id	sid	tid	token	lemma	pos
ejpam-4507	1	1	european	european	PROPN
ejpam-4507	1	2	journal	journal	PROPN
ejpam-4507	1	3	of	of	ADP
ejpam-4507	1	4	pure	pure	ADJ
ejpam-4507	1	5	and	and	CCONJ
ejpam-4507	1	6	applied	apply	VERB
ejpam-4507	1	7	mathematics	mathematic	NOUN
ejpam-4507	1	8	vol	vol	NOUN
ejpam-4507	1	9	.	.	PROPN
ejpam-4507	2	1	15	15	NUM
ejpam-4507	2	2	,	,	PUNCT
ejpam-4507	2	3	no	no	INTJ
ejpam-4507	2	4	.	.	NOUN
ejpam-4507	2	5	4	4	NUM
ejpam-4507	2	6	,	,	PUNCT
ejpam-4507	2	7	2022	2022	NUM
ejpam-4507	2	8	,	,	PUNCT
ejpam-4507	2	9	1662	1662	NUM
ejpam-4507	2	10	-	-	SYM
ejpam-4507	2	11	1682	1682	NUM
ejpam-4507	2	12	issn	issn	PROPN
ejpam-4507	2	13	1307	1307	NUM
ejpam-4507	2	14	-	-	SYM
ejpam-4507	2	15	5543	5543	NUM
ejpam-4507	2	16	–	–	PUNCT
ejpam-4507	2	17	ejpam.com	ejpam.com	X
ejpam-4507	2	18	published	publish	VERB
ejpam-4507	2	19	by	by	ADP
ejpam-4507	2	20	new	new	PROPN
ejpam-4507	2	21	york	york	PROPN
ejpam-4507	2	22	business	business	PROPN
ejpam-4507	2	23	global	global	PROPN
ejpam-4507	2	24	fourier	fourier	PROPN
ejpam-4507	2	25	series	series	NOUN
ejpam-4507	2	26	for	for	ADP
ejpam-4507	2	27	bernoulli	bernoulli	NOUN
ejpam-4507	2	28	-	-	PUNCT
ejpam-4507	2	29	type	type	NOUN
ejpam-4507	2	30	polynomials	polynomial	NOUN
ejpam-4507	2	31	,	,	PUNCT
ejpam-4507	2	32	euler	euler	NOUN
ejpam-4507	2	33	-	-	PUNCT
ejpam-4507	2	34	type	type	NOUN
ejpam-4507	2	35	polynomials	polynomial	NOUN
ejpam-4507	2	36	and	and	CCONJ
ejpam-4507	2	37	genocchi	genocchi	NOUN
ejpam-4507	2	38	-	-	PUNCT
ejpam-4507	2	39	type	type	NOUN
ejpam-4507	2	40	polynomials	polynomial	NOUN
ejpam-4507	2	41	of	of	ADP
ejpam-4507	2	42	integer	integer	NOUN
ejpam-4507	2	43	order	order	NOUN
ejpam-4507	2	44	cristina	cristina	PROPN
ejpam-4507	2	45	b.	b.	PROPN
ejpam-4507	2	46	corcino1,2	corcino1,2	PROPN
ejpam-4507	2	47	,	,	PUNCT
ejpam-4507	2	48	roberto	roberto	PROPN
ejpam-4507	2	49	b.	b.	PROPN
ejpam-4507	2	50	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-4507	2	51	1	1	NUM
ejpam-4507	2	52	research	research	NOUN
ejpam-4507	2	53	institute	institute	NOUN
ejpam-4507	2	54	for	for	ADP
ejpam-4507	2	55	computational	computational	ADJ
ejpam-4507	2	56	mathematics	mathematic	NOUN
ejpam-4507	2	57	and	and	CCONJ
ejpam-4507	2	58	physics	physics	NOUN
ejpam-4507	2	59	,	,	PUNCT
ejpam-4507	2	60	cebu	cebu	NOUN
ejpam-4507	2	61	normal	normal	ADJ
ejpam-4507	2	62	university	university	NOUN
ejpam-4507	2	63	,	,	PUNCT
ejpam-4507	2	64	6000	6000	NUM
ejpam-4507	2	65	cebu	cebu	NOUN
ejpam-4507	2	66	city	city	NOUN
ejpam-4507	2	67	,	,	PUNCT
ejpam-4507	2	68	philippines	philippines	PROPN
ejpam-4507	2	69	2	2	NUM
ejpam-4507	2	70	department	department	NOUN
ejpam-4507	2	71	of	of	ADP
ejpam-4507	2	72	mathematics	mathematic	NOUN
ejpam-4507	2	73	,	,	PUNCT
ejpam-4507	2	74	cebu	cebu	NOUN
ejpam-4507	2	75	normal	normal	ADJ
ejpam-4507	2	76	university	university	NOUN
ejpam-4507	2	77	,	,	PUNCT
ejpam-4507	2	78	6000	6000	NUM
ejpam-4507	2	79	cebu	cebu	NOUN
ejpam-4507	2	80	city	city	NOUN
ejpam-4507	2	81	,	,	PUNCT
ejpam-4507	2	82	philippines	philippine	NOUN
ejpam-4507	2	83	abstract	abstract	ADJ
ejpam-4507	2	84	.	.	PUNCT
ejpam-4507	3	1	parameters	parameter	NOUN
ejpam-4507	3	2	a	a	DET
ejpam-4507	3	3	,	,	PUNCT
ejpam-4507	3	4	b	b	PROPN
ejpam-4507	3	5	,	,	PUNCT
ejpam-4507	3	6	c	c	NOUN
ejpam-4507	3	7	,	,	PUNCT
ejpam-4507	3	8	and	and	CCONJ
ejpam-4507	3	9	α	α	NOUN
ejpam-4507	3	10	are	be	AUX
ejpam-4507	3	11	introduced	introduce	VERB
ejpam-4507	3	12	to	to	PART
ejpam-4507	3	13	form	form	VERB
ejpam-4507	3	14	the	the	DET
ejpam-4507	3	15	bernoulli	bernoulli	NOUN
ejpam-4507	3	16	-	-	PUNCT
ejpam-4507	3	17	type	type	NOUN
ejpam-4507	3	18	,	,	PUNCT
ejpam-4507	3	19	euler	euler	NOUN
ejpam-4507	3	20	-	-	PUNCT
ejpam-4507	3	21	type	type	NOUN
ejpam-4507	3	22	and	and	CCONJ
ejpam-4507	3	23	genocchi	genocchi	NOUN
ejpam-4507	3	24	-	-	PUNCT
ejpam-4507	3	25	type	type	NOUN
ejpam-4507	3	26	polynomilas	polynomila	NOUN
ejpam-4507	3	27	where	where	SCONJ
ejpam-4507	3	28	α	α	NOUN
ejpam-4507	3	29	is	be	AUX
ejpam-4507	3	30	the	the	DET
ejpam-4507	3	31	order	order	NOUN
ejpam-4507	3	32	of	of	ADP
ejpam-4507	3	33	the	the	DET
ejpam-4507	3	34	polynomial	polynomial	NOUN
ejpam-4507	3	35	and	and	CCONJ
ejpam-4507	3	36	is	be	AUX
ejpam-4507	3	37	a	a	DET
ejpam-4507	3	38	positive	positive	ADJ
ejpam-4507	3	39	integer	integer	NOUN
ejpam-4507	3	40	.	.	PUNCT
ejpam-4507	4	1	analytic	analytic	ADJ
ejpam-4507	4	2	methods	method	NOUN
ejpam-4507	4	3	are	be	AUX
ejpam-4507	4	4	used	use	VERB
ejpam-4507	4	5	here	here	ADV
ejpam-4507	4	6	to	to	PART
ejpam-4507	4	7	obtain	obtain	VERB
ejpam-4507	4	8	the	the	DET
ejpam-4507	4	9	fourier	fourier	ADJ
ejpam-4507	4	10	series	series	NOUN
ejpam-4507	4	11	for	for	ADP
ejpam-4507	4	12	these	these	DET
ejpam-4507	4	13	polynomials	polynomial	NOUN
ejpam-4507	4	14	.	.	PUNCT
ejpam-4507	5	1	2020	2020	NUM
ejpam-4507	5	2	mathematics	mathematic	NOUN
ejpam-4507	5	3	subject	subject	NOUN
ejpam-4507	5	4	classifications	classification	NOUN
ejpam-4507	5	5	:	:	PUNCT
ejpam-4507	5	6	11b68	11b68	NUM
ejpam-4507	5	7	,	,	PUNCT
ejpam-4507	5	8	42a16	42a16	NUM
ejpam-4507	5	9	,	,	PUNCT
ejpam-4507	5	10	11m35	11m35	NUM
ejpam-4507	5	11	key	key	ADJ
ejpam-4507	5	12	words	word	NOUN
ejpam-4507	5	13	and	and	CCONJ
ejpam-4507	5	14	phrases	phrase	NOUN
ejpam-4507	5	15	:	:	PUNCT
ejpam-4507	5	16	fourier	fourier	ADJ
ejpam-4507	5	17	series	series	NOUN
ejpam-4507	5	18	,	,	PUNCT
ejpam-4507	5	19	bernoulli	bernoulli	NOUN
ejpam-4507	5	20	polynomials	polynomial	NOUN
ejpam-4507	5	21	,	,	PUNCT
ejpam-4507	5	22	euler	euler	NOUN
ejpam-4507	5	23	polynomials	polynomial	NOUN
ejpam-4507	5	24	,	,	PUNCT
ejpam-4507	5	25	genocchi	genocchi	PROPN
ejpam-4507	5	26	polynomials	polynomial	VERB
ejpam-4507	5	27	1	1	NUM
ejpam-4507	5	28	.	.	PUNCT
ejpam-4507	6	1	introduction	introduction	NOUN
ejpam-4507	6	2	the	the	DET
ejpam-4507	6	3	polynomials	polynomial	NOUN
ejpam-4507	6	4	that	that	PRON
ejpam-4507	6	5	will	will	AUX
ejpam-4507	6	6	be	be	AUX
ejpam-4507	6	7	considered	consider	VERB
ejpam-4507	6	8	are	be	AUX
ejpam-4507	6	9	given	give	VERB
ejpam-4507	6	10	by	by	ADP
ejpam-4507	6	11	the	the	DET
ejpam-4507	6	12	generating	generating	NOUN
ejpam-4507	6	13	functions	function	NOUN
ejpam-4507	6	14	(	(	PUNCT
ejpam-4507	6	15	1)-(3	1)-(3	NUM
ejpam-4507	6	16	)	)	PUNCT
ejpam-4507	6	17	where	where	SCONJ
ejpam-4507	6	18	b	b	X
ejpam-4507	6	19	(	(	PUNCT
ejpam-4507	6	20	α	α	NOUN
ejpam-4507	6	21	)	)	PUNCT
ejpam-4507	6	22	n	n	PROPN
ejpam-4507	6	23	(	(	PUNCT
ejpam-4507	6	24	x	x	X
ejpam-4507	6	25	;	;	PUNCT
ejpam-4507	6	26	a	a	DET
ejpam-4507	6	27	,	,	PUNCT
ejpam-4507	6	28	b	b	NOUN
ejpam-4507	6	29	,	,	PUNCT
ejpam-4507	6	30	c	c	NOUN
ejpam-4507	6	31	)	)	PUNCT
ejpam-4507	6	32	denotes	denote	VERB
ejpam-4507	6	33	the	the	DET
ejpam-4507	6	34	bernoulli	bernoulli	NOUN
ejpam-4507	6	35	-	-	PUNCT
ejpam-4507	6	36	type	type	NOUN
ejpam-4507	6	37	polynomials	polynomial	NOUN
ejpam-4507	6	38	of	of	ADP
ejpam-4507	6	39	order	order	NOUN
ejpam-4507	6	40	α	α	NOUN
ejpam-4507	6	41	,	,	PUNCT
ejpam-4507	6	42	e	e	PROPN
ejpam-4507	6	43	(	(	PUNCT
ejpam-4507	6	44	α	α	NOUN
ejpam-4507	6	45	)	)	PUNCT
ejpam-4507	6	46	n	n	PROPN
ejpam-4507	6	47	(	(	PUNCT
ejpam-4507	6	48	x	x	X
ejpam-4507	6	49	;	;	PUNCT
ejpam-4507	6	50	a	a	DET
ejpam-4507	6	51	,	,	PUNCT
ejpam-4507	6	52	b	b	NOUN
ejpam-4507	6	53	,	,	PUNCT
ejpam-4507	6	54	c	c	NOUN
ejpam-4507	6	55	)	)	PUNCT
ejpam-4507	6	56	denotes	denote	VERB
ejpam-4507	6	57	the	the	DET
ejpam-4507	6	58	euler	euler	NOUN
ejpam-4507	6	59	-	-	PUNCT
ejpam-4507	6	60	type	type	NOUN
ejpam-4507	6	61	polynomials	polynomial	NOUN
ejpam-4507	6	62	of	of	ADP
ejpam-4507	6	63	order	order	NOUN
ejpam-4507	6	64	α	α	NOUN
ejpam-4507	6	65	and	and	CCONJ
ejpam-4507	6	66	g	g	PROPN
ejpam-4507	6	67	(	(	PUNCT
ejpam-4507	6	68	α	α	NOUN
ejpam-4507	6	69	)	)	PUNCT
ejpam-4507	6	70	n	n	PROPN
ejpam-4507	6	71	(	(	PUNCT
ejpam-4507	6	72	x	x	X
ejpam-4507	6	73	;	;	PUNCT
ejpam-4507	6	74	a	a	DET
ejpam-4507	6	75	,	,	PUNCT
ejpam-4507	6	76	b	b	NOUN
ejpam-4507	6	77	,	,	PUNCT
ejpam-4507	6	78	c	c	NOUN
ejpam-4507	6	79	)	)	PUNCT
ejpam-4507	6	80	denotes	denote	VERB
ejpam-4507	6	81	the	the	DET
ejpam-4507	6	82	genocchitype	genocchitype	NOUN
ejpam-4507	6	83	polynomials	polynomial	NOUN
ejpam-4507	6	84	of	of	ADP
ejpam-4507	6	85	order	order	NOUN
ejpam-4507	6	86	α	α	NOUN
ejpam-4507	6	87	with	with	ADP
ejpam-4507	6	88	α	α	PROPN
ejpam-4507	6	89	∈	∈	PROPN
ejpam-4507	6	90	z+	z+	X
ejpam-4507	6	91	,	,	PUNCT
ejpam-4507	6	92	a	a	DET
ejpam-4507	6	93	,	,	PUNCT
ejpam-4507	6	94	b	b	NOUN
ejpam-4507	6	95	,	,	PUNCT
ejpam-4507	6	96	c	c	PROPN
ejpam-4507	6	97	are	be	AUX
ejpam-4507	6	98	positive	positive	ADJ
ejpam-4507	6	99	real	real	ADJ
ejpam-4507	6	100	numbers	number	NOUN
ejpam-4507	6	101	and	and	CCONJ
ejpam-4507	6	102	b	b	X
ejpam-4507	6	103	=	=	SYM
ejpam-4507	6	104	ln	ln	PROPN
ejpam-4507	6	105	b−	b−	PROPN
ejpam-4507	7	1	ln	ln	ADV
ejpam-4507	7	2	a	a	PRON
ejpam-4507	7	3	>	>	X
ejpam-4507	7	4	0	0	NUM
ejpam-4507	7	5	.	.	PUNCT
ejpam-4507	8	1	(	(	PUNCT
ejpam-4507	8	2	t	t	NOUN
ejpam-4507	8	3	bt	bt	NOUN
ejpam-4507	8	4	−	−	PROPN
ejpam-4507	8	5	at	at	ADP
ejpam-4507	8	6	)	)	PUNCT
ejpam-4507	8	7	α	α	NOUN
ejpam-4507	8	8	cxt	cxt	NOUN
ejpam-4507	8	9	=	=	PUNCT
ejpam-4507	9	1	∞∑	∞∑	PROPN
ejpam-4507	9	2	n=0	n=0	NUM
ejpam-4507	9	3	b(α	b(α	NOUN
ejpam-4507	9	4	)	)	PUNCT
ejpam-4507	9	5	n	n	CCONJ
ejpam-4507	9	6	(	(	PUNCT
ejpam-4507	9	7	x	x	X
ejpam-4507	9	8	;	;	PUNCT
ejpam-4507	9	9	a	a	DET
ejpam-4507	9	10	,	,	PUNCT
ejpam-4507	9	11	b	b	NOUN
ejpam-4507	9	12	,	,	PUNCT
ejpam-4507	9	13	c	c	NOUN
ejpam-4507	9	14	)	)	PUNCT
ejpam-4507	9	15	tn	tn	PROPN
ejpam-4507	9	16	n	n	CCONJ
ejpam-4507	9	17	!	!	PUNCT
ejpam-4507	9	18	,	,	PUNCT
ejpam-4507	9	19	|t|	|t|	VERB
ejpam-4507	9	20	<	<	X
ejpam-4507	9	21	2π	2π	PROPN
ejpam-4507	9	22	b	b	X
ejpam-4507	9	23	(	(	PUNCT
ejpam-4507	9	24	1	1	NUM
ejpam-4507	9	25	)	)	PUNCT
ejpam-4507	9	26	(	(	PUNCT
ejpam-4507	9	27	2	2	NUM
ejpam-4507	9	28	bt	bt	NOUN
ejpam-4507	9	29	+	+	X
ejpam-4507	9	30	at	at	ADP
ejpam-4507	9	31	)	)	PUNCT
ejpam-4507	9	32	α	α	NOUN
ejpam-4507	9	33	cxt	cxt	NOUN
ejpam-4507	9	34	=	=	PUNCT
ejpam-4507	9	35	∞∑	∞∑	NUM
ejpam-4507	9	36	n=0	n=0	NUM
ejpam-4507	9	37	e(α	e(α	NOUN
ejpam-4507	9	38	)	)	PUNCT
ejpam-4507	9	39	n	n	CCONJ
ejpam-4507	9	40	(	(	PUNCT
ejpam-4507	9	41	x	x	X
ejpam-4507	9	42	;	;	PUNCT
ejpam-4507	9	43	a	a	DET
ejpam-4507	9	44	,	,	PUNCT
ejpam-4507	9	45	b	b	NOUN
ejpam-4507	9	46	,	,	PUNCT
ejpam-4507	9	47	c	c	NOUN
ejpam-4507	9	48	)	)	PUNCT
ejpam-4507	9	49	tn	tn	PROPN
ejpam-4507	9	50	n	n	CCONJ
ejpam-4507	9	51	!	!	PUNCT
ejpam-4507	9	52	,	,	PUNCT
ejpam-4507	9	53	|t|	|t|	VERB
ejpam-4507	9	54	<	<	X
ejpam-4507	9	55	π	π	PROPN
ejpam-4507	9	56	b	b	PROPN
ejpam-4507	9	57	(	(	PUNCT
ejpam-4507	9	58	2	2	NUM
ejpam-4507	9	59	)	)	PUNCT
ejpam-4507	9	60	(	(	PUNCT
ejpam-4507	9	61	2	2	NUM
ejpam-4507	9	62	t	t	NOUN
ejpam-4507	9	63	bt	bt	NOUN
ejpam-4507	9	64	+	+	CCONJ
ejpam-4507	9	65	at	at	ADP
ejpam-4507	9	66	)	)	PUNCT
ejpam-4507	9	67	α	α	NOUN
ejpam-4507	9	68	cxt	cxt	NOUN
ejpam-4507	9	69	=	=	PUNCT
ejpam-4507	9	70	∞∑	∞∑	PROPN
ejpam-4507	9	71	n=0	n=0	NUM
ejpam-4507	9	72	g(α	g(α	PROPN
ejpam-4507	9	73	)	)	PUNCT
ejpam-4507	9	74	n	n	CCONJ
ejpam-4507	9	75	(	(	PUNCT
ejpam-4507	9	76	x	x	X
ejpam-4507	9	77	;	;	PUNCT
ejpam-4507	9	78	a	a	DET
ejpam-4507	9	79	,	,	PUNCT
ejpam-4507	9	80	b	b	NOUN
ejpam-4507	9	81	,	,	PUNCT
ejpam-4507	9	82	c	c	NOUN
ejpam-4507	9	83	)	)	PUNCT
ejpam-4507	9	84	tn	tn	PROPN
ejpam-4507	9	85	n	n	CCONJ
ejpam-4507	9	86	!	!	PUNCT
ejpam-4507	9	87	,	,	PUNCT
ejpam-4507	9	88	|t|	|t|	VERB
ejpam-4507	9	89	<	<	X
ejpam-4507	9	90	π	π	PROPN
ejpam-4507	9	91	b	b	PROPN
ejpam-4507	9	92	.	.	PUNCT
ejpam-4507	10	1	(	(	PUNCT
ejpam-4507	10	2	3	3	X
ejpam-4507	10	3	)	)	PUNCT
ejpam-4507	10	4	∗corresponding	∗corresponde	VERB
ejpam-4507	10	5	author	author	NOUN
ejpam-4507	10	6	.	.	PUNCT
ejpam-4507	11	1	doi	doi	NOUN
ejpam-4507	11	2	:	:	PUNCT
ejpam-4507	11	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4507	https://doi.org/10.29020/nybg.ejpam.v15i4.4507	VERB
ejpam-4507	11	4	email	email	NOUN
ejpam-4507	11	5	addresses	address	NOUN
ejpam-4507	11	6	:	:	PUNCT
ejpam-4507	11	7	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-4507	11	8	(	(	PUNCT
ejpam-4507	11	9	c.	c.	PROPN
ejpam-4507	11	10	corcino	corcino	PROPN
ejpam-4507	11	11	)	)	PUNCT
ejpam-4507	11	12	,	,	PUNCT
ejpam-4507	11	13	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-4507	11	14	(	(	PUNCT
ejpam-4507	11	15	r.	r.	PROPN
ejpam-4507	11	16	corcino	corcino	PROPN
ejpam-4507	11	17	)	)	PUNCT
ejpam-4507	11	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4507	11	19	1662	1662	NUM
ejpam-4507	12	1	©	©	PROPN
ejpam-4507	12	2	2022	2022	NUM
ejpam-4507	12	3	ejpam	ejpam	VERB
ejpam-4507	12	4	all	all	DET
ejpam-4507	12	5	rights	right	NOUN
ejpam-4507	12	6	reserved	reserve	VERB
ejpam-4507	12	7	.	.	PUNCT
ejpam-4507	13	1	c.	c.	PROPN
ejpam-4507	13	2	corcino	corcino	PROPN
ejpam-4507	13	3	,	,	PUNCT
ejpam-4507	13	4	r.	r.	PROPN
ejpam-4507	13	5	corcino	corcino	PROPN
ejpam-4507	13	6	/	/	SYM
ejpam-4507	13	7	eur	eur	PROPN
ejpam-4507	13	8	.	.	PUNCT
ejpam-4507	14	1	j.	j.	PROPN
ejpam-4507	14	2	pure	pure	PROPN
ejpam-4507	14	3	appl	appl	PROPN
ejpam-4507	14	4	.	.	PROPN
ejpam-4507	14	5	math	math	PROPN
ejpam-4507	14	6	,	,	PUNCT
ejpam-4507	14	7	15	15	NUM
ejpam-4507	14	8	(	(	PUNCT
ejpam-4507	14	9	4	4	NUM
ejpam-4507	14	10	)	)	PUNCT
ejpam-4507	14	11	(	(	PUNCT
ejpam-4507	14	12	2022	2022	NUM
ejpam-4507	14	13	)	)	PUNCT
ejpam-4507	14	14	,	,	PUNCT
ejpam-4507	14	15	1662	1662	NUM
ejpam-4507	14	16	-	-	SYM
ejpam-4507	14	17	1682	1682	NUM
ejpam-4507	14	18	1663	1663	NUM
ejpam-4507	14	19	these	these	DET
ejpam-4507	14	20	polynomials	polynomial	NOUN
ejpam-4507	14	21	are	be	AUX
ejpam-4507	14	22	generalizations	generalization	NOUN
ejpam-4507	14	23	of	of	ADP
ejpam-4507	14	24	the	the	DET
ejpam-4507	14	25	classical	classical	ADJ
ejpam-4507	14	26	bernoulli	bernoulli	PROPN
ejpam-4507	14	27	,	,	PUNCT
ejpam-4507	14	28	euler	euler	VERB
ejpam-4507	14	29	and	and	CCONJ
ejpam-4507	14	30	genocchi	genocchi	PROPN
ejpam-4507	14	31	polynomials	polynomial	NOUN
ejpam-4507	14	32	,	,	PUNCT
ejpam-4507	14	33	respectively	respectively	ADV
ejpam-4507	14	34	.	.	PUNCT
ejpam-4507	15	1	the	the	DET
ejpam-4507	15	2	apostol	apostol	NOUN
ejpam-4507	15	3	-	-	PUNCT
ejpam-4507	15	4	type	type	NOUN
ejpam-4507	15	5	of	of	ADP
ejpam-4507	15	6	these	these	DET
ejpam-4507	15	7	polynomials	polynomial	NOUN
ejpam-4507	15	8	were	be	AUX
ejpam-4507	15	9	mentioned	mention	VERB
ejpam-4507	15	10	in	in	ADP
ejpam-4507	15	11	[	[	X
ejpam-4507	15	12	9	9	NUM
ejpam-4507	15	13	]	]	PUNCT
ejpam-4507	15	14	in	in	ADP
ejpam-4507	15	15	the	the	DET
ejpam-4507	15	16	introduction	introduction	NOUN
ejpam-4507	15	17	of	of	ADP
ejpam-4507	15	18	the	the	DET
ejpam-4507	15	19	paper	paper	NOUN
ejpam-4507	15	20	.	.	PUNCT
ejpam-4507	16	1	fourier	fourier	PROPN
ejpam-4507	16	2	series	series	PROPN
ejpam-4507	16	3	for	for	ADP
ejpam-4507	16	4	the	the	DET
ejpam-4507	16	5	tangent	tangent	ADJ
ejpam-4507	16	6	type	type	NOUN
ejpam-4507	16	7	of	of	ADP
ejpam-4507	16	8	these	these	DET
ejpam-4507	16	9	polynomials	polynomial	NOUN
ejpam-4507	16	10	were	be	AUX
ejpam-4507	16	11	obtained	obtain	VERB
ejpam-4507	16	12	in	in	ADP
ejpam-4507	16	13	[	[	X
ejpam-4507	16	14	7	7	NUM
ejpam-4507	16	15	]	]	PUNCT
ejpam-4507	16	16	while	while	SCONJ
ejpam-4507	16	17	the	the	DET
ejpam-4507	16	18	fourier	fourier	NOUN
ejpam-4507	16	19	series	series	NOUN
ejpam-4507	16	20	for	for	ADP
ejpam-4507	16	21	the	the	DET
ejpam-4507	16	22	apostol	apostol	NOUN
ejpam-4507	16	23	-	-	PUNCT
ejpam-4507	16	24	tangent	tangent	NOUN
ejpam-4507	16	25	polynomials	polynomial	NOUN
ejpam-4507	16	26	were	be	AUX
ejpam-4507	16	27	obtained	obtain	VERB
ejpam-4507	16	28	in	in	ADP
ejpam-4507	16	29	[	[	X
ejpam-4507	16	30	6	6	NUM
ejpam-4507	16	31	]	]	PUNCT
ejpam-4507	16	32	.	.	PUNCT
ejpam-4507	17	1	integral	integral	ADJ
ejpam-4507	17	2	representation	representation	NOUN
ejpam-4507	17	3	and	and	CCONJ
ejpam-4507	17	4	explicit	explicit	ADJ
ejpam-4507	17	5	formula	formula	NOUN
ejpam-4507	17	6	at	at	ADP
ejpam-4507	17	7	rational	rational	ADJ
ejpam-4507	17	8	arguments	argument	NOUN
ejpam-4507	17	9	of	of	ADP
ejpam-4507	17	10	tangent	tangent	ADJ
ejpam-4507	17	11	polynomials	polynomial	NOUN
ejpam-4507	17	12	of	of	ADP
ejpam-4507	17	13	higher	high	ADJ
ejpam-4507	17	14	order	order	NOUN
ejpam-4507	17	15	were	be	AUX
ejpam-4507	17	16	derived	derive	VERB
ejpam-4507	17	17	in	in	ADP
ejpam-4507	17	18	[	[	X
ejpam-4507	17	19	8	8	NUM
ejpam-4507	17	20	]	]	PUNCT
ejpam-4507	17	21	.	.	PUNCT
ejpam-4507	18	1	properties	property	NOUN
ejpam-4507	18	2	of	of	ADP
ejpam-4507	18	3	higher	high	ADJ
ejpam-4507	18	4	order	order	NOUN
ejpam-4507	18	5	apostol	apostol	NOUN
ejpam-4507	18	6	-	-	PUNCT
ejpam-4507	18	7	frobeniustype	frobeniustype	NOUN
ejpam-4507	18	8	poly	poly	ADJ
ejpam-4507	18	9	-	-	PUNCT
ejpam-4507	18	10	genocchi	genocchi	NOUN
ejpam-4507	18	11	polynomials	polynomial	NOUN
