id sid tid token lemma pos hvd.32044092008168 1 1 97 97 NUM hvd.32044092008168 1 2 ματη ματη NUM hvd.32044092008168 1 3 4008.93 4008.93 NUM hvd.32044092008168 1 4 08.93 08.93 NUM hvd.32044092008168 1 5 1 1 NUM hvd.32044092008168 1 6 math math NOUN hvd.32044092008168 1 7 4008.93 4008.93 NUM hvd.32044092008168 1 8 risto risto ADJ hvd.32044092008168 1 9 academial academial PROPN hvd.32044092008168 1 10 ver ver PROPN hvd.32044092008168 1 11 ro ro PROPN hvd.32044092008168 1 12 was be AUX hvd.32044092008168 1 13 tas tas PROPN hvd.32044092008168 1 14 ecclesi ecclesi PROPN hvd.32044092008168 1 15 e e PROPN hvd.32044092008168 1 16 in in ADP hvd.32044092008168 1 17 nov nov PROPN hvd.32044092008168 1 18 ony ony PROPN hvd.32044092008168 1 19 science science PROPN hvd.32044092008168 1 20 center center PROPN hvd.32044092008168 1 21 library library NOUN hvd.32044092008168 1 22 from from ADP hvd.32044092008168 1 23 the the DET hvd.32044092008168 1 24 author author NOUN hvd.32044092008168 1 25 . . PUNCT hvd.32044092008168 2 1 8 8 NUM hvd.32044092008168 2 2 sept sept PROPN hvd.32044092008168 2 3 . . PROPN hvd.32044092008168 2 4 18.93 18.93 NUM hvd.32044092008168 2 5 . . PUNCT hvd.32044092008168 3 1 complemente complemente PROPN hvd.32044092008168 3 2 i i PRON hvd.32044092008168 3 3 own own VERB hvd.32044092008168 3 4 's 's PART hvd.32044092008168 3 5 7 7 NUM hvd.32044092008168 3 6 horvard horvard PROPN hvd.32044092008168 3 7 89 89 NUM hvd.32044092008168 3 8 . . PUNCT hvd.32044092008168 4 1 07 07 NUM hvd.32044092008168 4 2 . . NOUN hvd.32044092008168 4 3 2 2 NUM hvd.32044092008168 4 4 a a DET hvd.32044092008168 4 5 math math NOUN hvd.32044092008168 4 6 4008.93 4008.93 NUM hvd.32044092008168 4 7 presentation presentation NOUN hvd.32044092008168 4 8 com com NOUN hvd.32044092008168 4 9 of of ADP hvd.32044092008168 4 10 the the DET hvd.32044092008168 4 11 theory theory NOUN hvd.32044092008168 4 12 of of ADP hvd.32044092008168 4 13 hermite hermite PROPN hvd.32044092008168 4 14 's 's PART hvd.32044092008168 4 15 form form NOUN hvd.32044092008168 4 16 of of ADP hvd.32044092008168 4 17 lamé lamé NOUN hvd.32044092008168 4 18 's 's PART hvd.32044092008168 4 19 equation equation NOUN hvd.32044092008168 4 20 with with ADP hvd.32044092008168 4 21 a a DET hvd.32044092008168 4 22 determination determination NOUN hvd.32044092008168 4 23 of of ADP hvd.32044092008168 4 24 the the DET hvd.32044092008168 4 25 explicit explicit ADJ hvd.32044092008168 4 26 forms form NOUN hvd.32044092008168 4 27 in in ADP hvd.32044092008168 4 28 terms term NOUN hvd.32044092008168 4 29 of of ADP hvd.32044092008168 4 30 the the DET hvd.32044092008168 4 31 p p NOUN hvd.32044092008168 4 32 function function NOUN hvd.32044092008168 4 33 for for ADP hvd.32044092008168 4 34 the the DET hvd.32044092008168 4 35 case case NOUN hvd.32044092008168 4 36 n n CCONJ hvd.32044092008168 4 37 equal equal ADJ hvd.32044092008168 4 38 to to ADP hvd.32044092008168 4 39 three three NUM hvd.32044092008168 4 40 . . PUNCT hvd.32044092008168 5 1 candidates candidate NOUN hvd.32044092008168 5 2 thesis thesis NOUN hvd.32044092008168 5 3 for for ADP hvd.32044092008168 5 4 the the DET hvd.32044092008168 5 5 degree degree NOUN hvd.32044092008168 5 6 of of ADP hvd.32044092008168 5 7 doctor doctor NOUN hvd.32044092008168 5 8 of of ADP hvd.32044092008168 5 9 philosophy philosophy NOUN hvd.32044092008168 5 10 presented present VERB hvd.32044092008168 5 11 by by ADP hvd.32044092008168 5 12 j. j. PROPN hvd.32044092008168 5 13 brace brace PROPN hvd.32044092008168 5 14 chittenden chittenden PROPN hvd.32044092008168 5 15 , , PUNCT hvd.32044092008168 5 16 a.m. a.m. PROPN hvd.32044092008168 5 17 , , PUNCT hvd.32044092008168 5 18 parker parker PROPN hvd.32044092008168 5 19 fellow fellow PROPN hvd.32044092008168 5 20 of of ADP hvd.32044092008168 5 21 harvard harvard PROPN hvd.32044092008168 5 22 univ univ PROPN hvd.32044092008168 5 23 . . PROPN hvd.32044092008168 5 24 , , PUNCT hvd.32044092008168 5 25 instructor instructor NOUN hvd.32044092008168 5 26 in in ADP hvd.32044092008168 5 27 princeton princeton PROPN hvd.32044092008168 5 28 college college PROPN hvd.32044092008168 5 29 . . PUNCT hvd.32044092008168 6 1 to to ADP hvd.32044092008168 6 2 the the DET hvd.32044092008168 6 3 philosophical philosophical ADJ hvd.32044092008168 6 4 faculty faculty NOUN hvd.32044092008168 6 5 of of ADP hvd.32044092008168 6 6 the the DET hvd.32044092008168 6 7 albertusuniversität albertusuniversität NOUN hvd.32044092008168 6 8 of of ADP hvd.32044092008168 6 9 königsberg königsberg PROPN hvd.32044092008168 6 10 in in ADP hvd.32044092008168 6 11 pr pr PROPN hvd.32044092008168 6 12 . . PROPN hvd.32044092008168 6 13 printed print VERB hvd.32044092008168 6 14 by by ADP hvd.32044092008168 6 15 b. b. PROPN hvd.32044092008168 6 16 g. g. PROPN hvd.32044092008168 6 17 teubner teubner PROPN hvd.32044092008168 6 18 , , PUNCT hvd.32044092008168 6 19 leipzig leipzig PROPN hvd.32044092008168 6 20 . . PUNCT hvd.32044092008168 7 1 1893 1893 NUM hvd.32044092008168 7 2 . . PUNCT hvd.32044092008168 8 1 a. a. NOUN hvd.32044092008168 8 2 $ $ PUNCT hvd.32044092008168 8 3 presentation presentation NOUN hvd.32044092008168 8 4 of of ADP hvd.32044092008168 8 5 the the DET hvd.32044092008168 8 6 theory theory NOUN hvd.32044092008168 8 7 of of ADP hvd.32044092008168 8 8 hermite hermite PROPN hvd.32044092008168 8 9 's 's PART hvd.32044092008168 8 10 form form NOUN hvd.32044092008168 8 11 of of ADP hvd.32044092008168 8 12 lamé lamé NOUN hvd.32044092008168 8 13 's 's PART hvd.32044092008168 8 14 equation equation NOUN hvd.32044092008168 8 15 with with ADP hvd.32044092008168 8 16 a a DET hvd.32044092008168 8 17 determination determination NOUN hvd.32044092008168 8 18 of of ADP hvd.32044092008168 8 19 the the DET hvd.32044092008168 8 20 explicit explicit ADJ hvd.32044092008168 8 21 forms form NOUN hvd.32044092008168 8 22 in in ADP hvd.32044092008168 8 23 terms term NOUN hvd.32044092008168 8 24 of of ADP hvd.32044092008168 8 25 the the DET hvd.32044092008168 8 26 pfunction pfunction NOUN hvd.32044092008168 8 27 for for ADP hvd.32044092008168 8 28 the the DET hvd.32044092008168 8 29 case case NOUN hvd.32044092008168 8 30 n n CCONJ hvd.32044092008168 8 31 equal equal ADJ hvd.32044092008168 8 32 to to ADP hvd.32044092008168 8 33 three three NUM hvd.32044092008168 8 34 . . PUNCT hvd.32044092008168 9 1 p p NOUN hvd.32044092008168 9 2 candidates candidate NOUN hvd.32044092008168 9 3 thesis thesis NOUN hvd.32044092008168 9 4 for for ADP hvd.32044092008168 9 5 the the DET hvd.32044092008168 9 6 degree degree NOUN hvd.32044092008168 9 7 of of ADP hvd.32044092008168 9 8 doctor doctor NOUN hvd.32044092008168 9 9 of of ADP hvd.32044092008168 9 10 philosophy philosophy NOUN hvd.32044092008168 9 11 presented present VERB hvd.32044092008168 9 12 by by ADP hvd.32044092008168 9 13 گر گر PROPN hvd.32044092008168 9 14 jonathan jonathan PROPN hvd.32044092008168 9 15 j. j. PROPN hvd.32044092008168 9 16 brace brace PROPN hvd.32044092008168 9 17 chittenden chittenden PROPN hvd.32044092008168 9 18 , , PUNCT hvd.32044092008168 9 19 a.m. a.m. PROPN hvd.32044092008168 9 20 , , PUNCT hvd.32044092008168 9 21 parker parker PROPN hvd.32044092008168 9 22 fellow fellow PROPN hvd.32044092008168 9 23 of of ADP hvd.32044092008168 9 24 harvard harvard PROPN hvd.32044092008168 9 25 univ univ PROPN hvd.32044092008168 9 26 . . PROPN hvd.32044092008168 9 27 , , PUNCT hvd.32044092008168 9 28 instructor instructor NOUN hvd.32044092008168 9 29 in in ADP hvd.32044092008168 9 30 princeton princeton PROPN hvd.32044092008168 9 31 college college PROPN hvd.32044092008168 9 32 . . PUNCT hvd.32044092008168 10 1 to to ADP hvd.32044092008168 10 2 the the DET hvd.32044092008168 10 3 philosophical philosophical ADJ hvd.32044092008168 10 4 faculty faculty NOUN hvd.32044092008168 10 5 of of ADP hvd.32044092008168 10 6 the the DET hvd.32044092008168 10 7 albertusuniversität albertusuniversität NOUN hvd.32044092008168 10 8 of of ADP hvd.32044092008168 10 9 königsberg königsberg PROPN hvd.32044092008168 10 10 in in ADP hvd.32044092008168 10 11 pr pr PROPN hvd.32044092008168 10 12 . . PROPN hvd.32044092008168 10 13 printed print VERB hvd.32044092008168 10 14 by by ADP hvd.32044092008168 10 15 b. b. PROPN hvd.32044092008168 10 16 g. g. PROPN hvd.32044092008168 10 17 teubner teubner PROPN hvd.32044092008168 10 18 , , PUNCT hvd.32044092008168 10 19 leipzig leipzig PROPN hvd.32044092008168 10 20 . . PUNCT hvd.32044092008168 11 1 1893 1893 NUM hvd.32044092008168 11 2 . . PUNCT hvd.32044092008168 12 1 ji ji PROPN hvd.32044092008168 12 2 , , PUNCT hvd.32044092008168 12 3 80 80 NUM hvd.32044092008168 12 4 8007.2 8007.2 NUM hvd.32044092008168 12 5 math math NOUN hvd.32044092008168 12 6 400893 400893 NUM hvd.32044092008168 12 7 , , PUNCT hvd.32044092008168 12 8 college college NOUN hvd.32044092008168 12 9 harvard harvard PROPN hvd.32044092008168 12 10 sep sep PROPN hvd.32044092008168 12 11 8 8 NUM hvd.32044092008168 12 12 1893 1893 NUM hvd.32044092008168 12 13 library library NOUN hvd.32044092008168 12 14 the the DET hvd.32044092008168 12 15 author author NOUN hvd.32044092008168 12 16 . . PUNCT hvd.32044092008168 13 1 dedicated dedicate VERB hvd.32044092008168 13 2 to to ADP hvd.32044092008168 13 3 the the DET hvd.32044092008168 13 4 first first ADJ hvd.32044092008168 13 5 of of ADP hvd.32044092008168 13 6 my my PRON hvd.32044092008168 13 7 many many ADJ hvd.32044092008168 13 8 teachers teacher NOUN hvd.32044092008168 13 9 , , PUNCT hvd.32044092008168 13 10 my my PRON hvd.32044092008168 13 11 mother mother NOUN hvd.32044092008168 13 12 who who PRON hvd.32044092008168 13 13 more more ADJ hvd.32044092008168 13 14 than than ADP hvd.32044092008168 13 15 all all DET hvd.32044092008168 13 16 others other NOUN hvd.32044092008168 13 17 has have AUX hvd.32044092008168 13 18 rendered render VERB hvd.32044092008168 13 19 the the DET hvd.32044092008168 13 20 realizations realization NOUN hvd.32044092008168 13 21 of of ADP hvd.32044092008168 13 22 my my PRON hvd.32044092008168 13 23 student student NOUN hvd.32044092008168 13 24 life life NOUN hvd.32044092008168 13 25 possible possible ADJ hvd.32044092008168 13 26 , , PUNCT hvd.32044092008168 13 27 for for ADP hvd.32044092008168 13 28 whom whom PRON hvd.32044092008168 13 29 no no DET hvd.32044092008168 13 30 sacrifice sacrifice NOUN hvd.32044092008168 13 31 has have AUX hvd.32044092008168 13 32 been be AUX hvd.32044092008168 13 33 to to PART hvd.32044092008168 13 34 great great ADJ hvd.32044092008168 13 35 in in ADP hvd.32044092008168 13 36 furthering further VERB hvd.32044092008168 13 37 the the DET hvd.32044092008168 13 38 interests interest NOUN hvd.32044092008168 13 39 of of ADP hvd.32044092008168 13 40 her her PRON hvd.32044092008168 13 41 sons son NOUN hvd.32044092008168 13 42 . . PUNCT hvd.32044092008168 14 1 introduction introduction NOUN hvd.32044092008168 14 2 . . PUNCT hvd.32044092008168 15 1 the the DET hvd.32044092008168 15 2 following follow VERB hvd.32044092008168 15 3 thesis thesis NOUN hvd.32044092008168 15 4 is be AUX hvd.32044092008168 15 5 practically practically ADV hvd.32044092008168 15 6 a a DET hvd.32044092008168 15 7 presentation presentation NOUN hvd.32044092008168 15 8 of of ADP hvd.32044092008168 15 9 the the DET hvd.32044092008168 15 10 general general ADJ hvd.32044092008168 15 11 analytical analytical ADJ hvd.32044092008168 15 12 theory theory NOUN hvd.32044092008168 15 13 of of ADP hvd.32044092008168 15 14 lamé lamé NOUN hvd.32044092008168 15 15 's 's PART hvd.32044092008168 15 16 differential differential ADJ hvd.32044092008168 15 17 equation equation NOUN hvd.32044092008168 15 18 of of ADP hvd.32044092008168 15 19 the the DET hvd.32044092008168 15 20 form form NOUN hvd.32044092008168 15 21 known know VERB hvd.32044092008168 15 22 as as ADP hvd.32044092008168 15 23 hermite hermite PROPN hvd.32044092008168 15 24 's 's PART hvd.32044092008168 15 25 . . PUNCT hvd.32044092008168 16 1 the the DET hvd.32044092008168 16 2 underlying underlie VERB hvd.32044092008168 16 3 principles principle NOUN hvd.32044092008168 16 4 and and CCONJ hvd.32044092008168 16 5 also also ADV hvd.32044092008168 16 6 the the DET hvd.32044092008168 16 7 general general ADJ hvd.32044092008168 16 8 solutions solution NOUN hvd.32044092008168 16 9 are be AUX hvd.32044092008168 16 10 therefore therefore ADV hvd.32044092008168 16 11 necessarily necessarily ADV hvd.32044092008168 16 12 based base VERB hvd.32044092008168 16 13 upon upon SCONJ hvd.32044092008168 16 14 the the DET hvd.32044092008168 16 15 original original ADJ hvd.32044092008168 16 16 work work NOUN hvd.32044092008168 16 17 of of ADP hvd.32044092008168 16 18 m. m. NOUN hvd.32044092008168 16 19 hermite hermite PROPN hvd.32044092008168 16 20 , , PUNCT hvd.32044092008168 16 21 published publish VERB hvd.32044092008168 16 22 for for ADP hvd.32044092008168 16 23 the the DET hvd.32044092008168 16 24 first first ADJ hvd.32044092008168 16 25 time time NOUN hvd.32044092008168 16 26 in in ADP hvd.32044092008168 16 27 paris paris PROPN hvd.32044092008168 16 28 in in ADP hvd.32044092008168 16 29 1877 1877 NUM hvd.32044092008168 16 30 in in ADP hvd.32044092008168 16 31 the the DET hvd.32044092008168 16 32 comptes compte NOUN hvd.32044092008168 16 33 rendus rendu VERB hvd.32044092008168 16 34 under under ADP hvd.32044092008168 16 35 the the DET hvd.32044092008168 16 36 title title NOUN hvd.32044092008168 16 37 “ " PUNCT hvd.32044092008168 16 38 sur sur X hvd.32044092008168 16 39 quelques quelques X hvd.32044092008168 16 40 applications application NOUN hvd.32044092008168 16 41 des des X hvd.32044092008168 16 42 fonctions fonction NOUN hvd.32044092008168 16 43 elliptiques elliptique NOUN hvd.32044092008168 16 44 ” " PUNCT hvd.32044092008168 16 45 and and CCONJ hvd.32044092008168 16 46 on on ADP hvd.32044092008168 16 47 a a DET hvd.32044092008168 16 48 later later ADJ hvd.32044092008168 16 49 treatment treatment NOUN hvd.32044092008168 16 50 of of ADP hvd.32044092008168 16 51 the the DET hvd.32044092008168 16 52 subject subject NOUN hvd.32044092008168 16 53 by by ADP hvd.32044092008168 16 54 halphen halphen ADV hvd.32044092008168 16 55 in in ADP hvd.32044092008168 16 56 his his PRON hvd.32044092008168 16 57 work work NOUN hvd.32044092008168 16 58 entitled entitle VERB hvd.32044092008168 16 59 " " PUNCT hvd.32044092008168 16 60 traité traité X hvd.32044092008168 16 61 des des PROPN hvd.32044092008168 16 62 fonctions fonction NOUN hvd.32044092008168 16 63 elliptiques elliptiques PROPN hvd.32044092008168 16 64 et et NOUN hvd.32044092008168 16 65 leur leur ADJ hvd.32044092008168 16 66 applications application NOUN hvd.32044092008168 16 67 " " PUNCT hvd.32044092008168 16 68 , , PUNCT hvd.32044092008168 16 69 vol vol NOUN hvd.32044092008168 16 70 . . PROPN hvd.32044092008168 16 71 ii ii PROPN hvd.32044092008168 16 72 , , PUNCT hvd.32044092008168 16 73 paris paris PROPN hvd.32044092008168 16 74 1888 1888 NUM hvd.32044092008168 16 75 . . PUNCT hvd.32044092008168 17 1 m. m. NOUN hvd.32044092008168 17 2 hermite hermite PROPN hvd.32044092008168 17 3 has have AUX hvd.32044092008168 17 4 employed employ VERB hvd.32044092008168 17 5 the the DET hvd.32044092008168 17 6 older old ADJ hvd.32044092008168 17 7 jacobian jacobian ADJ hvd.32044092008168 17 8 functions function NOUN hvd.32044092008168 17 9 while while SCONJ hvd.32044092008168 17 10 halphen halphen ADV hvd.32044092008168 17 11 has have AUX hvd.32044092008168 17 12 used use VERB hvd.32044092008168 17 13 in in ADP hvd.32044092008168 17 14 every every DET hvd.32044092008168 17 15 case case NOUN hvd.32044092008168 17 16 the the DET hvd.32044092008168 17 17 weierstrass weierstrass PROPN hvd.32044092008168 17 18 p p PROPN hvd.32044092008168 17 19 function function NOUN hvd.32044092008168 17 20 , , PUNCT hvd.32044092008168 17 21 and and CCONJ hvd.32044092008168 17 22 not not PART hvd.32044092008168 17 23 only only ADV hvd.32044092008168 17 24 the the DET hvd.32044092008168 17 25 notation notation NOUN hvd.32044092008168 17 26 but but CCONJ hvd.32044092008168 17 27 the the DET hvd.32044092008168 17 28 ultimate ultimate ADJ hvd.32044092008168 17 29 forms form NOUN hvd.32044092008168 17 30 as as ADV hvd.32044092008168 17 31 well well ADV hvd.32044092008168 17 32 as as ADP hvd.32044092008168 17 33 the the DET hvd.32044092008168 17 34 complex complex ADJ hvd.32044092008168 17 35 functions function NOUN hvd.32044092008168 17 36 in in ADP hvd.32044092008168 17 37 which which PRON hvd.32044092008168 17 38 they they PRON hvd.32044092008168 17 39 are be AUX hvd.32044092008168 17 40 expressed express VERB hvd.32044092008168 17 41 are be AUX hvd.32044092008168 17 42 in in ADP hvd.32044092008168 17 43 the the DET hvd.32044092008168 17 44 two two NUM hvd.32044092008168 17 45 works work NOUN hvd.32044092008168 17 46 intirely intirely ADV hvd.32044092008168 17 47 different different ADJ hvd.32044092008168 17 48 . . PUNCT hvd.32044092008168 18 1 as as ADV hvd.32044092008168 18 2 far far ADV hvd.32044092008168 18 3 as as SCONJ hvd.32044092008168 18 4 i i PRON hvd.32044092008168 18 5 know know VERB hvd.32044092008168 18 6 , , PUNCT hvd.32044092008168 18 7 no no DET hvd.32044092008168 18 8 attempt attempt NOUN hvd.32044092008168 18 9 has have AUX hvd.32044092008168 18 10 before before ADV hvd.32044092008168 18 11 been be AUX hvd.32044092008168 18 12 made make VERB hvd.32044092008168 18 13 to to PART hvd.32044092008168 18 14 establish establish VERB hvd.32044092008168 18 15 the the DET hvd.32044092008168 18 16 absolute absolute ADJ hvd.32044092008168 18 17 relations relation NOUN hvd.32044092008168 18 18 of of ADP hvd.32044092008168 18 19 these these DET hvd.32044092008168 18 20 different different ADJ hvd.32044092008168 18 21 functions function NOUN hvd.32044092008168 18 22 . . PUNCT hvd.32044092008168 19 1 in in ADP hvd.32044092008168 19 2 attempting attempt VERB hvd.32044092008168 19 3 to to PART hvd.32044092008168 19 4 do do VERB hvd.32044092008168 19 5 this this PRON hvd.32044092008168 19 6 , , PUNCT hvd.32044092008168 19 7 i i PRON hvd.32044092008168 19 8 have have AUX hvd.32044092008168 19 9 developed develop VERB hvd.32044092008168 19 10 the the DET hvd.32044092008168 19 11 intire intire ADJ hvd.32044092008168 19 12 theory theory NOUN hvd.32044092008168 19 13 in in ADP hvd.32044092008168 19 14 a a DET hvd.32044092008168 19 15 new new ADJ hvd.32044092008168 19 16 presentation presentation NOUN hvd.32044092008168 19 17 , , PUNCT hvd.32044092008168 19 18 working work VERB hvd.32044092008168 19 19 out out ADP hvd.32044092008168 19 20 the the DET hvd.32044092008168 19 21 results result NOUN hvd.32044092008168 19 22 of of ADP hvd.32044092008168 19 23 m. m. NOUN hvd.32044092008168 19 24 hermite hermite NOUN hvd.32044092008168 19 25 in in ADP hvd.32044092008168 19 26 terms term NOUN hvd.32044092008168 19 27 of of ADP hvd.32044092008168 19 28 the the DET hvd.32044092008168 19 29 p p NOUN hvd.32044092008168 19 30 function function NOUN hvd.32044092008168 19 31 , , PUNCT hvd.32044092008168 19 32 having have VERB hvd.32044092008168 19 33 principly principly ADV hvd.32044092008168 19 34 in in ADP hvd.32044092008168 19 35 view view NOUN hvd.32044092008168 19 36 a a DET hvd.32044092008168 19 37 determination determination NOUN hvd.32044092008168 19 38 of of ADP hvd.32044092008168 19 39 the the DET hvd.32044092008168 19 40 explicit explicit ADJ hvd.32044092008168 19 41 values value NOUN hvd.32044092008168 19 42 of of ADP hvd.32044092008168 19 43 all all DET hvd.32044092008168 19 44 the the DET hvd.32044092008168 19 45 forms form NOUN hvd.32044092008168 19 46 for for ADP hvd.32044092008168 19 47 the the DET hvd.32044092008168 19 48 special special ADJ hvd.32044092008168 19 49 case case NOUN hvd.32044092008168 19 50 n n ADP hvd.32044092008168 19 51 equal equal ADJ hvd.32044092008168 19 52 to to ADP hvd.32044092008168 19 53 three three NUM hvd.32044092008168 19 54 . . PUNCT hvd.32044092008168 20 1 i i PRON hvd.32044092008168 20 2 may may AUX hvd.32044092008168 20 3 add add VERB hvd.32044092008168 20 4 that that SCONJ hvd.32044092008168 20 5 owing owe VERB hvd.32044092008168 20 6 to to ADP hvd.32044092008168 20 7 the the DET hvd.32044092008168 20 8 exceptional exceptional ADJ hvd.32044092008168 20 9 privilege privilege NOUN hvd.32044092008168 20 10 granted grant VERB hvd.32044092008168 20 11 by by ADP hvd.32044092008168 20 12 the the DET hvd.32044092008168 20 13 minister minister NOUN hvd.32044092008168 20 14 of of ADP hvd.32044092008168 20 15 education education NOUN hvd.32044092008168 20 16 and and CCONJ hvd.32044092008168 20 17 the the DET hvd.32044092008168 20 18 philosophical philosophical ADJ hvd.32044092008168 20 19 faculty faculty NOUN hvd.32044092008168 20 20 of of ADP hvd.32044092008168 20 21 the the DET hvd.32044092008168 20 22 albertus albertus PROPN hvd.32044092008168 20 23 - - PUNCT hvd.32044092008168 20 24 universität universität NOUN hvd.32044092008168 20 25 allowing allow VERB hvd.32044092008168 20 26 the the DET hvd.32044092008168 20 27 publishing publishing NOUN hvd.32044092008168 20 28 of of ADP hvd.32044092008168 20 29 this this DET hvd.32044092008168 20 30 thesis thesis NOUN hvd.32044092008168 20 31 in in ADP hvd.32044092008168 20 32 english english PROPN hvd.32044092008168 20 33 , , PUNCT hvd.32044092008168 20 34 6 6 NUM hvd.32044092008168 20 35 introduction introduction NOUN hvd.32044092008168 20 36 . . PUNCT hvd.32044092008168 21 1 i i PRON hvd.32044092008168 21 2 am be AUX hvd.32044092008168 21 3 not not PART hvd.32044092008168 21 4 without without ADP hvd.32044092008168 21 5 hope hope NOUN hvd.32044092008168 21 6 that that SCONJ hvd.32044092008168 21 7 this this DET hvd.32044092008168 21 8 general general ADJ hvd.32044092008168 21 9 presentation presentation NOUN hvd.32044092008168 21 10 of of ADP hvd.32044092008168 21 11 the the DET hvd.32044092008168 21 12 theory theory NOUN hvd.32044092008168 21 13 of of ADP hvd.32044092008168 21 14 lamé lamé NOUN hvd.32044092008168 21 15 's 's PART hvd.32044092008168 21 16 functions function NOUN hvd.32044092008168 21 17 may may AUX hvd.32044092008168 21 18 prove prove VERB hvd.32044092008168 21 19 a a DET hvd.32044092008168 21 20 welcome welcome ADJ hvd.32044092008168 21 21 addition addition NOUN hvd.32044092008168 21 22 to to ADP hvd.32044092008168 21 23 the the DET hvd.32044092008168 21 24 literature literature NOUN hvd.32044092008168 21 25 of of ADP hvd.32044092008168 21 26 the the DET hvd.32044092008168 21 27 subject subject NOUN hvd.32044092008168 21 28 where where SCONJ hvd.32044092008168 21 29 in in ADP hvd.32044092008168 21 30 english english PROPN hvd.32044092008168 21 31 todhunter todhunter PROPN hvd.32044092008168 21 32 's 's PART hvd.32044092008168 21 33 “ " PUNCT hvd.32044092008168 21 34 lamé lamé NOUN hvd.32044092008168 21 35 's 's PART hvd.32044092008168 21 36 and and CCONJ hvd.32044092008168 21 37 bessel bessel PROPN hvd.32044092008168 21 38 's 's PART hvd.32044092008168 21 39 functions function NOUN hvd.32044092008168 21 40 ” " PUNCT hvd.32044092008168 21 41 is be AUX hvd.32044092008168 21 42 the the DET hvd.32044092008168 21 43 only only ADJ hvd.32044092008168 21 44 representative representative NOUN hvd.32044092008168 21 45 . . PUNCT hvd.32044092008168 22 1 finally finally ADV hvd.32044092008168 22 2 i i PRON hvd.32044092008168 22 3 must must AUX hvd.32044092008168 22 4 acknowledge acknowledge VERB hvd.32044092008168 22 5 my my PRON hvd.32044092008168 22 6 indebtedness indebtedness NOUN hvd.32044092008168 22 7 to to ADP hvd.32044092008168 22 8 prof prof PROPN hvd.32044092008168 22 9 . . PUNCT hvd.32044092008168 23 1 lindemann lindemann PROPN hvd.32044092008168 23 2 not not PART hvd.32044092008168 23 3 only only ADV hvd.32044092008168 23 4 for for ADP hvd.32044092008168 23 5 the the DET hvd.32044092008168 23 6 direction direction NOUN hvd.32044092008168 23 7 of of ADP hvd.32044092008168 23 8 a a DET hvd.32044092008168 23 9 most most ADV hvd.32044092008168 23 10 valuable valuable ADJ hvd.32044092008168 23 11 course course NOUN hvd.32044092008168 23 12 of of ADP hvd.32044092008168 23 13 reading reading NOUN hvd.32044092008168 23 14 but but CCONJ hvd.32044092008168 23 15 for for ADP hvd.32044092008168 23 16 a a DET hvd.32044092008168 23 17 general general NOUN hvd.32044092008168 23 18 although although ADV hvd.32044092008168 23 19 , , PUNCT hvd.32044092008168 23 20 owing owe VERB hvd.32044092008168 23 21 to to ADP hvd.32044092008168 23 22 a a DET hvd.32044092008168 23 23 lack lack NOUN hvd.32044092008168 23 24 of of ADP hvd.32044092008168 23 25 time time NOUN hvd.32044092008168 23 26 , , PUNCT hvd.32044092008168 23 27 a a PRON hvd.32044092008168 23 28 by by ADP hvd.32044092008168 23 29 no no DET hvd.32044092008168 23 30 means mean NOUN hvd.32044092008168 23 31 detailed detailed ADJ hvd.32044092008168 23 32 review review NOUN hvd.32044092008168 23 33 of of ADP hvd.32044092008168 23 34 the the DET hvd.32044092008168 23 35 work work NOUN hvd.32044092008168 23 36 . . PUNCT hvd.32044092008168 24 1 contents content NOUN hvd.32044092008168 24 2 . . PUNCT hvd.32044092008168 25 1 introduction introduction NOUN hvd.32044092008168 25 2 page page PROPN hvd.32044092008168 25 3 5 5 NUM hvd.32044092008168 25 4 part part NOUN hvd.32044092008168 25 5 1 1 NUM hvd.32044092008168 25 6 . . PUNCT hvd.32044092008168 25 7 history history NOUN hvd.32044092008168 25 8 and and CCONJ hvd.32044092008168 25 9 definitions definition NOUN hvd.32044092008168 25 10 . . PUNCT hvd.32044092008168 26 1 the the DET hvd.32044092008168 26 2 problem problem NOUN hvd.32044092008168 26 3 of of ADP hvd.32044092008168 26 4 lamé lamé NOUN hvd.32044092008168 26 5 . . PUNCT hvd.32044092008168 27 1 the the DET hvd.32044092008168 27 2 problem problem NOUN hvd.32044092008168 27 3 of of ADP hvd.32044092008168 27 4 hermite hermite PROPN hvd.32044092008168 27 5 . . PUNCT hvd.32044092008168 28 1 definitions definition NOUN hvd.32044092008168 28 2 11 11 NUM hvd.32044092008168 28 3 13 13 NUM hvd.32044092008168 28 4 15 15 NUM hvd.32044092008168 28 5 17 17 NUM hvd.32044092008168 28 6 20 20 NUM hvd.32044092008168 28 7 21 21 NUM hvd.32044092008168 28 8 23 23 NUM hvd.32044092008168 28 9 25 25 NUM hvd.32044092008168 28 10 . . PUNCT hvd.32044092008168 29 1 part part NOUN hvd.32044092008168 29 2 2 2 NUM hvd.32044092008168 29 3 . . PUNCT hvd.32044092008168 30 1 hermite hermite PROPN hvd.32044092008168 30 2 's 's PART hvd.32044092008168 30 3 integral integral ADJ hvd.32044092008168 30 4 as as ADP hvd.32044092008168 30 5 a a DET hvd.32044092008168 30 6 sum sum NOUN hvd.32044092008168 30 7 . . PUNCT hvd.32044092008168 31 1 the the DET hvd.32044092008168 31 2 function function NOUN hvd.32044092008168 31 3 of of ADP hvd.32044092008168 31 4 the the DET hvd.32044092008168 31 5 second second ADJ hvd.32044092008168 31 6 species species NOUN hvd.32044092008168 31 7 transformation transformation NOUN hvd.32044092008168 31 8 of of ADP hvd.32044092008168 31 9 hermite hermite PROPN hvd.32044092008168 31 10 's 's PART hvd.32044092008168 31 11 equation equation NOUN hvd.32044092008168 31 12 . . PUNCT hvd.32044092008168 32 1 development development NOUN hvd.32044092008168 32 2 of of ADP hvd.32044092008168 32 3 the the DET hvd.32044092008168 32 4 integral integral ADJ hvd.32044092008168 32 5 development development NOUN hvd.32044092008168 32 6 of of ADP hvd.32044092008168 32 7 the the DET hvd.32044092008168 32 8 eliment eliment NOUN hvd.32044092008168 32 9 of of ADP hvd.32044092008168 32 10 the the DET hvd.32044092008168 32 11 function function NOUN hvd.32044092008168 32 12 of of ADP hvd.32044092008168 32 13 the the DET hvd.32044092008168 32 14 second second ADJ hvd.32044092008168 32 15 species species NOUN hvd.32044092008168 32 16 determination determination NOUN hvd.32044092008168 32 17 of of ADP hvd.32044092008168 32 18 the the DET hvd.32044092008168 32 19 integral integral ADJ hvd.32044092008168 32 20 part part NOUN hvd.32044092008168 32 21 3 3 NUM hvd.32044092008168 32 22 . . PUNCT hvd.32044092008168 33 1 the the DET hvd.32044092008168 33 2 integral integral NOUN hvd.32044092008168 33 3 as as ADP hvd.32044092008168 33 4 a a DET hvd.32044092008168 33 5 product product NOUN hvd.32044092008168 33 6 . . PUNCT hvd.32044092008168 34 1 indirect indirect ADJ hvd.32044092008168 34 2 solution solution NOUN hvd.32044092008168 34 3 solution solution NOUN hvd.32044092008168 34 4 for for ADP hvd.32044092008168 34 5 n n NOUN hvd.32044092008168 34 6 = = SYM hvd.32044092008168 34 7 2 2 NUM hvd.32044092008168 34 8 the the DET hvd.32044092008168 34 9 product product NOUN hvd.32044092008168 34 10 y y PROPN hvd.32044092008168 34 11 of of ADP hvd.32044092008168 34 12 the the DET hvd.32044092008168 34 13 two two NUM hvd.32044092008168 34 14 solutions solution NOUN hvd.32044092008168 34 15 . . PUNCT hvd.32044092008168 35 1 direct direct ADJ hvd.32044092008168 35 2 solution solution NOUN hvd.32044092008168 35 3 determination determination NOUN hvd.32044092008168 35 4 of of ADP hvd.32044092008168 35 5 y y PROPN hvd.32044092008168 35 6 for for ADP hvd.32044092008168 35 7 n n CCONJ hvd.32044092008168 35 8 = = SYM hvd.32044092008168 35 9 3 3 NUM hvd.32044092008168 35 10 28 28 NUM hvd.32044092008168 35 11 30 30 NUM hvd.32044092008168 35 12 32 32 NUM hvd.32044092008168 35 13 37 37 NUM hvd.32044092008168 35 14 40 40 NUM hvd.32044092008168 35 15 . . PUNCT hvd.32044092008168 35 16 . . PUNCT hvd.32044092008168 36 1 part part NOUN hvd.32044092008168 36 2 4 4 NUM hvd.32044092008168 36 3 . . PUNCT hvd.32044092008168 37 1 the the DET hvd.32044092008168 37 2 special special ADJ hvd.32044092008168 37 3 functions function NOUN hvd.32044092008168 37 4 of of ADP hvd.32044092008168 37 5 lamé lamé NOUN hvd.32044092008168 37 6 . . PUNCT hvd.32044092008168 38 1 functions function NOUN hvd.32044092008168 38 2 of of ADP hvd.32044092008168 38 3 the the DET hvd.32044092008168 38 4 first first ADJ hvd.32044092008168 38 5 sort sort NOUN hvd.32044092008168 38 6 functions function NOUN hvd.32044092008168 38 7 of of ADP hvd.32044092008168 38 8 the the DET hvd.32044092008168 38 9 second second ADJ hvd.32044092008168 38 10 sort sort NOUN hvd.32044092008168 38 11 functions function NOUN hvd.32044092008168 38 12 of of ADP hvd.32044092008168 38 13 the the DET hvd.32044092008168 38 14 third third ADJ hvd.32044092008168 38 15 sort sort NOUN hvd.32044092008168 38 16 42 42 NUM hvd.32044092008168 38 17 43 43 NUM hvd.32044092008168 38 18 44 44 NUM hvd.32044092008168 38 19 3 3 NUM hvd.32044092008168 38 20 ” " PUNCT hvd.32044092008168 38 21 . . PUNCT hvd.32044092008168 39 1 45 45 NUM hvd.32044092008168 39 2 . . PUNCT hvd.32044092008168 40 1 part part NOUN hvd.32044092008168 40 2 5 5 NUM hvd.32044092008168 40 3 . . PUNCT hvd.32044092008168 40 4 reduction reduction NOUN hvd.32044092008168 40 5 of of ADP hvd.32044092008168 40 6 the the DET hvd.32044092008168 40 7 forms form NOUN hvd.32044092008168 40 8 " " PUNCT hvd.32044092008168 40 9 n n CCONJ hvd.32044092008168 40 10 identity identity NOUN hvd.32044092008168 40 11 of of ADP hvd.32044092008168 40 12 solutions solution NOUN hvd.32044092008168 40 13 determination determination NOUN hvd.32044092008168 40 14 of of ADP hvd.32044092008168 40 15 x x SYM hvd.32044092008168 40 16 and and CCONJ hvd.32044092008168 40 17 v. v. ADP hvd.32044092008168 40 18 first first ADJ hvd.32044092008168 40 19 method method PROPN hvd.32044092008168 40 20 x x PUNCT hvd.32044092008168 40 21 as as ADP hvd.32044092008168 40 22 function function NOUN hvd.32044092008168 40 23 of of ADP hvd.32044092008168 40 24 $ $ SYM hvd.32044092008168 40 25 factors factor NOUN hvd.32044092008168 40 26 of of ADP hvd.32044092008168 40 27 $ $ SYM hvd.32044092008168 40 28 case case NOUN hvd.32044092008168 40 29 0 0 NUM hvd.32044092008168 40 30 0 0 NUM hvd.32044092008168 40 31 definition definition NOUN hvd.32044092008168 40 32 of of ADP hvd.32044092008168 40 33 y y PROPN hvd.32044092008168 40 34 and and CCONJ hvd.32044092008168 40 35 p(v p(v PROPN hvd.32044092008168 40 36 ) ) PUNCT hvd.32044092008168 40 37 as as ADP hvd.32044092008168 40 38 function function NOUN hvd.32044092008168 40 39 of of ADP hvd.32044092008168 40 40 y y PROPN hvd.32044092008168 40 41 definition definition NOUN hvd.32044092008168 40 42 of of ADP hvd.32044092008168 40 43 x x PROPN hvd.32044092008168 40 44 and and CCONJ hvd.32044092008168 40 45 p p NOUN hvd.32044092008168 40 46 ' ' PUNCT hvd.32044092008168 40 47 ( ( PUNCT hvd.32044092008168 40 48 v v NOUN hvd.32044092008168 40 49 ) ) PUNCT hvd.32044092008168 40 50 as as ADP hvd.32044092008168 40 51 function function NOUN hvd.32044092008168 40 52 of of ADP hvd.32044092008168 40 53 x x NOUN hvd.32044092008168 40 54 reduction reduction NOUN hvd.32044092008168 40 55 of of ADP hvd.32044092008168 40 56 lamé lamé NOUN hvd.32044092008168 40 57 's 's PART hvd.32044092008168 40 58 functions function NOUN hvd.32044092008168 40 59 0 0 PUNCT hvd.32044092008168 40 60 = = SYM hvd.32044092008168 40 61 0 0 NUM hvd.32044092008168 40 62 integral integral PROPN hvd.32044092008168 40 63 x x SYM hvd.32044092008168 40 64 0 0 NUM hvd.32044092008168 40 65 case case NOUN hvd.32044092008168 40 66 d d X hvd.32044092008168 40 67 0 0 NUM hvd.32044092008168 40 68 47 47 NUM hvd.32044092008168 40 69 48 48 NUM hvd.32044092008168 40 70 49 49 NUM hvd.32044092008168 40 71 49 49 NUM hvd.32044092008168 40 72 50 50 NUM hvd.32044092008168 40 73 51 51 NUM hvd.32044092008168 40 74 51 51 NUM hvd.32044092008168 40 75 52 52 NUM hvd.32044092008168 40 76 52 52 NUM hvd.32044092008168 40 77 . . PUNCT hvd.32044092008168 41 1 8 8 NUM hvd.32044092008168 41 2 contents content NOUN hvd.32044092008168 41 3 . . PUNCT hvd.32044092008168 42 1 2 2 NUM hvd.32044092008168 42 2 0 0 NUM hvd.32044092008168 42 3 , , PUNCT hvd.32044092008168 42 4 q2 q2 PROPN hvd.32044092008168 42 5 0 0 NUM hvd.32044092008168 42 6 , , PUNCT hvd.32044092008168 42 7 23 23 NUM hvd.32044092008168 42 8 • • SYM hvd.32044092008168 42 9 3 3 NUM hvd.32044092008168 42 10 page page NOUN hvd.32044092008168 42 11 relation relation NOUN hvd.32044092008168 42 12 of of ADP hvd.32044092008168 42 13 y y PROPN hvd.32044092008168 42 14 and and CCONJ hvd.32044092008168 42 15 c c NOUN hvd.32044092008168 42 16 to to ADP hvd.32044092008168 42 17 the the DET hvd.32044092008168 42 18 special special ADJ hvd.32044092008168 42 19 functions function NOUN hvd.32044092008168 42 20 of of ADP hvd.32044092008168 42 21 lamé lamé NOUN hvd.32044092008168 42 22 : : PUNCT hvd.32044092008168 42 23 52 52 NUM hvd.32044092008168 42 24 analytic analytic ADJ hvd.32044092008168 42 25 form form NOUN hvd.32044092008168 42 26 of of ADP hvd.32044092008168 42 27 y y PROPN hvd.32044092008168 42 28 and and CCONJ hvd.32044092008168 42 29 y y PROPN hvd.32044092008168 42 30 53 53 NUM hvd.32044092008168 42 31 condition condition NOUN hvd.32044092008168 42 32 c c X hvd.32044092008168 42 33 = = SYM hvd.32044092008168 42 34 0 0 NUM hvd.32044092008168 42 35 . . PUNCT hvd.32044092008168 43 1 special special ADJ hvd.32044092008168 43 2 functions function NOUN hvd.32044092008168 43 3 of of ADP hvd.32044092008168 43 4 lamé lamé NOUN hvd.32044092008168 43 5 53 53 NUM hvd.32044092008168 43 6 condition condition NOUN hvd.32044092008168 43 7 p p NOUN hvd.32044092008168 43 8 0 0 NUM hvd.32044092008168 43 9 . . PUNCT hvd.32044092008168 43 10 functions function NOUN hvd.32044092008168 43 11 of of ADP hvd.32044092008168 43 12 first first ADJ hvd.32044092008168 43 13 sort sort ADJ hvd.32044092008168 43 14 54 54 NUM hvd.32044092008168 43 15 condition condition NOUN hvd.32044092008168 43 16 q q X hvd.32044092008168 43 17 0 0 NUM hvd.32044092008168 43 18 . . PUNCT hvd.32044092008168 43 19 functions function NOUN hvd.32044092008168 43 20 of of ADP hvd.32044092008168 43 21 second second ADJ hvd.32044092008168 43 22 sort sort NOUN hvd.32044092008168 43 23 55 55 NUM hvd.32044092008168 43 24 absolute absolute ADJ hvd.32044092008168 43 25 relations relation NOUN hvd.32044092008168 43 26 of of ADP hvd.32044092008168 43 27 q q NOUN hvd.32044092008168 43 28 , , PUNCT hvd.32044092008168 43 29 and and CCONJ hvd.32044092008168 43 30 on on ADP hvd.32044092008168 43 31 55 55 NUM hvd.32044092008168 43 32 determination determination NOUN hvd.32044092008168 43 33 of of ADP hvd.32044092008168 43 34 c c PROPN hvd.32044092008168 43 35 56 56 NUM hvd.32044092008168 43 36 the the DET hvd.32044092008168 43 37 integrals integral NOUN hvd.32044092008168 43 38 q1 q1 PROPN hvd.32044092008168 43 39 0 0 NUM hvd.32044092008168 43 40 . . PUNCT hvd.32044092008168 43 41 56 56 NUM hvd.32044092008168 44 1 the the DET hvd.32044092008168 44 2 discriminant discriminant NOUN hvd.32044092008168 44 3 of of ADP hvd.32044092008168 44 4 y y PROPN hvd.32044092008168 44 5 57 57 NUM hvd.32044092008168 44 6 resultant resultant NOUN hvd.32044092008168 44 7 of of ADP hvd.32044092008168 44 8 y y PROPN hvd.32044092008168 44 9 and and CCONJ hvd.32044092008168 44 10 o(a o(a SPACE hvd.32044092008168 44 11 ) ) PUNCT hvd.32044092008168 44 12 . . PUNCT hvd.32044092008168 45 1 57 57 NUM hvd.32044092008168 45 2 discriminant discriminant NOUN hvd.32044092008168 45 3 in in ADP hvd.32044092008168 45 4 terms term NOUN hvd.32044092008168 45 5 of of ADP hvd.32044092008168 45 6 this this DET hvd.32044092008168 45 7 resultant resultant ADJ hvd.32044092008168 45 8 58 58 NUM hvd.32044092008168 45 9 discriminant discriminant NOUN hvd.32044092008168 45 10 in in ADP hvd.32044092008168 45 11 terms term NOUN hvd.32044092008168 45 12 of of ADP hvd.32044092008168 45 13 p p PROPN hvd.32044092008168 45 14 and and CCONJ hvd.32044092008168 45 15 q q NOUN hvd.32044092008168 45 16 58 58 NUM hvd.32044092008168 45 17 special special ADJ hvd.32044092008168 45 18 results result NOUN hvd.32044092008168 45 19 , , PUNCT hvd.32044092008168 45 20 n n CCONJ hvd.32044092008168 45 21 59 59 NUM hvd.32044092008168 45 22 determination determination NOUN hvd.32044092008168 45 23 of of ADP hvd.32044092008168 45 24 x x SYM hvd.32044092008168 45 25 and and CCONJ hvd.32044092008168 45 26 v. v. ADP hvd.32044092008168 45 27 second second ADJ hvd.32044092008168 45 28 method method NOUN hvd.32044092008168 45 29 60 60 NUM hvd.32044092008168 45 30 reduction reduction NOUN hvd.32044092008168 45 31 of of ADP hvd.32044092008168 45 32 the the DET hvd.32044092008168 45 33 general general ADJ hvd.32044092008168 45 34 function function NOUN hvd.32044092008168 45 35 60 60 NUM hvd.32044092008168 45 36 development development NOUN hvd.32044092008168 45 37 of of ADP hvd.32044092008168 45 38 ( ( PUNCT hvd.32044092008168 45 39 n n CCONJ hvd.32044092008168 45 40 = = SYM hvd.32044092008168 45 41 3 3 NUM hvd.32044092008168 45 42 ) ) PUNCT hvd.32044092008168 45 43 62 62 NUM hvd.32044092008168 45 44 development development NOUN hvd.32044092008168 45 45 of of ADP hvd.32044092008168 45 46 ¥ ¥ PROPN hvd.32044092008168 45 47 ( ( PUNCT hvd.32044092008168 45 48 n n CCONJ hvd.32044092008168 45 49 3 3 X hvd.32044092008168 45 50 ) ) PUNCT hvd.32044092008168 45 51 64 64 NUM hvd.32044092008168 45 52 development development NOUN hvd.32044092008168 45 53 of of ADP hvd.32044092008168 45 54 en en PROPN hvd.32044092008168 45 55 3 3 NUM hvd.32044092008168 45 56 ) ) PUNCT hvd.32044092008168 45 57 65 65 NUM hvd.32044092008168 45 58 reduction reduction NOUN hvd.32044092008168 45 59 of of ADP hvd.32044092008168 45 60 x x SYM hvd.32044092008168 45 61 and and CCONJ hvd.32044092008168 45 62 v v NOUN hvd.32044092008168 45 63 from from ADP hvd.32044092008168 45 64 these these DET hvd.32044092008168 45 65 forms form NOUN hvd.32044092008168 45 66 66 66 NUM hvd.32044092008168 45 67 general general ADJ hvd.32044092008168 45 68 forms form NOUN hvd.32044092008168 45 69 for for ADP hvd.32044092008168 45 70 x x NUM hvd.32044092008168 45 71 , , PUNCT hvd.32044092008168 45 72 p p NOUN hvd.32044092008168 45 73 ( ( PUNCT hvd.32044092008168 45 74 v v NOUN hvd.32044092008168 45 75 ) ) PUNCT hvd.32044092008168 45 76 and and CCONJ hvd.32044092008168 45 77 p'(v p'(v NOUN hvd.32044092008168 45 78 ) ) PUNCT hvd.32044092008168 45 79 66 66 NUM hvd.32044092008168 45 80 determination determination NOUN hvd.32044092008168 45 81 of of ADP hvd.32044092008168 45 82 forms form NOUN hvd.32044092008168 45 83 ( ( PUNCT hvd.32044092008168 45 84 n n CCONJ hvd.32044092008168 45 85 3 3 X hvd.32044092008168 45 86 ) ) PUNCT hvd.32044092008168 45 87 68 68 NUM hvd.32044092008168 45 88 reduction reduction NOUN hvd.32044092008168 45 89 to to ADP hvd.32044092008168 45 90 the the DET hvd.32044092008168 45 91 first first ADJ hvd.32044092008168 45 92 forms form NOUN hvd.32044092008168 45 93 69 69 NUM hvd.32044092008168 45 94 determination determination NOUN hvd.32044092008168 45 95 of of ADP hvd.32044092008168 45 96 v. v. PROPN hvd.32044092008168 45 97 third third ADJ hvd.32044092008168 45 98 method method NOUN hvd.32044092008168 45 99 70 70 NUM hvd.32044092008168 45 100 value value NOUN hvd.32044092008168 45 101 of of ADP hvd.32044092008168 45 102 the the DET hvd.32044092008168 45 103 constant constant ADJ hvd.32044092008168 45 104 ky ky PROPN hvd.32044092008168 45 105 70 70 NUM hvd.32044092008168 45 106 general general ADJ hvd.32044092008168 45 107 form form NOUN hvd.32044092008168 45 108 as as ADP hvd.32044092008168 45 109 product product NOUN hvd.32044092008168 45 110 of of ADP hvd.32044092008168 45 111 0 0 NUM hvd.32044092008168 45 112 , , PUNCT hvd.32044092008168 45 113 0 0 NUM hvd.32044092008168 45 114 , , PUNCT hvd.32044092008168 45 115 , , PUNCT hvd.32044092008168 45 116 71 71 NUM hvd.32044092008168 45 117 the the DET hvd.32044092008168 45 118 functions function NOUN hvd.32044092008168 45 119 fi fi NOUN hvd.32044092008168 45 120 , , PUNCT hvd.32044092008168 45 121 f2 f2 PROPN hvd.32044092008168 45 122 , , PUNCT hvd.32044092008168 45 123 f f PROPN hvd.32044092008168 45 124 72 72 NUM hvd.32044092008168 45 125 forms form NOUN hvd.32044092008168 45 126 for for ADP hvd.32044092008168 45 127 p(v p(v PROPN hvd.32044092008168 45 128 ) ) PUNCT hvd.32044092008168 45 129 and and CCONJ hvd.32044092008168 45 130 p p NOUN hvd.32044092008168 45 131 ' ' PUNCT hvd.32044092008168 45 132 ( ( PUNCT hvd.32044092008168 45 133 v v NOUN hvd.32044092008168 45 134 ) ) PUNCT hvd.32044092008168 45 135 in in ADP hvd.32044092008168 45 136 terms term NOUN hvd.32044092008168 45 137 of of ADP hvd.32044092008168 45 138 fa fa PROPN hvd.32044092008168 45 139 and and CCONJ hvd.32044092008168 45 140 02 02 NUM hvd.32044092008168 45 141 72 72 NUM hvd.32044092008168 45 142 relation relation NOUN hvd.32044092008168 45 143 of of ADP hvd.32044092008168 45 144 f. f. PROPN hvd.32044092008168 45 145 to to ADP hvd.32044092008168 45 146 x x PROPN hvd.32044092008168 46 1 and and CCONJ hvd.32044092008168 46 2 the the DET hvd.32044092008168 46 3 factors factor NOUN hvd.32044092008168 46 4 of of ADP hvd.32044092008168 46 5 % % NOUN hvd.32044092008168 46 6 73 73 NUM hvd.32044092008168 46 7 reduction reduction NOUN hvd.32044092008168 46 8 to to ADP hvd.32044092008168 46 9 the the DET hvd.32044092008168 46 10 forms form NOUN hvd.32044092008168 46 11 of of ADP hvd.32044092008168 46 12 m. m. NOUN hvd.32044092008168 46 13 hermite hermite PROPN hvd.32044092008168 46 14 73 73 NUM hvd.32044092008168 46 15 general general ADJ hvd.32044092008168 46 16 discussion discussion NOUN hvd.32044092008168 46 17 . . PUNCT hvd.32044092008168 47 1 73 73 NUM hvd.32044092008168 47 2 review review NOUN hvd.32044092008168 47 3 of of ADP hvd.32044092008168 47 4 the the DET hvd.32044092008168 47 5 theory theory NOUN hvd.32044092008168 47 6 73 73 NUM hvd.32044092008168 47 7 general general ADJ hvd.32044092008168 47 8 integral integral ADJ hvd.32044092008168 47 9 p p PROPN hvd.32044092008168 47 10 0 0 NUM hvd.32044092008168 47 11 74 74 NUM hvd.32044092008168 47 12 integral integral ADJ hvd.32044092008168 47 13 q q PROPN hvd.32044092008168 47 14 , , PUNCT hvd.32044092008168 47 15 0 0 NUM hvd.32044092008168 47 16 , , PUNCT hvd.32044092008168 47 17 ν ν NOUN hvd.32044092008168 47 18 = = SYM hvd.32044092008168 47 19 0 0 NUM hvd.32044092008168 47 20 74 74 NUM hvd.32044092008168 47 21 integral integral ADJ hvd.32044092008168 47 22 f. f. NOUN hvd.32044092008168 47 23 0 0 PROPN hvd.32044092008168 47 24 , , PUNCT hvd.32044092008168 47 25 v v NOUN hvd.32044092008168 47 26 = = X hvd.32044092008168 47 27 x x PUNCT hvd.32044092008168 47 28 + + NUM hvd.32044092008168 47 29 0 0 NUM hvd.32044092008168 47 30 74 74 NUM hvd.32044092008168 47 31 case case NOUN hvd.32044092008168 47 32 v v NOUN hvd.32044092008168 47 33 = = NOUN hvd.32044092008168 47 34 0 0 NUM hvd.32044092008168 47 35 75 75 NUM hvd.32044092008168 47 36 functions function NOUN hvd.32044092008168 47 37 of of ADP hvd.32044092008168 47 38 m. m. NOUN hvd.32044092008168 47 39 mittag mittag ADJ hvd.32044092008168 47 40 - - PUNCT hvd.32044092008168 47 41 leffler leffler NOUN hvd.32044092008168 47 42 75 75 NUM hvd.32044092008168 47 43 relation relation NOUN hvd.32044092008168 47 44 to to ADP hvd.32044092008168 47 45 the the DET hvd.32044092008168 47 46 case case NOUN hvd.32044092008168 47 47 x x SYM hvd.32044092008168 47 48 0 0 NUM hvd.32044092008168 47 49 75 75 NUM hvd.32044092008168 47 50 definition definition NOUN hvd.32044092008168 47 51 of of ADP hvd.32044092008168 47 52 the the DET hvd.32044092008168 47 53 functions function NOUN hvd.32044092008168 47 54 . . PUNCT hvd.32044092008168 48 1 75 75 NUM hvd.32044092008168 48 2 determination determination NOUN hvd.32044092008168 48 3 as as ADP hvd.32044092008168 48 4 a a DET hvd.32044092008168 48 5 special special ADJ hvd.32044092008168 48 6 case case NOUN hvd.32044092008168 48 7 of of ADP hvd.32044092008168 48 8 the the DET hvd.32044092008168 48 9 doubly doubly ADV hvd.32044092008168 48 10 periodic periodic ADJ hvd.32044092008168 48 11 function function NOUN hvd.32044092008168 48 12 of of ADP hvd.32044092008168 48 13 the the DET hvd.32044092008168 48 14 second second ADJ hvd.32044092008168 48 15 species specie NOUN hvd.32044092008168 48 16 76 76 NUM hvd.32044092008168 48 17 determination determination NOUN hvd.32044092008168 48 18 of of ADP hvd.32044092008168 48 19 the the DET hvd.32044092008168 48 20 eliment eliment ADJ hvd.32044092008168 48 21 , , PUNCT hvd.32044092008168 48 22 v v ADP hvd.32044092008168 48 23 0 0 NUM hvd.32044092008168 48 24 77 77 NUM hvd.32044092008168 48 25 integral integral ADJ hvd.32044092008168 48 26 ( ( PUNCT hvd.32044092008168 48 27 v v NOUN hvd.32044092008168 48 28 = = SYM hvd.32044092008168 48 29 0 0 NUM hvd.32044092008168 48 30 ) ) PUNCT hvd.32044092008168 48 31 . . PUNCT hvd.32044092008168 48 32 . . PUNCT hvd.32044092008168 49 1 .78 .78 NUM hvd.32044092008168 49 2 table table NOUN hvd.32044092008168 49 3 of of ADP hvd.32044092008168 49 4 forms form NOUN hvd.32044092008168 49 5 and and CCONJ hvd.32044092008168 49 6 relations relation NOUN hvd.32044092008168 49 7 ( ( PUNCT hvd.32044092008168 49 8 n n NUM hvd.32044092008168 49 9 3 3 X hvd.32044092008168 49 10 ) ) PUNCT hvd.32044092008168 49 11 79 79 NUM hvd.32044092008168 49 12 3 3 NUM hvd.32044092008168 49 13 3 3 NUM hvd.32044092008168 49 14 n=3 n=3 NOUN hvd.32044092008168 50 1 ܕ002 ܕ002 PROPN hvd.32044092008168 50 2 c c NOUN hvd.32044092008168 50 3 = = PROPN hvd.32044092008168 50 4 0 0 NUM hvd.32044092008168 50 5 or or CCONJ hvd.32044092008168 50 6 x x SYM hvd.32044092008168 50 7 21 21 NUM hvd.32044092008168 50 8 = = NOUN hvd.32044092008168 50 9 thesis thesis NOUN hvd.32044092008168 50 10 . . PUNCT hvd.32044092008168 51 1 part part PROPN hvd.32044092008168 51 2 i. i. PROPN hvd.32044092008168 51 3 historical historical PROPN hvd.32044092008168 51 4 development development NOUN hvd.32044092008168 51 5 and and CCONJ hvd.32044092008168 51 6 definition definition NOUN hvd.32044092008168 51 7 of of ADP hvd.32044092008168 51 8 the the DET hvd.32044092008168 51 9 equation equation NOUN hvd.32044092008168 51 10 of of ADP hvd.32044092008168 51 11 lamé lamé NOUN hvd.32044092008168 51 12 . . PUNCT hvd.32044092008168 52 1 the the DET hvd.32044092008168 52 2 problem problem NOUN hvd.32044092008168 52 3 of of ADP hvd.32044092008168 52 4 lamé lamé NOUN hvd.32044092008168 52 5 . . PUNCT hvd.32044092008168 53 1 in in ADP hvd.32044092008168 53 2 order order NOUN hvd.32044092008168 53 3 to to PART hvd.32044092008168 53 4 arrive arrive VERB hvd.32044092008168 53 5 at at ADP hvd.32044092008168 53 6 an an DET hvd.32044092008168 53 7 understanding understanding NOUN hvd.32044092008168 53 8 of of ADP hvd.32044092008168 53 9 the the DET hvd.32044092008168 53 10 highly highly ADV hvd.32044092008168 53 11 generalized generalize VERB hvd.32044092008168 53 12 forms form NOUN hvd.32044092008168 53 13 that that PRON hvd.32044092008168 53 14 have have AUX hvd.32044092008168 53 15 taken take VERB hvd.32044092008168 53 16 the the DET hvd.32044092008168 53 17 name name NOUN hvd.32044092008168 53 18 of of ADP hvd.32044092008168 53 19 lamé lamé NOUN hvd.32044092008168 53 20 it it PRON hvd.32044092008168 53 21 is be AUX hvd.32044092008168 53 22 adivisable adivisable ADJ hvd.32044092008168 53 23 to to PART hvd.32044092008168 53 24 return return VERB hvd.32044092008168 53 25 for for ADP hvd.32044092008168 53 26 the the DET hvd.32044092008168 53 27 moment moment NOUN hvd.32044092008168 53 28 to to ADP hvd.32044092008168 53 29 the the DET hvd.32044092008168 53 30 original original ADJ hvd.32044092008168 53 31 problem problem NOUN hvd.32044092008168 53 32 of of ADP hvd.32044092008168 53 33 the the DET hvd.32044092008168 53 34 potential potential NOUN hvd.32044092008168 53 35 in in ADP hvd.32044092008168 53 36 which which PRON hvd.32044092008168 53 37 they they PRON hvd.32044092008168 53 38 claim claim VERB hvd.32044092008168 53 39 a a DET hvd.32044092008168 53 40 common common ADJ hvd.32044092008168 53 41 origin origin NOUN hvd.32044092008168 53 42 . . PUNCT hvd.32044092008168 54 1 lagrange lagrange PROPN hvd.32044092008168 54 2 and and CCONJ hvd.32044092008168 54 3 laplace laplace NOUN hvd.32044092008168 54 4 ( ( PUNCT hvd.32044092008168 54 5 1782 1782 NUM hvd.32044092008168 54 6 ) ) PUNCT hvd.32044092008168 54 7 in in ADP hvd.32044092008168 54 8 their their PRON hvd.32044092008168 54 9 researches research NOUN hvd.32044092008168 54 10 with with ADP hvd.32044092008168 54 11 respect respect NOUN hvd.32044092008168 54 12 to to ADP hvd.32044092008168 54 13 the the DET hvd.32044092008168 54 14 earth earth NOUN hvd.32044092008168 54 15 regarded regard VERB hvd.32044092008168 54 16 as as ADP hvd.32044092008168 54 17 a a DET hvd.32044092008168 54 18 solid solid ADJ hvd.32044092008168 54 19 sphere sphere NOUN hvd.32044092008168 54 20 developed develop VERB hvd.32044092008168 54 21 the the DET hvd.32044092008168 54 22 potential potential ADJ hvd.32044092008168 54 23 function function NOUN hvd.32044092008168 54 24 * * PUNCT hvd.32044092008168 54 25 ) ) PUNCT hvd.32044092008168 54 26 which which PRON hvd.32044092008168 54 27 led lead VERB hvd.32044092008168 54 28 to to ADP hvd.32044092008168 54 29 the the DET hvd.32044092008168 54 30 development development NOUN hvd.32044092008168 54 31 of of ADP hvd.32044092008168 54 32 the the DET hvd.32044092008168 54 33 theory theory NOUN hvd.32044092008168 54 34 of of ADP hvd.32044092008168 54 35 the the DET hvd.32044092008168 54 36 kugelfunction kugelfunction NOUN hvd.32044092008168 54 37 . . PUNCT hvd.32044092008168 55 1 from from ADP hvd.32044092008168 55 2 this this DET hvd.32044092008168 55 3 date date NOUN hvd.32044092008168 55 4 until until ADP hvd.32044092008168 55 5 1839 1839 NUM hvd.32044092008168 55 6 the the DET hvd.32044092008168 55 7 only only ADJ hvd.32044092008168 55 8 name name NOUN hvd.32044092008168 55 9 that that PRON hvd.32044092008168 55 10 need need VERB hvd.32044092008168 55 11 be be AUX hvd.32044092008168 55 12 mentioned mention VERB hvd.32044092008168 55 13 is be AUX hvd.32044092008168 55 14 that that PRON hvd.32044092008168 55 15 of of ADP hvd.32044092008168 55 16 fourier fourier NOUN hvd.32044092008168 55 17 ( ( PUNCT hvd.32044092008168 55 18 1822 1822 NUM hvd.32044092008168 55 19 ) ) PUNCT hvd.32044092008168 55 20 who who PRON hvd.32044092008168 55 21 , , PUNCT hvd.32044092008168 55 22 in in ADP hvd.32044092008168 55 23 developing develop VERB hvd.32044092008168 55 24 his his PRON hvd.32044092008168 55 25 theory theory NOUN hvd.32044092008168 55 26 of of ADP hvd.32044092008168 55 27 heat heat NOUN hvd.32044092008168 55 28 solved solve VERB hvd.32044092008168 55 29 the the DET hvd.32044092008168 55 30 problem problem NOUN hvd.32044092008168 55 31 with with ADP hvd.32044092008168 55 32 reference reference NOUN hvd.32044092008168 55 33 to to ADP hvd.32044092008168 55 34 a a DET hvd.32044092008168 55 35 right right ADJ hvd.32044092008168 55 36 angled angled NOUN hvd.32044092008168 55 37 cylinder cylinder NOUN hvd.32044092008168 55 38 discovering discover VERB hvd.32044092008168 55 39 the the DET hvd.32044092008168 55 40 series series NOUN hvd.32044092008168 55 41 named name VERB hvd.32044092008168 55 42 after after ADP hvd.32044092008168 55 43 him he PRON hvd.32044092008168 55 44 . . PUNCT hvd.32044092008168 56 1 in in ADP hvd.32044092008168 56 2 the the DET hvd.32044092008168 56 3 following following ADJ hvd.32044092008168 56 4 decade decade NOUN hvd.32044092008168 56 5 * * PUNCT hvd.32044092008168 56 6 * * NOUN hvd.32044092008168 56 7 ) ) PUNCT hvd.32044092008168 56 8 however however ADV hvd.32044092008168 56 9 lamé lamé NOUN hvd.32044092008168 56 10 * * PUNCT hvd.32044092008168 56 11 * * PUNCT hvd.32044092008168 56 12 * * PUNCT hvd.32044092008168 56 13 ) ) PUNCT hvd.32044092008168 56 14 generalized generalize VERB hvd.32044092008168 56 15 the the DET hvd.32044092008168 56 16 work work NOUN hvd.32044092008168 56 17 of of ADP hvd.32044092008168 56 18 his his PRON hvd.32044092008168 56 19 predicessors predicessor NOUN hvd.32044092008168 56 20 by by ADP hvd.32044092008168 56 21 solving solve VERB hvd.32044092008168 56 22 the the DET hvd.32044092008168 56 23 problem problem NOUN hvd.32044092008168 56 24 for for ADP hvd.32044092008168 56 25 an an DET hvd.32044092008168 56 26 ellipsoid ellipsoid NOUN hvd.32044092008168 56 27 with with ADP hvd.32044092008168 56 28 three three NUM hvd.32044092008168 56 29 unequal unequal ADJ hvd.32044092008168 56 30 axes axis NOUN hvd.32044092008168 56 31 thus thus ADV hvd.32044092008168 56 32 laying lay VERB hvd.32044092008168 56 33 the the DET hvd.32044092008168 56 34 foundation foundation NOUN hvd.32044092008168 56 35 for for ADP hvd.32044092008168 56 36 the the DET hvd.32044092008168 56 37 development development NOUN hvd.32044092008168 56 38 of of ADP hvd.32044092008168 56 39 functions function NOUN hvd.32044092008168 56 40 of of ADP hvd.32044092008168 56 41 which which PRON hvd.32044092008168 56 42 the the DET hvd.32044092008168 56 43 former former ADJ hvd.32044092008168 56 44 are be AUX hvd.32044092008168 56 45 but but CCONJ hvd.32044092008168 56 46 special special ADJ hvd.32044092008168 56 47 cases case NOUN hvd.32044092008168 56 48 . . PUNCT hvd.32044092008168 57 1 he he PRON hvd.32044092008168 57 2 used use VERB hvd.32044092008168 57 3 to to ADP hvd.32044092008168 57 4 this this DET hvd.32044092008168 57 5 end end NOUN hvd.32044092008168 57 6 the the DET hvd.32044092008168 57 7 inductive inductive ADJ hvd.32044092008168 57 8 method method NOUN hvd.32044092008168 57 9 arriving arrive VERB hvd.32044092008168 57 10 at at ADP hvd.32044092008168 57 11 special special ADJ hvd.32044092008168 57 12 solutions solution NOUN hvd.32044092008168 57 13 through through ADP hvd.32044092008168 57 14 a a DET hvd.32044092008168 57 15 study study NOUN hvd.32044092008168 57 16 of of ADP hvd.32044092008168 57 17 the the DET hvd.32044092008168 57 18 problem problem NOUN hvd.32044092008168 57 19 already already ADV hvd.32044092008168 57 20 solved solve VERB hvd.32044092008168 57 21 with with ADP hvd.32044092008168 57 22 reference reference NOUN hvd.32044092008168 57 23 too too ADV hvd.32044092008168 57 24 the the DET hvd.32044092008168 57 25 sphere sphere NOUN hvd.32044092008168 57 26 . . PUNCT hvd.32044092008168 58 1 the the DET hvd.32044092008168 58 2 problem problem NOUN hvd.32044092008168 58 3 of of ADP hvd.32044092008168 58 4 lamé lamé NOUN hvd.32044092008168 58 5 may may AUX hvd.32044092008168 58 6 be be AUX hvd.32044092008168 58 7 stated state VERB hvd.32044092008168 58 8 thus thus ADV hvd.32044092008168 58 9 : : PUNCT hvd.32044092008168 58 10 let let VERB hvd.32044092008168 58 11 the the DET hvd.32044092008168 58 12 surface surface NOUN hvd.32044092008168 58 13 of of ADP hvd.32044092008168 58 14 an an DET hvd.32044092008168 58 15 ellipsoid ellipsoid NOUN hvd.32044092008168 58 16 be be AUX hvd.32044092008168 58 17 given give VERB hvd.32044092008168 58 18 by by ADP hvd.32044092008168 58 19 the the DET hvd.32044092008168 58 20 equation equation NOUN hvd.32044092008168 58 21 u u PROPN hvd.32044092008168 58 22 uo uo PROPN hvd.32044092008168 58 23 ; ; PUNCT hvd.32044092008168 58 24 it it PRON hvd.32044092008168 58 25 is be AUX hvd.32044092008168 58 26 required require VERB hvd.32044092008168 58 27 to to PART hvd.32044092008168 58 28 find find VERB hvd.32044092008168 58 29 a a DET hvd.32044092008168 58 30 function function NOUN hvd.32044092008168 58 31 t t NOUN hvd.32044092008168 58 32 which which PRON hvd.32044092008168 58 33 will will AUX hvd.32044092008168 58 34 satisfy satisfy VERB hvd.32044092008168 58 35 the the DET hvd.32044092008168 58 36 equation equation NOUN hvd.32044092008168 58 37 of of ADP hvd.32044092008168 58 38 the the DET hvd.32044092008168 58 39 potential potential NOUN hvd.32044092008168 58 40 and and CCONJ hvd.32044092008168 58 41 which which PRON hvd.32044092008168 58 42 for for ADP hvd.32044092008168 58 43 the the DET hvd.32044092008168 58 44 value value NOUN hvd.32044092008168 58 45 u u PROPN hvd.32044092008168 58 46 = = PROPN hvd.32044092008168 58 47 u u PROPN hvd.32044092008168 58 48 , , PUNCT hvd.32044092008168 58 49 will will AUX hvd.32044092008168 58 50 reduce reduce VERB hvd.32044092008168 58 51 to to ADP hvd.32044092008168 58 52 a a DET hvd.32044092008168 58 53 given give VERB hvd.32044092008168 58 54 uy uy NOUN hvd.32044092008168 58 55 * * PUNCT hvd.32044092008168 58 56 ) ) PUNCT hvd.32044092008168 58 57 see see VERB hvd.32044092008168 58 58 note note NOUN hvd.32044092008168 58 59 heine heine NOUN hvd.32044092008168 58 60 , , PUNCT hvd.32044092008168 58 61 handbuch handbuch PROPN hvd.32044092008168 58 62 der der PROPN hvd.32044092008168 58 63 kugelfunctionen kugelfunctionen PROPN hvd.32044092008168 58 64 , , PUNCT hvd.32044092008168 58 65 p. p. NOUN hvd.32044092008168 58 66 2 2 NUM hvd.32044092008168 58 67 , , PUNCT hvd.32044092008168 58 68 berlin berlin PROPN hvd.32044092008168 58 69 1878 1878 NUM hvd.32044092008168 58 70 , , PUNCT hvd.32044092008168 58 71 and and CCONJ hvd.32044092008168 58 72 heine heine NOUN hvd.32044092008168 58 73 , , PUNCT hvd.32044092008168 58 74 2d 2d NUM hvd.32044092008168 58 75 vol vol NOUN hvd.32044092008168 58 76 . . PUNCT hvd.32044092008168 59 1 zusätze zusätze PROPN hvd.32044092008168 59 2 zum zum PROPN hvd.32044092008168 59 3 ersten ersten PROPN hvd.32044092008168 59 4 bande bande NOUN hvd.32044092008168 59 5 . . PUNCT hvd.32044092008168 60 1 * * PUNCT hvd.32044092008168 60 2 * * PUNCT hvd.32044092008168 60 3 ) ) PUNCT hvd.32044092008168 60 4 see see VERB hvd.32044092008168 60 5 also also ADV hvd.32044092008168 60 6 reference reference NOUN hvd.32044092008168 60 7 to to ADP hvd.32044092008168 60 8 green green PROPN hvd.32044092008168 60 9 heine heine PROPN hvd.32044092008168 60 10 p. p. PROPN hvd.32044092008168 60 11 1 1 NUM hvd.32044092008168 60 12 . . PUNCT hvd.32044092008168 61 1 * * PUNCT hvd.32044092008168 61 2 * * PUNCT hvd.32044092008168 61 3 * * PUNCT hvd.32044092008168 61 4 ) ) PUNCT hvd.32044092008168 61 5 memoire memoire PROPN hvd.32044092008168 61 6 sur sur X hvd.32044092008168 61 7 les les X hvd.32044092008168 61 8 axes axis NOUN hvd.32044092008168 61 9 des des X hvd.32044092008168 61 10 surfaces surface NOUN hvd.32044092008168 61 11 isothermes isothermes PROPN hvd.32044092008168 61 12 du du PROPN hvd.32044092008168 61 13 second second PROPN hvd.32044092008168 61 14 degree degree NOUN hvd.32044092008168 61 15 considérés considéré VERB hvd.32044092008168 61 16 comme comme X hvd.32044092008168 61 17 des des X hvd.32044092008168 61 18 fonctions fonction NOUN hvd.32044092008168 61 19 de de X hvd.32044092008168 61 20 la la X hvd.32044092008168 61 21 temperature temperature PROPN hvd.32044092008168 61 22 . . PUNCT hvd.32044092008168 62 1 journal journal PROPN hvd.32044092008168 62 2 des des X hvd.32044092008168 62 3 mathématiques mathématiques X hvd.32044092008168 62 4 pures pure NOUN hvd.32044092008168 62 5 et et NOUN hvd.32044092008168 62 6 appliqués appliqué NOUN hvd.32044092008168 62 7 . . PUNCT hvd.32044092008168 63 1 1re 1re PROPN hvd.32044092008168 63 2 série série PROPN hvd.32044092008168 63 3 . . PROPN hvd.32044092008168 63 4 t. t. PROPN hvd.32044092008168 63 5 iv iv PROPN hvd.32044092008168 63 6 , , PUNCT hvd.32044092008168 63 7 p. p. PROPN hvd.32044092008168 63 8 103 103 NUM hvd.32044092008168 63 9 . . PUNCT hvd.32044092008168 64 1 1839 1839 NUM hvd.32044092008168 64 2 . . PUNCT hvd.32044092008168 65 1 12 12 NUM hvd.32044092008168 65 2 part part NOUN hvd.32044092008168 65 3 i. i. PROPN hvd.32044092008168 65 4 dº dº PROPN hvd.32044092008168 65 5 u u PROPN hvd.32044092008168 65 6 . . PUNCT hvd.32044092008168 66 1 cz cz PROPN hvd.32044092008168 66 2 a a DET hvd.32044092008168 66 3 d2 d2 PROPN hvd.32044092008168 66 4 t t PROPN hvd.32044092008168 66 5 d2 d2 PROPN hvd.32044092008168 66 6 t t PROPN hvd.32044092008168 66 7 pv pv PROPN hvd.32044092008168 66 8 ) ) PUNCT hvd.32044092008168 66 9 dus dus NOUN hvd.32044092008168 66 10 . . PUNCT hvd.32044092008168 67 1 2 2 NUM hvd.32044092008168 67 2 where where SCONJ hvd.32044092008168 67 3 y y PROPN hvd.32044092008168 67 4 2 2 NUM hvd.32044092008168 67 5 function function NOUN hvd.32044092008168 67 6 of of ADP hvd.32044092008168 67 7 v v PROPN hvd.32044092008168 67 8 and and CCONJ hvd.32044092008168 67 9 w w PROPN hvd.32044092008168 67 10 , , PUNCT hvd.32044092008168 67 11 where where SCONJ hvd.32044092008168 67 12 t t PROPN hvd.32044092008168 67 13 is be AUX hvd.32044092008168 67 14 the the DET hvd.32044092008168 67 15 temperature temperature NOUN hvd.32044092008168 67 16 at at ADP hvd.32044092008168 67 17 a a DET hvd.32044092008168 67 18 point point NOUN hvd.32044092008168 67 19 whose whose DET hvd.32044092008168 67 20 elliptic elliptic ADJ hvd.32044092008168 67 21 coordinates coordinate NOUN hvd.32044092008168 67 22 are be AUX hvd.32044092008168 67 23 u u PROPN hvd.32044092008168 67 24 , , PUNCT hvd.32044092008168 67 25 v v NOUN hvd.32044092008168 67 26 and and CCONJ hvd.32044092008168 67 27 w. w. NOUN hvd.32044092008168 67 28 the the DET hvd.32044092008168 67 29 working work VERB hvd.32044092008168 67 30 eliments eliment NOUN hvd.32044092008168 67 31 are be AUX hvd.32044092008168 67 32 then then ADV hvd.32044092008168 67 33 , , PUNCT hvd.32044092008168 67 34 the the DET hvd.32044092008168 67 35 potential potential ADJ hvd.32044092008168 67 36 function function NOUN hvd.32044092008168 67 37 , , PUNCT hvd.32044092008168 67 38 generally generally ADV hvd.32044092008168 67 39 written write VERB hvd.32044092008168 67 40 [ [ X hvd.32044092008168 67 41 1 1 NUM hvd.32044092008168 67 42 ] ] PUNCT hvd.32044092008168 67 43 · · PUNCT hvd.32044092008168 67 44 0 0 NUM hvd.32044092008168 67 45 doc doc PROPN hvd.32044092008168 67 46 or or CCONJ hvd.32044092008168 67 47 transformed transform VERB hvd.32044092008168 67 48 in in ADP hvd.32044092008168 67 49 terms term NOUN hvd.32044092008168 67 50 of of ADP hvd.32044092008168 67 51 the the DET hvd.32044092008168 67 52 p p NOUN hvd.32044092008168 67 53 function function NOUN hvd.32044092008168 67 54 t t X hvd.32044092008168 68 1 [ [ X hvd.32044092008168 68 2 2 2 X hvd.32044092008168 68 3 ] ] PUNCT hvd.32044092008168 68 4 ( ( PUNCT hvd.32044092008168 68 5 pv pv INTJ hvd.32044092008168 68 6 — — PUNCT hvd.32044092008168 68 7 pu pu PROPN hvd.32044092008168 68 8 ) ) PUNCT hvd.32044092008168 68 9 and and CCONJ hvd.32044092008168 68 10 + + X hvd.32044092008168 68 11 ( ( PUNCT hvd.32044092008168 68 12 pu pu X hvd.32044092008168 68 13 — — PUNCT hvd.32044092008168 68 14 pulang pulang PROPN hvd.32044092008168 68 15 dv dv PROPN hvd.32044092008168 68 16 : : PUNCT hvd.32044092008168 68 17 + + CCONJ hvd.32044092008168 69 1 ( ( PUNCT hvd.32044092008168 69 2 pů pů INTJ hvd.32044092008168 69 3 – – PUNCT hvd.32044092008168 69 4 pv pv ADP hvd.32044092008168 69 5 ) ) PUNCT hvd.32044092008168 69 6 dan dan PROPN hvd.32044092008168 69 7 = = PROPN hvd.32044092008168 69 8 0 0 NUM hvd.32044092008168 69 9 dw2 dw2 NOUN hvd.32044092008168 69 10 the the DET hvd.32044092008168 69 11 relation relation NOUN hvd.32044092008168 69 12 , , PUNCT hvd.32044092008168 69 13 [ [ X hvd.32044092008168 69 14 3 3 X hvd.32044092008168 69 15 ] ] PUNCT hvd.32044092008168 69 16 · · PUNCT hvd.32044092008168 69 17 t t PROPN hvd.32044092008168 69 18 = = SYM hvd.32044092008168 69 19 f(u f(u PROPN hvd.32044092008168 69 20 ) ) PUNCT hvd.32044092008168 69 21 f(v f(v PROPN hvd.32044092008168 69 22 ) ) PUNCT hvd.32044092008168 69 23 f(w f(w PROPN hvd.32044092008168 69 24 ) ) PUNCT hvd.32044092008168 69 25 and and CCONJ hvd.32044092008168 69 26 the the DET hvd.32044092008168 69 27 equation equation NOUN hvd.32044092008168 69 28 day day NOUN hvd.32044092008168 69 29 [ [ X hvd.32044092008168 69 30 4 4 NUM hvd.32044092008168 69 31 ] ] PUNCT hvd.32044092008168 69 32 · · PUNCT hvd.32044092008168 69 33 du du X hvd.32044092008168 69 34 [ [ X hvd.32044092008168 69 35 apu apu X hvd.32044092008168 69 36 + + CCONJ hvd.32044092008168 69 37 b]y b]y PROPN hvd.32044092008168 69 38 f(u f(u PROPN hvd.32044092008168 69 39 ) ) PUNCT hvd.32044092008168 69 40 and and CCONJ hvd.32044092008168 69 41 a a PRON hvd.32044092008168 69 42 and and CCONJ hvd.32044092008168 69 43 b b NOUN hvd.32044092008168 69 44 are be AUX hvd.32044092008168 69 45 constants constant NOUN hvd.32044092008168 69 46 . . PUNCT hvd.32044092008168 70 1 if if SCONJ hvd.32044092008168 70 2 t t PROPN hvd.32044092008168 70 3 is be AUX hvd.32044092008168 70 4 developed develop VERB hvd.32044092008168 70 5 by by ADP hvd.32044092008168 70 6 maclaurin maclaurin PROPN hvd.32044092008168 70 7 's 's PART hvd.32044092008168 70 8 theorem theorem NOUN hvd.32044092008168 70 9 with with ADP hvd.32044092008168 70 10 respect respect NOUN hvd.32044092008168 70 11 to to ADP hvd.32044092008168 70 12 the the DET hvd.32044092008168 70 13 rectangular rectangular ADJ hvd.32044092008168 70 14 coordinates coordinate NOUN hvd.32044092008168 70 15 , , PUNCT hvd.32044092008168 70 16 we we PRON hvd.32044092008168 70 17 may may AUX hvd.32044092008168 70 18 write write VERB hvd.32044092008168 70 19 : : PUNCT hvd.32044092008168 70 20 * * PUNCT hvd.32044092008168 70 21 ) ) PUNCT hvd.32044092008168 71 1 [ [ X hvd.32044092008168 71 2 5 5 NUM hvd.32044092008168 71 3 ] ] PUNCT hvd.32044092008168 71 4 . . PUNCT hvd.32044092008168 72 1 t= t= PROPN hvd.32044092008168 72 2 t. t. PROPN hvd.32044092008168 72 3 + + CCONJ hvd.32044092008168 72 4 t t PROPN hvd.32044092008168 72 5 , , PUNCT hvd.32044092008168 72 6 + + PROPN hvd.32044092008168 72 7 t t PROPN hvd.32044092008168 72 8 , , PUNCT hvd.32044092008168 72 9 + + NUM hvd.32044092008168 72 10 ... ... PUNCT hvd.32044092008168 72 11 + + CCONJ hvd.32044092008168 72 12 in+ in+ ADJ hvd.32044092008168 72 13 ... ... PUNCT hvd.32044092008168 72 14 tn tn PROPN hvd.32044092008168 72 15 where where SCONJ hvd.32044092008168 72 16 tn tn PROPN hvd.32044092008168 72 17 in in ADP hvd.32044092008168 72 18 general general ADJ hvd.32044092008168 72 19 is be AUX hvd.32044092008168 72 20 an an DET hvd.32044092008168 72 21 intire intire ADJ hvd.32044092008168 72 22 homogenious homogenious ADJ hvd.32044092008168 72 23 polynomial polynomial NOUN hvd.32044092008168 72 24 of of ADP hvd.32044092008168 72 25 the the DET hvd.32044092008168 72 26 nth nth NOUN hvd.32044092008168 72 27 degree degree NOUN hvd.32044092008168 72 28 , , PUNCT hvd.32044092008168 72 29 it it PRON hvd.32044092008168 72 30 is be AUX hvd.32044092008168 72 31 observed observe VERB hvd.32044092008168 72 32 that that SCONJ hvd.32044092008168 72 33 each each PRON hvd.32044092008168 72 34 of of ADP hvd.32044092008168 72 35 the the DET hvd.32044092008168 72 36 functions function NOUN hvd.32044092008168 72 37 in in ADP hvd.32044092008168 72 38 will will AUX hvd.32044092008168 72 39 also also ADV hvd.32044092008168 72 40 satisfy satisfy VERB hvd.32044092008168 72 41 [ [ X hvd.32044092008168 72 42 1 1 NUM hvd.32044092008168 72 43 ] ] PUNCT hvd.32044092008168 72 44 , , PUNCT hvd.32044092008168 72 45 the the DET hvd.32044092008168 72 46 equation equation NOUN hvd.32044092008168 72 47 of of ADP hvd.32044092008168 72 48 the the DET hvd.32044092008168 72 49 potential potential NOUN hvd.32044092008168 72 50 , , PUNCT hvd.32044092008168 72 51 in in ADP hvd.32044092008168 72 52 which which DET hvd.32044092008168 72 53 case case NOUN hvd.32044092008168 72 54 [ [ X hvd.32044092008168 72 55 1 1 X hvd.32044092008168 72 56 ] ] PUNCT hvd.32044092008168 72 57 would would AUX hvd.32044092008168 72 58 be be AUX hvd.32044092008168 72 59 an an DET hvd.32044092008168 72 60 intire intire ADJ hvd.32044092008168 72 61 homogeneous homogeneous ADJ hvd.32044092008168 72 62 polynomial polynomial NOUN hvd.32044092008168 72 63 of of ADP hvd.32044092008168 72 64 the the DET hvd.32044092008168 72 65 ( ( PUNCT hvd.32044092008168 72 66 n n CCONJ hvd.32044092008168 72 67 − − PROPN hvd.32044092008168 72 68 2)d 2)d NOUN hvd.32044092008168 72 69 degree degree NOUN hvd.32044092008168 72 70 . . PUNCT hvd.32044092008168 73 1 this this DET hvd.32044092008168 73 2 polynomial polynomial NOUN hvd.32044092008168 73 3 must must AUX hvd.32044092008168 73 4 be be AUX hvd.32044092008168 73 5 identically identically ADV hvd.32044092008168 73 6 zero zero NUM hvd.32044092008168 73 7 which which PRON hvd.32044092008168 73 8 will will AUX hvd.32044092008168 73 9 impose impose VERB hvd.32044092008168 73 10 ( ( PUNCT hvd.32044092008168 73 11 n n CCONJ hvd.32044092008168 73 12 1)n 1)n NUM hvd.32044092008168 73 13 linear linear ADJ hvd.32044092008168 73 14 conditions condition NOUN hvd.32044092008168 73 15 . . PUNCT hvd.32044092008168 74 1 the the DET hvd.32044092008168 74 2 quantities quantity NOUN hvd.32044092008168 74 3 tn tn PROPN hvd.32044092008168 74 4 will will AUX hvd.32044092008168 74 5 have have VERB hvd.32044092008168 74 6 in in ADP hvd.32044092008168 74 7 all all PRON hvd.32044092008168 74 8 ( ( PUNCT hvd.32044092008168 74 9 n n CCONJ hvd.32044092008168 74 10 + + ADP hvd.32044092008168 74 11 1 1 X hvd.32044092008168 74 12 ) ) PUNCT hvd.32044092008168 74 13 ( ( PUNCT hvd.32044092008168 74 14 n n CCONJ hvd.32044092008168 74 15 + + CCONJ hvd.32044092008168 74 16 2 2 NUM hvd.32044092008168 74 17 ) ) PUNCT hvd.32044092008168 74 18 constants constant NOUN hvd.32044092008168 74 19 , , PUNCT hvd.32044092008168 74 20 which which PRON hvd.32044092008168 74 21 leaves leave VERB hvd.32044092008168 74 22 the the DET hvd.32044092008168 74 23 difference difference NOUN hvd.32044092008168 74 24 2n 2n NUM hvd.32044092008168 74 25 + + PUNCT hvd.32044092008168 74 26 1 1 NUM hvd.32044092008168 74 27 equal equal ADJ hvd.32044092008168 74 28 to to ADP hvd.32044092008168 74 29 the the DET hvd.32044092008168 74 30 number number NOUN hvd.32044092008168 74 31 of of ADP hvd.32044092008168 74 32 constants constant NOUN hvd.32044092008168 74 33 that that PRON hvd.32044092008168 74 34 may may AUX hvd.32044092008168 74 35 be be AUX hvd.32044092008168 74 36 considered consider VERB hvd.32044092008168 74 37 arbitrary arbitrary ADJ hvd.32044092008168 74 38 . . PUNCT hvd.32044092008168 75 1 now now ADV hvd.32044092008168 75 2 the the DET hvd.32044092008168 75 3 general general ADJ hvd.32044092008168 75 4 expression expression NOUN hvd.32044092008168 75 5 for for ADP hvd.32044092008168 75 6 x2 x2 PROPN hvd.32044092008168 75 7 in in ADP hvd.32044092008168 75 8 terms term NOUN hvd.32044092008168 75 9 of of ADP hvd.32044092008168 75 10 p p PROPN hvd.32044092008168 75 11 is be AUX hvd.32044092008168 75 12 known know VERB hvd.32044092008168 75 13 to to PART hvd.32044092008168 75 14 be be AUX hvd.32044092008168 75 15 ( ( PUNCT hvd.32044092008168 75 16 pu pu PROPN hvd.32044092008168 75 17 — — PUNCT hvd.32044092008168 75 18 ea ea PROPN hvd.32044092008168 75 19 ) ) PUNCT hvd.32044092008168 75 20 ( ( PUNCT hvd.32044092008168 75 21 pv pv PROPN hvd.32044092008168 75 22 — — PUNCT hvd.32044092008168 75 23 @c @c PROPN hvd.32044092008168 75 24 ) ) PUNCT hvd.32044092008168 75 25 ( ( PUNCT hvd.32044092008168 75 26 pw pw X hvd.32044092008168 75 27 — — PUNCT hvd.32044092008168 75 28 en en X hvd.32044092008168 75 29 ) ) PUNCT hvd.32044092008168 76 1 [ [ X hvd.32044092008168 76 2 6 6 X hvd.32044092008168 76 3 ] ] PUNCT hvd.32044092008168 76 4 ( ( PUNCT hvd.32044092008168 76 5 @p @p PROPN hvd.32044092008168 76 6 ) ) PUNCT hvd.32044092008168 76 7 ( ( PUNCT hvd.32044092008168 76 8 @a @a PROPN hvd.32044092008168 76 9 ey ey X hvd.32044092008168 76 10 ) ) PUNCT hvd.32044092008168 76 11 being be AUX hvd.32044092008168 76 12 a a DET hvd.32044092008168 76 13 constant constant ADJ hvd.32044092008168 76 14 , , PUNCT hvd.32044092008168 76 15 from from ADP hvd.32044092008168 76 16 which which PRON hvd.32044092008168 76 17 we we PRON hvd.32044092008168 76 18 see see VERB hvd.32044092008168 76 19 that that SCONJ hvd.32044092008168 76 20 by by ADP hvd.32044092008168 76 21 a a DET hvd.32044092008168 76 22 change change NOUN hvd.32044092008168 76 23 of of ADP hvd.32044092008168 76 24 variable variable ADJ hvd.32044092008168 76 25 tn tn PROPN hvd.32044092008168 76 26 may may AUX hvd.32044092008168 76 27 become become VERB hvd.32044092008168 76 28 an an DET hvd.32044092008168 76 29 intire intire ADJ hvd.32044092008168 76 30 homogeneous homogeneous ADJ hvd.32044092008168 76 31 function function NOUN hvd.32044092008168 76 32 of of ADP hvd.32044092008168 76 33 the the DET hvd.32044092008168 76 34 nth nth NOUN hvd.32044092008168 76 35 degree degree NOUN hvd.32044092008168 76 36 with with ADP hvd.32044092008168 76 37 respect respect NOUN hvd.32044092008168 76 38 to to ADP hvd.32044092008168 76 39 the the DET hvd.32044092008168 76 40 variables variable NOUN hvd.32044092008168 76 41 [ [ PUNCT hvd.32044092008168 76 42 7 7 NUM hvd.32044092008168 76 43 ] ] PUNCT hvd.32044092008168 76 44 vpu vpu NOUN hvd.32044092008168 76 45 — — PUNCT hvd.32044092008168 76 46 ez ez PROPN hvd.32044092008168 76 47 , , PUNCT hvd.32044092008168 76 48 vpu vpu PROPN hvd.32044092008168 76 49 ez ez PROPN hvd.32044092008168 76 50 quantities quantities PROPN hvd.32044092008168 76 51 proportional proportional ADJ hvd.32044092008168 76 52 to to ADP hvd.32044092008168 76 53 the the DET hvd.32044092008168 76 54 axes axis NOUN hvd.32044092008168 76 55 of of ADP hvd.32044092008168 76 56 the the DET hvd.32044092008168 76 57 ellipsoid ellipsoid NOUN hvd.32044092008168 76 58 , , PUNCT hvd.32044092008168 76 59 and and CCONJ hvd.32044092008168 76 60 of of ADP hvd.32044092008168 76 61 the the DET hvd.32044092008168 76 62 1st 1st ADJ hvd.32044092008168 76 63 degree degree NOUN hvd.32044092008168 76 64 , , PUNCT hvd.32044092008168 76 65 pu pu PROPN hvd.32044092008168 76 66 being be AUX hvd.32044092008168 76 67 of of ADP hvd.32044092008168 76 68 the the DET hvd.32044092008168 76 69 second second ADJ hvd.32044092008168 76 70 and and CCONJ hvd.32044092008168 76 71 p'u p'u ADV hvd.32044092008168 76 72 of of ADP hvd.32044092008168 76 73 the the DET hvd.32044092008168 76 74 third third NOUN hvd.32044092008168 76 75 . . PUNCT hvd.32044092008168 77 1 we we PRON hvd.32044092008168 77 2 have have VERB hvd.32044092008168 77 3 then then ADV hvd.32044092008168 77 4 that that SCONJ hvd.32044092008168 77 5 t t PROPN hvd.32044092008168 77 6 , , PUNCT hvd.32044092008168 77 7 the the DET hvd.32044092008168 77 8 function function NOUN hvd.32044092008168 77 9 sought seek VERB hvd.32044092008168 77 10 , , PUNCT hvd.32044092008168 77 11 is be AUX hvd.32044092008168 77 12 composed compose VERB hvd.32044092008168 77 13 of of ADP hvd.32044092008168 77 14 similar similar ADJ hvd.32044092008168 77 15 functions function NOUN hvd.32044092008168 77 16 in in ADP hvd.32044092008168 77 17 , , PUNCT hvd.32044092008168 77 18 where where SCONJ hvd.32044092008168 77 19 tn tn PROPN hvd.32044092008168 77 20 is be AUX hvd.32044092008168 77 21 of of ADP hvd.32044092008168 77 22 the the DET hvd.32044092008168 77 23 nth nth NOUN hvd.32044092008168 77 24 degree degree NOUN hvd.32044092008168 77 25 , , PUNCT hvd.32044092008168 77 26 is be AUX hvd.32044092008168 77 27 symmetrical symmetrical ADJ hvd.32044092008168 77 28 1 1 NUM hvd.32044092008168 77 29 ? ? SYM hvd.32044092008168 78 1 3 3 NUM hvd.32044092008168 78 2 . . X hvd.32044092008168 78 3 α α NOUN hvd.32044092008168 78 4 · · PUNCT hvd.32044092008168 78 5 vpu vpu NOUN hvd.32044092008168 78 6 – – PUNCT hvd.32044092008168 78 7 , , PUNCT hvd.32044092008168 78 8 @y @y NOUN hvd.32044092008168 78 9 27 27 NUM hvd.32044092008168 78 10 * * PUNCT hvd.32044092008168 78 11 ) ) PUNCT hvd.32044092008168 78 12 see see VERB hvd.32044092008168 78 13 halphen halphen ADV hvd.32044092008168 78 14 . . PUNCT hvd.32044092008168 79 1 vol vol NOUN hvd.32044092008168 79 2 . . PUNCT hvd.32044092008168 80 1 ii ii PROPN hvd.32044092008168 80 2 p. p. NOUN hvd.32044092008168 80 3 466 466 NUM hvd.32044092008168 80 4 . . PUNCT hvd.32044092008168 81 1 historical historical ADJ hvd.32044092008168 81 2 development development NOUN hvd.32044092008168 81 3 and and CCONJ hvd.32044092008168 81 4 definition definition NOUN hvd.32044092008168 81 5 of of ADP hvd.32044092008168 81 6 the the DET hvd.32044092008168 81 7 equation equation NOUN hvd.32044092008168 81 8 of of ADP hvd.32044092008168 81 9 lamé lamé NOUN hvd.32044092008168 81 10 . . PUNCT hvd.32044092008168 82 1 13 13 NUM hvd.32044092008168 82 2 u u PROPN hvd.32044092008168 82 3 . . PUNCT hvd.32044092008168 83 1 with with ADP hvd.32044092008168 83 2 respect respect NOUN hvd.32044092008168 83 3 to to ADP hvd.32044092008168 83 4 u u PROPN hvd.32044092008168 83 5 , , PUNCT hvd.32044092008168 83 6 v v NOUN hvd.32044092008168 83 7 and and CCONJ hvd.32044092008168 83 8 w w PROPN hvd.32044092008168 83 9 and and CCONJ hvd.32044092008168 83 10 having have VERB hvd.32044092008168 83 11 2n 2n NUM hvd.32044092008168 83 12 + + CCONJ hvd.32044092008168 83 13 1 1 NUM hvd.32044092008168 83 14 arbitrary arbitrary ADJ hvd.32044092008168 83 15 constants constant NOUN hvd.32044092008168 83 16 , , PUNCT hvd.32044092008168 83 17 is be AUX hvd.32044092008168 83 18 capable capable ADJ hvd.32044092008168 83 19 of of ADP hvd.32044092008168 83 20 satisfying satisfy VERB hvd.32044092008168 83 21 the the DET hvd.32044092008168 83 22 equation equation NOUN hvd.32044092008168 83 23 [ [ X hvd.32044092008168 83 24 2 2 X hvd.32044092008168 83 25 ] ] PUNCT hvd.32044092008168 83 26 of of ADP hvd.32044092008168 83 27 the the DET hvd.32044092008168 83 28 potential potential NOUN hvd.32044092008168 83 29 . . PUNCT hvd.32044092008168 84 1 from from ADP hvd.32044092008168 84 2 the the DET hvd.32044092008168 84 3 above above ADJ hvd.32044092008168 84 4 relations relation NOUN hvd.32044092008168 84 5 we we PRON hvd.32044092008168 84 6 derive derive VERB hvd.32044092008168 84 7 d2 d2 PROPN hvd.32044092008168 84 8 t t PROPN hvd.32044092008168 84 9 [ [ X hvd.32044092008168 84 10 8 8 NUM hvd.32044092008168 84 11 ] ] PUNCT hvd.32044092008168 84 12 · · PUNCT hvd.32044092008168 84 13 = = SYM hvd.32044092008168 84 14 f"ufvfw f"ufvfw NOUN hvd.32044092008168 84 15 " " PUNCT hvd.32044092008168 84 16 = = VERB hvd.32044092008168 84 17 1 1 NUM hvd.32044092008168 84 18 " " PUNCT hvd.32044092008168 84 19 " " PUNCT hvd.32044092008168 84 20 [ [ X hvd.32044092008168 84 21 apu apu X hvd.32044092008168 84 22 + + CCONJ hvd.32044092008168 84 23 b]t b]t NOUN hvd.32044092008168 84 24 du du NOUN hvd.32044092008168 84 25 ? ? PUNCT hvd.32044092008168 84 26 fu fu NOUN hvd.32044092008168 84 27 with with ADP hvd.32044092008168 84 28 corresponding corresponding ADJ hvd.32044092008168 84 29 equations equation NOUN hvd.32044092008168 84 30 for for ADP hvd.32044092008168 84 31 v v NOUN hvd.32044092008168 84 32 and and CCONJ hvd.32044092008168 84 33 w. w. NOUN hvd.32044092008168 84 34 if if SCONJ hvd.32044092008168 84 35 then then ADV hvd.32044092008168 84 36 one one PRON hvd.32044092008168 84 37 can can AUX hvd.32044092008168 84 38 find find VERB hvd.32044092008168 84 39 2n 2n NUM hvd.32044092008168 84 40 +1 +1 NOUN hvd.32044092008168 84 41 systems system NOUN hvd.32044092008168 84 42 of of ADP hvd.32044092008168 84 43 constants constant NOUN hvd.32044092008168 84 44 a a PRON hvd.32044092008168 84 45 and and CCONJ hvd.32044092008168 84 46 b b NOUN hvd.32044092008168 84 47 of of ADP hvd.32044092008168 84 48 such such ADJ hvd.32044092008168 84 49 sort sort NOUN hvd.32044092008168 84 50 that that DET hvd.32044092008168 84 51 for for ADP hvd.32044092008168 84 52 each each PRON hvd.32044092008168 84 53 of of ADP hvd.32044092008168 84 54 these these DET hvd.32044092008168 84 55 systems system NOUN hvd.32044092008168 84 56 there there ADV hvd.32044092008168 84 57 exists exist VERB hvd.32044092008168 84 58 a a DET hvd.32044092008168 84 59 solution solution NOUN hvd.32044092008168 84 60 y y NOUN hvd.32044092008168 84 61 = = NOUN hvd.32044092008168 84 62 fu fu PROPN hvd.32044092008168 84 63 = = NOUN hvd.32044092008168 84 64 of of ADP hvd.32044092008168 84 65 equation equation NOUN hvd.32044092008168 84 66 [ [ X hvd.32044092008168 84 67 4 4 X hvd.32044092008168 84 68 ] ] PUNCT hvd.32044092008168 84 69 where where SCONJ hvd.32044092008168 84 70 y y PROPN hvd.32044092008168 84 71 is be AUX hvd.32044092008168 84 72 an an DET hvd.32044092008168 84 73 intire intire ADJ hvd.32044092008168 84 74 function function NOUN hvd.32044092008168 84 75 of of ADP hvd.32044092008168 84 76 the the DET hvd.32044092008168 84 77 nth nth NOUN hvd.32044092008168 84 78 degree degree NOUN hvd.32044092008168 84 79 each each PRON hvd.32044092008168 84 80 of of ADP hvd.32044092008168 84 81 the the DET hvd.32044092008168 84 82 corresponding correspond VERB hvd.32044092008168 84 83 products product NOUN hvd.32044092008168 84 84 fu fu PROPN hvd.32044092008168 84 85 fv fv PROPN hvd.32044092008168 84 86 fw fw PROPN hvd.32044092008168 84 87 will will AUX hvd.32044092008168 84 88 furnish furnish VERB hvd.32044092008168 84 89 a a DET hvd.32044092008168 84 90 term term NOUN hvd.32044092008168 84 91 tn tn NOUN hvd.32044092008168 84 92 of of ADP hvd.32044092008168 84 93 t t PROPN hvd.32044092008168 84 94 and and CCONJ hvd.32044092008168 84 95 the the DET hvd.32044092008168 84 96 problem problem NOUN hvd.32044092008168 84 97 of of ADP hvd.32044092008168 84 98 lamé lamé NOUN hvd.32044092008168 84 99 will will AUX hvd.32044092008168 84 100 be be AUX hvd.32044092008168 84 101 solved solve VERB hvd.32044092008168 84 102 . . PUNCT hvd.32044092008168 85 1 the the DET hvd.32044092008168 85 2 value value NOUN hvd.32044092008168 85 3 of of ADP hvd.32044092008168 85 4 a a PRON hvd.32044092008168 85 5 for for ADP hvd.32044092008168 85 6 all all PRON hvd.32044092008168 85 7 of of ADP hvd.32044092008168 85 8 these these DET hvd.32044092008168 85 9 systems system NOUN hvd.32044092008168 85 10 is be AUX hvd.32044092008168 85 11 n(n n(n PROPN hvd.32044092008168 85 12 + + CCONJ hvd.32044092008168 85 13 1 1 X hvd.32044092008168 85 14 ) ) PUNCT hvd.32044092008168 85 15 where where SCONJ hvd.32044092008168 85 16 n n PROPN hvd.32044092008168 85 17 may may AUX hvd.32044092008168 85 18 be be AUX hvd.32044092008168 85 19 considered consider VERB hvd.32044092008168 85 20 as as ADP hvd.32044092008168 85 21 always always ADV hvd.32044092008168 85 22 positive positive ADJ hvd.32044092008168 85 23 , , PUNCT hvd.32044092008168 85 24 since since SCONJ hvd.32044092008168 85 25 the the DET hvd.32044092008168 85 26 substitution substitution NOUN hvd.32044092008168 85 27 n n ADP hvd.32044092008168 85 28 ( ( PUNCT hvd.32044092008168 85 29 n n X hvd.32044092008168 85 30 + + CCONJ hvd.32044092008168 85 31 1 1 X hvd.32044092008168 85 32 ) ) PUNCT hvd.32044092008168 85 33 does do AUX hvd.32044092008168 85 34 not not PART hvd.32044092008168 85 35 alter alter VERB hvd.32044092008168 85 36 the the DET hvd.32044092008168 85 37 value value NOUN hvd.32044092008168 85 38 of of ADP hvd.32044092008168 85 39 a. a. NOUN hvd.32044092008168 85 40 the the DET hvd.32044092008168 85 41 problem problem NOUN hvd.32044092008168 85 42 of of ADP hvd.32044092008168 85 43 hermite hermite PROPN hvd.32044092008168 85 44 . . PUNCT hvd.32044092008168 86 1 continuing continue VERB hvd.32044092008168 86 2 our our PRON hvd.32044092008168 86 3 review review NOUN hvd.32044092008168 86 4 we we PRON hvd.32044092008168 86 5 find find VERB hvd.32044092008168 86 6 that that SCONJ hvd.32044092008168 86 7 one one NUM hvd.32044092008168 86 8 of of ADP hvd.32044092008168 86 9 the the DET hvd.32044092008168 86 10 original original ADJ hvd.32044092008168 86 11 forms form NOUN hvd.32044092008168 86 12 of of ADP hvd.32044092008168 86 13 lamé lamé NOUN hvd.32044092008168 86 14 's 's PART hvd.32044092008168 86 15 equation equation NOUN hvd.32044092008168 86 16 expressed express VERB hvd.32044092008168 86 17 in in ADP hvd.32044092008168 86 18 terms term NOUN hvd.32044092008168 86 19 of of ADP hvd.32044092008168 86 20 the the DET hvd.32044092008168 86 21 jacobian jacobian ADJ hvd.32044092008168 86 22 function function NOUN hvd.32044092008168 86 23 is be AUX hvd.32044092008168 86 24 [ [ X hvd.32044092008168 86 25 9 9 NUM hvd.32044092008168 86 26 ] ] PUNCT hvd.32044092008168 86 27 · · PUNCT hvd.32044092008168 86 28 da da VERB hvd.32044092008168 86 29 — — PUNCT hvd.32044092008168 86 30 [ [ X hvd.32044092008168 86 31 n(n n(n X hvd.32044092008168 86 32 + + CCONJ hvd.32044092008168 86 33 1)kºsn*x 1)kºsn*x NUM hvd.32044092008168 86 34 + + SYM hvd.32044092008168 86 35 h]y=0 h]y=0 NOUN hvd.32044092008168 86 36 ) ) PUNCT hvd.32044092008168 86 37 corresponding correspond VERB hvd.32044092008168 86 38 to to ADP hvd.32044092008168 86 39 the the DET hvd.32044092008168 86 40 form form NOUN hvd.32044092008168 86 41 [ [ X hvd.32044092008168 86 42 4 4 NUM hvd.32044092008168 86 43 ] ] SYM hvd.32044092008168 86 44 * * PUNCT hvd.32044092008168 86 45 ) ) PUNCT hvd.32044092008168 86 46 dạy dạy PROPN hvd.32044092008168 86 47 da da PROPN hvd.32044092008168 86 48 y y PROPN hvd.32044092008168 87 1 [ [ X hvd.32044092008168 87 2 10 10 NUM hvd.32044092008168 87 3 ] ] PUNCT hvd.32044092008168 87 4 : : PUNCT hvd.32044092008168 87 5 [ [ X hvd.32044092008168 87 6 n(n n(n X hvd.32044092008168 87 7 + + CCONJ hvd.32044092008168 87 8 1 1 X hvd.32044092008168 87 9 ) ) PUNCT hvd.32044092008168 87 10 pu pu PROPN hvd.32044092008168 87 11 + + CCONJ hvd.32044092008168 87 12 b]y=0 b]y=0 NOUN hvd.32044092008168 87 13 d d PROPN hvd.32044092008168 87 14 u² u² PROPN hvd.32044092008168 87 15 where where SCONJ hvd.32044092008168 87 16 h h PROPN hvd.32044092008168 87 17 is be AUX hvd.32044092008168 87 18 an an DET hvd.32044092008168 87 19 arbitrary arbitrary ADJ hvd.32044092008168 87 20 constant constant NOUN hvd.32044092008168 87 21 and and CCONJ hvd.32044092008168 87 22 n n CCONJ hvd.32044092008168 87 23 a a DET hvd.32044092008168 87 24 positive positive ADJ hvd.32044092008168 87 25 whole whole ADJ hvd.32044092008168 87 26 number number NOUN hvd.32044092008168 87 27 . . PUNCT hvd.32044092008168 88 1 lamé lamé NOUN hvd.32044092008168 88 2 succeeded succeed VERB hvd.32044092008168 88 3 in in ADP hvd.32044092008168 88 4 finding find VERB hvd.32044092008168 88 5 the the DET hvd.32044092008168 88 6 requisite requisite ADJ hvd.32044092008168 88 7 number number NOUN hvd.32044092008168 88 8 of of ADP hvd.32044092008168 88 9 values value NOUN hvd.32044092008168 88 10 of of ADP hvd.32044092008168 88 11 h h NOUN hvd.32044092008168 88 12 to to PART hvd.32044092008168 88 13 complete complete VERB hvd.32044092008168 88 14 his his PRON hvd.32044092008168 88 15 solution solution NOUN hvd.32044092008168 88 16 for for ADP hvd.32044092008168 88 17 the the DET hvd.32044092008168 88 18 ellipsoid ellipsoid ADJ hvd.32044092008168 88 19 and and CCONJ hvd.32044092008168 88 20 the the DET hvd.32044092008168 88 21 solutions solution NOUN hvd.32044092008168 88 22 of of ADP hvd.32044092008168 88 23 [ [ PUNCT hvd.32044092008168 88 24 4 4 NUM hvd.32044092008168 88 25 ] ] PUNCT hvd.32044092008168 88 26 corresponding correspond VERB hvd.32044092008168 88 27 to to ADP hvd.32044092008168 88 28 these these DET hvd.32044092008168 88 29 values value NOUN hvd.32044092008168 88 30 are be AUX hvd.32044092008168 88 31 known know VERB hvd.32044092008168 88 32 as as ADP hvd.32044092008168 88 33 the the DET hvd.32044092008168 88 34 original original ADJ hvd.32044092008168 88 35 special special ADJ hvd.32044092008168 88 36 functions function NOUN hvd.32044092008168 88 37 of of ADP hvd.32044092008168 88 38 lamé lamé NOUN hvd.32044092008168 88 39 . . PUNCT hvd.32044092008168 89 1 the the DET hvd.32044092008168 89 2 problem problem NOUN hvd.32044092008168 89 3 then then ADV hvd.32044092008168 89 4 arose arise VERB hvd.32044092008168 89 5 : : PUNCT hvd.32044092008168 89 6 required require VERB hvd.32044092008168 89 7 to to PART hvd.32044092008168 89 8 determine determine VERB hvd.32044092008168 89 9 a a DET hvd.32044092008168 89 10 solution solution NOUN hvd.32044092008168 89 11 of of ADP hvd.32044092008168 89 12 lamé lamé NOUN hvd.32044092008168 89 13 's 's PART hvd.32044092008168 89 14 original original ADJ hvd.32044092008168 89 15 equation equation NOUN hvd.32044092008168 89 16 which which PRON hvd.32044092008168 89 17 shall shall AUX hvd.32044092008168 89 18 hold hold VERB hvd.32044092008168 89 19 for for ADP hvd.32044092008168 89 20 any any DET hvd.32044092008168 89 21 values value NOUN hvd.32044092008168 89 22 of of ADP hvd.32044092008168 89 23 h h PROPN hvd.32044092008168 89 24 and and CCONJ hvd.32044092008168 89 25 n. n. NOUN hvd.32044092008168 89 26 except except SCONJ hvd.32044092008168 89 27 for for ADP hvd.32044092008168 89 28 the the DET hvd.32044092008168 89 29 special special ADJ hvd.32044092008168 89 30 values value NOUN hvd.32044092008168 89 31 n n CCONJ hvd.32044092008168 89 32 = = X hvd.32044092008168 89 33 1 1 NUM hvd.32044092008168 89 34 and and CCONJ hvd.32044092008168 89 35 n= n= NUM hvd.32044092008168 89 36 2 2 NUM hvd.32044092008168 89 37 no no DET hvd.32044092008168 89 38 advance advance NOUN hvd.32044092008168 89 39 was be AUX hvd.32044092008168 89 40 made make VERB hvd.32044092008168 89 41 towards towards ADP hvd.32044092008168 89 42 a a DET hvd.32044092008168 89 43 solution solution NOUN hvd.32044092008168 89 44 until until ADP hvd.32044092008168 89 45 m. m. NOUN hvd.32044092008168 89 46 hermite hermite NOUN hvd.32044092008168 89 47 * * PUNCT hvd.32044092008168 89 48 * * PUNCT hvd.32044092008168 89 49 ) ) PUNCT hvd.32044092008168 89 50 , , PUNCT hvd.32044092008168 89 51 making make VERB hvd.32044092008168 89 52 use use NOUN hvd.32044092008168 89 53 of of ADP hvd.32044092008168 89 54 the the DET hvd.32044092008168 89 55 progress progress NOUN hvd.32044092008168 89 56 in in ADP hvd.32044092008168 89 57 the the DET hvd.32044092008168 89 58 theory theory NOUN hvd.32044092008168 89 59 of of ADP hvd.32044092008168 89 60 functions function NOUN hvd.32044092008168 89 61 inaugurated inaugurate VERB hvd.32044092008168 89 62 by by ADP hvd.32044092008168 89 63 cauchy cauchy NOUN hvd.32044092008168 89 64 , , PUNCT hvd.32044092008168 89 65 arrived arrive VERB hvd.32044092008168 89 66 at at ADP hvd.32044092008168 89 67 the the DET hvd.32044092008168 89 68 solution solution NOUN hvd.32044092008168 89 69 and and CCONJ hvd.32044092008168 89 70 by by ADP hvd.32044092008168 89 71 so so ADV hvd.32044092008168 89 72 doing do VERB hvd.32044092008168 89 73 opened open VERB hvd.32044092008168 89 74 a a DET hvd.32044092008168 89 75 new new ADJ hvd.32044092008168 89 76 field field NOUN hvd.32044092008168 89 77 for for ADP hvd.32044092008168 89 78 * * PUNCT hvd.32044092008168 89 79 ) ) PUNCT hvd.32044092008168 89 80 see see VERB hvd.32044092008168 89 81 transformation transformation NOUN hvd.32044092008168 89 82 p. p. NOUN hvd.32044092008168 89 83 20 20 NUM hvd.32044092008168 89 84 . . PUNCT hvd.32044092008168 90 1 * * PUNCT hvd.32044092008168 90 2 * * PUNCT hvd.32044092008168 90 3 ) ) PUNCT hvd.32044092008168 90 4 sur sur X hvd.32044092008168 90 5 quelques quelques X hvd.32044092008168 90 6 applications application NOUN hvd.32044092008168 90 7 des des X hvd.32044092008168 90 8 fonctions fonction NOUN hvd.32044092008168 90 9 elliptiques elliptique NOUN hvd.32044092008168 90 10 . . PUNCT hvd.32044092008168 91 1 comptes compte NOUN hvd.32044092008168 91 2 rendus rendus PROPN hvd.32044092008168 91 3 de de X hvd.32044092008168 91 4 l'académie l'académie X hvd.32044092008168 91 5 des des X hvd.32044092008168 91 6 sciences sciences PROPN hvd.32044092008168 91 7 de de X hvd.32044092008168 91 8 paris paris PROPN hvd.32044092008168 91 9 . . PUNCT hvd.32044092008168 92 1 1877 1877 NUM hvd.32044092008168 92 2 . . PUNCT hvd.32044092008168 93 1 14 14 NUM hvd.32044092008168 93 2 part part NOUN hvd.32044092008168 93 3 i. i. PROPN hvd.32044092008168 93 4 the the DET hvd.32044092008168 93 5 application application NOUN hvd.32044092008168 93 6 of of ADP hvd.32044092008168 93 7 the the DET hvd.32044092008168 93 8 elliptic elliptic ADJ hvd.32044092008168 93 9 functions function NOUN hvd.32044092008168 93 10 and and CCONJ hvd.32044092008168 93 11 leading lead VERB hvd.32044092008168 93 12 later later ADV hvd.32044092008168 93 13 to to ADP hvd.32044092008168 93 14 the the DET hvd.32044092008168 93 15 integration integration NOUN hvd.32044092008168 93 16 of of ADP hvd.32044092008168 93 17 a a DET hvd.32044092008168 93 18 large large ADJ hvd.32044092008168 93 19 class class NOUN hvd.32044092008168 93 20 of of ADP hvd.32044092008168 93 21 differential differential ADJ hvd.32044092008168 93 22 equations equation NOUN hvd.32044092008168 93 23 . . PUNCT hvd.32044092008168 94 1 * * PUNCT hvd.32044092008168 94 2 ) ) PUNCT hvd.32044092008168 94 3 in in ADP hvd.32044092008168 94 4 this this DET hvd.32044092008168 94 5 connection connection NOUN hvd.32044092008168 94 6 m. m. NOUN hvd.32044092008168 94 7 hermite hermite PROPN hvd.32044092008168 94 8 introduces introduce VERB hvd.32044092008168 94 9 the the DET hvd.32044092008168 94 10 functions function NOUN hvd.32044092008168 94 11 called call VERB hvd.32044092008168 94 12 by by ADP hvd.32044092008168 94 13 him he PRON hvd.32044092008168 94 14 doubly doubly ADV hvd.32044092008168 94 15 periodic periodic ADJ hvd.32044092008168 94 16 of of ADP hvd.32044092008168 94 17 the the DET hvd.32044092008168 94 18 second second ADJ hvd.32044092008168 94 19 species specie NOUN hvd.32044092008168 94 20 , , PUNCT hvd.32044092008168 94 21 which which PRON hvd.32044092008168 94 22 have have VERB hvd.32044092008168 94 23 the the DET hvd.32044092008168 94 24 special special ADJ hvd.32044092008168 94 25 property property NOUN hvd.32044092008168 94 26 , , PUNCT hvd.32044092008168 94 27 that that PRON hvd.32044092008168 94 28 save save VERB hvd.32044092008168 94 29 for for ADP hvd.32044092008168 94 30 a a DET hvd.32044092008168 94 31 constant constant ADJ hvd.32044092008168 94 32 factor factor NOUN hvd.32044092008168 94 33 they they PRON hvd.32044092008168 94 34 remain remain VERB hvd.32044092008168 94 35 unaltered unaltered ADJ hvd.32044092008168 94 36 upon upon SCONJ hvd.32044092008168 94 37 the the DET hvd.32044092008168 94 38 addition addition NOUN hvd.32044092008168 94 39 to to ADP hvd.32044092008168 94 40 the the DET hvd.32044092008168 94 41 argument argument NOUN hvd.32044092008168 94 42 of of ADP hvd.32044092008168 94 43 the the DET hvd.32044092008168 94 44 fundimental fundimental ADJ hvd.32044092008168 94 45 periods period NOUN hvd.32044092008168 94 46 . . PUNCT hvd.32044092008168 95 1 the the DET hvd.32044092008168 95 2 solution solution NOUN hvd.32044092008168 95 3 of of ADP hvd.32044092008168 95 4 m. m. NOUN hvd.32044092008168 95 5 hermite hermite PROPN hvd.32044092008168 95 6 developed develop VERB hvd.32044092008168 95 7 in in ADP hvd.32044092008168 95 8 terms term NOUN hvd.32044092008168 95 9 of of ADP hvd.32044092008168 95 10 snu snu NOUN hvd.32044092008168 95 11 and and CCONJ hvd.32044092008168 95 12 for for ADP hvd.32044092008168 95 13 n n CCONJ hvd.32044092008168 95 14 odd odd ADJ hvd.32044092008168 95 15 may may AUX hvd.32044092008168 95 16 be be AUX hvd.32044092008168 95 17 written write VERB hvd.32044092008168 95 18 in in ADP hvd.32044092008168 95 19 the the DET hvd.32044092008168 95 20 form form NOUN hvd.32044092008168 95 21 d2"-1f(u d2"-1f(u ADJ hvd.32044092008168 95 22 ) ) PUNCT hvd.32044092008168 95 23 d21 d21 NOUN hvd.32044092008168 95 24 2 2 NUM hvd.32044092008168 95 25 -3 -3 X hvd.32044092008168 95 26 u u NOUN hvd.32044092008168 96 1 [ [ X hvd.32044092008168 96 2 11 11 NUM hvd.32044092008168 96 3 ] ] PUNCT hvd.32044092008168 96 4 ] ] X hvd.32044092008168 96 5 h h NOUN hvd.32044092008168 96 6 , , PUNCT hvd.32044092008168 96 7 d% d% PROPN hvd.32044092008168 96 8 " " PUNCT hvd.32044092008168 96 9 – – PUNCT hvd.32044092008168 96 10 3f(u 3f(u NUM hvd.32044092008168 96 11 ) ) PUNCT hvd.32044092008168 96 12 t t PROPN hvd.32044092008168 96 13 ... ... PUNCT hvd.32044092008168 96 14 thx-1f(u thx-1f(u PROPN hvd.32044092008168 96 15 ) ) PUNCT hvd.32044092008168 96 16 . . PUNCT hvd.32044092008168 97 1 y y PROPN hvd.32044092008168 97 2 = = PROPN hvd.32044092008168 97 3 f(u f(u PROPN hvd.32044092008168 97 4 ) ) PUNCT hvd.32044092008168 97 5 + + CCONJ hvd.32044092008168 97 6 r(21 r(21 SPACE hvd.32044092008168 97 7 ) ) PUNCT hvd.32044092008168 97 8 r(2v r(2v ADP hvd.32044092008168 97 9 2 2 NUM hvd.32044092008168 97 10 2v 2v NOUN hvd.32044092008168 97 11 into into ADP hvd.32044092008168 97 12 o'(0 o'(0 NOUN hvd.32044092008168 97 13 ) ) PUNCT hvd.32044092008168 97 14 ® ® NOUN hvd.32044092008168 97 15 ( ( PUNCT hvd.32044092008168 97 16 w w PROPN hvd.32044092008168 97 17 ) ) PUNCT hvd.32044092008168 97 18 2 2 NUM hvd.32044092008168 97 19 k k PROPN hvd.32044092008168 97 20 x(u x(u PROPN hvd.32044092008168 97 21 ) ) PUNCT hvd.32044092008168 97 22 = = PROPN hvd.32044092008168 98 1 e e X hvd.32044092008168 98 2 where where SCONJ hvd.32044092008168 98 3 n n CCONJ hvd.32044092008168 98 4 = = SYM hvd.32044092008168 98 5 20 20 NUM hvd.32044092008168 98 6 — — PUNCT hvd.32044092008168 98 7 1 1 NUM hvd.32044092008168 98 8 , , PUNCT hvd.32044092008168 98 9 with with ADP hvd.32044092008168 98 10 a a DET hvd.32044092008168 98 11 corresponding corresponding ADJ hvd.32044092008168 98 12 form form NOUN hvd.32044092008168 98 13 for for ADP hvd.32044092008168 98 14 n n CCONJ hvd.32044092008168 98 15 even even ADV hvd.32044092008168 98 16 , , PUNCT hvd.32044092008168 98 17 where where SCONJ hvd.32044092008168 98 18 = = PROPN hvd.32044092008168 98 19 f(u f(u NOUN hvd.32044092008168 98 20 ) ) PUNCT hvd.32044092008168 98 21 is be AUX hvd.32044092008168 98 22 a a DET hvd.32044092008168 98 23 doubly doubly ADV hvd.32044092008168 98 24 periodic periodic ADJ hvd.32044092008168 98 25 function function NOUN hvd.32044092008168 98 26 of of ADP hvd.32044092008168 98 27 the the DET hvd.32044092008168 98 28 second second ADJ hvd.32044092008168 98 29 species specie NOUN hvd.32044092008168 98 30 , , PUNCT hvd.32044092008168 98 31 namely namely ADV hvd.32044092008168 98 32 , , PUNCT hvd.32044092008168 98 33 f(u f(u NOUN hvd.32044092008168 98 34 ) ) PUNCT hvd.32044092008168 98 35 = = PROPN hvd.32044092008168 98 36 eica eica PROPN hvd.32044092008168 98 37 — — PUNCT hvd.32044092008168 98 38 ik ik PROPN hvd.32044092008168 98 39 ' ' PUNCT hvd.32044092008168 98 40 ) ) PUNCT hvd.32044092008168 98 41 x(u x(u PROPN hvd.32044092008168 98 42 ) ) PUNCT hvd.32044092008168 98 43 where where SCONJ hvd.32044092008168 98 44 h h PROPN hvd.32044092008168 98 45 ( ( PUNCT hvd.32044092008168 98 46 0 0 NUM hvd.32044092008168 98 47 ) ) PUNCT hvd.32044092008168 98 48 h h PROPN hvd.32044092008168 98 49 ( ( PUNCT hvd.32044092008168 98 50 4 4 NUM hvd.32044092008168 98 51 + + NUM hvd.32044092008168 98 52 10 10 NUM hvd.32044092008168 98 53 ) ) PUNCT hvd.32044092008168 98 54 ( ( PUNCT hvd.32044092008168 98 55 ui ui PROPN hvd.32044092008168 98 56 k')+ k')+ PROPN hvd.32044092008168 98 57 ( ( PUNCT hvd.32044092008168 98 58 u u PROPN hvd.32044092008168 98 59 ) ) PUNCT hvd.32044092008168 98 60 ( ( PUNCT hvd.32044092008168 98 61 6 6 X hvd.32044092008168 98 62 ) ) PUNCT hvd.32044092008168 98 63 that that SCONJ hvd.32044092008168 98 64 this this PRON hvd.32044092008168 98 65 shall shall AUX hvd.32044092008168 98 66 be be AUX hvd.32044092008168 98 67 a a DET hvd.32044092008168 98 68 solution solution NOUN hvd.32044092008168 98 69 the the DET hvd.32044092008168 98 70 quantities quantity NOUN hvd.32044092008168 98 71 w w PROPN hvd.32044092008168 98 72 and and CCONJ hvd.32044092008168 98 73 a a PRON hvd.32044092008168 98 74 must must AUX hvd.32044092008168 98 75 be be AUX hvd.32044092008168 98 76 determined determine VERB hvd.32044092008168 98 77 to to PART hvd.32044092008168 98 78 correspond correspond VERB hvd.32044092008168 98 79 with with ADP hvd.32044092008168 98 80 definite definite ADJ hvd.32044092008168 98 81 conditions condition NOUN hvd.32044092008168 98 82 and and CCONJ hvd.32044092008168 98 83 herein herein ADV hvd.32044092008168 98 84 lies lie VERB hvd.32044092008168 98 85 the the DET hvd.32044092008168 98 86 chief chief ADJ hvd.32044092008168 98 87 difficulty difficulty NOUN hvd.32044092008168 98 88 when when SCONJ hvd.32044092008168 98 89 explicit explicit ADJ hvd.32044092008168 98 90 values value NOUN hvd.32044092008168 98 91 of of ADP hvd.32044092008168 98 92 the the DET hvd.32044092008168 98 93 functions function NOUN hvd.32044092008168 98 94 are be AUX hvd.32044092008168 98 95 sought seek VERB hvd.32044092008168 98 96 . . PUNCT hvd.32044092008168 99 1 moreover moreover ADV hvd.32044092008168 99 2 the the DET hvd.32044092008168 99 3 above above ADJ hvd.32044092008168 99 4 development development NOUN hvd.32044092008168 99 5 fails fail VERB hvd.32044092008168 99 6 as as SCONJ hvd.32044092008168 99 7 we we PRON hvd.32044092008168 99 8 shall shall AUX hvd.32044092008168 99 9 find find VERB hvd.32044092008168 99 10 when when SCONJ hvd.32044092008168 99 11 seeking seek VERB hvd.32044092008168 99 12 to to PART hvd.32044092008168 99 13 deduce deduce VERB hvd.32044092008168 99 14 the the DET hvd.32044092008168 99 15 special special ADJ hvd.32044092008168 99 16 functions function NOUN hvd.32044092008168 99 17 of of ADP hvd.32044092008168 99 18 m. m. NOUN hvd.32044092008168 99 19 mittag mittag ADJ hvd.32044092008168 99 20 - - PUNCT hvd.32044092008168 99 21 leffler leffler NOUN hvd.32044092008168 99 22 from from ADP hvd.32044092008168 99 23 the the DET hvd.32044092008168 99 24 general general ADJ hvd.32044092008168 99 25 form form NOUN hvd.32044092008168 99 26 . . PUNCT hvd.32044092008168 100 1 m. m. NOUN hvd.32044092008168 100 2 hermite hermite PROPN hvd.32044092008168 100 3 was be AUX hvd.32044092008168 100 4 thus thus ADV hvd.32044092008168 100 5 led lead VERB hvd.32044092008168 100 6 to to ADP hvd.32044092008168 100 7 a a DET hvd.32044092008168 100 8 new new ADJ hvd.32044092008168 100 9 presentation presentation NOUN hvd.32044092008168 100 10 of of ADP hvd.32044092008168 100 11 the the DET hvd.32044092008168 100 12 general general ADJ hvd.32044092008168 100 13 solution solution NOUN hvd.32044092008168 100 14 in in ADP hvd.32044092008168 100 15 the the DET hvd.32044092008168 100 16 form form NOUN hvd.32044092008168 100 17 of of ADP hvd.32044092008168 100 18 a a DET hvd.32044092008168 100 19 product product NOUN hvd.32044092008168 100 20 , , PUNCT hvd.32044092008168 100 21 namely namely ADV hvd.32044092008168 100 22 y y PROPN hvd.32044092008168 100 23 = = PRON hvd.32044092008168 100 24 it it PRON hvd.32044092008168 100 25 * * PUNCT hvd.32044092008168 100 26 o o X hvd.32044092008168 101 1 ( ( PUNCT hvd.32044092008168 101 2 u u PROPN hvd.32044092008168 101 3 + + CCONJ hvd.32044092008168 101 4 a a X hvd.32044092008168 101 5 ) ) PUNCT hvd.32044092008168 101 6 e e NOUN hvd.32044092008168 101 7 - - PROPN hvd.32044092008168 101 8 usa usa PROPN hvd.32044092008168 101 9 σα σα PROPN hvd.32044092008168 101 10 σω σω INTJ hvd.32044092008168 101 11 a a PRON hvd.32044092008168 101 12 = = NOUN hvd.32044092008168 101 13 a.b a.b X hvd.32044092008168 101 14 .. .. NOUN hvd.32044092008168 101 15 a a DET hvd.32044092008168 101 16 form form NOUN hvd.32044092008168 101 17 of of ADP hvd.32044092008168 101 18 solution solution NOUN hvd.32044092008168 101 19 suited suit VERB hvd.32044092008168 101 20 to to ADP hvd.32044092008168 101 21 every every DET hvd.32044092008168 101 22 case case NOUN hvd.32044092008168 101 23 . . PUNCT hvd.32044092008168 102 1 the the DET hvd.32044092008168 102 2 general general ADJ hvd.32044092008168 102 3 theory theory NOUN hvd.32044092008168 102 4 based base VERB hvd.32044092008168 102 5 upon upon SCONJ hvd.32044092008168 102 6 the the DET hvd.32044092008168 102 7 latter latter ADJ hvd.32044092008168 102 8 solution solution NOUN hvd.32044092008168 102 9 has have AUX hvd.32044092008168 102 10 been be AUX hvd.32044092008168 102 11 lately lately ADV hvd.32044092008168 102 12 perfected perfect VERB hvd.32044092008168 102 13 by by ADP hvd.32044092008168 102 14 halphen halphen ADV hvd.32044092008168 102 15 * * NOUN hvd.32044092008168 102 16 * * PUNCT hvd.32044092008168 102 17 ) ) PUNCT hvd.32044092008168 102 18 , , PUNCT hvd.32044092008168 102 19 who who PRON hvd.32044092008168 102 20 , , PUNCT hvd.32044092008168 102 21 confining confine VERB hvd.32044092008168 102 22 himself himself PRON hvd.32044092008168 102 23 in in ADP hvd.32044092008168 102 24 the the DET hvd.32044092008168 102 25 main main NOUN hvd.32044092008168 102 26 to to ADP hvd.32044092008168 102 27 the the DET hvd.32044092008168 102 28 use use NOUN hvd.32044092008168 102 29 of of ADP hvd.32044092008168 102 30 the the DET hvd.32044092008168 102 31 p p NOUN hvd.32044092008168 102 32 function function NOUN hvd.32044092008168 102 33 , , PUNCT hvd.32044092008168 102 34 presents present VERB hvd.32044092008168 102 35 the the DET hvd.32044092008168 102 36 subject subject NOUN hvd.32044092008168 102 37 in in ADP hvd.32044092008168 102 38 an an DET hvd.32044092008168 102 39 excellent excellent ADJ hvd.32044092008168 102 40 but but CCONJ hvd.32044092008168 102 41 highly highly ADV hvd.32044092008168 102 42 condensed condense VERB hvd.32044092008168 102 43 form form NOUN hvd.32044092008168 102 44 . . PUNCT hvd.32044092008168 103 1 * * PUNCT hvd.32044092008168 103 2 ) ) PUNCT hvd.32044092008168 103 3 equations equation NOUN hvd.32044092008168 103 4 of of ADP hvd.32044092008168 103 5 m. m. NOUN hvd.32044092008168 103 6 éimile éimile NOUN hvd.32044092008168 103 7 picard picard NOUN hvd.32044092008168 103 8 . . PUNCT hvd.32044092008168 104 1 comptes compte NOUN hvd.32044092008168 104 2 rendus rendus PROPN hvd.32044092008168 104 3 , , PUNCT hvd.32044092008168 104 4 t. t. PROPN hvd.32044092008168 104 5 xc xc PROPN hvd.32044092008168 104 6 , , PUNCT hvd.32044092008168 104 7 p. p. NOUN hvd.32044092008168 104 8 128 128 NUM hvd.32044092008168 104 9 and and CCONJ hvd.32044092008168 104 10 293 293 NUM hvd.32044092008168 104 11 . . PUNCT hvd.32044092008168 105 1 prof prof NOUN hvd.32044092008168 105 2 . . PUNCT hvd.32044092008168 105 3 fuchs fuchs PROPN hvd.32044092008168 105 4 , , PUNCT hvd.32044092008168 105 5 ueber ueber ADJ hvd.32044092008168 105 6 eine eine PROPN hvd.32044092008168 105 7 classe classe PROPN hvd.32044092008168 105 8 von von PROPN hvd.32044092008168 105 9 differenzialgleichungen differenzialgleichungen PROPN hvd.32044092008168 105 10 , , PUNCT hvd.32044092008168 105 11 welche welche PROPN hvd.32044092008168 105 12 durch durch PROPN hvd.32044092008168 105 13 abelsche abelsche PROPN hvd.32044092008168 105 14 oder oder PROPN hvd.32044092008168 105 15 elliptische elliptische PROPN hvd.32044092008168 105 16 functionen functionen PROPN hvd.32044092008168 105 17 integrirbar integrirbar PROPN hvd.32044092008168 105 18 sind sind PROPN hvd.32044092008168 105 19 . . PUNCT hvd.32044092008168 106 1 nachrichten nachrichten PROPN hvd.32044092008168 106 2 göttingen göttingen PROPN hvd.32044092008168 106 3 1878 1878 NUM hvd.32044092008168 106 4 , , PUNCT hvd.32044092008168 106 5 and and CCONJ hvd.32044092008168 106 6 hermite hermite NOUN hvd.32044092008168 106 7 : : PUNCT hvd.32044092008168 106 8 annali annali PROPN hvd.32044092008168 106 9 di di PROPN hvd.32044092008168 106 10 matematica matematica PROPN hvd.32044092008168 106 11 , , PUNCT hvd.32044092008168 106 12 serie serie PROPN hvd.32044092008168 106 13 ii ii PROPN hvd.32044092008168 106 14 , , PUNCT hvd.32044092008168 106 15 bd bd PROPN hvd.32044092008168 106 16 . . PROPN hvd.32044092008168 106 17 ix ix PROPN hvd.32044092008168 106 18 , , PUNCT hvd.32044092008168 106 19 1878 1878 NUM hvd.32044092008168 106 20 . . PUNCT hvd.32044092008168 107 1 * * PUNCT hvd.32044092008168 107 2 * * NOUN hvd.32044092008168 107 3 ) ) PUNCT hvd.32044092008168 107 4 traité traité NOUN hvd.32044092008168 107 5 des des PROPN hvd.32044092008168 107 6 fonctions fonction NOUN hvd.32044092008168 107 7 elliptiques elliptiques PROPN hvd.32044092008168 107 8 et et NOUN hvd.32044092008168 107 9 leur leur PROPN hvd.32044092008168 107 10 applications application NOUN hvd.32044092008168 107 11 . . PUNCT hvd.32044092008168 108 1 b. b. PROPN hvd.32044092008168 108 2 ii ii PROPN hvd.32044092008168 108 3 . . PROPN hvd.32044092008168 108 4 paris paris PROPN hvd.32044092008168 108 5 1888 1888 NUM hvd.32044092008168 108 6 . . PUNCT hvd.32044092008168 109 1 von von PROPN hvd.32044092008168 109 2 historical historical PROPN hvd.32044092008168 109 3 development development PROPN hvd.32044092008168 109 4 and and CCONJ hvd.32044092008168 109 5 definition definition NOUN hvd.32044092008168 109 6 of of ADP hvd.32044092008168 109 7 the the DET hvd.32044092008168 109 8 equation equation NOUN hvd.32044092008168 109 9 of of ADP hvd.32044092008168 109 10 lamé lamé NOUN hvd.32044092008168 109 11 . . PUNCT hvd.32044092008168 110 1 15 15 NUM hvd.32044092008168 110 2 definitions definition NOUN hvd.32044092008168 110 3 . . PUNCT hvd.32044092008168 111 1 returning return VERB hvd.32044092008168 111 2 to to PART hvd.32044092008168 111 3 form form VERB hvd.32044092008168 111 4 [ [ X hvd.32044092008168 111 5 9 9 NUM hvd.32044092008168 111 6 ] ] PUNCT hvd.32044092008168 111 7 of of ADP hvd.32044092008168 111 8 lamé lamé NOUN hvd.32044092008168 111 9 's 's PART hvd.32044092008168 111 10 equation equation NOUN hvd.32044092008168 111 11 we we PRON hvd.32044092008168 111 12 observe observe VERB hvd.32044092008168 111 13 that that SCONJ hvd.32044092008168 111 14 it it PRON hvd.32044092008168 111 15 has have VERB hvd.32044092008168 111 16 the the DET hvd.32044092008168 111 17 following follow VERB hvd.32044092008168 111 18 properties property NOUN hvd.32044092008168 111 19 : : PUNCT hvd.32044092008168 111 20 it it PRON hvd.32044092008168 111 21 has have VERB hvd.32044092008168 111 22 a a DET hvd.32044092008168 111 23 coefficient coefficient NOUN hvd.32044092008168 111 24 m m PROPN hvd.32044092008168 111 25 ( ( PUNCT hvd.32044092008168 111 26 1 1 NUM hvd.32044092008168 112 1 + + NUM hvd.32044092008168 112 2 1 1 NUM hvd.32044092008168 112 3 ) ) PUNCT hvd.32044092008168 112 4 kº kº PROPN hvd.32044092008168 112 5 snºx snºx PROPN hvd.32044092008168 113 1 + + PROPN hvd.32044092008168 113 2 1 1 NUM hvd.32044092008168 113 3 that that PRON hvd.32044092008168 113 4 is be AUX hvd.32044092008168 113 5 doubly doubly ADV hvd.32044092008168 113 6 periodic periodic ADJ hvd.32044092008168 113 7 and and CCONJ hvd.32044092008168 113 8 has have VERB hvd.32044092008168 113 9 only only ADV hvd.32044092008168 113 10 one one NUM hvd.32044092008168 113 11 infinite infinite NOUN hvd.32044092008168 113 12 x x SYM hvd.32044092008168 113 13 = = X hvd.32044092008168 113 14 ik ik PROPN hvd.32044092008168 113 15 ' ' PART hvd.32044092008168 113 16 and and CCONJ hvd.32044092008168 113 17 its its PRON hvd.32044092008168 113 18 congruents congruent NOUN hvd.32044092008168 113 19 , , PUNCT hvd.32044092008168 113 20 and and CCONJ hvd.32044092008168 113 21 it it PRON hvd.32044092008168 113 22 is be AUX hvd.32044092008168 113 23 known know VERB hvd.32044092008168 113 24 to to PART hvd.32044092008168 113 25 have have VERB hvd.32044092008168 113 26 an an DET hvd.32044092008168 113 27 integral integral ADJ hvd.32044092008168 113 28 which which PRON hvd.32044092008168 113 29 is be AUX hvd.32044092008168 113 30 a a DET hvd.32044092008168 113 31 rational rational ADJ hvd.32044092008168 113 32 function function NOUN hvd.32044092008168 113 33 of of ADP hvd.32044092008168 113 34 the the DET hvd.32044092008168 113 35 variable variable NOUN hvd.32044092008168 113 36 . . PUNCT hvd.32044092008168 114 1 conforming conform VERB hvd.32044092008168 114 2 with with ADP hvd.32044092008168 114 3 these these DET hvd.32044092008168 114 4 peculiarities peculiarity NOUN hvd.32044092008168 114 5 m. m. VERB hvd.32044092008168 114 6 mittag mittag ADJ hvd.32044092008168 114 7 - - PUNCT hvd.32044092008168 114 8 leffler leffler NOUN hvd.32044092008168 114 9 * * PROPN hvd.32044092008168 114 10 ) ) PUNCT hvd.32044092008168 114 11 defines define VERB hvd.32044092008168 114 12 the the DET hvd.32044092008168 114 13 general general ADJ hvd.32044092008168 114 14 hermite hermite PROPN hvd.32044092008168 114 15 's 's PART hvd.32044092008168 114 16 form form NOUN hvd.32044092008168 114 17 of of ADP hvd.32044092008168 114 18 lamé lamé NOUN hvd.32044092008168 114 19 's 's PART hvd.32044092008168 114 20 equation equation NOUN hvd.32044092008168 114 21 of of ADP hvd.32044092008168 114 22 the the DET hvd.32044092008168 114 23 nth nth NOUN hvd.32044092008168 114 24 order order NOUN hvd.32044092008168 114 25 as as ADP hvd.32044092008168 114 26 a a DET hvd.32044092008168 114 27 linear linear ADJ hvd.32044092008168 114 28 homogenious homogenious ADJ hvd.32044092008168 114 29 differential differential ADJ hvd.32044092008168 114 30 equation equation NOUN hvd.32044092008168 114 31 of of ADP hvd.32044092008168 114 32 the the DET hvd.32044092008168 114 33 order order NOUN hvd.32044092008168 114 34 n n CCONJ hvd.32044092008168 114 35 having have VERB hvd.32044092008168 114 36 coefficients coefficient NOUN hvd.32044092008168 114 37 that that PRON hvd.32044092008168 114 38 are be AUX hvd.32044092008168 114 39 doubly doubly ADV hvd.32044092008168 114 40 periodic periodic ADJ hvd.32044092008168 114 41 functions function NOUN hvd.32044092008168 114 42 , , PUNCT hvd.32044092008168 114 43 having have VERB hvd.32044092008168 114 44 the the DET hvd.32044092008168 114 45 fundimental fundimental ADJ hvd.32044092008168 114 46 periods period NOUN hvd.32044092008168 114 47 2k 2k NUM hvd.32044092008168 114 48 and and CCONJ hvd.32044092008168 114 49 2i 2i PROPN hvd.32044092008168 114 50 k k INTJ hvd.32044092008168 114 51 ' ' PUNCT hvd.32044092008168 114 52 and and CCONJ hvd.32044092008168 114 53 everywhere everywhere ADV hvd.32044092008168 114 54 finite finite NOUN hvd.32044092008168 114 55 save save VERB hvd.32044092008168 114 56 in in ADP hvd.32044092008168 114 57 the the DET hvd.32044092008168 114 58 point point NOUN hvd.32044092008168 114 59 x x PUNCT hvd.32044092008168 115 1 = = PUNCT hvd.32044092008168 115 2 i i INTJ hvd.32044092008168 115 3 k k PROPN hvd.32044092008168 115 4 ' ' PUNCT hvd.32044092008168 115 5 and and CCONJ hvd.32044092008168 115 6 its its PRON hvd.32044092008168 115 7 congruents congruent NOUN hvd.32044092008168 115 8 which which PRON hvd.32044092008168 115 9 alone alone ADV hvd.32044092008168 115 10 are be AUX hvd.32044092008168 115 11 infinite infinite ADJ hvd.32044092008168 115 12 and and CCONJ hvd.32044092008168 115 13 whose whose DET hvd.32044092008168 115 14 general general ADJ hvd.32044092008168 115 15 integral integral NOUN hvd.32044092008168 115 16 is be AUX hvd.32044092008168 115 17 a a DET hvd.32044092008168 115 18 rational rational ADJ hvd.32044092008168 115 19 function function NOUN hvd.32044092008168 115 20 of of ADP hvd.32044092008168 115 21 the the DET hvd.32044092008168 115 22 variable variable NOUN hvd.32044092008168 115 23 . . PUNCT hvd.32044092008168 116 1 the the DET hvd.32044092008168 116 2 general general ADJ hvd.32044092008168 116 3 theory theory NOUN hvd.32044092008168 116 4 of of ADP hvd.32044092008168 116 5 herrn herrn PROPN hvd.32044092008168 116 6 fuchs fuchs PROPN hvd.32044092008168 116 7 * * PUNCT hvd.32044092008168 116 8 * * PUNCT hvd.32044092008168 116 9 ) ) PUNCT hvd.32044092008168 116 10 then then ADV hvd.32044092008168 116 11 gives give VERB hvd.32044092008168 116 12 the the DET hvd.32044092008168 116 13 form form NOUN hvd.32044092008168 116 14 , , PUNCT hvd.32044092008168 116 15 namely namely ADV hvd.32044092008168 116 16 [ [ X hvd.32044092008168 116 17 12 12 NUM hvd.32044092008168 116 18 ] ] PUNCT hvd.32044092008168 116 19 · · PUNCT hvd.32044092008168 116 20 yn yn PROPN hvd.32044092008168 116 21 + + PROPN hvd.32044092008168 116 22 0,(x 0,(x NUM hvd.32044092008168 116 23 ) ) PUNCT hvd.32044092008168 116 24 y(n y(n PROPN hvd.32044092008168 116 25 — — PUNCT hvd.32044092008168 116 26 2 2 X hvd.32044092008168 116 27 ) ) PUNCT hvd.32044092008168 116 28 + + NUM hvd.32044092008168 116 29 + + CCONJ hvd.32044092008168 116 30 on on ADP hvd.32044092008168 116 31 ( ( PUNCT hvd.32044092008168 116 32 x)y x)y X hvd.32044092008168 116 33 = = PROPN hvd.32044092008168 116 34 0 0 NUM hvd.32044092008168 116 35 where where SCONJ hvd.32044092008168 116 36 φ φ PROPN hvd.32044092008168 116 37 , , PUNCT hvd.32044092008168 116 38 ( ( PUNCT hvd.32044092008168 116 39 α α X hvd.32044092008168 116 40 ) ) PUNCT hvd.32044092008168 116 41 do do VERB hvd.32044092008168 116 42 + + PROPN hvd.32044092008168 116 43 qysna qysna PROPN hvd.32044092008168 116 44 03 03 NUM hvd.32044092008168 116 45 ( ( PUNCT hvd.32044092008168 116 46 20 20 NUM hvd.32044092008168 116 47 ) ) PUNCT hvd.32044092008168 116 48 = = PUNCT hvd.32044092008168 116 49 be be AUX hvd.32044092008168 116 50 + + CCONJ hvd.32044092008168 116 51 basnax basnax NOUN hvd.32044092008168 117 1 + + CCONJ hvd.32044092008168 117 2 b2 b2 PROPN hvd.32044092008168 117 3 d2 d2 PROPN hvd.32044092008168 117 4 snax snax NOUN hvd.32044092008168 117 5 φ.(α φ.(α PROPN hvd.32044092008168 117 6 ) ) PUNCT hvd.32044092008168 117 7 yo yo PROPN hvd.32044092008168 117 8 + + PROPN hvd.32044092008168 117 9 715n 715n PROPN hvd.32044092008168 117 10 - - PUNCT hvd.32044092008168 117 11 x x NOUN hvd.32044092008168 117 12 + + CCONJ hvd.32044092008168 117 13 72 72 NUM hvd.32044092008168 117 14 drsna drsna PROPN hvd.32044092008168 117 15 x x PUNCT hvd.32044092008168 117 16 + + CCONJ hvd.32044092008168 117 17 73 73 NUM hvd.32044092008168 117 18 d d NOUN hvd.32044092008168 117 19 snạ snạ NOUN hvd.32044092008168 117 20 2 2 NUM hvd.32044092008168 118 1 2 2 NUM hvd.32044092008168 118 2 1 1 NUM hvd.32044092008168 118 3 1 1 NUM hvd.32044092008168 118 4 1 1 NUM hvd.32044092008168 118 5 1 1 NUM hvd.32044092008168 118 6 dy dy NOUN hvd.32044092008168 118 7 ) ) PUNCT hvd.32044092008168 118 8 +6 +6 PROPN hvd.32044092008168 118 9 + + NUM hvd.32044092008168 118 10 6 6 NUM hvd.32044092008168 118 11 + + NUM hvd.32044092008168 118 12 [ [ X hvd.32044092008168 118 13 13 13 NUM hvd.32044092008168 118 14 ] ] PUNCT hvd.32044092008168 118 15 do do AUX hvd.32044092008168 118 16 but but CCONJ hvd.32044092008168 118 17 a a DET hvd.32044092008168 118 18 better well ADJ hvd.32044092008168 118 19 generalization generalization NOUN hvd.32044092008168 118 20 based base VERB hvd.32044092008168 118 21 upon upon SCONJ hvd.32044092008168 118 22 a a DET hvd.32044092008168 118 23 full full ADJ hvd.32044092008168 118 24 representation representation NOUN hvd.32044092008168 118 25 of of ADP hvd.32044092008168 118 26 the the DET hvd.32044092008168 118 27 singular singular ADJ hvd.32044092008168 118 28 points point NOUN hvd.32044092008168 118 29 is be AUX hvd.32044092008168 118 30 given give VERB hvd.32044092008168 118 31 by by ADP hvd.32044092008168 118 32 prof prof PROPN hvd.32044092008168 118 33 . . PUNCT hvd.32044092008168 119 1 klein klein PROPN hvd.32044092008168 120 1 * * PUNCT hvd.32044092008168 120 2 * * PUNCT hvd.32044092008168 120 3 * * PUNCT hvd.32044092008168 120 4 ) ) PUNCT hvd.32044092008168 120 5 and and CCONJ hvd.32044092008168 120 6 later later ADV hvd.32044092008168 120 7 stated state VERB hvd.32044092008168 120 8 as as SCONJ hvd.32044092008168 120 9 follows follow VERB hvd.32044092008168 120 10 by by ADP hvd.32044092008168 120 11 dr dr PROPN hvd.32044092008168 120 12 . . PROPN hvd.32044092008168 120 13 bôchert bôchert PROPN hvd.32044092008168 120 14 ) ) PUNCT hvd.32044092008168 120 15 . . PUNCT hvd.32044092008168 120 16 ) ) PUNCT hvd.32044092008168 121 1 first first ADV hvd.32044092008168 121 2 the the DET hvd.32044092008168 121 3 ordinary ordinary ADJ hvd.32044092008168 121 4 form form NOUN hvd.32044092008168 121 5 of of ADP hvd.32044092008168 121 6 the the DET hvd.32044092008168 121 7 equation equation NOUN hvd.32044092008168 121 8 of of ADP hvd.32044092008168 121 9 lamé lamé NOUN hvd.32044092008168 121 10 may may AUX hvd.32044092008168 121 11 through through ADP hvd.32044092008168 122 1 transformation transformation PROPN hvd.32044092008168 122 2 becomett becomett PROPN hvd.32044092008168 122 3 ) ) PUNCT hvd.32044092008168 122 4 day day NOUN hvd.32044092008168 122 5 ax ax NOUN hvd.32044092008168 123 1 + + PROPN hvd.32044092008168 123 2 b b NOUN hvd.32044092008168 124 1 + + CCONJ hvd.32044092008168 124 2 dx dx X hvd.32044092008168 124 3 y y PROPN hvd.32044092008168 124 4 4 4 NUM hvd.32044092008168 124 5 ( ( PUNCT hvd.32044092008168 124 6 v v NOUN hvd.32044092008168 124 7 — — PUNCT hvd.32044092008168 124 8 ez ez PROPN hvd.32044092008168 124 9 ) ) PUNCT hvd.32044092008168 124 10 ( ( PUNCT hvd.32044092008168 124 11 oc oc PROPN hvd.32044092008168 124 12 ( ( PUNCT hvd.32044092008168 124 13 2 2 X hvd.32044092008168 124 14 ) ) PUNCT hvd.32044092008168 124 15 ( ( PUNCT hvd.32044092008168 124 16 ac ac PROPN hvd.32044092008168 124 17 ez ez PROPN hvd.32044092008168 124 18 ) ) PUNCT hvd.32044092008168 124 19 where where SCONJ hvd.32044092008168 124 20 the the DET hvd.32044092008168 124 21 exponents exponent NOUN hvd.32044092008168 124 22 of of ADP hvd.32044092008168 124 23 the the DET hvd.32044092008168 124 24 zeros zeros PROPN hvd.32044092008168 124 25 ez ez PROPN hvd.32044092008168 124 26 , , PUNCT hvd.32044092008168 124 27 ez ez PROPN hvd.32044092008168 124 28 , , PUNCT hvd.32044092008168 124 29 ez ez PROPN hvd.32044092008168 124 30 are be AUX hvd.32044092008168 124 31 0 0 PUNCT hvd.32044092008168 124 32 and and CCONJ hvd.32044092008168 124 33 and and CCONJ hvd.32044092008168 124 34 that that PRON hvd.32044092008168 124 35 of of ADP hvd.32044092008168 124 36 the the DET hvd.32044092008168 124 37 infinites infinite NOUN hvd.32044092008168 124 38 1 1 NUM hvd.32044092008168 124 39 + + NUM hvd.32044092008168 124 40 11 11 NUM hvd.32044092008168 124 41 + + NUM hvd.32044092008168 124 42 4a 4a NUM hvd.32044092008168 124 43 from from ADP hvd.32044092008168 124 44 this this DET hvd.32044092008168 124 45 generalizing generalizing NOUN hvd.32044092008168 124 46 by by ADP hvd.32044092008168 124 47 the the DET hvd.32044092008168 124 48 introduction introduction NOUN hvd.32044092008168 124 49 of of ADP hvd.32044092008168 124 50 n n CCONJ hvd.32044092008168 124 51 zeros zero NOUN hvd.32044092008168 124 52 we we PRON hvd.32044092008168 124 53 have have VERB hvd.32044092008168 124 54 the the DET hvd.32044092008168 124 55 following following ADJ hvd.32044092008168 124 56 definition definition NOUN hvd.32044092008168 124 57 : : PUNCT hvd.32044092008168 125 1 2 2 NUM hvd.32044092008168 125 2 ) ) PUNCT hvd.32044092008168 125 3 ei ei PROPN hvd.32044092008168 125 4 x x SYM hvd.32044092008168 125 5 eg eg PROPN hvd.32044092008168 125 6 2 2 NUM hvd.32044092008168 125 7 - - PUNCT hvd.32044092008168 125 8 e. e. NOUN hvd.32044092008168 125 9 2 2 NUM hvd.32044092008168 125 10 4 4 NUM hvd.32044092008168 125 11 * * SYM hvd.32044092008168 125 12 ) ) PUNCT hvd.32044092008168 125 13 annali annali PROPN hvd.32044092008168 125 14 di di PROPN hvd.32044092008168 125 15 matematica matematica PROPN hvd.32044092008168 125 16 , , PUNCT hvd.32044092008168 125 17 tomo tomo PROPN hvd.32044092008168 125 18 xi xi PROPN hvd.32044092008168 125 19 , , PUNCT hvd.32044092008168 125 20 1882 1882 NUM hvd.32044092008168 125 21 . . PUNCT hvd.32044092008168 126 1 * * PUNCT hvd.32044092008168 126 2 * * PUNCT hvd.32044092008168 126 3 ) ) PUNCT hvd.32044092008168 126 4 comptes compte VERB hvd.32044092008168 126 5 rendus rendus X hvd.32044092008168 126 6 etc etc X hvd.32044092008168 126 7 . . X hvd.32044092008168 126 8 1880 1880 NUM hvd.32044092008168 126 9 . . PUNCT hvd.32044092008168 127 1 p. p. NOUN hvd.32044092008168 127 2 64 64 NUM hvd.32044092008168 127 3 . . PUNCT hvd.32044092008168 128 1 * * PUNCT hvd.32044092008168 128 2 * * PUNCT hvd.32044092008168 128 3 * * PUNCT hvd.32044092008168 128 4 ) ) PUNCT hvd.32044092008168 128 5 math math NOUN hvd.32044092008168 128 6 . . PUNCT hvd.32044092008168 129 1 annal annal PROPN hvd.32044092008168 129 2 . . PUNCT hvd.32044092008168 130 1 bd bd PROPN hvd.32044092008168 130 2 . . PROPN hvd.32044092008168 130 3 38 38 NUM hvd.32044092008168 130 4 . . PUNCT hvd.32044092008168 131 1 † † PROPN hvd.32044092008168 131 2 ) ) PUNCT hvd.32044092008168 131 3 ueber ueber PROPN hvd.32044092008168 131 4 die die PROPN hvd.32044092008168 131 5 reihentwickelungen reihentwickelungen PROPN hvd.32044092008168 131 6 der der PROPN hvd.32044092008168 131 7 potentialtheorie potentialtheorie PROPN hvd.32044092008168 131 8 . . PUNCT hvd.32044092008168 132 1 göttingen göttingen PROPN hvd.32044092008168 132 2 1891 1891 NUM hvd.32044092008168 132 3 . . PUNCT hvd.32044092008168 133 1 †t †t PROPN hvd.32044092008168 133 2 ) ) PUNCT hvd.32044092008168 133 3 see see VERB hvd.32044092008168 133 4 also also ADV hvd.32044092008168 133 5 transformation transformation NOUN hvd.32044092008168 133 6 p. p. NOUN hvd.32044092008168 133 7 20 20 NUM hvd.32044092008168 133 8 . . PUNCT hvd.32044092008168 134 1 16 16 NUM hvd.32044092008168 134 2 part part NOUN hvd.32044092008168 134 3 i. i. PROPN hvd.32044092008168 134 4 historical historical PROPN hvd.32044092008168 134 5 development development NOUN hvd.32044092008168 134 6 and and CCONJ hvd.32044092008168 134 7 definition definition NOUN hvd.32044092008168 134 8 of of ADP hvd.32044092008168 134 9 the the DET hvd.32044092008168 134 10 equation equation NOUN hvd.32044092008168 134 11 of of ADP hvd.32044092008168 134 12 lamé lamé NOUN hvd.32044092008168 134 13 . . PUNCT hvd.32044092008168 135 1 „ „ PUNCT hvd.32044092008168 135 2 mit mit VERB hvd.32044092008168 135 3 dem dem PROPN hvd.32044092008168 135 4 namen namen PROPN hvd.32044092008168 135 5 lamésche lamésche PROPN hvd.32044092008168 135 6 gleichung gleichung PROPN hvd.32044092008168 135 7 bezeichnen bezeichnen PROPN hvd.32044092008168 135 8 wir wir PROPN hvd.32044092008168 135 9 eine eine PROPN hvd.32044092008168 135 10 überall überall NOUN hvd.32044092008168 135 11 reguläre reguläre PROPN hvd.32044092008168 135 12 homogene homogene PROPN hvd.32044092008168 135 13 differentialgleichung differentialgleichung PROPN hvd.32044092008168 135 14 zweiter zweiter PROPN hvd.32044092008168 135 15 ordnung ordnung PROPN hvd.32044092008168 135 16 mit mit PROPN hvd.32044092008168 135 17 rationalen rationalen PROPN hvd.32044092008168 135 18 coefficienten coefficienten PROPN hvd.32044092008168 135 19 , , PUNCT hvd.32044092008168 135 20 deren deren PROPN hvd.32044092008168 135 21 i i PRON hvd.32044092008168 135 22 m m VERB hvd.32044092008168 135 23 endlichen endlichen PROPN hvd.32044092008168 135 24 gelegene gelegene PROPN hvd.32044092008168 135 25 singuläre singuläre PROPN hvd.32044092008168 135 26 punkte punkte PROPN hvd.32044092008168 135 27 en en PROPN hvd.32044092008168 135 28 , , PUNCT hvd.32044092008168 135 29 l l PROPN hvd.32044092008168 135 30 , , PUNCT hvd.32044092008168 135 31 .. .. PUNCT hvd.32044092008168 135 32 en en X hvd.32044092008168 135 33 sämmtlich sämmtlich PROPN hvd.32044092008168 135 34 die die PROPN hvd.32044092008168 135 35 exponenten exponenten VERB hvd.32044092008168 135 36 0 0 NUM hvd.32044092008168 135 37 , , PUNCT hvd.32044092008168 135 38 1 1 NUM hvd.32044092008168 135 39 besetzen besetzen NOUN hvd.32044092008168 135 40 , , PUNCT hvd.32044092008168 135 41 und und ADV hvd.32044092008168 135 42 in in ADP hvd.32044092008168 135 43 unendlichen unendlichen PROPN hvd.32044092008168 135 44 nur nur PROPN hvd.32044092008168 135 45 einen einen PROPN hvd.32044092008168 135 46 , , PUNCT hvd.32044092008168 135 47 uneigentlich uneigentlich PROPN hvd.32044092008168 135 48 singularen singularen PROPN hvd.32044092008168 135 49 punkt punkt PROPN hvd.32044092008168 135 50 aufweist aufweist NOUN hvd.32044092008168 135 51 . . PUNCT hvd.32044092008168 136 1 “ " PUNCT hvd.32044092008168 136 2 lamé lamé NOUN hvd.32044092008168 136 3 's 's PART hvd.32044092008168 136 4 equation equation NOUN hvd.32044092008168 136 5 becomes become VERB hvd.32044092008168 136 6 in in ADP hvd.32044092008168 136 7 accordance accordance NOUN hvd.32044092008168 136 8 with with ADP hvd.32044092008168 136 9 this this DET hvd.32044092008168 136 10 definition definition NOUN hvd.32044092008168 136 11 and and CCONJ hvd.32044092008168 136 12 freed free VERB hvd.32044092008168 136 13 from from ADP hvd.32044092008168 136 14 the the DET hvd.32044092008168 136 15 possibility possibility NOUN hvd.32044092008168 136 16 of of ADP hvd.32044092008168 136 17 a a DET hvd.32044092008168 136 18 logarithmic logarithmic ADJ hvd.32044092008168 136 19 irrationality irrationality NOUN hvd.32044092008168 136 20 through through ADP hvd.32044092008168 136 21 a a DET hvd.32044092008168 136 22 determination determination NOUN hvd.32044092008168 136 23 of of ADP hvd.32044092008168 136 24 the the DET hvd.32044092008168 136 25 coefficient coefficient NOUN hvd.32044092008168 136 26 of of ADP hvd.32044092008168 136 27 xn-3 xn-3 SPACE hvd.32044092008168 136 28 . . PUNCT hvd.32044092008168 137 1 -3 -3 X hvd.32044092008168 137 2 dạy dạy X hvd.32044092008168 137 3 f f PROPN hvd.32044092008168 137 4 ' ' PUNCT hvd.32044092008168 137 5 ( ( PUNCT hvd.32044092008168 137 6 2 2 NUM hvd.32044092008168 137 7 ) ) PUNCT hvd.32044092008168 137 8 dy dy PROPN hvd.32044092008168 138 1 [ [ X hvd.32044092008168 138 2 14 14 NUM hvd.32044092008168 138 3 ] ] PUNCT hvd.32044092008168 138 4 · · PUNCT hvd.32044092008168 138 5 + + CCONJ hvd.32044092008168 138 6 daca daca PROPN hvd.32044092008168 138 7 2fx 2fx PROPN hvd.32044092008168 138 8 dx dx PROPN hvd.32044092008168 138 9 n n PROPN hvd.32044092008168 138 10 1 1 NUM hvd.32044092008168 138 11 n(n n(n PROPN hvd.32044092008168 138 12 — — PUNCT hvd.32044092008168 138 13 4 4 X hvd.32044092008168 138 14 ) ) PUNCT hvd.32044092008168 138 15 21—2 21—2 NOUN hvd.32044092008168 139 1 + + PUNCT hvd.32044092008168 139 2 -2 -2 X hvd.32044092008168 140 1 [ [ X hvd.32044092008168 140 2 " " PUNCT hvd.32044092008168 140 3 ( ( PUNCT hvd.32044092008168 140 4 n n CCONJ hvd.32044092008168 140 5 − − PROPN hvd.32044092008168 140 6 2)(n 2)(n NUM hvd.32044092008168 140 7 — — PUNCT hvd.32044092008168 140 8 4 4 X hvd.32044092008168 140 9 ) ) PUNCT hvd.32044092008168 140 10 e e NOUN hvd.32044092008168 140 11 ; ; PUNCT hvd.32044092008168 140 12 24–8 24–8 NUM hvd.32044092008168 140 13 + + NUM hvd.32044092008168 140 14 ar-4+.+m]y ar-4+.