id	sid	tid	token	lemma	pos
ejpam-3976	1	1	european	european	PROPN
ejpam-3976	1	2	journal	journal	PROPN
ejpam-3976	1	3	of	of	ADP
ejpam-3976	1	4	pure	pure	ADJ
ejpam-3976	1	5	and	and	CCONJ
ejpam-3976	1	6	applied	apply	VERB
ejpam-3976	1	7	mathematics	mathematic	NOUN
ejpam-3976	1	8	vol	vol	NOUN
ejpam-3976	1	9	.	.	PUNCT
ejpam-3976	2	1	14	14	NUM
ejpam-3976	2	2	,	,	PUNCT
ejpam-3976	2	3	no	no	INTJ
ejpam-3976	2	4	.	.	NOUN
ejpam-3976	2	5	3	3	NUM
ejpam-3976	2	6	,	,	PUNCT
ejpam-3976	2	7	2021	2021	NUM
ejpam-3976	2	8	,	,	PUNCT
ejpam-3976	2	9	666	666	NUM
ejpam-3976	2	10	-	-	SYM
ejpam-3976	2	11	684	684	NUM
ejpam-3976	2	12	issn	issn	PROPN
ejpam-3976	2	13	1307	1307	NUM
ejpam-3976	2	14	-	-	SYM
ejpam-3976	2	15	5543	5543	NUM
ejpam-3976	2	16	–	–	PUNCT
ejpam-3976	2	17	ejpam.com	ejpam.com	X
ejpam-3976	2	18	published	publish	VERB
ejpam-3976	2	19	by	by	ADP
ejpam-3976	2	20	new	new	PROPN
ejpam-3976	2	21	york	york	PROPN
ejpam-3976	2	22	business	business	PROPN
ejpam-3976	2	23	global	global	ADJ
ejpam-3976	2	24	asymptotic	asymptotic	ADJ
ejpam-3976	2	25	approximations	approximation	NOUN
ejpam-3976	2	26	of	of	ADP
ejpam-3976	2	27	apostol	apostol	NOUN
ejpam-3976	2	28	-	-	PUNCT
ejpam-3976	2	29	genocchi	genocchi	PROPN
ejpam-3976	2	30	numbers	number	NOUN
ejpam-3976	2	31	and	and	CCONJ
ejpam-3976	2	32	polynomials	polynomial	VERB
ejpam-3976	2	33	cristina	cristina	PROPN
ejpam-3976	2	34	b.	b.	PROPN
ejpam-3976	3	1	corcino1,2	corcino1,2	PROPN
ejpam-3976	3	2	1	1	NUM
ejpam-3976	3	3	research	research	NOUN
ejpam-3976	3	4	institute	institute	NOUN
ejpam-3976	3	5	for	for	ADP
ejpam-3976	3	6	computational	computational	ADJ
ejpam-3976	3	7	mathematics	mathematic	NOUN
ejpam-3976	3	8	and	and	CCONJ
ejpam-3976	3	9	physics	physics	NOUN
ejpam-3976	3	10	,	,	PUNCT
ejpam-3976	3	11	cebu	cebu	NOUN
ejpam-3976	3	12	normal	normal	ADJ
ejpam-3976	3	13	university	university	NOUN
ejpam-3976	3	14	,	,	PUNCT
ejpam-3976	3	15	6000	6000	NUM
ejpam-3976	3	16	cebu	cebu	NOUN
ejpam-3976	3	17	city	city	NOUN
ejpam-3976	3	18	,	,	PUNCT
ejpam-3976	3	19	philippines	philippine	NOUN
ejpam-3976	3	20	2	2	NUM
ejpam-3976	3	21	mathematics	mathematics	NOUN
ejpam-3976	3	22	department	department	NOUN
ejpam-3976	3	23	,	,	PUNCT
ejpam-3976	3	24	cebu	cebu	NOUN
ejpam-3976	3	25	normal	normal	ADJ
ejpam-3976	3	26	university	university	NOUN
ejpam-3976	3	27	,	,	PUNCT
ejpam-3976	3	28	6000	6000	NUM
ejpam-3976	3	29	cebu	cebu	NOUN
ejpam-3976	3	30	city	city	NOUN
ejpam-3976	3	31	,	,	PUNCT
ejpam-3976	3	32	philippines	philippine	NOUN
ejpam-3976	3	33	abstract	abstract	ADJ
ejpam-3976	3	34	.	.	PUNCT
ejpam-3976	4	1	asymptotic	asymptotic	ADJ
ejpam-3976	4	2	approximations	approximation	NOUN
ejpam-3976	4	3	of	of	ADP
ejpam-3976	4	4	the	the	DET
ejpam-3976	4	5	apostol	apostol	NOUN
ejpam-3976	4	6	-	-	PUNCT
ejpam-3976	4	7	genocchi	genocchi	PROPN
ejpam-3976	4	8	numbers	number	NOUN
ejpam-3976	4	9	and	and	CCONJ
ejpam-3976	4	10	polynomials	polynomial	NOUN
ejpam-3976	4	11	are	be	AUX
ejpam-3976	4	12	derived	derive	VERB
ejpam-3976	4	13	using	use	VERB
ejpam-3976	4	14	fourier	fourier	NOUN
ejpam-3976	4	15	series	series	NOUN
ejpam-3976	4	16	and	and	CCONJ
ejpam-3976	4	17	ordering	ordering	NOUN
ejpam-3976	4	18	of	of	ADP
ejpam-3976	4	19	poles	pole	NOUN
ejpam-3976	4	20	of	of	ADP
ejpam-3976	4	21	the	the	DET
ejpam-3976	4	22	generating	generate	VERB
ejpam-3976	4	23	function	function	NOUN
ejpam-3976	4	24	.	.	PUNCT
ejpam-3976	5	1	asymptotic	asymptotic	ADJ
ejpam-3976	5	2	formulas	formula	NOUN
ejpam-3976	5	3	for	for	ADP
ejpam-3976	5	4	the	the	DET
ejpam-3976	5	5	apostol	apostol	NOUN
ejpam-3976	5	6	-	-	PUNCT
ejpam-3976	5	7	euler	euler	NOUN
ejpam-3976	5	8	numbers	number	NOUN
ejpam-3976	5	9	and	and	CCONJ
ejpam-3976	5	10	polynomials	polynomial	NOUN
ejpam-3976	5	11	are	be	AUX
ejpam-3976	5	12	obtained	obtain	VERB
ejpam-3976	5	13	as	as	ADP
ejpam-3976	5	14	consequence	consequence	NOUN
ejpam-3976	5	15	.	.	PUNCT
ejpam-3976	6	1	asymptotic	asymptotic	ADJ
ejpam-3976	6	2	formulas	formula	NOUN
ejpam-3976	6	3	for	for	ADP
ejpam-3976	6	4	special	special	ADJ
ejpam-3976	6	5	cases	case	NOUN
ejpam-3976	6	6	which	which	PRON
ejpam-3976	6	7	include	include	VERB
ejpam-3976	6	8	the	the	DET
ejpam-3976	6	9	genocchi	genocchi	PROPN
ejpam-3976	6	10	numbers	number	NOUN
ejpam-3976	6	11	and	and	CCONJ
ejpam-3976	6	12	polynomials	polynomial	NOUN
ejpam-3976	6	13	are	be	AUX
ejpam-3976	6	14	also	also	ADV
ejpam-3976	6	15	explicitly	explicitly	ADV
ejpam-3976	6	16	stated	state	VERB
ejpam-3976	6	17	.	.	PUNCT
ejpam-3976	7	1	2020	2020	NUM
ejpam-3976	7	2	mathematics	mathematic	NOUN
ejpam-3976	7	3	subject	subject	NOUN
ejpam-3976	7	4	classifications	classification	NOUN
ejpam-3976	7	5	:	:	PUNCT
ejpam-3976	7	6	11b68	11b68	NUM
ejpam-3976	7	7	,	,	PUNCT
ejpam-3976	7	8	41a60	41a60	NUM
ejpam-3976	7	9	key	key	ADJ
ejpam-3976	7	10	words	word	NOUN
ejpam-3976	7	11	and	and	CCONJ
ejpam-3976	7	12	phrases	phrase	NOUN
ejpam-3976	7	13	:	:	PUNCT
ejpam-3976	7	14	asymptotic	asymptotic	ADJ
ejpam-3976	7	15	approximations	approximation	NOUN
ejpam-3976	7	16	,	,	PUNCT
ejpam-3976	7	17	genocchi	genocchi	PROPN
ejpam-3976	7	18	polynomials	polynomial	NOUN
ejpam-3976	7	19	,	,	PUNCT
ejpam-3976	7	20	bernoulli	bernoulli	NOUN
ejpam-3976	7	21	polynomials	polynomial	NOUN
ejpam-3976	7	22	,	,	PUNCT
ejpam-3976	7	23	euler	euler	NOUN
ejpam-3976	7	24	polynomials	polynomial	NOUN
ejpam-3976	7	25	,	,	PUNCT
ejpam-3976	7	26	apostol	apostol	NOUN
ejpam-3976	7	27	-	-	PUNCT
ejpam-3976	7	28	bernoulli	bernoulli	NOUN
ejpam-3976	7	29	polynomials	polynomial	NOUN
ejpam-3976	7	30	,	,	PUNCT
ejpam-3976	7	31	apostol	apostol	NOUN
ejpam-3976	7	32	-	-	PUNCT
ejpam-3976	7	33	euler	euler	NOUN
ejpam-3976	7	34	polynomials	polynomial	NOUN
ejpam-3976	7	35	,	,	PUNCT
ejpam-3976	7	36	apostolgenocchi	apostolgenocchi	NOUN
ejpam-3976	7	37	polynomials	polynomial	VERB
ejpam-3976	7	38	1	1	NUM
ejpam-3976	7	39	.	.	PUNCT
ejpam-3976	8	1	introduction	introduction	NOUN
ejpam-3976	8	2	the	the	DET
ejpam-3976	8	3	apostol	apostol	NOUN
ejpam-3976	8	4	-	-	PUNCT
ejpam-3976	8	5	genocchi	genocchi	PROPN
ejpam-3976	8	6	polynomials	polynomial	NOUN
ejpam-3976	8	7	gn(x;λ	gn(x;λ	PROPN
ejpam-3976	8	8	)	)	PUNCT
ejpam-3976	8	9	are	be	AUX
ejpam-3976	8	10	defined	define	VERB
ejpam-3976	8	11	by	by	ADP
ejpam-3976	8	12	the	the	DET
ejpam-3976	8	13	generating	generate	VERB
ejpam-3976	8	14	function	function	NOUN
ejpam-3976	8	15	2text	2text	NUM
ejpam-3976	8	16	λet	λet	NOUN
ejpam-3976	9	1	+	+	CCONJ
ejpam-3976	9	2	1	1	NUM
ejpam-3976	9	3	=	=	VERB
ejpam-3976	9	4	∞∑	∞∑	NUM
ejpam-3976	9	5	n=0	n=0	NUM
ejpam-3976	9	6	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	9	7	)	)	PUNCT
ejpam-3976	9	8	tn	tn	PROPN
ejpam-3976	9	9	n	n	PROPN
ejpam-3976	9	10	!	!	PROPN
ejpam-3976	9	11	,	,	PUNCT
ejpam-3976	9	12	(	(	PUNCT
ejpam-3976	9	13	1.1	1.1	NUM
ejpam-3976	9	14	)	)	PUNCT
ejpam-3976	9	15	where	where	SCONJ
ejpam-3976	9	16	|t|	|t|	ADP
ejpam-3976	9	17	<	<	X
ejpam-3976	9	18	π	π	PROPN
ejpam-3976	9	19	when	when	SCONJ
ejpam-3976	9	20	λ	λ	X
ejpam-3976	9	21	=	=	SYM
ejpam-3976	9	22	1	1	NUM
ejpam-3976	9	23	and	and	CCONJ
ejpam-3976	9	24	|t+log	|t+log	NUM
ejpam-3976	9	25	λ|	λ|	PROPN
ejpam-3976	9	26	<	<	X
ejpam-3976	9	27	π	π	PROPN
ejpam-3976	9	28	when	when	SCONJ
ejpam-3976	9	29	λ	λ	PROPN
ejpam-3976	9	30	6=	6=	PROPN
ejpam-3976	9	31	1	1	NUM
ejpam-3976	9	32	.	.	PUNCT
ejpam-3976	10	1	when	when	SCONJ
ejpam-3976	10	2	λ	λ	X
ejpam-3976	10	3	=	=	SYM
ejpam-3976	10	4	1	1	NUM
ejpam-3976	10	5	,	,	PUNCT
ejpam-3976	10	6	the	the	DET
ejpam-3976	10	7	above	above	ADJ
ejpam-3976	10	8	equation	equation	NOUN
ejpam-3976	10	9	gives	give	VERB
ejpam-3976	10	10	the	the	DET
ejpam-3976	10	11	generating	generate	VERB
ejpam-3976	10	12	function	function	NOUN
ejpam-3976	10	13	of	of	ADP
ejpam-3976	10	14	the	the	DET
ejpam-3976	10	15	genocchi	genocchi	PROPN
ejpam-3976	10	16	polynomials	polynomial	VERB
ejpam-3976	10	17	[	[	X
ejpam-3976	10	18	3	3	NUM
ejpam-3976	10	19	]	]	PUNCT
ejpam-3976	10	20	.	.	PUNCT
ejpam-3976	11	1	when	when	SCONJ
ejpam-3976	11	2	x	x	X
ejpam-3976	11	3	=	=	SYM
ejpam-3976	11	4	0	0	NUM
ejpam-3976	11	5	,	,	PUNCT
ejpam-3976	11	6	(	(	PUNCT
ejpam-3976	11	7	1.1	1.1	NUM
ejpam-3976	11	8	)	)	PUNCT
ejpam-3976	11	9	reduces	reduce	VERB
ejpam-3976	11	10	to	to	ADP
ejpam-3976	11	11	the	the	DET
ejpam-3976	11	12	generating	generate	VERB
ejpam-3976	11	13	function	function	NOUN
ejpam-3976	11	14	of	of	ADP
ejpam-3976	11	15	the	the	DET
ejpam-3976	11	16	apostol	apostol	NOUN
ejpam-3976	11	17	-	-	PUNCT
ejpam-3976	11	18	genocchi	genocchi	PROPN
ejpam-3976	11	19	numbers	number	NOUN
ejpam-3976	11	20	gn(0;λ	gn(0;λ	PROPN
ejpam-3976	11	21	)	)	PUNCT
ejpam-3976	11	22	given	give	VERB
ejpam-3976	11	23	by	by	ADP
ejpam-3976	11	24	2	2	NUM
ejpam-3976	11	25	t	t	NOUN
ejpam-3976	11	26	λet	λet	NOUN
ejpam-3976	12	1	+	+	NOUN
ejpam-3976	12	2	1	1	NUM
ejpam-3976	12	3	=	=	SYM
ejpam-3976	12	4	∞∑	∞∑	NUM
ejpam-3976	12	5	n=0	n=0	NUM
ejpam-3976	12	6	gn(0;λ	gn(0;λ	PROPN
ejpam-3976	12	7	)	)	PUNCT
ejpam-3976	12	8	tn	tn	PROPN
ejpam-3976	12	9	n	n	PROPN
ejpam-3976	12	10	!	!	PUNCT
ejpam-3976	12	11	.	.	PUNCT
ejpam-3976	13	1	(	(	PUNCT
ejpam-3976	13	2	1.2	1.2	NUM
ejpam-3976	13	3	)	)	PUNCT
ejpam-3976	13	4	for	for	ADP
ejpam-3976	13	5	λ	λ	X
ejpam-3976	13	6	not	not	PART
ejpam-3976	13	7	zero	zero	NUM
ejpam-3976	13	8	,	,	PUNCT
ejpam-3976	13	9	the	the	DET
ejpam-3976	13	10	set	set	NOUN
ejpam-3976	13	11	of	of	ADP
ejpam-3976	13	12	poles	pole	NOUN
ejpam-3976	13	13	of	of	ADP
ejpam-3976	13	14	the	the	DET
ejpam-3976	13	15	generating	generate	VERB
ejpam-3976	13	16	function	function	NOUN
ejpam-3976	13	17	(	(	PUNCT
ejpam-3976	13	18	1.1	1.1	NUM
ejpam-3976	13	19	)	)	PUNCT
ejpam-3976	13	20	is	be	AUX
ejpam-3976	13	21	tλ	tλ	ADP
ejpam-3976	13	22	:	:	PUNCT
ejpam-3976	13	23	=	=	SYM
ejpam-3976	13	24	{	{	PUNCT
ejpam-3976	13	25	(	(	PUNCT
ejpam-3976	13	26	2k	2k	NOUN
ejpam-3976	13	27	+	+	CCONJ
ejpam-3976	13	28	1)πi−	1)πi−	NUM
ejpam-3976	13	29	log	log	NOUN
ejpam-3976	13	30	λ	λ	INTJ
ejpam-3976	13	31	:	:	PUNCT
ejpam-3976	13	32	k	k	PROPN
ejpam-3976	13	33	∈	∈	PROPN
ejpam-3976	13	34	z	z	PROPN
ejpam-3976	13	35	}	}	PUNCT
ejpam-3976	13	36	,	,	PUNCT
ejpam-3976	13	37	(	(	PUNCT
ejpam-3976	13	38	1.3	1.3	NUM
ejpam-3976	13	39	)	)	PUNCT
ejpam-3976	13	40	doi	doi	NOUN
ejpam-3976	13	41	:	:	PUNCT
ejpam-3976	13	42	https://doi.org/10.29020/nybg.ejpam.v14i3.3976	https://doi.org/10.29020/nybg.ejpam.v14i3.3976	NOUN
ejpam-3976	13	43	email	email	NOUN
ejpam-3976	13	44	address	address	NOUN
ejpam-3976	13	45	:	:	PUNCT
ejpam-3976	13	46	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-3976	13	47	(	(	PUNCT
ejpam-3976	13	48	c.	c.	PROPN
ejpam-3976	13	49	corcino	corcino	PROPN
ejpam-3976	13	50	)	)	PUNCT
ejpam-3976	13	51	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3976	14	1	666	666	NUM
ejpam-3976	15	1	©	©	ADP
ejpam-3976	15	2	2021	2021	NUM
ejpam-3976	15	3	ejpam	ejpam	VERB
ejpam-3976	15	4	all	all	DET
ejpam-3976	15	5	rights	right	NOUN
ejpam-3976	15	6	reserved	reserve	VERB
ejpam-3976	15	7	.	.	PUNCT
ejpam-3976	16	1	c.	c.	PROPN
ejpam-3976	16	2	corcino	corcino	PROPN
ejpam-3976	16	3	/	/	SYM
ejpam-3976	16	4	eur	eur	PROPN
ejpam-3976	16	5	.	.	PUNCT
ejpam-3976	17	1	j.	j.	PROPN
ejpam-3976	17	2	pure	pure	PROPN
ejpam-3976	17	3	appl	appl	PROPN
ejpam-3976	17	4	.	.	PROPN
ejpam-3976	17	5	math	math	PROPN
ejpam-3976	17	6	,	,	PUNCT
ejpam-3976	17	7	14	14	NUM
ejpam-3976	17	8	(	(	PUNCT
ejpam-3976	17	9	3	3	NUM
ejpam-3976	17	10	)	)	PUNCT
ejpam-3976	17	11	(	(	PUNCT
ejpam-3976	17	12	2021	2021	NUM
ejpam-3976	17	13	)	)	PUNCT
ejpam-3976	17	14	,	,	PUNCT
ejpam-3976	17	15	666	666	NUM
ejpam-3976	17	16	-	-	SYM
ejpam-3976	17	17	684	684	NUM
ejpam-3976	17	18	667	667	NUM
ejpam-3976	17	19	which	which	PRON
ejpam-3976	17	20	is	be	AUX
ejpam-3976	17	21	also	also	ADV
ejpam-3976	17	22	the	the	DET
ejpam-3976	17	23	set	set	NOUN
ejpam-3976	17	24	of	of	ADP
ejpam-3976	17	25	poles	pole	NOUN
ejpam-3976	17	26	of	of	ADP
ejpam-3976	17	27	(	(	PUNCT
ejpam-3976	17	28	1.2	1.2	NUM
ejpam-3976	17	29	)	)	PUNCT
ejpam-3976	17	30	,	,	PUNCT
ejpam-3976	17	31	where	where	SCONJ
ejpam-3976	17	32	the	the	DET
ejpam-3976	17	33	logarithm	logarithm	NOUN
ejpam-3976	17	34	is	be	AUX
ejpam-3976	17	35	taken	take	VERB
ejpam-3976	17	36	to	to	PART
ejpam-3976	17	37	be	be	AUX
ejpam-3976	17	38	the	the	DET
ejpam-3976	17	39	principal	principal	ADJ
ejpam-3976	17	40	branch	branch	NOUN
ejpam-3976	17	41	.	.	PUNCT
ejpam-3976	18	1	bayad	bayad	X
ejpam-3976	19	1	[	[	X
ejpam-3976	19	2	2	2	X
ejpam-3976	19	3	]	]	PUNCT
ejpam-3976	19	4	and	and	CCONJ
ejpam-3976	19	5	luo	luo	PROPN
ejpam-3976	19	6	[	[	X
ejpam-3976	19	7	13	13	NUM
ejpam-3976	19	8	]	]	PUNCT
ejpam-3976	19	9	derived	derive	VERB
ejpam-3976	19	10	fourier	fourier	NOUN
ejpam-3976	19	11	series	series	NOUN
ejpam-3976	19	12	of	of	ADP
ejpam-3976	19	13	apostol	apostol	PROPN
ejpam-3976	19	14	-	-	PUNCT
ejpam-3976	19	15	genocchi	genocchi	PROPN
ejpam-3976	19	16	polynomials	polynomial	NOUN
ejpam-3976	19	17	expressed	express	VERB
ejpam-3976	19	18	in	in	ADP
ejpam-3976	19	19	terms	term	NOUN
ejpam-3976	19	20	of	of	ADP
ejpam-3976	19	21	these	these	DET
ejpam-3976	19	22	poles	pole	NOUN
ejpam-3976	19	23	.	.	PUNCT
ejpam-3976	20	1	the	the	DET
ejpam-3976	20	2	fourier	fourier	PROPN
ejpam-3976	20	3	series	series	NOUN
ejpam-3976	20	4	they	they	PRON
ejpam-3976	20	5	obtained	obtain	VERB
ejpam-3976	20	6	is	be	AUX
ejpam-3976	20	7	given	give	VERB
ejpam-3976	20	8	in	in	ADP
ejpam-3976	20	9	the	the	DET
ejpam-3976	20	10	next	next	ADJ
ejpam-3976	20	11	section	section	NOUN
ejpam-3976	20	12	.	.	PUNCT
ejpam-3976	21	1	fourier	fouri	ADJ
ejpam-3976	21	2	expansion	expansion	NOUN
ejpam-3976	21	3	of	of	ADP
ejpam-3976	21	4	higher	high	ADJ
ejpam-3976	21	5	-	-	PUNCT
ejpam-3976	21	6	order	order	NOUN
ejpam-3976	21	7	apostol	apostol	NOUN
ejpam-3976	21	8	-	-	PUNCT
ejpam-3976	21	9	genocchi	genocchi	PROPN
ejpam-3976	21	10	polynomials	polynomial	NOUN
ejpam-3976	21	11	was	be	AUX
ejpam-3976	21	12	derived	derive	VERB
ejpam-3976	21	13	in	in	ADP
ejpam-3976	21	14	[	[	X
ejpam-3976	21	15	4	4	NUM
ejpam-3976	21	16	]	]	PUNCT
ejpam-3976	21	17	and	and	CCONJ
ejpam-3976	21	18	was	be	AUX
ejpam-3976	21	19	shown	show	VERB
ejpam-3976	21	20	to	to	PART
ejpam-3976	21	21	be	be	AUX
ejpam-3976	21	22	reducible	reducible	ADJ
ejpam-3976	21	23	to	to	ADP
ejpam-3976	21	24	those	those	PRON
ejpam-3976	21	25	obtained	obtain	VERB
ejpam-3976	21	26	in	in	ADP
ejpam-3976	21	27	[	[	X
ejpam-3976	21	28	2	2	NUM
ejpam-3976	21	29	]	]	PUNCT
ejpam-3976	21	30	and	and	CCONJ
ejpam-3976	21	31	[	[	X
ejpam-3976	21	32	13	13	NUM
ejpam-3976	21	33	]	]	PUNCT
ejpam-3976	21	34	when	when	SCONJ
ejpam-3976	21	35	the	the	DET
ejpam-3976	21	36	order	order	NOUN
ejpam-3976	21	37	is	be	AUX
ejpam-3976	21	38	1	1	NUM
ejpam-3976	21	39	.	.	PUNCT
ejpam-3976	22	1	new	new	ADJ
ejpam-3976	22	2	identities	identity	NOUN
ejpam-3976	22	3	involving	involve	VERB
ejpam-3976	22	4	the	the	DET
ejpam-3976	22	5	apostol	apostol	NOUN
ejpam-3976	22	6	-	-	PUNCT
ejpam-3976	22	7	genocchi	genocchi	PROPN
ejpam-3976	22	8	polynomials	polynomial	NOUN
ejpam-3976	22	9	were	be	AUX
ejpam-3976	22	10	established	establish	VERB
ejpam-3976	22	11	in	in	ADP
ejpam-3976	22	12	[	[	X
ejpam-3976	22	13	9	9	NUM
ejpam-3976	22	14	]	]	PUNCT
ejpam-3976	22	15	.	.	PUNCT
ejpam-3976	23	1	some	some	DET
ejpam-3976	23	2	generalizations	generalization	NOUN
ejpam-3976	23	3	and	and	CCONJ
ejpam-3976	23	4	properties	property	NOUN
ejpam-3976	23	5	of	of	ADP
ejpam-3976	23	6	these	these	DET
ejpam-3976	23	7	polynomials	polynomial	NOUN
ejpam-3976	23	8	were	be	AUX
ejpam-3976	23	9	presented	present	VERB
ejpam-3976	23	10	in	in	ADP
ejpam-3976	23	11	[	[	X
ejpam-3976	23	12	14	14	NUM
ejpam-3976	23	13	]	]	PUNCT
ejpam-3976	23	14	.	.	PUNCT
ejpam-3976	24	1	multiplication	multiplication	NOUN
ejpam-3976	24	2	and	and	CCONJ
ejpam-3976	24	3	explicit	explicit	ADJ
ejpam-3976	24	4	recursive	recursive	ADJ
ejpam-3976	24	5	formulas	formula	NOUN
ejpam-3976	24	6	of	of	ADP
ejpam-3976	24	7	higher	high	ADJ
ejpam-3976	24	8	-	-	PUNCT
ejpam-3976	24	9	order	order	NOUN
ejpam-3976	24	10	apostol	apostol	NOUN
ejpam-3976	24	11	-	-	PUNCT
ejpam-3976	24	12	genocchi	genocchi	PROPN
ejpam-3976	24	13	polynomials	polynomial	NOUN
ejpam-3976	24	14	were	be	AUX
ejpam-3976	24	15	obtained	obtain	VERB
ejpam-3976	24	16	in	in	ADP
ejpam-3976	24	17	[	[	X
ejpam-3976	24	18	12	12	NUM
ejpam-3976	24	19	]	]	PUNCT
ejpam-3976	24	20	.	.	PUNCT
ejpam-3976	25	1	a	a	DET
ejpam-3976	25	2	new	new	ADJ
ejpam-3976	25	3	generalization	generalization	NOUN
ejpam-3976	25	4	of	of	ADP
ejpam-3976	25	5	apostol	apostol	PROPN
ejpam-3976	25	6	type	type	NOUN
ejpam-3976	25	7	hermite	hermite	PROPN
ejpam-3976	25	8	-	-	PUNCT
ejpam-3976	25	9	genocchi	genocchi	PROPN
ejpam-3976	25	10	polynomials	polynomial	NOUN
ejpam-3976	25	11	is	be	AUX
ejpam-3976	25	12	studied	study	VERB
ejpam-3976	25	13	in	in	ADP
ejpam-3976	25	14	[	[	X
ejpam-3976	25	15	1	1	NUM
ejpam-3976	25	16	]	]	PUNCT
ejpam-3976	25	17	while	while	SCONJ
ejpam-3976	25	18	products	product	NOUN
ejpam-3976	25	19	of	of	ADP
ejpam-3976	25	20	the	the	DET
ejpam-3976	25	21	apostol	apostol	NOUN
ejpam-3976	25	22	-	-	PUNCT
ejpam-3976	25	23	genocchi	genocchi	PROPN
ejpam-3976	25	24	polynomials	polynomial	NOUN
ejpam-3976	25	25	were	be	AUX
ejpam-3976	25	26	studied	study	VERB
ejpam-3976	25	27	in	in	ADP
ejpam-3976	25	28	[	[	X
ejpam-3976	25	29	10	10	NUM
ejpam-3976	25	30	]	]	PUNCT
ejpam-3976	25	31	.	.	PUNCT
ejpam-3976	26	1	moreover	moreover	ADV
ejpam-3976	26	2	,	,	PUNCT
ejpam-3976	26	3	the	the	DET
ejpam-3976	26	4	higher	high	ADJ
ejpam-3976	26	5	-	-	PUNCT
ejpam-3976	26	6	order	order	NOUN
ejpam-3976	26	7	convolutions	convolution	NOUN
ejpam-3976	26	8	of	of	ADP
ejpam-3976	26	9	these	these	DET
ejpam-3976	26	10	polynomials	polynomial	NOUN
ejpam-3976	26	11	using	use	VERB
ejpam-3976	26	12	generating	generating	NOUN
ejpam-3976	26	13	-	-	PUNCT
ejpam-3976	26	14	function	function	NOUN
ejpam-3976	26	15	methods	method	NOUN
ejpam-3976	26	16	and	and	CCONJ
ejpam-3976	26	17	summation	summation	NOUN
ejpam-3976	26	18	-	-	PUNCT
ejpam-3976	26	19	transform	transform	NOUN
ejpam-3976	26	20	techniques	technique	NOUN
ejpam-3976	26	21	were	be	AUX
ejpam-3976	26	22	established	establish	VERB
ejpam-3976	26	23	in	in	ADP
ejpam-3976	26	24	[	[	X
ejpam-3976	26	25	11	11	NUM
ejpam-3976	26	26	]	]	PUNCT
ejpam-3976	26	27	.	.	PUNCT
ejpam-3976	27	1	inspired	inspire	VERB
ejpam-3976	27	2	by	by	ADP
ejpam-3976	27	3	the	the	DET
ejpam-3976	27	4	work	work	NOUN
ejpam-3976	27	5	of	of	ADP
ejpam-3976	27	6	kim	kim	PROPN
ejpam-3976	27	7	and	and	CCONJ
ejpam-3976	27	8	kim	kim	PROPN
ejpam-3976	28	1	[	[	X
ejpam-3976	28	2	7	7	NUM
ejpam-3976	28	3	]	]	PUNCT
ejpam-3976	28	4	,	,	PUNCT
ejpam-3976	28	5	a	a	DET
ejpam-3976	28	6	new	new	ADJ
ejpam-3976	28	7	class	class	NOUN
ejpam-3976	28	8	of	of	ADP
ejpam-3976	28	9	the	the	DET
ejpam-3976	28	10	frobenius	frobenius	NOUN
ejpam-3976	28	11	-	-	PUNCT
ejpam-3976	28	12	genocchi	genocchi	NOUN
ejpam-3976	28	13	polynomials	polynomial	NOUN
ejpam-3976	28	14	was	be	AUX
ejpam-3976	28	15	considered	consider	VERB
ejpam-3976	28	16	in	in	ADP
ejpam-3976	28	17	[	[	X
ejpam-3976	28	18	6	6	NUM
ejpam-3976	28	19	]	]	PUNCT
ejpam-3976	28	20	by	by	ADP
ejpam-3976	28	21	means	mean	NOUN
ejpam-3976	28	22	of	of	ADP
ejpam-3976	28	23	the	the	DET
ejpam-3976	28	24	polyexponential	polyexponential	ADJ
ejpam-3976	28	25	function	function	NOUN
ejpam-3976	28	26	and	and	CCONJ
ejpam-3976	28	27	new	new	ADJ
ejpam-3976	28	28	relations	relation	NOUN
ejpam-3976	28	29	and	and	CCONJ
ejpam-3976	28	30	properties	property	NOUN
ejpam-3976	28	31	were	be	AUX
ejpam-3976	28	32	obtained	obtain	VERB
ejpam-3976	28	33	.	.	PUNCT
ejpam-3976	29	1	new	new	ADJ
ejpam-3976	29	2	relations	relation	NOUN
ejpam-3976	29	3	on	on	ADP
ejpam-3976	29	4	q	q	ADJ
ejpam-3976	29	5	-	-	PUNCT
ejpam-3976	29	6	genocchi	genocchi	ADJ
ejpam-3976	29	7	polynomials	polynomial	NOUN
ejpam-3976	29	8	where	where	SCONJ
ejpam-3976	29	9	the	the	DET
ejpam-3976	29	10	relations	relation	NOUN
ejpam-3976	29	11	were	be	AUX
ejpam-3976	29	12	stated	state	VERB
ejpam-3976	29	13	by	by	ADP
ejpam-3976	29	14	symmetric	symmetric	ADJ
ejpam-3976	29	15	group	group	NOUN
ejpam-3976	29	16	of	of	ADP
ejpam-3976	29	17	degree	degree	NOUN
ejpam-3976	29	18	n	n	PRON
ejpam-3976	29	19	were	be	AUX
ejpam-3976	29	20	done	do	VERB
ejpam-3976	29	21	in	in	ADP
ejpam-3976	29	22	[	[	X
ejpam-3976	29	23	5	5	NUM
ejpam-3976	29	24	]	]	PUNCT
ejpam-3976	29	25	.	.	PUNCT
ejpam-3976	30	1	navas	navas	PROPN
ejpam-3976	30	2	,	,	PUNCT
ejpam-3976	30	3	ruiz	ruiz	NOUN
ejpam-3976	30	4	and	and	CCONJ
ejpam-3976	30	5	varona	varona	NOUN
ejpam-3976	31	1	[	[	X
ejpam-3976	31	2	15	15	NUM
ejpam-3976	31	3	]	]	PUNCT
ejpam-3976	31	4	obtained	obtain	VERB
ejpam-3976	31	5	asymptotic	asymptotic	ADJ
ejpam-3976	31	6	estimates	estimate	NOUN
ejpam-3976	31	7	of	of	ADP
ejpam-3976	31	8	the	the	DET
ejpam-3976	31	9	apostol	apostol	NOUN
ejpam-3976	31	10	-	-	PUNCT
ejpam-3976	31	11	bernoulli	bernoulli	NOUN
ejpam-3976	31	12	and	and	CCONJ
ejpam-3976	31	13	apostol	apostol	NOUN
ejpam-3976	31	14	-	-	PUNCT
ejpam-3976	31	15	euler	euler	NOUN
ejpam-3976	31	16	numbers	number	NOUN
ejpam-3976	31	17	and	and	CCONJ
ejpam-3976	31	18	polynomials	polynomial	NOUN
ejpam-3976	31	19	and	and	CCONJ
ejpam-3976	31	20	further	far	ADV
ejpam-3976	31	21	analyzed	analyze	VERB
ejpam-3976	31	22	the	the	DET
ejpam-3976	31	23	asymptotic	asymptotic	ADJ
ejpam-3976	31	24	behavior	behavior	NOUN
ejpam-3976	31	25	of	of	ADP
ejpam-3976	31	26	the	the	DET
ejpam-3976	31	27	apostol	apostol	NOUN
ejpam-3976	31	28	-	-	PUNCT
ejpam-3976	31	29	bernoulli	bernoulli	NOUN
ejpam-3976	31	30	polynomials	polynomial	NOUN
ejpam-3976	31	31	in	in	ADP
ejpam-3976	31	32	detail	detail	NOUN
ejpam-3976	31	33	.	.	PUNCT
ejpam-3976	32	1	the	the	DET
ejpam-3976	32	2	starting	starting	NOUN
ejpam-3976	32	3	point	point	NOUN
ejpam-3976	32	4	of	of	ADP
ejpam-3976	32	5	their	their	PRON
ejpam-3976	32	6	analysis	analysis	NOUN
ejpam-3976	32	7	is	be	AUX
ejpam-3976	32	8	the	the	DET
ejpam-3976	32	9	fourier	fourier	ADJ
ejpam-3976	32	10	series	series	NOUN
ejpam-3976	32	11	of	of	ADP
ejpam-3976	32	12	the	the	DET
ejpam-3976	32	13	polynomials	polynomial	NOUN
ejpam-3976	32	14	on	on	ADP
ejpam-3976	32	15	the	the	DET
ejpam-3976	32	16	closed	closed	ADJ
ejpam-3976	32	17	interval	interval	NOUN
ejpam-3976	32	18	[	[	X
ejpam-3976	32	19	0	0	NUM
ejpam-3976	32	20	,	,	PUNCT
ejpam-3976	32	21	1	1	NUM
ejpam-3976	32	22	]	]	PUNCT
ejpam-3976	32	23	followed	follow	VERB
ejpam-3976	32	24	by	by	ADP
ejpam-3976	32	25	ordering	order	VERB
ejpam-3976	32	26	the	the	DET
ejpam-3976	32	27	poles	pole	NOUN
ejpam-3976	32	28	of	of	ADP
ejpam-3976	32	29	the	the	DET
ejpam-3976	32	30	generating	generate	VERB
ejpam-3976	32	31	function	function	NOUN
ejpam-3976	32	32	.	.	PUNCT
ejpam-3976	33	1	in	in	ADP
ejpam-3976	33	2	this	this	DET
ejpam-3976	33	3	paper	paper	NOUN
ejpam-3976	33	4	,	,	PUNCT
ejpam-3976	33	5	asymptotic	asymptotic	ADJ
ejpam-3976	33	6	approximations	approximation	NOUN
ejpam-3976	33	7	of	of	ADP
ejpam-3976	33	8	the	the	DET
ejpam-3976	33	9	apostol	apostol	NOUN
ejpam-3976	33	10	-	-	PUNCT
ejpam-3976	33	11	genocchi	genocchi	PROPN
ejpam-3976	33	12	numbers	number	NOUN
ejpam-3976	33	13	and	and	CCONJ
ejpam-3976	33	14	polynomials	polynomial	NOUN
ejpam-3976	33	15	for	for	ADP
ejpam-3976	33	16	λ	λ	PROPN
ejpam-3976	33	17	∈	∈	PROPN
ejpam-3976	33	18	c\{0	c\{0	PROPN
ejpam-3976	33	19	}	}	PUNCT
ejpam-3976	33	20	are	be	AUX
ejpam-3976	33	21	obtained	obtain	VERB
ejpam-3976	33	22	.	.	PUNCT
ejpam-3976	34	1	the	the	DET
ejpam-3976	34	2	method	method	NOUN
ejpam-3976	34	3	used	use	VERB
ejpam-3976	34	4	in	in	ADP
ejpam-3976	34	5	[	[	X
ejpam-3976	34	6	15	15	NUM
ejpam-3976	34	7	]	]	PUNCT
ejpam-3976	34	8	is	be	AUX
ejpam-3976	34	9	applied	apply	VERB
ejpam-3976	34	10	to	to	ADP
ejpam-3976	34	11	the	the	DET
ejpam-3976	34	12	apostolgenocchi	apostolgenocchi	ADJ
ejpam-3976	34	13	numbers	number	NOUN
ejpam-3976	34	14	and	and	CCONJ
ejpam-3976	34	15	polynomials	polynomial	NOUN
ejpam-3976	34	16	to	to	PART
ejpam-3976	34	17	obtain	obtain	VERB
ejpam-3976	34	18	asymptotic	asymptotic	ADJ
ejpam-3976	34	19	formulas	formula	NOUN
ejpam-3976	34	20	of	of	ADP
ejpam-3976	34	21	these	these	DET
ejpam-3976	34	22	numbers	number	NOUN
ejpam-3976	34	23	and	and	CCONJ
ejpam-3976	34	24	polynomials	polynomial	NOUN
ejpam-3976	34	25	.	.	PUNCT
ejpam-3976	35	1	a	a	DET
ejpam-3976	35	2	more	more	ADV
ejpam-3976	35	3	detailed	detailed	ADJ
ejpam-3976	35	4	proof	proof	NOUN
ejpam-3976	35	5	of	of	ADP
ejpam-3976	35	6	the	the	DET
ejpam-3976	35	7	results	result	NOUN
ejpam-3976	35	8	is	be	AUX
ejpam-3976	35	9	provided	provide	VERB
ejpam-3976	35	10	so	so	SCONJ
ejpam-3976	35	11	as	as	SCONJ
ejpam-3976	35	12	to	to	PART
ejpam-3976	35	13	reach	reach	VERB
ejpam-3976	35	14	a	a	DET
ejpam-3976	35	15	bigger	big	ADJ
ejpam-3976	35	16	group	group	NOUN
ejpam-3976	35	17	of	of	ADP
ejpam-3976	35	18	readers	reader	NOUN
ejpam-3976	35	19	.	.	PUNCT
ejpam-3976	36	1	asymptotic	asymptotic	ADJ
ejpam-3976	36	2	formulas	formula	NOUN
ejpam-3976	36	3	of	of	ADP
ejpam-3976	36	4	genocchi	genocchi	PROPN
ejpam-3976	36	5	numbers	number	NOUN
ejpam-3976	36	6	and	and	CCONJ
ejpam-3976	36	7	euler	euler	NOUN
ejpam-3976	36	8	numbers	number	NOUN
ejpam-3976	36	9	are	be	AUX
ejpam-3976	36	10	obtained	obtain	VERB
ejpam-3976	36	11	as	as	ADP
ejpam-3976	36	12	special	special	ADJ
ejpam-3976	36	13	cases	case	NOUN
ejpam-3976	36	14	.	.	PUNCT
ejpam-3976	37	1	asymptotic	asymptotic	ADJ
ejpam-3976	37	2	formulas	formula	NOUN
ejpam-3976	37	3	of	of	ADP
ejpam-3976	37	4	the	the	DET
ejpam-3976	37	5	apostol	apostol	NOUN
ejpam-3976	37	6	-	-	PUNCT
ejpam-3976	37	7	euler	euler	NOUN
ejpam-3976	37	8	numbers	number	NOUN
ejpam-3976	37	9	and	and	CCONJ
ejpam-3976	37	10	apostol	apostol	NOUN
ejpam-3976	37	11	-	-	PUNCT
ejpam-3976	37	12	euler	euler	NOUN