ejpam-4507	18	12	with	with	ADP
ejpam-4507	18	13	parameters	parameter	NOUN
ejpam-4507	18	14	a	a	DET
ejpam-4507	18	15	,	,	PUNCT
ejpam-4507	18	16	b	b	PROPN
ejpam-4507	18	17	and	and	CCONJ
ejpam-4507	18	18	c	c	PROPN
ejpam-4507	18	19	were	be	AUX
ejpam-4507	18	20	studied	study	VERB
ejpam-4507	18	21	in	in	ADP
ejpam-4507	18	22	[	[	X
ejpam-4507	18	23	10	10	NUM
ejpam-4507	18	24	]	]	PUNCT
ejpam-4507	18	25	.	.	PUNCT
ejpam-4507	19	1	other	other	ADJ
ejpam-4507	19	2	interesting	interesting	ADJ
ejpam-4507	19	3	polynomials	polynomial	NOUN
ejpam-4507	19	4	related	relate	VERB
ejpam-4507	19	5	to	to	ADP
ejpam-4507	19	6	bernoulli	bernoulli	PROPN
ejpam-4507	19	7	,	,	PUNCT
ejpam-4507	19	8	euler	euler	VERB
ejpam-4507	19	9	and	and	CCONJ
ejpam-4507	19	10	genocchi	genocchi	PROPN
ejpam-4507	19	11	were	be	AUX
ejpam-4507	19	12	studied	study	VERB
ejpam-4507	19	13	in	in	ADP
ejpam-4507	19	14	[	[	X
ejpam-4507	19	15	1–4	1–4	NOUN
ejpam-4507	19	16	]	]	X
ejpam-4507	19	17	.	.	PUNCT
ejpam-4507	20	1	in	in	ADP
ejpam-4507	20	2	this	this	DET
ejpam-4507	20	3	paper	paper	NOUN
ejpam-4507	20	4	,	,	PUNCT
ejpam-4507	20	5	the	the	DET
ejpam-4507	20	6	fourier	fourier	NOUN
ejpam-4507	20	7	series	series	NOUN
ejpam-4507	20	8	for	for	ADP
ejpam-4507	20	9	b	b	PROPN
ejpam-4507	20	10	(	(	PUNCT
ejpam-4507	20	11	α	α	NOUN
ejpam-4507	20	12	)	)	PUNCT
ejpam-4507	20	13	n	n	PROPN
ejpam-4507	20	14	(	(	PUNCT
ejpam-4507	20	15	x	x	X
ejpam-4507	20	16	;	;	PUNCT
ejpam-4507	20	17	a	a	DET
ejpam-4507	20	18	,	,	PUNCT
ejpam-4507	20	19	b	b	NOUN
ejpam-4507	20	20	,	,	PUNCT
ejpam-4507	20	21	c	c	NOUN
ejpam-4507	20	22	)	)	PUNCT
ejpam-4507	20	23	,	,	PUNCT
ejpam-4507	20	24	e	e	X
ejpam-4507	20	25	(	(	PUNCT
ejpam-4507	20	26	α	α	NOUN
ejpam-4507	20	27	)	)	PUNCT
ejpam-4507	20	28	n	n	PROPN
ejpam-4507	20	29	(	(	PUNCT
ejpam-4507	20	30	x	x	X
ejpam-4507	20	31	;	;	PUNCT
ejpam-4507	20	32	a	a	DET
ejpam-4507	20	33	,	,	PUNCT
ejpam-4507	20	34	b	b	NOUN
ejpam-4507	20	35	,	,	PUNCT
ejpam-4507	20	36	c	c	NOUN
ejpam-4507	20	37	)	)	PUNCT
ejpam-4507	20	38	and	and	CCONJ
ejpam-4507	20	39	g	g	PROPN
ejpam-4507	20	40	(	(	PUNCT
ejpam-4507	20	41	α	α	NOUN
ejpam-4507	20	42	)	)	PUNCT
ejpam-4507	20	43	n	n	PROPN
ejpam-4507	20	44	(	(	PUNCT
ejpam-4507	20	45	x	x	X
ejpam-4507	20	46	;	;	PUNCT
ejpam-4507	20	47	a	a	DET
ejpam-4507	20	48	,	,	PUNCT
ejpam-4507	20	49	b	b	NOUN
ejpam-4507	20	50	,	,	PUNCT
ejpam-4507	20	51	c	c	NOUN
ejpam-4507	20	52	)	)	PUNCT
ejpam-4507	20	53	of	of	ADP
ejpam-4507	20	54	positive	positive	ADJ
ejpam-4507	20	55	integer	integer	NOUN
ejpam-4507	20	56	order	order	NOUN
ejpam-4507	20	57	α	α	PRON
ejpam-4507	20	58	will	will	AUX
ejpam-4507	20	59	be	be	AUX
ejpam-4507	20	60	derived	derive	VERB
ejpam-4507	20	61	.	.	PUNCT
ejpam-4507	21	1	the	the	DET
ejpam-4507	21	2	method	method	NOUN
ejpam-4507	21	3	used	use	VERB
ejpam-4507	21	4	here	here	ADV
ejpam-4507	21	5	is	be	AUX
ejpam-4507	21	6	analytic	analytic	ADJ
ejpam-4507	21	7	.	.	PUNCT
ejpam-4507	22	1	in	in	ADP
ejpam-4507	22	2	particular	particular	ADJ
ejpam-4507	22	3	,	,	PUNCT
ejpam-4507	22	4	there	there	PRON
ejpam-4507	22	5	will	will	AUX
ejpam-4507	22	6	be	be	AUX
ejpam-4507	22	7	heavy	heavy	ADJ
ejpam-4507	22	8	use	use	NOUN
ejpam-4507	22	9	of	of	ADP
ejpam-4507	22	10	contour	contour	NOUN
ejpam-4507	22	11	integration	integration	NOUN
ejpam-4507	22	12	and	and	CCONJ
ejpam-4507	22	13	residue	residue	NOUN
ejpam-4507	22	14	theory	theory	NOUN
ejpam-4507	22	15	.	.	PUNCT
ejpam-4507	23	1	for	for	ADP
ejpam-4507	23	2	elaborate	elaborate	ADJ
ejpam-4507	23	3	discussion	discussion	NOUN
ejpam-4507	23	4	of	of	ADP
ejpam-4507	23	5	these	these	DET
ejpam-4507	23	6	topics	topic	NOUN
ejpam-4507	23	7	see	see	VERB
ejpam-4507	23	8	[	[	X
ejpam-4507	23	9	5	5	NUM
ejpam-4507	23	10	]	]	PUNCT
ejpam-4507	23	11	.	.	PUNCT
ejpam-4507	24	1	2	2	X
ejpam-4507	24	2	.	.	X
ejpam-4507	24	3	the	the	DET
ejpam-4507	24	4	case	case	NOUN
ejpam-4507	24	5	α	α	X
ejpam-4507	24	6	=	=	SYM
ejpam-4507	24	7	1	1	NUM
ejpam-4507	24	8	lemma	lemma	PROPN
ejpam-4507	24	9	2.1	2.1	NUM
ejpam-4507	24	10	.	.	PUNCT
ejpam-4507	25	1	let	let	VERB
ejpam-4507	25	2	n	n	PRON
ejpam-4507	25	3	≥	≥	NOUN
ejpam-4507	25	4	2	2	NUM
ejpam-4507	25	5	,	,	PUNCT
ejpam-4507	25	6	n	n	CCONJ
ejpam-4507	25	7	>	>	SYM
ejpam-4507	25	8	1	1	NUM
ejpam-4507	25	9	and	and	CCONJ
ejpam-4507	25	10	cn	cn	PROPN
ejpam-4507	25	11	be	be	AUX
ejpam-4507	25	12	the	the	DET
ejpam-4507	25	13	circle	circle	NOUN
ejpam-4507	25	14	about	about	ADP
ejpam-4507	25	15	zero	zero	NUM
ejpam-4507	25	16	of	of	ADP
ejpam-4507	25	17	radius	radius	NOUN
ejpam-4507	25	18	r	r	NOUN
ejpam-4507	25	19	=	=	PUNCT
ejpam-4507	25	20	(	(	PUNCT
ejpam-4507	25	21	2nπ−ε)/b	2nπ−ε)/b	NUM
ejpam-4507	25	22	,	,	PUNCT
ejpam-4507	25	23	where	where	SCONJ
ejpam-4507	25	24	0	0	X
ejpam-4507	25	25	<	<	X
ejpam-4507	25	26	ε	ε	X
ejpam-4507	25	27	<	<	X
ejpam-4507	25	28	1	1	NUM
ejpam-4507	25	29	and	and	CCONJ
ejpam-4507	25	30	b	b	NOUN
ejpam-4507	25	31	=	=	SYM
ejpam-4507	25	32	ln	ln	PROPN
ejpam-4507	25	33	b−	b−	PROPN
ejpam-4507	25	34	ln	ln	PROPN
ejpam-4507	25	35	a	a	PROPN
ejpam-4507	25	36	,	,	PUNCT
ejpam-4507	25	37	b	b	X
ejpam-4507	25	38	>	>	X
ejpam-4507	25	39	a.	a.	NOUN
ejpam-4507	25	40	for	for	ADP
ejpam-4507	25	41	0	0	NUM
ejpam-4507	25	42	<	<	X
ejpam-4507	25	43	x	x	X
ejpam-4507	25	44	<	<	X
ejpam-4507	25	45	(	(	PUNCT
ejpam-4507	25	46	ln	ln	X
ejpam-4507	25	47	a−	a−	PROPN
ejpam-4507	25	48	b	b	PROPN
ejpam-4507	25	49	2π	2π	PROPN
ejpam-4507	25	50	−	−	PROPN
ejpam-4507	25	51	ε	ε	PROPN
ejpam-4507	25	52	)	)	PUNCT
ejpam-4507	25	53	/	/	SYM
ejpam-4507	26	1	ln	ln	NOUN
ejpam-4507	26	2	c	c	NOUN
ejpam-4507	26	3	,	,	PUNCT
ejpam-4507	26	4	ln	ln	NOUN
ejpam-4507	26	5	c	c	NOUN
ejpam-4507	26	6	>	>	PUNCT
ejpam-4507	26	7	0	0	NUM
ejpam-4507	27	1	we	we	PRON
ejpam-4507	27	2	have	have	VERB
ejpam-4507	27	3	lim	lim	PROPN
ejpam-4507	27	4	n→+∞	n→+∞	PROPN
ejpam-4507	27	5	∫	∫	PROPN
ejpam-4507	27	6	cn	cn	PROPN
ejpam-4507	27	7	cxt	cxt	PROPN
ejpam-4507	27	8	bt	bt	PROPN
ejpam-4507	27	9	−	−	PROPN
ejpam-4507	27	10	at	at	ADP
ejpam-4507	27	11	dt	dt	PROPN
ejpam-4507	27	12	tn	tn	PROPN
ejpam-4507	28	1	=	=	SYM
ejpam-4507	28	2	0	0	X
ejpam-4507	28	3	.	.	PUNCT
ejpam-4507	29	1	proof	proof	NOUN
ejpam-4507	29	2	.	.	PUNCT
ejpam-4507	30	1	∣∣∣∣∫	∣∣∣∣∫	PROPN
ejpam-4507	30	2	cn	cn	PROPN
ejpam-4507	30	3	cxt	cxt	PROPN
ejpam-4507	30	4	(	(	PUNCT
ejpam-4507	30	5	bt	bt	NOUN
ejpam-4507	30	6	−	−	NOUN
ejpam-4507	30	7	at	at	ADP
ejpam-4507	30	8	)	)	PUNCT
ejpam-4507	30	9	dt	dt	PROPN
ejpam-4507	30	10	tn	tn	PROPN
ejpam-4507	30	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	30	12	≤	≤	NUM
ejpam-4507	30	13	∫	∫	PROPN
ejpam-4507	30	14	cn	cn	PROPN
ejpam-4507	30	15	|cxt|	|cxt|	PROPN
ejpam-4507	30	16	|bt	|bt	NOUN
ejpam-4507	30	17	−	−	NOUN
ejpam-4507	30	18	at|	at|	PROPN
ejpam-4507	30	19	|dt|	|dt|	PROPN
ejpam-4507	30	20	|tn|	|tn|	NOUN
ejpam-4507	30	21	.	.	PUNCT
ejpam-4507	31	1	we	we	PRON
ejpam-4507	31	2	will	will	AUX
ejpam-4507	31	3	show	show	VERB
ejpam-4507	31	4	that	that	SCONJ
ejpam-4507	31	5	under	under	ADP
ejpam-4507	31	6	the	the	DET
ejpam-4507	31	7	conditions	condition	NOUN
ejpam-4507	31	8	in	in	ADP
ejpam-4507	31	9	the	the	DET
ejpam-4507	31	10	lemma	lemma	PROPN
ejpam-4507	31	11	,	,	PUNCT
ejpam-4507	31	12	the	the	DET
ejpam-4507	31	13	function	function	NOUN
ejpam-4507	31	14	cxt	cxt	NOUN
ejpam-4507	31	15	(	(	PUNCT
ejpam-4507	31	16	bt	bt	NOUN
ejpam-4507	31	17	−	−	NOUN
ejpam-4507	31	18	at	at	ADP
ejpam-4507	31	19	)	)	PUNCT
ejpam-4507	31	20	is	be	AUX
ejpam-4507	31	21	bounded	bound	VERB
ejpam-4507	31	22	on	on	ADP
ejpam-4507	31	23	cn	cn	PROPN
ejpam-4507	31	24	.	.	PUNCT
ejpam-4507	32	1	write	write	VERB
ejpam-4507	32	2	cxt	cxt	NOUN
ejpam-4507	32	3	=	=	PUNCT
ejpam-4507	32	4	ext	ext	NOUN
ejpam-4507	32	5	ln	ln	NOUN
ejpam-4507	32	6	c	c	NOUN
ejpam-4507	32	7	,	,	PUNCT
ejpam-4507	32	8	bt	bt	X
ejpam-4507	33	1	=	=	VERB
ejpam-4507	33	2	et	et	PROPN
ejpam-4507	33	3	ln	ln	PROPN
ejpam-4507	33	4	b	b	PROPN
ejpam-4507	33	5	,	,	PUNCT
ejpam-4507	33	6	at	at	ADP
ejpam-4507	33	7	=	=	SYM
ejpam-4507	33	8	et	et	X
ejpam-4507	33	9	ln	ln	NOUN
ejpam-4507	33	10	a	a	X
ejpam-4507	33	11	,	,	PUNCT
ejpam-4507	34	1	where	where	SCONJ
ejpam-4507	34	2	t	t	PROPN
ejpam-4507	34	3	∈	∈	PROPN
ejpam-4507	34	4	cn	cn	PROPN
ejpam-4507	34	5	.	.	PUNCT
ejpam-4507	35	1	let	let	VERB
ejpam-4507	35	2	t	t	NOUN
ejpam-4507	35	3	=	=	PUNCT
ejpam-4507	35	4	γ	γ	X
ejpam-4507	35	5	+	+	X
ejpam-4507	35	6	iρ	iρ	NOUN
ejpam-4507	35	7	.	.	PUNCT
ejpam-4507	36	1	then	then	ADV
ejpam-4507	36	2	γ	γ	X
ejpam-4507	36	3	=	=	SYM
ejpam-4507	36	4	2nπ	2nπ	NOUN
ejpam-4507	36	5	−	−	PROPN
ejpam-4507	36	6	ε	ε	PROPN
ejpam-4507	36	7	b	b	PROPN
ejpam-4507	36	8	cos	cos	PROPN
ejpam-4507	36	9	θ	θ	PROPN
ejpam-4507	36	10	,	,	PUNCT
ejpam-4507	36	11	ρ	ρ	PROPN
ejpam-4507	36	12	=	=	SYM
ejpam-4507	36	13	2nπ	2nπ	NOUN
ejpam-4507	36	14	−	−	PROPN
ejpam-4507	36	15	ε	ε	PROPN
ejpam-4507	36	16	b	b	PROPN
ejpam-4507	36	17	sin	sin	NOUN
ejpam-4507	36	18	θ	θ	PROPN
ejpam-4507	36	19	,	,	PUNCT
ejpam-4507	36	20	where	where	SCONJ
ejpam-4507	36	21	0	0	NUM
ejpam-4507	36	22	≤	≤	NUM
ejpam-4507	36	23	θ	θ	NOUN
ejpam-4507	36	24	≤	≤	ADJ
ejpam-4507	36	25	2π	2π	NOUN
ejpam-4507	36	26	.	.	PUNCT
ejpam-4507	37	1	then	then	ADV
ejpam-4507	37	2	|cxt|	|cxt|	NOUN
ejpam-4507	37	3	|bt	|bt	NOUN
ejpam-4507	37	4	−	−	NOUN
ejpam-4507	37	5	at|	at|	NOUN
ejpam-4507	37	6	=	=	PUNCT
ejpam-4507	37	7	exγ	exγ	NOUN
ejpam-4507	37	8	ln	ln	PROPN
ejpam-4507	37	9	c	c	X
ejpam-4507	37	10	|e(γ+iρ	|e(γ+iρ	X
ejpam-4507	37	11	)	)	PUNCT
ejpam-4507	37	12	ln	ln	PROPN
ejpam-4507	37	13	b	b	NOUN
ejpam-4507	37	14	−	−	PROPN
ejpam-4507	37	15	e(γ+iρ	e(γ+iρ	NUM
ejpam-4507	37	16	)	)	PUNCT
ejpam-4507	37	17	ln	ln	PROPN
ejpam-4507	37	18	a|	a|	PROPN
ejpam-4507	37	19	=	=	PUNCT
ejpam-4507	37	20	exγ	exγ	NOUN
ejpam-4507	37	21	ln	ln	NOUN
ejpam-4507	37	22	c	c	NOUN
ejpam-4507	37	23	eγ	eγ	ADP
ejpam-4507	37	24	ln	ln	ADJ
ejpam-4507	37	25	a[e2γb	a[e2γb	X
ejpam-4507	37	26	−	−	PROPN
ejpam-4507	37	27	2eγb	2eγb	NUM
ejpam-4507	37	28	cos	cos	NOUN
ejpam-4507	37	29	ρb	ρb	PROPN
ejpam-4507	37	30	+	+	NOUN
ejpam-4507	37	31	1	1	NUM
ejpam-4507	37	32	]	]	SYM
ejpam-4507	37	33	1	1	NUM
ejpam-4507	37	34	2	2	NUM
ejpam-4507	37	35	c.	c.	NOUN
ejpam-4507	37	36	corcino	corcino	PROPN
ejpam-4507	37	37	,	,	PUNCT
ejpam-4507	37	38	r.	r.	PROPN
ejpam-4507	37	39	corcino	corcino	PROPN
ejpam-4507	37	40	/	/	SYM
ejpam-4507	37	41	eur	eur	PROPN
ejpam-4507	37	42	.	.	PUNCT
ejpam-4507	38	1	j.	j.	PROPN
ejpam-4507	38	2	pure	pure	PROPN
ejpam-4507	38	3	appl	appl	PROPN
ejpam-4507	38	4	.	.	PROPN
ejpam-4507	38	5	math	math	PROPN
ejpam-4507	38	6	,	,	PUNCT
ejpam-4507	38	7	15	15	NUM
ejpam-4507	38	8	(	(	PUNCT
ejpam-4507	38	9	4	4	NUM
ejpam-4507	38	10	)	)	PUNCT
ejpam-4507	38	11	(	(	PUNCT
ejpam-4507	38	12	2022	2022	NUM
ejpam-4507	38	13	)	)	PUNCT
ejpam-4507	38	14	,	,	PUNCT
ejpam-4507	38	15	1662	1662	NUM
ejpam-4507	38	16	-	-	SYM
ejpam-4507	38	17	1682	1682	NUM
ejpam-4507	38	18	1664	1664	NUM
ejpam-4507	38	19	=	=	SYM
ejpam-4507	38	20	1	1	NUM
ejpam-4507	38	21	eγ[ln	eγ[ln	PROPN
ejpam-4507	38	22	a−x	a−x	NOUN
ejpam-4507	38	23	ln	ln	NOUN
ejpam-4507	38	24	c][e2γb	c][e2γb	NUM
ejpam-4507	38	25	−	−	NOUN
ejpam-4507	38	26	2eγb	2eγb	NUM
ejpam-4507	38	27	cos	cos	NOUN
ejpam-4507	38	28	ρb	ρb	PROPN
ejpam-4507	38	29	+	+	NOUN
ejpam-4507	38	30	1	1	NUM
ejpam-4507	38	31	]	]	SYM
ejpam-4507	38	32	1	1	NUM
ejpam-4507	38	33	2	2	NUM
ejpam-4507	38	34	.	.	PUNCT
ejpam-4507	39	1	with	with	ADP
ejpam-4507	39	2	x	x	PUNCT
ejpam-4507	39	3	<	<	X
ejpam-4507	39	4	ln	ln	NOUN
ejpam-4507	39	5	a	a	DET
ejpam-4507	39	6	ln	ln	NOUN
ejpam-4507	39	7	c	c	NOUN
ejpam-4507	39	8	−	−	PROPN
ejpam-4507	39	9	b	b	PROPN
ejpam-4507	39	10	(	(	PUNCT
ejpam-4507	39	11	2π	2π	PROPN
ejpam-4507	39	12	−	−	PROPN
ejpam-4507	39	13	ε	ε	PROPN
ejpam-4507	39	14	)	)	PUNCT
ejpam-4507	39	15	ln	ln	NOUN
ejpam-4507	39	16	c	c	NOUN
ejpam-4507	39	17	=	=	NOUN
ejpam-4507	39	18	⇒	⇒	X
ejpam-4507	39	19	x	x	X
ejpam-4507	39	20	ln	ln	NOUN
ejpam-4507	39	21	c	c	X
ejpam-4507	39	22	<	<	X
ejpam-4507	39	23	ln	ln	X
ejpam-4507	39	24	a−	a−	PROPN
ejpam-4507	39	25	b	b	PROPN
ejpam-4507	39	26	2π	2π	PROPN
ejpam-4507	39	27	−	−	PROPN
ejpam-4507	39	28	ε	ε	PROPN
ejpam-4507	39	29	=	=	PRON
ejpam-4507	39	30	⇒	⇒	NOUN
ejpam-4507	39	31	x	x	X
ejpam-4507	39	32	ln	ln	ADJ
ejpam-4507	39	33	c−	c−	NOUN
ejpam-4507	39	34	ln	ln	NOUN
ejpam-4507	39	35	a	a	DET
ejpam-4507	39	36	<	<	X
ejpam-4507	39	37	−	−	PROPN
ejpam-4507	39	38	b	b	PROPN
ejpam-4507	39	39	2π	2π	NOUN
ejpam-4507	39	40	−	−	PROPN
ejpam-4507	39	41	ε	ε	PROPN
ejpam-4507	40	1	=	=	AUX
ejpam-4507	40	2	⇒	⇒	NOUN
ejpam-4507	40	3	ln	ln	ADJ
ejpam-4507	40	4	a−	a−	PROPN
ejpam-4507	40	5	x	x	X
ejpam-4507	40	6	ln	ln	PROPN
ejpam-4507	41	1	c	c	PROPN
ejpam-4507	41	2	>	>	X
ejpam-4507	41	3	b	b	PROPN
ejpam-4507	41	4	2π	2π	PROPN
ejpam-4507	41	5	−	−	PROPN
ejpam-4507	41	6	ε	ε	PROPN
ejpam-4507	41	7	≥	≥	NUM
ejpam-4507	42	1	b	b	NUM
ejpam-4507	42	2	2πn	2πn	ADJ
ejpam-4507	42	3	−	−	PROPN
ejpam-4507	42	4	ε	ε	PROPN
ejpam-4507	42	5	,	,	PUNCT
ejpam-4507	42	6	∀	∀	X
ejpam-4507	42	7	n	n	DET
ejpam-4507	42	8	≥	≥	NOUN
ejpam-4507	42	9	1	1	NUM
ejpam-4507	42	10	.	.	PUNCT
ejpam-4507	43	1	thus	thus	ADV
ejpam-4507	43	2	,	,	PUNCT
ejpam-4507	43	3	1	1	NUM
ejpam-4507	43	4	eγ[ln	eγ[ln	PROPN
ejpam-4507	43	5	a−x	a−x	NOUN
ejpam-4507	43	6	ln	ln	NOUN
ejpam-4507	43	7	c	c	NOUN
ejpam-4507	43	8	]	]	X
ejpam-4507	43	9	≤	≤	NUM
ejpam-4507	43	10	1	1	NUM
ejpam-4507	43	11	ecosθ	ecosθ	VERB
ejpam-4507	43	12	≤	≤	NUM
ejpam-4507	43	13	1	1	NUM
ejpam-4507	43	14	e−1	e−1	NOUN
ejpam-4507	43	15	=	=	SYM
ejpam-4507	43	16	e	e	NOUN
ejpam-4507	43	17	,	,	PUNCT
ejpam-4507	43	18	and	and	CCONJ
ejpam-4507	43	19	|cxt|	|cxt|	NOUN
ejpam-4507	43	20	|bt	|bt	NOUN
ejpam-4507	43	21	−	−	NOUN
ejpam-4507	43	22	at|	at|	ADP
ejpam-4507	43	23	≤	≤	NUM
ejpam-4507	43	24	e	e	NOUN
ejpam-4507	44	1	[	[	X
ejpam-4507	44	2	e2γb	e2γb	PUNCT
ejpam-4507	44	3	−	−	PROPN
ejpam-4507	44	4	2eγb	2eγb	NUM
ejpam-4507	44	5	cos	cos	NOUN
ejpam-4507	44	6	ρb	ρb	PROPN
ejpam-4507	44	7	+	+	NOUN
ejpam-4507	44	8	1	1	NUM
ejpam-4507	44	9	]	]	SYM
ejpam-4507	44	10	1	1	NUM
ejpam-4507	44	11	2	2	NUM
ejpam-4507	44	12	.	.	PUNCT
ejpam-4507	45	1	the	the	DET
ejpam-4507	45	2	denominator	denominator	NOUN
ejpam-4507	45	3	of	of	ADP
ejpam-4507	45	4	the	the	DET
ejpam-4507	45	5	preceding	precede	VERB
ejpam-4507	45	6	expression	expression	NOUN
ejpam-4507	45	7	must	must	AUX
ejpam-4507	45	8	not	not	PART
ejpam-4507	45	9	be	be	AUX
ejpam-4507	45	10	zero	zero	NUM
ejpam-4507	45	11	.	.	PUNCT
ejpam-4507	46	1	with	with	ADP
ejpam-4507	46	2	0	0	NUM
ejpam-4507	46	3	≤	≤	NUM
ejpam-4507	46	4	θ	θ	NOUN
ejpam-4507	46	5	≤	≤	ADJ
ejpam-4507	46	6	2π	2π	NOUN
ejpam-4507	46	7	,	,	PUNCT
ejpam-4507	46	8	we	we	PRON
ejpam-4507	46	9	look	look	VERB
ejpam-4507	46	10	at	at	ADP
ejpam-4507	46	11	3	3	NUM
ejpam-4507	46	12	cases	case	NOUN
ejpam-4507	46	13	:	:	PUNCT
ejpam-4507	46	14	case	case	NOUN
ejpam-4507	46	15	1	1	NUM
ejpam-4507	46	16	:	:	PUNCT
ejpam-4507	46	17	cos	cos	ADP
ejpam-4507	46	18	θ	θ	PROPN
ejpam-4507	46	19	<	<	X
ejpam-4507	46	20	0	0	PUNCT
ejpam-4507	46	21	as	as	ADP
ejpam-4507	46	22	n	n	PROPN
ejpam-4507	46	23	→	→	SYM
ejpam-4507	46	24	+	+	PROPN
ejpam-4507	46	25	∞	∞	PROPN
ejpam-4507	46	26	,	,	PUNCT
ejpam-4507	46	27	γ	γ	X
ejpam-4507	46	28	→	→	SYM
ejpam-4507	46	29	−∞	−∞	PROPN
ejpam-4507	46	30	and	and	CCONJ
ejpam-4507	46	31	e2γb	e2γb	SYM
ejpam-4507	46	32	−	−	PROPN
ejpam-4507	46	33	2eγb	2eγb	NUM
ejpam-4507	46	34	cos	cos	NOUN
ejpam-4507	46	35	ρb	ρb	PROPN
ejpam-4507	47	1	+	+	NOUN
ejpam-4507	47	2	1	1	NUM
ejpam-4507	47	3	−→	−→	NOUN
ejpam-4507	47	4	1	1	NUM
ejpam-4507	47	5	provided	provide	VERB
ejpam-4507	47	6	b	b	PROPN
ejpam-4507	47	7	>	>	X
ejpam-4507	47	8	0	0	NUM
ejpam-4507	47	9	.	.	PUNCT
ejpam-4507	47	10	case	case	NOUN
ejpam-4507	47	11	2	2	NUM
ejpam-4507	47	12	:	:	PUNCT
ejpam-4507	47	13	cos	cos	PART
ejpam-4507	47	14	θ	θ	PROPN
ejpam-4507	47	15	>	>	X
ejpam-4507	47	16	0	0	PUNCT
ejpam-4507	48	1	as	as	ADP
ejpam-4507	48	2	n	n	PROPN
ejpam-4507	48	3	→	→	SYM
ejpam-4507	48	4	+	+	PROPN
ejpam-4507	48	5	∞	∞	PROPN
ejpam-4507	48	6	,	,	PUNCT
ejpam-4507	48	7	γ	γ	X
ejpam-4507	48	8	→	→	SYM
ejpam-4507	48	9	+	+	PROPN
ejpam-4507	48	10	∞	∞	PROPN
ejpam-4507	48	11	and	and	CCONJ
ejpam-4507	48	12	e2γb	e2γb	SYM
ejpam-4507	48	13	−	−	PROPN
ejpam-4507	48	14	2eγb	2eγb	NUM
ejpam-4507	48	15	cos	cos	NOUN
ejpam-4507	48	16	ρb+1	ρb+1	NUM
ejpam-4507	48	17	=	=	SYM
ejpam-4507	48	18	e2γb	e2γb	PUNCT
ejpam-4507	48	19	(	(	PUNCT
ejpam-4507	48	20	1−	1−	NUM
ejpam-4507	48	21	2	2	NUM
ejpam-4507	48	22	cos	co	NOUN
ejpam-4507	48	23	ρb	ρb	PRON
ejpam-4507	48	24	eγb	eγb	VERB
ejpam-4507	48	25	+	+	CCONJ
ejpam-4507	48	26	1	1	NUM
ejpam-4507	48	27	eγb	eγb	NOUN
ejpam-4507	48	28	)	)	PUNCT
ejpam-4507	49	1	−→	−→	NOUN
ejpam-4507	49	2	+	+	ADJ
ejpam-4507	49	3	∞	∞	PROPN
ejpam-4507	49	4	,	,	PUNCT
ejpam-4507	49	5	provided	provide	VERB
ejpam-4507	49	6	b	b	PROPN
ejpam-4507	49	7	>	>	X
ejpam-4507	49	8	0	0	NUM
ejpam-4507	49	9	.	.	PUNCT
ejpam-4507	49	10	case	case	NOUN
ejpam-4507	49	11	3	3	NUM
ejpam-4507	49	12	:	:	PUNCT
