id	sid	tid	token	lemma	pos
ejpam-3839	1	1	european	european	PROPN
ejpam-3839	1	2	journal	journal	PROPN
ejpam-3839	1	3	of	of	ADP
ejpam-3839	1	4	pure	pure	ADJ
ejpam-3839	1	5	and	and	CCONJ
ejpam-3839	1	6	applied	apply	VERB
ejpam-3839	1	7	mathematics	mathematic	NOUN
ejpam-3839	1	8	vol	vol	NOUN
ejpam-3839	1	9	.	.	PROPN
ejpam-3839	2	1	13	13	NUM
ejpam-3839	2	2	,	,	PUNCT
ejpam-3839	2	3	no	no	INTJ
ejpam-3839	2	4	.	.	NOUN
ejpam-3839	2	5	4	4	NUM
ejpam-3839	2	6	,	,	PUNCT
ejpam-3839	2	7	2020	2020	NUM
ejpam-3839	2	8	,	,	PUNCT
ejpam-3839	2	9	948	948	NUM
ejpam-3839	2	10	-	-	SYM
ejpam-3839	2	11	963	963	NUM
ejpam-3839	2	12	issn	issn	PROPN
ejpam-3839	2	13	1307	1307	NUM
ejpam-3839	2	14	-	-	SYM
ejpam-3839	2	15	5543	5543	NUM
ejpam-3839	2	16	–	–	PUNCT
ejpam-3839	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3839	2	18	published	publish	VERB
ejpam-3839	2	19	by	by	ADP
ejpam-3839	2	20	new	new	PROPN
ejpam-3839	2	21	york	york	PROPN
ejpam-3839	2	22	business	business	PROPN
ejpam-3839	2	23	global	global	ADJ
ejpam-3839	2	24	truncated	truncate	VERB
ejpam-3839	2	25	tangent	tangent	NOUN
ejpam-3839	2	26	polynomials	polynomial	VERB
ejpam-3839	2	27	nestor	nestor	PROPN
ejpam-3839	2	28	g.	g.	PROPN
ejpam-3839	2	29	acala1,∗	acala1,∗	PROPN
ejpam-3839	2	30	,	,	PUNCT
ejpam-3839	2	31	maribeth	maribeth	PROPN
ejpam-3839	2	32	b.	b.	PROPN
ejpam-3839	3	1	montero1	montero1	PROPN
ejpam-3839	3	2	1	1	NUM
ejpam-3839	3	3	mathematics	mathematics	PROPN
ejpam-3839	3	4	department	department	NOUN
ejpam-3839	3	5	,	,	PUNCT
ejpam-3839	3	6	college	college	NOUN
ejpam-3839	3	7	of	of	ADP
ejpam-3839	3	8	natural	natural	ADJ
ejpam-3839	3	9	sciences	science	NOUN
ejpam-3839	3	10	and	and	CCONJ
ejpam-3839	3	11	mathematics	mathematic	NOUN
ejpam-3839	3	12	,	,	PUNCT
ejpam-3839	3	13	mindanao	mindanao	PROPN
ejpam-3839	3	14	state	state	PROPN
ejpam-3839	3	15	university	university	NOUN
ejpam-3839	3	16	-	-	PUNCT
ejpam-3839	3	17	main	main	ADJ
ejpam-3839	3	18	campus	campus	NOUN
ejpam-3839	3	19	,	,	PUNCT
ejpam-3839	3	20	marawi	marawi	PROPN
ejpam-3839	3	21	city	city	PROPN
ejpam-3839	3	22	,	,	PUNCT
ejpam-3839	3	23	lanao	lanao	PROPN
ejpam-3839	3	24	del	del	PROPN
ejpam-3839	3	25	sur	sur	PROPN
ejpam-3839	3	26	,	,	PUNCT
ejpam-3839	3	27	philippines	philippine	NOUN
ejpam-3839	3	28	abstract	abstract	ADJ
ejpam-3839	3	29	.	.	PUNCT
ejpam-3839	4	1	in	in	ADP
ejpam-3839	4	2	this	this	DET
ejpam-3839	4	3	paper	paper	NOUN
ejpam-3839	4	4	,	,	PUNCT
ejpam-3839	4	5	we	we	PRON
ejpam-3839	4	6	introduce	introduce	VERB
ejpam-3839	4	7	a	a	DET
ejpam-3839	4	8	class	class	NOUN
ejpam-3839	4	9	of	of	ADP
ejpam-3839	4	10	truncated	truncated	ADJ
ejpam-3839	4	11	tangent	tangent	NOUN
ejpam-3839	4	12	polynomials	polynomial	NOUN
ejpam-3839	4	13	which	which	PRON
ejpam-3839	4	14	generalizes	generalize	VERB
ejpam-3839	4	15	tangent	tangent	ADJ
ejpam-3839	4	16	numbers	number	NOUN
ejpam-3839	4	17	and	and	CCONJ
ejpam-3839	4	18	polynomials	polynomial	NOUN
ejpam-3839	4	19	,	,	PUNCT
ejpam-3839	4	20	and	and	CCONJ
ejpam-3839	4	21	establish	establish	VERB
ejpam-3839	4	22	various	various	ADJ
ejpam-3839	4	23	properties	property	NOUN
ejpam-3839	4	24	and	and	CCONJ
ejpam-3839	4	25	identities	identity	NOUN
ejpam-3839	4	26	.	.	PUNCT
ejpam-3839	5	1	moreover	moreover	ADV
ejpam-3839	5	2	,	,	PUNCT
ejpam-3839	5	3	we	we	PRON
ejpam-3839	5	4	obtain	obtain	VERB
ejpam-3839	5	5	some	some	DET
ejpam-3839	5	6	interesting	interesting	ADJ
ejpam-3839	5	7	correlations	correlation	NOUN
ejpam-3839	5	8	of	of	ADP
ejpam-3839	5	9	truncated	truncated	ADJ
ejpam-3839	5	10	tangent	tangent	NOUN
ejpam-3839	5	11	polynomials	polynomial	NOUN
ejpam-3839	5	12	with	with	ADP
ejpam-3839	5	13	the	the	DET
ejpam-3839	5	14	stirling	stirling	NOUN
ejpam-3839	5	15	numbers	number	NOUN
ejpam-3839	5	16	of	of	ADP
ejpam-3839	5	17	the	the	DET
ejpam-3839	5	18	second	second	ADJ
ejpam-3839	5	19	kind	kind	NOUN
ejpam-3839	5	20	and	and	CCONJ
ejpam-3839	5	21	with	with	ADP
ejpam-3839	5	22	the	the	DET
ejpam-3839	5	23	hypergeometric	hypergeometric	ADJ
ejpam-3839	5	24	bernoulli	bernoulli	NOUN
ejpam-3839	5	25	polynomials	polynomial	NOUN
ejpam-3839	5	26	.	.	PUNCT
ejpam-3839	6	1	2020	2020	NUM
ejpam-3839	6	2	mathematics	mathematic	NOUN
ejpam-3839	6	3	subject	subject	NOUN
ejpam-3839	6	4	classifications	classification	NOUN
ejpam-3839	6	5	:	:	PUNCT
ejpam-3839	6	6	11b68	11b68	NUM
ejpam-3839	6	7	,	,	PUNCT
ejpam-3839	6	8	11b73	11b73	NUM
ejpam-3839	6	9	,	,	PUNCT
ejpam-3839	6	10	11b83	11b83	NUM
ejpam-3839	6	11	,	,	PUNCT
ejpam-3839	6	12	33c15	33c15	NUM
ejpam-3839	6	13	key	key	ADJ
ejpam-3839	6	14	words	word	NOUN
ejpam-3839	6	15	and	and	CCONJ
ejpam-3839	6	16	phrases	phrase	NOUN
ejpam-3839	6	17	:	:	PUNCT
ejpam-3839	6	18	tangent	tangent	ADJ
ejpam-3839	6	19	numbers	number	NOUN
ejpam-3839	6	20	and	and	CCONJ
ejpam-3839	6	21	polynomials	polynomial	NOUN
ejpam-3839	6	22	,	,	PUNCT
ejpam-3839	6	23	truncated	truncated	ADJ
ejpam-3839	6	24	tangent	tangent	NOUN
ejpam-3839	6	25	polynomials	polynomial	NOUN
ejpam-3839	6	26	,	,	PUNCT
ejpam-3839	6	27	truncated	truncate	VERB
ejpam-3839	6	28	bernoulli	bernoulli	NOUN
ejpam-3839	6	29	polynomials	polynomial	NOUN
ejpam-3839	6	30	,	,	PUNCT
ejpam-3839	6	31	hypergeometric	hypergeometric	ADJ
ejpam-3839	6	32	bernoulli	bernoulli	NOUN
ejpam-3839	6	33	polynomials	polynomial	NOUN
ejpam-3839	6	34	,	,	PUNCT
ejpam-3839	6	35	stirling	stirling	NOUN
ejpam-3839	6	36	numbers	number	NOUN
ejpam-3839	6	37	of	of	ADP
ejpam-3839	6	38	the	the	DET
ejpam-3839	6	39	second	second	ADJ
ejpam-3839	6	40	kind	kind	NOUN
ejpam-3839	6	41	,	,	PUNCT
ejpam-3839	6	42	truncated	truncate	VERB
ejpam-3839	6	43	stirling	stirling	NOUN
ejpam-3839	6	44	numbers	number	NOUN
ejpam-3839	6	45	1	1	NUM
ejpam-3839	6	46	.	.	PUNCT
ejpam-3839	7	1	introduction	introduction	NOUN
ejpam-3839	7	2	the	the	DET
ejpam-3839	7	3	hypergeometric	hypergeometric	ADJ
ejpam-3839	7	4	bernoulli	bernoulli	NOUN
ejpam-3839	7	5	numbers	number	NOUN
ejpam-3839	7	6	bm	bm	PROPN
ejpam-3839	7	7	,	,	PUNCT
ejpam-3839	7	8	n	n	PROPN
ejpam-3839	7	9	(	(	PUNCT
ejpam-3839	7	10	see	see	VERB
ejpam-3839	7	11	[	[	X
ejpam-3839	7	12	8–11	8–11	NOUN
ejpam-3839	7	13	,	,	PUNCT
ejpam-3839	7	14	13	13	NUM
ejpam-3839	7	15	]	]	PUNCT
ejpam-3839	7	16	)	)	PUNCT
ejpam-3839	7	17	are	be	AUX
ejpam-3839	7	18	defined	define	VERB
ejpam-3839	7	19	by	by	ADP
ejpam-3839	7	20	1	1	NUM
ejpam-3839	7	21	1f1(1;m+	1f1(1;m+	NUM
ejpam-3839	7	22	1	1	NUM
ejpam-3839	7	23	;	;	PUNCT
ejpam-3839	7	24	t	t	X
ejpam-3839	7	25	)	)	PUNCT
ejpam-3839	7	26	=	=	PROPN
ejpam-3839	8	1	tm	tm	PROPN
ejpam-3839	8	2	m	m	PROPN
ejpam-3839	8	3	!	!	PUNCT
ejpam-3839	8	4	et	et	PROPN
ejpam-3839	9	1	−	−	PROPN
ejpam-3839	9	2	∑m−1	∑m−1	PROPN
ejpam-3839	9	3	j=0	j=0	PROPN
ejpam-3839	9	4	tj	tj	PROPN
ejpam-3839	9	5	j	j	PROPN
ejpam-3839	9	6	!	!	PUNCT
ejpam-3839	9	7	=	=	PUNCT
ejpam-3839	10	1	∞∑	∞∑	PRON
ejpam-3839	10	2	n=0	n=0	NUM
ejpam-3839	10	3	bm	bm	PROPN
ejpam-3839	10	4	,	,	PUNCT
ejpam-3839	10	5	n	n	PROPN
ejpam-3839	10	6	tn	tn	PROPN
ejpam-3839	10	7	n	n	CCONJ
ejpam-3839	10	8	!	!	PROPN
ejpam-3839	10	9	,	,	PUNCT
ejpam-3839	10	10	(	(	PUNCT
ejpam-3839	10	11	1	1	X
ejpam-3839	10	12	)	)	PUNCT
ejpam-3839	10	13	where	where	SCONJ
ejpam-3839	10	14	1f1(a	1f1(a	NUM
ejpam-3839	10	15	;	;	PUNCT
ejpam-3839	10	16	b	b	X
ejpam-3839	10	17	;	;	PUNCT
ejpam-3839	10	18	z	z	X
ejpam-3839	10	19	)	)	PUNCT
ejpam-3839	10	20	=	=	SYM
ejpam-3839	11	1	∞∑	∞∑	NUM
ejpam-3839	11	2	n=0	n=0	NUM
ejpam-3839	11	3	(	(	PUNCT
ejpam-3839	11	4	a)(n)zn	a)(n)zn	NOUN
ejpam-3839	11	5	(	(	PUNCT
ejpam-3839	11	6	b)(n)n	b)(n)n	X
ejpam-3839	11	7	!	!	PUNCT
ejpam-3839	12	1	(	(	PUNCT
ejpam-3839	12	2	2	2	X
ejpam-3839	12	3	)	)	PUNCT
ejpam-3839	12	4	is	be	AUX
ejpam-3839	12	5	the	the	DET
ejpam-3839	12	6	confluent	confluent	ADJ
ejpam-3839	12	7	hypergeometric	hypergeometric	ADJ
ejpam-3839	12	8	function	function	NOUN
ejpam-3839	12	9	with	with	ADP
ejpam-3839	12	10	(	(	PUNCT
ejpam-3839	12	11	x)(n	x)(n	PROPN
ejpam-3839	12	12	)	)	PUNCT
ejpam-3839	12	13	=	=	PUNCT
ejpam-3839	13	1	x(x+	x(x+	ADJ
ejpam-3839	13	2	1	1	NUM
ejpam-3839	13	3	)	)	PUNCT
ejpam-3839	13	4	·	·	PUNCT
ejpam-3839	14	1	·	·	PUNCT
ejpam-3839	14	2	·	·	PUNCT
ejpam-3839	14	3	(	(	PUNCT
ejpam-3839	14	4	x+	x+	X
ejpam-3839	14	5	n−	n−	NOUN
ejpam-3839	14	6	1	1	NUM
ejpam-3839	14	7	)	)	PUNCT
ejpam-3839	14	8	for	for	ADP
ejpam-3839	14	9	n	n	PRON
ejpam-3839	14	10	≥	≥	NUM
ejpam-3839	14	11	1	1	NUM
ejpam-3839	14	12	,	,	PUNCT
ejpam-3839	14	13	and	and	CCONJ
ejpam-3839	14	14	(	(	PUNCT
ejpam-3839	14	15	x)(0	x)(0	X
ejpam-3839	14	16	)	)	PUNCT
ejpam-3839	14	17	=	=	SYM
ejpam-3839	14	18	1	1	X
ejpam-3839	14	19	.	.	PUNCT
ejpam-3839	14	20	when	when	SCONJ
ejpam-3839	14	21	m	m	VERB
ejpam-3839	14	22	=	=	SYM
ejpam-3839	14	23	1	1	NUM
ejpam-3839	14	24	,	,	PUNCT
ejpam-3839	14	25	bn	bn	ADV
ejpam-3839	14	26	:	:	PUNCT
ejpam-3839	14	27	=	=	SYM
ejpam-3839	14	28	b1,n	b1,n	PROPN
ejpam-3839	14	29	are	be	AUX
ejpam-3839	14	30	the	the	DET
ejpam-3839	14	31	classical	classical	ADJ
ejpam-3839	14	32	bernoulli	bernoulli	NOUN
ejpam-3839	14	33	numbers	number	NOUN
ejpam-3839	14	34	given	give	VERB
ejpam-3839	14	35	by	by	ADP
ejpam-3839	14	36	t	t	PROPN
ejpam-3839	14	37	et	et	NOUN
ejpam-3839	14	38	−	−	NOUN
ejpam-3839	14	39	1	1	NUM
ejpam-3839	14	40	=	=	PUNCT
ejpam-3839	14	41	∞∑	∞∑	NUM
ejpam-3839	14	42	n=0	n=0	NUM
ejpam-3839	14	43	bn	bn	NUM
ejpam-3839	14	44	tn	tn	NOUN
ejpam-3839	14	45	n	n	CCONJ
ejpam-3839	14	46	!	!	PUNCT
ejpam-3839	14	47	.	.	PUNCT
ejpam-3839	15	1	∗corresponding	∗corresponde	VERB
ejpam-3839	15	2	author	author	NOUN
ejpam-3839	15	3	.	.	PUNCT
ejpam-3839	16	1	doi	doi	NOUN
ejpam-3839	16	2	:	:	PUNCT
ejpam-3839	16	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3839	https://doi.org/10.29020/nybg.ejpam.v13i4.3839	ADJ
ejpam-3839	16	4	email	email	NOUN
ejpam-3839	16	5	addresses	address	VERB
ejpam-3839	16	6	:	:	PUNCT
ejpam-3839	16	7	nestor.acala@msumain.edu.ph	nestor.acala@msumain.edu.ph	PROPN
ejpam-3839	16	8	(	(	PUNCT
ejpam-3839	16	9	n.	n.	NOUN
ejpam-3839	16	10	acala	acala	PROPN
ejpam-3839	16	11	)	)	PUNCT
ejpam-3839	16	12	,	,	PUNCT
ejpam-3839	16	13	maribeth.montero@msumain.edu.ph	maribeth.montero@msumain.edu.ph	PROPN
ejpam-3839	16	14	(	(	PUNCT
ejpam-3839	16	15	m.	m.	NOUN
ejpam-3839	16	16	montero	montero	PROPN
ejpam-3839	16	17	)	)	PUNCT
ejpam-3839	16	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3839	17	1	948	948	NUM
ejpam-3839	17	2	c	c	AUX
ejpam-3839	17	3	©	©	PROPN
ejpam-3839	17	4	2020	2020	NUM
ejpam-3839	17	5	ejpam	ejpam	VERB
ejpam-3839	17	6	all	all	DET
ejpam-3839	17	7	rights	right	NOUN
ejpam-3839	17	8	reserved	reserve	VERB
ejpam-3839	17	9	.	.	PUNCT
ejpam-3839	18	1	n.	n.	PROPN
ejpam-3839	18	2	acala	acala	PROPN
ejpam-3839	18	3	,	,	PUNCT
ejpam-3839	18	4	m.	m.	PROPN
ejpam-3839	18	5	montero	montero	PROPN
ejpam-3839	18	6	/	/	SYM
ejpam-3839	18	7	eur	eur	PROPN
ejpam-3839	18	8	.	.	PUNCT
ejpam-3839	19	1	j.	j.	PROPN
ejpam-3839	19	2	pure	pure	PROPN
ejpam-3839	19	3	appl	appl	PROPN
ejpam-3839	19	4	.	.	PROPN
ejpam-3839	19	5	math	math	PROPN
ejpam-3839	19	6	,	,	PUNCT
ejpam-3839	19	7	13	13	NUM
ejpam-3839	19	8	(	(	PUNCT
ejpam-3839	19	9	4	4	NUM
ejpam-3839	19	10	)	)	PUNCT
ejpam-3839	19	11	(	(	PUNCT
ejpam-3839	19	12	2020	2020	NUM
ejpam-3839	19	13	)	)	PUNCT
ejpam-3839	19	14	,	,	PUNCT
ejpam-3839	19	15	948	948	NUM
ejpam-3839	19	16	-	-	SYM
ejpam-3839	19	17	963	963	NUM
ejpam-3839	19	18	949	949	NUM
ejpam-3839	19	19	the	the	DET
ejpam-3839	19	20	hypergeometric	hypergeometric	ADJ
ejpam-3839	19	21	bernoulli	bernoulli	NOUN
ejpam-3839	19	22	polynomials	polynomial	VERB
ejpam-3839	19	23	bm	bm	PROPN
ejpam-3839	19	24	,	,	PUNCT
ejpam-3839	19	25	n(x	n(x	PROPN
ejpam-3839	19	26	)	)	PUNCT
ejpam-3839	19	27	were	be	AUX
ejpam-3839	19	28	also	also	ADV
ejpam-3839	19	29	introduced	introduce	VERB
ejpam-3839	19	30	in	in	ADP
ejpam-3839	19	31	[	[	X
ejpam-3839	19	32	8	8	NUM
ejpam-3839	19	33	,	,	PUNCT
ejpam-3839	19	34	9	9	NUM
ejpam-3839	19	35	]	]	PUNCT
ejpam-3839	19	36	and	and	CCONJ
ejpam-3839	19	37	defined	define	VERB
ejpam-3839	19	38	by	by	ADP
ejpam-3839	19	39	ext	ext	NOUN
ejpam-3839	19	40	1f1(1;m+	1f1(1;m+	PROPN
ejpam-3839	19	41	1	1	NUM
ejpam-3839	19	42	;	;	PUNCT
ejpam-3839	19	43	t	t	X
ejpam-3839	19	44	)	)	PUNCT
ejpam-3839	19	45	=	=	PROPN
ejpam-3839	20	1	tm	tm	PROPN
ejpam-3839	20	2	m!e	m!e	PROPN
ejpam-3839	20	3	xt	xt	PROPN
ejpam-3839	20	4	et	et	PROPN
ejpam-3839	20	5	−	−	PROPN
ejpam-3839	20	6	∑m−1	∑m−1	PROPN
ejpam-3839	20	7	j=0	j=0	PROPN
ejpam-3839	20	8	tj	tj	PROPN
ejpam-3839	20	9	j	j	PROPN
ejpam-3839	20	10	!	!	PUNCT
ejpam-3839	21	1	=	=	PUNCT
ejpam-3839	22	1	∞∑	∞∑	PRON
ejpam-3839	22	2	n=0	n=0	NUM
ejpam-3839	22	3	bm	bm	PROPN
ejpam-3839	22	4	,	,	PUNCT
ejpam-3839	22	5	n(x	n(x	PROPN
ejpam-3839	22	6	)	)	PUNCT
ejpam-3839	22	7	tn	tn	NOUN
ejpam-3839	22	8	n	n	NUM
ejpam-3839	22	9	!	!	PUNCT
ejpam-3839	22	10	.	.	PUNCT
ejpam-3839	23	1	(	(	PUNCT
ejpam-3839	23	2	3	3	X
ejpam-3839	23	3	)	)	PUNCT
ejpam-3839	23	4	when	when	SCONJ
ejpam-3839	23	5	m	m	VERB
ejpam-3839	23	6	=	=	SYM
ejpam-3839	23	7	1	1	NUM
ejpam-3839	23	8	,	,	PUNCT
ejpam-3839	23	9	bn(x	bn(x	NUM
ejpam-3839	23	10	)	)	PUNCT
ejpam-3839	23	11	:	:	PUNCT
ejpam-3839	23	12	=	=	PUNCT
ejpam-3839	23	13	b1,n(x	b1,n(x	X
ejpam-3839	23	14	)	)	PUNCT
ejpam-3839	23	15	are	be	AUX
ejpam-3839	23	16	the	the	DET
ejpam-3839	23	17	classical	classical	ADJ
ejpam-3839	23	18	bernoulli	bernoulli	NOUN
ejpam-3839	23	19	polynomials	polynomial	NOUN
ejpam-3839	23	20	given	give	VERB
ejpam-3839	23	21	by	by	ADP
ejpam-3839	23	22	the	the	DET
ejpam-3839	23	23	exponential	exponential	ADJ
ejpam-3839	23	24	generating	generating	NOUN
ejpam-3839	23	25	function	function	NOUN
ejpam-3839	23	26	tex	tex	PROPN
ejpam-3839	23	27	et	et	NOUN
ejpam-3839	23	28	−	−	NOUN
ejpam-3839	23	29	1	1	NUM
ejpam-3839	23	30	=	=	PUNCT
ejpam-3839	23	31	∞∑	∞∑	PRON
ejpam-3839	23	32	n=0	n=0	NUM
ejpam-3839	23	33	bn(x	bn(x	NUM
ejpam-3839	23	34	)	)	PUNCT
ejpam-3839	23	35	tn	tn	PROPN
ejpam-3839	23	36	n	n	PROPN
ejpam-3839	23	37	!	!	PUNCT
ejpam-3839	23	38	.	.	PUNCT
ejpam-3839	24	1	hypergeometric	hypergeometric	ADJ
ejpam-3839	24	2	bernoulli	bernoulli	NOUN
ejpam-3839	24	3	polynomials	polynomial	NOUN
ejpam-3839	24	4	(	(	PUNCT
ejpam-3839	24	5	numbers	number	NOUN
ejpam-3839	24	6	)	)	PUNCT
ejpam-3839	24	7	are	be	AUX
ejpam-3839	24	8	also	also	ADV
ejpam-3839	24	9	called	call	VERB
ejpam-3839	24	10	truncated	truncated	ADJ
ejpam-3839	24	11	bernoulli	bernoulli	NOUN
ejpam-3839	24	12	polynomials	polynomial	NOUN
ejpam-3839	24	13	(	(	PUNCT
ejpam-3839	24	14	numbers	number	NOUN
ejpam-3839	24	15	)	)	PUNCT
ejpam-3839	24	16	.	.	PUNCT
ejpam-3839	25	1	in	in	ADP
ejpam-3839	25	2	[	[	X
ejpam-3839	25	3	15	15	NUM
ejpam-3839	25	4	]	]	PUNCT
ejpam-3839	25	5	,	,	PUNCT
ejpam-3839	25	6	komatsu	komatsu	NOUN
ejpam-3839	25	7	and	and	CCONJ
ejpam-3839	25	8	pita	pita	NOUN
ejpam-3839	25	9	introduced	introduce	VERB
ejpam-3839	25	10	truncated	truncate	VERB
ejpam-3839	25	11	euler	euler	NOUN
ejpam-3839	25	12	polynomials	polynomial	NOUN
ejpam-3839	25	13	via	via	ADP
ejpam-3839	25	14	the	the	DET
ejpam-3839	25	15	generating	generate	VERB
ejpam-3839	25	16	function	function	NOUN
ejpam-3839	25	17	2tm	2tm	PROPN
ejpam-3839	25	18	m	m	PROPN
ejpam-3839	25	19	!	!	PUNCT
ejpam-3839	26	1	e	e	X
ejpam-3839	26	2	xt	xt	ADP
ejpam-3839	26	3	et	et	PROPN
ejpam-3839	26	4	+	+	CCONJ
ejpam-3839	26	5	1−	1−	NUM
ejpam-3839	26	6	∑m−1	∑m−1	NOUN
ejpam-3839	26	7	j=0	j=0	PROPN
ejpam-3839	26	8	tj	tj	PROPN
ejpam-3839	26	9	j	j	PROPN
ejpam-3839	26	10	!	!	PUNCT
ejpam-3839	26	11	=	=	PUNCT
ejpam-3839	27	1	∞∑	∞∑	PRON
ejpam-3839	27	2	n=0	n=0	NUM
ejpam-3839	27	3	em	em	NOUN
ejpam-3839	27	4	,	,	PUNCT
ejpam-3839	27	5	n(x	n(x	PROPN
ejpam-3839	27	6	)	)	PUNCT
ejpam-3839	27	7	tn	tn	NOUN
ejpam-3839	27	8	n	n	NUM
ejpam-3839	27	9	!	!	PUNCT
ejpam-3839	27	10	.	.	PUNCT
ejpam-3839	28	1	(	(	PUNCT
ejpam-3839	28	2	4	4	X
ejpam-3839	28	3	)	)	PUNCT
ejpam-3839	28	4	these	these	DET
ejpam-3839	28	5	polynomials	polynomial	NOUN
ejpam-3839	28	6	satisfy	satisfy	VERB
ejpam-3839	28	7	recurrence	recurrence	NOUN
ejpam-3839	28	8	relation	relation	PROPN
ejpam-3839	28	9	en	en	ADP
ejpam-3839	28	10	,	,	PUNCT
ejpam-3839	28	11	m(x	m(x	X
ejpam-3839	28	12	)	)	PUNCT
ejpam-3839	29	1	=	=	SYM
ejpam-3839	29	2	0	0	NUM
ejpam-3839	29	3	,	,	PUNCT
ejpam-3839	29	4	n	n	NOUN
ejpam-3839	29	5	=	=	SYM
ejpam-3839	29	6	0	0	NUM
ejpam-3839	29	7	,	,	PUNCT
ejpam-3839	29	8	1	1	NUM
ejpam-3839	29	9	,	,	PUNCT
ejpam-3839	29	10	2	2	NUM
ejpam-3839	29	11	,	,	PUNCT
ejpam-3839	29	12	·	·	PUNCT
ejpam-3839	29	13	·	·	PUNCT
ejpam-3839	29	14	·	·	PUNCT
ejpam-3839	29	15	,	,	PUNCT
ejpam-3839	29	16	m−	m−	PROPN
ejpam-3839	29	17	1	1	NUM
ejpam-3839	29	18	,	,	PUNCT
ejpam-3839	29	19	and	and	CCONJ
ejpam-3839	29	20	en	en	ADV
ejpam-3839	29	21	,	,	PUNCT
ejpam-3839	29	22	n+m(x	n+m(x	NOUN
ejpam-3839	29	23	)	)	PUNCT
ejpam-3839	29	24	=	=	SYM
ejpam-3839	29	25	2	2	NUM
ejpam-3839	29	26	(	(	PUNCT
ejpam-3839	29	27	n+m	n+m	NUM
ejpam-3839	29	28	n	n	CCONJ
ejpam-3839	29	29	)	)	PUNCT
ejpam-3839	29	30	xn	xn	PROPN
ejpam-3839	30	1	−	−	PROPN
ejpam-3839	30	2	n∑	n∑	PROPN
ejpam-3839	30	3	k=0	k=0	PROPN
ejpam-3839	30	4	(	(	PUNCT
ejpam-3839	30	5	n+m	n+m	NUM
ejpam-3839	30	6	k	k	X
ejpam-3839	30	7	)	)	PUNCT
ejpam-3839	30	8	en	en	ADP
ejpam-3839	30	9	,	,	PUNCT
ejpam-3839	30	10	k(x	k(x	PROPN
ejpam-3839	30	11	)	)	PUNCT
ejpam-3839	30	12	,	,	PUNCT
ejpam-3839	30	13	n	n	X
ejpam-3839	30	14	≥	≥	NOUN
ejpam-3839	30	15	0	0	NUM
ejpam-3839	30	16	.	.	PUNCT
ejpam-3839	31	1	when	when	SCONJ
ejpam-3839	31	2	m	m	VERB
ejpam-3839	31	3	=	=	X
ejpam-3839	31	4	0	0	NUM
ejpam-3839	31	5	in	in	ADP
ejpam-3839	31	6	(	(	PUNCT
ejpam-3839	31	7	4	4	NUM
ejpam-3839	31	8	)	)	PUNCT
ejpam-3839	31	9	,	,	PUNCT
ejpam-3839	31	10	en(x	en(x	ADP
ejpam-3839	31	11	)	)	PUNCT
ejpam-3839	31	12	:	:	PUNCT
ejpam-3839	31	13	=	=	SYM
ejpam-3839	31	14	e0,n(x	e0,n(x	X
ejpam-3839	31	15	)	)	PUNCT
ejpam-3839	31	16	are	be	AUX
ejpam-3839	31	17	the	the	DET
ejpam-3839	31	18	classical	classical	ADJ
ejpam-3839	31	19	euler	euler	NOUN
ejpam-3839	31	20	polynomials	polynomial	NOUN
ejpam-3839	31	21	given	give	VERB
ejpam-3839	31	22	by	by	ADP
ejpam-3839	31	23	2ex	2ex	ADJ
ejpam-3839	31	24	et	et	NOUN
ejpam-3839	31	25	+	+	CCONJ
ejpam-3839	32	1	1	1	X
ejpam-3839	32	2	=	=	SYM
ejpam-3839	32	3	∞∑	∞∑	NUM
ejpam-3839	32	4	n=0	n=0	NUM
ejpam-3839	32	5	en(x	en(x	PRON
ejpam-3839	32	6	)	)	PUNCT
ejpam-3839	32	7	tn	tn	PROPN
ejpam-3839	32	8	n	n	NUM
ejpam-3839	32	9	!	!	PUNCT
ejpam-3839	32	10	.	.	PUNCT
ejpam-3839	33	1	in	in	ADP
ejpam-3839	33	2	recent	recent	ADJ
ejpam-3839	33	3	years	year	NOUN
ejpam-3839	33	4	,	,	PUNCT
ejpam-3839	33	5	extensive	extensive	ADJ
ejpam-3839	33	6	researches	research	NOUN
ejpam-3839	33	7	on	on	ADP
ejpam-3839	33	8	various	various	ADJ
ejpam-3839	33	9	families	family	NOUN
ejpam-3839	33	10	of	of	ADP
ejpam-3839	33	11	truncated	truncated	ADJ
ejpam-3839	33	12	exponential	exponential	ADJ
ejpam-3839	33	13	polynomials	polynomial	NOUN
ejpam-3839	33	14	have	have	AUX
ejpam-3839	33	15	become	become	VERB
ejpam-3839	33	16	popular	popular	ADJ
ejpam-3839	33	17	.	.	PUNCT
ejpam-3839	34	1	truncation	truncation	NOUN
ejpam-3839	34	2	of	of	ADP
ejpam-3839	34	3	exponential	exponential	ADJ
ejpam-3839	34	4	polynomials	polynomial	NOUN
ejpam-3839	34	5	have	have	AUX
ejpam-3839	34	6	played	play	VERB
ejpam-3839	34	7	crucial	crucial	ADJ
ejpam-3839	34	8	importance	importance	NOUN
ejpam-3839	34	9	to	to	PART
ejpam-3839	34	10	evaluate	evaluate	VERB
ejpam-3839	34	11	integrals	integral	NOUN
ejpam-3839	34	12	including	include	VERB
ejpam-3839	34	13	products	product	NOUN
ejpam-3839	34	14	of	of	ADP
ejpam-3839	34	15	special	special	ADJ
ejpam-3839	34	16	functions	function	NOUN
ejpam-3839	34	17	[	[	X
ejpam-3839	34	18	4	4	NUM
ejpam-3839	34	19	]	]	PUNCT
ejpam-3839	34	20	.	.	PUNCT
ejpam-3839	35	1	some	some	PRON
ejpam-3839	35	2	of	of	ADP
ejpam-3839	35	3	the	the	DET
ejpam-3839	35	4	recent	recent	ADJ
ejpam-3839	35	5	works	work	NOUN
ejpam-3839	35	6	on	on	ADP
ejpam-3839	35	7	truncated	truncated	ADJ
ejpam-3839	35	8	numbers	number	NOUN
ejpam-3839	35	9	polynomials	polynomial	NOUN
ejpam-3839	35	10	include	include	VERB
ejpam-3839	35	11	truncated	truncate	VERB
ejpam-3839	35	12	fubini	fubini	ADJ
ejpam-3839	35	13	polynomials	polynomial	NOUN
ejpam-3839	35	14	[	[	X
ejpam-3839	35	15	5	5	NUM
ejpam-3839	35	16	]	]	PUNCT
ejpam-3839	35	17	,	,	PUNCT
ejpam-3839	35	18	truncated	truncate	VERB
ejpam-3839	35	19	-	-	PUNCT
ejpam-3839	35	20	exponential	exponential	NOUN
ejpam-3839	35	21	based	base	VERB
ejpam-3839	35	22	apostol	apostol	NOUN
ejpam-3839	35	23	-	-	PUNCT
ejpam-3839	35	24	type	type	NOUN
ejpam-3839	35	25	polynomials	polynomial	NOUN
ejpam-3839	35	26	[	[	X
ejpam-3839	35	27	26	26	NUM
ejpam-3839	35	28	]	]	PUNCT
ejpam-3839	35	29	,	,	PUNCT
ejpam-3839	35	30	truncated	truncate	VERB
ejpam-3839	35	31	-	-	PUNCT
ejpam-3839	35	32	exponentialbased	exponentialbase	VERB
ejpam-3839	35	33	frobenius	frobenius	NOUN
ejpam-3839	35	34	-	-	PUNCT
ejpam-3839	35	35	euler	euler	NOUN
ejpam-3839	35	36	polynomials	polynomial	NOUN
ejpam-3839	35	37	[	[	X
ejpam-3839	35	38	17	17	NUM
ejpam-3839	35	39	]	]	PUNCT
ejpam-3839	35	40	,	,	PUNCT
ejpam-3839	35	41	hypergeometric	hypergeometric	ADJ
ejpam-3839	35	42	cauchy	cauchy	ADJ
ejpam-3839	35	43	numbers	number	NOUN
ejpam-3839	35	44	[	[	X
ejpam-3839	35	45	13	13	NUM
ejpam-3839	35	46	]	]	PUNCT
ejpam-3839	35	47	,	,	PUNCT
ejpam-3839	35	48	truncated	truncate	VERB
ejpam-3839	35	49	bernoulli	bernoulli	PROPN
ejpam-3839	35	50	-	-	PUNCT
ejpam-3839	35	51	carlitz	carlitz	PROPN
ejpam-3839	35	52	and	and	CCONJ
ejpam-3839	35	53	truncated	truncated	ADJ
ejpam-3839	35	54	cauchy	cauchy	PROPN
ejpam-3839	35	55	-	-	PUNCT
ejpam-3839	35	56	carlitz	carlitz	PROPN
ejpam-3839	35	57	numbers	number	NOUN
ejpam-3839	35	58	[	[	X
ejpam-3839	35	59	14	14	NUM
ejpam-3839	35	60	,	,	PUNCT
ejpam-3839	35	61	16	16	NUM
ejpam-3839	35	62	]	]	PUNCT
ejpam-3839	35	63	,	,	PUNCT
ejpam-3839	35	64	truncated	truncate	VERB
ejpam-3839	35	65	exponentialbased	exponentialbase	VERB
ejpam-3839	35	66	appell	appell	ADJ
ejpam-3839	35	67	polynomials	polynomial	NOUN
ejpam-3839	35	68	[	[	X
ejpam-3839	35	69	12	12	NUM