ejpam-3976	37	13	polynomials	polynomial	NOUN
ejpam-3976	37	14	are	be	AUX
ejpam-3976	37	15	also	also	ADV
ejpam-3976	37	16	derived	derive	VERB
ejpam-3976	37	17	.	.	PUNCT
ejpam-3976	38	1	the	the	DET
ejpam-3976	38	2	results	result	NOUN
ejpam-3976	38	3	in	in	ADP
ejpam-3976	38	4	this	this	DET
ejpam-3976	38	5	paper	paper	NOUN
ejpam-3976	38	6	will	will	AUX
ejpam-3976	38	7	complete	complete	VERB
ejpam-3976	38	8	the	the	DET
ejpam-3976	38	9	results	result	NOUN
ejpam-3976	38	10	of	of	ADP
ejpam-3976	38	11	[	[	X
ejpam-3976	38	12	15	15	NUM
ejpam-3976	38	13	]	]	PUNCT
ejpam-3976	38	14	as	as	ADP
ejpam-3976	38	15	the	the	DET
ejpam-3976	38	16	latter	latter	ADJ
ejpam-3976	38	17	considered	consider	VERB
ejpam-3976	38	18	only	only	ADV
ejpam-3976	38	19	the	the	DET
ejpam-3976	38	20	apostol	apostol	NOUN
ejpam-3976	38	21	-	-	PUNCT
ejpam-3976	38	22	bernoulli	bernoulli	NOUN
ejpam-3976	38	23	and	and	CCONJ
ejpam-3976	38	24	apostol	apostol	NOUN
ejpam-3976	38	25	-	-	PUNCT
ejpam-3976	38	26	euler	euler	NOUN
ejpam-3976	38	27	polynomials	polynomial	NOUN
ejpam-3976	38	28	.	.	PUNCT
ejpam-3976	39	1	moreover	moreover	ADV
ejpam-3976	39	2	,	,	PUNCT
ejpam-3976	39	3	the	the	DET
ejpam-3976	39	4	results	result	NOUN
ejpam-3976	39	5	can	can	AUX
ejpam-3976	39	6	be	be	AUX
ejpam-3976	39	7	used	use	VERB
ejpam-3976	39	8	as	as	ADP
ejpam-3976	39	9	check	check	NOUN
ejpam-3976	39	10	formulas	formula	NOUN
ejpam-3976	39	11	of	of	ADP
ejpam-3976	39	12	those	those	PRON
ejpam-3976	39	13	in	in	ADP
ejpam-3976	39	14	[	[	X
ejpam-3976	39	15	15	15	NUM
ejpam-3976	39	16	]	]	SYM
ejpam-3976	39	17	.	.	PUNCT
ejpam-3976	40	1	2	2	X
ejpam-3976	40	2	.	.	X
ejpam-3976	40	3	asymptotic	asymptotic	ADJ
ejpam-3976	40	4	approximations	approximation	NOUN
ejpam-3976	40	5	fourier	fourier	NOUN
ejpam-3976	40	6	series	series	NOUN
ejpam-3976	40	7	of	of	ADP
ejpam-3976	40	8	the	the	DET
ejpam-3976	40	9	apostol	apostol	NOUN
ejpam-3976	40	10	-	-	PUNCT
ejpam-3976	40	11	genocchi	genocchi	PROPN
ejpam-3976	40	12	polynomials	polynomial	NOUN
ejpam-3976	40	13	in	in	ADP
ejpam-3976	40	14	terms	term	NOUN
ejpam-3976	40	15	of	of	ADP
ejpam-3976	40	16	the	the	DET
ejpam-3976	40	17	poles	pole	NOUN
ejpam-3976	40	18	in	in	ADP
ejpam-3976	40	19	tλ	tλ	ADV
ejpam-3976	40	20	is	be	AUX
ejpam-3976	40	21	given	give	VERB
ejpam-3976	40	22	in	in	ADP
ejpam-3976	40	23	the	the	DET
ejpam-3976	40	24	following	follow	VERB
ejpam-3976	40	25	theorem	theorem	NOUN
ejpam-3976	40	26	.	.	PUNCT
ejpam-3976	40	27	theorem	theorem	VERB
ejpam-3976	40	28	2.1	2.1	NUM
ejpam-3976	40	29	.	.	PUNCT
ejpam-3976	41	1	(	(	PUNCT
ejpam-3976	41	2	[	[	X
ejpam-3976	41	3	2	2	NUM
ejpam-3976	41	4	]	]	PUNCT
ejpam-3976	41	5	,	,	PUNCT
ejpam-3976	41	6	[	[	X
ejpam-3976	41	7	13	13	NUM
ejpam-3976	41	8	]	]	PUNCT
ejpam-3976	41	9	)	)	PUNCT
ejpam-3976	41	10	let	let	VERB
ejpam-3976	41	11	λ	λ	X
ejpam-3976	41	12	∈	∈	VERB
ejpam-3976	41	13	c\{0	c\{0	PROPN
ejpam-3976	41	14	}	}	PUNCT
ejpam-3976	41	15	.	.	PUNCT
ejpam-3976	42	1	for	for	ADP
ejpam-3976	42	2	n	n	PRON
ejpam-3976	42	3	≥	≥	NUM
ejpam-3976	42	4	1	1	NUM
ejpam-3976	42	5	,	,	PUNCT
ejpam-3976	42	6	0	0	NUM
ejpam-3976	42	7	≤	≤	NUM
ejpam-3976	42	8	x	x	SYM
ejpam-3976	42	9	≤	≤	NUM
ejpam-3976	42	10	1	1	NUM
ejpam-3976	42	11	,	,	PUNCT
ejpam-3976	42	12	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	42	13	)	)	PUNCT
ejpam-3976	42	14	n	n	CCONJ
ejpam-3976	42	15	!	!	PUNCT
ejpam-3976	42	16	=	=	SYM
ejpam-3976	42	17	2	2	NUM
ejpam-3976	42	18	λx	λx	NOUN
ejpam-3976	42	19	∑	∑	ADV
ejpam-3976	42	20	k∈z	k∈z	PROPN
ejpam-3976	42	21	e(2k+1)πix	e(2k+1)πix	PROPN
ejpam-3976	43	1	[	[	X
ejpam-3976	43	2	(	(	PUNCT
ejpam-3976	43	3	2k	2k	NUM
ejpam-3976	43	4	+	+	CCONJ
ejpam-3976	43	5	1)πi−	1)πi−	NUM
ejpam-3976	43	6	log	log	NOUN
ejpam-3976	43	7	λ]n	λ]n	NOUN
ejpam-3976	43	8	,	,	PUNCT
ejpam-3976	43	9	(	(	PUNCT
ejpam-3976	43	10	2.1	2.1	NUM
ejpam-3976	43	11	)	)	PUNCT
ejpam-3976	43	12	where	where	SCONJ
ejpam-3976	43	13	the	the	DET
ejpam-3976	43	14	logarithm	logarithm	NOUN
ejpam-3976	43	15	is	be	AUX
ejpam-3976	43	16	taken	take	VERB
ejpam-3976	43	17	to	to	PART
ejpam-3976	43	18	be	be	AUX
ejpam-3976	43	19	the	the	DET
ejpam-3976	43	20	principal	principal	ADJ
ejpam-3976	43	21	branch	branch	NOUN
ejpam-3976	43	22	.	.	PUNCT
ejpam-3976	44	1	c.	c.	PROPN
ejpam-3976	44	2	corcino	corcino	PROPN
ejpam-3976	44	3	/	/	SYM
ejpam-3976	44	4	eur	eur	PROPN
ejpam-3976	44	5	.	.	PUNCT
ejpam-3976	45	1	j.	j.	PROPN
ejpam-3976	45	2	pure	pure	PROPN
ejpam-3976	45	3	appl	appl	PROPN
ejpam-3976	45	4	.	.	PROPN
ejpam-3976	45	5	math	math	PROPN
ejpam-3976	45	6	,	,	PUNCT
ejpam-3976	45	7	14	14	NUM
ejpam-3976	45	8	(	(	PUNCT
ejpam-3976	45	9	3	3	NUM
ejpam-3976	45	10	)	)	PUNCT
ejpam-3976	45	11	(	(	PUNCT
ejpam-3976	45	12	2021	2021	NUM
ejpam-3976	45	13	)	)	PUNCT
ejpam-3976	45	14	,	,	PUNCT
ejpam-3976	45	15	666	666	NUM
ejpam-3976	45	16	-	-	SYM
ejpam-3976	45	17	684	684	NUM
ejpam-3976	45	18	668	668	NUM
ejpam-3976	45	19	taking	take	VERB
ejpam-3976	45	20	x	x	PUNCT
ejpam-3976	45	21	=	=	SYM
ejpam-3976	45	22	0	0	NUM
ejpam-3976	45	23	in	in	ADP
ejpam-3976	45	24	(	(	PUNCT
ejpam-3976	45	25	2.1	2.1	NUM
ejpam-3976	45	26	)	)	PUNCT
ejpam-3976	45	27	gives	give	VERB
ejpam-3976	45	28	the	the	DET
ejpam-3976	45	29	fourier	fourier	ADJ
ejpam-3976	45	30	series	series	NOUN
ejpam-3976	45	31	of	of	ADP
ejpam-3976	45	32	the	the	DET
ejpam-3976	45	33	apostol	apostol	NOUN
ejpam-3976	45	34	-	-	PUNCT
ejpam-3976	45	35	genocchi	genocchi	PROPN
ejpam-3976	45	36	numbers	number	NOUN
ejpam-3976	45	37	given	give	VERB
ejpam-3976	45	38	by	by	ADP
ejpam-3976	45	39	gn(0;λ	gn(0;λ	PROPN
ejpam-3976	45	40	)	)	PUNCT
ejpam-3976	45	41	n	n	CCONJ
ejpam-3976	45	42	!	!	PUNCT
ejpam-3976	46	1	=	=	SYM
ejpam-3976	46	2	2	2	NUM
ejpam-3976	46	3	∑	∑	ADV
ejpam-3976	46	4	k∈z	k∈z	NOUN
ejpam-3976	46	5	1	1	NUM
ejpam-3976	47	1	[	[	X
ejpam-3976	47	2	(	(	PUNCT
ejpam-3976	47	3	2k	2k	NOUN
ejpam-3976	47	4	+	+	CCONJ
ejpam-3976	47	5	1)πi−	1)πi−	NUM
ejpam-3976	47	6	log	log	NOUN
ejpam-3976	47	7	λ]n	λ]n	INTJ
ejpam-3976	47	8	,	,	PUNCT
ejpam-3976	47	9	(	(	PUNCT
ejpam-3976	47	10	2.2	2.2	NUM
ejpam-3976	47	11	)	)	PUNCT
ejpam-3976	47	12	where	where	SCONJ
ejpam-3976	47	13	the	the	DET
ejpam-3976	47	14	logarithm	logarithm	NOUN
ejpam-3976	47	15	is	be	AUX
ejpam-3976	47	16	taken	take	VERB
ejpam-3976	47	17	to	to	PART
ejpam-3976	47	18	be	be	AUX
ejpam-3976	47	19	the	the	DET
ejpam-3976	47	20	principal	principal	ADJ
ejpam-3976	47	21	branch	branch	NOUN
ejpam-3976	47	22	.	.	PUNCT
ejpam-3976	48	1	proceeding	proceed	VERB
ejpam-3976	48	2	as	as	ADP
ejpam-3976	48	3	in	in	ADP
ejpam-3976	48	4	[	[	X
ejpam-3976	48	5	15	15	NUM
ejpam-3976	48	6	]	]	PUNCT
ejpam-3976	48	7	,	,	PUNCT
ejpam-3976	48	8	ordering	order	VERB
ejpam-3976	48	9	of	of	ADP
ejpam-3976	48	10	the	the	DET
ejpam-3976	48	11	poles	pole	NOUN
ejpam-3976	48	12	of	of	ADP
ejpam-3976	48	13	the	the	DET
ejpam-3976	48	14	generating	generate	VERB
ejpam-3976	48	15	function	function	NOUN
ejpam-3976	48	16	(	(	PUNCT
ejpam-3976	48	17	1.1	1.1	NUM
ejpam-3976	48	18	)	)	PUNCT
ejpam-3976	48	19	is	be	AUX
ejpam-3976	48	20	done	do	VERB
ejpam-3976	48	21	in	in	ADP
ejpam-3976	48	22	the	the	DET
ejpam-3976	48	23	following	follow	VERB
ejpam-3976	48	24	lemma	lemma	PROPN
ejpam-3976	48	25	.	.	PUNCT
ejpam-3976	49	1	lemma	lemma	PROPN
ejpam-3976	49	2	2.2	2.2	NUM
ejpam-3976	49	3	.	.	PUNCT
ejpam-3976	50	1	let	let	VERB
ejpam-3976	50	2	uk	uk	PROPN
ejpam-3976	50	3	=	=	SYM
ejpam-3976	50	4	(	(	PUNCT
ejpam-3976	50	5	2k	2k	NUM
ejpam-3976	51	1	+	+	CCONJ
ejpam-3976	52	1	1)πi	1)πi	NUM
ejpam-3976	52	2	−	−	NOUN
ejpam-3976	52	3	log	log	NOUN
ejpam-3976	52	4	λ	λ	PROPN
ejpam-3976	52	5	with	with	ADP
ejpam-3976	52	6	k	k	PROPN
ejpam-3976	52	7	∈	∈	PROPN
ejpam-3976	52	8	z	z	PROPN
ejpam-3976	52	9	,	,	PUNCT
ejpam-3976	52	10	λ	λ	PROPN
ejpam-3976	52	11	∈	∈	PROPN
ejpam-3976	52	12	c\{0	c\{0	PROPN
ejpam-3976	52	13	}	}	PUNCT
ejpam-3976	52	14	and	and	CCONJ
ejpam-3976	52	15	γ	γ	X
ejpam-3976	52	16	=	=	X
ejpam-3976	52	17	(	(	PUNCT
ejpam-3976	52	18	log	log	NOUN
ejpam-3976	52	19	λ)/2πi	λ)/2πi	ADP
ejpam-3976	52	20	,	,	PUNCT
ejpam-3976	52	21	where	where	SCONJ
ejpam-3976	52	22	the	the	DET
ejpam-3976	52	23	logarithm	logarithm	NOUN
ejpam-3976	52	24	is	be	AUX
ejpam-3976	52	25	taken	take	VERB
ejpam-3976	52	26	to	to	PART
ejpam-3976	52	27	be	be	AUX
ejpam-3976	52	28	the	the	DET
ejpam-3976	52	29	principal	principal	ADJ
ejpam-3976	52	30	branch	branch	NOUN
ejpam-3976	52	31	.	.	PUNCT
ejpam-3976	53	1	a	a	DET
ejpam-3976	53	2	)	)	PUNCT
ejpam-3976	53	3	if	if	SCONJ
ejpam-3976	53	4	i	i	PRON
ejpam-3976	53	5	m	m	VERB
ejpam-3976	53	6	λ	λ	X
ejpam-3976	53	7	>	>	X
ejpam-3976	53	8	0	0	PUNCT
ejpam-3976	54	1	then	then	ADV
ejpam-3976	54	2	0	0	NUM
ejpam-3976	54	3	<	<	X
ejpam-3976	54	4	re	re	X
ejpam-3976	54	5	γ	γ	X
ejpam-3976	54	6	<	<	X
ejpam-3976	54	7	1	1	NUM
ejpam-3976	54	8	2	2	NUM
ejpam-3976	54	9	and	and	CCONJ
ejpam-3976	54	10	for	for	ADP
ejpam-3976	54	11	k	k	PROPN
ejpam-3976	54	12	≥	≥	PROPN
ejpam-3976	54	13	1	1	NUM
ejpam-3976	54	14	,	,	PUNCT
ejpam-3976	54	15	|u0|	|u0|	VERB
ejpam-3976	54	16	<	<	X
ejpam-3976	54	17	|u−1|	|u−1|	NOUN
ejpam-3976	54	18	<	<	X
ejpam-3976	54	19	|u1|	|u1|	X
ejpam-3976	54	20	<	<	X
ejpam-3976	54	21	|u−2|	|u−2|	X
ejpam-3976	54	22	<	<	X
ejpam-3976	54	23	|u2|	|u2|	ADJ
ejpam-3976	54	24	<	<	X
ejpam-3976	54	25	·	·	PUNCT
ejpam-3976	54	26	·	·	PUNCT
ejpam-3976	54	27	·	·	PUNCT
ejpam-3976	54	28	<	<	X
ejpam-3976	54	29	|u−k|	|u−k|	X
ejpam-3976	54	30	<	<	X
ejpam-3976	54	31	|uk|	|uk|	VERB
ejpam-3976	54	32	<	<	X
ejpam-3976	54	33	·	·	PUNCT
ejpam-3976	54	34	·	·	PUNCT
ejpam-3976	54	35	·	·	PUNCT
ejpam-3976	54	36	(	(	PUNCT
ejpam-3976	54	37	2.3	2.3	NUM
ejpam-3976	54	38	)	)	PUNCT
ejpam-3976	54	39	b	b	NOUN
ejpam-3976	54	40	)	)	PUNCT
ejpam-3976	54	41	if	if	SCONJ
ejpam-3976	54	42	i	i	PRON
ejpam-3976	54	43	m	m	VERB
ejpam-3976	54	44	λ	λ	X
ejpam-3976	54	45	<	<	X
ejpam-3976	54	46	0	0	X
ejpam-3976	54	47	then	then	ADV
ejpam-3976	54	48	−1	−1	NOUN
ejpam-3976	54	49	2	2	NUM
ejpam-3976	54	50	<	<	X
ejpam-3976	54	51	re	re	X
ejpam-3976	54	52	γ	γ	X
ejpam-3976	54	53	<	<	X
ejpam-3976	54	54	0	0	NUM
ejpam-3976	54	55	and	and	CCONJ
ejpam-3976	54	56	for	for	ADP
ejpam-3976	54	57	k	k	PROPN
ejpam-3976	54	58	≥	≥	PROPN
ejpam-3976	54	59	1	1	NUM
ejpam-3976	54	60	,	,	PUNCT
ejpam-3976	54	61	|u−1|	|u−1|	VERB
ejpam-3976	54	62	<	<	X
ejpam-3976	54	63	|u0|	|u0|	X
ejpam-3976	54	64	<	<	X
ejpam-3976	54	65	|u−2|	|u−2|	ADP
ejpam-3976	54	66	<	<	X
ejpam-3976	54	67	|u1|	|u1|	X
ejpam-3976	54	68	<	<	X
ejpam-3976	54	69	|u−3|	|u−3|	X
ejpam-3976	54	70	<	<	X
ejpam-3976	54	71	·	·	PUNCT
ejpam-3976	54	72	·	·	PUNCT
ejpam-3976	54	73	·	·	PUNCT
ejpam-3976	54	74	<	<	X
ejpam-3976	54	75	|u−k|	|u−k|	X
ejpam-3976	54	76	<	<	X
ejpam-3976	54	77	|uk−1|	|uk−1|	X
ejpam-3976	54	78	<	<	X
ejpam-3976	54	79	|u−(k+1)|	|u−(k+1)|	X
ejpam-3976	54	80	<	<	X
ejpam-3976	54	81	|uk|	|uk|	VERB
ejpam-3976	54	82	<	<	X
ejpam-3976	54	83	·	·	PUNCT
ejpam-3976	54	84	·	·	PUNCT
ejpam-3976	54	85	·	·	PUNCT
ejpam-3976	54	86	.	.	PUNCT
ejpam-3976	55	1	(	(	PUNCT
ejpam-3976	55	2	2.4	2.4	NUM
ejpam-3976	55	3	)	)	PUNCT
ejpam-3976	55	4	c	c	NOUN
ejpam-3976	55	5	)	)	PUNCT
ejpam-3976	55	6	if	if	SCONJ
ejpam-3976	55	7	λ	λ	X
ejpam-3976	55	8	>	>	X
ejpam-3976	55	9	0	0	PUNCT
ejpam-3976	56	1	(	(	PUNCT
ejpam-3976	56	2	positive	positive	ADJ
ejpam-3976	56	3	real	real	ADJ
ejpam-3976	56	4	number	number	NOUN
ejpam-3976	56	5	)	)	PUNCT
ejpam-3976	56	6	,	,	PUNCT
ejpam-3976	56	7	then	then	ADV
ejpam-3976	56	8	re	re	VERB
ejpam-3976	56	9	γ	γ	X
ejpam-3976	56	10	=	=	SYM
ejpam-3976	56	11	0	0	NUM
ejpam-3976	56	12	,	,	PUNCT
ejpam-3976	56	13	and	and	CCONJ
ejpam-3976	56	14	for	for	ADP
ejpam-3976	56	15	k	k	PROPN
ejpam-3976	56	16	≥	≥	NUM
ejpam-3976	56	17	1	1	NUM
ejpam-3976	56	18	,	,	PUNCT
ejpam-3976	56	19	|u0|	|u0|	X
ejpam-3976	56	20	=	=	SYM
ejpam-3976	56	21	|u−1|	|u−1|	NOUN
ejpam-3976	56	22	<	<	X
ejpam-3976	56	23	|u1|	|u1|	X
ejpam-3976	56	24	=	=	PUNCT
ejpam-3976	56	25	|u−2|	|u−2|	ADP
ejpam-3976	56	26	<	<	X
ejpam-3976	56	27	|u2|	|u2|	VERB
ejpam-3976	56	28	<	<	X
ejpam-3976	56	29	·	·	PUNCT
ejpam-3976	56	30	·	·	PUNCT
ejpam-3976	56	31	·	·	PUNCT
ejpam-3976	57	1	<	<	X
ejpam-3976	57	2	|u−k|	|u−k|	X
ejpam-3976	57	3	<	<	X
ejpam-3976	57	4	|uk|	|uk|	PROPN
ejpam-3976	57	5	=	=	PUNCT
ejpam-3976	57	6	|u−(k+1)|	|u−(k+1)|	X
ejpam-3976	57	7	<	<	X
ejpam-3976	57	8	|uk+1|	|uk+1|	X
ejpam-3976	57	9	<	<	X
ejpam-3976	57	10	·	·	PUNCT
ejpam-3976	57	11	·	·	PUNCT
ejpam-3976	57	12	·	·	PUNCT
ejpam-3976	57	13	.	.	PUNCT
ejpam-3976	58	1	(	(	PUNCT
ejpam-3976	58	2	2.5	2.5	NUM
ejpam-3976	58	3	)	)	PUNCT
ejpam-3976	58	4	d	d	NOUN
ejpam-3976	58	5	)	)	PUNCT
ejpam-3976	58	6	if	if	SCONJ
ejpam-3976	58	7	λ	λ	X
ejpam-3976	58	8	<	<	X
ejpam-3976	58	9	0	0	X
ejpam-3976	58	10	(	(	PUNCT
ejpam-3976	58	11	negative	negative	ADJ
ejpam-3976	58	12	real	real	ADJ
ejpam-3976	58	13	number	number	NOUN
ejpam-3976	58	14	)	)	PUNCT
ejpam-3976	58	15	,	,	PUNCT
ejpam-3976	58	16	then	then	ADV
ejpam-3976	58	17	re	re	VERB
ejpam-3976	58	18	γ	γ	X
ejpam-3976	58	19	=	=	SYM
ejpam-3976	58	20	1	1	NUM
ejpam-3976	58	21	2	2	NUM
ejpam-3976	58	22	,	,	PUNCT
ejpam-3976	58	23	and	and	CCONJ
ejpam-3976	58	24	for	for	ADP
ejpam-3976	58	25	k	k	PROPN
ejpam-3976	58	26	≥	≥	PROPN
ejpam-3976	58	27	1	1	NUM
ejpam-3976	58	28	,	,	PUNCT
ejpam-3976	58	29	|u0|	|u0|	VERB
ejpam-3976	58	30	<	<	X
ejpam-3976	58	31	|u1|	|u1|	PROPN
ejpam-3976	58	32	=	=	PUNCT
ejpam-3976	58	33	|u−1|	|u−1|	NOUN
ejpam-3976	58	34	<	<	X
ejpam-3976	58	35	|u2|	|u2|	X
ejpam-3976	58	36	=	=	SYM
ejpam-3976	58	37	|u−2|	|u−2|	ADP
ejpam-3976	58	38	<	<	X
ejpam-3976	58	39	·	·	PUNCT
ejpam-3976	58	40	·	·	PUNCT
ejpam-3976	58	41	·	·	PUNCT
ejpam-3976	58	42	<	<	X
ejpam-3976	58	43	|uk|	|uk|	PROPN
ejpam-3976	58	44	=	=	SYM
ejpam-3976	59	1	|u−k|	|u−k|	X
ejpam-3976	59	2	<	<	X
ejpam-3976	59	3	|uk+1|	|uk+1|	X
ejpam-3976	59	4	<	<	X
ejpam-3976	59	5	·	·	PUNCT
ejpam-3976	59	6	·	·	PUNCT
ejpam-3976	59	7	·	·	PUNCT
ejpam-3976	59	8	.	.	PUNCT
ejpam-3976	60	1	(	(	PUNCT
ejpam-3976	60	2	2.6	2.6	NUM
ejpam-3976	60	3	)	)	PUNCT
ejpam-3976	60	4	moreover	moreover	ADV
ejpam-3976	60	5	,	,	PUNCT
ejpam-3976	60	6	|uk|	|uk|	VERB
ejpam-3976	60	7	≥	≥	NOUN
ejpam-3976	60	8	2π(|k|	2π(|k|	NUM
ejpam-3976	60	9	−	−	NOUN
ejpam-3976	60	10	1	1	NUM
ejpam-3976	60	11	)	)	PUNCT
ejpam-3976	60	12	if	if	SCONJ
ejpam-3976	60	13	|k|	|k|	PRON
ejpam-3976	60	14	≥	≥	AUX
ejpam-3976	60	15	1	1	NUM
ejpam-3976	60	16	.	.	PUNCT
ejpam-3976	61	1	proof	proof	NOUN
ejpam-3976	61	2	.	.	PUNCT
ejpam-3976	62	1	with	with	SCONJ
ejpam-3976	62	2	the	the	DET
ejpam-3976	62	3	logarithm	logarithm	NOUN
ejpam-3976	62	4	taken	take	VERB
ejpam-3976	62	5	to	to	PART
ejpam-3976	62	6	be	be	AUX
ejpam-3976	62	7	the	the	DET
ejpam-3976	62	8	principal	principal	ADJ
ejpam-3976	62	9	branch	branch	NOUN
ejpam-3976	62	10	,	,	PUNCT
ejpam-3976	62	11	γ	γ	X
ejpam-3976	62	12	(	(	PUNCT
ejpam-3976	62	13	as	as	ADP
ejpam-3976	62	14	a	a	DET
ejpam-3976	62	15	function	function	NOUN
ejpam-3976	62	16	of	of	ADP
ejpam-3976	62	17	λ	λ	NOUN
ejpam-3976	62	18	)	)	PUNCT
ejpam-3976	62	19	maps	map	VERB
ejpam-3976	62	20	λ	λ	PROPN
ejpam-3976	62	21	∈	∈	PROPN
ejpam-3976	62	22	c\{0	c\{0	PROPN
ejpam-3976	62	23	}	}	PUNCT
ejpam-3976	62	24	to	to	ADP
ejpam-3976	62	25	the	the	DET
ejpam-3976	62	26	strip	strip	NOUN
ejpam-3976	62	27	−1	−1	NOUN
ejpam-3976	62	28	2	2	NUM
ejpam-3976	62	29	<	<	X
ejpam-3976	62	30	re	re	X
ejpam-3976	62	31	γ	γ	X
ejpam-3976	62	32	≤	≤	NUM
ejpam-3976	62	33	1	1	NUM
ejpam-3976	62	34	2	2	NUM
ejpam-3976	62	35	(	(	PUNCT
ejpam-3976	62	36	see	see	VERB
ejpam-3976	62	37	[	[	X
ejpam-3976	62	38	15	15	NUM
ejpam-3976	62	39	]	]	NUM
ejpam-3976	62	40	)	)	PUNCT
ejpam-3976	62	41	.	.	PUNCT
ejpam-3976	63	1	to	to	PART
ejpam-3976	63	2	see	see	VERB
ejpam-3976	63	3	this	this	DET
ejpam-3976	63	4	write	write	NOUN
ejpam-3976	63	5	γ	γ	NOUN
ejpam-3976	63	6	=	=	SYM
ejpam-3976	63	7	θ	θ	PROPN
ejpam-3976	63	8	2π	2π	NUM
ejpam-3976	63	9	−	−	PROPN
ejpam-3976	64	1	i	i	PRON
ejpam-3976	64	2	ln	ln	NOUN
ejpam-3976	64	3	|λ|	|λ|	VERB
ejpam-3976	64	4	2π	2π	NOUN
ejpam-3976	64	5	,	,	PUNCT
ejpam-3976	64	6	from	from	ADP
ejpam-3976	64	7	which	which	PRON
ejpam-3976	64	8	we	we	PRON
ejpam-3976	64	9	have	have	AUX
ejpam-3976	64	10	re	re	NOUN
ejpam-3976	64	11	γ	γ	X
ejpam-3976	64	12	=	=	SYM
ejpam-3976	64	13	θ	θ	PROPN
ejpam-3976	64	14	2π	2π	NOUN
ejpam-3976	64	15	and	and	CCONJ
ejpam-3976	64	16	i	i	PRON
ejpam-3976	64	17	m	m	VERB
ejpam-3976	64	18	γ	γ	NOUN
ejpam-3976	64	19	=	=	SYM
ejpam-3976	64	20	−	−	PROPN
ejpam-3976	64	21	ln	ln	ADJ
ejpam-3976	64	22	|λ|	|λ|	PROPN
ejpam-3976	64	23	2π	2π	PROPN
ejpam-3976	64	24	.	.	PUNCT
ejpam-3976	65	1	with	with	ADP
ejpam-3976	65	2	−π	−π	PROPN
ejpam-3976	65	3	<	<	X
ejpam-3976	65	4	θ	θ	PROPN
ejpam-3976	65	5	≤	≤	PROPN
ejpam-3976	65	6	π	π	PROPN
ejpam-3976	65	7	,	,	PUNCT
ejpam-3976	65	8	−π	−π	DET
ejpam-3976	65	9	2π	2π	PROPN
ejpam-3976	65	10	≤	≤	X
ejpam-3976	65	11	re	re	VERB
ejpam-3976	65	12	γ	γ	X
ejpam-3976	65	13	=	=	SYM
ejpam-3976	65	14	θ	θ	PROPN
ejpam-3976	65	15	2π	2π	NOUN
ejpam-3976	65	16	≤	≤	NUM
ejpam-3976	65	17	π	π	X
ejpam-3976	65	18	2π	2π	PROPN
ejpam-3976	65	19	⇒	⇒	VERB
ejpam-3976	65	20	−1	−1	ADV
ejpam-3976	65	21	2	2	NUM
ejpam-3976	65	22	<	<	X
ejpam-3976	65	23	re	re	X
ejpam-3976	65	24	γ	γ	X
ejpam-3976	65	25	≤	≤	NUM
ejpam-3976	65	26	1	1	NUM
ejpam-3976	65	27	2	2	NUM
ejpam-3976	65	28	,	,	PUNCT
ejpam-3976	65	29	c.	c.	PROPN
ejpam-3976	65	30	corcino	corcino	PROPN
ejpam-3976	65	31	/	/	SYM
ejpam-3976	65	32	eur	eur	PROPN
ejpam-3976	65	33	.	.	PUNCT
ejpam-3976	66	1	j.	j.	PROPN
ejpam-3976	66	2	pure	pure	PROPN
ejpam-3976	66	3	appl	appl	PROPN
ejpam-3976	66	4	.	.	PROPN
ejpam-3976	66	5	math	math	PROPN
ejpam-3976	66	6	,	,	PUNCT
ejpam-3976	66	7	14	14	NUM
ejpam-3976	66	8	(	(	PUNCT
ejpam-3976	66	9	3	3	NUM
ejpam-3976	66	10	)	)	PUNCT
ejpam-3976	66	11	(	(	PUNCT
ejpam-3976	66	12	2021	2021	NUM
ejpam-3976	66	13	)	)	PUNCT
ejpam-3976	66	14	,	,	PUNCT
ejpam-3976	66	15	666	666	NUM
ejpam-3976	66	16	-	-	SYM
ejpam-3976	66	17	684	684	NUM
ejpam-3976	66	18	669	669	NUM
ejpam-3976	66	19	where	where	SCONJ
ejpam-3976	66	20	re	re	ADP
ejpam-3976	66	21	γ	γ	X
ejpam-3976	66	22	=	=	SYM
ejpam-3976	66	23	0	0	PROPN
ejpam-3976	66	24	when	when	SCONJ
ejpam-3976	66	25	λ	λ	X
ejpam-3976	66	26	>	>	X
ejpam-3976	66	27	0	0	PUNCT
ejpam-3976	66	28	and	and	CCONJ
ejpam-3976	66	29	re	re	ADJ
ejpam-3976	66	30	γ	γ	X
ejpam-3976	66	31	=	=	SYM
ejpam-3976	66	32	1	1	NUM
ejpam-3976	66	33	2	2	NUM
ejpam-3976	66	34	when	when	SCONJ
ejpam-3976	66	35	λ	λ	X
ejpam-3976	66	36	<	<	X
ejpam-3976	66	37	0	0	NUM
ejpam-3976	66	38	.	.	PUNCT
ejpam-3976	67	1	if	if	SCONJ
ejpam-3976	67	2	i	i	PRON
ejpam-3976	67	3	m	m	VERB
ejpam-3976	67	4	λ	λ	X
ejpam-3976	67	5	>	>	X
ejpam-3976	67	6	0	0	PROPN
ejpam-3976	67	7	,	,	PUNCT
ejpam-3976	67	8	then	then	ADV
ejpam-3976	67	9	0	0	NUM
ejpam-3976	67	10	<	<	X
ejpam-3976	67	11	θ	θ	X
ejpam-3976	67	12	<	<	X
ejpam-3976	67	13	π	π	PROPN
ejpam-3976	67	14	,	,	PUNCT
ejpam-3976	67	15	hence	hence	ADV
ejpam-3976	67	16	0	0	NUM
ejpam-3976	67	17	<	<	X
ejpam-3976	67	18	re	re	X
ejpam-3976	67	19	γ	γ	X
ejpam-3976	67	20	<	<	X
ejpam-3976	67	21	1	1	NUM
ejpam-3976	67	22	2	2	NUM
ejpam-3976	67	23	.	.	PUNCT
ejpam-3976	68	1	if	if	SCONJ
ejpam-3976	68	2	i	i	PRON
ejpam-3976	68	3	m	m	VERB
ejpam-3976	68	4	λ	λ	X
ejpam-3976	68	5	<	<	X
ejpam-3976	68	6	0	0	NUM
ejpam-3976	68	7	,	,	PUNCT
ejpam-3976	68	8	then	then	ADV
ejpam-3976	68	9	−π	−π	ADV
ejpam-3976	68	10	<	<	X
ejpam-3976	68	11	θ	θ	X
ejpam-3976	68	12	<	<	X
ejpam-3976	68	13	0	0	NUM
ejpam-3976	68	14	,	,	PUNCT
ejpam-3976	68	15	hence	hence	ADV
ejpam-3976	68	16	−1	−1	NOUN
ejpam-3976	68	17	2	2	NUM
ejpam-3976	68	18	<	<	X
ejpam-3976	68	19	re	re	X
ejpam-3976	68	20	γ	γ	X
ejpam-3976	68	21	<	<	X
ejpam-3976	68	22	0	0	NUM
ejpam-3976	68	23	.	.	PUNCT
ejpam-3976	68	24	to	to	PART
ejpam-3976	68	25	verify	verify	VERB
ejpam-3976	68	26	the	the	DET
ejpam-3976	68	27	chains	chain	NOUN
ejpam-3976	68	28	in	in	ADP
ejpam-3976	68	29	(	(	PUNCT
ejpam-3976	68	30	2.3	2.3	NUM
ejpam-3976	68	31	)	)	PUNCT
ejpam-3976	68	32	,	,	PUNCT
ejpam-3976	68	33	(	(	PUNCT
ejpam-3976	68	34	2.4	2.4	NUM
ejpam-3976	68	35	)	)	PUNCT
ejpam-3976	68	36	,	,	PUNCT
ejpam-3976	68	37	(	(	PUNCT
ejpam-3976	68	38	2.5	2.5	NUM
ejpam-3976	68	39	)	)	PUNCT
ejpam-3976	68	40	,	,	PUNCT
ejpam-3976	68	41	(	(	PUNCT
ejpam-3976	68	42	2.6	2.6	NUM
ejpam-3976	68	43	)	)	PUNCT
ejpam-3976	68	44	,	,	PUNCT
ejpam-3976	68	45	let	let	VERB
ejpam-3976	68	46	x	x	SYM
ejpam-3976	68	47	=	=	SYM
ejpam-3976	68	48	re	re	ADP
ejpam-3976	68	49	γ	γ	PROPN
ejpam-3976	68	50	and	and	CCONJ
ejpam-3976	68	51	y	y	PROPN
ejpam-3976	68	52	=	=	PUNCT
ejpam-3976	69	1	i	i	PRON
ejpam-3976	69	2	m	m	VERB
ejpam-3976	69	3	γ	γ	X
ejpam-3976	69	4	.	.	PROPN
ejpam-3976	70	1	then	then	ADV
ejpam-3976	70	2	for	for	ADP
ejpam-3976	70	3	k	k	PROPN
ejpam-3976	70	4	∈	∈	PROPN
ejpam-3976	70	5	z	z	PROPN
ejpam-3976	70	6	,	,	PUNCT
ejpam-3976	70	7	uk	uk	PROPN
ejpam-3976	70	8	=	=	SYM
ejpam-3976	70	9	2π	2π	PROPN
ejpam-3976	70	10	√	√	VERB
ejpam-3976	70	11	(	(	PUNCT
ejpam-3976	70	12	k	k	PROPN
ejpam-3976	70	13	+	+	PROPN
ejpam-3976	70	14	1	1	NUM
ejpam-3976	70	15	2	2	NUM
ejpam-3976	70	16	−	−	NOUN
ejpam-3976	70	17	x	x	SYM
ejpam-3976	70	18	)	)	PUNCT
ejpam-3976	70	19	2	2	NUM
ejpam-3976	70	20	+	+	NUM
ejpam-3976	70	21	y2	y2	NOUN
ejpam-3976	70	22	.	.	PUNCT
ejpam-3976	71	1	a	a	X
ejpam-3976	71	2	)	)	PUNCT
ejpam-3976	71	3	if	if	SCONJ
ejpam-3976	71	4	i	i	PRON
ejpam-3976	71	5	m	m	VERB
ejpam-3976	71	6	λ	λ	X
ejpam-3976	71	7	>	>	X
ejpam-3976	71	8	0	0	PROPN
ejpam-3976	71	9	,	,	PUNCT
ejpam-3976	71	10	then	then	ADV
ejpam-3976	71	11	0	0	NUM
ejpam-3976	71	12	<	<	X
ejpam-3976	71	13	x	x	X
ejpam-3976	71	14	<	<	X
ejpam-3976	71	15	1	1	NUM
ejpam-3976	71	16	2	2	NUM
ejpam-3976	71	17	and	and	CCONJ
ejpam-3976	71	18	|u0|	|u0|	NOUN
ejpam-3976	71	19	=	=	SYM
ejpam-3976	71	20	2π	2π	NUM
ejpam-3976	71	21	√	√	VERB
ejpam-3976	71	22	(	(	PUNCT
ejpam-3976	71	23	1	1	NUM
ejpam-3976	71	24	2	2	NUM
ejpam-3976	71	25	−	−	NOUN
ejpam-3976	71	26	x	x	SYM
ejpam-3976	71	27	)	)	PUNCT
ejpam-3976	71	28	2	2	NUM
ejpam-3976	72	1	+	+	CCONJ
ejpam-3976	72	2	y2	y2	ADJ
ejpam-3976	72	3	|u1|	|u1|	ADJ
ejpam-3976	72	4	=	=	PUNCT
ejpam-3976	72	5	2π	2π	NUM
ejpam-3976	72	6	√	√	VERB
ejpam-3976	72	7	(	(	PUNCT
ejpam-3976	72	8	3	3	NUM
ejpam-3976	72	9	2	2	NUM
ejpam-3976	72	10	−	−	NOUN
ejpam-3976	72	11	x	x	SYM
ejpam-3976	72	12	)	)	PUNCT
ejpam-3976	72	13	2	2	NUM
ejpam-3976	72	14	+	+	CCONJ
ejpam-3976	72	15	y2	y2	NOUN
ejpam-3976	72	16	|u2|	|u2|	VERB
ejpam-3976	72	17	=	=	SYM
ejpam-3976	72	18	2π	2π	NUM
ejpam-3976	72	19	√	√	VERB
ejpam-3976	72	20	(	(	PUNCT
ejpam-3976	72	21	5	5	NUM
ejpam-3976	72	22	2	2	NUM
ejpam-3976	72	23	−	−	NOUN
ejpam-3976	72	24	x	x	SYM
ejpam-3976	72	25	)	)	PUNCT
ejpam-3976	72	26	2	2	NUM
ejpam-3976	72	27	+	+	NUM
ejpam-3976	72	28	y2	y2	NOUN
ejpam-3976	72	29	|u−1|	|u−1|	NOUN
ejpam-3976	72	30	=	=	SYM
ejpam-3976	72	31	2π	2π	NUM
ejpam-3976	72	32	√	√	VERB
ejpam-3976	72	33	(	(	PUNCT
ejpam-3976	72	34	−1	−1	NOUN
ejpam-3976	72	35	2	2	NUM
ejpam-3976	72	36	−	−	NOUN
ejpam-3976	72	37	x	x	SYM
ejpam-3976	72	38	)	)	PUNCT
ejpam-3976	72	39	2	2	NUM
ejpam-3976	72	40	+	+	CCONJ
ejpam-3976	72	41	y2	y2	NOUN
ejpam-3976	72	42	=	=	SYM
ejpam-3976	72	43	2π	2π	PROPN
ejpam-3976	72	44	√	√	VERB
ejpam-3976	72	45	(	(	PUNCT
ejpam-3976	72	46	1	1	NUM
ejpam-3976	72	47	2	2	NUM
ejpam-3976	72	48	+	+	NOUN
ejpam-3976	72	49	x	x	X
ejpam-3976	72	50	)	)	PUNCT
ejpam-3976	72	51	2	2	NUM
ejpam-3976	72	52	+	+	NUM
ejpam-3976	72	53	y2	y2	NOUN
ejpam-3976	72	54	|u−2|	|u−2|	NOUN
ejpam-3976	72	55	=	=	SYM
ejpam-3976	72	56	2π	2π	NUM
ejpam-3976	72	57	√	√	VERB
ejpam-3976	72	58	(	(	PUNCT
ejpam-3976	72	59	−3	−3	PROPN
ejpam-3976	72	60	2	2	NUM
ejpam-3976	72	61	−	−	NOUN
ejpam-3976	72	62	x	x	SYM
ejpam-3976	72	63	)	)	PUNCT
ejpam-3976	72	64	2	2	NUM
ejpam-3976	72	65	+	+	CCONJ
ejpam-3976	72	66	y2	y2	NOUN
ejpam-3976	72	67	=	=	SYM
ejpam-3976	72	68	2π	2π	PROPN
ejpam-3976	72	69	√	√	VERB
ejpam-3976	72	70	(	(	PUNCT
ejpam-3976	72	71	3	3	NUM
ejpam-3976	72	72	2	2	NUM
ejpam-3976	72	73	+	+	NOUN
ejpam-3976	72	74	x	x	X
ejpam-3976	72	75	)	)	PUNCT
ejpam-3976	72	76	2	2	NUM
ejpam-3976	72	77	+	+	NUM
ejpam-3976	72	78	y2	y2	NOUN
ejpam-3976	72	79	|u−3|	|u−3|	NOUN
ejpam-3976	72	80	=	=	SYM
ejpam-3976	72	81	2π	2π	NUM
ejpam-3976	72	82	√	√	VERB
ejpam-3976	72	83	(	(	PUNCT
ejpam-3976	72	84	−5	−5	ADV
ejpam-3976	72	85	2	2	NUM
ejpam-3976	72	86	−	−	NOUN
ejpam-3976	72	87	x	x	SYM
ejpam-3976	72	88	)	)	PUNCT
ejpam-3976	72	89	2	2	NUM
ejpam-3976	72	90	+	+	CCONJ
ejpam-3976	72	91	y2	y2	NOUN
ejpam-3976	72	92	=	=	SYM
ejpam-3976	72	93	2π	2π	PROPN
ejpam-3976	72	94	√	√	VERB
ejpam-3976	72	95	(	(	PUNCT
ejpam-3976	72	96	5	5	NUM
ejpam-3976	72	97	2	2	NUM
ejpam-3976	72	98	+	+	NOUN
ejpam-3976	72	99	x	x	X
ejpam-3976	72	100	)	)	PUNCT
ejpam-3976	72	101	2	2	NUM
ejpam-3976	72	102	+	+	NUM
ejpam-3976	72	103	y2	y2	NOUN
ejpam-3976	72	104	|u3|	|u3|	ADV
ejpam-3976	72	105	=	=	PUNCT
ejpam-3976	72	106	2π	2π	NUM
ejpam-3976	72	107	√	√	VERB
ejpam-3976	72	108	(	(	PUNCT
ejpam-3976	72	109	7	7	NUM
ejpam-3976	72	110	2	2	NUM
ejpam-3976	72	111	−	−	NOUN
ejpam-3976	72	112	x	x	SYM
ejpam-3976	72	113	)	)	PUNCT
ejpam-3976	72	114	2	2	NUM
ejpam-3976	72	115	+	+	CCONJ
ejpam-3976	72	116	y2	y2	PROPN
ejpam-3976	72	117	·	·	PUNCT
ejpam-3976	72	118	·	·	PUNCT
ejpam-3976	72	119	·	·	PUNCT
ejpam-3976	72	120	from	from	ADP
ejpam-3976	72	121	which	which	PRON
ejpam-3976	72	122	one	one	PRON
ejpam-3976	72	123	can	can	AUX
ejpam-3976	72	124	see	see	VERB
ejpam-3976	72	125	that	that	SCONJ
ejpam-3976	72	126	the	the	DET
ejpam-3976	72	127	order	order	NOUN
ejpam-3976	72	128	of	of	ADP
ejpam-3976	72	129	magnitude	magnitude	NOUN
ejpam-3976	72	130	of	of	ADP
ejpam-3976	72	131	uk	uk	PROPN
ejpam-3976	72	132	,	,	PUNCT
ejpam-3976	72	133	k	k	PROPN
ejpam-3976	72	134	∈	∈	PROPN
ejpam-3976	72	135	z	z	NOUN
ejpam-3976	72	136	given	give	VERB
ejpam-3976	72	137	in	in	ADP
ejpam-3976	72	138	(	(	PUNCT
ejpam-3976	72	139	2.3	2.3	NUM