ejpam-4507	49	13	cos	cos	PROPN
ejpam-4507	49	14	θ	θ	PROPN
ejpam-4507	49	15	=	=	SYM
ejpam-4507	49	16	0	0	NUM
ejpam-4507	49	17	then	then	ADV
ejpam-4507	49	18	γ	γ	X
ejpam-4507	49	19	=	=	SYM
ejpam-4507	49	20	0	0	NUM
ejpam-4507	49	21	and	and	CCONJ
ejpam-4507	49	22	e2γb	e2γb	SYM
ejpam-4507	49	23	−	−	PROPN
ejpam-4507	50	1	2eγb	2eγb	NUM
ejpam-4507	50	2	cos	cos	NOUN
ejpam-4507	50	3	ρb+1	ρb+1	NUM
ejpam-4507	50	4	=	=	SYM
ejpam-4507	50	5	2−	2−	NUM
ejpam-4507	50	6	2	2	NUM
ejpam-4507	50	7	cos	cos	ADP
ejpam-4507	50	8	ρb	ρb	PROPN
ejpam-4507	50	9	,	,	PUNCT
ejpam-4507	50	10	which	which	PRON
ejpam-4507	50	11	is	be	AUX
ejpam-4507	50	12	nonzero	nonzero	NOUN
ejpam-4507	50	13	provided	provide	VERB
ejpam-4507	50	14	that	that	SCONJ
ejpam-4507	50	15	cos	cos	ADP
ejpam-4507	50	16	ρb	ρb	PRON
ejpam-4507	50	17	̸=	̸=	PROPN
ejpam-4507	50	18	1	1	NUM
ejpam-4507	50	19	.	.	PUNCT
ejpam-4507	51	1	because	because	SCONJ
ejpam-4507	51	2	cos	cos	PROPN
ejpam-4507	51	3	θ	θ	PROPN
ejpam-4507	51	4	=	=	SYM
ejpam-4507	51	5	0	0	NUM
ejpam-4507	51	6	,	,	PUNCT
ejpam-4507	51	7	we	we	PRON
ejpam-4507	51	8	have	have	VERB
ejpam-4507	51	9	ρ	ρ	NOUN
ejpam-4507	51	10	=	=	SYM
ejpam-4507	51	11	±(2nπ	±(2nπ	NOUN
ejpam-4507	51	12	−	−	NOUN
ejpam-4507	51	13	ε)/b	ε)/b	NOUN
ejpam-4507	51	14	.	.	PUNCT
ejpam-4507	52	1	thus	thus	ADV
ejpam-4507	52	2	,	,	PUNCT
ejpam-4507	52	3	cos	cos	PROPN
ejpam-4507	52	4	ρb	ρb	ADP
ejpam-4507	52	5	=	=	SYM
ejpam-4507	52	6	cos[(±2nπ	cos[(±2nπ	PROPN
ejpam-4507	52	7	−	−	PROPN
ejpam-4507	52	8	ε	ε	PROPN
ejpam-4507	52	9	)	)	PUNCT
ejpam-4507	52	10	]	]	PUNCT
ejpam-4507	53	1	=	=	SYM
ejpam-4507	53	2	1	1	NUM
ejpam-4507	53	3	iff	iff	NOUN
ejpam-4507	53	4	2nπ	2nπ	NOUN
ejpam-4507	53	5	−	−	PROPN
ejpam-4507	53	6	ε	ε	PROPN
ejpam-4507	53	7	=	=	SYM
ejpam-4507	53	8	2kπ	2kπ	NOUN
ejpam-4507	53	9	,	,	PUNCT
ejpam-4507	53	10	for	for	ADP
ejpam-4507	53	11	some	some	DET
ejpam-4507	53	12	integer	integer	NOUN
ejpam-4507	53	13	k.	k.	PROPN
ejpam-4507	54	1	this	this	PRON
ejpam-4507	54	2	gives	give	VERB
ejpam-4507	54	3	2(n	2(n	NUM
ejpam-4507	54	4	−	−	PROPN
ejpam-4507	54	5	k)π	k)π	NOUN
ejpam-4507	54	6	=	=	SYM
ejpam-4507	54	7	ε	ε	PROPN
ejpam-4507	54	8	,	,	PUNCT
ejpam-4507	54	9	c.	c.	PROPN
ejpam-4507	54	10	corcino	corcino	PROPN
ejpam-4507	54	11	,	,	PUNCT
ejpam-4507	54	12	r.	r.	PROPN
ejpam-4507	54	13	corcino	corcino	PROPN
ejpam-4507	54	14	/	/	SYM
ejpam-4507	54	15	eur	eur	PROPN
ejpam-4507	54	16	.	.	PUNCT
ejpam-4507	55	1	j.	j.	PROPN
ejpam-4507	55	2	pure	pure	PROPN
ejpam-4507	55	3	appl	appl	PROPN
ejpam-4507	55	4	.	.	PROPN
ejpam-4507	55	5	math	math	PROPN
ejpam-4507	55	6	,	,	PUNCT
ejpam-4507	55	7	15	15	NUM
ejpam-4507	55	8	(	(	PUNCT
ejpam-4507	55	9	4	4	NUM
ejpam-4507	55	10	)	)	PUNCT
ejpam-4507	55	11	(	(	PUNCT
ejpam-4507	55	12	2022	2022	NUM
ejpam-4507	55	13	)	)	PUNCT
ejpam-4507	55	14	,	,	PUNCT
ejpam-4507	55	15	1662	1662	NUM
ejpam-4507	55	16	-	-	SYM
ejpam-4507	55	17	1682	1682	NUM
ejpam-4507	55	18	1665	1665	NUM
ejpam-4507	55	19	which	which	PRON
ejpam-4507	55	20	is	be	AUX
ejpam-4507	55	21	not	not	PART
ejpam-4507	55	22	possible	possible	ADJ
ejpam-4507	55	23	because	because	SCONJ
ejpam-4507	55	24	0	0	NUM
ejpam-4507	55	25	<	<	X
ejpam-4507	55	26	ε	ε	X
ejpam-4507	55	27	<	<	X
ejpam-4507	55	28	1	1	NUM
ejpam-4507	55	29	.	.	PUNCT
ejpam-4507	56	1	thus	thus	ADV
ejpam-4507	56	2	,	,	PUNCT
ejpam-4507	56	3	under	under	ADP
ejpam-4507	56	4	the	the	DET
ejpam-4507	56	5	conditions	condition	NOUN
ejpam-4507	56	6	in	in	ADP
ejpam-4507	56	7	the	the	DET
ejpam-4507	56	8	lemma	lemma	PROPN
ejpam-4507	56	9	,	,	PUNCT
ejpam-4507	56	10	in	in	ADP
ejpam-4507	56	11	all	all	DET
ejpam-4507	56	12	3	3	NUM
ejpam-4507	56	13	cases	case	NOUN
ejpam-4507	56	14	cxt/(bt	cxt/(bt	PROPN
ejpam-4507	56	15	−	−	NOUN
ejpam-4507	56	16	at	at	ADP
ejpam-4507	56	17	)	)	PUNCT
ejpam-4507	56	18	is	be	AUX
ejpam-4507	56	19	bounded	bound	VERB
ejpam-4507	56	20	∀t	∀t	PROPN
ejpam-4507	56	21	∈	∈	PROPN
ejpam-4507	56	22	cn	cn	PROPN
ejpam-4507	56	23	.	.	PUNCT
ejpam-4507	57	1	let	let	VERB
ejpam-4507	57	2	m	m	PRON
ejpam-4507	57	3	be	be	AUX
ejpam-4507	57	4	a	a	DET
ejpam-4507	57	5	positive	positive	ADJ
ejpam-4507	57	6	integer	integer	NOUN
ejpam-4507	57	7	such	such	ADJ
ejpam-4507	57	8	that∣∣∣∣	that∣∣∣∣	PROPN
ejpam-4507	57	9	cxt	cxt	PROPN
ejpam-4507	57	10	bt	bt	NOUN
ejpam-4507	57	11	−	−	PROPN
ejpam-4507	57	12	at	at	ADP
ejpam-4507	57	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4507	57	14	<	<	X
ejpam-4507	57	15	m	m	NOUN
ejpam-4507	57	16	.	.	PUNCT
ejpam-4507	58	1	then	then	ADV
ejpam-4507	58	2	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-4507	58	3	cn	cn	PROPN
ejpam-4507	58	4	cxt	cxt	PROPN
ejpam-4507	58	5	bt	bt	VERB
ejpam-4507	58	6	−	−	PROPN
ejpam-4507	58	7	at	at	ADP
ejpam-4507	58	8	dt	dt	PROPN
ejpam-4507	58	9	tn	tn	PROPN
ejpam-4507	58	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	58	11	<	<	X
ejpam-4507	58	12	m	m	NUM
ejpam-4507	58	13	∫	∫	PROPN
ejpam-4507	58	14	cn	cn	PROPN
ejpam-4507	58	15	|dt|	|dt|	PROPN
ejpam-4507	58	16	|tn|	|tn|	PROPN
ejpam-4507	58	17	=	=	PUNCT
ejpam-4507	58	18	m	m	AUX
ejpam-4507	58	19	·	·	PUNCT
ejpam-4507	58	20	(	(	PUNCT
ejpam-4507	58	21	2nπ	2nπ	NOUN
ejpam-4507	58	22	−	−	NOUN
ejpam-4507	58	23	ε)2π	ε)2π	NOUN
ejpam-4507	58	24	(	(	PUNCT
ejpam-4507	58	25	2nπ	2nπ	NOUN
ejpam-4507	58	26	−	−	PRON
ejpam-4507	58	27	ε)n	ε)n	PUNCT
ejpam-4507	59	1	bn−1	bn−1	PRON
ejpam-4507	59	2	=	=	SYM
ejpam-4507	59	3	2mπbn−1	2mπbn−1	NOUN
ejpam-4507	59	4	(	(	PUNCT
ejpam-4507	59	5	2nπ	2nπ	NOUN
ejpam-4507	59	6	−	−	NOUN
ejpam-4507	59	7	ε)n−1	ε)n−1	NOUN
ejpam-4507	59	8	−→	−→	NOUN
ejpam-4507	59	9	0	0	NUM
ejpam-4507	59	10	as	as	ADP
ejpam-4507	59	11	n	n	PRON
ejpam-4507	59	12	→	→	SYM
ejpam-4507	59	13	+	+	NOUN
ejpam-4507	59	14	∞	∞	PROPN
ejpam-4507	59	15	for	for	ADP
ejpam-4507	59	16	n	n	PRON
ejpam-4507	59	17	≥	≥	NUM
ejpam-4507	59	18	2	2	NUM
ejpam-4507	59	19	.	.	PUNCT
ejpam-4507	60	1	this	this	PRON
ejpam-4507	60	2	completes	complete	VERB
ejpam-4507	60	3	the	the	DET
ejpam-4507	60	4	proof	proof	NOUN
ejpam-4507	60	5	of	of	ADP
ejpam-4507	60	6	the	the	DET
ejpam-4507	60	7	lemma	lemma	PROPN
ejpam-4507	60	8	.	.	PUNCT
ejpam-4507	60	9	theorem	theorem	VERB
ejpam-4507	60	10	2.2	2.2	NUM
ejpam-4507	60	11	.	.	PUNCT
ejpam-4507	61	1	let	let	VERB
ejpam-4507	61	2	a	a	DET
ejpam-4507	61	3	,	,	PUNCT
ejpam-4507	61	4	b	b	NOUN
ejpam-4507	61	5	,	,	PUNCT
ejpam-4507	61	6	c	c	AUX
ejpam-4507	61	7	be	be	AUX
ejpam-4507	61	8	positive	positive	ADJ
ejpam-4507	61	9	real	real	ADJ
ejpam-4507	61	10	numbers	number	NOUN
ejpam-4507	61	11	.	.	PUNCT
ejpam-4507	62	1	the	the	DET
ejpam-4507	62	2	fourier	fourier	ADJ
ejpam-4507	62	3	series	series	NOUN
ejpam-4507	62	4	of	of	ADP
ejpam-4507	62	5	the	the	DET
ejpam-4507	62	6	bernoulli	bernoulli	NOUN
ejpam-4507	62	7	-	-	PUNCT
ejpam-4507	62	8	type	type	NOUN
ejpam-4507	62	9	polynomials	polynomial	NOUN
ejpam-4507	62	10	bn(x	bn(x	NOUN
ejpam-4507	62	11	;	;	PUNCT
ejpam-4507	62	12	a	a	DET
ejpam-4507	62	13	,	,	PUNCT
ejpam-4507	62	14	b	b	NOUN
ejpam-4507	62	15	,	,	PUNCT
ejpam-4507	62	16	c	c	NOUN
ejpam-4507	62	17	)	)	PUNCT
ejpam-4507	62	18	is	be	AUX
ejpam-4507	62	19	given	give	VERB
ejpam-4507	62	20	by	by	ADP
ejpam-4507	62	21	bn(x	bn(x	PROPN
ejpam-4507	62	22	;	;	PUNCT
ejpam-4507	62	23	a	a	DET
ejpam-4507	62	24	,	,	PUNCT
ejpam-4507	62	25	b	b	NOUN
ejpam-4507	62	26	,	,	PUNCT
ejpam-4507	62	27	c	c	NOUN
ejpam-4507	62	28	)	)	PUNCT
ejpam-4507	62	29	n	n	CCONJ
ejpam-4507	62	30	!	!	PUNCT
ejpam-4507	63	1	=	=	PUNCT
ejpam-4507	64	1	−	−	PROPN
ejpam-4507	64	2	1	1	NUM
ejpam-4507	64	3	b	b	X
ejpam-4507	64	4	∑	∑	PUNCT
ejpam-4507	64	5	k∈z+	k∈z+	PROPN
ejpam-4507	64	6	etk(x	etk(x	PROPN
ejpam-4507	64	7	ln	ln	ADJ
ejpam-4507	64	8	c−ln	c−ln	PROPN
ejpam-4507	64	9	a	a	X
ejpam-4507	64	10	)	)	PUNCT
ejpam-4507	64	11	tnk	tnk	PROPN
ejpam-4507	64	12	,	,	PUNCT
ejpam-4507	64	13	valid	valid	ADJ
ejpam-4507	64	14	for	for	ADP
ejpam-4507	64	15	0	0	NUM
ejpam-4507	64	16	<	<	X
ejpam-4507	64	17	x	x	X
ejpam-4507	64	18	<	<	X
ejpam-4507	64	19	(	(	PUNCT
ejpam-4507	64	20	ln	ln	X
ejpam-4507	64	21	a−	a−	PROPN
ejpam-4507	64	22	b	b	PROPN
ejpam-4507	64	23	2π	2π	PROPN
ejpam-4507	64	24	−	−	PROPN
ejpam-4507	64	25	ε	ε	PROPN
ejpam-4507	64	26	)	)	PUNCT
ejpam-4507	64	27	/	/	SYM
ejpam-4507	65	1	ln	ln	NOUN
ejpam-4507	65	2	c	c	NOUN
ejpam-4507	65	3	,	,	PUNCT
ejpam-4507	65	4	ln	ln	NOUN
ejpam-4507	65	5	c	c	NOUN
ejpam-4507	65	6	>	>	X
ejpam-4507	65	7	0	0	NUM
ejpam-4507	66	1	where	where	SCONJ
ejpam-4507	66	2	tk	tk	NOUN
ejpam-4507	66	3	=	=	NOUN
ejpam-4507	66	4	2kπi	2kπi	PROPN
ejpam-4507	66	5	/	/	SYM
ejpam-4507	66	6	b	b	PROPN
ejpam-4507	66	7	,	,	PUNCT
ejpam-4507	66	8	b	b	X
ejpam-4507	66	9	=	=	SYM
ejpam-4507	66	10	ln	ln	PROPN
ejpam-4507	66	11	b−	b−	PROPN
ejpam-4507	66	12	ln	ln	ADV
ejpam-4507	66	13	a	a	DET
ejpam-4507	66	14	>	>	X
ejpam-4507	66	15	0	0	X
ejpam-4507	66	16	.	.	PUNCT
ejpam-4507	66	17	proof	proof	NOUN
ejpam-4507	66	18	.	.	PUNCT
ejpam-4507	67	1	when	when	SCONJ
ejpam-4507	67	2	α	α	PRON
ejpam-4507	67	3	=	=	SYM
ejpam-4507	67	4	1	1	NUM
ejpam-4507	67	5	,	,	PUNCT
ejpam-4507	67	6	the	the	DET
ejpam-4507	67	7	generating	generate	VERB
ejpam-4507	67	8	function	function	NOUN
ejpam-4507	67	9	(	(	PUNCT
ejpam-4507	67	10	1	1	X
ejpam-4507	67	11	)	)	PUNCT
ejpam-4507	67	12	reduces	reduce	VERB
ejpam-4507	67	13	to	to	ADP
ejpam-4507	67	14	t	t	NOUN
ejpam-4507	67	15	bt	bt	NOUN
ejpam-4507	67	16	−	−	PROPN
ejpam-4507	67	17	at	at	ADP
ejpam-4507	67	18	cxt	cxt	NOUN
ejpam-4507	67	19	=	=	PUNCT
ejpam-4507	67	20	∞∑	∞∑	PROPN
ejpam-4507	67	21	n=0	n=0	NOUN
ejpam-4507	67	22	bn(x	bn(x	NUM
ejpam-4507	67	23	;	;	PUNCT
ejpam-4507	67	24	a	a	DET
ejpam-4507	67	25	,	,	PUNCT
ejpam-4507	67	26	b	b	NOUN
ejpam-4507	67	27	,	,	PUNCT
ejpam-4507	67	28	c	c	NOUN
ejpam-4507	67	29	)	)	PUNCT
ejpam-4507	67	30	tn	tn	PROPN
ejpam-4507	67	31	n	n	CCONJ
ejpam-4507	67	32	!	!	PUNCT
ejpam-4507	67	33	,	,	PUNCT
ejpam-4507	67	34	|t|	|t|	VERB
ejpam-4507	67	35	<	<	X
ejpam-4507	67	36	2π	2π	PROPN
ejpam-4507	67	37	b	b	X
ejpam-4507	67	38	.	.	PUNCT
ejpam-4507	68	1	applying	apply	VERB
ejpam-4507	68	2	the	the	DET
ejpam-4507	68	3	cauchy	cauchy	ADJ
ejpam-4507	68	4	integral	integral	ADJ
ejpam-4507	68	5	formula	formula	NOUN
ejpam-4507	68	6	yields	yield	NOUN
ejpam-4507	68	7	bn(x	bn(x	X
ejpam-4507	68	8	;	;	PUNCT
ejpam-4507	68	9	a	a	DET
ejpam-4507	68	10	,	,	PUNCT
ejpam-4507	68	11	b	b	NOUN
ejpam-4507	68	12	,	,	PUNCT
ejpam-4507	68	13	c	c	NOUN
ejpam-4507	68	14	)	)	PUNCT
ejpam-4507	68	15	n	n	CCONJ
ejpam-4507	68	16	!	!	PUNCT
ejpam-4507	69	1	=	=	SYM
ejpam-4507	69	2	1	1	NUM
ejpam-4507	69	3	2πi	2πi	ADJ
ejpam-4507	69	4	∫	∫	PROPN
ejpam-4507	69	5	c	c	PROPN
ejpam-4507	69	6	cxt	cxt	PROPN
ejpam-4507	69	7	bt	bt	VERB
ejpam-4507	69	8	−	−	PROPN
ejpam-4507	69	9	at	at	ADP
ejpam-4507	69	10	dt	dt	PROPN
ejpam-4507	69	11	tn	tn	PROPN
ejpam-4507	69	12	,	,	PUNCT
ejpam-4507	69	13	where	where	SCONJ
ejpam-4507	69	14	c	c	PROPN
ejpam-4507	69	15	is	be	AUX
ejpam-4507	69	16	a	a	DET
ejpam-4507	69	17	circle	circle	NOUN
ejpam-4507	69	18	with	with	ADP
ejpam-4507	69	19	center	center	NOUN
ejpam-4507	69	20	at	at	ADP
ejpam-4507	69	21	0	0	NUM
ejpam-4507	69	22	and	and	CCONJ
ejpam-4507	69	23	radius	radius	NOUN
ejpam-4507	69	24	less	less	ADJ
ejpam-4507	69	25	than	than	ADP
ejpam-4507	69	26	2π	2π	PROPN
ejpam-4507	69	27	b	b	X
ejpam-4507	69	28	.	.	PUNCT
ejpam-4507	70	1	let	let	VERB
ejpam-4507	70	2	f(t	f(t	NOUN
ejpam-4507	70	3	)	)	PUNCT
ejpam-4507	70	4	=	=	SYM
ejpam-4507	70	5	cxt	cxt	X
ejpam-4507	70	6	(	(	PUNCT
ejpam-4507	70	7	bt	bt	NOUN
ejpam-4507	70	8	−	−	PROPN
ejpam-4507	70	9	at)tn	at)tn	PROPN
ejpam-4507	70	10	.	.	PUNCT
ejpam-4507	71	1	c.	c.	PROPN
ejpam-4507	71	2	corcino	corcino	PROPN
ejpam-4507	71	3	,	,	PUNCT
ejpam-4507	71	4	r.	r.	PROPN
ejpam-4507	71	5	corcino	corcino	PROPN
ejpam-4507	71	6	/	/	SYM
ejpam-4507	71	7	eur	eur	PROPN
ejpam-4507	71	8	.	.	PUNCT
ejpam-4507	72	1	j.	j.	PROPN
ejpam-4507	72	2	pure	pure	PROPN
ejpam-4507	72	3	appl	appl	PROPN
ejpam-4507	72	4	.	.	PROPN
ejpam-4507	72	5	math	math	PROPN
ejpam-4507	72	6	,	,	PUNCT
ejpam-4507	72	7	15	15	NUM
ejpam-4507	72	8	(	(	PUNCT
ejpam-4507	72	9	4	4	NUM
ejpam-4507	72	10	)	)	PUNCT
ejpam-4507	72	11	(	(	PUNCT
ejpam-4507	72	12	2022	2022	NUM
ejpam-4507	72	13	)	)	PUNCT
ejpam-4507	72	14	,	,	PUNCT
ejpam-4507	72	15	1662	1662	NUM
ejpam-4507	72	16	-	-	SYM
ejpam-4507	72	17	1682	1682	NUM
ejpam-4507	72	18	1666	1666	NUM
ejpam-4507	72	19	the	the	DET
ejpam-4507	72	20	function	function	NOUN
ejpam-4507	72	21	f(t	f(t	PROPN
ejpam-4507	72	22	)	)	PUNCT
ejpam-4507	72	23	has	have	VERB
ejpam-4507	72	24	simple	simple	ADJ
ejpam-4507	72	25	poles	pole	NOUN
ejpam-4507	72	26	at	at	ADP
ejpam-4507	72	27	t	t	PROPN
ejpam-4507	72	28	such	such	ADJ
ejpam-4507	72	29	that	that	PRON
ejpam-4507	72	30	bt	bt	NOUN
ejpam-4507	72	31	−	−	NOUN
ejpam-4507	72	32	at	at	ADP
ejpam-4507	72	33	=	=	PROPN
ejpam-4507	72	34	0	0	PROPN
ejpam-4507	72	35	and	and	CCONJ
ejpam-4507	72	36	a	a	DET
ejpam-4507	72	37	pole	pole	NOUN
ejpam-4507	72	38	at	at	ADP
ejpam-4507	72	39	t	t	PROPN
ejpam-4507	72	40	=	=	SYM
ejpam-4507	72	41	0	0	NUM
ejpam-4507	73	1	of	of	ADP
ejpam-4507	73	2	order	order	NOUN
ejpam-4507	73	3	n.	n.	NOUN
ejpam-4507	73	4	let	let	VERB
ejpam-4507	73	5	tk	tk	PROPN
ejpam-4507	73	6	be	be	AUX
ejpam-4507	73	7	those	those	DET
ejpam-4507	73	8	values	value	NOUN
ejpam-4507	73	9	of	of	ADP
ejpam-4507	73	10	t	t	NOUN
ejpam-4507	73	11	such	such	ADJ
ejpam-4507	73	12	that	that	PRON
ejpam-4507	73	13	bt	bt	NOUN
ejpam-4507	73	14	−	−	NOUN
ejpam-4507	73	15	at	at	ADP
ejpam-4507	73	16	=	=	NOUN
ejpam-4507	73	17	0	0	PROPN
ejpam-4507	73	18	.	.	PUNCT
ejpam-4507	74	1	these	these	DET
ejpam-4507	74	2	values	value	NOUN
ejpam-4507	74	3	are	be	AUX
ejpam-4507	74	4	obtained	obtain	VERB
ejpam-4507	74	5	as	as	ADP
ejpam-4507	74	6	follows	follow	VERB
ejpam-4507	74	7	.	.	PUNCT
ejpam-4507	75	1	bt	bt	INTJ
ejpam-4507	75	2	−	−	NOUN
ejpam-4507	75	3	at	at	ADP
ejpam-4507	75	4	=	=	SYM
ejpam-4507	75	5	0	0	PUNCT
ejpam-4507	75	6	et	et	PROPN
ejpam-4507	75	7	ln	ln	PROPN
ejpam-4507	75	8	b	b	PROPN
ejpam-4507	75	9	−	−	X
ejpam-4507	75	10	et	et	NOUN
ejpam-4507	75	11	ln	ln	NOUN
ejpam-4507	75	12	a	a	PRON
ejpam-4507	75	13	=	=	SYM
ejpam-4507	75	14	0	0	PUNCT
ejpam-4507	76	1	(	(	PUNCT
ejpam-4507	76	2	et	et	PROPN
ejpam-4507	76	3	ln	ln	PROPN
ejpam-4507	76	4	b	b	PROPN
ejpam-4507	76	5	=	=	PUNCT
ejpam-4507	76	6	et	et	PROPN
ejpam-4507	76	7	ln	ln	NOUN
ejpam-4507	76	8	a)e−t	a)e−t	PROPN
ejpam-4507	77	1	ln	ln	ADV
ejpam-4507	77	2	a	a	DET
ejpam-4507	77	3	log(et(ln	log(et(ln	PROPN
ejpam-4507	77	4	b−ln	b−ln	NOUN
ejpam-4507	77	5	a	a	NOUN
ejpam-4507	77	6	)	)	PUNCT
ejpam-4507	77	7	=	=	SYM
ejpam-4507	77	8	1	1	X
ejpam-4507	77	9	)	)	PUNCT
ejpam-4507	77	10	t(ln	t(ln	PROPN
ejpam-4507	77	11	b−	b−	PROPN
ejpam-4507	77	12	ln	ln	PROPN
ejpam-4507	77	13	a	a	X
ejpam-4507	77	14	)	)	PUNCT
ejpam-4507	77	15	=	=	VERB
ejpam-4507	77	16	log	log	NOUN
ejpam-4507	77	17	1	1	NUM
ejpam-4507	78	1	=	=	NOUN
ejpam-4507	78	2	i	i	PRON
ejpam-4507	78	3	arg	arg	VERB
ejpam-4507	78	4	1	1	NUM
ejpam-4507	79	1	+	+	CCONJ
ejpam-4507	79	2	2kπi	2kπi	NUM
ejpam-4507	79	3	t	t	NOUN
ejpam-4507	79	4	=	=	PUNCT
ejpam-4507	79	5	2kπi	2kπi	NUM
ejpam-4507	79	6	b	b	PROPN
ejpam-4507	79	7	,	,	PUNCT
ejpam-4507	79	8	where	where	SCONJ
ejpam-4507	79	9	b	b	X
ejpam-4507	79	10	=	=	SYM
ejpam-4507	79	11	ln	ln	ADJ
ejpam-4507	79	12	b−	b−	PROPN
ejpam-4507	79	13	ln	ln	PROPN
ejpam-4507	79	14	a.	a.	NOUN
ejpam-4507	79	15	let	let	VERB
ejpam-4507	79	16	tk	tk	PROPN
ejpam-4507	79	17	=	=	PROPN
ejpam-4507	79	18	2kπi	2kπi	PROPN
ejpam-4507	79	19	/	/	SYM
ejpam-4507	79	20	b	b	NOUN
ejpam-4507	79	21	,	,	PUNCT
ejpam-4507	79	22	k	k	PROPN
ejpam-4507	79	23	∈	∈	PROPN
ejpam-4507	79	24	z.	z.	PROPN
ejpam-4507	79	25	now	now	ADV
ejpam-4507	79	26	let	let	VERB
ejpam-4507	79	27	cn	cn	PROPN
ejpam-4507	79	28	be	be	AUX
ejpam-4507	79	29	the	the	DET
ejpam-4507	79	30	circle	circle	NOUN
ejpam-4507	79	31	described	describe	VERB
ejpam-4507	79	32	in	in	ADP
ejpam-4507	79	33	lemma	lemma	PROPN
ejpam-4507	79	34	2.1	2.1	NUM
ejpam-4507	79	35	.	.	PUNCT
ejpam-4507	80	1	applying	apply	VERB
ejpam-4507	80	2	the	the	DET
ejpam-4507	80	3	residue	residue	NOUN
ejpam-4507	80	4	theorem	theorem	NOUN
ejpam-4507	80	5	,	,	PUNCT
ejpam-4507	80	6	we	we	PRON
ejpam-4507	80	7	have	have	VERB
ejpam-4507	80	8	lim	lim	PROPN
ejpam-4507	80	9	n→+∞	n→+∞	VERB
ejpam-4507	80	10	1	1	NUM
ejpam-4507	80	11	2πi	2πi	NOUN
ejpam-4507	80	12	∫	∫	PROPN
ejpam-4507	80	13	cn	cn	PROPN
ejpam-4507	80	14	cxt	cxt	PROPN
ejpam-4507	80	15	bt	bt	PROPN
ejpam-4507	80	16	−	−	PROPN
ejpam-4507	80	17	at	at	ADP
ejpam-4507	80	18	dt	dt	PROPN
ejpam-4507	80	19	tn	tn	NOUN
ejpam-4507	80	20	=	=	PUNCT
ejpam-4507	80	21	res(f(t	res(f(t	PROPN
ejpam-4507	80	22	)	)	PUNCT
ejpam-4507	80	23	,	,	PUNCT
ejpam-4507	80	24	t	t	PROPN
ejpam-4507	80	25	=	=	SYM
ejpam-4507	80	26	0	0	NUM
ejpam-4507	80	27	)	)	PUNCT
ejpam-4507	80	28	+	+	CCONJ
ejpam-4507	80	29	∑	∑	ADV
ejpam-4507	80	30	k∈z	k∈z	PROPN
ejpam-4507	80	31	,	,	PUNCT
ejpam-4507	80	32	k	k	PROPN
ejpam-4507	80	33	̸=0	̸=0	ADJ