ejpam-3839	35	70	]	]	PUNCT
ejpam-3839	35	71	and	and	CCONJ
ejpam-3839	35	72	many	many	ADJ
ejpam-3839	35	73	others	other	NOUN
ejpam-3839	35	74	.	.	PUNCT
ejpam-3839	36	1	in	in	ADP
ejpam-3839	36	2	[	[	X
ejpam-3839	36	3	6	6	NUM
ejpam-3839	36	4	]	]	PUNCT
ejpam-3839	36	5	,	,	PUNCT
ejpam-3839	36	6	duran	duran	NOUN
ejpam-3839	36	7	and	and	CCONJ
ejpam-3839	36	8	acikgoz	acikgoz	PROPN
ejpam-3839	36	9	introduced	introduce	VERB
ejpam-3839	36	10	degenerate	degenerate	ADJ
ejpam-3839	36	11	truncated	truncate	VERB
ejpam-3839	36	12	exponential	exponential	ADJ
ejpam-3839	36	13	polynomials	polynomial	NOUN
ejpam-3839	36	14	and	and	CCONJ
ejpam-3839	36	15	obtain	obtain	VERB
ejpam-3839	36	16	truncated	truncated	ADJ
ejpam-3839	36	17	degenerate	degenerate	ADJ
ejpam-3839	36	18	versions	version	NOUN
ejpam-3839	36	19	of	of	ADP
ejpam-3839	36	20	some	some	DET
ejpam-3839	36	21	special	special	ADJ
ejpam-3839	36	22	polynomials	polynomial	NOUN
ejpam-3839	36	23	such	such	ADJ
ejpam-3839	36	24	as	as	ADP
ejpam-3839	36	25	stirling	stirling	NOUN
ejpam-3839	36	26	polynomials	polynomial	NOUN
ejpam-3839	36	27	of	of	ADP
ejpam-3839	36	28	the	the	DET
ejpam-3839	36	29	second	second	ADJ
ejpam-3839	36	30	kind	kind	NOUN
ejpam-3839	36	31	,	,	PUNCT
ejpam-3839	36	32	bernoulli	bernoulli	NOUN
ejpam-3839	36	33	polynomials	polynomial	NOUN
ejpam-3839	36	34	,	,	PUNCT
ejpam-3839	36	35	euler	euler	NOUN
ejpam-3839	36	36	polynomials	polynomial	NOUN
ejpam-3839	36	37	,	,	PUNCT
ejpam-3839	36	38	and	and	CCONJ
ejpam-3839	36	39	bell	bell	NOUN
ejpam-3839	36	40	polynomials	polynomial	NOUN
ejpam-3839	36	41	.	.	PUNCT
ejpam-3839	37	1	in	in	ADP
ejpam-3839	37	2	the	the	DET
ejpam-3839	37	3	next	next	ADJ
ejpam-3839	37	4	section	section	NOUN
ejpam-3839	37	5	,	,	PUNCT
ejpam-3839	37	6	we	we	PRON
ejpam-3839	37	7	introduce	introduce	VERB
ejpam-3839	37	8	truncated	truncated	ADJ
ejpam-3839	37	9	tangent	tangent	NOUN
ejpam-3839	37	10	numbers	number	NOUN
ejpam-3839	37	11	and	and	CCONJ
ejpam-3839	37	12	polynomials	polynomial	NOUN
ejpam-3839	37	13	and	and	CCONJ
ejpam-3839	37	14	explore	explore	VERB
ejpam-3839	37	15	some	some	PRON
ejpam-3839	37	16	of	of	ADP
ejpam-3839	37	17	their	their	PRON
ejpam-3839	37	18	interesting	interesting	ADJ
ejpam-3839	37	19	properties	property	NOUN
ejpam-3839	37	20	and	and	CCONJ
ejpam-3839	37	21	formula	formula	NOUN
ejpam-3839	37	22	.	.	PUNCT
ejpam-3839	38	1	n.	n.	PROPN
ejpam-3839	38	2	acala	acala	PROPN
ejpam-3839	38	3	,	,	PUNCT
ejpam-3839	38	4	m.	m.	PROPN
ejpam-3839	38	5	montero	montero	PROPN
ejpam-3839	38	6	/	/	SYM
ejpam-3839	38	7	eur	eur	PROPN
ejpam-3839	38	8	.	.	PUNCT
ejpam-3839	39	1	j.	j.	PROPN
ejpam-3839	39	2	pure	pure	PROPN
ejpam-3839	39	3	appl	appl	PROPN
ejpam-3839	39	4	.	.	PROPN
ejpam-3839	39	5	math	math	PROPN
ejpam-3839	39	6	,	,	PUNCT
ejpam-3839	39	7	13	13	NUM
ejpam-3839	39	8	(	(	PUNCT
ejpam-3839	39	9	4	4	NUM
ejpam-3839	39	10	)	)	PUNCT
ejpam-3839	39	11	(	(	PUNCT
ejpam-3839	39	12	2020	2020	NUM
ejpam-3839	39	13	)	)	PUNCT
ejpam-3839	39	14	,	,	PUNCT
ejpam-3839	39	15	948	948	NUM
ejpam-3839	39	16	-	-	SYM
ejpam-3839	39	17	963	963	NUM
ejpam-3839	39	18	950	950	NUM
ejpam-3839	39	19	2	2	NUM
ejpam-3839	39	20	.	.	PUNCT
ejpam-3839	39	21	truncated	truncate	VERB
ejpam-3839	39	22	tangent	tangent	NOUN
ejpam-3839	39	23	polynomials	polynomial	NOUN
ejpam-3839	39	24	in	in	ADP
ejpam-3839	39	25	this	this	DET
ejpam-3839	39	26	section	section	NOUN
ejpam-3839	39	27	,	,	PUNCT
ejpam-3839	39	28	we	we	PRON
ejpam-3839	39	29	give	give	VERB
ejpam-3839	39	30	a	a	DET
ejpam-3839	39	31	generalization	generalization	NOUN
ejpam-3839	39	32	of	of	ADP
ejpam-3839	39	33	tangent	tangent	ADJ
ejpam-3839	39	34	polynomials	polynomial	NOUN
ejpam-3839	39	35	in	in	ADP
ejpam-3839	39	36	terms	term	NOUN
ejpam-3839	39	37	of	of	ADP
ejpam-3839	39	38	the	the	DET
ejpam-3839	39	39	truncated	truncated	ADJ
ejpam-3839	39	40	exponential	exponential	ADJ
ejpam-3839	39	41	function	function	NOUN
ejpam-3839	39	42	.	.	PUNCT
ejpam-3839	40	1	for	for	ADP
ejpam-3839	40	2	nonnegative	nonnegative	ADJ
ejpam-3839	40	3	integer	integer	NOUN
ejpam-3839	40	4	m	m	NOUN
ejpam-3839	40	5	,	,	PUNCT
ejpam-3839	40	6	we	we	PRON
ejpam-3839	40	7	define	define	VERB
ejpam-3839	40	8	the	the	DET
ejpam-3839	40	9	truncated	truncate	VERB
ejpam-3839	40	10	tangent	tangent	NOUN
ejpam-3839	40	11	polynomials	polynomial	VERB
ejpam-3839	40	12	tm	tm	NOUN
ejpam-3839	40	13	,	,	PUNCT
ejpam-3839	40	14	n(x	n(x	PROPN
ejpam-3839	40	15	)	)	PUNCT
ejpam-3839	40	16	through	through	ADP
ejpam-3839	40	17	the	the	DET
ejpam-3839	40	18	generating	generate	VERB
ejpam-3839	40	19	function	function	NOUN
ejpam-3839	40	20	2	2	NUM
ejpam-3839	40	21	tm	tm	PROPN
ejpam-3839	40	22	m	m	PROPN
ejpam-3839	40	23	!	!	PUNCT
ejpam-3839	41	1	e2	e2	PROPN
ejpam-3839	41	2	t	t	PROPN
ejpam-3839	41	3	+	+	CCONJ
ejpam-3839	41	4	1−	1−	NUM
ejpam-3839	41	5	∑m−1	∑m−1	NOUN
ejpam-3839	41	6	j=0	j=0	VERB
ejpam-3839	41	7	2j	2j	NUM
ejpam-3839	41	8	t	t	PROPN
ejpam-3839	41	9	j	j	PROPN
ejpam-3839	41	10	j	j	PROPN
ejpam-3839	41	11	!	!	PUNCT
ejpam-3839	41	12	ext	ext	PROPN
ejpam-3839	42	1	=	=	PUNCT
ejpam-3839	42	2	∞∑	∞∑	NUM
ejpam-3839	42	3	n=0	n=0	PUNCT
ejpam-3839	42	4	tm	tm	NOUN
ejpam-3839	42	5	,	,	PUNCT
ejpam-3839	42	6	n(x	n(x	PROPN
ejpam-3839	42	7	)	)	PUNCT
ejpam-3839	42	8	tn	tn	NOUN
ejpam-3839	42	9	n	n	NUM
ejpam-3839	42	10	!	!	PUNCT
ejpam-3839	42	11	.	.	PUNCT
ejpam-3839	43	1	(	(	PUNCT
ejpam-3839	43	2	5	5	X
ejpam-3839	43	3	)	)	PUNCT
ejpam-3839	43	4	when	when	SCONJ
ejpam-3839	43	5	m	m	VERB
ejpam-3839	43	6	=	=	SYM
ejpam-3839	43	7	0	0	NUM
ejpam-3839	43	8	,	,	PUNCT
ejpam-3839	43	9	tn(x	tn(x	PUNCT
ejpam-3839	43	10	)	)	PUNCT
ejpam-3839	43	11	:	:	PUNCT
ejpam-3839	44	1	=	=	SYM
ejpam-3839	44	2	t0,n(x	t0,n(x	X
ejpam-3839	44	3	)	)	PUNCT
ejpam-3839	44	4	are	be	AUX
ejpam-3839	44	5	the	the	DET
ejpam-3839	44	6	tangent	tangent	ADJ
ejpam-3839	44	7	polynomials	polynomial	NOUN
ejpam-3839	44	8	(	(	PUNCT
ejpam-3839	44	9	see	see	VERB
ejpam-3839	44	10	[	[	X
ejpam-3839	44	11	20	20	NUM
ejpam-3839	44	12	,	,	PUNCT
ejpam-3839	44	13	21	21	NUM
ejpam-3839	44	14	]	]	PUNCT
ejpam-3839	44	15	)	)	PUNCT
ejpam-3839	44	16	defined	define	VERB
ejpam-3839	44	17	by	by	ADP
ejpam-3839	44	18	2	2	NUM
ejpam-3839	44	19	e2	e2	PROPN
ejpam-3839	44	20	t	t	NOUN
ejpam-3839	44	21	+	+	CCONJ
ejpam-3839	44	22	1	1	NUM
ejpam-3839	44	23	=	=	SYM
ejpam-3839	44	24	∞∑	∞∑	NUM
ejpam-3839	44	25	n=0	n=0	NUM
ejpam-3839	44	26	tn(x	tn(x	NOUN
ejpam-3839	44	27	)	)	PUNCT
ejpam-3839	44	28	tn	tn	NOUN
ejpam-3839	44	29	n	n	X
ejpam-3839	44	30	!	!	PROPN
ejpam-3839	44	31	,	,	PUNCT
ejpam-3839	44	32	and	and	CCONJ
ejpam-3839	44	33	tn	tn	NOUN
ejpam-3839	44	34	:	:	PUNCT
ejpam-3839	45	1	=	=	SYM
ejpam-3839	45	2	tn(0	tn(0	PROPN
ejpam-3839	45	3	)	)	PUNCT
ejpam-3839	45	4	are	be	AUX
ejpam-3839	45	5	called	call	VERB
ejpam-3839	45	6	tangent	tangent	ADJ
ejpam-3839	45	7	numbers	number	NOUN
ejpam-3839	45	8	.	.	PUNCT
ejpam-3839	46	1	when	when	SCONJ
ejpam-3839	46	2	x	x	X
ejpam-3839	46	3	=	=	SYM
ejpam-3839	46	4	0	0	NUM
ejpam-3839	46	5	in	in	ADP
ejpam-3839	46	6	(	(	PUNCT
ejpam-3839	46	7	5	5	NUM
ejpam-3839	46	8	)	)	PUNCT
ejpam-3839	46	9	,	,	PUNCT
ejpam-3839	46	10	tm	tm	NOUN
ejpam-3839	46	11	,	,	PUNCT
ejpam-3839	46	12	n	n	PROPN
ejpam-3839	46	13	:	:	PUNCT
ejpam-3839	46	14	=	=	NUM
ejpam-3839	46	15	tm	tm	PROPN
ejpam-3839	46	16	,	,	PUNCT
ejpam-3839	46	17	n(0	n(0	PROPN
ejpam-3839	46	18	)	)	PUNCT
ejpam-3839	46	19	are	be	AUX
ejpam-3839	46	20	called	call	VERB
ejpam-3839	46	21	the	the	DET
ejpam-3839	46	22	truncated	truncate	VERB
ejpam-3839	46	23	tangent	tangent	NOUN
ejpam-3839	46	24	numbers	number	NOUN
ejpam-3839	46	25	given	give	VERB
ejpam-3839	46	26	by	by	ADP
ejpam-3839	46	27	2	2	NUM
ejpam-3839	46	28	tm	tm	PROPN
ejpam-3839	46	29	m	m	PROPN
ejpam-3839	46	30	!	!	PUNCT
ejpam-3839	47	1	e2	e2	PROPN
ejpam-3839	47	2	t	t	PROPN
ejpam-3839	47	3	+	+	CCONJ
ejpam-3839	47	4	1−	1−	NUM
ejpam-3839	47	5	∑m−1	∑m−1	NOUN
ejpam-3839	47	6	j=0	j=0	VERB
ejpam-3839	47	7	2j	2j	NUM
ejpam-3839	47	8	t	t	PROPN
ejpam-3839	47	9	j	j	PROPN
ejpam-3839	47	10	j	j	PROPN
ejpam-3839	47	11	!	!	PUNCT
ejpam-3839	47	12	=	=	PUNCT
ejpam-3839	48	1	∞∑	∞∑	PRON
ejpam-3839	48	2	n=0	n=0	PUNCT
ejpam-3839	48	3	tm	tm	NOUN
ejpam-3839	48	4	,	,	PUNCT
ejpam-3839	48	5	n	n	PROPN
ejpam-3839	48	6	tn	tn	PROPN
ejpam-3839	48	7	n	n	X
ejpam-3839	48	8	!	!	PUNCT
ejpam-3839	48	9	.	.	PUNCT
ejpam-3839	49	1	(	(	PUNCT
ejpam-3839	49	2	6	6	X
ejpam-3839	49	3	)	)	PUNCT
ejpam-3839	49	4	several	several	ADJ
ejpam-3839	49	5	extensions	extension	NOUN
ejpam-3839	49	6	and	and	CCONJ
ejpam-3839	49	7	generalizations	generalization	NOUN
ejpam-3839	49	8	of	of	ADP
ejpam-3839	49	9	tangent	tangent	ADJ
ejpam-3839	49	10	numbers	number	NOUN
ejpam-3839	49	11	and	and	CCONJ
ejpam-3839	49	12	polynomials	polynomial	NOUN
ejpam-3839	49	13	can	can	AUX
ejpam-3839	49	14	be	be	AUX
ejpam-3839	49	15	seen	see	VERB
ejpam-3839	49	16	in	in	ADP
ejpam-3839	49	17	[	[	X
ejpam-3839	49	18	1	1	NUM
ejpam-3839	49	19	,	,	PUNCT
ejpam-3839	49	20	22–25	22–25	NUM
ejpam-3839	49	21	]	]	PUNCT
ejpam-3839	49	22	.	.	PUNCT
ejpam-3839	50	1	the	the	DET
ejpam-3839	50	2	following	follow	VERB
ejpam-3839	50	3	identities	identity	NOUN
ejpam-3839	50	4	follow	follow	VERB
ejpam-3839	50	5	directly	directly	ADV
ejpam-3839	50	6	from	from	ADP
ejpam-3839	50	7	the	the	DET
ejpam-3839	50	8	generating	generate	VERB
ejpam-3839	50	9	function	function	NOUN
ejpam-3839	50	10	(	(	PUNCT
ejpam-3839	50	11	5	5	NUM
ejpam-3839	50	12	)	)	PUNCT
ejpam-3839	50	13	.	.	PUNCT
ejpam-3839	51	1	theorem	theorem	NOUN
ejpam-3839	51	2	1	1	NUM
ejpam-3839	51	3	.	.	X
ejpam-3839	51	4	for	for	ADP
ejpam-3839	51	5	m	m	PROPN
ejpam-3839	51	6	,	,	PUNCT
ejpam-3839	51	7	n	n	PRON
ejpam-3839	51	8	≥	≥	NOUN
ejpam-3839	51	9	0	0	NUM
ejpam-3839	51	10	,	,	PUNCT
ejpam-3839	51	11	tm	tm	NOUN
ejpam-3839	51	12	,	,	PUNCT
ejpam-3839	51	13	n(x	n(x	PROPN
ejpam-3839	51	14	)	)	PUNCT
ejpam-3839	51	15	=	=	SYM
ejpam-3839	51	16	n∑	n∑	NOUN
ejpam-3839	51	17	r=0	r=0	PROPN
ejpam-3839	51	18	(	(	PUNCT
ejpam-3839	51	19	n	n	NOUN
ejpam-3839	51	20	r	r	NOUN
ejpam-3839	51	21	)	)	PUNCT
ejpam-3839	51	22	tm	tm	NOUN
ejpam-3839	51	23	,	,	PUNCT
ejpam-3839	51	24	r	r	NOUN
ejpam-3839	51	25	·	·	PUNCT
ejpam-3839	51	26	xn−r	xn−r	NOUN
ejpam-3839	51	27	(	(	PUNCT
ejpam-3839	51	28	7	7	NUM
ejpam-3839	51	29	)	)	PUNCT
ejpam-3839	51	30	tm	tm	NOUN
ejpam-3839	51	31	,	,	PUNCT
ejpam-3839	51	32	n(x	n(x	PROPN
ejpam-3839	51	33	)	)	PUNCT
ejpam-3839	51	34	=	=	SYM
ejpam-3839	51	35	n∑	n∑	NOUN
ejpam-3839	51	36	r=0	r=0	PROPN
ejpam-3839	51	37	(	(	PUNCT
ejpam-3839	51	38	n	n	NOUN
ejpam-3839	51	39	r	r	NOUN
ejpam-3839	51	40	)	)	PUNCT
ejpam-3839	51	41	tm	tm	PROPN
ejpam-3839	51	42	,	,	PUNCT
ejpam-3839	51	43	r(y)(x−	r(y)(x−	NOUN
ejpam-3839	51	44	y)n−r	y)n−r	PROPN
ejpam-3839	51	45	(	(	PUNCT
ejpam-3839	51	46	8)	8)	NUM
ejpam-3839	51	47	tm	tm	NOUN
ejpam-3839	51	48	,	,	PUNCT
ejpam-3839	51	49	n(x+	n(x+	NOUN
ejpam-3839	51	50	y	y	NOUN
ejpam-3839	51	51	)	)	PUNCT
ejpam-3839	52	1	=	=	SYM
ejpam-3839	53	1	n∑	n∑	NOUN
ejpam-3839	53	2	r=0	r=0	PROPN
ejpam-3839	53	3	(	(	PUNCT
ejpam-3839	53	4	n	n	NOUN
ejpam-3839	53	5	r	r	NOUN
ejpam-3839	53	6	)	)	PUNCT
ejpam-3839	53	7	tm	tm	NOUN
ejpam-3839	53	8	,	,	PUNCT
ejpam-3839	53	9	r(x)yn−r	r(x)yn−r	NOUN
ejpam-3839	53	10	(	(	PUNCT
ejpam-3839	53	11	9	9	NUM
ejpam-3839	53	12	)	)	PUNCT
ejpam-3839	53	13	tm	tm	NOUN
ejpam-3839	53	14	,	,	PUNCT
ejpam-3839	53	15	n(px	n(px	X
ejpam-3839	53	16	)	)	PUNCT
ejpam-3839	53	17	=	=	SYM
ejpam-3839	54	1	n∑	n∑	NOUN
ejpam-3839	54	2	r=0	r=0	PROPN
ejpam-3839	54	3	(	(	PUNCT
ejpam-3839	54	4	n	n	NOUN
ejpam-3839	54	5	r	r	NOUN
ejpam-3839	54	6	)	)	PUNCT
ejpam-3839	54	7	tm	tm	NOUN
ejpam-3839	54	8	,	,	PUNCT
ejpam-3839	54	9	r(x)(p−	r(x)(p−	NOUN
ejpam-3839	54	10	1)n−rxn−r	1)n−rxn−r	NOUN
ejpam-3839	54	11	,	,	PUNCT
ejpam-3839	54	12	p	p	X
ejpam-3839	54	13	6=	6=	PROPN
ejpam-3839	54	14	1	1	NUM
ejpam-3839	54	15	.	.	PUNCT
ejpam-3839	55	1	(	(	PUNCT
ejpam-3839	55	2	10	10	NUM
ejpam-3839	55	3	)	)	PUNCT
ejpam-3839	55	4	the	the	DET
ejpam-3839	55	5	truncated	truncated	ADJ
ejpam-3839	55	6	tangent	tangent	NOUN
ejpam-3839	55	7	polynomials	polynomial	NOUN
ejpam-3839	55	8	satisfy	satisfy	VERB
ejpam-3839	55	9	the	the	DET
ejpam-3839	55	10	following	follow	VERB
ejpam-3839	55	11	derivative	derivative	ADJ
ejpam-3839	55	12	and	and	CCONJ
ejpam-3839	55	13	integral	integral	ADJ
ejpam-3839	55	14	properties	property	NOUN
ejpam-3839	55	15	.	.	PUNCT
ejpam-3839	56	1	theorem	theorem	NOUN
ejpam-3839	56	2	2	2	NUM
ejpam-3839	56	3	.	.	X
ejpam-3839	56	4	for	for	ADP
ejpam-3839	56	5	m	m	PROPN
ejpam-3839	56	6	≥	≥	NOUN
ejpam-3839	56	7	0	0	NUM
ejpam-3839	56	8	and	and	CCONJ
ejpam-3839	56	9	n	n	PRON
ejpam-3839	56	10	≥	≥	NOUN
ejpam-3839	56	11	1	1	NUM
ejpam-3839	56	12	,	,	PUNCT
ejpam-3839	56	13	d	d	PROPN
ejpam-3839	56	14	dx	dx	PROPN
ejpam-3839	56	15	tm	tm	PROPN
ejpam-3839	56	16	,	,	PUNCT
ejpam-3839	56	17	n(x	n(x	X
ejpam-3839	56	18	)	)	PUNCT
ejpam-3839	56	19	=	=	SYM
ejpam-3839	56	20	ntm	ntm	PROPN
ejpam-3839	56	21	,	,	PUNCT
ejpam-3839	56	22	n−1(x	n−1(x	PROPN
ejpam-3839	56	23	)	)	PUNCT
ejpam-3839	56	24	.	.	PUNCT
ejpam-3839	57	1	(	(	PUNCT
ejpam-3839	57	2	11	11	X
ejpam-3839	57	3	)	)	PUNCT
ejpam-3839	57	4	n.	n.	PROPN
ejpam-3839	57	5	acala	acala	PROPN
ejpam-3839	57	6	,	,	PUNCT
ejpam-3839	57	7	m.	m.	PROPN
ejpam-3839	57	8	montero	montero	PROPN
ejpam-3839	57	9	/	/	SYM
ejpam-3839	57	10	eur	eur	PROPN
ejpam-3839	57	11	.	.	PUNCT
ejpam-3839	58	1	j.	j.	PROPN
ejpam-3839	58	2	pure	pure	PROPN
ejpam-3839	58	3	appl	appl	PROPN
ejpam-3839	58	4	.	.	PROPN
ejpam-3839	58	5	math	math	PROPN
ejpam-3839	58	6	,	,	PUNCT
ejpam-3839	58	7	13	13	NUM
ejpam-3839	58	8	(	(	PUNCT
ejpam-3839	58	9	4	4	NUM
ejpam-3839	58	10	)	)	PUNCT
ejpam-3839	58	11	(	(	PUNCT
ejpam-3839	58	12	2020	2020	NUM
ejpam-3839	58	13	)	)	PUNCT
ejpam-3839	58	14	,	,	PUNCT
ejpam-3839	58	15	948	948	NUM
ejpam-3839	58	16	-	-	SYM
ejpam-3839	58	17	963	963	NUM
ejpam-3839	58	18	951∫	951∫	NUM
ejpam-3839	58	19	tm	tm	NOUN
ejpam-3839	58	20	,	,	PUNCT
ejpam-3839	58	21	n(x)dx	n(x)dx	ADV
ejpam-3839	58	22	=	=	SYM
ejpam-3839	58	23	1	1	NUM
ejpam-3839	58	24	n+	n+	SYM
ejpam-3839	58	25	1	1	NUM
ejpam-3839	58	26	tm	tm	NOUN
ejpam-3839	58	27	,	,	PUNCT
ejpam-3839	58	28	n+1	n+1	PROPN
ejpam-3839	58	29	(	(	PUNCT
ejpam-3839	58	30	12	12	NUM
ejpam-3839	58	31	)	)	PUNCT
ejpam-3839	58	32	tm	tm	NOUN
ejpam-3839	58	33	,	,	PUNCT
ejpam-3839	58	34	n(x	n(x	X
ejpam-3839	58	35	)	)	PUNCT
ejpam-3839	58	36	=	=	SYM
ejpam-3839	58	37	tm	tm	NOUN
ejpam-3839	58	38	,	,	PUNCT
ejpam-3839	58	39	n	n	PROPN
ejpam-3839	58	40	+	+	CCONJ
ejpam-3839	58	41	n	n	CCONJ
ejpam-3839	58	42	∫	∫	PROPN
ejpam-3839	58	43	x	x	SYM
ejpam-3839	58	44	0	0	NUM
ejpam-3839	58	45	tm	tm	PROPN
ejpam-3839	58	46	,	,	PUNCT
ejpam-3839	58	47	n−1(t)dt	n−1(t)dt	PROPN
ejpam-3839	58	48	.	.	PUNCT
ejpam-3839	59	1	(	(	PUNCT
ejpam-3839	59	2	13	13	NUM
ejpam-3839	59	3	)	)	PUNCT
ejpam-3839	59	4	proof	proof	NOUN
ejpam-3839	59	5	.	.	PUNCT
ejpam-3839	60	1	taking	take	VERB
ejpam-3839	60	2	the	the	DET
ejpam-3839	60	3	derivative	derivative	NOUN
ejpam-3839	60	4	of	of	ADP
ejpam-3839	60	5	both	both	DET
ejpam-3839	60	6	sides	side	NOUN
ejpam-3839	60	7	of	of	ADP
ejpam-3839	60	8	(	(	PUNCT
ejpam-3839	60	9	7	7	NUM
ejpam-3839	60	10	)	)	PUNCT
ejpam-3839	60	11	with	with	ADP
ejpam-3839	60	12	respect	respect	NOUN
ejpam-3839	60	13	to	to	ADP
ejpam-3839	60	14	x	x	SYM
ejpam-3839	60	15	,	,	PUNCT
ejpam-3839	60	16	we	we	PRON
ejpam-3839	60	17	obtain	obtain	VERB
ejpam-3839	60	18	d	d	PROPN
ejpam-3839	60	19	dx	dx	PROPN
ejpam-3839	60	20	tm	tm	PROPN
ejpam-3839	60	21	,	,	PUNCT
ejpam-3839	60	22	n(x	n(x	PROPN
ejpam-3839	60	23	)	)	PUNCT
ejpam-3839	60	24	=	=	SYM
ejpam-3839	60	25	n−1∑	n−1∑	PROPN
ejpam-3839	60	26	r=0	r=0	PROPN
ejpam-3839	60	27	(	(	PUNCT
ejpam-3839	60	28	n	n	NOUN
ejpam-3839	60	29	r	r	NOUN
ejpam-3839	60	30	)	)	PUNCT
ejpam-3839	60	31	(	(	PUNCT
ejpam-3839	60	32	n−	n−	PROPN
ejpam-3839	60	33	r)tm	r)tm	PROPN
ejpam-3839	60	34	,	,	PUNCT
ejpam-3839	60	35	r	r	NOUN
ejpam-3839	60	36	·	·	PUNCT
ejpam-3839	60	37	x(n−r−1	x(n−r−1	NUM
ejpam-3839	60	38	)	)	PUNCT
ejpam-3839	61	1	=	=	SYM
ejpam-3839	61	2	n	n	PROPN
ejpam-3839	61	3	n−1∑	n−1∑	PROPN
ejpam-3839	61	4	r=0	r=0	PROPN
ejpam-3839	61	5	(	(	PUNCT
ejpam-3839	61	6	n−	n−	NOUN
ejpam-3839	61	7	1	1	NUM
ejpam-3839	61	8	r	r	NOUN
ejpam-3839	61	9	)	)	PUNCT
ejpam-3839	61	10	tm	tm	NOUN
ejpam-3839	61	11	,	,	PUNCT
ejpam-3839	61	12	rx	rx	VERB
ejpam-3839	61	13	(	(	PUNCT
ejpam-3839	61	14	n−1)−r	n−1)−r	NOUN
ejpam-3839	61	15	=	=	SYM
ejpam-3839	61	16	ntm	ntm	PROPN
ejpam-3839	61	17	,	,	PUNCT
ejpam-3839	61	18	n−1(x	n−1(x	PROPN
ejpam-3839	61	19	)	)	PUNCT
ejpam-3839	61	20	.	.	PUNCT
ejpam-3839	62	1	equation	equation	NOUN
ejpam-3839	62	2	(	(	PUNCT
ejpam-3839	62	3	12	12	NUM
ejpam-3839	62	4	)	)	PUNCT
ejpam-3839	62	5	follows	follow	VERB
ejpam-3839	62	6	from	from	ADP
ejpam-3839	62	7	(	(	PUNCT
ejpam-3839	62	8	11	11	NUM
ejpam-3839	62	9	)	)	PUNCT
ejpam-3839	62	10	.	.	PUNCT
ejpam-3839	63	1	from	from	ADP
ejpam-3839	63	2	(	(	PUNCT
ejpam-3839	63	3	12	12	NUM
ejpam-3839	63	4	)	)	PUNCT
ejpam-3839	63	5	,	,	PUNCT
ejpam-3839	63	6	we	we	PRON
ejpam-3839	63	7	have∫	have∫	VERB
ejpam-3839	63	8	x	x	SYM
ejpam-3839	63	9	0	0	NUM
ejpam-3839	63	10	tm	tm	PROPN
ejpam-3839	63	11	,	,	PUNCT
ejpam-3839	63	12	n−1(t)dt	n−1(t)dt	NOUN
ejpam-3839	63	13	=	=	SYM
ejpam-3839	63	14	1	1	NUM
ejpam-3839	63	15	n	n	CCONJ
ejpam-3839	63	16	(	(	PUNCT
ejpam-3839	63	17	tm	tm	PROPN
ejpam-3839	63	18	,	,	PUNCT
ejpam-3839	63	19	n(x)−	n(x)−	PROPN
ejpam-3839	63	20	tm	tm	PROPN
ejpam-3839	63	21	,	,	PUNCT
ejpam-3839	63	22	n(0	n(0	PROPN
ejpam-3839	63	23	)	)	PUNCT
ejpam-3839	63	24	)	)	PUNCT
ejpam-3839	63	25	,	,	PUNCT
ejpam-3839	63	26	which	which	PRON
ejpam-3839	63	27	gives	give	VERB
ejpam-3839	63	28	(	(	PUNCT
ejpam-3839	63	29	13	13	NUM
ejpam-3839	63	30	)	)	PUNCT
ejpam-3839	63	31	.	.	PUNCT
ejpam-3839	64	1	theorem	theorem	NOUN
ejpam-3839	64	2	3	3	NUM
ejpam-3839	64	3	.	.	X
ejpam-3839	64	4	for	for	ADP
ejpam-3839	64	5	n	n	PRON
ejpam-3839	64	6	≥	≥	NOUN
ejpam-3839	64	7	0	0	NUM
ejpam-3839	64	8	,	,	PUNCT
ejpam-3839	64	9	t1,n(x	t1,n(x	X
ejpam-3839	64	10	)	)	PUNCT
ejpam-3839	64	11	=	=	SYM
ejpam-3839	64	12	2n(x−	2n(x−	NUM
ejpam-3839	64	13	2)n−1	2)n−1	NUM
ejpam-3839	64	14	.	.	PUNCT
ejpam-3839	65	1	(	(	PUNCT
ejpam-3839	65	2	14	14	NUM
ejpam-3839	65	3	)	)	PUNCT
ejpam-3839	65	4	proof	proof	NOUN
ejpam-3839	65	5	.	.	PUNCT
ejpam-3839	66	1	when	when	SCONJ
ejpam-3839	66	2	m	m	VERB
ejpam-3839	66	3	=	=	SYM
ejpam-3839	66	4	1	1	NUM
ejpam-3839	66	5	in	in	ADP
ejpam-3839	66	6	(	(	PUNCT
ejpam-3839	66	7	5	5	NUM
ejpam-3839	66	8	)	)	PUNCT
ejpam-3839	66	9	,	,	PUNCT
ejpam-3839	66	10	we	we	PRON
ejpam-3839	66	11	have	have	VERB
ejpam-3839	66	12	∞∑	∞∑	NUM
ejpam-3839	66	13	n=0	n=0	NUM
ejpam-3839	66	14	t1,n(x	t1,n(x	PART
ejpam-3839	66	15	)	)	PUNCT
ejpam-3839	66	16	tn−1	tn−1	PROPN
ejpam-3839	66	17	n	n	CCONJ
ejpam-3839	66	18	!	!	PUNCT
ejpam-3839	67	1	=	=	SYM
ejpam-3839	67	2	2te(x−2)t	2te(x−2)t	NUM
ejpam-3839	67	3	=	=	SYM
ejpam-3839	67	4	2	2	NUM
ejpam-3839	68	1	∞∑	∞∑	NUM
ejpam-3839	68	2	n=0	n=0	NUM
ejpam-3839	68	3	(	(	PUNCT
ejpam-3839	68	4	x−	x−	PROPN
ejpam-3839	68	5	2)n	2)n	NUM
ejpam-3839	68	6	tn+1	tn+1	NOUN
ejpam-3839	68	7	n	n	X
ejpam-3839	68	8	!	!	PUNCT
ejpam-3839	69	1	=	=	SYM
ejpam-3839	69	2	2	2	NUM
ejpam-3839	69	3	∞∑	∞∑	NUM
ejpam-3839	69	4	n=1	n=1	PROPN
ejpam-3839	69	5	n(x−	n(x−	ADP
ejpam-3839	69	6	2)n−1	2)n−1	NUM
ejpam-3839	69	7	tn	tn	NOUN
ejpam-3839	69	8	n	n	NOUN
ejpam-3839	69	9	!	!	PUNCT
ejpam-3839	70	1	=	=	SYM
ejpam-3839	70	2	2	2	NUM
ejpam-3839	71	1	∞∑	∞∑	NUM
ejpam-3839	71	2	n=0	n=0	NUM
ejpam-3839	71	3	n(x−	n(x−	ADP
ejpam-3839	71	4	2)n−1	2)n−1	NUM
ejpam-3839	71	5	tn	tn	NOUN
ejpam-3839	71	6	n	n	X
ejpam-3839	71	7	!	!	PUNCT
ejpam-3839	71	8	.	.	PUNCT
ejpam-3839	72	1	comparing	compare	VERB
ejpam-3839	72	2	the	the	DET
ejpam-3839	72	3	coefficients	coefficient	NOUN
ejpam-3839	72	4	of	of	ADP
ejpam-3839	72	5	tn	tn	NOUN
ejpam-3839	72	6	n	n	ADP
ejpam-3839	72	7	!	!	PROPN
ejpam-3839	72	8	completes	complete	VERB
ejpam-3839	72	9	the	the	DET
ejpam-3839	72	10	proof	proof	NOUN
ejpam-3839	72	11	.	.	PUNCT
ejpam-3839	73	1	theorem	theorem	ADJ
ejpam-3839	73	2	4	4	NUM
ejpam-3839	73	3	.	.	PUNCT
ejpam-3839	74	1	the	the	DET
ejpam-3839	74	2	truncated	truncated	ADJ
ejpam-3839	74	3	tangent	tangent	NOUN
ejpam-3839	74	4	polynomials	polynomial	NOUN
ejpam-3839	74	5	satisfy	satisfy	VERB
ejpam-3839	74	6	the	the	DET
ejpam-3839	74	7	following	follow	VERB
ejpam-3839	74	8	recurrence	recurrence	NOUN
ejpam-3839	74	9	relation	relation	PROPN
ejpam-3839	74	10	:	:	PUNCT
ejpam-3839	74	11	tm	tm	NOUN
ejpam-3839	74	12	,	,	PUNCT
ejpam-3839	74	13	n(x	n(x	PROPN
ejpam-3839	74	14	)	)	PUNCT
ejpam-3839	74	15	=	=	SYM
ejpam-3839	74	16	0	0	NUM
ejpam-3839	74	17	,	,	PUNCT
ejpam-3839	74	18	n	n	NOUN
ejpam-3839	74	19	=	=	SYM
ejpam-3839	74	20	0	0	NUM
ejpam-3839	74	21	,	,	PUNCT
ejpam-3839	74	22	1	1	NUM
ejpam-3839	74	23	,	,	PUNCT
ejpam-3839	74	24	2	2	NUM
ejpam-3839	74	25	,	,	PUNCT
ejpam-3839	74	26	·	·	PUNCT
ejpam-3839	74	27	·	·	PUNCT
ejpam-3839	74	28	·	·	PUNCT
ejpam-3839	74	29	,	,	PUNCT
ejpam-3839	74	30	m−	m−	PROPN
ejpam-3839	74	31	1	1	NUM
ejpam-3839	74	32	and	and	CCONJ
ejpam-3839	74	33	tm	tm	NOUN
ejpam-3839	74	34	,	,	PUNCT
ejpam-3839	74	35	n+m(x	n+m(x	NOUN
ejpam-3839	74	36	)	)	PUNCT
ejpam-3839	74	37	=	=	SYM
ejpam-3839	74	38	2	2	NUM
ejpam-3839	74	39	(	(	PUNCT
ejpam-3839	74	40	n+m	n+m	NUM
ejpam-3839	74	41	n	n	CCONJ
ejpam-3839	74	42	)	)	PUNCT
ejpam-3839	74	43	xn	xn	PROPN
ejpam-3839	75	1	−	−	PROPN
ejpam-3839	75	2	n∑	n∑	NOUN
ejpam-3839	75	3	j=0	j=0	PROPN
ejpam-3839	75	4	2n+m−j	2n+m−j	NUM
ejpam-3839	75	5	(	(	PUNCT
ejpam-3839	75	6	n+m	n+m	NUM
ejpam-3839	75	7	j	j	PROPN
ejpam-3839	75	8	)	)	PUNCT
ejpam-3839	75	9	tm	tm	PROPN
ejpam-3839	75	10	,	,	PUNCT
ejpam-3839	75	11	j	j	PROPN
ejpam-3839	75	12	,	,	PUNCT
ejpam-3839	75	13	n	n	CCONJ
ejpam-3839	75	14	≥	≥	NOUN
ejpam-3839	75	15	0	0	NUM
ejpam-3839	75	16	.	.	PUNCT
ejpam-3839	76	1	(	(	PUNCT
ejpam-3839	76	2	15	15	X
ejpam-3839	76	3	)	)	PUNCT
ejpam-3839	76	4	n.	n.	NOUN
ejpam-3839	76	5	acala	acala	PROPN
ejpam-3839	76	6	,	,	PUNCT
ejpam-3839	76	7	m.	m.	PROPN
ejpam-3839	76	8	montero	montero	PROPN
