id	sid	tid	token	lemma	pos
ejpam-4700	1	1	european	european	PROPN
ejpam-4700	1	2	journal	journal	PROPN
ejpam-4700	1	3	of	of	ADP
ejpam-4700	1	4	pure	pure	ADJ
ejpam-4700	1	5	and	and	CCONJ
ejpam-4700	1	6	applied	apply	VERB
ejpam-4700	1	7	mathematics	mathematic	NOUN
ejpam-4700	1	8	vol	vol	NOUN
ejpam-4700	1	9	.	.	PUNCT
ejpam-4700	2	1	16	16	NUM
ejpam-4700	2	2	,	,	PUNCT
ejpam-4700	2	3	no	no	INTJ
ejpam-4700	2	4	.	.	NOUN
ejpam-4700	2	5	2	2	NUM
ejpam-4700	2	6	,	,	PUNCT
ejpam-4700	2	7	2023	2023	NUM
ejpam-4700	2	8	,	,	PUNCT
ejpam-4700	2	9	1005	1005	NUM
ejpam-4700	2	10	-	-	SYM
ejpam-4700	2	11	1023	1023	NUM
ejpam-4700	2	12	issn	issn	PROPN
ejpam-4700	2	13	1307	1307	NUM
ejpam-4700	2	14	-	-	SYM
ejpam-4700	2	15	5543	5543	NUM
ejpam-4700	2	16	–	–	PUNCT
ejpam-4700	3	1	ejpam.com	ejpam.com	X
ejpam-4700	3	2	published	publish	VERB
ejpam-4700	3	3	by	by	ADP
ejpam-4700	3	4	new	new	PROPN
ejpam-4700	3	5	york	york	PROPN
ejpam-4700	3	6	business	business	PROPN
ejpam-4700	3	7	global	global	ADJ
ejpam-4700	3	8	construction	construction	NOUN
ejpam-4700	3	9	of	of	ADP
ejpam-4700	3	10	fourier	fourier	ADJ
ejpam-4700	3	11	series	series	NOUN
ejpam-4700	3	12	expansion	expansion	NOUN
ejpam-4700	3	13	of	of	ADP
ejpam-4700	3	14	apostol	apostol	NOUN
ejpam-4700	3	15	-	-	PUNCT
ejpam-4700	3	16	frobenius	frobenius	NOUN
ejpam-4700	3	17	-	-	PUNCT
ejpam-4700	3	18	type	type	NOUN
ejpam-4700	3	19	tangent	tangent	NOUN
ejpam-4700	3	20	and	and	CCONJ
ejpam-4700	3	21	genocchi	genocchi	PROPN
ejpam-4700	3	22	polynomials	polynomial	NOUN
ejpam-4700	3	23	of	of	ADP
ejpam-4700	3	24	higher	high	ADJ
ejpam-4700	3	25	-	-	PUNCT
ejpam-4700	3	26	order	order	NOUN
ejpam-4700	3	27	roberto	roberto	PROPN
ejpam-4700	3	28	b.	b.	PROPN
ejpam-4700	3	29	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-4700	3	30	,	,	PUNCT
ejpam-4700	3	31	cristina	cristina	PROPN
ejpam-4700	3	32	b.	b.	PROPN
ejpam-4700	3	33	corcino1,2	corcino1,2	PROPN
ejpam-4700	3	34	,	,	PUNCT
ejpam-4700	3	35	karl	karl	PROPN
ejpam-4700	3	36	patrick	patrick	PROPN
ejpam-4700	3	37	casas1,3	casas1,3	PROPN
ejpam-4700	3	38	,	,	PUNCT
ejpam-4700	3	39	allan	allan	PROPN
ejpam-4700	3	40	roy	roy	PROPN
ejpam-4700	3	41	elnar1,3	elnar1,3	PROPN
ejpam-4700	3	42	,	,	PUNCT
ejpam-4700	3	43	gibson	gibson	PROPN
ejpam-4700	3	44	maglasang1,3	maglasang1,3	PROPN
ejpam-4700	3	45	1	1	NUM
ejpam-4700	3	46	research	research	NOUN
ejpam-4700	3	47	institute	institute	NOUN
ejpam-4700	3	48	for	for	ADP
ejpam-4700	3	49	computational	computational	ADJ
ejpam-4700	3	50	mathematics	mathematic	NOUN
ejpam-4700	3	51	and	and	CCONJ
ejpam-4700	3	52	physics	physics	NOUN
ejpam-4700	3	53	,	,	PUNCT
ejpam-4700	3	54	cebu	cebu	NOUN
ejpam-4700	3	55	normal	normal	ADJ
ejpam-4700	3	56	university	university	NOUN
ejpam-4700	3	57	,	,	PUNCT
ejpam-4700	3	58	6000	6000	NUM
ejpam-4700	3	59	cebu	cebu	NOUN
ejpam-4700	3	60	city	city	NOUN
ejpam-4700	3	61	,	,	PUNCT
ejpam-4700	3	62	philippines	philippine	NOUN
ejpam-4700	3	63	2	2	NUM
ejpam-4700	3	64	mathematics	mathematics	NOUN
ejpam-4700	3	65	department	department	NOUN
ejpam-4700	3	66	,	,	PUNCT
ejpam-4700	3	67	cebu	cebu	NOUN
ejpam-4700	3	68	normal	normal	ADJ
ejpam-4700	3	69	university	university	NOUN
ejpam-4700	3	70	,	,	PUNCT
ejpam-4700	3	71	6000	6000	NUM
ejpam-4700	3	72	cebu	cebu	NOUN
ejpam-4700	3	73	city	city	NOUN
ejpam-4700	3	74	,	,	PUNCT
ejpam-4700	3	75	philippines	philippines	PROPN
ejpam-4700	3	76	2	2	NUM
ejpam-4700	3	77	physics	physics	NOUN
ejpam-4700	3	78	department	department	NOUN
ejpam-4700	3	79	,	,	PUNCT
ejpam-4700	3	80	cebu	cebu	NOUN
ejpam-4700	3	81	normal	normal	ADJ
ejpam-4700	3	82	university	university	NOUN
ejpam-4700	3	83	,	,	PUNCT
ejpam-4700	3	84	6000	6000	NUM
ejpam-4700	3	85	cebu	cebu	NOUN
ejpam-4700	3	86	city	city	NOUN
ejpam-4700	3	87	,	,	PUNCT
ejpam-4700	3	88	philippines	philippine	NOUN
ejpam-4700	3	89	abstract	abstract	ADJ
ejpam-4700	3	90	.	.	PUNCT
ejpam-4700	4	1	in	in	ADP
ejpam-4700	4	2	this	this	DET
ejpam-4700	4	3	study	study	NOUN
ejpam-4700	4	4	,	,	PUNCT
ejpam-4700	4	5	the	the	DET
ejpam-4700	4	6	fourier	fourier	NOUN
ejpam-4700	4	7	series	series	NOUN
ejpam-4700	4	8	expansions	expansion	NOUN
ejpam-4700	4	9	of	of	ADP
ejpam-4700	4	10	the	the	DET
ejpam-4700	4	11	apostol	apostol	NOUN
ejpam-4700	4	12	-	-	PUNCT
ejpam-4700	4	13	frobenius	frobenius	NOUN
ejpam-4700	4	14	type	type	NOUN
ejpam-4700	4	15	of	of	ADP
ejpam-4700	4	16	tangent	tangent	NOUN
ejpam-4700	4	17	and	and	CCONJ
ejpam-4700	4	18	genocchi	genocchi	PROPN
ejpam-4700	4	19	polynomials	polynomial	NOUN
ejpam-4700	4	20	of	of	ADP
ejpam-4700	4	21	higher	high	ADJ
ejpam-4700	4	22	order	order	NOUN
ejpam-4700	4	23	are	be	AUX
ejpam-4700	4	24	derived	derive	VERB
ejpam-4700	4	25	using	use	VERB
ejpam-4700	4	26	the	the	DET
ejpam-4700	4	27	cauchy	cauchy	ADJ
ejpam-4700	4	28	residue	residue	NOUN
ejpam-4700	4	29	theorem	theorem	VERB
ejpam-4700	4	30	.	.	PUNCT
ejpam-4700	5	1	some	some	DET
ejpam-4700	5	2	novel	novel	ADJ
ejpam-4700	5	3	and	and	CCONJ
ejpam-4700	5	4	intriguing	intriguing	ADJ
ejpam-4700	5	5	results	result	NOUN
ejpam-4700	5	6	are	be	AUX
ejpam-4700	5	7	obtained	obtain	VERB
ejpam-4700	5	8	by	by	ADP
ejpam-4700	5	9	applying	apply	VERB
ejpam-4700	5	10	the	the	DET
ejpam-4700	5	11	fourier	fourier	NOUN
ejpam-4700	5	12	series	series	NOUN
ejpam-4700	5	13	expansion	expansion	NOUN
ejpam-4700	5	14	of	of	ADP
ejpam-4700	5	15	these	these	DET
ejpam-4700	5	16	types	type	NOUN
ejpam-4700	5	17	of	of	ADP
ejpam-4700	5	18	polynomials	polynomial	NOUN
ejpam-4700	5	19	.	.	PUNCT
ejpam-4700	6	1	2020	2020	NUM
ejpam-4700	6	2	mathematics	mathematic	NOUN
ejpam-4700	6	3	subject	subject	NOUN
ejpam-4700	6	4	classifications	classification	NOUN
ejpam-4700	6	5	:	:	PUNCT
ejpam-4700	6	6	11b68	11b68	NUM
ejpam-4700	6	7	,	,	PUNCT
ejpam-4700	6	8	42a16	42a16	PRON
ejpam-4700	6	9	key	key	ADJ
ejpam-4700	6	10	words	word	NOUN
ejpam-4700	6	11	and	and	CCONJ
ejpam-4700	6	12	phrases	phrase	NOUN
ejpam-4700	6	13	:	:	PUNCT
ejpam-4700	6	14	cauchy	cauchy	ADJ
ejpam-4700	6	15	residue	residue	NOUN
ejpam-4700	6	16	theorem	theorem	NOUN
ejpam-4700	6	17	;	;	PUNCT
ejpam-4700	6	18	fourier	fourier	ADJ
ejpam-4700	6	19	series	series	NOUN
ejpam-4700	6	20	,	,	PUNCT
ejpam-4700	6	21	tangent	tangent	NOUN
ejpam-4700	6	22	polynomials	polynomial	NOUN
ejpam-4700	6	23	,	,	PUNCT
ejpam-4700	6	24	bernoulli	bernoulli	NOUN
ejpam-4700	6	25	polynomials	polynomial	NOUN
ejpam-4700	6	26	,	,	PUNCT
ejpam-4700	6	27	genocchi	genocchi	PROPN
ejpam-4700	6	28	polynomials	polynomial	VERB
ejpam-4700	6	29	1	1	NUM
ejpam-4700	6	30	.	.	PUNCT
ejpam-4700	7	1	introduction	introduction	NOUN
ejpam-4700	7	2	there	there	PRON
ejpam-4700	7	3	are	be	VERB
ejpam-4700	7	4	numerous	numerous	ADJ
ejpam-4700	7	5	well	well	ADV
ejpam-4700	7	6	-	-	PUNCT
ejpam-4700	7	7	known	know	VERB
ejpam-4700	7	8	special	special	ADJ
ejpam-4700	7	9	functions	function	NOUN
ejpam-4700	7	10	,	,	PUNCT
ejpam-4700	7	11	numbers	number	NOUN
ejpam-4700	7	12	,	,	PUNCT
ejpam-4700	7	13	and	and	CCONJ
ejpam-4700	7	14	polynomials	polynomial	NOUN
ejpam-4700	7	15	,	,	PUNCT
ejpam-4700	7	16	such	such	DET
ejpam-4700	7	17	the	the	DET
ejpam-4700	7	18	bernoulli	bernoulli	PROPN
ejpam-4700	7	19	,	,	PUNCT
ejpam-4700	7	20	tangent	tangent	NOUN
ejpam-4700	7	21	,	,	PUNCT
ejpam-4700	7	22	and	and	CCONJ
ejpam-4700	7	23	genocchi	genocchi	PROPN
ejpam-4700	7	24	numbers	number	NOUN
ejpam-4700	7	25	and	and	CCONJ
ejpam-4700	7	26	polynomials	polynomial	NOUN
ejpam-4700	7	27	,	,	PUNCT
ejpam-4700	7	28	and	and	CCONJ
ejpam-4700	7	29	derivative	derivative	ADJ
ejpam-4700	7	30	polynomials	polynomial	NOUN
ejpam-4700	7	31	,	,	PUNCT
ejpam-4700	7	32	that	that	PRON
ejpam-4700	7	33	are	be	AUX
ejpam-4700	7	34	well	well	ADV
ejpam-4700	7	35	studied	study	VERB
ejpam-4700	7	36	in	in	ADP
ejpam-4700	7	37	the	the	DET
ejpam-4700	7	38	current	current	ADJ
ejpam-4700	7	39	literature	literature	NOUN
ejpam-4700	7	40	due	due	ADP
ejpam-4700	7	41	to	to	ADP
ejpam-4700	7	42	their	their	PRON
ejpam-4700	7	43	broad	broad	ADJ
ejpam-4700	7	44	applications	application	NOUN
ejpam-4700	7	45	ranging	range	VERB
ejpam-4700	7	46	from	from	ADP
ejpam-4700	7	47	number	number	NOUN
ejpam-4700	7	48	theory	theory	NOUN
ejpam-4700	7	49	and	and	CCONJ
ejpam-4700	7	50	combinatorics	combinatoric	NOUN
ejpam-4700	7	51	to	to	ADP
ejpam-4700	7	52	other	other	ADJ
ejpam-4700	7	53	fields	field	NOUN
ejpam-4700	7	54	of	of	ADP
ejpam-4700	7	55	applied	apply	VERB
ejpam-4700	7	56	mathematics[5	mathematics[5	PROPN
ejpam-4700	7	57	,	,	PUNCT
ejpam-4700	7	58	6	6	NUM
ejpam-4700	7	59	,	,	PUNCT
ejpam-4700	7	60	13	13	NUM
ejpam-4700	7	61	]	]	PUNCT
ejpam-4700	7	62	.	.	PUNCT
ejpam-4700	8	1	in	in	ADP
ejpam-4700	8	2	the	the	DET
ejpam-4700	8	3	literature	literature	NOUN
ejpam-4700	8	4	,	,	PUNCT
ejpam-4700	8	5	other	other	ADJ
ejpam-4700	8	6	variants	variant	NOUN
ejpam-4700	8	7	and	and	CCONJ
ejpam-4700	8	8	extensions	extension	NOUN
ejpam-4700	8	9	of	of	ADP
ejpam-4700	8	10	these	these	DET
ejpam-4700	8	11	functions	function	NOUN
ejpam-4700	8	12	,	,	PUNCT
ejpam-4700	8	13	numbers	number	NOUN
ejpam-4700	8	14	,	,	PUNCT
ejpam-4700	8	15	and	and	CCONJ
ejpam-4700	8	16	polynomials	polynomial	NOUN
ejpam-4700	8	17	have	have	AUX
ejpam-4700	8	18	appeared	appear	VERB
ejpam-4700	8	19	.	.	PUNCT
ejpam-4700	9	1	some	some	DET
ejpam-4700	9	2	versions	version	NOUN
ejpam-4700	9	3	have	have	AUX
ejpam-4700	9	4	been	be	AUX
ejpam-4700	9	5	created	create	VERB
ejpam-4700	9	6	by	by	ADP
ejpam-4700	9	7	combining	combine	VERB
ejpam-4700	9	8	two	two	NUM
ejpam-4700	9	9	or	or	CCONJ
ejpam-4700	9	10	three	three	NUM
ejpam-4700	9	11	special	special	ADJ
ejpam-4700	9	12	functions	function	NOUN
ejpam-4700	9	13	,	,	PUNCT
ejpam-4700	9	14	integers	integer	NOUN
ejpam-4700	9	15	,	,	PUNCT
ejpam-4700	9	16	or	or	CCONJ
ejpam-4700	9	17	polynomials	polynomial	NOUN
ejpam-4700	9	18	.	.	PUNCT
ejpam-4700	10	1	poly	poly	ADJ
ejpam-4700	10	2	-	-	PUNCT
ejpam-4700	10	3	bernoulli	bernoulli	NOUN
ejpam-4700	10	4	numbers	number	NOUN
ejpam-4700	10	5	and	and	CCONJ
ejpam-4700	10	6	polynomials	polynomial	NOUN
ejpam-4700	10	7	,	,	PUNCT
ejpam-4700	10	8	for	for	ADP
ejpam-4700	10	9	example	example	NOUN
ejpam-4700	10	10	,	,	PUNCT
ejpam-4700	10	11	were	be	AUX
ejpam-4700	10	12	created	create	VERB
ejpam-4700	10	13	by	by	ADP
ejpam-4700	10	14	combining	combine	VERB
ejpam-4700	10	15	the	the	DET
ejpam-4700	10	16	notions	notion	NOUN
ejpam-4700	10	17	of	of	ADP
ejpam-4700	10	18	polylogarithm	polylogarithm	PROPN
ejpam-4700	10	19	and	and	CCONJ
ejpam-4700	10	20	bernoulli	bernoulli	NOUN
ejpam-4700	10	21	numbers	number	NOUN
ejpam-4700	10	22	and	and	CCONJ
ejpam-4700	10	23	polynomials[9	polynomials[9	PRON
ejpam-4700	10	24	,	,	PUNCT
ejpam-4700	10	25	14	14	NUM
ejpam-4700	10	26	]	]	PUNCT
ejpam-4700	10	27	.	.	PUNCT
ejpam-4700	11	1	∗corresponding	∗corresponde	VERB
ejpam-4700	11	2	author	author	NOUN
ejpam-4700	11	3	.	.	PUNCT
ejpam-4700	12	1	doi	doi	NOUN
ejpam-4700	12	2	:	:	PUNCT
ejpam-4700	12	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4700	https://doi.org/10.29020/nybg.ejpam.v16i2.4700	ADP
ejpam-4700	12	4	email	email	NOUN
ejpam-4700	12	5	addresses	address	NOUN
ejpam-4700	12	6	:	:	PUNCT
ejpam-4700	12	7	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-4700	12	8	(	(	PUNCT
ejpam-4700	12	9	r.	r.	PROPN
ejpam-4700	12	10	corcino	corcino	PROPN
ejpam-4700	12	11	)	)	PUNCT
ejpam-4700	12	12	,	,	PUNCT
ejpam-4700	12	13	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-4700	12	14	(	(	PUNCT
ejpam-4700	12	15	c.	c.	PROPN
ejpam-4700	12	16	corcino	corcino	PROPN
ejpam-4700	12	17	)	)	PUNCT
ejpam-4700	12	18	,	,	PUNCT
ejpam-4700	12	19	casask@cnu.edu.ph	casask@cnu.edu.ph	PROPN
ejpam-4700	12	20	(	(	PUNCT
ejpam-4700	12	21	k.	k.	PROPN
ejpam-4700	12	22	casas	casas	PROPN
ejpam-4700	12	23	)	)	PUNCT
ejpam-4700	12	24	,	,	PUNCT
ejpam-4700	12	25	elnara@cnu.edu.ph	elnara@cnu.edu.ph	PROPN
ejpam-4700	12	26	(	(	PUNCT
ejpam-4700	12	27	a.r	a.r	PROPN
ejpam-4700	12	28	.	.	PROPN
ejpam-4700	12	29	elnar	elnar	PROPN
ejpam-4700	12	30	)	)	PUNCT
ejpam-4700	12	31	,	,	PUNCT
ejpam-4700	12	32	maglasangg@cnu.edu.ph	maglasangg@cnu.edu.ph	PROPN
ejpam-4700	12	33	(	(	PUNCT
ejpam-4700	12	34	g.	g.	PROPN
ejpam-4700	12	35	maglasang	maglasang	PROPN
ejpam-4700	12	36	)	)	PUNCT
ejpam-4700	12	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4700	13	1	1005	1005	NUM
ejpam-4700	13	2	©	©	PROPN
ejpam-4700	13	3	2023	2023	NUM
ejpam-4700	13	4	ejpam	ejpam	NOUN
ejpam-4700	13	5	all	all	DET
ejpam-4700	13	6	rights	right	NOUN
ejpam-4700	13	7	reserved	reserve	VERB
ejpam-4700	13	8	.	.	PUNCT
ejpam-4700	14	1	r.	r.	PROPN
ejpam-4700	14	2	b.	b.	PROPN
ejpam-4700	14	3	corcino	corcino	PROPN
ejpam-4700	14	4	et	et	PROPN
ejpam-4700	14	5	al	al	PROPN
ejpam-4700	14	6	.	.	PUNCT
ejpam-4700	14	7	/	/	SYM
ejpam-4700	14	8	eur	eur	PROPN
ejpam-4700	14	9	.	.	PUNCT
ejpam-4700	15	1	j.	j.	PROPN
ejpam-4700	15	2	pure	pure	PROPN
ejpam-4700	15	3	appl	appl	PROPN
ejpam-4700	15	4	.	.	PROPN
ejpam-4700	15	5	math	math	PROPN
ejpam-4700	15	6	,	,	PUNCT
ejpam-4700	15	7	16	16	NUM
ejpam-4700	15	8	(	(	PUNCT
ejpam-4700	15	9	2	2	NUM
ejpam-4700	15	10	)	)	PUNCT
ejpam-4700	15	11	(	(	PUNCT
ejpam-4700	15	12	2023	2023	NUM
ejpam-4700	15	13	)	)	PUNCT
ejpam-4700	15	14	,	,	PUNCT
ejpam-4700	15	15	1005	1005	NUM
ejpam-4700	15	16	-	-	SYM
ejpam-4700	15	17	1023	1023	NUM
ejpam-4700	15	18	1006	1006	NUM
ejpam-4700	15	19	the	the	DET
ejpam-4700	15	20	principles	principle	NOUN
ejpam-4700	15	21	of	of	ADP
ejpam-4700	15	22	apostol	apostol	NOUN
ejpam-4700	15	23	,	,	PUNCT
ejpam-4700	15	24	frobenius	frobenius	NOUN
ejpam-4700	15	25	,	,	PUNCT
ejpam-4700	15	26	genocchi	genocchi	NOUN
ejpam-4700	15	27	,	,	PUNCT
ejpam-4700	15	28	and	and	CCONJ
ejpam-4700	15	29	euler	euler	NOUN
ejpam-4700	15	30	polynomials	polynomial	NOUN
ejpam-4700	15	31	were	be	AUX
ejpam-4700	15	32	combined	combine	VERB
ejpam-4700	15	33	to	to	PART
ejpam-4700	15	34	create	create	VERB
ejpam-4700	15	35	the	the	DET
ejpam-4700	15	36	apostol	apostol	NOUN
ejpam-4700	15	37	-	-	PUNCT
ejpam-4700	15	38	genocchi	genocchi	PROPN
ejpam-4700	15	39	polynomials	polynomial	NOUN
ejpam-4700	15	40	,	,	PUNCT
ejpam-4700	15	41	frobenius	frobenius	NOUN
ejpam-4700	15	42	-	-	PUNCT
ejpam-4700	15	43	euler	euler	NOUN
ejpam-4700	15	44	polynomials	polynomial	NOUN
ejpam-4700	15	45	,	,	PUNCT
ejpam-4700	15	46	frobeniusgenocchi	frobeniusgenocchi	ADJ
ejpam-4700	15	47	polynomials	polynomial	NOUN
ejpam-4700	15	48	,	,	PUNCT
ejpam-4700	15	49	and	and	CCONJ
ejpam-4700	15	50	apostol	apostol	NOUN
ejpam-4700	15	51	-	-	PUNCT
ejpam-4700	15	52	frobenius	frobenius	NOUN
ejpam-4700	15	53	-	-	PUNCT
ejpam-4700	15	54	type	type	NOUN
ejpam-4700	15	55	poly	poly	ADJ
ejpam-4700	15	56	-	-	PUNCT
ejpam-4700	15	57	genocchi	genocchi	NOUN
ejpam-4700	15	58	polynomials	polynomial	NOUN
ejpam-4700	15	59	in	in	ADP
ejpam-4700	15	60	the	the	DET
ejpam-4700	15	61	paper	paper	NOUN
ejpam-4700	15	62	of	of	ADP
ejpam-4700	15	63	ryoo	ryoo	NOUN
ejpam-4700	15	64	et.al.[10–12	et.al.[10–12	NOUN
ejpam-4700	15	65	]	]	PUNCT
ejpam-4700	15	66	.	.	PUNCT
ejpam-4700	16	1	another	another	DET
ejpam-4700	16	2	intriguing	intriguing	ADJ
ejpam-4700	16	3	combination	combination	NOUN
ejpam-4700	16	4	of	of	ADP
ejpam-4700	16	5	special	special	ADJ
ejpam-4700	16	6	polynomials	polynomial	NOUN
ejpam-4700	16	7	may	may	AUX
ejpam-4700	16	8	be	be	AUX
ejpam-4700	16	9	created	create	VERB
ejpam-4700	16	10	by	by	ADP
ejpam-4700	16	11	combining	combine	VERB
ejpam-4700	16	12	the	the	DET
ejpam-4700	16	13	principles	principle	NOUN
ejpam-4700	16	14	of	of	ADP
ejpam-4700	16	15	apostol	apostol	NOUN
ejpam-4700	16	16	and	and	CCONJ
ejpam-4700	16	17	frobenius	frobenius	ADJ
ejpam-4700	16	18	polynomials	polynomial	NOUN
ejpam-4700	16	19	with	with	ADP
ejpam-4700	16	20	tangent	tangent	NOUN
ejpam-4700	16	21	,	,	PUNCT
ejpam-4700	16	22	bernoulli	bernoulli	PROPN
ejpam-4700	16	23	,	,	PUNCT
ejpam-4700	16	24	and	and	CCONJ
ejpam-4700	16	25	genocchi	genocchi	PROPN
ejpam-4700	16	26	polynomials	polynomial	NOUN
ejpam-4700	16	27	,	,	PUNCT
ejpam-4700	16	28	which	which	PRON
ejpam-4700	16	29	will	will	AUX
ejpam-4700	16	30	be	be	AUX
ejpam-4700	16	31	the	the	DET
ejpam-4700	16	32	topic	topic	NOUN
ejpam-4700	16	33	direction	direction	NOUN
ejpam-4700	16	34	of	of	ADP
ejpam-4700	16	35	this	this	DET
ejpam-4700	16	36	paper	paper	NOUN
ejpam-4700	16	37	.	.	PUNCT
ejpam-4700	17	1	this	this	PRON
ejpam-4700	17	2	will	will	AUX
ejpam-4700	17	3	be	be	AUX
ejpam-4700	17	4	carried	carry	VERB
ejpam-4700	17	5	out	out	ADP
ejpam-4700	17	6	using	use	VERB
ejpam-4700	17	7	the	the	DET
ejpam-4700	17	8	fourier	fourier	NOUN
ejpam-4700	17	9	series	series	NOUN
ejpam-4700	17	10	expansion	expansion	NOUN
ejpam-4700	17	11	method[7	method[7	PROPN
ejpam-4700	17	12	]	]	PUNCT
ejpam-4700	17	13	.	.	PUNCT
ejpam-4700	18	1	currently	currently	ADV
ejpam-4700	18	2	,	,	PUNCT
ejpam-4700	18	3	there	there	PRON
ejpam-4700	18	4	was	be	VERB
ejpam-4700	18	5	no	no	DET
ejpam-4700	18	6	literature	literature	NOUN
ejpam-4700	18	7	or	or	CCONJ
ejpam-4700	18	8	related	related	ADJ
ejpam-4700	18	9	works	work	NOUN
ejpam-4700	18	10	that	that	PRON
ejpam-4700	18	11	mentioned	mention	VERB
ejpam-4700	18	12	the	the	DET
ejpam-4700	18	13	fourier	fourier	NOUN
ejpam-4700	18	14	series	series	NOUN
ejpam-4700	18	15	expansion	expansion	NOUN
ejpam-4700	18	16	of	of	ADP
ejpam-4700	18	17	apostolfrobenius	apostolfrobenius	NOUN
ejpam-4700	18	18	:	:	PUNCT
ejpam-4700	18	19	tangent	tangent	NOUN
ejpam-4700	18	20	,	,	PUNCT
ejpam-4700	18	21	bernoulli	bernoulli	PROPN
ejpam-4700	18	22	,	,	PUNCT
ejpam-4700	18	23	and	and	CCONJ
ejpam-4700	18	24	genocchi	genocchi	PROPN
ejpam-4700	18	25	polynomials	polynomial	VERB
ejpam-4700	18	26	that	that	PRON
ejpam-4700	18	27	were	be	AUX
ejpam-4700	18	28	accessible	accessible	ADJ
ejpam-4700	18	29	at	at	ADP
ejpam-4700	18	30	the	the	DET
ejpam-4700	18	31	time	time	NOUN
ejpam-4700	18	32	of	of	ADP
ejpam-4700	18	33	the	the	DET
ejpam-4700	18	34	research	research	NOUN
ejpam-4700	18	35	.	.	PUNCT
ejpam-4700	19	1	fourier	fourier	PROPN
ejpam-4700	19	2	series	series	PROPN
ejpam-4700	19	3	is	be	AUX
ejpam-4700	19	4	widely	widely	ADV
ejpam-4700	19	5	known	know	VERB
ejpam-4700	19	6	as	as	ADP
ejpam-4700	19	7	an	an	DET
ejpam-4700	19	8	expansion	expansion	NOUN
ejpam-4700	19	9	of	of	ADP
ejpam-4700	19	10	a	a	DET
ejpam-4700	19	11	periodic	periodic	ADJ
ejpam-4700	19	12	function	function	NOUN
ejpam-4700	19	13	f(x	f(x	PROPN
ejpam-4700	19	14	)	)	PUNCT
ejpam-4700	19	15	in	in	ADP
ejpam-4700	19	16	terms	term	NOUN
ejpam-4700	19	17	of	of	ADP
ejpam-4700	19	18	an	an	DET
ejpam-4700	19	19	infinite	infinite	ADJ
ejpam-4700	19	20	sum	sum	NOUN
ejpam-4700	19	21	of	of	ADP
ejpam-4700	19	22	sine	sine	NOUN
ejpam-4700	19	23	and	and	CCONJ
ejpam-4700	19	24	cosine	cosine	NOUN
ejpam-4700	19	25	functions	function	NOUN
ejpam-4700	19	26	.	.	PUNCT
ejpam-4700	20	1	it	it	PRON
ejpam-4700	20	2	makes	make	VERB
ejpam-4700	20	3	use	use	NOUN
ejpam-4700	20	4	of	of	ADP
ejpam-4700	20	5	the	the	DET
ejpam-4700	20	6	orthogonality	orthogonality	NOUN
ejpam-4700	20	7	relationships	relationship	NOUN
ejpam-4700	20	8	of	of	ADP
ejpam-4700	20	9	the	the	DET
ejpam-4700	20	10	sine	sine	NOUN
ejpam-4700	20	11	and	and	CCONJ
ejpam-4700	20	12	cosine	cosine	NOUN
ejpam-4700	20	13	functions	function	NOUN
ejpam-4700	20	14	.	.	PUNCT
ejpam-4700	21	1	fourier	fourier	PROPN
ejpam-4700	21	2	series	series	PROPN
ejpam-4700	21	3	is	be	AUX
ejpam-4700	21	4	expressed	express	VERB
ejpam-4700	21	5	as[1	as[1	NOUN
ejpam-4700	21	6	]	]	PUNCT
ejpam-4700	21	7	s(x	s(x	NOUN
ejpam-4700	21	8	)	)	PUNCT
ejpam-4700	21	9	=	=	SYM
ejpam-4700	21	10	a0	a0	NOUN
ejpam-4700	21	11	2	2	NUM
ejpam-4700	22	1	+	+	CCONJ
ejpam-4700	22	2	∞∑	∞∑	NUM
ejpam-4700	22	3	n=1	n=1	PROPN
ejpam-4700	22	4	[	[	PUNCT
ejpam-4700	22	5	an	an	DET
ejpam-4700	22	6	cos	cos	PROPN
ejpam-4700	22	7	(	(	PUNCT
ejpam-4700	22	8	2π	2π	PROPN
ejpam-4700	22	9	t	t	PROPN
ejpam-4700	22	10	nx	nx	PROPN
ejpam-4700	22	11	)	)	PUNCT
ejpam-4700	23	1	+	+	CCONJ
ejpam-4700	23	2	bn	bn	ADP
ejpam-4700	23	3	sin	sin	NOUN
ejpam-4700	23	4	(	(	PUNCT
ejpam-4700	23	5	2π	2π	NOUN
ejpam-4700	23	6	t	t	PROPN
ejpam-4700	23	7	nx	nx	PROPN
ejpam-4700	23	8	)	)	PUNCT
ejpam-4700	23	9	]	]	PUNCT
ejpam-4700	23	10	(	(	PUNCT
ejpam-4700	23	11	1	1	X
ejpam-4700	23	12	)	)	PUNCT
ejpam-4700	23	13	where	where	SCONJ
ejpam-4700	23	14	t	t	PROPN
ejpam-4700	23	15	is	be	AUX
ejpam-4700	23	16	the	the	DET
ejpam-4700	23	17	function	function	NOUN
ejpam-4700	23	18	’s	’s	PART
ejpam-4700	23	19	period	period	NOUN
ejpam-4700	23	20	.	.	PUNCT
ejpam-4700	24	1	the	the	DET
ejpam-4700	24	2	above	above	ADJ
ejpam-4700	24	3	expression	expression	NOUN
ejpam-4700	24	4	can	can	AUX
ejpam-4700	24	5	also	also	ADV
ejpam-4700	24	6	be	be	AUX
ejpam-4700	24	7	cast	cast	VERB
ejpam-4700	24	8	into	into	ADP
ejpam-4700	24	9	its	its	PRON
ejpam-4700	24	10	exponential	exponential	ADJ
ejpam-4700	24	11	form	form	NOUN
ejpam-4700	24	12	as	as	SCONJ
ejpam-4700	24	13	follows	follow	VERB
ejpam-4700	24	14	:	:	PUNCT
ejpam-4700	24	15	s(x	s(x	X
ejpam-4700	24	16	)	)	PUNCT
ejpam-4700	24	17	=	=	PUNCT
ejpam-4700	25	1	∞∑	∞∑	NUM
ejpam-4700	25	2	n=−∞	n=−∞	NUM
ejpam-4700	25	3	cn	cn	PROPN
ejpam-4700	25	4	·	·	PUNCT
ejpam-4700	25	5	ei2πnx	ei2πnx	PROPN
ejpam-4700	25	6	/	/	SYM
ejpam-4700	25	7	t	t	PROPN
ejpam-4700	25	8	(	(	PUNCT
ejpam-4700	25	9	2	2	NUM
ejpam-4700	25	10	)	)	PUNCT
ejpam-4700	25	11	where	where	SCONJ
ejpam-4700	25	12	the	the	DET
ejpam-4700	25	13	coefficients	coefficient	NOUN
ejpam-4700	25	14	cn	cn	PROPN
ejpam-4700	25	15	are	be	AUX
ejpam-4700	25	16	computed	compute	VERB
ejpam-4700	25	17	as	as	ADP
ejpam-4700	25	18	cn	cn	PROPN
ejpam-4700	25	19	=	=	SYM
ejpam-4700	25	20	1	1	NUM
ejpam-4700	25	21	t	t	NOUN
ejpam-4700	25	22	∫	∫	PROPN
ejpam-4700	25	23	t	t	PROPN
ejpam-4700	25	24	0	0	PUNCT
ejpam-4700	26	1	e−i2πnx	e−i2πnx	PROPN
ejpam-4700	26	2	/	/	SYM
ejpam-4700	26	3	t	t	PROPN
ejpam-4700	26	4	·	·	PUNCT
ejpam-4700	26	5	s(t)dt	s(t)dt	PROPN
ejpam-4700	26	6	(	(	PUNCT
ejpam-4700	26	7	3	3	NUM
ejpam-4700	26	8	)	)	PUNCT
ejpam-4700	26	9	the	the	DET
ejpam-4700	26	10	fourier	fourier	ADJ
ejpam-4700	26	11	expansion	expansion	NOUN
ejpam-4700	26	12	of	of	ADP
ejpam-4700	26	13	several	several	ADJ
ejpam-4700	26	14	well	well	ADV
ejpam-4700	26	15	-	-	PUNCT
ejpam-4700	26	16	known	know	VERB
ejpam-4700	26	17	polynomials	polynomial	NOUN
ejpam-4700	26	18	has	have	AUX
ejpam-4700	26	19	recently	recently	ADV
ejpam-4700	26	20	piqued	pique	VERB
ejpam-4700	26	21	the	the	DET
ejpam-4700	26	22	curiosity	curiosity	NOUN
ejpam-4700	26	23	of	of	ADP
ejpam-4700	26	24	mathematicians	mathematician	NOUN
ejpam-4700	26	25	.	.	PUNCT
ejpam-4700	27	1	the	the	DET
ejpam-4700	27	2	fourier	fourier	NOUN
ejpam-4700	27	3	expansions	expansion	NOUN
ejpam-4700	27	4	for	for	ADP
ejpam-4700	27	5	the	the	DET
ejpam-4700	27	6	apostol	apostol	NOUN
ejpam-4700	27	7	-	-	PUNCT
ejpam-4700	27	8	bernoulli	bernoulli	NOUN
ejpam-4700	27	9	and	and	CCONJ
ejpam-4700	27	10	apostol	apostol	NOUN
ejpam-4700	27	11	-	-	PUNCT
ejpam-4700	27	12	euler	euler	NOUN
ejpam-4700	27	13	polynomials	polynomial	NOUN
ejpam-4700	27	14	are	be	AUX
ejpam-4700	27	15	given	give	VERB
ejpam-4700	27	16	by	by	ADP
ejpam-4700	27	17	lou	lou	PROPN
ejpam-4700	27	18	(	(	PUNCT
ejpam-4700	27	19	2009	2009	NUM
ejpam-4700	27	20	)	)	PUNCT
ejpam-4700	27	21	.	.	PUNCT
ejpam-4700	28	1	using	use	VERB
ejpam-4700	28	2	the	the	DET
ejpam-4700	28	3	lipschitz	lipschitz	ADJ
ejpam-4700	28	4	summation	summation	NOUN
ejpam-4700	28	5	formula	formula	NOUN
ejpam-4700	28	6	,	,	PUNCT
ejpam-4700	28	7	lou	lou	PROPN
ejpam-4700	28	8	derives	derive	VERB
ejpam-4700	28	9	the	the	DET
ejpam-4700	28	10	fourier	fourier	NOUN
ejpam-4700	28	11	expansions	expansion	NOUN
ejpam-4700	28	12	and	and	CCONJ
ejpam-4700	28	13	integral	integral	ADJ
ejpam-4700	28	14	representation	representation	NOUN
ejpam-4700	28	15	for	for	ADP
ejpam-4700	28	16	genocchi	genocchi	PROPN
ejpam-4700	28	17	polynomials	polynomial	VERB
ejpam-4700	28	18	the	the	DET
ejpam-4700	28	19	same	same	ADJ
ejpam-4700	28	20	year	year	NOUN
ejpam-4700	28	21	.	.	PUNCT
ejpam-4700	29	1	araci	araci	NOUN
ejpam-4700	29	2	-	-	PUNCT
ejpam-4700	29	3	acikgoz	acikgoz	PROPN
ejpam-4700	29	4	(	(	PUNCT
ejpam-4700	29	5	2018	2018	NUM
ejpam-4700	29	6	)	)	PUNCT
ejpam-4700	29	7	made	make	VERB
ejpam-4700	29	8	a	a	DET
ejpam-4700	29	9	significant	significant	ADJ
ejpam-4700	29	10	finding	finding	NOUN
ejpam-4700	29	11	about	about	ADP
ejpam-4700	29	12	the	the	DET
ejpam-4700	29	13	fourier	fourier	ADJ
ejpam-4700	29	14	expansion	expansion	NOUN
ejpam-4700	29	15	of	of	ADP
ejpam-4700	29	16	the	the	DET
ejpam-4700	29	17	apostol	apostol	NOUN
ejpam-4700	29	18	frobenius	frobenius	NOUN
ejpam-4700	29	19	-	-	PUNCT
ejpam-4700	29	20	euler	euler	NOUN
ejpam-4700	29	21	and	and	CCONJ
ejpam-4700	29	22	genocchi	genocchi	PROPN
ejpam-4700	29	23	polynomials	polynomial	NOUN
ejpam-4700	29	24	.	.	PUNCT
ejpam-4700	30	1	with	with	ADP
ejpam-4700	30	2	this	this	DET
ejpam-4700	30	3	motivation	motivation	NOUN
ejpam-4700	30	4	,	,	PUNCT
ejpam-4700	30	5	we	we	PRON
ejpam-4700	30	6	are	be	AUX
ejpam-4700	30	7	interested	interested	ADJ
ejpam-4700	30	8	in	in	ADP
ejpam-4700	30	9	determining	determine	VERB
ejpam-4700	30	10	the	the	DET
ejpam-4700	30	11	fourier	fourier	ADJ
ejpam-4700	30	12	series	series	NOUN
ejpam-4700	30	13	expansions	expansion	NOUN
ejpam-4700	30	14	of	of	ADP
ejpam-4700	30	15	higher	high	ADJ
ejpam-4700	30	16	order	order	NOUN
ejpam-4700	30	17	apostol	apostol	NOUN
ejpam-4700	30	18	-	-	PUNCT
ejpam-4700	30	19	frobeniustype	frobeniustype	NOUN
ejpam-4700	30	20	tangent	tangent	NOUN
ejpam-4700	30	21	and	and	CCONJ
ejpam-4700	30	22	genocchi	genocchi	PROPN
ejpam-4700	30	23	polynomials	polynomial	NOUN
ejpam-4700	30	24	using	use	VERB
ejpam-4700	30	25	the	the	DET
ejpam-4700	30	26	cauchy	cauchy	ADJ
ejpam-4700	30	27	residue	residue	NOUN
ejpam-4700	30	28	theorem	theorem	NOUN
ejpam-4700	30	29	and	and	CCONJ
ejpam-4700	30	30	a	a	DET
ejpam-4700	30	31	complex	complex	ADJ
ejpam-4700	30	32	integral	integral	ADJ
ejpam-4700	30	33	over	over	ADP
ejpam-4700	30	34	a	a	DET
ejpam-4700	30	35	contour[2	contour[2	NOUN
ejpam-4700	30	36	]	]	PUNCT
ejpam-4700	30	37	,	,	PUNCT
ejpam-4700	30	38	which	which	PRON
ejpam-4700	30	39	they	they	PRON
ejpam-4700	30	40	found	find	VERB
ejpam-4700	30	41	to	to	PART
ejpam-4700	30	42	be	be	AUX
ejpam-4700	30	43	particularly	particularly	ADV
ejpam-4700	30	44	useful	useful	ADJ
ejpam-4700	30	45	.	.	PUNCT
ejpam-4700	31	1	2	2	X
ejpam-4700	31	2	.	.	X
ejpam-4700	31	3	main	main	ADJ
ejpam-4700	31	4	results	result	NOUN
ejpam-4700	31	5	in	in	ADP
ejpam-4700	31	6	this	this	DET
ejpam-4700	31	7	section	section	NOUN
ejpam-4700	31	8	,	,	PUNCT
ejpam-4700	31	9	we	we	PRON
ejpam-4700	31	10	use	use	VERB
ejpam-4700	31	11	the	the	DET
ejpam-4700	31	12	cauchy	cauchy	ADJ
ejpam-4700	31	13	residue	residue	NOUN
ejpam-4700	31	14	theorem	theorem	NOUN
ejpam-4700	31	15	and	and	CCONJ
ejpam-4700	31	16	bayad	bayad	PROPN
ejpam-4700	31	17	’s	’s	PART
ejpam-4700	31	18	method[2	method[2	NOUN
ejpam-4700	31	19	]	]	PUNCT
ejpam-4700	31	20	in	in	ADP
ejpam-4700	31	21	evaluating	evaluate	VERB
ejpam-4700	31	22	the	the	DET
ejpam-4700	31	23	complex	complex	ADJ
ejpam-4700	31	24	integral	integral	ADJ
ejpam-4700	31	25	over	over	ADP
ejpam-4700	31	26	a	a	DET
ejpam-4700	31	27	circle	circle	NOUN
ejpam-4700	31	28	c	c	NOUN
ejpam-4700	31	29	to	to	PART
ejpam-4700	31	30	obtain	obtain	VERB
ejpam-4700	31	31	the	the	DET
ejpam-4700	31	32	fourier	fourier	NOUN
ejpam-4700	31	33	series	series	NOUN
ejpam-4700	31	34	expansion	expansion	NOUN
ejpam-4700	31	35	for	for	ADP
ejpam-4700	31	36	the	the	DET
ejpam-4700	31	37	frobenius	frobenius	ADJ
ejpam-4700	31	38	type	type	NOUN
ejpam-4700	31	39	of	of	ADP
ejpam-4700	31	40	apostol	apostol	NOUN
ejpam-4700	31	41	-	-	PUNCT
ejpam-4700	31	42	tangent	tangent	NOUN
ejpam-4700	31	43	and	and	CCONJ
ejpam-4700	31	44	apostol	apostol	NOUN
ejpam-4700	31	45	-	-	PUNCT
ejpam-4700	31	46	genocchi	genocchi	PROPN
ejpam-4700	31	47	polynomials	polynomial	NOUN
ejpam-4700	31	48	.	.	PUNCT
ejpam-4700	32	1	r.	r.	PROPN
ejpam-4700	32	2	b.	b.	PROPN
ejpam-4700	32	3	corcino	corcino	PROPN
ejpam-4700	32	4	et	et	PROPN
ejpam-4700	32	5	al	al	PROPN
ejpam-4700	32	6	.	.	PUNCT
ejpam-4700	32	7	/	/	SYM
ejpam-4700	32	8	eur	eur	PROPN
ejpam-4700	32	9	.	.	PUNCT
ejpam-4700	33	1	j.	j.	PROPN
ejpam-4700	33	2	pure	pure	PROPN
ejpam-4700	33	3	appl	appl	PROPN
ejpam-4700	33	4	.	.	PROPN
ejpam-4700	33	5	math	math	PROPN
ejpam-4700	33	6	,	,	PUNCT
ejpam-4700	33	7	16	16	NUM
ejpam-4700	33	8	(	(	PUNCT
ejpam-4700	33	9	2	2	NUM
ejpam-4700	33	10	)	)	PUNCT
