id	sid	tid	token	lemma	pos
ejpam-4152	1	1	european	european	PROPN
ejpam-4152	1	2	journal	journal	PROPN
ejpam-4152	1	3	of	of	ADP
ejpam-4152	1	4	pure	pure	ADJ
ejpam-4152	1	5	and	and	CCONJ
ejpam-4152	1	6	applied	apply	VERB
ejpam-4152	1	7	mathematics	mathematic	NOUN
ejpam-4152	1	8	vol	vol	NOUN
ejpam-4152	1	9	.	.	PUNCT
ejpam-4152	2	1	14	14	NUM
ejpam-4152	2	2	,	,	PUNCT
ejpam-4152	2	3	no	no	INTJ
ejpam-4152	2	4	.	.	NOUN
ejpam-4152	2	5	4	4	NUM
ejpam-4152	2	6	,	,	PUNCT
ejpam-4152	2	7	2021	2021	NUM
ejpam-4152	2	8	,	,	PUNCT
ejpam-4152	2	9	1457	1457	NUM
ejpam-4152	2	10	-	-	SYM
ejpam-4152	2	11	1466	1466	NUM
ejpam-4152	2	12	issn	issn	PROPN
ejpam-4152	2	13	1307	1307	NUM
ejpam-4152	2	14	-	-	SYM
ejpam-4152	2	15	5543	5543	NUM
ejpam-4152	2	16	–	–	PUNCT
ejpam-4152	2	17	ejpam.com	ejpam.com	X
ejpam-4152	2	18	published	publish	VERB
ejpam-4152	2	19	by	by	ADP
ejpam-4152	2	20	new	new	PROPN
ejpam-4152	2	21	york	york	PROPN
ejpam-4152	2	22	business	business	PROPN
ejpam-4152	2	23	global	global	ADJ
ejpam-4152	2	24	fourier	fourier	NOUN
ejpam-4152	2	25	expansion	expansion	NOUN
ejpam-4152	2	26	,	,	PUNCT
ejpam-4152	2	27	integral	integral	ADJ
ejpam-4152	2	28	representation	representation	NOUN
ejpam-4152	2	29	and	and	CCONJ
ejpam-4152	2	30	explicit	explicit	ADJ
ejpam-4152	2	31	formula	formula	NOUN
ejpam-4152	2	32	at	at	ADP
ejpam-4152	2	33	rational	rational	ADJ
ejpam-4152	2	34	arguments	argument	NOUN
ejpam-4152	2	35	of	of	ADP
ejpam-4152	2	36	the	the	DET
ejpam-4152	2	37	tangent	tangent	ADJ
ejpam-4152	2	38	polynomials	polynomial	NOUN
ejpam-4152	2	39	of	of	ADP
ejpam-4152	2	40	higher	high	ADJ
ejpam-4152	2	41	-	-	PUNCT
ejpam-4152	2	42	order	order	NOUN
ejpam-4152	2	43	cristina	cristina	PROPN
ejpam-4152	2	44	b.	b.	PROPN
ejpam-4152	2	45	corcino1,2	corcino1,2	PROPN
ejpam-4152	2	46	,	,	PUNCT
ejpam-4152	3	1	roberto	roberto	PROPN
ejpam-4152	3	2	b.	b.	PROPN
ejpam-4152	3	3	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-4152	3	4	,	,	PUNCT
ejpam-4152	3	5	jeremar	jeremar	PROPN
ejpam-4152	3	6	s.	s.	PROPN
ejpam-4152	3	7	casquejo1	casquejo1	PROPN
ejpam-4152	4	1	1	1	NUM
ejpam-4152	4	2	research	research	NOUN
ejpam-4152	4	3	institute	institute	NOUN
ejpam-4152	4	4	for	for	ADP
ejpam-4152	4	5	computational	computational	ADJ
ejpam-4152	4	6	mathematics	mathematic	NOUN
ejpam-4152	4	7	and	and	CCONJ
ejpam-4152	4	8	physics	physics	NOUN
ejpam-4152	4	9	,	,	PUNCT
ejpam-4152	4	10	cebu	cebu	NOUN
ejpam-4152	4	11	normal	normal	ADJ
ejpam-4152	4	12	university	university	NOUN
ejpam-4152	4	13	,	,	PUNCT
ejpam-4152	4	14	6000	6000	NUM
ejpam-4152	4	15	cebu	cebu	NOUN
ejpam-4152	4	16	city	city	NOUN
ejpam-4152	4	17	,	,	PUNCT
ejpam-4152	4	18	philippines	philippine	NOUN
ejpam-4152	4	19	2	2	NUM
ejpam-4152	4	20	mathematics	mathematics	NOUN
ejpam-4152	4	21	department	department	NOUN
ejpam-4152	4	22	,	,	PUNCT
ejpam-4152	4	23	cebu	cebu	NOUN
ejpam-4152	4	24	normal	normal	ADJ
ejpam-4152	4	25	university	university	NOUN
ejpam-4152	4	26	,	,	PUNCT
ejpam-4152	4	27	6000	6000	NUM
ejpam-4152	4	28	cebu	cebu	NOUN
ejpam-4152	4	29	city	city	NOUN
ejpam-4152	4	30	,	,	PUNCT
ejpam-4152	4	31	philippines	philippine	NOUN
ejpam-4152	4	32	abstract	abstract	ADJ
ejpam-4152	4	33	.	.	PUNCT
ejpam-4152	5	1	in	in	ADP
ejpam-4152	5	2	this	this	DET
ejpam-4152	5	3	paper	paper	NOUN
ejpam-4152	5	4	,	,	PUNCT
ejpam-4152	5	5	fourier	fourier	NOUN
ejpam-4152	5	6	series	series	NOUN
ejpam-4152	5	7	expansion	expansion	NOUN
ejpam-4152	5	8	of	of	ADP
ejpam-4152	5	9	tangent	tangent	ADJ
ejpam-4152	5	10	polynomials	polynomial	NOUN
ejpam-4152	5	11	are	be	AUX
ejpam-4152	5	12	derived	derive	VERB
ejpam-4152	5	13	and	and	CCONJ
ejpam-4152	5	14	the	the	DET
ejpam-4152	5	15	integral	integral	ADJ
ejpam-4152	5	16	representation	representation	NOUN
ejpam-4152	5	17	and	and	CCONJ
ejpam-4152	5	18	explicit	explicit	ADJ
ejpam-4152	5	19	formula	formula	NOUN
ejpam-4152	5	20	at	at	ADP
ejpam-4152	5	21	rational	rational	ADJ
ejpam-4152	5	22	arguments	argument	NOUN
ejpam-4152	5	23	of	of	ADP
ejpam-4152	5	24	these	these	DET
ejpam-4152	5	25	polynomials	polynomial	NOUN
ejpam-4152	5	26	are	be	AUX
ejpam-4152	5	27	established	establish	VERB
ejpam-4152	5	28	.	.	PUNCT
ejpam-4152	6	1	2020	2020	NUM
ejpam-4152	6	2	mathematics	mathematics	PROPN
ejpam-4152	6	3	subject	subject	NOUN
ejpam-4152	6	4	classifications	classification	NOUN
ejpam-4152	6	5	:	:	PUNCT
ejpam-4152	6	6	11b68	11b68	NUM
ejpam-4152	6	7	,	,	PUNCT
ejpam-4152	6	8	42a16	42a16	NUM
ejpam-4152	6	9	,	,	PUNCT
ejpam-4152	6	10	11m35	11m35	NUM
ejpam-4152	6	11	key	key	ADJ
ejpam-4152	6	12	words	word	NOUN
ejpam-4152	6	13	and	and	CCONJ
ejpam-4152	6	14	phrases	phrase	NOUN
ejpam-4152	6	15	:	:	PUNCT
ejpam-4152	6	16	genocchi	genocchi	PROPN
ejpam-4152	6	17	polynomials	polynomial	NOUN
ejpam-4152	6	18	,	,	PUNCT
ejpam-4152	6	19	tangent	tangent	NOUN
ejpam-4152	6	20	polynomials	polynomial	NOUN
ejpam-4152	6	21	,	,	PUNCT
ejpam-4152	6	22	bernoulli	bernoulli	NOUN
ejpam-4152	6	23	polynomials	polynomial	NOUN
ejpam-4152	6	24	,	,	PUNCT
ejpam-4152	6	25	euler	euler	NOUN
ejpam-4152	6	26	polynomials	polynomial	NOUN
ejpam-4152	6	27	,	,	PUNCT
ejpam-4152	6	28	genocchi	genocchi	PROPN
ejpam-4152	6	29	polynomials	polynomial	NOUN
ejpam-4152	6	30	,	,	PUNCT
ejpam-4152	6	31	generating	generating	NOUN
ejpam-4152	6	32	functions	function	NOUN
ejpam-4152	6	33	,	,	PUNCT
ejpam-4152	6	34	fourier	fourier	NOUN
ejpam-4152	6	35	series	series	NOUN
ejpam-4152	6	36	,	,	PUNCT
ejpam-4152	6	37	integral	integral	ADJ
ejpam-4152	6	38	representation	representation	NOUN
ejpam-4152	6	39	1	1	NUM
ejpam-4152	6	40	.	.	PUNCT
ejpam-4152	6	41	introduction	introduction	NOUN
ejpam-4152	6	42	for	for	ADP
ejpam-4152	6	43	r	r	PROPN
ejpam-4152	6	44	∈	∈	PROPN
ejpam-4152	6	45	n	n	CCONJ
ejpam-4152	6	46	,	,	PUNCT
ejpam-4152	6	47	the	the	DET
ejpam-4152	6	48	higher	high	ADJ
ejpam-4152	6	49	-	-	PUNCT
ejpam-4152	6	50	order	order	NOUN
ejpam-4152	6	51	tangent	tangent	NOUN
ejpam-4152	6	52	polynomials	polynomial	NOUN
ejpam-4152	6	53	,	,	PUNCT
ejpam-4152	6	54	t	t	NOUN
ejpam-4152	6	55	r	r	NOUN
ejpam-4152	6	56	n(x	n(x	PROPN
ejpam-4152	6	57	)	)	PUNCT
ejpam-4152	6	58	(	(	PUNCT
ejpam-4152	6	59	n	n	X
ejpam-4152	6	60	≥	≥	NOUN
ejpam-4152	6	61	0	0	NUM
ejpam-4152	6	62	)	)	PUNCT
ejpam-4152	6	63	,	,	PUNCT
ejpam-4152	6	64	are	be	AUX
ejpam-4152	6	65	defined	define	VERB
ejpam-4152	6	66	by	by	ADP
ejpam-4152	6	67	the	the	DET
ejpam-4152	6	68	following	follow	VERB
ejpam-4152	6	69	generating	generating	NOUN
ejpam-4152	6	70	function	function	NOUN
ejpam-4152	6	71	(	(	PUNCT
ejpam-4152	6	72	see	see	VERB
ejpam-4152	6	73	[	[	X
ejpam-4152	6	74	1	1	NUM
ejpam-4152	6	75	]	]	NUM
ejpam-4152	6	76	)	)	PUNCT
ejpam-4152	6	77	(	(	PUNCT
ejpam-4152	6	78	2	2	NUM
ejpam-4152	6	79	e2	e2	PROPN
ejpam-4152	6	80	t	t	NOUN
ejpam-4152	6	81	+	+	NOUN
ejpam-4152	6	82	1	1	X
ejpam-4152	6	83	)	)	PUNCT
ejpam-4152	6	84	r	r	NOUN
ejpam-4152	6	85	ext	ext	NOUN
ejpam-4152	6	86	=	=	NOUN
ejpam-4152	6	87	∞∑	∞∑	NUM
ejpam-4152	6	88	n=0	n=0	NUM
ejpam-4152	6	89	t	t	NOUN
ejpam-4152	6	90	r	r	NOUN
ejpam-4152	6	91	n(x	n(x	X
ejpam-4152	6	92	)	)	PUNCT
ejpam-4152	6	93	tn	tn	NOUN
ejpam-4152	6	94	n	n	PROPN
ejpam-4152	6	95	!	!	PROPN
ejpam-4152	6	96	,	,	PUNCT
ejpam-4152	7	1	|2t|	|2t|	PROPN
ejpam-4152	7	2	<	<	X
ejpam-4152	7	3	π	π	PROPN
ejpam-4152	7	4	.	.	PUNCT
ejpam-4152	7	5	(	(	PUNCT
ejpam-4152	7	6	1	1	X
ejpam-4152	7	7	)	)	PUNCT
ejpam-4152	7	8	when	when	SCONJ
ejpam-4152	7	9	r	r	NOUN
ejpam-4152	7	10	=	=	SYM
ejpam-4152	7	11	1	1	NUM
ejpam-4152	7	12	,	,	PUNCT
ejpam-4152	7	13	the	the	DET
ejpam-4152	7	14	above	above	ADJ
ejpam-4152	7	15	equation	equation	NOUN
ejpam-4152	7	16	gives	give	VERB
ejpam-4152	7	17	the	the	DET
ejpam-4152	7	18	generating	generate	VERB
ejpam-4152	7	19	function	function	NOUN
ejpam-4152	7	20	for	for	ADP
ejpam-4152	7	21	the	the	DET
ejpam-4152	7	22	classical	classical	ADJ
ejpam-4152	7	23	tangent	tangent	NOUN
ejpam-4152	7	24	polynomials	polynomial	NOUN
ejpam-4152	7	25	(	(	PUNCT
ejpam-4152	7	26	see	see	VERB
ejpam-4152	7	27	[	[	X
ejpam-4152	7	28	2	2	NUM
ejpam-4152	7	29	]	]	NUM
ejpam-4152	7	30	)	)	PUNCT
ejpam-4152	7	31	.	.	PUNCT
ejpam-4152	8	1	the	the	DET
ejpam-4152	8	2	study	study	NOUN
ejpam-4152	8	3	of	of	ADP
ejpam-4152	8	4	tangent	tangent	NOUN
ejpam-4152	8	5	polynomials	polynomial	NOUN
ejpam-4152	8	6	has	have	AUX
ejpam-4152	8	7	become	become	VERB
ejpam-4152	8	8	an	an	DET
ejpam-4152	8	9	interesting	interesting	ADJ
ejpam-4152	8	10	area	area	NOUN
ejpam-4152	8	11	for	for	ADP
ejpam-4152	8	12	many	many	ADJ
ejpam-4152	8	13	mathematicians	mathematician	NOUN
ejpam-4152	8	14	for	for	SCONJ
ejpam-4152	8	15	they	they	PRON
ejpam-4152	8	16	possess	possess	VERB
ejpam-4152	8	17	significant	significant	ADJ
ejpam-4152	8	18	properties	property	NOUN
ejpam-4152	8	19	that	that	PRON
ejpam-4152	8	20	can	can	AUX
ejpam-4152	8	21	be	be	AUX
ejpam-4152	8	22	found	find	VERB
ejpam-4152	8	23	in	in	ADP
ejpam-4152	8	24	the	the	DET
ejpam-4152	8	25	field	field	NOUN
ejpam-4152	8	26	of	of	ADP
ejpam-4152	8	27	mathematics	mathematic	NOUN
ejpam-4152	8	28	and	and	CCONJ
ejpam-4152	8	29	physics	physics	NOUN
ejpam-4152	8	30	(	(	PUNCT
ejpam-4152	8	31	see	see	VERB
ejpam-4152	8	32	[	[	X
ejpam-4152	8	33	3	3	NUM
ejpam-4152	8	34	]	]	PUNCT
ejpam-4152	8	35	,	,	PUNCT
ejpam-4152	8	36	[	[	X
ejpam-4152	8	37	4	4	NUM
ejpam-4152	8	38	]	]	NUM
ejpam-4152	8	39	)	)	PUNCT
ejpam-4152	8	40	.	.	PUNCT
ejpam-4152	9	1	analogues	analogue	NOUN
ejpam-4152	9	2	,	,	PUNCT
ejpam-4152	9	3	explicit	explicit	ADJ
ejpam-4152	9	4	identities	identity	NOUN
ejpam-4152	9	5	and	and	CCONJ
ejpam-4152	9	6	symmetric	symmetric	ADJ
ejpam-4152	9	7	properties	property	NOUN
ejpam-4152	9	8	for	for	ADP
ejpam-4152	9	9	tangent	tangent	NOUN
ejpam-4152	9	10	polynomials	polynomial	NOUN
ejpam-4152	9	11	are	be	AUX
ejpam-4152	9	12	derived	derive	VERB
ejpam-4152	9	13	in	in	ADP
ejpam-4152	9	14	(	(	PUNCT
ejpam-4152	9	15	see	see	VERB
ejpam-4152	9	16	[	[	X
ejpam-4152	9	17	5	5	NUM
ejpam-4152	9	18	]	]	PUNCT
ejpam-4152	9	19	,	,	PUNCT
ejpam-4152	9	20	[	[	X
ejpam-4152	9	21	6	6	NUM
ejpam-4152	9	22	]	]	PUNCT
ejpam-4152	9	23	,	,	PUNCT
ejpam-4152	9	24	[	[	X
ejpam-4152	9	25	7	7	NUM
ejpam-4152	9	26	]	]	NUM
ejpam-4152	9	27	)	)	PUNCT
ejpam-4152	9	28	.	.	PUNCT
ejpam-4152	10	1	in	in	ADP
ejpam-4152	10	2	this	this	DET
ejpam-4152	10	3	paper	paper	NOUN
ejpam-4152	10	4	,	,	PUNCT
ejpam-4152	10	5	the	the	DET
ejpam-4152	10	6	researchers	researcher	NOUN
ejpam-4152	10	7	derive	derive	VERB
ejpam-4152	10	8	the	the	DET
ejpam-4152	10	9	fourier	fourier	ADJ
ejpam-4152	10	10	expansion	expansion	NOUN
ejpam-4152	10	11	and	and	CCONJ
ejpam-4152	10	12	integral	integral	ADJ
ejpam-4152	10	13	representation	representation	NOUN
ejpam-4152	10	14	of	of	ADP
ejpam-4152	10	15	the	the	DET
ejpam-4152	10	16	tangent	tangent	ADJ
ejpam-4152	10	17	polynomials	polynomial	NOUN
ejpam-4152	10	18	of	of	ADP
ejpam-4152	10	19	order	order	NOUN
ejpam-4152	10	20	r	r	NOUN
ejpam-4152	10	21	,	,	PUNCT
ejpam-4152	10	22	r	r	NOUN
ejpam-4152	10	23	∈	∈	PROPN
ejpam-4152	10	24	z+	z+	NUM
ejpam-4152	10	25	and	and	CCONJ
ejpam-4152	10	26	present	present	VERB
ejpam-4152	10	27	an	an	DET
ejpam-4152	10	28	explicit	explicit	ADJ
ejpam-4152	10	29	formula	formula	NOUN
ejpam-4152	10	30	of	of	ADP
ejpam-4152	10	31	these	these	DET
ejpam-4152	10	32	polynomials	polynomial	NOUN
ejpam-4152	10	33	at	at	ADP
ejpam-4152	10	34	rational	rational	ADJ
ejpam-4152	10	35	arguments	argument	NOUN
ejpam-4152	10	36	using	use	VERB
ejpam-4152	10	37	the	the	DET
ejpam-4152	10	38	method	method	NOUN
ejpam-4152	10	39	of	of	ADP
ejpam-4152	10	40	luo	luo	PROPN
ejpam-4152	11	1	[	[	X
ejpam-4152	11	2	8	8	NUM
ejpam-4152	11	3	]	]	PUNCT
ejpam-4152	11	4	.	.	PUNCT
ejpam-4152	12	1	∗corresponding	∗corresponde	VERB
ejpam-4152	12	2	author	author	NOUN
ejpam-4152	12	3	.	.	PUNCT
ejpam-4152	13	1	doi	doi	NOUN
ejpam-4152	13	2	:	:	PUNCT
ejpam-4152	13	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4152	https://doi.org/10.29020/nybg.ejpam.v14i4.4152	ADJ
ejpam-4152	13	4	email	email	NOUN
ejpam-4152	13	5	addresses	address	NOUN
ejpam-4152	13	6	:	:	PUNCT
ejpam-4152	13	7	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-4152	13	8	(	(	PUNCT
ejpam-4152	13	9	c.	c.	PROPN
ejpam-4152	13	10	corcino	corcino	PROPN
ejpam-4152	13	11	)	)	PUNCT
ejpam-4152	13	12	,	,	PUNCT
ejpam-4152	13	13	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-4152	13	14	(	(	PUNCT
ejpam-4152	13	15	r.	r.	PROPN
ejpam-4152	13	16	corcino	corcino	PROPN
ejpam-4152	13	17	)	)	PUNCT
ejpam-4152	13	18	,	,	PUNCT
ejpam-4152	13	19	casquejoj@cnu.edu.ph	casquejoj@cnu.edu.ph	PROPN
ejpam-4152	13	20	(	(	PUNCT
ejpam-4152	13	21	j.	j.	PROPN
ejpam-4152	13	22	casquejo	casquejo	PROPN
ejpam-4152	13	23	)	)	PUNCT
ejpam-4152	13	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4152	13	25	1457	1457	NUM
ejpam-4152	13	26	©	©	NOUN
ejpam-4152	13	27	2021	2021	NUM
ejpam-4152	13	28	ejpam	ejpam	VERB
ejpam-4152	13	29	all	all	DET
ejpam-4152	13	30	rights	right	NOUN
ejpam-4152	13	31	reserved	reserve	VERB
ejpam-4152	13	32	.	.	PUNCT
ejpam-4152	14	1	c.	c.	PROPN
ejpam-4152	14	2	corcino	corcino	PROPN
ejpam-4152	14	3	,	,	PUNCT
ejpam-4152	14	4	r.	r.	PROPN
ejpam-4152	14	5	corcino	corcino	PROPN
ejpam-4152	14	6	,	,	PUNCT
ejpam-4152	14	7	j.	j.	PROPN
ejpam-4152	14	8	casquejo	casquejo	PROPN
ejpam-4152	14	9	/	/	SYM
ejpam-4152	14	10	eur	eur	PROPN
ejpam-4152	14	11	.	.	PUNCT
ejpam-4152	15	1	j.	j.	PROPN
ejpam-4152	15	2	pure	pure	PROPN
ejpam-4152	15	3	appl	appl	PROPN
ejpam-4152	15	4	.	.	PROPN
ejpam-4152	15	5	math	math	PROPN
ejpam-4152	15	6	,	,	PUNCT
ejpam-4152	15	7	14	14	NUM
ejpam-4152	15	8	(	(	PUNCT
ejpam-4152	15	9	4	4	NUM
ejpam-4152	15	10	)	)	PUNCT
ejpam-4152	15	11	(	(	PUNCT
ejpam-4152	15	12	2021	2021	NUM
ejpam-4152	15	13	)	)	PUNCT
ejpam-4152	15	14	,	,	PUNCT
ejpam-4152	15	15	1457	1457	NUM
ejpam-4152	15	16	-	-	SYM
ejpam-4152	15	17	1466	1466	NUM
ejpam-4152	15	18	1458	1458	NUM
ejpam-4152	15	19	2	2	NUM
ejpam-4152	15	20	.	.	PUNCT
ejpam-4152	16	1	fourier	fourier	NOUN
ejpam-4152	16	2	expansions	expansion	NOUN
ejpam-4152	16	3	for	for	ADP
ejpam-4152	16	4	tangent	tangent	ADJ
ejpam-4152	16	5	polynomials	polynomial	NOUN
ejpam-4152	16	6	of	of	ADP