+m]y ADJ hvd.32044092008168 141 1 -3 -3 PUNCT hvd.32044092008168 141 2 :0 :0 NOUN hvd.32044092008168 141 3 4f 4f NUM hvd.32044092008168 141 4 ( ( PUNCT hvd.32044092008168 141 5 2 2 NUM hvd.32044092008168 141 6 ) ) PUNCT hvd.32044092008168 141 7 where where SCONJ hvd.32044092008168 141 8 xo xo PROPN hvd.32044092008168 141 9 f(x f(x PROPN hvd.32044092008168 141 10 ) ) PUNCT hvd.32044092008168 141 11 = = PROPN hvd.32044092008168 141 12 ( ( PUNCT hvd.32044092008168 141 13 x x PUNCT hvd.32044092008168 141 14 – – PUNCT hvd.32044092008168 141 15 e e X hvd.32044092008168 141 16 ) ) PUNCT hvd.32044092008168 141 17 ( ( PUNCT hvd.32044092008168 141 18 x x PUNCT hvd.32044092008168 141 19 – – PUNCT hvd.32044092008168 141 20 ez ez PROPN hvd.32044092008168 141 21 ) ) PUNCT hvd.32044092008168 141 22 ... ... PUNCT hvd.32044092008168 142 1 ( ( PUNCT hvd.32044092008168 142 2 x x PUNCT hvd.32044092008168 142 3 – – PUNCT hvd.32044092008168 142 4 en en ADV hvd.32044092008168 142 5 ) ) PUNCT hvd.32044092008168 142 6 . . PUNCT hvd.32044092008168 143 1 ac ac INTJ hvd.32044092008168 143 2 it it PRON hvd.32044092008168 143 3 is be AUX hvd.32044092008168 143 4 further far ADV hvd.32044092008168 143 5 evident evident ADJ hvd.32044092008168 143 6 that that SCONJ hvd.32044092008168 143 7 this this DET hvd.32044092008168 143 8 form form NOUN hvd.32044092008168 143 9 , , PUNCT hvd.32044092008168 143 10 like like ADP hvd.32044092008168 143 11 the the DET hvd.32044092008168 143 12 hermite hermite ADJ hvd.32044092008168 143 13 form form NOUN hvd.32044092008168 143 14 and and CCONJ hvd.32044092008168 143 15 as as ADV hvd.32044092008168 143 16 previously previously ADV hvd.32044092008168 143 17 developed develop VERB hvd.32044092008168 143 18 by by ADP hvd.32044092008168 143 19 prof prof PROPN hvd.32044092008168 143 20 . . PROPN hvd.32044092008168 143 21 heine heine PROPN hvd.32044092008168 143 22 , , PUNCT hvd.32044092008168 143 23 is be AUX hvd.32044092008168 143 24 but but CCONJ hvd.32044092008168 143 25 a a DET hvd.32044092008168 143 26 special special ADJ hvd.32044092008168 143 27 case case NOUN hvd.32044092008168 143 28 of of ADP hvd.32044092008168 143 29 a a DET hvd.32044092008168 143 30 general general ADJ hvd.32044092008168 143 31 equation equation NOUN hvd.32044092008168 143 32 of of ADP hvd.32044092008168 143 33 a a DET hvd.32044092008168 143 34 higher high ADJ hvd.32044092008168 143 35 order order NOUN hvd.32044092008168 143 36 . . PUNCT hvd.32044092008168 144 1 in in ADP hvd.32044092008168 144 2 speaking speak VERB hvd.32044092008168 144 3 of of ADP hvd.32044092008168 144 4 lamé lamé NOUN hvd.32044092008168 144 5 's 's PART hvd.32044092008168 144 6 equation equation NOUN hvd.32044092008168 144 7 we we PRON hvd.32044092008168 144 8 will will AUX hvd.32044092008168 144 9 understand understand VERB hvd.32044092008168 144 10 an an DET hvd.32044092008168 144 11 equation equation NOUN hvd.32044092008168 144 12 conforming conform VERB hvd.32044092008168 144 13 with with ADP hvd.32044092008168 144 14 the the DET hvd.32044092008168 144 15 above above ADJ hvd.32044092008168 144 16 definition definition NOUN hvd.32044092008168 144 17 whose whose DET hvd.32044092008168 144 18 general general ADJ hvd.32044092008168 144 19 form form NOUN hvd.32044092008168 144 20 is be AUX hvd.32044092008168 144 21 given give VERB hvd.32044092008168 144 22 by by ADP hvd.32044092008168 144 23 [ [ X hvd.32044092008168 144 24 14 14 NUM hvd.32044092008168 144 25 ] ] PUNCT hvd.32044092008168 144 26 and and CCONJ hvd.32044092008168 144 27 , , PUNCT hvd.32044092008168 144 28 if if SCONJ hvd.32044092008168 144 29 the the DET hvd.32044092008168 144 30 order order NOUN hvd.32044092008168 144 31 is be AUX hvd.32044092008168 144 32 higher high ADJ hvd.32044092008168 144 33 than than ADP hvd.32044092008168 144 34 the the DET hvd.32044092008168 144 35 second second ADJ hvd.32044092008168 144 36 , , PUNCT hvd.32044092008168 144 37 distinguish distinguish ADJ hvd.32044092008168 144 38 by by ADP hvd.32044092008168 144 39 mentioning mention VERB hvd.32044092008168 144 40 the the DET hvd.32044092008168 144 41 order order NOUN hvd.32044092008168 144 42 . . PUNCT hvd.32044092008168 145 1 forms form NOUN hvd.32044092008168 145 2 [ [ PUNCT hvd.32044092008168 145 3 9 9 NUM hvd.32044092008168 145 4 ] ] PUNCT hvd.32044092008168 145 5 and and CCONJ hvd.32044092008168 145 6 [ [ X hvd.32044092008168 145 7 10 10 X hvd.32044092008168 145 8 ] ] PUNCT hvd.32044092008168 145 9 will will AUX hvd.32044092008168 145 10 then then ADV hvd.32044092008168 145 11 be be AUX hvd.32044092008168 145 12 called call VERB hvd.32044092008168 145 13 hermite hermite PROPN hvd.32044092008168 145 14 's 's PART hvd.32044092008168 145 15 forms form NOUN hvd.32044092008168 145 16 of of ADP hvd.32044092008168 145 17 lamé lamé NOUN hvd.32044092008168 145 18 's 's PART hvd.32044092008168 145 19 equation equation NOUN hvd.32044092008168 145 20 or or CCONJ hvd.32044092008168 145 21 simply simply ADV hvd.32044092008168 145 22 hermite hermite PROPN hvd.32044092008168 145 23 's 's PART hvd.32044092008168 145 24 equation equation NOUN hvd.32044092008168 145 25 , , PUNCT hvd.32044092008168 145 26 where where SCONJ hvd.32044092008168 145 27 again again ADV hvd.32044092008168 145 28 the the DET hvd.32044092008168 145 29 order order NOUN hvd.32044092008168 145 30 need need AUX hvd.32044092008168 145 31 be be AUX hvd.32044092008168 145 32 mentioned mention VERB hvd.32044092008168 145 33 only only ADV hvd.32044092008168 145 34 if if SCONJ hvd.32044092008168 145 35 it it PRON hvd.32044092008168 145 36 be be VERB hvd.32044092008168 145 37 other other ADJ hvd.32044092008168 145 38 than than ADP hvd.32044092008168 145 39 the the DET hvd.32044092008168 145 40 second second ADJ hvd.32044092008168 145 41 . . PUNCT hvd.32044092008168 146 1 any any DET hvd.32044092008168 146 2 solution solution NOUN hvd.32044092008168 146 3 of of ADP hvd.32044092008168 146 4 any any DET hvd.32044092008168 146 5 form form NOUN hvd.32044092008168 146 6 of of ADP hvd.32044092008168 146 7 lamé lamé NOUN hvd.32044092008168 146 8 's 's PART hvd.32044092008168 146 9 equation equation NOUN hvd.32044092008168 146 10 will will AUX hvd.32044092008168 146 11 be be AUX hvd.32044092008168 146 12 a a DET hvd.32044092008168 146 13 function function NOUN hvd.32044092008168 146 14 of of ADP hvd.32044092008168 146 15 lamé lamé NOUN hvd.32044092008168 146 16 and and CCONJ hvd.32044092008168 146 17 if if SCONJ hvd.32044092008168 146 18 the the DET hvd.32044092008168 146 19 doubly doubly ADJ hvd.32044092008168 146 20 periodic periodic ADJ hvd.32044092008168 146 21 functions function NOUN hvd.32044092008168 146 22 first first ADV hvd.32044092008168 146 23 determined determine VERB hvd.32044092008168 146 24 by by ADP hvd.32044092008168 146 25 lamé lamé NOUN hvd.32044092008168 146 26 are be AUX hvd.32044092008168 146 27 mentioned mention VERB hvd.32044092008168 146 28 they they PRON hvd.32044092008168 146 29 will will AUX hvd.32044092008168 146 30 be be AUX hvd.32044092008168 146 31 designated designate VERB hvd.32044092008168 146 32 as as ADP hvd.32044092008168 146 33 the the DET hvd.32044092008168 146 34 special special ADJ hvd.32044092008168 146 35 functions function NOUN hvd.32044092008168 146 36 of of ADP hvd.32044092008168 146 37 lamé lamé NOUN hvd.32044092008168 146 38 . . PUNCT hvd.32044092008168 147 1 part part PROPN hvd.32044092008168 147 2 ii ii PROPN hvd.32044092008168 147 3 . . PUNCT hvd.32044092008168 148 1 hermite hermite PROPN hvd.32044092008168 148 2 's 's PART hvd.32044092008168 148 3 integral integral ADJ hvd.32044092008168 148 4 as as ADP hvd.32044092008168 148 5 a a DET hvd.32044092008168 148 6 sum sum NOUN hvd.32044092008168 148 7 . . PUNCT hvd.32044092008168 149 1 the the DET hvd.32044092008168 149 2 function function NOUN hvd.32044092008168 149 3 of of ADP hvd.32044092008168 149 4 the the DET hvd.32044092008168 149 5 second second ADJ hvd.32044092008168 149 6 species specie NOUN hvd.32044092008168 149 7 . . PUNCT hvd.32044092008168 150 1 da da PROPN hvd.32044092008168 150 2 y y INTJ hvd.32044092008168 150 3 we we PRON hvd.32044092008168 150 4 have have VERB hvd.32044092008168 150 5 the the DET hvd.32044092008168 150 6 problem problem NOUN hvd.32044092008168 150 7 required require VERB hvd.32044092008168 150 8 the the DET hvd.32044092008168 150 9 integral integral ADJ hvd.32044092008168 150 10 y y PROPN hvd.32044092008168 150 11 of of ADP hvd.32044092008168 150 12 the the DET hvd.32044092008168 150 13 equation equation NOUN hvd.32044092008168 150 14 [ [ X hvd.32044092008168 150 15 15 15 NUM hvd.32044092008168 150 16 ] ] PUNCT hvd.32044092008168 151 1 [ [ X hvd.32044092008168 151 2 n(n n(n X hvd.32044092008168 151 3 + + CCONJ hvd.32044092008168 151 4 1 1 NUM hvd.32044092008168 151 5 ) ) PUNCT hvd.32044092008168 151 6 snu snu NOUN hvd.32044092008168 151 7 + + CCONJ hvd.32044092008168 151 8 h]y h]y NOUN hvd.32044092008168 151 9 d d NOUN hvd.32044092008168 151 10 u² u² PROPN hvd.32044092008168 151 11 where where SCONJ hvd.32044092008168 151 12 h h NOUN hvd.32044092008168 151 13 is be AUX hvd.32044092008168 151 14 taken take VERB hvd.32044092008168 151 15 arbitrarily arbitrarily ADV hvd.32044092008168 151 16 , , PUNCT hvd.32044092008168 151 17 n n CCONJ hvd.32044092008168 151 18 is be AUX hvd.32044092008168 151 19 any any DET hvd.32044092008168 151 20 intire intire ADJ hvd.32044092008168 151 21 positive positive ADJ hvd.32044092008168 151 22 number number NOUN hvd.32044092008168 151 23 and and CCONJ hvd.32044092008168 151 24 k k PROPN hvd.32044092008168 151 25 is be AUX hvd.32044092008168 151 26 the the DET hvd.32044092008168 151 27 modulus modulus NOUN hvd.32044092008168 151 28 of of ADP hvd.32044092008168 151 29 the the DET hvd.32044092008168 151 30 elliptic elliptic ADJ hvd.32044092008168 151 31 function function NOUN hvd.32044092008168 151 32 . . PUNCT hvd.32044092008168 152 1 m. m. NOUN hvd.32044092008168 152 2 hermite hermite PROPN hvd.32044092008168 152 3 introduces introduce VERB hvd.32044092008168 152 4 to to ADP hvd.32044092008168 152 5 this this DET hvd.32044092008168 152 6 end end NOUN hvd.32044092008168 152 7 a a DET hvd.32044092008168 152 8 function function NOUN hvd.32044092008168 152 9 which which PRON hvd.32044092008168 152 10 he he PRON hvd.32044092008168 152 11 names name VERB hvd.32044092008168 152 12 doubly doubly ADV hvd.32044092008168 152 13 periodic periodic ADJ hvd.32044092008168 152 14 of of ADP hvd.32044092008168 152 15 the the DET hvd.32044092008168 152 16 second second ADJ hvd.32044092008168 152 17 species specie NOUN hvd.32044092008168 152 18 , , PUNCT hvd.32044092008168 152 19 which which PRON hvd.32044092008168 152 20 may may AUX hvd.32044092008168 152 21 be be AUX hvd.32044092008168 152 22 defined define VERB hvd.32044092008168 152 23 as as ADP hvd.32044092008168 152 24 a a DET hvd.32044092008168 152 25 product product NOUN hvd.32044092008168 152 26 of of ADP hvd.32044092008168 152 27 a a DET hvd.32044092008168 152 28 quotient quotient NOUN hvd.32044092008168 152 29 composed compose VERB hvd.32044092008168 152 30 of of ADP hvd.32044092008168 152 31 o o NOUN hvd.32044092008168 152 32 functions function NOUN hvd.32044092008168 152 33 , , PUNCT hvd.32044092008168 152 34 the the DET hvd.32044092008168 152 35 number number NOUN hvd.32044092008168 152 36 of of ADP hvd.32044092008168 152 37 zeros zero NOUN hvd.32044092008168 152 38 being be AUX hvd.32044092008168 152 39 equal equal ADJ hvd.32044092008168 152 40 to to ADP hvd.32044092008168 152 41 the the DET hvd.32044092008168 152 42 number number NOUN hvd.32044092008168 152 43 of of ADP hvd.32044092008168 152 44 the the DET hvd.32044092008168 152 45 infinites infinite NOUN hvd.32044092008168 152 46 , , PUNCT hvd.32044092008168 152 47 and and CCONJ hvd.32044092008168 152 48 an an DET hvd.32044092008168 152 49 exponential exponential NOUN hvd.32044092008168 152 50 , , PUNCT hvd.32044092008168 152 51 having have VERB hvd.32044092008168 152 52 the the DET hvd.32044092008168 152 53 property property NOUN hvd.32044092008168 152 54 of of ADP hvd.32044092008168 152 55 reproducing reproduce VERB hvd.32044092008168 152 56 itself itself PRON hvd.32044092008168 152 57 multiplied multiply VERB hvd.32044092008168 152 58 by by ADP hvd.32044092008168 152 59 an an DET hvd.32044092008168 152 60 exponential exponential ADJ hvd.32044092008168 152 61 factor factor NOUN hvd.32044092008168 152 62 when when SCONJ hvd.32044092008168 152 63 the the DET hvd.32044092008168 152 64 variable variable NOUN hvd.32044092008168 152 65 is be AUX hvd.32044092008168 152 66 increased increase VERB hvd.32044092008168 152 67 by by ADP hvd.32044092008168 152 68 the the DET hvd.32044092008168 152 69 periods period NOUN hvd.32044092008168 152 70 2k 2k NUM hvd.32044092008168 152 71 and and CCONJ hvd.32044092008168 152 72 2ik 2ik PROPN hvd.32044092008168 152 73 . . PUNCT hvd.32044092008168 153 1 it it PRON hvd.32044092008168 153 2 is be AUX hvd.32044092008168 153 3 defined define VERB hvd.32044092008168 153 4 then then ADV hvd.32044092008168 153 5 in in ADP hvd.32044092008168 153 6 general general ADJ hvd.32044092008168 153 7 by by ADP hvd.32044092008168 153 8 the the DET hvd.32044092008168 153 9 relations relation NOUN hvd.32044092008168 153 10 : : PUNCT hvd.32044092008168 153 11 f(u f(u PROPN hvd.32044092008168 153 12 + + NUM hvd.32044092008168 153 13 2k 2k NUM hvd.32044092008168 153 14 ) ) PUNCT hvd.32044092008168 153 15 = = PROPN hvd.32044092008168 154 1 u u PROPN hvd.32044092008168 154 2 f(u f(u PROPN hvd.32044092008168 154 3 ) ) PUNCT hvd.32044092008168 154 4 f f PROPN hvd.32044092008168 155 1 [ [ X hvd.32044092008168 155 2 16 16 NUM hvd.32044092008168 155 3 ] ] PUNCT hvd.32044092008168 155 4 f(u f(u PROPN hvd.32044092008168 155 5 + + NUM hvd.32044092008168 155 6 2ik 2ik PROPN hvd.32044092008168 155 7 ' ' PUNCT hvd.32044092008168 155 8 ) ) PUNCT hvd.32044092008168 155 9 = = PROPN hvd.32044092008168 155 10 u'f(u u'f(u PROPN hvd.32044092008168 155 11 ) ) PUNCT hvd.32044092008168 155 12 o(u o(u PROPN hvd.32044092008168 155 13 — — PUNCT hvd.32044092008168 155 14 @ @ NOUN hvd.32044092008168 155 15 ) ) PUNCT hvd.32044092008168 155 16 ( ( PUNCT hvd.32044092008168 155 17 u u PROPN hvd.32044092008168 155 18 — — PUNCT hvd.32044092008168 155 19 a.) a.) SPACE hvd.32044092008168 155 20 .... .... PUNCT hvd.32044092008168 155 21 (u (u PUNCT hvd.32044092008168 155 22 — — PUNCT hvd.32044092008168 155 23 q q X hvd.32044092008168 155 24 n-1 n-1 X hvd.32044092008168 155 25 ) ) PUNCT hvd.32044092008168 155 26 ao ao PROPN hvd.32044092008168 155 27 , , PUNCT hvd.32044092008168 155 28 — — PUNCT hvd.32044092008168 155 29 f(0 f(0 PROPN hvd.32044092008168 155 30 ) ) PUNCT hvd.32044092008168 155 31 o o NOUN hvd.32044092008168 156 1 ( ( PUNCT hvd.32044092008168 156 2 u u PROPN hvd.32044092008168 156 3 hy hy PROPN hvd.32044092008168 156 4 ) ) PUNCT hvd.32044092008168 156 5 o(u o(u PROPN hvd.32044092008168 156 6 — — PUNCT hvd.32044092008168 156 7 h,) h,) ADJ hvd.32044092008168 156 8 ... ... PUNCT hvd.32044092008168 156 9 0(u 0(u NUM hvd.32044092008168 157 1 ( ( PUNCT hvd.32044092008168 157 2 u u PROPN hvd.32044092008168 157 3 on-1 on-1 PROPN hvd.32044092008168 157 4 ) ) PUNCT hvd.32044092008168 157 5 the the DET hvd.32044092008168 157 6 factors factor NOUN hvd.32044092008168 157 7 u u PROPN hvd.32044092008168 157 8 and and CCONJ hvd.32044092008168 157 9 u u PROPN hvd.32044092008168 157 10 are be AUX hvd.32044092008168 157 11 called call VERB hvd.32044092008168 157 12 multiplicators multiplicator NOUN hvd.32044092008168 157 13 . . PUNCT hvd.32044092008168 158 1 m. m. NOUN hvd.32044092008168 158 2 hermite hermite PROPN hvd.32044092008168 158 3 might might AUX hvd.32044092008168 158 4 have have AUX hvd.32044092008168 158 5 been be AUX hvd.32044092008168 158 6 led lead VERB hvd.32044092008168 158 7 to to ADP hvd.32044092008168 158 8 the the DET hvd.32044092008168 158 9 employment employment NOUN hvd.32044092008168 158 10 of of ADP hvd.32044092008168 158 11 this this DET hvd.32044092008168 158 12 function function NOUN hvd.32044092008168 158 13 by by ADP hvd.32044092008168 158 14 the the DET hvd.32044092008168 158 15 following follow VERB hvd.32044092008168 158 16 analysis analysis NOUN hvd.32044092008168 158 17 which which PRON hvd.32044092008168 158 18 is be AUX hvd.32044092008168 158 19 essentially essentially ADV hvd.32044092008168 158 20 that that SCONJ hvd.32044092008168 158 21 given give VERB hvd.32044092008168 158 22 by by ADP hvd.32044092008168 158 23 halphen halphen ADV hvd.32044092008168 158 24 . . PUNCT hvd.32044092008168 158 25 * * PUNCT hvd.32044092008168 158 26 ) ) PUNCT hvd.32044092008168 158 27 consider consider VERB hvd.32044092008168 158 28 for for ADP hvd.32044092008168 158 29 the the DET hvd.32044092008168 158 30 moment moment NOUN hvd.32044092008168 158 31 that that PRON hvd.32044092008168 158 32 y y PROPN hvd.32044092008168 158 33 be be VERB hvd.32044092008168 158 34 such such DET hvd.32044092008168 158 35 a a DET hvd.32044092008168 158 36 function function NOUN hvd.32044092008168 158 37 of of ADP hvd.32044092008168 158 38 the the DET hvd.32044092008168 158 39 second second ADJ hvd.32044092008168 158 40 species specie NOUN hvd.32044092008168 158 41 but but CCONJ hvd.32044092008168 158 42 having have VERB hvd.32044092008168 158 43 instead instead ADV hvd.32044092008168 158 44 of of ADP hvd.32044092008168 158 45 the the DET hvd.32044092008168 158 46 n n CCONJ hvd.32044092008168 158 47 different different ADJ hvd.32044092008168 158 48 poles pole NOUN hvd.32044092008168 158 49 but but CCONJ hvd.32044092008168 158 50 one one NUM hvd.32044092008168 158 51 pole pole NOUN hvd.32044092008168 158 52 u u PROPN hvd.32044092008168 158 53 30 30 NUM hvd.32044092008168 158 54 of of ADP hvd.32044092008168 158 55 the the DET hvd.32044092008168 158 56 nth nth NOUN hvd.32044092008168 158 57 order order NOUN hvd.32044092008168 158 58 in in ADP hvd.32044092008168 158 59 which which DET hvd.32044092008168 158 60 case case NOUN hvd.32044092008168 158 61 the the DET hvd.32044092008168 158 62 function function NOUN hvd.32044092008168 158 63 will will AUX hvd.32044092008168 158 64 have have VERB hvd.32044092008168 158 65 n n VERB hvd.32044092008168 158 66 roots root NOUN hvd.32044092008168 158 67 . . PUNCT hvd.32044092008168 159 1 upon upon SCONJ hvd.32044092008168 159 2 developing develop VERB hvd.32044092008168 159 3 the the DET hvd.32044092008168 159 4 properties property NOUN hvd.32044092008168 159 5 of of ADP hvd.32044092008168 159 6 this this DET hvd.32044092008168 159 7 function function NOUN hvd.32044092008168 159 8 one one PRON hvd.32044092008168 159 9 finds find VERB hvd.32044092008168 159 10 that that SCONJ hvd.32044092008168 159 11 its its PRON hvd.32044092008168 159 12 second second ADJ hvd.32044092008168 159 13 derivative derivative NOUN hvd.32044092008168 159 14 has have VERB hvd.32044092008168 159 15 the the DET hvd.32044092008168 159 16 same same ADJ hvd.32044092008168 159 17 multiplicator multiplicator NOUN hvd.32044092008168 159 18 as as ADP hvd.32044092008168 159 19 the the DET hvd.32044092008168 159 20 function function NOUN hvd.32044092008168 159 21 n1 n1 PROPN hvd.32044092008168 159 22 elu elu PROPN hvd.32044092008168 159 23 . . PUNCT hvd.32044092008168 160 1 b b X hvd.32044092008168 160 2 * * PUNCT hvd.32044092008168 160 3 ) ) PUNCT hvd.32044092008168 160 4 bd bd PROPN hvd.32044092008168 160 5 . . PROPN hvd.32044092008168 160 6 ii ii PROPN hvd.32044092008168 160 7 p. p. PROPN hvd.32044092008168 160 8 495 495 NUM hvd.32044092008168 160 9 . . PUNCT hvd.32044092008168 161 1 2 2 NUM hvd.32044092008168 161 2 18 18 NUM hvd.32044092008168 161 3 part part NOUN hvd.32044092008168 161 4 ii ii PROPN hvd.32044092008168 161 5 . . PUNCT hvd.32044092008168 162 1 [ [ X hvd.32044092008168 162 2 17 17 NUM hvd.32044092008168 162 3 ] ] PUNCT hvd.32044092008168 162 4 itself itself PRON hvd.32044092008168 162 5 and and CCONJ hvd.32044092008168 162 6 that that SCONJ hvd.32044092008168 162 7 therefore therefore ADV hvd.32044092008168 162 8 the the DET hvd.32044092008168 162 9 quotient quotient NOUN hvd.32044092008168 162 10 y y PROPN hvd.32044092008168 162 11 " " PUNCT hvd.32044092008168 162 12 : : PUNCT hvd.32044092008168 162 13 y y PROPN hvd.32044092008168 162 14 will will AUX hvd.32044092008168 162 15 not not PART hvd.32044092008168 162 16 only only ADV hvd.32044092008168 162 17 be be AUX hvd.32044092008168 162 18 doubly doubly ADV hvd.32044092008168 162 19 periodic periodic ADJ hvd.32044092008168 162 20 but but CCONJ hvd.32044092008168 162 21 will will AUX hvd.32044092008168 162 22 have have VERB hvd.32044092008168 162 23 a a DET hvd.32044092008168 162 24 single single ADJ hvd.32044092008168 162 25 pole pole NOUN hvd.32044092008168 162 26 uo uo NOUN hvd.32044092008168 162 27 of of ADP hvd.32044092008168 162 28 the the DET hvd.32044092008168 162 29 second second ADJ hvd.32044092008168 162 30 order order NOUN hvd.32044092008168 162 31 . . PUNCT hvd.32044092008168 163 1 this this DET hvd.32044092008168 163 2 function function NOUN hvd.32044092008168 163 3 then then ADV hvd.32044092008168 163 4 satisfies satisfy VERB hvd.32044092008168 163 5 the the DET hvd.32044092008168 163 6 necessary necessary ADJ hvd.32044092008168 163 7 conditions condition NOUN hvd.32044092008168 163 8 and and CCONJ hvd.32044092008168 163 9 the the DET hvd.32044092008168 163 10 y y PROPN hvd.32044092008168 163 11 " " PUNCT hvd.32044092008168 163 12 corresponding correspond VERB hvd.32044092008168 163 13 quotient quotient NOUN hvd.32044092008168 163 14 may may AUX hvd.32044092008168 163 15 then then ADV hvd.32044092008168 163 16 be be AUX hvd.32044092008168 163 17 written write VERB hvd.32044092008168 163 18 equal equal ADJ hvd.32044092008168 163 19 to to ADP hvd.32044092008168 163 20 y y PROPN hvd.32044092008168 163 21 n(n n(n PROPN hvd.32044092008168 163 22 + + CCONJ hvd.32044092008168 163 23 1 1 X hvd.32044092008168 163 24 ) ) PUNCT hvd.32044092008168 163 25 sn² sn² NOUN hvd.32044092008168 163 26 x x PUNCT hvd.32044092008168 164 1 + + CCONJ hvd.32044092008168 164 2 h h NOUN hvd.32044092008168 164 3 where where SCONJ hvd.32044092008168 164 4 h h NOUN hvd.32044092008168 164 5 is be AUX hvd.32044092008168 164 6 a a DET hvd.32044092008168 164 7 constant constant ADJ hvd.32044092008168 164 8 . . PUNCT hvd.32044092008168 165 1 but but CCONJ hvd.32044092008168 165 2 we we PRON hvd.32044092008168 165 3 have have AUX hvd.32044092008168 165 4 taken take VERB hvd.32044092008168 165 5 this this DET hvd.32044092008168 165 6 function function NOUN hvd.32044092008168 165 7 with with ADP hvd.32044092008168 165 8 the the DET hvd.32044092008168 165 9 condition condition NOUN hvd.32044092008168 165 10 that that SCONJ hvd.32044092008168 165 11 it it PRON hvd.32044092008168 165 12 have have VERB hvd.32044092008168 165 13 but but CCONJ hvd.32044092008168 165 14 one one NUM hvd.32044092008168 165 15 pole pole NOUN hvd.32044092008168 165 16 of of ADP hvd.32044092008168 165 17 the the DET hvd.32044092008168 165 18 order order NOUN hvd.32044092008168 165 19 n n X hvd.32044092008168 165 20 subject subject NOUN hvd.32044092008168 165 21 to to ADP hvd.32044092008168 165 22 the the DET hvd.32044092008168 165 23 above above ADJ hvd.32044092008168 165 24 conditions condition NOUN hvd.32044092008168 165 25 which which PRON hvd.32044092008168 165 26 affords afford VERB hvd.32044092008168 165 27 n n CCONJ hvd.32044092008168 165 28 arbitrary arbitrary ADJ hvd.32044092008168 165 29 constants constant NOUN hvd.32044092008168 165 30 and and CCONJ hvd.32044092008168 165 31 employing employ VERB hvd.32044092008168 165 32 also also ADV hvd.32044092008168 165 33 an an DET hvd.32044092008168 165 34 arbitrary arbitrary ADJ hvd.32044092008168 165 35 constant constant ADJ hvd.32044092008168 165 36 factor factor NOUN hvd.32044092008168 165 37 we we PRON hvd.32044092008168 165 38 obtain obtain VERB hvd.32044092008168 165 39 ( ( PUNCT hvd.32044092008168 165 40 n n CCONJ hvd.32044092008168 165 41 + + CCONJ hvd.32044092008168 165 42 1 1 NUM hvd.32044092008168 165 43 ) ) PUNCT hvd.32044092008168 165 44 arbitraries arbitrarie NOUN hvd.32044092008168 165 45 in in ADP hvd.32044092008168 165 46 all all PRON hvd.32044092008168 165 47 . . PUNCT hvd.32044092008168 166 1 that that PRON hvd.32044092008168 166 2 is be AUX hvd.32044092008168 166 3 sufficient sufficient ADJ hvd.32044092008168 166 4 to to PART hvd.32044092008168 166 5 satisfy satisfy VERB hvd.32044092008168 166 6 all all DET hvd.32044092008168 166 7 the the DET hvd.32044092008168 166 8 conditions condition NOUN hvd.32044092008168 166 9 and and CCONJ hvd.32044092008168 166 10 leave leave VERB hvd.32044092008168 166 11 h h NOUN hvd.32044092008168 166 12 to to PART hvd.32044092008168 166 13 be be AUX hvd.32044092008168 166 14 chosen choose VERB hvd.32044092008168 166 15 at at ADP hvd.32044092008168 166 16 will will NOUN hvd.32044092008168 166 17 . . PUNCT hvd.32044092008168 167 1 hence hence ADV hvd.32044092008168 167 2 we we PRON hvd.32044092008168 167 3 must must AUX hvd.32044092008168 167 4 conclude conclude VERB hvd.32044092008168 167 5 that that SCONJ hvd.32044092008168 167 6 there there PRON hvd.32044092008168 167 7 is be VERB hvd.32044092008168 167 8 no no DET hvd.32044092008168 167 9 reason reason NOUN hvd.32044092008168 167 10 why why SCONJ hvd.32044092008168 167 11 y y PROPN hvd.32044092008168 167 12 should should AUX hvd.32044092008168 167 13 not not PART hvd.32044092008168 167 14 be be AUX hvd.32044092008168 167 15 a a DET hvd.32044092008168 167 16 doubly doubly ADV hvd.32044092008168 167 17 periodic periodic ADJ hvd.32044092008168 167 18 function function NOUN hvd.32044092008168 167 19 of of ADP hvd.32044092008168 167 20 the the DET hvd.32044092008168 167 21 second second ADJ hvd.32044092008168 167 22 species specie NOUN hvd.32044092008168 167 23 and and CCONJ hvd.32044092008168 167 24 our our PRON hvd.32044092008168 167 25 problem problem NOUN hvd.32044092008168 167 26 reduces reduce VERB hvd.32044092008168 167 27 to to ADP hvd.32044092008168 167 28 the the DET hvd.32044092008168 167 29 determination determination NOUN hvd.32044092008168 167 30 of of ADP hvd.32044092008168 167 31 a a DET hvd.32044092008168 167 32 function function NOUN hvd.32044092008168 167 33 whose whose DET hvd.32044092008168 167 34 general general ADJ hvd.32044092008168 167 35 form form NOUN hvd.32044092008168 167 36 and and CCONJ hvd.32044092008168 167 37 properties property NOUN hvd.32044092008168 168 1 [ [ PUNCT hvd.32044092008168 168 2 16 16 NUM hvd.32044092008168 168 3 ] ] PUNCT hvd.32044092008168 168 4 are be AUX hvd.32044092008168 168 5 known know VERB hvd.32044092008168 168 6 . . PUNCT hvd.32044092008168 169 1 from from ADP hvd.32044092008168 169 2 this this DET hvd.32044092008168 169 3 standpoint standpoint NOUN hvd.32044092008168 169 4 we we PRON hvd.32044092008168 169 5 have have AUX hvd.32044092008168 169 6 : : PUNCT hvd.32044092008168 169 7 required require VERB hvd.32044092008168 169 8 a a DET hvd.32044092008168 169 9 function function NOUN hvd.32044092008168 169 10 such such ADJ hvd.32044092008168 169 11 that that PRON hvd.32044092008168 169 12 define define VERB hvd.32044092008168 169 13 : : PUNCT hvd.32044092008168 169 14 whence whence PROPN hvd.32044092008168 169 15 ω ω PROPN hvd.32044092008168 169 16 2 2 NUM hvd.32044092008168 169 17 k k PROPN hvd.32044092008168 169 18 f(u+2)=µf(u f(u+2)=µf(u PROPN hvd.32044092008168 169 19 ) ) PUNCT hvd.32044092008168 169 20 , , PUNCT hvd.32044092008168 169 21 f(u+2)=u'f(u f(u+2)=u'f(u PROPN hvd.32044092008168 169 22 ) ) PUNCT hvd.32044092008168 169 23 , , PUNCT hvd.32044092008168 169 24 2 2 NUM hvd.32044092008168 169 25 ' ' PUNCT hvd.32044092008168 169 26 = = SYM hvd.32044092008168 169 27 2ik 2ik PROPN hvd.32044092008168 169 28 ' ' PUNCT hvd.32044092008168 169 29 . . PUNCT hvd.32044092008168 170 1 f(u f(u NOUN hvd.32044092008168 170 2 ) ) PUNCT hvd.32044092008168 171 1 = = X hvd.32044092008168 171 2 a a DET hvd.32044092008168 171 3 o o NOUN hvd.32044092008168 171 4 ( ( PUNCT hvd.32044092008168 171 5 u u PROPN hvd.32044092008168 171 6 + + NUM hvd.32044092008168 171 7 2 2 NUM hvd.32044092008168 171 8 ) ) PUNCT hvd.32044092008168 171 9 6(u 6(u NUM hvd.32044092008168 171 10 + + NUM hvd.32044092008168 171 11 2 2 NUM hvd.32044092008168 171 12 ' ' NUM hvd.32044092008168 171 13 ) ) PUNCT hvd.32044092008168 171 14 η η NOUN hvd.32044092008168 171 15 which which DET hvd.32044092008168 171 16 function function NOUN hvd.32044092008168 171 17 we we PRON hvd.32044092008168 171 18 will will AUX hvd.32044092008168 171 19 speak speak VERB hvd.32044092008168 171 20 of of ADP hvd.32044092008168 171 21 as as ADP hvd.32044092008168 171 22 the the DET hvd.32044092008168 171 23 eliment eliment NOUN hvd.32044092008168 171 24 the the DET hvd.32044092008168 171 25 general general ADJ hvd.32044092008168 171 26 form form NOUN hvd.32044092008168 171 27 [ [ PUNCT hvd.32044092008168 171 28 16 16 NUM hvd.32044092008168 171 29 ] ] PUNCT hvd.32044092008168 171 30 being be AUX hvd.32044092008168 171 31 a a DET hvd.32044092008168 171 32 product product NOUN hvd.32044092008168 171 33 of of ADP hvd.32044092008168 171 34 similar similar ADJ hvd.32044092008168 171 35 eliments eliment NOUN hvd.32044092008168 171 36 . . PUNCT hvd.32044092008168 172 1 we we PRON hvd.32044092008168 172 2 have have VERB hvd.32044092008168 172 3 the the DET hvd.32044092008168 172 4 fundimental fundimental ADJ hvd.32044092008168 172 5 relations relation NOUN hvd.32044092008168 172 6 : : PUNCT hvd.32044092008168 172 7 u u PROPN hvd.32044092008168 172 8 σ σ PROPN hvd.32044092008168 172 9 ( ( PUNCT hvd.32044092008168 172 10 u u PROPN hvd.32044092008168 172 11 + + CCONJ hvd.32044092008168 172 12 v v NOUN hvd.32044092008168 172 13 ) ) PUNCT hvd.32044092008168 172 14 σ σ PROPN hvd.32044092008168 172 15 ( ( PUNCT hvd.32044092008168 172 16 u u PROPN hvd.32044092008168 172 17 ) ) PUNCT hvd.32044092008168 172 18 = = NOUN hvd.32044092008168 172 19 = = VERB hvd.32044092008168 172 20 6 6 NUM hvd.32044092008168 172 21 ' ' PUNCT hvd.32044092008168 172 22 ―― ―― PROPN hvd.32044092008168 172 23 ( ( PUNCT hvd.32044092008168 172 24 2 2 X hvd.32044092008168 172 25 ) ) PUNCT hvd.32044092008168 172 26 = = X hvd.32044092008168 173 1 ehu ehu ADV hvd.32044092008168 173 2 * * PUNCT hvd.32044092008168 173 3 ) ) PUNCT hvd.32044092008168 173 4 = = PUNCT hvd.32044092008168 174 1 ― ― X hvd.32044092008168 174 2 σ σ PROPN hvd.32044092008168 174 3 ( ( PUNCT hvd.32044092008168 174 4 u u NOUN hvd.32044092008168 174 5 ) ) PUNCT hvd.32044092008168 174 6 e² e² PROPN hvd.32044092008168 174 7 nu+n nu+n PROPN hvd.32044092008168 174 8 σ σ PROPN hvd.32044092008168 174 9 ( ( PUNCT hvd.32044092008168 174 10 u u PROPN hvd.32044092008168 174 11 ) ) PUNCT hvd.32044092008168 174 12 e² e² PROPN hvd.32044092008168 174 13 n'u n'u PROPN hvd.32044092008168 174 14 + + CCONJ hvd.32044092008168 174 15 n n CCONJ hvd.32044092008168 174 16 ' ' PUNCT hvd.32044092008168 174 17 ' ' PUNCT hvd.32044092008168 174 18 ω ω PROPN hvd.32044092008168 174 19 f(u f(u PROPN hvd.32044092008168 174 20 + + PROPN hvd.32044092008168 174 21 2 2 X hvd.32044092008168 174 22 ) ) PUNCT hvd.32044092008168 174 23 = = PROPN hvd.32044092008168 174 24 1 1 NUM hvd.32044092008168 174 25 º º NUM hvd.32044092008168 174 26 ( ( PUNCT hvd.32044092008168 174 27 u u PROPN hvd.32044092008168 174 28 + + CCONJ hvd.32044092008168 174 29 v v NOUN hvd.32044092008168 174 30 ) ) PUNCT hvd.32044092008168 174 31 σ σ PROPN hvd.32044092008168 174 32 ( ( PUNCT hvd.32044092008168 174 33 u u NOUN hvd.32044092008168 174 34 ) ) PUNCT hvd.32044092008168 174 35 = = VERB hvd.32044092008168 174 36 f(u f(u NOUN hvd.32044092008168 174 37 ) ) PUNCT hvd.32044092008168 174 38 p¹ p¹ NOUN hvd.32044092008168 174 39 2 2 NUM hvd.32044092008168 174 40 + + NUM hvd.32044092008168 174 41 2 2 NUM hvd.32044092008168 174 42 ¹¹. ¹¹. NOUN hvd.32044092008168 174 43 choosing choose VERB hvd.32044092008168 174 44 then then ADV hvd.32044092008168 174 45 v v NOUN hvd.32044092008168 174 46 and and CCONJ hvd.32044092008168 174 47 λ λ PROPN hvd.32044092008168 174 48 correctly correctly ADV hvd.32044092008168 174 49 we we PRON hvd.32044092008168 174 50 may may AUX hvd.32044092008168 174 51 write write VERB hvd.32044092008168 174 52 eλ2 eλ2 NUM hvd.32044092008168 174 53 + + NUM hvd.32044092008168 174 54 217 217 NUM hvd.32044092008168 174 55 v v NOUN hvd.32044092008168 174 56 e² e² PROPN hvd.32044092008168 174 57 ( ( PUNCT hvd.32044092008168 174 58 u u PROPN hvd.32044092008168 174 59 +2)+2nv +2)+2nv PROPN hvd.32044092008168 174 60 * * PUNCT hvd.32044092008168 174 61 ) ) PUNCT hvd.32044092008168 174 62 hermite hermite NOUN hvd.32044092008168 174 63 , , PUNCT hvd.32044092008168 174 64 in in ADP hvd.32044092008168 174 65 the the DET hvd.32044092008168 174 66 following following ADJ hvd.32044092008168 174 67 analysis analysis NOUN hvd.32044092008168 174 68 , , PUNCT hvd.32044092008168 174 69 employs employ VERB hvd.32044092008168 174 70 the the DET hvd.32044092008168 174 71 function function NOUN hvd.32044092008168 174 72 given give VERB hvd.32044092008168 174 73 on on ADP hvd.32044092008168 174 74 p. p. PROPN hvd.32044092008168 174 75 11 11 NUM hvd.32044092008168 174 76 , , PUNCT hvd.32044092008168 174 77 namely namely ADV hvd.32044092008168 174 78 the the DET hvd.32044092008168 174 79 function function NOUN hvd.32044092008168 174 80 x x PUNCT hvd.32044092008168 174 81 expressed express VERB hvd.32044092008168 174 82 in in ADP hvd.32044092008168 174 83 terms term NOUN hvd.32044092008168 174 84 of of ADP hvd.32044092008168 174 85 the the DET hvd.32044092008168 174 86 function function NOUN hvd.32044092008168 174 87 . . PUNCT hvd.32044092008168 175 1 hermite hermite PROPN hvd.32044092008168 175 2 's 's PART hvd.32044092008168 175 3 integral integral ADJ hvd.32044092008168 175 4 as as ADP hvd.32044092008168 175 5 a a DET hvd.32044092008168 175 6 sum sum NOUN hvd.32044092008168 175 7 . . PUNCT hvd.32044092008168 176 1 19 19 NUM hvd.32044092008168 177 1 [ [ X hvd.32044092008168 177 2 18 18 NUM hvd.32044092008168 177 3 ] ] PUNCT hvd.32044092008168 177 4 with with ADP hvd.32044092008168 177 5 a a DET hvd.32044092008168 177 6 corresponding corresponding ADJ hvd.32044092008168 177 7 value value NOUN hvd.32044092008168 177 8 for for ADP hvd.32044092008168 177 9 u u PROPN hvd.32044092008168 177 10 ' ' PUNCT hvd.32044092008168 177 11 and and CCONJ hvd.32044092008168 177 12 we we PRON hvd.32044092008168 177 13 may may AUX hvd.32044092008168 177 14 then then ADV hvd.32044092008168 177 15 write write VERB hvd.32044092008168 177 16 f(u f(u PROPN hvd.32044092008168 177 17 ) ) PUNCT hvd.32044092008168 177 18 f(u f(u PROPN hvd.32044092008168 177 19 ) ) PUNCT hvd.32044092008168 177 20 φ(u φ(u SPACE hvd.32044092008168 177 21 ) ) PUNCT hvd.32044092008168 177 22 where where SCONJ hvd.32044092008168 177 23 is be AUX hvd.32044092008168 177 24 a a DET hvd.32044092008168 177 25 doubly doubly ADV hvd.32044092008168 177 26 periodic periodic ADJ hvd.32044092008168 177 27 function function NOUN hvd.32044092008168 177 28 , , PUNCT hvd.32044092008168 177 29 that that PRON hvd.32044092008168 177 30 is be AUX hvd.32044092008168 177 31 þ(u+m2+n2 þ(u+m2+n2 NOUN hvd.32044092008168 177 32 ' ' PUNCT hvd.32044092008168 177 33 ) ) PUNCT hvd.32044092008168 178 1 = = PUNCT hvd.32044092008168 178 2 þ(u þ(u SPACE hvd.32044092008168 178 3 ) ) PUNCT hvd.32044092008168 178 4 . . PUNCT hvd.32044092008168 179 1 · · PUNCT hvd.32044092008168 179 2 again again ADV hvd.32044092008168 179 3 and and CCONJ hvd.32044092008168 179 4 we we PRON hvd.32044092008168 179 5 derive derive VERB hvd.32044092008168 179 6 [ [ PUNCT hvd.32044092008168 179 7 19 19 NUM hvd.32044092008168 179 8 ] ] PUNCT hvd.32044092008168 179 9 · · PUNCT hvd.32044092008168 179 10 f(u f(u NOUN hvd.32044092008168 179 11 — — PUNCT hvd.32044092008168 179 12 2 2 X hvd.32044092008168 179 13 ) ) PUNCT hvd.32044092008168 179 14 = = PUNCT hvd.32044092008168 179 15 — — PUNCT hvd.32044092008168 179 16 f(u f(u NOUN hvd.32044092008168 179 17 ) ) PUNCT hvd.32044092008168 179 18 and and CCONJ hvd.32044092008168 179 19 ƒ ƒ X hvd.32044092008168 179 20 ( ( PUNCT hvd.32044092008168 179 21 u u PROPN hvd.32044092008168 179 22 — — PUNCT hvd.32044092008168 179 23 2′ 2′ X hvd.32044092008168 179 24 ) ) PUNCT hvd.32044092008168 179 25 — — PUNCT hvd.32044092008168 179 26 — — PUNCT hvd.32044092008168 179 27 , , PUNCT hvd.32044092008168 179 28 f(u f(u PROPN hvd.32044092008168 179 29 ) ) PUNCT hvd.32044092008168 179 30 . . PUNCT hvd.32044092008168 180 1 whence whence ADV hvd.32044092008168 180 2 f(u f(u PROPN hvd.32044092008168 180 3 — — PUNCT hvd.32044092008168 180 4 z z PROPN hvd.32044092008168 180 5 — — PUNCT hvd.32044092008168 180 6 2 2 X hvd.32044092008168 180 7 ) ) PUNCT hvd.32044092008168 180 8 — — PUNCT hvd.32044092008168 180 9 — — PUNCT hvd.32044092008168 180 10 f f X hvd.32044092008168 180 11 ( ( PUNCT hvd.32044092008168 180 12 u u PROPN hvd.32044092008168 180 13 — — PUNCT hvd.32044092008168 180 14 2 2 X hvd.32044092008168 180 15 ) ) PUNCT hvd.32044092008168 180 16 where where SCONJ hvd.32044092008168 180 17 f(≈ f(≈ PROPN hvd.32044092008168 180 18 + + PROPN hvd.32044092008168 180 19 2 2 NUM hvd.32044092008168 180 20 ) ) PUNCT hvd.32044092008168 180 21 = = X hvd.32044092008168 180 22 µf µf X hvd.32044092008168 180 23 ( ( PUNCT hvd.32044092008168 180 24 2 2 NUM hvd.32044092008168 180 25 ) ) PUNCT hvd.32044092008168 180 26 — — PUNCT hvd.32044092008168 180 27 = = PUNCT hvd.32044092008168 180 28 * * PUNCT hvd.32044092008168 180 29 where where SCONJ hvd.32044092008168 180 30 is be AUX hvd.32044092008168 180 31 doubly doubly ADV hvd.32044092008168 180 32 periodic periodic ADJ hvd.32044092008168 180 33 . . PUNCT hvd.32044092008168 181 1 from from ADP hvd.32044092008168 181 2 this this DET hvd.32044092008168 181 3 point point NOUN hvd.32044092008168 181 4 the the DET hvd.32044092008168 181 5 development development NOUN hvd.32044092008168 181 6 of of ADP hvd.32044092008168 181 7 f(u f(u NOUN hvd.32044092008168 181 8 ) ) PUNCT hvd.32044092008168 181 9 depends depend VERB hvd.32044092008168 181 10 upon upon SCONJ hvd.32044092008168 181 11 the the DET hvd.32044092008168 181 12 theory theory NOUN hvd.32044092008168 181 13 of of ADP hvd.32044092008168 181 14 cauchy cauchy NOUN hvd.32044092008168 181 15 , , PUNCT hvd.32044092008168 181 16 as as SCONJ hvd.32044092008168 181 17 it it PRON hvd.32044092008168 181 18 is be AUX hvd.32044092008168 181 19 obtained obtain VERB hvd.32044092008168 181 20 by by ADP hvd.32044092008168 181 21 calculating calculate VERB hvd.32044092008168 181 22 the the DET hvd.32044092008168 181 23 residuals residual NOUN hvd.32044092008168 181 24 of of ADP hvd.32044092008168 181 25 for for ADP hvd.32044092008168 181 26 the the DET hvd.32044092008168 181 27 values value NOUN hvd.32044092008168 181 28 of of ADP hvd.32044092008168 181 29 the the DET hvd.32044092008168 181 30 argument argument NOUN hvd.32044092008168 181 31 that that PRON hvd.32044092008168 181 32 render render VERB hvd.32044092008168 181 33 it it PRON hvd.32044092008168 181 34 infinite infinite ADJ hvd.32044092008168 181 35 and and CCONJ hvd.32044092008168 181 36 equating equate VERB hvd.32044092008168 181 37 the the DET hvd.32044092008168 181 38 sum sum NOUN hvd.32044092008168 181 39 to to ADP hvd.32044092008168 181 40 zero zero NUM hvd.32044092008168 181 41 as as SCONJ hvd.32044092008168 181 42 follows follow VERB hvd.32044092008168 181 43 . . PUNCT hvd.32044092008168 182 1 first first PROPN hvd.32044092008168 182 2 f(u f(u PROPN hvd.32044092008168 182 3 ) ) PUNCT hvd.32044092008168 182 4 becomes become VERB hvd.32044092008168 182 5 infinite infinite ADJ hvd.32044092008168 182 6 for for ADP hvd.32044092008168 182 7 the the DET hvd.32044092008168 182 8 value value NOUN hvd.32044092008168 182 9 u0 u0 PROPN hvd.32044092008168 182 10 whence whence ADV hvd.32044092008168 182 11 its its PRON hvd.32044092008168 182 12 residual residual ADJ hvd.32044092008168 182 13 eu eu NOUN hvd.32044092008168 182 14 = = X hvd.32044092008168 182 15 of of ADP hvd.32044092008168 182 16 ( ( PUNCT hvd.32044092008168 182 17 u u PROPN hvd.32044092008168 182 18 ) ) PUNCT hvd.32044092008168 182 19 of(u of(u PROPN hvd.32044092008168 182 20 ) ) PUNCT hvd.32044092008168 182 21 = = PUNCT hvd.32044092008168 183 1 [ [ X hvd.32044092008168 183 2 ufu]u ufu]u X hvd.32044092008168 183 3 : : PUNCT hvd.32044092008168 183 4 whence whence NOUN hvd.32044092008168 183 5 = = X hvd.32044092008168 183 6 þ(2 þ(2 SPACE hvd.32044092008168 183 7 ) ) PUNCT hvd.32044092008168 183 8 = = X hvd.32044092008168 183 9 f(2 f(2 PROPN hvd.32044092008168 183 10 ) ) PUNCT hvd.32044092008168 183 11 f(u f(u PROPN hvd.32044092008168 183 12 — — PUNCT hvd.32044092008168 183 13 — — PUNCT hvd.32044092008168 183 14 2 2 X hvd.32044092008168 183 15 ) ) PUNCT hvd.32044092008168 183 16 — — PUNCT hvd.32044092008168 183 17 = = PRON hvd.32044092008168 183 18 0 0 X hvd.32044092008168 183 19 = = PUNCT hvd.32044092008168 183 20 = = VERB hvd.32044092008168 183 21 a a PRON hvd.32044092008168 183 22 and and CCONJ hvd.32044092008168 183 23 becomes become VERB hvd.32044092008168 183 24 equal equal ADJ hvd.32044092008168 183 25 to to ADP hvd.32044092008168 183 26 unity unity NOUN hvd.32044092008168 183 27 if if SCONJ hvd.32044092008168 183 28 we we PRON hvd.32044092008168 183 29 take take VERB hvd.32044092008168 183 30 1 1 NUM hvd.32044092008168 183 31 a a DET hvd.32044092008168 183 32 6(v 6(v NUM hvd.32044092008168 183 33 ) ) PUNCT hvd.32044092008168 183 34 f(u f(u PROPN hvd.32044092008168 183 35 ) ) PUNCT hvd.32044092008168 184 1 [ [ X hvd.32044092008168 184 2 o o X hvd.32044092008168 184 3 ( ( PUNCT hvd.32044092008168 184 4 u u PROPN hvd.32044092008168 184 5 + + CCONJ hvd.32044092008168 184 6 v v NOUN hvd.32044092008168 184 7 ) ) PUNCT hvd.32044092008168 185 1 e¹u e¹u PROPN hvd.32044092008168 185 2 ] ] X hvd.32044092008168 185 3 , , PUNCT hvd.32044092008168 185 4 again again ADV hvd.32044092008168 185 5 lim lim PROPN hvd.32044092008168 185 6 eu eu PROPN hvd.32044092008168 185 7 ( ( PUNCT hvd.32044092008168 185 8 2 2 X hvd.32044092008168 185 9 ) ) PUNCT hvd.32044092008168 185 10 + + CCONJ hvd.32044092008168 185 11 = = PUNCT hvd.32044092008168 185 12 u u NOUN hvd.32044092008168 185 13 ( ( PUNCT hvd.32044092008168 185 14 ≈ ≈ PROPN hvd.32044092008168 185 15 − − PROPN hvd.32044092008168 185 16 u u PROPN hvd.32044092008168 185 17 ) ) PUNCT hvd.32044092008168 185 18 đ đ NUM hvd.32044092008168 185 19 ( ( PUNCT hvd.32044092008168 185 20 z z NOUN hvd.32044092008168 185 21 ) ) PUNCT hvd.32044092008168 185 22 2 2 NUM hvd.32044092008168 185 23 u u PROPN hvd.32044092008168 185 24 and and CCONJ hvd.32044092008168 185 25 developing develop VERB hvd.32044092008168 185 26 f(uz f(uz NOUN hvd.32044092008168 185 27 ) ) PUNCT hvd.32044092008168 185 28 we we PRON hvd.32044092008168 185 29 have have VERB hvd.32044092008168 185 30 [ [ X hvd.32044092008168 185 31 w w X hvd.32044092008168 185 32 ] ] X hvd.32044092008168 185 33 eu eu PROPN hvd.32044092008168 185 34 ( ( PUNCT hvd.32044092008168 185 35 2 2 X hvd.32044092008168 185 36 ) ) PUNCT hvd.32044092008168 185 37 o o NOUN hvd.32044092008168 185 38 ( ( PUNCT hvd.32044092008168 185 39 u u PROPN hvd.32044092008168 185 40 + + CCONJ hvd.32044092008168 185 41 v v NOUN hvd.32044092008168 185 42 ) ) PUNCT hvd.32044092008168 185 43 o o NOUN hvd.32044092008168 186 1 ( ( PUNCT hvd.32044092008168 186 2 u u PROPN hvd.32044092008168 186 3 ) ) PUNCT hvd.32044092008168 186 4 o o NOUN hvd.32044092008168 186 5 ( ( PUNCT hvd.32044092008168 186 6 v v NOUN hvd.32044092008168 186 7 ) ) PUNCT hvd.32044092008168 186 8 u u PROPN hvd.32044092008168 186 9 = = VERB hvd.32044092008168 186 10 0 0 NUM hvd.32044092008168 186 11 u u PROPN hvd.32044092008168 186 12 = = PROPN hvd.32044092008168 186 13 0 0 NUM hvd.32044092008168 186 14 ――――― ――――― PROPN hvd.32044092008168 186 15 elu elu PROPN hvd.32044092008168 186 16 = = X hvd.32044092008168 186 17 a a DET hvd.32044092008168 186 18 6(v 6(v NUM hvd.32044092008168 186 19 ) ) PUNCT hvd.32044092008168 186 20 ' ' PUNCT hvd.32044092008168 186 21 ( ( PUNCT hvd.32044092008168 186 22 0 0 NUM hvd.32044092008168 186 23 ) ) PUNCT hvd.32044092008168 186 24 lim lim PROPN hvd.32044092008168 186 25 z z PROPN hvd.32044092008168 186 26 = = PROPN hvd.32044092008168 186 27 u(≈ u(≈ PROPN hvd.32044092008168 186 28 — — PUNCT hvd.32044092008168 186 29 u u PROPN hvd.32044092008168 186 30 ) ) PUNCT hvd.32044092008168 186 31 f(z)f(u f(z)f(u PROPN hvd.32044092008168 186 32 — — PUNCT hvd.32044092008168 186 33 z z X hvd.32044092008168 186 34 ) ) PUNCT hvd.32044092008168 186 35 = = VERB hvd.32044092008168 186 36 f(u f(u PROPN hvd.32044092008168 186 37 ) ) PUNCT hvd.32044092008168 186 38 again again ADV hvd.32044092008168 186 39 let let VERB hvd.32044092008168 186 40 a a PRON hvd.32044092008168 186 41 be be AUX hvd.32044092008168 186 42 any any DET hvd.32044092008168 186 43 pole pole NOUN hvd.32044092008168 186 44 of of ADP hvd.32044092008168 186 45 f(u f(u NOUN hvd.32044092008168 186 46 ) ) PUNCT hvd.32044092008168 186 47 in in ADP hvd.32044092008168 186 48 which which DET hvd.32044092008168 186 49 case case NOUN hvd.32044092008168 186 50 , , PUNCT hvd.32044092008168 186 51 developing develop VERB hvd.32044092008168 186 52 by by ADP hvd.32044092008168 186 53 the the DET hvd.32044092008168 186 54 function function NOUN hvd.32044092008168 186 55 theory theory NOUN hvd.32044092008168 186 56 , , PUNCT hvd.32044092008168 186 57 we we PRON hvd.32044092008168 186 58 may may AUX hvd.32044092008168 186 59 write write VERB hvd.32044092008168 186 60 a6(v a6(v SPACE hvd.32044092008168 186 61 ) ) PUNCT hvd.32044092008168 186 62 + + CCONJ hvd.32044092008168 186 63 aa aa PROPN hvd.32044092008168 186 64 da da PROPN hvd.32044092008168 186 65 ε¬¹ ε¬¹ PUNCT hvd.32044092008168 187 1 + + PUNCT hvd.32044092008168 188 1 а а INTJ hvd.32044092008168 188 2 + + CCONJ hvd.32044092008168 189 1 α₁ α₁ VERB hvd.32044092008168 189 2 ε ε NOUN hvd.32044092008168 189 3 + + CCONJ hvd.32044092008168 189 4 а₂ а₂ NOUN hvd.32044092008168 189 5 ε² ε² PROPN hvd.32044092008168 189 6 + + NOUN hvd.32044092008168 189 7 · · PUNCT hvd.32044092008168 189 8 · · PUNCT hvd.32044092008168 189 9 -1 -1 PROPN hvd.32044092008168 189 10 1 1 NUM hvd.32044092008168 189 11 1 1 NUM hvd.32044092008168 189 12 1 1 NUM hvd.32044092008168 189 13 f(a f(a NUM hvd.32044092008168 189 14 + + PUNCT hvd.32044092008168 190 1 ε)=0 ε)=0 ADJ hvd.32044092008168 190 2 = = NOUN hvd.32044092008168 190 3 aɛ¬¹ aɛ¬¹ NOUN hvd.32044092008168 190 4 + + CCONJ hvd.32044092008168 190 5 a a DET hvd.32044092008168 190 6 , , PUNCT hvd.32044092008168 190 7 d d NOUN hvd.32044092008168 190 8 , , PUNCT hvd.32044092008168 190 9 ε~¹ ε~¹ NOUN hvd.32044092008168 190 10 + + PUNCT hvd.32044092008168 190 11 a½ a½ ADP hvd.32044092008168 190 12 d² d² PROPN hvd.32044092008168 190 13 ɛ¬¹ ɛ¬¹ NUM hvd.32044092008168 191 1 + + PUNCT hvd.32044092008168 191 2 · · PUNCT hvd.32044092008168 191 3 · · PUNCT hvd.32044092008168 191 4 2 2 NUM hvd.32044092008168 191 5 * * SYM hvd.32044092008168 191 6 20 20 NUM hvd.32044092008168 191 7 part part NOUN hvd.32044092008168 191 8 ii ii PROPN hvd.32044092008168 191 9 . . PROPN hvd.32044092008168 191 10 and and CCONJ hvd.32044092008168 191 11 2 2 NUM hvd.32044092008168 191 12 f(u f(u NOUN hvd.32044092008168 191 13 — — PUNCT hvd.32044092008168 191 14 a a PRON hvd.32044092008168 191 15 – – PUNCT hvd.32044092008168 191 16 – – PUNCT hvd.32044092008168 191 17 € € X hvd.32044092008168 191 18 ) ) PUNCT hvd.32044092008168 191 19 = = VERB hvd.32044092008168 191 20 f(u f(u PROPN hvd.32044092008168 191 21 — — PUNCT hvd.32044092008168 191 22 a a X hvd.32044092008168 191 23 ) ) PUNCT hvd.32044092008168 191 24 – – PUNCT hvd.32044092008168 191 25 duf(u duf(u PROPN hvd.32044092008168 191 26 — — PUNCT hvd.32044092008168 191 27 a a X hvd.32044092008168 191 28 ) ) PUNCT hvd.32044092008168 191 29 + + NUM hvd.32044092008168 191 30 1.d.f(u 1.d.f(u NUM hvd.32044092008168 191 31 – – PUNCT hvd.32044092008168 191 32 a a X hvd.32044092008168 191 33 ) ) PUNCT hvd.32044092008168 191 34 - - PUNCT hvd.32044092008168 191 35 .. .. PUNCT hvd.32044092008168 191 36 ( ( PUNCT hvd.32044092008168 191 37 -1 -1 X hvd.32044092008168 191 38 ) ) PUNCT hvd.32044092008168 191 39 " " PUNCT hvd.32044092008168 192 1 + + CCONJ hvd.32044092008168 192 2 1 1 NUM hvd.32044092008168 192 3 2 2 NUM hvd.32044092008168 192 4 difu difu VERB hvd.32044092008168 192 5 – – PUNCT hvd.32044092008168 192 6 a a X hvd.32044092008168 192 7 ) ) PUNCT hvd.32044092008168 192 8 + + NUM hvd.32044092008168 192 9 .. .. PUNCT hvd.32044092008168 193 1 • • X hvd.32044092008168 193 2 a a DET hvd.32044092008168 193 3 where where SCONJ hvd.32044092008168 193 4 . . PUNCT hvd.32044092008168 194 1 2 2 NUM hvd.32044092008168 194 2 n n CCONJ hvd.32044092008168 194 3 d%8 d%8 SPACE hvd.32044092008168 194 4 - - PUNCT hvd.32044092008168 194 5 1 1 NUM hvd.32044092008168 194 6 = = NOUN hvd.32044092008168 194 7 ( ( PUNCT hvd.32044092008168 194 8 -1 -1 X hvd.32044092008168 194 9 ) ) PUNCT hvd.32044092008168 194 10 " " PUNCT hvd.32044092008168 194 11 ? ? PUNCT hvd.32044092008168 195 1 anti anti INTJ hvd.32044092008168 195 2 we we PRON hvd.32044092008168 195 3 have have VERB hvd.32044092008168 195 4 then then ADV hvd.32044092008168 195 5 lim lim PROPN hvd.32044092008168 195 6 eε eε PROPN hvd.32044092008168 195 7 . . PROPN hvd.32044092008168 195 8 φ φ PROPN hvd.32044092008168 196 1 ' ' NOUN hvd.32044092008168 196 2 0 0 NUM hvd.32044092008168 196 3 & & CCONJ hvd.32044092008168 196 4 f(a f(a PROPN hvd.32044092008168 196 5 + + PROPN hvd.32044092008168 196 6 8)f(u 8)f(u NUM hvd.32044092008168 196 7 — — PUNCT hvd.32044092008168 196 8 a a X hvd.32044092008168 196 9 — — PUNCT hvd.32044092008168 196 10 8) 8) NUM hvd.32044092008168 196 11 દ દ NUM hvd.32044092008168 196 12 af(u af(u NUM hvd.32044092008168 196 13 -a -a NOUN hvd.32044092008168 196 14 ) ) PUNCT hvd.32044092008168 196 15 + + CCONJ hvd.32044092008168 196 16 a a DET hvd.32044092008168 196 17 , , PUNCT hvd.32044092008168 196 18 duf(u duf(u PROPN hvd.32044092008168 196 19 – – PUNCT hvd.32044092008168 196 20 a a NOUN hvd.32044092008168 196 21 ) ) PUNCT hvd.32044092008168 196 22 + + CCONJ hvd.32044092008168 196 23 a a DET hvd.32044092008168 196 24 , , PUNCT hvd.32044092008168 196 25 dif(u dif(u NOUN hvd.32044092008168 196 26 — — PUNCT hvd.32044092008168 196 27 a a X hvd.32044092008168 196 28 ) ) PUNCT hvd.32044092008168 196 29 + + PUNCT hvd.32044092008168 196 30 ... ... PUNCT hvd.32044092008168 197 1 + + CCONJ hvd.32044092008168 197 2 aqd4f(u aqd4f(u DET hvd.32044092008168 197 3 a a X hvd.32044092008168 197 4 ) ) PUNCT hvd.32044092008168 197 5 with with ADP hvd.32044092008168 197 6 similar similar ADJ hvd.32044092008168 197 7 expressions expression NOUN hvd.32044092008168 197 8 for for ADP hvd.32044092008168 197 9 e. e. PROPN hvd.32044092008168 197 10 , , PUNCT hvd.32044092008168 197 11 ec ec PROPN hvd.32044092008168 197 12 ... ... PUNCT hvd.32044092008168 198 1 but but CCONJ hvd.32044092008168 198 2 ở ở PROPN hvd.32044092008168 198 3 being be AUX hvd.32044092008168 198 4 a a DET hvd.32044092008168 198 5 doubly doubly ADV hvd.32044092008168 198 6 periodic periodic ADJ hvd.32044092008168 198 7 function function NOUN hvd.32044092008168 198 8 we we PRON hvd.32044092008168 198 9 know know VERB hvd.32044092008168 198 10 that that SCONJ hvd.32044092008168 198 11 the the DET hvd.32044092008168 198 12 sum sum NOUN hvd.32044092008168 198 13 of of ADP hvd.32044092008168 198 14 its its PRON hvd.32044092008168 198 15 residuals residual NOUN hvd.32044092008168 198 16 with with ADP hvd.32044092008168 198 17 respect respect NOUN hvd.32044092008168 198 18 to to ADP hvd.32044092008168 198 19 u u PROPN hvd.32044092008168 198 20 , , PUNCT hvd.32044092008168 198 21 a a DET hvd.32044092008168 198 22 , , PUNCT hvd.32044092008168 198 23 b b X hvd.32044092008168 198 24 .. .. PUNCT hvd.32044092008168 198 25 equals equal VERB hvd.32044092008168 198 26 zero zero NUM hvd.32044092008168 198 27 whence whence NOUN hvd.32044092008168 198 28 [ [ X hvd.32044092008168 198 29 20 20 NUM hvd.32044092008168 198 30 ] ] PUNCT hvd.32044092008168 198 31 f f PROPN hvd.32044092008168 198 32 ( ( PUNCT hvd.32044092008168 198 33 u u PROPN hvd.32044092008168 198 34 ) ) PUNCT hvd.32044092008168 198 35 = = PROPN hvd.32044092008168 198 36 { { PUNCT hvd.32044092008168 198 37 [ [ X hvd.32044092008168 198 38 af af X hvd.32044092008168 198 39 ( ( PUNCT hvd.32044092008168 198 40 u u PROPN hvd.32044092008168 198 41 — — PUNCT hvd.32044092008168 198 42 a a X hvd.32044092008168 198 43 ) ) PUNCT hvd.32044092008168 198 44 + + CCONJ hvd.32044092008168 198 45 a a DET hvd.32044092008168 198 46 , , PUNCT hvd.32044092008168 198 47 duf duf PROPN hvd.32044092008168 198 48 ( ( PUNCT hvd.32044092008168 198 49 u u X hvd.32044092008168 198 50 ] ] PUNCT hvd.32044092008168 198 51 σ σ X hvd.32044092008168 198 52 [ [ X hvd.32044092008168 198 53 ) ) PUNCT hvd.32044092008168 198 54 + + CCONJ hvd.32044092008168 198 55 a a X hvd.32044092008168 198 56 ) ) PUNCT hvd.32044092008168 198 57 + + CCONJ hvd.32044092008168 198 58 a a DET hvd.32044092008168 198 59 , , PUNCT hvd.32044092008168 198 60 dif dif PROPN hvd.32044092008168 198 61 ( ( PUNCT hvd.32044092008168 198 62 u u PROPN hvd.32044092008168 198 63 -a -a SPACE hvd.32044092008168 198 64 ) ) PUNCT hvd.32044092008168 198 65 + + PUNCT hvd.32044092008168 198 66 .. .. PUNCT hvd.32044092008168 199 1 + + CCONJ hvd.32044092008168 199 2 a a DET hvd.32044092008168 199 3 dif(u dif(u NOUN hvd.32044092008168 199 4 – – PUNCT hvd.32044092008168 199 5 a a X hvd.32044092008168 199 6 ) ) PUNCT hvd.32044092008168 199 7 ] ] PUNCT hvd.32044092008168 200 1 a a DET hvd.32044092008168 200 2 where where SCONJ hvd.32044092008168 200 3 ai ai VERB hvd.32044092008168 200 4 is be AUX hvd.32044092008168 200 5 determined determine VERB hvd.32044092008168 200 6 from from ADP hvd.32044092008168 200 7 the the DET hvd.32044092008168 200 8 first first ADJ hvd.32044092008168 200 9 development development NOUN hvd.32044092008168 200 10 . . PUNCT hvd.32044092008168 201 1 this this DET hvd.32044092008168 201 2 important important ADJ hvd.32044092008168 201 3 formula formula NOUN hvd.32044092008168 201 4 still still ADV hvd.32044092008168 201 5 further far ADV hvd.32044092008168 201 6 narrows narrow VERB hvd.32044092008168 201 7 our our PRON hvd.32044092008168 201 8 problem problem NOUN hvd.32044092008168 201 9 to to ADP hvd.32044092008168 201 10 a a DET hvd.32044092008168 201 11 consideration consideration NOUN hvd.32044092008168 201 12 of of ADP hvd.32044092008168 201 13 f(u f(u NOUN hvd.32044092008168 201 14 ) ) PUNCT hvd.32044092008168 201 15 in in ADP hvd.32044092008168 201 16 terms term NOUN hvd.32044092008168 201 17 of of ADP hvd.32044092008168 201 18 which which PRON hvd.32044092008168 201 19 and and CCONJ hvd.32044092008168 201 20 its its PRON hvd.32044092008168 201 21 derivatives derivative NOUN hvd.32044092008168 201 22 under under ADP hvd.32044092008168 201 23 conditions condition NOUN hvd.32044092008168 201 24 to to PART hvd.32044092008168 201 25 be be AUX hvd.32044092008168 201 26 determined determine VERB hvd.32044092008168 201 27 it it PRON hvd.32044092008168 201 28 is be AUX hvd.32044092008168 201 29 now now ADV hvd.32044092008168 201 30 evident evident ADJ hvd.32044092008168 201 31 that that SCONJ hvd.32044092008168 201 32 y y PROPN hvd.32044092008168 201 33 = = PROPN hvd.32044092008168 201 34 f f PROPN hvd.32044092008168 201 35 ( ( PUNCT hvd.32044092008168 201 36 u u PROPN hvd.32044092008168 201 37 ) ) PUNCT hvd.32044092008168 201 38 may may AUX hvd.32044092008168 201 39 be be AUX hvd.32044092008168 201 40 expressed express VERB hvd.32044092008168 201 41 . . PUNCT hvd.32044092008168 202 1 a a DET hvd.32044092008168 202 2 = = PROPN hvd.32044092008168 202 3 a a PROPN hvd.32044092008168 202 4 , , PUNCT hvd.32044092008168 202 5 b b NOUN hvd.32044092008168 202 6 , , PUNCT hvd.32044092008168 202 7 c c NOUN hvd.32044092008168 202 8 .. .. PUNCT hvd.32044092008168 202 9 a a DET hvd.32044092008168 202 10 transformation transformation NOUN hvd.32044092008168 202 11 of of ADP hvd.32044092008168 202 12 hermite hermite NOUN hvd.32044092008168 202 13 's 's PART hvd.32044092008168 202 14 equation equation NOUN hvd.32044092008168 202 15 . . PUNCT hvd.32044092008168 203 1 we we PRON hvd.32044092008168 203 2 have have AUX hvd.32044092008168 203 3 written write VERB hvd.32044092008168 203 4 hermite hermite PROPN hvd.32044092008168 203 5 's 's PART hvd.32044092008168 203 6 equation equation NOUN hvd.32044092008168 203 7 in in ADP hvd.32044092008168 203 8 its its PRON hvd.32044092008168 203 9 original original ADJ hvd.32044092008168 203 10 form form NOUN hvd.32044092008168 203 11 d'y d'y X hvd.32044092008168 203 12 [ [ X hvd.32044092008168 203 13 21 21 NUM hvd.32044092008168 203 14 ] ] PUNCT hvd.32044092008168 203 15 · · PUNCT hvd.32044092008168 203 16 =[ =[ X hvd.32044092008168 203 17 n n X hvd.32044092008168 203 18 [ [ X hvd.32044092008168 203 19 n(n n(n PROPN hvd.32044092008168 203 20 + + CCONJ hvd.32044092008168 203 21 1)ka 1)ka PROPN hvd.32044092008168 203 22 sna sna X hvd.32044092008168 203 23 x x PUNCT hvd.32044092008168 203 24 + + CCONJ hvd.32044092008168 203 25 h h PROPN hvd.32044092008168 203 26 ) ) PUNCT hvd.32044092008168 203 27 . . PUNCT hvd.32044092008168 204 1 d d X hvd.32044092008168 204 2 x2 x2 PROPN hvd.32044092008168 204 3 that that SCONJ hvd.32044092008168 204 4 this this PRON hvd.32044092008168 204 5 is be AUX hvd.32044092008168 204 6 however however ADV hvd.32044092008168 204 7 but but CCONJ hvd.32044092008168 204 8 a a DET hvd.32044092008168 204 9 special special ADJ hvd.32044092008168 204 10 case case NOUN hvd.32044092008168 204 11 of of ADP hvd.32044092008168 204 12 a a DET hvd.32044092008168 204 13 more more ADV hvd.32044092008168 204 14 general general ADJ hvd.32044092008168 204 15 form form NOUN hvd.32044092008168 204 16 is be AUX hvd.32044092008168 204 17 seen see VERB hvd.32044092008168 204 18 as as SCONJ hvd.32044092008168 204 19 follows follow NOUN hvd.32044092008168 204 20 . . PUNCT hvd.32044092008168 205 1 take take VERB hvd.32044092008168 205 2 the the DET hvd.32044092008168 205 3 integral integral ADJ hvd.32044092008168 205 4 2 2 NUM hvd.32044092008168 205 5 • • SYM hvd.32044092008168 205 6 da da NOUN hvd.32044092008168 205 7 v(1 v(1 VERB hvd.32044092008168 205 8 – – PUNCT hvd.32044092008168 205 9 12)(1 12)(1 NUM hvd.32044092008168 205 10 – – PUNCT hvd.32044092008168 205 11 k k PROPN hvd.32044092008168 205 12 22 22 X hvd.32044092008168 205 13 ) ) PUNCT hvd.32044092008168 206 1 ул ул ADP hvd.32044092008168 206 2 2 2 NUM hvd.32044092008168 206 3 x x SYM hvd.32044092008168 206 4 = = PUNCT hvd.32044092008168 206 5 ---we ---we PUNCT hvd.32044092008168 206 6 have have VERB hvd.32044092008168 206 7 dy dy X hvd.32044092008168 206 8 1 1 NUM hvd.32044092008168 206 9 dy dy X hvd.32044092008168 206 10 da da PROPN hvd.32044092008168 206 11 dy dy X hvd.32044092008168 206 12 dx dx X hvd.32044092008168 206 13 dx dx X hvd.32044092008168 206 14 da da PROPN hvd.32044092008168 206 15 dx dx X hvd.32044092008168 206 16 va va X hvd.32044092008168 206 17 or or CCONJ hvd.32044092008168 206 18 dy=17 dy=17 VERB hvd.32044092008168 206 19 dy dy PROPN hvd.32044092008168 206 20 da da PROPN hvd.32044092008168 206 21 hermite hermite PROPN hvd.32044092008168 206 22 's 's PART hvd.32044092008168 206 23 integral integral ADJ hvd.32044092008168 206 24 as as ADP hvd.32044092008168 206 25 a a DET hvd.32044092008168 206 26 sum sum NOUN hvd.32044092008168 206 27 . . PUNCT hvd.32044092008168 207 1 21 21 NUM hvd.32044092008168 207 2 whence whence NOUN hvd.32044092008168 207 3 [ [ X hvd.32044092008168 207 4 23 23 NUM hvd.32044092008168 207 5 ] ] PUNCT hvd.32044092008168 207 6 or or CCONJ hvd.32044092008168 207 7 [ [ X hvd.32044092008168 207 8 22 22 NUM hvd.32044092008168 207 9 ] ] PUNCT hvd.32044092008168 207 10 . . PUNCT hvd.32044092008168 208 1 [ [ X hvd.32044092008168 208 2 24 24 NUM hvd.32044092008168 208 3 ] ] SYM hvd.32044092008168 208 4 · · PUNCT hvd.32044092008168 208 5 p(u p(u PROPN hvd.32044092008168 208 6 ) ) PUNCT hvd.32044092008168 208 7 = = X hvd.32044092008168 209 1 es es X hvd.32044092008168 209 2 + + CCONJ hvd.32044092008168 209 3 we we PRON hvd.32044092008168 209 4 obtain obtain VERB hvd.32044092008168 209 5 : : PUNCT hvd.32044092008168 209 6 dy dy PROPN hvd.32044092008168 209 7 - - PUNCT hvd.32044092008168 209 8 ay-1 ay-1 PROPN hvd.32044092008168 209 9 - - PUNCT hvd.32044092008168 209 10 114x 114x PROPN hvd.32044092008168 209 11 dx² dx² VERB hvd.32044092008168 209 12 define define VERB hvd.32044092008168 209 13 d22 d22 NOUN hvd.32044092008168 209 14 day day NOUN hvd.32044092008168 209 15 du² du² CCONJ hvd.32044092008168 209 16 ( ( PUNCT hvd.32044092008168 209 17 e₁ e₁ PROPN hvd.32044092008168 209 18 e1 e1 PROPN hvd.32044092008168 209 19 sn²u sn²u PROPN hvd.32044092008168 209 20 ve ve VERB hvd.32044092008168 209 21 and and CCONJ hvd.32044092008168 209 22 making make VERB hvd.32044092008168 209 23 the the DET hvd.32044092008168 209 24 substitutions substitution NOUN hvd.32044092008168 209 25 : : PUNCT hvd.32044092008168 209 26 ― ― X hvd.32044092008168 209 27 d2y d2y VERB hvd.32044092008168 209 28 dx2 dx2 NOUN hvd.32044092008168 209 29 x x SYM hvd.32044092008168 209 30 = = ADP hvd.32044092008168 209 31 substituting substitute VERB hvd.32044092008168 209 32 we we PRON hvd.32044092008168 209 33 derive derive VERB hvd.32044092008168 209 34 the the DET hvd.32044092008168 209 35 ordinary ordinary ADJ hvd.32044092008168 209 36 form form NOUN hvd.32044092008168 209 37 of of ADP hvd.32044092008168 209 38 lamé lamé NOUN hvd.32044092008168 209 39 's 's PART hvd.32044092008168 209 40 equation equation NOUN hvd.32044092008168 209 41 dy dy PROPN hvd.32044092008168 209 42 dλ dλ NOUN hvd.32044092008168 209 43 d2y d2y NOUN hvd.32044092008168 209 44 1 1 NUM hvd.32044092008168 209 45 λ λ NOUN hvd.32044092008168 210 1 + + CCONJ hvd.32044092008168 210 2 δ δ NOUN hvd.32044092008168 210 3 ' ' PUNCT hvd.32044092008168 210 4 — — PUNCT hvd.32044092008168 211 1 [ [ X hvd.32044092008168 211 2 n n X hvd.32044092008168 211 3 ( ( PUNCT hvd.32044092008168 211 4 n n X hvd.32044092008168 211 5 + + CCONJ hvd.32044092008168 211 6 1 1 X hvd.32044092008168 211 7 ) ) PUNCT hvd.32044092008168 211 8 k² k² PROPN hvd.32044092008168 211 9 sn² sn² VERB hvd.32044092008168 211 10 x x PUNCT hvd.32044092008168 212 1 + + CCONJ hvd.32044092008168 212 2 h h X hvd.32044092008168 212 3 ] ] X hvd.32044092008168 213 1 = = X hvd.32044092008168 213 2 0 0 NUM hvd.32044092008168 213 3 . . PUNCT hvd.32044092008168 213 4 * * PUNCT hvd.32044092008168 213 5 ) ) PUNCT hvd.32044092008168 214 1 dλ2 dλ2 NOUN hvd.32044092008168 214 2 2 2 NUM hvd.32044092008168 214 3 = = NOUN hvd.32044092008168 214 4 the the DET hvd.32044092008168 214 5 value value NOUN hvd.32044092008168 214 6 of of ADP hvd.32044092008168 214 7 4 4 NUM hvd.32044092008168 214 8 gives give VERB hvd.32044092008168 214 9 as as ADP hvd.32044092008168 214 10 singular singular ADJ hvd.32044092008168 214 11 points point NOUN hvd.32044092008168 214 12 + + CCONJ hvd.32044092008168 214 13 1 1 NUM hvd.32044092008168 214 14 ; ; PUNCT hvd.32044092008168 214 15 and and CCONJ hvd.32044092008168 214 16 ∞. ∞. PROPN hvd.32044092008168 214 17 ± ± NOUN hvd.32044092008168 214 18 k k X hvd.32044092008168 214 19 for for ADP hvd.32044092008168 214 20 our our PRON hvd.32044092008168 214 21 present present ADJ hvd.32044092008168 214 22 purpose purpose NOUN hvd.32044092008168 214 23 however however ADV hvd.32044092008168 214 24 we we PRON hvd.32044092008168 214 25 need need VERB hvd.32044092008168 214 26 the the DET hvd.32044092008168 214 27 equation equation NOUN hvd.32044092008168 214 28 expressed express VERB hvd.32044092008168 214 29 in in ADP hvd.32044092008168 214 30 terms term NOUN hvd.32044092008168 214 31 of of ADP hvd.32044092008168 214 32 u u PROPN hvd.32044092008168 214 33 and and CCONJ hvd.32044092008168 214 34 pu pu PROPN hvd.32044092008168 214 35 which which PRON hvd.32044092008168 214 36 is be AUX hvd.32044092008168 214 37 derived derive VERB hvd.32044092008168 214 38 from from ADP hvd.32044092008168 214 39 ( ( PUNCT hvd.32044092008168 214 40 21 21 NUM hvd.32044092008168 214 41 ) ) PUNCT hvd.32044092008168 214 42 by by ADP hvd.32044092008168 214 43 means mean NOUN hvd.32044092008168 214 44 of of ADP hvd.32044092008168 214 45 the the DET hvd.32044092008168 214 46 relations relation NOUN hvd.32044092008168 214 47 1 1 NUM hvd.32044092008168 214 48 d2y d2y NOUN hvd.32044092008168 215 1 λ λ PROPN hvd.32044092008168 215 2 + + PROPN hvd.32044092008168 215 3 1/1/13 1/1/13 NUM hvd.32044092008168 215 4 d22 d22 NOUN hvd.32044092008168 215 5 2 2 NUM hvd.32044092008168 215 6 uve₁ uve₁ PROPN hvd.32044092008168 215 7 ve ve AUX hvd.32044092008168 215 8 dx² dx² VERB hvd.32044092008168 215 9 eg eg NOUN hvd.32044092008168 215 10 ) ) PUNCT hvd.32044092008168 215 11 eg eg X hvd.32044092008168 215 12 2 2 NUM hvd.32044092008168 215 13 = = SYM hvd.32044092008168 215 14 δ δ X hvd.32044092008168 215 15 ' ' PUNCT hvd.32044092008168 215 16 es es X hvd.32044092008168 215 17 = = X hvd.32044092008168 215 18 dy dy PROPN hvd.32044092008168 215 19 " " PUNCT hvd.32044092008168 215 20 dλ dλ NOUN hvd.32044092008168 215 21 k² k² PROPN hvd.32044092008168 215 22 sn² sn² VERB hvd.32044092008168 215 23 ( ( PUNCT hvd.32044092008168 215 24 u u PROPN hvd.32044092008168 215 25 + + X hvd.32044092008168 215 26 ik ik PROPN hvd.32044092008168 215 27 ' ' NOUN hvd.32044092008168 215 28 ) ) PUNCT hvd.32044092008168 215 29 u u PROPN hvd.32044092008168 215 30 ~u+ik ~u+ik SPACE hvd.32044092008168 215 31 ' ' PART hvd.32044092008168 215 32 l3 l3 NOUN hvd.32044092008168 216 1 du² du² PROPN hvd.32044092008168 216 2 ( ( PUNCT hvd.32044092008168 216 3 e₁ e₁ PROPN hvd.32044092008168 216 4 — — PUNCT hvd.32044092008168 216 5 e3 e3 PROPN hvd.32044092008168 216 6 ) ) PUNCT hvd.32044092008168 217 1 [ [ X hvd.32044092008168 217 2 n n X hvd.32044092008168 217 3 ( ( PUNCT hvd.32044092008168 217 4 n n X hvd.32044092008168 217 5 + + CCONJ hvd.32044092008168 217 6 1 1 X hvd.32044092008168 217 7 ) ) PUNCT hvd.32044092008168 217 8 pu pu X hvd.32044092008168 217 9 — — PUNCT hvd.32044092008168 217 10 es es X hvd.32044092008168 217 11 + + NOUN hvd.32044092008168 217 12 h h X hvd.32044092008168 217 13 ] ] X hvd.32044092008168 217 14 . . PUNCT hvd.32044092008168 218 1 e1 e1 NOUN hvd.32044092008168 218 2 = = PUNCT hvd.32044092008168 218 3 · · PUNCT hvd.32044092008168 218 4 b b X hvd.32044092008168 218 5 = = X hvd.32044092008168 218 6 h h NOUN hvd.32044092008168 218 7 ( ( PUNCT hvd.32044092008168 218 8 e₁ e₁ PROPN hvd.32044092008168 218 9 — — PUNCT hvd.32044092008168 218 10 е3 е3 NOUN hvd.32044092008168 218 11 ) ) PUNCT hvd.32044092008168 218 12 − − PROPN hvd.32044092008168 218 13 n n NOUN hvd.32044092008168 218 14 ( ( PUNCT hvd.32044092008168 218 15 n n X hvd.32044092008168 218 16 + + CCONJ hvd.32044092008168 218 17 1 1 X hvd.32044092008168 218 18 ) ) PUNCT hvd.32044092008168 218 19 ez ez PROPN hvd.32044092008168 218 20 · · PUNCT hvd.32044092008168 218 21 ― ― X hvd.32044092008168 219 1 1 1 NUM hvd.32044092008168 219 2 whence whence NOUN hvd.32044092008168 219 3 our our PRON hvd.32044092008168 219 4 equation equation NOUN hvd.32044092008168 219 5 may may AUX hvd.32044092008168 219 6 be be AUX hvd.32044092008168 219 7 written write VERB hvd.32044092008168 219 8 : : PUNCT hvd.32044092008168 219 9 y y PROPN hvd.32044092008168 219 10 ' ' PUNCT hvd.32044092008168 219 11 = = X hvd.32044092008168 220 1 [ [ X hvd.32044092008168 220 2 n n X hvd.32044092008168 220 3 ( ( PUNCT hvd.32044092008168 220 4 n n X hvd.32044092008168 220 5 + + CCONJ hvd.32044092008168 220 6 1 1 X hvd.32044092008168 220 7 ) ) PUNCT hvd.32044092008168 220 8 pu pu PROPN hvd.32044092008168 220 9 + + PROPN hvd.32044092008168 220 10 b]y b]y PROPN hvd.32044092008168 220 11 . . PUNCT hvd.32044092008168 220 12 1 1 NUM hvd.32044092008168 220 13 sn² sn² NUM hvd.32044092008168 220 14 u u PROPN hvd.32044092008168 220 15 development development NOUN hvd.32044092008168 220 16 of of ADP hvd.32044092008168 220 17 the the DET hvd.32044092008168 220 18 integral integral NOUN hvd.32044092008168 220 19 . . PUNCT hvd.32044092008168 221 1 we we PRON hvd.32044092008168 221 2 observe observe VERB hvd.32044092008168 221 3 , , PUNCT hvd.32044092008168 221 4 since since SCONJ hvd.32044092008168 221 5 snx snx NOUN hvd.32044092008168 221 6 reduces reduce VERB hvd.32044092008168 221 7 to to ADP hvd.32044092008168 221 8 zero zero NUM hvd.32044092008168 221 9 only only ADV hvd.32044092008168 221 10 for for ADP hvd.32044092008168 221 11 the the DET hvd.32044092008168 221 12 value value NOUN hvd.32044092008168 221 13 x x PUNCT hvd.32044092008168 221 14 = = PUNCT hvd.32044092008168 221 15 0 0 NUM hvd.32044092008168 221 16 , , PUNCT hvd.32044092008168 221 17 that that SCONJ hvd.32044092008168 221 18 we we PRON hvd.32044092008168 221 19 have have VERB hvd.32044092008168 221 20 but but CCONJ hvd.32044092008168 221 21 one one NUM hvd.32044092008168 221 22 pole pole NOUN hvd.32044092008168 221 23 of of ADP hvd.32044092008168 221 24 the the DET hvd.32044092008168 221 25 second second ADJ hvd.32044092008168 221 26 order order NOUN hvd.32044092008168 221 27 in in ADP hvd.32044092008168 221 28 hermite hermite PROPN hvd.32044092008168 221 29 's 's PART hvd.32044092008168 221 30 equation equation NOUN hvd.32044092008168 221 31 and and CCONJ hvd.32044092008168 221 32 that that SCONJ hvd.32044092008168 221 33 we we PRON hvd.32044092008168 221 34 may may AUX hvd.32044092008168 221 35 therefore therefore ADV hvd.32044092008168 221 36 develop develop VERB hvd.32044092008168 221 37 y y PROPN hvd.32044092008168 221 38 within within ADP hvd.32044092008168 221 39 a a DET hvd.32044092008168 221 40 cercle cercle NOUN hvd.32044092008168 221 41 whose whose DET hvd.32044092008168 221 42 radius radius NOUN hvd.32044092008168 221 43 is be AUX hvd.32044092008168 221 44 less less ADJ hvd.32044092008168 221 45 than than ADP hvd.32044092008168 221 46 2 2 NUM hvd.32044092008168 221 47 ' ' NOUN hvd.32044092008168 221 48 , , PUNCT hvd.32044092008168 221 49 the the DET hvd.32044092008168 221 50 form form NOUN hvd.32044092008168 221 51 being be AUX hvd.32044092008168 221 52 = = NOUN hvd.32044092008168 222 1 y y PROPN hvd.32044092008168 222 2 = = PROPN hvd.32044092008168 223 1 u² u² PROPN hvd.32044092008168 224 1 [ [ X hvd.32044092008168 224 2 y y X hvd.32044092008168 224 3 。 。 PROPN hvd.32044092008168 224 4 + + CCONJ hvd.32044092008168 224 5 y₁u y₁u X hvd.32044092008168 225 1 + + PUNCT hvd.32044092008168 225 2 y₂u² y₂u² PUNCT hvd.32044092008168 226 1 + + PUNCT hvd.32044092008168 226 2 · · PUNCT hvd.32044092008168 226 3 · · PUNCT hvd.32044092008168 226 4 • • SYM hvd.32044092008168 226 5 ] ] X hvd.32044092008168 226 6 whence whence ADP hvd.32044092008168 226 7 2 2 NUM hvd.32044092008168 226 8 y y PROPN hvd.32044092008168 226 9 = = SYM hvd.32044092008168 226 10 vu¹¹y vu¹¹y PROPN hvd.32044092008168 227 1 + + PROPN hvd.32044092008168 227 2 ( ( PUNCT hvd.32044092008168 227 3 v v ADP hvd.32044092008168 227 4 + + PROPN hvd.32044092008168 227 5 1 1 NUM hvd.32044092008168 227 6 ) ) PUNCT hvd.32044092008168 227 7 y₁ y₁ PROPN hvd.32044092008168 227 8 u² u² PROPN hvd.32044092008168 228 1 + + CCONJ hvd.32044092008168 228 2 ( ( PUNCT hvd.32044092008168 228 3 v v ADP hvd.32044092008168 228 4 + + PROPN hvd.32044092008168 228 5 2 2 NUM hvd.32044092008168 228 6 ) ) PUNCT hvd.32044092008168 228 7 u² u² PROPN hvd.32044092008168 228 8 + + PROPN hvd.32044092008168 228 9 ¹ ¹ NUM hvd.32044092008168 228 10 y₂ y₂ PROPN hvd.32044092008168 228 11 + + PROPN hvd.32044092008168 228 12 ( ( PUNCT hvd.32044092008168 228 13 v v ADP hvd.32044092008168 228 14 + + PROPN hvd.32044092008168 228 15 3 3 NUM hvd.32044092008168 228 16 ) ) PUNCT hvd.32044092008168 228 17 u¹ u¹ PROPN hvd.32044092008168 228 18 + + CCONJ hvd.32044092008168 228 19 ² ² NUM hvd.32044092008168 228 20 y y PROPN hvd.32044092008168 228 21 z z X hvd.32044092008168 229 1 + + CCONJ hvd.32044092008168 229 2 · · PUNCT hvd.32044092008168 229 3 · · PUNCT hvd.32044092008168 229 4 -2 -2 PROPN hvd.32044092008168 229 5 y y PROPN hvd.32044092008168 229 6 ' ' PUNCT hvd.32044092008168 229 7 — — PUNCT hvd.32044092008168 229 8 v v NOUN hvd.32044092008168 229 9 ( ( PUNCT hvd.32044092008168 229 10 v v NOUN hvd.32044092008168 229 11 — — PUNCT hvd.32044092008168 229 12 1 1 X hvd.32044092008168 229 13 ) ) PUNCT hvd.32044092008168 229 14 u u NOUN hvd.32044092008168 229 15 ' ' PUNCT hvd.32044092008168 229 16 — — PUNCT hvd.32044092008168 229 17 ²y ²y NOUN hvd.32044092008168 229 18 。 。 NOUN hvd.32044092008168 229 19 + + CCONJ hvd.32044092008168 229 20 v v NOUN hvd.32044092008168 229 21 ( ( PUNCT hvd.32044092008168 229 22 v v NOUN hvd.32044092008168 229 23 + + PROPN hvd.32044092008168 229 24 1 1 NUM hvd.32044092008168 229 25 ) ) PUNCT hvd.32044092008168 230 1 y₁ y₁ PROPN hvd.32044092008168 230 2 u¹−1 u¹−1 NOUN hvd.32044092008168 230 3 + + PROPN hvd.32044092008168 230 4 ( ( PUNCT hvd.32044092008168 230 5 v v ADP hvd.32044092008168 230 6 + + PROPN hvd.32044092008168 230 7 1 1 NUM hvd.32044092008168 230 8 ) ) PUNCT hvd.32044092008168 230 9 ( ( PUNCT hvd.32044092008168 230 10 v v NOUN hvd.32044092008168 230 11 + + PROPN hvd.32044092008168 230 12 2 2 NUM hvd.32044092008168 230 13 ) ) PUNCT hvd.32044092008168 230 14 u² u² PROPN hvd.32044092008168 230 15 y₂ y₂ PROPN hvd.32044092008168 231 1 + + CCONJ hvd.32044092008168 231 2 · · PUNCT hvd.32044092008168 231 3 · · PUNCT hvd.32044092008168 231 4 = = PUNCT hvd.32044092008168 231 5 * * NOUN hvd.32044092008168 231 6 ) ) PUNCT hvd.32044092008168 231 7 compair compair NOUN hvd.32044092008168 231 8 general general ADJ hvd.32044092008168 231 9 form form NOUN hvd.32044092008168 231 10 [ [ PUNCT hvd.32044092008168 231 11 14 14 NUM hvd.32044092008168 231 12 ] ] PUNCT hvd.32044092008168 231 13 p. p. NOUN hvd.32044092008168 231 14 16 16 NUM hvd.32044092008168 231 15 . . PUNCT hvd.32044092008168 232 1 22 22 NUM hvd.32044092008168 232 2 part part NOUN hvd.32044092008168 232 3 ii ii PROPN hvd.32044092008168 232 4 . . PUNCT hvd.32044092008168 233 1 we we PRON hvd.32044092008168 233 2 have have VERB hvd.32044092008168 233 3 also also ADV hvd.32044092008168 233 4 whence whence ADV hvd.32044092008168 233 5 : : PUNCT hvd.32044092008168 233 6 [ [ X hvd.32044092008168 233 7 25 25 NUM hvd.32044092008168 233 8 ] ] PUNCT hvd.32044092008168 233 9 . . PUNCT hvd.32044092008168 234 1 p(u p(u ADJ hvd.32044092008168 234 2 ) ) PUNCT hvd.32044092008168 235 1 these these DET hvd.32044092008168 235 2 values value NOUN hvd.32044092008168 235 3 in in ADP hvd.32044092008168 235 4 [ [ PUNCT hvd.32044092008168 235 5 24 24 NUM hvd.32044092008168 235 6 ] ] PUNCT hvd.32044092008168 235 7 give give VERB hvd.32044092008168 235 8 : : PUNCT hvd.32044092008168 235 9 v v NOUN hvd.32044092008168 235 10 ( ( PUNCT hvd.32044092008168 235 11 v v NOUN hvd.32044092008168 235 12 — — PUNCT hvd.32044092008168 235 13 1 1 X hvd.32044092008168 235 14 ) ) PUNCT hvd.32044092008168 235 15 yuv−2 yuv−2 PROPN hvd.32044092008168 235 16 + + PUNCT hvd.32044092008168 235 17 -[~ -[~ PROPN hvd.32044092008168 235 18 = = SYM hvd.32044092008168 235 19 u u PROPN hvd.32044092008168 235 20 ' ' PUNCT hvd.32044092008168 235 21 u u NOUN hvd.32044092008168 235 22 ' ' PUNCT hvd.32044092008168 235 23 • • SYM hvd.32044092008168 235 24 w w PROPN hvd.32044092008168 235 25 n n X hvd.32044092008168 235 26 v v NOUN hvd.32044092008168 235 27 ( ( PUNCT hvd.32044092008168 235 28 v v X hvd.32044092008168 235 29 − − PROPN hvd.32044092008168 235 30 1 1 NUM hvd.32044092008168 235 31 ) ) PUNCT hvd.32044092008168 235 32 = = PUNCT hvd.32044092008168 235 33 n n PROPN hvd.32044092008168 235 34 ( ( PUNCT hvd.32044092008168 235 35 n n X hvd.32044092008168 235 36 + + CCONJ hvd.32044092008168 235 37 1 1 X hvd.32044092008168 235 38 ) ) PUNCT hvd.32044092008168 235 39 n. n. NOUN hvd.32044092008168 236 1 this this DET hvd.32044092008168 236 2 value value NOUN hvd.32044092008168 236 3 gives give VERB hvd.32044092008168 236 4 since since SCONJ hvd.32044092008168 236 5 the the DET hvd.32044092008168 236 6 uneven uneven ADJ hvd.32044092008168 236 7 powers power NOUN hvd.32044092008168 236 8 fall fall VERB hvd.32044092008168 236 9 out out ADP hvd.32044092008168 236 10 h2 h2 PROPN hvd.32044092008168 236 11 + + CCONJ hvd.32044092008168 236 12 + + CCONJ hvd.32044092008168 236 13 n-4 n-4 X hvd.32044092008168 236 14 un un PROPN hvd.32044092008168 236 15 · · PUNCT hvd.32044092008168 236 16 + + CCONJ hvd.32044092008168 236 17 = = X hvd.32044092008168 236 18 n(n n(n PROPN hvd.32044092008168 236 19 + + CCONJ hvd.32044092008168 236 20 1 1 NUM hvd.32044092008168 236 21 ) ) PUNCT hvd.32044092008168 236 22 . . PUNCT hvd.32044092008168 237 1 n n CCONJ hvd.32044092008168 237 2 2 2 NUM hvd.32044092008168 237 3 y y NOUN hvd.32044092008168 237 4 + + PROPN hvd.32044092008168 237 5 1 1 NUM hvd.32044092008168 237 6 = = SYM hvd.32044092008168 237 7 + + ADJ hvd.32044092008168 237 8 b b X hvd.32044092008168 237 9 + + CCONJ hvd.32044092008168 237 10 n n CCONJ hvd.32044092008168 237 11 w w X hvd.32044092008168 237 12 + + PROPN hvd.32044092008168 237 13 ( ( PUNCT hvd.32044092008168 237 14 n−6 n−6 PROPN hvd.32044092008168 237 15 ) ) PUNCT hvd.32044092008168 237 16 ( ( PUNCT hvd.32044092008168 237 17 n n CCONJ hvd.32044092008168 237 18 − − PROPN hvd.32044092008168 237 19 5 5 X hvd.32044092008168 237 20 ) ) PUNCT hvd.32044092008168 237 21 h₁ h₁ PROPN hvd.32044092008168 237 22 n2 n2 PROPN hvd.32044092008168 237 23 u u PROPN hvd.32044092008168 237 24 1 1 NUM hvd.32044092008168 237 25 un un PROPN hvd.32044092008168 238 1 + + PROPN hvd.32044092008168 238 2 1 1 NUM hvd.32044092008168 238 3 un+ un+ PROPN hvd.32044092008168 238 4 2 2 NUM hvd.32044092008168 238 5 from from ADP hvd.32044092008168 238 6 which which PRON hvd.32044092008168 238 7 we we PRON hvd.32044092008168 238 8 again again ADV hvd.32044092008168 238 9 derive derive VERB hvd.32044092008168 238 10 y y PROPN hvd.32044092008168 238 11 ' ' PUNCT hvd.32044092008168 238 12 = = NOUN hvd.32044092008168 238 13 n(n n(n PROPN hvd.32044092008168 238 14 + + CCONJ hvd.32044092008168 238 15 1 1 NUM hvd.32044092008168 238 16 ) ) PUNCT hvd.32044092008168 238 17 + + NUM hvd.32044092008168 238 18 ( ( PUNCT hvd.32044092008168 238 19 n n CCONJ hvd.32044092008168 238 20 − − PROPN hvd.32044092008168 238 21 2 2 X hvd.32044092008168 238 22 ) ) PUNCT hvd.32044092008168 238 23 ( ( PUNCT hvd.32044092008168 238 24 n n CCONJ hvd.32044092008168 238 25 − − PROPN hvd.32044092008168 238 26 1 1 NUM hvd.32044092008168 238 27 ) ) PUNCT hvd.32044092008168 238 28 ¹¹ ¹¹ NUM hvd.32044092008168 238 29 + + NOUN hvd.32044092008168 238 30 ( ( PUNCT hvd.32044092008168 238 31 n n CCONJ hvd.32044092008168 238 32 − − PROPN hvd.32044092008168 238 33 4 4 NUM hvd.32044092008168 238 34 ) ) PUNCT hvd.32044092008168 238 35 ( ( PUNCT hvd.32044092008168 238 36 n n CCONJ hvd.32044092008168 238 37 − − PROPN hvd.32044092008168 238 38 3 3 NUM hvd.32044092008168 238 39 ) ) PUNCT hvd.32044092008168 238 40 1 1 NUM hvd.32044092008168 238 41 un+ un+ PROPN hvd.32044092008168 238 42 2 2 NUM hvd.32044092008168 238 43 h₁ h₁ PROPN hvd.32044092008168 238 44 un un PROPN hvd.32044092008168 238 45 + + CCONJ hvd.32044092008168 238 46 tn(n+1 tn(n+1 SPACE hvd.32044092008168 238 47 ) ) PUNCT hvd.32044092008168 238 48 ghi ghi PROPN hvd.32044092008168 238 49 h₂ h₂ PROPN hvd.32044092008168 238 50 + + CCONJ hvd.32044092008168 238 51 un-4 un-4 ADP hvd.32044092008168 238 52 bhi bhi PROPN hvd.32044092008168 238 53 n-2 n-2 PROPN hvd.32044092008168 238 54 un un PROPN hvd.32044092008168 238 55 h₁ h₁ PROPN hvd.32044092008168 238 56 n n ADP hvd.32044092008168 238 57 u u PROPN hvd.32044092008168 238 58 ' ' PART hvd.32044092008168 238 59 + + SYM hvd.32044092008168 238 60 h1 h1 X hvd.32044092008168 238 61 u2 u2 PROPN hvd.32044092008168 238 62 n n CCONJ hvd.32044092008168 238 63 2 2 NUM hvd.32044092008168 238 64 u u PROPN hvd.32044092008168 238 65 un+ un+ INTJ hvd.32044092008168 238 66 c₁u² c₁u² PUNCT hvd.32044092008168 239 1 + + PUNCT hvd.32044092008168 239 2 c₂u¹ c₂u¹ PUNCT hvd.32044092008168 240 1 + + X hvd.32044092008168 240 2 hg hg INTJ hvd.32044092008168 241 1 + + PROPN hvd.32044092008168 241 2 ( ( PUNCT hvd.32044092008168 241 3 n-4 n-4 SPACE hvd.32044092008168 241 4 ) ) PUNCT hvd.32044092008168 241 5 + + CCONJ hvd.32044092008168 241 6 + + CCONJ hvd.32044092008168 241 7 unbha unbha ADJ hvd.32044092008168 241 8 n-4 n-4 X hvd.32044092008168 241 9 ( ( PUNCT hvd.32044092008168 241 10 n n X hvd.32044092008168 241 11 + + CCONJ hvd.32044092008168 241 12 1 1 NUM hvd.32044092008168 241 13 ) ) PUNCT hvd.32044092008168 241 14 n n CCONJ hvd.32044092008168 241 15 + + CCONJ hvd.32044092008168 241 16 1 1 NUM hvd.32044092008168 241 17 2i+2 2i+2 NOUN hvd.32044092008168 241 18 2 2 NUM hvd.32044092008168 241 19 › › PROPN hvd.32044092008168 241 20 ( ( PUNCT hvd.32044092008168 241 21 n n CCONJ hvd.32044092008168 241 22 + + CCONJ hvd.32044092008168 241 23 1 1 X hvd.32044092008168 241 24 ) ) PUNCT hvd.32044092008168 241 25 you²² you²² PROPN hvd.32044092008168 242 1 + + CCONJ hvd.32044092008168 242 2 .. .. PUNCT hvd.32044092008168 243 1 u u PRON hvd.32044092008168 243 2 1 1 NUM hvd.32044092008168 243 3 + + CCONJ hvd.32044092008168 243 4 n n CCONJ hvd.32044092008168 243 5 ( ( PUNCT hvd.32044092008168 243 6 n n X hvd.32044092008168 243 7 + + CCONJ hvd.32044092008168 243 8 1 1 NUM hvd.32044092008168 243 9 ) ) PUNCT hvd.32044092008168 243 10 c1 c1 PROPN hvd.32044092008168 243 11 un—3 un—3 NOUN hvd.32044092008168 244 1 + + PUNCT hvd.32044092008168 244 2 n(n n(n PROPN hvd.32044092008168 244 3 + + CCONJ hvd.32044092008168 244 4 1 1 NUM hvd.32044092008168 244 5 ) ) PUNCT hvd.32044092008168 244 6 e̟h e̟h PROPN hvd.32044092008168 244 7 , , PUNCT hvd.32044092008168 244 8 2 2 NUM hvd.32044092008168 244 9 + + CCONJ hvd.32044092008168 244 10 + + NUM hvd.32044092008168 244 11 · · PUNCT hvd.32044092008168 244 12 + + CCONJ hvd.32044092008168 244 13 or or CCONJ hvd.32044092008168 244 14 ... ... PUNCT hvd.32044092008168 245 1 2 2 NUM hvd.32044092008168 245 2 i i PRON hvd.32044092008168 245 3 • • X hvd.32044092008168 245 4 w w X hvd.32044092008168 245 5 [ [ X hvd.32044092008168 245 6 n n X hvd.32044092008168 245 7 ( ( PUNCT hvd.32044092008168 245 8 n n NOUN hvd.32044092008168 245 9 ( ( PUNCT hvd.32044092008168 245 10 n n X hvd.32044092008168 245 11 + + ADP hvd.32044092008168 245 12 1 1 X hvd.32044092008168 245 13 ) ) PUNCT hvd.32044092008168 245 14 ( ( PUNCT hvd.32044092008168 245 15 ~ ~ PUNCT hvd.32044092008168 245 16 + + X hvd.32044092008168 245 17 qu² qu² ADJ hvd.32044092008168 245 18 + + NOUN hvd.32044092008168 245 19 cu¹ cu¹ NOUN hvd.32044092008168 245 20 + + CCONJ hvd.32044092008168 245 21 · · PUNCT hvd.32044092008168 245 22 · · PUNCT hvd.32044092008168 245 23 · · PUNCT hvd.32044092008168 245 24 ) ) PUNCT hvd.32044092008168 245 25 + + CCONJ hvd.32044092008168 246 1 b b X hvd.32044092008168 246 2 + + NOUN hvd.32044092008168 246 3 2 2 NUM hvd.32044092008168 246 4 = = SYM hvd.32044092008168 246 5 + + NUM hvd.32044092008168 246 6 ( ( PUNCT hvd.32044092008168 246 7 n-2i)(n2i+1 n-2i)(n2i+1 NOUN hvd.32044092008168 246 8 ) ) PUNCT hvd.32044092008168 246 9 h h NOUN hvd.32044092008168 246 10 ; ; PUNCT hvd.32044092008168 246 11 • • SYM hvd.32044092008168 247 1 + + CCONJ hvd.32044092008168 247 2 ] ] X hvd.32044092008168 247 3 bh bh NOUN hvd.32044092008168 247 4 n-2 n-2 PROPN hvd.32044092008168 247 5 i i NOUN hvd.32044092008168 247 6 + + CCONJ hvd.32044092008168 247 7 h h NOUN hvd.32044092008168 247 8 ; ; PUNCT hvd.32044092008168 247 9 un-2 un-2 NOUN hvd.32044092008168 247 10 i i PRON hvd.32044092008168 247 11 1/72 1/72 NUM hvd.32044092008168 247 12 | | NOUN hvd.32044092008168 247 13 ( ( PUNCT hvd.32044092008168 247 14 n n CCONJ hvd.32044092008168 247 15 − − PROPN hvd.32044092008168 247 16 2 2 X hvd.32044092008168 247 17 ) ) PUNCT hvd.32044092008168 247 18 ( ( PUNCT hvd.32044092008168 247 19 n n CCONJ hvd.32044092008168 247 20 − − PROPN hvd.32044092008168 247 21 1 1 X hvd.32044092008168 247 22 ) ) PUNCT hvd.32044092008168 247 23 h¸ h¸ PROPN hvd.32044092008168 247 24 − − PROPN hvd.32044092008168 247 25 n n CCONJ hvd.32044092008168 247 26 ( ( PUNCT hvd.32044092008168 247 27 n n X hvd.32044092008168 247 28 + + CCONJ hvd.32044092008168 247 29 1 1 X hvd.32044092008168 247 30 ) ) PUNCT hvd.32044092008168 248 1 h¸ h¸ PROPN hvd.32044092008168 248 2 + + CCONJ hvd.32044092008168 248 3 b b X hvd.32044092008168 248 4 · · PUNCT hvd.32044092008168 248 5 h₁ h₁ PROPN hvd.32044092008168 248 6 = = X hvd.32044092008168 248 7 un un PROPN hvd.32044092008168 249 1 + + PROPN hvd.32044092008168 249 2 1 1 NUM hvd.32044092008168 249 3 nw nw PROPN hvd.32044092008168 249 4 h h PROPN hvd.32044092008168 249 5 ; ; PUNCT hvd.32044092008168 249 6 n n NOUN hvd.32044092008168 249 7 ( ( PUNCT hvd.32044092008168 249 8 n n X hvd.32044092008168 249 9 + + CCONJ hvd.32044092008168 249 10 1 1 NUM hvd.32044092008168 249 11 ) ) PUNCT hvd.32044092008168 249 12 n-2 n-2 NOUN hvd.32044092008168 249 13 2i+2 2i+2 X hvd.32044092008168 249 14 w w NOUN hvd.32044092008168 249 15 + + CCONJ hvd.32044092008168 249 16 4 4 NUM hvd.32044092008168 249 17 + + PUNCT hvd.32044092008168 249 18 .. .. PUNCT hvd.32044092008168 249 19 ... ... PUNCT hvd.32044092008168 250 1 1 1 X hvd.32044092008168 250 2 | | NOUN hvd.32044092008168 250 3 ( ( PUNCT hvd.32044092008168 250 4 n n CCONJ hvd.32044092008168 250 5 − − PROPN hvd.32044092008168 250 6 4 4 NUM hvd.32044092008168 250 7 ) ) PUNCT hvd.32044092008168 250 8 ( ( PUNCT hvd.32044092008168 250 9 n n CCONJ hvd.32044092008168 250 10 − − PROPN hvd.32044092008168 250 11 3 3 X hvd.32044092008168 250 12 ) ) PUNCT hvd.32044092008168 250 13 h₂ h₂ PROPN hvd.32044092008168 250 14 = = X hvd.32044092008168 250 15 n n PROPN hvd.32044092008168 250 16 ( ( PUNCT hvd.32044092008168 250 17 n n X hvd.32044092008168 250 18 + + ADP hvd.32044092008168 250 19 1 1 X hvd.32044092008168 250 20 ) ) PUNCT hvd.32044092008168 250 21 [ [ PUNCT hvd.32044092008168 250 22 h₂ h₂ PROPN hvd.32044092008168 250 23 + + CCONJ hvd.32044092008168 250 24 ç ç X hvd.32044092008168 250 25 ] ] X hvd.32044092008168 250 26 + + CCONJ hvd.32044092008168 250 27 h₁ h₁ PROPN hvd.32044092008168 250 28 b b NOUN hvd.32044092008168 250 29 + + CCONJ hvd.32044092008168 250 30 n n NOUN hvd.32044092008168 250 31 ( ( PUNCT hvd.32044092008168 250 32 n n X hvd.32044092008168 250 33 + + CCONJ hvd.32044092008168 250 34 1 1 X hvd.32044092008168 250 35 ) ) PUNCT hvd.32044092008168 250 36 c½ c½ X hvd.32044092008168 250 37 2 2 NUM hvd.32044092008168 250 38 − − PROPN hvd.32044092008168 250 39 s s PART hvd.32044092008168 250 40 + + PROPN hvd.32044092008168 250 41 c₂ c₂ PROPN hvd.32044092008168 250 42 n-4 n-4 X hvd.32044092008168 250 43 u u PROPN hvd.32044092008168 250 44 ' ' PUNCT hvd.32044092008168 250 45 equating equate VERB hvd.32044092008168 250 46 the the DET hvd.32044092008168 250 47 coefficients coefficient NOUN hvd.32044092008168 250 48 of of ADP hvd.32044092008168 250 49 like like ADP hvd.32044092008168 250 50 powers power NOUN hvd.32044092008168 250 51 of of ADP hvd.32044092008168 250 52 u u PROPN hvd.32044092008168 250 53 in in ADP hvd.32044092008168 250 54 this this DET hvd.32044092008168 250 55 identity identity NOUN hvd.32044092008168 250 56 one one NOUN hvd.32044092008168 250 57 finds find VERB hvd.32044092008168 250 58 + + PUNCT hvd.32044092008168 250 59 ... ... PUNCT hvd.32044092008168 251 1 w w X hvd.32044092008168 251 2 ha ha INTJ hvd.32044092008168 251 3 n n CCONJ hvd.32044092008168 251 4 u u PROPN hvd.32044092008168 251 5 h h PROPN hvd.32044092008168 251 6 ; ; PUNCT hvd.32044092008168 251 7 n―2i+2 n―2i+2 NOUN hvd.32044092008168 251 8 | | NOUN hvd.32044092008168 251 9 ( ( PUNCT hvd.32044092008168 251 10 n n CCONJ hvd.32044092008168 251 11 − − PROPN hvd.32044092008168 251 12 6 6 NUM hvd.32044092008168 251 13 ) ) PUNCT hvd.32044092008168 251 14 ( ( PUNCT hvd.32044092008168 251 15 n n CCONJ hvd.32044092008168 251 16 − − PROPN hvd.32044092008168 251 17 5)kg 5)kg PROPN hvd.32044092008168 251 18 = = SYM hvd.32044092008168 251 19 n(n+1)(kstant)+h n(n+1)(kstant)+h PROPN hvd.32044092008168 251 20 b b PROPN hvd.32044092008168 251 21 4 4 NUM hvd.32044092008168 251 22 2 2 NUM hvd.32044092008168 251 23 hermite hermite NOUN hvd.32044092008168 251 24 's 's PART hvd.32044092008168 251 25 integral integral ADJ hvd.32044092008168 251 26 as as ADP hvd.32044092008168 251 27 a a DET hvd.32044092008168 251 28 sum sum NOUN hvd.32044092008168 251 29 . . PUNCT hvd.32044092008168 252 1 23 23 NUM hvd.32044092008168 252 2 1 1 NUM hvd.32044092008168 252 3 w w PROPN hvd.32044092008168 252 4 ło ło NOUN hvd.32044092008168 252 5 | | X hvd.32044092008168 252 6 ( ( PUNCT hvd.32044092008168 252 7 n n CCONJ hvd.32044092008168 252 8 -8 -8 X hvd.32044092008168 252 9 ) ) PUNCT hvd.32044092008168 252 10 ( ( PUNCT hvd.32044092008168 252 11 n n NOUN hvd.32044092008168 252 12 — — PUNCT hvd.32044092008168 252 13 7)h 7)h PROPN hvd.32044092008168 252 14 = = SYM hvd.32044092008168 252 15 n(n n(n PROPN hvd.32044092008168 252 16 + + CCONJ hvd.32044092008168 252 17 1 1 NUM hvd.32044092008168 252 18 ) ) PUNCT hvd.32044092008168 252 19 ( ( PUNCT hvd.32044092008168 252 20 hx+cho+cha+c3 hx+cho+cha+c3 PROPN hvd.32044092008168 252 21 ) ) PUNCT hvd.32044092008168 252 22 + + CCONJ hvd.32044092008168 252 23 hy hy PROPN hvd.32044092008168 252 24 b b PROPN hvd.32044092008168 252 25 in in ADP hvd.32044092008168 252 26 7 7 NUM hvd.32044092008168 252 27 0 0 NUM hvd.32044092008168 252 28 c c NOUN hvd.32044092008168 252 29 ) ) PUNCT hvd.32044092008168 252 30 b b PROPN hvd.32044092008168 252 31 6 6 NUM hvd.32044092008168 252 32 un un PROPN hvd.32044092008168 252 33 1 1 NUM hvd.32044092008168 252 34 -3 -3 PROPN hvd.32044092008168 252 35 u u PROPN hvd.32044092008168 252 36 n-2i+2(n-2i)(n-2i+1)h;=n(n+1)[hitchi-2+cahi-3 n-2i+2(n-2i)(n-2i+1)h;=n(n+1)[hitchi-2+cahi-3 PROPN hvd.32044092008168 253 1 + + NUM hvd.32044092008168 253 2 ... ... PUNCT hvd.32044092008168 254 1 + + CCONJ hvd.32044092008168 254 2 c-1 c-1 X hvd.32044092008168 254 3 ] ] X hvd.32044092008168 255 1 + + CCONJ hvd.32044092008168 255 2 hi-1 hi-1 X hvd.32044092008168 256 1 b. b. NOUN hvd.32044092008168 257 1 whence whence INTJ hvd.32044092008168 257 2 we we PRON hvd.32044092008168 257 3 obtain obtain VERB hvd.32044092008168 257 4 all all DET hvd.32044092008168 257 5 the the DET hvd.32044092008168 257 6 coefficients coefficient NOUN hvd.32044092008168 257 7 in in ADP hvd.32044092008168 257 8 the the DET hvd.32044092008168 257 9 development development NOUN hvd.32044092008168 257 10 for for ADP hvd.32044092008168 257 11 y y PROPN hvd.32044092008168 257 12 by by ADP hvd.32044092008168 257 13 means mean NOUN hvd.32044092008168 257 14 of of ADP hvd.32044092008168 257 15 the the DET hvd.32044092008168 257 16 recurring recur VERB hvd.32044092008168 257 17 formula formula NOUN hvd.32044092008168 257 18 . . PUNCT hvd.32044092008168 258 1 [ [ X hvd.32044092008168 258 2 26 26 NUM hvd.32044092008168 258 3 ] ] SYM hvd.32044092008168 258 4 2 2 NUM hvd.32044092008168 258 5 i(2 i(2 PROPN hvd.32044092008168 258 6 i i PRON hvd.32044092008168 258 7 — — PUNCT hvd.32044092008168 258 8 2n 2n NUM hvd.32044092008168 258 9 — — PUNCT hvd.32044092008168 258 10 1 1 X hvd.32044092008168 258 11 ) ) PUNCT hvd.32044092008168 258 12 hi hi PROPN hvd.32044092008168 258 13 = = PRON hvd.32044092008168 258 14 n(n n(n PROPN hvd.32044092008168 258 15 + + CCONJ hvd.32044092008168 258 16 1 1 X hvd.32044092008168 258 17 ) ) PUNCT hvd.32044092008168 259 1 [ [ X hvd.32044092008168 259 2 cı cı X hvd.32044092008168 259 3 hi-2 hi-2 X hvd.32044092008168 259 4 + + SYM hvd.32044092008168 259 5 cahi-3 cahi-3 PROPN hvd.32044092008168 259 6 + + CCONJ hvd.32044092008168 259 7 ... ... PUNCT hvd.32044092008168 260 1 + + CCONJ hvd.32044092008168 260 2 ci-2h ci-2h NOUN hvd.32044092008168 260 3 ; ; PUNCT hvd.32044092008168 260 4 + + NUM hvd.32044092008168 260 5 ci-1 ci-1 SPACE hvd.32044092008168 260 6 ] ] X hvd.32044092008168 261 1 + + CCONJ hvd.32044092008168 261 2 hi-1b hi-1b NOUN hvd.32044092008168 261 3 . . PUNCT hvd.32044092008168 262 1 since since SCONJ hvd.32044092008168 262 2 then then ADV hvd.32044092008168 262 3 hi hi INTJ hvd.32044092008168 262 4 is be AUX hvd.32044092008168 262 5 determined determine VERB hvd.32044092008168 262 6 we we PRON hvd.32044092008168 262 7 have have VERB hvd.32044092008168 262 8 when when SCONJ hvd.32044092008168 262 9 n n ADP hvd.32044092008168 262 10 is be AUX hvd.32044092008168 262 11 even even ADV hvd.32044092008168 262 12 and and CCONJ hvd.32044092008168 262 13 equal equal ADJ hvd.32044092008168 262 14 to to ADP hvd.32044092008168 262 15 2v 2v X hvd.32044092008168 262 16 h h PROPN hvd.32044092008168 262 17 , , PUNCT hvd.32044092008168 262 18 y y PROPN hvd.32044092008168 263 1 + + CCONJ hvd.32044092008168 263 2 + + CCONJ hvd.32044092008168 263 3 + + CCONJ hvd.32044092008168 263 4 th th X hvd.32044092008168 263 5 , , PUNCT hvd.32044092008168 264 1 u2v u2v ADJ hvd.32044092008168 264 2 u u PROPN hvd.32044092008168 264 3 ? ? PUNCT hvd.32044092008168 265 1 -2 -2 INTJ hvd.32044092008168 265 2 -3 -3 INTJ hvd.32044092008168 265 3 --1 --1 NOUN hvd.32044092008168 265 4 1 1 NUM hvd.32044092008168 265 5 hy-1 hy-1 X hvd.32044092008168 265 6 2 2 NUM hvd.32044092008168 265 7 v v NOUN hvd.32044092008168 265 8 -2 -2 PROPN hvd.32044092008168 265 9 w w PROPN hvd.32044092008168 266 1 and and CCONJ hvd.32044092008168 266 2 if if SCONJ hvd.32044092008168 266 3 n n CCONJ hvd.32044092008168 266 4 be be AUX hvd.32044092008168 266 5 odd odd ADJ hvd.32044092008168 266 6 and and CCONJ hvd.32044092008168 266 7 equal equal ADJ hvd.32044092008168 266 8 to to ADP hvd.32044092008168 266 9 2 2 NUM hvd.32044092008168 266 10 v v NOUN hvd.32044092008168 266 11 1 1 NUM hvd.32044092008168 266 12 1 1 NUM hvd.32044092008168 266 13 1 1 NUM hvd.32044092008168 266 14 hi hi NOUN hvd.32044092008168 266 15 v-1 v-1 X hvd.32044092008168 266 16 y y PROPN hvd.32044092008168 266 17 utrit utrit PROPN hvd.32044092008168 266 18 h h PROPN hvd.32044092008168 266 19 , , PUNCT hvd.32044092008168 266 20 + + CCONJ hvd.32044092008168 267 1 + + PUNCT hvd.32044092008168 268 1 + + PUNCT hvd.32044092008168 268 2 + + CCONJ hvd.32044092008168 268 3 hou hou NOUN hvd.32044092008168 268 4 2 2 NUM hvd.32044092008168 268 5 v-1 v-1 PROPN hvd.32044092008168 268 6 2v-2 2v-2 NUM hvd.32044092008168 269 1 u u PROPN hvd.32044092008168 269 2 urgt urgt ADJ hvd.32044092008168 269 3 where where SCONJ hvd.32044092008168 269 4 hi hi ADJ hvd.32044092008168 269 5 is be AUX hvd.32044092008168 269 6 given give VERB hvd.32044092008168 269 7 by by ADP hvd.32044092008168 269 8 ( ( PUNCT hvd.32044092008168 269 9 26 26 NUM hvd.32044092008168 269 10 ) ) PUNCT hvd.32044092008168 269 11 . . PUNCT hvd.32044092008168 270 1 elu elu PROPN hvd.32044092008168 270 2 6 6 NUM hvd.32044092008168 270 3 1 1 NUM hvd.32044092008168 270 4 u u PROPN hvd.32044092008168 270 5 development development NOUN hvd.32044092008168 270 6 of of ADP hvd.32044092008168 270 7 the the DET hvd.32044092008168 270 8 eliment eliment ADJ hvd.32044092008168 270 9 f(w f(w PROPN hvd.32044092008168 270 10 ) ) PUNCT hvd.32044092008168 270 11 . . PUNCT hvd.32044092008168 271 1 having have VERB hvd.32044092008168 271 2 now now ADV hvd.32044092008168 271 3 a a DET hvd.32044092008168 271 4 development development NOUN hvd.32044092008168 271 5 of of ADP hvd.32044092008168 271 6 y y PROPN hvd.32044092008168 271 7 we we PRON hvd.32044092008168 271 8 can can AUX hvd.32044092008168 271 9 , , PUNCT hvd.32044092008168 271 10 if if SCONJ hvd.32044092008168 271 11 we we PRON hvd.32044092008168 271 12 develop develop VERB hvd.32044092008168 271 13 f(u f(u NOUN hvd.32044092008168 271 14 ) ) PUNCT hvd.32044092008168 271 15 and and CCONJ hvd.32044092008168 271 16 substitute substitute VERB hvd.32044092008168 271 17 in in ADP hvd.32044092008168 271 18 the the DET hvd.32044092008168 271 19 development development NOUN hvd.32044092008168 271 20 of of ADP hvd.32044092008168 271 21 f(u f(u NOUN hvd.32044092008168 271 22 ) ) PUNCT hvd.32044092008168 271 23 , , PUNCT hvd.32044092008168 271 24 find find VERB hvd.32044092008168 271 25 by by ADP hvd.32044092008168 271 26 comparison comparison NOUN hvd.32044092008168 271 27 the the DET hvd.32044092008168 271 28 conditions condition NOUN hvd.32044092008168 271 29 necessary necessary ADJ hvd.32044092008168 271 30 that that SCONJ hvd.32044092008168 271 31 y y PROPN hvd.32044092008168 271 32 = = PROPN hvd.32044092008168 271 33 f f PROPN hvd.32044092008168 271 34 , , PUNCT hvd.32044092008168 271 35 ( ( PUNCT hvd.32044092008168 271 36 u u PROPN hvd.32044092008168 271 37 ) ) PUNCT hvd.32044092008168 271 38 be be AUX hvd.32044092008168 271 39 a a DET hvd.32044092008168 271 40 solution solution NOUN hvd.32044092008168 271 41 . . PUNCT hvd.32044092008168 272 1 we we PRON hvd.32044092008168 272 2 have have VERB hvd.32044092008168 272 3 then then ADV hvd.32044092008168 272 4 to to PART hvd.32044092008168 272 5 determine determine VERB hvd.32044092008168 272 6 the the DET hvd.32044092008168 272 7 development development NOUN hvd.32044092008168 272 8 of of ADP hvd.32044092008168 272 9 o(u o(u ADJ hvd.32044092008168 272 10 + + CCONJ hvd.32044092008168 272 11 v v NOUN hvd.32044092008168 272 12 ) ) PUNCT hvd.32044092008168 272 13 f(u f(u PROPN hvd.32044092008168 272 14 ) ) PUNCT hvd.32044092008168 272 15 o o PROPN hvd.32044092008168 272 16 ( ( PUNCT hvd.32044092008168 272 17 ) ) PUNCT hvd.32044092008168 272 18 ( ( PUNCT hvd.32044092008168 272 19 v v NOUN hvd.32044092008168 272 20 ) ) PUNCT hvd.32044092008168 272 21 + + CCONJ hvd.32044092008168 272 22 . . PUNCT hvd.32044092008168 273 1 since since SCONJ hvd.32044092008168 273 2 [ [ X hvd.32044092008168 273 3 uf uf PROPN hvd.32044092008168 273 4 ( ( PUNCT hvd.32044092008168 273 5 u)]u=0 u)]u=0 ADJ hvd.32044092008168 273 6 = = PRON hvd.32044092008168 273 7 1 1 NUM hvd.32044092008168 273 8 to to ADP hvd.32044092008168 273 9 this this DET hvd.32044092008168 273 10 end end NOUN hvd.32044092008168 273 11 we we PRON hvd.32044092008168 273 12 develop develop VERB hvd.32044092008168 273 13 first first ADV hvd.32044092008168 273 14 the the DET hvd.32044092008168 273 15 function function NOUN hvd.32044092008168 273 16 ou ou X hvd.32044092008168 273 17 + + CCONJ hvd.32044092008168 273 18 v v NOUN hvd.32044092008168 273 19 ) ) PUNCT hvd.32044092008168 273 20 [ [ X hvd.32044092008168 273 21 27 27 NUM hvd.32044092008168 273 22 ] ] PUNCT hvd.32044092008168 273 23 · · PUNCT hvd.32044092008168 273 24 9 9 NUM hvd.32044092008168 273 25 ( ( PUNCT hvd.32044092008168 273 26 u u NOUN hvd.32044092008168 273 27 ) ) PUNCT hvd.32044092008168 273 28 = = VERB hvd.32044092008168 273 29 f(u)e(1 f(u)e(1 PROPN hvd.32044092008168 273 30 + + PROPN hvd.32044092008168 273 31 5v)u 5v)u NUM hvd.32044092008168 273 32 ou ou NOUN hvd.32044092008168 273 33 ) ) PUNCT hvd.32044092008168 273 34 o o NOUN hvd.32044092008168 273 35 ( ( PUNCT hvd.32044092008168 273 36 v v NOUN hvd.32044092008168 273 37 ) ) PUNCT hvd.32044092008168 273 38 we we PRON hvd.32044092008168 273 39 have have VERB hvd.32044092008168 273 40 : : PUNCT hvd.32044092008168 273 41 deu deu PROPN hvd.32044092008168 273 42 d d PROPN hvd.32044092008168 273 43 pu pu PROPN hvd.32044092008168 273 44 + + CCONJ hvd.32044092008168 273 45 cu cu PROPN hvd.32044092008168 273 46 + + CCONJ hvd.32044092008168 273 47 cqu4 cqu4 PROPN hvd.32044092008168 273 48 t. t. PROPN hvd.32044092008168 273 49 whence whence PROPN hvd.32044092008168 273 50 23 23 NUM hvd.32044092008168 273 51 — — PUNCT hvd.32044092008168 273 52 ž ž X hvd.32044092008168 273 53 czu• czu• NOUN hvd.32044092008168 273 54 — — PUNCT hvd.32044092008168 273 55 c5 c5 PROPN hvd.32044092008168 273 56 2 2 NUM hvd.32044092008168 273 57 ? ? PUNCT hvd.32044092008168 273 58 ... ... PUNCT hvd.32044092008168 274 1 e e X hvd.32044092008168 274 2 - - PROPN hvd.32044092008168 274 3 uζν uζν PROPN hvd.32044092008168 274 4 0 0 NUM hvd.32044092008168 274 5 . . PUNCT hvd.32044092008168 274 6 o'u o'u PROPN hvd.32044092008168 274 7 pu pu PROPN hvd.32044092008168 274 8 du du PROPN hvd.32044092008168 274 9 au au X hvd.32044092008168 274 10 ou ou X hvd.32044092008168 274 11 1 1 NUM hvd.32044092008168 274 12 1 1 NUM hvd.32044092008168 274 13 6u 6u NUM hvd.32044092008168 274 14 u u PROPN hvd.32044092008168 274 15 3 3 NUM hvd.32044092008168 274 16 7cs 7cs PROPN hvd.32044092008168 274 17 u u PROPN hvd.32044092008168 274 18 ? ? PUNCT hvd.32044092008168 274 19 . . PUNCT hvd.32044092008168 275 1 24 24 NUM hvd.32044092008168 275 2 part part NOUN hvd.32044092008168 275 3 ii ii PROPN hvd.32044092008168 275 4 . . PUNCT hvd.32044092008168 276 1 by by ADP hvd.32044092008168 276 2 taylor taylor PROPN hvd.32044092008168 276 3 's 's PART hvd.32044092008168 276 4 theorem theorem NOUN hvd.32044092008168 276 5 : : PUNCT hvd.32044092008168 276 6 d2 d2 PROPN hvd.32044092008168 276 7 ( ( PUNCT hvd.32044092008168 276 8 v v NOUN hvd.32044092008168 276 9 ) ) PUNCT hvd.32044092008168 276 10 6 6 NUM hvd.32044092008168 276 11 d d NOUN hvd.32044092008168 276 12 ( ( PUNCT hvd.32044092008168 276 13 v v NOUN hvd.32044092008168 276 14 ) ) PUNCT hvd.32044092008168 276 15 + + CCONJ hvd.32044092008168 276 16 du du PROPN hvd.32044092008168 276 17 6 6 NUM hvd.32044092008168 276 18 u2 u2 ADJ hvd.32044092008168 276 19 1.2 1.2 NUM hvd.32044092008168 276 20 du du PROPN hvd.32044092008168 276 21 ? ? PUNCT hvd.32044092008168 276 22 u2 u2 PROPN hvd.32044092008168 276 23 1.2.30 1.2.30 SPACE hvd.32044092008168 276 24 " " PUNCT hvd.32044092008168 276 25 ( ( PUNCT hvd.32044092008168 276 26 » » X hvd.32044092008168 276 27 ) ) PUNCT hvd.32044092008168 276 28 ... ... PUNCT hvd.32044092008168 277 1 ó ó X hvd.32044092008168 277 2 o o NOUN hvd.32044092008168 277 3 ' ' NUM hvd.32044092008168 277 4 0 0 NUM hvd.32044092008168 277 5 6 6 NUM hvd.32044092008168 277 6 1 1 NUM hvd.32044092008168 277 7 u3 u3 PROPN hvd.32044092008168 277 8 ( ( PUNCT hvd.32044092008168 277 9 u u PROPN hvd.32044092008168 277 10 + + CCONJ hvd.32044092008168 277 11 v v NOUN hvd.32044092008168 277 12 ) ) PUNCT hvd.32044092008168 277 13 = = NOUN hvd.32044092008168 277 14 ( ( PUNCT hvd.32044092008168 277 15 v v NOUN hvd.32044092008168 277 16 ) ) PUNCT hvd.32044092008168 277 17 + + NUM hvd.32044092008168 277 18 + + PUNCT hvd.32044092008168 277 19 = = SYM hvd.32044092008168 277 20 $ $ SYM hvd.32044092008168 277 21 ( ( PUNCT hvd.32044092008168 277 22 v v NOUN hvd.32044092008168 277 23 ) ) PUNCT hvd.32044092008168 277 24 — — PUNCT hvd.32044092008168 277 25 up up ADV hvd.32044092008168 277 26 ( ( PUNCT hvd.32044092008168 277 27 v v NOUN hvd.32044092008168 277 28 ) ) PUNCT hvd.32044092008168 277 29 – – PUNCT hvd.32044092008168 277 30 1 1 X hvd.32044092008168 277 31 . . X hvd.32044092008168 277 32 r r NOUN hvd.32044092008168 277 33 ' ' PUNCT hvd.32044092008168 277 34 ( ( PUNCT hvd.32044092008168 277 35 v v NOUN hvd.32044092008168 277 36 ) ) PUNCT hvd.32044092008168 277 37 ) ) PUNCT hvd.32044092008168 277 38 v v NOUN hvd.32044092008168 277 39 passing pass VERB hvd.32044092008168 277 40 now now ADV hvd.32044092008168 277 41 to to ADP hvd.32044092008168 277 42 logarithms logarithm NOUN hvd.32044092008168 277 43 we we PRON hvd.32044092008168 277 44 derive derive VERB hvd.32044092008168 277 45 : : PUNCT hvd.32044092008168 277 46 ( ( PUNCT hvd.32044092008168 277 47 w w PROPN hvd.32044092008168 277 48 ) ) PUNCT hvd.32044092008168 277 49 ( ( PUNCT hvd.32044092008168 277 50 # # NOUN hvd.32044092008168 277 51 + + NUM hvd.32044092008168 277 52 v v NOUN hvd.32044092008168 277 53 ) ) PUNCT hvd.32044092008168 277 54 ( ( PUNCT hvd.32044092008168 277 55 n n NOUN hvd.32044092008168 277 56 ) ) PUNCT hvd.32044092008168 277 57 ) ) PUNCT hvd.32044092008168 278 1 u u PROPN hvd.32044092008168 278 2 u u PROPN hvd.32044092008168 278 3 ( ( PUNCT hvd.32044092008168 278 4 v v ADP hvd.32044092008168 278 5 up up ADP hvd.32044092008168 278 6 ( ( PUNCT hvd.32044092008168 278 7 » » X hvd.32044092008168 278 8 ) ) PUNCT hvd.32044092008168 278 9 * * PUNCT hvd.32044092008168 278 10 * * PUNCT hvd.32044092008168 278 11 * * PUNCT hvd.32044092008168 278 12 w w NOUN hvd.32044092008168 278 13 -(op -(op PUNCT hvd.32044092008168 278 14 ) ) PUNCT hvd.32044092008168 278 15 p'(v p'(v PROPN hvd.32044092008168 278 16 ) ) PUNCT hvd.32044092008168 278 17 * * PUNCT hvd.32044092008168 278 18 " " PUNCT hvd.32044092008168 278 19 ( ( PUNCT hvd.32044092008168 278 20 w w PROPN hvd.32044092008168 278 21 ) ) PUNCT hvd.32044092008168 278 22 , , PUNCT hvd.32044092008168 278 23 * * PUNCT hvd.32044092008168 278 24 " " PUNCT hvd.32044092008168 278 25 * * NOUN hvd.32044092008168 278 26 » » X hvd.32044092008168 278 27 ) ) PUNCT hvd.32044092008168 278 28 – – PUNCT hvd.32044092008168 278 29 ] ] PUNCT hvd.32044092008168 278 30 - - PUNCT hvd.32044092008168 278 31 ... ... X hvd.32044092008168 279 1 pv pv ADP hvd.32044092008168 279 2 + + ADJ hvd.32044092008168 279 3 agu agu INTJ hvd.32044092008168 279 4 + + PROPN hvd.32044092008168 279 5 1 1 NUM hvd.32044092008168 279 6 + + NUM hvd.32044092008168 279 7 23 23 NUM hvd.32044092008168 279 8 + + NUM hvd.32044092008168 279 9 .. .. PUNCT hvd.32044092008168 279 10 integrating integrate VERB hvd.32044092008168 279 11 we we PRON hvd.32044092008168 279 12 have have VERB hvd.32044092008168 279 13 : : PUNCT hvd.32044092008168 279 14 log log VERB hvd.32044092008168 279 15 u u PROPN hvd.32044092008168 279 16 + + CCONJ hvd.32044092008168 279 17 , , PUNCT hvd.32044092008168 279 18 * * PUNCT hvd.32044092008168 279 19 + + CCONJ hvd.32044092008168 279 20 a a DET hvd.32044092008168 279 21 + + NOUN hvd.32044092008168 279 22 + + PUNCT hvd.32044092008168 279 23 ... ... PUNCT hvd.32044092008168 280 1 + + CCONJ hvd.32044092008168 280 2 a2 a2 X hvd.32044092008168 280 3 az az X hvd.32044092008168 280 4 a4 a4 X hvd.32044092008168 281 1 + + CCONJ hvd.32044092008168 281 2 p p NOUN hvd.32044092008168 281 3 ” " PUNCT hvd.32044092008168 281 4 ( ( PUNCT hvd.32044092008168 281 5 v v PROPN hvd.32044092008168 281 6 ) ) PUNCT hvd.32044092008168 281 7 3 3 NUM hvd.32044092008168 281 8 ! ! NUM hvd.32044092008168 281 9 c c PROPN hvd.32044092008168 281 10 , , PUNCT hvd.32044092008168 281 11 v v NOUN hvd.32044092008168 282 1 20 20 NUM hvd.32044092008168 282 2 2 2 NUM hvd.32044092008168 282 3 3 3 NUM hvd.32044092008168 282 4 us us PROPN hvd.32044092008168 282 5 c2 c2 PROPN hvd.32044092008168 282 6 ! ! PUNCT hvd.32044092008168 283 1 67 67 NUM hvd.32044092008168 284 1 [ [ PUNCT hvd.32044092008168 284 2 a a DET hvd.32044092008168 284 3 , , PUNCT hvd.32044092008168 284 4 2 2 NUM hvd.32044092008168 284 5 ! ! PUNCT hvd.32044092008168 284 6 u² u² PROPN hvd.32044092008168 284 7 a a PRON hvd.32044092008168 284 8 , , PUNCT hvd.32044092008168 284 9 3 3 NUM hvd.32044092008168 284 10 ! ! PUNCT hvd.32044092008168 284 11 t t PROPN hvd.32044092008168 284 12 u u PROPN hvd.32044092008168 284 13 u2 u2 PROPN hvd.32044092008168 284 14 u3 u3 PROPN hvd.32044092008168 284 15 log log VERB hvd.32044092008168 284 16 9 9 NUM hvd.32044092008168 284 17 u u PROPN hvd.32044092008168 284 18 " " PUNCT hvd.32044092008168 284 19 4 4 NUM hvd.32044092008168 284 20 ! ! SYM hvd.32044092008168 284 21 2 2 NUM hvd.32044092008168 284 22 ! ! NUM hvd.32044092008168 284 23 3 3 NUM hvd.32044092008168 284 24 ! ! PUNCT hvd.32044092008168 285 1 whence whence NOUN hvd.32044092008168 285 2 1 1 NUM hvd.32044092008168 285 3 u u PROPN hvd.32044092008168 285 4 u u PROPN hvd.32044092008168 285 5 3 3 NUM hvd.32044092008168 285 6 a2 a2 PROPN hvd.32044092008168 285 7 + + CCONJ hvd.32044092008168 285 8 a a PRON hvd.32044092008168 285 9 , , PUNCT hvd.32044092008168 285 10 + + NUM hvd.32044092008168 285 11 2 2 X hvd.32044092008168 285 12 ! ! NUM hvd.32044092008168 285 13 31 31 NUM hvd.32044092008168 286 1 [ [ X hvd.32044092008168 286 2 28 28 NUM hvd.32044092008168 286 3 ] ] SYM hvd.32044092008168 286 4 9 9 NUM hvd.32044092008168 286 5 е е X hvd.32044092008168 286 6 u u NOUN hvd.32044092008168 286 7 [ [ X hvd.32044092008168 286 8 49 49 NUM hvd.32044092008168 286 9 + + NUM hvd.32044092008168 286 10 4 4 NUM hvd.32044092008168 286 11 + + NUM hvd.32044092008168 286 12 ... ... PUNCT hvd.32044092008168 286 13 ] ] PUNCT hvd.32044092008168 287 1 [ [ X hvd.32044092008168 287 2 1 1 NUM hvd.32044092008168 287 3 + + NUM hvd.32044092008168 287 4 4 4 NUM hvd.32044092008168 287 5 + + NUM hvd.32044092008168 287 6 4+ 4+ NUM hvd.32044092008168 287 7 .. .. PUNCT hvd.32044092008168 287 8 ]+:[4 ]+:[4 PUNCT hvd.32044092008168 287 9 + + X hvd.32044092008168 287 10 425*+ 425*+ NUM hvd.32044092008168 287 11 .. .. SYM hvd.32044092008168 287 12 14 14 NUM hvd.32044092008168 287 13 + + NUM hvd.32044092008168 287 14 ... ... PUNCT hvd.32044092008168 287 15 1 1 NUM hvd.32044092008168 287 16 , , PUNCT hvd.32044092008168 287 17 * * PUNCT hvd.32044092008168 287 18 * * PUNCT hvd.32044092008168 287 19 . . PUNCT hvd.32044092008168 287 20 " " PUNCT hvd.32044092008168 287 21 * * PUNCT hvd.32044092008168 287 22 + + CCONJ hvd.32044092008168 287 23 = = PUNCT hvd.32044092008168 288 1 [ [ X hvd.32044092008168 288 2 1 1 NUM hvd.32044092008168 288 3 + + NUM hvd.32044092008168 288 4 p p NOUN hvd.32044092008168 288 5 + + CCONJ hvd.32044092008168 288 6 p p NOUN hvd.32044092008168 288 7 + + CCONJ hvd.32044092008168 288 8 p p NOUN hvd.32044092008168 288 9 + + PUNCT hvd.32044092008168 288 10 ... ... PUNCT hvd.32044092008168 288 11 ] ] X hvd.32044092008168 289 1 u u PROPN hvd.32044092008168 289 2 ? ? PROPN hvd.32044092008168 289 3 72 72 NUM hvd.32044092008168 289 4 us we PRON hvd.32044092008168 289 5 3 3 NUM hvd.32044092008168 289 6 ! ! PUNCT hvd.32044092008168 290 1 us we PRON hvd.32044092008168 290 2 23 23 NUM hvd.32044092008168 290 3 . . PUNCT hvd.32044092008168 291 1 -2 -2 NOUN hvd.32044092008168 291 2 2 2 X hvd.32044092008168 291 3 ! ! PUNCT hvd.32044092008168 291 4 + + CCONJ hvd.32044092008168 291 5 a a PRON hvd.32044092008168 291 6 . . PUNCT hvd.32044092008168 292 1 u u PROPN hvd.32044092008168 292 2 2 2 NUM hvd.32044092008168 292 3 2 2 NUM hvd.32044092008168 292 4 ! ! NUM hvd.32044092008168 292 5 3 3 NUM hvd.32044092008168 292 6 3 3 NUM hvd.32044092008168 292 7 ! ! PUNCT hvd.32044092008168 293 1 u u PROPN hvd.32044092008168 293 2 ? ? PROPN hvd.32044092008168 293 3 , , PUNCT hvd.32044092008168 294 1 + + CCONJ hvd.32044092008168 294 2 us we PRON hvd.32044092008168 294 3 3 3 NUM hvd.32044092008168 294 4 ! ! NUM hvd.32044092008168 294 5 24 24 NUM hvd.32044092008168 294 6 4 4 NUM hvd.32044092008168 294 7 4 4 NUM hvd.32044092008168 294 8 ! ! NUM hvd.32044092008168 294 9 2 2 NUM hvd.32044092008168 294 10 3 3 NUM hvd.32044092008168 294 11 2 2 NUM hvd.32044092008168 294 12 2 2 NUM hvd.32044092008168 294 13 3 3 NUM hvd.32044092008168 294 14 pa pa PROPN hvd.32044092008168 294 15 where where SCONJ hvd.32044092008168 294 16 p p PROPN hvd.32044092008168 294 17 , , PUNCT hvd.32044092008168 294 18 = = NOUN hvd.32044092008168 294 19 a a PRON hvd.32044092008168 294 20 , , PUNCT hvd.32044092008168 294 21 = = NOUN hvd.32044092008168 294 22 p(v p(v PROPN hvd.32044092008168 294 23 ) ) PUNCT hvd.32044092008168 294 24 ; ; PUNCT hvd.32044092008168 294 25 p p NOUN hvd.32044092008168 294 26 = = SYM hvd.32044092008168 294 27 4 4 NUM hvd.32044092008168 294 28 , , PUNCT hvd.32044092008168 294 29 = = PROPN hvd.32044092008168 294 30 -p'(v -p'(v PROPN hvd.32044092008168 294 31 ) ) PUNCT hvd.32044092008168 294 32 ; ; PUNCT hvd.32044092008168 294 33 , , PUNCT hvd.32044092008168 294 34 = = NOUN hvd.32044092008168 294 35 3p(v 3p(v NUM hvd.32044092008168 294 36 ) ) PUNCT hvd.32044092008168 295 1 + + CCONJ hvd.32044092008168 296 1 92 92 NUM hvd.32044092008168 296 2 = = SYM hvd.32044092008168 296 3 a4 a4 X hvd.32044092008168 296 4 + + NUM hvd.32044092008168 296 5 3 3 NUM hvd.32044092008168 296 6 a a PRON hvd.32044092008168 296 7 , , PUNCT hvd.32044092008168 296 8 4 4 NUM hvd.32044092008168 296 9 p. p. NOUN hvd.32044092008168 296 10 3 3 NUM hvd.32044092008168 296 11 pvp'v pvp'v VERB hvd.32044092008168 296 12 = = NOUN hvd.32044092008168 296 13 a a PRON hvd.32044092008168 296 14 ; ; PUNCT hvd.32044092008168 296 15 + + NUM hvd.32044092008168 296 16 10 10 NUM hvd.32044092008168 296 17 a a DET hvd.32044092008168 296 18 , , PUNCT hvd.32044092008168 296 19 a a PRON hvd.32044092008168 296 20 ; ; PUNCT hvd.32044092008168 296 21 etc etc X hvd.32044092008168 296 22 . . X hvd.32044092008168 297 1 showing show VERB hvd.32044092008168 297 2 that that SCONJ hvd.32044092008168 297 3 the the DET hvd.32044092008168 297 4 coefficients coefficient NOUN hvd.32044092008168 297 5 pi pi NOUN hvd.32044092008168 297 6 are be AUX hvd.32044092008168 297 7 intire intire ADJ hvd.32044092008168 297 8 functions function NOUN hvd.32044092008168 297 9 of of ADP hvd.32044092008168 297 10 pv pv PROPN hvd.32044092008168 297 11 and and CCONJ hvd.32044092008168 297 12 p'v p'v PROPN hvd.32044092008168 297 13 . . PUNCT hvd.32044092008168 297 14 * * PUNCT hvd.32044092008168 297 15 ) ) PUNCT hvd.32044092008168 297 16 2 2 NUM hvd.32044092008168 297 17 5 5 NUM hvd.32044092008168 297 18 5 5 NUM hvd.32044092008168 297 19 * * PUNCT hvd.32044092008168 297 20 ) ) PUNCT hvd.32044092008168 297 21 the the DET hvd.32044092008168 297 22 functions function NOUN hvd.32044092008168 297 23 pi pi NOUN hvd.32044092008168 297 24 correspond correspond VERB hvd.32044092008168 297 25 to to ADP hvd.32044092008168 297 26 the the DET hvd.32044092008168 297 27 functions function NOUN hvd.32044092008168 297 28 2 2 NUM hvd.32044092008168 297 29 in in ADP hvd.32044092008168 297 30 hermite hermite PROPN hvd.32044092008168 297 31 's 's PART hvd.32044092008168 297 32 treatis treatis NOUN hvd.32044092008168 297 33 , , PUNCT hvd.32044092008168 297 34 for for ADP hvd.32044092008168 297 35 example example NOUN hvd.32044092008168 298 1 1 1 NUM hvd.32044092008168 299 1 + + CCONJ hvd.32044092008168 299 2 x2 x2 ADJ hvd.32044092008168 299 3 p,= p,= PROPN hvd.32044092008168 299 4 p(v p(v SPACE hvd.32044092008168 299 5 ) ) PUNCT hvd.32044092008168 299 6 zasnau zasnau NOUN hvd.32044092008168 299 7 3 3 NUM hvd.32044092008168 299 8 p. p. NOUN hvd.32044092008168 299 9 p'u p'u ADV hvd.32044092008168 299 10 2 2 NUM hvd.32044092008168 299 11 son son PROPN hvd.32044092008168 299 12 hasnu hasnu PROPN hvd.32044092008168 299 13 onu onu PROPN hvd.32044092008168 299 14 dnu dnu PROPN hvd.32044092008168 300 1 see see VERB hvd.32044092008168 300 2 p. p. NOUN hvd.32044092008168 300 3 126 126 NUM hvd.32044092008168 300 4 development development NOUN hvd.32044092008168 300 5 of of ADP hvd.32044092008168 300 6 % % NOUN hvd.32044092008168 300 7 . . PUNCT hvd.32044092008168 301 1 hermite hermite PROPN hvd.32044092008168 301 2 's 's PART hvd.32044092008168 301 3 integral integral ADJ hvd.32044092008168 301 4 as as ADP hvd.32044092008168 301 5 a a DET hvd.32044092008168 301 6 sum sum NOUN hvd.32044092008168 301 7 . . PUNCT hvd.32044092008168 302 1 25 25 NUM hvd.32044092008168 302 2 9 9 NUM hvd.32044092008168 302 3 u u NOUN hvd.32044092008168 302 4 1.2 1.2 NUM hvd.32044092008168 302 5 from from ADP hvd.32044092008168 302 6 these these DET hvd.32044092008168 302 7 forms form NOUN hvd.32044092008168 302 8 we we PRON hvd.32044092008168 302 9 pass pass VERB hvd.32044092008168 302 10 immediately immediately ADV hvd.32044092008168 302 11 to to ADP hvd.32044092008168 302 12 [ [ PUNCT hvd.32044092008168 302 13 29 29 NUM hvd.32044092008168 302 14 ] ] X hvd.32044092008168 302 15 f(u f(u NOUN hvd.32044092008168 302 16 ) ) PUNCT hvd.32044092008168 302 17 = = X hvd.32044092008168 302 18 q q PROPN hvd.32044092008168 302 19 ( ( PUNCT hvd.32044092008168 302 20 u u PROPN hvd.32044092008168 302 21 ) ) PUNCT hvd.32044092008168 302 22 e(2+$)u e(2+$)u NOUN hvd.32044092008168 302 23 = = PUNCT hvd.32044092008168 302 24 ( ( PUNCT hvd.32044092008168 302 25 n)[1 n)[1 PROPN hvd.32044092008168 302 26 + + CCONJ hvd.32044092008168 302 27 ( ( PUNCT hvd.32044092008168 302 28 8 8 NUM hvd.32044092008168 302 29 + + NUM hvd.32044092008168 302 30 $ $ SYM hvd.32044092008168 302 31 v v NOUN hvd.32044092008168 302 32 ) ) PUNCT hvd.32044092008168 302 33 + + NUM hvd.32044092008168 302 34 ( ( PUNCT hvd.32044092008168 302 35 8 8 NUM hvd.32044092008168 302 36 + + SYM hvd.32044092008168 302 37 bv)**+ bv)**+ PROPN hvd.32044092008168 302 38 ... ... PUNCT hvd.32044092008168 302 39 ] ] PUNCT hvd.32044092008168 302 40 9 9 NUM hvd.32044092008168 302 41 $ $ SYM hvd.32044092008168 302 42 ? ? PUNCT hvd.32044092008168 302 43 = = PUNCT hvd.32044092008168 303 1 { { PUNCT hvd.32044092008168 303 2 [ [ X hvd.32044092008168 303 3 1 1 NUM hvd.32044092008168 303 4 + + NUM hvd.32044092008168 303 5 ( ( PUNCT hvd.32044092008168 303 6 + + CCONJ hvd.32044092008168 303 7 $ $ SYM hvd.32044092008168 303 8 u)u u)u ADJ hvd.32044092008168 303 9 + + CCONJ hvd.32044092008168 303 10 ( ( PUNCT hvd.32044092008168 303 11 p. p. NOUN hvd.32044092008168 303 12 + + CCONJ hvd.32044092008168 303 13 ( ( PUNCT hvd.32044092008168 303 14 1 1 NUM hvd.32044092008168 303 15 + + NUM hvd.32044092008168 303 16 $ $ SYM hvd.32044092008168 303 17 u u NOUN hvd.32044092008168 303 18 ) ) PUNCT hvd.32044092008168 303 19 " " PUNCT hvd.32044092008168 303 20 ) ) PUNCT hvd.32044092008168 303 21 ... ... PUNCT hvd.32044092008168 303 22 ] ] PUNCT hvd.32044092008168 304 1 + + PUNCT hvd.32044092008168 304 2 [ [ X hvd.32044092008168 304 3 p p NOUN hvd.32044092008168 304 4 , , PUNCT hvd.32044092008168 304 5 + + NUM hvd.32044092008168 304 6 3 3 NUM hvd.32044092008168 304 7 p p NOUN hvd.32044092008168 304 8 , , PUNCT hvd.32044092008168 304 9 ( ( PUNCT hvd.32044092008168 304 10 1 1 NUM hvd.32044092008168 304 11 + + NUM hvd.32044092008168 304 12 $ $ SYM hvd.32044092008168 304 13 w w NOUN hvd.32044092008168 304 14 ) ) PUNCT hvd.32044092008168 305 1 + + NUM hvd.32044092008168 305 2 ( ( PUNCT hvd.32044092008168 305 3 1 1 NUM hvd.32044092008168 305 4 + + NUM hvd.32044092008168 305 5 $ $ SYM hvd.32044092008168 305 6 w"] w"] NOUN hvd.32044092008168 305 7 ... ... PUNCT hvd.32044092008168 306 1 + + NOUN hvd.32044092008168 306 2 . . PUNCT hvd.32044092008168 307 1 [ [ X hvd.32044092008168 307 2 ( ( PUNCT hvd.32044092008168 307 3 ( ( PUNCT hvd.32044092008168 307 4 ) ) PUNCT hvd.32044092008168 307 5 ... ... PUNCT hvd.32044092008168 307 6 } } PUNCT hvd.32044092008168 307 7 + + CCONJ hvd.32044092008168 307 8 h. h. NOUN hvd.32044092008168 307 9 + + CCONJ hvd.32044092008168 307 10 h h PROPN hvd.32044092008168 307 11 , , PUNCT hvd.32044092008168 307 12 u u PROPN hvd.32044092008168 307 13 + + X hvd.32044092008168 307 14 h2u2 h2u2 ADV hvd.32044092008168 307 15 + + SYM hvd.32044092008168 307 16 hyu+ hyu+ PROPN hvd.32044092008168 307 17 ... ... PUNCT hvd.32044092008168 307 18 h h PROPN hvd.32044092008168 307 19 , , PUNCT hvd.32044092008168 307 20 , , PUNCT hvd.32044092008168 307 21 u u PROPN hvd.32044092008168 307 22 ? ? PROPN hvd.32044092008168 307 23 2 2 NUM hvd.32044092008168 307 24 1 1 NUM hvd.32044092008168 307 25 23 23 NUM hvd.32044092008168 307 26 3 3 NUM hvd.32044092008168 307 27 2 2 NUM hvd.32044092008168 307 28 2 2 NUM hvd.32044092008168 307 29 3 3 NUM hvd.32044092008168 307 30 1 1 NUM hvd.32044092008168 307 31 u u NOUN hvd.32044092008168 307 32 take take VERB hvd.32044092008168 307 33 λ λ NOUN hvd.32044092008168 307 34 = = NOUN hvd.32044092008168 307 35 α α INTJ hvd.32044092008168 308 1 ζν ζν INTJ hvd.32044092008168 308 2 whence whence NOUN hvd.32044092008168 308 3 [ [ X hvd.32044092008168 308 4 30 30 NUM hvd.32044092008168 308 5 ] ] PUNCT hvd.32044092008168 308 6 · · PUNCT hvd.32044092008168 308 7 f(u f(u NOUN hvd.32044092008168 308 8 ) ) PUNCT hvd.32044092008168 308 9 o(u o(u PROPN hvd.32044092008168 308 10 + + NUM hvd.32044092008168 308 11 v v NOUN hvd.32044092008168 308 12 ) ) PUNCT hvd.32044092008168 308 13 e(x_{vu e(x_{vu NOUN hvd.32044092008168 308 14 o(u o(u PROPN hvd.32044092008168 308 15 ) ) PUNCT hvd.32044092008168 308 16 ( ( PUNCT hvd.32044092008168 308 17 v v NOUN hvd.32044092008168 308 18 ) ) PUNCT hvd.32044092008168 308 19 0 0 NUM hvd.32044092008168 309 1 u u PROPN hvd.32044092008168 309 2 u u PROPN hvd.32044092008168 309 3 + + PROPN hvd.32044092008168 309 4 * * PUNCT hvd.32044092008168 309 5 + + PUNCT hvd.32044092008168 309 6 ( ( PUNCT hvd.32044092008168 309 7 x2 x2 ADJ hvd.32044092008168 309 8 + + CCONJ hvd.32044092008168 309 9 p p NOUN hvd.32044092008168 309 10 , , PUNCT hvd.32044092008168 309 11 ) ) PUNCT hvd.32044092008168 309 12 + + CCONJ hvd.32044092008168 309 13 ( ( PUNCT hvd.32044092008168 309 14 x3 x3 PROPN hvd.32044092008168 309 15 + + CCONJ hvd.32044092008168 309 16 3 3 NUM hvd.32044092008168 309 17 p p NOUN hvd.32044092008168 309 18 x x PUNCT hvd.32044092008168 309 19 + + NUM hvd.32044092008168 309 20 p. p. NOUN hvd.32044092008168 309 21 ) ) PUNCT hvd.32044092008168 310 1 * * PUNCT hvd.32044092008168 310 2 * * PUNCT hvd.32044092008168 310 3 3 3 NUM hvd.32044092008168 310 4 ) ) PUNCT hvd.32044092008168 310 5 2.3 2.3 NUM hvd.32044092008168 310 6 + + NUM hvd.32044092008168 310 7 ( ( PUNCT hvd.32044092008168 310 8 x x PUNCT hvd.32044092008168 310 9 * * PUNCT hvd.32044092008168 310 10 * * PUNCT hvd.32044092008168 310 11 + + NUM hvd.32044092008168 310 12 6 6 NUM hvd.32044092008168 310 13 p.x2 p.x2 X hvd.32044092008168 310 14 + + NUM hvd.32044092008168 310 15 4 4 NUM hvd.32044092008168 310 16 p5x p5x NUM hvd.32044092008168 310 17 + + NUM hvd.32044092008168 310 18 p. p. NOUN hvd.32044092008168 310 19 ) ) PUNCT hvd.32044092008168 310 20 , , PUNCT hvd.32044092008168 310 21 at at ADP hvd.32044092008168 310 22 us we PRON hvd.32044092008168 310 23 3 3 NUM hvd.32044092008168 311 1 + + NUM hvd.32044092008168 311 2 4 4 NUM hvd.32044092008168 311 3 2 2 NUM hvd.32044092008168 311 4 = = SYM hvd.32044092008168 311 5 + + SYM hvd.32044092008168 311 6 h. h. NOUN hvd.32044092008168 311 7 + + CCONJ hvd.32044092008168 311 8 h h NOUN hvd.32044092008168 311 9 , , PUNCT hvd.32044092008168 311 10 ( ( PUNCT hvd.32044092008168 311 11 u u NOUN hvd.32044092008168 311 12 ) ) PUNCT hvd.32044092008168 311 13 + + CCONJ hvd.32044092008168 311 14 h h NOUN hvd.32044092008168 311 15 , , PUNCT hvd.32044092008168 311 16 ( ( PUNCT hvd.32044092008168 311 17 u)2 u)2 ADJ hvd.32044092008168 311 18 + + PRON hvd.32044092008168 311 19 h2u h2u X hvd.32044092008168 311 20 » » NOUN hvd.32044092008168 311 21 . . PUNCT hvd.32044092008168 312 1 1 1 NUM hvd.32044092008168 312 2 2 2 NUM hvd.32044092008168 312 3 u u NOUN hvd.32044092008168 312 4 where where SCONJ hvd.32044092008168 312 5 in in ADP hvd.32044092008168 312 6 hermite hermite PROPN hvd.32044092008168 312 7 's 's PART hvd.32044092008168 312 8 notation notation NOUN hvd.32044092008168 312 9 h. h. PROPN hvd.32044092008168 312 10 x. x. PROPN hvd.32044092008168 312 11 1 1 NUM hvd.32044092008168 312 12 2 2 NUM hvd.32044092008168 312 13 h h NOUN hvd.32044092008168 312 14 = = SYM hvd.32044092008168 312 15 ( ( PUNCT hvd.32044092008168 312 16 x2 x2 PROPN hvd.32044092008168 312 17 + + ADJ hvd.32044092008168 312 18 p. p. NOUN hvd.32044092008168 312 19 ) ) PUNCT hvd.32044092008168 312 20 . . PUNCT hvd.32044092008168 313 1 h h PROPN hvd.32044092008168 313 2 , , PUNCT hvd.32044092008168 313 3 = = NOUN hvd.32044092008168 313 4 ( ( PUNCT hvd.32044092008168 313 5 23 23 NUM hvd.32044092008168 313 6 + + NUM hvd.32044092008168 313 7 3 3 NUM hvd.32044092008168 313 8 p p NOUN hvd.32044092008168 313 9 x x SYM hvd.32044092008168 313 10 + + PROPN hvd.32044092008168 313 11 p3 p3 PROPN hvd.32044092008168 313 12 ) ) PUNCT hvd.32044092008168 313 13 p p PROPN hvd.32044092008168 313 14 , , PUNCT hvd.32044092008168 313 15 1 1 NUM hvd.32044092008168 313 16 [ [ X hvd.32044092008168 313 17 31 31 NUM hvd.32044092008168 313 18 ] ] PUNCT hvd.32044092008168 313 19 6 6 NUM hvd.32044092008168 313 20 1 1 NUM hvd.32044092008168 313 21 h h NOUN hvd.32044092008168 313 22 , , PUNCT hvd.32044092008168 313 23 ( ( PUNCT hvd.32044092008168 313 24 24 24 NUM hvd.32044092008168 313 25 + + NUM hvd.32044092008168 313 26 6 6 NUM hvd.32044092008168 313 27 pzx2 pzx2 ADJ hvd.32044092008168 313 28 + + PROPN hvd.32044092008168 313 29 4 4 NUM hvd.32044092008168 313 30 pz3 pz3 NOUN hvd.32044092008168 313 31 + + SYM hvd.32044092008168 313 32 pa pa PROPN hvd.32044092008168 313 33 ) ) PUNCT hvd.32044092008168 313 34 3 3 NUM hvd.32044092008168 313 35 24 24 NUM hvd.32044092008168 313 36 determination determination NOUN hvd.32044092008168 313 37 of of ADP hvd.32044092008168 313 38 the the DET hvd.32044092008168 313 39 integral integral NOUN hvd.32044092008168 313 40 . . PUNCT hvd.32044092008168 314 1 we we PRON hvd.32044092008168 314 2 are be AUX hvd.32044092008168 314 3 now now ADV hvd.32044092008168 314 4 enabled enable VERB hvd.32044092008168 314 5 to to PART hvd.32044092008168 314 6 determine determine VERB hvd.32044092008168 314 7 the the DET hvd.32044092008168 314 8 exact exact ADJ hvd.32044092008168 314 9 expression expression NOUN hvd.32044092008168 314 10 for for ADP hvd.32044092008168 314 11 f(u f(u NOUN hvd.32044092008168 314 12 ) ) PUNCT hvd.32044092008168 314 13 and and CCONJ hvd.32044092008168 314 14 the the DET hvd.32044092008168 314 15 conditions condition NOUN hvd.32044092008168 314 16 necessary necessary ADJ hvd.32044092008168 314 17 that that SCONJ hvd.32044092008168 314 18 it it PRON hvd.32044092008168 314 19 become become VERB hvd.32044092008168 314 20 equal equal ADJ hvd.32044092008168 314 21 to to ADP hvd.32044092008168 314 22 y y PROPN hvd.32044092008168 314 23 by by ADP hvd.32044092008168 314 24 a a DET hvd.32044092008168 314 25 process process NOUN hvd.32044092008168 314 26 of of ADP hvd.32044092008168 314 27 comparison comparison NOUN hvd.32044092008168 314 28 of of ADP hvd.32044092008168 314 29 the the DET hvd.32044092008168 314 30 several several ADJ hvd.32044092008168 314 31 developments development NOUN hvd.32044092008168 314 32 obtained obtain VERB hvd.32044092008168 314 33 . . PUNCT hvd.32044092008168 315 1 26 26 NUM hvd.32044092008168 315 2 part part PROPN hvd.32044092008168 315 3 ii ii PROPN hvd.32044092008168 315 4 . . PROPN hvd.32044092008168 316 1 first first ADV hvd.32044092008168 316 2 we we PRON hvd.32044092008168 316 3 have have VERB hvd.32044092008168 316 4 : : PUNCT hvd.32044092008168 316 5 1 1 NUM hvd.32044092008168 316 6 f(u f(u NOUN hvd.32044092008168 316 7 ) ) PUNCT hvd.32044092008168 316 8 + + CCONJ hvd.32044092008168 317 1 h h NOUN hvd.32044092008168 318 1 + + PUNCT hvd.32044092008168 318 2 h4 h4 NOUN hvd.32044092008168 318 3 + + CCONJ hvd.32044092008168 318 4 h21 h21 NOUN hvd.32044092008168 318 5 ° ° NOUN hvd.32044092008168 318 6 + + NUM hvd.32044092008168 319 1 + + CCONJ hvd.32044092008168 319 2 h4 h4 PROPN hvd.32044092008168 319 3 + + PUNCT hvd.32044092008168 319 4 .. .. PUNCT hvd.32044092008168 320 1 u u PROPN hvd.32044092008168 320 2 f'(u f'(u PROPN hvd.32044092008168 320 3 ) ) PUNCT hvd.32044092008168 320 4 1 1 NUM hvd.32044092008168 320 5 u u NOUN hvd.32044092008168 320 6 ? ? PUNCT hvd.32044092008168 321 1 + + CCONJ hvd.32044092008168 322 1 h+ h+ PROPN hvd.32044092008168 322 2 2 2 NUM hvd.32044092008168 322 3 h2u h2u PROPN hvd.32044092008168 323 1 + + PUNCT hvd.32044092008168 323 2 3 3 NUM hvd.32044092008168 323 3 h2u2 h2u2 ADV hvd.32044092008168 323 4 + + CCONJ hvd.32044092008168 323 5 + + CCONJ hvd.32044092008168 323 6 ih;u-1 ih;u-1 X hvd.32044092008168 324 1 + + ADJ hvd.32044092008168 324 2 ... ... PUNCT hvd.32044092008168 324 3 f”(u f”(u PROPN hvd.32044092008168 324 4 ) ) PUNCT hvd.32044092008168 324 5 + + CCONJ hvd.32044092008168 324 6 + + NUM hvd.32044092008168 324 7 2 2 NUM hvd.32044092008168 324 8 h2 h2 NOUN hvd.32044092008168 324 9 +2 +2 NUM hvd.32044092008168 324 10 . . PUNCT hvd.32044092008168 325 1 3 3 NUM hvd.32044092008168 325 2 h3u h3u NOUN hvd.32044092008168 325 3 + + PUNCT hvd.32044092008168 325 4 ... ... PUNCT hvd.32044092008168 325 5 . . PUNCT hvd.32044092008168 326 1 .. .. PUNCT hvd.32044092008168 326 2 tili tili PROPN hvd.32044092008168 326 3 — — PUNCT hvd.32044092008168 326 4 1 1 X hvd.32044092008168 326 5 ) ) PUNCT hvd.32044092008168 326 6 h;ui2 h;ui2 NUM hvd.32044092008168 326 7 2 2 NUM hvd.32044092008168 326 8 u2 u2 PROPN hvd.32044092008168 326 9 2.3 2.3 NUM hvd.32044092008168 326 10 f f NOUN hvd.32044092008168 326 11 '' '' PUNCT hvd.32044092008168 326 12 ( ( PUNCT hvd.32044092008168 326 13 u u PROPN hvd.32044092008168 326 14 ) ) PUNCT hvd.32044092008168 326 15 u4 u4 NOUN hvd.32044092008168 326 16 + + PROPN hvd.32044092008168 326 17 2 2 NUM hvd.32044092008168 326 18 · · SYM hvd.32044092008168 326 19 3 3 NUM hvd.32044092008168 326 20 h3 h3 NOUN hvd.32044092008168 326 21 + + NUM hvd.32044092008168 326 22 ... ... SYM hvd.32044092008168 326 23 2 2 NUM hvd.32044092008168 326 24 + + CCONJ hvd.32044092008168 326 25 tili tili PROPN hvd.32044092008168 326 26 1 1 NUM hvd.32044092008168 326 27 ) ) PUNCT hvd.32044092008168 326 28 ( ( PUNCT hvd.32044092008168 326 29 2 2 NUM hvd.32044092008168 326 30 — — SYM hvd.32044092008168 326 31 2 2 NUM hvd.32044092008168 326 32 ) ) PUNCT hvd.32044092008168 326 33 hu—3 hu—3 PROPN hvd.32044092008168 327 1 + + PUNCT hvd.32044092008168 327 2 ... ... PUNCT hvd.32044092008168 327 3 ( ( PUNCT hvd.32044092008168 327 4 n n X hvd.32044092008168 327 5 odd odd ADJ hvd.32044092008168 327 6 ) ) PUNCT hvd.32044092008168 327 7 1 1 NUM hvd.32044092008168 327 8 2 2 NUM hvd.32044092008168 327 9 .3 .3 NUM hvd.32044092008168 327 10 .•(n-1 .•(n-1 PUNCT hvd.32044092008168 327 11 ) ) PUNCT hvd.32044092008168 328 1 + + CCONJ hvd.32044092008168 328 2 + + NUM hvd.32044092008168 328 3 2 2 NUM hvd.32044092008168 328 4 .3 .3 NUM hvd.32044092008168 328 5 ... ... PUNCT hvd.32044092008168 329 1 ( ( PUNCT hvd.32044092008168 329 2 n n CCONJ hvd.32044092008168 329 3 − − PROPN hvd.32044092008168 329 4 1 1 X hvd.32044092008168 329 5 ) ) PUNCT hvd.32044092008168 329 6 hn-1 hn-1 X hvd.32044092008168 330 1 t t PROPN hvd.32044092008168 330 2 ... ... PUNCT hvd.32044092008168 330 3 un un PROPN hvd.32044092008168 330 4 tili tili PROPN hvd.32044092008168 330 5 — — PUNCT hvd.32044092008168 330 6 1) 1) NUM hvd.32044092008168 330 7 ... ... PUNCT hvd.32044092008168 330 8 (i (i PUNCT hvd.32044092008168 330 9 — — PUNCT hvd.32044092008168 330 10 n+1 n+1 X hvd.32044092008168 330 11 ) ) PUNCT hvd.32044092008168 330 12 hui hui PROPN hvd.32044092008168 330 13 - - PUNCT hvd.32044092008168 330 14 ntit ntit PROPN hvd.32044092008168 330 15 ... ... PUNCT hvd.32044092008168 331 1 again again ADV hvd.32044092008168 331 2 1 1 NUM hvd.32044092008168 331 3 hy hy X hvd.32044092008168 331 4 in1 in1 ADJ hvd.32044092008168 331 5 yn=2v-1 yn=2v-1 PROPN hvd.32044092008168 331 6 + + SYM hvd.32044092008168 331 7 to.it to.it PROPN hvd.32044092008168 332 1 + + CCONJ hvd.32044092008168 332 2 hou hou VERB hvd.32044092008168 332 3 ן ן PROPN hvd.32044092008168 332 4 2 2 NUM hvd.32044092008168 332 5 1 1 NUM hvd.32044092008168 332 6 2 2 NUM hvd.32044092008168 332 7 3 3 NUM hvd.32044092008168 332 8 u u PROPN hvd.32044092008168 332 9 u u PROPN hvd.32044092008168 332 10 u u PROPN hvd.32044092008168 332 11 1 1 NUM hvd.32044092008168 332 12 hr_1 hr_1 NOUN hvd.32044092008168 333 1 + + CCONJ hvd.32044092008168 333 2 2v 2v X hvd.32044092008168 334 1 u u PROPN hvd.32044092008168 334 2 2v 2v X hvd.32044092008168 334 3 — — PUNCT hvd.32044092008168 334 4 2 2 NUM hvd.32044092008168 334 5 u u NOUN hvd.32044092008168 334 6 2 2 NUM hvd.32044092008168 334 7 y y PROPN hvd.32044092008168 334 8 = = PROPN hvd.32044092008168 334 9 fiu fiu PROPN hvd.32044092008168 334 10 h h PROPN hvd.32044092008168 334 11 , , PUNCT hvd.32044092008168 334 12 yn yn PROPN hvd.32044092008168 334 13 = = PROPN hvd.32044092008168 334 14 lv lv PROPN hvd.32044092008168 334 15 + + PROPN hvd.32044092008168 334 16 + + NUM hvd.32044092008168 334 17 + + PUNCT hvd.32044092008168 334 18 hy hy PROPN hvd.32044092008168 334 19 . . PUNCT hvd.32044092008168 335 1 u2 u2 PROPN hvd.32044092008168 335 2 and and CCONJ hvd.32044092008168 335 3 in in ADP hvd.32044092008168 335 4 general general ADJ hvd.32044092008168 335 5 aaf(a aaf(a PROPN hvd.32044092008168 335 6 ) ) PUNCT hvd.32044092008168 335 7 + + CCONJ hvd.32044092008168 335 8 aa-1f aa-1f VERB hvd.32044092008168 335 9 ( ( PUNCT hvd.32044092008168 335 10 a-1 a-1 NOUN hvd.32044092008168 335 11 ) ) PUNCT hvd.32044092008168 335 12 + + NOUN hvd.32044092008168 335 13 ... ... PUNCT hvd.32044092008168 336 1 tf tf X hvd.32044092008168 336 2 aaf aaf PROPN hvd.32044092008168 336 3 ( ( PUNCT hvd.32044092008168 336 4 n-1 n-1 NOUN hvd.32044092008168 336 5 ) ) PUNCT hvd.32044092008168 336 6 + + CCONJ hvd.32044092008168 336 7 aa-2f aa-2f NOUN hvd.32044092008168 336 8 ( ( PUNCT hvd.32044092008168 336 9 n-3 n-3 NUM hvd.32044092008168 336 10 ) ) PUNCT hvd.32044092008168 336 11 + + PROPN hvd.32044092008168 336 12 + + CCONJ hvd.32044092008168 336 13 f f X hvd.32044092008168 336 14 ( ( PUNCT hvd.32044092008168 336 15 n n X hvd.32044092008168 336 16 odd odd ADJ hvd.32044092008168 336 17 ) ) PUNCT hvd.32044092008168 336 18 . . PUNCT hvd.32044092008168 337 1 now now ADV hvd.32044092008168 337 2 substituting substitute VERB hvd.32044092008168 337 3 the the DET hvd.32044092008168 337 4 values value NOUN hvd.32044092008168 337 5 f(x f(x PROPN hvd.32044092008168 337 6 ) ) PUNCT hvd.32044092008168 337 7 found find VERB hvd.32044092008168 337 8 above above ADV hvd.32044092008168 337 9 and and CCONJ hvd.32044092008168 337 10 ordering order VERB hvd.32044092008168 337 11 the the DET hvd.32044092008168 337 12 coefficients coefficient NOUN hvd.32044092008168 337 13 so so SCONJ hvd.32044092008168 337 14 that that SCONJ hvd.32044092008168 337 15 the the DET hvd.32044092008168 337 16 residual residual ADJ hvd.32044092008168 337 17 with with ADP hvd.32044092008168 337 18 respect respect NOUN hvd.32044092008168 337 19 to to ADP hvd.32044092008168 337 20 u u PROPN hvd.32044092008168 337 21 will will AUX hvd.32044092008168 337 22 be be AUX hvd.32044092008168 337 23 unity unity NOUN hvd.32044092008168 337 24 we we PRON hvd.32044092008168 337 25 find find VERB hvd.32044092008168 337 26 by by ADP hvd.32044092008168 337 27 comparison comparison NOUN hvd.32044092008168 337 28 that that SCONJ hvd.32044092008168 337 29 we we PRON hvd.32044092008168 337 30 may may AUX hvd.32044092008168 337 31 write write VERB hvd.32044092008168 337 32 1 1 NUM hvd.32044092008168 337 33 1 1 NUM hvd.32044092008168 337 34 ) ) PUNCT hvd.32044092008168 337 35 ; ; PUNCT hvd.32044092008168 337 36 f(n-1 f(n-1 VERB hvd.32044092008168 337 37 ) ) PUNCT hvd.32044092008168 337 38 + + CCONJ hvd.32044092008168 337 39 3 3 X hvd.32044092008168 337 40 ) ) PUNCT hvd.32044092008168 337 41 ; ; PUNCT hvd.32044092008168 337 42 hif hif PROPN hvd.32044092008168 337 43 ( ( PUNCT hvd.32044092008168 337 44 n—3 n—3 PROPN hvd.32044092008168 337 45 ) ) PUNCT hvd.32044092008168 338 1 + + NUM hvd.32044092008168 338 2 1 1 NUM hvd.32044092008168 339 1 [ [ X hvd.32044092008168 339 2 32 32 NUM hvd.32044092008168 339 3 ] ] PUNCT hvd.32044092008168 339 4 . . PUNCT hvd.32044092008168 340 1 • • PUNCT hvd.32044092008168 340 2 y y NOUN hvd.32044092008168 340 3 = = SYM hvd.32044092008168 340 4 f1(11 f1(11 PROPN hvd.32044092008168 340 5 ) ) PUNCT hvd.32044092008168 340 6 hif hif PROPN hvd.32044092008168 340 7 ( ( PUNCT hvd.32044092008168 340 8 n-3 n-3 NUM hvd.32044092008168 340 9 ) ) PUNCT hvd.32044092008168 341 1 + + CCONJ hvd.32044092008168 341 2 ... ... PUNCT hvd.32044092008168 341 3 hr hr NOUN hvd.32044092008168 341 4 - - PUNCT hvd.32044092008168 341 5 if if SCONJ hvd.32044092008168 341 6 ( ( PUNCT hvd.32044092008168 341 7 n n NOUN hvd.32044092008168 341 8 ( ( PUNCT hvd.32044092008168 341 9 n n NOUN hvd.32044092008168 341 10 ( ( PUNCT hvd.32044092008168 341 11 n n X hvd.32044092008168 341 12 odd odd ADJ hvd.32044092008168 341 13 and and CCONJ hvd.32044092008168 341 14 = = PRON hvd.32044092008168 341 15 2v 2v NUM hvd.32044092008168 341 16 — — PUNCT hvd.32044092008168 341 17 1 1 X hvd.32044092008168 341 18 ) ) PUNCT hvd.32044092008168 341 19 provided provide VERB hvd.32044092008168 341 20 x x PUNCT hvd.32044092008168 341 21 and and CCONJ hvd.32044092008168 341 22 v v NOUN hvd.32044092008168 341 23 be be AUX hvd.32044092008168 341 24 so so ADV hvd.32044092008168 341 25 taken take VERB hvd.32044092008168 341 26 that that SCONJ hvd.32044092008168 341 27 the the DET hvd.32044092008168 341 28 constant constant ADJ hvd.32044092008168 341 29 term term NOUN hvd.32044092008168 341 30 equal equal ADJ hvd.32044092008168 341 31 zero zero NUM hvd.32044092008168 341 32 and and CCONJ hvd.32044092008168 341 33 the the DET hvd.32044092008168 341 34 coefficient coefficient NOUN hvd.32044092008168 341 35 of of ADP hvd.32044092008168 341 36 the the DET hvd.32044092008168 341 37 next next ADJ hvd.32044092008168 341 38 term term NOUN hvd.32044092008168 341 39 equal equal ADJ hvd.32044092008168 341 40 hy hy PROPN hvd.32044092008168 341 41 and and CCONJ hvd.32044092008168 341 42 ha ha INTJ hvd.32044092008168 341 43 1)!f 1)!f NUM hvd.32044092008168 341 44 ( ( PUNCT hvd.32044092008168 341 45 n n CCONJ hvd.32044092008168 341 46 − − PROPN hvd.32044092008168 341 47 1 1 X hvd.32044092008168 341 48 ) ) PUNCT hvd.32044092008168 341 49 f(n—5 f(n—5 PROPN hvd.32044092008168 341 50 ) ) PUNCT hvd.32044092008168 341 51 ( ( PUNCT hvd.32044092008168 341 52 n n CCONJ hvd.32044092008168 341 53 − − PROPN hvd.32044092008168 341 54 3)!/(1 3)!