ejpam-3839	76	9	/	/	SYM
ejpam-3839	76	10	eur	eur	PROPN
ejpam-3839	76	11	.	.	PUNCT
ejpam-3839	77	1	j.	j.	PROPN
ejpam-3839	77	2	pure	pure	PROPN
ejpam-3839	77	3	appl	appl	PROPN
ejpam-3839	77	4	.	.	PROPN
ejpam-3839	77	5	math	math	PROPN
ejpam-3839	77	6	,	,	PUNCT
ejpam-3839	77	7	13	13	NUM
ejpam-3839	77	8	(	(	PUNCT
ejpam-3839	77	9	4	4	NUM
ejpam-3839	77	10	)	)	PUNCT
ejpam-3839	77	11	(	(	PUNCT
ejpam-3839	77	12	2020	2020	NUM
ejpam-3839	77	13	)	)	PUNCT
ejpam-3839	77	14	,	,	PUNCT
ejpam-3839	77	15	948	948	NUM
ejpam-3839	77	16	-	-	SYM
ejpam-3839	77	17	963	963	NUM
ejpam-3839	77	18	952	952	NUM
ejpam-3839	77	19	proof	proof	NOUN
ejpam-3839	77	20	.	.	PUNCT
ejpam-3839	78	1	it	it	PRON
ejpam-3839	78	2	follows	follow	VERB
ejpam-3839	78	3	from	from	ADP
ejpam-3839	78	4	(	(	PUNCT
ejpam-3839	78	5	5	5	NUM
ejpam-3839	78	6	)	)	PUNCT
ejpam-3839	78	7	that	that	SCONJ
ejpam-3839	78	8	2tm	2tm	NOUN
ejpam-3839	78	9	m	m	NOUN
ejpam-3839	78	10	!	!	PUNCT
ejpam-3839	79	1	∞∑	∞∑	ADJ
ejpam-3839	79	2	n=0	n=0	NUM
ejpam-3839	79	3	(	(	PUNCT
ejpam-3839	79	4	xt)n	xt)n	PROPN
ejpam-3839	79	5	n	n	CCONJ
ejpam-3839	79	6	!	!	PUNCT
ejpam-3839	79	7	=	=	NOUN
ejpam-3839	80	1	∞∑	∞∑	PRON
ejpam-3839	80	2	n=0	n=0	PUNCT
ejpam-3839	80	3	tm	tm	NOUN
ejpam-3839	80	4	,	,	PUNCT
ejpam-3839	80	5	n(x	n(x	PROPN
ejpam-3839	80	6	)	)	PUNCT
ejpam-3839	80	7	tn	tn	PROPN
ejpam-3839	80	8	n	n	PROPN
ejpam-3839	80	9	!	!	PUNCT
ejpam-3839	81	1	1	1	PROPN
ejpam-3839	81	2	+	+	CCONJ
ejpam-3839	82	1	∞∑	∞∑	NUM
ejpam-3839	82	2	j	j	X
ejpam-3839	82	3	=	=	NOUN
ejpam-3839	82	4	m	m	VERB
ejpam-3839	82	5	2j	2j	NUM
ejpam-3839	82	6	tj	tj	X
ejpam-3839	82	7	j	j	PROPN
ejpam-3839	82	8	!	!	PUNCT
ejpam-3839	83	1			PROPN
ejpam-3839	84	1	=	=	PUNCT
ejpam-3839	85	1	∞∑	∞∑	NUM
ejpam-3839	85	2	n=0	n=0	PUNCT
ejpam-3839	85	3	tm	tm	NOUN
ejpam-3839	85	4	,	,	PUNCT
ejpam-3839	85	5	n(x	n(x	PROPN
ejpam-3839	85	6	)	)	PUNCT
ejpam-3839	85	7	tn	tn	NOUN
ejpam-3839	85	8	n	n	CCONJ
ejpam-3839	85	9	!	!	PUNCT
ejpam-3839	86	1	+	+	CCONJ
ejpam-3839	86	2	(	(	PUNCT
ejpam-3839	86	3	∞∑	∞∑	NUM
ejpam-3839	86	4	n=0	n=0	NUM
ejpam-3839	86	5	tm	tm	NOUN
ejpam-3839	86	6	,	,	PUNCT
ejpam-3839	86	7	n(x	n(x	PROPN
ejpam-3839	86	8	)	)	PUNCT
ejpam-3839	86	9	tn	tn	NOUN
ejpam-3839	86	10	n	n	PROPN
ejpam-3839	86	11	!	!	PUNCT
ejpam-3839	86	12	)	)	PUNCT
ejpam-3839	87	1			PROPN
ejpam-3839	87	2	∞∑	∞∑	NUM
ejpam-3839	87	3	j	j	NOUN
ejpam-3839	87	4	=	=	NOUN
ejpam-3839	87	5	m	m	VERB
ejpam-3839	87	6	2j	2j	NUM
ejpam-3839	87	7	tj	tj	X
ejpam-3839	87	8	j	j	PROPN
ejpam-3839	87	9	!	!	PUNCT
ejpam-3839	88	1			PROPN
ejpam-3839	88	2	.	.	PUNCT
ejpam-3839	89	1	thus	thus	ADV
ejpam-3839	89	2	,	,	PUNCT
ejpam-3839	89	3	(	(	PUNCT
ejpam-3839	89	4	∞∑	∞∑	NUM
ejpam-3839	89	5	n=0	n=0	NUM
ejpam-3839	89	6	tm	tm	NOUN
ejpam-3839	89	7	,	,	PUNCT
ejpam-3839	89	8	n(x	n(x	PROPN
ejpam-3839	89	9	)	)	PUNCT
ejpam-3839	89	10	tn	tn	NOUN
ejpam-3839	89	11	n	n	PROPN
ejpam-3839	89	12	!	!	PUNCT
ejpam-3839	89	13	)	)	PUNCT
ejpam-3839	90	1			PROPN
ejpam-3839	90	2	∞∑	∞∑	NUM
ejpam-3839	90	3	j	j	NOUN
ejpam-3839	90	4	=	=	NOUN
ejpam-3839	90	5	m	m	VERB
ejpam-3839	90	6	2j	2j	NUM
ejpam-3839	90	7	tj	tj	X
ejpam-3839	90	8	j	j	PROPN
ejpam-3839	90	9	!	!	PUNCT
ejpam-3839	91	1			PROPN
ejpam-3839	91	2	(	(	PUNCT
ejpam-3839	91	3	16	16	NUM
ejpam-3839	91	4	)	)	PUNCT
ejpam-3839	91	5	=	=	NOUN
ejpam-3839	92	1	∞∑	∞∑	PRON
ejpam-3839	92	2	n=0	n=0	NUM
ejpam-3839	92	3	2xntn+m	2xntn+m	NUM
ejpam-3839	92	4	n!m	n!m	NUM
ejpam-3839	92	5	!	!	PUNCT
ejpam-3839	93	1	−	−	PROPN
ejpam-3839	94	1	∞∑	∞∑	NUM
ejpam-3839	94	2	n=0	n=0	PUNCT
ejpam-3839	94	3	tm	tm	NOUN
ejpam-3839	94	4	,	,	PUNCT
ejpam-3839	94	5	n+m(x	n+m(x	NOUN
ejpam-3839	94	6	)	)	PUNCT
ejpam-3839	94	7	tn+m	tn+m	PROPN
ejpam-3839	94	8	(	(	PUNCT
ejpam-3839	94	9	n+m	n+m	NUM
ejpam-3839	94	10	)	)	PUNCT
ejpam-3839	94	11	!	!	PUNCT
ejpam-3839	95	1	−	−	PROPN
ejpam-3839	96	1	m−1∑	m−1∑	PRON
ejpam-3839	96	2	n=0	n=0	PUNCT
ejpam-3839	96	3	tm	tm	NOUN
ejpam-3839	96	4	,	,	PUNCT
ejpam-3839	96	5	n(x	n(x	PROPN
ejpam-3839	96	6	)	)	PUNCT
ejpam-3839	96	7	tn	tn	NOUN
ejpam-3839	96	8	n	n	NOUN
ejpam-3839	96	9	!	!	PUNCT
ejpam-3839	96	10	=	=	NOUN
ejpam-3839	97	1	∞∑	∞∑	NUM
ejpam-3839	97	2	n=0	n=0	NUM
ejpam-3839	97	3	(	(	PUNCT
ejpam-3839	97	4	2	2	NUM
ejpam-3839	97	5	(	(	PUNCT
ejpam-3839	97	6	n+m	n+m	NUM
ejpam-3839	97	7	n	n	CCONJ
ejpam-3839	97	8	)	)	PUNCT
ejpam-3839	97	9	xn	xn	PUNCT
ejpam-3839	98	1	−	−	PROPN
ejpam-3839	98	2	tm	tm	NOUN
ejpam-3839	98	3	,	,	PUNCT
ejpam-3839	98	4	n+m(x	n+m(x	NOUN
ejpam-3839	98	5	)	)	PUNCT
ejpam-3839	98	6	)	)	PUNCT
ejpam-3839	98	7	tn+m	tn+m	PROPN
ejpam-3839	98	8	(	(	PUNCT
ejpam-3839	98	9	n+m	n+m	NUM
ejpam-3839	98	10	)	)	PUNCT
ejpam-3839	98	11	!	!	PUNCT
ejpam-3839	99	1	−	−	PROPN
ejpam-3839	100	1	m−1∑	m−1∑	PRON
ejpam-3839	100	2	n=0	n=0	PUNCT
ejpam-3839	100	3	tm	tm	NOUN
ejpam-3839	100	4	,	,	PUNCT
ejpam-3839	100	5	n(x	n(x	PROPN
ejpam-3839	100	6	)	)	PUNCT
ejpam-3839	100	7	tn	tn	NOUN
ejpam-3839	100	8	n	n	NUM
ejpam-3839	100	9	!	!	PUNCT
ejpam-3839	100	10	.	.	PUNCT
ejpam-3839	101	1	(	(	PUNCT
ejpam-3839	101	2	17	17	NUM
ejpam-3839	101	3	)	)	PUNCT
ejpam-3839	101	4	note	note	VERB
ejpam-3839	101	5	that	that	SCONJ
ejpam-3839	101	6	expression	expression	NOUN
ejpam-3839	101	7	(	(	PUNCT
ejpam-3839	101	8	16	16	NUM
ejpam-3839	101	9	)	)	PUNCT
ejpam-3839	101	10	can	can	AUX
ejpam-3839	101	11	be	be	AUX
ejpam-3839	101	12	written	write	VERB
ejpam-3839	101	13	as	as	ADP
ejpam-3839	101	14	(	(	PUNCT
ejpam-3839	101	15	∞∑	∞∑	NUM
ejpam-3839	101	16	n=0	n=0	NUM
ejpam-3839	101	17	tm	tm	NOUN
ejpam-3839	101	18	,	,	PUNCT
ejpam-3839	101	19	n(x	n(x	PROPN
ejpam-3839	101	20	)	)	PUNCT
ejpam-3839	101	21	tn	tn	NOUN
ejpam-3839	101	22	n	n	PROPN
ejpam-3839	101	23	!	!	PUNCT
ejpam-3839	101	24	)	)	PUNCT
ejpam-3839	102	1			PROPN
ejpam-3839	102	2	∞∑	∞∑	NUM
ejpam-3839	102	3	j	j	NOUN
ejpam-3839	102	4	=	=	NOUN
ejpam-3839	102	5	m	m	VERB
ejpam-3839	102	6	2j	2j	NUM
ejpam-3839	102	7	tj	tj	X
ejpam-3839	102	8	j	j	PROPN
ejpam-3839	102	9	!	!	PUNCT
ejpam-3839	102	10			PROPN
ejpam-3839	103	1	=	=	PUNCT
ejpam-3839	103	2	∞∑	∞∑	NUM
ejpam-3839	103	3	n=0	n=0	PROPN
ejpam-3839	103	4	n∑	n∑	PRON
ejpam-3839	103	5	j=0	j=0	PROPN
ejpam-3839	103	6	tm	tm	PROPN
ejpam-3839	103	7	,	,	PUNCT
ejpam-3839	103	8	j(x	j(x	PROPN
ejpam-3839	103	9	)	)	PUNCT
ejpam-3839	103	10	tj	tj	PROPN
ejpam-3839	103	11	j	j	PROPN
ejpam-3839	103	12	!	!	PUNCT
ejpam-3839	104	1	2n−j+m	2n−j+m	PROPN
ejpam-3839	104	2	tn−j+m	tn−j+m	PROPN
ejpam-3839	104	3	(	(	PUNCT
ejpam-3839	104	4	n−	n−	NOUN
ejpam-3839	104	5	j	j	PROPN
ejpam-3839	104	6	+	+	NOUN
ejpam-3839	104	7	m	m	NOUN
ejpam-3839	104	8	)	)	PUNCT
ejpam-3839	104	9	!	!	PUNCT
ejpam-3839	105	1	=	=	PUNCT
ejpam-3839	106	1	∞∑	∞∑	DET
ejpam-3839	106	2	n=0	n=0	NUM
ejpam-3839	106	3	n∑	n∑	X
ejpam-3839	106	4	j=0	j=0	PROPN
ejpam-3839	106	5	2n+m−j	2n+m−j	NUM
ejpam-3839	106	6	(	(	PUNCT
ejpam-3839	106	7	n+m	n+m	NUM
ejpam-3839	106	8	j	j	PROPN
ejpam-3839	106	9	)	)	PUNCT
ejpam-3839	106	10	tm	tm	PROPN
ejpam-3839	106	11	,	,	PUNCT
ejpam-3839	106	12	j(x	j(x	PROPN
ejpam-3839	106	13	)	)	PUNCT
ejpam-3839	106	14	tn+m	tn+m	PROPN
ejpam-3839	106	15	(	(	PUNCT
ejpam-3839	106	16	n+m	n+m	NUM
ejpam-3839	106	17	)	)	PUNCT
ejpam-3839	106	18	!	!	PUNCT
ejpam-3839	106	19	.	.	PUNCT
ejpam-3839	107	1	(	(	PUNCT
ejpam-3839	107	2	18	18	NUM
ejpam-3839	107	3	)	)	PUNCT
ejpam-3839	107	4	comparing	compare	VERB
ejpam-3839	107	5	(	(	PUNCT
ejpam-3839	107	6	17	17	NUM
ejpam-3839	107	7	)	)	PUNCT
ejpam-3839	107	8	and	and	CCONJ
ejpam-3839	107	9	(	(	PUNCT
ejpam-3839	107	10	18	18	NUM
ejpam-3839	107	11	)	)	PUNCT
ejpam-3839	107	12	gives	give	VERB
ejpam-3839	107	13	the	the	DET
ejpam-3839	107	14	desired	desire	VERB
ejpam-3839	107	15	result	result	NOUN
ejpam-3839	107	16	.	.	PUNCT
ejpam-3839	108	1	example	example	NOUN
ejpam-3839	109	1	1	1	NUM
ejpam-3839	109	2	.	.	X
ejpam-3839	110	1	for	for	ADP
ejpam-3839	110	2	m	m	PROPN
ejpam-3839	110	3	=	=	SYM
ejpam-3839	110	4	1	1	NUM
ejpam-3839	110	5	,	,	PUNCT
ejpam-3839	110	6	we	we	PRON
ejpam-3839	110	7	have	have	VERB
ejpam-3839	110	8	t1,0(x	t1,0(x	PROPN
ejpam-3839	110	9	)	)	PUNCT
ejpam-3839	110	10	=	=	SYM
ejpam-3839	111	1	0	0	X
ejpam-3839	111	2	.	.	X
ejpam-3839	111	3	using	use	VERB
ejpam-3839	111	4	recurrence	recurrence	NOUN
ejpam-3839	111	5	relation	relation	NOUN
ejpam-3839	111	6	(	(	PUNCT
ejpam-3839	111	7	15	15	NUM
ejpam-3839	111	8	)	)	PUNCT
ejpam-3839	111	9	,	,	PUNCT
ejpam-3839	111	10	we	we	PRON
ejpam-3839	111	11	obtain	obtain	VERB
ejpam-3839	111	12	t1,n+1(x	t1,n+1(x	NOUN
ejpam-3839	111	13	)	)	PUNCT
ejpam-3839	111	14	=	=	SYM
ejpam-3839	111	15	2	2	NUM
ejpam-3839	111	16	(	(	PUNCT
ejpam-3839	111	17	n+	n+	NUM
ejpam-3839	111	18	1	1	NUM
ejpam-3839	111	19	n	n	NOUN
ejpam-3839	111	20	)	)	PUNCT
ejpam-3839	111	21	xn	xn	PUNCT
ejpam-3839	112	1	−	−	PROPN
ejpam-3839	112	2	n∑	n∑	PROPN
ejpam-3839	112	3	j=0	j=0	PROPN
ejpam-3839	112	4	2n+1−j	2n+1−j	PROPN
ejpam-3839	112	5	(	(	PUNCT
ejpam-3839	112	6	n+	n+	ADP
ejpam-3839	112	7	1	1	NUM
ejpam-3839	112	8	j	j	NOUN
ejpam-3839	112	9	)	)	PUNCT
ejpam-3839	113	1	t1,j	t1,j	NOUN
ejpam-3839	113	2	.	.	PUNCT
ejpam-3839	114	1	(	(	PUNCT
ejpam-3839	114	2	19	19	NUM
ejpam-3839	114	3	)	)	PUNCT
ejpam-3839	114	4	computing	computing	NOUN
ejpam-3839	114	5	for	for	ADP
ejpam-3839	114	6	n	n	NOUN
ejpam-3839	114	7	=	=	SYM
ejpam-3839	114	8	0	0	NUM
ejpam-3839	114	9	,	,	PUNCT
ejpam-3839	114	10	1	1	NUM
ejpam-3839	114	11	,	,	PUNCT
ejpam-3839	114	12	2	2	NUM
ejpam-3839	114	13	,	,	PUNCT
ejpam-3839	114	14	3	3	NUM
ejpam-3839	114	15	,	,	PUNCT
ejpam-3839	114	16	4	4	NUM
ejpam-3839	114	17	,	,	PUNCT
ejpam-3839	114	18	we	we	PRON
ejpam-3839	114	19	get	get	VERB
ejpam-3839	114	20	the	the	DET
ejpam-3839	114	21	following	follow	VERB
ejpam-3839	114	22	polynomials	polynomial	NOUN
ejpam-3839	114	23	:	:	PUNCT
ejpam-3839	114	24	t1,1	t1,1	NOUN
ejpam-3839	114	25	=	=	SYM
ejpam-3839	114	26	2	2	NUM
ejpam-3839	114	27	t1,2	t1,2	NOUN
ejpam-3839	114	28	=	=	SYM
ejpam-3839	114	29	2	2	NUM
ejpam-3839	114	30	(	(	PUNCT
ejpam-3839	114	31	2	2	NUM
ejpam-3839	114	32	1	1	NUM
ejpam-3839	114	33	)	)	PUNCT
ejpam-3839	114	34	x−	x−	PROPN
ejpam-3839	114	35	2	2	NUM
ejpam-3839	114	36	(	(	PUNCT
ejpam-3839	114	37	2	2	NUM
ejpam-3839	114	38	1	1	NUM
ejpam-3839	114	39	)	)	PUNCT
ejpam-3839	114	40	t1,1	t1,1	NOUN
ejpam-3839	115	1	=	=	PUNCT
ejpam-3839	116	1	4x−	4x−	NOUN
ejpam-3839	116	2	8	8	NUM
ejpam-3839	116	3	=	=	SYM
ejpam-3839	116	4	4(x−	4(x−	NUM
ejpam-3839	116	5	2	2	NUM
ejpam-3839	116	6	)	)	PUNCT
ejpam-3839	116	7	t1,3	t1,3	NOUN
ejpam-3839	116	8	=	=	SYM
ejpam-3839	116	9	2	2	NUM
ejpam-3839	116	10	(	(	PUNCT
ejpam-3839	116	11	3	3	NUM
ejpam-3839	116	12	2	2	NUM
ejpam-3839	116	13	)	)	PUNCT
ejpam-3839	117	1	x2	x2	NOUN
ejpam-3839	118	1	−	−	PROPN
ejpam-3839	118	2	22	22	NUM
ejpam-3839	118	3	(	(	PUNCT
ejpam-3839	118	4	3	3	NUM
ejpam-3839	118	5	1	1	NUM
ejpam-3839	118	6	)	)	PUNCT
ejpam-3839	118	7	t1,1(x)−	t1,1(x)−	PROPN
ejpam-3839	118	8	2	2	NUM
ejpam-3839	118	9	(	(	PUNCT
ejpam-3839	118	10	3	3	NUM
ejpam-3839	118	11	2	2	NUM
ejpam-3839	118	12	)	)	PUNCT
ejpam-3839	118	13	t1,2(x	t1,2(x	PROPN
ejpam-3839	118	14	)	)	PUNCT
ejpam-3839	118	15	n.	n.	PROPN
ejpam-3839	118	16	acala	acala	PROPN
ejpam-3839	118	17	,	,	PUNCT
ejpam-3839	118	18	m.	m.	PROPN
ejpam-3839	118	19	montero	montero	PROPN
ejpam-3839	118	20	/	/	SYM
ejpam-3839	118	21	eur	eur	PROPN
ejpam-3839	118	22	.	.	PUNCT
ejpam-3839	119	1	j.	j.	PROPN
ejpam-3839	119	2	pure	pure	PROPN
ejpam-3839	119	3	appl	appl	PROPN
ejpam-3839	119	4	.	.	PROPN
ejpam-3839	119	5	math	math	PROPN
ejpam-3839	119	6	,	,	PUNCT
ejpam-3839	119	7	13	13	NUM
ejpam-3839	119	8	(	(	PUNCT
ejpam-3839	119	9	4	4	NUM
ejpam-3839	119	10	)	)	PUNCT
ejpam-3839	119	11	(	(	PUNCT
ejpam-3839	119	12	2020	2020	NUM
ejpam-3839	119	13	)	)	PUNCT
ejpam-3839	119	14	,	,	PUNCT
ejpam-3839	119	15	948	948	NUM
ejpam-3839	119	16	-	-	SYM
ejpam-3839	119	17	963	963	NUM
ejpam-3839	119	18	953	953	NUM
ejpam-3839	119	19	=	=	SYM
ejpam-3839	119	20	6x2	6x2	NUM
ejpam-3839	119	21	−	−	NUM
ejpam-3839	119	22	12(2)−	12(2)−	NUM
ejpam-3839	119	23	2(3)4(x−	2(3)4(x−	NUM
ejpam-3839	119	24	2	2	NUM
ejpam-3839	119	25	)	)	PUNCT
ejpam-3839	119	26	=	=	SYM
ejpam-3839	119	27	6(x−	6(x−	NUM
ejpam-3839	119	28	2)2	2)2	NUM
ejpam-3839	119	29	t1,4	t1,4	NOUN
ejpam-3839	119	30	=	=	SYM
ejpam-3839	119	31	2	2	NUM
ejpam-3839	119	32	(	(	PUNCT
ejpam-3839	119	33	4	4	NUM
ejpam-3839	119	34	3	3	NUM
ejpam-3839	119	35	)	)	PUNCT
ejpam-3839	120	1	x3	x3	ADV
ejpam-3839	120	2	−	−	PROPN
ejpam-3839	120	3	23	23	NUM
ejpam-3839	120	4	(	(	PUNCT
ejpam-3839	120	5	4	4	NUM
ejpam-3839	120	6	1	1	NUM
ejpam-3839	120	7	)	)	PUNCT
ejpam-3839	121	1	t1,1(x)−	t1,1(x)−	PROPN
ejpam-3839	121	2	22	22	NUM
ejpam-3839	121	3	(	(	PUNCT
ejpam-3839	121	4	4	4	NUM
ejpam-3839	121	5	2	2	NUM
ejpam-3839	121	6	)	)	PUNCT
ejpam-3839	121	7	t1,2(x)−	t1,2(x)−	PROPN
ejpam-3839	121	8	2	2	NUM
ejpam-3839	121	9	(	(	PUNCT
ejpam-3839	121	10	4	4	NUM
ejpam-3839	121	11	3	3	NUM
ejpam-3839	121	12	)	)	PUNCT
ejpam-3839	121	13	t1,3(x	t1,3(x	PROPN
ejpam-3839	121	14	)	)	PUNCT
ejpam-3839	121	15	=	=	SYM
ejpam-3839	121	16	8x3	8x3	NOUN
ejpam-3839	121	17	−	−	PROPN
ejpam-3839	121	18	8(4)(2)−	8(4)(2)−	NUM
ejpam-3839	121	19	24(4)(x−	24(4)(x−	PROPN
ejpam-3839	121	20	2)−	2)−	PROPN
ejpam-3839	121	21	8(6)(x−	8(6)(x−	NUM
ejpam-3839	121	22	2	2	NUM
ejpam-3839	121	23	)	)	PUNCT
ejpam-3839	121	24	=	=	SYM
ejpam-3839	121	25	8(x−	8(x−	NUM
ejpam-3839	121	26	2)3	2)3	NUM
ejpam-3839	121	27	.	.	PUNCT
ejpam-3839	121	28	note	note	VERB
ejpam-3839	121	29	that	that	SCONJ
ejpam-3839	121	30	the	the	DET
ejpam-3839	121	31	above	above	ADJ
ejpam-3839	121	32	computations	computation	NOUN
ejpam-3839	121	33	can	can	AUX
ejpam-3839	121	34	be	be	AUX
ejpam-3839	121	35	easily	easily	ADV
ejpam-3839	121	36	done	do	VERB
ejpam-3839	121	37	using	use	VERB
ejpam-3839	121	38	(	(	PUNCT
ejpam-3839	121	39	14	14	NUM
ejpam-3839	121	40	)	)	PUNCT
ejpam-3839	121	41	.	.	PUNCT
ejpam-3839	122	1	furthermore	furthermore	ADV
ejpam-3839	122	2	,	,	PUNCT
ejpam-3839	122	3	taking	take	VERB
ejpam-3839	122	4	m	m	NOUN
ejpam-3839	122	5	=	=	SYM
ejpam-3839	122	6	2	2	NUM
ejpam-3839	122	7	,	,	PUNCT
ejpam-3839	122	8	we	we	PRON
ejpam-3839	122	9	obtain	obtain	VERB
ejpam-3839	122	10	the	the	DET
ejpam-3839	122	11	recurrence	recurrence	NOUN
ejpam-3839	122	12	relation	relation	NOUN
ejpam-3839	122	13	:	:	PUNCT
ejpam-3839	122	14	t2,n+2(x	t2,n+2(x	NOUN
ejpam-3839	122	15	)	)	PUNCT
ejpam-3839	122	16	=	=	SYM
ejpam-3839	122	17	2	2	NUM
ejpam-3839	122	18	(	(	PUNCT
ejpam-3839	122	19	n+	n+	NUM
ejpam-3839	122	20	2	2	NUM
ejpam-3839	122	21	n	n	NOUN
ejpam-3839	122	22	)	)	PUNCT
ejpam-3839	122	23	xn	xn	PUNCT
ejpam-3839	123	1	−	−	PROPN
ejpam-3839	123	2	n∑	n∑	NOUN
ejpam-3839	123	3	j=0	j=0	PROPN
ejpam-3839	123	4	2n+2−j	2n+2−j	NUM
ejpam-3839	123	5	(	(	PUNCT
ejpam-3839	123	6	n+	n+	NUM
ejpam-3839	123	7	2	2	NUM
ejpam-3839	123	8	j	j	PROPN
ejpam-3839	123	9	)	)	PUNCT
ejpam-3839	123	10	t2,j	t2,j	PROPN
ejpam-3839	123	11	,	,	PUNCT
ejpam-3839	123	12	(	(	PUNCT
ejpam-3839	123	13	20	20	NUM
ejpam-3839	123	14	)	)	PUNCT
ejpam-3839	123	15	which	which	PRON
ejpam-3839	123	16	yields	yield	VERB
ejpam-3839	123	17	the	the	DET
ejpam-3839	123	18	following	follow	VERB
ejpam-3839	123	19	polynomials	polynomial	NOUN
ejpam-3839	123	20	:	:	PUNCT
ejpam-3839	123	21	t2,0(x	t2,0(x	NOUN
ejpam-3839	123	22	)	)	PUNCT
ejpam-3839	123	23	=	=	SYM
ejpam-3839	123	24	t2,1(x	t2,1(x	NOUN
ejpam-3839	123	25	)	)	PUNCT
ejpam-3839	123	26	=	=	SYM
ejpam-3839	123	27	0	0	NUM
ejpam-3839	123	28	t2,2(x	t2,2(x	NOUN
ejpam-3839	123	29	)	)	PUNCT
ejpam-3839	123	30	=	=	SYM
ejpam-3839	123	31	2	2	NUM
ejpam-3839	123	32	t2,3(x	t2,3(x	PROPN
ejpam-3839	123	33	)	)	PUNCT
ejpam-3839	123	34	=	=	SYM
ejpam-3839	123	35	6x	6x	NUM
ejpam-3839	123	36	t2,4(x	t2,4(x	PROPN
ejpam-3839	123	37	)	)	PUNCT
ejpam-3839	123	38	=	=	SYM
ejpam-3839	123	39	12(x2	12(x2	NOUN
ejpam-3839	124	1	−	−	NOUN
ejpam-3839	124	2	4	4	NUM
ejpam-3839	124	3	)	)	PUNCT
ejpam-3839	124	4	.	.	PUNCT
ejpam-3839	125	1	theorem	theorem	ADJ
ejpam-3839	125	2	5	5	NUM
ejpam-3839	125	3	.	.	PUNCT
ejpam-3839	126	1	for	for	ADP
ejpam-3839	126	2	m	m	PROPN
ejpam-3839	126	3	≥	≥	NOUN
ejpam-3839	126	4	0	0	NUM
ejpam-3839	126	5	and	and	CCONJ
ejpam-3839	126	6	n	n	CCONJ
ejpam-3839	126	7	>	>	ADP
ejpam-3839	126	8	0	0	PROPN
ejpam-3839	126	9	,	,	PUNCT
ejpam-3839	126	10	2m−1	2m−1	NUM
ejpam-3839	126	11	n∑	n∑	NOUN
ejpam-3839	126	12	k=0	k=0	PROPN
ejpam-3839	126	13	(	(	PUNCT
ejpam-3839	126	14	n	n	X
ejpam-3839	126	15	k	k	NOUN
ejpam-3839	126	16	)	)	PUNCT
ejpam-3839	126	17	tm	tm	PROPN
ejpam-3839	126	18	,	,	PUNCT
ejpam-3839	126	19	n−k(y)tm+1,k(x	n−k(y)tm+1,k(x	PROPN
ejpam-3839	126	20	)	)	PUNCT
ejpam-3839	127	1	=	=	SYM
ejpam-3839	127	2	n∑	n∑	NOUN
ejpam-3839	127	3	k=0	k=0	PROPN
ejpam-3839	127	4	(	(	PUNCT
ejpam-3839	127	5	n	n	X
ejpam-3839	127	6	k	k	PROPN
ejpam-3839	127	7	)	)	PUNCT
ejpam-3839	127	8	tm+1,n−k(x)yk−	tm+1,n−k(x)yk−	NOUN
ejpam-3839	127	9	n	n	CCONJ
ejpam-3839	127	10	m+	m+	NUM
ejpam-3839	127	11	1	1	NUM
ejpam-3839	127	12	n−1∑	n−1∑	PROPN
ejpam-3839	127	13	k=0	k=0	PROPN
ejpam-3839	128	1	(	(	PUNCT
ejpam-3839	128	2	n−	n−	NOUN
ejpam-3839	128	3	1	1	NUM
ejpam-3839	128	4	k	k	NOUN
ejpam-3839	128	5	)	)	PUNCT
ejpam-3839	128	6	tm	tm	PROPN
ejpam-3839	128	7	,	,	PUNCT
ejpam-3839	128	8	n−1−k(y)xk	n−1−k(y)xk	PROPN
ejpam-3839	128	9	.	.	PROPN
ejpam-3839	129	1	proof	proof	NOUN
ejpam-3839	129	2	.	.	PUNCT
ejpam-3839	130	1	it	it	PRON
ejpam-3839	130	2	follows	follow	VERB
ejpam-3839	130	3	from	from	ADP
ejpam-3839	130	4	(	(	PUNCT
ejpam-3839	130	5	5	5	NUM
ejpam-3839	130	6	)	)	PUNCT
ejpam-3839	131	1	that	that	SCONJ
ejpam-3839	131	2	2ext	2ext	PROPN
ejpam-3839	131	3	tm+1	tm+1	PROPN
ejpam-3839	131	4	(	(	PUNCT
ejpam-3839	131	5	m+	m+	NOUN
ejpam-3839	131	6	1	1	NUM
ejpam-3839	131	7	)	)	PUNCT
ejpam-3839	131	8	!	!	PUNCT
ejpam-3839	132	1	=	=	PUNCT
ejpam-3839	132	2	e2	e2	NOUN
ejpam-3839	132	3	t	t	NOUN
ejpam-3839	132	4	+	+	CCONJ
ejpam-3839	132	5	1−	1−	NUM
ejpam-3839	132	6	m∑	m∑	VERB
ejpam-3839	132	7	j=0	j=0	PROPN
ejpam-3839	132	8	(	(	PUNCT
ejpam-3839	132	9	2t)j	2t)j	NUM
ejpam-3839	132	10	j	j	NOUN
ejpam-3839	132	11	!	!	PUNCT
ejpam-3839	133	1			PROPN
ejpam-3839	133	2	∞∑	∞∑	ADJ
ejpam-3839	133	3	n=0	n=0	ADV
ejpam-3839	133	4	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	133	5	)	)	PUNCT
ejpam-3839	133	6	tn	tn	PROPN
ejpam-3839	133	7	n	n	NOUN
ejpam-3839	133	8	!	!	PUNCT
ejpam-3839	134	1	=	=	PUNCT
ejpam-3839	134	2	e2	e2	NOUN
ejpam-3839	134	3	t	t	NOUN
ejpam-3839	134	4	+	+	CCONJ
ejpam-3839	134	5	1−	1−	NUM
ejpam-3839	134	6	m−1∑	m−1∑	NUM
ejpam-3839	134	7	j=0	j=0	PROPN
ejpam-3839	134	8	(	(	PUNCT
ejpam-3839	134	9	2t)j	2t)j	NUM
ejpam-3839	134	10	j	j	NOUN
ejpam-3839	134	11	!	!	PUNCT
ejpam-3839	135	1			PROPN
ejpam-3839	135	2	∞∑	∞∑	ADJ
ejpam-3839	135	3	n=0	n=0	ADV
ejpam-3839	135	4	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	135	5	)	)	PUNCT
ejpam-3839	135	6	tn	tn	PROPN
ejpam-3839	136	1	n	n	PROPN
ejpam-3839	136	2	!	!	PUNCT
ejpam-3839	137	1	−	−	PUNCT
ejpam-3839	138	1	2mtm	2mtm	NUM
ejpam-3839	138	2	m	m	NOUN
ejpam-3839	138	3	!	!	PUNCT
ejpam-3839	139	1	∞∑	∞∑	PRON
ejpam-3839	139	2	n=0	n=0	ADJ
ejpam-3839	139	3	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	139	4	)	)	PUNCT
ejpam-3839	139	5	tn	tn	PROPN
ejpam-3839	139	6	n	n	PROPN
ejpam-3839	139	7	!	!	PUNCT
ejpam-3839	139	8	.	.	PUNCT
ejpam-3839	140	1	hence	hence	ADV
ejpam-3839	140	2	,	,	PUNCT
ejpam-3839	140	3	2ext	2ext	PROPN
ejpam-3839	140	4	tm+1	tm+1	PROPN
ejpam-3839	140	5	(	(	PUNCT
ejpam-3839	140	6	m+	m+	NOUN
ejpam-3839	140	7	1	1	NUM
ejpam-3839	140	8	)	)	PUNCT
ejpam-3839	140	9	!	!	PUNCT
ejpam-3839	141	1	∞∑	∞∑	PRON
ejpam-3839	141	2	n=0	n=0	PUNCT
ejpam-3839	141	3	tm	tm	NOUN
ejpam-3839	141	4	,	,	PUNCT
ejpam-3839	141	5	n(y	n(y	PROPN
ejpam-3839	141	6	)	)	PUNCT
ejpam-3839	141	7	tn	tn	PROPN
ejpam-3839	141	8	n	n	ADV
ejpam-3839	141	9	!	!	PUNCT
ejpam-3839	141	10	=	=	PUNCT
ejpam-3839	142	1	2tm	2tm	PROPN
ejpam-3839	142	2	m	m	PROPN
ejpam-3839	142	3	!	!	PUNCT
ejpam-3839	143	1	eyt	eyt	PROPN
ejpam-3839	144	1	∞∑	∞∑	PROPN
ejpam-3839	144	2	n=0	n=0	SYM
ejpam-3839	144	3	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	144	4	)	)	PUNCT
ejpam-3839	144	5	tn	tn	PROPN
ejpam-3839	144	6	n	n	PROPN
ejpam-3839	144	7	!	!	PUNCT
ejpam-3839	145	1	−	−	PUNCT
ejpam-3839	146	1	2mtm	2mtm	NUM
ejpam-3839	146	2	m	m	NOUN
ejpam-3839	146	3	!	!	PUNCT
ejpam-3839	147	1	∞∑	∞∑	PRON
ejpam-3839	147	2	n=0	n=0	PUNCT
ejpam-3839	147	3	tm	tm	NOUN
ejpam-3839	147	4	,	,	PUNCT
ejpam-3839	147	5	n(y	n(y	PROPN
ejpam-3839	147	6	)	)	PUNCT
ejpam-3839	147	7	tn	tn	PROPN
ejpam-3839	147	8	n	n	CCONJ
ejpam-3839	147	9	!	!	PUNCT
ejpam-3839	148	1	∞∑	∞∑	PRON
ejpam-3839	148	2	n=0	n=0	ADJ
ejpam-3839	148	3	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	148	4	)	)	PUNCT
ejpam-3839	148	5	tn	tn	PROPN
ejpam-3839	148	6	n	n	PROPN
ejpam-3839	148	7	!	!	PUNCT
ejpam-3839	148	8	.	.	PUNCT
ejpam-3839	149	1	consequently	consequently	ADV
ejpam-3839	149	2	,	,	PUNCT
ejpam-3839	149	3	∞∑	∞∑	ADJ
ejpam-3839	149	4	n=0	n=0	NUM
ejpam-3839	149	5	n∑	n∑	X
ejpam-3839	149	6	k=0	k=0	PROPN
ejpam-3839	149	7	(	(	PUNCT
ejpam-3839	149	8	n	n	X
ejpam-3839	149	9	k	k	NOUN
ejpam-3839	149	10	)	)	PUNCT
ejpam-3839	149	11	tm	tm	PROPN
ejpam-3839	149	12	,	,	PUNCT
ejpam-3839	149	13	n−k(y)xk	n−k(y)xk	PROPN
ejpam-3839	149	14	tn+1	tn+1	PROPN
ejpam-3839	149	15	(	(	PUNCT
ejpam-3839	149	16	m+	m+	NOUN
ejpam-3839	149	17	1)n	1)n	NUM
ejpam-3839	149	18	!	!	PUNCT
ejpam-3839	150	1	=	=	PUNCT
ejpam-3839	151	1	∞∑	∞∑	PRON
ejpam-3839	151	2	n=0	n=0	NUM
ejpam-3839	151	3	n∑	n∑	NOUN
ejpam-3839	151	4	k=0	k=0	PROPN
ejpam-3839	151	5	(	(	PUNCT
ejpam-3839	151	6	n	n	X
ejpam-3839	151	7	k	k	NOUN
ejpam-3839	151	8	)	)	PUNCT
ejpam-3839	151	9	tm+1,n−k(x)yk	tm+1,n−k(x)yk	VERB
ejpam-3839	151	10	tn	tn	PROPN
ejpam-3839	151	11	n	n	NOUN
ejpam-3839	151	12	!	!	PUNCT
ejpam-3839	152	1	−	−	PROPN
ejpam-3839	152	2	2m−1	2m−1	NUM
ejpam-3839	153	1	∞∑	∞∑	PRON
ejpam-3839	153	2	n=0	n=0	NUM
ejpam-3839	153	3	n∑	n∑	NOUN
ejpam-3839	153	4	k=0	k=0	PROPN
ejpam-3839	153	5	(	(	PUNCT
ejpam-3839	153	6	n	n	X
ejpam-3839	153	7	k	k	NOUN
ejpam-3839	153	8	)	)	PUNCT
ejpam-3839	153	9	tm	tm	PROPN
ejpam-3839	153	10	,	,	PUNCT