ejpam-4700	33	11	(	(	PUNCT
ejpam-4700	33	12	2023	2023	NUM
ejpam-4700	33	13	)	)	PUNCT
ejpam-4700	33	14	,	,	PUNCT
ejpam-4700	33	15	1005	1005	NUM
ejpam-4700	33	16	-	-	SYM
ejpam-4700	33	17	1023	1023	NUM
ejpam-4700	33	18	1007	1007	NUM
ejpam-4700	33	19	2.1	2.1	NUM
ejpam-4700	33	20	.	.	PUNCT
ejpam-4700	34	1	fourier	fouri	ADJ
ejpam-4700	34	2	expansion	expansion	NOUN
ejpam-4700	34	3	and	and	CCONJ
ejpam-4700	34	4	integral	integral	ADJ
ejpam-4700	34	5	representation	representation	NOUN
ejpam-4700	34	6	of	of	ADP
ejpam-4700	34	7	apostol	apostol	NOUN
ejpam-4700	34	8	-	-	PUNCT
ejpam-4700	34	9	frobeniustangent	frobeniustangent	ADJ
ejpam-4700	34	10	polynomials	polynomial	NOUN
ejpam-4700	34	11	:	:	PUNCT
ejpam-4700	34	12	the	the	DET
ejpam-4700	34	13	tangent	tangent	NOUN
ejpam-4700	34	14	polynomials	polynomial	VERB
ejpam-4700	34	15	with	with	ADP
ejpam-4700	34	16	complex	complex	ADJ
ejpam-4700	34	17	argument	argument	NOUN
ejpam-4700	34	18	x	x	PRON
ejpam-4700	34	19	are	be	AUX
ejpam-4700	34	20	defined	define	VERB
ejpam-4700	34	21	as	as	ADP
ejpam-4700	34	22	coefficients	coefficient	NOUN
ejpam-4700	34	23	of	of	ADP
ejpam-4700	34	24	the	the	DET
ejpam-4700	34	25	following	follow	VERB
ejpam-4700	34	26	generating	generate	VERB
ejpam-4700	34	27	function[8	function[8	NOUN
ejpam-4700	34	28	]	]	X
ejpam-4700	34	29	∞∑	∞∑	PRON
ejpam-4700	34	30	n=0	n=0	NUM
ejpam-4700	34	31	tn(x	tn(x	NOUN
ejpam-4700	34	32	)	)	PUNCT
ejpam-4700	34	33	tn	tn	NOUN
ejpam-4700	34	34	n	n	NOUN
ejpam-4700	34	35	!	!	PUNCT
ejpam-4700	35	1	=	=	PUNCT
ejpam-4700	35	2	(	(	PUNCT
ejpam-4700	35	3	2	2	NUM
ejpam-4700	35	4	e2	e2	PROPN
ejpam-4700	35	5	t	t	NOUN
ejpam-4700	35	6	+	+	CCONJ
ejpam-4700	35	7	1	1	X
ejpam-4700	35	8	)	)	PUNCT
ejpam-4700	35	9	ext	ext	NOUN
ejpam-4700	35	10	(	(	PUNCT
ejpam-4700	35	11	4	4	NUM
ejpam-4700	35	12	)	)	PUNCT
ejpam-4700	35	13	where	where	SCONJ
ejpam-4700	35	14	tn(0	tn(0	ADP
ejpam-4700	35	15	)	)	PUNCT
ejpam-4700	35	16	=	=	SYM
ejpam-4700	35	17	tn	tn	PROPN
ejpam-4700	35	18	.	.	PUNCT
ejpam-4700	36	1	the	the	DET
ejpam-4700	36	2	apostol	apostol	NOUN
ejpam-4700	36	3	-	-	PUNCT
ejpam-4700	36	4	frobenius	frobenius	NOUN
ejpam-4700	36	5	-	-	PUNCT
ejpam-4700	36	6	type	type	NOUN
ejpam-4700	36	7	tangent	tangent	NOUN
ejpam-4700	36	8	polynomials	polynomial	NOUN
ejpam-4700	36	9	,	,	PUNCT
ejpam-4700	36	10	which	which	PRON
ejpam-4700	36	11	are	be	AUX
ejpam-4700	36	12	another	another	DET
ejpam-4700	36	13	variation	variation	NOUN
ejpam-4700	36	14	of	of	ADP
ejpam-4700	36	15	the	the	DET
ejpam-4700	36	16	tangent	tangent	NOUN
ejpam-4700	36	17	polynomials	polynomial	NOUN
ejpam-4700	36	18	,	,	PUNCT
ejpam-4700	36	19	are	be	AUX
ejpam-4700	36	20	defined	define	VERB
ejpam-4700	36	21	as	as	SCONJ
ejpam-4700	36	22	follows	follow	VERB
ejpam-4700	36	23	:	:	PUNCT
ejpam-4700	36	24	∞∑	∞∑	NUM
ejpam-4700	36	25	n=0	n=0	NUM
ejpam-4700	36	26	tn(x;u	tn(x;u	NOUN
ejpam-4700	36	27	,	,	PUNCT
ejpam-4700	36	28	λ	λ	NOUN
ejpam-4700	36	29	)	)	PUNCT
ejpam-4700	36	30	tn	tn	PROPN
ejpam-4700	36	31	n	n	NOUN
ejpam-4700	36	32	!	!	PUNCT
ejpam-4700	37	1	=	=	SYM
ejpam-4700	38	1	1−	1−	NUM
ejpam-4700	38	2	u	u	NOUN
ejpam-4700	38	3	λe2	λe2	PROPN
ejpam-4700	38	4	t	t	PROPN
ejpam-4700	38	5	−	−	NOUN
ejpam-4700	38	6	u	u	NOUN
ejpam-4700	38	7	ext	ext	NOUN
ejpam-4700	38	8	(	(	PUNCT
ejpam-4700	38	9	5	5	NUM
ejpam-4700	38	10	)	)	PUNCT
ejpam-4700	38	11	where	where	SCONJ
ejpam-4700	38	12	u	u	NOUN
ejpam-4700	38	13	,	,	PUNCT
ejpam-4700	38	14	λ	λ	PROPN
ejpam-4700	38	15	∈	∈	PROPN
ejpam-4700	38	16	c	c	NOUN
ejpam-4700	38	17	with	with	ADP
ejpam-4700	38	18	u	u	NOUN
ejpam-4700	38	19	̸=	̸=	PROPN
ejpam-4700	38	20	1	1	NUM
ejpam-4700	38	21	,	,	PUNCT
ejpam-4700	38	22	λ	λ	PROPN
ejpam-4700	38	23	̸=	̸=	PROPN
ejpam-4700	38	24	1	1	NUM
ejpam-4700	38	25	and	and	CCONJ
ejpam-4700	38	26	u	u	PROPN
ejpam-4700	38	27	̸=	̸=	PROPN
ejpam-4700	38	28	λ	λ	PROPN
ejpam-4700	38	29	.	.	PUNCT
ejpam-4700	38	30	by	by	ADP
ejpam-4700	38	31	cauchy	cauchy	ADJ
ejpam-4700	38	32	integral	integral	ADJ
ejpam-4700	38	33	formula	formula	NOUN
ejpam-4700	38	34	,	,	PUNCT
ejpam-4700	38	35	we	we	PRON
ejpam-4700	38	36	have	have	VERB
ejpam-4700	38	37	tn(x;u	tn(x;u	NOUN
ejpam-4700	38	38	,	,	PUNCT
ejpam-4700	38	39	λ	λ	NOUN
ejpam-4700	38	40	)	)	PUNCT
ejpam-4700	38	41	n	n	CCONJ
ejpam-4700	38	42	!	!	PUNCT
ejpam-4700	39	1	=	=	SYM
ejpam-4700	39	2	1	1	NUM
ejpam-4700	39	3	2πi	2πi	ADJ
ejpam-4700	39	4	∫	∫	PROPN
ejpam-4700	39	5	c	c	NOUN
ejpam-4700	39	6	1−	1−	NUM
ejpam-4700	39	7	u	u	NOUN
ejpam-4700	39	8	λe2	λe2	PROPN
ejpam-4700	39	9	t	t	PROPN
ejpam-4700	39	10	−	−	NOUN
ejpam-4700	40	1	u	u	NOUN
ejpam-4700	40	2	ext	ext	NOUN
ejpam-4700	40	3	dt	dt	X
ejpam-4700	40	4	tn+1	tn+1	PROPN
ejpam-4700	40	5	(	(	PUNCT
ejpam-4700	40	6	6	6	NUM
ejpam-4700	40	7	)	)	PUNCT
ejpam-4700	40	8	consider	consider	VERB
ejpam-4700	40	9	now	now	ADV
ejpam-4700	40	10	the	the	DET
ejpam-4700	40	11	function	function	NOUN
ejpam-4700	40	12	inside	inside	ADP
ejpam-4700	40	13	the	the	DET
ejpam-4700	40	14	integral	integral	ADJ
ejpam-4700	40	15	f(t	f(t	NOUN
ejpam-4700	40	16	)	)	PUNCT
ejpam-4700	40	17	=	=	SYM
ejpam-4700	41	1	1−	1−	NUM
ejpam-4700	41	2	u	u	NOUN
ejpam-4700	41	3	λe2	λe2	PROPN
ejpam-4700	41	4	t	t	PROPN
ejpam-4700	41	5	−	−	NOUN
ejpam-4700	42	1	u	u	PROPN
ejpam-4700	42	2	ext	ext	NOUN
ejpam-4700	42	3	tn+1	tn+1	NOUN
ejpam-4700	42	4	(	(	PUNCT
ejpam-4700	42	5	7	7	NUM
ejpam-4700	42	6	)	)	PUNCT
ejpam-4700	42	7	which	which	PRON
ejpam-4700	42	8	has	have	VERB
ejpam-4700	42	9	a	a	DET
ejpam-4700	42	10	pole	pole	NOUN
ejpam-4700	42	11	at	at	ADP
ejpam-4700	42	12	t	t	PROPN
ejpam-4700	42	13	=	=	SYM
ejpam-4700	42	14	0	0	NUM
ejpam-4700	42	15	of	of	ADP
ejpam-4700	42	16	order	order	NOUN
ejpam-4700	42	17	n	n	X
ejpam-4700	42	18	+	+	NOUN
ejpam-4700	42	19	1	1	X
ejpam-4700	42	20	.	.	PUNCT
ejpam-4700	43	1	we	we	PRON
ejpam-4700	43	2	then	then	ADV
ejpam-4700	43	3	find	find	VERB
ejpam-4700	43	4	the	the	DET
ejpam-4700	43	5	other	other	ADJ
ejpam-4700	43	6	poles	pole	NOUN
ejpam-4700	43	7	of	of	ADP
ejpam-4700	43	8	the	the	DET
ejpam-4700	43	9	function	function	NOUN
ejpam-4700	43	10	fn(t	fn(t	PUNCT
ejpam-4700	43	11	)	)	PUNCT
ejpam-4700	43	12	as	as	SCONJ
ejpam-4700	43	13	follows	follow	VERB
ejpam-4700	43	14	:	:	PUNCT
ejpam-4700	44	1	λe2	λe2	PROPN
ejpam-4700	44	2	t	t	PROPN
ejpam-4700	44	3	−	−	NOUN
ejpam-4700	44	4	u	u	NOUN
ejpam-4700	44	5	=	=	NOUN
ejpam-4700	44	6	0	0	NUM
ejpam-4700	44	7	λe2	λe2	PROPN
ejpam-4700	44	8	t	t	NOUN
ejpam-4700	44	9	=	=	SYM
ejpam-4700	44	10	u	u	NOUN
ejpam-4700	44	11	λ	λ	PROPN
ejpam-4700	44	12	2	2	NUM
ejpam-4700	44	13	t	t	NOUN
ejpam-4700	44	14	=	=	PUNCT
ejpam-4700	44	15	log	log	VERB
ejpam-4700	44	16	u	u	NOUN
ejpam-4700	44	17	λ	λ	PROPN
ejpam-4700	44	18	+	+	PROPN
ejpam-4700	44	19	2kπi	2kπi	NUM
ejpam-4700	44	20	tk	tk	NOUN
ejpam-4700	44	21	:	:	PUNCT
ejpam-4700	44	22	=	=	SYM
ejpam-4700	44	23	t	t	PROPN
ejpam-4700	44	24	=	=	PUNCT
ejpam-4700	44	25	log	log	NOUN
ejpam-4700	44	26	(	(	PUNCT
ejpam-4700	44	27	u	u	NOUN
ejpam-4700	44	28	λ	λ	PROPN
ejpam-4700	44	29	)	)	PUNCT
ejpam-4700	44	30	1/2	1/2	NUM
ejpam-4700	45	1	+	+	NUM
ejpam-4700	45	2	kπi	kπi	NOUN
ejpam-4700	45	3	,	,	PUNCT
ejpam-4700	45	4	for	for	ADP
ejpam-4700	45	5	k	k	PROPN
ejpam-4700	45	6	∈	∈	PROPN
ejpam-4700	45	7	z	z	X
ejpam-4700	45	8	by	by	ADP
ejpam-4700	45	9	cauchy	cauchy	ADJ
ejpam-4700	45	10	residue	residue	NOUN
ejpam-4700	45	11	theorem	theorem	NOUN
ejpam-4700	45	12	,	,	PUNCT
ejpam-4700	45	13	we	we	PRON
ejpam-4700	45	14	have	have	VERB
ejpam-4700	45	15	1	1	NUM
ejpam-4700	45	16	2πi	2πi	ADJ
ejpam-4700	45	17	∫	∫	PROPN
ejpam-4700	45	18	cn	cn	PROPN
ejpam-4700	45	19	fn(t)dt	fn(t)dt	PROPN
ejpam-4700	45	20	=	=	PUNCT
ejpam-4700	45	21	res(f(t	res(f(t	NOUN
ejpam-4700	45	22	)	)	PUNCT
ejpam-4700	45	23	,	,	PUNCT
ejpam-4700	45	24	t	t	PROPN
ejpam-4700	45	25	=	=	SYM
ejpam-4700	45	26	0	0	NUM
ejpam-4700	45	27	)	)	PUNCT
ejpam-4700	45	28	+	+	CCONJ
ejpam-4700	45	29	∑	∑	ADV
ejpam-4700	45	30	k∈z	k∈z	PROPN
ejpam-4700	45	31	(	(	PUNCT
ejpam-4700	45	32	f(t	f(t	PROPN
ejpam-4700	45	33	)	)	PUNCT
ejpam-4700	45	34	,	,	PUNCT
ejpam-4700	45	35	t	t	PROPN
ejpam-4700	45	36	=	=	SYM
ejpam-4700	45	37	tk	tk	PROPN
ejpam-4700	45	38	)	)	PUNCT
ejpam-4700	45	39	(	(	PUNCT
ejpam-4700	45	40	8)	8)	NUM
ejpam-4700	45	41	in	in	ADP
ejpam-4700	45	42	eq	eq	ADP
ejpam-4700	45	43	.	.	PUNCT
ejpam-4700	46	1	(	(	PUNCT
ejpam-4700	46	2	8)	8)	NUM
ejpam-4700	46	3	,	,	PUNCT
ejpam-4700	46	4	we	we	PRON
ejpam-4700	46	5	integrate	integrate	VERB
ejpam-4700	46	6	fn(t	fn(t	NOUN
ejpam-4700	46	7	)	)	PUNCT
ejpam-4700	46	8	around	around	ADP
ejpam-4700	46	9	the	the	DET
ejpam-4700	46	10	circle	circle	NOUN
ejpam-4700	46	11	with	with	ADP
ejpam-4700	46	12	radius	radius	NOUN
ejpam-4700	46	13	(	(	PUNCT
ejpam-4700	46	14	n	n	X
ejpam-4700	46	15	+	+	X
ejpam-4700	46	16	ϵ)π	ϵ)π	X
ejpam-4700	46	17	where	where	SCONJ
ejpam-4700	46	18	ϵ	ϵ	PROPN
ejpam-4700	46	19	∈	∈	PROPN
ejpam-4700	46	20	r.	r.	PROPN
ejpam-4700	46	21	that	that	PRON
ejpam-4700	46	22	is	be	AUX
ejpam-4700	46	23	,	,	PUNCT
ejpam-4700	46	24	ϵπi	ϵπi	PROPN
ejpam-4700	46	25	±	±	NUM
ejpam-4700	46	26	log	log	NOUN
ejpam-4700	46	27	(	(	PUNCT
ejpam-4700	46	28	u	u	NOUN
ejpam-4700	46	29	λ	λ	PROPN
ejpam-4700	46	30	)	)	PUNCT
ejpam-4700	46	31	1/2	1/2	NUM
ejpam-4700	46	32	̸=	̸=	PROPN
ejpam-4700	46	33	0	0	NUM
ejpam-4700	46	34	(	(	PUNCT
ejpam-4700	46	35	mod	mod	PROPN
ejpam-4700	46	36	2πi	2πi	NOUN
ejpam-4700	46	37	)	)	PUNCT
ejpam-4700	46	38	.	.	PUNCT
ejpam-4700	47	1	this	this	DET
ejpam-4700	47	2	radius	radius	NOUN
ejpam-4700	47	3	guarantees	guarantee	VERB
ejpam-4700	47	4	that	that	SCONJ
ejpam-4700	47	5	the	the	DET
ejpam-4700	47	6	circle	circle	NOUN
ejpam-4700	47	7	cn	cn	PROPN
ejpam-4700	47	8	does	do	AUX
ejpam-4700	47	9	not	not	PART
ejpam-4700	47	10	pass	pass	VERB
ejpam-4700	47	11	through	through	ADP
ejpam-4700	47	12	any	any	PRON
ejpam-4700	47	13	of	of	ADP
ejpam-4700	47	14	the	the	DET
ejpam-4700	47	15	poles	pole	NOUN
ejpam-4700	47	16	tk	tk	PROPN
ejpam-4700	47	17	.	.	PUNCT
ejpam-4700	48	1	the	the	DET
ejpam-4700	48	2	following	follow	VERB
ejpam-4700	48	3	lemma	lemma	PROPN
ejpam-4700	48	4	contains	contain	VERB
ejpam-4700	48	5	the	the	DET
ejpam-4700	48	6	limit	limit	NOUN
ejpam-4700	48	7	of	of	ADP
ejpam-4700	48	8	the	the	DET
ejpam-4700	48	9	integral	integral	NOUN
ejpam-4700	48	10	in	in	ADP
ejpam-4700	48	11	eq	eq	ADP
ejpam-4700	48	12	.	.	PUNCT
ejpam-4700	49	1	(	(	PUNCT
ejpam-4700	49	2	8)	8)	NUM
ejpam-4700	49	3	as	as	ADP
ejpam-4700	49	4	n	n	NUM
ejpam-4700	49	5	→	→	SYM
ejpam-4700	49	6	∞	∞	PROPN
ejpam-4700	49	7	r.	r.	PROPN
ejpam-4700	49	8	b.	b.	PROPN
ejpam-4700	49	9	corcino	corcino	PROPN
ejpam-4700	49	10	et	et	PROPN
ejpam-4700	49	11	al	al	PROPN
ejpam-4700	49	12	.	.	PUNCT
ejpam-4700	49	13	/	/	SYM
ejpam-4700	49	14	eur	eur	PROPN
ejpam-4700	49	15	.	.	PUNCT
ejpam-4700	50	1	j.	j.	PROPN
ejpam-4700	50	2	pure	pure	PROPN
ejpam-4700	50	3	appl	appl	PROPN
ejpam-4700	50	4	.	.	PROPN
ejpam-4700	50	5	math	math	PROPN
ejpam-4700	50	6	,	,	PUNCT
ejpam-4700	50	7	16	16	NUM
ejpam-4700	50	8	(	(	PUNCT
ejpam-4700	50	9	2	2	NUM
ejpam-4700	50	10	)	)	PUNCT
ejpam-4700	50	11	(	(	PUNCT
ejpam-4700	50	12	2023	2023	NUM
ejpam-4700	50	13	)	)	PUNCT
ejpam-4700	50	14	,	,	PUNCT
ejpam-4700	50	15	1005	1005	NUM
ejpam-4700	50	16	-	-	SYM
ejpam-4700	50	17	1023	1023	NUM
ejpam-4700	50	18	1008	1008	NUM
ejpam-4700	50	19	lemma	lemma	PROPN
ejpam-4700	50	20	1	1	X
ejpam-4700	50	21	.	.	PUNCT
ejpam-4700	51	1	let	let	VERB
ejpam-4700	51	2	u	u	NOUN
ejpam-4700	51	3	,	,	PUNCT
ejpam-4700	51	4	λ	λ	PROPN
ejpam-4700	51	5	∈	∈	PROPN
ejpam-4700	51	6	c{0	c{0	NOUN
ejpam-4700	51	7	,	,	PUNCT
ejpam-4700	51	8	1	1	NUM
ejpam-4700	51	9	}	}	PUNCT
ejpam-4700	51	10	with	with	ADP
ejpam-4700	51	11	|λ|	|λ|	NOUN
ejpam-4700	51	12	=	=	PUNCT
ejpam-4700	51	13	̸	̸	NUM
ejpam-4700	51	14	|u|	|u|	PROPN
ejpam-4700	51	15	.	.	PUNCT
ejpam-4700	52	1	for	for	ADP
ejpam-4700	52	2	0	0	NUM
ejpam-4700	52	3	<	<	X
ejpam-4700	52	4	x	x	SYM
ejpam-4700	52	5	≤	≤	ADV
ejpam-4700	52	6	1	1	NUM
ejpam-4700	52	7	lim	lim	PROPN
ejpam-4700	52	8	n→∞	n→∞	NUM
ejpam-4700	52	9	∫	∫	PROPN
ejpam-4700	52	10	cn	cn	PROPN
ejpam-4700	52	11	fn(t)dt	fn(t)dt	PROPN
ejpam-4700	52	12	=	=	SYM
ejpam-4700	52	13	∫	∫	PROPN
ejpam-4700	52	14	cn	cn	PROPN
ejpam-4700	52	15	1−	1−	NUM
ejpam-4700	52	16	u	u	PROPN
ejpam-4700	52	17	λe2	λe2	PROPN
ejpam-4700	52	18	t	t	PROPN
ejpam-4700	52	19	−	−	NOUN
ejpam-4700	52	20	u	u	NOUN
ejpam-4700	52	21	ext	ext	NOUN
ejpam-4700	52	22	dt	dt	NOUN
ejpam-4700	52	23	tn+1	tn+1	PROPN
ejpam-4700	52	24	=	=	SYM
ejpam-4700	52	25	0	0	NUM
ejpam-4700	52	26	where	where	SCONJ
ejpam-4700	52	27	cn	cn	PROPN
ejpam-4700	52	28	=	=	PRON
ejpam-4700	52	29	{	{	PUNCT
ejpam-4700	52	30	t	t	PROPN
ejpam-4700	52	31	:	:	PUNCT
ejpam-4700	52	32	|t|	|t|	PROPN
ejpam-4700	52	33	=	=	X
ejpam-4700	52	34	(	(	PUNCT
ejpam-4700	52	35	n	n	X
ejpam-4700	52	36	+	+	X
ejpam-4700	52	37	ϵ)π	ϵ)π	NOUN
ejpam-4700	52	38	and	and	CCONJ
ejpam-4700	52	39	ϵ	ϵ	PRON
ejpam-4700	52	40	∈	∈	PROPN
ejpam-4700	52	41	r	r	NOUN
ejpam-4700	52	42	,	,	PUNCT
ejpam-4700	52	43	(	(	PUNCT
ejpam-4700	52	44	ϵπi±	ϵπi±	X
ejpam-4700	52	45	log(u	log(u	PROPN
ejpam-4700	52	46	/	/	SYM
ejpam-4700	52	47	λ)1/2	λ)1/2	PROPN
ejpam-4700	52	48	)	)	PUNCT
ejpam-4700	53	1	̸=	̸=	NOUN
ejpam-4700	53	2	0	0	NUM
ejpam-4700	53	3	}	}	PUNCT
ejpam-4700	53	4	proof	proof	NOUN
ejpam-4700	53	5	.	.	PUNCT
ejpam-4700	54	1	we	we	PRON
ejpam-4700	54	2	first	first	ADV
ejpam-4700	54	3	take	take	VERB
ejpam-4700	54	4	the	the	DET
ejpam-4700	54	5	modulus	modulus	NOUN
ejpam-4700	54	6	of	of	ADP
ejpam-4700	54	7	the	the	DET
ejpam-4700	54	8	integral	integral	ADJ
ejpam-4700	54	9	given	give	VERB
ejpam-4700	54	10	as∣∣∣∣∫	as∣∣∣∣∫	PROPN
ejpam-4700	54	11	cn	cn	PROPN
ejpam-4700	54	12	1−	1−	NUM
ejpam-4700	54	13	u	u	PROPN
ejpam-4700	54	14	λe2	λe2	PROPN
ejpam-4700	54	15	t	t	PROPN
ejpam-4700	54	16	−	−	NOUN
ejpam-4700	55	1	u	u	NOUN
ejpam-4700	55	2	ext	ext	NOUN
ejpam-4700	55	3	dt	dt	NOUN
ejpam-4700	55	4	tn+1	tn+1	PROPN
ejpam-4700	55	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4700	55	6	≤	≤	NUM
ejpam-4700	55	7	∫	∫	PROPN
ejpam-4700	55	8	cn	cn	PROPN
ejpam-4700	55	9	|1−	|1−	PROPN
ejpam-4700	55	10	u||ext|	u||ext|	PROPN
ejpam-4700	55	11	|λe2	|λe2	PROPN
ejpam-4700	55	12	t	t	NOUN
ejpam-4700	55	13	−	−	NOUN
ejpam-4700	55	14	u||tn+1||dt|	u||tn+1||dt|	PROPN
ejpam-4700	55	15	≤	≤	NUM
ejpam-4700	55	16	∫	∫	PROPN
ejpam-4700	55	17	cn	cn	PROPN
ejpam-4700	55	18	|ext|	|ext|	PROPN
ejpam-4700	55	19	|λe2	|λe2	NOUN
ejpam-4700	55	20	t	t	NOUN
ejpam-4700	55	21	−	−	NOUN
ejpam-4700	55	22	u|	u|	ADJ
ejpam-4700	55	23	|dt|	|dt|	NOUN
ejpam-4700	55	24	consider	consider	VERB
ejpam-4700	55	25	the	the	DET
ejpam-4700	55	26	function	function	NOUN
ejpam-4700	55	27	in	in	ADP
ejpam-4700	55	28	the	the	DET
ejpam-4700	55	29	last	last	ADJ
ejpam-4700	55	30	integral	integral	ADJ
ejpam-4700	55	31	|ext|	|ext|	PROPN
ejpam-4700	55	32	|λe2	|λe2	NOUN
ejpam-4700	55	33	t	t	NOUN
ejpam-4700	55	34	−	−	NOUN
ejpam-4700	55	35	u|	u|	PROPN
ejpam-4700	55	36	=	=	NOUN
ejpam-4700	55	37	|ext|	|ext|	PROPN
ejpam-4700	55	38	|	|	ADV
ejpam-4700	55	39	−	−	NOUN
ejpam-4700	56	1	u|	u|	PROPN
ejpam-4700	56	2	∣∣−u	∣∣−u	PROPN
ejpam-4700	56	3	λe	λe	ADP
ejpam-4700	56	4	2	2	NUM
ejpam-4700	56	5	t	t	NOUN
ejpam-4700	56	6	+	+	CCONJ
ejpam-4700	56	7	1	1	NUM
ejpam-4700	56	8	∣∣	∣∣	NUM
ejpam-4700	56	9	≤	≤	NUM
ejpam-4700	56	10	ere(t	ere(t	PROPN
ejpam-4700	56	11	)	)	PUNCT
ejpam-4700	56	12	|α||u||e2	|α||u||e2	PROPN
ejpam-4700	56	13	t	t	NOUN
ejpam-4700	56	14	+	+	CCONJ
ejpam-4700	56	15	1	1	NUM
ejpam-4700	56	16	α	α	NOUN
ejpam-4700	57	1	|	|	INTJ
ejpam-4700	57	2	,	,	PUNCT
ejpam-4700	57	3	where	where	SCONJ
ejpam-4700	57	4	α	α	NOUN
ejpam-4700	57	5	=	=	SYM
ejpam-4700	57	6	−λ	−λ	PROPN
ejpam-4700	57	7	u	u	NOUN
ejpam-4700	57	8	≤	≤	ADV
ejpam-4700	57	9	1	1	NUM
ejpam-4700	57	10	|	|	ADV
ejpam-4700	57	11	−	−	PROPN
ejpam-4700	57	12	λ|	λ|	NOUN
ejpam-4700	57	13	so	so	SCONJ
ejpam-4700	57	14	that	that	SCONJ
ejpam-4700	57	15	,	,	PUNCT
ejpam-4700	57	16	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-4700	57	17	cn	cn	NOUN
ejpam-4700	57	18	1−	1−	NUM
ejpam-4700	57	19	u	u	PROPN
ejpam-4700	58	1	λe2	λe2	PROPN
ejpam-4700	58	2	t	t	PROPN
ejpam-4700	58	3	−	−	NOUN
ejpam-4700	59	1	u	u	NOUN
ejpam-4700	59	2	ext	ext	NOUN
ejpam-4700	59	3	dt	dt	NOUN
ejpam-4700	59	4	tn+1	tn+1	PROPN
ejpam-4700	59	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4700	59	6	≤	≤	NUM
ejpam-4700	59	7	1	1	NUM
ejpam-4700	59	8	|	|	ADV
ejpam-4700	59	9	−	−	PROPN
ejpam-4700	60	1	λ|	λ|	PROPN
ejpam-4700	60	2	∫	∫	PROPN
ejpam-4700	60	3	cn	cn	PROPN
ejpam-4700	60	4	|dt|	|dt|	PROPN
ejpam-4700	60	5	|tn+1|	|tn+1|	PROPN
ejpam-4700	60	6	=	=	SYM
ejpam-4700	60	7	2n+1	2n+1	PROPN
ejpam-4700	60	8	|	|	ADV
ejpam-4700	60	9	−	−	NOUN
ejpam-4700	60	10	λ|((2n	λ|((2n	X
ejpam-4700	61	1	+	+	X
ejpam-4700	61	2	ϵ)π)n+1	ϵ)π)n+1	ADV
ejpam-4700	61	3	as	as	ADP
ejpam-4700	61	4	n	n	NOUN
ejpam-4700	61	5	→	→	SYM
ejpam-4700	61	6	∞	∞	NUM
ejpam-4700	61	7	for	for	ADP
ejpam-4700	61	8	n	n	PRON
ejpam-4700	61	9	≥	≥	NUM
ejpam-4700	61	10	1	1	NUM
ejpam-4700	61	11	∫	∫	PROPN
ejpam-4700	61	12	cn	cn	PROPN
ejpam-4700	61	13	1−	1−	NUM
ejpam-4700	61	14	u	u	PROPN
ejpam-4700	61	15	λe2	λe2	PROPN
ejpam-4700	61	16	t	t	PROPN
ejpam-4700	62	1	−	−	NOUN
ejpam-4700	62	2	u	u	NOUN
ejpam-4700	62	3	ext	ext	NOUN
ejpam-4700	62	4	dt	dt	NOUN
ejpam-4700	62	5	tn+1	tn+1	PROPN
ejpam-4700	62	6	→	→	SYM
ejpam-4700	62	7	0	0	NUM
ejpam-4700	62	8	using	use	VERB
ejpam-4700	62	9	lemma	lemma	PROPN
ejpam-4700	62	10	1	1	NUM
ejpam-4700	62	11	,	,	PUNCT
ejpam-4700	62	12	eq	eq	NOUN
ejpam-4700	62	13	.	.	PUNCT
ejpam-4700	63	1	(	(	PUNCT
ejpam-4700	63	2	8)	8)	NUM
ejpam-4700	63	3	becomes	become	VERB
ejpam-4700	63	4	res(fn(t	res(fn(t	PROPN
ejpam-4700	63	5	)	)	PUNCT
ejpam-4700	63	6	,	,	PUNCT
ejpam-4700	63	7	t	t	PROPN
ejpam-4700	63	8	=	=	SYM
ejpam-4700	63	9	0	0	NUM
ejpam-4700	63	10	)	)	PUNCT
ejpam-4700	63	11	=	=	SYM
ejpam-4700	64	1	−	−	PROPN
ejpam-4700	64	2	∑	∑	PUNCT
ejpam-4700	64	3	k∈z	k∈z	PROPN
ejpam-4700	64	4	res(fn(t	res(fn(t	PROPN
ejpam-4700	64	5	)	)	PUNCT
ejpam-4700	64	6	,	,	PUNCT
ejpam-4700	64	7	t	t	PROPN
ejpam-4700	64	8	=	=	SYM
ejpam-4700	64	9	tk	tk	PROPN
ejpam-4700	64	10	)	)	PUNCT
ejpam-4700	64	11	we	we	PRON
ejpam-4700	64	12	then	then	ADV
ejpam-4700	64	13	compute	compute	VERB
ejpam-4700	64	14	the	the	DET
ejpam-4700	64	15	res(fn(t	res(fn(t	PROPN
ejpam-4700	64	16	)	)	PUNCT
ejpam-4700	64	17	,	,	PUNCT
ejpam-4700	64	18	t	t	PROPN
ejpam-4700	64	19	=	=	SYM
ejpam-4700	64	20	0	0	NUM
ejpam-4700	64	21	,	,	PUNCT
ejpam-4700	64	22	)	)	PUNCT
ejpam-4700	64	23	and	and	CCONJ
ejpam-4700	64	24	∑	∑	PROPN
ejpam-4700	64	25	k∈zres(fn(t	k∈zres(fn(t	PROPN
ejpam-4700	64	26	)	)	PUNCT
ejpam-4700	64	27	,	,	PUNCT
ejpam-4700	64	28	t	t	PROPN
ejpam-4700	64	29	=	=	SYM
ejpam-4700	64	30	tk	tk	PROPN
ejpam-4700	64	31	)	)	PUNCT
ejpam-4700	64	32	to	to	PART
ejpam-4700	64	33	obtain	obtain	VERB
ejpam-4700	64	34	the	the	DET
ejpam-4700	64	35	fourier	fourier	NOUN
ejpam-4700	64	36	series	series	NOUN
ejpam-4700	64	37	expansion	expansion	NOUN
ejpam-4700	64	38	of	of	ADP
ejpam-4700	64	39	apostol	apostol	NOUN
ejpam-4700	64	40	-	-	PUNCT
ejpam-4700	64	41	frobenius	frobenius	NOUN
ejpam-4700	64	42	-	-	PUNCT
ejpam-4700	64	43	tangent	tangent	NOUN
ejpam-4700	64	44	polynomials	polynomial	NOUN
ejpam-4700	64	45	.	.	PUNCT
ejpam-4700	65	1	the	the	DET
ejpam-4700	65	2	following	follow	VERB
ejpam-4700	65	3	theorem	theorem	NOUN
ejpam-4700	65	4	explicitly	explicitly	ADV
ejpam-4700	65	5	shows	show	VERB
ejpam-4700	65	6	the	the	DET
ejpam-4700	65	7	fourier	fourier	PROPN
ejpam-4700	65	8	series	series	NOUN
ejpam-4700	65	9	representation	representation	NOUN
ejpam-4700	65	10	of	of	ADP
ejpam-4700	65	11	the	the	DET
ejpam-4700	65	12	said	say	VERB
ejpam-4700	65	13	polynomials	polynomial	NOUN
ejpam-4700	65	14	theorem	theorem	VERB
ejpam-4700	65	15	1	1	X
ejpam-4700	65	16	.	.	PUNCT
ejpam-4700	66	1	let	let	VERB
ejpam-4700	66	2	u	u	NOUN
ejpam-4700	66	3	,	,	PUNCT
ejpam-4700	66	4	λ	λ	PROPN
ejpam-4700	66	5	∈	∈	PROPN
ejpam-4700	66	6	c{0	c{0	NOUN
ejpam-4700	66	7	,	,	PUNCT
ejpam-4700	66	8	1	1	NUM
ejpam-4700	66	9	}	}	PUNCT
ejpam-4700	66	10	with	with	ADP
ejpam-4700	66	11	|λ|	|λ|	NOUN
ejpam-4700	66	12	=	=	PUNCT
ejpam-4700	66	13	̸	̸	NUM
ejpam-4700	66	14	|u|	|u|	PROPN
ejpam-4700	66	15	.	.	PUNCT
ejpam-4700	67	1	for	for	ADP
ejpam-4700	67	2	0	0	NUM
ejpam-4700	67	3	<	<	X
ejpam-4700	67	4	x	x	SYM
ejpam-4700	67	5	≤	≤	NUM
ejpam-4700	67	6	1	1	NUM
ejpam-4700	67	7	tn(x;u	tn(x;u	NOUN
ejpam-4700	67	8	,	,	PUNCT
ejpam-4700	67	9	λ	λ	NOUN
ejpam-4700	67	10	)	)	PUNCT
ejpam-4700	67	11	=	=	SYM
ejpam-4700	67	12	n	n	X
ejpam-4700	67	13	!	!	SYM
ejpam-4700	67	14	2	2	NUM
ejpam-4700	67	15	u−	u−	PROPN
ejpam-4700	67	16	1	1	NUM
ejpam-4700	67	17	u	u	NOUN
ejpam-4700	67	18	(	(	PUNCT
ejpam-4700	67	19	u	u	NOUN
ejpam-4700	67	20	λ	λ	PROPN
ejpam-4700	67	21	)	)	PUNCT
ejpam-4700	67	22	1	1	NUM
ejpam-4700	67	23	2	2	NUM
ejpam-4700	67	24	x∑	x∑	PRON
ejpam-4700	67	25	k∈z	k∈z	PROPN
ejpam-4700	67	26	eiπkx	eiπkx	PROPN
ejpam-4700	67	27	2λ	2λ	PROPN
ejpam-4700	67	28	[	[	PUNCT
ejpam-4700	67	29	log	log	NOUN
ejpam-4700	67	30	(	(	PUNCT
ejpam-4700	67	31	u	u	NOUN
ejpam-4700	67	32	λ	λ	PROPN
ejpam-4700	67	33	)	)	PUNCT
ejpam-4700	67	34	1/2	1/2	NUM
ejpam-4700	67	35	+	+	NUM
ejpam-4700	67	36	kπi	kπi	NOUN
ejpam-4700	67	37	]	]	X
ejpam-4700	67	38	n+1	n+1	PROPN
ejpam-4700	67	39	(	(	PUNCT
ejpam-4700	67	40	9	9	NUM
ejpam-4700	67	41	)	)	PUNCT
ejpam-4700	67	42	r.	r.	PROPN
ejpam-4700	67	43	b.	b.	PROPN
ejpam-4700	67	44	corcino	corcino	PROPN
ejpam-4700	67	45	et	et	PROPN
ejpam-4700	67	46	al	al	PROPN
ejpam-4700	67	47	.	.	PUNCT
ejpam-4700	67	48	/	/	SYM
ejpam-4700	67	49	eur	eur	PROPN
ejpam-4700	67	50	.	.	PUNCT
ejpam-4700	68	1	j.	j.	PROPN
ejpam-4700	68	2	pure	pure	PROPN
ejpam-4700	68	3	appl	appl	PROPN
ejpam-4700	68	4	.	.	PROPN
ejpam-4700	68	5	math	math	PROPN
ejpam-4700	68	6	,	,	PUNCT
ejpam-4700	68	7	16	16	NUM
ejpam-4700	68	8	(	(	PUNCT
ejpam-4700	68	9	2	2	NUM
ejpam-4700	68	10	)	)	PUNCT
ejpam-4700	68	11	(	(	PUNCT
ejpam-4700	68	12	2023	2023	NUM
ejpam-4700	68	13	)	)	PUNCT
ejpam-4700	68	14	,	,	PUNCT
ejpam-4700	68	15	1005	1005	NUM
ejpam-4700	68	16	-	-	SYM
ejpam-4700	68	17	1023	1023	NUM
ejpam-4700	68	18	1009	1009	NUM
ejpam-4700	68	19	proof	proof	NOUN
ejpam-4700	68	20	.	.	PUNCT
ejpam-4700	69	1	we	we	PRON
ejpam-4700	69	2	compute	compute	VERB
ejpam-4700	69	3	res(fn(t	res(fn(t	PROPN
ejpam-4700	69	4	)	)	PUNCT
ejpam-4700	69	5	,	,	PUNCT
ejpam-4700	69	6	t	t	PROPN
ejpam-4700	69	7	=	=	SYM
ejpam-4700	69	8	0	0	NUM
ejpam-4700	69	9	)	)	PUNCT
ejpam-4700	69	10	and	and	CCONJ
ejpam-4700	69	11	∑	∑	PROPN
ejpam-4700	69	12	k∈zres(fn(t	k∈zres(fn(t	PROPN
ejpam-4700	69	13	)	)	PUNCT
ejpam-4700	69	14	,	,	PUNCT
ejpam-4700	69	15	t	t	PROPN
ejpam-4700	69	16	=	=	SYM
ejpam-4700	69	17	tk	tk	PROPN
ejpam-4700	69	18	)	)	PUNCT
ejpam-4700	69	19	as	as	SCONJ
ejpam-4700	69	20	follows	follow	VERB
ejpam-4700	69	21	:	:	PUNCT
ejpam-4700	69	22	res(fn(t	res(fn(t	PROPN
ejpam-4700	69	23	)	)	PUNCT
ejpam-4700	69	24	,	,	PUNCT
ejpam-4700	69	25	t	t	PROPN
ejpam-4700	69	26	=	=	SYM
ejpam-4700	70	1	0	0	NUM
ejpam-4700	70	2	)	)	PUNCT
ejpam-4700	70	3	=	=	SYM
ejpam-4700	70	4	lim	lim	PROPN
ejpam-4700	70	5	t→0	t→0	PUNCT
ejpam-4700	70	6	1	1	NUM
ejpam-4700	70	7	n	n	X
ejpam-4700	70	8	!	!	PUNCT
ejpam-4700	71	1	dn	dn	PROPN
ejpam-4700	71	2	dtn	dtn	PROPN
ejpam-4700	71	3	(	(	PUNCT
ejpam-4700	71	4	t−	t−	PROPN
ejpam-4700	71	5	0)n+1	0)n+1	SYM
ejpam-4700	71	6	1	1	NUM
ejpam-4700	71	7	tn+1	tn+1	NOUN
ejpam-4700	71	8	∞∑	∞∑	PROPN
ejpam-4700	71	9	m=0	m=0	PROPN
ejpam-4700	71	10	tm(x	tm(x	X
ejpam-4700	71	11	;	;	PUNCT
ejpam-4700	71	12	,	,	PUNCT
ejpam-4700	71	13	u	u	NOUN
ejpam-4700	71	14	,	,	PUNCT
ejpam-4700	71	15	λ	λ	PROPN
ejpam-4700	71	16	)	)	PUNCT
ejpam-4700	71	17	tm	tm	PROPN
ejpam-4700	71	18	m	m	PROPN
ejpam-4700	71	19	!	!	PUNCT
ejpam-4700	72	1	=	=	PRON
ejpam-4700	72	2	lim	lim	PROPN
ejpam-4700	72	3	t→0	t→0	PUNCT
ejpam-4700	72	4	1	1	NUM
ejpam-4700	72	5	n	n	X
ejpam-4700	72	6	!	!	PUNCT
ejpam-4700	73	1	dn	dn	PROPN
ejpam-4700	73	2	dtn	dtn	PROPN
ejpam-4700	73	3	∞∑	∞∑	NUM
ejpam-4700	73	4	m=0	m=0	PROPN
ejpam-4700	73	5	tm(x;u	tm(x;u	NOUN
ejpam-4700	73	6	,	,	PUNCT
ejpam-4700	73	7	λ	λ	NOUN
ejpam-4700	73	8	)	)	PUNCT
ejpam-4700	73	9	=	=	SYM
ejpam-4700	73	10	lim	lim	PROPN
ejpam-4700	73	11	t→0	t→0	PUNCT
ejpam-4700	73	12	1	1	NUM
ejpam-4700	73	13	n	n	NOUN
ejpam-4700	73	14	!	!	PUNCT
ejpam-4700	74	1	∞∑	∞∑	PRON
ejpam-4700	74	2	m=0	m=0	PROPN
ejpam-4700	74	3	tm(x;u	tm(x;u	NOUN
ejpam-4700	74	4	,	,	PUNCT
ejpam-4700	74	5	λ	λ	NOUN
ejpam-4700	74	6	)	)	PUNCT
ejpam-4700	74	7	tm−n	tm−n	NOUN
ejpam-4700	74	8	(	(	PUNCT
ejpam-4700	74	9	m−	m−	PROPN
ejpam-4700	74	10	n	n	CCONJ
ejpam-4700	74	11	)	)	PUNCT
ejpam-4700	74	12	!	!	PUNCT
ejpam-4700	75	1	=	=	PUNCT
ejpam-4700	75	2	tm(x;u	tm(x;u	NOUN
ejpam-4700	75	3	,	,	PUNCT
ejpam-4700	75	4	λ	λ	NOUN
ejpam-4700	75	5	)	)	PUNCT
ejpam-4700	75	6	n	n	CCONJ
ejpam-4700	75	7	!	!	PUNCT
ejpam-4700	75	8	(	(	PUNCT
ejpam-4700	75	9	10	10	NUM
ejpam-4700	75	10	)	)	PUNCT
ejpam-4700	75	11	and	and	CCONJ
ejpam-4700	75	12	res(fn(t	res(fn(t	PROPN
ejpam-4700	75	13	)	)	PUNCT
ejpam-4700	75	14	,	,	PUNCT
ejpam-4700	75	15	t	t	PROPN
ejpam-4700	75	16	=	=	SYM
ejpam-4700	75	17	tk	tk	PROPN
ejpam-4700	75	18	)	)	PUNCT
ejpam-4700	75	19	=	=	PROPN
ejpam-4700	75	20	lim	lim	PROPN
ejpam-4700	75	21	t→tk	t→tk	PROPN
ejpam-4700	76	1	(	(	PUNCT
ejpam-4700	76	2	t−	t−	PROPN
ejpam-4700	76	3	tk	tk	PROPN
ejpam-4700	76	4	)	)	PUNCT
ejpam-4700	76	5	1−	1−	NUM
ejpam-4700	76	6	u	u	NOUN
ejpam-4700	76	7	λe2	λe2	PROPN
ejpam-4700	76	8	t	t	PROPN
ejpam-4700	76	9	−	−	NOUN
ejpam-4700	77	1	u	u	NOUN
ejpam-4700	77	2	ext	ext	VERB
ejpam-4700	77	3	1	1	NUM
ejpam-4700	77	4	tn+1	tn+1	NOUN
ejpam-4700	77	5	=	=	SYM
ejpam-4700	77	6	(	(	PUNCT
ejpam-4700	77	7	1−	1−	NUM
ejpam-4700	77	8	u	u	NOUN
ejpam-4700	77	9	)	)	PUNCT
ejpam-4700	77	10	tn+1	tn+1	PROPN
ejpam-4700	77	11	k	k	PROPN
ejpam-4700	77	12	extk	extk	PROPN
ejpam-4700	77	13	lim	lim	PROPN
ejpam-4700	77	14	t→tk	t→tk	PROPN
ejpam-4700	78	1	t−	t−	PROPN
ejpam-4700	78	2	tk	tk	PROPN
ejpam-4700	78	3	λe2	λe2	PROPN
ejpam-4700	78	4	t	t	PROPN
ejpam-4700	78	5	−	−	PROPN
ejpam-4700	78	6	u	u	NOUN
ejpam-4700	78	7	=	=	PROPN
ejpam-4700	78	8	1−	1−	NUM
ejpam-4700	78	9	u	u	NOUN
ejpam-4700	78	10	tn+1	tn+1	PROPN
ejpam-4700	78	11	k	k	PROPN
ejpam-4700	78	12	extk	extk	PROPN
ejpam-4700	78	13	lim	lim	PROPN
ejpam-4700	78	14	t→tk	t→tk	ADP
ejpam-4700	78	15	1	1	NUM
ejpam-4700	78	16	2λe2	2λe2	NUM
ejpam-4700	78	17	t	t	NOUN
ejpam-4700	78	18	=	=	SYM
ejpam-4700	78	19	(	(	PUNCT
ejpam-4700	78	20	1−	1−	NUM
ejpam-4700	78	21	u)e(x−2)tk	u)e(x−2)tk	PROPN
ejpam-4700	78	22	2λtn+1	2λtn+1	PROPN
ejpam-4700	78	23	k	k	PROPN
ejpam-4700	78	24	,	,	PUNCT
ejpam-4700	78	25	where	where	SCONJ
ejpam-4700	78	26	tk	tk	PROPN
ejpam-4700	78	27	=	=	NOUN
ejpam-4700	78	28	log	log	PROPN
ejpam-4700	78	29	(	(	PUNCT
ejpam-4700	78	30	u	u	NOUN
ejpam-4700	78	31	λ	λ	PROPN
ejpam-4700	78	32	)	)	PUNCT
ejpam-4700	78	33	1/2	1/2	NUM
ejpam-4700	78	34	+	+	NUM
ejpam-4700	78	35	kπi	kπi	NOUN
ejpam-4700	78	36	=	=	SYM
ejpam-4700	78	37	(	(	PUNCT
ejpam-4700	78	38	1−	1−	NUM
ejpam-4700	78	39	u	u	NOUN
ejpam-4700	78	40	)	)	PUNCT
ejpam-4700	78	41	exp	exp	NOUN
ejpam-4700	78	42	{	{	PUNCT
ejpam-4700	78	43	(	(	PUNCT
ejpam-4700	78	44	x−	x−	PROPN
ejpam-4700	78	45	2	2	NUM
ejpam-4700	78	46	)	)	PUNCT
ejpam-4700	78	47	[	[	PUNCT
ejpam-4700	78	48	log(u	log(u	PROPN
ejpam-4700	78	49	/	/	SYM
ejpam-4700	78	50	λ)1/2	λ)1/2	PROPN
ejpam-4700	79	1	+	+	CCONJ
ejpam-4700	79	2	kπi	kπi	NOUN
ejpam-4700	79	3	]	]	X
ejpam-4700	79	4	}	}	PUNCT
ejpam-4700	79	5	2λ	2λ	NOUN
ejpam-4700	79	6	[	[	PUNCT
ejpam-4700	79	7	log	log	NOUN
ejpam-4700	79	8	(	(	PUNCT
ejpam-4700	79	9	u	u	NOUN
ejpam-4700	79	10	λ	λ	PROPN
ejpam-4700	79	11	)	)	PUNCT
ejpam-4700	79	12	1/2	1/2	NUM
ejpam-4700	79	13	+	+	NUM
ejpam-4700	79	14	kπi	kπi	NOUN
ejpam-4700	79	15	]	]	X
ejpam-4700	79	16	n+1	n+1	X
ejpam-4700	79	17	=	=	SYM
ejpam-4700	79	18	(	(	PUNCT
ejpam-4700	79	19	1−	1−	NUM
ejpam-4700	79	20	u)ex	u)ex	PROPN
ejpam-4700	79	21	log(u	log(u	PROPN
ejpam-4700	79	22	/	/	SYM
ejpam-4700	79	23	λ)1/2ekπixe−2	λ)1/2ekπixe−2	NOUN
ejpam-4700	79	24	log(u	log(u	PROPN
ejpam-4700	79	25	/	/	SYM
ejpam-4700	79	26	λ)1/2e−2kπi	λ)1/2e−2kπi	PROPN
ejpam-4700	79	27	2λ	2λ	X
ejpam-4700	79	28	[	[	PUNCT
ejpam-4700	79	29	log	log	NOUN
ejpam-4700	79	30	(	(	PUNCT
ejpam-4700	79	31	u	u	NOUN
ejpam-4700	79	32	λ	λ	PROPN
ejpam-4700	79	33	)	)	PUNCT
ejpam-4700	79	34	1/2	1/2	NUM
ejpam-4700	79	35	+	+	NUM
ejpam-4700	79	36	kπi	kπi	NOUN
ejpam-4700	79	37	]	]	X
ejpam-4700	79	38	n+1	n+1	X
ejpam-4700	79	39	=	=	SYM
ejpam-4700	79	40	(	(	PUNCT
ejpam-4700	79	41	1−	1−	NUM