ejpam-3976	72	140	)	)	PUNCT
ejpam-3976	72	141	holds	hold	VERB
ejpam-3976	72	142	.	.	PUNCT
ejpam-3976	73	1	b	b	X
ejpam-3976	73	2	)	)	PUNCT
ejpam-3976	73	3	the	the	DET
ejpam-3976	73	4	second	second	ADJ
ejpam-3976	73	5	case	case	NOUN
ejpam-3976	73	6	can	can	AUX
ejpam-3976	73	7	be	be	AUX
ejpam-3976	73	8	derived	derive	VERB
ejpam-3976	73	9	similarly	similarly	ADV
ejpam-3976	73	10	.	.	PUNCT
ejpam-3976	74	1	the	the	DET
ejpam-3976	74	2	last	last	ADJ
ejpam-3976	74	3	two	two	NUM
ejpam-3976	74	4	cases	case	NOUN
ejpam-3976	74	5	are	be	AUX
ejpam-3976	74	6	belonging	belong	VERB
ejpam-3976	74	7	to	to	ADP
ejpam-3976	74	8	the	the	DET
ejpam-3976	74	9	case	case	NOUN
ejpam-3976	74	10	i	i	PRON
ejpam-3976	74	11	m	m	VERB
ejpam-3976	74	12	λ	λ	NOUN
ejpam-3976	74	13	=	=	NOUN
ejpam-3976	74	14	0	0	NUM
ejpam-3976	74	15	.	.	PUNCT
ejpam-3976	75	1	this	this	PRON
ejpam-3976	75	2	means	mean	VERB
ejpam-3976	75	3	that	that	SCONJ
ejpam-3976	75	4	λ	λ	NOUN
ejpam-3976	75	5	is	be	AUX
ejpam-3976	75	6	a	a	DET
ejpam-3976	75	7	real	real	ADJ
ejpam-3976	75	8	number	number	NOUN
ejpam-3976	75	9	which	which	PRON
ejpam-3976	75	10	is	be	AUX
ejpam-3976	75	11	either	either	CCONJ
ejpam-3976	75	12	positive	positive	ADJ
ejpam-3976	75	13	or	or	CCONJ
ejpam-3976	75	14	negative	negative	ADJ
ejpam-3976	75	15	but	but	CCONJ
ejpam-3976	75	16	not	not	PART
ejpam-3976	75	17	zero	zero	NUM
ejpam-3976	75	18	.	.	PUNCT
ejpam-3976	76	1	hence	hence	ADV
ejpam-3976	76	2	the	the	DET
ejpam-3976	76	3	cases	case	NOUN
ejpam-3976	76	4	c	c	NOUN
ejpam-3976	76	5	and	and	CCONJ
ejpam-3976	76	6	d.	d.	PROPN
ejpam-3976	76	7	c	c	PROPN
ejpam-3976	76	8	)	)	PUNCT
ejpam-3976	76	9	if	if	SCONJ
ejpam-3976	76	10	λ	λ	X
ejpam-3976	76	11	>	>	X
ejpam-3976	76	12	0	0	NUM
ejpam-3976	76	13	,	,	PUNCT
ejpam-3976	76	14	then	then	ADV
ejpam-3976	76	15	re	re	VERB
ejpam-3976	76	16	γ	γ	X
ejpam-3976	76	17	=	=	SYM
ejpam-3976	76	18	0	0	NUM
ejpam-3976	76	19	.	.	PUNCT
ejpam-3976	77	1	for	for	ADP
ejpam-3976	77	2	k	k	PROPN
ejpam-3976	77	3	≥	≥	PROPN
ejpam-3976	77	4	0	0	NUM
ejpam-3976	77	5	,	,	PUNCT
ejpam-3976	77	6	|uk|	|uk|	VERB
ejpam-3976	77	7	=	=	PUNCT
ejpam-3976	77	8	2π	2π	NUM
ejpam-3976	77	9	√	√	VERB
ejpam-3976	77	10	(	(	PUNCT
ejpam-3976	77	11	k	k	PROPN
ejpam-3976	77	12	+	+	PROPN
ejpam-3976	77	13	1	1	NUM
ejpam-3976	77	14	2	2	NUM
ejpam-3976	77	15	)	)	PUNCT
ejpam-3976	77	16	2	2	NUM
ejpam-3976	77	17	+	+	NUM
ejpam-3976	77	18	y2	y2	NOUN
ejpam-3976	77	19	.	.	PUNCT
ejpam-3976	78	1	c.	c.	PROPN
ejpam-3976	78	2	corcino	corcino	PROPN
ejpam-3976	78	3	/	/	SYM
ejpam-3976	78	4	eur	eur	PROPN
ejpam-3976	78	5	.	.	PUNCT
ejpam-3976	79	1	j.	j.	PROPN
ejpam-3976	79	2	pure	pure	PROPN
ejpam-3976	79	3	appl	appl	PROPN
ejpam-3976	79	4	.	.	PROPN
ejpam-3976	79	5	math	math	PROPN
ejpam-3976	79	6	,	,	PUNCT
ejpam-3976	79	7	14	14	NUM
ejpam-3976	79	8	(	(	PUNCT
ejpam-3976	79	9	3	3	NUM
ejpam-3976	79	10	)	)	PUNCT
ejpam-3976	79	11	(	(	PUNCT
ejpam-3976	79	12	2021	2021	NUM
ejpam-3976	79	13	)	)	PUNCT
ejpam-3976	79	14	,	,	PUNCT
ejpam-3976	79	15	666	666	NUM
ejpam-3976	79	16	-	-	SYM
ejpam-3976	79	17	684	684	NUM
ejpam-3976	79	18	670	670	NUM
ejpam-3976	79	19	in	in	ADP
ejpam-3976	79	20	particular	particular	ADJ
ejpam-3976	79	21	,	,	PUNCT
ejpam-3976	79	22	|u0|	|u0|	NOUN
ejpam-3976	79	23	=	=	SYM
ejpam-3976	79	24	2π	2π	NUM
ejpam-3976	79	25	√	√	VERB
ejpam-3976	79	26	(	(	PUNCT
ejpam-3976	79	27	1	1	NUM
ejpam-3976	79	28	2	2	NUM
ejpam-3976	79	29	)	)	PUNCT
ejpam-3976	79	30	2	2	NUM
ejpam-3976	79	31	+	+	CCONJ
ejpam-3976	79	32	y2	y2	ADJ
ejpam-3976	79	33	|u1|	|u1|	ADJ
ejpam-3976	79	34	=	=	PUNCT
ejpam-3976	79	35	2π	2π	NUM
ejpam-3976	79	36	√	√	VERB
ejpam-3976	79	37	(	(	PUNCT
ejpam-3976	79	38	1	1	NUM
ejpam-3976	79	39	+	+	NUM
ejpam-3976	79	40	1	1	NUM
ejpam-3976	79	41	2	2	NUM
ejpam-3976	79	42	)	)	PUNCT
ejpam-3976	79	43	2	2	NUM
ejpam-3976	79	44	+	+	CCONJ
ejpam-3976	79	45	y2	y2	NOUN
ejpam-3976	79	46	|u−1|	|u−1|	NOUN
ejpam-3976	79	47	=	=	SYM
ejpam-3976	79	48	2π	2π	NUM
ejpam-3976	79	49	√	√	VERB
ejpam-3976	79	50	(	(	PUNCT
ejpam-3976	79	51	−1	−1	NOUN
ejpam-3976	79	52	+	+	CCONJ
ejpam-3976	79	53	1	1	NUM
ejpam-3976	79	54	2	2	NUM
ejpam-3976	79	55	)	)	PUNCT
ejpam-3976	79	56	2	2	NUM
ejpam-3976	79	57	+	+	CCONJ
ejpam-3976	79	58	y2	y2	NOUN
ejpam-3976	79	59	|u2|	|u2|	VERB
ejpam-3976	79	60	=	=	SYM
ejpam-3976	79	61	2π	2π	NUM
ejpam-3976	79	62	√	√	VERB
ejpam-3976	79	63	(	(	PUNCT
ejpam-3976	79	64	2	2	NUM
ejpam-3976	79	65	+	+	CCONJ
ejpam-3976	79	66	1	1	NUM
ejpam-3976	79	67	2	2	NUM
ejpam-3976	79	68	)	)	PUNCT
ejpam-3976	79	69	2	2	NUM
ejpam-3976	80	1	+	+	NUM
ejpam-3976	80	2	y2	y2	NOUN
ejpam-3976	80	3	|u−2|	|u−2|	NOUN
ejpam-3976	80	4	=	=	SYM
ejpam-3976	80	5	2π	2π	NUM
ejpam-3976	80	6	√	√	VERB
ejpam-3976	80	7	(	(	PUNCT
ejpam-3976	80	8	−2	−2	NOUN
ejpam-3976	80	9	+	+	CCONJ
ejpam-3976	80	10	1	1	NUM
ejpam-3976	80	11	2	2	NUM
ejpam-3976	80	12	)	)	PUNCT
ejpam-3976	80	13	2	2	NUM
ejpam-3976	80	14	+	+	CCONJ
ejpam-3976	80	15	y2	y2	NOUN
ejpam-3976	80	16	|u3|	|u3|	ADV
ejpam-3976	80	17	=	=	PUNCT
ejpam-3976	80	18	2π	2π	NUM
ejpam-3976	80	19	√	√	VERB
ejpam-3976	80	20	(	(	PUNCT
ejpam-3976	80	21	3	3	NUM
ejpam-3976	80	22	+	+	CCONJ
ejpam-3976	80	23	1	1	NUM
ejpam-3976	80	24	2	2	NUM
ejpam-3976	80	25	)	)	PUNCT
ejpam-3976	80	26	2	2	NUM
ejpam-3976	80	27	+	+	CCONJ
ejpam-3976	80	28	y2	y2	VERB
ejpam-3976	80	29	from	from	ADP
ejpam-3976	80	30	which	which	PRON
ejpam-3976	80	31	we	we	PRON
ejpam-3976	80	32	have	have	VERB
ejpam-3976	80	33	the	the	DET
ejpam-3976	80	34	chain	chain	NOUN
ejpam-3976	80	35	|u0|	|u0|	NOUN
ejpam-3976	80	36	=	=	SYM
ejpam-3976	80	37	|u−1|	|u−1|	NOUN
ejpam-3976	80	38	<	<	X
ejpam-3976	80	39	|u1|	|u1|	X
ejpam-3976	80	40	=	=	PUNCT
ejpam-3976	80	41	|u−2|	|u−2|	ADP
ejpam-3976	80	42	<	<	X
ejpam-3976	80	43	|u2|	|u2|	VERB
ejpam-3976	80	44	<	<	X
ejpam-3976	80	45	·	·	PUNCT
ejpam-3976	80	46	·	·	PUNCT
ejpam-3976	80	47	·	·	PUNCT
ejpam-3976	81	1	<	<	X
ejpam-3976	81	2	|uk|	|uk|	PROPN
ejpam-3976	81	3	=	=	PUNCT
ejpam-3976	81	4	|u−(k+1)|	|u−(k+1)|	X
ejpam-3976	81	5	<	<	X
ejpam-3976	81	6	|uk+1|	|uk+1|	X
ejpam-3976	81	7	<	<	X
ejpam-3976	81	8	·	·	PUNCT
ejpam-3976	81	9	·	·	PUNCT
ejpam-3976	81	10	·	·	PUNCT
ejpam-3976	81	11	,	,	PUNCT
ejpam-3976	81	12	which	which	PRON
ejpam-3976	81	13	is	be	AUX
ejpam-3976	81	14	exactly	exactly	ADV
ejpam-3976	81	15	(	(	PUNCT
ejpam-3976	81	16	2.5	2.5	NUM
ejpam-3976	81	17	)	)	PUNCT
ejpam-3976	81	18	.	.	PUNCT
ejpam-3976	82	1	d	d	X
ejpam-3976	82	2	)	)	PUNCT
ejpam-3976	82	3	if	if	SCONJ
ejpam-3976	82	4	λ	λ	X
ejpam-3976	82	5	<	<	X
ejpam-3976	82	6	0	0	NUM
ejpam-3976	82	7	,	,	PUNCT
ejpam-3976	82	8	θ	θ	X
ejpam-3976	82	9	=	=	SYM
ejpam-3976	82	10	π	π	PROPN
ejpam-3976	82	11	,	,	PUNCT
ejpam-3976	82	12	hence	hence	ADV
ejpam-3976	82	13	x	x	PUNCT
ejpam-3976	82	14	=	=	SYM
ejpam-3976	82	15	1	1	NUM
ejpam-3976	82	16	2	2	NUM
ejpam-3976	82	17	.	.	PUNCT
ejpam-3976	83	1	for	for	ADP
ejpam-3976	83	2	k	k	PROPN
ejpam-3976	83	3	≥	≥	PROPN
ejpam-3976	83	4	0	0	NUM
ejpam-3976	83	5	,	,	PUNCT
ejpam-3976	83	6	|uk|	|uk|	VERB
ejpam-3976	83	7	=	=	PUNCT
ejpam-3976	83	8	2π	2π	NOUN
ejpam-3976	83	9	√	√	ADP
ejpam-3976	83	10	k2	k2	NOUN
ejpam-3976	83	11	+	+	CCONJ
ejpam-3976	83	12	y2	y2	NOUN
ejpam-3976	83	13	=	=	SYM
ejpam-3976	84	1	|u−k|	|u−k|	NOUN
ejpam-3976	84	2	,	,	PUNCT
ejpam-3976	84	3	from	from	ADP
ejpam-3976	84	4	which	which	PRON
ejpam-3976	84	5	it	it	PRON
ejpam-3976	84	6	can	can	AUX
ejpam-3976	84	7	be	be	AUX
ejpam-3976	84	8	observed	observe	VERB
ejpam-3976	84	9	easily	easily	ADV
ejpam-3976	84	10	that	that	PRON
ejpam-3976	84	11	|u0|	|u0|	VERB
ejpam-3976	84	12	<	<	X
ejpam-3976	84	13	|u1|	|u1|	PROPN
ejpam-3976	84	14	=	=	PUNCT
ejpam-3976	84	15	|u−1|	|u−1|	NOUN
ejpam-3976	84	16	<	<	X
ejpam-3976	84	17	|u2|	|u2|	X
ejpam-3976	84	18	=	=	SYM
ejpam-3976	84	19	|u−2|	|u−2|	ADP
ejpam-3976	84	20	<	<	X
ejpam-3976	84	21	|u3|	|u3|	NOUN
ejpam-3976	84	22	=	=	SYM
ejpam-3976	84	23	|u−3|	|u−3|	X
ejpam-3976	84	24	<	<	X
ejpam-3976	84	25	·	·	PUNCT
ejpam-3976	84	26	·	·	PUNCT
ejpam-3976	84	27	·	·	PUNCT
ejpam-3976	85	1	<	<	X
ejpam-3976	85	2	|uk|	|uk|	PROPN
ejpam-3976	85	3	=	=	SYM
ejpam-3976	85	4	|u−k|	|u−k|	X
ejpam-3976	85	5	<	<	X
ejpam-3976	85	6	·	·	PUNCT
ejpam-3976	85	7	·	·	PUNCT
ejpam-3976	85	8	·	·	PUNCT
ejpam-3976	85	9	,	,	PUNCT
ejpam-3976	85	10	which	which	PRON
ejpam-3976	85	11	is	be	AUX
ejpam-3976	85	12	exactly	exactly	ADV
ejpam-3976	85	13	the	the	DET
ejpam-3976	85	14	chain	chain	NOUN
ejpam-3976	85	15	in	in	ADP
ejpam-3976	85	16	(	(	PUNCT
ejpam-3976	85	17	2.6	2.6	NUM
ejpam-3976	85	18	)	)	PUNCT
ejpam-3976	85	19	.	.	PUNCT
ejpam-3976	86	1	moreover	moreover	ADV
ejpam-3976	86	2	,	,	PUNCT
ejpam-3976	86	3	|uk|	|uk|	VERB
ejpam-3976	86	4	=	=	PUNCT
ejpam-3976	86	5	2π	2π	NOUN
ejpam-3976	86	6	∣∣∣∣k	∣∣∣∣k	VERB
ejpam-3976	87	1	+	+	CCONJ
ejpam-3976	87	2	1	1	NUM
ejpam-3976	87	3	2	2	NUM
ejpam-3976	87	4	−	−	NOUN
ejpam-3976	87	5	γ	γ	X
ejpam-3976	87	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	87	7	=	=	PUNCT
ejpam-3976	87	8	2π	2π	PROPN
ejpam-3976	87	9	√	√	VERB
ejpam-3976	87	10	(	(	PUNCT
ejpam-3976	87	11	k	k	PROPN
ejpam-3976	87	12	+	+	PROPN
ejpam-3976	87	13	1	1	NUM
ejpam-3976	87	14	2	2	NUM
ejpam-3976	87	15	−	−	NOUN
ejpam-3976	87	16	x	x	SYM
ejpam-3976	87	17	)	)	PUNCT
ejpam-3976	87	18	2	2	NUM
ejpam-3976	88	1	+	+	CCONJ
ejpam-3976	88	2	y2	y2	PROPN
ejpam-3976	88	3	≥	≥	NOUN
ejpam-3976	88	4	2π	2π	PROPN
ejpam-3976	88	5	√	√	VERB
ejpam-3976	88	6	(	(	PUNCT
ejpam-3976	88	7	k	k	PROPN
ejpam-3976	88	8	+	+	PROPN
ejpam-3976	88	9	1	1	NUM
ejpam-3976	88	10	2	2	NUM
ejpam-3976	88	11	−	−	NOUN
ejpam-3976	88	12	x	x	SYM
ejpam-3976	88	13	)	)	PUNCT
ejpam-3976	88	14	2	2	NUM
ejpam-3976	88	15	c.	c.	NOUN
ejpam-3976	88	16	corcino	corcino	PROPN
ejpam-3976	88	17	/	/	SYM
ejpam-3976	88	18	eur	eur	PROPN
ejpam-3976	88	19	.	.	PUNCT
ejpam-3976	89	1	j.	j.	PROPN
ejpam-3976	89	2	pure	pure	PROPN
ejpam-3976	89	3	appl	appl	PROPN
ejpam-3976	89	4	.	.	PROPN
ejpam-3976	89	5	math	math	PROPN
ejpam-3976	89	6	,	,	PUNCT
ejpam-3976	89	7	14	14	NUM
ejpam-3976	89	8	(	(	PUNCT
ejpam-3976	89	9	3	3	NUM
ejpam-3976	89	10	)	)	PUNCT
ejpam-3976	89	11	(	(	PUNCT
ejpam-3976	89	12	2021	2021	NUM
ejpam-3976	89	13	)	)	PUNCT
ejpam-3976	89	14	,	,	PUNCT
ejpam-3976	89	15	666	666	NUM
ejpam-3976	89	16	-	-	SYM
ejpam-3976	89	17	684	684	NUM
ejpam-3976	89	18	671	671	NUM
ejpam-3976	89	19	=	=	NOUN
ejpam-3976	89	20	2π	2π	NOUN
ejpam-3976	89	21	∣∣∣∣k	∣∣∣∣k	VERB
ejpam-3976	89	22	+	+	CCONJ
ejpam-3976	89	23	1	1	NUM
ejpam-3976	89	24	2	2	NUM
ejpam-3976	89	25	−	−	NOUN
ejpam-3976	89	26	x	x	PUNCT
ejpam-3976	89	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	89	28	,	,	PUNCT
ejpam-3976	89	29	with	with	ADP
ejpam-3976	89	30	−	−	PROPN
ejpam-3976	89	31	1	1	NUM
ejpam-3976	89	32	2	2	NUM
ejpam-3976	89	33	≤	≤	NUM
ejpam-3976	89	34	x	x	PUNCT
ejpam-3976	89	35	≤	≤	NUM
ejpam-3976	89	36	1	1	NUM
ejpam-3976	89	37	2	2	NUM
ejpam-3976	89	38	=	=	NOUN
ejpam-3976	89	39	2π	2π	NOUN
ejpam-3976	89	40	∣∣∣∣k	∣∣∣∣k	VERB
ejpam-3976	89	41	−	−	NUM
ejpam-3976	90	1	(	(	PUNCT
ejpam-3976	90	2	x	x	SYM
ejpam-3976	90	3	−	−	PROPN
ejpam-3976	90	4	1	1	NUM
ejpam-3976	90	5	2	2	NUM
ejpam-3976	90	6	)	)	PUNCT
ejpam-3976	90	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3976	90	8	≥	≥	NOUN
ejpam-3976	90	9	2π	2π	NOUN
ejpam-3976	90	10	(	(	PUNCT
ejpam-3976	90	11	|k|	|k|	NOUN
ejpam-3976	90	12	−	−	NOUN
ejpam-3976	90	13	∣∣∣∣x−	∣∣∣∣x−	NUM
ejpam-3976	90	14	1	1	NUM
ejpam-3976	90	15	2	2	NUM
ejpam-3976	90	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	90	17	)	)	PUNCT
ejpam-3976	90	18	≥	≥	NOUN
ejpam-3976	90	19	2π	2π	NOUN
ejpam-3976	90	20	(	(	PUNCT
ejpam-3976	90	21	|k|	|k|	NOUN
ejpam-3976	90	22	−	−	PROPN
ejpam-3976	90	23	∣∣∣∣12	∣∣∣∣12	ADV
ejpam-3976	90	24	−	−	NOUN
ejpam-3976	90	25	x	x	SYM
ejpam-3976	90	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	90	27	)	)	PUNCT
ejpam-3976	90	28	≥	≥	NOUN
ejpam-3976	90	29	2π	2π	NOUN
ejpam-3976	90	30	(	(	PUNCT
ejpam-3976	90	31	|k|	|k|	NOUN
ejpam-3976	90	32	−	−	NOUN
ejpam-3976	90	33	1	1	NUM
ejpam-3976	90	34	)	)	PUNCT
ejpam-3976	90	35	.	.	PUNCT
ejpam-3976	91	1	an	an	DET
ejpam-3976	91	2	asymptotic	asymptotic	ADJ
ejpam-3976	91	3	expansion	expansion	NOUN
ejpam-3976	91	4	of	of	ADP
ejpam-3976	91	5	the	the	DET
ejpam-3976	91	6	apostol	apostol	NOUN
ejpam-3976	91	7	-	-	PUNCT
ejpam-3976	91	8	genocchi	genocchi	PROPN
ejpam-3976	91	9	numbers	number	NOUN
ejpam-3976	91	10	gn(0;λ	gn(0;λ	PROPN
ejpam-3976	91	11	)	)	PUNCT
ejpam-3976	91	12	is	be	AUX
ejpam-3976	91	13	given	give	VERB
ejpam-3976	91	14	in	in	ADP
ejpam-3976	91	15	the	the	DET
ejpam-3976	91	16	next	next	ADJ
ejpam-3976	91	17	theorem	theorem	PROPN
ejpam-3976	91	18	.	.	PUNCT
ejpam-3976	91	19	theorem	theorem	VERB
ejpam-3976	91	20	2.3	2.3	NUM
ejpam-3976	91	21	.	.	PUNCT
ejpam-3976	92	1	given	give	VERB
ejpam-3976	92	2	λ	λ	PROPN
ejpam-3976	92	3	∈	∈	PROPN
ejpam-3976	92	4	c\{0	c\{0	PROPN
ejpam-3976	92	5	}	}	PUNCT
ejpam-3976	92	6	,	,	PUNCT
ejpam-3976	92	7	let	let	VERB
ejpam-3976	92	8	h	h	PRON
ejpam-3976	92	9	be	be	AUX
ejpam-3976	92	10	a	a	DET
ejpam-3976	92	11	finite	finite	NOUN
ejpam-3976	92	12	subset	subset	NOUN
ejpam-3976	92	13	of	of	ADP
ejpam-3976	92	14	tλ	tλ	ADP
ejpam-3976	92	15	satisfying	satisfy	VERB
ejpam-3976	92	16	max	max	PROPN
ejpam-3976	92	17	{	{	PUNCT
ejpam-3976	92	18	|u|	|u|	PROPN
ejpam-3976	92	19	:	:	PUNCT
ejpam-3976	92	20	u	u	PROPN
ejpam-3976	92	21	∈	∈	PROPN
ejpam-3976	92	22	h	h	NOUN
ejpam-3976	92	23	}	}	PUNCT
ejpam-3976	92	24	<	<	X
ejpam-3976	92	25	min	min	X
ejpam-3976	92	26	{	{	PUNCT
ejpam-3976	92	27	|u|	|u|	ADV
ejpam-3976	92	28	:	:	PUNCT
ejpam-3976	92	29	u	u	NOUN
ejpam-3976	92	30	∈	∈	PROPN
ejpam-3976	92	31	tλ\h	tλ\h	ADP
ejpam-3976	92	32	}	}	PUNCT
ejpam-3976	92	33	:	:	PUNCT
ejpam-3976	92	34	=	=	PUNCT
ejpam-3976	93	1	ν	ν	X
ejpam-3976	93	2	.	.	PROPN
ejpam-3976	93	3	for	for	ADP
ejpam-3976	93	4	all	all	DET
ejpam-3976	93	5	integers	integer	NOUN
ejpam-3976	93	6	n	n	PRON
ejpam-3976	93	7	≥	≥	NUM
ejpam-3976	93	8	2	2	NUM
ejpam-3976	93	9	,	,	PUNCT
ejpam-3976	93	10	gn(0;λ	gn(0;λ	PROPN
ejpam-3976	93	11	)	)	PUNCT
ejpam-3976	93	12	n	n	CCONJ
ejpam-3976	93	13	!	!	PUNCT
ejpam-3976	94	1	=	=	SYM
ejpam-3976	94	2	2	2	NUM
ejpam-3976	94	3	∑	∑	ADV
ejpam-3976	94	4	u∈h	u∈h	ADJ
ejpam-3976	94	5	1	1	NUM
ejpam-3976	94	6	un	un	NOUN
ejpam-3976	94	7	+	+	NOUN
ejpam-3976	94	8	o(ν−n	o(ν−n	NOUN
ejpam-3976	94	9	)	)	PUNCT
ejpam-3976	94	10	.	.	PUNCT
ejpam-3976	95	1	proof	proof	NOUN
ejpam-3976	95	2	.	.	PUNCT
ejpam-3976	96	1	write	write	VERB
ejpam-3976	96	2	the	the	DET
ejpam-3976	96	3	series	series	NOUN
ejpam-3976	96	4	in	in	ADP
ejpam-3976	96	5	(	(	PUNCT
ejpam-3976	96	6	2.2	2.2	NUM
ejpam-3976	96	7	)	)	PUNCT
ejpam-3976	96	8	as	as	ADP
ejpam-3976	96	9	∑	∑	PROPN
ejpam-3976	96	10	k	k	PROPN
ejpam-3976	96	11	1	1	NUM
ejpam-3976	96	12	(	(	PUNCT
ejpam-3976	96	13	uk)n	uk)n	PROPN
ejpam-3976	96	14	.	.	PUNCT
ejpam-3976	97	1	by	by	ADP
ejpam-3976	97	2	lemma	lemma	PROPN
ejpam-3976	97	3	2.2	2.2	NUM
ejpam-3976	97	4	we	we	PRON
ejpam-3976	97	5	can	can	AUX
ejpam-3976	97	6	relabel	relabel	VERB
ejpam-3976	97	7	the	the	DET
ejpam-3976	97	8	set	set	NOUN
ejpam-3976	97	9	of	of	ADP
ejpam-3976	97	10	poles	pole	NOUN
ejpam-3976	97	11	in	in	ADP
ejpam-3976	97	12	increasing	increase	VERB
ejpam-3976	97	13	order	order	NOUN
ejpam-3976	97	14	of	of	ADP
ejpam-3976	97	15	magnitude	magnitude	NOUN
ejpam-3976	97	16	as	as	ADP
ejpam-3976	97	17	|µ0|	|µ0|	ADJ
ejpam-3976	97	18	≤	≤	NUM
ejpam-3976	97	19	|µ1|	|µ1|	NOUN
ejpam-3976	97	20	≤	≤	NOUN
ejpam-3976	97	21	·	·	PUNCT
ejpam-3976	97	22	·	·	PUNCT
ejpam-3976	97	23	·	·	PUNCT
ejpam-3976	98	1	≤	≤	NUM
ejpam-3976	98	2	|µm	|µm	PUNCT
ejpam-3976	98	3	|	|	ADV
ejpam-3976	98	4	≤	≤	NOUN
ejpam-3976	98	5	·	·	PUNCT
ejpam-3976	98	6	·	·	PUNCT
ejpam-3976	98	7	·	·	PUNCT
ejpam-3976	98	8	.	.	PUNCT
ejpam-3976	99	1	since	since	SCONJ
ejpam-3976	99	2	|µk|	|µk|	PROPN
ejpam-3976	99	3	≥	≥	NOUN
ejpam-3976	99	4	2π(|k|	2π(|k|	NUM
ejpam-3976	99	5	−	−	NUM
ejpam-3976	99	6	1	1	NUM
ejpam-3976	99	7	)	)	PUNCT
ejpam-3976	99	8	,	,	PUNCT
ejpam-3976	99	9	for	for	ADP
ejpam-3976	99	10	k	k	PROPN
ejpam-3976	99	11	≥	≥	NUM
ejpam-3976	99	12	2	2	NUM
ejpam-3976	99	13	,	,	PUNCT
ejpam-3976	99	14	the	the	DET
ejpam-3976	99	15	series	series	NOUN
ejpam-3976	99	16	∑	∑	PROPN
ejpam-3976	99	17	k	k	PROPN
ejpam-3976	99	18	1	1	NUM
ejpam-3976	99	19	(	(	PUNCT
ejpam-3976	99	20	µk)n	µk)n	PROPN
ejpam-3976	99	21	is	be	AUX
ejpam-3976	99	22	absolutely	absolutely	ADV
ejpam-3976	99	23	convergent	convergent	ADJ
ejpam-3976	99	24	for	for	ADP
ejpam-3976	99	25	n	n	PRON
ejpam-3976	99	26	≥	≥	NOUN
ejpam-3976	99	27	2	2	NUM
ejpam-3976	99	28	.	.	X
ejpam-3976	100	1	for	for	ADP
ejpam-3976	100	2	any	any	DET
ejpam-3976	100	3	m	m	NOUN
ejpam-3976	100	4	>	>	X
ejpam-3976	100	5	2	2	NUM
ejpam-3976	100	6	,	,	PUNCT
ejpam-3976	100	7	the	the	DET
ejpam-3976	100	8	tail	tail	NOUN
ejpam-3976	100	9	of	of	ADP
ejpam-3976	100	10	the	the	DET
ejpam-3976	100	11	series	series	NOUN
ejpam-3976	100	12	is	be	AUX
ejpam-3976	100	13	∞∑	∞∑	ADJ
ejpam-3976	100	14	k	k	X
ejpam-3976	100	15	=	=	ADJ
ejpam-3976	100	16	m+1	m+1	NUM
ejpam-3976	100	17	1	1	NUM
ejpam-3976	100	18	|µk|n	|µk|n	NOUN
ejpam-3976	100	19	=	=	SYM
ejpam-3976	100	20	1	1	NUM
ejpam-3976	100	21	|µm+1|n	|µm+1|n	NOUN
ejpam-3976	100	22	∞∑	∞∑	NUM
ejpam-3976	100	23	k	k	X
ejpam-3976	100	24	=	=	X
ejpam-3976	100	25	m+1	m+1	NOUN
ejpam-3976	100	26	∣∣∣∣µm+1	∣∣∣∣µm+1	VERB
ejpam-3976	100	27	µk	µk	NOUN
ejpam-3976	100	28	∣∣∣∣n	∣∣∣∣n	ADV
ejpam-3976	100	29	.	.	PUNCT
ejpam-3976	101	1	since	since	SCONJ
ejpam-3976	101	2	for	for	ADP
ejpam-3976	101	3	k	k	PROPN
ejpam-3976	101	4	>	>	X
ejpam-3976	101	5	m	m	VERB
ejpam-3976	101	6	+	+	ADJ
ejpam-3976	101	7	1	1	NUM
ejpam-3976	101	8	,	,	PUNCT
ejpam-3976	101	9	∣∣∣µm+1	∣∣∣µm+1	PROPN
ejpam-3976	101	10	µk	µk	PROPN
ejpam-3976	101	11	∣∣∣	∣∣∣	ADJ
ejpam-3976	101	12	≤	≤	NUM
ejpam-3976	101	13	1	1	NUM
ejpam-3976	101	14	,	,	PUNCT
ejpam-3976	101	15	we	we	PRON
ejpam-3976	101	16	have	have	VERB
ejpam-3976	101	17	∣∣∣µm+1	∣∣∣µm+1	PROPN
ejpam-3976	101	18	µk	µk	PROPN
ejpam-3976	101	19	∣∣∣n	∣∣∣n	PROPN
ejpam-3976	101	20	≤	≤	NUM
ejpam-3976	101	21	∣∣∣µm+1	∣∣∣µm+1	PROPN
ejpam-3976	101	22	µk	µk	PROPN
ejpam-3976	101	23	∣∣∣2	∣∣∣2	NOUN
ejpam-3976	101	24	for	for	ADP
ejpam-3976	101	25	n	n	X
ejpam-3976	101	26	≥	≥	NUM
ejpam-3976	101	27	2	2	NUM
ejpam-3976	101	28	.	.	PUNCT
ejpam-3976	102	1	hence	hence	ADV
ejpam-3976	102	2	,	,	PUNCT
ejpam-3976	102	3	∞∑	∞∑	ADJ
ejpam-3976	102	4	k	k	X
ejpam-3976	102	5	=	=	X
ejpam-3976	102	6	m+1	m+1	PROPN
ejpam-3976	102	7	1	1	NUM
ejpam-3976	102	8	|µk|n	|µk|n	PROPN
ejpam-3976	102	9	≤	≤	NUM
ejpam-3976	102	10	1	1	NUM
ejpam-3976	102	11	|µm+1|n	|µm+1|n	NOUN
ejpam-3976	102	12	∞∑	∞∑	NUM
ejpam-3976	102	13	k	k	X
ejpam-3976	102	14	=	=	X
ejpam-3976	102	15	m+1	m+1	NOUN
ejpam-3976	102	16	∣∣∣∣µm+1	∣∣∣∣µm+1	VERB
ejpam-3976	102	17	µk	µk	PRON
ejpam-3976	102	18	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	102	19	.	.	PUNCT
ejpam-3976	103	1	let	let	VERB
ejpam-3976	103	2	cm	cm	NOUN
ejpam-3976	103	3	,	,	PUNCT
ejpam-3976	103	4	λ	λ	X
ejpam-3976	103	5	=	=	SYM
ejpam-3976	103	6	∞∑	∞∑	NUM
ejpam-3976	103	7	k	k	NOUN
ejpam-3976	103	8	=	=	X
ejpam-3976	103	9	m+1	m+1	NOUN
ejpam-3976	103	10	∣∣∣∣µm+1	∣∣∣∣µm+1	VERB
ejpam-3976	103	11	µk	µk	PRON
ejpam-3976	103	12	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	103	13	.	.	PUNCT
ejpam-3976	104	1	then	then	ADV
ejpam-3976	104	2	∞∑	∞∑	NUM
ejpam-3976	104	3	k	k	NOUN
ejpam-3976	104	4	=	=	X
ejpam-3976	104	5	m+1	m+1	NUM
ejpam-3976	104	6	1	1	NUM
ejpam-3976	104	7	|µk|n	|µk|n	PROPN
ejpam-3976	104	8	≤	≤	NOUN
ejpam-3976	104	9	cm	cm	NOUN
ejpam-3976	104	10	,	,	PUNCT
ejpam-3976	104	11	λ	λ	PROPN
ejpam-3976	104	12	|µm+1|n	|µm+1|n	X
ejpam-3976	104	13	.	.	PUNCT
ejpam-3976	105	1	c.	c.	PROPN
ejpam-3976	105	2	corcino	corcino	PROPN
ejpam-3976	105	3	/	/	SYM
ejpam-3976	105	4	eur	eur	PROPN
ejpam-3976	105	5	.	.	PUNCT
ejpam-3976	106	1	j.	j.	PROPN
ejpam-3976	106	2	pure	pure	PROPN
ejpam-3976	106	3	appl	appl	PROPN
ejpam-3976	106	4	.	.	PROPN
ejpam-3976	106	5	math	math	PROPN
ejpam-3976	106	6	,	,	PUNCT
ejpam-3976	106	7	14	14	NUM
ejpam-3976	106	8	(	(	PUNCT
ejpam-3976	106	9	3	3	NUM
ejpam-3976	106	10	)	)	PUNCT
ejpam-3976	106	11	(	(	PUNCT
ejpam-3976	106	12	2021	2021	NUM
ejpam-3976	106	13	)	)	PUNCT
ejpam-3976	106	14	,	,	PUNCT
ejpam-3976	106	15	666	666	NUM
ejpam-3976	106	16	-	-	SYM
ejpam-3976	106	17	684	684	NUM
ejpam-3976	106	18	672	672	NUM
ejpam-3976	106	19	consider	consider	VERB
ejpam-3976	106	20	cm	cm	NOUN
ejpam-3976	106	21	,	,	PUNCT
ejpam-3976	106	22	λ	λ	NOUN
ejpam-3976	106	23	:	:	PUNCT
ejpam-3976	106	24	cm	cm	NOUN
ejpam-3976	106	25	,	,	PUNCT
ejpam-3976	106	26	λ	λ	X
ejpam-3976	106	27	=	=	SYM
ejpam-3976	107	1	∞∑	∞∑	NUM
ejpam-3976	107	2	k	k	X
ejpam-3976	107	3	=	=	ADJ
ejpam-3976	107	4	m+1	m+1	NUM
ejpam-3976	107	5	|µm+1|2	|µm+1|2	NOUN
ejpam-3976	107	6	|µk|2	|µk|2	PROPN
ejpam-3976	107	7	=	=	SYM
ejpam-3976	107	8	|µm+1|2	|µm+1|2	NOUN
ejpam-3976	107	9	∞∑	∞∑	NUM
ejpam-3976	107	10	k	k	NOUN
ejpam-3976	107	11	=	=	X
ejpam-3976	107	12	m+1	m+1	NUM
ejpam-3976	107	13	1	1	NUM
ejpam-3976	107	14	|µk|2	|µk|2	PROPN
ejpam-3976	107	15	=	=	SYM
ejpam-3976	107	16	(	(	PUNCT
ejpam-3976	107	17	2π)2	2π)2	NOUN
ejpam-3976	107	18	∣∣∣∣m	∣∣∣∣m	VERB
ejpam-3976	107	19	+	+	PROPN
ejpam-3976	107	20	1	1	NUM
ejpam-3976	107	21	+	+	SYM
ejpam-3976	107	22	1	1	NUM
ejpam-3976	107	23	2	2	NUM
ejpam-3976	107	24	−	−	NOUN
ejpam-3976	107	25	γ	γ	X
ejpam-3976	107	26	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	107	27	∞∑	∞∑	PROPN
ejpam-3976	107	28	k	k	NOUN
ejpam-3976	107	29	=	=	NOUN
ejpam-3976	107	30	m+1	m+1	NUM
ejpam-3976	107	31	1	1	NUM
ejpam-3976	107	32	(	(	PUNCT
ejpam-3976	107	33	2π)2	2π)2	NUM
ejpam-3976	107	34	∣∣k	∣∣k	PROPN
ejpam-3976	107	35	+	+	CCONJ
ejpam-3976	107	36	1	1	NUM
ejpam-3976	107	37	2	2	NUM
ejpam-3976	107	38	−	−	NOUN
ejpam-3976	107	39	γ	γ	PROPN
ejpam-3976	107	40	∣∣2	∣∣2	PROPN
ejpam-3976	107	41	≤	≤	NOUN
ejpam-3976	107	42	∣∣∣∣m	∣∣∣∣m	NOUN
ejpam-3976	107	43	+	+	CCONJ
ejpam-3976	107	44	3	3	NUM
ejpam-3976	107	45	2	2	NUM
ejpam-3976	107	46	−	−	NOUN
ejpam-3976	107	47	γ	γ	X
ejpam-3976	107	48	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	107	49	∞∑	∞∑	PROPN
ejpam-3976	107	50	k	k	NOUN
ejpam-3976	107	51	=	=	NOUN
ejpam-3976	107	52	m+1	m+1	NUM
ejpam-3976	107	53	1	1	NUM
ejpam-3976	107	54	(	(	PUNCT
ejpam-3976	107	55	|k|	|k|	NOUN
ejpam-3976	107	56	−	−	PROPN
ejpam-3976	107	57	1)2	1)2	NUM
ejpam-3976	107	58	≤	≤	ADJ
ejpam-3976	107	59	2	2	NUM
ejpam-3976	107	60	∣∣∣∣m	∣∣∣∣m	NOUN
ejpam-3976	107	61	+	+	CCONJ
ejpam-3976	107	62	3	3	NUM
ejpam-3976	107	63	2	2	NUM
ejpam-3976	107	64	−	−	NOUN
ejpam-3976	107	65	γ	γ	X
ejpam-3976	107	66	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	107	67	∞∑	∞∑	PROPN
ejpam-3976	107	68	l=0	l=0	PROPN
ejpam-3976	107	69	1	1	NUM
ejpam-3976	107	70	(	(	PUNCT
ejpam-3976	107	71	m	m	VERB
ejpam-3976	107	72	+	+	ADJ
ejpam-3976	107	73	l)2	l)2	ADJ
ejpam-3976	107	74	≤	≤	ADJ
ejpam-3976	107	75	2	2	NUM
ejpam-3976	107	76	∣∣∣∣m	∣∣∣∣m	NOUN
ejpam-3976	107	77	+	+	CCONJ
ejpam-3976	107	78	3	3	NUM
ejpam-3976	107	79	2	2	NUM
ejpam-3976	107	80	−	−	NOUN
ejpam-3976	107	81	γ	γ	X
ejpam-3976	107	82	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	107	83	(	(	PUNCT
ejpam-3976	107	84	1	1	NUM
ejpam-3976	107	85	m2	m2	NOUN
ejpam-3976	107	86	+	+	CCONJ
ejpam-3976	107	87	∞∑	∞∑	NUM
ejpam-3976	107	88	l=1	l=1	NOUN
ejpam-3976	107	89	1	1	NUM
ejpam-3976	107	90	(	(	PUNCT
ejpam-3976	107	91	m	m	VERB
ejpam-3976	107	92	+	+	ADJ
ejpam-3976	107	93	l)2	l)2	ADJ
ejpam-3976	107	94	)	)	PUNCT
ejpam-3976	107	95	.	.	PUNCT
ejpam-3976	108	1	with	with	ADP
ejpam-3976	108	2	∞∑	∞∑	NUM
ejpam-3976	108	3	l=1	l=1	NOUN
ejpam-3976	108	4	1	1	NUM
ejpam-3976	108	5	(	(	PUNCT
ejpam-3976	108	6	m	m	VERB
ejpam-3976	108	7	+	+	ADJ
ejpam-3976	108	8	l)2	l)2	PROPN
ejpam-3976	108	9	≤	≤	NUM
ejpam-3976	108	10	∫	∫	PROPN
ejpam-3976	108	11	∞	∞	NUM
ejpam-3976	108	12	1	1	NUM
ejpam-3976	108	13	1	1	NUM
ejpam-3976	108	14	(	(	PUNCT
ejpam-3976	108	15	m	m	VERB
ejpam-3976	108	16	+	+	ADJ
ejpam-3976	108	17	x)2	x)2	X
ejpam-3976	108	18	dx	dx	PROPN
ejpam-3976	108	19	=	=	SYM
ejpam-3976	109	1	1	1	NUM
ejpam-3976	109	2	m	m	NOUN
ejpam-3976	109	3	+	+	NUM
ejpam-3976	109	4	1	1	NUM
ejpam-3976	109	5	,	,	PUNCT
ejpam-3976	109	6	cm	cm	NOUN
ejpam-3976	109	7	,	,	PUNCT
ejpam-3976	109	8	λ	λ	PROPN
ejpam-3976	109	9	≤	≤	ADJ
ejpam-3976	109	10	2	2	NUM
ejpam-3976	109	11	∣∣∣∣m	∣∣∣∣m	NOUN
ejpam-3976	109	12	+	+	CCONJ
ejpam-3976	109	13	3	3	NUM
ejpam-3976	109	14	2	2	NUM
ejpam-3976	109	15	−	−	PROPN
ejpam-3976	109	16	γ	γ	X
ejpam-3976	109	17	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	109	18	(	(	PUNCT
ejpam-3976	109	19	1	1	NUM
ejpam-3976	109	20	m2	m2	PROPN
ejpam-3976	109	21	+	+	CCONJ
ejpam-3976	109	22	1	1	NUM
ejpam-3976	109	23	m	m	NOUN
ejpam-3976	109	24	+	+	NOUN
ejpam-3976	109	25	1	1	NUM
ejpam-3976	109	26	)	)	PUNCT
ejpam-3976	109	27	=	=	SYM
ejpam-3976	109	28	2	2	NUM
ejpam-3976	110	1	∣∣m	∣∣m	ADV
ejpam-3976	110	2	+	+	CCONJ
ejpam-3976	110	3	3	3	NUM
ejpam-3976	110	4	2	2	NUM
ejpam-3976	110	5	−	−	NOUN
ejpam-3976	110	6	γ	γ	PROPN
ejpam-3976	110	7	∣∣2	∣∣2	PROPN
ejpam-3976	110	8	m2	m2	PROPN
ejpam-3976	110	9	+	+	CCONJ
ejpam-3976	110	10	2	2	NUM
ejpam-3976	110	11	∣∣m	∣∣m	ADJ
ejpam-3976	110	12	+	+	CCONJ
ejpam-3976	110	13	3	3	NUM
ejpam-3976	110	14	2	2	NUM
ejpam-3976	110	15	−	−	NOUN
ejpam-3976	110	16	γ	γ	PROPN
ejpam-3976	110	17	∣∣2	∣∣2	PROPN
ejpam-3976	110	18	m	m	NOUN
ejpam-3976	110	19	+	+	NOUN
ejpam-3976	110	20	1	1	NUM
ejpam-3976	110	21	.	.	PUNCT
ejpam-3976	111	1	let	let	AUX
ejpam-3976	111	2	ε1	ε1	VERB
ejpam-3976	111	3	=	=	SYM
ejpam-3976	111	4	∣∣m	∣∣m	ADJ
ejpam-3976	111	5	+	+	CCONJ
ejpam-3976	111	6	3	3	NUM
ejpam-3976	111	7	2	2	NUM
ejpam-3976	111	8	−	−	NOUN
ejpam-3976	111	9	γ	γ	PROPN
ejpam-3976	111	10	∣∣2	∣∣2	PROPN
ejpam-3976	111	11	m2	m2	PROPN
ejpam-3976	111	12	≤	≤	PROPN
ejpam-3976	111	13	∣∣∣∣52	∣∣∣∣52	ADP
ejpam-3976	111	14	−	−	PROPN
ejpam-3976	111	15	γ	γ	X