ejpam-3839	153	11	n−k(y)tm+1,k(x	n−k(y)tm+1,k(x	PROPN
ejpam-3839	153	12	)	)	PUNCT
ejpam-3839	153	13	tn	tn	PROPN
ejpam-3839	153	14	n	n	PROPN
ejpam-3839	153	15	!	!	PROPN
ejpam-3839	153	16	,	,	PUNCT
ejpam-3839	153	17	which	which	PRON
ejpam-3839	153	18	provides	provide	VERB
ejpam-3839	153	19	the	the	DET
ejpam-3839	153	20	desired	desire	VERB
ejpam-3839	153	21	result	result	NOUN
ejpam-3839	153	22	.	.	PUNCT
ejpam-3839	154	1	n.	n.	PROPN
ejpam-3839	154	2	acala	acala	PROPN
ejpam-3839	154	3	,	,	PUNCT
ejpam-3839	154	4	m.	m.	PROPN
ejpam-3839	154	5	montero	montero	PROPN
ejpam-3839	154	6	/	/	SYM
ejpam-3839	154	7	eur	eur	PROPN
ejpam-3839	154	8	.	.	PUNCT
ejpam-3839	155	1	j.	j.	PROPN
ejpam-3839	155	2	pure	pure	PROPN
ejpam-3839	155	3	appl	appl	PROPN
ejpam-3839	155	4	.	.	PROPN
ejpam-3839	155	5	math	math	PROPN
ejpam-3839	155	6	,	,	PUNCT
ejpam-3839	155	7	13	13	NUM
ejpam-3839	155	8	(	(	PUNCT
ejpam-3839	155	9	4	4	NUM
ejpam-3839	155	10	)	)	PUNCT
ejpam-3839	155	11	(	(	PUNCT
ejpam-3839	155	12	2020	2020	NUM
ejpam-3839	155	13	)	)	PUNCT
ejpam-3839	155	14	,	,	PUNCT
ejpam-3839	155	15	948	948	NUM
ejpam-3839	155	16	-	-	SYM
ejpam-3839	155	17	963	963	NUM
ejpam-3839	155	18	954	954	NUM
ejpam-3839	155	19	theorem	theorem	NOUN
ejpam-3839	155	20	6	6	NUM
ejpam-3839	155	21	.	.	PUNCT
ejpam-3839	155	22	for	for	ADP
ejpam-3839	155	23	m	m	PROPN
ejpam-3839	155	24	,	,	PUNCT
ejpam-3839	155	25	n	n	PRON
ejpam-3839	155	26	≥	≥	NOUN
ejpam-3839	155	27	0	0	NUM
ejpam-3839	155	28	,	,	PUNCT
ejpam-3839	155	29	tn	tn	PROPN
ejpam-3839	155	30	,	,	PUNCT
ejpam-3839	155	31	m(x	m(x	PROPN
ejpam-3839	155	32	)	)	PUNCT
ejpam-3839	155	33	=	=	SYM
ejpam-3839	156	1	m!n	m!n	PROPN
ejpam-3839	156	2	!	!	PROPN
ejpam-3839	156	3	(	(	PUNCT
ejpam-3839	156	4	n+m	n+m	NUM
ejpam-3839	156	5	)	)	PUNCT
ejpam-3839	156	6	!	!	PUNCT
ejpam-3839	157	1	n∑	n∑	INTJ
ejpam-3839	158	1	l=0	l=0	PROPN
ejpam-3839	158	2	(	(	PUNCT
ejpam-3839	158	3	n+m	n+m	NUM
ejpam-3839	158	4	l	l	NOUN
ejpam-3839	158	5	)	)	PUNCT
ejpam-3839	158	6	l∑	l∑	PUNCT
ejpam-3839	159	1	k=0	k=0	PROPN
ejpam-3839	159	2	(	(	PUNCT
ejpam-3839	159	3	l	l	NOUN
ejpam-3839	159	4	k	k	X
ejpam-3839	159	5	)	)	PUNCT
ejpam-3839	159	6	tm	tm	PROPN
ejpam-3839	159	7	,	,	PUNCT
ejpam-3839	159	8	kbm	kbm	PROPN
ejpam-3839	159	9	,	,	PUNCT
ejpam-3839	159	10	l−k(x	l−k(x	PROPN
ejpam-3839	159	11	)	)	PUNCT
ejpam-3839	159	12	tn	tn	PROPN
ejpam-3839	159	13	n	n	PROPN
ejpam-3839	159	14	!	!	PUNCT
ejpam-3839	159	15	.	.	PUNCT
ejpam-3839	160	1	(	(	PUNCT
ejpam-3839	160	2	21	21	NUM
ejpam-3839	160	3	)	)	PUNCT
ejpam-3839	160	4	proof	proof	NOUN
ejpam-3839	160	5	.	.	PUNCT
ejpam-3839	161	1	applying	apply	VERB
ejpam-3839	161	2	(	(	PUNCT
ejpam-3839	161	3	5	5	NUM
ejpam-3839	161	4	)	)	PUNCT
ejpam-3839	161	5	,	,	PUNCT
ejpam-3839	161	6	we	we	PRON
ejpam-3839	161	7	have	have	VERB
ejpam-3839	161	8	∞∑	∞∑	NUM
ejpam-3839	161	9	n=0	n=0	NUM
ejpam-3839	161	10	tm	tm	NOUN
ejpam-3839	161	11	,	,	PUNCT
ejpam-3839	161	12	n(x	n(x	PROPN
ejpam-3839	161	13	,	,	PUNCT
ejpam-3839	161	14	y	y	PROPN
ejpam-3839	161	15	)	)	PUNCT
ejpam-3839	161	16	tn	tn	PROPN
ejpam-3839	161	17	n	n	NOUN
ejpam-3839	161	18	!	!	PUNCT
ejpam-3839	162	1	=	=	SYM
ejpam-3839	162	2	2	2	NUM
ejpam-3839	162	3	tm	tm	NOUN
ejpam-3839	162	4	m	m	PROPN
ejpam-3839	162	5	!	!	PUNCT
ejpam-3839	163	1	(	(	PUNCT
ejpam-3839	163	2	e2	e2	PROPN
ejpam-3839	163	3	t	t	PROPN
ejpam-3839	163	4	+	+	CCONJ
ejpam-3839	163	5	1−	1−	NUM
ejpam-3839	163	6	∑m−1	∑m−1	NOUN
ejpam-3839	163	7	j=0	j=0	VERB
ejpam-3839	163	8	2j	2j	NUM
ejpam-3839	163	9	t	t	PROPN
ejpam-3839	163	10	j	j	PROPN
ejpam-3839	163	11	j	j	PROPN
ejpam-3839	163	12	!	!	PUNCT
ejpam-3839	163	13	)	)	PUNCT
ejpam-3839	164	1	ext	ext	PROPN
ejpam-3839	164	2	tm	tm	PROPN
ejpam-3839	164	3	m	m	PROPN
ejpam-3839	164	4	!	!	PUNCT
ejpam-3839	165	1	(	(	PUNCT
ejpam-3839	165	2	et	et	PROPN
ejpam-3839	165	3	−	−	PROPN
ejpam-3839	165	4	∑m−1	∑m−1	PROPN
ejpam-3839	165	5	j=0	j=0	PROPN
ejpam-3839	165	6	tj	tj	PROPN
ejpam-3839	165	7	j	j	PROPN
ejpam-3839	165	8	!	!	PUNCT
ejpam-3839	165	9	)	)	PUNCT
ejpam-3839	165	10	·	·	PUNCT
ejpam-3839	166	1	(	(	PUNCT
ejpam-3839	166	2	et	et	NOUN
ejpam-3839	166	3	−	−	PROPN
ejpam-3839	166	4	∑m−1	∑m−1	PROPN
ejpam-3839	166	5	j=0	j=0	PROPN
ejpam-3839	166	6	tj	tj	PROPN
ejpam-3839	166	7	j	j	PROPN
ejpam-3839	166	8	!	!	PUNCT
ejpam-3839	166	9	)	)	PUNCT
ejpam-3839	167	1	tm	tm	DET
ejpam-3839	167	2	m	m	PROPN
ejpam-3839	167	3	!	!	PUNCT
ejpam-3839	168	1	=	=	PUNCT
ejpam-3839	169	1	m	m	PROPN
ejpam-3839	169	2	!	!	PUNCT
ejpam-3839	170	1	tm	tm	PROPN
ejpam-3839	170	2	(	(	PUNCT
ejpam-3839	170	3	∞∑	∞∑	PROPN
ejpam-3839	170	4	n=0	n=0	NUM
ejpam-3839	170	5	tm	tm	NOUN
ejpam-3839	170	6	,	,	PUNCT
ejpam-3839	170	7	n	n	PROPN
ejpam-3839	170	8	tn	tn	PROPN
ejpam-3839	170	9	n	n	CCONJ
ejpam-3839	170	10	!	!	PUNCT
ejpam-3839	171	1	∞∑	∞∑	PRON
ejpam-3839	171	2	n=0	n=0	NUM
ejpam-3839	171	3	bm	bm	PROPN
ejpam-3839	171	4	,	,	PUNCT
ejpam-3839	171	5	n(x	n(x	PROPN
ejpam-3839	171	6	)	)	PUNCT
ejpam-3839	171	7	tn	tn	NOUN
ejpam-3839	171	8	n	n	PROPN
ejpam-3839	171	9	!	!	PUNCT
ejpam-3839	171	10	)	)	PUNCT
ejpam-3839	172	1	∞∑	∞∑	PRON
ejpam-3839	172	2	j	j	X
ejpam-3839	172	3	=	=	NOUN
ejpam-3839	172	4	m	m	PROPN
ejpam-3839	172	5	tj	tj	PROPN
ejpam-3839	172	6	j	j	PROPN
ejpam-3839	172	7	!	!	PUNCT
ejpam-3839	172	8	=	=	PUNCT
ejpam-3839	173	1	m	m	VERB
ejpam-3839	173	2	!	!	PUNCT
ejpam-3839	174	1	∞∑	∞∑	PRON
ejpam-3839	174	2	n=0	n=0	NUM
ejpam-3839	174	3	n∑	n∑	NOUN
ejpam-3839	174	4	k=0	k=0	PROPN
ejpam-3839	174	5	(	(	PUNCT
ejpam-3839	174	6	n	n	X
ejpam-3839	174	7	k	k	NOUN
ejpam-3839	174	8	)	)	PUNCT
ejpam-3839	174	9	tm	tm	PROPN
ejpam-3839	174	10	,	,	PUNCT
ejpam-3839	174	11	kbm	kbm	NOUN
ejpam-3839	174	12	,	,	PUNCT
ejpam-3839	174	13	n−k(x	n−k(x	VERB
ejpam-3839	174	14	)	)	PUNCT
ejpam-3839	174	15	tn	tn	PROPN
ejpam-3839	175	1	n	n	CCONJ
ejpam-3839	175	2	!	!	PUNCT
ejpam-3839	176	1	∞∑	∞∑	NUM
ejpam-3839	176	2	j=0	j=0	PROPN
ejpam-3839	176	3	tj	tj	PROPN
ejpam-3839	176	4	(	(	PUNCT
ejpam-3839	176	5	j	j	PROPN
ejpam-3839	176	6	+	+	PROPN
ejpam-3839	176	7	m	m	NOUN
ejpam-3839	176	8	)	)	PUNCT
ejpam-3839	176	9	!	!	PUNCT
ejpam-3839	176	10	=	=	PUNCT
ejpam-3839	177	1	∞∑	∞∑	PRON
ejpam-3839	177	2	n=0	n=0	NUM
ejpam-3839	177	3	n∑	n∑	X
ejpam-3839	177	4	l=0	l=0	PROPN
ejpam-3839	177	5	m!n	m!n	PROPN
ejpam-3839	177	6	!	!	PUNCT
ejpam-3839	178	1	(	(	PUNCT
ejpam-3839	178	2	n+m	n+m	NUM
ejpam-3839	178	3	l	l	NOUN
ejpam-3839	178	4	)	)	PUNCT
ejpam-3839	178	5	(	(	PUNCT
ejpam-3839	178	6	n+m	n+m	NUM
ejpam-3839	178	7	)	)	PUNCT
ejpam-3839	178	8	!	!	PUNCT
ejpam-3839	179	1	l∑	l∑	X
ejpam-3839	180	1	k=0	k=0	PROPN
ejpam-3839	180	2	(	(	PUNCT
ejpam-3839	180	3	l	l	NOUN
ejpam-3839	180	4	k	k	X
ejpam-3839	180	5	)	)	PUNCT
ejpam-3839	180	6	tm	tm	PROPN
ejpam-3839	180	7	,	,	PUNCT
ejpam-3839	180	8	kbm	kbm	PROPN
ejpam-3839	180	9	,	,	PUNCT
ejpam-3839	180	10	l−k(x	l−k(x	PROPN
ejpam-3839	180	11	)	)	PUNCT
ejpam-3839	180	12	tn	tn	PROPN
ejpam-3839	180	13	n	n	PROPN
ejpam-3839	180	14	!	!	PUNCT
ejpam-3839	180	15	.	.	PUNCT
ejpam-3839	181	1	comparing	compare	VERB
ejpam-3839	181	2	the	the	DET
ejpam-3839	181	3	coefficients	coefficient	NOUN
ejpam-3839	181	4	of	of	ADP
ejpam-3839	181	5	tn	tn	NOUN
ejpam-3839	181	6	n	n	ADP
ejpam-3839	181	7	!	!	PROPN
ejpam-3839	181	8	completes	complete	VERB
ejpam-3839	181	9	the	the	DET
ejpam-3839	181	10	proof	proof	NOUN
ejpam-3839	181	11	.	.	PUNCT
ejpam-3839	182	1	3	3	X
ejpam-3839	182	2	.	.	X
ejpam-3839	182	3	relations	relation	NOUN
ejpam-3839	182	4	with	with	ADP
ejpam-3839	182	5	stirling	stirling	NOUN
ejpam-3839	182	6	numbers	number	NOUN
ejpam-3839	182	7	of	of	ADP
ejpam-3839	182	8	the	the	DET
ejpam-3839	182	9	second	second	ADJ
ejpam-3839	182	10	kind	kind	NOUN
ejpam-3839	182	11	and	and	CCONJ
ejpam-3839	182	12	its	its	PRON
ejpam-3839	182	13	associated	associate	VERB
ejpam-3839	182	14	truncated	truncate	VERB
ejpam-3839	182	15	stirling	stirling	NOUN
ejpam-3839	182	16	numbers	number	NOUN
ejpam-3839	182	17	the	the	DET
ejpam-3839	182	18	stirling	stirling	NOUN
ejpam-3839	182	19	numbers	number	NOUN
ejpam-3839	182	20	of	of	ADP
ejpam-3839	182	21	the	the	DET
ejpam-3839	182	22	second	second	ADJ
ejpam-3839	182	23	kind	kind	NOUN
ejpam-3839	182	24	are	be	AUX
ejpam-3839	182	25	given	give	VERB
ejpam-3839	182	26	by	by	ADP
ejpam-3839	182	27	the	the	DET
ejpam-3839	182	28	generating	generate	VERB
ejpam-3839	182	29	function	function	NOUN
ejpam-3839	182	30	(	(	PUNCT
ejpam-3839	182	31	et	et	NOUN
ejpam-3839	182	32	−	−	PROPN
ejpam-3839	182	33	1)k	1)k	NUM
ejpam-3839	182	34	k	k	X
ejpam-3839	182	35	!	!	PUNCT
ejpam-3839	182	36	=	=	PUNCT
ejpam-3839	183	1	∞∑	∞∑	DET
ejpam-3839	183	2	n=0	n=0	NUM
ejpam-3839	183	3	s2(n	s2(n	PROPN
ejpam-3839	183	4	,	,	PUNCT
ejpam-3839	183	5	k	k	NOUN
ejpam-3839	183	6	)	)	PUNCT
ejpam-3839	183	7	tn	tn	PROPN
ejpam-3839	183	8	n	n	PROPN
ejpam-3839	183	9	!	!	PROPN
ejpam-3839	183	10	,	,	PUNCT
ejpam-3839	183	11	(	(	PUNCT
ejpam-3839	183	12	22	22	NUM
ejpam-3839	183	13	)	)	PUNCT
ejpam-3839	183	14	or	or	CCONJ
ejpam-3839	183	15	by	by	ADP
ejpam-3839	183	16	the	the	DET
ejpam-3839	183	17	recurrence	recurrence	NOUN
ejpam-3839	183	18	relation	relation	NOUN
ejpam-3839	183	19	for	for	ADP
ejpam-3839	183	20	a	a	DET
ejpam-3839	183	21	fixed	fix	VERB
ejpam-3839	183	22	nonnegative	nonnegative	ADJ
ejpam-3839	183	23	integer	integer	NOUN
ejpam-3839	183	24	n	n	NOUN
ejpam-3839	183	25	,	,	PUNCT
ejpam-3839	183	26	xn	xn	PROPN
ejpam-3839	183	27	=	=	SYM
ejpam-3839	183	28	n∑	n∑	PROPN
ejpam-3839	183	29	k=0	k=0	PROPN
ejpam-3839	183	30	s2(n	s2(n	PROPN
ejpam-3839	183	31	,	,	PUNCT
ejpam-3839	183	32	k)(x)k	k)(x)k	PRON
ejpam-3839	183	33	,	,	PUNCT
ejpam-3839	183	34	(	(	PUNCT
ejpam-3839	183	35	23	23	NUM
ejpam-3839	183	36	)	)	PUNCT
ejpam-3839	183	37	where	where	SCONJ
ejpam-3839	183	38	(	(	PUNCT
ejpam-3839	183	39	x)(k	x)(k	PROPN
ejpam-3839	183	40	)	)	PUNCT
ejpam-3839	183	41	is	be	AUX
ejpam-3839	183	42	the	the	DET
ejpam-3839	183	43	falling	fall	VERB
ejpam-3839	183	44	factorial	factorial	NOUN
ejpam-3839	183	45	defined	define	VERB
ejpam-3839	183	46	as	as	ADP
ejpam-3839	183	47	(	(	PUNCT
ejpam-3839	183	48	x)k	x)k	NOUN
ejpam-3839	183	49	=	=	SYM
ejpam-3839	183	50	x(x−	x(x−	PROPN
ejpam-3839	183	51	1	1	NUM
ejpam-3839	183	52	)	)	PUNCT
ejpam-3839	183	53	·	·	PUNCT
ejpam-3839	183	54	·	·	PUNCT
ejpam-3839	183	55	·	·	PUNCT
ejpam-3839	184	1	(	(	PUNCT
ejpam-3839	184	2	x−	x−	PROPN
ejpam-3839	184	3	k	k	PROPN
ejpam-3839	184	4	+	+	PROPN
ejpam-3839	184	5	1	1	X
ejpam-3839	184	6	)	)	PUNCT
ejpam-3839	184	7	for	for	ADP
ejpam-3839	184	8	k	k	PROPN
ejpam-3839	184	9	≥	≥	PROPN
ejpam-3839	184	10	0	0	NUM
ejpam-3839	184	11	,	,	PUNCT
ejpam-3839	184	12	and	and	CCONJ
ejpam-3839	184	13	(	(	PUNCT
ejpam-3839	184	14	x)0	x)0	X
ejpam-3839	184	15	=	=	SYM
ejpam-3839	184	16	1	1	X
ejpam-3839	184	17	.	.	X
ejpam-3839	184	18	for	for	ADP
ejpam-3839	184	19	the	the	DET
ejpam-3839	184	20	detailed	detailed	ADJ
ejpam-3839	184	21	discussion	discussion	NOUN
ejpam-3839	184	22	of	of	ADP
ejpam-3839	184	23	stirling	stirling	NOUN
ejpam-3839	184	24	numbers	number	NOUN
ejpam-3839	184	25	of	of	ADP
ejpam-3839	184	26	the	the	DET
ejpam-3839	184	27	second	second	ADJ
ejpam-3839	184	28	kind	kind	NOUN
ejpam-3839	184	29	,	,	PUNCT
ejpam-3839	184	30	see	see	VERB
ejpam-3839	184	31	[	[	X
ejpam-3839	184	32	3	3	NUM
ejpam-3839	184	33	,	,	PUNCT
ejpam-3839	184	34	7	7	NUM
ejpam-3839	184	35	]	]	PUNCT
ejpam-3839	184	36	.	.	PUNCT
ejpam-3839	185	1	in	in	ADP
ejpam-3839	185	2	[	[	X
ejpam-3839	185	3	5	5	NUM
ejpam-3839	185	4	]	]	PUNCT
ejpam-3839	185	5	,	,	PUNCT
ejpam-3839	185	6	duran	duran	NOUN
ejpam-3839	185	7	and	and	CCONJ
ejpam-3839	185	8	acikgoz	acikgoz	PROPN
ejpam-3839	185	9	introduced	introduce	VERB
ejpam-3839	185	10	the	the	DET
ejpam-3839	185	11	truncated	truncated	ADJ
ejpam-3839	185	12	stirling	stirling	NOUN
ejpam-3839	185	13	numbers	number	NOUN
ejpam-3839	185	14	of	of	ADP
ejpam-3839	185	15	the	the	DET
ejpam-3839	185	16	second	second	ADJ
ejpam-3839	185	17	kind	kind	NOUN
ejpam-3839	185	18	:	:	PUNCT
ejpam-3839	185	19	(	(	PUNCT
ejpam-3839	185	20	et	et	NOUN
ejpam-3839	185	21	−	−	PROPN
ejpam-3839	185	22	1−	1−	NUM
ejpam-3839	185	23	∑m−1	∑m−1	PROPN
ejpam-3839	185	24	j=0	j=0	X
ejpam-3839	185	25	)	)	PUNCT
ejpam-3839	185	26	k	k	PROPN
ejpam-3839	186	1	k	k	X
ejpam-3839	186	2	!	!	PUNCT
ejpam-3839	186	3	=	=	PUNCT
ejpam-3839	187	1	∞∑	∞∑	PRON
ejpam-3839	187	2	n=0	n=0	NUM
ejpam-3839	187	3	s2,m(n	s2,m(n	NOUN
ejpam-3839	187	4	,	,	PUNCT
ejpam-3839	187	5	k	k	NOUN
ejpam-3839	187	6	)	)	PUNCT
ejpam-3839	187	7	tn	tn	PROPN
ejpam-3839	187	8	n	n	PROPN
ejpam-3839	187	9	!	!	PROPN
ejpam-3839	187	10	,	,	PUNCT
ejpam-3839	187	11	(	(	PUNCT
ejpam-3839	187	12	24	24	NUM
ejpam-3839	187	13	)	)	PUNCT
ejpam-3839	187	14	n.	n.	NOUN
ejpam-3839	187	15	acala	acala	PROPN
ejpam-3839	187	16	,	,	PUNCT
ejpam-3839	187	17	m.	m.	PROPN
ejpam-3839	187	18	montero	montero	PROPN
ejpam-3839	187	19	/	/	SYM
ejpam-3839	187	20	eur	eur	PROPN
ejpam-3839	187	21	.	.	PUNCT
ejpam-3839	188	1	j.	j.	PROPN
ejpam-3839	188	2	pure	pure	PROPN
ejpam-3839	188	3	appl	appl	PROPN
ejpam-3839	188	4	.	.	PROPN
ejpam-3839	188	5	math	math	PROPN
ejpam-3839	188	6	,	,	PUNCT
ejpam-3839	188	7	13	13	NUM
ejpam-3839	188	8	(	(	PUNCT
ejpam-3839	188	9	4	4	NUM
ejpam-3839	188	10	)	)	PUNCT
ejpam-3839	188	11	(	(	PUNCT
ejpam-3839	188	12	2020	2020	NUM
ejpam-3839	188	13	)	)	PUNCT
ejpam-3839	188	14	,	,	PUNCT
ejpam-3839	188	15	948	948	NUM
ejpam-3839	188	16	-	-	SYM
ejpam-3839	188	17	963	963	NUM
ejpam-3839	188	18	955	955	NUM
ejpam-3839	188	19	which	which	PRON
ejpam-3839	188	20	reduce	reduce	VERB
ejpam-3839	188	21	to	to	ADP
ejpam-3839	188	22	the	the	DET
ejpam-3839	188	23	stirling	stirling	NOUN
ejpam-3839	188	24	numbers	number	NOUN
ejpam-3839	188	25	of	of	ADP
ejpam-3839	188	26	the	the	DET
ejpam-3839	188	27	second	second	ADJ
ejpam-3839	188	28	kind	kind	NOUN
ejpam-3839	188	29	when	when	SCONJ
ejpam-3839	188	30	m	m	VERB
ejpam-3839	188	31	=	=	NOUN
ejpam-3839	188	32	0	0	NUM
ejpam-3839	188	33	.	.	PUNCT
ejpam-3839	189	1	in	in	ADP
ejpam-3839	189	2	this	this	DET
ejpam-3839	189	3	section	section	NOUN
ejpam-3839	189	4	,	,	PUNCT
ejpam-3839	189	5	we	we	PRON
ejpam-3839	189	6	derive	derive	VERB
ejpam-3839	189	7	some	some	DET
ejpam-3839	189	8	relationships	relationship	NOUN
ejpam-3839	189	9	between	between	ADP
ejpam-3839	189	10	the	the	DET
ejpam-3839	189	11	truncated	truncated	ADJ
ejpam-3839	189	12	tangent	tangent	NOUN
ejpam-3839	189	13	polynomials	polynomial	NOUN
ejpam-3839	189	14	and	and	CCONJ
ejpam-3839	189	15	stirling	stirling	NOUN
ejpam-3839	189	16	numbers	number	NOUN
ejpam-3839	189	17	of	of	ADP
ejpam-3839	189	18	the	the	DET
ejpam-3839	189	19	second	second	ADJ
ejpam-3839	189	20	kind	kind	NOUN
ejpam-3839	189	21	and	and	CCONJ
ejpam-3839	189	22	its	its	PRON
ejpam-3839	189	23	associated	associated	ADJ
ejpam-3839	189	24	truncated	truncated	ADJ
ejpam-3839	189	25	version	version	NOUN
ejpam-3839	189	26	.	.	PUNCT
ejpam-3839	190	1	theorem	theorem	VERB
ejpam-3839	190	2	7	7	NUM
ejpam-3839	190	3	.	.	NOUN
ejpam-3839	190	4	for	for	ADP
ejpam-3839	190	5	m	m	PROPN
ejpam-3839	190	6	,	,	PUNCT
ejpam-3839	190	7	n	n	PRON
ejpam-3839	190	8	≥	≥	NOUN
ejpam-3839	190	9	0	0	NUM
ejpam-3839	190	10	,	,	PUNCT
ejpam-3839	190	11	tm	tm	NOUN
ejpam-3839	190	12	,	,	PUNCT
ejpam-3839	190	13	n(x	n(x	PROPN
ejpam-3839	190	14	)	)	PUNCT
ejpam-3839	190	15	=	=	SYM
ejpam-3839	190	16	n∑	n∑	PROPN
ejpam-3839	190	17	k=0	k=0	PROPN
ejpam-3839	190	18	n∑	n∑	PUNCT
ejpam-3839	191	1	r	r	PROPN
ejpam-3839	191	2	=	=	SYM
ejpam-3839	191	3	k	k	X
ejpam-3839	191	4	(	(	PUNCT
ejpam-3839	191	5	n	n	NOUN
ejpam-3839	191	6	r	r	NOUN
ejpam-3839	191	7	)	)	PUNCT
ejpam-3839	191	8	s2(r	s2(r	PROPN
ejpam-3839	191	9	,	,	PUNCT
ejpam-3839	191	10	k)tm	k)tm	PROPN
ejpam-3839	191	11	,	,	PUNCT
ejpam-3839	191	12	n−r	n−r	NOUN
ejpam-3839	191	13	·	·	PUNCT
ejpam-3839	191	14	(	(	PUNCT
ejpam-3839	191	15	x)k	x)k	X
ejpam-3839	191	16	,	,	PUNCT
ejpam-3839	191	17	(	(	PUNCT
ejpam-3839	191	18	25	25	NUM
ejpam-3839	191	19	)	)	PUNCT
ejpam-3839	191	20	tm	tm	NOUN
ejpam-3839	191	21	,	,	PUNCT
ejpam-3839	191	22	n(x	n(x	PROPN
ejpam-3839	191	23	)	)	PUNCT
ejpam-3839	191	24	=	=	SYM
ejpam-3839	191	25	n∑	n∑	PROPN
ejpam-3839	191	26	k=0	k=0	PROPN
ejpam-3839	191	27	n∑	n∑	PUNCT
ejpam-3839	192	1	r	r	PROPN
ejpam-3839	192	2	=	=	SYM
ejpam-3839	192	3	k	k	X
ejpam-3839	192	4	(	(	PUNCT
ejpam-3839	192	5	n	n	NOUN
ejpam-3839	192	6	r	r	NOUN
ejpam-3839	192	7	)	)	PUNCT
ejpam-3839	192	8	s2(r	s2(r	PROPN
ejpam-3839	192	9	,	,	PUNCT
ejpam-3839	192	10	k)tm	k)tm	PROPN
ejpam-3839	192	11	,	,	PUNCT
ejpam-3839	192	12	n−r(−k)x(k	n−r(−k)x(k	NOUN
ejpam-3839	192	13	)	)	PUNCT
ejpam-3839	192	14	.	.	PUNCT
ejpam-3839	193	1	(	(	PUNCT
ejpam-3839	193	2	26	26	NUM
ejpam-3839	193	3	)	)	PUNCT
ejpam-3839	193	4	proof	proof	NOUN
ejpam-3839	193	5	.	.	PUNCT
ejpam-3839	194	1	applying	apply	VERB
ejpam-3839	194	2	relation	relation	NOUN
ejpam-3839	194	3	(	(	PUNCT
ejpam-3839	194	4	23	23	NUM
ejpam-3839	194	5	)	)	PUNCT
ejpam-3839	194	6	to	to	ADP
ejpam-3839	194	7	(	(	PUNCT
ejpam-3839	194	8	7	7	NUM
ejpam-3839	194	9	)	)	PUNCT
ejpam-3839	194	10	,	,	PUNCT
ejpam-3839	194	11	we	we	PRON
ejpam-3839	194	12	get	get	VERB
ejpam-3839	194	13	tm	tm	NOUN
ejpam-3839	194	14	,	,	PUNCT
ejpam-3839	194	15	n(x	n(x	X
ejpam-3839	194	16	)	)	PUNCT
ejpam-3839	194	17	=	=	SYM
ejpam-3839	195	1	n∑	n∑	NOUN
ejpam-3839	195	2	r=0	r=0	PROPN
ejpam-3839	195	3	(	(	PUNCT
ejpam-3839	195	4	n	n	NOUN
ejpam-3839	195	5	r	r	NOUN
ejpam-3839	195	6	)	)	PUNCT
ejpam-3839	195	7	tm	tm	NOUN
ejpam-3839	195	8	,	,	PUNCT
ejpam-3839	195	9	n−r	n−r	NOUN
ejpam-3839	195	10	r∑	r∑	NOUN
ejpam-3839	195	11	k=0	k=0	PROPN
ejpam-3839	195	12	s2(r	s2(r	PROPN
ejpam-3839	195	13	,	,	PUNCT
ejpam-3839	195	14	k)(x)k	k)(x)k	X
ejpam-3839	195	15	(	(	PUNCT
ejpam-3839	195	16	27	27	NUM
ejpam-3839	195	17	)	)	PUNCT
ejpam-3839	195	18	=	=	SYM
ejpam-3839	196	1	n∑	n∑	PROPN
ejpam-3839	196	2	k=0	k=0	PROPN
ejpam-3839	196	3	n∑	n∑	PUNCT
ejpam-3839	197	1	r	r	PROPN
ejpam-3839	197	2	=	=	SYM
ejpam-3839	197	3	k	k	X
ejpam-3839	197	4	(	(	PUNCT
ejpam-3839	197	5	n	n	NOUN
ejpam-3839	197	6	r	r	NOUN
ejpam-3839	197	7	)	)	PUNCT
ejpam-3839	197	8	s2(r	s2(r	PROPN
ejpam-3839	197	9	,	,	PUNCT
ejpam-3839	197	10	k)tm	k)tm	PROPN
ejpam-3839	197	11	,	,	PUNCT
ejpam-3839	197	12	n−r	n−r	NOUN
ejpam-3839	197	13	·	·	PUNCT
ejpam-3839	197	14	(	(	PUNCT
ejpam-3839	197	15	x)k	x)k	X
ejpam-3839	197	16	.	.	PUNCT
ejpam-3839	198	1	(	(	PUNCT
ejpam-3839	198	2	28	28	NUM
ejpam-3839	198	3	)	)	PUNCT
ejpam-3839	198	4	to	to	PART
ejpam-3839	198	5	do	do	VERB
ejpam-3839	198	6	(	(	PUNCT
ejpam-3839	198	7	26	26	NUM
ejpam-3839	198	8	)	)	PUNCT
ejpam-3839	198	9	,	,	PUNCT
ejpam-3839	198	10	we	we	PRON
ejpam-3839	198	11	note	note	VERB
ejpam-3839	198	12	that	that	SCONJ
ejpam-3839	198	13	ext	ext	NOUN
ejpam-3839	198	14	=	=	SYM
ejpam-3839	198	15	(	(	PUNCT
ejpam-3839	198	16	1−	1−	NUM
ejpam-3839	198	17	(	(	PUNCT
ejpam-3839	198	18	1−	1−	NUM
ejpam-3839	198	19	e−t)))−x	e−t)))−x	NOUN
ejpam-3839	198	20	.	.	PUNCT
ejpam-3839	199	1	hence	hence	ADV
ejpam-3839	199	2	,	,	PUNCT
ejpam-3839	199	3	equation	equation	NOUN
ejpam-3839	199	4	(	(	PUNCT
ejpam-3839	199	5	5	5	NUM
ejpam-3839	199	6	)	)	PUNCT
ejpam-3839	199	7	becomes	become	VERB
ejpam-3839	199	8	∞∑	∞∑	NUM
ejpam-3839	199	9	n=0	n=0	NUM
ejpam-3839	199	10	tm	tm	NOUN
ejpam-3839	199	11	,	,	PUNCT
ejpam-3839	199	12	n(x	n(x	PROPN
ejpam-3839	199	13	)	)	PUNCT
ejpam-3839	199	14	tn	tn	NOUN
ejpam-3839	199	15	n	n	NOUN
ejpam-3839	199	16	!	!	PUNCT
ejpam-3839	200	1	=	=	SYM
ejpam-3839	200	2	2	2	NUM
ejpam-3839	200	3	tm	tm	PROPN
ejpam-3839	200	4	m	m	PROPN
ejpam-3839	200	5	!	!	PUNCT
ejpam-3839	201	1	e2	e2	PROPN
ejpam-3839	201	2	t	t	PROPN
ejpam-3839	201	3	+	+	CCONJ
ejpam-3839	201	4	1−	1−	NUM
ejpam-3839	201	5	∑m−1	∑m−1	NOUN
ejpam-3839	201	6	j=0	j=0	VERB
ejpam-3839	201	7	2j	2j	NUM
ejpam-3839	201	8	t	t	PROPN
ejpam-3839	201	9	j	j	PROPN
ejpam-3839	201	10	j	j	PROPN
ejpam-3839	201	11	!	!	PUNCT
ejpam-3839	202	1	(	(	PUNCT
ejpam-3839	202	2	1−	1−	NUM
ejpam-3839	202	3	(	(	PUNCT
ejpam-3839	202	4	1−	1−	NUM
ejpam-3839	202	5	e−t)))−x	e−t)))−x	NOUN
ejpam-3839	202	6	=	=	SYM
ejpam-3839	202	7	2	2	NUM
ejpam-3839	202	8	tm	tm	PROPN
ejpam-3839	202	9	m	m	PROPN
ejpam-3839	202	10	!	!	PUNCT
ejpam-3839	203	1	e2	e2	PROPN
ejpam-3839	203	2	t	t	PROPN
ejpam-3839	203	3	+	+	CCONJ
ejpam-3839	203	4	1−	1−	NUM
ejpam-3839	203	5	∑m−1	∑m−1	NOUN
ejpam-3839	203	6	j=0	j=0	VERB
ejpam-3839	203	7	2j	2j	NUM
ejpam-3839	203	8	t	t	PROPN
ejpam-3839	203	9	j	j	PROPN
ejpam-3839	203	10	j	j	PROPN
ejpam-3839	203	11	!	!	PUNCT
ejpam-3839	204	1	∞∑	∞∑	ADJ
ejpam-3839	204	2	k=0	k=0	PROPN
ejpam-3839	204	3	(	(	PUNCT
ejpam-3839	204	4	x+	x+	X
ejpam-3839	204	5	k	k	NOUN
ejpam-3839	204	6	−	−	PROPN
ejpam-3839	204	7	1	1	NUM
ejpam-3839	204	8	k	k	NOUN
ejpam-3839	204	9	)	)	PUNCT
ejpam-3839	204	10	(	(	PUNCT
ejpam-3839	204	11	1−	1−	NUM
ejpam-3839	204	12	e−t)k	e−t)k	ADJ
ejpam-3839	204	13	=	=	PUNCT
ejpam-3839	204	14	2	2	NUM
ejpam-3839	204	15	tm	tm	PROPN
ejpam-3839	204	16	m	m	PROPN
ejpam-3839	204	17	!	!	PUNCT
ejpam-3839	205	1	e2	e2	PROPN
ejpam-3839	205	2	t	t	PROPN
ejpam-3839	205	3	+	+	CCONJ
ejpam-3839	205	4	1−	1−	NUM
ejpam-3839	205	5	∑m−1	∑m−1	NOUN
ejpam-3839	205	6	j=0	j=0	VERB
ejpam-3839	205	7	2j	2j	NUM
ejpam-3839	205	8	t	t	PROPN
ejpam-3839	205	9	j	j	PROPN
ejpam-3839	205	10	j	j	PROPN
ejpam-3839	205	11	!	!	PUNCT
ejpam-3839	206	1	∞∑	∞∑	PRON
ejpam-3839	206	2	k=0	k=0	PROPN
ejpam-3839	206	3	x(k	x(k	PROPN
ejpam-3839	206	4	)	)	PUNCT
ejpam-3839	206	5	(	(	PUNCT
ejpam-3839	206	6	et	et	NOUN
ejpam-3839	206	7	−	−	PROPN
ejpam-3839	206	8	1)k	1)k	NUM
ejpam-3839	206	9	k	k	X
ejpam-3839	206	10	!	!	PUNCT
ejpam-3839	206	11	e−kt	e−kt	NOUN
ejpam-3839	207	1	=	=	NOUN
ejpam-3839	208	1	∞∑	∞∑	ADJ
ejpam-3839	208	2	k=0	k=0	PROPN
ejpam-3839	208	3	x(k	x(k	PROPN
ejpam-3839	208	4	)	)	PUNCT
ejpam-3839	208	5	(	(	PUNCT
ejpam-3839	208	6	∞∑	∞∑	PROPN
ejpam-3839	208	7	n=0	n=0	PROPN
ejpam-3839	208	8	s2(n	s2(n	PROPN
ejpam-3839	208	9	,	,	PUNCT
ejpam-3839	208	10	k	k	NOUN
ejpam-3839	208	11	)	)	PUNCT
ejpam-3839	208	12	tn	tn	PROPN
ejpam-3839	208	13	n	n	PROPN
ejpam-3839	208	14	!	!	PUNCT
ejpam-3839	208	15	)	)	PUNCT
ejpam-3839	209	1	(	(	PUNCT
ejpam-3839	209	2	∞∑	∞∑	NUM
ejpam-3839	209	3	n=0	n=0	NUM