ejpam-4507	80	34	res(f(t	res(f(t	NOUN
ejpam-4507	80	35	)	)	PUNCT
ejpam-4507	80	36	,	,	PUNCT
ejpam-4507	80	37	t	t	PROPN
ejpam-4507	80	38	=	=	SYM
ejpam-4507	80	39	tk	tk	PROPN
ejpam-4507	80	40	)	)	PUNCT
ejpam-4507	80	41	.	.	PUNCT
ejpam-4507	81	1	by	by	ADP
ejpam-4507	81	2	lemma	lemma	PROPN
ejpam-4507	81	3	2.1	2.1	NUM
ejpam-4507	81	4	,	,	PUNCT
ejpam-4507	81	5	0	0	NUM
ejpam-4507	81	6	=	=	NUM
ejpam-4507	81	7	res(f(t	res(f(t	NOUN
ejpam-4507	81	8	)	)	PUNCT
ejpam-4507	81	9	,	,	PUNCT
ejpam-4507	81	10	t	t	PROPN
ejpam-4507	81	11	=	=	SYM
ejpam-4507	81	12	0	0	NUM
ejpam-4507	81	13	)	)	PUNCT
ejpam-4507	81	14	+	+	CCONJ
ejpam-4507	81	15	∑	∑	ADV
ejpam-4507	81	16	k∈z	k∈z	PROPN
ejpam-4507	81	17	,	,	PUNCT
ejpam-4507	81	18	k	k	PROPN
ejpam-4507	81	19	̸=0	̸=0	ADJ
ejpam-4507	81	20	res(f(t	res(f(t	NOUN
ejpam-4507	81	21	)	)	PUNCT
ejpam-4507	81	22	,	,	PUNCT
ejpam-4507	81	23	t	t	PROPN
ejpam-4507	81	24	=	=	SYM
ejpam-4507	81	25	tk	tk	PROPN
ejpam-4507	81	26	)	)	PUNCT
ejpam-4507	81	27	0	0	NUM
ejpam-4507	82	1	=	=	SYM
ejpam-4507	82	2	bn(x	bn(x	X
ejpam-4507	82	3	;	;	PUNCT
ejpam-4507	82	4	a	a	DET
ejpam-4507	82	5	,	,	PUNCT
ejpam-4507	82	6	b	b	NOUN
ejpam-4507	82	7	,	,	PUNCT
ejpam-4507	82	8	c	c	NOUN
ejpam-4507	82	9	)	)	PUNCT
ejpam-4507	82	10	n	n	CCONJ
ejpam-4507	82	11	!	!	PUNCT
ejpam-4507	83	1	+	+	CCONJ
ejpam-4507	83	2	∑	∑	ADV
ejpam-4507	83	3	k∈z	k∈z	PROPN
ejpam-4507	83	4	,	,	PUNCT
ejpam-4507	83	5	k	k	PROPN
ejpam-4507	83	6	̸=0	̸=0	ADJ
ejpam-4507	83	7	res(f(t	res(f(t	NOUN
ejpam-4507	83	8	)	)	PUNCT
ejpam-4507	83	9	,	,	PUNCT
ejpam-4507	83	10	t	t	PROPN
ejpam-4507	83	11	=	=	SYM
ejpam-4507	83	12	tk	tk	PROPN
ejpam-4507	83	13	)	)	PUNCT
ejpam-4507	83	14	=	=	NOUN
ejpam-4507	83	15	⇒bn(x	⇒bn(x	X
ejpam-4507	83	16	;	;	PUNCT
ejpam-4507	83	17	a	a	DET
ejpam-4507	83	18	,	,	PUNCT
ejpam-4507	83	19	b	b	NOUN
ejpam-4507	83	20	,	,	PUNCT
ejpam-4507	83	21	c	c	NOUN
ejpam-4507	83	22	)	)	PUNCT
ejpam-4507	83	23	n	n	CCONJ
ejpam-4507	83	24	!	!	PUNCT
ejpam-4507	84	1	=	=	PUNCT
ejpam-4507	85	1	−	−	PROPN
ejpam-4507	85	2	∑	∑	PUNCT
ejpam-4507	85	3	k∈z	k∈z	PROPN
ejpam-4507	85	4	,	,	PUNCT
ejpam-4507	85	5	k	k	PROPN
ejpam-4507	85	6	̸=0	̸=0	ADJ
ejpam-4507	85	7	res(f(t	res(f(t	NOUN
ejpam-4507	85	8	)	)	PUNCT
ejpam-4507	85	9	,	,	PUNCT
ejpam-4507	85	10	t	t	PROPN
ejpam-4507	85	11	=	=	SYM
ejpam-4507	85	12	tk	tk	PROPN
ejpam-4507	85	13	)	)	PUNCT
ejpam-4507	85	14	.	.	PUNCT
ejpam-4507	86	1	computing	compute	VERB
ejpam-4507	86	2	the	the	DET
ejpam-4507	86	3	residue	residue	NOUN
ejpam-4507	86	4	at	at	ADP
ejpam-4507	86	5	tk	tk	PROPN
ejpam-4507	86	6	:	:	PUNCT
ejpam-4507	86	7	res(f(t	res(f(t	PROPN
ejpam-4507	86	8	)	)	PUNCT
ejpam-4507	86	9	,	,	PUNCT
ejpam-4507	86	10	t	t	PROPN
ejpam-4507	86	11	=	=	SYM
ejpam-4507	86	12	tk	tk	PROPN
ejpam-4507	86	13	)	)	PUNCT
ejpam-4507	86	14	=	=	PROPN
ejpam-4507	86	15	lim	lim	PROPN
ejpam-4507	86	16	t→tk	t→tk	PROPN
ejpam-4507	87	1	(	(	PUNCT
ejpam-4507	87	2	t−	t−	PROPN
ejpam-4507	87	3	tk	tk	PROPN
ejpam-4507	87	4	)	)	PUNCT
ejpam-4507	87	5	2cxt	2cxt	PROPN
ejpam-4507	87	6	(	(	PUNCT
ejpam-4507	87	7	bt	bt	NOUN
ejpam-4507	87	8	−	−	NOUN
ejpam-4507	87	9	at)tn	at)tn	PUNCT
ejpam-4507	88	1	=	=	PUNCT
ejpam-4507	88	2	2cxtkt−n	2cxtkt−n	NUM
ejpam-4507	88	3	k	k	X
ejpam-4507	88	4	µ	µ	X
ejpam-4507	88	5	,	,	PUNCT
ejpam-4507	88	6	where	where	SCONJ
ejpam-4507	88	7	µ	µ	X
ejpam-4507	88	8	=	=	SYM
ejpam-4507	88	9	d	d	X
ejpam-4507	88	10	dt	dt	X
ejpam-4507	88	11	(	(	PUNCT
ejpam-4507	88	12	bt	bt	INTJ
ejpam-4507	88	13	−	−	PROPN
ejpam-4507	88	14	at)|t	at)|t	PROPN
ejpam-4507	88	15	=	=	NOUN
ejpam-4507	88	16	tk	tk	NOUN
ejpam-4507	88	17	=	=	SYM
ejpam-4507	88	18	d	d	NOUN
ejpam-4507	88	19	dt	dt	X
ejpam-4507	88	20	(	(	PUNCT
ejpam-4507	88	21	et	et	PROPN
ejpam-4507	88	22	ln	ln	PROPN
ejpam-4507	88	23	b	b	PROPN
ejpam-4507	88	24	−	−	X
ejpam-4507	88	25	et	et	NOUN
ejpam-4507	88	26	ln	ln	ADJ
ejpam-4507	88	27	a)|t	a)|t	PROPN
ejpam-4507	88	28	=	=	NOUN
ejpam-4507	88	29	tk	tk	NOUN
ejpam-4507	88	30	=	=	SYM
ejpam-4507	88	31	(	(	PUNCT
ejpam-4507	88	32	ln	ln	NOUN
ejpam-4507	88	33	b	b	PROPN
ejpam-4507	88	34	etk	etk	PROPN
ejpam-4507	88	35	ln	ln	PROPN
ejpam-4507	88	36	b	b	PROPN
ejpam-4507	88	37	−	−	X
ejpam-4507	88	38	ln	ln	ADV
ejpam-4507	88	39	a	a	DET
ejpam-4507	88	40	etk	etk	NOUN
ejpam-4507	88	41	ln	ln	PROPN
ejpam-4507	88	42	a	a	NOUN
ejpam-4507	88	43	)	)	PUNCT
ejpam-4507	88	44	e−tk	e−tk	NOUN
ejpam-4507	88	45	ln	ln	ADP
ejpam-4507	88	46	a	a	DET
ejpam-4507	88	47	e−tk	e−tk	NOUN
ejpam-4507	88	48	ln	ln	ADP
ejpam-4507	88	49	a	a	DET
ejpam-4507	88	50	c.	c.	PROPN
ejpam-4507	88	51	corcino	corcino	PROPN
ejpam-4507	88	52	,	,	PUNCT
ejpam-4507	88	53	r.	r.	PROPN
ejpam-4507	88	54	corcino	corcino	PROPN
ejpam-4507	88	55	/	/	SYM
ejpam-4507	88	56	eur	eur	PROPN
ejpam-4507	88	57	.	.	PUNCT
ejpam-4507	89	1	j.	j.	PROPN
ejpam-4507	89	2	pure	pure	PROPN
ejpam-4507	89	3	appl	appl	PROPN
ejpam-4507	89	4	.	.	PROPN
ejpam-4507	89	5	math	math	PROPN
ejpam-4507	89	6	,	,	PUNCT
ejpam-4507	89	7	15	15	NUM
ejpam-4507	89	8	(	(	PUNCT
ejpam-4507	89	9	4	4	NUM
ejpam-4507	89	10	)	)	PUNCT
ejpam-4507	89	11	(	(	PUNCT
ejpam-4507	89	12	2022	2022	NUM
ejpam-4507	89	13	)	)	PUNCT
ejpam-4507	89	14	,	,	PUNCT
ejpam-4507	89	15	1662	1662	NUM
ejpam-4507	89	16	-	-	SYM
ejpam-4507	89	17	1682	1682	NUM
ejpam-4507	89	18	1667	1667	NUM
ejpam-4507	89	19	=	=	SYM
ejpam-4507	89	20	etk	etk	PROPN
ejpam-4507	89	21	ln	ln	PROPN
ejpam-4507	89	22	a(ln	a(ln	PROPN
ejpam-4507	89	23	b	b	PROPN
ejpam-4507	89	24	etk(ln	etk(ln	NOUN
ejpam-4507	89	25	b−ln	b−ln	X
ejpam-4507	89	26	a	a	NOUN
ejpam-4507	89	27	)	)	PUNCT
ejpam-4507	89	28	−	−	PROPN
ejpam-4507	89	29	ln	ln	ADV
ejpam-4507	89	30	a	a	NOUN
ejpam-4507	89	31	)	)	PUNCT
ejpam-4507	89	32	=	=	SYM
ejpam-4507	89	33	etk	etk	PROPN
ejpam-4507	89	34	ln	ln	PROPN
ejpam-4507	89	35	a(ln	a(ln	PROPN
ejpam-4507	89	36	b−	b−	PROPN
ejpam-4507	89	37	ln	ln	PROPN
ejpam-4507	89	38	a	a	X
ejpam-4507	89	39	)	)	PUNCT
ejpam-4507	89	40	=	=	SYM
ejpam-4507	89	41	b	b	X
ejpam-4507	89	42	·	·	PUNCT
ejpam-4507	89	43	etk	etk	PROPN
ejpam-4507	89	44	ln	ln	PROPN
ejpam-4507	89	45	a.	a.	NOUN
ejpam-4507	89	46	thus	thus	ADV
ejpam-4507	89	47	,	,	PUNCT
ejpam-4507	89	48	res(f(t	res(f(t	PROPN
ejpam-4507	89	49	)	)	PUNCT
ejpam-4507	89	50	,	,	PUNCT
ejpam-4507	89	51	t	t	PROPN
ejpam-4507	89	52	=	=	SYM
ejpam-4507	89	53	tk	tk	PROPN
ejpam-4507	89	54	)	)	PUNCT
ejpam-4507	89	55	=	=	PROPN
ejpam-4507	89	56	cxtkt−n	cxtkt−n	PROPN
ejpam-4507	89	57	k	k	PROPN
ejpam-4507	89	58	b	b	PROPN
ejpam-4507	89	59	·	·	PUNCT
ejpam-4507	89	60	etk	etk	PROPN
ejpam-4507	89	61	ln	ln	NOUN
ejpam-4507	89	62	a	a	PROPN
ejpam-4507	89	63	=	=	SYM
ejpam-4507	89	64	etk(x	etk(x	PROPN
ejpam-4507	89	65	ln	ln	ADJ
ejpam-4507	89	66	c−ln	c−ln	PROPN
ejpam-4507	89	67	a	a	PRON
ejpam-4507	89	68	)	)	PUNCT
ejpam-4507	89	69	b	b	PROPN
ejpam-4507	89	70	·	·	PUNCT
ejpam-4507	89	71	tnk	tnk	PROPN
ejpam-4507	89	72	.	.	PUNCT
ejpam-4507	90	1	consequently	consequently	ADV
ejpam-4507	90	2	,	,	PUNCT
ejpam-4507	90	3	bn(x	bn(x	NUM
ejpam-4507	90	4	;	;	PUNCT
ejpam-4507	90	5	a	a	DET
ejpam-4507	90	6	,	,	PUNCT
ejpam-4507	90	7	b	b	NOUN
ejpam-4507	90	8	,	,	PUNCT
ejpam-4507	90	9	c	c	NOUN
ejpam-4507	90	10	)	)	PUNCT
ejpam-4507	90	11	n	n	CCONJ
ejpam-4507	90	12	!	!	PUNCT
ejpam-4507	91	1	=	=	PUNCT
ejpam-4507	92	1	−	−	PROPN
ejpam-4507	92	2	1	1	NUM
ejpam-4507	92	3	b	b	X
ejpam-4507	92	4	∑	∑	ADV
ejpam-4507	92	5	k∈z	k∈z	PROPN
ejpam-4507	92	6	,	,	PUNCT
ejpam-4507	92	7	k	k	PROPN
ejpam-4507	92	8	̸=0	̸=0	PROPN
ejpam-4507	92	9	etk(x	etk(x	PROPN
ejpam-4507	92	10	ln	ln	ADJ
ejpam-4507	92	11	c−ln	c−ln	PROPN
ejpam-4507	92	12	a	a	X
ejpam-4507	92	13	)	)	PUNCT
ejpam-4507	92	14	tnk	tnk	PROPN
ejpam-4507	92	15	.	.	PUNCT
ejpam-4507	93	1	lemma	lemma	PROPN
ejpam-4507	93	2	2.3	2.3	NUM
ejpam-4507	93	3	.	.	PUNCT
ejpam-4507	94	1	let	let	VERB
ejpam-4507	94	2	a	a	DET
ejpam-4507	94	3	,	,	PUNCT
ejpam-4507	94	4	b	b	NOUN
ejpam-4507	94	5	,	,	PUNCT
ejpam-4507	94	6	c	c	AUX
ejpam-4507	94	7	be	be	AUX
ejpam-4507	94	8	positive	positive	ADJ
ejpam-4507	94	9	real	real	ADJ
ejpam-4507	94	10	numbers	number	NOUN
ejpam-4507	94	11	.	.	PUNCT
ejpam-4507	95	1	let	let	VERB
ejpam-4507	95	2	n	n	PRON
ejpam-4507	95	3	≥	≥	NOUN
ejpam-4507	95	4	1	1	NUM
ejpam-4507	95	5	,	,	PUNCT
ejpam-4507	95	6	n	n	CCONJ
ejpam-4507	95	7	>	>	SYM
ejpam-4507	95	8	1	1	NUM
ejpam-4507	95	9	and	and	CCONJ
ejpam-4507	95	10	cn	cn	PROPN
ejpam-4507	95	11	be	be	AUX
ejpam-4507	95	12	the	the	DET
ejpam-4507	95	13	circle	circle	NOUN
ejpam-4507	95	14	about	about	ADP
ejpam-4507	95	15	zero	zero	NUM
ejpam-4507	95	16	of	of	ADP
ejpam-4507	95	17	radius	radius	NOUN
ejpam-4507	95	18	r	r	NOUN
ejpam-4507	95	19	=	=	SYM
ejpam-4507	95	20	(	(	PUNCT
ejpam-4507	95	21	(	(	PUNCT
ejpam-4507	95	22	2n	2n	NUM
ejpam-4507	95	23	+	+	CCONJ
ejpam-4507	95	24	1)π	1)π	NUM
ejpam-4507	96	1	−	−	NOUN
ejpam-4507	96	2	ε)/b	ε)/b	NOUN
ejpam-4507	96	3	,	,	PUNCT
ejpam-4507	96	4	where	where	SCONJ
ejpam-4507	96	5	0	0	X
ejpam-4507	96	6	<	<	X
ejpam-4507	96	7	ε	ε	X
ejpam-4507	96	8	<	<	X
ejpam-4507	96	9	1	1	NUM
ejpam-4507	96	10	and	and	CCONJ
ejpam-4507	96	11	b	b	NOUN
ejpam-4507	96	12	=	=	SYM
ejpam-4507	96	13	ln	ln	PROPN
ejpam-4507	96	14	b−	b−	PROPN
ejpam-4507	96	15	ln	ln	PROPN
ejpam-4507	96	16	a	a	PROPN
ejpam-4507	96	17	,	,	PUNCT
ejpam-4507	96	18	b	b	X
ejpam-4507	96	19	>	>	X
ejpam-4507	96	20	a.	a.	NOUN
ejpam-4507	96	21	for	for	ADP
ejpam-4507	96	22	0	0	NUM
ejpam-4507	96	23	<	<	X
ejpam-4507	96	24	x	x	X
ejpam-4507	96	25	<	<	X
ejpam-4507	96	26	(	(	PUNCT
ejpam-4507	96	27	ln	ln	X
ejpam-4507	96	28	a−	a−	PROPN
ejpam-4507	96	29	b	b	PROPN
ejpam-4507	96	30	π	π	NOUN
ejpam-4507	96	31	−	−	PROPN
ejpam-4507	96	32	ε	ε	PROPN
ejpam-4507	96	33	)	)	PUNCT
ejpam-4507	96	34	/	/	SYM
ejpam-4507	96	35	ln	ln	NOUN
ejpam-4507	96	36	c	c	NOUN
ejpam-4507	96	37	,	,	PUNCT
ejpam-4507	96	38	ln	ln	NOUN
ejpam-4507	96	39	c	c	NOUN
ejpam-4507	96	40	>	>	PUNCT
ejpam-4507	96	41	0	0	NUM
ejpam-4507	97	1	we	we	PRON
ejpam-4507	97	2	have	have	VERB
ejpam-4507	97	3	lim	lim	PROPN
ejpam-4507	97	4	n→+∞	n→+∞	PROPN
ejpam-4507	97	5	∫	∫	PROPN
ejpam-4507	97	6	cn	cn	PROPN
ejpam-4507	97	7	cxt	cxt	PROPN
ejpam-4507	97	8	bt	bt	PROPN
ejpam-4507	98	1	+	+	X
ejpam-4507	98	2	at	at	ADP
ejpam-4507	98	3	dt	dt	NOUN
ejpam-4507	98	4	tn+1	tn+1	PROPN
ejpam-4507	98	5	=	=	SYM
ejpam-4507	98	6	0	0	NUM
ejpam-4507	98	7	.	.	PUNCT
ejpam-4507	99	1	proof	proof	NOUN
ejpam-4507	99	2	.	.	PUNCT
ejpam-4507	100	1	we	we	PRON
ejpam-4507	100	2	will	will	AUX
ejpam-4507	100	3	show	show	VERB
ejpam-4507	100	4	that	that	SCONJ
ejpam-4507	100	5	the	the	DET
ejpam-4507	100	6	function	function	NOUN
ejpam-4507	100	7	cxt	cxt	NOUN
ejpam-4507	100	8	bt	bt	PROPN
ejpam-4507	101	1	+	+	CCONJ
ejpam-4507	101	2	at	at	ADP
ejpam-4507	101	3	is	be	AUX
ejpam-4507	101	4	bounded	bound	VERB
ejpam-4507	101	5	on	on	ADP
ejpam-4507	101	6	cn	cn	PROPN
ejpam-4507	101	7	under	under	ADP
ejpam-4507	101	8	the	the	DET
ejpam-4507	101	9	conditions	condition	NOUN
ejpam-4507	101	10	in	in	ADP
ejpam-4507	101	11	lemma	lemma	PROPN
ejpam-4507	101	12	2.3	2.3	NUM
ejpam-4507	101	13	.	.	PUNCT
ejpam-4507	102	1	from	from	ADP
ejpam-4507	102	2	the	the	DET
ejpam-4507	102	3	proof	proof	NOUN
ejpam-4507	102	4	of	of	ADP
ejpam-4507	102	5	lemma	lemma	PROPN
ejpam-4507	102	6	2.1	2.1	NUM
ejpam-4507	102	7	,	,	PUNCT
ejpam-4507	102	8	|cxt|	|cxt|	NOUN
ejpam-4507	102	9	|bt	|bt	NOUN
ejpam-4507	102	10	+	+	CCONJ
ejpam-4507	102	11	at|	at|	NOUN
ejpam-4507	102	12	=	=	NOUN
ejpam-4507	102	13	exγ	exγ	NOUN
ejpam-4507	102	14	ln	ln	NOUN
ejpam-4507	102	15	c	c	NOUN
ejpam-4507	102	16	eγ	eγ	ADP
ejpam-4507	102	17	ln	ln	ADJ
ejpam-4507	102	18	a[e2γb	a[e2γb	PROPN
ejpam-4507	102	19	+	+	X
ejpam-4507	102	20	2eγb	2eγb	NUM
ejpam-4507	102	21	cos	cos	NOUN
ejpam-4507	102	22	ρb	ρb	PROPN
ejpam-4507	102	23	+	+	NOUN
ejpam-4507	102	24	1	1	NUM
ejpam-4507	102	25	]	]	SYM
ejpam-4507	102	26	1	1	NUM
ejpam-4507	102	27	2	2	NUM
ejpam-4507	102	28	,	,	PUNCT
ejpam-4507	102	29	where	where	SCONJ
ejpam-4507	102	30	here	here	ADV
ejpam-4507	102	31	,	,	PUNCT
ejpam-4507	102	32	γ	γ	X
ejpam-4507	102	33	=	=	SYM
ejpam-4507	102	34	(	(	PUNCT
ejpam-4507	102	35	2n	2n	NUM
ejpam-4507	102	36	+	+	CCONJ
ejpam-4507	102	37	1)π	1)π	NUM
ejpam-4507	102	38	−	−	PROPN
ejpam-4507	102	39	ε	ε	PROPN
ejpam-4507	102	40	b	b	PROPN
ejpam-4507	102	41	cos	cos	PROPN
ejpam-4507	102	42	θ	θ	PROPN
ejpam-4507	102	43	,	,	PUNCT
ejpam-4507	102	44	ρ	ρ	NOUN
ejpam-4507	102	45	=	=	SYM
ejpam-4507	102	46	(	(	PUNCT
ejpam-4507	102	47	2n	2n	NUM
ejpam-4507	102	48	+	+	CCONJ
ejpam-4507	102	49	1)π	1)π	NUM
ejpam-4507	102	50	−	−	PROPN
ejpam-4507	102	51	ε	ε	PROPN
ejpam-4507	102	52	b	b	PROPN
ejpam-4507	102	53	sin	sin	PROPN
ejpam-4507	102	54	θ	θ	PROPN
ejpam-4507	102	55	,	,	PUNCT
ejpam-4507	102	56	0	0	NUM
ejpam-4507	102	57	≤	≤	NUM
ejpam-4507	102	58	θ	θ	NOUN
ejpam-4507	102	59	≤	≤	ADJ
ejpam-4507	102	60	2π	2π	NOUN
ejpam-4507	102	61	.	.	PUNCT
ejpam-4507	103	1	with	with	ADP
ejpam-4507	103	2	x	x	PUNCT
ejpam-4507	103	3	<	<	X
ejpam-4507	103	4	ln	ln	NOUN
ejpam-4507	103	5	a	a	DET
ejpam-4507	103	6	ln	ln	NOUN
ejpam-4507	103	7	c	c	NOUN
ejpam-4507	103	8	−	−	PROPN
ejpam-4507	103	9	b	b	PROPN
ejpam-4507	103	10	(	(	PUNCT
ejpam-4507	103	11	π	π	PROPN
ejpam-4507	103	12	−	−	PROPN
ejpam-4507	103	13	ε	ε	PROPN
ejpam-4507	103	14	)	)	PUNCT
ejpam-4507	103	15	ln	ln	NOUN
ejpam-4507	103	16	c	c	NOUN
ejpam-4507	103	17	=	=	NOUN
ejpam-4507	103	18	⇒	⇒	NOUN
ejpam-4507	103	19	ln	ln	ADJ
ejpam-4507	103	20	a−	a−	PROPN
ejpam-4507	103	21	x	x	X
ejpam-4507	103	22	ln	ln	PROPN
ejpam-4507	103	23	c	c	X
ejpam-4507	103	24	>	>	X
ejpam-4507	103	25	b	b	PROPN
ejpam-4507	104	1	π	π	X
ejpam-4507	104	2	−	−	PROPN
ejpam-4507	104	3	ε	ε	PROPN
ejpam-4507	104	4	≥	≥	PROPN
ejpam-4507	104	5	b	b	PROPN
ejpam-4507	104	6	(	(	PUNCT
ejpam-4507	104	7	2n	2n	NUM
ejpam-4507	104	8	+	+	CCONJ
ejpam-4507	104	9	1)π	1)π	NUM
ejpam-4507	104	10	−	−	PROPN
ejpam-4507	104	11	ε	ε	PROPN
ejpam-4507	104	12	,	,	PUNCT
ejpam-4507	104	13	∀	∀	PUNCT
ejpam-4507	104	14	n	n	PRON
ejpam-4507	104	15	≥	≥	NOUN
ejpam-4507	104	16	0	0	NUM
ejpam-4507	104	17	.	.	PUNCT
ejpam-4507	105	1	c.	c.	PROPN
ejpam-4507	105	2	corcino	corcino	PROPN
ejpam-4507	105	3	,	,	PUNCT
ejpam-4507	105	4	r.	r.	PROPN
ejpam-4507	105	5	corcino	corcino	PROPN
ejpam-4507	105	6	/	/	SYM
ejpam-4507	105	7	eur	eur	PROPN
ejpam-4507	105	8	.	.	PUNCT
ejpam-4507	106	1	j.	j.	PROPN
ejpam-4507	106	2	pure	pure	PROPN
ejpam-4507	106	3	appl	appl	PROPN
ejpam-4507	106	4	.	.	PROPN
ejpam-4507	106	5	math	math	PROPN
ejpam-4507	106	6	,	,	PUNCT
ejpam-4507	106	7	15	15	NUM
ejpam-4507	106	8	(	(	PUNCT
ejpam-4507	106	9	4	4	NUM
ejpam-4507	106	10	)	)	PUNCT
ejpam-4507	106	11	(	(	PUNCT
ejpam-4507	106	12	2022	2022	NUM
ejpam-4507	106	13	)	)	PUNCT
ejpam-4507	106	14	,	,	PUNCT
ejpam-4507	106	15	1662	1662	NUM
ejpam-4507	106	16	-	-	SYM
ejpam-4507	106	17	1682	1682	NUM
ejpam-4507	106	18	1668	1668	NUM
ejpam-4507	106	19	then	then	ADV
ejpam-4507	106	20	1	1	NUM
ejpam-4507	106	21	eγ(ln	eγ(ln	PROPN
ejpam-4507	106	22	a−x	a−x	NOUN
ejpam-4507	106	23	ln	ln	ADJ
ejpam-4507	106	24	c	c	NOUN
ejpam-4507	106	25	)	)	PUNCT
ejpam-4507	106	26	≤	≤	NOUN
ejpam-4507	106	27	1	1	NUM
ejpam-4507	106	28	ecos	ecos	PROPN
ejpam-4507	106	29	θ	θ	PROPN
ejpam-4507	106	30	≤	≤	NUM
ejpam-4507	106	31	1	1	NUM
ejpam-4507	106	32	e−1	e−1	PROPN
ejpam-4507	106	33	=	=	SYM
ejpam-4507	106	34	e.	e.	PROPN
ejpam-4507	106	35	thus	thus	ADV
ejpam-4507	106	36	,	,	PUNCT
ejpam-4507	106	37	|cxt|	|cxt|	NOUN
ejpam-4507	106	38	|bt	|bt	NOUN
ejpam-4507	106	39	+	+	CCONJ
ejpam-4507	106	40	at|	at|	ADP
ejpam-4507	106	41	≤	≤	NUM
ejpam-4507	106	42	e	e	NOUN
ejpam-4507	107	1	[	[	X
ejpam-4507	107	2	e2γb	e2γb	X
ejpam-4507	107	3	+	+	CCONJ
ejpam-4507	107	4	2eγb	2eγb	NUM
ejpam-4507	107	5	cos	cos	NOUN
ejpam-4507	107	6	ρb	ρb	PROPN
ejpam-4507	107	7	+	+	NOUN
ejpam-4507	107	8	1	1	NUM
ejpam-4507	107	9	]	]	SYM
ejpam-4507	107	10	1	1	NUM
ejpam-4507	107	11	2	2	NUM
ejpam-4507	107	12	.	.	PUNCT
ejpam-4507	108	1	the	the	DET
ejpam-4507	108	2	expression	expression	NOUN
ejpam-4507	108	3	e2γb+2eγb	e2γb+2eγb	NOUN
ejpam-4507	108	4	cos	cos	SCONJ
ejpam-4507	108	5	ρb+1	ρb+1	PRON
ejpam-4507	108	6	must	must	AUX
ejpam-4507	108	7	not	not	PART
ejpam-4507	108	8	be	be	AUX
ejpam-4507	108	9	zero	zero	NUM
ejpam-4507	108	10	.	.	PUNCT
ejpam-4507	109	1	the	the	DET
ejpam-4507	109	2	results	result	NOUN
ejpam-4507	109	3	for	for	ADP
ejpam-4507	109	4	the	the	DET
ejpam-4507	109	5	cases	case	NOUN
ejpam-4507	109	6	cos	cos	ADP
ejpam-4507	109	7	θ	θ	PROPN
ejpam-4507	109	8	<	<	X
ejpam-4507	109	9	0	0	PUNCT
ejpam-4507	109	10	and	and	CCONJ
ejpam-4507	109	11	cos	cos	ADP
ejpam-4507	109	12	θ	θ	PROPN
ejpam-4507	109	13	>	>	X
ejpam-4507	109	14	0	0	NUM
ejpam-4507	109	15	obtained	obtain	VERB
ejpam-4507	109	16	in	in	ADP
ejpam-4507	109	17	the	the	DET
ejpam-4507	109	18	proof	proof	NOUN
ejpam-4507	109	19	of	of	ADP
ejpam-4507	109	20	lemma	lemma	PROPN
ejpam-4507	109	21	2.1	2.1	NUM
ejpam-4507	109	22	still	still	ADV
ejpam-4507	109	23	hold	hold	VERB
ejpam-4507	109	24	.	.	PUNCT
ejpam-4507	110	1	we	we	PRON
ejpam-4507	110	2	reconsider	reconsider	VERB
ejpam-4507	110	3	here	here	ADV