/(1 NUM hvd.32044092008168 341 55 - - SYM hvd.32044092008168 341 56 3 3 NUM hvd.32044092008168 341 57 ) ) PUNCT hvd.32044092008168 341 58 . . PUNCT hvd.32044092008168 342 1 1 1 NUM hvd.32044092008168 342 2 h h NOUN hvd.32044092008168 342 3 [ [ X hvd.32044092008168 342 4 33 33 NUM hvd.32044092008168 342 5 ] ] PUNCT hvd.32044092008168 342 6 y y PROPN hvd.32044092008168 342 7 = = PUNCT hvd.32044092008168 342 8 f:(u f:(u X hvd.32044092008168 342 9 ) ) PUNCT hvd.32044092008168 342 10 ( ( PUNCT hvd.32044092008168 342 11 n n CCONJ hvd.32044092008168 342 12 − − PROPN hvd.32044092008168 342 13 1 1 NUM hvd.32044092008168 342 14 ) ) PUNCT hvd.32044092008168 342 15 ! ! PUNCT hvd.32044092008168 343 1 ( ( PUNCT hvd.32044092008168 343 2 n n X hvd.32044092008168 343 3 — — PUNCT hvd.32044092008168 343 4 5 5 X hvd.32044092008168 343 5 ) ) PUNCT hvd.32044092008168 343 6 ! ! PUNCT hvd.32044092008168 344 1 hr-1f hr-1f PROPN hvd.32044092008168 344 2 ' ' PUNCT hvd.32044092008168 344 3 ( ( PUNCT hvd.32044092008168 344 4 n n CCONJ hvd.32044092008168 344 5 even even ADV hvd.32044092008168 344 6 and and CCONJ hvd.32044092008168 344 7 = = PRON hvd.32044092008168 344 8 2 2 NUM hvd.32044092008168 344 9 v v NOUN hvd.32044092008168 344 10 ) ) PUNCT hvd.32044092008168 344 11 provided provide VERB hvd.32044092008168 344 12 x x PROPN hvd.32044092008168 344 13 and and CCONJ hvd.32044092008168 344 14 v v NOUN hvd.32044092008168 344 15 be be AUX hvd.32044092008168 344 16 so so ADV hvd.32044092008168 344 17 taken take VERB hvd.32044092008168 344 18 that that SCONJ hvd.32044092008168 344 19 the the DET hvd.32044092008168 344 20 constant constant ADJ hvd.32044092008168 344 21 term term NOUN hvd.32044092008168 344 22 equal equal ADJ hvd.32044092008168 344 23 h h NOUN hvd.32044092008168 344 24 , , PUNCT hvd.32044092008168 344 25 and and CCONJ hvd.32044092008168 344 26 the the DET hvd.32044092008168 344 27 coefficient coefficient NOUN hvd.32044092008168 344 28 of of ADP hvd.32044092008168 344 29 the the DET hvd.32044092008168 344 30 next next ADJ hvd.32044092008168 344 31 term term NOUN hvd.32044092008168 344 32 equal equal ADJ hvd.32044092008168 344 33 zero zero NUM hvd.32044092008168 344 34 or or CCONJ hvd.32044092008168 344 35 in in ADP hvd.32044092008168 344 36 general general ADJ hvd.32044092008168 344 37 1 1 NUM hvd.32044092008168 344 38 [ [ X hvd.32044092008168 344 39 34 34 NUM hvd.32044092008168 344 40 ] ] PUNCT hvd.32044092008168 344 41 ( ( PUNCT hvd.32044092008168 344 42 -1)n-17= -1)n-17= NOUN hvd.32044092008168 344 43 ( ( PUNCT hvd.32044092008168 344 44 n n CCONJ hvd.32044092008168 344 45 − − PROPN hvd.32044092008168 344 46 3 3 NUM hvd.32044092008168 344 47 ) ) PUNCT hvd.32044092008168 344 48 ! ! PUNCT hvd.32044092008168 345 1 h h NOUN hvd.32044092008168 345 2 , , PUNCT hvd.32044092008168 345 3 f f PROPN hvd.32044092008168 345 4 ( ( PUNCT hvd.32044092008168 345 5 n—3 n—3 PROPN hvd.32044092008168 345 6 + + PROPN hvd.32044092008168 345 7 hef hef PROPN hvd.32044092008168 345 8 ( ( PUNCT hvd.32044092008168 345 9 n—5 n—5 PROPN hvd.32044092008168 345 10 ) ) PUNCT hvd.32044092008168 345 11 + + NUM hvd.32044092008168 345 12 ... ... PUNCT hvd.32044092008168 345 13 ( ( PUNCT hvd.32044092008168 345 14 n n X hvd.32044092008168 345 15 — — PUNCT hvd.32044092008168 345 16 5 5 X hvd.32044092008168 345 17 ) ) PUNCT hvd.32044092008168 345 18 ! ! PUNCT hvd.32044092008168 346 1 1 1 NUM hvd.32044092008168 346 2 ( ( PUNCT hvd.32044092008168 346 3 n n CCONJ hvd.32044092008168 346 4 − − PROPN hvd.32044092008168 346 5 1 1 NUM hvd.32044092008168 346 6 ) ) PUNCT hvd.32044092008168 346 7 ! ! PUNCT hvd.32044092008168 347 1 f(n-1 f(n-1 NOUN hvd.32044092008168 347 2 ) ) PUNCT hvd.32044092008168 348 1 + + CCONJ hvd.32044092008168 348 2 hermite hermite PROPN hvd.32044092008168 348 3 's 's PART hvd.32044092008168 348 4 integral integral ADJ hvd.32044092008168 348 5 as as ADP hvd.32044092008168 348 6 a a DET hvd.32044092008168 348 7 sum sum NOUN hvd.32044092008168 348 8 . . PUNCT hvd.32044092008168 349 1 27 27 NUM hvd.32044092008168 349 2 where where SCONJ hvd.32044092008168 349 3 the the DET hvd.32044092008168 349 4 last last ADJ hvd.32044092008168 349 5 terms term NOUN hvd.32044092008168 349 6 are be AUX hvd.32044092008168 349 7 obtained obtain VERB hvd.32044092008168 349 8 to to ADP hvd.32044092008168 349 9 accord accord NOUN hvd.32044092008168 349 10 with with ADP hvd.32044092008168 349 11 the the DET hvd.32044092008168 349 12 above above ADJ hvd.32044092008168 349 13 conditions condition NOUN hvd.32044092008168 349 14 . . PUNCT hvd.32044092008168 350 1 substituting substitute VERB hvd.32044092008168 350 2 the the DET hvd.32044092008168 350 3 values value NOUN hvd.32044092008168 350 4 f(x f(x PROPN hvd.32044092008168 350 5 ) ) PUNCT hvd.32044092008168 351 1 we we PRON hvd.32044092008168 351 2 find find VERB hvd.32044092008168 351 3 the the DET hvd.32044092008168 351 4 conditions condition NOUN hvd.32044092008168 351 5 to to PART hvd.32044092008168 351 6 be be AUX hvd.32044092008168 351 7 ( ( PUNCT hvd.32044092008168 351 8 n n X hvd.32044092008168 351 9 odd odd ADJ hvd.32044092008168 351 10 ) ) PUNCT hvd.32044092008168 351 11 h2v-2 h2v-2 PROPN hvd.32044092008168 351 12 + + CCONJ hvd.32044092008168 351 13 h₁ h₁ NOUN hvd.32044092008168 351 14 h21 h21 NOUN hvd.32044092008168 351 15 - - PUNCT hvd.32044092008168 351 16 4 4 NUM hvd.32044092008168 351 17 + + NUM hvd.32044092008168 351 18 h₂ h₂ PROPN hvd.32044092008168 351 19 h2v-6 h2v-6 X hvd.32044092008168 351 20 + + CCONJ hvd.32044092008168 351 21 + + CCONJ hvd.32044092008168 351 22 hv−1 hv−1 INTJ hvd.32044092008168 351 23 ho ho PROPN hvd.32044092008168 351 24 = = X hvd.32044092008168 351 25 0 0 PUNCT hvd.32044092008168 352 1 [ [ X hvd.32044092008168 352 2 35 35 NUM hvd.32044092008168 352 3 ] ] PUNCT hvd.32044092008168 352 4 ( ( PUNCT hvd.32044092008168 352 5 2v 2v NUM hvd.32044092008168 352 6 1 1 X hvd.32044092008168 352 7 ) ) PUNCT hvd.32044092008168 352 8 h₂v-1 h₂v-1 SPACE hvd.32044092008168 352 9 + + CCONJ hvd.32044092008168 352 10 ( ( PUNCT hvd.32044092008168 352 11 2v 2v PROPN hvd.32044092008168 352 12 3 3 X hvd.32044092008168 352 13 ) ) PUNCT hvd.32044092008168 352 14 h₁ h₁ NOUN hvd.32044092008168 352 15 h₂v-3 h₂v-3 PROPN hvd.32044092008168 352 16 + + CCONJ hvd.32044092008168 352 17 ( ( PUNCT hvd.32044092008168 352 18 2v 2v NUM hvd.32044092008168 352 19 — — PUNCT hvd.32044092008168 352 20 5 5 X hvd.32044092008168 352 21 ) ) PUNCT hvd.32044092008168 352 22 hq hq PROPN hvd.32044092008168 352 23 h2 h2 NOUN hvd.32044092008168 352 24 v−5 v−5 X hvd.32044092008168 352 25 + + CCONJ hvd.32044092008168 352 26 : : PUNCT hvd.32044092008168 352 27 · · PUNCT hvd.32044092008168 352 28 · · PUNCT hvd.32044092008168 352 29 + + PROPN hvd.32044092008168 352 30 hy-1 hy-1 PROPN hvd.32044092008168 352 31 h₁h h₁h PROPN hvd.32044092008168 352 32 , , PUNCT hvd.32044092008168 352 33 0 0 NUM hvd.32044092008168 352 34 0 0 NUM hvd.32044092008168 352 35 — — PUNCT hvd.32044092008168 352 36 forms form NOUN hvd.32044092008168 352 37 ( ( PUNCT hvd.32044092008168 352 38 n n CCONJ hvd.32044092008168 352 39 even even ADV hvd.32044092008168 352 40 ) ) PUNCT hvd.32044092008168 352 41 h2v−1 h2v−1 PROPN hvd.32044092008168 352 42 + + SYM hvd.32044092008168 352 43 h₁ h₁ PROPN hvd.32044092008168 352 44 h2v−3 h2v−3 PROPN hvd.32044092008168 352 45 + + CCONJ hvd.32044092008168 352 46 h₂ h₂ PROPN hvd.32044092008168 352 47 h2v−5 h2v−5 PROPN hvd.32044092008168 352 48 + + SYM hvd.32044092008168 352 49 + + CCONJ hvd.32044092008168 353 1 hv−1 hv−1 INTJ hvd.32044092008168 353 2 h1 h1 X hvd.32044092008168 354 1 + + CCONJ hvd.32044092008168 354 2 hv hv NOUN hvd.32044092008168 355 1 [ [ X hvd.32044092008168 355 2 36 36 NUM hvd.32044092008168 355 3 ] ] PUNCT hvd.32044092008168 355 4 ( ( PUNCT hvd.32044092008168 355 5 2v 2v PROPN hvd.32044092008168 355 6 h₂v+(2 h₂v+(2 PROPN hvd.32044092008168 355 7 v v PROPN hvd.32044092008168 355 8 −2 −2 SPACE hvd.32044092008168 355 9 ) ) PUNCT hvd.32044092008168 355 10 h₁ h₁ PROPN hvd.32044092008168 355 11 h2 h2 PROPN hvd.32044092008168 355 12 v−2+(2 v−2+(2 ADJ hvd.32044092008168 355 13 v v NOUN hvd.32044092008168 355 14 — — PUNCT hvd.32044092008168 355 15 4 4 X hvd.32044092008168 355 16 ) ) PUNCT hvd.32044092008168 355 17 h2 h2 PROPN hvd.32044092008168 355 18 h2 h2 NOUN hvd.32044092008168 356 1 v−4 v−4 ADV hvd.32044092008168 356 2 + + NOUN hvd.32044092008168 356 3 · · PUNCT hvd.32044092008168 356 4 · · PUNCT hvd.32044092008168 356 5 · · PUNCT hvd.32044092008168 356 6 +2h,−1h2=0 +2h,−1h2=0 NOUN hvd.32044092008168 356 7 . . PUNCT hvd.32044092008168 357 1 these these DET hvd.32044092008168 357 2 conditions condition NOUN hvd.32044092008168 357 3 being be AUX hvd.32044092008168 357 4 satisfied satisfied ADJ hvd.32044092008168 357 5 y y PROPN hvd.32044092008168 357 6 f(u f(u PROPN hvd.32044092008168 357 7 ) ) PUNCT hvd.32044092008168 357 8 and and CCONJ hvd.32044092008168 357 9 we we PRON hvd.32044092008168 357 10 have have VERB hvd.32044092008168 357 11 two two NUM hvd.32044092008168 357 12 ... ... PUNCT hvd.32044092008168 358 1 = = X hvd.32044092008168 358 2 då då PROPN hvd.32044092008168 358 3 f f X hvd.32044092008168 358 4 ( ( PUNCT hvd.32044092008168 358 5 u u PROPN hvd.32044092008168 358 6 ) ) PUNCT hvd.32044092008168 358 7 — — PUNCT hvd.32044092008168 358 8 [ [ X hvd.32044092008168 358 9 n n X hvd.32044092008168 358 10 ( ( PUNCT hvd.32044092008168 358 11 n n X hvd.32044092008168 358 12 + + CCONJ hvd.32044092008168 358 13 1 1 X hvd.32044092008168 358 14 ) ) PUNCT hvd.32044092008168 358 15 pu pu PROPN hvd.32044092008168 358 16 + + PROPN hvd.32044092008168 358 17 b b ADP hvd.32044092008168 358 18 ] ] X hvd.32044092008168 358 19 f f X hvd.32044092008168 358 20 ' ' PUNCT hvd.32044092008168 358 21 ( ( PUNCT hvd.32044092008168 358 22 u u PROPN hvd.32044092008168 358 23 ) ) PUNCT hvd.32044092008168 358 24 = = SYM hvd.32044092008168 358 25 0 0 NUM hvd.32044092008168 358 26 ω ω PROPN hvd.32044092008168 358 27 since since SCONJ hvd.32044092008168 358 28 finite finite NOUN hvd.32044092008168 359 1 for for ADP hvd.32044092008168 359 2 u u PROPN hvd.32044092008168 359 3 = = X hvd.32044092008168 359 4 ik ik PROPN hvd.32044092008168 359 5 ' ' PART hvd.32044092008168 359 6 = = PRON hvd.32044092008168 359 7 2 2 NUM hvd.32044092008168 359 8 = = NOUN hvd.32044092008168 359 9 = = VERB hvd.32044092008168 359 10 a a DET hvd.32044092008168 359 11 second second ADJ hvd.32044092008168 359 12 solution solution NOUN hvd.32044092008168 359 13 being be AUX hvd.32044092008168 359 14 likewise likewise ADV hvd.32044092008168 359 15 obtained obtain VERB hvd.32044092008168 359 16 by by ADP hvd.32044092008168 359 17 making make VERB hvd.32044092008168 359 18 the the DET hvd.32044092008168 359 19 substitution substitution NOUN hvd.32044092008168 359 20 n n CCONJ hvd.32044092008168 359 21 ~ ~ PUNCT hvd.32044092008168 359 22 n n CCONJ hvd.32044092008168 359 23 the the DET hvd.32044092008168 359 24 general general ADJ hvd.32044092008168 359 25 integral integral NOUN hvd.32044092008168 359 26 may may AUX hvd.32044092008168 359 27 be be AUX hvd.32044092008168 359 28 written write VERB hvd.32044092008168 359 29 : : PUNCT hvd.32044092008168 359 30 [ [ X hvd.32044092008168 359 31 37 37 NUM hvd.32044092008168 359 32 ] ] PUNCT hvd.32044092008168 359 33 · · PUNCT hvd.32044092008168 359 34 y y PROPN hvd.32044092008168 359 35 = = PROPN hvd.32044092008168 359 36 cf(u)+c'f cf(u)+c'f PROPN hvd.32044092008168 359 37 ' ' PUNCT hvd.32044092008168 359 38 ( ( PUNCT hvd.32044092008168 359 39 — — PUNCT hvd.32044092008168 359 40 u u PROPN hvd.32044092008168 359 41 ) ) PUNCT hvd.32044092008168 359 42 . . PUNCT hvd.32044092008168 360 1 part part PROPN hvd.32044092008168 360 2 iii iii PROPN hvd.32044092008168 360 3 . . PUNCT hvd.32044092008168 360 4 integral integral ADJ hvd.32044092008168 360 5 as as ADP hvd.32044092008168 360 6 a a DET hvd.32044092008168 360 7 product product NOUN hvd.32044092008168 360 8 . . PUNCT hvd.32044092008168 361 1 indirect indirect ADJ hvd.32044092008168 361 2 solution solution NOUN hvd.32044092008168 361 3 . . PUNCT hvd.32044092008168 362 1 it it PRON hvd.32044092008168 362 2 will will AUX hvd.32044092008168 362 3 be be AUX hvd.32044092008168 362 4 shown show VERB hvd.32044092008168 362 5 in in ADP hvd.32044092008168 362 6 developing develop VERB hvd.32044092008168 362 7 the the DET hvd.32044092008168 362 8 forms form NOUN hvd.32044092008168 362 9 for for ADP hvd.32044092008168 362 10 the the DET hvd.32044092008168 362 11 case case NOUN hvd.32044092008168 362 12 n n X hvd.32044092008168 362 13 = = X hvd.32044092008168 362 14 3 3 NUM hvd.32044092008168 362 15 = = SYM hvd.32044092008168 362 16 3 3 NUM hvd.32044092008168 362 17 that that SCONJ hvd.32044092008168 362 18 the the DET hvd.32044092008168 362 19 original original ADJ hvd.32044092008168 362 20 solution solution NOUN hvd.32044092008168 362 21 of of ADP hvd.32044092008168 362 22 m. m. NOUN hvd.32044092008168 362 23 hermite hermite PROPN hvd.32044092008168 362 24 as as ADP hvd.32044092008168 362 25 a a DET hvd.32044092008168 362 26 sum sum NOUN hvd.32044092008168 362 27 will will AUX hvd.32044092008168 362 28 not not PART hvd.32044092008168 362 29 be be AUX hvd.32044092008168 362 30 applicable applicable ADJ hvd.32044092008168 362 31 in in ADP hvd.32044092008168 362 32 the the DET hvd.32044092008168 362 33 forms form NOUN hvd.32044092008168 362 34 given give VERB hvd.32044092008168 362 35 in in ADP hvd.32044092008168 362 36 the the DET hvd.32044092008168 362 37 last last ADJ hvd.32044092008168 362 38 chapter chapter NOUN hvd.32044092008168 362 39 , , PUNCT hvd.32044092008168 362 40 when when SCONJ hvd.32044092008168 362 41 b b PROPN hvd.32044092008168 362 42 is be AUX hvd.32044092008168 362 43 so so ADV hvd.32044092008168 362 44 taken take VERB hvd.32044092008168 362 45 as as ADP hvd.32044092008168 362 46 to to PART hvd.32044092008168 362 47 give give VERB hvd.32044092008168 362 48 a a DET hvd.32044092008168 362 49 value value NOUN hvd.32044092008168 362 50 , , PUNCT hvd.32044092008168 362 51 v v ADP hvd.32044092008168 362 52 equal equal ADJ hvd.32044092008168 362 53 to to ADP hvd.32044092008168 362 54 zero zero NUM hvd.32044092008168 362 55 , , PUNCT hvd.32044092008168 362 56 which which PRON hvd.32044092008168 362 57 leads lead VERB hvd.32044092008168 362 58 to to ADP hvd.32044092008168 362 59 a a DET hvd.32044092008168 362 60 second second ADJ hvd.32044092008168 362 61 development development NOUN hvd.32044092008168 362 62 in in ADP hvd.32044092008168 362 63 the the DET hvd.32044092008168 362 64 form form NOUN hvd.32044092008168 362 65 of of ADP hvd.32044092008168 362 66 a a DET hvd.32044092008168 362 67 product product NOUN hvd.32044092008168 362 68 , , PUNCT hvd.32044092008168 362 69 the the DET hvd.32044092008168 362 70 eliments eliment NOUN hvd.32044092008168 362 71 being be AUX hvd.32044092008168 362 72 as as ADP hvd.32044092008168 362 73 in in ADP hvd.32044092008168 362 74 the the DET hvd.32044092008168 362 75 first first ADJ hvd.32044092008168 362 76 case case NOUN hvd.32044092008168 362 77 doubly doubly ADV hvd.32044092008168 362 78 periodic periodic ADJ hvd.32044092008168 362 79 functions function NOUN hvd.32044092008168 362 80 of of ADP hvd.32044092008168 362 81 the the DET hvd.32044092008168 362 82 second second ADJ hvd.32044092008168 362 83 species specie NOUN hvd.32044092008168 362 84 . . PUNCT hvd.32044092008168 363 1 assume assume VERB hvd.32044092008168 363 2 that that SCONJ hvd.32044092008168 363 3 o(u o(u ADJ hvd.32044092008168 363 4 + + CCONJ hvd.32044092008168 363 5 a a X hvd.32044092008168 363 6 ) ) PUNCT hvd.32044092008168 364 1 [ [ PUNCT hvd.32044092008168 364 2 38 38 NUM hvd.32044092008168 364 3 ] ] X hvd.32044092008168 364 4 : : PUNCT hvd.32044092008168 364 5 y y PROPN hvd.32044092008168 364 6 e e PROPN hvd.32044092008168 364 7 - - PROPN hvd.32044092008168 364 8 uka uka ADJ hvd.32044092008168 364 9 , , PUNCT hvd.32044092008168 364 10 o(u o(u ADJ hvd.32044092008168 364 11 ) ) PUNCT hvd.32044092008168 364 12 o o NOUN hvd.32044092008168 364 13 ( ( PUNCT hvd.32044092008168 364 14 a a X hvd.32044092008168 364 15 ) ) PUNCT hvd.32044092008168 364 16 n n NOUN hvd.32044092008168 364 17 . . PUNCT hvd.32044092008168 364 18 . . PUNCT hvd.32044092008168 365 1 ii ii PROPN hvd.32044092008168 365 2 w0 w0 PROPN hvd.32044092008168 365 3 a a DET hvd.32044092008168 365 4 = = NOUN hvd.32044092008168 365 5 a.b a.b NOUN hvd.32044092008168 365 6 .. .. X hvd.32044092008168 365 7 1 1 NUM hvd.32044092008168 365 8 2 2 NUM hvd.32044092008168 365 9 u u NOUN hvd.32044092008168 365 10 where where SCONJ hvd.32044092008168 365 11 the the DET hvd.32044092008168 365 12 product product NOUN hvd.32044092008168 365 13 is be AUX hvd.32044092008168 365 14 composed compose VERB hvd.32044092008168 365 15 of of ADP hvd.32044092008168 365 16 n n CCONJ hvd.32044092008168 365 17 factors factor NOUN hvd.32044092008168 365 18 obtained obtain VERB hvd.32044092008168 365 19 by by ADP hvd.32044092008168 365 20 taking take VERB hvd.32044092008168 365 21 a a DET hvd.32044092008168 365 22 , , PUNCT hvd.32044092008168 365 23 b b NOUN hvd.32044092008168 365 24 , , PUNCT hvd.32044092008168 365 25 c c NOUN hvd.32044092008168 365 26 in in ADP hvd.32044092008168 365 27 place place NOUN hvd.32044092008168 365 28 of of ADP hvd.32044092008168 365 29 a. a. NOUN hvd.32044092008168 365 30 the the DET hvd.32044092008168 365 31 derivative derivative NOUN hvd.32044092008168 365 32 of of ADP hvd.32044092008168 365 33 the the DET hvd.32044092008168 365 34 logarithm logarithm NOUN hvd.32044092008168 365 35 is be AUX hvd.32044092008168 365 36 y y PROPN hvd.32044092008168 365 37 ' ' PART hvd.32044092008168 365 38 p'a p'a ADJ hvd.32044092008168 365 39 15(u 15(u NUM hvd.32044092008168 365 40 + + CCONJ hvd.32044092008168 365 41 a a X hvd.32044092008168 365 42 ) ) PUNCT hvd.32044092008168 365 43 — — PUNCT hvd.32044092008168 365 44 $ $ SYM hvd.32044092008168 365 45 ( ( PUNCT hvd.32044092008168 365 46 u u NOUN hvd.32044092008168 365 47 ) ) PUNCT hvd.32044092008168 365 48 – – PUNCT hvd.32044092008168 365 49 $ $ SYM hvd.32044092008168 365 50 ( ( PUNCT hvd.32044092008168 365 51 a a NOUN hvd.32044092008168 365 52 ) ) PUNCT hvd.32044092008168 365 53 ] ] PUNCT hvd.32044092008168 366 1 = = X hvd.32044092008168 366 2 2 2 NUM hvd.32044092008168 367 1 [ [ X hvd.32044092008168 367 2 ) ) PUNCT hvd.32044092008168 367 3 ри ри ADP hvd.32044092008168 367 4 ра ра INTJ hvd.32044092008168 367 5 while while SCONJ hvd.32044092008168 367 6 a a DET hvd.32044092008168 367 7 second second ADJ hvd.32044092008168 367 8 differentiation differentiation NOUN hvd.32044092008168 367 9 gives give VERB hvd.32044092008168 367 10 y y PROPN hvd.32044092008168 367 11 " " PUNCT hvd.32044092008168 367 12 2 2 NUM hvd.32044092008168 367 13 y y PROPN hvd.32044092008168 367 14 2 2 NUM hvd.32044092008168 367 15 ( ( PUNCT hvd.32044092008168 367 16 * * PUNCT hvd.32044092008168 367 17 ) ) PUNCT hvd.32044092008168 367 18 ( ( PUNCT hvd.32044092008168 367 19 pu pu PROPN hvd.32044092008168 367 20 – – PUNCT hvd.32044092008168 367 21 p p PROPN hvd.32044092008168 367 22 ( ( PUNCT hvd.32044092008168 367 23 u u NOUN hvd.32044092008168 367 24 + + CCONJ hvd.32044092008168 367 25 a a PRON hvd.32044092008168 367 26 ) ) PUNCT hvd.32044092008168 367 27 ] ] PUNCT hvd.32044092008168 367 28 . . PUNCT hvd.32044092008168 368 1 y y NOUN hvd.32044092008168 368 2 from from ADP hvd.32044092008168 368 3 the the DET hvd.32044092008168 368 4 first first ADJ hvd.32044092008168 368 5 equation equation NOUN hvd.32044092008168 368 6 2 2 NUM hvd.32044092008168 368 7 1 1 NUM hvd.32044092008168 368 8 1 1 NUM hvd.32044092008168 368 9 [= [= X hvd.32044092008168 368 10 > > SYM hvd.32044092008168 368 11 1 1 NUM hvd.32044092008168 368 12 ( ( PUNCT hvd.32044092008168 368 13 uma uma PROPN hvd.32044092008168 368 14 ) ) PUNCT hvd.32044092008168 368 15 + + CCONJ hvd.32044092008168 368 16 -σ -σ X hvd.32044092008168 368 17 :( :( PUNCT hvd.32044092008168 368 18 + + NUM hvd.32044092008168 368 19 : : PUNCT hvd.32044092008168 368 20 σ= σ= X hvd.32044092008168 368 21 pu pu PROPN hvd.32044092008168 368 22 pu pu PROPN hvd.32044092008168 368 23 p'u p'u ADV hvd.32044092008168 368 24 – – PUNCT hvd.32044092008168 368 25 p'a p'a ADJ hvd.32044092008168 368 26 pu pu PROPN hvd.32044092008168 368 27 – – PUNCT hvd.32044092008168 368 28 p'b p'b ADV hvd.32044092008168 368 29 pu pu PROPN hvd.32044092008168 368 30 pa pa PROPN hvd.32044092008168 368 31 pu pu PROPN hvd.32044092008168 368 32 4 4 NUM hvd.32044092008168 368 33 2 2 NUM hvd.32044092008168 368 34 y y PROPN hvd.32044092008168 368 35 ра ра PROPN hvd.32044092008168 368 36 , , PUNCT hvd.32044092008168 368 37 pb pb PROPN hvd.32044092008168 369 1 but but CCONJ hvd.32044092008168 369 2 the the DET hvd.32044092008168 369 3 addition addition NOUN hvd.32044092008168 369 4 theorem theorem NOUN hvd.32044092008168 369 5 gives give VERB hvd.32044092008168 369 6 : : PUNCT hvd.32044092008168 369 7 1 1 NUM hvd.32044092008168 369 8 p'r p'r X hvd.32044092008168 369 9 p'a p'a ADJ hvd.32044092008168 369 10 ри ри INTJ hvd.32044092008168 369 11 ра ра INTJ hvd.32044092008168 369 12 p(u p(u ADJ hvd.32044092008168 369 13 + + CCONJ hvd.32044092008168 369 14 a a PRON hvd.32044092008168 370 1 + + ADJ hvd.32044092008168 370 2 pu pu PROPN hvd.32044092008168 371 1 + + PROPN hvd.32044092008168 371 2 pa pa PROPN hvd.32044092008168 371 3 , , PUNCT hvd.32044092008168 371 4 4 4 NUM hvd.32044092008168 371 5 whence whence NOUN hvd.32044092008168 371 6 2npu 2npu NUM hvd.32044092008168 371 7 + + CCONJ hvd.32044092008168 371 8 pa+ pa+ ADJ hvd.32044092008168 371 9 ; ; PUNCT hvd.32044092008168 371 10 } } PUNCT hvd.32044092008168 371 11 pu pu X hvd.32044092008168 371 12 – – PUNCT hvd.32044092008168 371 13 p'a p'a PROPN hvd.32044092008168 371 14 p’u p’u NOUN hvd.32044092008168 371 15 -po -po X hvd.32044092008168 372 1 + + PUNCT hvd.32044092008168 372 2 + + CCONJ hvd.32044092008168 372 3 p'b p'b ADV hvd.32044092008168 372 4 pb pb X hvd.32044092008168 372 5 y y X hvd.32044092008168 372 6 ри ри X hvd.32044092008168 372 7 ра ра X hvd.32044092008168 372 8 ри ри PROPN hvd.32044092008168 372 9 integral integral PROPN hvd.32044092008168 372 10 as as ADP hvd.32044092008168 372 11 a a DET hvd.32044092008168 372 12 product product NOUN hvd.32044092008168 372 13 . . PUNCT hvd.32044092008168 373 1 29 29 NUM hvd.32044092008168 373 2 2 2 NUM hvd.32044092008168 373 3 pu pu NOUN hvd.32044092008168 373 4 ра ра X hvd.32044092008168 373 5 + + PROPN hvd.32044092008168 373 6 pb pb PROPN hvd.32044092008168 373 7 in in ADP hvd.32044092008168 373 8 order order NOUN hvd.32044092008168 373 9 to to PART hvd.32044092008168 373 10 decomposé decomposé PROPN hvd.32044092008168 373 11 the the DET hvd.32044092008168 373 12 last last ADJ hvd.32044092008168 373 13 term term NOUN hvd.32044092008168 373 14 in in ADP hvd.32044092008168 373 15 this this DET hvd.32044092008168 373 16 expression expression NOUN hvd.32044092008168 373 17 we we PRON hvd.32044092008168 373 18 write write VERB hvd.32044092008168 373 19 : : PUNCT hvd.32044092008168 373 20 1 1 NUM hvd.32044092008168 373 21 p'u p'u ADV hvd.32044092008168 373 22 – – PUNCT hvd.32044092008168 373 23 p'a p'a VERB hvd.32044092008168 373 24 p'r p'r X hvd.32044092008168 373 25 p'b p'b ADJ hvd.32044092008168 373 26 2 2 X hvd.32044092008168 373 27 ( ( PUNCT hvd.32044092008168 373 28 pu pu X hvd.32044092008168 373 29 + + PROPN hvd.32044092008168 373 30 pa pa PROPN hvd.32044092008168 373 31 + + PROPN hvd.32044092008168 373 32 pb pb PROPN hvd.32044092008168 373 33 ) ) PUNCT hvd.32044092008168 373 34 ри ри PROPN hvd.32044092008168 373 35 pb pb X hvd.32044092008168 373 36 p'a p'a X hvd.32044092008168 373 37 + + CCONJ hvd.32044092008168 373 38 p'b p'b ADV hvd.32044092008168 373 39 pa pa PROPN hvd.32044092008168 373 40 po po PROPN hvd.32044092008168 373 41 15(u 15(u NUM hvd.32044092008168 373 42 + + CCONJ hvd.32044092008168 373 43 a a X hvd.32044092008168 373 44 ) ) PUNCT hvd.32044092008168 373 45 – – PUNCT hvd.32044092008168 373 46 $ $ SYM hvd.32044092008168 373 47 ( ( PUNCT hvd.32044092008168 373 48 u u NOUN hvd.32044092008168 373 49 + + CCONJ hvd.32044092008168 373 50 b b NOUN hvd.32044092008168 373 51 ) ) PUNCT hvd.32044092008168 373 52 – – PUNCT hvd.32044092008168 373 53 $ $ SYM hvd.32044092008168 373 54 u u X hvd.32044092008168 373 55 +86 +86 NOUN hvd.32044092008168 373 56 ] ] PUNCT hvd.32044092008168 373 57 . . PUNCT hvd.32044092008168 374 1 [ [ PUNCT hvd.32044092008168 374 2 & & CCONJ hvd.32044092008168 374 3 ) ) PUNCT hvd.32044092008168 374 4 take take VERB hvd.32044092008168 374 5 the the DET hvd.32044092008168 374 6 value value NOUN hvd.32044092008168 374 7 u= u= ADJ hvd.32044092008168 374 8 ( ( PUNCT hvd.32044092008168 374 9 a a DET hvd.32044092008168 374 10 + + ADJ hvd.32044092008168 374 11 b b NOUN hvd.32044092008168 374 12 ) ) PUNCT hvd.32044092008168 374 13 , , PUNCT hvd.32044092008168 374 14 remembering remember VERB hvd.32044092008168 374 15 the the DET hvd.32044092008168 374 16 relations relation NOUN hvd.32044092008168 374 17 p p PROPN hvd.32044092008168 374 18 ( ( PUNCT hvd.32044092008168 374 19 ) ) PUNCT hvd.32044092008168 374 20 + + CCONJ hvd.32044092008168 374 21 pu pu ADV hvd.32044092008168 374 22 ; ; PUNCT hvd.32044092008168 374 23 p'(-u p'(-u SPACE hvd.32044092008168 374 24 ) ) PUNCT hvd.32044092008168 374 25 – – PUNCT hvd.32044092008168 374 26 p'(u p'(u PROPN hvd.32044092008168 374 27 ) ) PUNCT hvd.32044092008168 374 28 ; ; PUNCT hvd.32044092008168 374 29 $ $ SYM hvd.32044092008168 374 30 ( ( PUNCT hvd.32044092008168 374 31 -u -u PUNCT hvd.32044092008168 374 32 ) ) PUNCT hvd.32044092008168 374 33 = = X hvd.32044092008168 374 34 $ $ SYM hvd.32044092008168 374 35 ( ( PUNCT hvd.32044092008168 374 36 u u PROPN hvd.32044092008168 374 37 ) ) PUNCT hvd.32044092008168 374 38 . . PUNCT hvd.32044092008168 375 1 — — PUNCT hvd.32044092008168 375 2 writing write VERB hvd.32044092008168 375 3 then then ADV hvd.32044092008168 375 4 f(a f(a PROPN hvd.32044092008168 375 5 + + CCONJ hvd.32044092008168 375 6 b b X hvd.32044092008168 375 7 ) ) PUNCT hvd.32044092008168 375 8 for for ADP hvd.32044092008168 375 9 the the DET hvd.32044092008168 375 10 right right ADJ hvd.32044092008168 375 11 hand hand NOUN hvd.32044092008168 375 12 member member NOUN hvd.32044092008168 375 13 of of ADP hvd.32044092008168 375 14 the the DET hvd.32044092008168 375 15 above above ADJ hvd.32044092008168 375 16 equation equation NOUN hvd.32044092008168 375 17 under under ADP hvd.32044092008168 375 18 these these DET hvd.32044092008168 375 19 conditions condition NOUN hvd.32044092008168 375 20 we we PRON hvd.32044092008168 375 21 get get VERB hvd.32044092008168 375 22 f(a f(a PROPN hvd.32044092008168 375 23 + + CCONJ hvd.32044092008168 375 24 b b X hvd.32044092008168 375 25 ) ) PUNCT hvd.32044092008168 375 26 = = NOUN hvd.32044092008168 375 27 2np(a 2np(a NUM hvd.32044092008168 375 28 + + CCONJ hvd.32044092008168 375 29 b b X hvd.32044092008168 375 30 ) ) PUNCT hvd.32044092008168 375 31 + + CCONJ hvd.32044092008168 375 32 epa epa PROPN hvd.32044092008168 376 1 + + CCONJ hvd.32044092008168 376 2 2p(a 2p(a NOUN hvd.32044092008168 376 3 + + CCONJ hvd.32044092008168 376 4 b b X hvd.32044092008168 376 5 ) ) PUNCT hvd.32044092008168 376 6 + + CCONJ hvd.32044092008168 377 1 pa pa PROPN hvd.32044092008168 377 2 + + CCONJ hvd.32044092008168 377 3 pb pb X hvd.32044092008168 377 4 ) ) PUNCT hvd.32044092008168 377 5 + + CCONJ hvd.32044092008168 377 6 p'a p'a ADJ hvd.32044092008168 378 1 + + CCONJ hvd.32044092008168 378 2 p'b p'b ADJ hvd.32044092008168 378 3 [ [ X hvd.32044092008168 378 4 $ $ SYM hvd.32044092008168 378 5 ( ( PUNCT hvd.32044092008168 378 6 -6 -6 PROPN hvd.32044092008168 378 7 ) ) PUNCT hvd.32044092008168 378 8 $ $ SYM hvd.32044092008168 378 9 ( ( PUNCT hvd.32044092008168 378 10 -a -a NOUN hvd.32044092008168 378 11 ) ) PUNCT hvd.32044092008168 378 12 – – PUNCT hvd.32044092008168 378 13 $ $ SYM hvd.32044092008168 378 14 a a PRON hvd.32044092008168 378 15 + + NUM hvd.32044092008168 378 16 $ $ SYM hvd.32044092008168 378 17 b b NOUN hvd.32044092008168 378 18 ] ] X hvd.32044092008168 378 19 pa pa PROPN hvd.32044092008168 378 20 pb pb PROPN hvd.32044092008168 378 21 2 2 NUM hvd.32044092008168 378 22 ( ( PUNCT hvd.32044092008168 378 23 n n CCONJ hvd.32044092008168 378 24 + + CCONJ hvd.32044092008168 378 25 1 1 X hvd.32044092008168 378 26 ) ) PUNCT hvd.32044092008168 378 27 pu pu PROPN hvd.32044092008168 378 28 + + PROPN hvd.32044092008168 378 29 2 2 NUM hvd.32044092008168 378 30 epa epa PROPN hvd.32044092008168 378 31 . . PUNCT hvd.32044092008168 379 1 from from ADP hvd.32044092008168 379 2 which which PRON hvd.32044092008168 379 3 we we PRON hvd.32044092008168 379 4 see see VERB hvd.32044092008168 379 5 that that SCONJ hvd.32044092008168 379 6 in in ADP hvd.32044092008168 379 7 general general ADJ hvd.32044092008168 379 8 we we PRON hvd.32044092008168 379 9 would would AUX hvd.32044092008168 379 10 have have VERB hvd.32044092008168 379 11 y y PROPN hvd.32044092008168 379 12 " " PUNCT hvd.32044092008168 379 13 = = PROPN hvd.32044092008168 379 14 n(n n(n PROPN hvd.32044092008168 379 15 + + CCONJ hvd.32044092008168 379 16 1)pu 1)pu PROPN hvd.32044092008168 379 17 + + CCONJ hvd.32044092008168 379 18 ( ( PUNCT hvd.32044092008168 380 1 2n 2n NUM hvd.32044092008168 380 2 — — PUNCT hvd.32044092008168 380 3 1 1 X hvd.32044092008168 380 4 ) ) PUNCT hvd.32044092008168 380 5 epa epa PROPN hvd.32044092008168 380 6 у у PROPN hvd.32044092008168 380 7 a a PRON hvd.32044092008168 380 8 ; ; PUNCT hvd.32044092008168 380 9 p'a p'a ADJ hvd.32044092008168 380 10 = = X hvd.32044092008168 380 11 oc oc VERB hvd.32044092008168 380 12 the the DET hvd.32044092008168 380 13 quantity quantity NOUN hvd.32044092008168 380 14 in in ADP hvd.32044092008168 380 15 brackets bracket NOUN hvd.32044092008168 380 16 being be AUX hvd.32044092008168 380 17 equal equal ADJ hvd.32044092008168 380 18 to to ADP hvd.32044092008168 380 19 zero zero NUM hvd.32044092008168 380 20 . . PUNCT hvd.32044092008168 381 1 if if SCONJ hvd.32044092008168 381 2 now now ADV hvd.32044092008168 381 3 we we PRON hvd.32044092008168 381 4 reunite reunite VERB hvd.32044092008168 381 5 the the DET hvd.32044092008168 381 6 terms term NOUN hvd.32044092008168 381 7 $ $ SYM hvd.32044092008168 381 8 ( ( PUNCT hvd.32044092008168 381 9 u u PROPN hvd.32044092008168 381 10 + + CCONJ hvd.32044092008168 381 11 a a PRON hvd.32044092008168 381 12 ) ) PUNCT hvd.32044092008168 381 13 — — PUNCT hvd.32044092008168 381 14 & & CCONJ hvd.32044092008168 381 15 a a DET hvd.32044092008168 381 16 , , PUNCT hvd.32044092008168 381 17 $ $ SYM hvd.32044092008168 381 18 ( ( PUNCT hvd.32044092008168 381 19 u u NOUN hvd.32044092008168 381 20 + + NUM hvd.32044092008168 381 21 b b NOUN hvd.32044092008168 381 22 ) ) PUNCT hvd.32044092008168 381 23 – – PUNCT hvd.32044092008168 381 24 $ $ SYM hvd.32044092008168 381 25 b b X hvd.32044092008168 381 26 etc etc X hvd.32044092008168 381 27 . . X hvd.32044092008168 382 1 ( ( PUNCT hvd.32044092008168 382 2 in in ADP hvd.32044092008168 382 3 the the DET hvd.32044092008168 382 4 general general ADJ hvd.32044092008168 382 5 expression expression NOUN hvd.32044092008168 382 6 and and CCONJ hvd.32044092008168 382 7 make make VERB hvd.32044092008168 382 8 equal equal ADJ hvd.32044092008168 382 9 to to ADP hvd.32044092008168 382 10 zero zero NUM hvd.32044092008168 382 11 the the DET hvd.32044092008168 382 12 sum sum NOUN hvd.32044092008168 382 13 of of ADP hvd.32044092008168 382 14 their their PRON hvd.32044092008168 382 15 coefficients coefficient NOUN hvd.32044092008168 382 16 we we PRON hvd.32044092008168 382 17 obtain obtain VERB hvd.32044092008168 382 18 n n ADP hvd.32044092008168 382 19 equations equation NOUN hvd.32044092008168 382 20 of of ADP hvd.32044092008168 382 21 condition condition NOUN hvd.32044092008168 382 22 , , PUNCT hvd.32044092008168 382 23 namely namely ADV hvd.32044092008168 382 24 , , PUNCT hvd.32044092008168 382 25 writing write VERB hvd.32044092008168 382 26 ра ра ADP hvd.32044092008168 382 27 a a PRON hvd.32044092008168 382 28 ' ' NOUN hvd.32044092008168 382 29 ; ; PUNCT hvd.32044092008168 382 30 pb pb X hvd.32044092008168 382 31 = = PROPN hvd.32044092008168 382 32 b b PROPN hvd.32044092008168 382 33 ; ; PUNCT hvd.32044092008168 382 34 p'b p'b ADJ hvd.32044092008168 382 35 = = X hvd.32044092008168 382 36 b b ADP hvd.32044092008168 382 37 ' ' PUNCT hvd.32044092008168 382 38 ; ; PUNCT hvd.32044092008168 382 39 a a DET hvd.32044092008168 382 40 ' ' PUNCT hvd.32044092008168 382 41 + + CCONJ hvd.32044092008168 382 42 b b X hvd.32044092008168 382 43 ' ' PUNCT hvd.32044092008168 382 44 d'+y d'+y SPACE hvd.32044092008168 382 45 ' ' PUNCT hvd.32044092008168 382 46 a a DET hvd.32044092008168 382 47 ' ' PUNCT hvd.32044092008168 382 48 + + CCONJ hvd.32044092008168 382 49 d d X hvd.32044092008168 382 50 ' ' PUNCT hvd.32044092008168 382 51 + + NUM hvd.32044092008168 382 52 0 0 NUM hvd.32044092008168 382 53 в в PROPN hvd.32044092008168 382 54 b b NOUN hvd.32044092008168 382 55 ' ' PUNCT hvd.32044092008168 382 56 t. t. X hvd.32044092008168 382 57 a a DET hvd.32044092008168 382 58 b b NOUN hvd.32044092008168 382 59 ' ' PUNCT hvd.32044092008168 382 60 + + NUM hvd.32044092008168 382 61 g g NOUN hvd.32044092008168 382 62 ' ' PART hvd.32044092008168 382 63 ß ß NOUN hvd.32044092008168 382 64 ' ' PUNCT hvd.32044092008168 382 65 td td NOUN hvd.32044092008168 383 1 + + CCONJ hvd.32044092008168 383 2 + + NUM hvd.32044092008168 383 3 + + PUNCT hvd.32044092008168 383 4 0 0 NUM hvd.32044092008168 383 5 b b X hvd.32044092008168 383 6 b b X hvd.32044092008168 383 7 b b X hvd.32044092008168 383 8 g g NOUN hvd.32044092008168 383 9 ' ' PUNCT hvd.32044092008168 383 10 to to PART hvd.32044092008168 383 11 ' ' PUNCT hvd.32044092008168 383 12 y y NOUN hvd.32044092008168 383 13 ' ' PUNCT hvd.32044092008168 383 14 + + CCONJ hvd.32044092008168 383 15 b b ADP hvd.32044092008168 383 16 ' ' PUNCT hvd.32044092008168 383 17 y y NOUN hvd.32044092008168 383 18 ' ' PUNCT hvd.32044092008168 383 19 + + ADJ hvd.32044092008168 383 20 d d X hvd.32044092008168 384 1 + + PUNCT hvd.32044092008168 384 2 + + NUM hvd.32044092008168 384 3 0 0 NUM hvd.32044092008168 384 4 b b NOUN hvd.32044092008168 384 5 . . PUNCT hvd.32044092008168 385 1 + + PUNCT hvd.32044092008168 386 1 + + CCONJ hvd.32044092008168 386 2 α α X hvd.32044092008168 386 3 q q X hvd.32044092008168 386 4 n n CCONJ hvd.32044092008168 386 5 oc oc X hvd.32044092008168 386 6 d d X hvd.32044092008168 386 7 [ [ X hvd.32044092008168 386 8 39 39 NUM hvd.32044092008168 386 9 ] ] PUNCT hvd.32044092008168 386 10 a a DET hvd.32044092008168 386 11 d d NOUN hvd.32044092008168 386 12 . . PUNCT hvd.32044092008168 387 1 + + PUNCT hvd.32044092008168 387 2 g g NOUN hvd.32044092008168 387 3 a a DET hvd.32044092008168 387 4 7 7 NUM hvd.32044092008168 387 5 g g NOUN hvd.32044092008168 387 6 d d NOUN hvd.32044092008168 387 7 12 12 NUM hvd.32044092008168 387 8 oc oc NOUN hvd.32044092008168 388 1 [ [ X hvd.32044092008168 388 2 40 40 NUM hvd.32044092008168 388 3 ] ] PUNCT hvd.32044092008168 388 4 93 93 NUM hvd.32044092008168 388 5 if if SCONJ hvd.32044092008168 388 6 then then ADV hvd.32044092008168 388 7 we we PRON hvd.32044092008168 388 8 can can AUX hvd.32044092008168 388 9 solve solve VERB hvd.32044092008168 388 10 the the DET hvd.32044092008168 388 11 equations equation NOUN hvd.32044092008168 388 12 considered consider VERB hvd.32044092008168 388 13 as as ADP hvd.32044092008168 388 14 simultanious simultanious ADJ hvd.32044092008168 388 15 403 403 NUM hvd.32044092008168 388 16 920 920 NUM hvd.32044092008168 388 17 93 93 NUM hvd.32044092008168 388 18 b'2 b'2 NUM hvd.32044092008168 388 19 483 483 NUM hvd.32044092008168 388 20 — — PUNCT hvd.32044092008168 388 21 92b 92b NOUN hvd.32044092008168 388 22 together together ADV hvd.32044092008168 388 23 with with ADP hvd.32044092008168 388 24 the the DET hvd.32044092008168 388 25 relation relation NOUN hvd.32044092008168 388 26 ( ( PUNCT hvd.32044092008168 388 27 2n 2n NUM hvd.32044092008168 388 28 — — PUNCT hvd.32044092008168 388 29 1)(a 1)(a NUM hvd.32044092008168 388 30 + + PUNCT hvd.32044092008168 388 31 b b X hvd.32044092008168 388 32 + + PUNCT hvd.32044092008168 388 33 y y NOUN hvd.32044092008168 389 1 + + CCONJ hvd.32044092008168 389 2 :) :) PUNCT hvd.32044092008168 390 1 в в PUNCT hvd.32044092008168 390 2 we we PRON hvd.32044092008168 390 3 will will AUX hvd.32044092008168 390 4 satisfy satisfy VERB hvd.32044092008168 390 5 the the DET hvd.32044092008168 390 6 necessary necessary ADJ hvd.32044092008168 390 7 conditions condition NOUN hvd.32044092008168 390 8 to to PART hvd.32044092008168 390 9 enable enable VERB hvd.32044092008168 390 10 us we PRON hvd.32044092008168 390 11 to to PART hvd.32044092008168 390 12 write write VERB hvd.32044092008168 390 13 : : PUNCT hvd.32044092008168 390 14 y y PROPN hvd.32044092008168 390 15 " " PUNCT hvd.32044092008168 390 16 = = PROPN hvd.32044092008168 390 17 n(n n(n PROPN hvd.32044092008168 390 18 + + CCONJ hvd.32044092008168 390 19 1)pu 1)pu PROPN hvd.32044092008168 390 20 + + SYM hvd.32044092008168 391 1 b. b. PROPN hvd.32044092008168 391 2 y y PROPN hvd.32044092008168 391 3 30 30 NUM hvd.32044092008168 391 4 part part NOUN hvd.32044092008168 391 5 iii iii NUM hvd.32044092008168 391 6 . . PUNCT hvd.32044092008168 392 1 y= y= X hvd.32044092008168 393 1 e e PROPN hvd.32044092008168 393 2 - - NOUN hvd.32044092008168 393 3 uta uta PROPN hvd.32044092008168 393 4 that that PRON hvd.32044092008168 393 5 is be AUX hvd.32044092008168 393 6 6(u 6(u NUM hvd.32044092008168 393 7 + + CCONJ hvd.32044092008168 393 8 a a X hvd.32044092008168 393 9 ) ) PUNCT hvd.32044092008168 393 10 y y NOUN hvd.32044092008168 393 11 it it PRON hvd.32044092008168 393 12 6 6 NUM hvd.32044092008168 393 13 ( ( PUNCT hvd.32044092008168 393 14 u u NOUN hvd.32044092008168 393 15 ) ) PUNCT hvd.32044092008168 393 16 o o NOUN hvd.32044092008168 393 17 ( ( PUNCT hvd.32044092008168 393 18 a a X hvd.32044092008168 393 19 ) ) PUNCT hvd.32044092008168 393 20 is be AUX hvd.32044092008168 393 21 a a DET hvd.32044092008168 393 22 solution solution NOUN hvd.32044092008168 393 23 of of ADP hvd.32044092008168 393 24 hermite hermite PROPN hvd.32044092008168 393 25 's 's PART hvd.32044092008168 393 26 equation equation NOUN hvd.32044092008168 393 27 whatever whatever PRON hvd.32044092008168 393 28 be be VERB hvd.32044092008168 393 29 the the DET hvd.32044092008168 393 30 value value NOUN hvd.32044092008168 393 31 of of ADP hvd.32044092008168 393 32 b b NUM hvd.32044092008168 393 33 , , PUNCT hvd.32044092008168 393 34 provided provide VERB hvd.32044092008168 393 35 a a PRON hvd.32044092008168 393 36 , , PUNCT hvd.32044092008168 393 37 b b NOUN hvd.32044092008168 393 38 , , PUNCT hvd.32044092008168 393 39 c c X hvd.32044092008168 393 40 .. .. PUNCT hvd.32044092008168 393 41 fulfil fulfil VERB hvd.32044092008168 393 42 the the DET hvd.32044092008168 393 43 above above ADJ hvd.32044092008168 393 44 conditions condition NOUN hvd.32044092008168 393 45 . . PUNCT hvd.32044092008168 394 1 solution solution NOUN hvd.32044092008168 394 2 for for ADP hvd.32044092008168 394 3 n n CCONJ hvd.32044092008168 394 4 = = SYM hvd.32044092008168 394 5 2 2 X hvd.32044092008168 394 6 . . X hvd.32044092008168 395 1 it it PRON hvd.32044092008168 395 2 is be AUX hvd.32044092008168 395 3 clear clear ADJ hvd.32044092008168 395 4 that that SCONJ hvd.32044092008168 395 5 , , PUNCT hvd.32044092008168 395 6 save save VERB hvd.32044092008168 395 7 for for ADP hvd.32044092008168 395 8 small small ADJ hvd.32044092008168 395 9 values value NOUN hvd.32044092008168 395 10 of of ADP hvd.32044092008168 395 11 n n NOUN hvd.32044092008168 395 12 , , PUNCT hvd.32044092008168 395 13 an an DET hvd.32044092008168 395 14 attempt attempt NOUN hvd.32044092008168 395 15 to to PART hvd.32044092008168 395 16 solve solve VERB hvd.32044092008168 395 17 the the DET hvd.32044092008168 395 18 above above ADJ hvd.32044092008168 395 19 equations equation NOUN hvd.32044092008168 395 20 by by ADP hvd.32044092008168 395 21 the the DET hvd.32044092008168 395 22 ordinary ordinary ADJ hvd.32044092008168 395 23 methods method NOUN hvd.32044092008168 395 24 would would AUX hvd.32044092008168 395 25 give give VERB hvd.32044092008168 395 26 rise rise NOUN hvd.32044092008168 395 27 to to ADP hvd.32044092008168 395 28 insurmountable insurmountable ADJ hvd.32044092008168 395 29 difficulties difficulty NOUN hvd.32044092008168 395 30 . . PUNCT hvd.32044092008168 396 1 the the DET hvd.32044092008168 396 2 case case NOUN hvd.32044092008168 396 3 n=2 n=2 VERB hvd.32044092008168 396 4 however however ADV hvd.32044092008168 396 5 , , PUNCT hvd.32044092008168 396 6 which which PRON hvd.32044092008168 396 7 is be AUX hvd.32044092008168 396 8 famous famous ADJ hvd.32044092008168 396 9 = = NOUN hvd.32044092008168 396 10 as as ADP hvd.32044092008168 396 11 affording afford VERB hvd.32044092008168 396 12 a a DET hvd.32044092008168 396 13 solution solution NOUN hvd.32044092008168 396 14 to to ADP hvd.32044092008168 396 15 the the DET hvd.32044092008168 396 16 problem problem NOUN hvd.32044092008168 396 17 of of ADP hvd.32044092008168 396 18 a a DET hvd.32044092008168 396 19 pendulum pendulum NOUN hvd.32044092008168 396 20 , , PUNCT hvd.32044092008168 396 21 constrained constrain VERB hvd.32044092008168 396 22 to to PART hvd.32044092008168 396 23 move move VERB hvd.32044092008168 396 24 upon upon SCONJ hvd.32044092008168 396 25 a a DET hvd.32044092008168 396 26 sphere sphere NOUN hvd.32044092008168 396 27 , , PUNCT hvd.32044092008168 396 28 can can AUX hvd.32044092008168 396 29 be be AUX hvd.32044092008168 396 30 readily readily ADV hvd.32044092008168 396 31 solved solve VERB hvd.32044092008168 396 32 as as SCONJ hvd.32044092008168 396 33 follows follow VERB hvd.32044092008168 396 34 : : PUNCT hvd.32044092008168 396 35 given give VERB hvd.32044092008168 396 36 n n CCONJ hvd.32044092008168 396 37 = = SYM hvd.32044092008168 396 38 2 2 NUM hvd.32044092008168 396 39 : : PUNCT hvd.32044092008168 396 40 we we PRON hvd.32044092008168 396 41 have have VERB hvd.32044092008168 396 42 the the DET hvd.32044092008168 396 43 conditions condition NOUN hvd.32044092008168 396 44 12 12 NUM hvd.32044092008168 396 45 a a DET hvd.32044092008168 396 46 12 12 NUM hvd.32044092008168 397 1 [ [ X hvd.32044092008168 397 2 41 41 NUM hvd.32044092008168 397 3 ] ] PUNCT hvd.32044092008168 397 4 [ [ PUNCT hvd.32044092008168 397 5 p'?a= p'?a= NOUN hvd.32044092008168 397 6 4ą% 4ą% NUM hvd.32044092008168 397 7 92a 92a NUM hvd.32044092008168 397 8 93 93 NUM hvd.32044092008168 397 9 b'2 b'2 NUM hvd.32044092008168 397 10 483 483 NUM hvd.32044092008168 397 11 – – PUNCT hvd.32044092008168 397 12 92b 92b NUM hvd.32044092008168 397 13 – – PUNCT hvd.32044092008168 397 14 9 9 NUM hvd.32044092008168 397 15 : : PUNCT hvd.32044092008168 397 16 pa pa PROPN hvd.32044092008168 397 17 + + CCONJ hvd.32044092008168 397 18 pb pb X hvd.32044092008168 397 19 = = PROPN hvd.32044092008168 397 20 b b PROPN hvd.32044092008168 397 21 b b NOUN hvd.32044092008168 397 22 a a NOUN hvd.32044092008168 397 23 ' ' NOUN hvd.32044092008168 397 24 ? ? PUNCT hvd.32044092008168 398 1 + + CCONJ hvd.32044092008168 398 2 b b ADP hvd.32044092008168 398 3 ’ ' PUNCT hvd.32044092008168 398 4 ? ? PUNCT hvd.32044092008168 399 1 = = SYM hvd.32044092008168 399 2 0 0 X hvd.32044092008168 399 3 . . PUNCT hvd.32044092008168 400 1 p'26 p'26 NOUN hvd.32044092008168 400 2 1 1 NUM hvd.32044092008168 400 3 2 2 NUM hvd.32044092008168 400 4 or or CCONJ hvd.32044092008168 400 5 3 3 NUM hvd.32044092008168 400 6 observe observe VERB hvd.32044092008168 400 7 that that SCONJ hvd.32044092008168 400 8 by by ADP hvd.32044092008168 400 9 designating designate VERB hvd.32044092008168 400 10 pb pb PROPN hvd.32044092008168 400 11 by by ADP hvd.32044092008168 400 12 — — PUNCT hvd.32044092008168 400 13 b b X hvd.32044092008168 400 14 the the DET hvd.32044092008168 400 15 above above ADJ hvd.32044092008168 400 16 relations relation NOUN hvd.32044092008168 400 17 remain remain VERB hvd.32044092008168 400 18 unaltered unaltered ADJ hvd.32044092008168 400 19 and and CCONJ hvd.32044092008168 400 20 that that SCONJ hvd.32044092008168 400 21 we we PRON hvd.32044092008168 400 22 may may AUX hvd.32044092008168 400 23 therefore therefore ADV hvd.32044092008168 400 24 write write VERB hvd.32044092008168 400 25 403 403 NUM hvd.32044092008168 400 26 92a 92a NUM hvd.32044092008168 400 27 93 93 NUM hvd.32044092008168 400 28 48 48 NUM hvd.32044092008168 400 29 % % NOUN hvd.32044092008168 400 30 + + CCONJ hvd.32044092008168 400 31 92b 92b NUM hvd.32044092008168 400 32 — — PUNCT hvd.32044092008168 400 33 93 93 NUM hvd.32044092008168 400 34 or or CCONJ hvd.32044092008168 400 35 4 4 NUM hvd.32044092008168 400 36 ( ( PUNCT hvd.32044092008168 400 37 a+ a+ PUNCT hvd.32044092008168 400 38 ) ) PUNCT hvd.32044092008168 400 39 92(a 92(a NUM hvd.32044092008168 401 1 + + NUM hvd.32044092008168 401 2 b b X hvd.32044092008168 401 3 ) ) PUNCT hvd.32044092008168 401 4 = = PROPN hvd.32044092008168 401 5 0 0 NUM hvd.32044092008168 401 6 ) ) PUNCT hvd.32044092008168 401 7 . . PUNCT hvd.32044092008168 402 1 whence whence ADV hvd.32044092008168 402 2 ? ? PUNCT hvd.32044092008168 402 3 – – PUNCT hvd.32044092008168 403 1 αβ αβ NOUN hvd.32044092008168 403 2 + + CCONJ hvd.32044092008168 403 3 β2 β2 ADJ hvd.32044092008168 403 4 a a PRON hvd.32044092008168 403 5 ? ? PUNCT hvd.32044092008168 404 1 — — PUNCT hvd.32044092008168 404 2 « « PUNCT hvd.32044092008168 404 3 ß ß NOUN hvd.32044092008168 404 4 + + CCONJ hvd.32044092008168 404 5 b2 b2 PROPN hvd.32044092008168 404 6 – – PUNCT hvd.32044092008168 404 7 192 192 NUM hvd.32044092008168 404 8 = = SYM hvd.32044092008168 404 9 0 0 NUM hvd.32044092008168 404 10 . . PUNCT hvd.32044092008168 404 11 = = PUNCT hvd.32044092008168 405 1 but but CCONJ hvd.32044092008168 405 2 b b X hvd.32044092008168 405 3 = = NOUN hvd.32044092008168 405 4 a a PRON hvd.32044092008168 405 5 -b -b PUNCT hvd.32044092008168 405 6 whence whence ADP hvd.32044092008168 405 7 the the DET hvd.32044092008168 405 8 equation equation NOUN hvd.32044092008168 405 9 that that PRON hvd.32044092008168 405 10 determines determine VERB hvd.32044092008168 405 11 the the DET hvd.32044092008168 405 12 values value NOUN hvd.32044092008168 405 13 of of ADP hvd.32044092008168 405 14 b. b. PROPN hvd.32044092008168 406 1 [ [ X hvd.32044092008168 406 2 42 42 NUM hvd.32044092008168 406 3 ] ] PUNCT hvd.32044092008168 406 4 : : PUNCT hvd.32044092008168 406 5 · · PUNCT hvd.32044092008168 406 6 bº bº ADP hvd.32044092008168 406 7 – – PUNCT hvd.32044092008168 406 8 ja ja PROPN hvd.32044092008168 406 9 b b PROPN hvd.32044092008168 406 10 + + NOUN hvd.32044092008168 406 11 a a NOUN hvd.32044092008168 406 12 ? ? PUNCT hvd.32044092008168 406 13 — — PUNCT hvd.32044092008168 406 14 192 192 NUM hvd.32044092008168 406 15 = = SYM hvd.32044092008168 406 16 0 0 NUM hvd.32044092008168 406 17 and and CCONJ hvd.32044092008168 406 18 also also ADV hvd.32044092008168 406 19 b2 b2 PROPN hvd.32044092008168 406 20 şa şa PROPN hvd.32044092008168 406 21 o o PROPN hvd.32044092008168 406 22 and and CCONJ hvd.32044092008168 406 23 also also ADV hvd.32044092008168 406 24 b=0 b=0 ADV hvd.32044092008168 406 25 . . PUNCT hvd.32044092008168 406 26 * * PUNCT hvd.32044092008168 406 27 ) ) PUNCT hvd.32044092008168 406 28 if if SCONJ hvd.32044092008168 406 29 then then ADV hvd.32044092008168 406 30 n= n= ADJ hvd.32044092008168 406 31 2 2 NUM hvd.32044092008168 406 32 and and CCONJ hvd.32044092008168 406 33 a a PRON hvd.32044092008168 406 34 and and CCONJ hvd.32044092008168 406 35 b b NOUN hvd.32044092008168 406 36 , , PUNCT hvd.32044092008168 406 37 the the DET hvd.32044092008168 406 38 arguments argument NOUN hvd.32044092008168 406 39 of of ADP hvd.32044092008168 406 40 a=(pag a=(pag PROPN hvd.32044092008168 406 41 ) ) PUNCT hvd.32044092008168 406 42 , , PUNCT hvd.32044092008168 406 43 ( ( PUNCT hvd.32044092008168 406 44 , , PUNCT hvd.32044092008168 406 45 are be AUX hvd.32044092008168 406 46 so so ADV hvd.32044092008168 406 47 taken take VERB hvd.32044092008168 406 48 that that SCONJ hvd.32044092008168 406 49 b b NOUN hvd.32044092008168 406 50 shall shall AUX hvd.32044092008168 406 51 have have VERB hvd.32044092008168 406 52 the the DET hvd.32044092008168 406 53 values value NOUN hvd.32044092008168 406 54 of of ADP hvd.32044092008168 406 55 the the DET hvd.32044092008168 406 56 roots root NOUN hvd.32044092008168 406 57 of of ADP hvd.32044092008168 406 58 equation equation NOUN hvd.32044092008168 406 59 ( ( PUNCT hvd.32044092008168 406 60 42 42 NUM hvd.32044092008168 406 61 ) ) PUNCT hvd.32044092008168 406 62 hermite hermite PROPN hvd.32044092008168 406 63 's 's PART hvd.32044092008168 406 64 equation equation NOUN hvd.32044092008168 406 65 will will AUX hvd.32044092008168 406 66 have have VERB hvd.32044092008168 406 67 the the DET hvd.32044092008168 406 68 solution solution NOUN hvd.32044092008168 406 69 1 1 NUM hvd.32044092008168 406 70 . . PUNCT hvd.32044092008168 407 1 9 9 NUM hvd.32044092008168 407 2 4 4 NUM hvd.32044092008168 407 3 1 1 NUM hvd.32044092008168 407 4 * * PUNCT hvd.32044092008168 407 5 ) ) PUNCT hvd.32044092008168 407 6 if if SCONJ hvd.32044092008168 407 7 in in ADP hvd.32044092008168 407 8 this this DET hvd.32044092008168 407 9 result result NOUN hvd.32044092008168 407 10 we we PRON hvd.32044092008168 407 11 take take VERB hvd.32044092008168 407 12 b b PROPN hvd.32044092008168 407 13 ś ś ADP hvd.32044092008168 407 14 we we PRON hvd.32044092008168 407 15 obtain obtain VERB hvd.32044092008168 407 16 the the DET hvd.32044092008168 407 17 formula formula NOUN hvd.32044092008168 407 18 3 3 NUM hvd.32044092008168 407 19 & & CCONJ hvd.32044092008168 407 20 2 2 NUM hvd.32044092008168 407 21 — — PUNCT hvd.32044092008168 407 22 as as ADP hvd.32044092008168 407 23 ta ta NOUN hvd.32044092008168 407 24 ? ? PUNCT hvd.32044092008168 408 1 1 1 NUM hvd.32044092008168 408 2 92 92 NUM hvd.32044092008168 408 3 4 4 NUM hvd.32044092008168 408 4 0 0 NUM hvd.32044092008168 408 5 , , PUNCT hvd.32044092008168 408 6 see see VERB hvd.32044092008168 408 7 halphen halphen PROPN hvd.32044092008168 409 1 ii ii PROPN hvd.32044092008168 409 2 p. p. PROPN hvd.32044092008168 409 3 131 131 NUM hvd.32044092008168 409 4 . . PUNCT hvd.32044092008168 410 1 integral integral ADJ hvd.32044092008168 410 2 as as ADP hvd.32044092008168 410 3 a a DET hvd.32044092008168 410 4 product product NOUN hvd.32044092008168 410 5 . . PUNCT hvd.32044092008168 411 1 31 31 NUM hvd.32044092008168 411 2 o(u o(u PROPN hvd.32044092008168 411 3 — — PUNCT hvd.32044092008168 411 4 a a X hvd.32044092008168 411 5 ) ) PUNCT hvd.32044092008168 411 6 o o NOUN hvd.32044092008168 411 7 ( ( PUNCT hvd.32044092008168 411 8 u u NOUN hvd.32044092008168 411 9 + + CCONJ hvd.32044092008168 411 10 b b X hvd.32044092008168 411 11 ) ) PUNCT hvd.32044092008168 411 12 [ [ X hvd.32044092008168 411 13 43 43 NUM hvd.32044092008168 411 14 ] ] PUNCT hvd.32044092008168 411 15 · · PUNCT hvd.32044092008168 411 16 y y PROPN hvd.32044092008168 411 17 = = PROPN hvd.32044092008168 411 18 elta6u elta6u X hvd.32044092008168 411 19 cou cou PROPN hvd.32044092008168 411 20 a a PRON hvd.32044092008168 411 21 + + PROPN hvd.32044092008168 411 22 b b X hvd.32044092008168 411 23 ) ) PUNCT hvd.32044092008168 411 24 c c X hvd.32044092008168 411 25 elša–5)u elša–5)u PROPN hvd.32044092008168 411 26 ] ] PUNCT hvd.32044092008168 411 27 du du PROPN hvd.32044092008168 411 28 би би X hvd.32044092008168 411 29 c c NOUN hvd.32044092008168 411 30 ' ' PUNCT hvd.32044092008168 411 31 los los NOUN hvd.32044092008168 411 32 a a PRON hvd.32044092008168 412 1 so so ADV hvd.32044092008168 412 2 ( ( PUNCT hvd.32044092008168 412 3 u u NOUN hvd.32044092008168 412 4 + + CCONJ hvd.32044092008168 412 5 » » NOUN hvd.32044092008168 412 6 ) ) PUNCT hvd.32044092008168 412 7 ere–50 ere–50 PROPN hvd.32044092008168 412 8 ) ) PUNCT hvd.32044092008168 412 9 ] ] PUNCT hvd.32044092008168 413 1 d d NOUN hvd.32044092008168 413 2 [ [ X hvd.32044092008168 413 3 šv šv X hvd.32044092008168 413 4 ) ) PUNCT hvd.32044092008168 413 5 du du PROPN hvd.32044092008168 413 6 6u 6u PROPN hvd.32044092008168 413 7 6 6 NUM hvd.32044092008168 413 8 u u PROPN hvd.32044092008168 413 9 where where SCONJ hvd.32044092008168 413 10 v v ADP hvd.32044092008168 413 11 = = PUNCT hvd.32044092008168 413 12 a a PRON hvd.32044092008168 413 13 + + PROPN hvd.32044092008168 413 14 b. b. NOUN hvd.32044092008168 413 15 * * PUNCT hvd.32044092008168 413 16 ) ) PUNCT hvd.32044092008168 413 17 that that SCONJ hvd.32044092008168 413 18 our our PRON hvd.32044092008168 413 19 solution solution NOUN hvd.32044092008168 413 20 given give VERB hvd.32044092008168 413 21 above above ADV hvd.32044092008168 413 22 be be AUX hvd.32044092008168 413 23 complete complete ADJ hvd.32044092008168 413 24 we we PRON hvd.32044092008168 413 25 must must AUX hvd.32044092008168 413 26 obtain obtain VERB hvd.32044092008168 413 27 the the DET hvd.32044092008168 413 28 corresponding corresponding ADJ hvd.32044092008168 413 29 values value NOUN hvd.32044092008168 413 30 of of ADP hvd.32044092008168 413 31 x x SYM hvd.32044092008168 413 32 and and CCONJ hvd.32044092008168 413 33 v v NOUN hvd.32044092008168 413 34 as as SCONJ hvd.32044092008168 413 35 follows follow VERB hvd.32044092008168 413 36 : : PUNCT hvd.32044092008168 413 37 d d PROPN hvd.32044092008168 413 38 co co PROPN hvd.32044092008168 413 39 ( ( PUNCT hvd.32044092008168 413 40 u u PROPN hvd.32044092008168 413 41 + + CCONJ hvd.32044092008168 413 42 v v NOUN hvd.32044092008168 413 43 ) ) PUNCT hvd.32044092008168 413 44 y y PROPN hvd.32044092008168 413 45 du du PROPN hvd.32044092008168 413 46 [ [ PUNCT hvd.32044092008168 413 47 ele-50u ele-50u PROPN hvd.32044092008168 413 48 ( ( PUNCT hvd.32044092008168 413 49 ) ) PUNCT hvd.32044092008168 413 50 ] ] PUNCT hvd.32044092008168 414 1 we we PRON hvd.32044092008168 414 2 have have VERB hvd.32044092008168 414 3 also also ADV hvd.32044092008168 414 4 [ [ X hvd.32044092008168 414 5 44 44 NUM hvd.32044092008168 414 6 ] ] PUNCT hvd.32044092008168 414 7 : : PUNCT hvd.32044092008168 414 8 1 1 NUM hvd.32044092008168 414 9 p'a p'a ADJ hvd.32044092008168 414 10 + + CCONJ hvd.32044092008168 414 11 p'b p'b ADJ hvd.32044092008168 414 12 pv pv INTJ hvd.32044092008168 414 13 + + CCONJ hvd.32044092008168 414 14 pa pa PROPN hvd.32044092008168 414 15 + + CCONJ hvd.32044092008168 414 16 pb= pb= INTJ hvd.32044092008168 414 17 p'a p'a NOUN hvd.32044092008168 414 18 , , PUNCT hvd.32044092008168 414 19 6 6 NUM hvd.32044092008168 414 20 pa pa PROPN hvd.32044092008168 414 21 pb pb X hvd.32044092008168 414 22 pb pb PROPN hvd.32044092008168 414 23 ) ) PUNCT hvd.32044092008168 414 24 since since SCONJ hvd.32044092008168 414 25 p'a p'a ADJ hvd.32044092008168 414 26 = = VERB hvd.32044092008168 414 27 p'b p'b ADJ hvd.32044092008168 414 28 = = PRON hvd.32044092008168 414 29 a a PRON hvd.32044092008168 414 30 ' ' NOUN hvd.32044092008168 414 31 . . PUNCT hvd.32044092008168 415 1 again again ADV hvd.32044092008168 415 2 we we PRON hvd.32044092008168 415 3 have have VERB hvd.32044092008168 415 4 ξ2 ξ2 NUM hvd.32044092008168 415 5 – – PUNCT hvd.32044092008168 415 6 αζ αζ NOUN hvd.32044092008168 415 7 + + CCONJ hvd.32044092008168 415 8 α α NOUN hvd.32044092008168 415 9 ? ? NOUN hvd.32044092008168 415 10 4 4 NUM hvd.32044092008168 415 11 92 92 NUM hvd.32044092008168 415 12 = = SYM hvd.32044092008168 415 13 0 0 NUM hvd.32044092008168 415 14 4 4 NUM hvd.32044092008168 415 15 pa pa PROPN hvd.32044092008168 415 16 1 1 NUM hvd.32044092008168 415 17 or or CCONJ hvd.32044092008168 415 18 α α PRON hvd.32044092008168 415 19 1 1 NUM hvd.32044092008168 415 20 2 2 NUM hvd.32044092008168 415 21 α α NOUN hvd.32044092008168 415 22 2 2 NUM hvd.32044092008168 415 23 α α NOUN hvd.32044092008168 415 24 1 1 NUM hvd.32044092008168 415 25 2 2 NUM hvd.32044092008168 415 26 2 2 NUM hvd.32044092008168 415 27 + + NUM hvd.32044092008168 415 28 v92 v92 VERB hvd.32044092008168 415 29 – – PUNCT hvd.32044092008168 415 30 30 30 NUM hvd.32044092008168 415 31 % % NOUN hvd.32044092008168 415 32 . . PUNCT hvd.32044092008168 416 1 hence hence ADV hvd.32044092008168 416 2 p(a p(a NOUN hvd.32044092008168 416 3 ) ) PUNCT hvd.32044092008168 417 1 = = PROPN hvd.32044092008168 418 1 + + CCONJ hvd.32044092008168 418 2 v v ADP hvd.32044092008168 418 3 9 9 NUM hvd.32044092008168 418 4 . . NUM hvd.32044092008168 418 5 302 302 NUM hvd.32044092008168 418 6 p p NOUN hvd.32044092008168 418 7 ( ( PUNCT hvd.32044092008168 418 8 b b NOUN hvd.32044092008168 418 9 ) ) PUNCT hvd.32044092008168 418 10 v9,3a2 v9,3a2 NOUN hvd.32044092008168 418 11 whence whence ADP hvd.32044092008168 418 12 pa pa PROPN hvd.32044092008168 418 13 pb pb PROPN hvd.32044092008168 418 14 = = PROPN hvd.32044092008168 418 15 v9 v9 PROPN hvd.32044092008168 418 16 . . PUNCT hvd.32044092008168 419 1 – – PUNCT hvd.32044092008168 419 2 30 30 NUM hvd.32044092008168 419 3 pa pa PROPN hvd.32044092008168 419 4 + + CCONJ hvd.32044092008168 419 5 pb pb X hvd.32044092008168 419 6 p'a p'a INTJ hvd.32044092008168 419 7 , , PUNCT hvd.32044092008168 419 8 = = NOUN hvd.32044092008168 419 9 – – PUNCT hvd.32044092008168 419 10 40 40 NUM hvd.32044092008168 419 11 % % NOUN hvd.32044092008168 419 12 + + CCONJ hvd.32044092008168 419 13 9,0 9,0 NUM hvd.32044092008168 419 14 – – PUNCT hvd.32044092008168 419 15 93 93 NUM hvd.32044092008168 419 16 . . PUNCT hvd.32044092008168 420 1 these these DET hvd.32044092008168 420 2 values value NOUN hvd.32044092008168 420 3 in in ADP hvd.32044092008168 420 4 ( ( PUNCT hvd.32044092008168 420 5 44 44 NUM hvd.32044092008168 420 6 ) ) PUNCT hvd.32044092008168 420 7 give give VERB hvd.32044092008168 420 8 : : PUNCT hvd.32044092008168 420 9 403 403 NUM hvd.32044092008168 420 10 + + CCONJ hvd.32044092008168 420 11 9,0 9,0 NUM hvd.32044092008168 420 12 – – PUNCT hvd.32044092008168 420 13 93 93 NUM hvd.32044092008168 420 14 · · SYM hvd.32044092008168 420 15 p(v p(v PROPN hvd.32044092008168 420 16 ) ) PUNCT hvd.32044092008168 420 17 92 92 NUM hvd.32044092008168 420 18 3 3 NUM hvd.32044092008168 420 19 2 2 NUM hvd.32044092008168 420 20 92 92 NUM hvd.32044092008168 420 21 = = PUNCT hvd.32044092008168 420 22 [ [ X hvd.32044092008168 420 23 45 45 NUM hvd.32044092008168 420 24 ] ] PUNCT hvd.32044092008168 420 25 . . PUNCT hvd.32044092008168 421 1 a a DET hvd.32044092008168 421 2 q3 q3 PROPN hvd.32044092008168 421 3 + + CCONJ hvd.32044092008168 421 4 93 93 NUM hvd.32044092008168 421 5 3a 3a NUM hvd.32044092008168 421 6 92 92 NUM hvd.32044092008168 421 7 * * PUNCT hvd.32044092008168 421 8 ) ) PUNCT hvd.32044092008168 421 9 the the DET hvd.32044092008168 421 10 last last ADJ hvd.32044092008168 421 11 is be AUX hvd.32044092008168 421 12 the the DET hvd.32044092008168 421 13 form form NOUN hvd.32044092008168 421 14 given give VERB hvd.32044092008168 421 15 for for ADP hvd.32044092008168 421 16 the the DET hvd.32044092008168 421 17 expression expression NOUN hvd.32044092008168 421 18 cos cos ADP hvd.32044092008168 422 1 cx cx X hvd.32044092008168 423 1 + + CCONJ hvd.32044092008168 423 2 i i PRON hvd.32044092008168 423 3 cos cos ADP hvd.32044092008168 423 4 cy cy PROPN hvd.32044092008168 423 5 in in ADP hvd.32044092008168 423 6 the the DET hvd.32044092008168 423 7 solution solution NOUN hvd.32044092008168 423 8 of of ADP hvd.32044092008168 423 9 the the DET hvd.32044092008168 423 10 pendulum pendulum NOUN hvd.32044092008168 423 11 problem problem NOUN hvd.32044092008168 423 12 in in ADP hvd.32044092008168 423 13 the the DET hvd.32044092008168 423 14 direct direct ADJ hvd.32044092008168 423 15 investigation investigation NOUN hvd.32044092008168 423 16 of of ADP hvd.32044092008168 423 17 which which PRON hvd.32044092008168 423 18 one one PRON hvd.32044092008168 423 19 arrives arrive VERB hvd.32044092008168 423 20 at at ADP hvd.32044092008168 423 21 the the DET hvd.32044092008168 423 22 expressions expression NOUN hvd.32044092008168 423 23 d d NOUN hvd.32044092008168 423 24 ? ? PUNCT hvd.32044092008168 423 25 x x PUNCT hvd.32044092008168 424 1 d2 d2 PROPN hvd.32044092008168 424 2 y y PROPN hvd.32044092008168 424 3 nx nx PROPN hvd.32044092008168 424 4 ; ; PUNCT hvd.32044092008168 424 5 ny ny PROPN hvd.32044092008168 424 6 ; ; PUNCT hvd.32044092008168 424 7 dta dta VERB hvd.32044092008168 424 8 dt2 dt2 DET hvd.32044092008168 424 9 dt dt PROPN hvd.32044092008168 424 10 ? ? PUNCT hvd.32044092008168 424 11 where where SCONJ hvd.32044092008168 424 12 n n PROPN hvd.32044092008168 424 13 is be AUX hvd.32044092008168 424 14 found find VERB hvd.32044092008168 424 15 to to PART hvd.32044092008168 424 16 be be AUX hvd.32044092008168 424 17 3 3 NUM hvd.32044092008168 424 18 r2 r2 PROPN hvd.32044092008168 424 19 ( ( PUNCT hvd.32044092008168 424 20 2 2 NUM hvd.32044092008168 424 21 pu pu X hvd.32044092008168 424 22 — — PUNCT hvd.32044092008168 424 23 pa pa PROPN hvd.32044092008168 424 24 , , PUNCT hvd.32044092008168 424 25 ) ) PUNCT hvd.32044092008168 424 26 which which PRON hvd.32044092008168 424 27 causes cause VERB hvd.32044092008168 424 28 the the DET hvd.32044092008168 424 29 solution solution NOUN hvd.32044092008168 424 30 to to PART hvd.32044092008168 424 31 depend depend VERB hvd.32044092008168 424 32 upon upon SCONJ hvd.32044092008168 424 33 lamé lamé NOUN hvd.32044092008168 424 34 's 's PART hvd.32044092008168 424 35 functions function NOUN hvd.32044092008168 424 36 . . PUNCT hvd.32044092008168 425 1 d2 d2 PROPN hvd.32044092008168 425 2 % % NOUN hvd.32044092008168 425 3 nz nz PROPN hvd.32044092008168 426 1 + + CCONJ hvd.32044092008168 426 2 g g NOUN hvd.32044092008168 426 3 32 32 NUM hvd.32044092008168 426 4 part part NOUN hvd.32044092008168 426 5 iii iii NUM hvd.32044092008168 426 6 . . PUNCT hvd.32044092008168 426 7 o o PUNCT hvd.32044092008168 426 8 ' ' PUNCT hvd.32044092008168 426 9 · · PUNCT hvd.32044092008168 426 10 92 92 NUM hvd.32044092008168 426 11 if if SCONJ hvd.32044092008168 426 12 we we PRON hvd.32044092008168 426 13 take take VERB hvd.32044092008168 426 14 a a PRON hvd.32044092008168 426 15 = = NOUN hvd.32044092008168 426 16 2b 2b NUM hvd.32044092008168 426 17 we we PRON hvd.32044092008168 426 18 have have VERB hvd.32044092008168 426 19 8b3 8b3 NUM hvd.32044092008168 426 20 + + SYM hvd.32044092008168 426 21 9 9 NUM hvd.32044092008168 426 22 bo bo NOUN hvd.32044092008168 426 23 ' ' NOUN hvd.32044092008168 426 24 0 0 NUM hvd.32044092008168 427 1 [ [ X hvd.32044092008168 427 2 46 46 NUM hvd.32044092008168 427 3 ] ] PUNCT hvd.32044092008168 427 4 · · PUNCT hvd.32044092008168 427 5 p p PROPN hvd.32044092008168 427 6 ( ( PUNCT hvd.32044092008168 427 7 v v NOUN hvd.32044092008168 427 8 ) ) PUNCT hvd.32044092008168 427 9 12b2 12b2 NUM hvd.32044092008168 427 10 92 92 NUM hvd.32044092008168 427 11 9 9 NUM hvd.32044092008168 427 12 where where SCONJ hvd.32044092008168 427 13 ф ф PROPN hvd.32044092008168 427 14 433 433 NUM hvd.32044092008168 427 15 92b 92b NUM hvd.32044092008168 427 16 -93 -93 PUNCT hvd.32044092008168 427 17 and and CCONJ hvd.32044092008168 427 18 1262 1262 NUM hvd.32044092008168 427 19 for for ADP hvd.32044092008168 427 20 x x PUNCT hvd.32044092008168 427 21 we we PRON hvd.32044092008168 427 22 have have VERB hvd.32044092008168 427 23 : : PUNCT hvd.32044092008168 427 24 1 1 NUM hvd.32044092008168 427 25 p p NOUN hvd.32044092008168 427 26 ' ' PUNCT hvd.32044092008168 427 27 ( ( PUNCT hvd.32044092008168 427 28 b b PROPN hvd.32044092008168 427 29 -a -a X hvd.32044092008168 427 30 ) ) PUNCT hvd.32044092008168 427 31 + + CCONJ hvd.32044092008168 427 32 p'b p'b ADV hvd.32044092008168 427 33 [ [ X hvd.32044092008168 427 34 47 47 NUM hvd.32044092008168 427 35 ] ] PUNCT hvd.32044092008168 427 36 x x PUNCT hvd.32044092008168 427 37 = = X hvd.32044092008168 427 38 $ $ SYM hvd.32044092008168 427 39 ( ( PUNCT hvd.32044092008168 427 40 a a DET hvd.32044092008168 427 41 b b NOUN hvd.32044092008168 427 42 ) ) PUNCT hvd.32044092008168 427 43 + + CCONJ hvd.32044092008168 427 44 $ $ SYM hvd.32044092008168 427 45 a a PRON hvd.32044092008168 427 46 – – PUNCT hvd.32044092008168 427 47 $ $ SYM hvd.32044092008168 427 48 b b NOUN hvd.32044092008168 427 49 = = X hvd.32044092008168 427 50 s s VERB hvd.32044092008168 427 51 = = PRON hvd.32044092008168 427 52 2 2 NUM hvd.32044092008168 427 53 p p NOUN hvd.32044092008168 427 54 ( ( PUNCT hvd.32044092008168 427 55 b b NOUN hvd.32044092008168 427 56 − − NOUN hvd.32044092008168 427 57 a a X hvd.32044092008168 427 58 ) ) PUNCT hvd.32044092008168 427 59 – – PUNCT hvd.32044092008168 427 60 pb pb PROPN hvd.32044092008168 427 61 1 1 NUM hvd.32044092008168 427 62 p p NOUN hvd.32044092008168 427 63 ' ' PUNCT hvd.32044092008168 427 64 ( ( PUNCT hvd.32044092008168 427 65 b b NOUN hvd.32044092008168 427 66 − − NOUN hvd.32044092008168 427 67 a a PRON hvd.32044092008168 427 68 ) ) PUNCT hvd.32044092008168 427 69 -p'(a -p'(a PROPN hvd.32044092008168 427 70 ) ) PUNCT hvd.32044092008168 427 71 a a DET hvd.32044092008168 427 72 p p NOUN hvd.32044092008168 427 73 ' ' PUNCT hvd.32044092008168 427 74 ( ( PUNCT hvd.32044092008168 427 75 b b NOUN hvd.32044092008168 427 76 − − NOUN hvd.32044092008168 427 77 a a X hvd.32044092008168 427 78 ) ) PUNCT hvd.32044092008168 427 79 + + CCONJ hvd.32044092008168 427 80 p'b p'b ADV hvd.32044092008168 427 81 p'a p'a ADJ hvd.32044092008168 427 82 p p X hvd.32044092008168 427 83 ( ( PUNCT hvd.32044092008168 427 84 b b NOUN hvd.32044092008168 427 85 a a PRON hvd.32044092008168 427 86 ) ) PUNCT hvd.32044092008168 427 87 2 2 NUM hvd.32044092008168 427 88 p p PROPN hvd.32044092008168 427 89 b b NOUN hvd.32044092008168 427 90 -a -a X hvd.32044092008168 427 91 ) ) PUNCT hvd.32044092008168 427 92 pb pb PROPN hvd.32044092008168 427 93 pa pa PROPN hvd.32044092008168 427 94 ( ( PUNCT hvd.32044092008168 427 95 — — PUNCT hvd.32044092008168 427 96 — — PUNCT hvd.32044092008168 427 97 = = X hvd.32044092008168 427 98 p'v p'v X hvd.32044092008168 427 99 2pv 2pv NOUN hvd.32044092008168 427 100 2 2 NUM hvd.32044092008168 427 101 p p NOUN hvd.32044092008168 427 102 ( ( PUNCT hvd.32044092008168 427 103 a a X hvd.32044092008168 427 104 ) ) PUNCT hvd.32044092008168 427 105 cz cz PROPN hvd.32044092008168 427 106 3 3 NUM hvd.32044092008168 427 107 bo bo NOUN hvd.32044092008168 427 108 ' ' PART hvd.32044092008168 427 109 9 9 NUM hvd.32044092008168 427 110 -1 -1 NOUN hvd.32044092008168 427 111 since since SCONJ hvd.32044092008168 427 112 p'a p'a ADJ hvd.32044092008168 427 113 — — PUNCT hvd.32044092008168 427 114 p'b=0 p'b=0 PROPN hvd.32044092008168 427 115 pa pa PROPN hvd.32044092008168 427 116 + + CCONJ hvd.32044092008168 427 117 pb pb PROPN hvd.32044092008168 427 118 combining combine VERB hvd.32044092008168 427 119 these these DET hvd.32044092008168 427 120 relations relation NOUN hvd.32044092008168 427 121 we we PRON hvd.32044092008168 427 122 obtain obtain VERB hvd.32044092008168 427 123 : : PUNCT hvd.32044092008168 427 124 = = SYM hvd.32044092008168 427 125 a. a. NOUN hvd.32044092008168 427 126 p'v p'v NOUN hvd.32044092008168 427 127 + + CCONJ hvd.32044092008168 427 128 pv pv ADP hvd.32044092008168 427 129 = = NOUN hvd.32044092008168 427 130 b b PROPN hvd.32044092008168 427 131 2 2 NUM hvd.32044092008168 427 132 x x SYM hvd.32044092008168 427 133 9 9 NUM hvd.32044092008168 427 134 9 9 NUM hvd.32044092008168 427 135 . . PUNCT hvd.32044092008168 427 136 1 1 NUM hvd.32044092008168 427 137 9 9 NUM hvd.32044092008168 427 138 29 29 NUM hvd.32044092008168 427 139 9 9 NUM hvd.32044092008168 427 140 i i PRON hvd.32044092008168 427 141 and and CCONJ hvd.32044092008168 427 142 /369 /369 SPACE hvd.32044092008168 427 143 ' ' PUNCT hvd.32044092008168 428 1 bo bo NOUN hvd.32044092008168 428 2 ' ' PUNCT hvd.32044092008168 428 3 3 3 NUM hvd.32044092008168 428 4 bo bo NOUN hvd.32044092008168 428 5 ' ' PUNCT hvd.32044092008168 428 6 p'v=2(b p'v=2(b NOUN hvd.32044092008168 428 7 – – PUNCT hvd.32044092008168 428 8 pv pv ADP hvd.32044092008168 428 9 ) ) PUNCT hvd.32044092008168 428 10 v v ADP hvd.32044092008168 428 11 201 201 NUM hvd.32044092008168 428 12 9 9 NUM hvd.32044092008168 428 13 ) ) PUNCT hvd.32044092008168 428 14 v v ADP hvd.32044092008168 428 15 9 9 NUM hvd.32044092008168 428 16 90 90 NUM hvd.32044092008168 428 17 3 3 NUM hvd.32044092008168 428 18 bo bo NOUN hvd.32044092008168 428 19 ' ' PUNCT hvd.32044092008168 428 20 v v NOUN hvd.32044092008168 428 21 * * PROPN hvd.32044092008168 428 22 ) ) PUNCT hvd.32044092008168 428 23 9 9 NUM hvd.32044092008168 428 24 finally finally ADV hvd.32044092008168 428 25 we we PRON hvd.32044092008168 428 26 observe observe VERB hvd.32044092008168 428 27 that that SCONJ hvd.32044092008168 428 28 if if SCONJ hvd.32044092008168 428 29 -u -u VERB hvd.32044092008168 428 30 is be AUX hvd.32044092008168 428 31 substituted substitute VERB hvd.32044092008168 428 32 for for ADP hvd.32044092008168 428 33 u u PROPN hvd.32044092008168 428 34 in in ADP hvd.32044092008168 428 35 hermite hermite PROPN hvd.32044092008168 428 36 's 's PART hvd.32044092008168 428 37 equation equation NOUN hvd.32044092008168 428 38 it it PRON hvd.32044092008168 428 39 remains remain VERB hvd.32044092008168 428 40 unaltered unaltered ADJ hvd.32044092008168 428 41 which which PRON hvd.32044092008168 428 42 gives give VERB hvd.32044092008168 428 43 us we PRON hvd.32044092008168 428 44 the the DET hvd.32044092008168 428 45 second second ADJ hvd.32044092008168 428 46 solution solution NOUN hvd.32044092008168 428 47 , , PUNCT hvd.32044092008168 428 48 namely namely ADV hvd.32044092008168 428 49 6 6 NUM hvd.32044092008168 428 50 ( ( PUNCT hvd.32044092008168 428 51 a a DET hvd.32044092008168 428 52 u u NOUN hvd.32044092008168 428 53 ) ) PUNCT hvd.32044092008168 429 1 [ [ X hvd.32044092008168 429 2 48 48 NUM hvd.32044092008168 429 3 ] ] PUNCT hvd.32044092008168 429 4 · · PUNCT hvd.32044092008168 429 5 -it -it X hvd.32044092008168 429 6 . . PUNCT hvd.32044092008168 429 7 o(a o(a SPACE hvd.32044092008168 429 8 ) ) PUNCT hvd.32044092008168 429 9 o o NOUN hvd.32044092008168 429 10 ( ( PUNCT hvd.32044092008168 429 11 u u PROPN hvd.32044092008168 429 12 ) ) PUNCT hvd.32044092008168 429 13 x x PUNCT hvd.32044092008168 430 1 and and CCONJ hvd.32044092008168 430 2 v v NOUN hvd.32044092008168 430 3 remaining remain VERB hvd.32044092008168 430 4 as as ADV hvd.32044092008168 430 5 before before ADV hvd.32044092008168 430 6 . . PUNCT hvd.32044092008168 430 7 . . PUNCT hvd.32044092008168 431 1 2 2 NUM hvd.32044092008168 431 2 euta euta PROPN hvd.32044092008168 431 3 2 2 NUM hvd.32044092008168 431 4 product product NOUN hvd.32044092008168 431 5 of of ADP hvd.32044092008168 431 6 the the DET hvd.32044092008168 431 7 two two NUM hvd.32044092008168 431 8 solutions solution NOUN hvd.32044092008168 431 9 . . PUNCT hvd.32044092008168 432 1 it it PRON hvd.32044092008168 432 2 becomes become VERB hvd.32044092008168 432 3 evident evident ADJ hvd.32044092008168 432 4 from from ADP hvd.32044092008168 432 5 the the DET hvd.32044092008168 432 6 illustration illustration NOUN hvd.32044092008168 432 7 in in ADP hvd.32044092008168 432 8 the the DET hvd.32044092008168 432 9 previous previous ADJ hvd.32044092008168 432 10 paragraph paragraph NOUN hvd.32044092008168 432 11 that that SCONJ hvd.32044092008168 432 12 while while SCONJ hvd.32044092008168 432 13 in in ADP hvd.32044092008168 432 14 general general ADJ hvd.32044092008168 432 15 the the DET hvd.32044092008168 432 16 theory theory NOUN hvd.32044092008168 432 17 involved involve VERB hvd.32044092008168 432 18 in in ADP hvd.32044092008168 432 19 the the DET hvd.32044092008168 432 20 solution solution NOUN hvd.32044092008168 432 21 just just ADV hvd.32044092008168 432 22 given give VERB hvd.32044092008168 432 23 holds hold VERB hvd.32044092008168 432 24 it it PRON hvd.32044092008168 432 25 is be AUX hvd.32044092008168 432 26 practically practically ADV hvd.32044092008168 432 27 inapplicable inapplicable ADJ hvd.32044092008168 432 28 for for ADP hvd.32044092008168 432 29 other other ADJ hvd.32044092008168 432 30 values value NOUN hvd.32044092008168 432 31 of of ADP hvd.32044092008168 432 32 n n NOUN hvd.32044092008168 432 33 than than ADP hvd.32044092008168 432 34 two two NUM hvd.32044092008168 432 35 or or CCONJ hvd.32044092008168 432 36 at at ADP hvd.32044092008168 432 37 most most ADV hvd.32044092008168 432 38 three three NUM hvd.32044092008168 432 39 whence whence NOUN hvd.32044092008168 432 40 one one NUM hvd.32044092008168 432 41 is be AUX hvd.32044092008168 432 42 led lead VERB hvd.32044092008168 432 43 to to ADP hvd.32044092008168 432 44 a a DET hvd.32044092008168 432 45 study study NOUN hvd.32044092008168 432 46 of of ADP hvd.32044092008168 432 47 functions function NOUN hvd.32044092008168 432 48 of of ADP hvd.32044092008168 432 49 the the DET hvd.32044092008168 432 50 integral integral NOUN hvd.32044092008168 432 51 in in ADP hvd.32044092008168 432 52 the the DET hvd.32044092008168 432 53 hope hope NOUN hvd.32044092008168 432 54 of of ADP hvd.32044092008168 432 55 discovering discover VERB hvd.32044092008168 432 56 inherent inherent ADJ hvd.32044092008168 432 57 properties property NOUN hvd.32044092008168 432 58 * * PUNCT hvd.32044092008168 432 59 ) ) PUNCT hvd.32044092008168 432 60 compair compair NOUN hvd.32044092008168 432 61 results result NOUN hvd.32044092008168 432 62 obtained obtain VERB hvd.32044092008168 432 63 by by ADP hvd.32044092008168 432 64 m. m. NOUN hvd.32044092008168 432 65 halphen halphen ADV hvd.32044092008168 432 66 and and CCONJ hvd.32044092008168 432 67 obtained obtain VERB hvd.32044092008168 432 68 in in ADP hvd.32044092008168 432 69 a a DET hvd.32044092008168 432 70 different different ADJ hvd.32044092008168 432 71 manner manner NOUN hvd.32044092008168 432 72 , , PUNCT hvd.32044092008168 432 73 ii ii PROPN hvd.32044092008168 432 74 p. p. NOUN hvd.32044092008168 432 75 131 131 NUM hvd.32044092008168 432 76 and and CCONJ hvd.32044092008168 432 77 527 527 NUM hvd.32044092008168 432 78 . . PUNCT hvd.32044092008168 433 1 integral integral ADJ hvd.32044092008168 433 2 as as ADP hvd.32044092008168 433 3 a a DET hvd.32044092008168 433 4 product product NOUN hvd.32044092008168 433 5 . . PUNCT hvd.32044092008168 434 1 33 33 NUM hvd.32044092008168 434 2 that that PRON hvd.32044092008168 434 3 will will AUX hvd.32044092008168 434 4 lead lead VERB hvd.32044092008168 434 5 to to ADP hvd.32044092008168 434 6 a a DET hvd.32044092008168 434 7 more more ADV hvd.32044092008168 434 8 practical practical ADJ hvd.32044092008168 434 9 result result NOUN hvd.32044092008168 434 10 . . PUNCT hvd.32044092008168 435 1 the the DET hvd.32044092008168 435 2 first first ADJ hvd.32044092008168 435 3 of of ADP hvd.32044092008168 435 4 such such ADJ hvd.32044092008168 435 5 functions function NOUN hvd.32044092008168 435 6 to to PART hvd.32044092008168 435 7 command command VERB hvd.32044092008168 435 8 attention attention NOUN hvd.32044092008168 435 9 would would AUX hvd.32044092008168 435 10 be be AUX hvd.32044092008168 435 11 the the DET hvd.32044092008168 435 12 product product NOUN hvd.32044092008168 435 13 of of ADP hvd.32044092008168 435 14 the the DET hvd.32044092008168 435 15 two two NUM hvd.32044092008168 435 16 integrals integral NOUN hvd.32044092008168 435 17 [ [ PUNCT hvd.32044092008168 435 18 49 49 NUM hvd.32044092008168 435 19 ] ] PUNCT hvd.32044092008168 435 20 : : PUNCT hvd.32044092008168 435 21 y y PROPN hvd.32044092008168 435 22 y% y% PROPN hvd.32044092008168 435 23 which which PRON hvd.32044092008168 435 24 we we PRON hvd.32044092008168 435 25 will will AUX hvd.32044092008168 435 26 proceed proceed VERB hvd.32044092008168 435 27 to to PART hvd.32044092008168 435 28 develop develop VERB hvd.32044092008168 435 29 as as SCONJ hvd.32044092008168 435 30 follows follow VERB hvd.32044092008168 435 31 : : PUNCT hvd.32044092008168 435 32 we we PRON hvd.32044092008168 435 33 would would AUX hvd.32044092008168 435 34 find find VERB hvd.32044092008168 435 35 from from ADP hvd.32044092008168 435 36 the the DET hvd.32044092008168 435 37 integral integral ADJ hvd.32044092008168 435 38 % % NOUN hvd.32044092008168 435 39 as as ADP hvd.32044092008168 435 40 in in ADP hvd.32044092008168 435 41 the the DET hvd.32044092008168 435 42 case case NOUN hvd.32044092008168 435 43 of of ADP hvd.32044092008168 435 44 y y PROPN hvd.32044092008168 435 45 z z PROPN hvd.32044092008168 435 46 ' ' PUNCT hvd.32044092008168 435 47 = = PUNCT hvd.32044092008168 435 48 t t PROPN hvd.32044092008168 435 49 ; ; PUNCT hvd.32044092008168 436 1 ( ( PUNCT hvd.32044092008168 436 2 a a DET hvd.32044092008168 436 3 — — PUNCT hvd.32044092008168 436 4 u u NOUN hvd.32044092008168 436 5 ) ) PUNCT hvd.32044092008168 436 6 — — PUNCT hvd.32044092008168 436 7 6u 6u NUM hvd.32044092008168 436 8 + + NUM hvd.32044092008168 436 9 $ $ SYM hvd.32044092008168 436 10 a a NOUN hvd.32044092008168 436 11 ] ] PUNCT hvd.32044092008168 436 12 -σεξ -σεξ PROPN hvd.32044092008168 436 13 ( ( PUNCT hvd.32044092008168 436 14 α α NOUN hvd.32044092008168 436 15 — — PUNCT hvd.32044092008168 436 16 ga ga ADJ hvd.32044092008168 436 17 and and CCONJ hvd.32044092008168 436 18 combining combine VERB hvd.32044092008168 436 19 with with ADP hvd.32044092008168 436 20 y y PROPN hvd.32044092008168 436 21 ' ' PUNCT hvd.32044092008168 436 22 a a DET hvd.32044092008168 436 23 1 1 NUM hvd.32044092008168 436 24 [ [ PUNCT hvd.32044092008168 436 25 5 5 NUM hvd.32044092008168 436 26 ( ( PUNCT hvd.32044092008168 436 27 a a DET hvd.32044092008168 436 28 + + ADJ hvd.32044092008168 436 29 u u PROPN hvd.32044092008168 436 30 ) ) PUNCT hvd.32044092008168 436 31 — — PUNCT hvd.32044092008168 436 32 $ $ SYM hvd.32044092008168 436 33 ( ( PUNCT hvd.32044092008168 436 34 u u NOUN hvd.32044092008168 436 35 ) ) PUNCT hvd.32044092008168 436 36 – – PUNCT hvd.32044092008168 436 37 ça ça X hvd.32044092008168 436 38 ] ] X hvd.32044092008168 436 39 we we PRON hvd.32044092008168 436 40 obtain obtain VERB hvd.32044092008168 436 41 y y PROPN hvd.32044092008168 436 42 ' ' PUNCT hvd.32044092008168 436 43 is be AUX hvd.32044092008168 436 44 ( ( PUNCT hvd.32044092008168 436 45 v v ADP hvd.32044092008168 436 46 + + PRON hvd.32044092008168 436 47 a a X hvd.32044092008168 436 48 ) ) PUNCT hvd.32044092008168 436 49 — — PUNCT hvd.32044092008168 436 50 $ $ SYM hvd.32044092008168 436 51 ( ( PUNCT hvd.32044092008168 436 52 u u PROPN hvd.32044092008168 436 53 — — PUNCT hvd.32044092008168 436 54 a a X hvd.32044092008168 436 55 ) ) PUNCT hvd.32044092008168 436 56 — — PUNCT hvd.32044092008168 436 57 25a 25a NOUN hvd.32044092008168 436 58 ] ] PUNCT hvd.32044092008168 436 59 p'a p'a PUNCT hvd.32044092008168 436 60 but but CCONJ hvd.32044092008168 436 61 co co VERB hvd.32044092008168 436 62 ( ( PUNCT hvd.32044092008168 436 63 a a DET hvd.32044092008168 436 64 + + ADJ hvd.32044092008168 436 65 u u NOUN hvd.32044092008168 436 66 ) ) PUNCT hvd.32044092008168 436 67 o o NOUN hvd.32044092008168 437 1 ( ( PUNCT hvd.32044092008168 437 2 a a DET hvd.32044092008168 437 3 u u NOUN hvd.32044092008168 437 4 ) ) PUNCT hvd.32044092008168 437 5 y y PROPN hvd.32044092008168 437 6 y y PROPN hvd.32044092008168 437 7 ? ? PUNCT hvd.32044092008168 438 1 -it -it X hvd.32044092008168 438 2 = = SYM hvd.32044092008168 438 3 17(pu 17(pu NUM hvd.32044092008168 438 4 - - PUNCT hvd.32044092008168 438 5 pa pa PROPN hvd.32044092008168 438 6 ) ) PUNCT hvd.32044092008168 438 7 . . PUNCT hvd.32044092008168 439 1 * * PUNCT hvd.32044092008168 439 2 ) ) PUNCT hvd.32044092008168 439 3 whence whence ADP hvd.32044092008168 439 4 p'a p'a ADJ hvd.32044092008168 439 5 · · PUNCT hvd.32044092008168 440 1 y y PROPN hvd.32044092008168 440 2 z z X hvd.32044092008168 440 3 ра ра INTJ hvd.32044092008168 440 4 p'a p'a INTJ hvd.32044092008168 440 5 -σ -σ SPACE hvd.32044092008168 440 6 , , PUNCT hvd.32044092008168 440 7 при при X hvd.32044092008168 440 8 ) ) PUNCT hvd.32044092008168 440 9 2c 2c NUM hvd.32044092008168 440 10 ра ра ADP hvd.32044092008168 440 11 y y PROPN hvd.32044092008168 440 12 pu pu PROPN hvd.32044092008168 440 13 - - PROPN hvd.32044092008168 440 14 pa pa PROPN hvd.32044092008168 440 15 y y PROPN hvd.32044092008168 440 16 2 2 NUM hvd.32044092008168 440 17 62a 62a NUM hvd.32044092008168 440 18 62 62 NUM hvd.32044092008168 441 1 u u PROPN hvd.32044092008168 442 1 y y PROPN hvd.32044092008168 442 2 e e PROPN hvd.32044092008168 442 3 ' ' PUNCT hvd.32044092008168 442 4 – – PUNCT hvd.32044092008168 442 5 by by ADP hvd.32044092008168 442 6 = = NOUN hvd.32044092008168 442 7 pu pu PROPN hvd.32044092008168 442 8 ? ? PUNCT hvd.32044092008168 442 9 " " PUNCT hvd.32044092008168 443 1 pa pa PROPN hvd.32044092008168 443 2 pur-“ra pur-“ra PROPN hvd.32044092008168 443 3 17(pu 17(pu NUM hvd.32044092008168 443 4 – – PUNCT hvd.32044092008168 443 5 pa pa PROPN hvd.32044092008168 443 6 ) ) PUNCT hvd.32044092008168 443 7 = = VERB hvd.32044092008168 443 8 20 20 NUM hvd.32044092008168 443 9 or or CCONJ hvd.32044092008168 443 10 > > X hvd.32044092008168 443 11 + + CCONJ hvd.32044092008168 443 12 a a DET hvd.32044092008168 443 13 t t PROPN hvd.32044092008168 443 14 t t PROPN hvd.32044092008168 443 15 y y PROPN hvd.32044092008168 443 16 2 2 NUM hvd.32044092008168 443 17 = = SYM hvd.32044092008168 443 18 p'a p'a INTJ hvd.32044092008168 443 19 20 20 NUM hvd.32044092008168 443 20 σ σ NOUN hvd.32044092008168 443 21 ри ри X hvd.32044092008168 443 22 pa pa PROPN hvd.32044092008168 443 23 ii ii PROPN hvd.32044092008168 444 1 ( ( PUNCT hvd.32044092008168 444 2 pu pu PROPN hvd.32044092008168 444 3 pa pa PROPN hvd.32044092008168 444 4 ) ) PUNCT hvd.32044092008168 444 5 ? ? PUNCT hvd.32044092008168 445 1 c c X hvd.32044092008168 445 2 being be AUX hvd.32044092008168 445 3 a a DET hvd.32044092008168 445 4 constant constant ADJ hvd.32044092008168 445 5 or or CCONJ hvd.32044092008168 445 6 expanding expand VERB hvd.32044092008168 445 7 and and CCONJ hvd.32044092008168 445 8 writing write VERB hvd.32044092008168 445 9 t t PROPN hvd.32044092008168 445 10 = = NOUN hvd.32044092008168 445 11 pu pu NOUN hvd.32044092008168 445 12 we we PRON hvd.32044092008168 445 13 have have VERB hvd.32044092008168 445 14 a a DET hvd.32044092008168 445 15 ' ' PUNCT hvd.32044092008168 445 16 b b NOUN hvd.32044092008168 445 17 ' ' PUNCT hvd.32044092008168 445 18 g g NOUN hvd.32044092008168 445 19 2 2 NUM hvd.32044092008168 445 20 c c NOUN hvd.32044092008168 445 21 [ [ X hvd.32044092008168 445 22 50 50 NUM hvd.32044092008168 445 23 ] ] PUNCT hvd.32044092008168 446 1 + + NUM hvd.32044092008168 446 2 + + PUNCT hvd.32044092008168 446 3 b b X hvd.32044092008168 446 4 ( ( PUNCT hvd.32044092008168 446 5 t t PROPN hvd.32044092008168 446 6 a a X hvd.32044092008168 446 7 ) ) PUNCT hvd.32044092008168 446 8 ( ( PUNCT hvd.32044092008168 446 9 t t PROPN hvd.32044092008168 446 10 b b PROPN hvd.32044092008168 446 11 ) ) PUNCT hvd.32044092008168 446 12 ( ( PUNCT hvd.32044092008168 446 13 t t PROPN hvd.32044092008168 446 14 – – PUNCT hvd.32044092008168 446 15 y y PROPN hvd.32044092008168 446 16 ) ) PUNCT hvd.32044092008168 446 17 ... ... PUNCT hvd.32044092008168 447 1 an an DET hvd.32044092008168 447 2 identity identity NOUN hvd.32044092008168 447 3 independant independant NOUN hvd.32044092008168 447 4 of of ADP hvd.32044092008168 447 5 the the DET hvd.32044092008168 447 6 value value NOUN hvd.32044092008168 447 7 of of ADP hvd.32044092008168 447 8 t. t. PROPN hvd.32044092008168 447 9 to to PART hvd.32044092008168 447 10 determine determine VERB hvd.32044092008168 447 11 a a DET hvd.32044092008168 447 12 ' ' PUNCT hvd.32044092008168 447 13 , , PUNCT hvd.32044092008168 447 14 b b NOUN hvd.32044092008168 447 15 ' ' NUM hvd.32044092008168 447 16 ... ... PUNCT hvd.32044092008168 447 17 multiply multiply VERB hvd.32044092008168 447 18 both both DET hvd.32044092008168 447 19 members member NOUN hvd.32044092008168 447 20 by by ADP hvd.32044092008168 447 21 ( ( PUNCT hvd.32044092008168 447 22 t t PROPN hvd.32044092008168 447 23 a a PRON hvd.32044092008168 447 24 ) ) PUNCT hvd.32044092008168 447 25 , , PUNCT hvd.32044092008168 447 26 ( ( PUNCT hvd.32044092008168 447 27 t t NOUN hvd.32044092008168 447 28 – – PUNCT hvd.32044092008168 447 29 b b NOUN hvd.32044092008168 447 30 ) ) PUNCT hvd.32044092008168 447 31 ... ... PUNCT hvd.32044092008168 447 32 and and CCONJ hvd.32044092008168 447 33 take take VERB hvd.32044092008168 447 34 t t PROPN hvd.32044092008168 447 35 = = NOUN hvd.32044092008168 447 36 a a DET hvd.32044092008168 447 37 , , PUNCT hvd.32044092008168 447 38 b b X hvd.32044092008168 447 39 ... ... PUNCT hvd.32044092008168 447 40 for for ADP hvd.32044092008168 447 41 example example NOUN hvd.32044092008168 447 42 a a PRON hvd.32044092008168 447 43 ) ) PUNCT hvd.32044092008168 447 44 n'at n'at NOUN hvd.32044092008168 447 45 a a PRON hvd.32044092008168 447 46 ) ) PUNCT hvd.32044092008168 447 47 20 20 NUM hvd.32044092008168 447 48 a'+ a'+ NOUN hvd.32044092008168 447 49 + + CCONJ hvd.32044092008168 447 50 + + CCONJ hvd.32044092008168 447 51 ( ( PUNCT hvd.32044092008168 447 52 t t PROPN hvd.32044092008168 447 53 b b PROPN hvd.32044092008168 447 54 ) ) PUNCT hvd.32044092008168 447 55 ( ( PUNCT hvd.32044092008168 447 56 t t PROPN hvd.32044092008168 447 57 b b PROPN hvd.32044092008168 447 58 ) ) PUNCT hvd.32044092008168 447 59 ( ( PUNCT hvd.32044092008168 447 60 t t PROPN hvd.32044092008168 447 61 y y PROPN hvd.32044092008168 447 62 ) ) PUNCT hvd.32044092008168 447 63 ... ... PUNCT hvd.32044092008168 447 64 — — PUNCT hvd.32044092008168 447 65 whence whence NOUN hvd.32044092008168 447 66 making make VERB hvd.32044092008168 447 67 t= t= ADJ hvd.32044092008168 447 68 a a PRON hvd.32044092008168 447 69 we we PRON hvd.32044092008168 447 70 have have VERB hvd.32044092008168 447 71 = = NOUN hvd.32044092008168 447 72 2c 2c NUM hvd.32044092008168 448 1 [ [ X hvd.32044092008168 448 2 51 51 NUM hvd.32044092008168 448 3 ] ] PUNCT hvd.32044092008168 448 4 . . PUNCT hvd.32044092008168 449 1 a'r a'r PROPN hvd.32044092008168 449 2 ( ( PUNCT hvd.32044092008168 449 3 a a DET hvd.32044092008168 449 4 b b NOUN hvd.32044092008168 449 5 ) ) PUNCT hvd.32044092008168 449 6 ( ( PUNCT hvd.32044092008168 449 7 a a DET hvd.32044092008168 449 8 — — PUNCT hvd.32044092008168 449 9 y y PROPN hvd.32044092008168 449 10 ) ) PUNCT hvd.32044092008168 449 11 ... ... PUNCT hvd.32044092008168 450 1 and and CCONJ hvd.32044092008168 450 2 in in ADP hvd.32044092008168 450 3 a a DET hvd.32044092008168 450 4 similar similar ADJ hvd.32044092008168 450 5 manner manner NOUN hvd.32044092008168 450 6 we we PRON hvd.32044092008168 450 7 find find VERB hvd.32044092008168 450 8 b b NOUN hvd.32044092008168 450 9 ' ' PUNCT hvd.32044092008168 450 10 ( ( PUNCT hvd.32044092008168 450 11 t t PROPN hvd.32044092008168 450 12 t t PROPN hvd.32044092008168 450 13 . . PUNCT hvd.32044092008168 451 1 a a DET hvd.32044092008168 451 2 20 20 NUM hvd.32044092008168 451 3 b b NOUN hvd.32044092008168 451 4 ' ' PUNCT hvd.32044092008168 451 5 ( ( PUNCT hvd.32044092008168 451 6 b b PROPN hvd.32044092008168 451 7 a a X hvd.32044092008168 451 8 ) ) PUNCT hvd.32044092008168 451 9 ( ( PUNCT hvd.32044092008168 451 10 b b PROPN hvd.32044092008168 451 11 y y PROPN hvd.32044092008168 451 12 ) ) PUNCT hvd.32044092008168 451 13 ... ... PUNCT hvd.32044092008168 452 1 * * PUNCT hvd.32044092008168 452 2 ) ) PUNCT hvd.32044092008168 452 3 see see VERB hvd.32044092008168 452 4 theory theory NOUN hvd.32044092008168 452 5 of of ADP hvd.32044092008168 452 6 p p PROPN hvd.32044092008168 452 7 and and CCONJ hvd.32044092008168 452 8 o o NOUN hvd.32044092008168 452 9 functions function NOUN hvd.32044092008168 452 10 . . PUNCT hvd.32044092008168 453 1 34 34 NUM hvd.32044092008168 453 2 part part NOUN hvd.32044092008168 453 3 iii iii NUM hvd.32044092008168 453 4 . . PUNCT hvd.32044092008168 454 1 these these DET hvd.32044092008168 454 2 values value NOUN hvd.32044092008168 454 3 of of ADP hvd.32044092008168 454 4 a a PRON hvd.32044092008168 454 5 ' ' PUNCT hvd.32044092008168 454 6 and and CCONJ hvd.32044092008168 454 7 b b X hvd.32044092008168 454 8 ' ' PUNCT hvd.32044092008168 454 9 ... ... PUNCT hvd.32044092008168 454 10 determine determine VERB hvd.32044092008168 454 11 the the DET hvd.32044092008168 454 12 constants constant NOUN hvd.32044092008168 454 13 a a DET hvd.32044092008168 454 14 , , PUNCT hvd.32044092008168 454 15 b b X hvd.32044092008168 454 16 ... ... PUNCT hvd.32044092008168 454 17 provided provide VERB hvd.32044092008168 454 18 we we PRON hvd.32044092008168 454 19 can can AUX hvd.32044092008168 454 20 find find VERB hvd.32044092008168 454 21 the the DET hvd.32044092008168 454 22 value value NOUN hvd.32044092008168 454 23 of of ADP hvd.32044092008168 454 24 the the DET hvd.32044092008168 454 25 constant constant ADJ hvd.32044092008168 454 26 c. c. NOUN hvd.32044092008168 454 27 it it PRON hvd.32044092008168 454 28 is be AUX hvd.32044092008168 454 29 also also ADV hvd.32044092008168 454 30 clear clear ADJ hvd.32044092008168 454 31 that that SCONJ hvd.32044092008168 454 32 c c PROPN hvd.32044092008168 454 33 must must AUX hvd.32044092008168 454 34 be be AUX hvd.32044092008168 454 35 a a DET hvd.32044092008168 454 36 constant constant NOUN hvd.32044092008168 454 37 involved involve VERB hvd.32044092008168 454 38 in in ADP hvd.32044092008168 454 39 the the DET hvd.32044092008168 454 40 relation relation PROPN hvd.32044092008168 454 41 y y PROPN hvd.32044092008168 454 42 = = PRON hvd.32044092008168 454 43 ya ya PROPN hvd.32044092008168 454 44 . . PUNCT hvd.32044092008168 455 1 2 2 NUM hvd.32044092008168 455 2 2 2 NUM hvd.32044092008168 455 3 2 2 NUM hvd.32044092008168 456 1 and and CCONJ hvd.32044092008168 456 2 we we PRON hvd.32044092008168 456 3 are be AUX hvd.32044092008168 456 4 thus thus ADV hvd.32044092008168 456 5 led lead VERB hvd.32044092008168 456 6 first first ADV hvd.32044092008168 456 7 to to ADP hvd.32044092008168 456 8 a a DET hvd.32044092008168 456 9 development development NOUN hvd.32044092008168 456 10 of of ADP hvd.32044092008168 456 11 y y PROPN hvd.32044092008168 456 12 according accord VERB hvd.32044092008168 456 13 to to ADP hvd.32044092008168 456 14 the the DET hvd.32044092008168 456 15 powers power NOUN hvd.32044092008168 456 16 of of ADP hvd.32044092008168 456 17 t t NOUN hvd.32044092008168 456 18 and and CCONJ hvd.32044092008168 456 19 to to ADP hvd.32044092008168 456 20 the the DET hvd.32044092008168 456 21 finding finding NOUN hvd.32044092008168 456 22 of of ADP hvd.32044092008168 456 23 the the DET hvd.32044092008168 456 24 relation relation NOUN hvd.32044092008168 456 25 between between ADP hvd.32044092008168 456 26 the the DET hvd.32044092008168 456 27 coefficients coefficient NOUN hvd.32044092008168 456 28 . . PUNCT hvd.32044092008168 457 1 thus thus ADV hvd.32044092008168 457 2 y y PROPN hvd.32044092008168 457 3 becomes become VERB hvd.32044092008168 457 4 available available ADJ hvd.32044092008168 457 5 in in ADP hvd.32044092008168 457 6 a a DET hvd.32044092008168 457 7 practical practical ADJ hvd.32044092008168 457 8 form form NOUN hvd.32044092008168 457 9 and and CCONJ hvd.32044092008168 457 10 c c NOUN hvd.32044092008168 457 11 being be AUX hvd.32044092008168 457 12 determined determine VERB hvd.32044092008168 457 13 as as ADP hvd.32044092008168 457 14 a a DET hvd.32044092008168 457 15 function function NOUN hvd.32044092008168 457 16 of of ADP hvd.32044092008168 457 17 y y PROPN hvd.32044092008168 457 18 and and CCONJ hvd.32044092008168 457 19 its its PRON hvd.32044092008168 457 20 derivatives derivative NOUN hvd.32044092008168 457 21 we we PRON hvd.32044092008168 457 22 have have VERB hvd.32044092008168 457 23 our our PRON hvd.32044092008168 457 24 relation relation NOUN hvd.32044092008168 457 25 in in ADP hvd.32044092008168 457 26 a a DET hvd.32044092008168 457 27 new new ADJ hvd.32044092008168 457 28 form form NOUN hvd.32044092008168 457 29 [ [ PUNCT hvd.32044092008168 457 30 52 52 NUM hvd.32044092008168 457 31 ] ] PUNCT hvd.32044092008168 458 1 y y NOUN hvd.32044092008168 458 2 = = PUNCT hvd.32044092008168 458 3 + + NUM hvd.32044092008168 458 4 vy vy NOUN hvd.32044092008168 458 5 . . PUNCT hvd.32044092008168 459 1 i i PRON hvd.32044092008168 459 2 expand expand VERB hvd.32044092008168 459 3 these these DET hvd.32044092008168 459 4 principles principle NOUN hvd.32044092008168 459 5 of of ADP hvd.32044092008168 459 6 m. m. NOUN hvd.32044092008168 459 7 hermite hermite PROPN hvd.32044092008168 459 8 * * PUNCT hvd.32044092008168 459 9 ) ) PUNCT hvd.32044092008168 459 10 ( ( PUNCT hvd.32044092008168 459 11 annali annali PROPN hvd.32044092008168 459 12 di di X hvd.32044092008168 459 13 math math PROPN hvd.32044092008168 459 14 . . PUNCT hvd.32044092008168 459 15 ) ) PUNCT hvd.32044092008168 460 1 and and CCONJ hvd.32044092008168 460 2 halphen halphen ADV hvd.32044092008168 460 3 * * SYM hvd.32044092008168 460 4 * * PUNCT hvd.32044092008168 460 5 ) ) PUNCT hvd.32044092008168 460 6 as as SCONJ hvd.32044092008168 460 7 follows follow VERB hvd.32044092008168 460 8 : : PUNCT hvd.32044092008168 460 9 lamé lamé NOUN hvd.32044092008168 460 10 's 's PART hvd.32044092008168 460 11 equation equation NOUN hvd.32044092008168 460 12 may may AUX hvd.32044092008168 460 13 be be AUX hvd.32044092008168 460 14 written write VERB hvd.32044092008168 460 15 [ [ PUNCT hvd.32044092008168 460 16 53 53 NUM hvd.32044092008168 460 17 ] ] PUNCT hvd.32044092008168 460 18 g”= g”= NOUN hvd.32044092008168 460 19 pu pu PROPN hvd.32044092008168 460 20 where where SCONJ hvd.32044092008168 460 21 p p PROPN hvd.32044092008168 460 22 = = NOUN hvd.32044092008168 460 23 n(n.+ n(n.+ PROPN hvd.32044092008168 460 24 1 1 NUM hvd.32044092008168 460 25 ) ) PUNCT hvd.32044092008168 460 26 pu pu PROPN hvd.32044092008168 460 27 + + PROPN hvd.32044092008168 460 28 b b PROPN hvd.32044092008168 461 1 and and CCONJ hvd.32044092008168 461 2 y y PROPN hvd.32044092008168 461 3 = = PROPN hvd.32044092008168 461 4 vy vy PROPN hvd.32044092008168 461 5 . . PUNCT hvd.32044092008168 462 1 = = PUNCT hvd.32044092008168 462 2 seeking seek VERB hvd.32044092008168 462 3 the the DET hvd.32044092008168 462 4 equation equation NOUN hvd.32044092008168 462 5 in in ADP hvd.32044092008168 462 6 terms term NOUN hvd.32044092008168 462 7 of of ADP hvd.32044092008168 462 8 y y PROPN hvd.32044092008168 462 9 we we PRON hvd.32044092008168 462 10 write write VERB hvd.32044092008168 462 11 y y PROPN hvd.32044092008168 462 12 ' ' PUNCT hvd.32044092008168 462 13 = = SYM hvd.32044092008168 462 14 2yy 2yy PROPN hvd.32044092008168 462 15 ' ' PUNCT hvd.32044092008168 462 16 whence whence PROPN hvd.32044092008168 462 17 y y PROPN hvd.32044092008168 462 18 '' '' PUNCT hvd.32044092008168 462 19 = = VERB hvd.32044092008168 462 20 2y 2y NUM hvd.32044092008168 462 21 ' ' NOUN hvd.32044092008168 462 22 ? ? PUNCT hvd.32044092008168 463 1 + + NUM hvd.32044092008168 463 2 2yy 2yy PROPN hvd.32044092008168 463 3 ” " PUNCT hvd.32044092008168 463 4 = = VERB hvd.32044092008168 464 1 2y 2y NUM hvd.32044092008168 464 2 ' ' NOUN hvd.32044092008168 464 3 ? ? PUNCT hvd.32044092008168 465 1 + + CCONJ hvd.32044092008168 465 2 2 2 NUM hvd.32044092008168 465 3 py py X hvd.32044092008168 465 4 = = PUNCT hvd.32044092008168 465 5 2y 2y PROPN hvd.32044092008168 465 6 ' ' NOUN hvd.32044092008168 465 7 ? ? PUNCT hvd.32044092008168 466 1 + + PUNCT hvd.32044092008168 466 2 2py 2py ADJ hvd.32044092008168 466 3 , , PUNCT hvd.32044092008168 466 4 also also ADV hvd.32044092008168 466 5 ( ( PUNCT hvd.32044092008168 466 6 y y PROPN hvd.32044092008168 466 7 ” " PUNCT hvd.32044092008168 466 8 – – PUNCT hvd.32044092008168 466 9 2py 2py PROPN hvd.32044092008168 466 10 ) ) PUNCT hvd.32044092008168 466 11 = = NOUN hvd.32044092008168 466 12 4y'y 4y'y NUM hvd.32044092008168 466 13 " " PUNCT hvd.32044092008168 466 14 = = VERB hvd.32044092008168 466 15 4 4 NUM hvd.32044092008168 466 16 pyy pyy NOUN hvd.32044092008168 466 17 ' ' PART hvd.32044092008168 466 18 2py 2py PROPN hvd.32044092008168 466 19 y y PROPN hvd.32044092008168 466 20 " " PUNCT hvd.32044092008168 466 21 ' ' PUNCT hvd.32044092008168 466 22 " " PUNCT hvd.32044092008168 466 23 = = NOUN hvd.32044092008168 467 1 whence whence NOUN hvd.32044092008168 467 2 [ [ X hvd.32044092008168 467 3 54 54 NUM hvd.32044092008168 467 4 ] ] PUNCT hvd.32044092008168 467 5 y y PROPN hvd.32044092008168 467 6 " " PUNCT hvd.32044092008168 467 7 " " PUNCT hvd.32044092008168 467 8 – – PUNCT hvd.32044092008168 467 9 4py 4py NOUN hvd.32044092008168 467 10 ' ' PUNCT hvd.32044092008168 467 11 – – PUNCT hvd.32044092008168 467 12 2p'y=0 2p'y=0 NUM hvd.32044092008168 467 13 a a DET hvd.32044092008168 467 14 linear linear ADJ hvd.32044092008168 467 15 differential differential ADJ hvd.32044092008168 467 16 equation equation NOUN hvd.32044092008168 467 17 in in ADP hvd.32044092008168 467 18 y y PROPN hvd.32044092008168 467 19 of of ADP hvd.32044092008168 467 20 the the DET hvd.32044092008168 467 21 third third ADJ hvd.32044092008168 467 22 order order NOUN hvd.32044092008168 467 23 . . PUNCT hvd.32044092008168 468 1 from from ADP hvd.32044092008168 468 2 the the DET hvd.32044092008168 468 3 theory theory NOUN hvd.32044092008168 468 4 of of ADP hvd.32044092008168 468 5 the the DET hvd.32044092008168 468 6 linear linear ADJ hvd.32044092008168 468 7 differential differential ADJ hvd.32044092008168 468 8 equation equation NOUN hvd.32044092008168 468 9 , , PUNCT hvd.32044092008168 468 10 if if SCONJ hvd.32044092008168 468 11 y y PROPN hvd.32044092008168 468 12 and and CCONJ hvd.32044092008168 468 13 2 2 NUM hvd.32044092008168 468 14 are be AUX hvd.32044092008168 468 15 solutions solution NOUN hvd.32044092008168 468 16 of of ADP hvd.32044092008168 468 17 ( ( PUNCT hvd.32044092008168 468 18 53 53 NUM hvd.32044092008168 468 19 ) ) PUNCT hvd.32044092008168 468 20 vy+will vy+will NOUN hvd.32044092008168 468 21 also also ADV hvd.32044092008168 468 22 be be AUX hvd.32044092008168 468 23 a a DET hvd.32044092008168 468 24 solution solution NOUN hvd.32044092008168 468 25 y y PROPN hvd.32044092008168 468 26 and and CCONJ hvd.32044092008168 468 27 q q X hvd.32044092008168 468 28 being be AUX hvd.32044092008168 468 29 arbitrary arbitrary ADJ hvd.32044092008168 468 30 constants constant NOUN hvd.32044092008168 468 31 , , PUNCT hvd.32044092008168 468 32 and and CCONJ hvd.32044092008168 468 33 we we PRON hvd.32044092008168 468 34 derive derive VERB hvd.32044092008168 468 35 also also ADV hvd.32044092008168 468 36 as as ADP hvd.32044092008168 468 37 distinct distinct ADJ hvd.32044092008168 468 38 solutions solution NOUN hvd.32044092008168 468 39 of of ADP hvd.32044092008168 468 40 the the DET hvd.32044092008168 468 41 transformed transformed ADJ hvd.32044092008168 468 42 ( ( PUNCT hvd.32044092008168 468 43 54 54 NUM hvd.32044092008168 468 44 ) ) PUNCT hvd.32044092008168 468 45 y y PROPN hvd.32044092008168 468 46 , , PUNCT hvd.32044092008168 468 47 yx yx PROPN hvd.32044092008168 468 48 and and CCONJ hvd.32044092008168 468 49 m2 m2 PROPN hvd.32044092008168 468 50 obtained obtain VERB hvd.32044092008168 468 51 from from ADP hvd.32044092008168 468 52 the the DET hvd.32044092008168 468 53 complex complex ADJ hvd.32044092008168 468 54 form form NOUN hvd.32044092008168 468 55 ( ( PUNCT hvd.32044092008168 468 56 ry ry NOUN hvd.32044092008168 468 57 + + PROPN hvd.32044092008168 468 58 92 92 NUM hvd.32044092008168 468 59 ) ) PUNCT hvd.32044092008168 468 60 p p PROPN hvd.32044092008168 468 61 ' ' PUNCT hvd.32044092008168 468 62 = = SYM hvd.32044092008168 468 63 n(n n(n X hvd.32044092008168 468 64 + + CCONJ hvd.32044092008168 468 65 1 1 NUM hvd.32044092008168 468 66 ) ) PUNCT hvd.32044092008168 468 67 p'u p'u ADV hvd.32044092008168 468 68 and and CCONJ hvd.32044092008168 468 69 the the DET hvd.32044092008168 468 70 transformed transformed NOUN hvd.32044092008168 468 71 may may AUX hvd.32044092008168 468 72 be be AUX hvd.32044092008168 468 73 written write VERB hvd.32044092008168 468 74 : : PUNCT hvd.32044092008168 468 75 [ [ X hvd.32044092008168 468 76 55 55 NUM hvd.32044092008168 468 77 ] ] PUNCT hvd.32044092008168 468 78 · · PUNCT hvd.32044092008168 468 79 y y PROPN hvd.32044092008168 468 80 '' '' PUNCT hvd.32044092008168 468 81 ' ' PUNCT hvd.32044092008168 468 82 — — PUNCT hvd.32044092008168 468 83 4 4 NUM hvd.32044092008168 468 84 [ [ X hvd.32044092008168 468 85 n(n n(n PROPN hvd.32044092008168 468 86 + + CCONJ hvd.32044092008168 468 87 1 1 X hvd.32044092008168 468 88 ) ) PUNCT hvd.32044092008168 468 89 pu pu PROPN hvd.32044092008168 468 90 + + PROPN hvd.32044092008168 468 91 b b ADP hvd.32044092008168 468 92 ] ] X hvd.32044092008168 468 93 y y NOUN hvd.32044092008168 468 94 ' ' PUNCT hvd.32044092008168 468 95 — — PUNCT hvd.32044092008168 468 96 2n(n 2n(n NUM hvd.32044092008168 468 97 + + NUM hvd.32044092008168 468 98 1 1 NUM hvd.32044092008168 468 99 ) ) PUNCT hvd.32044092008168 468 100 p’u p’u PROPN hvd.32044092008168 469 1 y y PROPN hvd.32044092008168 469 2 = = PUNCT hvd.32044092008168 469 3 0 0 NUM hvd.32044092008168 469 4 where where SCONJ hvd.32044092008168 469 5 to(a to(a PUNCT hvd.32044092008168 469 6 + + PROPN hvd.32044092008168 469 7 u u PROPN hvd.32044092008168 469 8 ) ) PUNCT hvd.32044092008168 469 9 ( ( PUNCT hvd.32044092008168 469 10 a a DET hvd.32044092008168 469 11 u u NOUN hvd.32044092008168 469 12 ) ) PUNCT hvd.32044092008168 469 13 y y PROPN hvd.32044092008168 470 1 = = PRON hvd.32044092008168 470 2 it it PRON hvd.32044092008168 470 3 o o X hvd.32044092008168 470 4 ua ua PROPN hvd.32044092008168 470 5 ) ) PUNCT hvd.32044092008168 470 6 . . PUNCT hvd.32044092008168 471 1 = = PROPN hvd.32044092008168 471 2 ii ii PROPN hvd.32044092008168 471 3 ( ( PUNCT hvd.32044092008168 471 4 pu pu X hvd.32044092008168 471 5 gº gº X hvd.32044092008168 471 6 a a DET hvd.32044092008168 471 7 gau gau PROPN hvd.32044092008168 471 8 this this DET hvd.32044092008168 471 9 value value NOUN hvd.32044092008168 471 10 indicates indicate VERB hvd.32044092008168 471 11 that that SCONJ hvd.32044092008168 471 12 ( ( PUNCT hvd.32044092008168 471 13 55 55 NUM hvd.32044092008168 471 14 ) ) PUNCT hvd.32044092008168 471 15 has have VERB hvd.32044092008168 471 16 n n PRON hvd.32044092008168 471 17 solutions solution NOUN hvd.32044092008168 471 18 in in ADP hvd.32044092008168 471 19 terms term NOUN hvd.32044092008168 471 20 of of ADP hvd.32044092008168 471 21 p p PROPN hvd.32044092008168 471 22 ( ( PUNCT hvd.32044092008168 471 23 u u PROPN hvd.32044092008168 471 24 ) ) PUNCT hvd.32044092008168 471 25 : : PUNCT hvd.32044092008168 471 26 * * PUNCT hvd.32044092008168 471 27 ) ) PUNCT hvd.32044092008168 471 28 bd bd PROPN hvd.32044092008168 471 29 . . PROPN hvd.32044092008168 471 30 ii ii PROPN hvd.32044092008168 471 31 . . PUNCT hvd.32044092008168 472 1 p. p. NOUN hvd.32044092008168 472 2 498 498 NUM hvd.32044092008168 472 3 . . PUNCT hvd.32044092008168 473 1 * * PUNCT hvd.32044092008168 473 2 * * PUNCT hvd.32044092008168 473 3 ) ) PUNCT hvd.32044092008168 473 4 bd bd PROPN hvd.32044092008168 473 5 . . PROPN hvd.32044092008168 473 6 ii ii PROPN hvd.32044092008168 473 7 . . PUNCT hvd.32044092008168 474 1 p. p. NOUN hvd.32044092008168 474 2 498 498 NUM hvd.32044092008168 474 3 . . PUNCT hvd.32044092008168 475 1 integral integral ADJ hvd.32044092008168 475 2 as as ADP hvd.32044092008168 475 3 a a DET hvd.32044092008168 475 4 product product NOUN hvd.32044092008168 475 5 . . PUNCT hvd.32044092008168 476 1 35 35 NUM hvd.32044092008168 476 2 from from ADP hvd.32044092008168 476 3 which which PRON hvd.32044092008168 476 4 it it PRON hvd.32044092008168 476 5 follows follow VERB hvd.32044092008168 476 6 also also ADV hvd.32044092008168 476 7 that that SCONJ hvd.32044092008168 476 8 y y PROPN hvd.32044092008168 476 9 may may AUX hvd.32044092008168 476 10 be be AUX hvd.32044092008168 476 11 written write VERB hvd.32044092008168 476 12 as as ADP hvd.32044092008168 476 13 an an DET hvd.32044092008168 476 14 intire intire ADJ hvd.32044092008168 476 15 polynomial polynomial NOUN hvd.32044092008168 476 16 of of ADP hvd.32044092008168 476 17 the the DET hvd.32044092008168 476 18 nth nth NOUN hvd.32044092008168 476 19 degree degree NOUN hvd.32044092008168 476 20 in in ADP hvd.32044092008168 476 21 t t PROPN hvd.32044092008168 476 22 = = PROPN hvd.32044092008168 476 23 pu pu PROPN hvd.32044092008168 476 24 . . PUNCT hvd.32044092008168 477 1 that that PRON hvd.32044092008168 477 2 is be AUX hvd.32044092008168 477 3 [ [ X hvd.32044092008168 477 4 56 56 NUM hvd.32044092008168 477 5 ] ] PUNCT hvd.32044092008168 477 6 · · PUNCT hvd.32044092008168 477 7 ... ... PUNCT hvd.32044092008168 478 1 yt yt PROPN hvd.32044092008168 478 2 + + CCONJ hvd.32044092008168 478 3 α₁tn−1 α₁tn−1 PROPN hvd.32044092008168 478 4 + + CCONJ hvd.32044092008168 478 5 αtn-² αtn-² ADP hvd.32044092008168 478 6 + + PROPN hvd.32044092008168 478 7 -1 -1 PROPN hvd.32044092008168 479 1 -2 -2 NOUN hvd.32044092008168 479 2 · · PUNCT hvd.32044092008168 479 3 + + PROPN hvd.32044092008168 479 4 an an X hvd.32044092008168 479 5 - - PUNCT hvd.32044092008168 479 6 it it PRON hvd.32044092008168 479 7 + + CCONJ hvd.32044092008168 479 8 an an PRON hvd.32044092008168 479 9 . . PUNCT hvd.32044092008168 480 1 equation equation NOUN hvd.32044092008168 481 1 [ [ X hvd.32044092008168 481 2 55 55 NUM hvd.32044092008168 481 3 ] ] PUNCT hvd.32044092008168 481 4 is be AUX hvd.32044092008168 481 5 written write VERB hvd.32044092008168 481 6 in in ADP hvd.32044092008168 481 7 terms term NOUN hvd.32044092008168 481 8 of of ADP hvd.32044092008168 481 9 derivatives derivative NOUN hvd.32044092008168 481 10 with with ADP hvd.32044092008168 481 11 respect respect NOUN hvd.32044092008168 481 12 to to ADP hvd.32044092008168 481 13 u u PROPN hvd.32044092008168 481 14 whence whence NOUN hvd.32044092008168 481 15 to to PART hvd.32044092008168 481 16 determine determine VERB hvd.32044092008168 481 17 the the DET hvd.32044092008168 481 18 coefficients coefficient NOUN hvd.32044092008168 481 19 in in ADP hvd.32044092008168 481 20 ( ( PUNCT hvd.32044092008168 481 21 56 56 NUM hvd.32044092008168 481 22 ) ) PUNCT hvd.32044092008168 481 23 we we PRON hvd.32044092008168 481 24 must must AUX hvd.32044092008168 481 25 express express VERB hvd.32044092008168 481 26 ( ( PUNCT hvd.32044092008168 481 27 55 55 NUM hvd.32044092008168 481 28 ) ) PUNCT hvd.32044092008168 481 29 also also ADV hvd.32044092008168 481 30 in in ADP hvd.32044092008168 481 31 terms term NOUN hvd.32044092008168 481 32 of of ADP hvd.32044092008168 481 33 derivatives derivative NOUN hvd.32044092008168 481 34 of of ADP hvd.32044092008168 481 35 t t PROPN hvd.32044092008168 481 36 = = PROPN hvd.32044092008168 481 37 pu pu PROPN hvd.32044092008168 481 38 and and CCONJ hvd.32044092008168 481 39 equate equate VERB hvd.32044092008168 481 40 the the DET hvd.32044092008168 481 41 coefficients coefficient NOUN hvd.32044092008168 481 42 of of ADP hvd.32044092008168 481 43 like like ADJ hvd.32044092008168 481 44 powers power NOUN hvd.32044092008168 481 45 in in ADP hvd.32044092008168 481 46 the the DET hvd.32044092008168 481 47 two two NUM hvd.32044092008168 481 48 identities identity NOUN hvd.32044092008168 481 49 thus thus ADV hvd.32044092008168 481 50 obtained obtain VERB hvd.32044092008168 481 51 . . PUNCT hvd.32044092008168 482 1 take take VERB hvd.32044092008168 482 2 whence whence NOUN hvd.32044092008168 482 3 d₁u d₁u ADP hvd.32044092008168 482 4 = = X hvd.32044092008168 482 5 q q X hvd.32044092008168 482 6 ꭰ ꭰ NOUN hvd.32044092008168 483 1 and and CCONJ hvd.32044092008168 483 2 du du PROPN hvd.32044092008168 483 3 y y PROPN hvd.32044092008168 483 4 dydut dydut VERB hvd.32044092008168 483 5 1 1 NUM hvd.32044092008168 483 6 „ „ PUNCT hvd.32044092008168 483 7 ³ ³ ADJ hvd.32044092008168 483 8 ; ; PUNCT hvd.32044092008168 483 9 diu diu PROPN hvd.32044092008168 483 10 2 2 NUM hvd.32044092008168 483 11 då då NOUN hvd.32044092008168 483 12 da da NOUN hvd.32044092008168 483 13 y= y= PROPN hvd.32044092008168 483 14 = = X hvd.32044092008168 483 15 d³ d³ PROPN hvd.32044092008168 483 16 y y PROPN hvd.32044092008168 483 17 — — PUNCT hvd.32044092008168 483 18 = = PROPN hvd.32044092008168 483 19 d2 d2 PROPN hvd.32044092008168 483 20 y y PROPN hvd.32044092008168 483 21 dt2 dt2 PROPN hvd.32044092008168 483 22 d³ d³ PROPN hvd.32044092008168 483 23 y y PROPN hvd.32044092008168 483 24 dt3 dt3 NOUN hvd.32044092008168 483 25 2 2 NUM hvd.32044092008168 483 26 9 9 NUM hvd.32044092008168 483 27 = = SYM hvd.32044092008168 483 28 9 9 NUM hvd.32044092008168 483 29 ( ( PUNCT hvd.32044092008168 483 30 t t PROPN hvd.32044092008168 483 31 ) ) PUNCT hvd.32044092008168 483 32 = = PROPN hvd.32044092008168 483 33 4t³ 4t³ NUM hvd.32044092008168 483 34 — — PUNCT hvd.32044092008168 483 35 j₂t j₂t NOUN hvd.32044092008168 483 36 — — PUNCT hvd.32044092008168 483 37 93 93 NUM hvd.32044092008168 483 38 = = SYM hvd.32044092008168 483 39 p² p² VERB hvd.32044092008168 483 40 ² ² X hvd.32044092008168 483 41 u u PROPN hvd.32044092008168 484 1 [ [ X hvd.32044092008168 484 2 57 57 NUM hvd.32044092008168 484 3 ] ] PUNCT hvd.32044092008168 484 4 ( ( PUNCT hvd.32044092008168 484 5 4t³ 4t³ NUM hvd.32044092008168 484 6 — — PUNCT hvd.32044092008168 484 7 g₂t g₂t PROPN hvd.32044092008168 484 8 — — PUNCT hvd.32044092008168 484 9 93 93 NUM hvd.32044092008168 484 10 ) ) PUNCT hvd.32044092008168 484 11 --3 --3 NOUN hvd.32044092008168 485 1 u u NOUN hvd.32044092008168 485 2 = = VERB hvd.32044092008168 485 3 19 19 NUM hvd.32044092008168 485 4 29 29 NUM hvd.32044092008168 485 5 ; ; PUNCT hvd.32044092008168 485 6 du du PROPN hvd.32044092008168 485 7 ф ф X hvd.32044092008168 485 8 ዎ ዎ X hvd.32044092008168 485 9 = = SYM hvd.32044092008168 485 10 1 1 NUM hvd.32044092008168 485 11 92 92 NUM hvd.32044092008168 485 12 d d NOUN hvd.32044092008168 485 13 , , PUNCT hvd.32044092008168 485 14 y y PROPN hvd.32044092008168 485 15 du du PROPN hvd.32044092008168 485 16 dy dy PROPN hvd.32044092008168 485 17 d d PROPN hvd.32044092008168 485 18 , , PUNCT hvd.32044092008168 485 19 y y PROPN hvd.32044092008168 485 20 du du PROPN hvd.32044092008168 485 21 3 3 NUM hvd.32044092008168 485 22 ( ( PUNCT hvd.32044092008168 485 23 du du PROPN hvd.32044092008168 485 24 ) ) PUNCT hvd.32044092008168 485 25 these these DET hvd.32044092008168 485 26 substitutions substitution NOUN hvd.32044092008168 485 27 give give VERB hvd.32044092008168 485 28 : : PUNCT hvd.32044092008168 485 29 ... ... PUNCT hvd.32044092008168 485 30 3 3 NUM hvd.32044092008168 485 31 1 1 NUM hvd.32044092008168 485 32 3 3 NUM hvd.32044092008168 485 33 1 1 NUM hvd.32044092008168 485 34 2 2 NUM hvd.32044092008168 485 35 " " PUNCT hvd.32044092008168 485 36 — — PUNCT hvd.32044092008168 485 37 9 9 NUM hvd.32044092008168 485 38 ¹³ ¹³ NUM hvd.32044092008168 485 39 d d NOUN hvd.32044092008168 485 40 ; ; PUNCT hvd.32044092008168 485 41 y y PROPN hvd.32044092008168 485 42 + + PROPN hvd.32044092008168 485 43 9 9 NUM hvd.32044092008168 485 44 ³ ³ X hvd.32044092008168 485 45 q q X hvd.32044092008168 485 46 ´ ´ INTJ hvd.32044092008168 485 47 d d NOUN hvd.32044092008168 485 48 ; ; PUNCT hvd.32044092008168 485 49 y y PROPN hvd.32044092008168 485 50 — — PUNCT hvd.32044092008168 485 51 — — PUNCT hvd.32044092008168 485 52 9 9 NUM hvd.32044092008168 485 53 ³ ³ NUM hvd.32044092008168 485 54 9″ 9″ NUM hvd.32044092008168 485 55 d d NOUN hvd.32044092008168 485 56 , , PUNCT hvd.32044092008168 485 57 y y PROPN hvd.32044092008168 485 58 2 2 NUM hvd.32044092008168 485 59 = = SYM hvd.32044092008168 485 60 2 2 NUM hvd.32044092008168 485 61 2 2 NUM hvd.32044092008168 485 62 2 2 NUM hvd.32044092008168 485 63 u u PROPN hvd.32044092008168 485 64 = = PROPN hvd.32044092008168 485 65 ዎ ዎ PRON hvd.32044092008168 485 66 3 3 NUM hvd.32044092008168 485 67 4 4 NUM hvd.32044092008168 485 68 5 5 NUM hvd.32044092008168 485 69 2 2 NUM hvd.32044092008168 485 70 φ φ PROPN hvd.32044092008168 485 71 ― ― PROPN hvd.32044092008168 485 72 /2 /2 PROPN hvd.32044092008168 485 73 ▬ ▬ PROPN hvd.32044092008168 485 74 ▬ ▬ NUM hvd.32044092008168 485 75 ▬ ▬ NUM hvd.32044092008168 485 76 ▬ ▬ NUM hvd.32044092008168 485 77 ▬ ▬ NUM hvd.32044092008168 485 78 ▬ ▬ NUM hvd.32044092008168 485 79 ▬ ▬ NUM hvd.32044092008168 485 80 ▬ ▬ NUM hvd.32044092008168 485 81 ▬ ▬ NUM hvd.32044092008168 485 82 ▬ ▬ NUM hvd.32044092008168 485 83 ▬ ▬ NUM hvd.32044092008168 485 84 ▬ ▬ PROPN hvd.32044092008168 485 85 ▬ ▬ PROPN hvd.32044092008168 485 86 ( ( PUNCT hvd.32044092008168 485 87 d¸u)² d¸u)² NOUN hvd.32044092008168 485 88 d³ d³ PROPN hvd.32044092008168 485 89 y y PROPN hvd.32044092008168 485 90 — — PUNCT hvd.32044092008168 485 91 d¸u d¸u CCONJ hvd.32044092008168 485 92 d¾ d¾ PROPN hvd.32044092008168 485 93 u u PROPN hvd.32044092008168 485 94 d¸ d¸ PROPN hvd.32044092008168 485 95 y y PROPN hvd.32044092008168 485 96 — — PUNCT hvd.32044092008168 485 97 3 3 NUM hvd.32044092008168 485 98 d¸u d¸u NUM hvd.32044092008168 485 99 d¾ d¾ NOUN hvd.32044092008168 485 100 u u PROPN hvd.32044092008168 485 101 d¸ d¸ PROPN hvd.32044092008168 485 102 y y PROPN hvd.32044092008168 485 103 + + PROPN hvd.32044092008168 485 104 3 3 NUM hvd.32044092008168 485 105 ( ( PUNCT hvd.32044092008168 485 106 d² d² PROPN hvd.32044092008168 485 107 u)² u)² NOUN hvd.32044092008168 485 108 d¸y d¸y PUNCT hvd.32044092008168 486 1 t t PROPN hvd.32044092008168 486 2 t t PROPN hvd.32044092008168 486 3 ( ( PUNCT hvd.32044092008168 486 4 d d PROPN hvd.32044092008168 486 5 , , PUNCT hvd.32044092008168 486 6 u u PROPN hvd.32044092008168 486 7 ) ) PUNCT hvd.32044092008168 486 8 d2 d2 PROPN hvd.32044092008168 486 9 y y PROPN hvd.32044092008168 486 10 d³ d³ PROPN hvd.32044092008168 486 11 y y PROPN hvd.32044092008168 486 12 dt3 dt3 PROPN hvd.32044092008168 486 13 + + PROPN hvd.32044092008168 486 14 3 3 NUM hvd.32044092008168 486 15 ( ( PUNCT hvd.32044092008168 486 16 61² 61² NUM hvd.32044092008168 486 17 — — PUNCT hvd.32044092008168 486 18 1 1 NUM hvd.32044092008168 486 19 92 92 NUM hvd.32044092008168 486 20 ) ) PUNCT hvd.32044092008168 486 21 2 2 NUM hvd.32044092008168 486 22 − − PROPN hvd.32044092008168 486 23 4 4 NUM hvd.32044092008168 486 24 [ [ X hvd.32044092008168 486 25 ( ( PUNCT hvd.32044092008168 486 26 n²+ n²+ X hvd.32044092008168 486 27 n n CCONJ hvd.32044092008168 486 28 − − PROPN hvd.32044092008168 486 29 3 3 X hvd.32044092008168 486 30 ) ) PUNCT hvd.32044092008168 486 31 t t PROPN hvd.32044092008168 486 32 + + SYM hvd.32044092008168 486 33 b b X hvd.32044092008168 486 34 ] ] X hvd.32044092008168 486 35 dr dr PROPN hvd.32044092008168 486 36 dy dy PROPN hvd.32044092008168 486 37 dt dt PROPN hvd.32044092008168 486 38 2 2 NUM hvd.32044092008168 486 39 dt2 dt2 PROPN hvd.32044092008168 486 40 2n 2n NUM hvd.32044092008168 486 41 ( ( PUNCT hvd.32044092008168 486 42 n n X hvd.32044092008168 486 43 + + CCONJ hvd.32044092008168 486 44 1 1 X hvd.32044092008168 486 45 ) ) PUNCT hvd.32044092008168 486 46 y y PROPN hvd.32044092008168 486 47 = = NOUN hvd.32044092008168 486 48 0 0 NUM hvd.32044092008168 486 49 . . PUNCT hvd.32044092008168 486 50 from from ADP hvd.32044092008168 486 51 [ [ X hvd.32044092008168 486 52 56 56 NUM hvd.32044092008168 486 53 ] ] PUNCT hvd.32044092008168 486 54 we we PRON hvd.32044092008168 486 55 obtain obtain VERB hvd.32044092008168 486 56 the the DET hvd.32044092008168 486 57 values value NOUN hvd.32044092008168 486 58 of of ADP hvd.32044092008168 486 59 these these DET hvd.32044092008168 486 60 derivatives derivative NOUN hvd.32044092008168 486 61 , , PUNCT hvd.32044092008168 486 62 namely namely ADV hvd.32044092008168 486 63 dy dy DET hvd.32044092008168 486 64 dt dt PROPN hvd.32044092008168 486 65 1 1 NUM hvd.32044092008168 486 66 2 2 NUM hvd.32044092008168 486 67 9 9 NUM hvd.32044092008168 486 68 = = NOUN hvd.32044092008168 486 69 ntn−1 ntn−1 ADJ hvd.32044092008168 486 70 + + CCONJ hvd.32044092008168 486 71 a₁ a₁ NOUN hvd.32044092008168 486 72 ( ( PUNCT hvd.32044092008168 486 73 n n CCONJ hvd.32044092008168 486 74 − − NOUN hvd.32044092008168 486 75 1)tn—² 1)tn—² NUM hvd.32044092008168 486 76 + + CCONJ hvd.32044092008168 486 77 α α NOUN hvd.32044092008168 486 78 , , PUNCT hvd.32044092008168 486 79 ( ( PUNCT hvd.32044092008168 486 80 n n CCONJ hvd.32044092008168 486 81 − − PROPN hvd.32044092008168 486 82 2 2 X hvd.32044092008168 486 83 ) ) PUNCT hvd.32044092008168 486 84 tn−³ tn−³ ADV hvd.32044092008168 486 85 + + CCONJ hvd.32044092008168 486 86 az az PROPN hvd.32044092008168 486 87 ( ( PUNCT hvd.32044092008168 486 88 n n CCONJ hvd.32044092008168 486 89 − − PROPN hvd.32044092008168 486 90 3 3 X hvd.32044092008168 486 91 ) ) PUNCT hvd.32044092008168 486 92 t”—4 t”—4 NOUN hvd.32044092008168 486 93 a₂ a₂ PROPN hvd.32044092008168 486 94 2 2 NUM hvd.32044092008168 486 95 -3 -3 X hvd.32044092008168 486 96 -4 -4 X hvd.32044092008168 486 97 3 3 NUM hvd.32044092008168 486 98 4 4 NUM hvd.32044092008168 486 99 ) ) PUNCT hvd.32044092008168 486 100 t−5 t−5 PROPN hvd.32044092008168 487 1 + + PUNCT hvd.32044092008168 487 2 .. .. PUNCT hvd.32044092008168 488 1 + + PUNCT hvd.32044092008168 488 2 α α NOUN hvd.32044092008168 488 3 ( ( PUNCT hvd.32044092008168 488 4 n n CCONJ hvd.32044092008168 488 5 − − PROPN hvd.32044092008168 488 6 4 4 X hvd.32044092008168 488 7 ) ) PUNCT hvd.32044092008168 488 8 tn−5 tn−5 PROPN hvd.32044092008168 489 1 n(n−1)!"-+a(n n(n−1)!"-+a(n NOUN hvd.32044092008168 489 2 −1)(n −1)(n X hvd.32044092008168 489 3 −2)!"-sta −2)!"