ejpam-3839	209	4	tm	tm	NOUN
ejpam-3839	209	5	,	,	PUNCT
ejpam-3839	209	6	n(−k	n(−k	ADJ
ejpam-3839	209	7	)	)	PUNCT
ejpam-3839	209	8	tn	tn	NOUN
ejpam-3839	209	9	n	n	NOUN
ejpam-3839	209	10	!	!	PUNCT
ejpam-3839	209	11	)	)	PUNCT
ejpam-3839	210	1	=	=	PUNCT
ejpam-3839	211	1	∞∑	∞∑	NUM
ejpam-3839	211	2	k=0	k=0	PUNCT
ejpam-3839	211	3	x(k	x(k	PROPN
ejpam-3839	211	4	)	)	PUNCT
ejpam-3839	212	1	∞∑	∞∑	PRON
ejpam-3839	212	2	n=0	n=0	NUM
ejpam-3839	212	3	n∑	n∑	NOUN
ejpam-3839	212	4	r=0	r=0	PROPN
ejpam-3839	212	5	(	(	PUNCT
ejpam-3839	212	6	n	n	NOUN
ejpam-3839	212	7	r	r	NOUN
ejpam-3839	212	8	)	)	PUNCT
ejpam-3839	212	9	s2(r	s2(r	PROPN
ejpam-3839	212	10	,	,	PUNCT
ejpam-3839	212	11	k)tm	k)tm	PROPN
ejpam-3839	212	12	,	,	PUNCT
ejpam-3839	212	13	n−r(−k	n−r(−k	NOUN
ejpam-3839	212	14	)	)	PUNCT
ejpam-3839	212	15	tn	tn	NOUN
ejpam-3839	212	16	n	n	NOUN
ejpam-3839	212	17	!	!	PUNCT
ejpam-3839	212	18	=	=	NOUN
ejpam-3839	213	1	∞∑	∞∑	PRON
ejpam-3839	213	2	n=0	n=0	NUM
ejpam-3839	213	3	n∑	n∑	ADP
ejpam-3839	213	4	k=0	k=0	PROPN
ejpam-3839	213	5	n∑	n∑	PUNCT
ejpam-3839	214	1	r	r	PROPN
ejpam-3839	214	2	=	=	SYM
ejpam-3839	214	3	k	k	X
ejpam-3839	214	4	(	(	PUNCT
ejpam-3839	214	5	n	n	NOUN
ejpam-3839	214	6	r	r	NOUN
ejpam-3839	214	7	)	)	PUNCT
ejpam-3839	214	8	s2(r	s2(r	PROPN
ejpam-3839	214	9	,	,	PUNCT
ejpam-3839	214	10	k)tm	k)tm	PROPN
ejpam-3839	214	11	,	,	PUNCT
ejpam-3839	214	12	n−r(−k)x(k	n−r(−k)x(k	PROPN
ejpam-3839	214	13	)	)	PUNCT
ejpam-3839	214	14	tn	tn	PROPN
ejpam-3839	214	15	n	n	PROPN
ejpam-3839	214	16	!	!	PUNCT
ejpam-3839	214	17	.	.	PUNCT
ejpam-3839	215	1	comparing	compare	VERB
ejpam-3839	215	2	the	the	DET
ejpam-3839	215	3	coefficients	coefficient	NOUN
ejpam-3839	215	4	of	of	ADP
ejpam-3839	215	5	tn	tn	NOUN
ejpam-3839	215	6	n	n	ADP
ejpam-3839	215	7	!	!	PROPN
ejpam-3839	216	1	gives	give	VERB
ejpam-3839	216	2	(	(	PUNCT
ejpam-3839	216	3	26	26	NUM
ejpam-3839	216	4	)	)	PUNCT
ejpam-3839	216	5	.	.	PUNCT
ejpam-3839	217	1	theorem	theorem	ADJ
ejpam-3839	217	2	8	8	NUM
ejpam-3839	217	3	.	.	PUNCT
ejpam-3839	218	1	for	for	ADP
ejpam-3839	218	2	m	m	PROPN
ejpam-3839	218	3	,	,	PUNCT
ejpam-3839	218	4	n	n	PRON
ejpam-3839	218	5	≥	≥	NOUN
ejpam-3839	218	6	0	0	NUM
ejpam-3839	218	7	,	,	PUNCT
ejpam-3839	218	8	tm	tm	NOUN
ejpam-3839	218	9	,	,	PUNCT
ejpam-3839	218	10	n+m(x	n+m(x	NOUN
ejpam-3839	218	11	)	)	PUNCT
ejpam-3839	218	12	=	=	SYM
ejpam-3839	218	13	n∑	n∑	NOUN
ejpam-3839	218	14	k=0	k=0	PROPN
ejpam-3839	218	15	(	(	PUNCT
ejpam-3839	218	16	n+m	n+m	NUM
ejpam-3839	218	17	m	m	VERB
ejpam-3839	218	18	)	)	PUNCT
ejpam-3839	218	19	(	(	PUNCT
ejpam-3839	218	20	−1)kk!2n−ks2,m(n	−1)kk!2n−ks2,m(n	X
ejpam-3839	218	21	,	,	PUNCT
ejpam-3839	218	22	k	k	NOUN
ejpam-3839	218	23	)	)	PUNCT
ejpam-3839	218	24	.	.	PUNCT
ejpam-3839	219	1	(	(	PUNCT
ejpam-3839	219	2	29	29	NUM
ejpam-3839	219	3	)	)	PUNCT
ejpam-3839	219	4	n.	n.	PROPN
ejpam-3839	219	5	acala	acala	PROPN
ejpam-3839	219	6	,	,	PUNCT
ejpam-3839	219	7	m.	m.	PROPN
ejpam-3839	219	8	montero	montero	PROPN
ejpam-3839	219	9	/	/	SYM
ejpam-3839	219	10	eur	eur	PROPN
ejpam-3839	219	11	.	.	PUNCT
ejpam-3839	220	1	j.	j.	PROPN
ejpam-3839	220	2	pure	pure	PROPN
ejpam-3839	220	3	appl	appl	PROPN
ejpam-3839	220	4	.	.	PROPN
ejpam-3839	220	5	math	math	PROPN
ejpam-3839	220	6	,	,	PUNCT
ejpam-3839	220	7	13	13	NUM
ejpam-3839	220	8	(	(	PUNCT
ejpam-3839	220	9	4	4	NUM
ejpam-3839	220	10	)	)	PUNCT
ejpam-3839	220	11	(	(	PUNCT
ejpam-3839	220	12	2020	2020	NUM
ejpam-3839	220	13	)	)	PUNCT
ejpam-3839	220	14	,	,	PUNCT
ejpam-3839	220	15	948	948	NUM
ejpam-3839	220	16	-	-	SYM
ejpam-3839	220	17	963	963	NUM
ejpam-3839	220	18	956	956	NUM
ejpam-3839	220	19	proof	proof	NOUN
ejpam-3839	220	20	.	.	PUNCT
ejpam-3839	221	1	note	note	VERB
ejpam-3839	221	2	that	that	SCONJ
ejpam-3839	221	3	(	(	PUNCT
ejpam-3839	221	4	5	5	X
ejpam-3839	221	5	)	)	PUNCT
ejpam-3839	221	6	can	can	AUX
ejpam-3839	221	7	be	be	AUX
ejpam-3839	221	8	expressed	express	VERB
ejpam-3839	221	9	as	as	ADP
ejpam-3839	221	10	∞∑	∞∑	NUM
ejpam-3839	221	11	n=0	n=0	NUM
ejpam-3839	221	12	tm	tm	NOUN
ejpam-3839	221	13	,	,	PUNCT
ejpam-3839	221	14	n(x	n(x	PROPN
ejpam-3839	221	15	)	)	PUNCT
ejpam-3839	221	16	tn	tn	NOUN
ejpam-3839	221	17	n	n	NOUN
ejpam-3839	221	18	!	!	PUNCT
ejpam-3839	222	1	=	=	PUNCT
ejpam-3839	222	2	tm	tm	PROPN
ejpam-3839	222	3	m	m	PROPN
ejpam-3839	222	4	!	!	PUNCT
ejpam-3839	223	1	(	(	PUNCT
ejpam-3839	223	2	1	1	NUM
ejpam-3839	223	3	+	+	CCONJ
ejpam-3839	223	4	1	1	NUM
ejpam-3839	223	5	2	2	NUM
ejpam-3839	223	6	(	(	PUNCT
ejpam-3839	223	7	e2	e2	PROPN
ejpam-3839	223	8	t	t	PROPN
ejpam-3839	223	9	−	−	PROPN
ejpam-3839	223	10	1−	1−	NUM
ejpam-3839	223	11	∑m−1	∑m−1	PROPN
ejpam-3839	223	12	j=0	j=0	PROPN
ejpam-3839	223	13	(	(	PUNCT
ejpam-3839	223	14	2t)j	2t)j	NUM
ejpam-3839	223	15	j	j	NOUN
ejpam-3839	223	16	!	!	PUNCT
ejpam-3839	223	17	)	)	PUNCT
ejpam-3839	223	18	)	)	PUNCT
ejpam-3839	223	19	(	(	PUNCT
ejpam-3839	223	20	30	30	NUM
ejpam-3839	223	21	)	)	PUNCT
ejpam-3839	223	22	=	=	NOUN
ejpam-3839	223	23	tm	tm	PROPN
ejpam-3839	223	24	m	m	PROPN
ejpam-3839	223	25	!	!	PUNCT
ejpam-3839	224	1	∞∑	∞∑	ADJ
ejpam-3839	224	2	k=0	k=0	PROPN
ejpam-3839	224	3	(	(	PUNCT
ejpam-3839	224	4	−1	−1	NOUN
ejpam-3839	224	5	2	2	NUM
ejpam-3839	224	6	)	)	PUNCT
ejpam-3839	224	7	k	k	PROPN
ejpam-3839	224	8	e2	e2	NOUN
ejpam-3839	224	9	t	t	PROPN
ejpam-3839	224	10	−	−	PROPN
ejpam-3839	224	11	1−	1−	NUM
ejpam-3839	224	12	m−1∑	m−1∑	PROPN
ejpam-3839	224	13	j=0	j=0	PROPN
ejpam-3839	224	14	(	(	PUNCT
ejpam-3839	224	15	2t)j	2t)j	NUM
ejpam-3839	224	16	j	j	NOUN
ejpam-3839	224	17	!	!	PROPN
ejpam-3839	224	18	k	k	PUNCT
ejpam-3839	224	19	(	(	PUNCT
ejpam-3839	224	20	31	31	NUM
ejpam-3839	224	21	)	)	PUNCT
ejpam-3839	224	22	=	=	NOUN
ejpam-3839	224	23	tm	tm	PROPN
ejpam-3839	224	24	m	m	PROPN
ejpam-3839	224	25	!	!	PUNCT
ejpam-3839	225	1	∞∑	∞∑	ADJ
ejpam-3839	225	2	k=0	k=0	PROPN
ejpam-3839	225	3	(	(	PUNCT
ejpam-3839	225	4	−1)kk!2−k	−1)kk!2−k	NOUN
ejpam-3839	225	5	∞∑	∞∑	NUM
ejpam-3839	225	6	n=0	n=0	NUM
ejpam-3839	225	7	s2,m(n	s2,m(n	NOUN
ejpam-3839	225	8	,	,	PUNCT
ejpam-3839	225	9	k	k	NOUN
ejpam-3839	225	10	)	)	PUNCT
ejpam-3839	225	11	(	(	PUNCT
ejpam-3839	225	12	2t)n	2t)n	NUM
ejpam-3839	225	13	n	n	CCONJ
ejpam-3839	225	14	!	!	PUNCT
ejpam-3839	226	1	(	(	PUNCT
ejpam-3839	226	2	32	32	NUM
ejpam-3839	226	3	)	)	PUNCT
ejpam-3839	226	4	=	=	NOUN
ejpam-3839	227	1	∞∑	∞∑	NUM
ejpam-3839	227	2	n=0	n=0	NUM
ejpam-3839	227	3	∞∑	∞∑	NUM
ejpam-3839	227	4	k=0	k=0	PROPN
ejpam-3839	227	5	(	(	PUNCT
ejpam-3839	227	6	−1)kk!2n−ks2,m(n	−1)kk!2n−ks2,m(n	X
ejpam-3839	227	7	,	,	PUNCT
ejpam-3839	227	8	k	k	NOUN
ejpam-3839	227	9	)	)	PUNCT
ejpam-3839	227	10	tn+m	tn+m	PROPN
ejpam-3839	228	1	m!n	m!n	PROPN
ejpam-3839	228	2	!	!	PROPN
ejpam-3839	229	1	(	(	PUNCT
ejpam-3839	229	2	33	33	NUM
ejpam-3839	229	3	)	)	PUNCT
ejpam-3839	229	4	=	=	PUNCT
ejpam-3839	230	1	∞∑	∞∑	NUM
ejpam-3839	230	2	n=0	n=0	NUM
ejpam-3839	230	3	n∑	n∑	NOUN
ejpam-3839	230	4	k=0	k=0	PROPN
ejpam-3839	230	5	(	(	PUNCT
ejpam-3839	230	6	n+m	n+m	NUM
ejpam-3839	230	7	m	m	VERB
ejpam-3839	230	8	)	)	PUNCT
ejpam-3839	230	9	(	(	PUNCT
ejpam-3839	230	10	−1)kk!2n−ks2,m(n	−1)kk!2n−ks2,m(n	X
ejpam-3839	230	11	,	,	PUNCT
ejpam-3839	230	12	k	k	NOUN
ejpam-3839	230	13	)	)	PUNCT
ejpam-3839	230	14	tn+m	tn+m	PROPN
ejpam-3839	230	15	(	(	PUNCT
ejpam-3839	230	16	n+m	n+m	NUM
ejpam-3839	230	17	)	)	PUNCT
ejpam-3839	230	18	!	!	PUNCT
ejpam-3839	231	1	,	,	PUNCT
ejpam-3839	231	2	(	(	PUNCT
ejpam-3839	231	3	34	34	NUM
ejpam-3839	231	4	)	)	PUNCT
ejpam-3839	231	5	which	which	PRON
ejpam-3839	231	6	gives	give	VERB
ejpam-3839	231	7	the	the	DET
ejpam-3839	231	8	desired	desire	VERB
ejpam-3839	231	9	result	result	NOUN
ejpam-3839	231	10	.	.	PUNCT
ejpam-3839	232	1	the	the	DET
ejpam-3839	232	2	case	case	NOUN
ejpam-3839	232	3	when	when	SCONJ
ejpam-3839	232	4	m	m	VERB
ejpam-3839	232	5	=	=	SYM
ejpam-3839	232	6	1	1	NUM
ejpam-3839	232	7	,	,	PUNCT
ejpam-3839	232	8	we	we	PRON
ejpam-3839	232	9	obtain	obtain	VERB
ejpam-3839	232	10	an	an	DET
ejpam-3839	232	11	interesting	interesting	ADJ
ejpam-3839	232	12	identity	identity	NOUN
ejpam-3839	232	13	involving	involve	VERB
ejpam-3839	232	14	apostol	apostol	NOUN
ejpam-3839	232	15	-	-	PUNCT
ejpam-3839	232	16	type	type	NOUN
ejpam-3839	232	17	stirling	stirling	NOUN
ejpam-3839	232	18	numbers	number	NOUN
ejpam-3839	232	19	of	of	ADP
ejpam-3839	232	20	the	the	DET
ejpam-3839	232	21	second	second	ADJ
ejpam-3839	232	22	kind	kind	NOUN
ejpam-3839	232	23	.	.	PUNCT
ejpam-3839	233	1	these	these	DET
ejpam-3839	233	2	numbers	number	NOUN
ejpam-3839	233	3	are	be	AUX
ejpam-3839	233	4	defined	define	VERB
ejpam-3839	233	5	(	(	PUNCT
ejpam-3839	233	6	see	see	VERB
ejpam-3839	233	7	[	[	X
ejpam-3839	233	8	18	18	NUM
ejpam-3839	233	9	]	]	PUNCT
ejpam-3839	233	10	by	by	ADP
ejpam-3839	233	11	means	mean	NOUN
ejpam-3839	233	12	of	of	ADP
ejpam-3839	233	13	the	the	DET
ejpam-3839	233	14	generating	generate	VERB
ejpam-3839	233	15	function	function	NOUN
ejpam-3839	233	16	(	(	PUNCT
ejpam-3839	233	17	λet	λet	ADV
ejpam-3839	233	18	−	−	NUM
ejpam-3839	233	19	1	1	NUM
ejpam-3839	233	20	)	)	PUNCT
ejpam-3839	233	21	k	k	PROPN
ejpam-3839	234	1	k	k	X
ejpam-3839	234	2	!	!	PUNCT
ejpam-3839	234	3	=	=	PUNCT
ejpam-3839	235	1	∞∑	∞∑	DET
ejpam-3839	235	2	n=0	n=0	NUM
ejpam-3839	235	3	s2(n	s2(n	PROPN
ejpam-3839	235	4	,	,	PUNCT
ejpam-3839	235	5	k;λ	k;λ	PROPN
ejpam-3839	235	6	)	)	PUNCT
ejpam-3839	235	7	tn	tn	PROPN
ejpam-3839	235	8	n	n	PROPN
ejpam-3839	235	9	!	!	PUNCT
ejpam-3839	235	10	.	.	PUNCT
ejpam-3839	236	1	(	(	PUNCT
ejpam-3839	236	2	35	35	NUM
ejpam-3839	236	3	)	)	PUNCT
ejpam-3839	236	4	theorem	theorem	NOUN
ejpam-3839	236	5	9	9	NUM
ejpam-3839	236	6	.	.	PUNCT
ejpam-3839	236	7	for	for	ADP
ejpam-3839	236	8	n	n	PRON
ejpam-3839	236	9	≥	≥	NOUN
ejpam-3839	236	10	0	0	NUM
ejpam-3839	236	11	,	,	PUNCT
ejpam-3839	236	12	t1,n+1(x	t1,n+1(x	NUM
ejpam-3839	236	13	)	)	PUNCT
ejpam-3839	236	14	=	=	SYM
ejpam-3839	237	1	(	(	PUNCT
ejpam-3839	237	2	n+	n+	NUM
ejpam-3839	237	3	1)2n	1)2n	NUM
ejpam-3839	238	1	∞∑	∞∑	ADJ
ejpam-3839	238	2	k=0	k=0	PROPN
ejpam-3839	238	3	(	(	PUNCT
ejpam-3839	238	4	−1)kk!s2	−1)kk!s2	PROPN
ejpam-3839	238	5	(	(	PUNCT
ejpam-3839	238	6	n	n	CCONJ
ejpam-3839	238	7	,	,	PUNCT
ejpam-3839	238	8	k	k	NOUN
ejpam-3839	238	9	;	;	PUNCT
ejpam-3839	238	10	1	1	NUM
ejpam-3839	238	11	2	2	NUM
ejpam-3839	238	12	)	)	PUNCT
ejpam-3839	238	13	.	.	PUNCT
ejpam-3839	239	1	(	(	PUNCT
ejpam-3839	239	2	36	36	NUM
ejpam-3839	239	3	)	)	PUNCT
ejpam-3839	239	4	proof	proof	NOUN
ejpam-3839	239	5	.	.	PUNCT
ejpam-3839	240	1	when	when	SCONJ
ejpam-3839	240	2	m	m	VERB
ejpam-3839	240	3	=	=	SYM
ejpam-3839	240	4	1	1	NUM
ejpam-3839	240	5	in	in	ADP
ejpam-3839	240	6	(	(	PUNCT
ejpam-3839	240	7	5	5	NUM
ejpam-3839	240	8	)	)	PUNCT
ejpam-3839	240	9	,	,	PUNCT
ejpam-3839	240	10	we	we	PRON
ejpam-3839	240	11	have	have	VERB
ejpam-3839	240	12	∞∑	∞∑	NUM
ejpam-3839	240	13	n=0	n=0	NUM
ejpam-3839	240	14	t1,n(x	t1,n(x	ADP
ejpam-3839	240	15	)	)	PUNCT
ejpam-3839	240	16	tn	tn	PROPN
ejpam-3839	240	17	n	n	NOUN
ejpam-3839	240	18	!	!	PUNCT
ejpam-3839	241	1	=	=	SYM
ejpam-3839	241	2	t	t	PROPN
ejpam-3839	241	3	(	(	PUNCT
ejpam-3839	241	4	1	1	NUM
ejpam-3839	241	5	2e	2e	NUM
ejpam-3839	241	6	2	2	NUM
ejpam-3839	241	7	t	t	NOUN
ejpam-3839	241	8	−	−	NOUN
ejpam-3839	241	9	1	1	NUM
ejpam-3839	241	10	)	)	PUNCT
ejpam-3839	241	11	+	+	CCONJ
ejpam-3839	241	12	1	1	NUM
ejpam-3839	241	13	=	=	SYM
ejpam-3839	241	14	t	t	NOUN
ejpam-3839	241	15	∞∑	∞∑	PROPN
ejpam-3839	241	16	k=0	k=0	PROPN
ejpam-3839	241	17	(	(	PUNCT
ejpam-3839	241	18	−1)k	−1)k	PROPN
ejpam-3839	241	19	(	(	PUNCT
ejpam-3839	241	20	1	1	NUM
ejpam-3839	241	21	2	2	NUM
ejpam-3839	241	22	e2	e2	PROPN
ejpam-3839	241	23	t	t	PROPN
ejpam-3839	241	24	−	−	PROPN
ejpam-3839	241	25	1	1	NUM
ejpam-3839	241	26	)	)	PUNCT
ejpam-3839	241	27	k	k	NOUN
ejpam-3839	242	1	=	=	PUNCT
ejpam-3839	242	2	t	t	PROPN
ejpam-3839	242	3	∞∑	∞∑	PROPN
ejpam-3839	242	4	k=0	k=0	PROPN
ejpam-3839	242	5	(	(	PUNCT
ejpam-3839	242	6	−1)kk	−1)kk	PROPN
ejpam-3839	242	7	!	!	PUNCT
ejpam-3839	243	1	(	(	PUNCT
ejpam-3839	243	2	1	1	NUM
ejpam-3839	243	3	2e	2e	NUM
ejpam-3839	243	4	2	2	NUM
ejpam-3839	243	5	t	t	NOUN
ejpam-3839	243	6	−	−	NOUN
ejpam-3839	243	7	1	1	NUM
ejpam-3839	243	8	)	)	PUNCT
ejpam-3839	243	9	k	k	PROPN
ejpam-3839	243	10	k	k	X
ejpam-3839	243	11	!	!	PUNCT
ejpam-3839	243	12	=	=	PUNCT
ejpam-3839	244	1	t	t	PROPN
ejpam-3839	244	2	∞∑	∞∑	NUM
ejpam-3839	244	3	k=0	k=0	PROPN
ejpam-3839	244	4	(	(	PUNCT
ejpam-3839	244	5	−1)kk	−1)kk	PROPN
ejpam-3839	244	6	!	!	PUNCT
ejpam-3839	245	1	∞∑	∞∑	ADJ
ejpam-3839	245	2	n=0	n=0	ADJ
ejpam-3839	245	3	s2	s2	NOUN
ejpam-3839	245	4	(	(	PUNCT
ejpam-3839	245	5	n	n	CCONJ
ejpam-3839	245	6	,	,	PUNCT
ejpam-3839	245	7	k	k	NOUN
ejpam-3839	245	8	;	;	PUNCT
ejpam-3839	245	9	1	1	NUM
ejpam-3839	245	10	2	2	NUM
ejpam-3839	245	11	)	)	PUNCT
ejpam-3839	245	12	(	(	PUNCT
ejpam-3839	245	13	2t)n	2t)n	NUM
ejpam-3839	245	14	n	n	CCONJ
ejpam-3839	245	15	!	!	PUNCT
ejpam-3839	245	16	=	=	PUNCT
ejpam-3839	246	1	∑	∑	PUNCT
ejpam-3839	246	2	n=0	n=0	NUM
ejpam-3839	246	3	(	(	PUNCT
ejpam-3839	246	4	n+	n+	NUM
ejpam-3839	246	5	1)2n	1)2n	NUM
ejpam-3839	246	6	∞∑	∞∑	ADJ
ejpam-3839	246	7	k=0	k=0	PROPN
ejpam-3839	246	8	(	(	PUNCT
ejpam-3839	246	9	−1)kk!s2	−1)kk!s2	PROPN
ejpam-3839	246	10	(	(	PUNCT
ejpam-3839	246	11	n	n	CCONJ
ejpam-3839	246	12	,	,	PUNCT
ejpam-3839	246	13	k	k	NOUN
ejpam-3839	246	14	;	;	PUNCT
ejpam-3839	246	15	1	1	NUM
ejpam-3839	246	16	2	2	NUM
ejpam-3839	246	17	)	)	PUNCT
ejpam-3839	246	18	tn+1	tn+1	NOUN
ejpam-3839	246	19	(	(	PUNCT
ejpam-3839	246	20	n+	n+	NOUN
ejpam-3839	246	21	1	1	NUM
ejpam-3839	246	22	)	)	PUNCT
ejpam-3839	246	23	!	!	PUNCT
ejpam-3839	247	1	,	,	PUNCT
ejpam-3839	247	2	which	which	PRON
ejpam-3839	247	3	gives	give	VERB
ejpam-3839	247	4	the	the	DET
ejpam-3839	247	5	desired	desire	VERB
ejpam-3839	247	6	result	result	NOUN
ejpam-3839	247	7	.	.	PUNCT
ejpam-3839	248	1	n.	n.	PROPN
ejpam-3839	248	2	acala	acala	PROPN
ejpam-3839	248	3	,	,	PUNCT
ejpam-3839	248	4	m.	m.	PROPN
ejpam-3839	248	5	montero	montero	PROPN
ejpam-3839	248	6	/	/	SYM
ejpam-3839	248	7	eur	eur	PROPN
ejpam-3839	248	8	.	.	PUNCT
ejpam-3839	249	1	j.	j.	PROPN
ejpam-3839	249	2	pure	pure	PROPN
ejpam-3839	249	3	appl	appl	PROPN
ejpam-3839	249	4	.	.	PROPN
ejpam-3839	249	5	math	math	PROPN
ejpam-3839	249	6	,	,	PUNCT
ejpam-3839	249	7	13	13	NUM
ejpam-3839	249	8	(	(	PUNCT
ejpam-3839	249	9	4	4	NUM
ejpam-3839	249	10	)	)	PUNCT
ejpam-3839	249	11	(	(	PUNCT
ejpam-3839	249	12	2020	2020	NUM
ejpam-3839	249	13	)	)	PUNCT
ejpam-3839	249	14	,	,	PUNCT
ejpam-3839	249	15	948	948	NUM
ejpam-3839	249	16	-	-	SYM
ejpam-3839	249	17	963	963	NUM
ejpam-3839	249	18	957	957	NUM
ejpam-3839	249	19	4	4	NUM
ejpam-3839	249	20	.	.	PUNCT
ejpam-3839	250	1	relations	relation	NOUN
ejpam-3839	250	2	with	with	ADP
ejpam-3839	250	3	hypergeometric	hypergeometric	ADJ
ejpam-3839	250	4	bernoulli	bernoulli	NOUN
ejpam-3839	250	5	polynomials	polynomial	NOUN
ejpam-3839	250	6	in	in	ADP
ejpam-3839	250	7	this	this	DET
ejpam-3839	250	8	section	section	NOUN
ejpam-3839	250	9	,	,	PUNCT
ejpam-3839	250	10	we	we	PRON
ejpam-3839	250	11	show	show	VERB
ejpam-3839	250	12	several	several	ADJ
ejpam-3839	250	13	relations	relation	NOUN
ejpam-3839	250	14	of	of	ADP
ejpam-3839	250	15	truncated	truncated	ADJ
ejpam-3839	250	16	tangent	tangent	NOUN
ejpam-3839	250	17	polynomials	polynomial	NOUN
ejpam-3839	250	18	with	with	ADP
ejpam-3839	250	19	hypergeometric	hypergeometric	ADJ
ejpam-3839	250	20	bernoulli	bernoulli	NOUN
ejpam-3839	250	21	polynomials	polynomial	NOUN
ejpam-3839	250	22	and	and	CCONJ
ejpam-3839	250	23	hypergeometric	hypergeometric	ADJ
ejpam-3839	250	24	bernoulli	bernoulli	NOUN
ejpam-3839	250	25	numbers	number	NOUN
ejpam-3839	250	26	.	.	PUNCT
ejpam-3839	251	1	theorem	theorem	VERB
ejpam-3839	251	2	10	10	NUM
ejpam-3839	251	3	.	.	PUNCT
ejpam-3839	252	1	for	for	ADP
ejpam-3839	252	2	m	m	PROPN
ejpam-3839	252	3	,	,	PUNCT
ejpam-3839	252	4	n	n	PRON
ejpam-3839	252	5	≥	≥	NOUN
ejpam-3839	252	6	0	0	NUM
ejpam-3839	252	7	,	,	PUNCT
ejpam-3839	252	8	(	(	PUNCT
ejpam-3839	252	9	n+m	n+m	NUM
ejpam-3839	252	10	n	n	CCONJ
ejpam-3839	252	11	)	)	PUNCT
ejpam-3839	252	12	n∑	n∑	PUNCT
ejpam-3839	252	13	k=0	k=0	PROPN
ejpam-3839	252	14	(	(	PUNCT
ejpam-3839	252	15	n	n	X
ejpam-3839	252	16	k	k	NOUN
ejpam-3839	252	17	)	)	PUNCT
ejpam-3839	252	18	(	(	PUNCT
ejpam-3839	252	19	2k−(n+m)bm	2k−(n+m)bm	NUM
ejpam-3839	252	20	,	,	PUNCT
ejpam-3839	252	21	k(x)yn−k	k(x)yn−k	NOUN
ejpam-3839	252	22	−	−	PROPN
ejpam-3839	252	23	2−(k+1)tm	2−(k+1)tm	NUM
ejpam-3839	252	24	,	,	PUNCT
ejpam-3839	252	25	k(y)xn−k	k(y)xn−k	NOUN
ejpam-3839	252	26	)	)	PUNCT
ejpam-3839	252	27	(	(	PUNCT
ejpam-3839	252	28	37	37	NUM
ejpam-3839	252	29	)	)	PUNCT
ejpam-3839	252	30	=	=	PUNCT
ejpam-3839	252	31	n+m∑	n+m∑	PROPN
ejpam-3839	252	32	k=0	k=0	X
ejpam-3839	252	33	(	(	PUNCT
ejpam-3839	252	34	n+m	n+m	NUM
ejpam-3839	252	35	k	k	X
ejpam-3839	252	36	)	)	PUNCT
ejpam-3839	252	37	2−(k+1)tm	2−(k+1)tm	NUM
ejpam-3839	252	38	,	,	PUNCT
ejpam-3839	252	39	k(y)bm	k(y)bm	PROPN
ejpam-3839	252	40	,	,	PUNCT
ejpam-3839	252	41	n+m−k(x	n+m−k(x	NUM
ejpam-3839	252	42	)	)	PUNCT
ejpam-3839	252	43	.	.	PUNCT
ejpam-3839	253	1	(	(	PUNCT
ejpam-3839	253	2	38	38	NUM
ejpam-3839	253	3	)	)	PUNCT
ejpam-3839	253	4	proof	proof	NOUN
ejpam-3839	253	5	.	.	PUNCT
ejpam-3839	254	1	applying	apply	VERB
ejpam-3839	254	2	(	(	PUNCT
ejpam-3839	254	3	5	5	NUM
ejpam-3839	254	4	)	)	PUNCT
ejpam-3839	254	5	,	,	PUNCT
ejpam-3839	254	6	we	we	PRON
ejpam-3839	254	7	obtain	obtain	VERB
ejpam-3839	254	8	2tm	2tm	PROPN
ejpam-3839	254	9	m	m	PROPN
ejpam-3839	254	10	!	!	PUNCT
ejpam-3839	255	1	eyt	eyt	PROPN
ejpam-3839	255	2	=	=	PROPN
ejpam-3839	256	1	(	(	PUNCT
ejpam-3839	256	2	∞∑	∞∑	NUM
ejpam-3839	256	3	n=0	n=0	NUM
ejpam-3839	256	4	tm	tm	NOUN
ejpam-3839	256	5	,	,	PUNCT
ejpam-3839	256	6	n(y	n(y	PROPN
ejpam-3839	256	7	)	)	PUNCT
ejpam-3839	256	8	tn	tn	PROPN
ejpam-3839	256	9	n	n	PROPN
ejpam-3839	256	10	!	!	PUNCT
ejpam-3839	256	11	)	)	PUNCT
ejpam-3839	257	1	e2	e2	NOUN
ejpam-3839	257	2	t	t	NOUN
ejpam-3839	257	3	+	+	CCONJ
ejpam-3839	257	4	1−	1−	NUM
ejpam-3839	257	5	m−1∑	m−1∑	NUM
ejpam-3839	257	6	j=0	j=0	PROPN
ejpam-3839	257	7	(	(	PUNCT
ejpam-3839	257	8	2t)j	2t)j	NUM
ejpam-3839	257	9	j	j	NOUN
ejpam-3839	257	10	!	!	PUNCT
ejpam-3839	258	1			PROPN
ejpam-3839	259	1	=	=	PUNCT
ejpam-3839	260	1	(	(	PUNCT
ejpam-3839	260	2	∞∑	∞∑	NUM
ejpam-3839	260	3	n=0	n=0	NUM
ejpam-3839	260	4	tm	tm	NOUN
ejpam-3839	260	5	,	,	PUNCT
ejpam-3839	260	6	n(y	n(y	PROPN
ejpam-3839	260	7	)	)	PUNCT
ejpam-3839	260	8	tn	tn	PROPN
ejpam-3839	260	9	n	n	PROPN
ejpam-3839	260	10	!	!	PUNCT
ejpam-3839	260	11	)	)	PUNCT
ejpam-3839	260	12	e2	e2	NOUN
ejpam-3839	260	13	t	t	NOUN
ejpam-3839	260	14	−	−	PROPN
ejpam-3839	260	15	m−1∑	m−1∑	PROPN
ejpam-3839	260	16	j=0	j=0	PROPN
ejpam-3839	260	17	(	(	PUNCT
ejpam-3839	260	18	2t)j	2t)j	NUM
ejpam-3839	260	19	j	j	PROPN
ejpam-3839	260	20	!	!	PUNCT
ejpam-3839	261	1	+	+	PROPN
ejpam-3839	261	2	(	(	PUNCT
ejpam-3839	261	3	∞∑	∞∑	NUM
ejpam-3839	261	4	n=0	n=0	NUM
ejpam-3839	261	5	tm	tm	NOUN
ejpam-3839	261	6	,	,	PUNCT
ejpam-3839	261	7	n(y	n(y	PROPN
ejpam-3839	261	8	)	)	PUNCT
ejpam-3839	261	9	tn	tn	PROPN
ejpam-3839	261	10	n	n	PROPN
ejpam-3839	261	11	!	!	PUNCT
ejpam-3839	261	12	)	)	PUNCT
ejpam-3839	261	13	.	.	PUNCT
ejpam-3839	262	1	thus	thus	ADV
ejpam-3839	262	2	,	,	PUNCT
ejpam-3839	262	3	2tm	2tm	PROPN
ejpam-3839	262	4	m	m	PROPN
ejpam-3839	262	5	!	!	PUNCT
ejpam-3839	262	6	eyt	eyt	PROPN
ejpam-3839	263	1	∞∑	∞∑	PROPN
ejpam-3839	263	2	n=0	n=0	PROPN
ejpam-3839	263	3	bm	bm	PROPN
ejpam-3839	263	4	,	,	PUNCT
ejpam-3839	263	5	n(x	n(x	PROPN
ejpam-3839	263	6	)	)	PUNCT
ejpam-3839	263	7	(	(	PUNCT
ejpam-3839	263	8	2t)n	2t)n	NUM
ejpam-3839	263	9	n	n	CCONJ
ejpam-3839	263	10	!	!	PUNCT
ejpam-3839	263	11	=	=	PUNCT
ejpam-3839	263	12	(	(	PUNCT
ejpam-3839	263	13	2t)m	2t)m	NUM
ejpam-3839	263	14	m	m	NOUN
ejpam-3839	263	15	!	!	PUNCT
ejpam-3839	263	16	e2xt	e2xt	PUNCT
ejpam-3839	263	17	(	(	PUNCT
ejpam-3839	263	18	∞∑	∞∑	NUM
ejpam-3839	263	19	n=0	n=0	NUM
ejpam-3839	263	20	tm	tm	NOUN
ejpam-3839	263	21	,	,	PUNCT
ejpam-3839	263	22	n(y	n(y	PROPN
ejpam-3839	263	23	)	)	PUNCT
ejpam-3839	263	24	tn	tn	PROPN
ejpam-3839	263	25	n	n	PROPN
ejpam-3839	263	26	!	!	PUNCT
ejpam-3839	263	27	)	)	PUNCT
ejpam-3839	264	1	+	+	CCONJ
ejpam-3839	264	2	(	(	PUNCT
ejpam-3839	264	3	∞∑	∞∑	NUM
ejpam-3839	264	4	n=0	n=0	NUM
ejpam-3839	264	5	tm	tm	NOUN
ejpam-3839	264	6	,	,	PUNCT
ejpam-3839	264	7	n(y	n(y	PROPN
ejpam-3839	264	8	)	)	PUNCT
ejpam-3839	264	9	tn	tn	PROPN
ejpam-3839	264	10	n	n	PROPN
ejpam-3839	264	11	!	!	PUNCT
ejpam-3839	264	12	)	)	PUNCT
ejpam-3839	265	1	∞∑	∞∑	PRON
ejpam-3839	265	2	n=0	n=0	NUM
ejpam-3839	265	3	bm	bm	PROPN
ejpam-3839	265	4	,	,	PUNCT
ejpam-3839	265	5	n(x	n(x	PROPN
ejpam-3839	265	6	)	)	PUNCT
ejpam-3839	265	7	(	(	PUNCT
ejpam-3839	265	8	2t)n	2t)n	NUM
ejpam-3839	265	9	n	n	CCONJ
ejpam-3839	265	10	!	!	PUNCT
ejpam-3839	265	11	.	.	PUNCT
ejpam-3839	266	1	expanding	expand	VERB
ejpam-3839	266	2	the	the	DET
ejpam-3839	266	3	exponential	exponential	ADJ
ejpam-3839	266	4	functions	function	NOUN
ejpam-3839	266	5	into	into	ADP
ejpam-3839	266	6	series	series	NOUN
ejpam-3839	266	7	and	and	CCONJ
ejpam-3839	266	8	applying	apply	VERB
ejpam-3839	266	9	cauchy	cauchy	NOUN
ejpam-3839	266	10	product	product	NOUN
ejpam-3839	266	11	,	,	PUNCT
ejpam-3839	266	12	we	we	PRON
ejpam-3839	266	13	have	have	VERB
ejpam-3839	266	14	tm	tm	PRON
ejpam-3839	266	15	m	m	NOUN
ejpam-3839	266	16	!	!	PUNCT
ejpam-3839	267	1	∞∑	∞∑	ADJ
ejpam-3839	267	2	n=0	n=0	NUM
ejpam-3839	267	3	(	(	PUNCT
ejpam-3839	267	4	n∑	n∑	NOUN
ejpam-3839	267	5	k=0	k=0	PROPN
ejpam-3839	267	6	(	(	PUNCT
ejpam-3839	267	7	n	n	X
ejpam-3839	267	8	k	k	NOUN
ejpam-3839	267	9	)	)	PUNCT
ejpam-3839	267	10	(	(	PUNCT
ejpam-3839	267	11	2k+1bm	2k+1bm	NUM
ejpam-3839	267	12	,	,	PUNCT
ejpam-3839	267	13	k(x)yn−k	k(x)yn−k	PROPN
ejpam-3839	267	14	−	−	PROPN
ejpam-3839	267	15	2m+n−ktm	2m+n−ktm	NUM
ejpam-3839	267	16	,	,	PUNCT
ejpam-3839	267	17	k(y)xn−k	k(y)xn−k	NOUN
ejpam-3839	267	18	)	)	PUNCT
ejpam-3839	267	19	)	)	PUNCT
ejpam-3839	267	20	tn	tn	PROPN
ejpam-3839	267	21	n	n	CCONJ
ejpam-3839	267	22	!	!	PUNCT