ejpam-4700	79	42	u)(u	u)(u	PROPN
ejpam-4700	79	43	/	/	SYM
ejpam-4700	79	44	λ	λ	NOUN
ejpam-4700	79	45	)	)	PUNCT
ejpam-4700	79	46	1	1	NUM
ejpam-4700	79	47	2	2	NUM
ejpam-4700	79	48	x−1ekπix	x−1ekπix	NOUN
ejpam-4700	79	49	2λ	2λ	NOUN
ejpam-4700	79	50	[	[	PUNCT
ejpam-4700	79	51	log	log	NOUN
ejpam-4700	79	52	(	(	PUNCT
ejpam-4700	79	53	u	u	NOUN
ejpam-4700	79	54	λ	λ	PROPN
ejpam-4700	79	55	)	)	PUNCT
ejpam-4700	79	56	1/2	1/2	NUM
ejpam-4700	79	57	+	+	NUM
ejpam-4700	79	58	kπi	kπi	NOUN
ejpam-4700	80	1	]	]	X
ejpam-4700	80	2	n+1	n+1	PROPN
ejpam-4700	80	3	(	(	PUNCT
ejpam-4700	80	4	11	11	NUM
ejpam-4700	80	5	)	)	PUNCT
ejpam-4700	80	6	combining	combine	VERB
ejpam-4700	80	7	the	the	DET
ejpam-4700	80	8	results	result	NOUN
ejpam-4700	80	9	of	of	ADP
ejpam-4700	80	10	the	the	DET
ejpam-4700	80	11	residues	residue	NOUN
ejpam-4700	80	12	equations	equation	NOUN
ejpam-4700	80	13	(	(	PUNCT
ejpam-4700	80	14	10	10	NUM
ejpam-4700	80	15	)	)	PUNCT
ejpam-4700	80	16	and	and	CCONJ
ejpam-4700	80	17	(	(	PUNCT
ejpam-4700	80	18	11	11	NUM
ejpam-4700	80	19	)	)	PUNCT
ejpam-4700	80	20	and	and	CCONJ
ejpam-4700	80	21	substitute	substitute	VERB
ejpam-4700	80	22	it	it	PRON
ejpam-4700	80	23	to	to	ADP
ejpam-4700	80	24	eq	eq	PROPN
ejpam-4700	80	25	.	.	PUNCT
ejpam-4700	81	1	(	(	PUNCT
ejpam-4700	81	2	8)	8)	NUM
ejpam-4700	81	3	,	,	PUNCT
ejpam-4700	81	4	we	we	PRON
ejpam-4700	81	5	get	get	VERB
ejpam-4700	81	6	tn(x;u	tn(x;u	NOUN
ejpam-4700	81	7	,	,	PUNCT
ejpam-4700	81	8	λ	λ	NOUN
ejpam-4700	81	9	)	)	PUNCT
ejpam-4700	81	10	n	n	CCONJ
ejpam-4700	81	11	!	!	PUNCT
ejpam-4700	82	1	=	=	PUNCT
ejpam-4700	83	1	−	−	PROPN
ejpam-4700	83	2	∑	∑	ADV
ejpam-4700	83	3	k∈z	k∈z	PROPN
ejpam-4700	83	4	(	(	PUNCT
ejpam-4700	83	5	1−	1−	NUM
ejpam-4700	83	6	u	u	NOUN
ejpam-4700	83	7	)	)	PUNCT
ejpam-4700	83	8	(	(	PUNCT
ejpam-4700	83	9	u	u	NOUN
ejpam-4700	83	10	λ	λ	PROPN
ejpam-4700	83	11	)	)	PUNCT
ejpam-4700	83	12	1	1	NUM
ejpam-4700	83	13	2	2	NUM
ejpam-4700	83	14	x−1	x−1	NOUN
ejpam-4700	83	15	ekπix	ekπix	ADJ
ejpam-4700	83	16	2λ	2λ	PROPN
ejpam-4700	83	17	[	[	PUNCT
ejpam-4700	83	18	log	log	NOUN
ejpam-4700	83	19	(	(	PUNCT
ejpam-4700	83	20	u	u	NOUN
ejpam-4700	83	21	λ	λ	PROPN
ejpam-4700	83	22	)	)	PUNCT
ejpam-4700	83	23	1/2	1/2	NUM
ejpam-4700	83	24	+	+	NUM
ejpam-4700	83	25	kπi	kπi	NOUN
ejpam-4700	83	26	]	]	X
ejpam-4700	83	27	n+1	n+1	NUM
ejpam-4700	83	28	simplifying	simplify	VERB
ejpam-4700	83	29	the	the	DET
ejpam-4700	83	30	above	above	ADJ
ejpam-4700	83	31	expression	expression	NOUN
ejpam-4700	83	32	we	we	PRON
ejpam-4700	83	33	then	then	ADV
ejpam-4700	83	34	have	have	AUX
ejpam-4700	83	35	tn(x;u	tn(x;u	NOUN
ejpam-4700	83	36	,	,	PUNCT
ejpam-4700	83	37	λ	λ	NOUN
ejpam-4700	83	38	)	)	PUNCT
ejpam-4700	83	39	=	=	SYM
ejpam-4700	83	40	n	n	X
ejpam-4700	83	41	!	!	SYM
ejpam-4700	83	42	2	2	NUM
ejpam-4700	83	43	u−	u−	PROPN
ejpam-4700	83	44	1	1	NUM
ejpam-4700	83	45	u	u	NOUN
ejpam-4700	83	46	(	(	PUNCT
ejpam-4700	83	47	u	u	NOUN
ejpam-4700	83	48	λ	λ	PROPN
ejpam-4700	83	49	)	)	PUNCT
ejpam-4700	83	50	1	1	NUM
ejpam-4700	83	51	2	2	NUM
ejpam-4700	83	52	x∑	x∑	PRON
ejpam-4700	83	53	k∈z	k∈z	PROPN
ejpam-4700	83	54	eiπkx	eiπkx	PROPN
ejpam-4700	83	55	[	[	X
ejpam-4700	83	56	log	log	NOUN
ejpam-4700	83	57	(	(	PUNCT
ejpam-4700	83	58	u	u	NOUN
ejpam-4700	83	59	λ	λ	PROPN
ejpam-4700	83	60	)	)	PUNCT
ejpam-4700	83	61	1/2	1/2	NUM
ejpam-4700	84	1	+	+	NUM
ejpam-4700	84	2	kπi	kπi	NOUN
ejpam-4700	84	3	]	]	X
ejpam-4700	84	4	n+1	n+1	PROPN
ejpam-4700	84	5	r.	r.	PROPN
ejpam-4700	84	6	b.	b.	PROPN
ejpam-4700	84	7	corcino	corcino	PROPN
ejpam-4700	84	8	et	et	PROPN
ejpam-4700	84	9	al	al	PROPN
ejpam-4700	84	10	.	.	PUNCT
ejpam-4700	84	11	/	/	SYM
ejpam-4700	84	12	eur	eur	PROPN
ejpam-4700	84	13	.	.	PUNCT
ejpam-4700	85	1	j.	j.	PROPN
ejpam-4700	85	2	pure	pure	PROPN
ejpam-4700	85	3	appl	appl	PROPN
ejpam-4700	85	4	.	.	PROPN
ejpam-4700	85	5	math	math	PROPN
ejpam-4700	85	6	,	,	PUNCT
ejpam-4700	85	7	16	16	NUM
ejpam-4700	85	8	(	(	PUNCT
ejpam-4700	85	9	2	2	NUM
ejpam-4700	85	10	)	)	PUNCT
ejpam-4700	85	11	(	(	PUNCT
ejpam-4700	85	12	2023	2023	NUM
ejpam-4700	85	13	)	)	PUNCT
ejpam-4700	85	14	,	,	PUNCT
ejpam-4700	85	15	1005	1005	NUM
ejpam-4700	85	16	-	-	SYM
ejpam-4700	85	17	1023	1023	NUM
ejpam-4700	85	18	1010	1010	NUM
ejpam-4700	85	19	when	when	SCONJ
ejpam-4700	85	20	u	u	PROPN
ejpam-4700	85	21	=	=	PROPN
ejpam-4700	85	22	−1	−1	PROPN
ejpam-4700	85	23	,	,	PUNCT
ejpam-4700	85	24	the	the	DET
ejpam-4700	85	25	above	above	ADJ
ejpam-4700	85	26	expression	expression	NOUN
ejpam-4700	85	27	will	will	AUX
ejpam-4700	85	28	then	then	ADV
ejpam-4700	85	29	be	be	AUX
ejpam-4700	85	30	tn(x;−1	tn(x;−1	NOUN
ejpam-4700	85	31	,	,	PUNCT
ejpam-4700	85	32	λ	λ	NOUN
ejpam-4700	85	33	)	)	PUNCT
ejpam-4700	85	34	=	=	SYM
ejpam-4700	85	35	t	t	PROPN
ejpam-4700	85	36	(	(	PUNCT
ejpam-4700	85	37	x;λ	x;λ	PROPN
ejpam-4700	85	38	)	)	PUNCT
ejpam-4700	85	39	.	.	PUNCT
ejpam-4700	86	1	that	that	PRON
ejpam-4700	86	2	is	be	AUX
ejpam-4700	86	3	tn(x;u	tn(x;u	NOUN
ejpam-4700	86	4	=	=	SYM
ejpam-4700	86	5	−1	−1	NOUN
ejpam-4700	86	6	,	,	PUNCT
ejpam-4700	86	7	λ	λ	NOUN
ejpam-4700	86	8	)	)	PUNCT
ejpam-4700	86	9	=	=	SYM
ejpam-4700	86	10	n	n	X
ejpam-4700	86	11	!	!	X
ejpam-4700	86	12	2	2	NUM
ejpam-4700	86	13	(	(	PUNCT
ejpam-4700	86	14	−1	−1	NOUN
ejpam-4700	86	15	λ	λ	NOUN
ejpam-4700	86	16	)	)	PUNCT
ejpam-4700	86	17	1	1	NUM
ejpam-4700	86	18	2	2	NUM
ejpam-4700	86	19	x∑	x∑	DET
ejpam-4700	86	20	k∈z	k∈z	NOUN
ejpam-4700	86	21	eikπx	eikπx	NOUN
ejpam-4700	87	1	·	·	PUNCT
ejpam-4700	87	2	2n+1	2n+1	PROPN
ejpam-4700	87	3	[	[	PUNCT
ejpam-4700	87	4	log	log	NOUN
ejpam-4700	87	5	(	(	PUNCT
ejpam-4700	87	6	−1	−1	NOUN
ejpam-4700	87	7	λ	λ	PROPN
ejpam-4700	87	8	)	)	PUNCT
ejpam-4700	88	1	+	+	CCONJ
ejpam-4700	88	2	2kπi	2kπi	NUM
ejpam-4700	88	3	]	]	SYM
ejpam-4700	88	4	n+1	n+1	PUNCT
ejpam-4700	88	5	=	=	SYM
ejpam-4700	88	6	n	n	X
ejpam-4700	88	7	!	!	X
ejpam-4700	88	8	2	2	NUM
ejpam-4700	88	9	e−iπk	e−iπk	NOUN
ejpam-4700	88	10	x	x	SYM
ejpam-4700	88	11	2	2	NUM
ejpam-4700	88	12	λ	λ	NOUN
ejpam-4700	88	13	1	1	NUM
ejpam-4700	88	14	2	2	NUM
ejpam-4700	88	15	x	x	SYM
ejpam-4700	88	16	∑	∑	PUNCT
ejpam-4700	88	17	k∈z	k∈z	PROPN
ejpam-4700	88	18	eiπkx	eiπkx	PROPN
ejpam-4700	88	19	·	·	PUNCT
ejpam-4700	88	20	2n+1	2n+1	PROPN
ejpam-4700	89	1	[	[	X
ejpam-4700	89	2	(	(	PUNCT
ejpam-4700	89	3	2k	2k	NUM
ejpam-4700	89	4	−	−	PROPN
ejpam-4700	89	5	1)π	1)π	NUM
ejpam-4700	89	6	−	−	NOUN
ejpam-4700	89	7	log	log	PROPN
ejpam-4700	89	8	λ]n+1	λ]n+1	NOUN
ejpam-4700	89	9	=	=	SYM
ejpam-4700	89	10	n	n	X
ejpam-4700	89	11	!	!	X
ejpam-4700	89	12	2	2	NUM
ejpam-4700	89	13	1	1	NUM
ejpam-4700	89	14	(	(	PUNCT
ejpam-4700	89	15	λ	λ	NOUN
ejpam-4700	89	16	)	)	PUNCT
ejpam-4700	89	17	1	1	NUM
ejpam-4700	89	18	2	2	NUM
ejpam-4700	89	19	x	x	NOUN
ejpam-4700	89	20	∑	∑	ADP
ejpam-4700	89	21	k∈z	k∈z	PROPN
ejpam-4700	89	22	eiπkxe−iπ	eiπkxe−iπ	NOUN
ejpam-4700	89	23	x	x	SYM
ejpam-4700	89	24	2	2	NUM
ejpam-4700	89	25	·	·	SYM
ejpam-4700	89	26	2n+1	2n+1	PROPN
ejpam-4700	89	27	[	[	PUNCT
ejpam-4700	89	28	log	log	NOUN
ejpam-4700	89	29	(	(	PUNCT
ejpam-4700	89	30	−1	−1	NOUN
ejpam-4700	89	31	λ	λ	PROPN
ejpam-4700	89	32	)	)	PUNCT
ejpam-4700	90	1	+	+	CCONJ
ejpam-4700	90	2	2kπi	2kπi	NUM
ejpam-4700	90	3	]	]	SYM
ejpam-4700	90	4	n+1	n+1	PROPN
ejpam-4700	90	5	t	t	PROPN
ejpam-4700	90	6	(	(	PUNCT
ejpam-4700	90	7	x;λ	x;λ	PROPN
ejpam-4700	90	8	)	)	PUNCT
ejpam-4700	90	9	=	=	SYM
ejpam-4700	91	1	n	n	X
ejpam-4700	91	2	!	!	X
ejpam-4700	91	3	2	2	NUM
ejpam-4700	91	4	1	1	NUM
ejpam-4700	91	5	(	(	PUNCT
ejpam-4700	91	6	λ	λ	NOUN
ejpam-4700	91	7	)	)	PUNCT
ejpam-4700	91	8	1	1	NUM
ejpam-4700	91	9	2	2	NUM
ejpam-4700	91	10	x	x	NOUN
ejpam-4700	91	11	∑	∑	PUNCT
ejpam-4700	91	12	k∈z	k∈z	PART
ejpam-4700	91	13	e	e	X
ejpam-4700	91	14	x	x	SYM
ejpam-4700	91	15	2	2	NUM
ejpam-4700	91	16	(	(	PUNCT
ejpam-4700	91	17	2k−1)πi	2k−1)πi	NUM
ejpam-4700	91	18	·	·	SYM
ejpam-4700	91	19	2n+1	2n+1	X
ejpam-4700	92	1	[	[	X
ejpam-4700	92	2	(	(	PUNCT
ejpam-4700	92	3	2k	2k	NUM
ejpam-4700	92	4	−	−	PROPN
ejpam-4700	92	5	1)πi−	1)πi−	NUM
ejpam-4700	92	6	log	log	PROPN
ejpam-4700	92	7	λ]n+1	λ]n+1	NOUN
ejpam-4700	92	8	note	note	VERB
ejpam-4700	92	9	that	that	SCONJ
ejpam-4700	92	10	,	,	PUNCT
ejpam-4700	92	11	the	the	DET
ejpam-4700	92	12	above	above	ADJ
ejpam-4700	92	13	expression	expression	NOUN
ejpam-4700	92	14	is	be	AUX
ejpam-4700	92	15	the	the	DET
ejpam-4700	92	16	known	know	VERB
ejpam-4700	92	17	apostol	apostol	NOUN
ejpam-4700	92	18	-	-	PUNCT
ejpam-4700	92	19	tangent	tangent	NOUN
ejpam-4700	92	20	polynomial	polynomial	NOUN
ejpam-4700	92	21	as	as	SCONJ
ejpam-4700	92	22	shown	show	VERB
ejpam-4700	92	23	in	in	ADP
ejpam-4700	92	24	the	the	DET
ejpam-4700	92	25	paper	paper	NOUN
ejpam-4700	92	26	of	of	ADP
ejpam-4700	92	27	corcino	corcino	PROPN
ejpam-4700	92	28	et	et	PROPN
ejpam-4700	92	29	al.[3	al.[3	PROPN
ejpam-4700	92	30	]	]	PUNCT
ejpam-4700	92	31	now	now	ADV
ejpam-4700	92	32	,	,	PUNCT
ejpam-4700	92	33	consider	consider	VERB
ejpam-4700	92	34	an	an	DET
ejpam-4700	92	35	integral	integral	ADJ
ejpam-4700	92	36	formulation	formulation	NOUN
ejpam-4700	92	37	of	of	ADP
ejpam-4700	92	38	the	the	DET
ejpam-4700	92	39	polynomials	polynomial	NOUN
ejpam-4700	92	40	apostol	apostol	NOUN
ejpam-4700	92	41	-	-	PUNCT
ejpam-4700	92	42	frobenius	frobenius	NOUN
ejpam-4700	92	43	-	-	PUNCT
ejpam-4700	92	44	tangent	tangent	NOUN
ejpam-4700	92	45	.	.	PUNCT
ejpam-4700	93	1	theorem	theorem	NOUN
ejpam-4700	93	2	2	2	NUM
ejpam-4700	93	3	.	.	X
ejpam-4700	93	4	for	for	ADP
ejpam-4700	93	5	n	n	PRON
ejpam-4700	93	6	∈	∈	PROPN
ejpam-4700	93	7	n	n	CCONJ
ejpam-4700	93	8	(	(	PUNCT
ejpam-4700	93	9	set	set	NOUN
ejpam-4700	93	10	of	of	ADP
ejpam-4700	93	11	natural	natural	ADJ
ejpam-4700	93	12	numbers	number	NOUN
ejpam-4700	93	13	)	)	PUNCT
ejpam-4700	93	14	,	,	PUNCT
ejpam-4700	93	15	0	0	PUNCT
ejpam-4700	93	16	<	<	X
ejpam-4700	93	17	x	x	X
ejpam-4700	93	18	<	<	X
ejpam-4700	93	19	1	1	NUM
ejpam-4700	93	20	,	,	PUNCT
ejpam-4700	93	21	ξ	ξ	X
ejpam-4700	93	22	<	<	X
ejpam-4700	93	23	1	1	NUM
ejpam-4700	93	24	2	2	NUM
ejpam-4700	93	25	,	,	PUNCT
ejpam-4700	93	26	ξ	ξ	PROPN
ejpam-4700	93	27	∈	∈	PROPN
ejpam-4700	93	28	r	r	NOUN
ejpam-4700	93	29	,	,	PUNCT
ejpam-4700	93	30	we	we	PRON
ejpam-4700	93	31	have	have	VERB
ejpam-4700	93	32	tn	tn	NOUN
ejpam-4700	93	33	(	(	PUNCT
ejpam-4700	93	34	x;u;−ue2ξπi	x;u;−ue2ξπi	NUM
ejpam-4700	93	35	)	)	PUNCT
ejpam-4700	94	1	=	=	PRON
ejpam-4700	94	2	(	(	PUNCT
ejpam-4700	94	3	u−	u−	PROPN
ejpam-4700	94	4	1	1	NUM
ejpam-4700	94	5	u	u	NOUN
ejpam-4700	94	6	)	)	PUNCT
ejpam-4700	94	7	2n−1e−ξπix	2n−1e−ξπix	NUM
ejpam-4700	94	8	×	×	NOUN
ejpam-4700	95	1	[	[	X
ejpam-4700	95	2	∫	∫	X
ejpam-4700	95	3	∞	∞	PROPN
ejpam-4700	95	4	0	0	NUM
ejpam-4700	95	5	m(n;x	m(n;x	PROPN
ejpam-4700	95	6	;	;	PUNCT
ejpam-4700	95	7	v	v	NOUN
ejpam-4700	95	8	)	)	PUNCT
ejpam-4700	95	9	cosh(2ξπv	cosh(2ξπv	PROPN
ejpam-4700	95	10	)	)	PUNCT
ejpam-4700	96	1	+	+	NUM
ejpam-4700	96	2	in(n;x	in(n;x	PROPN
ejpam-4700	96	3	;	;	PUNCT
ejpam-4700	96	4	v	v	X
ejpam-4700	96	5	)	)	PUNCT
ejpam-4700	96	6	sinh(2ξπv	sinh(2ξπv	NOUN
ejpam-4700	96	7	)	)	PUNCT
ejpam-4700	96	8	cosh(2πvs	cosh(2πvs	NOUN
ejpam-4700	96	9	.	.	PUNCT
ejpam-4700	96	10	)	)	PUNCT
ejpam-4700	97	1	+	+	PUNCT
ejpam-4700	97	2	cos(πx	cos(πx	NOUN
ejpam-4700	97	3	)	)	PUNCT
ejpam-4700	97	4	vndv	vndv	NOUN
ejpam-4700	97	5	]	]	PUNCT
ejpam-4700	97	6	(	(	PUNCT
ejpam-4700	97	7	12	12	NUM
ejpam-4700	97	8	)	)	PUNCT
ejpam-4700	97	9	where	where	SCONJ
ejpam-4700	97	10	m(n;x	m(n;x	NOUN
ejpam-4700	97	11	;	;	PUNCT
ejpam-4700	97	12	v	v	NOUN
ejpam-4700	97	13	)	)	PUNCT
ejpam-4700	97	14	=	=	SYM
ejpam-4700	97	15	eπv	eπv	PROPN
ejpam-4700	97	16	cos	cos	INTJ
ejpam-4700	97	17	(	(	PUNCT
ejpam-4700	97	18	−π	−π	ADV
ejpam-4700	97	19	2	2	NUM
ejpam-4700	97	20	x+	x+	X
ejpam-4700	97	21	(	(	PUNCT
ejpam-4700	97	22	n+	n+	NUM
ejpam-4700	97	23	1)π	1)π	NUM
ejpam-4700	97	24	2	2	NUM
ejpam-4700	97	25	)	)	PUNCT
ejpam-4700	97	26	−	−	PROPN
ejpam-4700	98	1	e−πv	e−πv	PROPN
ejpam-4700	98	2	cos	cos	PROPN
ejpam-4700	98	3	(	(	PUNCT
ejpam-4700	98	4	π	π	PROPN
ejpam-4700	98	5	2	2	NUM
ejpam-4700	98	6	x+	x+	X
ejpam-4700	98	7	(	(	PUNCT
ejpam-4700	98	8	n+	n+	NUM
ejpam-4700	98	9	1)π	1)π	NUM
ejpam-4700	98	10	2	2	NUM
ejpam-4700	98	11	)	)	PUNCT
ejpam-4700	98	12	(	(	PUNCT
ejpam-4700	98	13	13	13	NUM
ejpam-4700	98	14	)	)	PUNCT
ejpam-4700	98	15	n(nn;x	n(nn;x	PROPN
ejpam-4700	98	16	;	;	PUNCT
ejpam-4700	98	17	v	v	NOUN
ejpam-4700	98	18	)	)	PUNCT
ejpam-4700	98	19	=	=	SYM
ejpam-4700	98	20	eπv	eπv	ADJ
ejpam-4700	98	21	sin	sin	NOUN
ejpam-4700	98	22	(	(	PUNCT
ejpam-4700	98	23	−π	−π	ADV
ejpam-4700	98	24	2	2	NUM
ejpam-4700	98	25	x+	x+	X
ejpam-4700	98	26	(	(	PUNCT
ejpam-4700	98	27	n+	n+	NUM
ejpam-4700	98	28	1)π	1)π	NUM
ejpam-4700	98	29	2	2	NUM
ejpam-4700	98	30	)	)	PUNCT
ejpam-4700	98	31	−	−	PROPN
ejpam-4700	98	32	e−πv	e−πv	ADJ
ejpam-4700	98	33	sin	sin	NOUN
ejpam-4700	98	34	(	(	PUNCT
ejpam-4700	98	35	π	π	PROPN
ejpam-4700	98	36	2	2	NUM
ejpam-4700	98	37	x+	x+	X
ejpam-4700	98	38	(	(	PUNCT
ejpam-4700	98	39	n+	n+	NUM
ejpam-4700	98	40	1)π	1)π	NUM
ejpam-4700	98	41	2	2	NUM
ejpam-4700	98	42	)	)	PUNCT
ejpam-4700	98	43	(	(	PUNCT
ejpam-4700	98	44	14	14	X
ejpam-4700	98	45	)	)	PUNCT
ejpam-4700	98	46	proof	proof	NOUN
ejpam-4700	98	47	.	.	PUNCT
ejpam-4700	98	48	from	from	ADP
ejpam-4700	98	49	eq.(9	eq.(9	ADJ
ejpam-4700	98	50	)	)	PUNCT
ejpam-4700	98	51	,	,	PUNCT
ejpam-4700	98	52	we	we	PRON
ejpam-4700	98	53	let	let	VERB
ejpam-4700	98	54	λ	λ	X
ejpam-4700	98	55	=	=	SYM
ejpam-4700	99	1	−ue2ξπi	−ue2ξπi	NOUN
ejpam-4700	99	2	and	and	CCONJ
ejpam-4700	99	3	k	k	PROPN
ejpam-4700	99	4	7→	7→	PROPN
ejpam-4700	99	5	−k	−k	PROPN
ejpam-4700	99	6	t	t	PROPN
ejpam-4700	99	7	(	(	PUNCT
ejpam-4700	99	8	x;u;−ue2ξπi	x;u;−ue2ξπi	NUM
ejpam-4700	99	9	)	)	PUNCT
ejpam-4700	100	1	=	=	SYM
ejpam-4700	100	2	u−	u−	PROPN
ejpam-4700	100	3	1	1	NUM
ejpam-4700	100	4	u	u	NOUN
ejpam-4700	100	5	2n	2n	NUM
ejpam-4700	100	6	(	(	PUNCT
ejpam-4700	100	7	−e−2ξπi	−e−2ξπi	NUM
ejpam-4700	100	8	)	)	PUNCT
ejpam-4700	100	9	1	1	NUM
ejpam-4700	100	10	2	2	NUM
ejpam-4700	100	11	x	x	SYM
ejpam-4700	100	12	n	n	X
ejpam-4700	100	13	!	!	PUNCT
ejpam-4700	100	14	∑	∑	ADV
ejpam-4700	100	15	k∈z	k∈z	X
ejpam-4700	100	16	e−iπkx	e−iπkx	PUNCT
ejpam-4700	101	1	[	[	X
ejpam-4700	101	2	−2kπi+	−2kπi+	ADJ
ejpam-4700	101	3	log(e−πi	log(e−πi	ADV
ejpam-4700	101	4	·	·	PUNCT
ejpam-4700	101	5	e−2ξπi	e−2ξπi	NOUN
ejpam-4700	101	6	)	)	PUNCT
ejpam-4700	101	7	]	]	PUNCT
ejpam-4700	102	1	n+1	n+1	PROPN
ejpam-4700	102	2	=	=	SYM
ejpam-4700	102	3	u−	u−	PROPN
ejpam-4700	102	4	1	1	NUM
ejpam-4700	102	5	u	u	NOUN
ejpam-4700	102	6	2n	2n	NUM
ejpam-4700	102	7	(	(	PUNCT
ejpam-4700	102	8	e−πi−2ξπi	e−πi−2ξπi	PROPN
ejpam-4700	102	9	)	)	PUNCT
ejpam-4700	102	10	1	1	NUM
ejpam-4700	102	11	2	2	NUM
ejpam-4700	102	12	x	x	SYM
ejpam-4700	102	13	n	n	X
ejpam-4700	102	14	!	!	PUNCT
ejpam-4700	102	15	∑	∑	ADV
ejpam-4700	102	16	k∈z	k∈z	X
ejpam-4700	102	17	e−iπkx	e−iπkx	PUNCT
ejpam-4700	103	1	[	[	X
ejpam-4700	103	2	−2kπi−	−2kπi−	X
ejpam-4700	103	3	πi−	πi−	PUNCT
ejpam-4700	103	4	2ξπi]n+1	2ξπi]n+1	ADJ
ejpam-4700	103	5	=	=	SYM
ejpam-4700	103	6	u−	u−	PROPN
ejpam-4700	103	7	1	1	NUM
ejpam-4700	103	8	u	u	NOUN
ejpam-4700	103	9	2n	2n	NUM
ejpam-4700	103	10	(	(	PUNCT
ejpam-4700	103	11	e−	e−	X
ejpam-4700	103	12	(	(	PUNCT
ejpam-4700	103	13	1	1	NUM
ejpam-4700	103	14	2	2	NUM
ejpam-4700	103	15	+	+	NOUN
ejpam-4700	103	16	ξ)πix	ξ)πix	ADJ
ejpam-4700	103	17	)	)	PUNCT
ejpam-4700	103	18	n	n	CCONJ
ejpam-4700	103	19	!	!	PUNCT
ejpam-4700	103	20	∑	∑	ADV
ejpam-4700	103	21	k∈z	k∈z	X
ejpam-4700	103	22	e−iπkx	e−iπkx	PROPN
ejpam-4700	103	23	(	(	PUNCT
ejpam-4700	103	24	−πi)n+1(2k	−πi)n+1(2k	PROPN
ejpam-4700	103	25	+	+	NUM
ejpam-4700	103	26	2ξ	2ξ	NUM
ejpam-4700	103	27	+	+	SYM
ejpam-4700	103	28	1)n+1	1)n+1	NUM
ejpam-4700	103	29	=	=	SYM
ejpam-4700	103	30	u−	u−	PROPN
ejpam-4700	103	31	1	1	NUM
ejpam-4700	103	32	u	u	NOUN
ejpam-4700	103	33	2n	2n	NUM
ejpam-4700	103	34	e−	e−	PROPN
ejpam-4700	103	35	(	(	PUNCT
ejpam-4700	103	36	1	1	NUM
ejpam-4700	103	37	2	2	NUM
ejpam-4700	103	38	+	+	NOUN
ejpam-4700	103	39	ξ)πix	ξ)πix	ADJ
ejpam-4700	103	40	(	(	PUNCT
ejpam-4700	103	41	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	103	42	n	n	X
ejpam-4700	103	43	!	!	PUNCT
ejpam-4700	103	44	∑	∑	ADV
ejpam-4700	103	45	k∈z	k∈z	X
ejpam-4700	103	46	e−iπkx	e−iπkx	PROPN
ejpam-4700	103	47	(	(	PUNCT
ejpam-4700	103	48	2k	2k	NOUN
ejpam-4700	103	49	+	+	CCONJ
ejpam-4700	103	50	2ξ	2ξ	NUM
ejpam-4700	103	51	+	+	SYM
ejpam-4700	103	52	1)n+1	1)n+1	NUM
ejpam-4700	103	53	r.	r.	PROPN
ejpam-4700	103	54	b.	b.	PROPN
ejpam-4700	103	55	corcino	corcino	PROPN
ejpam-4700	103	56	et	et	PROPN
ejpam-4700	103	57	al	al	PROPN
ejpam-4700	103	58	.	.	PUNCT
ejpam-4700	103	59	/	/	SYM
ejpam-4700	103	60	eur	eur	PROPN
ejpam-4700	103	61	.	.	PUNCT
ejpam-4700	104	1	j.	j.	PROPN
ejpam-4700	104	2	pure	pure	PROPN
ejpam-4700	104	3	appl	appl	PROPN
ejpam-4700	104	4	.	.	PROPN
ejpam-4700	104	5	math	math	PROPN
ejpam-4700	104	6	,	,	PUNCT
ejpam-4700	104	7	16	16	NUM
ejpam-4700	104	8	(	(	PUNCT
ejpam-4700	104	9	2	2	NUM
ejpam-4700	104	10	)	)	PUNCT
ejpam-4700	104	11	(	(	PUNCT
ejpam-4700	104	12	2023	2023	NUM
ejpam-4700	104	13	)	)	PUNCT
ejpam-4700	104	14	,	,	PUNCT
ejpam-4700	104	15	1005	1005	NUM
ejpam-4700	104	16	-	-	SYM
ejpam-4700	104	17	1023	1023	NUM
ejpam-4700	104	18	1011	1011	NUM
ejpam-4700	104	19	=	=	SYM
ejpam-4700	104	20	u−	u−	PROPN
ejpam-4700	104	21	1	1	NUM
ejpam-4700	104	22	u	u	NOUN
ejpam-4700	104	23	2n	2n	NUM
ejpam-4700	104	24	e−	e−	PROPN
ejpam-4700	104	25	(	(	PUNCT
ejpam-4700	104	26	1	1	NUM
ejpam-4700	104	27	2	2	NUM
ejpam-4700	104	28	+	+	NOUN
ejpam-4700	104	29	ξ)πix	ξ)πix	ADJ
ejpam-4700	104	30	(	(	PUNCT
ejpam-4700	104	31	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	104	32	n	n	X
ejpam-4700	104	33	!	!	PUNCT
ejpam-4700	105	1	[	[	PUNCT
ejpam-4700	105	2	∞∑	∞∑	PROPN
ejpam-4700	105	3	k=0	k=0	PROPN
ejpam-4700	105	4	e−πkx	e−πkx	NOUN
ejpam-4700	105	5	(	(	PUNCT
ejpam-4700	105	6	2k	2k	NOUN
ejpam-4700	105	7	+	+	CCONJ
ejpam-4700	105	8	2ξ	2ξ	NUM
ejpam-4700	105	9	+	+	SYM
ejpam-4700	105	10	1)n+1	1)n+1	NUM
ejpam-4700	106	1	+	+	CCONJ
ejpam-4700	106	2	∞∑	∞∑	NUM
ejpam-4700	106	3	k=1	k=1	X
ejpam-4700	106	4	eiπkx	eiπkx	PROPN
ejpam-4700	106	5	(	(	PUNCT
ejpam-4700	106	6	−2k	−2k	PROPN
ejpam-4700	106	7	+	+	CCONJ
ejpam-4700	106	8	2ξ	2ξ	NUM
ejpam-4700	106	9	+	+	SYM
ejpam-4700	106	10	1)n+1	1)n+1	NUM
ejpam-4700	106	11	]	]	PUNCT
ejpam-4700	107	1	=	=	SYM
ejpam-4700	107	2	u−	u−	PROPN
ejpam-4700	107	3	1	1	NUM
ejpam-4700	107	4	u	u	NOUN
ejpam-4700	107	5	2n	2n	NUM
ejpam-4700	107	6	e−	e−	PROPN
ejpam-4700	107	7	(	(	PUNCT
ejpam-4700	107	8	1	1	NUM
ejpam-4700	107	9	2	2	NUM
ejpam-4700	107	10	+	+	NOUN
ejpam-4700	107	11	ξ)πix	ξ)πix	ADJ
ejpam-4700	107	12	(	(	PUNCT
ejpam-4700	107	13	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	107	14	n	n	X
ejpam-4700	107	15	!	!	PUNCT
ejpam-4700	108	1	[	[	PUNCT
ejpam-4700	108	2	∞∑	∞∑	PROPN
ejpam-4700	108	3	k=0	k=0	PROPN
ejpam-4700	108	4	e−πkx	e−πkx	NOUN
ejpam-4700	108	5	(	(	PUNCT
ejpam-4700	108	6	2k	2k	NOUN
ejpam-4700	108	7	+	+	CCONJ
ejpam-4700	108	8	2ξ	2ξ	NUM
ejpam-4700	108	9	+	+	SYM
ejpam-4700	108	10	1)n+1	1)n+1	NUM
ejpam-4700	109	1	+	+	CCONJ
ejpam-4700	109	2	(	(	PUNCT
ejpam-4700	109	3	−1)n+1	−1)n+1	VERB
ejpam-4700	109	4	∞∑	∞∑	NUM
ejpam-4700	109	5	k=1	k=1	X
ejpam-4700	109	6	eiπkx	eiπkx	PROPN
ejpam-4700	109	7	(	(	PUNCT
ejpam-4700	109	8	2k	2k	NOUN
ejpam-4700	109	9	−	−	PROPN
ejpam-4700	109	10	2ξ	2ξ	NUM
ejpam-4700	109	11	−	−	PROPN
ejpam-4700	109	12	1)n+1	1)n+1	NUM
ejpam-4700	109	13	]	]	PUNCT
ejpam-4700	110	1	=	=	SYM
ejpam-4700	110	2	u−	u−	PROPN
ejpam-4700	110	3	1	1	NUM
ejpam-4700	110	4	u	u	NOUN
ejpam-4700	110	5	2n	2n	NUM
ejpam-4700	110	6	e−	e−	PROPN
ejpam-4700	110	7	(	(	PUNCT
ejpam-4700	110	8	1	1	NUM
ejpam-4700	110	9	2	2	NUM
ejpam-4700	110	10	+	+	NOUN
ejpam-4700	110	11	ξ)πix	ξ)πix	ADJ
ejpam-4700	110	12	(	(	PUNCT
ejpam-4700	110	13	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	110	14	[	[	PUNCT
ejpam-4700	110	15	∞∑	∞∑	PROPN
ejpam-4700	110	16	k=0	k=0	PROPN
ejpam-4700	110	17	e−iπkx	e−iπkx	X
ejpam-4700	110	18	n	n	X
ejpam-4700	110	19	!	!	PUNCT
ejpam-4700	111	1	(	(	PUNCT
ejpam-4700	111	2	2k	2k	NOUN
ejpam-4700	111	3	+	+	CCONJ
ejpam-4700	111	4	2ξ	2ξ	NUM
ejpam-4700	111	5	+	+	SYM
ejpam-4700	111	6	1)n+1	1)n+1	NUM
ejpam-4700	112	1	+	+	CCONJ
ejpam-4700	112	2	(	(	PUNCT
ejpam-4700	112	3	−1)n+1	−1)n+1	VERB
ejpam-4700	112	4	∞∑	∞∑	NUM
ejpam-4700	112	5	k=1	k=1	PUNCT
ejpam-4700	112	6	eiπkx	eiπkx	PROPN
ejpam-4700	112	7	n	n	PROPN
ejpam-4700	112	8	!	!	PUNCT
ejpam-4700	113	1	(	(	PUNCT
ejpam-4700	113	2	2k	2k	NOUN
ejpam-4700	113	3	−	−	PROPN
ejpam-4700	113	4	2ξ	2ξ	NUM
ejpam-4700	113	5	−	−	PROPN
ejpam-4700	113	6	1)n+1	1)n+1	NUM
ejpam-4700	113	7	]	]	PUNCT
ejpam-4700	113	8	where	where	SCONJ
ejpam-4700	113	9	(	(	PUNCT
ejpam-4700	113	10	2k	2k	NOUN
ejpam-4700	113	11	+	+	CCONJ
ejpam-4700	113	12	2ξ	2ξ	NUM
ejpam-4700	113	13	+	+	CCONJ
ejpam-4700	113	14	1	1	NUM
ejpam-4700	113	15	)	)	PUNCT
ejpam-4700	113	16	>	>	X
ejpam-4700	113	17	0	0	PUNCT
ejpam-4700	114	1	if	if	SCONJ
ejpam-4700	114	2	|ξ|	|ξ|	PROPN
ejpam-4700	114	3	<	<	X
ejpam-4700	114	4	1	1	NUM
ejpam-4700	114	5	2	2	NUM
ejpam-4700	114	6	,	,	PUNCT
ejpam-4700	114	7	ξ	ξ	PROPN
ejpam-4700	114	8	∈	∈	PROPN
ejpam-4700	114	9	r	r	NOUN
ejpam-4700	114	10	and	and	CCONJ
ejpam-4700	114	11	k	k	PROPN
ejpam-4700	114	12	≥	≥	PROPN
ejpam-4700	114	13	0	0	NUM
ejpam-4700	114	14	,	,	PUNCT
ejpam-4700	114	15	(	(	PUNCT
ejpam-4700	114	16	2k	2k	NOUN
ejpam-4700	115	1	−	−	PROPN
ejpam-4700	115	2	2ξ	2ξ	NUM
ejpam-4700	115	3	−	−	PROPN
ejpam-4700	115	4	1	1	NUM
ejpam-4700	115	5	)	)	PUNCT
ejpam-4700	115	6	>	>	X
ejpam-4700	115	7	0	0	PUNCT
ejpam-4700	116	1	if	if	SCONJ
ejpam-4700	116	2	|ξ|	|ξ|	PROPN
ejpam-4700	116	3	<	<	X
ejpam-4700	116	4	1	1	NUM
ejpam-4700	116	5	2	2	NUM
ejpam-4700	116	6	,	,	PUNCT
ejpam-4700	116	7	ξ	ξ	PROPN
ejpam-4700	116	8	∈	∈	PROPN
ejpam-4700	116	9	r	r	NOUN
ejpam-4700	116	10	and	and	CCONJ
ejpam-4700	116	11	k	k	PROPN
ejpam-4700	116	12	≥	≥	PROPN
ejpam-4700	116	13	0	0	NUM
ejpam-4700	116	14	.	.	PUNCT
ejpam-4700	117	1	we	we	PRON
ejpam-4700	117	2	then	then	ADV
ejpam-4700	117	3	apply	apply	VERB
ejpam-4700	117	4	the	the	DET
ejpam-4700	117	5	integral	integral	ADJ
ejpam-4700	117	6	formula	formula	NOUN
ejpam-4700	117	7	given	give	VERB
ejpam-4700	117	8	as∫	as∫	PROPN
ejpam-4700	117	9	∞	∞	PROPN
ejpam-4700	117	10	0	0	PUNCT
ejpam-4700	118	1	tne−atdt	tne−atdt	VERB
ejpam-4700	118	2	=	=	SYM
ejpam-4700	118	3	n	n	X
ejpam-4700	118	4	!	!	X
ejpam-4700	118	5	an+1	an+1	X
ejpam-4700	118	6	(	(	PUNCT
ejpam-4700	118	7	n	n	NOUN
ejpam-4700	118	8	=	=	SYM
ejpam-4700	118	9	0	0	NUM
ejpam-4700	118	10	,	,	PUNCT
ejpam-4700	118	11	1	1	NUM
ejpam-4700	118	12	,	,	PUNCT
ejpam-4700	118	13	...	...	PUNCT
ejpam-4700	118	14	;	;	PUNCT
ejpam-4700	118	15	r(a	r(a	X
ejpam-4700	118	16	)	)	PUNCT
ejpam-4700	118	17	>	>	X
ejpam-4700	118	18	0	0	NUM
ejpam-4700	118	19	)	)	PUNCT
ejpam-4700	118	20	so	so	SCONJ
ejpam-4700	118	21	that	that	SCONJ
ejpam-4700	118	22	,	,	PUNCT
ejpam-4700	118	23	t	t	PROPN
ejpam-4700	118	24	(	(	PUNCT
ejpam-4700	118	25	x;u;−ue2ξπi	x;u;−ue2ξπi	NUM
ejpam-4700	118	26	)	)	PUNCT
ejpam-4700	119	1	=	=	SYM
ejpam-4700	119	2	u−	u−	PROPN
ejpam-4700	119	3	1	1	NUM
ejpam-4700	119	4	u	u	NOUN
ejpam-4700	119	5	2n	2n	NUM
ejpam-4700	119	6	e−	e−	PROPN
ejpam-4700	119	7	(	(	PUNCT
ejpam-4700	119	8	1	1	NUM
ejpam-4700	119	9	2	2	NUM
ejpam-4700	119	10	+	+	NOUN
ejpam-4700	119	11	ξ)πix	ξ)πix	ADJ
ejpam-4700	119	12	(	(	PUNCT
ejpam-4700	119	13	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	119	14	[	[	PUNCT
ejpam-4700	119	15	∞∑	∞∑	PROPN
ejpam-4700	119	16	k=0	k=0	PROPN
ejpam-4700	119	17	e−iπkx	e−iπkx	X
ejpam-4700	119	18	∫	∫	PROPN
ejpam-4700	119	19	∞	∞	NUM
ejpam-4700	119	20	0	0	NUM
ejpam-4700	120	1	tne−(2k+2ξ+1)tdt	tne−(2k+2ξ+1)tdt	CCONJ
ejpam-4700	120	2	+	+	CCONJ
ejpam-4700	120	3	(	(	PUNCT
ejpam-4700	120	4	−1)n+1	−1)n+1	VERB
ejpam-4700	120	5	∞∑	∞∑	NUM
ejpam-4700	120	6	k=1	k=1	X
ejpam-4700	120	7	eiπkx	eiπkx	PROPN
ejpam-4700	120	8	∫	∫	PROPN
ejpam-4700	120	9	∞	∞	PROPN
ejpam-4700	120	10	0	0	NUM
ejpam-4700	121	1	tne−(2k−2ξ−1)tdt	tne−(2k−2ξ−1)tdt	VERB
ejpam-4700	121	2	]	]	X
ejpam-4700	122	1	=	=	SYM
ejpam-4700	122	2	u−	u−	PROPN
ejpam-4700	122	3	1	1	NUM
ejpam-4700	122	4	u	u	NOUN
ejpam-4700	122	5	2n	2n	NUM
ejpam-4700	122	6	e−	e−	PROPN
ejpam-4700	122	7	(	(	PUNCT
ejpam-4700	122	8	1	1	NUM
ejpam-4700	122	9	2	2	NUM
ejpam-4700	122	10	+	+	NOUN
ejpam-4700	122	11	ξ)πix	ξ)πix	ADJ
ejpam-4700	122	12	(	(	PUNCT
ejpam-4700	122	13	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	122	14	[	[	X
ejpam-4700	122	15	∫	∫	PROPN
ejpam-4700	122	16	∞	∞	NUM
ejpam-4700	122	17	0	0	NUM
ejpam-4700	123	1	tne−(2ξ+1)t	tne−(2ξ+1)t	PROPN
ejpam-4700	123	2	∞∑	∞∑	PRON
ejpam-4700	123	3	k=0	k=0	ADV
ejpam-4700	123	4	e−(iπx+2t)kdt	e−(iπx+2t)kdt	PROPN
ejpam-4700	123	5	+	+	CCONJ
ejpam-4700	123	6	(	(	PUNCT
ejpam-4700	123	7	−1)n+1	−1)n+1	VERB
ejpam-4700	123	8	∫	∫	X
ejpam-4700	123	9	∞	∞	NUM
ejpam-4700	123	10	0	0	NUM
ejpam-4700	124	1	e(2ξ+1)t	e(2ξ+1)t	PROPN
ejpam-4700	125	1	∞∑	∞∑	NUM
ejpam-4700	125	2	k=1	k=1	NOUN
ejpam-4700	125	3	e(iπx−2t)ktndt	e(iπx−2t)ktndt	PUNCT
ejpam-4700	125	4	]	]	PUNCT
ejpam-4700	126	1	=	=	SYM
ejpam-4700	126	2	u−	u−	PROPN
ejpam-4700	126	3	1	1	NUM
ejpam-4700	126	4	u	u	NOUN
ejpam-4700	126	5	2n	2n	NUM
ejpam-4700	126	6	e−	e−	PROPN
ejpam-4700	126	7	(	(	PUNCT
ejpam-4700	126	8	1	1	NUM
ejpam-4700	126	9	2	2	NUM
ejpam-4700	126	10	+	+	NOUN
ejpam-4700	126	11	ξ)πix	ξ)πix	ADJ
ejpam-4700	126	12	(	(	PUNCT
ejpam-4700	126	13	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	126	14	[	[	X
ejpam-4700	126	15	∫	∫	PROPN
ejpam-4700	126	16	∞	∞	NUM
ejpam-4700	126	17	0	0	NUM
ejpam-4700	127	1	tne−(2ξ+1)t	tne−(2ξ+1)t	NOUN
ejpam-4700	127	2	1	1	NUM
ejpam-4700	127	3	1−	1−	NUM
ejpam-4700	127	4	e−(iπx+2	e−(iπx+2	PROPN
ejpam-4700	127	5	t	t	PROPN
ejpam-4700	127	6	)	)	PUNCT
ejpam-4700	127	7	dt	dt	PUNCT
ejpam-4700	128	1	+	+	CCONJ
ejpam-4700	128	2	(	(	PUNCT
ejpam-4700	128	3	−1)n+1	−1)n+1	VERB
ejpam-4700	128	4	∫	∫	X
ejpam-4700	128	5	∞	∞	NUM
ejpam-4700	128	6	0	0	NUM
ejpam-4700	129	1	e(2ξ+1)t	e(2ξ+1)t	PROPN
ejpam-4700	129	2	eiπx−2	eiπx−2	PROPN
ejpam-4700	129	3	t	t	PROPN
ejpam-4700	129	4	1−	1−	NUM
ejpam-4700	129	5	eiπx−2	eiπx−2	ADP
ejpam-4700	129	6	t	t	NOUN
ejpam-4700	129	7	tndt	tndt	NOUN
ejpam-4700	130	1	=	=	SYM
ejpam-4700	130	2	u−	u−	PROPN
ejpam-4700	130	3	1	1	NUM
ejpam-4700	130	4	u	u	NOUN
ejpam-4700	130	5	2n	2n	NUM
ejpam-4700	130	6	e−	e−	PROPN
ejpam-4700	130	7	(	(	PUNCT
ejpam-4700	130	8	1	1	NUM
ejpam-4700	130	9	2	2	NUM
ejpam-4700	130	10	+	+	NOUN
ejpam-4700	130	11	ξ)πix	ξ)πix	ADJ
ejpam-4700	130	12	(	(	PUNCT
ejpam-4700	130	13	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	130	14	[	[	X
ejpam-4700	130	15	∫	∫	PROPN
ejpam-4700	130	16	∞	∞	NUM
ejpam-4700	130	17	0	0	NUM
ejpam-4700	131	1	tne−(2ξ+1)t	tne−(2ξ+1)t	PROPN
ejpam-4700	131	2	eiπx	eiπx	PROPN
ejpam-4700	131	3	eiπx	eiπx	PROPN
ejpam-4700	131	4	−	−	PROPN
ejpam-4700	132	1	e−2	e−2	PROPN
ejpam-4700	132	2	t	t	PROPN
ejpam-4700	132	3	dt	dt	X
ejpam-4700	132	4	+	+	CCONJ
ejpam-4700	132	5	(	(	PUNCT
ejpam-4700	132	6	−1)n+1	−1)n+1	VERB
ejpam-4700	132	7	∫	∫	X
ejpam-4700	132	8	∞	∞	NUM
ejpam-4700	132	9	0	0	NUM
ejpam-4700	133	1	e(2ξ+1)t	e(2ξ+1)t	PROPN
ejpam-4700	133	2	eiπx	eiπx	PROPN
ejpam-4700	133	3	e2t−eiπx	e2t−eiπx	X
ejpam-4700	133	4	t	t	PROPN
ejpam-4700	133	5	ndt	ndt	PROPN
ejpam-4700	133	6	r.	r.	PROPN
ejpam-4700	133	7	b.	b.	PROPN
ejpam-4700	133	8	corcino	corcino	PROPN
ejpam-4700	133	9	et	et	PROPN
ejpam-4700	133	10	al	al	PROPN
ejpam-4700	133	11	.	.	PUNCT
ejpam-4700	133	12	/	/	SYM
ejpam-4700	133	13	eur	eur	PROPN
ejpam-4700	133	14	.	.	PUNCT
ejpam-4700	134	1	j.	j.	PROPN
ejpam-4700	134	2	pure	pure	PROPN
ejpam-4700	134	3	appl	appl	PROPN
ejpam-4700	134	4	.	.	PROPN
ejpam-4700	134	5	math	math	PROPN
ejpam-4700	134	6	,	,	PUNCT
ejpam-4700	134	7	16	16	NUM
ejpam-4700	134	8	(	(	PUNCT
ejpam-4700	134	9	2	2	NUM
ejpam-4700	134	10	)	)	PUNCT
ejpam-4700	134	11	(	(	PUNCT
ejpam-4700	134	12	2023	2023	NUM
ejpam-4700	134	13	)	)	PUNCT
ejpam-4700	134	14	,	,	PUNCT
ejpam-4700	134	15	1005	1005	NUM
ejpam-4700	134	16	-	-	SYM
ejpam-4700	134	17	1023	1023	NUM
ejpam-4700	134	18	1012	1012	NUM
ejpam-4700	134	19	=	=	SYM
ejpam-4700	134	20	u−	u−	PROPN
ejpam-4700	134	21	1	1	NUM
ejpam-4700	134	22	u	u	NOUN
ejpam-4700	134	23	2n	2n	NUM
ejpam-4700	134	24	e−ξπix	e−ξπix	X
ejpam-4700	134	25	(	(	PUNCT
ejpam-4700	134	26	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	134	27	[	[	X
ejpam-4700	134	28	∫	∫	X
ejpam-4700	134	29	∞	∞	NUM
ejpam-4700	134	30	0	0	PUNCT
ejpam-4700	134	31	e	e	NOUN