-sta X hvd.32044092008168 489 4 ( ( PUNCT hvd.32044092008168 489 5 n−2)(n−3)-4 n−2)(n−3)-4 X hvd.32044092008168 489 6 -3 -3 X hvd.32044092008168 489 7 + + CCONJ hvd.32044092008168 489 8 as as ADP hvd.32044092008168 489 9 ( ( PUNCT hvd.32044092008168 489 10 n n CCONJ hvd.32044092008168 489 11 − − PROPN hvd.32044092008168 489 12 3 3 X hvd.32044092008168 489 13 ) ) PUNCT hvd.32044092008168 489 14 ( ( PUNCT hvd.32044092008168 489 15 n n CCONJ hvd.32044092008168 489 16 − − PROPN hvd.32044092008168 489 17 4 4 X hvd.32044092008168 489 18 ) ) PUNCT hvd.32044092008168 489 19 tr−5 tr−5 PROPN hvd.32044092008168 489 20 + + PROPN hvd.32044092008168 489 21 · · PUNCT hvd.32044092008168 489 22 · · PUNCT hvd.32044092008168 489 23 · · PUNCT hvd.32044092008168 489 24 " " PUNCT hvd.32044092008168 489 25 = = X hvd.32044092008168 489 26 a a DET hvd.32044092008168 489 27 n n NOUN hvd.32044092008168 489 28 ( ( PUNCT hvd.32044092008168 489 29 n n CCONJ hvd.32044092008168 489 30 − − PROPN hvd.32044092008168 489 31 1 1 X hvd.32044092008168 489 32 ) ) PUNCT hvd.32044092008168 489 33 ( ( PUNCT hvd.32044092008168 489 34 n n CCONJ hvd.32044092008168 489 35 − − PROPN hvd.32044092008168 489 36 2 2 X hvd.32044092008168 489 37 ) ) PUNCT hvd.32044092008168 489 38 t−3 t−3 NOUN hvd.32044092008168 489 39 + + CCONJ hvd.32044092008168 489 40 a a PRON hvd.32044092008168 489 41 ( ( PUNCT hvd.32044092008168 489 42 n n CCONJ hvd.32044092008168 489 43 − − PROPN hvd.32044092008168 489 44 1 1 NUM hvd.32044092008168 489 45 ) ) PUNCT hvd.32044092008168 489 46 ( ( PUNCT hvd.32044092008168 489 47 n n CCONJ hvd.32044092008168 489 48 − − PROPN hvd.32044092008168 489 49 2 2 X hvd.32044092008168 489 50 ) ) PUNCT hvd.32044092008168 489 51 ( ( PUNCT hvd.32044092008168 489 52 n n CCONJ hvd.32044092008168 489 53 − − PROPN hvd.32044092008168 489 54 3 3 NUM hvd.32044092008168 489 55 ) ) PUNCT hvd.32044092008168 489 56 -3 -3 PUNCT hvd.32044092008168 489 57 — — PUNCT hvd.32044092008168 489 58 · · PUNCT hvd.32044092008168 489 59 -5 -5 PROPN hvd.32044092008168 489 60 ta ta X hvd.32044092008168 489 61 ( ( PUNCT hvd.32044092008168 489 62 n-2 n-2 PROPN hvd.32044092008168 489 63 ) ) PUNCT hvd.32044092008168 489 64 ( ( PUNCT hvd.32044092008168 489 65 n n CCONJ hvd.32044092008168 489 66 − − PROPN hvd.32044092008168 489 67 3 3 X hvd.32044092008168 489 68 ) ) PUNCT hvd.32044092008168 489 69 ( ( PUNCT hvd.32044092008168 489 70 n n CCONJ hvd.32044092008168 489 71 − − PROPN hvd.32044092008168 489 72 4 4 X hvd.32044092008168 489 73 ) ) PUNCT hvd.32044092008168 489 74 tt tt PROPN hvd.32044092008168 489 75 and and CCONJ hvd.32044092008168 489 76 equating equate VERB hvd.32044092008168 489 77 the the DET hvd.32044092008168 489 78 coefficients coefficient NOUN hvd.32044092008168 489 79 to to ADP hvd.32044092008168 489 80 zero zero NUM hvd.32044092008168 489 81 we we PRON hvd.32044092008168 489 82 have have VERB hvd.32044092008168 489 83 : : PUNCT hvd.32044092008168 489 84 3 3 NUM hvd.32044092008168 489 85 * * SYM hvd.32044092008168 489 86 36 36 NUM hvd.32044092008168 489 87 part part NOUN hvd.32044092008168 489 88 iii iii NUM hvd.32044092008168 489 89 . . PUNCT hvd.32044092008168 489 90 n n CCONJ hvd.32044092008168 489 91 3 3 NUM hvd.32044092008168 489 92 n n CCONJ hvd.32044092008168 489 93 – – PUNCT hvd.32044092008168 489 94 3 3 NUM hvd.32044092008168 489 95 : : SYM hvd.32044092008168 489 96 4a3 4a3 NUM hvd.32044092008168 489 97 ( ( PUNCT hvd.32044092008168 489 98 n n CCONJ hvd.32044092008168 489 99 − − PROPN hvd.32044092008168 489 100 3 3 NUM hvd.32044092008168 489 101 ) ) PUNCT hvd.32044092008168 489 102 ( ( PUNCT hvd.32044092008168 489 103 n n NOUN hvd.32044092008168 489 104 — — PUNCT hvd.32044092008168 489 105 4 4 X hvd.32044092008168 489 106 ) ) PUNCT hvd.32044092008168 489 107 ( ( PUNCT hvd.32044092008168 489 108 n n NOUN hvd.32044092008168 489 109 – – PUNCT hvd.32044092008168 489 110 5 5 X hvd.32044092008168 489 111 ) ) PUNCT hvd.32044092008168 489 112 – – PUNCT hvd.32044092008168 489 113 9,0(n 9,0(n NUM hvd.32044092008168 489 114 1)(n 1)(n PROPN hvd.32044092008168 489 115 − − PROPN hvd.32044092008168 489 116 2)(n 2)(n PROPN hvd.32044092008168 489 117 − − PROPN hvd.32044092008168 489 118 3 3 NUM hvd.32044092008168 489 119 ) ) PUNCT hvd.32044092008168 489 120 3 3 NUM hvd.32044092008168 489 121 n n CCONJ hvd.32044092008168 489 122 5 5 NUM hvd.32044092008168 489 123 — — PUNCT hvd.32044092008168 489 124 92a 92a NUM hvd.32044092008168 489 125 — — PUNCT hvd.32044092008168 489 126 ) ) PUNCT hvd.32044092008168 489 127 izn izn PROPN hvd.32044092008168 489 128 ( ( PUNCT hvd.32044092008168 489 129 n n CCONJ hvd.32044092008168 489 130 − − PROPN hvd.32044092008168 489 131 1 1 X hvd.32044092008168 489 132 ) ) PUNCT hvd.32044092008168 489 133 ( ( PUNCT hvd.32044092008168 489 134 n n CCONJ hvd.32044092008168 489 135 − − PROPN hvd.32044092008168 489 136 2 2 NUM hvd.32044092008168 489 137 ) ) PUNCT hvd.32044092008168 489 138 + + CCONJ hvd.32044092008168 489 139 18ag 18ag NOUN hvd.32044092008168 489 140 ( ( PUNCT hvd.32044092008168 489 141 n n CCONJ hvd.32044092008168 489 142 − − PROPN hvd.32044092008168 489 143 3 3 X hvd.32044092008168 489 144 ) ) PUNCT hvd.32044092008168 489 145 ( ( PUNCT hvd.32044092008168 489 146 n n NOUN hvd.32044092008168 489 147 — — PUNCT hvd.32044092008168 489 148 4 4 X hvd.32044092008168 489 149 ) ) PUNCT hvd.32044092008168 489 150 + + CCONJ hvd.32044092008168 489 151 * * PUNCT hvd.32044092008168 489 152 , , PUNCT hvd.32044092008168 489 153 a a PRON hvd.32044092008168 489 154 ( ( PUNCT hvd.32044092008168 489 155 – – PUNCT hvd.32044092008168 489 156 1)(x 1)(x NUM hvd.32044092008168 489 157 – – SYM hvd.32044092008168 489 158 2 2 NUM hvd.32044092008168 489 159 ) ) PUNCT hvd.32044092008168 489 160 4 4 NUM hvd.32044092008168 489 161 ( ( PUNCT hvd.32044092008168 489 162 x x PUNCT hvd.32044092008168 489 163 + + NUM hvd.32044092008168 489 164 m m NOUN hvd.32044092008168 489 165 – – PUNCT hvd.32044092008168 489 166 3 3 NUM hvd.32044092008168 489 167 ) ) PUNCT hvd.32044092008168 489 168 ( ( PUNCT hvd.32044092008168 489 169 x x SYM hvd.32044092008168 489 170 3)a 3)a NUM hvd.32044092008168 489 171 , , PUNCT hvd.32044092008168 489 172 g( g( NOUN hvd.32044092008168 489 173 ° ° NOUN hvd.32044092008168 489 174 + + NUM hvd.32044092008168 489 175 n n CCONJ hvd.32044092008168 489 176 n n X hvd.32044092008168 489 177 4 4 NUM hvd.32044092008168 489 178 bag bag NOUN hvd.32044092008168 489 179 ( ( PUNCT hvd.32044092008168 489 180 n n NOUN hvd.32044092008168 489 181 — — PUNCT hvd.32044092008168 489 182 2 2 X hvd.32044092008168 489 183 ) ) PUNCT hvd.32044092008168 489 184 – – PUNCT hvd.32044092008168 489 185 2n(n 2n(n NUM hvd.32044092008168 489 186 + + NUM hvd.32044092008168 489 187 1 1 NUM hvd.32044092008168 489 188 ) ) PUNCT hvd.32044092008168 489 189 ag ag PROPN hvd.32044092008168 489 190 = = NOUN hvd.32044092008168 489 191 0 0 PUNCT hvd.32044092008168 489 192 + + CCONJ hvd.32044092008168 489 193 n n ADP hvd.32044092008168 489 194 --4 --4 X hvd.32044092008168 489 195 : : PUNCT hvd.32044092008168 489 196 4a 4a PROPN hvd.32044092008168 489 197 ( ( PUNCT hvd.32044092008168 489 198 n n CCONJ hvd.32044092008168 489 199 − − PROPN hvd.32044092008168 489 200 3)(n 3)(n NUM hvd.32044092008168 489 201 — — PUNCT hvd.32044092008168 489 202 4)(n 4)(n PROPN hvd.32044092008168 489 203 — — PUNCT hvd.32044092008168 489 204 5 5 X hvd.32044092008168 489 205 ) ) PUNCT hvd.32044092008168 489 206 — — PUNCT hvd.32044092008168 490 1 920,(n 920,(n NUM hvd.32044092008168 490 2 -2)(n -2)(n PROPN hvd.32044092008168 490 3 -3)(n -3)(n PROPN hvd.32044092008168 490 4 — — PUNCT hvd.32044092008168 490 5 4 4 X hvd.32044092008168 490 6 ) ) PUNCT hvd.32044092008168 490 7 — — PUNCT hvd.32044092008168 490 8 3 3 NUM hvd.32044092008168 490 9 93a 93a NUM hvd.32044092008168 490 10 , , PUNCT hvd.32044092008168 490 11 ( ( PUNCT hvd.32044092008168 490 12 n n CCONJ hvd.32044092008168 490 13 − − PROPN hvd.32044092008168 490 14 1)(n 1)(n PROPN hvd.32044092008168 490 15 − − PROPN hvd.32044092008168 490 16 2)(n 2)(n PROPN hvd.32044092008168 490 17 − − PROPN hvd.32044092008168 490 18 3 3 NUM hvd.32044092008168 490 19 ) ) PUNCT hvd.32044092008168 490 20 + + NUM hvd.32044092008168 490 21 18a 18a NUM hvd.32044092008168 490 22 , , PUNCT hvd.32044092008168 490 23 ( ( PUNCT hvd.32044092008168 490 24 n n NOUN hvd.32044092008168 490 25 — — PUNCT hvd.32044092008168 490 26 4)(n 4)(n PROPN hvd.32044092008168 490 27 — — PUNCT hvd.32044092008168 490 28 5 5 NUM hvd.32044092008168 490 29 ) ) PUNCT hvd.32044092008168 490 30 920,(n 920,(n NUM hvd.32044092008168 490 31 − − PROPN hvd.32044092008168 490 32 2)(n-3 2)(n-3 NUM hvd.32044092008168 490 33 ) ) PUNCT hvd.32044092008168 490 34 — — PUNCT hvd.32044092008168 490 35 4 4 NUM hvd.32044092008168 490 36 ( ( PUNCT hvd.32044092008168 490 37 n n NOUN hvd.32044092008168 490 38 + + CCONJ hvd.32044092008168 490 39 n-3 n-3 NUM hvd.32044092008168 490 40 ) ) PUNCT hvd.32044092008168 490 41 ( ( PUNCT hvd.32044092008168 490 42 n n NOUN hvd.32044092008168 490 43 — — PUNCT hvd.32044092008168 490 44 4 4 X hvd.32044092008168 490 45 ) ) PUNCT hvd.32044092008168 490 46 , , PUNCT hvd.32044092008168 490 47 nº nº PROPN hvd.32044092008168 490 48 0 0 NUM hvd.32044092008168 490 49 – – PUNCT hvd.32044092008168 490 50 0 0 NUM hvd.32044092008168 490 51 – – PUNCT hvd.32044092008168 490 52 a a X hvd.32044092008168 490 53 , , PUNCT hvd.32044092008168 490 54 – – PUNCT hvd.32044092008168 490 55 4b(n 4b(n PROPN hvd.32044092008168 490 56 — — PUNCT hvd.32044092008168 490 57 3 3 X hvd.32044092008168 490 58 ) ) PUNCT hvd.32044092008168 490 59 az az PROPN hvd.32044092008168 490 60 — — PUNCT hvd.32044092008168 490 61 2n(n 2n(n NUM hvd.32044092008168 490 62 + + NUM hvd.32044092008168 490 63 1 1 X hvd.32044092008168 490 64 ) ) PUNCT hvd.32044092008168 490 65 aq aq PROPN hvd.32044092008168 490 66 = = NOUN hvd.32044092008168 490 67 0 0 NUM hvd.32044092008168 490 68 = = PUNCT hvd.32044092008168 490 69 ) ) PUNCT hvd.32044092008168 490 70 3 3 NUM hvd.32044092008168 490 71 2 2 NUM hvd.32044092008168 490 72 . . PUNCT hvd.32044092008168 491 1 -3 -3 X hvd.32044092008168 491 2 3 3 NUM hvd.32044092008168 491 3 2 2 NUM hvd.32044092008168 491 4 k k X hvd.32044092008168 491 5 = = NOUN hvd.32044092008168 491 6 = = SYM hvd.32044092008168 491 7 n n X hvd.32044092008168 491 8 1 1 NUM hvd.32044092008168 491 9 n n CCONJ hvd.32044092008168 491 10 — — PUNCT hvd.32044092008168 491 11 k k X hvd.32044092008168 491 12 : : PUNCT hvd.32044092008168 491 13 4ax 4ax NOUN hvd.32044092008168 491 14 ( ( PUNCT hvd.32044092008168 491 15 n n NOUN hvd.32044092008168 491 16 – – PUNCT hvd.32044092008168 491 17 k k PROPN hvd.32044092008168 491 18 ) ) PUNCT hvd.32044092008168 491 19 ( ( PUNCT hvd.32044092008168 491 20 – – PUNCT hvd.32044092008168 491 21 k k PROPN hvd.32044092008168 491 22 – – PUNCT hvd.32044092008168 491 23 1 1 X hvd.32044092008168 491 24 ) ) PUNCT hvd.32044092008168 491 25 ( ( PUNCT hvd.32044092008168 491 26 n n NOUN hvd.32044092008168 491 27 — — PUNCT hvd.32044092008168 491 28 k k PROPN hvd.32044092008168 491 29 — — PUNCT hvd.32044092008168 491 30 2 2 X hvd.32044092008168 491 31 ) ) PUNCT hvd.32044092008168 491 32 – – PUNCT hvd.32044092008168 491 33 920x-2 920x-2 NUM hvd.32044092008168 491 34 ( ( PUNCT hvd.32044092008168 491 35 n n NOUN hvd.32044092008168 491 36 – – PUNCT hvd.32044092008168 491 37 k k PROPN hvd.32044092008168 491 38 + + PROPN hvd.32044092008168 491 39 2 2 X hvd.32044092008168 491 40 ) ) PUNCT hvd.32044092008168 491 41 ( ( PUNCT hvd.32044092008168 491 42 n n CCONJ hvd.32044092008168 491 43 k k X hvd.32044092008168 491 44 + + PROPN hvd.32044092008168 491 45 1 1 X hvd.32044092008168 491 46 ) ) PUNCT hvd.32044092008168 491 47 ( ( PUNCT hvd.32044092008168 491 48 n n NOUN hvd.32044092008168 491 49 — — PUNCT hvd.32044092008168 491 50 k k X hvd.32044092008168 491 51 ) ) PUNCT hvd.32044092008168 491 52 9304–3 9304–3 NUM hvd.32044092008168 491 53 ( ( PUNCT hvd.32044092008168 491 54 n n X hvd.32044092008168 491 55 -k -k X hvd.32044092008168 491 56 + + CCONJ hvd.32044092008168 491 57 3 3 X hvd.32044092008168 491 58 ) ) PUNCT hvd.32044092008168 491 59 ( ( PUNCT hvd.32044092008168 491 60 n n NOUN hvd.32044092008168 491 61 – – PUNCT hvd.32044092008168 491 62 k k PROPN hvd.32044092008168 491 63 + + PROPN hvd.32044092008168 491 64 2)(n 2)(n NUM hvd.32044092008168 492 1 k k X hvd.32044092008168 492 2 + + PROPN hvd.32044092008168 492 3 1 1 X hvd.32044092008168 492 4 ) ) PUNCT hvd.32044092008168 492 5 k k PROPN hvd.32044092008168 492 6 2 2 NUM hvd.32044092008168 492 7 1 1 NUM hvd.32044092008168 492 8 + + NUM hvd.32044092008168 492 9 18ax(n 18ax(n NUM hvd.32044092008168 492 10 = = SYM hvd.32044092008168 492 11 k k PROPN hvd.32044092008168 492 12 ) ) PUNCT hvd.32044092008168 492 13 ( ( PUNCT hvd.32044092008168 492 14 n n CCONJ hvd.32044092008168 492 15 -k -k PUNCT hvd.32044092008168 492 16 – – PUNCT hvd.32044092008168 492 17 1 1 X hvd.32044092008168 492 18 ) ) PUNCT hvd.32044092008168 492 19 k k PROPN hvd.32044092008168 492 20 920x-2 920x-2 NUM hvd.32044092008168 492 21 ( ( PUNCT hvd.32044092008168 492 22 n n X hvd.32044092008168 492 23 — — PUNCT hvd.32044092008168 492 24 k k PROPN hvd.32044092008168 492 25 + + PROPN hvd.32044092008168 492 26 2 2 X hvd.32044092008168 492 27 ) ) PUNCT hvd.32044092008168 492 28 ( ( PUNCT hvd.32044092008168 492 29 n n NOUN hvd.32044092008168 492 30 — — PUNCT hvd.32044092008168 492 31 k k PROPN hvd.32044092008168 492 32 + + PROPN hvd.32044092008168 492 33 1 1 NUM hvd.32044092008168 492 34 ) ) PUNCT hvd.32044092008168 492 35 4(n2 4(n2 NUM hvd.32044092008168 492 36 + + NUM hvd.32044092008168 492 37 1 1 NUM hvd.32044092008168 492 38 3)(n 3)(n NUM hvd.32044092008168 492 39 – – PUNCT hvd.32044092008168 492 40 k)ax k)ax X hvd.32044092008168 492 41 — — PUNCT hvd.32044092008168 492 42 4b 4b NUM hvd.32044092008168 492 43 ( ( PUNCT hvd.32044092008168 492 44 n n NOUN hvd.32044092008168 492 45 - - PUNCT hvd.32044092008168 492 46 k+1 k+1 NUM hvd.32044092008168 492 47 ) ) PUNCT hvd.32044092008168 492 48 ax--1 ax--1 PROPN hvd.32044092008168 492 49 n n X hvd.32044092008168 492 50 — — PUNCT hvd.32044092008168 492 51 2n(n 2n(n NUM hvd.32044092008168 492 52 + + NUM hvd.32044092008168 492 53 1 1 NUM hvd.32044092008168 492 54 ) ) PUNCT hvd.32044092008168 492 55 ax ax NOUN hvd.32044092008168 492 56 = = PROPN hvd.32044092008168 492 57 0 0 NUM hvd.32044092008168 492 58 . . PUNCT hvd.32044092008168 493 1 from from ADP hvd.32044092008168 493 2 the the DET hvd.32044092008168 493 3 last last ADJ hvd.32044092008168 493 4 value value NOUN hvd.32044092008168 493 5 we we PRON hvd.32044092008168 493 6 pass pass VERB hvd.32044092008168 493 7 to to ADP hvd.32044092008168 493 8 the the DET hvd.32044092008168 493 9 nth nth NOUN hvd.32044092008168 493 10 by by ADP hvd.32044092008168 493 11 writing write VERB hvd.32044092008168 493 12 m m ADV hvd.32044092008168 493 13 whence whence ADP hvd.32044092008168 493 14 the the DET hvd.32044092008168 493 15 recurring recur VERB hvd.32044092008168 493 16 formula formula NOUN hvd.32044092008168 493 17 : : PUNCT hvd.32044092008168 494 1 [ [ X hvd.32044092008168 494 2 58 58 NUM hvd.32044092008168 494 3 ] ] PUNCT hvd.32044092008168 494 4 2 2 NUM hvd.32044092008168 494 5 ( ( PUNCT hvd.32044092008168 494 6 3 3 NUM hvd.32044092008168 494 7 -4)(2n -4)(2n X hvd.32044092008168 494 8 + + NUM hvd.32044092008168 494 9 1)(x 1)(x NUM hvd.32044092008168 494 10 + + NUM hvd.32044092008168 494 11 m m NOUN hvd.32044092008168 494 12 + + PROPN hvd.32044092008168 494 13 1 1 NUM hvd.32044092008168 494 14 ) ) PUNCT hvd.32044092008168 494 15 a a DET hvd.32044092008168 494 16 = = NOUN hvd.32044092008168 494 17 + + NUM hvd.32044092008168 494 18 4 4 NUM hvd.32044092008168 494 19 ( ( PUNCT hvd.32044092008168 494 20 4 4 NUM hvd.32044092008168 494 21 + + NUM hvd.32044092008168 494 22 1 1 NUM hvd.32044092008168 494 23 ) ) PUNCT hvd.32044092008168 494 24 ban-4 ban-4 SPACE hvd.32044092008168 494 25 - - PUNCT hvd.32044092008168 494 26 1 1 NUM hvd.32044092008168 494 27 ] ] PUNCT hvd.32044092008168 494 28 ( ( PUNCT hvd.32044092008168 494 29 n n CCONJ hvd.32044092008168 494 30 u1u u1u PROPN hvd.32044092008168 494 31 n n CCONJ hvd.32044092008168 494 32 an an PRON hvd.32044092008168 494 33 . . PUNCT hvd.32044092008168 495 1 inx inx PROPN hvd.32044092008168 495 2 u u PROPN hvd.32044092008168 495 3 4—1 4—1 NUM hvd.32044092008168 495 4 +92 +92 PROPN hvd.32044092008168 495 5 ( ( PUNCT hvd.32044092008168 495 6 n n NOUN hvd.32044092008168 495 7 + + ADP hvd.32044092008168 495 8 1 1 X hvd.32044092008168 495 9 ) ) PUNCT hvd.32044092008168 495 10 ( ( PUNCT hvd.32044092008168 495 11 u u PROPN hvd.32044092008168 495 12 + + NUM hvd.32044092008168 495 13 2 2 NUM hvd.32044092008168 495 14 ) ) PUNCT hvd.32044092008168 495 15 ( ( PUNCT hvd.32044092008168 495 16 2 2 NUM hvd.32044092008168 495 17 u u NOUN hvd.32044092008168 495 18 + + NUM hvd.32044092008168 495 19 3 3 X hvd.32044092008168 495 20 ) ) PUNCT hvd.32044092008168 495 21 an an DET hvd.32044092008168 495 22 — — PUNCT hvd.32044092008168 495 23 u—2 u—2 NOUN hvd.32044092008168 495 24 + + NUM hvd.32044092008168 495 25 93 93 NUM hvd.32044092008168 496 1 ( ( PUNCT hvd.32044092008168 496 2 u u NOUN hvd.32044092008168 496 3 + + PROPN hvd.32044092008168 496 4 1 1 NUM hvd.32044092008168 496 5 ) ) PUNCT hvd.32044092008168 496 6 ( ( PUNCT hvd.32044092008168 496 7 u u PROPN hvd.32044092008168 496 8 + + NUM hvd.32044092008168 496 9 2 2 X hvd.32044092008168 496 10 ) ) PUNCT hvd.32044092008168 496 11 ( ( PUNCT hvd.32044092008168 496 12 u u NOUN hvd.32044092008168 496 13 + + NUM hvd.32044092008168 496 14 3 3 X hvd.32044092008168 496 15 ) ) PUNCT hvd.32044092008168 496 16 an—^—3 an—^—3 X hvd.32044092008168 496 17 from from ADP hvd.32044092008168 496 18 which which PRON hvd.32044092008168 496 19 equation equation NOUN hvd.32044092008168 496 20 we we PRON hvd.32044092008168 496 21 find find VERB hvd.32044092008168 496 22 the the DET hvd.32044092008168 496 23 unknown unknown ADJ hvd.32044092008168 496 24 coefficients coefficient NOUN hvd.32044092008168 496 25 ai ai VERB hvd.32044092008168 496 26 by by ADP hvd.32044092008168 496 27 making make VERB hvd.32044092008168 496 28 u u PROPN hvd.32044092008168 496 29 2 2 NUM hvd.32044092008168 496 30 , , PUNCT hvd.32044092008168 496 31 ... ... PUNCT hvd.32044092008168 497 1 k k X hvd.32044092008168 497 2 1.2 1.2 NUM hvd.32044092008168 497 3 ... ... PUNCT hvd.32044092008168 497 4 these these DET hvd.32044092008168 497 5 results result NOUN hvd.32044092008168 497 6 are be AUX hvd.32044092008168 497 7 simplified simplify VERB hvd.32044092008168 497 8 by by ADP hvd.32044092008168 497 9 employing employ VERB hvd.32044092008168 497 10 the the DET hvd.32044092008168 497 11 notation notation NOUN hvd.32044092008168 497 12 introduced introduce VERB hvd.32044092008168 497 13 by by ADP hvd.32044092008168 497 14 brioschi brioschi PROPN hvd.32044092008168 497 15 , , PUNCT hvd.32044092008168 497 16 namely namely ADV hvd.32044092008168 497 17 : : PUNCT hvd.32044092008168 497 18 : : PUNCT hvd.32044092008168 497 19 set set NOUN hvd.32044092008168 497 20 - - PUNCT hvd.32044092008168 497 21 b b NOUN hvd.32044092008168 497 22 : : PUNCT hvd.32044092008168 497 23 b. b. PROPN hvd.32044092008168 497 24 9(t)=4 9(t)=4 NUM hvd.32044092008168 497 25 t t PROPN hvd.32044092008168 497 26 — — PUNCT hvd.32044092008168 497 27 92 92 NUM hvd.32044092008168 497 28 - - SYM hvd.32044092008168 497 29 93 93 NUM hvd.32044092008168 497 30 = = SYM hvd.32044092008168 497 31 9 9 NUM hvd.32044092008168 497 32 . . PUNCT hvd.32044092008168 498 1 t t PROPN hvd.32044092008168 498 2 = = PROPN hvd.32044092008168 498 3 pu pu PROPN hvd.32044092008168 498 4 , , PUNCT hvd.32044092008168 498 5 n n NOUN hvd.32044092008168 498 6 ( ( PUNCT hvd.32044092008168 498 7 2n 2n NUM hvd.32044092008168 498 8 1 1 X hvd.32044092008168 498 9 ) ) PUNCT hvd.32044092008168 498 10 by by ADP hvd.32044092008168 498 11 means mean NOUN hvd.32044092008168 498 12 of of ADP hvd.32044092008168 498 13 which which PRON hvd.32044092008168 498 14 the the DET hvd.32044092008168 498 15 above above ADJ hvd.32044092008168 498 16 forms form NOUN hvd.32044092008168 498 17 are be AUX hvd.32044092008168 498 18 expressed express VERB hvd.32044092008168 498 19 as as SCONJ hvd.32044092008168 498 20 follows follow VERB hvd.32044092008168 498 21 : : PUNCT hvd.32044092008168 499 1 703 703 NUM hvd.32044092008168 499 2 y y X hvd.32044092008168 499 3 d d X hvd.32044092008168 499 4 ? ? PUNCT hvd.32044092008168 500 1 y y PROPN hvd.32044092008168 501 1 [ [ X hvd.32044092008168 501 2 59 59 NUM hvd.32044092008168 501 3 ] ] PUNCT hvd.32044092008168 502 1 [ [ X hvd.32044092008168 502 2 48 48 NUM hvd.32044092008168 502 3 % % NOUN hvd.32044092008168 502 4 + + CCONJ hvd.32044092008168 502 5 $ $ SYM hvd.32044092008168 502 6 9"s 9"s NUM hvd.32044092008168 502 7 ? ? PUNCT hvd.32044092008168 503 1 +0 +0 PROPN hvd.32044092008168 503 2 's 's PART hvd.32044092008168 503 3 + + NOUN hvd.32044092008168 503 4 glas gla NOUN hvd.32044092008168 503 5 + + CCONJ hvd.32044092008168 503 6 ( ( PUNCT hvd.32044092008168 503 7 1882 1882 NUM hvd.32044092008168 503 8 +30"s +30"s PROPN hvd.32044092008168 503 9 + + CCONJ hvd.32044092008168 503 10 9 9 NUM hvd.32044092008168 503 11 oʻs oʻs NOUN hvd.32044092008168 503 12 +9 +9 NUM hvd.32044092008168 503 13 9 9 NUM hvd.32044092008168 503 14 ' ' NUM hvd.32044092008168 503 15 ) ) PUNCT hvd.32044092008168 503 16 d82 d82 NOUN hvd.32044092008168 503 17 [ [ PUNCT hvd.32044092008168 503 18 4(n2 4(n2 NOUN hvd.32044092008168 503 19 + + ADP hvd.32044092008168 503 20 n n NOUN hvd.32044092008168 503 21 — — PUNCT hvd.32044092008168 503 22 3)s+ 3)s+ NOUN hvd.32044092008168 503 23 ds ds NOUN hvd.32044092008168 503 24 2n(n 2n(n NUM hvd.32044092008168 503 25 + + NUM hvd.32044092008168 503 26 1 1 NUM hvd.32044092008168 503 27 ) ) PUNCT hvd.32044092008168 503 28 y=0 y=0 X hvd.32044092008168 504 1 [ [ PUNCT hvd.32044092008168 504 2 60 60 NUM hvd.32044092008168 504 3 ] ] X hvd.32044092008168 504 4 y y PROPN hvd.32044092008168 504 5 sn sn PROPN hvd.32044092008168 504 6 + + CCONJ hvd.32044092008168 504 7 a a DET hvd.32044092008168 504 8 , , PUNCT hvd.32044092008168 504 9 sn—2 sn—2 NOUN hvd.32044092008168 504 10 + + X hvd.32044092008168 504 11 ag ag INTJ hvd.32044092008168 504 12 sn—3 sn—3 PROPN hvd.32044092008168 504 13 + + NUM hvd.32044092008168 504 14 + + CCONJ hvd.32044092008168 504 15 an an DET hvd.32044092008168 504 16 = = NOUN hvd.32044092008168 504 17 0 0 NUM hvd.32044092008168 504 18 n n CCONJ hvd.32044092008168 504 19 -1 -1 PROPN hvd.32044092008168 504 20 , , PUNCT hvd.32044092008168 504 21 n n NOUN hvd.32044092008168 504 22 or or CCONJ hvd.32044092008168 504 23 1 1 NUM hvd.32044092008168 504 24 sc sc NOUN hvd.32044092008168 504 25 1 1 NUM hvd.32044092008168 504 26 3 3 NUM hvd.32044092008168 504 27 2 2 NUM hvd.32044092008168 504 28 d d NOUN hvd.32044092008168 504 29 2 2 NUM hvd.32044092008168 504 30 2 2 NUM hvd.32044092008168 504 31 n n NOUN hvd.32044092008168 504 32 ? ? NOUN hvd.32044092008168 504 33 1 1 NUM hvd.32044092008168 504 34 2 2 NUM hvd.32044092008168 504 35 9 9 NUM hvd.32044092008168 504 36 " " PUNCT hvd.32044092008168 504 37 ) ) PUNCT hvd.32044092008168 504 38 ay ay NOUN hvd.32044092008168 504 39 integral integral ADJ hvd.32044092008168 504 40 as as ADP hvd.32044092008168 504 41 a a DET hvd.32044092008168 504 42 product product NOUN hvd.32044092008168 504 43 . . PUNCT hvd.32044092008168 505 1 37 37 NUM hvd.32044092008168 505 2 1 1 NUM hvd.32044092008168 505 3 2 2 NUM hvd.32044092008168 505 4 [ [ PUNCT hvd.32044092008168 505 5 61 61 NUM hvd.32044092008168 505 6 ] ] PUNCT hvd.32044092008168 505 7 2 2 NUM hvd.32044092008168 505 8 ( ( PUNCT hvd.32044092008168 505 9 n n NOUN hvd.32044092008168 505 10 – – PUNCT hvd.32044092008168 505 11 u u PROPN hvd.32044092008168 505 12 ) ) PUNCT hvd.32044092008168 505 13 ( ( PUNCT hvd.32044092008168 505 14 2 2 NUM hvd.32044092008168 505 15 u u NOUN hvd.32044092008168 505 16 + + NUM hvd.32044092008168 505 17 1 1 NUM hvd.32044092008168 505 18 ) ) PUNCT hvd.32044092008168 505 19 ( ( PUNCT hvd.32044092008168 505 20 u u NOUN hvd.32044092008168 505 21 + + NOUN hvd.32044092008168 505 22 n n CCONJ hvd.32044092008168 505 23 + + CCONJ hvd.32044092008168 505 24 1 1 NUM hvd.32044092008168 505 25 ) ) PUNCT hvd.32044092008168 505 26 an an DET hvd.32044092008168 505 27 - - PUNCT hvd.32044092008168 505 28 m m NOUN hvd.32044092008168 505 29 u u PROPN hvd.32044092008168 505 30 = = PROPN hvd.32044092008168 505 31 12 12 NUM hvd.32044092008168 505 32 ( ( PUNCT hvd.32044092008168 505 33 u u NOUN hvd.32044092008168 505 34 + + NUM hvd.32044092008168 505 35 1 1 NUM hvd.32044092008168 505 36 ) ) PUNCT hvd.32044092008168 505 37 ( ( PUNCT hvd.32044092008168 505 38 n n CCONJ hvd.32044092008168 505 39 + + ADP hvd.32044092008168 505 40 1 1 NUM hvd.32044092008168 505 41 – – PUNCT hvd.32044092008168 505 42 n n CCONJ hvd.32044092008168 505 43 ) ) PUNCT hvd.32044092008168 505 44 ( ( PUNCT hvd.32044092008168 505 45 v v X hvd.32044092008168 505 46 +1 +1 NOUN hvd.32044092008168 505 47 + + SYM hvd.32044092008168 505 48 r r X hvd.32044092008168 505 49 ) ) PUNCT hvd.32044092008168 505 50 an—-—1 an—-—1 PROPN hvd.32044092008168 505 51 1 1 NUM hvd.32044092008168 506 1 nu nu PROPN hvd.32044092008168 506 2 nb nb X hvd.32044092008168 506 3 u u PROPN hvd.32044092008168 506 4 + + CCONJ hvd.32044092008168 507 1 ( ( PUNCT hvd.32044092008168 507 2 u u NOUN hvd.32044092008168 507 3 + + NUM hvd.32044092008168 507 4 1 1 NUM hvd.32044092008168 507 5 ) ) PUNCT hvd.32044092008168 507 6 ( ( PUNCT hvd.32044092008168 507 7 u u PROPN hvd.32044092008168 507 8 + + NUM hvd.32044092008168 507 9 2 2 NUM hvd.32044092008168 507 10 ) ) PUNCT hvd.32044092008168 507 11 ( ( PUNCT hvd.32044092008168 507 12 2u 2u PROPN hvd.32044092008168 507 13 + + PROPN hvd.32044092008168 507 14 3 3 X hvd.32044092008168 507 15 ) ) PUNCT hvd.32044092008168 507 16 9 9 NUM hvd.32044092008168 507 17 ' ' PUNCT hvd.32044092008168 507 18 ( ( PUNCT hvd.32044092008168 507 19 b b NOUN hvd.32044092008168 507 20 ) ) PUNCT hvd.32044092008168 507 21 an an DET hvd.32044092008168 507 22 — — PUNCT hvd.32044092008168 507 23 u—-2 u—-2 NOUN hvd.32044092008168 507 24 + + DET hvd.32044092008168 507 25 ( ( PUNCT hvd.32044092008168 507 26 u u NOUN hvd.32044092008168 507 27 + + NUM hvd.32044092008168 507 28 1 1 NUM hvd.32044092008168 507 29 ) ) PUNCT hvd.32044092008168 507 30 ( ( PUNCT hvd.32044092008168 507 31 u u PROPN hvd.32044092008168 507 32 + + NUM hvd.32044092008168 507 33 2 2 X hvd.32044092008168 507 34 ) ) PUNCT hvd.32044092008168 507 35 ( ( PUNCT hvd.32044092008168 507 36 u u PROPN hvd.32044092008168 507 37 + + NUM hvd.32044092008168 507 38 3 3 NUM hvd.32044092008168 507 39 ) ) PUNCT hvd.32044092008168 507 40 4 4 NUM hvd.32044092008168 507 41 ( ( PUNCT hvd.32044092008168 507 42 6 6 NUM hvd.32044092008168 507 43 ) ) PUNCT hvd.32044092008168 507 44 an—-—3 an—-—3 NOUN hvd.32044092008168 507 45 . . PUNCT hvd.32044092008168 508 1 taking take VERB hvd.32044092008168 508 2 u u PROPN hvd.32044092008168 508 3 1 1 NUM hvd.32044092008168 508 4 we we PRON hvd.32044092008168 508 5 find find VERB hvd.32044092008168 508 6 a a DET hvd.32044092008168 508 7 = = NOUN hvd.32044092008168 508 8 0 0 NUM hvd.32044092008168 508 9 n n X hvd.32044092008168 508 10 in in ADP hvd.32044092008168 508 11 1 1 NUM hvd.32044092008168 508 12 ) ) PUNCT hvd.32044092008168 508 13 u u NOUN hvd.32044092008168 508 14 2 2 NUM hvd.32044092008168 508 15 : : PUNCT hvd.32044092008168 508 16 a2= a2= PROPN hvd.32044092008168 508 17 8 8 NUM hvd.32044092008168 508 18 ( ( PUNCT hvd.32044092008168 508 19 2n 2n NUM hvd.32044092008168 508 20 3 3 X hvd.32044092008168 508 21 ) ) PUNCT hvd.32044092008168 508 22 nan nan PROPN hvd.32044092008168 508 23 nan nan PROPN hvd.32044092008168 508 24 1 1 NUM hvd.32044092008168 508 25 ) ) PUNCT hvd.32044092008168 508 26 ( ( PUNCT hvd.32044092008168 508 27 n n PROPN hvd.32044092008168 508 28 2 2 X hvd.32044092008168 508 29 ) ) PUNCT hvd.32044092008168 508 30 3 3 NUM hvd.32044092008168 508 31 : : PUNCT hvd.32044092008168 508 32 az az PROPN hvd.32044092008168 508 33 = = NOUN hvd.32044092008168 508 34 m m VERB hvd.32044092008168 508 35 bo'(b bo'(b NOUN hvd.32044092008168 508 36 ) ) PUNCT hvd.32044092008168 508 37 . . PUNCT hvd.32044092008168 509 1 12 12 NUM hvd.32044092008168 509 2 ( ( PUNCT hvd.32044092008168 509 3 2n 2n NUM hvd.32044092008168 509 4 5 5 NUM hvd.32044092008168 509 5 ) ) PUNCT hvd.32044092008168 509 6 2 2 NUM hvd.32044092008168 509 7 ( ( PUNCT hvd.32044092008168 509 8 2n 2n NUM hvd.32044092008168 509 9 3 3 X hvd.32044092008168 509 10 ) ) PUNCT hvd.32044092008168 509 11 ( ( PUNCT hvd.32044092008168 509 12 2n 2n NUM hvd.32044092008168 509 13 — — PUNCT hvd.32044092008168 509 14 5 5 X hvd.32044092008168 509 15 ) ) PUNCT hvd.32044092008168 509 16 = = PUNCT hvd.32044092008168 509 17 n n CCONJ hvd.32044092008168 509 18 i i PRON hvd.32044092008168 509 19 en en X hvd.32044092008168 509 20 φ φ X hvd.32044092008168 509 21 ' ' PUNCT hvd.32044092008168 509 22 ( ( PUNCT hvd.32044092008168 509 23 0 0 NUM hvd.32044092008168 509 24 ) ) PUNCT hvd.32044092008168 509 25 2 2 NUM hvd.32044092008168 509 26 n n CCONJ hvd.32044092008168 509 27 3 3 NUM hvd.32044092008168 509 28 9 9 NUM hvd.32044092008168 509 29 ( ( PUNCT hvd.32044092008168 509 30 6 6 NUM hvd.32044092008168 509 31 ) ) PUNCT hvd.32044092008168 509 32 = = PROPN hvd.32044092008168 509 33 1 1 X hvd.32044092008168 509 34 ) ) PUNCT hvd.32044092008168 509 35 b b NOUN hvd.32044092008168 509 36 ( ( PUNCT hvd.32044092008168 509 37 2n 2n NUM hvd.32044092008168 509 38 and and CCONJ hvd.32044092008168 509 39 the the DET hvd.32044092008168 509 40 term term NOUN hvd.32044092008168 509 41 containing contain VERB hvd.32044092008168 509 42 the the DET hvd.32044092008168 509 43 highest high ADJ hvd.32044092008168 509 44 power power NOUN hvd.32044092008168 509 45 of of ADP hvd.32044092008168 509 46 b b PROPN hvd.32044092008168 509 47 is be AUX hvd.32044092008168 509 48 obtained obtain VERB hvd.32044092008168 509 49 as as SCONJ hvd.32044092008168 509 50 follows follow VERB hvd.32044092008168 509 51 : : PUNCT hvd.32044092008168 510 1 и и PUNCT hvd.32044092008168 510 2 u u PROPN hvd.32044092008168 510 3 = = X hvd.32044092008168 510 4 n n X hvd.32044092008168 510 5 — — PUNCT hvd.32044092008168 510 6 2 2 NUM hvd.32044092008168 510 7 : : SYM hvd.32044092008168 510 8 2.2 2.2 NUM hvd.32044092008168 510 9 ( ( PUNCT hvd.32044092008168 510 10 2n 2n NUM hvd.32044092008168 510 11 — — PUNCT hvd.32044092008168 510 12 3 3 X hvd.32044092008168 510 13 ) ) PUNCT hvd.32044092008168 510 14 ( ( PUNCT hvd.32044092008168 510 15 2n 2n NUM hvd.32044092008168 510 16 — — PUNCT hvd.32044092008168 510 17 1 1 X hvd.32044092008168 510 18 ) ) PUNCT hvd.32044092008168 510 19 ag ag PROPN hvd.32044092008168 510 20 4 4 NUM hvd.32044092008168 510 21 ( ( PUNCT hvd.32044092008168 510 22 n n CCONJ hvd.32044092008168 510 23 − − PROPN hvd.32044092008168 510 24 1 1 X hvd.32044092008168 510 25 ) ) PUNCT hvd.32044092008168 510 26 b b NOUN hvd.32044092008168 510 27 ( ( PUNCT hvd.32044092008168 510 28 n n NOUN hvd.32044092008168 510 29 or or CCONJ hvd.32044092008168 510 30 az az PROPN hvd.32044092008168 510 31 1 1 NUM hvd.32044092008168 510 32 ) ) PUNCT hvd.32044092008168 510 33 ( ( PUNCT hvd.32044092008168 510 34 2 2 NUM hvd.32044092008168 510 35 n n CCONJ hvd.32044092008168 510 36 3 3 NUM hvd.32044092008168 510 37 ) ) PUNCT hvd.32044092008168 510 38 4 4 NUM hvd.32044092008168 510 39 = = SYM hvd.32044092008168 510 40 0 0 NUM hvd.32044092008168 510 41 – – PUNCT hvd.32044092008168 510 42 3 3 NUM hvd.32044092008168 510 43 : : PUNCT hvd.32044092008168 510 44 ( ( PUNCT hvd.32044092008168 510 45 n n NOUN hvd.32044092008168 510 46 и и X hvd.32044092008168 510 47 – – PUNCT hvd.32044092008168 510 48 1 1 X hvd.32044092008168 510 49 ) ) PUNCT hvd.32044092008168 510 50 ( ( PUNCT hvd.32044092008168 510 51 2n 2n NUM hvd.32044092008168 510 52 5 5 X hvd.32044092008168 510 53 ) ) PUNCT hvd.32044092008168 510 54 ( ( PUNCT hvd.32044092008168 510 55 n n PROPN hvd.32044092008168 510 56 2 2 X hvd.32044092008168 510 57 ) ) PUNCT hvd.32044092008168 510 58 ( ( PUNCT hvd.32044092008168 510 59 n n X hvd.32044092008168 510 60 un un PROPN hvd.32044092008168 510 61 4 4 NUM hvd.32044092008168 510 62 : : SYM hvd.32044092008168 510 63 2 2 NUM hvd.32044092008168 510 64 · · SYM hvd.32044092008168 510 65 3 3 NUM hvd.32044092008168 510 66 · · PUNCT hvd.32044092008168 510 67 ( ( PUNCT hvd.32044092008168 510 68 2n 2n NUM hvd.32044092008168 510 69 1 1 X hvd.32044092008168 510 70 ) ) PUNCT hvd.32044092008168 510 71 ( ( PUNCT hvd.32044092008168 510 72 2 2 NUM hvd.32044092008168 510 73 n n CCONJ hvd.32044092008168 510 74 3 3 NUM hvd.32044092008168 510 75 ) ) PUNCT hvd.32044092008168 510 76 ( ( PUNCT hvd.32044092008168 510 77 2n 2n NUM hvd.32044092008168 510 78 5 5 X hvd.32044092008168 510 79 ) ) PUNCT hvd.32044092008168 510 80 ( ( PUNCT hvd.32044092008168 510 81 2n 2n NUM hvd.32044092008168 510 82 3 3 X hvd.32044092008168 510 83 ) ) PUNCT hvd.32044092008168 510 84 ( ( PUNCT hvd.32044092008168 510 85 n n CCONJ hvd.32044092008168 510 86 u u PROPN hvd.32044092008168 510 87 + + PUNCT hvd.32044092008168 510 88 ... ... PUNCT hvd.32044092008168 510 89 2.3.5(2n-1)(2n3)(2n5)(2n 2.3.5(2n-1)(2n3)(2n5)(2n NUM hvd.32044092008168 510 90 -7)(2n-9 -7)(2n-9 NOUN hvd.32044092008168 510 91 ) ) PUNCT hvd.32044092008168 510 92 3 3 NUM hvd.32044092008168 510 93 : : PUNCT hvd.32044092008168 510 94 az az PROPN hvd.32044092008168 510 95 2 2 X hvd.32044092008168 510 96 ) ) PUNCT hvd.32044092008168 510 97 b2 b2 PROPN hvd.32044092008168 510 98 3 3 NUM hvd.32044092008168 510 99 ( ( PUNCT hvd.32044092008168 510 100 2n 2n NUM hvd.32044092008168 510 101 4 4 NUM hvd.32044092008168 510 102 : : SYM hvd.32044092008168 510 103 24 24 NUM hvd.32044092008168 510 104 3 3 NUM hvd.32044092008168 510 105 ) ) PUNCT hvd.32044092008168 510 106 b3 b3 PROPN hvd.32044092008168 510 107 . . PUNCT hvd.32044092008168 511 1 7 7 X hvd.32044092008168 511 2 ) ) PUNCT hvd.32044092008168 511 3 x x PUNCT hvd.32044092008168 511 4 ( ( PUNCT hvd.32044092008168 511 5 n n CCONJ hvd.32044092008168 511 6 5 5 NUM hvd.32044092008168 511 7 : : PUNCT hvd.32044092008168 511 8 a5 a5 NUM hvd.32044092008168 511 9 4 4 X hvd.32044092008168 511 10 ) ) PUNCT hvd.32044092008168 511 11 b4 b4 PROPN hvd.32044092008168 511 12 [ [ X hvd.32044092008168 512 1 62 62 NUM hvd.32044092008168 512 2 ] ] PUNCT hvd.32044092008168 512 3 u u NOUN hvd.32044092008168 512 4 = = NOUN hvd.32044092008168 512 5 1 1 NUM hvd.32044092008168 512 6 : : PUNCT hvd.32044092008168 512 7 an-1= an-1= NOUN hvd.32044092008168 512 8 [ [ X hvd.32044092008168 512 9 3 3 NUM hvd.32044092008168 512 10 ( ( PUNCT hvd.32044092008168 512 11 -1 -1 X hvd.32044092008168 512 12 ) ) PUNCT hvd.32044092008168 512 13 " " PUNCT hvd.32044092008168 512 14 b b NOUN hvd.32044092008168 512 15 ” " PUNCT hvd.32044092008168 512 16 5 5 NUM hvd.32044092008168 512 17 7 7 NUM hvd.32044092008168 512 18 2n 2n NUM hvd.32044092008168 512 19 + + NUM hvd.32044092008168 512 20 . . PUNCT hvd.32044092008168 512 21 . . PUNCT hvd.32044092008168 512 22 . . PUNCT hvd.32044092008168 513 1 1 1 NUM hvd.32044092008168 513 2 ] ] X hvd.32044092008168 513 3 ya ya PROPN hvd.32044092008168 513 4 c c X hvd.32044092008168 513 5 direct direct ADJ hvd.32044092008168 513 6 solution solution NOUN hvd.32044092008168 513 7 . . PUNCT hvd.32044092008168 514 1 having have VERB hvd.32044092008168 514 2 y y PROPN hvd.32044092008168 514 3 = = PROPN hvd.32044092008168 514 4 ys ys PROPN hvd.32044092008168 514 5 , , PUNCT hvd.32044092008168 514 6 we we PRON hvd.32044092008168 514 7 are be AUX hvd.32044092008168 514 8 enabled enable VERB hvd.32044092008168 514 9 to to PART hvd.32044092008168 514 10 obtain obtain VERB hvd.32044092008168 514 11 a a DET hvd.32044092008168 514 12 rigid rigid ADJ hvd.32044092008168 514 13 and and CCONJ hvd.32044092008168 514 14 direct direct ADJ hvd.32044092008168 514 15 solution solution NOUN hvd.32044092008168 514 16 of of ADP hvd.32044092008168 514 17 hermite hermite PROPN hvd.32044092008168 514 18 's 's PART hvd.32044092008168 514 19 equation equation NOUN hvd.32044092008168 514 20 in in ADP hvd.32044092008168 514 21 the the DET hvd.32044092008168 514 22 form form NOUN hvd.32044092008168 514 23 of of ADP hvd.32044092008168 514 24 a a DET hvd.32044092008168 514 25 product product NOUN hvd.32044092008168 514 26 as as SCONJ hvd.32044092008168 514 27 follows follow VERB hvd.32044092008168 514 28 : : PUNCT hvd.32044092008168 514 29 in in ADP hvd.32044092008168 514 30 addition addition NOUN hvd.32044092008168 514 31 to to ADP hvd.32044092008168 514 32 y y PROPN hvd.32044092008168 514 33 we we PRON hvd.32044092008168 514 34 have have VERB hvd.32044092008168 514 35 : : PUNCT hvd.32044092008168 514 36 y y PROPN hvd.32044092008168 514 37 ' ' PUNCT hvd.32044092008168 514 38 = = X hvd.32044092008168 514 39 ys ys NOUN hvd.32044092008168 514 40 ' ' PUNCT hvd.32044092008168 514 41 + + CCONJ hvd.32044092008168 514 42 xy xy PRON hvd.32044092008168 514 43 ' ' PUNCT hvd.32044092008168 514 44 = = PRON hvd.32044092008168 514 45 yz yz PROPN hvd.32044092008168 514 46 and and CCONJ hvd.32044092008168 514 47 yz yz NOUN hvd.32044092008168 514 48 ' ' PUNCT hvd.32044092008168 514 49 – – PUNCT hvd.32044092008168 514 50 zy'=2c zy'=2c PROPN hvd.32044092008168 514 51 . . PUNCT hvd.32044092008168 515 1 = = PUNCT hvd.32044092008168 516 1 whence whence ADP hvd.32044092008168 516 2 2c+y 2c+y NUM hvd.32044092008168 516 3 2 2 NUM hvd.32044092008168 517 1 yz'= yz'= PROPN hvd.32044092008168 517 2 20 20 NUM hvd.32044092008168 517 3 + + NUM hvd.32044092008168 517 4 y y NOUN hvd.32044092008168 517 5 ' ' PUNCT hvd.32044092008168 517 6 , , PUNCT hvd.32044092008168 517 7 = = SYM hvd.32044092008168 517 8 2 2 NUM hvd.32044092008168 517 9 y y PROPN hvd.32044092008168 517 10 and and CCONJ hvd.32044092008168 517 11 y y PROPN hvd.32044092008168 517 12 y y PROPN hvd.32044092008168 517 13 ' ' PUNCT hvd.32044092008168 517 14 – – PUNCT hvd.32044092008168 517 15 20 20 NUM hvd.32044092008168 517 16 — — SYM hvd.32044092008168 517 17 2 2 NUM hvd.32044092008168 517 18 zy'=2c zy'=2c PROPN hvd.32044092008168 517 19 – – PUNCT hvd.32044092008168 517 20 y y PROPN hvd.32044092008168 517 21 ' ' PUNCT hvd.32044092008168 517 22 , , PUNCT hvd.32044092008168 517 23 whence whence PROPN hvd.32044092008168 517 24 yy yy INTJ hvd.32044092008168 517 25 " " PUNCT hvd.32044092008168 517 26 y y PROPN hvd.32044092008168 517 27 ' ' PUNCT hvd.32044092008168 517 28 ? ? PUNCT hvd.32044092008168 518 1 yy yy INTJ hvd.32044092008168 518 2 " " PUNCT hvd.32044092008168 519 1 y'2 y'2 NOUN hvd.32044092008168 519 2 y y PROPN hvd.32044092008168 519 3 ? ? PUNCT hvd.32044092008168 520 1 y y PROPN hvd.32044092008168 520 2 2 2 NUM hvd.32044092008168 520 3 y y PROPN hvd.32044092008168 520 4 2 2 NUM hvd.32044092008168 520 5 or or CCONJ hvd.32044092008168 520 6 2 2 NUM hvd.32044092008168 520 7 or or CCONJ hvd.32044092008168 520 8 y y PROPN hvd.32044092008168 520 9 2 2 PROPN hvd.32044092008168 520 10 y y PROPN hvd.32044092008168 520 11 2 2 NUM hvd.32044092008168 520 12 2 2 NUM hvd.32044092008168 520 13 y y PROPN hvd.32044092008168 520 14 " " PUNCT hvd.32044092008168 520 15 ( ( PUNCT hvd.32044092008168 520 16 o)= o)= PROPN hvd.32044092008168 520 17 2 2 NUM hvd.32044092008168 520 18 or or CCONJ hvd.32044092008168 520 19 2 2 NUM hvd.32044092008168 520 20 yy yy INTJ hvd.32044092008168 520 21 " " PUNCT hvd.32044092008168 520 22 y y PROPN hvd.32044092008168 520 23 " " PUNCT hvd.32044092008168 520 24 y y PROPN hvd.32044092008168 520 25 y y PROPN hvd.32044092008168 520 26 ' ' PUNCT hvd.32044092008168 520 27 ? ? PUNCT hvd.32044092008168 521 1 + + NUM hvd.32044092008168 521 2 4c 4c NUM hvd.32044092008168 521 3 4 4 NUM hvd.32044092008168 521 4 y2 y2 PROPN hvd.32044092008168 521 5 38 38 NUM hvd.32044092008168 521 6 part part NOUN hvd.32044092008168 522 1 iii iii NUM hvd.32044092008168 522 2 . . PUNCT hvd.32044092008168 523 1 [ [ X hvd.32044092008168 523 2 63 63 NUM hvd.32044092008168 523 3 ] ] PUNCT hvd.32044092008168 524 1 [ [ X hvd.32044092008168 524 2 64 64 NUM hvd.32044092008168 524 3 ] ] PUNCT hvd.32044092008168 524 4 . . PUNCT hvd.32044092008168 524 5 . . PUNCT hvd.32044092008168 525 1 this this DET hvd.32044092008168 525 2 value value NOUN hvd.32044092008168 525 3 in in ADP hvd.32044092008168 525 4 hermite hermite PROPN hvd.32044092008168 525 5 's 's PART hvd.32044092008168 525 6 equation equation NOUN hvd.32044092008168 525 7 gives give VERB hvd.32044092008168 525 8 : : PUNCT hvd.32044092008168 525 9 · · PUNCT hvd.32044092008168 525 10 2 2 NUM hvd.32044092008168 525 11 yy yy NOUN hvd.32044092008168 525 12 " " PUNCT hvd.32044092008168 525 13 — — PUNCT hvd.32044092008168 525 14 y y PROPN hvd.32044092008168 525 15 ' ' PUNCT hvd.32044092008168 525 16 ? ? PUNCT hvd.32044092008168 526 1 + + NUM hvd.32044092008168 526 2 4c 4c NUM hvd.32044092008168 526 3 = = PUNCT hvd.32044092008168 527 1 [ [ X hvd.32044092008168 527 2 n(n n(n PROPN hvd.32044092008168 527 3 + + CCONJ hvd.32044092008168 527 4 1)pu 1)pu PROPN hvd.32044092008168 527 5 + + PUNCT hvd.32044092008168 527 6 b]4y b]4y PROPN hvd.32044092008168 527 7 ? ? PUNCT hvd.32044092008168 527 8 . . PUNCT hvd.32044092008168 528 1 whence whence ADV hvd.32044092008168 528 2 we we PRON hvd.32044092008168 528 3 derive derive VERB hvd.32044092008168 528 4 the the DET hvd.32044092008168 528 5 value value NOUN hvd.32044092008168 528 6 of of ADP hvd.32044092008168 528 7 c c PROPN hvd.32044092008168 528 8 sought seek VERB hvd.32044092008168 528 9 , , PUNCT hvd.32044092008168 528 10 namely namely ADV hvd.32044092008168 528 11 4c2 4c2 NUM hvd.32044092008168 528 12 = = SYM hvd.32044092008168 528 13 y y NOUN hvd.32044092008168 528 14 ' ' PUNCT hvd.32044092008168 528 15 ? ? PUNCT hvd.32044092008168 528 16 – – PUNCT hvd.32044092008168 528 17 2yy 2yy PROPN hvd.32044092008168 528 18 " " PUNCT hvd.32044092008168 528 19 + + NUM hvd.32044092008168 528 20 4[n(n 4[n(n NUM hvd.32044092008168 528 21 + + SYM hvd.32044092008168 528 22 1)pu 1)pu NUM hvd.32044092008168 528 23 + + CCONJ hvd.32044092008168 528 24 b b NOUN hvd.32044092008168 528 25 ] ] X hvd.32044092008168 528 26 y. y. NOUN hvd.32044092008168 528 27 y'2 y'2 X hvd.32044092008168 528 28 ( ( PUNCT hvd.32044092008168 528 29 let let VERB hvd.32044092008168 528 30 a a DET hvd.32044092008168 528 31 , , PUNCT hvd.32044092008168 528 32 b b NOUN hvd.32044092008168 528 33 , , PUNCT hvd.32044092008168 528 34 p p NOUN hvd.32044092008168 528 35 ... ... PUNCT hvd.32044092008168 528 36 = = PROPN hvd.32044092008168 528 37 pa pa PROPN hvd.32044092008168 528 38 , , PUNCT hvd.32044092008168 528 39 pb pb PROPN hvd.32044092008168 528 40 , , PUNCT hvd.32044092008168 528 41 py py PROPN hvd.32044092008168 528 42 ... ... PUNCT hvd.32044092008168 528 43 be be AUX hvd.32044092008168 528 44 roots root NOUN hvd.32044092008168 528 45 of of ADP hvd.32044092008168 528 46 y. y. NOUN hvd.32044092008168 528 47 = = PROPN hvd.32044092008168 528 48 then then ADV hvd.32044092008168 528 49 yu yu PROPN hvd.32044092008168 528 50 = = VERB hvd.32044092008168 528 51 a a X hvd.32044092008168 528 52 ... ... PUNCT hvd.32044092008168 528 53 = = SYM hvd.32044092008168 528 54 " " PUNCT hvd.32044092008168 528 55 + + CCONJ hvd.32044092008168 528 56 a a PRON hvd.32044092008168 528 57 , , PUNCT hvd.32044092008168 528 58 th-1 th-1 PUNCT hvd.32044092008168 529 1 + + CCONJ hvd.32044092008168 529 2 = = ADJ hvd.32044092008168 529 3 tn tn NOUN hvd.32044092008168 529 4 0 0 NUM hvd.32044092008168 529 5 yu yu PROPN hvd.32044092008168 529 6 = = NOUN hvd.32044092008168 529 7 a a PRON hvd.32044092008168 529 8 .... .... PUNCT hvd.32044092008168 529 9 = = PUNCT hvd.32044092008168 529 10 nt not PART hvd.32044092008168 529 11 " " PUNCT hvd.32044092008168 529 12 – – PUNCT hvd.32044092008168 529 13 1 1 NUM hvd.32044092008168 529 14 t t PROPN hvd.32044092008168 529 15 ' ' PUNCT hvd.32044092008168 529 16 + + CCONJ hvd.32044092008168 529 17 a a PRON hvd.32044092008168 529 18 , , PUNCT hvd.32044092008168 529 19 ( ( PUNCT hvd.32044092008168 529 20 n n X hvd.32044092008168 529 21 ntn—1 ntn—1 X hvd.32044092008168 529 22 t t PROPN hvd.32044092008168 529 23 ' ' PUNCT hvd.32044092008168 529 24 + + CCONJ hvd.32044092008168 529 25 ay(n ay(n ADJ hvd.32044092008168 529 26 − − NOUN hvd.32044092008168 529 27 1)tr 1)tr NUM hvd.32044092008168 529 28 — — PUNCT hvd.32044092008168 529 29 2 2 NUM hvd.32044092008168 529 30 % % NOUN hvd.32044092008168 529 31 + + NUM hvd.32044092008168 529 32 . . PUNCT hvd.32044092008168 530 1 ( ( PUNCT hvd.32044092008168 530 2 ... ... PUNCT hvd.32044092008168 530 3 = = NOUN hvd.32044092008168 530 4 0 0 NUM hvd.32044092008168 530 5 0 0 NUM hvd.32044092008168 530 6 -1 -1 PUNCT hvd.32044092008168 530 7 = = PUNCT hvd.32044092008168 530 8 = = PRON hvd.32044092008168 530 9 a.b a.b ADP hvd.32044092008168 530 10 or or CCONJ hvd.32044092008168 530 11 ' ' PUNCT hvd.32044092008168 530 12 u u PROPN hvd.32044092008168 530 13 y y PROPN hvd.32044092008168 530 14 : : PUNCT hvd.32044092008168 530 15 -p'2 -p'2 SPACE hvd.32044092008168 530 16 * * PUNCT hvd.32044092008168 530 17 * * NOUN hvd.32044092008168 530 18 4c 4c NUM hvd.32044092008168 530 19 ° ° NUM hvd.32044092008168 530 20 = = PUNCT hvd.32044092008168 530 21 p"?(a p"?(a PROPN hvd.32044092008168 530 22 ) ) PUNCT hvd.32044092008168 530 23 [ [ X hvd.32044092008168 530 24 " " PUNCT hvd.32044092008168 530 25 y y INTJ hvd.32044092008168 530 26 i i PRON hvd.32044092008168 530 27 _ _ PRON hvd.32044092008168 530 28 = = PUNCT hvd.32044092008168 531 1 ye ye INTJ hvd.32044092008168 531 2 = = PUNCT hvd.32044092008168 531 3 p“()(h p“()(h NOUN hvd.32044092008168 531 4 ) ) PUNCT hvd.32044092008168 531 5 x x PUNCT hvd.32044092008168 532 1 = = PROPN hvd.32044092008168 532 2 y y PROPN hvd.32044092008168 532 3 ; ; PUNCT hvd.32044092008168 532 4 ... ... PUNCT hvd.32044092008168 532 5 12 12 NUM hvd.32044092008168 532 6 dy dy PROPN hvd.32044092008168 532 7 np(un-1p'u np(un-1p'u X hvd.32044092008168 532 8 . . PUNCT hvd.32044092008168 533 1 du du PROPN hvd.32044092008168 533 2 whence whence PROPN hvd.32044092008168 533 3 d d PROPN hvd.32044092008168 533 4 y y PROPN hvd.32044092008168 533 5 dt dt PROPN hvd.32044092008168 533 6 and and CCONJ hvd.32044092008168 533 7 dy72 dy72 PROPN hvd.32044092008168 533 8 d d NOUN hvd.32044092008168 533 9 y/2 y/2 NOUN hvd.32044092008168 533 10 : : PUNCT hvd.32044092008168 534 1 dt dt PROPN hvd.32044092008168 534 2 dt dt PROPN hvd.32044092008168 534 3 = = PROPN hvd.32044092008168 534 4 but but CCONJ hvd.32044092008168 534 5 from from ADP hvd.32044092008168 534 6 algebra algebra NOUN hvd.32044092008168 534 7 we we PRON hvd.32044092008168 534 8 have have VERB hvd.32044092008168 534 9 dy dy NOUN hvd.32044092008168 534 10 = = NOUN hvd.32044092008168 534 11 ( ( PUNCT hvd.32044092008168 534 12 a a DET hvd.32044092008168 534 13 — — PUNCT hvd.32044092008168 534 14 b b X hvd.32044092008168 534 15 ) ) PUNCT hvd.32044092008168 534 16 ( ( PUNCT hvd.32044092008168 534 17 a a DET hvd.32044092008168 534 18 – – PUNCT hvd.32044092008168 534 19 v v NOUN hvd.32044092008168 534 20 ) ) PUNCT hvd.32044092008168 534 21 ... ... PUNCT hvd.32044092008168 534 22 — — PUNCT hvd.32044092008168 535 1 dt dt PROPN hvd.32044092008168 535 2 whence whence NOUN hvd.32044092008168 535 3 [ [ X hvd.32044092008168 535 4 65 65 NUM hvd.32044092008168 535 5 ] ] PUNCT hvd.32044092008168 535 6 · · PUNCT hvd.32044092008168 535 7 2c 2c NUM hvd.32044092008168 535 8 = = PRON hvd.32044092008168 535 9 a a NOUN hvd.32044092008168 535 10 ' ' PUNCT hvd.32044092008168 535 11 ( ( PUNCT hvd.32044092008168 535 12 a a DET hvd.32044092008168 535 13 b b NOUN hvd.32044092008168 535 14 ) ) PUNCT hvd.32044092008168 535 15 ( ( PUNCT hvd.32044092008168 535 16 a a DET hvd.32044092008168 535 17 – – PUNCT hvd.32044092008168 535 18 v v NOUN hvd.32044092008168 535 19 ) ) PUNCT hvd.32044092008168 535 20 ... ... PUNCT hvd.32044092008168 536 1 a'la a'la SCONJ hvd.32044092008168 536 2 with with ADP hvd.32044092008168 536 3 like like INTJ hvd.32044092008168 536 4 expressions expression NOUN hvd.32044092008168 536 5 for for ADP hvd.32044092008168 536 6 the the DET hvd.32044092008168 536 7 other other ADJ hvd.32044092008168 536 8 roots root NOUN hvd.32044092008168 536 9 which which PRON hvd.32044092008168 536 10 we we PRON hvd.32044092008168 536 11 observe observe VERB hvd.32044092008168 536 12 are be AUX hvd.32044092008168 536 13 the the DET hvd.32044092008168 536 14 values value NOUN hvd.32044092008168 536 15 obtain obtain VERB hvd.32044092008168 536 16 before before ADV hvd.32044092008168 536 17 ( ( PUNCT hvd.32044092008168 536 18 see see VERB hvd.32044092008168 536 19 [ [ X hvd.32044092008168 536 20 51 51 NUM hvd.32044092008168 536 21 ] ] PUNCT hvd.32044092008168 536 22 ) ) PUNCT hvd.32044092008168 536 23 , , PUNCT hvd.32044092008168 536 24 namely namely ADV hvd.32044092008168 536 25 20 20 NUM hvd.32044092008168 536 26 ( ( PUNCT hvd.32044092008168 536 27 a a DET hvd.32044092008168 536 28 – – PUNCT hvd.32044092008168 536 29 b b NOUN hvd.32044092008168 536 30 ) ) PUNCT hvd.32044092008168 536 31 ( ( PUNCT hvd.32044092008168 536 32 a a DET hvd.32044092008168 536 33 y y NOUN hvd.32044092008168 536 34 ) ) PUNCT hvd.32044092008168 536 35 ... ... PUNCT hvd.32044092008168 537 1 2 2 NUM hvd.32044092008168 537 2 c c X hvd.32044092008168 537 3 b b NOUN hvd.32044092008168 537 4 ' ' PUNCT hvd.32044092008168 537 5 = = X hvd.32044092008168 537 6 ( ( PUNCT hvd.32044092008168 537 7 b b X hvd.32044092008168 537 8 a a X hvd.32044092008168 537 9 ) ) PUNCT hvd.32044092008168 537 10 ( ( PUNCT hvd.32044092008168 537 11 b b X hvd.32044092008168 537 12 — — PUNCT hvd.32044092008168 537 13 v v NOUN hvd.32044092008168 537 14 ... ... PUNCT hvd.32044092008168 537 15 ( ( PUNCT hvd.32044092008168 537 16 = = X hvd.32044092008168 537 17 a a DET hvd.32044092008168 537 18 a a DET hvd.32044092008168 537 19 ' ' PUNCT hvd.32044092008168 537 20 y. y. NOUN hvd.32044092008168 537 21 to to PART hvd.32044092008168 537 22 obtain obtain VERB hvd.32044092008168 537 23 y y PROPN hvd.32044092008168 537 24 we we PRON hvd.32044092008168 537 25 have have VERB hvd.32044092008168 537 26 : : PUNCT hvd.32044092008168 537 27 2c= 2c= NUM hvd.32044092008168 537 28 ya ya PROPN hvd.32044092008168 537 29 y y PROPN hvd.32044092008168 537 30 ; ; PUNCT hvd.32044092008168 537 31 + + NUM hvd.32044092008168 537 32 a a DET hvd.32044092008168 537 33 , , PUNCT hvd.32044092008168 537 34 +1 +1 PROPN hvd.32044092008168 537 35 , , PUNCT hvd.32044092008168 537 36 + + PROPN hvd.32044092008168 537 37 c c ADP hvd.32044092008168 537 38 being be AUX hvd.32044092008168 537 39 the the DET hvd.32044092008168 537 40 roots root NOUN hvd.32044092008168 537 41 of of ADP hvd.32044092008168 537 42 y y PROPN hvd.32044092008168 537 43 = = PROPN hvd.32044092008168 537 44 f(u f(u PROPN hvd.32044092008168 537 45 ) ) PUNCT hvd.32044092008168 537 46 . . PUNCT hvd.32044092008168 538 1 we we PRON hvd.32044092008168 538 2 have have VERB hvd.32044092008168 538 3 also also ADV hvd.32044092008168 538 4 : : PUNCT hvd.32044092008168 538 5 2c 2c NUM hvd.32044092008168 538 6 = = X hvd.32044092008168 538 7 yz yz INTJ hvd.32044092008168 538 8 ' ' PUNCT hvd.32044092008168 538 9 --zy --zy NOUN hvd.32044092008168 538 10 ' ' PUNCT hvd.32044092008168 538 11 = = SYM hvd.32044092008168 538 12 > > X hvd.32044092008168 538 13 15(u 15(u NUM hvd.32044092008168 538 14 + + CCONJ hvd.32044092008168 538 15 a a X hvd.32044092008168 538 16 ) ) PUNCT hvd.32044092008168 538 17 – – PUNCT hvd.32044092008168 538 18 $ $ SYM hvd.32044092008168 538 19 ( ( PUNCT hvd.32044092008168 538 20 u u PROPN hvd.32044092008168 538 21 — — PUNCT hvd.32044092008168 538 22 a a X hvd.32044092008168 538 23 ) ) PUNCT hvd.32044092008168 538 24 28(a)]yz 28(a)]yz NUM hvd.32044092008168 538 25 15(v 15(v NUM hvd.32044092008168 538 26 + + CCONJ hvd.32044092008168 538 27 a a X hvd.32044092008168 538 28 ) ) PUNCT hvd.32044092008168 538 29 – – PUNCT hvd.32044092008168 538 30 $ $ SYM hvd.32044092008168 538 31 ( ( PUNCT hvd.32044092008168 538 32 u u PROPN hvd.32044092008168 538 33 — — PUNCT hvd.32044092008168 538 34 a a X hvd.32044092008168 538 35 ) ) PUNCT hvd.32044092008168 538 36 — — PUNCT hvd.32044092008168 538 37 28(a 28(a NUM hvd.32044092008168 538 38 ) ) PUNCT hvd.32044092008168 538 39 ] ] PUNCT hvd.32044092008168 538 40 . . PUNCT hvd.32044092008168 539 1 n n CCONJ hvd.32044092008168 539 2 + + PUNCT hvd.32044092008168 539 3 ) ) PUNCT hvd.32044092008168 539 4 & & CCONJ hvd.32044092008168 539 5 . . PUNCT hvd.32044092008168 540 1 but but CCONJ hvd.32044092008168 540 2 p'r p'r X hvd.32044092008168 540 3 [ [ PUNCT hvd.32044092008168 540 4 $ $ SYM hvd.32044092008168 540 5 ( ( PUNCT hvd.32044092008168 540 6 u u PROPN hvd.32044092008168 540 7 + + CCONJ hvd.32044092008168 540 8 a a PRON hvd.32044092008168 540 9 ) ) PUNCT hvd.32044092008168 540 10 + + CCONJ hvd.32044092008168 540 11 $ $ SYM hvd.32044092008168 540 12 ( ( PUNCT hvd.32044092008168 540 13 u u PROPN hvd.32044092008168 540 14 — — PUNCT hvd.32044092008168 540 15 a a X hvd.32044092008168 540 16 ) ) PUNCT hvd.32044092008168 540 17 — — PUNCT hvd.32044092008168 540 18 28a 28a NUM hvd.32044092008168 540 19 ] ] PUNCT hvd.32044092008168 540 20 pa pa PROPN hvd.32044092008168 540 21 ) ) PUNCT hvd.32044092008168 540 22 or or CCONJ hvd.32044092008168 540 23 20 20 NUM hvd.32044092008168 540 24 2 2 NUM hvd.32044092008168 540 25 ( ( PUNCT hvd.32044092008168 540 26 ри ри NOUN hvd.32044092008168 540 27 integral integral ADJ hvd.32044092008168 540 28 as as ADP hvd.32044092008168 540 29 a a DET hvd.32044092008168 540 30 product product NOUN hvd.32044092008168 540 31 . . PUNCT hvd.32044092008168 541 1 39 39 NUM hvd.32044092008168 541 2 whence whence NOUN hvd.32044092008168 541 3 с с PROPN hvd.32044092008168 541 4 2 2 NUM hvd.32044092008168 541 5 ( ( PUNCT hvd.32044092008168 541 6 pú pú ADP hvd.32044092008168 541 7 – – PUNCT hvd.32044092008168 541 8 pa pa PROPN hvd.32044092008168 541 9 ) ) PUNCT hvd.32044092008168 541 10 — — PUNCT hvd.32044092008168 541 11 śu śu INTJ hvd.32044092008168 541 12 — — PUNCT hvd.32044092008168 541 13 $ $ SYM hvd.32044092008168 541 14 a a PRON hvd.32044092008168 541 15 ] ] PUNCT hvd.32044092008168 541 16 p'u p'u ADV hvd.32044092008168 541 17 d d PROPN hvd.32044092008168 541 18 du du PROPN hvd.32044092008168 541 19 pa pa PROPN hvd.32044092008168 541 20 log log PROPN hvd.32044092008168 541 21 ou ou X hvd.32044092008168 541 22 į į X hvd.32044092008168 541 23 = = X hvd.32044092008168 541 24 > > X hvd.32044092008168 542 1 [ [ X hvd.32044092008168 542 2 s(v s(v X hvd.32044092008168 542 3 + + CCONJ hvd.32044092008168 542 4 a a X hvd.32044092008168 542 5 ) ) PUNCT hvd.32044092008168 542 6 σ(+ σ(+ NOUN hvd.32044092008168 542 7 ) ) PUNCT hvd.32044092008168 543 1 [ [ X hvd.32044092008168 543 2 logo logo NOUN hvd.32044092008168 543 3 ( ( PUNCT hvd.32044092008168 543 4 v v NOUN hvd.32044092008168 543 5 + + PRON hvd.32044092008168 543 6 a a X hvd.32044092008168 543 7 ) ) PUNCT hvd.32044092008168 543 8 – – PUNCT hvd.32044092008168 543 9 log log PROPN hvd.32044092008168 543 10 vpu vpu PROPN hvd.32044092008168 543 11 u u PROPN hvd.32044092008168 543 12 uça uça PROPN hvd.32044092008168 543 13 ] ] X hvd.32044092008168 543 14 it it PRON hvd.32044092008168 543 15 log log VERB hvd.32044092008168 543 16 ii ii PROPN hvd.32044092008168 543 17 au au X hvd.32044092008168 543 18 log|tvpu log|tvpu NOUN hvd.32044092008168 543 19 -pa -pa SPACE hvd.32044092008168 543 20 . . PUNCT hvd.32044092008168 544 1 d d PROPN hvd.32044092008168 544 2 du du PROPN hvd.32044092008168 544 3 log log VERB hvd.32044092008168 544 4 e e PROPN hvd.32044092008168 544 5 - - ADJ hvd.32044092008168 544 6 uζα uζα ADJ hvd.32044092008168 544 7 o(u o(u ADJ hvd.32044092008168 544 8 + + CCONJ hvd.32044092008168 544 9 a a X hvd.32044092008168 544 10 ) ) PUNCT hvd.32044092008168 544 11 vpu vpu NOUN hvd.32044092008168 545 1 pa pa PROPN hvd.32044092008168 545 2 • • X hvd.32044092008168 545 3 си си PROPN hvd.32044092008168 545 4 co(u co(u ADJ hvd.32044092008168 545 5 + + CCONJ hvd.32044092008168 545 6 a a X hvd.32044092008168 545 7 ) ) PUNCT hvd.32044092008168 545 8 d d PROPN hvd.32044092008168 545 9 d d X hvd.32044092008168 545 10 du du X hvd.32044092008168 545 11 e e PROPN hvd.32044092008168 545 12 - - NOUN hvd.32044092008168 545 13 uga uga PROPN hvd.32044092008168 545 14 σι σι INTJ hvd.32044092008168 545 15 but but CCONJ hvd.32044092008168 545 16 1 1 NUM hvd.32044092008168 545 17 1 1 NUM hvd.32044092008168 545 18 пури пури NOUN hvd.32044092008168 545 19 ttvpu ttvpu ADJ hvd.32044092008168 545 20 – – PUNCT hvd.32044092008168 545 21 pa pa PROPN hvd.32044092008168 545 22 = = SYM hvd.32044092008168 545 23 yon yon PROPN hvd.32044092008168 545 24 2 2 NUM hvd.32044092008168 545 25 2 2 NUM hvd.32044092008168 545 26 1 1 NUM hvd.32044092008168 545 27 с с X hvd.32044092008168 545 28 y y PROPN hvd.32044092008168 545 29 d d PROPN hvd.32044092008168 545 30 d d X hvd.32044092008168 545 31 du du PROPN hvd.32044092008168 545 32 ( ( PUNCT hvd.32044092008168 545 33 ) ) PUNCT hvd.32044092008168 545 34 1 1 NUM hvd.32044092008168 545 35 2 2 NUM hvd.32044092008168 545 36 log[/ºu log[/ºu NOUN hvd.32044092008168 545 37 + + CCONJ hvd.32044092008168 545 38 a a X hvd.32044092008168 545 39 ) ) PUNCT hvd.32044092008168 545 40 ewζα ewζα X hvd.32044092008168 545 41 log log VERB hvd.32044092008168 545 42 ya ya PRON hvd.32044092008168 545 43 2 2 NUM hvd.32044092008168 545 44 би би X hvd.32044092008168 545 45 du du X hvd.32044092008168 545 46 o o X hvd.32044092008168 545 47 ( ( PUNCT hvd.32044092008168 545 48 u u PROPN hvd.32044092008168 545 49 + + CCONJ hvd.32044092008168 545 50 a a PRON hvd.32044092008168 545 51 ) ) PUNCT hvd.32044092008168 545 52 d d PROPN hvd.32044092008168 545 53 du du X hvd.32044092008168 545 54 log log VERB hvd.32044092008168 545 55 [ [ X hvd.32044092008168 545 56 ] ] X hvd.32044092008168 545 57 ti ti PROPN hvd.32044092008168 545 58 é é PROPN hvd.32044092008168 545 59 uša uša PROPN hvd.32044092008168 545 60 1 1 NUM hvd.32044092008168 545 61 yz yz PROPN hvd.32044092008168 545 62 ' ' PUNCT hvd.32044092008168 545 63 + + CCONJ hvd.32044092008168 545 64 zy zy INTJ hvd.32044092008168 545 65 ' ' PUNCT hvd.32044092008168 545 66 y y PROPN hvd.32044092008168 545 67 ? ? PUNCT hvd.32044092008168 546 1 6u 6u NUM hvd.32044092008168 546 2 2 2 NUM hvd.32044092008168 547 1 y y PROPN hvd.32044092008168 547 2 ' ' PART hvd.32044092008168 547 3 6 6 NUM hvd.32044092008168 547 4 d d NOUN hvd.32044092008168 547 5 + + NOUN hvd.32044092008168 547 6 du du PROPN hvd.32044092008168 547 7 logit logit NOUN hvd.32044092008168 547 8 ( ( PUNCT hvd.32044092008168 547 9 u u NOUN hvd.32044092008168 547 10 + + CCONJ hvd.32044092008168 547 11 a a PRON hvd.32044092008168 547 12 ) ) PUNCT hvd.32044092008168 547 13 0(u 0(u NUM hvd.32044092008168 547 14 ) ) PUNCT hvd.32044092008168 547 15 « « PUNCT hvd.32044092008168 547 16 ζα ζα PROPN hvd.32044092008168 547 17 . . PROPN hvd.32044092008168 547 18 2 2 NUM hvd.32044092008168 547 19 y y PROPN hvd.32044092008168 547 20 whence whence NOUN hvd.32044092008168 547 21 d d PROPN hvd.32044092008168 547 22 y y PROPN hvd.32044092008168 547 23 ' ' PUNCT hvd.32044092008168 547 24 – – PUNCT hvd.32044092008168 547 25 20 20 NUM hvd.32044092008168 547 26 2 2 NUM hvd.32044092008168 547 27 y y PROPN hvd.32044092008168 547 28 co co PROPN hvd.32044092008168 547 29 ) ) PUNCT hvd.32044092008168 547 30 = = PUNCT hvd.32044092008168 548 1 e e X hvd.32044092008168 548 2 - - NOUN hvd.32044092008168 548 3 uζα uζα ADJ hvd.32044092008168 548 4 log[t•(-+ log[t•(-+ ADJ hvd.32044092008168 548 5 a a PRON hvd.32044092008168 548 6 ) ) PUNCT hvd.32044092008168 548 7 у у PROPN hvd.32044092008168 548 8 du du X hvd.32044092008168 548 9 σι σι INTJ hvd.32044092008168 548 10 or or CCONJ hvd.32044092008168 548 11 6 6 NUM hvd.32044092008168 548 12 logy logy NOUN hvd.32044092008168 548 13 log log NOUN hvd.32044092008168 548 14 / / SYM hvd.32044092008168 548 15 t"(u t"(u X hvd.32044092008168 548 16 + + CCONJ hvd.32044092008168 548 17 a a X hvd.32044092008168 548 18 ) ) PUNCT hvd.32044092008168 548 19 e e NOUN hvd.32044092008168 549 1 - - PROPN hvd.32044092008168 549 2 uša uša PROPN hvd.32044092008168 549 3 log log PROPN hvd.32044092008168 549 4 c c PROPN hvd.32044092008168 549 5 σω σω INTJ hvd.32044092008168 549 6 . . PUNCT hvd.32044092008168 549 7 . . PUNCT hvd.32044092008168 550 1 бо бо INTJ hvd.32044092008168 550 2 а а X hvd.32044092008168 550 3 c c NOUN hvd.32044092008168 550 4 = = SYM hvd.32044092008168 550 5 16 16 NUM hvd.32044092008168 550 6 a. a. NOUN hvd.32044092008168 550 7 whence whence NOUN hvd.32044092008168 550 8 the the DET hvd.32044092008168 550 9 value value NOUN hvd.32044092008168 550 10 of of ADP hvd.32044092008168 550 11 y y PROPN hvd.32044092008168 550 12 is be AUX hvd.32044092008168 550 13 obtained obtain VERB hvd.32044092008168 550 14 directly directly ADV hvd.32044092008168 550 15 , , PUNCT hvd.32044092008168 550 16 namely namely ADV hvd.32044092008168 550 17 co(u co(u ADJ hvd.32044092008168 550 18 + + CCONJ hvd.32044092008168 550 19 a a X hvd.32044092008168 550 20 ) ) PUNCT hvd.32044092008168 551 1 [ [ X hvd.32044092008168 551 2 66 66 NUM hvd.32044092008168 551 3 ] ] PUNCT hvd.32044092008168 551 4 y y PROPN hvd.32044092008168 551 5 - - PUNCT hvd.32044092008168 551 6 it it PRON hvd.32044092008168 551 7 e e NOUN hvd.32044092008168 551 8 - - NOUN hvd.32044092008168 551 9 uζα uζα ADJ hvd.32044092008168 551 10 the the DET hvd.32044092008168 551 11 third third ADJ hvd.32044092008168 551 12 method method NOUN hvd.32044092008168 551 13 of of ADP hvd.32044092008168 551 14 integration integration NOUN hvd.32044092008168 551 15 is be AUX hvd.32044092008168 551 16 then then ADV hvd.32044092008168 551 17 the the DET hvd.32044092008168 551 18 following follow VERB hvd.32044092008168 551 19 : : PUNCT hvd.32044092008168 551 20 calculate calculate VERB hvd.32044092008168 551 21 the the DET hvd.32044092008168 551 22 polynomial polynomial ADJ hvd.32044092008168 551 23 y y NOUN hvd.32044092008168 551 24 by by ADP hvd.32044092008168 551 25 the the DET hvd.32044092008168 551 26 aid aid NOUN hvd.32044092008168 551 27 of of ADP hvd.32044092008168 551 28 the the DET hvd.32044092008168 551 29 relation relation NOUN hvd.32044092008168 551 30 [ [ X hvd.32044092008168 551 31 58 58 NUM hvd.32044092008168 551 32 ] ] PUNCT hvd.32044092008168 551 33 or or CCONJ hvd.32044092008168 551 34 [ [ X hvd.32044092008168 551 35 61 61 NUM hvd.32044092008168 551 36 ] ] PUNCT hvd.32044092008168 551 37 from from ADP hvd.32044092008168 551 38 which which PRON hvd.32044092008168 551 39 derive derive VERB hvd.32044092008168 551 40 the the DET hvd.32044092008168 551 41 constant constant ADJ hvd.32044092008168 551 42 c2 c2 NOUN hvd.32044092008168 551 43 by by ADP hvd.32044092008168 551 44 means mean NOUN hvd.32044092008168 551 45 of of ADP hvd.32044092008168 551 46 equation equation NOUN hvd.32044092008168 551 47 [ [ X hvd.32044092008168 551 48 64 64 NUM hvd.32044092008168 551 49 ] ] PUNCT hvd.32044092008168 551 50 extracting extract VERB hvd.32044092008168 551 51 the the DET hvd.32044092008168 551 52 square square ADJ hvd.32044092008168 551 53 root root NOUN hvd.32044092008168 551 54 to to PART hvd.32044092008168 551 55 obtain obtain VERB hvd.32044092008168 551 56 c c PROPN hvd.32044092008168 551 57 and and CCONJ hvd.32044092008168 551 58 finally finally ADV hvd.32044092008168 551 59 obtain obtain VERB hvd.32044092008168 551 60 the the DET hvd.32044092008168 551 61 constants constants ADJ hvd.32044092008168 551 62 20 20 NUM hvd.32044092008168 551 63 20 20 NUM hvd.32044092008168 551 64 p'a p'a NOUN hvd.32044092008168 551 65 = = NOUN hvd.32044092008168 551 66 ( ( PUNCT hvd.32044092008168 551 67 a a DET hvd.32044092008168 551 68 b b NOUN hvd.32044092008168 551 69 ) ) PUNCT hvd.32044092008168 551 70 ( ( PUNCT hvd.32044092008168 551 71 a a DET hvd.32044092008168 551 72 y y NOUN hvd.32044092008168 551 73 ) ) PUNCT hvd.32044092008168 551 74 . . PUNCT hvd.32044092008168 552 1 ( ( PUNCT hvd.32044092008168 552 2 b b X hvd.32044092008168 552 3 a a X hvd.32044092008168 552 4 ) ) PUNCT hvd.32044092008168 552 5 b b PROPN hvd.32044092008168 552 6 v v NOUN hvd.32044092008168 552 7 ... ... PUNCT hvd.32044092008168 552 8 — — PUNCT hvd.32044092008168 552 9 y y PROPN hvd.32044092008168 552 10 ) ) PUNCT hvd.32044092008168 552 11 when when SCONJ hvd.32044092008168 552 12 a a DET hvd.32044092008168 552 13 = = NOUN hvd.32044092008168 552 14 pa pa PROPN hvd.32044092008168 552 15 , , PUNCT hvd.32044092008168 552 16 b b PROPN hvd.32044092008168 552 17 yb yb X hvd.32044092008168 552 18 ... ... PUNCT hvd.32044092008168 552 19 are be AUX hvd.32044092008168 552 20 the the DET hvd.32044092008168 552 21 roots root NOUN hvd.32044092008168 552 22 of of ADP hvd.32044092008168 552 23 y. y. NOUN hvd.32044092008168 552 24 these these DET hvd.32044092008168 552 25 relations relation NOUN hvd.32044092008168 552 26 determine determine VERB hvd.32044092008168 552 27 the the DET hvd.32044092008168 552 28 arguments argument NOUN hvd.32044092008168 552 29 a·b.c a·b.c ADV hvd.32044092008168 552 30 ... ... PUNCT hvd.32044092008168 552 31 , , PUNCT hvd.32044092008168 552 32 having have VERB hvd.32044092008168 552 33 which which PRON hvd.32044092008168 552 34 the the DET hvd.32044092008168 552 35 solution solution NOUN hvd.32044092008168 552 36 is be AUX hvd.32044092008168 552 37 co(u co(u ADJ hvd.32044092008168 552 38 + + CCONJ hvd.32044092008168 552 39 a a X hvd.32044092008168 552 40 ) ) PUNCT hvd.32044092008168 552 41 y y PROPN hvd.32044092008168 552 42 = = PRON hvd.32044092008168 552 43 it it PRON hvd.32044092008168 552 44 : : PUNCT hvd.32044092008168 552 45 if if SCONJ hvd.32044092008168 552 46 we we PRON hvd.32044092008168 552 47 take take VERB hvd.32044092008168 552 48 the the DET hvd.32044092008168 552 49 second second ADJ hvd.32044092008168 552 50 root root NOUN hvd.32044092008168 552 51 of of ADP hvd.32044092008168 552 52 c2 c2 PROPN hvd.32044092008168 552 53 we we PRON hvd.32044092008168 552 54 obtain obtain VERB hvd.32044092008168 552 55 the the DET hvd.32044092008168 552 56 integral integral NOUN hvd.32044092008168 552 57 obtained obtain VERB hvd.32044092008168 552 58 also also ADV hvd.32044092008168 552 59 from from ADP hvd.32044092008168 552 60 y y PROPN hvd.32044092008168 552 61 by by ADP hvd.32044092008168 552 62 changing change VERB hvd.32044092008168 552 63 u u PROPN hvd.32044092008168 552 64 into into ADP hvd.32044092008168 552 65 – – PUNCT hvd.32044092008168 552 66 u. u. PROPN hvd.32044092008168 552 67 p'o p'o PROPN hvd.32044092008168 552 68 > > X hvd.32044092008168 552 69 e e PROPN hvd.32044092008168 552 70 - - PROPN hvd.32044092008168 552 71 usa usa PROPN hvd.32044092008168 552 72 . . PROPN hvd.32044092008168 552 73 σω σω PROPN hvd.32044092008168 552 74 u. u. PROPN hvd.32044092008168 552 75 40 40 NUM hvd.32044092008168 552 76 part part NOUN hvd.32044092008168 552 77 iii iii NOUN hvd.32044092008168 552 78 . . PUNCT hvd.32044092008168 553 1 determination determination NOUN hvd.32044092008168 553 2 of of ADP hvd.32044092008168 553 3 y y PROPN hvd.32044092008168 553 4 for for ADP hvd.32044092008168 553 5 n n CCONJ hvd.32044092008168 553 6 = = SYM hvd.32044092008168 553 7 3 3 X hvd.32044092008168 553 8 . . PUNCT hvd.32044092008168 554 1 the the DET hvd.32044092008168 554 2 foregoing forego VERB hvd.32044092008168 554 3 solution solution NOUN hvd.32044092008168 554 4 while while SCONJ hvd.32044092008168 554 5 complete complete ADJ hvd.32044092008168 554 6 and and CCONJ hvd.32044092008168 554 7 rigid rigid ADJ hvd.32044092008168 554 8 from from ADP hvd.32044092008168 554 9 a a DET hvd.32044092008168 554 10 theoretical theoretical ADJ hvd.32044092008168 554 11 standpoint standpoint NOUN hvd.32044092008168 554 12 needs need VERB hvd.32044092008168 554 13 to to PART hvd.32044092008168 554 14 be be AUX hvd.32044092008168 554 15 greatly greatly ADV hvd.32044092008168 554 16 perfected perfect VERB hvd.32044092008168 554 17 before before SCONJ hvd.32044092008168 554 18 it it PRON hvd.32044092008168 554 19 becomes become VERB hvd.32044092008168 554 20 practically practically ADV hvd.32044092008168 554 21 applicable applicable ADJ hvd.32044092008168 554 22 . . PUNCT hvd.32044092008168 555 1 it it PRON hvd.32044092008168 555 2 is be AUX hvd.32044092008168 555 3 indeed indeed ADV hvd.32044092008168 555 4 but but CCONJ hvd.32044092008168 555 5 another another DET hvd.32044092008168 555 6 example example NOUN hvd.32044092008168 555 7 , , PUNCT hvd.32044092008168 555 8 the the DET hvd.32044092008168 555 9 invariant invariant ADJ hvd.32044092008168 555 10 theory theory NOUN hvd.32044092008168 555 11 being be AUX hvd.32044092008168 555 12 a a DET hvd.32044092008168 555 13 second second NOUN hvd.32044092008168 555 14 of of ADP hvd.32044092008168 555 15 the the DET hvd.32044092008168 555 16 fact fact NOUN hvd.32044092008168 555 17 that that SCONJ hvd.32044092008168 555 18 it it PRON hvd.32044092008168 555 19 is be AUX hvd.32044092008168 555 20 often often ADV hvd.32044092008168 555 21 an an DET hvd.32044092008168 555 22 easier easy ADJ hvd.32044092008168 555 23 task task NOUN hvd.32044092008168 555 24 to to PART hvd.32044092008168 555 25 obtain obtain VERB hvd.32044092008168 555 26 a a DET hvd.32044092008168 555 27 general general NOUN hvd.32044092008168 555 28 than than ADP hvd.32044092008168 555 29 an an DET hvd.32044092008168 555 30 explicit explicit ADJ hvd.32044092008168 555 31 form form NOUN hvd.32044092008168 555 32 . . PUNCT hvd.32044092008168 556 1 having having AUX hvd.32044092008168 556 2 determined determine VERB hvd.32044092008168 556 3 the the DET hvd.32044092008168 556 4 explicit explicit ADJ hvd.32044092008168 556 5 forms form NOUN hvd.32044092008168 556 6 for for ADP hvd.32044092008168 556 7 n n X hvd.32044092008168 556 8 2 2 NUM hvd.32044092008168 556 9 let let VERB hvd.32044092008168 556 10 us we PRON hvd.32044092008168 556 11 attempt attempt VERB hvd.32044092008168 556 12 to to PART hvd.32044092008168 556 13 apply apply VERB hvd.32044092008168 556 14 the the DET hvd.32044092008168 556 15 above above ADJ hvd.32044092008168 556 16 rule rule NOUN hvd.32044092008168 556 17 to to ADP hvd.32044092008168 556 18 the the DET hvd.32044092008168 556 19 next next ADJ hvd.32044092008168 556 20 case case NOUN hvd.32044092008168 556 21 n n X hvd.32044092008168 556 22 = = X hvd.32044092008168 556 23 3 3 X hvd.32044092008168 556 24 . . PUNCT hvd.32044092008168 556 25 = = PUNCT hvd.32044092008168 556 26 given give VERB hvd.32044092008168 556 27 n n CCONJ hvd.32044092008168 556 28 = = SYM hvd.32044092008168 556 29 3 3 NUM hvd.32044092008168 556 30 where where SCONJ hvd.32044092008168 556 31 a₂ a₂ PROPN hvd.32044092008168 556 32 as as ADP hvd.32044092008168 556 33 from from ADP hvd.32044092008168 556 34 ( ( PUNCT hvd.32044092008168 556 35 60 60 NUM hvd.32044092008168 556 36 ) ) PUNCT hvd.32044092008168 556 37 and and CCONJ hvd.32044092008168 556 38 ( ( PUNCT hvd.32044092008168 556 39 61 61 X hvd.32044092008168 556 40 ) ) PUNCT hvd.32044092008168 556 41 we we PRON hvd.32044092008168 556 42 obtain obtain VERB hvd.32044092008168 556 43 . . PUNCT hvd.32044092008168 557 1 [ [ X hvd.32044092008168 557 2 67 67 NUM hvd.32044092008168 557 3 ] ] PUNCT hvd.32044092008168 557 4 · · PUNCT hvd.32044092008168 557 5 n(n n(n PROPN hvd.32044092008168 557 6 8(2n 8(2n NUM hvd.32044092008168 557 7 [ [ X hvd.32044092008168 557 8 68 68 NUM hvd.32044092008168 557 9 ] ] PUNCT hvd.32044092008168 557 10 · · PUNCT hvd.32044092008168 557 11 hence hence ADV hvd.32044092008168 557 12 • • SYM hvd.32044092008168 557 13 n(n n(n PROPN hvd.32044092008168 557 14 12 12 NUM hvd.32044092008168 557 15 ( ( PUNCT hvd.32044092008168 557 16 2n 2n NUM hvd.32044092008168 557 17 : : PUNCT hvd.32044092008168 557 18 : : PUNCT hvd.32044092008168 557 19 s3 s3 PROPN hvd.32044092008168 557 20 -again -again PROPN hvd.32044092008168 557 21 st st PROPN hvd.32044092008168 557 22 b b PROPN hvd.32044092008168 557 23 = = X hvd.32044092008168 557 24 ― ― X hvd.32044092008168 557 25 = = X hvd.32044092008168 557 26 = = X hvd.32044092008168 557 27 yn=3 yn=3 NOUN hvd.32044092008168 557 28 : : PUNCT hvd.32044092008168 557 29 . . PUNCT hvd.32044092008168 558 1 ( ( PUNCT hvd.32044092008168 558 2 t t PROPN hvd.32044092008168 558 3 ) ) PUNCT hvd.32044092008168 558 4 = = VERB hvd.32044092008168 558 5 4(s+ 4(s+ NUM hvd.32044092008168 558 6 b)³ b)³ NOUN hvd.32044092008168 558 7 — — PUNCT hvd.32044092008168 558 8 g₂ g₂ PROPN hvd.32044092008168 558 9 ( ( PUNCT hvd.32044092008168 558 10 s s X hvd.32044092008168 558 11 + + CCONJ hvd.32044092008168 558 12 b b NOUN hvd.32044092008168 558 13 ) ) PUNCT hvd.32044092008168 558 14 — — PUNCT hvd.32044092008168 558 15 93 93 NUM hvd.32044092008168 558 16 1 1 NUM hvd.32044092008168 558 17 ) ) PUNCT hvd.32044092008168 558 18 - - PUNCT hvd.32044092008168 558 19 · · PROPN hvd.32044092008168 558 20 1 1 NUM hvd.32044092008168 558 21 ( ( PUNCT hvd.32044092008168 558 22 44b³ 44b³ NUM hvd.32044092008168 558 23 — — PUNCT hvd.32044092008168 558 24 3g₂b 3g₂b PROPN hvd.32044092008168 558 25 + + CCONJ hvd.32044092008168 558 26 93 93 NUM hvd.32044092008168 558 27 ) ) PUNCT hvd.32044092008168 558 28 . . PUNCT hvd.32044092008168 559 1 3 3 X hvd.32044092008168 559 2 ) ) PUNCT hvd.32044092008168 559 3 2 2 NUM hvd.32044092008168 559 4 ) ) PUNCT hvd.32044092008168 559 5 5 5 NUM hvd.32044092008168 559 6 ) ) PUNCT hvd.32044092008168 559 7 1 1 NUM hvd.32044092008168 559 8 1 1 NUM hvd.32044092008168 559 9 g'(b g'(b NUM hvd.32044092008168 559 10 ) ) PUNCT hvd.32044092008168 559 11 — — PUNCT hvd.32044092008168 559 12 — — PUNCT hvd.32044092008168 559 13 9′(b 9′(b NUM hvd.32044092008168 559 14 ) ) PUNCT hvd.32044092008168 559 15 = = PUNCT hvd.32044092008168 560 1 ¦ ¦ ADP hvd.32044092008168 560 2 ( ( PUNCT hvd.32044092008168 560 3 126² 126² NUM hvd.32044092008168 560 4 — — PUNCT hvd.32044092008168 560 5 — — PUNCT hvd.32044092008168 560 6 92 92 NUM hvd.32044092008168 560 7 ) ) PUNCT hvd.32044092008168 560 8 4 4 NUM hvd.32044092008168 560 9 9 9 NUM hvd.32044092008168 560 10 ( ( PUNCT hvd.32044092008168 560 11 b b NOUN hvd.32044092008168 560 12 ) ) PUNCT hvd.32044092008168 560 13 = = PUNCT hvd.32044092008168 560 14 yn=3 yn=3 PUNCT hvd.32044092008168 560 15 = = PUNCT hvd.32044092008168 561 1 s³ s³ PROPN hvd.32044092008168 561 2 + + CCONJ hvd.32044092008168 561 3 a‚s a‚s PROPN hvd.32044092008168 561 4 + + CCONJ hvd.32044092008168 561 5 㸠㸠X hvd.32044092008168 561 6 = = X hvd.32044092008168 561 7 = = PROPN hvd.32044092008168 561 8 2 2 NUM hvd.32044092008168 561 9 ) ) PUNCT hvd.32044092008168 561 10 n(n n(n PROPN hvd.32044092008168 561 11 1 1 NUM hvd.32044092008168 561 12 ) ) PUNCT hvd.32044092008168 561 13 ( ( PUNCT hvd.32044092008168 561 14 n n PROPN hvd.32044092008168 561 15 2(2n-3 2(2n-3 NUM hvd.32044092008168 561 16 ) ) PUNCT hvd.32044092008168 561 17 ( ( PUNCT hvd.32044092008168 561 18 2n 2n NUM hvd.32044092008168 561 19 — — PUNCT hvd.32044092008168 561 20 5 5 X hvd.32044092008168 561 21 ) ) PUNCT hvd.32044092008168 561 22 483126s2 483126s2 NUM hvd.32044092008168 562 1 + + NUM hvd.32044092008168 562 2 1262s+4b3gsbg293 1262s+4b3gsbg293 NUM hvd.32044092008168 563 1 19 19 NUM hvd.32044092008168 563 2 ( ( PUNCT hvd.32044092008168 563 3 t t PROPN hvd.32044092008168 563 4 ) ) PUNCT hvd.32044092008168 563 5 — — PUNCT hvd.32044092008168 563 6 3b82 3b82 NUM hvd.32044092008168 563 7 --12bs² --12bs² PUNCT hvd.32044092008168 563 8 48 48 NUM hvd.32044092008168 563 9 +12682 +12682 ADV hvd.32044092008168 563 10 + + ADP hvd.32044092008168 563 11 ( ( PUNCT hvd.32044092008168 563 12 126292 126292 NUM hvd.32044092008168 563 13 ) ) PUNCT hvd.32044092008168 563 14 s+4b³ s+4b³ PROPN hvd.32044092008168 563 15 — — PUNCT hvd.32044092008168 563 16 bg bg INTJ hvd.32044092008168 563 17 — — PUNCT hvd.32044092008168 563 18 9s 9s NUM hvd.32044092008168 563 19 4s³ 4s³ NUM hvd.32044092008168 563 20 + + NUM hvd.32044092008168 563 21 12bs² 12bs² NUM hvd.32044092008168 564 1 + + PUNCT hvd.32044092008168 564 2 ❤ ❤ PUNCT hvd.32044092008168 565 1 ´ ´ PRON hvd.32044092008168 565 2 s s PROPN hvd.32044092008168 565 3 + + PROPN hvd.32044092008168 565 4 9 9 NUM hvd.32044092008168 565 5 . . SYM hvd.32044092008168 565 6 3 3 NUM hvd.32044092008168 565 7 = = SYM hvd.32044092008168 565 8 = = PRON hvd.32044092008168 566 1 s³ s³ NOUN hvd.32044092008168 566 2 + + CCONJ hvd.32044092008168 566 3 a₂s a₂s PROPN hvd.32044092008168 566 4 + + PROPN hvd.32044092008168 566 5 ag ag PROPN hvd.32044092008168 566 6 19 19 NUM hvd.32044092008168 566 7 's 's PART hvd.32044092008168 566 8 19 19 NUM hvd.32044092008168 566 9 . . SYM hvd.32044092008168 567 1 4 4 NUM hvd.32044092008168 567 2 s³ s³ PROPN hvd.32044092008168 567 3 + + NUM hvd.32044092008168 567 4 1 1 NUM hvd.32044092008168 567 5 9 9 NUM hvd.32044092008168 567 6 's 's PART hvd.32044092008168 567 7 + + PROPN hvd.32044092008168 567 8 1 1 NUM hvd.32044092008168 567 9 9 9 NUM hvd.32044092008168 567 10 — — PUNCT hvd.32044092008168 567 11 bq bq NOUN hvd.32044092008168 567 12 ' ' PUNCT hvd.32044092008168 567 13 ዎ ዎ DET hvd.32044092008168 567 14 4 4 NUM hvd.32044092008168 567 15 1 1 NUM hvd.32044092008168 567 16 = = SYM hvd.32044092008168 567 17 s³ s³ PROPN hvd.32044092008168 567 18 + + CCONJ hvd.32044092008168 567 19 ( ( PUNCT hvd.32044092008168 567 20 3b² 3b² NUM hvd.32044092008168 567 21 — — PUNCT hvd.32044092008168 567 22 — — PUNCT hvd.32044092008168 567 23 92 92 NUM hvd.32044092008168 567 24 ) ) PUNCT hvd.32044092008168 567 25 s s NOUN hvd.32044092008168 567 26 — — PUNCT hvd.32044092008168 567 27 ¦ ¦ PROPN hvd.32044092008168 567 28 ( ( PUNCT hvd.32044092008168 567 29 446³ 446³ NUM hvd.32044092008168 567 30 — — PUNCT hvd.32044092008168 567 31 392 392 NUM hvd.32044092008168 567 32 b b NOUN hvd.32044092008168 567 33 + + NUM hvd.32044092008168 567 34 93 93 NUM hvd.32044092008168 567 35 ) ) PUNCT hvd.32044092008168 567 36 ❤ ❤ ADP hvd.32044092008168 567 37 ( ( PUNCT hvd.32044092008168 567 38 t t PROPN hvd.32044092008168 567 39 ) ) PUNCT hvd.32044092008168 567 40 − − PROPN hvd.32044092008168 567 41 b(ø′+ b(ø′+ NOUN hvd.32044092008168 567 42 3s² 3s² NUM hvd.32044092008168 567 43 ) ) PUNCT hvd.32044092008168 567 44 bq bq NOUN hvd.32044092008168 567 45 ' ' PUNCT hvd.32044092008168 567 46 b b NOUN hvd.32044092008168 567 47 = = X hvd.32044092008168 567 48 = = X hvd.32044092008168 567 49 q(b q(b PROPN hvd.32044092008168 567 50 ) ) PUNCT hvd.32044092008168 567 51 — — PUNCT hvd.32044092008168 567 52 bq'b bq'b PROPN hvd.32044092008168 567 53 1 1 NUM hvd.32044092008168 567 54 ø ø NOUN hvd.32044092008168 567 55 ( ( PUNCT hvd.32044092008168 567 56 t t PROPN hvd.32044092008168 567 57 ) ) PUNCT hvd.32044092008168 567 58 = = X hvd.32044092008168 567 59 b b X hvd.32044092008168 568 1 [ [ X hvd.32044092008168 568 2 ' ' PUNCT hvd.32044092008168 568 3 + + CCONJ hvd.32044092008168 568 4 3 3 NUM hvd.32044092008168 568 5 ( ( PUNCT hvd.32044092008168 568 6 t t PROPN hvd.32044092008168 568 7 − − PROPN hvd.32044092008168 568 8 b)³ b)³ NOUN hvd.32044092008168 568 9 ] ] PUNCT hvd.32044092008168 568 10 4 4 NUM hvd.32044092008168 568 11 whence whence PRON hvd.32044092008168 568 12 y y PROPN hvd.32044092008168 568 13 ' ' PUNCT hvd.32044092008168 568 14 = = PRON hvd.32044092008168 568 15 3s² 3s² NUM hvd.32044092008168 568 16 + + CCONJ hvd.32044092008168 568 17 a2 a2 PROPN hvd.32044092008168 568 18 , , PUNCT hvd.32044092008168 568 19 y"= y"= VERB hvd.32044092008168 568 20 6s 6s PROPN hvd.32044092008168 568 21 , , PUNCT hvd.32044092008168 568 22 2 2 NUM hvd.32044092008168 568 23 yy yy NOUN hvd.32044092008168 568 24 " " PUNCT hvd.32044092008168 568 25 : : PUNCT hvd.32044092008168 568 26 and and CCONJ hvd.32044092008168 568 27 substituting substitute VERB hvd.32044092008168 568 28 in in ADP hvd.32044092008168 568 29 ( ( PUNCT hvd.32044092008168 568 30 64 64 NUM hvd.32044092008168 568 31 ) ) PUNCT hvd.32044092008168 568 32 we we PRON hvd.32044092008168 568 33 have have VERB hvd.32044092008168 568 34 1 1 NUM hvd.32044092008168 568 35 1 1 NUM hvd.32044092008168 568 36 = = SYM hvd.32044092008168 568 37 t³ t³ PROPN hvd.32044092008168 568 38 — — PUNCT hvd.32044092008168 568 39 3bt² 3bt² PROPN hvd.32044092008168 568 40 + + CCONJ hvd.32044092008168 568 41 ( ( PUNCT hvd.32044092008168 568 42 6b² 6b² NUM hvd.32044092008168 568 43 — — PUNCT hvd.32044092008168 568 44 9%)t 9%)t NUM hvd.32044092008168 568 45 ( ( PUNCT hvd.32044092008168 568 46 156³ 156³ NUM hvd.32044092008168 568 47 — — PUNCT hvd.32044092008168 568 48 gab gab NOUN hvd.32044092008168 568 49 + + CCONJ hvd.32044092008168 568 50 1 1 NUM hvd.32044092008168 568 51 93 93 NUM hvd.32044092008168 568 52 ) ) PUNCT hvd.32044092008168 568 53 . . PUNCT hvd.32044092008168 569 1 = = PUNCT hvd.32044092008168 569 2 12s 12s NUM hvd.32044092008168 569 3 ( ( PUNCT hvd.32044092008168 569 4 s³ s³ PROPN hvd.32044092008168 569 5 + + CCONJ hvd.32044092008168 569 6 a₂ a₂ PROPN hvd.32044092008168 569 7 s+ s+ VERB hvd.32044092008168 569 8 ag ag PROPN hvd.32044092008168 569 9 ) ) PUNCT hvd.32044092008168 569 10 c2 c2 PROPN hvd.32044092008168 569 11 ( ( PUNCT hvd.32044092008168 569 12 382 382 NUM hvd.32044092008168 569 13 + + SYM hvd.32044092008168 569 14 a,)² a,)² PROPN hvd.32044092008168 569 15 3s 3s NOUN hvd.32044092008168 569 16 ( ( PUNCT hvd.32044092008168 569 17 s³ s³ PROPN hvd.32044092008168 569 18 + + CCONJ hvd.32044092008168 569 19 a a PRON hvd.32044092008168 569 20 , , PUNCT hvd.32044092008168 569 21 s s X hvd.32044092008168 569 22 + + PRON hvd.32044092008168 569 23 a3 a3 PROPN hvd.32044092008168 569 24 ) ) PUNCT hvd.32044092008168 569 25 + + NUM hvd.32044092008168 569 26 3(4s+ 3(4s+ NUM hvd.32044092008168 569 27 qb qb PROPN hvd.32044092008168 569 28 ) ) PUNCT hvd.32044092008168 569 29 ( ( PUNCT hvd.32044092008168 569 30 s³ s³ PROPN hvd.32044092008168 569 31 + + CCONJ hvd.32044092008168 569 32 a a PRON hvd.32044092008168 569 33 , , PUNCT hvd.32044092008168 569 34 s s X hvd.32044092008168 569 35 + + PROPN hvd.32044092008168 569 36 ag)² ag)² PROPN hvd.32044092008168 569 37 . . PUNCT hvd.32044092008168 569 38 integral integral ADJ hvd.32044092008168 569 39 as as ADP hvd.32044092008168 569 40 a a DET hvd.32044092008168 569 41 product product NOUN hvd.32044092008168 569 42 . . PUNCT hvd.32044092008168 570 1 41 41 NUM hvd.32044092008168 570 2 to to PART hvd.32044092008168 570 3 attempt attempt VERB hvd.32044092008168 570 4 to to PART hvd.32044092008168 570 5 extract extract VERB hvd.32044092008168 570 6 the the DET hvd.32044092008168 570 7 square square ADJ hvd.32044092008168 570 8 roots root NOUN hvd.32044092008168 570 9 of of ADP hvd.32044092008168 570 10 this this DET hvd.32044092008168 570 11 equation equation NOUN hvd.32044092008168 570 12 in in ADP hvd.32044092008168 570 13 accordance accordance NOUN hvd.32044092008168 570 14 with with ADP hvd.32044092008168 570 15 the the DET hvd.32044092008168 570 16 theory theory NOUN hvd.32044092008168 570 17 , , PUNCT hvd.32044092008168 570 18 c² c² PROPN hvd.32044092008168 570 19 being be AUX hvd.32044092008168 570 20 expressed express VERB hvd.32044092008168 570 21 as as ADP hvd.32044092008168 570 22 an an DET hvd.32044092008168 570 23 equation equation NOUN hvd.32044092008168 570 24 of of ADP hvd.32044092008168 570 25 the the DET hvd.32044092008168 570 26 7th 7th ADJ hvd.32044092008168 570 27 degree degree NOUN hvd.32044092008168 570 28 in in ADP hvd.32044092008168 570 29 s s PROPN hvd.32044092008168 570 30 or or CCONJ hvd.32044092008168 570 31 t t PROPN hvd.32044092008168 570 32 were be AUX hvd.32044092008168 570 33 clearly clearly ADV hvd.32044092008168 570 34 impossible impossible ADJ hvd.32044092008168 570 35 without without SCONJ hvd.32044092008168 570 36 some some DET hvd.32044092008168 570 37 further further ADJ hvd.32044092008168 570 38 knowledge knowledge NOUN hvd.32044092008168 570 39 of of ADP hvd.32044092008168 570 40 the the DET hvd.32044092008168 570 41 properties property NOUN hvd.32044092008168 570 42 of of ADP hvd.32044092008168 570 43 c. c. PROPN hvd.32044092008168 570 44 to to PART hvd.32044092008168 570 45 arrive arrive VERB hvd.32044092008168 570 46 at at ADP hvd.32044092008168 570 47 such such ADJ hvd.32044092008168 570 48 knowledge knowledge NOUN hvd.32044092008168 570 49 we we PRON hvd.32044092008168 570 50 are be AUX hvd.32044092008168 570 51 led lead VERB hvd.32044092008168 570 52 ultimately ultimately ADV hvd.32044092008168 570 53 back back ADV hvd.32044092008168 570 54 to to ADP hvd.32044092008168 570 55 a a DET hvd.32044092008168 570 56 study study NOUN hvd.32044092008168 570 57 of of ADP hvd.32044092008168 570 58 the the DET hvd.32044092008168 570 59 special special ADJ hvd.32044092008168 570 60 functions function NOUN hvd.32044092008168 570 61 of of ADP hvd.32044092008168 570 62 lamé lamé NOUN hvd.32044092008168 570 63 . . PUNCT hvd.32044092008168 571 1 part part NOUN hvd.32044092008168 571 2 iv iv PROPN hvd.32044092008168 571 3 . . PUNCT hvd.32044092008168 572 1 the the DET hvd.32044092008168 572 2 special special ADJ hvd.32044092008168 572 3 functions function NOUN hvd.32044092008168 572 4 of of ADP hvd.32044092008168 572 5 lamé lamé NOUN hvd.32044092008168 572 6 . . PUNCT hvd.32044092008168 573 1 functions function NOUN hvd.32044092008168 573 2 of of ADP hvd.32044092008168 573 3 the the DET hvd.32044092008168 573 4 first first ADJ hvd.32044092008168 573 5 sort sort NOUN hvd.32044092008168 573 6 . . PUNCT hvd.32044092008168 574 1 > > X hvd.32044092008168 575 1 [ [ X hvd.32044092008168 575 2 69 69 NUM hvd.32044092008168 575 3 ] ] PUNCT hvd.32044092008168 575 4 . . PUNCT hvd.32044092008168 575 5 . . PUNCT hvd.32044092008168 576 1 lamé lamé NOUN hvd.32044092008168 576 2 derived derive VERB hvd.32044092008168 576 3 originally originally ADV hvd.32044092008168 576 4 functions function NOUN hvd.32044092008168 576 5 of of ADP hvd.32044092008168 576 6 three three NUM hvd.32044092008168 576 7 different different ADJ hvd.32044092008168 576 8 sorts sort NOUN hvd.32044092008168 576 9 , , PUNCT hvd.32044092008168 576 10 values value NOUN hvd.32044092008168 576 11 for for ADP hvd.32044092008168 576 12 y y PROPN hvd.32044092008168 576 13 , , PUNCT hvd.32044092008168 576 14 depending depend VERB hvd.32044092008168 576 15 on on ADP hvd.32044092008168 576 16 the the DET hvd.32044092008168 576 17 value value NOUN hvd.32044092008168 576 18 of of ADP hvd.32044092008168 576 19 n n NOUN hvd.32044092008168 576 20 and and CCONJ hvd.32044092008168 576 21 corresponding correspond VERB hvd.32044092008168 576 22 in in ADP hvd.32044092008168 576 23 each each DET hvd.32044092008168 576 24 case case NOUN hvd.32044092008168 576 25 to to ADP hvd.32044092008168 576 26 a a DET hvd.32044092008168 576 27 specific specific ADJ hvd.32044092008168 576 28 value value NOUN hvd.32044092008168 576 29 of of ADP hvd.32044092008168 576 30 b b NOUN hvd.32044092008168 576 31 , , PUNCT hvd.32044092008168 576 32 the the DET hvd.32044092008168 576 33 chief chief ADJ hvd.32044092008168 576 34 peculiarity peculiarity NOUN hvd.32044092008168 576 35 being be AUX hvd.32044092008168 576 36 that that SCONJ hvd.32044092008168 576 37 for for ADP hvd.32044092008168 576 38 these these DET hvd.32044092008168 576 39 values value NOUN hvd.32044092008168 576 40 y y PROPN hvd.32044092008168 576 41 is be AUX hvd.32044092008168 576 42 doubly doubly ADV hvd.32044092008168 576 43 periodic periodic ADJ hvd.32044092008168 576 44 . . PUNCT hvd.32044092008168 577 1 the the DET hvd.32044092008168 577 2 functions function NOUN hvd.32044092008168 577 3 of of ADP hvd.32044092008168 577 4 the the DET hvd.32044092008168 577 5 first first ADJ hvd.32044092008168 577 6 class class NOUN hvd.32044092008168 577 7 are be AUX hvd.32044092008168 577 8 characterized characterize VERB hvd.32044092008168 577 9 as as ADP hvd.32044092008168 577 10 developable developable ADJ hvd.32044092008168 577 11 in in ADP hvd.32044092008168 577 12 the the DET hvd.32044092008168 577 13 form form NOUN hvd.32044092008168 577 14 y y PROPN hvd.32044092008168 577 15 = = NOUN hvd.32044092008168 577 16 pln—2 pln—2 SPACE hvd.32044092008168 577 17 ) ) PUNCT hvd.32044092008168 577 18 + + CCONJ hvd.32044092008168 577 19 ay ay INTJ hvd.32044092008168 577 20 pine pine NOUN hvd.32044092008168 577 21 — — PUNCT hvd.32044092008168 577 22 4 4 X hvd.32044092008168 577 23 ) ) PUNCT hvd.32044092008168 577 24 + + CCONJ hvd.32044092008168 577 25 azpín—6 azpín—6 VERB hvd.32044092008168 577 26 ) ) PUNCT hvd.32044092008168 577 27 + + CCONJ hvd.32044092008168 577 28 .. .. PUNCT hvd.32044092008168 577 29 and and CCONJ hvd.32044092008168 577 30 that that SCONJ hvd.32044092008168 577 31 such such DET hvd.32044092008168 577 32 an an DET hvd.32044092008168 577 33 integral integral ADJ hvd.32044092008168 577 34 may may AUX hvd.32044092008168 577 35 exist exist VERB hvd.32044092008168 577 36 is be AUX hvd.32044092008168 577 37 seen see VERB hvd.32044092008168 577 38 from from ADP hvd.32044092008168 577 39 the the DET hvd.32044092008168 577 40 following follow VERB hvd.32044092008168 577 41 : : PUNCT hvd.32044092008168 577 42 writing write VERB hvd.32044092008168 577 43 the the DET hvd.32044092008168 577 44 corresponding corresponding ADJ hvd.32044092008168 577 45 function function NOUN hvd.32044092008168 577 46 of of ADP hvd.32044092008168 577 47 the the DET hvd.32044092008168 577 48 same same ADJ hvd.32044092008168 577 49 sort sort NOUN hvd.32044092008168 577 50 y.p(u y.p(u SPACE hvd.32044092008168 577 51 ) ) PUNCT hvd.32044092008168 577 52 we we PRON hvd.32044092008168 577 53 have have VERB hvd.32044092008168 577 54 n(n n(n PROPN hvd.32044092008168 577 55 + + CCONJ hvd.32044092008168 577 56 1)yp(u 1)yp(u NUM hvd.32044092008168 577 57 ) ) PUNCT hvd.32044092008168 577 58 = = NOUN hvd.32044092008168 577 59 pin pin X hvd.32044092008168 577 60 ) ) PUNCT hvd.32044092008168 577 61 + + CCONJ hvd.32044092008168 577 62 a4p(2 a4p(2 PROPN hvd.32044092008168 577 63 - - SYM hvd.32044092008168 577 64 2 2 NUM hvd.32044092008168 577 65 ) ) PUNCT hvd.32044092008168 577 66 + + CCONJ hvd.32044092008168 577 67 a2p(n—4 a2p(n—4 SPACE hvd.32044092008168 577 68 ) ) PUNCT hvd.32044092008168 577 69 + + CCONJ hvd.32044092008168 577 70 whence whence NOUN hvd.32044092008168 577 71 by by ADP hvd.32044092008168 577 72 subtraction subtraction NOUN hvd.32044092008168 577 73 y y NOUN hvd.32044092008168 577 74 ” " PUNCT hvd.32044092008168 577 75 – – PUNCT hvd.32044092008168 577 76 n(n n(n PROPN hvd.32044092008168 577 77 + + CCONJ hvd.32044092008168 577 78 1)yp 1)yp NUM hvd.32044092008168 577 79 = = SYM hvd.32044092008168 577 80 ( ( PUNCT hvd.32044092008168 577 81 a a PRON hvd.32044092008168 577 82 , , PUNCT hvd.32044092008168 577 83 – – PUNCT hvd.32044092008168 577 84 a,)pn—2 a,)pn—2 ADJ hvd.32044092008168 577 85 ) ) PUNCT hvd.32044092008168 578 1 + + CCONJ hvd.32044092008168 578 2 ( ( PUNCT hvd.32044092008168 578 3 az az PROPN hvd.32044092008168 578 4 — — PUNCT hvd.32044092008168 578 5 a,)pn—4 a,)pn—4 ADV hvd.32044092008168 578 6 ) ) PUNCT hvd.32044092008168 578 7 + + CCONJ hvd.32044092008168 578 8 ву ву X hvd.32044092008168 578 9 b b PROPN hvd.32044092008168 578 10 : : PUNCT hvd.32044092008168 578 11 02 02 NUM hvd.32044092008168 578 12 that that PRON hvd.32044092008168 578 13 is be AUX hvd.32044092008168 578 14 a a DET hvd.32044092008168 578 15 function function NOUN hvd.32044092008168 578 16 of of ADP hvd.32044092008168 578 17 the the DET hvd.32044092008168 578 18 first first ADJ hvd.32044092008168 578 19 sort sort NOUN hvd.32044092008168 578 20 will will AUX hvd.32044092008168 578 21 be be AUX hvd.32044092008168 578 22 a a DET hvd.32044092008168 578 23 root root NOUN hvd.32044092008168 578 24 of of ADP hvd.32044092008168 578 25 hermite hermite PROPN hvd.32044092008168 578 26 's 's PART hvd.32044092008168 578 27 equation equation NOUN hvd.32044092008168 578 28 provided provide VERB hvd.32044092008168 578 29 01 01 NUM hvd.32044092008168 578 30 a a DET hvd.32044092008168 578 31 a2 a2 PROPN hvd.32044092008168 578 32 baz baz PROPN hvd.32044092008168 578 33 : : PUNCT hvd.32044092008168 578 34 0 0 NUM hvd.32044092008168 578 35 g g NOUN hvd.32044092008168 578 36 – – PUNCT hvd.32044092008168 578 37 ag ag PROPN hvd.32044092008168 578 38 = = PROPN hvd.32044092008168 578 39 ba ba PROPN hvd.32044092008168 578 40 , , PUNCT hvd.32044092008168 578 41 etc etc X hvd.32044092008168 578 42 . . X hvd.32044092008168 579 1 az az PROPN hvd.32044092008168 579 2 where where SCONJ hvd.32044092008168 579 3 the the DET hvd.32044092008168 579 4 quantities quantity NOUN hvd.32044092008168 579 5 ( ( PUNCT hvd.32044092008168 579 6 a a X hvd.32044092008168 579 7 ) ) PUNCT hvd.32044092008168 579 8 are be AUX hvd.32044092008168 579 9 linear linear ADJ hvd.32044092008168 579 10 functions function NOUN hvd.32044092008168 579 11 of of ADP hvd.32044092008168 579 12 the the DET hvd.32044092008168 579 13 quantities quantity NOUN hvd.32044092008168 579 14 ( ( PUNCT hvd.32044092008168 579 15 a a X hvd.32044092008168 579 16 ) ) PUNCT hvd.32044092008168 579 17 . . PUNCT hvd.32044092008168 580 1 but but CCONJ hvd.32044092008168 580 2 since since SCONJ hvd.32044092008168 580 3 the the DET hvd.32044092008168 580 4 number number NOUN hvd.32044092008168 580 5 of of ADP hvd.32044092008168 580 6 these these DET hvd.32044092008168 580 7 condition condition NOUN hvd.32044092008168 580 8 equations equation NOUN hvd.32044092008168 580 9 is be AUX hvd.32044092008168 580 10 greater great ADJ hvd.32044092008168 580 11 by by ADP hvd.32044092008168 580 12 unity unity NOUN hvd.32044092008168 580 13 than than ADP hvd.32044092008168 580 14 the the DET hvd.32044092008168 580 15 number number NOUN hvd.32044092008168 580 16 of of ADP hvd.32044092008168 580 17 unknown unknown ADJ hvd.32044092008168 580 18 ( ( PUNCT hvd.32044092008168 580 19 a a X hvd.32044092008168 580 20 ) ) PUNCT hvd.32044092008168 580 21 it it PRON hvd.32044092008168 580 22 follows follow VERB hvd.32044092008168 580 23 that that SCONJ hvd.32044092008168 580 24 upon upon SCONJ hvd.32044092008168 580 25 their their PRON hvd.32044092008168 580 26 ellimination ellimination NOUN hvd.32044092008168 580 27 we we PRON hvd.32044092008168 580 28 obtain obtain VERB hvd.32044092008168 580 29 an an DET hvd.32044092008168 580 30 equation equation NOUN hvd.32044092008168 580 31 in in ADP hvd.32044092008168 580 32 b b PROPN hvd.32044092008168 580 33 whose whose DET hvd.32044092008168 580 34 degree degree NOUN hvd.32044092008168 580 35 will will AUX hvd.32044092008168 580 36 equal equal VERB hvd.32044092008168 580 37 the the DET hvd.32044092008168 580 38 number number NOUN hvd.32044092008168 580 39 of of ADP hvd.32044092008168 580 40 equations equation NOUN hvd.32044092008168 580 41 , , PUNCT hvd.32044092008168 580 42 that that PRON hvd.32044092008168 580 43 is be AUX hvd.32044092008168 580 44 n n X hvd.32044092008168 580 45 +1 +1 PROPN hvd.32044092008168 580 46 if if SCONJ hvd.32044092008168 580 47 n n ADP hvd.32044092008168 580 48 is be AUX hvd.32044092008168 580 49 even even ADV hvd.32044092008168 580 50 and and CCONJ hvd.32044092008168 580 51 ; ; PUNCT hvd.32044092008168 580 52 ( ( PUNCT hvd.32044092008168 580 53 n n CCONJ hvd.32044092008168 580 54 1 1 X hvd.32044092008168 580 55 ) ) PUNCT hvd.32044092008168 580 56 if if SCONJ hvd.32044092008168 580 57 n n ADV hvd.32044092008168 580 58 is be AUX hvd.32044092008168 580 59 uneven uneven ADJ hvd.32044092008168 580 60 : : PUNCT hvd.32044092008168 580 61 for for ADP hvd.32044092008168 580 62 example example NOUN hvd.32044092008168 580 63 take take VERB hvd.32044092008168 580 64 n n CCONJ hvd.32044092008168 580 65 = = SYM hvd.32044092008168 580 66 2 2 NUM hvd.32044092008168 580 67 , , PUNCT hvd.32044092008168 580 68 whence whence ADP hvd.32044092008168 580 69 y y PROPN hvd.32044092008168 580 70 = = PROPN hvd.32044092008168 580 71 p p PROPN hvd.32044092008168 580 72 + + CCONJ hvd.32044092008168 580 73 a a PRON hvd.32044092008168 580 74 , , PUNCT hvd.32044092008168 580 75 and and CCONJ hvd.32044092008168 580 76 y"=p y"=p SPACE hvd.32044092008168 580 77 " " PUNCT hvd.32044092008168 580 78 and and CCONJ hvd.32044092008168 580 79 we we PRON hvd.32044092008168 580 80 derive derive VERB hvd.32044092008168 580 81 p p NOUN hvd.32044092008168 580 82 " " PUNCT hvd.32044092008168 580 83 -6(2 -6(2 CCONJ hvd.32044092008168 580 84 + + CCONJ hvd.32044092008168 580 85 a)p a)p ADJ hvd.32044092008168 580 86 bp bp PROPN hvd.32044092008168 580 87 – – PUNCT hvd.32044092008168 580 88 bay bay PROPN hvd.32044092008168 580 89 or or CCONJ hvd.32044092008168 580 90 1 1 NUM hvd.32044092008168 580 91 ba ba NOUN hvd.32044092008168 580 92 , , PUNCT hvd.32044092008168 580 93 + + NUM hvd.32044092008168 580 94 9 9 NUM hvd.32044092008168 580 95 = = SYM hvd.32044092008168 580 96 0 0 NUM hvd.32044092008168 580 97 , , PUNCT hvd.32044092008168 580 98 ź ź ADP hvd.32044092008168 580 99 92 92 NUM hvd.32044092008168 580 100 also also ADV hvd.32044092008168 580 101 611 611 NUM hvd.32044092008168 580 102 + + ADV hvd.32044092008168 580 103 b=0 b=0 ADP hvd.32044092008168 580 104 2 2 NUM hvd.32044092008168 580 105 the the DET hvd.32044092008168 580 106 special special ADJ hvd.32044092008168 580 107 functions function NOUN hvd.32044092008168 580 108 of of ADP hvd.32044092008168 580 109 lamé lamé NOUN hvd.32044092008168 580 110 . . PUNCT hvd.32044092008168 581 1 43 43 NUM hvd.32044092008168 581 2 b b PROPN hvd.32044092008168 581 3 6 6 NUM hvd.32044092008168 581 4 1 1 NUM hvd.32044092008168 581 5 6 6 NUM hvd.32044092008168 581 6 whence whence NOUN hvd.32044092008168 581 7 a1 a1 PROPN hvd.32044092008168 581 8 6 6 NUM hvd.32044092008168 582 1 and and CCONJ hvd.32044092008168 582 2 we we PRON hvd.32044092008168 582 3 find find VERB hvd.32044092008168 582 4 y y PROPN hvd.32044092008168 582 5 = = PROPN hvd.32044092008168 582 6 p p PROPN hvd.32044092008168 582 7 b b NOUN hvd.32044092008168 582 8 where where SCONJ hvd.32044092008168 582 9 b4 b4 PROPN hvd.32044092008168 582 10 – – PUNCT hvd.32044092008168 582 11 392 392 NUM hvd.32044092008168 582 12 = = SYM hvd.32044092008168 582 13 0 0 NUM hvd.32044092008168 582 14 . . PUNCT hvd.32044092008168 583 1 b2 b2 PROPN hvd.32044092008168 583 2 = = PROPN hvd.32044092008168 583 3 again again ADV hvd.32044092008168 583 4 let let VERB hvd.32044092008168 583 5 n n CCONJ hvd.32044092008168 583 6 = = X hvd.32044092008168 583 7 3 3 NUM hvd.32044092008168 583 8 in in ADP hvd.32044092008168 583 9 which which DET hvd.32044092008168 583 10 case case NOUN hvd.32044092008168 583 11 the the DET hvd.32044092008168 583 12 equation equation NOUN hvd.32044092008168 583 13 in in ADP hvd.32044092008168 583 14 b b PROPN hvd.32044092008168 583 15 would would AUX hvd.32044092008168 583 16 be be AUX hvd.32044092008168 583 17 of of ADP hvd.32044092008168 583 18 degree degree NOUN hvd.32044092008168 583 19 i(n i(n PROPN hvd.32044092008168 583 20 − − PROPN hvd.32044092008168 583 21 1 1 NUM hvd.32044092008168 583 22 ) ) PUNCT hvd.32044092008168 583 23 1 1 NUM hvd.32044092008168 583 24 ) ) PUNCT hvd.32044092008168 583 25 = = PROPN hvd.32044092008168 583 26 1 1 NUM hvd.32044092008168 583 27 , , PUNCT hvd.32044092008168 583 28 that that PRON hvd.32044092008168 583 29 is be AUX hvd.32044092008168 583 30 b b PROPN hvd.32044092008168 583 31 0 0 NUM hvd.32044092008168 583 32 , , PUNCT hvd.32044092008168 583 33 for for ADP hvd.32044092008168 583 34 which which DET hvd.32044092008168 583 35 value value NOUN hvd.32044092008168 583 36 we we PRON hvd.32044092008168 583 37 have have VERB hvd.32044092008168 583 38 at at ADP hvd.32044092008168 583 39 once once ADV hvd.32044092008168 583 40 y y PROPN hvd.32044092008168 583 41 = = PROPN hvd.32044092008168 583 42 p'(u p'(u PROPN hvd.32044092008168 583 43 ) ) PUNCT hvd.32044092008168 583 44 . . PUNCT hvd.32044092008168 584 1 substituting substitute VERB hvd.32044092008168 584 2 indeed indeed ADV hvd.32044092008168 584 3 this this DET hvd.32044092008168 584 4 value value NOUN hvd.32044092008168 584 5 in in ADP hvd.32044092008168 584 6 hermite hermite PROPN hvd.32044092008168 584 7 's 's PART hvd.32044092008168 584 8 equation equation NOUN hvd.32044092008168 584 9 for for ADP hvd.32044092008168 584 10 n n NOUN hvd.32044092008168 584 11 = = AUX hvd.32044092008168 584 12 3 3 NUM hvd.32044092008168 584 13 we we PRON hvd.32044092008168 584 14 derive derive VERB hvd.32044092008168 584 15 at at ADP hvd.32044092008168 584 16 once once ADV hvd.32044092008168 584 17 p p NOUN hvd.32044092008168 584 18 " " PUNCT hvd.32044092008168 584 19 — — PUNCT hvd.32044092008168 584 20 12p'p=0 12p'p=0 NUM hvd.32044092008168 584 21 a a DET hvd.32044092008168 584 22 well well ADV hvd.32044092008168 584 23 known know VERB hvd.32044092008168 584 24 identity identity NOUN hvd.32044092008168 584 25 . . PUNCT hvd.32044092008168 585 1 define define VERB hvd.32044092008168 585 2 ( ( PUNCT hvd.32044092008168 585 3 p=0 p=0 NOUN hvd.32044092008168 585 4 ) ) PUNCT hvd.32044092008168 585 5 equal equal ADJ hvd.32044092008168 585 6 to to ADP hvd.32044092008168 585 7 the the DET hvd.32044092008168 585 8 equation equation NOUN hvd.32044092008168 585 9 in in ADP hvd.32044092008168 585 10 b b PROPN hvd.32044092008168 585 11 of of ADP hvd.32044092008168 585 12 degree degree NOUN hvd.32044092008168 585 13 } } PUNCT hvd.32044092008168 585 14 ( ( PUNCT hvd.32044092008168 585 15 n n CCONJ hvd.32044092008168 585 16 − − PROPN hvd.32044092008168 585 17 1 1 X hvd.32044092008168 585 18 ) ) PUNCT hvd.32044092008168 585 19 that that SCONJ hvd.32044092008168 585 20 in in ADP hvd.32044092008168 585 21 any any DET hvd.32044092008168 585 22 case case NOUN hvd.32044092008168 585 23 determines determine VERB hvd.32044092008168 585 24 the the DET hvd.32044092008168 585 25 values value NOUN hvd.32044092008168 585 26 of of ADP hvd.32044092008168 585 27 b b PRON hvd.32044092008168 585 28 giving giving NOUN hvd.32044092008168 585 29 rise rise NOUN hvd.32044092008168 585 30 to to ADP hvd.32044092008168 585 31 an an DET hvd.32044092008168 585 32 integral integral NOUN hvd.32044092008168 585 33 of of ADP hvd.32044092008168 585 34 the the DET hvd.32044092008168 585 35 first first ADJ hvd.32044092008168 585 36 sort sort NOUN hvd.32044092008168 585 37 . . PUNCT hvd.32044092008168 586 1 we we PRON hvd.32044092008168 586 2 have have VERB hvd.32044092008168 586 3 then then ADV hvd.32044092008168 586 4 that that SCONJ hvd.32044092008168 586 5 when when SCONJ hvd.32044092008168 586 6 p=0 p=0 ADV hvd.32044092008168 586 7 the the DET hvd.32044092008168 586 8 general general ADJ hvd.32044092008168 586 9 solution solution NOUN hvd.32044092008168 586 10 of of ADP hvd.32044092008168 586 11 hermite hermite NOUN hvd.32044092008168 586 12 as as ADP hvd.32044092008168 586 13 a a DET hvd.32044092008168 586 14 sum sum NOUN hvd.32044092008168 586 15 has have VERB hvd.32044092008168 586 16 in in ADP hvd.32044092008168 586 17 place place NOUN hvd.32044092008168 586 18 of of ADP hvd.32044092008168 586 19 f(u f(u NOUN hvd.32044092008168 586 20 ) ) PUNCT hvd.32044092008168 586 21 the the DET hvd.32044092008168 586 22 p(u p(u PROPN hvd.32044092008168 586 23 ) ) PUNCT hvd.32044092008168 586 24 and and CCONJ hvd.32044092008168 586 25 may may AUX hvd.32044092008168 586 26 be be AUX hvd.32044092008168 586 27 written write VERB hvd.32044092008168 586 28 [ [ PUNCT hvd.32044092008168 586 29 70 70 NUM hvd.32044092008168 586 30 ] ] PUNCT hvd.32044092008168 586 31 · · PUNCT hvd.32044092008168 586 32 ( ( PUNCT hvd.32044092008168 586 33 -1)"y -1)"y ADJ hvd.32044092008168 586 34 pin pin NOUN hvd.32044092008168 586 35 — — PUNCT hvd.32044092008168 586 36 2 2 X hvd.32044092008168 586 37 ) ) PUNCT hvd.32044092008168 586 38 ( ( PUNCT hvd.32044092008168 586 39 u u PROPN hvd.32044092008168 586 40 ) ) PUNCT hvd.32044092008168 586 41 + + CCONJ hvd.32044092008168 586 42 h h NOUN hvd.32044092008168 586 43 , , PUNCT hvd.32044092008168 586 44 pin pin NOUN hvd.32044092008168 586 45 — — PUNCT hvd.32044092008168 586 46 4)(u 4)(u NUM hvd.32044092008168 586 47 ) ) PUNCT hvd.32044092008168 586 48 1 1 NUM hvd.32044092008168 586 49 ) ) PUNCT hvd.32044092008168 586 50 ! ! PUNCT hvd.32044092008168 587 1 ( ( PUNCT hvd.32044092008168 587 2 n n CCONJ hvd.32044092008168 587 3 3 3 X hvd.32044092008168 587 4 ) ) PUNCT hvd.32044092008168 587 5 ! ! PUNCT hvd.32044092008168 588 1 1 1 NUM hvd.32044092008168 588 2 2 2 NUM hvd.32044092008168 588 3 a a DET hvd.32044092008168 588 4 1 1 NUM hvd.32044092008168 588 5 1 1 NUM hvd.32044092008168 588 6 in in ADP hvd.32044092008168 588 7 1 1 NUM hvd.32044092008168 588 8 + + NUM hvd.32044092008168 588 9 họpl2 họpl2 PROPN hvd.32044092008168 588 10 - - PUNCT hvd.32044092008168 588 11 6)(u 6)(u NUM hvd.32044092008168 588 12 ) ) PUNCT hvd.32044092008168 588 13 + + NOUN hvd.32044092008168 588 14 . . PUNCT hvd.32044092008168 589 1 ( ( PUNCT hvd.32044092008168 589 2 n n NUM hvd.32044092008168 589 3 5 5 X hvd.32044092008168 589 4 ) ) PUNCT hvd.32044092008168 589 5 ! ! PUNCT hvd.32044092008168 590 1 the the DET hvd.32044092008168 590 2 coefficients coefficient NOUN hvd.32044092008168 590 3 being be AUX hvd.32044092008168 590 4 the the DET hvd.32044092008168 590 5 same same ADJ hvd.32044092008168 590 6 as as ADP hvd.32044092008168 590 7 in in ADP hvd.32044092008168 590 8 the the DET hvd.32044092008168 590 9 corresponding corresponding ADJ hvd.32044092008168 590 10 general general ADJ hvd.32044092008168 590 11 development development NOUN hvd.32044092008168 590 12 . . PUNCT hvd.32044092008168 590 13 * * SYM hvd.32044092008168 590 14 ) ) PUNCT hvd.32044092008168 590 15 functions function NOUN hvd.32044092008168 590 16 of of ADP hvd.32044092008168 590 17 the the DET hvd.32044092008168 590 18 second second ADJ hvd.32044092008168 590 19 sort sort NOUN hvd.32044092008168 590 20 . . PUNCT hvd.32044092008168 590 21 . . PUNCT hvd.32044092008168 591 1 q=1 q=1 PROPN hvd.32044092008168 591 2 . . PUNCT hvd.32044092008168 592 1 2.3 2.3 NUM hvd.32044092008168 592 2 to to PART hvd.32044092008168 592 3 attain attain VERB hvd.32044092008168 592 4 a a DET hvd.32044092008168 592 5 function function NOUN hvd.32044092008168 592 6 of of ADP hvd.32044092008168 592 7 the the DET hvd.32044092008168 592 8 second second ADJ hvd.32044092008168 592 9 sort sort NOUN hvd.32044092008168 592 10 assume assume VERB hvd.32044092008168 592 11 that that SCONJ hvd.32044092008168 592 12 n n CCONJ hvd.32044092008168 592 13 is be AUX hvd.32044092008168 592 14 odd odd ADJ hvd.32044092008168 592 15 and and CCONJ hvd.32044092008168 592 16 that that SCONJ hvd.32044092008168 592 17 the the DET hvd.32044092008168 592 18 solution solution NOUN hvd.32044092008168 592 19 has have VERB hvd.32044092008168 592 20 the the DET hvd.32044092008168 592 21 form form NOUN hvd.32044092008168 592 22 [ [ X hvd.32044092008168 592 23 71 71 NUM hvd.32044092008168 592 24 ] ] PUNCT hvd.32044092008168 592 25 · · PUNCT hvd.32044092008168 592 26 y y PROPN hvd.32044092008168 592 27 y=%vpu y=%vpu PUNCT hvd.32044092008168 592 28 – – PUNCT hvd.32044092008168 592 29 este este PROPN hvd.32044092008168 592 30 la la ADV hvd.32044092008168 592 31 where where SCONJ hvd.32044092008168 592 32 may may AUX hvd.32044092008168 592 33 be be AUX hvd.32044092008168 592 34 developed develop VERB hvd.32044092008168 592 35 in in ADP hvd.32044092008168 592 36 the the DET hvd.32044092008168 592 37 form form NOUN hvd.32044092008168 592 38 % % NOUN hvd.32044092008168 592 39 = = NOUN hvd.32044092008168 592 40 pin pin PROPN hvd.32044092008168 592 41 3 3 NUM hvd.32044092008168 592 42 ) ) PUNCT hvd.32044092008168 592 43 + + NUM hvd.32044092008168 592 44 apin-5 apin-5 X hvd.32044092008168 592 45 ) ) PUNCT hvd.32044092008168 592 46 + + CCONJ hvd.32044092008168 592 47 a,261 a,261 NUM hvd.32044092008168 592 48 — — PUNCT hvd.32044092008168 592 49 7 7 X hvd.32044092008168 592 50 ) ) PUNCT hvd.32044092008168 592 51 equation equation NOUN hvd.32044092008168 592 52 in in ADP hvd.32044092008168 592 53 p p PROPN hvd.32044092008168 592 54 differing differ VERB hvd.32044092008168 592 55 from from ADP hvd.32044092008168 592 56 ( ( PUNCT hvd.32044092008168 592 57 70 70 NUM hvd.32044092008168 592 58 ) ) PUNCT hvd.32044092008168 592 59 in in ADP hvd.32044092008168 592 60 the the DET hvd.32044092008168 592 61 degree degree NOUN hvd.32044092008168 592 62 of of ADP hvd.32044092008168 592 63 the the DET hvd.32044092008168 592 64 derivatives derivative NOUN hvd.32044092008168 592 65 only only ADV hvd.32044092008168 592 66 . . PUNCT hvd.32044092008168 593 1 proceeding proceed VERB hvd.32044092008168 593 2 as as ADP hvd.32044092008168 593 3 in in ADP hvd.32044092008168 593 4 the the DET hvd.32044092008168 593 5 former former ADJ hvd.32044092008168 593 6 case case NOUN hvd.32044092008168 593 7 by by ADP hvd.32044092008168 593 8 substituting substitute VERB hvd.32044092008168 593 9 in in ADP hvd.32044092008168 593 10 hermite hermite PROPN hvd.32044092008168 593 11 's 's PART hvd.32044092008168 593 12 equation equation NOUN hvd.32044092008168 593 13 one one PRON hvd.32044092008168 593 14 finds find VERB hvd.32044092008168 593 15 that that SCONJ hvd.32044092008168 593 16 the the DET hvd.32044092008168 593 17 solution solution NOUN hvd.32044092008168 593 18 holds holds AUX hvd.32044092008168 593 19 provided provide VERB hvd.32044092008168 593 20 b b ADP hvd.32044092008168 593 21 be be AUX hvd.32044092008168 593 22 now now ADV hvd.32044092008168 593 23 taken take VERB hvd.32044092008168 593 24 equal equal ADJ hvd.32044092008168 593 25 to to ADP hvd.32044092008168 593 26 any any DET hvd.32044092008168 593 27 one one NUM hvd.32044092008168 593 28 of of ADP hvd.32044092008168 593 29 the the DET hvd.32044092008168 593 30 roots root NOUN hvd.32044092008168 593 31 of of ADP hvd.32044092008168 593 32 a a DET hvd.32044092008168 593 33 perfectly perfectly ADV hvd.32044092008168 593 34 determined determined ADJ hvd.32044092008168 593 35 equation equation NOUN hvd.32044092008168 593 36 of of ADP hvd.32044092008168 593 37 degree degree NOUN hvd.32044092008168 593 38 ( ( PUNCT hvd.32044092008168 593 39 n n CCONJ hvd.32044092008168 593 40 + + CCONJ hvd.32044092008168 593 41 1 1 NUM hvd.32044092008168 593 42 ) ) PUNCT hvd.32044092008168 593 43 , , PUNCT hvd.32044092008168 593 44 the the DET hvd.32044092008168 593 45 right right ADJ hvd.32044092008168 593 46 hand hand NOUN hvd.32044092008168 593 47 member member NOUN hvd.32044092008168 593 48 of of ADP hvd.32044092008168 593 49 which which PRON hvd.32044092008168 593 50 we we PRON hvd.32044092008168 593 51 will will AUX hvd.32044092008168 593 52 define define VERB hvd.32044092008168 593 53 as as ADP hvd.32044092008168 593 54 qu qu PROPN hvd.32044092008168 593 55 which which PRON hvd.32044092008168 593 56 is be AUX hvd.32044092008168 593 57 equal equal ADJ hvd.32044092008168 593 58 to to ADP hvd.32044092008168 593 59 zero zero NUM hvd.32044092008168 593 60 . . PUNCT hvd.32044092008168 594 1 1 1 NUM hvd.32044092008168 594 2 * * PUNCT hvd.32044092008168 594 3 ) ) PUNCT hvd.32044092008168 594 4 see see VERB hvd.32044092008168 594 5 ( ( PUNCT hvd.32044092008168 594 6 34 34 NUM hvd.32044092008168 594 7 ) ) PUNCT hvd.32044092008168 594 8 and and CCONJ hvd.32044092008168 594 9 ( ( PUNCT hvd.32044092008168 594 10 26 26 NUM hvd.32044092008168 594 11 ) ) PUNCT hvd.32044092008168 594 12 . . PUNCT hvd.32044092008168 595 1 44 44 NUM hvd.32044092008168 596 1 [ [ PUNCT hvd.32044092008168 596 2 73 73 NUM hvd.32044092008168 596 3 ] ] PUNCT hvd.32044092008168 596 4 part part NOUN hvd.32044092008168 596 5 iv iv PROPN hvd.32044092008168 596 6 . . PUNCT hvd.32044092008168 597 1 the the DET hvd.32044092008168 597 2 special special ADJ hvd.32044092008168 597 3 functions function NOUN hvd.32044092008168 597 4 of of ADP hvd.32044092008168 597 5 lamé lamé NOUN hvd.32044092008168 597 6 . . PUNCT hvd.32044092008168 598 1 writing write VERB hvd.32044092008168 598 2 for for ADP hvd.32044092008168 598 3 convenience convenience NOUN hvd.32044092008168 598 4 hermite hermite NOUN hvd.32044092008168 598 5 's 's PART hvd.32044092008168 598 6 equation equation NOUN hvd.32044092008168 598 7 in in ADP hvd.32044092008168 598 8 terms term NOUN hvd.32044092008168 598 9 of of ADP hvd.32044092008168 598 10 the the DET hvd.32044092008168 598 11 derivatives derivative NOUN hvd.32044092008168 598 12 of of ADP hvd.32044092008168 598 13 z z PROPN hvd.32044092008168 598 14 with with ADP hvd.32044092008168 598 15 respect respect NOUN hvd.32044092008168 598 16 to to ADP hvd.32044092008168 598 17 pu pu PROPN hvd.32044092008168 598 18 by by ADP hvd.32044092008168 598 19 aid aid NOUN hvd.32044092008168 598 20 of of ADP hvd.32044092008168 598 21 the the DET hvd.32044092008168 598 22 identity identity NOUN hvd.32044092008168 598 23 p² p² PROPN hvd.32044092008168 598 24 4p³ 4p³ NUM hvd.32044092008168 598 25 92p 92p NUM hvd.32044092008168 598 26 93 93 NUM hvd.32044092008168 598 27 we we PRON hvd.32044092008168 598 28 have have VERB hvd.32044092008168 598 29 * * PUNCT hvd.32044092008168 598 30 ) ) PUNCT hvd.32044092008168 599 1 [ [ X hvd.32044092008168 599 2 72 72 NUM hvd.32044092008168 599 3 ] ] PUNCT hvd.32044092008168 599 4 · · PUNCT hvd.32044092008168 599 5 0 0 NUM hvd.32044092008168 599 6 or or CCONJ hvd.32044092008168 599 7 and and CCONJ hvd.32044092008168 599 8 ( ( PUNCT hvd.32044092008168 599 9 72 72 NUM hvd.32044092008168 599 10 ) ) PUNCT hvd.32044092008168 599 11 becomes become VERB hvd.32044092008168 599 12 ( ( PUNCT hvd.32044092008168 599 13 4p³ 4p³ NUM hvd.32044092008168 599 14 — — PUNCT hvd.32044092008168 599 15 i¿p i¿p NOUN hvd.32044092008168 599 16 — — PUNCT hvd.32044092008168 599 17 i3 i3 PROPN hvd.32044092008168 599 18 ) ) PUNCT hvd.32044092008168 599 19 and and CCONJ hvd.32044092008168 599 20 whence whence NOUN hvd.32044092008168 599 21 = = X hvd.32044092008168 599 22 • • PUNCT hvd.32044092008168 600 1 [ [ X hvd.32044092008168 600 2 75 75 NUM hvd.32044092008168 600 3 ] ] PUNCT hvd.32044092008168 600 4 · · PUNCT hvd.32044092008168 600 5 • • PUNCT hvd.32044092008168 600 6 = = PUNCT hvd.32044092008168 601 1 [ [ X hvd.32044092008168 601 2 ( ( PUNCT hvd.32044092008168 601 3 n n X hvd.32044092008168 601 4 − − PROPN hvd.32044092008168 601 5 and and CCONJ hvd.32044092008168 601 6 differentiating differentiate VERB hvd.32044092008168 601 7 we we PRON hvd.32044092008168 601 8 have have VERB hvd.32044092008168 601 9 4 4 NUM hvd.32044092008168 601 10 la la ADV hvd.32044092008168 601 11 = = PROPN hvd.32044092008168 601 12 d² d² PROPN hvd.32044092008168 601 13 z z PROPN hvd.32044092008168 601 14 dp dp PROPN hvd.32044092008168 601 15 * * PUNCT hvd.32044092008168 601 16 take take VERB hvd.32044092008168 601 17 now now ADV hvd.32044092008168 601 18 for for ADP hvd.32044092008168 601 19 example example NOUN hvd.32044092008168 601 20 n n CCONJ hvd.32044092008168 601 21 = = SYM hvd.32044092008168 601 22 3 3 NUM hvd.32044092008168 601 23 . . PUNCT hvd.32044092008168 602 1 whence whence ADV hvd.32044092008168 602 2 = = PROPN hvd.32044092008168 602 3 z z PROPN hvd.32044092008168 602 4 = = ADP hvd.32044092008168 602 5 p p PROPN hvd.32044092008168 602 6 + + CCONJ hvd.32044092008168 602 7 a a DET hvd.32044092008168 602 8 ― ― X hvd.32044092008168 602 9 dp dp PROPN hvd.32044092008168 602 10 + + CCONJ hvd.32044092008168 602 11 ( ( PUNCT hvd.32044092008168 602 12 10p² 10p² X hvd.32044092008168 603 1 + + NUM hvd.32044092008168 603 2 4e¸p 4e¸p NUM hvd.32044092008168 603 3 + + NUM hvd.32044092008168 603 4 4c² 4c² NUM hvd.32044092008168 603 5 − − NOUN hvd.32044092008168 603 6 292 292 NUM hvd.32044092008168 603 7 ) ) PUNCT hvd.32044092008168 603 8 dz dz PROPN hvd.32044092008168 603 9 1 1 X hvd.32044092008168 603 10 ) ) PUNCT hvd.32044092008168 603 11 ( ( PUNCT hvd.32044092008168 603 12 n n CCONJ hvd.32044092008168 603 13 + + CCONJ hvd.32044092008168 603 14 2 2 NUM hvd.32044092008168 603 15 ) ) PUNCT hvd.32044092008168 603 16 p p NOUN hvd.32044092008168 604 1 + + CCONJ hvd.32044092008168 604 2 b b NOUN hvd.32044092008168 604 3 − − NOUN hvd.32044092008168 604 4 € € SYM hvd.32044092008168 604 5 a a PRON hvd.32044092008168 604 6 ] ] PUNCT hvd.32044092008168 605 1 ≈. ≈. PROPN hvd.32044092008168 605 2 • • SYM hvd.32044092008168 605 3 = = PUNCT hvd.32044092008168 605 4 qa qa INTJ hvd.32044092008168 605 5 an an DET hvd.32044092008168 605 6 equation equation NOUN hvd.32044092008168 605 7 whose whose DET hvd.32044092008168 605 8 degree degree NOUN hvd.32044092008168 605 9 is be AUX hvd.32044092008168 605 10 3 3 NUM hvd.32044092008168 605 11 10p²+4eap+4c292 10p²+4eap+4c292 NUM hvd.32044092008168 605 12 ( ( PUNCT hvd.32044092008168 605 13 10p+ 10p+ NUM hvd.32044092008168 605 14 bea bea PROPN hvd.32044092008168 605 15 ) ) PUNCT hvd.32044092008168 606 1 ( ( PUNCT hvd.32044092008168 606 2 p p NOUN hvd.32044092008168 606 3 + + CCONJ hvd.32044092008168 606 4 a₁ a₁ PROPN hvd.32044092008168 606 5 ) ) PUNCT hvd.32044092008168 606 6 dz dz X hvd.32044092008168 606 7 dp dp PROPN hvd.32044092008168 606 8 = = PROPN hvd.32044092008168 606 9 1 1 NUM hvd.32044092008168 606 10 a₁ a₁ PROPN hvd.32044092008168 606 11 = = SYM hvd.32044092008168 606 12 1/2 1/2 NUM hvd.32044092008168 606 13 ea ea NOUN hvd.32044092008168 606 14 11 11 NUM hvd.32044092008168 606 15 b b NOUN hvd.32044092008168 606 16 αι αι PRON hvd.32044092008168 606 17 10 10 NUM hvd.32044092008168 606 18 10a₁+ 10a₁+ NOUN hvd.32044092008168 607 1 bla bla INTJ hvd.32044092008168 607 2 z z PROPN hvd.32044092008168 607 3 = = X hvd.32044092008168 607 4 p p PROPN hvd.32044092008168 607 5 + + PROPN hvd.32044092008168 607 6 1/1 1/1 NUM hvd.32044092008168 607 7 ea ea NOUN hvd.32044092008168 607 8 1/1 1/1 NUM hvd.32044092008168 607 9 b b NOUN hvd.32044092008168 607 10 2 2 NUM hvd.32044092008168 607 11 10 10 NUM hvd.32044092008168 607 12 = = SYM hvd.32044092008168 607 13 d2z d2z X hvd.32044092008168 607 14 dp² dp² NOUN hvd.32044092008168 607 15 b2 b2 PROPN hvd.32044092008168 607 16 - - PUNCT hvd.32044092008168 607 17 6ea 6ea NOUN hvd.32044092008168 607 18 b+45e-1592 b+45e-1592 PROPN hvd.32044092008168 607 19 — — PUNCT hvd.32044092008168 608 1 ( ( PUNCT hvd.32044092008168 608 2 n n CCONJ hvd.32044092008168 608 3 + + CCONJ hvd.32044092008168 608 4 1 1 X hvd.32044092008168 608 5 ) ) PUNCT hvd.32044092008168 608 6 = = PROPN hvd.32044092008168 608 7 2 2 NUM hvd.32044092008168 608 8 , , PUNCT hvd.32044092008168 608 9 2 2 NUM hvd.32044092008168 608 10 compair compair NOUN hvd.32044092008168 608 11 transformation transformation NOUN hvd.32044092008168 608 12 p. p. NOUN hvd.32044092008168 608 13 35 35 NUM hvd.32044092008168 608 14 . . PUNCT hvd.32044092008168 609 1 = = PUNCT hvd.32044092008168 609 2 and and CCONJ hvd.32044092008168 609 3 as as ADP hvd.32044092008168 609 4 a a PRON hvd.32044092008168 609 5 may may AUX hvd.32044092008168 609 6 have have VERB hvd.32044092008168 609 7 the the DET hvd.32044092008168 609 8 values value NOUN hvd.32044092008168 609 9 1 1 NUM hvd.32044092008168 609 10 , , PUNCT hvd.32044092008168 609 11 2 2 NUM hvd.32044092008168 609 12 or or CCONJ hvd.32044092008168 609 13 3 3 NUM hvd.32044092008168 609 14 we we PRON hvd.32044092008168 609 15 have have VERB hvd.32044092008168 609 16 in in ADP hvd.32044092008168 609 17 all all DET hvd.32044092008168 609 18 six six NUM hvd.32044092008168 609 19 values value NOUN hvd.32044092008168 609 20 of of ADP hvd.32044092008168 609 21 b b NOUN hvd.32044092008168 609 22 giving give VERB hvd.32044092008168 609 23 a a DET hvd.32044092008168 609 24 doubly doubly ADV hvd.32044092008168 609 25 periodic periodic ADJ hvd.32044092008168 609 26 solution solution NOUN hvd.32044092008168 609 27 of of ADP hvd.32044092008168 609 28 the the DET hvd.32044092008168 609 29 second second ADJ hvd.32044092008168 609 30 sort sort NOUN hvd.32044092008168 609 31 and and CCONJ hvd.32044092008168 609 32 determined determine VERB hvd.32044092008168 609 33 by by ADP hvd.32044092008168 609 34 an an DET hvd.32044092008168 609 35 equation equation NOUN hvd.32044092008168 609 36 of of ADP hvd.32044092008168 609 37 the the DET hvd.32044092008168 609 38 sixth sixth ADJ hvd.32044092008168 609 39 degree degree NOUN hvd.32044092008168 609 40 defined define VERB hvd.32044092008168 609 41 as as ADP hvd.32044092008168 609 42 [ [ X hvd.32044092008168 609 43 74 74 NUM hvd.32044092008168 609 44 ] ] PUNCT hvd.32044092008168 609 45 · · PUNCT hvd.32044092008168 609 46 q q X hvd.32044092008168 609 47 q1 q1 PROPN hvd.32044092008168 609 48 q2 q2 PROPN hvd.32044092008168 609 49 q3 q3 PROPN hvd.32044092008168 609 50 0 0 NUM hvd.32044092008168 609 51 functions function NOUN hvd.32044092008168 609 52 of of ADP hvd.32044092008168 609 53 the the DET hvd.32044092008168 609 54 third third ADJ hvd.32044092008168 609 55 sort sort NOUN hvd.32044092008168 609 56 . . PUNCT hvd.32044092008168 610 1 we we PRON hvd.32044092008168 610 2 have have VERB hvd.32044092008168 610 3 finally finally ADV hvd.32044092008168 610 4 solutions solution NOUN hvd.32044092008168 610 5 that that PRON hvd.32044092008168 610 6 are be AUX hvd.32044092008168 610 7 doubly doubly ADV hvd.32044092008168 610 8 periodic periodic ADJ hvd.32044092008168 610 9 of of ADP hvd.32044092008168 610 10 a a DET hvd.32044092008168 610 11 third third ADJ hvd.32044092008168 610 12 sort sort NOUN hvd.32044092008168 610 13 the the DET hvd.32044092008168 610 14 integral integral ADJ hvd.32044092008168 610 15 being be AUX hvd.32044092008168 610 16 written write VERB hvd.32044092008168 610 17 in in ADP hvd.32044092008168 610 18 the the DET hvd.32044092008168 610 19 form form NOUN hvd.32044092008168 610 20 : : PUNCT hvd.32044092008168 610 21 y y PROPN hvd.32044092008168 610 22 = = PROPN hvd.32044092008168 610 23 z√(pu z√(pu PROPN hvd.32044092008168 610 24 — — PUNCT hvd.32044092008168 610 25 es es INTJ hvd.32044092008168 610 26 ) ) PUNCT hvd.32044092008168 610 27 ( ( PUNCT hvd.32044092008168 610 28 pu pu PROPN hvd.32044092008168 610 29 cα cα PROPN hvd.32044092008168 610 30 ) ) PUNCT hvd.32044092008168 610 31 -where -where ADV hvd.32044092008168 610 32 n n ADV hvd.32044092008168 610 33 is be AUX hvd.32044092008168 610 34 restricted restrict VERB hvd.32044092008168 610 35 to to ADP hvd.32044092008168 610 36 an an DET hvd.32044092008168 610 37 even even ADV hvd.32044092008168 610 38 member member NOUN hvd.32044092008168 610 39 and and CCONJ hvd.32044092008168 610 40 z z PROPN hvd.32044092008168 610 41 has have VERB hvd.32044092008168 610 42 the the DET hvd.32044092008168 610 43 form form NOUN hvd.32044092008168 610 44 2 2 NUM hvd.32044092008168 610 45 = = SYM hvd.32044092008168 610 46 ... ... PUNCT hvd.32044092008168 610 47 p(n−4 p(n−4 NOUN hvd.32044092008168 610 48 ) ) PUNCT hvd.32044092008168 610 49 + + CCONJ hvd.32044092008168 610 50 α¸p(n−6 α¸p(n−6 SPACE hvd.32044092008168 610 51 ) ) PUNCT hvd.32044092008168 610 52 + + CCONJ hvd.32044092008168 610 53 α¿p(n−8 α¿p(n−8 ADP hvd.32044092008168 610 54 ) ) PUNCT hvd.32044092008168 610 55 + + CCONJ hvd.32044092008168 610 56 · · PUNCT hvd.32044092008168 610 57 and and CCONJ hvd.32044092008168 610 58 a a DET hvd.32044092008168 610 59 similar similar ADJ hvd.32044092008168 610 60 analysis analysis NOUN hvd.32044092008168 610 61 to to ADP hvd.32044092008168 610 62 the the DET hvd.32044092008168 610 63 former former ADJ hvd.32044092008168 610 64 cases case NOUN hvd.32044092008168 610 65 shows show VERB hvd.32044092008168 610 66 that that SCONJ hvd.32044092008168 610 67 this this DET hvd.32044092008168 610 68 solution solution NOUN hvd.32044092008168 610 69 holds hold VERB hvd.32044092008168 610 70 when when SCONJ hvd.32044092008168 610 71 b b PROPN hvd.32044092008168 610 72 is be AUX hvd.32044092008168 610 73 the the DET hvd.32044092008168 610 74 root root NOUN hvd.32044092008168 610 75 of of ADP hvd.32044092008168 610 76 a a DET hvd.32044092008168 610 77 determinate determinate ADJ hvd.32044092008168 610 78 equation equation NOUN hvd.32044092008168 610 79 whose whose DET hvd.32044092008168 610 80 degree degree NOUN hvd.32044092008168 610 81 is be AUX hvd.32044092008168 610 82 n. n. PROPN hvd.32044092008168 610 83 15g₂ 15g₂ NUM hvd.32044092008168 610 84 = = SYM hvd.32044092008168 610 85 0 0 NUM hvd.32044092008168 610 86 identity identity NOUN hvd.32044092008168 610 87 of of ADP hvd.32044092008168 610 88 solutions solution NOUN hvd.32044092008168 610 89 . . PUNCT hvd.32044092008168 611 1 having having AUX hvd.32044092008168 611 2 developed develop VERB hvd.32044092008168 611 3 in in ADP hvd.32044092008168 611 4 the the DET hvd.32044092008168 611 5 foregoing forego VERB hvd.32044092008168 611 6 the the DET hvd.32044092008168 611 7 necessary necessary ADJ hvd.32044092008168 611 8 underlying underlying ADJ hvd.32044092008168 611 9 principles principle NOUN hvd.32044092008168 611 10 we we PRON hvd.32044092008168 611 11 return return VERB hvd.32044092008168 611 12 to to ADP hvd.32044092008168 611 13 the the DET hvd.32044092008168 611 14 case case NOUN hvd.32044092008168 611 15 where where SCONJ hvd.32044092008168 611 16 n n CCONJ hvd.32044092008168 611 17 equals equal VERB hvd.32044092008168 611 18 three three NUM hvd.32044092008168 611 19 , , PUNCT hvd.32044092008168 611 20 that that PRON hvd.32044092008168 611 21 is be AUX hvd.32044092008168 611 22 to to ADP hvd.32044092008168 611 23 a a DET hvd.32044092008168 611 24 determination determination NOUN hvd.32044092008168 611 25 of of ADP hvd.32044092008168 611 26 the the DET hvd.32044092008168 611 27 integral integral NOUN hvd.32044092008168 611 28 of of ADP hvd.32044092008168 611 29 the the DET hvd.32044092008168 611 30 equation equation NOUN hvd.32044092008168 611 31 [ [ X hvd.32044092008168 611 32 76 76 NUM hvd.32044092008168 611 33 ] ] PUNCT hvd.32044092008168 611 34 · · PUNCT hvd.32044092008168 611 35 y"= y"= NOUN hvd.32044092008168 612 1 [ [ X hvd.32044092008168 612 2 12p(u 12p(u NUM hvd.32044092008168 612 3 ) ) PUNCT hvd.32044092008168 613 1 + + CCONJ hvd.32044092008168 613 2 b]y b]y PUNCT hvd.32044092008168 614 1 [ [ X hvd.32044092008168 614 2 77 77 NUM hvd.32044092008168 614 3 ] ] PUNCT hvd.32044092008168 614 4 where where SCONJ hvd.32044092008168 614 5 b b PROPN hvd.32044092008168 614 6 is be AUX hvd.32044092008168 614 7 to to PART hvd.32044092008168 614 8 be be AUX hvd.32044092008168 614 9 arbitrarily arbitrarily ADV hvd.32044092008168 614 10 chosen choose VERB hvd.32044092008168 614 11 . . PUNCT hvd.32044092008168 615 1 the the DET hvd.32044092008168 615 2 first first ADJ hvd.32044092008168 615 3 form form NOUN hvd.32044092008168 615 4 obtain obtain VERB hvd.32044092008168 615 5 from from ADP hvd.32044092008168 615 6 ( ( PUNCT hvd.32044092008168 615 7 32 32 NUM hvd.32044092008168 615 8 ) ) PUNCT hvd.32044092008168 615 9 is be AUX hvd.32044092008168 615 10 y y PROPN hvd.32044092008168 615 11 = = SYM hvd.32044092008168 615 12 1/2 1/2 NUM hvd.32044092008168 615 13 f f X hvd.32044092008168 615 14 " " PUNCT hvd.32044092008168 615 15 + + PROPN hvd.32044092008168 615 16 h₁ h₁ PROPN hvd.32044092008168 615 17 f f PROPN hvd.32044092008168 615 18 and and CCONJ hvd.32044092008168 615 19 from from ADP hvd.32044092008168 615 20 the the DET hvd.32044092008168 615 21 first first ADJ hvd.32044092008168 615 22 of of ADP hvd.32044092008168 615 23 equations equation NOUN hvd.32044092008168 615 24 ( ( PUNCT hvd.32044092008168 615 25 26 26 NUM hvd.32044092008168 615 26 ) ) PUNCT hvd.32044092008168 615 27 we we PRON hvd.32044092008168 615 28 have have VERB hvd.32044092008168 615 29 b b PROPN hvd.32044092008168 615 30 10 10 NUM hvd.32044092008168 615 31 • • SYM hvd.32044092008168 615 32 part part NOUN hvd.32044092008168 615 33 v. v. ADP hvd.32044092008168 615 34 reduction reduction NOUN hvd.32044092008168 615 35 of of ADP hvd.32044092008168 615 36 the the DET hvd.32044092008168 615 37 forms form NOUN hvd.32044092008168 615 38 when when SCONJ hvd.32044092008168 615 39 n n SYM hvd.32044092008168 615 40 equals equal VERB hvd.32044092008168 615 41 three three NUM hvd.32044092008168 615 42 . . PUNCT hvd.32044092008168 616 1 where where SCONJ hvd.32044092008168 616 2 h₁ h₁ NOUN hvd.32044092008168 616 3 hence hence ADV hvd.32044092008168 616 4 disregarding disregard VERB hvd.32044092008168 616 5 the the DET hvd.32044092008168 616 6 constant constant ADJ hvd.32044092008168 616 7 the the DET hvd.32044092008168 616 8 integral integral NOUN hvd.32044092008168 616 9 is be AUX hvd.32044092008168 616 10 y y PROPN hvd.32044092008168 616 11 = = X hvd.32044092008168 616 12 f f X hvd.32044092008168 616 13 " " PUNCT hvd.32044092008168 616 14 — — PUNCT hvd.32044092008168 616 15 3bf 3bf ADJ hvd.32044092008168 616 16 σ σ NOUN hvd.32044092008168 616 17 ( ( PUNCT hvd.32044092008168 616 18 u u PROPN hvd.32044092008168 616 19 + + CCONJ hvd.32044092008168 616 20 v v NOUN hvd.32044092008168 616 21 ) ) PUNCT hvd.32044092008168 616 22 o o NOUN hvd.32044092008168 616 23 ( ( PUNCT hvd.32044092008168 616 24 u u PROPN hvd.32044092008168 616 25 ) ) PUNCT hvd.32044092008168 616 26 o o NOUN hvd.32044092008168 616 27 ( ( PUNCT hvd.32044092008168 616 28 v v NOUN hvd.32044092008168 616 29 ) ) PUNCT hvd.32044092008168 616 30 and and CCONJ hvd.32044092008168 616 31 x x PUNCT hvd.32044092008168 616 32 and and CCONJ hvd.32044092008168 616 33 satisfy satisfy VERB hvd.32044092008168 616 34 the the DET hvd.32044092008168 616 35 conditions condition NOUN hvd.32044092008168 616 36 ( ( PUNCT hvd.32044092008168 616 37 35 35 NUM hvd.32044092008168 616 38 ) ) PUNCT hvd.32044092008168 616 39 where where SCONJ hvd.32044092008168 616 40 b b X hvd.32044092008168 616 41 f f X hvd.32044092008168 616 42 : : PUNCT hvd.32044092008168 616 43 ←← ←← NUM hvd.32044092008168 616 44 e(x-5v e(x-5v X hvd.32044092008168 616 45 ) ) PUNCT hvd.32044092008168 616 46 u u PROPN hvd.32044092008168 616 47 = = PUNCT hvd.32044092008168 617 1 [ [ X hvd.32044092008168 617 2 h₂+ h₂+ X hvd.32044092008168 617 3 h₁ h₁ NOUN hvd.32044092008168 617 4 h₁ h₁ NOUN hvd.32044092008168 617 5 = = SYM hvd.32044092008168 617 6 0 0 NUM hvd.32044092008168 617 7 ho ho PROPN hvd.32044092008168 617 8 2 2 NUM hvd.32044092008168 617 9 156 156 NUM hvd.32044092008168 618 1 [ [ X hvd.32044092008168 618 2 78 78 NUM hvd.32044092008168 618 3 ] ] PUNCT hvd.32044092008168 618 4 where where SCONJ hvd.32044092008168 618 5 \ \ PROPN hvd.32044092008168 618 6 3 3 NUM hvd.32044092008168 618 7 h₂ h₂ PROPN hvd.32044092008168 618 8 + + SYM hvd.32044092008168 618 9 h₁ h₁ PROPN hvd.32044092008168 618 10 h₁ h₁ PROPN hvd.32044092008168 618 11 = = PROPN hvd.32044092008168 618 12 h₂ h₂ PROPN hvd.32044092008168 618 13 ζα ζα PROPN hvd.32044092008168 618 14 x x ADP hvd.32044092008168 618 15 = = PROPN hvd.32044092008168 618 16 ev ev INTJ hvd.32044092008168 618 17 — — PUNCT hvd.32044092008168 618 18 ea ea PROPN hvd.32044092008168 618 19 — — PUNCT hvd.32044092008168 618 20 eb eb PROPN hvd.32044092008168 618 21 — — PUNCT hvd.32044092008168 618 22 ec ec PROPN hvd.32044092008168 618 23 v v ADP hvd.32044092008168 618 24 = = X hvd.32044092008168 618 25 a+b+c a+b+c ADV hvd.32044092008168 618 26 . . PUNCT hvd.32044092008168 619 1 ( ( PUNCT hvd.32044092008168 619 2 p. p. NOUN hvd.32044092008168 619 3 17 17 NUM hvd.32044092008168 619 4 and and CCONJ hvd.32044092008168 619 5 p. p. NOUN hvd.32044092008168 619 6 16 16 NUM hvd.32044092008168 619 7 . . PUNCT hvd.32044092008168 619 8 ) ) PUNCT hvd.32044092008168 620 1 1st 1st NOUN hvd.32044092008168 620 2 solution solution NOUN hvd.32044092008168 620 3 . . PUNCT hvd.32044092008168 621 1 46 46 NUM hvd.32044092008168 621 2 part part NOUN hvd.32044092008168 621 3 v. v. ADP hvd.32044092008168 621 4 [ [ X hvd.32044092008168 621 5 79 79 NUM hvd.32044092008168 621 6 ] ] PUNCT hvd.32044092008168 621 7 euša euša ADJ hvd.32044092008168 621 8 y=17 y=17 PROPN hvd.32044092008168 621 9 ° ° X hvd.32044092008168 621 10 (u (u PUNCT hvd.32044092008168 621 11 + + CCONJ hvd.32044092008168 621 12 a a X hvd.32044092008168 621 13 ) ) PUNCT hvd.32044092008168 621 14 11 11 NUM hvd.32044092008168 621 15 . . PUNCT hvd.32044092008168 622 1 ( ( PUNCT hvd.32044092008168 622 2 a a X hvd.32044092008168 622 3 ) ) PUNCT hvd.32044092008168 622 4 0 0 NUM hvd.32044092008168 622 5 ( ( PUNCT hvd.32044092008168 622 6 0 0 NUM hvd.32044092008168 622 7 ) ) PUNCT hvd.32044092008168 622 8 eu eu PROPN hvd.32044092008168 622 9 ša ša PROPN hvd.32044092008168 622 10 σα σα PROPN hvd.32044092008168 622 11 σε σε PROPN hvd.32044092008168 622 12 the the DET hvd.32044092008168 622 13 second second ADJ hvd.32044092008168 622 14 form form NOUN hvd.32044092008168 622 15 obtained obtain VERB hvd.32044092008168 622 16 from from ADP hvd.32044092008168 622 17 ( ( PUNCT hvd.32044092008168 622 18 66 66 NUM hvd.32044092008168 622 19 ) ) PUNCT hvd.32044092008168 622 20 is be AUX hvd.32044092008168 622 21 u u PROPN hvd.32044092008168 622 22 ( ( PUNCT hvd.32044092008168 622 23 4 4 NUM hvd.32044092008168 622 24 a a X hvd.32044092008168 622 25 ) ) PUNCT hvd.32044092008168 622 26 ) ) PUNCT hvd.32044092008168 623 1 u u PROPN hvd.32044092008168 623 2 o(u o(u PROPN hvd.32044092008168 623 3 a a DET hvd.32044092008168 623 4 ) ) PUNCT hvd.32044092008168 623 5 o(u o(u PROPN hvd.32044092008168 623 6 b b PROPN hvd.32044092008168 623 7 ) ) PUNCT hvd.32044092008168 623 8 o(u o(u PROPN hvd.32044092008168 623 9 c c PROPN hvd.32044092008168 623 10 ) ) PUNCT hvd.32044092008168 623 11 elsa elsa ADJ hvd.32044092008168 623 12 +56+$cu +56+$cu NUM hvd.32044092008168 623 13 o(a o(a SPACE hvd.32044092008168 623 14 ) ) PUNCT hvd.32044092008168 623 15 ( ( PUNCT hvd.32044092008168 623 16 b b PROPN hvd.32044092008168 623 17 ) ) PUNCT hvd.32044092008168 623 18 o(c o(c PROPN hvd.32044092008168 623 19 ) ) PUNCT hvd.32044092008168 623 20 03 03 NUM hvd.32044092008168 623 21 0 0 NUM hvd.32044092008168 623 22 where where SCONJ hvd.32044092008168 623 23 20 20 NUM hvd.32044092008168 623 24 a'rp'(a a'rp'(a PROPN hvd.32044092008168 623 25 ) ) PUNCT hvd.32044092008168 623 26 ( ( PUNCT hvd.32044092008168 623 27 a a DET hvd.32044092008168 623 28 b b NOUN hvd.32044092008168 623 29 ) ) PUNCT hvd.32044092008168 623 30 ( ( PUNCT hvd.32044092008168 623 31 a a DET hvd.32044092008168 623 32 y y PROPN hvd.32044092008168 623 33 ) ) PUNCT hvd.32044092008168 623 34 20 20 NUM hvd.32044092008168 623 35 b b NOUN hvd.32044092008168 623 36 ' ' PUNCT hvd.32044092008168 623 37 = = NOUN hvd.32044092008168 623 38 p'(b p'(b NOUN hvd.32044092008168 623 39 ) ) PUNCT hvd.32044092008168 623 40 ( ( PUNCT hvd.32044092008168 623 41 b b PROPN hvd.32044092008168 623 42 a a X hvd.32044092008168 623 43 ) ) PUNCT hvd.32044092008168 623 44 ( ( PUNCT hvd.32044092008168 623 45 y y PROPN hvd.32044092008168 623 46 ) ) PUNCT hvd.32044092008168 623 47 20 20 NUM hvd.32044092008168 623 48 y'rp'(c y'rp'(c PROPN hvd.32044092008168 623 49 ) ) PUNCT hvd.32044092008168 623 50 ( ( PUNCT hvd.32044092008168 623 51 y y PROPN hvd.32044092008168 623 52 a a X hvd.32044092008168 623 53 ) ) PUNCT hvd.32044092008168 623 54 ( ( PUNCT hvd.32044092008168 623 55 y y PROPN hvd.32044092008168 623 56 – – PUNCT hvd.32044092008168 623 57 b b NOUN hvd.32044092008168 623 58 ) ) PUNCT hvd.32044092008168 623 59 and and CCONJ hvd.32044092008168 623 60 (= (= NOUN hvd.32044092008168 623 61 + + NUM hvd.32044092008168 623 62 vy vy NOUN hvd.32044092008168 623 63 ; ; PUNCT hvd.32044092008168 623 64 y y PROPN hvd.32044092008168 623 65 = = PROPN hvd.32044092008168 623 66 s% s% PROPN hvd.32044092008168 623 67 + + CCONJ hvd.32044092008168 623 68 a a PRON hvd.32044092008168 623 69 , , PUNCT hvd.32044092008168 623 70 s s X hvd.32044092008168 623 71 + + PROPN hvd.32044092008168 623 72 az az PROPN hvd.32044092008168 623 73 s s NOUN hvd.32044092008168 623 74 = = PROPN hvd.32044092008168 623 75 t—6 t—6 PROPN hvd.32044092008168 623 76 ; ; PUNCT hvd.32044092008168 623 77 4 4 X hvd.32044092008168 623 78 , , PUNCT hvd.32044092008168 623 79 = = VERB hvd.32044092008168 623 80 + + CCONJ hvd.32044092008168 623 81 ( ( PUNCT hvd.32044092008168 623 82 1262 1262 NUM hvd.32044092008168 623 83 – – PUNCT hvd.32044092008168 623 84 į į NUM hvd.32044092008168 623 85 92 92 NUM hvd.32044092008168 623 86 ) ) PUNCT hvd.32044092008168 623 87 ; ; PUNCT hvd.32044092008168 623 88 ag ag PROPN hvd.32044092008168 623 89 = = PROPN hvd.32044092008168 623 90 – – PUNCT hvd.32044092008168 623 91 4 4 NUM hvd.32044092008168 623 92 ( ( PUNCT hvd.32044092008168 623 93 446 446 NUM hvd.32044092008168 623 94 * * PUNCT hvd.32044092008168 623 95 — — PUNCT hvd.32044092008168 623 96 39,6 39,6 NUM hvd.32044092008168 623 97 +93 +93 PROPN hvd.32044092008168 623 98 ) ) PUNCT hvd.32044092008168 623 99 . . PUNCT hvd.32044092008168 623 100 ) ) PUNCT hvd.32044092008168 624 1 ba= ba= VERB hvd.32044092008168 624 2 the the DET hvd.32044092008168 624 3 transformation transformation NOUN hvd.32044092008168 624 4 of of ADP hvd.32044092008168 624 5 form form NOUN hvd.32044092008168 624 6 ( ( PUNCT hvd.32044092008168 624 7 79 79 NUM hvd.32044092008168 624 8 ) ) PUNCT hvd.32044092008168 624 9 to to PART hvd.32044092008168 624 10 form form VERB hvd.32044092008168 624 11 ( ( PUNCT hvd.32044092008168 624 12 77 77 NUM hvd.32044092008168 624 13 ) ) PUNCT hvd.32044092008168 624 14 may may AUX hvd.32044092008168 624 15 be be AUX hvd.32044092008168 624 16 accomplished accomplish VERB hvd.32044092008168 624 17 as as SCONJ hvd.32044092008168 624 18 follows follow NOUN hvd.32044092008168 624 19 . . PUNCT hvd.32044092008168 625 1 taking take VERB hvd.32044092008168 625 2 the the DET hvd.32044092008168 625 3 eliments eliment NOUN hvd.32044092008168 625 4 we we PRON hvd.32044092008168 625 5 have have VERB hvd.32044092008168 625 6 2d 2d PRON hvd.32044092008168 625 7 solution solution NOUN hvd.32044092008168 625 8 . . PUNCT hvd.32044092008168 626 1 c= c= NOUN hvd.32044092008168 626 2 ( ( PUNCT hvd.32044092008168 626 3 p. p. NOUN hvd.32044092008168 626 4 40 40 NUM hvd.32044092008168 626 5 . . PUNCT hvd.32044092008168 626 6 ) ) PUNCT hvd.32044092008168 626 7 4 4 NUM hvd.32044092008168 626 8 0 0 NUM hvd.32044092008168 626 9 ( ( PUNCT hvd.32044092008168 626 10 u u NOUN hvd.32044092008168 626 11 + + CCONJ hvd.32044092008168 626 12 a a PRON hvd.32044092008168 626 13 ) ) PUNCT hvd.32044092008168 626 14 e1 e1 PROPN hvd.32044092008168 626 15 u u PROPN hvd.32044092008168 626 16 e e PROPN hvd.32044092008168 626 17 - - PROPN hvd.32044092008168 626 18 usa usa PROPN hvd.32044092008168 626 19 σω σω INTJ hvd.32044092008168 626 20 σα σα PROPN hvd.32044092008168 626 21 pa pa PROPN hvd.32044092008168 626 22 + + PROPN hvd.32044092008168 626 23 2 2 NUM hvd.32044092008168 626 24 u u PROPN hvd.32044092008168 626 25 o(u o(u PROPN hvd.32044092008168 626 26 + + CCONJ hvd.32044092008168 626 27 b b X hvd.32044092008168 626 28 ) ) PUNCT hvd.32044092008168 626 29 1 1 NUM hvd.32044092008168 626 30 u u PROPN hvd.32044092008168 626 31 e e PROPN hvd.32044092008168 626 32 uto uto PROPN hvd.32044092008168 626 33 pb pb PROPN hvd.32044092008168 626 34 + + PROPN hvd.32044092008168 626 35 .. .. PUNCT hvd.32044092008168 626 36 ( ( PUNCT hvd.32044092008168 626 37 u u PROPN hvd.32044092008168 626 38 ) ) PUNCT hvd.32044092008168 626 39 ob ob PROPN hvd.32044092008168 626 40 u u PROPN hvd.32044092008168 626 41 2 2 NUM hvd.32044092008168 626 42 u u PROPN hvd.32044092008168 626 43 o(u o(u PROPN hvd.32044092008168 626 44 + + CCONJ hvd.32044092008168 626 45 c c X hvd.32044092008168 626 46 ) ) PUNCT hvd.32044092008168 626 47 σασο σασο PROPN hvd.32044092008168 626 48 e e PROPN hvd.32044092008168 626 49 - - PROPN hvd.32044092008168 626 50 usc usc PROPN hvd.32044092008168 626 51 pet pet PROPN hvd.32044092008168 626 52 .. .. PUNCT hvd.32044092008168 626 53 u u PRON hvd.32044092008168 626 54 2 2 NUM hvd.32044092008168 626 55 whence whence NOUN hvd.32044092008168 626 56 0 0 NUM hvd.32044092008168 626 57 6 6 NUM hvd.32044092008168 626 58 ou ou ADV hvd.32044092008168 626 59 + + CCONJ hvd.32044092008168 626 60 a a X hvd.32044092008168 626 61 ) ) PUNCT hvd.32044092008168 626 62 ou ou X hvd.32044092008168 626 63 + + PROPN hvd.32044092008168 626 64 b b X hvd.32044092008168 626 65 ) ) PUNCT hvd.32044092008168 626 66 ( ( PUNCT hvd.32044092008168 626 67 u u PROPN hvd.32044092008168 626 68 + + CCONJ hvd.32044092008168 626 69 c c NOUN hvd.32044092008168 626 70 ) ) PUNCT hvd.32044092008168 626 71 o(a o(a NUM hvd.32044092008168 626 72 ) ) PUNCT hvd.32044092008168 626 73 ( ( PUNCT hvd.32044092008168 626 74 b b NOUN hvd.32044092008168 626 75 ) ) PUNCT hvd.32044092008168 626 76 ( ( PUNCT hvd.32044092008168 626 77 c c NOUN hvd.32044092008168 626 78 ) ) PUNCT hvd.32044092008168 626 79 o'r o'r ADJ hvd.32044092008168 627 1 e-(sa+$6 e-(sa+$6 PROPN hvd.32044092008168 627 2 + + NUM hvd.32044092008168 627 3 50 50 NUM hvd.32044092008168 627 4 ) ) PUNCT hvd.32044092008168 627 5 u u PROPN hvd.32044092008168 627 6 y y PROPN hvd.32044092008168 627 7 1 1 NUM hvd.32044092008168 627 8 u u NOUN hvd.32044092008168 627 9 [ [ PUNCT hvd.32044092008168 627 10 mt(pa mt(pa VERB hvd.32044092008168 627 11 + + CCONJ hvd.32044092008168 627 12 pb)+]6 pb)+]6 PROPN hvd.32044092008168 627 13 pcc pcc NOUN hvd.32044092008168 627 14 ) ) PUNCT hvd.32044092008168 627 15 + + PROPN hvd.32044092008168 627 16 ) ) PUNCT hvd.32044092008168 627 17 ( ( PUNCT hvd.32044092008168 627 18 2 2 NUM hvd.32044092008168 627 19 u u NOUN hvd.32044092008168 627 20 2 2 NUM hvd.32044092008168 627 21 take take NOUN hvd.32044092008168 627 22 ( ( PUNCT hvd.32044092008168 627 23 11 11 NUM hvd.32044092008168 627 24 + + CCONJ hvd.32044092008168 627 25 a a PRON hvd.32044092008168 627 26 + + ADJ hvd.32044092008168 627 27 b b NOUN hvd.32044092008168 627 28 + + CCONJ hvd.32044092008168 627 29 c c NOUN hvd.32044092008168 627 30 ) ) PUNCT hvd.32044092008168 627 31 f= f= NOUN hvd.32044092008168 627 32 o(a o(a ADP hvd.32044092008168 627 33 + + NOUN hvd.32044092008168 627 34 b b NOUN hvd.32044092008168 627 35 + + CCONJ hvd.32044092008168 627 36 c c X hvd.32044092008168 627 37 ) ) PUNCT hvd.32044092008168 627 38 ou ou X hvd.32044092008168 627 39 0 0 NUM hvd.32044092008168 628 1 ( ( PUNCT hvd.32044092008168 628 2 u u PROPN hvd.32044092008168 628 3 + + CCONJ hvd.32044092008168 628 4 v v PROPN hvd.32044092008168 628 5 ) ) PUNCT hvd.32044092008168 628 6 p(x- p(x- PROPN hvd.32044092008168 628 7 > > SYM hvd.32044092008168 628 8 » » PUNCT hvd.32044092008168 628 9 ) ) PUNCT hvd.32044092008168 628 10 u u PROPN hvd.32044092008168 628 11 e e PROPN hvd.32044092008168 628 12 - - ADJ hvd.32044092008168 628 13 u(sa+56 u(sa+56 ADJ hvd.32044092008168 628 14 + + NUM hvd.32044092008168 628 15 50 50 NUM hvd.32044092008168 628 16 ) ) PUNCT hvd.32044092008168 628 17 e e NOUN hvd.32044092008168 628 18 — — PUNCT hvd.32044092008168 628 19 šv šv INTJ hvd.32044092008168 628 20 σι σι INTJ hvd.32044092008168 628 21 σν σν INTJ hvd.32044092008168 628 22 1 1 NUM hvd.32044092008168 628 23 u u PROPN hvd.32044092008168 628 24 u u PROPN hvd.32044092008168 628 25 2 2 NUM hvd.32044092008168 629 1 ( ( PUNCT hvd.32044092008168 629 2 pa pa PROPN hvd.32044092008168 629 3 + + CCONJ hvd.32044092008168 629 4 pb pb X hvd.32044092008168 629 5 + + PROPN hvd.32044092008168 629 6 pc)+ pc)+ PROPN hvd.32044092008168 629 7 . . PUNCT hvd.32044092008168 630 1 į į X hvd.32044092008168 630 2 ( ( PUNCT hvd.32044092008168 630 3 pa pa PROPN hvd.32044092008168 630 4 + + CCONJ hvd.32044092008168 630 5 pb pb X hvd.32044092008168 630 6 + + PROPN hvd.32044092008168 630 7 pe pe X hvd.32044092008168 630 8 ) ) PUNCT hvd.32044092008168 630 9 + + PUNCT hvd.32044092008168 630 10 ... ... PUNCT hvd.32044092008168 630 11 . . PUNCT hvd.32044092008168 631 1 1 1 NUM hvd.32044092008168 631 2 f'= f'= PROPN hvd.32044092008168 631 3 1 1 NUM hvd.32044092008168 631 4 u u PROPN hvd.32044092008168 631 5 2 2 NUM hvd.32044092008168 631 6 2 2 NUM hvd.32044092008168 631 7 f f X hvd.32044092008168 631 8 " " PUNCT hvd.32044092008168 631 9 = = X hvd.32044092008168 631 10 + + CCONJ hvd.32044092008168 631 11 u3 u3 ADJ hvd.32044092008168 631 12 whence whence INTJ hvd.32044092008168 631 13 we we PRON hvd.32044092008168 631 14 observe observe VERB hvd.32044092008168 631 15 that that SCONJ hvd.32044092008168 631 16 we we PRON hvd.32044092008168 631 17 may may AUX hvd.32044092008168 631 18 write write VERB hvd.32044092008168 631 19 y y PROPN hvd.32044092008168 631 20 y=[f"u y=[f"u PROPN hvd.32044092008168 631 21 — — PUNCT hvd.32044092008168 632 1 ( ( PUNCT hvd.32044092008168 632 2 pa pa PROPN hvd.32044092008168 632 3 + + CCONJ hvd.32044092008168 632 4 pb pb PROPN hvd.32044092008168 632 5 + + PROPN hvd.32044092008168 632 6 pe pe PROPN hvd.32044092008168 632 7 ) ) PUNCT hvd.32044092008168 632 8 fu fu PROPN hvd.32044092008168 632 9 ] ] PUNCT hvd.32044092008168 632 10 . . PUNCT hvd.32044092008168 633 1 but but CCONJ hvd.32044092008168 633 2 pa pa PROPN hvd.32044092008168 633 3 + + CCONJ hvd.32044092008168 633 4 pb pb X hvd.32044092008168 634 1 + + X hvd.32044092008168 634 2 pe pe X hvd.32044092008168 634 3 = = X hvd.32044092008168 634 4 b=31 b=31 PRON hvd.32044092008168 634 5 pc pc NOUN hvd.32044092008168 635 1 в в NOUN hvd.32044092008168 635 2 1 1 NUM hvd.32044092008168 635 3 5 5 NUM hvd.32044092008168 635 4 reduction reduction NOUN hvd.32044092008168 635 5 of of ADP hvd.32044092008168 635 6 the the DET hvd.32044092008168 635 7 forms form NOUN hvd.32044092008168 635 8 when when SCONJ hvd.32044092008168 635 9 n n SYM hvd.32044092008168 635 10 equals equal VERB hvd.32044092008168 635 11 three three NUM hvd.32044092008168 635 12 . . PUNCT hvd.32044092008168 636 1 47 47 NUM hvd.32044092008168 636 2 and and CCONJ hvd.32044092008168 636 3 , , PUNCT hvd.32044092008168 636 4 disregarding disregard VERB hvd.32044092008168 636 5 the the DET hvd.32044092008168 636 6 factor factor NOUN hvd.32044092008168 636 7 , , PUNCT hvd.32044092008168 636 8 we we PRON hvd.32044092008168 636 9 obtain obtain VERB hvd.32044092008168 636 10 the the DET hvd.32044092008168 636 11 first first ADJ hvd.32044092008168 636 12 form form NOUN hvd.32044092008168 636 13 : : PUNCT hvd.32044092008168 636 14 y y PROPN hvd.32044092008168 636 15 = = X hvd.32044092008168 636 16 f f X hvd.32044092008168 636 17 " " PUNCT hvd.32044092008168 636 18 — — PUNCT hvd.32044092008168 636 19 3bf 3bf ADJ hvd.32044092008168 636 20 . . PUNCT hvd.32044092008168 637 1 having have VERB hvd.32044092008168 637 2 then then ADV hvd.32044092008168 637 3 a a DET hvd.32044092008168 637 4 method method NOUN hvd.32044092008168 637 5 of of ADP hvd.32044092008168 637 6 reduction reduction NOUN hvd.32044092008168 637 7 the the DET hvd.32044092008168 637 8 determination determination NOUN hvd.32044092008168 637 9 of of ADP hvd.32044092008168 637 10 abc abc PROPN hvd.32044092008168 637 11 is be AUX hvd.32044092008168 637 12 involved involve VERB hvd.32044092008168 637 13 in in ADP hvd.32044092008168 637 14 the the DET hvd.32044092008168 637 15 determinate determinate NOUN hvd.32044092008168 637 16 of of ADP hvd.32044092008168 637 17 v. v. NOUN hvd.32044092008168 637 18 determination determination NOUN hvd.32044092008168 637 19 of of ADP hvd.32044092008168 637 20 x x SYM hvd.32044092008168 637 21 and and CCONJ hvd.32044092008168 637 22 v. v. ADP hvd.32044092008168 637 23 first first ADJ hvd.32044092008168 637 24 method method NOUN hvd.32044092008168 637 25 . . PUNCT hvd.32044092008168 638 1 to to ADP hvd.32044092008168 638 2 this this DET hvd.32044092008168 638 3 end end NOUN hvd.32044092008168 638 4 we we PRON hvd.32044092008168 638 5 have have VERB hvd.32044092008168 638 6 from from ADP hvd.32044092008168 638 7 ( ( PUNCT hvd.32044092008168 638 8 31 31 NUM hvd.32044092008168 638 9 ) ) PUNCT hvd.32044092008168 638 10 and and CCONJ hvd.32044092008168 638 11 ( ( PUNCT hvd.32044092008168 638 12 26 26 NUM hvd.32044092008168 638 13 ) ) PUNCT hvd.32044092008168 638 14 1 1 NUM hvd.32044092008168 638 15 h₁ h₁ PROPN hvd.32044092008168 638 16 = = SYM hvd.32044092008168 638 17 ½-½ ½-½ X hvd.32044092008168 638 18 ( ( PUNCT hvd.32044092008168 638 19 x² x² PROPN hvd.32044092008168 638 20 + + CCONJ hvd.32044092008168 638 21 p₂ p₂ PROPN hvd.32044092008168 638 22 ) ) PUNCT hvd.32044092008168 638 23 ; ; PUNCT hvd.32044092008168 639 1 2 2 NUM hvd.32044092008168 639 2 and and CCONJ hvd.32044092008168 639 3 also also ADV hvd.32044092008168 639 4 set set VERB hvd.32044092008168 639 5 h₁ h₁ PROPN hvd.32044092008168 639 6 = = NOUN hvd.32044092008168 639 7 x x PUNCT hvd.32044092008168 639 8 ; ; PUNCT hvd.32044092008168 639 9 ho ho PROPN hvd.32044092008168 639 10 h₂ h₂ PROPN hvd.32044092008168 639 11 whence whence ADP hvd.32044092008168 639 12 relations relation NOUN hvd.32044092008168 639 13 ( ( PUNCT hvd.32044092008168 639 14 78 78 NUM hvd.32044092008168 639 15 ) ) PUNCT hvd.32044092008168 639 16 become become VERB hvd.32044092008168 639 17 1 1 NUM hvd.32044092008168 639 18 b b X hvd.32044092008168 639 19 — — PUNCT hvd.32044092008168 639 20 ( ( PUNCT hvd.32044092008168 639 21 x³ x³ PROPN hvd.32044092008168 639 22 + + CCONJ hvd.32044092008168 639 23 3 3 NUM hvd.32044092008168 639 24 p₂ p₂ PROPN hvd.32044092008168 639 25 x x PUNCT hvd.32044092008168 640 1 + + CCONJ hvd.32044092008168 640 2 p₂ p₂ PROPN hvd.32044092008168 640 3 ) ) PUNCT hvd.32044092008168 640 4 — — PUNCT hvd.32044092008168 640 5 3 3 NUM hvd.32044092008168 640 6 2 2 NUM hvd.32044092008168 640 7 ι ι NOUN hvd.32044092008168 640 8 = = SYM hvd.32044092008168 640 9 1 1 NUM hvd.32044092008168 640 10 5 5 NUM hvd.32044092008168 640 11 and and CCONJ hvd.32044092008168 640 12 the the DET hvd.32044092008168 640 13 useful useful ADJ hvd.32044092008168 640 14 relation relation NOUN hvd.32044092008168 640 15 b2 b2 PROPN hvd.32044092008168 640 16 120 120 NUM hvd.32044092008168 640 17 1 1 NUM hvd.32044092008168 640 18 b b NOUN hvd.32044092008168 640 19 ¦ ¦ PROPN hvd.32044092008168 640 20 ( ( PUNCT hvd.32044092008168 640 21 x² x² PROPN hvd.32044092008168 640 22 + + NUM hvd.32044092008168 640 23 6p¸x² 6p¸x² NUM hvd.32044092008168 640 24 + + NUM hvd.32044092008168 640 25 4p¸x 4p¸x NUM hvd.32044092008168 640 26 + + NUM hvd.32044092008168 640 27 p₁ p₁ NOUN hvd.32044092008168 640 28 ) ) PUNCT hvd.32044092008168 640 29 − − PROPN hvd.32044092008168 640 30 ²² ²² NUM hvd.32044092008168 641 1 ( ( PUNCT hvd.32044092008168 641 2 x² x² PROPN hvd.32044092008168 641 3 + + CCONJ hvd.32044092008168 641 4 p₂ p₂ PROPN hvd.32044092008168 641 5 ) ) PUNCT hvd.32044092008168 641 6 2 2 NUM hvd.32044092008168 641 7 = = PUNCT hvd.32044092008168 641 8 h₂ h₂ PROPN hvd.32044092008168 641 9 = = PROPN hvd.32044092008168 641 10 ( ( PUNCT hvd.32044092008168 641 11 x² x² PROPN hvd.32044092008168 641 12 + + SYM hvd.32044092008168 641 13 3 3 NUM hvd.32044092008168 641 14 p₂x p₂x NOUN hvd.32044092008168 641 15 + + CCONJ hvd.32044092008168 641 16 p3 p3 X hvd.32044092008168 641 17 ) ) PUNCT hvd.32044092008168 641 18 b b PROPN hvd.32044092008168 641 19 or or CCONJ hvd.32044092008168 641 20 b b NOUN hvd.32044092008168 641 21 10 10 NUM hvd.32044092008168 641 22 1/2 1/2 NUM hvd.32044092008168 641 23 x x PUNCT hvd.32044092008168 641 24 = = PUNCT hvd.32044092008168 641 25 0 0 NUM hvd.32044092008168 641 26 92 92 NUM hvd.32044092008168 641 27 20 20 NUM hvd.32044092008168 641 28 h₁ h₁ PROPN hvd.32044092008168 641 29 = = NOUN hvd.32044092008168 642 1 ι ι X hvd.32044092008168 642 2 3 3 NUM hvd.32044092008168 642 3 and and CCONJ hvd.32044092008168 642 4 take take VERB hvd.32044092008168 642 5 from from ADP hvd.32044092008168 642 6 ( ( PUNCT hvd.32044092008168 642 7 p. p. NOUN hvd.32044092008168 642 8 24 24 NUM hvd.32044092008168 642 9 ) ) PUNCT hvd.32044092008168 643 1 p p PROPN hvd.32044092008168 643 2 3 3 NUM hvd.32044092008168 643 3 pa pa PROPN hvd.32044092008168 643 4 p₁ p₁ NOUN hvd.32044092008168 643 5 = = VERB hvd.32044092008168 643 6 3p² 3p² NUM hvd.32044092008168 643 7 v v NOUN hvd.32044092008168 643 8 + + CCONJ hvd.32044092008168 643 9 $ $ SYM hvd.32044092008168 643 10 98 98 NUM hvd.32044092008168 643 11 +92 +92 NUM hvd.32044092008168 644 1 p₂ p₂ PROPN hvd.32044092008168 644 2 = = ADP hvd.32044092008168 644 3 pv pv ADV hvd.32044092008168 644 4 ; ; PUNCT hvd.32044092008168 644 5 pv pv ADP hvd.32044092008168 644 6 ; ; PUNCT hvd.32044092008168 644 7 which which DET hvd.32044092008168 644 8 values value NOUN hvd.32044092008168 644 9 reduce reduce VERB hvd.32044092008168 644 10 our our PRON hvd.32044092008168 644 11 relations relation NOUN hvd.32044092008168 644 12 to to ADP hvd.32044092008168 644 13 the the DET hvd.32044092008168 644 14 form form NOUN hvd.32044092008168 644 15 = = X hvd.32044092008168 644 16 ( ( PUNCT hvd.32044092008168 644 17 a a X hvd.32044092008168 644 18 ) ) PUNCT hvd.32044092008168 644 19 | | PROPN hvd.32044092008168 644 20 x³ x³ PROPN hvd.32044092008168 644 21 — — PUNCT hvd.32044092008168 644 22 3p(v)x 3p(v)x NUM hvd.32044092008168 644 23 — — PUNCT hvd.32044092008168 644 24 p′(v p′(v NOUN hvd.32044092008168 644 25 ) ) PUNCT hvd.32044092008168 644 26 — — PUNCT hvd.32044092008168 644 27 3lx 3lx NOUN hvd.32044092008168 644 28 — — PUNCT hvd.32044092008168 644 29 0 0 NUM hvd.32044092008168 645 1 [ [ X hvd.32044092008168 645 2 80 80 NUM hvd.32044092008168 645 3 ] ] PUNCT hvd.32044092008168 645 4 ( ( PUNCT hvd.32044092008168 645 5 b b NOUN hvd.32044092008168 645 6 ) ) PUNCT hvd.32044092008168 645 7 | | PROPN hvd.32044092008168 645 8 x¹ x¹ PROPN hvd.32044092008168 645 9 — — PUNCT hvd.32044092008168 645 10 6p(v)x² 6p(v)x² NUM hvd.32044092008168 645 11 — — PUNCT hvd.32044092008168 645 12 4p′ 4p′ NUM hvd.32044092008168 645 13 ( ( PUNCT hvd.32044092008168 645 14 v)x v)x NOUN hvd.32044092008168 645 15 — — PUNCT hvd.32044092008168 645 16 3p³ 3p³ NUM hvd.32044092008168 645 17 ( ( PUNCT hvd.32044092008168 645 18 v v NOUN hvd.32044092008168 645 19 ) ) PUNCT hvd.32044092008168 645 20 — — PUNCT hvd.32044092008168 645 21 21 21 NUM hvd.32044092008168 645 22 + + CCONJ hvd.32044092008168 645 23 2lp 2lp PROPN hvd.32044092008168 645 24 ( ( PUNCT hvd.32044092008168 645 25 v v NOUN hvd.32044092008168 645 26 ) ) PUNCT hvd.32044092008168 645 27 = = PUNCT hvd.32044092008168 645 28 = = SYM hvd.32044092008168 645 29 b2 b2 PROPN hvd.32044092008168 645 30 30 30 NUM hvd.32044092008168 645 31 h₁ h₁ PROPN hvd.32044092008168 645 32 = = PUNCT hvd.32044092008168 645 33 = = PUNCT hvd.32044092008168 645 34 ( ( PUNCT hvd.32044092008168 645 35 x² x² PROPN hvd.32044092008168 645 36 — — PUNCT hvd.32044092008168 645 37 p(v p(v PROPN hvd.32044092008168 645 38 ) ) PUNCT hvd.32044092008168 645 39 ) ) PUNCT hvd.32044092008168 645 40 , , PUNCT hvd.32044092008168 645 41 or or CCONJ hvd.32044092008168 645 42 p(v p(v PROPN hvd.32044092008168 645 43 ) ) PUNCT hvd.32044092008168 645 44 = = PROPN hvd.32044092008168 646 1 x² x² PROPN hvd.32044092008168 646 2 · · PUNCT hvd.32044092008168 646 3 2 2 NUM hvd.32044092008168 646 4 92 92 NUM hvd.32044092008168 646 5 5 5 NUM hvd.32044092008168 646 6 572 572 NUM hvd.32044092008168 646 7 3 3 NUM hvd.32044092008168 646 8 92 92 NUM hvd.32044092008168 646 9 which which PRON hvd.32044092008168 646 10 are be AUX hvd.32044092008168 646 11 reduced reduce VERB hvd.32044092008168 646 12 forms form NOUN hvd.32044092008168 646 13 of of ADP hvd.32044092008168 646 14 the the DET hvd.32044092008168 646 15 equations equation NOUN hvd.32044092008168 646 16 of of ADP hvd.32044092008168 646 17 condition condition NOUN hvd.32044092008168 646 18 that that SCONJ hvd.32044092008168 646 19 y y PROPN hvd.32044092008168 646 20 = = PUNCT hvd.32044092008168 646 21 f(x f(x PROPN hvd.32044092008168 646 22 ) ) PUNCT hvd.32044092008168 646 23 be be AUX hvd.32044092008168 646 24 a a DET hvd.32044092008168 646 25 solution solution NOUN hvd.32044092008168 646 26 in in ADP hvd.32044092008168 646 27 addition addition NOUN hvd.32044092008168 646 28 to to ADP hvd.32044092008168 646 29 which which PRON hvd.32044092008168 646 30 we we PRON hvd.32044092008168 646 31 have have VERB hvd.32044092008168 646 32 the the DET hvd.32044092008168 646 33 identity identity NOUN hvd.32044092008168 646 34 p′(v)² p′(v)² VERB hvd.32044092008168 646 35 = = VERB hvd.32044092008168 646 36 4p³(v 4p³(v NUM hvd.32044092008168 646 37 ) ) PUNCT hvd.32044092008168 646 38 — — PUNCT hvd.32044092008168 646 39 j₂p j₂p PROPN hvd.32044092008168 646 40 ( ( PUNCT hvd.32044092008168 646 41 v v NOUN hvd.32044092008168 646 42 ) ) PUNCT hvd.32044092008168 646 43 — — PUNCT hvd.32044092008168 646 44 i3 i3 NOUN hvd.32044092008168 646 45 2 2 NUM hvd.32044092008168 646 46 h₁. h₁. ADJ hvd.32044092008168 646 47 the the DET hvd.32044092008168 646 48 product product NOUN hvd.32044092008168 646 49 of of ADP hvd.32044092008168 646 50 equations equation NOUN hvd.32044092008168 646 51 ( ( PUNCT hvd.32044092008168 646 52 80 80 NUM hvd.32044092008168 646 53 ) ) PUNCT hvd.32044092008168 646 54 is be AUX hvd.32044092008168 646 55 an an DET hvd.32044092008168 646 56 equation equation NOUN hvd.32044092008168 646 57 of of ADP hvd.32044092008168 646 58 the the DET hvd.32044092008168 646 59 seventh seventh ADJ hvd.32044092008168 646 60 degree degree NOUN hvd.32044092008168 646 61 in in ADP hvd.32044092008168 646 62 x x PROPN hvd.32044092008168 646 63 the the DET hvd.32044092008168 646 64 roots root NOUN hvd.32044092008168 646 65 of of ADP hvd.32044092008168 646 66 which which PRON hvd.32044092008168 646 67 are be AUX hvd.32044092008168 646 68 functions function NOUN hvd.32044092008168 646 69 of of ADP hvd.32044092008168 646 70 v v PROPN hvd.32044092008168 646 71 and and CCONJ hvd.32044092008168 646 72 b b PROPN hvd.32044092008168 646 73 and and CCONJ hvd.32044092008168 646 74 hence hence ADV hvd.32044092008168 646 75 the the DET hvd.32044092008168 646 76 values value NOUN hvd.32044092008168 646 77 of of ADP hvd.32044092008168 646 78 b b PROPN hvd.32044092008168 646 79 that that PRON hvd.32044092008168 646 80 will will AUX hvd.32044092008168 646 81 reduce reduce VERB hvd.32044092008168 646 82 x x PROPN hvd.32044092008168 646 83 to to ADP hvd.32044092008168 646 84 zero zero NUM hvd.32044092008168 646 85 are be AUX hvd.32044092008168 646 86 in in ADP hvd.32044092008168 646 87 number number NOUN hvd.32044092008168 646 88 not not PART hvd.32044092008168 646 89 more more ADJ hvd.32044092008168 646 90 than than ADP hvd.32044092008168 646 91 seven seven NUM hvd.32044092008168 646 92 . . PUNCT hvd.32044092008168 647 1 but but CCONJ hvd.32044092008168 647 2 when when SCONJ hvd.32044092008168 647 3 x x PUNCT hvd.32044092008168 647 4 equals equal VERB hvd.32044092008168 647 5 zero zero NUM hvd.32044092008168 647 6 ( ( PUNCT hvd.32044092008168 647 7 and and CCONJ hvd.32044092008168 647 8 v v ADP hvd.32044092008168 647 9 = = PROPN hvd.32044092008168 647 10 wa wa PROPN hvd.32044092008168 647 11 ) ) PUNCT hvd.32044092008168 647 12 , , PUNCT hvd.32044092008168 647 13 y y PROPN hvd.32044092008168 647 14 is be AUX hvd.32044092008168 647 15 in in ADP hvd.32044092008168 647 16 general general ADJ hvd.32044092008168 647 17 a a DET hvd.32044092008168 647 18 doubly doubly ADV hvd.32044092008168 647 19 periodic periodic ADJ hvd.32044092008168 647 20 function function NOUN hvd.32044092008168 647 21 and and CCONJ hvd.32044092008168 647 22 the the DET hvd.32044092008168 647 23 doubly doubly ADV hvd.32044092008168 647 24 periodic periodic ADJ hvd.32044092008168 647 25 special special ADJ hvd.32044092008168 647 26 functions function NOUN hvd.32044092008168 647 27 of of ADP hvd.32044092008168 647 28 lamé lamé NOUN hvd.32044092008168 647 29 48 48 NUM hvd.32044092008168 647 30 part part NOUN hvd.32044092008168 647 31 v. v. ADV hvd.32044092008168 647 32 are be AUX hvd.32044092008168 647 33 in in ADP hvd.32044092008168 647 34 all all DET hvd.32044092008168 647 35 seven seven NUM hvd.32044092008168 647 36 in in ADP hvd.32044092008168 647 37 number number NOUN hvd.32044092008168 647 38 for for ADP hvd.32044092008168 647 39 n n NOUN hvd.32044092008168 647 40 equals equal VERB hvd.32044092008168 647 41 three three NUM hvd.32044092008168 647 42 one one NUM hvd.32044092008168 647 43 being being NOUN hvd.32044092008168 647 44 of of ADP hvd.32044092008168 647 45 the the DET hvd.32044092008168 647 46 first first ADJ hvd.32044092008168 647 47 sort sort NOUN hvd.32044092008168 647 48 and and CCONJ hvd.32044092008168 647 49 six six NUM hvd.32044092008168 647 50 of of ADP hvd.32044092008168 647 51 the the DET hvd.32044092008168 647 52 second second ADJ hvd.32044092008168 647 53 . . PUNCT hvd.32044092008168 648 1 it it PRON hvd.32044092008168 648 2 follows follow VERB hvd.32044092008168 648 3 then then ADV hvd.32044092008168 648 4 that that SCONJ hvd.32044092008168 648 5 by by ADP hvd.32044092008168 648 6 elliminating elliminate VERB hvd.32044092008168 648 7 p(v p(v PROPN hvd.32044092008168 648 8 ) ) PUNCT hvd.32044092008168 648 9 and and CCONJ hvd.32044092008168 648 10 p´(v p´(v PROPN hvd.32044092008168 648 11 ) ) PUNCT hvd.32044092008168 648 12 , , PUNCT hvd.32044092008168 648 13 we we PRON hvd.32044092008168 648 14 should should AUX hvd.32044092008168 648 15 obtain obtain VERB hvd.32044092008168 648 16 x x PUNCT hvd.32044092008168 648 17 as as ADP hvd.32044092008168 648 18 a a DET hvd.32044092008168 648 19 function function NOUN hvd.32044092008168 648 20 of of ADP hvd.32044092008168 648 21 where where SCONJ hvd.32044092008168 648 22 is be AUX hvd.32044092008168 648 23 a a DET hvd.32044092008168 648 24 function function NOUN hvd.32044092008168 648 25 of of ADP hvd.32044092008168 648 26 b b NOUN hvd.32044092008168 648 27 the the DET hvd.32044092008168 648 28 vanishing vanishing NOUN hvd.32044092008168 648 29 of of ADP hvd.32044092008168 648 30 which which PRON hvd.32044092008168 648 31 will will AUX hvd.32044092008168 648 32 be be AUX hvd.32044092008168 648 33 the the DET hvd.32044092008168 648 34 condition condition NOUN hvd.32044092008168 648 35 for for ADP hvd.32044092008168 648 36 the the DET hvd.32044092008168 648 37 special special ADJ hvd.32044092008168 648 38 functions function NOUN hvd.32044092008168 648 39 of of ADP hvd.32044092008168 648 40 lamé lamé NOUN hvd.32044092008168 648 41 . . PUNCT hvd.32044092008168 649 1 this this DET hvd.32044092008168 649 2 complicated complicated ADJ hvd.32044092008168 649 3 ellimination ellimination NOUN hvd.32044092008168 649 4 , , PUNCT hvd.32044092008168 649 5 suggesting suggest VERB hvd.32044092008168 649 6 the the DET hvd.32044092008168 649 7 practical practical ADJ hvd.32044092008168 649 8 uselesness uselesness NOUN hvd.32044092008168 649 9 of of ADP hvd.32044092008168 649 10 this this DET hvd.32044092008168 649 11 method method NOUN hvd.32044092008168 649 12 for for ADP hvd.32044092008168 649 13 any any DET hvd.32044092008168 649 14 higher high ADJ hvd.32044092008168 649 15 value value NOUN hvd.32044092008168 649 16 of of ADP hvd.32044092008168 649 17 n n CCONJ hvd.32044092008168 649 18 is be AUX hvd.32044092008168 649 19 performed perform VERB hvd.32044092008168 649 20 as as SCONJ hvd.32044092008168 649 21 follows follow NOUN hvd.32044092008168 649 22 . . PUNCT hvd.32044092008168 650 1 multiplying multiply VERB hvd.32044092008168 650 2 the the DET hvd.32044092008168 650 3 first first ADJ hvd.32044092008168 650 4 equation equation NOUN hvd.32044092008168 650 5 by by ADP hvd.32044092008168 650 6 four four NUM hvd.32044092008168 650 7 and and CCONJ hvd.32044092008168 650 8 subtracting subtract VERB hvd.32044092008168 650 9 we we PRON hvd.32044092008168 650 10 obtain obtain VERB hvd.32044092008168 650 11 3x4 3x4 NUM hvd.32044092008168 650 12 - - PUNCT hvd.32044092008168 650 13 6p(v 6p(v NUM hvd.32044092008168 650 14 ) ) PUNCT hvd.32044092008168 650 15 x²-101x2 x²-101x2 PROPN hvd.32044092008168 650 16 2lp(v 2lp(v NUM hvd.32044092008168 650 17 ) ) PUNCT hvd.32044092008168 651 1 + + NUM hvd.32044092008168 651 2 3p³ 3p³ NUM hvd.32044092008168 651 3 ( ( PUNCT hvd.32044092008168 651 4 v v NOUN hvd.32044092008168 651 5 ) ) PUNCT hvd.32044092008168 651 6 = = NOUN hvd.32044092008168 651 7 +92 +92 VERB hvd.32044092008168 651 8 whence whence SCONJ hvd.32044092008168 651 9 the the DET hvd.32044092008168 651 10 relation relation NOUN hvd.32044092008168 651 11 gives give VERB hvd.32044092008168 651 12 ( ( PUNCT hvd.32044092008168 651 13 c c NOUN hvd.32044092008168 651 14 ) ) PUNCT hvd.32044092008168 651 15 p(v p(v PROPN hvd.32044092008168 651 16 ) ) PUNCT hvd.32044092008168 652 1 = = PROPN hvd.32044092008168 652 2 = = PROPN hvd.32044092008168 652 3 x² x² PROPN hvd.32044092008168 652 4 or or CCONJ hvd.32044092008168 652 5 2 2 NUM hvd.32044092008168 652 6 h₁ h₁ NOUN hvd.32044092008168 652 7 2 2 NUM hvd.32044092008168 652 8 36 36 NUM hvd.32044092008168 652 9 hi-36bx² hi-36bx² PROPN hvd.32044092008168 652 10 + + CCONJ hvd.32044092008168 652 11 121 121 NUM hvd.32044092008168 652 12 h h NOUN hvd.32044092008168 652 13 , , PUNCT hvd.32044092008168 652 14 + + NUM hvd.32044092008168 652 15 512 512 NUM hvd.32044092008168 652 16 — — PUNCT hvd.32044092008168 652 17 again again ADV hvd.32044092008168 652 18 from from ADP hvd.32044092008168 652 19 ( ( PUNCT hvd.32044092008168 652 20 b b NOUN hvd.32044092008168 652 21 ) ) PUNCT hvd.32044092008168 652 22 and and CCONJ hvd.32044092008168 652 23 the the DET hvd.32044092008168 652 24 identity identity NOUN hvd.32044092008168 652 25 p p NOUN hvd.32044092008168 652 26 ' ' PUNCT hvd.32044092008168 652 27 ( ( PUNCT hvd.32044092008168 652 28 v)² v)² ADJ hvd.32044092008168 652 29 = = SYM hvd.32044092008168 652 30 ( ( PUNCT hvd.32044092008168 652 31 3bx+3p(v 3bx+3p(v NUM hvd.32044092008168 652 32 ) ) PUNCT hvd.32044092008168 652 33 x x PUNCT hvd.32044092008168 653 1 − − PROPN hvd.32044092008168 653 2 x³)²=9b²x²+9p² x³)²=9b²x²+9p² PROPN hvd.32044092008168 653 3 ( ( PUNCT hvd.32044092008168 653 4 v v NOUN hvd.32044092008168 653 5 ) ) PUNCT hvd.32044092008168 653 6 x²+x6 x²+x6 PROPN hvd.32044092008168 653 7 + + NUM hvd.32044092008168 653 8 18bp(v)x² 18bp(v)x² NUM hvd.32044092008168 653 9 -6bx¹ -6bx¹ PROPN hvd.32044092008168 653 10 6p(v)x4 6p(v)x4 PROPN hvd.32044092008168 653 11 3g₂ 3g₂ NUM hvd.32044092008168 653 12 = = SYM hvd.32044092008168 653 13 0 0 NUM hvd.32044092008168 653 14 . . PUNCT hvd.32044092008168 653 15 = = PROPN hvd.32044092008168 653 16 96²x²+9x²(x² 96²x²+9x²(x² NUM hvd.32044092008168 653 17 4x² 4x² NUM hvd.32044092008168 653 18 h h NOUN hvd.32044092008168 653 19 , , PUNCT hvd.32044092008168 653 20 +4h₁ +4h₁ SPACE hvd.32044092008168 653 21 ) ) PUNCT hvd.32044092008168 654 1 + + CCONJ hvd.32044092008168 654 2 x x PUNCT hvd.32044092008168 655 1 + + NUM hvd.32044092008168 655 2 18bx² 18bx² NUM hvd.32044092008168 655 3 ( ( PUNCT hvd.32044092008168 655 4 x² x² PROPN hvd.32044092008168 655 5 2 2 NUM hvd.32044092008168 655 6 h₁ h₁ PROPN hvd.32044092008168 655 7 ) ) PUNCT hvd.32044092008168 655 8 -6bx46x4 -6bx46x4 PROPN hvd.32044092008168 656 1 ( ( PUNCT hvd.32044092008168 656 2 x² x² PROPN hvd.32044092008168 656 3 2 2 NUM hvd.32044092008168 656 4 h₁ h₁ PROPN hvd.32044092008168 656 5 ) ) PUNCT hvd.32044092008168 656 6 = = PUNCT hvd.32044092008168 656 7 — — PUNCT hvd.32044092008168 656 8 4(x6 4(x6 NUM hvd.32044092008168 656 9 — — PUNCT hvd.32044092008168 656 10 6x¹h 6x¹h NUM hvd.32044092008168 656 11 , , PUNCT hvd.32044092008168 656 12 + + NUM hvd.32044092008168 656 13 12x² 12x² NUM hvd.32044092008168 656 14 h h NOUN hvd.32044092008168 656 15 — — PUNCT hvd.32044092008168 656 16 8h³ 8h³ NUM hvd.32044092008168 656 17 ) ) PUNCT hvd.32044092008168 656 18 — — PUNCT hvd.32044092008168 656 19 9₂ 9₂ NUM hvd.32044092008168 656 20 ( ( PUNCT hvd.32044092008168 656 21 x² x² PROPN hvd.32044092008168 656 22 2 2 NUM hvd.32044092008168 656 23 h h NOUN hvd.32044092008168 656 24 ) ) PUNCT hvd.32044092008168 656 25 — — PUNCT hvd.32044092008168 656 26 93 93 NUM hvd.32044092008168 656 27 -or -or NOUN hvd.32044092008168 656 28 multiplying multiply VERB hvd.32044092008168 656 29 by by ADP hvd.32044092008168 656 30 9 9 NUM hvd.32044092008168 656 31 1 1 NUM hvd.32044092008168 656 32 ( ( PUNCT hvd.32044092008168 656 33 d d NOUN hvd.32044092008168 656 34 ) ) PUNCT hvd.32044092008168 656 35 817²x² 817²x² NUM hvd.32044092008168 656 36 108x² 108x² NUM hvd.32044092008168 656 37 hi+ hi+ PROPN hvd.32044092008168 656 38 1087x¹ 1087x¹ NUM hvd.32044092008168 656 39 — — PUNCT hvd.32044092008168 657 1 9 9 NUM hvd.32044092008168 657 2 . . SYM hvd.32044092008168 657 3 361 361 NUM hvd.32044092008168 657 4 h₁x²+9 h₁x²+9 NOUN hvd.32044092008168 657 5 · · PUNCT hvd.32044092008168 657 6 32 32 NUM hvd.32044092008168 657 7 hi hi INTJ hvd.32044092008168 657 8 +992x²-1892 +992x²-1892 NOUN hvd.32044092008168 657 9 h₁ h₁ VERB hvd.32044092008168 657 10 +993 +993 X hvd.32044092008168 657 11 0 0 NUM hvd.32044092008168 657 12 . . PUNCT hvd.32044092008168 657 13 from from ADP hvd.32044092008168 657 14 ( ( PUNCT hvd.32044092008168 657 15 a a NOUN hvd.32044092008168 657 16 ) ) PUNCT hvd.32044092008168 657 17 , , PUNCT hvd.32044092008168 657 18 ( ( PUNCT hvd.32044092008168 657 19 b b NOUN hvd.32044092008168 657 20 ) ) PUNCT hvd.32044092008168 657 21 and and CCONJ hvd.32044092008168 657 22 the the DET hvd.32044092008168 657 23 value value NOUN hvd.32044092008168 657 24 for for ADP hvd.32044092008168 657 25 p(v p(v NOUN hvd.32044092008168 657 26 ) ) PUNCT hvd.32044092008168 657 27 x¹ x¹ PROPN hvd.32044092008168 657 28 — — PUNCT hvd.32044092008168 657 29 — — PUNCT hvd.32044092008168 657 30 6 6 NUM hvd.32044092008168 657 31 x² x² PROPN hvd.32044092008168 657 32 ( ( PUNCT hvd.32044092008168 657 33 x² x² PROPN hvd.32044092008168 657 34 — — PUNCT hvd.32044092008168 657 35 2 2 NUM hvd.32044092008168 657 36 h₁ h₁ PROPN hvd.32044092008168 657 37 ) ) PUNCT hvd.32044092008168 657 38 — — PUNCT hvd.32044092008168 657 39 4 4 NUM hvd.32044092008168 657 40 x x SYM hvd.32044092008168 657 41 ( ( PUNCT hvd.32044092008168 657 42 x³ x³ PROPN hvd.32044092008168 657 43 — — PUNCT hvd.32044092008168 657 44 3 3 NUM hvd.32044092008168 657 45 p(v p(v PROPN hvd.32044092008168 657 46 ) ) PUNCT hvd.32044092008168 657 47 x x PUNCT hvd.32044092008168 657 48 − − PROPN hvd.32044092008168 658 1 3 3 NUM hvd.32044092008168 658 2 b b NOUN hvd.32044092008168 658 3 x x NUM hvd.32044092008168 658 4 ) ) PUNCT hvd.32044092008168 658 5 — — PUNCT hvd.32044092008168 658 6 3 3 NUM hvd.32044092008168 658 7 ( ( PUNCT hvd.32044092008168 658 8 x² x² PROPN hvd.32044092008168 658 9 4x² 4x² NUM hvd.32044092008168 658 10 h₁+4h h₁+4h PROPN hvd.32044092008168 658 11 ;) ;) PUNCT hvd.32044092008168 659 1 21x² 21x² NUM hvd.32044092008168 659 2 + + NUM hvd.32044092008168 659 3 21(x² 21(x² NUM hvd.32044092008168 659 4 − − NOUN hvd.32044092008168 659 5 2 2 NUM hvd.32044092008168 659 6 h h NOUN hvd.32044092008168 659 7 ‚ ‚ NUM hvd.32044092008168 659 8 ) ) PUNCT hvd.32044092008168 659 9 — — PUNCT hvd.32044092008168 659 10 377312 377312 NUM hvd.32044092008168 659 11 3 3 NUM hvd.32044092008168 659 12 92 92 NUM hvd.32044092008168 659 13 572 572 NUM hvd.32044092008168 659 14 3 3 NUM hvd.32044092008168 659 15 ― ― NOUN hvd.32044092008168 659 16 ( ( PUNCT hvd.32044092008168 659 17 e e NOUN hvd.32044092008168 659 18 ) ) PUNCT hvd.32044092008168 659 19 12lx² 12lx² NUM hvd.32044092008168 659 20 12h 12h PROPN hvd.32044092008168 659 21 , , PUNCT hvd.32044092008168 659 22 4b 4b PROPN hvd.32044092008168 659 23 h₁ h₁ VERB hvd.32044092008168 659 24 572 572 NUM hvd.32044092008168 659 25 3 3 NUM hvd.32044092008168 659 26 and and CCONJ hvd.32044092008168 659 27 multiplying multiply VERB hvd.32044092008168 659 28 ( ( PUNCT hvd.32044092008168 659 29 e e NOUN hvd.32044092008168 659 30 ) ) PUNCT hvd.32044092008168 659 31 by by ADP hvd.32044092008168 659 32 3 3 NUM hvd.32044092008168 659 33 and and CCONJ hvd.32044092008168 659 34 8h₁ 8h₁ NUM hvd.32044092008168 659 35 it it PRON hvd.32044092008168 659 36 becomes become VERB hvd.32044092008168 659 37 ( ( PUNCT hvd.32044092008168 659 38 f f X hvd.32044092008168 659 39 ) ) PUNCT hvd.32044092008168 659 40 36.81x2h 36.81x2h NUM hvd.32044092008168 659 41 , , PUNCT hvd.32044092008168 659 42 368h961h4012 368h961h4012 PROPN hvd.32044092008168 659 43 h₁-24 h₁-24 NOUN hvd.32044092008168 659 44 g g PROPN hvd.32044092008168 659 45 , , PUNCT hvd.32044092008168 659 46 h₁ h₁ PROPN hvd.32044092008168 659 47 = = SYM hvd.32044092008168 659 48 92 92 NUM hvd.32044092008168 659 49 whence whence ADV hvd.32044092008168 659 50 from from ADP hvd.32044092008168 659 51 ( ( PUNCT hvd.32044092008168 659 52 c c NOUN hvd.32044092008168 659 53 ) ) PUNCT hvd.32044092008168 659 54 eliminating eliminate VERB hvd.32044092008168 659 55 hi hi INTJ hvd.32044092008168 659 56 ―――――――― ―――――――― PROPN hvd.32044092008168 659 57 993 993 NUM hvd.32044092008168 659 58 . . PUNCT hvd.32044092008168 660 1 ( ( PUNCT hvd.32044092008168 660 2 g g NOUN hvd.32044092008168 660 3 ) ) PUNCT hvd.32044092008168 660 4 817²x² 817²x² NUM hvd.32044092008168 661 1 108a2h+ 108a2h+ NUM hvd.32044092008168 661 2 1081 1081 NUM hvd.32044092008168 661 3 - - PUNCT hvd.32044092008168 661 4 361h 361h PROPN hvd.32044092008168 661 5 , , PUNCT hvd.32044092008168 661 6 x²-961 x²-961 PROPN hvd.32044092008168 661 7 h h PROPN hvd.32044092008168 661 8 } } PUNCT hvd.32044092008168 661 9 = = VERB hvd.32044092008168 661 10 401² 401² NUM hvd.32044092008168 661 11 h₁ h₁ PROPN hvd.32044092008168 661 12 -69 -69 NUM hvd.32044092008168 661 13 , , PUNCT hvd.32044092008168 661 14 h₁ h₁ NOUN hvd.32044092008168 661 15 992x² 992x² NUM hvd.32044092008168 661 16 reduction reduction NOUN hvd.32044092008168 661 17 of of ADP hvd.32044092008168 661 18 the the DET hvd.32044092008168 661 19 forms form NOUN hvd.32044092008168 661 20 when when SCONJ hvd.32044092008168 661 21 n n SYM hvd.32044092008168 661 22 equals equal VERB hvd.32044092008168 661 23 three three NUM hvd.32044092008168 661 24 . . PUNCT hvd.32044092008168 661 25 49 49 NUM hvd.32044092008168 662 1 whence whence NOUN hvd.32044092008168 662 2 a a DET hvd.32044092008168 662 3 further further ADJ hvd.32044092008168 662 4 combination combination NOUN hvd.32044092008168 662 5 with with ADP hvd.32044092008168 662 6 ( ( PUNCT hvd.32044092008168 662 7 c c NOUN hvd.32044092008168 662 8 ) ) PUNCT hvd.32044092008168 662 9 gives give VERB hvd.32044092008168 662 10 ( ( PUNCT hvd.32044092008168 662 11 h h PROPN hvd.32044092008168 662 12 ) ) PUNCT hvd.32044092008168 662 13 721²x² 721²x² NUM hvd.32044092008168 663 1 721h 721h PROPN hvd.32044092008168 663 2 321 321 NUM hvd.32044092008168 663 3 h₂+ h₂+ SYM hvd.32044092008168 663 4 6g₂h₁ 6g₂h₁ NUM hvd.32044092008168 663 5 + + NUM hvd.32044092008168 663 6 1073 1073 NUM hvd.32044092008168 663 7 3 3 NUM hvd.32044092008168 663 8 and and CCONJ hvd.32044092008168 663 9 again again ADV hvd.32044092008168 663 10 ( ( PUNCT hvd.32044092008168 663 11 i i NOUN hvd.32044092008168 663 12 ) ) PUNCT hvd.32044092008168 663 13 whence whence NOUN hvd.32044092008168 663 14 [ [ X hvd.32044092008168 663 15 81 81 NUM hvd.32044092008168 663 16 ] ] PUNCT hvd.32044092008168 663 17 · · PUNCT hvd.32044092008168 663 18 where where SCONJ hvd.32044092008168 663 19 [ [ X hvd.32044092008168 663 20 82 82 NUM hvd.32044092008168 663 21 ] ] PUNCT hvd.32044092008168 663 22 · · PUNCT hvd.32044092008168 663 23 where where SCONJ hvd.32044092008168 663 24 φ(0 φ(0 SPACE hvd.32044092008168 663 25 ) ) PUNCT hvd.32044092008168 663 26 = = PUNCT hvd.32044092008168 663 27 • • NUM hvd.32044092008168 663 28 812 812 NUM hvd.32044092008168 663 29 h₁ h₁ NOUN hvd.32044092008168 663 30 392 392 NUM hvd.32044092008168 663 31 = = NOUN hvd.32044092008168 663 32 a₁ a₁ NOUN hvd.32044092008168 663 33 = = SYM hvd.32044092008168 663 34 3 3 NUM hvd.32044092008168 663 35 9 9 NUM hvd.32044092008168 663 36 2 2 NUM hvd.32044092008168 663 37 — — PUNCT hvd.32044092008168 663 38 4 4 NUM hvd.32044092008168 663 39 ―― ―― PROPN hvd.32044092008168 663 40 φ(0 φ(0 SPACE hvd.32044092008168 663 41 ) ) PUNCT hvd.32044092008168 663 42 sd2 sd2 X hvd.32044092008168 663 43 12576 12576 NUM hvd.32044092008168 663 44 69½ 69½ NUM hvd.32044092008168 663 45 h₁ h₁ PROPN hvd.32044092008168 663 46 a₁ a₁ PROPN hvd.32044092008168 663 47 h₁ h₁ PROPN hvd.32044092008168 664 1 = = NOUN hvd.32044092008168 665 1 = = PUNCT hvd.32044092008168 665 2 392 392 NUM hvd.32044092008168 665 3 4 4 NUM hvd.32044092008168 665 4 210 210 NUM hvd.32044092008168 665 5 a₁ a₁ PROPN hvd.32044092008168 665 6 74 74 NUM hvd.32044092008168 665 7 -210a -210a NOUN hvd.32044092008168 665 8 , , PUNCT hvd.32044092008168 665 9 14 14 NUM hvd.32044092008168 665 10 ― ― NOUN hvd.32044092008168 665 11 d d NOUN hvd.32044092008168 665 12 4073 4073 NUM hvd.32044092008168 665 13 27 27 NUM hvd.32044092008168 665 14 107³ 107³ NUM hvd.32044092008168 665 15 — — PUNCT hvd.32044092008168 665 16 67g½ 67g½ NUM hvd.32044092008168 665 17 + + NUM hvd.32044092008168 665 18 93 93 NUM hvd.32044092008168 665 19 1 1 NUM hvd.32044092008168 665 20 4 4 NUM hvd.32044092008168 665 21 1073 1073 NUM hvd.32044092008168 665 22 and and CCONJ hvd.32044092008168 665 23 b₁ b₁ PROPN hvd.32044092008168 665 24 from from ADP hvd.32044092008168 665 25 this this DET hvd.32044092008168 665 26 value value NOUN hvd.32044092008168 665 27 of of ADP hvd.32044092008168 665 28 h₁ h₁ PROPN hvd.32044092008168 665 29 we we PRON hvd.32044092008168 665 30 have have VERB hvd.32044092008168 665 31 by by ADP hvd.32044092008168 665 32 substituting substitute VERB hvd.32044092008168 665 33 in in ADP hvd.32044092008168 665 34 ( ( PUNCT hvd.32044092008168 665 35 c c NOUN hvd.32044092008168 665 36 ) ) PUNCT hvd.32044092008168 665 37 1 1 NUM hvd.32044092008168 665 38 12576 12576 NUM hvd.32044092008168 665 39 x² x² PROPN hvd.32044092008168 666 1 22b¸ 22b¸ NUM hvd.32044092008168 666 2 1³ 1³ NUM hvd.32044092008168 666 3 † † NOUN hvd.32044092008168 666 4 93 93 NUM hvd.32044092008168 666 5 a a PRON hvd.32044092008168 666 6 } } PUNCT hvd.32044092008168 666 7 1² 1² NUM hvd.32044092008168 666 8 + + NUM hvd.32044092008168 666 9 18 18 NUM hvd.32044092008168 666 10 a a DET hvd.32044092008168 666 11 , , PUNCT hvd.32044092008168 666 12 b₁l b₁l ADJ hvd.32044092008168 666 13 + + CCONJ hvd.32044092008168 666 14 b² b² PROPN hvd.32044092008168 666 15 — — PUNCT hvd.32044092008168 666 16 4a³ 4a³ NUM hvd.32044092008168 666 17 361(1a 361(1a NUM hvd.32044092008168 666 18 ) ) PUNCT hvd.32044092008168 666 19 2 2 NUM hvd.32044092008168 666 20 s=361 s=361 NOUN hvd.32044092008168 666 21 , , PUNCT hvd.32044092008168 666 22 1 1 NUM hvd.32044092008168 666 23 1 1 NUM hvd.32044092008168 666 24 ( ( PUNCT hvd.32044092008168 666 25 1 1 NUM hvd.32044092008168 666 26 — — PUNCT hvd.32044092008168 666 27 k² k² PROPN hvd.32044092008168 666 28 + + CCONJ hvd.32044092008168 666 29 k´¹ k´¹ PROPN hvd.32044092008168 666 30 ) ) PUNCT hvd.32044092008168 666 31 ; ; PUNCT hvd.32044092008168 666 32 b₁ b₁ PROPN hvd.32044092008168 666 33 = = PROPN hvd.32044092008168 666 34 ( ( PUNCT hvd.32044092008168 666 35 1 1 NUM hvd.32044092008168 666 36 22 22 NUM hvd.32044092008168 666 37 = = SYM hvd.32044092008168 666 38 3 3 NUM hvd.32044092008168 666 39 — — PUNCT hvd.32044092008168 666 40 6 6 NUM hvd.32044092008168 666 41 ( ( PUNCT hvd.32044092008168 666 42 12 12 NUM hvd.32044092008168 666 43 — — PUNCT hvd.32044092008168 666 44 11 11 NUM hvd.32044092008168 666 45 92 92 NUM hvd.32044092008168 666 46 ) ) PUNCT hvd.32044092008168 666 47 4 4 NUM hvd.32044092008168 666 48 6 6 NUM hvd.32044092008168 666 49 ( ( PUNCT hvd.32044092008168 666 50 12 12 NUM hvd.32044092008168 666 51 4(a)(11739a 4(a)(11739a NUM hvd.32044092008168 666 52 , , PUNCT hvd.32044092008168 666 53 l l NOUN hvd.32044092008168 666 54 b₁)² b₁)² PROPN hvd.32044092008168 666 55 361 361 NUM hvd.32044092008168 666 56 ( ( PUNCT hvd.32044092008168 666 57 12 12 NUM hvd.32044092008168 666 58 a₁)2 a₁)2 DET hvd.32044092008168 666 59 ι ι PROPN hvd.32044092008168 666 60 993 993 NUM hvd.32044092008168 666 61 +8lg₂ +8lg₂ PROPN hvd.32044092008168 666 62 = = PUNCT hvd.32044092008168 666 63 0 0 NUM hvd.32044092008168 666 64 . . PROPN hvd.32044092008168 666 65 8 8 NUM hvd.32044092008168 666 66 al al PROPN hvd.32044092008168 666 67 a₁ a₁ PROPN hvd.32044092008168 666 68 ) ) PUNCT hvd.32044092008168 666 69 1 1 NUM hvd.32044092008168 666 70 by by ADP hvd.32044092008168 666 71 226,1 226,1 NUM hvd.32044092008168 666 72 +93 +93 NOUN hvd.32044092008168 666 73 a a DET hvd.32044092008168 666 74 12 12 NUM hvd.32044092008168 666 75 + + NUM hvd.32044092008168 666 76 18ab₁l 18ab₁l NUM hvd.32044092008168 666 77 + + NUM hvd.32044092008168 666 78 b² b² PROPN hvd.32044092008168 666 79 4a³ 4a³ NUM hvd.32044092008168 666 80 ( ( PUNCT hvd.32044092008168 666 81 1² 1² NUM hvd.32044092008168 666 82 — — PUNCT hvd.32044092008168 666 83 a₁ a₁ NOUN hvd.32044092008168 666 84 ) ) PUNCT hvd.32044092008168 666 85 , , PUNCT hvd.32044092008168 666 86 l l PROPN hvd.32044092008168 666 87 = = VERB hvd.32044092008168 666 88 b₁ b₁ PROPN hvd.32044092008168 666 89 27 27 NUM hvd.32044092008168 666 90 493 493 NUM hvd.32044092008168 666 91 . . PUNCT hvd.32044092008168 667 1 1 1 NUM hvd.32044092008168 667 2 23 23 NUM hvd.32044092008168 667 3 +9g3 +9g3 SPACE hvd.32044092008168 667 4 - - NOUN hvd.32044092008168 667 5 21g2 21g2 NUM hvd.32044092008168 667 6 − − NOUN hvd.32044092008168 667 7 = = SYM hvd.32044092008168 667 8 b b PROPN hvd.32044092008168 667 9 5 5 NUM hvd.32044092008168 667 10 27 27 NUM hvd.32044092008168 667 11 4 4 NUM hvd.32044092008168 667 12 93 93 NUM hvd.32044092008168 667 13 ( ( PUNCT hvd.32044092008168 667 14 1+k² 1+k² PROPN hvd.32044092008168 667 15 ) ) PUNCT hvd.32044092008168 667 16 ( ( PUNCT hvd.32044092008168 667 17 2 2 NUM hvd.32044092008168 667 18 — — PUNCT hvd.32044092008168 667 19 k² k² PROPN hvd.32044092008168 667 20 ) ) PUNCT hvd.32044092008168 667 21 ( ( PUNCT hvd.32044092008168 667 22 1—2k² 1—2k² NUM hvd.32044092008168 667 23 ) ) PUNCT hvd.32044092008168 667 24 . . PUNCT hvd.32044092008168 668 1 * * PUNCT hvd.32044092008168 668 2 ) ) PUNCT hvd.32044092008168 668 3 = = PUNCT hvd.32044092008168 668 4 = = PUNCT hvd.32044092008168 668 5 = = X hvd.32044092008168 668 6 þ(1 þ(1 ADJ hvd.32044092008168 668 7 ) ) PUNCT hvd.32044092008168 668 8 o o NOUN hvd.32044092008168 668 9 is be AUX hvd.32044092008168 668 10 then then ADV hvd.32044092008168 668 11 the the DET hvd.32044092008168 668 12 condition condition NOUN hvd.32044092008168 668 13 for for ADP hvd.32044092008168 668 14 the the DET hvd.32044092008168 668 15 existence existence NOUN hvd.32044092008168 668 16 of of ADP hvd.32044092008168 668 17 the the DET hvd.32044092008168 668 18 special special ADJ hvd.32044092008168 668 19 functions function NOUN hvd.32044092008168 668 20 of of ADP hvd.32044092008168 668 21 lamé lamé NOUN hvd.32044092008168 668 22 the the DET hvd.32044092008168 668 23 seventh seventh ADJ hvd.32044092008168 668 24 value value NOUN hvd.32044092008168 668 25 of of ADP hvd.32044092008168 668 26 b b PRON hvd.32044092008168 668 27 , , PUNCT hvd.32044092008168 668 28 as as SCONJ hvd.32044092008168 668 29 we we PRON hvd.32044092008168 668 30 have have AUX hvd.32044092008168 668 31 already already ADV hvd.32044092008168 668 32 seen see VERB hvd.32044092008168 668 33 ( ( PUNCT hvd.32044092008168 668 34 p. p. NOUN hvd.32044092008168 668 35 43 43 NUM hvd.32044092008168 668 36 ) ) PUNCT hvd.32044092008168 668 37 , , PUNCT hvd.32044092008168 668 38 being be AUX hvd.32044092008168 668 39 b b ADP hvd.32044092008168 668 40 = = NOUN hvd.32044092008168 668 41 0 0 NUM hvd.32044092008168 668 42 . . PUNCT hvd.32044092008168 669 1 ( ( PUNCT hvd.32044092008168 669 2 1 1 X hvd.32044092008168 669 3 ) ) PUNCT hvd.32044092008168 669 4 must must AUX hvd.32044092008168 669 5 then then ADV hvd.32044092008168 669 6 be be AUX hvd.32044092008168 669 7 q(7 q(7 PROPN hvd.32044092008168 669 8 ) ) PUNCT hvd.32044092008168 669 9 times time NOUN hvd.32044092008168 669 10 a a DET hvd.32044092008168 669 11 constant constant ADJ hvd.32044092008168 669 12 and and CCONJ hvd.32044092008168 669 13 as as SCONJ hvd.32044092008168 669 14 we we PRON hvd.32044092008168 669 15 have have AUX hvd.32044092008168 669 16 seen see VERB hvd.32044092008168 669 17 that that PRON hvd.32044092008168 669 18 is be AUX hvd.32044092008168 669 19 separable separable ADJ hvd.32044092008168 669 20 into into ADP hvd.32044092008168 669 21 three three NUM hvd.32044092008168 669 22 factors factor NOUN hvd.32044092008168 669 23 of of ADP hvd.32044092008168 669 24 the the DET hvd.32044092008168 669 25 second second ADJ hvd.32044092008168 669 26 degree degree NOUN hvd.32044092008168 669 27 it it PRON hvd.32044092008168 669 28 follows follow VERB hvd.32044092008168 669 29 that that SCONJ hvd.32044092008168 669 30 ( ( PUNCT hvd.32044092008168 669 31 1 1 X hvd.32044092008168 669 32 ) ) PUNCT hvd.32044092008168 669 33 is be AUX hvd.32044092008168 669 34 a a DET hvd.32044092008168 669 35 reducable reducable ADJ hvd.32044092008168 669 36 equation equation NOUN hvd.32044092008168 669 37 of of ADP hvd.32044092008168 669 38 the the DET hvd.32044092008168 669 39 sixth sixth ADJ hvd.32044092008168 669 40 degree degree NOUN hvd.32044092008168 669 41 . . PUNCT hvd.32044092008168 670 1 * * PUNCT hvd.32044092008168 670 2 * * PUNCT hvd.32044092008168 670 3 ) ) PUNCT hvd.32044092008168 670 4 moreover moreover ADV hvd.32044092008168 670 5 if if SCONJ hvd.32044092008168 670 6 we we PRON hvd.32044092008168 670 7 make make VERB hvd.32044092008168 670 8 the the DET hvd.32044092008168 670 9 transformation transformation NOUN hvd.32044092008168 670 10 3b 3b INTJ hvd.32044092008168 670 11 = = SYM hvd.32044092008168 670 12 0 0 PUNCT hvd.32044092008168 670 13 * * PUNCT hvd.32044092008168 670 14 ) ) PUNCT hvd.32044092008168 671 1 the the DET hvd.32044092008168 671 2 expressions expression NOUN hvd.32044092008168 671 3 used use VERB hvd.32044092008168 671 4 here here ADV hvd.32044092008168 671 5 are be AUX hvd.32044092008168 671 6 essentially essentially ADV hvd.32044092008168 671 7 the the DET hvd.32044092008168 671 8 same same ADJ hvd.32044092008168 671 9 as as ADP hvd.32044092008168 671 10 those those PRON hvd.32044092008168 671 11 of of ADP hvd.32044092008168 671 12 m. m. NOUN hvd.32044092008168 671 13 hermite hermite NOUN hvd.32044092008168 671 14 in in ADP hvd.32044092008168 671 15 his his PRON hvd.32044092008168 671 16 celebrated celebrated ADJ hvd.32044092008168 671 17 memoir memoir PROPN hvd.32044092008168 671 18 . . PUNCT hvd.32044092008168 672 1 the the DET hvd.32044092008168 672 2 following follow VERB hvd.32044092008168 672 3 reduction reduction NOUN hvd.32044092008168 672 4 of of ADP hvd.32044092008168 672 5 the the DET hvd.32044092008168 672 6 function function NOUN hvd.32044092008168 672 7 ( ( PUNCT hvd.32044092008168 672 8 ) ) PUNCT hvd.32044092008168 672 9 is be AUX hvd.32044092008168 672 10 also also ADV hvd.32044092008168 672 11 indicated indicate VERB hvd.32044092008168 672 12 by by ADP hvd.32044092008168 672 13 hermite hermite NOUN hvd.32044092008168 672 14 . . PUNCT hvd.32044092008168 673 1 * * PUNCT hvd.32044092008168 673 2 * * PUNCT hvd.32044092008168 673 3 ) ) PUNCT hvd.32044092008168 673 4 it it PRON hvd.32044092008168 673 5 is be AUX hvd.32044092008168 673 6 interesting interesting ADJ hvd.32044092008168 673 7 to to PART hvd.32044092008168 673 8 note note VERB hvd.32044092008168 673 9 that that SCONJ hvd.32044092008168 673 10 it it PRON hvd.32044092008168 673 11 is be AUX hvd.32044092008168 673 12 not not PART hvd.32044092008168 673 13 given give VERB hvd.32044092008168 673 14 under under ADP hvd.32044092008168 673 15 the the DET hvd.32044092008168 673 16 head head NOUN hvd.32044092008168 673 17 of of ADP hvd.32044092008168 673 18 reducable reducable ADJ hvd.32044092008168 673 19 forms form NOUN hvd.32044092008168 673 20 of of ADP hvd.32044092008168 673 21 the the DET hvd.32044092008168 673 22 sixth sixth ADJ hvd.32044092008168 673 23 degree degree NOUN hvd.32044092008168 673 24 by by ADP hvd.32044092008168 673 25 either either DET hvd.32044092008168 673 26 clebsch clebsch PROPN hvd.32044092008168 673 27 or or CCONJ hvd.32044092008168 673 28 gordan gordan PROPN hvd.32044092008168 673 29 . . PUNCT hvd.32044092008168 674 1 4 4 NUM hvd.32044092008168 674 2 50 50 NUM hvd.32044092008168 674 3 part part NOUN hvd.32044092008168 674 4 v. v. ADP hvd.32044092008168 674 5 the the DET hvd.32044092008168 674 6 coefficients coefficient NOUN hvd.32044092008168 674 7 of of ADP hvd.32044092008168 674 8 variant variant NOUN hvd.32044092008168 674 9 of of ADP hvd.32044092008168 674 10 the the DET hvd.32044092008168 674 11 fourth fourth ADJ hvd.32044092008168 674 12 degree degree NOUN hvd.32044092008168 674 13 = = VERB hvd.32044092008168 674 14 α1 α1 PROPN hvd.32044092008168 674 15 [ [ X hvd.32044092008168 674 16 83 83 NUM hvd.32044092008168 674 17 ] ] PUNCT hvd.32044092008168 674 18 · · PUNCT hvd.32044092008168 674 19 þ(§₁ þ(§₁ NOUN hvd.32044092008168 674 20 ) ) PUNCT hvd.32044092008168 674 21 • • X hvd.32044092008168 675 1 [ [ X hvd.32044092008168 675 2 84 84 NUM hvd.32044092008168 675 3 ] ] PUNCT hvd.32044092008168 675 4 · · PUNCT hvd.32044092008168 675 5 bi bi NOUN hvd.32044092008168 675 6 1 1 NUM hvd.32044092008168 675 7 and and CCONJ hvd.32044092008168 675 8 we we PRON hvd.32044092008168 675 9 have have VERB hvd.32044092008168 675 10 the the DET hvd.32044092008168 675 11 form form NOUN hvd.32044092008168 675 12 : : PUNCT hvd.32044092008168 675 13 [ [ X hvd.32044092008168 675 14 85 85 NUM hvd.32044092008168 675 15 ] ] PUNCT hvd.32044092008168 675 16 · · PUNCT hvd.32044092008168 675 17 [ [ X hvd.32044092008168 675 18 86 86 NUM hvd.32044092008168 675 19 ] ] PUNCT hvd.32044092008168 675 20 · · PUNCT hvd.32044092008168 675 21 = = PUNCT hvd.32044092008168 675 22 and and CCONJ hvd.32044092008168 675 23 c³ c³ INTJ hvd.32044092008168 675 24 define define VERB hvd.32044092008168 675 25 4 4 NUM hvd.32044092008168 675 26 ( ( PUNCT hvd.32044092008168 675 27 1 1 NUM hvd.32044092008168 675 28 ) ) PUNCT hvd.32044092008168 675 29 210c§¹ 210c§¹ NUM hvd.32044092008168 675 30 +1 +1 NUM hvd.32044092008168 675 31 - - PUNCT hvd.32044092008168 675 32 4c³ 4c³ NUM hvd.32044092008168 675 33 0 0 NUM hvd.32044092008168 675 34 . . PUNCT hvd.32044092008168 676 1 = = PUNCT hvd.32044092008168 676 2 if if SCONJ hvd.32044092008168 676 3 then then ADV hvd.32044092008168 676 4 this this DET hvd.32044092008168 676 5 equation equation NOUN hvd.32044092008168 676 6 be be AUX hvd.32044092008168 676 7 written write VERB hvd.32044092008168 676 8 in in ADP hvd.32044092008168 676 9 its its PRON hvd.32044092008168 676 10 expanded expand VERB hvd.32044092008168 676 11 form form NOUN hvd.32044092008168 676 12 in in ADP hvd.32044092008168 676 13 terms term NOUN hvd.32044092008168 676 14 of of ADP hvd.32044092008168 676 15 the the DET hvd.32044092008168 676 16 modulus modulus NOUN hvd.32044092008168 676 17 k k INTJ hvd.32044092008168 676 18 it it PRON hvd.32044092008168 676 19 will will AUX hvd.32044092008168 676 20 not not PART hvd.32044092008168 676 21 be be AUX hvd.32044092008168 676 22 difficult difficult ADJ hvd.32044092008168 676 23 to to PART hvd.32044092008168 676 24 see see VERB hvd.32044092008168 676 25 by by ADP hvd.32044092008168 676 26 inspection inspection NOUN hvd.32044092008168 676 27 ( ( PUNCT hvd.32044092008168 676 28 for for ADP hvd.32044092008168 676 29 rigorous rigorous ADJ hvd.32044092008168 676 30 proof proof NOUN hvd.32044092008168 676 31 see see VERB hvd.32044092008168 676 32 p. p. NOUN hvd.32044092008168 676 33 56 56 NUM hvd.32044092008168 676 34 ) ) PUNCT hvd.32044092008168 676 35 that that SCONJ hvd.32044092008168 676 36 if if SCONJ hvd.32044092008168 676 37 we we PRON hvd.32044092008168 676 38 write write VERB hvd.32044092008168 676 39 φ φ X hvd.32044092008168 676 40 d d X hvd.32044092008168 676 41 ( ( PUNCT hvd.32044092008168 676 42 b3 b3 PROPN hvd.32044092008168 676 43 § § SPACE hvd.32044092008168 676 44 ) ) PUNCT hvd.32044092008168 676 45 b2 b2 PROPN hvd.32044092008168 676 46 • • PUNCT hvd.32044092008168 676 47 d3 d3 PROPN hvd.32044092008168 676 48 = = X hvd.32044092008168 676 49 = = PUNCT hvd.32044092008168 676 50 = = NOUN hvd.32044092008168 676 51 all all PRON hvd.32044092008168 676 52 reduce reduce VERB hvd.32044092008168 676 53 to to ADP hvd.32044092008168 676 54 functions function NOUN hvd.32044092008168 676 55 of of ADP hvd.32044092008168 676 56 the the DET hvd.32044092008168 676 57 absolute absolute ADJ hvd.32044092008168 676 58 in= in= NOUN hvd.32044092008168 676 59 1 1 NUM hvd.32044092008168 676 60 2 2 NUM hvd.32044092008168 676 61 these these DET hvd.32044092008168 676 62 factors factor NOUN hvd.32044092008168 676 63 of of ADP hvd.32044092008168 676 64 ø¸ ø¸ NOUN hvd.32044092008168 676 65 ð½ ð½ PUNCT hvd.32044092008168 676 66 ð³ ð³ PROPN hvd.32044092008168 676 67 corresponding correspond VERB hvd.32044092008168 676 68 to to ADP hvd.32044092008168 676 69 the the DET hvd.32044092008168 676 70 special special ADJ hvd.32044092008168 676 71 functions function NOUN hvd.32044092008168 676 72 of of ADP hvd.32044092008168 676 73 the the DET hvd.32044092008168 676 74 second second ADJ hvd.32044092008168 676 75 sort sort NOUN hvd.32044092008168 676 76 are be AUX hvd.32044092008168 676 77 , , PUNCT hvd.32044092008168 676 78 as as SCONJ hvd.32044092008168 676 79 given give VERB hvd.32044092008168 676 80 by by ADP hvd.32044092008168 676 81 m. m. NOUN hvd.32044092008168 676 82 hermite hermite PROPN hvd.32044092008168 676 83 : : PUNCT hvd.32044092008168 676 84 φι φι INTJ hvd.32044092008168 676 85 572 572 NUM hvd.32044092008168 676 86 2 2 NUM hvd.32044092008168 677 1 ( ( PUNCT hvd.32044092008168 677 2 k² k² PROPN hvd.32044092008168 677 3 2)1 2)1 NUM hvd.32044092008168 677 4 374 374 NUM hvd.32044092008168 677 5 φ φ X hvd.32044092008168 677 6 — — PUNCT hvd.32044092008168 677 7 572 572 NUM hvd.32044092008168 677 8 — — PUNCT hvd.32044092008168 677 9 2(1 2(1 NUM hvd.32044092008168 677 10 — — PUNCT hvd.32044092008168 677 11 2k²)l 2k²)l NUM hvd.32044092008168 677 12 — — PUNCT hvd.32044092008168 677 13 3 3 NUM hvd.32044092008168 677 14 = = SYM hvd.32044092008168 677 15 3 3 NUM hvd.32044092008168 677 16 α α NOUN hvd.32044092008168 677 17 b2 b2 PROPN hvd.32044092008168 677 18 12586 12586 NUM hvd.32044092008168 677 19 p p NOUN hvd.32044092008168 677 20 = = SYM hvd.32044092008168 677 21 512 512 NUM hvd.32044092008168 677 22 — — PUNCT hvd.32044092008168 677 23 2(1 2(1 X hvd.32044092008168 677 24 = = PUNCT hvd.32044092008168 677 25 = = PUNCT hvd.32044092008168 677 26 when when SCONJ hvd.32044092008168 677 27 o o X hvd.32044092008168 677 28 we we PRON hvd.32044092008168 677 29 have have VERB hvd.32044092008168 677 30 x x PUNCT hvd.32044092008168 677 31 o o X hvd.32044092008168 677 32 whence whence ADV hvd.32044092008168 677 33 , , PUNCT hvd.32044092008168 677 34 as as SCONJ hvd.32044092008168 677 35 before before ADV hvd.32044092008168 677 36 stated state VERB hvd.32044092008168 677 37 , , PUNCT hvd.32044092008168 677 38 ø ø ADP hvd.32044092008168 677 39 0 0 NUM hvd.32044092008168 677 40 is be AUX hvd.32044092008168 677 41 a a DET hvd.32044092008168 677 42 necessary necessary ADJ hvd.32044092008168 677 43 condition condition NOUN hvd.32044092008168 677 44 for for ADP hvd.32044092008168 677 45 the the DET hvd.32044092008168 677 46 existence existence NOUN hvd.32044092008168 677 47 of of ADP hvd.32044092008168 677 48 a a DET hvd.32044092008168 677 49 doubly doubly ADV hvd.32044092008168 677 50 periodic periodic ADJ hvd.32044092008168 677 51 function function NOUN hvd.32044092008168 677 52 . . PUNCT hvd.32044092008168 678 1 but but CCONJ hvd.32044092008168 678 2 in in ADP hvd.32044092008168 678 3 order order NOUN hvd.32044092008168 678 4 to to PART hvd.32044092008168 678 5 be be AUX hvd.32044092008168 678 6 a a DET hvd.32044092008168 678 7 sufficient sufficient ADJ hvd.32044092008168 678 8 condition condition NOUN hvd.32044092008168 678 9 it it PRON hvd.32044092008168 678 10 must must AUX hvd.32044092008168 678 11 involve involve VERB hvd.32044092008168 678 12 a a DET hvd.32044092008168 678 13 definite definite ADJ hvd.32044092008168 678 14 value value NOUN hvd.32044092008168 678 15 of of ADP hvd.32044092008168 678 16 v v NOUN hvd.32044092008168 678 17 , , PUNCT hvd.32044092008168 678 18 that that PRON hvd.32044092008168 678 19 is be AUX hvd.32044092008168 678 20 v v NOUN hvd.32044092008168 678 21 must must AUX hvd.32044092008168 678 22 be be AUX hvd.32044092008168 678 23 a a DET hvd.32044092008168 678 24 half half ADJ hvd.32044092008168 678 25 - - PUNCT hvd.32044092008168 678 26 period period NOUN hvd.32044092008168 678 27 . . PUNCT hvd.32044092008168 679 1 that that SCONJ hvd.32044092008168 679 2 this this PRON hvd.32044092008168 679 3 is be AUX hvd.32044092008168 679 4 the the DET hvd.32044092008168 679 5 case case NOUN hvd.32044092008168 679 6 , , PUNCT hvd.32044092008168 679 7 although although SCONJ hvd.32044092008168 679 8 the the DET hvd.32044092008168 679 9 reverse reverse NOUN hvd.32044092008168 679 10 as as SCONJ hvd.32044092008168 679 11 we we PRON hvd.32044092008168 679 12 shall shall AUX hvd.32044092008168 679 13 find find VERB hvd.32044092008168 679 14 later later ADV hvd.32044092008168 679 15 does do AUX hvd.32044092008168 679 16 not not PART hvd.32044092008168 679 17 hold hold VERB hvd.32044092008168 679 18 , , PUNCT hvd.32044092008168 679 19 is be AUX hvd.32044092008168 679 20 seen see VERB hvd.32044092008168 679 21 by by ADP hvd.32044092008168 679 22 a a DET hvd.32044092008168 679 23 determination determination NOUN hvd.32044092008168 679 24 of of ADP hvd.32044092008168 679 25 v v NOUN hvd.32044092008168 679 26 as as SCONJ hvd.32044092008168 679 27 follows follow VERB hvd.32044092008168 679 28 : : PUNCT hvd.32044092008168 679 29 we we PRON hvd.32044092008168 679 30 have have VERB hvd.32044092008168 679 31 ( ( PUNCT hvd.32044092008168 679 32 p. p. NOUN hvd.32044092008168 679 33 47 47 NUM hvd.32044092008168 679 34 ) ) PUNCT hvd.32044092008168 679 35 p(v p(v PROPN hvd.32044092008168 679 36 ): ): PUNCT hvd.32044092008168 680 1 x² x² PROPN hvd.32044092008168 680 2 = = PROPN hvd.32044092008168 680 3 1 1 NUM hvd.32044092008168 680 4 92 92 NUM hvd.32044092008168 680 5 108 108 NUM hvd.32044092008168 680 6 2 2 NUM hvd.32044092008168 680 7 93 93 NUM hvd.32044092008168 680 8 = = NOUN hvd.32044092008168 680 9 whence whence INTJ hvd.32044092008168 680 10 we we PRON hvd.32044092008168 680 11 write write VERB hvd.32044092008168 680 12 p(v p(v PROPN hvd.32044092008168 680 13 ): ): PUNCT hvd.32044092008168 680 14 returning return VERB hvd.32044092008168 680 15 to to ADP hvd.32044092008168 680 16 ( ( PUNCT hvd.32044092008168 680 17 80 80 NUM hvd.32044092008168 680 18 , , PUNCT hvd.32044092008168 680 19 a a X hvd.32044092008168 680 20 ) ) PUNCT hvd.32044092008168 680 21 we we PRON hvd.32044092008168 680 22 have have VERB hvd.32044092008168 680 23 k2 k2 PROPN hvd.32044092008168 680 24 sn² sn² VERB hvd.32044092008168 680 25 w w PROPN hvd.32044092008168 680 26 ( ( PUNCT hvd.32044092008168 680 27 1 1 NUM hvd.32044092008168 680 28 ) ) PUNCT hvd.32044092008168 680 29 127 127 NUM hvd.32044092008168 680 30 ( ( PUNCT hvd.32044092008168 680 31 12a 12a NUM hvd.32044092008168 680 32 ) ) PUNCT hvd.32044092008168 680 33 ( ( PUNCT hvd.32044092008168 680 34 1073516 1073516 NUM hvd.32044092008168 680 35 + + NUM hvd.32044092008168 680 36 6α₁l 6α₁l NOUN hvd.32044092008168 680 37 ( ( PUNCT hvd.32044092008168 680 38 1k2k4)3 1k2k4)3 NUM hvd.32044092008168 680 39 ( ( PUNCT hvd.32044092008168 680 40 1 1 NUM hvd.32044092008168 680 41 ) ) PUNCT hvd.32044092008168 680 42 ( ( PUNCT hvd.32044092008168 680 43 2 2 NUM hvd.32044092008168 680 44 k³ k³ NUM hvd.32044092008168 680 45 ) ) PUNCT hvd.32044092008168 680 46 * * PUNCT hvd.32044092008168 681 1 ( ( PUNCT hvd.32044092008168 681 2 1 1 NUM hvd.32044092008168 681 3 — — PUNCT hvd.32044092008168 681 4 2k³ 2k³ NUM hvd.32044092008168 681 5 ) ) PUNCT hvd.32044092008168 681 6 * * PUNCT hvd.32044092008168 681 7 · · PUNCT hvd.32044092008168 681 8 ――― ――― NOUN hvd.32044092008168 681 9 2 2 NUM hvd.32044092008168 681 10 h₁ h₁ NOUN hvd.32044092008168 681 11 þ(1 þ(1 ADJ hvd.32044092008168 681 12 ) ) PUNCT hvd.32044092008168 681 13 — — PUNCT hvd.32044092008168 681 14 127 127 NUM hvd.32044092008168 681 15 ( ( PUNCT hvd.32044092008168 681 16 12 12 NUM hvd.32044092008168 681 17 — — PUNCT hvd.32044092008168 681 18 a₁ a₁ NOUN hvd.32044092008168 681 19 ) ) PUNCT hvd.32044092008168 681 20 ( ( PUNCT hvd.32044092008168 681 21 10788a₁l 10788a₁l NUM hvd.32044092008168 681 22 - - PUNCT hvd.32044092008168 681 23 b₁ b₁ PROPN hvd.32044092008168 681 24 ) ) PUNCT hvd.32044092008168 681 25 367 367 NUM hvd.32044092008168 681 26 ( ( PUNCT hvd.32044092008168 681 27 12a 12a NUM hvd.32044092008168 681 28 ) ) PUNCT hvd.32044092008168 681 29 2 2 NUM hvd.32044092008168 681 30 xx xx X hvd.32044092008168 681 31 -+ -+ X hvd.32044092008168 681 32 k²)l k²)l NOUN hvd.32044092008168 681 33 — — PUNCT hvd.32044092008168 681 34 3(1 3(1 NUM hvd.32044092008168 681 35 − − PROPN hvd.32044092008168 681 36 k²)² k²)² NOUN hvd.32044092008168 681 37 . . PROPN hvd.32044092008168 681 38 8 8 NUM hvd.32044092008168 681 39 a₁l a₁l PROPN hvd.32044092008168 681 40 — — PUNCT hvd.32044092008168 681 41 b₁ b₁ PROPN hvd.32044092008168 681 42 ) ) PUNCT hvd.32044092008168 681 43 10b,1 10b,1 NUM hvd.32044092008168 681 44 - - SYM hvd.32044092008168 681 45 3a² 3a² NUM hvd.32044092008168 681 46 + + NUM hvd.32044092008168 681 47 6a₁b₁l 6a₁b₁l NUM hvd.32044092008168 681 48 + + CCONJ hvd.32044092008168 681 49 b² b² PROPN hvd.32044092008168 681 50 — — PUNCT hvd.32044092008168 681 51 4a³. 4a³. NUM hvd.32044092008168 681 52 22393c²² 22393c²² NUM hvd.32044092008168 681 53 + + NUM hvd.32044092008168 682 1 18c§ 18c§ NOUN hvd.32044092008168 682 2 1+k² 1+k² PROPN hvd.32044092008168 682 3 3 3 NUM hvd.32044092008168 682 4 187(1 187(1 NUM hvd.32044092008168 682 5 a₁ a₁ PROPN hvd.32044092008168 682 6 ) ) PUNCT hvd.32044092008168 682 7 2 2 NUM hvd.32044092008168 682 8 ° ° NUM hvd.32044092008168 682 9 ― ― X hvd.32044092008168 682 10 p p NOUN hvd.32044092008168 682 11 ' ' PUNCT hvd.32044092008168 682 12 ( ( PUNCT hvd.32044092008168 682 13 v v NOUN hvd.32044092008168 682 14 ) ) PUNCT hvd.32044092008168 682 15 = = SYM hvd.32044092008168 682 16 x(x² x(x² PUNCT hvd.32044092008168 682 17 — — PUNCT hvd.32044092008168 682 18 3pv 3pv ADV hvd.32044092008168 682 19 — — PUNCT hvd.32044092008168 682 20 31 31 NUM hvd.32044092008168 682 21 ) ) PUNCT hvd.32044092008168 682 22 367 367 NUM hvd.32044092008168 682 23 ( ( PUNCT hvd.32044092008168 682 24 12 12 NUM hvd.32044092008168 682 25 4(1 4(1 NUM hvd.32044092008168 682 26 ) ) PUNCT hvd.32044092008168 682 27 ¸p(7 ¸p(7 NOUN hvd.32044092008168 682 28 ) ) PUNCT hvd.32044092008168 682 29 — — PUNCT hvd.32044092008168 682 30 3 3 NUM hvd.32044092008168 682 31 4 4 NUM hvd.32044092008168 682 32 ( ( PUNCT hvd.32044092008168 682 33 7 7 NUM hvd.32044092008168 682 34 ) ) PUNCT hvd.32044092008168 682 35 — — PUNCT hvd.32044092008168 682 36 10872 10872 NUM hvd.32044092008168 682 37 ( ( PUNCT hvd.32044092008168 682 38 72 72 NUM hvd.32044092008168 682 39 — — PUNCT hvd.32044092008168 682 40 a₁)² a₁)² X hvd.32044092008168 682 41 þ(1 þ(1 ADJ hvd.32044092008168 682 42 ) ) PUNCT hvd.32044092008168 682 43 xc xc PROPN hvd.32044092008168 682 44 367(1a 367(1a NUM hvd.32044092008168 682 45 ) ) PUNCT hvd.32044092008168 682 46 a₁)2 a₁)2 ADP hvd.32044092008168 682 47 reduction reduction NOUN hvd.32044092008168 682 48 of of ADP hvd.32044092008168 682 49 the the DET hvd.32044092008168 682 50 forms form NOUN hvd.32044092008168 682 51 when when SCONJ hvd.32044092008168 682 52 n n SYM hvd.32044092008168 682 53 equals equal VERB hvd.32044092008168 682 54 three three NUM hvd.32044092008168 682 55 . . PUNCT hvd.32044092008168 683 1 51 51 NUM hvd.32044092008168 684 1 [ [ X hvd.32044092008168 684 2 87 87 NUM hvd.32044092008168 684 3 ] ] PUNCT hvd.32044092008168 684 4 · · PUNCT hvd.32044092008168 684 5 [ [ X hvd.32044092008168 684 6 88 88 NUM hvd.32044092008168 684 7 ] ] PUNCT hvd.32044092008168 684 8 . . PUNCT hvd.32044092008168 685 1 where where SCONJ hvd.32044092008168 685 2 we we PRON hvd.32044092008168 685 3 define define VERB hvd.32044092008168 685 4 where where SCONJ hvd.32044092008168 685 5 or or CCONJ hvd.32044092008168 685 6 y y PROPN hvd.32044092008168 685 7 . . PUNCT hvd.32044092008168 685 8 x x PUNCT hvd.32044092008168 686 1 = = PUNCT hvd.32044092008168 686 2 // // PUNCT hvd.32044092008168 687 1 [ [ X hvd.32044092008168 687 2 þ(1 þ(1 ADJ hvd.32044092008168 687 3 ) ) PUNCT hvd.32044092008168 687 4 — — PUNCT hvd.32044092008168 687 5 34(1 34(1 NUM hvd.32044092008168 687 6 ) ) PUNCT hvd.32044092008168 687 7 10812 10812 NUM hvd.32044092008168 687 8 ( ( PUNCT hvd.32044092008168 687 9 12 12 NUM hvd.32044092008168 687 10 — — PUNCT hvd.32044092008168 687 11 a₁)2 a₁)2 ADV hvd.32044092008168 687 12 ] ] X hvd.32044092008168 687 13 = = SYM hvd.32044092008168 687 14 16 16 NUM hvd.32044092008168 687 15 — — PUNCT hvd.32044092008168 687 16 6a 6a NUM hvd.32044092008168 687 17 , , PUNCT hvd.32044092008168 687 18 1² 1² NUM hvd.32044092008168 687 19 + + NUM hvd.32044092008168 687 20 4b₁13 4b₁13 NUM hvd.32044092008168 687 21 — — PUNCT hvd.32044092008168 687 22 3 3 NUM hvd.32044092008168 687 23 alb² alb² NOUN hvd.32044092008168 687 24 + + SYM hvd.32044092008168 687 25 4a³ 4a³ NUM hvd.32044092008168 687 26 = = NOUN hvd.32044092008168 687 27 a.b.c a.b.c NOUN hvd.32044092008168 687 28 . . PUNCT hvd.32044092008168 687 29 * * PUNCT hvd.32044092008168 687 30 ) ) PUNCT hvd.32044092008168 688 1 • • PUNCT hvd.32044092008168 688 2 refering refer VERB hvd.32044092008168 688 3 then then ADV hvd.32044092008168 688 4 to to PART hvd.32044092008168 688 5 note note VERB hvd.32044092008168 688 6 ( ( PUNCT hvd.32044092008168 688 7 p. p. NOUN hvd.32044092008168 688 8 24 24 NUM hvd.32044092008168 688 9 ) ) PUNCT hvd.32044092008168 689 1 we we PRON hvd.32044092008168 689 2 have have VERB hvd.32044092008168 689 3 : : PUNCT hvd.32044092008168 689 4 k¹su²v k¹su²v X hvd.32044092008168 689 5 · · PUNCT hvd.32044092008168 689 6 cn²v cn²v NOUN hvd.32044092008168 689 7 · · PUNCT hvd.32044092008168 689 8 dn² dn² NOUN hvd.32044092008168 689 9 v v NOUN hvd.32044092008168 689 10 = = X hvd.32044092008168 689 11 p p NOUN hvd.32044092008168 689 12 ' ' PUNCT hvd.32044092008168 689 13 ( ( PUNCT hvd.32044092008168 689 14 v v NOUN hvd.32044092008168 689 15 ) ) PUNCT hvd.32044092008168 689 16 = = X hvd.32044092008168 689 17 = = VERB hvd.32044092008168 689 18 a a DET hvd.32044092008168 689 19 = = NOUN hvd.32044092008168 689 20 12 12 NUM hvd.32044092008168 689 21 — — PUNCT hvd.32044092008168 689 22 ( ( PUNCT hvd.32044092008168 689 23 1 1 NUM hvd.32044092008168 689 24 + + NUM hvd.32044092008168 689 25 k² k² PROPN hvd.32044092008168 689 26 ) ) PUNCT hvd.32044092008168 689 27 — — PUNCT hvd.32044092008168 689 28 3k² 3k² NUM hvd.32044092008168 689 29 72 72 NUM hvd.32044092008168 689 30 l l X hvd.32044092008168 689 31 ་ ་ X hvd.32044092008168 689 32 = = SYM hvd.32044092008168 689 33 2 2 NUM hvd.32044092008168 689 34 b b NOUN hvd.32044092008168 689 35 — — PUNCT hvd.32044092008168 689 36 l² l² PROPN hvd.32044092008168 689 37 — — PUNCT hvd.32044092008168 689 38 ( ( PUNCT hvd.32044092008168 689 39 1 1 NUM hvd.32044092008168 689 40 — — PUNCT hvd.32044092008168 689 41 2k²)1 2k²)1 NOUN hvd.32044092008168 689 42 + + NUM hvd.32044092008168 689 43 3 3 NUM hvd.32044092008168 689 44 ( ( PUNCT hvd.32044092008168 689 45 k² k² PROPN hvd.32044092008168 689 46 12 12 NUM hvd.32044092008168 689 47 c c NOUN hvd.32044092008168 689 48 = = SYM hvd.32044092008168 689 49 12 12 NUM hvd.32044092008168 689 50 — — PUNCT hvd.32044092008168 689 51 2 2 NUM hvd.32044092008168 689 52 ) ) PUNCT hvd.32044092008168 689 53 — — PUNCT hvd.32044092008168 689 54 3 3 NUM hvd.32044092008168 689 55 ( ( PUNCT hvd.32044092008168 689 56 1 1 NUM hvd.32044092008168 689 57 — — PUNCT hvd.32044092008168 689 58 ( ( PUNCT hvd.32044092008168 689 59 k² k² PROPN hvd.32044092008168 689 60 that that PRON hvd.32044092008168 689 61 is be AUX hvd.32044092008168 689 62 p(v p(v SPACE hvd.32044092008168 689 63 ) ) PUNCT hvd.32044092008168 689 64 vanishes vanish VERB hvd.32044092008168 689 65 where where SCONJ hvd.32044092008168 689 66 x x PROPN hvd.32044092008168 689 67 vanishes vanish VERB hvd.32044092008168 689 68 a a DET hvd.32044092008168 689 69 semi semi ADJ hvd.32044092008168 689 70 - - NOUN hvd.32044092008168 689 71 period period NOUN hvd.32044092008168 689 72 , , PUNCT hvd.32044092008168 689 73 and and CCONJ hvd.32044092008168 689 74 in in ADP hvd.32044092008168 689 75 consequence consequence NOUN hvd.32044092008168 689 76 , , PUNCT hvd.32044092008168 689 77 when when SCONJ hvd.32044092008168 689 78 e e NOUN hvd.32044092008168 689 79 - - NOUN hvd.32044092008168 689 80 us us PROPN hvd.32044092008168 689 81 ( ( PUNCT hvd.32044092008168 689 82 w₂ w₂ PROPN hvd.32044092008168 689 83 ) ) PUNCT hvd.32044092008168 689 84 ―――― ―――― PROPN hvd.32044092008168 689 85 ――――――― ――――――― PROPN hvd.32044092008168 689 86 ―――――― ―――――― PROPN hvd.32044092008168 689 87 = = VERB hvd.32044092008168 689 88 hence hence ADV hvd.32044092008168 689 89 1 1 NUM hvd.32044092008168 689 90 y y NOUN hvd.32044092008168 689 91 = = PUNCT hvd.32044092008168 690 1 [ [ X hvd.32044092008168 690 2 2p(u 2p(u NUM hvd.32044092008168 690 3 ) ) PUNCT hvd.32044092008168 691 1 + + CCONJ hvd.32044092008168 691 2 ca can AUX hvd.32044092008168 691 3 − − PROPN hvd.32044092008168 691 4 ¦ ¦ ADJ hvd.32044092008168 691 5 ( ( PUNCT hvd.32044092008168 691 6 1 1 NUM hvd.32044092008168 691 7 + + NUM hvd.32044092008168 691 8 k² k² PROPN hvd.32044092008168 691 9 ) ) PUNCT hvd.32044092008168 691 10 — — PUNCT hvd.32044092008168 692 1 ea ea PROPN hvd.32044092008168 692 2 f₁ f₁ PROPN hvd.32044092008168 692 3 o o PROPN hvd.32044092008168 692 4 ( ( PUNCT hvd.32044092008168 692 5 u u PROPN hvd.32044092008168 692 6 + + CCONJ hvd.32044092008168 692 7 w₂ w₂ PROPN hvd.32044092008168 692 8 ) ) PUNCT hvd.32044092008168 692 9 ou ou PROPN hvd.32044092008168 692 10 o o PROPN hvd.32044092008168 692 11 ( ( PUNCT hvd.32044092008168 692 12 wx wx X hvd.32044092008168 692 13 ) ) PUNCT hvd.32044092008168 692 14 the the DET hvd.32044092008168 692 15 value value NOUN hvd.32044092008168 692 16 of of ADP hvd.32044092008168 692 17 the the DET hvd.32044092008168 692 18 function function NOUN hvd.32044092008168 692 19 of of ADP hvd.32044092008168 692 20 lamé lamé NOUN hvd.32044092008168 692 21 corresponding correspond VERB hvd.32044092008168 692 22 to to ADP hvd.32044092008168 692 23 any any DET hvd.32044092008168 692 24 value value NOUN hvd.32044092008168 692 25 of of ADP hvd.32044092008168 692 26 b b NOUN hvd.32044092008168 692 27 giving giving NOUN hvd.32044092008168 692 28 rise rise NOUN hvd.32044092008168 692 29 to to ADP hvd.32044092008168 692 30 the the DET hvd.32044092008168 692 31 condition condition NOUN hvd.32044092008168 692 32 = = PUNCT hvd.32044092008168 692 33 0 0 PUNCT hvd.32044092008168 692 34 is be AUX hvd.32044092008168 692 35 then then ADV hvd.32044092008168 692 36 deduced deduce VERB hvd.32044092008168 692 37 as as SCONJ hvd.32044092008168 692 38 follows follow VERB hvd.32044092008168 692 39 . . PUNCT hvd.32044092008168 693 1 from from ADP hvd.32044092008168 693 2 p p PROPN hvd.32044092008168 693 3 o o X hvd.32044092008168 693 4 we we PRON hvd.32044092008168 693 5 derive derive VERB hvd.32044092008168 693 6 : : PUNCT hvd.32044092008168 693 7 b b X hvd.32044092008168 693 8 = = X hvd.32044092008168 693 9 5l 5l X hvd.32044092008168 693 10 = = PUNCT hvd.32044092008168 693 11 1 1 NUM hvd.32044092008168 693 12 + + CCONJ hvd.32044092008168 693 13 k² k² PROPN hvd.32044092008168 693 14 + + NUM hvd.32044092008168 693 15 21/19(1 21/19(1 NUM hvd.32044092008168 693 16 — — PUNCT hvd.32044092008168 693 17 k²)² k²)² X hvd.32044092008168 693 18 + + CCONJ hvd.32044092008168 693 19 k² k² PROPN hvd.32044092008168 693 20 and and CCONJ hvd.32044092008168 693 21 the the DET hvd.32044092008168 693 22 special special ADJ hvd.32044092008168 693 23 equation equation NOUN hvd.32044092008168 693 24 of of ADP hvd.32044092008168 693 25 lamé lamé NOUN hvd.32044092008168 693 26 becomes become VERB hvd.32044092008168 693 27 y y NOUN hvd.32044092008168 693 28 ' ' PUNCT hvd.32044092008168 693 29 = = X hvd.32044092008168 694 1 [ [ X hvd.32044092008168 694 2 12p 12p NOUN hvd.32044092008168 694 3 ( ( PUNCT hvd.32044092008168 694 4 u u PROPN hvd.32044092008168 694 5 ) ) PUNCT hvd.32044092008168 694 6 + + NUM hvd.32044092008168 694 7 1 1 NUM hvd.32044092008168 695 1 + + PUNCT hvd.32044092008168 695 2 k² k² PROPN hvd.32044092008168 695 3 + + CCONJ hvd.32044092008168 695 4 2 2 NUM hvd.32044092008168 695 5 √19(1 √19(1 NOUN hvd.32044092008168 695 6 — — PUNCT hvd.32044092008168 695 7 k²)² k²)² PROPN hvd.32044092008168 695 8 + + PROPN hvd.32044092008168 695 9 k² k² PROPN hvd.32044092008168 695 10 ] ] PUNCT hvd.32044092008168 695 11 y y PROPN hvd.32044092008168 695 12 = = PUNCT hvd.32044092008168 695 13 · · PUNCT hvd.32044092008168 696 1 [ [ X hvd.32044092008168 696 2 2 2 NUM hvd.32044092008168 696 3 pu pu NOUN hvd.32044092008168 696 4 + + CCONJ hvd.32044092008168 696 5 e e NOUN hvd.32044092008168 696 6 − − NOUN hvd.32044092008168 696 7 / / SYM hvd.32044092008168 696 8 ( ( PUNCT hvd.32044092008168 696 9 1 1 NUM hvd.32044092008168 696 10 + + NUM hvd.32044092008168 696 11 k² k² PROPN hvd.32044092008168 696 12 ) ) PUNCT hvd.32044092008168 696 13 − − PROPN hvd.32044092008168 696 14 — — PUNCT hvd.32044092008168 696 15 5 5 NUM hvd.32044092008168 696 16 and and CCONJ hvd.32044092008168 696 17 from from ADP hvd.32044092008168 696 18 the the DET hvd.32044092008168 696 19 general general ADJ hvd.32044092008168 696 20 form form NOUN hvd.32044092008168 696 21 of of ADP hvd.32044092008168 696 22 the the DET hvd.32044092008168 696 23 integral integral ADJ hvd.32044092008168 696 24 [ [ X hvd.32044092008168 696 25 77 77 NUM hvd.32044092008168 696 26 ] ] PUNCT hvd.32044092008168 696 27 1 1 NUM hvd.32044092008168 696 28 y y NOUN hvd.32044092008168 696 29 = = VERB hvd.32044092008168 696 30 f f X hvd.32044092008168 696 31 ' ' PUNCT hvd.32044092008168 696 32 { { PUNCT hvd.32044092008168 696 33 ' ' PUNCT hvd.32044092008168 696 34 — — PUNCT hvd.32044092008168 696 35 } } PUNCT hvd.32044092008168 696 36 { { PUNCT hvd.32044092008168 696 37 1 1 NUM hvd.32044092008168 696 38 + + CCONJ hvd.32044092008168 696 39 k² k² PROPN hvd.32044092008168 696 40 + + CCONJ hvd.32044092008168 696 41 2 2 NUM hvd.32044092008168 696 42 √/19 √/19 ADV hvd.32044092008168 696 43 ( ( PUNCT hvd.32044092008168 696 44 1 1 NUM hvd.32044092008168 696 45 − − NOUN hvd.32044092008168 696 46 k²)² k²)² X hvd.32044092008168 696 47 + + PROPN hvd.32044092008168 696 48 1;² 1;² NUM hvd.32044092008168 696 49 } } PUNCT hvd.32044092008168 696 50 f₁• f₁• NOUN hvd.32044092008168 696 51 but but CCONJ hvd.32044092008168 696 52 differentiating differentiate VERB hvd.32044092008168 696 53 f₁ f₁ NOUN hvd.32044092008168 697 1 we we PRON hvd.32044092008168 697 2 have have VERB hvd.32044092008168 697 3 f₁ f₁ ADJ hvd.32044092008168 697 4 = = PUNCT hvd.32044092008168 698 1 [ [ X hvd.32044092008168 698 2 2p(u)+p(w₂ 2p(u)+p(w₂ NUM hvd.32044092008168 698 3 ) ) PUNCT hvd.32044092008168 698 4 ] ] PUNCT hvd.32044092008168 698 5 fi fi NOUN hvd.32044092008168 699 1 [ [ X hvd.32044092008168 699 2 2p(u 2p(u NUM hvd.32044092008168 699 3 ) ) PUNCT hvd.32044092008168 699 4 + + PUNCT hvd.32044092008168 699 5 ea ea X hvd.32044092008168 699 6 ] ] X hvd.32044092008168 699 7 f1 f1 NOUN hvd.32044092008168 699 8 . . PUNCT hvd.32044092008168 700 1 ― ― PUNCT hvd.32044092008168 700 2 · · PUNCT hvd.32044092008168 700 3 — — PUNCT hvd.32044092008168 700 4 k² k² PROPN hvd.32044092008168 700 5 ) ) PUNCT hvd.32044092008168 700 6 k² k² PROPN hvd.32044092008168 700 7 ) ) PUNCT hvd.32044092008168 700 8 . . PUNCT hvd.32044092008168 700 9 . . PUNCT hvd.32044092008168 701 1 x(1 x(1 PROPN hvd.32044092008168 701 2 ) ) PUNCT hvd.32044092008168 702 1 · · PUNCT hvd.32044092008168 702 2 x x SYM hvd.32044092008168 702 3 187 187 NUM hvd.32044092008168 702 4 ( ( PUNCT hvd.32044092008168 702 5 la la ADV hvd.32044092008168 702 6 ) ) PUNCT hvd.32044092008168 702 7 = = PUNCT hvd.32044092008168 702 8 = = PUNCT hvd.32044092008168 702 9 2 2 NUM hvd.32044092008168 702 10 [ [ X hvd.32044092008168 702 11 p(u p(u NOUN hvd.32044092008168 702 12 ) ) PUNCT hvd.32044092008168 702 13 + + CCONJ hvd.32044092008168 702 14 1 1 NUM hvd.32044092008168 702 15 la la ADV hvd.32044092008168 702 16 − − NOUN hvd.32044092008168 702 17 ¦ ¦ ADJ hvd.32044092008168 702 18 ¦ ¦ PROPN hvd.32044092008168 702 19 b]vpu b]vpu NOUN hvd.32044092008168 702 20 — — PUNCT hvd.32044092008168 702 21 ea ea NOUN hvd.32044092008168 702 22 10 10 NUM hvd.32044092008168 702 23 ° ° NOUN hvd.32044092008168 702 24 which which PRON hvd.32044092008168 702 25 gives give VERB hvd.32044092008168 702 26 v v X hvd.32044092008168 702 27 w₂ w₂ PROPN hvd.32044092008168 702 28 = = PROPN hvd.32044092008168 702 29 0 0 NUM hvd.32044092008168 702 30 , , PUNCT hvd.32044092008168 702 31 f f PROPN hvd.32044092008168 702 32 reduces reduce VERB hvd.32044092008168 702 33 to to ADP hvd.32044092008168 702 34 α α PROPN hvd.32044092008168 702 35 ( ( PUNCT hvd.32044092008168 702 36 u u NOUN hvd.32044092008168 702 37 ) ) NUM hvd.32044092008168 702 38 6(u 6(u NUM hvd.32044092008168 702 39 ) ) PUNCT hvd.32044092008168 702 40 • • CCONJ hvd.32044092008168 702 41 2 2 NUM hvd.32044092008168 702 42 ( ( PUNCT hvd.32044092008168 702 43 u u NOUN hvd.32044092008168 702 44 ) ) PUNCT hvd.32044092008168 702 45 ¦ ¦ ADP hvd.32044092008168 702 46 √/ √/ PROPN hvd.32044092008168 702 47 19 19 NUM hvd.32044092008168 702 48 ( ( PUNCT hvd.32044092008168 702 49 1 1 NUM hvd.32044092008168 702 50 − − NOUN hvd.32044092008168 702 51 k²)² k²)² X hvd.32044092008168 702 52 + + PROPN hvd.32044092008168 702 53 k² k² PROPN hvd.32044092008168 702 54 ] ] PUNCT hvd.32044092008168 702 55 a a PRON hvd.32044092008168 702 56 ) ) PUNCT hvd.32044092008168 702 57 5 5 NUM hvd.32044092008168 702 58 v v NOUN hvd.32044092008168 702 59 pu pu PROPN hvd.32044092008168 702 60 la la PROPN hvd.32044092008168 702 61 where where SCONJ hvd.32044092008168 702 62 ( ( PUNCT hvd.32044092008168 702 63 p. p. NOUN hvd.32044092008168 702 64 44 44 NUM hvd.32044092008168 702 65 ) ) PUNCT hvd.32044092008168 702 66 . . PUNCT hvd.32044092008168 703 1 * * PUNCT hvd.32044092008168 703 2 ) ) PUNCT hvd.32044092008168 703 3 compair compair NOUN hvd.32044092008168 704 1 [ [ X hvd.32044092008168 704 2 161 161 NUM hvd.32044092008168 704 3 ] ] PUNCT hvd.32044092008168 704 4 p. p. NOUN hvd.32044092008168 704 5 73 73 NUM hvd.32044092008168 704 6 . . PUNCT hvd.32044092008168 705 1 has have VERB hvd.32044092008168 705 2 the the DET hvd.32044092008168 705 3 value value NOUN hvd.32044092008168 705 4 determined determine VERB hvd.32044092008168 705 5 by by ADP hvd.32044092008168 705 6 the the DET hvd.32044092008168 705 7 elimentary elimentary ADJ hvd.32044092008168 705 8 consideration consideration NOUN hvd.32044092008168 705 9 α=1 α=1 ADP hvd.32044092008168 705 10 , , PUNCT hvd.32044092008168 705 11 2 2 NUM hvd.32044092008168 705 12 , , PUNCT hvd.32044092008168 705 13 3 3 NUM hvd.32044092008168 705 14 ( ( PUNCT hvd.32044092008168 705 15 w)=n₂ w)=n₂ NOUN hvd.32044092008168 705 16 3 3 NUM hvd.32044092008168 705 17 √19(1 √19(1 NOUN hvd.32044092008168 705 18 − − PROPN hvd.32044092008168 705 19 k²)² k²)² X hvd.32044092008168 705 20 + + SYM hvd.32044092008168 705 21 k²]vpu k²]vpu NOUN hvd.32044092008168 705 22 — — PUNCT hvd.32044092008168 705 23 ca can AUX hvd.32044092008168 705 24 4 4 NUM hvd.32044092008168 705 25 * * SYM hvd.32044092008168 705 26 52 52 NUM hvd.32044092008168 705 27 part part NOUN hvd.32044092008168 705 28 v. v. ADP hvd.32044092008168 705 29 if if SCONJ hvd.32044092008168 705 30 x x SYM hvd.32044092008168 705 31 case case NOUN hvd.32044092008168 705 32 x x PUNCT hvd.32044092008168 705 33 = = PUNCT hvd.32044092008168 705 34 0 0 NUM hvd.32044092008168 705 35 . . PUNCT hvd.32044092008168 706 1 ( ( PUNCT hvd.32044092008168 706 2 we we PRON hvd.32044092008168 706 3 have have VERB hvd.32044092008168 706 4 a a DET hvd.32044092008168 706 5 second second ADJ hvd.32044092008168 706 6 case case NOUN hvd.32044092008168 706 7 in in ADP hvd.32044092008168 706 8 which which PRON hvd.32044092008168 706 9 the the DET hvd.32044092008168 706 10 p'(v p'(v NOUN hvd.32044092008168 706 11 ) ) PUNCT hvd.32044092008168 706 12 vanishes vanishe NOUN hvd.32044092008168 706 13 , , PUNCT hvd.32044092008168 706 14 v v ADP hvd.32044092008168 706 15 taking take VERB hvd.32044092008168 706 16 the the DET hvd.32044092008168 706 17 value value NOUN hvd.32044092008168 706 18 of of ADP hvd.32044092008168 706 19 a a DET hvd.32044092008168 706 20 semi semi ADJ hvd.32044092008168 706 21 - - NOUN hvd.32044092008168 706 22 period period NOUN hvd.32044092008168 706 23 , , PUNCT hvd.32044092008168 706 24 but but CCONJ hvd.32044092008168 706 25 as as SCONJ hvd.32044092008168 706 26 this this PRON hvd.32044092008168 706 27 may may AUX hvd.32044092008168 706 28 occur occur VERB hvd.32044092008168 706 29 without without ADP hvd.32044092008168 706 30 reducing reduce VERB hvd.32044092008168 706 31 x x PROPN hvd.32044092008168 706 32 to to PART hvd.32044092008168 706 33 zero zero NUM hvd.32044092008168 706 34 the the DET hvd.32044092008168 706 35 eliment eliment NOUN hvd.32044092008168 706 36 will will AUX hvd.32044092008168 706 37 not not PART hvd.32044092008168 706 38 be be AUX hvd.32044092008168 706 39 doubly doubly ADV hvd.32044092008168 706 40 periodic periodic ADJ hvd.32044092008168 706 41 since since SCONJ hvd.32044092008168 706 42 it it PRON hvd.32044092008168 706 43 will will AUX hvd.32044092008168 706 44 contain contain VERB hvd.32044092008168 706 45 an an DET hvd.32044092008168 706 46 exponential exponential ADJ hvd.32044092008168 706 47 factor factor NOUN hvd.32044092008168 706 48 eit eit PROPN hvd.32044092008168 706 49 u. u. PROPN hvd.32044092008168 706 50 if if SCONJ hvd.32044092008168 706 51 then then ADV hvd.32044092008168 706 52 x x SYM hvd.32044092008168 706 53 = = PUNCT hvd.32044092008168 706 54 0 0 X hvd.32044092008168 706 55 ) ) PUNCT hvd.32044092008168 706 56 we we PRON hvd.32044092008168 706 57 will will AUX hvd.32044092008168 706 58 have have VERB hvd.32044092008168 706 59 from from ADP hvd.32044092008168 706 60 ( ( PUNCT hvd.32044092008168 706 61 87 87 NUM hvd.32044092008168 706 62 ) ) PUNCT hvd.32044092008168 706 63 six six NUM hvd.32044092008168 706 64 values value NOUN hvd.32044092008168 706 65 of of ADP hvd.32044092008168 706 66 b b PROPN hvd.32044092008168 706 67 for for ADP hvd.32044092008168 706 68 which which PRON hvd.32044092008168 706 69 the the DET hvd.32044092008168 706 70 integral integral NOUN hvd.32044092008168 706 71 will will AUX hvd.32044092008168 706 72 take take VERB hvd.32044092008168 706 73 the the DET hvd.32044092008168 706 74 form form NOUN hvd.32044092008168 706 75 o(u o(u ADJ hvd.32044092008168 706 76 + + CCONJ hvd.32044092008168 706 77 wn wn X hvd.32044092008168 706 78 ) ) PUNCT hvd.32044092008168 706 79 y y PROPN hvd.32044092008168 706 80 = = PROPN hvd.32044092008168 706 81 fbf fbf NOUN hvd.32044092008168 706 82 where where SCONJ hvd.32044092008168 706 83 fa fa PROPN hvd.32044092008168 706 84 e+ e+ X hvd.32044092008168 706 85 ( ( PUNCT hvd.32044092008168 706 86 x x SYM hvd.32044092008168 706 87 − − PROPN hvd.32044092008168 706 88 ¢wn ¢wn SPACE hvd.32044092008168 706 89 ) ) PUNCT hvd.32044092008168 706 90 2 2 NUM hvd.32044092008168 706 91 σε σε PROPN hvd.32044092008168 706 92 σωλ σωλ X hvd.32044092008168 706 93 ба ба X hvd.32044092008168 706 94 и и PROPN hvd.32044092008168 706 95 u u PROPN hvd.32044092008168 706 96 exu exu NOUN hvd.32044092008168 706 97 . . PUNCT hvd.32044092008168 707 1 σα σα PROPN hvd.32044092008168 707 2 moreover moreover ADV hvd.32044092008168 707 3 the the DET hvd.32044092008168 707 4 second second ADJ hvd.32044092008168 707 5 integral integral NOUN hvd.32044092008168 707 6 will will AUX hvd.32044092008168 707 7 be be AUX hvd.32044092008168 707 8 са са X hvd.32044092008168 707 9 и и X hvd.32044092008168 707 10 f f PROPN hvd.32044092008168 707 11 -mu -mu PUNCT hvd.32044092008168 707 12 6u 6u NUM hvd.32044092008168 707 13 a a PRON hvd.32044092008168 707 14 or or CCONJ hvd.32044092008168 707 15 4 4 NUM hvd.32044092008168 707 16 3 3 NUM hvd.32044092008168 707 17 the the DET hvd.32044092008168 707 18 form form NOUN hvd.32044092008168 707 19 remaining remain VERB hvd.32044092008168 707 20 unchanged unchanged ADJ hvd.32044092008168 707 21 which which PRON hvd.32044092008168 707 22 is be AUX hvd.32044092008168 707 23 not not PART hvd.32044092008168 707 24 as as SCONJ hvd.32044092008168 707 25 we we PRON hvd.32044092008168 707 26 have have AUX hvd.32044092008168 707 27 seen see VERB hvd.32044092008168 707 28 in in ADP hvd.32044092008168 707 29 general general ADJ hvd.32044092008168 707 30 the the DET hvd.32044092008168 707 31 case case NOUN hvd.32044092008168 707 32 . . PUNCT hvd.32044092008168 708 1 case case NOUN hvd.32044092008168 708 2 d=0 d=0 SPACE hvd.32044092008168 708 3 . . PUNCT hvd.32044092008168 709 1 the the DET hvd.32044092008168 709 2 only only ADJ hvd.32044092008168 709 3 remaining remain VERB hvd.32044092008168 709 4 case case NOUN hvd.32044092008168 709 5 to to PART hvd.32044092008168 709 6 be be AUX hvd.32044092008168 709 7 considered consider VERB hvd.32044092008168 709 8 is be AUX hvd.32044092008168 709 9 where where SCONJ hvd.32044092008168 709 10 d d NOUN hvd.32044092008168 709 11 = = NOUN hvd.32044092008168 709 12 0 0 NUM hvd.32044092008168 709 13 , , PUNCT hvd.32044092008168 709 14 or or CCONJ hvd.32044092008168 709 15 72 72 NUM hvd.32044092008168 709 16 — — PUNCT hvd.32044092008168 709 17 ay ay NOUN hvd.32044092008168 709 18 = = PROPN hvd.32044092008168 709 19 12 12 NUM hvd.32044092008168 709 20 – – PUNCT hvd.32044092008168 709 21 1 1 NUM hvd.32044092008168 709 22 + + NUM hvd.32044092008168 709 23 ka ka X hvd.32044092008168 709 24 k4 k4 PROPN hvd.32044092008168 709 25 = = PUNCT hvd.32044092008168 709 26 0 0 NUM hvd.32044092008168 709 27 : : PUNCT hvd.32044092008168 709 28 — — PUNCT hvd.32044092008168 709 29 l=+(1 l=+(1 INTJ hvd.32044092008168 709 30 — — PUNCT hvd.32044092008168 709 31 " " PUNCT hvd.32044092008168 709 32 * * PUNCT hvd.32044092008168 709 33 + + NOUN hvd.32044092008168 709 34 : : PUNCT hvd.32044092008168 709 35 $ $ SYM hvd.32044092008168 709 36 4)% 4)% NUM hvd.32044092008168 709 37 = = SYM hvd.32044092008168 709 38 + + NUM hvd.32044092008168 709 39 v39 v39 NOUN hvd.32044092008168 709 40 , , PUNCT hvd.32044092008168 709 41 — — PUNCT hvd.32044092008168 709 42 ka ka PROPN hvd.32044092008168 709 43 + + CCONJ hvd.32044092008168 709 44 since since SCONJ hvd.32044092008168 709 45 aga aga NOUN hvd.32044092008168 709 46 = = SYM hvd.32044092008168 709 47 ( ( PUNCT hvd.32044092008168 709 48 1 1 NUM hvd.32044092008168 709 49 — — PUNCT hvd.32044092008168 709 50 k+ k+ X hvd.32044092008168 709 51 k4 k4 PROPN hvd.32044092008168 709 52 ) ) PUNCT hvd.32044092008168 709 53 . . PUNCT hvd.32044092008168 710 1 also also ADV hvd.32044092008168 710 2 l l PRON hvd.32044092008168 710 3 = = VERB hvd.32044092008168 710 4 36 36 NUM hvd.32044092008168 711 1 whence whence ADV hvd.32044092008168 711 2 b b ADP hvd.32044092008168 711 3 = = SYM hvd.32044092008168 711 4 v% v% PROPN hvd.32044092008168 711 5 12 12 NUM hvd.32044092008168 711 6 62 62 NUM hvd.32044092008168 711 7 92 92 NUM hvd.32044092008168 711 8 = = NOUN hvd.32044092008168 711 9 9'(6)=0 9'(6)=0 NUM hvd.32044092008168 711 10 . . PUNCT hvd.32044092008168 712 1 that that PRON hvd.32044092008168 712 2 is be AUX hvd.32044092008168 712 3 d d X hvd.32044092008168 712 4 = = NOUN hvd.32044092008168 712 5 ( ( PUNCT hvd.32044092008168 712 6 ) ) PUNCT hvd.32044092008168 712 7 and and CCONJ hvd.32044092008168 712 8 g'(b g'(b NOUN hvd.32044092008168 712 9 ) ) PUNCT hvd.32044092008168 712 10 : : PUNCT hvd.32044092008168 712 11 0 0 NUM hvd.32044092008168 712 12 are be AUX hvd.32044092008168 712 13 conditions condition NOUN hvd.32044092008168 712 14 for for ADP hvd.32044092008168 712 15 one one NUM hvd.32044092008168 712 16 and and CCONJ hvd.32044092008168 712 17 the the DET hvd.32044092008168 712 18 same same ADJ hvd.32044092008168 712 19 function function NOUN hvd.32044092008168 712 20 of of ADP hvd.32044092008168 712 21 lamé lamé NOUN hvd.32044092008168 712 22 . . PUNCT hvd.32044092008168 713 1 in in ADP hvd.32044092008168 713 2 this this DET hvd.32044092008168 713 3 case case NOUN hvd.32044092008168 713 4 p(v p(v SPACE hvd.32044092008168 713 5 ) ) PUNCT hvd.32044092008168 713 6 and and CCONJ hvd.32044092008168 713 7 also also ADV hvd.32044092008168 713 8 the the DET hvd.32044092008168 713 9 p'(v p'(v NOUN hvd.32044092008168 713 10 ) ) PUNCT hvd.32044092008168 713 11 become become VERB hvd.32044092008168 713 12 infinite infinite ADJ hvd.32044092008168 713 13 which which PRON hvd.32044092008168 713 14 gives give VERB hvd.32044092008168 713 15 v= v= NOUN hvd.32044092008168 713 16 0 0 NUM hvd.32044092008168 713 17 or or CCONJ hvd.32044092008168 713 18 the the DET hvd.32044092008168 713 19 congruent congruent ADJ hvd.32044092008168 713 20 values value NOUN hvd.32044092008168 713 21 2 2 NUM hvd.32044092008168 713 22 mw mw NOUN hvd.32044092008168 713 23 + + CCONJ hvd.32044092008168 713 24 2 2 NUM hvd.32044092008168 713 25 m'w m'w SPACE hvd.32044092008168 713 26 ' ' PUNCT hvd.32044092008168 713 27 . . PUNCT hvd.32044092008168 714 1 the the DET hvd.32044092008168 714 2 general general ADJ hvd.32044092008168 714 3 form form NOUN hvd.32044092008168 714 4 of of ADP hvd.32044092008168 714 5 our our PRON hvd.32044092008168 714 6 integral integral ADJ hvd.32044092008168 714 7 will will AUX hvd.32044092008168 714 8 not not PART hvd.32044092008168 714 9 hold hold VERB hvd.32044092008168 714 10 for for ADP hvd.32044092008168 714 11 this this DET hvd.32044092008168 714 12 exceptional exceptional ADJ hvd.32044092008168 714 13 case case NOUN hvd.32044092008168 714 14 and and CCONJ hvd.32044092008168 714 15 we we PRON hvd.32044092008168 714 16 are be AUX hvd.32044092008168 714 17 obliged oblige VERB hvd.32044092008168 714 18 to to PART hvd.32044092008168 714 19 return return VERB hvd.32044092008168 714 20 to to ADP hvd.32044092008168 714 21 the the DET hvd.32044092008168 714 22 treatment treatment NOUN hvd.32044092008168 714 23 of of ADP hvd.32044092008168 714 24 the the DET hvd.32044092008168 714 25 subject subject NOUN hvd.32044092008168 714 26 from from ADP hvd.32044092008168 714 27 the the DET hvd.32044092008168 714 28 standpoint standpoint NOUN hvd.32044092008168 714 29 of of ADP hvd.32044092008168 714 30 a a DET hvd.32044092008168 714 31 product product NOUN hvd.32044092008168 714 32 . . PUNCT hvd.32044092008168 715 1 92 92 NUM hvd.32044092008168 715 2 3 3 NUM hvd.32044092008168 715 3 2 2 NUM hvd.32044092008168 715 4 or or CCONJ hvd.32044092008168 715 5 relation relation NOUN hvd.32044092008168 715 6 of of ADP hvd.32044092008168 715 7 y y PROPN hvd.32044092008168 715 8 and and CCONJ hvd.32044092008168 715 9 c c NOUN hvd.32044092008168 715 10 to to ADP hvd.32044092008168 715 11 the the DET hvd.32044092008168 715 12 special special ADJ hvd.32044092008168 715 13 functions function NOUN hvd.32044092008168 715 14 of of ADP hvd.32044092008168 715 15 lamé lamé NOUN hvd.32044092008168 715 16 . . PUNCT hvd.32044092008168 716 1 returning return VERB hvd.32044092008168 716 2 first first ADV hvd.32044092008168 716 3 to to ADP hvd.32044092008168 716 4 ( ( PUNCT hvd.32044092008168 716 5 part part NOUN hvd.32044092008168 716 6 iv iv X hvd.32044092008168 716 7 , , PUNCT hvd.32044092008168 716 8 p. p. NOUN hvd.32044092008168 716 9 42 42 NUM hvd.32044092008168 716 10 ) ) PUNCT hvd.32044092008168 716 11 , , PUNCT hvd.32044092008168 716 12 the the DET hvd.32044092008168 716 13 elimentary elimentary ADJ hvd.32044092008168 716 14 determination determination NOUN hvd.32044092008168 716 15 of of ADP hvd.32044092008168 716 16 the the DET hvd.32044092008168 716 17 special special ADJ hvd.32044092008168 716 18 functions function NOUN hvd.32044092008168 716 19 of of ADP hvd.32044092008168 716 20 lamé lamé NOUN hvd.32044092008168 716 21 , , PUNCT hvd.32044092008168 716 22 we we PRON hvd.32044092008168 716 23 there there ADV hvd.32044092008168 716 24 found find VERB hvd.32044092008168 716 25 with with ADP hvd.32044092008168 716 26 reference reference NOUN hvd.32044092008168 716 27 to to ADP hvd.32044092008168 716 28 b b PROPN hvd.32044092008168 716 29 that that PRON hvd.32044092008168 716 30 , , PUNCT hvd.32044092008168 716 31 first first ADV hvd.32044092008168 716 32 , , PUNCT hvd.32044092008168 716 33 if if SCONJ hvd.32044092008168 716 34 n n CCONJ hvd.32044092008168 716 35 be be AUX hvd.32044092008168 716 36 odd odd ADJ hvd.32044092008168 716 37 , , PUNCT hvd.32044092008168 716 38 it it PRON hvd.32044092008168 716 39 is be AUX hvd.32044092008168 716 40 determined determine VERB hvd.32044092008168 716 41 by by ADP hvd.32044092008168 716 42 two two NUM hvd.32044092008168 716 43 sorts sort NOUN hvd.32044092008168 716 44 of of ADP hvd.32044092008168 716 45 equations equation NOUN hvd.32044092008168 716 46 , , PUNCT hvd.32044092008168 716 47 one one NUM hvd.32044092008168 716 48 of of ADP hvd.32044092008168 716 49 degree degree NOUN hvd.32044092008168 716 50 ( ( PUNCT hvd.32044092008168 716 51 n n CCONJ hvd.32044092008168 716 52 --1 --1 SPACE hvd.32044092008168 716 53 ) ) PUNCT hvd.32044092008168 716 54 giving give VERB hvd.32044092008168 716 55 rise rise NOUN hvd.32044092008168 716 56 to to ADP hvd.32044092008168 716 57 functions function NOUN hvd.32044092008168 716 58 of of ADP hvd.32044092008168 716 59 the the DET hvd.32044092008168 716 60 > > X hvd.32044092008168 716 61 1 1 NUM hvd.32044092008168 716 62 2 2 NUM hvd.32044092008168 716 63 reduction reduction NOUN hvd.32044092008168 716 64 of of ADP hvd.32044092008168 716 65 the the DET hvd.32044092008168 716 66 forms form NOUN hvd.32044092008168 716 67 when when SCONJ hvd.32044092008168 716 68 n n SYM hvd.32044092008168 716 69 equals equal VERB hvd.32044092008168 716 70 three three NUM hvd.32044092008168 716 71 . . PUNCT hvd.32044092008168 717 1 53 53 NUM hvd.32044092008168 717 2 2 2 NUM hvd.32044092008168 717 3 3 3 NUM hvd.32044092008168 717 4 1 1 NUM hvd.32044092008168 717 5 > > SYM hvd.32044092008168 717 6 1 1 NUM hvd.32044092008168 717 7 2 2 NUM hvd.32044092008168 717 8 v v NOUN hvd.32044092008168 717 9 ... ... PUNCT hvd.32044092008168 717 10 first first ADJ hvd.32044092008168 717 11 sort sort NOUN hvd.32044092008168 717 12 , , PUNCT hvd.32044092008168 717 13 and and CCONJ hvd.32044092008168 717 14 the the DET hvd.32044092008168 717 15 other other ADJ hvd.32044092008168 717 16 , , PUNCT hvd.32044092008168 717 17 three three NUM hvd.32044092008168 717 18 in in ADP hvd.32044092008168 717 19 all all PRON hvd.32044092008168 717 20 , , PUNCT hvd.32044092008168 717 21 of of ADP hvd.32044092008168 717 22 degree degree NOUN hvd.32044092008168 717 23 ( ( PUNCT hvd.32044092008168 717 24 n n CCONJ hvd.32044092008168 717 25 + + CCONJ hvd.32044092008168 717 26 1 1 X hvd.32044092008168 717 27 ) ) PUNCT hvd.32044092008168 717 28 giving give VERB hvd.32044092008168 717 29 rise rise NOUN hvd.32044092008168 717 30 to to ADP hvd.32044092008168 717 31 functions function NOUN hvd.32044092008168 717 32 of of ADP hvd.32044092008168 717 33 the the DET hvd.32044092008168 717 34 second second ADJ hvd.32044092008168 717 35 sort sort NOUN hvd.32044092008168 717 36 ; ; PUNCT hvd.32044092008168 718 1 whence whence ADV hvd.32044092008168 718 2 combining combine VERB hvd.32044092008168 718 3 we we PRON hvd.32044092008168 718 4 have have VERB hvd.32044092008168 718 5 , , PUNCT hvd.32044092008168 718 6 n n CCONJ hvd.32044092008168 718 7 being be AUX hvd.32044092008168 718 8 odd odd ADJ hvd.32044092008168 718 9 , , PUNCT hvd.32044092008168 718 10 b b X hvd.32044092008168 718 11 determined determine VERB hvd.32044092008168 718 12 by by ADP hvd.32044092008168 718 13 an an DET hvd.32044092008168 718 14 equation equation NOUN hvd.32044092008168 718 15 of of ADP hvd.32044092008168 718 16 degree degree NOUN hvd.32044092008168 718 17 ( ( PUNCT hvd.32044092008168 718 18 n+1)+(n-1 n+1)+(n-1 NOUN hvd.32044092008168 718 19 ) ) PUNCT hvd.32044092008168 718 20 = = SYM hvd.32044092008168 718 21 2n 2n NUM hvd.32044092008168 718 22 + + CCONJ hvd.32044092008168 718 23 1 1 X hvd.32044092008168 718 24 . . PUNCT hvd.32044092008168 719 1 if if SCONJ hvd.32044092008168 719 2 n n ADV hvd.32044092008168 719 3 is be AUX hvd.32044092008168 719 4 even even ADV hvd.32044092008168 719 5 we we PRON hvd.32044092008168 719 6 find find VERB hvd.32044092008168 719 7 but but CCONJ hvd.32044092008168 719 8 one one NUM hvd.32044092008168 719 9 equation equation NOUN hvd.32044092008168 719 10 , , PUNCT hvd.32044092008168 719 11 degree degree NOUN hvd.32044092008168 719 12 n n ADP hvd.32044092008168 719 13 +1 +1 PROPN hvd.32044092008168 719 14 , , PUNCT hvd.32044092008168 719 15 + + NUM hvd.32044092008168 719 16 for for ADP hvd.32044092008168 719 17 functions function NOUN hvd.32044092008168 719 18 of of ADP hvd.32044092008168 719 19 the the DET hvd.32044092008168 719 20 first first ADJ hvd.32044092008168 719 21 sort sort NOUN hvd.32044092008168 719 22 and and CCONJ hvd.32044092008168 719 23 three three NUM hvd.32044092008168 719 24 equations equation NOUN hvd.32044092008168 719 25 , , PUNCT hvd.32044092008168 719 26 degreen degreen VERB hvd.32044092008168 719 27 , , PUNCT hvd.32044092008168 719 28 for for ADP hvd.32044092008168 719 29 those those PRON hvd.32044092008168 719 30 of of ADP hvd.32044092008168 719 31 the the DET hvd.32044092008168 719 32 second second ADJ hvd.32044092008168 719 33 sort sort NOUN hvd.32044092008168 719 34 making make VERB hvd.32044092008168 719 35 a a DET hvd.32044092008168 719 36 single single ADJ hvd.32044092008168 719 37 equation equation NOUN hvd.32044092008168 719 38 whose whose DET hvd.32044092008168 719 39 degree degree NOUN hvd.32044092008168 719 40 as as ADP hvd.32044092008168 719 41 in in ADP hvd.32044092008168 719 42 the the DET hvd.32044092008168 719 43 first first ADJ hvd.32044092008168 719 44 case case NOUN hvd.32044092008168 719 45 is be AUX hvd.32044092008168 719 46 2n 2n NUM hvd.32044092008168 719 47 + + CCONJ hvd.32044092008168 719 48 1 1 X hvd.32044092008168 719 49 . . PUNCT hvd.32044092008168 720 1 if if SCONJ hvd.32044092008168 720 2 then then ADV hvd.32044092008168 720 3 these these DET hvd.32044092008168 720 4 roots root NOUN hvd.32044092008168 720 5 are be AUX hvd.32044092008168 720 6 all all ADV hvd.32044092008168 720 7 different different ADJ hvd.32044092008168 720 8 we we PRON hvd.32044092008168 720 9 have have VERB hvd.32044092008168 720 10 in in ADP hvd.32044092008168 720 11 all all DET hvd.32044092008168 720 12 2n 2n NUM hvd.32044092008168 720 13 +1 +1 NOUN hvd.32044092008168 720 14 special special ADJ hvd.32044092008168 720 15 functions function NOUN hvd.32044092008168 720 16 of of ADP hvd.32044092008168 720 17 lamé lamé NOUN hvd.32044092008168 720 18 . . PUNCT hvd.32044092008168 721 1 returning return VERB hvd.32044092008168 721 2 now now ADV hvd.32044092008168 721 3 to to ADP hvd.32044092008168 721 4 the the DET hvd.32044092008168 721 5 forms form NOUN hvd.32044092008168 721 6 ( ( PUNCT hvd.32044092008168 721 7 65 65 NUM hvd.32044092008168 721 8 ) ) PUNCT hvd.32044092008168 721 9 2c 2c NUM hvd.32044092008168 721 10 = = X hvd.32044092008168 721 11 a(a a(a PROPN hvd.32044092008168 721 12 – – PUNCT hvd.32044092008168 721 13 b b X hvd.32044092008168 721 14 ) ) PUNCT hvd.32044092008168 721 15 ( ( PUNCT hvd.32044092008168 721 16 a a PRON hvd.32044092008168 721 17 — — PUNCT hvd.32044092008168 721 18 » » NOUN hvd.32044092008168 721 19 ) ) PUNCT hvd.32044092008168 721 20 . . PUNCT hvd.32044092008168 722 1 a'la a'la PROPN hvd.32044092008168 722 2 ( ( PUNCT hvd.32044092008168 722 3 we we PRON hvd.32044092008168 722 4 have have VERB hvd.32044092008168 722 5 the the DET hvd.32044092008168 722 6 half half ADJ hvd.32044092008168 722 7 periods period NOUN hvd.32044092008168 722 8 or or CCONJ hvd.32044092008168 722 9 values value NOUN hvd.32044092008168 722 10 of of ADP hvd.32044092008168 722 11 the the DET hvd.32044092008168 722 12 roots root NOUN hvd.32044092008168 722 13 a a DET hvd.32044092008168 722 14 , , PUNCT hvd.32044092008168 722 15 b b NOUN hvd.32044092008168 722 16 that that PRON hvd.32044092008168 722 17 will will AUX hvd.32044092008168 722 18 reduce reduce VERB hvd.32044092008168 722 19 them they PRON hvd.32044092008168 722 20 to to ADP hvd.32044092008168 722 21 zero zero NUM hvd.32044092008168 722 22 . . PUNCT hvd.32044092008168 723 1 moreover moreover ADV hvd.32044092008168 723 2 they they PRON hvd.32044092008168 723 3 will will AUX hvd.32044092008168 723 4 not not PART hvd.32044092008168 723 5 be be AUX hvd.32044092008168 723 6 double double ADJ hvd.32044092008168 723 7 roots root NOUN hvd.32044092008168 723 8 , , PUNCT hvd.32044092008168 723 9 for for SCONJ hvd.32044092008168 723 10 consider consider VERB hvd.32044092008168 723 11 t t PROPN hvd.32044092008168 723 12 en en PROPN hvd.32044092008168 723 13 as as ADP hvd.32044092008168 723 14 a a DET hvd.32044092008168 723 15 double double ADJ hvd.32044092008168 723 16 root root NOUN hvd.32044092008168 723 17 of of ADP hvd.32044092008168 723 18 y y PROPN hvd.32044092008168 723 19 in in ADP hvd.32044092008168 723 20 which which DET hvd.32044092008168 723 21 case case NOUN hvd.32044092008168 723 22 all all DET hvd.32044092008168 723 23 the the DET hvd.32044092008168 723 24 terms term NOUN hvd.32044092008168 723 25 of of ADP hvd.32044092008168 723 26 equation equation NOUN hvd.32044092008168 723 27 ( ( PUNCT hvd.32044092008168 723 28 57 57 NUM hvd.32044092008168 723 29 ) ) PUNCT hvd.32044092008168 723 30 will will AUX hvd.32044092008168 723 31 reduce reduce VERB hvd.32044092008168 723 32 to to ADP hvd.32044092008168 723 33 zero zero NUM hvd.32044092008168 723 34 save save VERB hvd.32044092008168 723 35 the the DET hvd.32044092008168 723 36 second second ADJ hvd.32044092008168 723 37 which which PRON hvd.32044092008168 723 38 will will AUX hvd.32044092008168 723 39 be be AUX hvd.32044092008168 723 40 identically identically ADV hvd.32044092008168 723 41 zero zero NUM hvd.32044092008168 723 42 , , PUNCT hvd.32044092008168 723 43 which which PRON hvd.32044092008168 723 44 is be AUX hvd.32044092008168 723 45 a a DET hvd.32044092008168 723 46 condition condition NOUN hvd.32044092008168 723 47 that that SCONJ hvd.32044092008168 723 48 the the DET hvd.32044092008168 723 49 root root NOUN hvd.32044092008168 723 50 be be AUX hvd.32044092008168 723 51 tripple tripple NOUN hvd.32044092008168 723 52 . . PUNCT hvd.32044092008168 724 1 differentiating differentiate VERB hvd.32044092008168 724 2 we we PRON hvd.32044092008168 724 3 find find VERB hvd.32044092008168 724 4 an an DET hvd.32044092008168 724 5 analogous analogous ADJ hvd.32044092008168 724 6 equation equation NOUN hvd.32044092008168 724 7 and and CCONJ hvd.32044092008168 724 8 a a DET hvd.32044092008168 724 9 similar similar ADJ hvd.32044092008168 724 10 course course NOUN hvd.32044092008168 724 11 of of ADP hvd.32044092008168 724 12 reasoning reasoning NOUN hvd.32044092008168 724 13 shows show VERB hvd.32044092008168 724 14 that that SCONJ hvd.32044092008168 724 15 the the DET hvd.32044092008168 724 16 root root NOUN hvd.32044092008168 724 17 must must AUX hvd.32044092008168 724 18 be be AUX hvd.32044092008168 724 19 quadruple quadruple ADJ hvd.32044092008168 724 20 and and CCONJ hvd.32044092008168 724 21 so so ADV hvd.32044092008168 724 22 on on ADP hvd.32044092008168 724 23 which which PRON hvd.32044092008168 724 24 is be AUX hvd.32044092008168 724 25 absurde absurde ADJ hvd.32044092008168 724 26 . . PUNCT hvd.32044092008168 725 1 hence hence ADV hvd.32044092008168 725 2 the the DET hvd.32044092008168 725 3 roots root NOUN hvd.32044092008168 725 4 that that PRON hvd.32044092008168 725 5 are be AUX hvd.32044092008168 725 6 half half ADJ hvd.32044092008168 725 7 - - PUNCT hvd.32044092008168 725 8 periods period NOUN hvd.32044092008168 725 9 are be AUX hvd.32044092008168 725 10 not not PART hvd.32044092008168 725 11 double double ADJ hvd.32044092008168 725 12 . . PUNCT hvd.32044092008168 726 1 on on ADP hvd.32044092008168 726 2 the the DET hvd.32044092008168 726 3 other other ADJ hvd.32044092008168 726 4 hand hand NOUN hvd.32044092008168 726 5 any any DET hvd.32044092008168 726 6 other other ADJ hvd.32044092008168 726 7 root root NOUN hvd.32044092008168 726 8 of of ADP hvd.32044092008168 726 9 y y PROPN hvd.32044092008168 726 10 may may AUX hvd.32044092008168 726 11 be be AUX hvd.32044092008168 726 12 double double ADJ hvd.32044092008168 726 13 but but CCONJ hvd.32044092008168 726 14 as as ADP hvd.32044092008168 726 15 a a DET hvd.32044092008168 726 16 similar similar ADJ hvd.32044092008168 726 17 course course NOUN hvd.32044092008168 726 18 of of ADP hvd.32044092008168 726 19 reasoning reasoning NOUN hvd.32044092008168 726 20 shows show VERB hvd.32044092008168 726 21 it it PRON hvd.32044092008168 726 22 could could AUX hvd.32044092008168 726 23 not not PART hvd.32044092008168 726 24 be be AUX hvd.32044092008168 726 25 tripple tripple NOUN hvd.32044092008168 726 26 . . PUNCT hvd.32044092008168 727 1 if if SCONJ hvd.32044092008168 727 2 then then ADV hvd.32044092008168 727 3 c=0 c=0 VERB hvd.32044092008168 727 4 all all DET hvd.32044092008168 727 5 the the DET hvd.32044092008168 727 6 roots root NOUN hvd.32044092008168 727 7 will will AUX hvd.32044092008168 727 8 be be AUX hvd.32044092008168 727 9 double double ADJ hvd.32044092008168 727 10 unless unless SCONJ hvd.32044092008168 727 11 they they PRON hvd.32044092008168 727 12 are be AUX hvd.32044092008168 727 13 semi semi ADJ hvd.32044092008168 727 14 - - NOUN hvd.32044092008168 727 15 periods period NOUN hvd.32044092008168 727 16 and and CCONJ hvd.32044092008168 727 17 we we PRON hvd.32044092008168 727 18 may may AUX hvd.32044092008168 727 19 write write VERB hvd.32044092008168 727 20 [ [ X hvd.32044092008168 727 21 89 89 NUM hvd.32044092008168 727 22 ] ] PUNCT hvd.32044092008168 727 23 · · PUNCT hvd.32044092008168 727 24 y= y= NUM hvd.32044092008168 727 25 — — PUNCT hvd.32044092008168 727 26 * * PUNCT hvd.32044092008168 727 27 ( ( PUNCT hvd.32044092008168 727 28 pu pu PROPN hvd.32044092008168 727 29 e e PROPN hvd.32044092008168 727 30 ) ) PUNCT hvd.32044092008168 727 31 ( ( PUNCT hvd.32044092008168 727 32 pu pu PROPN hvd.32044092008168 727 33 ex)'(pu ex)'(pu PROPN hvd.32044092008168 727 34 — — PUNCT hvd.32044092008168 727 35 ez ez PROPN hvd.32044092008168 727 36 ) ) PUNCT hvd.32044092008168 727 37 ? ? PUNCT hvd.32044092008168 727 38 " " PUNCT hvd.32044092008168 728 1 ii ii PROPN hvd.32044092008168 728 2 ( ( PUNCT hvd.32044092008168 728 3 pu pu PROPN hvd.32044092008168 728 4 pa pa PROPN hvd.32044092008168 728 5 ) ) PUNCT hvd.32044092008168 728 6 ? ? PUNCT hvd.32044092008168 729 1 e e X hvd.32044092008168 729 2 . . PUNCT hvd.32044092008168 730 1 whence whence INTJ hvd.32044092008168 730 2 . . PUNCT hvd.32044092008168 730 3 . . PUNCT hvd.32044092008168 731 1 င် င် PROPN hvd.32044092008168 732 1 [ [ X hvd.32044092008168 732 2 90 90 NUM hvd.32044092008168 732 3 ] ] PUNCT hvd.32044092008168 732 4 : : PUNCT hvd.32044092008168 732 5 · · PUNCT hvd.32044092008168 732 6 y y PROPN hvd.32044092008168 732 7 = = PRON hvd.32044092008168 732 8 v(pu v(pu X hvd.32044092008168 732 9 – – PUNCT hvd.32044092008168 732 10 e)'(puey e)'(puey VERB hvd.32044092008168 732 11 ) ) PUNCT hvd.32044092008168 732 12 " " PUNCT hvd.32044092008168 732 13 ( ( PUNCT hvd.32044092008168 732 14 pu pu PROPN hvd.32044092008168 732 15 — — PUNCT hvd.32044092008168 732 16 ez ez PROPN hvd.32044092008168 732 17 ) ) PUNCT hvd.32044092008168 732 18 " " PUNCT hvd.32044092008168 732 19 " " PUNCT hvd.32044092008168 732 20 ii ii PROPN hvd.32044092008168 732 21 ( ( PUNCT hvd.32044092008168 732 22 pu pu PROPN hvd.32044092008168 732 23 pa pa PROPN hvd.32044092008168 732 24 ) ) PUNCT hvd.32044092008168 732 25 where where SCONJ hvd.32044092008168 732 26 e e NOUN hvd.32044092008168 732 27 , , PUNCT hvd.32044092008168 732 28 ' ' PUNCT hvd.32044092008168 732 29 , , PUNCT hvd.32044092008168 732 30 0 0 NUM hvd.32044092008168 732 31 or or CCONJ hvd.32044092008168 732 32 1 1 NUM hvd.32044092008168 732 33 . . PUNCT hvd.32044092008168 733 1 but but CCONJ hvd.32044092008168 733 2 this this DET hvd.32044092008168 733 3 form form NOUN hvd.32044092008168 733 4 we we PRON hvd.32044092008168 733 5 observe observe VERB hvd.32044092008168 733 6 at at ADP hvd.32044092008168 733 7 once once ADV hvd.32044092008168 733 8 is be AUX hvd.32044092008168 733 9 that that PRON hvd.32044092008168 733 10 assumed assume VERB hvd.32044092008168 733 11 in in ADP hvd.32044092008168 733 12 every every DET hvd.32044092008168 733 13 case case NOUN hvd.32044092008168 733 14 by by ADP hvd.32044092008168 733 15 the the DET hvd.32044092008168 733 16 special special ADJ hvd.32044092008168 733 17 functions function NOUN hvd.32044092008168 733 18 of of ADP hvd.32044092008168 733 19 lamé lamé NOUN hvd.32044092008168 733 20 where where SCONJ hvd.32044092008168 733 21 we we PRON hvd.32044092008168 733 22 found find VERB hvd.32044092008168 733 23 y y PROPN hvd.32044092008168 733 24 always always ADV hvd.32044092008168 733 25 equal equal ADJ hvd.32044092008168 733 26 to to ADP hvd.32044092008168 733 27 a a DET hvd.32044092008168 733 28 ( ( PUNCT hvd.32044092008168 733 29 polynomial polynomial NOUN hvd.32044092008168 733 30 in in ADP hvd.32044092008168 733 31 p(u p(u PROPN hvd.32044092008168 733 32 ) ) PUNCT hvd.32044092008168 733 33 times time NOUN hvd.32044092008168 733 34 some some DET hvd.32044092008168 733 35 one one NUM hvd.32044092008168 733 36 or or CCONJ hvd.32044092008168 733 37 more more ADJ hvd.32044092008168 733 38 of of ADP hvd.32044092008168 733 39 the the DET hvd.32044092008168 733 40 factors factor NOUN hvd.32044092008168 733 41 ( ( PUNCT hvd.32044092008168 733 42 pu pu PROPN hvd.32044092008168 733 43 – – PUNCT hvd.32044092008168 733 44 ea)% ea)% PROPN hvd.32044092008168 733 45 . . PUNCT hvd.32044092008168 734 1 ex% ex% NOUN hvd.32044092008168 734 2 that that PRON hvd.32044092008168 734 3 is be AUX hvd.32044092008168 734 4 c c PROPN hvd.32044092008168 734 5 = = SYM hvd.32044092008168 734 6 0 0 NUM hvd.32044092008168 734 7 is be AUX hvd.32044092008168 734 8 a a DET hvd.32044092008168 734 9 condition condition NOUN hvd.32044092008168 734 10 that that SCONJ hvd.32044092008168 734 11 the the DET hvd.32044092008168 734 12 integrals integral NOUN hvd.32044092008168 734 13 be be AUX hvd.32044092008168 734 14 the the DET hvd.32044092008168 734 15 special special ADJ hvd.32044092008168 734 16 double double ADJ hvd.32044092008168 734 17 periodic periodic ADJ hvd.32044092008168 734 18 functions function NOUN hvd.32044092008168 734 19 of of ADP hvd.32044092008168 734 20 lamé lamé NOUN hvd.32044092008168 734 21 . . PUNCT hvd.32044092008168 735 1 by by ADP hvd.32044092008168 735 2 a a DET hvd.32044092008168 735 3 transformation transformation NOUN hvd.32044092008168 735 4 similar similar ADJ hvd.32044092008168 735 5 to to ADP hvd.32044092008168 735 6 that that PRON hvd.32044092008168 735 7 on on ADP hvd.32044092008168 735 8 p. p. NOUN hvd.32044092008168 735 9 35 35 NUM hvd.32044092008168 735 10 we we PRON hvd.32044092008168 735 11 may may AUX hvd.32044092008168 735 12 write write VERB hvd.32044092008168 735 13 equation equation NOUN hvd.32044092008168 735 14 ( ( PUNCT hvd.32044092008168 735 15 64 64 NUM hvd.32044092008168 735 16 , , PUNCT hvd.32044092008168 735 17 p. p. NOUN hvd.32044092008168 735 18 38 38 NUM hvd.32044092008168 735 19 ) ) PUNCT hvd.32044092008168 735 20 in in ADP hvd.32044092008168 735 21 the the DET hvd.32044092008168 735 22 form form NOUN hvd.32044092008168 735 23 : : PUNCT hvd.32044092008168 735 24 54 54 NUM hvd.32044092008168 735 25 part part NOUN hvd.32044092008168 735 26 v. v. ADP hvd.32044092008168 735 27 4 4 NUM hvd.32044092008168 735 28 c c NOUN hvd.32044092008168 735 29 * * PUNCT hvd.32044092008168 735 30 = = SYM hvd.32044092008168 735 31 ( ( PUNCT hvd.32044092008168 735 32 4 4 NUM hvd.32044092008168 735 33 * * PUNCT hvd.32044092008168 735 34 * * PUNCT hvd.32044092008168 735 35 – – PUNCT hvd.32044092008168 735 36 9 9 NUM hvd.32044092008168 735 37 : : PUNCT hvd.32044092008168 735 38 t t PROPN hvd.32044092008168 735 39 – – PUNCT hvd.32044092008168 735 40 9:)[(a 9:)[(a NUM hvd.32044092008168 735 41 ) ) PUNCT hvd.32044092008168 735 42 – – PUNCT hvd.32044092008168 735 43 2 2 NUM hvd.32044092008168 735 44 ro ro X hvd.32044092008168 735 45 ] ] X hvd.32044092008168 735 46 – – PUNCT hvd.32044092008168 735 47 ( ( PUNCT hvd.32044092008168 735 48 12ť 12ť NOUN hvd.32044092008168 735 49 – – PUNCT hvd.32044092008168 735 50 9 9 NUM hvd.32044092008168 735 51 . . PUNCT hvd.32044092008168 735 52 ) ) PUNCT hvd.32044092008168 736 1 y y PROPN hvd.32044092008168 736 2 y y PROPN hvd.32044092008168 736 3 ; ; PUNCT hvd.32044092008168 736 4 ) ) PUNCT hvd.32044092008168 736 5 2 2 NUM hvd.32044092008168 736 6 n n CCONJ hvd.32044092008168 736 7 . . PUNCT hvd.32044092008168 737 1 as as ADP hvd.32044092008168 737 2 d d X hvd.32044092008168 737 3 dy dy X hvd.32044092008168 737 4 dy dy PROPN hvd.32044092008168 737 5 2 2 PROPN hvd.32044092008168 737 6 y y PROPN hvd.32044092008168 737 7 dt dt PROPN hvd.32044092008168 737 8 dt dt PROPN hvd.32044092008168 737 9 dt dt PROPN hvd.32044092008168 737 10 + + PROPN hvd.32044092008168 737 11 4 4 NUM hvd.32044092008168 737 12 [ [ PUNCT hvd.32044092008168 737 13 ( ( PUNCT hvd.32044092008168 737 14 + + PROPN hvd.32044092008168 737 15 1)t 1)t NUM hvd.32044092008168 737 16 + + PUNCT hvd.32044092008168 737 17 b]y b]y PROPN hvd.32044092008168 737 18 ? ? PUNCT hvd.32044092008168 738 1 and and CCONJ hvd.32044092008168 738 2 we we PRON hvd.32044092008168 738 3 have have VERB hvd.32044092008168 738 4 ( ( PUNCT hvd.32044092008168 738 5 62 62 NUM hvd.32044092008168 738 6 , , PUNCT hvd.32044092008168 738 7 p. p. NOUN hvd.32044092008168 738 8 37 37 NUM hvd.32044092008168 738 9 ) ) PUNCT hvd.32044092008168 738 10 ( ( PUNCT hvd.32044092008168 738 11 1)"b 1)"b PUNCT hvd.32044092008168 738 12 " " PUNCT hvd.32044092008168 738 13 y y PROPN hvd.32044092008168 738 14 t t PROPN hvd.32044092008168 738 15 ... ... PUNCT hvd.32044092008168 739 1 [ [ X hvd.32044092008168 739 2 3 3 NUM hvd.32044092008168 739 3 · · SYM hvd.32044092008168 739 4 5 5 NUM hvd.32044092008168 739 5 7 7 NUM hvd.32044092008168 739 6 1 1 NUM hvd.32044092008168 739 7 ] ] PUNCT hvd.32044092008168 739 8 ” " PUNCT hvd.32044092008168 739 9 from from ADP hvd.32044092008168 739 10 which which PRON hvd.32044092008168 739 11 relations relation NOUN hvd.32044092008168 739 12 we we PRON hvd.32044092008168 739 13 see see VERB hvd.32044092008168 739 14 that that SCONJ hvd.32044092008168 739 15 the the DET hvd.32044092008168 739 16 highest high ADJ hvd.32044092008168 739 17 power power NOUN hvd.32044092008168 739 18 of of ADP hvd.32044092008168 739 19 b b PROPN hvd.32044092008168 739 20 in in ADP hvd.32044092008168 739 21 c c PROPN hvd.32044092008168 739 22 is be AUX hvd.32044092008168 739 23 2n 2n NUM hvd.32044092008168 739 24 + + CCONJ hvd.32044092008168 739 25 1 1 NUM hvd.32044092008168 740 1 and and CCONJ hvd.32044092008168 740 2 that that SCONJ hvd.32044092008168 740 3 the the DET hvd.32044092008168 740 4 condition condition NOUN hvd.32044092008168 740 5 c= c= VERB hvd.32044092008168 740 6 0 0 NUM hvd.32044092008168 740 7 ) ) PUNCT hvd.32044092008168 740 8 gives give VERB hvd.32044092008168 740 9 rise rise NOUN hvd.32044092008168 740 10 to to ADP hvd.32044092008168 740 11 an an DET hvd.32044092008168 740 12 equation equation NOUN hvd.32044092008168 740 13 of of ADP hvd.32044092008168 740 14 o o DET hvd.32044092008168 740 15 the the DET hvd.32044092008168 740 16 2n 2n NUM hvd.32044092008168 740 17 + + NUM hvd.32044092008168 740 18 1st 1st ADJ hvd.32044092008168 740 19 degree degree NOUN hvd.32044092008168 740 20 in in ADP hvd.32044092008168 740 21 b b PROPN hvd.32044092008168 740 22 which which PRON hvd.32044092008168 740 23 is be AUX hvd.32044092008168 740 24 as as ADP hvd.32044092008168 740 25 the the DET hvd.32044092008168 740 26 number number NOUN hvd.32044092008168 740 27 of of ADP hvd.32044092008168 740 28 the the DET hvd.32044092008168 740 29 special special ADJ hvd.32044092008168 740 30 functions function NOUN hvd.32044092008168 740 31 of of ADP hvd.32044092008168 740 32 lamé lamé NOUN hvd.32044092008168 740 33 . . PUNCT hvd.32044092008168 741 1 refering refer VERB hvd.32044092008168 741 2 to to ADP hvd.32044092008168 741 3 ( ( PUNCT hvd.32044092008168 741 4 68 68 NUM hvd.32044092008168 741 5 , , PUNCT hvd.32044092008168 741 6 p. p. NOUN hvd.32044092008168 741 7 40 40 NUM hvd.32044092008168 741 8 ) ) PUNCT hvd.32044092008168 741 9 we we PRON hvd.32044092008168 741 10 see see VERB hvd.32044092008168 741 11 that that SCONJ hvd.32044092008168 741 12 c² c² PROPN hvd.32044092008168 741 13 = = PROPN hvd.32044092008168 741 14 0 0 NUM hvd.32044092008168 741 15 has have AUX hvd.32044092008168 741 16 been be AUX hvd.32044092008168 741 17 found find VERB hvd.32044092008168 741 18 an an DET hvd.32044092008168 741 19 equation equation NOUN hvd.32044092008168 741 20 of of ADP hvd.32044092008168 741 21 the the DET hvd.32044092008168 741 22 seventh seventh ADJ hvd.32044092008168 741 23 degree degree NOUN hvd.32044092008168 741 24 in in ADP hvd.32044092008168 741 25 b b PROPN hvd.32044092008168 741 26 as as SCONJ hvd.32044092008168 741 27 required require VERB hvd.32044092008168 741 28 by by ADP hvd.32044092008168 741 29 the the DET hvd.32044092008168 741 30 above above ADJ hvd.32044092008168 741 31 theory theory NOUN hvd.32044092008168 741 32 . . PUNCT hvd.32044092008168 742 1 functions function NOUN hvd.32044092008168 742 2 of of ADP hvd.32044092008168 742 3 the the DET hvd.32044092008168 742 4 first first ADJ hvd.32044092008168 742 5 sort sort NOUN hvd.32044092008168 742 6 . . PUNCT hvd.32044092008168 743 1 following follow VERB hvd.32044092008168 743 2 the the DET hvd.32044092008168 743 3 notation notation NOUN hvd.32044092008168 743 4 of of ADP hvd.32044092008168 743 5 m. m. PROPN hvd.32044092008168 743 6 halphen halphen ADV hvd.32044092008168 743 7 designate designate ADJ hvd.32044092008168 743 8 by by ADP hvd.32044092008168 743 9 p p PROPN hvd.32044092008168 743 10 the the DET hvd.32044092008168 743 11 first first ADJ hvd.32044092008168 743 12 member member NOUN hvd.32044092008168 743 13 of of ADP hvd.32044092008168 743 14 the the DET hvd.32044092008168 743 15 equation equation NOUN hvd.32044092008168 743 16 that that PRON hvd.32044092008168 743 17 determines determine VERB hvd.32044092008168 743 18 b b PROPN hvd.32044092008168 743 19 corresponding correspond VERB hvd.32044092008168 743 20 to to ADP hvd.32044092008168 743 21 functions function NOUN hvd.32044092008168 743 22 of of ADP hvd.32044092008168 743 23 the the DET hvd.32044092008168 743 24 first first ADJ hvd.32044092008168 743 25 sort sort NOUN hvd.32044092008168 743 26 . . PUNCT hvd.32044092008168 744 1 refering refer VERB hvd.32044092008168 744 2 again again ADV hvd.32044092008168 744 3 to to ADP hvd.32044092008168 744 4 ( ( PUNCT hvd.32044092008168 744 5 part part NOUN hvd.32044092008168 744 6 iv iv X hvd.32044092008168 744 7 ) ) PUNCT hvd.32044092008168 744 8 we we PRON hvd.32044092008168 744 9 observe observe VERB hvd.32044092008168 744 10 that that SCONJ hvd.32044092008168 744 11 if if SCONJ hvd.32044092008168 744 12 n n ADP hvd.32044092008168 744 13 is be AUX hvd.32044092008168 744 14 odd odd ADJ hvd.32044092008168 744 15 each each PRON hvd.32044092008168 744 16 of of ADP hvd.32044092008168 744 17 these these DET hvd.32044092008168 744 18 functions function NOUN hvd.32044092008168 744 19 contains contain VERB hvd.32044092008168 744 20 the the DET hvd.32044092008168 744 21 factor factor NOUN hvd.32044092008168 744 22 pu pu PROPN hvd.32044092008168 744 23 . . PUNCT hvd.32044092008168 745 1 for for ADP hvd.32044092008168 745 2 example example NOUN hvd.32044092008168 745 3 we we PRON hvd.32044092008168 745 4 have have VERB hvd.32044092008168 745 5 : : PUNCT hvd.32044092008168 745 6 n n CCONJ hvd.32044092008168 745 7 = = X hvd.32044092008168 745 8 3 3 NUM hvd.32044092008168 745 9 : : PUNCT hvd.32044092008168 745 10 y= y= PROPN hvd.32044092008168 746 1 p p NOUN hvd.32044092008168 746 2 where where SCONJ hvd.32044092008168 746 3 : : PUNCT hvd.32044092008168 746 4 = = PROPN hvd.32044092008168 746 5 p p PROPN hvd.32044092008168 746 6 where where SCONJ hvd.32044092008168 746 7 b=0 b=0 ADV hvd.32044092008168 746 8 , , PUNCT hvd.32044092008168 746 9 the the DET hvd.32044092008168 746 10 degree degree NOUN hvd.32044092008168 746 11 in in ADP hvd.32044092008168 746 12 b b PROPN hvd.32044092008168 746 13 being be AUX hvd.32044092008168 746 14 unity unity NOUN hvd.32044092008168 746 15 . . PUNCT hvd.32044092008168 747 1 n=5 n=5 ADJ hvd.32044092008168 747 2 : : PUNCT hvd.32044092008168 747 3 y y PROPN hvd.32044092008168 747 4 = = X hvd.32044092008168 747 5 p p NOUN hvd.32044092008168 747 6 " " PUNCT hvd.32044092008168 747 7 – – PUNCT hvd.32044092008168 747 8 bp bp PROPN hvd.32044092008168 747 9 ' ' PUNCT hvd.32044092008168 747 10 = = NOUN hvd.32044092008168 747 11 p p PROPN hvd.32044092008168 747 12 ( ( PUNCT hvd.32044092008168 747 13 12 12 NUM hvd.32044092008168 747 14 p p NOUN hvd.32044092008168 747 15 — — PUNCT hvd.32044092008168 747 16 b b NOUN hvd.32044092008168 747 17 ) ) PUNCT hvd.32044092008168 747 18 where where SCONJ hvd.32044092008168 747 19 b b NOUN hvd.32044092008168 747 20 ’ ' PUNCT hvd.32044092008168 747 21 — — PUNCT hvd.32044092008168 747 22 2792 2792 NUM hvd.32044092008168 747 23 = = SYM hvd.32044092008168 747 24 0 0 NUM hvd.32044092008168 747 25 yp yp PROPN hvd.32044092008168 747 26 ' ' PUNCT hvd.32044092008168 747 27 the the DET hvd.32044092008168 747 28 degree degree NOUN hvd.32044092008168 747 29 being be AUX hvd.32044092008168 747 30 two two NUM hvd.32044092008168 747 31 , , PUNCT hvd.32044092008168 747 32 etc etc X hvd.32044092008168 747 33 . . X hvd.32044092008168 748 1 but but CCONJ hvd.32044092008168 748 2 p p NOUN hvd.32044092008168 748 3 ' ' PUNCT hvd.32044092008168 748 4 ( ( PUNCT hvd.32044092008168 748 5 u)=4(pu u)=4(pu PROPN hvd.32044092008168 748 6 e)(pu e)(pu PROPN hvd.32044092008168 748 7 — — PUNCT hvd.32044092008168 748 8 ez ez PROPN hvd.32044092008168 748 9 ) ) PUNCT hvd.32044092008168 748 10 ( ( PUNCT hvd.32044092008168 748 11 pu pu PROPN hvd.32044092008168 748 12 – – PUNCT hvd.32044092008168 748 13 es es PROPN hvd.32044092008168 748 14 ) ) PUNCT hvd.32044092008168 748 15 whence whence NOUN hvd.32044092008168 748 16 for for ADP hvd.32044092008168 748 17 n n CCONJ hvd.32044092008168 748 18 odd odd ADJ hvd.32044092008168 748 19 -or -or NUM hvd.32044092008168 748 20 equal equal ADJ hvd.32044092008168 748 21 to to ADP hvd.32044092008168 748 22 three three NUM hvd.32044092008168 748 23 , , PUNCT hvd.32044092008168 748 24 & & CCONJ hvd.32044092008168 748 25 , , PUNCT hvd.32044092008168 748 26 é é X hvd.32044092008168 748 27 , , PUNCT hvd.32044092008168 748 28 " " PUNCT hvd.32044092008168 748 29 are be AUX hvd.32044092008168 748 30 all all PRON hvd.32044092008168 748 31 equal equal ADJ hvd.32044092008168 748 32 to to ADP hvd.32044092008168 748 33 unity unity NOUN hvd.32044092008168 748 34 . . PUNCT hvd.32044092008168 749 1 moreover moreover ADV hvd.32044092008168 749 2 we we PRON hvd.32044092008168 749 3 have have AUX hvd.32044092008168 749 4 obtained obtain VERB hvd.32044092008168 749 5 y y PROPN hvd.32044092008168 749 6 ( ( PUNCT hvd.32044092008168 749 7 67 67 NUM hvd.32044092008168 749 8 , , PUNCT hvd.32044092008168 749 9 p. p. NOUN hvd.32044092008168 749 10 40 40 NUM hvd.32044092008168 749 11 ) ) PUNCT hvd.32044092008168 749 12 expressed express VERB hvd.32044092008168 749 13 as as ADP hvd.32044092008168 749 14 a a DET hvd.32044092008168 749 15 polynomial polynomial NOUN hvd.32044092008168 749 16 in in ADP hvd.32044092008168 749 17 t t PROPN hvd.32044092008168 749 18 and and CCONJ hvd.32044092008168 749 19 b b PROPN hvd.32044092008168 749 20 in in ADP hvd.32044092008168 749 21 the the DET hvd.32044092008168 749 22 form form NOUN hvd.32044092008168 749 23 yn=3 yn=3 PUNCT hvd.32044092008168 749 24 = = PUNCT hvd.32044092008168 749 25 * * PUNCT hvd.32044092008168 749 26 $ $ SYM hvd.32044092008168 749 27 ( ( PUNCT hvd.32044092008168 749 28 t t PROPN hvd.32044092008168 749 29 ) ) PUNCT hvd.32044092008168 749 30 b[g b[g PROPN hvd.32044092008168 749 31 ' ' PUNCT hvd.32044092008168 749 32 + + NUM hvd.32044092008168 749 33 3 3 NUM hvd.32044092008168 749 34 ( ( PUNCT hvd.32044092008168 749 35 t t NOUN hvd.32044092008168 749 36 — — PUNCT hvd.32044092008168 749 37 b b X hvd.32044092008168 749 38 ) ) PUNCT hvd.32044092008168 749 39 ? ? PUNCT hvd.32044092008168 749 40 ] ] X hvd.32044092008168 750 1 – – PUNCT hvd.32044092008168 750 2 0 0 NUM hvd.32044092008168 750 3 ) ) PUNCT hvd.32044092008168 750 4 ] ] PUNCT hvd.32044092008168 750 5 and and CCONJ hvd.32044092008168 750 6 since since SCONJ hvd.32044092008168 750 7 p p PROPN hvd.32044092008168 750 8 ' ' PUNCT hvd.32044092008168 750 9 ( ( PUNCT hvd.32044092008168 750 10 en en PROPN hvd.32044092008168 750 11 ) ) PUNCT hvd.32044092008168 750 12 = = PUNCT hvd.32044092008168 750 13 ť ť X hvd.32044092008168 750 14 ( ( PUNCT hvd.32044092008168 750 15 e e NOUN hvd.32044092008168 750 16 ) ) PUNCT hvd.32044092008168 750 17 = = PUNCT hvd.32044092008168 750 18 0 0 NUM hvd.32044092008168 751 1 we we PRON hvd.32044092008168 751 2 derive derive VERB hvd.32044092008168 751 3 [ [ X hvd.32044092008168 751 4 91 91 NUM hvd.32044092008168 751 5 ] ] PUNCT hvd.32044092008168 751 6 · · PUNCT hvd.32044092008168 751 7 yn=3(en yn=3(en PRON hvd.32044092008168 751 8 ) ) PUNCT hvd.32044092008168 751 9 b b NOUN hvd.32044092008168 752 1 [ [ X hvd.32044092008168 752 2 0 0 NOUN hvd.32044092008168 752 3 ' ' PUNCT hvd.32044092008168 752 4 + + NUM hvd.32044092008168 752 5 3 3 NUM hvd.32044092008168 752 6 ( ( PUNCT hvd.32044092008168 752 7 en en X hvd.32044092008168 752 8 — — PUNCT hvd.32044092008168 752 9 b b X hvd.32044092008168 752 10 ) ) PUNCT hvd.32044092008168 752 11 ] ] PUNCT hvd.32044092008168 752 12 . . PUNCT hvd.32044092008168 753 1 hence hence ADV hvd.32044092008168 753 2 pn=3 pn=3 CCONJ hvd.32044092008168 753 3 = = PRON hvd.32044092008168 753 4 b=15b b=15b PROPN hvd.32044092008168 753 5 is be AUX hvd.32044092008168 753 6 a a DET hvd.32044092008168 753 7 factor factor NOUN hvd.32044092008168 753 8 of of ADP hvd.32044092008168 753 9 yn=3(en yn=3(en NOUN hvd.32044092008168 753 10 ) ) PUNCT hvd.32044092008168 753 11 times time NOUN hvd.32044092008168 753 12 a a DET hvd.32044092008168 753 13 3 3 NUM hvd.32044092008168 753 14 constant constant ADJ hvd.32044092008168 753 15 . . PUNCT hvd.32044092008168 754 1 if if SCONJ hvd.32044092008168 754 2 on on ADP hvd.32044092008168 754 3 the the DET hvd.32044092008168 754 4 other other ADJ hvd.32044092008168 754 5 hand hand NOUN hvd.32044092008168 754 6 n n CCONJ hvd.32044092008168 754 7 be be AUX hvd.32044092008168 754 8 even even ADV hvd.32044092008168 754 9 none none NOUN hvd.32044092008168 754 10 of of ADP hvd.32044092008168 754 11 the the DET hvd.32044092008168 754 12 functions function NOUN hvd.32044092008168 754 13 of of ADP hvd.32044092008168 754 14 the the DET hvd.32044092008168 754 15 first first ADJ hvd.32044092008168 754 16 sort sort NOUN hvd.32044092008168 754 17 contain contain VERB hvd.32044092008168 754 18 a a DET hvd.32044092008168 754 19 factor factor NOUN hvd.32044092008168 754 20 vpu vpu NOUN hvd.32044092008168 754 21 en en ADV hvd.32044092008168 754 22 and and CCONJ hvd.32044092008168 754 23 pn=2x pn=2x ADJ hvd.32044092008168 754 24 will will AUX hvd.32044092008168 754 25 not not PART hvd.32044092008168 754 26 be be AUX hvd.32044092008168 754 27 a a DET hvd.32044092008168 754 28 factor factor NOUN hvd.32044092008168 754 29 of of ADP hvd.32044092008168 754 30 y=%(ea y=%(ea SPACE hvd.32044092008168 754 31 ) ) PUNCT hvd.32044092008168 754 32 . . PUNCT hvd.32044092008168 755 1 3 3 NUM hvd.32044092008168 755 2 3 3 NUM hvd.32044092008168 755 3 e e SYM hvd.32044092008168 755 4 2 2 NUM hvd.32044092008168 755 5 1 1 NUM hvd.32044092008168 755 6 en en ADV hvd.32044092008168 755 7 . . PUNCT hvd.32044092008168 756 1 = = NOUN hvd.32044092008168 756 2 n2x n2x PROPN hvd.32044092008168 756 3 reduction reduction NOUN hvd.32044092008168 756 4 of of ADP hvd.32044092008168 756 5 the the DET hvd.32044092008168 756 6 forms form NOUN hvd.32044092008168 756 7 when when SCONJ hvd.32044092008168 756 8 n n SYM hvd.32044092008168 756 9 equals equal VERB hvd.32044092008168 756 10 three three NUM hvd.32044092008168 756 11 . . PUNCT hvd.32044092008168 757 1 55 55 NUM hvd.32044092008168 757 2 1 1 NUM hvd.32044092008168 757 3 2 2 NUM hvd.32044092008168 757 4 1 1 NUM hvd.32044092008168 757 5 2 2 NUM hvd.32044092008168 757 6 > > PUNCT hvd.32044092008168 757 7 • • PUNCT hvd.32044092008168 757 8 08 08 NUM hvd.32044092008168 758 1 • • SYM hvd.32044092008168 758 2 2 2 NUM hvd.32044092008168 758 3 2 2 NUM hvd.32044092008168 758 4 1592 1592 NUM hvd.32044092008168 758 5 =3 =3 VERB hvd.32044092008168 758 6 2 2 NUM hvd.32044092008168 758 7 =3 =3 VERB hvd.32044092008168 758 8 9(b 9(b NUM hvd.32044092008168 758 9 ) ) PUNCT hvd.32044092008168 758 10 n n CCONJ hvd.32044092008168 758 11 functions function NOUN hvd.32044092008168 758 12 of of ADP hvd.32044092008168 758 13 the the DET hvd.32044092008168 758 14 second second ADJ hvd.32044092008168 758 15 sort sort NOUN hvd.32044092008168 758 16 . . PUNCT hvd.32044092008168 759 1 we we PRON hvd.32044092008168 759 2 have have AUX hvd.32044092008168 759 3 found find VERB hvd.32044092008168 759 4 three three NUM hvd.32044092008168 759 5 equations equation NOUN hvd.32044092008168 759 6 each each PRON hvd.32044092008168 759 7 of of ADP hvd.32044092008168 759 8 degree degree NOUN hvd.32044092008168 759 9 ( ( PUNCT hvd.32044092008168 759 10 n n CCONJ hvd.32044092008168 759 11 + + CCONJ hvd.32044092008168 759 12 1 1 NUM hvd.32044092008168 759 13 ) ) PUNCT hvd.32044092008168 759 14 or or CCONJ hvd.32044092008168 759 15 n n CCONJ hvd.32044092008168 759 16 as as ADP hvd.32044092008168 759 17 n n ADV hvd.32044092008168 759 18 is be AUX hvd.32044092008168 759 19 taken take VERB hvd.32044092008168 759 20 odd odd ADJ hvd.32044092008168 759 21 or or CCONJ hvd.32044092008168 759 22 even even ADV hvd.32044092008168 759 23 , , PUNCT hvd.32044092008168 759 24 that that PRON hvd.32044092008168 759 25 give give VERB hvd.32044092008168 759 26 values value NOUN hvd.32044092008168 759 27 of of ADP hvd.32044092008168 759 28 b b NOUN hvd.32044092008168 759 29 that that PRON hvd.32044092008168 759 30 , , PUNCT hvd.32044092008168 759 31 if if SCONJ hvd.32044092008168 759 32 n n CCONJ hvd.32044092008168 759 33 be be AUX hvd.32044092008168 759 34 odd odd ADJ hvd.32044092008168 759 35 , , PUNCT hvd.32044092008168 759 36 correspond correspond VERB hvd.32044092008168 759 37 to to ADP hvd.32044092008168 759 38 functions function NOUN hvd.32044092008168 759 39 of of ADP hvd.32044092008168 759 40 the the DET hvd.32044092008168 759 41 second second ADJ hvd.32044092008168 759 42 sort sort NOUN hvd.32044092008168 759 43 , , PUNCT hvd.32044092008168 759 44 or or CCONJ hvd.32044092008168 759 45 , , PUNCT hvd.32044092008168 759 46 if if SCONJ hvd.32044092008168 759 47 n n CCONJ hvd.32044092008168 759 48 be be AUX hvd.32044092008168 759 49 even even ADV hvd.32044092008168 759 50 , , PUNCT hvd.32044092008168 759 51 to to ADP hvd.32044092008168 759 52 functions function NOUN hvd.32044092008168 759 53 of of ADP hvd.32044092008168 759 54 the the DET hvd.32044092008168 759 55 third third ADJ hvd.32044092008168 759 56 sort sort NOUN hvd.32044092008168 759 57 . . PUNCT hvd.32044092008168 760 1 designate designate ADJ hvd.32044092008168 760 2 the the DET hvd.32044092008168 760 3 first first ADJ hvd.32044092008168 760 4 members member NOUN hvd.32044092008168 760 5 , , PUNCT hvd.32044092008168 760 6 by by ADP hvd.32044092008168 760 7 q1 q1 NOUN hvd.32044092008168 760 8 , , PUNCT hvd.32044092008168 760 9 q2 q2 NOUN hvd.32044092008168 760 10 , , PUNCT hvd.32044092008168 760 11 and and CCONJ hvd.32044092008168 760 12 q3 q3 PROPN hvd.32044092008168 760 13 . . PUNCT hvd.32044092008168 761 1 refering refer VERB hvd.32044092008168 761 2 again again ADV hvd.32044092008168 761 3 to to ADP hvd.32044092008168 761 4 lamé lamé NOUN hvd.32044092008168 761 5 's 's PART hvd.32044092008168 761 6 special special ADJ hvd.32044092008168 761 7 functions function NOUN hvd.32044092008168 761 8 we we PRON hvd.32044092008168 761 9 see see VERB hvd.32044092008168 761 10 that that SCONJ hvd.32044092008168 761 11 if if SCONJ hvd.32044092008168 761 12 q1 q1 PROPN hvd.32044092008168 761 13 o o VERB hvd.32044092008168 761 14 the the DET hvd.32044092008168 761 15 function function NOUN hvd.32044092008168 761 16 of of ADP hvd.32044092008168 761 17 lamé lamé NOUN hvd.32044092008168 761 18 corresponding corresponding NOUN hvd.32044092008168 761 19 contains contain VERB hvd.32044092008168 761 20 the the DET hvd.32044092008168 761 21 factor factor NOUN hvd.32044092008168 761 22 vpu vpu NOUN hvd.32044092008168 761 23 & & CCONJ hvd.32044092008168 761 24 if if SCONJ hvd.32044092008168 761 25 n n ADV hvd.32044092008168 761 26 is be AUX hvd.32044092008168 761 27 odd odd ADJ hvd.32044092008168 761 28 and and CCONJ hvd.32044092008168 761 29 the the DET hvd.32044092008168 761 30 two two NUM hvd.32044092008168 761 31 corresponding corresponding ADJ hvd.32044092008168 761 32 factors factor NOUN hvd.32044092008168 761 33 vpu vpu NOUN hvd.32044092008168 761 34 € € PROPN hvd.32044092008168 761 35 , , PUNCT hvd.32044092008168 761 36 vpu vpu NOUN hvd.32044092008168 761 37 – – PUNCT hvd.32044092008168 761 38 ez ez PROPN hvd.32044092008168 761 39 if if SCONJ hvd.32044092008168 761 40 n n CCONJ hvd.32044092008168 761 41 is be AUX hvd.32044092008168 761 42 even even ADV hvd.32044092008168 761 43 . . PUNCT hvd.32044092008168 762 1 in in ADP hvd.32044092008168 762 2 the the DET hvd.32044092008168 762 3 first first ADJ hvd.32044092008168 762 4 case case NOUN hvd.32044092008168 762 5 q. q. NOUN hvd.32044092008168 762 6 is be AUX hvd.32044092008168 762 7 a a DET hvd.32044092008168 762 8 factor factor NOUN hvd.32044092008168 762 9 ез ез VERB hvd.32044092008168 762 10 of of ADP hvd.32044092008168 762 11 y(21 y(21 SPACE hvd.32044092008168 762 12 ) ) PUNCT hvd.32044092008168 762 13 and and CCONJ hvd.32044092008168 762 14 in in ADP hvd.32044092008168 762 15 the the DET hvd.32044092008168 762 16 second second ADJ hvd.32044092008168 762 17 case case NOUN hvd.32044092008168 762 18 of of ADP hvd.32044092008168 762 19 y y PROPN hvd.32044092008168 762 20 ( ( PUNCT hvd.32044092008168 762 21 ez ez PROPN hvd.32044092008168 762 22 ) ) PUNCT hvd.32044092008168 762 23 and and CCONJ hvd.32044092008168 762 24 of of ADP hvd.32044092008168 762 25 y y PROPN hvd.32044092008168 762 26 ( ( PUNCT hvd.32044092008168 762 27 cz cz PROPN hvd.32044092008168 762 28 ) ) PUNCT hvd.32044092008168 762 29 , , PUNCT hvd.32044092008168 762 30 while while SCONJ hvd.32044092008168 762 31 in in ADP hvd.32044092008168 762 32 the the DET hvd.32044092008168 762 33 second second ADJ hvd.32044092008168 762 34 case case NOUN hvd.32044092008168 762 35 we we PRON hvd.32044092008168 762 36 have have VERB hvd.32044092008168 762 37 also also ADV hvd.32044092008168 762 38 y(e y(e VERB hvd.32044092008168 762 39 ) ) PUNCT hvd.32044092008168 762 40 contains contain VERB hvd.32044092008168 762 41 the the DET hvd.32044092008168 762 42 factor factor NOUN hvd.32044092008168 762 43 q2 q2 PROPN hvd.32044092008168 762 44 23 23 NUM hvd.32044092008168 762 45 . . PUNCT hvd.32044092008168 763 1 returning return VERB hvd.32044092008168 763 2 to to ADP hvd.32044092008168 763 3 n=3 n=3 NOUN hvd.32044092008168 763 4 we we PRON hvd.32044092008168 763 5 have have AUX hvd.32044092008168 763 6 ( ( PUNCT hvd.32044092008168 763 7 see see VERB hvd.32044092008168 763 8 ( ( PUNCT hvd.32044092008168 763 9 73 73 NUM hvd.32044092008168 763 10 ) ) PUNCT hvd.32044092008168 763 11 p. p. NOUN hvd.32044092008168 763 12 44 44 NUM hvd.32044092008168 763 13 ) ) PUNCT hvd.32044092008168 764 1 p p NOUN hvd.32044092008168 765 1 [ [ X hvd.32044092008168 765 2 q1]n= q1]n= X hvd.32044092008168 765 3 b2 b2 PROPN hvd.32044092008168 765 4 64 64 NUM hvd.32044092008168 765 5 b b PROPN hvd.32044092008168 765 6 + + CCONJ hvd.32044092008168 765 7 45e 45e NUM hvd.32044092008168 765 8 , , PUNCT hvd.32044092008168 765 9 ? ? PUNCT hvd.32044092008168 765 10 — — PUNCT hvd.32044092008168 765 11 1592 1592 NUM hvd.32044092008168 765 12 [ [ X hvd.32044092008168 765 13 92 92 NUM hvd.32044092008168 765 14 ] ] PUNCT hvd.32044092008168 765 15 · · PUNCT hvd.32044092008168 765 16 [ [ X hvd.32044092008168 765 17 q2]n= q2]n= PRON hvd.32044092008168 765 18 b2 b2 PROPN hvd.32044092008168 765 19 6 6 NUM hvd.32044092008168 765 20 ez ez PROPN hvd.32044092008168 765 21 b b PROPN hvd.32044092008168 765 22 + + PROPN hvd.32044092008168 765 23 45 45 NUM hvd.32044092008168 765 24 e e NOUN hvd.32044092008168 765 25 , , PUNCT hvd.32044092008168 765 26 [ [ X hvd.32044092008168 765 27 23]n= 23]n= PROPN hvd.32044092008168 765 28 b2 b2 PROPN hvd.32044092008168 765 29 6 6 NUM hvd.32044092008168 765 30 6 6 NUM hvd.32044092008168 765 31 ez ez PROPN hvd.32044092008168 765 32 b b PROPN hvd.32044092008168 765 33 + + PROPN hvd.32044092008168 765 34 45 45 NUM hvd.32044092008168 765 35 ez ez PROPN hvd.32044092008168 765 36 ? ? PUNCT hvd.32044092008168 765 37 — — PUNCT hvd.32044092008168 765 38 159 159 NUM hvd.32044092008168 765 39 , , PUNCT hvd.32044092008168 765 40 or or CCONJ hvd.32044092008168 765 41 in in ADP hvd.32044092008168 765 42 general general ADJ hvd.32044092008168 765 43 writing writing NOUN hvd.32044092008168 765 44 b b PROPN hvd.32044092008168 765 45 15 15 NUM hvd.32044092008168 765 46 b b NOUN hvd.32044092008168 765 47 and and CCONJ hvd.32044092008168 765 48 o o NOUN hvd.32044092008168 765 49 468 468 NUM hvd.32044092008168 765 50 — — PUNCT hvd.32044092008168 765 51 92b 92b NUM hvd.32044092008168 765 52 — — PUNCT hvd.32044092008168 765 53 93 93 NUM hvd.32044092008168 765 54 -[93 -[93 X hvd.32044092008168 765 55 ] ] X hvd.32044092008168 765 56 · · PUNCT hvd.32044092008168 765 57 [ [ X hvd.32044092008168 765 58 qı]n=3 qı]n=3 X hvd.32044092008168 765 59 = = PRON hvd.32044092008168 765 60 32.5 32.5 NUM hvd.32044092008168 765 61 [ [ X hvd.32044092008168 765 62 9 9 NUM hvd.32044092008168 765 63 ' ' PUNCT hvd.32044092008168 765 64 + + NUM hvd.32044092008168 765 65 3(e2 3(e2 NUM hvd.32044092008168 765 66 – – PUNCT hvd.32044092008168 765 67 ) ) PUNCT hvd.32044092008168 765 68 ? ? PUNCT hvd.32044092008168 765 69 ] ] PUNCT hvd.32044092008168 765 70 . . PUNCT hvd.32044092008168 766 1 also also ADV hvd.32044092008168 766 2 from from ADP hvd.32044092008168 766 3 ( ( PUNCT hvd.32044092008168 766 4 91 91 NUM hvd.32044092008168 766 5 ) ) PUNCT hvd.32044092008168 766 6 . . PUNCT hvd.32044092008168 767 1 [ [ X hvd.32044092008168 767 2 94 94 NUM hvd.32044092008168 767 3 ] ] PUNCT hvd.32044092008168 767 4 · · PUNCT hvd.32044092008168 767 5 y(ez y(ez PROPN hvd.32044092008168 767 6 ) ) PUNCT hvd.32044092008168 767 7 b b X hvd.32044092008168 767 8 [ [ X hvd.32044092008168 767 9 g g X hvd.32044092008168 767 10 ' ' PUNCT hvd.32044092008168 767 11 + + NUM hvd.32044092008168 767 12 3(e 3(e NUM hvd.32044092008168 767 13 – – PUNCT hvd.32044092008168 767 14 ) ) PUNCT hvd.32044092008168 767 15 ] ] PUNCT hvd.32044092008168 767 16 ) ) PUNCT hvd.32044092008168 767 17 ] ] PUNCT hvd.32044092008168 768 1 b b X hvd.32044092008168 768 2 [ [ X hvd.32044092008168 768 3 15 15 NUM hvd.32044092008168 768 4 b2 b2 PROPN hvd.32044092008168 768 5 + + CCONJ hvd.32044092008168 768 6 30 30 NUM hvd.32044092008168 768 7 , , PUNCT hvd.32044092008168 768 8 6e4b 6e4b NOUN hvd.32044092008168 768 9 — — PUNCT hvd.32044092008168 768 10 92 92 NUM hvd.32044092008168 768 11 ] ] X hvd.32044092008168 768 12 ве ве PROPN hvd.32044092008168 768 13 , , PUNCT hvd.32044092008168 768 14 в в PROPN hvd.32044092008168 768 15 + + CCONJ hvd.32044092008168 768 16 3e 3e NUM hvd.32044092008168 768 17 ; ; PUNCT hvd.32044092008168 768 18 " " PUNCT hvd.32044092008168 768 19 – – PUNCT hvd.32044092008168 768 20 9 9 NUM hvd.32044092008168 768 21 cb cb X hvd.32044092008168 768 22 [ [ X hvd.32044092008168 768 23 b b NOUN hvd.32044092008168 768 24 ? ? PUNCT hvd.32044092008168 768 25 6e 6e PROPN hvd.32044092008168 768 26 , , PUNCT hvd.32044092008168 768 27 b b PROPN hvd.32044092008168 768 28 + + CCONJ hvd.32044092008168 768 29 45e 45e NUM hvd.32044092008168 768 30 , , PUNCT hvd.32044092008168 768 31 " " PUNCT hvd.32044092008168 768 32 – – PUNCT hvd.32044092008168 768 33 15 15 NUM hvd.32044092008168 768 34 92 92 NUM hvd.32044092008168 768 35 ] ] PUNCT hvd.32044092008168 768 36 g g NOUN hvd.32044092008168 768 37 cʻq1p cʻq1p PROPN hvd.32044092008168 768 38 where where SCONJ hvd.32044092008168 768 39 in in ADP hvd.32044092008168 768 40 general general ADJ hvd.32044092008168 768 41 [ [ X hvd.32044092008168 768 42 95 95 NUM hvd.32044092008168 768 43 ] ] PUNCT hvd.32044092008168 768 44 · · PUNCT hvd.32044092008168 768 45 the the DET hvd.32044092008168 768 46 quantities quantity NOUN hvd.32044092008168 768 47 q q PROPN hvd.32044092008168 768 48 are be AUX hvd.32044092008168 768 49 also also ADV hvd.32044092008168 768 50 necessarily necessarily ADV hvd.32044092008168 768 51 the the DET hvd.32044092008168 768 52 functions function NOUN hvd.32044092008168 768 53 0 0 PUNCT hvd.32044092008168 768 54 times time NOUN hvd.32044092008168 768 55 a a DET hvd.32044092008168 768 56 factor factor NOUN hvd.32044092008168 768 57 as as SCONJ hvd.32044092008168 768 58 is be AUX hvd.32044092008168 768 59 shown show VERB hvd.32044092008168 768 60 by by ADP hvd.32044092008168 768 61 taking take VERB hvd.32044092008168 768 62 the the DET hvd.32044092008168 768 63 substitutions substitution NOUN hvd.32044092008168 768 64 ei ei PROPN hvd.32044092008168 768 65 ( ( PUNCT hvd.32044092008168 768 66 2 2 NUM hvd.32044092008168 768 67 — — PUNCT hvd.32044092008168 768 68 k k X hvd.32044092008168 768 69 “ " PUNCT hvd.32044092008168 768 70 ) ) PUNCT hvd.32044092008168 768 71 , , PUNCT hvd.32044092008168 768 72 k k PROPN hvd.32044092008168 768 73 “ " PUNCT hvd.32044092008168 768 74 ) ) PUNCT hvd.32044092008168 768 75 , , PUNCT hvd.32044092008168 768 76 o2 o2 PROPN hvd.32044092008168 768 77 ( ( PUNCT hvd.32044092008168 768 78 2k 2k NUM hvd.32044092008168 768 79 ” " PUNCT hvd.32044092008168 768 80 – – PUNCT hvd.32044092008168 768 81 1 1 X hvd.32044092008168 768 82 ) ) PUNCT hvd.32044092008168 768 83 , , PUNCT hvd.32044092008168 768 84 ez ez PROPN hvd.32044092008168 768 85 ез ез PROPN hvd.32044092008168 768 86 ( ( PUNCT hvd.32044092008168 768 87 1 1 NUM hvd.32044092008168 768 88 + + NUM hvd.32044092008168 768 89 ka ka PROPN hvd.32044092008168 768 90 ) ) PUNCT hvd.32044092008168 768 91 , , PUNCT hvd.32044092008168 768 92 gº gº PROPN hvd.32044092008168 768 93 ( ( PUNCT hvd.32044092008168 768 94 1 1 NUM hvd.32044092008168 768 95 – – PUNCT hvd.32044092008168 768 96 k2 k2 PROPN hvd.32044092008168 768 97 + + CCONJ hvd.32044092008168 768 98 k k PROPN hvd.32044092008168 768 99 ) ) PUNCT hvd.32044092008168 768 100 ka ka PROPN hvd.32044092008168 768 101 whence whence NOUN hvd.32044092008168 768 102 : : PUNCT hvd.32044092008168 768 103 [ [ X hvd.32044092008168 768 104 qi]n=3 qi]n=3 X hvd.32044092008168 768 105 b2 b2 PROPN hvd.32044092008168 768 106 ( ( PUNCT hvd.32044092008168 768 107 2 2 NUM hvd.32044092008168 768 108 – – PUNCT hvd.32044092008168 768 109 k2)b[q2]n=3 k2)b[q2]n=3 ADJ hvd.32044092008168 768 110 b2 b2 X hvd.32044092008168 768 111 à à X hvd.32044092008168 768 112 ( ( PUNCT hvd.32044092008168 768 113 1 1 NUM hvd.32044092008168 768 114 — — SYM hvd.32044092008168 768 115 2 2 NUM hvd.32044092008168 768 116 ) ) PUNCT hvd.32044092008168 768 117 b b NOUN hvd.32044092008168 768 118 ka ka NOUN hvd.32044092008168 768 119 3 3 NUM hvd.32044092008168 768 120 : : SYM hvd.32044092008168 768 121 5 5 NUM hvd.32044092008168 768 122 ( ( PUNCT hvd.32044092008168 768 123 1 1 NUM hvd.32044092008168 768 124 – – SYM hvd.32044092008168 768 125 12 12 NUM hvd.32044092008168 768 126 ) ) PUNCT hvd.32044092008168 769 1 [ [ X hvd.32044092008168 769 2 q3]n=3 q3]n=3 X hvd.32044092008168 769 3 b2 b2 X hvd.32044092008168 769 4 à à X hvd.32044092008168 769 5 ( ( PUNCT hvd.32044092008168 769 6 1 1 NUM hvd.32044092008168 769 7 + + CCONJ hvd.32044092008168 769 8 k k X hvd.32044092008168 769 9 ? ? PUNCT hvd.32044092008168 769 10 ) ) PUNCT hvd.32044092008168 770 1 b b PROPN hvd.32044092008168 770 2 2 2 NUM hvd.32044092008168 770 3 в в NOUN hvd.32044092008168 770 4 гв гв NOUN hvd.32044092008168 770 5 ? ? PROPN hvd.32044092008168 770 6 15 15 NUM hvd.32044092008168 770 7 l l NOUN hvd.32044092008168 770 8 15 15 NUM hvd.32044092008168 770 9 15 15 NUM hvd.32044092008168 770 10 с с NUM hvd.32044092008168 770 11 1 1 NUM hvd.32044092008168 770 12 с с NUM hvd.32044092008168 770 13 3 3 NUM hvd.32044092008168 770 14 . . PUNCT hvd.32044092008168 771 1 5 5 NUM hvd.32044092008168 771 2 2n 2n NUM hvd.32044092008168 771 3 1 1 NUM hvd.32044092008168 771 4 1 1 NUM hvd.32044092008168 771 5 31 31 NUM hvd.32044092008168 771 6 32 32 NUM hvd.32044092008168 771 7 32 32 NUM hvd.32044092008168 771 8 4 4 NUM hvd.32044092008168 771 9 32 32 NUM hvd.32044092008168 771 10 2 2 NUM hvd.32044092008168 771 11 2 2 NUM hvd.32044092008168 771 12 ܘܬ ܘܬ NOUN hvd.32044092008168 771 13 ܐܚܝܢ ܐܚܝܢ VERB hvd.32044092008168 771 14 < < X hvd.32044092008168 771 15 5 5 NUM hvd.32044092008168 771 16 · · SYM hvd.32044092008168 771 17 3 3 NUM hvd.32044092008168 771 18 k4 k4 PROPN hvd.32044092008168 771 19 22 22 NUM hvd.32044092008168 771 20 5 5 NUM hvd.32044092008168 771 21 . . PUNCT hvd.32044092008168 771 22 3 3 NUM hvd.32044092008168 771 23 22 22 NUM hvd.32044092008168 771 24 2 2 NUM hvd.32044092008168 771 25 =3 =3 VERB hvd.32044092008168 771 26 2 2 NUM hvd.32044092008168 771 27 2 2 NUM hvd.32044092008168 771 28 22 22 NUM hvd.32044092008168 771 29 56 56 NUM hvd.32044092008168 771 30 part part NOUN hvd.32044092008168 771 31 v. v. ADP hvd.32044092008168 771 32 , , PUNCT hvd.32044092008168 771 33 n3 n3 PROPN hvd.32044092008168 771 34 5 5 NUM hvd.32044092008168 771 35 03 03 NUM hvd.32044092008168 771 36 q1 q1 PROPN hvd.32044092008168 771 37 q2q q2q PROPN hvd.32044092008168 771 38 1 1 NUM hvd.32044092008168 771 39 3 3 NUM hvd.32044092008168 771 40 s s VERB hvd.32044092008168 771 41 3 3 NUM hvd.32044092008168 771 42 1 1 NUM hvd.32044092008168 771 43 108 108 NUM hvd.32044092008168 771 44 2 2 NUM hvd.32044092008168 771 45 hence hence ADV hvd.32044092008168 771 46 making make VERB hvd.32044092008168 771 47 a a PRON hvd.32044092008168 771 48 = = NOUN hvd.32044092008168 771 49 constant constant ADJ hvd.32044092008168 771 50 , , PUNCT hvd.32044092008168 771 51 equal equal ADJ hvd.32044092008168 771 52 1 1 NUM hvd.32044092008168 771 53 and and CCONJ hvd.32044092008168 771 54 b-57 b-57 ADJ hvd.32044092008168 771 55 156 156 NUM hvd.32044092008168 772 1 we we PRON hvd.32044092008168 772 2 obtain obtain VERB hvd.32044092008168 772 3 [ [ X hvd.32044092008168 772 4 q1]n=3 q1]n=3 PROPN hvd.32044092008168 772 5 50 50 NUM hvd.32044092008168 772 6 = = SYM hvd.32044092008168 772 7 5 5 NUM hvd.32044092008168 773 1 [ [ PUNCT hvd.32044092008168 773 2 512 512 NUM hvd.32044092008168 773 3 — — PUNCT hvd.32044092008168 773 4 2 2 NUM hvd.32044092008168 773 5 ( ( PUNCT hvd.32044092008168 773 6 k k PROPN hvd.32044092008168 773 7 — — PUNCT hvd.32044092008168 773 8 2)1 2)1 NUM hvd.32044092008168 773 9 – – PUNCT hvd.32044092008168 773 10 3 3 NUM hvd.32044092008168 773 11 ] ] PUNCT hvd.32044092008168 773 12 ki ki PROPN hvd.32044092008168 774 1 [ [ X hvd.32044092008168 774 2 96 96 NUM hvd.32044092008168 774 3 ] ] PUNCT hvd.32044092008168 774 4 [ [ X hvd.32044092008168 774 5 q2]n=3 q2]n=3 VERB hvd.32044092008168 774 6 50 50 NUM hvd.32044092008168 774 7 , , PUNCT hvd.32044092008168 774 8 = = PROPN hvd.32044092008168 774 9 5[512 5[512 NUM hvd.32044092008168 774 10 – – PUNCT hvd.32044092008168 774 11 2 2 NUM hvd.32044092008168 774 12 ( ( PUNCT hvd.32044092008168 774 13 1 1 NUM hvd.32044092008168 774 14 – – SYM hvd.32044092008168 774 15 2 2 NUM hvd.32044092008168 774 16 k)1 k)1 NOUN hvd.32044092008168 774 17 – – PUNCT hvd.32044092008168 774 18 3 3 NUM hvd.32044092008168 774 19 ] ] SYM hvd.32044092008168 774 20 2 2 NUM hvd.32044092008168 774 21 [ [ X hvd.32044092008168 774 22 q3]n q3]n SPACE hvd.32044092008168 774 23 - - PUNCT hvd.32044092008168 774 24 s s NOUN hvd.32044092008168 774 25 5 5 NUM hvd.32044092008168 775 1 [ [ PUNCT hvd.32044092008168 775 2 512 512 NUM hvd.32044092008168 775 3 -2(1 -2(1 NOUN hvd.32044092008168 775 4 + + PUNCT hvd.32044092008168 775 5 k4)1 k4)1 SPACE hvd.32044092008168 775 6 , , PUNCT hvd.32044092008168 775 7 – – PUNCT hvd.32044092008168 775 8 3(1 3(1 NOUN hvd.32044092008168 775 9 — — PUNCT hvd.32044092008168 775 10 kº kº PROPN hvd.32044092008168 775 11 ) ) PUNCT hvd.32044092008168 775 12 ? ? PUNCT hvd.32044092008168 775 13 ] ] PUNCT hvd.32044092008168 775 14 . . PUNCT hvd.32044092008168 776 1 – – PUNCT hvd.32044092008168 776 2 hence hence ADV hvd.32044092008168 776 3 also also ADV hvd.32044092008168 776 4 : : PUNCT hvd.32044092008168 776 5 [ [ X hvd.32044092008168 776 6 97 97 NUM hvd.32044092008168 776 7 ] ] PUNCT hvd.32044092008168 776 8 q q X hvd.32044092008168 776 9 = = X hvd.32044092008168 776 10 k1122 k1122 NOUN hvd.32044092008168 776 11 : : PUNCT hvd.32044092008168 776 12 = = SYM hvd.32044092008168 776 13 50 50 NUM hvd.32044092008168 776 14 ( ( PUNCT hvd.32044092008168 776 15 1 1 NUM hvd.32044092008168 776 16 ) ) PUNCT hvd.32044092008168 776 17 = = VERB hvd.32044092008168 776 18 5 5 NUM hvd.32044092008168 776 19 ° ° NUM hvd.32044092008168 776 20 0 0 NUM hvd.32044092008168 776 21 , , PUNCT hvd.32044092008168 776 22 0,03 0,03 NUM hvd.32044092008168 776 23 ) ) PUNCT hvd.32044092008168 776 24 5 5 NUM hvd.32044092008168 776 25 : : SYM hvd.32044092008168 776 26 53 53 NUM hvd.32044092008168 776 27 [ [ PUNCT hvd.32044092008168 776 28 4 4 NUM hvd.32044092008168 776 29 ( ( PUNCT hvd.32044092008168 776 30 72 72 NUM hvd.32044092008168 776 31 — — PUNCT hvd.32044092008168 776 32 a a X hvd.32044092008168 776 33 ) ) PUNCT hvd.32044092008168 776 34 + + NUM hvd.32044092008168 776 35 ( ( PUNCT hvd.32044092008168 776 36 11 11 NUM hvd.32044092008168 776 37 73 73 NUM hvd.32044092008168 776 38 – – PUNCT hvd.32044092008168 776 39 9al 9al NOUN hvd.32044092008168 776 40 6 6 NUM hvd.32044092008168 776 41 . . PUNCT hvd.32044092008168 776 42 ) ) PUNCT hvd.32044092008168 776 43 ' ' PUNCT hvd.32044092008168 776 44 ] ] PUNCT hvd.32044092008168 776 45 b b X hvd.32044092008168 776 46 ? ? NOUN hvd.32044092008168 776 47 53 53 NUM hvd.32044092008168 777 1 [ [ X hvd.32044092008168 777 2 125 125 NUM hvd.32044092008168 777 3 g g NOUN hvd.32044092008168 777 4 210 210 NUM hvd.32044092008168 777 5 0,84 0,84 NUM hvd.32044092008168 777 6 2258 2258 NUM hvd.32044092008168 777 7 + + SYM hvd.32044092008168 777 8 93 93 NUM hvd.32044092008168 777 9 c252 c252 PROPN hvd.32044092008168 777 10 + + NUM hvd.32044092008168 777 11 18 18 NUM hvd.32044092008168 778 1 c c NOUN hvd.32044092008168 778 2 +1 +1 NOUN hvd.32044092008168 778 3 40 40 NUM hvd.32044092008168 778 4 , , PUNCT hvd.32044092008168 778 5 * * PUNCT hvd.32044092008168 778 6 ] ] X hvd.32044092008168 778 7 c c X hvd.32044092008168 778 8 etc etc X hvd.32044092008168 778 9 . . X hvd.32044092008168 779 1 where where SCONJ hvd.32044092008168 779 2 ai ai AUX hvd.32044092008168 779 3 ( ( PUNCT hvd.32044092008168 779 4 1 1 NUM hvd.32044092008168 779 5 — — PUNCT hvd.32044092008168 779 6 kº kº PROPN hvd.32044092008168 779 7 + + PROPN hvd.32044092008168 779 8 k4)3 k4)3 NOUN hvd.32044092008168 779 9 q=-=108 q=-=108 X hvd.32044092008168 779 10 b b NOUN hvd.32044092008168 779 11 , , PUNCT hvd.32044092008168 779 12 2 2 NUM hvd.32044092008168 779 13 93 93 NUM hvd.32044092008168 779 14 ( ( PUNCT hvd.32044092008168 779 15 1 1 NUM hvd.32044092008168 779 16 + + NUM hvd.32044092008168 779 17 ka ka PROPN hvd.32044092008168 779 18 ) ) PUNCT hvd.32044092008168 779 19 ( ( PUNCT hvd.32044092008168 779 20 2 2 NUM hvd.32044092008168 779 21 k k X hvd.32044092008168 779 22 ) ) PUNCT hvd.32044092008168 779 23 ( ( PUNCT hvd.32044092008168 779 24 1 1 NUM hvd.32044092008168 779 25 2 2 NUM hvd.32044092008168 779 26 k k NUM hvd.32044092008168 779 27 ): ): PUNCT hvd.32044092008168 779 28 kº)2 kº)2 PROPN hvd.32044092008168 779 29 – – PUNCT hvd.32044092008168 779 30 k22 k22 NOUN hvd.32044092008168 779 31 we we PRON hvd.32044092008168 779 32 have have AUX hvd.32044092008168 779 33 moreover moreover ADV hvd.32044092008168 779 34 that that SCONJ hvd.32044092008168 779 35 the the DET hvd.32044092008168 779 36 conditions condition NOUN hvd.32044092008168 779 37 that that PRON hvd.32044092008168 779 38 the the DET hvd.32044092008168 779 39 integrals integral NOUN hvd.32044092008168 779 40 be be VERB hvd.32044092008168 779 41 special special ADJ hvd.32044092008168 779 42 functions function NOUN hvd.32044092008168 779 43 of of ADP hvd.32044092008168 779 44 lamé lamé NOUN hvd.32044092008168 779 45 are be AUX hvd.32044092008168 779 46 that that SCONJ hvd.32044092008168 779 47 q1 q1 NOUN hvd.32044092008168 779 48 , , PUNCT hvd.32044092008168 779 49 q2 q2 PROPN hvd.32044092008168 779 50 , , PUNCT hvd.32044092008168 779 51 qg qg PROPN hvd.32044092008168 779 52 and and CCONJ hvd.32044092008168 779 53 p p PROPN hvd.32044092008168 779 54 vanish vanish VERB hvd.32044092008168 779 55 . . PUNCT hvd.32044092008168 780 1 but but CCONJ hvd.32044092008168 780 2 c2=0 c2=0 PROPN hvd.32044092008168 780 3 was be AUX hvd.32044092008168 780 4 also also ADV hvd.32044092008168 780 5 found find VERB hvd.32044092008168 780 6 to to PART hvd.32044092008168 780 7 be be AUX hvd.32044092008168 780 8 a a DET hvd.32044092008168 780 9 condition condition NOUN hvd.32044092008168 780 10 and and CCONJ hvd.32044092008168 780 11 we we PRON hvd.32044092008168 780 12 note note VERB hvd.32044092008168 780 13 that that SCONJ hvd.32044092008168 780 14 the the DET hvd.32044092008168 780 15 sum sum NOUN hvd.32044092008168 780 16 of of ADP hvd.32044092008168 780 17 the the DET hvd.32044092008168 780 18 degrees degree NOUN hvd.32044092008168 780 19 of of ADP hvd.32044092008168 780 20 q q NOUN hvd.32044092008168 780 21 , , PUNCT hvd.32044092008168 780 22 and and CCONJ hvd.32044092008168 780 23 p p PROPN hvd.32044092008168 780 24 is be AUX hvd.32044092008168 780 25 equal equal ADJ hvd.32044092008168 780 26 to to ADP hvd.32044092008168 780 27 the the DET hvd.32044092008168 780 28 degree degree NOUN hvd.32044092008168 780 29 of of ADP hvd.32044092008168 780 30 cwhich cwhich PRON hvd.32044092008168 780 31 qa qa X hvd.32044092008168 780 32 equals equal VERB hvd.32044092008168 780 33 the the DET hvd.32044092008168 780 34 number number NOUN hvd.32044092008168 780 35 of of ADP hvd.32044092008168 780 36 the the DET hvd.32044092008168 780 37 functions function NOUN hvd.32044092008168 780 38 of of ADP hvd.32044092008168 780 39 lamé lamé NOUN hvd.32044092008168 780 40 . . PUNCT hvd.32044092008168 781 1 we we PRON hvd.32044092008168 781 2 must must AUX hvd.32044092008168 781 3 have have VERB hvd.32044092008168 781 4 then then ADV hvd.32044092008168 781 5 the the DET hvd.32044092008168 781 6 relation relation NOUN hvd.32044092008168 781 7 c c NOUN hvd.32044092008168 781 8 ' ' PUNCT hvd.32044092008168 781 9 q1 q1 PROPN hvd.32044092008168 781 10 q2 q2 PROPN hvd.32044092008168 781 11 q3 q3 PROPN hvd.32044092008168 781 12 p. p. NOUN hvd.32044092008168 782 1 but but CCONJ hvd.32044092008168 782 2 we we PRON hvd.32044092008168 782 3 have have AUX hvd.32044092008168 782 4 shown show VERB hvd.32044092008168 782 5 that that SCONJ hvd.32044092008168 782 6 the the DET hvd.32044092008168 782 7 highest high ADJ hvd.32044092008168 782 8 power power NOUN hvd.32044092008168 782 9 of of ADP hvd.32044092008168 782 10 b b PROPN hvd.32044092008168 782 11 in in ADP hvd.32044092008168 782 12 the the DET hvd.32044092008168 782 13 development development NOUN hvd.32044092008168 782 14 of of ADP hvd.32044092008168 782 15 4c2 4c2 NUM hvd.32044092008168 782 16 is be AUX hvd.32044092008168 782 17 ( ( PUNCT hvd.32044092008168 782 18 p. p. NOUN hvd.32044092008168 782 19 38 38 NUM hvd.32044092008168 782 20 ) ) PUNCT hvd.32044092008168 782 21 4b 4b NUM hvd.32044092008168 782 22 - - SYM hvd.32044092008168 782 23 b2n b2n PROPN hvd.32044092008168 783 1 402 402 NUM hvd.32044092008168 783 2 = = PUNCT hvd.32044092008168 783 3 4by 4by NOUN hvd.32044092008168 783 4 ? ? PUNCT hvd.32044092008168 784 1 + + PUNCT hvd.32044092008168 785 1 + + PUNCT hvd.32044092008168 785 2 [ [ X hvd.32044092008168 785 3 3 3 NUM hvd.32044092008168 785 4 · · SYM hvd.32044092008168 785 5 5 5 NUM hvd.32044092008168 785 6 ( ( PUNCT hvd.32044092008168 785 7 2n 2n NUM hvd.32044092008168 785 8 whence whence NOUN hvd.32044092008168 785 9 1 1 NUM hvd.32044092008168 785 10 c c X hvd.32044092008168 785 11 [ [ X hvd.32044092008168 785 12 3 3 NUM hvd.32044092008168 785 13 · · SYM hvd.32044092008168 785 14 5 5 NUM hvd.32044092008168 785 15 ( ( PUNCT hvd.32044092008168 785 16 2n 2n NUM hvd.32044092008168 785 17 which which PRON hvd.32044092008168 785 18 for for ADP hvd.32044092008168 785 19 n= n= PROPN hvd.32044092008168 785 20 3 3 NUM hvd.32044092008168 785 21 gives give VERB hvd.32044092008168 785 22 as as ADP hvd.32044092008168 785 23 before before ADP hvd.32044092008168 785 24 taken take VERB hvd.32044092008168 785 25 c c PROPN hvd.32044092008168 785 26 we we PRON hvd.32044092008168 785 27 have have VERB hvd.32044092008168 785 28 then then ADV hvd.32044092008168 785 29 in in ADP hvd.32044092008168 785 30 general general ADJ hvd.32044092008168 785 31 [ [ X hvd.32044092008168 785 32 98 98 NUM hvd.32044092008168 785 33 ] ] PUNCT hvd.32044092008168 785 34 c2 c2 PROPN hvd.32044092008168 785 35 c4 c4 PROPN hvd.32044092008168 785 36 pq1q2q3 pq1q2q3 PROPN hvd.32044092008168 785 37 and and CCONJ hvd.32044092008168 785 38 when when SCONJ hvd.32044092008168 785 39 n= n= ADJ hvd.32044092008168 785 40 .3 .3 X hvd.32044092008168 786 1 [ [ X hvd.32044092008168 786 2 99 99 NUM hvd.32044092008168 786 3 ] ] PUNCT hvd.32044092008168 786 4 · · PUNCT hvd.32044092008168 786 5 c2 c2 PROPN hvd.32044092008168 786 6 qp=3175 qp=3175 PROPN hvd.32044092008168 786 7 pq pq PROPN hvd.32044092008168 786 8 . . PUNCT hvd.32044092008168 787 1 ( ( PUNCT hvd.32044092008168 787 2 15 15 NUM hvd.32044092008168 787 3 ) ) PUNCT hvd.32044092008168 787 4 34.5 34.5 NUM hvd.32044092008168 787 5 if if SCONJ hvd.32044092008168 787 6 then then ADV hvd.32044092008168 787 7 we we PRON hvd.32044092008168 787 8 take take VERB hvd.32044092008168 787 9 q q PROPN hvd.32044092008168 787 10 , , PUNCT hvd.32044092008168 787 11 = = PRON hvd.32044092008168 787 12 0 0 NUM hvd.32044092008168 787 13 : : PUNCT hvd.32044092008168 787 14 b=3e b=3e SPACE hvd.32044092008168 787 15 , , PUNCT hvd.32044092008168 787 16 +134–12c +134–12c PROPN hvd.32044092008168 787 17 ; ; PUNCT hvd.32044092008168 787 18 +592)=h +592)=h PROPN hvd.32044092008168 787 19 ? ? PROPN hvd.32044092008168 787 20 — — PUNCT hvd.32044092008168 787 21 2 2 NUM hvd.32044092008168 787 22 + + NUM hvd.32044092008168 787 23 1(162 1(162 NUM hvd.32044092008168 787 24 — — PUNCT hvd.32044092008168 788 1 2)2 2)2 NUM hvd.32044092008168 788 2 + + NUM hvd.32044092008168 788 3 15k4 15k4 NUM hvd.32044092008168 788 4 =( =( NOUN hvd.32044092008168 788 5 -12e -12e ADJ hvd.32044092008168 788 6 y={p y={p PROPN hvd.32044092008168 788 7 + + PROPN hvd.32044092008168 788 8 1 1 NUM hvd.32044092008168 788 9 1 1 NUM hvd.32044092008168 788 10 ( ( PUNCT hvd.32044092008168 788 11 3e 3e X hvd.32044092008168 788 12 , , PUNCT hvd.32044092008168 788 13 +63(592 +63(592 PROPN hvd.32044092008168 788 14 – – PUNCT hvd.32044092008168 788 15 12cz 12cz PROPN hvd.32044092008168 788 16 ) ) PUNCT hvd.32044092008168 788 17 ) ) PUNCT hvd.32044092008168 788 18 } } PUNCT hvd.32044092008168 788 19 vp vp PROPN hvd.32044092008168 788 20 – – PUNCT hvd.32044092008168 788 21 en en X hvd.32044092008168 788 22 p p X hvd.32044092008168 788 23 en en X hvd.32044092008168 788 24 ei ei PROPN hvd.32044092008168 788 25 = = PROPN hvd.32044092008168 788 26 { { PUNCT hvd.32044092008168 788 27 p+ p+ VERB hvd.32044092008168 788 28 is be AUX hvd.32044092008168 788 29 ( ( PUNCT hvd.32044092008168 788 30 — — PUNCT hvd.32044092008168 788 31 2 2 X hvd.32044092008168 788 32 ) ) PUNCT hvd.32044092008168 788 33 + + CCONJ hvd.32044092008168 788 34 " " PUNCT hvd.32044092008168 788 35 v v ADJ hvd.32044092008168 788 36 ( ( PUNCT hvd.32044092008168 788 37 k2 k2 ADJ hvd.32044092008168 788 38 — — PUNCT hvd.32044092008168 788 39 2)*+ 2)*+ NUM hvd.32044092008168 788 40 1544 1544 NUM hvd.32044092008168 788 41 } } PUNCT hvd.32044092008168 788 42 vp}(k vp}(k ADP hvd.32044092008168 788 43 ? ? PUNCT hvd.32044092008168 788 44 — — PUNCT hvd.32044092008168 788 45 2 2 X hvd.32044092008168 788 46 ) ) PUNCT hvd.32044092008168 788 47 ka ka PROPN hvd.32044092008168 788 48 152 152 NUM hvd.32044092008168 788 49 c2 c2 PROPN hvd.32044092008168 788 50 1 1 NUM hvd.32044092008168 788 51 ) ) PUNCT hvd.32044092008168 788 52 ] ] X hvd.32044092008168 789 1 * * PUNCT hvd.32044092008168 789 2 a a X hvd.32044092008168 789 3 . . PUNCT hvd.32044092008168 790 1 1)]4 1)]4 NUM hvd.32044092008168 790 2 1 1 NUM hvd.32044092008168 790 3 . . PUNCT hvd.32044092008168 791 1 3 3 NUM hvd.32044092008168 791 2 5 5 NUM hvd.32044092008168 791 3 . . PUNCT hvd.32044092008168 791 4 1 1 NUM hvd.32044092008168 791 5 2 2 NUM hvd.32044092008168 791 6 10 10 NUM hvd.32044092008168 791 7 1 1 NUM hvd.32044092008168 791 8 15 15 NUM hvd.32044092008168 791 9 10 10 NUM hvd.32044092008168 791 10 3 3 NUM hvd.32044092008168 791 11 reduction reduction NOUN hvd.32044092008168 791 12 of of ADP hvd.32044092008168 791 13 the the DET hvd.32044092008168 791 14 forms form NOUN hvd.32044092008168 791 15 when when SCONJ hvd.32044092008168 791 16 n n SYM hvd.32044092008168 791 17 equals equal VERB hvd.32044092008168 791 18 three three NUM hvd.32044092008168 791 19 . . PUNCT hvd.32044092008168 792 1 57 57 NUM hvd.32044092008168 792 2 1 1 NUM hvd.32044092008168 792 3 2 2 NUM hvd.32044092008168 792 4 10 10 NUM hvd.32044092008168 792 5 ez ez PROPN hvd.32044092008168 792 6 1 1 NUM hvd.32044092008168 792 7 15 15 NUM hvd.32044092008168 792 8 3 3 NUM hvd.32044092008168 792 9 1 1 NUM hvd.32044092008168 792 10 2 2 NUM hvd.32044092008168 792 11 10 10 NUM hvd.32044092008168 792 12 1 1 NUM hvd.32044092008168 792 13 15 15 NUM hvd.32044092008168 792 14 5 5 NUM hvd.32044092008168 792 15 3 3 NUM hvd.32044092008168 792 16 [ [ X hvd.32044092008168 792 17 100 100 NUM hvd.32044092008168 792 18 ] ] PUNCT hvd.32044092008168 792 19 ( ( PUNCT hvd.32044092008168 792 20 2=0 2=0 NUM hvd.32044092008168 792 21 : : PUNCT hvd.32044092008168 792 22 b=3e b=3e SPACE hvd.32044092008168 792 23 , , PUNCT hvd.32044092008168 792 24 + + PROPN hvd.32044092008168 792 25 v3(592 v3(592 NUM hvd.32044092008168 792 26 — — PUNCT hvd.32044092008168 792 27 12e 12e X hvd.32044092008168 792 28 , , PUNCT hvd.32044092008168 792 29 ) ) PUNCT hvd.32044092008168 792 30 = = X hvd.32044092008168 792 31 1 1 NUM hvd.32044092008168 792 32 2k+v(1 2k+v(1 NUM hvd.32044092008168 792 33 — — PUNCT hvd.32044092008168 792 34 2k 2k NUM hvd.32044092008168 792 35 ? ? PUNCT hvd.32044092008168 792 36 ? ? PUNCT hvd.32044092008168 793 1 + + CCONJ hvd.32044092008168 793 2 15 15 NUM hvd.32044092008168 793 3 q2 q2 PROPN hvd.32044092008168 793 4 ) ) PUNCT hvd.32044092008168 793 5 y={p y={p PROPN hvd.32044092008168 793 6 + + PROPN hvd.32044092008168 793 7 e e PROPN hvd.32044092008168 793 8 , , PUNCT hvd.32044092008168 793 9 1 1 NUM hvd.32044092008168 793 10 ( ( PUNCT hvd.32044092008168 793 11 3e 3e X hvd.32044092008168 793 12 , , PUNCT hvd.32044092008168 793 13 +13 +13 NUM hvd.32044092008168 793 14 ( ( PUNCT hvd.32044092008168 793 15 59 59 NUM hvd.32044092008168 793 16 . . PUNCT hvd.32044092008168 794 1 — — PUNCT hvd.32044092008168 794 2 12cz 12cz PROPN hvd.32044092008168 794 3 ) ) PUNCT hvd.32044092008168 794 4 ) ) PUNCT hvd.32044092008168 794 5 } } PUNCT hvd.32044092008168 794 6 vp vp PROPN hvd.32044092008168 794 7 — — PUNCT hvd.32044092008168 794 8 € € PROPN hvd.32044092008168 794 9 , , PUNCT hvd.32044092008168 794 10 = = NOUN hvd.32044092008168 794 11 { { PUNCT hvd.32044092008168 794 12 p+1 p+1 X hvd.32044092008168 794 13 ( ( PUNCT hvd.32044092008168 794 14 1–22 1–22 NUM hvd.32044092008168 794 15 ) ) PUNCT hvd.32044092008168 794 16 + + PROPN hvd.32044092008168 794 17 -v(1—2k+ -v(1—2k+ X hvd.32044092008168 794 18 ) ) PUNCT hvd.32044092008168 794 19 ? ? PUNCT hvd.32044092008168 794 20 +15}vp}(1–21:- +15}vp}(1–21:- SPACE hvd.32044092008168 794 21 ) ) PUNCT hvd.32044092008168 794 22 q3ez q3ez ADJ hvd.32044092008168 794 23 v3 v3 PROPN hvd.32044092008168 794 24 ; ; PUNCT hvd.32044092008168 794 25 = = PUNCT hvd.32044092008168 794 26 0 0 NUM hvd.32044092008168 794 27 : : PUNCT hvd.32044092008168 794 28 b=363 b=363 NUM hvd.32044092008168 794 29 +13 +13 NUM hvd.32044092008168 794 30 ( ( PUNCT hvd.32044092008168 794 31 59 59 NUM hvd.32044092008168 794 32 . . PUNCT hvd.32044092008168 794 33 – – PUNCT hvd.32044092008168 794 34 12c 12c PROPN hvd.32044092008168 794 35 ) ) PUNCT hvd.32044092008168 794 36 = = VERB hvd.32044092008168 795 1 1+**+2v(2 1+**+2v(2 NUM hvd.32044092008168 795 2 k k X hvd.32044092008168 795 3 * * PUNCT hvd.32044092008168 795 4 ) ) PUNCT hvd.32044092008168 795 5 — — PUNCT hvd.32044092008168 795 6 3k 3k NUM hvd.32044092008168 795 7 km km NOUN hvd.32044092008168 795 8 y={p y={p PROPN hvd.32044092008168 795 9 + + PROPN hvd.32044092008168 795 10 5e3 5e3 NUM hvd.32044092008168 795 11 – – PUNCT hvd.32044092008168 795 12 ( ( PUNCT hvd.32044092008168 795 13 3e3 3e3 NUM hvd.32044092008168 795 14 + + CCONJ hvd.32044092008168 795 15 v3 v3 PROPN hvd.32044092008168 795 16 ( ( PUNCT hvd.32044092008168 795 17 592 592 NUM hvd.32044092008168 795 18 — — PUNCT hvd.32044092008168 795 19 12e 12e X hvd.32044092008168 795 20 ;) ;) PUNCT hvd.32044092008168 795 21 } } PUNCT hvd.32044092008168 795 22 vp vp PROPN hvd.32044092008168 795 23 e e PROPN hvd.32044092008168 795 24 ; ; PUNCT hvd.32044092008168 795 25 y y PROPN hvd.32044092008168 795 26 ) ) PUNCT hvd.32044092008168 795 27 = = PROPN hvd.32044092008168 795 28 { { PUNCT hvd.32044092008168 795 29 p+ p+ X hvd.32044092008168 795 30 ( ( PUNCT hvd.32044092008168 795 31 1 1 NUM hvd.32044092008168 795 32 + + NUM hvd.32044092008168 795 33 2k 2k NUM hvd.32044092008168 795 34 “ " PUNCT hvd.32044092008168 795 35 ) ) PUNCT hvd.32044092008168 795 36 +5v2 +5v2 NOUN hvd.32044092008168 795 37 — — PUNCT hvd.32044092008168 795 38 : : PUNCT hvd.32044092008168 795 39 2 2 NUM hvd.32044092008168 795 40 ) ) PUNCT hvd.32044092008168 795 41 2 2 NUM hvd.32044092008168 795 42 — — PUNCT hvd.32044092008168 795 43 3k 3k NUM hvd.32044092008168 795 44 } } PUNCT hvd.32044092008168 795 45 vp vp PROPN hvd.32044092008168 795 46 -1 -1 PROPN hvd.32044092008168 795 47 ( ( PUNCT hvd.32044092008168 795 48 1+% 1+% NUM hvd.32044092008168 795 49 * * PUNCT hvd.32044092008168 795 50 ) ) PUNCT hvd.32044092008168 795 51 + + CCONJ hvd.32044092008168 795 52 all all PRON hvd.32044092008168 795 53 of of ADP hvd.32044092008168 795 54 which which PRON hvd.32044092008168 795 55 are be AUX hvd.32044092008168 795 56 special special ADJ hvd.32044092008168 795 57 functions function NOUN hvd.32044092008168 795 58 of of ADP hvd.32044092008168 795 59 lamé lamé NOUN hvd.32044092008168 795 60 of of ADP hvd.32044092008168 795 61 the the DET hvd.32044092008168 795 62 second second ADJ hvd.32044092008168 795 63 species specie NOUN hvd.32044092008168 795 64 , , PUNCT hvd.32044092008168 795 65 the the DET hvd.32044092008168 795 66 general general ADJ hvd.32044092008168 795 67 form form NOUN hvd.32044092008168 795 68 being be AUX hvd.32044092008168 795 69 9 9 NUM hvd.32044092008168 795 70 vpu vpu NOUN hvd.32044092008168 795 71 – – PUNCT hvd.32044092008168 795 72 where where SCONJ hvd.32044092008168 795 73 p(n-3 p(n-3 PROPN hvd.32044092008168 795 74 ) ) PUNCT hvd.32044092008168 795 75 + + CCONJ hvd.32044092008168 795 76 a a DET hvd.32044092008168 795 77 , , PUNCT hvd.32044092008168 795 78 pin—5)+ pin—5)+ NOUN hvd.32044092008168 795 79 ... ... PUNCT hvd.32044092008168 795 80 +c +c PROPN hvd.32044092008168 795 81 , , PUNCT hvd.32044092008168 795 82 and and CCONJ hvd.32044092008168 795 83 as as SCONJ hvd.32044092008168 795 84 given give VERB hvd.32044092008168 795 85 ( ( PUNCT hvd.32044092008168 795 86 p. p. NOUN hvd.32044092008168 795 87 43 43 NUM hvd.32044092008168 795 88 ) ) PUNCT hvd.32044092008168 795 89 the the DET hvd.32044092008168 795 90 general general ADJ hvd.32044092008168 795 91 form form NOUN hvd.32044092008168 795 92 for for ADP hvd.32044092008168 795 93 n= n= ADJ hvd.32044092008168 795 94 3 3 NUM hvd.32044092008168 795 95 including include VERB hvd.32044092008168 795 96 the the DET hvd.32044092008168 795 97 above above ADJ hvd.32044092008168 795 98 is be AUX hvd.32044092008168 795 99 [ [ X hvd.32044092008168 795 100 101 101 NUM hvd.32044092008168 795 101 ] ] PUNCT hvd.32044092008168 795 102 y y PROPN hvd.32044092008168 795 103 ( ( PUNCT hvd.32044092008168 795 104 + + PROPN hvd.32044092008168 795 105 b b X hvd.32044092008168 795 106 ) ) PUNCT hvd.32044092008168 795 107 về về PROPN hvd.32044092008168 795 108 ) ) PUNCT hvd.32044092008168 796 1 where where SCONJ hvd.32044092008168 796 2 b=3ea b=3ea PROPN hvd.32044092008168 796 3 + + CCONJ hvd.32044092008168 796 4 v3(592 v3(592 NUM hvd.32044092008168 796 5 – – PUNCT hvd.32044092008168 796 6 12c 12c PROPN hvd.32044092008168 796 7 ) ) PUNCT hvd.32044092008168 796 8 . . PUNCT hvd.32044092008168 797 1 la la ADV hvd.32044092008168 797 2 ca can AUX hvd.32044092008168 797 3 ea ea X hvd.32044092008168 797 4 10 10 NUM hvd.32044092008168 797 5 the the DET hvd.32044092008168 797 6 discriminant discriminant NOUN hvd.32044092008168 797 7 of of ADP hvd.32044092008168 797 8 y. y. PROPN hvd.32044092008168 797 9 a a PRON hvd.32044092008168 797 10 from from ADP hvd.32044092008168 797 11 ( ( PUNCT hvd.32044092008168 797 12 65 65 NUM hvd.32044092008168 797 13 ) ) PUNCT hvd.32044092008168 797 14 p. p. NOUN hvd.32044092008168 797 15 38 38 NUM hvd.32044092008168 797 16 . . PUNCT hvd.32044092008168 798 1 we we PRON hvd.32044092008168 798 2 have have VERB hvd.32044092008168 798 3 2c 2c NUM hvd.32044092008168 798 4 = = X hvd.32044092008168 798 5 a a PRON hvd.32044092008168 798 6 ' ' PUNCT hvd.32044092008168 798 7 ( ( PUNCT hvd.32044092008168 798 8 « « PUNCT hvd.32044092008168 798 9 — — PUNCT hvd.32044092008168 798 10 b b X hvd.32044092008168 798 11 ) ) PUNCT hvd.32044092008168 798 12 ( ( PUNCT hvd.32044092008168 798 13 a a PRON hvd.32044092008168 798 14 — — PUNCT hvd.32044092008168 798 15 » » NOUN hvd.32044092008168 798 16 ) ) PUNCT hvd.32044092008168 798 17 ... ... PUNCT hvd.32044092008168 798 18 = = VERB hvd.32044092008168 798 19 b'(b b'(b VERB hvd.32044092008168 798 20 – – PUNCT hvd.32044092008168 798 21 a a X hvd.32044092008168 798 22 ) ) PUNCT hvd.32044092008168 798 23 ( ( PUNCT hvd.32044092008168 798 24 b b X hvd.32044092008168 798 25 — — PUNCT hvd.32044092008168 798 26 y y PROPN hvd.32044092008168 798 27 ) ) PUNCT hvd.32044092008168 798 28 . . PUNCT hvd.32044092008168 799 1 v v ADP hvd.32044092008168 799 2 7 7 NUM hvd.32044092008168 799 3 . . PUNCT hvd.32044092008168 799 4 = = PROPN hvd.32044092008168 799 5 v9 v9 PROPN hvd.32044092008168 799 6 ( ( PUNCT hvd.32044092008168 799 7 a a NOUN hvd.32044092008168 799 8 ) ) PUNCT hvd.32044092008168 799 9 ( ( PUNCT hvd.32044092008168 799 10 a a DET hvd.32044092008168 799 11 – – PUNCT hvd.32044092008168 799 12 b b NOUN hvd.32044092008168 799 13 ) ) PUNCT hvd.32044092008168 799 14 ( ( PUNCT hvd.32044092008168 799 15 a a DET hvd.32044092008168 799 16 — — PUNCT hvd.32044092008168 799 17 v) v) VERB hvd.32044092008168 799 18 ... ... PUNCT hvd.32044092008168 799 19 v9 v9 NOUN hvd.32044092008168 799 20 ( ( PUNCT hvd.32044092008168 799 21 6 6 NUM hvd.32044092008168 799 22 ) ) PUNCT hvd.32044092008168 799 23 ( ( PUNCT hvd.32044092008168 799 24 8 8 NUM hvd.32044092008168 799 25 — — PUNCT hvd.32044092008168 799 26 « « NOUN hvd.32044092008168 799 27 ) ) PUNCT hvd.32044092008168 799 28 ( ( PUNCT hvd.32044092008168 799 29 b b X hvd.32044092008168 799 30 – – PUNCT hvd.32044092008168 799 31 v v NOUN hvd.32044092008168 799 32 ) ) PUNCT hvd.32044092008168 799 33 . . PUNCT hvd.32044092008168 800 1 ( ( PUNCT hvd.32044092008168 800 2 b b X hvd.32044092008168 800 3 a a DET hvd.32044092008168 800 4 where where SCONJ hvd.32044092008168 800 5 9 9 NUM hvd.32044092008168 800 6 ( ( PUNCT hvd.32044092008168 800 7 a a X hvd.32044092008168 800 8 ) ) PUNCT hvd.32044092008168 800 9 = = PROPN hvd.32044092008168 800 10 4(pu 4(pu NUM hvd.32044092008168 800 11 – – PUNCT hvd.32044092008168 800 12 e e NOUN hvd.32044092008168 800 13 ) ) PUNCT hvd.32044092008168 800 14 ( ( PUNCT hvd.32044092008168 800 15 pu pu PROPN hvd.32044092008168 800 16 – – PUNCT hvd.32044092008168 800 17 ez ez PROPN hvd.32044092008168 800 18 ) ) PUNCT hvd.32044092008168 800 19 ( ( PUNCT hvd.32044092008168 800 20 pu pu PROPN hvd.32044092008168 800 21 – – PUNCT hvd.32044092008168 800 22 es es PROPN hvd.32044092008168 800 23 ) ) PUNCT hvd.32044092008168 800 24 y y PROPN hvd.32044092008168 800 25 = = PROPN hvd.32044092008168 800 26 ( ( PUNCT hvd.32044092008168 800 27 pu pu X hvd.32044092008168 800 28 e)(pu e)(pu PROPN hvd.32044092008168 800 29 — — PUNCT hvd.32044092008168 800 30 € € X hvd.32044092008168 800 31 ) ) PUNCT hvd.32044092008168 800 32 * * PUNCT hvd.32044092008168 800 33 ' ' PUNCT hvd.32044092008168 800 34 ( ( PUNCT hvd.32044092008168 800 35 pu pu PROPN hvd.32044092008168 800 36 – – PUNCT hvd.32044092008168 800 37 ez ez PROPN hvd.32044092008168 800 38 ) ) PUNCT hvd.32044092008168 800 39 * * PUNCT hvd.32044092008168 800 40 " " PUNCT hvd.32044092008168 800 41 ii ii PROPN hvd.32044092008168 800 42 ( ( PUNCT hvd.32044092008168 800 43 pu pu PROPN hvd.32044092008168 800 44 pa pa PROPN hvd.32044092008168 800 45 ) ) PUNCT hvd.32044092008168 800 46 . . PUNCT hvd.32044092008168 800 47 . . PUNCT hvd.32044092008168 801 1 eg eg PROPN hvd.32044092008168 801 2 ” " PUNCT hvd.32044092008168 801 3 the the DET hvd.32044092008168 801 4 roots root NOUN hvd.32044092008168 801 5 of of ADP hvd.32044092008168 801 6 9 9 NUM hvd.32044092008168 801 7 ( ( PUNCT hvd.32044092008168 801 8 a)=0 a)=0 PROPN hvd.32044092008168 801 9 en en PROPN hvd.32044092008168 801 10 , , PUNCT hvd.32044092008168 801 11 ez ez PROPN hvd.32044092008168 801 12 , , PUNCT hvd.32044092008168 801 13 ez ez PROPN hvd.32044092008168 801 14 . . PUNCT hvd.32044092008168 802 1 the the DET hvd.32044092008168 802 2 roots root NOUN hvd.32044092008168 802 3 of of ADP hvd.32044092008168 802 4 y=0 y=0 NUM hvd.32044092008168 802 5 c1 c1 PROPN hvd.32044092008168 802 6 , , PUNCT hvd.32044092008168 802 7 c2 c2 PROPN hvd.32044092008168 802 8 , , PUNCT hvd.32044092008168 802 9 c3 c3 PROPN hvd.32044092008168 802 10 , , PUNCT hvd.32044092008168 802 11 quß quß PROPN hvd.32044092008168 802 12 ... ... PUNCT hvd.32044092008168 802 13 whence whence ADP hvd.32044092008168 802 14 the the DET hvd.32044092008168 802 15 resultant resultant NOUN hvd.32044092008168 802 16 of of ADP hvd.32044092008168 802 17 q q PROPN hvd.32044092008168 802 18 ( ( PUNCT hvd.32044092008168 802 19 a a X hvd.32044092008168 802 20 ) ) PUNCT hvd.32044092008168 802 21 and and CCONJ hvd.32044092008168 802 22 y y PROPN hvd.32044092008168 802 23 written write VERB hvd.32044092008168 802 24 as as ADP hvd.32044092008168 802 25 the the DET hvd.32044092008168 802 26 product product NOUN hvd.32044092008168 802 27 of of ADP hvd.32044092008168 802 28 the the DET hvd.32044092008168 802 29 differences difference NOUN hvd.32044092008168 802 30 of of ADP hvd.32044092008168 802 31 the the DET hvd.32044092008168 802 32 roots root NOUN hvd.32044092008168 802 33 is be AUX hvd.32044092008168 802 34 r=1l r=1l PRON hvd.32044092008168 802 35 ( ( PUNCT hvd.32044092008168 802 36 a a DET hvd.32044092008168 802 37 — — PUNCT hvd.32044092008168 802 38 ea ea NOUN hvd.32044092008168 802 39 ) ) PUNCT hvd.32044092008168 802 40 , , PUNCT hvd.32044092008168 802 41 where where SCONJ hvd.32044092008168 802 42 a a DET hvd.32044092008168 802 43 = = NOUN hvd.32044092008168 802 44 a a X hvd.32044092008168 802 45 , , PUNCT hvd.32044092008168 802 46 b b NOUN hvd.32044092008168 802 47 , , PUNCT hvd.32044092008168 802 48 .. .. PUNCT hvd.32044092008168 802 49 to to ADP hvd.32044092008168 802 50 n n ADP hvd.32044092008168 802 51 letters letter NOUN hvd.32044092008168 802 52 and and CCONJ hvd.32044092008168 802 53 1=1 1=1 NUM hvd.32044092008168 802 54 , , PUNCT hvd.32044092008168 802 55 2 2 NUM hvd.32044092008168 802 56 or or CCONJ hvd.32044092008168 802 57 3 3 NUM hvd.32044092008168 802 58 ii ii PROPN hvd.32044092008168 802 59 n n X hvd.32044092008168 802 60 a a PRON hvd.32044092008168 802 61 [ [ X hvd.32044092008168 802 62 ( ( PUNCT hvd.32044092008168 802 63 a a DET hvd.32044092008168 802 64 — — PUNCT hvd.32044092008168 802 65 e e NOUN hvd.32044092008168 802 66 ) ) PUNCT hvd.32044092008168 802 67 ( ( PUNCT hvd.32044092008168 802 68 a a DET hvd.32044092008168 802 69 – – PUNCT hvd.32044092008168 802 70 e e NOUN hvd.32044092008168 802 71 ) ) PUNCT hvd.32044092008168 802 72 ( ( PUNCT hvd.32044092008168 802 73 a a DET hvd.32044092008168 802 74 — — PUNCT hvd.32044092008168 802 75 e e NOUN hvd.32044092008168 802 76 ) ) PUNCT hvd.32044092008168 802 77 ] ] PUNCT hvd.32044092008168 803 1 [ [ PUNCT hvd.32044092008168 803 2 ( ( PUNCT hvd.32044092008168 803 3 b b X hvd.32044092008168 803 4 -e -e NOUN hvd.32044092008168 803 5 ) ) PUNCT hvd.32044092008168 803 6 ( ( PUNCT hvd.32044092008168 803 7 b b X hvd.32044092008168 803 8 – – PUNCT hvd.32044092008168 803 9 en en NOUN hvd.32044092008168 803 10 ) ) PUNCT hvd.32044092008168 803 11 ( ( PUNCT hvd.32044092008168 803 12 b b X hvd.32044092008168 803 13 – – PUNCT hvd.32044092008168 803 14 ez ez PROPN hvd.32044092008168 803 15 ) ) PUNCT hvd.32044092008168 803 16 ] ] PUNCT hvd.32044092008168 803 17 ... ... PUNCT hvd.32044092008168 803 18 πφ πφ NOUN hvd.32044092008168 803 19 ( ( PUNCT hvd.32044092008168 803 20 α α PROPN hvd.32044092008168 803 21 ) ) PUNCT hvd.32044092008168 803 22 . . PUNCT hvd.32044092008168 804 1 ( ( PUNCT hvd.32044092008168 804 2 are be AUX hvd.32044092008168 804 3 are be AUX hvd.32044092008168 804 4 58 58 NUM hvd.32044092008168 804 5 part part NOUN hvd.32044092008168 804 6 v. v. ADP hvd.32044092008168 804 7 1 1 NUM hvd.32044092008168 804 8 4 4 NUM hvd.32044092008168 804 9 " " PUNCT hvd.32044092008168 804 10 a. a. NOUN hvd.32044092008168 804 11 2 2 NUM hvd.32044092008168 804 12 2 2 NUM hvd.32044092008168 804 13 -c -c PUNCT hvd.32044092008168 804 14 : : PUNCT hvd.32044092008168 804 15 1 1 X hvd.32044092008168 805 1 [ [ X hvd.32044092008168 805 2 ] ] X hvd.32044092008168 805 3 ( ( PUNCT hvd.32044092008168 805 4 « « PUNCT hvd.32044092008168 805 5 — — PUNCT hvd.32044092008168 805 6 c c X hvd.32044092008168 805 7 ) ) PUNCT hvd.32044092008168 805 8 = = PROPN hvd.32044092008168 805 9 119(a 119(a NUM hvd.32044092008168 805 10 ) ) PUNCT hvd.32044092008168 805 11 = = PROPN hvd.32044092008168 805 12 ( ( PUNCT hvd.32044092008168 805 13 – – PUNCT hvd.32044092008168 805 14 1 1 X hvd.32044092008168 805 15 ) ) PUNCT hvd.32044092008168 805 16 " " PUNCT hvd.32044092008168 805 17 ] ] X hvd.32044092008168 805 18 ] ] X hvd.32044092008168 805 19 y(en)= y(en)= SPACE hvd.32044092008168 805 20 { { PUNCT hvd.32044092008168 805 21 * * PROPN hvd.32044092008168 805 22 * * ADJ hvd.32044092008168 805 23 , , PUNCT hvd.32044092008168 805 24 n n CCONJ hvd.32044092008168 805 25 even even ADV hvd.32044092008168 805 26 . . PUNCT hvd.32044092008168 806 1 but but CCONJ hvd.32044092008168 806 2 again again ADV hvd.32044092008168 806 3 y(e y(e PROPN hvd.32044092008168 806 4 ) ) PUNCT hvd.32044092008168 806 5 = = PUNCT hvd.32044092008168 807 1 [ [ X hvd.32044092008168 807 2 ( ( PUNCT hvd.32044092008168 807 3 a a X hvd.32044092008168 807 4 --e --e NOUN hvd.32044092008168 807 5 ) ) PUNCT hvd.32044092008168 807 6 ( ( PUNCT hvd.32044092008168 807 7 6 6 NUM hvd.32044092008168 807 8 -e -e X hvd.32044092008168 807 9 ) ) PUNCT hvd.32044092008168 807 10 ( ( PUNCT hvd.32044092008168 807 11 y y PROPN hvd.32044092008168 807 12 -- -- PUNCT hvd.32044092008168 807 13 ) ) PUNCT hvd.32044092008168 807 14 ] ] X hvd.32044092008168 807 15 ... ... PUNCT hvd.32044092008168 808 1 e e PROPN hvd.32044092008168 808 2 e. e. PROPN hvd.32044092008168 808 3 y(e y(e PROPN hvd.32044092008168 808 4 ) ) PUNCT hvd.32044092008168 808 5 = = PUNCT hvd.32044092008168 809 1 [ [ X hvd.32044092008168 809 2 ( ( PUNCT hvd.32044092008168 809 3 a a DET hvd.32044092008168 809 4 — — PUNCT hvd.32044092008168 809 5 ey ey NOUN hvd.32044092008168 809 6 ) ) PUNCT hvd.32044092008168 809 7 ( ( PUNCT hvd.32044092008168 809 8 b b X hvd.32044092008168 809 9 — — PUNCT hvd.32044092008168 809 10 ey ey NOUN hvd.32044092008168 809 11 ) ) PUNCT hvd.32044092008168 809 12 ( ( PUNCT hvd.32044092008168 809 13 y y PROPN hvd.32044092008168 809 14 = = SYM hvd.32044092008168 809 15 e e X hvd.32044092008168 809 16 ) ) PUNCT hvd.32044092008168 809 17 ] ] PUNCT hvd.32044092008168 809 18 ... ... PUNCT hvd.32044092008168 809 19 . . PUNCT hvd.32044092008168 810 1 y(e y(e PROPN hvd.32044092008168 810 2 ) ) PUNCT hvd.32044092008168 811 1 = = PUNCT hvd.32044092008168 812 1 [ [ X hvd.32044092008168 812 2 ( ( PUNCT hvd.32044092008168 812 3 a a DET hvd.32044092008168 812 4 – – PUNCT hvd.32044092008168 812 5 ez ez PROPN hvd.32044092008168 812 6 ) ) PUNCT hvd.32044092008168 812 7 ( ( PUNCT hvd.32044092008168 812 8 b b PROPN hvd.32044092008168 812 9 – – PUNCT hvd.32044092008168 812 10 ) ) PUNCT hvd.32044092008168 812 11 ( ( PUNCT hvd.32044092008168 812 12 – – PUNCT hvd.32044092008168 812 13 ex ex NOUN hvd.32044092008168 812 14 ) ) PUNCT hvd.32044092008168 812 15 ] ] PUNCT hvd.32044092008168 812 16 . . PUNCT hvd.32044092008168 812 17 . . PUNCT hvd.32044092008168 813 1 e3 e3 PROPN hvd.32044092008168 814 1 whence whence ADP hvd.32044092008168 814 2 r r NOUN hvd.32044092008168 814 3 - - PUNCT hvd.32044092008168 814 4 i i PRON hvd.32044092008168 814 5 [ [ X hvd.32044092008168 814 6 ( ( PUNCT hvd.32044092008168 814 7 « « PUNCT hvd.32044092008168 814 8 — — PUNCT hvd.32044092008168 814 9 e e NOUN hvd.32044092008168 814 10 ) ) PUNCT hvd.32044092008168 814 11 = = PUNCT hvd.32044092008168 815 1 [ [ X hvd.32044092008168 815 2 ( ( PUNCT hvd.32044092008168 815 3 ) ) PUNCT hvd.32044092008168 815 4 – – PUNCT hvd.32044092008168 815 5 ( ( PUNCT hvd.32044092008168 815 6 -1)"]]y(c -1)"]]y(c SPACE hvd.32044092008168 815 7 ) ) PUNCT hvd.32044092008168 815 8 . . PUNCT hvd.32044092008168 816 1 πφ πφ INTJ hvd.32044092008168 816 2 α α PROPN hvd.32044092008168 816 3 ) ) PUNCT hvd.32044092008168 817 1 [ [ X hvd.32044092008168 817 2 ty ty X hvd.32044092008168 817 3 again again ADV hvd.32044092008168 817 4 we we PRON hvd.32044092008168 817 5 have have AUX hvd.32044092008168 817 6 shown show VERB hvd.32044092008168 817 7 ( ( PUNCT hvd.32044092008168 817 8 94 94 NUM hvd.32044092008168 817 9 , , PUNCT hvd.32044092008168 817 10 p. p. NOUN hvd.32044092008168 817 11 55 55 NUM hvd.32044092008168 817 12 ) ) PUNCT hvd.32044092008168 817 13 that that SCONJ hvd.32044092008168 817 14 for for ADP hvd.32044092008168 817 15 n n CCONJ hvd.32044092008168 817 16 = = SYM hvd.32044092008168 817 17 3 3 NUM hvd.32044092008168 817 18 ; ; PUNCT hvd.32044092008168 817 19 and and CCONJ hvd.32044092008168 817 20 the the DET hvd.32044092008168 817 21 same same ADJ hvd.32044092008168 817 22 method method NOUN hvd.32044092008168 817 23 gives give VERB hvd.32044092008168 817 24 in in ADP hvd.32044092008168 817 25 general general ADJ hvd.32044092008168 817 26 for for ADP hvd.32044092008168 817 27 n n ADP hvd.32044092008168 817 28 odd odd ADJ hvd.32044092008168 817 29 : : PUNCT hvd.32044092008168 817 30 n n ADP hvd.32044092008168 817 31 odd odd ADJ hvd.32044092008168 817 32 : : PUNCT hvd.32044092008168 817 33 y(0)= y(0)= X hvd.32044092008168 817 34 – – PUNCT hvd.32044092008168 817 35 cº cº NOUN hvd.32044092008168 817 36 pq pq PROPN hvd.32044092008168 817 37 ; ; PUNCT hvd.32044092008168 817 38 y(en y(en PROPN hvd.32044092008168 817 39 ) ) PUNCT hvd.32044092008168 817 40 = = PUNCT hvd.32044092008168 818 1 -6 -6 PROPN hvd.32044092008168 818 2 % % NOUN hvd.32044092008168 818 3 pqz pqz PROPN hvd.32044092008168 818 4 ; ; PUNCT hvd.32044092008168 818 5 y(e y(e PROPN hvd.32044092008168 818 6 ) ) PUNCT hvd.32044092008168 818 7 = = PROPN hvd.32044092008168 819 1 -6 -6 INTJ hvd.32044092008168 819 2 pq pq X hvd.32044092008168 819 3 : : PUNCT hvd.32044092008168 819 4 e. e. PROPN hvd.32044092008168 819 5 -c -c PUNCT hvd.32044092008168 819 6 ) ) PUNCT hvd.32044092008168 819 7 and and CCONJ hvd.32044092008168 819 8 likewise likewise ADV hvd.32044092008168 819 9 n n ADV hvd.32044092008168 819 10 even even ADV hvd.32044092008168 819 11 : : PUNCT hvd.32044092008168 819 12 ye ye PRON hvd.32044092008168 819 13 ) ) PUNCT hvd.32044092008168 819 14 = = PUNCT hvd.32044092008168 820 1 c*q2qz c*q2qz NOUN hvd.32044092008168 820 2 ; ; PUNCT hvd.32044092008168 820 3 y(e y(e PROPN hvd.32044092008168 820 4 ) ) PUNCT hvd.32044092008168 820 5 = = PROPN hvd.32044092008168 820 6 cºq3 cºq3 PROPN hvd.32044092008168 820 7 qı qı PROPN hvd.32044092008168 820 8 y(0 y(0 PROPN hvd.32044092008168 820 9 ) ) PUNCT hvd.32044092008168 820 10 = = X hvd.32044092008168 820 11 cq.q2 cq.q2 X hvd.32044092008168 821 1 ( ( PUNCT hvd.32044092008168 821 2 + + CCONJ hvd.32044092008168 821 3 whence whence INTJ hvd.32044092008168 821 4 we we PRON hvd.32044092008168 821 5 finally finally ADV hvd.32044092008168 821 6 derive derive VERB hvd.32044092008168 821 7 [ [ PUNCT hvd.32044092008168 821 8 102]r 102]r NUM hvd.32044092008168 821 9 - - PUNCT hvd.32044092008168 821 10 ii ii PROPN hvd.32044092008168 821 11 1 1 NUM hvd.32044092008168 821 12 cm cm PROPN hvd.32044092008168 821 13 pq pq PROPN hvd.32044092008168 821 14 , , PUNCT hvd.32044092008168 821 15 nodd nodd NOUN hvd.32044092008168 821 16 now now ADV hvd.32044092008168 821 17 the the DET hvd.32044092008168 821 18 discriminant discriminant NOUN hvd.32044092008168 821 19 of of ADP hvd.32044092008168 821 20 y y PROPN hvd.32044092008168 821 21 equals equal VERB hvd.32044092008168 821 22 the the DET hvd.32044092008168 821 23 product product NOUN hvd.32044092008168 821 24 of of ADP hvd.32044092008168 821 25 the the DET hvd.32044092008168 821 26 squares square NOUN hvd.32044092008168 821 27 of of ADP hvd.32044092008168 821 28 the the DET hvd.32044092008168 821 29 differences difference NOUN hvd.32044092008168 821 30 of of ADP hvd.32044092008168 821 31 the the DET hvd.32044092008168 821 32 roots root NOUN hvd.32044092008168 821 33 and and CCONJ hvd.32044092008168 821 34 may may AUX hvd.32044092008168 821 35 be be AUX hvd.32044092008168 821 36 written write VERB hvd.32044092008168 821 37 : : PUNCT hvd.32044092008168 821 38 a=(a a=(a NUM hvd.32044092008168 821 39 – – PUNCT hvd.32044092008168 821 40 b)'(a b)'(a PROPN hvd.32044092008168 821 41 – – PUNCT hvd.32044092008168 821 42 v v NOUN hvd.32044092008168 821 43 ) ) PUNCT hvd.32044092008168 821 44 ... ... PUNCT hvd.32044092008168 822 1 whence whence ADV hvd.32044092008168 822 2 from from ADP hvd.32044092008168 822 3 ( ( PUNCT hvd.32044092008168 822 4 65 65 NUM hvd.32044092008168 822 5 ) ) PUNCT hvd.32044092008168 822 6 22 22 NUM hvd.32044092008168 823 1 c22202 c22202 PROPN hvd.32044092008168 823 2 22n 22n NUM hvd.32044092008168 823 3 cºn cºn ADJ hvd.32044092008168 823 4 a a DET hvd.32044092008168 823 5 ? ? NUM hvd.32044092008168 823 6 9(a 9(a NUM hvd.32044092008168 823 7 ) ) PUNCT hvd.32044092008168 823 8 ( ( PUNCT hvd.32044092008168 823 9 b b NOUN hvd.32044092008168 823 10 ) ) PUNCT hvd.32044092008168 823 11 ii ii PROPN hvd.32044092008168 823 12 9 9 NUM hvd.32044092008168 823 13 ( ( PUNCT hvd.32044092008168 823 14 a a X hvd.32044092008168 823 15 ) ) PUNCT hvd.32044092008168 823 16 but but CCONJ hvd.32044092008168 823 17 we we PRON hvd.32044092008168 823 18 have have AUX hvd.32044092008168 823 19 first first ADV hvd.32044092008168 823 20 found find VERB hvd.32044092008168 823 21 ii ii PROPN hvd.32044092008168 823 22 9 9 NUM hvd.32044092008168 823 23 ( ( PUNCT hvd.32044092008168 823 24 a a X hvd.32044092008168 824 1 ) ) PUNCT hvd.32044092008168 824 2 4 4 NUM hvd.32044092008168 824 3 " " PUNCT hvd.32044092008168 824 4 r r NOUN hvd.32044092008168 824 5 whence whence NOUN hvd.32044092008168 824 6 can can AUX hvd.32044092008168 824 7 a2 a2 X hvd.32044092008168 824 8 r r VERB hvd.32044092008168 824 9 again again ADV hvd.32044092008168 824 10 c2 c2 PROPN hvd.32044092008168 824 11 = = NOUN hvd.32044092008168 824 12 pq pq NOUN hvd.32044092008168 824 13 ( ( PUNCT hvd.32044092008168 824 14 from from ADP hvd.32044092008168 824 15 99 99 NUM hvd.32044092008168 824 16 ) ) PUNCT hvd.32044092008168 824 17 and and CCONJ hvd.32044092008168 824 18 we we PRON hvd.32044092008168 824 19 derive derive VERB hvd.32044092008168 824 20 from from ADP hvd.32044092008168 824 21 these these PRON hvd.32044092008168 824 22 n n CCONJ hvd.32044092008168 824 23 being be AUX hvd.32044092008168 824 24 odd odd ADJ hvd.32044092008168 824 25 c2n c2n NOUN hvd.32044092008168 824 26 ( ( PUNCT hvd.32044092008168 824 27 c c NOUN hvd.32044092008168 824 28 ) ) PUNCT hvd.32044092008168 824 29 " " PUNCT hvd.32044092008168 824 30 c4n c4n PROPN hvd.32044092008168 824 31 p"q p"q PROPN hvd.32044092008168 824 32 " " PUNCT hvd.32044092008168 824 33 a a PROPN hvd.32044092008168 824 34 ? ? PUNCT hvd.32044092008168 824 35 c2(2n—3 c2(2n—3 PROPN hvd.32044092008168 824 36 ) ) PUNCT hvd.32044092008168 824 37 pn—3 pn—3 NOUN hvd.32044092008168 824 38 qn-1 qn-1 ADP hvd.32044092008168 824 39 r r X hvd.32044092008168 824 40 r r X hvd.32044092008168 824 41 c c PROPN hvd.32044092008168 824 42 psq psq PROPN hvd.32044092008168 824 43 q. q. PROPN hvd.32044092008168 824 44 2 2 NUM hvd.32044092008168 824 45 n n CCONJ hvd.32044092008168 824 46 2 2 NUM hvd.32044092008168 824 47 -1 -1 PROPN hvd.32044092008168 824 48 or or CCONJ hvd.32044092008168 824 49 nn-3 nn-3 X hvd.32044092008168 824 50 n-1 n-1 X hvd.32044092008168 825 1 a=(-1)"7*cºn-5 a=(-1)"7*cºn-5 X hvd.32044092008168 825 2 p p NOUN hvd.32044092008168 825 3 3 3 NUM hvd.32044092008168 825 4 3 3 NUM hvd.32044092008168 825 5 2 2 NUM hvd.32044092008168 825 6 : : PUNCT hvd.32044092008168 825 7 n n CCONJ hvd.32044092008168 825 8 odd odd ADJ hvd.32044092008168 825 9 2 2 NUM hvd.32044092008168 825 10 q q X hvd.32044092008168 825 11 [ [ X hvd.32044092008168 825 12 103 103 NUM hvd.32044092008168 825 13 ] ] PUNCT hvd.32044092008168 825 14 and and CCONJ hvd.32044092008168 825 15 in in ADP hvd.32044092008168 825 16 like like ADJ hvd.32044092008168 825 17 manner manner NOUN hvd.32044092008168 825 18 we we PRON hvd.32044092008168 825 19 derive derive VERB hvd.32044092008168 825 20 ( ( PUNCT hvd.32044092008168 825 21 sign sign VERB hvd.32044092008168 825 22 ambiguous ambiguous ADJ hvd.32044092008168 825 23 ) ) PUNCT hvd.32044092008168 825 24 =( =( PRON hvd.32044092008168 825 25 1 1 NUM hvd.32044092008168 825 26 ) ) PUNCT hvd.32044092008168 825 27 ? ? PUNCT hvd.32044092008168 826 1 can—3 can—3 INTJ hvd.32044092008168 827 1 p p NOUN hvd.32044092008168 827 2 2 2 NUM hvd.32044092008168 827 3 " " PUNCT hvd.32044092008168 827 4 q q NOUN hvd.32044092008168 827 5 : : PUNCT hvd.32044092008168 827 6 n n CCONJ hvd.32044092008168 827 7 even even ADV hvd.32044092008168 828 1 and and CCONJ hvd.32044092008168 828 2 we we PRON hvd.32044092008168 828 3 have have VERB hvd.32044092008168 828 4 also also ADV hvd.32044092008168 828 5 a a PRON hvd.32044092008168 828 6 ( ( PUNCT hvd.32044092008168 828 7 since since SCONJ hvd.32044092008168 828 8 y y PROPN hvd.32044092008168 828 9 has have AUX hvd.32044092008168 828 10 at at ADV hvd.32044092008168 828 11 least least ADV hvd.32044092008168 828 12 one one NUM hvd.32044092008168 828 13 double double ADJ hvd.32044092008168 828 14 root root NOUN hvd.32044092008168 828 15 . . PUNCT hvd.32044092008168 829 1 1 1 NUM hvd.32044092008168 829 2 1 1 NUM hvd.32044092008168 829 3 1 1 NUM hvd.32044092008168 829 4 . . PUNCT hvd.32044092008168 829 5 n n CCONJ hvd.32044092008168 829 6 n-1 n-1 X hvd.32044092008168 829 7 a a DET hvd.32044092008168 829 8 reduction reduction NOUN hvd.32044092008168 829 9 of of ADP hvd.32044092008168 829 10 the the DET hvd.32044092008168 829 11 forms form NOUN hvd.32044092008168 829 12 when when SCONJ hvd.32044092008168 829 13 n n SYM hvd.32044092008168 829 14 equals equal VERB hvd.32044092008168 829 15 three three NUM hvd.32044092008168 829 16 . . PUNCT hvd.32044092008168 830 1 59 59 NUM hvd.32044092008168 830 2 1 1 NUM hvd.32044092008168 830 3 43 43 NUM hvd.32044092008168 830 4 as as ADP hvd.32044092008168 830 5 1 1 NUM hvd.32044092008168 830 6 3 3 NUM hvd.32044092008168 830 7 153 153 NUM hvd.32044092008168 830 8 ( ( PUNCT hvd.32044092008168 830 9 see see VERB hvd.32044092008168 830 10 ( ( PUNCT hvd.32044092008168 830 11 94 94 NUM hvd.32044092008168 830 12 ) ) PUNCT hvd.32044092008168 830 13 ) ) PUNCT hvd.32044092008168 830 14 case case NOUN hvd.32044092008168 830 15 n n ADP hvd.32044092008168 830 16 = = X hvd.32044092008168 830 17 : : PUNCT hvd.32044092008168 831 1 3 3 X hvd.32044092008168 831 2 . . X hvd.32044092008168 831 3 [ [ X hvd.32044092008168 831 4 104 104 NUM hvd.32044092008168 831 5 ] ] PUNCT hvd.32044092008168 831 6 r=(a r=(a NOUN hvd.32044092008168 831 7 — — PUNCT hvd.32044092008168 831 8 e e X hvd.32044092008168 831 9 ) ) PUNCT hvd.32044092008168 831 10 ( ( PUNCT hvd.32044092008168 831 11 a a DET hvd.32044092008168 831 12 — — PUNCT hvd.32044092008168 831 13 ex)(a ex)(a VERB hvd.32044092008168 831 14 — — PUNCT hvd.32044092008168 831 15 ez)(e)(b ez)(e)(b ADJ hvd.32044092008168 831 16 - - PUNCT hvd.32044092008168 831 17 ex)(-es)(y ex)(-es)(y SPACE hvd.32044092008168 831 18 - - PUNCT hvd.32044092008168 831 19 e)(y-2)(y e)(y-2)(y PROPN hvd.32044092008168 831 20 -- -- PUNCT hvd.32044092008168 831 21 es es PROPN hvd.32044092008168 831 22 ) ) PUNCT hvd.32044092008168 831 23 ( ( PUNCT hvd.32044092008168 831 24 -,q -,q PROPN hvd.32044092008168 831 25 – – PUNCT hvd.32044092008168 831 26 ) ) PUNCT hvd.32044092008168 831 27 ( ( PUNCT hvd.32044092008168 831 28 – – PUNCT hvd.32044092008168 831 29 ( ( PUNCT hvd.32044092008168 831 30 0 0 NUM hvd.32044092008168 831 31 920 920 NUM hvd.32044092008168 831 32 93 93 NUM hvd.32044092008168 831 33 ) ) PUNCT hvd.32044092008168 831 34 ( ( PUNCT hvd.32044092008168 831 35 23 23 NUM hvd.32044092008168 831 36 . . PUNCT hvd.32044092008168 831 37 92 92 NUM hvd.32044092008168 831 38 b93 b93 PROPN hvd.32044092008168 831 39 ) ) PUNCT hvd.32044092008168 831 40 ( ( PUNCT hvd.32044092008168 831 41 73 73 NUM hvd.32044092008168 831 42 – – PUNCT hvd.32044092008168 831 43 927 927 NUM hvd.32044092008168 831 44 – – PUNCT hvd.32044092008168 831 45 93 93 NUM hvd.32044092008168 831 46 ) ) PUNCT hvd.32044092008168 831 47 63 63 NUM hvd.32044092008168 831 48 13 13 NUM hvd.32044092008168 832 1 [ [ PUNCT hvd.32044092008168 832 2 9 9 NUM hvd.32044092008168 832 3 ' ' NUM hvd.32044092008168 832 4 + + NUM hvd.32044092008168 832 5 3(e1 3(e1 NUM hvd.32044092008168 832 6 — — PUNCT hvd.32044092008168 832 7 b b NOUN hvd.32044092008168 832 8 ) ) PUNCT hvd.32044092008168 832 9 ] ] PUNCT hvd.32044092008168 833 1 [ [ X hvd.32044092008168 833 2 9 9 NUM hvd.32044092008168 833 3 ' ' PUNCT hvd.32044092008168 833 4 + + NUM hvd.32044092008168 833 5 3 3 NUM hvd.32044092008168 833 6 ( ( PUNCT hvd.32044092008168 833 7 0 0 NUM hvd.32044092008168 833 8 , , PUNCT hvd.32044092008168 833 9 - - PUNCT hvd.32044092008168 833 10 . . PUNCT hvd.32044092008168 833 11 b b X hvd.32044092008168 833 12 ) ) PUNCT hvd.32044092008168 833 13 ] ] PUNCT hvd.32044092008168 834 1 [ [ X hvd.32044092008168 834 2 9 9 NUM hvd.32044092008168 834 3 ' ' PUNCT hvd.32044092008168 834 4 + + CCONJ hvd.32044092008168 834 5 3(ez 3(ez NUM hvd.32044092008168 834 6 — — PUNCT hvd.32044092008168 834 7 b b X hvd.32044092008168 834 8 ) ) PUNCT hvd.32044092008168 834 9 ? ? PUNCT hvd.32044092008168 834 10 ] ] PUNCT hvd.32044092008168 834 11 ? ? PUNCT hvd.32044092008168 834 12 e e X hvd.32044092008168 834 13 ? ? PUNCT hvd.32044092008168 834 14 ] ] PUNCT hvd.32044092008168 835 1 ( ( PUNCT hvd.32044092008168 835 2 3 3 NUM hvd.32044092008168 835 3 ) ) PUNCT hvd.32044092008168 835 4 3 3 NUM hvd.32044092008168 836 1 [ [ X hvd.32044092008168 836 2 105 105 NUM hvd.32044092008168 836 3 ] ] SYM hvd.32044092008168 836 4 4 4 NUM hvd.32044092008168 836 5 . . X hvd.32044092008168 836 6 pºq pºq PROPN hvd.32044092008168 836 7 ( ( PUNCT hvd.32044092008168 836 8 15 15 NUM hvd.32044092008168 836 9 ) ) PUNCT hvd.32044092008168 836 10 q q NOUN hvd.32044092008168 836 11 21 21 NUM hvd.32044092008168 836 12 22 22 NUM hvd.32044092008168 836 13 23 23 NUM hvd.32044092008168 836 14 38 38 NUM hvd.32044092008168 837 1 [ [ PUNCT hvd.32044092008168 837 2 ' ' PUNCT hvd.32044092008168 837 3 + + CCONJ hvd.32044092008168 837 4 3(ez 3(ez NUM hvd.32044092008168 837 5 – – PUNCT hvd.32044092008168 837 6 b b NOUN hvd.32044092008168 837 7 ) ) PUNCT hvd.32044092008168 837 8 ] ] PUNCT hvd.32044092008168 838 1 [ [ X hvd.32044092008168 838 2 ' ' PUNCT hvd.32044092008168 838 3 + + ADJ hvd.32044092008168 838 4 .3(e .3(e NUM hvd.32044092008168 838 5 — — PUNCT hvd.32044092008168 838 6 b b NOUN hvd.32044092008168 838 7 ) ) PUNCT hvd.32044092008168 838 8 ? ? PUNCT hvd.32044092008168 838 9 ] ] X hvd.32044092008168 839 1 [ [ X hvd.32044092008168 839 2 9 9 NUM hvd.32044092008168 839 3 ' ' PUNCT hvd.32044092008168 839 4 + + NUM hvd.32044092008168 839 5 3(en 3(en NUM hvd.32044092008168 839 6 -b -b X hvd.32044092008168 839 7 ) ) PUNCT hvd.32044092008168 839 8 ] ] PUNCT hvd.32044092008168 839 9 9 9 NUM hvd.32044092008168 839 10 which which DET hvd.32044092008168 839 11 for for ADP hvd.32044092008168 839 12 the the DET hvd.32044092008168 839 13 special special ADJ hvd.32044092008168 839 14 case case NOUN hvd.32044092008168 839 15 n n X hvd.32044092008168 839 16 = = X hvd.32044092008168 839 17 3 3 NUM hvd.32044092008168 839 18 furnishes furnishe NOUN hvd.32044092008168 839 19 the the DET hvd.32044092008168 839 20 interesting interesting ADJ hvd.32044092008168 839 21 relation relation NOUN hvd.32044092008168 839 22 , , PUNCT hvd.32044092008168 839 23 q q X hvd.32044092008168 839 24 differs differ VERB hvd.32044092008168 839 25 only only ADV hvd.32044092008168 839 26 by by ADP hvd.32044092008168 839 27 a a DET hvd.32044092008168 839 28 constant constant ADJ hvd.32044092008168 839 29 factor factor NOUN hvd.32044092008168 839 30 from from ADP hvd.32044092008168 839 31 the the DET hvd.32044092008168 839 32 discriminant discriminant NOUN hvd.32044092008168 839 33 of of ADP hvd.32044092008168 839 34 y. y. PROPN hvd.32044092008168 839 35 remembering remembering NOUN hvd.32044092008168 839 36 that that SCONJ hvd.32044092008168 839 37 a a PRON hvd.32044092008168 839 38 has have AUX hvd.32044092008168 839 39 been be AUX hvd.32044092008168 839 40 determined determine VERB hvd.32044092008168 839 41 equal equal ADJ hvd.32044092008168 839 42 to to ADP hvd.32044092008168 839 43 ( ( PUNCT hvd.32044092008168 839 44 1 1 X hvd.32044092008168 839 45 ) ) PUNCT hvd.32044092008168 839 46 we we PRON hvd.32044092008168 839 47 have have VERB hvd.32044092008168 839 48 from from ADP hvd.32044092008168 839 49 ( ( PUNCT hvd.32044092008168 839 50 97 97 NUM hvd.32044092008168 839 51 ) ) PUNCT hvd.32044092008168 839 52 q q PROPN hvd.32044092008168 839 53 53 53 NUM hvd.32044092008168 840 1 [ [ X hvd.32044092008168 840 2 4 4 NUM hvd.32044092008168 840 3 ( ( PUNCT hvd.32044092008168 840 4 72 72 NUM hvd.32044092008168 840 5 — — PUNCT hvd.32044092008168 840 6 a a X hvd.32044092008168 840 7 , , PUNCT hvd.32044092008168 840 8 ) ) PUNCT hvd.32044092008168 840 9 + + CCONJ hvd.32044092008168 840 10 ( ( PUNCT hvd.32044092008168 840 11 1113 1113 NUM hvd.32044092008168 840 12 — — PUNCT hvd.32044092008168 840 13 9al 9al NOUN hvd.32044092008168 840 14 — — PUNCT hvd.32044092008168 840 15 b b X hvd.32044092008168 840 16 ) ) PUNCT hvd.32044092008168 840 17 ” " PUNCT hvd.32044092008168 840 18 ] ] X hvd.32044092008168 840 19 and and CCONJ hvd.32044092008168 840 20 the the DET hvd.32044092008168 840 21 relations relation NOUN hvd.32044092008168 840 22 : : PUNCT hvd.32044092008168 840 23 1 1 NUM hvd.32044092008168 840 24 = = NUM hvd.32044092008168 840 25 3b 3b NUM hvd.32044092008168 840 26 : : PUNCT hvd.32044092008168 840 27 a a X hvd.32044092008168 840 28 , , PUNCT hvd.32044092008168 840 29 = = PROPN hvd.32044092008168 840 30 * * PUNCT hvd.32044092008168 840 31 92 92 NUM hvd.32044092008168 840 32 b b NOUN hvd.32044092008168 840 33 = = PUNCT hvd.32044092008168 840 34 * * PUNCT hvd.32044092008168 840 35 93 93 NUM hvd.32044092008168 840 36 : : PUNCT hvd.32044092008168 840 37 a,= a,= PROPN hvd.32044092008168 840 38 1 1 NUM hvd.32044092008168 840 39 ( ( PUNCT hvd.32044092008168 840 40 1262 1262 NUM hvd.32044092008168 840 41 — — PUNCT hvd.32044092008168 840 42 92 92 NUM hvd.32044092008168 840 43 ): ): PUNCT hvd.32044092008168 840 44 az az PROPN hvd.32044092008168 840 45 = = PROPN hvd.32044092008168 840 46 ( ( PUNCT hvd.32044092008168 840 47 4463 4463 NUM hvd.32044092008168 840 48 — — PUNCT hvd.32044092008168 840 49 392b 392b PROPN hvd.32044092008168 840 50 +93 +93 PROPN hvd.32044092008168 840 51 ) ) PUNCT hvd.32044092008168 840 52 a a X hvd.32044092008168 840 53 ) ) PUNCT hvd.32044092008168 840 54 } } PUNCT hvd.32044092008168 840 55 = = PROPN hvd.32044092008168 840 56 4.27 4.27 NUM hvd.32044092008168 840 57 a% a% PROPN hvd.32044092008168 840 58 : : PUNCT hvd.32044092008168 840 59 1113 1113 NUM hvd.32044092008168 840 60 — — PUNCT hvd.32044092008168 840 61 9a 9a NUM hvd.32044092008168 840 62 , , PUNCT hvd.32044092008168 840 63 1 1 NUM hvd.32044092008168 840 64 — — PUNCT hvd.32044092008168 840 65 b b X hvd.32044092008168 840 66 ) ) PUNCT hvd.32044092008168 840 67 = = PROPN hvd.32044092008168 840 68 -27a -27a PROPN hvd.32044092008168 840 69 , , PUNCT hvd.32044092008168 840 70 3 3 NUM hvd.32044092008168 840 71 · · PUNCT hvd.32044092008168 840 72 ? ? PUNCT hvd.32044092008168 841 1 [ [ X hvd.32044092008168 841 2 106 106 NUM hvd.32044092008168 841 3 ] ] PUNCT hvd.32044092008168 841 4 : : PUNCT hvd.32044092008168 841 5 q q X hvd.32044092008168 841 6 = = NOUN hvd.32044092008168 841 7 38.53 38.53 NUM hvd.32044092008168 841 8 [ [ X hvd.32044092008168 841 9 4 4 NUM hvd.32044092008168 841 10 a3 a3 NOUN hvd.32044092008168 841 11 + + NUM hvd.32044092008168 841 12 27 27 NUM hvd.32044092008168 841 13 a a X hvd.32044092008168 841 14 } } PUNCT hvd.32044092008168 841 15 ] ] X hvd.32044092008168 841 16 [ [ X hvd.32044092008168 841 17 107 107 NUM hvd.32044092008168 841 18 ] ] PUNCT hvd.32044092008168 841 19 a a PRON hvd.32044092008168 841 20 = = X hvd.32044092008168 841 21 [ [ X hvd.32044092008168 841 22 4 4 NUM hvd.32044092008168 841 23 a3 a3 NOUN hvd.32044092008168 841 24 + + CCONJ hvd.32044092008168 841 25 27 27 NUM hvd.32044092008168 841 26 a3 a3 NUM hvd.32044092008168 841 27 ] ] PUNCT hvd.32044092008168 841 28 which which DET hvd.32044092008168 841 29 latter latter ADJ hvd.32044092008168 841 30 value value NOUN hvd.32044092008168 841 31 we we PRON hvd.32044092008168 841 32 would would AUX hvd.32044092008168 841 33 have have AUX hvd.32044092008168 841 34 derived derive VERB hvd.32044092008168 841 35 directly directly ADV hvd.32044092008168 841 36 from from ADP hvd.32044092008168 841 37 the the DET hvd.32044092008168 841 38 form form NOUN hvd.32044092008168 841 39 y y PROPN hvd.32044092008168 841 40 = = VERB hvd.32044092008168 841 41 $ $ SYM hvd.32044092008168 841 42 $ $ SYM hvd.32044092008168 841 43 + + NUM hvd.32044092008168 841 44 a a PRON hvd.32044092008168 841 45 , , PUNCT hvd.32044092008168 841 46 s s X hvd.32044092008168 841 47 + + PROPN hvd.32044092008168 841 48 az az PROPN hvd.32044092008168 841 49 . . PUNCT hvd.32044092008168 842 1 s s AUX hvd.32044092008168 842 2 + + CCONJ hvd.32044092008168 842 3 writing write VERB hvd.32044092008168 842 4 a a PRON hvd.32044092008168 842 5 , , PUNCT hvd.32044092008168 842 6 = = NOUN hvd.32044092008168 842 7 ' ' PUNCT hvd.32044092008168 842 8 and and CCONJ hvd.32044092008168 842 9 ag ag PROPN hvd.32044092008168 842 10 = = PROPN hvd.32044092008168 842 11 1 1 NUM hvd.32044092008168 842 12 g g NOUN hvd.32044092008168 842 13 — — PUNCT hvd.32044092008168 842 14 bo'we bo'we PROPN hvd.32044092008168 842 15 a a DET hvd.32044092008168 842 16 9 9 NUM hvd.32044092008168 842 17 – – PUNCT hvd.32044092008168 842 18 derive derive VERB hvd.32044092008168 842 19 still still ADV hvd.32044092008168 842 20 another another DET hvd.32044092008168 842 21 form form NOUN hvd.32044092008168 842 22 for for ADP hvd.32044092008168 842 23 q q PROPN hvd.32044092008168 842 24 namely namely ADV hvd.32044092008168 842 25 * * SYM hvd.32044092008168 842 26 1108 1108 NUM hvd.32044092008168 842 27 ] ] PUNCT hvd.32044092008168 842 28 : : PUNCT hvd.32044092008168 842 29 q q X hvd.32044092008168 843 1 [ [ X hvd.32044092008168 843 2 9'3 9'3 NUM hvd.32044092008168 843 3 + + NUM hvd.32044092008168 843 4 2792 2792 NUM hvd.32044092008168 843 5 – – PUNCT hvd.32044092008168 843 6 8.27b90 8.27b90 NOUN hvd.32044092008168 843 7 ' ' PUNCT hvd.32044092008168 843 8 + + CCONJ hvd.32044092008168 843 9 16.27620'2 16.27620'2 NUM hvd.32044092008168 843 10 ] ] PUNCT hvd.32044092008168 843 11 . . PUNCT hvd.32044092008168 844 1 3 3 NUM hvd.32044092008168 844 2 4 4 NUM hvd.32044092008168 844 3 ܝ ܝ NUM hvd.32044092008168 844 4 27 27 NUM hvd.32044092008168 844 5 1 1 NUM hvd.32044092008168 844 6 4(1 4(1 NOUN hvd.32044092008168 844 7 . . PUNCT hvd.32044092008168 845 1 1 1 NUM hvd.32044092008168 845 2 4 4 NUM hvd.32044092008168 845 3 4 4 NUM hvd.32044092008168 845 4 ( ( PUNCT hvd.32044092008168 845 5 15 15 NUM hvd.32044092008168 845 6 ) ) PUNCT hvd.32044092008168 845 7 3 3 NUM hvd.32044092008168 845 8 16 16 NUM hvd.32044092008168 845 9 again again ADV hvd.32044092008168 845 10 we we PRON hvd.32044092008168 845 11 find find VERB hvd.32044092008168 845 12 φ φ X hvd.32044092008168 845 13 ( ( PUNCT hvd.32044092008168 845 14 0 0 NUM hvd.32044092008168 845 15 ) ) PUNCT hvd.32044092008168 845 16 x2 x2 PROPN hvd.32044092008168 845 17 367(72 367(72 NUM hvd.32044092008168 845 18 — — PUNCT hvd.32044092008168 845 19 a a X hvd.32044092008168 845 20 ) ) PUNCT hvd.32044092008168 845 21 2 2 NUM hvd.32044092008168 845 22 4233 4233 NUM hvd.32044092008168 845 23 36 36 NUM hvd.32044092008168 845 24 · · PUNCT hvd.32044092008168 845 25 38b9 38b9 NUM hvd.32044092008168 845 26 ' ' PUNCT hvd.32044092008168 845 27 [ [ X hvd.32044092008168 845 28 109 109 NUM hvd.32044092008168 845 29 ] ] PUNCT hvd.32044092008168 845 30 · · PUNCT hvd.32044092008168 845 31 ( ( PUNCT hvd.32044092008168 845 32 va va X hvd.32044092008168 845 33 2 2 NUM hvd.32044092008168 845 34 39 39 NUM hvd.32044092008168 845 35 ' ' PUNCT hvd.32044092008168 845 36 . . PUNCT hvd.32044092008168 846 1 2 2 NUM hvd.32044092008168 846 2 2 2 NUM hvd.32044092008168 846 3 { { PUNCT hvd.32044092008168 846 4 v v ADP hvd.32044092008168 846 5 44 44 NUM hvd.32044092008168 846 6 % % NOUN hvd.32044092008168 846 7 + + NUM hvd.32044092008168 846 8 274 274 NUM hvd.32044092008168 846 9 " " PUNCT hvd.32044092008168 846 10 39 39 NUM hvd.32044092008168 846 11 b b NOUN hvd.32044092008168 846 12 from from ADP hvd.32044092008168 846 13 which which DET hvd.32044092008168 846 14 value value NOUN hvd.32044092008168 846 15 we we PRON hvd.32044092008168 846 16 again again ADV hvd.32044092008168 846 17 see see VERB hvd.32044092008168 846 18 that that SCONJ hvd.32044092008168 846 19 the the DET hvd.32044092008168 846 20 vanishing vanishing NOUN hvd.32044092008168 846 21 of of ADP hvd.32044092008168 846 22 g g PROPN hvd.32044092008168 846 23 ' ' PUNCT hvd.32044092008168 846 24 is be AUX hvd.32044092008168 846 25 equivalent equivalent ADJ hvd.32044092008168 846 26 to to ADP hvd.32044092008168 846 27 the the DET hvd.32044092008168 846 28 vanishing vanishing NOUN hvd.32044092008168 846 29 of of ADP hvd.32044092008168 846 30 d. d. PROPN hvd.32044092008168 846 31 ( ( PUNCT hvd.32044092008168 846 32 compair compair PROPN hvd.32044092008168 846 33 p. p. NOUN hvd.32044092008168 846 34 49 49 NUM hvd.32044092008168 846 35 and and CCONJ hvd.32044092008168 846 36 52 52 NUM hvd.32044092008168 846 37 . . PUNCT hvd.32044092008168 846 38 ) ) PUNCT hvd.32044092008168 847 1 60 60 NUM hvd.32044092008168 847 2 part part NOUN hvd.32044092008168 847 3 v. v. ADP hvd.32044092008168 847 4 v v PROPN hvd.32044092008168 847 5 pi(u pi(u PROPN hvd.32044092008168 847 6 ) ) PUNCT hvd.32044092008168 847 7 ao ao ADP hvd.32044092008168 847 8 6 6 NUM hvd.32044092008168 847 9 ( ( PUNCT hvd.32044092008168 847 10 u u NOUN hvd.32044092008168 847 11 2 2 NUM hvd.32044092008168 847 12 determination determination NOUN hvd.32044092008168 847 13 of of ADP hvd.32044092008168 847 14 x x SYM hvd.32044092008168 847 15 and and CCONJ hvd.32044092008168 847 16 v. v. ADP hvd.32044092008168 847 17 second second ADJ hvd.32044092008168 847 18 method method NOUN hvd.32044092008168 847 19 . . PUNCT hvd.32044092008168 848 1 we we PRON hvd.32044092008168 848 2 have have VERB hvd.32044092008168 848 3 the the DET hvd.32044092008168 848 4 general general ADJ hvd.32044092008168 848 5 theorem theorem NOUN hvd.32044092008168 848 6 : : PUNCT hvd.32044092008168 848 7 every every DET hvd.32044092008168 848 8 rational rational ADJ hvd.32044092008168 848 9 function function NOUN hvd.32044092008168 848 10 of of ADP hvd.32044092008168 848 11 pu pu PROPN hvd.32044092008168 848 12 and and CCONJ hvd.32044092008168 848 13 p'u p'u ADV hvd.32044092008168 848 14 can can AUX hvd.32044092008168 848 15 be be AUX hvd.32044092008168 848 16 written write VERB hvd.32044092008168 848 17 in in ADP hvd.32044092008168 848 18 the the DET hvd.32044092008168 848 19 form form NOUN hvd.32044092008168 848 20 : : PUNCT hvd.32044092008168 848 21 a. a. NOUN hvd.32044092008168 848 22 ( ( PUNCT hvd.32044092008168 848 23 u u PROPN hvd.32044092008168 848 24 v. v. PROPN hvd.32044092008168 848 25 ) ) PUNCT hvd.32044092008168 848 26 ( ( PUNCT hvd.32044092008168 848 27 u u PROPN hvd.32044092008168 848 28 -vy -vy SPACE hvd.32044092008168 848 29 ) ) PUNCT hvd.32044092008168 848 30 ... ... PUNCT hvd.32044092008168 849 1 ( ( PUNCT hvd.32044092008168 849 2 u u INTJ hvd.32044092008168 849 3 – – PUNCT hvd.32044092008168 849 4 » » PUNCT hvd.32044092008168 849 5 ) ) PUNCT hvd.32044092008168 849 6 o o NOUN hvd.32044092008168 849 7 6 6 NUM hvd.32044092008168 849 8 ' ' NOUN hvd.32044092008168 849 9 m m VERB hvd.32044092008168 849 10 vi vi NOUN hvd.32044092008168 849 11 ' ' NOUN hvd.32044092008168 849 12 ) ) PUNCT hvd.32044092008168 849 13 o o NOUN hvd.32044092008168 849 14 ( ( PUNCT hvd.32044092008168 849 15 u u PROPN hvd.32044092008168 849 16 ve ve NOUN hvd.32044092008168 849 17 ' ' NOUN hvd.32044092008168 849 18 ) ) PUNCT hvd.32044092008168 849 19 o(u o(u PROPN hvd.32044092008168 849 20 ) ) PUNCT hvd.32044092008168 849 21 where where SCONJ hvd.32044092008168 849 22 the the DET hvd.32044092008168 849 23 number number NOUN hvd.32044092008168 849 24 of of ADP hvd.32044092008168 849 25 o o NOUN hvd.32044092008168 849 26 functions function NOUN hvd.32044092008168 849 27 in in ADP hvd.32044092008168 849 28 the the DET hvd.32044092008168 849 29 numerator numerator NOUN hvd.32044092008168 849 30 equals equal VERB hvd.32044092008168 849 31 the the DET hvd.32044092008168 849 32 number number NOUN hvd.32044092008168 849 33 in in ADP hvd.32044092008168 849 34 the the DET hvd.32044092008168 849 35 denominator denominator NOUN hvd.32044092008168 849 36 , , PUNCT hvd.32044092008168 849 37 making make VERB hvd.32044092008168 849 38 the the DET hvd.32044092008168 849 39 number number NOUN hvd.32044092008168 849 40 of of ADP hvd.32044092008168 849 41 zeros zero NOUN hvd.32044092008168 849 42 equal equal ADJ hvd.32044092008168 849 43 to to ADP hvd.32044092008168 849 44 the the DET hvd.32044092008168 849 45 number number NOUN hvd.32044092008168 849 46 of of ADP hvd.32044092008168 849 47 infinites infinite NOUN hvd.32044092008168 849 48 . . PUNCT hvd.32044092008168 850 1 the the DET hvd.32044092008168 850 2 reverse reverse ADJ hvd.32044092008168 850 3 theorem theorem NOUN hvd.32044092008168 850 4 is be AUX hvd.32044092008168 850 5 also also ADV hvd.32044092008168 850 6 known know VERB hvd.32044092008168 850 7 and and CCONJ hvd.32044092008168 850 8 we we PRON hvd.32044092008168 850 9 may may AUX hvd.32044092008168 850 10 write write VERB hvd.32044092008168 850 11 : : PUNCT hvd.32044092008168 850 12 ) ) PUNCT hvd.32044092008168 851 1 o o X hvd.32044092008168 851 2 bc bc PROPN hvd.32044092008168 851 3 [ [ X hvd.32044092008168 851 4 110](-1)”k 110](-1)”k PROPN hvd.32044092008168 851 5 , , PUNCT hvd.32044092008168 851 6 ( ( PUNCT hvd.32044092008168 851 7 t t PROPN hvd.32044092008168 851 8 – – PUNCT hvd.32044092008168 851 9 a a X hvd.32044092008168 851 10 ) ) PUNCT hvd.32044092008168 851 11 0 0 NUM hvd.32044092008168 852 1 ( ( PUNCT hvd.32044092008168 852 2 u u PROPN hvd.32044092008168 852 3 — — PUNCT hvd.32044092008168 852 4 6 6 X hvd.32044092008168 852 5 ) ) PUNCT hvd.32044092008168 852 6 ( ( PUNCT hvd.32044092008168 852 7 u u PROPN hvd.32044092008168 852 8 — — PUNCT hvd.32044092008168 852 9 c)o(u c)o(u PROPN hvd.32044092008168 852 10 + + CCONJ hvd.32044092008168 852 11 v v NOUN hvd.32044092008168 852 12 ) ) PUNCT hvd.32044092008168 852 13 0 0 NUM hvd.32044092008168 853 1 oa oa INTJ hvd.32044092008168 853 2 ob ob PROPN hvd.32044092008168 853 3 oc oc PROPN hvd.32044092008168 853 4 ( ( PUNCT hvd.32044092008168 853 5 ou ou PROPN hvd.32044092008168 853 6 ) ) PUNCT hvd.32044092008168 853 7 ( ( PUNCT hvd.32044092008168 853 8 pu pu PROPN hvd.32044092008168 853 9 ) ) PUNCT hvd.32044092008168 853 10 — — PUNCT hvd.32044092008168 853 11 ac ac PROPN hvd.32044092008168 853 12 p'up p'up PROPN hvd.32044092008168 853 13 ( ( PUNCT hvd.32044092008168 853 14 pu pu PROPN hvd.32044092008168 853 15 ) ) PUNCT hvd.32044092008168 853 16 20 20 NUM hvd.32044092008168 853 17 where where SCONJ hvd.32044092008168 853 18 q q PROPN hvd.32044092008168 854 1 and and CCONJ hvd.32044092008168 854 2 i i PRON hvd.32044092008168 854 3 are be AUX hvd.32044092008168 854 4 intire intire ADJ hvd.32044092008168 854 5 polynomials polynomial NOUN hvd.32044092008168 854 6 in in ADP hvd.32044092008168 854 7 pu pu PROPN hvd.32044092008168 854 8 and and CCONJ hvd.32044092008168 854 9 p'u p'u ADV hvd.32044092008168 854 10 , , PUNCT hvd.32044092008168 854 11 k k PROPN hvd.32044092008168 854 12 , , PUNCT hvd.32044092008168 854 13 a a DET hvd.32044092008168 854 14 constant constant NOUN hvd.32044092008168 854 15 to to PART hvd.32044092008168 854 16 be be AUX hvd.32044092008168 854 17 determined determine VERB hvd.32044092008168 854 18 and and CCONJ hvd.32044092008168 854 19 the the DET hvd.32044092008168 854 20 relation relation NOUN hvd.32044092008168 854 21 exists exist VERB hvd.32044092008168 854 22 a a DET hvd.32044092008168 854 23 + + ADJ hvd.32044092008168 854 24 b+c b+c SPACE hvd.32044092008168 854 25 = = NOUN hvd.32044092008168 854 26 v. v. X hvd.32044092008168 854 27 also also ADV hvd.32044092008168 854 28 , , PUNCT hvd.32044092008168 854 29 from from ADP hvd.32044092008168 854 30 the the DET hvd.32044092008168 854 31 general general ADJ hvd.32044092008168 854 32 theory theory NOUN hvd.32044092008168 854 33 , , PUNCT hvd.32044092008168 854 34 the the DET hvd.32044092008168 854 35 degree degree NOUN hvd.32044092008168 854 36 of of ADP hvd.32044092008168 854 37 the the DET hvd.32044092008168 854 38 right right ADJ hvd.32044092008168 854 39 hand hand NOUN hvd.32044092008168 854 40 member member NOUN hvd.32044092008168 854 41 is be AUX hvd.32044092008168 854 42 four four NUM hvd.32044092008168 854 43 , , PUNCT hvd.32044092008168 854 44 p p NOUN hvd.32044092008168 854 45 ( ( PUNCT hvd.32044092008168 854 46 u u NOUN hvd.32044092008168 854 47 ) ) PUNCT hvd.32044092008168 854 48 being be AUX hvd.32044092008168 854 49 considered consider VERB hvd.32044092008168 854 50 as as ADP hvd.32044092008168 854 51 of of ADP hvd.32044092008168 854 52 the the DET hvd.32044092008168 854 53 second second ADJ hvd.32044092008168 854 54 degree degree NOUN hvd.32044092008168 854 55 and and CCONJ hvd.32044092008168 854 56 p p NOUN hvd.32044092008168 854 57 ' ' PUNCT hvd.32044092008168 854 58 ( ( PUNCT hvd.32044092008168 854 59 u u PROPN hvd.32044092008168 854 60 ) ) PUNCT hvd.32044092008168 854 61 of of ADP hvd.32044092008168 854 62 the the DET hvd.32044092008168 854 63 third third ADJ hvd.32044092008168 854 64 . . PUNCT hvd.32044092008168 855 1 the the DET hvd.32044092008168 855 2 degree degree NOUN hvd.32044092008168 855 3 of of ADP hvd.32044092008168 855 4 $ $ SYM hvd.32044092008168 855 5 and and CCONJ hvd.32044092008168 855 6 sare sare NOUN hvd.32044092008168 855 7 thus thus ADV hvd.32044092008168 855 8 determined determine VERB hvd.32044092008168 855 9 as as SCONJ hvd.32044092008168 855 10 follows follow VERB hvd.32044092008168 855 11 : : PUNCT hvd.32044092008168 855 12 φ φ PROPN hvd.32044092008168 855 13 y y PROPN hvd.32044092008168 855 14 ( ( PUNCT hvd.32044092008168 855 15 n n X hvd.32044092008168 855 16 + + CCONJ hvd.32044092008168 855 17 1 1 X hvd.32044092008168 855 18 ) ) PUNCT hvd.32044092008168 855 19 an an DET hvd.32044092008168 855 20 3 3 NUM hvd.32044092008168 855 21 ) ) PUNCT hvd.32044092008168 855 22 1 1 NUM hvd.32044092008168 855 23 1 1 NUM hvd.32044092008168 855 24 n n ADP hvd.32044092008168 855 25 odd odd ADJ hvd.32044092008168 855 26 : : PUNCT hvd.32044092008168 855 27 2 2 NUM hvd.32044092008168 855 28 1 1 NUM hvd.32044092008168 855 29 n n CCONJ hvd.32044092008168 855 30 even even ADV hvd.32044092008168 855 31 n n CCONJ hvd.32044092008168 855 32 n n X hvd.32044092008168 855 33 1 1 NUM hvd.32044092008168 855 34 2 2 NUM hvd.32044092008168 855 35 2 2 NUM hvd.32044092008168 855 36 n n CCONJ hvd.32044092008168 855 37 1 1 NUM hvd.32044092008168 855 38 . . PUNCT hvd.32044092008168 856 1 a a DET hvd.32044092008168 856 2 3 3 NUM hvd.32044092008168 856 3 0 0 NUM hvd.32044092008168 856 4 . . PUNCT hvd.32044092008168 857 1 the the DET hvd.32044092008168 857 2 n n ADJ hvd.32044092008168 857 3 roots root NOUN hvd.32044092008168 857 4 of of ADP hvd.32044092008168 857 5 the the DET hvd.32044092008168 857 6 first first ADJ hvd.32044092008168 857 7 member member NOUN hvd.32044092008168 857 8 in in ADP hvd.32044092008168 857 9 the the DET hvd.32044092008168 857 10 general general ADJ hvd.32044092008168 857 11 case case NOUN hvd.32044092008168 857 12 being be AUX hvd.32044092008168 857 13 a a DET hvd.32044092008168 857 14 , , PUNCT hvd.32044092008168 857 15 b b NOUN hvd.32044092008168 857 16 , , PUNCT hvd.32044092008168 857 17 c c X hvd.32044092008168 857 18 ... ... PUNCT hvd.32044092008168 857 19 we we PRON hvd.32044092008168 857 20 have have VERB hvd.32044092008168 857 21 : : PUNCT hvd.32044092008168 857 22 [ [ X hvd.32044092008168 857 23 111 111 NUM hvd.32044092008168 857 24 ] ] SYM hvd.32044092008168 857 25 0(a 0(a NUM hvd.32044092008168 857 26 ) ) PUNCT hvd.32044092008168 857 27 — — PUNCT hvd.32044092008168 857 28 20 20 NUM hvd.32044092008168 857 29 a a DET hvd.32044092008168 857 30 ' ' PUNCT hvd.32044092008168 857 31 f f X hvd.32044092008168 857 32 ( ( PUNCT hvd.32044092008168 857 33 ) ) PUNCT hvd.32044092008168 857 34 = = PUNCT hvd.32044092008168 857 35 0 0 NUM hvd.32044092008168 857 36 φ φ PROPN hvd.32044092008168 857 37 ( ( PUNCT hvd.32044092008168 857 38 α α NOUN hvd.32044092008168 857 39 ) ) PUNCT hvd.32044092008168 857 40 a a DET hvd.32044092008168 857 41 where where SCONJ hvd.32044092008168 857 42 a'rp a'rp NOUN hvd.32044092008168 857 43 ' ' PUNCT hvd.32044092008168 857 44 ( ( PUNCT hvd.32044092008168 857 45 a a NOUN hvd.32044092008168 857 46 ) ) PUNCT hvd.32044092008168 857 47 , , PUNCT hvd.32044092008168 857 48 a a DET hvd.32044092008168 857 49 = = NOUN hvd.32044092008168 857 50 p(a p(a NOUN hvd.32044092008168 857 51 ): ): PUNCT hvd.32044092008168 857 52 from from ADP hvd.32044092008168 857 53 ( ( PUNCT hvd.32044092008168 857 54 p. p. NOUN hvd.32044092008168 857 55 38 38 NUM hvd.32044092008168 857 56 ) ) PUNCT hvd.32044092008168 857 57 dy dy PROPN hvd.32044092008168 857 58 20 20 NUM hvd.32044092008168 857 59 ( ( PUNCT hvd.32044092008168 857 60 a a DET hvd.32044092008168 857 61 — — PUNCT hvd.32044092008168 857 62 b b X hvd.32044092008168 857 63 ) ) PUNCT hvd.32044092008168 857 64 ( ( PUNCT hvd.32044092008168 857 65 a a DET hvd.32044092008168 857 66 y y PROPN hvd.32044092008168 857 67 ) ) PUNCT hvd.32044092008168 857 68 ... ... PUNCT hvd.32044092008168 858 1 dt dt PROPN hvd.32044092008168 858 2 . . PUNCT hvd.32044092008168 859 1 whence whence PROPN hvd.32044092008168 859 2 a'=(ai a'=(ai ADJ hvd.32044092008168 859 3 ) ) PUNCT hvd.32044092008168 859 4 , , PUNCT hvd.32044092008168 859 5 dy dy PROPN hvd.32044092008168 859 6 and and CCONJ hvd.32044092008168 859 7 [ [ X hvd.32044092008168 859 8 111 111 NUM hvd.32044092008168 859 9 ] ] PUNCT hvd.32044092008168 859 10 becomes become VERB hvd.32044092008168 859 11 dy dy PROPN hvd.32044092008168 859 12 [ [ X hvd.32044092008168 859 13 112 112 NUM hvd.32044092008168 859 14 ] ] PUNCT hvd.32044092008168 860 1 [ [ PUNCT hvd.32044092008168 860 2 = = NOUN hvd.32044092008168 860 3 0 0 NUM hvd.32044092008168 860 4 . . PUNCT hvd.32044092008168 861 1 dt dt PROPN hvd.32044092008168 861 2 jt jt PROPN hvd.32044092008168 861 3 = = PROPN hvd.32044092008168 861 4 α α PROPN hvd.32044092008168 861 5 , , PUNCT hvd.32044092008168 861 6 β β X hvd.32044092008168 861 7 , , PUNCT hvd.32044092008168 861 8 γ γ PROPN hvd.32044092008168 861 9 , , PUNCT hvd.32044092008168 861 10 but but CCONJ hvd.32044092008168 861 11 a a DET hvd.32044092008168 861 12 , , PUNCT hvd.32044092008168 861 13 b b NOUN hvd.32044092008168 861 14 , , PUNCT hvd.32044092008168 861 15 y y PROPN hvd.32044092008168 861 16 , , PUNCT hvd.32044092008168 861 17 ... ... PUNCT hvd.32044092008168 861 18 are be AUX hvd.32044092008168 861 19 also also ADV hvd.32044092008168 861 20 roots root NOUN hvd.32044092008168 861 21 of of ADP hvd.32044092008168 861 22 y y PROPN hvd.32044092008168 861 23 , , PUNCT hvd.32044092008168 861 24 whence whence ADP hvd.32044092008168 861 25 the the DET hvd.32044092008168 861 26 relation relation NOUN hvd.32044092008168 861 27 dy dy X hvd.32044092008168 862 1 [ [ X hvd.32044092008168 862 2 113 113 NUM hvd.32044092008168 862 3 ] ] PUNCT hvd.32044092008168 862 4 = = PRON hvd.32044092008168 862 5 ey ey INTJ hvd.32044092008168 862 6 y y PROPN hvd.32044092008168 862 7 where where SCONJ hvd.32044092008168 862 8 e e NOUN hvd.32044092008168 862 9 is be AUX hvd.32044092008168 862 10 also also ADV hvd.32044092008168 862 11 in in ADP hvd.32044092008168 862 12 general general ADJ hvd.32044092008168 862 13 an an DET hvd.32044092008168 862 14 intire intire ADJ hvd.32044092008168 862 15 polynomial polynomial NOUN hvd.32044092008168 862 16 in in ADP hvd.32044092008168 862 17 t t PROPN hvd.32044092008168 862 18 whence whence ADV hvd.32044092008168 862 19 φ φ X hvd.32044092008168 863 1 dυ dυ X hvd.32044092008168 863 2 y y X hvd.32044092008168 864 1 [ [ X hvd.32044092008168 864 2 114 114 NUM hvd.32044092008168 864 3 ] ] X hvd.32044092008168 864 4 y y PROPN hvd.32044092008168 864 5 dt dt PROPN hvd.32044092008168 864 6 y y PROPN hvd.32044092008168 864 7 1 1 NUM hvd.32044092008168 865 1 dt dt PROPN hvd.32044092008168 865 2 20 20 NUM hvd.32044092008168 865 3 t t PROPN hvd.32044092008168 865 4 = = NOUN hvd.32044092008168 865 5 q q PROPN hvd.32044092008168 865 6 v v X hvd.32044092008168 865 7 ] ] X hvd.32044092008168 865 8 _ _ PROPN hvd.32044092008168 866 1 dt dt PROPN hvd.32044092008168 866 2 -e+ -e+ PROPN hvd.32044092008168 866 3 reduction reduction NOUN hvd.32044092008168 866 4 of of ADP hvd.32044092008168 866 5 the the DET hvd.32044092008168 866 6 forms form NOUN hvd.32044092008168 866 7 when when SCONJ hvd.32044092008168 866 8 n n SYM hvd.32044092008168 866 9 equals equal VERB hvd.32044092008168 866 10 three three NUM hvd.32044092008168 866 11 . . PUNCT hvd.32044092008168 867 1 61 61 NUM hvd.32044092008168 867 2 we we PRON hvd.32044092008168 867 3 have have VERB hvd.32044092008168 867 4 also also ADV hvd.32044092008168 867 5 dy dy PROPN hvd.32044092008168 867 6 dt dt PROPN hvd.32044092008168 867 7 . . PUNCT hvd.32044092008168 868 1 y y PROPN hvd.32044092008168 868 2 = = PUNCT hvd.32044092008168 868 3 0 0 NUM hvd.32044092008168 868 4 tb tb PROPN hvd.32044092008168 868 5 etc etc X hvd.32044092008168 868 6 . . X hvd.32044092008168 869 1 for for ADP hvd.32044092008168 869 2 the the DET hvd.32044092008168 869 3 other other ADJ hvd.32044092008168 869 4 roots root NOUN hvd.32044092008168 869 5 of of ADP hvd.32044092008168 869 6 y. y. NOUN hvd.32044092008168 869 7 the the DET hvd.32044092008168 869 8 degrees degree NOUN hvd.32044092008168 869 9 of of ADP hvd.32044092008168 869 10 [ [ PUNCT hvd.32044092008168 869 11 114 114 NUM hvd.32044092008168 869 12 ] ] PUNCT hvd.32044092008168 869 13 are be AUX hvd.32044092008168 869 14 y y PROPN hvd.32044092008168 869 15 y y PROPN hvd.32044092008168 869 16 φ φ PROPN hvd.32044092008168 870 1 1 1 NUM hvd.32044092008168 870 2 1 1 NUM hvd.32044092008168 870 3 n n CCONJ hvd.32044092008168 870 4 = = SYM hvd.32044092008168 870 5 2 2 NUM hvd.32044092008168 870 6 2 2 NUM hvd.32044092008168 870 7 2 2 NUM hvd.32044092008168 870 8 n n ADP hvd.32044092008168 870 9 odd odd ADJ hvd.32044092008168 870 10 : : PUNCT hvd.32044092008168 870 11 ( ( PUNCT hvd.32044092008168 870 12 n n CCONJ hvd.32044092008168 870 13 − − PROPN hvd.32044092008168 870 14 3 3 X hvd.32044092008168 870 15 ) ) PUNCT hvd.32044092008168 870 16 ( ( PUNCT hvd.32044092008168 870 17 3 3 X hvd.32044092008168 870 18 ) ) PUNCT hvd.32044092008168 870 19 ( ( PUNCT hvd.32044092008168 870 20 n n CCONJ hvd.32044092008168 870 21 + + CCONJ hvd.32044092008168 870 22 3 3 X hvd.32044092008168 870 23 ) ) PUNCT hvd.32044092008168 870 24 ' ' NUM hvd.32044092008168 870 25 1 1 X hvd.32044092008168 870 26 ) ) PUNCT hvd.32044092008168 870 27 ( ( PUNCT hvd.32044092008168 870 28 n n CCONJ hvd.32044092008168 870 29 + + CCONJ hvd.32044092008168 870 30 3 3 X hvd.32044092008168 870 31 ) ) PUNCT hvd.32044092008168 870 32 — — PUNCT hvd.32044092008168 870 33 1 1 NUM hvd.32044092008168 870 34 n n CCONJ hvd.32044092008168 870 35 even even ADV hvd.32044092008168 870 36 : : PUNCT hvd.32044092008168 870 37 § § NUM hvd.32044092008168 870 38 ( ( PUNCT hvd.32044092008168 870 39 n n NOUN hvd.32044092008168 870 40 ) ) PUNCT hvd.32044092008168 870 41 1 1 NUM hvd.32044092008168 870 42 -=- -=- SPACE hvd.32044092008168 870 43 (; (; X hvd.32044092008168 870 44 n+1 n+1 X hvd.32044092008168 870 45 ) ) PUNCT hvd.32044092008168 870 46 , , PUNCT hvd.32044092008168 870 47 n n CCONJ hvd.32044092008168 870 48 , , PUNCT hvd.32044092008168 870 49 (; (; X hvd.32044092008168 870 50 n n X hvd.32044092008168 870 51 + + ADP hvd.32044092008168 870 52 1 1 X hvd.32044092008168 870 53 ) ) PUNCT hvd.32044092008168 870 54 — — PUNCT hvd.32044092008168 870 55 1 1 X hvd.32044092008168 870 56 . . SYM hvd.32044092008168 870 57 1 1 NUM hvd.32044092008168 871 1 we we PRON hvd.32044092008168 871 2 have have VERB hvd.32044092008168 871 3 1 1 NUM hvd.32044092008168 871 4 n n CCONJ hvd.32044092008168 871 5 : : PUNCT hvd.32044092008168 871 6 2 2 NUM hvd.32044092008168 871 7 2 2 NUM hvd.32044092008168 871 8 c c X hvd.32044092008168 871 9 y y PROPN hvd.32044092008168 871 10 = = X hvd.32044092008168 871 11 t t PROPN hvd.32044092008168 871 12 " " PUNCT hvd.32044092008168 871 13 + + CCONJ hvd.32044092008168 871 14 a a PRON hvd.32044092008168 871 15 , , PUNCT hvd.32044092008168 871 16 ta-1 ta-1 INTJ hvd.32044092008168 872 1 + + CCONJ hvd.32044092008168 872 2 a a DET hvd.32044092008168 872 3 , , PUNCT hvd.32044092008168 872 4 tu-+ tu-+ ADV hvd.32044092008168 872 5 ... ... PUNCT hvd.32044092008168 872 6 + + NOUN hvd.32044092008168 873 1 an-1t+ an-1t+ ADP hvd.32044092008168 873 2 an an DET hvd.32044092008168 873 3 y y PROPN hvd.32044092008168 873 4 y y PROPN hvd.32044092008168 873 5 ' ' PUNCT hvd.32044092008168 873 6 = = NOUN hvd.32044092008168 873 7 ntn-1 ntn-1 SYM hvd.32044092008168 873 8 + + NOUN hvd.32044092008168 873 9 ( ( PUNCT hvd.32044092008168 873 10 n n PROPN hvd.32044092008168 873 11 -1 -1 X hvd.32044092008168 873 12 ) ) PUNCT hvd.32044092008168 873 13 a a DET hvd.32044092008168 873 14 , , PUNCT hvd.32044092008168 873 15 tn tn PROPN hvd.32044092008168 873 16 -2 -2 PROPN hvd.32044092008168 873 17 + + PRON hvd.32044092008168 873 18 ( ( PUNCT hvd.32044092008168 873 19 n n CCONJ hvd.32044092008168 873 20 − − PROPN hvd.32044092008168 873 21 2 2 X hvd.32044092008168 873 22 ) ) PUNCT hvd.32044092008168 873 23 a a DET hvd.32044092008168 873 24 , , PUNCT hvd.32044092008168 873 25 tu tu PROPN hvd.32044092008168 873 26 - - PUNCT hvd.32044092008168 873 27 s s PROPN hvd.32044092008168 873 28 + + PROPN hvd.32044092008168 873 29 0 0 NUM hvd.32044092008168 873 30 2 2 NUM hvd.32044092008168 873 31 ) ) PUNCT hvd.32044092008168 873 32 a a PRON hvd.32044092008168 873 33 , , PUNCT hvd.32044092008168 873 34 tn^3 tn^3 PROPN hvd.32044092008168 873 35 + + PUNCT hvd.32044092008168 873 36 ... ... PUNCT hvd.32044092008168 873 37 + + PUNCT hvd.32044092008168 873 38 an-1 an-1 PUNCT hvd.32044092008168 873 39 . . PUNCT hvd.32044092008168 874 1 and and CCONJ hvd.32044092008168 874 2 y y PROPN hvd.32044092008168 874 3 ' ' PUNCT hvd.32044092008168 874 4 nth-1 nth-1 PRON hvd.32044092008168 874 5 + + CCONJ hvd.32044092008168 874 6 a a PRON hvd.32044092008168 874 7 , , PUNCT hvd.32044092008168 874 8 ( ( PUNCT hvd.32044092008168 874 9 n n CCONJ hvd.32044092008168 874 10 1 1 X hvd.32044092008168 874 11 ) ) PUNCT hvd.32044092008168 874 12 t»—2 t»—2 NOUN hvd.32044092008168 875 1 + + PUNCT hvd.32044092008168 875 2 .. .. PUNCT hvd.32044092008168 876 1 b. b. PROPN hvd.32044092008168 876 2 bi bi PROPN hvd.32044092008168 876 3 b b PROPN hvd.32044092008168 876 4 + + NOUN hvd.32044092008168 876 5 + + NOUN hvd.32044092008168 876 6 en en INTJ hvd.32044092008168 877 1 + + PUNCT hvd.32044092008168 877 2 + + PUNCT hvd.32044092008168 877 3 y y X hvd.32044092008168 877 4 to to ADP hvd.32044092008168 877 5 ta ta PROPN hvd.32044092008168 877 6 , , PUNCT hvd.32044092008168 877 7 tht tht PROPN hvd.32044092008168 877 8 . . PUNCT hvd.32044092008168 878 1 -1 -1 PROPN hvd.32044092008168 878 2 1 1 NUM hvd.32044092008168 879 1 t t PROPN hvd.32044092008168 879 2 + + CCONJ hvd.32044092008168 879 3 a a PRON hvd.32044092008168 879 4 , , PUNCT hvd.32044092008168 879 5 th—2 th—2 NOUN hvd.32044092008168 879 6 or or CCONJ hvd.32044092008168 879 7 -1 -1 PROPN hvd.32044092008168 879 8 1 1 NUM hvd.32044092008168 879 9 -2 -2 NOUN hvd.32044092008168 879 10 2 2 NUM hvd.32044092008168 879 11 -3 -3 X hvd.32044092008168 879 12 n n CCONJ hvd.32044092008168 879 13 ' ' PUNCT hvd.32044092008168 879 14 ay ay PROPN hvd.32044092008168 879 15 ( ( PUNCT hvd.32044092008168 879 16 n n ADV hvd.32044092008168 879 17 ai ai VERB hvd.32044092008168 879 18 b2 b2 PROPN hvd.32044092008168 879 19 nta-1 nta-1 ADP hvd.32044092008168 879 20 + + CCONJ hvd.32044092008168 879 21 a a PRON hvd.32044092008168 879 22 , , PUNCT hvd.32044092008168 879 23 ( ( PUNCT hvd.32044092008168 879 24 n n CCONJ hvd.32044092008168 879 25 − − PROPN hvd.32044092008168 879 26 1 1 X hvd.32044092008168 879 27 ) ) PUNCT hvd.32044092008168 879 28 { { PUNCT hvd.32044092008168 879 29 r^2 r^2 PROPN hvd.32044092008168 879 30 + + PROPN hvd.32044092008168 879 31 az az PROPN hvd.32044092008168 879 32 ( ( PUNCT hvd.32044092008168 879 33 n n PROPN hvd.32044092008168 879 34 --2 --2 X hvd.32044092008168 879 35 ) ) PUNCT hvd.32044092008168 879 36 { { PUNCT hvd.32044092008168 879 37 n—3 n—3 PROPN hvd.32044092008168 879 38 + + PROPN hvd.32044092008168 879 39 ( ( PUNCT hvd.32044092008168 879 40 – – PUNCT hvd.32044092008168 879 41 + + NOUN hvd.32044092008168 879 42 = = SYM hvd.32044092008168 879 43 b b NOUN hvd.32044092008168 879 44 , , PUNCT hvd.32044092008168 879 45 ( ( PUNCT hvd.32044092008168 879 46 in-1 in-1 NOUN hvd.32044092008168 879 47 + + ADP hvd.32044092008168 879 48 antr-+ antr-+ NUM hvd.32044092008168 879 49 ... ... PUNCT hvd.32044092008168 879 50 ) ) PUNCT hvd.32044092008168 880 1 + + CCONJ hvd.32044092008168 880 2 b b X hvd.32044092008168 880 3 ( ( PUNCT hvd.32044092008168 880 4 tn–2 tn–2 PROPN hvd.32044092008168 880 5 + + NOUN hvd.32044092008168 880 6 axtn—+ axtn—+ PUNCT hvd.32044092008168 880 7 ... ... PUNCT hvd.32044092008168 880 8 ) ) PUNCT hvd.32044092008168 881 1 and and CCONJ hvd.32044092008168 881 2 equating equate VERB hvd.32044092008168 881 3 the the DET hvd.32044092008168 881 4 corresponding corresponding ADJ hvd.32044092008168 881 5 coefficients coefficient NOUN hvd.32044092008168 881 6 we we PRON hvd.32044092008168 881 7 obtain obtain VERB hvd.32044092008168 881 8 : : PUNCT hvd.32044092008168 881 9 bo bo PROPN hvd.32044092008168 881 10 1 1 NUM hvd.32044092008168 881 11 ) ) PUNCT hvd.32044092008168 881 12 na na ADP hvd.32044092008168 881 13 + + NOUN hvd.32044092008168 881 14 bi bi NOUN hvd.32044092008168 882 1 or or CCONJ hvd.32044092008168 882 2 [ [ X hvd.32044092008168 882 3 115 115 NUM hvd.32044092008168 882 4 ] ] PUNCT hvd.32044092008168 882 5 · · PUNCT hvd.32044092008168 882 6 2a2 2a2 NUM hvd.32044092008168 882 7 + + NUM hvd.32044092008168 882 8 ai ai VERB hvd.32044092008168 882 9 bz bz PROPN hvd.32044092008168 882 10 3az 3az PROPN hvd.32044092008168 883 1 + + CCONJ hvd.32044092008168 883 2 az az PROPN hvd.32044092008168 883 3 az az PROPN hvd.32044092008168 883 4 ai ai PROPN hvd.32044092008168 883 5 etc etc PROPN hvd.32044092008168 883 6 . . X hvd.32044092008168 884 1 proceeding proceed VERB hvd.32044092008168 884 2 in in ADP hvd.32044092008168 884 3 like like ADJ hvd.32044092008168 884 4 manner manner NOUN hvd.32044092008168 884 5 we we PRON hvd.32044092008168 884 6 write write VERB hvd.32044092008168 884 7 : : PUNCT hvd.32044092008168 884 8 q q X hvd.32044092008168 884 9 = = SYM hvd.32044092008168 884 10 b b PROPN hvd.32044092008168 884 11 , , PUNCT hvd.32044092008168 884 12 t t PROPN hvd.32044092008168 884 13 + + CCONJ hvd.32044092008168 884 14 b b PROPN hvd.32044092008168 884 15 , , PUNCT hvd.32044092008168 884 16 t"-1 t"-1 ADJ hvd.32044092008168 884 17 + + VERB hvd.32044092008168 884 18 ... ... PUNCT hvd.32044092008168 884 19 " " PUNCT hvd.32044092008168 884 20 . . PUNCT hvd.32044092008168 885 1 + + CCONJ hvd.32044092008168 885 2 bn-1t+ bn-1t+ X hvd.32044092008168 885 3 b b PROPN hvd.32044092008168 885 4 , , PUNCT hvd.32044092008168 885 5 where where SCONJ hvd.32044092008168 885 6 v v ADP hvd.32044092008168 885 7 = = X hvd.32044092008168 885 8 [ [ X hvd.32044092008168 885 9 ] ] X hvd.32044092008168 885 10 ( ( PUNCT hvd.32044092008168 885 11 n n CCONJ hvd.32044092008168 885 12 + + CCONJ hvd.32044092008168 885 13 1 1 NUM hvd.32044092008168 885 14 ) ) PUNCT hvd.32044092008168 885 15 , , PUNCT hvd.32044092008168 885 16 į į X hvd.32044092008168 885 17 n n X hvd.32044092008168 885 18 ] ] X hvd.32044092008168 885 19 = = NOUN hvd.32044092008168 885 20 whence whence ADV hvd.32044092008168 885 21 be be AUX hvd.32044092008168 885 22 or or CCONJ hvd.32044092008168 885 23 + + NUM hvd.32044092008168 885 24 + + CCONJ hvd.32044092008168 885 25 + + PUNCT hvd.32044092008168 885 26 .. .. PUNCT hvd.32044092008168 886 1 + + PUNCT hvd.32044092008168 886 2 ... ... PUNCT hvd.32044092008168 886 3 ) ) PUNCT hvd.32044092008168 886 4 ( ( PUNCT hvd.32044092008168 886 5 b.t b.t PROPN hvd.32044092008168 886 6 " " PUNCT hvd.32044092008168 886 7 + + CCONJ hvd.32044092008168 886 8 b,8 b,8 NOUN hvd.32044092008168 886 9 - - SYM hvd.32044092008168 886 10 1 1 NUM hvd.32044092008168 886 11 + + CCONJ hvd.32044092008168 886 12 + + CCONJ hvd.32044092008168 886 13 bt bt ADP hvd.32044092008168 886 14 + + PROPN hvd.32044092008168 886 15 b b NOUN hvd.32044092008168 886 16 ) ) PUNCT hvd.32044092008168 886 17 bo bo PROPN hvd.32044092008168 886 18 ( ( PUNCT hvd.32044092008168 886 19 b b PROPN hvd.32044092008168 886 20 , , PUNCT hvd.32044092008168 886 21 t=1 t=1 SPACE hvd.32044092008168 886 22 + + NUM hvd.32044092008168 886 23 3,8 3,8 NUM hvd.32044092008168 886 24 - - SYM hvd.32044092008168 886 25 2+ 2+ NUM hvd.32044092008168 886 26 ... ... PUNCT hvd.32044092008168 886 27 +by-1 +by-1 NUM hvd.32044092008168 886 28 + + PUNCT hvd.32044092008168 886 29 ) ) PUNCT hvd.32044092008168 886 30 + + CCONJ hvd.32044092008168 886 31 b b X hvd.32044092008168 886 32 , , PUNCT hvd.32044092008168 886 33 ( ( PUNCT hvd.32044092008168 886 34 bot”-3 bot”-3 SPACE hvd.32044092008168 886 35 + + PROPN hvd.32044092008168 886 36 bt-3 bt-3 SPACE hvd.32044092008168 886 37 + + CCONJ hvd.32044092008168 886 38 + + CCONJ hvd.32044092008168 886 39 b-2 b-2 ADJ hvd.32044092008168 886 40 + + CCONJ hvd.32044092008168 886 41 by-17 by-17 ADP hvd.32044092008168 886 42 - - PUNCT hvd.32044092008168 886 43 1 1 NUM hvd.32044092008168 886 44 + + NUM hvd.32044092008168 886 45 b b NOUN hvd.32044092008168 886 46 , , PUNCT hvd.32044092008168 886 47 t2 t2 PROPN hvd.32044092008168 886 48 ) ) PUNCT hvd.32044092008168 886 49 + + PROPN hvd.32044092008168 886 50 b2 b2 PROPN hvd.32044092008168 886 51 ( ( PUNCT hvd.32044092008168 886 52 botr=3 botr=3 PROPN hvd.32044092008168 886 53 + + ADJ hvd.32044092008168 886 54 b b PROPN hvd.32044092008168 886 55 , , PUNCT hvd.32044092008168 886 56 tr–4 tr–4 PROPN hvd.32044092008168 886 57 + + PUNCT hvd.32044092008168 886 58 ... ... PUNCT hvd.32044092008168 887 1 + + CCONJ hvd.32044092008168 887 2 2 2 NUM hvd.32044092008168 887 3 > > SYM hvd.32044092008168 887 4 2 2 NUM hvd.32044092008168 887 5 b b NOUN hvd.32044092008168 887 6 1 1 NUM hvd.32044092008168 887 7 be be AUX hvd.32044092008168 887 8 t3 t3 PROPN hvd.32044092008168 887 9 t t PROPN hvd.32044092008168 887 10 ta ta ADP hvd.32044092008168 887 11 bn bn PROPN hvd.32044092008168 887 12 0 0 NUM hvd.32044092008168 887 13 1 1 NUM hvd.32044092008168 888 1 t t PROPN hvd.32044092008168 888 2 -2 -2 PROPN hvd.32044092008168 888 3 1 1 NUM hvd.32044092008168 888 4 v v NOUN hvd.32044092008168 888 5 -3 -3 X hvd.32044092008168 888 6 62 62 NUM hvd.32044092008168 888 7 part part NOUN hvd.32044092008168 888 8 . . PUNCT hvd.32044092008168 889 1 v. v. ADP hvd.32044092008168 889 2 0 0 NUM hvd.32044092008168 889 3 v-3 v-3 X hvd.32044092008168 889 4 0 0 NUM hvd.32044092008168 889 5 v v PROPN hvd.32044092008168 889 6 v-2 v-2 X hvd.32044092008168 889 7 -3 -3 PROPN hvd.32044092008168 889 8 -1 -1 PROPN hvd.32044092008168 889 9 -1 -1 PROPN hvd.32044092008168 889 10 and and CCONJ hvd.32044092008168 889 11 6 6 NUM hvd.32044092008168 889 12 , , PUNCT hvd.32044092008168 889 13 b,+1+b b,+1+b PROPN hvd.32044092008168 889 14 , , PUNCT hvd.32044092008168 889 15 b,-1+b b,-1+b PROPN hvd.32044092008168 889 16 , , PUNCT hvd.32044092008168 889 17 b,-2t+b b,-2t+b SPACE hvd.32044092008168 889 18 , , PUNCT hvd.32044092008168 889 19 b,—32 b,—32 CCONJ hvd.32044092008168 890 1 + + PUNCT hvd.32044092008168 890 2 ... ... PUNCT hvd.32044092008168 891 1 + + PUNCT hvd.32044092008168 891 2 b b X hvd.32044092008168 891 3 , , PUNCT hvd.32044092008168 891 4 b b NOUN hvd.32044092008168 891 5 , , PUNCT hvd.32044092008168 891 6 tv-2 tv-2 PROPN hvd.32044092008168 891 7 +1 +1 PROPN hvd.32044092008168 891 8 , , PUNCT hvd.32044092008168 891 9 b b NOUN hvd.32044092008168 891 10 , , PUNCT hvd.32044092008168 891 11 tr-1 tr-1 ADJ hvd.32044092008168 891 12 +6 +6 NOUN hvd.32044092008168 891 13 , , PUNCT hvd.32044092008168 891 14 beta beta NOUN hvd.32044092008168 891 15 + + CCONJ hvd.32044092008168 891 16 b b NOUN hvd.32044092008168 891 17 , , PUNCT hvd.32044092008168 891 18 b,-1 b,-1 NOUN hvd.32044092008168 891 19 + + NUM hvd.32044092008168 891 20 1+bb,-+ 1+bb,-+ NUM hvd.32044092008168 891 21 6 6 NUM hvd.32044092008168 891 22 , , PUNCT hvd.32044092008168 891 23 b,-st b,-st VERB hvd.32044092008168 891 24 + + PUNCT hvd.32044092008168 891 25 ... ... PUNCT hvd.32044092008168 892 1 + + PUNCT hvd.32044092008168 892 2 + + PUNCT hvd.32044092008168 892 3 br-1b br-1b NOUN hvd.32044092008168 892 4 , , PUNCT hvd.32044092008168 892 5 tv tv PROPN hvd.32044092008168 892 6 + + CCONJ hvd.32044092008168 892 7 br-1b,-1t(n-1 br-1b,-1t(n-1 PROPN hvd.32044092008168 892 8 ) ) PUNCT hvd.32044092008168 893 1 + + PUNCT hvd.32044092008168 893 2 ... ... PUNCT hvd.32044092008168 894 1 + + CCONJ hvd.32044092008168 894 2 br-1 br-1 X hvd.32044092008168 894 3 b. b. PROPN hvd.32044092008168 894 4 b b PROPN hvd.32044092008168 894 5 , , PUNCT hvd.32044092008168 894 6 t—1 t—1 PROPN hvd.32044092008168 894 7 + + CCONJ hvd.32044092008168 894 8 b b PROPN hvd.32044092008168 894 9 , , PUNCT hvd.32044092008168 894 10 b,-1 b,-1 PROPN hvd.32044092008168 894 11 t t PROPN hvd.32044092008168 894 12 " " PUNCT hvd.32044092008168 894 13 + + CCONJ hvd.32044092008168 894 14 b b NOUN hvd.32044092008168 894 15 , , PUNCT hvd.32044092008168 894 16 b,-2t+1 b,-2t+1 PROPN hvd.32044092008168 894 17 + + SYM hvd.32044092008168 894 18 + + SYM hvd.32044092008168 894 19 bb bb NOUN hvd.32044092008168 894 20 , , PUNCT hvd.32044092008168 894 21 t2v-2 t2v-2 PROPN hvd.32044092008168 894 22 + + CCONJ hvd.32044092008168 894 23 b b ADP hvd.32044092008168 894 24 b.t2v-1 b.t2v-1 NOUN hvd.32044092008168 894 25 + + CCONJ hvd.32044092008168 894 26 b b NOUN hvd.32044092008168 894 27 , , PUNCT hvd.32044092008168 894 28 b b PROPN hvd.32044092008168 894 29 , , PUNCT hvd.32044092008168 894 30 t"=2 t"=2 NOUN hvd.32044092008168 894 31 + + NUM hvd.32044092008168 894 32 6 6 NUM hvd.32044092008168 894 33 , , PUNCT hvd.32044092008168 894 34 b,-14"-1 b,-14"-1 PROPN hvd.32044092008168 894 35 + + PROPN hvd.32044092008168 894 36 b b ADP hvd.32044092008168 894 37 by-24 by-24 PROPN hvd.32044092008168 894 38 + + CCONJ hvd.32044092008168 894 39 .. .. PUNCT hvd.32044092008168 895 1 from from ADP hvd.32044092008168 895 2 whence whence ADP hvd.32044092008168 895 3 the the DET hvd.32044092008168 895 4 relations relation NOUN hvd.32044092008168 895 5 : : PUNCT hvd.32044092008168 895 6 b b X hvd.32044092008168 895 7 , , PUNCT hvd.32044092008168 895 8 b b NOUN hvd.32044092008168 895 9 , , PUNCT hvd.32044092008168 895 10 + + NUM hvd.32044092008168 895 11 b b NOUN hvd.32044092008168 895 12 , , PUNCT hvd.32044092008168 895 13 b,-1 b,-1 NOUN hvd.32044092008168 895 14 + + CCONJ hvd.32044092008168 895 15 1 1 NUM hvd.32044092008168 895 16 , , PUNCT hvd.32044092008168 895 17 b,-:+ b,-:+ PROPN hvd.32044092008168 895 18 ... ... SYM hvd.32044092008168 895 19 +b +b PROPN hvd.32044092008168 895 20 , , PUNCT hvd.32044092008168 895 21 b b NOUN hvd.32044092008168 895 22 = = SYM hvd.32044092008168 895 23 0 0 PUNCT hvd.32044092008168 896 1 [ [ X hvd.32044092008168 896 2 116 116 NUM hvd.32044092008168 896 3 ] ] PUNCT hvd.32044092008168 896 4 b b NOUN hvd.32044092008168 896 5 , , PUNCT hvd.32044092008168 896 6 b b NOUN hvd.32044092008168 896 7 , , PUNCT hvd.32044092008168 896 8 + + NUM hvd.32044092008168 896 9 b b NOUN hvd.32044092008168 896 10 , , PUNCT hvd.32044092008168 896 11 b,-1 b,-1 NOUN hvd.32044092008168 896 12 + + NUM hvd.32044092008168 896 13 b3 b3 PROPN hvd.32044092008168 896 14 b,-2 b,-2 NUM hvd.32044092008168 896 15 + + NOUN hvd.32044092008168 896 16 . . PUNCT hvd.32044092008168 897 1 + + CCONJ hvd.32044092008168 897 2 bx+1b bx+1b PROPN hvd.32044092008168 897 3 , , PUNCT hvd.32044092008168 897 4 0 0 NUM hvd.32044092008168 897 5 --2 --2 NOUN hvd.32044092008168 897 6 0 0 NUM hvd.32044092008168 897 7 -1 -1 PROPN hvd.32044092008168 897 8 22 22 NUM hvd.32044092008168 897 9 v-2 v-2 NUM hvd.32044092008168 897 10 v v ADP hvd.32044092008168 897 11 0 0 NUM hvd.32044092008168 897 12 v+ v+ PRON hvd.32044092008168 897 13 ber-1b ber-1b PROPN hvd.32044092008168 897 14 = = PROPN hvd.32044092008168 897 15 0 0 NUM hvd.32044092008168 897 16 v v NOUN hvd.32044092008168 897 17 1 1 NUM hvd.32044092008168 897 18 br br PROPN hvd.32044092008168 897 19 -1b -1b PROPN hvd.32044092008168 897 20 , , PUNCT hvd.32044092008168 897 21 + + PROPN hvd.32044092008168 897 22 b b NOUN hvd.32044092008168 897 23 , , PUNCT hvd.32044092008168 897 24 b,-1 b,-1 NOUN hvd.32044092008168 897 25 + + SYM hvd.32044092008168 897 26 bx+1b,-2 bx+1b,-2 SPACE hvd.32044092008168 898 1 + + CCONJ hvd.32044092008168 898 2 we we PRON hvd.32044092008168 898 3 will will AUX hvd.32044092008168 898 4 define define VERB hvd.32044092008168 898 5 : : PUNCT hvd.32044092008168 898 6 bob bob PROPN hvd.32044092008168 898 7 b b PROPN hvd.32044092008168 898 8 , , PUNCT hvd.32044092008168 898 9 b b PROPN hvd.32044092008168 898 10 , , PUNCT hvd.32044092008168 898 11 b b NOUN hvd.32044092008168 898 12 , , PUNCT hvd.32044092008168 898 13 by by ADP hvd.32044092008168 898 14 be be AUX hvd.32044092008168 898 15 bg bg INTJ hvd.32044092008168 899 1 [ [ X hvd.32044092008168 899 2 117 117 NUM hvd.32044092008168 899 3 ] ] PUNCT hvd.32044092008168 899 4 ... ... PUNCT hvd.32044092008168 899 5 bm bm PROPN hvd.32044092008168 899 6 ... ... PUNCT hvd.32044092008168 900 1 bm+1 bm+1 PROPN hvd.32044092008168 900 2 om om PROPN hvd.32044092008168 900 3 т т PROPN hvd.32044092008168 900 4 dr-1 dr-1 PROPN hvd.32044092008168 900 5 2 2 NUM hvd.32044092008168 901 1 • • SYM hvd.32044092008168 901 2 -1 -1 PUNCT hvd.32044092008168 901 3 > > X hvd.32044092008168 901 4 bmbm+1bm+2 bmbm+1bm+2 NOUN hvd.32044092008168 901 5 bam bam NOUN hvd.32044092008168 901 6 we we PRON hvd.32044092008168 901 7 will will AUX hvd.32044092008168 901 8 define define VERB hvd.32044092008168 901 9 b b PROPN hvd.32044092008168 901 10 = = SYM hvd.32044092008168 902 1 and and CCONJ hvd.32044092008168 902 2 we we PRON hvd.32044092008168 902 3 will will AUX hvd.32044092008168 902 4 then then ADV hvd.32044092008168 902 5 have have VERB hvd.32044092008168 902 6 from from ADP hvd.32044092008168 902 7 the the DET hvd.32044092008168 902 8 above above ADJ hvd.32044092008168 902 9 conditions condition NOUN hvd.32044092008168 902 10 , , PUNCT hvd.32044092008168 902 11 all all DET hvd.32044092008168 902 12 the the DET hvd.32044092008168 902 13 coefficients coefficient NOUN hvd.32044092008168 902 14 b b PROPN hvd.32044092008168 902 15 , , PUNCT hvd.32044092008168 902 16 b b PROPN hvd.32044092008168 902 17 , , PUNCT hvd.32044092008168 902 18 ... ... PUNCT hvd.32044092008168 902 19 as as ADP hvd.32044092008168 902 20 intire intire ADJ hvd.32044092008168 902 21 functions function NOUN hvd.32044092008168 902 22 of of ADP hvd.32044092008168 902 23 b b ADP hvd.32044092008168 902 24 , , PUNCT hvd.32044092008168 902 25 bı bı PROPN hvd.32044092008168 902 26 ... ... PUNCT hvd.32044092008168 902 27 which which PRON hvd.32044092008168 902 28 are be AUX hvd.32044092008168 902 29 in in ADP hvd.32044092008168 902 30 turn turn NOUN hvd.32044092008168 902 31 functions function NOUN hvd.32044092008168 902 32 of of ADP hvd.32044092008168 902 33 an an PRON hvd.32044092008168 902 34 , , PUNCT hvd.32044092008168 902 35 a a PRON hvd.32044092008168 902 36 , , PUNCT hvd.32044092008168 902 37 ... ... PUNCT hvd.32044092008168 902 38 which which PRON hvd.32044092008168 902 39 finally finally ADV hvd.32044092008168 902 40 are be AUX hvd.32044092008168 902 41 expressed express VERB hvd.32044092008168 902 42 as as ADP hvd.32044092008168 902 43 functions function NOUN hvd.32044092008168 902 44 of of ADP hvd.32044092008168 902 45 b b PROPN hvd.32044092008168 902 46 , , PUNCT hvd.32044092008168 902 47 92 92 NUM hvd.32044092008168 902 48 and and CCONJ hvd.32044092008168 902 49 93 93 NUM hvd.32044092008168 902 50 . . PUNCT hvd.32044092008168 903 1 that that PRON hvd.32044092008168 903 2 is be AUX hvd.32044092008168 903 3 we we PRON hvd.32044092008168 903 4 have have AUX hvd.32044092008168 903 5 obtained obtain VERB hvd.32044092008168 903 6 ø ø NOUN hvd.32044092008168 903 7 , , PUNCT hvd.32044092008168 903 8 of of ADP hvd.32044092008168 903 9 which which PRON hvd.32044092008168 903 10 the the DET hvd.32044092008168 903 11 first first ADJ hvd.32044092008168 903 12 coefficient coefficient NOUN hvd.32044092008168 903 13 shall shall AUX hvd.32044092008168 903 14 be be AUX hvd.32044092008168 903 15 dr- dr- SPACE hvd.32044092008168 903 16 , , PUNCT hvd.32044092008168 903 17 intire intire NOUN hvd.32044092008168 903 18 in in ADP hvd.32044092008168 903 19 terms term NOUN hvd.32044092008168 903 20 of of ADP hvd.32044092008168 903 21 t t PROPN hvd.32044092008168 903 22 , , PUNCT hvd.32044092008168 903 23 b b PROPN hvd.32044092008168 903 24 , , PUNCT hvd.32044092008168 903 25 9 9 NUM hvd.32044092008168 903 26 , , PUNCT hvd.32044092008168 903 27 and and CCONJ hvd.32044092008168 903 28 93 93 NUM hvd.32044092008168 903 29 : : SYM hvd.32044092008168 903 30 92 92 NUM hvd.32044092008168 903 31 case case NOUN hvd.32044092008168 903 32 n n X hvd.32044092008168 903 33 3 3 NUM hvd.32044092008168 903 34 we we PRON hvd.32044092008168 903 35 have have VERB hvd.32044092008168 903 36 : : PUNCT hvd.32044092008168 903 37 from from ADP hvd.32044092008168 903 38 ( ( PUNCT hvd.32044092008168 903 39 p. p. NOUN hvd.32044092008168 903 40 36 36 NUM hvd.32044092008168 903 41 ) ) PUNCT hvd.32044092008168 903 42 b b ADP hvd.32044092008168 903 43 ' ' PUNCT hvd.32044092008168 903 44 m m NOUN hvd.32044092008168 903 45 2 2 NUM hvd.32044092008168 903 46 : : SYM hvd.32044092008168 903 47 2.1.5 2.1.5 NUM hvd.32044092008168 903 48 . . NUM hvd.32044092008168 903 49 6a 6a NUM hvd.32044092008168 903 50 , , PUNCT hvd.32044092008168 903 51 + + NUM hvd.32044092008168 903 52 4.3b=0 4.3b=0 NUM hvd.32044092008168 903 53 or or CCONJ hvd.32044092008168 903 54 ay ay NOUN hvd.32044092008168 903 55 2 2 NUM hvd.32044092008168 903 56 b2 b2 PROPN hvd.32044092008168 903 57 93 93 NUM hvd.32044092008168 903 58 u u NOUN hvd.32044092008168 903 59 = = VERB hvd.32044092008168 903 60 1 1 NUM hvd.32044092008168 903 61 : : PUNCT hvd.32044092008168 903 62 a2 a2 PROPN hvd.32044092008168 903 63 3 3 NUM hvd.32044092008168 903 64 . . PUNCT hvd.32044092008168 903 65 52 52 NUM hvd.32044092008168 903 66 4 4 NUM hvd.32044092008168 903 67 b3 b3 PROPN hvd.32044092008168 903 68 93 93 NUM hvd.32044092008168 903 69 m m NOUN hvd.32044092008168 903 70 0 0 NUM hvd.32044092008168 903 71 : : SYM hvd.32044092008168 903 72 03 03 NUM hvd.32044092008168 903 73 + + NUM hvd.32044092008168 903 74 3252 3252 NUM hvd.32044092008168 903 75 3.5 3.5 NUM hvd.32044092008168 903 76 4 4 NUM hvd.32044092008168 903 77 and and CCONJ hvd.32044092008168 903 78 from from ADP hvd.32044092008168 903 79 ( ( PUNCT hvd.32044092008168 903 80 115 115 NUM hvd.32044092008168 903 81 ) ) PUNCT hvd.32044092008168 903 82 tn-1 tn-1 SPACE hvd.32044092008168 903 83 : : PUNCT hvd.32044092008168 903 84 tn-2 tn-2 SPACE hvd.32044092008168 903 85 : : PUNCT hvd.32044092008168 903 86 a a X hvd.32044092008168 903 87 , , PUNCT hvd.32044092008168 903 88 ( ( PUNCT hvd.32044092008168 903 89 n n CCONJ hvd.32044092008168 903 90 − − PROPN hvd.32044092008168 903 91 1 1 X hvd.32044092008168 903 92 ) ) PUNCT hvd.32044092008168 903 93 = = X hvd.32044092008168 903 94 b b PROPN hvd.32044092008168 903 95 , , PUNCT hvd.32044092008168 903 96 aj aj PROPN hvd.32044092008168 903 97 ; ; PUNCT hvd.32044092008168 903 98 by by ADP hvd.32044092008168 903 99 : : PUNCT hvd.32044092008168 903 100 ay ay INTJ hvd.32044092008168 903 101 -th-3 -th-3 SPACE hvd.32044092008168 903 102 : : PUNCT hvd.32044092008168 903 103 a a X hvd.32044092008168 903 104 , , PUNCT hvd.32044092008168 903 105 ( ( PUNCT hvd.32044092008168 903 106 m m PROPN hvd.32044092008168 903 107 2 2 NUM hvd.32044092008168 903 108 ) ) PUNCT hvd.32044092008168 903 109 2 2 NUM hvd.32044092008168 903 110 ) ) PUNCT hvd.32044092008168 903 111 = = X hvd.32044092008168 903 112 b b PROPN hvd.32044092008168 903 113 , , PUNCT hvd.32044092008168 903 114 a a PRON hvd.32044092008168 903 115 , , PUNCT hvd.32044092008168 903 116 + + NUM hvd.32044092008168 903 117 by by ADP hvd.32044092008168 903 118 an an DET hvd.32044092008168 903 119 + + ADJ hvd.32044092008168 903 120 ba ba NOUN hvd.32044092008168 903 121 ; ; PUNCT hvd.32044092008168 903 122 b2 b2 PROPN hvd.32044092008168 903 123 b b PROPN hvd.32044092008168 903 124 , , PUNCT hvd.32044092008168 903 125 2a 2a NUM hvd.32044092008168 903 126 , , PUNCT hvd.32044092008168 903 127 ba ba PROPN hvd.32044092008168 903 128 — — PUNCT hvd.32044092008168 903 129 tn–4 tn–4 PROPN hvd.32044092008168 903 130 : : PUNCT hvd.32044092008168 903 131 az az PROPN hvd.32044092008168 903 132 ( ( PUNCT hvd.32044092008168 903 133 n n PROPN hvd.32044092008168 903 134 3)=+ 3)=+ NUM hvd.32044092008168 903 135 ba ba PROPN hvd.32044092008168 903 136 , , PUNCT hvd.32044092008168 903 137 b b PROPN hvd.32044092008168 903 138 , , PUNCT hvd.32044092008168 903 139 az az PROPN hvd.32044092008168 903 140 + + PROPN hvd.32044092008168 903 141 6,4 6,4 NUM hvd.32044092008168 903 142 , , PUNCT hvd.32044092008168 903 143 + + NUM hvd.32044092008168 903 144 b b X hvd.32044092008168 903 145 , , PUNCT hvd.32044092008168 903 146 a a PRON hvd.32044092008168 903 147 , , PUNCT hvd.32044092008168 903 148 + + NUM hvd.32044092008168 903 149 b3 b3 PROPN hvd.32044092008168 903 150 ; ; PUNCT hvd.32044092008168 903 151 b3 b3 PROPN hvd.32044092008168 903 152 = = PRON hvd.32044092008168 903 153 3a,4,3az 3a,4,3az NUM hvd.32044092008168 903 154 a a DET hvd.32044092008168 903 155 5 5 NUM hvd.32044092008168 903 156 b92 b92 NOUN hvd.32044092008168 903 157 n n CCONJ hvd.32044092008168 903 158 = = ADP hvd.32044092008168 903 159 bo bo NOUN hvd.32044092008168 903 160 n n NOUN hvd.32044092008168 903 161 reduction reduction NOUN hvd.32044092008168 903 162 of of ADP hvd.32044092008168 903 163 the the DET hvd.32044092008168 903 164 forms form NOUN hvd.32044092008168 903 165 when when SCONJ hvd.32044092008168 903 166 n n SYM hvd.32044092008168 903 167 equals equal VERB hvd.32044092008168 903 168 three three NUM hvd.32044092008168 903 169 . . PUNCT hvd.32044092008168 904 1 63 63 NUM hvd.32044092008168 904 2 s s NOUN hvd.32044092008168 904 3 0 0 NUM hvd.32044092008168 904 4 2 2 NUM hvd.32044092008168 904 5 2 2 NUM hvd.32044092008168 904 6 = = SYM hvd.32044092008168 904 7 2 2 NUM hvd.32044092008168 904 8 62 62 NUM hvd.32044092008168 904 9 , , PUNCT hvd.32044092008168 904 10 0 0 NUM hvd.32044092008168 904 11 . . NOUN hvd.32044092008168 904 12 3 3 NUM hvd.32044092008168 904 13 3 3 NUM hvd.32044092008168 904 14 3 3 NUM hvd.32044092008168 904 15 12 12 NUM hvd.32044092008168 904 16 6 6 NUM hvd.32044092008168 904 17 a a PRON hvd.32044092008168 904 18 , , PUNCT hvd.32044092008168 904 19 2 2 NUM hvd.32044092008168 904 20 2 2 NUM hvd.32044092008168 904 21 2 2 NUM hvd.32044092008168 904 22 the the DET hvd.32044092008168 904 23 conditions condition NOUN hvd.32044092008168 904 24 ( ( PUNCT hvd.32044092008168 904 25 116 116 NUM hvd.32044092008168 904 26 ) ) PUNCT hvd.32044092008168 904 27 become become VERB hvd.32044092008168 904 28 : : PUNCT hvd.32044092008168 904 29 b b X hvd.32044092008168 904 30 , , PUNCT hvd.32044092008168 904 31 b b NOUN hvd.32044092008168 904 32 , , PUNCT hvd.32044092008168 904 33 + + PROPN hvd.32044092008168 904 34 b b X hvd.32044092008168 904 35 b. b. PROPN hvd.32044092008168 904 36 + + CCONJ hvd.32044092008168 904 37 b b PROPN hvd.32044092008168 904 38 , , PUNCT hvd.32044092008168 904 39 b. b. PROPN hvd.32044092008168 904 40 = = PROPN hvd.32044092008168 904 41 b b PROPN hvd.32044092008168 904 42 , , PUNCT hvd.32044092008168 904 43 b b NOUN hvd.32044092008168 904 44 , , PUNCT hvd.32044092008168 904 45 + + PROPN hvd.32044092008168 904 46 b b X hvd.32044092008168 904 47 b. b. PROPN hvd.32044092008168 904 48 + + SYM hvd.32044092008168 904 49 b3 b3 PROPN hvd.32044092008168 904 50 b=0 b=0 ADV hvd.32044092008168 904 51 = = PROPN hvd.32044092008168 904 52 whence whence NOUN hvd.32044092008168 904 53 ( ( PUNCT hvd.32044092008168 904 54 bob bob PROPN hvd.32044092008168 904 55 , , PUNCT hvd.32044092008168 904 56 — — PUNCT hvd.32044092008168 904 57 bî bî PROPN hvd.32044092008168 904 58 ) ) PUNCT hvd.32044092008168 904 59 b. b. PROPN hvd.32044092008168 904 60 — — PUNCT hvd.32044092008168 904 61 ( ( PUNCT hvd.32044092008168 904 62 — — PUNCT hvd.32044092008168 904 63 b b X hvd.32044092008168 904 64 ) ) PUNCT hvd.32044092008168 904 65 b. b. PROPN hvd.32044092008168 904 66 , , PUNCT hvd.32044092008168 904 67 – – PUNCT hvd.32044092008168 904 68 64bz 64bz NOUN hvd.32044092008168 904 69 ( ( PUNCT hvd.32044092008168 904 70 1,5 1,5 NUM hvd.32044092008168 904 71 , , PUNCT hvd.32044092008168 904 72 -bi -bi SPACE hvd.32044092008168 904 73 ) ) PUNCT hvd.32044092008168 904 74 b b NOUN hvd.32044092008168 904 75 = = PUNCT hvd.32044092008168 904 76 ( ( PUNCT hvd.32044092008168 904 77 1,62 1,62 NUM hvd.32044092008168 904 78 — — PUNCT hvd.32044092008168 904 79 6,63 6,63 NUM hvd.32044092008168 904 80 ) ) PUNCT hvd.32044092008168 904 81 by by ADP hvd.32044092008168 904 82 . . PUNCT hvd.32044092008168 905 1 but but CCONJ hvd.32044092008168 905 2 b. b. PROPN hvd.32044092008168 905 3 = = PROPN hvd.32044092008168 905 4 b b PROPN hvd.32044092008168 905 5 , , PUNCT hvd.32044092008168 905 6 by by ADP hvd.32044092008168 905 7 --= --= X hvd.32044092008168 905 8 9 9 NUM hvd.32044092008168 905 9 : : SYM hvd.32044092008168 905 10 b b X hvd.32044092008168 905 11 ’ ' PUNCT hvd.32044092008168 905 12 = = SYM hvd.32044092008168 905 13 9 9 NUM hvd.32044092008168 905 14 : : PUNCT hvd.32044092008168 905 15 — — PUNCT hvd.32044092008168 905 16 181= 181= ADJ hvd.32044092008168 905 17 = = SYM hvd.32044092008168 905 18 b2 b2 PROPN hvd.32044092008168 905 19 92 92 NUM hvd.32044092008168 905 20 — — PUNCT hvd.32044092008168 905 21 -0 -0 PUNCT hvd.32044092008168 905 22 whence whence NOUN hvd.32044092008168 905 23 b,= b,= ADJ hvd.32044092008168 905 24 ( ( PUNCT hvd.32044092008168 905 25 -a -a NOUN hvd.32044092008168 905 26 ) ) PUNCT hvd.32044092008168 905 27 ( ( PUNCT hvd.32044092008168 905 28 3a 3a PROPN hvd.32044092008168 905 29 , , PUNCT hvd.32044092008168 905 30 0 0 NUM hvd.32044092008168 905 31 , , PUNCT hvd.32044092008168 905 32 — — PUNCT hvd.32044092008168 905 33 3az 3az ADJ hvd.32044092008168 905 34 — — PUNCT hvd.32044092008168 905 35 a a X hvd.32044092008168 905 36 ;) ;) PUNCT hvd.32044092008168 905 37 – – PUNCT hvd.32044092008168 905 38 ( ( PUNCT hvd.32044092008168 905 39 4a 4a NUM hvd.32044092008168 905 40 ; ; PUNCT hvd.32044092008168 905 41 — — PUNCT hvd.32044092008168 905 42 4a;az 4a;az NUM hvd.32044092008168 905 43 + + CCONJ hvd.32044092008168 905 44 af af ADV hvd.32044092008168 905 45 ) ) PUNCT hvd.32044092008168 905 46 a a DET hvd.32044092008168 905 47 a2 a2 PROPN hvd.32044092008168 905 48 + + CCONJ hvd.32044092008168 905 49 3a 3a NUM hvd.32044092008168 905 50 ; ; PUNCT hvd.32044092008168 905 51 qg qg PROPN hvd.32044092008168 905 52 — — PUNCT hvd.32044092008168 905 53 4a 4a PROPN hvd.32044092008168 905 54 19 19 NUM hvd.32044092008168 905 55 g g NOUN hvd.32044092008168 905 56 = = SYM hvd.32044092008168 905 57 32.564 32.564 NUM hvd.32044092008168 905 58 + + NUM hvd.32044092008168 905 59 * * PUNCT hvd.32044092008168 905 60 9962 9962 NUM hvd.32044092008168 906 1 +93bg +93bg PROPN hvd.32044092008168 906 2 b=(-a b=(-a NUM hvd.32044092008168 906 3 ) ) PUNCT hvd.32044092008168 906 4 ( ( PUNCT hvd.32044092008168 906 5 a a X hvd.32044092008168 906 6 } } PUNCT hvd.32044092008168 906 7 – – PUNCT hvd.32044092008168 906 8 2a 2a NUM hvd.32044092008168 906 9 ) ) PUNCT hvd.32044092008168 906 10 — — PUNCT hvd.32044092008168 906 11 3 3 NUM hvd.32044092008168 906 12 ( ( PUNCT hvd.32044092008168 906 13 3a 3a NUM hvd.32044092008168 906 14 , , PUNCT hvd.32044092008168 906 15 0 0 NUM hvd.32044092008168 906 16 , , PUNCT hvd.32044092008168 906 17 – – PUNCT hvd.32044092008168 906 18 3az 3az ADJ hvd.32044092008168 906 19 a a PRON hvd.32044092008168 906 20 ;) ;) NUM hvd.32044092008168 906 21 — — PUNCT hvd.32044092008168 906 22 ) ) PUNCT hvd.32044092008168 906 23 2a 2a NUM hvd.32044092008168 906 24 ; ; PUNCT hvd.32044092008168 906 25 – – PUNCT hvd.32044092008168 906 26 7a+ 7a+ NUM hvd.32044092008168 906 27 9az 9az ADJ hvd.32044092008168 906 28 3?g 3?g NOUN hvd.32044092008168 906 29 2 2 NUM hvd.32044092008168 906 30 b4 b4 PROPN hvd.32044092008168 906 31 32.53 32.53 NUM hvd.32044092008168 906 32 92b2 92b2 NUM hvd.32044092008168 906 33 + + NUM hvd.32044092008168 906 34 1 1 NUM hvd.32044092008168 906 35 + + NUM hvd.32044092008168 906 36 393 393 NUM hvd.32044092008168 906 37 b b NOUN hvd.32044092008168 906 38 3.4.52 3.4.52 NUM hvd.32044092008168 906 39 4 4 NUM hvd.32044092008168 906 40 · · SYM hvd.32044092008168 906 41 5 5 NUM hvd.32044092008168 906 42 4 4 NUM hvd.32044092008168 906 43 3 3 NUM hvd.32044092008168 906 44 9 9 NUM hvd.32044092008168 906 45 1 1 NUM hvd.32044092008168 906 46 4 4 NUM hvd.32044092008168 906 47 4 4 NUM hvd.32044092008168 906 48 4 4 NUM hvd.32044092008168 906 49 7b3 7b3 NUM hvd.32044092008168 906 50 3 3 NUM hvd.32044092008168 906 51 . . PUNCT hvd.32044092008168 906 52 53 53 NUM hvd.32044092008168 906 53 + + NUM hvd.32044092008168 906 54 9 9 NUM hvd.32044092008168 906 55 , , PUNCT hvd.32044092008168 906 56 b b PROPN hvd.32044092008168 906 57 4 4 NUM hvd.32044092008168 906 58 4 4 NUM hvd.32044092008168 906 59 9 9 NUM hvd.32044092008168 906 60 15 15 NUM hvd.32044092008168 906 61 4 4 NUM hvd.32044092008168 906 62 926 926 NUM hvd.32044092008168 906 63 9 9 NUM hvd.32044092008168 906 64 15 15 NUM hvd.32044092008168 906 65 4 4 NUM hvd.32044092008168 906 66 4 4 NUM hvd.32044092008168 906 67 3 3 NUM hvd.32044092008168 906 68 9 9 NUM hvd.32044092008168 906 69 1 1 NUM hvd.32044092008168 906 70 2 2 NUM hvd.32044092008168 906 71 bg bg NOUN hvd.32044092008168 906 72 32763 32763 NUM hvd.32044092008168 906 73 + + NUM hvd.32044092008168 906 74 * * PUNCT hvd.32044092008168 906 75 995 995 NUM hvd.32044092008168 906 76 93 93 NUM hvd.32044092008168 906 77 -943 -943 PROPN hvd.32044092008168 906 78 + + NUM hvd.32044092008168 906 79 12b 12b SYM hvd.32044092008168 906 80 a,=;9 a,=;9 PROPN hvd.32044092008168 906 81 — — PUNCT hvd.32044092008168 906 82 6bq 6bq PROPN hvd.32044092008168 906 83 ' ' PUNCT hvd.32044092008168 906 84 . . PUNCT hvd.32044092008168 907 1 az az PROPN hvd.32044092008168 907 2 we we PRON hvd.32044092008168 907 3 derive derive VERB hvd.32044092008168 907 4 then then ADV hvd.32044092008168 907 5 finally finally ADV hvd.32044092008168 907 6 φ φ X hvd.32044092008168 907 7 q q X hvd.32044092008168 907 8 = = NOUN hvd.32044092008168 907 9 bť+ bť+ PROPN hvd.32044092008168 907 10 b b PROPN hvd.32044092008168 907 11 , , PUNCT hvd.32044092008168 907 12 t t PROPN hvd.32044092008168 907 13 + + CCONJ hvd.32044092008168 907 14 b b PROPN hvd.32044092008168 907 15 , , PUNCT hvd.32044092008168 907 16 6 6 NUM hvd.32044092008168 907 17 ( ( PUNCT hvd.32044092008168 907 18 36 36 NUM hvd.32044092008168 907 19 ? ? PUNCT hvd.32044092008168 907 20 – – PUNCT hvd.32044092008168 907 21 à à ADP hvd.32044092008168 907 22 92 92 NUM hvd.32044092008168 907 23 ) ) PUNCT hvd.32044092008168 907 24 ( ( PUNCT hvd.32044092008168 907 25 s. s. X hvd.32044092008168 907 26 +268 +268 NOUN hvd.32044092008168 907 27 + + CCONJ hvd.32044092008168 907 28 b2 b2 PROPN hvd.32044092008168 907 29 ) ) PUNCT hvd.32044092008168 907 30 + + NUM hvd.32044092008168 907 31 ( ( PUNCT hvd.32044092008168 907 32 6363 6363 NUM hvd.32044092008168 907 33 + + NUM hvd.32044092008168 907 34 * * PUNCT hvd.32044092008168 907 35 996 996 NUM hvd.32044092008168 907 36 – – PUNCT hvd.32044092008168 907 37 193 193 NUM hvd.32044092008168 907 38 ) ) PUNCT hvd.32044092008168 907 39 ( ( PUNCT hvd.32044092008168 907 40 s s VERB hvd.32044092008168 907 41 + + ADJ hvd.32044092008168 907 42 b b NOUN hvd.32044092008168 907 43 ) ) PUNCT hvd.32044092008168 907 44 + + NUM hvd.32044092008168 907 45 32.5264 32.5264 NUM hvd.32044092008168 907 46 + + NUM hvd.32044092008168 907 47 * * SYM hvd.32044092008168 907 48 99b2 99b2 NUM hvd.32044092008168 907 49 + + NUM hvd.32044092008168 907 50 i i NOUN hvd.32044092008168 907 51 b93 b93 PROPN hvd.32044092008168 907 52 - - PUNCT hvd.32044092008168 907 53 3 3 NUM hvd.32044092008168 907 54 gå gå PROPN hvd.32044092008168 907 55 . . PUNCT hvd.32044092008168 908 1 ꮽ+ ꮽ+ DET hvd.32044092008168 908 2 coef coef PROPN hvd.32044092008168 908 3 . . PUNCT hvd.32044092008168 909 1 s s X hvd.32044092008168 909 2 is be AUX hvd.32044092008168 909 3 – – PUNCT hvd.32044092008168 909 4 6 6 NUM hvd.32044092008168 909 5 ( ( PUNCT hvd.32044092008168 909 6 362 362 NUM hvd.32044092008168 909 7 – – PUNCT hvd.32044092008168 909 8 1 1 NUM hvd.32044092008168 909 9 92 92 NUM hvd.32044092008168 909 10 ) ) PUNCT hvd.32044092008168 909 11 9(1169 9(1169 NUM hvd.32044092008168 910 1 + + NUM hvd.32044092008168 910 2 $ $ SYM hvd.32044092008168 910 3 936 936 NUM hvd.32044092008168 910 4 93 93 NUM hvd.32044092008168 910 5 ) ) PUNCT hvd.32044092008168 910 6 – – PUNCT hvd.32044092008168 911 1 943 943 NUM hvd.32044092008168 911 2 so so ADV hvd.32044092008168 911 3 – – PUNCT hvd.32044092008168 911 4 4 4 NUM hvd.32044092008168 911 5 ( ( PUNCT hvd.32044092008168 911 6 362 362 NUM hvd.32044092008168 911 7 – – SYM hvd.32044092008168 911 8 192 192 NUM hvd.32044092008168 911 9 ) ) PUNCT hvd.32044092008168 911 10 = = NOUN hvd.32044092008168 911 11 – – PUNCT hvd.32044092008168 911 12 4 4 NUM hvd.32044092008168 911 13 a a DET hvd.32044092008168 911 14 hence hence ADV hvd.32044092008168 911 15 [ [ X hvd.32044092008168 911 16 118 118 NUM hvd.32044092008168 911 17 ] ] PUNCT hvd.32044092008168 911 18 φ φ NOUN hvd.32044092008168 911 19 362 362 NUM hvd.32044092008168 911 20 6(31 6(31 NUM hvd.32044092008168 911 21 – – PUNCT hvd.32044092008168 911 22 1 1 NUM hvd.32044092008168 911 23 92 92 NUM hvd.32044092008168 911 24 ) ) PUNCT hvd.32044092008168 911 25 s s PROPN hvd.32044092008168 911 26 ? ? PUNCT hvd.32044092008168 911 27 +9(--116 +9(--116 VERB hvd.32044092008168 912 1 + + PUNCT hvd.32044092008168 912 2 * * NUM hvd.32044092008168 912 3 936–193 936–193 NUM hvd.32044092008168 912 4 ) ) PUNCT hvd.32044092008168 912 5 s-4(362–192 s-4(362–192 PROPN hvd.32044092008168 912 6 ) ) PUNCT hvd.32044092008168 912 7 å å PROPN hvd.32044092008168 912 8 92b 92b PROPN hvd.32044092008168 912 9 — — PUNCT hvd.32044092008168 912 10 6a 6a NUM hvd.32044092008168 912 11 , , PUNCT hvd.32044092008168 912 12 s?+ s?+ X hvd.32044092008168 912 13 9 9 NUM hvd.32044092008168 912 14 a a DET hvd.32044092008168 912 15 , , PUNCT hvd.32044092008168 912 16 s s NOUN hvd.32044092008168 912 17 - - PUNCT hvd.32044092008168 912 18 — — PUNCT hvd.32044092008168 912 19 4 4 NUM hvd.32044092008168 912 20 a a DET hvd.32044092008168 912 21 9a3s 9a3s NOUN hvd.32044092008168 912 22 44 44 NUM hvd.32044092008168 912 23 having having AUX hvd.32044092008168 912 24 obtained obtain VERB hvd.32044092008168 912 25 ø ø NOUN hvd.32044092008168 912 26 , , PUNCT hvd.32044092008168 912 27 the the DET hvd.32044092008168 912 28 calculation calculation NOUN hvd.32044092008168 912 29 of of ADP hvd.32044092008168 912 30 y y PROPN hvd.32044092008168 912 31 and and CCONJ hvd.32044092008168 912 32 e e PROPN hvd.32044092008168 912 33 is be AUX hvd.32044092008168 912 34 simplified simplify VERB hvd.32044092008168 912 35 by by ADP hvd.32044092008168 912 36 the the DET hvd.32044092008168 912 37 following follow VERB hvd.32044092008168 912 38 considerations consideration NOUN hvd.32044092008168 912 39 : : PUNCT hvd.32044092008168 912 40 642 642 NUM hvd.32044092008168 912 41 4 4 NUM hvd.32044092008168 912 42 3 3 NUM hvd.32044092008168 912 43 s s PART hvd.32044092008168 912 44 is be AUX hvd.32044092008168 912 45 4 4 NUM hvd.32044092008168 912 46 1 1 NUM hvd.32044092008168 912 47 2 2 NUM hvd.32044092008168 912 48 442 442 NUM hvd.32044092008168 912 49 3 3 NUM hvd.32044092008168 912 50 2 2 NUM hvd.32044092008168 912 51 4 4 NUM hvd.32044092008168 912 52 4 4 NUM hvd.32044092008168 912 53 64 64 NUM hvd.32044092008168 912 54 part part NOUN hvd.32044092008168 912 55 v. v. ADP hvd.32044092008168 912 56 [ [ X hvd.32044092008168 912 57 119 119 NUM hvd.32044092008168 912 58 ] ] PUNCT hvd.32044092008168 912 59 ― ― X hvd.32044092008168 912 60 1 1 X hvd.32044092008168 912 61 let let VERB hvd.32044092008168 912 62 n n ADV hvd.32044092008168 912 63 be be AUX hvd.32044092008168 912 64 taken take VERB hvd.32044092008168 912 65 odd odd ADJ hvd.32044092008168 912 66 and and CCONJ hvd.32044092008168 912 67 take take VERB hvd.32044092008168 912 68 for for ADP hvd.32044092008168 912 69 b b PROPN hvd.32044092008168 912 70 a a DET hvd.32044092008168 912 71 root root NOUN hvd.32044092008168 912 72 of of ADP hvd.32044092008168 912 73 the the DET hvd.32044092008168 912 74 equation equation NOUN hvd.32044092008168 912 75 q₁ q₁ PROPN hvd.32044092008168 912 76 = = PROPN hvd.32044092008168 912 77 0 0 NUM hvd.32044092008168 912 78 . . PUNCT hvd.32044092008168 913 1 in in ADP hvd.32044092008168 913 2 this this DET hvd.32044092008168 913 3 case case NOUN hvd.32044092008168 913 4 ( ( PUNCT hvd.32044092008168 913 5 see see VERB hvd.32044092008168 913 6 p. p. NOUN hvd.32044092008168 913 7 54 54 NUM hvd.32044092008168 913 8 ) ) PUNCT hvd.32044092008168 914 1 we we PRON hvd.32044092008168 914 2 have have VERB hvd.32044092008168 914 3 y y PROPN hvd.32044092008168 914 4 as as ADP hvd.32044092008168 914 5 a a DET hvd.32044092008168 914 6 product product NOUN hvd.32044092008168 914 7 of of ADP hvd.32044092008168 914 8 t t NOUN hvd.32044092008168 914 9 by by ADP hvd.32044092008168 914 10 a a DET hvd.32044092008168 914 11 polynomial polynomial ADJ hvd.32044092008168 914 12 u² u² PROPN hvd.32044092008168 914 13 where where SCONJ hvd.32044092008168 914 14 u u PROPN hvd.32044092008168 914 15 has have VERB hvd.32044092008168 914 16 the the DET hvd.32044092008168 914 17 degree degree NOUN hvd.32044092008168 914 18 ( ( PUNCT hvd.32044092008168 914 19 n n CCONJ hvd.32044092008168 914 20 1 1 NUM hvd.32044092008168 914 21 ) ) PUNCT hvd.32044092008168 914 22 . . PUNCT hvd.32044092008168 915 1 moreover moreover ADV hvd.32044092008168 915 2 u u PROPN hvd.32044092008168 915 3 enters enter VERB hvd.32044092008168 915 4 as as ADP hvd.32044092008168 915 5 a a DET hvd.32044092008168 915 6 double double ADJ hvd.32044092008168 915 7 factor factor NOUN hvd.32044092008168 915 8 and and CCONJ hvd.32044092008168 915 9 is be AUX hvd.32044092008168 915 10 therefore therefore ADV hvd.32044092008168 915 11 also also ADV hvd.32044092008168 915 12 a a DET hvd.32044092008168 915 13 factor factor NOUN hvd.32044092008168 915 14 of of ADP hvd.32044092008168 915 15 y y PROPN hvd.32044092008168 915 16 ' ' PUNCT hvd.32044092008168 915 17 , , PUNCT hvd.32044092008168 915 18 whence whence ADV hvd.32044092008168 915 19 , , PUNCT hvd.32044092008168 915 20 from from ADP hvd.32044092008168 915 21 the the DET hvd.32044092008168 915 22 form form NOUN hvd.32044092008168 915 23 2 2 NUM hvd.32044092008168 915 24 = = NOUN hvd.32044092008168 915 25 φ φ X hvd.32044092008168 915 26 ψ ψ X hvd.32044092008168 916 1 ey ey INTJ hvd.32044092008168 916 2 = = NOUN hvd.32044092008168 916 3 1 1 NUM hvd.32044092008168 916 4 we we PRON hvd.32044092008168 916 5 find find VERB hvd.32044092008168 916 6 that that SCONJ hvd.32044092008168 916 7 u u PROPN hvd.32044092008168 916 8 must must AUX hvd.32044092008168 916 9 also also ADV hvd.32044092008168 916 10 be be AUX hvd.32044092008168 916 11 a a DET hvd.32044092008168 916 12 factor factor NOUN hvd.32044092008168 916 13 of of ADP hvd.32044092008168 916 14 t. t. PROPN hvd.32044092008168 916 15 this this PRON hvd.32044092008168 916 16 , , PUNCT hvd.32044092008168 916 17 however however ADV hvd.32044092008168 916 18 , , PUNCT hvd.32044092008168 916 19 we we PRON hvd.32044092008168 916 20 know know VERB hvd.32044092008168 916 21 to to PART hvd.32044092008168 916 22 be be AUX hvd.32044092008168 916 23 impossible impossible ADJ hvd.32044092008168 916 24 since since SCONJ hvd.32044092008168 916 25 the the DET hvd.32044092008168 916 26 degree degree NOUN hvd.32044092008168 916 27 of of ADP hvd.32044092008168 916 28 u u PROPN hvd.32044092008168 916 29 is be AUX hvd.32044092008168 916 30 ( ( PUNCT hvd.32044092008168 916 31 n n CCONJ hvd.32044092008168 916 32 − − PROPN hvd.32044092008168 916 33 1 1 NUM hvd.32044092008168 916 34 ) ) PUNCT hvd.32044092008168 916 35 and and CCONJ hvd.32044092008168 916 36 that that PRON hvd.32044092008168 916 37 of of ADP hvd.32044092008168 916 38 only only ADV hvd.32044092008168 916 39 ( ( PUNCT hvd.32044092008168 916 40 n n CCONJ hvd.32044092008168 916 41 − − PROPN hvd.32044092008168 916 42 3 3 X hvd.32044092008168 916 43 ) ) PUNCT hvd.32044092008168 916 44 ( ( PUNCT hvd.32044092008168 916 45 p. p. NOUN hvd.32044092008168 916 46 60 60 NUM hvd.32044092008168 916 47 ) ) PUNCT hvd.32044092008168 916 48 . . PUNCT hvd.32044092008168 917 1 1 1 NUM hvd.32044092008168 917 2 2 2 NUM hvd.32044092008168 917 3 dy dy X hvd.32044092008168 917 4 dt dt PROPN hvd.32044092008168 917 5 v v PROPN hvd.32044092008168 917 6 of of ADP hvd.32044092008168 917 7 degree degree NOUN hvd.32044092008168 917 8 n n ADP hvd.32044092008168 917 9 where where SCONJ hvd.32044092008168 917 10 2 2 NUM hvd.32044092008168 917 11 consequence consequence NOUN hvd.32044092008168 917 12 one one NOUN hvd.32044092008168 917 13 has have VERB hvd.32044092008168 917 14 the the DET hvd.32044092008168 917 15 only only ADJ hvd.32044092008168 917 16 conclusion conclusion NOUN hvd.32044092008168 917 17 possible possible ADJ hvd.32044092008168 917 18 then then ADV hvd.32044092008168 917 19 is be AUX hvd.32044092008168 917 20 that that PRON hvd.32044092008168 917 21 contains contain VERB hvd.32044092008168 917 22 a a DET hvd.32044092008168 917 23 zero zero NUM hvd.32044092008168 917 24 factor factor NOUN hvd.32044092008168 917 25 . . PUNCT hvd.32044092008168 918 1 we we PRON hvd.32044092008168 918 2 know know VERB hvd.32044092008168 918 3 also also ADV hvd.32044092008168 918 4 that that SCONJ hvd.32044092008168 918 5 b b NOUN hvd.32044092008168 918 6 being be AUX hvd.32044092008168 918 7 any any DET hvd.32044092008168 918 8 value value NOUN hvd.32044092008168 918 9 whatever whatever PRON hvd.32044092008168 918 10 , , PUNCT hvd.32044092008168 918 11 ¥ ¥ PRON hvd.32044092008168 918 12 considered consider VERB hvd.32044092008168 918 13 as as ADP hvd.32044092008168 918 14 a a DET hvd.32044092008168 918 15 function function NOUN hvd.32044092008168 918 16 of of ADP hvd.32044092008168 918 17 b b PROPN hvd.32044092008168 918 18 contains contain VERB hvd.32044092008168 918 19 the the DET hvd.32044092008168 918 20 factors factor NOUN hvd.32044092008168 918 21 q1 q1 NOUN hvd.32044092008168 918 22 , , PUNCT hvd.32044092008168 918 23 q2 q2 PROPN hvd.32044092008168 918 24 and and CCONJ hvd.32044092008168 918 25 q q NOUN hvd.32044092008168 918 26 , , PUNCT hvd.32044092008168 918 27 and and CCONJ hvd.32044092008168 918 28 it it PRON hvd.32044092008168 918 29 follows follow VERB hvd.32044092008168 918 30 that that SCONJ hvd.32044092008168 918 31 we we PRON hvd.32044092008168 918 32 may may AUX hvd.32044092008168 918 33 write write VERB hvd.32044092008168 918 34 hence hence ADV hvd.32044092008168 918 35 we we PRON hvd.32044092008168 918 36 write write VERB hvd.32044092008168 918 37 : : PUNCT hvd.32044092008168 918 38 n n ADP hvd.32044092008168 918 39 odd odd ADJ hvd.32044092008168 918 40 : : PUNCT hvd.32044092008168 918 41 t t PROPN hvd.32044092008168 918 42 where where SCONJ hvd.32044092008168 918 43 q0 q0 PROPN hvd.32044092008168 918 44 , , PUNCT hvd.32044092008168 918 45 if if SCONJ hvd.32044092008168 918 46 b b NOUN hvd.32044092008168 918 47 be be AUX hvd.32044092008168 918 48 taken take VERB hvd.32044092008168 918 49 as as ADP hvd.32044092008168 918 50 a a DET hvd.32044092008168 918 51 root root NOUN hvd.32044092008168 918 52 of of ADP hvd.32044092008168 918 53 q₁ q₁ PROPN hvd.32044092008168 918 54 = = PROPN hvd.32044092008168 918 55 0 0 NUM hvd.32044092008168 918 56 , , PUNCT hvd.32044092008168 918 57 q₂ q₂ PROPN hvd.32044092008168 918 58 = = PROPN hvd.32044092008168 918 59 0 0 NUM hvd.32044092008168 918 60 , , PUNCT hvd.32044092008168 918 61 or or CCONJ hvd.32044092008168 918 62 0 0 NUM hvd.32044092008168 918 63 , , PUNCT hvd.32044092008168 918 64 and and CCONJ hvd.32044092008168 918 65 fo fo NOUN hvd.32044092008168 918 66 ( ( PUNCT hvd.32044092008168 918 67 t t PROPN hvd.32044092008168 918 68 ) ) PUNCT hvd.32044092008168 918 69 . . PUNCT hvd.32044092008168 919 1 = = PUNCT hvd.32044092008168 919 2 n n X hvd.32044092008168 919 3 odd odd ADJ hvd.32044092008168 919 4 qo qo PROPN hvd.32044092008168 919 5 by by ADP hvd.32044092008168 919 6 a a DET hvd.32044092008168 919 7 similar similar ADJ hvd.32044092008168 919 8 course course NOUN hvd.32044092008168 919 9 of of ADP hvd.32044092008168 919 10 reasoning reasoning NOUN hvd.32044092008168 919 11 we we PRON hvd.32044092008168 919 12 show show VERB hvd.32044092008168 919 13 that that SCONJ hvd.32044092008168 919 14 if if SCONJ hvd.32044092008168 919 15 b b NOUN hvd.32044092008168 919 16 be be AUX hvd.32044092008168 919 17 taken take VERB hvd.32044092008168 919 18 as as ADP hvd.32044092008168 919 19 a a DET hvd.32044092008168 919 20 root root NOUN hvd.32044092008168 919 21 of of ADP hvd.32044092008168 919 22 p p NOUN hvd.32044092008168 919 23 , , PUNCT hvd.32044092008168 919 24 n n CCONJ hvd.32044092008168 919 25 being be AUX hvd.32044092008168 919 26 even even ADV hvd.32044092008168 919 27 , , PUNCT hvd.32044092008168 919 28 y y PROPN hvd.32044092008168 919 29 will will AUX hvd.32044092008168 919 30 be be AUX hvd.32044092008168 919 31 the the DET hvd.32044092008168 919 32 square square NOUN hvd.32044092008168 919 33 of of ADP hvd.32044092008168 919 34 a a DET hvd.32044092008168 919 35 polynomial polynomial ADJ hvd.32044092008168 919 36 1 1 NUM hvd.32044092008168 919 37 , , PUNCT hvd.32044092008168 919 38 and and CCONJ hvd.32044092008168 919 39 that that SCONJ hvd.32044092008168 919 40 in in ADP hvd.32044092008168 919 41 n n CCONJ hvd.32044092008168 919 42 even even ADV hvd.32044092008168 919 43 : : PUNCT hvd.32044092008168 919 44 1 1 NUM hvd.32044092008168 919 45 is be AUX hvd.32044092008168 919 46 only only ADV hvd.32044092008168 919 47 of of ADP hvd.32044092008168 919 48 degree degree NOUN hvd.32044092008168 919 49 n n CCONJ hvd.32044092008168 919 50 yn yn PROPN hvd.32044092008168 919 51 even even ADV hvd.32044092008168 919 52 φ φ PROPN hvd.32044092008168 919 53 dy dy PROPN hvd.32044092008168 919 54 dt dt PROPN hvd.32044092008168 919 55 dy dy PROPN hvd.32044092008168 919 56 dt dt PROPN hvd.32044092008168 919 57 = = PROPN hvd.32044092008168 919 58 ρθ ρθ ADP hvd.32044092008168 919 59 q0= q0= PROPN hvd.32044092008168 919 60 po po PROPN hvd.32044092008168 919 61 = = X hvd.32044092008168 920 1 ܡܘ ܡܘ INTJ hvd.32044092008168 921 1 e1 e1 X hvd.32044092008168 922 1 ey ey INTJ hvd.32044092008168 922 2 ey ey INTJ hvd.32044092008168 922 3 ... ... PUNCT hvd.32044092008168 922 4 where where SCONJ hvd.32044092008168 922 5 all all DET hvd.32044092008168 922 6 the the DET hvd.32044092008168 922 7 functions function NOUN hvd.32044092008168 922 8 are be AUX hvd.32044092008168 922 9 intire intire ADJ hvd.32044092008168 922 10 in in ADP hvd.32044092008168 922 11 t. t. PROPN hvd.32044092008168 922 12 as as SCONJ hvd.32044092008168 922 13 we we PRON hvd.32044092008168 922 14 have have AUX hvd.32044092008168 922 15 before before ADP hvd.32044092008168 922 16 determined determine VERB hvd.32044092008168 922 17 the the DET hvd.32044092008168 922 18 first first ADJ hvd.32044092008168 922 19 coefficient coefficient NOUN hvd.32044092008168 922 20 of of ADP hvd.32044092008168 922 21 is be AUX hvd.32044092008168 922 22 the the DET hvd.32044092008168 922 23 determinant determinant ADJ hvd.32044092008168 922 24 d d NOUN hvd.32044092008168 922 25 , , PUNCT hvd.32044092008168 922 26 . . PUNCT hvd.32044092008168 923 1 and and CCONJ hvd.32044092008168 923 2 in in ADP hvd.32044092008168 923 3 like like ADJ hvd.32044092008168 923 4 manner manner NOUN hvd.32044092008168 923 5 we we PRON hvd.32044092008168 923 6 find find VERB hvd.32044092008168 923 7 the the DET hvd.32044092008168 923 8 first first ADJ hvd.32044092008168 923 9 coefficient coefficient NOUN hvd.32044092008168 923 10 of of ADP hvd.32044092008168 923 11 t t PROPN hvd.32044092008168 923 12 to to PART hvd.32044092008168 923 13 be be AUX hvd.32044092008168 923 14 v-1 v-1 NOUN hvd.32044092008168 924 1 [ [ PUNCT hvd.32044092008168 924 2 120 120 NUM hvd.32044092008168 924 3 ] ] PUNCT hvd.32044092008168 924 4 8,b 8,b NOUN hvd.32044092008168 924 5 , , PUNCT hvd.32044092008168 924 6 b,+by+1by-1 b,+by+1by-1 VERB hvd.32044092008168 924 7 + + NOUN hvd.32044092008168 924 8 hence hence ADV hvd.32044092008168 924 9 if if SCONJ hvd.32044092008168 924 10 we we PRON hvd.32044092008168 924 11 divide divide VERB hvd.32044092008168 924 12 d d NOUN hvd.32044092008168 924 13 , , PUNCT hvd.32044092008168 924 14 by by ADP hvd.32044092008168 924 15 q q PROPN hvd.32044092008168 924 16 , , PUNCT hvd.32044092008168 924 17 n n CCONJ hvd.32044092008168 924 18 being be AUX hvd.32044092008168 924 19 odd odd ADJ hvd.32044092008168 924 20 we we PRON hvd.32044092008168 924 21 will will AUX hvd.32044092008168 924 22 have have VERB hvd.32044092008168 924 23 y y PROPN hvd.32044092008168 924 24 , , PUNCT hvd.32044092008168 924 25 the the DET hvd.32044092008168 924 26 first first ADJ hvd.32044092008168 924 27 coefficient coefficient NOUN hvd.32044092008168 924 28 of of ADP hvd.32044092008168 924 29 . . PUNCT hvd.32044092008168 925 1 + + PROPN hvd.32044092008168 925 2 bạ bạ PROPN hvd.32044092008168 925 3 , , PUNCT hvd.32044092008168 925 4 ba ba PROPN hvd.32044092008168 925 5 ν ν PROPN hvd.32044092008168 925 6 reduction reduction NOUN hvd.32044092008168 925 7 of of ADP hvd.32044092008168 925 8 the the DET hvd.32044092008168 925 9 forms form NOUN hvd.32044092008168 925 10 when when SCONJ hvd.32044092008168 925 11 n n SYM hvd.32044092008168 925 12 equals equal VERB hvd.32044092008168 925 13 three three NUM hvd.32044092008168 925 14 . . PUNCT hvd.32044092008168 926 1 65 65 NUM hvd.32044092008168 926 2 2 2 NUM hvd.32044092008168 926 3 1 1 NUM hvd.32044092008168 926 4 2 2 NUM hvd.32044092008168 926 5 1 1 NUM hvd.32044092008168 926 6 2 2 NUM hvd.32044092008168 926 7 to to PART hvd.32044092008168 926 8 find find VERB hvd.32044092008168 926 9 e e NOUN hvd.32044092008168 926 10 , , PUNCT hvd.32044092008168 926 11 n n CCONJ hvd.32044092008168 926 12 = = SYM hvd.32044092008168 926 13 3 3 X hvd.32044092008168 926 14 . . PUNCT hvd.32044092008168 927 1 the the DET hvd.32044092008168 927 2 degree degree NOUN hvd.32044092008168 927 3 of of ADP hvd.32044092008168 927 4 0 0 NUM hvd.32044092008168 927 5 is be AUX hvd.32044092008168 927 6 ( ( PUNCT hvd.32044092008168 927 7 n n X hvd.32044092008168 927 8 + + CCONJ hvd.32044092008168 927 9 1 1 NUM hvd.32044092008168 927 10 ) ) PUNCT hvd.32044092008168 927 11 , , PUNCT hvd.32044092008168 927 12 the the DET hvd.32044092008168 927 13 degree degree NOUN hvd.32044092008168 927 14 of of ADP hvd.32044092008168 927 15 y y PROPN hvd.32044092008168 927 16 is be AUX hvd.32044092008168 927 17 n n ADJ hvd.32044092008168 927 18 — — PUNCT hvd.32044092008168 927 19 1 1 NUM hvd.32044092008168 927 20 and and CCONJ hvd.32044092008168 927 21 1 1 NUM hvd.32044092008168 927 22 the the DET hvd.32044092008168 927 23 degree degree NOUN hvd.32044092008168 927 24 of of ADP hvd.32044092008168 927 25 t t PROPN hvd.32044092008168 927 26 is be AUX hvd.32044092008168 927 27 ; ; PUNCT hvd.32044092008168 927 28 ( ( PUNCT hvd.32044092008168 927 29 n n CCONJ hvd.32044092008168 927 30 − − PROPN hvd.32044092008168 927 31 3 3 X hvd.32044092008168 927 32 ) ) PUNCT hvd.32044092008168 927 33 less less ADJ hvd.32044092008168 927 34 than than ADP hvd.32044092008168 927 35 y y PROPN hvd.32044092008168 927 36 ' ' PUNCT hvd.32044092008168 927 37 . . PUNCT hvd.32044092008168 928 1 hence hence ADV hvd.32044092008168 928 2 from from ADP hvd.32044092008168 928 3 the the DET hvd.32044092008168 928 4 relays relay NOUN hvd.32044092008168 928 5 tion tion NOUN hvd.32044092008168 928 6 on on ADP hvd.32044092008168 928 7 p(64 p(64 NOUN hvd.32044092008168 928 8 ) ) PUNCT hvd.32044092008168 928 9 , , PUNCT hvd.32044092008168 928 10 the the DET hvd.32044092008168 928 11 degree degree NOUN hvd.32044092008168 928 12 of of ADP hvd.32044092008168 928 13 ey ey PRON hvd.32044092008168 928 14 must must AUX hvd.32044092008168 928 15 be be AUX hvd.32044092008168 928 16 1 1 NUM hvd.32044092008168 928 17 ( ( PUNCT hvd.32044092008168 928 18 n n CCONJ hvd.32044092008168 928 19 + + ADP hvd.32044092008168 928 20 1 1 NUM hvd.32044092008168 928 21 ) ) PUNCT hvd.32044092008168 928 22 + + NUM hvd.32044092008168 928 23 ( ( PUNCT hvd.32044092008168 928 24 n n CCONJ hvd.32044092008168 928 25 − − PROPN hvd.32044092008168 928 26 1 1 X hvd.32044092008168 928 27 ) ) PUNCT hvd.32044092008168 928 28 = = PROPN hvd.32044092008168 928 29 { { PUNCT hvd.32044092008168 928 30 ( ( PUNCT hvd.32044092008168 928 31 3n 3n NUM hvd.32044092008168 928 32 – – PUNCT hvd.32044092008168 928 33 1 1 X hvd.32044092008168 928 34 ) ) PUNCT hvd.32044092008168 928 35 . . PUNCT hvd.32044092008168 929 1 1 1 NUM hvd.32044092008168 929 2 but but CCONJ hvd.32044092008168 929 3 the the DET hvd.32044092008168 929 4 degree degree NOUN hvd.32044092008168 929 5 of of ADP hvd.32044092008168 929 6 y y PROPN hvd.32044092008168 929 7 is be AUX hvd.32044092008168 929 8 ' ' NOUN hvd.32044092008168 929 9 n n NOUN hvd.32044092008168 929 10 and and CCONJ hvd.32044092008168 929 11 hence hence ADV hvd.32044092008168 929 12 the the DET hvd.32044092008168 929 13 degree degree NOUN hvd.32044092008168 929 14 of of ADP hvd.32044092008168 929 15 e e NOUN hvd.32044092008168 929 16 is be AUX hvd.32044092008168 929 17 į į X hvd.32044092008168 929 18 ( ( PUNCT hvd.32044092008168 929 19 n n CCONJ hvd.32044092008168 929 20 − − PROPN hvd.32044092008168 929 21 1 1 NUM hvd.32044092008168 929 22 ) ) PUNCT hvd.32044092008168 929 23 . . PUNCT hvd.32044092008168 930 1 we we PRON hvd.32044092008168 930 2 have have AUX hvd.32044092008168 930 3 then then ADV hvd.32044092008168 930 4 [ [ X hvd.32044092008168 930 5 121 121 NUM hvd.32044092008168 930 6 ] ] PUNCT hvd.32044092008168 930 7 en=3 en=3 PUNCT hvd.32044092008168 930 8 = = NOUN hvd.32044092008168 930 9 = = PUNCT hvd.32044092008168 930 10 nt not PART hvd.32044092008168 930 11 + + CCONJ hvd.32044092008168 930 12 ni ni ADJ hvd.32044092008168 930 13 and and CCONJ hvd.32044092008168 930 14 reduces reduce VERB hvd.32044092008168 930 15 to to ADP hvd.32044092008168 930 16 a a DET hvd.32044092008168 930 17 constant constant ADJ hvd.32044092008168 930 18 , , PUNCT hvd.32044092008168 930 19 namely namely ADV hvd.32044092008168 930 20 : : PUNCT hvd.32044092008168 930 21 [ [ X hvd.32044092008168 930 22 122 122 NUM hvd.32044092008168 930 23 ] ] PUNCT hvd.32044092008168 930 24 we we PRON hvd.32044092008168 930 25 have have VERB hvd.32044092008168 930 26 : : PUNCT hvd.32044092008168 930 27 yz yz PROPN hvd.32044092008168 930 28 s s VERB hvd.32044092008168 930 29 + + CCONJ hvd.32044092008168 930 30 a a PRON hvd.32044092008168 930 31 , , PUNCT hvd.32044092008168 930 32 s s X hvd.32044092008168 930 33 + + PROPN hvd.32044092008168 930 34 ag ag PROPN hvd.32044092008168 930 35 y y PROPN hvd.32044092008168 930 36 ; ; PUNCT hvd.32044092008168 930 37 3 3 NUM hvd.32044092008168 930 38 s2 s2 PROPN hvd.32044092008168 930 39 + + CCONJ hvd.32044092008168 930 40 a2 a2 PROPN hvd.32044092008168 930 41 6 6 NUM hvd.32044092008168 930 42 a a PRON hvd.32044092008168 930 43 , , PUNCT hvd.32044092008168 930 44 s s NOUN hvd.32044092008168 930 45 ? ? PUNCT hvd.32044092008168 931 1 + + NUM hvd.32044092008168 931 2 9 9 NUM hvd.32044092008168 931 3 a a PRON hvd.32044092008168 931 4 , , PUNCT hvd.32044092008168 931 5 s s NOUN hvd.32044092008168 931 6 – – PUNCT hvd.32044092008168 931 7 a a PRON hvd.32044092008168 931 8 , , PUNCT hvd.32044092008168 931 9 and and CCONJ hvd.32044092008168 931 10 substituting substitute VERB hvd.32044092008168 931 11 we we PRON hvd.32044092008168 931 12 derive derive VERB hvd.32044092008168 931 13 ( ( PUNCT hvd.32044092008168 931 14 382 382 NUM hvd.32044092008168 931 15 + + NUM hvd.32044092008168 931 16 a,)(-64,s?