ejpam-3839	267	23	=	=	NOUN
ejpam-3839	268	1	∞∑	∞∑	PRON
ejpam-3839	268	2	n=0	n=0	NUM
ejpam-3839	268	3	n∑	n∑	NOUN
ejpam-3839	268	4	k=0	k=0	PROPN
ejpam-3839	268	5	(	(	PUNCT
ejpam-3839	268	6	n	n	X
ejpam-3839	268	7	k	k	PROPN
ejpam-3839	268	8	)	)	PUNCT
ejpam-3839	268	9	2n−ktm	2n−ktm	NUM
ejpam-3839	268	10	,	,	PUNCT
ejpam-3839	268	11	k(y)bm	k(y)bm	PROPN
ejpam-3839	268	12	,	,	PUNCT
ejpam-3839	268	13	n−k(x	n−k(x	VERB
ejpam-3839	268	14	)	)	PUNCT
ejpam-3839	268	15	tn	tn	PROPN
ejpam-3839	268	16	n	n	PROPN
ejpam-3839	268	17	!	!	PUNCT
ejpam-3839	268	18	.	.	PUNCT
ejpam-3839	269	1	avoiding	avoid	VERB
ejpam-3839	269	2	the	the	DET
ejpam-3839	269	3	zero	zero	NUM
ejpam-3839	269	4	-	-	PUNCT
ejpam-3839	269	5	terms	term	NOUN
ejpam-3839	269	6	on	on	ADP
ejpam-3839	269	7	the	the	DET
ejpam-3839	269	8	right	right	ADJ
ejpam-3839	269	9	-	-	PUNCT
ejpam-3839	269	10	hand	hand	NOUN
ejpam-3839	269	11	side	side	NOUN
ejpam-3839	269	12	of	of	ADP
ejpam-3839	269	13	the	the	DET
ejpam-3839	269	14	above	above	ADJ
ejpam-3839	269	15	equation	equation	NOUN
ejpam-3839	269	16	leads	lead	VERB
ejpam-3839	269	17	to	to	ADP
ejpam-3839	269	18	1	1	NUM
ejpam-3839	269	19	m	m	NOUN
ejpam-3839	269	20	!	!	PUNCT
ejpam-3839	270	1	∞∑	∞∑	ADJ
ejpam-3839	270	2	n=0	n=0	NUM
ejpam-3839	270	3	(	(	PUNCT
ejpam-3839	270	4	n∑	n∑	NOUN
ejpam-3839	270	5	k=0	k=0	PROPN
ejpam-3839	270	6	(	(	PUNCT
ejpam-3839	270	7	n	n	X
ejpam-3839	270	8	k	k	NOUN
ejpam-3839	270	9	)	)	PUNCT
ejpam-3839	270	10	[	[	PUNCT
ejpam-3839	270	11	2k+1bm	2k+1bm	NOUN
ejpam-3839	270	12	,	,	PUNCT
ejpam-3839	270	13	k(x)yn−k	k(x)yn−k	PROPN
ejpam-3839	270	14	−	−	PROPN
ejpam-3839	270	15	2m+n−ktm	2m+n−ktm	NUM
ejpam-3839	270	16	,	,	PUNCT
ejpam-3839	270	17	k(y)xn−k	k(y)xn−k	X
ejpam-3839	270	18	]	]	PUNCT
ejpam-3839	270	19	)	)	PUNCT
ejpam-3839	270	20	tn+m	tn+m	PROPN
ejpam-3839	270	21	n	n	X
ejpam-3839	270	22	!	!	PUNCT
ejpam-3839	270	23	=	=	NOUN
ejpam-3839	271	1	∞∑	∞∑	PRON
ejpam-3839	271	2	n=0	n=0	NUM
ejpam-3839	271	3	n+m∑	n+m∑	PROPN
ejpam-3839	271	4	k=0	k=0	PROPN
ejpam-3839	271	5	(	(	PUNCT
ejpam-3839	271	6	n+m	n+m	NUM
ejpam-3839	271	7	k	k	X
ejpam-3839	271	8	)	)	PUNCT
ejpam-3839	271	9	2n+m−ktm	2n+m−ktm	NUM
ejpam-3839	271	10	,	,	PUNCT
ejpam-3839	271	11	k(y)bm	k(y)bm	PROPN
ejpam-3839	271	12	,	,	PUNCT
ejpam-3839	271	13	n+m−k(x	n+m−k(x	PROPN
ejpam-3839	271	14	)	)	PUNCT
ejpam-3839	271	15	tn+m	tn+m	PROPN
ejpam-3839	271	16	(	(	PUNCT
ejpam-3839	271	17	n+m	n+m	NUM
ejpam-3839	271	18	)	)	PUNCT
ejpam-3839	271	19	!	!	PUNCT
ejpam-3839	271	20	.	.	PUNCT
ejpam-3839	272	1	comparing	compare	VERB
ejpam-3839	272	2	the	the	DET
ejpam-3839	272	3	coefficients	coefficient	NOUN
ejpam-3839	272	4	of	of	ADP
ejpam-3839	272	5	both	both	DET
ejpam-3839	272	6	sides	side	NOUN
ejpam-3839	272	7	gives	give	VERB
ejpam-3839	272	8	2n+m+1	2n+m+1	NUM
ejpam-3839	272	9	n!m	n!m	PROPN
ejpam-3839	272	10	!	!	PUNCT
ejpam-3839	273	1	n∑	n∑	NOUN
ejpam-3839	273	2	k=0	k=0	PROPN
ejpam-3839	273	3	(	(	PUNCT
ejpam-3839	273	4	n	n	X
ejpam-3839	273	5	k	k	NOUN
ejpam-3839	273	6	)	)	PUNCT
ejpam-3839	274	1	[	[	PUNCT
ejpam-3839	274	2	2k−(n+m)bm	2k−(n+m)bm	NUM
ejpam-3839	274	3	,	,	PUNCT
ejpam-3839	274	4	k(x)yn−k	k(x)yn−k	NOUN
ejpam-3839	274	5	−	−	PROPN
ejpam-3839	274	6	2−(k+1)tm	2−(k+1)tm	NUM
ejpam-3839	274	7	,	,	PUNCT
ejpam-3839	274	8	j(y)xn−k	j(y)xn−k	NOUN
ejpam-3839	274	9	]	]	PUNCT
ejpam-3839	274	10	n.	n.	PROPN
ejpam-3839	274	11	acala	acala	PROPN
ejpam-3839	274	12	,	,	PUNCT
ejpam-3839	274	13	m.	m.	PROPN
ejpam-3839	274	14	montero	montero	PROPN
ejpam-3839	274	15	/	/	SYM
ejpam-3839	274	16	eur	eur	PROPN
ejpam-3839	274	17	.	.	PUNCT
ejpam-3839	275	1	j.	j.	PROPN
ejpam-3839	275	2	pure	pure	PROPN
ejpam-3839	275	3	appl	appl	PROPN
ejpam-3839	275	4	.	.	PROPN
ejpam-3839	275	5	math	math	PROPN
ejpam-3839	275	6	,	,	PUNCT
ejpam-3839	275	7	13	13	NUM
ejpam-3839	275	8	(	(	PUNCT
ejpam-3839	275	9	4	4	NUM
ejpam-3839	275	10	)	)	PUNCT
ejpam-3839	275	11	(	(	PUNCT
ejpam-3839	275	12	2020	2020	NUM
ejpam-3839	275	13	)	)	PUNCT
ejpam-3839	275	14	,	,	PUNCT
ejpam-3839	275	15	948	948	NUM
ejpam-3839	275	16	-	-	SYM
ejpam-3839	275	17	963	963	NUM
ejpam-3839	275	18	958	958	NUM
ejpam-3839	275	19	=	=	SYM
ejpam-3839	275	20	2n+m+1	2n+m+1	NUM
ejpam-3839	275	21	(	(	PUNCT
ejpam-3839	275	22	n+m	n+m	NUM
ejpam-3839	275	23	)	)	PUNCT
ejpam-3839	275	24	!	!	PUNCT
ejpam-3839	276	1	n+m∑	n+m∑	PROPN
ejpam-3839	276	2	k=0	k=0	PROPN
ejpam-3839	276	3	(	(	PUNCT
ejpam-3839	276	4	n+m	n+m	NUM
ejpam-3839	276	5	k	k	X
ejpam-3839	276	6	)	)	PUNCT
ejpam-3839	276	7	2−(k+1)tm	2−(k+1)tm	NUM
ejpam-3839	276	8	,	,	PUNCT
ejpam-3839	276	9	k(y)bm	k(y)bm	PROPN
ejpam-3839	276	10	,	,	PUNCT
ejpam-3839	276	11	n+m−k(x	n+m−k(x	PROPN
ejpam-3839	276	12	)	)	PUNCT
ejpam-3839	276	13	,	,	PUNCT
ejpam-3839	276	14	from	from	ADP
ejpam-3839	276	15	where	where	SCONJ
ejpam-3839	276	16	the	the	DET
ejpam-3839	276	17	desired	desire	VERB
ejpam-3839	276	18	result	result	NOUN
ejpam-3839	276	19	follows	follow	VERB
ejpam-3839	276	20	.	.	PUNCT
ejpam-3839	277	1	lemma	lemma	PROPN
ejpam-3839	277	2	1	1	NUM
ejpam-3839	277	3	.	.	PUNCT
ejpam-3839	278	1	(	(	PUNCT
ejpam-3839	278	2	see	see	VERB
ejpam-3839	278	3	theorem	theorem	ADJ
ejpam-3839	278	4	1[19	1[19	NUM
ejpam-3839	278	5	]	]	PUNCT
ejpam-3839	278	6	)	)	PUNCT
ejpam-3839	278	7	the	the	DET
ejpam-3839	278	8	polynomial	polynomial	ADJ
ejpam-3839	278	9	identity	identity	NOUN
ejpam-3839	278	10	n∑	n∑	PROPN
ejpam-3839	278	11	k=0	k=0	PROPN
ejpam-3839	278	12	an	an	DET
ejpam-3839	278	13	,	,	PUNCT
ejpam-3839	278	14	k(x+	k(x+	ADJ
ejpam-3839	278	15	α)k	α)k	NOUN
ejpam-3839	279	1	=	=	SYM
ejpam-3839	279	2	n∑	n∑	PRON
ejpam-3839	279	3	k=0	k=0	PROPN
ejpam-3839	279	4	bn	bn	PROPN
ejpam-3839	279	5	,	,	PUNCT
ejpam-3839	279	6	k(x+	k(x+	ADJ
ejpam-3839	279	7	β)k	β)k	X
ejpam-3839	279	8	(	(	PUNCT
ejpam-3839	279	9	39	39	NUM
ejpam-3839	279	10	)	)	PUNCT
ejpam-3839	279	11	implies	imply	VERB
ejpam-3839	279	12	the	the	DET
ejpam-3839	279	13	bernoulli	bernoulli	PROPN
ejpam-3839	279	14	polynomials	polynomial	NOUN
ejpam-3839	279	15	identiy	identiy	VERB
ejpam-3839	279	16	n∑	n∑	PROPN
ejpam-3839	279	17	k=0	k=0	PROPN
ejpam-3839	279	18	an	an	PROPN
ejpam-3839	279	19	,	,	PUNCT
ejpam-3839	279	20	kbk(x+	kbk(x+	NOUN
ejpam-3839	279	21	α	α	X
ejpam-3839	279	22	)	)	PUNCT
ejpam-3839	280	1	=	=	SYM
ejpam-3839	280	2	n∑	n∑	PROPN
ejpam-3839	280	3	k=0	k=0	PROPN
ejpam-3839	280	4	bn	bn	PROPN
ejpam-3839	280	5	,	,	PUNCT
ejpam-3839	280	6	kbk(x+	kbk(x+	NOUN
ejpam-3839	280	7	β	β	NOUN
ejpam-3839	280	8	)	)	PUNCT
ejpam-3839	280	9	.	.	PUNCT
ejpam-3839	281	1	(	(	PUNCT
ejpam-3839	281	2	40	40	NUM
ejpam-3839	281	3	)	)	PUNCT
ejpam-3839	281	4	when	when	SCONJ
ejpam-3839	281	5	m	m	VERB
ejpam-3839	281	6	=	=	SYM
ejpam-3839	281	7	0	0	NUM
ejpam-3839	281	8	in	in	ADP
ejpam-3839	281	9	theorem	theorem	NOUN
ejpam-3839	281	10	10	10	NUM
ejpam-3839	281	11	,	,	PUNCT
ejpam-3839	281	12	we	we	PRON
ejpam-3839	281	13	obtain	obtain	VERB
ejpam-3839	281	14	the	the	DET
ejpam-3839	281	15	following	follow	VERB
ejpam-3839	281	16	corollary	corollary	NOUN
ejpam-3839	281	17	.	.	PUNCT
ejpam-3839	282	1	corollary	corollary	ADJ
ejpam-3839	282	2	1	1	NUM
ejpam-3839	282	3	.	.	PUNCT
ejpam-3839	283	1	for	for	ADP
ejpam-3839	283	2	n	n	PRON
ejpam-3839	283	3	≥	≥	NOUN
ejpam-3839	283	4	0	0	NUM
ejpam-3839	283	5	,	,	PUNCT
ejpam-3839	283	6	n∑	n∑	DET
ejpam-3839	283	7	k=0	k=0	PROPN
ejpam-3839	283	8	(	(	PUNCT
ejpam-3839	283	9	n	n	X
ejpam-3839	283	10	k	k	NOUN
ejpam-3839	283	11	)	)	PUNCT
ejpam-3839	283	12	2−(k+1)tk(y	2−(k+1)tk(y	NUM
ejpam-3839	283	13	)	)	PUNCT
ejpam-3839	284	1	(	(	PUNCT
ejpam-3839	284	2	(	(	PUNCT
ejpam-3839	284	3	x−	x−	PROPN
ejpam-3839	284	4	1)n−k	1)n−k	NUM
ejpam-3839	284	5	+	+	NUM
ejpam-3839	284	6	xn−k	xn−k	PROPN
ejpam-3839	284	7	)	)	PUNCT
ejpam-3839	285	1	=	=	PRON
ejpam-3839	285	2	(	(	PUNCT
ejpam-3839	285	3	x−	x−	PROPN
ejpam-3839	285	4	1	1	NUM
ejpam-3839	285	5	+	+	NUM
ejpam-3839	285	6	y	y	PROPN
ejpam-3839	285	7	2	2	NUM
ejpam-3839	285	8	)	)	PUNCT
ejpam-3839	285	9	n	n	CCONJ
ejpam-3839	285	10	,	,	PUNCT
ejpam-3839	285	11	(	(	PUNCT
ejpam-3839	285	12	41	41	NUM
ejpam-3839	285	13	)	)	PUNCT
ejpam-3839	285	14	n∑	n∑	NOUN
ejpam-3839	286	1	k=0	k=0	PROPN
ejpam-3839	286	2	(	(	PUNCT
ejpam-3839	286	3	n	n	X
ejpam-3839	286	4	k	k	NOUN
ejpam-3839	286	5	)	)	PUNCT
ejpam-3839	286	6	2−(k+1)tk(y	2−(k+1)tk(y	NUM
ejpam-3839	286	7	)	)	PUNCT
ejpam-3839	286	8	(	(	PUNCT
ejpam-3839	286	9	bn−k(x−	bn−k(x−	X
ejpam-3839	286	10	1	1	NUM
ejpam-3839	286	11	)	)	PUNCT
ejpam-3839	286	12	+	+	NOUN
ejpam-3839	286	13	bn−k(x	bn−k(x	NOUN
ejpam-3839	286	14	)	)	PUNCT
ejpam-3839	286	15	)	)	PUNCT
ejpam-3839	287	1	=	=	PUNCT
ejpam-3839	287	2	bn	bn	INTJ
ejpam-3839	287	3	(	(	PUNCT
ejpam-3839	287	4	x−	x−	PROPN
ejpam-3839	287	5	1	1	NUM
ejpam-3839	287	6	+	+	NUM
ejpam-3839	287	7	y	y	PROPN
ejpam-3839	287	8	2	2	NUM
ejpam-3839	287	9	)	)	PUNCT
ejpam-3839	287	10	.	.	PUNCT
ejpam-3839	288	1	(	(	PUNCT
ejpam-3839	288	2	42	42	X
ejpam-3839	288	3	)	)	PUNCT
ejpam-3839	288	4	proof	proof	NOUN
ejpam-3839	288	5	.	.	PUNCT
ejpam-3839	289	1	note	note	VERB
ejpam-3839	289	2	that	that	SCONJ
ejpam-3839	289	3	b0,n(x	b0,n(x	ADP
ejpam-3839	289	4	)	)	PUNCT
ejpam-3839	289	5	=	=	SYM
ejpam-3839	289	6	(	(	PUNCT
ejpam-3839	289	7	x−	x−	PROPN
ejpam-3839	289	8	1)n	1)n	PROPN
ejpam-3839	289	9	and	and	CCONJ
ejpam-3839	289	10	t0,n(x	t0,n(x	X
ejpam-3839	289	11	)	)	PUNCT
ejpam-3839	289	12	=	=	SYM
ejpam-3839	289	13	tn(x	tn(x	NOUN
ejpam-3839	289	14	)	)	PUNCT
ejpam-3839	289	15	.	.	PUNCT
ejpam-3839	290	1	setting	set	VERB
ejpam-3839	290	2	m	m	VERB
ejpam-3839	290	3	=	=	X
ejpam-3839	290	4	0	0	NUM
ejpam-3839	290	5	in	in	ADP
ejpam-3839	290	6	theorem	theorem	NOUN
ejpam-3839	290	7	10	10	NUM
ejpam-3839	290	8	,	,	PUNCT
ejpam-3839	290	9	we	we	PRON
ejpam-3839	290	10	get	get	VERB
ejpam-3839	290	11	n∑	n∑	NOUN
ejpam-3839	290	12	k=0	k=0	PROPN
ejpam-3839	290	13	(	(	PUNCT
ejpam-3839	290	14	n	n	X
ejpam-3839	290	15	k	k	NOUN
ejpam-3839	290	16	)	)	PUNCT
ejpam-3839	290	17	2−(k+1)tk(y	2−(k+1)tk(y	NUM
ejpam-3839	290	18	)	)	PUNCT
ejpam-3839	290	19	(	(	PUNCT
ejpam-3839	290	20	(	(	PUNCT
ejpam-3839	290	21	x−	x−	PROPN
ejpam-3839	290	22	1)n−k	1)n−k	NUM
ejpam-3839	290	23	+	+	NUM
ejpam-3839	290	24	xn−k	xn−k	PROPN
ejpam-3839	290	25	)	)	PUNCT
ejpam-3839	291	1	=	=	PUNCT
ejpam-3839	292	1	n∑	n∑	NOUN
ejpam-3839	292	2	k=0	k=0	PROPN
ejpam-3839	292	3	(	(	PUNCT
ejpam-3839	292	4	n	n	X
ejpam-3839	292	5	k	k	X
ejpam-3839	292	6	)	)	PUNCT
ejpam-3839	292	7	2k−n(x−	2k−n(x−	PROPN
ejpam-3839	292	8	1)kyn−k	1)kyn−k	NUM
ejpam-3839	292	9	(	(	PUNCT
ejpam-3839	292	10	43	43	NUM
ejpam-3839	292	11	)	)	PUNCT
ejpam-3839	292	12	=	=	PRON
ejpam-3839	293	1	(	(	PUNCT
ejpam-3839	293	2	x−	x−	PROPN
ejpam-3839	293	3	1	1	NUM
ejpam-3839	293	4	+	+	NUM
ejpam-3839	293	5	y	y	PROPN
ejpam-3839	293	6	2	2	NUM
ejpam-3839	293	7	)	)	PUNCT
ejpam-3839	293	8	n	n	X
ejpam-3839	293	9	.	.	PUNCT
ejpam-3839	294	1	applying	apply	VERB
ejpam-3839	294	2	lemma	lemma	PROPN
ejpam-3839	294	3	1	1	NUM
ejpam-3839	294	4	in	in	ADP
ejpam-3839	294	5	(	(	PUNCT
ejpam-3839	294	6	43	43	NUM
ejpam-3839	294	7	)	)	PUNCT
ejpam-3839	294	8	,	,	PUNCT
ejpam-3839	294	9	we	we	PRON
ejpam-3839	294	10	obtain	obtain	VERB
ejpam-3839	294	11	n∑	n∑	ADJ
ejpam-3839	294	12	k=0	k=0	PROPN
ejpam-3839	294	13	(	(	PUNCT
ejpam-3839	294	14	n	n	X
ejpam-3839	294	15	k	k	NOUN
ejpam-3839	294	16	)	)	PUNCT
ejpam-3839	294	17	2−(k+1)tk(y	2−(k+1)tk(y	NUM
ejpam-3839	294	18	)	)	PUNCT
ejpam-3839	294	19	(	(	PUNCT
ejpam-3839	294	20	bn−k(x−	bn−k(x−	X
ejpam-3839	294	21	1	1	NUM
ejpam-3839	294	22	)	)	PUNCT
ejpam-3839	294	23	+	+	NOUN
ejpam-3839	294	24	bn−k(x	bn−k(x	NOUN
ejpam-3839	294	25	)	)	PUNCT
ejpam-3839	294	26	)	)	PUNCT
ejpam-3839	295	1	=	=	PUNCT
ejpam-3839	296	1	n∑	n∑	NOUN
ejpam-3839	296	2	k=0	k=0	PROPN
ejpam-3839	296	3	(	(	PUNCT
ejpam-3839	296	4	n	n	X
ejpam-3839	296	5	k	k	PROPN
ejpam-3839	296	6	)	)	PUNCT
ejpam-3839	297	1	2k−nbk(x−	2k−nbk(x−	NUM
ejpam-3839	297	2	1)yn−k	1)yn−k	NOUN
ejpam-3839	297	3	=	=	SYM
ejpam-3839	297	4	bn	bn	PROPN
ejpam-3839	297	5	(	(	PUNCT
ejpam-3839	297	6	x−	x−	PROPN
ejpam-3839	297	7	1	1	NUM
ejpam-3839	297	8	+	+	NUM
ejpam-3839	297	9	y	y	PROPN
ejpam-3839	297	10	2	2	NUM
ejpam-3839	297	11	)	)	PUNCT
ejpam-3839	297	12	.	.	PUNCT
ejpam-3839	298	1	corollary	corollary	ADJ
ejpam-3839	298	2	2	2	NUM
ejpam-3839	298	3	.	.	PUNCT
ejpam-3839	298	4	for	for	ADP
ejpam-3839	298	5	n	n	PRON
ejpam-3839	298	6	≥	≥	NOUN
ejpam-3839	298	7	0	0	NUM
ejpam-3839	298	8	,	,	PUNCT
ejpam-3839	298	9	n∑	n∑	DET
ejpam-3839	298	10	k=0	k=0	PROPN
ejpam-3839	298	11	(	(	PUNCT
ejpam-3839	298	12	n	n	X
ejpam-3839	298	13	k	k	NOUN
ejpam-3839	298	14	)	)	PUNCT
ejpam-3839	298	15	(	(	PUNCT
ejpam-3839	298	16	2k−n−1bk(x)yn−k	2k−n−1bk(x)yn−k	NUM
ejpam-3839	298	17	−	−	NUM
ejpam-3839	298	18	2−kk(y	2−kk(y	NUM
ejpam-3839	298	19	−	−	PROPN
ejpam-3839	298	20	2)k−1xn−k	2)k−1xn−k	X
ejpam-3839	298	21	)	)	PUNCT
ejpam-3839	298	22	n.	n.	PROPN
ejpam-3839	298	23	acala	acala	PROPN
ejpam-3839	298	24	,	,	PUNCT
ejpam-3839	298	25	m.	m.	PROPN
ejpam-3839	298	26	montero	montero	PROPN
ejpam-3839	298	27	/	/	SYM
ejpam-3839	298	28	eur	eur	PROPN
ejpam-3839	298	29	.	.	PUNCT
ejpam-3839	299	1	j.	j.	PROPN
ejpam-3839	299	2	pure	pure	PROPN
ejpam-3839	299	3	appl	appl	PROPN
ejpam-3839	299	4	.	.	PROPN
ejpam-3839	299	5	math	math	PROPN
ejpam-3839	299	6	,	,	PUNCT
ejpam-3839	299	7	13	13	NUM
ejpam-3839	299	8	(	(	PUNCT
ejpam-3839	299	9	4	4	NUM
ejpam-3839	299	10	)	)	PUNCT
ejpam-3839	299	11	(	(	PUNCT
ejpam-3839	299	12	2020	2020	NUM
ejpam-3839	299	13	)	)	PUNCT
ejpam-3839	299	14	,	,	PUNCT
ejpam-3839	299	15	948	948	NUM
ejpam-3839	299	16	-	-	SYM
ejpam-3839	299	17	963	963	NUM
ejpam-3839	299	18	959	959	NUM
ejpam-3839	299	19	=	=	SYM
ejpam-3839	299	20	1	1	NUM
ejpam-3839	299	21	n+	n+	SYM
ejpam-3839	299	22	1	1	NUM
ejpam-3839	299	23	n∑	n∑	NOUN
ejpam-3839	299	24	k=0	k=0	PROPN
ejpam-3839	299	25	(	(	PUNCT
ejpam-3839	299	26	n+	n+	NUM
ejpam-3839	299	27	1	1	NUM
ejpam-3839	299	28	n−	n−	NOUN
ejpam-3839	299	29	k	k	X
ejpam-3839	299	30	)	)	PUNCT
ejpam-3839	299	31	2−k−1(k	2−k−1(k	NUM
ejpam-3839	300	1	+	+	CCONJ
ejpam-3839	300	2	1)(y	1)(y	NUM
ejpam-3839	300	3	−	−	PROPN
ejpam-3839	300	4	2)kbn−k(x	2)kbn−k(x	NUM
ejpam-3839	300	5	)	)	PUNCT
ejpam-3839	300	6	.	.	PUNCT
ejpam-3839	301	1	(	(	PUNCT
ejpam-3839	301	2	44	44	NUM
ejpam-3839	301	3	)	)	PUNCT
ejpam-3839	301	4	n∑	n∑	NOUN
ejpam-3839	301	5	k=0	k=0	PROPN
ejpam-3839	301	6	(	(	PUNCT
ejpam-3839	301	7	n	n	X
ejpam-3839	301	8	k	k	NOUN
ejpam-3839	301	9	)	)	PUNCT
ejpam-3839	301	10	(	(	PUNCT
ejpam-3839	301	11	2k−n−1bk(x)bn−k(y)−	2k−n−1bk(x)bn−k(y)−	NUM
ejpam-3839	301	12	2−kkbk−1(y	2−kkbk−1(y	NUM
ejpam-3839	301	13	−	−	PROPN
ejpam-3839	301	14	2)xn−k	2)xn−k	NOUN
ejpam-3839	301	15	)	)	PUNCT
ejpam-3839	301	16	=	=	SYM
ejpam-3839	301	17	1	1	NUM
ejpam-3839	301	18	n+	n+	SYM
ejpam-3839	301	19	1	1	NUM
ejpam-3839	301	20	n∑	n∑	NOUN
ejpam-3839	301	21	k=0	k=0	PROPN
ejpam-3839	301	22	(	(	PUNCT
ejpam-3839	301	23	n+	n+	NUM
ejpam-3839	301	24	1	1	NUM
ejpam-3839	301	25	n−	n−	NOUN
ejpam-3839	301	26	k	k	X
ejpam-3839	301	27	)	)	PUNCT
ejpam-3839	301	28	2−k−1(k	2−k−1(k	NUM
ejpam-3839	302	1	+	+	CCONJ
ejpam-3839	303	1	1)bk(y	1)bk(y	NUM
ejpam-3839	303	2	−	−	NOUN
ejpam-3839	304	1	2)bn−k(x	2)bn−k(x	NUM
ejpam-3839	304	2	)	)	PUNCT
ejpam-3839	304	3	.	.	PUNCT
ejpam-3839	305	1	(	(	PUNCT
ejpam-3839	305	2	45	45	NUM
ejpam-3839	305	3	)	)	PUNCT
ejpam-3839	305	4	proof	proof	NOUN
ejpam-3839	305	5	.	.	PUNCT
ejpam-3839	306	1	using	use	VERB
ejpam-3839	306	2	b1,n(x	b1,n(x	NOUN
ejpam-3839	306	3	)	)	PUNCT
ejpam-3839	306	4	=	=	SYM
ejpam-3839	306	5	bn(x	bn(x	X
ejpam-3839	306	6	)	)	PUNCT
ejpam-3839	306	7	and	and	CCONJ
ejpam-3839	306	8	t1,n(x	t1,n(x	X
ejpam-3839	306	9	)	)	PUNCT
ejpam-3839	306	10	=	=	SYM
ejpam-3839	306	11	2n(x−	2n(x−	NUM
ejpam-3839	306	12	2)n−1	2)n−1	NUM
ejpam-3839	306	13	,	,	PUNCT
ejpam-3839	306	14	and	and	CCONJ
ejpam-3839	306	15	applying	apply	VERB
ejpam-3839	306	16	theorem	theorem	NOUN
ejpam-3839	306	17	10	10	NUM
ejpam-3839	306	18	when	when	SCONJ
ejpam-3839	306	19	m	m	VERB
ejpam-3839	306	20	=	=	SYM
ejpam-3839	306	21	1	1	NUM
ejpam-3839	306	22	,	,	PUNCT
ejpam-3839	306	23	we	we	PRON
ejpam-3839	306	24	obtain	obtain	VERB
ejpam-3839	306	25	(	(	PUNCT
ejpam-3839	306	26	n+	n+	NOUN
ejpam-3839	306	27	1	1	NUM
ejpam-3839	306	28	)	)	PUNCT
ejpam-3839	306	29	n∑	n∑	NOUN
ejpam-3839	306	30	k=0	k=0	PROPN
ejpam-3839	306	31	(	(	PUNCT
ejpam-3839	306	32	n	n	X
ejpam-3839	306	33	k	k	NOUN
ejpam-3839	306	34	)	)	PUNCT
ejpam-3839	306	35	(	(	PUNCT
ejpam-3839	306	36	2k−n−1bk(x)yn−k	2k−n−1bk(x)yn−k	NUM
ejpam-3839	306	37	−	−	NUM
ejpam-3839	306	38	2−kk(y	2−kk(y	NUM
ejpam-3839	306	39	−	−	PROPN
ejpam-3839	306	40	2)k−1xn−k	2)k−1xn−k	NUM
ejpam-3839	306	41	)	)	PUNCT
ejpam-3839	306	42	(	(	PUNCT
ejpam-3839	306	43	46	46	NUM
ejpam-3839	306	44	)	)	PUNCT
ejpam-3839	306	45	=	=	SYM
ejpam-3839	307	1	n+1∑	n+1∑	ADJ
ejpam-3839	307	2	k=0	k=0	PROPN
ejpam-3839	307	3	(	(	PUNCT
ejpam-3839	307	4	n+	n+	ADP
ejpam-3839	307	5	1	1	NUM
ejpam-3839	307	6	k	k	NOUN
ejpam-3839	307	7	)	)	PUNCT
ejpam-3839	307	8	2−kk(y	2−kk(y	NUM
ejpam-3839	307	9	−	−	NOUN
ejpam-3839	307	10	2)k−1bn+1−k(x	2)k−1bn+1−k(x	NUM
ejpam-3839	307	11	)	)	PUNCT
ejpam-3839	307	12	(	(	PUNCT
ejpam-3839	307	13	47	47	NUM
ejpam-3839	307	14	)	)	PUNCT
ejpam-3839	307	15	=	=	SYM
ejpam-3839	307	16	n∑	n∑	NOUN
ejpam-3839	307	17	k=0	k=0	PROPN
ejpam-3839	307	18	(	(	PUNCT
ejpam-3839	307	19	n+	n+	NUM
ejpam-3839	307	20	1	1	NUM
ejpam-3839	307	21	n−	n−	NOUN
ejpam-3839	307	22	k	k	X
ejpam-3839	307	23	)	)	PUNCT
ejpam-3839	307	24	2−(k+1)(k	2−(k+1)(k	NUM
ejpam-3839	308	1	+	+	CCONJ
ejpam-3839	308	2	1)(y	1)(y	NUM
ejpam-3839	308	3	−	−	PROPN
ejpam-3839	308	4	2)kbn−k(x	2)kbn−k(x	NUM
ejpam-3839	308	5	)	)	PUNCT
ejpam-3839	308	6	,	,	PUNCT
ejpam-3839	308	7	(	(	PUNCT
ejpam-3839	308	8	48	48	NUM
ejpam-3839	308	9	)	)	PUNCT
ejpam-3839	308	10	which	which	PRON
ejpam-3839	308	11	gives	give	VERB
ejpam-3839	308	12	(	(	PUNCT
ejpam-3839	308	13	44	44	NUM
ejpam-3839	308	14	)	)	PUNCT
ejpam-3839	308	15	.	.	PUNCT
ejpam-3839	309	1	applying	apply	VERB
ejpam-3839	309	2	lemma	lemma	PROPN
ejpam-3839	309	3	1	1	NUM
ejpam-3839	309	4	in	in	ADP
ejpam-3839	309	5	(	(	PUNCT
ejpam-3839	309	6	44	44	NUM
ejpam-3839	309	7	)	)	PUNCT
ejpam-3839	309	8	,	,	PUNCT
ejpam-3839	309	9	we	we	PRON
ejpam-3839	309	10	obtain	obtain	VERB
ejpam-3839	309	11	(	(	PUNCT
ejpam-3839	309	12	45	45	NUM
ejpam-3839	309	13	)	)	PUNCT
ejpam-3839	309	14	.	.	PUNCT
ejpam-3839	310	1	theorem	theorem	VERB
ejpam-3839	310	2	11	11	NUM
ejpam-3839	310	3	.	.	PUNCT
ejpam-3839	311	1	n∑	n∑	NOUN
ejpam-3839	311	2	k=0	k=0	PROPN
ejpam-3839	311	3	(	(	PUNCT
ejpam-3839	311	4	n	n	X
ejpam-3839	311	5	k	k	PROPN
ejpam-3839	311	6	)	)	PUNCT
ejpam-3839	311	7	tm+1,n−k(x)yk−	tm+1,n−k(x)yk−	NOUN
ejpam-3839	311	8	n	n	CCONJ
ejpam-3839	311	9	m+	m+	NUM
ejpam-3839	311	10	1	1	NUM
ejpam-3839	311	11	n−1∑	n−1∑	PROPN
ejpam-3839	311	12	k=0	k=0	PROPN
ejpam-3839	311	13	(	(	PUNCT
ejpam-3839	311	14	n−	n−	NOUN
ejpam-3839	311	15	1	1	NUM
ejpam-3839	311	16	k	k	NOUN
ejpam-3839	311	17	)	)	PUNCT
ejpam-3839	311	18	tm	tm	PROPN
ejpam-3839	311	19	,	,	PUNCT
ejpam-3839	311	20	n−k−1(y)xk	n−k−1(y)xk	PROPN
ejpam-3839	311	21	=	=	PUNCT
ejpam-3839	312	1	2m−1	2m−1	NUM
ejpam-3839	312	2	n∑	n∑	NOUN
ejpam-3839	312	3	k=0	k=0	PROPN
ejpam-3839	312	4	(	(	PUNCT
ejpam-3839	312	5	n	n	CCONJ
ejpam-3839	312	6	k	k	NOUN
ejpam-3839	312	7	)	)	PUNCT
ejpam-3839	312	8	tm+1,n−k(x)tm	tm+1,n−k(x)tm	PROPN
ejpam-3839	312	9	,	,	PUNCT
ejpam-3839	312	10	k(y	k(y	PROPN
ejpam-3839	312	11	)	)	PUNCT
ejpam-3839	312	12	.	.	PUNCT
ejpam-3839	313	1	proof	proof	NOUN
ejpam-3839	313	2	.	.	PUNCT
ejpam-3839	314	1	from	from	ADP
ejpam-3839	314	2	(	(	PUNCT
ejpam-3839	314	3	5	5	NUM
ejpam-3839	314	4	)	)	PUNCT
ejpam-3839	314	5	,	,	PUNCT
ejpam-3839	314	6	2tm+1	2tm+1	NUM
ejpam-3839	314	7	(	(	PUNCT
ejpam-3839	314	8	m+	m+	NOUN
ejpam-3839	314	9	1	1	NUM
ejpam-3839	314	10	)	)	PUNCT
ejpam-3839	314	11	!	!	PUNCT
ejpam-3839	315	1	ext	ext	NOUN
ejpam-3839	315	2	=	=	PUNCT
ejpam-3839	315	3	e2	e2	NOUN
ejpam-3839	315	4	t	t	NOUN
ejpam-3839	315	5	+	+	CCONJ
ejpam-3839	315	6	1−	1−	NUM
ejpam-3839	315	7	m−1∑	m−1∑	NUM
ejpam-3839	315	8	j=0	j=0	PROPN
ejpam-3839	315	9	(	(	PUNCT
ejpam-3839	315	10	2t)j	2t)j	NUM
ejpam-3839	315	11	j	j	NOUN
ejpam-3839	315	12	!	!	PUNCT
ejpam-3839	316	1	−	−	PROPN
ejpam-3839	317	1	2mtm	2mtm	NUM
ejpam-3839	317	2	m	m	NOUN
ejpam-3839	317	3	!	!	PUNCT
ejpam-3839	318	1			PROPN
ejpam-3839	318	2	∞∑	∞∑	ADJ
ejpam-3839	318	3	n=0	n=0	ADV
ejpam-3839	318	4	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	318	5	)	)	PUNCT
ejpam-3839	318	6	tn	tn	PROPN
ejpam-3839	318	7	n	n	NOUN
ejpam-3839	318	8	!	!	PUNCT
ejpam-3839	319	1	=	=	PUNCT
ejpam-3839	319	2	e2	e2	NOUN
ejpam-3839	319	3	t	t	NOUN
ejpam-3839	319	4	+	+	CCONJ
ejpam-3839	319	5	1−	1−	NUM
ejpam-3839	319	6	m−1∑	m−1∑	NUM
ejpam-3839	319	7	j=0	j=0	PROPN
ejpam-3839	319	8	(	(	PUNCT
ejpam-3839	319	9	2t)j	2t)j	NUM
ejpam-3839	319	10	j	j	NOUN
ejpam-3839	319	11	!	!	PUNCT
ejpam-3839	320	1			PROPN
ejpam-3839	320	2	∞∑	∞∑	ADJ
ejpam-3839	320	3	n=0	n=0	ADV
ejpam-3839	320	4	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	320	5	)	)	PUNCT
ejpam-3839	320	6	tn	tn	PROPN
ejpam-3839	321	1	n	n	PROPN
ejpam-3839	321	2	!	!	PUNCT
ejpam-3839	322	1	−	−	PUNCT
ejpam-3839	323	1	2mtm	2mtm	NUM
ejpam-3839	323	2	m	m	NOUN
ejpam-3839	323	3	!	!	PUNCT
ejpam-3839	324	1	∞∑	∞∑	PRON
ejpam-3839	324	2	n=0	n=0	ADJ
ejpam-3839	324	3	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	324	4	)	)	PUNCT
ejpam-3839	324	5	tn	tn	PROPN
ejpam-3839	324	6	n	n	PROPN
ejpam-3839	324	7	!	!	PUNCT
ejpam-3839	324	8	.	.	PUNCT
ejpam-3839	325	1	consequently	consequently	ADV
ejpam-3839	325	2	,	,	PUNCT
ejpam-3839	325	3	2tm+1	2tm+1	NUM
ejpam-3839	325	4	(	(	PUNCT
ejpam-3839	325	5	m+	m+	NOUN
ejpam-3839	325	6	1	1	NUM
ejpam-3839	325	7	)	)	PUNCT
ejpam-3839	325	8	!	!	PUNCT
ejpam-3839	326	1	ext	ext	VERB
ejpam-3839	326	2	∞∑	∞∑	PRON
ejpam-3839	326	3	n=0	n=0	PUNCT
ejpam-3839	326	4	tm	tm	NOUN
ejpam-3839	326	5	,	,	PUNCT
ejpam-3839	326	6	n(y	n(y	PROPN
ejpam-3839	326	7	)	)	PUNCT
ejpam-3839	326	8	tn	tn	PROPN
ejpam-3839	326	9	n	n	ADV
ejpam-3839	326	10	!	!	PUNCT
ejpam-3839	327	1	=	=	PUNCT