ejpam-4700	134	32	1	1	NUM
ejpam-4700	134	33	2	2	NUM
ejpam-4700	134	34	πix	πix	NOUN
ejpam-4700	134	35	eπix	eπix	NOUN
ejpam-4700	134	36	−	−	PROPN
ejpam-4700	134	37	e−2	e−2	PROPN
ejpam-4700	134	38	t	t	PROPN
ejpam-4700	134	39	e−(2ξ+1)ttndt	e−(2ξ+1)ttndt	X
ejpam-4700	135	1	+	+	CCONJ
ejpam-4700	135	2	(	(	PUNCT
ejpam-4700	135	3	−1)n+1	−1)n+1	VERB
ejpam-4700	135	4	∫	∫	X
ejpam-4700	135	5	∞	∞	NOUN
ejpam-4700	135	6	0	0	PUNCT
ejpam-4700	135	7	e	e	NOUN
ejpam-4700	135	8	1	1	NUM
ejpam-4700	135	9	2	2	NUM
ejpam-4700	135	10	πix	πix	ADJ
ejpam-4700	135	11	e2	e2	PROPN
ejpam-4700	135	12	t	t	PROPN
ejpam-4700	135	13	−	−	PROPN
ejpam-4700	135	14	eiπx	eiπx	NOUN
ejpam-4700	135	15	e(2ξ+1)ttndt	e(2ξ+1)ttndt	ADV
ejpam-4700	135	16	]	]	PUNCT
ejpam-4700	135	17	=	=	SYM
ejpam-4700	135	18	u−	u−	PROPN
ejpam-4700	135	19	1	1	NUM
ejpam-4700	135	20	u	u	NOUN
ejpam-4700	135	21	2n	2n	NUM
ejpam-4700	135	22	e−ξπix	e−ξπix	X
ejpam-4700	135	23	(	(	PUNCT
ejpam-4700	135	24	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	136	1	[	[	X
ejpam-4700	136	2	∫	∫	PROPN
ejpam-4700	136	3	∞	∞	NUM
ejpam-4700	136	4	0	0	NUM
ejpam-4700	136	5	e−(2ξ+1)t	e−(2ξ+1)t	NOUN
ejpam-4700	136	6	e	e	NOUN
ejpam-4700	136	7	1	1	NUM
ejpam-4700	136	8	2	2	NUM
ejpam-4700	136	9	πix	πix	VERB
ejpam-4700	136	10	−	−	PROPN
ejpam-4700	136	11	e−2t−	e−2t−	PROPN
ejpam-4700	136	12	1	1	NUM
ejpam-4700	136	13	2	2	NUM
ejpam-4700	136	14	πix	πix	ADJ
ejpam-4700	136	15	tndt	tndt	INTJ
ejpam-4700	136	16	+	+	CCONJ
ejpam-4700	136	17	(	(	PUNCT
ejpam-4700	136	18	−1)n+1	−1)n+1	VERB
ejpam-4700	136	19	∫	∫	X
ejpam-4700	136	20	∞	∞	NUM
ejpam-4700	136	21	0	0	NUM
ejpam-4700	137	1	e(2ξ+1)t	e(2ξ+1)t	PROPN
ejpam-4700	137	2	e2t−	e2t−	NOUN
ejpam-4700	137	3	1	1	NUM
ejpam-4700	137	4	2	2	NUM
ejpam-4700	137	5	πix	πix	VERB
ejpam-4700	137	6	−	−	PROPN
ejpam-4700	137	7	e	e	NOUN
ejpam-4700	137	8	1	1	NUM
ejpam-4700	137	9	2	2	NUM
ejpam-4700	137	10	πix	πix	ADJ
ejpam-4700	137	11	tndt	tndt	ADP
ejpam-4700	137	12	]	]	PUNCT
ejpam-4700	138	1	=	=	SYM
ejpam-4700	138	2	u−	u−	PROPN
ejpam-4700	138	3	1	1	NUM
ejpam-4700	138	4	u	u	NOUN
ejpam-4700	138	5	2n	2n	NUM
ejpam-4700	138	6	e−ξπix	e−ξπix	X
ejpam-4700	138	7	(	(	PUNCT
ejpam-4700	138	8	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	138	9	[	[	X
ejpam-4700	138	10	∫	∫	PROPN
ejpam-4700	138	11	∞	∞	NUM
ejpam-4700	138	12	0	0	NUM
ejpam-4700	138	13	e−(2ξ+1)t	e−(2ξ+1)t	NOUN
ejpam-4700	138	14	e	e	NOUN
ejpam-4700	138	15	1	1	NUM
ejpam-4700	138	16	2	2	NUM
ejpam-4700	138	17	πix	πix	VERB
ejpam-4700	138	18	−	−	PROPN
ejpam-4700	138	19	e−2t−	e−2t−	PROPN
ejpam-4700	138	20	1	1	NUM
ejpam-4700	138	21	2	2	NUM
ejpam-4700	138	22	πix	πix	ADJ
ejpam-4700	138	23	·	·	PUNCT
ejpam-4700	138	24	(	(	PUNCT
ejpam-4700	138	25	e2	e2	PROPN
ejpam-4700	138	26	t	t	PROPN
ejpam-4700	138	27	−	−	PROPN
ejpam-4700	138	28	eπix	eπix	NOUN
ejpam-4700	138	29	)	)	PUNCT
ejpam-4700	139	1	e−	e−	ADV
ejpam-4700	139	2	1	1	NUM
ejpam-4700	139	3	2	2	NUM
ejpam-4700	139	4	πix	πix	ADJ
ejpam-4700	139	5	e2t−	e2t−	NOUN
ejpam-4700	139	6	1	1	NUM
ejpam-4700	139	7	2	2	NUM
ejpam-4700	139	8	πix	πix	VERB
ejpam-4700	139	9	−	−	PROPN
ejpam-4700	139	10	e	e	NOUN
ejpam-4700	139	11	1	1	NUM
ejpam-4700	139	12	2	2	NUM
ejpam-4700	139	13	πix	πix	ADJ
ejpam-4700	139	14	tndt	tndt	INTJ
ejpam-4700	139	15	+	+	CCONJ
ejpam-4700	139	16	(	(	PUNCT
ejpam-4700	139	17	−1)n+1	−1)n+1	VERB
ejpam-4700	139	18	∫	∫	X
ejpam-4700	139	19	∞	∞	NUM
ejpam-4700	139	20	0	0	NUM
ejpam-4700	140	1	e(2ξ+1)t	e(2ξ+1)t	PROPN
ejpam-4700	140	2	e2t−	e2t−	NOUN
ejpam-4700	140	3	1	1	NUM
ejpam-4700	140	4	2	2	NUM
ejpam-4700	140	5	πix	πix	VERB
ejpam-4700	140	6	−	−	PROPN
ejpam-4700	140	7	e	e	NOUN
ejpam-4700	140	8	1	1	NUM
ejpam-4700	140	9	2	2	NUM
ejpam-4700	140	10	πix	πix	ADJ
ejpam-4700	140	11	·	·	PUNCT
ejpam-4700	140	12	(	(	PUNCT
ejpam-4700	140	13	eπix	eπix	VERB
ejpam-4700	140	14	−	−	PROPN
ejpam-4700	140	15	e−2	e−2	PROPN
ejpam-4700	140	16	t	t	PROPN
ejpam-4700	140	17	)	)	PUNCT
ejpam-4700	141	1	e−	e−	ADV
ejpam-4700	141	2	1	1	NUM
ejpam-4700	141	3	2	2	NUM
ejpam-4700	141	4	πix	πix	ADJ
ejpam-4700	141	5	e	e	NOUN
ejpam-4700	141	6	1	1	NUM
ejpam-4700	141	7	2	2	NUM
ejpam-4700	141	8	πix	πix	VERB
ejpam-4700	141	9	−	−	PROPN
ejpam-4700	141	10	e−2t−	e−2t−	PROPN
ejpam-4700	141	11	1	1	NUM
ejpam-4700	141	12	2	2	NUM
ejpam-4700	141	13	πix	πix	ADJ
ejpam-4700	141	14	tndt	tndt	ADP
ejpam-4700	141	15	]	]	PUNCT
ejpam-4700	142	1	=	=	SYM
ejpam-4700	142	2	u−	u−	PROPN
ejpam-4700	142	3	1	1	NUM
ejpam-4700	142	4	u	u	NOUN
ejpam-4700	142	5	2n−1	2n−1	NUM
ejpam-4700	142	6	e−ξπix	e−ξπix	PROPN
ejpam-4700	142	7	(	(	PUNCT
ejpam-4700	142	8	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	142	9	[	[	X
ejpam-4700	142	10	∫	∫	PROPN
ejpam-4700	142	11	∞	∞	PROPN
ejpam-4700	142	12	0	0	NUM
ejpam-4700	142	13	e−(2ξ+1)t(e2	e−(2ξ+1)t(e2	PROPN
ejpam-4700	142	14	t	t	PROPN
ejpam-4700	142	15	−	−	PROPN
ejpam-4700	142	16	eπix)e−	eπix)e−	PROPN
ejpam-4700	142	17	1	1	NUM
ejpam-4700	142	18	2	2	NUM
ejpam-4700	142	19	πix	πix	ADJ
ejpam-4700	142	20	cosh(2t)−	cosh(2t)−	PROPN
ejpam-4700	142	21	cos(πx	cos(πx	NOUN
ejpam-4700	142	22	)	)	PUNCT
ejpam-4700	142	23	tndt	tndt	VERB
ejpam-4700	143	1	+	+	CCONJ
ejpam-4700	143	2	(	(	PUNCT
ejpam-4700	143	3	−1)n+1	−1)n+1	VERB
ejpam-4700	143	4	∫	∫	X
ejpam-4700	143	5	∞	∞	PROPN
ejpam-4700	143	6	0	0	PROPN
ejpam-4700	144	1	e(2ξ+1)t(eπix	e(2ξ+1)t(eπix	PROPN
ejpam-4700	144	2	−	−	PROPN
ejpam-4700	144	3	e2t)e−	e2t)e−	NOUN
ejpam-4700	144	4	1	1	NUM
ejpam-4700	144	5	2	2	NUM
ejpam-4700	144	6	πix	πix	ADJ
ejpam-4700	144	7	cosh(2t)−	cosh(2t)−	PROPN
ejpam-4700	144	8	cos(πx	cos(πx	NOUN
ejpam-4700	144	9	)	)	PUNCT
ejpam-4700	144	10	tndt	tndt	ADP
ejpam-4700	144	11	]	]	PUNCT
ejpam-4700	145	1	we	we	PRON
ejpam-4700	145	2	then	then	ADV
ejpam-4700	145	3	make	make	VERB
ejpam-4700	145	4	the	the	DET
ejpam-4700	145	5	substitution	substitution	NOUN
ejpam-4700	145	6	t	t	NOUN
ejpam-4700	145	7	=	=	SYM
ejpam-4700	145	8	πv	πv	PROPN
ejpam-4700	145	9	,	,	PUNCT
ejpam-4700	145	10	(	(	PUNCT
ejpam-4700	145	11	−1	−1	NOUN
ejpam-4700	145	12	/	/	SYM
ejpam-4700	145	13	i)n+1	i)n+1	ADJ
ejpam-4700	145	14	=	=	SYM
ejpam-4700	145	15	e(n+1)πi/2	e(n+1)πi/2	NOUN
ejpam-4700	145	16	and	and	CCONJ
ejpam-4700	145	17	(	(	PUNCT
ejpam-4700	145	18	−1)n+1	−1)n+1	NOUN
ejpam-4700	145	19	=	=	PUNCT
ejpam-4700	145	20	e−(n+1)πi	e−(n+1)πi	NOUN
ejpam-4700	145	21	,	,	PUNCT
ejpam-4700	145	22	we	we	PRON
ejpam-4700	145	23	find	find	VERB
ejpam-4700	145	24	that	that	SCONJ
ejpam-4700	145	25	t	t	PROPN
ejpam-4700	145	26	(	(	PUNCT
ejpam-4700	145	27	x;u;−ue2ξπi	x;u;−ue2ξπi	NUM
ejpam-4700	145	28	)	)	PUNCT
ejpam-4700	146	1	=	=	SYM
ejpam-4700	146	2	u−	u−	PROPN
ejpam-4700	146	3	1	1	NUM
ejpam-4700	146	4	u	u	NOUN
ejpam-4700	146	5	2n−1	2n−1	NUM
ejpam-4700	146	6	e−ξπix	e−ξπix	PROPN
ejpam-4700	146	7	(	(	PUNCT
ejpam-4700	146	8	−πi)n+1	−πi)n+1	PROPN
ejpam-4700	147	1	[	[	X
ejpam-4700	147	2	∫	∫	PROPN
ejpam-4700	147	3	∞	∞	NUM
ejpam-4700	147	4	0	0	NUM
ejpam-4700	148	1	e−(2ξ+1)πv(e2πv	e−(2ξ+1)πv(e2πv	CCONJ
ejpam-4700	148	2	−	−	PROPN
ejpam-4700	148	3	eπix)e−	eπix)e−	PROPN
ejpam-4700	148	4	1	1	NUM
ejpam-4700	148	5	2	2	NUM
ejpam-4700	148	6	πix	πix	ADJ
ejpam-4700	148	7	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	148	8	cos(πx	cos(πx	NOUN
ejpam-4700	148	9	)	)	PUNCT
ejpam-4700	148	10	(	(	PUNCT
ejpam-4700	148	11	πv)nπdv	πv)nπdv	NOUN
ejpam-4700	148	12	+	+	CCONJ
ejpam-4700	148	13	(	(	PUNCT
ejpam-4700	148	14	−1)n+1	−1)n+1	VERB
ejpam-4700	148	15	∫	∫	X
ejpam-4700	148	16	∞	∞	NUM
ejpam-4700	148	17	0	0	NUM
ejpam-4700	148	18	e(2ξ+1)πv(eπix	e(2ξ+1)πv(eπix	VERB
ejpam-4700	148	19	−	−	PROPN
ejpam-4700	148	20	e2πv)e−	e2πv)e−	VERB
ejpam-4700	148	21	1	1	NUM
ejpam-4700	148	22	2	2	NUM
ejpam-4700	148	23	πix	πix	ADJ
ejpam-4700	148	24	cosh(2πvs)−	cosh(2πvs)−	PROPN
ejpam-4700	148	25	cos(πx	cos(πx	NOUN
ejpam-4700	148	26	)	)	PUNCT
ejpam-4700	148	27	(	(	PUNCT
ejpam-4700	148	28	πv)nπdv	πv)nπdv	X
ejpam-4700	148	29	]	]	PUNCT
ejpam-4700	149	1	=	=	SYM
ejpam-4700	149	2	u−	u−	PROPN
ejpam-4700	149	3	1	1	NUM
ejpam-4700	149	4	u	u	NOUN
ejpam-4700	149	5	2n−1	2n−1	NUM
ejpam-4700	149	6	e	e	NOUN
ejpam-4700	149	7	−ξπix	−ξπix	X
ejpam-4700	149	8	πn+1	πn+1	NUM
ejpam-4700	149	9	[	[	X
ejpam-4700	149	10	∫	∫	X
ejpam-4700	149	11	∞	∞	NUM
ejpam-4700	149	12	0	0	NUM
ejpam-4700	149	13	e(n+1)πi/2(e2πv	e(n+1)πi/2(e2πv	NOUN
ejpam-4700	149	14	−	−	PROPN
ejpam-4700	149	15	eπix)e−(2ξ+1)πve−	eπix)e−(2ξ+1)πve−	PROPN
ejpam-4700	149	16	1	1	NUM
ejpam-4700	149	17	2	2	NUM
ejpam-4700	149	18	πix	πix	ADJ
ejpam-4700	149	19	cosh(2πvs)−	cosh(2πvs)−	PROPN
ejpam-4700	149	20	cos(πx	cos(πx	NOUN
ejpam-4700	149	21	)	)	PUNCT
ejpam-4700	149	22	πn+1vndv	πn+1vndv	PROPN
ejpam-4700	150	1	+	+	CCONJ
ejpam-4700	150	2	(	(	PUNCT
ejpam-4700	150	3	−1)n+1	−1)n+1	VERB
ejpam-4700	150	4	∫	∫	X
ejpam-4700	150	5	∞	∞	PROPN
ejpam-4700	150	6	0	0	PROPN
ejpam-4700	151	1	e−(n+1)πi/2(eπx	e−(n+1)πi/2(eπx	PROPN
ejpam-4700	151	2	−	−	PROPN
ejpam-4700	152	1	e2πv)e(2ξ+1)πve−	e2πv)e(2ξ+1)πve−	CCONJ
ejpam-4700	152	2	1	1	NUM
ejpam-4700	152	3	2	2	NUM
ejpam-4700	152	4	πix	πix	ADJ
ejpam-4700	152	5	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	152	6	cos(πx	cos(πx	NOUN
ejpam-4700	152	7	)	)	PUNCT
ejpam-4700	152	8	πn+1vndv	πn+1vndv	NOUN
ejpam-4700	152	9	]	]	PUNCT
ejpam-4700	152	10	=	=	SYM
ejpam-4700	152	11	u−	u−	PROPN
ejpam-4700	153	1	1	1	NUM
ejpam-4700	153	2	u	u	NOUN
ejpam-4700	153	3	2n−1e−ξπix	2n−1e−ξπix	NUM
ejpam-4700	154	1	[	[	X
ejpam-4700	154	2	∫	∫	X
ejpam-4700	154	3	∞	∞	NUM
ejpam-4700	154	4	0	0	NUM
ejpam-4700	154	5	eπve	eπve	NOUN
ejpam-4700	155	1	i	i	PRON
ejpam-4700	155	2	[	[	PUNCT
ejpam-4700	155	3	−π	−π	PROPN
ejpam-4700	155	4	2	2	NUM
ejpam-4700	155	5	x+	x+	NUM
ejpam-4700	155	6	(	(	PUNCT
ejpam-4700	155	7	n+1)π	n+1)π	PROPN
ejpam-4700	155	8	2	2	NUM
ejpam-4700	155	9	]	]	PUNCT
ejpam-4700	155	10	e−2ξπv	e−2ξπv	ADP
ejpam-4700	155	11	−	−	PROPN
ejpam-4700	155	12	e−πve	e−πve	NOUN
ejpam-4700	156	1	i	i	PRON
ejpam-4700	156	2	[	[	PUNCT
ejpam-4700	156	3	π	π	PROPN
ejpam-4700	156	4	2	2	NUM
ejpam-4700	156	5	x+	x+	PUNCT
ejpam-4700	156	6	(	(	PUNCT
ejpam-4700	156	7	n+1)π	n+1)π	PROPN
ejpam-4700	156	8	2	2	NUM
ejpam-4700	156	9	]	]	PUNCT
ejpam-4700	156	10	e−2ξπv	e−2ξπv	ADP
ejpam-4700	156	11	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	156	12	cos(πx	cos(πx	NOUN
ejpam-4700	156	13	)	)	PUNCT
ejpam-4700	156	14	vndv	vndv	NOUN
ejpam-4700	156	15	+	+	CCONJ
ejpam-4700	157	1	∫	∫	PROPN
ejpam-4700	157	2	∞	∞	PROPN
ejpam-4700	157	3	0	0	NUM
ejpam-4700	157	4	eπve	eπve	NOUN
ejpam-4700	158	1	i	i	PRON
ejpam-4700	158	2	[	[	PUNCT
ejpam-4700	158	3	π	π	PROPN
ejpam-4700	158	4	2	2	NUM
ejpam-4700	158	5	x−	x−	PROPN
ejpam-4700	158	6	(	(	PUNCT
ejpam-4700	158	7	n+1)π	n+1)π	PROPN
ejpam-4700	158	8	2	2	NUM
ejpam-4700	158	9	]	]	PUNCT
ejpam-4700	158	10	e2ξπv	e2ξπv	PROPN
ejpam-4700	158	11	−	−	PROPN
ejpam-4700	158	12	e−πve	e−πve	NOUN
ejpam-4700	159	1	i	i	PRON
ejpam-4700	159	2	[	[	PUNCT
ejpam-4700	159	3	−π	−π	PROPN
ejpam-4700	159	4	2	2	NUM
ejpam-4700	159	5	x−	x−	PROPN
ejpam-4700	159	6	(	(	PUNCT
ejpam-4700	159	7	n+1)π	n+1)π	PROPN
ejpam-4700	159	8	2	2	NUM
ejpam-4700	159	9	]	]	PUNCT
ejpam-4700	159	10	e2ξπv	e2ξπv	PROPN
ejpam-4700	159	11	cosh(2πvs)−	cosh(2πvs)−	PROPN
ejpam-4700	159	12	cos(πx	cos(πx	NOUN
ejpam-4700	159	13	)	)	PUNCT
ejpam-4700	159	14	vndv	vndv	NOUN
ejpam-4700	159	15	]	]	PUNCT
ejpam-4700	159	16	r.	r.	PROPN
ejpam-4700	159	17	b.	b.	PROPN
ejpam-4700	159	18	corcino	corcino	PROPN
ejpam-4700	159	19	et	et	PROPN
ejpam-4700	159	20	al	al	PROPN
ejpam-4700	159	21	.	.	PUNCT
ejpam-4700	159	22	/	/	SYM
ejpam-4700	159	23	eur	eur	PROPN
ejpam-4700	159	24	.	.	PUNCT
ejpam-4700	160	1	j.	j.	PROPN
ejpam-4700	160	2	pure	pure	PROPN
ejpam-4700	160	3	appl	appl	PROPN
ejpam-4700	160	4	.	.	PROPN
ejpam-4700	160	5	math	math	PROPN
ejpam-4700	160	6	,	,	PUNCT
ejpam-4700	160	7	16	16	NUM
ejpam-4700	160	8	(	(	PUNCT
ejpam-4700	160	9	2	2	NUM
ejpam-4700	160	10	)	)	PUNCT
ejpam-4700	160	11	(	(	PUNCT
ejpam-4700	160	12	2023	2023	NUM
ejpam-4700	160	13	)	)	PUNCT
ejpam-4700	160	14	,	,	PUNCT
ejpam-4700	160	15	1005	1005	NUM
ejpam-4700	160	16	-	-	SYM
ejpam-4700	160	17	1023	1023	NUM
ejpam-4700	160	18	1013	1013	NUM
ejpam-4700	160	19	let	let	VERB
ejpam-4700	160	20	a	a	DET
ejpam-4700	160	21	=	=	NOUN
ejpam-4700	160	22	−π	−π	NUM
ejpam-4700	160	23	2x+	2x+	NUM
ejpam-4700	160	24	(	(	PUNCT
ejpam-4700	160	25	n+1)π	n+1)π	PROPN
ejpam-4700	160	26	2	2	NUM
ejpam-4700	160	27	and	and	CCONJ
ejpam-4700	160	28	b	b	NOUN
ejpam-4700	160	29	=	=	SYM
ejpam-4700	160	30	π	π	PROPN
ejpam-4700	160	31	2x+	2x+	NUM
ejpam-4700	160	32	(	(	PUNCT
ejpam-4700	160	33	n+1)π	n+1)π	PROPN
ejpam-4700	160	34	2	2	NUM
ejpam-4700	160	35	.	.	PUNCT
ejpam-4700	161	1	so	so	ADV
ejpam-4700	161	2	that	that	SCONJ
ejpam-4700	161	3	,	,	PUNCT
ejpam-4700	161	4	t	t	PROPN
ejpam-4700	161	5	(	(	PUNCT
ejpam-4700	161	6	x;u;−ue2ξπi	x;u;−ue2ξπi	NUM
ejpam-4700	161	7	)	)	PUNCT
ejpam-4700	162	1	=	=	SYM
ejpam-4700	162	2	u−	u−	PROPN
ejpam-4700	162	3	1	1	NUM
ejpam-4700	162	4	u	u	NOUN
ejpam-4700	162	5	2n−1e−ξπix	2n−1e−ξπix	NUM
ejpam-4700	163	1	[	[	X
ejpam-4700	163	2	∫	∫	X
ejpam-4700	163	3	∞	∞	NUM
ejpam-4700	163	4	0	0	NUM
ejpam-4700	163	5	eπveiae−2ξπv	eπveiae−2ξπv	ADJ
ejpam-4700	163	6	−	−	PROPN
ejpam-4700	163	7	e−πveibe−2ξπv	e−πveibe−2ξπv	PROPN
ejpam-4700	163	8	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	163	9	cos(πx	cos(πx	NOUN
ejpam-4700	163	10	)	)	PUNCT
ejpam-4700	163	11	vndv	vndv	NOUN
ejpam-4700	163	12	+	+	CCONJ
ejpam-4700	163	13	∫	∫	PROPN
ejpam-4700	163	14	∞	∞	NOUN
ejpam-4700	163	15	0	0	X
ejpam-4700	164	1	eπve−iae2ξπv	eπve−iae2ξπv	PROPN
ejpam-4700	164	2	−	−	PROPN
ejpam-4700	164	3	e−πve−ibe2ξπv	e−πve−ibe2ξπv	PROPN
ejpam-4700	164	4	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	164	5	cos(πx	cos(πx	NOUN
ejpam-4700	164	6	)	)	PUNCT
ejpam-4700	164	7	vndv	vndv	NOUN
ejpam-4700	164	8	]	]	PUNCT
ejpam-4700	165	1	=	=	SYM
ejpam-4700	165	2	u−	u−	PROPN
ejpam-4700	165	3	1	1	NUM
ejpam-4700	165	4	u	u	NOUN
ejpam-4700	165	5	2n−1e−ξπix	2n−1e−ξπix	NUM
ejpam-4700	166	1	[	[	X
ejpam-4700	166	2	∫	∫	X
ejpam-4700	166	3	∞	∞	NUM
ejpam-4700	166	4	0	0	NUM
ejpam-4700	167	1	(	(	PUNCT
ejpam-4700	167	2	eπv	eπv	PROPN
ejpam-4700	167	3	cosa−	cosa−	NOUN
ejpam-4700	167	4	e−πv	e−πv	ADJ
ejpam-4700	167	5	cosb)(e−2ξπv	cosb)(e−2ξπv	PUNCT
ejpam-4700	168	1	+	+	CCONJ
ejpam-4700	168	2	e2ξπv	e2ξπv	ADJ
ejpam-4700	168	3	)	)	PUNCT
ejpam-4700	168	4	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	168	5	cos(πx	cos(πx	NOUN
ejpam-4700	168	6	)	)	PUNCT
ejpam-4700	168	7	vndv	vndv	NOUN
ejpam-4700	169	1	+	+	CCONJ
ejpam-4700	170	1	i	i	PRON
ejpam-4700	170	2	∫	∫	VERB
ejpam-4700	170	3	∞	∞	PROPN
ejpam-4700	170	4	0	0	NUM
ejpam-4700	170	5	(	(	PUNCT
ejpam-4700	170	6	eπv	eπv	PROPN
ejpam-4700	170	7	sina−	sina−	NOUN
ejpam-4700	170	8	e−πv	e−πv	PROPN
ejpam-4700	170	9	sinb)(e2ξπv	sinb)(e2ξπv	NOUN
ejpam-4700	170	10	−	−	ADP
ejpam-4700	170	11	e2ξπv	e2ξπv	PROPN
ejpam-4700	170	12	)	)	PUNCT
ejpam-4700	170	13	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	170	14	cos(πx	cos(πx	NOUN
ejpam-4700	170	15	)	)	PUNCT
ejpam-4700	170	16	vndv	vndv	NOUN
ejpam-4700	170	17	]	]	PUNCT
ejpam-4700	171	1	=	=	SYM
ejpam-4700	171	2	u−	u−	PROPN
ejpam-4700	171	3	1	1	NUM
ejpam-4700	171	4	u	u	NOUN
ejpam-4700	171	5	2n−1e−ξπix	2n−1e−ξπix	NUM
ejpam-4700	172	1	[	[	X
ejpam-4700	172	2	∫	∫	X
ejpam-4700	172	3	∞	∞	NUM
ejpam-4700	172	4	0	0	NUM
ejpam-4700	173	1	(	(	PUNCT
ejpam-4700	173	2	eπv	eπv	PROPN
ejpam-4700	173	3	cosa−	cosa−	X
ejpam-4700	173	4	e−πv	e−πv	PROPN
ejpam-4700	173	5	cosb)(cosh(2ξπv	cosb)(cosh(2ξπv	NOUN
ejpam-4700	173	6	)	)	PUNCT
ejpam-4700	173	7	)	)	PUNCT
ejpam-4700	173	8	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	173	9	cos(πx	cos(πx	NOUN
ejpam-4700	173	10	)	)	PUNCT
ejpam-4700	173	11	vndv	vndv	NOUN
ejpam-4700	174	1	+	+	CCONJ
ejpam-4700	175	1	i	i	PRON
ejpam-4700	175	2	∫	∫	VERB
ejpam-4700	175	3	∞	∞	PROPN
ejpam-4700	175	4	0	0	NUM
ejpam-4700	175	5	(	(	PUNCT
ejpam-4700	175	6	eπv	eπv	PROPN
ejpam-4700	175	7	sina−	sina−	VERB
ejpam-4700	175	8	e−πv	e−πv	ADJ
ejpam-4700	175	9	sinb)(sinh(2ξπv	sinb)(sinh(2ξπv	NOUN
ejpam-4700	175	10	)	)	PUNCT
ejpam-4700	175	11	)	)	PUNCT
ejpam-4700	175	12	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	175	13	cos(πx	cos(πx	NOUN
ejpam-4700	175	14	)	)	PUNCT
ejpam-4700	175	15	vndv	vndv	NOUN
ejpam-4700	175	16	]	]	PUNCT
ejpam-4700	175	17	simplifying	simplify	VERB
ejpam-4700	175	18	the	the	DET
ejpam-4700	175	19	above	above	ADJ
ejpam-4700	175	20	equation	equation	NOUN
ejpam-4700	175	21	gives	give	VERB
ejpam-4700	175	22	us	we	PRON
ejpam-4700	175	23	the	the	DET
ejpam-4700	175	24	integral	integral	ADJ
ejpam-4700	175	25	representation	representation	NOUN
ejpam-4700	175	26	of	of	ADP
ejpam-4700	175	27	the	the	DET
ejpam-4700	175	28	apostol	apostol	NOUN
ejpam-4700	175	29	-	-	PUNCT
ejpam-4700	175	30	frobeniustangent	frobeniustangent	ADJ
ejpam-4700	175	31	polynomials	polynomial	NOUN
ejpam-4700	175	32	t	t	PROPN
ejpam-4700	175	33	(	(	PUNCT
ejpam-4700	175	34	x;u;−ue2ξπi	x;u;−ue2ξπi	NUM
ejpam-4700	175	35	)	)	PUNCT
ejpam-4700	176	1	=	=	SYM
ejpam-4700	176	2	u−	u−	PROPN
ejpam-4700	176	3	1	1	NUM
ejpam-4700	176	4	u	u	NOUN
ejpam-4700	176	5	2n−1e−ξπix	2n−1e−ξπix	NUM
ejpam-4700	177	1	[	[	X
ejpam-4700	177	2	∫	∫	X
ejpam-4700	177	3	∞	∞	PROPN
ejpam-4700	177	4	0	0	NUM
ejpam-4700	177	5	m(n;x	m(n;x	PROPN
ejpam-4700	177	6	;	;	PUNCT
ejpam-4700	177	7	v	v	NOUN
ejpam-4700	177	8	)	)	PUNCT
ejpam-4700	177	9	cosh(2ξπv	cosh(2ξπv	PROPN
ejpam-4700	177	10	)	)	PUNCT
ejpam-4700	177	11	+	+	NUM
ejpam-4700	177	12	in(n;x	in(n;x	PROPN
ejpam-4700	177	13	;	;	PUNCT
ejpam-4700	177	14	v	v	X
ejpam-4700	177	15	)	)	PUNCT
ejpam-4700	177	16	sinh(2ξπv	sinh(2ξπv	PROPN
ejpam-4700	177	17	)	)	PUNCT
ejpam-4700	177	18	cosh(2πvs.)−	cosh(2πvs.)−	PROPN
ejpam-4700	177	19	cos(πx	cos(πx	NOUN
ejpam-4700	177	20	)	)	PUNCT
ejpam-4700	177	21	vndv	vndv	NOUN
ejpam-4700	177	22	]	]	PUNCT
ejpam-4700	177	23	(	(	PUNCT
ejpam-4700	177	24	15	15	NUM
ejpam-4700	177	25	)	)	PUNCT
ejpam-4700	177	26	where	where	SCONJ
ejpam-4700	177	27	m(n;x	m(n;x	NOUN
ejpam-4700	177	28	;	;	PUNCT
ejpam-4700	177	29	v	v	NOUN
ejpam-4700	177	30	)	)	PUNCT
ejpam-4700	177	31	=	=	SYM
ejpam-4700	177	32	eπv	eπv	PROPN
ejpam-4700	177	33	cos	cos	INTJ
ejpam-4700	177	34	(	(	PUNCT
ejpam-4700	177	35	−π	−π	ADV
ejpam-4700	177	36	2	2	NUM
ejpam-4700	177	37	x+	x+	X
ejpam-4700	177	38	(	(	PUNCT
ejpam-4700	177	39	n+	n+	NUM
ejpam-4700	177	40	1)π	1)π	NUM
ejpam-4700	177	41	2	2	NUM
ejpam-4700	177	42	)	)	PUNCT
ejpam-4700	177	43	−	−	PROPN
ejpam-4700	178	1	e−πv	e−πv	PROPN
ejpam-4700	178	2	cos	cos	PROPN
ejpam-4700	178	3	(	(	PUNCT
ejpam-4700	178	4	π	π	PROPN
ejpam-4700	178	5	2	2	NUM
ejpam-4700	178	6	x+	x+	X
ejpam-4700	178	7	(	(	PUNCT
ejpam-4700	178	8	n+	n+	NUM
ejpam-4700	178	9	1)π	1)π	NUM
ejpam-4700	178	10	2	2	NUM
ejpam-4700	178	11	)	)	PUNCT
ejpam-4700	178	12	n(nn;x	n(nn;x	PROPN
ejpam-4700	178	13	;	;	PUNCT
ejpam-4700	178	14	v	v	NOUN
ejpam-4700	178	15	)	)	PUNCT
ejpam-4700	178	16	=	=	SYM
ejpam-4700	178	17	eπv	eπv	ADJ
ejpam-4700	178	18	sin	sin	NOUN
ejpam-4700	178	19	(	(	PUNCT
ejpam-4700	178	20	−π	−π	ADV
ejpam-4700	178	21	2	2	NUM
ejpam-4700	178	22	x+	x+	X
ejpam-4700	178	23	(	(	PUNCT
ejpam-4700	178	24	n+	n+	NUM
ejpam-4700	178	25	1)π	1)π	NUM
ejpam-4700	178	26	2	2	NUM
ejpam-4700	178	27	)	)	PUNCT
ejpam-4700	178	28	−	−	PROPN
ejpam-4700	179	1	e−πv	e−πv	ADJ
ejpam-4700	179	2	sin	sin	NOUN
ejpam-4700	179	3	(	(	PUNCT
ejpam-4700	179	4	π	π	PROPN
ejpam-4700	179	5	2	2	NUM
ejpam-4700	179	6	x+	x+	X
ejpam-4700	179	7	(	(	PUNCT
ejpam-4700	179	8	n+	n+	NUM
ejpam-4700	179	9	1)π	1)π	NUM
ejpam-4700	179	10	2	2	NUM
ejpam-4700	179	11	)	)	PUNCT
ejpam-4700	179	12	2.2	2.2	NUM
ejpam-4700	179	13	.	.	PUNCT
ejpam-4700	180	1	fourier	fouri	ADJ
ejpam-4700	180	2	expansion	expansion	NOUN
ejpam-4700	180	3	of	of	ADP
ejpam-4700	180	4	apostol	apostol	NOUN
ejpam-4700	180	5	-	-	PUNCT
ejpam-4700	180	6	frobenius	frobenius	NOUN
ejpam-4700	180	7	-	-	PUNCT
ejpam-4700	180	8	tangent	tangent	NOUN
ejpam-4700	180	9	polynomials	polynomial	NOUN
ejpam-4700	180	10	of	of	ADP
ejpam-4700	180	11	higherorder	higherorder	NOUN
ejpam-4700	180	12	the	the	DET
ejpam-4700	180	13	apostol	apostol	NOUN
ejpam-4700	180	14	-	-	PUNCT
ejpam-4700	180	15	frobenius	frobenius	NOUN
ejpam-4700	180	16	-	-	PUNCT
ejpam-4700	180	17	tangent	tangent	NOUN
ejpam-4700	180	18	polynomials	polynomial	NOUN
ejpam-4700	180	19	of	of	ADP
ejpam-4700	180	20	higher	high	ADJ
ejpam-4700	180	21	order	order	NOUN
ejpam-4700	180	22	,	,	PUNCT
ejpam-4700	180	23	denoted	denote	VERB
ejpam-4700	180	24	by	by	ADP
ejpam-4700	180	25	t	t	PROPN
ejpam-4700	180	26	(	(	PUNCT
ejpam-4700	180	27	r	r	NOUN
ejpam-4700	180	28	)	)	PUNCT
ejpam-4700	180	29	n	n	CCONJ
ejpam-4700	180	30	(	(	PUNCT
ejpam-4700	180	31	x;u	x;u	PROPN
ejpam-4700	180	32	,	,	PUNCT
ejpam-4700	180	33	λ	λ	PROPN
ejpam-4700	180	34	)	)	PUNCT
ejpam-4700	180	35	,	,	PUNCT
ejpam-4700	180	36	are	be	AUX
ejpam-4700	180	37	defined	define	VERB
ejpam-4700	180	38	as	as	ADP
ejpam-4700	180	39	coefficients	coefficient	NOUN
ejpam-4700	180	40	of	of	ADP
ejpam-4700	180	41	the	the	DET
ejpam-4700	180	42	following	follow	VERB
ejpam-4700	180	43	generating	generate	VERB
ejpam-4700	180	44	function	function	NOUN
ejpam-4700	180	45	∞∑	∞∑	PROPN
ejpam-4700	180	46	n=0	n=0	SYM
ejpam-4700	180	47	t	t	NOUN
ejpam-4700	180	48	(	(	PUNCT
ejpam-4700	180	49	r	r	NOUN
ejpam-4700	180	50	)	)	PUNCT
ejpam-4700	180	51	n	n	CCONJ
ejpam-4700	180	52	(	(	PUNCT
ejpam-4700	180	53	x;u	x;u	PROPN
ejpam-4700	180	54	,	,	PUNCT
ejpam-4700	180	55	λ	λ	NOUN
ejpam-4700	180	56	)	)	PUNCT
ejpam-4700	180	57	tn	tn	PROPN
ejpam-4700	180	58	n	n	PROPN
ejpam-4700	180	59	!	!	PUNCT
ejpam-4700	181	1	=	=	PUNCT
ejpam-4700	181	2	(	(	PUNCT
ejpam-4700	181	3	1−	1−	NUM
ejpam-4700	181	4	u	u	NOUN
ejpam-4700	181	5	λe2	λe2	PROPN
ejpam-4700	181	6	t	t	PROPN
ejpam-4700	181	7	−	−	PROPN
ejpam-4700	181	8	u	u	NOUN
ejpam-4700	181	9	)	)	PUNCT
ejpam-4700	181	10	r	r	NOUN
ejpam-4700	181	11	ext	ext	NOUN
ejpam-4700	181	12	(	(	PUNCT
ejpam-4700	181	13	16	16	NUM
ejpam-4700	181	14	)	)	PUNCT
ejpam-4700	181	15	where	where	SCONJ
ejpam-4700	181	16	r	r	NOUN
ejpam-4700	181	17	≥	≥	NUM
ejpam-4700	181	18	1	1	NUM
ejpam-4700	181	19	,	,	PUNCT
ejpam-4700	181	20	u	u	NOUN
ejpam-4700	181	21	,	,	PUNCT
ejpam-4700	181	22	λ	λ	PROPN
ejpam-4700	181	23	∈	∈	PROPN
ejpam-4700	181	24	c	c	NOUN
ejpam-4700	181	25	with	with	ADP
ejpam-4700	181	26	u	u	NOUN
ejpam-4700	181	27	̸=	̸=	PROPN
ejpam-4700	181	28	1	1	NUM
ejpam-4700	181	29	,	,	PUNCT
ejpam-4700	181	30	λ	λ	PROPN
ejpam-4700	181	31	̸=	̸=	PROPN
ejpam-4700	181	32	1	1	NUM
ejpam-4700	181	33	and	and	CCONJ
ejpam-4700	181	34	u	u	PROPN
ejpam-4700	181	35	̸=	̸=	PROPN
ejpam-4700	181	36	λ	λ	PROPN
ejpam-4700	181	37	.	.	PUNCT
ejpam-4700	182	1	in	in	ADP
ejpam-4700	182	2	this	this	DET
ejpam-4700	182	3	section	section	NOUN
ejpam-4700	182	4	,	,	PUNCT
ejpam-4700	182	5	we	we	PRON
ejpam-4700	182	6	derive	derive	VERB
ejpam-4700	182	7	the	the	DET
ejpam-4700	182	8	fourier	fourier	ADJ
ejpam-4700	182	9	expansion	expansion	NOUN
ejpam-4700	182	10	for	for	ADP
ejpam-4700	182	11	apostol	apostol	NOUN
ejpam-4700	182	12	-	-	PUNCT
ejpam-4700	182	13	frobenius	frobenius	NOUN
ejpam-4700	182	14	-	-	PUNCT
ejpam-4700	182	15	tangent	tangent	NOUN
ejpam-4700	182	16	polynomials	polynomial	NOUN
ejpam-4700	182	17	of	of	ADP
ejpam-4700	182	18	higher	high	ADJ
ejpam-4700	182	19	order	order	NOUN
ejpam-4700	182	20	as	as	SCONJ
ejpam-4700	182	21	shown	show	VERB
ejpam-4700	182	22	in	in	ADP
ejpam-4700	182	23	the	the	DET
ejpam-4700	182	24	following	following	NOUN
ejpam-4700	182	25	theorem	theorem	PROPN
ejpam-4700	182	26	.	.	PROPN
ejpam-4700	182	27	r.	r.	PROPN
ejpam-4700	182	28	b.	b.	PROPN
ejpam-4700	182	29	corcino	corcino	PROPN
ejpam-4700	182	30	et	et	PROPN
ejpam-4700	182	31	al	al	PROPN
ejpam-4700	182	32	.	.	PUNCT
ejpam-4700	182	33	/	/	SYM
ejpam-4700	182	34	eur	eur	PROPN
ejpam-4700	182	35	.	.	PUNCT
ejpam-4700	183	1	j.	j.	PROPN
ejpam-4700	183	2	pure	pure	PROPN
ejpam-4700	183	3	appl	appl	PROPN
ejpam-4700	183	4	.	.	PROPN
ejpam-4700	183	5	math	math	PROPN
ejpam-4700	183	6	,	,	PUNCT
ejpam-4700	183	7	16	16	NUM
ejpam-4700	183	8	(	(	PUNCT
ejpam-4700	183	9	2	2	NUM
ejpam-4700	183	10	)	)	PUNCT
ejpam-4700	183	11	(	(	PUNCT
ejpam-4700	183	12	2023	2023	NUM
ejpam-4700	183	13	)	)	PUNCT
ejpam-4700	183	14	,	,	PUNCT
ejpam-4700	183	15	1005	1005	NUM
ejpam-4700	183	16	-	-	SYM
ejpam-4700	183	17	1023	1023	NUM
ejpam-4700	183	18	1014	1014	NUM
ejpam-4700	183	19	theorem	theorem	VERB
ejpam-4700	183	20	3	3	NUM
ejpam-4700	183	21	.	.	PUNCT
ejpam-4700	184	1	for	for	ADP
ejpam-4700	184	2	0	0	NUM
ejpam-4700	184	3	≤	≤	NUM
ejpam-4700	184	4	x	x	SYM
ejpam-4700	184	5	≤	≤	NUM
ejpam-4700	184	6	1	1	NUM
ejpam-4700	184	7	,	,	PUNCT
ejpam-4700	184	8	t	t	PROPN
ejpam-4700	184	9	(	(	PUNCT
ejpam-4700	184	10	r	r	NOUN
ejpam-4700	184	11	)	)	PUNCT
ejpam-4700	184	12	n	n	CCONJ
ejpam-4700	184	13	(	(	PUNCT
ejpam-4700	184	14	x;u	x;u	PROPN
ejpam-4700	184	15	,	,	PUNCT
ejpam-4700	184	16	λ	λ	NOUN
ejpam-4700	184	17	)	)	PUNCT
ejpam-4700	184	18	=	=	PUNCT
ejpam-4700	184	19	−n	−n	ADJ
ejpam-4700	184	20	!	!	PUNCT
ejpam-4700	185	1	∑	∑	ADV
ejpam-4700	185	2	k∈z	k∈z	PROPN
ejpam-4700	185	3	(	(	PUNCT
ejpam-4700	185	4	1−	1−	NUM
ejpam-4700	185	5	u	u	NOUN
ejpam-4700	185	6	2u	2u	NOUN
ejpam-4700	185	7	)	)	PUNCT
ejpam-4700	185	8	r	r	NOUN
ejpam-4700	185	9	r−1∑	r−1∑	PROPN
ejpam-4700	185	10	j=0	j=0	PROPN
ejpam-4700	185	11	(	(	PUNCT
ejpam-4700	185	12	−1)j−12j	−1)j−12j	NOUN
ejpam-4700	185	13	(	(	PUNCT
ejpam-4700	185	14	n+	n+	INTJ
ejpam-4700	185	15	r	r	NOUN
ejpam-4700	185	16	−	−	PROPN
ejpam-4700	185	17	1−	1−	NUM
ejpam-4700	186	1	j	j	PROPN
ejpam-4700	186	2	r	r	NOUN
ejpam-4700	186	3	−	−	PROPN
ejpam-4700	186	4	1−	1−	NUM
ejpam-4700	186	5	j	j	PROPN
ejpam-4700	186	6	)	)	PUNCT
ejpam-4700	186	7	b	b	PROPN
ejpam-4700	186	8	(	(	PUNCT
ejpam-4700	186	9	r	r	NOUN
ejpam-4700	186	10	)	)	PUNCT
ejpam-4700	186	11	l	l	NOUN
ejpam-4700	186	12	(	(	PUNCT
ejpam-4700	186	13	x	x	SYM
ejpam-4700	186	14	2	2	X
ejpam-4700	186	15	)	)	PUNCT
ejpam-4700	186	16	j	j	NOUN
ejpam-4700	186	17	!	!	PUNCT
ejpam-4700	187	1	(	(	PUNCT
ejpam-4700	187	2	u	u	NOUN
ejpam-4700	187	3	λ	λ	PROPN
ejpam-4700	187	4	)	)	PUNCT
ejpam-4700	187	5	x	x	SYM
ejpam-4700	187	6	2	2	NUM
ejpam-4700	187	7	exkπi	exkπi	PROPN
ejpam-4700	187	8	[	[	PUNCT
ejpam-4700	187	9	log	log	NOUN
ejpam-4700	187	10	(	(	PUNCT
ejpam-4700	187	11	u	u	NOUN
ejpam-4700	187	12	λ	λ	PROPN
ejpam-4700	187	13	)	)	PUNCT
ejpam-4700	187	14	1	1	NUM
ejpam-4700	187	15	2	2	NUM
ejpam-4700	187	16	+	+	NUM
ejpam-4700	187	17	kπi	kπi	NOUN
ejpam-4700	187	18	]	]	X
ejpam-4700	187	19	r+n−j	r+n−j	X
ejpam-4700	187	20	(	(	PUNCT
ejpam-4700	187	21	17	17	NUM
ejpam-4700	187	22	)	)	PUNCT
ejpam-4700	187	23	where	where	SCONJ
ejpam-4700	187	24	b	b	X
ejpam-4700	187	25	(	(	PUNCT
ejpam-4700	187	26	r	r	NOUN
ejpam-4700	187	27	)	)	PUNCT
ejpam-4700	187	28	n	n	NOUN
ejpam-4700	187	29	(	(	PUNCT
ejpam-4700	187	30	x	x	SYM
ejpam-4700	187	31	2	2	X
ejpam-4700	187	32	)	)	PUNCT
ejpam-4700	187	33	is	be	AUX
ejpam-4700	187	34	the	the	DET
ejpam-4700	187	35	bernoulli	bernoulli	NOUN
ejpam-4700	187	36	polynomials	polynomial	NOUN
ejpam-4700	187	37	of	of	ADP
ejpam-4700	187	38	order	order	NOUN
ejpam-4700	187	39	r	r	NOUN
ejpam-4700	187	40	defined	define	VERB
ejpam-4700	187	41	by	by	ADP
ejpam-4700	187	42	(	(	PUNCT
ejpam-4700	187	43	t	t	NOUN
ejpam-4700	187	44	et	et	NOUN
ejpam-4700	187	45	−	−	NOUN
ejpam-4700	187	46	1	1	X
ejpam-4700	187	47	)	)	PUNCT
ejpam-4700	187	48	r	r	NOUN
ejpam-4700	187	49	ext	ext	NOUN
ejpam-4700	188	1	=	=	NOUN
ejpam-4700	188	2	∞∑	∞∑	NUM
ejpam-4700	188	3	n=0	n=0	NUM
ejpam-4700	188	4	b(r	b(r	NOUN
ejpam-4700	188	5	)	)	PUNCT
ejpam-4700	188	6	n	n	CCONJ
ejpam-4700	188	7	(	(	PUNCT
ejpam-4700	188	8	x	x	X
ejpam-4700	188	9	)	)	PUNCT
ejpam-4700	188	10	tn	tn	PROPN
ejpam-4700	188	11	n	n	NOUN
ejpam-4700	188	12	!	!	PUNCT
ejpam-4700	188	13	proof	proof	NOUN
ejpam-4700	188	14	.	.	PUNCT
ejpam-4700	189	1	by	by	ADP
ejpam-4700	189	2	cauchy	cauchy	PROPN
ejpam-4700	189	3	residue	residue	NOUN
ejpam-4700	189	4	theorem	theorem	VERB
ejpam-4700	189	5	,	,	PUNCT
ejpam-4700	189	6	1	1	NUM
ejpam-4700	189	7	2πi	2πi	NOUN
ejpam-4700	189	8	∫	∫	PROPN
ejpam-4700	189	9	cn	cn	PROPN
ejpam-4700	189	10	f(t)dt	f(t)dt	PROPN
ejpam-4700	189	11	=	=	PROPN
ejpam-4700	189	12	res(f(t	res(f(t	PROPN
ejpam-4700	189	13	)	)	PUNCT
ejpam-4700	189	14	,	,	PUNCT
ejpam-4700	189	15	t	t	PROPN
ejpam-4700	189	16	=	=	SYM
ejpam-4700	189	17	0	0	NUM
ejpam-4700	189	18	)	)	PUNCT
ejpam-4700	190	1	+	+	CCONJ
ejpam-4700	190	2	∑	∑	PROPN
ejpam-4700	190	3	k∈z	k∈z	PROPN
ejpam-4700	190	4	res(f(t	res(f(t	PROPN
ejpam-4700	190	5	)	)	PUNCT