ejpam-4152	16	7	higher	high	ADJ
ejpam-4152	16	8	-	-	PUNCT
ejpam-4152	16	9	order	order	NOUN
ejpam-4152	16	10	in	in	ADP
ejpam-4152	16	11	this	this	DET
ejpam-4152	16	12	section	section	NOUN
ejpam-4152	16	13	,	,	PUNCT
ejpam-4152	16	14	we	we	PRON
ejpam-4152	16	15	give	give	VERB
ejpam-4152	16	16	fourier	fourier	ADJ
ejpam-4152	16	17	expansion	expansion	NOUN
ejpam-4152	16	18	for	for	ADP
ejpam-4152	16	19	tangent	tangent	ADJ
ejpam-4152	16	20	polynomials	polynomial	NOUN
ejpam-4152	16	21	of	of	ADP
ejpam-4152	16	22	higher	high	ADJ
ejpam-4152	16	23	order	order	NOUN
ejpam-4152	16	24	.	.	PUNCT
ejpam-4152	17	1	theorem	theorem	VERB
ejpam-4152	17	2	2.1	2.1	NUM
ejpam-4152	17	3	.	.	PUNCT
ejpam-4152	18	1	for	for	ADP
ejpam-4152	18	2	0	0	NUM
ejpam-4152	18	3	≤	≤	NUM
ejpam-4152	18	4	x	x	SYM
ejpam-4152	18	5	≤	≤	NUM
ejpam-4152	18	6	1	1	NUM
ejpam-4152	18	7	,	,	PUNCT
ejpam-4152	18	8	t	t	NOUN
ejpam-4152	18	9	r	r	NOUN
ejpam-4152	18	10	n(x	n(x	PROPN
ejpam-4152	18	11	)	)	PUNCT
ejpam-4152	18	12	=	=	SYM
ejpam-4152	18	13	2	2	NUM
ejpam-4152	18	14	·	·	PUNCT
ejpam-4152	18	15	n	n	X
ejpam-4152	18	16	!	!	PUNCT
ejpam-4152	19	1	(	(	PUNCT
ejpam-4152	19	2	2	2	NUM
ejpam-4152	19	3	π	π	NOUN
ejpam-4152	19	4	)	)	PUNCT
ejpam-4152	19	5	r+n	r+n	NOUN
ejpam-4152	20	1	∞∑	∞∑	PROPN
ejpam-4152	20	2	k=0	k=0	PUNCT
ejpam-4152	20	3	r−1∑	r−1∑	NUM
ejpam-4152	20	4	j=0	j=0	PROPN
ejpam-4152	20	5	(	(	PUNCT
ejpam-4152	20	6	−1)j	−1)j	X
ejpam-4152	20	7	(	(	PUNCT
ejpam-4152	20	8	r	r	NOUN
ejpam-4152	20	9	+	+	NUM
ejpam-4152	20	10	n−	n−	PROPN
ejpam-4152	20	11	j	j	NOUN
ejpam-4152	20	12	−	−	NOUN
ejpam-4152	20	13	1	1	NUM
ejpam-4152	20	14	r	r	NOUN
ejpam-4152	20	15	−	−	PROPN
ejpam-4152	20	16	j	j	NOUN
ejpam-4152	20	17	−	−	PROPN
ejpam-4152	20	18	1	1	NUM
ejpam-4152	20	19	)	)	PUNCT
ejpam-4152	20	20	πj	πj	VERB
ejpam-4152	20	21	j	j	PROPN
ejpam-4152	20	22	!	!	PUNCT
ejpam-4152	20	23	br	br	PROPN
ejpam-4152	21	1	j	j	PROPN
ejpam-4152	21	2	(	(	PUNCT
ejpam-4152	21	3	x	x	SYM
ejpam-4152	21	4	2	2	X
ejpam-4152	21	5	)	)	PUNCT
ejpam-4152	21	6	×	×	NOUN
ejpam-4152	21	7	cos	cos	PROPN
ejpam-4152	22	1	[	[	X
ejpam-4152	22	2	(	(	PUNCT
ejpam-4152	22	3	2k	2k	NOUN
ejpam-4152	22	4	+	+	CCONJ
ejpam-4152	22	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	22	6	(	(	PUNCT
ejpam-4152	22	7	r	r	NOUN
ejpam-4152	22	8	+	+	PROPN
ejpam-4152	22	9	n−	n−	NOUN
ejpam-4152	22	10	j)π/2	j)π/2	VERB
ejpam-4152	22	11	]	]	PUNCT
ejpam-4152	22	12	(	(	PUNCT
ejpam-4152	22	13	2k	2k	NOUN
ejpam-4152	22	14	+	+	CCONJ
ejpam-4152	22	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	22	16	,	,	PUNCT
ejpam-4152	22	17	(	(	PUNCT
ejpam-4152	22	18	2	2	X
ejpam-4152	22	19	)	)	PUNCT
ejpam-4152	22	20	where	where	SCONJ
ejpam-4152	22	21	br	br	PROPN
ejpam-4152	22	22	j	j	PROPN
ejpam-4152	22	23	(	(	PUNCT
ejpam-4152	22	24	x	x	SYM
ejpam-4152	22	25	2	2	X
ejpam-4152	22	26	)	)	PUNCT
ejpam-4152	22	27	denotes	denote	VERB
ejpam-4152	22	28	the	the	DET
ejpam-4152	22	29	bernoulli	bernoulli	PROPN
ejpam-4152	22	30	polynomials	polynomial	NOUN
ejpam-4152	22	31	of	of	ADP
ejpam-4152	22	32	order	order	NOUN
ejpam-4152	22	33	r	r	NOUN
ejpam-4152	22	34	defined	define	VERB
ejpam-4152	22	35	by	by	ADP
ejpam-4152	22	36	(	(	PUNCT
ejpam-4152	22	37	w	w	NOUN
ejpam-4152	22	38	ew	ew	NOUN
ejpam-4152	22	39	−	−	PROPN
ejpam-4152	22	40	1	1	NUM
ejpam-4152	22	41	)	)	PUNCT
ejpam-4152	22	42	r	r	NOUN
ejpam-4152	22	43	exw	exw	NOUN
ejpam-4152	23	1	=	=	PUNCT
ejpam-4152	23	2	∞∑	∞∑	NUM
ejpam-4152	23	3	j=0	j=0	PROPN
ejpam-4152	23	4	br	br	PROPN
ejpam-4152	23	5	j	j	PROPN
ejpam-4152	23	6	(	(	PUNCT
ejpam-4152	23	7	x	x	PROPN
ejpam-4152	23	8	)	)	PUNCT
ejpam-4152	23	9	wn	wn	PROPN
ejpam-4152	23	10	n	n	X
ejpam-4152	23	11	!	!	PUNCT
ejpam-4152	23	12	.	.	PUNCT
ejpam-4152	24	1	proof	proof	NOUN
ejpam-4152	24	2	.	.	PUNCT
ejpam-4152	25	1	for	for	ADP
ejpam-4152	25	2	r	r	NOUN
ejpam-4152	25	3	≥	≥	NUM
ejpam-4152	25	4	2	2	NUM
ejpam-4152	25	5	,	,	PUNCT
ejpam-4152	25	6	res	re	NOUN
ejpam-4152	25	7	(	(	PUNCT
ejpam-4152	25	8	f(t	f(t	PROPN
ejpam-4152	25	9	)	)	PUNCT
ejpam-4152	25	10	,	,	PUNCT
ejpam-4152	25	11	t	t	PROPN
ejpam-4152	25	12	=	=	SYM
ejpam-4152	25	13	tk	tk	PROPN
ejpam-4152	25	14	)	)	PUNCT
ejpam-4152	25	15	=	=	SYM
ejpam-4152	25	16	1	1	NUM
ejpam-4152	25	17	(	(	PUNCT
ejpam-4152	25	18	r	r	NOUN
ejpam-4152	25	19	−	−	NOUN
ejpam-4152	25	20	1	1	NUM
ejpam-4152	25	21	)	)	PUNCT
ejpam-4152	25	22	!	!	PUNCT
ejpam-4152	26	1	lim	lim	PROPN
ejpam-4152	26	2	t→tk	t→tk	VERB
ejpam-4152	27	1	dr−1	dr−1	PROPN
ejpam-4152	27	2	dtr−1	dtr−1	PROPN
ejpam-4152	27	3	(	(	PUNCT
ejpam-4152	27	4	t−	t−	PROPN
ejpam-4152	27	5	tk	tk	PROPN
ejpam-4152	27	6	)	)	PUNCT
ejpam-4152	27	7	r	r	NOUN
ejpam-4152	27	8	(	(	PUNCT
ejpam-4152	27	9	2	2	NUM
ejpam-4152	27	10	e2	e2	PROPN
ejpam-4152	27	11	t	t	NOUN
ejpam-4152	27	12	+	+	NOUN
ejpam-4152	27	13	1	1	X
ejpam-4152	27	14	)	)	PUNCT
ejpam-4152	27	15	r	r	NOUN
ejpam-4152	27	16	ext	ext	NOUN
ejpam-4152	27	17	tn+1	tn+1	NOUN
ejpam-4152	27	18	.	.	PUNCT
ejpam-4152	28	1	consider	consider	VERB
ejpam-4152	28	2	the	the	DET
ejpam-4152	28	3	function	function	NOUN
ejpam-4152	28	4	(	(	PUNCT
ejpam-4152	28	5	t−	t−	PROPN
ejpam-4152	28	6	tk	tk	PROPN
ejpam-4152	28	7	)	)	PUNCT
ejpam-4152	28	8	r	r	NOUN
ejpam-4152	28	9	(	(	PUNCT
ejpam-4152	28	10	2	2	NUM
ejpam-4152	28	11	e2	e2	PROPN
ejpam-4152	28	12	t	t	NOUN
ejpam-4152	28	13	+	+	NOUN
ejpam-4152	28	14	1	1	X
ejpam-4152	28	15	)	)	PUNCT
ejpam-4152	28	16	r	r	NOUN
ejpam-4152	28	17	ext	ext	NOUN
ejpam-4152	28	18	tn+1	tn+1	NOUN
ejpam-4152	28	19	=	=	SYM
ejpam-4152	28	20	2r	2r	NUM
ejpam-4152	28	21	(	(	PUNCT
ejpam-4152	28	22	t−	t−	PROPN
ejpam-4152	28	23	tk	tk	PROPN
ejpam-4152	28	24	)	)	PUNCT
ejpam-4152	28	25	r	r	PROPN
ejpam-4152	28	26	(	(	PUNCT
ejpam-4152	28	27	e2	e2	PROPN
ejpam-4152	28	28	t	t	PROPN
ejpam-4152	28	29	+	+	CCONJ
ejpam-4152	28	30	1)r	1)r	NUM
ejpam-4152	28	31	ext	ext	NOUN
ejpam-4152	28	32	tn+1	tn+1	NOUN
ejpam-4152	28	33	.	.	PUNCT
ejpam-4152	29	1	writing	write	VERB
ejpam-4152	29	2	(	(	PUNCT
ejpam-4152	29	3	e2	e2	PROPN
ejpam-4152	29	4	t	t	PROPN
ejpam-4152	29	5	+	+	CCONJ
ejpam-4152	29	6	1	1	X
ejpam-4152	29	7	)	)	PUNCT
ejpam-4152	29	8	r	r	NOUN
ejpam-4152	29	9	as	as	ADP
ejpam-4152	29	10	(	(	PUNCT
ejpam-4152	29	11	e2	e2	PROPN
ejpam-4152	29	12	t	t	PROPN
ejpam-4152	29	13	+	+	CCONJ
ejpam-4152	29	14	1	1	X
ejpam-4152	29	15	)	)	PUNCT
ejpam-4152	29	16	r	r	NOUN
ejpam-4152	29	17	=	=	SYM
ejpam-4152	29	18	(	(	PUNCT
ejpam-4152	29	19	−1)r	−1)r	X
ejpam-4152	29	20	(	(	PUNCT
ejpam-4152	29	21	e2t(−1)−	e2t(−1)−	PROPN
ejpam-4152	29	22	1	1	NUM
ejpam-4152	29	23	)	)	PUNCT
ejpam-4152	29	24	r	r	NOUN
ejpam-4152	29	25	=	=	SYM
ejpam-4152	29	26	(	(	PUNCT
ejpam-4152	29	27	−1)r	−1)r	X
ejpam-4152	29	28	(	(	PUNCT
ejpam-4152	29	29	e2	e2	PROPN
ejpam-4152	29	30	t	t	PROPN
ejpam-4152	29	31	·	·	PUNCT
ejpam-4152	29	32	e−2tk	e−2tk	NOUN
ejpam-4152	29	33	−	−	NOUN
ejpam-4152	29	34	1	1	X
ejpam-4152	29	35	)	)	PUNCT
ejpam-4152	29	36	r	r	NOUN
ejpam-4152	29	37	=	=	SYM
ejpam-4152	29	38	(	(	PUNCT
ejpam-4152	29	39	−1)r	−1)r	X
ejpam-4152	29	40	(	(	PUNCT
ejpam-4152	29	41	e2(t−tk	e2(t−tk	ADJ
ejpam-4152	29	42	)	)	PUNCT
ejpam-4152	29	43	−	−	PROPN
ejpam-4152	29	44	1	1	NUM
ejpam-4152	29	45	)	)	PUNCT
ejpam-4152	29	46	r	r	NOUN
ejpam-4152	29	47	,	,	PUNCT
ejpam-4152	29	48	and	and	CCONJ
ejpam-4152	29	49	since	since	SCONJ
ejpam-4152	29	50	e−2tk	e−2tk	NOUN
ejpam-4152	29	51	=	=	PUNCT
ejpam-4152	29	52	e−2(2k+1)π	e−2(2k+1)π	NOUN
ejpam-4152	29	53	2	2	NUM
ejpam-4152	30	1	i	i	NOUN
ejpam-4152	30	2	=	=	NOUN
ejpam-4152	30	3	e−(2k+1)πi	e−(2k+1)πi	NOUN
ejpam-4152	30	4	=	=	SYM
ejpam-4152	30	5	−1	−1	NOUN
ejpam-4152	30	6	,	,	PUNCT
ejpam-4152	30	7	we	we	PRON
ejpam-4152	30	8	have	have	VERB
ejpam-4152	30	9	(	(	PUNCT
ejpam-4152	30	10	t−	t−	PROPN
ejpam-4152	30	11	tk	tk	PROPN
ejpam-4152	30	12	)	)	PUNCT
ejpam-4152	30	13	r	r	NOUN
ejpam-4152	30	14	(	(	PUNCT
ejpam-4152	30	15	2	2	NUM
ejpam-4152	30	16	e2	e2	PROPN
ejpam-4152	30	17	t	t	NOUN
ejpam-4152	30	18	+	+	NOUN
ejpam-4152	30	19	1	1	X
ejpam-4152	30	20	)	)	PUNCT
ejpam-4152	30	21	r	r	NOUN
ejpam-4152	30	22	ext	ext	NOUN
ejpam-4152	30	23	tn+1	tn+1	NOUN
ejpam-4152	30	24	=	=	SYM
ejpam-4152	30	25	2r(t−	2r(t−	NUM
ejpam-4152	30	26	tk	tk	PROPN
ejpam-4152	30	27	)	)	PUNCT
ejpam-4152	30	28	r	r	NOUN
ejpam-4152	30	29	(	(	PUNCT
ejpam-4152	30	30	−1)r	−1)r	X
ejpam-4152	30	31	(	(	PUNCT
ejpam-4152	30	32	e2(t−tk	e2(t−tk	ADJ
ejpam-4152	30	33	)	)	PUNCT
ejpam-4152	30	34	−	−	PROPN
ejpam-4152	30	35	1	1	NUM
ejpam-4152	30	36	)	)	PUNCT
ejpam-4152	30	37	r	r	NOUN
ejpam-4152	30	38	·	·	PUNCT
ejpam-4152	30	39	ext	ext	NOUN
ejpam-4152	30	40	tn+1	tn+1	NOUN
ejpam-4152	30	41	=	=	SYM
ejpam-4152	30	42	(	(	PUNCT
ejpam-4152	30	43	−1)r	−1)r	X
ejpam-4152	30	44	(	(	PUNCT
ejpam-4152	30	45	2(t−	2(t−	NUM
ejpam-4152	30	46	tk	tk	NOUN
ejpam-4152	30	47	)	)	PUNCT
ejpam-4152	30	48	)	)	PUNCT
ejpam-4152	31	1	r	r	NOUN
ejpam-4152	31	2	(	(	PUNCT
ejpam-4152	31	3	e2(t−tk	e2(t−tk	ADJ
ejpam-4152	31	4	)	)	PUNCT
ejpam-4152	31	5	−	−	PROPN
ejpam-4152	31	6	1)r	1)r	NUM
ejpam-4152	31	7	·	·	PUNCT
ejpam-4152	31	8	ext	ext	NOUN
ejpam-4152	31	9	tn+1	tn+1	NUM
ejpam-4152	31	10	=	=	SYM
ejpam-4152	31	11	(	(	PUNCT
ejpam-4152	31	12	−1)r	−1)r	X
ejpam-4152	31	13	(	(	PUNCT
ejpam-4152	31	14	∞∑	∞∑	NUM
ejpam-4152	31	15	n=0	n=0	NUM
ejpam-4152	31	16	br	br	NOUN
ejpam-4152	31	17	n	n	CCONJ
ejpam-4152	31	18	(	(	PUNCT
ejpam-4152	31	19	2(t−	2(t−	NUM
ejpam-4152	31	20	tk	tk	NOUN
ejpam-4152	31	21	)	)	PUNCT
ejpam-4152	31	22	)	)	PUNCT
ejpam-4152	31	23	n	n	PRON
ejpam-4152	31	24	n	n	CCONJ
ejpam-4152	31	25	!	!	PUNCT
ejpam-4152	31	26	)	)	PUNCT
ejpam-4152	32	1	ext	ext	PROPN
ejpam-4152	32	2	t−(n+1	t−(n+1	PROPN
ejpam-4152	32	3	)	)	PUNCT
ejpam-4152	32	4	,	,	PUNCT
ejpam-4152	32	5	where	where	SCONJ
ejpam-4152	32	6	br	br	PROPN
ejpam-4152	32	7	n	n	PROPN
ejpam-4152	32	8	denotes	denote	VERB
ejpam-4152	32	9	the	the	DET
ejpam-4152	32	10	bernoulli	bernoulli	PROPN
ejpam-4152	32	11	numbers	number	NOUN
ejpam-4152	32	12	of	of	ADP
ejpam-4152	32	13	order	order	NOUN
ejpam-4152	32	14	r	r	NOUN
ejpam-4152	32	15	defined	define	VERB
ejpam-4152	32	16	by	by	ADP
ejpam-4152	32	17	the	the	DET
ejpam-4152	32	18	generating	generate	VERB
ejpam-4152	32	19	function	function	NOUN
ejpam-4152	32	20	c.	c.	PROPN
ejpam-4152	32	21	corcino	corcino	PROPN
ejpam-4152	32	22	,	,	PUNCT
ejpam-4152	32	23	r.	r.	PROPN
ejpam-4152	32	24	corcino	corcino	PROPN
ejpam-4152	32	25	,	,	PUNCT
ejpam-4152	32	26	j.	j.	PROPN
ejpam-4152	32	27	casquejo	casquejo	PROPN
ejpam-4152	32	28	/	/	SYM
ejpam-4152	32	29	eur	eur	PROPN
ejpam-4152	32	30	.	.	PUNCT
ejpam-4152	33	1	j.	j.	PROPN
ejpam-4152	33	2	pure	pure	PROPN
ejpam-4152	33	3	appl	appl	PROPN
ejpam-4152	33	4	.	.	PROPN
ejpam-4152	33	5	math	math	PROPN
ejpam-4152	33	6	,	,	PUNCT
ejpam-4152	33	7	14	14	NUM
ejpam-4152	33	8	(	(	PUNCT
ejpam-4152	33	9	4	4	NUM
ejpam-4152	33	10	)	)	PUNCT
ejpam-4152	33	11	(	(	PUNCT
ejpam-4152	33	12	2021	2021	NUM
ejpam-4152	33	13	)	)	PUNCT
ejpam-4152	33	14	,	,	PUNCT
ejpam-4152	33	15	1457	1457	NUM
ejpam-4152	33	16	-	-	SYM
ejpam-4152	33	17	1466	1466	NUM
ejpam-4152	33	18	1459	1459	NUM
ejpam-4152	33	19	(	(	PUNCT
ejpam-4152	34	1	w	w	NOUN
ejpam-4152	34	2	ew	ew	INTJ
ejpam-4152	34	3	−	−	PROPN
ejpam-4152	34	4	1	1	NUM
ejpam-4152	34	5	)	)	PUNCT
ejpam-4152	34	6	r	r	NOUN
ejpam-4152	34	7	=	=	SYM
ejpam-4152	35	1	∞∑	∞∑	NUM
ejpam-4152	35	2	n=0	n=0	NUM
ejpam-4152	35	3	br	br	NOUN
ejpam-4152	35	4	n	n	ADP
ejpam-4152	35	5	wn	wn	NOUN
ejpam-4152	35	6	n	n	X
ejpam-4152	35	7	!	!	PUNCT
ejpam-4152	35	8	.	.	PUNCT
ejpam-4152	36	1	to	to	PART
ejpam-4152	36	2	get	get	VERB
ejpam-4152	36	3	the	the	DET
ejpam-4152	36	4	derivative	derivative	NOUN
ejpam-4152	36	5	,	,	PUNCT
ejpam-4152	36	6	applying	apply	VERB
ejpam-4152	36	7	the	the	DET
ejpam-4152	36	8	leibniz	leibniz	NOUN
ejpam-4152	36	9	rule	rule	NOUN
ejpam-4152	36	10	yields	yield	NOUN
ejpam-4152	37	1	dr−1	dr−1	PROPN
ejpam-4152	37	2	dtr−1	dtr−1	PROPN
ejpam-4152	37	3	{	{	PUNCT
ejpam-4152	37	4	(	(	PUNCT
ejpam-4152	37	5	t−	t−	PROPN
ejpam-4152	37	6	tk	tk	PROPN
ejpam-4152	37	7	)	)	PUNCT
ejpam-4152	37	8	r	r	NOUN
ejpam-4152	37	9	(	(	PUNCT
ejpam-4152	37	10	2	2	NUM
ejpam-4152	37	11	e2	e2	PROPN
ejpam-4152	37	12	t	t	NOUN
ejpam-4152	37	13	+	+	NOUN
ejpam-4152	37	14	1	1	X
ejpam-4152	37	15	)	)	PUNCT
ejpam-4152	37	16	r	r	NOUN
ejpam-4152	37	17	ext	ext	NOUN
ejpam-4152	37	18	tn+1	tn+1	NOUN
ejpam-4152	37	19	}	}	PUNCT
ejpam-4152	37	20	=	=	PUNCT
ejpam-4152	38	1	dr−1	dr−1	PROPN
ejpam-4152	38	2	dtr−1	dtr−1	PROPN
ejpam-4152	38	3	{	{	PUNCT
ejpam-4152	38	4	(	(	PUNCT
ejpam-4152	38	5	−1)r	−1)r	X
ejpam-4152	38	6	(	(	PUNCT
ejpam-4152	38	7	∞∑	∞∑	NUM
ejpam-4152	38	8	n=0	n=0	NUM
ejpam-4152	38	9	br	br	NOUN
ejpam-4152	38	10	n	n	CCONJ
ejpam-4152	38	11	(	(	PUNCT
ejpam-4152	38	12	2(t−	2(t−	NUM
ejpam-4152	38	13	tk	tk	NOUN
ejpam-4152	38	14	)	)	PUNCT
ejpam-4152	38	15	)	)	PUNCT
ejpam-4152	38	16	n	n	PRON
ejpam-4152	38	17	n	n	CCONJ
ejpam-4152	38	18	!	!	PUNCT
ejpam-4152	38	19	)	)	PUNCT
ejpam-4152	39	1	ext	ext	PROPN
ejpam-4152	39	2	t−(n+1	t−(n+1	PROPN
ejpam-4152	39	3	)	)	PUNCT
ejpam-4152	39	4	}	}	PUNCT
ejpam-4152	40	1	=	=	SYM
ejpam-4152	40	2	(	(	PUNCT
ejpam-4152	40	3	−1)r	−1)r	AUX
ejpam-4152	40	4	dr−1	dr−1	ADV
ejpam-4152	40	5	dtr−1	dtr−1	PROPN
ejpam-4152	40	6	{	{	PUNCT
ejpam-4152	40	7	(	(	PUNCT
ejpam-4152	40	8	ext	ext	VERB
ejpam-4152	40	9	∞∑	∞∑	NUM
ejpam-4152	40	10	n=0	n=0	NUM
ejpam-4152	40	11	br	br	NOUN
ejpam-4152	40	12	n	n	CCONJ
ejpam-4152	40	13	(	(	PUNCT
ejpam-4152	40	14	2(t−	2(t−	NUM
ejpam-4152	40	15	tk	tk	NOUN
ejpam-4152	40	16	)	)	PUNCT
ejpam-4152	40	17	)	)	PUNCT
ejpam-4152	40	18	n	n	CCONJ
ejpam-4152	40	19	n	n	CCONJ
ejpam-4152	40	20	!	!	PUNCT
ejpam-4152	40	21	)	)	PUNCT
ejpam-4152	40	22	t−(n+1	t−(n+1	NOUN
ejpam-4152	40	23	)	)	PUNCT
ejpam-4152	40	24	}	}	PUNCT
ejpam-4152	41	1	=	=	SYM
ejpam-4152	41	2	(	(	PUNCT
ejpam-4152	41	3	−1)r	−1)r	X
ejpam-4152	41	4	r−1∑	r−1∑	NUM
ejpam-4152	41	5	j=0	j=0	PROPN
ejpam-4152	41	6	(	(	PUNCT
ejpam-4152	41	7	r	r	NOUN
ejpam-4152	41	8	−	−	PROPN
ejpam-4152	41	9	1	1	NUM
ejpam-4152	41	10	j	j	NOUN
ejpam-4152	41	11	)	)	PUNCT
ejpam-4152	41	12	dr−1−j	dr−1−j	PROPN
ejpam-4152	41	13	dtr−1−j	dtr−1−j	PROPN
ejpam-4152	41	14	t−(n+1	t−(n+1	NOUN
ejpam-4152	41	15	)	)	PUNCT
ejpam-4152	41	16	·	·	PUNCT