ejpam-3976	111	16	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-3976	111	17	,	,	PUNCT
ejpam-3976	111	18	and	and	CCONJ
ejpam-3976	111	19	ε2	ε2	NOUN
ejpam-3976	111	20	=	=	PUNCT
ejpam-3976	111	21	∣∣m	∣∣m	ADJ
ejpam-3976	111	22	+	+	CCONJ
ejpam-3976	111	23	3	3	NUM
ejpam-3976	111	24	2	2	NUM
ejpam-3976	111	25	−	−	NOUN
ejpam-3976	111	26	γ	γ	X
ejpam-3976	111	27	∣∣	∣∣	VERB
ejpam-3976	111	28	m	m	PROPN
ejpam-3976	111	29	+	+	X
ejpam-3976	111	30	1	1	NUM
ejpam-3976	111	31	≤	≤	NUM
ejpam-3976	111	32	1	1	NUM
ejpam-3976	111	33	+	+	CCONJ
ejpam-3976	111	34	|1/2−	|1/2−	PROPN
ejpam-3976	111	35	γ|	γ|	PROPN
ejpam-3976	111	36	|m	|m	NOUN
ejpam-3976	111	37	+	+	CCONJ
ejpam-3976	111	38	1|	1|	NUM
ejpam-3976	111	39	≤	≤	NUM
ejpam-3976	111	40	1	1	NUM
ejpam-3976	112	1	+	+	CCONJ
ejpam-3976	112	2	∣∣∣∣12	∣∣∣∣12	ADJ
ejpam-3976	112	3	−	−	NOUN
ejpam-3976	113	1	γ	γ	PROPN
ejpam-3976	113	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	113	3	.	.	PUNCT
ejpam-3976	114	1	consequently	consequently	ADV
ejpam-3976	114	2	,	,	PUNCT
ejpam-3976	114	3	cm	cm	PROPN
ejpam-3976	114	4	,	,	PUNCT
ejpam-3976	114	5	λ	λ	X
ejpam-3976	114	6	|µm+1|n	|µm+1|n	NUM
ejpam-3976	114	7	≤	≤	NUM
ejpam-3976	114	8	2	2	NUM
ejpam-3976	114	9	ε1	ε1	NOUN
ejpam-3976	114	10	|µm+1|n	|µm+1|n	NOUN
ejpam-3976	114	11	+	+	CCONJ
ejpam-3976	114	12	2	2	NUM
ejpam-3976	114	13	ε2	ε2	ADJ
ejpam-3976	114	14	|µm+1|n	|µm+1|n	NOUN
ejpam-3976	114	15	·	·	PUNCT
ejpam-3976	114	16	∣∣∣∣m	∣∣∣∣m	VERB
ejpam-3976	114	17	+	+	CCONJ
ejpam-3976	114	18	3	3	NUM
ejpam-3976	114	19	2	2	NUM
ejpam-3976	114	20	−	−	NOUN
ejpam-3976	114	21	γ	γ	PROPN
ejpam-3976	114	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	114	23	≤	≤	NOUN
ejpam-3976	114	24	2ε1	2ε1	NUM
ejpam-3976	114	25	|µm+1|n	|µm+1|n	NOUN
ejpam-3976	115	1	+	+	X
ejpam-3976	115	2	2ε2	2ε2	NUM
ejpam-3976	115	3	·	·	PUNCT
ejpam-3976	115	4	|m	|m	NOUN
ejpam-3976	115	5	+	+	CCONJ
ejpam-3976	115	6	3/2−	3/2−	PROPN
ejpam-3976	115	7	γ|	γ|	AUX
ejpam-3976	115	8	|µm+1|n	|µm+1|n	NOUN
ejpam-3976	115	9	,	,	PUNCT
ejpam-3976	115	10	c.	c.	PROPN
ejpam-3976	115	11	corcino	corcino	PROPN
ejpam-3976	115	12	/	/	SYM
ejpam-3976	115	13	eur	eur	PROPN
ejpam-3976	115	14	.	.	PUNCT
ejpam-3976	116	1	j.	j.	PROPN
ejpam-3976	116	2	pure	pure	PROPN
ejpam-3976	116	3	appl	appl	PROPN
ejpam-3976	116	4	.	.	PROPN
ejpam-3976	116	5	math	math	PROPN
ejpam-3976	116	6	,	,	PUNCT
ejpam-3976	116	7	14	14	NUM
ejpam-3976	116	8	(	(	PUNCT
ejpam-3976	116	9	3	3	NUM
ejpam-3976	116	10	)	)	PUNCT
ejpam-3976	116	11	(	(	PUNCT
ejpam-3976	116	12	2021	2021	NUM
ejpam-3976	116	13	)	)	PUNCT
ejpam-3976	116	14	,	,	PUNCT
ejpam-3976	116	15	666	666	NUM
ejpam-3976	116	16	-	-	SYM
ejpam-3976	116	17	684	684	NUM
ejpam-3976	116	18	673	673	NUM
ejpam-3976	116	19	where	where	SCONJ
ejpam-3976	116	20	|µm+1|	|µm+1|	PROPN
ejpam-3976	116	21	=	=	PUNCT
ejpam-3976	116	22	∣∣∣∣m	∣∣∣∣m	PROPN
ejpam-3976	116	23	+	+	CCONJ
ejpam-3976	116	24	3	3	NUM
ejpam-3976	116	25	2	2	NUM
ejpam-3976	116	26	−	−	NOUN
ejpam-3976	116	27	γ	γ	X
ejpam-3976	116	28	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3976	116	29	=	=	PUNCT
ejpam-3976	116	30	√	√	PROPN
ejpam-3976	116	31	(	(	PUNCT
ejpam-3976	116	32	m	m	PROPN
ejpam-3976	116	33	+	+	NOUN
ejpam-3976	116	34	3	3	NUM
ejpam-3976	116	35	2	2	NUM
ejpam-3976	116	36	−re	−re	NOUN
ejpam-3976	116	37	γ	γ	X
ejpam-3976	116	38	)	)	PUNCT
ejpam-3976	116	39	2	2	NUM
ejpam-3976	116	40	+	+	CCONJ
ejpam-3976	116	41	(	(	PUNCT
ejpam-3976	116	42	i	i	NOUN
ejpam-3976	116	43	m	m	VERB
ejpam-3976	116	44	γ)2	γ)2	NOUN
ejpam-3976	116	45	≥	≥	NOUN
ejpam-3976	116	46	|m	|m	NOUN
ejpam-3976	116	47	|	|	ADV
ejpam-3976	116	48	−	−	PROPN
ejpam-3976	116	49	2	2	NUM
ejpam-3976	116	50	.	.	PUNCT
ejpam-3976	116	51	cm	cm	NOUN
ejpam-3976	116	52	,	,	PUNCT
ejpam-3976	116	53	λ	λ	PROPN
ejpam-3976	116	54	≤	≤	NUM
ejpam-3976	116	55	ε1	ε1	VERB
ejpam-3976	116	56	2n−1πn	2n−1πn	NUM
ejpam-3976	116	57	|m	|m	NOUN
ejpam-3976	116	58	+	+	CCONJ
ejpam-3976	116	59	3/2−	3/2−	NUM
ejpam-3976	116	60	γ|n	γ|n	VERB
ejpam-3976	117	1	+	+	CCONJ
ejpam-3976	117	2	ε2	ε2	ADJ
ejpam-3976	117	3	2n−1πn	2n−1πn	NUM
ejpam-3976	117	4	|m	|m	NOUN
ejpam-3976	117	5	+	+	CCONJ
ejpam-3976	117	6	3/2−	3/2−	NUM
ejpam-3976	117	7	γ|n−1	γ|n−1	ADV
ejpam-3976	117	8	≤	≤	PROPN
ejpam-3976	117	9	ε1	ε1	VERB
ejpam-3976	117	10	2n−1πn	2n−1πn	NUM
ejpam-3976	117	11	(	(	PUNCT
ejpam-3976	117	12	|m	|m	NOUN
ejpam-3976	117	13	|	|	ADV
ejpam-3976	117	14	−	−	PROPN
ejpam-3976	117	15	2)n	2)n	NUM
ejpam-3976	117	16	+	+	CCONJ
ejpam-3976	117	17	ε2	ε2	ADJ
ejpam-3976	117	18	2n−1πn	2n−1πn	NUM
ejpam-3976	117	19	(	(	PUNCT
ejpam-3976	117	20	|m	|m	NOUN
ejpam-3976	117	21	|	|	ADV
ejpam-3976	117	22	−	−	PROPN
ejpam-3976	117	23	2)n	2)n	NOUN
ejpam-3976	117	24	≤	≤	NOUN
ejpam-3976	117	25	|5/2−	|5/2−	ADP
ejpam-3976	118	1	γ|2	γ|2	ADJ
ejpam-3976	118	2	2n−1πn	2n−1πn	PROPN
ejpam-3976	118	3	(	(	PUNCT
ejpam-3976	118	4	|m	|m	NOUN
ejpam-3976	118	5	|	|	ADV
ejpam-3976	118	6	−	−	NOUN
ejpam-3976	118	7	2)n	2)n	NUM
ejpam-3976	118	8	+	+	SYM
ejpam-3976	118	9	1	1	NUM
ejpam-3976	118	10	+	+	CCONJ
ejpam-3976	118	11	|1/2−	|1/2−	PROPN
ejpam-3976	118	12	γ|	γ|	PROPN
ejpam-3976	118	13	2n−1πn	2n−1πn	NUM
ejpam-3976	118	14	(	(	PUNCT
ejpam-3976	118	15	|m	|m	NOUN
ejpam-3976	118	16	|	|	ADV
ejpam-3976	118	17	−	−	PROPN
ejpam-3976	118	18	2)n	2)n	NOUN
ejpam-3976	118	19	≤	≤	NUM
ejpam-3976	118	20	|5/2−	|5/2−	SYM
ejpam-3976	118	21	γ|	γ|	PROPN
ejpam-3976	118	22	2	2	NUM
ejpam-3976	118	23	2n−1πn	2n−1πn	NUM
ejpam-3976	118	24	+	+	CCONJ
ejpam-3976	118	25	1	1	NUM
ejpam-3976	118	26	+	+	CCONJ
ejpam-3976	118	27	|1/2−	|1/2−	PROPN
ejpam-3976	118	28	γ|	γ|	PROPN
ejpam-3976	118	29	2n−1πn	2n−1πn	NOUN
ejpam-3976	118	30	.	.	PUNCT
ejpam-3976	119	1	we	we	PRON
ejpam-3976	119	2	can	can	AUX
ejpam-3976	119	3	see	see	VERB
ejpam-3976	119	4	that	that	DET
ejpam-3976	119	5	cm	cm	NOUN
ejpam-3976	119	6	,	,	PUNCT
ejpam-3976	119	7	λ	λ	X
ejpam-3976	119	8	→	→	SYM
ejpam-3976	119	9	0	0	PROPN
ejpam-3976	119	10	as	as	ADP
ejpam-3976	119	11	n→∞	n→∞	NUM
ejpam-3976	119	12	for	for	ADP
ejpam-3976	119	13	|m	|m	NOUN
ejpam-3976	119	14	|	|	ADV
ejpam-3976	119	15	>	>	X
ejpam-3976	119	16	2	2	NUM
ejpam-3976	119	17	.	.	PUNCT
ejpam-3976	120	1	thus	thus	ADV
ejpam-3976	120	2	,	,	PUNCT
ejpam-3976	120	3	the	the	DET
ejpam-3976	120	4	tail	tail	NOUN
ejpam-3976	120	5	of	of	ADP
ejpam-3976	120	6	the	the	DET
ejpam-3976	120	7	series	series	NOUN
ejpam-3976	120	8	,	,	PUNCT
ejpam-3976	120	9	∞∑	∞∑	PROPN
ejpam-3976	120	10	k	k	NOUN
ejpam-3976	120	11	=	=	NOUN
ejpam-3976	120	12	m+1	m+1	PROPN
ejpam-3976	120	13	1	1	NUM
ejpam-3976	120	14	|µk|n	|µk|n	PUNCT
ejpam-3976	120	15	→	→	SYM
ejpam-3976	120	16	0	0	NUM
ejpam-3976	120	17	as	as	ADP
ejpam-3976	120	18	n→∞.	n→∞.	ADJ
ejpam-3976	120	19	moreover	moreover	ADV
ejpam-3976	120	20	,	,	PUNCT
ejpam-3976	120	21	for	for	ADP
ejpam-3976	120	22	fixed	fix	VERB
ejpam-3976	120	23	m	m	VERB
ejpam-3976	120	24	>	>	X
ejpam-3976	120	25	2	2	NUM
ejpam-3976	120	26	and	and	CCONJ
ejpam-3976	120	27	n	n	PRON
ejpam-3976	120	28	�	�	PROPN
ejpam-3976	120	29	0	0	NUM
ejpam-3976	120	30	,	,	PUNCT
ejpam-3976	120	31	cm	cm	NUM
ejpam-3976	120	32	,	,	PUNCT
ejpam-3976	120	33	λ	λ	PROPN
ejpam-3976	120	34	is	be	AUX
ejpam-3976	120	35	bounded	bound	VERB
ejpam-3976	120	36	and	and	CCONJ
ejpam-3976	120	37	independent	independent	ADJ
ejpam-3976	120	38	of	of	ADP
ejpam-3976	120	39	m	m	PROPN
ejpam-3976	120	40	.	.	PUNCT
ejpam-3976	121	1	hence	hence	ADV
ejpam-3976	121	2	,	,	PUNCT
ejpam-3976	121	3	we	we	PRON
ejpam-3976	121	4	can	can	AUX
ejpam-3976	121	5	replace	replace	VERB
ejpam-3976	121	6	cm	cm	NOUN
ejpam-3976	121	7	,	,	PUNCT
ejpam-3976	121	8	λ	λ	X
ejpam-3976	121	9	by	by	ADP
ejpam-3976	121	10	cλ	cλ	PROPN
ejpam-3976	121	11	.	.	PUNCT
ejpam-3976	122	1	this	this	PRON
ejpam-3976	122	2	completes	complete	VERB
ejpam-3976	122	3	the	the	DET
ejpam-3976	122	4	proof	proof	NOUN
ejpam-3976	122	5	of	of	ADP
ejpam-3976	122	6	the	the	DET
ejpam-3976	122	7	theorem	theorem	NOUN
ejpam-3976	122	8	.	.	PUNCT
ejpam-3976	123	1	when	when	SCONJ
ejpam-3976	123	2	λ	λ	X
ejpam-3976	123	3	=	=	SYM
ejpam-3976	123	4	1	1	NUM
ejpam-3976	123	5	,	,	PUNCT
ejpam-3976	123	6	log	log	VERB
ejpam-3976	123	7	λ	λ	NOUN
ejpam-3976	123	8	=	=	SYM
ejpam-3976	123	9	0	0	PROPN
ejpam-3976	123	10	and	and	CCONJ
ejpam-3976	123	11	uk	uk	PROPN
ejpam-3976	123	12	=	=	SYM
ejpam-3976	123	13	(	(	PUNCT
ejpam-3976	123	14	2k+	2k+	NUM
ejpam-3976	123	15	1)πi	1)πi	NUM
ejpam-3976	123	16	,	,	PUNCT
ejpam-3976	123	17	k	k	PROPN
ejpam-3976	123	18	∈	∈	PROPN
ejpam-3976	123	19	z.	z.	PROPN
ejpam-3976	123	20	take	take	VERB
ejpam-3976	123	21	h	h	NOUN
ejpam-3976	123	22	=	=	PUNCT
ejpam-3976	123	23	{	{	PUNCT
ejpam-3976	123	24	πi,−πi	πi,−πi	NOUN
ejpam-3976	123	25	}	}	PUNCT
ejpam-3976	123	26	.	.	PUNCT
ejpam-3976	124	1	then	then	ADV
ejpam-3976	124	2	ν	ν	X
ejpam-3976	124	3	=	=	NOUN
ejpam-3976	124	4	3π	3π	NOUN
ejpam-3976	124	5	and	and	CCONJ
ejpam-3976	124	6	the	the	DET
ejpam-3976	124	7	ordinary	ordinary	ADJ
ejpam-3976	124	8	genocchi	genocchi	NOUN
ejpam-3976	124	9	numbers	number	NOUN
ejpam-3976	124	10	gn	gn	PROPN
ejpam-3976	124	11	=	=	PUNCT
ejpam-3976	124	12	gn(0	gn(0	PROPN
ejpam-3976	124	13	;	;	PUNCT
ejpam-3976	124	14	1	1	X
ejpam-3976	124	15	)	)	PUNCT
ejpam-3976	124	16	satisfy	satisfy	NOUN
ejpam-3976	124	17	gn	gn	PROPN
ejpam-3976	124	18	2(n	2(n	NUM
ejpam-3976	124	19	!	!	PUNCT
ejpam-3976	124	20	)	)	PUNCT
ejpam-3976	125	1	=	=	PUNCT
ejpam-3976	126	1	gn(0	gn(0	NOUN
ejpam-3976	126	2	;	;	PUNCT
ejpam-3976	126	3	1	1	NUM
ejpam-3976	126	4	)	)	PUNCT
ejpam-3976	126	5	2(n	2(n	NUM
ejpam-3976	126	6	!	!	PUNCT
ejpam-3976	126	7	)	)	PUNCT
ejpam-3976	127	1	=	=	SYM
ejpam-3976	127	2	1	1	NUM
ejpam-3976	127	3	(	(	PUNCT
ejpam-3976	127	4	πi)n	πi)n	PROPN
ejpam-3976	127	5	+	+	NUM
ejpam-3976	127	6	1	1	NUM
ejpam-3976	127	7	(	(	PUNCT
ejpam-3976	127	8	−πi)n	−πi)n	PROPN
ejpam-3976	127	9	+	+	PROPN
ejpam-3976	127	10	o((3π)−n	o((3π)−n	ADV
ejpam-3976	127	11	)	)	PUNCT
ejpam-3976	127	12	.	.	PUNCT
ejpam-3976	128	1	(	(	PUNCT
ejpam-3976	128	2	2.7	2.7	NUM
ejpam-3976	128	3	)	)	PUNCT
ejpam-3976	128	4	an	an	DET
ejpam-3976	128	5	approximation	approximation	NOUN
ejpam-3976	128	6	of	of	ADP
ejpam-3976	128	7	gn(0	gn(0	NOUN
ejpam-3976	128	8	;	;	PUNCT
ejpam-3976	128	9	1	1	NUM
ejpam-3976	128	10	)	)	PUNCT
ejpam-3976	128	11	is	be	AUX
ejpam-3976	128	12	given	give	VERB
ejpam-3976	128	13	by	by	ADP
ejpam-3976	128	14	gn	gn	PROPN
ejpam-3976	128	15	2(n	2(n	NUM
ejpam-3976	128	16	!	!	PUNCT
ejpam-3976	128	17	)	)	PUNCT
ejpam-3976	129	1	≈	≈	PROPN
ejpam-3976	129	2	1	1	NUM
ejpam-3976	129	3	(	(	PUNCT
ejpam-3976	129	4	πi)n	πi)n	PROPN
ejpam-3976	129	5	+	+	PROPN
ejpam-3976	129	6	1	1	NUM
ejpam-3976	129	7	(	(	PUNCT
ejpam-3976	129	8	−πi)n	−πi)n	PROPN
ejpam-3976	129	9	.	.	PUNCT
ejpam-3976	130	1	(	(	PUNCT
ejpam-3976	130	2	2.8	2.8	NUM
ejpam-3976	130	3	)	)	PUNCT
ejpam-3976	130	4	for	for	ADP
ejpam-3976	130	5	odd	odd	ADJ
ejpam-3976	130	6	n	n	CCONJ
ejpam-3976	130	7	,	,	PUNCT
ejpam-3976	130	8	n	n	PRON
ejpam-3976	130	9	≥	≥	NOUN
ejpam-3976	130	10	3	3	NUM
ejpam-3976	130	11	,	,	PUNCT
ejpam-3976	130	12	it	it	PRON
ejpam-3976	130	13	is	be	AUX
ejpam-3976	130	14	known	know	VERB
ejpam-3976	130	15	that	that	SCONJ
ejpam-3976	130	16	gn	gn	PROPN
ejpam-3976	130	17	=	=	PUNCT
ejpam-3976	130	18	0	0	NUM
ejpam-3976	130	19	which	which	PRON
ejpam-3976	130	20	is	be	AUX
ejpam-3976	130	21	also	also	ADV
ejpam-3976	130	22	true	true	ADJ
ejpam-3976	130	23	when	when	SCONJ
ejpam-3976	130	24	we	we	PRON
ejpam-3976	130	25	use	use	VERB
ejpam-3976	130	26	(	(	PUNCT
ejpam-3976	130	27	2.8	2.8	NUM
ejpam-3976	130	28	)	)	PUNCT
ejpam-3976	130	29	.	.	PUNCT
ejpam-3976	131	1	for	for	ADP
ejpam-3976	131	2	even	even	ADV
ejpam-3976	131	3	indices	index	NOUN
ejpam-3976	131	4	,	,	PUNCT
ejpam-3976	131	5	g2n	g2n	PROPN
ejpam-3976	131	6	≈	≈	PROPN
ejpam-3976	131	7	(	(	PUNCT
ejpam-3976	131	8	−1)n4((2n	−1)n4((2n	PROPN
ejpam-3976	131	9	)	)	PUNCT
ejpam-3976	131	10	!	!	PUNCT
ejpam-3976	131	11	)	)	PUNCT
ejpam-3976	132	1	π2n	π2n	PROPN
ejpam-3976	132	2	,	,	PUNCT
ejpam-3976	132	3	n	n	X
ejpam-3976	132	4	≥	≥	NUM
ejpam-3976	132	5	2	2	NUM
ejpam-3976	132	6	(	(	PUNCT
ejpam-3976	132	7	2.9	2.9	NUM
ejpam-3976	132	8	)	)	PUNCT
ejpam-3976	132	9	taking	take	VERB
ejpam-3976	132	10	n	n	NOUN
ejpam-3976	132	11	=	=	SYM
ejpam-3976	132	12	4	4	NUM
ejpam-3976	132	13	,	,	PUNCT
ejpam-3976	132	14	g8	g8	PROPN
ejpam-3976	132	15	≈	≈	PROPN
ejpam-3976	132	16	4(8	4(8	PROPN
ejpam-3976	132	17	!	!	PUNCT
ejpam-3976	132	18	)	)	PUNCT
ejpam-3976	133	1	π8	π8	PROPN
ejpam-3976	134	1	≈	≈	PROPN
ejpam-3976	134	2	16.99	16.99	NUM
ejpam-3976	134	3	.	.	PUNCT
ejpam-3976	135	1	this	this	DET
ejpam-3976	135	2	value	value	NOUN
ejpam-3976	135	3	is	be	AUX
ejpam-3976	135	4	very	very	ADV
ejpam-3976	135	5	close	close	ADJ
ejpam-3976	135	6	to	to	ADP
ejpam-3976	135	7	the	the	DET
ejpam-3976	135	8	exact	exact	ADJ
ejpam-3976	135	9	value	value	NOUN
ejpam-3976	135	10	of	of	ADP
ejpam-3976	135	11	g8	g8	PROPN
ejpam-3976	135	12	which	which	PRON
ejpam-3976	135	13	is	be	AUX
ejpam-3976	135	14	17	17	NUM
ejpam-3976	135	15	.	.	PUNCT
ejpam-3976	136	1	it	it	PRON
ejpam-3976	136	2	is	be	AUX
ejpam-3976	136	3	proved	prove	VERB
ejpam-3976	136	4	in	in	ADP
ejpam-3976	136	5	the	the	DET
ejpam-3976	136	6	next	next	ADJ
ejpam-3976	136	7	theorem	theorem	NOUN
ejpam-3976	136	8	that	that	SCONJ
ejpam-3976	136	9	an	an	DET
ejpam-3976	136	10	asymptotic	asymptotic	ADJ
ejpam-3976	136	11	approximation	approximation	NOUN
ejpam-3976	136	12	of	of	ADP
ejpam-3976	136	13	the	the	DET
ejpam-3976	136	14	apostolgenocchi	apostolgenocchi	NOUN
ejpam-3976	136	15	polynomials	polynomial	NOUN
ejpam-3976	136	16	can	can	AUX
ejpam-3976	136	17	be	be	AUX
ejpam-3976	136	18	obtained	obtain	VERB
ejpam-3976	136	19	from	from	ADP
ejpam-3976	136	20	its	its	PRON
ejpam-3976	136	21	fourier	fourier	NOUN
ejpam-3976	136	22	series	series	NOUN
ejpam-3976	136	23	(	(	PUNCT
ejpam-3976	136	24	2.1	2.1	NUM
ejpam-3976	136	25	)	)	PUNCT
ejpam-3976	136	26	by	by	ADP
ejpam-3976	136	27	choosing	choose	VERB
ejpam-3976	136	28	an	an	DET
ejpam-3976	136	29	appropriate	appropriate	ADJ
ejpam-3976	136	30	subset	subset	NOUN
ejpam-3976	136	31	of	of	ADP
ejpam-3976	136	32	tλ	tλ	ADP
ejpam-3976	136	33	.	.	PUNCT
ejpam-3976	137	1	c.	c.	PROPN
ejpam-3976	137	2	corcino	corcino	PROPN
ejpam-3976	137	3	/	/	SYM
ejpam-3976	137	4	eur	eur	PROPN
ejpam-3976	137	5	.	.	PUNCT
ejpam-3976	138	1	j.	j.	PROPN
ejpam-3976	138	2	pure	pure	PROPN
ejpam-3976	138	3	appl	appl	PROPN
ejpam-3976	138	4	.	.	PROPN
ejpam-3976	138	5	math	math	PROPN
ejpam-3976	138	6	,	,	PUNCT
ejpam-3976	138	7	14	14	NUM
ejpam-3976	138	8	(	(	PUNCT
ejpam-3976	138	9	3	3	NUM
ejpam-3976	138	10	)	)	PUNCT
ejpam-3976	138	11	(	(	PUNCT
ejpam-3976	138	12	2021	2021	NUM
ejpam-3976	138	13	)	)	PUNCT
ejpam-3976	138	14	,	,	PUNCT
ejpam-3976	138	15	666	666	NUM
ejpam-3976	138	16	-	-	SYM
ejpam-3976	138	17	684	684	NUM
ejpam-3976	138	18	674	674	NUM
ejpam-3976	138	19	theorem	theorem	VERB
ejpam-3976	138	20	2.4	2.4	NUM
ejpam-3976	138	21	.	.	PUNCT
ejpam-3976	138	22	given	give	VERB
ejpam-3976	138	23	λ	λ	PROPN
ejpam-3976	138	24	∈	∈	PROPN
ejpam-3976	138	25	c\{0	c\{0	PROPN
ejpam-3976	138	26	}	}	PUNCT
ejpam-3976	138	27	,	,	PUNCT
ejpam-3976	138	28	let	let	VERB
ejpam-3976	138	29	h	h	PRON
ejpam-3976	138	30	be	be	AUX
ejpam-3976	138	31	a	a	DET
ejpam-3976	138	32	finite	finite	NOUN
ejpam-3976	138	33	subset	subset	NOUN
ejpam-3976	138	34	of	of	ADP
ejpam-3976	138	35	tλ	tλ	ADP
ejpam-3976	138	36	satisfying	satisfying	NOUN
ejpam-3976	138	37	max{|u|	max{|u|	NOUN
ejpam-3976	138	38	:	:	PUNCT
ejpam-3976	138	39	u	u	PROPN
ejpam-3976	138	40	∈	∈	PROPN
ejpam-3976	138	41	h	h	NOUN
ejpam-3976	138	42	}	}	PUNCT
ejpam-3976	138	43	<	<	X
ejpam-3976	138	44	min{|u|	min{|u|	NOUN
ejpam-3976	138	45	:	:	PUNCT
ejpam-3976	138	46	u	u	NOUN
ejpam-3976	138	47	∈	∈	PROPN
ejpam-3976	138	48	tλ	tλ	ADP
ejpam-3976	138	49	\h	\h	NUM
ejpam-3976	138	50	}	}	PUNCT
ejpam-3976	138	51	:	:	PUNCT
ejpam-3976	138	52	=	=	PUNCT
ejpam-3976	139	1	ν	ν	X
ejpam-3976	139	2	.	.	PROPN
ejpam-3976	139	3	for	for	ADP
ejpam-3976	139	4	all	all	DET
ejpam-3976	139	5	integers	integer	NOUN
ejpam-3976	139	6	n	n	PRON
ejpam-3976	139	7	≥	≥	NOUN
ejpam-3976	139	8	2	2	NUM
ejpam-3976	139	9	,	,	PUNCT
ejpam-3976	139	10	we	we	PRON
ejpam-3976	139	11	have	have	VERB
ejpam-3976	139	12	,	,	PUNCT
ejpam-3976	139	13	uniformly	uniformly	ADV
ejpam-3976	139	14	for	for	ADP
ejpam-3976	139	15	x	x	PUNCT
ejpam-3976	139	16	in	in	ADP
ejpam-3976	139	17	a	a	DET
ejpam-3976	139	18	compact	compact	ADJ
ejpam-3976	139	19	subset	subset	NOUN
ejpam-3976	140	1	k	k	PROPN
ejpam-3976	140	2	of	of	ADP
ejpam-3976	140	3	c	c	PROPN
ejpam-3976	140	4	,	,	PUNCT
ejpam-3976	140	5	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	140	6	)	)	PUNCT
ejpam-3976	140	7	n	n	CCONJ
ejpam-3976	140	8	!	!	PUNCT
ejpam-3976	141	1	=	=	SYM
ejpam-3976	141	2	2	2	NUM
ejpam-3976	141	3	∑	∑	PART
ejpam-3976	141	4	u	u	PROPN
ejpam-3976	141	5	∈	∈	PROPN
ejpam-3976	141	6	h	h	PROPN
ejpam-3976	141	7	eux	eux	X
ejpam-3976	141	8	un	un	PROPN
ejpam-3976	142	1	+	+	PROPN
ejpam-3976	142	2	o	o	X
ejpam-3976	142	3	(	(	PUNCT
ejpam-3976	142	4	eν|x|	eν|x|	NOUN
ejpam-3976	142	5	νn	νn	PROPN
ejpam-3976	142	6	)	)	PUNCT
ejpam-3976	142	7	,	,	PUNCT
ejpam-3976	142	8	where	where	SCONJ
ejpam-3976	142	9	the	the	DET
ejpam-3976	142	10	constant	constant	ADJ
ejpam-3976	142	11	implicit	implicit	NOUN
ejpam-3976	142	12	in	in	ADP
ejpam-3976	142	13	the	the	DET
ejpam-3976	142	14	order	order	NOUN
ejpam-3976	142	15	term	term	NOUN
ejpam-3976	142	16	depends	depend	VERB
ejpam-3976	142	17	on	on	ADP
ejpam-3976	142	18	λ	λ	PROPN
ejpam-3976	142	19	,	,	PUNCT
ejpam-3976	142	20	h	h	NOUN
ejpam-3976	142	21	and	and	CCONJ
ejpam-3976	142	22	k.	k.	PROPN
ejpam-3976	143	1	moreover	moreover	ADV
ejpam-3976	143	2	,	,	PUNCT
ejpam-3976	143	3	for	for	ADP
ejpam-3976	143	4	n	n	CCONJ
ejpam-3976	143	5	�	�	PROPN
ejpam-3976	143	6	0	0	NUM
ejpam-3976	143	7	,	,	PUNCT
ejpam-3976	143	8	this	this	DET
ejpam-3976	143	9	constant	constant	ADJ
ejpam-3976	143	10	can	can	AUX
ejpam-3976	143	11	be	be	AUX
ejpam-3976	143	12	made	make	VERB
ejpam-3976	143	13	independent	independent	ADJ
ejpam-3976	143	14	of	of	ADP
ejpam-3976	143	15	k	k	PROPN
ejpam-3976	143	16	,	,	PUNCT
ejpam-3976	143	17	equal	equal	ADJ
ejpam-3976	143	18	to	to	ADP
ejpam-3976	143	19	the	the	DET
ejpam-3976	143	20	constant	constant	NOUN
ejpam-3976	143	21	for	for	ADP
ejpam-3976	143	22	the	the	DET
ejpam-3976	143	23	apostolgenocchi	apostolgenocchi	ADJ
ejpam-3976	143	24	numbers	number	NOUN
ejpam-3976	143	25	,	,	PUNCT
ejpam-3976	143	26	corresponding	correspond	VERB
ejpam-3976	143	27	to	to	ADP
ejpam-3976	143	28	the	the	DET
ejpam-3976	143	29	case	case	NOUN
ejpam-3976	143	30	x	x	X
ejpam-3976	144	1	=	=	NOUN
ejpam-3976	144	2	0	0	X
ejpam-3976	144	3	.	.	PUNCT
ejpam-3976	145	1	proof	proof	NOUN
ejpam-3976	145	2	.	.	PUNCT
ejpam-3976	146	1	from	from	ADP
ejpam-3976	146	2	the	the	DET
ejpam-3976	146	3	generating	generate	VERB
ejpam-3976	146	4	function	function	NOUN
ejpam-3976	146	5	(	(	PUNCT
ejpam-3976	146	6	1.1	1.1	NUM
ejpam-3976	146	7	)	)	PUNCT
ejpam-3976	146	8	we	we	PRON
ejpam-3976	146	9	have	have	VERB
ejpam-3976	146	10	2ze(x+y)z	2ze(x+y)z	NUM
ejpam-3976	146	11	λez	λez	NOUN
ejpam-3976	146	12	+	+	X
ejpam-3976	146	13	1	1	NUM
ejpam-3976	146	14	=	=	SYM
ejpam-3976	146	15	∞∑	∞∑	PRON
ejpam-3976	146	16	n=0	n=0	PROPN
ejpam-3976	146	17	gn(x+	gn(x+	NOUN
ejpam-3976	146	18	y;λ	y;λ	PROPN
ejpam-3976	146	19	)	)	PUNCT
ejpam-3976	146	20	zn	zn	PROPN
ejpam-3976	146	21	n	n	PRON
ejpam-3976	146	22	!	!	PUNCT
ejpam-3976	146	23	.	.	PUNCT
ejpam-3976	147	1	the	the	DET
ejpam-3976	147	2	lhs	lhs	PROPN
ejpam-3976	147	3	can	can	AUX
ejpam-3976	147	4	be	be	AUX
ejpam-3976	147	5	written	write	VERB
ejpam-3976	147	6	2zexz	2zexz	NUM
ejpam-3976	147	7	λez	λez	NOUN
ejpam-3976	147	8	+	+	SYM
ejpam-3976	147	9	1	1	NUM
ejpam-3976	147	10	·	·	PUNCT
ejpam-3976	147	11	eyz	eyz	NOUN
ejpam-3976	148	1	=	=	PUNCT
ejpam-3976	149	1	(	(	PUNCT
ejpam-3976	149	2	∞∑	∞∑	NUM
ejpam-3976	149	3	n=0	n=0	ADJ
ejpam-3976	149	4	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	149	5	)	)	PUNCT
ejpam-3976	149	6	zn	zn	PROPN
ejpam-3976	149	7	n	n	CCONJ
ejpam-3976	149	8	!	!	PUNCT
ejpam-3976	149	9	)	)	PUNCT
ejpam-3976	150	1	(	(	PUNCT
ejpam-3976	150	2	∞∑	∞∑	NUM
ejpam-3976	150	3	n=0	n=0	NUM
ejpam-3976	150	4	(	(	PUNCT
ejpam-3976	150	5	yz)n	yz)n	PROPN
ejpam-3976	150	6	n	n	PRON
ejpam-3976	150	7	!	!	PUNCT
ejpam-3976	150	8	)	)	PUNCT
ejpam-3976	151	1	=	=	PUNCT
ejpam-3976	152	1	∞∑	∞∑	NUM
ejpam-3976	152	2	n=0	n=0	NUM
ejpam-3976	152	3	n∑	n∑	PRON
ejpam-3976	152	4	k=0	k=0	PROPN
ejpam-3976	152	5	gn−k(x;λ	gn−k(x;λ	NOUN
ejpam-3976	152	6	)	)	PUNCT
ejpam-3976	152	7	zn−k	zn−k	PROPN
ejpam-3976	152	8	(	(	PUNCT
ejpam-3976	152	9	n−	n−	NOUN
ejpam-3976	152	10	k	k	NOUN
ejpam-3976	152	11	)	)	PUNCT
ejpam-3976	152	12	!	!	PUNCT
ejpam-3976	153	1	(	(	PUNCT
ejpam-3976	153	2	yz)k	yz)k	PROPN
ejpam-3976	153	3	k	k	NOUN
ejpam-3976	153	4	!	!	PUNCT
ejpam-3976	153	5	=	=	PUNCT
ejpam-3976	154	1	∞∑	∞∑	PRON
ejpam-3976	154	2	n=0	n=0	NUM
ejpam-3976	154	3	(	(	PUNCT
ejpam-3976	154	4	n∑	n∑	NOUN
ejpam-3976	154	5	k=0	k=0	PROPN
ejpam-3976	154	6	(	(	PUNCT
ejpam-3976	154	7	n	n	CCONJ
ejpam-3976	154	8	k	k	X
ejpam-3976	154	9	)	)	PUNCT
ejpam-3976	154	10	gn−k(x;λ)yk	gn−k(x;λ)yk	NOUN
ejpam-3976	154	11	)	)	PUNCT
ejpam-3976	154	12	zn	zn	PROPN
ejpam-3976	154	13	n	n	CCONJ
ejpam-3976	154	14	!	!	PROPN
ejpam-3976	154	15	,	,	PUNCT
ejpam-3976	154	16	from	from	ADP
ejpam-3976	154	17	which	which	PRON
ejpam-3976	154	18	gn(x+	gn(x+	NOUN
ejpam-3976	154	19	y;λ	y;λ	NOUN
ejpam-3976	154	20	)	)	PUNCT
ejpam-3976	154	21	=	=	SYM
ejpam-3976	155	1	n∑	n∑	NOUN
ejpam-3976	155	2	k=0	k=0	PROPN
ejpam-3976	155	3	(	(	PUNCT
ejpam-3976	155	4	n	n	CCONJ
ejpam-3976	155	5	k	k	ADJ
ejpam-3976	155	6	)	)	PUNCT
ejpam-3976	155	7	gn−k(x;λ)yk	gn−k(x;λ)yk	PROPN
ejpam-3976	155	8	.	.	PUNCT
ejpam-3976	156	1	for	for	ADP
ejpam-3976	156	2	z	z	PROPN
ejpam-3976	156	3	∈	∈	PROPN
ejpam-3976	156	4	c	c	NOUN
ejpam-3976	156	5	,	,	PUNCT
ejpam-3976	156	6	writing	write	VERB
ejpam-3976	156	7	z	z	NOUN
ejpam-3976	156	8	=	=	SYM
ejpam-3976	156	9	0	0	PUNCT
ejpam-3976	157	1	+	+	CCONJ
ejpam-3976	157	2	z	z	NOUN
ejpam-3976	157	3	(	(	PUNCT
ejpam-3976	157	4	here	here	ADV
ejpam-3976	157	5	y	y	PROPN
ejpam-3976	157	6	=	=	SYM
ejpam-3976	157	7	z	z	PROPN
ejpam-3976	157	8	,	,	PUNCT
ejpam-3976	157	9	x	x	SYM
ejpam-3976	157	10	=	=	NOUN
ejpam-3976	157	11	0	0	NUM
ejpam-3976	157	12	)	)	PUNCT
ejpam-3976	157	13	,	,	PUNCT
ejpam-3976	157	14	gn(z;λ	gn(z;λ	PROPN
ejpam-3976	157	15	)	)	PUNCT
ejpam-3976	158	1	=	=	SYM
ejpam-3976	158	2	n∑	n∑	NOUN
ejpam-3976	158	3	k=0	k=0	PROPN
ejpam-3976	158	4	(	(	PUNCT
ejpam-3976	158	5	n	n	CCONJ
ejpam-3976	158	6	k	k	PROPN
ejpam-3976	158	7	)	)	PUNCT
ejpam-3976	158	8	gn−k(0	gn−k(0	PROPN
ejpam-3976	158	9	,	,	PUNCT
ejpam-3976	158	10	λ)zk	λ)zk	PROPN
ejpam-3976	158	11	,	,	PUNCT
ejpam-3976	158	12	gn(z;λ	gn(z;λ	PROPN
ejpam-3976	158	13	)	)	PUNCT
ejpam-3976	158	14	n	n	CCONJ
ejpam-3976	158	15	!	!	PUNCT
ejpam-3976	158	16	=	=	PUNCT
ejpam-3976	159	1	n∑	n∑	PROPN
ejpam-3976	159	2	k=0	k=0	PROPN
ejpam-3976	159	3	gn−k(0;λ	gn−k(0;λ	PROPN
ejpam-3976	159	4	)	)	PUNCT
ejpam-3976	159	5	(	(	PUNCT
ejpam-3976	159	6	n−	n−	NOUN
ejpam-3976	159	7	k	k	NOUN
ejpam-3976	159	8	)	)	PUNCT
ejpam-3976	159	9	!	!	PUNCT
ejpam-3976	160	1	zk	zk	PROPN
ejpam-3976	161	1	k	k	X
ejpam-3976	161	2	!	!	PUNCT
ejpam-3976	162	1	=	=	SYM
ejpam-3976	162	2	2	2	NUM
ejpam-3976	162	3	n∑	n∑	NOUN
ejpam-3976	162	4	k=0	k=0	PROPN
ejpam-3976	162	5	(	(	PUNCT
ejpam-3976	162	6	∑	∑	PUNCT
ejpam-3976	162	7	u	u	NOUN
ejpam-3976	162	8	∈	∈	PROPN
ejpam-3976	162	9	h	h	NOUN
ejpam-3976	162	10	1	1	NUM
ejpam-3976	162	11	un−k	un−k	ADJ
ejpam-3976	162	12	+	+	NOUN
ejpam-3976	162	13	o(ν−(n−k	o(ν−(n−k	NOUN
ejpam-3976	162	14	)	)	PUNCT
ejpam-3976	162	15	)	)	PUNCT
ejpam-3976	162	16	)	)	PUNCT
ejpam-3976	163	1	zk	zk	PROPN
ejpam-3976	164	1	k	k	X
ejpam-3976	164	2	!	!	PUNCT
ejpam-3976	164	3	(	(	PUNCT
ejpam-3976	164	4	by	by	ADP
ejpam-3976	164	5	theorem	theorem	NOUN
ejpam-3976	164	6	2.3	2.3	NUM
ejpam-3976	164	7	)	)	PUNCT
ejpam-3976	164	8	=	=	SYM
ejpam-3976	164	9	2	2	NUM
ejpam-3976	164	10	n∑	n∑	NOUN
ejpam-3976	164	11	k=0	k=0	PROPN
ejpam-3976	164	12	(	(	PUNCT
ejpam-3976	164	13	∑	∑	ADP
ejpam-3976	164	14	u∈	u∈	VERB
ejpam-3976	164	15	h	h	NOUN
ejpam-3976	164	16	1	1	NUM
ejpam-3976	164	17	un−k	un−k	PROPN
ejpam-3976	164	18	zk	zk	PROPN
ejpam-3976	164	19	k	k	PROPN
ejpam-3976	164	20	!	!	PUNCT
ejpam-3976	164	21	)	)	PUNCT
ejpam-3976	165	1	+	+	CCONJ
ejpam-3976	165	2	n∑	n∑	PROPN
ejpam-3976	165	3	k=0	k=0	PROPN
ejpam-3976	165	4	o(ν−(n−k	o(ν−(n−k	PROPN
ejpam-3976	165	5	)	)	PUNCT
ejpam-3976	165	6	)	)	PUNCT
ejpam-3976	166	1	zk	zk	PROPN
ejpam-3976	167	1	k	k	X
ejpam-3976	167	2	!	!	PROPN
ejpam-3976	167	3	,	,	PUNCT
ejpam-3976	167	4	c.	c.	PROPN
ejpam-3976	167	5	corcino	corcino	PROPN
ejpam-3976	167	6	/	/	SYM
ejpam-3976	167	7	eur	eur	PROPN
ejpam-3976	167	8	.	.	PUNCT
ejpam-3976	168	1	j.	j.	PROPN
ejpam-3976	168	2	pure	pure	PROPN
ejpam-3976	168	3	appl	appl	PROPN
ejpam-3976	168	4	.	.	PROPN
ejpam-3976	168	5	math	math	PROPN
ejpam-3976	168	6	,	,	PUNCT
ejpam-3976	168	7	14	14	NUM
ejpam-3976	168	8	(	(	PUNCT
ejpam-3976	168	9	3	3	NUM
ejpam-3976	168	10	)	)	PUNCT
ejpam-3976	168	11	(	(	PUNCT
ejpam-3976	168	12	2021	2021	NUM
ejpam-3976	168	13	)	)	PUNCT
ejpam-3976	168	14	,	,	PUNCT
ejpam-3976	168	15	666	666	NUM
ejpam-3976	168	16	-	-	SYM
ejpam-3976	168	17	684	684	NUM
ejpam-3976	168	18	675	675	NUM
ejpam-3976	168	19	where	where	SCONJ
ejpam-3976	168	20	the	the	DET
ejpam-3976	168	21	implicit	implicit	ADJ
ejpam-3976	168	22	constant	constant	ADJ
ejpam-3976	168	23	c	c	NOUN
ejpam-3976	168	24	in	in	ADP
ejpam-3976	168	25	the	the	DET
ejpam-3976	168	26	order	order	NOUN
ejpam-3976	168	27	term	term	NOUN
ejpam-3976	168	28	is	be	AUX
ejpam-3976	169	1	that	that	SCONJ
ejpam-3976	169	2	corresponding	correspond	VERB
ejpam-3976	169	3	to	to	ADP
ejpam-3976	169	4	z	z	NOUN