ejpam-4700	190	6	,	,	PUNCT
ejpam-4700	190	7	t	t	PROPN
ejpam-4700	190	8	=	=	SYM
ejpam-4700	190	9	tk	tk	PROPN
ejpam-4700	190	10	)	)	PUNCT
ejpam-4700	191	1	where	where	SCONJ
ejpam-4700	191	2	tk	tk	PROPN
ejpam-4700	191	3	=	=	NOUN
ejpam-4700	191	4	log	log	PROPN
ejpam-4700	191	5	(	(	PUNCT
ejpam-4700	191	6	u	u	NOUN
ejpam-4700	191	7	λ	λ	PROPN
ejpam-4700	191	8	)	)	PUNCT
ejpam-4700	191	9	1	1	NUM
ejpam-4700	191	10	2	2	NUM
ejpam-4700	191	11	+	+	CCONJ
ejpam-4700	191	12	kπi	kπi	NOUN
ejpam-4700	191	13	,	,	PUNCT
ejpam-4700	191	14	k	k	PROPN
ejpam-4700	191	15	∈	∈	PROPN
ejpam-4700	191	16	z	z	NOUN
ejpam-4700	191	17	f(t	f(t	PROPN
ejpam-4700	191	18	)	)	PUNCT
ejpam-4700	191	19	=	=	PRON
ejpam-4700	191	20	(	(	PUNCT
ejpam-4700	191	21	1−	1−	NUM
ejpam-4700	191	22	u	u	NOUN
ejpam-4700	191	23	λe2	λe2	PROPN
ejpam-4700	191	24	t	t	PROPN
ejpam-4700	191	25	−	−	PROPN
ejpam-4700	191	26	u	u	NOUN
ejpam-4700	191	27	)	)	PUNCT
ejpam-4700	191	28	r	r	NOUN
ejpam-4700	191	29	ext	ext	NOUN
ejpam-4700	191	30	tn+1	tn+1	NOUN
ejpam-4700	191	31	consider	consider	VERB
ejpam-4700	191	32	the	the	DET
ejpam-4700	191	33	left	leave	VERB
ejpam-4700	191	34	-	-	PUNCT
ejpam-4700	191	35	hand	hand	NOUN
ejpam-4700	191	36	side	side	NOUN
ejpam-4700	191	37	of	of	ADP
ejpam-4700	191	38	the	the	DET
ejpam-4700	191	39	equation	equation	NOUN
ejpam-4700	191	40	in	in	ADP
ejpam-4700	191	41	the	the	DET
ejpam-4700	191	42	cauchy	cauchy	ADJ
ejpam-4700	191	43	residue	residue	NOUN
ejpam-4700	191	44	theorem	theorem	NOUN
ejpam-4700	191	45	as	as	ADP
ejpam-4700	191	46	n	n	PROPN
ejpam-4700	191	47	→	→	SYM
ejpam-4700	191	48	∞	∞	PROPN
ejpam-4700	191	49	,	,	PUNCT
ejpam-4700	191	50	we	we	PRON
ejpam-4700	191	51	have	have	VERB
ejpam-4700	191	52	lim	lim	PROPN
ejpam-4700	191	53	n→∞	n→∞	NUM
ejpam-4700	192	1	∫	∫	PROPN
ejpam-4700	192	2	cn	cn	PROPN
ejpam-4700	192	3	f(t)dt	f(t)dt	PROPN
ejpam-4700	192	4	=	=	PROPN
ejpam-4700	192	5	lim	lim	PROPN
ejpam-4700	192	6	n→∞	n→∞	NUM
ejpam-4700	193	1	∫	∫	PROPN
ejpam-4700	193	2	cn	cn	PROPN
ejpam-4700	193	3	(	(	PUNCT
ejpam-4700	193	4	1−	1−	NUM
ejpam-4700	193	5	u	u	NOUN
ejpam-4700	193	6	λe2	λe2	PROPN
ejpam-4700	193	7	t	t	PROPN
ejpam-4700	193	8	−	−	PROPN
ejpam-4700	193	9	u	u	NOUN
ejpam-4700	193	10	)	)	PUNCT
ejpam-4700	193	11	r	r	NOUN
ejpam-4700	193	12	ext	ext	NOUN
ejpam-4700	193	13	dt	dt	NOUN
ejpam-4700	193	14	tn+1	tn+1	PROPN
ejpam-4700	193	15	=	=	SYM
ejpam-4700	193	16	0	0	NUM
ejpam-4700	193	17	we	we	PRON
ejpam-4700	193	18	use	use	VERB
ejpam-4700	193	19	the	the	DET
ejpam-4700	193	20	same	same	ADJ
ejpam-4700	193	21	proof	proof	NOUN
ejpam-4700	193	22	as	as	ADP
ejpam-4700	193	23	in	in	ADP
ejpam-4700	193	24	the	the	DET
ejpam-4700	193	25	case	case	NOUN
ejpam-4700	193	26	when	when	SCONJ
ejpam-4700	193	27	r	r	NOUN
ejpam-4700	193	28	=	=	SYM
ejpam-4700	193	29	1	1	NUM
ejpam-4700	193	30	as	as	SCONJ
ejpam-4700	193	31	shown	show	VERB
ejpam-4700	193	32	in	in	ADP
ejpam-4700	193	33	lemma	lemma	PROPN
ejpam-4700	193	34	1	1	NUM
ejpam-4700	193	35	.	.	PUNCT
ejpam-4700	194	1	we	we	PRON
ejpam-4700	194	2	shall	shall	AUX
ejpam-4700	194	3	evaluate	evaluate	VERB
ejpam-4700	194	4	the	the	DET
ejpam-4700	194	5	first	first	ADJ
ejpam-4700	194	6	term	term	NOUN
ejpam-4700	194	7	of	of	ADP
ejpam-4700	194	8	the	the	DET
ejpam-4700	194	9	right	right	ADJ
ejpam-4700	194	10	-	-	PUNCT
ejpam-4700	194	11	hand	hand	NOUN
ejpam-4700	194	12	side	side	NOUN
ejpam-4700	194	13	of	of	ADP
ejpam-4700	194	14	the	the	DET
ejpam-4700	194	15	equation	equation	NOUN
ejpam-4700	194	16	in	in	ADP
ejpam-4700	194	17	the	the	DET
ejpam-4700	194	18	cauchy	cauchy	ADJ
ejpam-4700	194	19	residue	residue	NOUN
ejpam-4700	194	20	theorem	theorem	NOUN
ejpam-4700	194	21	as	as	ADP
ejpam-4700	194	22	t	t	PROPN
ejpam-4700	194	23	=	=	SYM
ejpam-4700	194	24	0	0	NUM
ejpam-4700	194	25	,	,	PUNCT
ejpam-4700	194	26	we	we	PRON
ejpam-4700	194	27	have	have	VERB
ejpam-4700	194	28	res(f(t	res(f(t	NOUN
ejpam-4700	194	29	)	)	PUNCT
ejpam-4700	194	30	,	,	PUNCT
ejpam-4700	194	31	t	t	PROPN
ejpam-4700	194	32	=	=	SYM
ejpam-4700	195	1	0	0	NUM
ejpam-4700	195	2	)	)	PUNCT
ejpam-4700	195	3	=	=	SYM
ejpam-4700	195	4	lim	lim	PROPN
ejpam-4700	195	5	t→0	t→0	PUNCT
ejpam-4700	195	6	1	1	NUM
ejpam-4700	195	7	n	n	X
ejpam-4700	195	8	!	!	PUNCT
ejpam-4700	196	1	dn	dn	PROPN
ejpam-4700	196	2	dtn	dtn	PROPN
ejpam-4700	196	3	(	(	PUNCT
ejpam-4700	196	4	t−	t−	PROPN
ejpam-4700	196	5	0)n+1	0)n+1	SYM
ejpam-4700	196	6	1	1	NUM
ejpam-4700	196	7	tn+1	tn+1	NOUN
ejpam-4700	196	8	∞∑	∞∑	PROPN
ejpam-4700	196	9	m=0	m=0	PROPN
ejpam-4700	196	10	t	t	PROPN
ejpam-4700	196	11	(	(	PUNCT
ejpam-4700	196	12	r	r	NOUN
ejpam-4700	196	13	)	)	PUNCT
ejpam-4700	196	14	m	m	PROPN
ejpam-4700	196	15	(	(	PUNCT
ejpam-4700	196	16	x;u	x;u	PROPN
ejpam-4700	196	17	,	,	PUNCT
ejpam-4700	196	18	λ	λ	NOUN
ejpam-4700	196	19	)	)	PUNCT
ejpam-4700	196	20	tm	tm	PROPN
ejpam-4700	196	21	m	m	PROPN
ejpam-4700	196	22	!	!	PUNCT
ejpam-4700	197	1	=	=	SYM
ejpam-4700	197	2	1	1	NUM
ejpam-4700	197	3	n	n	NUM
ejpam-4700	197	4	!	!	PUNCT
ejpam-4700	198	1	t	t	NOUN
ejpam-4700	198	2	(	(	PUNCT
ejpam-4700	198	3	r	r	NOUN
ejpam-4700	198	4	)	)	PUNCT
ejpam-4700	198	5	n	n	CCONJ
ejpam-4700	198	6	(	(	PUNCT
ejpam-4700	198	7	x;u	x;u	PROPN
ejpam-4700	198	8	,	,	PUNCT
ejpam-4700	198	9	λ	λ	PROPN
ejpam-4700	198	10	)	)	PUNCT
ejpam-4700	198	11	.	.	PUNCT
ejpam-4700	199	1	now	now	ADV
ejpam-4700	199	2	we	we	PRON
ejpam-4700	199	3	will	will	AUX
ejpam-4700	199	4	evaluate	evaluate	VERB
ejpam-4700	199	5	the	the	DET
ejpam-4700	199	6	second	second	ADJ
ejpam-4700	199	7	term	term	NOUN
ejpam-4700	199	8	of	of	ADP
ejpam-4700	199	9	the	the	DET
ejpam-4700	199	10	right	right	ADJ
ejpam-4700	199	11	-	-	PUNCT
ejpam-4700	199	12	hand	hand	NOUN
ejpam-4700	199	13	side	side	NOUN
ejpam-4700	199	14	of	of	ADP
ejpam-4700	199	15	the	the	DET
ejpam-4700	199	16	equation	equation	NOUN
ejpam-4700	199	17	of	of	ADP
ejpam-4700	199	18	the	the	DET
ejpam-4700	199	19	cauchy	cauchy	ADJ
ejpam-4700	199	20	residue	residue	NOUN
ejpam-4700	199	21	theorem	theorem	NOUN
ejpam-4700	199	22	as	as	ADP
ejpam-4700	199	23	t	t	PROPN
ejpam-4700	199	24	=	=	SYM
ejpam-4700	199	25	tk	tk	PROPN
ejpam-4700	199	26	.	.	PROPN
ejpam-4700	199	27	that	that	PRON
ejpam-4700	199	28	is	be	AUX
ejpam-4700	199	29	,	,	PUNCT
ejpam-4700	199	30	for	for	ADP
ejpam-4700	199	31	r	r	NOUN
ejpam-4700	199	32	≥	≥	NUM
ejpam-4700	199	33	2	2	NUM
ejpam-4700	199	34	res(f(t	res(f(t	NOUN
ejpam-4700	199	35	)	)	PUNCT
ejpam-4700	199	36	,	,	PUNCT
ejpam-4700	199	37	t	t	PROPN
ejpam-4700	199	38	=	=	SYM
ejpam-4700	199	39	tk	tk	PROPN
ejpam-4700	199	40	)	)	PUNCT
ejpam-4700	199	41	=	=	SYM
ejpam-4700	199	42	1	1	NUM
ejpam-4700	199	43	(	(	PUNCT
ejpam-4700	199	44	r	r	NOUN
ejpam-4700	199	45	−	−	NOUN
ejpam-4700	199	46	1	1	NUM
ejpam-4700	199	47	)	)	PUNCT
ejpam-4700	199	48	!	!	PUNCT
ejpam-4700	200	1	lim	lim	PROPN
ejpam-4700	200	2	t→tk	t→tk	VERB
ejpam-4700	201	1	dr−1	dr−1	PROPN
ejpam-4700	201	2	dtr−1	dtr−1	PROPN
ejpam-4700	201	3	(	(	PUNCT
ejpam-4700	201	4	t−	t−	PROPN
ejpam-4700	201	5	tk	tk	PROPN
ejpam-4700	201	6	)	)	PUNCT
ejpam-4700	201	7	r	r	NOUN
ejpam-4700	201	8	(	(	PUNCT
ejpam-4700	201	9	1−	1−	NUM
ejpam-4700	201	10	u	u	NOUN
ejpam-4700	201	11	λe2	λe2	PROPN
ejpam-4700	201	12	t	t	PROPN
ejpam-4700	201	13	−	−	PROPN
ejpam-4700	201	14	u	u	NOUN
ejpam-4700	201	15	)	)	PUNCT
ejpam-4700	201	16	r	r	NOUN
ejpam-4700	201	17	ext	ext	NOUN
ejpam-4700	201	18	tn+1	tn+1	NOUN
ejpam-4700	201	19	consider	consider	VERB
ejpam-4700	201	20	the	the	DET
ejpam-4700	201	21	function	function	NOUN
ejpam-4700	201	22	(	(	PUNCT
ejpam-4700	201	23	t−	t−	PROPN
ejpam-4700	201	24	tk	tk	PROPN
ejpam-4700	201	25	)	)	PUNCT
ejpam-4700	201	26	r	r	NOUN
ejpam-4700	201	27	(	(	PUNCT
ejpam-4700	201	28	1−	1−	NUM
ejpam-4700	201	29	u	u	NOUN
ejpam-4700	201	30	λe2	λe2	PROPN
ejpam-4700	201	31	t	t	PROPN
ejpam-4700	201	32	−	−	PROPN
ejpam-4700	201	33	u	u	NOUN
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ejpam-4700	201	35	r	r	NOUN
ejpam-4700	201	36	ext	ext	NOUN
ejpam-4700	201	37	tn+1	tn+1	NOUN
ejpam-4700	201	38	=	=	SYM
ejpam-4700	201	39	(	(	PUNCT
ejpam-4700	201	40	t−	t−	PROPN
ejpam-4700	201	41	tk	tk	PROPN
ejpam-4700	201	42	)	)	PUNCT
ejpam-4700	201	43	r	r	NOUN
ejpam-4700	201	44	(	(	PUNCT
ejpam-4700	201	45	1−	1−	NUM
ejpam-4700	201	46	u)r	u)r	NOUN
ejpam-4700	201	47	(	(	PUNCT
ejpam-4700	201	48	λ	λ	X
ejpam-4700	201	49	ue	ue	PROPN
ejpam-4700	201	50	2	2	NUM
ejpam-4700	201	51	t	t	NOUN
ejpam-4700	201	52	−	−	NOUN
ejpam-4700	201	53	1	1	NUM
ejpam-4700	201	54	)	)	PUNCT
ejpam-4700	202	1	r	r	NOUN
ejpam-4700	202	2	1	1	NUM
ejpam-4700	202	3	ur	ur	NOUN
ejpam-4700	202	4	ext	ext	PROPN
ejpam-4700	202	5	tn+1	tn+1	PROPN
ejpam-4700	202	6	r.	r.	PROPN
ejpam-4700	202	7	b.	b.	PROPN
ejpam-4700	202	8	corcino	corcino	PROPN
ejpam-4700	202	9	et	et	PROPN
ejpam-4700	202	10	al	al	PROPN
ejpam-4700	202	11	.	.	PUNCT
ejpam-4700	202	12	/	/	SYM
ejpam-4700	202	13	eur	eur	PROPN
ejpam-4700	202	14	.	.	PUNCT
ejpam-4700	203	1	j.	j.	PROPN
ejpam-4700	203	2	pure	pure	PROPN
ejpam-4700	203	3	appl	appl	PROPN
ejpam-4700	203	4	.	.	PROPN
ejpam-4700	203	5	math	math	PROPN
ejpam-4700	203	6	,	,	PUNCT
ejpam-4700	203	7	16	16	NUM
ejpam-4700	203	8	(	(	PUNCT
ejpam-4700	203	9	2	2	NUM
ejpam-4700	203	10	)	)	PUNCT
ejpam-4700	203	11	(	(	PUNCT
ejpam-4700	203	12	2023	2023	NUM
ejpam-4700	203	13	)	)	PUNCT
ejpam-4700	203	14	,	,	PUNCT
ejpam-4700	203	15	1005	1005	NUM
ejpam-4700	203	16	-	-	SYM
ejpam-4700	203	17	1023	1023	NUM
ejpam-4700	203	18	1015	1015	NUM
ejpam-4700	203	19	=	=	SYM
ejpam-4700	203	20	(	(	PUNCT
ejpam-4700	203	21	t−	t−	PROPN
ejpam-4700	203	22	tk	tk	PROPN
ejpam-4700	203	23	)	)	PUNCT
ejpam-4700	203	24	r	r	NOUN
ejpam-4700	203	25	(	(	PUNCT
ejpam-4700	203	26	1−	1−	NUM
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ejpam-4700	203	29	λ	λ	X
ejpam-4700	203	30	ue	ue	PROPN
ejpam-4700	203	31	2	2	NUM
ejpam-4700	203	32	t	t	NOUN
ejpam-4700	203	33	−	−	NOUN
ejpam-4700	203	34	1	1	NUM
ejpam-4700	203	35	)	)	PUNCT
ejpam-4700	203	36	r	r	NOUN
ejpam-4700	203	37	extt−(n+1	extt−(n+1	PROPN
ejpam-4700	203	38	)	)	PUNCT
ejpam-4700	203	39	=	=	SYM
ejpam-4700	203	40	(	(	PUNCT
ejpam-4700	203	41	t−	t−	PROPN
ejpam-4700	203	42	tk	tk	PROPN
ejpam-4700	203	43	)	)	PUNCT
ejpam-4700	203	44	r	r	NOUN
ejpam-4700	203	45	(	(	PUNCT
ejpam-4700	203	46	1−	1−	NUM
ejpam-4700	203	47	u)ru−r	u)ru−r	NOUN
ejpam-4700	203	48	(	(	PUNCT
ejpam-4700	203	49	λ	λ	X
ejpam-4700	203	50	ue	ue	PROPN
ejpam-4700	203	51	2	2	NUM
ejpam-4700	203	52	t	t	NOUN
ejpam-4700	203	53	−	−	NOUN
ejpam-4700	203	54	1	1	NUM
ejpam-4700	203	55	)	)	PUNCT
ejpam-4700	203	56	r	r	NOUN
ejpam-4700	203	57	extt−(n+1	extt−(n+1	PROPN
ejpam-4700	203	58	)	)	PUNCT
ejpam-4700	203	59	=	=	SYM
ejpam-4700	203	60	(	(	PUNCT
ejpam-4700	203	61	t−	t−	PROPN
ejpam-4700	203	62	tk	tk	PROPN
ejpam-4700	203	63	)	)	PUNCT
ejpam-4700	203	64	r	r	NOUN
ejpam-4700	203	65	(	(	PUNCT
ejpam-4700	203	66	1−	1−	NUM
ejpam-4700	203	67	u)ru−r	u)ru−r	NOUN
ejpam-4700	203	68	(	(	PUNCT
ejpam-4700	203	69	λ	λ	X
ejpam-4700	203	70	ue	ue	NOUN
ejpam-4700	203	71	2(t−tk	2(t−tk	NUM
ejpam-4700	203	72	)	)	PUNCT
ejpam-4700	203	73	u	u	NOUN
ejpam-4700	203	74	λ	λ	NOUN
ejpam-4700	203	75	−	−	NOUN
ejpam-4700	203	76	1	1	NUM
ejpam-4700	203	77	)	)	PUNCT
ejpam-4700	203	78	r	r	NOUN
ejpam-4700	203	79	extt−(n+1	extt−(n+1	PROPN
ejpam-4700	203	80	)	)	PUNCT
ejpam-4700	203	81	since	since	SCONJ
ejpam-4700	203	82	u	u	NOUN
ejpam-4700	203	83	λ	λ	X
ejpam-4700	203	84	e−2tk	e−2tk	NOUN
ejpam-4700	203	85	=	=	SYM
ejpam-4700	203	86	1	1	NUM
ejpam-4700	203	87	=	=	SYM
ejpam-4700	203	88	(	(	PUNCT
ejpam-4700	203	89	1−	1−	NUM
ejpam-4700	203	90	u)r	u)r	X
ejpam-4700	203	91	(	(	PUNCT
ejpam-4700	203	92	2u)r	2u)r	NUM
ejpam-4700	204	1	[	[	X
ejpam-4700	204	2	2(t−	2(t−	NUM
ejpam-4700	204	3	tk	tk	NOUN
ejpam-4700	204	4	)	)	PUNCT
ejpam-4700	204	5	]	]	X
ejpam-4700	205	1	r	r	NOUN
ejpam-4700	205	2	(	(	PUNCT
ejpam-4700	205	3	e2(t−tk	e2(t−tk	ADJ
ejpam-4700	205	4	)	)	PUNCT
ejpam-4700	205	5	−	−	PROPN
ejpam-4700	205	6	1)r	1)r	NUM
ejpam-4700	205	7	ext	ext	NOUN
ejpam-4700	205	8	tn+1	tn+1	NOUN
ejpam-4700	205	9	=	=	SYM
ejpam-4700	205	10	(	(	PUNCT
ejpam-4700	205	11	1−	1−	NUM
ejpam-4700	205	12	u)r	u)r	NOUN
ejpam-4700	205	13	(	(	PUNCT
ejpam-4700	205	14	2u)r	2u)r	NUM
ejpam-4700	205	15	∞∑	∞∑	NUM
ejpam-4700	205	16	n=0	n=0	NUM
ejpam-4700	205	17	b(r	b(r	NOUN
ejpam-4700	205	18	)	)	PUNCT
ejpam-4700	205	19	n	n	CCONJ
ejpam-4700	206	1	[	[	X
ejpam-4700	206	2	2(t−	2(t−	NUM
ejpam-4700	206	3	tk	tk	NOUN
ejpam-4700	206	4	)	)	PUNCT
ejpam-4700	206	5	]	]	PUNCT
ejpam-4700	207	1	r	r	NOUN
ejpam-4700	207	2	n	n	NOUN
ejpam-4700	207	3	!	!	PUNCT
ejpam-4700	207	4	t−(n+1)ext	t−(n+1)ext	PROPN
ejpam-4700	207	5	where	where	SCONJ
ejpam-4700	207	6	(	(	PUNCT
ejpam-4700	207	7	w	w	NOUN
ejpam-4700	207	8	ew	ew	INTJ
ejpam-4700	207	9	−	−	PROPN
ejpam-4700	207	10	1	1	NUM
ejpam-4700	207	11	)	)	PUNCT
ejpam-4700	207	12	r	r	NOUN
ejpam-4700	207	13	=	=	SYM
ejpam-4700	207	14	∞∑	∞∑	NUM
ejpam-4700	207	15	n=0	n=0	NUM
ejpam-4700	207	16	b(r	b(r	NOUN
ejpam-4700	207	17	)	)	PUNCT
ejpam-4700	207	18	n	n	PROPN
ejpam-4700	207	19	wn	wn	NOUN
ejpam-4700	207	20	n	n	CCONJ
ejpam-4700	207	21	!	!	PUNCT
ejpam-4700	208	1	to	to	PART
ejpam-4700	208	2	get	get	VERB
ejpam-4700	208	3	the	the	DET
ejpam-4700	208	4	derivative	derivative	NOUN
ejpam-4700	208	5	,	,	PUNCT
ejpam-4700	208	6	we	we	PRON
ejpam-4700	208	7	employ	employ	VERB
ejpam-4700	208	8	the	the	DET
ejpam-4700	208	9	leibniz	leibniz	PROPN
ejpam-4700	208	10	rule	rule	NOUN
ejpam-4700	208	11	which	which	PRON
ejpam-4700	208	12	gives	give	VERB
ejpam-4700	208	13	us	we	PRON
ejpam-4700	208	14	dr−1	dr−1	PROPN
ejpam-4700	208	15	dtr−1	dtr−1	PROPN
ejpam-4700	208	16	{	{	PUNCT
ejpam-4700	208	17	(	(	PUNCT
ejpam-4700	208	18	t−	t−	PROPN
ejpam-4700	208	19	tk	tk	PROPN
ejpam-4700	208	20	)	)	PUNCT
ejpam-4700	208	21	r	r	NOUN
ejpam-4700	208	22	(	(	PUNCT
ejpam-4700	208	23	1−	1−	NUM
ejpam-4700	208	24	u	u	NOUN
ejpam-4700	208	25	λe2	λe2	PROPN
ejpam-4700	208	26	t	t	PROPN
ejpam-4700	208	27	−	−	PROPN
ejpam-4700	208	28	u	u	NOUN
ejpam-4700	208	29	)	)	PUNCT
ejpam-4700	208	30	r	r	NOUN
ejpam-4700	208	31	ext	ext	NOUN
ejpam-4700	208	32	tn+1	tn+1	NOUN
ejpam-4700	208	33	}	}	PUNCT
ejpam-4700	208	34	=	=	PUNCT
ejpam-4700	208	35	(	(	PUNCT
ejpam-4700	208	36	1−	1−	NUM
ejpam-4700	208	37	u	u	NOUN
ejpam-4700	208	38	2u	2u	NOUN
ejpam-4700	208	39	)	)	PUNCT
ejpam-4700	209	1	r	r	NOUN
ejpam-4700	209	2	dr−1	dr−1	PROPN
ejpam-4700	209	3	dtr−1	dtr−1	PROPN
ejpam-4700	209	4	{	{	PUNCT
ejpam-4700	209	5	(	(	PUNCT
ejpam-4700	209	6	t−	t−	PROPN
ejpam-4700	209	7	tk	tk	PROPN
ejpam-4700	209	8	)	)	PUNCT
ejpam-4700	209	9	r	r	NOUN
ejpam-4700	209	10	[	[	PUNCT
ejpam-4700	209	11	∞∑	∞∑	NUM
ejpam-4700	209	12	n=0	n=0	NUM
ejpam-4700	209	13	b(r	b(r	NOUN
ejpam-4700	209	14	)	)	PUNCT
ejpam-4700	209	15	n	n	CCONJ
ejpam-4700	210	1	[	[	X
ejpam-4700	210	2	2(t−	2(t−	NUM
ejpam-4700	210	3	tk	tk	NOUN
ejpam-4700	210	4	)	)	PUNCT
ejpam-4700	210	5	]	]	PUNCT
ejpam-4700	211	1	n	n	PRON
ejpam-4700	211	2	n	n	X
ejpam-4700	211	3	!	!	PUNCT
ejpam-4700	211	4	]	]	PUNCT
ejpam-4700	212	1	extt−(n+1	extt−(n+1	X
ejpam-4700	212	2	)	)	PUNCT
ejpam-4700	212	3	}	}	PUNCT
ejpam-4700	212	4	=	=	PUNCT
ejpam-4700	212	5	(	(	PUNCT
ejpam-4700	212	6	1−	1−	NUM
ejpam-4700	212	7	u	u	NOUN
ejpam-4700	212	8	2u	2u	NOUN
ejpam-4700	212	9	)	)	PUNCT
ejpam-4700	212	10	r	r	NOUN
ejpam-4700	213	1	dr−1	dr−1	PROPN
ejpam-4700	213	2	dtr−1	dtr−1	PROPN
ejpam-4700	213	3	{	{	PUNCT
ejpam-4700	213	4	(	(	PUNCT
ejpam-4700	213	5	[	[	PUNCT
ejpam-4700	213	6	b(r	b(r	NOUN
ejpam-4700	213	7	)	)	PUNCT
ejpam-4700	213	8	n	n	CCONJ
ejpam-4700	214	1	[	[	X
ejpam-4700	214	2	2(t−	2(t−	NUM
ejpam-4700	214	3	tk	tk	NOUN
ejpam-4700	214	4	)	)	PUNCT
ejpam-4700	214	5	]	]	PUNCT
ejpam-4700	215	1	n	n	PRON
ejpam-4700	215	2	n	n	CCONJ
ejpam-4700	215	3	!	!	PUNCT
ejpam-4700	215	4	]	]	PUNCT
ejpam-4700	216	1	ext	ext	X
ejpam-4700	216	2	)	)	PUNCT
ejpam-4700	216	3	t−(n+1	t−(n+1	PROPN
ejpam-4700	216	4	)	)	PUNCT
ejpam-4700	216	5	}	}	PUNCT
ejpam-4700	217	1	=	=	PUNCT
ejpam-4700	217	2	(	(	PUNCT
ejpam-4700	217	3	1−	1−	NUM
ejpam-4700	217	4	u	u	NOUN
ejpam-4700	217	5	2u	2u	NOUN
ejpam-4700	217	6	)	)	PUNCT
ejpam-4700	217	7	r	r	NOUN
ejpam-4700	217	8	r−1∑	r−1∑	NUM
ejpam-4700	217	9	j=0	j=0	PROPN
ejpam-4700	217	10	(	(	PUNCT
ejpam-4700	217	11	r	r	NOUN
ejpam-4700	217	12	−	−	PROPN
ejpam-4700	217	13	1	1	NUM
ejpam-4700	217	14	j	j	NOUN
ejpam-4700	217	15	)	)	PUNCT
ejpam-4700	217	16	dr−1−j	dr−1−j	PROPN
ejpam-4700	217	17	dtr−1−j	dtr−1−j	PROPN
ejpam-4700	217	18	t−(n+1	t−(n+1	NOUN
ejpam-4700	217	19	)	)	PUNCT
ejpam-4700	218	1	d	d	X
ejpam-4700	218	2	j	j	PROPN
ejpam-4700	218	3	dtj	dtj	NOUN
ejpam-4700	218	4	ext	ext	NOUN
ejpam-4700	218	5	∞∑	∞∑	PRON
ejpam-4700	218	6	n=0	n=0	NUM
ejpam-4700	218	7	b(r	b(r	NOUN
ejpam-4700	218	8	)	)	PUNCT
ejpam-4700	218	9	n	n	PRON
ejpam-4700	218	10	2n	2n	NUM
ejpam-4700	218	11	(	(	PUNCT
ejpam-4700	218	12	t−	t−	PROPN
ejpam-4700	218	13	tk	tk	PROPN
ejpam-4700	218	14	)	)	PUNCT
ejpam-4700	218	15	n	n	PROPN
ejpam-4700	218	16	n!︸	n!︸	PROPN
ejpam-4700	218	17	︷︷	︷︷	PROPN
ejpam-4700	218	18	︸	︸	ADP
ejpam-4700	218	19	h(t	h(t	PROPN
ejpam-4700	218	20	)	)	PUNCT
ejpam-4700	218	21			NOUN
ejpam-4700	218	22	consider	consider	VERB
ejpam-4700	218	23	now	now	ADV
ejpam-4700	218	24	,	,	PUNCT
ejpam-4700	218	25	dj	dj	VERB
ejpam-4700	218	26	dtj	dtj	NOUN
ejpam-4700	218	27	(	(	PUNCT
ejpam-4700	218	28	h(t	h(t	PROPN
ejpam-4700	218	29	)	)	PUNCT
ejpam-4700	218	30	)	)	PUNCT
ejpam-4700	219	1	=	=	PUNCT
ejpam-4700	220	1	j∑	j∑	PROPN
ejpam-4700	221	1	l=0	l=0	PROPN
ejpam-4700	221	2	(	(	PUNCT
ejpam-4700	221	3	j	j	PROPN
ejpam-4700	221	4	l	l	NOUN
ejpam-4700	221	5	)	)	PUNCT
ejpam-4700	221	6	xj−lext	xj−lext	PUNCT
ejpam-4700	222	1	∞∑	∞∑	PRON
ejpam-4700	222	2	n=0	n=0	NUM
ejpam-4700	222	3	b(r	b(r	NOUN
ejpam-4700	222	4	)	)	PUNCT
ejpam-4700	222	5	n	n	CCONJ
ejpam-4700	222	6	2n(n)l	2n(n)l	NUM
ejpam-4700	222	7	n	n	X
ejpam-4700	222	8	!	!	PUNCT
ejpam-4700	223	1	(	(	PUNCT
ejpam-4700	223	2	t−	t−	PROPN
ejpam-4700	223	3	tk	tk	PROPN
ejpam-4700	223	4	)	)	PUNCT
ejpam-4700	223	5	n−l	n−l	NOUN
ejpam-4700	223	6	=	=	PUNCT
ejpam-4700	224	1	ext	ext	NOUN
ejpam-4700	224	2	j∑	j∑	PROPN
ejpam-4700	224	3	l=0	l=0	PROPN
ejpam-4700	225	1	(	(	PUNCT
ejpam-4700	225	2	j	j	PROPN
ejpam-4700	225	3	l	l	NOUN
ejpam-4700	225	4	)	)	PUNCT
ejpam-4700	226	1	xj−l	xj−l	PROPN
ejpam-4700	226	2	∞∑	∞∑	NUM
ejpam-4700	226	3	n=0	n=0	NUM
ejpam-4700	226	4	b(r	b(r	NOUN
ejpam-4700	226	5	)	)	PUNCT
ejpam-4700	226	6	n	n	PRON
ejpam-4700	226	7	2n	2n	NUM
ejpam-4700	226	8	(	(	PUNCT
ejpam-4700	226	9	t−	t−	PROPN
ejpam-4700	226	10	tk	tk	PROPN
ejpam-4700	226	11	)	)	PUNCT
ejpam-4700	226	12	n−l	n−l	NOUN
ejpam-4700	226	13	(	(	PUNCT
ejpam-4700	226	14	n−	n−	NOUN
ejpam-4700	226	15	l	l	NOUN
ejpam-4700	226	16	)	)	PUNCT
ejpam-4700	226	17	!	!	PUNCT
ejpam-4700	227	1	so	so	ADV
ejpam-4700	227	2	that	that	SCONJ
ejpam-4700	227	3	,	,	PUNCT
ejpam-4700	227	4	the	the	DET
ejpam-4700	227	5	derivative	derivative	NOUN
ejpam-4700	227	6	becomes	become	VERB
ejpam-4700	227	7	dr−1	dr−1	PROPN
ejpam-4700	227	8	dtr−1	dtr−1	PROPN
ejpam-4700	227	9	{	{	PUNCT
ejpam-4700	227	10	(	(	PUNCT
ejpam-4700	227	11	t−	t−	PROPN
ejpam-4700	227	12	tk	tk	PROPN
ejpam-4700	227	13	)	)	PUNCT
ejpam-4700	227	14	r	r	NOUN
ejpam-4700	227	15	(	(	PUNCT
ejpam-4700	227	16	1−	1−	NUM
ejpam-4700	227	17	u	u	NOUN
ejpam-4700	227	18	λe2	λe2	PROPN
ejpam-4700	227	19	t	t	PROPN
ejpam-4700	227	20	−	−	PROPN
ejpam-4700	227	21	u	u	NOUN
ejpam-4700	227	22	)	)	PUNCT
ejpam-4700	227	23	r	r	NOUN
ejpam-4700	227	24	ext	ext	NOUN
ejpam-4700	227	25	tn+1	tn+1	NOUN
ejpam-4700	227	26	}	}	PUNCT
ejpam-4700	227	27	=	=	PUNCT
ejpam-4700	227	28	(	(	PUNCT
ejpam-4700	227	29	1−	1−	NUM
ejpam-4700	227	30	u	u	NOUN
ejpam-4700	227	31	2u	2u	NOUN
ejpam-4700	227	32	)	)	PUNCT
ejpam-4700	227	33	r	r	NOUN
ejpam-4700	227	34	r−1∑	r−1∑	NUM
ejpam-4700	227	35	j=0	j=0	PROPN
ejpam-4700	227	36	(	(	PUNCT
ejpam-4700	227	37	r	r	NOUN
ejpam-4700	227	38	−	−	PROPN
ejpam-4700	227	39	1	1	NUM
ejpam-4700	227	40	j	j	NOUN
ejpam-4700	227	41	)	)	PUNCT
ejpam-4700	227	42	dr−1−j	dr−1−j	PROPN
ejpam-4700	227	43	dtr−1−j	dtr−1−j	PROPN
ejpam-4700	227	44	t−(n+1	t−(n+1	PROPN
ejpam-4700	227	45	)	)	PUNCT
ejpam-4700	227	46	r.	r.	PROPN
ejpam-4700	227	47	b.	b.	PROPN
ejpam-4700	227	48	corcino	corcino	PROPN
ejpam-4700	227	49	et	et	PROPN
ejpam-4700	227	50	al	al	PROPN
ejpam-4700	227	51	.	.	PUNCT
ejpam-4700	227	52	/	/	SYM
ejpam-4700	227	53	eur	eur	PROPN
ejpam-4700	227	54	.	.	PUNCT
ejpam-4700	228	1	j.	j.	PROPN
ejpam-4700	228	2	pure	pure	PROPN
ejpam-4700	228	3	appl	appl	PROPN
ejpam-4700	228	4	.	.	PROPN
ejpam-4700	228	5	math	math	PROPN
ejpam-4700	228	6	,	,	PUNCT
ejpam-4700	228	7	16	16	NUM
ejpam-4700	228	8	(	(	PUNCT
ejpam-4700	228	9	2	2	NUM
ejpam-4700	228	10	)	)	PUNCT
ejpam-4700	228	11	(	(	PUNCT
ejpam-4700	228	12	2023	2023	NUM
ejpam-4700	228	13	)	)	PUNCT
ejpam-4700	228	14	,	,	PUNCT
ejpam-4700	228	15	1005	1005	NUM
ejpam-4700	228	16	-	-	SYM
ejpam-4700	228	17	1023	1023	NUM
ejpam-4700	228	18	1016	1016	NUM
ejpam-4700	228	19	×	×	NOUN
ejpam-4700	228	20	ext	ext	NOUN
ejpam-4700	228	21	j∑	j∑	PROPN
ejpam-4700	228	22	l=0	l=0	PROPN
ejpam-4700	229	1	(	(	PUNCT
ejpam-4700	229	2	j	j	PROPN
ejpam-4700	229	3	l	l	NOUN
ejpam-4700	229	4	)	)	PUNCT
ejpam-4700	230	1	xj−l	xj−l	PROPN
ejpam-4700	230	2	∞∑	∞∑	NUM
ejpam-4700	230	3	n=0	n=0	NUM
ejpam-4700	230	4	b(r	b(r	NOUN
ejpam-4700	230	5	)	)	PUNCT
ejpam-4700	230	6	n	n	PRON
ejpam-4700	230	7	2n	2n	NUM
ejpam-4700	230	8	(	(	PUNCT
ejpam-4700	230	9	t−	t−	PROPN
ejpam-4700	230	10	tk	tk	PROPN
ejpam-4700	230	11	)	)	PUNCT
ejpam-4700	230	12	n−l	n−l	NOUN
ejpam-4700	230	13	(	(	PUNCT
ejpam-4700	230	14	n−	n−	NOUN
ejpam-4700	230	15	l	l	NOUN
ejpam-4700	230	16	)	)	PUNCT
ejpam-4700	230	17	!	!	PUNCT
ejpam-4700	231	1	thus	thus	ADV
ejpam-4700	231	2	,	,	PUNCT
ejpam-4700	231	3	res(f(t	res(f(t	PROPN
ejpam-4700	231	4	)	)	PUNCT
ejpam-4700	231	5	,	,	PUNCT
ejpam-4700	231	6	t	t	PROPN
ejpam-4700	231	7	=	=	SYM
ejpam-4700	231	8	tk	tk	PROPN
ejpam-4700	231	9	)	)	PUNCT
ejpam-4700	231	10	=	=	SYM
ejpam-4700	232	1	1	1	NUM
ejpam-4700	232	2	(	(	PUNCT
ejpam-4700	232	3	r	r	NOUN
ejpam-4700	232	4	−	−	NOUN
ejpam-4700	232	5	1	1	NUM
ejpam-4700	232	6	)	)	PUNCT
ejpam-4700	232	7	!	!	PUNCT
ejpam-4700	233	1	lim	lim	PROPN
ejpam-4700	233	2	t→tk	t→tk	VERB
ejpam-4700	234	1	dr−1	dr−1	PROPN
ejpam-4700	234	2	dtr−1	dtr−1	PROPN
ejpam-4700	234	3	(	(	PUNCT
ejpam-4700	234	4	t−	t−	PROPN
ejpam-4700	234	5	tk	tk	PROPN
ejpam-4700	234	6	)	)	PUNCT
ejpam-4700	234	7	r	r	NOUN
ejpam-4700	234	8	(	(	PUNCT
ejpam-4700	234	9	1−	1−	NUM
ejpam-4700	234	10	u	u	NOUN
ejpam-4700	234	11	λe2	λe2	PROPN
ejpam-4700	234	12	t	t	PROPN
ejpam-4700	234	13	−	−	PROPN
ejpam-4700	234	14	u	u	NOUN
ejpam-4700	234	15	)	)	PUNCT
ejpam-4700	234	16	r	r	NOUN
ejpam-4700	234	17	ext	ext	NOUN
ejpam-4700	234	18	tn+1	tn+1	NOUN
ejpam-4700	234	19	=	=	SYM
ejpam-4700	234	20	1	1	NUM
ejpam-4700	234	21	(	(	PUNCT
ejpam-4700	234	22	r	r	NOUN
ejpam-4700	234	23	−	−	NOUN
ejpam-4700	234	24	1	1	NUM
ejpam-4700	234	25	)	)	PUNCT
ejpam-4700	234	26	!	!	PUNCT
ejpam-4700	235	1	lim	lim	PROPN
ejpam-4700	235	2	t→tk	t→tk	PROPN
ejpam-4700	236	1	(	(	PUNCT
ejpam-4700	236	2	1−	1−	NUM
ejpam-4700	236	3	u	u	NOUN
ejpam-4700	236	4	2u	2u	NOUN
ejpam-4700	236	5	)	)	PUNCT
ejpam-4700	236	6	r	r	NOUN
ejpam-4700	236	7	r−1∑	r−1∑	NUM
ejpam-4700	236	8	j=0	j=0	PROPN
ejpam-4700	236	9	(	(	PUNCT
ejpam-4700	236	10	r	r	NOUN
ejpam-4700	236	11	−	−	PROPN
ejpam-4700	236	12	1	1	NUM
ejpam-4700	236	13	j	j	NOUN
ejpam-4700	236	14	)	)	PUNCT
ejpam-4700	236	15	dr−1−j	dr−1−j	PROPN
ejpam-4700	236	16	dtr−1−j	dtr−1−j	PROPN
ejpam-4700	236	17	t−(n+1	t−(n+1	PROPN
ejpam-4700	236	18	)	)	PUNCT
ejpam-4700	236	19	×	×	NOUN
ejpam-4700	236	20	ext	ext	NOUN
ejpam-4700	236	21	j∑	j∑	PROPN
ejpam-4700	236	22	l=0	l=0	PROPN
ejpam-4700	236	23	(	(	PUNCT
ejpam-4700	236	24	j	j	PROPN
ejpam-4700	236	25	l	l	NOUN
ejpam-4700	236	26	)	)	PUNCT
ejpam-4700	237	1	xj−l	xj−l	PROPN
ejpam-4700	237	2	∞∑	∞∑	NUM
ejpam-4700	237	3	n=0	n=0	NUM
ejpam-4700	237	4	b(r	b(r	NOUN
ejpam-4700	237	5	)	)	PUNCT
ejpam-4700	237	6	n	n	PRON
ejpam-4700	237	7	2n	2n	NUM
ejpam-4700	237	8	(	(	PUNCT
ejpam-4700	237	9	t−	t−	PROPN
ejpam-4700	237	10	tk	tk	PROPN
ejpam-4700	237	11	)	)	PUNCT
ejpam-4700	237	12	n−l	n−l	NOUN
ejpam-4700	237	13	(	(	PUNCT
ejpam-4700	237	14	n−	n−	NOUN
ejpam-4700	237	15	l	l	NOUN
ejpam-4700	237	16	)	)	PUNCT
ejpam-4700	237	17	!	!	PUNCT
ejpam-4700	238	1	note	note	VERB
ejpam-4700	238	2	that	that	SCONJ
ejpam-4700	238	3	b	b	X
ejpam-4700	238	4	(	(	PUNCT
ejpam-4700	238	5	r	r	NOUN
ejpam-4700	238	6	)	)	PUNCT
ejpam-4700	238	7	n	n	CCONJ
ejpam-4700	238	8	(	(	PUNCT
ejpam-4700	238	9	t−tk	t−tk	PROPN
ejpam-4700	238	10	)	)	PUNCT
ejpam-4700	238	11	n−l	n−l	NOUN
ejpam-4700	238	12	(	(	PUNCT
ejpam-4700	238	13	n−l	n−l	PROPN
ejpam-4700	238	14	)	)	PUNCT
ejpam-4700	238	15	!	!	PUNCT
ejpam-4700	239	1	→	→	SYM
ejpam-4700	239	2	0	0	PUNCT
ejpam-4700	239	3	as	as	ADP
ejpam-4700	239	4	t	t	PROPN
ejpam-4700	239	5	→	→	SYM
ejpam-4700	239	6	tk	tk	PROPN
ejpam-4700	239	7	except	except	SCONJ
ejpam-4700	239	8	when	when	SCONJ
ejpam-4700	239	9	n	n	PROPN
ejpam-4700	239	10	=	=	SYM
ejpam-4700	239	11	l.	l.	PROPN
ejpam-4700	239	12	so	so	SCONJ
ejpam-4700	239	13	that	that	SCONJ
ejpam-4700	239	14	res(f(t	res(f(t	NOUN
ejpam-4700	239	15	)	)	PUNCT
ejpam-4700	239	16	,	,	PUNCT
ejpam-4700	239	17	t	t	PROPN
ejpam-4700	239	18	=	=	SYM
ejpam-4700	239	19	tk	tk	PROPN
ejpam-4700	239	20	)	)	PUNCT
ejpam-4700	239	21	=	=	SYM
ejpam-4700	239	22	1	1	NUM
ejpam-4700	239	23	(	(	PUNCT
ejpam-4700	239	24	r	r	NOUN
ejpam-4700	239	25	−	−	NOUN
ejpam-4700	239	26	1	1	NUM
ejpam-4700	239	27	)	)	PUNCT
ejpam-4700	239	28	!	!	PUNCT
ejpam-4700	240	1	(	(	PUNCT
ejpam-4700	240	2	1−	1−	NUM
ejpam-4700	240	3	u	u	NOUN
ejpam-4700	240	4	2u	2u	NOUN
ejpam-4700	240	5	)	)	PUNCT
ejpam-4700	240	6	r	r	NOUN
ejpam-4700	240	7	r−1∑	r−1∑	NUM
ejpam-4700	240	8	j=0	j=0	PROPN
ejpam-4700	240	9	(	(	PUNCT
ejpam-4700	240	10	r	r	NOUN
ejpam-4700	240	11	−	−	PROPN
ejpam-4700	240	12	1	1	NUM
ejpam-4700	240	13	j	j	NOUN
ejpam-4700	240	14	)	)	PUNCT
ejpam-4700	240	15	(	(	PUNCT
ejpam-4700	240	16	−1)r−1−j(n+	−1)r−1−j(n+	PUNCT
ejpam-4700	240	17	r	r	NOUN
ejpam-4700	240	18	−	−	PROPN
ejpam-4700	240	19	1−	1−	NUM
ejpam-4700	240	20	j)r−1−jt	j)r−1−jt	NUM
ejpam-4700	240	21	−(n+r−j	−(n+r−j	NOUN
ejpam-4700	240	22	)	)	PUNCT
ejpam-4700	240	23	k	k	NOUN
ejpam-4700	240	24	×	×	PROPN
ejpam-4700	240	25	extk	extk	INTJ
ejpam-4700	240	26	j∑	j∑	PROPN
ejpam-4700	240	27	l=0	l=0	PROPN
ejpam-4700	241	1	(	(	PUNCT
ejpam-4700	241	2	j	j	PROPN
ejpam-4700	241	3	l	l	NOUN
ejpam-4700	241	4	)	)	PUNCT
ejpam-4700	242	1	xj−l2	xj−l2	PROPN
ejpam-4700	242	2	lb	lb	X
ejpam-4700	242	3	(	(	PUNCT
ejpam-4700	242	4	r	r	NOUN
ejpam-4700	242	5	)	)	PUNCT
ejpam-4700	242	6	l	l	NOUN
ejpam-4700	242	7	=	=	SYM
ejpam-4700	242	8	1	1	NUM
ejpam-4700	242	9	(	(	PUNCT
ejpam-4700	242	10	r	r	NOUN
ejpam-4700	242	11	−	−	NOUN
ejpam-4700	242	12	1	1	NUM
ejpam-4700	242	13	)	)	PUNCT
ejpam-4700	242	14	!	!	PUNCT
ejpam-4700	243	1	(	(	PUNCT
ejpam-4700	243	2	1−	1−	NUM
ejpam-4700	243	3	u)r	u)r	X
ejpam-4700	243	4	(	(	PUNCT
ejpam-4700	243	5	2u)r	2u)r	PROPN
ejpam-4700	243	6	r−1∑	r−1∑	NUM
ejpam-4700	243	7	j=0	j=0	PROPN
ejpam-4700	243	8	(	(	PUNCT
ejpam-4700	243	9	r	r	NOUN
ejpam-4700	243	10	−	−	NOUN
ejpam-4700	243	11	1	1	NUM
ejpam-4700	243	12	)	)	PUNCT
ejpam-4700	243	13	!	!	PUNCT
ejpam-4700	244	1	j!(r	j!(r	PROPN
ejpam-4700	245	1	−	−	PROPN
ejpam-4700	245	2	1−	1−	NUM
ejpam-4700	245	3	j	j	PROPN
ejpam-4700	245	4	)	)	PUNCT
ejpam-4700	245	5	!	!	PUNCT
ejpam-4700	246	1	(	(	PUNCT
ejpam-4700	246	2	−1)r−1−j(n+	−1)r−1−j(n+	PUNCT
ejpam-4700	246	3	r	r	NOUN
ejpam-4700	246	4	−	−	PROPN
ejpam-4700	246	5	1−	1−	NUM
ejpam-4700	246	6	j)r−1−jt	j)r−1−jt	NUM
ejpam-4700	246	7	−(n+r−j	−(n+r−j	NOUN
ejpam-4700	246	8	)	)	PUNCT
ejpam-4700	246	9	k	k	NOUN
ejpam-4700	246	10	×	×	PROPN
ejpam-4700	247	1	extk	extk	INTJ
ejpam-4700	247	2	j∑	j∑	PROPN
ejpam-4700	248	1	l=0	l=0	PROPN
ejpam-4700	248	2	(	(	PUNCT
ejpam-4700	248	3	j	j	PROPN
ejpam-4700	248	4	l	l	NOUN
ejpam-4700	248	5	)	)	PUNCT
ejpam-4700	249	1	xj−l2	xj−l2	PROPN
ejpam-4700	249	2	lb	lb	X
ejpam-4700	249	3	(	(	PUNCT
ejpam-4700	249	4	r	r	NOUN
ejpam-4700	249	5	)	)	PUNCT
ejpam-4700	249	6	l	l	NOUN
ejpam-4700	250	1	=	=	SYM
ejpam-4700	250	2	(	(	PUNCT
ejpam-4700	250	3	u−	u−	PROPN
ejpam-4700	250	4	1	1	NUM
ejpam-4700	250	5	2u	2u	NOUN
ejpam-4700	250	6	)	)	PUNCT
ejpam-4700	250	7	r	r	NOUN
ejpam-4700	250	8	r−1∑	r−1∑	VERB
ejpam-4700	250	9	j=0	j=0	PROPN
ejpam-4700	250	10	(	(	PUNCT
ejpam-4700	250	11	n+	n+	INTJ
ejpam-4700	250	12	r	r	NOUN
ejpam-4700	250	13	−	−	PROPN
ejpam-4700	250	14	1−	1−	NUM
ejpam-4700	250	15	j	j	PROPN
ejpam-4700	250	16	r	r	NOUN