ejpam-4507	110	4	the	the	DET
ejpam-4507	110	5	case	case	NOUN
ejpam-4507	110	6	cos	cos	PROPN
ejpam-4507	110	7	θ	θ	PROPN
ejpam-4507	110	8	=	=	SYM
ejpam-4507	110	9	0	0	X
ejpam-4507	110	10	.	.	PUNCT
ejpam-4507	111	1	in	in	ADP
ejpam-4507	111	2	the	the	DET
ejpam-4507	111	3	case	case	NOUN
ejpam-4507	111	4	θ	θ	NOUN
ejpam-4507	111	5	=	=	SYM
ejpam-4507	111	6	0	0	NUM
ejpam-4507	111	7	,	,	PUNCT
ejpam-4507	111	8	γ	γ	NOUN
ejpam-4507	111	9	=	=	SYM
ejpam-4507	111	10	0	0	NUM
ejpam-4507	111	11	and	and	CCONJ
ejpam-4507	111	12	e2γb	e2γb	PUNCT
ejpam-4507	112	1	+	+	CCONJ
ejpam-4507	112	2	2eγb	2eγb	NUM
ejpam-4507	112	3	cos	cos	NOUN
ejpam-4507	112	4	ρb	ρb	PROPN
ejpam-4507	112	5	+	+	NOUN
ejpam-4507	112	6	1	1	NUM
ejpam-4507	112	7	=	=	SYM
ejpam-4507	112	8	2	2	NUM
ejpam-4507	112	9	+	+	SYM
ejpam-4507	112	10	2	2	NUM
ejpam-4507	112	11	cos	cos	ADP
ejpam-4507	112	12	ρb	ρb	PROPN
ejpam-4507	112	13	,	,	PUNCT
ejpam-4507	112	14	which	which	PRON
ejpam-4507	112	15	is	be	AUX
ejpam-4507	112	16	nonzero	nonzero	NOUN
ejpam-4507	112	17	provided	provide	VERB
ejpam-4507	112	18	that	that	SCONJ
ejpam-4507	112	19	cos	cos	ADP
ejpam-4507	112	20	ρb	ρb	PRON
ejpam-4507	112	21	̸=	̸=	PROPN
ejpam-4507	112	22	−1	−1	NOUN
ejpam-4507	112	23	.	.	PUNCT
ejpam-4507	113	1	since	since	SCONJ
ejpam-4507	113	2	cos	cos	PROPN
ejpam-4507	113	3	θ	θ	PROPN
ejpam-4507	113	4	=	=	SYM
ejpam-4507	113	5	0	0	NUM
ejpam-4507	113	6	,	,	PUNCT
ejpam-4507	113	7	we	we	PRON
ejpam-4507	113	8	have	have	VERB
ejpam-4507	113	9	ρ	ρ	NOUN
ejpam-4507	113	10	=	=	SYM
ejpam-4507	113	11	(	(	PUNCT
ejpam-4507	113	12	±1	±1	PROPN
ejpam-4507	113	13	)	)	PUNCT
ejpam-4507	113	14	(	(	PUNCT
ejpam-4507	113	15	2n	2n	NUM
ejpam-4507	113	16	+	+	CCONJ
ejpam-4507	113	17	1)π	1)π	NUM
ejpam-4507	113	18	−	−	PROPN
ejpam-4507	113	19	ε	ε	PROPN
ejpam-4507	113	20	b	b	PROPN
ejpam-4507	113	21	.	.	PUNCT
ejpam-4507	114	1	thus	thus	ADV
ejpam-4507	114	2	,	,	PUNCT
ejpam-4507	114	3	cos	cos	PROPN
ejpam-4507	114	4	ρb	ρb	NOUN
ejpam-4507	114	5	=	=	PUNCT
ejpam-4507	114	6	cos(±(2n	cos(±(2n	NOUN
ejpam-4507	114	7	+	+	CCONJ
ejpam-4507	114	8	1)π	1)π	NUM
ejpam-4507	114	9	−	−	NOUN
ejpam-4507	114	10	ε	ε	PROPN
ejpam-4507	114	11	)	)	PUNCT
ejpam-4507	114	12	=	=	SYM
ejpam-4507	114	13	−1	−1	NOUN
ejpam-4507	114	14	iff	iff	PROPN
ejpam-4507	114	15	(	(	PUNCT
ejpam-4507	114	16	2n	2n	NUM
ejpam-4507	114	17	+	+	CCONJ
ejpam-4507	114	18	1)π	1)π	NUM
ejpam-4507	114	19	−	−	PROPN
ejpam-4507	114	20	ε	ε	PROPN
ejpam-4507	114	21	=	=	PUNCT
ejpam-4507	114	22	(	(	PUNCT
ejpam-4507	114	23	2k	2k	PROPN
ejpam-4507	114	24	+	+	CCONJ
ejpam-4507	114	25	1)π	1)π	NUM
ejpam-4507	114	26	,	,	PUNCT
ejpam-4507	114	27	for	for	ADP
ejpam-4507	114	28	some	some	DET
ejpam-4507	114	29	integer	integer	NOUN
ejpam-4507	114	30	k.	k.	PROPN
ejpam-4507	114	31	equivalently	equivalently	PROPN
ejpam-4507	114	32	,	,	PUNCT
ejpam-4507	114	33	(	(	PUNCT
ejpam-4507	114	34	2n	2n	X
ejpam-4507	114	35	+	+	CCONJ
ejpam-4507	114	36	1)π	1)π	NUM
ejpam-4507	114	37	−	−	PROPN
ejpam-4507	114	38	(	(	PUNCT
ejpam-4507	114	39	2k	2k	NUM
ejpam-4507	114	40	+	+	CCONJ
ejpam-4507	114	41	1)π	1)π	NUM
ejpam-4507	114	42	=	=	SYM
ejpam-4507	114	43	ε	ε	PROPN
ejpam-4507	114	44	2(n	2(n	NUM
ejpam-4507	114	45	−	−	PROPN
ejpam-4507	114	46	k)π	k)π	NOUN
ejpam-4507	114	47	=	=	SYM
ejpam-4507	114	48	ε	ε	PROPN
ejpam-4507	114	49	,	,	PUNCT
ejpam-4507	114	50	which	which	PRON
ejpam-4507	114	51	is	be	AUX
ejpam-4507	114	52	not	not	PART
ejpam-4507	114	53	possible	possible	ADJ
ejpam-4507	114	54	because	because	SCONJ
ejpam-4507	114	55	0	0	NUM
ejpam-4507	114	56	<	<	X
ejpam-4507	114	57	ε	ε	X
ejpam-4507	114	58	<	<	X
ejpam-4507	114	59	1	1	NUM
ejpam-4507	114	60	.	.	PUNCT
ejpam-4507	114	61	thus	thus	ADV
ejpam-4507	114	62	,	,	PUNCT
ejpam-4507	114	63	under	under	ADP
ejpam-4507	114	64	the	the	DET
ejpam-4507	114	65	conditions	condition	NOUN
ejpam-4507	114	66	in	in	ADP
ejpam-4507	114	67	the	the	DET
ejpam-4507	114	68	lemma	lemma	PROPN
ejpam-4507	114	69	,	,	PUNCT
ejpam-4507	114	70	the	the	DET
ejpam-4507	114	71	function	function	NOUN
ejpam-4507	114	72	cxt	cxt	NOUN
ejpam-4507	114	73	bt	bt	PROPN
ejpam-4507	115	1	+	+	CCONJ
ejpam-4507	115	2	at	at	ADP
ejpam-4507	115	3	is	be	AUX
ejpam-4507	115	4	bounded	bound	VERB
ejpam-4507	115	5	on	on	ADP
ejpam-4507	115	6	cn	cn	PROPN
ejpam-4507	115	7	as	as	ADP
ejpam-4507	115	8	n	n	PROPN
ejpam-4507	115	9	→	→	PUNCT
ejpam-4507	115	10	+	+	NOUN
ejpam-4507	115	11	∞.	∞.	PROPN
ejpam-4507	115	12	let	let	VERB
ejpam-4507	115	13	m∗	m∗	NOUN
ejpam-4507	115	14	be	be	AUX
ejpam-4507	115	15	a	a	DET
ejpam-4507	115	16	positive	positive	ADJ
ejpam-4507	115	17	integer	integer	NOUN
ejpam-4507	115	18	such	such	ADJ
ejpam-4507	115	19	that	that	SCONJ
ejpam-4507	115	20	|cxt|	|cxt|	NOUN
ejpam-4507	115	21	|bt	|bt	NOUN
ejpam-4507	115	22	+	+	CCONJ
ejpam-4507	115	23	at|	at|	PROPN
ejpam-4507	115	24	<	<	X
ejpam-4507	115	25	m∗	m∗	NOUN
ejpam-4507	115	26	,	,	PUNCT
ejpam-4507	115	27	∀t	∀t	PROPN
ejpam-4507	115	28	∈	∈	PROPN
ejpam-4507	115	29	cn	cn	PROPN
ejpam-4507	115	30	.	.	PUNCT
ejpam-4507	116	1	then	then	ADV
ejpam-4507	116	2	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-4507	116	3	cn	cn	PROPN
ejpam-4507	116	4	cxt	cxt	PROPN
ejpam-4507	116	5	bt	bt	PROPN
ejpam-4507	116	6	+	+	X
ejpam-4507	116	7	at	at	ADP
ejpam-4507	116	8	·	·	PUNCT
ejpam-4507	116	9	dt	dt	ADP
ejpam-4507	116	10	tn+1	tn+1	PROPN
ejpam-4507	116	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	116	12	≤	≤	NUM
ejpam-4507	116	13	∫	∫	PROPN
ejpam-4507	116	14	cn	cn	PROPN
ejpam-4507	116	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	116	16	cxt	cxt	NOUN
ejpam-4507	116	17	bt	bt	NOUN
ejpam-4507	117	1	+	+	CCONJ
ejpam-4507	117	2	at	at	ADP
ejpam-4507	117	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	117	4	|dt|	|dt|	PROPN
ejpam-4507	117	5	|tn+1|	|tn+1|	PROPN
ejpam-4507	117	6	<	<	X
ejpam-4507	117	7	m∗	m∗	PROPN
ejpam-4507	117	8	(	(	PUNCT
ejpam-4507	117	9	2n	2n	NUM
ejpam-4507	117	10	+	+	CCONJ
ejpam-4507	118	1	1)π	1)π	NUM
ejpam-4507	118	2	−	−	PROPN
ejpam-4507	118	3	ε	ε	PROPN
ejpam-4507	118	4	b	b	PROPN
ejpam-4507	118	5	·	·	PUNCT
ejpam-4507	118	6	2π	2π	NOUN
ejpam-4507	118	7	(	(	PUNCT
ejpam-4507	118	8	(	(	PUNCT
ejpam-4507	118	9	2n	2n	NUM
ejpam-4507	118	10	+	+	CCONJ
ejpam-4507	118	11	1)π	1)π	NUM
ejpam-4507	118	12	−	−	PROPN
ejpam-4507	118	13	ε	ε	PROPN
ejpam-4507	118	14	b	b	PROPN
ejpam-4507	118	15	)	)	PUNCT
ejpam-4507	118	16	n+1	n+1	PROPN
ejpam-4507	118	17	<	<	X
ejpam-4507	118	18	2m∗πbn	2m∗πbn	PROPN
ejpam-4507	118	19	(	(	PUNCT
ejpam-4507	118	20	(	(	PUNCT
ejpam-4507	118	21	2n	2n	NUM
ejpam-4507	118	22	+	+	CCONJ
ejpam-4507	118	23	1)π	1)π	NUM
ejpam-4507	118	24	−	−	NOUN
ejpam-4507	118	25	ε)n	ε)n	PUNCT
ejpam-4507	118	26	,	,	PUNCT
ejpam-4507	118	27	which	which	PRON
ejpam-4507	118	28	goes	go	VERB
ejpam-4507	118	29	to	to	ADP
ejpam-4507	118	30	zero	zero	NUM
ejpam-4507	118	31	as	as	ADP
ejpam-4507	118	32	n	n	PROPN
ejpam-4507	118	33	→	→	SYM
ejpam-4507	118	34	+	+	PROPN
ejpam-4507	118	35	∞.	∞.	PROPN
ejpam-4507	118	36	c.	c.	PROPN
ejpam-4507	118	37	corcino	corcino	PROPN
ejpam-4507	118	38	,	,	PUNCT
ejpam-4507	118	39	r.	r.	PROPN
ejpam-4507	118	40	corcino	corcino	PROPN
ejpam-4507	118	41	/	/	SYM
ejpam-4507	118	42	eur	eur	PROPN
ejpam-4507	118	43	.	.	PUNCT
ejpam-4507	119	1	j.	j.	PROPN
ejpam-4507	119	2	pure	pure	PROPN
ejpam-4507	119	3	appl	appl	PROPN
ejpam-4507	119	4	.	.	PROPN
ejpam-4507	119	5	math	math	PROPN
ejpam-4507	119	6	,	,	PUNCT
ejpam-4507	119	7	15	15	NUM
ejpam-4507	119	8	(	(	PUNCT
ejpam-4507	119	9	4	4	NUM
ejpam-4507	119	10	)	)	PUNCT
ejpam-4507	119	11	(	(	PUNCT
ejpam-4507	119	12	2022	2022	NUM
ejpam-4507	119	13	)	)	PUNCT
ejpam-4507	119	14	,	,	PUNCT
ejpam-4507	119	15	1662	1662	NUM
ejpam-4507	119	16	-	-	SYM
ejpam-4507	119	17	1682	1682	NUM
ejpam-4507	119	18	1669	1669	NUM
ejpam-4507	119	19	theorem	theorem	VERB
ejpam-4507	119	20	2.4	2.4	NUM
ejpam-4507	119	21	.	.	PUNCT
ejpam-4507	120	1	let	let	VERB
ejpam-4507	120	2	a	a	DET
ejpam-4507	120	3	,	,	PUNCT
ejpam-4507	120	4	b	b	NOUN
ejpam-4507	120	5	,	,	PUNCT
ejpam-4507	120	6	c	c	AUX
ejpam-4507	120	7	be	be	AUX
ejpam-4507	120	8	positive	positive	ADJ
ejpam-4507	120	9	real	real	ADJ
ejpam-4507	120	10	numbers	number	NOUN
ejpam-4507	120	11	.	.	PUNCT
ejpam-4507	121	1	the	the	DET
ejpam-4507	121	2	fourier	fourier	ADJ
ejpam-4507	121	3	series	series	NOUN
ejpam-4507	121	4	of	of	ADP
ejpam-4507	121	5	the	the	DET
ejpam-4507	121	6	euler	euler	NOUN
ejpam-4507	121	7	-	-	PUNCT
ejpam-4507	121	8	type	type	NOUN
ejpam-4507	121	9	polynomials	polynomial	NOUN
ejpam-4507	121	10	en(x	en(x	ADP
ejpam-4507	121	11	;	;	PUNCT
ejpam-4507	121	12	a	a	DET
ejpam-4507	121	13	,	,	PUNCT
ejpam-4507	121	14	b	b	NOUN
ejpam-4507	121	15	,	,	PUNCT
ejpam-4507	121	16	c	c	NOUN
ejpam-4507	121	17	)	)	PUNCT
ejpam-4507	121	18	is	be	AUX
ejpam-4507	121	19	given	give	VERB
ejpam-4507	121	20	by	by	ADP
ejpam-4507	121	21	en(x	en(x	NOUN
ejpam-4507	121	22	;	;	PUNCT
ejpam-4507	121	23	a	a	DET
ejpam-4507	121	24	,	,	PUNCT
ejpam-4507	121	25	b	b	NOUN
ejpam-4507	121	26	,	,	PUNCT
ejpam-4507	121	27	c	c	NOUN
ejpam-4507	121	28	)	)	PUNCT
ejpam-4507	121	29	n	n	CCONJ
ejpam-4507	121	30	!	!	PUNCT
ejpam-4507	122	1	=	=	SYM
ejpam-4507	122	2	2	2	NUM
ejpam-4507	122	3	b	b	NOUN
ejpam-4507	122	4	∑	∑	ADV
ejpam-4507	122	5	k∈z	k∈z	PROPN
ejpam-4507	122	6	etk(x	etk(x	PROPN
ejpam-4507	122	7	ln	ln	ADJ
ejpam-4507	122	8	c−ln	c−ln	PROPN
ejpam-4507	122	9	a	a	X
ejpam-4507	122	10	)	)	PUNCT
ejpam-4507	122	11	tn+1	tn+1	NOUN
ejpam-4507	122	12	k	k	PROPN
ejpam-4507	122	13	,	,	PUNCT
ejpam-4507	122	14	valid	valid	ADJ
ejpam-4507	122	15	for	for	ADP
ejpam-4507	122	16	0	0	NUM
ejpam-4507	122	17	<	<	X
ejpam-4507	122	18	x	x	X
ejpam-4507	122	19	<	<	X
ejpam-4507	122	20	(	(	PUNCT
ejpam-4507	122	21	ln	ln	X
ejpam-4507	122	22	a−	a−	PROPN
ejpam-4507	122	23	b	b	PROPN
ejpam-4507	122	24	π	π	NOUN
ejpam-4507	122	25	−	−	PROPN
ejpam-4507	122	26	ε	ε	PROPN
ejpam-4507	122	27	)	)	PUNCT
ejpam-4507	122	28	/	/	SYM
ejpam-4507	123	1	ln	ln	NOUN
ejpam-4507	123	2	c	c	NOUN
ejpam-4507	123	3	,	,	PUNCT
ejpam-4507	123	4	ln	ln	NOUN
ejpam-4507	123	5	c	c	NOUN
ejpam-4507	123	6	>	>	X
ejpam-4507	123	7	0	0	NUM
ejpam-4507	124	1	where	where	SCONJ
ejpam-4507	124	2	tk	tk	PROPN
ejpam-4507	124	3	=	=	X
ejpam-4507	124	4	(	(	PUNCT
ejpam-4507	124	5	2k	2k	NOUN
ejpam-4507	124	6	+	+	CCONJ
ejpam-4507	124	7	1)πi	1)πi	NUM
ejpam-4507	124	8	/	/	SYM
ejpam-4507	124	9	b	b	PROPN
ejpam-4507	124	10	,	,	PUNCT
ejpam-4507	124	11	b	b	X
ejpam-4507	124	12	=	=	SYM
ejpam-4507	124	13	ln	ln	PROPN
ejpam-4507	124	14	b−	b−	PROPN
ejpam-4507	124	15	ln	ln	ADV
ejpam-4507	124	16	a	a	DET
ejpam-4507	124	17	>	>	X
ejpam-4507	124	18	0	0	X
ejpam-4507	124	19	.	.	PUNCT
ejpam-4507	124	20	proof	proof	NOUN
ejpam-4507	124	21	.	.	PUNCT
ejpam-4507	125	1	when	when	SCONJ
ejpam-4507	125	2	α	α	PRON
ejpam-4507	125	3	=	=	SYM
ejpam-4507	125	4	1	1	NUM
ejpam-4507	125	5	,	,	PUNCT
ejpam-4507	125	6	the	the	DET
ejpam-4507	125	7	generating	generate	VERB
ejpam-4507	125	8	function	function	NOUN
ejpam-4507	125	9	(	(	PUNCT
ejpam-4507	125	10	2	2	X
ejpam-4507	125	11	)	)	PUNCT
ejpam-4507	125	12	reduces	reduce	VERB
ejpam-4507	125	13	to	to	ADP
ejpam-4507	125	14	(	(	PUNCT
ejpam-4507	125	15	2	2	NUM
ejpam-4507	125	16	bt	bt	NOUN
ejpam-4507	125	17	+	+	X
ejpam-4507	125	18	at	at	ADP
ejpam-4507	125	19	)	)	PUNCT
ejpam-4507	125	20	cxt	cxt	NOUN
ejpam-4507	125	21	=	=	PUNCT
ejpam-4507	125	22	∞∑	∞∑	PROPN
ejpam-4507	125	23	n=0	n=0	NUM
ejpam-4507	125	24	en(x	en(x	ADP
ejpam-4507	125	25	;	;	PUNCT
ejpam-4507	125	26	a	a	DET
ejpam-4507	125	27	,	,	PUNCT
ejpam-4507	125	28	b	b	NOUN
ejpam-4507	125	29	,	,	PUNCT
ejpam-4507	125	30	c	c	NOUN
ejpam-4507	125	31	)	)	PUNCT
ejpam-4507	125	32	tn	tn	PROPN
ejpam-4507	125	33	n	n	CCONJ
ejpam-4507	125	34	!	!	PUNCT
ejpam-4507	125	35	,	,	PUNCT
ejpam-4507	125	36	|t|	|t|	VERB
ejpam-4507	125	37	<	<	X
ejpam-4507	125	38	π	π	PROPN
ejpam-4507	125	39	b	b	PROPN
ejpam-4507	125	40	.	.	PUNCT
ejpam-4507	126	1	applying	apply	VERB
ejpam-4507	126	2	the	the	DET
ejpam-4507	126	3	cauchy	cauchy	ADJ
ejpam-4507	126	4	integral	integral	ADJ
ejpam-4507	126	5	formula	formula	NOUN
ejpam-4507	126	6	,	,	PUNCT
ejpam-4507	126	7	en(x	en(x	ADP
ejpam-4507	126	8	;	;	PUNCT
ejpam-4507	126	9	a	a	DET
ejpam-4507	126	10	,	,	PUNCT
ejpam-4507	126	11	b	b	NOUN
ejpam-4507	126	12	,	,	PUNCT
ejpam-4507	126	13	c	c	NOUN
ejpam-4507	126	14	)	)	PUNCT
ejpam-4507	126	15	n	n	CCONJ
ejpam-4507	126	16	!	!	PUNCT
ejpam-4507	127	1	=	=	SYM
ejpam-4507	127	2	1	1	NUM
ejpam-4507	127	3	2πi	2πi	ADJ
ejpam-4507	127	4	∫	∫	PROPN
ejpam-4507	128	1	c	c	PROPN
ejpam-4507	128	2	2cxt	2cxt	NUM
ejpam-4507	128	3	(	(	PUNCT
ejpam-4507	128	4	bt	bt	X
ejpam-4507	128	5	+	+	CCONJ
ejpam-4507	128	6	at)tn+1	at)tn+1	ADJ
ejpam-4507	128	7	dt	dt	NOUN
ejpam-4507	128	8	,	,	PUNCT
ejpam-4507	128	9	where	where	SCONJ
ejpam-4507	128	10	c	c	PROPN
ejpam-4507	128	11	is	be	AUX
ejpam-4507	128	12	a	a	DET
ejpam-4507	128	13	circle	circle	NOUN
ejpam-4507	128	14	about	about	ADP
ejpam-4507	128	15	zero	zero	NUM
ejpam-4507	128	16	of	of	ADP
ejpam-4507	128	17	radius	radius	NOUN
ejpam-4507	128	18	π	π	PROPN
ejpam-4507	128	19	b	b	PROPN
ejpam-4507	128	20	.	.	PUNCT
ejpam-4507	129	1	let	let	VERB
ejpam-4507	129	2	g(t	g(t	PROPN
ejpam-4507	129	3	)	)	PUNCT
ejpam-4507	130	1	=	=	PUNCT
ejpam-4507	130	2	2cxt	2cxt	NUM
ejpam-4507	130	3	(	(	PUNCT
ejpam-4507	130	4	bt	bt	X
ejpam-4507	130	5	+	+	CCONJ
ejpam-4507	130	6	at)tn+1	at)tn+1	ADJ
ejpam-4507	130	7	.	.	PUNCT
ejpam-4507	131	1	the	the	DET
ejpam-4507	131	2	function	function	PROPN
ejpam-4507	131	3	g(t	g(t	PROPN
ejpam-4507	131	4	)	)	PUNCT
ejpam-4507	131	5	has	have	VERB
ejpam-4507	131	6	a	a	DET
ejpam-4507	131	7	pole	pole	NOUN
ejpam-4507	131	8	at	at	ADP
ejpam-4507	131	9	t	t	PROPN
ejpam-4507	131	10	=	=	SYM
ejpam-4507	131	11	0	0	NUM
ejpam-4507	131	12	of	of	ADP
ejpam-4507	131	13	order	order	NOUN
ejpam-4507	131	14	n+1	n+1	X
ejpam-4507	131	15	and	and	CCONJ
ejpam-4507	131	16	simple	simple	ADJ
ejpam-4507	131	17	poles	pole	NOUN
ejpam-4507	131	18	at	at	ADP
ejpam-4507	131	19	the	the	DET
ejpam-4507	131	20	values	value	NOUN
ejpam-4507	131	21	of	of	ADP
ejpam-4507	131	22	t	t	NOUN
ejpam-4507	131	23	such	such	ADJ
ejpam-4507	131	24	that	that	DET
ejpam-4507	131	25	bt	bt	NOUN
ejpam-4507	132	1	+	+	CCONJ
ejpam-4507	132	2	at	at	ADP
ejpam-4507	132	3	=	=	NOUN
ejpam-4507	132	4	0	0	NUM
ejpam-4507	132	5	.	.	PUNCT
ejpam-4507	133	1	these	these	DET
ejpam-4507	133	2	values	value	NOUN
ejpam-4507	133	3	are	be	AUX
ejpam-4507	133	4	tk	tk	NOUN
ejpam-4507	133	5	=	=	SYM
ejpam-4507	133	6	(	(	PUNCT
ejpam-4507	133	7	2k	2k	NOUN
ejpam-4507	133	8	+	+	CCONJ
ejpam-4507	134	1	1)πi	1)πi	NUM
ejpam-4507	134	2	/	/	SYM
ejpam-4507	134	3	b	b	NOUN
ejpam-4507	134	4	,	,	PUNCT
ejpam-4507	134	5	k	k	PROPN
ejpam-4507	134	6	∈	∈	PROPN
ejpam-4507	134	7	z	z	NOUN
ejpam-4507	134	8	which	which	PRON
ejpam-4507	134	9	are	be	AUX
ejpam-4507	134	10	obtained	obtain	VERB
ejpam-4507	134	11	similarly	similarly	ADV
ejpam-4507	134	12	as	as	ADP
ejpam-4507	134	13	those	those	PRON
ejpam-4507	134	14	in	in	ADP
ejpam-4507	134	15	theorem	theorem	NOUN
ejpam-4507	134	16	2.2	2.2	NUM
ejpam-4507	134	17	.	.	PUNCT
ejpam-4507	135	1	let	let	VERB
ejpam-4507	135	2	cn	cn	PROPN
ejpam-4507	135	3	be	be	AUX
ejpam-4507	135	4	the	the	DET
ejpam-4507	135	5	circle	circle	NOUN
ejpam-4507	135	6	described	describe	VERB
ejpam-4507	135	7	in	in	ADP
ejpam-4507	135	8	lemma	lemma	PROPN
ejpam-4507	135	9	2.3	2.3	NUM
ejpam-4507	135	10	.	.	PUNCT
ejpam-4507	136	1	from	from	ADP
ejpam-4507	136	2	the	the	DET
ejpam-4507	136	3	residue	residue	NOUN
ejpam-4507	136	4	theorem	theorem	NOUN
ejpam-4507	136	5	,	,	PUNCT
ejpam-4507	136	6	lim	lim	PROPN
ejpam-4507	136	7	n→+∞	n→+∞	VERB
ejpam-4507	136	8	1	1	NUM
ejpam-4507	136	9	2πi	2πi	NOUN
ejpam-4507	136	10	∫	∫	PROPN
ejpam-4507	136	11	cn	cn	PROPN
ejpam-4507	136	12	g(t)d(t	g(t)d(t	NOUN
ejpam-4507	136	13	)	)	PUNCT
ejpam-4507	136	14	=	=	SYM
ejpam-4507	136	15	res(g(t	res(g(t	NOUN
ejpam-4507	136	16	)	)	PUNCT
ejpam-4507	136	17	,	,	PUNCT
ejpam-4507	136	18	t	t	PROPN
ejpam-4507	136	19	=	=	SYM
ejpam-4507	136	20	0	0	NUM
ejpam-4507	136	21	)	)	PUNCT
ejpam-4507	137	1	+	+	CCONJ
ejpam-4507	137	2	∑	∑	ADP
ejpam-4507	137	3	k∈z	k∈z	PROPN
ejpam-4507	137	4	res(g(t	res(g(t	NOUN
ejpam-4507	137	5	)	)	PUNCT
ejpam-4507	137	6	,	,	PUNCT
ejpam-4507	137	7	t	t	PROPN
ejpam-4507	137	8	=	=	SYM
ejpam-4507	137	9	tk	tk	PROPN
ejpam-4507	137	10	)	)	PUNCT
ejpam-4507	137	11	.	.	PUNCT
ejpam-4507	138	1	by	by	ADP
ejpam-4507	138	2	lemma	lemma	PROPN
ejpam-4507	138	3	2.3	2.3	NUM
ejpam-4507	138	4	,	,	PUNCT
ejpam-4507	138	5	we	we	PRON
ejpam-4507	138	6	have	have	VERB
ejpam-4507	138	7	en(x	en(x	NOUN
ejpam-4507	138	8	;	;	PUNCT
ejpam-4507	138	9	a	a	DET
ejpam-4507	138	10	,	,	PUNCT
ejpam-4507	138	11	b	b	NOUN
ejpam-4507	138	12	,	,	PUNCT
ejpam-4507	138	13	c	c	NOUN
ejpam-4507	138	14	)	)	PUNCT
ejpam-4507	138	15	n	n	CCONJ
ejpam-4507	138	16	!	!	PUNCT
ejpam-4507	139	1	=	=	PUNCT
ejpam-4507	140	1	−	−	PROPN
ejpam-4507	140	2	∑	∑	PUNCT
ejpam-4507	140	3	k∈z	k∈z	PROPN