ejpam-3976	169	5	=	=	SYM
ejpam-3976	169	6	0	0	PUNCT
ejpam-3976	169	7	and	and	CCONJ
ejpam-3976	169	8	only	only	ADV
ejpam-3976	169	9	depends	depend	VERB
ejpam-3976	169	10	on	on	ADP
ejpam-3976	169	11	h	h	NOUN
ejpam-3976	169	12	and	and	CCONJ
ejpam-3976	169	13	λ	λ	PROPN
ejpam-3976	169	14	.	.	PROPN
ejpam-3976	169	15	note	note	PROPN
ejpam-3976	169	16	also	also	ADV
ejpam-3976	169	17	that∣∣∣∣∣	that∣∣∣∣∣	PROPN
ejpam-3976	169	18	n∑	n∑	PROPN
ejpam-3976	169	19	k=0	k=0	PROPN
ejpam-3976	169	20	o(ν−n+k	o(ν−n+k	X
ejpam-3976	169	21	)	)	PUNCT
ejpam-3976	169	22	zk	zk	PROPN
ejpam-3976	169	23	k	k	PROPN
ejpam-3976	169	24	!	!	PUNCT
ejpam-3976	170	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-3976	170	2	≤	≤	NOUN
ejpam-3976	170	3	n∑	n∑	NOUN
ejpam-3976	170	4	k=0	k=0	PROPN
ejpam-3976	171	1	cν−n+k	cν−n+k	AUX
ejpam-3976	171	2	|zk|	|zk|	VERB
ejpam-3976	171	3	k	k	NOUN
ejpam-3976	171	4	!	!	PUNCT
ejpam-3976	172	1	=	=	PUNCT
ejpam-3976	172	2	cν−n	cν−n	PROPN
ejpam-3976	172	3	n∑	n∑	NOUN
ejpam-3976	172	4	k=0	k=0	PROPN
ejpam-3976	172	5	νk	νk	NOUN
ejpam-3976	172	6	|zk|	|zk|	PROPN
ejpam-3976	172	7	k	k	NOUN
ejpam-3976	172	8	!	!	PUNCT
ejpam-3976	172	9	≤	≤	NUM
ejpam-3976	172	10	cv−nen(ν|z|	cv−nen(ν|z|	NOUN
ejpam-3976	172	11	)	)	PUNCT
ejpam-3976	172	12	,	,	PUNCT
ejpam-3976	172	13	where	where	SCONJ
ejpam-3976	172	14	en	en	ADV
ejpam-3976	172	15	=	=	SYM
ejpam-3976	172	16	∑n	∑n	PROPN
ejpam-3976	172	17	k=0	k=0	PROPN
ejpam-3976	172	18	wk	wk	ADP
ejpam-3976	173	1	k	k	PROPN
ejpam-3976	173	2	!	!	PUNCT
ejpam-3976	173	3	.	.	PUNCT
ejpam-3976	174	1	to	to	PART
ejpam-3976	174	2	prove	prove	VERB
ejpam-3976	174	3	the	the	DET
ejpam-3976	174	4	theorem	theorem	NOUN
ejpam-3976	174	5	,	,	PUNCT
ejpam-3976	174	6	it	it	PRON
ejpam-3976	174	7	remains	remain	VERB
ejpam-3976	174	8	to	to	PART
ejpam-3976	174	9	show	show	VERB
ejpam-3976	174	10	that	that	SCONJ
ejpam-3976	174	11	e∗n(uz	e∗n(uz	NOUN
ejpam-3976	174	12	)	)	PUNCT
ejpam-3976	174	13	un	un	PROPN
ejpam-3976	175	1	=	=	PROPN
ejpam-3976	175	2	euz	euz	NOUN
ejpam-3976	175	3	−	−	PROPN
ejpam-3976	175	4	en(uz	en(uz	PROPN
ejpam-3976	175	5	)	)	PUNCT
ejpam-3976	175	6	un	un	PROPN
ejpam-3976	175	7	is	be	AUX
ejpam-3976	175	8	bounded	bound	VERB
ejpam-3976	175	9	.	.	PUNCT
ejpam-3976	176	1	using	use	VERB
ejpam-3976	176	2	mvt	mvt	PROPN
ejpam-3976	176	3	for	for	ADP
ejpam-3976	176	4	banach	banach	NOUN
ejpam-3976	176	5	spaces	space	NOUN
ejpam-3976	176	6	(	(	PUNCT
ejpam-3976	176	7	see	see	VERB
ejpam-3976	176	8	also	also	ADV
ejpam-3976	176	9	[	[	X
ejpam-3976	176	10	15	15	NUM
ejpam-3976	176	11	]	]	SYM
ejpam-3976	176	12	)	)	PUNCT
ejpam-3976	176	13	e∗n(w	e∗n(w	X
ejpam-3976	176	14	)	)	PUNCT
ejpam-3976	176	15	=	=	SYM
ejpam-3976	176	16	wn+1	wn+1	X
ejpam-3976	176	17	(	(	PUNCT
ejpam-3976	176	18	n+	n+	NOUN
ejpam-3976	176	19	1	1	NUM
ejpam-3976	176	20	)	)	PUNCT
ejpam-3976	176	21	!	!	PUNCT
ejpam-3976	177	1	+	+	CCONJ
ejpam-3976	177	2	wn+2	wn+2	NOUN
ejpam-3976	177	3	(	(	PUNCT
ejpam-3976	177	4	n+	n+	NOUN
ejpam-3976	177	5	2	2	NUM
ejpam-3976	177	6	)	)	PUNCT
ejpam-3976	177	7	!	!	PUNCT
ejpam-3976	178	1	+	+	CCONJ
ejpam-3976	178	2	·	·	PUNCT
ejpam-3976	178	3	·	·	PUNCT
ejpam-3976	178	4	·	·	PUNCT
ejpam-3976	178	5	=	=	PUNCT
ejpam-3976	178	6	wn+1	wn+1	X
ejpam-3976	178	7	(	(	PUNCT
ejpam-3976	178	8	n+	n+	NOUN
ejpam-3976	178	9	1	1	NUM
ejpam-3976	178	10	)	)	PUNCT
ejpam-3976	178	11	!	!	PUNCT
ejpam-3976	178	12	{	{	PUNCT
ejpam-3976	179	1	1	1	NUM
ejpam-3976	179	2	+	+	X
ejpam-3976	179	3	w	w	VERB
ejpam-3976	179	4	n+	n+	ADJ
ejpam-3976	179	5	2	2	NUM
ejpam-3976	179	6	+	+	NOUN
ejpam-3976	179	7	w2	w2	NOUN
ejpam-3976	179	8	(	(	PUNCT
ejpam-3976	179	9	n+	n+	NOUN
ejpam-3976	179	10	3)(n+	3)(n+	NUM
ejpam-3976	179	11	2	2	NUM
ejpam-3976	179	12	)	)	PUNCT
ejpam-3976	179	13	+	+	CCONJ
ejpam-3976	179	14	·	·	PUNCT
ejpam-3976	179	15	·	·	PUNCT
ejpam-3976	179	16	·	·	PUNCT
ejpam-3976	179	17	}	}	PUNCT
ejpam-3976	179	18	,	,	PUNCT
ejpam-3976	179	19	from	from	ADP
ejpam-3976	179	20	which	which	PRON
ejpam-3976	179	21	|e∗n(w)|	|e∗n(w)|	ADP
ejpam-3976	179	22	≤	≤	NUM
ejpam-3976	179	23	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	179	24	wn+1	wn+1	NOUN
ejpam-3976	179	25	(	(	PUNCT
ejpam-3976	179	26	n+	n+	NOUN
ejpam-3976	179	27	1	1	NUM
ejpam-3976	179	28	)	)	PUNCT
ejpam-3976	179	29	!	!	PUNCT
ejpam-3976	180	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	180	2	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-3976	180	3	+	+	CCONJ
ejpam-3976	180	4	w	w	NOUN
ejpam-3976	180	5	n+	n+	ADJ
ejpam-3976	180	6	2	2	NUM
ejpam-3976	180	7	+	+	NOUN
ejpam-3976	180	8	w2	w2	NOUN
ejpam-3976	180	9	(	(	PUNCT
ejpam-3976	180	10	n+	n+	NOUN
ejpam-3976	180	11	3)(n+	3)(n+	NUM
ejpam-3976	180	12	2	2	NUM
ejpam-3976	180	13	)	)	PUNCT
ejpam-3976	180	14	+	+	NUM
ejpam-3976	180	15	·	·	PUNCT
ejpam-3976	180	16	·	·	PUNCT
ejpam-3976	180	17	·	·	PUNCT
ejpam-3976	180	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3976	180	19	≤	≤	NOUN
ejpam-3976	180	20	|w|	|w|	VERB
ejpam-3976	180	21	n+1	n+1	PROPN
ejpam-3976	180	22	(	(	PUNCT
ejpam-3976	180	23	n+	n+	NOUN
ejpam-3976	180	24	1	1	NUM
ejpam-3976	180	25	)	)	PUNCT
ejpam-3976	180	26	!	!	PUNCT
ejpam-3976	181	1	ere+(w	ere+(w	PROPN
ejpam-3976	181	2	)	)	PUNCT
ejpam-3976	181	3	,	,	PUNCT
ejpam-3976	181	4	where	where	SCONJ
ejpam-3976	181	5	re+(w	re+(w	NOUN
ejpam-3976	181	6	)	)	PUNCT
ejpam-3976	181	7	=	=	SYM
ejpam-3976	181	8	max{re(w	max{re(w	PROPN
ejpam-3976	181	9	)	)	PUNCT
ejpam-3976	181	10	,	,	PUNCT
ejpam-3976	181	11	0	0	NUM
ejpam-3976	181	12	}	}	PUNCT
ejpam-3976	181	13	.	.	PUNCT
ejpam-3976	182	1	since	since	SCONJ
ejpam-3976	182	2	|u|	|u|	PROPN
ejpam-3976	182	3	≤	≤	NOUN
ejpam-3976	182	4	ν	ν	NOUN
ejpam-3976	182	5	,	,	PUNCT
ejpam-3976	182	6	for	for	ADP
ejpam-3976	182	7	all	all	DET
ejpam-3976	182	8	u	u	PROPN
ejpam-3976	182	9	∈	∈	PROPN
ejpam-3976	182	10	h	h	NOUN
ejpam-3976	182	11	,	,	PUNCT
ejpam-3976	182	12	we	we	PRON
ejpam-3976	182	13	have	have	VERB
ejpam-3976	182	14	|e∗n(uz)|	|e∗n(uz)|	NOUN
ejpam-3976	182	15	|un|	|un|	VERB
ejpam-3976	182	16	≤	≤	NUM
ejpam-3976	182	17	e|uz||uz|n+1	e|uz||uz|n+1	PROPN
ejpam-3976	182	18	|un|(n+	|un|(n+	NOUN
ejpam-3976	182	19	1	1	NUM
ejpam-3976	182	20	)	)	PUNCT
ejpam-3976	182	21	!	!	PUNCT
ejpam-3976	183	1	=	=	PUNCT
ejpam-3976	183	2	|u|e|uz|	|u|e|uz|	PROPN
ejpam-3976	183	3	|z	|z	X
ejpam-3976	183	4	n+1|	n+1|	PROPN
ejpam-3976	183	5	(	(	PUNCT
ejpam-3976	183	6	n+	n+	NOUN
ejpam-3976	183	7	1	1	NUM
ejpam-3976	183	8	)	)	PUNCT
ejpam-3976	183	9	!	!	PUNCT
ejpam-3976	184	1	<	<	X
ejpam-3976	184	2	νeν|z|	νeν|z|	NOUN
ejpam-3976	184	3	|z|n+1	|z|n+1	X
ejpam-3976	184	4	(	(	PUNCT
ejpam-3976	184	5	n+	n+	NOUN
ejpam-3976	184	6	1	1	NUM
ejpam-3976	184	7	)	)	PUNCT
ejpam-3976	184	8	!	!	PUNCT
ejpam-3976	185	1	,	,	PUNCT
ejpam-3976	185	2	so	so	SCONJ
ejpam-3976	185	3	that	that	SCONJ
ejpam-3976	185	4	∣∣∣∣∣∑	∣∣∣∣∣∑	NOUN
ejpam-3976	185	5	u∈h	u∈h	ADJ
ejpam-3976	185	6	e∗n(uz	e∗n(uz	NOUN
ejpam-3976	185	7	)	)	PUNCT
ejpam-3976	185	8	un	un	PROPN
ejpam-3976	186	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3976	186	2	≤	≤	PROPN
ejpam-3976	186	3	∑	∑	PUNCT
ejpam-3976	186	4	u	u	NOUN
ejpam-3976	186	5	∈	∈	PROPN
ejpam-3976	186	6	h	h	NOUN
ejpam-3976	187	1	|e∗n(uz)|	|e∗n(uz)|	PROPN
ejpam-3976	187	2	|un|	|un|	VERB
ejpam-3976	187	3	c.	c.	PROPN
ejpam-3976	187	4	corcino	corcino	PROPN
ejpam-3976	187	5	/	/	SYM
ejpam-3976	187	6	eur	eur	PROPN
ejpam-3976	187	7	.	.	PUNCT
ejpam-3976	188	1	j.	j.	PROPN
ejpam-3976	188	2	pure	pure	PROPN
ejpam-3976	188	3	appl	appl	PROPN
ejpam-3976	188	4	.	.	PROPN
ejpam-3976	188	5	math	math	PROPN
ejpam-3976	188	6	,	,	PUNCT
ejpam-3976	188	7	14	14	NUM
ejpam-3976	188	8	(	(	PUNCT
ejpam-3976	188	9	3	3	NUM
ejpam-3976	188	10	)	)	PUNCT
ejpam-3976	188	11	(	(	PUNCT
ejpam-3976	188	12	2021	2021	NUM
ejpam-3976	188	13	)	)	PUNCT
ejpam-3976	188	14	,	,	PUNCT
ejpam-3976	188	15	666	666	NUM
ejpam-3976	188	16	-	-	SYM
ejpam-3976	188	17	684	684	NUM
ejpam-3976	188	18	676	676	NUM
ejpam-3976	188	19	<	<	NOUN
ejpam-3976	188	20	#	#	SYM
ejpam-3976	188	21	hνeν|z|	hνeν|z|	NOUN
ejpam-3976	188	22	|z|n+1	|z|n+1	X
ejpam-3976	188	23	(	(	PUNCT
ejpam-3976	188	24	n+	n+	NOUN
ejpam-3976	188	25	1	1	NUM
ejpam-3976	188	26	)	)	PUNCT
ejpam-3976	188	27	!	!	PUNCT
ejpam-3976	189	1	,	,	PUNCT
ejpam-3976	189	2	where	where	SCONJ
ejpam-3976	189	3	#	#	NOUN
ejpam-3976	189	4	h	h	NOUN
ejpam-3976	189	5	=	=	NOUN
ejpam-3976	189	6	no	no	INTJ
ejpam-3976	189	7	.	.	PUNCT
ejpam-3976	190	1	of	of	ADP
ejpam-3976	190	2	elements	element	NOUN
ejpam-3976	190	3	in	in	ADP
ejpam-3976	190	4	h.	h.	PROPN
ejpam-3976	190	5	we	we	PRON
ejpam-3976	190	6	give	give	VERB
ejpam-3976	190	7	the	the	DET
ejpam-3976	190	8	argument	argument	NOUN
ejpam-3976	190	9	that	that	SCONJ
ejpam-3976	190	10	#	#	SYM
ejpam-3976	190	11	hνeν|z|	hνeν|z|	NOUN
ejpam-3976	190	12	|z|n+1	|z|n+1	X
ejpam-3976	190	13	(	(	PUNCT
ejpam-3976	190	14	n+	n+	NOUN
ejpam-3976	190	15	1	1	NUM
ejpam-3976	190	16	)	)	PUNCT
ejpam-3976	190	17	!	!	PUNCT
ejpam-3976	191	1	<	<	X
ejpam-3976	192	1	ceν|z|ν−n	ceν|z|ν−n	NOUN
ejpam-3976	192	2	if	if	SCONJ
ejpam-3976	192	3	#	#	SYM
ejpam-3976	192	4	h	h	NOUN
ejpam-3976	192	5	(	(	PUNCT
ejpam-3976	192	6	ν|z|)n+1	ν|z|)n+1	PROPN
ejpam-3976	192	7	(	(	PUNCT
ejpam-3976	192	8	n+	n+	NOUN
ejpam-3976	192	9	1	1	NUM
ejpam-3976	192	10	)	)	PUNCT
ejpam-3976	192	11	!	!	PUNCT
ejpam-3976	193	1	<	<	X
ejpam-3976	194	1	c	c	X
ejpam-3976	194	2	,	,	PUNCT
ejpam-3976	194	3	which	which	PRON
ejpam-3976	194	4	certainly	certainly	ADV
ejpam-3976	194	5	holds	hold	VERB
ejpam-3976	194	6	for	for	ADP
ejpam-3976	194	7	n	n	X
ejpam-3976	194	8	�	�	PROPN
ejpam-3976	194	9	0	0	NUM
ejpam-3976	194	10	,	,	PUNCT
ejpam-3976	194	11	uniformly	uniformly	ADV
ejpam-3976	194	12	for	for	ADP
ejpam-3976	194	13	z	z	NOUN
ejpam-3976	194	14	in	in	ADP
ejpam-3976	194	15	a	a	DET
ejpam-3976	194	16	compact	compact	ADJ
ejpam-3976	194	17	subset	subset	NOUN
ejpam-3976	194	18	k	k	PROPN
ejpam-3976	194	19	⊂	⊂	PROPN
ejpam-3976	194	20	c.	c.	PROPN
ejpam-3976	194	21	corollary	corollary	PROPN
ejpam-3976	194	22	2.5	2.5	NUM
ejpam-3976	194	23	.	.	PUNCT
ejpam-3976	195	1	let	let	VERB
ejpam-3976	195	2	k	k	PRON
ejpam-3976	195	3	be	be	AUX
ejpam-3976	195	4	an	an	DET
ejpam-3976	195	5	arbitrary	arbitrary	ADJ
ejpam-3976	195	6	compact	compact	ADJ
ejpam-3976	195	7	subset	subset	NOUN
ejpam-3976	195	8	of	of	ADP
ejpam-3976	195	9	c.	c.	PROPN
ejpam-3976	195	10	the	the	DET
ejpam-3976	195	11	genocchi	genocchi	PROPN
ejpam-3976	195	12	polynomials	polynomial	NOUN
ejpam-3976	195	13	satisfy	satisfy	VERB
ejpam-3976	195	14	uniformly	uniformly	ADV
ejpam-3976	195	15	on	on	ADP
ejpam-3976	195	16	k	k	PROPN
ejpam-3976	195	17	the	the	DET
ejpam-3976	195	18	estimates	estimate	NOUN
ejpam-3976	195	19	g2n(x	g2n(x	PROPN
ejpam-3976	195	20	)	)	PUNCT
ejpam-3976	195	21	(	(	PUNCT
ejpam-3976	195	22	2n	2n	NUM
ejpam-3976	195	23	)	)	PUNCT
ejpam-3976	195	24	!	!	PUNCT
ejpam-3976	196	1	=	=	PUNCT
ejpam-3976	196	2	(	(	PUNCT
ejpam-3976	196	3	−1)n	−1)n	PROPN
ejpam-3976	196	4	4	4	NUM
ejpam-3976	196	5	cosπx	cosπx	NOUN
ejpam-3976	196	6	π2n	π2n	PROPN
ejpam-3976	197	1	+	+	ADP
ejpam-3976	197	2	o	o	X
ejpam-3976	197	3	(	(	PUNCT
ejpam-3976	197	4	e3π|x|	e3π|x|	X
ejpam-3976	197	5	(	(	PUNCT
ejpam-3976	197	6	3π)n	3π)n	NUM
ejpam-3976	197	7	)	)	PUNCT
ejpam-3976	197	8	,	,	PUNCT
ejpam-3976	197	9	n	n	X
ejpam-3976	197	10	≥	≥	NOUN
ejpam-3976	197	11	2	2	NUM
ejpam-3976	197	12	,	,	PUNCT
ejpam-3976	197	13	g2n+1(x	g2n+1(x	NUM
ejpam-3976	197	14	)	)	PUNCT
ejpam-3976	197	15	(	(	PUNCT
ejpam-3976	197	16	2n+	2n+	NUM
ejpam-3976	197	17	1	1	NUM
ejpam-3976	197	18	)	)	PUNCT
ejpam-3976	197	19	!	!	PUNCT
ejpam-3976	198	1	=	=	PUNCT
ejpam-3976	198	2	(	(	PUNCT
ejpam-3976	198	3	−1)n	−1)n	PROPN
ejpam-3976	198	4	4	4	NUM
ejpam-3976	198	5	sinπx	sinπx	NOUN
ejpam-3976	198	6	π2n+1	π2n+1	NOUN
ejpam-3976	198	7	+	+	NOUN
ejpam-3976	198	8	o	o	X
ejpam-3976	198	9	(	(	PUNCT
ejpam-3976	198	10	e3π|x|	e3π|x|	X
ejpam-3976	198	11	(	(	PUNCT
ejpam-3976	198	12	3π)n	3π)n	NUM
ejpam-3976	198	13	)	)	PUNCT
ejpam-3976	198	14	,	,	PUNCT
ejpam-3976	198	15	n	n	X
ejpam-3976	198	16	≥	≥	NOUN
ejpam-3976	198	17	3	3	NUM
ejpam-3976	198	18	,	,	PUNCT
ejpam-3976	198	19	where	where	SCONJ
ejpam-3976	198	20	the	the	DET
ejpam-3976	198	21	implicit	implicit	ADJ
ejpam-3976	198	22	constant	constant	ADJ
ejpam-3976	198	23	in	in	ADP
ejpam-3976	198	24	the	the	DET
ejpam-3976	198	25	order	order	NOUN
ejpam-3976	198	26	term	term	NOUN
ejpam-3976	198	27	depends	depend	VERB
ejpam-3976	198	28	on	on	ADP
ejpam-3976	198	29	the	the	DET
ejpam-3976	198	30	set	set	NOUN
ejpam-3976	198	31	k.	k.	PROPN
ejpam-3976	198	32	moreover	moreover	ADV
ejpam-3976	198	33	,	,	PUNCT
ejpam-3976	198	34	for	for	ADP
ejpam-3976	198	35	n	n	PRON
ejpam-3976	198	36	�	�	PROPN
ejpam-3976	198	37	0	0	NUM
ejpam-3976	198	38	,	,	PUNCT
ejpam-3976	198	39	this	this	DET
ejpam-3976	198	40	constant	constant	ADJ
ejpam-3976	198	41	can	can	AUX
ejpam-3976	198	42	be	be	AUX
ejpam-3976	198	43	made	make	VERB
ejpam-3976	198	44	independent	independent	ADJ
ejpam-3976	198	45	of	of	ADP
ejpam-3976	198	46	k	k	PROPN
ejpam-3976	198	47	,	,	PUNCT
ejpam-3976	198	48	equal	equal	ADJ
ejpam-3976	198	49	to	to	ADP
ejpam-3976	198	50	the	the	DET
ejpam-3976	198	51	constant	constant	NOUN
ejpam-3976	198	52	for	for	ADP
ejpam-3976	198	53	the	the	DET
ejpam-3976	198	54	genocchi	genocchi	PROPN
ejpam-3976	198	55	numbers	number	NOUN
ejpam-3976	198	56	,	,	PUNCT
ejpam-3976	198	57	corresponding	correspond	VERB
ejpam-3976	198	58	to	to	ADP
ejpam-3976	198	59	the	the	DET
ejpam-3976	198	60	case	case	NOUN
ejpam-3976	198	61	x	x	X
ejpam-3976	199	1	=	=	NOUN
ejpam-3976	199	2	0	0	X
ejpam-3976	199	3	.	.	PUNCT
ejpam-3976	200	1	proof	proof	NOUN
ejpam-3976	200	2	.	.	PUNCT
ejpam-3976	201	1	the	the	DET
ejpam-3976	201	2	genocchi	genocchi	PROPN
ejpam-3976	201	3	polynomials	polynomial	NOUN
ejpam-3976	201	4	correspond	correspond	VERB
ejpam-3976	201	5	to	to	ADP
ejpam-3976	201	6	the	the	DET
ejpam-3976	201	7	case	case	NOUN
ejpam-3976	201	8	λ	λ	X
ejpam-3976	201	9	=	=	SYM
ejpam-3976	201	10	1	1	NUM
ejpam-3976	201	11	so	so	SCONJ
ejpam-3976	201	12	that	that	SCONJ
ejpam-3976	201	13	uk	uk	PROPN
ejpam-3976	201	14	=	=	SYM
ejpam-3976	201	15	(	(	PUNCT
ejpam-3976	201	16	2k+1)πi	2k+1)πi	NUM
ejpam-3976	201	17	,	,	PUNCT
ejpam-3976	201	18	for	for	ADP
ejpam-3976	201	19	k	k	PROPN
ejpam-3976	201	20	∈	∈	PROPN
ejpam-3976	201	21	z.	z.	PROPN
ejpam-3976	201	22	thus	thus	ADV
ejpam-3976	201	23	,	,	PUNCT
ejpam-3976	201	24	t1	t1	NOUN
ejpam-3976	201	25	=	=	PUNCT
ejpam-3976	201	26	{	{	PUNCT
ejpam-3976	201	27	(	(	PUNCT
ejpam-3976	201	28	2k	2k	NOUN
ejpam-3976	202	1	+	+	CCONJ
ejpam-3976	203	1	1)πi	1)πi	NUM
ejpam-3976	203	2	:	:	PUNCT
ejpam-3976	203	3	k	k	PROPN
ejpam-3976	203	4	∈	∈	PROPN
ejpam-3976	203	5	z	z	X
ejpam-3976	203	6	}	}	PUNCT
ejpam-3976	203	7	.	.	PUNCT
ejpam-3976	204	1	taking	take	VERB
ejpam-3976	204	2	h	h	NOUN
ejpam-3976	204	3	=	=	PRON
ejpam-3976	204	4	{	{	PUNCT
ejpam-3976	204	5	(	(	PUNCT
ejpam-3976	204	6	2k	2k	NOUN
ejpam-3976	204	7	+	+	CCONJ
ejpam-3976	205	1	1)πi	1)πi	NUM
ejpam-3976	205	2	|	|	ADV
ejpam-3976	205	3	k	k	PROPN
ejpam-3976	205	4	=	=	SYM
ejpam-3976	205	5	−1	−1	NOUN
ejpam-3976	205	6	,	,	PUNCT
ejpam-3976	205	7	0	0	NUM
ejpam-3976	205	8	}	}	PUNCT
ejpam-3976	205	9	=	=	PRON
ejpam-3976	205	10	{	{	PUNCT
ejpam-3976	205	11	−πi	−πi	NOUN
ejpam-3976	205	12	,	,	PUNCT
ejpam-3976	205	13	πi	πi	ADV
ejpam-3976	205	14	}	}	PUNCT
ejpam-3976	205	15	,	,	PUNCT
ejpam-3976	205	16	then	then	ADV
ejpam-3976	205	17	ν	ν	X
ejpam-3976	205	18	=	=	SYM
ejpam-3976	205	19	|3πi|	|3πi|	NUM
ejpam-3976	205	20	=	=	NOUN
ejpam-3976	205	21	3π	3π	NOUN
ejpam-3976	205	22	.	.	PUNCT
ejpam-3976	206	1	from	from	ADP
ejpam-3976	206	2	theorem	theorem	ADJ
ejpam-3976	206	3	2.4	2.4	NUM
ejpam-3976	206	4	,	,	PUNCT
ejpam-3976	206	5	gn(x	gn(x	CCONJ
ejpam-3976	206	6	;	;	PUNCT
ejpam-3976	206	7	1	1	X
ejpam-3976	206	8	)	)	PUNCT
ejpam-3976	206	9	n	n	CCONJ
ejpam-3976	206	10	!	!	PUNCT
ejpam-3976	207	1	=	=	SYM
ejpam-3976	207	2	2	2	NUM
ejpam-3976	207	3	∑	∑	PROPN
ejpam-3976	207	4	u∈h	u∈h	PROPN
ejpam-3976	207	5	eux	eux	X
ejpam-3976	207	6	un	un	PROPN
ejpam-3976	208	1	+	+	PROPN
ejpam-3976	208	2	o	o	X
ejpam-3976	208	3	(	(	PUNCT
ejpam-3976	208	4	eν|x|	eν|x|	NOUN
ejpam-3976	208	5	νn	νn	PART
ejpam-3976	208	6	)	)	PUNCT
ejpam-3976	208	7	=	=	SYM
ejpam-3976	208	8	2	2	NUM
ejpam-3976	208	9	(	(	PUNCT
ejpam-3976	208	10	e−πix	e−πix	NOUN
ejpam-3976	208	11	(	(	PUNCT
ejpam-3976	208	12	−πi)n	−πi)n	PROPN
ejpam-3976	208	13	+	+	CCONJ
ejpam-3976	208	14	eπix	eπix	NOUN
ejpam-3976	208	15	(	(	PUNCT
ejpam-3976	208	16	πi)n	πi)n	PROPN
ejpam-3976	208	17	)	)	PUNCT
ejpam-3976	209	1	+	+	NOUN
ejpam-3976	209	2	o	o	X
ejpam-3976	209	3	(	(	PUNCT
ejpam-3976	209	4	e3π|x|	e3π|x|	X
ejpam-3976	209	5	(	(	PUNCT
ejpam-3976	209	6	3π)n	3π)n	NUM
ejpam-3976	209	7	)	)	PUNCT
ejpam-3976	209	8	.	.	PUNCT
ejpam-3976	210	1	for	for	ADP
ejpam-3976	210	2	even	even	ADV
ejpam-3976	210	3	indices	index	NOUN
ejpam-3976	210	4	,	,	PUNCT
ejpam-3976	210	5	g2n(x	g2n(x	PROPN
ejpam-3976	210	6	)	)	PUNCT
ejpam-3976	210	7	(	(	PUNCT
ejpam-3976	210	8	2n	2n	NUM
ejpam-3976	210	9	)	)	PUNCT
ejpam-3976	210	10	!	!	PUNCT
ejpam-3976	211	1	=	=	PUNCT
ejpam-3976	211	2	g2n(x	g2n(x	X
ejpam-3976	211	3	;	;	PUNCT
ejpam-3976	211	4	1	1	NUM
ejpam-3976	211	5	)	)	PUNCT
ejpam-3976	211	6	(	(	PUNCT
ejpam-3976	211	7	2n	2n	NUM
ejpam-3976	211	8	)	)	PUNCT
ejpam-3976	211	9	!	!	PUNCT
ejpam-3976	212	1	=	=	SYM
ejpam-3976	212	2	2	2	NUM
ejpam-3976	212	3	(	(	PUNCT
ejpam-3976	212	4	e−πix	e−πix	ADJ
ejpam-3976	212	5	(	(	PUNCT
ejpam-3976	212	6	πi)2n	πi)2n	ADV
ejpam-3976	212	7	+	+	CCONJ
ejpam-3976	212	8	eπix	eπix	ADJ
ejpam-3976	212	9	(	(	PUNCT
ejpam-3976	212	10	πi)2n	πi)2n	NOUN
ejpam-3976	212	11	)	)	PUNCT
ejpam-3976	213	1	+	+	NOUN
ejpam-3976	213	2	o	o	X
ejpam-3976	213	3	(	(	PUNCT
ejpam-3976	213	4	e3π|x|	e3π|x|	X
ejpam-3976	213	5	(	(	PUNCT
ejpam-3976	213	6	3π)2n	3π)2n	NUM
ejpam-3976	213	7	)	)	PUNCT
ejpam-3976	213	8	=	=	SYM
ejpam-3976	213	9	4	4	NUM
ejpam-3976	213	10	cosπx	cosπx	NOUN
ejpam-3976	213	11	(	(	PUNCT
ejpam-3976	213	12	πi)2n	πi)2n	ADV
ejpam-3976	213	13	+	+	ADJ
ejpam-3976	213	14	o	o	X
ejpam-3976	213	15	(	(	PUNCT
ejpam-3976	213	16	e3π|x|	e3π|x|	X
ejpam-3976	213	17	(	(	PUNCT
ejpam-3976	213	18	3π)2n	3π)2n	PROPN
ejpam-3976	213	19	)	)	PUNCT
ejpam-3976	213	20	c.	c.	PROPN
ejpam-3976	213	21	corcino	corcino	PROPN
ejpam-3976	213	22	/	/	SYM
ejpam-3976	213	23	eur	eur	PROPN
ejpam-3976	213	24	.	.	PUNCT
ejpam-3976	214	1	j.	j.	PROPN
ejpam-3976	214	2	pure	pure	PROPN
ejpam-3976	214	3	appl	appl	PROPN
ejpam-3976	214	4	.	.	PROPN
ejpam-3976	214	5	math	math	PROPN
ejpam-3976	214	6	,	,	PUNCT
ejpam-3976	214	7	14	14	NUM
ejpam-3976	214	8	(	(	PUNCT
ejpam-3976	214	9	3	3	NUM
ejpam-3976	214	10	)	)	PUNCT
ejpam-3976	214	11	(	(	PUNCT
ejpam-3976	214	12	2021	2021	NUM
ejpam-3976	214	13	)	)	PUNCT
ejpam-3976	214	14	,	,	PUNCT
ejpam-3976	214	15	666	666	NUM
ejpam-3976	214	16	-	-	SYM
ejpam-3976	214	17	684	684	NUM
ejpam-3976	214	18	677	677	NUM
ejpam-3976	214	19	=	=	SYM
ejpam-3976	214	20	(	(	PUNCT
ejpam-3976	214	21	−1)n	−1)n	PROPN
ejpam-3976	214	22	4	4	NUM
ejpam-3976	214	23	cosπx	cosπx	NOUN
ejpam-3976	214	24	π2n	π2n	PROPN
ejpam-3976	215	1	+	+	ADP
ejpam-3976	215	2	o	o	X
ejpam-3976	215	3	(	(	PUNCT
ejpam-3976	215	4	e3π|x|	e3π|x|	X
ejpam-3976	215	5	(	(	PUNCT
ejpam-3976	215	6	3π)n	3π)n	NUM
ejpam-3976	215	7	)	)	PUNCT
ejpam-3976	215	8	.	.	PUNCT
ejpam-3976	216	1	for	for	ADP
ejpam-3976	216	2	odd	odd	ADJ
ejpam-3976	216	3	indices	index	NOUN
ejpam-3976	216	4	,	,	PUNCT
ejpam-3976	216	5	g2n+1(x	g2n+1(x	NUM
ejpam-3976	216	6	)	)	PUNCT
ejpam-3976	216	7	(	(	PUNCT
ejpam-3976	216	8	2n+	2n+	NUM
ejpam-3976	216	9	1	1	NUM
ejpam-3976	216	10	)	)	PUNCT
ejpam-3976	216	11	!	!	PUNCT
ejpam-3976	217	1	=	=	PUNCT
ejpam-3976	217	2	g2n+1(x	g2n+1(x	NOUN
ejpam-3976	217	3	;	;	PUNCT
ejpam-3976	217	4	1	1	X
ejpam-3976	217	5	)	)	PUNCT
ejpam-3976	217	6	(	(	PUNCT
ejpam-3976	217	7	2n+	2n+	NUM
ejpam-3976	217	8	1	1	NUM
ejpam-3976	217	9	)	)	PUNCT
ejpam-3976	217	10	!	!	PUNCT
ejpam-3976	218	1	=	=	SYM
ejpam-3976	218	2	2	2	NUM
ejpam-3976	218	3	(	(	PUNCT
ejpam-3976	218	4	e−πix	e−πix	ADJ
ejpam-3976	218	5	(	(	PUNCT
ejpam-3976	218	6	−πi)2n+1	−πi)2n+1	NOUN
ejpam-3976	218	7	+	+	CCONJ
ejpam-3976	218	8	eπix	eπix	NOUN
ejpam-3976	218	9	(	(	PUNCT
ejpam-3976	218	10	πi)2n+1	πi)2n+1	NOUN
ejpam-3976	218	11	)	)	PUNCT
ejpam-3976	219	1	+	+	NOUN
ejpam-3976	219	2	o	o	X
ejpam-3976	219	3	(	(	PUNCT
ejpam-3976	219	4	e3π|x|	e3π|x|	X
ejpam-3976	219	5	(	(	PUNCT
ejpam-3976	219	6	3π)2n+1	3π)2n+1	NUM
ejpam-3976	219	7	)	)	PUNCT
ejpam-3976	219	8	=	=	SYM
ejpam-3976	219	9	2	2	NUM
ejpam-3976	219	10	(	(	PUNCT
ejpam-3976	219	11	(	(	PUNCT
ejpam-3976	219	12	−1)n	−1)n	X
ejpam-3976	219	13	2	2	NUM
ejpam-3976	219	14	sinπx	sinπx	NOUN
ejpam-3976	219	15	(	(	PUNCT
ejpam-3976	219	16	π)2n+1	π)2n+1	NOUN
ejpam-3976	219	17	)	)	PUNCT
ejpam-3976	220	1	+	+	ADP
ejpam-3976	220	2	o	o	X
ejpam-3976	220	3	(	(	PUNCT
ejpam-3976	220	4	e3π|x|	e3π|x|	X
ejpam-3976	220	5	(	(	PUNCT
ejpam-3976	220	6	3π)2n+1	3π)2n+1	NUM
ejpam-3976	220	7	)	)	PUNCT
ejpam-3976	220	8	=	=	SYM
ejpam-3976	220	9	(	(	PUNCT
ejpam-3976	220	10	−1)n(4	−1)n(4	PROPN
ejpam-3976	220	11	sinπx	sinπx	ADJ
ejpam-3976	220	12	)	)	PUNCT
ejpam-3976	220	13	π2n+1	π2n+1	NOUN
ejpam-3976	220	14	+	+	NOUN
ejpam-3976	220	15	o	o	X
ejpam-3976	220	16	(	(	PUNCT
ejpam-3976	220	17	e3π|x|	e3π|x|	X
ejpam-3976	220	18	(	(	PUNCT
ejpam-3976	220	19	3π)n	3π)n	NUM
ejpam-3976	220	20	)	)	PUNCT
ejpam-3976	220	21	.	.	PUNCT
ejpam-3976	221	1	notice	notice	VERB
ejpam-3976	221	2	the	the	DET
ejpam-3976	221	3	resemblance	resemblance	NOUN
ejpam-3976	221	4	of	of	ADP
ejpam-3976	221	5	the	the	DET
ejpam-3976	221	6	results	result	NOUN
ejpam-3976	221	7	in	in	ADP
ejpam-3976	221	8	corollary	corollary	ADJ
ejpam-3976	221	9	2.5	2.5	NUM
ejpam-3976	221	10	and	and	CCONJ
ejpam-3976	221	11	of	of	ADP
ejpam-3976	221	12	(	(	PUNCT
ejpam-3976	221	13	33	33	NUM
ejpam-3976	221	14	)	)	PUNCT
ejpam-3976	221	15	in	in	ADP
ejpam-3976	221	16	[	[	X
ejpam-3976	221	17	3	3	NUM
ejpam-3976	221	18	]	]	PUNCT
ejpam-3976	221	19	.	.	PUNCT
ejpam-3976	222	1	since	since	SCONJ
ejpam-3976	222	2	,	,	PUNCT
ejpam-3976	222	3	for	for	ADP
ejpam-3976	222	4	k	k	PROPN
ejpam-3976	222	5	=	=	SYM
ejpam-3976	222	6	2n	2n	NUM
ejpam-3976	222	7	,	,	PUNCT
ejpam-3976	222	8	cos	cos	PROPN
ejpam-3976	222	9	(	(	PUNCT
ejpam-3976	222	10	πx−	πx−	PUNCT
ejpam-3976	222	11	kπ	kπ	PROPN
ejpam-3976	222	12	2	2	NUM
ejpam-3976	222	13	)	)	PUNCT
ejpam-3976	222	14	=	=	SYM
ejpam-3976	222	15	±	±	NUM
ejpam-3976	222	16	cosπx	cosπx	NOUN
ejpam-3976	222	17	=	=	SYM
ejpam-3976	222	18	(	(	PUNCT
ejpam-3976	222	19	−1)n	−1)n	PROPN
ejpam-3976	222	20	cosπx	cosπx	PROPN
ejpam-3976	222	21	,	,	PUNCT
ejpam-3976	222	22	(	(	PUNCT
ejpam-3976	222	23	33	33	NUM
ejpam-3976	222	24	)	)	PUNCT
ejpam-3976	222	25	in	in	ADP
ejpam-3976	222	26	[	[	X
ejpam-3976	222	27	3	3	X
ejpam-3976	222	28	]	]	PUNCT
ejpam-3976	222	29	can	can	AUX
ejpam-3976	222	30	be	be	AUX
ejpam-3976	222	31	written	write	VERB
ejpam-3976	222	32	as	as	ADP
ejpam-3976	222	33	g2n(x	g2n(x	PROPN
ejpam-3976	222	34	)	)	PUNCT
ejpam-3976	222	35	=	=	SYM
ejpam-3976	223	1	4((2n	4((2n	NUM
ejpam-3976	223	2	)	)	PUNCT
ejpam-3976	223	3	!	!	PUNCT
ejpam-3976	223	4	)	)	PUNCT
ejpam-3976	224	1	π2n	π2n	PROPN
ejpam-3976	224	2	[	[	PUNCT
ejpam-3976	224	3	(	(	PUNCT
ejpam-3976	224	4	−1)n	−1)n	PROPN
ejpam-3976	224	5	cosπx+o(3−n	cosπx+o(3−n	PROPN
ejpam-3976	224	6	)	)	PUNCT
ejpam-3976	224	7	]	]	X
ejpam-3976	224	8	g2n(x	g2n(x	PROPN
ejpam-3976	224	9	)	)	PUNCT
ejpam-3976	224	10	(	(	PUNCT
ejpam-3976	224	11	2n	2n	NUM
ejpam-3976	224	12	)	)	PUNCT
ejpam-3976	224	13	!	!	PUNCT
ejpam-3976	225	1	=	=	PUNCT
ejpam-3976	225	2	(	(	PUNCT
ejpam-3976	225	3	−1)n4	−1)n4	NOUN
ejpam-3976	225	4	cosπx	cosπx	NOUN
ejpam-3976	225	5	π2n	π2n	PROPN
ejpam-3976	226	1	+	+	ADP
ejpam-3976	226	2	o	o	X
ejpam-3976	226	3	(	(	PUNCT
ejpam-3976	226	4	3−n	3−n	NUM
ejpam-3976	226	5	π2n	π2n	X
ejpam-3976	226	6	)	)	PUNCT
ejpam-3976	227	1	=	=	PUNCT
ejpam-3976	227	2	(	(	PUNCT
ejpam-3976	227	3	−1)n4	−1)n4	NOUN
ejpam-3976	227	4	cosπx	cosπx	NOUN
ejpam-3976	227	5	π2n	π2n	PROPN
ejpam-3976	228	1	+	+	ADP
ejpam-3976	228	2	o	o	X
ejpam-3976	228	3	(	(	PUNCT
ejpam-3976	228	4	1	1	NUM
ejpam-3976	228	5	(	(	PUNCT
ejpam-3976	228	6	3π)n	3π)n	NUM
ejpam-3976	228	7	)	)	PUNCT
ejpam-3976	228	8	=	=	SYM
ejpam-3976	228	9	(	(	PUNCT
ejpam-3976	228	10	−1)n4	−1)n4	NOUN
ejpam-3976	228	11	cosπx	cosπx	NOUN
ejpam-3976	228	12	π2n	π2n	PROPN
ejpam-3976	229	1	+	+	ADP
ejpam-3976	229	2	o	o	X
ejpam-3976	229	3	(	(	PUNCT
ejpam-3976	229	4	e3π|x|	e3π|x|	X
ejpam-3976	229	5	(	(	PUNCT
ejpam-3976	229	6	3π)n	3π)n	NUM
ejpam-3976	229	7	)	)	PUNCT
ejpam-3976	229	8	,	,	PUNCT
ejpam-3976	229	9	for	for	ADP
ejpam-3976	229	10	x	x	PROPN
ejpam-3976	229	11	∈	∈	PROPN
ejpam-3976	229	12	k.	k.	PROPN
ejpam-3976	229	13	for	for	ADP
ejpam-3976	229	14	odd	odd	ADJ
ejpam-3976	229	15	k	k	PROPN
ejpam-3976	229	16	(	(	PUNCT
ejpam-3976	229	17	k	k	NOUN
ejpam-3976	229	18	=	=	SYM
ejpam-3976	229	19	2n+	2n+	NUM
ejpam-3976	229	20	1	1	NUM
ejpam-3976	229	21	)	)	PUNCT
ejpam-3976	229	22	,	,	PUNCT
ejpam-3976	229	23	cosπx−	cosπx−	PROPN
ejpam-3976	229	24	kπ	kπ	VERB
ejpam-3976	229	25	2	2	NUM
ejpam-3976	229	26	=	=	SYM
ejpam-3976	229	27	(	(	PUNCT
ejpam-3976	229	28	−1)n	−1)n	PROPN
ejpam-3976	229	29	sinπx	sinπx	NOUN
ejpam-3976	229	30	.	.	PUNCT
ejpam-3976	230	1	then	then	ADV
ejpam-3976	230	2	(	(	PUNCT
ejpam-3976	230	3	33	33	NUM
ejpam-3976	230	4	)	)	PUNCT
ejpam-3976	230	5	in	in	ADP
ejpam-3976	230	6	[	[	X
ejpam-3976	230	7	3	3	X
ejpam-3976	230	8	]	]	PUNCT
ejpam-3976	230	9	can	can	AUX
ejpam-3976	230	10	be	be	AUX
ejpam-3976	230	11	written	write	VERB
ejpam-3976	230	12	as	as	ADP
ejpam-3976	230	13	g2n+1(x	g2n+1(x	NOUN
ejpam-3976	230	14	)	)	PUNCT
ejpam-3976	230	15	=	=	PUNCT
ejpam-3976	231	1	4((2n+	4((2n+	NUM
ejpam-3976	231	2	1	1	NUM
ejpam-3976	231	3	)	)	PUNCT
ejpam-3976	231	4	!	!	PUNCT