ejpam-4700	250	17	−	−	PROPN
ejpam-4700	250	18	1−	1−	NUM
ejpam-4700	250	19	j	j	PROPN
ejpam-4700	250	20	)	)	PUNCT
ejpam-4700	250	21	(	(	PUNCT
ejpam-4700	250	22	−1)−j−1	−1)−j−1	PROPN
ejpam-4700	250	23	t	t	PROPN
ejpam-4700	250	24	j−n−r	j−n−r	PROPN
ejpam-4700	250	25	j	j	PROPN
ejpam-4700	250	26	!	!	PUNCT
ejpam-4700	250	27	extk2j	extk2j	PROPN
ejpam-4700	251	1	j∑	j∑	VERB
ejpam-4700	251	2	l=0	l=0	PROPN
ejpam-4700	251	3	(	(	PUNCT
ejpam-4700	251	4	j	j	PROPN
ejpam-4700	251	5	l	l	NOUN
ejpam-4700	251	6	)	)	PUNCT
ejpam-4700	252	1	xj−l	xj−l	PROPN
ejpam-4700	252	2	2j−l	2j−l	NUM
ejpam-4700	252	3	b(r	b(r	PROPN
ejpam-4700	252	4	)	)	PUNCT
ejpam-4700	252	5	n	n	NOUN
ejpam-4700	252	6	.	.	PUNCT
ejpam-4700	253	1	we	we	PRON
ejpam-4700	253	2	use	use	VERB
ejpam-4700	253	3	the	the	DET
ejpam-4700	253	4	identity	identity	NOUN
ejpam-4700	253	5	that	that	PRON
ejpam-4700	253	6	b	b	X
ejpam-4700	253	7	(	(	PUNCT
ejpam-4700	253	8	r	r	NOUN
ejpam-4700	253	9	)	)	PUNCT
ejpam-4700	253	10	l	l	NOUN
ejpam-4700	253	11	=	=	PUNCT
ejpam-4700	254	1	∑j	∑j	NOUN
ejpam-4700	254	2	j=0	j=0	PROPN
ejpam-4700	254	3	(	(	PUNCT
ejpam-4700	254	4	j	j	PROPN
ejpam-4700	254	5	l	l	NOUN
ejpam-4700	254	6	)	)	PUNCT
ejpam-4700	254	7	b	b	NOUN
ejpam-4700	254	8	(	(	PUNCT
ejpam-4700	254	9	r	r	NOUN
ejpam-4700	254	10	)	)	PUNCT
ejpam-4700	254	11	l	l	NOUN
ejpam-4700	254	12	(	(	PUNCT
ejpam-4700	254	13	x	x	SYM
ejpam-4700	254	14	2	2	X
ejpam-4700	254	15	)	)	PUNCT
ejpam-4700	254	16	j−l	j−l	NOUN
ejpam-4700	254	17	.	.	PUNCT
ejpam-4700	255	1	thus	thus	ADV
ejpam-4700	255	2	,	,	PUNCT
ejpam-4700	255	3	res(f(t	res(f(t	PROPN
ejpam-4700	255	4	)	)	PUNCT
ejpam-4700	255	5	,	,	PUNCT
ejpam-4700	255	6	t	t	PROPN
ejpam-4700	255	7	=	=	SYM
ejpam-4700	255	8	tk	tk	PROPN
ejpam-4700	255	9	)	)	PUNCT
ejpam-4700	255	10	=	=	PUNCT
ejpam-4700	256	1	(	(	PUNCT
ejpam-4700	256	2	u−	u−	PROPN
ejpam-4700	256	3	1	1	NUM
ejpam-4700	256	4	2u	2u	NOUN
ejpam-4700	256	5	)	)	PUNCT
ejpam-4700	257	1	r	r	NOUN
ejpam-4700	257	2	r−1∑	r−1∑	VERB
ejpam-4700	257	3	j=0	j=0	PROPN
ejpam-4700	257	4	(	(	PUNCT
ejpam-4700	257	5	n+	n+	INTJ
ejpam-4700	257	6	r	r	NOUN
ejpam-4700	257	7	−	−	PROPN
ejpam-4700	257	8	1−	1−	NUM
ejpam-4700	257	9	j	j	PROPN
ejpam-4700	257	10	r	r	NOUN
ejpam-4700	257	11	−	−	PROPN
ejpam-4700	257	12	1−	1−	NUM
ejpam-4700	257	13	j	j	PROPN
ejpam-4700	257	14	)	)	PUNCT
ejpam-4700	257	15	(	(	PUNCT
ejpam-4700	257	16	−1)j−1b	−1)j−1b	X
ejpam-4700	257	17	(	(	PUNCT
ejpam-4700	257	18	r	r	NOUN
ejpam-4700	257	19	)	)	PUNCT
ejpam-4700	257	20	l	l	NOUN
ejpam-4700	257	21	(	(	PUNCT
ejpam-4700	257	22	x	x	SYM
ejpam-4700	257	23	2	2	X
ejpam-4700	257	24	)	)	PUNCT
ejpam-4700	257	25	j	j	PROPN
ejpam-4700	257	26	!	!	PUNCT
ejpam-4700	258	1	extk	extk	INTJ
ejpam-4700	259	1	tr+n−j	tr+n−j	INTJ
ejpam-4700	259	2	k	k	ADJ
ejpam-4700	259	3	substituting	substitute	VERB
ejpam-4700	259	4	tk	tk	PROPN
ejpam-4700	259	5	=	=	NOUN
ejpam-4700	259	6	log	log	PROPN
ejpam-4700	259	7	(	(	PUNCT
ejpam-4700	259	8	u	u	NOUN
ejpam-4700	259	9	λ	λ	PROPN
ejpam-4700	259	10	)	)	PUNCT
ejpam-4700	259	11	1	1	NUM
ejpam-4700	259	12	2	2	NUM
ejpam-4700	259	13	+	+	CCONJ
ejpam-4700	259	14	kπi	kπi	NOUN
ejpam-4700	259	15	,	,	PUNCT
ejpam-4700	259	16	we	we	PRON
ejpam-4700	259	17	get	get	VERB
ejpam-4700	259	18	res(f(t	res(f(t	NOUN
ejpam-4700	259	19	)	)	PUNCT
ejpam-4700	259	20	,	,	PUNCT
ejpam-4700	259	21	t	t	PROPN
ejpam-4700	259	22	=	=	SYM
ejpam-4700	259	23	tk	tk	PROPN
ejpam-4700	259	24	)	)	PUNCT
ejpam-4700	259	25	=	=	PUNCT
ejpam-4700	260	1	(	(	PUNCT
ejpam-4700	260	2	u−	u−	PROPN
ejpam-4700	260	3	1	1	NUM
ejpam-4700	260	4	2u	2u	NOUN
ejpam-4700	260	5	)	)	PUNCT
ejpam-4700	261	1	r	r	NOUN
ejpam-4700	261	2	r−1∑	r−1∑	VERB
ejpam-4700	261	3	j=0	j=0	PROPN
ejpam-4700	261	4	(	(	PUNCT
ejpam-4700	261	5	n+	n+	INTJ
ejpam-4700	261	6	r	r	NOUN
ejpam-4700	261	7	−	−	PROPN
ejpam-4700	261	8	1−	1−	NUM
ejpam-4700	261	9	j	j	PROPN
ejpam-4700	261	10	r	r	NOUN
ejpam-4700	261	11	−	−	PROPN
ejpam-4700	261	12	1−	1−	NUM
ejpam-4700	261	13	j	j	PROPN
ejpam-4700	261	14	)	)	PUNCT
ejpam-4700	261	15	(	(	PUNCT
ejpam-4700	261	16	−1)j−1b	−1)j−1b	X
ejpam-4700	261	17	(	(	PUNCT
ejpam-4700	261	18	r	r	NOUN
ejpam-4700	261	19	)	)	PUNCT
ejpam-4700	261	20	l	l	NOUN
ejpam-4700	261	21	(	(	PUNCT
ejpam-4700	261	22	x	x	SYM
ejpam-4700	261	23	2	2	X
ejpam-4700	261	24	)	)	PUNCT
ejpam-4700	261	25	j	j	NOUN
ejpam-4700	261	26	!	!	PUNCT
ejpam-4700	262	1	e	e	X
ejpam-4700	262	2	x	x	X
ejpam-4700	262	3	(	(	PUNCT
ejpam-4700	262	4	log(u	log(u	PROPN
ejpam-4700	262	5	λ	λ	NOUN
ejpam-4700	262	6	)	)	PUNCT
ejpam-4700	262	7	1	1	NUM
ejpam-4700	262	8	2+kπi	2+kπi	NUM
ejpam-4700	262	9	)	)	PUNCT
ejpam-4700	262	10	1	1	NUM
ejpam-4700	262	11	2	2	NUM
ejpam-4700	262	12	[	[	PUNCT
ejpam-4700	262	13	log	log	NOUN
ejpam-4700	262	14	(	(	PUNCT
ejpam-4700	262	15	u	u	NOUN
ejpam-4700	262	16	λ	λ	PROPN
ejpam-4700	262	17	)	)	PUNCT
ejpam-4700	262	18	1	1	NUM
ejpam-4700	262	19	2	2	NUM
ejpam-4700	262	20	+	+	NUM
ejpam-4700	262	21	kπi	kπi	NOUN
ejpam-4700	262	22	]	]	X
ejpam-4700	262	23	r+n−j	r+n−j	PROPN
ejpam-4700	262	24	r.	r.	PROPN
ejpam-4700	262	25	b.	b.	PROPN
ejpam-4700	262	26	corcino	corcino	PROPN
ejpam-4700	262	27	et	et	PROPN
ejpam-4700	262	28	al	al	PROPN
ejpam-4700	262	29	.	.	PUNCT
ejpam-4700	262	30	/	/	SYM
ejpam-4700	262	31	eur	eur	PROPN
ejpam-4700	262	32	.	.	PUNCT
ejpam-4700	263	1	j.	j.	PROPN
ejpam-4700	263	2	pure	pure	PROPN
ejpam-4700	263	3	appl	appl	PROPN
ejpam-4700	263	4	.	.	PROPN
ejpam-4700	263	5	math	math	PROPN
ejpam-4700	263	6	,	,	PUNCT
ejpam-4700	263	7	16	16	NUM
ejpam-4700	263	8	(	(	PUNCT
ejpam-4700	263	9	2	2	NUM
ejpam-4700	263	10	)	)	PUNCT
ejpam-4700	263	11	(	(	PUNCT
ejpam-4700	263	12	2023	2023	NUM
ejpam-4700	263	13	)	)	PUNCT
ejpam-4700	263	14	,	,	PUNCT
ejpam-4700	263	15	1005	1005	NUM
ejpam-4700	263	16	-	-	SYM
ejpam-4700	263	17	1023	1023	NUM
ejpam-4700	263	18	1017	1017	NUM
ejpam-4700	263	19	this	this	PRON
ejpam-4700	263	20	gives	give	VERB
ejpam-4700	263	21	t	t	PROPN
ejpam-4700	263	22	(	(	PUNCT
ejpam-4700	263	23	r	r	NOUN
ejpam-4700	263	24	)	)	PUNCT
ejpam-4700	263	25	n	n	CCONJ
ejpam-4700	263	26	(	(	PUNCT
ejpam-4700	263	27	x;u	x;u	PROPN
ejpam-4700	263	28	,	,	PUNCT
ejpam-4700	263	29	λ	λ	NOUN
ejpam-4700	263	30	)	)	PUNCT
ejpam-4700	263	31	=	=	PUNCT
ejpam-4700	264	1	−n	−n	ADJ
ejpam-4700	264	2	!	!	PUNCT
ejpam-4700	265	1	∑	∑	ADV
ejpam-4700	265	2	k∈z	k∈z	PROPN
ejpam-4700	265	3	(	(	PUNCT
ejpam-4700	265	4	u−	u−	PROPN
ejpam-4700	265	5	1	1	NUM
ejpam-4700	265	6	2u	2u	NOUN
ejpam-4700	265	7	)	)	PUNCT
ejpam-4700	265	8	r	r	NOUN
ejpam-4700	265	9	r−1∑	r−1∑	PROPN
ejpam-4700	265	10	j=0	j=0	PROPN
ejpam-4700	265	11	(	(	PUNCT
ejpam-4700	265	12	−1)j−12j	−1)j−12j	NOUN
ejpam-4700	265	13	(	(	PUNCT
ejpam-4700	265	14	n+	n+	INTJ
ejpam-4700	266	1	r	r	NOUN
ejpam-4700	266	2	−	−	PROPN
ejpam-4700	266	3	1−	1−	NUM
ejpam-4700	267	1	j	j	PROPN
ejpam-4700	267	2	r	r	NOUN
ejpam-4700	267	3	−	−	PROPN
ejpam-4700	267	4	1−	1−	NUM
ejpam-4700	267	5	j	j	PROPN
ejpam-4700	267	6	)	)	PUNCT
ejpam-4700	267	7	b	b	PROPN
ejpam-4700	267	8	(	(	PUNCT
ejpam-4700	267	9	r	r	NOUN
ejpam-4700	267	10	)	)	PUNCT
ejpam-4700	267	11	l	l	NOUN
ejpam-4700	267	12	(	(	PUNCT
ejpam-4700	267	13	x	x	SYM
ejpam-4700	267	14	2	2	X
ejpam-4700	267	15	)	)	PUNCT
ejpam-4700	267	16	j	j	NOUN
ejpam-4700	267	17	!	!	PUNCT
ejpam-4700	268	1	(	(	PUNCT
ejpam-4700	268	2	u	u	NOUN
ejpam-4700	268	3	λ	λ	PROPN
ejpam-4700	268	4	)	)	PUNCT
ejpam-4700	268	5	x/2	x/2	PUNCT
ejpam-4700	269	1	exkπi	exkπi	PROPN
ejpam-4700	269	2	[	[	PUNCT
ejpam-4700	269	3	log	log	NOUN
ejpam-4700	269	4	(	(	PUNCT
ejpam-4700	269	5	u	u	NOUN
ejpam-4700	269	6	λ	λ	PROPN
ejpam-4700	269	7	)	)	PUNCT
ejpam-4700	269	8	1	1	NUM
ejpam-4700	269	9	2	2	NUM
ejpam-4700	269	10	+	+	NUM
ejpam-4700	269	11	kπi	kπi	NOUN
ejpam-4700	270	1	]	]	X
ejpam-4700	270	2	r+n−j	r+n−j	X
ejpam-4700	270	3	where	where	SCONJ
ejpam-4700	270	4	(	(	PUNCT
ejpam-4700	270	5	t	t	NOUN
ejpam-4700	270	6	et	et	NOUN
ejpam-4700	270	7	−	−	NOUN
ejpam-4700	270	8	1	1	X
ejpam-4700	270	9	)	)	PUNCT
ejpam-4700	270	10	r	r	NOUN
ejpam-4700	270	11	ext	ext	NOUN
ejpam-4700	270	12	=	=	NOUN
ejpam-4700	270	13	∞∑	∞∑	NUM
ejpam-4700	270	14	n=0	n=0	NUM
ejpam-4700	270	15	b(r	b(r	NOUN
ejpam-4700	270	16	)	)	PUNCT
ejpam-4700	270	17	n	n	CCONJ
ejpam-4700	270	18	(	(	PUNCT
ejpam-4700	270	19	x	x	X
ejpam-4700	270	20	)	)	PUNCT
ejpam-4700	270	21	tn	tn	PROPN
ejpam-4700	270	22	n	n	PROPN
ejpam-4700	270	23	!	!	PROPN
ejpam-4700	270	24	2.3	2.3	NUM
ejpam-4700	270	25	.	.	PUNCT
ejpam-4700	271	1	fourier	fouri	ADJ
ejpam-4700	271	2	expansion	expansion	NOUN
ejpam-4700	271	3	of	of	ADP
ejpam-4700	271	4	apostol	apostol	NOUN
ejpam-4700	271	5	-	-	PUNCT
ejpam-4700	271	6	frobenius	frobenius	NOUN
ejpam-4700	271	7	-	-	PUNCT
ejpam-4700	271	8	genocchi	genocchi	NOUN
ejpam-4700	271	9	polynomials	polynomial	NOUN
ejpam-4700	271	10	of	of	ADP
ejpam-4700	271	11	higher	high	ADJ
ejpam-4700	271	12	order	order	NOUN
ejpam-4700	271	13	the	the	DET
ejpam-4700	271	14	genocchi	genocchi	PROPN
ejpam-4700	271	15	polynomials	polynomial	NOUN
ejpam-4700	271	16	can	can	AUX
ejpam-4700	271	17	be	be	AUX
ejpam-4700	271	18	defined	define	VERB
ejpam-4700	271	19	as	as	ADP
ejpam-4700	271	20	[	[	X
ejpam-4700	271	21	4	4	NUM
ejpam-4700	271	22	]	]	X
ejpam-4700	271	23	∞∑	∞∑	NUM
ejpam-4700	271	24	n=0	n=0	NUM
ejpam-4700	271	25	gn(x	gn(x	NOUN
ejpam-4700	271	26	)	)	PUNCT
ejpam-4700	271	27	tn	tn	NOUN
ejpam-4700	271	28	n	n	NOUN
ejpam-4700	271	29	!	!	PUNCT
ejpam-4700	272	1	=	=	PUNCT
ejpam-4700	272	2	(	(	PUNCT
ejpam-4700	272	3	2	2	NUM
ejpam-4700	272	4	t	t	NOUN
ejpam-4700	272	5	et	et	NOUN
ejpam-4700	273	1	+	+	CCONJ
ejpam-4700	273	2	1	1	X
ejpam-4700	273	3	)	)	PUNCT
ejpam-4700	273	4	ext	ext	NOUN
ejpam-4700	273	5	(	(	PUNCT
ejpam-4700	273	6	18	18	NUM
ejpam-4700	273	7	)	)	PUNCT
ejpam-4700	273	8	the	the	DET
ejpam-4700	273	9	apostol	apostol	NOUN
ejpam-4700	273	10	-	-	PUNCT
ejpam-4700	273	11	frobenius	frobenius	NOUN
ejpam-4700	273	12	-	-	PUNCT
ejpam-4700	273	13	genocchi	genocchi	NOUN
ejpam-4700	273	14	polynomials	polynomial	NOUN
ejpam-4700	273	15	which	which	PRON
ejpam-4700	273	16	are	be	AUX
ejpam-4700	273	17	certain	certain	ADJ
ejpam-4700	273	18	variation	variation	NOUN
ejpam-4700	273	19	of	of	ADP
ejpam-4700	273	20	the	the	DET
ejpam-4700	273	21	genocchi	genocchi	PROPN
ejpam-4700	273	22	polynomials	polynomial	NOUN
ejpam-4700	273	23	are	be	AUX
ejpam-4700	273	24	defined	define	VERB
ejpam-4700	273	25	by	by	ADP
ejpam-4700	273	26	araci	araci	NOUN
ejpam-4700	273	27	and	and	CCONJ
ejpam-4700	273	28	acikgoz	acikgoz	ADJ
ejpam-4700	274	1	[	[	X
ejpam-4700	274	2	1	1	NUM
ejpam-4700	274	3	]	]	PUNCT
ejpam-4700	274	4	as	as	ADP
ejpam-4700	274	5	coefficients	coefficient	NOUN
ejpam-4700	274	6	of	of	ADP
ejpam-4700	274	7	the	the	DET
ejpam-4700	274	8	following	follow	VERB
ejpam-4700	274	9	generating	generate	VERB
ejpam-4700	274	10	function	function	NOUN
ejpam-4700	274	11	:	:	PUNCT
ejpam-4700	274	12	∞∑	∞∑	NUM
ejpam-4700	274	13	n=0	n=0	ADJ
ejpam-4700	274	14	gn(x;u	gn(x;u	NOUN
ejpam-4700	274	15	,	,	PUNCT
ejpam-4700	274	16	λ	λ	NOUN
ejpam-4700	274	17	)	)	PUNCT
ejpam-4700	274	18	tn	tn	PROPN
ejpam-4700	274	19	n	n	PROPN
ejpam-4700	274	20	!	!	PUNCT
ejpam-4700	275	1	=	=	PUNCT
ejpam-4700	276	1	(	(	PUNCT
ejpam-4700	276	2	1−	1−	NUM
ejpam-4700	276	3	u)t	u)t	X
ejpam-4700	276	4	λet	λet	ADP
ejpam-4700	276	5	−	−	NUM
ejpam-4700	276	6	u	u	NOUN
ejpam-4700	276	7	ext	ext	NOUN
ejpam-4700	276	8	(	(	PUNCT
ejpam-4700	276	9	19	19	NUM
ejpam-4700	276	10	)	)	PUNCT
ejpam-4700	276	11	where	where	SCONJ
ejpam-4700	276	12	u	u	NOUN
ejpam-4700	276	13	,	,	PUNCT
ejpam-4700	276	14	λ	λ	PROPN
ejpam-4700	276	15	∈	∈	PROPN
ejpam-4700	276	16	c	c	NOUN
ejpam-4700	276	17	with	with	ADP
ejpam-4700	276	18	u	u	NOUN
ejpam-4700	276	19	̸=	̸=	PROPN
ejpam-4700	276	20	1	1	NUM
ejpam-4700	276	21	,	,	PUNCT
ejpam-4700	276	22	λ	λ	PROPN
ejpam-4700	276	23	̸=	̸=	PROPN
ejpam-4700	276	24	1	1	NUM
ejpam-4700	276	25	and	and	CCONJ
ejpam-4700	276	26	u	u	PROPN
ejpam-4700	276	27	̸=	̸=	PROPN
ejpam-4700	276	28	λ	λ	PROPN
ejpam-4700	276	29	.	.	PUNCT
ejpam-4700	276	30	by	by	ADP
ejpam-4700	276	31	cauchy	cauchy	ADJ
ejpam-4700	276	32	integral	integral	ADJ
ejpam-4700	276	33	formula	formula	NOUN
ejpam-4700	276	34	,	,	PUNCT
ejpam-4700	276	35	we	we	PRON
ejpam-4700	276	36	observe	observe	VERB
ejpam-4700	276	37	that	that	DET
ejpam-4700	276	38	gn(x;u	gn(x;u	NOUN
ejpam-4700	276	39	,	,	PUNCT
ejpam-4700	276	40	λ	λ	NOUN
ejpam-4700	276	41	)	)	PUNCT
ejpam-4700	276	42	n	n	CCONJ
ejpam-4700	276	43	!	!	PUNCT
ejpam-4700	277	1	=	=	SYM
ejpam-4700	277	2	1	1	NUM
ejpam-4700	277	3	2πi	2πi	NOUN
ejpam-4700	277	4	∫	∫	PROPN
ejpam-4700	277	5	c	c	X
ejpam-4700	277	6	(	(	PUNCT
ejpam-4700	277	7	1−	1−	NUM
ejpam-4700	277	8	u)t	u)t	X
ejpam-4700	277	9	λet	λet	ADP
ejpam-4700	277	10	−	−	NUM
ejpam-4700	277	11	u	u	NOUN
ejpam-4700	277	12	ext	ext	NOUN
ejpam-4700	277	13	dt	dt	NOUN
ejpam-4700	277	14	tn+1	tn+1	PROPN
ejpam-4700	277	15	if	if	SCONJ
ejpam-4700	277	16	we	we	PRON
ejpam-4700	277	17	consider	consider	VERB
ejpam-4700	277	18	the	the	DET
ejpam-4700	277	19	function	function	NOUN
ejpam-4700	277	20	f(t	f(t	NOUN
ejpam-4700	277	21	)	)	PUNCT
ejpam-4700	277	22	=	=	PUNCT
ejpam-4700	277	23	(	(	PUNCT
ejpam-4700	277	24	1−	1−	NUM
ejpam-4700	277	25	u	u	NOUN
ejpam-4700	277	26	)	)	PUNCT
ejpam-4700	278	1	λet	λet	ADP
ejpam-4700	278	2	−	−	PROPN
ejpam-4700	278	3	u	u	NOUN
ejpam-4700	278	4	ext	ext	VERB
ejpam-4700	278	5	tn	tn	PROPN
ejpam-4700	278	6	,	,	PUNCT
ejpam-4700	278	7	then	then	ADV
ejpam-4700	278	8	it	it	PRON
ejpam-4700	278	9	has	have	VERB
ejpam-4700	278	10	a	a	DET
ejpam-4700	278	11	pole	pole	NOUN
ejpam-4700	278	12	at	at	ADP
ejpam-4700	278	13	t	t	PROPN
ejpam-4700	278	14	=	=	SYM
ejpam-4700	278	15	0	0	NUM
ejpam-4700	278	16	of	of	ADP
ejpam-4700	278	17	order	order	NOUN
ejpam-4700	278	18	n.	n.	VERB
ejpam-4700	278	19	the	the	DET
ejpam-4700	278	20	other	other	ADJ
ejpam-4700	278	21	poles	pole	NOUN
ejpam-4700	278	22	are	be	AUX
ejpam-4700	278	23	found	find	VERB
ejpam-4700	278	24	to	to	PART
ejpam-4700	278	25	be	be	AUX
ejpam-4700	278	26	at	at	ADP
ejpam-4700	278	27	λet	λet	ADV
ejpam-4700	278	28	−	−	NUM
ejpam-4700	278	29	u	u	NOUN
ejpam-4700	278	30	=	=	NOUN
ejpam-4700	278	31	0	0	NUM
ejpam-4700	278	32	λet	λet	NOUN
ejpam-4700	278	33	=	=	SYM
ejpam-4700	278	34	u	u	NOUN
ejpam-4700	278	35	et	et	NOUN
ejpam-4700	278	36	=	=	SYM
ejpam-4700	278	37	u	u	NOUN
ejpam-4700	278	38	λ	λ	X
ejpam-4700	278	39	tk	tk	NOUN
ejpam-4700	278	40	:	:	PUNCT
ejpam-4700	278	41	=	=	SYM
ejpam-4700	278	42	t	t	PROPN
ejpam-4700	278	43	=	=	PUNCT
ejpam-4700	278	44	log	log	NOUN
ejpam-4700	278	45	(	(	PUNCT
ejpam-4700	278	46	u	u	NOUN
ejpam-4700	278	47	λ	λ	PROPN
ejpam-4700	278	48	)	)	PUNCT
ejpam-4700	279	1	+	+	CCONJ
ejpam-4700	279	2	2kπi	2kπi	NUM
ejpam-4700	279	3	by	by	ADP
ejpam-4700	279	4	cauchy	cauchy	ADJ
ejpam-4700	279	5	residue	residue	NOUN
ejpam-4700	279	6	theorem	theorem	NOUN
ejpam-4700	279	7	,	,	PUNCT
ejpam-4700	279	8	we	we	PRON
ejpam-4700	279	9	have	have	VERB
ejpam-4700	279	10	1	1	NUM
ejpam-4700	279	11	2πi	2πi	ADJ
ejpam-4700	279	12	∫	∫	PROPN
ejpam-4700	279	13	cn	cn	PROPN
ejpam-4700	279	14	fn(t)dt	fn(t)dt	PROPN
ejpam-4700	279	15	=	=	SYM
ejpam-4700	279	16	res(fn(t	res(fn(t	PROPN
ejpam-4700	279	17	)	)	PUNCT
ejpam-4700	279	18	,	,	PUNCT
ejpam-4700	279	19	t	t	PROPN
ejpam-4700	279	20	=	=	SYM
ejpam-4700	279	21	0	0	NUM
ejpam-4700	279	22	)	)	PUNCT
ejpam-4700	280	1	+	+	CCONJ
ejpam-4700	280	2	∑	∑	ADV
ejpam-4700	280	3	k∈z	k∈z	PROPN
ejpam-4700	280	4	res(fn(t	res(fn(t	PROPN
ejpam-4700	280	5	)	)	PUNCT
ejpam-4700	280	6	,	,	PUNCT
ejpam-4700	280	7	t	t	PROPN
ejpam-4700	280	8	=	=	SYM
ejpam-4700	280	9	tk	tk	PROPN
ejpam-4700	280	10	)	)	PUNCT
ejpam-4700	280	11	(	(	PUNCT
ejpam-4700	280	12	20	20	NUM
ejpam-4700	280	13	)	)	PUNCT
ejpam-4700	280	14	in	in	ADP
ejpam-4700	280	15	eq	eq	ADP
ejpam-4700	280	16	.	.	PUNCT
ejpam-4700	281	1	(	(	PUNCT
ejpam-4700	281	2	20	20	NUM
ejpam-4700	281	3	)	)	PUNCT
ejpam-4700	281	4	,	,	PUNCT
ejpam-4700	281	5	we	we	PRON
ejpam-4700	281	6	take	take	VERB
ejpam-4700	281	7	the	the	DET
ejpam-4700	281	8	limit	limit	NOUN
ejpam-4700	281	9	of	of	ADP
ejpam-4700	281	10	the	the	DET
ejpam-4700	281	11	integral	integral	ADJ
ejpam-4700	281	12	,	,	PUNCT
ejpam-4700	281	13	∫	∫	PROPN
ejpam-4700	281	14	cn	cn	PROPN
ejpam-4700	281	15	fn(t)dt	fn(t)dt	PROPN
ejpam-4700	281	16	as	as	ADP
ejpam-4700	281	17	n	n	PROPN
ejpam-4700	281	18	→	→	SYM
ejpam-4700	281	19	∞	∞	PROPN
ejpam-4700	281	20	as	as	SCONJ
ejpam-4700	281	21	explicitly	explicitly	ADV
ejpam-4700	281	22	shown	show	VERB
ejpam-4700	281	23	in	in	ADP
ejpam-4700	281	24	the	the	DET
ejpam-4700	281	25	following	follow	VERB
ejpam-4700	281	26	lemma	lemma	PROPN
ejpam-4700	281	27	r.	r.	PROPN
ejpam-4700	281	28	b.	b.	PROPN
ejpam-4700	281	29	corcino	corcino	PROPN
ejpam-4700	281	30	et	et	PROPN
ejpam-4700	281	31	al	al	PROPN
ejpam-4700	281	32	.	.	PUNCT
ejpam-4700	281	33	/	/	SYM
ejpam-4700	281	34	eur	eur	PROPN
ejpam-4700	281	35	.	.	PUNCT
ejpam-4700	282	1	j.	j.	PROPN
ejpam-4700	282	2	pure	pure	PROPN
ejpam-4700	282	3	appl	appl	PROPN
ejpam-4700	282	4	.	.	PROPN
ejpam-4700	282	5	math	math	PROPN
ejpam-4700	282	6	,	,	PUNCT
ejpam-4700	282	7	16	16	NUM
ejpam-4700	282	8	(	(	PUNCT
ejpam-4700	282	9	2	2	NUM
ejpam-4700	282	10	)	)	PUNCT
ejpam-4700	282	11	(	(	PUNCT
ejpam-4700	282	12	2023	2023	NUM
ejpam-4700	282	13	)	)	PUNCT
ejpam-4700	282	14	,	,	PUNCT
ejpam-4700	282	15	1005	1005	NUM
ejpam-4700	282	16	-	-	SYM
ejpam-4700	282	17	1023	1023	NUM
ejpam-4700	282	18	1018	1018	NUM
ejpam-4700	282	19	lemma	lemma	PROPN
ejpam-4700	282	20	2	2	X
ejpam-4700	282	21	.	.	PUNCT
ejpam-4700	283	1	let	let	VERB
ejpam-4700	283	2	u	u	NOUN
ejpam-4700	283	3	,	,	PUNCT
ejpam-4700	283	4	λ	λ	PROPN
ejpam-4700	283	5	∈	∈	PROPN
ejpam-4700	283	6	c{0	c{0	NOUN
ejpam-4700	283	7	,	,	PUNCT
ejpam-4700	283	8	1	1	NUM
ejpam-4700	283	9	}	}	PUNCT
ejpam-4700	283	10	with	with	ADP
ejpam-4700	283	11	|λ|	|λ|	NOUN
ejpam-4700	283	12	=	=	PUNCT
ejpam-4700	283	13	̸	̸	NUM
ejpam-4700	283	14	|u|	|u|	PROPN
ejpam-4700	283	15	.	.	PUNCT
ejpam-4700	284	1	for	for	ADP
ejpam-4700	284	2	0	0	NUM
ejpam-4700	284	3	<	<	X
ejpam-4700	284	4	x	x	SYM
ejpam-4700	284	5	≤	≤	PROPN
ejpam-4700	284	6	1∫	1∫	NUM
ejpam-4700	284	7	cn	cn	NOUN
ejpam-4700	284	8	(	(	PUNCT
ejpam-4700	284	9	1−	1−	NUM
ejpam-4700	284	10	u)text	u)text	PROPN
ejpam-4700	284	11	(	(	PUNCT
ejpam-4700	284	12	λet	λet	NOUN
ejpam-4700	284	13	−	−	PROPN
ejpam-4700	284	14	u)tn+1	u)tn+1	ADJ
ejpam-4700	284	15	dt	dt	NOUN
ejpam-4700	284	16	=	=	SYM
ejpam-4700	284	17	0	0	NUM
ejpam-4700	284	18	proof	proof	NOUN
ejpam-4700	284	19	.	.	PUNCT
ejpam-4700	285	1	consider∣∣∣∣∫	consider∣∣∣∣∫	NOUN
ejpam-4700	285	2	cn	cn	PROPN
ejpam-4700	285	3	(	(	PUNCT
ejpam-4700	285	4	1−	1−	NUM
ejpam-4700	285	5	u)text	u)text	INTJ
ejpam-4700	285	6	λet	λet	PRON
ejpam-4700	285	7	−	−	NUM
ejpam-4700	285	8	u	u	NOUN
ejpam-4700	285	9	dt	dt	X
ejpam-4700	285	10	tn+1	tn+1	PROPN
ejpam-4700	285	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4700	285	12	≤	≤	NUM
ejpam-4700	285	13	∫	∫	PROPN
ejpam-4700	285	14	cn	cn	PROPN
ejpam-4700	285	15	|1−	|1−	PROPN
ejpam-4700	285	16	u||ext||dt|	u||ext||dt|	ADJ
ejpam-4700	285	17	|λet	|λet	NOUN
ejpam-4700	285	18	−	−	PROPN
ejpam-4700	285	19	u||tn|	u||tn|	NOUN
ejpam-4700	285	20	=	=	SYM
ejpam-4700	285	21	∫	∫	PROPN
ejpam-4700	285	22	cn	cn	PROPN
ejpam-4700	285	23	|1−	|1−	PROPN
ejpam-4700	285	24	u||ext||dt|	u||ext||dt|	ADJ
ejpam-4700	285	25	|αu|	|αu|	PROPN
ejpam-4700	285	26	∣∣et	∣∣et	NOUN
ejpam-4700	285	27	+	+	CCONJ
ejpam-4700	285	28	1	1	NUM
ejpam-4700	285	29	α	α	NOUN
ejpam-4700	285	30	∣∣	∣∣	X
ejpam-4700	285	31	|tn|	|tn|	NOUN
ejpam-4700	285	32	,	,	PUNCT
ejpam-4700	285	33	where	where	SCONJ
ejpam-4700	285	34	α	α	NOUN
ejpam-4700	285	35	=	=	SYM
ejpam-4700	285	36	−λ	−λ	PROPN
ejpam-4700	285	37	u∫	u∫	NOUN
ejpam-4700	285	38	cn	cn	PROPN
ejpam-4700	285	39	|1−	|1−	VERB
ejpam-4700	285	40	u||dt|	u||dt|	ADJ
ejpam-4700	286	1	|	|	ADV
ejpam-4700	286	2	−	−	X
ejpam-4700	286	3	λ||tn|	λ||tn|	PRON
ejpam-4700	286	4	so	so	SCONJ
ejpam-4700	286	5	that	that	SCONJ
ejpam-4700	286	6	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-4700	287	1	cn	cn	X
ejpam-4700	288	1	(	(	PUNCT
ejpam-4700	288	2	1−	1−	NUM
ejpam-4700	288	3	u)text	u)text	INTJ
ejpam-4700	289	1	λet	λet	PRON
ejpam-4700	289	2	−	−	NUM
ejpam-4700	289	3	u	u	NOUN
ejpam-4700	289	4	dt	dt	X
ejpam-4700	289	5	tn+1	tn+1	PROPN
ejpam-4700	289	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4700	289	7	≤	≤	NOUN
ejpam-4700	289	8	|1−	|1−	VERB
ejpam-4700	289	9	u|	u|	PROPN
ejpam-4700	290	1	|	|	ADV
ejpam-4700	290	2	−	−	PROPN
ejpam-4700	290	3	λ|	λ|	PROPN
ejpam-4700	290	4	∫	∫	PROPN
ejpam-4700	291	1	cn	cn	PROPN
ejpam-4700	291	2	|dt|	|dt|	PROPN
ejpam-4700	291	3	|tn|	|tn|	PROPN
ejpam-4700	291	4	=	=	SYM
ejpam-4700	291	5	1	1	NUM
ejpam-4700	291	6	(	(	PUNCT
ejpam-4700	291	7	(	(	PUNCT
ejpam-4700	291	8	2n	2n	X
ejpam-4700	291	9	+	+	CCONJ
ejpam-4700	291	10	ϵ)π)n	ϵ)π)n	NOUN
ejpam-4700	291	11	as	as	ADP
ejpam-4700	291	12	n	n	PROPN
ejpam-4700	291	13	→	→	SYM
ejpam-4700	291	14	∞	∞	NUM
ejpam-4700	291	15	∫	∫	PROPN
ejpam-4700	291	16	cn	cn	PROPN
ejpam-4700	291	17	(	(	PUNCT
ejpam-4700	291	18	1−	1−	NUM
ejpam-4700	291	19	u)text	u)text	INTJ
ejpam-4700	292	1	λet	λet	DET
ejpam-4700	292	2	−	−	NUM
ejpam-4700	292	3	u	u	INTJ
ejpam-4700	292	4	dt	dt	X
ejpam-4700	292	5	tn+1	tn+1	NOUN
ejpam-4700	292	6	dt	dt	X
ejpam-4700	292	7	→	→	SYM
ejpam-4700	292	8	0	0	NUM
ejpam-4700	292	9	using	use	VERB
ejpam-4700	292	10	lemma	lemma	PROPN
ejpam-4700	292	11	2	2	NUM
ejpam-4700	292	12	,	,	PUNCT
ejpam-4700	292	13	eq	eq	NOUN
ejpam-4700	292	14	.	.	PUNCT
ejpam-4700	293	1	(	(	PUNCT
ejpam-4700	293	2	20	20	NUM
ejpam-4700	293	3	)	)	PUNCT
ejpam-4700	293	4	becomes	become	VERB
ejpam-4700	293	5	res(fn(t	res(fn(t	PROPN
ejpam-4700	293	6	)	)	PUNCT
ejpam-4700	293	7	,	,	PUNCT
ejpam-4700	293	8	t	t	PROPN
ejpam-4700	293	9	=	=	SYM
ejpam-4700	293	10	0	0	NUM
ejpam-4700	293	11	)	)	PUNCT
ejpam-4700	293	12	=	=	SYM
ejpam-4700	294	1	−	−	PROPN
ejpam-4700	294	2	∑	∑	PUNCT
ejpam-4700	294	3	k∈z	k∈z	PROPN
ejpam-4700	294	4	res(fn(t	res(fn(t	PROPN
ejpam-4700	294	5	)	)	PUNCT
ejpam-4700	294	6	,	,	PUNCT
ejpam-4700	294	7	t	t	PROPN
ejpam-4700	294	8	=	=	SYM
ejpam-4700	294	9	tk	tk	PROPN
ejpam-4700	294	10	)	)	PUNCT
ejpam-4700	294	11	with	with	ADP
ejpam-4700	294	12	these	these	PRON
ejpam-4700	294	13	,	,	PUNCT
ejpam-4700	294	14	araci	araci	NOUN
ejpam-4700	294	15	and	and	CCONJ
ejpam-4700	294	16	acikgoz	acikgoz	ADJ
ejpam-4700	295	1	[	[	X
ejpam-4700	295	2	1	1	NUM
ejpam-4700	295	3	]	]	PUNCT
ejpam-4700	295	4	obtained	obtain	VERB
ejpam-4700	295	5	the	the	DET
ejpam-4700	295	6	following	follow	VERB
ejpam-4700	295	7	fourier	fourier	NOUN
ejpam-4700	295	8	series	series	NOUN
ejpam-4700	295	9	expansion	expansion	NOUN
ejpam-4700	295	10	by	by	ADP
ejpam-4700	295	11	calculating	calculate	VERB
ejpam-4700	295	12	the	the	DET
ejpam-4700	295	13	residues	residue	NOUN
ejpam-4700	295	14	of	of	ADP
ejpam-4700	295	15	the	the	DET
ejpam-4700	295	16	function	function	NOUN
ejpam-4700	295	17	fn(t	fn(t	PUNCT
ejpam-4700	295	18	)	)	PUNCT
ejpam-4700	295	19	at	at	ADP
ejpam-4700	295	20	t	t	PROPN
ejpam-4700	295	21	=	=	SYM
ejpam-4700	295	22	0	0	PROPN
ejpam-4700	295	23	and	and	CCONJ
ejpam-4700	295	24	t	t	PROPN
ejpam-4700	295	25	=	=	SYM
ejpam-4700	295	26	tk	tk	PROPN
ejpam-4700	295	27	,	,	PUNCT
ejpam-4700	295	28	respectively	respectively	ADV
ejpam-4700	295	29	:	:	PUNCT
ejpam-4700	295	30	gn(x;u	gn(x;u	NOUN
ejpam-4700	295	31	,	,	PUNCT
ejpam-4700	295	32	λ	λ	NOUN
ejpam-4700	295	33	)	)	PUNCT
ejpam-4700	295	34	=	=	SYM
ejpam-4700	296	1	n	n	X
ejpam-4700	296	2	!	!	NOUN
ejpam-4700	296	3	1−	1−	NUM
ejpam-4700	297	1	u	u	SYM
ejpam-4700	297	2	u	u	NOUN
ejpam-4700	297	3	(	(	PUNCT
ejpam-4700	297	4	u	u	NOUN
ejpam-4700	297	5	λ	λ	PROPN
ejpam-4700	297	6	)	)	PUNCT
ejpam-4700	297	7	x∑	x∑	PRON
ejpam-4700	297	8	k∈z	k∈z	NOUN
ejpam-4700	297	9	ei2πkx	ei2πkx	PROPN
ejpam-4700	298	1	[	[	X
ejpam-4700	298	2	log(u	log(u	PROPN
ejpam-4700	298	3	/	/	SYM
ejpam-4700	298	4	λ	λ	NOUN
ejpam-4700	298	5	)	)	PUNCT
ejpam-4700	299	1	+	+	CCONJ
ejpam-4700	299	2	2kπi]−n	2kπi]−n	NUM
ejpam-4700	299	3	(	(	PUNCT
ejpam-4700	299	4	21	21	NUM
ejpam-4700	299	5	)	)	PUNCT
ejpam-4700	299	6	where	where	SCONJ
ejpam-4700	299	7	u	u	NOUN
ejpam-4700	299	8	,	,	PUNCT
ejpam-4700	299	9	λ	λ	PROPN
ejpam-4700	299	10	∈	∈	PROPN
ejpam-4700	299	11	c{0	c{0	NOUN
ejpam-4700	299	12	,	,	PUNCT
ejpam-4700	299	13	1	1	NUM
ejpam-4700	299	14	}	}	PUNCT
ejpam-4700	299	15	with	with	ADP
ejpam-4700	299	16	|λ|	|λ|	NOUN
ejpam-4700	299	17	=	=	SYM
ejpam-4700	299	18	̸	̸	NUM
ejpam-4700	299	19	|u|	|u|	PROPN
ejpam-4700	299	20	and	and	CCONJ
ejpam-4700	299	21	0	0	NUM
ejpam-4700	299	22	<	<	X
ejpam-4700	299	23	x	x	SYM
ejpam-4700	299	24	≤	≤	NUM
ejpam-4700	299	25	1	1	NUM
ejpam-4700	299	26	.	.	PUNCT
ejpam-4700	299	27	note	note	VERB
ejpam-4700	299	28	that	that	SCONJ
ejpam-4700	299	29	,	,	PUNCT
ejpam-4700	299	30	when	when	SCONJ
ejpam-4700	299	31	we	we	PRON
ejpam-4700	299	32	take	take	VERB
ejpam-4700	299	33	u	u	NOUN
ejpam-4700	299	34	=	=	NOUN
ejpam-4700	299	35	−1	−1	NOUN
ejpam-4700	299	36	,	,	PUNCT
ejpam-4700	299	37	we	we	PRON
ejpam-4700	299	38	have	have	VERB
ejpam-4700	299	39	g(x;u	g(x;u	NOUN
ejpam-4700	299	40	=	=	SYM
ejpam-4700	299	41	−1	−1	NOUN
ejpam-4700	299	42	,	,	PUNCT
ejpam-4700	299	43	λ	λ	NOUN
ejpam-4700	299	44	)	)	PUNCT
ejpam-4700	299	45	=	=	SYM
ejpam-4700	299	46	n	n	X
ejpam-4700	299	47	!	!	PUNCT
ejpam-4700	300	1	−1−	−1−	NOUN
ejpam-4700	300	2	1	1	NUM
ejpam-4700	300	3	−1	−1	NOUN
ejpam-4700	300	4	(	(	PUNCT
ejpam-4700	300	5	−1	−1	NOUN
ejpam-4700	300	6	λ	λ	NOUN
ejpam-4700	300	7	)	)	PUNCT
ejpam-4700	300	8	x∑	x∑	DET
ejpam-4700	300	9	k∈z	k∈z	PROPN
ejpam-4700	300	10	e2kπix	e2kπix	PROPN
ejpam-4700	300	11	[	[	PUNCT
ejpam-4700	300	12	log	log	NOUN
ejpam-4700	300	13	(	(	PUNCT
ejpam-4700	300	14	−1	−1	NOUN
ejpam-4700	300	15	λ	λ	PROPN
ejpam-4700	300	16	)	)	PUNCT
ejpam-4700	301	1	+	+	CCONJ
ejpam-4700	301	2	2kπi	2kπi	NUM
ejpam-4700	301	3	]	]	PUNCT
ejpam-4700	301	4	−n	−n	NOUN
ejpam-4700	301	5	=	=	PUNCT
ejpam-4700	301	6	2n	2n	NUM
ejpam-4700	301	7	!	!	PUNCT
ejpam-4700	302	1	(	(	PUNCT
ejpam-4700	302	2	−1)x	−1)x	AUX
ejpam-4700	302	3	λx	λx	PART
ejpam-4700	302	4	∑	∑	ADV
ejpam-4700	302	5	k∈z	k∈z	PROPN
ejpam-4700	302	6	e2kπix[log(−1)−	e2kπix[log(−1)−	PROPN
ejpam-4700	302	7	log	log	PROPN
ejpam-4700	302	8	λ+	λ+	PUNCT
ejpam-4700	302	9	2kπi]−n	2kπi]−n	NUM
ejpam-4700	302	10	=	=	SYM
ejpam-4700	302	11	2n	2n	NUM
ejpam-4700	302	12	!	!	PUNCT
ejpam-4700	302	13	eπix	eπix	PROPN
ejpam-4700	303	1	λx	λx	PROPN
ejpam-4700	303	2	∑	∑	ADV
ejpam-4700	303	3	k∈z	k∈z	PROPN
ejpam-4700	303	4	e2kπix[πi−	e2kπix[πi−	PROPN
ejpam-4700	303	5	log	log	NOUN
ejpam-4700	303	6	λ+	λ+	PUNCT
ejpam-4700	303	7	2kπi]−n	2kπi]−n	NUM
ejpam-4700	303	8	g(x;λ	g(x;λ	PROPN
ejpam-4700	303	9	)	)	PUNCT
ejpam-4700	303	10	=	=	SYM
ejpam-4700	303	11	2n	2n	NUM
ejpam-4700	303	12	!	!	PUNCT
ejpam-4700	304	1	λx	λx	NOUN
ejpam-4700	304	2	∑	∑	ADV
ejpam-4700	304	3	k∈z	k∈z	PROPN
ejpam-4700	304	4	e(2k+1)πix	e(2k+1)πix	PROPN
ejpam-4700	305	1	[	[	X
ejpam-4700	305	2	−	−	X
ejpam-4700	305	3	log	log	NOUN
ejpam-4700	305	4	λ+	λ+	X
ejpam-4700	305	5	(	(	PUNCT
ejpam-4700	305	6	2k	2k	NUM
ejpam-4700	305	7	+	+	CCONJ
ejpam-4700	305	8	1)πi]n	1)πi]n	NUM
ejpam-4700	305	9	(	(	PUNCT
ejpam-4700	305	10	22	22	NUM
ejpam-4700	305	11	)	)	PUNCT
ejpam-4700	305	12	r.	r.	PROPN
ejpam-4700	305	13	b.	b.	PROPN
ejpam-4700	305	14	corcino	corcino	PROPN
ejpam-4700	305	15	et	et	PROPN
ejpam-4700	305	16	al	al	PROPN
ejpam-4700	305	17	.	.	PUNCT
ejpam-4700	305	18	/	/	SYM
ejpam-4700	305	19	eur	eur	PROPN
ejpam-4700	305	20	.	.	PUNCT
ejpam-4700	306	1	j.	j.	PROPN
ejpam-4700	306	2	pure	pure	PROPN
ejpam-4700	306	3	appl	appl	PROPN
ejpam-4700	306	4	.	.	PROPN
ejpam-4700	306	5	math	math	PROPN
ejpam-4700	306	6	,	,	PUNCT
ejpam-4700	306	7	16	16	NUM
ejpam-4700	306	8	(	(	PUNCT
ejpam-4700	306	9	2	2	NUM
ejpam-4700	306	10	)	)	PUNCT
ejpam-4700	306	11	(	(	PUNCT
ejpam-4700	306	12	2023	2023	NUM
ejpam-4700	306	13	)	)	PUNCT
ejpam-4700	306	14	,	,	PUNCT
ejpam-4700	306	15	1005	1005	NUM
ejpam-4700	306	16	-	-	SYM
ejpam-4700	306	17	1023	1023	NUM
ejpam-4700	306	18	1019	1019	NUM
ejpam-4700	306	19	note	note	NOUN
ejpam-4700	306	20	that	that	SCONJ
ejpam-4700	306	21	eq.(22	eq.(22	NOUN
ejpam-4700	306	22	)	)	PUNCT
ejpam-4700	306	23	is	be	AUX
ejpam-4700	306	24	the	the	DET
ejpam-4700	306	25	apostol	apostol	NOUN
ejpam-4700	306	26	-	-	PUNCT
ejpam-4700	306	27	genocchi	genocchi	PROPN
ejpam-4700	306	28	polynomials	polynomial	NOUN
ejpam-4700	306	29	obtained	obtain	VERB
ejpam-4700	306	30	in	in	ADP
ejpam-4700	306	31	the	the	DET
ejpam-4700	306	32	paper	paper	NOUN