ejpam-4152	42	1	dj	dj	ADP
ejpam-4152	42	2	dtj	dtj	NOUN
ejpam-4152	42	3	(	(	PUNCT
ejpam-4152	42	4	ext	ext	VERB
ejpam-4152	42	5	∞∑	∞∑	NUM
ejpam-4152	42	6	n=0	n=0	NUM
ejpam-4152	42	7	br	br	NOUN
ejpam-4152	42	8	n	n	CCONJ
ejpam-4152	42	9	(	(	PUNCT
ejpam-4152	42	10	2(t−	2(t−	NUM
ejpam-4152	42	11	tk	tk	NOUN
ejpam-4152	42	12	)	)	PUNCT
ejpam-4152	42	13	)	)	PUNCT
ejpam-4152	42	14	n	n	PRON
ejpam-4152	42	15	n	n	CCONJ
ejpam-4152	42	16	!	!	PUNCT
ejpam-4152	42	17	)	)	PUNCT
ejpam-4152	42	18	,	,	PUNCT
ejpam-4152	42	19	dj	dj	VERB
ejpam-4152	42	20	dtj	dtj	NOUN
ejpam-4152	42	21	(	(	PUNCT
ejpam-4152	42	22	ext	ext	VERB
ejpam-4152	42	23	∞∑	∞∑	NUM
ejpam-4152	43	1	n=0	n=0	NUM
ejpam-4152	43	2	br	br	NOUN
ejpam-4152	43	3	n	n	NUM
ejpam-4152	43	4	2n(t−	2n(t−	NUM
ejpam-4152	43	5	tk	tk	PROPN
ejpam-4152	43	6	)	)	PUNCT
ejpam-4152	43	7	n	n	CCONJ
ejpam-4152	43	8	)	)	PUNCT
ejpam-4152	43	9	n	n	CCONJ
ejpam-4152	43	10	!	!	PUNCT
ejpam-4152	43	11	)	)	PUNCT
ejpam-4152	44	1	=	=	PUNCT
ejpam-4152	45	1	j∑	j∑	PROPN
ejpam-4152	46	1	l=0	l=0	PROPN
ejpam-4152	46	2	(	(	PUNCT
ejpam-4152	46	3	j	j	PROPN
ejpam-4152	46	4	l	l	NOUN
ejpam-4152	46	5	)	)	PUNCT
ejpam-4152	46	6	xj−lext	xj−lext	PUNCT
ejpam-4152	47	1	∞∑	∞∑	NUM
ejpam-4152	47	2	n	n	CCONJ
ejpam-4152	47	3	=	=	SYM
ejpam-4152	47	4	l	l	NOUN
ejpam-4152	47	5	br	br	NOUN
ejpam-4152	47	6	n	n	ADV
ejpam-4152	47	7	2n	2n	NUM
ejpam-4152	47	8	n	n	X
ejpam-4152	47	9	!	!	PUNCT
ejpam-4152	47	10	(	(	PUNCT
ejpam-4152	47	11	n)l	n)l	X
ejpam-4152	47	12	(	(	PUNCT
ejpam-4152	47	13	t−	t−	PROPN
ejpam-4152	47	14	tk	tk	PROPN
ejpam-4152	47	15	)	)	PUNCT
ejpam-4152	47	16	n−l	n−l	NOUN
ejpam-4152	47	17	=	=	PUNCT
ejpam-4152	47	18	ext	ext	NOUN
ejpam-4152	47	19	j∑	j∑	PROPN
ejpam-4152	47	20	l=0	l=0	PROPN
ejpam-4152	47	21	(	(	PUNCT
ejpam-4152	47	22	j	j	PROPN
ejpam-4152	47	23	l	l	NOUN
ejpam-4152	47	24	)	)	PUNCT
ejpam-4152	48	1	xj−l	xj−l	PROPN
ejpam-4152	48	2	∞∑	∞∑	NUM
ejpam-4152	48	3	n	n	CCONJ
ejpam-4152	48	4	=	=	SYM
ejpam-4152	48	5	l	l	NOUN
ejpam-4152	48	6	2nbr	2nbr	PROPN
ejpam-4152	48	7	n	n	ADP
ejpam-4152	48	8	(	(	PUNCT
ejpam-4152	48	9	t−	t−	PROPN
ejpam-4152	48	10	tk	tk	PROPN
ejpam-4152	48	11	)	)	PUNCT
ejpam-4152	48	12	n−l	n−l	NOUN
ejpam-4152	48	13	(	(	PUNCT
ejpam-4152	48	14	n−	n−	NOUN
ejpam-4152	48	15	l	l	NOUN
ejpam-4152	48	16	)	)	PUNCT
ejpam-4152	48	17	!	!	PUNCT
ejpam-4152	49	1	,	,	PUNCT
ejpam-4152	50	1	dr−1	dr−1	INTJ
ejpam-4152	50	2	dtr−1	dtr−1	PROPN
ejpam-4152	50	3	(	(	PUNCT
ejpam-4152	50	4	(	(	PUNCT
ejpam-4152	50	5	t−	t−	PROPN
ejpam-4152	50	6	tk	tk	PROPN
ejpam-4152	50	7	)	)	PUNCT
ejpam-4152	50	8	r	r	NOUN
ejpam-4152	50	9	(	(	PUNCT
ejpam-4152	50	10	2	2	NUM
ejpam-4152	50	11	e2	e2	PROPN
ejpam-4152	50	12	t	t	NOUN
ejpam-4152	50	13	+	+	NOUN
ejpam-4152	50	14	1	1	X
ejpam-4152	50	15	)	)	PUNCT
ejpam-4152	50	16	r	r	NOUN
ejpam-4152	50	17	ext	ext	NOUN
ejpam-4152	50	18	tn+1	tn+1	NOUN
ejpam-4152	50	19	)	)	PUNCT
ejpam-4152	50	20	=	=	PRON
ejpam-4152	50	21	(	(	PUNCT
ejpam-4152	50	22	−1)r	−1)r	X
ejpam-4152	50	23	r−1∑	r−1∑	NUM
ejpam-4152	50	24	j=0	j=0	PROPN
ejpam-4152	50	25	(	(	PUNCT
ejpam-4152	50	26	r	r	NOUN
ejpam-4152	50	27	−	−	PROPN
ejpam-4152	50	28	1	1	NUM
ejpam-4152	50	29	j	j	NOUN
ejpam-4152	50	30	)	)	PUNCT
ejpam-4152	50	31	dr−1−j	dr−1−j	PROPN
ejpam-4152	50	32	dtr−1−j	dtr−1−j	PROPN
ejpam-4152	50	33	t−(n+1	t−(n+1	PROPN
ejpam-4152	50	34	)	)	PUNCT
ejpam-4152	50	35	×	×	NOUN
ejpam-4152	50	36	ext	ext	NOUN
ejpam-4152	50	37	j∑	j∑	PROPN
ejpam-4152	50	38	l=0	l=0	PROPN
ejpam-4152	50	39	(	(	PUNCT
ejpam-4152	50	40	j	j	PROPN
ejpam-4152	50	41	l	l	NOUN
ejpam-4152	50	42	)	)	PUNCT
ejpam-4152	51	1	xj−l	xj−l	PROPN
ejpam-4152	51	2	∞∑	∞∑	NUM
ejpam-4152	51	3	n	n	CCONJ
ejpam-4152	51	4	=	=	SYM
ejpam-4152	51	5	l	l	NOUN
ejpam-4152	51	6	2nbr	2nbr	PROPN
ejpam-4152	51	7	n	n	ADP
ejpam-4152	51	8	(	(	PUNCT
ejpam-4152	51	9	t−	t−	PROPN
ejpam-4152	51	10	tk	tk	PROPN
ejpam-4152	51	11	)	)	PUNCT
ejpam-4152	51	12	n−l	n−l	NOUN
ejpam-4152	51	13	(	(	PUNCT
ejpam-4152	51	14	n−	n−	NOUN
ejpam-4152	51	15	l	l	NOUN
ejpam-4152	51	16	)	)	PUNCT
ejpam-4152	51	17	!	!	PUNCT
ejpam-4152	51	18	.	.	PUNCT
ejpam-4152	52	1	thus	thus	ADV
ejpam-4152	52	2	,	,	PUNCT
ejpam-4152	52	3	res	re	NOUN
ejpam-4152	52	4	(	(	PUNCT
ejpam-4152	52	5	f(t	f(t	PROPN
ejpam-4152	52	6	)	)	PUNCT
ejpam-4152	52	7	,	,	PUNCT
ejpam-4152	52	8	t	t	PROPN
ejpam-4152	52	9	=	=	SYM
ejpam-4152	52	10	tk	tk	PROPN
ejpam-4152	52	11	)	)	PUNCT
ejpam-4152	52	12	=	=	SYM
ejpam-4152	52	13	1	1	NUM
ejpam-4152	52	14	(	(	PUNCT
ejpam-4152	52	15	r	r	NOUN
ejpam-4152	52	16	−	−	NOUN
ejpam-4152	52	17	1	1	NUM
ejpam-4152	52	18	)	)	PUNCT
ejpam-4152	52	19	!	!	PUNCT
ejpam-4152	53	1	lim	lim	PROPN
ejpam-4152	53	2	t→tk	t→tk	PROPN
ejpam-4152	53	3	(	(	PUNCT
ejpam-4152	53	4	−1)r	−1)r	X
ejpam-4152	53	5	r−1∑	r−1∑	NUM
ejpam-4152	53	6	j=0	j=0	PROPN
ejpam-4152	53	7	(	(	PUNCT
ejpam-4152	53	8	r	r	NOUN
ejpam-4152	53	9	−	−	PROPN
ejpam-4152	53	10	1	1	NUM
ejpam-4152	53	11	j	j	NOUN
ejpam-4152	53	12	)	)	PUNCT
ejpam-4152	53	13	dr−1−j	dr−1−j	PROPN
ejpam-4152	53	14	dtr−1−j	dtr−1−j	PROPN
ejpam-4152	53	15	t−(n+1	t−(n+1	PROPN
ejpam-4152	53	16	)	)	PUNCT
ejpam-4152	54	1	×	×	PROPN
ejpam-4152	54	2	lim	lim	PROPN
ejpam-4152	54	3	t→tk	t→tk	PROPN
ejpam-4152	54	4	ext	ext	PROPN
ejpam-4152	54	5	j∑	j∑	PROPN
ejpam-4152	55	1	l=0	l=0	PROPN
ejpam-4152	55	2	(	(	PUNCT
ejpam-4152	55	3	j	j	PROPN
ejpam-4152	55	4	l	l	NOUN
ejpam-4152	55	5	)	)	PUNCT
ejpam-4152	56	1	xj−l	xj−l	PROPN
ejpam-4152	56	2	∞∑	∞∑	NUM
ejpam-4152	56	3	n	n	CCONJ
ejpam-4152	56	4	=	=	SYM
ejpam-4152	56	5	l	l	NOUN
ejpam-4152	56	6	2nbr	2nbr	PROPN
ejpam-4152	56	7	n	n	ADP
ejpam-4152	56	8	(	(	PUNCT
ejpam-4152	56	9	t−	t−	PROPN
ejpam-4152	56	10	tk	tk	PROPN
ejpam-4152	56	11	)	)	PUNCT
ejpam-4152	56	12	n−l	n−l	NOUN
ejpam-4152	56	13	(	(	PUNCT
ejpam-4152	56	14	n−	n−	NOUN
ejpam-4152	56	15	l	l	NOUN
ejpam-4152	56	16	)	)	PUNCT
ejpam-4152	56	17	!	!	PUNCT
ejpam-4152	56	18	.	.	PUNCT
ejpam-4152	57	1	c.	c.	PROPN
ejpam-4152	57	2	corcino	corcino	PROPN
ejpam-4152	57	3	,	,	PUNCT
ejpam-4152	57	4	r.	r.	PROPN
ejpam-4152	57	5	corcino	corcino	PROPN
ejpam-4152	57	6	,	,	PUNCT
ejpam-4152	57	7	j.	j.	PROPN
ejpam-4152	57	8	casquejo	casquejo	PROPN
ejpam-4152	57	9	/	/	SYM
ejpam-4152	57	10	eur	eur	PROPN
ejpam-4152	57	11	.	.	PUNCT
ejpam-4152	58	1	j.	j.	PROPN
ejpam-4152	58	2	pure	pure	PROPN
ejpam-4152	58	3	appl	appl	PROPN
ejpam-4152	58	4	.	.	PROPN
ejpam-4152	58	5	math	math	PROPN
ejpam-4152	58	6	,	,	PUNCT
ejpam-4152	58	7	14	14	NUM
ejpam-4152	58	8	(	(	PUNCT
ejpam-4152	58	9	4	4	NUM
ejpam-4152	58	10	)	)	PUNCT
ejpam-4152	58	11	(	(	PUNCT
ejpam-4152	58	12	2021	2021	NUM
ejpam-4152	58	13	)	)	PUNCT
ejpam-4152	58	14	,	,	PUNCT
ejpam-4152	58	15	1457	1457	NUM
ejpam-4152	58	16	-	-	SYM
ejpam-4152	58	17	1466	1466	NUM
ejpam-4152	58	18	1460	1460	NUM
ejpam-4152	58	19	note	note	NOUN
ejpam-4152	58	20	that	that	SCONJ
ejpam-4152	58	21	br	br	VERB
ejpam-4152	58	22	n	n	PROPN
ejpam-4152	58	23	(	(	PUNCT
ejpam-4152	58	24	t−tk	t−tk	PROPN
ejpam-4152	58	25	)	)	PUNCT
ejpam-4152	58	26	n−l	n−l	NOUN
ejpam-4152	58	27	(	(	PUNCT
ejpam-4152	58	28	n−l	n−l	PROPN
ejpam-4152	58	29	)	)	PUNCT
ejpam-4152	58	30	!	!	PUNCT
ejpam-4152	59	1	→	→	SYM
ejpam-4152	59	2	0	0	PUNCT
ejpam-4152	59	3	as	as	ADP
ejpam-4152	59	4	t	t	PROPN
ejpam-4152	59	5	→	→	SYM
ejpam-4152	59	6	tk	tk	PROPN
ejpam-4152	59	7	except	except	SCONJ
ejpam-4152	59	8	when	when	SCONJ
ejpam-4152	59	9	n	n	PROPN
ejpam-4152	59	10	=	=	SYM
ejpam-4152	59	11	l.	l.	NOUN
ejpam-4152	59	12	this	this	PRON
ejpam-4152	59	13	gives	give	VERB
ejpam-4152	59	14	res	re	NOUN
ejpam-4152	59	15	(	(	PUNCT
ejpam-4152	59	16	f(t	f(t	PROPN
ejpam-4152	59	17	)	)	PUNCT
ejpam-4152	59	18	,	,	PUNCT
ejpam-4152	59	19	t	t	PROPN
ejpam-4152	59	20	=	=	SYM
ejpam-4152	59	21	tk	tk	PROPN
ejpam-4152	59	22	)	)	PUNCT
ejpam-4152	59	23	=	=	SYM
ejpam-4152	60	1	1	1	NUM
ejpam-4152	60	2	(	(	PUNCT
ejpam-4152	60	3	r	r	NOUN
ejpam-4152	60	4	−	−	NOUN
ejpam-4152	60	5	1	1	NUM
ejpam-4152	60	6	)	)	PUNCT
ejpam-4152	60	7	!	!	PUNCT
ejpam-4152	61	1	(	(	PUNCT
ejpam-4152	61	2	−1)r	−1)r	X
ejpam-4152	61	3	r−1∑	r−1∑	NUM
ejpam-4152	61	4	j=0	j=0	PROPN
ejpam-4152	61	5	(	(	PUNCT
ejpam-4152	61	6	r	r	NOUN
ejpam-4152	61	7	−	−	PROPN
ejpam-4152	61	8	1	1	NUM
ejpam-4152	61	9	j	j	NOUN
ejpam-4152	61	10	)	)	PUNCT
ejpam-4152	61	11	(	(	PUNCT
ejpam-4152	61	12	−1)r−1−j(n+	−1)r−1−j(n+	CCONJ
ejpam-4152	61	13	r	r	NOUN
ejpam-4152	61	14	−	−	PROPN
ejpam-4152	61	15	1−	1−	NUM
ejpam-4152	61	16	j)r−1−j	j)r−1−j	NOUN
ejpam-4152	61	17	t	t	PROPN
ejpam-4152	61	18	−(n+r−j	−(n+r−j	PROPN
ejpam-4152	61	19	)	)	PUNCT
ejpam-4152	61	20	k	k	NOUN
ejpam-4152	61	21	×	×	PROPN
ejpam-4152	61	22	extk	extk	INTJ
ejpam-4152	61	23	j∑	j∑	PROPN
ejpam-4152	61	24	l=0	l=0	PROPN
ejpam-4152	61	25	(	(	PUNCT
ejpam-4152	61	26	j	j	PROPN
ejpam-4152	61	27	l	l	NOUN
ejpam-4152	61	28	)	)	PUNCT
ejpam-4152	62	1	xj−l2lbr	xj−l2lbr	PROPN
ejpam-4152	62	2	l	l	NOUN
ejpam-4152	62	3	=	=	SYM
ejpam-4152	62	4	(	(	PUNCT
ejpam-4152	62	5	−1)r	−1)r	X
ejpam-4152	62	6	(	(	PUNCT
ejpam-4152	62	7	r	r	NOUN
ejpam-4152	62	8	−	−	NOUN
ejpam-4152	62	9	1	1	NUM
ejpam-4152	62	10	)	)	PUNCT
ejpam-4152	62	11	!	!	PUNCT
ejpam-4152	63	1	r−1∑	r−1∑	PROPN
ejpam-4152	63	2	j=0	j=0	PROPN
ejpam-4152	63	3	(	(	PUNCT
ejpam-4152	63	4	r	r	NOUN
ejpam-4152	63	5	−	−	NOUN
ejpam-4152	63	6	1	1	NUM
ejpam-4152	63	7	)	)	PUNCT
ejpam-4152	63	8	!	!	PUNCT
ejpam-4152	64	1	j!(r	j!(r	PROPN
ejpam-4152	65	1	−	−	PROPN
ejpam-4152	65	2	1−	1−	NUM
ejpam-4152	65	3	j	j	PROPN
ejpam-4152	65	4	)	)	PUNCT
ejpam-4152	65	5	!	!	PUNCT
ejpam-4152	66	1	(	(	PUNCT
ejpam-4152	66	2	−1)r−1−j(n+	−1)r−1−j(n+	PUNCT
ejpam-4152	66	3	r	r	NOUN
ejpam-4152	66	4	−	−	PROPN
ejpam-4152	66	5	1−	1−	NUM
ejpam-4152	66	6	j)r−1−j	j)r−1−j	NOUN
ejpam-4152	66	7	t	t	PROPN
ejpam-4152	66	8	−(n+r−j	−(n+r−j	PROPN
ejpam-4152	66	9	)	)	PUNCT
ejpam-4152	66	10	k	k	NOUN
ejpam-4152	66	11	×	×	PROPN
ejpam-4152	66	12	extk	extk	INTJ
ejpam-4152	66	13	j∑	j∑	PROPN
ejpam-4152	66	14	l=0	l=0	PROPN
ejpam-4152	66	15	(	(	PUNCT
ejpam-4152	66	16	j	j	PROPN
ejpam-4152	66	17	l	l	NOUN
ejpam-4152	66	18	)	)	PUNCT
ejpam-4152	66	19	xj−l2lbr	xj−l2lbr	PROPN
ejpam-4152	66	20	l	l	NOUN
ejpam-4152	66	21	=	=	SYM
ejpam-4152	66	22	r−1∑	r−1∑	PROPN
ejpam-4152	66	23	j=0	j=0	PROPN
ejpam-4152	66	24	(	(	PUNCT
ejpam-4152	66	25	−1)j−1	−1)j−1	PROPN
ejpam-4152	66	26	(	(	PUNCT
ejpam-4152	66	27	n+	n+	INTJ
ejpam-4152	66	28	r	r	NOUN
ejpam-4152	66	29	−	−	PROPN
ejpam-4152	66	30	1−	1−	NUM
ejpam-4152	66	31	j	j	PROPN
ejpam-4152	66	32	r	r	NOUN
ejpam-4152	66	33	−	−	PROPN
ejpam-4152	66	34	1−	1−	NUM
ejpam-4152	66	35	j	j	PROPN
ejpam-4152	66	36	)	)	PUNCT
ejpam-4152	66	37	tj−n−r	tj−n−r	VERB
ejpam-4152	67	1	k	k	PROPN
ejpam-4152	67	2	j	j	PROPN
ejpam-4152	67	3	!	!	PUNCT
ejpam-4152	67	4	extk2j	extk2j	PROPN
ejpam-4152	67	5	j∑	j∑	VERB
ejpam-4152	68	1	l=0	l=0	PROPN
ejpam-4152	68	2	(	(	PUNCT
ejpam-4152	68	3	j	j	PROPN
ejpam-4152	68	4	l	l	NOUN
ejpam-4152	68	5	)	)	PUNCT
ejpam-4152	69	1	xj−l	xj−l	PROPN
ejpam-4152	69	2	2j−l	2j−l	NUM
ejpam-4152	70	1	br	br	INTJ
ejpam-4152	70	2	l	l	NOUN
ejpam-4152	70	3	.	.	PUNCT
ejpam-4152	71	1	recall	recall	VERB
ejpam-4152	71	2	that	that	PRON
ejpam-4152	72	1	br	br	PROPN
ejpam-4152	72	2	j	j	PROPN
ejpam-4152	72	3	(	(	PUNCT
ejpam-4152	72	4	x	x	SYM
ejpam-4152	72	5	2	2	X
ejpam-4152	72	6	)	)	PUNCT
ejpam-4152	72	7	=	=	NOUN
ejpam-4152	73	1	∑j	∑j	ADJ
ejpam-4152	73	2	l=0	l=0	PROPN
ejpam-4152	73	3	(	(	PUNCT
ejpam-4152	73	4	j	j	PROPN
ejpam-4152	73	5	l	l	NOUN
ejpam-4152	73	6	)	)	PUNCT
ejpam-4152	74	1	br	br	ADP
ejpam-4152	74	2	l	l	NOUN
ejpam-4152	74	3	(	(	PUNCT
ejpam-4152	74	4	x	x	SYM
ejpam-4152	74	5	2	2	X
ejpam-4152	74	6	)	)	PUNCT
ejpam-4152	74	7	j−l	j−l	NOUN
ejpam-4152	74	8	.	.	PUNCT
ejpam-4152	75	1	thus	thus	ADV
ejpam-4152	75	2	,	,	PUNCT
ejpam-4152	75	3	res	re	NOUN
ejpam-4152	75	4	(	(	PUNCT
ejpam-4152	75	5	f(t	f(t	PROPN
ejpam-4152	75	6	)	)	PUNCT
ejpam-4152	75	7	,	,	PUNCT
ejpam-4152	75	8	t	t	PROPN
ejpam-4152	75	9	=	=	SYM
ejpam-4152	75	10	tk	tk	PROPN
ejpam-4152	75	11	)	)	PUNCT
ejpam-4152	75	12	=	=	PROPN
ejpam-4152	75	13	r−1∑	r−1∑	PROPN
ejpam-4152	75	14	j=0	j=0	PROPN
ejpam-4152	75	15	(	(	PUNCT
ejpam-4152	75	16	−1)j−12j	−1)j−12j	NOUN
ejpam-4152	75	17	(	(	PUNCT
ejpam-4152	75	18	n+	n+	INTJ
ejpam-4152	75	19	r	r	NOUN
ejpam-4152	75	20	−	−	PROPN
ejpam-4152	75	21	1−	1−	NUM
ejpam-4152	75	22	j	j	PROPN
ejpam-4152	75	23	r	r	NOUN
ejpam-4152	75	24	−	−	PROPN
ejpam-4152	75	25	1−	1−	NUM
ejpam-4152	75	26	j	j	PROPN
ejpam-4152	75	27	)	)	PUNCT
ejpam-4152	75	28	tj−n−r	tj−n−r	VERB
ejpam-4152	75	29	k	k	PROPN
ejpam-4152	75	30	j	j	PROPN
ejpam-4152	75	31	!	!	PUNCT
ejpam-4152	76	1	extkbr	extkbr	PROPN
ejpam-4152	76	2	j	j	PROPN
ejpam-4152	76	3	(	(	PUNCT
ejpam-4152	76	4	x	x	NOUN
ejpam-4152	76	5	2	2	X
ejpam-4152	76	6	)	)	PUNCT
ejpam-4152	76	7	=	=	SYM
ejpam-4152	76	8	r−1∑	r−1∑	PROPN
ejpam-4152	76	9	j=0	j=0	PROPN
ejpam-4152	76	10	(	(	PUNCT
ejpam-4152	76	11	−1)j−12j	−1)j−12j	NOUN
ejpam-4152	76	12	(	(	PUNCT
ejpam-4152	76	13	n+	n+	INTJ
ejpam-4152	76	14	r	r	NOUN
ejpam-4152	76	15	−	−	PROPN
ejpam-4152	76	16	1−	1−	NUM
ejpam-4152	77	1	j	j	PROPN
ejpam-4152	77	2	r	r	NOUN
ejpam-4152	77	3	−	−	PROPN
ejpam-4152	77	4	1−	1−	NUM
ejpam-4152	77	5	j	j	PROPN
ejpam-4152	77	6	)	)	PUNCT
ejpam-4152	78	1	br	br	PROPN
ejpam-4152	78	2	j	j	PROPN
ejpam-4152	78	3	(	(	PUNCT
ejpam-4152	78	4	x	x	SYM
ejpam-4152	78	5	2	2	X
ejpam-4152	78	6	)	)	PUNCT
ejpam-4152	78	7	j	j	PROPN
ejpam-4152	78	8	!	!	PUNCT
ejpam-4152	79	1	extk	extk	INTJ
ejpam-4152	79	2	tn+r−j	tn+r−j	PROPN
ejpam-4152	80	1	k	k	PROPN
ejpam-4152	80	2	=	=	PROPN
ejpam-4152	80	3	r−1∑	r−1∑	PROPN
ejpam-4152	80	4	j=0	j=0	PROPN
ejpam-4152	80	5	(	(	PUNCT
ejpam-4152	80	6	−1)j−12j	−1)j−12j	NOUN
ejpam-4152	80	7	(	(	PUNCT
ejpam-4152	80	8	r	r	NOUN
ejpam-4152	80	9	+	+	NUM
ejpam-4152	80	10	n−	n−	PROPN
ejpam-4152	80	11	j	j	NOUN
ejpam-4152	80	12	−	−	NOUN
ejpam-4152	80	13	1	1	NUM
ejpam-4152	80	14	r	r	NOUN
ejpam-4152	80	15	−	−	PROPN
ejpam-4152	80	16	j	j	NOUN
ejpam-4152	80	17	−	−	PROPN
ejpam-4152	80	18	1	1	NUM
ejpam-4152	80	19	)	)	PUNCT
ejpam-4152	80	20	br	br	PROPN
ejpam-4152	81	1	j	j	PROPN
ejpam-4152	81	2	(	(	PUNCT
ejpam-4152	81	3	x	x	SYM
ejpam-4152	81	4	2	2	X
ejpam-4152	81	5	)	)	PUNCT
ejpam-4152	81	6	j	j	PROPN
ejpam-4152	81	7	!	!	PUNCT