ejpam-4507	140	4	res(g(t	res(g(t	NOUN
ejpam-4507	140	5	)	)	PUNCT
ejpam-4507	140	6	,	,	PUNCT
ejpam-4507	140	7	t	t	PROPN
ejpam-4507	140	8	=	=	SYM
ejpam-4507	140	9	tk	tk	PROPN
ejpam-4507	140	10	)	)	PUNCT
ejpam-4507	140	11	.	.	PUNCT
ejpam-4507	141	1	computing	compute	VERB
ejpam-4507	141	2	the	the	DET
ejpam-4507	141	3	residues	residue	NOUN
ejpam-4507	141	4	of	of	ADP
ejpam-4507	141	5	g(t	g(t	PROPN
ejpam-4507	141	6	)	)	PUNCT
ejpam-4507	141	7	at	at	ADP
ejpam-4507	141	8	tk	tk	PROPN
ejpam-4507	141	9	:	:	PUNCT
ejpam-4507	141	10	res(g(t	res(g(t	PROPN
ejpam-4507	141	11	)	)	PUNCT
ejpam-4507	141	12	,	,	PUNCT
ejpam-4507	141	13	t	t	PROPN
ejpam-4507	141	14	=	=	SYM
ejpam-4507	141	15	tk	tk	PROPN
ejpam-4507	141	16	)	)	PUNCT
ejpam-4507	141	17	=	=	PROPN
ejpam-4507	141	18	lim	lim	PROPN
ejpam-4507	141	19	t→tk	t→tk	PROPN
ejpam-4507	142	1	(	(	PUNCT
ejpam-4507	142	2	t−	t−	PROPN
ejpam-4507	142	3	tk	tk	PROPN
ejpam-4507	142	4	)	)	PUNCT
ejpam-4507	142	5	2ext	2ext	PROPN
ejpam-4507	142	6	ln	ln	NOUN
ejpam-4507	142	7	c	c	NOUN
ejpam-4507	142	8	bt	bt	NOUN
ejpam-4507	143	1	+	+	X
ejpam-4507	143	2	at	at	ADP
ejpam-4507	143	3	t−n−1	t−n−1	PROPN
ejpam-4507	143	4	=	=	PUNCT
ejpam-4507	144	1	2extk	2extk	NUM
ejpam-4507	144	2	ln	ln	NOUN
ejpam-4507	144	3	ct−n−1	ct−n−1	X
ejpam-4507	144	4	k	k	PROPN
ejpam-4507	144	5	ν	ν	PROPN
ejpam-4507	144	6	,	,	PUNCT
ejpam-4507	144	7	c.	c.	PROPN
ejpam-4507	144	8	corcino	corcino	PROPN
ejpam-4507	144	9	,	,	PUNCT
ejpam-4507	144	10	r.	r.	PROPN
ejpam-4507	144	11	corcino	corcino	PROPN
ejpam-4507	144	12	/	/	SYM
ejpam-4507	144	13	eur	eur	PROPN
ejpam-4507	144	14	.	.	PUNCT
ejpam-4507	145	1	j.	j.	PROPN
ejpam-4507	145	2	pure	pure	PROPN
ejpam-4507	145	3	appl	appl	PROPN
ejpam-4507	145	4	.	.	PROPN
ejpam-4507	145	5	math	math	PROPN
ejpam-4507	145	6	,	,	PUNCT
ejpam-4507	145	7	15	15	NUM
ejpam-4507	145	8	(	(	PUNCT
ejpam-4507	145	9	4	4	NUM
ejpam-4507	145	10	)	)	PUNCT
ejpam-4507	145	11	(	(	PUNCT
ejpam-4507	145	12	2022	2022	NUM
ejpam-4507	145	13	)	)	PUNCT
ejpam-4507	145	14	,	,	PUNCT
ejpam-4507	145	15	1662	1662	NUM
ejpam-4507	145	16	-	-	SYM
ejpam-4507	145	17	1682	1682	NUM
ejpam-4507	145	18	1670	1670	NUM
ejpam-4507	146	1	where	where	SCONJ
ejpam-4507	146	2	ν	ν	X
ejpam-4507	146	3	=	=	SYM
ejpam-4507	146	4	d	d	X
ejpam-4507	146	5	dt	dt	X
ejpam-4507	146	6	(	(	PUNCT
ejpam-4507	146	7	bt	bt	X
ejpam-4507	146	8	+	+	CCONJ
ejpam-4507	146	9	at)|t	at)|t	ADJ
ejpam-4507	146	10	=	=	ADJ
ejpam-4507	146	11	tk	tk	NOUN
ejpam-4507	146	12	=	=	SYM
ejpam-4507	146	13	(	(	PUNCT
ejpam-4507	146	14	(	(	PUNCT
ejpam-4507	146	15	ln	ln	PROPN
ejpam-4507	146	16	b)etk	b)etk	PROPN
ejpam-4507	146	17	ln	ln	PROPN
ejpam-4507	146	18	b	b	PROPN
ejpam-4507	146	19	+	+	CCONJ
ejpam-4507	146	20	(	(	PUNCT
ejpam-4507	146	21	ln	ln	PROPN
ejpam-4507	146	22	a)etk	a)etk	PROPN
ejpam-4507	146	23	ln	ln	PROPN
ejpam-4507	146	24	a	a	NOUN
ejpam-4507	146	25	)	)	PUNCT
ejpam-4507	146	26	e−tk	e−tk	NOUN
ejpam-4507	146	27	ln	ln	ADP
ejpam-4507	146	28	a	a	DET
ejpam-4507	146	29	e−tk	e−tk	NOUN
ejpam-4507	146	30	ln	ln	ADP
ejpam-4507	146	31	a	a	DET
ejpam-4507	146	32	=	=	X
ejpam-4507	146	33	etk	etk	PROPN
ejpam-4507	146	34	ln	ln	PROPN
ejpam-4507	146	35	a[(ln	a[(ln	PROPN
ejpam-4507	146	36	b)etk(ln	b)etk(ln	PROPN
ejpam-4507	146	37	b−ln	b−ln	X
ejpam-4507	146	38	a	a	NOUN
ejpam-4507	146	39	)	)	PUNCT
ejpam-4507	147	1	+	+	CCONJ
ejpam-4507	147	2	ln	ln	ADV
ejpam-4507	147	3	a	a	X
ejpam-4507	147	4	]	]	X
ejpam-4507	147	5	=	=	SYM
ejpam-4507	147	6	etk	etk	PROPN
ejpam-4507	147	7	ln	ln	PROPN
ejpam-4507	147	8	a[−	a[−	PROPN
ejpam-4507	147	9	ln	ln	ADP
ejpam-4507	147	10	b+	b+	X
ejpam-4507	147	11	ln	ln	ADV
ejpam-4507	147	12	a	a	X
ejpam-4507	147	13	]	]	X
ejpam-4507	147	14	=	=	SYM
ejpam-4507	147	15	−b	−b	ADJ
ejpam-4507	147	16	·	·	PUNCT
ejpam-4507	147	17	etk	etk	PROPN
ejpam-4507	147	18	ln	ln	ADJ
ejpam-4507	147	19	a.	a.	NOUN
ejpam-4507	147	20	thus	thus	ADV
ejpam-4507	147	21	,	,	PUNCT
ejpam-4507	147	22	res(g(t	res(g(t	NOUN
ejpam-4507	147	23	)	)	PUNCT
ejpam-4507	147	24	,	,	PUNCT
ejpam-4507	147	25	t	t	PROPN
ejpam-4507	147	26	=	=	SYM
ejpam-4507	147	27	tk	tk	PROPN
ejpam-4507	147	28	)	)	PUNCT
ejpam-4507	147	29	=	=	PUNCT
ejpam-4507	148	1	2etkx	2etkx	NUM
ejpam-4507	148	2	ln	ln	SYM
ejpam-4507	148	3	ct−n−1	ct−n−1	X
ejpam-4507	148	4	k	k	NOUN
ejpam-4507	148	5	−b	−b	ADJ
ejpam-4507	148	6	·	·	PUNCT
ejpam-4507	148	7	etk	etk	PROPN
ejpam-4507	148	8	ln	ln	NOUN
ejpam-4507	148	9	a	a	PROPN
ejpam-4507	148	10	=	=	SYM
ejpam-4507	148	11	2etk(x	2etk(x	NUM
ejpam-4507	148	12	ln	ln	ADJ
ejpam-4507	148	13	c−ln	c−ln	PROPN
ejpam-4507	148	14	a	a	X
ejpam-4507	148	15	)	)	PUNCT
ejpam-4507	148	16	−b	−b	NOUN
ejpam-4507	148	17	·	·	PUNCT
ejpam-4507	148	18	tn+1	tn+1	PROPN
ejpam-4507	148	19	k	k	X
ejpam-4507	148	20	.	.	PUNCT
ejpam-4507	149	1	consequently	consequently	ADV
ejpam-4507	149	2	,	,	PUNCT
ejpam-4507	149	3	en(x	en(x	ADP
ejpam-4507	149	4	;	;	PUNCT
ejpam-4507	149	5	a	a	DET
ejpam-4507	149	6	,	,	PUNCT
ejpam-4507	149	7	b	b	NOUN
ejpam-4507	149	8	,	,	PUNCT
ejpam-4507	149	9	c	c	NOUN
ejpam-4507	149	10	)	)	PUNCT
ejpam-4507	149	11	n	n	CCONJ
ejpam-4507	149	12	!	!	PUNCT
ejpam-4507	150	1	=	=	SYM
ejpam-4507	151	1	2	2	NUM
ejpam-4507	151	2	b	b	NOUN
ejpam-4507	151	3	∑	∑	ADV
ejpam-4507	151	4	k∈z	k∈z	PROPN
ejpam-4507	151	5	etk(x	etk(x	PROPN
ejpam-4507	151	6	ln	ln	ADJ
ejpam-4507	151	7	c−ln	c−ln	PROPN
ejpam-4507	151	8	a	a	X
ejpam-4507	151	9	)	)	PUNCT
ejpam-4507	151	10	tn+1	tn+1	PROPN
ejpam-4507	151	11	k	k	X
ejpam-4507	151	12	.	.	PUNCT
ejpam-4507	152	1	theorem	theorem	VERB
ejpam-4507	152	2	2.5	2.5	NUM
ejpam-4507	152	3	.	.	PUNCT
ejpam-4507	153	1	let	let	VERB
ejpam-4507	153	2	a	a	DET
ejpam-4507	153	3	,	,	PUNCT
ejpam-4507	153	4	b	b	NOUN
ejpam-4507	153	5	,	,	PUNCT
ejpam-4507	153	6	c	c	AUX
ejpam-4507	153	7	be	be	AUX
ejpam-4507	153	8	positive	positive	ADJ
ejpam-4507	153	9	real	real	ADJ
ejpam-4507	153	10	numbers	number	NOUN
ejpam-4507	153	11	.	.	PUNCT
ejpam-4507	154	1	the	the	DET
ejpam-4507	154	2	fourier	fourier	ADJ
ejpam-4507	154	3	series	series	NOUN
ejpam-4507	154	4	of	of	ADP
ejpam-4507	154	5	the	the	DET
ejpam-4507	154	6	genocchi	genocchi	NOUN
ejpam-4507	154	7	-	-	PUNCT
ejpam-4507	154	8	type	type	NOUN
ejpam-4507	154	9	polynomials	polynomial	NOUN
ejpam-4507	154	10	gn(x	gn(x	PUNCT
ejpam-4507	154	11	;	;	PUNCT
ejpam-4507	154	12	a	a	DET
ejpam-4507	154	13	,	,	PUNCT
ejpam-4507	154	14	b	b	NOUN
ejpam-4507	154	15	,	,	PUNCT
ejpam-4507	154	16	c	c	NOUN
ejpam-4507	154	17	)	)	PUNCT
ejpam-4507	154	18	is	be	AUX
ejpam-4507	154	19	given	give	VERB
ejpam-4507	154	20	by	by	ADP
ejpam-4507	154	21	gn(x	gn(x	PUNCT
ejpam-4507	154	22	;	;	PUNCT
ejpam-4507	154	23	a	a	DET
ejpam-4507	154	24	,	,	PUNCT
ejpam-4507	154	25	b	b	NOUN
ejpam-4507	154	26	,	,	PUNCT
ejpam-4507	154	27	c	c	NOUN
ejpam-4507	154	28	)	)	PUNCT
ejpam-4507	154	29	n	n	CCONJ
ejpam-4507	154	30	!	!	PUNCT
ejpam-4507	155	1	=	=	SYM
ejpam-4507	155	2	2	2	NUM
ejpam-4507	155	3	b	b	NOUN
ejpam-4507	155	4	∑	∑	ADV
ejpam-4507	155	5	k∈z	k∈z	PROPN
ejpam-4507	155	6	etk(x	etk(x	PROPN
ejpam-4507	155	7	ln	ln	ADJ
ejpam-4507	155	8	c−ln	c−ln	PROPN
ejpam-4507	155	9	a	a	X
ejpam-4507	155	10	)	)	PUNCT
ejpam-4507	155	11	tnk	tnk	PROPN
ejpam-4507	155	12	,	,	PUNCT
ejpam-4507	155	13	valid	valid	ADJ
ejpam-4507	155	14	for	for	ADP
ejpam-4507	155	15	0	0	NUM
ejpam-4507	155	16	<	<	X
ejpam-4507	155	17	x	x	X
ejpam-4507	155	18	<	<	X
ejpam-4507	155	19	(	(	PUNCT
ejpam-4507	155	20	ln	ln	X
ejpam-4507	155	21	a−	a−	PROPN
ejpam-4507	155	22	b	b	PROPN
ejpam-4507	155	23	π	π	NOUN
ejpam-4507	155	24	−	−	PROPN
ejpam-4507	155	25	ε	ε	PROPN
ejpam-4507	155	26	)	)	PUNCT
ejpam-4507	155	27	/	/	SYM
ejpam-4507	156	1	ln	ln	NOUN
ejpam-4507	156	2	c	c	NOUN
ejpam-4507	156	3	,	,	PUNCT
ejpam-4507	156	4	ln	ln	NOUN
ejpam-4507	156	5	c	c	NOUN
ejpam-4507	156	6	>	>	X
ejpam-4507	156	7	0	0	NUM
ejpam-4507	157	1	where	where	SCONJ
ejpam-4507	157	2	tk	tk	PROPN
ejpam-4507	157	3	=	=	X
ejpam-4507	157	4	(	(	PUNCT
ejpam-4507	157	5	2k	2k	NOUN
ejpam-4507	157	6	+	+	CCONJ
ejpam-4507	157	7	1)πi	1)πi	NUM
ejpam-4507	157	8	/	/	SYM
ejpam-4507	157	9	b	b	PROPN
ejpam-4507	157	10	,	,	PUNCT
ejpam-4507	157	11	b	b	X
ejpam-4507	157	12	=	=	SYM
ejpam-4507	157	13	ln	ln	PROPN
ejpam-4507	157	14	b−	b−	PROPN
ejpam-4507	157	15	ln	ln	ADV
ejpam-4507	157	16	a	a	DET
ejpam-4507	157	17	>	>	X
ejpam-4507	157	18	0	0	X
ejpam-4507	157	19	.	.	PUNCT
ejpam-4507	157	20	proof	proof	NOUN
ejpam-4507	157	21	.	.	PUNCT
ejpam-4507	158	1	the	the	DET
ejpam-4507	158	2	theorem	theorem	NOUN
ejpam-4507	158	3	follows	follow	VERB
ejpam-4507	158	4	from	from	ADP
ejpam-4507	158	5	theorem	theorem	ADJ
ejpam-4507	158	6	2.4	2.4	NUM
ejpam-4507	158	7	.	.	PUNCT
ejpam-4507	159	1	3	3	X
ejpam-4507	159	2	.	.	X
ejpam-4507	160	1	the	the	DET
ejpam-4507	160	2	case	case	NOUN
ejpam-4507	160	3	α	α	NOUN
ejpam-4507	160	4	≥	≥	NUM
ejpam-4507	160	5	2	2	NUM
ejpam-4507	160	6	lemma	lemma	PROPN
ejpam-4507	160	7	3.1	3.1	NUM
ejpam-4507	160	8	.	.	PUNCT
ejpam-4507	161	1	let	let	VERB
ejpam-4507	161	2	a	a	DET
ejpam-4507	161	3	,	,	PUNCT
ejpam-4507	161	4	b	b	NOUN
ejpam-4507	161	5	,	,	PUNCT
ejpam-4507	161	6	c	c	AUX
ejpam-4507	161	7	be	be	AUX
ejpam-4507	161	8	positive	positive	ADJ
ejpam-4507	161	9	real	real	ADJ
ejpam-4507	161	10	numbers	number	NOUN
ejpam-4507	161	11	.	.	PUNCT
ejpam-4507	162	1	let	let	VERB
ejpam-4507	162	2	n	n	PRON
ejpam-4507	162	3	≥	≥	NOUN
ejpam-4507	162	4	α	α	PRON
ejpam-4507	162	5	≥	≥	NUM
ejpam-4507	162	6	2	2	NUM
ejpam-4507	162	7	,	,	PUNCT
ejpam-4507	162	8	α	α	PROPN
ejpam-4507	162	9	∈	∈	PROPN
ejpam-4507	162	10	z+	z+	NUM
ejpam-4507	162	11	,	,	PUNCT
ejpam-4507	162	12	n	n	CCONJ
ejpam-4507	162	13	>	>	SYM
ejpam-4507	162	14	1	1	NUM
ejpam-4507	162	15	and	and	CCONJ
ejpam-4507	162	16	cn	cn	PROPN
ejpam-4507	162	17	be	be	AUX
ejpam-4507	162	18	the	the	DET
ejpam-4507	162	19	circle	circle	NOUN
ejpam-4507	162	20	about	about	ADP
ejpam-4507	162	21	zero	zero	NUM
ejpam-4507	162	22	of	of	ADP
ejpam-4507	162	23	radius	radius	NOUN
ejpam-4507	162	24	r	r	NOUN
ejpam-4507	162	25	=	=	PUNCT
ejpam-4507	162	26	(	(	PUNCT
ejpam-4507	162	27	2nπ−	2nπ−	NUM
ejpam-4507	162	28	ε)/b	ε)/b	NOUN
ejpam-4507	162	29	,	,	PUNCT
ejpam-4507	162	30	where	where	SCONJ
ejpam-4507	162	31	0	0	X
ejpam-4507	162	32	<	<	X
ejpam-4507	162	33	ε	ε	X
ejpam-4507	162	34	<	<	X
ejpam-4507	162	35	1	1	NUM
ejpam-4507	162	36	and	and	CCONJ
ejpam-4507	162	37	b	b	NOUN
ejpam-4507	162	38	=	=	SYM
ejpam-4507	162	39	ln	ln	PROPN
ejpam-4507	162	40	b−	b−	PROPN
ejpam-4507	162	41	ln	ln	ADV
ejpam-4507	162	42	a	a	PRON
ejpam-4507	162	43	>	>	X
ejpam-4507	162	44	0	0	NUM
ejpam-4507	162	45	.	.	PUNCT
ejpam-4507	163	1	for	for	ADP
ejpam-4507	163	2	0	0	NUM
ejpam-4507	163	3	<	<	X
ejpam-4507	163	4	x	x	X
ejpam-4507	163	5	<	<	X
ejpam-4507	163	6	(	(	PUNCT
ejpam-4507	163	7	α	α	X
ejpam-4507	163	8	ln	ln	ADJ
ejpam-4507	163	9	a−	a−	PROPN
ejpam-4507	163	10	b	b	PROPN
ejpam-4507	163	11	2π	2π	PROPN
ejpam-4507	163	12	−	−	PROPN
ejpam-4507	163	13	ε	ε	PROPN
ejpam-4507	163	14	)	)	PUNCT
ejpam-4507	163	15	/	/	SYM
ejpam-4507	163	16	ln	ln	NOUN
ejpam-4507	163	17	c	c	NOUN
ejpam-4507	163	18	,	,	PUNCT
ejpam-4507	163	19	ln	ln	NOUN
ejpam-4507	163	20	c	c	NOUN
ejpam-4507	163	21	>	>	PUNCT
ejpam-4507	163	22	0	0	NUM
ejpam-4507	164	1	we	we	PRON
ejpam-4507	164	2	have	have	VERB
ejpam-4507	164	3	lim	lim	PROPN
ejpam-4507	164	4	n→+∞	n→+∞	PROPN
ejpam-4507	164	5	∫	∫	PROPN
ejpam-4507	164	6	cn	cn	PROPN
ejpam-4507	164	7	cxt	cxt	PROPN
ejpam-4507	164	8	(	(	PUNCT
ejpam-4507	164	9	bt	bt	NOUN
ejpam-4507	164	10	−	−	PROPN
ejpam-4507	164	11	at)α	at)α	PROPN
ejpam-4507	164	12	dt	dt	NOUN
ejpam-4507	164	13	tn−α+1	tn−α+1	NOUN
ejpam-4507	164	14	=	=	SYM
ejpam-4507	164	15	0	0	X
ejpam-4507	164	16	.	.	PUNCT
ejpam-4507	165	1	c.	c.	PROPN
ejpam-4507	165	2	corcino	corcino	PROPN
ejpam-4507	165	3	,	,	PUNCT
ejpam-4507	165	4	r.	r.	PROPN
ejpam-4507	165	5	corcino	corcino	PROPN
ejpam-4507	165	6	/	/	SYM
ejpam-4507	165	7	eur	eur	PROPN
ejpam-4507	165	8	.	.	PUNCT
ejpam-4507	166	1	j.	j.	PROPN
ejpam-4507	166	2	pure	pure	PROPN
ejpam-4507	166	3	appl	appl	PROPN
ejpam-4507	166	4	.	.	PROPN
ejpam-4507	166	5	math	math	PROPN
ejpam-4507	166	6	,	,	PUNCT
ejpam-4507	166	7	15	15	NUM
ejpam-4507	166	8	(	(	PUNCT
ejpam-4507	166	9	4	4	NUM
ejpam-4507	166	10	)	)	PUNCT
ejpam-4507	166	11	(	(	PUNCT
ejpam-4507	166	12	2022	2022	NUM
ejpam-4507	166	13	)	)	PUNCT
ejpam-4507	166	14	,	,	PUNCT
ejpam-4507	166	15	1662	1662	NUM
ejpam-4507	166	16	-	-	SYM
ejpam-4507	166	17	1682	1682	NUM
ejpam-4507	166	18	1671	1671	NUM
ejpam-4507	166	19	proof	proof	NOUN
ejpam-4507	166	20	.	.	PUNCT
ejpam-4507	167	1	we	we	PRON
ejpam-4507	167	2	will	will	AUX
ejpam-4507	167	3	show	show	VERB
ejpam-4507	167	4	that	that	SCONJ
ejpam-4507	167	5	the	the	DET
ejpam-4507	167	6	function	function	NOUN
ejpam-4507	167	7	cxt	cxt	NOUN
ejpam-4507	167	8	(	(	PUNCT
ejpam-4507	167	9	bt	bt	NOUN
ejpam-4507	167	10	−	−	PROPN
ejpam-4507	167	11	at)α	at)α	PROPN
ejpam-4507	167	12	is	be	AUX
ejpam-4507	167	13	bounded	bound	VERB
ejpam-4507	167	14	on	on	ADP
ejpam-4507	167	15	cn	cn	PROPN
ejpam-4507	167	16	.	.	PUNCT
ejpam-4507	168	1	from	from	ADP
ejpam-4507	168	2	lemma	lemma	PROPN
ejpam-4507	168	3	2.1	2.1	NUM
ejpam-4507	168	4	,	,	PUNCT
ejpam-4507	168	5	|bt	|bt	NUM
ejpam-4507	168	6	−	−	NOUN
ejpam-4507	168	7	at|	at|	PROPN
ejpam-4507	168	8	=	=	PUNCT
ejpam-4507	168	9	eγ	eγ	PART
ejpam-4507	168	10	ln	ln	ADJ
ejpam-4507	168	11	a[e2γb	a[e2γb	X
ejpam-4507	168	12	−	−	PROPN
ejpam-4507	168	13	2eγb	2eγb	NUM
ejpam-4507	168	14	cos	cos	NOUN
ejpam-4507	168	15	ρb	ρb	PROPN
ejpam-4507	169	1	+	+	NOUN
ejpam-4507	169	2	1	1	NUM
ejpam-4507	169	3	]	]	SYM
ejpam-4507	169	4	1	1	NUM
ejpam-4507	169	5	2	2	NUM
ejpam-4507	169	6	,	,	PUNCT
ejpam-4507	169	7	where	where	SCONJ
ejpam-4507	169	8	t	t	PROPN
ejpam-4507	169	9	∈	∈	PROPN
ejpam-4507	169	10	cn	cn	PROPN
ejpam-4507	169	11	,	,	PUNCT
ejpam-4507	169	12	t	t	PROPN
ejpam-4507	169	13	=	=	SYM
ejpam-4507	169	14	γ	γ	X
ejpam-4507	169	15	+	+	X
ejpam-4507	169	16	iρ	iρ	NOUN
ejpam-4507	169	17	.	.	PUNCT
ejpam-4507	170	1	that	that	PRON
ejpam-4507	170	2	is	be	AUX
ejpam-4507	170	3	,	,	PUNCT
ejpam-4507	170	4	γ	γ	NOUN
ejpam-4507	170	5	=	=	SYM
ejpam-4507	170	6	2nπ	2nπ	NOUN
ejpam-4507	170	7	−	−	PROPN
ejpam-4507	170	8	ε	ε	PROPN
ejpam-4507	170	9	b	b	PROPN
ejpam-4507	170	10	cos	cos	PROPN
ejpam-4507	170	11	θ	θ	PROPN
ejpam-4507	170	12	,	,	PUNCT
ejpam-4507	170	13	ρ	ρ	PROPN
ejpam-4507	170	14	=	=	SYM
ejpam-4507	170	15	2nπ	2nπ	NOUN
ejpam-4507	170	16	−	−	PROPN
ejpam-4507	170	17	ε	ε	PROPN
ejpam-4507	170	18	b	b	PROPN
ejpam-4507	170	19	sin	sin	PROPN
ejpam-4507	170	20	θ	θ	PROPN
ejpam-4507	170	21	,	,	PUNCT
ejpam-4507	170	22	0	0	NUM
ejpam-4507	170	23	≤	≤	NUM
ejpam-4507	170	24	θ	θ	NOUN
ejpam-4507	170	25	≤	≤	ADJ
ejpam-4507	170	26	2π	2π	NOUN
ejpam-4507	170	27	.	.	PUNCT
ejpam-4507	171	1	then	then	ADV
ejpam-4507	171	2	|bt	|bt	NUM
ejpam-4507	171	3	−	−	NOUN
ejpam-4507	171	4	at|α	at|α	NOUN
ejpam-4507	172	1	=	=	PUNCT
ejpam-4507	172	2	eαγ	eαγ	PROPN
ejpam-4507	172	3	ln	ln	ADJ
ejpam-4507	172	4	a[e2γb	a[e2γb	X
ejpam-4507	172	5	−	−	PROPN
ejpam-4507	172	6	2eγb	2eγb	NUM
ejpam-4507	172	7	cos	cos	NOUN
ejpam-4507	172	8	ρb	ρb	PROPN
ejpam-4507	172	9	+	+	NOUN
ejpam-4507	172	10	1	1	NUM
ejpam-4507	172	11	]	]	PUNCT
ejpam-4507	172	12	α	α	PRON
ejpam-4507	172	13	2	2	NUM
ejpam-4507	172	14	,	,	PUNCT
ejpam-4507	172	15	and	and	CCONJ
ejpam-4507	172	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	172	17	cxt	cxt	NOUN
ejpam-4507	172	18	(	(	PUNCT
ejpam-4507	172	19	bt	bt	NOUN
ejpam-4507	172	20	−	−	PROPN
ejpam-4507	172	21	at)α	at)α	PROPN
ejpam-4507	172	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4507	172	23	=	=	NOUN
ejpam-4507	172	24	exγ	exγ	NOUN
ejpam-4507	172	25	ln	ln	NOUN
ejpam-4507	172	26	c	c	PROPN
ejpam-4507	172	27	eαγ	eαγ	PROPN
ejpam-4507	172	28	ln	ln	ADV
ejpam-4507	172	29	a[e2γb	a[e2γb	X
ejpam-4507	172	30	−	−	PROPN
ejpam-4507	173	1	2eγbcosρb	2eγbcosρb	NUM
ejpam-4507	173	2	+	+	CCONJ
ejpam-4507	173	3	1	1	NUM
ejpam-4507	173	4	]	]	PUNCT
ejpam-4507	173	5	α	α	DET
ejpam-4507	173	6	2	2	NUM
ejpam-4507	173	7	.	.	PUNCT
ejpam-4507	173	8	impose	impose	VERB
ejpam-4507	173	9	that	that	SCONJ
ejpam-4507	173	10	α	α	PRON
ejpam-4507	173	11	ln	ln	ADJ
ejpam-4507	173	12	a−	a−	PROPN
ejpam-4507	173	13	x	x	X
ejpam-4507	173	14	ln	ln	PROPN
ejpam-4507	173	15	c	c	X
ejpam-4507	173	16	>	>	X
ejpam-4507	173	17	b	b	PROPN
ejpam-4507	174	1	2nπ	2nπ	NOUN
ejpam-4507	174	2	−	−	PROPN
ejpam-4507	174	3	ε	ε	PROPN
ejpam-4507	174	4	,	,	PUNCT
ejpam-4507	174	5	∀n	∀n	NUM
ejpam-4507	174	6	≥	≥	NOUN
ejpam-4507	174	7	1	1	X
ejpam-4507	174	8	.	.	PUNCT
ejpam-4507	175	1	this	this	PRON
ejpam-4507	175	2	is	be	AUX
ejpam-4507	175	3	satisfied	satisfied	ADJ
ejpam-4507	175	4	when	when	SCONJ
ejpam-4507	175	5	α	α	DET
ejpam-4507	175	6	ln	ln	ADJ
ejpam-4507	175	7	a−	a−	PROPN
ejpam-4507	175	8	x	x	X
ejpam-4507	175	9	ln	ln	PROPN
ejpam-4507	175	10	c	c	PROPN
ejpam-4507	175	11	>	>	X
ejpam-4507	175	12	b	b	PROPN
ejpam-4507	175	13	2π	2π	PROPN
ejpam-4507	175	14	−	−	PROPN
ejpam-4507	175	15	ε	ε	PROPN
ejpam-4507	175	16	.	.	PUNCT
ejpam-4507	176	1	equivalently	equivalently	ADV