ejpam-4700	306	33	of	of	ADP
ejpam-4700	306	34	corcino	corcino	NOUN
ejpam-4700	306	35	,	,	PUNCT
ejpam-4700	306	36	et.al.[2	et.al.[2	NOUN
ejpam-4700	306	37	]	]	PUNCT
ejpam-4700	306	38	.	.	PUNCT
ejpam-4700	307	1	that	that	PRON
ejpam-4700	307	2	is	be	AUX
ejpam-4700	307	3	,	,	PUNCT
ejpam-4700	307	4	g(x;u	g(x;u	PROPN
ejpam-4700	307	5	=	=	SYM
ejpam-4700	307	6	−1	−1	NOUN
ejpam-4700	307	7	,	,	PUNCT
ejpam-4700	307	8	λ	λ	NOUN
ejpam-4700	307	9	)	)	PUNCT
ejpam-4700	307	10	=	=	SYM
ejpam-4700	307	11	g(x;λ	g(x;λ	PROPN
ejpam-4700	307	12	)	)	PUNCT
ejpam-4700	307	13	.	.	PUNCT
ejpam-4700	308	1	the	the	DET
ejpam-4700	308	2	apostol	apostol	NOUN
ejpam-4700	308	3	-	-	PUNCT
ejpam-4700	308	4	frobenius	frobenius	NOUN
ejpam-4700	308	5	-	-	PUNCT
ejpam-4700	308	6	genocchi	genocchi	NOUN
ejpam-4700	308	7	polynomials	polynomial	NOUN
ejpam-4700	308	8	of	of	ADP
ejpam-4700	308	9	higher	high	ADJ
ejpam-4700	308	10	order	order	NOUN
ejpam-4700	308	11	,	,	PUNCT
ejpam-4700	308	12	denoted	denote	VERB
ejpam-4700	308	13	by	by	ADP
ejpam-4700	308	14	g	g	PROPN
ejpam-4700	308	15	(	(	PUNCT
ejpam-4700	308	16	r	r	NOUN
ejpam-4700	308	17	)	)	PUNCT
ejpam-4700	308	18	n	n	CCONJ
ejpam-4700	308	19	(	(	PUNCT
ejpam-4700	308	20	x;u	x;u	PROPN
ejpam-4700	308	21	,	,	PUNCT
ejpam-4700	308	22	λ	λ	PROPN
ejpam-4700	308	23	)	)	PUNCT
ejpam-4700	308	24	,	,	PUNCT
ejpam-4700	308	25	are	be	AUX
ejpam-4700	308	26	defined	define	VERB
ejpam-4700	308	27	as	as	ADP
ejpam-4700	308	28	coefficients	coefficient	NOUN
ejpam-4700	308	29	of	of	ADP
ejpam-4700	308	30	the	the	DET
ejpam-4700	308	31	following	follow	VERB
ejpam-4700	308	32	generating	generate	VERB
ejpam-4700	308	33	function	function	NOUN
ejpam-4700	308	34	:	:	PUNCT
ejpam-4700	308	35	∞∑	∞∑	NUM
ejpam-4700	308	36	n=0	n=0	PROPN
ejpam-4700	308	37	g(r	g(r	NOUN
ejpam-4700	308	38	)	)	PUNCT
ejpam-4700	308	39	n	n	CCONJ
ejpam-4700	308	40	(	(	PUNCT
ejpam-4700	308	41	x;u	x;u	PROPN
ejpam-4700	308	42	,	,	PUNCT
ejpam-4700	308	43	λ	λ	NOUN
ejpam-4700	308	44	)	)	PUNCT
ejpam-4700	308	45	tn	tn	PROPN
ejpam-4700	308	46	n	n	PROPN
ejpam-4700	308	47	!	!	PUNCT
ejpam-4700	309	1	=	=	PUNCT
ejpam-4700	309	2	(	(	PUNCT
ejpam-4700	309	3	(	(	PUNCT
ejpam-4700	309	4	1−	1−	NUM
ejpam-4700	309	5	u)t	u)t	X
ejpam-4700	309	6	λet	λet	ADP
ejpam-4700	309	7	−	−	PROPN
ejpam-4700	309	8	u	u	NOUN
ejpam-4700	309	9	)	)	PUNCT
ejpam-4700	309	10	r	r	NOUN
ejpam-4700	309	11	ext	ext	NOUN
ejpam-4700	309	12	(	(	PUNCT
ejpam-4700	309	13	23	23	NUM
ejpam-4700	309	14	)	)	PUNCT
ejpam-4700	309	15	where	where	SCONJ
ejpam-4700	309	16	r	r	NOUN
ejpam-4700	309	17	≥	≥	NUM
ejpam-4700	309	18	1	1	NUM
ejpam-4700	309	19	,	,	PUNCT
ejpam-4700	309	20	u	u	NOUN
ejpam-4700	309	21	,	,	PUNCT
ejpam-4700	309	22	λ	λ	PROPN
ejpam-4700	309	23	∈	∈	PROPN
ejpam-4700	309	24	c	c	NOUN
ejpam-4700	309	25	with	with	ADP
ejpam-4700	309	26	u	u	NOUN
ejpam-4700	309	27	̸=	̸=	PROPN
ejpam-4700	309	28	1	1	NUM
ejpam-4700	309	29	,	,	PUNCT
ejpam-4700	309	30	λ	λ	PROPN
ejpam-4700	309	31	̸=	̸=	PROPN
ejpam-4700	309	32	1	1	NUM
ejpam-4700	309	33	and	and	CCONJ
ejpam-4700	309	34	u	u	PROPN
ejpam-4700	309	35	̸=	̸=	PROPN
ejpam-4700	309	36	λ	λ	PROPN
ejpam-4700	309	37	.	.	PUNCT
ejpam-4700	310	1	the	the	DET
ejpam-4700	310	2	following	follow	VERB
ejpam-4700	310	3	theorem	theorem	NOUN
ejpam-4700	310	4	contains	contain	VERB
ejpam-4700	310	5	the	the	DET
ejpam-4700	310	6	fourier	fourier	ADJ
ejpam-4700	310	7	expansion	expansion	NOUN
ejpam-4700	310	8	of	of	ADP
ejpam-4700	310	9	these	these	DET
ejpam-4700	310	10	polynomials	polynomial	NOUN
ejpam-4700	310	11	.	.	PUNCT
ejpam-4700	311	1	theorem	theorem	ADJ
ejpam-4700	311	2	4	4	NUM
ejpam-4700	311	3	.	.	PUNCT
ejpam-4700	312	1	for	for	ADP
ejpam-4700	312	2	0	0	NUM
ejpam-4700	312	3	≤	≤	NUM
ejpam-4700	312	4	x	x	SYM
ejpam-4700	312	5	≤	≤	NUM
ejpam-4700	312	6	1	1	NUM
ejpam-4700	312	7	g(r	g(r	NOUN
ejpam-4700	312	8	)	)	PUNCT
ejpam-4700	312	9	n	n	CCONJ
ejpam-4700	312	10	(	(	PUNCT
ejpam-4700	312	11	x;u	x;u	PROPN
ejpam-4700	312	12	,	,	PUNCT
ejpam-4700	312	13	λ	λ	NOUN
ejpam-4700	312	14	)	)	PUNCT
ejpam-4700	312	15	=	=	PUNCT
ejpam-4700	312	16	−n	−n	ADJ
ejpam-4700	312	17	!	!	PUNCT
ejpam-4700	313	1	(	(	PUNCT
ejpam-4700	313	2	u−	u−	PROPN
ejpam-4700	313	3	1	1	NUM
ejpam-4700	313	4	u	u	NOUN
ejpam-4700	313	5	)	)	PUNCT
ejpam-4700	313	6	r∑	r∑	NOUN
ejpam-4700	313	7	k∈z	k∈z	NOUN
ejpam-4700	313	8	r−1∑	r−1∑	PROPN
ejpam-4700	313	9	j=0	j=0	PROPN
ejpam-4700	313	10	(	(	PUNCT
ejpam-4700	313	11	−1)j−1	−1)j−1	PROPN
ejpam-4700	313	12	(	(	PUNCT
ejpam-4700	313	13	n−	n−	NOUN
ejpam-4700	313	14	1−	1−	NUM
ejpam-4700	313	15	j	j	PROPN
ejpam-4700	314	1	r	r	NOUN
ejpam-4700	315	1	−	−	PROPN
ejpam-4700	316	1	1−	1−	NUM
ejpam-4700	316	2	j	j	PROPN
ejpam-4700	316	3	)	)	PUNCT
ejpam-4700	316	4	b	b	PROPN
ejpam-4700	316	5	(	(	PUNCT
ejpam-4700	316	6	r	r	NOUN
ejpam-4700	316	7	)	)	PUNCT
ejpam-4700	316	8	l	l	NOUN
ejpam-4700	316	9	(	(	PUNCT
ejpam-4700	316	10	x	x	NOUN
ejpam-4700	316	11	)	)	PUNCT
ejpam-4700	316	12	j	j	PROPN
ejpam-4700	316	13	!	!	PUNCT
ejpam-4700	317	1	(	(	PUNCT
ejpam-4700	317	2	u	u	NOUN
ejpam-4700	317	3	λ	λ	PROPN
ejpam-4700	317	4	)	)	PUNCT
ejpam-4700	317	5	x	x	SYM
ejpam-4700	318	1	e2xkπi	e2xkπi	ADJ
ejpam-4700	318	2	[	[	PUNCT
ejpam-4700	318	3	log	log	NOUN
ejpam-4700	318	4	(	(	PUNCT
ejpam-4700	318	5	u	u	NOUN
ejpam-4700	318	6	λ	λ	PROPN
ejpam-4700	318	7	)	)	PUNCT
ejpam-4700	319	1	+	+	CCONJ
ejpam-4700	319	2	2kπi	2kπi	NUM
ejpam-4700	319	3	]	]	PUNCT
ejpam-4700	319	4	n−j	n−j	X
ejpam-4700	319	5	(	(	PUNCT
ejpam-4700	319	6	24	24	NUM
ejpam-4700	319	7	)	)	PUNCT
ejpam-4700	319	8	where	where	SCONJ
ejpam-4700	319	9	b	b	X
ejpam-4700	319	10	(	(	PUNCT
ejpam-4700	319	11	r	r	NOUN
ejpam-4700	319	12	)	)	PUNCT
ejpam-4700	319	13	n	n	NOUN
ejpam-4700	319	14	(	(	PUNCT
ejpam-4700	319	15	x	x	X
ejpam-4700	319	16	)	)	PUNCT
ejpam-4700	319	17	is	be	AUX
ejpam-4700	319	18	the	the	DET
ejpam-4700	319	19	bernoulli	bernoulli	NOUN
ejpam-4700	319	20	polynomials	polynomial	NOUN
ejpam-4700	319	21	of	of	ADP
ejpam-4700	319	22	order	order	NOUN
ejpam-4700	319	23	r.	r.	NOUN
ejpam-4700	319	24	proof	proof	NOUN
ejpam-4700	319	25	.	.	PUNCT
ejpam-4700	320	1	using	use	VERB
ejpam-4700	320	2	the	the	DET
ejpam-4700	320	3	cauchy	cauchy	ADJ
ejpam-4700	320	4	residue	residue	NOUN
ejpam-4700	320	5	theorem	theorem	NOUN
ejpam-4700	320	6	(	(	PUNCT
ejpam-4700	320	7	crt	crt	ADJ
ejpam-4700	320	8	)	)	PUNCT
ejpam-4700	320	9	,	,	PUNCT
ejpam-4700	320	10	1	1	NUM
ejpam-4700	320	11	2πi	2πi	NOUN
ejpam-4700	320	12	∫	∫	PROPN
ejpam-4700	320	13	cn	cn	PROPN
ejpam-4700	320	14	f(t)dt	f(t)dt	PROPN
ejpam-4700	320	15	=	=	PROPN
ejpam-4700	320	16	res(f(t	res(f(t	PROPN
ejpam-4700	320	17	)	)	PUNCT
ejpam-4700	320	18	,	,	PUNCT
ejpam-4700	320	19	t	t	PROPN
ejpam-4700	320	20	=	=	SYM
ejpam-4700	320	21	0	0	NUM
ejpam-4700	320	22	)	)	PUNCT
ejpam-4700	320	23	+	+	CCONJ
ejpam-4700	320	24	∑	∑	PROPN
ejpam-4700	320	25	k∈z	k∈z	PROPN
ejpam-4700	320	26	res(f(t	res(f(t	PROPN
ejpam-4700	320	27	)	)	PUNCT
ejpam-4700	320	28	,	,	PUNCT
ejpam-4700	320	29	t	t	PROPN
ejpam-4700	320	30	=	=	SYM
ejpam-4700	320	31	tk	tk	PROPN
ejpam-4700	320	32	)	)	PUNCT
ejpam-4700	321	1	where	where	SCONJ
ejpam-4700	321	2	tk	tk	PROPN
ejpam-4700	321	3	=	=	NOUN
ejpam-4700	321	4	log	log	PROPN
ejpam-4700	321	5	(	(	PUNCT
ejpam-4700	321	6	u	u	NOUN
ejpam-4700	321	7	λ	λ	PROPN
ejpam-4700	321	8	)	)	PUNCT
ejpam-4700	322	1	+	+	CCONJ
ejpam-4700	322	2	2kπi	2kπi	NUM
ejpam-4700	322	3	,	,	PUNCT
ejpam-4700	322	4	k	k	PROPN
ejpam-4700	322	5	∈	∈	PROPN
ejpam-4700	322	6	z	z	NOUN
ejpam-4700	322	7	f(t	f(t	PROPN
ejpam-4700	322	8	)	)	PUNCT
ejpam-4700	322	9	=	=	SYM
ejpam-4700	322	10	(	(	PUNCT
ejpam-4700	322	11	(	(	PUNCT
ejpam-4700	322	12	1−	1−	NUM
ejpam-4700	322	13	u)t	u)t	X
ejpam-4700	322	14	λet	λet	ADP
ejpam-4700	322	15	−	−	PROPN
ejpam-4700	322	16	u	u	NOUN
ejpam-4700	322	17	)	)	PUNCT
ejpam-4700	322	18	r	r	NOUN
ejpam-4700	322	19	ext	ext	NOUN
ejpam-4700	322	20	tn+1	tn+1	NOUN
ejpam-4700	322	21	=	=	SYM
ejpam-4700	322	22	(	(	PUNCT
ejpam-4700	322	23	1−	1−	NUM
ejpam-4700	322	24	u	u	NOUN
ejpam-4700	322	25	λet	λet	ADP
ejpam-4700	322	26	−	−	NUM
ejpam-4700	322	27	u	u	NOUN
ejpam-4700	322	28	)	)	PUNCT
ejpam-4700	322	29	r	r	NOUN
ejpam-4700	322	30	ext	ext	NOUN
ejpam-4700	322	31	tn+1−r	tn+1−r	NOUN
ejpam-4700	322	32	consider	consider	VERB
ejpam-4700	322	33	the	the	DET
ejpam-4700	322	34	left	leave	VERB
ejpam-4700	322	35	-	-	PUNCT
ejpam-4700	322	36	hand	hand	NOUN
ejpam-4700	322	37	side	side	NOUN
ejpam-4700	322	38	of	of	ADP
ejpam-4700	322	39	the	the	DET
ejpam-4700	322	40	equation	equation	NOUN
ejpam-4700	322	41	in	in	ADP
ejpam-4700	322	42	the	the	DET
ejpam-4700	322	43	crt	crt	NOUN
ejpam-4700	322	44	as	as	ADP
ejpam-4700	322	45	n	n	PROPN
ejpam-4700	322	46	→	→	SYM
ejpam-4700	322	47	∞	∞	PROPN
ejpam-4700	322	48	,	,	PUNCT
ejpam-4700	322	49	we	we	PRON
ejpam-4700	322	50	have	have	VERB
ejpam-4700	322	51	lim	lim	PROPN
ejpam-4700	322	52	n→∞	n→∞	NUM
ejpam-4700	323	1	∫	∫	PROPN
ejpam-4700	323	2	cn	cn	PROPN
ejpam-4700	323	3	f(t)dt	f(t)dt	PROPN
ejpam-4700	323	4	=	=	PROPN
ejpam-4700	323	5	lim	lim	PROPN
ejpam-4700	323	6	n→∞	n→∞	NUM
ejpam-4700	324	1	∫	∫	PROPN
ejpam-4700	324	2	cn	cn	PROPN
ejpam-4700	324	3	(	(	PUNCT
ejpam-4700	324	4	(	(	PUNCT
ejpam-4700	324	5	1−	1−	NUM
ejpam-4700	324	6	u	u	NOUN
ejpam-4700	324	7	)	)	PUNCT
ejpam-4700	324	8	λet	λet	ADP
ejpam-4700	324	9	−	−	PROPN
ejpam-4700	324	10	u	u	NOUN
ejpam-4700	324	11	)	)	PUNCT
ejpam-4700	324	12	r	r	NOUN
ejpam-4700	324	13	ext	ext	NOUN
ejpam-4700	324	14	dt	dt	NOUN
ejpam-4700	324	15	tn+1−r	tn+1−r	ADJ
ejpam-4700	324	16	=	=	NOUN
ejpam-4700	324	17	0	0	NUM
ejpam-4700	324	18	,	,	PUNCT
ejpam-4700	324	19	which	which	PRON
ejpam-4700	324	20	can	can	AUX
ejpam-4700	324	21	easily	easily	ADV
ejpam-4700	324	22	be	be	AUX
ejpam-4700	324	23	shown	show	VERB
ejpam-4700	324	24	using	use	VERB
ejpam-4700	324	25	the	the	DET
ejpam-4700	324	26	same	same	ADJ
ejpam-4700	324	27	proof	proof	NOUN
ejpam-4700	324	28	as	as	ADP
ejpam-4700	324	29	in	in	ADP
ejpam-4700	324	30	the	the	DET
ejpam-4700	324	31	case	case	NOUN
ejpam-4700	324	32	when	when	SCONJ
ejpam-4700	324	33	r	r	NOUN
ejpam-4700	324	34	=	=	SYM
ejpam-4700	324	35	1	1	NUM
ejpam-4700	324	36	as	as	SCONJ
ejpam-4700	324	37	shown	show	VERB
ejpam-4700	324	38	in	in	ADP
ejpam-4700	324	39	lemma	lemma	PROPN
ejpam-4700	324	40	2	2	NUM
ejpam-4700	324	41	.	.	PUNCT
ejpam-4700	325	1	we	we	PRON
ejpam-4700	325	2	shall	shall	AUX
ejpam-4700	325	3	evaluate	evaluate	VERB
ejpam-4700	325	4	the	the	DET
ejpam-4700	325	5	first	first	ADJ
ejpam-4700	325	6	term	term	NOUN
ejpam-4700	325	7	of	of	ADP
ejpam-4700	325	8	the	the	DET
ejpam-4700	325	9	right	right	ADJ
ejpam-4700	325	10	-	-	PUNCT
ejpam-4700	325	11	hand	hand	NOUN
ejpam-4700	325	12	side	side	NOUN
ejpam-4700	325	13	of	of	ADP
ejpam-4700	325	14	the	the	DET
ejpam-4700	325	15	equation	equation	NOUN
ejpam-4700	325	16	in	in	ADP
ejpam-4700	325	17	the	the	DET
ejpam-4700	325	18	cauchy	cauchy	ADJ
ejpam-4700	325	19	residue	residue	NOUN
ejpam-4700	325	20	theorem	theorem	NOUN
ejpam-4700	325	21	as	as	ADP
ejpam-4700	325	22	t	t	PROPN
ejpam-4700	325	23	=	=	SYM
ejpam-4700	325	24	0	0	NUM
ejpam-4700	325	25	,	,	PUNCT
ejpam-4700	325	26	we	we	PRON
ejpam-4700	325	27	have	have	VERB
ejpam-4700	325	28	res(f(t	res(f(t	NOUN
ejpam-4700	325	29	)	)	PUNCT
ejpam-4700	325	30	,	,	PUNCT
ejpam-4700	325	31	t	t	PROPN
ejpam-4700	325	32	=	=	SYM
ejpam-4700	326	1	0	0	NUM
ejpam-4700	326	2	)	)	PUNCT
ejpam-4700	326	3	=	=	SYM
ejpam-4700	326	4	lim	lim	PROPN
ejpam-4700	326	5	t→0	t→0	PUNCT
ejpam-4700	326	6	1	1	NUM
ejpam-4700	326	7	n	n	X
ejpam-4700	326	8	!	!	PUNCT
ejpam-4700	327	1	dn	dn	PROPN
ejpam-4700	327	2	dtn	dtn	PROPN
ejpam-4700	327	3	(	(	PUNCT
ejpam-4700	327	4	t−	t−	PROPN
ejpam-4700	327	5	0)n+1	0)n+1	SYM
ejpam-4700	327	6	1	1	NUM
ejpam-4700	327	7	tn+1	tn+1	NUM
ejpam-4700	327	8	∞∑	∞∑	PROPN
ejpam-4700	327	9	m=0	m=0	PROPN
ejpam-4700	327	10	g(r	g(r	PROPN
ejpam-4700	327	11	)	)	PUNCT
ejpam-4700	327	12	m	m	PROPN
ejpam-4700	327	13	(	(	PUNCT
ejpam-4700	327	14	x;u	x;u	PROPN
ejpam-4700	327	15	,	,	PUNCT
ejpam-4700	327	16	λ	λ	NOUN
ejpam-4700	327	17	)	)	PUNCT
ejpam-4700	327	18	tm	tm	PROPN
ejpam-4700	327	19	m	m	PROPN
ejpam-4700	327	20	!	!	PUNCT
ejpam-4700	328	1	=	=	PRON
ejpam-4700	328	2	lim	lim	PROPN
ejpam-4700	328	3	t→0	t→0	PUNCT
ejpam-4700	328	4	1	1	NUM
ejpam-4700	328	5	n	n	X
ejpam-4700	328	6	!	!	PUNCT
ejpam-4700	329	1	dn	dn	PROPN
ejpam-4700	329	2	dtn	dtn	PROPN
ejpam-4700	329	3	∞∑	∞∑	PROPN
ejpam-4700	329	4	m=0	m=0	PROPN
ejpam-4700	329	5	g(r	g(r	PROPN
ejpam-4700	329	6	)	)	PUNCT
ejpam-4700	329	7	m	m	PROPN
ejpam-4700	329	8	(	(	PUNCT
ejpam-4700	329	9	x;u	x;u	PROPN
ejpam-4700	329	10	,	,	PUNCT
ejpam-4700	329	11	λ	λ	NOUN
ejpam-4700	329	12	)	)	PUNCT
ejpam-4700	329	13	tm	tm	PROPN
ejpam-4700	329	14	m	m	PROPN
ejpam-4700	329	15	!	!	PUNCT
ejpam-4700	329	16	r.	r.	PROPN
ejpam-4700	329	17	b.	b.	PROPN
ejpam-4700	329	18	corcino	corcino	PROPN
ejpam-4700	329	19	et	et	PROPN
ejpam-4700	329	20	al	al	PROPN
ejpam-4700	329	21	.	.	PUNCT
ejpam-4700	329	22	/	/	SYM
ejpam-4700	329	23	eur	eur	PROPN
ejpam-4700	329	24	.	.	PUNCT
ejpam-4700	330	1	j.	j.	PROPN
ejpam-4700	330	2	pure	pure	PROPN
ejpam-4700	330	3	appl	appl	PROPN
ejpam-4700	330	4	.	.	PROPN
ejpam-4700	330	5	math	math	PROPN
ejpam-4700	330	6	,	,	PUNCT
ejpam-4700	330	7	16	16	NUM
ejpam-4700	330	8	(	(	PUNCT
ejpam-4700	330	9	2	2	NUM
ejpam-4700	330	10	)	)	PUNCT
ejpam-4700	330	11	(	(	PUNCT
ejpam-4700	330	12	2023	2023	NUM
ejpam-4700	330	13	)	)	PUNCT
ejpam-4700	330	14	,	,	PUNCT
ejpam-4700	330	15	1005	1005	NUM
ejpam-4700	330	16	-	-	SYM
ejpam-4700	330	17	1023	1023	NUM
ejpam-4700	330	18	1020	1020	NUM
ejpam-4700	330	19	=	=	SYM
ejpam-4700	330	20	lim	lim	PROPN
ejpam-4700	330	21	t→0	t→0	PUNCT
ejpam-4700	330	22	1	1	NUM
ejpam-4700	330	23	n	n	NOUN
ejpam-4700	330	24	!	!	PUNCT
ejpam-4700	331	1	∞∑	∞∑	NUM
ejpam-4700	331	2	m=0	m=0	PROPN
ejpam-4700	331	3	g(r	g(r	PROPN
ejpam-4700	331	4	)	)	PUNCT
ejpam-4700	331	5	m	m	PROPN
ejpam-4700	331	6	(	(	PUNCT
ejpam-4700	331	7	x;u	x;u	PROPN
ejpam-4700	331	8	,	,	PUNCT
ejpam-4700	331	9	λ	λ	NOUN
ejpam-4700	331	10	)	)	PUNCT
ejpam-4700	331	11	(	(	PUNCT
ejpam-4700	331	12	m)n	m)n	X
ejpam-4700	331	13	m	m	PROPN
ejpam-4700	331	14	!	!	PUNCT
ejpam-4700	332	1	tm−n	tm−n	PROPN
ejpam-4700	332	2	=	=	SYM
ejpam-4700	332	3	lim	lim	PROPN
ejpam-4700	332	4	t→0	t→0	PUNCT
ejpam-4700	332	5	1	1	NUM
ejpam-4700	332	6	n	n	NOUN
ejpam-4700	332	7	!	!	PUNCT
ejpam-4700	333	1	∞∑	∞∑	NUM
ejpam-4700	333	2	m=0	m=0	PROPN
ejpam-4700	333	3	g(r	g(r	PROPN
ejpam-4700	333	4	)	)	PUNCT
ejpam-4700	333	5	m	m	PROPN
ejpam-4700	333	6	(	(	PUNCT
ejpam-4700	333	7	x;u	x;u	PROPN
ejpam-4700	333	8	,	,	PUNCT
ejpam-4700	333	9	λ	λ	NOUN
ejpam-4700	333	10	)	)	PUNCT
ejpam-4700	333	11	tm−n	tm−n	NOUN
ejpam-4700	333	12	(	(	PUNCT
ejpam-4700	333	13	m−	m−	PROPN
ejpam-4700	333	14	n	n	CCONJ
ejpam-4700	333	15	)	)	PUNCT
ejpam-4700	333	16	!	!	PUNCT
ejpam-4700	334	1	=	=	SYM
ejpam-4700	334	2	1	1	NUM
ejpam-4700	334	3	n	n	NOUN
ejpam-4700	334	4	!	!	PUNCT
ejpam-4700	335	1	g(r	g(r	NOUN
ejpam-4700	335	2	)	)	PUNCT
ejpam-4700	335	3	n	n	CCONJ
ejpam-4700	335	4	(	(	PUNCT
ejpam-4700	335	5	x;u	x;u	PROPN
ejpam-4700	335	6	,	,	PUNCT
ejpam-4700	335	7	λ	λ	NOUN
ejpam-4700	335	8	)	)	PUNCT
ejpam-4700	335	9	now	now	ADV
ejpam-4700	335	10	we	we	PRON
ejpam-4700	335	11	will	will	AUX
ejpam-4700	335	12	evaluate	evaluate	VERB
ejpam-4700	335	13	the	the	DET
ejpam-4700	335	14	second	second	ADJ
ejpam-4700	335	15	term	term	NOUN
ejpam-4700	335	16	of	of	ADP
ejpam-4700	335	17	the	the	DET
ejpam-4700	335	18	right	right	ADJ
ejpam-4700	335	19	-	-	PUNCT
ejpam-4700	335	20	hand	hand	NOUN
ejpam-4700	335	21	side	side	NOUN
ejpam-4700	335	22	of	of	ADP
ejpam-4700	335	23	the	the	DET
ejpam-4700	335	24	equation	equation	NOUN
ejpam-4700	335	25	of	of	ADP
ejpam-4700	335	26	the	the	DET
ejpam-4700	335	27	cauchy	cauchy	ADJ
ejpam-4700	335	28	residue	residue	NOUN
ejpam-4700	335	29	theorem	theorem	NOUN
ejpam-4700	335	30	as	as	ADP
ejpam-4700	335	31	t	t	PROPN
ejpam-4700	335	32	=	=	SYM
ejpam-4700	335	33	tk	tk	PROPN
ejpam-4700	335	34	.	.	PROPN
ejpam-4700	335	35	that	that	PRON
ejpam-4700	335	36	is	be	AUX
ejpam-4700	335	37	,	,	PUNCT
ejpam-4700	335	38	for	for	ADP
ejpam-4700	335	39	r	r	NOUN
ejpam-4700	335	40	≥	≥	NUM
ejpam-4700	335	41	2	2	NUM
ejpam-4700	335	42	res(f(t	res(f(t	NOUN
ejpam-4700	335	43	)	)	PUNCT
ejpam-4700	335	44	,	,	PUNCT
ejpam-4700	335	45	t	t	PROPN
ejpam-4700	335	46	=	=	SYM
ejpam-4700	335	47	tk	tk	PROPN
ejpam-4700	335	48	)	)	PUNCT
ejpam-4700	335	49	=	=	SYM
ejpam-4700	335	50	1	1	NUM
ejpam-4700	335	51	(	(	PUNCT
ejpam-4700	335	52	r	r	NOUN
ejpam-4700	335	53	−	−	NOUN
ejpam-4700	335	54	1	1	NUM
ejpam-4700	335	55	)	)	PUNCT
ejpam-4700	335	56	!	!	PUNCT
ejpam-4700	336	1	lim	lim	PROPN
ejpam-4700	336	2	t→tk	t→tk	VERB
ejpam-4700	337	1	dr−1	dr−1	PROPN
ejpam-4700	337	2	dtr−1	dtr−1	PROPN
ejpam-4700	337	3	(	(	PUNCT
ejpam-4700	337	4	t−	t−	PROPN
ejpam-4700	337	5	tk	tk	PROPN
ejpam-4700	337	6	)	)	PUNCT
ejpam-4700	337	7	r	r	NOUN
ejpam-4700	337	8	(	(	PUNCT
ejpam-4700	337	9	1−	1−	NUM
ejpam-4700	337	10	u	u	NOUN
ejpam-4700	337	11	λet	λet	ADP
ejpam-4700	337	12	−	−	NUM
ejpam-4700	337	13	u	u	NOUN
ejpam-4700	337	14	)	)	PUNCT
ejpam-4700	337	15	r	r	NOUN
ejpam-4700	337	16	extk	extk	ADJ
ejpam-4700	337	17	tn−r+1	tn−r+1	NOUN
ejpam-4700	337	18	consider	consider	VERB
ejpam-4700	337	19	now	now	ADV
ejpam-4700	337	20	the	the	DET
ejpam-4700	337	21	function	function	NOUN
ejpam-4700	337	22	(	(	PUNCT
ejpam-4700	337	23	t−	t−	PROPN
ejpam-4700	337	24	tk	tk	PROPN
ejpam-4700	337	25	)	)	PUNCT
ejpam-4700	337	26	r	r	NOUN
ejpam-4700	337	27	(	(	PUNCT
ejpam-4700	337	28	1−	1−	NUM
ejpam-4700	337	29	u	u	NOUN
ejpam-4700	337	30	λet	λet	ADP
ejpam-4700	337	31	−	−	NUM
ejpam-4700	337	32	u	u	NOUN
ejpam-4700	337	33	)	)	PUNCT
ejpam-4700	337	34	r	r	NOUN
ejpam-4700	337	35	extk	extk	ADJ
ejpam-4700	337	36	tn−r+1	tn−r+1	NOUN
ejpam-4700	337	37	=	=	SYM
ejpam-4700	337	38	(	(	PUNCT
ejpam-4700	337	39	1−	1−	NUM
ejpam-4700	337	40	u)r	u)r	X
ejpam-4700	337	41	ur	ur	INTJ
ejpam-4700	337	42	(	(	PUNCT
ejpam-4700	337	43	t−	t−	PROPN
ejpam-4700	337	44	tk	tk	PROPN
ejpam-4700	337	45	λ	λ	PROPN
ejpam-4700	337	46	ue	ue	PROPN
ejpam-4700	337	47	t	t	PROPN
ejpam-4700	337	48	−	−	NOUN
ejpam-4700	337	49	1	1	X
ejpam-4700	337	50	)	)	PUNCT
ejpam-4700	337	51	r	r	NOUN
ejpam-4700	337	52	extk	extk	ADJ
ejpam-4700	337	53	tn−r+1	tn−r+1	NOUN
ejpam-4700	337	54	=	=	SYM
ejpam-4700	337	55	(	(	PUNCT
ejpam-4700	337	56	1−	1−	NUM
ejpam-4700	337	57	u)r	u)r	X
ejpam-4700	337	58	ur	ur	INTJ
ejpam-4700	337	59	(	(	PUNCT
ejpam-4700	337	60	t−	t−	PROPN
ejpam-4700	337	61	tk	tk	PROPN
ejpam-4700	337	62	λ	λ	PROPN
ejpam-4700	337	63	ue	ue	PROPN
ejpam-4700	337	64	t−tk	t−tk	PROPN
ejpam-4700	337	65	u	u	NOUN
ejpam-4700	337	66	λ	λ	NOUN
ejpam-4700	337	67	−	−	NOUN
ejpam-4700	337	68	1	1	NUM
ejpam-4700	337	69	)	)	PUNCT
ejpam-4700	337	70	r	r	NOUN
ejpam-4700	337	71	extk	extk	ADJ
ejpam-4700	337	72	tn−r+1	tn−r+1	PROPN
ejpam-4700	337	73	,	,	PUNCT
ejpam-4700	337	74	since	since	SCONJ
ejpam-4700	337	75	u	u	NOUN
ejpam-4700	337	76	λ	λ	PROPN
ejpam-4700	337	77	e−tk	e−tk	NOUN
ejpam-4700	337	78	=	=	SYM
ejpam-4700	337	79	1	1	NUM
ejpam-4700	337	80	=	=	SYM
ejpam-4700	337	81	(	(	PUNCT
ejpam-4700	337	82	1−	1−	NUM
ejpam-4700	337	83	u	u	NOUN
ejpam-4700	337	84	u	u	NOUN
ejpam-4700	337	85	)	)	PUNCT
ejpam-4700	337	86	r	r	NOUN
ejpam-4700	337	87	(	(	PUNCT
ejpam-4700	337	88	t−	t−	PROPN
ejpam-4700	337	89	tk	tk	PROPN
ejpam-4700	337	90	et−tk	et−tk	NUM
ejpam-4700	337	91	−	−	NUM
ejpam-4700	337	92	1	1	NUM
ejpam-4700	337	93	)	)	PUNCT
ejpam-4700	337	94	r	r	NOUN
ejpam-4700	337	95	extk	extk	ADJ
ejpam-4700	337	96	tn−r+1	tn−r+1	NOUN
ejpam-4700	337	97	=	=	PUNCT
ejpam-4700	337	98	(	(	PUNCT
ejpam-4700	337	99	1−	1−	NUM
ejpam-4700	337	100	u	u	NOUN
ejpam-4700	337	101	u	u	NOUN
ejpam-4700	337	102	)	)	PUNCT
ejpam-4700	337	103	r	r	NOUN
ejpam-4700	337	104	∞∑	∞∑	NUM
ejpam-4700	337	105	n=0	n=0	NUM
ejpam-4700	337	106	b(r	b(r	NOUN
ejpam-4700	337	107	)	)	PUNCT
ejpam-4700	337	108	n	n	CCONJ
ejpam-4700	337	109	(	(	PUNCT
ejpam-4700	337	110	t−	t−	PROPN
ejpam-4700	337	111	tk	tk	PROPN
ejpam-4700	337	112	)	)	PUNCT
ejpam-4700	337	113	n	n	ADP
ejpam-4700	337	114	n	n	CCONJ
ejpam-4700	337	115	!	!	PUNCT
ejpam-4700	337	116	extk	extk	ADJ
ejpam-4700	337	117	tn−r+1	tn−r+1	PROPN
ejpam-4700	337	118	where	where	SCONJ
ejpam-4700	337	119	(	(	PUNCT
ejpam-4700	337	120	w	w	NOUN
ejpam-4700	337	121	ew	ew	INTJ
ejpam-4700	337	122	−	−	PROPN
ejpam-4700	337	123	1	1	NUM
ejpam-4700	337	124	)	)	PUNCT
ejpam-4700	337	125	r	r	NOUN
ejpam-4700	337	126	=	=	SYM
ejpam-4700	337	127	∞∑	∞∑	NUM
ejpam-4700	337	128	n=0	n=0	NUM
ejpam-4700	337	129	b(r	b(r	NOUN
ejpam-4700	337	130	)	)	PUNCT
ejpam-4700	337	131	n	n	PROPN
ejpam-4700	337	132	wn	wn	NOUN
ejpam-4700	337	133	n	n	CCONJ
ejpam-4700	337	134	!	!	PUNCT
ejpam-4700	338	1	using	use	VERB
ejpam-4700	338	2	the	the	DET
ejpam-4700	338	3	leibniz	leibniz	PROPN
ejpam-4700	338	4	rule	rule	NOUN
ejpam-4700	338	5	,	,	PUNCT
ejpam-4700	338	6	the	the	DET
ejpam-4700	338	7	derivative	derivative	ADJ
ejpam-4700	338	8	part	part	NOUN
ejpam-4700	338	9	for	for	ADP
ejpam-4700	338	10	our	our	PRON
ejpam-4700	338	11	residue	residue	NOUN
ejpam-4700	338	12	at	at	ADP
ejpam-4700	338	13	t	t	PROPN
ejpam-4700	338	14	=	=	SYM
ejpam-4700	338	15	tk	tk	PROPN
ejpam-4700	338	16	,	,	PUNCT
ejpam-4700	338	17	we	we	PRON
ejpam-4700	338	18	get	get	VERB
ejpam-4700	338	19	dr−1	dr−1	PROPN
ejpam-4700	338	20	dtr−1	dtr−1	PROPN
ejpam-4700	338	21	(	(	PUNCT
ejpam-4700	338	22	t−	t−	PROPN
ejpam-4700	338	23	tk	tk	PROPN
ejpam-4700	338	24	et−tk	et−tk	NUM
ejpam-4700	338	25	−	−	NUM
ejpam-4700	338	26	1	1	NUM
ejpam-4700	338	27	)	)	PUNCT
ejpam-4700	338	28	r	r	NOUN
ejpam-4700	338	29	extk	extk	ADJ
ejpam-4700	338	30	tn−r+1	tn−r+1	NOUN
ejpam-4700	338	31	=	=	PUNCT
ejpam-4700	339	1	dr−1	dr−1	PROPN
ejpam-4700	339	2	dtr−1	dtr−1	PROPN
ejpam-4700	339	3	{	{	PUNCT
ejpam-4700	339	4	[	[	PUNCT
ejpam-4700	339	5	∞∑	∞∑	NUM
ejpam-4700	339	6	n=0	n=0	NUM
ejpam-4700	339	7	b(r	b(r	NOUN
ejpam-4700	339	8	)	)	PUNCT
ejpam-4700	339	9	n	n	CCONJ
ejpam-4700	339	10	(	(	PUNCT
ejpam-4700	339	11	t−	t−	PROPN
ejpam-4700	339	12	tk	tk	PROPN
ejpam-4700	339	13	)	)	PUNCT
ejpam-4700	339	14	n	n	PRON
ejpam-4700	339	15	n	n	X
ejpam-4700	339	16	!	!	PUNCT
ejpam-4700	339	17	]	]	PUNCT
ejpam-4700	340	1	extk	extk	ADV
ejpam-4700	340	2	tn−r+1	tn−r+1	NOUN
ejpam-4700	340	3	}	}	PUNCT
ejpam-4700	340	4	=	=	PUNCT
ejpam-4700	341	1	dr−1	dr−1	PROPN
ejpam-4700	341	2	dtr−1	dtr−1	PROPN
ejpam-4700	341	3	{	{	PUNCT
ejpam-4700	341	4	[	[	PUNCT
ejpam-4700	341	5	∞∑	∞∑	NUM
ejpam-4700	341	6	n=0	n=0	NUM
ejpam-4700	341	7	b(r	b(r	NOUN
ejpam-4700	341	8	)	)	PUNCT
ejpam-4700	341	9	n	n	CCONJ
ejpam-4700	341	10	(	(	PUNCT
ejpam-4700	341	11	t−	t−	PROPN
ejpam-4700	341	12	tk	tk	PROPN
ejpam-4700	341	13	)	)	PUNCT
ejpam-4700	341	14	n	n	PRON
ejpam-4700	341	15	n	n	X
ejpam-4700	341	16	!	!	PUNCT
ejpam-4700	341	17	]	]	PUNCT
ejpam-4700	342	1	extk	extk	ADV
ejpam-4700	342	2	}	}	PUNCT
ejpam-4700	342	3	t−(n−r+1	t−(n−r+1	PROPN
ejpam-4700	342	4	)	)	PUNCT
ejpam-4700	342	5	performing	perform	VERB
ejpam-4700	342	6	the	the	DET
ejpam-4700	342	7	leibniz	leibniz	NOUN
ejpam-4700	342	8	derivative	derivative	ADJ
ejpam-4700	342	9	rule	rule	NOUN
ejpam-4700	342	10	on	on	ADP
ejpam-4700	342	11	the	the	DET
ejpam-4700	342	12	above	above	ADJ
ejpam-4700	342	13	equation	equation	NOUN
ejpam-4700	342	14	,	,	PUNCT
ejpam-4700	342	15	we	we	PRON
ejpam-4700	342	16	get	get	VERB
ejpam-4700	342	17	dr−1	dr−1	PROPN
ejpam-4700	342	18	dtr−1	dtr−1	PROPN
ejpam-4700	342	19	{	{	PUNCT
ejpam-4700	342	20	[	[	PUNCT
ejpam-4700	342	21	∞∑	∞∑	NUM
ejpam-4700	342	22	n=0	n=0	NUM
ejpam-4700	342	23	b(r	b(r	NOUN
ejpam-4700	342	24	)	)	PUNCT
ejpam-4700	342	25	n	n	CCONJ
ejpam-4700	342	26	(	(	PUNCT
ejpam-4700	342	27	t−	t−	PROPN
ejpam-4700	342	28	tk	tk	PROPN
ejpam-4700	342	29	)	)	PUNCT
ejpam-4700	342	30	n	n	PRON
ejpam-4700	342	31	n	n	X
ejpam-4700	342	32	!	!	PUNCT
ejpam-4700	342	33	]	]	PUNCT
ejpam-4700	343	1	extk	extk	ADV
ejpam-4700	343	2	}	}	PUNCT
ejpam-4700	343	3	t−(n−r+1	t−(n−r+1	PROPN
ejpam-4700	343	4	)	)	PUNCT
ejpam-4700	343	5	=	=	SYM
ejpam-4700	343	6	r−1∑	r−1∑	PROPN
ejpam-4700	343	7	j=0	j=0	PROPN
ejpam-4700	343	8	(	(	PUNCT
ejpam-4700	343	9	r	r	NOUN
ejpam-4700	343	10	−	−	PROPN
ejpam-4700	343	11	1	1	NUM
ejpam-4700	343	12	j	j	NOUN
ejpam-4700	343	13	)	)	PUNCT
ejpam-4700	343	14	dr−1−j	dr−1−j	PROPN
ejpam-4700	343	15	dtr−1−j	dtr−1−j	PROPN
ejpam-4700	343	16	t−(n−r+1	t−(n−r+1	PROPN
ejpam-4700	343	17	)	)	PUNCT
ejpam-4700	343	18	r.	r.	PROPN
ejpam-4700	343	19	b.	b.	PROPN
ejpam-4700	343	20	corcino	corcino	PROPN
ejpam-4700	343	21	et	et	PROPN
ejpam-4700	343	22	al	al	PROPN
ejpam-4700	343	23	.	.	PUNCT
ejpam-4700	343	24	/	/	SYM
ejpam-4700	343	25	eur	eur	PROPN
ejpam-4700	343	26	.	.	PUNCT
ejpam-4700	344	1	j.	j.	PROPN
ejpam-4700	344	2	pure	pure	PROPN
ejpam-4700	344	3	appl	appl	PROPN
ejpam-4700	344	4	.	.	PROPN
ejpam-4700	344	5	math	math	PROPN
ejpam-4700	344	6	,	,	PUNCT
ejpam-4700	344	7	16	16	NUM
ejpam-4700	344	8	(	(	PUNCT
ejpam-4700	344	9	2	2	NUM
ejpam-4700	344	10	)	)	PUNCT
ejpam-4700	344	11	(	(	PUNCT
ejpam-4700	344	12	2023	2023	NUM
ejpam-4700	344	13	)	)	PUNCT
ejpam-4700	344	14	,	,	PUNCT
ejpam-4700	344	15	1005	1005	NUM
ejpam-4700	344	16	-	-	SYM
ejpam-4700	344	17	1023	1023	NUM
ejpam-4700	344	18	1021	1021	NUM
ejpam-4700	344	19	×	×	NOUN
ejpam-4700	344	20	dj	dj	NOUN
ejpam-4700	344	21	dtj	dtj	NOUN
ejpam-4700	344	22	extk	extk	PROPN
ejpam-4700	344	23	∞∑	∞∑	PRON
ejpam-4700	344	24	n=0	n=0	NUM
ejpam-4700	344	25	b(r	b(r	NOUN
ejpam-4700	344	26	)	)	PUNCT
ejpam-4700	344	27	n	n	CCONJ
ejpam-4700	344	28	(	(	PUNCT
ejpam-4700	344	29	t−	t−	PROPN
ejpam-4700	344	30	tk	tk	PROPN
ejpam-4700	344	31	)	)	PUNCT
ejpam-4700	344	32	n	n	PROPN
ejpam-4700	344	33	n!︸	n!︸	PROPN
ejpam-4700	344	34	︷︷	︷︷	PROPN
ejpam-4700	344	35	︸	︸	ADP
ejpam-4700	344	36	h(t	h(t	PROPN
ejpam-4700	344	37	)	)	PUNCT
ejpam-4700	344	38			NOUN
ejpam-4700	344	39	now	now	ADV
ejpam-4700	344	40	,	,	PUNCT
ejpam-4700	344	41	consider	consider	VERB
ejpam-4700	344	42	the	the	DET
ejpam-4700	344	43	derivative	derivative	ADJ
ejpam-4700	344	44	dj	dj	NOUN
ejpam-4700	344	45	dtj	dtj	NOUN
ejpam-4700	344	46	(	(	PUNCT
ejpam-4700	344	47	extkh(t	extkh(t	NOUN
ejpam-4700	344	48	)	)	PUNCT
ejpam-4700	344	49	)	)	PUNCT
ejpam-4700	345	1	=	=	SYM
ejpam-4700	346	1	j∑	j∑	PROPN
ejpam-4700	346	2	l=0	l=0	PROPN
ejpam-4700	346	3	(	(	PUNCT
ejpam-4700	346	4	j	j	PROPN
ejpam-4700	346	5	l	l	NOUN
ejpam-4700	346	6	)	)	PUNCT
ejpam-4700	347	1	xj−lextk	xj−lextk	PROPN
ejpam-4700	348	1	∞∑	∞∑	PRON
ejpam-4700	348	2	n=0	n=0	PROPN
ejpam-4700	348	3	b	b	NOUN
ejpam-4700	348	4	(	(	PUNCT
ejpam-4700	348	5	r	r	NOUN
ejpam-4700	348	6	)	)	PUNCT
ejpam-4700	348	7	n	n	PRON
ejpam-4700	348	8	n	n	CCONJ
ejpam-4700	348	9	!	!	PUNCT
ejpam-4700	349	1	(	(	PUNCT
ejpam-4700	349	2	n)l(t−	n)l(t−	PROPN
ejpam-4700	349	3	tk	tk	PROPN
ejpam-4700	349	4	)	)	PUNCT
ejpam-4700	349	5	n−l	n−l	NOUN
ejpam-4700	349	6	=	=	SYM
ejpam-4700	349	7	extk	extk	ADV
ejpam-4700	349	8	l∑	l∑	PUNCT
ejpam-4700	350	1	l=0	l=0	PROPN
ejpam-4700	350	2	(	(	PUNCT
ejpam-4700	350	3	j	j	PROPN
ejpam-4700	350	4	l	l	NOUN
ejpam-4700	350	5	)	)	PUNCT
ejpam-4700	351	1	xj−l	xj−l	PROPN
ejpam-4700	351	2	∞∑	∞∑	NUM
ejpam-4700	351	3	n=0	n=0	NUM
ejpam-4700	351	4	b(r	b(r	NOUN
ejpam-4700	351	5	)	)	PUNCT
ejpam-4700	351	6	n	n	CCONJ
ejpam-4700	351	7	(	(	PUNCT
ejpam-4700	351	8	t−	t−	PROPN
ejpam-4700	351	9	tk	tk	PROPN
ejpam-4700	351	10	)	)	PUNCT
ejpam-4700	351	11	n	n	PROPN
ejpam-4700	351	12	(	(	PUNCT
ejpam-4700	351	13	n−	n−	NOUN
ejpam-4700	351	14	l	l	NOUN
ejpam-4700	351	15	)	)	PUNCT
ejpam-4700	351	16	!	!	PUNCT
ejpam-4700	352	1	so	so	ADV
ejpam-4700	352	2	that	that	SCONJ
ejpam-4700	352	3	,	,	PUNCT
ejpam-4700	352	4	res(f(t	res(f(t	PROPN
ejpam-4700	352	5	)	)	PUNCT
ejpam-4700	352	6	,	,	PUNCT
ejpam-4700	352	7	t	t	PROPN
ejpam-4700	352	8	=	=	SYM
ejpam-4700	352	9	tk	tk	PROPN
ejpam-4700	352	10	)	)	PUNCT
ejpam-4700	352	11	=	=	SYM
ejpam-4700	352	12	1	1	NUM
ejpam-4700	352	13	(	(	PUNCT
ejpam-4700	352	14	r	r	NOUN
ejpam-4700	352	15	−	−	NOUN
ejpam-4700	352	16	1	1	NUM
ejpam-4700	352	17	)	)	PUNCT
ejpam-4700	352	18	!	!	PUNCT
ejpam-4700	353	1	(	(	PUNCT
ejpam-4700	353	2	1−	1−	NUM
ejpam-4700	353	3	u	u	NOUN
ejpam-4700	353	4	u	u	NOUN
ejpam-4700	353	5	)	)	PUNCT
ejpam-4700	353	6	r	r	NOUN
ejpam-4700	353	7	lim	lim	PROPN
ejpam-4700	353	8	t→tk	t→tk	PROPN
ejpam-4700	353	9	r−1∑	r−1∑	PROPN
ejpam-4700	353	10	j=0	j=0	PROPN
ejpam-4700	353	11	(	(	PUNCT
ejpam-4700	353	12	r	r	NOUN
ejpam-4700	353	13	−	−	PROPN
ejpam-4700	353	14	1	1	NUM
ejpam-4700	353	15	j	j	NOUN
ejpam-4700	353	16	)	)	PUNCT