ejpam-3976	231	5	)	)	PUNCT
ejpam-3976	232	1	π2n+1	π2n+1	NOUN
ejpam-3976	232	2	[	[	PUNCT
ejpam-3976	232	3	(	(	PUNCT
ejpam-3976	232	4	−1)n	−1)n	PROPN
ejpam-3976	232	5	sinπx+o	sinπx+o	PROPN
ejpam-3976	232	6	(	(	PUNCT
ejpam-3976	232	7	3−(2n+1	3−(2n+1	PROPN
ejpam-3976	232	8	)	)	PUNCT
ejpam-3976	232	9	)	)	PUNCT
ejpam-3976	232	10	]	]	PUNCT
ejpam-3976	232	11	g2n+1(x	g2n+1(x	X
ejpam-3976	232	12	)	)	PUNCT
ejpam-3976	232	13	(	(	PUNCT
ejpam-3976	232	14	2n+	2n+	NUM
ejpam-3976	232	15	1	1	NUM
ejpam-3976	232	16	)	)	PUNCT
ejpam-3976	232	17	!	!	PUNCT
ejpam-3976	233	1	=	=	PUNCT
ejpam-3976	233	2	(	(	PUNCT
ejpam-3976	233	3	−1)n	−1)n	PROPN
ejpam-3976	233	4	4	4	NUM
ejpam-3976	233	5	sinπx	sinπx	NOUN
ejpam-3976	233	6	π2n+1	π2n+1	NOUN
ejpam-3976	233	7	+	+	NOUN
ejpam-3976	233	8	o	o	X
ejpam-3976	233	9	(	(	PUNCT
ejpam-3976	233	10	3−(2n+1	3−(2n+1	PROPN
ejpam-3976	233	11	)	)	PUNCT
ejpam-3976	233	12	π2n+1	π2n+1	NOUN
ejpam-3976	233	13	)	)	PUNCT
ejpam-3976	234	1	=	=	SYM
ejpam-3976	234	2	(	(	PUNCT
ejpam-3976	234	3	−1)n	−1)n	PROPN
ejpam-3976	234	4	4	4	NUM
ejpam-3976	234	5	sinπx	sinπx	NOUN
ejpam-3976	234	6	π2n+1	π2n+1	NOUN
ejpam-3976	235	1	+	+	NOUN
ejpam-3976	235	2	o	o	X
ejpam-3976	235	3	(	(	PUNCT
ejpam-3976	235	4	1	1	NUM
ejpam-3976	235	5	(	(	PUNCT
ejpam-3976	235	6	3π)2n+1	3π)2n+1	NUM
ejpam-3976	235	7	)	)	PUNCT
ejpam-3976	235	8	c.	c.	PROPN
ejpam-3976	235	9	corcino	corcino	PROPN
ejpam-3976	235	10	/	/	SYM
ejpam-3976	235	11	eur	eur	PROPN
ejpam-3976	235	12	.	.	PUNCT
ejpam-3976	236	1	j.	j.	PROPN
ejpam-3976	236	2	pure	pure	PROPN
ejpam-3976	236	3	appl	appl	PROPN
ejpam-3976	236	4	.	.	PROPN
ejpam-3976	236	5	math	math	PROPN
ejpam-3976	236	6	,	,	PUNCT
ejpam-3976	236	7	14	14	NUM
ejpam-3976	236	8	(	(	PUNCT
ejpam-3976	236	9	3	3	NUM
ejpam-3976	236	10	)	)	PUNCT
ejpam-3976	236	11	(	(	PUNCT
ejpam-3976	236	12	2021	2021	NUM
ejpam-3976	236	13	)	)	PUNCT
ejpam-3976	236	14	,	,	PUNCT
ejpam-3976	236	15	666	666	NUM
ejpam-3976	236	16	-	-	SYM
ejpam-3976	236	17	684	684	NUM
ejpam-3976	236	18	678	678	NUM
ejpam-3976	236	19	=	=	SYM
ejpam-3976	236	20	(	(	PUNCT
ejpam-3976	236	21	−1)n	−1)n	PROPN
ejpam-3976	236	22	4	4	NUM
ejpam-3976	236	23	sinπx	sinπx	NOUN
ejpam-3976	236	24	π2n+1	π2n+1	NOUN
ejpam-3976	236	25	+	+	NOUN
ejpam-3976	236	26	o	o	X
ejpam-3976	236	27	(	(	PUNCT
ejpam-3976	236	28	e3π|x|	e3π|x|	X
ejpam-3976	236	29	(	(	PUNCT
ejpam-3976	236	30	3π)2n+1	3π)2n+1	NUM
ejpam-3976	236	31	)	)	PUNCT
ejpam-3976	236	32	=	=	SYM
ejpam-3976	237	1	(	(	PUNCT
ejpam-3976	237	2	−1)n	−1)n	PROPN
ejpam-3976	237	3	4	4	NUM
ejpam-3976	237	4	sinπx	sinπx	NOUN
ejpam-3976	237	5	π2n+1	π2n+1	NOUN
ejpam-3976	238	1	+	+	NOUN
ejpam-3976	238	2	o	o	X
ejpam-3976	238	3	(	(	PUNCT
ejpam-3976	238	4	e3π|x|	e3π|x|	X
ejpam-3976	238	5	(	(	PUNCT
ejpam-3976	238	6	3π)n	3π)n	NUM
ejpam-3976	238	7	)	)	PUNCT
ejpam-3976	238	8	.	.	PUNCT
ejpam-3976	239	1	thus	thus	ADV
ejpam-3976	239	2	,	,	PUNCT
ejpam-3976	239	3	the	the	DET
ejpam-3976	239	4	asymptotic	asymptotic	ADJ
ejpam-3976	239	5	formulas	formula	NOUN
ejpam-3976	239	6	in	in	ADP
ejpam-3976	239	7	corollary	corollary	ADJ
ejpam-3976	239	8	2.5	2.5	NUM
ejpam-3976	239	9	are	be	AUX
ejpam-3976	239	10	equivalent	equivalent	ADJ
ejpam-3976	239	11	to	to	ADP
ejpam-3976	239	12	(	(	PUNCT
ejpam-3976	239	13	33	33	NUM
ejpam-3976	239	14	)	)	PUNCT
ejpam-3976	239	15	in	in	ADP
ejpam-3976	239	16	[	[	X
ejpam-3976	239	17	3	3	NUM
ejpam-3976	239	18	]	]	PUNCT
ejpam-3976	239	19	.	.	PUNCT
ejpam-3976	240	1	3	3	X
ejpam-3976	240	2	.	.	X
ejpam-3976	240	3	λ	λ	NOUN
ejpam-3976	240	4	is	be	AUX
ejpam-3976	240	5	a	a	DET
ejpam-3976	240	6	negative	negative	ADJ
ejpam-3976	240	7	real	real	ADJ
ejpam-3976	240	8	number	number	NOUN
ejpam-3976	240	9	when	when	SCONJ
ejpam-3976	240	10	λ	λ	PROPN
ejpam-3976	240	11	is	be	AUX
ejpam-3976	240	12	a	a	DET
ejpam-3976	240	13	negative	negative	ADJ
ejpam-3976	240	14	real	real	ADJ
ejpam-3976	240	15	number	number	NOUN
ejpam-3976	240	16	,	,	PUNCT
ejpam-3976	240	17	writing	write	VERB
ejpam-3976	240	18	λ	λ	X
ejpam-3976	240	19	=	=	PUNCT
ejpam-3976	240	20	−|λ|	−|λ|	PROPN
ejpam-3976	240	21	,	,	PUNCT
ejpam-3976	240	22	the	the	DET
ejpam-3976	240	23	generating	generate	VERB
ejpam-3976	240	24	function	function	NOUN
ejpam-3976	240	25	is	be	AUX
ejpam-3976	240	26	given	give	VERB
ejpam-3976	240	27	by	by	ADP
ejpam-3976	240	28	2text	2text	NUM
ejpam-3976	240	29	−|λ|et	−|λ|et	NUM
ejpam-3976	240	30	+	+	CCONJ
ejpam-3976	240	31	1	1	NUM
ejpam-3976	240	32	=	=	VERB
ejpam-3976	240	33	∞∑	∞∑	NUM
ejpam-3976	240	34	n=0	n=0	NUM
ejpam-3976	240	35	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	240	36	)	)	PUNCT
ejpam-3976	240	37	tn	tn	PROPN
ejpam-3976	240	38	n	n	PROPN
ejpam-3976	240	39	!	!	PUNCT
ejpam-3976	240	40	.	.	PUNCT
ejpam-3976	241	1	(	(	PUNCT
ejpam-3976	241	2	3.1	3.1	NUM
ejpam-3976	241	3	)	)	PUNCT
ejpam-3976	241	4	the	the	DET
ejpam-3976	241	5	poles	pole	NOUN
ejpam-3976	241	6	of	of	ADP
ejpam-3976	241	7	the	the	DET
ejpam-3976	241	8	generating	generate	VERB
ejpam-3976	241	9	function	function	NOUN
ejpam-3976	241	10	(	(	PUNCT
ejpam-3976	241	11	3.1	3.1	NUM
ejpam-3976	241	12	)	)	PUNCT
ejpam-3976	241	13	is	be	AUX
ejpam-3976	241	14	t−|λ|	t−|λ|	NOUN
ejpam-3976	241	15	=	=	PUNCT
ejpam-3976	241	16	{	{	PUNCT
ejpam-3976	241	17	2kπi−	2kπi−	INTJ
ejpam-3976	241	18	log	log	NOUN
ejpam-3976	241	19	|λ|	|λ|	NOUN
ejpam-3976	241	20	:	:	PUNCT
ejpam-3976	241	21	k	k	PROPN
ejpam-3976	241	22	∈	∈	PROPN
ejpam-3976	241	23	z	z	PROPN
ejpam-3976	241	24	}	}	PUNCT
ejpam-3976	241	25	.	.	PUNCT
ejpam-3976	242	1	the	the	DET
ejpam-3976	242	2	next	next	ADJ
ejpam-3976	242	3	theorem	theorem	NOUN
ejpam-3976	242	4	follows	follow	VERB
ejpam-3976	242	5	from	from	ADP
ejpam-3976	242	6	theorem	theorem	ADJ
ejpam-3976	242	7	2.4	2.4	NUM
ejpam-3976	242	8	.	.	PUNCT
ejpam-3976	243	1	theorem	theorem	VERB
ejpam-3976	243	2	3.1	3.1	NUM
ejpam-3976	243	3	.	.	PUNCT
ejpam-3976	244	1	given	give	VERB
ejpam-3976	244	2	that	that	PRON
ejpam-3976	244	3	λ	λ	PROPN
ejpam-3976	244	4	is	be	AUX
ejpam-3976	244	5	a	a	DET
ejpam-3976	244	6	negative	negative	ADJ
ejpam-3976	244	7	real	real	ADJ
ejpam-3976	244	8	number	number	NOUN
ejpam-3976	244	9	,	,	PUNCT
ejpam-3976	244	10	let	let	VERB
ejpam-3976	244	11	f	f	PRON
ejpam-3976	244	12	be	be	AUX
ejpam-3976	244	13	a	a	DET
ejpam-3976	244	14	finite	finite	NOUN
ejpam-3976	244	15	subset	subset	NOUN
ejpam-3976	244	16	of	of	ADP
ejpam-3976	244	17	t−|λ|	t−|λ|	NOUN
ejpam-3976	244	18	satisfying	satisfy	VERB
ejpam-3976	244	19	max	max	PROPN
ejpam-3976	244	20	{	{	PUNCT
ejpam-3976	244	21	|a|	|a|	NOUN
ejpam-3976	244	22	:	:	PUNCT
ejpam-3976	244	23	a	a	DET
ejpam-3976	244	24	∈	∈	ADJ
ejpam-3976	244	25	f	f	NOUN
ejpam-3976	244	26	}	}	PUNCT
ejpam-3976	244	27	<	<	X
ejpam-3976	244	28	min	min	X
ejpam-3976	244	29	{	{	PUNCT
ejpam-3976	244	30	|a|	|a|	NOUN
ejpam-3976	244	31	:	:	PUNCT
ejpam-3976	244	32	a	a	DET
ejpam-3976	244	33	∈	∈	NOUN
ejpam-3976	244	34	t−|λ|\f	t−|λ|\f	NUM
ejpam-3976	244	35	}	}	PUNCT
ejpam-3976	244	36	:	:	PUNCT
ejpam-3976	244	37	=	=	PUNCT
ejpam-3976	244	38	µ.	µ.	NOUN
ejpam-3976	244	39	for	for	ADP
ejpam-3976	244	40	all	all	DET
ejpam-3976	244	41	integers	integer	NOUN
ejpam-3976	244	42	n	n	PRON
ejpam-3976	244	43	≥	≥	NOUN
ejpam-3976	244	44	2	2	NUM
ejpam-3976	244	45	,	,	PUNCT
ejpam-3976	244	46	we	we	PRON
ejpam-3976	244	47	have	have	AUX
ejpam-3976	244	48	,	,	PUNCT
ejpam-3976	244	49	uniformly	uniformly	ADV
ejpam-3976	244	50	for	for	ADP
ejpam-3976	244	51	x	x	PUNCT
ejpam-3976	244	52	in	in	ADP
ejpam-3976	244	53	a	a	DET
ejpam-3976	244	54	compact	compact	ADJ
ejpam-3976	244	55	subset	subset	NOUN
ejpam-3976	244	56	k	k	PROPN
ejpam-3976	244	57	of	of	ADP
ejpam-3976	244	58	c	c	PROPN
ejpam-3976	244	59	,	,	PUNCT
ejpam-3976	244	60	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	244	61	)	)	PUNCT
ejpam-3976	244	62	n	n	CCONJ
ejpam-3976	244	63	!	!	PUNCT
ejpam-3976	245	1	=	=	SYM
ejpam-3976	245	2	2	2	NUM
ejpam-3976	245	3	∑	∑	PROPN
ejpam-3976	245	4	a∈f	a∈f	NOUN
ejpam-3976	245	5	eax	eax	VERB
ejpam-3976	245	6	an	an	DET
ejpam-3976	245	7	+	+	PROPN
ejpam-3976	245	8	o	o	X
ejpam-3976	245	9	(	(	PUNCT
ejpam-3976	245	10	eµ|x|	eµ|x|	NOUN
ejpam-3976	245	11	µn	µn	PROPN
ejpam-3976	245	12	)	)	PUNCT
ejpam-3976	245	13	,	,	PUNCT
ejpam-3976	245	14	(	(	PUNCT
ejpam-3976	245	15	3.2	3.2	NUM
ejpam-3976	245	16	)	)	PUNCT
ejpam-3976	245	17	where	where	SCONJ
ejpam-3976	245	18	the	the	DET
ejpam-3976	245	19	constant	constant	ADJ
ejpam-3976	245	20	implicit	implicit	NOUN
ejpam-3976	245	21	in	in	ADP
ejpam-3976	245	22	the	the	DET
ejpam-3976	245	23	order	order	NOUN
ejpam-3976	245	24	term	term	NOUN
ejpam-3976	245	25	depends	depend	VERB
ejpam-3976	245	26	on	on	ADP
ejpam-3976	245	27	λ	λ	PROPN
ejpam-3976	245	28	,	,	PUNCT
ejpam-3976	245	29	f	f	PROPN
ejpam-3976	245	30	and	and	CCONJ
ejpam-3976	245	31	k.	k.	PROPN
ejpam-3976	245	32	the	the	DET
ejpam-3976	245	33	apostol	apostol	PROPN
ejpam-3976	245	34	-	-	PUNCT
ejpam-3976	245	35	genocchi	genocchi	PROPN
ejpam-3976	245	36	numbers	number	NOUN
ejpam-3976	245	37	gn(0;−1	gn(0;−1	PROPN
ejpam-3976	245	38	)	)	PUNCT
ejpam-3976	245	39	corresponding	correspond	VERB
ejpam-3976	245	40	to	to	ADP
ejpam-3976	245	41	the	the	DET
ejpam-3976	245	42	case	case	NOUN
ejpam-3976	245	43	λ	λ	NOUN
ejpam-3976	245	44	=	=	PRON
ejpam-3976	245	45	−1	−1	NOUN
ejpam-3976	245	46	has	have	AUX
ejpam-3976	245	47	generating	generate	VERB
ejpam-3976	245	48	function	function	NOUN
ejpam-3976	245	49	2	2	NUM
ejpam-3976	245	50	t	t	NOUN
ejpam-3976	245	51	−et	−et	NOUN
ejpam-3976	246	1	+	+	CCONJ
ejpam-3976	246	2	1	1	X
ejpam-3976	246	3	=	=	VERB
ejpam-3976	246	4	∞∑	∞∑	NUM
ejpam-3976	246	5	n=0	n=0	ADJ
ejpam-3976	246	6	gn(0;−1	gn(0;−1	NOUN
ejpam-3976	246	7	)	)	PUNCT
ejpam-3976	246	8	tn	tn	PROPN
ejpam-3976	246	9	n	n	PROPN
ejpam-3976	246	10	!	!	PROPN
ejpam-3976	246	11	,	,	PUNCT
ejpam-3976	246	12	(	(	PUNCT
ejpam-3976	246	13	3.3	3.3	NUM
ejpam-3976	246	14	)	)	PUNCT
ejpam-3976	246	15	the	the	DET
ejpam-3976	246	16	set	set	NOUN
ejpam-3976	246	17	of	of	ADP
ejpam-3976	246	18	poles	pole	NOUN
ejpam-3976	246	19	is	be	AUX
ejpam-3976	246	20	t−1	t−1	PROPN
ejpam-3976	246	21	=	=	PUNCT
ejpam-3976	246	22	{	{	PUNCT
ejpam-3976	246	23	2kπi	2kπi	NUM
ejpam-3976	246	24	:	:	PUNCT
ejpam-3976	246	25	k	k	PROPN
ejpam-3976	246	26	∈	∈	PROPN
ejpam-3976	246	27	z\{0	z\{0	PROPN
ejpam-3976	246	28	}	}	PUNCT
ejpam-3976	246	29	}	}	PUNCT
ejpam-3976	246	30	.	.	PUNCT
ejpam-3976	247	1	an	an	DET
ejpam-3976	247	2	asymptotic	asymptotic	ADJ
ejpam-3976	247	3	formula	formula	NOUN
ejpam-3976	247	4	for	for	ADP
ejpam-3976	247	5	gn(0;−1	gn(0;−1	NOUN
ejpam-3976	247	6	)	)	PUNCT
ejpam-3976	247	7	is	be	AUX
ejpam-3976	247	8	given	give	VERB
ejpam-3976	247	9	in	in	ADP
ejpam-3976	247	10	the	the	DET
ejpam-3976	247	11	following	follow	VERB
ejpam-3976	247	12	theorem	theorem	NOUN
ejpam-3976	247	13	.	.	PUNCT
ejpam-3976	247	14	theorem	theorem	PROPN
ejpam-3976	247	15	3.2	3.2	NUM
ejpam-3976	247	16	.	.	PUNCT
ejpam-3976	248	1	for	for	ADP
ejpam-3976	248	2	n	n	PRON
ejpam-3976	248	3	≥	≥	NUM
ejpam-3976	248	4	3	3	NUM
ejpam-3976	248	5	,	,	PUNCT
ejpam-3976	248	6	the	the	DET
ejpam-3976	248	7	apostol	apostol	NOUN
ejpam-3976	248	8	-	-	PUNCT
ejpam-3976	248	9	genocchi	genocchi	PROPN
ejpam-3976	248	10	numbers	number	NOUN
ejpam-3976	248	11	gn(0;−1	gn(0;−1	PROPN
ejpam-3976	248	12	)	)	PUNCT
ejpam-3976	248	13	satisfy	satisfy	NOUN
ejpam-3976	248	14	gn(0;−1	gn(0;−1	PROPN
ejpam-3976	248	15	)	)	PUNCT
ejpam-3976	248	16	n	n	CCONJ
ejpam-3976	248	17	!	!	PUNCT
ejpam-3976	249	1	=	=	SYM
ejpam-3976	249	2	2	2	NUM
ejpam-3976	249	3	(	(	PUNCT
ejpam-3976	249	4	1	1	NUM
ejpam-3976	249	5	(	(	PUNCT
ejpam-3976	249	6	−2πi)n	−2πi)n	NOUN
ejpam-3976	249	7	+	+	CCONJ
ejpam-3976	249	8	1	1	NUM
ejpam-3976	249	9	(	(	PUNCT
ejpam-3976	249	10	2πi)n	2πi)n	PROPN
ejpam-3976	249	11	)	)	PUNCT
ejpam-3976	250	1	+	+	NOUN
ejpam-3976	250	2	o	o	X
ejpam-3976	250	3	(	(	PUNCT
ejpam-3976	250	4	(	(	PUNCT
ejpam-3976	250	5	4π)−n	4π)−n	PROPN
ejpam-3976	250	6	)	)	PUNCT
ejpam-3976	250	7	.	.	PUNCT
ejpam-3976	251	1	(	(	PUNCT
ejpam-3976	251	2	3.4	3.4	NUM
ejpam-3976	251	3	)	)	PUNCT
ejpam-3976	251	4	in	in	ADP
ejpam-3976	251	5	particular	particular	ADJ
ejpam-3976	251	6	,	,	PUNCT
ejpam-3976	251	7	g2n(0;−1	g2n(0;−1	X
ejpam-3976	251	8	)	)	PUNCT
ejpam-3976	251	9	(	(	PUNCT
ejpam-3976	251	10	2n	2n	NUM
ejpam-3976	251	11	)	)	PUNCT
ejpam-3976	251	12	!	!	PUNCT
ejpam-3976	252	1	=	=	PUNCT
ejpam-3976	252	2	(	(	PUNCT
ejpam-3976	252	3	−1)n4	−1)n4	X
ejpam-3976	252	4	(	(	PUNCT
ejpam-3976	252	5	2π)2n	2π)2n	NUM
ejpam-3976	253	1	+	+	NOUN
ejpam-3976	253	2	o	o	X
ejpam-3976	253	3	(	(	PUNCT
ejpam-3976	253	4	(	(	PUNCT
ejpam-3976	253	5	4π)−2n	4π)−2n	PROPN
ejpam-3976	253	6	)	)	PUNCT
ejpam-3976	253	7	,	,	PUNCT
ejpam-3976	253	8	n	n	X
ejpam-3976	253	9	≥	≥	NOUN
ejpam-3976	253	10	2	2	NUM
ejpam-3976	253	11	.	.	PUNCT
ejpam-3976	253	12	(	(	PUNCT
ejpam-3976	253	13	3.5	3.5	NUM
ejpam-3976	253	14	)	)	PUNCT
ejpam-3976	253	15	c.	c.	PROPN
ejpam-3976	253	16	corcino	corcino	PROPN
ejpam-3976	253	17	/	/	SYM
ejpam-3976	253	18	eur	eur	PROPN
ejpam-3976	253	19	.	.	PUNCT
ejpam-3976	254	1	j.	j.	PROPN
ejpam-3976	254	2	pure	pure	PROPN
ejpam-3976	254	3	appl	appl	PROPN
ejpam-3976	254	4	.	.	PROPN
ejpam-3976	254	5	math	math	PROPN
ejpam-3976	254	6	,	,	PUNCT
ejpam-3976	254	7	14	14	NUM
ejpam-3976	254	8	(	(	PUNCT
ejpam-3976	254	9	3	3	NUM
ejpam-3976	254	10	)	)	PUNCT
ejpam-3976	254	11	(	(	PUNCT
ejpam-3976	254	12	2021	2021	NUM
ejpam-3976	254	13	)	)	PUNCT
ejpam-3976	254	14	,	,	PUNCT
ejpam-3976	254	15	666	666	NUM
ejpam-3976	254	16	-	-	SYM
ejpam-3976	254	17	684	684	NUM
ejpam-3976	254	18	679	679	NUM
ejpam-3976	254	19	proof	proof	NOUN
ejpam-3976	254	20	.	.	PUNCT
ejpam-3976	255	1	taking	take	VERB
ejpam-3976	255	2	x	x	PUNCT
ejpam-3976	255	3	=	=	SYM
ejpam-3976	255	4	0	0	NUM
ejpam-3976	255	5	,	,	PUNCT
ejpam-3976	255	6	f	f	X
ejpam-3976	255	7	=	=	PRON
ejpam-3976	255	8	{	{	PUNCT
ejpam-3976	255	9	−2πi	−2πi	X
ejpam-3976	255	10	,	,	PUNCT
ejpam-3976	255	11	2πi	2πi	ADJ
ejpam-3976	255	12	}	}	PUNCT
ejpam-3976	255	13	in	in	ADP
ejpam-3976	255	14	theorem	theorem	ADJ
ejpam-3976	255	15	3.1	3.1	NUM
ejpam-3976	255	16	,	,	PUNCT
ejpam-3976	255	17	then	then	ADV
ejpam-3976	255	18	µ	µ	X
ejpam-3976	255	19	=	=	SYM
ejpam-3976	255	20	4π	4π	NUM
ejpam-3976	255	21	.	.	PUNCT
ejpam-3976	256	1	hence	hence	ADV
ejpam-3976	256	2	,	,	PUNCT
ejpam-3976	256	3	−1	−1	NOUN
ejpam-3976	256	4	2gn(0;−1	2gn(0;−1	NUM
ejpam-3976	256	5	)	)	PUNCT
ejpam-3976	256	6	n	n	CCONJ
ejpam-3976	256	7	!	!	PUNCT
ejpam-3976	257	1	=	=	PUNCT
ejpam-3976	258	1	−	−	PROPN
ejpam-3976	258	2	(	(	PUNCT
ejpam-3976	258	3	1	1	NUM
ejpam-3976	258	4	(	(	PUNCT
ejpam-3976	258	5	−2πi)n	−2πi)n	NOUN
ejpam-3976	258	6	+	+	CCONJ
ejpam-3976	258	7	1	1	NUM
ejpam-3976	258	8	(	(	PUNCT
ejpam-3976	258	9	2πi)n	2πi)n	PROPN
ejpam-3976	258	10	)	)	PUNCT
ejpam-3976	259	1	+	+	NOUN
ejpam-3976	259	2	o	o	X
ejpam-3976	259	3	(	(	PUNCT
ejpam-3976	259	4	(	(	PUNCT
ejpam-3976	259	5	4π)−n	4π)−n	PROPN
ejpam-3976	259	6	)	)	PUNCT
ejpam-3976	259	7	,	,	PUNCT
ejpam-3976	259	8	(	(	PUNCT
ejpam-3976	259	9	3.6	3.6	NUM
ejpam-3976	259	10	)	)	PUNCT
ejpam-3976	259	11	from	from	ADP
ejpam-3976	259	12	which	which	PRON
ejpam-3976	259	13	(	(	PUNCT
ejpam-3976	259	14	3.4	3.4	NUM
ejpam-3976	259	15	)	)	PUNCT
ejpam-3976	259	16	follows	follow	VERB
ejpam-3976	259	17	.	.	PUNCT
ejpam-3976	260	1	for	for	ADP
ejpam-3976	260	2	(	(	PUNCT
ejpam-3976	260	3	n	n	X
ejpam-3976	260	4	≥	≥	NOUN
ejpam-3976	260	5	3	3	NUM
ejpam-3976	260	6	)	)	PUNCT
ejpam-3976	260	7	,	,	PUNCT
ejpam-3976	260	8	(	(	PUNCT
ejpam-3976	260	9	3.6	3.6	NUM
ejpam-3976	260	10	)	)	PUNCT
ejpam-3976	260	11	gives	give	VERB
ejpam-3976	260	12	g2n+1(0;−1	g2n+1(0;−1	NOUN
ejpam-3976	260	13	)	)	PUNCT
ejpam-3976	261	1	≈	≈	PROPN
ejpam-3976	261	2	0	0	NUM
ejpam-3976	261	3	.	.	PUNCT
ejpam-3976	262	1	indeed	indeed	ADV
ejpam-3976	262	2	g2n+1(0;−1	g2n+1(0;−1	NOUN
ejpam-3976	262	3	)	)	PUNCT
ejpam-3976	263	1	=	=	SYM
ejpam-3976	263	2	0	0	NUM
ejpam-3976	263	3	,	,	PUNCT
ejpam-3976	263	4	∀n	∀n	NUM
ejpam-3976	263	5	≥	≥	NOUN
ejpam-3976	263	6	1	1	NUM
ejpam-3976	263	7	.	.	PUNCT
ejpam-3976	263	8	for	for	ADP
ejpam-3976	263	9	n	n	PRON
ejpam-3976	263	10	≥	≥	NUM
ejpam-3976	263	11	2	2	NUM
ejpam-3976	263	12	,	,	PUNCT
ejpam-3976	263	13	g2n(0;−1	g2n(0;−1	X
ejpam-3976	263	14	)	)	PUNCT
ejpam-3976	263	15	(	(	PUNCT
ejpam-3976	263	16	2n	2n	NUM
ejpam-3976	263	17	)	)	PUNCT
ejpam-3976	263	18	!	!	PUNCT
ejpam-3976	264	1	=	=	SYM
ejpam-3976	264	2	4	4	NUM
ejpam-3976	264	3	(	(	PUNCT
ejpam-3976	264	4	(	(	PUNCT
ejpam-3976	264	5	−1)n	−1)n	X
ejpam-3976	264	6	(	(	PUNCT
ejpam-3976	264	7	2π)2n	2π)2n	NUM
ejpam-3976	264	8	)	)	PUNCT
ejpam-3976	265	1	+	+	NOUN
ejpam-3976	265	2	o	o	X
ejpam-3976	265	3	(	(	PUNCT
ejpam-3976	265	4	(	(	PUNCT
ejpam-3976	265	5	4π)−2n	4π)−2n	PROPN
ejpam-3976	265	6	)	)	PUNCT
ejpam-3976	265	7	.	.	PUNCT
ejpam-3976	266	1	(	(	PUNCT
ejpam-3976	266	2	3.7	3.7	NUM
ejpam-3976	266	3	)	)	PUNCT
ejpam-3976	266	4	from	from	ADP
ejpam-3976	266	5	(	(	PUNCT
ejpam-3976	266	6	3.7	3.7	NUM
ejpam-3976	266	7	)	)	PUNCT
ejpam-3976	266	8	we	we	PRON
ejpam-3976	266	9	have	have	VERB
ejpam-3976	266	10	the	the	DET
ejpam-3976	266	11	approximation	approximation	NOUN
ejpam-3976	266	12	g2n(0;−1	g2n(0;−1	X
ejpam-3976	266	13	)	)	PUNCT
ejpam-3976	267	1	≈	≈	PROPN
ejpam-3976	267	2	(	(	PUNCT
ejpam-3976	267	3	−1)n	−1)n	PROPN
ejpam-3976	267	4	4(2n	4(2n	NUM
ejpam-3976	267	5	)	)	PUNCT
ejpam-3976	267	6	!	!	PUNCT
ejpam-3976	268	1	(	(	PUNCT
ejpam-3976	268	2	2π)2n	2π)2n	NUM
ejpam-3976	268	3	.	.	PUNCT
ejpam-3976	269	1	(	(	PUNCT
ejpam-3976	269	2	3.8	3.8	NUM
ejpam-3976	269	3	)	)	PUNCT
ejpam-3976	269	4	taking	take	VERB
ejpam-3976	269	5	n	n	NOUN
ejpam-3976	269	6	=	=	SYM
ejpam-3976	269	7	4	4	NUM
ejpam-3976	269	8	,	,	PUNCT
ejpam-3976	269	9	g8(0;−1	g8(0;−1	NOUN
ejpam-3976	269	10	)	)	PUNCT
ejpam-3976	269	11	=	=	SYM
ejpam-3976	269	12	4(8	4(8	NOUN
ejpam-3976	269	13	!	!	PUNCT
ejpam-3976	269	14	)	)	PUNCT
ejpam-3976	270	1	(	(	PUNCT
ejpam-3976	270	2	2π)8	2π)8	NUM
ejpam-3976	270	3	≈	≈	PROPN
ejpam-3976	270	4	.06638	.06638	PROPN
ejpam-3976	270	5	.	.	PUNCT
ejpam-3976	271	1	the	the	DET
ejpam-3976	271	2	actual	actual	ADJ
ejpam-3976	271	3	value	value	NOUN
ejpam-3976	271	4	of	of	ADP
ejpam-3976	271	5	g8(0;−1	g8(0;−1	NOUN
ejpam-3976	271	6	)	)	PUNCT
ejpam-3976	272	1	=	=	PUNCT
ejpam-3976	272	2	−2b8	−2b8	X
ejpam-3976	272	3	=	=	SYM
ejpam-3976	272	4	1	1	NUM
ejpam-3976	272	5	15	15	NUM
ejpam-3976	273	1	≈	≈	NUM
ejpam-3976	273	2	.06667	.06667	PROPN
ejpam-3976	273	3	.	.	PUNCT
ejpam-3976	274	1	the	the	DET
ejpam-3976	274	2	apostol	apostol	NOUN
ejpam-3976	274	3	-	-	PUNCT
ejpam-3976	274	4	genocchi	genocchi	PROPN
ejpam-3976	274	5	polynomials	polynomial	NOUN
ejpam-3976	274	6	,	,	PUNCT
ejpam-3976	274	7	gn(x;−1	gn(x;−1	NOUN
ejpam-3976	274	8	)	)	PUNCT
ejpam-3976	274	9	correspond	correspond	NOUN
ejpam-3976	274	10	to	to	ADP
ejpam-3976	274	11	the	the	DET
ejpam-3976	274	12	case	case	NOUN
ejpam-3976	274	13	λ	λ	X
ejpam-3976	274	14	=	=	SYM
ejpam-3976	274	15	−1	−1	NOUN
ejpam-3976	274	16	.	.	PUNCT
ejpam-3976	275	1	these	these	DET
ejpam-3976	275	2	polynomials	polynomial	NOUN
ejpam-3976	275	3	have	have	AUX
ejpam-3976	275	4	generating	generate	VERB
ejpam-3976	275	5	function	function	NOUN
ejpam-3976	275	6	2text	2text	NUM
ejpam-3976	275	7	−et	−et	NOUN
ejpam-3976	275	8	+	+	CCONJ
ejpam-3976	275	9	1	1	NUM
ejpam-3976	275	10	=	=	VERB
ejpam-3976	275	11	∞∑	∞∑	NUM
ejpam-3976	275	12	n=0	n=0	NUM
ejpam-3976	275	13	gn(x;−1	gn(x;−1	NOUN
ejpam-3976	275	14	)	)	PUNCT
ejpam-3976	275	15	tn	tn	NOUN
ejpam-3976	275	16	n	n	NUM
ejpam-3976	275	17	!	!	PUNCT
ejpam-3976	275	18	.	.	PUNCT
ejpam-3976	276	1	(	(	PUNCT
ejpam-3976	276	2	3.9	3.9	NUM
ejpam-3976	276	3	)	)	PUNCT
ejpam-3976	276	4	we	we	PRON
ejpam-3976	276	5	will	will	AUX
ejpam-3976	276	6	prove	prove	VERB
ejpam-3976	276	7	the	the	DET
ejpam-3976	276	8	following	follow	VERB
ejpam-3976	276	9	theorem	theorem	VERB
ejpam-3976	276	10	.	.	PUNCT
ejpam-3976	276	11	theorem	theorem	VERB
ejpam-3976	276	12	3.3	3.3	NUM
ejpam-3976	276	13	.	.	PUNCT
ejpam-3976	277	1	let	let	VERB
ejpam-3976	277	2	k	k	PRON
ejpam-3976	277	3	be	be	AUX
ejpam-3976	277	4	a	a	DET
ejpam-3976	277	5	compact	compact	ADJ
ejpam-3976	277	6	subset	subset	NOUN
ejpam-3976	277	7	of	of	ADP
ejpam-3976	277	8	c.	c.	PROPN
ejpam-3976	277	9	the	the	DET
ejpam-3976	277	10	apostol	apostol	PROPN
ejpam-3976	277	11	-	-	PUNCT
ejpam-3976	277	12	genocchi	genocchi	PROPN
ejpam-3976	277	13	polynomials	polynomial	VERB
ejpam-3976	277	14	gn(x;−1	gn(x;−1	NOUN
ejpam-3976	277	15	)	)	PUNCT
ejpam-3976	277	16	satisfy	satisfy	VERB
ejpam-3976	277	17	uniformly	uniformly	ADV
ejpam-3976	277	18	on	on	ADP
ejpam-3976	277	19	k	k	PROPN
ejpam-3976	277	20	the	the	DET
ejpam-3976	277	21	estimates	estimate	NOUN
ejpam-3976	277	22	g2n(x;−1	g2n(x;−1	PROPN
ejpam-3976	277	23	)	)	PUNCT
ejpam-3976	277	24	(	(	PUNCT
ejpam-3976	277	25	2n	2n	NUM
ejpam-3976	277	26	)	)	PUNCT
ejpam-3976	277	27	!	!	PUNCT
ejpam-3976	278	1	=	=	PUNCT
ejpam-3976	278	2	(	(	PUNCT
ejpam-3976	278	3	−1)n4	−1)n4	PROPN
ejpam-3976	278	4	cos	cos	NOUN
ejpam-3976	278	5	2πx	2πx	ADJ
ejpam-3976	278	6	(	(	PUNCT
ejpam-3976	278	7	2π)2n	2π)2n	NUM
ejpam-3976	278	8	+	+	NOUN
ejpam-3976	278	9	o	o	X
ejpam-3976	278	10	(	(	PUNCT
ejpam-3976	278	11	e4π|x|	e4π|x|	PROPN
ejpam-3976	278	12	(	(	PUNCT
ejpam-3976	278	13	4π)n	4π)n	NUM
ejpam-3976	278	14	)	)	PUNCT
ejpam-3976	278	15	,	,	PUNCT
ejpam-3976	278	16	(	(	PUNCT
ejpam-3976	278	17	3.10	3.10	NUM
ejpam-3976	278	18	)	)	PUNCT
ejpam-3976	278	19	g2n+1(x;−1	g2n+1(x;−1	PROPN
ejpam-3976	278	20	)	)	PUNCT
ejpam-3976	278	21	(	(	PUNCT
ejpam-3976	278	22	2n+	2n+	NUM
ejpam-3976	278	23	1	1	NUM
ejpam-3976	278	24	)	)	PUNCT
ejpam-3976	278	25	!	!	PUNCT
ejpam-3976	279	1	=	=	PUNCT
ejpam-3976	279	2	(	(	PUNCT
ejpam-3976	279	3	−1)n4	−1)n4	NOUN
ejpam-3976	279	4	sin	sin	NOUN
ejpam-3976	279	5	2πx	2πx	NOUN
ejpam-3976	279	6	(	(	PUNCT
ejpam-3976	279	7	2π)2n+1	2π)2n+1	NUM
ejpam-3976	280	1	+	+	NOUN
ejpam-3976	280	2	o	o	X
ejpam-3976	280	3	(	(	PUNCT
ejpam-3976	280	4	e4π|x|	e4π|x|	PROPN
ejpam-3976	280	5	(	(	PUNCT
ejpam-3976	280	6	4π)n	4π)n	NUM
ejpam-3976	280	7	)	)	PUNCT
ejpam-3976	280	8	,	,	PUNCT
ejpam-3976	280	9	(	(	PUNCT
ejpam-3976	280	10	3.11	3.11	NUM
ejpam-3976	280	11	)	)	PUNCT
ejpam-3976	280	12	where	where	SCONJ
ejpam-3976	280	13	the	the	DET
ejpam-3976	280	14	implicit	implicit	ADJ
ejpam-3976	280	15	constant	constant	ADJ
ejpam-3976	280	16	in	in	ADP
ejpam-3976	280	17	the	the	DET
ejpam-3976	280	18	order	order	NOUN
ejpam-3976	280	19	term	term	NOUN
ejpam-3976	280	20	depends	depend	VERB
ejpam-3976	280	21	on	on	ADP
ejpam-3976	280	22	the	the	DET
ejpam-3976	280	23	set	set	NOUN
ejpam-3976	280	24	k.	k.	PROPN
ejpam-3976	280	25	moreover	moreover	ADV
ejpam-3976	280	26	,	,	PUNCT
ejpam-3976	280	27	for	for	ADP
ejpam-3976	280	28	n	n	CCONJ
ejpam-3976	280	29	�	�	PROPN
ejpam-3976	280	30	0	0	NUM
ejpam-3976	280	31	,	,	PUNCT
ejpam-3976	280	32	this	this	DET
ejpam-3976	280	33	constant	constant	ADJ
ejpam-3976	280	34	can	can	AUX
ejpam-3976	280	35	be	be	AUX
ejpam-3976	280	36	made	make	VERB
ejpam-3976	280	37	independent	independent	ADJ
ejpam-3976	280	38	of	of	ADP
ejpam-3976	280	39	k	k	PROPN
ejpam-3976	280	40	,	,	PUNCT
ejpam-3976	280	41	equal	equal	ADJ
ejpam-3976	280	42	to	to	ADP
ejpam-3976	280	43	the	the	DET
ejpam-3976	280	44	constant	constant	NOUN
ejpam-3976	280	45	for	for	ADP
ejpam-3976	280	46	the	the	DET
ejpam-3976	280	47	apostol	apostol	NOUN
ejpam-3976	280	48	-	-	PUNCT
ejpam-3976	280	49	genocchi	genocchi	PROPN
ejpam-3976	280	50	numbers	number	NOUN
ejpam-3976	280	51	gn(0;−1	gn(0;−1	PROPN
ejpam-3976	280	52	)	)	PUNCT
ejpam-3976	280	53	corresponding	correspond	VERB
ejpam-3976	280	54	to	to	ADP
ejpam-3976	280	55	the	the	DET
ejpam-3976	280	56	case	case	NOUN
ejpam-3976	280	57	x	x	X
ejpam-3976	281	1	=	=	SYM
ejpam-3976	281	2	0	0	PROPN
ejpam-3976	281	3	.	.	PUNCT
ejpam-3976	282	1	c.	c.	PROPN
ejpam-3976	282	2	corcino	corcino	PROPN
ejpam-3976	282	3	/	/	SYM
ejpam-3976	282	4	eur	eur	PROPN
ejpam-3976	282	5	.	.	PUNCT
ejpam-3976	283	1	j.	j.	PROPN
ejpam-3976	283	2	pure	pure	PROPN
ejpam-3976	283	3	appl	appl	PROPN
ejpam-3976	283	4	.	.	PROPN
ejpam-3976	283	5	math	math	PROPN
ejpam-3976	283	6	,	,	PUNCT
ejpam-3976	283	7	14	14	NUM
ejpam-3976	283	8	(	(	PUNCT
ejpam-3976	283	9	3	3	NUM
ejpam-3976	283	10	)	)	PUNCT
ejpam-3976	283	11	(	(	PUNCT
ejpam-3976	283	12	2021	2021	NUM
ejpam-3976	283	13	)	)	PUNCT
ejpam-3976	283	14	,	,	PUNCT
ejpam-3976	283	15	666	666	NUM
ejpam-3976	283	16	-	-	SYM
ejpam-3976	283	17	684	684	NUM
ejpam-3976	283	18	680	680	NUM
ejpam-3976	283	19	proof	proof	NOUN
ejpam-3976	283	20	.	.	PUNCT
ejpam-3976	284	1	taking	take	VERB
ejpam-3976	284	2	f	f	NOUN
ejpam-3976	284	3	=	=	X
ejpam-3976	284	4	{	{	PUNCT
ejpam-3976	284	5	−2πi	−2πi	X
ejpam-3976	284	6	,	,	PUNCT
ejpam-3976	284	7	2πi	2πi	ADJ
ejpam-3976	284	8	}	}	PUNCT
ejpam-3976	284	9	,	,	PUNCT
ejpam-3976	284	10	then	then	ADV
ejpam-3976	284	11	µ	µ	X
ejpam-3976	284	12	=	=	SYM
ejpam-3976	284	13	4π	4π	NUM
ejpam-3976	284	14	.	.	PUNCT
ejpam-3976	285	1	hence	hence	ADV
ejpam-3976	285	2	,	,	PUNCT
ejpam-3976	285	3	it	it	PRON
ejpam-3976	285	4	follows	follow	VERB
ejpam-3976	285	5	from	from	ADP
ejpam-3976	285	6	theorem	theorem	ADJ
ejpam-3976	285	7	3.1	3.1	NUM
ejpam-3976	285	8	that	that	DET
ejpam-3976	285	9	−1	−1	NOUN
ejpam-3976	285	10	2	2	NUM
ejpam-3976	285	11	gn(x;−1	gn(x;−1	NOUN
ejpam-3976	285	12	)	)	PUNCT
ejpam-3976	285	13	n	n	CCONJ
ejpam-3976	285	14	!	!	PUNCT
ejpam-3976	286	1	=	=	PUNCT
ejpam-3976	287	1	−	−	PROPN
ejpam-3976	287	2	e2πix	e2πix	PROPN
ejpam-3976	287	3	(	(	PUNCT
ejpam-3976	287	4	2πi)n	2πi)n	PROPN
ejpam-3976	287	5	−	−	PROPN
ejpam-3976	288	1	e−2πix	e−2πix	INTJ
ejpam-3976	288	2	(	(	PUNCT
ejpam-3976	288	3	−2πi)n	−2πi)n	NUM
ejpam-3976	289	1	+	+	NOUN
ejpam-3976	289	2	o	o	X
ejpam-3976	289	3	(	(	PUNCT
ejpam-3976	289	4	e4π|x|	e4π|x|	PROPN
ejpam-3976	289	5	(	(	PUNCT
ejpam-3976	289	6	4π)n	4π)n	NUM