ejpam-4152	82	1	extk	extk	INTJ
ejpam-4152	83	1	tr+n−j	tr+n−j	ADV
ejpam-4152	83	2	k	k	X
ejpam-4152	83	3	.	.	PUNCT
ejpam-4152	84	1	taking	take	VERB
ejpam-4152	84	2	tk	tk	NOUN
ejpam-4152	84	3	=	=	NOUN
ejpam-4152	84	4	1	1	NUM
ejpam-4152	84	5	2(2k	2(2k	NUM
ejpam-4152	85	1	+	+	SYM
ejpam-4152	85	2	1)πi	1)πi	NUM
ejpam-4152	85	3	,	,	PUNCT
ejpam-4152	85	4	we	we	PRON
ejpam-4152	85	5	get	get	VERB
ejpam-4152	85	6	res	re	NOUN
ejpam-4152	85	7	(	(	PUNCT
ejpam-4152	85	8	f(t	f(t	PROPN
ejpam-4152	85	9	)	)	PUNCT
ejpam-4152	85	10	,	,	PUNCT
ejpam-4152	85	11	t	t	PROPN
ejpam-4152	85	12	=	=	SYM
ejpam-4152	85	13	tk	tk	PROPN
ejpam-4152	85	14	)	)	PUNCT
ejpam-4152	85	15	=	=	PROPN
ejpam-4152	85	16	r−1∑	r−1∑	PROPN
ejpam-4152	85	17	j=0	j=0	PROPN
ejpam-4152	85	18	(	(	PUNCT
ejpam-4152	85	19	−1)j−12j	−1)j−12j	NOUN
ejpam-4152	85	20	(	(	PUNCT
ejpam-4152	85	21	r	r	NOUN
ejpam-4152	85	22	+	+	NUM
ejpam-4152	85	23	n−	n−	PROPN
ejpam-4152	85	24	j	j	NOUN
ejpam-4152	85	25	−	−	NOUN
ejpam-4152	85	26	1	1	NUM
ejpam-4152	85	27	r	r	NOUN
ejpam-4152	85	28	−	−	PROPN
ejpam-4152	85	29	j	j	NOUN
ejpam-4152	85	30	−	−	PROPN
ejpam-4152	85	31	1	1	NUM
ejpam-4152	85	32	)	)	PUNCT
ejpam-4152	85	33	br	br	PROPN
ejpam-4152	86	1	j	j	PROPN
ejpam-4152	86	2	(	(	PUNCT
ejpam-4152	86	3	x	x	SYM
ejpam-4152	86	4	2	2	X
ejpam-4152	86	5	)	)	PUNCT
ejpam-4152	86	6	j	j	NOUN
ejpam-4152	86	7	!	!	PUNCT
ejpam-4152	87	1	e	e	NOUN
ejpam-4152	87	2	1	1	NUM
ejpam-4152	87	3	2	2	NUM
ejpam-4152	87	4	(	(	PUNCT
ejpam-4152	87	5	2k+1)πix	2k+1)πix	NUM
ejpam-4152	87	6	(	(	PUNCT
ejpam-4152	87	7	1	1	NUM
ejpam-4152	87	8	2(2k	2(2k	NUM
ejpam-4152	87	9	+	+	NUM
ejpam-4152	87	10	1)πi	1)πi	NUM
ejpam-4152	87	11	)	)	PUNCT
ejpam-4152	87	12	r+n−j	r+n−j	NOUN
ejpam-4152	87	13	=	=	SYM
ejpam-4152	87	14	1	1	NUM
ejpam-4152	87	15	(	(	PUNCT
ejpam-4152	87	16	1	1	NUM
ejpam-4152	87	17	2πi	2πi	NOUN
ejpam-4152	87	18	)	)	PUNCT
ejpam-4152	87	19	r+n	r+n	PROPN
ejpam-4152	87	20	r−1∑	r−1∑	PROPN
ejpam-4152	87	21	j=0	j=0	PROPN
ejpam-4152	87	22	(	(	PUNCT
ejpam-4152	87	23	−1)j−12j	−1)j−12j	NOUN
ejpam-4152	87	24	(	(	PUNCT
ejpam-4152	87	25	r	r	NOUN
ejpam-4152	87	26	+	+	NUM
ejpam-4152	87	27	n−	n−	PROPN
ejpam-4152	87	28	j	j	NOUN
ejpam-4152	87	29	−	−	NOUN
ejpam-4152	87	30	1	1	NUM
ejpam-4152	87	31	r	r	NOUN
ejpam-4152	87	32	−	−	PROPN
ejpam-4152	87	33	j	j	NOUN
ejpam-4152	87	34	−	−	NOUN
ejpam-4152	87	35	1	1	NUM
ejpam-4152	87	36	)	)	PUNCT
ejpam-4152	87	37	(	(	PUNCT
ejpam-4152	87	38	1	1	NUM
ejpam-4152	87	39	2πi	2πi	NOUN
ejpam-4152	87	40	)	)	PUNCT
ejpam-4152	88	1	j	j	PROPN
ejpam-4152	88	2	j	j	PROPN
ejpam-4152	88	3	!	!	PUNCT
ejpam-4152	88	4	br	br	PROPN
ejpam-4152	89	1	j	j	PROPN
ejpam-4152	89	2	(	(	PUNCT
ejpam-4152	89	3	x	x	PROPN
ejpam-4152	89	4	2	2	X
ejpam-4152	89	5	)	)	PUNCT
ejpam-4152	89	6	e	e	NOUN
ejpam-4152	89	7	1	1	NUM
ejpam-4152	89	8	2	2	NUM
ejpam-4152	89	9	(	(	PUNCT
ejpam-4152	89	10	2k+1)πix	2k+1)πix	NUM
ejpam-4152	89	11	(	(	PUNCT
ejpam-4152	89	12	2k	2k	NOUN
ejpam-4152	89	13	+	+	CCONJ
ejpam-4152	89	14	1)r+n−j	1)r+n−j	NUM
ejpam-4152	89	15	.	.	PUNCT
ejpam-4152	90	1	this	this	PRON
ejpam-4152	90	2	gives	give	VERB
ejpam-4152	90	3	t	t	NOUN
ejpam-4152	90	4	r	r	NOUN
ejpam-4152	90	5	n(x	n(x	X
ejpam-4152	90	6	)	)	PUNCT
ejpam-4152	90	7	=	=	SYM
ejpam-4152	90	8	n	n	X
ejpam-4152	90	9	!	!	PUNCT
ejpam-4152	91	1	(	(	PUNCT
ejpam-4152	91	2	2	2	NUM
ejpam-4152	91	3	πi	πi	CCONJ
ejpam-4152	91	4	)	)	PUNCT
ejpam-4152	91	5	r+n∑	r+n∑	PROPN
ejpam-4152	91	6	k∈z	k∈z	NOUN
ejpam-4152	91	7	r−1∑	r−1∑	PROPN
ejpam-4152	91	8	j=0	j=0	PROPN
ejpam-4152	91	9	(	(	PUNCT
ejpam-4152	91	10	−1)j	−1)j	X
ejpam-4152	91	11	(	(	PUNCT
ejpam-4152	91	12	r	r	NOUN
ejpam-4152	91	13	+	+	NUM
ejpam-4152	91	14	n−	n−	PROPN
ejpam-4152	91	15	j	j	NOUN
ejpam-4152	92	1	−	−	NOUN
ejpam-4152	92	2	1	1	NUM
ejpam-4152	92	3	r	r	NOUN
ejpam-4152	92	4	−	−	PROPN
ejpam-4152	92	5	j	j	NOUN
ejpam-4152	92	6	−	−	PROPN
ejpam-4152	92	7	1	1	NUM
ejpam-4152	92	8	)	)	PUNCT
ejpam-4152	92	9	(	(	PUNCT
ejpam-4152	92	10	πi)j	πi)j	PROPN
ejpam-4152	92	11	j	j	PROPN
ejpam-4152	92	12	!	!	PUNCT
ejpam-4152	92	13	br	br	PROPN
ejpam-4152	93	1	j	j	PROPN
ejpam-4152	93	2	(	(	PUNCT
ejpam-4152	93	3	x	x	NOUN
ejpam-4152	93	4	2	2	X
ejpam-4152	93	5	)	)	PUNCT
ejpam-4152	93	6			PROPN
ejpam-4152	93	7	e	e	NOUN
ejpam-4152	93	8	1	1	NUM
ejpam-4152	93	9	2	2	NUM
ejpam-4152	93	10	(	(	PUNCT
ejpam-4152	93	11	2k+1)πi	2k+1)πi	NUM
ejpam-4152	93	12	2	2	NUM
ejpam-4152	93	13	x	x	X
ejpam-4152	93	14	(	(	PUNCT
ejpam-4152	93	15	2k	2k	NOUN
ejpam-4152	93	16	+	+	CCONJ
ejpam-4152	93	17	1)r+n−j	1)r+n−j	NUM
ejpam-4152	93	18	.	.	PUNCT
ejpam-4152	94	1	(	(	PUNCT
ejpam-4152	94	2	3	3	X
ejpam-4152	94	3	)	)	PUNCT
ejpam-4152	94	4	c.	c.	NOUN
ejpam-4152	94	5	corcino	corcino	PROPN
ejpam-4152	94	6	,	,	PUNCT
ejpam-4152	94	7	r.	r.	PROPN
ejpam-4152	94	8	corcino	corcino	PROPN
ejpam-4152	94	9	,	,	PUNCT
ejpam-4152	94	10	j.	j.	PROPN
ejpam-4152	94	11	casquejo	casquejo	PROPN
ejpam-4152	94	12	/	/	SYM
ejpam-4152	94	13	eur	eur	PROPN
ejpam-4152	94	14	.	.	PUNCT
ejpam-4152	95	1	j.	j.	PROPN
ejpam-4152	95	2	pure	pure	PROPN
ejpam-4152	95	3	appl	appl	PROPN
ejpam-4152	95	4	.	.	PROPN
ejpam-4152	95	5	math	math	PROPN
ejpam-4152	95	6	,	,	PUNCT
ejpam-4152	95	7	14	14	NUM
ejpam-4152	95	8	(	(	PUNCT
ejpam-4152	95	9	4	4	NUM
ejpam-4152	95	10	)	)	PUNCT
ejpam-4152	95	11	(	(	PUNCT
ejpam-4152	95	12	2021	2021	NUM
ejpam-4152	95	13	)	)	PUNCT
ejpam-4152	95	14	,	,	PUNCT
ejpam-4152	95	15	1457	1457	NUM
ejpam-4152	95	16	-	-	SYM
ejpam-4152	95	17	1466	1466	NUM
ejpam-4152	95	18	1461	1461	NUM
ejpam-4152	95	19	now	now	ADV
ejpam-4152	95	20	,	,	PUNCT
ejpam-4152	95	21	from	from	ADP
ejpam-4152	95	22	(	(	PUNCT
ejpam-4152	95	23	3	3	NUM
ejpam-4152	95	24	)	)	PUNCT
ejpam-4152	95	25	,	,	PUNCT
ejpam-4152	95	26	we	we	PRON
ejpam-4152	95	27	look	look	VERB
ejpam-4152	95	28	at	at	ADP
ejpam-4152	95	29	i−(r+n−j	i−(r+n−j	NOUN
ejpam-4152	95	30	)	)	PUNCT
ejpam-4152	95	31	∑	∑	ADV
ejpam-4152	95	32	k∈z	k∈z	VERB
ejpam-4152	95	33	e(2k+1)πi	e(2k+1)πi	ADP
ejpam-4152	95	34	2	2	NUM
ejpam-4152	95	35	x	x	SYM
ejpam-4152	95	36	(	(	PUNCT
ejpam-4152	95	37	2k	2k	NOUN
ejpam-4152	95	38	+	+	CCONJ
ejpam-4152	95	39	1)r+n−j	1)r+n−j	NUM
ejpam-4152	95	40	.	.	PUNCT
ejpam-4152	96	1	(	(	PUNCT
ejpam-4152	96	2	4	4	X
ejpam-4152	96	3	)	)	PUNCT
ejpam-4152	96	4	noting	note	VERB
ejpam-4152	96	5	that	that	SCONJ
ejpam-4152	96	6	i−(r+n−j	i−(r+n−j	NOUN
ejpam-4152	96	7	)	)	PUNCT
ejpam-4152	96	8	=	=	SYM
ejpam-4152	96	9	e−(r+n−j)πi/2	e−(r+n−j)πi/2	NOUN
ejpam-4152	96	10	and	and	CCONJ
ejpam-4152	96	11	(	(	PUNCT
ejpam-4152	96	12	−1)r+n−j	−1)r+n−j	ADV
ejpam-4152	96	13	=	=	PUNCT
ejpam-4152	96	14	e(r+n−j)πi	e(r+n−j)πi	NOUN
ejpam-4152	96	15	,	,	PUNCT
ejpam-4152	96	16	we	we	PRON
ejpam-4152	96	17	see	see	VERB
ejpam-4152	96	18	that	that	SCONJ
ejpam-4152	96	19	i−(r+n−j	i−(r+n−j	ADV
ejpam-4152	96	20	)	)	PUNCT
ejpam-4152	96	21	∑	∑	ADV
ejpam-4152	96	22	k∈z	k∈z	VERB
ejpam-4152	96	23	e(2k+1)πi	e(2k+1)πi	ADP
ejpam-4152	96	24	2	2	NUM
ejpam-4152	96	25	x	x	SYM
ejpam-4152	96	26	(	(	PUNCT
ejpam-4152	96	27	2k	2k	NOUN
ejpam-4152	96	28	+	+	CCONJ
ejpam-4152	96	29	1)r+n−j	1)r+n−j	NUM
ejpam-4152	96	30	=	=	SYM
ejpam-4152	96	31	i−(r+n−j	i−(r+n−j	NOUN
ejpam-4152	96	32	)	)	PUNCT
ejpam-4152	96	33	{	{	PUNCT
ejpam-4152	96	34	∞∑	∞∑	PROPN
ejpam-4152	96	35	k=0	k=0	PROPN
ejpam-4152	96	36	e(2k+1)πi	e(2k+1)πi	ADP
ejpam-4152	96	37	2	2	NUM
ejpam-4152	96	38	x	x	X
ejpam-4152	96	39	(	(	PUNCT
ejpam-4152	96	40	2k	2k	NOUN
ejpam-4152	96	41	+	+	CCONJ
ejpam-4152	96	42	1)r+n−j	1)r+n−j	NUM
ejpam-4152	96	43	+	+	CCONJ
ejpam-4152	96	44	(	(	PUNCT
ejpam-4152	96	45	−1)r+n−j	−1)r+n−j	VERB
ejpam-4152	96	46	∞∑	∞∑	NUM
ejpam-4152	96	47	k=0	k=0	PROPN
ejpam-4152	96	48	e−(2k+1)πi	e−(2k+1)πi	NOUN
ejpam-4152	96	49	2	2	NUM
ejpam-4152	96	50	x	x	SYM
ejpam-4152	96	51	(	(	PUNCT
ejpam-4152	96	52	2k	2k	NOUN
ejpam-4152	96	53	+	+	CCONJ
ejpam-4152	96	54	1)r+n−j	1)r+n−j	NUM
ejpam-4152	96	55	}	}	PUNCT
ejpam-4152	96	56	=	=	PUNCT
ejpam-4152	97	1	∞∑	∞∑	NUM
ejpam-4152	97	2	k=0	k=0	PUNCT
ejpam-4152	97	3	e[(2k+1)x/2−(r+n−j)/2]πi	e[(2k+1)x/2−(r+n−j)/2]πi	SYM
ejpam-4152	98	1	+	+	CCONJ
ejpam-4152	98	2	e−[(2k+1)x/2−(r+n−j)/2]πi	e−[(2k+1)x/2−(r+n−j)/2]πi	PROPN
ejpam-4152	98	3	(	(	PUNCT
ejpam-4152	98	4	2k	2k	NOUN
ejpam-4152	98	5	+	+	CCONJ
ejpam-4152	98	6	1)r+n−j	1)r+n−j	NUM
ejpam-4152	98	7	=	=	PUNCT
ejpam-4152	99	1	∞∑	∞∑	NUM
ejpam-4152	99	2	k=0	k=0	PROPN
ejpam-4152	99	3	2	2	NUM
ejpam-4152	99	4	cos	cos	NOUN
ejpam-4152	99	5	[	[	X
ejpam-4152	99	6	(	(	PUNCT
ejpam-4152	99	7	2k	2k	NOUN
ejpam-4152	99	8	+	+	CCONJ
ejpam-4152	99	9	1)πx/2−	1)πx/2−	NUM
ejpam-4152	99	10	(	(	PUNCT
ejpam-4152	99	11	r	r	NOUN
ejpam-4152	99	12	+	+	PROPN
ejpam-4152	99	13	n−	n−	NOUN
ejpam-4152	99	14	j)π/2	j)π/2	VERB
ejpam-4152	99	15	]	]	PUNCT
ejpam-4152	99	16	(	(	PUNCT
ejpam-4152	99	17	2k	2k	NOUN
ejpam-4152	99	18	+	+	CCONJ
ejpam-4152	99	19	1)r+n−j	1)r+n−j	NUM
ejpam-4152	99	20	=	=	SYM
ejpam-4152	99	21	2	2	NUM
ejpam-4152	100	1	∞∑	∞∑	NUM
ejpam-4152	100	2	k=0	k=0	PUNCT
ejpam-4152	100	3	cos	cos	PUNCT
ejpam-4152	101	1	[	[	X
ejpam-4152	101	2	(	(	PUNCT
ejpam-4152	101	3	2k	2k	NOUN
ejpam-4152	101	4	+	+	CCONJ
ejpam-4152	101	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	101	6	(	(	PUNCT
ejpam-4152	101	7	r	r	NOUN
ejpam-4152	101	8	+	+	PROPN
ejpam-4152	101	9	n−	n−	NOUN
ejpam-4152	101	10	j)π/2	j)π/2	VERB
ejpam-4152	101	11	]	]	PUNCT
ejpam-4152	101	12	(	(	PUNCT
ejpam-4152	101	13	2k	2k	NOUN
ejpam-4152	101	14	+	+	CCONJ
ejpam-4152	101	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	101	16	.	.	PUNCT
ejpam-4152	102	1	(	(	PUNCT
ejpam-4152	102	2	5	5	X
ejpam-4152	102	3	)	)	PUNCT
ejpam-4152	102	4	replacing	replace	VERB
ejpam-4152	102	5	(	(	PUNCT
ejpam-4152	102	6	4	4	NUM
ejpam-4152	102	7	)	)	PUNCT
ejpam-4152	102	8	with	with	ADP
ejpam-4152	102	9	(	(	PUNCT
ejpam-4152	102	10	5	5	NUM
ejpam-4152	102	11	)	)	PUNCT
ejpam-4152	102	12	in	in	ADP
ejpam-4152	102	13	(	(	PUNCT
ejpam-4152	102	14	3	3	NUM
ejpam-4152	102	15	)	)	PUNCT
ejpam-4152	102	16	,	,	PUNCT
ejpam-4152	102	17	we	we	PRON
ejpam-4152	102	18	get	get	VERB
ejpam-4152	102	19	the	the	DET
ejpam-4152	102	20	desired	desire	VERB
ejpam-4152	102	21	formula	formula	NOUN
ejpam-4152	102	22	(	(	PUNCT
ejpam-4152	102	23	2	2	NUM
ejpam-4152	102	24	)	)	PUNCT
ejpam-4152	102	25	.	.	PUNCT
ejpam-4152	103	1	3	3	X
ejpam-4152	103	2	.	.	X
ejpam-4152	103	3	integral	integral	ADJ
ejpam-4152	103	4	representation	representation	NOUN
ejpam-4152	103	5	for	for	ADP
ejpam-4152	103	6	tangent	tangent	NOUN
ejpam-4152	103	7	polynomials	polynomial	NOUN
ejpam-4152	103	8	of	of	ADP
ejpam-4152	103	9	higher	high	ADJ
ejpam-4152	103	10	-	-	PUNCT
ejpam-4152	103	11	order	order	NOUN
ejpam-4152	103	12	in	in	ADP
ejpam-4152	103	13	this	this	DET
ejpam-4152	103	14	section	section	NOUN
ejpam-4152	103	15	,	,	PUNCT
ejpam-4152	103	16	we	we	PRON
ejpam-4152	103	17	establish	establish	VERB
ejpam-4152	103	18	an	an	DET
ejpam-4152	103	19	integral	integral	ADJ
ejpam-4152	103	20	representation	representation	NOUN
ejpam-4152	103	21	for	for	ADP
ejpam-4152	103	22	tangent	tangent	NOUN
ejpam-4152	103	23	polynomials	polynomial	NOUN
ejpam-4152	103	24	of	of	ADP
ejpam-4152	103	25	higher	high	ADJ
ejpam-4152	103	26	order	order	NOUN
ejpam-4152	103	27	.	.	PUNCT
ejpam-4152	104	1	theorem	theorem	VERB
ejpam-4152	104	2	3.1	3.1	NUM
ejpam-4152	104	3	.	.	PUNCT
ejpam-4152	105	1	for	for	ADP
ejpam-4152	105	2	n	n	PRON
ejpam-4152	105	3	∈	∈	PROPN
ejpam-4152	105	4	n	n	CCONJ
ejpam-4152	105	5	,	,	PUNCT
ejpam-4152	105	6	r	r	NOUN
ejpam-4152	105	7	≥	≥	NOUN
ejpam-4152	105	8	2	2	NUM
ejpam-4152	105	9	,	,	PUNCT
ejpam-4152	105	10	and	and	CCONJ
ejpam-4152	105	11	0	0	NUM
ejpam-4152	105	12	≤	≤	NUM
ejpam-4152	105	13	r(x	r(x	PROPN
ejpam-4152	105	14	)	)	PUNCT
ejpam-4152	105	15	≤	≤	NUM
ejpam-4152	105	16	1	1	NUM
ejpam-4152	105	17	,	,	PUNCT
ejpam-4152	105	18	t	t	NOUN
ejpam-4152	105	19	r	r	NOUN
ejpam-4152	105	20	n(x	n(x	PROPN
ejpam-4152	105	21	)	)	PUNCT
ejpam-4152	105	22	=	=	SYM
ejpam-4152	105	23	2r+n	2r+n	NUM
ejpam-4152	105	24	r−1∑	r−1∑	PROPN
ejpam-4152	105	25	j=0	j=0	PROPN
ejpam-4152	105	26	(	(	PUNCT
ejpam-4152	105	27	−1)j	−1)j	NOUN
ejpam-4152	105	28	j	j	X
ejpam-4152	105	29	!	!	PUNCT
ejpam-4152	105	30	·	·	PUNCT
ejpam-4152	106	1	br	br	PROPN
ejpam-4152	106	2	j	j	PROPN
ejpam-4152	106	3	(	(	PUNCT
ejpam-4152	106	4	x	x	SYM
ejpam-4152	106	5	2	2	X
ejpam-4152	106	6	)	)	PUNCT
ejpam-4152	106	7	(	(	PUNCT
ejpam-4152	106	8	r	r	NOUN
ejpam-4152	106	9	−	−	PROPN
ejpam-4152	106	10	j	j	NOUN
ejpam-4152	106	11	−	−	PROPN
ejpam-4152	106	12	1	1	NUM
ejpam-4152	106	13	)	)	PUNCT
ejpam-4152	106	14	!	!	PUNCT
ejpam-4152	106	15	{	{	PUNCT
ejpam-4152	107	1	∫	∫	PROPN
ejpam-4152	107	2	∞	∞	NUM
ejpam-4152	107	3	0	0	NUM
ejpam-4152	107	4	eπt	eπt	NOUN
ejpam-4152	107	5	cos	cos	PUNCT
ejpam-4152	108	1	[	[	X
ejpam-4152	108	2	πx/2−	πx/2−	X
ejpam-4152	108	3	(	(	PUNCT
ejpam-4152	108	4	r	r	NOUN
ejpam-4152	108	5	+	+	PROPN
ejpam-4152	108	6	n−	n−	NOUN
ejpam-4152	108	7	j)π/2	j)π/2	VERB
ejpam-4152	108	8	]	]	PUNCT
ejpam-4152	108	9	cosh	cosh	NOUN
ejpam-4152	108	10	(	(	PUNCT
ejpam-4152	108	11	2πt)−	2πt)−	PROPN
ejpam-4152	108	12	cos	cos	X
ejpam-4152	108	13	(	(	PUNCT
ejpam-4152	108	14	πx	πx	NOUN
ejpam-4152	108	15	)	)	PUNCT
ejpam-4152	108	16	tr+n−j−1	tr+n−j−1	NOUN
ejpam-4152	108	17	dt	dt	NOUN
ejpam-4152	108	18	−	−	NOUN
ejpam-4152	108	19	∫	∫	PROPN
ejpam-4152	108	20	∞	∞	PROPN
ejpam-4152	108	21	0	0	NUM
ejpam-4152	108	22	e−πt	e−πt	NOUN
ejpam-4152	108	23	cos	cos	ADP
ejpam-4152	109	1	[	[	X
ejpam-4152	109	2	πx/2	πx/2	NOUN
ejpam-4152	109	3	+	+	CCONJ
ejpam-4152	109	4	(	(	PUNCT
ejpam-4152	109	5	r	r	NOUN
ejpam-4152	109	6	+	+	PROPN
ejpam-4152	109	7	n−	n−	NOUN
ejpam-4152	109	8	j)π/2	j)π/2	VERB
ejpam-4152	109	9	]	]	PUNCT
ejpam-4152	109	10	cosh	cosh	NOUN
ejpam-4152	109	11	(	(	PUNCT
ejpam-4152	109	12	2πt)−	2πt)−	PROPN
ejpam-4152	109	13	cos	cos	X
ejpam-4152	109	14	(	(	PUNCT
ejpam-4152	109	15	πx	πx	NOUN
ejpam-4152	109	16	)	)	PUNCT
ejpam-4152	109	17	tr+n−j−1	tr+n−j−1	NOUN
ejpam-4152	109	18	dt	dt	NOUN
ejpam-4152	109	19	}	}	PUNCT
ejpam-4152	109	20	.	.	PUNCT
ejpam-4152	110	1	(	(	PUNCT
ejpam-4152	110	2	6	6	X
ejpam-4152	110	3	)	)	PUNCT
ejpam-4152	110	4	proof	proof	NOUN
ejpam-4152	110	5	.	.	PUNCT
ejpam-4152	111	1	from	from	ADP