ejpam-4700	353	17	dr−1−j	dr−1−j	PROPN
ejpam-4700	353	18	dtr−1−j	dtr−1−j	NOUN
ejpam-4700	353	19	t−(n−r+1)extk	t−(n−r+1)extk	ADP
ejpam-4700	353	20	×	×	NOUN
ejpam-4700	353	21	j∑	j∑	PROPN
ejpam-4700	354	1	l=0	l=0	PROPN
ejpam-4700	354	2	(	(	PUNCT
ejpam-4700	354	3	j	j	PROPN
ejpam-4700	354	4	l	l	NOUN
ejpam-4700	354	5	)	)	PUNCT
ejpam-4700	355	1	xj−l	xj−l	PROPN
ejpam-4700	355	2	∞∑	∞∑	NUM
ejpam-4700	355	3	n=0	n=0	NUM
ejpam-4700	355	4	b(r	b(r	NOUN
ejpam-4700	355	5	)	)	PUNCT
ejpam-4700	355	6	n	n	CCONJ
ejpam-4700	355	7	(	(	PUNCT
ejpam-4700	355	8	t−	t−	PROPN
ejpam-4700	355	9	tk	tk	PROPN
ejpam-4700	355	10	)	)	PUNCT
ejpam-4700	355	11	n	n	PROPN
ejpam-4700	355	12	(	(	PUNCT
ejpam-4700	355	13	n−	n−	NOUN
ejpam-4700	355	14	l	l	NOUN
ejpam-4700	355	15	)	)	PUNCT
ejpam-4700	355	16	!	!	PUNCT
ejpam-4700	356	1	note	note	VERB
ejpam-4700	356	2	that	that	SCONJ
ejpam-4700	356	3	b	b	X
ejpam-4700	356	4	(	(	PUNCT
ejpam-4700	356	5	r	r	NOUN
ejpam-4700	356	6	)	)	PUNCT
ejpam-4700	356	7	n	n	CCONJ
ejpam-4700	356	8	(	(	PUNCT
ejpam-4700	356	9	t−tk	t−tk	PROPN
ejpam-4700	356	10	)	)	PUNCT
ejpam-4700	356	11	n−l	n−l	NOUN
ejpam-4700	356	12	(	(	PUNCT
ejpam-4700	356	13	n−l	n−l	PROPN
ejpam-4700	356	14	)	)	PUNCT
ejpam-4700	356	15	!	!	PUNCT
ejpam-4700	357	1	→	→	SYM
ejpam-4700	357	2	0	0	PUNCT
ejpam-4700	357	3	as	as	ADP
ejpam-4700	357	4	t	t	PROPN
ejpam-4700	357	5	→	→	SYM
ejpam-4700	357	6	tk	tk	PROPN
ejpam-4700	357	7	except	except	SCONJ
ejpam-4700	357	8	when	when	SCONJ
ejpam-4700	357	9	n	n	PROPN
ejpam-4700	357	10	=	=	SYM
ejpam-4700	357	11	l	l	NOUN
ejpam-4700	357	12	res(f(t	res(f(t	NOUN
ejpam-4700	357	13	)	)	PUNCT
ejpam-4700	357	14	,	,	PUNCT
ejpam-4700	357	15	t	t	PROPN
ejpam-4700	357	16	=	=	SYM
ejpam-4700	357	17	tk	tk	PROPN
ejpam-4700	357	18	)	)	PUNCT
ejpam-4700	357	19	=	=	SYM
ejpam-4700	357	20	1	1	NUM
ejpam-4700	357	21	(	(	PUNCT
ejpam-4700	357	22	r	r	NOUN
ejpam-4700	357	23	−	−	NOUN
ejpam-4700	357	24	1	1	NUM
ejpam-4700	357	25	)	)	PUNCT
ejpam-4700	357	26	!	!	PUNCT
ejpam-4700	358	1	(	(	PUNCT
ejpam-4700	358	2	1−	1−	NUM
ejpam-4700	358	3	u	u	NOUN
ejpam-4700	358	4	u	u	NOUN
ejpam-4700	358	5	)	)	PUNCT
ejpam-4700	358	6	r	r	NOUN
ejpam-4700	358	7	r−1∑	r−1∑	PROPN
ejpam-4700	358	8	j=0	j=0	PROPN
ejpam-4700	358	9	(	(	PUNCT
ejpam-4700	358	10	r	r	NOUN
ejpam-4700	358	11	−	−	PROPN
ejpam-4700	358	12	1	1	NUM
ejpam-4700	358	13	j	j	NOUN
ejpam-4700	358	14	)	)	PUNCT
ejpam-4700	358	15	(	(	PUNCT
ejpam-4700	358	16	−1)r−1−j(n−	−1)r−1−j(n−	NOUN
ejpam-4700	358	17	1−	1−	NUM
ejpam-4700	358	18	j)r−1−jt	j)r−1−jt	ADJ
ejpam-4700	358	19	−(n−j	−(n−j	X
ejpam-4700	358	20	)	)	PUNCT
ejpam-4700	359	1	k	k	X
ejpam-4700	359	2	×	×	PROPN
ejpam-4700	359	3	extk	extk	INTJ
ejpam-4700	359	4	j∑	j∑	PROPN
ejpam-4700	360	1	l=0	l=0	PROPN
ejpam-4700	360	2	(	(	PUNCT
ejpam-4700	360	3	j	j	PROPN
ejpam-4700	360	4	l	l	NOUN
ejpam-4700	360	5	)	)	PUNCT
ejpam-4700	360	6	xj−lb	xj−lb	X
ejpam-4700	361	1	(	(	PUNCT
ejpam-4700	361	2	r	r	NOUN
ejpam-4700	361	3	)	)	PUNCT
ejpam-4700	361	4	l	l	NOUN
ejpam-4700	361	5	=	=	PUNCT
ejpam-4700	361	6	(	(	PUNCT
ejpam-4700	361	7	1−	1−	NUM
ejpam-4700	361	8	u	u	NOUN
ejpam-4700	361	9	u	u	NOUN
ejpam-4700	361	10	)	)	PUNCT
ejpam-4700	361	11	r	r	NOUN
ejpam-4700	361	12	r−1∑	r−1∑	PROPN
ejpam-4700	361	13	j=0	j=0	PROPN
ejpam-4700	361	14	(	(	PUNCT
ejpam-4700	361	15	−1)r−1−j	−1)r−1−j	NOUN
ejpam-4700	361	16	j!(r	j!(r	PRON
ejpam-4700	361	17	−	−	PROPN
ejpam-4700	361	18	1−	1−	NUM
ejpam-4700	361	19	j	j	PROPN
ejpam-4700	361	20	)	)	PUNCT
ejpam-4700	361	21	!	!	PUNCT
ejpam-4700	362	1	(	(	PUNCT
ejpam-4700	362	2	n−	n−	NOUN
ejpam-4700	362	3	1−	1−	NUM
ejpam-4700	362	4	j)r−1−jt	j)r−1−jt	ADJ
ejpam-4700	362	5	−(n−j	−(n−j	X
ejpam-4700	362	6	)	)	PUNCT
ejpam-4700	363	1	k	k	X
ejpam-4700	363	2	×	×	PROPN
ejpam-4700	363	3	extk	extk	INTJ
ejpam-4700	363	4	j∑	j∑	PROPN
ejpam-4700	364	1	l=0	l=0	PROPN
ejpam-4700	364	2	(	(	PUNCT
ejpam-4700	364	3	j	j	PROPN
ejpam-4700	364	4	l	l	NOUN
ejpam-4700	364	5	)	)	PUNCT
ejpam-4700	364	6	xj−lb	xj−lb	X
ejpam-4700	365	1	(	(	PUNCT
ejpam-4700	365	2	r	r	NOUN
ejpam-4700	365	3	)	)	PUNCT
ejpam-4700	365	4	l	l	NOUN
ejpam-4700	365	5	=	=	PUNCT
ejpam-4700	365	6	(	(	PUNCT
ejpam-4700	365	7	1−	1−	NUM
ejpam-4700	365	8	u	u	NOUN
ejpam-4700	365	9	u	u	NOUN
ejpam-4700	365	10	)	)	PUNCT
ejpam-4700	365	11	r	r	NOUN
ejpam-4700	365	12	r−1∑	r−1∑	VERB
ejpam-4700	365	13	j=0	j=0	PROPN
ejpam-4700	365	14	(	(	PUNCT
ejpam-4700	365	15	n−	n−	NOUN
ejpam-4700	365	16	1−	1−	NUM
ejpam-4700	366	1	j	j	PROPN
ejpam-4700	366	2	r	r	NOUN
ejpam-4700	366	3	−	−	PROPN
ejpam-4700	366	4	1−	1−	NUM
ejpam-4700	366	5	j	j	PROPN
ejpam-4700	366	6	)	)	PUNCT
ejpam-4700	366	7	(	(	PUNCT
ejpam-4700	366	8	−1)−j−1	−1)−j−1	NOUN
ejpam-4700	366	9	t	t	PROPN
ejpam-4700	366	10	j−n	j−n	PROPN
ejpam-4700	367	1	k	k	PROPN
ejpam-4700	367	2	j	j	PROPN
ejpam-4700	367	3	!	!	PUNCT
ejpam-4700	368	1	×	×	PROPN
ejpam-4700	369	1	extk	extk	INTJ
ejpam-4700	369	2	j∑	j∑	PROPN
ejpam-4700	370	1	l=0	l=0	PROPN
ejpam-4700	370	2	(	(	PUNCT
ejpam-4700	370	3	j	j	PROPN
ejpam-4700	370	4	l	l	NOUN
ejpam-4700	370	5	)	)	PUNCT
ejpam-4700	370	6	xj−lb	xj−lb	X
ejpam-4700	371	1	(	(	PUNCT
ejpam-4700	371	2	r	r	NOUN
ejpam-4700	371	3	)	)	PUNCT
ejpam-4700	371	4	l	l	NOUN
ejpam-4700	371	5	recall	recall	NOUN
ejpam-4700	371	6	that	that	SCONJ
ejpam-4700	371	7	b	b	X
ejpam-4700	371	8	(	(	PUNCT
ejpam-4700	371	9	r	r	NOUN
ejpam-4700	371	10	)	)	PUNCT
ejpam-4700	371	11	l	l	NOUN
ejpam-4700	371	12	(	(	PUNCT
ejpam-4700	371	13	x	x	X
ejpam-4700	371	14	)	)	PUNCT
ejpam-4700	371	15	=	=	SYM
ejpam-4700	372	1	∑j	∑j	ADJ
ejpam-4700	372	2	l=0	l=0	PROPN
ejpam-4700	372	3	(	(	PUNCT
ejpam-4700	372	4	j	j	PROPN
ejpam-4700	372	5	l	l	NOUN
ejpam-4700	372	6	)	)	PUNCT
ejpam-4700	372	7	b	b	NOUN
ejpam-4700	372	8	(	(	PUNCT
ejpam-4700	372	9	r	r	NOUN
ejpam-4700	372	10	)	)	PUNCT
ejpam-4700	372	11	l	l	NOUN
ejpam-4700	372	12	(	(	PUNCT
ejpam-4700	372	13	x)j−l	x)j−l	NOUN
ejpam-4700	372	14	.	.	PUNCT
ejpam-4700	373	1	thus	thus	ADV
ejpam-4700	373	2	,	,	PUNCT
ejpam-4700	373	3	res(f(t	res(f(t	PROPN
ejpam-4700	373	4	)	)	PUNCT
ejpam-4700	373	5	,	,	PUNCT
ejpam-4700	373	6	t	t	PROPN
ejpam-4700	373	7	=	=	SYM
ejpam-4700	373	8	tk	tk	PROPN
ejpam-4700	373	9	)	)	PUNCT
ejpam-4700	373	10	=	=	PUNCT
ejpam-4700	374	1	(	(	PUNCT
ejpam-4700	374	2	1−	1−	NUM
ejpam-4700	374	3	u	u	NOUN
ejpam-4700	374	4	u	u	NOUN
ejpam-4700	374	5	)	)	PUNCT
ejpam-4700	374	6	r	r	NOUN
ejpam-4700	374	7	r−1∑	r−1∑	VERB
ejpam-4700	374	8	j=0	j=0	PROPN
ejpam-4700	374	9	(	(	PUNCT
ejpam-4700	374	10	n−	n−	NOUN
ejpam-4700	374	11	1−	1−	NUM
ejpam-4700	374	12	j	j	PROPN
ejpam-4700	375	1	r	r	NOUN
ejpam-4700	375	2	−	−	PROPN
ejpam-4700	375	3	1−	1−	NUM
ejpam-4700	375	4	j	j	PROPN
ejpam-4700	375	5	)	)	PUNCT
ejpam-4700	375	6	(	(	PUNCT
ejpam-4700	375	7	−1)−j−1b	−1)−j−1b	PROPN
ejpam-4700	375	8	(	(	PUNCT
ejpam-4700	375	9	r	r	NOUN
ejpam-4700	375	10	)	)	PUNCT
ejpam-4700	375	11	l	l	NOUN
ejpam-4700	376	1	j	j	X
ejpam-4700	376	2	!	!	PUNCT
ejpam-4700	376	3	extk	extk	ADJ
ejpam-4700	376	4	tn−j	tn−j	ADJ
ejpam-4700	376	5	references	reference	NOUN
ejpam-4700	376	6	1022	1022	NUM
ejpam-4700	376	7	substituting	substitute	VERB
ejpam-4700	376	8	tk	tk	PROPN
ejpam-4700	376	9	=	=	NOUN
ejpam-4700	376	10	log	log	NOUN
ejpam-4700	376	11	u	u	NOUN
ejpam-4700	376	12	λ	λ	NOUN
ejpam-4700	376	13	+	+	PROPN
ejpam-4700	376	14	2kπi	2kπi	NUM
ejpam-4700	377	1	,	,	PUNCT
ejpam-4700	377	2	we	we	PRON
ejpam-4700	377	3	get	get	VERB
ejpam-4700	377	4	res(f(t	res(f(t	NOUN
ejpam-4700	377	5	)	)	PUNCT
ejpam-4700	377	6	,	,	PUNCT
ejpam-4700	377	7	t	t	PROPN
ejpam-4700	377	8	=	=	SYM
ejpam-4700	377	9	tk	tk	PROPN
ejpam-4700	377	10	)	)	PUNCT
ejpam-4700	377	11	=	=	PUNCT
ejpam-4700	378	1	(	(	PUNCT
ejpam-4700	378	2	1−	1−	NUM
ejpam-4700	378	3	u	u	NOUN
ejpam-4700	378	4	u	u	NOUN
ejpam-4700	378	5	)	)	PUNCT
ejpam-4700	378	6	r	r	NOUN
ejpam-4700	378	7	r−1∑	r−1∑	VERB
ejpam-4700	378	8	j=0	j=0	PROPN
ejpam-4700	378	9	(	(	PUNCT
ejpam-4700	378	10	n−	n−	NOUN
ejpam-4700	378	11	1−	1−	NUM
ejpam-4700	378	12	j	j	PROPN
ejpam-4700	379	1	r	r	NOUN
ejpam-4700	379	2	−	−	PROPN
ejpam-4700	379	3	1−	1−	NUM
ejpam-4700	379	4	j	j	PROPN
ejpam-4700	379	5	)	)	PUNCT
ejpam-4700	379	6	(	(	PUNCT
ejpam-4700	379	7	−1)−j−1b	−1)−j−1b	PROPN
ejpam-4700	379	8	(	(	PUNCT
ejpam-4700	379	9	r	r	NOUN
ejpam-4700	379	10	)	)	PUNCT
ejpam-4700	379	11	l	l	NOUN
ejpam-4700	379	12	j	j	PROPN
ejpam-4700	379	13	!	!	PROPN
ejpam-4700	379	14	ex(log	ex(log	PROPN
ejpam-4700	379	15	u	u	PROPN
ejpam-4700	379	16	λ	λ	X
ejpam-4700	379	17	+2kπi	+2kπi	PROPN
ejpam-4700	379	18	)	)	PUNCT
ejpam-4700	379	19	[	[	PUNCT
ejpam-4700	379	20	log	log	VERB
ejpam-4700	379	21	u	u	NOUN
ejpam-4700	379	22	λ	λ	PROPN
ejpam-4700	379	23	+	+	PROPN
ejpam-4700	379	24	2kπi	2kπi	NUM
ejpam-4700	379	25	]	]	PUNCT
ejpam-4700	379	26	n−j	n−j	PUNCT
ejpam-4700	379	27	this	this	PRON
ejpam-4700	379	28	gives	give	VERB
ejpam-4700	379	29	,	,	PUNCT
ejpam-4700	379	30	g(r	g(r	NOUN
ejpam-4700	379	31	)	)	PUNCT
ejpam-4700	379	32	n	n	CCONJ
ejpam-4700	379	33	(	(	PUNCT
ejpam-4700	379	34	x;u	x;u	PROPN
ejpam-4700	379	35	,	,	PUNCT
ejpam-4700	379	36	λ	λ	NOUN
ejpam-4700	379	37	)	)	PUNCT
ejpam-4700	379	38	=	=	PUNCT
ejpam-4700	380	1	−n	−n	ADJ
ejpam-4700	380	2	!	!	PUNCT
ejpam-4700	381	1	∑	∑	ADV
ejpam-4700	381	2	k∈z	k∈z	PROPN
ejpam-4700	382	1	(	(	PUNCT
ejpam-4700	382	2	1−	1−	NUM
ejpam-4700	382	3	u	u	NOUN
ejpam-4700	382	4	u	u	NOUN
ejpam-4700	382	5	)	)	PUNCT
ejpam-4700	382	6	r	r	NOUN
ejpam-4700	382	7	r−1∑	r−1∑	VERB
ejpam-4700	382	8	j=0	j=0	PROPN
ejpam-4700	382	9	(	(	PUNCT
ejpam-4700	382	10	n−	n−	NOUN
ejpam-4700	382	11	1−	1−	NUM
ejpam-4700	382	12	j	j	PROPN
ejpam-4700	382	13	r	r	NOUN
ejpam-4700	382	14	−	−	PROPN
ejpam-4700	382	15	1−	1−	NUM
ejpam-4700	382	16	j	j	PROPN
ejpam-4700	382	17	)	)	PUNCT
ejpam-4700	382	18	(	(	PUNCT
ejpam-4700	382	19	−1)−j−1b	−1)−j−1b	PROPN
ejpam-4700	382	20	(	(	PUNCT
ejpam-4700	382	21	r	r	NOUN
ejpam-4700	382	22	)	)	PUNCT
ejpam-4700	382	23	l	l	NOUN
ejpam-4700	382	24	j	j	PROPN
ejpam-4700	382	25	!	!	PUNCT
ejpam-4700	383	1	(	(	PUNCT
ejpam-4700	383	2	u	u	NOUN
ejpam-4700	383	3	λ	λ	PROPN
ejpam-4700	383	4	)	)	PUNCT
ejpam-4700	383	5	x	x	PROPN
ejpam-4700	383	6	e2kxπi	e2kxπi	PROPN
ejpam-4700	383	7	[	[	PUNCT
ejpam-4700	383	8	log	log	VERB
ejpam-4700	383	9	u	u	NOUN
ejpam-4700	383	10	λ	λ	PROPN
ejpam-4700	383	11	+	+	PROPN
ejpam-4700	383	12	2kπi	2kπi	NUM
ejpam-4700	383	13	]	]	PUNCT
ejpam-4700	383	14	n−j	n−j	X
ejpam-4700	383	15	.	.	PUNCT
ejpam-4700	384	1	3	3	X
ejpam-4700	384	2	.	.	X
ejpam-4700	384	3	conclusion	conclusion	NOUN
ejpam-4700	384	4	the	the	DET
ejpam-4700	384	5	researchers	researcher	NOUN
ejpam-4700	384	6	were	be	AUX
ejpam-4700	384	7	able	able	ADJ
ejpam-4700	384	8	to	to	PART
ejpam-4700	384	9	obtain	obtain	VERB
ejpam-4700	384	10	the	the	DET
ejpam-4700	384	11	fourier	fourier	NOUN
ejpam-4700	384	12	series	series	NOUN
ejpam-4700	384	13	expansion	expansion	NOUN
ejpam-4700	384	14	of	of	ADP
ejpam-4700	384	15	the	the	DET
ejpam-4700	384	16	apostolfrobenius	apostolfrobenius	NOUN
ejpam-4700	384	17	type	type	NOUN
ejpam-4700	384	18	of	of	ADP
ejpam-4700	384	19	:	:	PUNCT
ejpam-4700	384	20	tangent	tangent	NOUN
ejpam-4700	384	21	and	and	CCONJ
ejpam-4700	384	22	genocchi	genocchi	PROPN
ejpam-4700	384	23	polynomials	polynomial	NOUN
ejpam-4700	384	24	of	of	ADP
ejpam-4700	384	25	higher	high	ADJ
ejpam-4700	384	26	order	order	NOUN
ejpam-4700	384	27	.	.	PUNCT
ejpam-4700	385	1	taking	take	VERB
ejpam-4700	385	2	into	into	ADP
ejpam-4700	385	3	consideration	consideration	NOUN
ejpam-4700	385	4	all	all	PRON
ejpam-4700	385	5	of	of	ADP
ejpam-4700	385	6	the	the	DET
ejpam-4700	385	7	generating	generate	VERB
ejpam-4700	385	8	function	function	NOUN
ejpam-4700	385	9	’s	’s	PART
ejpam-4700	385	10	residues	residue	NOUN
ejpam-4700	385	11	,	,	PUNCT
ejpam-4700	385	12	together	together	ADV
ejpam-4700	385	13	with	with	ADP
ejpam-4700	385	14	the	the	DET
ejpam-4700	385	15	cauchy	cauchy	ADJ
ejpam-4700	385	16	residue	residue	NOUN
ejpam-4700	385	17	theorem	theorem	NOUN
ejpam-4700	385	18	,	,	PUNCT
ejpam-4700	385	19	proved	prove	VERB
ejpam-4700	385	20	to	to	PART
ejpam-4700	385	21	be	be	AUX
ejpam-4700	385	22	a	a	DET
ejpam-4700	385	23	useful	useful	ADJ
ejpam-4700	385	24	strategy	strategy	NOUN
ejpam-4700	385	25	for	for	ADP
ejpam-4700	385	26	deriving	derive	VERB
ejpam-4700	385	27	the	the	DET
ejpam-4700	385	28	fourier	fourier	ADJ
ejpam-4700	385	29	series	series	NOUN
ejpam-4700	385	30	of	of	ADP
ejpam-4700	385	31	these	these	DET
ejpam-4700	385	32	polynomials	polynomial	NOUN
ejpam-4700	385	33	of	of	ADP
ejpam-4700	385	34	higher	high	ADJ
ejpam-4700	385	35	order	order	NOUN
ejpam-4700	385	36	.	.	PUNCT
ejpam-4700	386	1	for	for	ADP
ejpam-4700	386	2	future	future	ADJ
ejpam-4700	386	3	study	study	NOUN
ejpam-4700	386	4	,	,	PUNCT
ejpam-4700	386	5	it	it	PRON
ejpam-4700	386	6	will	will	AUX
ejpam-4700	386	7	be	be	AUX
ejpam-4700	386	8	interesting	interesting	ADJ
ejpam-4700	386	9	to	to	PART
ejpam-4700	386	10	derive	derive	VERB
ejpam-4700	386	11	the	the	DET
ejpam-4700	386	12	integral	integral	ADJ
ejpam-4700	386	13	representations	representation	NOUN
ejpam-4700	386	14	of	of	ADP
ejpam-4700	386	15	these	these	DET
ejpam-4700	386	16	higher	high	ADJ
ejpam-4700	386	17	order	order	NOUN
ejpam-4700	386	18	polynomials	polynomial	NOUN
ejpam-4700	386	19	.	.	PUNCT
ejpam-4700	387	1	acknowledgements	acknowledgement	NOUN
ejpam-4700	387	2	the	the	DET
ejpam-4700	387	3	authors	author	NOUN
ejpam-4700	387	4	are	be	AUX
ejpam-4700	387	5	grateful	grateful	ADJ
ejpam-4700	387	6	to	to	PART
ejpam-4700	387	7	cebu	cebu	VERB
ejpam-4700	387	8	normal	normal	ADJ
ejpam-4700	387	9	university	university	NOUN
ejpam-4700	387	10	(	(	PUNCT
ejpam-4700	387	11	cnu	cnu	PROPN
ejpam-4700	387	12	)	)	PUNCT
ejpam-4700	387	13	for	for	ADP
ejpam-4700	387	14	funding	fund	VERB
ejpam-4700	387	15	this	this	DET
ejpam-4700	387	16	research	research	NOUN
ejpam-4700	387	17	project	project	NOUN
ejpam-4700	387	18	through	through	ADP
ejpam-4700	387	19	its	its	PRON
ejpam-4700	387	20	research	research	NOUN
ejpam-4700	387	21	institute	institute	NOUN
ejpam-4700	387	22	for	for	ADP
ejpam-4700	387	23	computational	computational	ADJ
ejpam-4700	387	24	mathematics	mathematic	NOUN
ejpam-4700	387	25	and	and	CCONJ
ejpam-4700	387	26	physics	physics	PROPN
ejpam-4700	387	27	(	(	PUNCT
ejpam-4700	387	28	ricmp	ricmp	PROPN
ejpam-4700	387	29	)	)	PUNCT
ejpam-4700	387	30	.	.	PUNCT
ejpam-4700	388	1	they	they	PRON
ejpam-4700	388	2	are	be	AUX
ejpam-4700	388	3	also	also	ADV
ejpam-4700	388	4	grateful	grateful	ADJ
ejpam-4700	388	5	to	to	ADP
ejpam-4700	388	6	the	the	DET
ejpam-4700	388	7	referees	referee	NOUN
ejpam-4700	388	8	for	for	ADP
ejpam-4700	388	9	their	their	PRON
ejpam-4700	388	10	valuable	valuable	ADJ
ejpam-4700	388	11	time	time	NOUN
ejpam-4700	388	12	in	in	ADP
ejpam-4700	388	13	reviewing	review	VERB
ejpam-4700	388	14	the	the	DET
ejpam-4700	388	15	paper	paper	NOUN
ejpam-4700	388	16	.	.	PUNCT
ejpam-4700	389	1	references	reference	NOUN
ejpam-4700	389	2	[	[	X
ejpam-4700	389	3	1	1	X
ejpam-4700	389	4	]	]	PUNCT
ejpam-4700	389	5	s.	s.	PROPN
ejpam-4700	389	6	araci	araci	PROPN
ejpam-4700	389	7	and	and	CCONJ
ejpam-4700	389	8	m.	m.	NOUN
ejpam-4700	389	9	acikgoz	acikgoz	VERB
ejpam-4700	389	10	.	.	PUNCT
ejpam-4700	390	1	construction	construction	NOUN
ejpam-4700	390	2	of	of	ADP
ejpam-4700	390	3	fourier	fourier	ADJ
ejpam-4700	390	4	expansion	expansion	NOUN
ejpam-4700	390	5	of	of	ADP
ejpam-4700	390	6	apostol	apostol	NOUN
ejpam-4700	390	7	frobenius	frobenius	NOUN
ejpam-4700	390	8	-	-	PUNCT
ejpam-4700	390	9	euler	euler	NOUN
ejpam-4700	390	10	polynomials	polynomial	NOUN
ejpam-4700	390	11	and	and	CCONJ
ejpam-4700	390	12	its	its	PRON
ejpam-4700	390	13	applications	application	NOUN
ejpam-4700	390	14	.	.	PUNCT
ejpam-4700	391	1	advances	advance	NOUN
ejpam-4700	391	2	in	in	ADP
ejpam-4700	391	3	difference	difference	NOUN
ejpam-4700	391	4	equations	equation	NOUN
ejpam-4700	391	5	,	,	PUNCT
ejpam-4700	391	6	2018(1):1–14	2018(1):1–14	PROPN
ejpam-4700	391	7	.	.	PUNCT
ejpam-4700	391	8	,	,	PUNCT
ejpam-4700	391	9	2018	2018	NUM
ejpam-4700	391	10	.	.	PUNCT
ejpam-4700	392	1	[	[	X
ejpam-4700	392	2	2	2	NUM
ejpam-4700	392	3	]	]	PUNCT
ejpam-4700	392	4	a.	a.	NOUN
ejpam-4700	392	5	bayad	bayad	NOUN
ejpam-4700	392	6	and	and	CCONJ
ejpam-4700	392	7	y.	y.	PROPN
ejpam-4700	392	8	hamahata	hamahata	PROPN
ejpam-4700	392	9	.	.	PUNCT
ejpam-4700	393	1	polylogarithms	polylogarithm	NOUN
ejpam-4700	393	2	and	and	CCONJ
ejpam-4700	393	3	poly	poly	ADJ
ejpam-4700	393	4	-	-	PUNCT
ejpam-4700	393	5	bernoulli	bernoulli	NOUN
ejpam-4700	393	6	polynomials	polynomial	NOUN
ejpam-4700	393	7	.	.	PUNCT
ejpam-4700	394	1	kyushu	kyushu	PROPN
ejpam-4700	394	2	j.	j.	PROPN
ejpam-4700	394	3	math	math	PROPN
ejpam-4700	394	4	,	,	PUNCT
ejpam-4700	394	5	65:15–24	65:15–24	PROPN
ejpam-4700	394	6	.	.	PROPN
ejpam-4700	394	7	,	,	PUNCT
ejpam-4700	394	8	2011	2011	NUM
ejpam-4700	394	9	.	.	PUNCT
ejpam-4700	395	1	[	[	X
ejpam-4700	395	2	3	3	NUM
ejpam-4700	395	3	]	]	X
ejpam-4700	395	4	b.a	b.a	PROPN
ejpam-4700	395	5	.	.	PROPN
ejpam-4700	395	6	damgo	damgo	PROPN
ejpam-4700	395	7	c.	c.	PROPN
ejpam-4700	395	8	b.	b.	PROPN
ejpam-4700	395	9	corcino	corcino	PROPN
ejpam-4700	395	10	,	,	PUNCT
ejpam-4700	395	11	r.	r.	PROPN
ejpam-4700	395	12	b.	b.	PROPN
ejpam-4700	395	13	corcino	corcino	PROPN
ejpam-4700	395	14	and	and	CCONJ
ejpam-4700	395	15	j.a.a	j.a.a	PROPN
ejpam-4700	395	16	.	.	PUNCT
ejpam-4700	396	1	ca	can	AUX
ejpam-4700	396	2	nete	nete	VERB
ejpam-4700	396	3	.	.	PUNCT
ejpam-4700	397	1	integral	integral	ADJ
ejpam-4700	397	2	representation	representation	NOUN
ejpam-4700	397	3	and	and	CCONJ
ejpam-4700	397	4	explicit	explicit	ADJ
ejpam-4700	397	5	formula	formula	NOUN
ejpam-4700	397	6	at	at	ADP
ejpam-4700	397	7	rational	rational	ADJ
ejpam-4700	397	8	arguments	argument	NOUN
ejpam-4700	397	9	for	for	ADP
ejpam-4700	397	10	apostol	apostol	NOUN
ejpam-4700	397	11	-	-	PUNCT
ejpam-4700	397	12	tangent	tangent	NOUN
ejpam-4700	397	13	polynomials	polynomial	NOUN
ejpam-4700	397	14	.	.	PUNCT
ejpam-4700	398	1	symmetry	symmetry	NOUN
ejpam-4700	398	2	,	,	PUNCT
ejpam-4700	398	3	14(1):article	14(1):article	PROPN
ejpam-4700	398	4	35	35	NUM
ejpam-4700	398	5	,	,	PUNCT
ejpam-4700	398	6	2021	2021	NUM
ejpam-4700	398	7	.	.	PUNCT
ejpam-4700	399	1	[	[	X
ejpam-4700	399	2	4	4	NUM
ejpam-4700	399	3	]	]	X
ejpam-4700	399	4	a.f	a.f	PROPN
ejpam-4700	399	5	.	.	PUNCT
ejpam-4700	399	6	horadam	horadam	PROPN
ejpam-4700	399	7	.	.	PUNCT
ejpam-4700	400	1	applications	application	NOUN
ejpam-4700	400	2	of	of	ADP
ejpam-4700	400	3	fibonacci	fibonacci	NOUN
ejpam-4700	400	4	numbers	number	NOUN
ejpam-4700	400	5	,	,	PUNCT
ejpam-4700	400	6	chapter	chapter	NOUN
ejpam-4700	400	7	genocchi	genocchi	PROPN
ejpam-4700	400	8	polynomials	polynomial	VERB
ejpam-4700	400	9	,	,	PUNCT
ejpam-4700	400	10	pages	page	NOUN
ejpam-4700	400	11	145–166	145–166	NUM
ejpam-4700	400	12	.	.	PUNCT
ejpam-4700	400	13	springer	springer	NOUN
ejpam-4700	400	14	,	,	PUNCT
ejpam-4700	400	15	1991	1991	NUM
ejpam-4700	400	16	.	.	PUNCT
ejpam-4700	401	1	[	[	X
ejpam-4700	401	2	5	5	X
ejpam-4700	401	3	]	]	PUNCT
ejpam-4700	401	4	t.	t.	PROPN
ejpam-4700	401	5	kim	kim	PROPN
ejpam-4700	401	6	.	.	PUNCT
ejpam-4700	401	7	euler	euler	PROPN
ejpam-4700	401	8	numbers	number	NOUN
ejpam-4700	401	9	and	and	CCONJ
ejpam-4700	401	10	polynomials	polynomial	NOUN
ejpam-4700	401	11	associated	associate	VERB
ejpam-4700	401	12	with	with	ADP
ejpam-4700	401	13	zeta	zeta	NOUN
ejpam-4700	401	14	functions	function	NOUN
ejpam-4700	401	15	.	.	PUNCT
ejpam-4700	402	1	abstract	abstract	ADJ
ejpam-4700	402	2	and	and	CCONJ
ejpam-4700	402	3	applied	apply	VERB
ejpam-4700	402	4	analysis	analysis	NOUN
ejpam-4700	402	5	,	,	PUNCT
ejpam-4700	402	6	2008	2008	NUM
ejpam-4700	402	7	:	:	PUNCT
ejpam-4700	402	8	article	article	NOUN
ejpam-4700	402	9	i	i	PROPN
ejpam-4700	402	10	d	d	PROPN
ejpam-4700	402	11	581582	581582	NUM
ejpam-4700	402	12	,	,	PUNCT
ejpam-4700	402	13	11	11	NUM
ejpam-4700	402	14	pages	page	NOUN
ejpam-4700	402	15	,	,	PUNCT
ejpam-4700	402	16	doi:10.1155/2008/581582	doi:10.1155/2008/581582	PROPN
ejpam-4700	402	17	,	,	PUNCT
ejpam-4700	402	18	2008	2008	NUM
ejpam-4700	402	19	.	.	PUNCT
ejpam-4700	403	1	references	reference	NOUN
ejpam-4700	403	2	1023	1023	NUM
ejpam-4700	403	3	[	[	X
ejpam-4700	403	4	6	6	NUM
ejpam-4700	403	5	]	]	PUNCT
ejpam-4700	403	6	t.	t.	PROPN
ejpam-4700	403	7	kim	kim	PROPN
ejpam-4700	403	8	.	.	PUNCT
ejpam-4700	404	1	note	note	NOUN
ejpam-4700	404	2	on	on	ADP
ejpam-4700	404	3	the	the	DET
ejpam-4700	404	4	euler	euler	NOUN
ejpam-4700	404	5	numbers	number	NOUN
ejpam-4700	404	6	and	and	CCONJ
ejpam-4700	404	7	polynomials	polynomial	NOUN
ejpam-4700	404	8	.	.	PUNCT
ejpam-4700	405	1	adv	adv	PROPN
ejpam-4700	405	2	.	.	PUNCT
ejpam-4700	405	3	stud	stud	PROPN
ejpam-4700	405	4	.	.	PUNCT
ejpam-4700	406	1	contemp	contemp	NOUN
ejpam-4700	406	2	.	.	PUNCT
ejpam-4700	407	1	math	math	NOUN
ejpam-4700	407	2	.	.	PUNCT
ejpam-4700	407	3	,	,	PUNCT
ejpam-4700	407	4	17(2):109–116	17(2):109–116	NUM
ejpam-4700	407	5	,	,	PUNCT
ejpam-4700	407	6	2008	2008	NUM
ejpam-4700	407	7	.	.	PUNCT
ejpam-4700	408	1	[	[	X
ejpam-4700	408	2	7	7	NUM
ejpam-4700	408	3	]	]	SYM
ejpam-4700	408	4	fixed	fixed	ADJ
ejpam-4700	408	5	point	point	NOUN
ejpam-4700	408	6	.	.	PUNCT
ejpam-4700	409	1	real	real	ADJ
ejpam-4700	409	2	world	world	NOUN
ejpam-4700	409	3	application	application	NOUN
ejpam-4700	409	4	of	of	ADP
ejpam-4700	409	5	fourier	fourier	ADJ
ejpam-4700	409	6	series	series	NOUN
ejpam-4700	409	7	.	.	PUNCT
ejpam-4700	410	1	https://math.stackexchange.com/q/579695	https://math.stackexchange.com/q/579695	NOUN
ejpam-4700	410	2	,	,	PUNCT
ejpam-4700	410	3	11	11	NUM
ejpam-4700	410	4	2013	2013	NUM
ejpam-4700	410	5	.	.	PUNCT
ejpam-4700	411	1	[	[	X
ejpam-4700	411	2	8	8	NUM
ejpam-4700	411	3	]	]	X
ejpam-4700	411	4	c.	c.	PROPN
ejpam-4700	411	5	s.	s.	PROPN
ejpam-4700	411	6	ryoo	ryoo	PROPN
ejpam-4700	411	7	.	.	PUNCT
ejpam-4700	412	1	a	a	DET
ejpam-4700	412	2	note	note	NOUN
ejpam-4700	412	3	on	on	ADP
ejpam-4700	412	4	the	the	DET
ejpam-4700	412	5	tangent	tangent	ADJ
ejpam-4700	412	6	numbers	number	NOUN
ejpam-4700	412	7	and	and	CCONJ
ejpam-4700	412	8	polynomials	polynomial	NOUN
ejpam-4700	412	9	.	.	PUNCT
ejpam-4700	413	1	adv	adv	PROPN
ejpam-4700	413	2	.	.	PUNCT
ejpam-4700	414	1	studies	study	NOUN
ejpam-4700	414	2	theor	theor	PROPN
ejpam-4700	414	3	.	.	PUNCT
ejpam-4700	415	1	phys	phy	NOUN
ejpam-4700	415	2	,	,	PUNCT
ejpam-4700	415	3	7(9):447–454	7(9):447–454	NUM
ejpam-4700	415	4	,	,	PUNCT
ejpam-4700	415	5	2013	2013	NUM
ejpam-4700	415	6	.	.	PUNCT
ejpam-4700	416	1	[	[	X
ejpam-4700	416	2	9	9	NUM
ejpam-4700	416	3	]	]	X
ejpam-4700	416	4	c.s	c.s	PROPN
ejpam-4700	416	5	.	.	PROPN
ejpam-4700	416	6	ryoo	ryoo	NOUN
ejpam-4700	416	7	.	.	PUNCT
ejpam-4700	417	1	on	on	ADP
ejpam-4700	417	2	the	the	DET
ejpam-4700	417	3	twisted	twisted	ADJ
ejpam-4700	417	4	q	q	ADJ
ejpam-4700	417	5	-	-	PUNCT
ejpam-4700	417	6	tangent	tangent	ADJ
ejpam-4700	417	7	numbers	number	NOUN
ejpam-4700	417	8	and	and	CCONJ
ejpam-4700	417	9	polynomials	polynomial	NOUN
ejpam-4700	417	10	.	.	PUNCT
ejpam-4700	418	1	appl	appl	PROPN
ejpam-4700	418	2	.	.	PROPN
ejpam-4700	418	3	math	math	PROPN
ejpam-4700	418	4	.	.	PUNCT
ejpam-4700	419	1	sci	sci	PROPN
ejpam-4700	419	2	.	.	PROPN
ejpam-4700	419	3	,	,	PUNCT
ejpam-4700	419	4	7(99):4935–4941	7(99):4935–4941	NUM
ejpam-4700	419	5	.	.	PUNCT
ejpam-4700	420	1	[	[	X
ejpam-4700	420	2	10	10	NUM
ejpam-4700	420	3	]	]	X
ejpam-4700	420	4	c.s	c.s	PROPN
ejpam-4700	420	5	.	.	PROPN
ejpam-4700	420	6	ryoo	ryoo	PROPN
ejpam-4700	420	7	.	.	PUNCT
ejpam-4700	421	1	a	a	DET
ejpam-4700	421	2	note	note	NOUN
ejpam-4700	421	3	on	on	ADP
ejpam-4700	421	4	the	the	DET
ejpam-4700	421	5	symmetric	symmetric	ADJ
ejpam-4700	421	6	properties	property	NOUN
ejpam-4700	421	7	for	for	ADP
ejpam-4700	421	8	the	the	DET
ejpam-4700	421	9	tangent	tangent	NOUN
ejpam-4700	421	10	polynomials	polynomial	NOUN
ejpam-4700	421	11	.	.	PUNCT
ejpam-4700	422	1	int	int	NOUN
ejpam-4700	422	2	.	.	PUNCT
ejpam-4700	423	1	j.	j.	PROPN
ejpam-4700	423	2	math	math	PROPN
ejpam-4700	423	3	.	.	PUNCT
ejpam-4700	424	1	anal	anal	PROPN
ejpam-4700	424	2	.	.	PUNCT
ejpam-4700	424	3	,	,	PUNCT
ejpam-4700	424	4	7(52):2575–2581	7(52):2575–2581	PROPN
ejpam-4700	424	5	.	.	PUNCT
ejpam-4700	424	6	,	,	PUNCT
ejpam-4700	424	7	2013	2013	NUM
ejpam-4700	424	8	.	.	PUNCT
ejpam-4700	425	1	[	[	X
ejpam-4700	425	2	11	11	NUM
ejpam-4700	425	3	]	]	X
ejpam-4700	425	4	c.s	c.s	PROPN
ejpam-4700	425	5	.	.	PROPN
ejpam-4700	425	6	ryoo	ryoo	PROPN
ejpam-4700	425	7	.	.	PUNCT
ejpam-4700	426	1	a	a	DET
ejpam-4700	426	2	numerical	numerical	ADJ
ejpam-4700	426	3	investigation	investigation	NOUN
ejpam-4700	426	4	on	on	ADP
ejpam-4700	426	5	the	the	DET
ejpam-4700	426	6	zeros	zero	NOUN
ejpam-4700	426	7	of	of	ADP
ejpam-4700	426	8	the	the	DET
ejpam-4700	426	9	tangent	tangent	NOUN
ejpam-4700	426	10	polynomials	polynomial	NOUN
ejpam-4700	426	11	.	.	PUNCT
ejpam-4700	427	1	j.	j.	PROPN
ejpam-4700	427	2	appl	appl	PROPN
ejpam-4700	427	3	.	.	PROPN
ejpam-4700	427	4	math	math	PROPN
ejpam-4700	427	5	.	.	PUNCT
ejpam-4700	428	1	info	info	PROPN
ejpam-4700	428	2	.	.	PUNCT
ejpam-4700	428	3	,	,	PUNCT
ejpam-4700	428	4	32(3	32(3	NUM
ejpam-4700	428	5	-	-	SYM
ejpam-4700	428	6	4):315–322	4):315–322	NUM
ejpam-4700	428	7	.	.	PROPN
ejpam-4700	428	8	,	,	PUNCT
ejpam-4700	428	9	2014	2014	NUM
ejpam-4700	428	10	.	.	PUNCT
ejpam-4700	429	1	[	[	X
ejpam-4700	429	2	12	12	NUM
ejpam-4700	429	3	]	]	X
ejpam-4700	429	4	c.s	c.s	PROPN
ejpam-4700	429	5	.	.	PROPN
ejpam-4700	429	6	ryoo	ryoo	NOUN
ejpam-4700	429	7	.	.	PUNCT
ejpam-4700	430	1	explicit	explicit	ADJ
ejpam-4700	430	2	identities	identity	NOUN
ejpam-4700	430	3	for	for	ADP
ejpam-4700	430	4	the	the	DET
ejpam-4700	430	5	generalized	generalize	VERB
ejpam-4700	430	6	tangent	tangent	NOUN
ejpam-4700	430	7	polynomials	polynomial	NOUN
ejpam-4700	430	8	.	.	PUNCT
ejpam-4700	431	1	nonlinear	nonlinear	ADJ
ejpam-4700	431	2	analysis	analysis	NOUN
ejpam-4700	431	3	and	and	CCONJ
ejpam-4700	431	4	differential	differential	ADJ
ejpam-4700	431	5	equations	equation	NOUN
ejpam-4700	431	6	,	,	PUNCT
ejpam-4700	431	7	6(1):43–51	6(1):43–51	NUM
ejpam-4700	431	8	,	,	PUNCT
ejpam-4700	431	9	2018	2018	NUM
ejpam-4700	431	10	.	.	PUNCT
ejpam-4700	432	1	[	[	X
ejpam-4700	432	2	13	13	NUM
ejpam-4700	432	3	]	]	X
ejpam-4700	432	4	e.	e.	PROPN
ejpam-4700	432	5	sen	sen	PROPN
ejpam-4700	432	6	s.	s.	PROPN
ejpam-4700	432	7	araci	araci	PROPN
ejpam-4700	432	8	,	,	PUNCT
ejpam-4700	432	9	m.	m.	NOUN
ejpam-4700	432	10	acikgoz	acikgoz	PROPN
ejpam-4700	432	11	.	.	PUNCT
ejpam-4700	433	1	some	some	DET
ejpam-4700	433	2	new	new	ADJ
ejpam-4700	433	3	formulae	formulae	NOUN
ejpam-4700	433	4	for	for	ADP
ejpam-4700	433	5	genocchi	genocchi	PROPN
ejpam-4700	433	6	numbers	number	NOUN
ejpam-4700	433	7	and	and	CCONJ
ejpam-4700	433	8	polynomials	polynomial	NOUN
ejpam-4700	433	9	involving	involve	VERB
ejpam-4700	433	10	bernoulli	bernoulli	NOUN
ejpam-4700	433	11	and	and	CCONJ
ejpam-4700	433	12	euler	euler	NOUN
ejpam-4700	433	13	polynomials	polynomial	NOUN
ejpam-4700	433	14	.	.	PUNCT
ejpam-4700	434	1	international	international	ADJ
ejpam-4700	434	2	journal	journal	PROPN
ejpam-4700	434	3	of	of	ADP
ejpam-4700	434	4	mathematics	mathematics	PROPN
ejpam-4700	434	5	and	and	CCONJ
ejpam-4700	434	6	mathematical	mathematical	ADJ
ejpam-4700	434	7	sciences	science	NOUN
ejpam-4700	434	8	,	,	PUNCT
ejpam-4700	434	9	2014	2014	NUM
ejpam-4700	434	10	:	:	PUNCT
ejpam-4700	434	11	article	article	NOUN
ejpam-4700	434	12	i	i	PROPN
ejpam-4700	434	13	d	d	PROPN
ejpam-4700	434	14	760613	760613	NUM
ejpam-4700	434	15	.	.	PUNCT
ejpam-4700	434	16	,	,	PUNCT
ejpam-4700	434	17	2014	2014	NUM
ejpam-4700	434	18	.	.	PUNCT
ejpam-4700	435	1	[	[	X
ejpam-4700	435	2	14	14	NUM
ejpam-4700	435	3	]	]	X
ejpam-4700	435	4	y.	y.	NOUN
ejpam-4700	435	5	simsek	simsek	PROPN
ejpam-4700	435	6	.	.	PUNCT
ejpam-4700	436	1	on	on	ADP
ejpam-4700	436	2	twisted	twisted	ADJ
ejpam-4700	436	3	generalized	generalized	ADJ
ejpam-4700	436	4	euler	euler	NOUN
ejpam-4700	436	5	numbers	number	NOUN
ejpam-4700	436	6	.	.	PUNCT
ejpam-4700	437	1	bull	bull	NOUN
ejpam-4700	437	2	.	.	PUNCT
ejpam-4700	438	1	korean	korean	ADJ
ejpam-4700	438	2	math	math	PROPN
ejpam-4700	438	3	.	.	PUNCT
ejpam-4700	439	1	soc	soc	PROPN
ejpam-4700	439	2	.	.	PUNCT
ejpam-4700	439	3	,	,	PUNCT
ejpam-4700	439	4	41(2):299	41(2):299	NOUN
ejpam-4700	439	5	–	–	PUNCT
ejpam-4700	439	6	306	306	NUM
ejpam-4700	439	7	.	.	NUM
ejpam-4700	439	8	,	,	PUNCT
ejpam-4700	439	9	2004	2004	NUM
ejpam-4700	439	10	.	.	PUNCT