ejpam-3976	289	7	)	)	PUNCT
ejpam-3976	289	8	.	.	PUNCT
ejpam-3976	290	1	(	(	PUNCT
ejpam-3976	290	2	3.12	3.12	NUM
ejpam-3976	290	3	)	)	PUNCT
ejpam-3976	290	4	for	for	ADP
ejpam-3976	290	5	odd	odd	ADJ
ejpam-3976	290	6	indices	index	NOUN
ejpam-3976	290	7	,	,	PUNCT
ejpam-3976	290	8	−1	−1	NOUN
ejpam-3976	290	9	2	2	NUM
ejpam-3976	290	10	g2n+1(x;−1	g2n+1(x;−1	PROPN
ejpam-3976	290	11	)	)	PUNCT
ejpam-3976	290	12	(	(	PUNCT
ejpam-3976	290	13	2n+	2n+	NUM
ejpam-3976	290	14	1	1	NUM
ejpam-3976	290	15	)	)	PUNCT
ejpam-3976	290	16	!	!	PUNCT
ejpam-3976	291	1	=	=	PUNCT
ejpam-3976	292	1	−	−	PROPN
ejpam-3976	292	2	(	(	PUNCT
ejpam-3976	292	3	e2πix	e2πix	PROPN
ejpam-3976	292	4	(	(	PUNCT
ejpam-3976	292	5	2πi)2n+1	2πi)2n+1	NUM
ejpam-3976	292	6	+	+	CCONJ
ejpam-3976	292	7	e−2πix	e−2πix	INTJ
ejpam-3976	292	8	(	(	PUNCT
ejpam-3976	292	9	−2πi)2n+1	−2πi)2n+1	NOUN
ejpam-3976	292	10	)	)	PUNCT
ejpam-3976	293	1	+	+	NOUN
ejpam-3976	293	2	o	o	X
ejpam-3976	293	3	(	(	PUNCT
ejpam-3976	293	4	e4π|x|	e4π|x|	X
ejpam-3976	293	5	(	(	PUNCT
ejpam-3976	293	6	4π)2n+1	4π)2n+1	NOUN
ejpam-3976	293	7	)	)	PUNCT
ejpam-3976	293	8	(	(	PUNCT
ejpam-3976	293	9	3.13	3.13	NUM
ejpam-3976	293	10	)	)	PUNCT
ejpam-3976	293	11	g2n+1(x;−1	g2n+1(x;−1	PROPN
ejpam-3976	293	12	)	)	PUNCT
ejpam-3976	293	13	(	(	PUNCT
ejpam-3976	293	14	2n+	2n+	NUM
ejpam-3976	293	15	1	1	NUM
ejpam-3976	293	16	)	)	PUNCT
ejpam-3976	293	17	!	!	PUNCT
ejpam-3976	294	1	=	=	PUNCT
ejpam-3976	294	2	(	(	PUNCT
ejpam-3976	294	3	−1)n4	−1)n4	NOUN
ejpam-3976	294	4	sin	sin	NOUN
ejpam-3976	294	5	2πx	2πx	NOUN
ejpam-3976	294	6	(	(	PUNCT
ejpam-3976	294	7	2π)2n+1	2π)2n+1	NUM
ejpam-3976	295	1	+	+	NOUN
ejpam-3976	295	2	o	o	X
ejpam-3976	295	3	(	(	PUNCT
ejpam-3976	295	4	e4π|x|	e4π|x|	PROPN
ejpam-3976	295	5	(	(	PUNCT
ejpam-3976	295	6	4π)n	4π)n	NUM
ejpam-3976	295	7	)	)	PUNCT
ejpam-3976	295	8	.	.	PUNCT
ejpam-3976	296	1	(	(	PUNCT
ejpam-3976	296	2	3.14	3.14	NUM
ejpam-3976	296	3	)	)	PUNCT
ejpam-3976	296	4	for	for	ADP
ejpam-3976	296	5	even	even	ADV
ejpam-3976	296	6	indices	index	NOUN
ejpam-3976	296	7	,	,	PUNCT
ejpam-3976	296	8	g2n(x;−1	g2n(x;−1	NOUN
ejpam-3976	296	9	)	)	PUNCT
ejpam-3976	296	10	(	(	PUNCT
ejpam-3976	296	11	2n	2n	NUM
ejpam-3976	296	12	)	)	PUNCT
ejpam-3976	296	13	!	!	PUNCT
ejpam-3976	297	1	=	=	SYM
ejpam-3976	297	2	2	2	NUM
ejpam-3976	297	3	(	(	PUNCT
ejpam-3976	297	4	e2πix	e2πix	PROPN
ejpam-3976	297	5	(	(	PUNCT
ejpam-3976	297	6	2πi)2n	2πi)2n	NUM
ejpam-3976	297	7	+	+	CCONJ
ejpam-3976	297	8	e−2πix	e−2πix	PROPN
ejpam-3976	297	9	(	(	PUNCT
ejpam-3976	297	10	−2πi)2n	−2πi)2n	NOUN
ejpam-3976	297	11	)	)	PUNCT
ejpam-3976	298	1	+	+	NOUN
ejpam-3976	298	2	o	o	X
ejpam-3976	298	3	(	(	PUNCT
ejpam-3976	298	4	e4π|x|	e4π|x|	X
ejpam-3976	298	5	(	(	PUNCT
ejpam-3976	298	6	4π)2n	4π)2n	NUM
ejpam-3976	298	7	)	)	PUNCT
ejpam-3976	298	8	(	(	PUNCT
ejpam-3976	298	9	3.15	3.15	NUM
ejpam-3976	298	10	)	)	PUNCT
ejpam-3976	298	11	=	=	SYM
ejpam-3976	298	12	(	(	PUNCT
ejpam-3976	298	13	−1)n4	−1)n4	PROPN
ejpam-3976	298	14	cos	cos	NOUN
ejpam-3976	298	15	2πx	2πx	ADJ
ejpam-3976	298	16	(	(	PUNCT
ejpam-3976	298	17	2π)2n	2π)2n	NUM
ejpam-3976	299	1	+	+	NOUN
ejpam-3976	299	2	o	o	X
ejpam-3976	299	3	(	(	PUNCT
ejpam-3976	299	4	e4π|x|	e4π|x|	PROPN
ejpam-3976	299	5	(	(	PUNCT
ejpam-3976	299	6	4π)n	4π)n	NUM
ejpam-3976	299	7	)	)	PUNCT
ejpam-3976	299	8	.	.	PUNCT
ejpam-3976	300	1	(	(	PUNCT
ejpam-3976	300	2	3.16	3.16	NUM
ejpam-3976	300	3	)	)	PUNCT
ejpam-3976	300	4	4	4	NUM
ejpam-3976	300	5	.	.	X
ejpam-3976	300	6	apostol	apostol	NOUN
ejpam-3976	300	7	-	-	PUNCT
ejpam-3976	300	8	euler	euler	NOUN
ejpam-3976	300	9	numbers	number	NOUN
ejpam-3976	300	10	and	and	CCONJ
ejpam-3976	300	11	polynomials	polynomial	VERB
ejpam-3976	300	12	the	the	DET
ejpam-3976	300	13	apostol	apostol	NOUN
ejpam-3976	300	14	-	-	PUNCT
ejpam-3976	300	15	euler	euler	NOUN
ejpam-3976	300	16	numbers	number	NOUN
ejpam-3976	300	17	are	be	AUX
ejpam-3976	300	18	defined	define	VERB
ejpam-3976	300	19	by	by	ADP
ejpam-3976	300	20	the	the	DET
ejpam-3976	300	21	generating	generate	VERB
ejpam-3976	300	22	function	function	NOUN
ejpam-3976	300	23	2	2	NUM
ejpam-3976	300	24	λet	λet	NOUN
ejpam-3976	301	1	+	+	NOUN
ejpam-3976	301	2	1	1	NUM
ejpam-3976	301	3	=	=	SYM
ejpam-3976	301	4	∞∑	∞∑	NUM
ejpam-3976	301	5	n=0	n=0	NUM
ejpam-3976	301	6	en(0;λ	en(0;λ	PROPN
ejpam-3976	301	7	)	)	PUNCT
ejpam-3976	301	8	tn	tn	PROPN
ejpam-3976	301	9	n	n	PROPN
ejpam-3976	301	10	!	!	PUNCT
ejpam-3976	301	11	.	.	PUNCT
ejpam-3976	302	1	(	(	PUNCT
ejpam-3976	302	2	4.1	4.1	NUM
ejpam-3976	302	3	)	)	PUNCT
ejpam-3976	302	4	multiplying	multiply	VERB
ejpam-3976	302	5	both	both	DET
ejpam-3976	302	6	sides	side	NOUN
ejpam-3976	302	7	of	of	ADP
ejpam-3976	302	8	(	(	PUNCT
ejpam-3976	302	9	4.1	4.1	NUM
ejpam-3976	302	10	)	)	PUNCT
ejpam-3976	302	11	by	by	ADP
ejpam-3976	302	12	t	t	PROPN
ejpam-3976	302	13	gives	give	VERB
ejpam-3976	302	14	∞∑	∞∑	DET
ejpam-3976	302	15	n=0	n=0	NUM
ejpam-3976	302	16	gn(0;λ	gn(0;λ	PROPN
ejpam-3976	302	17	)	)	PUNCT
ejpam-3976	302	18	tn	tn	PROPN
ejpam-3976	302	19	n	n	ADV
ejpam-3976	302	20	!	!	PUNCT
ejpam-3976	303	1	=	=	NOUN
ejpam-3976	304	1	∞∑	∞∑	PRON
ejpam-3976	304	2	n=0	n=0	NUM
ejpam-3976	304	3	(	(	PUNCT
ejpam-3976	304	4	n+	n+	X
ejpam-3976	304	5	1)en(0;λ	1)en(0;λ	NUM
ejpam-3976	304	6	)	)	PUNCT
ejpam-3976	304	7	tn+1	tn+1	NOUN
ejpam-3976	304	8	(	(	PUNCT
ejpam-3976	304	9	n+	n+	NOUN
ejpam-3976	304	10	1	1	NUM
ejpam-3976	304	11	)	)	PUNCT
ejpam-3976	304	12	!	!	PUNCT
ejpam-3976	304	13	,	,	PUNCT
ejpam-3976	304	14	from	from	ADP
ejpam-3976	304	15	which	which	PRON
ejpam-3976	304	16	we	we	PRON
ejpam-3976	304	17	have	have	VERB
ejpam-3976	304	18	,	,	PUNCT
ejpam-3976	304	19	for	for	ADP
ejpam-3976	304	20	n	n	NUM
ejpam-3976	304	21	≥	≥	NUM
ejpam-3976	304	22	1	1	NUM
ejpam-3976	304	23	en−1(0;λ	en−1(0;λ	NOUN
ejpam-3976	304	24	)	)	PUNCT
ejpam-3976	304	25	=	=	SYM
ejpam-3976	304	26	gn(0;λ	gn(0;λ	PROPN
ejpam-3976	304	27	)	)	PUNCT
ejpam-3976	304	28	n	n	NOUN
ejpam-3976	304	29	=	=	PUNCT
ejpam-3976	304	30	(	(	PUNCT
ejpam-3976	304	31	n−	n−	NOUN
ejpam-3976	304	32	1	1	NUM
ejpam-3976	304	33	)	)	PUNCT
ejpam-3976	304	34	!	!	PUNCT
ejpam-3976	305	1	gn(0;λ	gn(0;λ	NUM
ejpam-3976	305	2	)	)	PUNCT
ejpam-3976	305	3	n	n	CCONJ
ejpam-3976	305	4	!	!	PUNCT
ejpam-3976	305	5	.	.	PUNCT
ejpam-3976	306	1	(	(	PUNCT
ejpam-3976	306	2	4.2	4.2	NUM
ejpam-3976	306	3	)	)	PUNCT
ejpam-3976	306	4	thus	thus	ADV
ejpam-3976	306	5	,	,	PUNCT
ejpam-3976	306	6	from	from	ADP
ejpam-3976	306	7	theorem	theorem	ADJ
ejpam-3976	306	8	2.3	2.3	NUM
ejpam-3976	306	9	,	,	PUNCT
ejpam-3976	306	10	en−1(0;λ	en−1(0;λ	NOUN
ejpam-3976	306	11	)	)	PUNCT
ejpam-3976	306	12	=	=	PUNCT
ejpam-3976	307	1	2(n−	2(n−	NUM
ejpam-3976	307	2	1	1	NUM
ejpam-3976	307	3	)	)	PUNCT
ejpam-3976	307	4	!	!	PUNCT
ejpam-3976	308	1	[	[	PUNCT
ejpam-3976	308	2	∞∑	∞∑	NUM
ejpam-3976	308	3	n=0	n=0	SYM
ejpam-3976	308	4	1	1	NUM
ejpam-3976	308	5	un	un	NOUN
ejpam-3976	308	6	+	+	PROPN
ejpam-3976	308	7	o	o	X
ejpam-3976	308	8	(	(	PUNCT
ejpam-3976	308	9	ν−n	ν−n	NOUN
ejpam-3976	308	10	)	)	PUNCT
ejpam-3976	308	11	]	]	PUNCT
ejpam-3976	308	12	,	,	PUNCT
ejpam-3976	308	13	(	(	PUNCT
ejpam-3976	308	14	4.3	4.3	NUM
ejpam-3976	308	15	)	)	PUNCT
ejpam-3976	308	16	where	where	SCONJ
ejpam-3976	308	17	f	f	PROPN
ejpam-3976	308	18	⊆	⊆	NUM
ejpam-3976	308	19	tλ	tλ	NOUN
ejpam-3976	308	20	=	=	PUNCT
ejpam-3976	308	21	{	{	PUNCT
ejpam-3976	308	22	(	(	PUNCT
ejpam-3976	308	23	2k	2k	NOUN
ejpam-3976	308	24	+	+	CCONJ
ejpam-3976	308	25	1)πi−	1)πi−	NUM
ejpam-3976	308	26	log	log	NOUN
ejpam-3976	308	27	λ	λ	INTJ
ejpam-3976	308	28	|	|	ADV
ejpam-3976	308	29	k	k	PROPN
ejpam-3976	308	30	∈	∈	PROPN
ejpam-3976	309	1	z	z	PROPN
ejpam-3976	309	2	}	}	PUNCT
ejpam-3976	309	3	and	and	CCONJ
ejpam-3976	309	4	f	f	PROPN
ejpam-3976	309	5	satisfies	satisfy	VERB
ejpam-3976	309	6	c.	c.	PROPN
ejpam-3976	309	7	corcino	corcino	PROPN
ejpam-3976	309	8	/	/	SYM
ejpam-3976	309	9	eur	eur	PROPN
ejpam-3976	309	10	.	.	PUNCT
ejpam-3976	310	1	j.	j.	PROPN
ejpam-3976	310	2	pure	pure	PROPN
ejpam-3976	310	3	appl	appl	PROPN
ejpam-3976	310	4	.	.	PROPN
ejpam-3976	310	5	math	math	PROPN
ejpam-3976	310	6	,	,	PUNCT
ejpam-3976	310	7	14	14	NUM
ejpam-3976	310	8	(	(	PUNCT
ejpam-3976	310	9	3	3	NUM
ejpam-3976	310	10	)	)	PUNCT
ejpam-3976	310	11	(	(	PUNCT
ejpam-3976	310	12	2021	2021	NUM
ejpam-3976	310	13	)	)	PUNCT
ejpam-3976	310	14	,	,	PUNCT
ejpam-3976	310	15	666	666	NUM
ejpam-3976	310	16	-	-	SYM
ejpam-3976	310	17	684	684	NUM
ejpam-3976	310	18	681	681	NUM
ejpam-3976	310	19	max{|u|	max{|u|	NOUN
ejpam-3976	310	20	:	:	PUNCT
ejpam-3976	310	21	u	u	NOUN
ejpam-3976	310	22	∈	∈	PROPN
ejpam-3976	310	23	f	f	X
ejpam-3976	310	24	}	}	PUNCT
ejpam-3976	310	25	<	<	X
ejpam-3976	310	26	min{|u|	min{|u|	NOUN
ejpam-3976	310	27	:	:	PUNCT
ejpam-3976	310	28	u	u	NOUN
ejpam-3976	310	29	∈	∈	PROPN
ejpam-3976	310	30	tλ\f	tλ\f	PRON
ejpam-3976	310	31	}	}	PUNCT
ejpam-3976	310	32	=	=	SYM
ejpam-3976	310	33	ν	ν	X
ejpam-3976	310	34	.	.	PROPN
ejpam-3976	310	35	for	for	ADP
ejpam-3976	310	36	odd	odd	ADJ
ejpam-3976	310	37	n	n	CCONJ
ejpam-3976	310	38	,	,	PUNCT
ejpam-3976	310	39	say	say	VERB
ejpam-3976	310	40	n	n	PRON
ejpam-3976	310	41	=	=	SYM
ejpam-3976	310	42	2k	2k	PROPN
ejpam-3976	310	43	+	+	CCONJ
ejpam-3976	310	44	1	1	NUM
ejpam-3976	310	45	,	,	PUNCT
ejpam-3976	310	46	from	from	ADP
ejpam-3976	310	47	(	(	PUNCT
ejpam-3976	310	48	4.2	4.2	NUM
ejpam-3976	310	49	)	)	PUNCT
ejpam-3976	310	50	,	,	PUNCT
ejpam-3976	310	51	we	we	PRON
ejpam-3976	310	52	have	have	VERB
ejpam-3976	310	53	e2k(0;λ	e2k(0;λ	PRON
ejpam-3976	310	54	)	)	PUNCT
ejpam-3976	311	1	=	=	PUNCT
ejpam-3976	311	2	g2k+1(0;λ	g2k+1(0;λ	NOUN
ejpam-3976	311	3	)	)	PUNCT
ejpam-3976	311	4	2k	2k	NOUN
ejpam-3976	311	5	+	+	CCONJ
ejpam-3976	311	6	1	1	NUM
ejpam-3976	311	7	,	,	PUNCT
ejpam-3976	311	8	(	(	PUNCT
ejpam-3976	311	9	4.4	4.4	NUM
ejpam-3976	311	10	)	)	PUNCT
ejpam-3976	311	11	while	while	SCONJ
ejpam-3976	311	12	for	for	ADP
ejpam-3976	311	13	even	even	ADV
ejpam-3976	311	14	n	n	CCONJ
ejpam-3976	311	15	,	,	PUNCT
ejpam-3976	311	16	say	say	VERB
ejpam-3976	311	17	n	n	PROPN
ejpam-3976	311	18	=	=	SYM
ejpam-3976	311	19	2k	2k	NUM
ejpam-3976	311	20	,	,	PUNCT
ejpam-3976	311	21	e2k−1(0;λ	e2k−1(0;λ	NOUN
ejpam-3976	311	22	)	)	PUNCT
ejpam-3976	311	23	=	=	SYM
ejpam-3976	311	24	g2k(0;λ	g2k(0;λ	NOUN
ejpam-3976	311	25	)	)	PUNCT
ejpam-3976	311	26	2k	2k	NOUN
ejpam-3976	311	27	.	.	PUNCT
ejpam-3976	312	1	(	(	PUNCT
ejpam-3976	312	2	4.5	4.5	NUM
ejpam-3976	312	3	)	)	PUNCT
ejpam-3976	312	4	the	the	DET
ejpam-3976	312	5	case	case	NOUN
ejpam-3976	312	6	λ	λ	X
ejpam-3976	312	7	=	=	SYM
ejpam-3976	312	8	1	1	NUM
ejpam-3976	312	9	,	,	PUNCT
ejpam-3976	312	10	corresponds	correspond	VERB
ejpam-3976	312	11	to	to	ADP
ejpam-3976	312	12	the	the	DET
ejpam-3976	312	13	euler	euler	NOUN
ejpam-3976	312	14	numbers	number	NOUN
ejpam-3976	312	15	en	en	ADP
ejpam-3976	312	16	.	.	PUNCT
ejpam-3976	313	1	from	from	ADP
ejpam-3976	313	2	(	(	PUNCT
ejpam-3976	313	3	4.2	4.2	NUM
ejpam-3976	313	4	)	)	PUNCT
ejpam-3976	313	5	,	,	PUNCT
ejpam-3976	313	6	en−1	en−1	PROPN
ejpam-3976	313	7	=	=	SYM
ejpam-3976	313	8	gn	gn	PROPN
ejpam-3976	313	9	n	n	ADV
ejpam-3976	313	10	.	.	PUNCT
ejpam-3976	314	1	(	(	PUNCT
ejpam-3976	314	2	4.6	4.6	NUM
ejpam-3976	314	3	)	)	PUNCT
ejpam-3976	314	4	since	since	SCONJ
ejpam-3976	314	5	gn	gn	PROPN
ejpam-3976	314	6	=	=	NOUN
ejpam-3976	314	7	0	0	PROPN
ejpam-3976	314	8	for	for	ADP
ejpam-3976	314	9	all	all	PRON
ejpam-3976	314	10	odd	odd	ADJ
ejpam-3976	314	11	n	n	PRON
ejpam-3976	314	12	≥	≥	NUM
ejpam-3976	314	13	3	3	NUM
ejpam-3976	314	14	,	,	PUNCT
ejpam-3976	314	15	e2k	e2k	NOUN
ejpam-3976	314	16	=	=	SYM
ejpam-3976	314	17	0	0	NUM
ejpam-3976	314	18	for	for	ADP
ejpam-3976	314	19	k	k	PROPN
ejpam-3976	314	20	≥	≥	PROPN
ejpam-3976	314	21	1	1	NUM
ejpam-3976	314	22	.	.	PUNCT
ejpam-3976	315	1	for	for	ADP
ejpam-3976	315	2	odd	odd	ADJ
ejpam-3976	315	3	indices	index	NOUN
ejpam-3976	315	4	,	,	PUNCT
ejpam-3976	315	5	using	use	VERB
ejpam-3976	315	6	(	(	PUNCT
ejpam-3976	315	7	2.9	2.9	NUM
ejpam-3976	315	8	)	)	PUNCT
ejpam-3976	315	9	we	we	PRON
ejpam-3976	315	10	have	have	VERB
ejpam-3976	315	11	e2n−1	e2n−1	NUM
ejpam-3976	315	12	=	=	SYM
ejpam-3976	315	13	(	(	PUNCT
ejpam-3976	315	14	2n−	2n−	PROPN
ejpam-3976	315	15	1	1	NUM
ejpam-3976	315	16	)	)	PUNCT
ejpam-3976	315	17	!	!	PUNCT
ejpam-3976	316	1	g2n	g2n	PROPN
ejpam-3976	316	2	(	(	PUNCT
ejpam-3976	316	3	2n	2n	NUM
ejpam-3976	316	4	)	)	PUNCT
ejpam-3976	316	5	!	!	PUNCT
ejpam-3976	317	1	=	=	PUNCT
ejpam-3976	318	1	(	(	PUNCT
ejpam-3976	318	2	2n−	2n−	PROPN
ejpam-3976	318	3	1	1	NUM
ejpam-3976	318	4	)	)	PUNCT
ejpam-3976	318	5	!	!	PUNCT
ejpam-3976	319	1	(	(	PUNCT
ejpam-3976	319	2	(	(	PUNCT
ejpam-3976	319	3	−1)n(4	−1)n(4	PROPN
ejpam-3976	319	4	)	)	PUNCT
ejpam-3976	319	5	π2n	π2n	PROPN
ejpam-3976	320	1	+	+	PROPN
ejpam-3976	320	2	o	o	X
ejpam-3976	320	3	(	(	PUNCT
ejpam-3976	320	4	(	(	PUNCT
ejpam-3976	320	5	3π)−n	3π)−n	NOUN
ejpam-3976	320	6	)	)	PUNCT
ejpam-3976	320	7	)	)	PUNCT
ejpam-3976	320	8	,	,	PUNCT
ejpam-3976	320	9	n	n	X
ejpam-3976	320	10	≥	≥	NOUN
ejpam-3976	320	11	2	2	NUM
ejpam-3976	320	12	.	.	PUNCT
ejpam-3976	320	13	(	(	PUNCT
ejpam-3976	320	14	4.7	4.7	NUM
ejpam-3976	320	15	)	)	PUNCT
ejpam-3976	320	16	taking	take	VERB
ejpam-3976	320	17	n	n	NOUN
ejpam-3976	320	18	=	=	SYM
ejpam-3976	320	19	2	2	NUM
ejpam-3976	320	20	,	,	PUNCT
ejpam-3976	320	21	e3	e3	VERB
ejpam-3976	320	22	≈	≈	PROPN
ejpam-3976	320	23	3	3	NUM
ejpam-3976	320	24	!	!	PUNCT
ejpam-3976	321	1	(	(	PUNCT
ejpam-3976	321	2	4	4	NUM
ejpam-3976	321	3	π4	π4	NOUN
ejpam-3976	321	4	)	)	PUNCT
ejpam-3976	322	1	=	=	SYM
ejpam-3976	322	2	24	24	NUM
ejpam-3976	322	3	π4	π4	NOUN
ejpam-3976	322	4	=	=	SYM
ejpam-3976	322	5	0.24638	0.24638	NUM
ejpam-3976	322	6	.	.	PUNCT
ejpam-3976	323	1	the	the	DET
ejpam-3976	323	2	actual	actual	ADJ
ejpam-3976	323	3	value	value	NOUN
ejpam-3976	323	4	of	of	ADP
ejpam-3976	323	5	e3	e3	NOUN
ejpam-3976	323	6	=	=	NOUN
ejpam-3976	323	7	0.25	0.25	NUM
ejpam-3976	323	8	.	.	PUNCT
ejpam-3976	324	1	the	the	DET
ejpam-3976	324	2	apostol	apostol	NOUN
ejpam-3976	324	3	-	-	PUNCT
ejpam-3976	324	4	euler	euler	NOUN
ejpam-3976	324	5	polynomials	polynomial	NOUN
ejpam-3976	324	6	en(x;λ	en(x;λ	NOUN
ejpam-3976	324	7	)	)	PUNCT
ejpam-3976	324	8	are	be	AUX
ejpam-3976	324	9	defined	define	VERB
ejpam-3976	324	10	by	by	ADP
ejpam-3976	324	11	the	the	DET
ejpam-3976	324	12	generating	generate	VERB
ejpam-3976	324	13	function	function	NOUN
ejpam-3976	324	14	2ext	2ext	PRON
ejpam-3976	324	15	λet	λet	VERB
ejpam-3976	324	16	+	+	NOUN
ejpam-3976	324	17	1	1	NUM
ejpam-3976	324	18	=	=	VERB
ejpam-3976	324	19	∞∑	∞∑	NUM
ejpam-3976	324	20	n=0	n=0	SYM
ejpam-3976	324	21	en(x;λ	en(x;λ	NOUN
ejpam-3976	324	22	)	)	PUNCT
ejpam-3976	324	23	tn	tn	PROPN
ejpam-3976	324	24	n	n	PROPN
ejpam-3976	324	25	!	!	PROPN
ejpam-3976	324	26	,	,	PUNCT
ejpam-3976	324	27	(	(	PUNCT
ejpam-3976	324	28	4.8	4.8	NUM
ejpam-3976	324	29	)	)	PUNCT
ejpam-3976	324	30	which	which	PRON
ejpam-3976	324	31	can	can	AUX
ejpam-3976	324	32	be	be	AUX
ejpam-3976	324	33	written	write	VERB
ejpam-3976	324	34	∞∑	∞∑	DET
ejpam-3976	324	35	n=0	n=0	NUM
ejpam-3976	324	36	gn(x;λ)tn	gn(x;λ)tn	NOUN
ejpam-3976	324	37	n	n	NOUN
ejpam-3976	324	38	!	!	PUNCT
ejpam-3976	324	39	=	=	NOUN
ejpam-3976	325	1	∞∑	∞∑	PRON
ejpam-3976	325	2	n=0	n=0	NUM
ejpam-3976	325	3	(	(	PUNCT
ejpam-3976	325	4	n+	n+	NOUN
ejpam-3976	325	5	1)en(x;λ	1)en(x;λ	PROPN
ejpam-3976	325	6	)	)	PUNCT
ejpam-3976	325	7	tn+1	tn+1	NOUN
ejpam-3976	325	8	(	(	PUNCT
ejpam-3976	325	9	n+	n+	NOUN
ejpam-3976	325	10	1	1	NUM
ejpam-3976	325	11	)	)	PUNCT
ejpam-3976	325	12	!	!	PUNCT
ejpam-3976	325	13	.	.	PUNCT
ejpam-3976	326	1	(	(	PUNCT
ejpam-3976	326	2	4.9	4.9	NUM
ejpam-3976	326	3	)	)	PUNCT
ejpam-3976	326	4	thus	thus	ADV
ejpam-3976	326	5	,	,	PUNCT
ejpam-3976	326	6	en−1(x;λ	en−1(x;λ	ADJ
ejpam-3976	326	7	)	)	PUNCT
ejpam-3976	326	8	=	=	SYM
ejpam-3976	326	9	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	326	10	)	)	PUNCT
ejpam-3976	326	11	n	n	CCONJ
ejpam-3976	326	12	.	.	PUNCT
ejpam-3976	327	1	(	(	PUNCT
ejpam-3976	327	2	4.10	4.10	NUM
ejpam-3976	327	3	)	)	PUNCT
ejpam-3976	327	4	from	from	ADP
ejpam-3976	327	5	theorem	theorem	ADJ
ejpam-3976	327	6	2.4	2.4	NUM
ejpam-3976	327	7	,	,	PUNCT
ejpam-3976	327	8	en−1(x;λ	en−1(x;λ	ADJ
ejpam-3976	327	9	)	)	PUNCT
ejpam-3976	327	10	=	=	SYM
ejpam-3976	327	11	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	327	12	)	)	PUNCT
ejpam-3976	327	13	n	n	PROPN
ejpam-3976	327	14	·	·	PUNCT
ejpam-3976	327	15	(	(	PUNCT
ejpam-3976	327	16	n−	n−	NOUN
ejpam-3976	327	17	1	1	NUM
ejpam-3976	327	18	)	)	PUNCT
ejpam-3976	327	19	!	!	PUNCT
ejpam-3976	328	1	(	(	PUNCT
ejpam-3976	328	2	n−	n−	NOUN
ejpam-3976	328	3	1	1	NUM
ejpam-3976	328	4	)	)	PUNCT
ejpam-3976	328	5	!	!	PUNCT
ejpam-3976	329	1	=	=	PUNCT
ejpam-3976	329	2	(	(	PUNCT
ejpam-3976	329	3	n−	n−	NOUN
ejpam-3976	329	4	1	1	NUM
ejpam-3976	329	5	)	)	PUNCT
ejpam-3976	329	6	!	!	PUNCT
ejpam-3976	330	1	gn(x;λ	gn(x;λ	NOUN
ejpam-3976	330	2	)	)	PUNCT
ejpam-3976	331	1	n	n	CCONJ
ejpam-3976	331	2	!	!	PUNCT
ejpam-3976	332	1	=	=	PUNCT
ejpam-3976	332	2	(	(	PUNCT
ejpam-3976	332	3	n−	n−	NOUN
ejpam-3976	332	4	1	1	NUM
ejpam-3976	332	5	)	)	PUNCT
ejpam-3976	332	6	!	!	PUNCT
ejpam-3976	333	1	(	(	PUNCT
ejpam-3976	333	2	2	2	NUM
ejpam-3976	333	3	∑	∑	NUM
ejpam-3976	333	4	u∈f	u∈f	NOUN
ejpam-3976	333	5	euz	euz	NOUN
ejpam-3976	333	6	un	un	PROPN
ejpam-3976	334	1	+	+	PROPN
ejpam-3976	334	2	o	o	X
ejpam-3976	334	3	(	(	PUNCT
ejpam-3976	334	4	eν|x|	eν|x|	NOUN
ejpam-3976	334	5	νn	νn	ADJ
ejpam-3976	334	6	)	)	PUNCT
ejpam-3976	334	7	)	)	PUNCT
ejpam-3976	334	8	.	.	PUNCT
ejpam-3976	335	1	hence	hence	ADV
ejpam-3976	335	2	,	,	PUNCT
ejpam-3976	335	3	we	we	PRON
ejpam-3976	335	4	have	have	VERB
ejpam-3976	335	5	the	the	DET
ejpam-3976	335	6	following	follow	VERB
ejpam-3976	335	7	corollary	corollary	NOUN
ejpam-3976	335	8	.	.	PUNCT
ejpam-3976	336	1	c.	c.	PROPN
ejpam-3976	336	2	corcino	corcino	PROPN
ejpam-3976	336	3	/	/	SYM
ejpam-3976	336	4	eur	eur	PROPN
ejpam-3976	336	5	.	.	PUNCT
ejpam-3976	337	1	j.	j.	PROPN
ejpam-3976	337	2	pure	pure	PROPN
ejpam-3976	337	3	appl	appl	PROPN
ejpam-3976	337	4	.	.	PROPN
ejpam-3976	337	5	math	math	PROPN
ejpam-3976	337	6	,	,	PUNCT
ejpam-3976	337	7	14	14	NUM
ejpam-3976	337	8	(	(	PUNCT
ejpam-3976	337	9	3	3	NUM
ejpam-3976	337	10	)	)	PUNCT
ejpam-3976	337	11	(	(	PUNCT
ejpam-3976	337	12	2021	2021	NUM
ejpam-3976	337	13	)	)	PUNCT
ejpam-3976	337	14	,	,	PUNCT
ejpam-3976	337	15	666	666	NUM
ejpam-3976	337	16	-	-	SYM
ejpam-3976	337	17	684	684	NUM
ejpam-3976	337	18	682	682	NUM
ejpam-3976	337	19	corollary	corollary	ADJ
ejpam-3976	337	20	4.1	4.1	NUM
ejpam-3976	337	21	.	.	PUNCT
ejpam-3976	338	1	given	give	VERB
ejpam-3976	338	2	λ	λ	PROPN
ejpam-3976	338	3	∈	∈	PROPN
ejpam-3976	338	4	c\{0	c\{0	PROPN
ejpam-3976	338	5	}	}	PUNCT
ejpam-3976	338	6	,	,	PUNCT
ejpam-3976	338	7	let	let	VERB
ejpam-3976	338	8	f	f	PRON
ejpam-3976	338	9	be	be	AUX
ejpam-3976	338	10	a	a	DET
ejpam-3976	338	11	finite	finite	NOUN
ejpam-3976	338	12	subset	subset	NOUN
ejpam-3976	338	13	of	of	ADP
ejpam-3976	338	14	tλ	tλ	ADP
ejpam-3976	338	15	satisfying	satisfying	NOUN
ejpam-3976	338	16	max{|u|	max{|u|	NOUN
ejpam-3976	338	17	:	:	PUNCT
ejpam-3976	338	18	u	u	NOUN
ejpam-3976	338	19	∈	∈	PROPN
ejpam-3976	338	20	f	f	X
ejpam-3976	338	21	}	}	PUNCT
ejpam-3976	338	22	<	<	X
ejpam-3976	338	23	min{|u|	min{|u|	NOUN
ejpam-3976	338	24	:	:	PUNCT
ejpam-3976	338	25	u	u	NOUN
ejpam-3976	338	26	∈	∈	PROPN
ejpam-3976	338	27	tλ\f	tλ\f	PRON
ejpam-3976	338	28	}	}	PUNCT
ejpam-3976	338	29	=	=	SYM
ejpam-3976	338	30	ν	ν	X
ejpam-3976	338	31	.	.	PUNCT
ejpam-3976	338	32	let	let	VERB
ejpam-3976	338	33	k	k	PRON
ejpam-3976	338	34	be	be	AUX
ejpam-3976	338	35	an	an	DET
ejpam-3976	338	36	arbitrary	arbitrary	ADJ
ejpam-3976	338	37	compact	compact	ADJ
ejpam-3976	338	38	subset	subset	NOUN
ejpam-3976	338	39	of	of	ADP
ejpam-3976	338	40	c.	c.	PROPN
ejpam-3976	338	41	the	the	DET
ejpam-3976	338	42	apostol	apostol	PROPN
ejpam-3976	338	43	-	-	PUNCT
ejpam-3976	338	44	euler	euler	NOUN
ejpam-3976	338	45	polynomials	polynomial	NOUN
ejpam-3976	338	46	satisfy	satisfy	VERB
ejpam-3976	338	47	uniformly	uniformly	ADV
ejpam-3976	338	48	on	on	ADP
ejpam-3976	338	49	k	k	PROPN
ejpam-3976	338	50	the	the	DET
ejpam-3976	338	51	estimates	estimate	NOUN
ejpam-3976	338	52	,	,	PUNCT
ejpam-3976	338	53	en−1(x;λ	en−1(x;λ	NOUN
ejpam-3976	338	54	)	)	PUNCT
ejpam-3976	338	55	(	(	PUNCT
ejpam-3976	338	56	n−	n−	NOUN
ejpam-3976	338	57	1	1	NUM
ejpam-3976	338	58	)	)	PUNCT
ejpam-3976	338	59	!	!	PUNCT
ejpam-3976	339	1	=	=	SYM
ejpam-3976	339	2	2	2	NUM
ejpam-3976	339	3	∑	∑	PUNCT
ejpam-3976	339	4	u∈f	u∈f	NOUN
ejpam-3976	339	5	eux	eux	X
ejpam-3976	339	6	un	un	PROPN
ejpam-3976	340	1	+	+	PROPN
ejpam-3976	340	2	o	o	X
ejpam-3976	340	3	(	(	PUNCT
ejpam-3976	340	4	eν|x|	eν|x|	NOUN
ejpam-3976	340	5	νn	νn	PROPN
ejpam-3976	340	6	)	)	PUNCT
ejpam-3976	340	7	,	,	PUNCT
ejpam-3976	340	8	where	where	SCONJ
ejpam-3976	340	9	the	the	DET
ejpam-3976	340	10	constant	constant	ADJ
ejpam-3976	340	11	implicit	implicit	NOUN
ejpam-3976	340	12	in	in	ADP
ejpam-3976	340	13	the	the	DET
ejpam-3976	340	14	order	order	NOUN
ejpam-3976	340	15	term	term	NOUN
ejpam-3976	340	16	depends	depend	VERB
ejpam-3976	340	17	on	on	ADP
ejpam-3976	340	18	λ	λ	PROPN
ejpam-3976	340	19	,	,	PUNCT
ejpam-3976	340	20	f	f	PROPN
ejpam-3976	340	21	and	and	CCONJ
ejpam-3976	340	22	k.	k.	PROPN
ejpam-3976	340	23	moreover	moreover	ADV
ejpam-3976	340	24	,	,	PUNCT
ejpam-3976	340	25	for	for	ADP
ejpam-3976	340	26	n	n	CCONJ
ejpam-3976	340	27	�	�	PROPN
ejpam-3976	340	28	0	0	NUM
ejpam-3976	340	29	,	,	PUNCT
ejpam-3976	340	30	this	this	DET
ejpam-3976	340	31	constant	constant	ADJ
ejpam-3976	340	32	can	can	AUX
ejpam-3976	340	33	be	be	AUX
ejpam-3976	340	34	made	make	VERB
ejpam-3976	340	35	independent	independent	ADJ
ejpam-3976	340	36	of	of	ADP
ejpam-3976	340	37	k	k	PROPN
ejpam-3976	340	38	,	,	PUNCT
ejpam-3976	340	39	equal	equal	ADJ
ejpam-3976	340	40	to	to	ADP
ejpam-3976	340	41	the	the	DET
ejpam-3976	340	42	constant	constant	NOUN
ejpam-3976	340	43	for	for	ADP
ejpam-3976	340	44	the	the	DET
ejpam-3976	340	45	apostol	apostol	NOUN
ejpam-3976	340	46	-	-	PUNCT
ejpam-3976	340	47	euler	euler	NOUN
ejpam-3976	340	48	numbers	number	NOUN
ejpam-3976	340	49	,	,	PUNCT
ejpam-3976	340	50	corresponding	correspond	VERB
ejpam-3976	340	51	to	to	ADP
ejpam-3976	340	52	the	the	DET
ejpam-3976	340	53	case	case	NOUN
ejpam-3976	340	54	x	x	X
ejpam-3976	341	1	=	=	NOUN
ejpam-3976	341	2	0	0	X
ejpam-3976	341	3	.	.	PUNCT
ejpam-3976	342	1	it	it	PRON
ejpam-3976	342	2	follows	follow	VERB
ejpam-3976	342	3	from	from	ADP
ejpam-3976	342	4	corollary	corollary	ADJ
ejpam-3976	342	5	2.5	2.5	NUM
ejpam-3976	342	6	that	that	PRON
ejpam-3976	342	7	the	the	DET
ejpam-3976	342	8	euler	euler	NOUN
ejpam-3976	342	9	polynomials	polynomial	NOUN
ejpam-3976	342	10	which	which	PRON
ejpam-3976	342	11	correspond	correspond	VERB
ejpam-3976	342	12	to	to	ADP
ejpam-3976	342	13	λ	λ	PROPN
ejpam-3976	342	14	=	=	SYM
ejpam-3976	342	15	1	1	NUM
ejpam-3976	342	16	,	,	PUNCT
ejpam-3976	342	17	satisfy	satisfy	VERB
ejpam-3976	342	18	,	,	PUNCT
ejpam-3976	342	19	uniformly	uniformly	ADV
ejpam-3976	342	20	on	on	ADP
ejpam-3976	342	21	a	a	DET
ejpam-3976	342	22	compact	compact	ADJ
ejpam-3976	342	23	subset	subset	NOUN
ejpam-3976	342	24	k	k	PROPN
ejpam-3976	342	25	of	of	ADP
ejpam-3976	342	26	c	c	PROPN
ejpam-3976	342	27	the	the	DET
ejpam-3976	342	28	estimates	estimate	NOUN
ejpam-3976	342	29	e2n−1(x	e2n−1(x	VERB
ejpam-3976	342	30	)	)	PUNCT
ejpam-3976	342	31	(	(	PUNCT
ejpam-3976	342	32	2n−	2n−	PROPN
ejpam-3976	342	33	1	1	NUM
ejpam-3976	342	34	)	)	PUNCT
ejpam-3976	342	35	!	!	PUNCT
ejpam-3976	343	1	=	=	SYM
ejpam-3976	343	2	g2n(x	g2n(x	PROPN
ejpam-3976	343	3	)	)	PUNCT
ejpam-3976	343	4	(	(	PUNCT
ejpam-3976	343	5	2n	2n	NUM
ejpam-3976	343	6	)	)	PUNCT
ejpam-3976	343	7	!	!	PUNCT
ejpam-3976	344	1	=	=	PUNCT
ejpam-3976	344	2	(	(	PUNCT
ejpam-3976	344	3	−1)n4	−1)n4	NOUN
ejpam-3976	344	4	cosπx	cosπx	NOUN
ejpam-3976	344	5	π2n	π2n	PROPN
ejpam-3976	345	1	+	+	ADP
ejpam-3976	345	2	o	o	X
ejpam-3976	345	3	(	(	PUNCT
ejpam-3976	345	4	e3π|x|	e3π|x|	X
ejpam-3976	345	5	(	(	PUNCT
ejpam-3976	345	6	3π)n	3π)n	NUM
ejpam-3976	345	7	)	)	PUNCT
ejpam-3976	345	8	,	,	PUNCT
ejpam-3976	345	9	(	(	PUNCT
ejpam-3976	345	10	4.11	4.11	NUM
ejpam-3976	345	11	)	)	PUNCT
ejpam-3976	345	12	e2n(x	e2n(x	PROPN
ejpam-3976	345	13	)	)	PUNCT
ejpam-3976	345	14	(	(	PUNCT
ejpam-3976	345	15	2n	2n	NUM
ejpam-3976	345	16	)	)	PUNCT
ejpam-3976	345	17	!	!	PUNCT
ejpam-3976	346	1	=	=	PUNCT
ejpam-3976	346	2	g2n+1(x	g2n+1(x	NOUN
ejpam-3976	346	3	)	)	PUNCT
ejpam-3976	346	4	(	(	PUNCT
ejpam-3976	346	5	2n+	2n+	NUM
ejpam-3976	346	6	1	1	NUM
ejpam-3976	346	7	)	)	PUNCT
ejpam-3976	346	8	!	!	PUNCT
ejpam-3976	347	1	=	=	PUNCT
ejpam-3976	347	2	(	(	PUNCT
ejpam-3976	347	3	−1)n4	−1)n4	X
ejpam-3976	347	4	sinπx	sinπx	X
ejpam-3976	347	5	π2n+1	π2n+1	NOUN
ejpam-3976	348	1	+	+	NOUN
ejpam-3976	348	2	o	o	X
ejpam-3976	348	3	(	(	PUNCT
ejpam-3976	348	4	e3π|x|	e3π|x|	X
ejpam-3976	348	5	(	(	PUNCT
ejpam-3976	348	6	3π)n	3π)n	NUM
ejpam-3976	348	7	)	)	PUNCT
ejpam-3976	348	8	,	,	PUNCT
ejpam-3976	348	9	(	(	PUNCT
ejpam-3976	348	10	4.12	4.12	NUM
ejpam-3976	348	11	)	)	PUNCT
ejpam-3976	348	12	as	as	ADP
ejpam-3976	348	13	n→∞	n→∞	NUM
ejpam-3976	348	14	,	,	PUNCT
ejpam-3976	348	15	for	for	ADP
ejpam-3976	348	16	n	n	PRON
ejpam-3976	348	17	≥	≥	NUM
ejpam-3976	348	18	1	1	NUM
ejpam-3976	348	19	.	.	PUNCT
ejpam-3976	349	1	the	the	DET
ejpam-3976	349	2	apostol	apostol	NOUN
ejpam-3976	349	3	-	-	PUNCT
ejpam-3976	349	4	euler	euler	NOUN
ejpam-3976	349	5	polynomials	polynomial	NOUN
ejpam-3976	349	6	en−1(x;−1	en−1(x;−1	NOUN
ejpam-3976	349	7	)	)	PUNCT
ejpam-3976	349	8	correspond	correspond	VERB
ejpam-3976	349	9	to	to	ADP
ejpam-3976	349	10	the	the	DET
ejpam-3976	349	11	special	special	ADJ