ejpam-4152	111	2	(	(	PUNCT
ejpam-4152	111	3	2	2	NUM
ejpam-4152	111	4	)	)	PUNCT
ejpam-4152	111	5	,	,	PUNCT
ejpam-4152	111	6	we	we	PRON
ejpam-4152	111	7	get	get	VERB
ejpam-4152	111	8	t	t	NOUN
ejpam-4152	111	9	r	r	NOUN
ejpam-4152	111	10	n(x	n(x	X
ejpam-4152	111	11	)	)	PUNCT
ejpam-4152	111	12	=	=	SYM
ejpam-4152	111	13	2	2	NUM
ejpam-4152	111	14	·	·	PUNCT
ejpam-4152	111	15	n	n	X
ejpam-4152	111	16	!	!	PUNCT
ejpam-4152	112	1	(	(	PUNCT
ejpam-4152	112	2	2	2	NUM
ejpam-4152	112	3	π	π	NOUN
ejpam-4152	112	4	)	)	PUNCT
ejpam-4152	112	5	r+n	r+n	NOUN
ejpam-4152	113	1	∞∑	∞∑	PROPN
ejpam-4152	113	2	k=0	k=0	PUNCT
ejpam-4152	113	3	r−1∑	r−1∑	NUM
ejpam-4152	113	4	j=0	j=0	PROPN
ejpam-4152	113	5	(	(	PUNCT
ejpam-4152	113	6	−1)j	−1)j	X
ejpam-4152	113	7	(	(	PUNCT
ejpam-4152	113	8	r	r	NOUN
ejpam-4152	113	9	+	+	NUM
ejpam-4152	113	10	n−	n−	PROPN
ejpam-4152	113	11	j	j	NOUN
ejpam-4152	113	12	−	−	NOUN
ejpam-4152	113	13	1	1	NUM
ejpam-4152	113	14	)	)	PUNCT
ejpam-4152	113	15	!	!	PUNCT
ejpam-4152	114	1	(	(	PUNCT
ejpam-4152	114	2	r	r	NOUN
ejpam-4152	114	3	−	−	PROPN
ejpam-4152	114	4	j	j	NOUN
ejpam-4152	114	5	−	−	PROPN
ejpam-4152	114	6	1	1	NUM
ejpam-4152	114	7	)	)	PUNCT
ejpam-4152	114	8	!	!	PUNCT
ejpam-4152	115	1	n	n	X
ejpam-4152	115	2	!	!	PUNCT
ejpam-4152	115	3	·	·	PUNCT
ejpam-4152	116	1	π	π	X
ejpam-4152	116	2	j	j	PROPN
ejpam-4152	116	3	j	j	PROPN
ejpam-4152	116	4	!	!	PUNCT
ejpam-4152	116	5	br	br	PROPN
ejpam-4152	117	1	j	j	PROPN
ejpam-4152	117	2	(	(	PUNCT
ejpam-4152	117	3	x	x	SYM
ejpam-4152	117	4	2	2	X
ejpam-4152	117	5	)	)	PUNCT
ejpam-4152	117	6	×	×	NOUN
ejpam-4152	117	7	cos	cos	PROPN
ejpam-4152	118	1	[	[	X
ejpam-4152	118	2	(	(	PUNCT
ejpam-4152	118	3	2k	2k	NOUN
ejpam-4152	118	4	+	+	CCONJ
ejpam-4152	118	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	118	6	(	(	PUNCT
ejpam-4152	118	7	r	r	NOUN
ejpam-4152	118	8	+	+	PROPN
ejpam-4152	118	9	n−	n−	NOUN
ejpam-4152	118	10	j)π/2	j)π/2	VERB
ejpam-4152	118	11	]	]	PUNCT
ejpam-4152	118	12	(	(	PUNCT
ejpam-4152	118	13	2k	2k	NOUN
ejpam-4152	118	14	+	+	CCONJ
ejpam-4152	118	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	118	16	=	=	SYM
ejpam-4152	118	17	2r+n+1	2r+n+1	NUM
ejpam-4152	118	18	r−1∑	r−1∑	PROPN
ejpam-4152	118	19	j=0	j=0	PROPN
ejpam-4152	118	20	(	(	PUNCT
ejpam-4152	118	21	−1)j	−1)j	NOUN
ejpam-4152	118	22	br	br	PROPN
ejpam-4152	118	23	j	j	PROPN
ejpam-4152	118	24	(	(	PUNCT
ejpam-4152	118	25	x	x	SYM
ejpam-4152	118	26	2	2	X
ejpam-4152	118	27	)	)	PUNCT
ejpam-4152	118	28	(	(	PUNCT
ejpam-4152	118	29	r	r	NOUN
ejpam-4152	118	30	−	−	PROPN
ejpam-4152	118	31	j	j	NOUN
ejpam-4152	118	32	−	−	PROPN
ejpam-4152	118	33	1	1	NUM
ejpam-4152	118	34	)	)	PUNCT
ejpam-4152	118	35	!	!	PUNCT
ejpam-4152	119	1	j	j	X
ejpam-4152	119	2	!	!	PUNCT
ejpam-4152	119	3	·	·	PUNCT
ejpam-4152	120	1	(	(	PUNCT
ejpam-4152	120	2	r	r	NOUN
ejpam-4152	120	3	+	+	NUM
ejpam-4152	120	4	n−	n−	PROPN
ejpam-4152	120	5	j	j	NOUN
ejpam-4152	120	6	−	−	NOUN
ejpam-4152	120	7	1	1	NUM
ejpam-4152	120	8	)	)	PUNCT
ejpam-4152	120	9	!	!	PUNCT
ejpam-4152	121	1	πr+n−j	πr+n−j	VERB
ejpam-4152	121	2	∞∑	∞∑	DET
ejpam-4152	121	3	k=0	k=0	PUNCT
ejpam-4152	121	4	cos	cos	PUNCT
ejpam-4152	122	1	[	[	X
ejpam-4152	122	2	(	(	PUNCT
ejpam-4152	122	3	2k	2k	NOUN
ejpam-4152	122	4	+	+	CCONJ
ejpam-4152	122	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	122	6	(	(	PUNCT
ejpam-4152	122	7	r	r	NOUN
ejpam-4152	122	8	+	+	PROPN
ejpam-4152	122	9	n−	n−	NOUN
ejpam-4152	122	10	j)π/2	j)π/2	VERB
ejpam-4152	122	11	]	]	PUNCT
ejpam-4152	122	12	(	(	PUNCT
ejpam-4152	122	13	2k	2k	NOUN
ejpam-4152	122	14	+	+	CCONJ
ejpam-4152	122	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	122	16	.	.	PUNCT
ejpam-4152	123	1	(	(	PUNCT
ejpam-4152	123	2	7	7	X
ejpam-4152	123	3	)	)	PUNCT
ejpam-4152	123	4	c.	c.	NOUN
ejpam-4152	123	5	corcino	corcino	PROPN
ejpam-4152	123	6	,	,	PUNCT
ejpam-4152	123	7	r.	r.	PROPN
ejpam-4152	123	8	corcino	corcino	PROPN
ejpam-4152	123	9	,	,	PUNCT
ejpam-4152	123	10	j.	j.	PROPN
ejpam-4152	123	11	casquejo	casquejo	PROPN
ejpam-4152	123	12	/	/	SYM
ejpam-4152	123	13	eur	eur	PROPN
ejpam-4152	123	14	.	.	PUNCT
ejpam-4152	124	1	j.	j.	PROPN
ejpam-4152	124	2	pure	pure	PROPN
ejpam-4152	124	3	appl	appl	PROPN
ejpam-4152	124	4	.	.	PROPN
ejpam-4152	124	5	math	math	PROPN
ejpam-4152	124	6	,	,	PUNCT
ejpam-4152	124	7	14	14	NUM
ejpam-4152	124	8	(	(	PUNCT
ejpam-4152	124	9	4	4	NUM
ejpam-4152	124	10	)	)	PUNCT
ejpam-4152	124	11	(	(	PUNCT
ejpam-4152	124	12	2021	2021	NUM
ejpam-4152	124	13	)	)	PUNCT
ejpam-4152	124	14	,	,	PUNCT
ejpam-4152	124	15	1457	1457	NUM
ejpam-4152	124	16	-	-	SYM
ejpam-4152	124	17	1466	1466	NUM
ejpam-4152	124	18	1462	1462	NUM
ejpam-4152	124	19	we	we	PRON
ejpam-4152	124	20	look	look	VERB
ejpam-4152	124	21	at	at	ADP
ejpam-4152	124	22	(	(	PUNCT
ejpam-4152	124	23	r	r	NOUN
ejpam-4152	124	24	+	+	NUM
ejpam-4152	124	25	n−	n−	PROPN
ejpam-4152	124	26	j	j	NOUN
ejpam-4152	124	27	−	−	NOUN
ejpam-4152	124	28	1	1	NUM
ejpam-4152	124	29	)	)	PUNCT
ejpam-4152	124	30	!	!	PUNCT
ejpam-4152	125	1	πr+n−j	πr+n−j	VERB
ejpam-4152	125	2	∞∑	∞∑	DET
ejpam-4152	125	3	k=0	k=0	PUNCT
ejpam-4152	125	4	cos	cos	PUNCT
ejpam-4152	126	1	[	[	X
ejpam-4152	126	2	(	(	PUNCT
ejpam-4152	126	3	2k	2k	NOUN
ejpam-4152	126	4	+	+	CCONJ
ejpam-4152	126	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	126	6	(	(	PUNCT
ejpam-4152	126	7	r	r	NOUN
ejpam-4152	126	8	+	+	PROPN
ejpam-4152	126	9	n−	n−	NOUN
ejpam-4152	126	10	j)π/2	j)π/2	VERB
ejpam-4152	126	11	]	]	PUNCT
ejpam-4152	126	12	(	(	PUNCT
ejpam-4152	126	13	2k	2k	NOUN
ejpam-4152	126	14	+	+	CCONJ
ejpam-4152	126	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	126	16	=	=	SYM
ejpam-4152	126	17	1	1	NUM
ejpam-4152	126	18	πr+n−j	πr+n−j	VERB
ejpam-4152	126	19	∞∑	∞∑	NUM
ejpam-4152	126	20	k=0	k=0	PUNCT
ejpam-4152	126	21	cos	cos	PUNCT
ejpam-4152	127	1	[	[	X
ejpam-4152	127	2	(	(	PUNCT
ejpam-4152	127	3	2k	2k	NOUN
ejpam-4152	127	4	+	+	CCONJ
ejpam-4152	127	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	127	6	(	(	PUNCT
ejpam-4152	127	7	r	r	NOUN
ejpam-4152	127	8	+	+	PROPN
ejpam-4152	127	9	n−	n−	NOUN
ejpam-4152	127	10	j)π/2	j)π/2	VERB
ejpam-4152	127	11	]	]	PUNCT
ejpam-4152	127	12	(	(	PUNCT
ejpam-4152	127	13	r	r	NOUN
ejpam-4152	127	14	+	+	NUM
ejpam-4152	127	15	n−	n−	PROPN
ejpam-4152	127	16	j	j	NOUN
ejpam-4152	127	17	−	−	NOUN
ejpam-4152	127	18	1	1	NUM
ejpam-4152	127	19	)	)	PUNCT
ejpam-4152	127	20	!	!	PUNCT
ejpam-4152	128	1	(	(	PUNCT
ejpam-4152	128	2	2k	2k	NOUN
ejpam-4152	128	3	+	+	CCONJ
ejpam-4152	128	4	1)r+n−j	1)r+n−j	NUM
ejpam-4152	128	5	.	.	PUNCT
ejpam-4152	129	1	(	(	PUNCT
ejpam-4152	129	2	8)	8)	NUM
ejpam-4152	129	3	applying	apply	VERB
ejpam-4152	129	4	the	the	DET
ejpam-4152	129	5	integral	integral	ADJ
ejpam-4152	129	6	formula	formula	NOUN
ejpam-4152	129	7	∫	∫	PROPN
ejpam-4152	129	8	∞	∞	NUM
ejpam-4152	129	9	0	0	NUM
ejpam-4152	129	10	tne−at	tne−at	ADJ
ejpam-4152	129	11	dt	dt	NOUN
ejpam-4152	129	12	=	=	SYM
ejpam-4152	129	13	n	n	X
ejpam-4152	129	14	!	!	NOUN
ejpam-4152	129	15	an+1	an+1	NOUN
ejpam-4152	129	16	,	,	PUNCT
ejpam-4152	129	17	for	for	ADP
ejpam-4152	129	18	n	n	PRON
ejpam-4152	129	19	≥	≥	NOUN
ejpam-4152	129	20	0	0	NUM
ejpam-4152	129	21	and	and	CCONJ
ejpam-4152	129	22	r(a	r(a	NUM
ejpam-4152	129	23	)	)	PUNCT
ejpam-4152	129	24	>	>	X
ejpam-4152	130	1	0	0	NUM
ejpam-4152	130	2	,	,	PUNCT
ejpam-4152	130	3	then	then	ADV
ejpam-4152	130	4	(	(	PUNCT
ejpam-4152	130	5	8)	8)	NUM
ejpam-4152	130	6	becomes	become	VERB
ejpam-4152	130	7	(	(	PUNCT
ejpam-4152	130	8	r	r	NOUN
ejpam-4152	130	9	+	+	NUM
ejpam-4152	130	10	n−	n−	PROPN
ejpam-4152	130	11	j	j	NOUN
ejpam-4152	130	12	−	−	NOUN
ejpam-4152	130	13	1	1	NUM
ejpam-4152	130	14	)	)	PUNCT
ejpam-4152	130	15	!	!	PUNCT
ejpam-4152	131	1	πr+n−j	πr+n−j	VERB
ejpam-4152	131	2	∞∑	∞∑	DET
ejpam-4152	131	3	k=0	k=0	PUNCT
ejpam-4152	131	4	cos	cos	PUNCT
ejpam-4152	132	1	[	[	X
ejpam-4152	132	2	(	(	PUNCT
ejpam-4152	132	3	2k	2k	NOUN
ejpam-4152	132	4	+	+	CCONJ
ejpam-4152	132	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	132	6	(	(	PUNCT
ejpam-4152	132	7	r	r	NOUN
ejpam-4152	132	8	+	+	PROPN
ejpam-4152	132	9	n−	n−	NOUN
ejpam-4152	132	10	j)π/2	j)π/2	VERB
ejpam-4152	132	11	]	]	PUNCT
ejpam-4152	132	12	(	(	PUNCT
ejpam-4152	132	13	2k	2k	NOUN
ejpam-4152	132	14	+	+	CCONJ
ejpam-4152	132	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	132	16	=	=	SYM
ejpam-4152	132	17	1	1	NUM
ejpam-4152	132	18	πr+n−j	πr+n−j	VERB
ejpam-4152	132	19	∞∑	∞∑	NUM
ejpam-4152	132	20	k=0	k=0	PUNCT
ejpam-4152	132	21	cos	cos	PUNCT
ejpam-4152	133	1	[	[	X
ejpam-4152	133	2	(	(	PUNCT
ejpam-4152	133	3	2k	2k	NOUN
ejpam-4152	133	4	+	+	CCONJ
ejpam-4152	133	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	133	6	(	(	PUNCT
ejpam-4152	133	7	r	r	NOUN
ejpam-4152	133	8	+	+	PROPN
ejpam-4152	133	9	n−	n−	NOUN
ejpam-4152	133	10	j)π/2	j)π/2	VERB
ejpam-4152	133	11	]	]	PUNCT
ejpam-4152	133	12	∫	∫	PROPN
ejpam-4152	134	1	∞	∞	NUM
ejpam-4152	134	2	0	0	NUM
ejpam-4152	134	3	tr+n−j−1e−(2k+1)t	tr+n−j−1e−(2k+1)t	NOUN
ejpam-4152	134	4	dt	dt	X
ejpam-4152	135	1	=	=	SYM
ejpam-4152	135	2	1	1	NUM
ejpam-4152	135	3	πr+n−j	πr+n−j	VERB
ejpam-4152	135	4	∫	∫	PROPN
ejpam-4152	135	5	∞	∞	NUM
ejpam-4152	135	6	0	0	PROPN
ejpam-4152	136	1	tr+n−j−1	tr+n−j−1	NUM
ejpam-4152	136	2	∞∑	∞∑	PROPN
ejpam-4152	136	3	k=0	k=0	PROPN
ejpam-4152	136	4	e−(2k+1)t	e−(2k+1)t	PROPN
ejpam-4152	136	5	cos	cos	PROPN
ejpam-4152	137	1	[	[	X
ejpam-4152	137	2	(	(	PUNCT
ejpam-4152	137	3	2k	2k	NOUN
ejpam-4152	137	4	+	+	CCONJ
ejpam-4152	137	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	137	6	(	(	PUNCT
ejpam-4152	137	7	r	r	NOUN
ejpam-4152	137	8	+	+	PROPN
ejpam-4152	137	9	n−	n−	NOUN
ejpam-4152	137	10	j)π/2	j)π/2	VERB
ejpam-4152	137	11	]	]	PUNCT
ejpam-4152	137	12	dt	dt	X
ejpam-4152	137	13	=	=	SYM
ejpam-4152	137	14	1	1	NUM
ejpam-4152	137	15	πr+n−j	πr+n−j	VERB
ejpam-4152	137	16	∫	∫	PROPN
ejpam-4152	138	1	∞	∞	NUM
ejpam-4152	138	2	0	0	PROPN
ejpam-4152	139	1	tr+n−j−1	tr+n−j−1	NUM
ejpam-4152	139	2	∞∑	∞∑	PROPN
ejpam-4152	139	3	k=0	k=0	PROPN
ejpam-4152	139	4	e−(2k+1)t	e−(2k+1)t	PROPN
ejpam-4152	139	5	{	{	PUNCT
ejpam-4152	139	6	cos	cos	PROPN
ejpam-4152	139	7	[	[	X
ejpam-4152	139	8	(	(	PUNCT
ejpam-4152	139	9	2k	2k	NOUN
ejpam-4152	139	10	+	+	CCONJ
ejpam-4152	139	11	1)πx/2	1)πx/2	NUM
ejpam-4152	139	12	]	]	X
ejpam-4152	139	13	cos	cos	PROPN
ejpam-4152	140	1	[	[	X
ejpam-4152	140	2	(	(	PUNCT
ejpam-4152	140	3	r	r	NOUN
ejpam-4152	140	4	+	+	PROPN
ejpam-4152	140	5	n−	n−	NOUN
ejpam-4152	140	6	j)π/2	j)π/2	VERB
ejpam-4152	140	7	]	]	PUNCT
ejpam-4152	141	1	+	+	CCONJ
ejpam-4152	141	2	sin	sin	NOUN
ejpam-4152	141	3	[	[	X
ejpam-4152	141	4	(	(	PUNCT
ejpam-4152	141	5	2k	2k	NOUN
ejpam-4152	141	6	+	+	CCONJ
ejpam-4152	141	7	1)πx/2	1)πx/2	NUM
ejpam-4152	141	8	]	]	PUNCT
ejpam-4152	141	9	sin	sin	NOUN
ejpam-4152	141	10	[	[	X
ejpam-4152	141	11	(	(	PUNCT
ejpam-4152	141	12	r	r	NOUN
ejpam-4152	141	13	+	+	NUM
ejpam-4152	141	14	n−	n−	NOUN
ejpam-4152	141	15	j)π/2	j)π/2	VERB
ejpam-4152	141	16	]	]	PUNCT
ejpam-4152	141	17	}	}	PUNCT
ejpam-4152	141	18	dt	dt	X
ejpam-4152	141	19	=	=	SYM
ejpam-4152	141	20	1	1	NUM
ejpam-4152	141	21	πr+n−j	πr+n−j	VERB
ejpam-4152	141	22	∫	∫	PROPN
ejpam-4152	141	23	∞	∞	PROPN
ejpam-4152	141	24	0	0	NUM
ejpam-4152	141	25	{	{	PUNCT
ejpam-4152	141	26	cos	cos	X
ejpam-4152	142	1	[	[	X
ejpam-4152	142	2	(	(	PUNCT
ejpam-4152	142	3	r	r	NOUN
ejpam-4152	142	4	+	+	PROPN
ejpam-4152	142	5	n−	n−	NOUN
ejpam-4152	142	6	j)π/2	j)π/2	VERB
ejpam-4152	142	7	]	]	PUNCT
ejpam-4152	143	1	∞∑	∞∑	PROPN
ejpam-4152	143	2	k=0	k=0	PROPN
ejpam-4152	143	3	e−(2k+1)t	e−(2k+1)t	PROPN
ejpam-4152	143	4	cos	cos	PROPN
ejpam-4152	143	5	[	[	X
ejpam-4152	143	6	(	(	PUNCT
ejpam-4152	143	7	2k	2k	NOUN
ejpam-4152	143	8	+	+	CCONJ
ejpam-4152	143	9	1)πx/2	1)πx/2	NUM
ejpam-4152	143	10	]	]	PUNCT
ejpam-4152	143	11	+	+	CCONJ
ejpam-4152	143	12	sin	sin	NOUN
ejpam-4152	143	13	[	[	X
ejpam-4152	143	14	(	(	PUNCT
ejpam-4152	143	15	r	r	NOUN
ejpam-4152	143	16	+	+	NUM
ejpam-4152	143	17	n−	n−	NOUN
ejpam-4152	143	18	j)π/2	j)π/2	VERB
ejpam-4152	143	19	]	]	PUNCT
ejpam-4152	144	1	∞∑	∞∑	PROPN
ejpam-4152	144	2	k=0	k=0	PROPN
ejpam-4152	144	3	e−(2k+1)t	e−(2k+1)t	PROPN
ejpam-4152	144	4	sin	sin	VERB
ejpam-4152	144	5	[	[	X
ejpam-4152	144	6	(	(	PUNCT
ejpam-4152	144	7	2k	2k	NOUN
ejpam-4152	144	8	+	+	CCONJ
ejpam-4152	144	9	1)πx/2	1)πx/2	NUM
ejpam-4152	144	10	]	]	PUNCT
ejpam-4152	144	11	}	}	PUNCT
ejpam-4152	144	12	tr+n−j−1	tr+n−j−1	NUM
ejpam-4152	144	13	dt	dt	NOUN
ejpam-4152	144	14	.	.	PUNCT
ejpam-4152	145	1	(	(	PUNCT
ejpam-4152	145	2	9	9	NUM
ejpam-4152	145	3	)	)	PUNCT
ejpam-4152	145	4	by	by	ADP
ejpam-4152	145	5	making	make	VERB
ejpam-4152	145	6	use	use	NOUN
ejpam-4152	145	7	of	of	ADP
ejpam-4152	145	8	∞∑	∞∑	PRON
ejpam-4152	145	9	k=0	k=0	PROPN
ejpam-4152	145	10	e−(2k+1)t	e−(2k+1)t	PROPN
ejpam-4152	145	11	sin	sin	VERB
ejpam-4152	145	12	[	[	X
ejpam-4152	145	13	(	(	PUNCT
ejpam-4152	145	14	2k	2k	NOUN
ejpam-4152	145	15	+	+	CCONJ
ejpam-4152	145	16	1)x	1)x	NUM
ejpam-4152	145	17	]	]	X
ejpam-4152	145	18	=	=	SYM
ejpam-4152	145	19	sinx	sinx	PROPN
ejpam-4152	145	20	cosh	cosh	PROPN
ejpam-4152	145	21	t	t	PROPN
ejpam-4152	145	22	cosh	cosh	PROPN
ejpam-4152	145	23	(	(	PUNCT
ejpam-4152	145	24	2t)−	2t)−	PROPN
ejpam-4152	145	25	cos	cos	PROPN
ejpam-4152	145	26	(	(	PUNCT
ejpam-4152	145	27	2x	2x	NUM
ejpam-4152	145	28	)	)	PUNCT
ejpam-4152	145	29	,	,	PUNCT
ejpam-4152	145	30	and	and	CCONJ
ejpam-4152	145	31	∞∑	∞∑	PRON
ejpam-4152	145	32	k=0	k=0	PROPN
ejpam-4152	145	33	e−(2k+1)t	e−(2k+1)t	PROPN
ejpam-4152	145	34	cos	cos	PROPN
ejpam-4152	146	1	[	[	X
ejpam-4152	146	2	(	(	PUNCT
ejpam-4152	146	3	2k	2k	NOUN
ejpam-4152	146	4	+	+	CCONJ
ejpam-4152	146	5	1)x	1)x	NUM
ejpam-4152	146	6	]	]	X
ejpam-4152	146	7	=	=	SYM
ejpam-4152	146	8	cosx	cosx	PROPN
ejpam-4152	146	9	sinh	sinh	PROPN
ejpam-4152	146	10	t	t	PROPN
ejpam-4152	146	11	cosh	cosh	PROPN
ejpam-4152	146	12	(	(	PUNCT
ejpam-4152	146	13	2t)−	2t)−	PROPN
ejpam-4152	146	14	cos	cos	PROPN
ejpam-4152	146	15	(	(	PUNCT
ejpam-4152	146	16	2x	2x	NUM
ejpam-4152	146	17	)	)	PUNCT
ejpam-4152	146	18	,	,	PUNCT
ejpam-4152	146	19	which	which	PRON
ejpam-4152	146	20	may	may	AUX
ejpam-4152	146	21	be	be	AUX
ejpam-4152	146	22	deduced	deduce	VERB