+ a,)(-64,s?+ PROPN hvd.32044092008168 931 17 9 9 NUM hvd.32044092008168 931 18 az az NOUN hvd.32044092008168 931 19 s-4 s-4 NOUN hvd.32044092008168 931 20 a,*)=(n8 a,*)=(n8 SPACE hvd.32044092008168 932 1 + + CCONJ hvd.32044092008168 932 2 n)(s3 n)(s3 PROPN hvd.32044092008168 932 3 + + VERB hvd.32044092008168 932 4 a a PRON hvd.32044092008168 932 5 , , PUNCT hvd.32044092008168 932 6 s+ s+ ADV hvd.32044092008168 932 7 a2)+pq a2)+pq PROPN hvd.32044092008168 932 8 and and CCONJ hvd.32044092008168 932 9 from from ADP hvd.32044092008168 932 10 these these PRON hvd.32044092008168 932 11 we we PRON hvd.32044092008168 932 12 have have VERB hvd.32044092008168 932 13 7 7 NUM hvd.32044092008168 932 14 n3 n3 PROPN hvd.32044092008168 932 15 p p X hvd.32044092008168 932 16 q q X hvd.32044092008168 932 17 φ φ X hvd.32044092008168 932 18 3 3 NUM hvd.32044092008168 932 19 η η NOUN hvd.32044092008168 932 20 : : PUNCT hvd.32044092008168 932 21 18 18 NUM hvd.32044092008168 932 22 ag ag PROPN hvd.32044092008168 932 23 ; ; PUNCT hvd.32044092008168 932 24 mi mi PROPN hvd.32044092008168 933 1 27 27 NUM hvd.32044092008168 933 2 az az PROPN hvd.32044092008168 933 3 er er INTJ hvd.32044092008168 933 4 2 2 NUM hvd.32044092008168 933 5 1 1 NUM hvd.32044092008168 933 6 2 2 NUM hvd.32044092008168 933 7 c c NOUN hvd.32044092008168 933 8 1 1 NUM hvd.32044092008168 933 9 ф ф NOUN hvd.32044092008168 933 10 . . PUNCT hvd.32044092008168 934 1 a a DET hvd.32044092008168 934 2 c c PROPN hvd.32044092008168 934 3 20 20 NUM hvd.32044092008168 934 4 whence whence NOUN hvd.32044092008168 934 5 [ [ X hvd.32044092008168 934 6 123 123 NUM hvd.32044092008168 934 7 ] ] PUNCT hvd.32044092008168 934 8 9 9 NUM hvd.32044092008168 935 1 [ [ X hvd.32044092008168 935 2 2 2 NUM hvd.32044092008168 935 3 a a PRON hvd.32044092008168 935 4 , , PUNCT hvd.32044092008168 935 5 s s NOUN hvd.32044092008168 935 6 — — PUNCT hvd.32044092008168 935 7 3 3 NUM hvd.32044092008168 935 8 a3 a3 NUM hvd.32044092008168 935 9 ] ] PUNCT hvd.32044092008168 935 10 . . PUNCT hvd.32044092008168 936 1 returning return VERB hvd.32044092008168 936 2 to to ADP hvd.32044092008168 936 3 our our PRON hvd.32044092008168 936 4 original original ADJ hvd.32044092008168 936 5 form form NOUN hvd.32044092008168 936 6 we we PRON hvd.32044092008168 936 7 find find VERB hvd.32044092008168 936 8 that that SCONJ hvd.32044092008168 936 9 when when SCONJ hvd.32044092008168 936 10 n n SYM hvd.32044092008168 936 11 is be AUX hvd.32044092008168 936 12 three three NUM hvd.32044092008168 936 13 we we PRON hvd.32044092008168 936 14 may may AUX hvd.32044092008168 936 15 write write VERB hvd.32044092008168 936 16 : : PUNCT hvd.32044092008168 937 1 [ [ X hvd.32044092008168 937 2 124 124 NUM hvd.32044092008168 937 3 ] ] PUNCT hvd.32044092008168 937 4 ( ( PUNCT hvd.32044092008168 937 5 — — PUNCT hvd.32044092008168 937 6 1 1 X hvd.32044092008168 937 7 ) ) PUNCT hvd.32044092008168 937 8 " " PUNCT hvd.32044092008168 937 9 " " PUNCT hvd.32044092008168 937 10 , , PUNCT hvd.32044092008168 937 11 " " PUNCT hvd.32044092008168 937 12 ( ( PUNCT hvd.32044092008168 937 13 « « PUNCT hvd.32044092008168 937 14 — — PUNCT hvd.32044092008168 937 15 a a X hvd.32044092008168 937 16 ) ) PUNCT hvd.32044092008168 937 17 o o NOUN hvd.32044092008168 937 18 co co NOUN hvd.32044092008168 937 19 chocolate)o chocolate)o PROPN hvd.32044092008168 937 20 ( ( PUNCT hvd.32044092008168 937 21 16 16 NUM hvd.32044092008168 937 22 + + NUM hvd.32044092008168 937 23 » » PUNCT hvd.32044092008168 937 24 ) ) PUNCT hvd.32044092008168 937 25 = = X hvd.32044092008168 937 26 ( ( PUNCT hvd.32044092008168 937 27 pu pu PROPN hvd.32044092008168 937 28 ) ) PUNCT hvd.32044092008168 937 29 u u PROPN hvd.32044092008168 937 30 ( ( PUNCT hvd.32044092008168 937 31 u u PROPN hvd.32044092008168 937 32 — — PUNCT hvd.32044092008168 937 33 b b X hvd.32044092008168 937 34 ) ) PUNCT hvd.32044092008168 937 35 ( ( PUNCT hvd.32044092008168 937 36 u u PROPN hvd.32044092008168 937 37 — — PUNCT hvd.32044092008168 937 38 u u PROPN hvd.32044092008168 937 39 v v PROPN hvd.32044092008168 937 40 ) ) PUNCT hvd.32044092008168 937 41 φ φ PROPN hvd.32044092008168 937 42 ( ( PUNCT hvd.32044092008168 937 43 ) ) PUNCT hvd.32044092008168 937 44 ga ga PROPN hvd.32044092008168 937 45 ob ob PROPN hvd.32044092008168 937 46 ( ( PUNCT hvd.32044092008168 937 47 ) ) PUNCT hvd.32044092008168 937 48 p'u p'u ADV hvd.32044092008168 937 49 f f PROPN hvd.32044092008168 937 50 ( ( PUNCT hvd.32044092008168 937 51 pu pu PROPN hvd.32044092008168 937 52 ) ) PUNCT hvd.32044092008168 937 53 0 0 NUM hvd.32044092008168 937 54 - - SYM hvd.32044092008168 937 55 2 2 NUM hvd.32044092008168 937 56 s'yq=(-6a s'yq=(-6a SPACE hvd.32044092008168 937 57 , , PUNCT hvd.32044092008168 937 58 sp+9a sp+9a ADJ hvd.32044092008168 937 59 , , PUNCT hvd.32044092008168 937 60 s—44,9 s—44,9 SPACE hvd.32044092008168 937 61 + + NOUN hvd.32044092008168 937 62 , , PUNCT hvd.32044092008168 937 63 cs'(44,9 cs'(44,9 SPACE hvd.32044092008168 937 64 + + NUM hvd.32044092008168 937 65 274,2 274,2 NUM hvd.32044092008168 937 66 ) ) PUNCT hvd.32044092008168 937 67 . . PUNCT hvd.32044092008168 938 1 +9 +9 NUM hvd.32044092008168 938 2 ) ) PUNCT hvd.32044092008168 939 1 + + PUNCT hvd.32044092008168 939 2 . . PUNCT hvd.32044092008168 940 1 having have VERB hvd.32044092008168 940 2 this this DET hvd.32044092008168 940 3 development development NOUN hvd.32044092008168 940 4 , , PUNCT hvd.32044092008168 940 5 the the DET hvd.32044092008168 940 6 determination determination NOUN hvd.32044092008168 940 7 of of ADP hvd.32044092008168 940 8 x x SYM hvd.32044092008168 940 9 and and CCONJ hvd.32044092008168 940 10 v v NOUN hvd.32044092008168 940 11 is be AUX hvd.32044092008168 940 12 made make VERB hvd.32044092008168 940 13 possible possible ADJ hvd.32044092008168 940 14 as as SCONJ hvd.32044092008168 940 15 follows follow VERB hvd.32044092008168 940 16 : : PUNCT hvd.32044092008168 940 17 – – PUNCT hvd.32044092008168 940 18 taking take VERB hvd.32044092008168 940 19 the the DET hvd.32044092008168 940 20 derivative derivative NOUN hvd.32044092008168 940 21 of of ADP hvd.32044092008168 940 22 the the DET hvd.32044092008168 940 23 log log NOUN hvd.32044092008168 940 24 . . PUNCT hvd.32044092008168 941 1 of of ADP hvd.32044092008168 941 2 the the DET hvd.32044092008168 941 3 first first ADJ hvd.32044092008168 941 4 member member NOUN hvd.32044092008168 941 5 , , PUNCT hvd.32044092008168 941 6 a a PRON hvd.32044092008168 941 7 , , PUNCT hvd.32044092008168 941 8 and and CCONJ hvd.32044092008168 941 9 developing develop VERB hvd.32044092008168 941 10 according accord VERB hvd.32044092008168 941 11 to to ADP hvd.32044092008168 941 12 the the DET hvd.32044092008168 941 13 powers power NOUN hvd.32044092008168 941 14 of of ADP hvd.32044092008168 941 15 u u PROPN hvd.32044092008168 941 16 we we PRON hvd.32044092008168 941 17 write write VERB hvd.32044092008168 941 18 in in ADP hvd.32044092008168 941 19 general general ADJ hvd.32044092008168 941 20 a a DET hvd.32044092008168 941 21 = = NOUN hvd.32044092008168 941 22 [ [ X hvd.32044092008168 941 23 $ $ SYM hvd.32044092008168 941 24 ( ( PUNCT hvd.32044092008168 941 25 u u PROPN hvd.32044092008168 941 26 — — PUNCT hvd.32044092008168 941 27 a a X hvd.32044092008168 941 28 ) ) PUNCT hvd.32044092008168 941 29 + + CCONJ hvd.32044092008168 941 30 $ $ SYM hvd.32044092008168 941 31 ( ( PUNCT hvd.32044092008168 941 32 u u PROPN hvd.32044092008168 941 33 -b -b PUNCT hvd.32044092008168 941 34 ) ) PUNCT hvd.32044092008168 941 35 + + CCONJ hvd.32044092008168 941 36 $ $ SYM hvd.32044092008168 941 37 ( ( PUNCT hvd.32044092008168 941 38 u u PROPN hvd.32044092008168 941 39 — — PUNCT hvd.32044092008168 941 40 c) c) PUNCT hvd.32044092008168 941 41 ... ... PUNCT hvd.32044092008168 942 1 $(1 $(1 PROPN hvd.32044092008168 942 2 + + PROPN hvd.32044092008168 942 3 v)-(n v)-(n NOUN hvd.32044092008168 942 4 + + NUM hvd.32044092008168 942 5 1)&u 1)&u NUM hvd.32044092008168 942 6 . . PUNCT hvd.32044092008168 943 1 c c X hvd.32044092008168 943 2 , , PUNCT hvd.32044092008168 943 3 [ [ X hvd.32044092008168 943 4 ૬ ૬ NUM hvd.32044092008168 943 5 ( ( PUNCT hvd.32044092008168 943 6 au au X hvd.32044092008168 943 7 but but CCONJ hvd.32044092008168 943 8 the the DET hvd.32044092008168 943 9 developments development NOUN hvd.32044092008168 943 10 are be AUX hvd.32044092008168 943 11 known know VERB hvd.32044092008168 943 12 : : PUNCT hvd.32044092008168 943 13 $ $ SYM hvd.32044092008168 943 14 ( ( PUNCT hvd.32044092008168 943 15 u u PROPN hvd.32044092008168 943 16 + + NUM hvd.32044092008168 943 17 v v NOUN hvd.32044092008168 943 18 ) ) PUNCT hvd.32044092008168 943 19 — — PUNCT hvd.32044092008168 943 20 gu gu NOUN hvd.32044092008168 943 21 = = SYM hvd.32044092008168 943 22 $ $ SYM hvd.32044092008168 943 23 ( ( PUNCT hvd.32044092008168 943 24 v v NOUN hvd.32044092008168 943 25 ) ) PUNCT hvd.32044092008168 943 26 up up NOUN hvd.32044092008168 943 27 ( ( PUNCT hvd.32044092008168 943 28 v v NOUN hvd.32044092008168 943 29 ) ) PUNCT hvd.32044092008168 943 30 . . PUNCT hvd.32044092008168 944 1 v v PROPN hvd.32044092008168 944 2 ६0 ६0 NUM hvd.32044092008168 944 3 v v NOUN hvd.32044092008168 944 4 ) ) PUNCT hvd.32044092008168 944 5 $ $ SYM hvd.32044092008168 945 1 ( ( PUNCT hvd.32044092008168 945 2 u u PROPN hvd.32044092008168 945 3 – – PUNCT hvd.32044092008168 945 4 a a X hvd.32044092008168 945 5 ) ) PUNCT hvd.32044092008168 945 6 – – PUNCT hvd.32044092008168 945 7 $ $ SYM hvd.32044092008168 945 8 ( ( PUNCT hvd.32044092008168 945 9 u u PROPN hvd.32044092008168 945 10 ) ) PUNCT hvd.32044092008168 945 11 ६ ६ ADP hvd.32044092008168 945 12 ( ( PUNCT hvd.32044092008168 945 13 ça ça X hvd.32044092008168 945 14 upa upa INTJ hvd.32044092008168 945 15 1 1 NUM hvd.32044092008168 945 16 u u PROPN hvd.32044092008168 945 17 ? ? PROPN hvd.32044092008168 945 18 0 0 NUM hvd.32044092008168 945 19 ) ) PUNCT hvd.32044092008168 945 20 p'v p'v PROPN hvd.32044092008168 945 21 .. .. PROPN hvd.32044092008168 945 22 u u PROPN hvd.32044092008168 945 23 2 2 NUM hvd.32044092008168 945 24 uz uz PROPN hvd.32044092008168 945 25 pa pa PROPN hvd.32044092008168 945 26 ... ... PUNCT hvd.32044092008168 946 1 w w PROPN hvd.32044092008168 946 2 2 2 NUM hvd.32044092008168 946 3 1 1 NUM hvd.32044092008168 946 4 & & CCONJ hvd.32044092008168 946 5 ( ( PUNCT hvd.32044092008168 946 6 u u PROPN hvd.32044092008168 946 7 — — PUNCT hvd.32044092008168 946 8 b b X hvd.32044092008168 946 9 ) ) PUNCT hvd.32044092008168 946 10 — — PUNCT hvd.32044092008168 946 11 § § PROPN hvd.32044092008168 946 12 ( ( PUNCT hvd.32044092008168 946 13 u u PROPN hvd.32044092008168 946 14 ) ) PUNCT hvd.32044092008168 946 15 ६० ६० NUM hvd.32044092008168 947 1 upb upb ADJ hvd.32044092008168 947 2 u u PROPN hvd.32044092008168 947 3 ? ? PUNCT hvd.32044092008168 948 1 pb pb PROPN hvd.32044092008168 948 2 ... ... PUNCT hvd.32044092008168 948 3 2 2 NUM hvd.32044092008168 948 4 u u PROPN hvd.32044092008168 948 5 5 5 NUM hvd.32044092008168 948 6 66 66 NUM hvd.32044092008168 948 7 part part NOUN hvd.32044092008168 948 8 v. v. ADV hvd.32044092008168 949 1 and and CCONJ hvd.32044092008168 949 2 we we PRON hvd.32044092008168 949 3 may may AUX hvd.32044092008168 949 4 write write VERB hvd.32044092008168 949 5 a a DET hvd.32044092008168 949 6 ( ( PUNCT hvd.32044092008168 949 7 $ $ SYM hvd.32044092008168 949 8 у у PROPN hvd.32044092008168 949 9 — — PUNCT hvd.32044092008168 949 10 a a DET hvd.32044092008168 949 11 — — PUNCT hvd.32044092008168 949 12 0 0 NUM hvd.32044092008168 949 13 — — PUNCT hvd.32044092008168 949 14 с с X hvd.32044092008168 949 15 . . PUNCT hvd.32044092008168 949 16 :) :) PUNCT hvd.32044092008168 950 1 n+ n+ PUNCT hvd.32044092008168 950 2 1 1 NUM hvd.32044092008168 950 3 ( ( PUNCT hvd.32044092008168 950 4 pv pv ADP hvd.32044092008168 950 5 + + CCONJ hvd.32044092008168 950 6 a a PRON hvd.32044092008168 950 7 + + ADJ hvd.32044092008168 950 8 b b NOUN hvd.32044092008168 950 9 + + NOUN hvd.32044092008168 950 10 p+ p+ VERB hvd.32044092008168 950 11 .. .. PUNCT hvd.32044092008168 950 12 ) ) PUNCT hvd.32044092008168 951 1 u u PROPN hvd.32044092008168 951 2 u u PROPN hvd.32044092008168 951 3 22 22 NUM hvd.32044092008168 951 4 ( ( PUNCT hvd.32044092008168 951 5 p'v p'v PROPN hvd.32044092008168 951 6 + + CCONJ hvd.32044092008168 951 7 p'a p'a ADJ hvd.32044092008168 951 8 + + PUNCT hvd.32044092008168 951 9 p'b+ p'b+ X hvd.32044092008168 951 10 .. .. PUNCT hvd.32044092008168 951 11 ) ) PUNCT hvd.32044092008168 951 12 ... ... PUNCT hvd.32044092008168 952 1 + + CCONJ hvd.32044092008168 952 2 + + PUNCT hvd.32044092008168 952 3 + + CCONJ hvd.32044092008168 952 4 2 2 NUM hvd.32044092008168 952 5 but but CCONJ hvd.32044092008168 952 6 = = SYM hvd.32044092008168 952 7 x x SYM hvd.32044092008168 952 8 2 2 NUM hvd.32044092008168 952 9 u u PROPN hvd.32044092008168 952 10 2 2 NUM hvd.32044092008168 952 11 су су NOUN hvd.32044092008168 952 12 — — PUNCT hvd.32044092008168 952 13 $ $ SYM hvd.32044092008168 952 14 a a PRON hvd.32044092008168 952 15 — — PUNCT hvd.32044092008168 952 16 fb fb PROPN hvd.32044092008168 952 17 — — PUNCT hvd.32044092008168 952 18 fc fc PROPN hvd.32044092008168 952 19 and and CCONJ hvd.32044092008168 952 20 p'a p'a ADJ hvd.32044092008168 952 21 + + CCONJ hvd.32044092008168 952 22 p'b p'b ADJ hvd.32044092008168 952 23 + + CCONJ hvd.32044092008168 952 24 p'ct p'ct NOUN hvd.32044092008168 952 25 .. .. PUNCT hvd.32044092008168 952 26 =0 =0 VERB hvd.32044092008168 952 27 ( ( PUNCT hvd.32044092008168 952 28 see see VERB hvd.32044092008168 952 29 pages page NOUN hvd.32044092008168 952 30 25 25 NUM hvd.32044092008168 952 31 and and CCONJ hvd.32044092008168 952 32 45 45 NUM hvd.32044092008168 952 33 ) ) PUNCT hvd.32044092008168 952 34 , , PUNCT hvd.32044092008168 952 35 whence whence ADP hvd.32044092008168 952 36 n+1 n+1 X hvd.32044092008168 952 37 u u PROPN hvd.32044092008168 952 38 ? ? PUNCT hvd.32044092008168 953 1 [ [ X hvd.32044092008168 953 2 125 125 NUM hvd.32044092008168 953 3 ] ] PUNCT hvd.32044092008168 953 4 a a X hvd.32044092008168 953 5 + + NOUN hvd.32044092008168 953 6 x x SYM hvd.32044092008168 953 7 ( ( PUNCT hvd.32044092008168 953 8 a a X hvd.32044092008168 953 9 + + ADJ hvd.32044092008168 953 10 b b NOUN hvd.32044092008168 953 11 + + NOUN hvd.32044092008168 953 12 pt pt PROPN hvd.32044092008168 953 13 . . PUNCT hvd.32044092008168 954 1 + + PROPN hvd.32044092008168 954 2 pv pv ADP hvd.32044092008168 954 3 ) ) PUNCT hvd.32044092008168 954 4 u u PROPN hvd.32044092008168 954 5 p'v p'v PROPN hvd.32044092008168 954 6 t t PROPN hvd.32044092008168 954 7 ... ... PUNCT hvd.32044092008168 955 1 the the DET hvd.32044092008168 955 2 degree degree NOUN hvd.32044092008168 955 3 of of ADP hvd.32044092008168 955 4 q q NOUN hvd.32044092008168 955 5 is be AUX hvd.32044092008168 955 6 ( ( PUNCT hvd.32044092008168 955 7 n n X hvd.32044092008168 955 8 + + CCONJ hvd.32044092008168 955 9 1 1 NUM hvd.32044092008168 955 10 ) ) PUNCT hvd.32044092008168 955 11 , , PUNCT hvd.32044092008168 955 12 of of ADP hvd.32044092008168 955 13 s s NOUN hvd.32044092008168 955 14 ' ' NOUN hvd.32044092008168 955 15 , , PUNCT hvd.32044092008168 955 16 3 3 NUM hvd.32044092008168 955 17 , , PUNCT hvd.32044092008168 955 18 of of ADP hvd.32044092008168 955 19 , , PUNCT hvd.32044092008168 955 20 ( ( PUNCT hvd.32044092008168 955 21 n n NOUN hvd.32044092008168 955 22 — — PUNCT hvd.32044092008168 955 23 3 3 NUM hvd.32044092008168 955 24 ) ) PUNCT hvd.32044092008168 955 25 , , PUNCT hvd.32044092008168 955 26 and and CCONJ hvd.32044092008168 955 27 ' ' PUNCT hvd.32044092008168 955 28 of of ADP hvd.32044092008168 955 29 p p NOUN hvd.32044092008168 955 30 ' ' PUNCT hvd.32044092008168 955 31 , , PUNCT hvd.32044092008168 955 32 , , PUNCT hvd.32044092008168 955 33 which which PRON hvd.32044092008168 955 34 gives give VERB hvd.32044092008168 955 35 the the DET hvd.32044092008168 955 36 degree degree NOUN hvd.32044092008168 955 37 of of ADP hvd.32044092008168 955 38 the the DET hvd.32044092008168 955 39 second second ADJ hvd.32044092008168 955 40 member member NOUN hvd.32044092008168 955 41 as as ADP hvd.32044092008168 955 42 ( ( PUNCT hvd.32044092008168 955 43 n n NOUN hvd.32044092008168 955 44 + + CCONJ hvd.32044092008168 955 45 1 1 NUM hvd.32044092008168 955 46 ) ) PUNCT hvd.32044092008168 955 47 , , PUNCT hvd.32044092008168 955 48 also also ADV hvd.32044092008168 955 49 + + CCONJ hvd.32044092008168 955 50 whence whence ADV hvd.32044092008168 955 51 pero pero NOUN hvd.32044092008168 955 52 pā pā PROPN hvd.32044092008168 955 53 + + CCONJ hvd.32044092008168 955 54 + + ADJ hvd.32044092008168 955 55 . . NOUN hvd.32044092008168 956 1 1 1 NUM hvd.32044092008168 956 2 1 1 NUM hvd.32044092008168 956 3 2 2 NUM hvd.32044092008168 956 4 2 2 NUM hvd.32044092008168 956 5 3 3 NUM hvd.32044092008168 956 6 1 1 NUM hvd.32044092008168 956 7 2 2 NUM hvd.32044092008168 956 8 1 1 NUM hvd.32044092008168 956 9 1 1 NUM hvd.32044092008168 956 10 ( ( PUNCT hvd.32044092008168 956 11 n+1 n+1 PROPN hvd.32044092008168 956 12 ) ) PUNCT hvd.32044092008168 956 13 1 1 NUM hvd.32044092008168 956 14 1 1 NUM hvd.32044092008168 956 15 ри ри NOUN hvd.32044092008168 956 16 2 2 NUM hvd.32044092008168 956 17 u u PROPN hvd.32044092008168 956 18 2 2 NUM hvd.32044092008168 956 19 u u PROPN hvd.32044092008168 956 20 nt not PART hvd.32044092008168 956 21 unti unti ADV hvd.32044092008168 956 22 and and CCONJ hvd.32044092008168 956 23 developing develop VERB hvd.32044092008168 956 24 the the DET hvd.32044092008168 956 25 second second ADJ hvd.32044092008168 956 26 member member NOUN hvd.32044092008168 956 27 ( ( PUNCT hvd.32044092008168 956 28 b b NOUN hvd.32044092008168 956 29 ) ) PUNCT hvd.32044092008168 956 30 we we PRON hvd.32044092008168 956 31 write write VERB hvd.32044092008168 956 32 , , PUNCT hvd.32044092008168 956 33 disregarding disregard VERB hvd.32044092008168 956 34 the the DET hvd.32044092008168 956 35 constant constant ADJ hvd.32044092008168 956 36 factor factor NOUN hvd.32044092008168 956 37 1 1 NUM hvd.32044092008168 956 38 b b NOUN hvd.32044092008168 956 39 = = PUNCT hvd.32044092008168 956 40 + + NUM hvd.32044092008168 956 41 21 21 NUM hvd.32044092008168 956 42 + + NUM hvd.32044092008168 956 43 92 92 NUM hvd.32044092008168 956 44 u u NOUN hvd.32044092008168 956 45 ” " PUNCT hvd.32044092008168 956 46 + + CCONJ hvd.32044092008168 956 47 93 93 NUM hvd.32044092008168 956 48 2 2 NUM hvd.32044092008168 956 49 t t PROPN hvd.32044092008168 956 50 .. .. PUNCT hvd.32044092008168 956 51 n n ADP hvd.32044092008168 956 52 n n X hvd.32044092008168 956 53 1 1 NUM hvd.32044092008168 956 54 nunti nunti PROPN hvd.32044092008168 956 55 u u PROPN hvd.32044092008168 956 56 u u PROPN hvd.32044092008168 956 57 whence whence ADV hvd.32044092008168 956 58 n n X hvd.32044092008168 956 59 + + PROPN hvd.32044092008168 956 60 1 1 NUM hvd.32044092008168 956 61 nai nai PROPN hvd.32044092008168 956 62 1 1 NUM hvd.32044092008168 956 63 ) ) PUNCT hvd.32044092008168 956 64 92 92 NUM hvd.32044092008168 956 65 ( ( PUNCT hvd.32044092008168 956 66 n n NOUN hvd.32044092008168 956 67 ( ( PUNCT hvd.32044092008168 956 68 n n X hvd.32044092008168 956 69 [ [ X hvd.32044092008168 956 70 126]d 126]d NUM hvd.32044092008168 956 71 log log NOUN hvd.32044092008168 956 72 b b PROPN hvd.32044092008168 956 73 2 2 NUM hvd.32044092008168 956 74 ) ) PUNCT hvd.32044092008168 956 75 93 93 NUM hvd.32044092008168 956 76 unt2 unt2 VERB hvd.32044092008168 956 77 unti unti ADV hvd.32044092008168 956 78 u u PROPN hvd.32044092008168 956 79 " " PUNCT hvd.32044092008168 956 80 un-1 un-1 ADP hvd.32044092008168 956 81 1 1 NUM hvd.32044092008168 956 82 + + NUM hvd.32044092008168 956 83 91 91 NUM hvd.32044092008168 956 84 u u NOUN hvd.32044092008168 956 85 " " PUNCT hvd.32044092008168 956 86 + + CCONJ hvd.32044092008168 956 87 92 92 NUM hvd.32044092008168 956 88 n-1 n-1 X hvd.32044092008168 956 89 + + NUM hvd.32044092008168 956 90 93 93 NUM hvd.32044092008168 956 91 n n CCONJ hvd.32044092008168 956 92 2 2 NUM hvd.32044092008168 956 93 u u NOUN hvd.32044092008168 956 94 + + CCONJ hvd.32044092008168 956 95 unti unti ADV hvd.32044092008168 956 96 un1 un1 NUM hvd.32044092008168 956 97 2 2 NUM hvd.32044092008168 956 98 ) ) PUNCT hvd.32044092008168 956 99 93 93 NUM hvd.32044092008168 956 100 u3 u3 PROPN hvd.32044092008168 956 101 + + NUM hvd.32044092008168 956 102 . . PUNCT hvd.32044092008168 957 1 ( ( PUNCT hvd.32044092008168 957 2 n n CCONJ hvd.32044092008168 957 3 + + CCONJ hvd.32044092008168 957 4 1 1 NUM hvd.32044092008168 957 5 ) ) PUNCT hvd.32044092008168 957 6 + + CCONJ hvd.32044092008168 957 7 nuqi nuqi PROPN hvd.32044092008168 957 8 + + PROPN hvd.32044092008168 957 9 ( ( PUNCT hvd.32044092008168 957 10 n n CCONJ hvd.32044092008168 957 11 + + CCONJ hvd.32044092008168 957 12 1)92 1)92 NUM hvd.32044092008168 957 13 u+ u+ NOUN hvd.32044092008168 957 14 ( ( PUNCT hvd.32044092008168 957 15 n n NOUN hvd.32044092008168 957 16 1 1 NUM hvd.32044092008168 957 17 + + NUM hvd.32044092008168 957 18 au+ au+ PROPN hvd.32044092008168 957 19 9 9 NUM hvd.32044092008168 957 20 . . PUNCT hvd.32044092008168 957 21 u^ u^ PROPN hvd.32044092008168 958 1 + + NUM hvd.32044092008168 958 2 93 93 NUM hvd.32044092008168 958 3 23 23 NUM hvd.32044092008168 958 4 + + NUM hvd.32044092008168 958 5 u u X hvd.32044092008168 958 6 n n X hvd.32044092008168 958 7 + + CCONJ hvd.32044092008168 958 8 1 1 NUM hvd.32044092008168 958 9 +4+(2qp +4+(2qp NUM hvd.32044092008168 958 10 - - PUNCT hvd.32044092008168 958 11 q q PROPN hvd.32044092008168 958 12 ° ° X hvd.32044092008168 958 13 )+(3q )+(3q PUNCT hvd.32044092008168 958 14 – – PUNCT hvd.32044092008168 958 15 3q 3q NUM hvd.32044092008168 958 16 , , PUNCT hvd.32044092008168 958 17 q+g q+g SPACE hvd.32044092008168 958 18 ° ° NOUN hvd.32044092008168 958 19 )(*+ )(*+ PROPN hvd.32044092008168 958 20 ... ... PUNCT hvd.32044092008168 959 1 u u PROPN hvd.32044092008168 959 2 . . PUNCT hvd.32044092008168 960 1 again again ADV hvd.32044092008168 960 2 : : PUNCT hvd.32044092008168 960 3 1 1 NUM hvd.32044092008168 960 4 1 1 NUM hvd.32044092008168 960 5 botza botza NOUN hvd.32044092008168 960 6 1 1 NUM hvd.32044092008168 960 7 ( ( PUNCT hvd.32044092008168 960 8 n+1 n+1 X hvd.32044092008168 960 9 ) ) PUNCT hvd.32044092008168 960 10 ( ( PUNCT hvd.32044092008168 960 11 n-1 n-1 NOUN hvd.32044092008168 960 12 ) ) PUNCT hvd.32044092008168 960 13 + + CCONJ hvd.32044092008168 960 14 bit bit NOUN hvd.32044092008168 960 15 ? ? PUNCT hvd.32044092008168 961 1 t. t. PROPN hvd.32044092008168 961 2 = = PROPN hvd.32044092008168 961 3 yt yt PROPN hvd.32044092008168 961 4 ( ( PUNCT hvd.32044092008168 961 5 n-3 n-3 NUM hvd.32044092008168 961 6 ) ) PUNCT hvd.32044092008168 961 7 ( ( PUNCT hvd.32044092008168 961 8 n n CCONJ hvd.32044092008168 961 9 −5 −5 X hvd.32044092008168 961 10 ) ) PUNCT hvd.32044092008168 961 11 ? ? PUNCT hvd.32044092008168 962 1 + + CCONJ hvd.32044092008168 962 2 p p NOUN hvd.32044092008168 962 3 = = SYM hvd.32044092008168 962 4 ( ( PUNCT hvd.32044092008168 962 5 ( ( PUNCT hvd.32044092008168 962 6 4 4 NUM hvd.32044092008168 962 7 të të X hvd.32044092008168 962 8 — — PUNCT hvd.32044092008168 962 9 tg2 tg2 PROPN hvd.32044092008168 962 10 + + PROPN hvd.32044092008168 962 11 93 93 NUM hvd.32044092008168 962 12 ) ) PUNCT hvd.32044092008168 962 13 t t PROPN hvd.32044092008168 962 14 .. .. PUNCT hvd.32044092008168 963 1 + + CCONJ hvd.32044092008168 963 2 y1 y1 PROPN hvd.32044092008168 963 3 t2 t2 PROPN hvd.32044092008168 963 4 2 2 NUM hvd.32044092008168 963 5 u3 u3 NOUN hvd.32044092008168 963 6 whence whence NOUN hvd.32044092008168 963 7 1 1 NUM hvd.32044092008168 963 8 1 1 NUM hvd.32044092008168 963 9 1 1 NUM hvd.32044092008168 963 10 ( ( PUNCT hvd.32044092008168 963 11 n+1 n+1 PROPN hvd.32044092008168 963 12 ) ) PUNCT hvd.32044092008168 963 13 b.t2 b.t2 SPACE hvd.32044092008168 963 14 b=(5,60+p+by b=(5,60+p+by PROPN hvd.32044092008168 963 15 tě tě PROPN hvd.32044092008168 963 16 ( ( PUNCT hvd.32044092008168 963 17 n="+ n="+ PROPN hvd.32044092008168 963 18 ... ... PUNCT hvd.32044092008168 963 19 ) ) PUNCT hvd.32044092008168 963 20 , , PUNCT hvd.32044092008168 963 21 2 2 NUM hvd.32044092008168 963 22 ( ( PUNCT hvd.32044092008168 963 23 46–194–95)"btico 46–194–95)"btico NUM hvd.32044092008168 963 24 _ _ PUNCT hvd.32044092008168 963 25 _ _ PUNCT hvd.32044092008168 963 26 :( :( PUNCT hvd.32044092008168 964 1 n-1 n-1 X hvd.32044092008168 964 2 ) ) PUNCT hvd.32044092008168 964 3 ( ( PUNCT hvd.32044092008168 964 4 n n CCONJ hvd.32044092008168 964 5 3 3 X hvd.32044092008168 964 6 be be AUX hvd.32044092008168 964 7 -5 -5 PROPN hvd.32044092008168 964 8 ) ) PUNCT hvd.32044092008168 964 9 + + CCONJ hvd.32044092008168 964 10 lytzen lytzen NOUN hvd.32044092008168 964 11 + + NOUN hvd.32044092008168 964 12 .... .... PUNCT hvd.32044092008168 965 1 20 20 NUM hvd.32044092008168 965 2 bo bo PROPN hvd.32044092008168 965 3 b b X hvd.32044092008168 965 4 qx1 qx1 PUNCT hvd.32044092008168 965 5 + + CCONJ hvd.32044092008168 965 6 qy qy INTJ hvd.32044092008168 965 7 cu cu PROPN hvd.32044092008168 965 8 " " PUNCT hvd.32044092008168 965 9 + + CCONJ hvd.32044092008168 965 10 + + CCONJ hvd.32044092008168 965 11 an an DET hvd.32044092008168 965 12 unti unti PROPN hvd.32044092008168 965 13 un un PROPN hvd.32044092008168 965 14 1 1 NUM hvd.32044092008168 965 15 ) ) PUNCT hvd.32044092008168 965 16 + + NUM hvd.32044092008168 965 17 cun cun PROPN hvd.32044092008168 965 18 2 2 NUM hvd.32044092008168 965 19 reduction reduction NOUN hvd.32044092008168 965 20 of of ADP hvd.32044092008168 965 21 the the DET hvd.32044092008168 965 22 forms form NOUN hvd.32044092008168 965 23 when when SCONJ hvd.32044092008168 965 24 n n SYM hvd.32044092008168 965 25 equals equal VERB hvd.32044092008168 965 26 three three NUM hvd.32044092008168 965 27 . . PUNCT hvd.32044092008168 966 1 67 67 NUM hvd.32044092008168 966 2 and and CCONJ hvd.32044092008168 966 3 2 2 NUM hvd.32044092008168 966 4 qv qv PROPN hvd.32044092008168 966 5 127]d 127]d NUM hvd.32044092008168 966 6 log log NOUN hvd.32044092008168 966 7 . . PUNCT hvd.32044092008168 967 1 b b X hvd.32044092008168 967 2 = = PUNCT hvd.32044092008168 967 3 bo bo X hvd.32044092008168 967 4 [ [ PUNCT hvd.32044092008168 967 5 – – PUNCT hvd.32044092008168 967 6 * * ADJ hvd.32044092008168 967 7 * * SYM hvd.32044092008168 967 8 1 1 NUM hvd.32044092008168 967 9 + + NUM hvd.32044092008168 967 10 $ $ SYM hvd.32044092008168 967 11 8 8 NUM hvd.32044092008168 967 12 + + NUM hvd.32044092008168 967 13 ( ( PUNCT hvd.32044092008168 967 14 2b 2b NUM hvd.32044092008168 967 15 , , PUNCT hvd.32044092008168 967 16 – – PUNCT hvd.32044092008168 967 17 qx*)u+($% qx*)u+($% PROPN hvd.32044092008168 967 18 ! ! PUNCT hvd.32044092008168 967 19 _ _ PUNCT hvd.32044092008168 968 1 3qyb,+b;')]uº+ 3qyb,+b;')]uº+ NUM hvd.32044092008168 968 2 .. .. PUNCT hvd.32044092008168 969 1 +1 +1 PROPN hvd.32044092008168 969 2 b b INTJ hvd.32044092008168 969 3 qy qy INTJ hvd.32044092008168 969 4 ? ? PUNCT hvd.32044092008168 970 1 c2 c2 PROPN hvd.32044092008168 970 2 ? ? PUNCT hvd.32044092008168 971 1 y y NOUN hvd.32044092008168 971 2 1 1 NUM hvd.32044092008168 971 3 c c X hvd.32044092008168 971 4 qy qy ADP hvd.32044092008168 971 5 сво сво PROPN hvd.32044092008168 971 6 cb cb PROPN hvd.32044092008168 971 7 ' ' PART hvd.32044092008168 971 8 0 0 NUM hvd.32044092008168 971 9 x x PUNCT hvd.32044092008168 971 10 = = PROPN hvd.32044092008168 971 11 cb cb PROPN hvd.32044092008168 971 12 . . PROPN hvd.32044092008168 971 13 2 2 NUM hvd.32044092008168 971 14 2 2 NUM hvd.32044092008168 971 15 b b NOUN hvd.32044092008168 971 16 , , PUNCT hvd.32044092008168 971 17 2 2 NUM hvd.32044092008168 971 18 2 2 NUM hvd.32044092008168 971 19 6 6 NUM hvd.32044092008168 971 20 q. q. NOUN hvd.32044092008168 972 1 + + NUM hvd.32044092008168 972 2 2 2 NUM hvd.32044092008168 972 3 3 3 NUM hvd.32044092008168 972 4 ( ( PUNCT hvd.32044092008168 972 5 21 21 NUM hvd.32044092008168 972 6 1 1 NUM hvd.32044092008168 972 7 γ γ NOUN hvd.32044092008168 972 8 x x PUNCT hvd.32044092008168 972 9 c"b c"b NOUN hvd.32044092008168 972 10 , , PUNCT hvd.32044092008168 972 11 from from ADP hvd.32044092008168 972 12 developments development NOUN hvd.32044092008168 972 13 [ [ X hvd.32044092008168 972 14 126 126 NUM hvd.32044092008168 972 15 ] ] PUNCT hvd.32044092008168 972 16 and and CCONJ hvd.32044092008168 972 17 [ [ X hvd.32044092008168 972 18 127 127 X hvd.32044092008168 972 19 ] ] PUNCT hvd.32044092008168 972 20 we we PRON hvd.32044092008168 972 21 find find VERB hvd.32044092008168 972 22 b b NOUN hvd.32044092008168 972 23 qy1 qy1 NOUN hvd.32044092008168 972 24 128 128 NUM hvd.32044092008168 972 25 ] ] SYM hvd.32044092008168 972 26 91 91 NUM hvd.32044092008168 972 27 ; ; PUNCT hvd.32044092008168 972 28 92 92 NUM hvd.32044092008168 972 29 ; ; PUNCT hvd.32044092008168 972 30 93 93 NUM hvd.32044092008168 972 31 n n CCONJ hvd.32044092008168 972 32 being be AUX hvd.32044092008168 972 33 odd odd ADJ hvd.32044092008168 972 34 , , PUNCT hvd.32044092008168 972 35 b. b. PROPN hvd.32044092008168 972 36 and and CCONJ hvd.32044092008168 972 37 from from ADP hvd.32044092008168 972 38 developments development NOUN hvd.32044092008168 972 39 [ [ X hvd.32044092008168 972 40 125 125 NUM hvd.32044092008168 972 41 ] ] PUNCT hvd.32044092008168 972 42 and and CCONJ hvd.32044092008168 972 43 [ [ X hvd.32044092008168 972 44 126 126 NUM hvd.32044092008168 972 45 ] ] X hvd.32044092008168 972 46 qy qy ADP hvd.32044092008168 972 47 91 91 NUM hvd.32044092008168 972 48 q?y q?y NOUN hvd.32044092008168 972 49 ? ? PUNCT hvd.32044092008168 973 1 129 129 NUM hvd.32044092008168 973 2 ] ] PUNCT hvd.32044092008168 973 3 { { PUNCT hvd.32044092008168 973 4 a a X hvd.32044092008168 973 5 + + PROPN hvd.32044092008168 973 6 b b NOUN hvd.32044092008168 973 7 + + NUM hvd.32044092008168 973 8 y y NOUN hvd.32044092008168 973 9 + + PUNCT hvd.32044092008168 973 10 .. .. PUNCT hvd.32044092008168 973 11 + + PUNCT hvd.32044092008168 973 12 pv pv ADP hvd.32044092008168 973 13 ) ) PUNCT hvd.32044092008168 973 14 = = VERB hvd.32044092008168 973 15 9 9 NUM hvd.32044092008168 973 16 , , PUNCT hvd.32044092008168 973 17 ’ ' PUNCT hvd.32044092008168 973 18 – – PUNCT hvd.32044092008168 973 19 292 292 NUM hvd.32044092008168 973 20 cb cb X hvd.32044092008168 973 21 , , PUNCT hvd.32044092008168 973 22 b. b. PROPN hvd.32044092008168 973 23 6qyb 6qyb PROPN hvd.32044092008168 973 24 2 2 NUM hvd.32044092008168 973 25 qy qy ADP hvd.32044092008168 973 26 p'v p'v NOUN hvd.32044092008168 973 27 = = SYM hvd.32044092008168 973 28 2 2 NUM hvd.32044092008168 973 29 ( ( PUNCT hvd.32044092008168 973 30 34192 34192 NUM hvd.32044092008168 973 31 – – PUNCT hvd.32044092008168 973 32 393 393 NUM hvd.32044092008168 973 33 +91 +91 NUM hvd.32044092008168 973 34 % % NOUN hvd.32044092008168 973 35 ) ) PUNCT hvd.32044092008168 973 36 сво сво PROPN hvd.32044092008168 973 37 ? ? PUNCT hvd.32044092008168 974 1 cb cb PROPN hvd.32044092008168 974 2 c'b c'b SPACE hvd.32044092008168 974 3 ' ' PUNCT hvd.32044092008168 974 4 these these DET hvd.32044092008168 974 5 fornis forni NOUN hvd.32044092008168 974 6 are be AUX hvd.32044092008168 974 7 transformed transform VERB hvd.32044092008168 974 8 by by ADP hvd.32044092008168 974 9 the the DET hvd.32044092008168 974 10 aid aid NOUN hvd.32044092008168 974 11 of of ADP hvd.32044092008168 974 12 the the DET hvd.32044092008168 974 13 relations relation NOUN hvd.32044092008168 974 14 c c X hvd.32044092008168 974 15 = = SYM hvd.32044092008168 974 16 ( ( PUNCT hvd.32044092008168 974 17 vpq vpq NOUN hvd.32044092008168 974 18 ( ( PUNCT hvd.32044092008168 974 19 p. p. NOUN hvd.32044092008168 974 20 56 56 NUM hvd.32044092008168 974 21 ) ) PUNCT hvd.32044092008168 974 22 ; ; PUNCT hvd.32044092008168 974 23 ( ( PUNCT hvd.32044092008168 974 24 2n 2n NUM hvd.32044092008168 974 25 — — PUNCT hvd.32044092008168 974 26 1)(a 1)(a NUM hvd.32044092008168 975 1 + + PUNCT hvd.32044092008168 975 2 b b X hvd.32044092008168 975 3 + + PUNCT hvd.32044092008168 975 4 y y NOUN hvd.32044092008168 975 5 + + PUNCT hvd.32044092008168 975 6 .. .. PUNCT hvd.32044092008168 975 7 ) ) PUNCT hvd.32044092008168 976 1 = = PROPN hvd.32044092008168 976 2 b b X hvd.32044092008168 976 3 ( ( PUNCT hvd.32044092008168 976 4 p. p. NOUN hvd.32044092008168 976 5 29 29 NUM hvd.32044092008168 976 6 ) ) PUNCT hvd.32044092008168 976 7 b b NOUN hvd.32044092008168 976 8 ( ( PUNCT hvd.32044092008168 976 9 2n 2n NUM hvd.32044092008168 976 10 – – PUNCT hvd.32044092008168 976 11 1)a 1)a NUM hvd.32044092008168 976 12 , , PUNCT hvd.32044092008168 976 13 = = NOUN hvd.32044092008168 976 14 -b -b X hvd.32044092008168 976 15 ( ( PUNCT hvd.32044092008168 976 16 p. p. NOUN hvd.32044092008168 976 17 36 36 NUM hvd.32044092008168 976 18 ) ) PUNCT hvd.32044092008168 977 1 whence whence NOUN hvd.32044092008168 977 2 ( ( PUNCT hvd.32044092008168 977 3 a a DET hvd.32044092008168 977 4 + + ADJ hvd.32044092008168 977 5 b+r+ b+r+ NOUN hvd.32044092008168 977 6 ... ... PUNCT hvd.32044092008168 977 7 )=-a )=-a PUNCT hvd.32044092008168 977 8 , , PUNCT hvd.32044092008168 977 9 pgiving pgiving NOUN hvd.32044092008168 977 10 as as ADP hvd.32044092008168 977 11 result result NOUN hvd.32044092008168 977 12 : : PUNCT hvd.32044092008168 977 13 oy oy PROPN hvd.32044092008168 977 14 vio vio PROPN hvd.32044092008168 977 15 q q PROPN hvd.32044092008168 977 16 n n PROPN hvd.32044092008168 977 17 odd odd ADJ hvd.32044092008168 977 18 . . PUNCT hvd.32044092008168 978 1 св св PROPN hvd.32044092008168 978 2 . . PROPN hvd.32044092008168 979 1 p p PROPN hvd.32044092008168 979 2 qy qy ADP hvd.32044092008168 979 3 2 2 NUM hvd.32044092008168 979 4 b b NOUN hvd.32044092008168 979 5 , , PUNCT hvd.32044092008168 979 6 b b X hvd.32044092008168 979 7 pv pv X hvd.32044092008168 979 8 c c PROPN hvd.32044092008168 979 9 pb pb PROPN hvd.32044092008168 979 10 . . PUNCT hvd.32044092008168 980 1 b b PROPN hvd.32044092008168 980 2 2 2 NUM hvd.32044092008168 980 3 3 3 NUM hvd.32044092008168 980 4 y y PROPN hvd.32044092008168 980 5 b b PROPN hvd.32044092008168 980 6 p'v p'v PROPN hvd.32044092008168 980 7 130 130 NUM hvd.32044092008168 980 8 ] ] PUNCT hvd.32044092008168 980 9 le le PROPN hvd.32044092008168 980 10 pb pb PROPN hvd.32044092008168 980 11 . . PROPN hvd.32044092008168 980 12 } } PUNCT hvd.32044092008168 980 13 v v PROPN hvd.32044092008168 980 14 ? ? PROPN hvd.32044092008168 980 15 b. b. PROPN hvd.32044092008168 980 16 b. b. PROPN hvd.32044092008168 980 17 and and CCONJ hvd.32044092008168 980 18 from from ADP hvd.32044092008168 980 19 these these PRON hvd.32044092008168 980 20 the the DET hvd.32044092008168 980 21 combined combine VERB hvd.32044092008168 980 22 forms form NOUN hvd.32044092008168 980 23 arise arise VERB hvd.32044092008168 980 24 pv pv INTJ hvd.32044092008168 980 25 qy qy NOUN hvd.32044092008168 980 26 ? ? PUNCT hvd.32044092008168 981 1 3b 3b NUM hvd.32044092008168 981 2 + + CCONJ hvd.32044092008168 981 3 cpb cpb PROPN hvd.32044092008168 981 4 b. b. PROPN hvd.32044092008168 981 5 y y PROPN hvd.32044092008168 981 6 b b PROPN hvd.32044092008168 981 7 b. b. PROPN hvd.32044092008168 981 8 1 1 NUM hvd.32044092008168 981 9 these these DET hvd.32044092008168 981 10 formules formule NOUN hvd.32044092008168 981 11 are be AUX hvd.32044092008168 981 12 perfectly perfectly ADV hvd.32044092008168 981 13 general general ADJ hvd.32044092008168 981 14 for for ADP hvd.32044092008168 981 15 n n ADP hvd.32044092008168 981 16 odd odd ADJ hvd.32044092008168 981 17 and and CCONJ hvd.32044092008168 981 18 the the DET hvd.32044092008168 981 19 corresponding correspond VERB hvd.32044092008168 981 20 forms form NOUN hvd.32044092008168 981 21 n n CCONJ hvd.32044092008168 981 22 even even ADV hvd.32044092008168 981 23 obtained obtain VERB hvd.32044092008168 981 24 in in ADP hvd.32044092008168 981 25 like like ADJ hvd.32044092008168 981 26 manner manner NOUN hvd.32044092008168 981 27 are be AUX hvd.32044092008168 981 28 q q PROPN hvd.32044092008168 981 29 py py PROPN hvd.32044092008168 981 30 p p PROPN hvd.32044092008168 981 31 c4 c4 PROPN hvd.32044092008168 981 32 qb qb PROPN hvd.32044092008168 981 33 . . PROPN hvd.32044092008168 981 34 27 27 NUM hvd.32044092008168 981 35 . . PUNCT hvd.32044092008168 982 1 b b X hvd.32044092008168 982 2 pv pv PROPN hvd.32044092008168 982 3 py py PROPN hvd.32044092008168 982 4 ? ? PUNCT hvd.32044092008168 982 5 b b NOUN hvd.32044092008168 982 6 q q X hvd.32044092008168 982 7 p'v p'v PROPN hvd.32044092008168 982 8 2 2 NUM hvd.32044092008168 982 9 c2 c2 NOUN hvd.32044092008168 982 10 } } PUNCT hvd.32044092008168 982 11 py8 py8 CCONJ hvd.32044092008168 982 12 p p PROPN hvd.32044092008168 982 13 p p NOUN hvd.32044092008168 982 14 ' ' PUNCT hvd.32044092008168 982 15 v v NOUN hvd.32044092008168 982 16 2 2 PROPN hvd.32044092008168 982 17 b b PROPN hvd.32044092008168 982 18 b b PROPN hvd.32044092008168 982 19 2 2 NUM hvd.32044092008168 982 20 2n 2n NUM hvd.32044092008168 982 21 1 1 NUM hvd.32044092008168 983 1 i i PRON hvd.32044092008168 983 2 3 3 NUM hvd.32044092008168 983 3 yi yi PROPN hvd.32044092008168 983 4 + + NUM hvd.32044092008168 983 5 3 3 NUM hvd.32044092008168 983 6 2 2 NUM hvd.32044092008168 983 7 p p PROPN hvd.32044092008168 983 8 371 371 NUM hvd.32044092008168 983 9 23 23 NUM hvd.32044092008168 983 10 2 2 NUM hvd.32044092008168 983 11 p'o p'o NOUN hvd.32044092008168 983 12 by by ADP hvd.32044092008168 983 13 3 3 NUM hvd.32044092008168 983 14 y1 y1 NOUN hvd.32044092008168 983 15 + + CCONJ hvd.32044092008168 983 16 pv pv ADP hvd.32044092008168 983 17 2x 2x NUM hvd.32044092008168 983 18 2 2 NUM hvd.32044092008168 983 19 n n CCONJ hvd.32044092008168 983 20 сво сво PROPN hvd.32044092008168 983 21 c2b c2b PROPN hvd.32044092008168 983 22 . . PUNCT hvd.32044092008168 984 1 х х PROPN hvd.32044092008168 984 2 v v PROPN hvd.32044092008168 984 3 n n CCONJ hvd.32044092008168 984 4 even even ADV hvd.32044092008168 984 5 . . PUNCT hvd.32044092008168 985 1 n n CCONJ hvd.32044092008168 985 2 2 2 NUM hvd.32044092008168 985 3 n n CCONJ hvd.32044092008168 985 4 131 131 NUM hvd.32044092008168 985 5 ] ] PUNCT hvd.32044092008168 985 6 1 1 NUM hvd.32044092008168 985 7 c4 c4 NOUN hvd.32044092008168 985 8 qb qb PROPN hvd.32044092008168 985 9 . . PUNCT hvd.32044092008168 986 1 3 3 NUM hvd.32044092008168 986 2 0 0 NUM hvd.32044092008168 986 3 3 3 NUM hvd.32044092008168 986 4 3b 3b NUM hvd.32044092008168 986 5 , , PUNCT hvd.32044092008168 986 6 71 71 NUM hvd.32044092008168 986 7 + + NUM hvd.32044092008168 986 8 3v 3v NUM hvd.32044092008168 986 9 2 2 NUM hvd.32044092008168 986 10 71 71 NUM hvd.32044092008168 986 11 + + NUM hvd.32044092008168 986 12 pv pv ADP hvd.32044092008168 986 13 2 2 NUM hvd.32044092008168 986 14 x x X hvd.32044092008168 987 1 во во X hvd.32044092008168 987 2 y y PROPN hvd.32044092008168 987 3 2n 2n PROPN hvd.32044092008168 987 4 1 1 NUM hvd.32044092008168 987 5 the the DET hvd.32044092008168 987 6 superiority superiority NOUN hvd.32044092008168 987 7 of of ADP hvd.32044092008168 987 8 these these DET hvd.32044092008168 987 9 forms form NOUN hvd.32044092008168 987 10 over over ADP hvd.32044092008168 987 11 those those PRON hvd.32044092008168 987 12 first first ADJ hvd.32044092008168 987 13 derived derive VERB hvd.32044092008168 987 14 , , PUNCT hvd.32044092008168 987 15 showing show VERB hvd.32044092008168 987 16 as as SCONJ hvd.32044092008168 987 17 they they PRON hvd.32044092008168 987 18 do do VERB hvd.32044092008168 987 19 at at ADP hvd.32044092008168 987 20 a a DET hvd.32044092008168 987 21 glance glance NOUN hvd.32044092008168 987 22 the the DET hvd.32044092008168 987 23 synthetic synthetic ADJ hvd.32044092008168 987 24 relations relation NOUN hvd.32044092008168 987 25 , , PUNCT hvd.32044092008168 987 26 is be AUX hvd.32044092008168 987 27 unquestionable unquestionable ADJ hvd.32044092008168 987 28 5 5 NUM hvd.32044092008168 987 29 * * SYM hvd.32044092008168 987 30 68 68 NUM hvd.32044092008168 987 31 part part NOUN hvd.32044092008168 987 32 v. v. ADP hvd.32044092008168 987 33 and and CCONJ hvd.32044092008168 987 34 the the DET hvd.32044092008168 987 35 explicit explicit ADJ hvd.32044092008168 987 36 forms form NOUN hvd.32044092008168 987 37 for for ADP hvd.32044092008168 987 38 our our PRON hvd.32044092008168 987 39 case case NOUN hvd.32044092008168 987 40 n n X hvd.32044092008168 987 41 equals equal VERB hvd.32044092008168 987 42 three three NUM hvd.32044092008168 987 43 and and CCONJ hvd.32044092008168 987 44 also also ADV hvd.32044092008168 987 45 for for ADP hvd.32044092008168 987 46 n n X hvd.32044092008168 987 47 equals equal VERB hvd.32044092008168 987 48 four four NUM hvd.32044092008168 987 49 and and CCONJ hvd.32044092008168 987 50 to to ADP hvd.32044092008168 987 51 some some DET hvd.32044092008168 987 52 extent extent NOUN hvd.32044092008168 987 53 for for ADP hvd.32044092008168 987 54 yet yet ADV hvd.32044092008168 987 55 higher high ADJ hvd.32044092008168 987 56 values value NOUN hvd.32044092008168 987 57 , , PUNCT hvd.32044092008168 987 58 are be AUX hvd.32044092008168 987 59 obtainable obtainable ADJ hvd.32044092008168 987 60 with with ADP hvd.32044092008168 987 61 greater great ADJ hvd.32044092008168 987 62 easy easy ADJ hvd.32044092008168 987 63 than than ADP hvd.32044092008168 987 64 by by ADP hvd.32044092008168 987 65 the the DET hvd.32044092008168 987 66 first first ADJ hvd.32044092008168 987 67 method method NOUN hvd.32044092008168 987 68 . . PUNCT hvd.32044092008168 988 1 even even ADV hvd.32044092008168 988 2 here here ADV hvd.32044092008168 988 3 however however ADV hvd.32044092008168 988 4 the the DET hvd.32044092008168 988 5 forms form NOUN hvd.32044092008168 988 6 increase increase VERB hvd.32044092008168 988 7 in in ADP hvd.32044092008168 988 8 complexity complexity NOUN hvd.32044092008168 988 9 so so ADV hvd.32044092008168 988 10 rapidly rapidly ADV hvd.32044092008168 988 11 that that SCONJ hvd.32044092008168 988 12 n n CCONJ hvd.32044092008168 988 13 is be AUX hvd.32044092008168 988 14 practically practically ADV hvd.32044092008168 988 15 restricted restrict VERB hvd.32044092008168 988 16 to to ADP hvd.32044092008168 988 17 the the DET hvd.32044092008168 988 18 lowest low ADJ hvd.32044092008168 988 19 values value NOUN hvd.32044092008168 988 20 . . PUNCT hvd.32044092008168 989 1 > > X hvd.32044092008168 989 2 3 3 NUM hvd.32044092008168 989 3 2 2 NUM hvd.32044092008168 989 4 for for ADP hvd.32044092008168 989 5 case case NOUN hvd.32044092008168 989 6 n n X hvd.32044092008168 989 7 = = X hvd.32044092008168 989 8 3 3 X hvd.32044092008168 989 9 . . X hvd.32044092008168 990 1 we we PRON hvd.32044092008168 990 2 have have AUX hvd.32044092008168 990 3 found find VERB hvd.32044092008168 990 4 all all DET hvd.32044092008168 990 5 the the DET hvd.32044092008168 990 6 eliments eliment NOUN hvd.32044092008168 990 7 except except SCONJ hvd.32044092008168 990 8 7ı 7ı NUM hvd.32044092008168 990 9 which which PRON hvd.32044092008168 990 10 is be AUX hvd.32044092008168 990 11 derived derive VERB hvd.32044092008168 990 12 from from ADP hvd.32044092008168 990 13 development development NOUN hvd.32044092008168 990 14 of of ADP hvd.32044092008168 990 15 ® ® PROPN hvd.32044092008168 990 16 , , PUNCT hvd.32044092008168 990 17 or or CCONJ hvd.32044092008168 990 18 more more ADV hvd.32044092008168 990 19 easily easily ADV hvd.32044092008168 990 20 as as SCONJ hvd.32044092008168 990 21 follows follow NOUN hvd.32044092008168 990 22 . . PUNCT hvd.32044092008168 991 1 from from ADP hvd.32044092008168 991 2 ( ( PUNCT hvd.32044092008168 991 3 106 106 NUM hvd.32044092008168 991 4 , , PUNCT hvd.32044092008168 991 5 p. p. NOUN hvd.32044092008168 991 6 59 59 NUM hvd.32044092008168 991 7 ) ) PUNCT hvd.32044092008168 991 8 q=(15 q=(15 PROPN hvd.32044092008168 991 9 ) ) PUNCT hvd.32044092008168 991 10 * * PUNCT hvd.32044092008168 992 1 [ [ X hvd.32044092008168 992 2 4 4 NUM hvd.32044092008168 992 3 4 4 NUM hvd.32044092008168 992 4 + + NUM hvd.32044092008168 992 5 27 27 NUM hvd.32044092008168 992 6 4 4 NUM hvd.32044092008168 992 7 ] ] PUNCT hvd.32044092008168 992 8 and and CCONJ hvd.32044092008168 992 9 from from ADP hvd.32044092008168 992 10 ( ( PUNCT hvd.32044092008168 992 11 p. p. NOUN hvd.32044092008168 992 12 65 65 NUM hvd.32044092008168 992 13 ) ) PUNCT hvd.32044092008168 992 14 qy qy NOUN hvd.32044092008168 992 15 ( ( PUNCT hvd.32044092008168 992 16 38 38 NUM hvd.32044092008168 992 17 ? ? PUNCT hvd.32044092008168 993 1 + + CCONJ hvd.32044092008168 993 2 a a X hvd.32044092008168 993 3 ) ) PUNCT hvd.32044092008168 993 4 6 6 NUM hvd.32044092008168 993 5 a a PRON hvd.32044092008168 993 6 , , PUNCT hvd.32044092008168 993 7 s2 s2 PROPN hvd.32044092008168 994 1 + + NUM hvd.32044092008168 994 2 9 9 NUM hvd.32044092008168 994 3 a a PRON hvd.32044092008168 994 4 , , PUNCT hvd.32044092008168 994 5 s s NOUN hvd.32044092008168 994 6 – – PUNCT hvd.32044092008168 994 7 4 4 NUM hvd.32044092008168 994 8 12 12 NUM hvd.32044092008168 994 9 ) ) PUNCT hvd.32044092008168 994 10 4 4 NUM hvd.32044092008168 994 11 + + NUM hvd.32044092008168 994 12 9(2a 9(2a NUM hvd.32044092008168 994 13 , , PUNCT hvd.32044092008168 994 14 s s VERB hvd.32044092008168 994 15 3 3 NUM hvd.32044092008168 994 16 ag ag PROPN hvd.32044092008168 994 17 ) ) PUNCT hvd.32044092008168 994 18 ( ( PUNCT hvd.32044092008168 994 19 s8 s8 NOUN hvd.32044092008168 994 20 + + CCONJ hvd.32044092008168 994 21 4,8 4,8 NUM hvd.32044092008168 994 22 + + NUM hvd.32044092008168 994 23 43 43 NUM hvd.32044092008168 994 24 ) ) PUNCT hvd.32044092008168 994 25 3 3 NUM hvd.32044092008168 994 26 3 3 NUM hvd.32044092008168 994 27 a2s a2s NOUN hvd.32044092008168 994 28 ( ( PUNCT hvd.32044092008168 994 29 4 4 NUM hvd.32044092008168 994 30 + + NUM hvd.32044092008168 994 31 27 27 NUM hvd.32044092008168 994 32 a a PRON hvd.32044092008168 994 33 ) ) PUNCT hvd.32044092008168 994 34 and and CCONJ hvd.32044092008168 994 35 a a DET hvd.32044092008168 994 36 comparison comparison NOUN hvd.32044092008168 994 37 gives give VERB hvd.32044092008168 994 38 immediately immediately ADV hvd.32044092008168 994 39 1 1 NUM hvd.32044092008168 994 40 ( ( PUNCT hvd.32044092008168 994 41 132 132 NUM hvd.32044092008168 994 42 ] ] PUNCT hvd.32044092008168 994 43 ( ( PUNCT hvd.32044092008168 994 44 15 15 X hvd.32044092008168 994 45 ) ) PUNCT hvd.32044092008168 994 46 the the DET hvd.32044092008168 994 47 other other ADJ hvd.32044092008168 994 48 values value NOUN hvd.32044092008168 994 49 for for ADP hvd.32044092008168 994 50 the the DET hvd.32044092008168 994 51 eliments eliment NOUN hvd.32044092008168 994 52 have have AUX hvd.32044092008168 994 53 been be AUX hvd.32044092008168 994 54 found find VERB hvd.32044092008168 994 55 , , PUNCT hvd.32044092008168 994 56 namely namely ADV hvd.32044092008168 994 57 : : PUNCT hvd.32044092008168 994 58 yn=3 yn=3 NUM hvd.32044092008168 994 59 2 2 NUM hvd.32044092008168 994 60 3 3 NUM hvd.32044092008168 994 61 2 2 NUM hvd.32044092008168 994 62 r r NOUN hvd.32044092008168 994 63 3 3 NUM hvd.32044092008168 994 64 2 2 NUM hvd.32044092008168 994 65 1 1 NUM hvd.32044092008168 994 66 с с X hvd.32044092008168 994 67 p=0 p=0 PROPN hvd.32044092008168 994 68 o'= o'= NUM hvd.32044092008168 994 69 1262 1262 NUM hvd.32044092008168 994 70 15 15 NUM hvd.32044092008168 994 71 92 92 NUM hvd.32044092008168 994 72 1 1 NUM hvd.32044092008168 994 73 p p NOUN hvd.32044092008168 994 74 156 156 NUM hvd.32044092008168 994 75 1 1 NUM hvd.32044092008168 994 76 4 4 NUM hvd.32044092008168 994 77 7 7 NUM hvd.32044092008168 994 78 30 30 NUM hvd.32044092008168 994 79 3 3 NUM hvd.32044092008168 994 80 a,= a,= PROPN hvd.32044092008168 994 81 = = NOUN hvd.32044092008168 995 1 a a DET hvd.32044092008168 995 2 = = NOUN hvd.32044092008168 995 3 19 19 NUM hvd.32044092008168 995 4 – – PUNCT hvd.32044092008168 995 5 bo bo NOUN hvd.32044092008168 995 6 ' ' NUM hvd.32044092008168 995 7 463 463 NUM hvd.32044092008168 995 8 3 3 NUM hvd.32044092008168 995 9 -92 -92 SYM hvd.32044092008168 995 10 a a DET hvd.32044092008168 995 11 4 4 NUM hvd.32044092008168 995 12 2 2 NUM hvd.32044092008168 995 13 b b NOUN hvd.32044092008168 995 14 = = NOUN hvd.32044092008168 995 15 , , PUNCT hvd.32044092008168 995 16 = = X hvd.32044092008168 995 17 b=9 b=9 ADP hvd.32044092008168 995 18 o o NOUN hvd.32044092008168 995 19 ' ' PUNCT hvd.32044092008168 995 20 6bg 6bg PROPN hvd.32044092008168 995 21 ' ' PART hvd.32044092008168 995 22 9 9 NUM hvd.32044092008168 995 23 27 27 NUM hvd.32044092008168 995 24 99 99 NUM hvd.32044092008168 995 25 b92 b92 NOUN hvd.32044092008168 995 26 — — PUNCT hvd.32044092008168 995 27 93 93 NUM hvd.32044092008168 995 28 ba ba NOUN hvd.32044092008168 995 29 4 4 NUM hvd.32044092008168 995 30 4 4 NUM hvd.32044092008168 995 31 93 93 NUM hvd.32044092008168 995 32 we we PRON hvd.32044092008168 995 33 have have VERB hvd.32044092008168 995 34 then then ADV hvd.32044092008168 995 35 for for ADP hvd.32044092008168 995 36 n n NOUN hvd.32044092008168 995 37 equals equal VERB hvd.32044092008168 995 38 three three NUM hvd.32044092008168 995 39 va va X hvd.32044092008168 995 40 [ [ X hvd.32044092008168 995 41 133 133 NUM hvd.32044092008168 995 42 ] ] PUNCT hvd.32044092008168 995 43 q q NOUN hvd.32044092008168 995 44 ( ( PUNCT hvd.32044092008168 995 45 15 15 NUM hvd.32044092008168 995 46 ) ) PUNCT hvd.32044092008168 995 47 1/(15)9 1/(15)9 NUM hvd.32044092008168 995 48 ( ( PUNCT hvd.32044092008168 995 49 4 4 NUM hvd.32044092008168 995 50 a3 a3 NOUN hvd.32044092008168 995 51 + + NUM hvd.32044092008168 995 52 274 274 NUM hvd.32044092008168 995 53 ) ) PUNCT hvd.32044092008168 995 54 ) ) PUNCT hvd.32044092008168 996 1 + + CCONJ hvd.32044092008168 997 1 p p NOUN hvd.32044092008168 997 2 ( ( PUNCT hvd.32044092008168 997 3 15)3 15)3 NUM hvd.32044092008168 997 4 39 39 NUM hvd.32044092008168 997 5 ' ' NUM hvd.32044092008168 997 6 v v NOUN hvd.32044092008168 997 7 -2 -2 PROPN hvd.32044092008168 997 8 c2b c2b PROPN hvd.32044092008168 997 9 . . PROPN hvd.32044092008168 997 10 156 156 NUM hvd.32044092008168 997 11 0 0 NUM hvd.32044092008168 997 12 3 3 NUM hvd.32044092008168 997 13 2 2 NUM hvd.32044092008168 997 14 v v NUM hvd.32044092008168 997 15 44 44 NUM hvd.32044092008168 997 16 % % NOUN hvd.32044092008168 997 17 + + NUM hvd.32044092008168 997 18 2743 2743 NUM hvd.32044092008168 997 19 ( ( PUNCT hvd.32044092008168 997 20 compair compair NOUN hvd.32044092008168 997 21 109 109 NUM hvd.32044092008168 997 22 , , PUNCT hvd.32044092008168 997 23 p. p. NOUN hvd.32044092008168 997 24 59 59 NUM hvd.32044092008168 997 25 . . PUNCT hvd.32044092008168 997 26 ) ) PUNCT hvd.32044092008168 998 1 3 3 NUM hvd.32044092008168 998 2 ф ф NOUN hvd.32044092008168 998 3 1 1 NUM hvd.32044092008168 998 4 3 3 NUM hvd.32044092008168 998 5 1 1 NUM hvd.32044092008168 998 6 19"+ 19"+ NUM hvd.32044092008168 998 7 2792 2792 NUM hvd.32044092008168 998 8 ( ( PUNCT hvd.32044092008168 998 9 2 2 NUM hvd.32044092008168 998 10 8(27)b90 8(27)b90 NUM hvd.32044092008168 998 11 ' ' PART hvd.32044092008168 998 12 + + NUM hvd.32044092008168 998 13 16(27)629 16(27)629 NUM hvd.32044092008168 998 14 b b NOUN hvd.32044092008168 998 15 myny myny NOUN hvd.32044092008168 998 16 60 60 NUM hvd.32044092008168 998 17 ' ' PUNCT hvd.32044092008168 998 18 squaring squaring NOUN hvd.32044092008168 998 19 we we PRON hvd.32044092008168 998 20 have have VERB hvd.32044092008168 998 21 : : PUNCT hvd.32044092008168 998 22 reduction reduction NOUN hvd.32044092008168 998 23 of of ADP hvd.32044092008168 998 24 the the DET hvd.32044092008168 998 25 forms form NOUN hvd.32044092008168 998 26 when when SCONJ hvd.32044092008168 998 27 n n SYM hvd.32044092008168 998 28 equals equal VERB hvd.32044092008168 998 29 three three NUM hvd.32044092008168 998 30 . . PUNCT hvd.32044092008168 999 1 69 69 NUM hvd.32044092008168 999 2 for for ADP hvd.32044092008168 999 3 tere tere PROPN hvd.32044092008168 999 4 t t PROPN hvd.32044092008168 999 5 tea tea NOUN hvd.32044092008168 999 6 miss miss VERB hvd.32044092008168 999 7 e e X hvd.32044092008168 1000 1 [ [ X hvd.32044092008168 1000 2 134 134 NUM hvd.32044092008168 1000 3 ] ] PUNCT hvd.32044092008168 1000 4 . . PUNCT hvd.32044092008168 1001 1 [ [ X hvd.32044092008168 1001 2 135 135 NUM hvd.32044092008168 1001 3 ] ] PUNCT hvd.32044092008168 1001 4 . . PUNCT hvd.32044092008168 1002 1 whence whence NOUN hvd.32044092008168 1002 2 [ [ X hvd.32044092008168 1002 3 [ [ X hvd.32044092008168 1002 4 136 136 NUM hvd.32044092008168 1002 5 ] ] PUNCT hvd.32044092008168 1002 6 pv pv ADP hvd.32044092008168 1002 7 — — PUNCT hvd.32044092008168 1002 8 b b X hvd.32044092008168 1002 9 [ [ X hvd.32044092008168 1002 10 138 138 NUM hvd.32044092008168 1002 11 ] ] PUNCT hvd.32044092008168 1002 12 whence whence NOUN hvd.32044092008168 1002 13 [ [ X hvd.32044092008168 1002 14 137 137 NUM hvd.32044092008168 1002 15 ] ] PUNCT hvd.32044092008168 1003 1 pv pv ADP hvd.32044092008168 1003 2 again again ADV hvd.32044092008168 1003 3 we we PRON hvd.32044092008168 1003 4 have have VERB hvd.32044092008168 1003 5 : : PUNCT hvd.32044092008168 1003 6 qy2 qy2 PROPN hvd.32044092008168 1003 7 cpb cpb PROPN hvd.32044092008168 1003 8 x² x² PROPN hvd.32044092008168 1003 9 where where SCONJ hvd.32044092008168 1003 10 pv pv ADV hvd.32044092008168 1003 11 ― ― X hvd.32044092008168 1003 12 pv pv ADP hvd.32044092008168 1003 13 = = PUNCT hvd.32044092008168 1003 14 writing write VERB hvd.32044092008168 1003 15 ዎ ዎ DET hvd.32044092008168 1003 16 272 272 NUM hvd.32044092008168 1003 17 108b 108b NOUN hvd.32044092008168 1003 18 ❤ ❤ SPACE hvd.32044092008168 1003 19 ❤ ❤ PUNCT hvd.32044092008168 1003 20 = = PUNCT hvd.32044092008168 1003 21 = = PUNCT hvd.32044092008168 1003 22 ' ' NUM hvd.32044092008168 1003 23 3 3 NUM hvd.32044092008168 1003 24 1 1 NUM hvd.32044092008168 1003 25 3 3 NUM hvd.32044092008168 1003 26 3 3 NUM hvd.32044092008168 1003 27 2 2 NUM hvd.32044092008168 1003 28 4(36² 4(36² NUM hvd.32044092008168 1003 29 — — PUNCT hvd.32044092008168 1003 30 — — PUNCT hvd.32044092008168 1003 31 92)³ 92)³ NUM hvd.32044092008168 1003 32 + + NUM hvd.32044092008168 1003 33 27 27 NUM hvd.32044092008168 1003 34 ( ( PUNCT hvd.32044092008168 1003 35 116³ 116³ NUM hvd.32044092008168 1003 36 — — PUNCT hvd.32044092008168 1003 37 — — PUNCT hvd.32044092008168 1003 38 bg bg INTJ hvd.32044092008168 1003 39 . . PUNCT hvd.32044092008168 1004 1 + + NUM hvd.32044092008168 1005 1 193)² 193)² NOUN hvd.32044092008168 1006 1 -4 -4 X hvd.32044092008168 1006 2 4 4 NUM hvd.32044092008168 1006 3 . . SYM hvd.32044092008168 1006 4 4 4 NUM hvd.32044092008168 1006 5 / / SYM hvd.32044092008168 1006 6 4 4 NUM hvd.32044092008168 1006 7 ( ( PUNCT hvd.32044092008168 1006 8 1² 1² NUM hvd.32044092008168 1006 9 — — PUNCT hvd.32044092008168 1006 10 a₁)³ a₁)³ X hvd.32044092008168 1007 1 + + PROPN hvd.32044092008168 1007 2 ( ( PUNCT hvd.32044092008168 1007 3 1163 1163 NUM hvd.32044092008168 1007 4 9a 9a NUM hvd.32044092008168 1007 5 , , PUNCT hvd.32044092008168 1007 6 b,—b)2 b,—b)2 PROPN hvd.32044092008168 1007 7 361(13 361(13 NUM hvd.32044092008168 1007 8 - - PUNCT hvd.32044092008168 1007 9 a)2 a)2 NOUN hvd.32044092008168 1007 10 $ $ SYM hvd.32044092008168 1007 11 ( ( PUNCT hvd.32044092008168 1007 12 1 1 NUM hvd.32044092008168 1007 13 ) ) PUNCT hvd.32044092008168 1007 14 361 361 NUM hvd.32044092008168 1007 15 ( ( PUNCT hvd.32044092008168 1007 16 1a 1a NUM hvd.32044092008168 1007 17 ) ) PUNCT hvd.32044092008168 1007 18 " " PUNCT hvd.32044092008168 1007 19 φ φ PROPN hvd.32044092008168 1007 20 , , PUNCT hvd.32044092008168 1007 21 φ φ PROPN hvd.32044092008168 1007 22 . . PUNCT hvd.32044092008168 1007 23 φ φ PROPN hvd.32044092008168 1007 24 . . PROPN hvd.32044092008168 1007 25 1 1 NUM hvd.32044092008168 1007 26 3 3 NUM hvd.32044092008168 1007 27 367 367 NUM hvd.32044092008168 1007 28 ( ( PUNCT hvd.32044092008168 1007 29 la la ADV hvd.32044092008168 1007 30 ) ) PUNCT hvd.32044092008168 1007 31 pv pv ADP hvd.32044092008168 1007 32 = = X hvd.32044092008168 1007 33 = = X hvd.32044092008168 1007 34 = = X hvd.32044092008168 1007 35 ― ― PUNCT hvd.32044092008168 1007 36 ' ' NUM hvd.32044092008168 1007 37 3279² 3279² NUM hvd.32044092008168 1007 38 108bqo 108bqo NUM hvd.32044092008168 1007 39 ' ' PART hvd.32044092008168 1007 40 36bq 36bq NOUN hvd.32044092008168 1007 41 2 2 NUM hvd.32044092008168 1007 42 1 1 NUM hvd.32044092008168 1007 43 2 2 NUM hvd.32044092008168 1007 44 36b 36b NOUN hvd.32044092008168 1007 45 ( ( PUNCT hvd.32044092008168 1007 46 30 30 NUM hvd.32044092008168 1007 47 — — PUNCT hvd.32044092008168 1007 48 — — PUNCT hvd.32044092008168 1007 49 92 92 NUM hvd.32044092008168 1007 50 ) ) PUNCT hvd.32044092008168 1007 51 * * PUNCT hvd.32044092008168 1007 52 1 1 NUM hvd.32044092008168 1007 53 9 9 NUM hvd.32044092008168 1007 54 4[4 4[4 NUM hvd.32044092008168 1007 55 43 43 NUM hvd.32044092008168 1008 1 + + NUM hvd.32044092008168 1008 2 2743 2743 NUM hvd.32044092008168 1008 3 ] ] PUNCT hvd.32044092008168 1008 4 , , PUNCT hvd.32044092008168 1008 5 4(† 4(† NUM hvd.32044092008168 1008 6 9 9 NUM hvd.32044092008168 1008 7 — — PUNCT hvd.32044092008168 1008 8 6 6 NUM hvd.32044092008168 1008 9 b b NOUN hvd.32044092008168 1008 10 4 4 NUM hvd.32044092008168 1008 11 + + NUM hvd.32044092008168 1008 12 99'2b 99'2b NUM hvd.32044092008168 1008 13 39 39 NUM hvd.32044092008168 1008 14 = = SYM hvd.32044092008168 1008 15 ω ω PROPN hvd.32044092008168 1009 1 2b 2b NUM hvd.32044092008168 1009 2 , , PUNCT hvd.32044092008168 1009 3 bo bo PROPN hvd.32044092008168 1009 4 ――― ――― PROPN hvd.32044092008168 1009 5 ' ' NUM hvd.32044092008168 1009 6 3 3 NUM hvd.32044092008168 1009 7 2 2 NUM hvd.32044092008168 1009 8 4 4 NUM hvd.32044092008168 1009 9 [ [ X hvd.32044092008168 1009 10 1 1 NUM hvd.32044092008168 1009 11 , , PUNCT hvd.32044092008168 1009 12 9'³ 9'³ NUM hvd.32044092008168 1009 13 + + NUM hvd.32044092008168 1009 14 27 27 NUM hvd.32044092008168 1009 15 ( ( PUNCT hvd.32044092008168 1009 16 17 17 NUM hvd.32044092008168 1009 17 , , PUNCT hvd.32044092008168 1009 18 9² 9² NUM hvd.32044092008168 1009 19 1 1 NUM hvd.32044092008168 1009 20 bq bq X hvd.32044092008168 1009 21 q q X hvd.32044092008168 1009 22 ' ' PUNCT hvd.32044092008168 1009 23 + + CCONJ hvd.32044092008168 1009 24 b² b² PROPN hvd.32044092008168 1009 25 q q X hvd.32044092008168 1009 26 ' ' NUM hvd.32044092008168 1009 27 ³ ³ PROPN hvd.32044092008168 1009 28 ) ) PUNCT hvd.32044092008168 1009 29 ] ] PUNCT hvd.32044092008168 1010 1 + + CCONJ hvd.32044092008168 1010 2 10 10 NUM hvd.32044092008168 1010 3 ° ° X hvd.32044092008168 1010 4 q q X hvd.32044092008168 1010 5 q′b q′b NOUN hvd.32044092008168 1010 6 — — PUNCT hvd.32044092008168 1010 7 72b² 72b² NUM hvd.32044092008168 1010 8 q¹² q¹² PROPN hvd.32044092008168 1010 9 -16 -16 NUM hvd.32044092008168 1010 10 16 16 NUM hvd.32044092008168 1010 11 2 2 NUM hvd.32044092008168 1010 12 4 4 NUM hvd.32044092008168 1010 13 99'2b 99'2b NUM hvd.32044092008168 1010 14 q1 q1 NOUN hvd.32044092008168 1010 15 q2 q2 PROPN hvd.32044092008168 1010 16 q3 q3 PROPN hvd.32044092008168 1010 17 53627 53627 NUM hvd.32044092008168 1010 18 ( ( PUNCT hvd.32044092008168 1010 19 12 12 NUM hvd.32044092008168 1010 20 a₁)² a₁)² ADV hvd.32044092008168 1010 21 again again ADV hvd.32044092008168 1010 22 from from ADP hvd.32044092008168 1010 23 the the DET hvd.32044092008168 1010 24 first first ADJ hvd.32044092008168 1010 25 method method NOUN hvd.32044092008168 1010 26 1 1 NUM hvd.32044092008168 1010 27 + + CCONJ hvd.32044092008168 1010 28 k² k² PROPN hvd.32044092008168 1010 29 3 3 NUM hvd.32044092008168 1010 30 ――― ――― NOUN hvd.32044092008168 1010 31 = = SYM hvd.32044092008168 1010 32 b b PROPN hvd.32044092008168 1010 33 2n 2n NUM hvd.32044092008168 1010 34 and and CCONJ hvd.32044092008168 1010 35 ' ' PUNCT hvd.32044092008168 1010 36 in in ADP hvd.32044092008168 1010 37 terms term NOUN hvd.32044092008168 1010 38 of of ADP hvd.32044092008168 1010 39 99 99 NUM hvd.32044092008168 1010 40 and and CCONJ hvd.32044092008168 1010 41 b b X hvd.32044092008168 1010 42 we we PRON hvd.32044092008168 1010 43 have have VERB hvd.32044092008168 1010 44 : : PUNCT hvd.32044092008168 1010 45 € € SYM hvd.32044092008168 1010 46 172866 172866 NUM hvd.32044092008168 1010 47 . . PUNCT hvd.32044092008168 1011 1 432b¹g₂+ 432b¹g₂+ NUM hvd.32044092008168 1011 2 36b2g2 36b2g2 NUM hvd.32044092008168 1011 3 — — PUNCT hvd.32044092008168 1011 4 gå gå PROPN hvd.32044092008168 1011 5 36bo 36bo PROPN hvd.32044092008168 1011 6 43266 43266 NUM hvd.32044092008168 1011 7 - - SYM hvd.32044092008168 1011 8 216b¹g₂+27bg-216b³g 216b¹g₂+27bg-216b³g NUM hvd.32044092008168 1011 9 +27g3 +27g3 NOUN hvd.32044092008168 1011 10 + + NUM hvd.32044092008168 1011 11 549293b 549293b NUM hvd.32044092008168 1011 12 . . PUNCT hvd.32044092008168 1012 1 · · PUNCT hvd.32044092008168 1012 2 5184b6 5184b6 NUM hvd.32044092008168 1012 3 + + NUM hvd.32044092008168 1012 4 1728b¹g₂-108 1728b¹g₂-108 NUM hvd.32044092008168 1012 5 b² b² PROPN hvd.32044092008168 1012 6 g²+1296b³g g²+1296b³g PROPN hvd.32044092008168 1012 7 — — PUNCT hvd.32044092008168 1012 8 108bg29 108bg29 NUM hvd.32044092008168 1012 9 3 3 NUM hvd.32044092008168 1013 1 21606 21606 NUM hvd.32044092008168 1014 1 +2166*g₂ +2166*g₂ NOUN hvd.32044092008168 1014 2 + + CCONJ hvd.32044092008168 1014 3 1080b³g 1080b³g NUM hvd.32044092008168 1014 4 — — PUNCT hvd.32044092008168 1014 5 9b² 9b² NUM hvd.32044092008168 1014 6 gå gå PROPN hvd.32044092008168 1014 7 — — PUNCT hvd.32044092008168 1014 8 54b9 54b9 NUM hvd.32044092008168 1014 9 , , PUNCT hvd.32044092008168 1014 10 93 93 NUM hvd.32044092008168 1014 11 93 93 NUM hvd.32044092008168 1014 12 + + NUM hvd.32044092008168 1014 13 27 27 NUM hvd.32044092008168 1014 14 g g NOUN hvd.32044092008168 1014 15 36b 36b NOUN hvd.32044092008168 1015 1 ( ( PUNCT hvd.32044092008168 1015 2 144b24b²g 144b24b²g NUM hvd.32044092008168 1015 3 + + NUM hvd.32044092008168 1015 4 93)² 93)² NUM hvd.32044092008168 1015 5 . . NUM hvd.32044092008168 1015 6 12 12 NUM hvd.32044092008168 1015 7 = = NOUN hvd.32044092008168 1015 8 ―――― ―――― PROPN hvd.32044092008168 1015 9 pqr pqr PROPN hvd.32044092008168 1015 10 sd2 sd2 PROPN hvd.32044092008168 1015 11 3b 3b NUM hvd.32044092008168 1016 1 k2sn² k2sn² X hvd.32044092008168 1016 2 v v NOUN hvd.32044092008168 1016 3 ( ( PUNCT hvd.32044092008168 1016 4 compair compair NOUN hvd.32044092008168 1016 5 82 82 NUM hvd.32044092008168 1016 6 , , PUNCT hvd.32044092008168 1016 7 p. p. NOUN hvd.32044092008168 1016 8 49 49 NUM hvd.32044092008168 1016 9 . . PUNCT hvd.32044092008168 1016 10 ) ) PUNCT hvd.32044092008168 1016 11 etc etc X hvd.32044092008168 1016 12 . . X hvd.32044092008168 1016 13 * * PUNCT hvd.32044092008168 1016 14 ) ) PUNCT hvd.32044092008168 1016 15 2 2 NUM hvd.32044092008168 1016 16 ¥ ¥ SYM hvd.32044092008168 1016 17 = = SYM hvd.32044092008168 1016 18 5(3b)6 5(3b)6 NUM hvd.32044092008168 1016 19 + + NUM hvd.32044092008168 1016 20 6a 6a NUM hvd.32044092008168 1016 21 , , PUNCT hvd.32044092008168 1016 22 ( ( PUNCT hvd.32044092008168 1016 23 3b)¹ 3b)¹ NUM hvd.32044092008168 1016 24 — — PUNCT hvd.32044092008168 1016 25 10b 10b NUM hvd.32044092008168 1016 26 , , PUNCT hvd.32044092008168 1016 27 ( ( PUNCT hvd.32044092008168 1016 28 3b)³ 3b)³ NUM hvd.32044092008168 1016 29 — — PUNCT hvd.32044092008168 1016 30 3a² 3a² NUM hvd.32044092008168 1016 31 ( ( PUNCT hvd.32044092008168 1016 32 3b)²+6a 3b)²+6a NUM hvd.32044092008168 1016 33 , , PUNCT hvd.32044092008168 1016 34 b₁(3b)+b²−4a³ b₁(3b)+b²−4a³ NOUN hvd.32044092008168 1016 35 or or CCONJ hvd.32044092008168 1016 36 expanding expand VERB hvd.32044092008168 1016 37 we we PRON hvd.32044092008168 1016 38 again again ADV hvd.32044092008168 1016 39 obtain obtain VERB hvd.32044092008168 1016 40 2 2 NUM hvd.32044092008168 1016 41 2 2 NUM hvd.32044092008168 1016 42 2160b6 2160b6 NUM hvd.32044092008168 1016 43 + + NUM hvd.32044092008168 1016 44 216b¹g 216b¹g NUM hvd.32044092008168 1016 45 + + NUM hvd.32044092008168 1016 46 1080 1080 NUM hvd.32044092008168 1016 47 g g PROPN hvd.32044092008168 1016 48 , , PUNCT hvd.32044092008168 1016 49 b³ b³ PROPN hvd.32044092008168 1016 50 — — PUNCT hvd.32044092008168 1016 51 9b²g 9b²g NUM hvd.32044092008168 1016 52 — — PUNCT hvd.32044092008168 1016 53 5 5 NUM hvd.32044092008168 1016 54 4 4 NUM hvd.32044092008168 1016 55 b b ADP hvd.32044092008168 1016 56 j₂ j₂ PROPN hvd.32044092008168 1016 57 9 9 NUM hvd.32044092008168 1016 58 3 3 NUM hvd.32044092008168 1016 59 — — PUNCT hvd.32044092008168 1016 60 93 93 NUM hvd.32044092008168 1017 1 + + NUM hvd.32044092008168 1017 2 27g3 27g3 NUM hvd.32044092008168 1017 3 g g NOUN hvd.32044092008168 1017 4 2 2 NUM hvd.32044092008168 1017 5 g g NOUN hvd.32044092008168 1017 6 92 92 NUM hvd.32044092008168 1017 7 36b 36b NOUN hvd.32044092008168 1017 8 ( ( PUNCT hvd.32044092008168 1017 9 144b24b2g½ 144b24b2g½ NUM hvd.32044092008168 1018 1 + + CCONJ hvd.32044092008168 1018 2 g²)² g²)² NUM hvd.32044092008168 1018 3 2 2 NUM hvd.32044092008168 1018 4 9'32792 9'32792 NUM hvd.32044092008168 1019 1 108b36b2q 108b36b2q SPACE hvd.32044092008168 1019 2 ' ' PART hvd.32044092008168 1019 3 y y PROPN hvd.32044092008168 1019 4 ( ( PUNCT hvd.32044092008168 1019 5 3b 3b NUM hvd.32044092008168 1019 6 ) ) PUNCT hvd.32044092008168 1019 7 1086 1086 NUM hvd.32044092008168 1019 8 ( ( PUNCT hvd.32044092008168 1019 9 9ba₁)² 9ba₁)² NUM hvd.32044092008168 1019 10 * * SYM hvd.32044092008168 1019 11 ) ) PUNCT hvd.32044092008168 1019 12 compair compair PROPN hvd.32044092008168 1019 13 hermite hermite NOUN hvd.32044092008168 1019 14 where where SCONJ hvd.32044092008168 1019 15 p= p= PROPN hvd.32044092008168 1019 16 þ₁ þ₁ PROPN hvd.32044092008168 1019 17 , , PUNCT hvd.32044092008168 1019 18 q q X hvd.32044092008168 1019 19 = = NOUN hvd.32044092008168 1019 20 q₂ q₂ PROPN hvd.32044092008168 1019 21 , , PUNCT hvd.32044092008168 1019 22 r= r= PROPN hvd.32044092008168 1019 23 q3 q3 PROPN hvd.32044092008168 1019 24 , , PUNCT hvd.32044092008168 1019 25 s=361 s=361 NOUN hvd.32044092008168 1019 26 , , PUNCT hvd.32044092008168 1019 27 d d NOUN hvd.32044092008168 1019 28 = = PUNCT hvd.32044092008168 1019 29 ( ( PUNCT hvd.32044092008168 1019 30 1² 1² NUM hvd.32044092008168 1019 31 — — PUNCT hvd.32044092008168 1019 32 a a X hvd.32044092008168 1019 33 ) ) PUNCT hvd.32044092008168 1019 34 , , PUNCT hvd.32044092008168 1019 35 a a PRON hvd.32044092008168 1019 36 = = NOUN hvd.32044092008168 1019 37 a a PRON hvd.32044092008168 1019 38 , , NOUN hvd.32044092008168 1019 39 . . PUNCT hvd.32044092008168 1020 1 19 19 NUM hvd.32044092008168 1020 2 21 21 NUM hvd.32044092008168 1020 3 70 70 NUM hvd.32044092008168 1020 4 part part NOUN hvd.32044092008168 1020 5 v. v. ADP hvd.32044092008168 1020 6 it it PRON hvd.32044092008168 1020 7 is be AUX hvd.32044092008168 1020 8 , , PUNCT hvd.32044092008168 1020 9 finally finally ADV hvd.32044092008168 1020 10 , , PUNCT hvd.32044092008168 1020 11 evident evident ADJ hvd.32044092008168 1020 12 from from ADP hvd.32044092008168 1020 13 the the DET hvd.32044092008168 1020 14 general general ADJ hvd.32044092008168 1020 15 forms form NOUN hvd.32044092008168 1020 16 that that SCONJ hvd.32044092008168 1020 17 if if SCONJ hvd.32044092008168 1020 18 it it PRON hvd.32044092008168 1020 19 be be AUX hvd.32044092008168 1020 20 required require VERB hvd.32044092008168 1020 21 to to PART hvd.32044092008168 1020 22 determine determine VERB hvd.32044092008168 1020 23 p'v p'v PROPN hvd.32044092008168 1020 24 it it PRON hvd.32044092008168 1020 25 will will AUX hvd.32044092008168 1020 26 be be AUX hvd.32044092008168 1020 27 easier easy ADJ hvd.32044092008168 1020 28 first first ADV hvd.32044092008168 1020 29 to to PART hvd.32044092008168 1020 30 find find VERB hvd.32044092008168 1020 31 p'v p'v PROPN hvd.32044092008168 1020 32 b b PRON hvd.32044092008168 1020 33 bu bu NOUN hvd.32044092008168 1020 34 371 371 NUM hvd.32044092008168 1021 1 + + NUM hvd.32044092008168 1021 2 pv pv ADP hvd.32044092008168 1021 3 2 2 NUM hvd.32044092008168 1021 4 x x SYM hvd.32044092008168 1021 5 b. b. PROPN hvd.32044092008168 1021 6 v v PROPN hvd.32044092008168 1021 7 2n 2n PROPN hvd.32044092008168 1021 8 1 1 NUM hvd.32044092008168 1021 9 9 9 NUM hvd.32044092008168 1021 10 . . PUNCT hvd.32044092008168 1022 1 6 6 NUM hvd.32044092008168 1022 2 bo bo NOUN hvd.32044092008168 1022 3 ' ' PART hvd.32044092008168 1022 4 36 36 NUM hvd.32044092008168 1022 5 2bg 2bg PROPN hvd.32044092008168 1022 6 ' ' PUNCT hvd.32044092008168 1022 7 – – PUNCT hvd.32044092008168 1022 8 39 39 NUM hvd.32044092008168 1022 9 29 29 NUM hvd.32044092008168 1022 10 ' ' NUM hvd.32044092008168 1022 11 3 3 NUM hvd.32044092008168 1022 12 . . PUNCT hvd.32044092008168 1022 13 2 2 NUM hvd.32044092008168 1022 14 90 90 NUM hvd.32044092008168 1022 15 = = SYM hvd.32044092008168 1022 16 b b ADP hvd.32044092008168 1022 17 3 3 NUM hvd.32044092008168 1022 18 ф ф SYM hvd.32044092008168 1022 19 2 2 NUM hvd.32044092008168 1022 20 818 818 NUM hvd.32044092008168 1022 21 whence whence NOUN hvd.32044092008168 1022 22 3 3 NUM hvd.32044092008168 1022 23 p p NOUN hvd.32044092008168 1022 24 p'v= p'v= X hvd.32044092008168 1022 25 ( ( PUNCT hvd.32044092008168 1022 26 6 6 NUM hvd.32044092008168 1022 27 pv pv NOUN hvd.32044092008168 1022 28 ) ) PUNCT hvd.32044092008168 1022 29 2x 2x NUM hvd.32044092008168 1022 30 = = X hvd.32044092008168 1022 31 -{(pv -{(pv PROPN hvd.32044092008168 1022 32 b b NOUN hvd.32044092008168 1022 33 ) ) PUNCT hvd.32044092008168 1022 34 + + NUM hvd.32044092008168 1022 35 * * PUNCT hvd.32044092008168 1022 36 2 2 NUM hvd.32044092008168 1022 37 = = PUNCT hvd.32044092008168 1022 38 -p -p PUNCT hvd.32044092008168 1022 39 – – PUNCT hvd.32044092008168 1022 40 } } PUNCT hvd.32044092008168 1022 41 3 3 NUM hvd.32044092008168 1022 42 p p NOUN hvd.32044092008168 1022 43 2 2 NUM hvd.32044092008168 1022 44 q q NOUN hvd.32044092008168 1022 45 x x SYM hvd.32044092008168 1022 46 p p NOUN hvd.32044092008168 1022 47 162 162 NUM hvd.32044092008168 1022 48 οφφ΄ οφφ΄ NOUN hvd.32044092008168 1022 49 2702 2702 NUM hvd.32044092008168 1022 50 9'3 9'3 NUM hvd.32044092008168 1022 51 ' ' NUM hvd.32044092008168 1022 52 2 2 NUM hvd.32044092008168 1022 53 v8'3 v8'3 PROPN hvd.32044092008168 1022 54 + + CCONJ hvd.32044092008168 1022 55 27 27 NUM hvd.32044092008168 1022 56 g g NOUN hvd.32044092008168 1022 57 ? ? NOUN hvd.32044092008168 1022 58 216 216 NUM hvd.32044092008168 1022 59 690 690 NUM hvd.32044092008168 1022 60 ' ' PUNCT hvd.32044092008168 1022 61 + + NUM hvd.32044092008168 1022 62 432o 432o NUM hvd.32044092008168 1022 63 ' ' NOUN hvd.32044092008168 1022 64 ? ? PUNCT hvd.32044092008168 1022 65 108 108 NUM hvd.32044092008168 1022 66 9'37 9'37 NUM hvd.32044092008168 1022 67 determination determination NOUN hvd.32044092008168 1022 68 of of ADP hvd.32044092008168 1022 69 v. v. PROPN hvd.32044092008168 1022 70 third third ADJ hvd.32044092008168 1022 71 method method NOUN hvd.32044092008168 1022 72 . . PUNCT hvd.32044092008168 1023 1 the the DET hvd.32044092008168 1023 2 formulae formulae PROPN hvd.32044092008168 1023 3 may may AUX hvd.32044092008168 1023 4 be be AUX hvd.32044092008168 1023 5 obtained obtain VERB hvd.32044092008168 1023 6 by by ADP hvd.32044092008168 1023 7 a a DET hvd.32044092008168 1023 8 third third ADJ hvd.32044092008168 1023 9 method method NOUN hvd.32044092008168 1023 10 and and CCONJ hvd.32044092008168 1023 11 in in ADP hvd.32044092008168 1023 12 yet yet ADV hvd.32044092008168 1023 13 different different ADJ hvd.32044092008168 1023 14 forms form NOUN hvd.32044092008168 1023 15 as as SCONJ hvd.32044092008168 1023 16 follows follow VERB hvd.32044092008168 1023 17 : : PUNCT hvd.32044092008168 1023 18 starting start VERB hvd.32044092008168 1023 19 anew anew ADV hvd.32044092008168 1023 20 with with ADP hvd.32044092008168 1023 21 equation equation NOUN hvd.32044092008168 1023 22 [ [ X hvd.32044092008168 1023 23 110 110 NUM hvd.32044092008168 1023 24 ] ] PUNCT hvd.32044092008168 1023 25 we we PRON hvd.32044092008168 1023 26 write write VERB hvd.32044092008168 1023 27 a a DET hvd.32044092008168 1023 28 ) ) PUNCT hvd.32044092008168 1023 29 o(u o(u PROPN hvd.32044092008168 1023 30 b b NOUN hvd.32044092008168 1023 31 ) ) PUNCT hvd.32044092008168 1023 32 ... ... PUNCT hvd.32044092008168 1024 1 ( ( PUNCT hvd.32044092008168 1024 2 u u NOUN hvd.32044092008168 1024 3 + + CCONJ hvd.32044092008168 1024 4 v v NOUN hvd.32044092008168 1024 5 ) ) PUNCT hvd.32044092008168 1025 1 [ [ X hvd.32044092008168 1025 2 139 139 NUM hvd.32044092008168 1025 3 ] ] PUNCT hvd.32044092008168 1025 4 ( ( PUNCT hvd.32044092008168 1025 5 -1)"k -1)"k X hvd.32044092008168 1025 6 0(pu 0(pu NUM hvd.32044092008168 1025 7 ) ) PUNCT hvd.32044092008168 1025 8 – – PUNCT hvd.32044092008168 1025 9 ap'u ap'u NUM hvd.32044092008168 1025 10 ' ' PUNCT hvd.32044092008168 1025 11 ( ( PUNCT hvd.32044092008168 1025 12 pu pu PROPN hvd.32044092008168 1025 13 ) ) PUNCT hvd.32044092008168 1025 14 . . PUNCT hvd.32044092008168 1026 1 σασ σασ PROPN hvd.32044092008168 1026 2 . . PUNCT hvd.32044092008168 1027 1 also also ADV hvd.32044092008168 1027 2 ( ( PUNCT hvd.32044092008168 1027 3 u u PROPN hvd.32044092008168 1027 4 n n X hvd.32044092008168 1027 5 2c 2c NUM hvd.32044092008168 1027 6 ov(ou)+1 ov(ou)+1 NUM hvd.32044092008168 1027 7 force force NOUN hvd.32044092008168 1027 8 cas cas X hvd.32044092008168 1027 9 l_o l_o X hvd.32044092008168 1027 10 ) ) PUNCT hvd.32044092008168 1027 11 1 1 NUM hvd.32044092008168 1027 12 u=0 u=0 ADJ hvd.32044092008168 1027 13 whence whence NOUN hvd.32044092008168 1027 14 it it PRON hvd.32044092008168 1027 15 follows follow VERB hvd.32044092008168 1027 16 that that SCONJ hvd.32044092008168 1027 17 the the DET hvd.32044092008168 1027 18 left left ADJ hvd.32044092008168 1027 19 hand hand NOUN hvd.32044092008168 1027 20 member member NOUN hvd.32044092008168 1027 21 of of ADP hvd.32044092008168 1027 22 ( ( PUNCT hvd.32044092008168 1027 23 139 139 NUM hvd.32044092008168 1027 24 ) ) PUNCT hvd.32044092008168 1027 25 depends depend VERB hvd.32044092008168 1027 26 for for ADP hvd.32044092008168 1027 27 its its PRON hvd.32044092008168 1027 28 value value NOUN hvd.32044092008168 1027 29 on on ADP hvd.32044092008168 1027 30 the the DET hvd.32044092008168 1027 31 terms term NOUN hvd.32044092008168 1027 32 ( ( PUNCT hvd.32044092008168 1027 33 -1)"k -1)"k X hvd.32044092008168 1027 34 n n X hvd.32044092008168 1027 35 ( ( PUNCT hvd.32044092008168 1027 36 u u PROPN hvd.32044092008168 1027 37 ) ) PUNCT hvd.32044092008168 1027 38 * * PUNCT hvd.32044092008168 1027 39 +1 +1 INTJ hvd.32044092008168 1028 1 but but CCONJ hvd.32044092008168 1028 2 we we PRON hvd.32044092008168 1028 3 have have AUX hvd.32044092008168 1028 4 again again ADV hvd.32044092008168 1028 5 ve ve VERB hvd.32044092008168 1028 6 buro buro PROPN hvd.32044092008168 1028 7 1 1 PROPN hvd.32044092008168 1028 8 u u PROPN hvd.32044092008168 1028 9 ki ki PROPN hvd.32044092008168 1029 1 whence whence NOUN hvd.32044092008168 1029 2 we we PRON hvd.32044092008168 1029 3 may may AUX hvd.32044092008168 1029 4 write write VERB hvd.32044092008168 1029 5 , , PUNCT hvd.32044092008168 1029 6 taking take VERB hvd.32044092008168 1029 7 n n CCONJ hvd.32044092008168 1029 8 odd odd ADJ hvd.32044092008168 1029 9 ( ( PUNCT hvd.32044092008168 1029 10 u u NOUN hvd.32044092008168 1029 11 + + NOUN hvd.32044092008168 1029 12 a) a) NOUN hvd.32044092008168 1029 13 ... ... PUNCT hvd.32044092008168 1030 1 (u (u PUNCT hvd.32044092008168 1031 1 + + CCONJ hvd.32044092008168 1031 2 v v X hvd.32044092008168 1031 3 ) ) PUNCT hvd.32044092008168 1031 4 ” " PUNCT hvd.32044092008168 1031 5 k k X hvd.32044092008168 1031 6 ( ( PUNCT hvd.32044092008168 1031 7 a a X hvd.32044092008168 1031 8 ) ) PUNCT hvd.32044092008168 1031 9 ( ( PUNCT hvd.32044092008168 1031 10 b b NOUN hvd.32044092008168 1031 11 ) ) PUNCT hvd.32044092008168 1031 12 ... ... PUNCT hvd.32044092008168 1031 13 6(v 6(v NUM hvd.32044092008168 1031 14 ) ) PUNCT hvd.32044092008168 1031 15 ( ( PUNCT hvd.32044092008168 1031 16 ou)"+1 ou)"+1 NOUN hvd.32044092008168 1031 17 o o NOUN hvd.32044092008168 1031 18 ) ) PUNCT hvd.32044092008168 1031 19 0 0 NUM hvd.32044092008168 1031 20 n n ADP hvd.32044092008168 1031 21 and and CCONJ hvd.32044092008168 1031 22 from from ADP hvd.32044092008168 1031 23 p. p. NOUN hvd.32044092008168 1031 24 66 66 NUM hvd.32044092008168 1032 1 [ [ PUNCT hvd.32044092008168 1032 2 ( ( PUNCT hvd.32044092008168 1032 3 1)^2 1)^2 NUM hvd.32044092008168 1032 4 ; ; PUNCT hvd.32044092008168 1032 5 del del PROPN hvd.32044092008168 1032 6 + + PROPN hvd.32044092008168 1032 7 6 6 NUM hvd.32044092008168 1032 8 unti unti ADV hvd.32044092008168 1032 9 u=0 u=0 NUM hvd.32044092008168 1033 1 bo bo PROPN hvd.32044092008168 1033 2 1 1 NUM hvd.32044092008168 1033 3 qy qy ADV hvd.32044092008168 1033 4 + + ADV hvd.32044092008168 1033 5 boy+ boy+ ADJ hvd.32044092008168 1033 6 unti unti ADV hvd.32044092008168 1033 7 n n SYM hvd.32044092008168 1033 8 c c X hvd.32044092008168 1033 9 that that PRON hvd.32044092008168 1033 10 is be AUX hvd.32044092008168 1033 11 n n ADP hvd.32044092008168 1033 12 being be AUX hvd.32044092008168 1033 13 odd odd ADJ hvd.32044092008168 1033 14 k k PROPN hvd.32044092008168 1033 15 = = SYM hvd.32044092008168 1033 16 b b X hvd.32044092008168 1033 17 .. .. PUNCT hvd.32044092008168 1033 18 and and CCONJ hvd.32044092008168 1033 19 a a DET hvd.32044092008168 1033 20 similar similar ADJ hvd.32044092008168 1033 21 investigation investigation NOUN hvd.32044092008168 1033 22 gives give VERB hvd.32044092008168 1033 23 n n ADP hvd.32044092008168 1033 24 being be AUX hvd.32044092008168 1033 25 even even ADV hvd.32044092008168 1033 26 pγ pγ NOUN hvd.32044092008168 1033 27 . . PUNCT hvd.32044092008168 1034 1 k k PROPN hvd.32044092008168 1034 2 с с PROPN hvd.32044092008168 1034 3 reduction reduction NOUN hvd.32044092008168 1034 4 of of ADP hvd.32044092008168 1034 5 the the DET hvd.32044092008168 1034 6 forms form NOUN hvd.32044092008168 1034 7 when when SCONJ hvd.32044092008168 1034 8 n n SYM hvd.32044092008168 1034 9 equals equal VERB hvd.32044092008168 1034 10 three three NUM hvd.32044092008168 1034 11 . . PUNCT hvd.32044092008168 1035 1 71 71 NUM hvd.32044092008168 1035 2 since since SCONJ hvd.32044092008168 1035 3 v= v= VERB hvd.32044092008168 1035 4 a a PRON hvd.32044092008168 1035 5 + + PROPN hvd.32044092008168 1035 6 b b NOUN hvd.32044092008168 1036 1 + + CCONJ hvd.32044092008168 1036 2 c c NOUN hvd.32044092008168 1036 3 we we PRON hvd.32044092008168 1036 4 may may AUX hvd.32044092008168 1036 5 write write VERB hvd.32044092008168 1036 6 e e PROPN hvd.32044092008168 1036 7 - - PROPN hvd.32044092008168 1036 8 a+u+c+ a+u+c+ PROPN hvd.32044092008168 1036 9 ... ... PUNCT hvd.32044092008168 1036 10 --")ni --")ni X hvd.32044092008168 1036 11 1 1 NUM hvd.32044092008168 1036 12 and and CCONJ hvd.32044092008168 1036 13 multiplying multiply VERB hvd.32044092008168 1036 14 by by ADP hvd.32044092008168 1036 15 this this DET hvd.32044092008168 1036 16 factor factor NOUN hvd.32044092008168 1036 17 we we PRON hvd.32044092008168 1036 18 can can AUX hvd.32044092008168 1036 19 separate separate VERB hvd.32044092008168 1036 20 the the DET hvd.32044092008168 1036 21 left left ADJ hvd.32044092008168 1036 22 hand hand NOUN hvd.32044092008168 1036 23 member member NOUN hvd.32044092008168 1036 24 into into ADP hvd.32044092008168 1036 25 factors factor NOUN hvd.32044092008168 1036 26 of of ADP hvd.32044092008168 1036 27 the the DET hvd.32044092008168 1036 28 form form NOUN hvd.32044092008168 1036 29 o(a o(a ADP hvd.32044092008168 1036 30 + + PROPN hvd.32044092008168 1036 31 u u NOUN hvd.32044092008168 1036 32 ) ) PUNCT hvd.32044092008168 1036 33 o o NOUN hvd.32044092008168 1036 34 , , PUNCT hvd.32044092008168 1036 35 a a DET hvd.32044092008168 1036 36 ( ( PUNCT hvd.32044092008168 1036 37 140 140 NUM hvd.32044092008168 1036 38 ] ] PUNCT hvd.32044092008168 1036 39 ani ani PROPN hvd.32044092008168 1036 40 = = PROPN hvd.32044092008168 1036 41 . . PUNCT hvd.32044092008168 1037 1 e e X hvd.32044092008168 1037 2 - - PUNCT hvd.32044092008168 1037 3 a a DET hvd.32044092008168 1037 4 би би X hvd.32044092008168 1037 5 ба ба ADP hvd.32044092008168 1037 6 6 6 NUM hvd.32044092008168 1037 7 a a PRON hvd.32044092008168 1037 8 for for ADP hvd.32044092008168 1037 9 u u PROPN hvd.32044092008168 1037 10 = = ADJ hvd.32044092008168 1037 11 w1 w1 NOUN hvd.32044092008168 1037 12 but but CCONJ hvd.32044092008168 1037 13 for for ADP hvd.32044092008168 1037 14 this this DET hvd.32044092008168 1037 15 value value NOUN hvd.32044092008168 1037 16 p'(w p'(w NOUN hvd.32044092008168 1037 17 ) ) PUNCT hvd.32044092008168 1037 18 = = PROPN hvd.32044092008168 1037 19 0 0 NUM hvd.32044092008168 1037 20 and and CCONJ hvd.32044092008168 1037 21 our our PRON hvd.32044092008168 1037 22 relation relation NOUN hvd.32044092008168 1037 23 becomes become VERB hvd.32044092008168 1037 24 p p PROPN hvd.32044092008168 1037 25 φ(φω φ(φω PROPN hvd.32044092008168 1037 26 , , PUNCT hvd.32044092008168 1037 27 ) ) PUNCT hvd.32044092008168 1037 28 φ(e φ(e SPACE hvd.32044092008168 1037 29 , , PUNCT hvd.32044092008168 1037 30 ) ) PUNCT hvd.32044092008168 1037 31 = = X hvd.32044092008168 1038 1 φ φ PROPN hvd.32044092008168 1038 2 . . PUNCT hvd.32044092008168 1039 1 k k PROPN hvd.32044092008168 1039 2 9 9 NUM hvd.32044092008168 1039 3 b b PROPN hvd.32044092008168 1039 4 9 9 NUM hvd.32044092008168 1039 5 , , PUNCT hvd.32044092008168 1039 6 ao ao PROPN hvd.32044092008168 1039 7 , , PUNCT hvd.32044092008168 1039 8 b b PROPN hvd.32044092008168 1039 9 o o X hvd.32044092008168 1039 10 aob aob PROPN hvd.32044092008168 1039 11 " " PUNCT hvd.32044092008168 1039 12 σν σν X hvd.32044092008168 1039 13 li li PROPN hvd.32044092008168 1039 14 σν σν PROPN hvd.32044092008168 1039 15 63 63 NUM hvd.32044092008168 1039 16 v v NOUN hvd.32044092008168 1039 17 03 03 NUM hvd.32044092008168 1039 18 ••• ••• PROPN hvd.32044092008168 1039 19 σν σν X hvd.32044092008168 1039 20 [ [ X hvd.32044092008168 1039 21 141 141 NUM hvd.32044092008168 1039 22 ] ] PUNCT hvd.32044092008168 1040 1 and and CCONJ hvd.32044092008168 1040 2 we we PRON hvd.32044092008168 1040 3 obtain obtain VERB hvd.32044092008168 1040 4 in in ADP hvd.32044092008168 1040 5 a a DET hvd.32044092008168 1040 6 similar similar ADJ hvd.32044092008168 1040 7 manner manner NOUN hvd.32044092008168 1040 8 k k X hvd.32044092008168 1040 9 0 0 NUM hvd.32044092008168 1040 10 , , PUNCT hvd.32044092008168 1040 11 a a DET hvd.32044092008168 1040 12 6 6 NUM hvd.32044092008168 1040 13 , , PUNCT hvd.32044092008168 1040 14 b b X hvd.32044092008168 1040 15 og og PROPN hvd.32044092008168 1040 16 v v NOUN hvd.32044092008168 1040 17 ( ( PUNCT hvd.32044092008168 1040 18 ) ) PUNCT hvd.32044092008168 1040 19 φ(pw φ(pw PROPN hvd.32044092008168 1040 20 , , PUNCT hvd.32044092008168 1040 21 ) ) PUNCT hvd.32044092008168 1040 22 = = X hvd.32044092008168 1040 23 φ(c φ(c PROPN hvd.32044092008168 1040 24 . . PUNCT hvd.32044092008168 1040 25 ) ) PUNCT hvd.32044092008168 1041 1 ( ( PUNCT hvd.32044092008168 1041 2 ) ) PUNCT hvd.32044092008168 1041 3 φ φ PROPN hvd.32044092008168 1041 4 , , PUNCT hvd.32044092008168 1041 5 σασή σασή PROPN hvd.32044092008168 1041 6 and and CCONJ hvd.32044092008168 1041 7 63 63 NUM hvd.32044092008168 1041 8 63 63 NUM hvd.32044092008168 1041 9 0 0 NUM hvd.32044092008168 1041 10 ( ( PUNCT hvd.32044092008168 1041 11 pw3 pw3 NOUN hvd.32044092008168 1041 12 ) ) PUNCT hvd.32044092008168 1041 13 φ(e φ(e SPACE hvd.32044092008168 1041 14 . . PUNCT hvd.32044092008168 1041 15 ) ) PUNCT hvd.32044092008168 1042 1 σασο σασο PROPN hvd.32044092008168 1042 2 recalling recall VERB hvd.32044092008168 1042 3 the the DET hvd.32044092008168 1042 4 known know VERB hvd.32044092008168 1042 5 relation relation NOUN hvd.32044092008168 1042 6 о о PROPN hvd.32044092008168 1042 7 , , PUNCT hvd.32044092008168 1042 8 иб иб PROPN hvd.32044092008168 1042 9 , , PUNCT hvd.32044092008168 1042 10 иб иб PROPN hvd.32044092008168 1042 11 , , PUNCT hvd.32044092008168 1042 12 и и ADP hvd.32044092008168 1042 13 2 2 NUM hvd.32044092008168 1042 14 p'r p'r X hvd.32044092008168 1042 15 = = PUNCT hvd.32044092008168 1042 16 63 63 NUM hvd.32044092008168 1042 17 u u NOUN hvd.32044092008168 1042 18 we we PRON hvd.32044092008168 1042 19 have have VERB hvd.32044092008168 1042 20 upon upon SCONJ hvd.32044092008168 1042 21 taking take VERB hvd.32044092008168 1042 22 the the DET hvd.32044092008168 1042 23 product product NOUN hvd.32044092008168 1042 24 of of ADP hvd.32044092008168 1042 25 the the DET hvd.32044092008168 1042 26 above above ADJ hvd.32044092008168 1042 27 equations equation NOUN hvd.32044092008168 1042 28 [ [ PUNCT hvd.32044092008168 1042 29 142 142 NUM hvd.32044092008168 1042 30 ] ] PUNCT hvd.32044092008168 1042 31 kp'ap'b kp'ap'b ADV hvd.32044092008168 1042 32 ... ... PUNCT hvd.32044092008168 1043 1 p'v=(2)"+1 p'v=(2)"+1 ADV hvd.32044092008168 1043 2 0,0,0 0,0,0 PUNCT hvd.32044092008168 1043 3 again again ADV hvd.32044092008168 1043 4 from from ADP hvd.32044092008168 1043 5 the the DET hvd.32044092008168 1043 6 relations relation NOUN hvd.32044092008168 1043 7 ( ( PUNCT hvd.32044092008168 1043 8 65 65 NUM hvd.32044092008168 1043 9 ) ) PUNCT hvd.32044092008168 1043 10 20 20 NUM hvd.32044092008168 1043 11 á á PROPN hvd.32044092008168 1043 12 etc etc X hvd.32044092008168 1043 13 . . X hvd.32044092008168 1044 1 ( ( PUNCT hvd.32044092008168 1044 2 a a DET hvd.32044092008168 1044 3 b b NOUN hvd.32044092008168 1044 4 ) ) PUNCT hvd.32044092008168 1044 5 ( ( PUNCT hvd.32044092008168 1044 6 a a DET hvd.32044092008168 1044 7 v v NOUN hvd.32044092008168 1044 8 ) ) PUNCT hvd.32044092008168 1044 9 ( ( PUNCT hvd.32044092008168 1044 10 a a DET hvd.32044092008168 1044 11 d d NOUN hvd.32044092008168 1044 12 ) ) PUNCT hvd.32044092008168 1044 13 to to ADP hvd.32044092008168 1044 14 n n CCONJ hvd.32044092008168 1044 15 terms term NOUN hvd.32044092008168 1044 16 and and CCONJ hvd.32044092008168 1044 17 we we PRON hvd.32044092008168 1044 18 obtain obtain VERB hvd.32044092008168 1044 19 the the DET hvd.32044092008168 1044 20 product product NOUN hvd.32044092008168 1044 21 ) ) PUNCT hvd.32044092008168 1045 1 [ [ X hvd.32044092008168 1045 2 143 143 NUM hvd.32044092008168 1045 3 ] ] PUNCT hvd.32044092008168 1045 4 a'b'y' a'b'y' PROPN hvd.32044092008168 1045 5 ... ... PUNCT hvd.32044092008168 1045 6 = = PROPN hvd.32044092008168 1045 7 2"c 2"c PROPN hvd.32044092008168 1045 8 " " PUNCT hvd.32044092008168 1045 9 – – PUNCT hvd.32044092008168 1045 10 1,1.2.- 1,1.2.- PROPN hvd.32044092008168 1045 11 * * PUNCT hvd.32044092008168 1045 12 — — PUNCT hvd.32044092008168 1045 13 1 1 X hvd.32044092008168 1045 14 ) ) PUNCT hvd.32044092008168 1045 15 = = X hvd.32044092008168 1045 16 ( ( PUNCT hvd.32044092008168 1045 17 – – PUNCT hvd.32044092008168 1045 18 1)£u 1)£u PROPN hvd.32044092008168 1045 19 ( ( PUNCT hvd.32044092008168 1045 20 n n CCONJ hvd.32044092008168 1045 21 − − NOUN hvd.32044092008168 1045 22 1)(2)"c 1)(2)"c NUM hvd.32044092008168 1045 23 " " PUNCT hvd.32044092008168 1046 1 [ [ X hvd.32044092008168 1046 2 ] ] X hvd.32044092008168 1046 3 ' ' PUNCT hvd.32044092008168 1046 4 . . PUNCT hvd.32044092008168 1046 5 " " PUNCT hvd.32044092008168 1047 1 ( ( PUNCT hvd.32044092008168 1047 2 ) ) PUNCT hvd.32044092008168 1047 3 ( ( PUNCT hvd.32044092008168 1047 4 a a DET hvd.32044092008168 1047 5 b)2 b)2 X hvd.32044092008168 1047 6 ( ( PUNCT hvd.32044092008168 1047 7 a a DET hvd.32044092008168 1047 8 y)2 y)2 NOUN hvd.32044092008168 1047 9 ( ( PUNCT hvd.32044092008168 1047 10 a a PRON hvd.32044092008168 1047 11 d d NOUN hvd.32044092008168 1047 12 ) ) PUNCT hvd.32044092008168 1047 13 ? ? PUNCT hvd.32044092008168 1047 14 ... ... PUNCT hvd.32044092008168 1048 1 ( ( PUNCT hvd.32044092008168 1048 2 b b X hvd.32044092008168 1048 3 ) ) PUNCT hvd.32044092008168 1048 4 2 2 NUM hvd.32044092008168 1048 5 ( ( PUNCT hvd.32044092008168 1048 6 b b X hvd.32044092008168 1048 7 – – PUNCT hvd.32044092008168 1048 8 d d NOUN hvd.32044092008168 1048 9 ) ) PUNCT hvd.32044092008168 1048 10 ... ... PUNCT hvd.32044092008168 1049 1 ( ( PUNCT hvd.32044092008168 1049 2 y y X hvd.32044092008168 1049 3 -d -d PUNCT hvd.32044092008168 1049 4 ) ) PUNCT hvd.32044092008168 1049 5 ? ? PUNCT hvd.32044092008168 1049 6 ... ... PUNCT hvd.32044092008168 1050 1 ( ( PUNCT hvd.32044092008168 1050 2 -1){n(n -1){n(n SPACE hvd.32044092008168 1050 3 — — PUNCT hvd.32044092008168 1050 4 1 1 X hvd.32044092008168 1050 5 ) ) PUNCT hvd.32044092008168 1050 6 ( ( PUNCT hvd.32044092008168 1050 7 2)"c 2)"c NUM hvd.32044092008168 1050 8 " " SYM hvd.32044092008168 1050 9 3 3 NUM hvd.32044092008168 1050 10 . . PUNCT hvd.32044092008168 1050 11 n n CCONJ hvd.32044092008168 1050 12 n n X hvd.32044092008168 1050 13 nn nn X hvd.32044092008168 1050 14 n n X hvd.32044092008168 1050 15 д д PROPN hvd.32044092008168 1050 16 1 1 NUM hvd.32044092008168 1050 17 1 1 NUM hvd.32044092008168 1050 18 n n CCONJ hvd.32044092008168 1050 19 n n NOUN hvd.32044092008168 1050 20 . . PUNCT hvd.32044092008168 1051 1 a a PRON hvd.32044092008168 1051 2 being be AUX hvd.32044092008168 1051 3 the the DET hvd.32044092008168 1051 4 discriminant discriminant NOUN hvd.32044092008168 1051 5 of of ADP hvd.32044092008168 1051 6 y. y. PROPN hvd.32044092008168 1051 7 substituting substitute VERB hvd.32044092008168 1051 8 this this DET hvd.32044092008168 1051 9 value value NOUN hvd.32044092008168 1051 10 in in ADP hvd.32044092008168 1051 11 [ [ X hvd.32044092008168 1051 12 142 142 NUM hvd.32044092008168 1051 13 ] ] PUNCT hvd.32044092008168 1051 14 we we PRON hvd.32044092008168 1051 15 derive derive VERB hvd.32044092008168 1051 16 [ [ PUNCT hvd.32044092008168 1051 17 144 144 NUM hvd.32044092008168 1051 18 ] ] PUNCT hvd.32044092008168 1051 19 ( ( PUNCT hvd.32044092008168 1051 20 1)ğmen–12 1)ğmen–12 NUM hvd.32044092008168 1051 21 " " PUNCT hvd.32044092008168 1051 22 cºp'v cºp'v NOUN hvd.32044092008168 1051 23 = = X hvd.32044092008168 1051 24 ( ( PUNCT hvd.32044092008168 1051 25 – – PUNCT hvd.32044092008168 1051 26 1)*+120,0,0,0 1)*+120,0,0,0 NUM hvd.32044092008168 1051 27 . . PUNCT hvd.32044092008168 1052 1 again again ADV hvd.32044092008168 1052 2 squaring square VERB hvd.32044092008168 1052 3 we we PRON hvd.32044092008168 1052 4 get get VERB hvd.32044092008168 1052 5 of of ADP hvd.32044092008168 1052 6 a a DET hvd.32044092008168 1052 7 ob ob X hvd.32044092008168 1052 8 ... ... SYM hvd.32044092008168 1052 9 0 0 NUM hvd.32044092008168 1052 10 22 22 NUM hvd.32044092008168 1052 11 0”(@)=(-1)"kº(pa 0”(@)=(-1)"kº(pa PROPN hvd.32044092008168 1052 12 – – PUNCT hvd.32044092008168 1052 13 e)(pb e)(pb NUM hvd.32044092008168 1052 14 – – PUNCT hvd.32044092008168 1052 15 en en ADJ hvd.32044092008168 1052 16 ) ) PUNCT hvd.32044092008168 1052 17 ... ... PUNCT hvd.32044092008168 1053 1 ( ( PUNCT hvd.32044092008168 1053 2 pv pv INTJ hvd.32044092008168 1053 3 — — PUNCT hvd.32044092008168 1053 4 e e X hvd.32044092008168 1053 5 ) ) PUNCT hvd.32044092008168 1053 6 σα σα PROPN hvd.32044092008168 1053 7 σου σου PROPN hvd.32044092008168 1053 8 . . PUNCT hvd.32044092008168 1054 1 or or CCONJ hvd.32044092008168 1054 2 ( ( PUNCT hvd.32044092008168 1054 3 see see VERB hvd.32044092008168 1054 4 [ [ X hvd.32044092008168 1054 5 89 89 NUM hvd.32044092008168 1054 6 ] ] PUNCT hvd.32044092008168 1054 7 ) ) PUNCT hvd.32044092008168 1055 1 [ [ X hvd.32044092008168 1055 2 145 145 NUM hvd.32044092008168 1055 3 ] ] PUNCT hvd.32044092008168 1055 4 · · PUNCT hvd.32044092008168 1055 5 ( ( PUNCT hvd.32044092008168 1055 6 -1)"k -1)"k PROPN hvd.32044092008168 1055 7 ? ? PUNCT hvd.32044092008168 1055 8 y(en y(en PROPN hvd.32044092008168 1055 9 ) ) PUNCT hvd.32044092008168 1055 10 ( ( PUNCT hvd.32044092008168 1055 11 pv pv ADP hvd.32044092008168 1055 12 – – PUNCT hvd.32044092008168 1055 13 e e NOUN hvd.32044092008168 1055 14 ) ) PUNCT hvd.32044092008168 1055 15 kề kề PROPN hvd.32044092008168 1055 16 04(e 04(e PROPN hvd.32044092008168 1055 17 ) ) PUNCT hvd.32044092008168 1055 18 and and CCONJ hvd.32044092008168 1055 19 we we PRON hvd.32044092008168 1055 20 have have VERB hvd.32044092008168 1055 21 also also ADV hvd.32044092008168 1055 22 the the DET hvd.32044092008168 1055 23 two two NUM hvd.32044092008168 1055 24 corresponding corresponding ADJ hvd.32044092008168 1055 25 expressions expression NOUN hvd.32044092008168 1055 26 . . PUNCT hvd.32044092008168 1056 1 62 62 NUM hvd.32044092008168 1056 2 v v NOUN hvd.32044092008168 1056 3 . . PUNCT hvd.32044092008168 1056 4 . . PUNCT hvd.32044092008168 1057 1 72 72 NUM hvd.32044092008168 1057 2 part part NOUN hvd.32044092008168 1057 3 v. v. ADP hvd.32044092008168 1057 4 . . PUNCT hvd.32044092008168 1058 1 02 02 NUM hvd.32044092008168 1058 2 . . PUNCT hvd.32044092008168 1059 1 : : PUNCT hvd.32044092008168 1059 2 2 2 NUM hvd.32044092008168 1059 3 we we PRON hvd.32044092008168 1059 4 have have AUX hvd.32044092008168 1059 5 shown show VERB hvd.32044092008168 1059 6 ( ( PUNCT hvd.32044092008168 1059 7 see see VERB hvd.32044092008168 1059 8 p. p. NOUN hvd.32044092008168 1059 9 58 58 NUM hvd.32044092008168 1059 10 ) ) PUNCT hvd.32044092008168 1060 1 that that SCONJ hvd.32044092008168 1060 2 when when SCONJ hvd.32044092008168 1060 3 t= t= PROPN hvd.32044092008168 1060 4 e e PROPN hvd.32044092008168 1060 5 , , PUNCT hvd.32044092008168 1060 6 we we PRON hvd.32044092008168 1060 7 have have VERB hvd.32044092008168 1060 8 ei ei PROPN hvd.32044092008168 1060 9 y(e y(e PROPN hvd.32044092008168 1060 10 ) ) PUNCT hvd.32044092008168 1060 11 = = PROPN hvd.32044092008168 1060 12 = = PUNCT hvd.32044092008168 1060 13 -cpq -cpq X hvd.32044092008168 1060 14 whence whence NOUN hvd.32044092008168 1060 15 it it PRON hvd.32044092008168 1060 16 follows follow VERB hvd.32044092008168 1060 17 from from ADP hvd.32044092008168 1060 18 this this PRON hvd.32044092008168 1060 19 and and CCONJ hvd.32044092008168 1060 20 relation relation NOUN hvd.32044092008168 1060 21 ( ( PUNCT hvd.32044092008168 1060 22 145 145 NUM hvd.32044092008168 1060 23 ) ) PUNCT hvd.32044092008168 1060 24 that that SCONJ hvd.32044092008168 1060 25 0(e 0(e NUM hvd.32044092008168 1060 26 ) ) PUNCT hvd.32044092008168 1060 27 is be AUX hvd.32044092008168 1060 28 divisable divisable ADJ hvd.32044092008168 1060 29 by by ADP hvd.32044092008168 1060 30 and and CCONJ hvd.32044092008168 1060 31 in in ADP hvd.32044092008168 1060 32 general general ADJ hvd.32044092008168 1060 33 ° ° PROPN hvd.32044092008168 1060 34 ( ( PUNCT hvd.32044092008168 1060 35 en en PROPN hvd.32044092008168 1060 36 ) ) PUNCT hvd.32044092008168 1060 37 by by ADP hvd.32044092008168 1060 38 qu qu PROPN hvd.32044092008168 1060 39 . . PUNCT hvd.32044092008168 1061 1 φ φ PROPN hvd.32044092008168 1061 2 ( ( PUNCT hvd.32044092008168 1061 3 , , PUNCT hvd.32044092008168 1061 4 ) ) PUNCT hvd.32044092008168 1061 5 qi qi PROPN hvd.32044092008168 1061 6 0 0 X hvd.32044092008168 1061 7 ) ) PUNCT hvd.32044092008168 1061 8 we we PRON hvd.32044092008168 1061 9 thus thus ADV hvd.32044092008168 1061 10 derive derive VERB hvd.32044092008168 1061 11 the the DET hvd.32044092008168 1061 12 relations relation NOUN hvd.32044092008168 1061 13 [ [ X hvd.32044092008168 1061 14 146 146 NUM hvd.32044092008168 1061 15 ] ] PUNCT hvd.32044092008168 1061 16 0,= 0,= NUM hvd.32044092008168 1061 17 q.f q.f PROPN hvd.32044092008168 1061 18 q.f q.f PROPN hvd.32044092008168 1061 19 : : PUNCT hvd.32044092008168 1061 20 0 0 NUM hvd.32044092008168 1061 21 , , PUNCT hvd.32044092008168 1061 22 q.f q.f PROPN hvd.32044092008168 1061 23 , , PUNCT hvd.32044092008168 1061 24 : : PUNCT hvd.32044092008168 1061 25 : : PUNCT hvd.32044092008168 1061 26 ф ф X hvd.32044092008168 1061 27 . . PUNCT hvd.32044092008168 1062 1 23 23 NUM hvd.32044092008168 1062 2 f3 f3 PROPN hvd.32044092008168 1062 3 . . PUNCT hvd.32044092008168 1063 1 we we PRON hvd.32044092008168 1063 2 have have AUX hvd.32044092008168 1063 3 also also ADV hvd.32044092008168 1063 4 found find VERB hvd.32044092008168 1063 5 n n ADP hvd.32044092008168 1063 6 being be AUX hvd.32044092008168 1063 7 odd odd ADJ hvd.32044092008168 1063 8 : : PUNCT hvd.32044092008168 1063 9 n-3 n-3 PROPN hvd.32044092008168 1063 10 ) ) PUNCT hvd.32044092008168 1063 11 k k PROPN hvd.32044092008168 1063 12 b.:(= b.:(= PROPN hvd.32044092008168 1063 13 vpq vpq PROPN hvd.32044092008168 1063 14 : : PUNCT hvd.32044092008168 1063 15 a=(-1)7c2n–3 a=(-1)7c2n–3 PROPN hvd.32044092008168 1063 16 pz pz PROPN hvd.32044092008168 1063 17 ( ( PUNCT hvd.32044092008168 1063 18 a a PRON hvd.32044092008168 1063 19 – – PUNCT hvd.32044092008168 1063 20 ? ? PUNCT hvd.32044092008168 1063 21 . . PUNCT hvd.32044092008168 1064 1 ( ( PUNCT hvd.32044092008168 1064 2 -1 -1 X hvd.32044092008168 1064 3 ) ) PUNCT hvd.32044092008168 1064 4 qzony(g qzony(g PROPN hvd.32044092008168 1064 5 ) ) PUNCT hvd.32044092008168 1064 6 cpqi cpqi VERB hvd.32044092008168 1064 7 these these DET hvd.32044092008168 1064 8 values value NOUN hvd.32044092008168 1064 9 in in ADP hvd.32044092008168 1064 10 [ [ PUNCT hvd.32044092008168 1064 11 144 144 NUM hvd.32044092008168 1064 12 ] ] PUNCT hvd.32044092008168 1064 13 give give VERB hvd.32044092008168 1064 14 n-1 n-1 NOUN hvd.32044092008168 1064 15 1 1 NUM hvd.32044092008168 1064 16 1 1 NUM hvd.32044092008168 1064 17 ( ( PUNCT hvd.32044092008168 1064 18 1 1 NUM hvd.32044092008168 1064 19 ) ) PUNCT hvd.32044092008168 1064 20 3 3 NUM hvd.32044092008168 1064 21 n n CCONJ hvd.32044092008168 1064 22 n n X hvd.32044092008168 1064 23 ( ( PUNCT hvd.32044092008168 1064 24 n-1 n-1 NOUN hvd.32044092008168 1064 25 ) ) PUNCT hvd.32044092008168 1064 26 n n CCONJ hvd.32044092008168 1064 27 ) ) PUNCT hvd.32044092008168 1064 28 b3c2n b3c2n X hvd.32044092008168 1065 1 p2 p2 PROPN hvd.32044092008168 1065 2 qp'v qp'v PROPN hvd.32044092008168 1065 3 ( ( PUNCT hvd.32044092008168 1065 4 -15 -15 NUM hvd.32044092008168 1065 5 > > SYM hvd.32044092008168 1065 6 --(-1,6 --(-1,6 SPACE hvd.32044092008168 1065 7 + + PROPN hvd.32044092008168 1065 8 0+*3 0+*3 NUM hvd.32044092008168 1065 9 * * PUNCT hvd.32044092008168 1065 10 2 2 NUM hvd.32044092008168 1065 11 * * NUM hvd.32044092008168 1065 12 3–1 3–1 NUM hvd.32044092008168 1065 13 pro-*-"qf pro-*-"qf NOUN hvd.32044092008168 1065 14 , , PUNCT hvd.32044092008168 1065 15 e e PROPN hvd.32044092008168 1065 16 , , PUNCT hvd.32044092008168 1065 17 f f PROPN hvd.32044092008168 1065 18 , , PUNCT hvd.32044092008168 1065 19 -3 -3 PROPN hvd.32044092008168 1065 20 1 1 NUM hvd.32044092008168 1065 21 ( ( PUNCT hvd.32044092008168 1065 22 n n X hvd.32044092008168 1065 23 ) ) PUNCT hvd.32044092008168 1065 24 n-1 n-1 NUM hvd.32044092008168 1065 25 2 2 NUM hvd.32044092008168 1065 26 ( ( PUNCT hvd.32044092008168 1065 27 n n X hvd.32044092008168 1065 28 in in ADP hvd.32044092008168 1065 29 ) ) PUNCT hvd.32044092008168 1065 30 = = PROPN hvd.32044092008168 1065 31 -1)(19 -1)(19 PUNCT hvd.32044092008168 1065 32 1 1 NUM hvd.32044092008168 1065 33 3 3 NUM hvd.32044092008168 1065 34 ) ) PUNCT hvd.32044092008168 1065 35 02 02 NUM hvd.32044092008168 1065 36 2 2 NUM hvd.32044092008168 1065 37 c2np2 c2np2 PROPN hvd.32044092008168 1065 38 f f PROPN hvd.32044092008168 1065 39 2 2 NUM hvd.32044092008168 1065 40 3 3 NUM hvd.32044092008168 1065 41 or or CCONJ hvd.32044092008168 1065 42 2f 2f NOUN hvd.32044092008168 1065 43 , , PUNCT hvd.32044092008168 1065 44 f f PROPN hvd.32044092008168 1065 45 , , PUNCT hvd.32044092008168 1065 46 fed fed PROPN hvd.32044092008168 1065 47 1 1 NUM hvd.32044092008168 1065 48 2 2 NUM hvd.32044092008168 1065 49 1 1 NUM hvd.32044092008168 1065 50 3 3 NUM hvd.32044092008168 1065 51 v v NOUN hvd.32044092008168 1065 52 p p PROPN hvd.32044092008168 1065 53 n n X hvd.32044092008168 1065 54 odd odd ADJ hvd.32044092008168 1065 55 . . PUNCT hvd.32044092008168 1066 1 1 1 NUM hvd.32044092008168 1066 2 2 2 NUM hvd.32044092008168 1066 3 qf qf NOUN hvd.32044092008168 1066 4 ff ff PROPN hvd.32044092008168 1066 5 . . PUNCT hvd.32044092008168 1067 1 f f PROPN hvd.32044092008168 1067 2 q q X hvd.32044092008168 1068 1 [ [ X hvd.32044092008168 1068 2 147 147 NUM hvd.32044092008168 1068 3 ] ] PUNCT hvd.32044092008168 1068 4 p'v p'v PROPN hvd.32044092008168 1068 5 c c X hvd.32044092008168 1068 6 * * SYM hvd.32044092008168 1068 7 p p PROPN hvd.32044092008168 1068 8 b. b. PROPN hvd.32044092008168 1068 9 'q 'q PART hvd.32044092008168 1068 10 q q PROPN hvd.32044092008168 1068 11 ? ? PUNCT hvd.32044092008168 1068 12 cºpb cºpb ADJ hvd.32044092008168 1068 13 , , PUNCT hvd.32044092008168 1068 14 and and CCONJ hvd.32044092008168 1068 15 from from ADP hvd.32044092008168 1068 16 [ [ X hvd.32044092008168 1068 17 145 145 NUM hvd.32044092008168 1068 18 ] ] PUNCT hvd.32044092008168 1068 19 b%cº b%cº PROPN hvd.32044092008168 1068 20 pq1 pq1 PROPN hvd.32044092008168 1068 21 ( ( PUNCT hvd.32044092008168 1068 22 pv pv PROPN hvd.32044092008168 1068 23 — — PUNCT hvd.32044092008168 1068 24 4 4 X hvd.32044092008168 1068 25 ) ) PUNCT hvd.32044092008168 1068 26 ( ( PUNCT hvd.32044092008168 1068 27 1 1 X hvd.32044092008168 1068 28 ) ) PUNCT hvd.32044092008168 1068 29 = = PUNCT hvd.32044092008168 1068 30 0 0 PUNCT hvd.32044092008168 1068 31 = = PUNCT hvd.32044092008168 1068 32 of of ADP hvd.32044092008168 1068 33 whence whence NOUN hvd.32044092008168 1068 34 we we PRON hvd.32044092008168 1068 35 have have VERB hvd.32044092008168 1068 36 in in ADP hvd.32044092008168 1068 37 general general ADJ hvd.32044092008168 1068 38 2 2 NUM hvd.32044092008168 1068 39 . . PUNCT hvd.32044092008168 1069 1 f f X hvd.32044092008168 1069 2 ? ? PUNCT hvd.32044092008168 1070 1 [ [ X hvd.32044092008168 1070 2 148 148 X hvd.32044092008168 1070 3 ] ] PUNCT hvd.32044092008168 1070 4 pv pv ADP hvd.32044092008168 1070 5 la la PROPN hvd.32044092008168 1070 6 cb cb PROPN hvd.32044092008168 1070 7 :p :p PROPN hvd.32044092008168 1070 8 the the DET hvd.32044092008168 1070 9 corresponding correspond VERB hvd.32044092008168 1070 10 expressions expression NOUN hvd.32044092008168 1070 11 for for ADP hvd.32044092008168 1070 12 n n CCONJ hvd.32044092008168 1070 13 even even ADV hvd.32044092008168 1070 14 are be AUX hvd.32044092008168 1070 15 2c0 2c0 NUM hvd.32044092008168 1070 16 , , PUNCT hvd.32044092008168 1070 17 0,3 0,3 NUM hvd.32044092008168 1070 18 q q X hvd.32044092008168 1071 1 yp yp X hvd.32044092008168 1072 1 [ [ X hvd.32044092008168 1072 2 149 149 NUM hvd.32044092008168 1072 3 ] ] PUNCT hvd.32044092008168 1072 4 c c X hvd.32044092008168 1072 5 * * PUNCT hvd.32044092008168 1072 6 q,03 q,03 VERB hvd.32044092008168 1072 7 ca ca NOUN hvd.32044092008168 1072 8 2 2 NUM hvd.32044092008168 1072 9 0 0 NUM hvd.32044092008168 1072 10 2 2 NUM hvd.32044092008168 1072 11 va va NOUN hvd.32044092008168 1072 12 1 1 NUM hvd.32044092008168 1072 13 3 3 NUM hvd.32044092008168 1072 14 ? ? PUNCT hvd.32044092008168 1073 1 ש ש NUM hvd.32044092008168 1073 2 10 10 NUM hvd.32044092008168 1074 1 | | NOUN hvd.32044092008168 1074 2 y?p y?p NOUN hvd.32044092008168 1074 3 3 3 NUM hvd.32044092008168 1074 4 p'v=-(-v p'v=-(-v NOUN hvd.32044092008168 1074 5 3 3 NUM hvd.32044092008168 1074 6 2 2 NUM hvd.32044092008168 1074 7 . . PUNCT hvd.32044092008168 1075 1 2 2 NUM hvd.32044092008168 1075 2 va va NOUN hvd.32044092008168 1075 3 2 2 NUM hvd.32044092008168 1075 4 again again ADV hvd.32044092008168 1075 5 from from ADP hvd.32044092008168 1075 6 [ [ X hvd.32044092008168 1075 7 130 130 NUM hvd.32044092008168 1075 8 ] ] PUNCT hvd.32044092008168 1075 9 21 21 NUM hvd.32044092008168 1075 10 qys qys ADV hvd.32044092008168 1075 11 3 3 NUM hvd.32044092008168 1075 12 y y PROPN hvd.32044092008168 1075 13 b b X hvd.32044092008168 1075 14 q q X hvd.32044092008168 1075 15 = = X hvd.32044092008168 1075 16 c2 c2 PROPN hvd.32044092008168 1075 17 a a DET hvd.32044092008168 1075 18 lc lc NOUN hvd.32044092008168 1075 19 pbs pbs PROPN hvd.32044092008168 1075 20 b. b. PROPN hvd.32044092008168 1075 21 p p PROPN hvd.32044092008168 1075 22 2 2 PROPN hvd.32044092008168 1075 23 f f PROPN hvd.32044092008168 1075 24 f f X hvd.32044092008168 1075 25 f f X hvd.32044092008168 1075 26 q q PROPN hvd.32044092008168 1075 27 c'b'p c'b'p PROPN hvd.32044092008168 1076 1 iqy iqy PROPN hvd.32044092008168 1076 2 3 3 NUM hvd.32044092008168 1076 3 y y PROPN hvd.32044092008168 1076 4 b b PROPN hvd.32044092008168 1076 5 , , PUNCT hvd.32044092008168 1076 6 c'b c'b NOUN hvd.32044092008168 1076 7 , , PUNCT hvd.32044092008168 1076 8 pu pu PROPN hvd.32044092008168 1076 9 c c PROPN hvd.32044092008168 1076 10 ” " PUNCT hvd.32044092008168 1076 11 b.p b.p PROPN hvd.32044092008168 1076 12 1 1 NUM hvd.32044092008168 1076 13 03 03 NUM hvd.32044092008168 1076 14 c'b c'b NOUN hvd.32044092008168 1076 15 . . PUNCT hvd.32044092008168 1077 1 'p 'p PUNCT hvd.32044092008168 1077 2 p p PROPN hvd.32044092008168 1077 3 2 2 PROPN hvd.32044092008168 1077 4 y y PROPN hvd.32044092008168 1077 5 ( ( PUNCT hvd.32044092008168 1077 6 qx8 qx8 ADJ hvd.32044092008168 1077 7 = = NOUN hvd.32044092008168 1077 8 qy-3b qy-3b PROPN hvd.32044092008168 1077 9 , , PUNCT hvd.32044092008168 1077 10 b b PROPN hvd.32044092008168 1077 11 , , PUNCT hvd.32044092008168 1077 12 pet pet NOUN hvd.32044092008168 1077 13 q q PROPN hvd.32044092008168 1077 14 c c X hvd.32044092008168 1077 15 : : PUNCT hvd.32044092008168 1077 16 b. b. PROPN hvd.32044092008168 1077 17 'p 'p NUM hvd.32044092008168 1077 18 cº cº NOUN hvd.32044092008168 1077 19 p p NOUN hvd.32044092008168 1077 20 compairing compaire VERB hvd.32044092008168 1077 21 the the DET hvd.32044092008168 1077 22 second second ADJ hvd.32044092008168 1077 23 and and CCONJ hvd.32044092008168 1077 24 fourth fourth ADJ hvd.32044092008168 1077 25 forms form NOUN hvd.32044092008168 1077 26 we we PRON hvd.32044092008168 1077 27 have have VERB hvd.32044092008168 1077 28 [ [ X hvd.32044092008168 1077 29 150 150 NUM hvd.32044092008168 1077 30 ] ] PUNCT hvd.32044092008168 1077 31 · · PUNCT hvd.32044092008168 1077 32 f f PROPN hvd.32044092008168 1077 33 , , PUNCT hvd.32044092008168 1077 34 f f PROPN hvd.32044092008168 1077 35 , , PUNCT hvd.32044092008168 1077 36 f f PROPN hvd.32044092008168 1077 37 , , PUNCT hvd.32044092008168 1077 38 ( ( PUNCT hvd.32044092008168 1077 39 qy qy NOUN hvd.32044092008168 1077 40 ? ? NOUN hvd.32044092008168 1077 41 4 4 NUM hvd.32044092008168 1077 42 0 0 NUM hvd.32044092008168 1077 43 3 3 NUM hvd.32044092008168 1077 44 3 3 NUM hvd.32044092008168 1077 45 3 3 NUM hvd.32044092008168 1077 46 v v NOUN hvd.32044092008168 1077 47 v. v. PROPN hvd.32044092008168 1077 48 1 1 NUM hvd.32044092008168 1077 49 3 3 NUM hvd.32044092008168 1077 50 3 3 NUM hvd.32044092008168 1077 51 ( ( PUNCT hvd.32044092008168 1077 52 2 2 NUM hvd.32044092008168 1077 53 – – PUNCT hvd.32044092008168 1077 54 3 3 NUM hvd.32044092008168 1077 55 b b NOUN hvd.32044092008168 1077 56 , , PUNCT hvd.32044092008168 1077 57 b b PROPN hvd.32044092008168 1077 58 , , PUNCT hvd.32044092008168 1077 59 p4 p4 PROPN hvd.32044092008168 1077 60 ) ) PUNCT hvd.32044092008168 1077 61 . . PUNCT hvd.32044092008168 1078 1 3 3 NUM hvd.32044092008168 1078 2 reduction reduction NOUN hvd.32044092008168 1078 3 of of ADP hvd.32044092008168 1078 4 the the DET hvd.32044092008168 1078 5 forms form NOUN hvd.32044092008168 1078 6 when when SCONJ hvd.32044092008168 1078 7 n n SYM hvd.32044092008168 1078 8 equals equal VERB hvd.32044092008168 1078 9 three three NUM hvd.32044092008168 1078 10 . . PUNCT hvd.32044092008168 1078 11 73 73 NUM hvd.32044092008168 1078 12 substituting substitute VERB hvd.32044092008168 1078 13 the the DET hvd.32044092008168 1078 14 values value NOUN hvd.32044092008168 1078 15 n n CCONJ hvd.32044092008168 1078 16 = = X hvd.32044092008168 1078 17 3 3 NUM hvd.32044092008168 1078 18 ( ( PUNCT hvd.32044092008168 1078 19 p. p. NOUN hvd.32044092008168 1078 20 68 68 NUM hvd.32044092008168 1078 21 ) ) PUNCT hvd.32044092008168 1078 22 and and CCONJ hvd.32044092008168 1078 23 refering refer VERB hvd.32044092008168 1078 24 to to ADP hvd.32044092008168 1078 25 the the DET hvd.32044092008168 1078 26 value value NOUN hvd.32044092008168 1078 27 of of ADP hvd.32044092008168 1078 28 x. x. PROPN hvd.32044092008168 1078 29 ( ( PUNCT hvd.32044092008168 1078 30 p. p. NOUN hvd.32044092008168 1078 31 51 51 NUM hvd.32044092008168 1078 32 ) ) PUNCT hvd.32044092008168 1079 1 we we PRON hvd.32044092008168 1079 2 find find VERB hvd.32044092008168 1079 3 the the DET hvd.32044092008168 1079 4 relation relation NOUN hvd.32044092008168 1079 5 [ [ X hvd.32044092008168 1079 6 160 160 NUM hvd.32044092008168 1079 7 ] ] PUNCT hvd.32044092008168 1079 8 . . PUNCT hvd.32044092008168 1080 1 fn=3 fn=3 ADJ hvd.32044092008168 1081 1 [ [ X hvd.32044092008168 1081 2 161 161 NUM hvd.32044092008168 1081 3 ] ] PUNCT hvd.32044092008168 1081 4 · · PUNCT hvd.32044092008168 1081 5 [ [ X hvd.32044092008168 1081 6 163 163 NUM hvd.32044092008168 1081 7 ] ] PUNCT hvd.32044092008168 1081 8 • • PUNCT hvd.32044092008168 1081 9 abc abc PROPN hvd.32044092008168 1081 10 . . PUNCT hvd.32044092008168 1082 1 it it PRON hvd.32044092008168 1082 2 follows follow VERB hvd.32044092008168 1082 3 then then ADV hvd.32044092008168 1082 4 that that SCONJ hvd.32044092008168 1082 5 x x X hvd.32044092008168 1082 6 , , PUNCT hvd.32044092008168 1082 7 if if SCONJ hvd.32044092008168 1082 8 expressed express VERB hvd.32044092008168 1082 9 in in ADP hvd.32044092008168 1082 10 terms term NOUN hvd.32044092008168 1082 11 of of ADP hvd.32044092008168 1082 12 the the DET hvd.32044092008168 1082 13 modulus modulus NOUN hvd.32044092008168 1082 14 k k PROPN hvd.32044092008168 1082 15 and and CCONJ hvd.32044092008168 1082 16 b b PROPN hvd.32044092008168 1082 17 or or CCONJ hvd.32044092008168 1082 18 as as ADP hvd.32044092008168 1082 19 a a DET hvd.32044092008168 1082 20 function function NOUN hvd.32044092008168 1082 21 of of ADP hvd.32044092008168 1082 22 b b PROPN hvd.32044092008168 1082 23 , , PUNCT hvd.32044092008168 1082 24 ez ez PROPN hvd.32044092008168 1082 25 , , PUNCT hvd.32044092008168 1082 26 92 92 NUM hvd.32044092008168 1082 27 and and CCONJ hvd.32044092008168 1082 28 gз gз PROPN hvd.32044092008168 1082 29 , , PUNCT hvd.32044092008168 1082 30 will will AUX hvd.32044092008168 1082 31 be be AUX hvd.32044092008168 1082 32 separable separable ADJ hvd.32044092008168 1082 33 into into ADP hvd.32044092008168 1082 34 three three NUM hvd.32044092008168 1082 35 factors factor NOUN hvd.32044092008168 1082 36 which which PRON hvd.32044092008168 1082 37 from from ADP hvd.32044092008168 1082 38 the the DET hvd.32044092008168 1082 39 expressions expression NOUN hvd.32044092008168 1082 40 for for ADP hvd.32044092008168 1082 41 are be AUX hvd.32044092008168 1082 42 seen see VERB hvd.32044092008168 1082 43 to to PART hvd.32044092008168 1082 44 be be AUX hvd.32044092008168 1082 45 of of ADP hvd.32044092008168 1082 46 the the DET hvd.32044092008168 1082 47 same same ADJ hvd.32044092008168 1082 48 degree degree NOUN hvd.32044092008168 1082 49 in in ADP hvd.32044092008168 1082 50 b b PROPN hvd.32044092008168 1082 51 , , PUNCT hvd.32044092008168 1082 52 namely namely ADV hvd.32044092008168 1082 53 , , PUNCT hvd.32044092008168 1082 54 the the DET hvd.32044092008168 1082 55 second second ADJ hvd.32044092008168 1082 56 . . PUNCT hvd.32044092008168 1083 1 the the DET hvd.32044092008168 1083 2 factors factor NOUN hvd.32044092008168 1083 3 of of ADP hvd.32044092008168 1083 4 x x PUNCT hvd.32044092008168 1083 5 which which PRON hvd.32044092008168 1083 6 we we PRON hvd.32044092008168 1083 7 before before ADV hvd.32044092008168 1083 8 obtained obtain VERB hvd.32044092008168 1083 9 by by ADP hvd.32044092008168 1083 10 inspection inspection NOUN hvd.32044092008168 1083 11 ( ( PUNCT hvd.32044092008168 1083 12 see see VERB hvd.32044092008168 1083 13 p. p. NOUN hvd.32044092008168 1083 14 51 51 NUM hvd.32044092008168 1084 1 [ [ PUNCT hvd.32044092008168 1084 2 87 87 NUM hvd.32044092008168 1084 3 ] ] PUNCT hvd.32044092008168 1084 4 ) ) PUNCT hvd.32044092008168 1084 5 are be AUX hvd.32044092008168 1084 6 [ [ X hvd.32044092008168 1084 7 162 162 NUM hvd.32044092008168 1084 8 ] ] PUNCT hvd.32044092008168 1084 9 . . PUNCT hvd.32044092008168 1085 1 a a DET hvd.32044092008168 1085 2 = = NOUN hvd.32044092008168 1085 3 1² 1² NUM hvd.32044092008168 1085 4 − − NOUN hvd.32044092008168 1085 5 ( ( PUNCT hvd.32044092008168 1085 6 1 1 NUM hvd.32044092008168 1085 7 + + NUM hvd.32044092008168 1085 8 k² k² PROPN hvd.32044092008168 1085 9 ) ) PUNCT hvd.32044092008168 1085 10 l l PROPN hvd.32044092008168 1085 11 — — PUNCT hvd.32044092008168 1085 12 3k² 3k² NUM hvd.32044092008168 1085 13 b b NOUN hvd.32044092008168 1085 14 12 12 NUM hvd.32044092008168 1085 15 12 12 NUM hvd.32044092008168 1086 1 and and CCONJ hvd.32044092008168 1086 2 we we PRON hvd.32044092008168 1086 3 find find VERB hvd.32044092008168 1086 4 the the DET hvd.32044092008168 1086 5 relations relation NOUN hvd.32044092008168 1086 6 : : PUNCT hvd.32044092008168 1086 7 k² k² PROPN hvd.32044092008168 1086 8 sn² sn² VERB hvd.32044092008168 1086 9 ∞ ∞ NUM hvd.32044092008168 1086 10 = = NOUN hvd.32044092008168 1087 1 whence whence ADV hvd.32044092008168 1087 2 = = PROPN hvd.32044092008168 1087 3 k² k² PROPN hvd.32044092008168 1087 4 cn² cn² VERB hvd.32044092008168 1087 5 ∞ ∞ NUM hvd.32044092008168 1087 6 dn² dn² NOUN hvd.32044092008168 1087 7 a a DET hvd.32044092008168 1087 8 с с X hvd.32044092008168 1087 9 ―――― ―――― PROPN hvd.32044092008168 1087 10 [ [ X hvd.32044092008168 1087 11 f₁ f₁ PROPN hvd.32044092008168 1087 12 f₂ f₂ PROPN hvd.32044092008168 1087 13 f3]n=3 f3]n=3 VERB hvd.32044092008168 1087 14 2 2 NUM hvd.32044092008168 1087 15 = = SYM hvd.32044092008168 1087 16 ➖ ➖ ADJ hvd.32044092008168 1087 17 ➖ ➖ ADJ hvd.32044092008168 1087 18 fc fc X hvd.32044092008168 1087 19 . . PROPN hvd.32044092008168 1087 20 72 72 NUM hvd.32044092008168 1087 21 · · PUNCT hvd.32044092008168 1087 22 taking take VERB hvd.32044092008168 1087 23 now now ADV hvd.32044092008168 1087 24 s s PART hvd.32044092008168 1087 25 361 361 NUM hvd.32044092008168 1087 26 and and CCONJ hvd.32044092008168 1087 27 d d X hvd.32044092008168 1087 28 = = NOUN hvd.32044092008168 1087 29 1² 1² NUM hvd.32044092008168 1087 30 — — PUNCT hvd.32044092008168 1087 31 a₁ a₁ PROPN hvd.32044092008168 1087 32 = = NOUN hvd.32044092008168 1087 33 l² l² PROPN hvd.32044092008168 1087 34 − − PROPN hvd.32044092008168 1087 35 1 1 NUM hvd.32044092008168 1087 36 + + CCONJ hvd.32044092008168 1087 37 k² k² PROPN hvd.32044092008168 1087 38 — — PUNCT hvd.32044092008168 1087 39 k¹ k¹ PROPN hvd.32044092008168 1087 40 we we PRON hvd.32044092008168 1087 41 find find VERB hvd.32044092008168 1087 42 the the DET hvd.32044092008168 1087 43 following follow VERB hvd.32044092008168 1087 44 relations relation NOUN hvd.32044092008168 1087 45 of of ADP hvd.32044092008168 1087 46 m. m. NOUN hvd.32044092008168 1087 47 hermite hermite PROPN hvd.32044092008168 1087 48 x² x² PROPN hvd.32044092008168 1087 49 f₁ f₁ PROPN hvd.32044092008168 1087 50 = = NOUN hvd.32044092008168 1087 51 φ(0 φ(0 SPACE hvd.32044092008168 1087 52 ) ) PUNCT hvd.32044092008168 1087 53 367 367 NUM hvd.32044092008168 1087 54 ( ( PUNCT hvd.32044092008168 1087 55 12 12 NUM hvd.32044092008168 1087 56 a₁ a₁ NOUN hvd.32044092008168 1087 57 ) ) PUNCT hvd.32044092008168 1087 58 — — PUNCT hvd.32044092008168 1087 59 p'v p'v PROPN hvd.32044092008168 1087 60 = = PROPN hvd.32044092008168 1087 61 q₁ q₁ PROPN hvd.32044092008168 1087 62 = = VERB hvd.32044092008168 1087 63 k² k² PROPN hvd.32044092008168 1087 64 snu snu NOUN hvd.32044092008168 1087 65 cnu cnu PROPN hvd.32044092008168 1087 66 dnu dnu PROPN hvd.32044092008168 1087 67 45 45 NUM hvd.32044092008168 1087 68 = = SYM hvd.32044092008168 1087 69 a a PRON hvd.32044092008168 1087 70 ; ; PUNCT hvd.32044092008168 1087 71 ― ― X hvd.32044092008168 1087 72 where where SCONJ hvd.32044092008168 1087 73 x x PUNCT hvd.32044092008168 1087 74 and and CCONJ hvd.32044092008168 1087 75 a₁ a₁ PROPN hvd.32044092008168 1087 76 ― ― PRON hvd.32044092008168 1087 77 ( ( PUNCT hvd.32044092008168 1087 78 1 1 NUM hvd.32044092008168 1087 79 — — PUNCT hvd.32044092008168 1087 80 2k²)1 2k²)1 NOUN hvd.32044092008168 1087 81 + + NUM hvd.32044092008168 1087 82 3(k² 3(k² NUM hvd.32044092008168 1087 83 — — PUNCT hvd.32044092008168 1087 84 k¹ k¹ PROPN hvd.32044092008168 1087 85 ) ) PUNCT hvd.32044092008168 1087 86 ( ( PUNCT hvd.32044092008168 1087 87 k² k² PROPN hvd.32044092008168 1087 88 — — PUNCT hvd.32044092008168 1087 89 2 2 NUM hvd.32044092008168 1087 90 ) ) PUNCT hvd.32044092008168 1087 91 7 7 NUM hvd.32044092008168 1087 92 — — PUNCT hvd.32044092008168 1087 93 3(1 3(1 NUM hvd.32044092008168 1087 94 — — PUNCT hvd.32044092008168 1087 95 k² k² PROPN hvd.32044092008168 1087 96 ) ) PUNCT hvd.32044092008168 1087 97 = = PROPN hvd.32044092008168 1087 98 8 8 NUM hvd.32044092008168 1087 99 33153 33153 NUM hvd.32044092008168 1087 100 x x PUNCT hvd.32044092008168 1087 101 = = PUNCT hvd.32044092008168 1087 102 f₁ f₁ PROPN hvd.32044092008168 1087 103 = = SYM hvd.32044092008168 1087 104 b b NOUN hvd.32044092008168 1087 105 ; ; PUNCT hvd.32044092008168 1087 106 f2 f2 PROPN hvd.32044092008168 1087 107 p p X hvd.32044092008168 1087 108 q q X hvd.32044092008168 1087 109 r r NOUN hvd.32044092008168 1087 110 sd2 sd2 NOUN hvd.32044092008168 1087 111 = = PROPN hvd.32044092008168 1087 112 ψ ψ PROPN hvd.32044092008168 1088 1 1+k² 1+k² PROPN hvd.32044092008168 1088 2 3 3 NUM hvd.32044092008168 1088 3 361 361 NUM hvd.32044092008168 1088 4 ( ( PUNCT hvd.32044092008168 1088 5 1² 1² NUM hvd.32044092008168 1088 6 — — PUNCT hvd.32044092008168 1088 7 a₁)² a₁)² ADV hvd.32044092008168 1088 8 --2 --2 NOUN hvd.32044092008168 1088 9 45 45 NUM hvd.32044092008168 1088 10 8 8 NUM hvd.32044092008168 1088 11 3653 3653 NUM hvd.32044092008168 1088 12 x\1 x\1 PROPN hvd.32044092008168 1088 13 ) ) PUNCT hvd.32044092008168 1088 14 x x PUNCT hvd.32044092008168 1089 1 367(-a 367(-a PROPN hvd.32044092008168 1089 2 ) ) PUNCT hvd.32044092008168 1089 3 ―――― ―――― PROPN hvd.32044092008168 1089 4 127(a 127(a NUM hvd.32044092008168 1089 5 ) ) PUNCT hvd.32044092008168 1089 6 a₁)³ a₁)³ PROPN hvd.32044092008168 1089 7 ( ( PUNCT hvd.32044092008168 1089 8 2 2 NUM hvd.32044092008168 1089 9 k² k² PROPN hvd.32044092008168 1089 10 — — PUNCT hvd.32044092008168 1089 11 1 1 X hvd.32044092008168 1089 12 ) ) PUNCT hvd.32044092008168 1089 13 + + NUM hvd.32044092008168 1089 14 4 4 NUM hvd.32044092008168 1089 15 ( ( PUNCT hvd.32044092008168 1089 16 l l NOUN hvd.32044092008168 1089 17 ) ) PUNCT hvd.32044092008168 1089 18 367 367 NUM hvd.32044092008168 1089 19 ( ( PUNCT hvd.32044092008168 1089 20 1 1 NUM hvd.32044092008168 1089 21 — — PUNCT hvd.32044092008168 1089 22 a₁ a₁ NOUN hvd.32044092008168 1089 23 ) ) PUNCT hvd.32044092008168 1089 24 127 127 NUM hvd.32044092008168 1089 25 ( ( PUNCT hvd.32044092008168 1089 26 1² 1² NUM hvd.32044092008168 1089 27 — — PUNCT hvd.32044092008168 1089 28 a a X hvd.32044092008168 1089 29 , , PUNCT hvd.32044092008168 1089 30 ) ) PUNCT hvd.32044092008168 1089 31 ( ( PUNCT hvd.32044092008168 1089 32 2 2 NUM hvd.32044092008168 1089 33 − − PROPN hvd.32044092008168 1089 34 k² k² PROPN hvd.32044092008168 1089 35 ) ) PUNCT hvd.32044092008168 1089 36 + + CCONJ hvd.32044092008168 1089 37 4 4 NUM hvd.32044092008168 1089 38 ( ( PUNCT hvd.32044092008168 1089 39 1 1 NUM hvd.32044092008168 1089 40 ) ) PUNCT hvd.32044092008168 1089 41 367 367 NUM hvd.32044092008168 1089 42 ( ( PUNCT hvd.32044092008168 1089 43 12 12 NUM hvd.32044092008168 1089 44 α₁)² α₁)² SYM hvd.32044092008168 1089 45 2 2 NUM hvd.32044092008168 1089 46 = = ADP hvd.32044092008168 1089 47 a a PRON hvd.32044092008168 1089 48 and and CCONJ hvd.32044092008168 1089 49 ∞ ∞ NUM hvd.32044092008168 1089 50 = = PUNCT hvd.32044092008168 1089 51 v. v. ADP hvd.32044092008168 1089 52 127 127 NUM hvd.32044092008168 1089 53 ( ( PUNCT hvd.32044092008168 1089 54 l² l² PROPN hvd.32044092008168 1089 55 — — PUNCT hvd.32044092008168 1089 56 a a PRON hvd.32044092008168 1089 57 , , PUNCT hvd.32044092008168 1089 58 ) ) PUNCT hvd.32044092008168 1089 59 ² ² X hvd.32044092008168 1089 60 ( ( PUNCT hvd.32044092008168 1089 61 1 1 NUM hvd.32044092008168 1089 62 + + NUM hvd.32044092008168 1089 63 k² k² PROPN hvd.32044092008168 1089 64 ) ) PUNCT hvd.32044092008168 1089 65 — — PUNCT hvd.32044092008168 1089 66 4 4 NUM hvd.32044092008168 1089 67 ( ( PUNCT hvd.32044092008168 1089 68 7 7 NUM hvd.32044092008168 1089 69 ) ) PUNCT hvd.32044092008168 1089 70 367 367 NUM hvd.32044092008168 1089 71 ( ( PUNCT hvd.32044092008168 1089 72 1² 1² NUM hvd.32044092008168 1089 73 — — PUNCT hvd.32044092008168 1089 74 a₁)² a₁)² X hvd.32044092008168 1089 75 qb2 qb2 X hvd.32044092008168 1089 76 sd2 sd2 PROPN hvd.32044092008168 1089 77 abcx abcx PROPN hvd.32044092008168 1089 78 sd2 sd2 PROPN hvd.32044092008168 1089 79 rc2 rc2 NOUN hvd.32044092008168 1089 80 sd2 sd2 PRON hvd.32044092008168 1089 81 pa2 pa2 NOUN hvd.32044092008168 1089 82 sd2 sd2 VERB hvd.32044092008168 1089 83 ( ( PUNCT hvd.32044092008168 1089 84 see see VERB hvd.32044092008168 1089 85 also also ADV hvd.32044092008168 1089 86 note note VERB hvd.32044092008168 1089 87 p. p. NOUN hvd.32044092008168 1089 88 69 69 NUM hvd.32044092008168 1089 89 ) ) PUNCT hvd.32044092008168 1089 90 general general ADJ hvd.32044092008168 1089 91 discussion discussion NOUN hvd.32044092008168 1089 92 . . PUNCT hvd.32044092008168 1090 1 = = SYM hvd.32044092008168 1090 2 3 3 NUM hvd.32044092008168 1090 3 reviewing review VERB hvd.32044092008168 1090 4 the the DET hvd.32044092008168 1090 5 foregoing forego VERB hvd.32044092008168 1090 6 theory theory NOUN hvd.32044092008168 1090 7 we we PRON hvd.32044092008168 1090 8 have have AUX hvd.32044092008168 1090 9 found find VERB hvd.32044092008168 1091 1 that that SCONJ hvd.32044092008168 1091 2 when when SCONJ hvd.32044092008168 1091 3 n n ADP hvd.32044092008168 1091 4 = = X hvd.32044092008168 1091 5 y y PROPN hvd.32044092008168 1091 6 = = X hvd.32044092008168 1091 7 f f X hvd.32044092008168 1091 8 " " PUNCT hvd.32044092008168 1091 9 — — PUNCT hvd.32044092008168 1091 10 3bf 3bf ADJ hvd.32044092008168 1091 11 and and CCONJ hvd.32044092008168 1091 12 that that SCONJ hvd.32044092008168 1091 13 in in ADP hvd.32044092008168 1091 14 general general PROPN hvd.32044092008168 1091 15 y y PROPN hvd.32044092008168 1091 16 is be AUX hvd.32044092008168 1091 17 a a DET hvd.32044092008168 1091 18 function function NOUN hvd.32044092008168 1091 19 of of ADP hvd.32044092008168 1091 20 f f PROPN hvd.32044092008168 1091 21 where where SCONJ hvd.32044092008168 1091 22 we we PRON hvd.32044092008168 1091 23 write write VERB hvd.32044092008168 1091 24 o o NOUN hvd.32044092008168 1091 25 ( ( PUNCT hvd.32044092008168 1091 26 u u PROPN hvd.32044092008168 1091 27 + + CCONJ hvd.32044092008168 1091 28 v v NOUN hvd.32044092008168 1091 29 ) ) PUNCT hvd.32044092008168 1091 30 f= f= NOUN hvd.32044092008168 1091 31 e(x-5v e(x-5v SPACE hvd.32044092008168 1091 32 ) ) PUNCT hvd.32044092008168 1091 33 u u PROPN hvd.32044092008168 1091 34 συ συ ADP hvd.32044092008168 1091 35 the the DET hvd.32044092008168 1091 36 one one NUM hvd.32044092008168 1091 37 exception exception NOUN hvd.32044092008168 1091 38 occurring occur VERB hvd.32044092008168 1091 39 where where SCONJ hvd.32044092008168 1091 40 v v NOUN hvd.32044092008168 1091 41 equals equal VERB hvd.32044092008168 1091 42 zero zero NUM hvd.32044092008168 1091 43 . . PUNCT hvd.32044092008168 1092 1 74 74 NUM hvd.32044092008168 1092 2 part part NOUN hvd.32044092008168 1092 3 v. v. ADP hvd.32044092008168 1092 4 ve ve PROPN hvd.32044092008168 1092 5 x x SYM hvd.32044092008168 1092 6 = = PROPN hvd.32044092008168 1092 7 cb cb PROPN hvd.32044092008168 1092 8 c?b c?b SPACE hvd.32044092008168 1092 9 . . PROPN hvd.32044092008168 1093 1 b b PROPN hvd.32044092008168 1093 2 1 1 NUM hvd.32044092008168 1093 3 2 2 NUM hvd.32044092008168 1093 4 b b NOUN hvd.32044092008168 1093 5 we we PRON hvd.32044092008168 1093 6 find find VERB hvd.32044092008168 1093 7 further far ADV hvd.32044092008168 1093 8 , , PUNCT hvd.32044092008168 1093 9 that that SCONJ hvd.32044092008168 1093 10 where where SCONJ hvd.32044092008168 1093 11 q q PROPN hvd.32044092008168 1093 12 or or CCONJ hvd.32044092008168 1093 13 vanish vanish VERB hvd.32044092008168 1093 14 in in ADP hvd.32044092008168 1093 15 which which DET hvd.32044092008168 1093 16 case case NOUN hvd.32044092008168 1093 17 x x PUNCT hvd.32044092008168 1093 18 and and CCONJ hvd.32044092008168 1093 19 p'v p'v AUX hvd.32044092008168 1093 20 also also ADV hvd.32044092008168 1093 21 vanish vanish VERB hvd.32044092008168 1093 22 , , PUNCT hvd.32044092008168 1093 23 our our PRON hvd.32044092008168 1093 24 integrals integral NOUN hvd.32044092008168 1093 25 , , PUNCT hvd.32044092008168 1093 26 six six NUM hvd.32044092008168 1093 27 in in ADP hvd.32044092008168 1093 28 number number NOUN hvd.32044092008168 1093 29 ( ( PUNCT hvd.32044092008168 1093 30 n n CCONJ hvd.32044092008168 1093 31 = = SYM hvd.32044092008168 1093 32 3 3 NUM hvd.32044092008168 1093 33 ) ) PUNCT hvd.32044092008168 1093 34 , , PUNCT hvd.32044092008168 1093 35 become become VERB hvd.32044092008168 1093 36 doubly doubly ADV hvd.32044092008168 1093 37 periodic periodic ADJ hvd.32044092008168 1093 38 and and CCONJ hvd.32044092008168 1093 39 are be AUX hvd.32044092008168 1093 40 in in ADP hvd.32044092008168 1093 41 fact fact NOUN hvd.32044092008168 1093 42 the the DET hvd.32044092008168 1093 43 original original ADJ hvd.32044092008168 1093 44 special special ADJ hvd.32044092008168 1093 45 functions function NOUN hvd.32044092008168 1093 46 of of ADP hvd.32044092008168 1093 47 lamé lamé NOUN hvd.32044092008168 1093 48 of of ADP hvd.32044092008168 1093 49 the the DET hvd.32044092008168 1093 50 second second ADJ hvd.32044092008168 1093 51 and and CCONJ hvd.32044092008168 1093 52 third third ADJ hvd.32044092008168 1093 53 sort sort NOUN hvd.32044092008168 1093 54 . . PUNCT hvd.32044092008168 1094 1 we we PRON hvd.32044092008168 1094 2 have have AUX hvd.32044092008168 1094 3 found find VERB hvd.32044092008168 1094 4 for for ADP hvd.32044092008168 1094 5 x x PUNCT hvd.32044092008168 1094 6 the the DET hvd.32044092008168 1094 7 general general ADJ hvd.32044092008168 1094 8 value value NOUN hvd.32044092008168 1094 9 @ @ ADP hvd.32044092008168 1094 10 p p NOUN hvd.32044092008168 1094 11 from from ADP hvd.32044092008168 1094 12 which which PRON hvd.32044092008168 1094 13 form form NOUN hvd.32044092008168 1094 14 we we PRON hvd.32044092008168 1094 15 see see VERB hvd.32044092008168 1094 16 that that PRON hvd.32044092008168 1094 17 x x PUNCT hvd.32044092008168 1094 18 will will AUX hvd.32044092008168 1094 19 be be AUX hvd.32044092008168 1094 20 zero zero NUM hvd.32044092008168 1094 21 when when SCONJ hvd.32044092008168 1094 22 y y PROPN hvd.32044092008168 1094 23 and and CCONJ hvd.32044092008168 1094 24 q q X hvd.32044092008168 1094 25 vanish vanish VERB hvd.32044092008168 1094 26 and and CCONJ hvd.32044092008168 1094 27 will will AUX hvd.32044092008168 1094 28 be be AUX hvd.32044092008168 1094 29 infinite infinite ADJ hvd.32044092008168 1094 30 where where SCONJ hvd.32044092008168 1094 31 b b PROPN hvd.32044092008168 1094 32 or or CCONJ hvd.32044092008168 1094 33 p p NOUN hvd.32044092008168 1094 34 vanish vanish VERB hvd.32044092008168 1094 35 . . PUNCT hvd.32044092008168 1095 1 but but CCONJ hvd.32044092008168 1095 2 from from ADP hvd.32044092008168 1095 3 the the DET hvd.32044092008168 1095 4 form form NOUN hvd.32044092008168 1095 5 qy qy ADP hvd.32044092008168 1095 6 ? ? NOUN hvd.32044092008168 1095 7 2 2 NUM hvd.32044092008168 1095 8 b b NOUN hvd.32044092008168 1095 9 pv pv X hvd.32044092008168 1095 10 = = PROPN hvd.32044092008168 1095 11 c'pb c'pb PROPN hvd.32044092008168 1095 12 . . PUNCT hvd.32044092008168 1095 13 2n 2n PROPN hvd.32044092008168 1096 1 + + CCONJ hvd.32044092008168 1096 2 1 1 NUM hvd.32044092008168 1096 3 we we PRON hvd.32044092008168 1096 4 observe observe VERB hvd.32044092008168 1096 5 that that SCONJ hvd.32044092008168 1096 6 pv pv NOUN hvd.32044092008168 1096 7 is be AUX hvd.32044092008168 1096 8 also also ADV hvd.32044092008168 1096 9 infinite infinite ADJ hvd.32044092008168 1096 10 where where SCONJ hvd.32044092008168 1096 11 x x PROPN hvd.32044092008168 1096 12 becomes become VERB hvd.32044092008168 1096 13 infinite infinite ADJ hvd.32044092008168 1096 14 through through ADP hvd.32044092008168 1096 15 the the DET hvd.32044092008168 1096 16 vanishing vanishing NOUN hvd.32044092008168 1096 17 of of ADP hvd.32044092008168 1096 18 bo bo PROPN hvd.32044092008168 1096 19 . . PUNCT hvd.32044092008168 1097 1 we we PRON hvd.32044092008168 1097 2 have have VERB hvd.32044092008168 1097 3 further far ADV hvd.32044092008168 1097 4 that that SCONJ hvd.32044092008168 1097 5 in in ADP hvd.32044092008168 1097 6 case case NOUN hvd.32044092008168 1097 7 p p NOUN hvd.32044092008168 1097 8 vanish vanish VERB hvd.32044092008168 1097 9 the the DET hvd.32044092008168 1097 10 integral integral NOUN hvd.32044092008168 1097 11 becomes become VERB hvd.32044092008168 1097 12 a a DET hvd.32044092008168 1097 13 function function NOUN hvd.32044092008168 1097 14 of of ADP hvd.32044092008168 1097 15 lamé lamé NOUN hvd.32044092008168 1097 16 of of ADP hvd.32044092008168 1097 17 the the DET hvd.32044092008168 1097 18 first first ADJ hvd.32044092008168 1097 19 sort sort NOUN hvd.32044092008168 1097 20 in in ADP hvd.32044092008168 1097 21 which which PRON hvd.32044092008168 1097 22 p p PROPN hvd.32044092008168 1097 23 takes take VERB hvd.32044092008168 1097 24 the the DET hvd.32044092008168 1097 25 place place NOUN hvd.32044092008168 1097 26 of of ADP hvd.32044092008168 1097 27 f f PROPN hvd.32044092008168 1097 28 in in ADP hvd.32044092008168 1097 29 the the DET hvd.32044092008168 1097 