ejpam-3839	328	1	2tm	2tm	PROPN
ejpam-3839	328	2	m	m	PROPN
ejpam-3839	328	3	!	!	PUNCT
ejpam-3839	329	1	eyt	eyt	PROPN
ejpam-3839	330	1	∞∑	∞∑	PROPN
ejpam-3839	330	2	n=0	n=0	SYM
ejpam-3839	330	3	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	330	4	)	)	PUNCT
ejpam-3839	330	5	tn	tn	PROPN
ejpam-3839	330	6	n	n	PROPN
ejpam-3839	330	7	!	!	PUNCT
ejpam-3839	331	1	n.	n.	PROPN
ejpam-3839	331	2	acala	acala	PROPN
ejpam-3839	331	3	,	,	PUNCT
ejpam-3839	331	4	m.	m.	PROPN
ejpam-3839	331	5	montero	montero	PROPN
ejpam-3839	331	6	/	/	SYM
ejpam-3839	331	7	eur	eur	PROPN
ejpam-3839	331	8	.	.	PUNCT
ejpam-3839	332	1	j.	j.	PROPN
ejpam-3839	332	2	pure	pure	PROPN
ejpam-3839	332	3	appl	appl	PROPN
ejpam-3839	332	4	.	.	PROPN
ejpam-3839	332	5	math	math	PROPN
ejpam-3839	332	6	,	,	PUNCT
ejpam-3839	332	7	13	13	NUM
ejpam-3839	332	8	(	(	PUNCT
ejpam-3839	332	9	4	4	NUM
ejpam-3839	332	10	)	)	PUNCT
ejpam-3839	332	11	(	(	PUNCT
ejpam-3839	332	12	2020	2020	NUM
ejpam-3839	332	13	)	)	PUNCT
ejpam-3839	332	14	,	,	PUNCT
ejpam-3839	332	15	948	948	NUM
ejpam-3839	332	16	-	-	SYM
ejpam-3839	332	17	963	963	NUM
ejpam-3839	332	18	960	960	NUM
ejpam-3839	332	19	−	−	NUM
ejpam-3839	332	20	2mtm	2mtm	NUM
ejpam-3839	332	21	m	m	NOUN
ejpam-3839	332	22	!	!	PUNCT
ejpam-3839	333	1	∞∑	∞∑	PRON
ejpam-3839	333	2	n=0	n=0	ADJ
ejpam-3839	333	3	tm+1,n(x	tm+1,n(x	NOUN
ejpam-3839	333	4	)	)	PUNCT
ejpam-3839	333	5	tn	tn	PROPN
ejpam-3839	333	6	n	n	CCONJ
ejpam-3839	333	7	!	!	PUNCT
ejpam-3839	334	1	∞∑	∞∑	PRON
ejpam-3839	334	2	n=0	n=0	PUNCT
ejpam-3839	334	3	tm	tm	NOUN
ejpam-3839	334	4	,	,	PUNCT
ejpam-3839	334	5	n(y	n(y	PROPN
ejpam-3839	334	6	)	)	PUNCT
ejpam-3839	334	7	tn	tn	PROPN
ejpam-3839	334	8	n	n	PROPN
ejpam-3839	334	9	!	!	PUNCT
ejpam-3839	334	10	.	.	PUNCT
ejpam-3839	335	1	expanding	expand	VERB
ejpam-3839	335	2	the	the	DET
ejpam-3839	335	3	exponential	exponential	ADJ
ejpam-3839	335	4	functions	function	NOUN
ejpam-3839	335	5	into	into	ADP
ejpam-3839	335	6	series	series	NOUN
ejpam-3839	335	7	and	and	CCONJ
ejpam-3839	335	8	applying	apply	VERB
ejpam-3839	335	9	cauchy	cauchy	NOUN
ejpam-3839	335	10	product	product	NOUN
ejpam-3839	335	11	,	,	PUNCT
ejpam-3839	335	12	we	we	PRON
ejpam-3839	335	13	get	get	VERB
ejpam-3839	335	14	n	n	PRON
ejpam-3839	335	15	m+	m+	NOUN
ejpam-3839	335	16	1	1	NUM
ejpam-3839	335	17	∞∑	∞∑	NUM
ejpam-3839	335	18	n=1	n=1	PROPN
ejpam-3839	335	19	(	(	PUNCT
ejpam-3839	335	20	n−1∑	n−1∑	PROPN
ejpam-3839	335	21	k=0	k=0	PROPN
ejpam-3839	335	22	(	(	PUNCT
ejpam-3839	335	23	n−	n−	NOUN
ejpam-3839	335	24	1	1	NUM
ejpam-3839	335	25	k	k	NOUN
ejpam-3839	335	26	)	)	PUNCT
ejpam-3839	335	27	tm	tm	PROPN
ejpam-3839	335	28	,	,	PUNCT
ejpam-3839	335	29	n−1−k(y)xk	n−1−k(y)xk	PROPN
ejpam-3839	335	30	)	)	PUNCT
ejpam-3839	335	31	tn	tn	PROPN
ejpam-3839	335	32	n	n	CCONJ
ejpam-3839	335	33	!	!	PUNCT
ejpam-3839	336	1	=	=	NOUN
ejpam-3839	337	1	∞∑	∞∑	NUM
ejpam-3839	337	2	n=1	n=1	PROPN
ejpam-3839	337	3	n∑	n∑	PROPN
ejpam-3839	337	4	k=0	k=0	PROPN
ejpam-3839	337	5	(	(	PUNCT
ejpam-3839	337	6	n	n	X
ejpam-3839	337	7	k	k	NOUN
ejpam-3839	337	8	)	)	PUNCT
ejpam-3839	337	9	tm+1,n−k(x)yk	tm+1,n−k(x)yk	VERB
ejpam-3839	337	10	tn	tn	PROPN
ejpam-3839	337	11	n	n	NOUN
ejpam-3839	337	12	!	!	PUNCT
ejpam-3839	338	1	−	−	PROPN
ejpam-3839	339	1	2m−1	2m−1	NUM
ejpam-3839	339	2	∞∑	∞∑	NUM
ejpam-3839	339	3	n=1	n=1	PROPN
ejpam-3839	339	4	n∑	n∑	PROPN
ejpam-3839	339	5	k=0	k=0	PROPN
ejpam-3839	339	6	(	(	PUNCT
ejpam-3839	339	7	n	n	CCONJ
ejpam-3839	339	8	k	k	NOUN
ejpam-3839	339	9	)	)	PUNCT
ejpam-3839	339	10	tm+1,n−k(x)tm	tm+1,n−k(x)tm	PROPN
ejpam-3839	339	11	,	,	PUNCT
ejpam-3839	339	12	k(y	k(y	PROPN
ejpam-3839	339	13	)	)	PUNCT
ejpam-3839	339	14	tn	tn	PROPN
ejpam-3839	339	15	n	n	PRON
ejpam-3839	339	16	!	!	PUNCT
ejpam-3839	339	17	.	.	PUNCT
ejpam-3839	340	1	comparing	compare	VERB
ejpam-3839	340	2	the	the	DET
ejpam-3839	340	3	coeeficients	coeeficient	NOUN
ejpam-3839	340	4	of	of	ADP
ejpam-3839	340	5	tn	tn	NOUN
ejpam-3839	340	6	n	n	ADP
ejpam-3839	340	7	!	!	PROPN
ejpam-3839	340	8	completes	complete	VERB
ejpam-3839	340	9	the	the	DET
ejpam-3839	340	10	proof	proof	NOUN
ejpam-3839	340	11	.	.	PUNCT
ejpam-3839	341	1	corollary	corollary	ADJ
ejpam-3839	341	2	3	3	NUM
ejpam-3839	341	3	.	.	PUNCT
ejpam-3839	341	4	for	for	ADP
ejpam-3839	341	5	n	n	PRON
ejpam-3839	341	6	≥	≥	NOUN
ejpam-3839	341	7	0	0	NUM
ejpam-3839	341	8	,	,	PUNCT
ejpam-3839	341	9	n∑	n∑	DET
ejpam-3839	341	10	k=0	k=0	PROPN
ejpam-3839	341	11	(	(	PUNCT
ejpam-3839	341	12	n	n	X
ejpam-3839	341	13	k	k	NOUN
ejpam-3839	341	14	)	)	PUNCT
ejpam-3839	341	15	(	(	PUNCT
ejpam-3839	341	16	2(x−	2(x−	NUM
ejpam-3839	341	17	2)n−kyk	2)n−kyk	NUM
ejpam-3839	341	18	−	−	NOUN
ejpam-3839	341	19	tn−k(y)xk	tn−k(y)xk	PRON
ejpam-3839	341	20	)	)	PUNCT
ejpam-3839	342	1	=	=	SYM
ejpam-3839	342	2	tn(x−	tn(x−	PART
ejpam-3839	342	3	2	2	NUM
ejpam-3839	342	4	+	+	NUM
ejpam-3839	342	5	y	y	NOUN
ejpam-3839	342	6	)	)	PUNCT
ejpam-3839	342	7	(	(	PUNCT
ejpam-3839	342	8	49	49	NUM
ejpam-3839	342	9	)	)	PUNCT
ejpam-3839	343	1	n∑	n∑	NOUN
ejpam-3839	343	2	k=0	k=0	PROPN
ejpam-3839	343	3	(	(	PUNCT
ejpam-3839	343	4	n	n	X
ejpam-3839	343	5	k	k	NOUN
ejpam-3839	343	6	)	)	PUNCT
ejpam-3839	343	7	(	(	PUNCT
ejpam-3839	343	8	2bn−k(x−	2bn−k(x−	NUM
ejpam-3839	343	9	2)yk	2)yk	NOUN
ejpam-3839	343	10	−	−	PROPN
ejpam-3839	343	11	tn−k(y)bk(x	tn−k(y)bk(x	PROPN
ejpam-3839	343	12	)	)	PUNCT
ejpam-3839	343	13	)	)	PUNCT
ejpam-3839	344	1	=	=	PUNCT
ejpam-3839	345	1	n∑	n∑	NOUN
ejpam-3839	345	2	k=0	k=0	PROPN
ejpam-3839	345	3	(	(	PUNCT
ejpam-3839	345	4	n	n	X
ejpam-3839	345	5	k	k	NOUN
ejpam-3839	345	6	)	)	PUNCT
ejpam-3839	345	7	bn−k(x−	bn−k(x−	PROPN
ejpam-3839	345	8	2)tk(y	2)tk(y	NUM
ejpam-3839	345	9	)	)	PUNCT
ejpam-3839	345	10	.	.	PUNCT
ejpam-3839	346	1	(	(	PUNCT
ejpam-3839	346	2	50	50	NUM
ejpam-3839	346	3	)	)	PUNCT
ejpam-3839	346	4	proof	proof	NOUN
ejpam-3839	346	5	.	.	PUNCT
ejpam-3839	347	1	setting	set	VERB
ejpam-3839	347	2	m	m	NOUN
ejpam-3839	347	3	=	=	X
ejpam-3839	347	4	0	0	NUM
ejpam-3839	347	5	in	in	ADP
ejpam-3839	347	6	theorem	theorem	NOUN
ejpam-3839	347	7	11	11	NUM
ejpam-3839	347	8	,	,	PUNCT
ejpam-3839	347	9	we	we	PRON
ejpam-3839	347	10	have	have	VERB
ejpam-3839	347	11	n−1∑	n−1∑	NUM
ejpam-3839	347	12	k=0	k=0	PROPN
ejpam-3839	347	13	(	(	PUNCT
ejpam-3839	347	14	n	n	X
ejpam-3839	347	15	k	k	PROPN
ejpam-3839	347	16	)	)	PUNCT
ejpam-3839	348	1	2(n−	2(n−	NUM
ejpam-3839	348	2	k)(x−	k)(x−	PROPN
ejpam-3839	348	3	2)n−k−1yk	2)n−k−1yk	NUM
ejpam-3839	348	4	−	−	PROPN
ejpam-3839	348	5	n	n	CCONJ
ejpam-3839	348	6	n−1∑	n−1∑	PROPN
ejpam-3839	348	7	k=0	k=0	PROPN
ejpam-3839	348	8	(	(	PUNCT
ejpam-3839	348	9	n−	n−	NOUN
ejpam-3839	348	10	1	1	NUM
ejpam-3839	348	11	k	k	NOUN
ejpam-3839	348	12	)	)	PUNCT
ejpam-3839	348	13	tn−k−1(y)xk	tn−k−1(y)xk	PROPN
ejpam-3839	348	14	=	=	PUNCT
ejpam-3839	349	1	=	=	NOUN
ejpam-3839	349	2	n−1∑	n−1∑	PROPN
ejpam-3839	349	3	k=0	k=0	PROPN
ejpam-3839	349	4	(	(	PUNCT
ejpam-3839	349	5	n	n	X
ejpam-3839	349	6	k	k	NOUN
ejpam-3839	349	7	)	)	PUNCT
ejpam-3839	349	8	(	(	PUNCT
ejpam-3839	349	9	n−	n−	NOUN
ejpam-3839	349	10	k)(x−	k)(x−	PROPN
ejpam-3839	349	11	2)n−k−1tk(y	2)n−k−1tk(y	PROPN
ejpam-3839	349	12	)	)	PUNCT
ejpam-3839	349	13	.	.	PUNCT
ejpam-3839	350	1	using	use	VERB
ejpam-3839	350	2	the	the	DET
ejpam-3839	350	3	identity	identity	NOUN
ejpam-3839	350	4	(	(	PUNCT
ejpam-3839	350	5	n	n	NOUN
ejpam-3839	350	6	k	k	NOUN
ejpam-3839	350	7	)	)	PUNCT
ejpam-3839	350	8	(	(	PUNCT
ejpam-3839	350	9	n−	n−	NOUN
ejpam-3839	350	10	k	k	NOUN
ejpam-3839	350	11	)	)	PUNCT
ejpam-3839	350	12	=	=	SYM
ejpam-3839	351	1	(	(	PUNCT
ejpam-3839	351	2	n−1	n−1	PROPN
ejpam-3839	351	3	k	k	PROPN
ejpam-3839	351	4	)	)	PUNCT
ejpam-3839	351	5	n	n	CCONJ
ejpam-3839	351	6	,	,	PUNCT
ejpam-3839	351	7	the	the	DET
ejpam-3839	351	8	above	above	ADJ
ejpam-3839	351	9	equation	equation	NOUN
ejpam-3839	351	10	simplifies	simplifie	NOUN
ejpam-3839	351	11	to	to	ADP
ejpam-3839	351	12	n−1∑	n−1∑	PROPN
ejpam-3839	351	13	k=0	k=0	PROPN
ejpam-3839	351	14	(	(	PUNCT
ejpam-3839	351	15	n−	n−	NOUN
ejpam-3839	351	16	1	1	NUM
ejpam-3839	351	17	k	k	NOUN
ejpam-3839	351	18	)	)	PUNCT
ejpam-3839	351	19	(	(	PUNCT
ejpam-3839	351	20	2(x−	2(x−	NUM
ejpam-3839	351	21	2)n−k−1yk	2)n−k−1yk	NUM
ejpam-3839	351	22	−	−	NOUN
ejpam-3839	351	23	tn−k−1(y)xk	tn−k−1(y)xk	PROPN
ejpam-3839	351	24	)	)	PUNCT
ejpam-3839	352	1	=	=	SYM
ejpam-3839	352	2	n−1∑	n−1∑	PROPN
ejpam-3839	352	3	k=0	k=0	PROPN
ejpam-3839	352	4	(	(	PUNCT
ejpam-3839	352	5	n−	n−	NOUN
ejpam-3839	352	6	1	1	NUM
ejpam-3839	352	7	k	k	NOUN
ejpam-3839	352	8	)	)	PUNCT
ejpam-3839	352	9	(	(	PUNCT
ejpam-3839	352	10	x−	x−	PROPN
ejpam-3839	352	11	2)n−k−1tk(y	2)n−k−1tk(y	NUM
ejpam-3839	352	12	)	)	PUNCT
ejpam-3839	352	13	,	,	PUNCT
ejpam-3839	352	14	which	which	PRON
ejpam-3839	352	15	is	be	AUX
ejpam-3839	352	16	equivalent	equivalent	ADJ
ejpam-3839	352	17	to	to	ADP
ejpam-3839	352	18	n∑	n∑	PROPN
ejpam-3839	352	19	k=0	k=0	PROPN
ejpam-3839	352	20	(	(	PUNCT
ejpam-3839	352	21	n	n	X
ejpam-3839	352	22	k	k	NOUN
ejpam-3839	352	23	)	)	PUNCT
ejpam-3839	352	24	(	(	PUNCT
ejpam-3839	352	25	2(x−	2(x−	NUM
ejpam-3839	352	26	2)n−kyk	2)n−kyk	NUM
ejpam-3839	352	27	−	−	NOUN
ejpam-3839	352	28	tn−k(y)xk	tn−k(y)xk	PRON
ejpam-3839	352	29	)	)	PUNCT
ejpam-3839	353	1	=	=	SYM
ejpam-3839	353	2	n∑	n∑	NOUN
ejpam-3839	353	3	k=0	k=0	PROPN
ejpam-3839	353	4	(	(	PUNCT
ejpam-3839	353	5	n	n	X
ejpam-3839	353	6	k	k	NOUN
ejpam-3839	353	7	)	)	PUNCT
ejpam-3839	353	8	(	(	PUNCT
ejpam-3839	353	9	x−	x−	PROPN
ejpam-3839	353	10	2)n−ktk(y	2)n−ktk(y	PROPN
ejpam-3839	353	11	)	)	PUNCT
ejpam-3839	353	12	(	(	PUNCT
ejpam-3839	353	13	51	51	NUM
ejpam-3839	353	14	)	)	PUNCT
ejpam-3839	353	15	=	=	SYM
ejpam-3839	353	16	tn(x−	tn(x−	PART
ejpam-3839	353	17	2	2	NUM
ejpam-3839	353	18	+	+	NUM
ejpam-3839	353	19	y	y	NOUN
ejpam-3839	353	20	)	)	PUNCT
ejpam-3839	353	21	.	.	PUNCT
ejpam-3839	354	1	applying	apply	VERB
ejpam-3839	354	2	lemma	lemma	PROPN
ejpam-3839	354	3	1	1	NUM
ejpam-3839	354	4	to	to	ADP
ejpam-3839	354	5	(	(	PUNCT
ejpam-3839	354	6	51	51	NUM
ejpam-3839	354	7	)	)	PUNCT
ejpam-3839	354	8	,	,	PUNCT
ejpam-3839	354	9	we	we	PRON
ejpam-3839	354	10	obtain	obtain	VERB
ejpam-3839	354	11	(	(	PUNCT
ejpam-3839	354	12	50	50	NUM
ejpam-3839	354	13	)	)	PUNCT
ejpam-3839	354	14	.	.	PUNCT
ejpam-3839	355	1	lastly	lastly	ADV
ejpam-3839	355	2	,	,	PUNCT
ejpam-3839	355	3	we	we	PRON
ejpam-3839	355	4	obtain	obtain	VERB
ejpam-3839	355	5	a	a	DET
ejpam-3839	355	6	relation	relation	NOUN
ejpam-3839	355	7	of	of	ADP
ejpam-3839	355	8	truncated	truncated	ADJ
ejpam-3839	355	9	tangent	tangent	NOUN
ejpam-3839	355	10	polynomials	polynomial	NOUN
ejpam-3839	355	11	with	with	ADP
ejpam-3839	355	12	the	the	DET
ejpam-3839	355	13	frobenius	frobenius	NOUN
ejpam-3839	355	14	-	-	PUNCT
ejpam-3839	355	15	euler	euler	NOUN
ejpam-3839	355	16	polynomials	polynomial	NOUN
ejpam-3839	355	17	.	.	PUNCT
ejpam-3839	356	1	references	reference	NOUN
ejpam-3839	356	2	961	961	NUM
ejpam-3839	356	3	theorem	theorem	VERB
ejpam-3839	356	4	12	12	NUM
ejpam-3839	356	5	.	.	PUNCT
ejpam-3839	357	1	for	for	ADP
ejpam-3839	357	2	m	m	PROPN
ejpam-3839	357	3	,	,	PUNCT
ejpam-3839	357	4	n	n	PRON
ejpam-3839	357	5	≥	≥	NOUN
ejpam-3839	357	6	0	0	NUM
ejpam-3839	357	7	,	,	PUNCT
ejpam-3839	357	8	tm	tm	NOUN
ejpam-3839	357	9	,	,	PUNCT
ejpam-3839	357	10	n(x	n(x	PROPN
ejpam-3839	357	11	)	)	PUNCT
ejpam-3839	357	12	=	=	SYM
ejpam-3839	357	13	n∑	n∑	NOUN
ejpam-3839	357	14	k=0	k=0	PROPN
ejpam-3839	357	15	(	(	PUNCT
ejpam-3839	357	16	n	n	X
ejpam-3839	357	17	k	k	NOUN
ejpam-3839	357	18	)	)	PUNCT
ejpam-3839	357	19	(	(	PUNCT
ejpam-3839	357	20	1−	1−	NUM
ejpam-3839	357	21	λ)r	λ)r	X
ejpam-3839	357	22	r∑	r∑	X
ejpam-3839	357	23	j=0	j=0	PROPN
ejpam-3839	357	24	(	(	PUNCT
ejpam-3839	357	25	r	r	NOUN
ejpam-3839	357	26	j	j	PROPN
ejpam-3839	357	27	)	)	PUNCT
ejpam-3839	357	28	(	(	PUNCT
ejpam-3839	357	29	−λ)r−jtm	−λ)r−jtm	PROPN
ejpam-3839	357	30	,	,	PUNCT
ejpam-3839	357	31	n−k(j)h	n−k(j)h	PROPN
ejpam-3839	357	32	(	(	PUNCT
ejpam-3839	357	33	r	r	NOUN
ejpam-3839	357	34	)	)	PUNCT
ejpam-3839	357	35	k	k	NOUN
ejpam-3839	357	36	(	(	PUNCT
ejpam-3839	357	37	x|λ	x|λ	ADV
ejpam-3839	357	38	)	)	PUNCT
ejpam-3839	357	39	,	,	PUNCT
ejpam-3839	357	40	(	(	PUNCT
ejpam-3839	357	41	52	52	NUM
ejpam-3839	357	42	)	)	PUNCT
ejpam-3839	357	43	where	where	SCONJ
ejpam-3839	357	44	(	(	PUNCT
ejpam-3839	357	45	1−	1−	NUM
ejpam-3839	357	46	λ	λ	X
ejpam-3839	357	47	et	et	NOUN
ejpam-3839	357	48	−	−	PROPN
ejpam-3839	358	1	λ	λ	PROPN
ejpam-3839	358	2	)	)	PUNCT
ejpam-3839	358	3	s	s	PART
ejpam-3839	358	4	ext	ext	NOUN
ejpam-3839	358	5	=	=	PUNCT
ejpam-3839	358	6	∞∑	∞∑	NUM
ejpam-3839	358	7	n=0	n=0	NUM
ejpam-3839	358	8	h(s	h(	NOUN
ejpam-3839	358	9	)	)	PUNCT
ejpam-3839	358	10	n	n	CCONJ
ejpam-3839	358	11	(	(	PUNCT
ejpam-3839	358	12	x;λ	x;λ	NUM
ejpam-3839	358	13	)	)	PUNCT
ejpam-3839	358	14	tn	tn	PROPN
ejpam-3839	358	15	n	n	PROPN
ejpam-3839	358	16	!	!	PROPN
ejpam-3839	358	17	are	be	AUX
ejpam-3839	358	18	the	the	DET
ejpam-3839	358	19	frobenius	frobenius	NOUN
ejpam-3839	358	20	-	-	PUNCT
ejpam-3839	358	21	euler	euler	NOUN
ejpam-3839	358	22	polynomials	polynomial	NOUN
ejpam-3839	358	23	(	(	PUNCT
ejpam-3839	358	24	see	see	VERB
ejpam-3839	358	25	[	[	X
ejpam-3839	358	26	2	2	NUM
ejpam-3839	358	27	]	]	NUM
ejpam-3839	358	28	)	)	PUNCT
ejpam-3839	358	29	.	.	PUNCT
ejpam-3839	359	1	proof	proof	NOUN
ejpam-3839	359	2	.	.	PUNCT
ejpam-3839	360	1	we	we	PRON
ejpam-3839	360	2	express	express	VERB
ejpam-3839	360	3	(	(	PUNCT
ejpam-3839	360	4	5	5	NUM
ejpam-3839	360	5	)	)	PUNCT
ejpam-3839	360	6	as	as	ADP
ejpam-3839	360	7	∞∑	∞∑	NUM
ejpam-3839	360	8	n=0	n=0	NUM
ejpam-3839	360	9	tm	tm	NOUN
ejpam-3839	360	10	,	,	PUNCT
ejpam-3839	360	11	n(x	n(x	PROPN
ejpam-3839	360	12	)	)	PUNCT
ejpam-3839	360	13	tn	tn	NOUN
ejpam-3839	360	14	n	n	NOUN
ejpam-3839	360	15	!	!	PUNCT
ejpam-3839	360	16	=	=	PUNCT
ejpam-3839	361	1	(	(	PUNCT
ejpam-3839	361	2	1−	1−	NUM
ejpam-3839	361	3	λ	λ	X
ejpam-3839	361	4	et	et	NOUN
ejpam-3839	361	5	−	−	PROPN
ejpam-3839	361	6	λ	λ	NOUN
ejpam-3839	361	7	)	)	PUNCT
ejpam-3839	361	8	r	r	NOUN
ejpam-3839	361	9	ext	ext	NOUN
ejpam-3839	361	10	(	(	PUNCT
ejpam-3839	361	11	et	et	NOUN
ejpam-3839	361	12	−	−	PROPN
ejpam-3839	361	13	λ	λ	PROPN
ejpam-3839	361	14	1−	1−	NUM
ejpam-3839	361	15	λ	λ	NOUN
ejpam-3839	361	16	)	)	PUNCT
ejpam-3839	361	17	2	2	NUM
ejpam-3839	361	18	tm	tm	PROPN
ejpam-3839	361	19	m	m	PROPN
ejpam-3839	361	20	!	!	PUNCT
ejpam-3839	362	1	e2	e2	PROPN
ejpam-3839	362	2	t	t	PROPN
ejpam-3839	362	3	+	+	CCONJ
ejpam-3839	362	4	1−	1−	NUM
ejpam-3839	362	5	∑m−1	∑m−1	NOUN
ejpam-3839	362	6	j=0	j=0	VERB
ejpam-3839	362	7	2j	2j	NUM
ejpam-3839	362	8	t	t	PROPN
ejpam-3839	362	9	j	j	PROPN
ejpam-3839	362	10	j	j	PROPN
ejpam-3839	362	11	!	!	PUNCT
ejpam-3839	363	1	=	=	SYM
ejpam-3839	363	2	1	1	NUM
ejpam-3839	363	3	(	(	PUNCT
ejpam-3839	363	4	1−	1−	NUM
ejpam-3839	363	5	λ)r	λ)r	PUNCT
ejpam-3839	363	6	(	(	PUNCT
ejpam-3839	363	7	∞∑	∞∑	NUM
ejpam-3839	363	8	n=0	n=0	NUM
ejpam-3839	363	9	h(r	h(r	NOUN
ejpam-3839	363	10	)	)	PUNCT
ejpam-3839	363	11	n	n	CCONJ
ejpam-3839	363	12	(	(	PUNCT
ejpam-3839	363	13	x|λ	x|λ	X
ejpam-3839	363	14	)	)	PUNCT
ejpam-3839	363	15	tn	tn	PROPN
ejpam-3839	363	16	n	n	PROPN
ejpam-3839	363	17	!	!	PUNCT
ejpam-3839	363	18	)	)	PUNCT
ejpam-3839	364	1			PROPN
ejpam-3839	364	2	r∑	r∑	NOUN
ejpam-3839	364	3	j=0	j=0	PROPN
ejpam-3839	364	4	(	(	PUNCT
ejpam-3839	364	5	r	r	NOUN
ejpam-3839	364	6	j	j	PROPN
ejpam-3839	364	7	)	)	PUNCT
ejpam-3839	364	8	(	(	PUNCT
ejpam-3839	364	9	−λ)r−j	−λ)r−j	NOUN
ejpam-3839	364	10			PROPN
ejpam-3839	364	11	2	2	NUM
ejpam-3839	364	12	tm	tm	PRON
ejpam-3839	364	13	m!e	m!e	PROPN
ejpam-3839	364	14	jt	jt	PROPN
ejpam-3839	364	15	e2	e2	PROPN
ejpam-3839	364	16	t	t	PROPN
ejpam-3839	364	17	+	+	CCONJ
ejpam-3839	364	18	1−	1−	NUM
ejpam-3839	364	19	∑m−1	∑m−1	NOUN
ejpam-3839	364	20	j=0	j=0	VERB
ejpam-3839	364	21	2j	2j	NUM
ejpam-3839	364	22	t	t	PROPN
ejpam-3839	364	23	j	j	PROPN
ejpam-3839	364	24	j	j	PROPN
ejpam-3839	364	25	!	!	PUNCT
ejpam-3839	365	1	=	=	SYM
ejpam-3839	365	2	1	1	NUM
ejpam-3839	365	3	(	(	PUNCT
ejpam-3839	365	4	1−	1−	NUM
ejpam-3839	365	5	λ)r	λ)r	X
ejpam-3839	365	6	r∑	r∑	X
ejpam-3839	365	7	j=0	j=0	PROPN
ejpam-3839	365	8	(	(	PUNCT
ejpam-3839	365	9	r	r	NOUN
ejpam-3839	365	10	j	j	PROPN
ejpam-3839	365	11	)	)	PUNCT
ejpam-3839	365	12	(	(	PUNCT
ejpam-3839	365	13	−λ)r−j	−λ)r−j	NOUN
ejpam-3839	365	14	(	(	PUNCT
ejpam-3839	365	15	∞∑	∞∑	NUM
ejpam-3839	365	16	n=0	n=0	NUM
ejpam-3839	365	17	h(r	h(r	NOUN
ejpam-3839	365	18	)	)	PUNCT
ejpam-3839	365	19	n	n	CCONJ
ejpam-3839	365	20	(	(	PUNCT
ejpam-3839	365	21	x|λ	x|λ	X
ejpam-3839	365	22	)	)	PUNCT
ejpam-3839	365	23	tn	tn	PROPN
ejpam-3839	365	24	n	n	PROPN
ejpam-3839	365	25	!	!	PUNCT
ejpam-3839	365	26	)	)	PUNCT
ejpam-3839	366	1	(	(	PUNCT
ejpam-3839	366	2	∞∑	∞∑	NUM
ejpam-3839	366	3	n=0	n=0	PUNCT
ejpam-3839	366	4	tm	tm	NOUN
ejpam-3839	366	5	,	,	PUNCT
ejpam-3839	366	6	n(j	n(j	PROPN
ejpam-3839	366	7	)	)	PUNCT
ejpam-3839	366	8	tn	tn	PROPN
ejpam-3839	366	9	n	n	PROPN
ejpam-3839	366	10	!	!	PUNCT
ejpam-3839	366	11	)	)	PUNCT
ejpam-3839	367	1	=	=	SYM
ejpam-3839	367	2	1	1	NUM
ejpam-3839	367	3	(	(	PUNCT
ejpam-3839	367	4	1−	1−	NUM
ejpam-3839	367	5	λ)r	λ)r	X
ejpam-3839	367	6	r∑	r∑	X
ejpam-3839	367	7	j=0	j=0	PROPN
ejpam-3839	367	8	(	(	PUNCT
ejpam-3839	367	9	r	r	NOUN
ejpam-3839	367	10	j	j	PROPN
ejpam-3839	367	11	)	)	PUNCT
ejpam-3839	367	12	(	(	PUNCT
ejpam-3839	367	13	−λ)r−j	−λ)r−j	VERB
ejpam-3839	368	1	∞∑	∞∑	NOUN
ejpam-3839	368	2	n=0	n=0	NUM
ejpam-3839	368	3	(	(	PUNCT
ejpam-3839	368	4	n∑	n∑	NOUN
ejpam-3839	368	5	k=0	k=0	PROPN
ejpam-3839	368	6	(	(	PUNCT
ejpam-3839	368	7	n	n	X
ejpam-3839	368	8	k	k	NOUN
ejpam-3839	368	9	)	)	PUNCT
ejpam-3839	368	10	h	h	NOUN
ejpam-3839	368	11	(	(	PUNCT
ejpam-3839	368	12	r	r	NOUN
ejpam-3839	368	13	)	)	PUNCT
ejpam-3839	368	14	k	k	NOUN
ejpam-3839	368	15	(	(	PUNCT
ejpam-3839	368	16	x|λ)tm	x|λ)tm	PROPN
ejpam-3839	368	17	,	,	PUNCT
ejpam-3839	368	18	n−k(j	n−k(j	NOUN
ejpam-3839	368	19	)	)	PUNCT
ejpam-3839	368	20	)	)	PUNCT
ejpam-3839	368	21	tn	tn	PROPN
ejpam-3839	368	22	n	n	CCONJ
ejpam-3839	368	23	!	!	PUNCT
ejpam-3839	368	24	=	=	NOUN
ejpam-3839	369	1	∞∑	∞∑	PRON
ejpam-3839	369	2	n=0	n=0	PUNCT
ejpam-3839	369	3			PROPN
ejpam-3839	369	4	n∑	n∑	NOUN
ejpam-3839	369	5	k=0	k=0	PROPN
ejpam-3839	369	6	(	(	PUNCT
ejpam-3839	369	7	n	n	X
ejpam-3839	369	8	k	k	NOUN
ejpam-3839	369	9	)	)	PUNCT
ejpam-3839	369	10	(	(	PUNCT
ejpam-3839	369	11	1−	1−	NUM
ejpam-3839	369	12	λ)r	λ)r	X
ejpam-3839	369	13	r∑	r∑	X
ejpam-3839	369	14	j=0	j=0	PROPN
ejpam-3839	369	15	(	(	PUNCT
ejpam-3839	369	16	r	r	NOUN
ejpam-3839	369	17	j	j	PROPN
ejpam-3839	369	18	)	)	PUNCT
ejpam-3839	369	19	(	(	PUNCT
ejpam-3839	369	20	−λ)r−jtm	−λ)r−jtm	PROPN
ejpam-3839	369	21	,	,	PUNCT
ejpam-3839	369	22	n−k(j)h	n−k(j)h	PROPN
ejpam-3839	369	23	(	(	PUNCT
ejpam-3839	369	24	r	r	NOUN
ejpam-3839	369	25	)	)	PUNCT
ejpam-3839	369	26	k	k	NOUN
ejpam-3839	369	27	(	(	PUNCT
ejpam-3839	369	28	x|λ	x|λ	ADV
ejpam-3839	369	29	)	)	PUNCT
ejpam-3839	369	30			PROPN
ejpam-3839	369	31	tn	tn	PROPN
ejpam-3839	369	32	n	n	CCONJ
ejpam-3839	369	33	!	!	PUNCT
ejpam-3839	369	34	.	.	PUNCT
ejpam-3839	370	1	comparing	compare	VERB
ejpam-3839	370	2	the	the	DET
ejpam-3839	370	3	coefficients	coefficient	NOUN
ejpam-3839	370	4	of	of	ADP
ejpam-3839	370	5	tn	tn	NOUN
ejpam-3839	370	6	n	n	ADP
ejpam-3839	370	7	!	!	PROPN
ejpam-3839	370	8	completes	complete	VERB
ejpam-3839	370	9	the	the	DET
ejpam-3839	370	10	proof	proof	NOUN
ejpam-3839	370	11	.	.	PUNCT
ejpam-3839	371	1	references	reference	NOUN
ejpam-3839	371	2	[	[	X
ejpam-3839	371	3	1	1	NUM
ejpam-3839	371	4	]	]	X
ejpam-3839	371	5	r	r	NOUN
ejpam-3839	371	6	p	p	NOUN
ejpam-3839	371	7	agarawal	agarawal	NOUN
ejpam-3839	371	8	,	,	PUNCT
ejpam-3839	371	9	j	j	PROPN
ejpam-3839	371	10	y	y	PROPN
ejpam-3839	371	11	kang	kang	PROPN
ejpam-3839	371	12	,	,	PUNCT
ejpam-3839	371	13	and	and	CCONJ
ejpam-3839	371	14	c	c	NOUN
ejpam-3839	371	15	s	s	NOUN
ejpam-3839	371	16	ryoo	ryoo	NOUN
ejpam-3839	371	17	.	.	PUNCT
ejpam-3839	372	1	some	some	DET
ejpam-3839	372	2	properties	property	NOUN
ejpam-3839	372	3	of	of	ADP
ejpam-3839	372	4	(	(	PUNCT
ejpam-3839	372	5	p	p	X
ejpam-3839	372	6	,	,	PUNCT
ejpam-3839	372	7	q)-tangent	q)-tangent	ADJ
ejpam-3839	372	8	polynomials	polynomial	NOUN
ejpam-3839	372	9	.	.	PUNCT
ejpam-3839	373	1	j.	j.	PROPN
ejpam-3839	373	2	comp	comp	PROPN
ejpam-3839	373	3	.	.	PUNCT
ejpam-3839	374	1	anal	anal	PROPN
ejpam-3839	374	2	.	.	PUNCT
ejpam-3839	375	1	appl	appl	PROPN
ejpam-3839	375	2	.	.	PROPN
ejpam-3839	375	3	,	,	PUNCT
ejpam-3839	375	4	24(8):1439–1454	24(8):1439–1454	NUM
ejpam-3839	375	5	,	,	PUNCT
ejpam-3839	375	6	2018	2018	NUM
ejpam-3839	375	7	.	.	PUNCT
ejpam-3839	376	1	[	[	X
ejpam-3839	376	2	2	2	NUM
ejpam-3839	376	3	]	]	X
ejpam-3839	376	4	s	s	PART
ejpam-3839	376	5	araci	araci	NOUN
ejpam-3839	376	6	and	and	CCONJ
ejpam-3839	376	7	m	m	VERB
ejpam-3839	376	8	acikgoz	acikgoz	ADJ
ejpam-3839	376	9	.	.	PUNCT
ejpam-3839	377	1	a	a	DET
ejpam-3839	377	2	note	note	NOUN
ejpam-3839	377	3	on	on	ADP
ejpam-3839	377	4	the	the	DET
ejpam-3839	377	5	frobenius	frobenius	NOUN
ejpam-3839	377	6	-	-	PUNCT
ejpam-3839	377	7	euler	euler	NOUN
ejpam-3839	377	8	numbers	number	NOUN
ejpam-3839	377	9	and	and	CCONJ
ejpam-3839	377	10	polynomials	polynomial	NOUN
ejpam-3839	377	11	associated	associate	VERB
ejpam-3839	377	12	with	with	ADP
ejpam-3839	377	13	bernstein	bernstein	PROPN
ejpam-3839	377	14	polynomials	polynomials	PROPN
ejpam-3839	377	15	.	.	PUNCT
ejpam-3839	378	1	adv	adv	PROPN
ejpam-3839	378	2	.	.	PUNCT
ejpam-3839	378	3	stud	stud	PROPN
ejpam-3839	378	4	.	.	PUNCT
ejpam-3839	379	1	contemp	contemp	NOUN
ejpam-3839	379	2	.	.	PUNCT
ejpam-3839	380	1	math	math	NOUN
ejpam-3839	380	2	.	.	PUNCT
ejpam-3839	380	3	,	,	PUNCT
ejpam-3839	380	4	22(3):399–406	22(3):399–406	NUM
ejpam-3839	380	5	,	,	PUNCT
ejpam-3839	380	6	2012	2012	NUM
ejpam-3839	380	7	.	.	PUNCT
ejpam-3839	381	1	[	[	X
ejpam-3839	381	2	3	3	NUM
ejpam-3839	381	3	]	]	X
ejpam-3839	381	4	l	l	NOUN
ejpam-3839	381	5	comtet	comtet	NOUN
ejpam-3839	381	6	.	.	PUNCT
ejpam-3839	382	1	advanced	advanced	ADJ
ejpam-3839	382	2	combinatorics	combinatoric	NOUN