ejpam-4152	146	23	from	from	ADP
ejpam-4152	146	24	∞∑	∞∑	PRON
ejpam-4152	146	25	k=0	k=0	PROPN
ejpam-4152	146	26	e(xi−t)(2k+1	e(xi−t)(2k+1	NOUN
ejpam-4152	146	27	)	)	PUNCT
ejpam-4152	146	28	=	=	SYM
ejpam-4152	146	29	cosx	cosx	PROPN
ejpam-4152	146	30	sinh	sinh	PROPN
ejpam-4152	146	31	t+	t+	PUNCT
ejpam-4152	146	32	i	i	PROPN
ejpam-4152	146	33	sinx	sinx	PROPN
ejpam-4152	146	34	cosh	cosh	PROPN
ejpam-4152	146	35	t	t	PROPN
ejpam-4152	146	36	cosh	cosh	PROPN
ejpam-4152	146	37	(	(	PUNCT
ejpam-4152	146	38	2t)−	2t)−	PROPN
ejpam-4152	146	39	cos	cos	PROPN
ejpam-4152	146	40	(	(	PUNCT
ejpam-4152	146	41	2x	2x	NUM
ejpam-4152	146	42	)	)	PUNCT
ejpam-4152	146	43	,	,	PUNCT
ejpam-4152	146	44	c.	c.	PROPN
ejpam-4152	146	45	corcino	corcino	PROPN
ejpam-4152	146	46	,	,	PUNCT
ejpam-4152	146	47	r.	r.	PROPN
ejpam-4152	146	48	corcino	corcino	PROPN
ejpam-4152	146	49	,	,	PUNCT
ejpam-4152	146	50	j.	j.	PROPN
ejpam-4152	146	51	casquejo	casquejo	PROPN
ejpam-4152	146	52	/	/	SYM
ejpam-4152	146	53	eur	eur	PROPN
ejpam-4152	146	54	.	.	PUNCT
ejpam-4152	147	1	j.	j.	PROPN
ejpam-4152	147	2	pure	pure	PROPN
ejpam-4152	147	3	appl	appl	PROPN
ejpam-4152	147	4	.	.	PROPN
ejpam-4152	147	5	math	math	PROPN
ejpam-4152	147	6	,	,	PUNCT
ejpam-4152	147	7	14	14	NUM
ejpam-4152	147	8	(	(	PUNCT
ejpam-4152	147	9	4	4	NUM
ejpam-4152	147	10	)	)	PUNCT
ejpam-4152	147	11	(	(	PUNCT
ejpam-4152	147	12	2021	2021	NUM
ejpam-4152	147	13	)	)	PUNCT
ejpam-4152	147	14	,	,	PUNCT
ejpam-4152	147	15	1457	1457	NUM
ejpam-4152	147	16	-	-	SYM
ejpam-4152	147	17	1466	1466	NUM
ejpam-4152	147	18	1463	1463	NUM
ejpam-4152	147	19	for	for	ADP
ejpam-4152	147	20	t	t	PROPN
ejpam-4152	147	21	>	>	X
ejpam-4152	147	22	0	0	NUM
ejpam-4152	147	23	,	,	PUNCT
ejpam-4152	147	24	(	(	PUNCT
ejpam-4152	147	25	9	9	NUM
ejpam-4152	147	26	)	)	PUNCT
ejpam-4152	147	27	then	then	ADV
ejpam-4152	147	28	becomes	become	VERB
ejpam-4152	147	29	(	(	PUNCT
ejpam-4152	147	30	r	r	NOUN
ejpam-4152	147	31	+	+	NUM
ejpam-4152	147	32	n−	n−	PROPN
ejpam-4152	147	33	j	j	NOUN
ejpam-4152	147	34	−	−	NOUN
ejpam-4152	147	35	1	1	NUM
ejpam-4152	147	36	)	)	PUNCT
ejpam-4152	147	37	!	!	PUNCT
ejpam-4152	148	1	πr+n−j	πr+n−j	VERB
ejpam-4152	148	2	∞∑	∞∑	DET
ejpam-4152	148	3	k=0	k=0	PUNCT
ejpam-4152	148	4	cos	cos	PUNCT
ejpam-4152	149	1	[	[	X
ejpam-4152	149	2	(	(	PUNCT
ejpam-4152	149	3	2k	2k	NOUN
ejpam-4152	149	4	+	+	CCONJ
ejpam-4152	149	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	149	6	(	(	PUNCT
ejpam-4152	149	7	r	r	NOUN
ejpam-4152	149	8	+	+	PROPN
ejpam-4152	149	9	n−	n−	NOUN
ejpam-4152	149	10	j)π/2	j)π/2	VERB
ejpam-4152	149	11	]	]	PUNCT
ejpam-4152	149	12	(	(	PUNCT
ejpam-4152	149	13	2k	2k	NOUN
ejpam-4152	149	14	+	+	CCONJ
ejpam-4152	149	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	149	16	=	=	SYM
ejpam-4152	149	17	1	1	NUM
ejpam-4152	149	18	πr+n−j	πr+n−j	VERB
ejpam-4152	149	19	∫	∫	PROPN
ejpam-4152	149	20	∞	∞	PROPN
ejpam-4152	149	21	0	0	NUM
ejpam-4152	149	22	{	{	PUNCT
ejpam-4152	149	23	cos	cos	X
ejpam-4152	150	1	[	[	X
ejpam-4152	150	2	(	(	PUNCT
ejpam-4152	150	3	r	r	NOUN
ejpam-4152	150	4	+	+	PROPN
ejpam-4152	150	5	n−	n−	NOUN
ejpam-4152	150	6	j)π/2	j)π/2	VERB
ejpam-4152	150	7	]	]	PUNCT
ejpam-4152	150	8	cos	cos	ADP
ejpam-4152	150	9	πx	πx	NUM
ejpam-4152	150	10	2	2	NUM
ejpam-4152	150	11	sinh	sinh	NOUN
ejpam-4152	150	12	t	t	PROPN
ejpam-4152	150	13	cosh	cosh	NOUN
ejpam-4152	150	14	(	(	PUNCT
ejpam-4152	150	15	2t)−	2t)−	PROPN
ejpam-4152	150	16	cos	cos	PROPN
ejpam-4152	150	17	(	(	PUNCT
ejpam-4152	150	18	πx	πx	NOUN
ejpam-4152	150	19	)	)	PUNCT
ejpam-4152	150	20	+	+	CCONJ
ejpam-4152	150	21	sin	sin	NOUN
ejpam-4152	150	22	[	[	X
ejpam-4152	150	23	(	(	PUNCT
ejpam-4152	150	24	r	r	NOUN
ejpam-4152	150	25	+	+	NUM
ejpam-4152	150	26	n−	n−	NOUN
ejpam-4152	150	27	j)π/2	j)π/2	VERB
ejpam-4152	150	28	]	]	PUNCT
ejpam-4152	150	29	sin	sin	NOUN
ejpam-4152	150	30	πx	πx	PUNCT
ejpam-4152	150	31	2	2	NUM
ejpam-4152	150	32	cosh	cosh	NOUN
ejpam-4152	150	33	t	t	PROPN
ejpam-4152	150	34	cosh	cosh	NOUN
ejpam-4152	150	35	(	(	PUNCT
ejpam-4152	150	36	2t)−	2t)−	PROPN
ejpam-4152	150	37	cos	cos	PROPN
ejpam-4152	150	38	(	(	PUNCT
ejpam-4152	150	39	πx	πx	NOUN
ejpam-4152	150	40	)	)	PUNCT
ejpam-4152	150	41	}	}	PUNCT
ejpam-4152	150	42	tr+n−j−1	tr+n−j−1	NUM
ejpam-4152	150	43	dt	dt	NOUN
ejpam-4152	150	44	.	.	PUNCT
ejpam-4152	151	1	(	(	PUNCT
ejpam-4152	151	2	10	10	NUM
ejpam-4152	151	3	)	)	PUNCT
ejpam-4152	151	4	applying	apply	VERB
ejpam-4152	151	5	the	the	DET
ejpam-4152	151	6	transformation	transformation	NOUN
ejpam-4152	151	7	t	t	NOUN
ejpam-4152	151	8	=	=	PUNCT
ejpam-4152	151	9	πt	πt	PROPN
ejpam-4152	151	10	,	,	PUNCT
ejpam-4152	151	11	(	(	PUNCT
ejpam-4152	151	12	10	10	NUM
ejpam-4152	151	13	)	)	PUNCT
ejpam-4152	151	14	becomes	become	VERB
ejpam-4152	151	15	(	(	PUNCT
ejpam-4152	151	16	r	r	NOUN
ejpam-4152	151	17	+	+	NUM
ejpam-4152	151	18	n−	n−	PROPN
ejpam-4152	151	19	j	j	NOUN
ejpam-4152	151	20	−	−	NOUN
ejpam-4152	151	21	1	1	NUM
ejpam-4152	151	22	)	)	PUNCT
ejpam-4152	151	23	!	!	PUNCT
ejpam-4152	152	1	πr+n−j	πr+n−j	VERB
ejpam-4152	152	2	∞∑	∞∑	DET
ejpam-4152	152	3	k=0	k=0	PUNCT
ejpam-4152	152	4	cos	cos	PUNCT
ejpam-4152	153	1	[	[	X
ejpam-4152	153	2	(	(	PUNCT
ejpam-4152	153	3	2k	2k	NOUN
ejpam-4152	153	4	+	+	CCONJ
ejpam-4152	153	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	153	6	(	(	PUNCT
ejpam-4152	153	7	r	r	NOUN
ejpam-4152	153	8	+	+	PROPN
ejpam-4152	153	9	n−	n−	NOUN
ejpam-4152	153	10	j)π/2	j)π/2	VERB
ejpam-4152	153	11	]	]	PUNCT
ejpam-4152	153	12	(	(	PUNCT
ejpam-4152	153	13	2k	2k	NOUN
ejpam-4152	153	14	+	+	CCONJ
ejpam-4152	153	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	153	16	=	=	SYM
ejpam-4152	153	17	1	1	NUM
ejpam-4152	153	18	πr+n−j	πr+n−j	VERB
ejpam-4152	153	19	∫	∫	PROPN
ejpam-4152	153	20	∞	∞	PROPN
ejpam-4152	153	21	0	0	NUM
ejpam-4152	153	22	{	{	PUNCT
ejpam-4152	153	23	cos	cos	X
ejpam-4152	154	1	[	[	X
ejpam-4152	154	2	(	(	PUNCT
ejpam-4152	154	3	r	r	NOUN
ejpam-4152	154	4	+	+	PROPN
ejpam-4152	154	5	n−	n−	NOUN
ejpam-4152	154	6	j)π/2	j)π/2	VERB
ejpam-4152	154	7	]	]	PUNCT
ejpam-4152	155	1	cos	cos	ADP
ejpam-4152	155	2	πx	πx	PROPN
ejpam-4152	155	3	2	2	NUM
ejpam-4152	155	4	sinhπt	sinhπt	PROPN
ejpam-4152	155	5	cosh	cosh	PROPN
ejpam-4152	155	6	(	(	PUNCT
ejpam-4152	155	7	2πt)−	2πt)−	PROPN
ejpam-4152	155	8	cos	cos	X
ejpam-4152	155	9	(	(	PUNCT
ejpam-4152	155	10	πx	πx	NOUN
ejpam-4152	155	11	)	)	PUNCT
ejpam-4152	155	12	+	+	CCONJ
ejpam-4152	155	13	sin	sin	NOUN
ejpam-4152	155	14	[	[	X
ejpam-4152	155	15	(	(	PUNCT
ejpam-4152	155	16	r	r	NOUN
ejpam-4152	155	17	+	+	NUM
ejpam-4152	155	18	n−	n−	NOUN
ejpam-4152	155	19	j)π/2	j)π/2	VERB
ejpam-4152	155	20	]	]	PUNCT
ejpam-4152	155	21	sin	sin	NOUN
ejpam-4152	155	22	πx	πx	PUNCT
ejpam-4152	155	23	2	2	NUM
ejpam-4152	155	24	coshπt	coshπt	NOUN
ejpam-4152	155	25	cosh	cosh	PROPN
ejpam-4152	155	26	(	(	PUNCT
ejpam-4152	155	27	2πt)−	2πt)−	PROPN
ejpam-4152	155	28	cos	cos	X
ejpam-4152	155	29	(	(	PUNCT
ejpam-4152	155	30	πx	πx	NOUN
ejpam-4152	155	31	)	)	PUNCT
ejpam-4152	155	32	}	}	PUNCT
ejpam-4152	156	1	πr+n−jtr+n−j−1	πr+n−jtr+n−j−1	ADP
ejpam-4152	156	2	dt	dt	NOUN
ejpam-4152	156	3	=	=	SYM
ejpam-4152	156	4	∫	∫	PROPN
ejpam-4152	156	5	∞	∞	PROPN
ejpam-4152	156	6	0	0	NUM
ejpam-4152	156	7	{	{	PUNCT
ejpam-4152	156	8	cos	cos	X
ejpam-4152	156	9	[	[	X
ejpam-4152	156	10	(	(	PUNCT
ejpam-4152	156	11	r	r	NOUN
ejpam-4152	156	12	+	+	PROPN
ejpam-4152	156	13	n−	n−	NOUN
ejpam-4152	156	14	j)π/2	j)π/2	VERB
ejpam-4152	156	15	]	]	PUNCT
ejpam-4152	156	16	cos	cos	ADP
ejpam-4152	156	17	πx	πx	X
ejpam-4152	156	18	2	2	NUM
ejpam-4152	156	19	(	(	PUNCT
ejpam-4152	156	20	eπs	eπ	NOUN
ejpam-4152	156	21	−	−	NOUN
ejpam-4152	156	22	e−πs	e−πs	NOUN
ejpam-4152	156	23	)	)	PUNCT
ejpam-4152	156	24	2	2	NUM
ejpam-4152	157	1	[	[	X
ejpam-4152	157	2	cosh	cosh	X
ejpam-4152	157	3	(	(	PUNCT
ejpam-4152	157	4	2πt)−	2πt)−	PROPN
ejpam-4152	157	5	cos	cos	X
ejpam-4152	157	6	(	(	PUNCT
ejpam-4152	157	7	πx	πx	NOUN
ejpam-4152	157	8	)	)	PUNCT
ejpam-4152	157	9	]	]	PUNCT
ejpam-4152	157	10	+	+	CCONJ
ejpam-4152	157	11	sin	sin	NOUN
ejpam-4152	157	12	[	[	X
ejpam-4152	157	13	(	(	PUNCT
ejpam-4152	157	14	r	r	NOUN
ejpam-4152	157	15	+	+	NUM
ejpam-4152	157	16	n−	n−	NOUN
ejpam-4152	157	17	j)π/2	j)π/2	VERB
ejpam-4152	157	18	]	]	PUNCT
ejpam-4152	157	19	sin	sin	NOUN
ejpam-4152	157	20	πx	πx	ADP
ejpam-4152	157	21	2	2	NUM
ejpam-4152	157	22	(	(	PUNCT
ejpam-4152	157	23	eπs	eπs	NOUN
ejpam-4152	157	24	+	+	CCONJ
ejpam-4152	157	25	e−πs	e−πs	NOUN
ejpam-4152	157	26	)	)	PUNCT
ejpam-4152	157	27	2	2	NUM
ejpam-4152	158	1	[	[	X
ejpam-4152	158	2	cosh	cosh	X
ejpam-4152	158	3	(	(	PUNCT
ejpam-4152	158	4	2πt)−	2πt)−	PROPN
ejpam-4152	158	5	cos	cos	X
ejpam-4152	158	6	(	(	PUNCT
ejpam-4152	158	7	πx	πx	NOUN
ejpam-4152	158	8	)	)	PUNCT
ejpam-4152	158	9	]	]	PUNCT
ejpam-4152	158	10	}	}	PUNCT
ejpam-4152	158	11	tr+n−j−1	tr+n−j−1	NUM
ejpam-4152	158	12	dt	dt	NOUN
ejpam-4152	158	13	=	=	SYM
ejpam-4152	158	14	1	1	NUM
ejpam-4152	158	15	2	2	NUM
ejpam-4152	158	16	∫	∫	NOUN
ejpam-4152	158	17	∞	∞	NOUN
ejpam-4152	158	18	0	0	NUM
ejpam-4152	158	19	{	{	PUNCT
ejpam-4152	158	20	eπs	eπs	X
ejpam-4152	158	21	(	(	PUNCT
ejpam-4152	158	22	cos	cos	X
ejpam-4152	158	23	[	[	X
ejpam-4152	158	24	(	(	PUNCT
ejpam-4152	158	25	r	r	NOUN
ejpam-4152	158	26	+	+	PROPN
ejpam-4152	158	27	n−	n−	NOUN
ejpam-4152	158	28	j)π/2	j)π/2	VERB
ejpam-4152	158	29	]	]	PUNCT
ejpam-4152	158	30	cos	cos	ADP
ejpam-4152	158	31	πx	πx	PROPN
ejpam-4152	158	32	2	2	NUM
ejpam-4152	158	33	+	+	NUM
ejpam-4152	158	34	sin	sin	NOUN
ejpam-4152	158	35	[	[	X
ejpam-4152	158	36	(	(	PUNCT
ejpam-4152	158	37	r	r	NOUN
ejpam-4152	158	38	+	+	NUM
ejpam-4152	158	39	n−	n−	NOUN
ejpam-4152	158	40	j)π/2	j)π/2	VERB
ejpam-4152	158	41	]	]	PUNCT
ejpam-4152	158	42	sin	sin	NOUN
ejpam-4152	158	43	πx	πx	ADP
ejpam-4152	158	44	2	2	NUM
ejpam-4152	158	45	)	)	PUNCT
ejpam-4152	158	46	cosh	cosh	NOUN
ejpam-4152	158	47	(	(	PUNCT
ejpam-4152	158	48	2πt)−	2πt)−	PROPN
ejpam-4152	158	49	cos	cos	X
ejpam-4152	158	50	(	(	PUNCT
ejpam-4152	158	51	πx	πx	NOUN
ejpam-4152	158	52	)	)	PUNCT
ejpam-4152	158	53	−	−	NOUN
ejpam-4152	158	54	e−πs	e−πs	NOUN
ejpam-4152	158	55	(	(	PUNCT
ejpam-4152	158	56	cos	cos	X
ejpam-4152	158	57	[	[	X
ejpam-4152	158	58	(	(	PUNCT
ejpam-4152	158	59	r	r	NOUN
ejpam-4152	158	60	+	+	PROPN
ejpam-4152	158	61	n−	n−	NOUN
ejpam-4152	158	62	j)π/2	j)π/2	VERB
ejpam-4152	158	63	]	]	PUNCT
ejpam-4152	158	64	cos	cos	ADP
ejpam-4152	158	65	πx	πx	ADP
ejpam-4152	158	66	2	2	NUM
ejpam-4152	158	67	−	−	NOUN
ejpam-4152	158	68	sin	sin	NOUN
ejpam-4152	158	69	[	[	X
ejpam-4152	158	70	(	(	PUNCT
ejpam-4152	158	71	r	r	NOUN
ejpam-4152	158	72	+	+	NUM
ejpam-4152	158	73	n−	n−	NOUN
ejpam-4152	158	74	j)π/2	j)π/2	VERB
ejpam-4152	158	75	]	]	PUNCT
ejpam-4152	158	76	sin	sin	NOUN
ejpam-4152	158	77	πx	πx	ADP
ejpam-4152	158	78	2	2	NUM
ejpam-4152	158	79	)	)	PUNCT
ejpam-4152	158	80	cosh	cosh	NOUN
ejpam-4152	158	81	(	(	PUNCT
ejpam-4152	158	82	2πt)−	2πt)−	PROPN
ejpam-4152	158	83	cos	cos	X
ejpam-4152	158	84	(	(	PUNCT
ejpam-4152	158	85	πx	πx	NOUN
ejpam-4152	158	86	)	)	PUNCT
ejpam-4152	158	87	}	}	PUNCT
ejpam-4152	159	1	tr+n−j−1	tr+n−j−1	NOUN
ejpam-4152	159	2	dt	dt	NOUN
ejpam-4152	160	1	=	=	SYM
ejpam-4152	160	2	1	1	NUM
ejpam-4152	160	3	2	2	NUM
ejpam-4152	160	4	∫	∫	NOUN
ejpam-4152	160	5	∞	∞	NOUN
ejpam-4152	160	6	0	0	NUM
ejpam-4152	160	7	eπs	eπs	X
ejpam-4152	160	8	cos	cos	PUNCT
ejpam-4152	161	1	[	[	X
ejpam-4152	161	2	πx/2−	πx/2−	X
ejpam-4152	161	3	(	(	PUNCT
ejpam-4152	161	4	r	r	NOUN
ejpam-4152	161	5	+	+	NUM
ejpam-4152	161	6	n−	n−	NOUN
ejpam-4152	161	7	j)π/2]−	j)π/2]−	ADJ
ejpam-4152	161	8	e−πs	e−πs	NOUN
ejpam-4152	161	9	cos	cos	PUNCT
ejpam-4152	162	1	[	[	X
ejpam-4152	162	2	πx/2	πx/2	NOUN
ejpam-4152	162	3	+	+	CCONJ
ejpam-4152	162	4	(	(	PUNCT
ejpam-4152	162	5	r	r	NOUN
ejpam-4152	162	6	+	+	PROPN
ejpam-4152	162	7	n−	n−	NOUN
ejpam-4152	162	8	j)π/2	j)π/2	VERB
ejpam-4152	162	9	]	]	PUNCT
ejpam-4152	162	10	cosh	cosh	NOUN
ejpam-4152	162	11	(	(	PUNCT
ejpam-4152	162	12	2πt)−	2πt)−	PROPN
ejpam-4152	162	13	cos	cos	X
ejpam-4152	162	14	(	(	PUNCT
ejpam-4152	162	15	πx	πx	NOUN
ejpam-4152	162	16	)	)	PUNCT
ejpam-4152	162	17	tr+n−j−1	tr+n−j−1	NUM
ejpam-4152	162	18	dt	dt	NOUN
ejpam-4152	162	19	.	.	PUNCT
ejpam-4152	163	1	(	(	PUNCT
ejpam-4152	163	2	11	11	X
ejpam-4152	163	3	)	)	PUNCT
ejpam-4152	163	4	applying	apply	VERB
ejpam-4152	163	5	(	(	PUNCT
ejpam-4152	163	6	11	11	NUM
ejpam-4152	163	7	)	)	PUNCT
ejpam-4152	163	8	to	to	ADP
ejpam-4152	163	9	(	(	PUNCT
ejpam-4152	163	10	7	7	NUM
ejpam-4152	163	11	)	)	PUNCT
ejpam-4152	163	12	,	,	PUNCT
ejpam-4152	163	13	we	we	PRON
ejpam-4152	163	14	get	get	VERB
ejpam-4152	163	15	the	the	DET
ejpam-4152	163	16	desired	desire	VERB
ejpam-4152	163	17	formula	formula	NOUN
ejpam-4152	163	18	(	(	PUNCT
ejpam-4152	163	19	6	6	NUM
ejpam-4152	163	20	)	)	PUNCT
ejpam-4152	163	21	.	.	PUNCT
ejpam-4152	164	1	4	4	X
ejpam-4152	164	2	.	.	X
ejpam-4152	164	3	explicit	explicit	ADJ
ejpam-4152	164	4	formula	formula	NOUN
ejpam-4152	164	5	for	for	ADP
ejpam-4152	164	6	tangent	tangent	ADJ
ejpam-4152	164	7	polynomials	polynomial	NOUN
ejpam-4152	164	8	of	of	ADP
ejpam-4152	164	9	higher	high	ADJ
ejpam-4152	164	10	-	-	PUNCT
ejpam-4152	164	11	order	order	NOUN
ejpam-4152	164	12	at	at	ADP
ejpam-4152	164	13	rational	rational	ADJ
ejpam-4152	164	14	arguments	argument	NOUN
ejpam-4152	164	15	in	in	ADP
ejpam-4152	164	16	this	this	DET
ejpam-4152	164	17	section	section	NOUN
ejpam-4152	164	18	,	,	PUNCT
ejpam-4152	164	19	we	we	PRON
ejpam-4152	164	20	obtain	obtain	VERB
ejpam-4152	164	21	an	an	DET
ejpam-4152	164	22	explicit	explicit	ADJ
ejpam-4152	164	23	formula	formula	NOUN
ejpam-4152	164	24	for	for	ADP
ejpam-4152	164	25	tangent	tangent	ADJ
ejpam-4152	164	26	polynomials	polynomial	NOUN
ejpam-4152	164	27	of	of	ADP
ejpam-4152	164	28	higher	high	ADJ
ejpam-4152	164	29	order	order	NOUN
ejpam-4152	164	30	at	at	ADP
ejpam-4152	164	31	rational	rational	ADJ
ejpam-4152	164	32	arguments	argument	NOUN
ejpam-4152	164	33	by	by	ADP
ejpam-4152	164	34	applying	apply	VERB
ejpam-4152	164	35	the	the	DET
ejpam-4152	164	36	fourier	fourier	ADJ
ejpam-4152	164	37	expansion	expansion	NOUN
ejpam-4152	164	38	(	(	PUNCT
ejpam-4152	164	39	2	2	NUM