ejpam-4507	176	2	,	,	PUNCT
ejpam-4507	176	3	impose	impose	VERB
ejpam-4507	176	4	that	that	SCONJ
ejpam-4507	176	5	0	0	PUNCT
ejpam-4507	176	6	<	<	X
ejpam-4507	176	7	x	x	X
ejpam-4507	176	8	<	<	X
ejpam-4507	176	9	(	(	PUNCT
ejpam-4507	176	10	α	α	X
ejpam-4507	176	11	ln	ln	ADJ
ejpam-4507	176	12	a−	a−	PROPN
ejpam-4507	176	13	b	b	PROPN
ejpam-4507	176	14	2π	2π	PROPN
ejpam-4507	176	15	−	−	PROPN
ejpam-4507	176	16	ε	ε	PROPN
ejpam-4507	176	17	)	)	PUNCT
ejpam-4507	176	18	/	/	SYM
ejpam-4507	176	19	ln	ln	ADJ
ejpam-4507	176	20	c.	c.	NOUN
ejpam-4507	176	21	then	then	ADV
ejpam-4507	176	22	1	1	NUM
ejpam-4507	176	23	eγ(α	eγ(α	NOUN
ejpam-4507	176	24	ln	ln	ADJ
ejpam-4507	176	25	a−x	a−x	NOUN
ejpam-4507	176	26	ln	ln	NOUN
ejpam-4507	176	27	c	c	NOUN
ejpam-4507	176	28	)	)	PUNCT
ejpam-4507	176	29	<	<	X
ejpam-4507	176	30	1	1	NUM
ejpam-4507	176	31	ecos	ecos	PROPN
ejpam-4507	176	32	θ	θ	PROPN
ejpam-4507	176	33	≤	≤	NUM
ejpam-4507	176	34	1	1	NUM
ejpam-4507	176	35	e−1	e−1	PROPN
ejpam-4507	176	36	=	=	SYM
ejpam-4507	176	37	e.	e.	PROPN
ejpam-4507	176	38	consequently	consequently	ADV
ejpam-4507	176	39	,	,	PUNCT
ejpam-4507	176	40	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4507	176	41	cxt	cxt	NOUN
ejpam-4507	176	42	(	(	PUNCT
ejpam-4507	176	43	bt	bt	NOUN
ejpam-4507	176	44	−	−	PROPN
ejpam-4507	176	45	at)α	at)α	PROPN
ejpam-4507	176	46	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	176	47	<	<	X
ejpam-4507	176	48	e	e	X
ejpam-4507	177	1	[	[	X
ejpam-4507	177	2	e2γb	e2γb	PUNCT
ejpam-4507	177	3	−	−	PROPN
ejpam-4507	177	4	2eγb	2eγb	NUM
ejpam-4507	177	5	cos	cos	NOUN
ejpam-4507	177	6	ρb	ρb	PROPN
ejpam-4507	177	7	+	+	NOUN
ejpam-4507	177	8	1	1	NUM
ejpam-4507	177	9	]	]	PUNCT
ejpam-4507	177	10	α	α	DET
ejpam-4507	177	11	2	2	NUM
ejpam-4507	177	12	.	.	PUNCT
ejpam-4507	178	1	it	it	PRON
ejpam-4507	178	2	follows	follow	VERB
ejpam-4507	178	3	from	from	ADP
ejpam-4507	178	4	lemma	lemma	PROPN
ejpam-4507	178	5	2.1	2.1	NUM
ejpam-4507	178	6	that	that	SCONJ
ejpam-4507	178	7	the	the	DET
ejpam-4507	178	8	right	right	ADJ
ejpam-4507	178	9	hand	hand	NOUN
ejpam-4507	178	10	side	side	NOUN
ejpam-4507	178	11	above	above	ADV
ejpam-4507	178	12	is	be	AUX
ejpam-4507	178	13	bounded	bound	VERB
ejpam-4507	178	14	on	on	ADP
ejpam-4507	178	15	cn	cn	PROPN
ejpam-4507	178	16	as	as	ADP
ejpam-4507	178	17	n	n	PROPN
ejpam-4507	178	18	→	→	PUNCT
ejpam-4507	178	19	+	+	PROPN
ejpam-4507	178	20	∞.	∞.	PROPN
ejpam-4507	178	21	that	that	PRON
ejpam-4507	178	22	is	be	AUX
ejpam-4507	178	23	,	,	PUNCT
ejpam-4507	178	24	there	there	PRON
ejpam-4507	178	25	is	be	VERB
ejpam-4507	178	26	a	a	DET
ejpam-4507	178	27	constant	constant	ADJ
ejpam-4507	178	28	m	m	NOUN
ejpam-4507	178	29	such	such	ADJ
ejpam-4507	178	30	that∣∣∣∣	that∣∣∣∣	PROPN
ejpam-4507	178	31	cxt	cxt	PROPN
ejpam-4507	178	32	(	(	PUNCT
ejpam-4507	178	33	bt	bt	NOUN
ejpam-4507	178	34	−	−	PROPN
ejpam-4507	178	35	at)α	at)α	PROPN
ejpam-4507	178	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	178	37	<	<	X
ejpam-4507	178	38	m	m	PROPN
ejpam-4507	178	39	,	,	PUNCT
ejpam-4507	178	40	t	t	PROPN
ejpam-4507	178	41	∈	∈	PROPN
ejpam-4507	178	42	cn	cn	PROPN
ejpam-4507	178	43	and	and	CCONJ
ejpam-4507	179	1	0	0	NUM
ejpam-4507	179	2	<	<	X
ejpam-4507	179	3	x	x	X
ejpam-4507	179	4	<	<	X
ejpam-4507	179	5	(	(	PUNCT
ejpam-4507	179	6	α	α	X
ejpam-4507	179	7	ln	ln	ADJ
ejpam-4507	179	8	a−	a−	PROPN
ejpam-4507	179	9	b	b	PROPN
ejpam-4507	179	10	2π	2π	PROPN
ejpam-4507	179	11	−	−	PROPN
ejpam-4507	179	12	ε	ε	PROPN
ejpam-4507	179	13	)	)	PUNCT
ejpam-4507	179	14	/	/	SYM
ejpam-4507	179	15	ln	ln	ADJ
ejpam-4507	179	16	c.	c.	PROPN
ejpam-4507	179	17	thus	thus	ADV
ejpam-4507	179	18	,	,	PUNCT
ejpam-4507	179	19	∣∣∣∣∫	∣∣∣∣∫	DET
ejpam-4507	179	20	cn	cn	PROPN
ejpam-4507	179	21	cxt	cxt	PROPN
ejpam-4507	179	22	(	(	PUNCT
ejpam-4507	179	23	bt	bt	NOUN
ejpam-4507	179	24	−	−	PROPN
ejpam-4507	179	25	at)α	at)α	PROPN
ejpam-4507	179	26	dt	dt	NOUN
ejpam-4507	179	27	tn−α+1	tn−α+1	PROPN
ejpam-4507	179	28	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	179	29	<	<	X
ejpam-4507	179	30	m	m	NUM
ejpam-4507	179	31	∫	∫	PROPN
ejpam-4507	179	32	cn	cn	PROPN
ejpam-4507	179	33	|dt|	|dt|	PROPN
ejpam-4507	179	34	|tn−α+1|	|tn−α+1|	PROPN
ejpam-4507	179	35	<	<	X
ejpam-4507	179	36	m	m	PROPN
ejpam-4507	179	37	·	·	PUNCT
ejpam-4507	179	38	2nπ	2nπ	NOUN
ejpam-4507	179	39	−	−	PROPN
ejpam-4507	179	40	ε	ε	PROPN
ejpam-4507	179	41	b	b	PROPN
ejpam-4507	179	42	·	·	PUNCT
ejpam-4507	179	43	2π	2π	NOUN
ejpam-4507	179	44	(	(	PUNCT
ejpam-4507	179	45	2nπ	2nπ	NOUN
ejpam-4507	179	46	−	−	PROPN
ejpam-4507	179	47	ε	ε	PROPN
ejpam-4507	179	48	b	b	PROPN
ejpam-4507	179	49	)	)	PUNCT
ejpam-4507	179	50	n−α+1	n−α+1	PROPN
ejpam-4507	179	51	c.	c.	PROPN
ejpam-4507	179	52	corcino	corcino	PROPN
ejpam-4507	179	53	,	,	PUNCT
ejpam-4507	179	54	r.	r.	PROPN
ejpam-4507	179	55	corcino	corcino	PROPN
ejpam-4507	179	56	/	/	SYM
ejpam-4507	179	57	eur	eur	PROPN
ejpam-4507	179	58	.	.	PUNCT
ejpam-4507	180	1	j.	j.	PROPN
ejpam-4507	180	2	pure	pure	PROPN
ejpam-4507	180	3	appl	appl	PROPN
ejpam-4507	180	4	.	.	PROPN
ejpam-4507	180	5	math	math	PROPN
ejpam-4507	180	6	,	,	PUNCT
ejpam-4507	180	7	15	15	NUM
ejpam-4507	180	8	(	(	PUNCT
ejpam-4507	180	9	4	4	NUM
ejpam-4507	180	10	)	)	PUNCT
ejpam-4507	180	11	(	(	PUNCT
ejpam-4507	180	12	2022	2022	NUM
ejpam-4507	180	13	)	)	PUNCT
ejpam-4507	180	14	,	,	PUNCT
ejpam-4507	180	15	1662	1662	NUM
ejpam-4507	180	16	-	-	SYM
ejpam-4507	180	17	1682	1682	NUM
ejpam-4507	180	18	1672	1672	NUM
ejpam-4507	180	19	=	=	SYM
ejpam-4507	180	20	2πmbα−n	2πmbα−n	NUM
ejpam-4507	180	21	(	(	PUNCT
ejpam-4507	180	22	2nπ	2nπ	NOUN
ejpam-4507	180	23	−	−	NOUN
ejpam-4507	180	24	ε)n−α	ε)n−α	NOUN
ejpam-4507	180	25	,	,	PUNCT
ejpam-4507	180	26	n	n	X
ejpam-4507	180	27	≥	≥	NOUN
ejpam-4507	180	28	α	α	NOUN
ejpam-4507	180	29	.	.	PUNCT
ejpam-4507	181	1	−→	−→	NOUN
ejpam-4507	181	2	0	0	NUM
ejpam-4507	182	1	as	as	ADP
ejpam-4507	182	2	n	n	PRON
ejpam-4507	182	3	→	→	PUNCT
ejpam-4507	182	4	+	+	NUM
ejpam-4507	182	5	∞.	∞.	PROPN
ejpam-4507	182	6	lemma	lemma	PROPN
ejpam-4507	182	7	3.2	3.2	NUM
ejpam-4507	182	8	.	.	PUNCT
ejpam-4507	183	1	for	for	ADP
ejpam-4507	183	2	a	a	DET
ejpam-4507	183	3	,	,	PUNCT
ejpam-4507	183	4	b	b	NOUN
ejpam-4507	183	5	,	,	PUNCT
ejpam-4507	183	6	c	c	PROPN
ejpam-4507	183	7	∈	∈	PROPN
ejpam-4507	183	8	r+	r+	X
ejpam-4507	183	9	,	,	PUNCT
ejpam-4507	183	10	x	x	PUNCT
ejpam-4507	183	11	∈	∈	PROPN
ejpam-4507	183	12	r	r	NOUN
ejpam-4507	183	13	,	,	PUNCT
ejpam-4507	183	14	ν	ν	PROPN
ejpam-4507	183	15	,	,	PUNCT
ejpam-4507	183	16	α	α	PROPN
ejpam-4507	183	17	∈	∈	PROPN
ejpam-4507	183	18	z+	z+	NUM
ejpam-4507	183	19	with	with	ADP
ejpam-4507	183	20	fixed	fix	VERB
ejpam-4507	183	21	ν	ν	NOUN
ejpam-4507	183	22	≥	≥	PROPN
ejpam-4507	183	23	α	α	NOUN
ejpam-4507	183	24	,	,	PUNCT
ejpam-4507	183	25	b(α	b(α	NOUN
ejpam-4507	183	26	)	)	PUNCT
ejpam-4507	183	27	ν	ν	NOUN
ejpam-4507	183	28	(	(	PUNCT
ejpam-4507	183	29	x	x	NOUN
ejpam-4507	183	30	;	;	PUNCT
ejpam-4507	183	31	a	a	DET
ejpam-4507	183	32	,	,	PUNCT
ejpam-4507	183	33	b	b	NOUN
ejpam-4507	183	34	,	,	PUNCT
ejpam-4507	183	35	c	c	NOUN
ejpam-4507	183	36	)	)	PUNCT
ejpam-4507	183	37	=	=	SYM
ejpam-4507	183	38	ν∑	ν∑	PROPN
ejpam-4507	184	1	l=0	l=0	PROPN
ejpam-4507	184	2	(	(	PUNCT
ejpam-4507	184	3	ν	ν	X
ejpam-4507	184	4	l	l	NOUN
ejpam-4507	184	5	)	)	PUNCT
ejpam-4507	184	6	b	b	PROPN
ejpam-4507	184	7	(	(	PUNCT
ejpam-4507	184	8	α	α	NOUN
ejpam-4507	184	9	)	)	PUNCT
ejpam-4507	184	10	l	l	NOUN
ejpam-4507	184	11	(	(	PUNCT
ejpam-4507	184	12	0	0	NUM
ejpam-4507	184	13	;	;	PUNCT
ejpam-4507	184	14	a	a	DET
ejpam-4507	184	15	,	,	PUNCT
ejpam-4507	184	16	b	b	NOUN
ejpam-4507	184	17	,	,	PUNCT
ejpam-4507	184	18	c)(x	c)(x	PROPN
ejpam-4507	184	19	ln	ln	PROPN
ejpam-4507	184	20	c)ν−l	c)ν−l	PROPN
ejpam-4507	184	21	.	.	PUNCT
ejpam-4507	185	1	proof	proof	NOUN
ejpam-4507	185	2	.	.	PUNCT
ejpam-4507	186	1	(	(	PUNCT
ejpam-4507	186	2	t	t	NOUN
ejpam-4507	186	3	bt	bt	NOUN
ejpam-4507	186	4	−	−	PROPN
ejpam-4507	186	5	at	at	ADP
ejpam-4507	186	6	)	)	PUNCT
ejpam-4507	186	7	α	α	PROPN
ejpam-4507	186	8	cxt	cxt	NOUN
ejpam-4507	186	9	·	·	PUNCT
ejpam-4507	186	10	cyt	cyt	NOUN
ejpam-4507	186	11	=	=	PUNCT
ejpam-4507	186	12	(	(	PUNCT
ejpam-4507	186	13	∞∑	∞∑	NUM
ejpam-4507	186	14	n=0	n=0	NUM
ejpam-4507	186	15	b(α	b(α	NOUN
ejpam-4507	186	16	)	)	PUNCT
ejpam-4507	186	17	n	n	CCONJ
ejpam-4507	186	18	(	(	PUNCT
ejpam-4507	186	19	x	x	X
ejpam-4507	186	20	;	;	PUNCT
ejpam-4507	186	21	a	a	DET
ejpam-4507	186	22	,	,	PUNCT
ejpam-4507	186	23	b	b	NOUN
ejpam-4507	186	24	,	,	PUNCT
ejpam-4507	186	25	c	c	NOUN
ejpam-4507	186	26	)	)	PUNCT
ejpam-4507	186	27	tn	tn	PROPN
ejpam-4507	186	28	n	n	CCONJ
ejpam-4507	186	29	!	!	PUNCT
ejpam-4507	186	30	)	)	PUNCT
ejpam-4507	187	1	(	(	PUNCT
ejpam-4507	187	2	∞∑	∞∑	NUM
ejpam-4507	187	3	n=0	n=0	NUM
ejpam-4507	187	4	(	(	PUNCT
ejpam-4507	187	5	yt	yt	PROPN
ejpam-4507	187	6	ln	ln	PROPN
ejpam-4507	187	7	c)n	c)n	PROPN
ejpam-4507	187	8	n	n	CCONJ
ejpam-4507	187	9	!	!	PUNCT
ejpam-4507	187	10	)	)	PUNCT
ejpam-4507	188	1	(	(	PUNCT
ejpam-4507	188	2	t	t	NOUN
ejpam-4507	188	3	bt	bt	NOUN
ejpam-4507	188	4	−	−	PROPN
ejpam-4507	188	5	at	at	ADP
ejpam-4507	188	6	)	)	PUNCT
ejpam-4507	188	7	α	α	NOUN
ejpam-4507	188	8	c(x+y)t	c(x+y)t	NOUN
ejpam-4507	188	9	=	=	PUNCT
ejpam-4507	189	1	∞∑	∞∑	PRON
ejpam-4507	189	2	n=0	n=0	NUM
ejpam-4507	189	3	n∑	n∑	NOUN
ejpam-4507	189	4	l=0	l=0	PROPN
ejpam-4507	189	5	b	b	PROPN
ejpam-4507	189	6	(	(	PUNCT
ejpam-4507	189	7	α	α	NOUN
ejpam-4507	189	8	)	)	PUNCT
ejpam-4507	189	9	l	l	NOUN
ejpam-4507	189	10	(	(	PUNCT
ejpam-4507	189	11	x	x	NOUN
ejpam-4507	189	12	;	;	PUNCT
ejpam-4507	189	13	a	a	DET
ejpam-4507	189	14	,	,	PUNCT
ejpam-4507	189	15	b	b	NOUN
ejpam-4507	189	16	,	,	PUNCT
ejpam-4507	189	17	c	c	NOUN
ejpam-4507	189	18	)	)	PUNCT
ejpam-4507	189	19	tl	tl	PROPN
ejpam-4507	189	20	l	l	NOUN
ejpam-4507	189	21	!	!	PUNCT
ejpam-4507	190	1	(	(	PUNCT
ejpam-4507	190	2	yt	yt	INTJ
ejpam-4507	190	3	ln	ln	ADV
ejpam-4507	190	4	c)n−l	c)n−l	PROPN
ejpam-4507	190	5	(	(	PUNCT
ejpam-4507	190	6	n−	n−	NOUN
ejpam-4507	190	7	l	l	NOUN
ejpam-4507	190	8	)	)	PUNCT
ejpam-4507	190	9	!	!	PUNCT
ejpam-4507	190	10	·	·	PUNCT
ejpam-4507	191	1	n	n	CCONJ
ejpam-4507	191	2	!	!	NUM
ejpam-4507	191	3	n	n	CCONJ
ejpam-4507	191	4	!	!	PUNCT
ejpam-4507	192	1	∞∑	∞∑	PRON
ejpam-4507	192	2	n=0	n=0	NUM
ejpam-4507	192	3	b(α	b(α	NOUN
ejpam-4507	192	4	)	)	PUNCT
ejpam-4507	192	5	n	n	CCONJ
ejpam-4507	192	6	(	(	PUNCT
ejpam-4507	192	7	x+	x+	PROPN
ejpam-4507	192	8	y	y	PROPN
ejpam-4507	192	9	;	;	PUNCT
ejpam-4507	192	10	a	a	DET
ejpam-4507	192	11	,	,	PUNCT
ejpam-4507	192	12	b	b	NOUN
ejpam-4507	192	13	,	,	PUNCT
ejpam-4507	192	14	c	c	NOUN
ejpam-4507	192	15	)	)	PUNCT
ejpam-4507	192	16	ty	ty	NOUN
ejpam-4507	192	17	n	n	ADV
ejpam-4507	192	18	!	!	PUNCT
ejpam-4507	192	19	=	=	NOUN
ejpam-4507	193	1	∞∑	∞∑	PRON
ejpam-4507	193	2	n=0	n=0	NUM
ejpam-4507	193	3	n∑	n∑	X
ejpam-4507	193	4	l=0	l=0	PROPN
ejpam-4507	193	5	(	(	PUNCT
ejpam-4507	193	6	n	n	X
ejpam-4507	193	7	l	l	NOUN
ejpam-4507	193	8	)	)	PUNCT
ejpam-4507	193	9	b	b	PROPN
ejpam-4507	193	10	(	(	PUNCT
ejpam-4507	193	11	α	α	NOUN
ejpam-4507	193	12	)	)	PUNCT
ejpam-4507	193	13	l	l	NOUN
ejpam-4507	193	14	(	(	PUNCT
ejpam-4507	193	15	x	x	NOUN
ejpam-4507	193	16	;	;	PUNCT
ejpam-4507	193	17	a	a	DET
ejpam-4507	193	18	,	,	PUNCT
ejpam-4507	193	19	b	b	NOUN
ejpam-4507	193	20	,	,	PUNCT
ejpam-4507	193	21	c)(y	c)(y	ADV
ejpam-4507	193	22	ln	ln	ADV
ejpam-4507	193	23	c)n−l	c)n−l	PROPN
ejpam-4507	193	24	t	t	PROPN
ejpam-4507	193	25	n	n	PROPN
ejpam-4507	193	26	n	n	CCONJ
ejpam-4507	193	27	!	!	PUNCT
ejpam-4507	193	28	.	.	PUNCT
ejpam-4507	194	1	thus	thus	ADV
ejpam-4507	194	2	,	,	PUNCT
ejpam-4507	194	3	b(α	b(α	NOUN
ejpam-4507	194	4	)	)	PUNCT
ejpam-4507	194	5	n	n	CCONJ
ejpam-4507	194	6	(	(	PUNCT
ejpam-4507	194	7	x+	x+	PROPN
ejpam-4507	194	8	y	y	PROPN
ejpam-4507	194	9	;	;	PUNCT
ejpam-4507	194	10	a	a	DET
ejpam-4507	194	11	,	,	PUNCT
ejpam-4507	194	12	b	b	NOUN
ejpam-4507	194	13	,	,	PUNCT
ejpam-4507	194	14	c	c	NOUN
ejpam-4507	194	15	)	)	PUNCT
ejpam-4507	194	16	=	=	SYM
ejpam-4507	194	17	n∑	n∑	NOUN
ejpam-4507	194	18	l=0	l=0	PROPN
ejpam-4507	194	19	(	(	PUNCT
ejpam-4507	194	20	n	n	X
ejpam-4507	194	21	l	l	NOUN
ejpam-4507	194	22	)	)	PUNCT
ejpam-4507	194	23	b	b	PROPN
ejpam-4507	194	24	(	(	PUNCT
ejpam-4507	194	25	α	α	NOUN
ejpam-4507	194	26	)	)	PUNCT
ejpam-4507	194	27	l	l	NOUN
ejpam-4507	194	28	(	(	PUNCT
ejpam-4507	194	29	x	x	NOUN
ejpam-4507	194	30	;	;	PUNCT
ejpam-4507	194	31	a	a	DET
ejpam-4507	194	32	,	,	PUNCT
ejpam-4507	194	33	b	b	NOUN
ejpam-4507	194	34	,	,	PUNCT
ejpam-4507	194	35	c)(y	c)(y	ADV
ejpam-4507	194	36	ln	ln	ADJ
ejpam-4507	194	37	c)n−l	c)n−l	PROPN
ejpam-4507	194	38	.	.	PUNCT
ejpam-4507	195	1	take	take	VERB
ejpam-4507	195	2	y	y	NOUN
ejpam-4507	195	3	=	=	SYM
ejpam-4507	195	4	z	z	PROPN
ejpam-4507	195	5	,	,	PUNCT
ejpam-4507	195	6	x	x	SYM
ejpam-4507	195	7	=	=	PUNCT
ejpam-4507	195	8	0	0	X
ejpam-4507	195	9	.	.	PUNCT
ejpam-4507	196	1	then	then	ADV
ejpam-4507	196	2	bα	bα	PROPN
ejpam-4507	196	3	n	n	PROPN
ejpam-4507	196	4	(	(	PUNCT
ejpam-4507	196	5	z	z	NOUN
ejpam-4507	196	6	;	;	PUNCT
ejpam-4507	196	7	a	a	DET
ejpam-4507	196	8	,	,	PUNCT
ejpam-4507	196	9	b	b	NOUN
ejpam-4507	196	10	,	,	PUNCT
ejpam-4507	196	11	c	c	NOUN
ejpam-4507	196	12	)	)	PUNCT
ejpam-4507	196	13	=	=	SYM
ejpam-4507	197	1	n∑	n∑	NOUN
ejpam-4507	197	2	l=0	l=0	PROPN
ejpam-4507	197	3	(	(	PUNCT
ejpam-4507	197	4	n	n	X
ejpam-4507	197	5	l	l	NOUN
ejpam-4507	197	6	)	)	PUNCT
ejpam-4507	197	7	b	b	PROPN
ejpam-4507	197	8	(	(	PUNCT
ejpam-4507	197	9	α	α	NOUN
ejpam-4507	197	10	)	)	PUNCT
ejpam-4507	197	11	l	l	NOUN
ejpam-4507	197	12	(	(	PUNCT
ejpam-4507	197	13	0	0	NUM
ejpam-4507	197	14	;	;	PUNCT
ejpam-4507	197	15	a	a	DET
ejpam-4507	197	16	,	,	PUNCT
ejpam-4507	197	17	b	b	NOUN
ejpam-4507	197	18	,	,	PUNCT
ejpam-4507	197	19	c)(z	c)(z	AUX
ejpam-4507	197	20	ln	ln	INTJ
ejpam-4507	197	21	c)n−l	c)n−l	PROPN
ejpam-4507	197	22	now	now	ADV
ejpam-4507	197	23	take	take	VERB
ejpam-4507	197	24	n	n	PRON
ejpam-4507	197	25	=	=	SYM
ejpam-4507	197	26	ν	ν	NOUN
ejpam-4507	197	27	and	and	CCONJ
ejpam-4507	197	28	z	z	NOUN
ejpam-4507	197	29	=	=	SYM
ejpam-4507	197	30	x	x	NOUN
ejpam-4507	197	31	,	,	PUNCT
ejpam-4507	197	32	we	we	PRON
ejpam-4507	197	33	have	have	VERB
ejpam-4507	197	34	b(α	b(α	NOUN
ejpam-4507	197	35	)	)	PUNCT
ejpam-4507	197	36	ν	ν	NOUN
ejpam-4507	197	37	(	(	PUNCT
ejpam-4507	197	38	x	x	NOUN
ejpam-4507	197	39	;	;	PUNCT
ejpam-4507	197	40	a	a	DET
ejpam-4507	197	41	,	,	PUNCT
ejpam-4507	197	42	b	b	NOUN
ejpam-4507	197	43	,	,	PUNCT
ejpam-4507	197	44	c	c	NOUN
ejpam-4507	197	45	)	)	PUNCT
ejpam-4507	197	46	=	=	SYM
ejpam-4507	198	1	ν∑	ν∑	PROPN
ejpam-4507	199	1	l=0	l=0	PROPN
ejpam-4507	199	2	(	(	PUNCT
ejpam-4507	199	3	ν	ν	X
ejpam-4507	199	4	l	l	NOUN
ejpam-4507	199	5	)	)	PUNCT
ejpam-4507	199	6	b	b	PROPN
ejpam-4507	199	7	(	(	PUNCT
ejpam-4507	199	8	α	α	NOUN
ejpam-4507	199	9	)	)	PUNCT
ejpam-4507	199	10	l	l	NOUN
ejpam-4507	199	11	(	(	PUNCT
ejpam-4507	199	12	0	0	NUM
ejpam-4507	199	13	;	;	PUNCT
ejpam-4507	199	14	a	a	DET
ejpam-4507	199	15	,	,	PUNCT
ejpam-4507	199	16	b	b	NOUN
ejpam-4507	199	17	,	,	PUNCT
ejpam-4507	199	18	c)(x	c)(x	PROPN
ejpam-4507	199	19	ln	ln	ADV
ejpam-4507	199	20	c)v−l	c)v−l	PROPN
ejpam-4507	199	21	.	.	PUNCT
ejpam-4507	200	1	theorem	theorem	VERB
ejpam-4507	200	2	3.3	3.3	NUM
ejpam-4507	200	3	.	.	PUNCT
ejpam-4507	201	1	let	let	VERB
ejpam-4507	201	2	a	a	DET
ejpam-4507	201	3	,	,	PUNCT
ejpam-4507	201	4	b	b	NOUN
ejpam-4507	201	5	,	,	PUNCT
ejpam-4507	201	6	c	c	AUX
ejpam-4507	201	7	be	be	AUX
ejpam-4507	201	8	positive	positive	ADJ
ejpam-4507	201	9	real	real	ADJ
ejpam-4507	201	10	numbers	number	NOUN
ejpam-4507	201	11	,	,	PUNCT
ejpam-4507	201	12	n	n	CCONJ
ejpam-4507	201	13	,	,	PUNCT
ejpam-4507	201	14	n	n	CCONJ
ejpam-4507	201	15	,	,	PUNCT
ejpam-4507	201	16	α	α	PROPN
ejpam-4507	201	17	∈	∈	PROPN
ejpam-4507	201	18	z+	z+	NUM
ejpam-4507	201	19	with	with	ADP
ejpam-4507	201	20	n	n	PRON
ejpam-4507	201	21	≥	≥	NOUN
ejpam-4507	201	22	α	α	PRON
ejpam-4507	201	23	≥	≥	NUM
ejpam-4507	201	24	2	2	NUM
ejpam-4507	201	25	,	,	PUNCT
ejpam-4507	201	26	n	n	CCONJ
ejpam-4507	201	27	>	>	SYM
ejpam-4507	201	28	1	1	NUM
ejpam-4507	201	29	and	and	CCONJ
ejpam-4507	201	30	cn	cn	PROPN
ejpam-4507	201	31	be	be	AUX
ejpam-4507	201	32	the	the	DET
ejpam-4507	201	33	circle	circle	NOUN
ejpam-4507	201	34	about	about	ADP
ejpam-4507	201	35	zero	zero	NUM
ejpam-4507	201	36	of	of	ADP
ejpam-4507	201	37	radius	radius	NOUN
ejpam-4507	201	38	r	r	NOUN
ejpam-4507	201	39	=	=	PUNCT
ejpam-4507	201	40	(	(	PUNCT
ejpam-4507	201	41	2nπ	2nπ	NOUN
ejpam-4507	201	42	−	−	NOUN
ejpam-4507	201	43	ε)/b	ε)/b	NOUN
ejpam-4507	201	44	,	,	PUNCT
ejpam-4507	201	45	where	where	SCONJ
ejpam-4507	201	46	0	0	X
ejpam-4507	201	47	<	<	X
ejpam-4507	201	48	ε	ε	X
ejpam-4507	201	49	<	<	X
ejpam-4507	201	50	1	1	NUM
ejpam-4507	201	51	and	and	CCONJ
ejpam-4507	201	52	b	b	X
ejpam-4507	201	53	=	=	SYM
ejpam-4507	201	54	ln	ln	PROPN
ejpam-4507	201	55	b	b	PROPN