ejpam-3839	382	3	.	.	PUNCT
ejpam-3839	383	1	reidel	reidel	PROPN
ejpam-3839	383	2	publishing	publishing	PROPN
ejpam-3839	383	3	company	company	NOUN
ejpam-3839	383	4	,	,	PUNCT
ejpam-3839	383	5	1974	1974	NUM
ejpam-3839	383	6	.	.	PUNCT
ejpam-3839	384	1	[	[	X
ejpam-3839	384	2	4	4	X
ejpam-3839	384	3	]	]	X
ejpam-3839	384	4	g	g	NOUN
ejpam-3839	384	5	dattoli	dattoli	NOUN
ejpam-3839	384	6	,	,	PUNCT
ejpam-3839	384	7	c	c	PROPN
ejpam-3839	384	8	cesarano	cesarano	ADV
ejpam-3839	384	9	,	,	PUNCT
ejpam-3839	384	10	and	and	CCONJ
ejpam-3839	384	11	d	d	PRON
ejpam-3839	384	12	sacchetti	sacchetti	VERB
ejpam-3839	384	13	.	.	PUNCT
ejpam-3839	385	1	a	a	DET
ejpam-3839	385	2	note	note	NOUN
ejpam-3839	385	3	on	on	ADP
ejpam-3839	385	4	truncated	truncated	ADJ
ejpam-3839	385	5	polynomials	polynomial	NOUN
ejpam-3839	385	6	.	.	PUNCT
ejpam-3839	386	1	appl	appl	PROPN
ejpam-3839	386	2	.	.	PROPN
ejpam-3839	386	3	math	math	PROPN
ejpam-3839	386	4	.	.	PUNCT
ejpam-3839	387	1	comput	comput	NOUN
ejpam-3839	387	2	.	.	PUNCT
ejpam-3839	387	3	,	,	PUNCT
ejpam-3839	387	4	134:595–605	134:595–605	NUM
ejpam-3839	387	5	,	,	PUNCT
ejpam-3839	387	6	2003	2003	NUM
ejpam-3839	387	7	.	.	PUNCT
ejpam-3839	388	1	[	[	X
ejpam-3839	388	2	5	5	NUM
ejpam-3839	388	3	]	]	SYM
ejpam-3839	388	4	u	u	PROPN
ejpam-3839	388	5	duran	duran	NOUN
ejpam-3839	388	6	and	and	CCONJ
ejpam-3839	388	7	m	m	VERB
ejpam-3839	388	8	acikgoz	acikgoz	ADJ
ejpam-3839	388	9	.	.	PUNCT
ejpam-3839	389	1	truncated	truncate	VERB
ejpam-3839	389	2	fubini	fubini	ADJ
ejpam-3839	389	3	polynomials	polynomial	NOUN
ejpam-3839	389	4	.	.	PUNCT
ejpam-3839	390	1	mathematics	mathematic	NOUN
ejpam-3839	390	2	,	,	PUNCT
ejpam-3839	390	3	7,431	7,431	NUM
ejpam-3839	390	4	,	,	PUNCT
ejpam-3839	390	5	2019	2019	NUM
ejpam-3839	390	6	.	.	PUNCT
ejpam-3839	391	1	references	reference	NOUN
ejpam-3839	391	2	962	962	NUM
ejpam-3839	392	1	[	[	X
ejpam-3839	392	2	6	6	NUM
ejpam-3839	392	3	]	]	SYM
ejpam-3839	392	4	u	u	PROPN
ejpam-3839	392	5	duran	duran	NOUN
ejpam-3839	392	6	and	and	CCONJ
ejpam-3839	392	7	m	m	VERB
ejpam-3839	392	8	acikgoz	acikgoz	ADJ
ejpam-3839	392	9	.	.	PUNCT
ejpam-3839	393	1	on	on	ADP
ejpam-3839	393	2	degenerate	degenerate	ADJ
ejpam-3839	393	3	truncated	truncate	VERB
ejpam-3839	393	4	special	special	ADJ
ejpam-3839	393	5	polynomials	polynomial	NOUN
ejpam-3839	393	6	.	.	PUNCT
ejpam-3839	394	1	mathematics	mathematic	NOUN
ejpam-3839	394	2	,	,	PUNCT
ejpam-3839	394	3	8(1):144	8(1):144	NUM
ejpam-3839	394	4	,	,	PUNCT
ejpam-3839	394	5	2020	2020	NUM
ejpam-3839	394	6	.	.	PUNCT
ejpam-3839	395	1	[	[	X
ejpam-3839	395	2	7	7	NUM
ejpam-3839	395	3	]	]	SYM
ejpam-3839	395	4	r	r	NOUN
ejpam-3839	395	5	l	l	NOUN
ejpam-3839	395	6	graham	graham	PROPN
ejpam-3839	395	7	,	,	PUNCT
ejpam-3839	395	8	d	d	PROPN
ejpam-3839	395	9	e	e	PROPN
ejpam-3839	395	10	knuth	knuth	PROPN
ejpam-3839	395	11	,	,	PUNCT
ejpam-3839	395	12	and	and	CCONJ
ejpam-3839	395	13	o	o	X
ejpam-3839	395	14	patashnik	patashnik	X
ejpam-3839	395	15	.	.	PUNCT
ejpam-3839	396	1	concrete	concrete	ADJ
ejpam-3839	396	2	mathematics	mathematic	NOUN
ejpam-3839	396	3	.	.	PUNCT
ejpam-3839	397	1	addison	addison	PROPN
ejpam-3839	397	2	-	-	PUNCT
ejpam-3839	397	3	wesley	wesley	PROPN
ejpam-3839	397	4	publ	publ	PROPN
ejpam-3839	397	5	.	.	PUNCT
ejpam-3839	398	1	co.	co.	PROPN
ejpam-3839	398	2	,	,	PUNCT
ejpam-3839	398	3	new	new	PROPN
ejpam-3839	398	4	york	york	PROPN
ejpam-3839	398	5	,	,	PUNCT
ejpam-3839	398	6	1994	1994	NUM
ejpam-3839	398	7	.	.	PUNCT
ejpam-3839	399	1	[	[	X
ejpam-3839	399	2	8	8	NUM
ejpam-3839	399	3	]	]	PUNCT
ejpam-3839	399	4	a	a	DET
ejpam-3839	399	5	hassen	hassen	NOUN
ejpam-3839	399	6	and	and	CCONJ
ejpam-3839	399	7	h	h	NOUN
ejpam-3839	399	8	d	d	NOUN
ejpam-3839	399	9	nguyen	nguyen	NOUN
ejpam-3839	399	10	.	.	PUNCT
ejpam-3839	400	1	hypergeometric	hypergeometric	ADJ
ejpam-3839	400	2	bernoulli	bernoulli	NOUN
ejpam-3839	400	3	polynomials	polynomial	NOUN
ejpam-3839	400	4	and	and	CCONJ
ejpam-3839	400	5	appell	appell	ADJ
ejpam-3839	400	6	sequences	sequence	NOUN
ejpam-3839	400	7	.	.	PUNCT
ejpam-3839	401	1	int	int	NOUN
ejpam-3839	401	2	.	.	PUNCT
ejpam-3839	402	1	j.	j.	PROPN
ejpam-3839	402	2	number	number	PROPN
ejpam-3839	402	3	theory	theory	NOUN
ejpam-3839	402	4	,	,	PUNCT
ejpam-3839	402	5	4:767–774	4:767–774	NOUN
ejpam-3839	402	6	,	,	PUNCT
ejpam-3839	402	7	2008	2008	NUM
ejpam-3839	402	8	.	.	PUNCT
ejpam-3839	403	1	[	[	X
ejpam-3839	403	2	9	9	NUM
ejpam-3839	403	3	]	]	PUNCT
ejpam-3839	403	4	a	a	DET
ejpam-3839	403	5	hassen	hassen	NOUN
ejpam-3839	403	6	and	and	CCONJ
ejpam-3839	403	7	h	h	NOUN
ejpam-3839	403	8	d	d	NOUN
ejpam-3839	403	9	nguyen	nguyen	NOUN
ejpam-3839	403	10	.	.	PUNCT
ejpam-3839	404	1	hypergeometric	hypergeometric	ADJ
ejpam-3839	404	2	zeta	zeta	NOUN
ejpam-3839	404	3	functions	function	NOUN
ejpam-3839	404	4	.	.	PUNCT
ejpam-3839	405	1	int	int	NOUN
ejpam-3839	405	2	.	.	PUNCT
ejpam-3839	406	1	j.	j.	PROPN
ejpam-3839	406	2	number	number	PROPN
ejpam-3839	406	3	theory	theory	NOUN
ejpam-3839	406	4	,	,	PUNCT
ejpam-3839	406	5	6:99–126	6:99–126	NUM
ejpam-3839	406	6	,	,	PUNCT
ejpam-3839	406	7	2010	2010	NUM
ejpam-3839	406	8	.	.	PUNCT
ejpam-3839	407	1	[	[	X
ejpam-3839	407	2	10	10	NUM
ejpam-3839	407	3	]	]	X
ejpam-3839	407	4	f	f	PROPN
ejpam-3839	407	5	t	t	PROPN
ejpam-3839	407	6	howard	howard	PROPN
ejpam-3839	407	7	.	.	PUNCT
ejpam-3839	408	1	some	some	DET
ejpam-3839	408	2	sequences	sequence	NOUN
ejpam-3839	408	3	of	of	ADP
ejpam-3839	408	4	rational	rational	ADJ
ejpam-3839	408	5	numbers	number	NOUN
ejpam-3839	408	6	related	relate	VERB
ejpam-3839	408	7	to	to	ADP
ejpam-3839	408	8	the	the	DET
ejpam-3839	408	9	exponential	exponential	ADJ
ejpam-3839	408	10	function	function	NOUN
ejpam-3839	408	11	.	.	PUNCT
ejpam-3839	409	1	duke	duke	PROPN
ejpam-3839	409	2	math	math	PROPN
ejpam-3839	409	3	.	.	PUNCT
ejpam-3839	410	1	j.	j.	PROPN
ejpam-3839	410	2	,	,	PUNCT
ejpam-3839	410	3	34:701–716	34:701–716	PROPN
ejpam-3839	410	4	,	,	PUNCT
ejpam-3839	410	5	1967	1967	NUM
ejpam-3839	410	6	.	.	PUNCT
ejpam-3839	411	1	[	[	X
ejpam-3839	411	2	11	11	NUM
ejpam-3839	411	3	]	]	X
ejpam-3839	411	4	k	k	PROPN
ejpam-3839	411	5	kamano	kamano	NOUN
ejpam-3839	411	6	.	.	PUNCT
ejpam-3839	412	1	sums	sum	NOUN
ejpam-3839	412	2	of	of	ADP
ejpam-3839	412	3	products	product	NOUN
ejpam-3839	412	4	of	of	ADP
ejpam-3839	412	5	hypergeometric	hypergeometric	ADJ
ejpam-3839	412	6	bernoulli	bernoulli	NOUN
ejpam-3839	412	7	numbers	number	NOUN
ejpam-3839	412	8	.	.	PUNCT
ejpam-3839	413	1	int	int	NOUN
ejpam-3839	413	2	.	.	PUNCT
ejpam-3839	414	1	j.	j.	PROPN
ejpam-3839	414	2	number	number	PROPN
ejpam-3839	414	3	theory	theory	NOUN
ejpam-3839	414	4	,	,	PUNCT
ejpam-3839	414	5	130:2259–2271	130:2259–2271	NUM
ejpam-3839	414	6	,	,	PUNCT
ejpam-3839	414	7	2010	2010	NUM
ejpam-3839	414	8	.	.	PUNCT
ejpam-3839	415	1	[	[	X
ejpam-3839	415	2	12	12	NUM
ejpam-3839	415	3	]	]	X
ejpam-3839	415	4	s	s	PART
ejpam-3839	415	5	khan	khan	PROPN
ejpam-3839	415	6	,	,	PUNCT
ejpam-3839	415	7	g	g	PROPN
ejpam-3839	415	8	yasmin	yasmin	PROPN
ejpam-3839	415	9	,	,	PUNCT
ejpam-3839	415	10	and	and	CCONJ
ejpam-3839	415	11	m	m	PROPN
ejpam-3839	415	12	ahmad	ahmad	PROPN
ejpam-3839	415	13	.	.	PUNCT
ejpam-3839	416	1	a	a	DET
ejpam-3839	416	2	note	note	NOUN
ejpam-3839	416	3	on	on	ADP
ejpam-3839	416	4	truncated	truncated	ADJ
ejpam-3839	416	5	exponential	exponential	NOUN
ejpam-3839	416	6	-	-	PUNCT
ejpam-3839	416	7	based	base	VERB
ejpam-3839	416	8	appell	appell	NOUN
ejpam-3839	416	9	polynomials	polynomial	NOUN
ejpam-3839	416	10	.	.	PUNCT
ejpam-3839	417	1	bull	bull	NOUN
ejpam-3839	417	2	.	.	PUNCT
ejpam-3839	418	1	malays	malays	PROPN
ejpam-3839	418	2	.	.	PUNCT
ejpam-3839	419	1	math	math	NOUN
ejpam-3839	419	2	.	.	PUNCT
ejpam-3839	420	1	sci	sci	PROPN
ejpam-3839	420	2	.	.	PROPN
ejpam-3839	420	3	soc	soc	PROPN
ejpam-3839	420	4	.	.	PUNCT
ejpam-3839	420	5	,	,	PUNCT
ejpam-3839	420	6	40:373–388	40:373–388	PROPN
ejpam-3839	420	7	,	,	PUNCT
ejpam-3839	420	8	2017	2017	NUM
ejpam-3839	420	9	.	.	PUNCT
ejpam-3839	421	1	[	[	X
ejpam-3839	421	2	13	13	NUM
ejpam-3839	421	3	]	]	PUNCT
ejpam-3839	421	4	t	t	PROPN
ejpam-3839	421	5	komatsu	komatsu	NOUN
ejpam-3839	421	6	.	.	PUNCT
ejpam-3839	422	1	hypergeometric	hypergeometric	ADJ
ejpam-3839	422	2	cauchy	cauchy	ADJ
ejpam-3839	422	3	numbers	number	NOUN
ejpam-3839	422	4	.	.	PUNCT
ejpam-3839	423	1	int	int	NOUN
ejpam-3839	423	2	.	.	PUNCT
ejpam-3839	424	1	j.	j.	PROPN
ejpam-3839	424	2	number	number	PROPN
ejpam-3839	424	3	theory	theory	NOUN
ejpam-3839	424	4	,	,	PUNCT
ejpam-3839	424	5	9:545–560	9:545–560	PROPN
ejpam-3839	424	6	,	,	PUNCT
ejpam-3839	424	7	2013	2013	NUM
ejpam-3839	424	8	.	.	PUNCT
ejpam-3839	425	1	[	[	X
ejpam-3839	425	2	14	14	NUM
ejpam-3839	425	3	]	]	PUNCT
ejpam-3839	425	4	t	t	PROPN
ejpam-3839	425	5	komatsu	komatsu	PROPN
ejpam-3839	425	6	.	.	PUNCT
ejpam-3839	426	1	truncated	truncate	VERB
ejpam-3839	426	2	bernoulli	bernoulli	PROPN
ejpam-3839	426	3	-	-	PUNCT
ejpam-3839	426	4	carlitz	carlitz	PROPN
ejpam-3839	426	5	and	and	CCONJ
ejpam-3839	426	6	truncated	truncated	ADJ
ejpam-3839	426	7	cauchy	cauchy	PROPN
ejpam-3839	426	8	-	-	PUNCT
ejpam-3839	426	9	carlitz	carlitz	PROPN
ejpam-3839	426	10	numbers	number	NOUN
ejpam-3839	426	11	.	.	PUNCT
ejpam-3839	427	1	tokyo	tokyo	PROPN
ejpam-3839	427	2	j.	j.	PROPN
ejpam-3839	427	3	math	math	PROPN
ejpam-3839	427	4	.	.	PUNCT
ejpam-3839	427	5	,	,	PUNCT
ejpam-3839	427	6	41:541–556	41:541–556	PROPN
ejpam-3839	427	7	,	,	PUNCT
ejpam-3839	427	8	2018	2018	NUM
ejpam-3839	427	9	.	.	PUNCT
ejpam-3839	428	1	[	[	X
ejpam-3839	428	2	15	15	NUM
ejpam-3839	428	3	]	]	X
ejpam-3839	428	4	t	t	PROPN
ejpam-3839	428	5	komatsu	komatsu	PROPN
ejpam-3839	428	6	and	and	CCONJ
ejpam-3839	428	7	c	c	PROPN
ejpam-3839	428	8	pita	pita	NOUN
ejpam-3839	428	9	-	-	PUNCT
ejpam-3839	428	10	ruiz	ruiz	NOUN
ejpam-3839	428	11	.	.	PUNCT
ejpam-3839	429	1	truncated	truncate	VERB
ejpam-3839	429	2	euler	euler	NOUN
ejpam-3839	429	3	polynomials	polynomial	NOUN
ejpam-3839	429	4	.	.	PUNCT
ejpam-3839	430	1	mathematica	mathematica	PROPN
ejpam-3839	430	2	slovaca	slovaca	PROPN
ejpam-3839	430	3	,	,	PUNCT
ejpam-3839	430	4	68(3):527–536	68(3):527–536	NUM
ejpam-3839	430	5	,	,	PUNCT
ejpam-3839	430	6	2018	2018	NUM
ejpam-3839	430	7	.	.	PUNCT
ejpam-3839	431	1	[	[	X
ejpam-3839	431	2	16	16	NUM
ejpam-3839	431	3	]	]	PUNCT
ejpam-3839	431	4	t	t	PROPN
ejpam-3839	431	5	komatsu	komatsu	PROPN
ejpam-3839	431	6	and	and	CCONJ
ejpam-3839	431	7	w	w	PROPN
ejpam-3839	431	8	zhang	zhang	PROPN
ejpam-3839	431	9	.	.	PUNCT
ejpam-3839	432	1	several	several	ADJ
ejpam-3839	432	2	expressions	expression	NOUN
ejpam-3839	432	3	of	of	ADP
ejpam-3839	432	4	truncated	truncated	ADJ
ejpam-3839	432	5	bernoulli	bernoulli	PROPN
ejpam-3839	432	6	-	-	PUNCT
ejpam-3839	432	7	carlitz	carlitz	PROPN
ejpam-3839	432	8	and	and	CCONJ
ejpam-3839	432	9	truncated	truncated	ADJ
ejpam-3839	432	10	cauchy	cauchy	PROPN
ejpam-3839	432	11	-	-	PUNCT
ejpam-3839	432	12	carlitz	carlitz	NOUN
ejpam-3839	432	13	numbers	number	NOUN
ejpam-3839	432	14	.	.	PUNCT
ejpam-3839	433	1	aims	aim	VERB
ejpam-3839	433	2	mathematics	mathematic	NOUN
ejpam-3839	433	3	,	,	PUNCT
ejpam-3839	433	4	5(6):5939–5954	5(6):5939–5954	PROPN
ejpam-3839	433	5	,	,	PUNCT
ejpam-3839	433	6	2020	2020	NUM
ejpam-3839	433	7	.	.	PUNCT
ejpam-3839	434	1	[	[	X
ejpam-3839	434	2	17	17	NUM
ejpam-3839	434	3	]	]	X
ejpam-3839	434	4	w	w	PROPN
ejpam-3839	434	5	kumam	kumam	PROPN
ejpam-3839	434	6	,	,	PUNCT
ejpam-3839	434	7	h	h	PROPN
ejpam-3839	434	8	m	m	PROPN
ejpam-3839	434	9	srivastava	srivastava	PROPN
ejpam-3839	434	10	,	,	PUNCT
ejpam-3839	434	11	s	s	VERB
ejpam-3839	434	12	a	a	DET
ejpam-3839	434	13	wani	wani	PROPN
ejpam-3839	434	14	,	,	PUNCT
ejpam-3839	434	15	s	s	PART
ejpam-3839	434	16	araci	araci	NOUN
ejpam-3839	434	17	,	,	PUNCT
ejpam-3839	434	18	and	and	CCONJ
ejpam-3839	434	19	p	p	NOUN
ejpam-3839	434	20	kumam	kumam	NOUN
ejpam-3839	434	21	.	.	PUNCT
ejpam-3839	435	1	truncatedexponential	truncatedexponential	NOUN
ejpam-3839	435	2	-	-	PUNCT
ejpam-3839	435	3	based	base	VERB
ejpam-3839	435	4	frobenius	frobenius	NOUN
ejpam-3839	435	5	-	-	PUNCT
ejpam-3839	435	6	euler	euler	NOUN
ejpam-3839	435	7	polynomials	polynomial	NOUN
ejpam-3839	435	8	.	.	PUNCT
ejpam-3839	436	1	advances	advance	NOUN
ejpam-3839	436	2	in	in	ADP
ejpam-3839	436	3	difference	difference	NOUN
ejpam-3839	436	4	equations	equation	NOUN
ejpam-3839	436	5	,	,	PUNCT
ejpam-3839	436	6	2019(530	2019(530	NUM
ejpam-3839	436	7	)	)	PUNCT
ejpam-3839	436	8	,	,	PUNCT
ejpam-3839	436	9	2019	2019	NUM
ejpam-3839	436	10	.	.	PUNCT
ejpam-3839	437	1	[	[	X
ejpam-3839	437	2	18	18	NUM
ejpam-3839	437	3	]	]	X
ejpam-3839	437	4	q	q	X
ejpam-3839	437	5	m	m	X
ejpam-3839	437	6	luo	luo	PROPN
ejpam-3839	437	7	and	and	CCONJ
ejpam-3839	437	8	h	h	PROPN
ejpam-3839	437	9	m	m	PROPN
ejpam-3839	437	10	srivastava	srivastava	PROPN
ejpam-3839	437	11	.	.	PUNCT
ejpam-3839	438	1	some	some	DET
ejpam-3839	438	2	generalizations	generalization	NOUN
ejpam-3839	438	3	of	of	ADP
ejpam-3839	438	4	the	the	DET
ejpam-3839	438	5	apostol	apostol	NOUN
ejpam-3839	438	6	-	-	PUNCT
ejpam-3839	438	7	genocchi	genocchi	PROPN
ejpam-3839	438	8	polynomials	polynomial	NOUN
ejpam-3839	438	9	and	and	CCONJ
ejpam-3839	438	10	the	the	DET
ejpam-3839	438	11	stirling	stirling	NOUN
ejpam-3839	438	12	numbers	number	NOUN
ejpam-3839	438	13	of	of	ADP
ejpam-3839	438	14	the	the	DET
ejpam-3839	438	15	second	second	ADJ
ejpam-3839	438	16	kind	kind	NOUN
ejpam-3839	438	17	.	.	PUNCT
ejpam-3839	439	1	appl	appl	PROPN
ejpam-3839	439	2	.	.	PROPN
ejpam-3839	439	3	math	math	PROPN
ejpam-3839	439	4	.	.	PUNCT
ejpam-3839	440	1	comput	comput	NOUN
ejpam-3839	440	2	.	.	PUNCT
ejpam-3839	440	3	,	,	PUNCT
ejpam-3839	440	4	217:5702	217:5702	NUM
ejpam-3839	440	5	–	–	PUNCT
ejpam-3839	440	6	5728	5728	NUM
ejpam-3839	440	7	,	,	PUNCT
ejpam-3839	440	8	2011	2011	NUM
ejpam-3839	440	9	.	.	PUNCT
ejpam-3839	441	1	[	[	X
ejpam-3839	441	2	19	19	NUM
ejpam-3839	441	3	]	]	X
ejpam-3839	441	4	c	c	PROPN
ejpam-3839	441	5	pita	pita	NOUN
ejpam-3839	441	6	-	-	PUNCT
ejpam-3839	441	7	ruiz	ruiz	NOUN
ejpam-3839	441	8	.	.	PUNCT
ejpam-3839	442	1	carlitz	carlitz	NOUN
ejpam-3839	442	2	-	-	PUNCT
ejpam-3839	442	3	type	type	NOUN
ejpam-3839	442	4	and	and	CCONJ
ejpam-3839	442	5	other	other	ADJ
ejpam-3839	442	6	bernoulli	bernoulli	PROPN
ejpam-3839	442	7	identities	identity	NOUN
ejpam-3839	442	8	.	.	PUNCT
ejpam-3839	443	1	j.	j.	PROPN
ejpam-3839	443	2	integer	integer	PROPN
ejpam-3839	443	3	seq	seq	PROPN
ejpam-3839	443	4	.	.	PROPN
ejpam-3839	443	5	,	,	PUNCT
ejpam-3839	443	6	19	19	NUM
ejpam-3839	443	7	:	:	PUNCT
ejpam-3839	443	8	article	article	NOUN
ejpam-3839	443	9	16.1.8	16.1.8	NUM
ejpam-3839	443	10	.	.	PROPN
ejpam-3839	443	11	,	,	PUNCT
ejpam-3839	443	12	2016	2016	NUM
ejpam-3839	443	13	.	.	PUNCT
ejpam-3839	444	1	[	[	X
ejpam-3839	444	2	20	20	NUM
ejpam-3839	444	3	]	]	SYM
ejpam-3839	444	4	c	c	PROPN
ejpam-3839	444	5	s	s	NOUN
ejpam-3839	444	6	ryoo	ryoo	NOUN
ejpam-3839	444	7	.	.	PUNCT
ejpam-3839	445	1	a	a	DET
ejpam-3839	445	2	note	note	NOUN
ejpam-3839	445	3	on	on	ADP
ejpam-3839	445	4	the	the	DET
ejpam-3839	445	5	tangent	tangent	ADJ
ejpam-3839	445	6	numbers	number	NOUN
ejpam-3839	445	7	and	and	CCONJ
ejpam-3839	445	8	polynomials	polynomial	NOUN
ejpam-3839	445	9	.	.	PUNCT
ejpam-3839	446	1	adv	adv	PROPN
ejpam-3839	446	2	.	.	PUNCT
ejpam-3839	447	1	studies	study	NOUN
ejpam-3839	447	2	theor	theor	PROPN
ejpam-3839	447	3	.	.	PUNCT
ejpam-3839	448	1	phys	phy	NOUN
ejpam-3839	448	2	.	.	PUNCT
ejpam-3839	448	3	,	,	PUNCT
ejpam-3839	448	4	7(9):447–454	7(9):447–454	NUM
ejpam-3839	448	5	,	,	PUNCT
ejpam-3839	448	6	2013	2013	NUM
ejpam-3839	448	7	.	.	PUNCT
ejpam-3839	449	1	[	[	X
ejpam-3839	449	2	21	21	NUM
ejpam-3839	449	3	]	]	X
ejpam-3839	449	4	c	c	PROPN
ejpam-3839	449	5	s	s	NOUN
ejpam-3839	449	6	ryoo	ryoo	NOUN
ejpam-3839	449	7	.	.	PUNCT
ejpam-3839	450	1	a	a	DET
ejpam-3839	450	2	numerical	numerical	ADJ
ejpam-3839	450	3	investigation	investigation	NOUN
ejpam-3839	450	4	on	on	ADP
ejpam-3839	450	5	the	the	DET
ejpam-3839	450	6	zeros	zero	NOUN
ejpam-3839	450	7	of	of	ADP
ejpam-3839	450	8	the	the	DET
ejpam-3839	450	9	tangent	tangent	NOUN
ejpam-3839	450	10	polynomials	polynomial	NOUN
ejpam-3839	450	11	.	.	PUNCT
ejpam-3839	451	1	j.	j.	PROPN
ejpam-3839	451	2	app	app	PROPN
ejpam-3839	451	3	.	.	PROPN
ejpam-3839	451	4	math	math	PROPN
ejpam-3839	451	5	.	.	PUNCT
ejpam-3839	452	1	informatics	informatic	NOUN
ejpam-3839	452	2	,	,	PUNCT
ejpam-3839	452	3	3(3	3(3	NUM
ejpam-3839	452	4	-	-	SYM
ejpam-3839	452	5	4):315–322	4):315–322	NUM
ejpam-3839	452	6	,	,	PUNCT
ejpam-3839	452	7	2014	2014	NUM
ejpam-3839	452	8	.	.	PUNCT
ejpam-3839	453	1	references	reference	NOUN
ejpam-3839	453	2	963	963	NUM
ejpam-3839	454	1	[	[	X
ejpam-3839	454	2	22	22	NUM
ejpam-3839	454	3	]	]	X
ejpam-3839	454	4	c	c	PROPN
ejpam-3839	454	5	s	s	NOUN
ejpam-3839	454	6	ryoo	ryoo	NOUN
ejpam-3839	454	7	.	.	PUNCT
ejpam-3839	455	1	some	some	DET
ejpam-3839	455	2	properties	property	NOUN
ejpam-3839	455	3	of	of	ADP
ejpam-3839	455	4	two	two	NUM
ejpam-3839	455	5	dimensional	dimensional	ADJ
ejpam-3839	455	6	q	q	ADJ
ejpam-3839	455	7	-	-	PUNCT
ejpam-3839	455	8	tangent	tangent	ADJ
ejpam-3839	455	9	numbers	number	NOUN
ejpam-3839	455	10	and	and	CCONJ
ejpam-3839	455	11	polynomials	polynomial	NOUN
ejpam-3839	455	12	.	.	PUNCT
ejpam-3839	456	1	global	global	ADJ
ejpam-3839	456	2	j.	j.	PROPN
ejpam-3839	456	3	pure	pure	PROPN
ejpam-3839	456	4	appl	appl	PROPN
ejpam-3839	456	5	.	.	PUNCT
ejpam-3839	456	6	math	math	PROPN
ejpam-3839	456	7	.	.	PUNCT
ejpam-3839	456	8	,	,	PUNCT
ejpam-3839	456	9	12(4):2999–3007	12(4):2999–3007	NUM
ejpam-3839	456	10	,	,	PUNCT
ejpam-3839	456	11	2016	2016	NUM
ejpam-3839	456	12	.	.	PUNCT
ejpam-3839	457	1	[	[	X
ejpam-3839	457	2	23	23	NUM
ejpam-3839	457	3	]	]	X
ejpam-3839	457	4	c	c	PROPN
ejpam-3839	457	5	s	s	NOUN
ejpam-3839	457	6	ryoo	ryoo	NOUN
ejpam-3839	457	7	.	.	PUNCT
ejpam-3839	458	1	on	on	ADP
ejpam-3839	458	2	poly	poly	ADJ
ejpam-3839	458	3	-	-	PUNCT
ejpam-3839	458	4	tangent	tangent	NOUN
ejpam-3839	458	5	numbers	number	NOUN
ejpam-3839	458	6	and	and	CCONJ
ejpam-3839	458	7	polynomials	polynomial	NOUN
ejpam-3839	458	8	and	and	CCONJ
ejpam-3839	458	9	distribution	distribution	NOUN
ejpam-3839	458	10	of	of	ADP
ejpam-3839	458	11	their	their	PRON
ejpam-3839	458	12	zeros	zero	NOUN
ejpam-3839	458	13	.	.	PUNCT
ejpam-3839	459	1	global	global	ADJ
ejpam-3839	459	2	j.	j.	PROPN
ejpam-3839	459	3	pure	pure	PROPN
ejpam-3839	459	4	appl	appl	PROPN
ejpam-3839	459	5	.	.	PUNCT
ejpam-3839	459	6	math	math	PROPN
ejpam-3839	459	7	.	.	PUNCT
ejpam-3839	459	8	,	,	PUNCT
ejpam-3839	459	9	12(5):4411–4425	12(5):4411–4425	NUM
ejpam-3839	459	10	,	,	PUNCT
ejpam-3839	459	11	2016	2016	NUM
ejpam-3839	459	12	.	.	PUNCT
ejpam-3839	460	1	[	[	X
ejpam-3839	460	2	24	24	NUM
ejpam-3839	460	3	]	]	X
ejpam-3839	460	4	c	c	PROPN
ejpam-3839	460	5	s	s	NOUN
ejpam-3839	460	6	ryoo	ryoo	NOUN
ejpam-3839	460	7	and	and	CCONJ
ejpam-3839	460	8	r	r	NOUN
ejpam-3839	460	9	p	p	PROPN
ejpam-3839	460	10	agarwal	agarwal	PROPN
ejpam-3839	460	11	.	.	PUNCT
ejpam-3839	461	1	some	some	DET
ejpam-3839	461	2	identities	identity	NOUN
ejpam-3839	461	3	involving	involve	VERB
ejpam-3839	461	4	q	q	ADJ
ejpam-3839	461	5	-	-	PUNCT
ejpam-3839	461	6	poly	poly	ADJ
ejpam-3839	461	7	-	-	PUNCT
ejpam-3839	461	8	tangent	tangent	NOUN
ejpam-3839	461	9	numbers	number	NOUN
ejpam-3839	461	10	and	and	CCONJ
ejpam-3839	461	11	polynomials	polynomial	NOUN
ejpam-3839	461	12	and	and	CCONJ
ejpam-3839	461	13	distribution	distribution	NOUN
ejpam-3839	461	14	of	of	ADP
ejpam-3839	461	15	their	their	PRON
ejpam-3839	461	16	zeros	zero	NOUN
ejpam-3839	461	17	.	.	PUNCT
ejpam-3839	462	1	advances	advance	NOUN
ejpam-3839	462	2	in	in	ADP
ejpam-3839	462	3	difference	difference	NOUN
ejpam-3839	462	4	equations	equation	NOUN
ejpam-3839	462	5	,	,	PUNCT
ejpam-3839	462	6	2017(213	2017(213	NUM
ejpam-3839	462	7	)	)	PUNCT
ejpam-3839	462	8	,	,	PUNCT
ejpam-3839	462	9	2017	2017	NUM
ejpam-3839	462	10	.	.	PUNCT
ejpam-3839	463	1	[	[	X
ejpam-3839	463	2	25	25	NUM
ejpam-3839	463	3	]	]	X
ejpam-3839	463	4	h	h	NOUN
ejpam-3839	463	5	shin	shin	NOUN
ejpam-3839	463	6	and	and	CCONJ
ejpam-3839	463	7	j	j	PROPN
ejpam-3839	463	8	zeng	zeng	PROPN
ejpam-3839	463	9	.	.	PUNCT
ejpam-3839	464	1	the	the	DET
ejpam-3839	464	2	q	q	NOUN
ejpam-3839	464	3	-	-	PUNCT
ejpam-3839	464	4	tangent	tangent	NOUN
ejpam-3839	464	5	and	and	CCONJ
ejpam-3839	464	6	q	q	ADJ
ejpam-3839	464	7	-	-	PUNCT
ejpam-3839	464	8	secant	secant	ADJ
ejpam-3839	464	9	numbers	number	NOUN
ejpam-3839	464	10	via	via	ADP
ejpam-3839	464	11	continued	continue	VERB
ejpam-3839	464	12	fractions	fraction	NOUN
ejpam-3839	464	13	.	.	PUNCT
ejpam-3839	465	1	european	european	PROPN
ejpam-3839	465	2	j.	j.	PROPN
ejpam-3839	465	3	combin	combin	PROPN
ejpam-3839	465	4	.	.	PROPN
ejpam-3839	465	5	,	,	PUNCT
ejpam-3839	465	6	31:1689–1705	31:1689–1705	NUM
ejpam-3839	465	7	,	,	PUNCT
ejpam-3839	465	8	2010	2010	NUM
ejpam-3839	465	9	.	.	PUNCT
ejpam-3839	466	1	[	[	X
ejpam-3839	466	2	26	26	NUM
ejpam-3839	466	3	]	]	X
ejpam-3839	466	4	h	h	PROPN
ejpam-3839	466	5	m	m	PROPN
ejpam-3839	466	6	srivastava	srivastava	PROPN
ejpam-3839	466	7	,	,	PUNCT
ejpam-3839	466	8	s	s	PART
ejpam-3839	466	9	araci	araci	NOUN
ejpam-3839	466	10	,	,	PUNCT
ejpam-3839	466	11	w	w	ADP
ejpam-3839	466	12	a	a	DET
ejpam-3839	466	13	khan	khan	PROPN
ejpam-3839	466	14	,	,	PUNCT
ejpam-3839	466	15	and	and	CCONJ
ejpam-3839	466	16	m	m	AUX
ejpam-3839	466	17	acikgoz	acikgoz	ADJ
ejpam-3839	466	18	.	.	PUNCT
ejpam-3839	467	1	a	a	DET
ejpam-3839	467	2	note	note	NOUN
ejpam-3839	467	3	on	on	ADP
ejpam-3839	467	4	the	the	DET
ejpam-3839	467	5	truncatedexponential	truncatedexponential	NOUN
ejpam-3839	467	6	based	base	VERB
ejpam-3839	467	7	apostol	apostol	NOUN
ejpam-3839	467	8	-	-	PUNCT
ejpam-3839	467	9	type	type	NOUN
ejpam-3839	467	10	polynomials	polynomial	NOUN
ejpam-3839	467	11	.	.	PUNCT
ejpam-3839	468	1	symmetry	symmetry	NOUN
ejpam-3839	468	2	,	,	PUNCT
ejpam-3839	468	3	11,538	11,538	NUM
ejpam-3839	468	4	,	,	PUNCT
ejpam-3839	468	5	2019	2019	NUM
ejpam-3839	468	6	.	.	PUNCT