ejpam-4152	164	40	)	)	PUNCT
ejpam-4152	164	41	.	.	PUNCT
ejpam-4152	165	1	here	here	ADV
ejpam-4152	165	2	let	let	VERB
ejpam-4152	165	3	z−	z−	PROPN
ejpam-4152	165	4	0	0	PUNCT
ejpam-4152	166	1	=	=	SYM
ejpam-4152	166	2	{	{	PUNCT
ejpam-4152	166	3	0,−1,−2	0,−1,−2	NUM
ejpam-4152	166	4	,	,	PUNCT
ejpam-4152	166	5	·	·	PUNCT
ejpam-4152	166	6	·	·	PUNCT
ejpam-4152	166	7	·	·	PUNCT
ejpam-4152	166	8	}	}	PUNCT
ejpam-4152	166	9	denote	denote	VERB
ejpam-4152	166	10	the	the	DET
ejpam-4152	166	11	set	set	NOUN
ejpam-4152	166	12	of	of	ADP
ejpam-4152	166	13	nonpositive	nonpositive	ADJ
ejpam-4152	166	14	integers	integer	NOUN
ejpam-4152	166	15	.	.	PUNCT
ejpam-4152	167	1	theorem	theorem	VERB
ejpam-4152	167	2	4.1	4.1	NUM
ejpam-4152	167	3	.	.	PUNCT
ejpam-4152	168	1	for	for	ADP
ejpam-4152	168	2	n	n	CCONJ
ejpam-4152	168	3	,	,	PUNCT
ejpam-4152	168	4	q	q	PUNCT
ejpam-4152	168	5	∈	∈	PROPN
ejpam-4152	168	6	n	n	NOUN
ejpam-4152	168	7	and	and	CCONJ
ejpam-4152	168	8	p	p	NOUN
ejpam-4152	168	9	∈	∈	PROPN
ejpam-4152	169	1	z	z	PROPN
ejpam-4152	169	2	,	,	PUNCT
ejpam-4152	169	3	t	t	PROPN
ejpam-4152	169	4	r	r	NOUN
ejpam-4152	169	5	n	n	PROPN
ejpam-4152	169	6	(	(	PUNCT
ejpam-4152	169	7	2p	2p	NUM
ejpam-4152	169	8	q	q	NOUN
ejpam-4152	169	9	)	)	PUNCT
ejpam-4152	169	10	=	=	SYM
ejpam-4152	169	11	2	2	NUM
ejpam-4152	169	12	·	·	PUNCT
ejpam-4152	169	13	n	n	X
ejpam-4152	169	14	!	!	PUNCT
ejpam-4152	169	15	(	(	PUNCT
ejpam-4152	169	16	qπ)r+n	qπ)r+n	NOUN
ejpam-4152	169	17	r−1∑	r−1∑	PROPN
ejpam-4152	169	18	j=0	j=0	PROPN
ejpam-4152	169	19	(	(	PUNCT
ejpam-4152	169	20	−1)j	−1)j	X
ejpam-4152	169	21	(	(	PUNCT
ejpam-4152	169	22	r	r	NOUN
ejpam-4152	169	23	+	+	NUM
ejpam-4152	169	24	n−	n−	PROPN
ejpam-4152	169	25	j	j	NOUN
ejpam-4152	169	26	−	−	NOUN
ejpam-4152	169	27	1	1	NUM
ejpam-4152	170	1	r	r	NOUN
ejpam-4152	170	2	−	−	PROPN
ejpam-4152	170	3	j	j	NOUN
ejpam-4152	170	4	−	−	PROPN
ejpam-4152	170	5	1	1	NUM
ejpam-4152	170	6	)	)	PUNCT
ejpam-4152	170	7	(	(	PUNCT
ejpam-4152	170	8	2qπ)j	2qπ)j	PROPN
ejpam-4152	170	9	j	j	PROPN
ejpam-4152	170	10	!	!	PUNCT
ejpam-4152	170	11	br	br	PROPN
ejpam-4152	171	1	j	j	PROPN
ejpam-4152	171	2	(	(	PUNCT
ejpam-4152	171	3	p	p	NOUN
ejpam-4152	171	4	q	q	PROPN
ejpam-4152	171	5	)	)	PUNCT
ejpam-4152	171	6	c.	c.	PROPN
ejpam-4152	171	7	corcino	corcino	PROPN
ejpam-4152	171	8	,	,	PUNCT
ejpam-4152	171	9	r.	r.	PROPN
ejpam-4152	171	10	corcino	corcino	PROPN
ejpam-4152	171	11	,	,	PUNCT
ejpam-4152	171	12	j.	j.	PROPN
ejpam-4152	171	13	casquejo	casquejo	PROPN
ejpam-4152	171	14	/	/	SYM
ejpam-4152	171	15	eur	eur	PROPN
ejpam-4152	171	16	.	.	PUNCT
ejpam-4152	172	1	j.	j.	PROPN
ejpam-4152	172	2	pure	pure	PROPN
ejpam-4152	172	3	appl	appl	PROPN
ejpam-4152	172	4	.	.	PROPN
ejpam-4152	172	5	math	math	PROPN
ejpam-4152	172	6	,	,	PUNCT
ejpam-4152	172	7	14	14	NUM
ejpam-4152	172	8	(	(	PUNCT
ejpam-4152	172	9	4	4	NUM
ejpam-4152	172	10	)	)	PUNCT
ejpam-4152	172	11	(	(	PUNCT
ejpam-4152	172	12	2021	2021	NUM
ejpam-4152	172	13	)	)	PUNCT
ejpam-4152	172	14	,	,	PUNCT
ejpam-4152	172	15	1457	1457	NUM
ejpam-4152	172	16	-	-	SYM
ejpam-4152	172	17	1466	1466	NUM
ejpam-4152	172	18	1464	1464	NUM
ejpam-4152	172	19	×	×	NOUN
ejpam-4152	172	20	q∑	q∑	PROPN
ejpam-4152	173	1	l=1	l=1	NOUN
ejpam-4152	173	2	ζ	ζ	INTJ
ejpam-4152	173	3	(	(	PUNCT
ejpam-4152	173	4	r	r	NOUN
ejpam-4152	173	5	+	+	NUM
ejpam-4152	173	6	n−	n−	PROPN
ejpam-4152	173	7	j	j	PROPN
ejpam-4152	173	8	,	,	PUNCT
ejpam-4152	173	9	2l	2l	NUM
ejpam-4152	173	10	−	−	NOUN
ejpam-4152	173	11	1	1	NUM
ejpam-4152	173	12	2q	2q	NUM
ejpam-4152	173	13	)	)	PUNCT
ejpam-4152	174	1	cos	cos	PROPN
ejpam-4152	174	2	[	[	PUNCT
ejpam-4152	174	3	(	(	PUNCT
ejpam-4152	174	4	2l	2l	NUM
ejpam-4152	174	5	−	−	PROPN
ejpam-4152	174	6	1)pπ	1)pπ	NUM
ejpam-4152	174	7	q	q	NOUN
ejpam-4152	174	8	−	−	PROPN
ejpam-4152	175	1	(	(	PUNCT
ejpam-4152	175	2	r	r	AUX
ejpam-4152	175	3	+	+	NUM
ejpam-4152	175	4	n−	n−	NOUN
ejpam-4152	175	5	j)π	j)π	NOUN
ejpam-4152	175	6	2	2	NUM
ejpam-4152	175	7	]	]	PUNCT
ejpam-4152	175	8	,	,	PUNCT
ejpam-4152	175	9	(	(	PUNCT
ejpam-4152	175	10	12	12	NUM
ejpam-4152	175	11	)	)	PUNCT
ejpam-4152	175	12	where	where	SCONJ
ejpam-4152	175	13	ζ(s	ζ(s	PROPN
ejpam-4152	175	14	,	,	PUNCT
ejpam-4152	175	15	a	a	PRON
ejpam-4152	175	16	)	)	PUNCT
ejpam-4152	175	17	=	=	SYM
ejpam-4152	176	1	∞∑	∞∑	PRON
ejpam-4152	176	2	n=0	n=0	NUM
ejpam-4152	176	3	1	1	NUM
ejpam-4152	176	4	(	(	PUNCT
ejpam-4152	176	5	n+	n+	X
ejpam-4152	176	6	a)s	a)s	NOUN
ejpam-4152	176	7	,	,	PUNCT
ejpam-4152	176	8	(	(	PUNCT
ejpam-4152	176	9	13	13	NUM
ejpam-4152	176	10	)	)	PUNCT
ejpam-4152	176	11	for	for	ADP
ejpam-4152	176	12	r(s	r(s	PROPN
ejpam-4152	176	13	)	)	PUNCT
ejpam-4152	176	14	>	>	X
ejpam-4152	176	15	1	1	NUM
ejpam-4152	176	16	and	and	CCONJ
ejpam-4152	176	17	a	a	DET
ejpam-4152	176	18	/∈	/∈	INTJ
ejpam-4152	176	19	z−	z−	NOUN
ejpam-4152	176	20	0	0	PUNCT
ejpam-4152	176	21	is	be	AUX
ejpam-4152	176	22	hurwitz	hurwitz	PROPN
ejpam-4152	176	23	zeta	zeta	PROPN
ejpam-4152	176	24	function	function	NOUN
ejpam-4152	176	25	.	.	PUNCT
ejpam-4152	177	1	proof	proof	NOUN
ejpam-4152	177	2	.	.	PUNCT
ejpam-4152	178	1	we	we	PRON
ejpam-4152	178	2	look	look	VERB
ejpam-4152	178	3	at	at	ADP
ejpam-4152	178	4	∞∑	∞∑	PRON
ejpam-4152	178	5	k=0	k=0	PUNCT
ejpam-4152	178	6	cos	cos	PUNCT
ejpam-4152	179	1	[	[	X
ejpam-4152	179	2	(	(	PUNCT
ejpam-4152	179	3	2k	2k	NOUN
ejpam-4152	179	4	+	+	CCONJ
ejpam-4152	179	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	179	6	(	(	PUNCT
ejpam-4152	179	7	r	r	NOUN
ejpam-4152	179	8	+	+	PROPN
ejpam-4152	179	9	n−	n−	NOUN
ejpam-4152	179	10	j)π/2	j)π/2	VERB
ejpam-4152	179	11	]	]	PUNCT
ejpam-4152	179	12	(	(	PUNCT
ejpam-4152	179	13	2k	2k	NOUN
ejpam-4152	179	14	+	+	CCONJ
ejpam-4152	179	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	179	16	.	.	PUNCT
ejpam-4152	180	1	(	(	PUNCT
ejpam-4152	180	2	14	14	NUM
ejpam-4152	180	3	)	)	PUNCT
ejpam-4152	180	4	replacing	replace	VERB
ejpam-4152	180	5	k	k	PROPN
ejpam-4152	180	6	with	with	ADP
ejpam-4152	180	7	k	k	PROPN
ejpam-4152	180	8	−	−	PROPN
ejpam-4152	180	9	1	1	NUM
ejpam-4152	180	10	:	:	PUNCT
ejpam-4152	180	11	∞∑	∞∑	NUM
ejpam-4152	180	12	k=0	k=0	PUNCT
ejpam-4152	180	13	cos	cos	PUNCT
ejpam-4152	181	1	[	[	X
ejpam-4152	181	2	(	(	PUNCT
ejpam-4152	181	3	2k	2k	NOUN
ejpam-4152	181	4	+	+	CCONJ
ejpam-4152	181	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	181	6	(	(	PUNCT
ejpam-4152	181	7	r	r	NOUN
ejpam-4152	181	8	+	+	PROPN
ejpam-4152	181	9	n−	n−	NOUN
ejpam-4152	181	10	j)π/2	j)π/2	VERB
ejpam-4152	181	11	]	]	PUNCT
ejpam-4152	181	12	(	(	PUNCT
ejpam-4152	181	13	2k	2k	NOUN
ejpam-4152	181	14	+	+	CCONJ
ejpam-4152	181	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	181	16	=	=	SYM
ejpam-4152	182	1	∞∑	∞∑	NUM
ejpam-4152	182	2	k=1	k=1	X
ejpam-4152	182	3	cos	cos	PROPN
ejpam-4152	183	1	[	[	X
ejpam-4152	183	2	(	(	PUNCT
ejpam-4152	183	3	r	r	NOUN
ejpam-4152	183	4	+	+	NUM
ejpam-4152	183	5	n−	n−	PROPN
ejpam-4152	183	6	j)π/2−	j)π/2−	PROPN
ejpam-4152	183	7	(	(	PUNCT
ejpam-4152	183	8	2k	2k	NOUN
ejpam-4152	183	9	−	−	PROPN
ejpam-4152	183	10	1)πx/2	1)πx/2	NOUN
ejpam-4152	183	11	]	]	PUNCT
ejpam-4152	183	12	(	(	PUNCT
ejpam-4152	183	13	2k	2k	NOUN
ejpam-4152	183	14	−	−	PROPN
ejpam-4152	183	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	183	16	.	.	PUNCT
ejpam-4152	184	1	(	(	PUNCT
ejpam-4152	184	2	15	15	X
ejpam-4152	184	3	)	)	PUNCT
ejpam-4152	184	4	applying	apply	VERB
ejpam-4152	184	5	the	the	DET
ejpam-4152	184	6	elementary	elementary	ADJ
ejpam-4152	184	7	series	series	PROPN
ejpam-4152	184	8	identity	identity	NOUN
ejpam-4152	184	9	∞∑	∞∑	NUM
ejpam-4152	184	10	k=1	k=1	ADJ
ejpam-4152	184	11	f(k	f(k	VERB
ejpam-4152	184	12	)	)	PUNCT
ejpam-4152	184	13	=	=	PUNCT
ejpam-4152	185	1	q∑	q∑	PROPN
ejpam-4152	186	1	l=1	l=1	PROPN
ejpam-4152	186	2	∞∑	∞∑	PRON
ejpam-4152	186	3	k=0	k=0	NOUN
ejpam-4152	186	4	f(qk	f(qk	PROPN
ejpam-4152	186	5	+	+	CCONJ
ejpam-4152	186	6	l	l	NOUN
ejpam-4152	186	7	)	)	PUNCT
ejpam-4152	186	8	,	,	PUNCT
ejpam-4152	186	9	q	q	PROPN
ejpam-4152	186	10	∈	∈	PROPN
ejpam-4152	186	11	n	n	CCONJ
ejpam-4152	186	12	,	,	PUNCT
ejpam-4152	186	13	(	(	PUNCT
ejpam-4152	186	14	15	15	NUM
ejpam-4152	186	15	)	)	PUNCT
ejpam-4152	186	16	becomes	become	VERB
ejpam-4152	186	17	∞∑	∞∑	DET
ejpam-4152	186	18	k=0	k=0	PUNCT
ejpam-4152	187	1	cos	cos	PUNCT
ejpam-4152	188	1	[	[	X
ejpam-4152	188	2	(	(	PUNCT
ejpam-4152	188	3	2k	2k	NOUN
ejpam-4152	188	4	+	+	CCONJ
ejpam-4152	188	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	188	6	(	(	PUNCT
ejpam-4152	188	7	r	r	NOUN
ejpam-4152	188	8	+	+	PROPN
ejpam-4152	188	9	n−	n−	NOUN
ejpam-4152	188	10	j)π/2	j)π/2	VERB
ejpam-4152	188	11	]	]	PUNCT
ejpam-4152	188	12	(	(	PUNCT
ejpam-4152	188	13	2k	2k	NOUN
ejpam-4152	188	14	+	+	CCONJ
ejpam-4152	188	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	188	16	=	=	PUNCT
ejpam-4152	189	1	q∑	q∑	PROPN
ejpam-4152	190	1	l=1	l=1	PROPN
ejpam-4152	190	2	∞∑	∞∑	DET
ejpam-4152	190	3	k=0	k=0	PUNCT
ejpam-4152	190	4	cos	cos	PUNCT
ejpam-4152	191	1	[	[	X
ejpam-4152	191	2	(	(	PUNCT
ejpam-4152	191	3	r	r	NOUN
ejpam-4152	191	4	+	+	NUM
ejpam-4152	191	5	n−	n−	PROPN
ejpam-4152	191	6	j)π/2−	j)π/2−	PROPN
ejpam-4152	191	7	(	(	PUNCT
ejpam-4152	191	8	2qk	2qk	ADJ
ejpam-4152	191	9	+	+	CCONJ
ejpam-4152	191	10	2l	2l	NUM
ejpam-4152	191	11	−	−	NOUN
ejpam-4152	191	12	1)πx/2	1)πx/2	NOUN
ejpam-4152	191	13	]	]	PUNCT
ejpam-4152	191	14	(	(	PUNCT
ejpam-4152	191	15	2qk	2qk	ADJ
ejpam-4152	191	16	+	+	CCONJ
ejpam-4152	191	17	2l	2l	NUM
ejpam-4152	191	18	−	−	PROPN
ejpam-4152	191	19	1)r+n−j	1)r+n−j	NUM
ejpam-4152	191	20	=	=	PUNCT
ejpam-4152	192	1	q∑	q∑	PROPN
ejpam-4152	193	1	l=1	l=1	VERB
ejpam-4152	193	2	∞∑	∞∑	DET
ejpam-4152	193	3	k=0	k=0	PUNCT
ejpam-4152	193	4	cos	cos	PUNCT
ejpam-4152	194	1	[	[	X
ejpam-4152	194	2	(	(	PUNCT
ejpam-4152	194	3	r	r	NOUN
ejpam-4152	194	4	+	+	NUM
ejpam-4152	194	5	n−	n−	PROPN
ejpam-4152	194	6	j)π/2−	j)π/2−	PROPN
ejpam-4152	194	7	(	(	PUNCT
ejpam-4152	194	8	2l	2l	NUM
ejpam-4152	194	9	−	−	PROPN
ejpam-4152	194	10	1)πx/2−	1)πx/2−	NUM
ejpam-4152	194	11	qkπx	qkπx	NOUN
ejpam-4152	194	12	]	]	X
ejpam-4152	194	13	[	[	PUNCT
ejpam-4152	194	14	2q	2q	NUM
ejpam-4152	194	15	(	(	PUNCT
ejpam-4152	194	16	k	k	X
ejpam-4152	194	17	+	+	NUM
ejpam-4152	194	18	2l−1	2l−1	NUM
ejpam-4152	194	19	2q	2q	NOUN
ejpam-4152	194	20	)	)	PUNCT
ejpam-4152	195	1	]	]	PUNCT
ejpam-4152	195	2	r+n−j	r+n−j	NOUN
ejpam-4152	195	3	=	=	PUNCT
ejpam-4152	195	4	q∑	q∑	PROPN
ejpam-4152	195	5	l=1	l=1	PROPN
ejpam-4152	195	6	∞∑	∞∑	DET
ejpam-4152	195	7	k=0	k=0	PUNCT
ejpam-4152	195	8	cos	cos	PUNCT
ejpam-4152	196	1	[	[	X
ejpam-4152	196	2	(	(	PUNCT
ejpam-4152	196	3	r	r	NOUN
ejpam-4152	196	4	+	+	NUM
ejpam-4152	196	5	n−	n−	PROPN
ejpam-4152	196	6	j)π/2−	j)π/2−	PROPN
ejpam-4152	196	7	(	(	PUNCT
ejpam-4152	196	8	2l	2l	NUM
ejpam-4152	196	9	−	−	PROPN
ejpam-4152	196	10	1)πx/2−	1)πx/2−	NUM
ejpam-4152	196	11	qkπx	qkπx	NOUN
ejpam-4152	196	12	]	]	X
ejpam-4152	196	13	(	(	PUNCT
ejpam-4152	196	14	2q)r+n−j	2q)r+n−j	NUM
ejpam-4152	196	15	·	·	SYM
ejpam-4152	196	16	1	1	NUM
ejpam-4152	196	17	(	(	PUNCT
ejpam-4152	196	18	k	k	NOUN
ejpam-4152	196	19	+	+	NUM
ejpam-4152	196	20	2l−1	2l−1	NUM
ejpam-4152	196	21	2q	2q	NOUN
ejpam-4152	196	22	)	)	PUNCT
ejpam-4152	196	23	r+n−j	r+n−j	NOUN
ejpam-4152	196	24	.	.	PUNCT
ejpam-4152	197	1	(	(	PUNCT
ejpam-4152	197	2	16	16	NUM
ejpam-4152	197	3	)	)	PUNCT
ejpam-4152	197	4	setting	set	VERB
ejpam-4152	197	5	x	x	PUNCT
ejpam-4152	197	6	=	=	SYM
ejpam-4152	197	7	2p	2p	NUM
ejpam-4152	197	8	/	/	SYM
ejpam-4152	197	9	q	q	NOUN
ejpam-4152	197	10	,	,	PUNCT
ejpam-4152	197	11	(	(	PUNCT
ejpam-4152	197	12	16	16	NUM
ejpam-4152	197	13	)	)	PUNCT
ejpam-4152	197	14	becomes	become	VERB
ejpam-4152	197	15	∞∑	∞∑	DET
ejpam-4152	197	16	k=0	k=0	PUNCT
ejpam-4152	197	17	cos	cos	PUNCT
ejpam-4152	198	1	[	[	X
ejpam-4152	198	2	(	(	PUNCT
ejpam-4152	198	3	2k	2k	NOUN
ejpam-4152	198	4	+	+	CCONJ
ejpam-4152	198	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	198	6	(	(	PUNCT
ejpam-4152	198	7	r	r	NOUN
ejpam-4152	198	8	+	+	PROPN
ejpam-4152	198	9	n−	n−	NOUN
ejpam-4152	198	10	j)π/2	j)π/2	VERB
ejpam-4152	198	11	]	]	PUNCT
ejpam-4152	198	12	(	(	PUNCT
ejpam-4152	198	13	2k	2k	NOUN
ejpam-4152	198	14	+	+	CCONJ
ejpam-4152	198	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	198	16	=	=	PUNCT
ejpam-4152	199	1	q∑	q∑	PROPN
ejpam-4152	200	1	l=1	l=1	PROPN
ejpam-4152	200	2	∞∑	∞∑	DET
ejpam-4152	200	3	k=0	k=0	PUNCT
ejpam-4152	200	4	cos	cos	PUNCT
ejpam-4152	201	1	[	[	X
ejpam-4152	201	2	(	(	PUNCT
ejpam-4152	201	3	r	r	NOUN
ejpam-4152	201	4	+	+	NUM
ejpam-4152	201	5	n−	n−	PROPN
ejpam-4152	201	6	j)π/2−	j)π/2−	PROPN
ejpam-4152	201	7	(	(	PUNCT
ejpam-4152	201	8	2l	2l	NUM
ejpam-4152	201	9	−	−	PROPN
ejpam-4152	201	10	1)pπ	1)pπ	NUM
ejpam-4152	201	11	/	/	SYM
ejpam-4152	201	12	q	q	NOUN
ejpam-4152	201	13	−	−	NOUN
ejpam-4152	201	14	2π(pk	2π(pk	NUM
ejpam-4152	201	15	)	)	PUNCT
ejpam-4152	201	16	]	]	PUNCT
ejpam-4152	201	17	(	(	PUNCT
ejpam-4152	201	18	2q)r+n−j	2q)r+n−j	NUM
ejpam-4152	201	19	·	·	SYM
ejpam-4152	201	20	1	1	NUM
ejpam-4152	201	21	(	(	PUNCT
ejpam-4152	201	22	k	k	NOUN
ejpam-4152	201	23	+	+	NUM
ejpam-4152	201	24	2l−1	2l−1	NUM
ejpam-4152	201	25	2q	2q	NOUN
ejpam-4152	201	26	)	)	PUNCT
ejpam-4152	201	27	r+n−j	r+n−j	NOUN
ejpam-4152	201	28	references	reference	NOUN
ejpam-4152	201	29	1465	1465	NUM
ejpam-4152	201	30	=	=	SYM
ejpam-4152	201	31	1	1	NUM
ejpam-4152	201	32	(	(	PUNCT
ejpam-4152	201	33	2q)r+n−j	2q)r+n−j	NUM
ejpam-4152	201	34	q∑	q∑	NOUN
ejpam-4152	202	1	l=1	l=1	VERB
ejpam-4152	202	2	∞∑	∞∑	DET
ejpam-4152	202	3	k=0	k=0	PUNCT
ejpam-4152	202	4	cos	cos	PUNCT
ejpam-4152	203	1	[	[	X
ejpam-4152	203	2	(	(	PUNCT
ejpam-4152	203	3	r	r	NOUN
ejpam-4152	203	4	+	+	NUM
ejpam-4152	203	5	n−	n−	PROPN
ejpam-4152	203	6	j)π/2−	j)π/2−	PROPN
ejpam-4152	203	7	(	(	PUNCT
ejpam-4152	203	8	2l	2l	NUM
ejpam-4152	203	9	−	−	PROPN
ejpam-4152	203	10	1)pπ	1)pπ	NUM
ejpam-4152	203	11	/	/	SYM
ejpam-4152	203	12	q	q	NOUN
ejpam-4152	203	13	]	]	X
ejpam-4152	203	14	·	·	PUNCT
ejpam-4152	203	15	1	1	X
ejpam-4152	203	16	(	(	PUNCT
ejpam-4152	203	17	k	k	NOUN
ejpam-4152	203	18	+	+	NUM
ejpam-4152	203	19	2l−1	2l−1	NUM
ejpam-4152	203	20	2q	2q	NOUN
ejpam-4152	203	21	)	)	PUNCT