30 general general ADJ hvd.32044092008168 1097 31 solution solution NOUN hvd.32044092008168 1097 32 the the DET hvd.32044092008168 1097 33 form form NOUN hvd.32044092008168 1097 34 being be AUX hvd.32044092008168 1097 35 1 1 NUM hvd.32044092008168 1097 36 [ [ X hvd.32044092008168 1097 37 164 164 NUM hvd.32044092008168 1097 38 ] ] PUNCT hvd.32044092008168 1097 39 ( ( PUNCT hvd.32044092008168 1097 40 1)"y= 1)"y= PROPN hvd.32044092008168 1097 41 2 2 X hvd.32044092008168 1097 42 ) ) PUNCT hvd.32044092008168 1097 43 u u PROPN hvd.32044092008168 1097 44 + + PROPN hvd.32044092008168 1097 45 92p(x-4u+ 92p(x-4u+ NUM hvd.32044092008168 1097 46 ( ( PUNCT hvd.32044092008168 1097 47 n(n n(n PROPN hvd.32044092008168 1097 48 − − PROPN hvd.32044092008168 1097 49 3 3 NUM hvd.32044092008168 1097 50 ) ) PUNCT hvd.32044092008168 1097 51 ! ! PUNCT hvd.32044092008168 1098 1 ( ( PUNCT hvd.32044092008168 1098 2 n n NOUN hvd.32044092008168 1098 3 – – PUNCT hvd.32044092008168 1098 4 5 5 NUM hvd.32044092008168 1098 5 ): ): SYM hvd.32044092008168 1098 6 94p(n—6 94p(n—6 NUM hvd.32044092008168 1098 7 ) ) PUNCT hvd.32044092008168 1098 8 u u PROPN hvd.32044092008168 1098 9 t t PROPN hvd.32044092008168 1098 10 ... ... PUNCT hvd.32044092008168 1099 1 the the DET hvd.32044092008168 1099 2 values value NOUN hvd.32044092008168 1099 3 of of ADP hvd.32044092008168 1099 4 b b NOUN hvd.32044092008168 1099 5 conforming conform VERB hvd.32044092008168 1099 6 with with ADP hvd.32044092008168 1099 7 the the DET hvd.32044092008168 1099 8 above above ADJ hvd.32044092008168 1099 9 cases case NOUN hvd.32044092008168 1099 10 being be AUX hvd.32044092008168 1099 11 roots root NOUN hvd.32044092008168 1099 12 of of ADP hvd.32044092008168 1099 13 the the DET hvd.32044092008168 1099 14 equations equation NOUN hvd.32044092008168 1099 15 p p PROPN hvd.32044092008168 1099 16 = = SYM hvd.32044092008168 1099 17 0 0 NUM hvd.32044092008168 1099 18 , , PUNCT hvd.32044092008168 1099 19 y y PROPN hvd.32044092008168 1099 20 = = PROPN hvd.32044092008168 1099 21 0 0 NUM hvd.32044092008168 1099 22 , , PUNCT hvd.32044092008168 1099 23 1 1 NUM hvd.32044092008168 1099 24 , , PUNCT hvd.32044092008168 1099 25 = = SYM hvd.32044092008168 1099 26 0 0 NUM hvd.32044092008168 1099 27 , , PUNCT hvd.32044092008168 1099 28 03 03 NUM hvd.32044092008168 1099 29 = = SYM hvd.32044092008168 1099 30 0 0 NUM hvd.32044092008168 1099 31 . . PUNCT hvd.32044092008168 1099 32 = = PUNCT hvd.32044092008168 1100 1 r2 r2 X hvd.32044092008168 1100 2 moreover moreover ADV hvd.32044092008168 1100 3 when when SCONJ hvd.32044092008168 1100 4 q q PROPN hvd.32044092008168 1100 5 vanishes vanish VERB hvd.32044092008168 1100 6 w w PROPN hvd.32044092008168 1100 7 and and CCONJ hvd.32044092008168 1100 8 p'v p'v PROPN hvd.32044092008168 1100 9 will will AUX hvd.32044092008168 1100 10 vanish vanish VERB hvd.32044092008168 1100 11 simultaniously simultaniously ADV hvd.32044092008168 1100 12 which which PRON hvd.32044092008168 1100 13 makes make VERB hvd.32044092008168 1100 14 v v ADP hvd.32044092008168 1100 15 one one NUM hvd.32044092008168 1100 16 of of ADP hvd.32044092008168 1100 17 the the DET hvd.32044092008168 1100 18 semi semi NOUN hvd.32044092008168 1100 19 - - ADJ hvd.32044092008168 1100 20 periods period NOUN hvd.32044092008168 1100 21 wa wa NOUN hvd.32044092008168 1100 22 , , PUNCT hvd.32044092008168 1100 23 and and CCONJ hvd.32044092008168 1100 24 f f PROPN hvd.32044092008168 1100 25 may may AUX hvd.32044092008168 1100 26 be be AUX hvd.32044092008168 1100 27 written write VERB hvd.32044092008168 1100 28 1 1 NUM hvd.32044092008168 1100 29 1 1 NUM hvd.32044092008168 1100 30 ) ) PUNCT hvd.32044092008168 1100 31 0 0 NUM hvd.32044092008168 1100 32 ( ( PUNCT hvd.32044092008168 1100 33 ou ou X hvd.32044092008168 1100 34 ou ou X hvd.32044092008168 1100 35 a a DET hvd.32044092008168 1100 36 [ [ X hvd.32044092008168 1100 37 165 165 NUM hvd.32044092008168 1100 38 ] ] PUNCT hvd.32044092008168 1100 39 fq=0 fq=0 PROPN hvd.32044092008168 1100 40 + + CCONJ hvd.32044092008168 1100 41 again again ADV hvd.32044092008168 1100 42 , , PUNCT hvd.32044092008168 1100 43 observing observe VERB hvd.32044092008168 1100 44 the the DET hvd.32044092008168 1100 45 last last ADJ hvd.32044092008168 1100 46 forms form NOUN hvd.32044092008168 1100 47 obtained obtain VERB hvd.32044092008168 1100 48 , , PUNCT hvd.32044092008168 1100 49 we we PRON hvd.32044092008168 1100 50 see see VERB hvd.32044092008168 1100 51 that that SCONJ hvd.32044092008168 1100 52 v v NOUN hvd.32044092008168 1100 53 can can AUX hvd.32044092008168 1100 54 also also ADV hvd.32044092008168 1100 55 be be AUX hvd.32044092008168 1100 56 a a DET hvd.32044092008168 1100 57 half half ADJ hvd.32044092008168 1100 58 period period NOUN hvd.32044092008168 1100 59 if if SCONJ hvd.32044092008168 1100 60 fr fr PROPN hvd.32044092008168 1100 61 , , PUNCT hvd.32044092008168 1100 62 n n CCONJ hvd.32044092008168 1100 63 being be AUX hvd.32044092008168 1100 64 odd odd ADJ hvd.32044092008168 1100 65 , , PUNCT hvd.32044092008168 1100 66 or or CCONJ hvd.32044092008168 1100 67 on on ADP hvd.32044092008168 1100 68 , , PUNCT hvd.32044092008168 1100 69 n n CCONJ hvd.32044092008168 1100 70 being be AUX hvd.32044092008168 1100 71 even even ADV hvd.32044092008168 1100 72 , , PUNCT hvd.32044092008168 1100 73 vanish vanish VERB hvd.32044092008168 1100 74 , , PUNCT hvd.32044092008168 1100 75 but but CCONJ hvd.32044092008168 1100 76 it it PRON hvd.32044092008168 1100 77 does do AUX hvd.32044092008168 1100 78 not not PART hvd.32044092008168 1100 79 follow follow VERB hvd.32044092008168 1100 80 that that PRON hvd.32044092008168 1100 81 will will AUX hvd.32044092008168 1100 82 also also ADV hvd.32044092008168 1100 83 reduce reduce VERB hvd.32044092008168 1100 84 to to ADP hvd.32044092008168 1100 85 zero zero NUM hvd.32044092008168 1100 86 . . PUNCT hvd.32044092008168 1101 1 that that PRON hvd.32044092008168 1101 2 is be AUX hvd.32044092008168 1101 3 the the DET hvd.32044092008168 1101 4 integral integral ADJ hvd.32044092008168 1101 5 will will NOUN hvd.32044092008168 1101 6 in in ADP hvd.32044092008168 1101 7 general general ADJ hvd.32044092008168 1101 8 have have VERB hvd.32044092008168 1101 9 the the DET hvd.32044092008168 1101 10 form form NOUN hvd.32044092008168 1101 11 0(u 0(u NUM hvd.32044092008168 1102 1 + + PUNCT hvd.32044092008168 1102 2 wa wa X hvd.32044092008168 1102 3 ) ) PUNCT hvd.32044092008168 1103 1 [ [ X hvd.32044092008168 1103 2 166 166 NUM hvd.32044092008168 1103 3 ] ] PUNCT hvd.32044092008168 1103 4 · · PUNCT hvd.32044092008168 1103 5 fi fi NOUN hvd.32044092008168 1103 6 ele-$(wa))u ele-$(wa))u NOUN hvd.32044092008168 1103 7 exu exu NOUN hvd.32044092008168 1103 8 when when SCONJ hvd.32044092008168 1103 9 f2=0 f2=0 PROPN hvd.32044092008168 1103 10 , , PUNCT hvd.32044092008168 1103 11 or or CCONJ hvd.32044092008168 1103 12 02 02 NUM hvd.32044092008168 1103 13 0 0 NUM hvd.32044092008168 1103 14 , , PUNCT hvd.32044092008168 1103 15 or or CCONJ hvd.32044092008168 1103 16 x x SYM hvd.32044092008168 1103 17 = = PUNCT hvd.32044092008168 1103 18 0 0 NUM hvd.32044092008168 1103 19 , , PUNCT hvd.32044092008168 1103 20 or or CCONJ hvd.32044092008168 1103 21 a a DET hvd.32044092008168 1103 22 = = NOUN hvd.32044092008168 1103 23 0 0 NUM hvd.32044092008168 1103 24 , , PUNCT hvd.32044092008168 1103 25 or or CCONJ hvd.32044092008168 1103 26 b. b. PROPN hvd.32044092008168 1103 27 = = PROPN hvd.32044092008168 1103 28 0 0 NUM hvd.32044092008168 1103 29 , , PUNCT hvd.32044092008168 1103 30 or or CCONJ hvd.32044092008168 1103 31 c c X hvd.32044092008168 1103 32 = = SYM hvd.32044092008168 1103 33 0 0 NUM hvd.32044092008168 1103 34 . . PUNCT hvd.32044092008168 1104 1 in in ADP hvd.32044092008168 1104 2 this this DET hvd.32044092008168 1104 3 case case NOUN hvd.32044092008168 1104 4 as as SCONJ hvd.32044092008168 1104 5 in in ADP hvd.32044092008168 1104 6 general general ADJ hvd.32044092008168 1104 7 two two NUM hvd.32044092008168 1104 8 distinct distinct ADJ hvd.32044092008168 1104 9 integrals integral NOUN hvd.32044092008168 1104 10 exist exist VERB hvd.32044092008168 1104 11 which which PRON hvd.32044092008168 1104 12 are be AUX hvd.32044092008168 1104 13 doubly doubly ADV hvd.32044092008168 1104 14 periodic periodic ADJ hvd.32044092008168 1104 15 of of ADP hvd.32044092008168 1104 16 the the DET hvd.32044092008168 1104 17 second second ADJ hvd.32044092008168 1104 18 species species NOUN hvd.32044092008168 1104 19 the the DET hvd.32044092008168 1104 20 second second ADJ hvd.32044092008168 1104 21 integral integral ADJ hvd.32044092008168 1104 22 being be AUX hvd.32044092008168 1104 23 6 6 NUM hvd.32044092008168 1104 24 onu onu NOUN hvd.32044092008168 1104 25 σω σω INTJ hvd.32044092008168 1104 26 6u 6u PROPN hvd.32044092008168 1104 27 oqu oqu PROPN hvd.32044092008168 1104 28 u u PROPN hvd.32044092008168 1104 29 f2 f2 PROPN hvd.32044092008168 1104 30 σι σι INTJ hvd.32044092008168 1104 31 a a DET hvd.32044092008168 1104 32 form form NOUN hvd.32044092008168 1104 33 which which PRON hvd.32044092008168 1104 34 does do AUX hvd.32044092008168 1104 35 not not PART hvd.32044092008168 1104 36 differ differ VERB hvd.32044092008168 1104 37 from from ADP hvd.32044092008168 1104 38 f f PROPN hvd.32044092008168 1104 39 , , PUNCT hvd.32044092008168 1104 40 a a DET hvd.32044092008168 1104 41 peculiarity peculiarity NOUN hvd.32044092008168 1104 42 which which PRON hvd.32044092008168 1104 43 does do AUX hvd.32044092008168 1104 44 not not PART hvd.32044092008168 1104 45 appear appear VERB hvd.32044092008168 1104 46 in in ADP hvd.32044092008168 1104 47 the the DET hvd.32044092008168 1104 48 special special ADJ hvd.32044092008168 1104 49 functions function NOUN hvd.32044092008168 1104 50 of of ADP hvd.32044092008168 1104 51 lamé lamé NOUN hvd.32044092008168 1104 52 . . PUNCT hvd.32044092008168 1105 1 reduction reduction NOUN hvd.32044092008168 1105 2 of of ADP hvd.32044092008168 1105 3 the the DET hvd.32044092008168 1105 4 forms form NOUN hvd.32044092008168 1105 5 when when SCONJ hvd.32044092008168 1105 6 n n SYM hvd.32044092008168 1105 7 equals equal VERB hvd.32044092008168 1105 8 three three NUM hvd.32044092008168 1105 9 . . PUNCT hvd.32044092008168 1106 1 75 75 NUM hvd.32044092008168 1106 2 ν ν PROPN hvd.32044092008168 1106 3 -0 -0 PROPN hvd.32044092008168 1106 4 we we PRON hvd.32044092008168 1106 5 have have AUX hvd.32044092008168 1106 6 finally finally ADV hvd.32044092008168 1106 7 but but CCONJ hvd.32044092008168 1106 8 one one NUM hvd.32044092008168 1106 9 more more ADJ hvd.32044092008168 1106 10 case case NOUN hvd.32044092008168 1106 11 to to PART hvd.32044092008168 1106 12 consider consider VERB hvd.32044092008168 1106 13 , , PUNCT hvd.32044092008168 1106 14 namely namely ADV hvd.32044092008168 1106 15 when when SCONJ hvd.32044092008168 1106 16 0 0 NUM hvd.32044092008168 1106 17 , , PUNCT hvd.32044092008168 1106 18 a a DET hvd.32044092008168 1106 19 condition condition NOUN hvd.32044092008168 1106 20 arising arise VERB hvd.32044092008168 1106 21 when when SCONJ hvd.32044092008168 1106 22 b b NOUN hvd.32044092008168 1106 23 , , PUNCT hvd.32044092008168 1106 24 or or CCONJ hvd.32044092008168 1106 25 y y PROPN hvd.32044092008168 1106 26 , , PUNCT hvd.32044092008168 1106 27 common common ADJ hvd.32044092008168 1106 28 to to ADP hvd.32044092008168 1106 29 the the DET hvd.32044092008168 1106 30 functions function NOUN hvd.32044092008168 1106 31 x x PUNCT hvd.32044092008168 1106 32 , , PUNCT hvd.32044092008168 1106 33 pv pv NOUN hvd.32044092008168 1106 34 and and CCONJ hvd.32044092008168 1106 35 p'v p'v SPACE hvd.32044092008168 1106 36 , , PUNCT hvd.32044092008168 1106 37 vanish vanish VERB hvd.32044092008168 1106 38 , , PUNCT hvd.32044092008168 1106 39 in in ADP hvd.32044092008168 1106 40 which which DET hvd.32044092008168 1106 41 case case NOUN hvd.32044092008168 1106 42 the the DET hvd.32044092008168 1106 43 integrals integral NOUN hvd.32044092008168 1106 44 become become VERB hvd.32044092008168 1106 45 functions function NOUN hvd.32044092008168 1106 46 named name VERB hvd.32044092008168 1106 47 after after ADP hvd.32044092008168 1106 48 their their PRON hvd.32044092008168 1106 49 discoverer discoverer NOUN hvd.32044092008168 1106 50 . . PUNCT hvd.32044092008168 1107 1 * * PUNCT hvd.32044092008168 1107 2 2 2 NUM hvd.32044092008168 1107 3 6 6 NUM hvd.32044092008168 1107 4 a a PRON hvd.32044092008168 1107 5 , , PUNCT hvd.32044092008168 1107 6 ) ) PUNCT hvd.32044092008168 1107 7 6 6 NUM hvd.32044092008168 1107 8 elu elu NOUN hvd.32044092008168 1107 9 ( ( PUNCT hvd.32044092008168 1107 10 800 800 NUM hvd.32044092008168 1107 11 ( ( PUNCT hvd.32044092008168 1107 12 16 16 NUM hvd.32044092008168 1107 13 ) ) PUNCT hvd.32044092008168 1107 14 p. p. NOUN hvd.32044092008168 1107 15 17 17 NUM hvd.32044092008168 1107 16 . . PUNCT hvd.32044092008168 1107 17 ) ) PUNCT hvd.32044092008168 1107 18 functions function NOUN hvd.32044092008168 1107 19 of of ADP hvd.32044092008168 1107 20 m. m. NOUN hvd.32044092008168 1107 21 mittag mittag ADJ hvd.32044092008168 1107 22 - - PUNCT hvd.32044092008168 1107 23 leffler leffler NOUN hvd.32044092008168 1107 24 . . PUNCT hvd.32044092008168 1108 1 as as SCONJ hvd.32044092008168 1108 2 m. m. NOUN hvd.32044092008168 1108 3 hermite hermite PROPN hvd.32044092008168 1108 4 observes observe VERB hvd.32044092008168 1108 5 ( ( PUNCT hvd.32044092008168 1108 6 p. p. NOUN hvd.32044092008168 1108 7 28 28 NUM hvd.32044092008168 1108 8 ) ) PUNCT hvd.32044092008168 1108 9 the the DET hvd.32044092008168 1108 10 vanishing vanishing NOUN hvd.32044092008168 1108 11 of of ADP hvd.32044092008168 1108 12 a a DET hvd.32044092008168 1108 13 , , PUNCT hvd.32044092008168 1108 14 b b NOUN hvd.32044092008168 1108 15 , , PUNCT hvd.32044092008168 1108 16 c c PROPN hvd.32044092008168 1108 17 and and CCONJ hvd.32044092008168 1108 18 d d NOUN hvd.32044092008168 1108 19 are be AUX hvd.32044092008168 1108 20 necessary necessary ADJ hvd.32044092008168 1108 21 conditions condition NOUN hvd.32044092008168 1108 22 that that PRON hvd.32044092008168 1108 23 the the DET hvd.32044092008168 1108 24 integrals integral NOUN hvd.32044092008168 1108 25 shall shall AUX hvd.32044092008168 1108 26 be be AUX hvd.32044092008168 1108 27 functions function NOUN hvd.32044092008168 1108 28 which which PRON hvd.32044092008168 1108 29 he he PRON hvd.32044092008168 1108 30 first first ADV hvd.32044092008168 1108 31 called call VERB hvd.32044092008168 1108 32 functions function NOUN hvd.32044092008168 1108 33 of of ADP hvd.32044092008168 1108 34 m. m. NOUN hvd.32044092008168 1108 35 mittag mittag ADJ hvd.32044092008168 1108 36 - - PUNCT hvd.32044092008168 1108 37 leffler leffler NOUN hvd.32044092008168 1108 38 , , PUNCT hvd.32044092008168 1108 39 but but CCONJ hvd.32044092008168 1108 40 they they PRON hvd.32044092008168 1108 41 are be AUX hvd.32044092008168 1108 42 not not PART hvd.32044092008168 1108 43 sufficient sufficient ADJ hvd.32044092008168 1108 44 conditions condition NOUN hvd.32044092008168 1108 45 . . PUNCT hvd.32044092008168 1109 1 the the DET hvd.32044092008168 1109 2 functions function NOUN hvd.32044092008168 1109 3 are be AUX hvd.32044092008168 1109 4 in in ADP hvd.32044092008168 1109 5 fact fact NOUN hvd.32044092008168 1109 6 special special ADJ hvd.32044092008168 1109 7 cases case NOUN hvd.32044092008168 1109 8 of of ADP hvd.32044092008168 1109 9 fi fi PROPN hvd.32044092008168 1109 10 and and CCONJ hvd.32044092008168 1109 11 f2 f2 PROPN hvd.32044092008168 1109 12 having have VERB hvd.32044092008168 1109 13 the the DET hvd.32044092008168 1109 14 additional additional ADJ hvd.32044092008168 1109 15 property property NOUN hvd.32044092008168 1109 16 that that PRON hvd.32044092008168 1109 17 the the DET hvd.32044092008168 1109 18 logarithms logarithm NOUN hvd.32044092008168 1109 19 of of ADP hvd.32044092008168 1109 20 the the DET hvd.32044092008168 1109 21 so so ADV hvd.32044092008168 1109 22 called call VERB hvd.32044092008168 1109 23 multiplicators multiplicator NOUN hvd.32044092008168 1109 24 are be AUX hvd.32044092008168 1109 25 proportional proportional ADJ hvd.32044092008168 1109 26 to to ADP hvd.32044092008168 1109 27 the the DET hvd.32044092008168 1109 28 corresponding correspond VERB hvd.32044092008168 1109 29 periods period NOUN hvd.32044092008168 1109 30 . . PUNCT hvd.32044092008168 1110 1 in in ADP hvd.32044092008168 1110 2 this this DET hvd.32044092008168 1110 3 case case NOUN hvd.32044092008168 1110 4 the the DET hvd.32044092008168 1110 5 integrals integral NOUN hvd.32044092008168 1110 6 assume assume VERB hvd.32044092008168 1110 7 a a DET hvd.32044092008168 1110 8 special special ADJ hvd.32044092008168 1110 9 form form NOUN hvd.32044092008168 1110 10 where where SCONJ hvd.32044092008168 1110 11 the the DET hvd.32044092008168 1110 12 elimentary elimentary NOUN hvd.32044092008168 1110 13 function function NOUN hvd.32044092008168 1110 14 is be AUX hvd.32044092008168 1110 15 a a DET hvd.32044092008168 1110 16 function function NOUN hvd.32044092008168 1110 17 of of ADP hvd.32044092008168 1110 18 p p PROPN hvd.32044092008168 1110 19 and and CCONJ hvd.32044092008168 1110 20 p p NOUN hvd.32044092008168 1110 21 ' ' PUNCT hvd.32044092008168 1110 22 multiplied multiply VERB hvd.32044092008168 1110 23 by by ADP hvd.32044092008168 1110 24 a a DET hvd.32044092008168 1110 25 determinate determinate ADJ hvd.32044092008168 1110 26 exponential exponential NOUN hvd.32044092008168 1110 27 having have VERB hvd.32044092008168 1110 28 the the DET hvd.32044092008168 1110 29 above above ADJ hvd.32044092008168 1110 30 property property NOUN hvd.32044092008168 1110 31 . . PUNCT hvd.32044092008168 1111 1 we we PRON hvd.32044092008168 1111 2 can can AUX hvd.32044092008168 1111 3 show show VERB hvd.32044092008168 1111 4 that that SCONJ hvd.32044092008168 1111 5 these these PRON hvd.32044092008168 1111 6 are be AUX hvd.32044092008168 1111 7 but but CCONJ hvd.32044092008168 1111 8 special special ADJ hvd.32044092008168 1111 9 cases case NOUN hvd.32044092008168 1111 10 of of ADP hvd.32044092008168 1111 11 the the DET hvd.32044092008168 1111 12 general general ADJ hvd.32044092008168 1111 13 doubly doubly ADV hvd.32044092008168 1111 14 periodic periodic ADJ hvd.32044092008168 1111 15 function function NOUN hvd.32044092008168 1111 16 of of ADP hvd.32044092008168 1111 17 the the DET hvd.32044092008168 1111 18 second second ADJ hvd.32044092008168 1111 19 species specie NOUN hvd.32044092008168 1111 20 of of ADP hvd.32044092008168 1111 21 m. m. NOUN hvd.32044092008168 1111 22 hermite hermite PROPN hvd.32044092008168 1111 23 as as SCONJ hvd.32044092008168 1111 24 follows follow VERB hvd.32044092008168 1111 25 : : PUNCT hvd.32044092008168 1111 26 we we PRON hvd.32044092008168 1111 27 have have VERB hvd.32044092008168 1111 28 as as ADP hvd.32044092008168 1111 29 the the DET hvd.32044092008168 1111 30 general general ADJ hvd.32044092008168 1111 31 form form NOUN hvd.32044092008168 1111 32 ( ( PUNCT hvd.32044092008168 1111 33 u u X hvd.32044092008168 1111 34 a a X hvd.32044092008168 1111 35 ) ) PUNCT hvd.32044092008168 1112 1 o o NOUN hvd.32044092008168 1112 2 ( ( PUNCT hvd.32044092008168 1112 3 u u PROPN hvd.32044092008168 1112 4 q(u q(u PROPN hvd.32044092008168 1112 5 an-1 an-1 SPACE hvd.32044092008168 1112 6 ) ) PUNCT hvd.32044092008168 1113 1 [ [ X hvd.32044092008168 1113 2 167 167 NUM hvd.32044092008168 1113 3 ] ] PUNCT hvd.32044092008168 1113 4 · · PUNCT hvd.32044092008168 1113 5 f(u f(u NOUN hvd.32044092008168 1113 6 ) ) PUNCT hvd.32044092008168 1113 7 o(u o(u PROPN hvd.32044092008168 1113 8 b b NOUN hvd.32044092008168 1113 9 ) ) PUNCT hvd.32044092008168 1113 10 ( ( PUNCT hvd.32044092008168 1113 11 u u PROPN hvd.32044092008168 1113 12 b b PROPN hvd.32044092008168 1113 13 ) ) PUNCT hvd.32044092008168 1113 14 ( ( PUNCT hvd.32044092008168 1113 15 u u PROPN hvd.32044092008168 1113 16 – – PUNCT hvd.32044092008168 1113 17 0,-1 0,-1 X hvd.32044092008168 1113 18 ) ) PUNCT hvd.32044092008168 1113 19 o o NUM hvd.32044092008168 1113 20 b b X hvd.32044092008168 1113 21 a a DET hvd.32044092008168 1113 22 function function NOUN hvd.32044092008168 1113 23 of of ADP hvd.32044092008168 1113 24 the the DET hvd.32044092008168 1113 25 second second ADJ hvd.32044092008168 1113 26 species specie NOUN hvd.32044092008168 1113 27 upon upon SCONJ hvd.32044092008168 1113 28 the the DET hvd.32044092008168 1113 29 addition addition NOUN hvd.32044092008168 1113 30 to to ADP hvd.32044092008168 1113 31 the the DET hvd.32044092008168 1113 32 arguments argument NOUN hvd.32044092008168 1113 33 of of ADP hvd.32044092008168 1113 34 the the DET hvd.32044092008168 1113 35 periods period NOUN hvd.32044092008168 1113 36 2w 2w NUM hvd.32044092008168 1113 37 and and CCONJ hvd.32044092008168 1113 38 2w 2w NUM hvd.32044092008168 1113 39 ' ' PUNCT hvd.32044092008168 1113 40 the the DET hvd.32044092008168 1113 41 function function NOUN hvd.32044092008168 1113 42 remains remain VERB hvd.32044092008168 1113 43 unchanged unchanged ADJ hvd.32044092008168 1113 44 save save NOUN hvd.32044092008168 1113 45 in in ADP hvd.32044092008168 1113 46 the the DET hvd.32044092008168 1113 47 exponential exponential ADJ hvd.32044092008168 1113 48 factor factor NOUN hvd.32044092008168 1113 49 which which PRON hvd.32044092008168 1113 50 takes take VERB hvd.32044092008168 1113 51 the the DET hvd.32044092008168 1113 52 forms form NOUN hvd.32044092008168 1113 53 respectively respectively ADV hvd.32044092008168 1113 54 u u PROPN hvd.32044092008168 1113 55 [ [ X hvd.32044092008168 1113 56 170 170 NUM hvd.32044092008168 1113 57 ] ] PUNCT hvd.32044092008168 1113 58 200 200 NUM hvd.32044092008168 1113 59 c*n c*n PROPN hvd.32044092008168 1113 60 ( ( PUNCT hvd.32044092008168 1113 61 b b NOUN hvd.32044092008168 1113 62 − − NOUN hvd.32044092008168 1113 63 a a X hvd.32044092008168 1113 64 ) ) PUNCT hvd.32044092008168 1114 1 + + CCONJ hvd.32044092008168 1114 2 2 2 NUM hvd.32044092008168 1114 3 ou ou X hvd.32044092008168 1114 4 u u NOUN hvd.32044092008168 1114 5 ' ' PUNCT hvd.32044092008168 1114 6 = = NOUN hvd.32044092008168 1114 7 62''(b 62''(b NUM hvd.32044092008168 1114 8 a a PRON hvd.32044092008168 1114 9 ) ) PUNCT hvd.32044092008168 1114 10 + + PUNCT hvd.32044092008168 1115 1 2ow 2ow PROPN hvd.32044092008168 1115 2 ' ' PUNCT hvd.32044092008168 1115 3 m m VERB hvd.32044092008168 1115 4 when when SCONJ hvd.32044092008168 1115 5 b b ADP hvd.32044092008168 1115 6 = = SYM hvd.32044092008168 1115 7 b b NOUN hvd.32044092008168 1115 8 , , PUNCT hvd.32044092008168 1115 9 + + NUM hvd.32044092008168 1115 10 b b X hvd.32044092008168 1116 1 + + PUNCT hvd.32044092008168 1116 2 : : PUNCT hvd.32044092008168 1116 3 + + CCONJ hvd.32044092008168 1116 4 br-1 br-1 X hvd.32044092008168 1117 1 b b ADP hvd.32044092008168 1117 2 bn bn X hvd.32044092008168 1117 3 a a PRON hvd.32044092008168 1117 4 a a DET hvd.32044092008168 1117 5 + + NOUN hvd.32044092008168 1117 6 da da ADJ hvd.32044092008168 1117 7 + + NOUN hvd.32044092008168 1117 8 .. .. PUNCT hvd.32044092008168 1118 1 + + X hvd.32044092008168 1118 2 ( ( PUNCT hvd.32044092008168 1118 3 – – PUNCT hvd.32044092008168 1118 4 1 1 NUM hvd.32044092008168 1118 5 and and CCONJ hvd.32044092008168 1118 6 n n NOUN hvd.32044092008168 1118 7 and and CCONJ hvd.32044092008168 1118 8 n n CCONJ hvd.32044092008168 1118 9 ' ' PUNCT hvd.32044092008168 1118 10 are be AUX hvd.32044092008168 1118 11 constants constant NOUN hvd.32044092008168 1118 12 . . PUNCT hvd.32044092008168 1119 1 the the DET hvd.32044092008168 1119 2 factors factor NOUN hvd.32044092008168 1119 3 and and CCONJ hvd.32044092008168 1119 4 u u PROPN hvd.32044092008168 1119 5 ' ' PUNCT hvd.32044092008168 1119 6 are be AUX hvd.32044092008168 1119 7 general general ADJ hvd.32044092008168 1119 8 and and CCONJ hvd.32044092008168 1119 9 we we PRON hvd.32044092008168 1119 10 may may AUX hvd.32044092008168 1119 11 if if SCONJ hvd.32044092008168 1119 12 we we PRON hvd.32044092008168 1119 13 choose choose VERB hvd.32044092008168 1119 14 take take VERB hvd.32044092008168 1119 15 them they PRON hvd.32044092008168 1119 16 at at ADP hvd.32044092008168 1119 17 pleasure pleasure NOUN hvd.32044092008168 1119 18 and and CCONJ hvd.32044092008168 1119 19 then then ADV hvd.32044092008168 1119 20 seek seek VERB hvd.32044092008168 1119 21 the the DET hvd.32044092008168 1119 22 corresponding corresponding ADJ hvd.32044092008168 1119 23 function function NOUN hvd.32044092008168 1119 24 . . PUNCT hvd.32044092008168 1120 1 doing do VERB hvd.32044092008168 1120 2 this this PRON hvd.32044092008168 1120 3 we we PRON hvd.32044092008168 1120 4 have have VERB hvd.32044092008168 1120 5 u u PROPN hvd.32044092008168 1120 6 and and CCONJ hvd.32044092008168 1120 7 u u PROPN hvd.32044092008168 1120 8 ' ' PUNCT hvd.32044092008168 1120 9 given give VERB hvd.32044092008168 1120 10 and and CCONJ hvd.32044092008168 1120 11 also also ADV hvd.32044092008168 1120 12 o o X hvd.32044092008168 1120 13 to to PART hvd.32044092008168 1120 14 determine determine VERB hvd.32044092008168 1120 15 b b PROPN hvd.32044092008168 1120 16 a a PRON hvd.32044092008168 1120 17 from from ADP hvd.32044092008168 1120 18 the the DET hvd.32044092008168 1120 19 relations relation NOUN hvd.32044092008168 1120 20 [ [ X hvd.32044092008168 1120 21 170 170 NUM hvd.32044092008168 1120 22 ] ] PUNCT hvd.32044092008168 1120 23 . . PUNCT hvd.32044092008168 1121 1 solving solve VERB hvd.32044092008168 1121 2 we we PRON hvd.32044092008168 1121 3 have have VERB hvd.32044092008168 1121 4 2n(b 2n(b NUM hvd.32044092008168 1121 5 – – PUNCT hvd.32044092008168 1121 6 a a X hvd.32044092008168 1121 7 ) ) PUNCT hvd.32044092008168 1121 8 + + PUNCT hvd.32044092008168 1122 1 2ow 2ow PROPN hvd.32044092008168 1122 2 log log VERB hvd.32044092008168 1122 3 u u PROPN hvd.32044092008168 1122 4 ' ' PUNCT hvd.32044092008168 1122 5 = = NOUN hvd.32044092008168 1122 6 2n(b 2n(b NUM hvd.32044092008168 1122 7 -a -a SYM hvd.32044092008168 1122 8 ) ) PUNCT hvd.32044092008168 1122 9 + + SYM hvd.32044092008168 1123 1 2ow 2ow PROPN hvd.32044092008168 1123 2 ' ' PUNCT hvd.32044092008168 1123 3 ' ' PUNCT hvd.32044092008168 1123 4 ( ( PUNCT hvd.32044092008168 1123 5 + + CCONJ hvd.32044092008168 1123 6 and and CCONJ hvd.32044092008168 1123 7 as as ADP hvd.32044092008168 1123 8 e2 e2 PROPN hvd.32044092008168 1123 9 1 1 NUM hvd.32044092008168 1123 10 ( ( PUNCT hvd.32044092008168 1123 11 see see VERB hvd.32044092008168 1123 12 p. p. NOUN hvd.32044092008168 1123 13 17 17 NUM hvd.32044092008168 1123 14 . . PUNCT hvd.32044092008168 1123 15 ) ) PUNCT hvd.32044092008168 1124 1 log log VERB hvd.32044092008168 1124 2 u u PROPN hvd.32044092008168 1124 3 * * PUNCT hvd.32044092008168 1124 4 ) ) PUNCT hvd.32044092008168 1124 5 see see VERB hvd.32044092008168 1124 6 mittag mittag ADJ hvd.32044092008168 1124 7 - - PUNCT hvd.32044092008168 1124 8 leffler leffler NOUN hvd.32044092008168 1124 9 , , PUNCT hvd.32044092008168 1124 10 comptes compte NOUN hvd.32044092008168 1124 11 rendus rendus PROPN hvd.32044092008168 1124 12 t. t. PROPN hvd.32044092008168 1124 13 xc xc PROPN hvd.32044092008168 1124 14 , , PUNCT hvd.32044092008168 1124 15 1880 1880 NUM hvd.32044092008168 1124 16 , , PUNCT hvd.32044092008168 1124 17 p. p. NOUN hvd.32044092008168 1124 18 178 178 NUM hvd.32044092008168 1124 19 . . PUNCT hvd.32044092008168 1125 1 76 76 NUM hvd.32044092008168 1125 2 part part NOUN hvd.32044092008168 1125 3 v. v. ADP hvd.32044092008168 1125 4 [ [ X hvd.32044092008168 1125 5 171 171 NUM hvd.32044092008168 1125 6 ] ] PUNCT hvd.32044092008168 1125 7 whence whence NOUN hvd.32044092008168 1125 8 n n CCONJ hvd.32044092008168 1125 9 log log PROPN hvd.32044092008168 1125 10 u u PROPN hvd.32044092008168 1125 11 ' ' PART hvd.32044092008168 1125 12 n n CCONJ hvd.32044092008168 1125 13 ' ' PUNCT hvd.32044092008168 1125 14 log log NOUN hvd.32044092008168 1125 15 μ μ PROPN hvd.32044092008168 1125 16 w w PROPN hvd.32044092008168 1125 17 ' ' PART hvd.32044092008168 1125 18 log log NOUN hvd.32044092008168 1125 19 μ μ X hvd.32044092008168 1125 20 w w AUX hvd.32044092008168 1125 21 log log VERB hvd.32044092008168 1125 22 μ μ NOUN hvd.32044092008168 1125 23 2(b 2(b NUM hvd.32044092008168 1125 24 — — PUNCT hvd.32044092008168 1125 25 a a X hvd.32044092008168 1125 26 ) ) PUNCT hvd.32044092008168 1125 27 ( ( PUNCT hvd.32044092008168 1125 28 ŋw ŋw PROPN hvd.32044092008168 1125 29 ' ' PUNCT hvd.32044092008168 1125 30 — — PUNCT hvd.32044092008168 1125 31 n n CCONJ hvd.32044092008168 1125 32 ' ' NOUN hvd.32044092008168 1125 33 w w NOUN hvd.32044092008168 1125 34 ) ) PUNCT hvd.32044092008168 1125 35 — — PUNCT hvd.32044092008168 1125 36 ( ( PUNCT hvd.32044092008168 1125 37 b b X hvd.32044092008168 1125 38 — — PUNCT hvd.32044092008168 1125 39 a)ñi a)ñi X hvd.32044092008168 1125 40 . . PUNCT hvd.32044092008168 1126 1 = = PROPN hvd.32044092008168 1126 2 this this DET hvd.32044092008168 1126 3 solution solution NOUN hvd.32044092008168 1126 4 however however ADV hvd.32044092008168 1126 5 becomes become VERB hvd.32044092008168 1126 6 indeterminate indeterminate ADJ hvd.32044092008168 1126 7 when when SCONJ hvd.32044092008168 1126 8 f(x f(x PROPN hvd.32044092008168 1126 9 ) ) PUNCT hvd.32044092008168 1126 10 becomes become VERB hvd.32044092008168 1126 11 doubly doubly ADV hvd.32044092008168 1126 12 periodic periodic ADJ hvd.32044092008168 1126 13 , , PUNCT hvd.32044092008168 1126 14 for for ADP hvd.32044092008168 1126 15 then then ADV hvd.32044092008168 1126 16 0 0 NUM hvd.32044092008168 1126 17 and and CCONJ hvd.32044092008168 1126 18 b― b― VERB hvd.32044092008168 1126 19 a a DET hvd.32044092008168 1126 20 2mw 2mw NOUN hvd.32044092008168 1126 21 + + NUM hvd.32044092008168 1126 22 2m'w 2m'w NUM hvd.32044092008168 1126 23 ' ' PUNCT hvd.32044092008168 1126 24 . . PUNCT hvd.32044092008168 1127 1 whence whence ADP hvd.32044092008168 1127 2 this this PRON hvd.32044092008168 1127 3 gives gives AUX hvd.32044092008168 1127 4 we we PRON hvd.32044092008168 1127 5 have have VERB hvd.32044092008168 1127 6 [ [ PUNCT hvd.32044092008168 1127 7 172 172 NUM hvd.32044092008168 1127 8 ] ] PUNCT hvd.32044092008168 1127 9 · · PUNCT hvd.32044092008168 1127 10 we we PRON hvd.32044092008168 1127 11 observe observe VERB hvd.32044092008168 1127 12 that that SCONJ hvd.32044092008168 1127 13 when when SCONJ hvd.32044092008168 1127 14 where where SCONJ hvd.32044092008168 1127 15 where where SCONJ hvd.32044092008168 1127 16 where where SCONJ hvd.32044092008168 1127 17 = = PROPN hvd.32044092008168 1127 18 [ [ X hvd.32044092008168 1127 19 173 173 NUM hvd.32044092008168 1127 20 ] ] PUNCT hvd.32044092008168 1127 21 . . PUNCT hvd.32044092008168 1128 1 2º 2º NUM hvd.32044092008168 1128 2 ( ( PUNCT hvd.32044092008168 1128 3 nw nw PROPN hvd.32044092008168 1128 4 ' ' PUNCT hvd.32044092008168 1128 5 — — PUNCT hvd.32044092008168 1128 6 n'w n'w PROPN hvd.32044092008168 1128 7 ) ) PUNCT hvd.32044092008168 1128 8 — — PUNCT hvd.32044092008168 1128 9 — — PUNCT hvd.32044092008168 1128 10 o̟xi o̟xi NUM hvd.32044092008168 1128 11 ; ; PUNCT hvd.32044092008168 1128 12 · · PUNCT hvd.32044092008168 1128 13 ( ( PUNCT hvd.32044092008168 1128 14 nw nw PROPN hvd.32044092008168 1128 15 ' ' PUNCT hvd.32044092008168 1128 16 — — PUNCT hvd.32044092008168 1128 17 n'w n'w PROPN hvd.32044092008168 1128 18 = = X hvd.32044092008168 1128 19 xi xi PUNCT hvd.32044092008168 1128 20 ) ) PUNCT hvd.32044092008168 1128 21 = = X hvd.32044092008168 1129 1 y y X hvd.32044092008168 1129 2 in in ADP hvd.32044092008168 1129 3 ( ( PUNCT hvd.32044092008168 1129 4 2mw 2mw NOUN hvd.32044092008168 1129 5 + + NUM hvd.32044092008168 1129 6 2m'w 2m'w NOUN hvd.32044092008168 1129 7 ' ' NUM hvd.32044092008168 1129 8 ) ) PUNCT hvd.32044092008168 1129 9 w w PROPN hvd.32044092008168 1129 10 w w PROPN hvd.32044092008168 1129 11 which which PRON hvd.32044092008168 1129 12 means mean VERB hvd.32044092008168 1129 13 that that SCONJ hvd.32044092008168 1129 14 the the DET hvd.32044092008168 1129 15 logs log NOUN hvd.32044092008168 1129 16 of of ADP hvd.32044092008168 1129 17 the the DET hvd.32044092008168 1129 18 multiplicators multiplicator NOUN hvd.32044092008168 1129 19 are be AUX hvd.32044092008168 1129 20 proportional proportional ADJ hvd.32044092008168 1129 21 to to ADP hvd.32044092008168 1129 22 their their PRON hvd.32044092008168 1129 23 corresponding correspond VERB hvd.32044092008168 1129 24 periods period NOUN hvd.32044092008168 1129 25 . . PUNCT hvd.32044092008168 1130 1 returning return VERB hvd.32044092008168 1130 2 to to ADP hvd.32044092008168 1130 3 the the DET hvd.32044092008168 1130 4 form form NOUN hvd.32044092008168 1130 5 = = PROPN hvd.32044092008168 1130 6 f f X hvd.32044092008168 1130 7 = = SYM hvd.32044092008168 1130 8 w w PROPN hvd.32044092008168 1130 9 ' ' PUNCT hvd.32044092008168 1130 10 log log NOUN hvd.32044092008168 1130 11 μ μ NOUN hvd.32044092008168 1130 12 log log VERB hvd.32044092008168 1130 13 u u PROPN hvd.32044092008168 1131 1 2inm 2inm NUM hvd.32044092008168 1131 2 log log NOUN hvd.32044092008168 1131 3 u'+2inm u'+2inm PROPN hvd.32044092008168 1131 4 ' ' PART hvd.32044092008168 1131 5 o o NOUN hvd.32044092008168 1131 6 ( ( PUNCT hvd.32044092008168 1131 7 u u PROPN hvd.32044092008168 1131 8 + + CCONJ hvd.32044092008168 1131 9 v v NOUN hvd.32044092008168 1131 10 ) ) PUNCT hvd.32044092008168 1131 11 6 6 NUM hvd.32044092008168 1131 12 6 6 NUM hvd.32044092008168 1131 13 σ σ PROPN hvd.32044092008168 1131 14 ( ( PUNCT hvd.32044092008168 1131 15 u u PROPN hvd.32044092008168 1131 16 ) ) PUNCT hvd.32044092008168 1131 17 2 2 NUM hvd.32044092008168 1131 18 = = X hvd.32044092008168 1131 19 а а NOUN hvd.32044092008168 1131 20 ₁ ₁ PUNCT hvd.32044092008168 1132 1 + + PUNCT hvd.32044092008168 1132 2 a₂+ a₂+ SYM hvd.32044092008168 1133 1 v v NOUN hvd.32044092008168 1133 2 = = NOUN hvd.32044092008168 1133 3 2mw+2m'w 2mw+2m'w NUM hvd.32044092008168 1133 4 ' ' PUNCT hvd.32044092008168 1134 1 this this DET hvd.32044092008168 1134 2 case case NOUN hvd.32044092008168 1134 3 . . PUNCT hvd.32044092008168 1135 1 = = PROPN hvd.32044092008168 1135 2 and and CCONJ hvd.32044092008168 1135 3 f f PROPN hvd.32044092008168 1135 4 vanishes vanish VERB hvd.32044092008168 1135 5 showing show VERB hvd.32044092008168 1135 6 that that SCONJ hvd.32044092008168 1135 7 this this DET hvd.32044092008168 1135 8 eliment eliment NOUN hvd.32044092008168 1135 9 can can AUX hvd.32044092008168 1135 10 not not PART hvd.32044092008168 1135 11 be be AUX hvd.32044092008168 1135 12 utilized utilize VERB hvd.32044092008168 1135 13 in in ADP hvd.32044092008168 1135 14 written write VERB hvd.32044092008168 1135 15 as as ADP hvd.32044092008168 1135 16 a a DET hvd.32044092008168 1135 17 product product NOUN hvd.32044092008168 1135 18 however however ADV hvd.32044092008168 1135 19 and and CCONJ hvd.32044092008168 1135 20 for for ADP hvd.32044092008168 1135 21 u u PROPN hvd.32044092008168 1135 22 3 3 NUM hvd.32044092008168 1135 23 we we PRON hvd.32044092008168 1135 24 have have VERB hvd.32044092008168 1135 25 o o X hvd.32044092008168 1135 26 ( ( PUNCT hvd.32044092008168 1135 27 u u PROPN hvd.32044092008168 1135 28 + + CCONJ hvd.32044092008168 1135 29 a a X hvd.32044092008168 1135 30 ) ) PUNCT hvd.32044092008168 1135 31 o o NOUN hvd.32044092008168 1135 32 ( ( PUNCT hvd.32044092008168 1135 33 u u NOUN hvd.32044092008168 1135 34 + + CCONJ hvd.32044092008168 1135 35 b b NOUN hvd.32044092008168 1135 36 ) ) PUNCT hvd.32044092008168 1135 37 o o X hvd.32044092008168 1136 1 íu íu NOUN hvd.32044092008168 1136 2 + + PRON hvd.32044092008168 1136 3 c c X hvd.32044092008168 1137 1 ) ) PUNCT hvd.32044092008168 1137 2 63 63 NUM hvd.32044092008168 1137 3 u u PROPN hvd.32044092008168 1137 4 = = X hvd.32044092008168 1137 5 e e PUNCT hvd.32044092008168 1137 6 = = VERB hvd.32044092008168 1137 7 u&a+b+c u&a+b+c ADV hvd.32044092008168 1137 8 ) ) PUNCT hvd.32044092008168 1137 9 • • X hvd.32044092008168 1137 10 ― ― PUNCT hvd.32044092008168 1137 11 = = PUNCT hvd.32044092008168 1137 12 · · PUNCT hvd.32044092008168 1137 13 0 0 NUM hvd.32044092008168 1137 14 a+b+c a+b+c ADV hvd.32044092008168 1137 15 = = SYM hvd.32044092008168 1137 16 v v NOUN hvd.32044092008168 1137 17 = = NOUN hvd.32044092008168 1137 18 0 0 NUM hvd.32044092008168 1137 19 and and CCONJ hvd.32044092008168 1137 20 our our PRON hvd.32044092008168 1137 21 eliment eliment NOUN hvd.32044092008168 1137 22 may may AUX hvd.32044092008168 1137 23 be be AUX hvd.32044092008168 1137 24 taken take VERB hvd.32044092008168 1137 25 as as ADP hvd.32044092008168 1137 26 a a DET hvd.32044092008168 1137 27 rational rational ADJ hvd.32044092008168 1137 28 function function NOUN hvd.32044092008168 1137 29 of of ADP hvd.32044092008168 1137 30 pu pu PROPN hvd.32044092008168 1137 31 and and CCONJ hvd.32044092008168 1137 32 p'u p'u ADV hvd.32044092008168 1137 33 multiplied multiply VERB hvd.32044092008168 1137 34 by by ADP hvd.32044092008168 1137 35 a a DET hvd.32044092008168 1137 36 factor factor NOUN hvd.32044092008168 1137 37 of of ADP hvd.32044092008168 1137 38 the the DET hvd.32044092008168 1137 39 form form NOUN hvd.32044092008168 1137 40 e e NOUN hvd.32044092008168 1137 41 " " PUNCT hvd.32044092008168 1137 42 . . PUNCT hvd.32044092008168 1138 1 it it PRON hvd.32044092008168 1138 2 is be AUX hvd.32044092008168 1138 3 moreover moreover ADV hvd.32044092008168 1138 4 known know VERB hvd.32044092008168 1138 5 that that SCONJ hvd.32044092008168 1138 6 any any DET hvd.32044092008168 1138 7 function function NOUN hvd.32044092008168 1138 8 f(u f(u NOUN hvd.32044092008168 1138 9 ) ) PUNCT hvd.32044092008168 1138 10 of of ADP hvd.32044092008168 1138 11 p p PROPN hvd.32044092008168 1138 12 and and CCONJ hvd.32044092008168 1138 13 p p PROPN hvd.32044092008168 1138 14 ' ' PUNCT hvd.32044092008168 1138 15 may may AUX hvd.32044092008168 1138 16 be be AUX hvd.32044092008168 1138 17 resolved resolve VERB hvd.32044092008168 1138 18 in in ADP hvd.32044092008168 1138 19 the the DET hvd.32044092008168 1138 20 form form NOUN hvd.32044092008168 1138 21 f(u f(u NOUN hvd.32044092008168 1138 22 ) ) PUNCT hvd.32044092008168 1138 23 = = X hvd.32044092008168 1139 1 l l NOUN hvd.32044092008168 1139 2 + + CCONJ hvd.32044092008168 1139 3 p p X hvd.32044092008168 1139 4 w w PROPN hvd.32044092008168 1139 5 log log PROPN hvd.32044092008168 1139 6 u u PROPN hvd.32044092008168 1139 7 l l NOUN hvd.32044092008168 1139 8 = = PRON hvd.32044092008168 1139 9 1 1 NUM hvd.32044092008168 1139 10 , , PUNCT hvd.32044092008168 1139 11 ¿ ¿ NUM hvd.32044092008168 1139 12 ( ( PUNCT hvd.32044092008168 1139 13 u u PROPN hvd.32044092008168 1139 14 — — PUNCT hvd.32044092008168 1139 15 v₁ v₁ PROPN hvd.32044092008168 1139 16 ) ) PUNCT hvd.32044092008168 1139 17 + + NUM hvd.32044092008168 1139 18 1½§ 1½§ NUM hvd.32044092008168 1139 19 ( ( PUNCT hvd.32044092008168 1139 20 u u PROPN hvd.32044092008168 1139 21 — — PUNCT hvd.32044092008168 1139 22 v₂ v₂ INTJ hvd.32044092008168 1139 23 ) ) PUNCT hvd.32044092008168 1139 24 + + CCONJ hvd.32044092008168 1139 25 13 13 NUM hvd.32044092008168 1139 26 § § PROPN hvd.32044092008168 1139 27 ( ( PUNCT hvd.32044092008168 1139 28 u u PROPN hvd.32044092008168 1139 29 — — PUNCT hvd.32044092008168 1139 30 v3 v3 PROPN hvd.32044092008168 1139 31 ) ) PUNCT hvd.32044092008168 1139 32 + + CCONJ hvd.32044092008168 1139 33 · · PUNCT hvd.32044092008168 1139 34 · · PUNCT hvd.32044092008168 1139 35 ( ( PUNCT hvd.32044092008168 1139 36 u u X hvd.32044092008168 1139 37 p= p= X hvd.32044092008168 1139 38 c c PROPN hvd.32044092008168 1139 39 + + SYM hvd.32044092008168 1139 40 σm σm NOUN hvd.32044092008168 1139 41 p‹¹ p‹¹ SPACE hvd.32044092008168 1139 42 ) ) PUNCT hvd.32044092008168 1139 43 ( ( PUNCT hvd.32044092008168 1139 44 u u PROPN hvd.32044092008168 1139 45 — — PUNCT hvd.32044092008168 1139 46 v v NOUN hvd.32044092008168 1139 47 ) ) PUNCT hvd.32044092008168 1139 48 4 4 NUM hvd.32044092008168 1139 49 + + NUM hvd.32044092008168 1139 50 12 12 NUM hvd.32044092008168 1139 51 + + SYM hvd.32044092008168 1139 52 l3 l3 NOUN hvd.32044092008168 1140 1 + + CCONJ hvd.32044092008168 1140 2 this this DET hvd.32044092008168 1140 3 property property NOUN hvd.32044092008168 1140 4 being be AUX hvd.32044092008168 1140 5 general general ADJ hvd.32044092008168 1140 6 , , PUNCT hvd.32044092008168 1140 7 we we PRON hvd.32044092008168 1140 8 have have VERB hvd.32044092008168 1140 9 , , PUNCT hvd.32044092008168 1140 10 f f PROPN hvd.32044092008168 1140 11 being be AUX hvd.32044092008168 1140 12 doubly doubly ADV hvd.32044092008168 1140 13 periodic periodic ADJ hvd.32044092008168 1140 14 , , PUNCT hvd.32044092008168 1140 15 but but CCONJ hvd.32044092008168 1140 16 to to PART hvd.32044092008168 1140 17 multiply multiply VERB hvd.32044092008168 1140 18 by by ADP hvd.32044092008168 1140 19 eeu eeu PROPN hvd.32044092008168 1140 20 to to PART hvd.32044092008168 1140 21 find find VERB hvd.32044092008168 1140 22 a a DET hvd.32044092008168 1140 23 development development NOUN hvd.32044092008168 1140 24 for for ADP hvd.32044092008168 1140 25 the the DET hvd.32044092008168 1140 26 eliment eliment NOUN hvd.32044092008168 1140 27 required require VERB hvd.32044092008168 1140 28 in in ADP hvd.32044092008168 1140 29 [ [ X hvd.32044092008168 1140 30 172 172 NUM hvd.32044092008168 1140 31 ] ] PUNCT hvd.32044092008168 1140 32 namely namely ADV hvd.32044092008168 1140 33 d(u d(u PROPN hvd.32044092008168 1140 34 ) ) PUNCT hvd.32044092008168 1140 35 = = PROPN hvd.32044092008168 1141 1 eeu eeu PROPN hvd.32044092008168 1141 2 { { PUNCT hvd.32044092008168 1141 3 ( ( PUNCT hvd.32044092008168 1141 4 u u PROPN hvd.32044092008168 1141 5 ) ) PUNCT hvd.32044092008168 1141 6 = = SYM hvd.32044092008168 1141 7 0 0 NUM hvd.32044092008168 1141 8 . . PUNCT hvd.32044092008168 1141 9 reduction reduction NOUN hvd.32044092008168 1141 10 of of ADP hvd.32044092008168 1141 11 the the DET hvd.32044092008168 1141 12 forms form NOUN hvd.32044092008168 1141 13 when when SCONJ hvd.32044092008168 1141 14 n n SYM hvd.32044092008168 1141 15 equals equal VERB hvd.32044092008168 1141 16 three three NUM hvd.32044092008168 1141 17 . . PUNCT hvd.32044092008168 1142 1 77 77 NUM hvd.32044092008168 1142 2 s. s. NOUN hvd.32044092008168 1142 3 من من X hvd.32044092008168 1143 1 من من INTJ hvd.32044092008168 1143 2 مد مد INTJ hvd.32044092008168 1144 1 we we PRON hvd.32044092008168 1144 2 have have VERB hvd.32044092008168 1144 3 then then ADV hvd.32044092008168 1144 4 $ $ SYM hvd.32044092008168 1144 5 ( ( PUNCT hvd.32044092008168 1144 6 u u NOUN hvd.32044092008168 1144 7 ) ) PUNCT hvd.32044092008168 1144 8 ф(и ф(и SPACE hvd.32044092008168 1144 9 ) ) PUNCT hvd.32044092008168 1144 10 ери ери PROPN hvd.32044092008168 1144 11 & & CCONJ hvd.32044092008168 1144 12 ' ' PUNCT hvd.32044092008168 1144 13 ( ( PUNCT hvd.32044092008168 1144 14 u u PROPN hvd.32044092008168 1144 15 ) ) PUNCT hvd.32044092008168 1144 16 o'(u)equ o'(u)equ PROPN hvd.32044092008168 1144 17 equ equ PROPN hvd.32044092008168 1144 18 — — PUNCT hvd.32044092008168 1144 19 00(11 00(11 X hvd.32044092008168 1144 20 ) ) PUNCT hvd.32044092008168 1144 21 e e NOUN hvd.32044092008168 1144 22 - - PUNCT hvd.32044092008168 1144 23 on on ADP hvd.32044092008168 1144 24 š š PROPN hvd.32044092008168 1144 25 " " PUNCT hvd.32044092008168 1144 26 ( ( PUNCT hvd.32044092008168 1144 27 u u PROPN hvd.32044092008168 1144 28 ) ) PUNCT hvd.32044092008168 1144 29 o”(u)equ o”(u)equ ADP hvd.32044092008168 1144 30 200'(11)cou 200'(11)cou NUM hvd.32044092008168 1144 31 + + NUM hvd.32044092008168 1144 32 p'd(u)cou p'd(u)cou NOUN hvd.32044092008168 1144 33 ç(3 ç(3 PROPN hvd.32044092008168 1144 34 ) ) PUNCT hvd.32044092008168 1144 35 ( ( PUNCT hvd.32044092008168 1144 36 u u PROPN hvd.32044092008168 1144 37 ) ) PUNCT hvd.32044092008168 1144 38 0"(u)e–94—300"(u)e 0"(u)e–94—300"(u)e PROPN hvd.32044092008168 1144 39 - - PUNCT hvd.32044092008168 1144 40 qu qu PROPN hvd.32044092008168 1144 41 +3p2 +3p2 PROPN hvd.32044092008168 1144 42 ó'(u)c ó'(u)c PROPN hvd.32044092008168 1144 43 - - PUNCT hvd.32044092008168 1144 44 gu gu NOUN hvd.32044092008168 1144 45 — — PUNCT hvd.32044092008168 1144 46 08 08 NUM hvd.32044092008168 1144 47 0 0 NUM hvd.32044092008168 1144 48 ( ( PUNCT hvd.32044092008168 1144 49 u)e u)e ADJ hvd.32044092008168 1144 50 - - PUNCT hvd.32044092008168 1144 51 eu eu PROPN hvd.32044092008168 1144 52 . . PUNCT hvd.32044092008168 1145 1 и и ADP hvd.32044092008168 1145 2 whence whence NOUN hvd.32044092008168 1145 3 n n ADP hvd.32044092008168 1145 4 φ φ X hvd.32044092008168 1145 5 ( ( PUNCT hvd.32044092008168 1145 6 ( ( PUNCT hvd.32044092008168 1145 7 ) ) PUNCT hvd.32044092008168 1145 8 non non ADJ hvd.32044092008168 1145 9 — — PUNCT hvd.32044092008168 1145 10 1 1 X hvd.32044092008168 1145 11 ) ) PUNCT hvd.32044092008168 1145 12 12 12 NUM hvd.32044092008168 1145 13 o o NUM hvd.32044092008168 1145 14 ° ° NUM hvd.32044092008168 1145 15 p”2)(x)+ p”2)(x)+ NUM hvd.32044092008168 1145 16 .. .. PUNCT hvd.32044092008168 1145 17 1 1 NUM hvd.32044092008168 1146 1 [ [ X hvd.32044092008168 1146 2 174 174 NUM hvd.32044092008168 1146 3 ] ] PUNCT hvd.32044092008168 1146 4 eru eru PROPN hvd.32044092008168 1146 5 çin çin PROPN hvd.32044092008168 1146 6 ) ) PUNCT hvd.32044092008168 1146 7 ( ( PUNCT hvd.32044092008168 1146 8 u u PROPN hvd.32044092008168 1146 9 ) ) PUNCT hvd.32044092008168 1146 10 = = SYM hvd.32044092008168 1146 11 o(n o(n PROPN hvd.32044092008168 1146 12 ) ) PUNCT hvd.32044092008168 1146 13 ( ( PUNCT hvd.32044092008168 1146 14 u u PROPN hvd.32044092008168 1146 15 ) ) PUNCT hvd.32044092008168 1146 16 ( ( PUNCT hvd.32044092008168 1146 17 ( ( PUNCT hvd.32044092008168 1146 18 i i X hvd.32044092008168 1146 19 pon pon PROPN hvd.32044092008168 1146 20 1)(u 1)(u NUM hvd.32044092008168 1146 21 ) ) PUNCT hvd.32044092008168 1146 22 ọ ọ NOUN hvd.32044092008168 1146 23 - - PUNCT hvd.32044092008168 1146 24 ) ) PUNCT hvd.32044092008168 1146 25 + + CCONJ hvd.32044092008168 1146 26 we we PRON hvd.32044092008168 1146 27 have have VERB hvd.32044092008168 1146 28 then then ADV hvd.32044092008168 1146 29 a a DET hvd.32044092008168 1146 30 decomposition decomposition NOUN hvd.32044092008168 1146 31 in in ADP hvd.32044092008168 1146 32 the the DET hvd.32044092008168 1146 33 form form NOUN hvd.32044092008168 1146 34 [ [ X hvd.32044092008168 1146 35 175 175 NUM hvd.32044092008168 1146 36 ] ] PUNCT hvd.32044092008168 1146 37 · · PUNCT hvd.32044092008168 1146 38 fi fi PROPN hvd.32044092008168 1146 39 ( ( PUNCT hvd.32044092008168 1146 40 u u NOUN hvd.32044092008168 1146 41 ) ) PUNCT hvd.32044092008168 1146 42 = = X hvd.32044092008168 1147 1 ce ce PROPN hvd.32044092008168 1147 2 * * PUNCT hvd.32044092008168 1147 3 * * PUNCT hvd.32044092008168 1147 4 + + NUM hvd.32044092008168 1147 5 2x4 2x4 NUM hvd.32044092008168 1147 6 gom gom NOUN hvd.32044092008168 1147 7 ( ( PUNCT hvd.32044092008168 1147 8 = = ADJ hvd.32044092008168 1147 9 c c NOUN hvd.32044092008168 1147 10 + + PROPN hvd.32044092008168 1147 11 σσα σσα PROPN hvd.32044092008168 1147 12 , , PUNCT hvd.32044092008168 1147 13 q(v q(v PROPN hvd.32044092008168 1147 14 ) ) PUNCT hvd.32044092008168 1147 15 u u PROPN hvd.32044092008168 1147 16 . . PUNCT hvd.32044092008168 1148 1 vn vn PROPN hvd.32044092008168 1148 2 ) ) PUNCT hvd.32044092008168 1148 3 m m VERB hvd.32044092008168 1148 4 v v ADP hvd.32044092008168 1148 5 where where SCONJ hvd.32044092008168 1148 6 vn vn PROPN hvd.32044092008168 1148 7 stands stand VERB hvd.32044092008168 1148 8 for for ADP hvd.32044092008168 1148 9 the the DET hvd.32044092008168 1148 10 several several ADJ hvd.32044092008168 1148 11 infinites infinite NOUN hvd.32044092008168 1148 12 of of ADP hvd.32044092008168 1148 13 fi(u fi(u PROPN hvd.32044092008168 1148 14 ) ) PUNCT hvd.32044092008168 1148 15 and and CCONJ hvd.32044092008168 1148 16 q q X hvd.32044092008168 1148 17 ( ( PUNCT hvd.32044092008168 1148 18 ) ) PUNCT hvd.32044092008168 1148 19 for for ADP hvd.32044092008168 1148 20 the the DET hvd.32044092008168 1148 21 derivatives derivative NOUN hvd.32044092008168 1148 22 where where SCONJ hvd.32044092008168 1148 23 v v PROPN hvd.32044092008168 1148 24 must must AUX hvd.32044092008168 1148 25 be be AUX hvd.32044092008168 1148 26 of of ADP hvd.32044092008168 1148 27 an an DET hvd.32044092008168 1148 28 order order NOUN hvd.32044092008168 1148 29 one one NUM hvd.32044092008168 1148 30 degree degree NOUN hvd.32044092008168 1148 31 less less ADJ hvd.32044092008168 1148 32 than than ADP hvd.32044092008168 1148 33 the the DET hvd.32044092008168 1148 34 multiplicity multiplicity NOUN hvd.32044092008168 1148 35 of of ADP hvd.32044092008168 1148 36 the the DET hvd.32044092008168 1148 37 infinites infinite NOUN hvd.32044092008168 1148 38 . . PUNCT hvd.32044092008168 1149 1 the the DET hvd.32044092008168 1149 2 coefficients coefficient NOUN hvd.32044092008168 1149 3 a a PRON hvd.32044092008168 1149 4 will will AUX hvd.32044092008168 1149 5 be be AUX hvd.32044092008168 1149 6 determined determine VERB hvd.32044092008168 1149 7 in in ADP hvd.32044092008168 1149 8 general general ADJ hvd.32044092008168 1149 9 by by ADP hvd.32044092008168 1149 10 developing develop VERB hvd.32044092008168 1149 11 fi(u fi(u PROPN hvd.32044092008168 1149 12 ) ) PUNCT hvd.32044092008168 1149 13 according accord VERB hvd.32044092008168 1149 14 to to ADP hvd.32044092008168 1149 15 the the DET hvd.32044092008168 1149 16 powers power NOUN hvd.32044092008168 1149 17 of of ADP hvd.32044092008168 1149 18 ( ( PUNCT hvd.32044092008168 1149 19 u u PROPN hvd.32044092008168 1149 20 — — PUNCT hvd.32044092008168 1149 21 vn vn PROPN hvd.32044092008168 1149 22 ) ) PUNCT hvd.32044092008168 1149 23 while while SCONJ hvd.32044092008168 1149 24 c c PROPN hvd.32044092008168 1149 25 will will AUX hvd.32044092008168 1149 26 be be AUX hvd.32044092008168 1149 27 a a DET hvd.32044092008168 1149 28 fixed fix VERB hvd.32044092008168 1149 29 value value NOUN hvd.32044092008168 1149 30 depending depend VERB hvd.32044092008168 1149 31 upon upon SCONJ hvd.32044092008168 1149 32 the the DET hvd.32044092008168 1149 33 given give VERB hvd.32044092008168 1149 34 conditions condition NOUN hvd.32044092008168 1149 35 . . PUNCT hvd.32044092008168 1150 1 in in ADP hvd.32044092008168 1150 2 our our PRON hvd.32044092008168 1150 3 case case NOUN hvd.32044092008168 1150 4 then then ADV hvd.32044092008168 1150 5 we we PRON hvd.32044092008168 1150 6 may may AUX hvd.32044092008168 1150 7 write write VERB hvd.32044092008168 1150 8 [ [ X hvd.32044092008168 1150 9 176 176 NUM hvd.32044092008168 1150 10 ] ] PUNCT hvd.32044092008168 1150 11 · · PUNCT hvd.32044092008168 1150 12 f1 f1 PROPN hvd.32044092008168 1150 13 ( ( PUNCT hvd.32044092008168 1150 14 u u PROPN hvd.32044092008168 1150 15 ) ) PUNCT hvd.32044092008168 1150 16 celu celu X hvd.32044092008168 1150 17 + + PROPN hvd.32044092008168 1150 18 fu fu PROPN hvd.32044092008168 1150 19 elu elu PROPN hvd.32044092008168 1150 20 . . PUNCT hvd.32044092008168 1151 1 this this DET hvd.32044092008168 1151 2 function function NOUN hvd.32044092008168 1151 3 when when SCONJ hvd.32044092008168 1151 4 v v ADP hvd.32044092008168 1151 5 is be AUX hvd.32044092008168 1151 6 zero zero NUM hvd.32044092008168 1151 7 , , PUNCT hvd.32044092008168 1151 8 in in ADP hvd.32044092008168 1151 9 which which DET hvd.32044092008168 1151 10 case case NOUN hvd.32044092008168 1151 11 o=0 o=0 PROPN hvd.32044092008168 1151 12 and and CCONJ hvd.32044092008168 1151 13 d=0 d=0 SPACE hvd.32044092008168 1151 14 , , PUNCT hvd.32044092008168 1151 15 takes take VERB hvd.32044092008168 1151 16 the the DET hvd.32044092008168 1151 17 place place NOUN hvd.32044092008168 1151 18 of of ADP hvd.32044092008168 1151 19 f(u f(u NOUN hvd.32044092008168 1151 20 ) ) PUNCT hvd.32044092008168 1151 21 and and CCONJ hvd.32044092008168 1151 22 hence hence ADV hvd.32044092008168 1151 23 the the DET hvd.32044092008168 1151 24 general general ADJ hvd.32044092008168 1151 25 solution solution NOUN hvd.32044092008168 1151 26 is be AUX hvd.32044092008168 1151 27 y y PROPN hvd.32044092008168 1151 28 = = X hvd.32044092008168 1151 29 fi fi PROPN hvd.32044092008168 1151 30 " " PUNCT hvd.32044092008168 1151 31 ( ( PUNCT hvd.32044092008168 1151 32 u u PROPN hvd.32044092008168 1151 33 ) ) PUNCT hvd.32044092008168 1151 34 — — PUNCT hvd.32044092008168 1151 35 3 3 NUM hvd.32044092008168 1151 36 bf bf NOUN hvd.32044092008168 1151 37 , , PUNCT hvd.32044092008168 1151 38 u u PROPN hvd.32044092008168 1151 39 yı yı X hvd.32044092008168 1151 40 — — PUNCT hvd.32044092008168 1151 41 = = SYM hvd.32044092008168 1151 42 ( ( PUNCT hvd.32044092008168 1151 43 celu celu X hvd.32044092008168 1151 44 + + PROPN hvd.32044092008168 1151 45 çu.epu çu.epu PROPN hvd.32044092008168 1151 46 ) ) PUNCT hvd.32044092008168 1151 47 " " PUNCT hvd.32044092008168 1151 48 – – PUNCT hvd.32044092008168 1151 49 3b 3b NUM hvd.32044092008168 1151 50 ( ( PUNCT hvd.32044092008168 1151 51 $ $ SYM hvd.32044092008168 1151 52 1.epu 1.epu NUM hvd.32044092008168 1151 53 + + SYM hvd.32044092008168 1151 54 ceer ceer NOUN hvd.32044092008168 1151 55 ) ) PUNCT hvd.32044092008168 1151 56 + + CCONJ hvd.32044092008168 1151 57 fi fi NOUN hvd.32044092008168 1151 58 ' ' PUNCT hvd.32044092008168 1151 59 ( ( PUNCT hvd.32044092008168 1151 60 u u PROPN hvd.32044092008168 1151 61 ) ) PUNCT hvd.32044092008168 1151 62 pcelu pcelu NOUN hvd.32044092008168 1151 63 + + CCONJ hvd.32044092008168 1151 64 sueou sueou NOUN hvd.32044092008168 1151 65 tos to NOUN hvd.32044092008168 1151 66 ( ( PUNCT hvd.32044092008168 1151 67 ) ) PUNCT hvd.32044092008168 1151 68 elu elu PROPN hvd.32044092008168 1151 69 fi fi PROPN hvd.32044092008168 1151 70 ” " PUNCT hvd.32044092008168 1151 71 ( ( PUNCT hvd.32044092008168 1151 72 u u PROPN hvd.32044092008168 1151 73 ) ) PUNCT hvd.32044092008168 1151 74 pcepu pcepu NOUN hvd.32044092008168 1151 75 + + CCONJ hvd.32044092008168 1151 76 sueou sueou NOUN hvd.32044092008168 1151 77 + + NUM hvd.32044092008168 1151 78 2 2 NUM hvd.32044092008168 1151 79 08 08 NUM hvd.32044092008168 1151 80 ' ' PUNCT hvd.32044092008168 1151 81 ( ( PUNCT hvd.32044092008168 1151 82 u)epu u)epu PROPN hvd.32044092008168 1151 83 + + PROPN hvd.32044092008168 1151 84 9%84(u 9%84(u NUM hvd.32044092008168 1151 85 ) ) PUNCT hvd.32044092008168 1151 86 eeu eeu NOUN hvd.32044092008168 1151 87 whence whence NOUN hvd.32044092008168 1151 88 ( ( PUNCT hvd.32044092008168 1151 89 suceu suceu NOUN hvd.32044092008168 1151 90 ) ) PUNCT hvd.32044092008168 1151 91 ” " PUNCT hvd.32044092008168 1151 92 = = VERB hvd.32044092008168 1151 93 6 6 NUM hvd.32044092008168 1151 94 " " PUNCT hvd.32044092008168 1151 95 uctu uctu ADJ hvd.32044092008168 1151 96 + + PROPN hvd.32044092008168 1151 97 2 2 NUM hvd.32044092008168 1151 98 congu congu NOUN hvd.32044092008168 1152 1 + + CCONJ hvd.32044092008168 1152 2 p*ccugu p*ccugu INTJ hvd.32044092008168 1153 1 uçu uçu INTJ hvd.32044092008168 1154 1 and and CCONJ hvd.32044092008168 1154 2 we we PRON hvd.32044092008168 1154 3 have have VERB hvd.32044092008168 1154 4 [ [ PUNCT hvd.32044092008168 1154 5 177 177 NUM hvd.32044092008168 1154 6 ] ] PUNCT hvd.32044092008168 1154 7 yı yı PROPN hvd.32044092008168 1154 8 ( ( PUNCT hvd.32044092008168 1154 9 & & CCONJ hvd.32044092008168 1154 10 u u PROPN hvd.32044092008168 1154 11 elu elu PROPN hvd.32044092008168 1154 12 3 3 NUM hvd.32044092008168 1154 13 bucou bucou PROPN hvd.32044092008168 1154 14 + + SYM hvd.32044092008168 1154 15 c'eru c'eru PROPN hvd.32044092008168 1154 16 = = SYM hvd.32044092008168 1154 17 4 4 NUM hvd.32044092008168 1154 18 * * PUNCT hvd.32044092008168 1155 1 [ [ X hvd.32044092008168 1155 2 s s X hvd.32044092008168 1155 3 " " PUNCT hvd.32044092008168 1155 4 u u PROPN hvd.32044092008168 1155 5 + + PROPN hvd.32044092008168 1155 6 2 2 NUM hvd.32044092008168 1155 7 08'u 08'u ADJ hvd.32044092008168 1156 1 + + PUNCT hvd.32044092008168 1156 2 ( ( PUNCT hvd.32044092008168 1156 3 o o NOUN hvd.32044092008168 1156 4 ? ? PUNCT hvd.32044092008168 1156 5 — — PUNCT hvd.32044092008168 1156 6 36 36 NUM hvd.32044092008168 1156 7 ) ) PUNCT hvd.32044092008168 1156 8 81 81 NUM hvd.32044092008168 1156 9 + + CCONJ hvd.32044092008168 1156 10 c c X hvd.32044092008168 1156 11 ) ) PUNCT hvd.32044092008168 1156 12 . . PUNCT hvd.32044092008168 1157 1 but but CCONJ hvd.32044092008168 1157 2 from from ADP hvd.32044092008168 1157 3 the the DET hvd.32044092008168 1157 4 foregoing forego VERB hvd.32044092008168 1157 5 theory theory NOUN hvd.32044092008168 1157 6 in in ADP hvd.32044092008168 1157 7 this this DET hvd.32044092008168 1157 8 case case NOUN hvd.32044092008168 1157 9 we we PRON hvd.32044092008168 1157 10 have have VERB hvd.32044092008168 1157 11 the the DET hvd.32044092008168 1157 12 coefficients coefficient NOUN hvd.32044092008168 1157 13 of of ADP hvd.32044092008168 1157 14 $ $ SYM hvd.32044092008168 1157 15 ( ( PUNCT hvd.32044092008168 1157 16 u u PROPN hvd.32044092008168 1157 17 ) ) PUNCT hvd.32044092008168 1157 18 equal equal ADJ hvd.32044092008168 1157 19 to to ADP hvd.32044092008168 1157 20 zero zero NUM hvd.32044092008168 1157 21 , , PUNCT hvd.32044092008168 1157 22 i. i. PROPN hvd.32044092008168 1157 23 e. e. PROPN hvd.32044092008168 1157 24 u u PROPN hvd.32044092008168 1157 25 or or CCONJ hvd.32044092008168 1157 26 02 02 NUM hvd.32044092008168 1157 27 36 36 NUM hvd.32044092008168 1157 28 0 0 NUM hvd.32044092008168 1158 1 [ [ X hvd.32044092008168 1158 2 178 178 NUM hvd.32044092008168 1158 3 ] ] PUNCT hvd.32044092008168 1158 4 : : PUNCT hvd.32044092008168 1158 5 e e X hvd.32044092008168 1158 6 ? ? PUNCT hvd.32044092008168 1159 1 3b 3b NUM hvd.32044092008168 1159 2 . . PUNCT hvd.32044092008168 1160 1 78 78 NUM hvd.32044092008168 1160 2 part part NOUN hvd.32044092008168 1160 3 v. v. ADP hvd.32044092008168 1160 4 reduction reduction NOUN hvd.32044092008168 1160 5 of of ADP hvd.32044092008168 1160 6 the the DET hvd.32044092008168 1160 7 forms form NOUN hvd.32044092008168 1160 8 when when SCONJ hvd.32044092008168 1160 9 n n SYM hvd.32044092008168 1160 10 equals equal VERB hvd.32044092008168 1160 11 three three NUM hvd.32044092008168 1160 12 . . PUNCT hvd.32044092008168 1161 1 to to PART hvd.32044092008168 1161 2 find find VERB hvd.32044092008168 1161 3 c c PROPN hvd.32044092008168 1161 4 we we PRON hvd.32044092008168 1161 5 proceed proceed VERB hvd.32044092008168 1161 6 as as SCONJ hvd.32044092008168 1161 7 follows follow VERB hvd.32044092008168 1161 8 : : PUNCT hvd.32044092008168 1161 9 1 1 NUM hvd.32044092008168 1161 10 eu eu PROPN hvd.32044092008168 1161 11 92 92 NUM hvd.32044092008168 1161 12 u u PROPN hvd.32044092008168 1161 13 3 3 NUM hvd.32044092008168 1161 14 u u PROPN hvd.32044092008168 1161 15 20 20 NUM hvd.32044092008168 1161 16 3 3 NUM hvd.32044092008168 1161 17 t'u t'u DET hvd.32044092008168 1161 18 11 11 NUM hvd.32044092008168 1161 19 u2 u2 PROPN hvd.32044092008168 1161 20 .. .. PUNCT hvd.32044092008168 1161 21 2 2 NUM hvd.32044092008168 1161 22 u u PROPN hvd.32044092008168 1161 23 ? ? PROPN hvd.32044092008168 1161 24 20 20 NUM hvd.32044092008168 1161 25 & & CCONJ hvd.32044092008168 1161 26 " " PUNCT hvd.32044092008168 1161 27 u u PROPN hvd.32044092008168 1161 28 u u PROPN hvd.32044092008168 1161 29 92 92 NUM hvd.32044092008168 1161 30 u u PROPN hvd.32044092008168 1161 31 10 10 NUM hvd.32044092008168 1161 32 . . PUNCT hvd.32044092008168 1162 1 us we PRON hvd.32044092008168 1162 2 p?u p?u PROPN hvd.32044092008168 1162 3 ? ? PROPN hvd.32044092008168 1162 4 0 0 NUM hvd.32044092008168 1162 5 ° ° NUM hvd.32044092008168 1162 6 43 43 NUM hvd.32044092008168 1162 7 clu clu PROPN hvd.32044092008168 1162 8 6 6 NUM hvd.32044092008168 1162 9 3 3 NUM hvd.32044092008168 1162 10 2 2 NUM hvd.32044092008168 1162 11 92 92 NUM hvd.32044092008168 1162 12 10 10 NUM hvd.32044092008168 1162 13 u u NOUN hvd.32044092008168 1162 14 3 3 NUM hvd.32044092008168 1162 15 ga ga NOUN hvd.32044092008168 1162 16 20 20 NUM hvd.32044092008168 1162 17 u² u² PROPN hvd.32044092008168 1162 18 . . PUNCT hvd.32044092008168 1163 1 1 1 NUM hvd.32044092008168 1163 2 + + CCONJ hvd.32044092008168 1163 3 ou ou X hvd.32044092008168 1163 4 + + PROPN hvd.32044092008168 1163 5 t t PROPN hvd.32044092008168 1163 6 .. .. PUNCT hvd.32044092008168 1164 1 hence hence ADV hvd.32044092008168 1164 2 ou ou ADV hvd.32044092008168 1164 3 " " PUNCT hvd.32044092008168 1164 4 y y PROPN hvd.32044092008168 1164 5 = = PROPN hvd.32044092008168 1164 6 ( ( PUNCT hvd.32044092008168 1164 7 1 1 NUM hvd.32044092008168 1164 8 + + X hvd.32044092008168 1164 9 ou ou NOUN hvd.32044092008168 1164 10 + + NOUN hvd.32044092008168 1164 11 pu pu NOUN hvd.32044092008168 1164 12 ? ? PUNCT hvd.32044092008168 1165 1 + + PUNCT hvd.32044092008168 1166 1 + + PUNCT hvd.32044092008168 1166 2 - - PUNCT hvd.32044092008168 1166 3 ] ] X hvd.32044092008168 1166 4 { { PUNCT hvd.32044092008168 1166 5 [ [ PUNCT hvd.32044092008168 1166 6 % % INTJ hvd.32044092008168 1166 7 + + DET hvd.32044092008168 1166 8 - - PUNCT hvd.32044092008168 1166 9 ] ] X hvd.32044092008168 1166 10 6 6 NUM hvd.32044092008168 1166 11 20 20 NUM hvd.32044092008168 1167 1 [ [ PUNCT hvd.32044092008168 1167 2 + + NUM hvd.32044092008168 1167 3 + + NUM hvd.32044092008168 1167 4 0 0 NUM hvd.32044092008168 1167 5 * * NUM hvd.32044092008168 1167 6 20 20 NUM hvd.32044092008168 1167 7 * * PUNCT hvd.32044092008168 1167 8 + + PUNCT hvd.32044092008168 1167 9 ... ... PUNCT hvd.32044092008168 1167 10 ] ] X hvd.32044092008168 1168 1 + + PUNCT hvd.32044092008168 1168 2 c+ c+ X hvd.32044092008168 1168 3 ... ... PUNCT hvd.32044092008168 1168 4 } } PUNCT hvd.32044092008168 1168 5 and and CCONJ hvd.32044092008168 1168 6 taking take VERB hvd.32044092008168 1168 7 c c NOUN hvd.32044092008168 1168 8 so so SCONJ hvd.32044092008168 1168 9 that that SCONJ hvd.32044092008168 1168 10 the the DET hvd.32044092008168 1168 11 constant constant ADJ hvd.32044092008168 1168 12 term term NOUN hvd.32044092008168 1168 13 equal equal ADJ hvd.32044092008168 1168 14 zero zero NUM hvd.32044092008168 1168 15 we we PRON hvd.32044092008168 1168 16 have have VERB hvd.32044092008168 1168 17 [ [ X hvd.32044092008168 1168 18 179 179 NUM hvd.32044092008168 1168 19 ] ] SYM hvd.32044092008168 1168 20 03 03 NUM hvd.32044092008168 1168 21 = = SYM hvd.32044092008168 1168 22 2 2 NUM hvd.32044092008168 1168 23 pb pb PROPN hvd.32044092008168 1168 24 . . PUNCT hvd.32044092008168 1168 25 2ob 2ob PROPN hvd.32044092008168 1169 1 the the DET hvd.32044092008168 1169 2 general general ADJ hvd.32044092008168 1169 3 solution solution NOUN hvd.32044092008168 1169 4 ( ( PUNCT hvd.32044092008168 1169 5 v v NOUN hvd.32044092008168 1169 6 = = SYM hvd.32044092008168 1169 7 0 0 NUM hvd.32044092008168 1169 8 ) ) PUNCT hvd.32044092008168 1169 9 is be AUX hvd.32044092008168 1169 10 then then ADV hvd.32044092008168 1169 11 : : PUNCT hvd.32044092008168 1169 12 ) ) PUNCT hvd.32044092008168 1169 13 yi yi PROPN hvd.32044092008168 1169 14 ( ( PUNCT hvd.32044092008168 1169 15 su su PROPN hvd.32044092008168 1169 16 eo eo PROPN hvd.32044092008168 1169 17 u u PROPN hvd.32044092008168 1169 18 ) ) PUNCT hvd.32044092008168 1169 19 " " PUNCT hvd.32044092008168 1169 20 – – PUNCT hvd.32044092008168 1169 21 36(su 36(su NUM hvd.32044092008168 1169 22 •efu •efu SPACE hvd.32044092008168 1169 23 ) ) PUNCT hvd.32044092008168 1169 24 + + CCONJ hvd.32044092008168 1169 25 2 2 NUM hvd.32044092008168 1169 26 obegu obegu NOUN hvd.32044092008168 1169 27 where where SCONJ hvd.32044092008168 1169 28 v3b v3b PROPN hvd.32044092008168 1169 29 . . PROPN hvd.32044092008168 1170 1 2 2 NUM hvd.32044092008168 1170 2 c c PROPN hvd.32044092008168 1170 3 = = NOUN hvd.32044092008168 1170 4 . . PUNCT hvd.32044092008168 1171 1 3 3 NUM hvd.32044092008168 1171 2 finis fini NOUN hvd.32044092008168 1171 3 . . PUNCT hvd.32044092008168 1172 1 table table NOUN hvd.32044092008168 1172 2 of of ADP hvd.32044092008168 1172 3 forms form NOUN hvd.32044092008168 1172 4 n n CCONJ hvd.32044092008168 1172 5 3 3 NUM hvd.32044092008168 1172 6 . . PUNCT hvd.32044092008168 1173 1 where where SCONJ hvd.32044092008168 1173 2 and and CCONJ hvd.32044092008168 1173 3 the the DET hvd.32044092008168 1173 4 complete complete ADJ hvd.32044092008168 1173 5 integral integral NOUN hvd.32044092008168 1173 6 is be AUX hvd.32044092008168 1173 7 where where SCONJ hvd.32044092008168 1173 8 y y PROPN hvd.32044092008168 1173 9 y y PROPN hvd.32044092008168 1173 10 = = X hvd.32044092008168 1173 11 = = PUNCT hvd.32044092008168 1173 12 y₁cf(u)+c'f y₁cf(u)+c'f SPACE hvd.32044092008168 1173 13 ' ' PUNCT hvd.32044092008168 1173 14 ( ( PUNCT hvd.32044092008168 1173 15 — — PUNCT hvd.32044092008168 1173 16 u u PROPN hvd.32044092008168 1173 17 ) ) PUNCT hvd.32044092008168 1173 18 f(u f(u PROPN hvd.32044092008168 1173 19 ) ) PUNCT hvd.32044092008168 1173 20 = = X hvd.32044092008168 1173 21 f f X hvd.32044092008168 1173 22 '' '' PUNCT hvd.32044092008168 1173 23 ( ( PUNCT hvd.32044092008168 1173 24 u u PROPN hvd.32044092008168 1173 25 ) ) PUNCT hvd.32044092008168 1173 26 — — PUNCT hvd.32044092008168 1173 27 3bf 3bf ADJ hvd.32044092008168 1173 28 ( ( PUNCT hvd.32044092008168 1173 29 u u PROPN hvd.32044092008168 1173 30 ) ) PUNCT hvd.32044092008168 1173 31 e(x-(v)u e(x-(v)u VERB hvd.32044092008168 1173 32 the the DET hvd.32044092008168 1173 33 ordinary ordinary ADJ hvd.32044092008168 1173 34 form form NOUN hvd.32044092008168 1173 35 of of ADP hvd.32044092008168 1173 36 the the DET hvd.32044092008168 1173 37 equation equation NOUN hvd.32044092008168 1173 38 of of ADP hvd.32044092008168 1173 39 hermite hermite NOUN hvd.32044092008168 1173 40 for for ADP hvd.32044092008168 1173 41 n n PROPN hvd.32044092008168 1173 42 ii ii AUX hvd.32044092008168 1173 43 a a X hvd.32044092008168 1173 44 = = PROPN hvd.32044092008168 1173 45 a a PRON hvd.32044092008168 1173 46 , , PUNCT hvd.32044092008168 1173 47 b b NOUN hvd.32044092008168 1173 48 , , PUNCT hvd.32044092008168 1173 49 c c PROPN hvd.32044092008168 1173 50 o o PROPN hvd.32044092008168 1173 51 ( ( PUNCT hvd.32044092008168 1173 52 u u PROPN hvd.32044092008168 1173 53 forms form VERB hvd.32044092008168 1173 54 for for ADP hvd.32044092008168 1173 55 n n CCONJ hvd.32044092008168 1173 56 = = SYM hvd.32044092008168 1173 57 3 3 X hvd.32044092008168 1173 58 . . PUNCT hvd.32044092008168 1173 59 = = NOUN hvd.32044092008168 1174 1 a a DET hvd.32044092008168 1174 2 second second ADJ hvd.32044092008168 1174 3 form form NOUN hvd.32044092008168 1174 4 of of ADP hvd.32044092008168 1174 5 the the DET hvd.32044092008168 1174 6 integral integral NOUN hvd.32044092008168 1174 7 is be AUX hvd.32044092008168 1174 8 : : PUNCT hvd.32044092008168 1174 9 o o X hvd.32044092008168 1174 10 ( ( PUNCT hvd.32044092008168 1174 11 u u PROPN hvd.32044092008168 1174 12 + + CCONJ hvd.32044092008168 1174 13 a a X hvd.32044092008168 1174 14 ) ) PUNCT hvd.32044092008168 1174 15 ба ба ADP hvd.32044092008168 1174 16 би би PROPN hvd.32044092008168 1174 17 f(u f(u PROPN hvd.32044092008168 1174 18 ) ) PUNCT hvd.32044092008168 1174 19 x x PUNCT hvd.32044092008168 1175 1 = = X hvd.32044092008168 1175 2 ev ev INTJ hvd.32044092008168 1175 3 — — PUNCT hvd.32044092008168 1175 4 = = PRON hvd.32044092008168 1175 5 d2y d2y VERB hvd.32044092008168 1175 6 du2 du2 DET hvd.32044092008168 1175 7 σ σ PROPN hvd.32044092008168 1175 8 ( ( PUNCT hvd.32044092008168 1175 9 u u PROPN hvd.32044092008168 1175 10 + + CCONJ hvd.32044092008168 1175 11 v v NOUN hvd.32044092008168 1175 12 ) ) PUNCT hvd.32044092008168 1175 13 συσν συσν PROPN hvd.32044092008168 1175 14 = = PROPN hvd.32044092008168 1176 1 [ [ X hvd.32044092008168 1176 2 12p(u 12p(u NUM hvd.32044092008168 1176 3 ) ) PUNCT hvd.32044092008168 1176 4 + + PUNCT hvd.32044092008168 1176 5 b]y b]y PROPN hvd.32044092008168 1176 6 . . PUNCT hvd.32044092008168 1177 1 ― ― PROPN hvd.32044092008168 1178 1 a a X hvd.32044092008168 1178 2 ) ) PUNCT hvd.32044092008168 1178 3 o o NOUN hvd.32044092008168 1179 1 ( ( PUNCT hvd.32044092008168 1179 2 u u PROPN hvd.32044092008168 1179 3 ca can AUX hvd.32044092008168 1179 4 ob ob PROPN hvd.32044092008168 1179 5 oc oc PROPN hvd.32044092008168 1179 6 ( ( PUNCT hvd.32044092008168 1179 7 ou)3 ou)3 NOUN hvd.32044092008168 1179 8 e e NOUN hvd.32044092008168 1179 9 — — PUNCT hvd.32044092008168 1179 10 u$a u$a NOUN hvd.32044092008168 1179 11 = = X hvd.32044092008168 1179 12 ] ] X hvd.32044092008168 1179 13 ] ] X hvd.32044092008168 1179 14 º º NOUN hvd.32044092008168 1179 15 ( ( PUNCT hvd.32044092008168 1179 16 u u PROPN hvd.32044092008168 1179 17 — — PUNCT hvd.32044092008168 1179 18 a a X hvd.32044092008168 1179 19 ) ) PUNCT hvd.32044092008168 1179 20 ii ii PROPN hvd.32044092008168 1179 21 баб баб PROPN hvd.32044092008168 1179 22 0 0 NUM hvd.32044092008168 1179 23 a a DET hvd.32044092008168 1179 24 = = PROPN hvd.32044092008168 1179 25 a a DET hvd.32044092008168 1179 26 , , PUNCT hvd.32044092008168 1179 27 b b NOUN hvd.32044092008168 1179 28 , , PUNCT hvd.32044092008168 1179 29 c c PROPN hvd.32044092008168 1179 30 b b NOUN hvd.32044092008168 1179 31 ) ) PUNCT hvd.32044092008168 1179 32 o o NOUN hvd.32044092008168 1180 1 ( ( PUNCT hvd.32044092008168 1180 2 u u PROPN hvd.32044092008168 1180 3 ea ea PROPN hvd.32044092008168 1180 4 — — PUNCT hvd.32044092008168 1180 5 eb eb PROPN hvd.32044092008168 1180 6 — — PUNCT hvd.32044092008168 1180 7 ec ec PROPN hvd.32044092008168 1180 8 ફ્ ફ્ PROPN hvd.32044092008168 1180 9 = = VERB hvd.32044092008168 1180 10 v v ADP hvd.32044092008168 1180 11 = = NOUN hvd.32044092008168 1180 12 a+b+c a+b+c ADV hvd.32044092008168 1180 13 and and CCONJ hvd.32044092008168 1180 14 b b PRON hvd.32044092008168 1180 15 156 156 NUM hvd.32044092008168 1180 16 which which PRON hvd.32044092008168 1180 17 is be AUX hvd.32044092008168 1180 18 intirely intirely ADV hvd.32044092008168 1180 19 arbitrary arbitrary ADJ hvd.32044092008168 1180 20 and and CCONJ hvd.32044092008168 1180 21 is be AUX hvd.32044092008168 1180 22 originally originally ADV hvd.32044092008168 1180 23 expressed express VERB hvd.32044092008168 1180 24 in in ADP hvd.32044092008168 1180 25 the the DET hvd.32044092008168 1180 26 form form NOUN hvd.32044092008168 1180 27 b b PROPN hvd.32044092008168 1180 28 = = NOUN hvd.32044092008168 1180 29 h h NOUN hvd.32044092008168 1180 30 ( ( PUNCT hvd.32044092008168 1180 31 e₁ e₁ PROPN hvd.32044092008168 1180 32 — — PUNCT hvd.32044092008168 1180 33 e3 e3 PROPN hvd.32044092008168 1180 34 ) ) PUNCT hvd.32044092008168 1180 35 — — PUNCT hvd.32044092008168 1180 36 n n NOUN hvd.32044092008168 1180 37 ( ( PUNCT hvd.32044092008168 1180 38 n n X hvd.32044092008168 1180 39 + + CCONJ hvd.32044092008168 1180 40 1 1 X hvd.32044092008168 1180 41 ) ) PUNCT hvd.32044092008168 1180 42 ez ez PROPN hvd.32044092008168 1180 43 = = PROPN hvd.32044092008168 1180 44 in in ADP hvd.32044092008168 1180 45 which which DET hvd.32044092008168 1180 46 case case NOUN hvd.32044092008168 1180 47 the the DET hvd.32044092008168 1180 48 equation equation NOUN hvd.32044092008168 1180 49 of of ADP hvd.32044092008168 1180 50 hermite hermite PROPN hvd.32044092008168 1180 51 is be AUX hvd.32044092008168 1180 52 d2y d2y NOUN hvd.32044092008168 1180 53 dx2 dx2 PROPN hvd.32044092008168 1180 54 c c X hvd.32044092008168 1180 55 ) ) PUNCT hvd.32044092008168 1180 56 we we PRON hvd.32044092008168 1180 57 have have VERB hvd.32044092008168 1180 58 also also ADV hvd.32044092008168 1180 59 the the DET hvd.32044092008168 1180 60 general general ADJ hvd.32044092008168 1180 61 form form NOUN hvd.32044092008168 1180 62 : : PUNCT hvd.32044092008168 1180 63 y y PROPN hvd.32044092008168 1180 64 = = PRON hvd.32044092008168 1180 65 ±vy=√(pu ±vy=√(pu PROPN hvd.32044092008168 1180 66 — — PUNCT hvd.32044092008168 1180 67 e¸ e¸ X hvd.32044092008168 1180 68 ) ) PUNCT hvd.32044092008168 1180 69 * * PUNCT hvd.32044092008168 1181 1 ( ( PUNCT hvd.32044092008168 1181 2 pu pu PROPN hvd.32044092008168 1181 3 e e PROPN hvd.32044092008168 1181 4 , , PUNCT hvd.32044092008168 1181 5 é é PROPN hvd.32044092008168 1181 6 , , PUNCT hvd.32044092008168 1181 7 é é X hvd.32044092008168 1181 8 " " PUNCT hvd.32044092008168 1181 9 [ [ PUNCT hvd.32044092008168 1181 10 12 12 NUM hvd.32044092008168 1181 11 k² k² PROPN hvd.32044092008168 1181 12 sn² sn² VERB hvd.32044092008168 1181 13 x x PUNCT hvd.32044092008168 1181 14 + + CCONJ hvd.32044092008168 1181 15 h h X hvd.32044092008168 1181 16 ] ] X hvd.32044092008168 1181 17 . . PUNCT hvd.32044092008168 1182 1 e($a+56 e($a+56 PROPN hvd.32044092008168 1182 2 + + PROPN hvd.32044092008168 1182 3 5c 5c NUM hvd.32044092008168 1182 4 ) ) PUNCT hvd.32044092008168 1182 5 u u PROPN hvd.32044092008168 1182 6 ―― ―― PROPN hvd.32044092008168 1182 7 = = PROPN hvd.32044092008168 1182 8 ρυζα ρυζα NOUN hvd.32044092008168 1182 9 3 3 NUM hvd.32044092008168 1182 10 being be AUX hvd.32044092008168 1182 11 : : PUNCT hvd.32044092008168 1182 12 € € SYM hvd.32044092008168 1182 13 3)º 3)º NUM hvd.32044092008168 1182 14 ' ' PUNCT hvd.32044092008168 1182 15 ( ( PUNCT hvd.32044092008168 1182 16 pu pu PROPN hvd.32044092008168 1182 17 — — PUNCT hvd.32044092008168 1182 18 € € SYM hvd.32044092008168 1182 19 3)º″ 3)º″ NUM hvd.32044092008168 1182 20 ii ii PROPN hvd.32044092008168 1182 21 ( ( PUNCT hvd.32044092008168 1182 22 pu pu X hvd.32044092008168 1182 23 — — PUNCT hvd.32044092008168 1182 24 pa pa PROPN hvd.32044092008168 1182 25 ) ) PUNCT hvd.32044092008168 1182 26 : : PUNCT hvd.32044092008168 1182 27 0 0 NUM hvd.32044092008168 1182 28 or or CCONJ hvd.32044092008168 1182 29 1 1 NUM hvd.32044092008168 1182 30 . . PUNCT hvd.32044092008168 1182 31 82 82 NUM hvd.32044092008168 1182 32 table table NOUN hvd.32044092008168 1182 33 of of ADP hvd.32044092008168 1182 34 forms form NOUN hvd.32044092008168 1182 35 n n CCONJ hvd.32044092008168 1182 36 = = X hvd.32044092008168 1182 37 3 3 NUM hvd.32044092008168 1182 38 . . PUNCT hvd.32044092008168 1183 1 the the DET hvd.32044092008168 1183 2 functions function NOUN hvd.32044092008168 1183 3 developed develop VERB hvd.32044092008168 1183 4 in in ADP hvd.32044092008168 1183 5 the the DET hvd.32044092008168 1183 6 general general ADJ hvd.32044092008168 1183 7 theory theory NOUN hvd.32044092008168 1183 8 have have VERB hvd.32044092008168 1183 9 values value NOUN hvd.32044092008168 1183 10 as as SCONJ hvd.32044092008168 1183 11 follows follow VERB hvd.32044092008168 1183 12 : : PUNCT hvd.32044092008168 1183 13 ዎ ዎ DET hvd.32044092008168 1183 14 ø ø X hvd.32044092008168 1183 15 ' ' PUNCT hvd.32044092008168 1183 16 ዎ ዎ DET hvd.32044092008168 1183 17 ι ι PROPN hvd.32044092008168 1183 18 a1 a1 PROPN hvd.32044092008168 1183 19 b₁ b₁ PROPN hvd.32044092008168 1184 1 = = ADP hvd.32044092008168 1185 1 = = PUNCT hvd.32044092008168 1185 2 = = X hvd.32044092008168 1185 3 x² x² PROPN hvd.32044092008168 1185 4 = = X hvd.32044092008168 1185 5 = = PUNCT hvd.32044092008168 1185 6 1262 1262 NUM hvd.32044092008168 1185 7 3b==/ 3b==/ NUM hvd.32044092008168 1185 8 b b NOUN hvd.32044092008168 1185 9 4bs 4bs ADJ hvd.32044092008168 1185 10 - - PUNCT hvd.32044092008168 1185 11 bg2 bg2 NOUN hvd.32044092008168 1185 12 - - PUNCT hvd.32044092008168 1185 13 93 93 NUM hvd.32044092008168 1185 14 y(e₁ y(e₁ NOUN hvd.32044092008168 1185 15 ) ) PUNCT hvd.32044092008168 1185 16 3 3 NUM hvd.32044092008168 1185 17 4 4 NUM hvd.32044092008168 1185 18 where where SCONJ hvd.32044092008168 1185 19 φ φ PROPN hvd.32044092008168 1185 20 ( ( PUNCT hvd.32044092008168 1185 21 1 1 NUM hvd.32044092008168 1185 22 ) ) PUNCT hvd.32044092008168 1185 23 92 92 NUM hvd.32044092008168 1185 24 27 27 NUM hvd.32044092008168 1185 25 4 4 NUM hvd.32044092008168 1185 26 93 93 NUM hvd.32044092008168 1185 27 or or CCONJ hvd.32044092008168 1185 28 ø ø X hvd.32044092008168 1185 29 ( ( PUNCT hvd.32044092008168 1185 30 1 1 X hvd.32044092008168 1185 31 ) ) PUNCT hvd.32044092008168 1185 32 = = SYM hvd.32044092008168 1185 33 p(u p(u PROPN hvd.32044092008168 1185 34 ) ) PUNCT hvd.32044092008168 1185 35 6bq 6bq PROPN hvd.32044092008168 1185 36 ' ' PART hvd.32044092008168 1185 37 t'p'u[4 t'p'u[4 NUM hvd.32044092008168 1185 38 t³ t³ PROPN hvd.32044092008168 1185 39 — — PUNCT hvd.32044092008168 1185 40 tg₂-g3]2 tg₂-g3]2 X hvd.32044092008168 1185 41 21=0 21=0 NUM hvd.32044092008168 1185 42 s s VERB hvd.32044092008168 1185 43 t t PROPN hvd.32044092008168 1185 44 — — PUNCT hvd.32044092008168 1185 45 b b NOUN hvd.32044092008168 1185 46 ❤ ❤ NOUN hvd.32044092008168 1185 47 ( ( PUNCT hvd.32044092008168 1185 48 t t PROPN hvd.32044092008168 1185 49 ) ) PUNCT hvd.32044092008168 1185 50 = = VERB hvd.32044092008168 1185 51 4s³ 4s³ NUM hvd.32044092008168 1185 52 + + NUM hvd.32044092008168 1185 53 12bs² 12bs² NUM hvd.32044092008168 1185 54 + + PUNCT hvd.32044092008168 1185 55 ( ( PUNCT hvd.32044092008168 1185 56 1262 1262 NUM hvd.32044092008168 1185 57 — — PUNCT hvd.32044092008168 1185 58 g2 g2 PROPN hvd.32044092008168 1185 59 ) ) PUNCT hvd.32044092008168 1185 60 g g PROPN hvd.32044092008168 1186 1 +46³ +46³ X hvd.32044092008168 1186 2 — — PUNCT hvd.32044092008168 1186 3 bg2 bg2 CCONJ hvd.32044092008168 1186 4 = = PRON hvd.32044092008168 1186 5 483 483 NUM hvd.32044092008168 1186 6 + + NUM hvd.32044092008168 1186 7 12682 12682 NUM hvd.32044092008168 1186 8 + + PUNCT hvd.32044092008168 1187 1 ¢´s ¢´s X hvd.32044092008168 1188 1 + + NOUN hvd.32044092008168 1188 2 ❤ ❤ SYM hvd.32044092008168 1188 3 92 92 NUM hvd.32044092008168 1188 4 = = NOUN hvd.32044092008168 1188 5 = = X hvd.32044092008168 1188 6 p p PROPN hvd.32044092008168 1188 7 ―――― ―――― PROPN hvd.32044092008168 1188 8 c c PROPN hvd.32044092008168 1188 9 = = PROPN hvd.32044092008168 1188 10 bo bo PROPN hvd.32044092008168 1188 11 φ φ PROPN hvd.32044092008168 1188 12 ( ( PUNCT hvd.32044092008168 1188 13 0 0 X hvd.32044092008168 1188 14 ) ) PUNCT hvd.32044092008168 1188 15 sd2 sd2 X hvd.32044092008168 1188 16 = = PUNCT hvd.32044092008168 1188 17 — — PUNCT hvd.32044092008168 1188 18 9 9 NUM hvd.32044092008168 1188 19 ( ( PUNCT hvd.32044092008168 1188 20 t t PROPN hvd.32044092008168 1188 21 ) ) PUNCT hvd.32044092008168 1188 22 − − PROPN hvd.32044092008168 1189 1 b b X hvd.32044092008168 1190 1 [ [ X hvd.32044092008168 1190 2 ø ø X hvd.32044092008168 1190 3 ' ' PUNCT hvd.32044092008168 1190 4 + + NUM hvd.32044092008168 1190 5 3 3 NUM hvd.32044092008168 1190 6 ( ( PUNCT hvd.32044092008168 1190 7 t t NOUN hvd.32044092008168 1190 8 — — PUNCT hvd.32044092008168 1190 9 b)² b)² X hvd.32044092008168 1190 10 ] ] X hvd.32044092008168 1190 11 4 4 NUM hvd.32044092008168 1190 12 = = SYM hvd.32044092008168 1190 13 = = VERB hvd.32044092008168 1190 14 b₁ b₁ PROPN hvd.32044092008168 1190 15 -y -y PUNCT hvd.32044092008168 1190 16 = = PROPN hvd.32044092008168 1190 17 s³+ s³+ X hvd.32044092008168 1190 18 a‚s a‚s PROPN hvd.32044092008168 1190 19 + + PROPN hvd.32044092008168 1190 20 a¸= a¸= NOUN hvd.32044092008168 1190 21 s³ s³ NOUN hvd.32044092008168 1190 22 + + CCONJ hvd.32044092008168 1190 23 ¦ ¦ PROPN hvd.32044092008168 1190 24 9 9 NUM hvd.32044092008168 1190 25 ' ' PUNCT hvd.32044092008168 1190 26 s s NOUN hvd.32044092008168 1190 27 + + CCONJ hvd.32044092008168 1190 28 ¦ ¦ NOUN hvd.32044092008168 1190 29 ❤ ❤ PRON hvd.32044092008168 1190 30 — — PUNCT hvd.32044092008168 1190 31 bø′ bø′ NOUN hvd.32044092008168 1190 32 ዎ ዎ X hvd.32044092008168 1190 33 · · PUNCT hvd.32044092008168 1190 34 bo bo X hvd.32044092008168 1190 35 ' ' NOUN hvd.32044092008168 1190 36 4 4 NUM hvd.32044092008168 1190 37 = = SYM hvd.32044092008168 1190 38 1 1 NUM hvd.32044092008168 1190 39 15 15 NUM hvd.32044092008168 1190 40 = = PUNCT hvd.32044092008168 1190 41 · · PUNCT hvd.32044092008168 1190 42 s³ s³ PROPN hvd.32044092008168 1190 43 + + CCONJ hvd.32044092008168 1190 44 ( ( PUNCT hvd.32044092008168 1190 45 3 3 NUM hvd.32044092008168 1190 46 b² b² PROPN hvd.32044092008168 1190 47 — — PUNCT hvd.32044092008168 1190 48 — — PUNCT hvd.32044092008168 1190 49 9 9 NUM hvd.32044092008168 1190 50 ½ ½ X hvd.32044092008168 1190 51 ) ) PUNCT hvd.32044092008168 1190 52 § § NUM hvd.32044092008168 1190 53 — — PUNCT hvd.32044092008168 1190 54 1 1 NUM hvd.32044092008168 1190 55 ( ( PUNCT hvd.32044092008168 1190 56 44b³—3g₂b+93 44b³—3g₂b+93 NUM hvd.32044092008168 1190 57 ) ) PUNCT hvd.32044092008168 1190 58 = = X hvd.32044092008168 1190 59 19(t 19(t NUM hvd.32044092008168 1190 60 ) ) PUNCT hvd.32044092008168 1190 61 − − PROPN hvd.32044092008168 1190 62 b b PROPN hvd.32044092008168 1190 63 ( ( PUNCT hvd.32044092008168 1190 64 œ'+3,8² œ'+3,8² PROPN hvd.32044092008168 1190 65 ) ) PUNCT hvd.32044092008168 1190 66 ―――― ―――― PROPN hvd.32044092008168 1190 67 4 4 NUM hvd.32044092008168 1190 68 c3 c3 PROPN hvd.32044092008168 1190 69 15 15 NUM hvd.32044092008168 1190 70 b b NOUN hvd.32044092008168 1190 71 = = NOUN hvd.32044092008168 1190 72 t³ t³ PROPN hvd.32044092008168 1190 73 — — PUNCT hvd.32044092008168 1190 74 3bt² 3bt² PROPN hvd.32044092008168 1190 75 + + CCONJ hvd.32044092008168 1190 76 ( ( PUNCT hvd.32044092008168 1190 77 6b² 6b² NUM hvd.32044092008168 1190 78 — — PUNCT hvd.32044092008168 1190 79 — — PUNCT hvd.32044092008168 1190 80 92 92 NUM hvd.32044092008168 1190 81 ) ) PUNCT hvd.32044092008168 1190 82 t t PROPN hvd.32044092008168 1190 83 — — PUNCT hvd.32044092008168 1190 84 ( ( PUNCT hvd.32044092008168 1190 85 156³ 156³ NUM hvd.32044092008168 1190 86 — — PUNCT hvd.32044092008168 1190 87 g₂b g₂b NOUN hvd.32044092008168 1190 88 + + NUM hvd.32044092008168 1190 89 1—1 1—1 NUM hvd.32044092008168 1190 90 93 93 NUM hvd.32044092008168 1190 91 ) ) PUNCT hvd.32044092008168 1190 92 • • CCONJ hvd.32044092008168 1190 93 9 9 NUM hvd.32044092008168 1190 94 1 1 NUM hvd.32044092008168 1190 95 s= s= PROPN hvd.32044092008168 1190 96 s s PART hvd.32044092008168 1190 97 = = PROPN hvd.32044092008168 1190 98 1 1 NUM hvd.32044092008168 1190 99 9 9 NUM hvd.32044092008168 1190 100 ( ( PUNCT hvd.32044092008168 1190 101 t t PROPN hvd.32044092008168 1190 102 ) ) PUNCT hvd.32044092008168 1190 103 — — PUNCT hvd.32044092008168 1190 104 3 3 NUM hvd.32044092008168 1190 105 b b X hvd.32044092008168 1190 106 s² s² X hvd.32044092008168 1190 107 — — PUNCT hvd.32044092008168 1190 108 — — PUNCT hvd.32044092008168 1190 109 ¢´s ¢´s PROPN hvd.32044092008168 1190 110 — — PUNCT hvd.32044092008168 1190 111 — — PUNCT hvd.32044092008168 1190 112 9 9 X hvd.32044092008168 1190 113 . . SYM hvd.32044092008168 1190 114 · · PUNCT hvd.32044092008168 1190 115 2 2 NUM hvd.32044092008168 1190 116 3 3 NUM hvd.32044092008168 1190 117 / / SYM hvd.32044092008168 1190 118 2 2 NUM hvd.32044092008168 1190 119 ዎ ዎ DET hvd.32044092008168 1190 120 b b X hvd.32044092008168 1191 1 [ [ X hvd.32044092008168 1191 2 ø'+ ø'+ X hvd.32044092008168 1191 3 3 3 NUM hvd.32044092008168 1191 4 ( ( PUNCT hvd.32044092008168 1191 5 e̟₁ e̟₁ NOUN hvd.32044092008168 1191 6 — — PUNCT hvd.32044092008168 1191 7 b)² b)² X hvd.32044092008168 1191 8 ] ] X hvd.32044092008168 1191 9 в в PROPN hvd.32044092008168 1191 10 гв гв PROPN hvd.32044092008168 1191 11 6e 6e PROPN hvd.32044092008168 1191 12 , , PUNCT hvd.32044092008168 1191 13 b b PROPN hvd.32044092008168 1191 14 15 15 NUM hvd.32044092008168 1191 15 15 15 NUM hvd.32044092008168 1191 16 l l NOUN hvd.32044092008168 1191 17 15 15 NUM hvd.32044092008168 1191 18 s=361 s=361 NOUN hvd.32044092008168 1191 19 a₁s a₁s VERB hvd.32044092008168 1191 20 b₁ b₁ PROPN hvd.32044092008168 1191 21 ዎ ዎ X hvd.32044092008168 1191 22 4 4 NUM hvd.32044092008168 1191 23 ( ( PUNCT hvd.32044092008168 1191 24 1² 1² NUM hvd.32044092008168 1191 25 — — PUNCT hvd.32044092008168 1191 26 a₁)³ a₁)³ X hvd.32044092008168 1191 27 + + PROPN hvd.32044092008168 1191 28 ( ( PUNCT hvd.32044092008168 1191 29 117³ 117³ NUM hvd.32044092008168 1191 30 — — PUNCT hvd.32044092008168 1191 31 9 9 NUM hvd.32044092008168 1191 32 α α NOUN hvd.32044092008168 1191 33 , , PUNCT hvd.32044092008168 1191 34 l l NOUN hvd.32044092008168 1191 35 — — PUNCT hvd.32044092008168 1191 36 b₁)² b₁)² ADV hvd.32044092008168 1191 37 361 361 NUM hvd.32044092008168 1191 38 ( ( PUNCT hvd.32044092008168 1191 39 12 12 NUM hvd.32044092008168 1191 40 — — PUNCT hvd.32044092008168 1191 41 a₁)² a₁)² X hvd.32044092008168 1191 42 +36₁2 +36₁2 NOUN hvd.32044092008168 1191 43 - - SYM hvd.32044092008168 1191 44 92 92 NUM hvd.32044092008168 1191 45 ] ] PUNCT hvd.32044092008168 1191 46 2 2 NUM hvd.32044092008168 1191 47 cb cb X hvd.32044092008168 1192 1 [ [ X hvd.32044092008168 1192 2 b² b² PROPN hvd.32044092008168 1192 3 — — PUNCT hvd.32044092008168 1192 4 6e̟₁b 6e̟₁b NUM hvd.32044092008168 1192 5 + + NUM hvd.32044092008168 1192 6 45e̟₁² 45e̟₁² PROPN hvd.32044092008168 1192 7 — — PUNCT hvd.32044092008168 1192 8 15 15 NUM hvd.32044092008168 1192 9 g g X hvd.32044092008168 1192 10 ] ] X hvd.32044092008168 1192 11 c² c² PROPN hvd.32044092008168 1192 12 q₁p q₁p PROPN hvd.32044092008168 1192 13 = = PROPN hvd.32044092008168 1192 14 1257º 1257º NUM hvd.32044092008168 1192 15 — — PUNCT hvd.32044092008168 1192 16 210a 210a NUM hvd.32044092008168 1192 17 , , PUNCT hvd.32044092008168 1192 18 l¹ l¹ PROPN hvd.32044092008168 1192 19 — — PUNCT hvd.32044092008168 1192 20 22b 22b NUM hvd.32044092008168 1192 21 , , PUNCT hvd.32044092008168 1192 22 1ª 1ª NUM hvd.32044092008168 1192 23 + + NUM hvd.32044092008168 1192 24 93 93 NUM hvd.32044092008168 1192 25 a a PRON hvd.32044092008168 1192 26 , , PUNCT hvd.32044092008168 1192 27 l² l² PROPN hvd.32044092008168 1192 28 + + PROPN hvd.32044092008168 1192 29 18 18 NUM hvd.32044092008168 1192 30 a a DET hvd.32044092008168 1192 31 , , PUNCT hvd.32044092008168 1192 32 b b NOUN hvd.32044092008168 1192 33 , , PUNCT hvd.32044092008168 1192 34 l l NOUN hvd.32044092008168 1192 35 + + CCONJ hvd.32044092008168 1192 36 b₁² b₁² VERB hvd.32044092008168 1192 37 — — PUNCT hvd.32044092008168 1192 38 4a,³ 4a,³ PROPN hvd.32044092008168 1192 39 361 361 NUM hvd.32044092008168 1192 40 ( ( PUNCT hvd.32044092008168 1192 41 12 12 NUM hvd.32044092008168 1192 42 - - PUNCT hvd.32044092008168 1192 43 a₁ a₁ NOUN hvd.32044092008168 1192 44 ) ) PUNCT hvd.32044092008168 1192 45 a₁ a₁ PROPN hvd.32044092008168 1192 46 = = SYM hvd.32044092008168 1192 47 a2 a2 PROPN hvd.32044092008168 1192 48 d d NOUN hvd.32044092008168 1192 49 3 3 NUM hvd.32044092008168 1192 50 1 1 NUM hvd.32044092008168 1192 51 925 925 NUM hvd.32044092008168 1192 52 108 108 NUM hvd.32044092008168 1192 53 93 93 NUM hvd.32044092008168 1192 54 2 2 NUM hvd.32044092008168 1192 55 a₁ a₁ NOUN hvd.32044092008168 1192 56 = = SYM hvd.32044092008168 1192 57 19 19 NUM hvd.32044092008168 1192 58 bø bø NOUN hvd.32044092008168 1192 59 a3 a3 PROPN hvd.32044092008168 1192 60 4 4 NUM hvd.32044092008168 1192 61 t t NOUN hvd.32044092008168 1192 62 1 1 NUM hvd.32044092008168 1192 63 = = SYM hvd.32044092008168 1192 64 3 3 NUM hvd.32044092008168 1192 65 12576210a 12576210a NUM hvd.32044092008168 1192 66 , , PUNCT hvd.32044092008168 1192 67 226,193a 226,193a NUM hvd.32044092008168 1192 68 , , PUNCT hvd.32044092008168 1192 69 +18a +18a PROPN hvd.32044092008168 1192 70 , , PUNCT hvd.32044092008168 1192 71 b b PROPN hvd.32044092008168 1192 72 , , PUNCT hvd.32044092008168 1192 73 l l NOUN hvd.32044092008168 1192 74 + + CCONJ hvd.32044092008168 1192 75 b₁³ b₁³ VERB hvd.32044092008168 1192 76 4a,3 4a,3 NUM hvd.32044092008168 1192 77 9 9 NUM hvd.32044092008168 1192 78 ' ' PUNCT hvd.32044092008168 1192 79 = = VERB hvd.32044092008168 1192 80 121256210c¹22 121256210c¹22 NUM hvd.32044092008168 1192 81 § § NUM hvd.32044092008168 1192 82 ³ ³ X hvd.32044092008168 1192 83 + + NUM hvd.32044092008168 1192 84 93 93 NUM hvd.32044092008168 1192 85 c²²+18c§ c²²+18c§ NOUN hvd.32044092008168 1192 86 + + NUM hvd.32044092008168 1192 87 1 1 NUM hvd.32044092008168 1192 88 — — PUNCT hvd.32044092008168 1192 89 4c³ 4c³ NUM hvd.32044092008168 1192 90 1 1 NUM hvd.32044092008168 1192 91 a1 a1 PROPN hvd.32044092008168 1192 92 b b X hvd.32044092008168 1193 1 [ [ X hvd.32044092008168 1193 2 15b²+ 15b²+ NUM hvd.32044092008168 1193 3 3e̟² 3e̟² NUM hvd.32044092008168 1193 4 — — PUNCT hvd.32044092008168 1193 5 6e̟b 6e̟b NUM hvd.32044092008168 1193 6 — — PUNCT hvd.32044092008168 1193 7 9½ 9½ NUM hvd.32044092008168 1193 8 ] ] PUNCT hvd.32044092008168 1193 9 93 93 NUM hvd.32044092008168 1193 10 § § PUNCT hvd.32044092008168 1193 11 — — PUNCT hvd.32044092008168 1193 12 b₁ b₁ PROPN hvd.32044092008168 1193 13 = = PUNCT hvd.32044092008168 1193 14 31 31 NUM hvd.32044092008168 1193 15 ( ( PUNCT hvd.32044092008168 1193 16 1 1 NUM hvd.32044092008168 1193 17 — — PUNCT hvd.32044092008168 1193 18 k² k² PROPN hvd.32044092008168 1193 19 + + CCONJ hvd.32044092008168 1193 20 k¹)³ k¹)³ NUM hvd.32044092008168 1193 21 k4)3 k4)3 NOUN hvd.32044092008168 1193 22 ( ( PUNCT hvd.32044092008168 1193 23 1 1 NUM hvd.32044092008168 1193 24 + + NUM hvd.32044092008168 1193 25 k²)² k²)² X hvd.32044092008168 1193 26 ( ( PUNCT hvd.32044092008168 1193 27 2 2 NUM hvd.32044092008168 1193 28 — — PUNCT hvd.32044092008168 1193 29 k²)² k²)² X hvd.32044092008168 1193 30 ( ( PUNCT hvd.32044092008168 1193 31 1 1 NUM hvd.32044092008168 1193 32 — — PUNCT hvd.32044092008168 1193 33 2 2 NUM hvd.32044092008168 1193 34 k²)² k²)² NOUN hvd.32044092008168 1193 35 forms form NOUN hvd.32044092008168 1193 36 for for ADP hvd.32044092008168 1193 37 n n CCONJ hvd.32044092008168 1193 38 = = ADP hvd.32044092008168 1193 39 83 83 NUM hvd.32044092008168 1193 40 = = SYM hvd.32044092008168 1193 41 3 3 NUM hvd.32044092008168 1193 42 . . PUNCT hvd.32044092008168 1194 1 also also ADV hvd.32044092008168 1194 2 : : PUNCT hvd.32044092008168 1194 3 where where SCONJ hvd.32044092008168 1194 4 γρ γρ DET hvd.32044092008168 1194 5 q2= q2= NOUN hvd.32044092008168 1194 6 q₁ q₁ PROPN hvd.32044092008168 1194 7 q₂ q₂ VERB hvd.32044092008168 1194 8 q3 q3 PROPN hvd.32044092008168 1194 9 = = X hvd.32044092008168 1194 10 e₁ e₁ PROPN hvd.32044092008168 1194 11 = = PROPN hvd.32044092008168 1194 12 = = ADP hvd.32044092008168 1194 13 = = X hvd.32044092008168 1194 14 q q X hvd.32044092008168 1194 15 = = SYM hvd.32044092008168 1194 16 q1 q1 PROPN hvd.32044092008168 1194 17 q2 q2 PROPN hvd.32044092008168 1194 18 q3 q3 PROPN hvd.32044092008168 1194 19 = = PROPN hvd.32044092008168 1194 20 ( ( PUNCT hvd.32044092008168 1194 21 15 15 NUM hvd.32044092008168 1194 22 ) ) PUNCT hvd.32044092008168 1194 23 4 4 NUM hvd.32044092008168 1195 1 = = SYM hvd.32044092008168 1195 2 = = X hvd.32044092008168 1195 3 x= x= X hvd.32044092008168 1195 4 p p PROPN hvd.32044092008168 1195 5 ( ( PUNCT hvd.32044092008168 1195 6 v v NOUN hvd.32044092008168 1195 7 ) ) PUNCT hvd.32044092008168 1195 8 = = PROPN hvd.32044092008168 1195 9 1 1 NUM hvd.32044092008168 1195 10 32 32 NUM hvd.32044092008168 1195 11 = = PUNCT hvd.32044092008168 1195 12 = = NOUN hvd.32044092008168 1195 13 ( ( PUNCT hvd.32044092008168 1195 14 2 2 NUM hvd.32044092008168 1195 15 qr qr NOUN hvd.32044092008168 1195 16 cb cb NOUN hvd.32044092008168 1196 1 。 。 X hvd.32044092008168 1196 2 ф ф X hvd.32044092008168 1196 3 = = PUNCT hvd.32044092008168 1196 4 k²sn² k²sn² X hvd.32044092008168 1196 5 w w PROPN hvd.32044092008168 1196 6 qy2 qy2 VERB hvd.32044092008168 1196 7 epb epb PRON hvd.32044092008168 1196 8 / / PUNCT hvd.32044092008168 1196 9 = = PUNCT hvd.32044092008168 1196 10 = = PUNCT hvd.32044092008168 1196 11 — — PUNCT hvd.32044092008168 1196 12 1:2 1:2 X hvd.32044092008168 1196 13 ) ) PUNCT hvd.32044092008168 1196 14 ――― ――― NOUN hvd.32044092008168 1196 15 ύ ύ NOUN hvd.32044092008168 1197 1 * * PUNCT hvd.32044092008168 1197 2 bo bo NOUN hvd.32044092008168 1197 3 3 3 NUM hvd.32044092008168 1197 4 ( ( PUNCT hvd.32044092008168 1197 5 4a,³= 4a,³= NUM hvd.32044092008168 1197 6 27 27 NUM hvd.32044092008168 1197 7 ag² ag² NOUN hvd.32044092008168 1197 8 ) ) PUNCT hvd.32044092008168 1197 9 — — PUNCT hvd.32044092008168 1197 10 — — PUNCT hvd.32044092008168 1197 11 4 4 NUM hvd.32044092008168 1197 12 = = SYM hvd.32044092008168 1197 13 δ δ PROPN hvd.32044092008168 1197 14 √ √ PROPN hvd.32044092008168 1197 15 121 121 NUM hvd.32044092008168 1197 16 p p NOUN hvd.32044092008168 1197 17 1 1 NUM hvd.32044092008168 1197 18 ' ' NUM hvd.32044092008168 1197 19 ³+ ³+ NUM hvd.32044092008168 1197 20 27 27 NUM hvd.32044092008168 1197 21 p² p² PROPN hvd.32044092008168 1197 22 8 8 NUM hvd.32044092008168 1197 23 ( ( PUNCT hvd.32044092008168 1197 24 27 27 NUM hvd.32044092008168 1197 25 ) ) PUNCT hvd.32044092008168 1197 26 bøy′+ bøy′+ CCONJ hvd.32044092008168 1197 27 16 16 NUM hvd.32044092008168 1197 28 ( ( PUNCT hvd.32044092008168 1197 29 27 27 NUM hvd.32044092008168 1197 30 ) ) PUNCT hvd.32044092008168 1197 31 b²ø′ b²ø′ NOUN hvd.32044092008168 1197 32 6 6 NUM hvd.32044092008168 1197 33 9 9 NUM hvd.32044092008168 1197 34 b b X hvd.32044092008168 1197 35 þ þ PROPN hvd.32044092008168 1197 36 ( ( PUNCT hvd.32044092008168 1197 37 1 1 NUM hvd.32044092008168 1197 38 ) ) PUNCT hvd.32044092008168 1197 39 2 2 NUM hvd.32044092008168 1197 40 b₁ b₁ PROPN hvd.32044092008168 1197 41 bo bo PROPN hvd.32044092008168 1197 42 δ δ PROPN hvd.32044092008168 1197 43 1 1 NUM hvd.32044092008168 1197 44 + + PROPN hvd.32044092008168 1197 45 k² k² PROPN hvd.32044092008168 1197 46 3 3 NUM hvd.32044092008168 1197 47 2 2 NUM hvd.32044092008168 1197 48 f f PROPN hvd.32044092008168 1197 49 , , PUNCT hvd.32044092008168 1197 50 f f PROPN hvd.32044092008168 1197 51 , , PUNCT hvd.32044092008168 1197 52 fs fs PROPN hvd.32044092008168 1197 53 v v PROPN hvd.32044092008168 1197 54 1 1 NUM hvd.32044092008168 1197 55 2 2 NUM hvd.32044092008168 1197 56 c³ c³ NOUN hvd.32044092008168 1197 57 pb3 pb3 NOUN hvd.32044092008168 1197 58 = = PUNCT hvd.32044092008168 1197 59 = = PRON hvd.32044092008168 1197 60 2 2 NUM hvd.32044092008168 1197 61 c2 c2 PROPN hvd.32044092008168 1197 62 92 92 NUM hvd.32044092008168 1197 63 p p NOUN hvd.32044092008168 1197 64 = = NOUN hvd.32044092008168 1197 65 = = X hvd.32044092008168 1197 66 32.5 32.5 NUM hvd.32044092008168 1198 1 [ [ PUNCT hvd.32044092008168 1198 2 ' ' NOUN hvd.32044092008168 1198 3 + + CCONJ hvd.32044092008168 1198 4 3 3 NUM hvd.32044092008168 1198 5 ( ( PUNCT hvd.32044092008168 1198 6 c₂ c₂ PROPN hvd.32044092008168 1198 7 — — PUNCT hvd.32044092008168 1198 8 b)² b)² X hvd.32044092008168 1198 9 ] ] X hvd.32044092008168 1198 10 — — PUNCT hvd.32044092008168 1198 11 5 5 NUM hvd.32044092008168 1198 12 þa þa NOUN hvd.32044092008168 1198 13 b² b² PROPN hvd.32044092008168 1198 14 — — PUNCT hvd.32044092008168 1198 15 6e̟₁b 6e̟₁b NUM hvd.32044092008168 1198 16 + + NUM hvd.32044092008168 1198 17 45e2—15g,=.5 45e2—15g,=.5 NUM hvd.32044092008168 1199 1 [ [ X hvd.32044092008168 1199 2 5 5 NUM hvd.32044092008168 1199 3 1² 1² NUM hvd.32044092008168 1199 4 — — PUNCT hvd.32044092008168 1199 5 2 2 NUM hvd.32044092008168 1199 6 ( ( PUNCT hvd.32044092008168 1199 7 k² k² PROPN hvd.32044092008168 1199 8 — — PUNCT hvd.32044092008168 1199 9 2 2 X hvd.32044092008168 1199 10 ) ) PUNCT hvd.32044092008168 1199 11 1 1 NUM hvd.32044092008168 1199 12 — — PUNCT hvd.32044092008168 1199 13 3k¹ 3k¹ NUM hvd.32044092008168 1199 14 ] ] PUNCT hvd.32044092008168 1199 15 = = X hvd.32044092008168 1199 16 5 5 NUM hvd.32044092008168 1199 17 þ₁ þ₁ PROPN hvd.32044092008168 1199 18 b² b² PROPN hvd.32044092008168 1199 19 — — PUNCT hvd.32044092008168 1199 20 6e 6e PROPN hvd.32044092008168 1199 21 , , PUNCT hvd.32044092008168 1199 22 b+45e,2 b+45e,2 SPACE hvd.32044092008168 1199 23 - - SYM hvd.32044092008168 1199 24 15g-5[57² 15g-5[57² NUM hvd.32044092008168 1199 25 — — PUNCT hvd.32044092008168 1199 26 2 2 NUM hvd.32044092008168 1199 27 ( ( PUNCT hvd.32044092008168 1199 28 1 1 NUM hvd.32044092008168 1199 29 — — SYM hvd.32044092008168 1199 30 2 2 NUM hvd.32044092008168 1199 31 k²)l k²)l NOUN hvd.32044092008168 1199 32 — — PUNCT hvd.32044092008168 1199 33 3 3 X hvd.32044092008168 1199 34 ] ] PUNCT hvd.32044092008168 1199 35 = = PUNCT hvd.32044092008168 1199 36 5º 5º NOUN hvd.32044092008168 1199 37 , , PUNCT hvd.32044092008168 1199 38 b² b² PROPN hvd.32044092008168 1199 39 — — PUNCT hvd.32044092008168 1199 40 6e3 6e3 NUM hvd.32044092008168 1199 41 b+45e32 b+45e32 PROPN hvd.32044092008168 1199 42 - - PUNCT hvd.32044092008168 1199 43 15g=5[57² 15g=5[57² NUM hvd.32044092008168 1199 44 — — PUNCT hvd.32044092008168 1199 45 2 2 NUM hvd.32044092008168 1199 46 ( ( PUNCT hvd.32044092008168 1199 47 1 1 NUM hvd.32044092008168 1199 48 + + NUM hvd.32044092008168 1199 49 k² k² PROPN hvd.32044092008168 1199 50 ) ) PUNCT hvd.32044092008168 1199 51 l l PROPN hvd.32044092008168 1199 52 − − PROPN hvd.32044092008168 1199 53 3 3 NUM hvd.32044092008168 1199 54 ( ( PUNCT hvd.32044092008168 1199 55 1 1 NUM hvd.32044092008168 1199 56 — — PUNCT hvd.32044092008168 1199 57 7²)² 7²)² NUM hvd.32044092008168 1199 58 ] ] SYM hvd.32044092008168 1199 59 2n 2n NUM hvd.32044092008168 1199 60 1 1 NUM hvd.32044092008168 1199 61 ( ( PUNCT hvd.32044092008168 1199 62 15)3 15)3 NUM hvd.32044092008168 1199 63 3 3 NUM hvd.32044092008168 1199 64 q q PROPN hvd.32044092008168 1199 65 b b PROPN hvd.32044092008168 1199 66 2 2 NUM hvd.32044092008168 1199 67 þ₁ þ₁ PROPN hvd.32044092008168 1199 68 ð½ ð½ X hvd.32044092008168 1199 69 ð³ ð³ PROPN hvd.32044092008168 1199 70 1 1 NUM hvd.32044092008168 1199 71 4 4 NUM hvd.32044092008168 1199 72 32 32 NUM hvd.32044092008168 1199 73 2 2 NUM hvd.32044092008168 1199 74 3 3 NUM hvd.32044092008168 1199 75 516a 516a NUM hvd.32044092008168 1199 76 , , PUNCT hvd.32044092008168 1199 77 110b 110b PROPN hvd.32044092008168 1199 78 , , PUNCT hvd.32044092008168 1199 79 1³ 1³ NUM hvd.32044092008168 1199 80 — — PUNCT hvd.32044092008168 1199 81 3a 3a NUM hvd.32044092008168 1199 82 , , PUNCT hvd.32044092008168 1199 83 1º 1º NUM hvd.32044092008168 1199 84 + + NUM hvd.32044092008168 1199 85 6a 6a NUM hvd.32044092008168 1199 86 , , PUNCT hvd.32044092008168 1199 87 b b NOUN hvd.32044092008168 1199 88 , , PUNCT hvd.32044092008168 1199 89 l+ l+ PRON hvd.32044092008168 1199 90 b b PROPN hvd.32044092008168 1199 91 , , PUNCT hvd.32044092008168 1199 92 ² ² SYM hvd.32044092008168 1199 93 4a 4a NUM hvd.32044092008168 1199 94 , , PUNCT hvd.32044092008168 1199 95 ³ ³ NUM hvd.32044092008168 1199 96 v v X hvd.32044092008168 1199 97 q q X hvd.32044092008168 1199 98 ' ' NUM hvd.32044092008168 1199 99 3 3 NUM hvd.32044092008168 1199 100 162 162 NUM hvd.32044092008168 1199 101 bpp bpp NOUN hvd.32044092008168 1199 102 ' ' PUNCT hvd.32044092008168 1199 103 — — PUNCT hvd.32044092008168 1199 104 27 27 NUM hvd.32044092008168 1199 105 ❤ ❤ SYM hvd.32044092008168 1199 106 ² ² NUM hvd.32044092008168 1199 107 — — PUNCT hvd.32044092008168 1199 108 ❤ ❤ ADP hvd.32044092008168 1199 109 ' ' NUM hvd.32044092008168 1199 110 108´³½ 108´³½ NUM hvd.32044092008168 1199 111 3 3 NUM hvd.32044092008168 1200 1 [ [ PUNCT hvd.32044092008168 1200 2 4a₂³+ 4a₂³+ NUM hvd.32044092008168 1200 3 27 27 NUM hvd.32044092008168 1200 4 ag² ag² NOUN hvd.32044092008168 1200 5 ] ] X hvd.32044092008168 1200 6 2 2 NUM hvd.32044092008168 1200 7 3 3 NUM hvd.32044092008168 1200 8 p'(v p'(v NOUN hvd.32044092008168 1200 9 ): ): PUNCT hvd.32044092008168 1201 1 k2 k2 PROPN hvd.32044092008168 1201 2 sn²v sn²v PROPN hvd.32044092008168 1201 3 cn2v cn2v ADP hvd.32044092008168 1201 4 dn² dn² NOUN hvd.32044092008168 1201 5 v v NOUN hvd.32044092008168 1201 6 = = NOUN hvd.32044092008168 1201 7 1 1 NUM hvd.32044092008168 1201 8 1 1 NUM hvd.32044092008168 1201 9 32 32 NUM hvd.32044092008168 1201 10 ( ( PUNCT hvd.32044092008168 1201 11 212 212 NUM hvd.32044092008168 1201 12 = = NOUN hvd.32044092008168 1201 13 = = SYM hvd.32044092008168 1201 14 361 361 NUM hvd.32044092008168 1201 15 ( ( PUNCT hvd.32044092008168 1201 16 12 12 NUM hvd.32044092008168 1201 17 — — PUNCT hvd.32044092008168 1201 18 a₁)² a₁)² X hvd.32044092008168 1201 19 . . NOUN hvd.32044092008168 1201 20 ข ข NOUN hvd.32044092008168 1201 21 ( ( PUNCT hvd.32044092008168 1201 22 1 1 NUM hvd.32044092008168 1201 23 ) ) PUNCT hvd.32044092008168 1201 24 361 361 NUM hvd.32044092008168 1201 25 ( ( PUNCT hvd.32044092008168 1201 26 12 12 NUM hvd.32044092008168 1201 27 = = SYM hvd.32044092008168 1201 28 3 3 NUM hvd.32044092008168 1201 29 4 4 NUM hvd.32044092008168 1201 30 a¸³+ a¸³+ PROPN hvd.32044092008168 1201 31 21 21 NUM hvd.32044092008168 1201 32 a¸² a¸² PROPN hvd.32044092008168 1201 33 2 2 NUM hvd.32044092008168 1201 34 3 3 NUM hvd.32044092008168 1201 35 b b NUM hvd.32044092008168 1201 36 1 1 NUM hvd.32044092008168 1201 37 ( ( PUNCT hvd.32044092008168 1201 38 5)3 5)3 NUM hvd.32044092008168 1201 39 50 50 NUM hvd.32044092008168 1201 40 g. g. NOUN hvd.32044092008168 1201 41 ――――― ――――― PROPN hvd.32044092008168 1201 42 ( ( PUNCT hvd.32044092008168 1201 43 1 1 NUM hvd.32044092008168 1201 44 — — PUNCT hvd.32044092008168 1201 45 k² k² PROPN hvd.32044092008168 1201 46 + + CCONJ hvd.32044092008168 1201 47 k¹ k¹ PROPN hvd.32044092008168 1201 48 ) ) PUNCT hvd.32044092008168 1201 49 --1 --1 PROPN hvd.32044092008168 1201 50 ) ) PUNCT hvd.32044092008168 1201 51 a₁)2 a₁)2 X hvd.32044092008168 1201 52 qi qi PROPN hvd.32044092008168 1201 53 f₂2 f₂2 PROPN hvd.32044092008168 1201 54 ん ん PROPN hvd.32044092008168 1201 55 ​c2 ​c2 PROPN hvd.32044092008168 1201 56 b2 b2 PROPN hvd.32044092008168 1201 57 p p NOUN hvd.32044092008168 1201 58 = = SYM hvd.32044092008168 1201 59 c c NOUN hvd.32044092008168 1201 60 = = SYM hvd.32044092008168 1201 61 c¹ c¹ X hvd.32044092008168 1201 62 pq1 pq1 PROPN hvd.32044092008168 1201 63 q2 q2 PROPN hvd.32044092008168 1201 64 q3 q3 PROPN hvd.32044092008168 1201 65 у у PROPN hvd.32044092008168 1201 66 ( ( PUNCT hvd.32044092008168 1201 67 15)3 15)3 NUM hvd.32044092008168 1201 68 qi qi PROPN hvd.32044092008168 1201 69 qy qy PROPN hvd.32044092008168 1201 70 q3 q3 PROPN hvd.32044092008168 1201 71 2 2 NUM hvd.32044092008168 1201 72 + + NUM hvd.32044092008168 1201 73 ex ex X hvd.32044092008168 1201 74 --39 --39 INTJ hvd.32044092008168 1201 75 c3 c3 PROPN hvd.32044092008168 1202 1 g g NOUN hvd.32044092008168 1202 2 21606216b¹g 21606216b¹g NUM hvd.32044092008168 1202 3 + + NUM hvd.32044092008168 1202 4 1080 1080 NUM hvd.32044092008168 1202 5 g g NOUN hvd.32044092008168 1202 6 , , PUNCT hvd.32044092008168 1202 7 b9b2g54b92 b9b2g54b92 SYM hvd.32044092008168 1202 8 93 93 NUM hvd.32044092008168 1202 9 923 923 NUM hvd.32044092008168 1202 10 + + NUM hvd.32044092008168 1202 11 27 27 NUM hvd.32044092008168 1202 12 932 932 NUM hvd.32044092008168 1202 13 36b 36b NOUN hvd.32044092008168 1202 14 ( ( PUNCT hvd.32044092008168 1202 15 144b24b9₂+923 144b24b9₂+923 NUM hvd.32044092008168 1202 16 ) ) PUNCT hvd.32044092008168 1202 17 * * PUNCT hvd.32044092008168 1202 18 ' ' NUM hvd.32044092008168 1202 19 32792 32792 NUM hvd.32044092008168 1202 20 - - PUNCT hvd.32044092008168 1202 21 108bq 108bq NOUN hvd.32044092008168 1202 22 q'+36bq q'+36bq NOUN hvd.32044092008168 1202 23 ' ' PART hvd.32044092008168 1202 24 2 2 NUM hvd.32044092008168 1202 25 b² b² PROPN hvd.32044092008168 1202 26 36b 36b NOUN hvd.32044092008168 1203 1 2 2 NUM hvd.32044092008168 1203 2 7 7 NUM hvd.32044092008168 1203 3 1 1 NUM hvd.32044092008168 1203 4 2 2 NUM hvd.32044092008168 1203 5 710 710 NUM hvd.32044092008168 1203 6 1/11 1/11 NUM hvd.32044092008168 1203 7 32 32 NUM hvd.32044092008168 1203 8 2 2 NUM hvd.32044092008168 1203 9 x x SYM hvd.32044092008168 1203 10 ( ( PUNCT hvd.32044092008168 1203 11 ) ) PUNCT hvd.32044092008168 1203 12 x x SYM hvd.32044092008168 1203 13 187 187 NUM hvd.32044092008168 1203 14 ( ( PUNCT hvd.32044092008168 1203 15 72 72 NUM hvd.32044092008168 1203 16 a₁ a₁ NOUN hvd.32044092008168 1203 17 ) ) PUNCT hvd.32044092008168 1204 1 v9'³ v9'³ PROPN hvd.32044092008168 1204 2 +279² +279² PROPN hvd.32044092008168 1204 3 216bøø′+ 216bøø′+ NUM hvd.32044092008168 1204 4 432b²ø 432b²ø NUM hvd.32044092008168 1204 5 ( ( PUNCT hvd.32044092008168 1204 6 1 1 NUM hvd.32044092008168 1204 7 + + NUM hvd.32044092008168 1204 8 k² k² PROPN hvd.32044092008168 1204 9 ) ) PUNCT hvd.32044092008168 1204 10 12 12 NUM hvd.32044092008168 1204 11 6 6 NUM hvd.32044092008168 1204 12 * * SYM hvd.32044092008168 1204 13 84 84 NUM hvd.32044092008168 1204 14 table table NOUN hvd.32044092008168 1204 15 of of ADP hvd.32044092008168 1204 16 forms form NOUN hvd.32044092008168 1204 17 n= n= PROPN hvd.32044092008168 1204 18 = = VERB hvd.32044092008168 1204 19 3 3 NUM hvd.32044092008168 1204 20 . . NOUN hvd.32044092008168 1204 21 3 3 NUM hvd.32044092008168 1204 22 pν pν NOUN hvd.32044092008168 1204 23 q'+ q'+ PROPN hvd.32044092008168 1204 24 27q 27q NOUN hvd.32044092008168 1204 25 ? ? PUNCT hvd.32044092008168 1204 26 – – PUNCT hvd.32044092008168 1204 27 108 108 NUM hvd.32044092008168 1204 28 99 99 NUM hvd.32044092008168 1204 29 90 90 NUM hvd.32044092008168 1204 30 ' ' NUM hvd.32044092008168 1204 31 36 36 NUM hvd.32044092008168 1204 32 9'26 9'26 NUM hvd.32044092008168 1204 33 q. q. X hvd.32044092008168 1204 34 f f X hvd.32044092008168 1204 35 ? ? NOUN hvd.32044092008168 1204 36 2 2 NUM hvd.32044092008168 1204 37 2 2 NUM hvd.32044092008168 1204 38 pv pv X hvd.32044092008168 1204 39 — — PUNCT hvd.32044092008168 1204 40 22cºb 22cºb X hvd.32044092008168 1204 41 p p X hvd.32044092008168 1204 42 [ [ X hvd.32044092008168 1204 43 0'+ 0'+ PROPN hvd.32044092008168 1204 44 3(€ 3(€ NUM hvd.32044092008168 1204 45 – – PUNCT hvd.32044092008168 1204 46 6 6 NUM hvd.32044092008168 1204 47 ) ) PUNCT hvd.32044092008168 1204 48 ? ? PUNCT hvd.32044092008168 1204 49 ] ] X hvd.32044092008168 1205 1 [ [ X hvd.32044092008168 1205 2 12 12 NUM hvd.32044092008168 1205 3 ( ( PUNCT hvd.32044092008168 1205 4 6 6 NUM hvd.32044092008168 1205 5 — — PUNCT hvd.32044092008168 1205 6 ex ex NOUN hvd.32044092008168 1205 7 ) ) PUNCT hvd.32044092008168 1205 8 ( ( PUNCT hvd.32044092008168 1205 9 2b 2b NUM hvd.32044092008168 1205 10 – – PUNCT hvd.32044092008168 1205 11 en en ADV hvd.32044092008168 1205 12 ) ) PUNCT hvd.32044092008168 1205 13 — — PUNCT hvd.32044092008168 1205 14 ' ' PUNCT hvd.32044092008168 1205 15 ? ? PUNCT hvd.32044092008168 1205 16 ] ] PUNCT hvd.32044092008168 1205 17 ? ? PUNCT hvd.32044092008168 1206 1 36 36 NUM hvd.32044092008168 1206 2 9'2 9'2 NUM hvd.32044092008168 1206 3 ] ] PUNCT hvd.32044092008168 1206 4 pv pv ADP hvd.32044092008168 1206 5 = = PROPN hvd.32044092008168 1206 6 b b X hvd.32044092008168 1206 7 p'o p'o NOUN hvd.32044092008168 1206 8 3 3 NUM hvd.32044092008168 1206 9 99 99 NUM hvd.32044092008168 1206 10 2 2 NUM hvd.32044092008168 1206 11 9 9 NUM hvd.32044092008168 1206 12 . . PUNCT hvd.32044092008168 1206 13 2 2 NUM hvd.32044092008168 1206 14 x x SYM hvd.32044092008168 1206 15 ( ( PUNCT hvd.32044092008168 1206 16 ) ) PUNCT hvd.32044092008168 1206 17 2 2 NUM hvd.32044092008168 1206 18 1 1 NUM hvd.32044092008168 1206 19 ) ) PUNCT hvd.32044092008168 1206 20 3 3 NUM hvd.32044092008168 1206 21 where where SCONJ hvd.32044092008168 1206 22 ♡ ♡ PUNCT hvd.32044092008168 1206 23 ( ( PUNCT hvd.32044092008168 1206 24 1 1 NUM hvd.32044092008168 1206 25 ) ) PUNCT hvd.32044092008168 1206 26 0(l 0(l NUM hvd.32044092008168 1206 27 ) ) PUNCT hvd.32044092008168 1206 28 — — PUNCT hvd.32044092008168 1206 29 121(1 121(1 NUM hvd.32044092008168 1206 30 » » PUNCT hvd.32044092008168 1206 31 – – PUNCT hvd.32044092008168 1206 32 az az PROPN hvd.32044092008168 1206 33 ) ) PUNCT hvd.32044092008168 1206 34 ( ( PUNCT hvd.32044092008168 1206 35 1073 1073 NUM hvd.32044092008168 1206 36 — — PUNCT hvd.32044092008168 1206 37 8a71 8a71 NUM hvd.32044092008168 1206 38 — — PUNCT hvd.32044092008168 1206 39 b b X hvd.32044092008168 1206 40 ) ) PUNCT hvd.32044092008168 1206 41 ) ) PUNCT hvd.32044092008168 1206 42 l l NOUN hvd.32044092008168 1206 43 — — PUNCT hvd.32044092008168 1206 44 = = PRON hvd.32044092008168 1206 45 576 576 NUM hvd.32044092008168 1206 46 + + NUM hvd.32044092008168 1206 47 6a,1 6a,1 NUM hvd.32044092008168 1206 48 – – PUNCT hvd.32044092008168 1206 49 106,7 106,7 NUM hvd.32044092008168 1206 50 – – PUNCT hvd.32044092008168 1206 51 3a,+ 3a,+ NUM hvd.32044092008168 1206 52 6a,6,7 6a,6,7 NUM hvd.32044092008168 1206 53 + + NUM hvd.32044092008168 1206 54 – – PUNCT hvd.32044092008168 1206 55 4a 4a NUM hvd.32044092008168 1206 56 , , PUNCT hvd.32044092008168 1206 57 . . PUNCT hvd.32044092008168 1207 1 212 212 NUM hvd.32044092008168 1207 2 12 12 NUM hvd.32044092008168 1207 3 bi bi PROPN hvd.32044092008168 1207 4 x(1 x(1 PROPN hvd.32044092008168 1207 5 ) ) PUNCT hvd.32044092008168 1207 6 = = PUNCT hvd.32044092008168 1208 1 [ [ X hvd.32044092008168 1208 2 0(1 0(1 ADJ hvd.32044092008168 1208 3 ) ) PUNCT hvd.32044092008168 1208 4 34(1 34(1 NUM hvd.32044092008168 1208 5 ) ) PUNCT hvd.32044092008168 1208 6 — — PUNCT hvd.32044092008168 1208 7 108 108 NUM hvd.32044092008168 1208 8 14 14 NUM hvd.32044092008168 1208 9 ( ( PUNCT hvd.32044092008168 1208 10 72 72 NUM hvd.32044092008168 1208 11 — — PUNCT hvd.32044092008168 1208 12 a a X hvd.32044092008168 1208 13 , , PUNCT hvd.32044092008168 1208 14 ) ) PUNCT hvd.32044092008168 1208 15 ? ? PUNCT hvd.32044092008168 1209 1 [ [ X hvd.32044092008168 1209 2 φ φ X hvd.32044092008168 1209 3 ( ( PUNCT hvd.32044092008168 1209 4 ( ( PUNCT hvd.32044092008168 1209 5 ) ) PUNCT hvd.32044092008168 1209 6 = = PROPN hvd.32044092008168 1209 7 18 18 NUM hvd.32044092008168 1209 8 – – PUNCT hvd.32044092008168 1209 9 6a74 6a74 NUM hvd.32044092008168 1209 10 + + CCONJ hvd.32044092008168 1209 11 46,78 46,78 NUM hvd.32044092008168 1209 12 -3a,41 -3a,41 PROPN hvd.32044092008168 1209 13 – – PUNCT hvd.32044092008168 1209 14 6,2 6,2 NUM hvd.32044092008168 1209 15 + + NUM hvd.32044092008168 1209 16 4a 4a NUM hvd.32044092008168 1209 17 ' ' PUNCT hvd.32044092008168 1209 18 = = PUNCT hvd.32044092008168 1209 19 a·b.c a·b.c ADV hvd.32044092008168 1209 20 = = VERB hvd.32044092008168 1210 1 a a X hvd.32044092008168 1210 2 à à X hvd.32044092008168 1210 3 = = X hvd.32044092008168 1210 4 12 12 NUM hvd.32044092008168 1210 5 – – PUNCT hvd.32044092008168 1210 6 ( ( PUNCT hvd.32044092008168 1210 7 1 1 NUM hvd.32044092008168 1210 8 + + CCONJ hvd.32044092008168 1210 9 k k X hvd.32044092008168 1210 10 ? ? PUNCT hvd.32044092008168 1210 11 ) ) PUNCT hvd.32044092008168 1210 12 1 1 NUM hvd.32044092008168 1210 13 — — PUNCT hvd.32044092008168 1210 14 37 37 NUM hvd.32044092008168 1210 15 . . PUNCT hvd.32044092008168 1210 16 * * PUNCT hvd.32044092008168 1211 1 = = X hvd.32044092008168 1211 2 f f X hvd.32044092008168 1211 3 72 72 NUM hvd.32044092008168 1211 4 b b NOUN hvd.32044092008168 1211 5 = = SYM hvd.32044092008168 1211 6 12 12 NUM hvd.32044092008168 1211 7 — — PUNCT hvd.32044092008168 1211 8 ( ( PUNCT hvd.32044092008168 1211 9 1 1 NUM hvd.32044092008168 1211 10 – – SYM hvd.32044092008168 1211 11 2k 2k NUM hvd.32044092008168 1211 12 ) ) PUNCT hvd.32044092008168 1211 13 7 7 NUM hvd.32044092008168 1211 14 + + NUM hvd.32044092008168 1211 15 3(kº 3(kº NUM hvd.32044092008168 1211 16 -14 -14 PUNCT hvd.32044092008168 1211 17 ) ) PUNCT hvd.32044092008168 1211 18 = = X hvd.32044092008168 1212 1 f f PROPN hvd.32044092008168 1212 2 , , PUNCT hvd.32044092008168 1212 3 72 72 NUM hvd.32044092008168 1212 4 ) ) PUNCT hvd.32044092008168 1212 5 c c NOUN hvd.32044092008168 1212 6 72 72 NUM hvd.32044092008168 1212 7 — — PUNCT hvd.32044092008168 1212 8 ( ( PUNCT hvd.32044092008168 1212 9 k k PROPN hvd.32044092008168 1212 10 ? ? PUNCT hvd.32044092008168 1212 11 — — PUNCT hvd.32044092008168 1212 12 2)2 2)2 NUM hvd.32044092008168 1212 13 – – PUNCT hvd.32044092008168 1212 14 3(1 3(1 NOUN hvd.32044092008168 1212 15 — — PUNCT hvd.32044092008168 1212 16 k k X hvd.32044092008168 1212 17 ? ? PUNCT hvd.32044092008168 1212 18 ) ) PUNCT hvd.32044092008168 1212 19 ( ( PUNCT hvd.32044092008168 1212 20 — — PUNCT hvd.32044092008168 1212 21 = = PROPN hvd.32044092008168 1212 22 fs fs X hvd.32044092008168 1212 23 f f PROPN hvd.32044092008168 1212 24 f f X hvd.32044092008168 1212 25 = = PROPN hvd.32044092008168 1212 26 f f PROPN hvd.32044092008168 1212 27 , , PUNCT hvd.32044092008168 1212 28 f f PROPN hvd.32044092008168 1212 29 , , PUNCT hvd.32044092008168 1212 30 f3 f3 PROPN hvd.32044092008168 1212 31 = = SYM hvd.32044092008168 1212 32 30 30 NUM hvd.32044092008168 1212 33 ga ga PROPN hvd.32044092008168 1212 34 x x PUNCT hvd.32044092008168 1212 35 a.b.c a.b.c PROPN hvd.32044092008168 1212 36 . . PROPN hvd.32044092008168 1212 37 45 45 NUM hvd.32044092008168 1212 38 2 2 NUM hvd.32044092008168 1212 39 1 1 NUM hvd.32044092008168 1212 40 45 45 NUM hvd.32044092008168 1212 41 2 2 NUM hvd.32044092008168 1212 42 45 45 NUM hvd.32044092008168 1212 43 2 2 NUM hvd.32044092008168 1212 44 8 8 NUM hvd.32044092008168 1212 45 8 8 NUM hvd.32044092008168 1212 46 3653 3653 NUM hvd.32044092008168 1212 47 1 1 NUM hvd.32044092008168 1212 48 2 2 NUM hvd.32044092008168 1212 49 3653 3653 NUM hvd.32044092008168 1212 50 case case NOUN hvd.32044092008168 1212 51 1 1 NUM hvd.32044092008168 1212 52 . . PUNCT hvd.32044092008168 1213 1 p p NOUN hvd.32044092008168 1213 2 = = SYM hvd.32044092008168 1213 3 0 0 NUM hvd.32044092008168 1213 4 . . PROPN hvd.32044092008168 1213 5 integral integral PROPN hvd.32044092008168 1213 6 a a DET hvd.32044092008168 1213 7 special special ADJ hvd.32044092008168 1213 8 function function NOUN hvd.32044092008168 1213 9 of of ADP hvd.32044092008168 1213 10 lamé lamé NOUN hvd.32044092008168 1213 11 of of ADP hvd.32044092008168 1213 12 the the DET hvd.32044092008168 1213 13 first first ADJ hvd.32044092008168 1213 14 sort sort NOUN hvd.32044092008168 1213 15 . . PUNCT hvd.32044092008168 1214 1 y y PROPN hvd.32044092008168 1214 2 = = PROPN hvd.32044092008168 1214 3 p p NOUN hvd.32044092008168 1214 4 ' ' NOUN hvd.32044092008168 1214 5 . . PUNCT hvd.32044092008168 1215 1 b b X hvd.32044092008168 1215 2 = = SYM hvd.32044092008168 1215 3 0 0 NUM hvd.32044092008168 1215 4 . . PROPN hvd.32044092008168 1215 5 case case PROPN hvd.32044092008168 1215 6 2 2 NUM hvd.32044092008168 1215 7 . . PUNCT hvd.32044092008168 1216 1 q q X hvd.32044092008168 1216 2 ; ; PUNCT hvd.32044092008168 1216 3 φ(0 φ(0 SPACE hvd.32044092008168 1216 4 ) ) PUNCT hvd.32044092008168 1216 5 0 0 NUM hvd.32044092008168 1216 6 ; ; PUNCT hvd.32044092008168 1216 7 0(1 0(1 NUM hvd.32044092008168 1216 8 ) ) PUNCT hvd.32044092008168 1216 9 = = NOUN hvd.32044092008168 1216 10 0 0 NUM hvd.32044092008168 1216 11 ; ; PUNCT hvd.32044092008168 1216 12 q. q. X hvd.32044092008168 1216 13 q1 q1 PROPN hvd.32044092008168 1216 14 0 0 NUM hvd.32044092008168 1216 15 ; ; PUNCT hvd.32044092008168 1216 16 q2 q2 NOUN hvd.32044092008168 1216 17 = = SYM hvd.32044092008168 1216 18 0 0 NUM hvd.32044092008168 1216 19 ; ; PUNCT hvd.32044092008168 1216 20 23 23 NUM hvd.32044092008168 1216 21 0 0 NUM hvd.32044092008168 1216 22 ; ; PUNCT hvd.32044092008168 1216 23 x x PUNCT hvd.32044092008168 1216 24 = = PUNCT hvd.32044092008168 1216 25 0 0 NUM hvd.32044092008168 1216 26 ; ; PUNCT hvd.32044092008168 1216 27 p'v p'v NOUN hvd.32044092008168 1216 28 = = NOUN hvd.32044092008168 1216 29 0 0 NUM hvd.32044092008168 1216 30 ; ; PUNCT hvd.32044092008168 1216 31 v v X hvd.32044092008168 1216 32 = = X hvd.32044092008168 1216 33 wa wa PROPN hvd.32044092008168 1216 34 . . PROPN hvd.32044092008168 1216 35 integrals integral NOUN hvd.32044092008168 1216 36 , , PUNCT hvd.32044092008168 1216 37 six six NUM hvd.32044092008168 1216 38 in in ADP hvd.32044092008168 1216 39 number number NOUN hvd.32044092008168 1216 40 , , PUNCT hvd.32044092008168 1216 41 of of ADP hvd.32044092008168 1216 42 the the DET hvd.32044092008168 1216 43 second second ADJ hvd.32044092008168 1216 44 sort sort NOUN hvd.32044092008168 1216 45 . . PUNCT hvd.32044092008168 1217 1 ба ба X hvd.32044092008168 1217 2 и и X hvd.32044092008168 1217 3 ( ( PUNCT hvd.32044092008168 1217 4 u u PROPN hvd.32044092008168 1217 5 + + CCONJ hvd.32044092008168 1217 6 w w PROPN hvd.32044092008168 1217 7 ) ) PUNCT hvd.32044092008168 1217 8 a=1 a=1 VERB hvd.32044092008168 1217 9 , , PUNCT hvd.32044092008168 1217 10 2 2 NUM hvd.32044092008168 1217 11 , , PUNCT hvd.32044092008168 1217 12 3 3 NUM hvd.32044092008168 1217 13 f=+ f=+ ADP hvd.32044092008168 1217 14 u u PROPN hvd.32044092008168 1217 15 & & CCONJ hvd.32044092008168 1217 16 ( ( PUNCT hvd.32044092008168 1217 17 w w PROPN hvd.32044092008168 1217 18 ? ? PUNCT hvd.32044092008168 1217 19 ) ) PUNCT hvd.32044092008168 1217 20 $ $ SYM hvd.32044092008168 1217 21 ( ( PUNCT hvd.32044092008168 1217 22 w2)=12 w2)=12 PROPN hvd.32044092008168 1217 23 10(w 10(w NUM hvd.32044092008168 1217 24 ) ) PUNCT hvd.32044092008168 1218 1 vpu vpu NOUN hvd.32044092008168 1219 1 ea ea X hvd.32044092008168 1219 2 би би X hvd.32044092008168 1219 3 = = SYM hvd.32044092008168 1219 4 2 2 NUM hvd.32044092008168 1219 5 where where SCONJ hvd.32044092008168 1219 6 1 1 NUM hvd.32044092008168 1219 7 1 1 NUM hvd.32044092008168 1219 8 2 2 NUM hvd.32044092008168 1219 9 la la PRON hvd.32044092008168 1219 10 b b NOUN hvd.32044092008168 1219 11 10 10 NUM hvd.32044092008168 1219 12 b b NOUN hvd.32044092008168 1219 13 ри ри X hvd.32044092008168 1219 14 — — PUNCT hvd.32044092008168 1219 15 ( ( PUNCT hvd.32044092008168 1219 16 a a X hvd.32044092008168 1219 17 ) ) PUNCT hvd.32044092008168 1219 18 qı= qı= PROPN hvd.32044092008168 1219 19 0 0 NUM hvd.32044092008168 1219 20 3e 3e PROPN hvd.32044092008168 1219 21 , , PUNCT hvd.32044092008168 1219 22 + + CCONJ hvd.32044092008168 1219 23 v3(12e v3(12e ADJ hvd.32044092008168 1219 24 + + PRON hvd.32044092008168 1219 25 592 592 NUM hvd.32044092008168 1219 26 ) ) PUNCT hvd.32044092008168 1219 27 = = PROPN hvd.32044092008168 1219 28 kº kº PROPN hvd.32044092008168 1219 29 — — PUNCT hvd.32044092008168 1219 30 2 2 NUM hvd.32044092008168 1219 31 + + CCONJ hvd.32044092008168 1219 32 v v NOUN hvd.32044092008168 1219 33 ( ( PUNCT hvd.32044092008168 1219 34 12 12 NUM hvd.32044092008168 1219 35 — — SYM hvd.32044092008168 1219 36 2 2 NUM hvd.32044092008168 1219 37 ) ) PUNCT hvd.32044092008168 1219 38 ? ? PUNCT hvd.32044092008168 1220 1 + + CCONJ hvd.32044092008168 1220 2 15k4 15k4 NUM hvd.32044092008168 1220 3 y y NOUN hvd.32044092008168 1220 4 = = X hvd.32044092008168 1220 5 { { PUNCT hvd.32044092008168 1220 6 p p PROPN hvd.32044092008168 1220 7 + + CCONJ hvd.32044092008168 1220 8 ja ja PROPN hvd.32044092008168 1220 9 ( ( PUNCT hvd.32044092008168 1220 10 34 34 NUM hvd.32044092008168 1220 11 ; ; PUNCT hvd.32044092008168 1220 12 + + NUM hvd.32044092008168 1220 13 v3(592 v3(592 NUM hvd.32044092008168 1220 14 — — PUNCT hvd.32044092008168 1220 15 12c 12c NUM hvd.32044092008168 1220 16 ) ) PUNCT hvd.32044092008168 1220 17 ) ) PUNCT hvd.32044092008168 1220 18 } } PUNCT hvd.32044092008168 1220 19 vp vp X hvd.32044092008168 1220 20 – – PUNCT hvd.32044092008168 1220 21 en en ADP hvd.32044092008168 1220 22 + + CCONJ hvd.32044092008168 1220 23 { { PUNCT hvd.32044092008168 1220 24 p+ p+ ADJ hvd.32044092008168 1220 25 1 1 NUM hvd.32044092008168 1220 26 ( ( PUNCT hvd.32044092008168 1220 27 1:4 1:4 NUM hvd.32044092008168 1220 28 — — PUNCT hvd.32044092008168 1220 29 2 2 NUM hvd.32044092008168 1220 30 ) ) PUNCT hvd.32044092008168 1220 31 + + NUM hvd.32044092008168 1220 32 v v ADP hvd.32044092008168 1220 33 ( ( PUNCT hvd.32044092008168 1220 34 1:2 1:2 NUM hvd.32044092008168 1220 35 — — PUNCT hvd.32044092008168 1220 36 2)2 2)2 NUM hvd.32044092008168 1220 37 + + NUM hvd.32044092008168 1220 38 1574 1574 NUM hvd.32044092008168 1220 39 } } PUNCT hvd.32044092008168 1220 40 vp vp X hvd.32044092008168 1220 41 ( ( PUNCT hvd.32044092008168 1220 42 k2 k2 PROPN hvd.32044092008168 1220 43 -2 -2 PROPN hvd.32044092008168 1220 44 ) ) PUNCT hvd.32044092008168 1220 45 . . PUNCT hvd.32044092008168 1221 1 2 2 NUM hvd.32044092008168 1221 2 2 2 NUM hvd.32044092008168 1221 3 to to PART hvd.32044092008168 1221 4 ? ? PUNCT hvd.32044092008168 1222 1 — — PUNCT hvd.32044092008168 1222 2 k2 k2 PROPN hvd.32044092008168 1222 3 1 1 NUM hvd.32044092008168 1222 4 1 1 NUM hvd.32044092008168 1222 5 10 10 NUM hvd.32044092008168 1222 6 -e1 -e1 NOUN hvd.32044092008168 1222 7 ey ey INTJ hvd.32044092008168 1222 8 2 2 NUM hvd.32044092008168 1222 9 1 1 NUM hvd.32044092008168 1222 10 pt pt PROPN hvd.32044092008168 1222 11 15 15 NUM hvd.32044092008168 1222 12 3 3 NUM hvd.32044092008168 1222 13 forms form NOUN hvd.32044092008168 1222 14 for for ADP hvd.32044092008168 1222 15 n n CCONJ hvd.32044092008168 1222 16 = = ADP hvd.32044092008168 1222 17 85 85 NUM hvd.32044092008168 1222 18 = = SYM hvd.32044092008168 1222 19 3 3 NUM hvd.32044092008168 1222 20 . . PUNCT hvd.32044092008168 1223 1 ( ( PUNCT hvd.32044092008168 1223 2 c c NOUN hvd.32044092008168 1223 3 ) ) PUNCT hvd.32044092008168 1223 4 ( ( PUNCT hvd.32044092008168 1223 5 b b X hvd.32044092008168 1223 6 ) ) PUNCT hvd.32044092008168 1223 7 q₂ q₂ NOUN hvd.32044092008168 1223 8 = = SYM hvd.32044092008168 1223 9 0 0 NUM hvd.32044092008168 1223 10 q2 q2 PROPN hvd.32044092008168 1223 11 = = SYM hvd.32044092008168 1223 12 b=3e₂ b=3e₂ PROPN hvd.32044092008168 1223 13 ±√3 ±√3 NOUN hvd.32044092008168 1223 14 ( ( PUNCT hvd.32044092008168 1223 15 59₂ 59₂ NUM hvd.32044092008168 1223 16 — — PUNCT hvd.32044092008168 1223 17 12е 12е PROPN hvd.32044092008168 1223 18 ) ) PUNCT hvd.32044092008168 1223 19 — — PUNCT hvd.32044092008168 1224 1 1 1 NUM hvd.32044092008168 1224 2 — — PUNCT hvd.32044092008168 1224 3 2k² 2k² NUM hvd.32044092008168 1224 4 + + NOUN hvd.32044092008168 1224 5 √(1 √(1 ADJ hvd.32044092008168 1224 6 − − PROPN hvd.32044092008168 1224 7 2k² 2k² NUM hvd.32044092008168 1224 8 ) ) PUNCT hvd.32044092008168 1224 9 + + CCONJ hvd.32044092008168 1224 10 15 15 NUM hvd.32044092008168 1224 11 y y PROPN hvd.32044092008168 1224 12 = = SYM hvd.32044092008168 1224 13 { { PUNCT hvd.32044092008168 1224 14 p p NOUN hvd.32044092008168 1224 15 + + CCONJ hvd.32044092008168 1224 16 1 1 NUM hvd.32044092008168 1224 17 e e NOUN hvd.32044092008168 1224 18 , , PUNCT hvd.32044092008168 1224 19 — — PUNCT hvd.32044092008168 1224 20 1 1 X hvd.32044092008168 1224 21 — — PUNCT hvd.32044092008168 1224 22 ( ( PUNCT hvd.32044092008168 1224 23 3e 3e X hvd.32044092008168 1224 24 , , PUNCT hvd.32044092008168 1224 25 ±√3 ±√3 NOUN hvd.32044092008168 1224 26 ( ( PUNCT hvd.32044092008168 1224 27 5 5 NUM hvd.32044092008168 1224 28 g g NOUN hvd.32044092008168 1224 29 , , PUNCT hvd.32044092008168 1224 30 — — PUNCT hvd.32044092008168 1224 31 12c 12c NUM hvd.32044092008168 1224 32 ;) ;) PUNCT hvd.32044092008168 1224 33 ) ) PUNCT hvd.32044092008168 1224 34 } } PUNCT hvd.32044092008168 1224 35 vp vp PROPN hvd.32044092008168 1224 36 — — PUNCT hvd.32044092008168 1224 37 ez ez PROPN hvd.32044092008168 1224 38 2 2 PROPN hvd.32044092008168 1224 39 10 10 NUM hvd.32044092008168 1224 40 f₂ f₂ PROPN hvd.32044092008168 1224 41 or or CCONJ hvd.32044092008168 1224 42 q3 q3 PROPN hvd.32044092008168 1224 43 or or CCONJ hvd.32044092008168 1224 44 = = X hvd.32044092008168 1224 45 { { PUNCT hvd.32044092008168 1224 46 p p NOUN hvd.32044092008168 1224 47 + + PROPN hvd.32044092008168 1224 48 1/3 1/3 NUM hvd.32044092008168 1224 49 ( ( PUNCT hvd.32044092008168 1224 50 1 1 NUM hvd.32044092008168 1224 51 − − NOUN hvd.32044092008168 1224 52 15 15 NUM hvd.32044092008168 1224 53 = = SYM hvd.32044092008168 1224 54 = = SYM hvd.32044092008168 1224 55 0 0 NUM hvd.32044092008168 1225 1 y y PROPN hvd.32044092008168 1225 2 = = SYM hvd.32044092008168 1225 3 { { PUNCT hvd.32044092008168 1225 4 p p NOUN hvd.32044092008168 1225 5 + + NOUN hvd.32044092008168 1225 6 case case NOUN hvd.32044092008168 1225 7 3 3 NUM hvd.32044092008168 1225 8 . . PUNCT hvd.32044092008168 1225 9 where where SCONJ hvd.32044092008168 1225 10 b=3eg±√3 b=3eg±√3 NOUN hvd.32044092008168 1225 11 ( ( PUNCT hvd.32044092008168 1225 12 5 5 NUM hvd.32044092008168 1225 13 g g NOUN hvd.32044092008168 1225 14 12c 12c NUM hvd.32044092008168 1225 15 1 1 NUM hvd.32044092008168 1225 16 + + CCONJ hvd.32044092008168 1225 17 k² k² PROPN hvd.32044092008168 1225 18 + + CCONJ hvd.32044092008168 1225 19 2 2 NUM hvd.32044092008168 1225 20 √ √ PROPN hvd.32044092008168 1225 21 ( ( PUNCT hvd.32044092008168 1225 22 2 2 NUM hvd.32044092008168 1225 23 — — PUNCT hvd.32044092008168 1225 24 k²)2 k²)2 SYM hvd.32044092008168 1225 25 3k 3k NUM hvd.32044092008168 1225 26 = = SYM hvd.32044092008168 1225 27 { { PUNCT hvd.32044092008168 1225 28 p p NOUN hvd.32044092008168 1225 29 + + NUM hvd.32044092008168 1225 30 0 0 NUM hvd.32044092008168 1225 31 ; ; PUNCT hvd.32044092008168 1225 32 1 1 NUM hvd.32044092008168 1225 33 e e NOUN hvd.32044092008168 1225 34 2 2 NUM hvd.32044092008168 1225 35 1/ 1/ NUM hvd.32044092008168 1225 36 x x SYM hvd.32044092008168 1225 37 = = PUNCT hvd.32044092008168 1225 38 0 0 NUM hvd.32044092008168 1225 39 ; ; PUNCT hvd.32044092008168 1225 40 ( ( PUNCT hvd.32044092008168 1225 41 1 1 NUM hvd.32044092008168 1225 42 + + CCONJ hvd.32044092008168 1225 43 2 2 NUM hvd.32044092008168 1225 44 k² k² PROPN hvd.32044092008168 1225 45 ) ) PUNCT hvd.32044092008168 1225 46 + + CCONJ hvd.32044092008168 1226 1 2k²)± 2k²)± NUM hvd.32044092008168 1226 2 62u 62u NOUN hvd.32044092008168 1226 3 би би PROPN hvd.32044092008168 1226 4 y1 y1 PROPN hvd.32044092008168 1226 5 ―― ―― PROPN hvd.32044092008168 1226 6 φ φ PROPN hvd.32044092008168 1226 7 e e X hvd.32044092008168 1226 8 2 2 NUM hvd.32044092008168 1226 9 k² k² PROPN hvd.32044092008168 1226 10 ) ) PUNCT hvd.32044092008168 1226 11 ± ± NOUN hvd.32044092008168 1226 12 1%√(1 1%√(1 NUM hvd.32044092008168 1226 13 − − NOUN hvd.32044092008168 1226 14 2k²)² 2k²)² NUM hvd.32044092008168 1226 15 + + NUM hvd.32044092008168 1226 16 15 15 NUM hvd.32044092008168 1226 17 } } PUNCT hvd.32044092008168 1226 18 vp vp PROPN hvd.32044092008168 1226 19 — — PUNCT hvd.32044092008168 1226 20 1 1 NUM hvd.32044092008168 1226 21 ( ( PUNCT hvd.32044092008168 1226 22 1 1 NUM hvd.32044092008168 1226 23 — — PUNCT hvd.32044092008168 1226 24 2k² 2k² NUM hvd.32044092008168 1226 25 ) ) PUNCT hvd.32044092008168 1226 26 10 10 NUM hvd.32044092008168 1226 27 3 3 NUM hvd.32044092008168 1226 28 f= f= NOUN hvd.32044092008168 1226 29 e(x-(0%)u e(x-(0%)u NUM hvd.32044092008168 1226 30 ) ) PUNCT hvd.32044092008168 1226 31 . . PUNCT hvd.32044092008168 1227 1 six six NUM hvd.32044092008168 1227 2 values value NOUN hvd.32044092008168 1227 3 of of ADP hvd.32044092008168 1227 4 this this DET hvd.32044092008168 1227 5 form form NOUN hvd.32044092008168 1227 6 corresponding correspond VERB hvd.32044092008168 1227 7 to to ADP hvd.32044092008168 1227 8 the the DET hvd.32044092008168 1227 9 roots root NOUN hvd.32044092008168 1227 10 of of ADP hvd.32044092008168 1227 11 a a DET hvd.32044092008168 1227 12 = = SYM hvd.32044092008168 1227 13 0 0 NUM hvd.32044092008168 1227 14 ; ; PUNCT hvd.32044092008168 1227 15 b= b= PUNCT hvd.32044092008168 1227 16 0 0 NUM hvd.32044092008168 1227 17 ; ; PUNCT hvd.32044092008168 1227 18 c c X hvd.32044092008168 1227 19 = = SYM hvd.32044092008168 1227 20 0 0 NUM hvd.32044092008168 1227 21 , , PUNCT hvd.32044092008168 1227 22 namely namely ADV hvd.32044092008168 1227 23 ψ ψ PROPN hvd.32044092008168 1227 24 1/1 1/1 NUM hvd.32044092008168 1227 25 ( ( PUNCT hvd.32044092008168 1227 26 3e 3e X hvd.32044092008168 1227 27 , , PUNCT hvd.32044092008168 1227 28 ± ± PROPN hvd.32044092008168 1227 29 √3 √3 PROPN hvd.32044092008168 1227 30 ( ( PUNCT hvd.32044092008168 1227 31 5 5 NUM hvd.32044092008168 1227 32 g g NOUN hvd.32044092008168 1227 33 , , PUNCT hvd.32044092008168 1227 34 — — PUNCT hvd.32044092008168 1227 35 12 12 NUM hvd.32044092008168 1227 36 € € NUM hvd.32044092008168 1227 37 ;) ;) NUM hvd.32044092008168 1227 38 ) ) PUNCT hvd.32044092008168 1227 39 } } PUNCT hvd.32044092008168 1227 40 vp vp PROPN hvd.32044092008168 1227 41 — — PUNCT hvd.32044092008168 1227 42 es es X hvd.32044092008168 1227 43 10 10 NUM hvd.32044092008168 1227 44 5 5 NUM hvd.32044092008168 1227 45 b b NOUN hvd.32044092008168 1227 46 = = NOUN hvd.32044092008168 1227 47 ½/ ½/ NOUN hvd.32044092008168 1227 48 ( ( PUNCT hvd.32044092008168 1227 49 1 1 NUM hvd.32044092008168 1227 50 + + NUM hvd.32044092008168 1227 51 k² k² PROPN hvd.32044092008168 1227 52 ) ) PUNCT hvd.32044092008168 1227 53 ± ± NOUN hvd.32044092008168 1227 54 √ √ PROPN hvd.32044092008168 1227 55 ( ( PUNCT hvd.32044092008168 1227 56 1 1 NUM hvd.32044092008168 1227 57 + + NUM hvd.32044092008168 1227 58 k²)² k²)² X hvd.32044092008168 1227 59 + + NUM hvd.32044092008168 1227 60 6k² 6k² NUM hvd.32044092008168 1227 61 2 2 NUM hvd.32044092008168 1227 62 = = SYM hvd.32044092008168 1227 63 5 5 NUM hvd.32044092008168 1227 64 5 5 NUM hvd.32044092008168 1227 65 b b NOUN hvd.32044092008168 1227 66 = = SYM hvd.32044092008168 1227 67 1 1 NUM hvd.32044092008168 1227 68 / / SYM hvd.32044092008168 1227 69 ( ( PUNCT hvd.32044092008168 1227 70 1 1 NUM hvd.32044092008168 1227 71 − − NOUN hvd.32044092008168 1227 72 2k² 2k² NUM hvd.32044092008168 1227 73 ) ) PUNCT hvd.32044092008168 1227 74 + + CCONJ hvd.32044092008168 1227 75 ½ ½ ADP hvd.32044092008168 1227 76 √(1 √(1 PRON hvd.32044092008168 1227 77 − − PROPN hvd.32044092008168 1227 78 2k² 2k² NUM hvd.32044092008168 1227 79 ) ) PUNCT hvd.32044092008168 1227 80 — — PUNCT hvd.32044092008168 1227 81 6 6 NUM hvd.32044092008168 1227 82 ( ( PUNCT hvd.32044092008168 1227 83 k² k² PROPN hvd.32044092008168 1227 84 — — PUNCT hvd.32044092008168 1227 85 k¹ k¹ PROPN hvd.32044092008168 1227 86 ) ) PUNCT hvd.32044092008168 1227 87 2 2 NUM hvd.32044092008168 1227 88 2 2 NUM hvd.32044092008168 1227 89 which which PRON hvd.32044092008168 1227 90 determine determine VERB hvd.32044092008168 1227 91 corresponding corresponding ADJ hvd.32044092008168 1227 92 values value NOUN hvd.32044092008168 1227 93 for for ADP hvd.32044092008168 1227 94 x. x. NOUN hvd.32044092008168 1227 95 = = VERB hvd.32044092008168 1227 96 a a PRON hvd.32044092008168 1227 97 = = NOUN hvd.32044092008168 1227 98 0 0 NUM hvd.32044092008168 1227 99 ; ; PUNCT hvd.32044092008168 1227 100 b b X hvd.32044092008168 1227 101 = = X hvd.32044092008168 1227 102 ex ex PROPN hvd.32044092008168 1227 103 u u NOUN hvd.32044092008168 1227 104 5 5 NUM hvd.32044092008168 1227 105 b b NOUN hvd.32044092008168 1227 106 = = SYM hvd.32044092008168 1227 107 1 1 NUM hvd.32044092008168 1227 108 / / SYM hvd.32044092008168 1227 109 ( ( PUNCT hvd.32044092008168 1227 110 k²2 k²2 NOUN hvd.32044092008168 1227 111 − − PROPN hvd.32044092008168 1227 112 2 2 NUM hvd.32044092008168 1227 113 ) ) PUNCT hvd.32044092008168 1227 114 + + CCONJ hvd.32044092008168 1227 115 ½ ½ NUM hvd.32044092008168 1227 116 √(k² √(k² PROPN hvd.32044092008168 1227 117 − − PROPN hvd.32044092008168 1227 118 2 2 NUM hvd.32044092008168 1227 119 ) ) PUNCT hvd.32044092008168 1227 120 + + CCONJ hvd.32044092008168 1227 121 6 6 NUM hvd.32044092008168 1227 122 ( ( PUNCT hvd.32044092008168 1227 123 1 1 NUM hvd.32044092008168 1227 124 — — PUNCT hvd.32044092008168 1227 125 k² k² PROPN hvd.32044092008168 1227 126 ) ) PUNCT hvd.32044092008168 1227 127 · · PUNCT hvd.32044092008168 1227 128 2 2 NUM hvd.32044092008168 1227 129 = = NOUN hvd.32044092008168 1227 130 = = X hvd.32044092008168 1227 131 case case NOUN hvd.32044092008168 1227 132 4 4 NUM hvd.32044092008168 1227 133 . . PUNCT hvd.32044092008168 1228 1 conditions condition NOUN hvd.32044092008168 1228 2 as as ADP hvd.32044092008168 1228 3 in in ADP hvd.32044092008168 1228 4 case case NOUN hvd.32044092008168 1228 5 ( ( PUNCT hvd.32044092008168 1228 6 3 3 NUM hvd.32044092008168 1228 7 ) ) PUNCT hvd.32044092008168 1228 8 with with ADP hvd.32044092008168 1228 9 the the DET hvd.32044092008168 1228 10 additional additional ADJ hvd.32044092008168 1228 11 condition condition NOUN hvd.32044092008168 1228 12 of of ADP hvd.32044092008168 1228 13 the the DET hvd.32044092008168 1228 14 functions function NOUN hvd.32044092008168 1228 15 of of ADP hvd.32044092008168 1228 16 m. m. NOUN hvd.32044092008168 1228 17 mittag mittag ADJ hvd.32044092008168 1228 18 - - PUNCT hvd.32044092008168 1228 19 leffler leffler NOUN hvd.32044092008168 1228 20 . . PUNCT hvd.32044092008168 1229 1 the the DET hvd.32044092008168 1229 2 integral integral NOUN hvd.32044092008168 1229 3 is be AUX hvd.32044092008168 1229 4 : : PUNCT hvd.32044092008168 1229 5 — — PUNCT hvd.32044092008168 1229 6 } } PUNCT hvd.32044092008168 1229 7 √(2 √(2 X hvd.32044092008168 1229 8 − − X hvd.32044092008168 1229 9 k²)² k²)² PROPN hvd.32044092008168 1229 10 − − PROPN hvd.32044092008168 1229 11 3k 3k NUM hvd.32044092008168 1229 12 } } PUNCT hvd.32044092008168 1229 13 v v X hvd.32044092008168 1229 14 p p PROPN hvd.32044092008168 1229 15 − − NOUN hvd.32044092008168 1229 16 } } PUNCT hvd.32044092008168 1229 17 ( ( PUNCT hvd.32044092008168 1229 18 1 1 NUM hvd.32044092008168 1229 19 + + NUM hvd.32044092008168 1229 20 k² k² PROPN hvd.32044092008168 1229 21 ) ) PUNCT hvd.32044092008168 1229 22 · · PUNCT hvd.32044092008168 1229 23 x x PUNCT hvd.32044092008168 1229 24 = = PUNCT hvd.32044092008168 1229 25 0 0 NUM hvd.32044092008168 1229 26 o o NOUN hvd.32044092008168 1229 27 ( ( PUNCT hvd.32044092008168 1229 28 u u PROPN hvd.32044092008168 1229 29 — — PUNCT hvd.32044092008168 1229 30 w₂ w₂ PROPN hvd.32044092008168 1229 31 ) ) PUNCT hvd.32044092008168 1229 32 би би NOUN hvd.32044092008168 1229 33 0 0 NUM hvd.32044092008168 1229 34 ; ; PUNCT hvd.32044092008168 1229 35 ( ( PUNCT hvd.32044092008168 1229 36 sue sue VERB hvd.32044092008168 1229 37 ) ) PUNCT hvd.32044092008168 1229 38 " " PUNCT hvd.32044092008168 1229 39 — — PUNCT hvd.32044092008168 1229 40 3b 3b NUM hvd.32044092008168 1229 41 ( ( PUNCT hvd.32044092008168 1229 42 gueou gueou NOUN hvd.32044092008168 1229 43 ) ) PUNCT hvd.32044092008168 1229 44 + + NUM hvd.32044092008168 1229 45 2gbeou 2gbeou NUM hvd.32044092008168 1229 46 vq vq NOUN hvd.32044092008168 1229 47 . . PUNCT hvd.32044092008168 1230 1 c c NOUN hvd.32044092008168 1230 2 = = SYM hvd.32044092008168 1230 3 0 0 NUM hvd.32044092008168 1230 4 ; ; PUNCT hvd.32044092008168 1230 5 v v X hvd.32044092008168 1230 6 = = NOUN hvd.32044092008168 1230 7 = = NOUN hvd.32044092008168 1230 8 02 02 NUM hvd.32044092008168 1230 9 ; ; PUNCT hvd.32044092008168 1230 10 ୧ ୧ NUM hvd.32044092008168 1230 11 v36 v36 PROPN hvd.32044092008168 1230 12 6 6 NUM hvd.32044092008168 1230 13 a a DET hvd.32044092008168 1230 14 s² s² X hvd.32044092008168 1230 15 + + NUM hvd.32044092008168 1230 16 9 9 NUM hvd.32044092008168 1230 17 as as ADP hvd.32044092008168 1230 18 a² a² NOUN hvd.32044092008168 1230 19 9 9 NUM hvd.32044092008168 1230 20 [ [ X hvd.32044092008168 1230 21 2 2 NUM hvd.32044092008168 1230 22 as3 as3 ADV hvd.32044092008168 1230 23 a a PRON hvd.32044092008168 1230 24 ] ] PUNCT hvd.32044092008168 1230 25 2 2 NUM hvd.32044092008168 1230 26 due due ADJ hvd.32044092008168 1230 27 jan jan PROPN hvd.32044092008168 1230 28 1 1 NUM hvd.32044092008168 1230 29 1911 1911 NUM hvd.32044092008168 1230 30 math math NOUN hvd.32044092008168 1230 31 4008.93 4008.93 NUM hvd.32044092008168 1230 32 ( ( PUNCT hvd.32044092008168 1230 33 a a DET hvd.32044092008168 1230 34 presentation presentation NOUN hvd.32044092008168 1230 35 of of ADP hvd.32044092008168 1230 36 the the DET hvd.32044092008168 1230 37 theory theory NOUN hvd.32044092008168 1230 38 of of ADP hvd.32044092008168 1230 39 he he PRON hvd.32044092008168 1230 40 cabot cabot NOUN hvd.32044092008168 1230 41 science science NOUN hvd.32044092008168 1230 42 003006941 003006941 NUM hvd.32044092008168 1230 43 3 3 NUM hvd.32044092008168 1230 44 2044 2044 NUM hvd.32044092008168 1230 45 092 092 NUM hvd.32044092008168 1230 46 008 008 NUM hvd.32044092008168 1230 47 168 168 NUM