ejpam-3976	349	12	case	case	NOUN
ejpam-3976	349	13	λ	λ	X
ejpam-3976	349	14	=	=	SYM
ejpam-3976	349	15	−1	−1	NOUN
ejpam-3976	349	16	.	.	PUNCT
ejpam-3976	350	1	from	from	ADP
ejpam-3976	350	2	(	(	PUNCT
ejpam-3976	350	3	4.10	4.10	NUM
ejpam-3976	350	4	)	)	PUNCT
ejpam-3976	350	5	,	,	PUNCT
ejpam-3976	350	6	en−1(x;−1	en−1(x;−1	PROPN
ejpam-3976	350	7	)	)	PUNCT
ejpam-3976	350	8	=	=	SYM
ejpam-3976	350	9	gn(x;−1	gn(x;−1	NOUN
ejpam-3976	350	10	)	)	PUNCT
ejpam-3976	350	11	n	n	NOUN
ejpam-3976	350	12	.	.	PUNCT
ejpam-3976	351	1	(	(	PUNCT
ejpam-3976	351	2	4.13	4.13	X
ejpam-3976	351	3	)	)	PUNCT
ejpam-3976	351	4	it	it	PRON
ejpam-3976	351	5	follows	follow	VERB
ejpam-3976	351	6	from	from	ADP
ejpam-3976	351	7	(	(	PUNCT
ejpam-3976	351	8	3.10	3.10	NUM
ejpam-3976	351	9	)	)	PUNCT
ejpam-3976	351	10	and	and	CCONJ
ejpam-3976	351	11	(	(	PUNCT
ejpam-3976	351	12	3.11	3.11	NUM
ejpam-3976	351	13	)	)	PUNCT
ejpam-3976	351	14	,	,	PUNCT
ejpam-3976	351	15	respectively	respectively	ADV
ejpam-3976	351	16	that	that	SCONJ
ejpam-3976	351	17	e2n(x;−1	e2n(x;−1	ADJ
ejpam-3976	351	18	)	)	PUNCT
ejpam-3976	351	19	(	(	PUNCT
ejpam-3976	351	20	2n	2n	NUM
ejpam-3976	351	21	)	)	PUNCT
ejpam-3976	351	22	!	!	PUNCT
ejpam-3976	352	1	=	=	PUNCT
ejpam-3976	352	2	(	(	PUNCT
ejpam-3976	352	3	−1)n4	−1)n4	NOUN
ejpam-3976	352	4	sin	sin	NOUN
ejpam-3976	352	5	2πx	2πx	NOUN
ejpam-3976	352	6	(	(	PUNCT
ejpam-3976	352	7	2π)2n+1	2π)2n+1	NUM
ejpam-3976	353	1	+	+	NOUN
ejpam-3976	353	2	o	o	X
ejpam-3976	353	3	(	(	PUNCT
ejpam-3976	353	4	e4π|x|	e4π|x|	PROPN
ejpam-3976	353	5	(	(	PUNCT
ejpam-3976	353	6	4π)n	4π)n	NUM
ejpam-3976	353	7	)	)	PUNCT
ejpam-3976	353	8	,	,	PUNCT
ejpam-3976	353	9	(	(	PUNCT
ejpam-3976	353	10	4.14	4.14	NUM
ejpam-3976	353	11	)	)	PUNCT
ejpam-3976	353	12	e2n−1(x;−1	e2n−1(x;−1	PROPN
ejpam-3976	353	13	)	)	PUNCT
ejpam-3976	353	14	(	(	PUNCT
ejpam-3976	353	15	2n−	2n−	PROPN
ejpam-3976	353	16	1	1	NUM
ejpam-3976	353	17	)	)	PUNCT
ejpam-3976	353	18	!	!	PUNCT
ejpam-3976	354	1	=	=	PUNCT
ejpam-3976	354	2	(	(	PUNCT
ejpam-3976	354	3	−1)n4	−1)n4	PROPN
ejpam-3976	354	4	cos	cos	NOUN
ejpam-3976	354	5	2πx	2πx	ADJ
ejpam-3976	354	6	(	(	PUNCT
ejpam-3976	354	7	2π)2n	2π)2n	NUM
ejpam-3976	354	8	+	+	NOUN
ejpam-3976	354	9	o	o	X
ejpam-3976	354	10	(	(	PUNCT
ejpam-3976	354	11	e4π|x|	e4π|x|	PROPN
ejpam-3976	354	12	(	(	PUNCT
ejpam-3976	354	13	4π)n	4π)n	NUM
ejpam-3976	354	14	)	)	PUNCT
ejpam-3976	354	15	,	,	PUNCT
ejpam-3976	354	16	(	(	PUNCT
ejpam-3976	354	17	4.15	4.15	NUM
ejpam-3976	354	18	)	)	PUNCT
ejpam-3976	354	19	on	on	ADP
ejpam-3976	354	20	a	a	DET
ejpam-3976	354	21	compact	compact	ADJ
ejpam-3976	354	22	subset	subset	NOUN
ejpam-3976	354	23	k	k	PROPN
ejpam-3976	354	24	of	of	ADP
ejpam-3976	354	25	c.	c.	PROPN
ejpam-3976	354	26	5	5	NUM
ejpam-3976	354	27	.	.	PUNCT
ejpam-3976	355	1	conclusion	conclusion	NOUN
ejpam-3976	355	2	asymptotic	asymptotic	ADJ
ejpam-3976	355	3	approximations	approximation	NOUN
ejpam-3976	355	4	of	of	ADP
ejpam-3976	355	5	the	the	DET
ejpam-3976	355	6	apostol	apostol	NOUN
ejpam-3976	355	7	-	-	PUNCT
ejpam-3976	355	8	genocchi	genocchi	PROPN
ejpam-3976	355	9	numbers	number	NOUN
ejpam-3976	355	10	and	and	CCONJ
ejpam-3976	355	11	polynomials	polynomial	NOUN
ejpam-3976	355	12	were	be	AUX
ejpam-3976	355	13	obtained	obtain	VERB
ejpam-3976	355	14	for	for	ADP
ejpam-3976	355	15	values	value	NOUN
ejpam-3976	355	16	of	of	ADP
ejpam-3976	355	17	the	the	DET
ejpam-3976	355	18	parameter	parameter	NOUN
ejpam-3976	355	19	λ	λ	PROPN
ejpam-3976	355	20	in	in	ADP
ejpam-3976	355	21	c\{0	c\{0	NOUN
ejpam-3976	355	22	}	}	PUNCT
ejpam-3976	355	23	.	.	PUNCT
ejpam-3976	356	1	unlike	unlike	ADP
ejpam-3976	356	2	in	in	ADP
ejpam-3976	356	3	[	[	X
ejpam-3976	356	4	15	15	NUM
ejpam-3976	356	5	]	]	X
ejpam-3976	356	6	we	we	PRON
ejpam-3976	356	7	have	have	AUX
ejpam-3976	356	8	considered	consider	VERB
ejpam-3976	356	9	explicitly	explicitly	ADV
ejpam-3976	356	10	the	the	DET
ejpam-3976	356	11	case	case	NOUN
ejpam-3976	356	12	when	when	SCONJ
ejpam-3976	356	13	λ	λ	PROPN
ejpam-3976	356	14	is	be	AUX
ejpam-3976	356	15	negative	negative	ADJ
ejpam-3976	356	16	and	and	CCONJ
ejpam-3976	356	17	obtained	obtain	VERB
ejpam-3976	356	18	corresponding	corresponding	ADJ
ejpam-3976	356	19	asymptotic	asymptotic	ADJ
ejpam-3976	356	20	formulas	formula	NOUN
ejpam-3976	356	21	.	.	PUNCT
ejpam-3976	357	1	references	reference	NOUN
ejpam-3976	357	2	683	683	NUM
ejpam-3976	357	3	moreover	moreover	ADV
ejpam-3976	357	4	,	,	PUNCT
ejpam-3976	357	5	the	the	DET
ejpam-3976	357	6	asymptotic	asymptotic	ADJ
ejpam-3976	357	7	formulas	formula	NOUN
ejpam-3976	357	8	for	for	ADP
ejpam-3976	357	9	λ	λ	NOUN
ejpam-3976	357	10	=	=	SYM
ejpam-3976	357	11	1	1	NUM
ejpam-3976	357	12	are	be	AUX
ejpam-3976	357	13	explicitly	explicitly	ADV
ejpam-3976	357	14	obtained	obtain	VERB
ejpam-3976	357	15	for	for	ADP
ejpam-3976	357	16	each	each	PRON
ejpam-3976	357	17	of	of	ADP
ejpam-3976	357	18	the	the	DET
ejpam-3976	357	19	apostolgenocchi	apostolgenocchi	NOUN
ejpam-3976	357	20	and	and	CCONJ
ejpam-3976	357	21	apostol	apostol	NOUN
ejpam-3976	357	22	-	-	PUNCT
ejpam-3976	357	23	euler	euler	NOUN
ejpam-3976	357	24	numbers	number	NOUN
ejpam-3976	357	25	and	and	CCONJ
ejpam-3976	357	26	polynomials	polynomial	NOUN
ejpam-3976	357	27	.	.	PUNCT
ejpam-3976	358	1	the	the	DET
ejpam-3976	358	2	tangent	tangent	NOUN
ejpam-3976	358	3	polynomials	polynomial	VERB
ejpam-3976	358	4	[	[	X
ejpam-3976	358	5	8	8	NUM
ejpam-3976	358	6	]	]	PUNCT
ejpam-3976	358	7	have	have	AUX
ejpam-3976	358	8	generating	generate	VERB
ejpam-3976	358	9	function	function	NOUN
ejpam-3976	358	10	very	very	ADV
ejpam-3976	358	11	similar	similar	ADJ
ejpam-3976	358	12	to	to	ADP
ejpam-3976	358	13	that	that	PRON
ejpam-3976	358	14	of	of	ADP
ejpam-3976	358	15	the	the	DET
ejpam-3976	358	16	apostol	apostol	NOUN
ejpam-3976	358	17	-	-	PUNCT
ejpam-3976	358	18	genocchi	genocchi	PROPN
ejpam-3976	358	19	polynomials	polynomial	NOUN
ejpam-3976	358	20	.	.	PUNCT
ejpam-3976	359	1	the	the	DET
ejpam-3976	359	2	author	author	NOUN
ejpam-3976	359	3	recommends	recommend	VERB
ejpam-3976	359	4	finding	find	VERB
ejpam-3976	359	5	fourier	fourier	ADJ
ejpam-3976	359	6	expansion	expansion	NOUN
ejpam-3976	359	7	and	and	CCONJ
ejpam-3976	359	8	asymptotic	asymptotic	ADJ
ejpam-3976	359	9	approximations	approximation	NOUN
ejpam-3976	359	10	of	of	ADP
ejpam-3976	359	11	these	these	DET
ejpam-3976	359	12	polynomials	polynomial	NOUN
ejpam-3976	359	13	.	.	PUNCT
ejpam-3976	360	1	acknowledgements	acknowledgement	NOUN
ejpam-3976	360	2	this	this	DET
ejpam-3976	360	3	research	research	NOUN
ejpam-3976	360	4	project	project	NOUN
ejpam-3976	360	5	is	be	AUX
ejpam-3976	360	6	funded	fund	VERB
ejpam-3976	360	7	by	by	ADP
ejpam-3976	360	8	cebu	cebu	PROPN
ejpam-3976	360	9	normal	normal	ADJ
ejpam-3976	360	10	university	university	NOUN
ejpam-3976	360	11	through	through	ADP
ejpam-3976	360	12	its	its	PRON
ejpam-3976	360	13	center	center	NOUN
ejpam-3976	360	14	for	for	ADP
ejpam-3976	360	15	research	research	NOUN
ejpam-3976	360	16	and	and	CCONJ
ejpam-3976	360	17	development	development	NOUN
ejpam-3976	360	18	.	.	PUNCT
ejpam-3976	361	1	references	reference	NOUN
ejpam-3976	361	2	[	[	X
ejpam-3976	361	3	1	1	NUM
ejpam-3976	361	4	]	]	PUNCT
ejpam-3976	361	5	s.	s.	PROPN
ejpam-3976	361	6	araci	araci	PROPN
ejpam-3976	361	7	,	,	PUNCT
ejpam-3976	361	8	w.a	w.a	PROPN
ejpam-3976	361	9	khan	khan	PROPN
ejpam-3976	361	10	,	,	PUNCT
ejpam-3976	361	11	m.	m.	NOUN
ejpam-3976	361	12	acikgoz	acikgoz	PROPN
ejpam-3976	361	13	,	,	PUNCT
ejpam-3976	361	14	c.	c.	PROPN
ejpam-3976	361	15	ozel	ozel	PROPN
ejpam-3976	361	16	and	and	CCONJ
ejpam-3976	361	17	p.	p.	PROPN
ejpam-3976	361	18	kumam	kumam	PROPN
ejpam-3976	361	19	,	,	PUNCT
ejpam-3976	361	20	a	a	DET
ejpam-3976	361	21	new	new	ADJ
ejpam-3976	361	22	generaliztion	generaliztion	NOUN
ejpam-3976	361	23	of	of	ADP
ejpam-3976	361	24	apostol	apostol	PROPN
ejpam-3976	361	25	type	type	NOUN
ejpam-3976	361	26	hermite	hermite	PROPN
ejpam-3976	361	27	-	-	PUNCT
ejpam-3976	361	28	genocchi	genocchi	PROPN
ejpam-3976	361	29	polynomials	polynomial	NOUN
ejpam-3976	361	30	and	and	CCONJ
ejpam-3976	361	31	its	its	PRON
ejpam-3976	361	32	applications	application	NOUN
ejpam-3976	361	33	,	,	PUNCT
ejpam-3976	361	34	springerplus	springerplus	NOUN
ejpam-3976	361	35	,	,	PUNCT
ejpam-3976	361	36	5(2016	5(2016	NUM
ejpam-3976	361	37	)	)	PUNCT
ejpam-3976	361	38	,	,	PUNCT
ejpam-3976	361	39	art	art	NOUN
ejpam-3976	361	40	.	.	PUNCT
ejpam-3976	362	1	i	i	PRON
ejpam-3976	362	2	d	d	PROPN
ejpam-3976	362	3	860	860	NUM
ejpam-3976	362	4	.	.	PUNCT
ejpam-3976	363	1	[	[	X
ejpam-3976	363	2	2	2	NUM
ejpam-3976	363	3	]	]	PUNCT
ejpam-3976	363	4	a.	a.	NOUN
ejpam-3976	363	5	bayad	bayad	PROPN
ejpam-3976	363	6	,	,	PUNCT
ejpam-3976	363	7	fourier	fourier	NOUN
ejpam-3976	363	8	expansions	expansion	NOUN
ejpam-3976	363	9	for	for	ADP
ejpam-3976	363	10	apostol	apostol	NOUN
ejpam-3976	363	11	-	-	PUNCT
ejpam-3976	363	12	bernoulli	bernoulli	PROPN
ejpam-3976	363	13	,	,	PUNCT
ejpam-3976	363	14	apostoleuler	apostoleuler	NOUN
ejpam-3976	363	15	and	and	CCONJ
ejpam-3976	363	16	apostolgenocchi	apostolgenocchi	NOUN
ejpam-3976	363	17	polynomials	polynomial	NOUN
ejpam-3976	363	18	,	,	PUNCT
ejpam-3976	363	19	math	math	NOUN
ejpam-3976	363	20	comp	comp	PROPN
ejpam-3976	363	21	.	.	PUNCT
ejpam-3976	363	22	,	,	PUNCT
ejpam-3976	363	23	80	80	NUM
ejpam-3976	363	24	(	(	PUNCT
ejpam-3976	363	25	2011	2011	NUM
ejpam-3976	363	26	)	)	PUNCT
ejpam-3976	363	27	,	,	PUNCT
ejpam-3976	363	28	2219–2221	2219–2221	NOUN
ejpam-3976	363	29	.	.	PUNCT
ejpam-3976	364	1	[	[	X
ejpam-3976	364	2	3	3	X
ejpam-3976	364	3	]	]	X
ejpam-3976	364	4	c.	c.	PROPN
ejpam-3976	364	5	b.	b.	PROPN
ejpam-3976	364	6	corcino	corcino	PROPN
ejpam-3976	364	7	,	,	PUNCT
ejpam-3976	364	8	r.b	r.b	PROPN
ejpam-3976	364	9	.	.	PROPN
ejpam-3976	364	10	corcino	corcino	PROPN
ejpam-3976	364	11	,	,	PUNCT
ejpam-3976	364	12	asymptotics	asymptotic	NOUN
ejpam-3976	364	13	of	of	ADP
ejpam-3976	364	14	genocchi	genocchi	PROPN
ejpam-3976	364	15	polynomials	polynomial	NOUN
ejpam-3976	364	16	and	and	CCONJ
ejpam-3976	364	17	higher	high	ADJ
ejpam-3976	364	18	order	order	NOUN
ejpam-3976	364	19	genocchi	genocchi	NOUN
ejpam-3976	364	20	polynomials	polynomial	VERB
ejpam-3976	364	21	using	use	VERB
ejpam-3976	364	22	residues	residue	NOUN
ejpam-3976	364	23	.	.	PUNCT
ejpam-3976	365	1	afr	afr	PROPN
ejpam-3976	365	2	.	.	PUNCT
ejpam-3976	365	3	math	math	NOUN
ejpam-3976	365	4	.	.	PUNCT
ejpam-3976	366	1	(	(	PUNCT
ejpam-3976	366	2	2020	2020	NUM
ejpam-3976	366	3	)	)	PUNCT
ejpam-3976	366	4	,	,	PUNCT
ejpam-3976	366	5	https://doi.org/10.1007/s13370-019-00759-z	https://doi.org/10.1007/s13370-019-00759-z	NOUN
ejpam-3976	366	6	[	[	X
ejpam-3976	366	7	4	4	NUM
ejpam-3976	366	8	]	]	PUNCT
ejpam-3976	366	9	c.	c.	PROPN
ejpam-3976	366	10	b.	b.	PROPN
ejpam-3976	366	11	corcino	corcino	PROPN
ejpam-3976	366	12	,	,	PUNCT
ejpam-3976	366	13	r.b	r.b	PROPN
ejpam-3976	366	14	.	.	PROPN
ejpam-3976	366	15	corcino	corcino	PROPN
ejpam-3976	366	16	,	,	PUNCT
ejpam-3976	366	17	fourier	fourier	NOUN
ejpam-3976	366	18	expansions	expansion	NOUN
ejpam-3976	366	19	for	for	ADP
ejpam-3976	366	20	higher	high	ADJ
ejpam-3976	366	21	-	-	PUNCT
ejpam-3976	366	22	order	order	NOUN
ejpam-3976	366	23	apostol	apostol	NOUN
ejpam-3976	366	24	-	-	PUNCT
ejpam-3976	366	25	genocchi	genocchi	NOUN
ejpam-3976	366	26	,	,	PUNCT
ejpam-3976	366	27	apostol	apostol	NOUN
ejpam-3976	366	28	-	-	PUNCT
ejpam-3976	366	29	bernoulli	bernoulli	NOUN
ejpam-3976	366	30	and	and	CCONJ
ejpam-3976	366	31	apostol	apostol	NOUN
ejpam-3976	366	32	-	-	PUNCT
ejpam-3976	366	33	euler	euler	NOUN
ejpam-3976	366	34	polynomials	polynomial	NOUN
ejpam-3976	366	35	,	,	PUNCT
ejpam-3976	366	36	advances	advance	NOUN
ejpam-3976	366	37	in	in	ADP
ejpam-3976	366	38	difference	difference	NOUN
ejpam-3976	366	39	equations	equation	NOUN
ejpam-3976	366	40	,	,	PUNCT
ejpam-3976	366	41	2020(1	2020(1	NUM
ejpam-3976	366	42	)	)	PUNCT
ejpam-3976	366	43	,	,	PUNCT
ejpam-3976	366	44	1	1	NUM
ejpam-3976	366	45	-	-	SYM
ejpam-3976	366	46	13	13	NUM
ejpam-3976	366	47	.	.	PUNCT
ejpam-3976	367	1	[	[	X
ejpam-3976	367	2	5	5	NUM
ejpam-3976	367	3	]	]	PUNCT
ejpam-3976	367	4	a.	a.	NOUN
ejpam-3976	367	5	duran	duran	PROPN
ejpam-3976	367	6	,	,	PUNCT
ejpam-3976	367	7	m.	m.	NOUN
ejpam-3976	367	8	acikgoz	acikgoz	PROPN
ejpam-3976	367	9	,	,	PUNCT
ejpam-3976	367	10	s.	s.	PROPN
ejpam-3976	367	11	araci	araci	PROPN
ejpam-3976	367	12	,	,	PUNCT
ejpam-3976	367	13	a	a	DET
ejpam-3976	367	14	note	note	NOUN
ejpam-3976	367	15	on	on	ADP
ejpam-3976	367	16	the	the	DET
ejpam-3976	367	17	symmetric	symmetric	ADJ
ejpam-3976	367	18	relations	relation	NOUN
ejpam-3976	367	19	of	of	ADP
ejpam-3976	367	20	q	q	ADJ
ejpam-3976	367	21	-	-	PUNCT
ejpam-3976	367	22	genocchi	genocchi	ADJ
ejpam-3976	367	23	polynomials	polynomial	NOUN
ejpam-3976	367	24	under	under	ADP
ejpam-3976	367	25	symmetric	symmetric	ADJ
ejpam-3976	367	26	group	group	NOUN
ejpam-3976	367	27	of	of	ADP
ejpam-3976	367	28	degree	degree	NOUN
ejpam-3976	367	29	n	n	CCONJ
ejpam-3976	367	30	,	,	PUNCT
ejpam-3976	367	31	tamap	tamap	NOUN
ejpam-3976	367	32	journal	journal	NOUN
ejpam-3976	367	33	of	of	ADP
ejpam-3976	367	34	mathematics	mathematic	NOUN
ejpam-3976	367	35	and	and	CCONJ
ejpam-3976	367	36	statistics	statistic	NOUN
ejpam-3976	367	37	,	,	PUNCT
ejpam-3976	367	38	2017	2017	NUM
ejpam-3976	367	39	(	(	PUNCT
ejpam-3976	367	40	article	article	NOUN
ejpam-3976	367	41	i	i	PROPN
ejpam-3976	367	42	d	d	PROPN
ejpam-3976	367	43	7	7	NUM
ejpam-3976	367	44	)	)	PUNCT
ejpam-3976	367	45	,	,	PUNCT
ejpam-3976	367	46	8	8	NUM
ejpam-3976	367	47	pages	page	NOUN
ejpam-3976	367	48	.	.	PUNCT
ejpam-3976	368	1	[	[	X
ejpam-3976	368	2	6	6	NUM
ejpam-3976	368	3	]	]	X
ejpam-3976	368	4	u.	u.	PROPN
ejpam-3976	368	5	duran	duran	PROPN
ejpam-3976	368	6	,	,	PUNCT
ejpam-3976	368	7	m.	m.	NOUN
ejpam-3976	368	8	acikgoz	acikgoz	PROPN
ejpam-3976	368	9	,	,	PUNCT
ejpam-3976	368	10	s.	s.	PROPN
ejpam-3976	368	11	araci	araci	PROPN
ejpam-3976	368	12	,	,	PUNCT
ejpam-3976	368	13	construction	construction	NOUN
ejpam-3976	368	14	of	of	ADP
ejpam-3976	368	15	the	the	DET
ejpam-3976	368	16	type	type	NOUN
ejpam-3976	368	17	2	2	NUM
ejpam-3976	368	18	poly	poly	ADJ
ejpam-3976	368	19	-	-	PUNCT
ejpam-3976	368	20	frobenius	frobenius	NOUN
ejpam-3976	368	21	-	-	PUNCT
ejpam-3976	368	22	genocchi	genocchi	NOUN
ejpam-3976	368	23	polynomials	polynomial	VERB
ejpam-3976	368	24	with	with	ADP
ejpam-3976	368	25	their	their	PRON
ejpam-3976	368	26	certain	certain	ADJ
ejpam-3976	368	27	applications	application	NOUN
ejpam-3976	368	28	,	,	PUNCT
ejpam-3976	368	29	advances	advance	NOUN
ejpam-3976	368	30	in	in	ADP
ejpam-3976	368	31	difference	difference	NOUN
ejpam-3976	368	32	equations	equation	NOUN
ejpam-3976	368	33	,	,	PUNCT
ejpam-3976	368	34	2020	2020	NUM
ejpam-3976	368	35	,	,	PUNCT
ejpam-3976	368	36	432(2020	432(2020	NUM
ejpam-3976	368	37	)	)	PUNCT
ejpam-3976	368	38	.	.	PUNCT
ejpam-3976	369	1	[	[	X
ejpam-3976	369	2	7	7	NUM
ejpam-3976	369	3	]	]	PUNCT
ejpam-3976	369	4	d.-s	d.-	NOUN
ejpam-3976	369	5	.	.	PUNCT
ejpam-3976	370	1	kim	kim	PROPN
ejpam-3976	370	2	,	,	PUNCT
ejpam-3976	370	3	t.	t.	PROPN
ejpam-3976	370	4	kim	kim	PROPN
ejpam-3976	370	5	,	,	PUNCT
ejpam-3976	370	6	a	a	DET
ejpam-3976	370	7	note	note	NOUN
ejpam-3976	370	8	on	on	ADP
ejpam-3976	370	9	polyexponential	polyexponential	ADJ
ejpam-3976	370	10	and	and	CCONJ
ejpam-3976	370	11	unipoly	unipoly	ADJ
ejpam-3976	370	12	functions	function	NOUN
ejpam-3976	370	13	,	,	PUNCT
ejpam-3976	370	14	russ	russ	PROPN
ejpam-3976	370	15	.	.	PUNCT
ejpam-3976	371	1	j.	j.	PROPN
ejpam-3976	371	2	math	math	PROPN
ejpam-3976	371	3	.	.	PUNCT
ejpam-3976	372	1	phys	phy	NOUN
ejpam-3976	372	2	.	.	PUNCT
ejpam-3976	373	1	2019	2019	NUM
ejpam-3976	373	2	26(1	26(1	NUM
ejpam-3976	373	3	)	)	PUNCT
ejpam-3976	373	4	,	,	PUNCT
ejpam-3976	373	5	40	40	NUM
ejpam-3976	373	6	-	-	SYM
ejpam-3976	373	7	49	49	NUM
ejpam-3976	373	8	.	.	PUNCT
ejpam-3976	374	1	[	[	X
ejpam-3976	374	2	8	8	NUM
ejpam-3976	374	3	]	]	X
ejpam-3976	374	4	b.	b.	PROPN
ejpam-3976	374	5	kurt	kurt	PROPN
ejpam-3976	374	6	,	,	PUNCT
ejpam-3976	374	7	identities	identity	NOUN
ejpam-3976	374	8	and	and	CCONJ
ejpam-3976	374	9	relations	relation	NOUN
ejpam-3976	374	10	on	on	ADP
ejpam-3976	374	11	hermite	hermite	PROPN
ejpam-3976	374	12	-	-	PUNCT
ejpam-3976	374	13	based	base	VERB
ejpam-3976	374	14	tangent	tangent	NOUN
ejpam-3976	374	15	polynomials	polynomial	NOUN
ejpam-3976	374	16	,	,	PUNCT
ejpam-3976	374	17	arxiv:1811.03587v1[math.nt]8	arxiv:1811.03587v1[math.nt]8	ADJ
ejpam-3976	374	18	nov	nov	PROPN
ejpam-3976	374	19	2018	2018	NUM
ejpam-3976	374	20	.	.	PUNCT
ejpam-3976	375	1	[	[	X
ejpam-3976	375	2	9	9	NUM
ejpam-3976	375	3	]	]	X
ejpam-3976	375	4	y.	y.	NOUN
ejpam-3976	375	5	he	he	PRON
ejpam-3976	375	6	,	,	PUNCT
ejpam-3976	375	7	s.	s.	PROPN
ejpam-3976	375	8	araci	araci	PROPN
ejpam-3976	375	9	,	,	PUNCT
ejpam-3976	375	10	h.m	h.m	PROPN
ejpam-3976	375	11	.	.	PROPN
ejpam-3976	375	12	srivastava	srivastava	PROPN
ejpam-3976	375	13	and	and	CCONJ
ejpam-3976	375	14	m.	m.	NOUN
ejpam-3976	375	15	acikgoz	acikgoz	PROPN
ejpam-3976	375	16	,	,	PUNCT
ejpam-3976	375	17	some	some	DET
ejpam-3976	375	18	new	new	ADJ
ejpam-3976	375	19	identities	identity	NOUN
ejpam-3976	375	20	for	for	ADP
ejpam-3976	375	21	the	the	DET
ejpam-3976	375	22	apostolbernoulli	apostolbernoulli	NOUN
ejpam-3976	375	23	polynomials	polynomial	NOUN
ejpam-3976	375	24	and	and	CCONJ
ejpam-3976	375	25	the	the	DET
ejpam-3976	375	26	apostol	apostol	NOUN
ejpam-3976	375	27	-	-	PUNCT
ejpam-3976	375	28	genocchi	genocchi	PROPN
ejpam-3976	375	29	polynomials	polynomial	NOUN
ejpam-3976	375	30	,	,	PUNCT
ejpam-3976	375	31	appl	appl	PROPN
ejpam-3976	375	32	.	.	PROPN
ejpam-3976	375	33	math	math	PROPN
ejpam-3976	375	34	.	.	PUNCT
ejpam-3976	376	1	comput	comput	NOUN
ejpam-3976	376	2	.	.	PUNCT
ejpam-3976	376	3	,	,	PUNCT
ejpam-3976	376	4	262	262	NUM
ejpam-3976	376	5	(	(	PUNCT
ejpam-3976	376	6	2015	2015	NUM
ejpam-3976	376	7	)	)	PUNCT
ejpam-3976	376	8	,	,	PUNCT
ejpam-3976	376	9	31	31	NUM
ejpam-3976	376	10	-	-	SYM
ejpam-3976	376	11	41	41	NUM
ejpam-3976	376	12	.	.	PUNCT
ejpam-3976	377	1	references	reference	NOUN
ejpam-3976	377	2	684	684	NUM
ejpam-3976	378	1	[	[	X
ejpam-3976	378	2	10	10	NUM
ejpam-3976	378	3	]	]	X
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ejpam-3976	378	5	he	he	PRON
ejpam-3976	378	6	,	,	PUNCT
ejpam-3976	378	7	some	some	DET
ejpam-3976	378	8	new	new	ADJ
ejpam-3976	378	9	results	result	NOUN
ejpam-3976	378	10	on	on	ADP
ejpam-3976	378	11	products	product	NOUN
ejpam-3976	378	12	of	of	ADP
ejpam-3976	378	13	the	the	DET
ejpam-3976	378	14	apostol	apostol	NOUN
ejpam-3976	378	15	-	-	PUNCT
ejpam-3976	378	16	genocchi	genocchi	PROPN
ejpam-3976	378	17	polynomials	polynomial	NOUN
ejpam-3976	378	18	,	,	PUNCT
ejpam-3976	378	19	j.	j.	PROPN
ejpam-3976	378	20	comput	comput	PROPN
ejpam-3976	378	21	.	.	PUNCT
ejpam-3976	379	1	anal	anal	PROPN
ejpam-3976	379	2	.	.	PUNCT
ejpam-3976	379	3	appl	appl	PROPN
ejpam-3976	379	4	.	.	PROPN
ejpam-3976	379	5	,	,	PUNCT
ejpam-3976	379	6	22(4	22(4	NUM
ejpam-3976	379	7	)	)	PUNCT
ejpam-3976	379	8	(	(	PUNCT
ejpam-3976	379	9	2017	2017	NUM
ejpam-3976	379	10	)	)	PUNCT
ejpam-3976	379	11	,	,	PUNCT
ejpam-3976	379	12	591	591	NUM
ejpam-3976	379	13	-	-	SYM
ejpam-3976	379	14	600	600	NUM
ejpam-3976	379	15	.	.	PUNCT
ejpam-3976	380	1	[	[	X
ejpam-3976	380	2	11	11	NUM
ejpam-3976	380	3	]	]	X
ejpam-3976	380	4	y.	y.	NOUN
ejpam-3976	380	5	he	he	PRON
ejpam-3976	380	6	,	,	PUNCT
ejpam-3976	380	7	s.	s.	PROPN
ejpam-3976	380	8	araci	araci	PROPN
ejpam-3976	380	9	,	,	PUNCT
ejpam-3976	380	10	h.m	h.m	PROPN
ejpam-3976	380	11	.	.	PROPN
ejpam-3976	380	12	srivastava	srivastava	PROPN
ejpam-3976	380	13	and	and	CCONJ
ejpam-3976	380	14	m.	m.	PROPN
ejpam-3976	380	15	abdel	abdel	PROPN
ejpam-3976	380	16	-	-	PUNCT
ejpam-3976	380	17	aty	aty	PROPN
ejpam-3976	380	18	,	,	PUNCT
ejpam-3976	380	19	higher	high	ADJ
ejpam-3976	380	20	-	-	PUNCT
ejpam-3976	380	21	order	order	NOUN
ejpam-3976	380	22	convolutions	convolution	NOUN
ejpam-3976	380	23	for	for	ADP
ejpam-3976	380	24	apostol	apostol	NOUN
ejpam-3976	380	25	-	-	PUNCT
ejpam-3976	380	26	bernoulli	bernoulli	NOUN
ejpam-3976	380	27	,	,	PUNCT
ejpam-3976	380	28	apostol	apostol	NOUN
ejpam-3976	380	29	-	-	PUNCT
ejpam-3976	380	30	euler	euler	NOUN
ejpam-3976	380	31	and	and	CCONJ
ejpam-3976	380	32	apostol	apostol	NOUN
ejpam-3976	380	33	-	-	PUNCT
ejpam-3976	380	34	genocchi	genocchi	PROPN
ejpam-3976	380	35	polynomials	polynomial	NOUN
ejpam-3976	380	36	.	.	PUNCT
ejpam-3976	381	1	mathematics	mathematic	NOUN
ejpam-3976	381	2	6	6	NUM
ejpam-3976	381	3	,	,	PUNCT
ejpam-3976	381	4	article	article	NOUN
ejpam-3976	381	5	i	i	PROPN
ejpam-3976	381	6	d	d	PROPN
ejpam-3976	381	7	329	329	NUM
ejpam-3976	381	8	(	(	PUNCT
ejpam-3976	381	9	2019	2019	NUM
ejpam-3976	381	10	)	)	PUNCT
ejpam-3976	381	11	.	.	PUNCT
ejpam-3976	382	1	https://doi.org/10.3390/math6120329	https://doi.org/10.3390/math6120329	VERB
ejpam-3976	383	1	[	[	X
ejpam-3976	383	2	12	12	NUM
ejpam-3976	383	3	]	]	X
ejpam-3976	383	4	h.	h.	PROPN
ejpam-3976	383	5	jolany	jolany	PROPN
ejpam-3976	383	6	and	and	CCONJ
ejpam-3976	383	7	h.	h.	PROPN
ejpam-3976	383	8	sharifi	sharifi	PROPN
ejpam-3976	383	9	,	,	PUNCT
ejpam-3976	383	10	some	some	PRON
ejpam-3976	383	11	results	result	VERB
ejpam-3976	383	12	for	for	ADP
ejpam-3976	383	13	the	the	DET
ejpam-3976	383	14	apostol	apostol	NOUN
ejpam-3976	383	15	-	-	PUNCT
ejpam-3976	383	16	genocchi	genocchi	PROPN
ejpam-3976	383	17	polynomials	polynomial	NOUN
ejpam-3976	383	18	of	of	ADP
ejpam-3976	383	19	higher	high	ADJ
ejpam-3976	383	20	order	order	NOUN
ejpam-3976	383	21	,	,	PUNCT
ejpam-3976	383	22	arxiv	arxiv	PROPN
ejpam-3976	383	23	preprint	preprint	NOUN
ejpam-3976	383	24	arxiv:1104.1501.,(2011	arxiv:1104.1501.,(2011	NOUN
ejpam-3976	383	25	)	)	PUNCT
ejpam-3976	384	1	[	[	X
ejpam-3976	384	2	13	13	NUM
ejpam-3976	384	3	]	]	X
ejpam-3976	384	4	q.m	q.m	PROPN
ejpam-3976	384	5	.	.	PROPN
ejpam-3976	384	6	luo	luo	PROPN
ejpam-3976	384	7	,	,	PUNCT
ejpam-3976	384	8	extensions	extension	NOUN
ejpam-3976	384	9	of	of	ADP
ejpam-3976	384	10	the	the	DET
ejpam-3976	384	11	genocchi	genocchi	PROPN
ejpam-3976	384	12	polynomials	polynomial	NOUN
ejpam-3976	384	13	and	and	CCONJ
ejpam-3976	384	14	their	their	PRON
ejpam-3976	384	15	fourier	fourier	NOUN
ejpam-3976	384	16	expansions	expansion	NOUN
ejpam-3976	384	17	and	and	CCONJ
ejpam-3976	384	18	integral	integral	ADJ
ejpam-3976	384	19	representations	representation	NOUN
ejpam-3976	384	20	.	.	PUNCT
ejpam-3976	385	1	osaka	osaka	PROPN
ejpam-3976	385	2	j.	j.	PROPN
ejpam-3976	385	3	math	math	PROPN
ejpam-3976	385	4	.	.	PUNCT
ejpam-3976	386	1	48	48	NUM
ejpam-3976	386	2	,	,	PUNCT
ejpam-3976	386	3	291309	291309	NUM
ejpam-3976	386	4	(	(	PUNCT
ejpam-3976	386	5	2011	2011	NUM
ejpam-3976	386	6	)	)	PUNCT
ejpam-3976	387	1	[	[	X
ejpam-3976	387	2	14	14	NUM
ejpam-3976	387	3	]	]	X
ejpam-3976	387	4	q.	q.	PROPN
ejpam-3976	387	5	m.	m.	PROPN
ejpam-3976	387	6	luo	luo	PROPN
ejpam-3976	387	7	,	,	PUNCT
ejpam-3976	387	8	h.	h.	PROPN
ejpam-3976	387	9	m.	m.	PROPN
ejpam-3976	387	10	srivastava	srivastava	PROPN
ejpam-3976	387	11	,	,	PUNCT
ejpam-3976	387	12	some	some	DET
ejpam-3976	387	13	generalizations	generalization	NOUN
ejpam-3976	387	14	of	of	ADP
ejpam-3976	387	15	the	the	DET
ejpam-3976	387	16	apostol	apostol	NOUN
ejpam-3976	387	17	-	-	PUNCT
ejpam-3976	387	18	genocchi	genocchi	PROPN
ejpam-3976	387	19	polynomials	polynomial	NOUN
ejpam-3976	387	20	and	and	CCONJ
ejpam-3976	387	21	the	the	DET
ejpam-3976	387	22	stirling	stirling	NOUN
ejpam-3976	387	23	numbers	number	NOUN
ejpam-3976	387	24	of	of	ADP
ejpam-3976	387	25	the	the	DET
ejpam-3976	387	26	second	second	ADJ
ejpam-3976	387	27	kind	kind	NOUN
ejpam-3976	387	28	,	,	PUNCT
ejpam-3976	387	29	appl	appl	PROPN
ejpam-3976	387	30	.	.	PROPN
ejpam-3976	387	31	math	math	PROPN
ejpam-3976	387	32	.	.	PUNCT
ejpam-3976	388	1	comput	comput	NOUN
ejpam-3976	388	2	.	.	PUNCT
ejpam-3976	388	3	,	,	PUNCT
ejpam-3976	388	4	217(12),(2011	217(12),(2011	NUM
ejpam-3976	388	5	)	)	PUNCT
ejpam-3976	388	6	,	,	PUNCT
ejpam-3976	388	7	5702	5702	NUM
ejpam-3976	388	8	-	-	SYM
ejpam-3976	388	9	5728	5728	NUM
ejpam-3976	388	10	.	.	PUNCT
ejpam-3976	389	1	[	[	X
ejpam-3976	389	2	15	15	NUM
ejpam-3976	389	3	]	]	X
ejpam-3976	389	4	l.	l.	PROPN
ejpam-3976	389	5	navas	navas	PROPN
ejpam-3976	389	6	,	,	PUNCT
ejpam-3976	389	7	f.	f.	PROPN
ejpam-3976	389	8	ruiz	ruiz	PROPN
ejpam-3976	389	9	,	,	PUNCT
ejpam-3976	389	10	and	and	CCONJ
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ejpam-3976	389	12	,	,	PUNCT
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ejpam-3976	389	14	estimates	estimate	NOUN
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ejpam-3976	389	16	apostol	apostol	NOUN
ejpam-3976	389	17	-	-	PUNCT
ejpam-3976	389	18	bernoulli	bernoulli	NOUN
ejpam-3976	389	19	and	and	CCONJ
ejpam-3976	389	20	apostol	apostol	NOUN
ejpam-3976	389	21	-	-	PUNCT
ejpam-3976	389	22	euler	euler	NOUN
ejpam-3976	389	23	polynomials	polynomial	NOUN
ejpam-3976	389	24	,	,	PUNCT
ejpam-3976	389	25	mathematics	mathematic	NOUN
ejpam-3976	389	26	of	of	ADP
ejpam-3976	389	27	computation	computation	NOUN
ejpam-3976	389	28	,	,	PUNCT
ejpam-3976	389	29	volume	volume	NOUN
ejpam-3976	389	30	81	81	NUM
ejpam-3976	389	31	,	,	PUNCT
ejpam-3976	389	32	(	(	PUNCT
ejpam-3976	389	33	number	number	NOUN
ejpam-3976	389	34	279	279	NUM
ejpam-3976	389	35	)	)	PUNCT
ejpam-3976	389	36	,	,	PUNCT
ejpam-3976	389	37	(	(	PUNCT
ejpam-3976	389	38	july	july	PROPN
ejpam-3976	389	39	2012	2012	NUM
ejpam-3976	389	40	)	)	PUNCT
ejpam-3976	389	41	,	,	PUNCT
ejpam-3976	389	42	1707	1707	NUM
ejpam-3976	389	43	-	-	SYM
ejpam-3976	389	44	1722	1722	NUM
ejpam-3976	389	45	.	.	PUNCT