ejpam-4152	204	1	r+n−j	r+n−j	NOUN
ejpam-4152	204	2	=	=	SYM
ejpam-4152	204	3	1	1	NUM
ejpam-4152	204	4	(	(	PUNCT
ejpam-4152	204	5	2q)r+n−j	2q)r+n−j	NUM
ejpam-4152	204	6	q∑	q∑	NOUN
ejpam-4152	205	1	l=1	l=1	X
ejpam-4152	205	2	cos	cos	X
ejpam-4152	206	1	[	[	X
ejpam-4152	206	2	(	(	PUNCT
ejpam-4152	206	3	r	r	NOUN
ejpam-4152	206	4	+	+	NUM
ejpam-4152	206	5	n−	n−	PROPN
ejpam-4152	206	6	j)π/2−	j)π/2−	PROPN
ejpam-4152	206	7	(	(	PUNCT
ejpam-4152	206	8	2l	2l	NUM
ejpam-4152	206	9	−	−	PROPN
ejpam-4152	206	10	1)pπ	1)pπ	NUM
ejpam-4152	206	11	/	/	SYM
ejpam-4152	206	12	q	q	NOUN
ejpam-4152	206	13	]	]	X
ejpam-4152	206	14	∞∑	∞∑	PRON
ejpam-4152	206	15	k=0	k=0	PROPN
ejpam-4152	206	16	1	1	NUM
ejpam-4152	206	17	(	(	PUNCT
ejpam-4152	206	18	k	k	NOUN
ejpam-4152	206	19	+	+	NUM
ejpam-4152	206	20	2l−1	2l−1	NUM
ejpam-4152	206	21	2q	2q	NOUN
ejpam-4152	206	22	)	)	PUNCT
ejpam-4152	206	23	r+n−j	r+n−j	NOUN
ejpam-4152	206	24	.	.	PUNCT
ejpam-4152	207	1	(	(	PUNCT
ejpam-4152	207	2	17	17	NUM
ejpam-4152	207	3	)	)	PUNCT
ejpam-4152	207	4	by	by	ADP
ejpam-4152	207	5	(	(	PUNCT
ejpam-4152	207	6	13	13	NUM
ejpam-4152	207	7	)	)	PUNCT
ejpam-4152	207	8	,	,	PUNCT
ejpam-4152	207	9	(	(	PUNCT
ejpam-4152	207	10	17	17	NUM
ejpam-4152	207	11	)	)	PUNCT
ejpam-4152	207	12	becomes	become	VERB
ejpam-4152	207	13	∞∑	∞∑	DET
ejpam-4152	207	14	k=0	k=0	PUNCT
ejpam-4152	207	15	cos	cos	PUNCT
ejpam-4152	208	1	[	[	X
ejpam-4152	208	2	(	(	PUNCT
ejpam-4152	208	3	2k	2k	NOUN
ejpam-4152	208	4	+	+	CCONJ
ejpam-4152	208	5	1)πx/2−	1)πx/2−	NUM
ejpam-4152	208	6	(	(	PUNCT
ejpam-4152	208	7	r	r	NOUN
ejpam-4152	208	8	+	+	PROPN
ejpam-4152	208	9	n−	n−	NOUN
ejpam-4152	208	10	j)π/2	j)π/2	VERB
ejpam-4152	208	11	]	]	PUNCT
ejpam-4152	208	12	(	(	PUNCT
ejpam-4152	208	13	2k	2k	NOUN
ejpam-4152	208	14	+	+	CCONJ
ejpam-4152	208	15	1)r+n−j	1)r+n−j	NUM
ejpam-4152	208	16	=	=	SYM
ejpam-4152	208	17	1	1	NUM
ejpam-4152	208	18	(	(	PUNCT
ejpam-4152	208	19	2q)r+n−j	2q)r+n−j	NUM
ejpam-4152	208	20	q∑	q∑	INTJ
ejpam-4152	209	1	l=1	l=1	X
ejpam-4152	209	2	cos	cos	INTJ
ejpam-4152	209	3	[	[	PUNCT
ejpam-4152	209	4	(	(	PUNCT
ejpam-4152	209	5	2l	2l	NUM
ejpam-4152	209	6	−	−	PROPN
ejpam-4152	209	7	1)pπ	1)pπ	NUM
ejpam-4152	209	8	q	q	NOUN
ejpam-4152	210	1	−	−	PROPN
ejpam-4152	210	2	(	(	PUNCT
ejpam-4152	210	3	r	r	NOUN
ejpam-4152	210	4	+	+	NUM
ejpam-4152	210	5	n−	n−	NOUN
ejpam-4152	210	6	j)π	j)π	NOUN
ejpam-4152	210	7	2	2	NUM
ejpam-4152	210	8	]	]	SYM
ejpam-4152	210	9	ζ	ζ	NOUN
ejpam-4152	210	10	(	(	PUNCT
ejpam-4152	210	11	r	r	NOUN
ejpam-4152	210	12	+	+	NUM
ejpam-4152	210	13	n−	n−	PROPN
ejpam-4152	210	14	j	j	PROPN
ejpam-4152	210	15	,	,	PUNCT
ejpam-4152	210	16	2l	2l	NUM
ejpam-4152	210	17	−	−	NOUN
ejpam-4152	210	18	1	1	NUM
ejpam-4152	210	19	2q	2q	NUM
ejpam-4152	210	20	)	)	PUNCT
ejpam-4152	210	21	.	.	PUNCT
ejpam-4152	211	1	(	(	PUNCT
ejpam-4152	211	2	18	18	NUM
ejpam-4152	211	3	)	)	PUNCT
ejpam-4152	211	4	replacing	replace	VERB
ejpam-4152	211	5	(	(	PUNCT
ejpam-4152	211	6	14	14	NUM
ejpam-4152	211	7	)	)	PUNCT
ejpam-4152	211	8	with	with	ADP
ejpam-4152	211	9	(	(	PUNCT
ejpam-4152	211	10	18	18	NUM
ejpam-4152	211	11	)	)	PUNCT
ejpam-4152	211	12	in	in	ADP
ejpam-4152	211	13	(	(	PUNCT
ejpam-4152	211	14	2	2	NUM
ejpam-4152	211	15	)	)	PUNCT
ejpam-4152	211	16	,	,	PUNCT
ejpam-4152	211	17	we	we	PRON
ejpam-4152	211	18	obtain	obtain	VERB
ejpam-4152	211	19	the	the	DET
ejpam-4152	211	20	desired	desire	VERB
ejpam-4152	211	21	formula	formula	NOUN
ejpam-4152	211	22	(	(	PUNCT
ejpam-4152	211	23	12	12	NUM
ejpam-4152	211	24	)	)	PUNCT
ejpam-4152	211	25	.	.	PUNCT
ejpam-4152	212	1	acknowledgements	acknowledgement	NOUN
ejpam-4152	212	2	the	the	DET
ejpam-4152	212	3	authors	author	NOUN
ejpam-4152	212	4	would	would	AUX
ejpam-4152	212	5	like	like	VERB
ejpam-4152	212	6	to	to	PART
ejpam-4152	212	7	thank	thank	VERB
ejpam-4152	212	8	the	the	DET
ejpam-4152	212	9	anonymous	anonymous	ADJ
ejpam-4152	212	10	referees	referee	NOUN
ejpam-4152	212	11	for	for	ADP
ejpam-4152	212	12	reviewing	review	VERB
ejpam-4152	212	13	the	the	DET
ejpam-4152	212	14	paper	paper	NOUN
ejpam-4152	212	15	thoroughly	thoroughly	ADV
ejpam-4152	212	16	the	the	DET
ejpam-4152	212	17	authors	author	NOUN
ejpam-4152	212	18	would	would	AUX
ejpam-4152	212	19	also	also	ADV
ejpam-4152	212	20	like	like	VERB
ejpam-4152	212	21	to	to	PART
ejpam-4152	212	22	thank	thank	VERB
ejpam-4152	212	23	cebu	cebu	NOUN
ejpam-4152	212	24	normal	normal	ADJ
ejpam-4152	212	25	university	university	NOUN
ejpam-4152	212	26	(	(	PUNCT
ejpam-4152	212	27	cnu	cnu	PROPN
ejpam-4152	212	28	)	)	PUNCT
ejpam-4152	212	29	for	for	ADP
ejpam-4152	212	30	funding	fund	VERB
ejpam-4152	212	31	this	this	DET
ejpam-4152	212	32	research	research	NOUN
ejpam-4152	212	33	project	project	NOUN
ejpam-4152	212	34	through	through	ADP
ejpam-4152	212	35	its	its	PRON
ejpam-4152	212	36	research	research	NOUN
ejpam-4152	212	37	institute	institute	NOUN
ejpam-4152	212	38	for	for	ADP
ejpam-4152	212	39	computational	computational	ADJ
ejpam-4152	212	40	mathematics	mathematic	NOUN
ejpam-4152	212	41	and	and	CCONJ
ejpam-4152	212	42	physics	physics	PROPN
ejpam-4152	212	43	(	(	PUNCT
ejpam-4152	212	44	ricmp	ricmp	PROPN
ejpam-4152	212	45	)	)	PUNCT
ejpam-4152	212	46	.	.	PUNCT
ejpam-4152	213	1	references	reference	NOUN
ejpam-4152	213	2	[	[	X
ejpam-4152	213	3	1	1	NUM
ejpam-4152	213	4	]	]	PUNCT
ejpam-4152	213	5	ryoo	ryoo	NOUN
ejpam-4152	213	6	,	,	PUNCT
ejpam-4152	213	7	c.	c.	PROPN
ejpam-4152	213	8	s.	s.	PROPN
ejpam-4152	213	9	,	,	PUNCT
ejpam-4152	213	10	multiple	multiple	ADJ
ejpam-4152	213	11	tangent	tangent	NOUN
ejpam-4152	213	12	zeta	zeta	NOUN
ejpam-4152	213	13	function	function	NOUN
ejpam-4152	213	14	and	and	CCONJ
ejpam-4152	213	15	tangent	tangent	NOUN
ejpam-4152	213	16	polynomials	polynomial	NOUN
ejpam-4152	213	17	of	of	ADP
ejpam-4152	213	18	higher	high	ADJ
ejpam-4152	213	19	order	order	NOUN
ejpam-4152	213	20	,	,	PUNCT
ejpam-4152	213	21	adv	adv	PROPN
ejpam-4152	213	22	.	.	PUNCT
ejpam-4152	214	1	studies	studies	PROPN
ejpam-4152	214	2	theor	theor	PROPN
ejpam-4152	214	3	.	.	PUNCT
ejpam-4152	215	1	phys	phy	NOUN
ejpam-4152	215	2	8(10	8(10	NUM
ejpam-4152	215	3	)	)	PUNCT
ejpam-4152	215	4	(	(	PUNCT
ejpam-4152	215	5	2014	2014	NUM
ejpam-4152	215	6	)	)	PUNCT
ejpam-4152	215	7	,	,	PUNCT
ejpam-4152	215	8	457	457	NUM
ejpam-4152	215	9	-	-	SYM
ejpam-4152	215	10	462	462	NUM
ejpam-4152	215	11	.	.	PUNCT
ejpam-4152	216	1	[	[	X
ejpam-4152	216	2	2	2	NUM
ejpam-4152	216	3	]	]	PUNCT
ejpam-4152	216	4	ryoo	ryoo	NOUN
ejpam-4152	216	5	,	,	PUNCT
ejpam-4152	216	6	c.	c.	PROPN
ejpam-4152	216	7	s.	s.	PROPN
ejpam-4152	216	8	,	,	PUNCT
ejpam-4152	216	9	a	a	DET
ejpam-4152	216	10	note	note	NOUN
ejpam-4152	216	11	on	on	ADP
ejpam-4152	216	12	the	the	DET
ejpam-4152	216	13	tangent	tangent	ADJ
ejpam-4152	216	14	numbers	number	NOUN
ejpam-4152	216	15	and	and	CCONJ
ejpam-4152	216	16	polynomials	polynomial	NOUN
ejpam-4152	216	17	,	,	PUNCT
ejpam-4152	216	18	adv	adv	PROPN
ejpam-4152	216	19	.	.	PUNCT
ejpam-4152	216	20	studies	studies	PROPN
ejpam-4152	216	21	theor	theor	PROPN
ejpam-4152	216	22	.	.	PUNCT
ejpam-4152	217	1	phys	phy	NOUN
ejpam-4152	217	2	7(9	7(9	NUM
ejpam-4152	217	3	)	)	PUNCT
ejpam-4152	217	4	(	(	PUNCT
ejpam-4152	217	5	2013	2013	NUM
ejpam-4152	217	6	)	)	PUNCT
ejpam-4152	217	7	,	,	PUNCT
ejpam-4152	217	8	447	447	NUM
ejpam-4152	217	9	-	-	SYM
ejpam-4152	217	10	454	454	NUM
ejpam-4152	217	11	.	.	PUNCT
ejpam-4152	218	1	[	[	X
ejpam-4152	218	2	3	3	NUM
ejpam-4152	218	3	]	]	X
ejpam-4152	218	4	ryoo	ryoo	NOUN
ejpam-4152	218	5	,	,	PUNCT
ejpam-4152	218	6	c.	c.	PROPN
ejpam-4152	218	7	s.	s.	PROPN
ejpam-4152	218	8	,	,	PUNCT
ejpam-4152	218	9	a	a	DET
ejpam-4152	218	10	numerical	numerical	ADJ
ejpam-4152	218	11	investigation	investigation	NOUN
ejpam-4152	218	12	on	on	ADP
ejpam-4152	218	13	the	the	DET
ejpam-4152	218	14	zeros	zero	NOUN
ejpam-4152	218	15	of	of	ADP
ejpam-4152	218	16	the	the	DET
ejpam-4152	218	17	tangent	tangent	NOUN
ejpam-4152	218	18	polynomials	polynomial	NOUN
ejpam-4152	218	19	,	,	PUNCT
ejpam-4152	218	20	j.	j.	PROPN
ejpam-4152	218	21	appl	appl	PROPN
ejpam-4152	218	22	.	.	PROPN
ejpam-4152	218	23	math	math	PROPN
ejpam-4152	218	24	.	.	PUNCT
ejpam-4152	219	1	info	info	NOUN
ejpam-4152	219	2	.	.	PUNCT
ejpam-4152	220	1	32(3	32(3	NUM
ejpam-4152	220	2	-	-	SYM
ejpam-4152	220	3	4	4	NUM
ejpam-4152	220	4	)	)	PUNCT
ejpam-4152	220	5	(	(	PUNCT
ejpam-4152	220	6	2014	2014	NUM
ejpam-4152	220	7	)	)	PUNCT
ejpam-4152	220	8	,	,	PUNCT
ejpam-4152	220	9	315	315	NUM
ejpam-4152	220	10	-	-	SYM
ejpam-4152	220	11	322	322	NUM
ejpam-4152	220	12	.	.	PUNCT
ejpam-4152	221	1	[	[	X
ejpam-4152	221	2	4	4	NUM
ejpam-4152	221	3	]	]	SYM
ejpam-4152	221	4	ryoo	ryoo	NOUN
ejpam-4152	221	5	,	,	PUNCT
ejpam-4152	221	6	c.	c.	PROPN
ejpam-4152	221	7	s.	s.	PROPN
ejpam-4152	221	8	,	,	PUNCT
ejpam-4152	221	9	on	on	ADP
ejpam-4152	221	10	the	the	DET
ejpam-4152	221	11	twisted	twisted	ADJ
ejpam-4152	221	12	q	q	ADJ
ejpam-4152	221	13	-	-	PUNCT
ejpam-4152	221	14	tangent	tangent	ADJ
ejpam-4152	221	15	numbers	number	NOUN
ejpam-4152	221	16	and	and	CCONJ
ejpam-4152	221	17	polynomials	polynomial	NOUN
ejpam-4152	221	18	,	,	PUNCT
ejpam-4152	221	19	appll	appll	PROPN
ejpam-4152	221	20	.	.	PUNCT
ejpam-4152	222	1	math	math	PROPN
ejpam-4152	222	2	.	.	PUNCT
ejpam-4152	223	1	sci	sci	PROPN
ejpam-4152	223	2	.	.	PROPN
ejpam-4152	224	1	7(99	7(99	NUM
ejpam-4152	224	2	)	)	PUNCT
ejpam-4152	224	3	(	(	PUNCT
ejpam-4152	224	4	2013	2013	NUM
ejpam-4152	224	5	)	)	PUNCT
ejpam-4152	224	6	,	,	PUNCT
ejpam-4152	224	7	4935	4935	NUM
ejpam-4152	224	8	-	-	SYM
ejpam-4152	224	9	4941	4941	NUM
ejpam-4152	224	10	.	.	PUNCT
ejpam-4152	225	1	[	[	X
ejpam-4152	225	2	5	5	NUM
ejpam-4152	225	3	]	]	PUNCT
ejpam-4152	225	4	ryoo	ryoo	NOUN
ejpam-4152	225	5	,	,	PUNCT
ejpam-4152	225	6	c.	c.	PROPN
ejpam-4152	225	7	s.	s.	PROPN
ejpam-4152	225	8	,	,	PUNCT
ejpam-4152	225	9	explicit	explicit	ADJ
ejpam-4152	225	10	identities	identity	NOUN
ejpam-4152	225	11	for	for	ADP
ejpam-4152	225	12	the	the	DET
ejpam-4152	225	13	generalized	generalize	VERB
ejpam-4152	225	14	tangent	tangent	NOUN
ejpam-4152	225	15	polynomials	polynomial	NOUN
ejpam-4152	225	16	,	,	PUNCT
ejpam-4152	225	17	nonlinear	nonlinear	ADJ
ejpam-4152	225	18	analysis	analysis	NOUN
ejpam-4152	225	19	and	and	CCONJ
ejpam-4152	225	20	differential	differential	ADJ
ejpam-4152	225	21	equations	equation	NOUN
ejpam-4152	225	22	6(1	6(1	NUM
ejpam-4152	225	23	)	)	PUNCT
ejpam-4152	225	24	(	(	PUNCT
ejpam-4152	225	25	2018	2018	NUM
ejpam-4152	225	26	)	)	PUNCT
ejpam-4152	225	27	,	,	PUNCT
ejpam-4152	225	28	43	43	NUM
ejpam-4152	225	29	51	51	NUM
ejpam-4152	225	30	.	.	PUNCT
ejpam-4152	226	1	[	[	X
ejpam-4152	226	2	6	6	NUM
ejpam-4152	226	3	]	]	SYM
ejpam-4152	226	4	ryoo	ryoo	NOUN
ejpam-4152	226	5	,	,	PUNCT
ejpam-4152	226	6	c.	c.	PROPN
ejpam-4152	226	7	s.	s.	PROPN
ejpam-4152	226	8	,	,	PUNCT
ejpam-4152	226	9	on	on	ADP
ejpam-4152	226	10	the	the	DET
ejpam-4152	226	11	analogues	analogue	NOUN
ejpam-4152	226	12	of	of	ADP
ejpam-4152	226	13	tangent	tangent	ADJ
ejpam-4152	226	14	numbers	number	NOUN
ejpam-4152	226	15	and	and	CCONJ
ejpam-4152	226	16	polynomials	polynomial	NOUN
ejpam-4152	226	17	associated	associate	VERB
ejpam-4152	226	18	with	with	ADP
ejpam-4152	226	19	p	p	NOUN
ejpam-4152	226	20	-	-	PUNCT
ejpam-4152	226	21	adic	adic	NOUN
ejpam-4152	226	22	integral	integral	NOUN
ejpam-4152	226	23	on	on	ADP
ejpam-4152	226	24	zp	zp	PROPN
ejpam-4152	226	25	,	,	PUNCT
ejpam-4152	226	26	appl	appl	PROPN
ejpam-4152	226	27	.	.	PROPN
ejpam-4152	226	28	math	math	PROPN
ejpam-4152	226	29	.	.	PUNCT
ejpam-4152	227	1	sci	sci	PROPN
ejpam-4152	227	2	.	.	PUNCT
ejpam-4152	228	1	7(64	7(64	NOUN
ejpam-4152	228	2	)	)	PUNCT
ejpam-4152	228	3	(	(	PUNCT
ejpam-4152	228	4	2013	2013	NUM
ejpam-4152	228	5	)	)	PUNCT
ejpam-4152	228	6	,	,	PUNCT
ejpam-4152	228	7	3177	3177	NUM
ejpam-4152	228	8	-	-	SYM
ejpam-4152	228	9	3183	3183	NUM
ejpam-4152	228	10	.	.	PUNCT
ejpam-4152	229	1	[	[	X
ejpam-4152	229	2	7	7	NUM
ejpam-4152	229	3	]	]	SYM
ejpam-4152	229	4	ryoo	ryoo	NOUN
ejpam-4152	229	5	,	,	PUNCT
ejpam-4152	229	6	c.	c.	PROPN
ejpam-4152	229	7	s.	s.	PROPN
ejpam-4152	229	8	,	,	PUNCT
ejpam-4152	229	9	a	a	DET
ejpam-4152	229	10	note	note	NOUN
ejpam-4152	229	11	on	on	ADP
ejpam-4152	229	12	the	the	DET
ejpam-4152	229	13	symmetric	symmetric	ADJ
ejpam-4152	229	14	properties	property	NOUN
ejpam-4152	229	15	for	for	ADP
ejpam-4152	229	16	the	the	DET
ejpam-4152	229	17	tangent	tangent	NOUN
ejpam-4152	229	18	polynomials	polynomial	NOUN
ejpam-4152	229	19	,	,	PUNCT
ejpam-4152	229	20	int	int	NOUN
ejpam-4152	229	21	.	.	PUNCT
ejpam-4152	230	1	j.	j.	PROPN
ejpam-4152	230	2	math	math	PROPN
ejpam-4152	230	3	.	.	PUNCT
ejpam-4152	231	1	anal	anal	ADJ
ejpam-4152	231	2	.	.	PUNCT
ejpam-4152	232	1	7(52	7(52	NUM
ejpam-4152	232	2	)	)	PUNCT
ejpam-4152	232	3	(	(	PUNCT
ejpam-4152	232	4	2013	2013	NUM
ejpam-4152	232	5	)	)	PUNCT
ejpam-4152	232	6	,	,	PUNCT
ejpam-4152	232	7	2575	2575	NUM
ejpam-4152	232	8	-	-	SYM
ejpam-4152	232	9	2581	2581	NUM
ejpam-4152	232	10	.	.	PUNCT
ejpam-4152	233	1	references	reference	NOUN
ejpam-4152	233	2	1466	1466	NUM
ejpam-4152	233	3	[	[	X
ejpam-4152	233	4	8	8	NUM
ejpam-4152	233	5	]	]	X
ejpam-4152	233	6	luo	luo	PROPN
ejpam-4152	233	7	,	,	PUNCT
ejpam-4152	233	8	q	q	NOUN
ejpam-4152	233	9	-	-	PUNCT
ejpam-4152	233	10	m.	m.	NOUN
ejpam-4152	233	11	,	,	PUNCT
ejpam-4152	233	12	fourier	fourier	NOUN
ejpam-4152	233	13	expansions	expansion	NOUN
ejpam-4152	233	14	and	and	CCONJ
ejpam-4152	233	15	integral	integral	ADJ
ejpam-4152	233	16	representations	representation	NOUN
ejpam-4152	233	17	for	for	ADP
ejpam-4152	233	18	the	the	DET
ejpam-4152	233	19	genocchi	genocchi	PROPN
ejpam-4152	233	20	polynomials	polynomial	NOUN
ejpam-4152	233	21	,	,	PUNCT
ejpam-4152	233	22	j.	j.	PROPN
ejpam-4152	233	23	integer	integer	PROPN
ejpam-4152	233	24	seq	seq	PROPN
ejpam-4152	233	25	.	.	PUNCT
ejpam-4152	233	26	12(1	12(1	NUM
ejpam-4152	233	27	)	)	PUNCT
ejpam-4152	233	28	(	(	PUNCT
ejpam-4152	233	29	2009	2009	NUM
ejpam-4152	233	30	)	)	PUNCT
ejpam-4152	233	31	,	,	PUNCT
ejpam-4152	233	32	article	article	NOUN
ejpam-4152	233	33	09.1.4	09.1.4	NOUN
ejpam-4152	233	34	.	.	PUNCT