ejpam-4507	201	56	−	−	NOUN
ejpam-4507	202	1	ln	ln	ADV
ejpam-4507	202	2	a	a	X
ejpam-4507	202	3	>	>	X
ejpam-4507	202	4	0	0	NUM
ejpam-4507	202	5	.	.	PUNCT
ejpam-4507	203	1	the	the	DET
ejpam-4507	203	2	fourier	fourier	ADJ
ejpam-4507	203	3	series	series	NOUN
ejpam-4507	203	4	of	of	ADP
ejpam-4507	203	5	the	the	DET
ejpam-4507	203	6	bernoulli	bernoulli	NOUN
ejpam-4507	203	7	-	-	PUNCT
ejpam-4507	203	8	type	type	NOUN
ejpam-4507	203	9	polynomials	polynomial	NOUN
ejpam-4507	203	10	b	b	PROPN
ejpam-4507	203	11	(	(	PUNCT
ejpam-4507	203	12	α	α	NOUN
ejpam-4507	203	13	)	)	PUNCT
ejpam-4507	203	14	n	n	PROPN
ejpam-4507	203	15	(	(	PUNCT
ejpam-4507	203	16	x	x	X
ejpam-4507	203	17	;	;	PUNCT
ejpam-4507	203	18	a	a	DET
ejpam-4507	203	19	,	,	PUNCT
ejpam-4507	203	20	b	b	NOUN
ejpam-4507	203	21	,	,	PUNCT
ejpam-4507	203	22	c	c	NOUN
ejpam-4507	203	23	)	)	PUNCT
ejpam-4507	203	24	of	of	ADP
ejpam-4507	203	25	order	order	NOUN
ejpam-4507	203	26	α	α	NOUN
ejpam-4507	203	27	is	be	AUX
ejpam-4507	203	28	given	give	VERB
ejpam-4507	203	29	by	by	ADP
ejpam-4507	203	30	c.	c.	PROPN
ejpam-4507	203	31	corcino	corcino	PROPN
ejpam-4507	203	32	,	,	PUNCT
ejpam-4507	203	33	r.	r.	PROPN
ejpam-4507	203	34	corcino	corcino	PROPN
ejpam-4507	203	35	/	/	SYM
ejpam-4507	203	36	eur	eur	PROPN
ejpam-4507	203	37	.	.	PUNCT
ejpam-4507	204	1	j.	j.	PROPN
ejpam-4507	204	2	pure	pure	PROPN
ejpam-4507	204	3	appl	appl	PROPN
ejpam-4507	204	4	.	.	PROPN
ejpam-4507	204	5	math	math	PROPN
ejpam-4507	204	6	,	,	PUNCT
ejpam-4507	204	7	15	15	NUM
ejpam-4507	204	8	(	(	PUNCT
ejpam-4507	204	9	4	4	NUM
ejpam-4507	204	10	)	)	PUNCT
ejpam-4507	204	11	(	(	PUNCT
ejpam-4507	204	12	2022	2022	NUM
ejpam-4507	204	13	)	)	PUNCT
ejpam-4507	204	14	,	,	PUNCT
ejpam-4507	204	15	1662	1662	NUM
ejpam-4507	204	16	-	-	SYM
ejpam-4507	204	17	1682	1682	NUM
ejpam-4507	204	18	1673	1673	NUM
ejpam-4507	204	19	b	b	PROPN
ejpam-4507	204	20	(	(	PUNCT
ejpam-4507	204	21	α	α	NOUN
ejpam-4507	204	22	)	)	PUNCT
ejpam-4507	204	23	n	n	PROPN
ejpam-4507	204	24	(	(	PUNCT
ejpam-4507	204	25	x	x	X
ejpam-4507	204	26	;	;	PUNCT
ejpam-4507	204	27	a	a	DET
ejpam-4507	204	28	,	,	PUNCT
ejpam-4507	204	29	b	b	NOUN
ejpam-4507	204	30	,	,	PUNCT
ejpam-4507	204	31	c	c	NOUN
ejpam-4507	204	32	)	)	PUNCT
ejpam-4507	204	33	n	n	CCONJ
ejpam-4507	204	34	!	!	PUNCT
ejpam-4507	204	35	=	=	PUNCT
ejpam-4507	205	1	−	−	PROPN
ejpam-4507	205	2	∑	∑	PUNCT
ejpam-4507	205	3	k∈z	k∈z	PROPN
ejpam-4507	205	4	,	,	PUNCT
ejpam-4507	205	5	k	k	PROPN
ejpam-4507	205	6	̸=0	̸=0	PROPN
ejpam-4507	205	7	(	(	PUNCT
ejpam-4507	205	8	α−1∑	α−1∑	NUM
ejpam-4507	205	9	ν=0	ν=0	PROPN
ejpam-4507	205	10	(	(	PUNCT
ejpam-4507	205	11	α−	α−	ADP
ejpam-4507	205	12	n−	n−	NOUN
ejpam-4507	205	13	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	205	14	ν!(α−	ν!(α−	VERB
ejpam-4507	205	15	1−	1−	NUM
ejpam-4507	205	16	ν	ν	NOUN
ejpam-4507	205	17	)	)	PUNCT
ejpam-4507	205	18	!	!	PUNCT
ejpam-4507	206	1	(	(	PUNCT
ejpam-4507	206	2	2kπi)νb(α	2kπi)νb(α	NUM
ejpam-4507	206	3	)	)	PUNCT
ejpam-4507	206	4	ν	ν	NOUN
ejpam-4507	206	5	(	(	PUNCT
ejpam-4507	206	6	x	x	NOUN
ejpam-4507	206	7	;	;	PUNCT
ejpam-4507	206	8	a	a	DET
ejpam-4507	206	9	,	,	PUNCT
ejpam-4507	206	10	b	b	NOUN
ejpam-4507	206	11	,	,	PUNCT
ejpam-4507	206	12	c	c	NOUN
ejpam-4507	206	13	)	)	PUNCT
ejpam-4507	206	14	)	)	PUNCT
ejpam-4507	207	1	e2kπi(x	e2kπi(x	PROPN
ejpam-4507	208	1	ln	ln	ADJ
ejpam-4507	208	2	c−α	c−α	NOUN
ejpam-4507	208	3	ln	ln	PROPN
ejpam-4507	208	4	b	b	NOUN
ejpam-4507	208	5	)	)	PUNCT
ejpam-4507	208	6	(	(	PUNCT
ejpam-4507	208	7	2kπi)n	2kπi)n	NUM
ejpam-4507	208	8	,	,	PUNCT
ejpam-4507	208	9	valid	valid	ADJ
ejpam-4507	208	10	for	for	ADP
ejpam-4507	208	11	0	0	NUM
ejpam-4507	208	12	<	<	X
ejpam-4507	208	13	x	x	X
ejpam-4507	208	14	<	<	X
ejpam-4507	208	15	(	(	PUNCT
ejpam-4507	208	16	α	α	X
ejpam-4507	208	17	ln	ln	ADJ
ejpam-4507	208	18	a−	a−	PROPN
ejpam-4507	208	19	b	b	PROPN
ejpam-4507	208	20	2π	2π	PROPN
ejpam-4507	208	21	−	−	PROPN
ejpam-4507	208	22	ε	ε	PROPN
ejpam-4507	208	23	)	)	PUNCT
ejpam-4507	208	24	/	/	SYM
ejpam-4507	209	1	ln	ln	NOUN
ejpam-4507	209	2	c	c	NOUN
ejpam-4507	209	3	,	,	PUNCT
ejpam-4507	209	4	ln	ln	NOUN
ejpam-4507	209	5	c	c	NOUN
ejpam-4507	209	6	>	>	X
ejpam-4507	209	7	0	0	PROPN
ejpam-4507	209	8	,	,	PUNCT
ejpam-4507	209	9	where	where	SCONJ
ejpam-4507	209	10	b	b	X
ejpam-4507	209	11	(	(	PUNCT
ejpam-4507	209	12	α	α	NOUN
ejpam-4507	209	13	)	)	PUNCT
ejpam-4507	209	14	ν	ν	NOUN
ejpam-4507	209	15	(	(	PUNCT
ejpam-4507	209	16	x	x	NOUN
ejpam-4507	209	17	;	;	PUNCT
ejpam-4507	209	18	a	a	DET
ejpam-4507	209	19	,	,	PUNCT
ejpam-4507	209	20	b	b	NOUN
ejpam-4507	209	21	,	,	PUNCT
ejpam-4507	209	22	c	c	NOUN
ejpam-4507	209	23	)	)	PUNCT
ejpam-4507	209	24	is	be	AUX
ejpam-4507	209	25	given	give	VERB
ejpam-4507	209	26	in	in	ADP
ejpam-4507	209	27	lemma	lemma	PROPN
ejpam-4507	209	28	3.2	3.2	NUM
ejpam-4507	209	29	.	.	PUNCT
ejpam-4507	210	1	proof	proof	NOUN
ejpam-4507	210	2	.	.	PUNCT
ejpam-4507	211	1	applying	apply	VERB
ejpam-4507	211	2	the	the	DET
ejpam-4507	211	3	cauchy	cauchy	ADJ
ejpam-4507	211	4	integral	integral	ADJ
ejpam-4507	211	5	formula	formula	NOUN
ejpam-4507	211	6	to	to	ADP
ejpam-4507	211	7	(	(	PUNCT
ejpam-4507	211	8	1	1	NUM
ejpam-4507	211	9	)	)	PUNCT
ejpam-4507	211	10	,	,	PUNCT
ejpam-4507	211	11	b	b	X
ejpam-4507	211	12	(	(	PUNCT
ejpam-4507	211	13	α	α	NOUN
ejpam-4507	211	14	)	)	PUNCT
ejpam-4507	211	15	n	n	PROPN
ejpam-4507	211	16	(	(	PUNCT
ejpam-4507	211	17	x	x	X
ejpam-4507	211	18	;	;	PUNCT
ejpam-4507	211	19	a	a	DET
ejpam-4507	211	20	,	,	PUNCT
ejpam-4507	211	21	b	b	NOUN
ejpam-4507	211	22	,	,	PUNCT
ejpam-4507	211	23	c	c	NOUN
ejpam-4507	211	24	)	)	PUNCT
ejpam-4507	211	25	n	n	CCONJ
ejpam-4507	211	26	!	!	PUNCT
ejpam-4507	212	1	=	=	SYM
ejpam-4507	212	2	1	1	NUM
ejpam-4507	212	3	2πi	2πi	ADJ
ejpam-4507	212	4	∫	∫	PROPN
ejpam-4507	212	5	c	c	PROPN
ejpam-4507	212	6	cxt	cxt	PROPN
ejpam-4507	212	7	(	(	PUNCT
ejpam-4507	212	8	bt	bt	NOUN
ejpam-4507	212	9	−	−	PROPN
ejpam-4507	212	10	at)α	at)α	PROPN
ejpam-4507	212	11	dt	dt	NOUN
ejpam-4507	212	12	tn+1−α	tn+1−α	NOUN
ejpam-4507	212	13	,	,	PUNCT
ejpam-4507	212	14	where	where	SCONJ
ejpam-4507	212	15	c	c	PROPN
ejpam-4507	212	16	is	be	AUX
ejpam-4507	212	17	a	a	DET
ejpam-4507	212	18	circle	circle	NOUN
ejpam-4507	212	19	about	about	ADP
ejpam-4507	212	20	the	the	DET
ejpam-4507	212	21	origin	origin	NOUN
ejpam-4507	212	22	with	with	ADP
ejpam-4507	212	23	radius	radius	NOUN
ejpam-4507	212	24	less	less	ADJ
ejpam-4507	212	25	than	than	ADP
ejpam-4507	212	26	2π	2π	PROPN
ejpam-4507	212	27	b	b	X
ejpam-4507	212	28	.	.	PUNCT
ejpam-4507	213	1	let	let	VERB
ejpam-4507	213	2	fα(t	fα(t	PUNCT
ejpam-4507	213	3	)	)	PUNCT
ejpam-4507	213	4	=	=	SYM
ejpam-4507	213	5	cxt	cxt	PROPN
ejpam-4507	213	6	(	(	PUNCT
ejpam-4507	213	7	bt	bt	NOUN
ejpam-4507	213	8	−	−	PROPN
ejpam-4507	213	9	at)αtn−α+1	at)αtn−α+1	PROPN
ejpam-4507	213	10	,	,	PUNCT
ejpam-4507	213	11	n	n	CCONJ
ejpam-4507	213	12	>	>	X
ejpam-4507	213	13	α	α	X
ejpam-4507	213	14	.	.	PUNCT
ejpam-4507	214	1	the	the	DET
ejpam-4507	214	2	function	function	NOUN
ejpam-4507	214	3	fα(t	fα(t	PUNCT
ejpam-4507	214	4	)	)	PUNCT
ejpam-4507	214	5	has	have	VERB
ejpam-4507	214	6	a	a	DET
ejpam-4507	214	7	pole	pole	NOUN
ejpam-4507	214	8	of	of	ADP
ejpam-4507	214	9	order	order	NOUN
ejpam-4507	214	10	n	n	PRON
ejpam-4507	214	11	−	−	PROPN
ejpam-4507	214	12	α	α	NOUN
ejpam-4507	214	13	+	+	NOUN
ejpam-4507	214	14	1	1	NUM
ejpam-4507	214	15	at	at	ADP
ejpam-4507	214	16	t	t	NOUN
ejpam-4507	214	17	=	=	SYM
ejpam-4507	214	18	0	0	PROPN
ejpam-4507	214	19	and	and	CCONJ
ejpam-4507	214	20	a	a	DET
ejpam-4507	214	21	pole	pole	NOUN
ejpam-4507	214	22	of	of	ADP
ejpam-4507	214	23	order	order	NOUN
ejpam-4507	214	24	α	α	NOUN
ejpam-4507	214	25	at	at	ADP
ejpam-4507	214	26	the	the	DET
ejpam-4507	214	27	zeros	zero	NOUN
ejpam-4507	214	28	of	of	ADP
ejpam-4507	214	29	bt	bt	NOUN
ejpam-4507	214	30	−	−	PROPN
ejpam-4507	214	31	at	at	ADP
ejpam-4507	214	32	which	which	PRON
ejpam-4507	214	33	are	be	AUX
ejpam-4507	214	34	given	give	VERB
ejpam-4507	214	35	by	by	ADP
ejpam-4507	214	36	tk	tk	PROPN
ejpam-4507	214	37	=	=	PROPN
ejpam-4507	214	38	2kπi	2kπi	PROPN
ejpam-4507	214	39	b	b	PROPN
ejpam-4507	214	40	,	,	PUNCT
ejpam-4507	214	41	k	k	PROPN
ejpam-4507	214	42	∈	∈	PROPN
ejpam-4507	214	43	z.	z.	PROPN
ejpam-4507	214	44	now	now	ADV
ejpam-4507	214	45	let	let	VERB
ejpam-4507	214	46	cn	cn	PROPN
ejpam-4507	214	47	,	,	PUNCT
ejpam-4507	214	48	n	n	PROPN
ejpam-4507	214	49	>	>	X
ejpam-4507	214	50	1	1	NUM
ejpam-4507	214	51	be	be	VERB
ejpam-4507	214	52	the	the	DET
ejpam-4507	214	53	circle	circle	NOUN
ejpam-4507	214	54	described	describe	VERB
ejpam-4507	214	55	in	in	ADP
ejpam-4507	214	56	lemma	lemma	PROPN
ejpam-4507	214	57	3.1	3.1	NUM
ejpam-4507	214	58	.	.	PUNCT
ejpam-4507	215	1	applying	apply	VERB
ejpam-4507	215	2	the	the	DET
ejpam-4507	215	3	residue	residue	NOUN
ejpam-4507	215	4	theorem	theorem	NOUN
ejpam-4507	215	5	,	,	PUNCT
ejpam-4507	215	6	lim	lim	PROPN
ejpam-4507	215	7	n→+∞	n→+∞	VERB
ejpam-4507	215	8	1	1	NUM
ejpam-4507	215	9	2πi	2πi	NOUN
ejpam-4507	215	10	∫	∫	PROPN
ejpam-4507	215	11	cn	cn	PROPN
ejpam-4507	215	12	cxt	cxt	PROPN
ejpam-4507	215	13	(	(	PUNCT
ejpam-4507	215	14	bt	bt	NOUN
ejpam-4507	215	15	−	−	PROPN
ejpam-4507	215	16	at)α	at)α	PROPN
ejpam-4507	215	17	dt	dt	NOUN
ejpam-4507	215	18	tn−α+1	tn−α+1	NOUN
ejpam-4507	215	19	=	=	SYM
ejpam-4507	215	20	res(fα(t	res(fα(t	PROPN
ejpam-4507	215	21	)	)	PUNCT
ejpam-4507	215	22	,	,	PUNCT
ejpam-4507	215	23	t	t	NOUN
ejpam-4507	215	24	=	=	SYM
ejpam-4507	215	25	0	0	NUM
ejpam-4507	215	26	)	)	PUNCT
ejpam-4507	216	1	+	+	CCONJ
ejpam-4507	216	2	∑	∑	ADV
ejpam-4507	216	3	k∈z	k∈z	PROPN
ejpam-4507	216	4	,	,	PUNCT
ejpam-4507	216	5	k	k	X
ejpam-4507	216	6	̸=0	̸=0	ADJ
ejpam-4507	216	7	res(fα(t	res(fα(t	NOUN
ejpam-4507	216	8	)	)	PUNCT
ejpam-4507	216	9	,	,	PUNCT
ejpam-4507	216	10	t	t	PROPN
ejpam-4507	216	11	=	=	SYM
ejpam-4507	216	12	tk	tk	PROPN
ejpam-4507	216	13	)	)	PUNCT
ejpam-4507	216	14	.	.	PUNCT
ejpam-4507	217	1	by	by	ADP
ejpam-4507	217	2	lemma	lemma	PROPN
ejpam-4507	217	3	3.1	3.1	NUM
ejpam-4507	217	4	,	,	PUNCT
ejpam-4507	217	5	0	0	NUM
ejpam-4507	217	6	=	=	SYM
ejpam-4507	217	7	res(fα(t	res(fα(t	NOUN
ejpam-4507	217	8	)	)	PUNCT
ejpam-4507	217	9	,	,	PUNCT
ejpam-4507	217	10	t	t	NOUN
ejpam-4507	217	11	=	=	SYM
ejpam-4507	217	12	0	0	NUM
ejpam-4507	217	13	)	)	PUNCT
ejpam-4507	217	14	+	+	CCONJ
ejpam-4507	217	15	∑	∑	ADV
ejpam-4507	217	16	k∈z	k∈z	PROPN
ejpam-4507	217	17	,	,	PUNCT
ejpam-4507	217	18	k	k	X
ejpam-4507	217	19	̸=0	̸=0	ADJ
ejpam-4507	217	20	res(fα(t	res(fα(t	NOUN
ejpam-4507	217	21	)	)	PUNCT
ejpam-4507	217	22	,	,	PUNCT
ejpam-4507	217	23	t	t	PROPN
ejpam-4507	217	24	=	=	SYM
ejpam-4507	217	25	tk	tk	PROPN
ejpam-4507	217	26	)	)	PUNCT
ejpam-4507	217	27	0	0	NUM
ejpam-4507	218	1	=	=	SYM
ejpam-4507	218	2	b	b	PROPN
ejpam-4507	218	3	(	(	PUNCT
ejpam-4507	218	4	α	α	NOUN
ejpam-4507	218	5	)	)	PUNCT
ejpam-4507	218	6	n	n	PROPN
ejpam-4507	218	7	(	(	PUNCT
ejpam-4507	218	8	x	x	X
ejpam-4507	218	9	;	;	PUNCT
ejpam-4507	218	10	a	a	DET
ejpam-4507	218	11	,	,	PUNCT
ejpam-4507	218	12	b	b	NOUN
ejpam-4507	218	13	,	,	PUNCT
ejpam-4507	218	14	c	c	NOUN
ejpam-4507	218	15	)	)	PUNCT
ejpam-4507	218	16	n	n	CCONJ
ejpam-4507	218	17	!	!	PUNCT
ejpam-4507	219	1	+	+	CCONJ
ejpam-4507	219	2	∑	∑	ADV
ejpam-4507	219	3	k∈z	k∈z	PROPN
ejpam-4507	219	4	,	,	PUNCT
ejpam-4507	219	5	k	k	X
ejpam-4507	219	6	̸=0	̸=0	ADJ
ejpam-4507	219	7	res(fα(t	res(fα(t	NOUN
ejpam-4507	219	8	)	)	PUNCT
ejpam-4507	219	9	,	,	PUNCT
ejpam-4507	219	10	t	t	PROPN
ejpam-4507	219	11	=	=	SYM
ejpam-4507	219	12	tk	tk	PROPN
ejpam-4507	219	13	)	)	PUNCT
ejpam-4507	219	14	⇐	⇐	ADJ
ejpam-4507	219	15	⇒	⇒	PROPN
ejpam-4507	219	16	bα	bα	PROPN
ejpam-4507	219	17	n	n	CCONJ
ejpam-4507	219	18	(	(	PUNCT
ejpam-4507	219	19	x	x	NOUN
ejpam-4507	219	20	;	;	PUNCT
ejpam-4507	219	21	a	a	DET
ejpam-4507	219	22	,	,	PUNCT
ejpam-4507	219	23	b	b	NOUN
ejpam-4507	219	24	,	,	PUNCT
ejpam-4507	219	25	c	c	NOUN
ejpam-4507	219	26	)	)	PUNCT
ejpam-4507	219	27	n	n	CCONJ
ejpam-4507	219	28	!	!	PUNCT
ejpam-4507	220	1	=	=	PUNCT
ejpam-4507	221	1	−	−	PROPN
ejpam-4507	221	2	∑	∑	PUNCT
ejpam-4507	221	3	k∈z	k∈z	PROPN
ejpam-4507	221	4	,	,	PUNCT
ejpam-4507	221	5	k	k	X
ejpam-4507	221	6	̸=0	̸=0	ADJ
ejpam-4507	221	7	res(fα(t	res(fα(t	NOUN
ejpam-4507	221	8	)	)	PUNCT
ejpam-4507	221	9	,	,	PUNCT
ejpam-4507	221	10	t	t	PROPN
ejpam-4507	221	11	=	=	SYM
ejpam-4507	221	12	tk	tk	PROPN
ejpam-4507	221	13	)	)	PUNCT
ejpam-4507	221	14	.	.	PUNCT
ejpam-4507	222	1	(	(	PUNCT
ejpam-4507	222	2	4	4	X
ejpam-4507	222	3	)	)	PUNCT
ejpam-4507	222	4	computing	compute	VERB
ejpam-4507	222	5	the	the	DET
ejpam-4507	222	6	residues	residue	NOUN
ejpam-4507	222	7	at	at	ADP
ejpam-4507	222	8	tk	tk	NOUN
ejpam-4507	222	9	:	:	PUNCT
ejpam-4507	222	10	res(fα(t	res(fα(t	ADJ
ejpam-4507	222	11	)	)	PUNCT
ejpam-4507	222	12	,	,	PUNCT
ejpam-4507	222	13	t	t	PROPN
ejpam-4507	222	14	=	=	SYM
ejpam-4507	222	15	k	k	X
ejpam-4507	222	16	)	)	PUNCT
ejpam-4507	222	17	=	=	SYM
ejpam-4507	222	18	1	1	NUM
ejpam-4507	222	19	(	(	PUNCT
ejpam-4507	222	20	α−	α−	ADP
ejpam-4507	222	21	1	1	NUM
ejpam-4507	222	22	)	)	PUNCT
ejpam-4507	222	23	!	!	PUNCT
ejpam-4507	223	1	lim	lim	PROPN
ejpam-4507	223	2	t→tk	t→tk	PROPN
ejpam-4507	223	3	dα−1	dα−1	PROPN
ejpam-4507	223	4	dtα−1	dtα−1	PROPN
ejpam-4507	223	5	(	(	PUNCT
ejpam-4507	223	6	t−	t−	PROPN
ejpam-4507	223	7	tk	tk	PROPN
ejpam-4507	223	8	)	)	PUNCT
ejpam-4507	223	9	α	α	PROPN
ejpam-4507	223	10	(	(	PUNCT
ejpam-4507	223	11	ext	ext	PROPN
ejpam-4507	223	12	ln	ln	PROPN
ejpam-4507	223	13	c	c	PROPN
ejpam-4507	223	14	(	(	PUNCT
ejpam-4507	223	15	bt	bt	NOUN
ejpam-4507	223	16	−	−	PROPN
ejpam-4507	223	17	at)α	at)α	PROPN
ejpam-4507	223	18	)	)	PUNCT
ejpam-4507	223	19	1	1	NUM
ejpam-4507	223	20	tn−α+1	tn−α+1	NOUN
ejpam-4507	223	21	=	=	SYM
ejpam-4507	223	22	1	1	NUM
ejpam-4507	223	23	(	(	PUNCT
ejpam-4507	223	24	α−	α−	ADP
ejpam-4507	223	25	1	1	NUM
ejpam-4507	223	26	)	)	PUNCT
ejpam-4507	223	27	!	!	PUNCT
ejpam-4507	224	1	lim	lim	PROPN
ejpam-4507	224	2	t→tk	t→tk	PROPN
ejpam-4507	224	3	dα−1	dα−1	PROPN
ejpam-4507	224	4	dtα−1	dtα−1	PROPN
ejpam-4507	224	5	[	[	PUNCT
ejpam-4507	224	6	(	(	PUNCT
ejpam-4507	224	7	t−	t−	PROPN
ejpam-4507	224	8	tk	tk	PROPN
ejpam-4507	224	9	)	)	PUNCT
ejpam-4507	224	10	α	α	PROPN
ejpam-4507	224	11	(	(	PUNCT
ejpam-4507	224	12	bt	bt	NOUN
ejpam-4507	224	13	−	−	PROPN
ejpam-4507	224	14	at)α	at)α	PROPN
ejpam-4507	224	15	ext	ext	NOUN
ejpam-4507	224	16	ln	ln	NOUN
ejpam-4507	224	17	c	c	NOUN
ejpam-4507	224	18	tn−α+1	tn−α+1	PROPN
ejpam-4507	224	19	]	]	PUNCT
ejpam-4507	224	20	.	.	PUNCT
ejpam-4507	225	1	(	(	PUNCT
ejpam-4507	225	2	5	5	X
ejpam-4507	225	3	)	)	PUNCT
ejpam-4507	225	4	c.	c.	NOUN
ejpam-4507	225	5	corcino	corcino	PROPN
ejpam-4507	225	6	,	,	PUNCT
ejpam-4507	225	7	r.	r.	PROPN
ejpam-4507	225	8	corcino	corcino	PROPN
ejpam-4507	225	9	/	/	SYM
ejpam-4507	225	10	eur	eur	PROPN
ejpam-4507	225	11	.	.	PUNCT
ejpam-4507	226	1	j.	j.	PROPN
ejpam-4507	226	2	pure	pure	PROPN
ejpam-4507	226	3	appl	appl	PROPN
ejpam-4507	226	4	.	.	PROPN
ejpam-4507	226	5	math	math	PROPN
ejpam-4507	226	6	,	,	PUNCT
ejpam-4507	226	7	15	15	NUM
ejpam-4507	226	8	(	(	PUNCT
ejpam-4507	226	9	4	4	NUM
ejpam-4507	226	10	)	)	PUNCT
ejpam-4507	226	11	(	(	PUNCT
ejpam-4507	226	12	2022	2022	NUM
ejpam-4507	226	13	)	)	PUNCT
ejpam-4507	226	14	,	,	PUNCT
ejpam-4507	226	15	1662	1662	NUM
ejpam-4507	226	16	-	-	SYM
ejpam-4507	226	17	1682	1682	NUM
ejpam-4507	226	18	1674	1674	NUM
ejpam-4507	226	19	taking	take	VERB
ejpam-4507	226	20	x	x	PUNCT
ejpam-4507	226	21	=	=	SYM
ejpam-4507	226	22	0	0	NUM
ejpam-4507	226	23	in	in	ADP
ejpam-4507	226	24	(	(	PUNCT
ejpam-4507	226	25	1	1	X
ejpam-4507	226	26	)	)	PUNCT
ejpam-4507	226	27	gives	give	VERB
ejpam-4507	226	28	(	(	PUNCT
ejpam-4507	226	29	t	t	NOUN
ejpam-4507	226	30	bt	bt	NOUN
ejpam-4507	226	31	−	−	PROPN
ejpam-4507	226	32	at	at	ADP
ejpam-4507	226	33	)	)	PUNCT
ejpam-4507	226	34	α	α	NOUN
ejpam-4507	226	35	=	=	PUNCT
ejpam-4507	227	1	∞∑	∞∑	NUM
ejpam-4507	227	2	n=0	n=0	NUM
ejpam-4507	227	3	b(α	b(α	NOUN
ejpam-4507	227	4	)	)	PUNCT
ejpam-4507	227	5	n	n	CCONJ
ejpam-4507	227	6	(	(	PUNCT
ejpam-4507	227	7	0	0	NUM
ejpam-4507	227	8	;	;	PUNCT
ejpam-4507	227	9	a	a	DET
ejpam-4507	227	10	,	,	PUNCT
ejpam-4507	227	11	b	b	NOUN
ejpam-4507	227	12	,	,	PUNCT
ejpam-4507	227	13	c	c	NOUN
ejpam-4507	227	14	)	)	PUNCT
ejpam-4507	227	15	tn	tn	PROPN
ejpam-4507	227	16	n	n	CCONJ
ejpam-4507	227	17	!	!	PUNCT
ejpam-4507	227	18	.	.	PUNCT
ejpam-4507	228	1	replacing	replace	VERB
ejpam-4507	228	2	t	t	PROPN
ejpam-4507	228	3	7→	7→	NUM
ejpam-4507	229	1	t−	t−	PROPN
ejpam-4507	229	2	tk	tk	PROPN
ejpam-4507	229	3	and	and	CCONJ
ejpam-4507	229	4	writing	write	VERB
ejpam-4507	229	5	bt	bt	NOUN
ejpam-4507	229	6	=	=	PUNCT
ejpam-4507	229	7	et	et	PROPN
ejpam-4507	229	8	ln	ln	PROPN
ejpam-4507	229	9	b	b	PROPN
ejpam-4507	229	10	,	,	PUNCT
ejpam-4507	229	11	at	at	ADP
ejpam-4507	229	12	=	=	SYM
ejpam-4507	229	13	et	et	X
ejpam-4507	229	14	ln	ln	NOUN
ejpam-4507	229	15	a	a	X
ejpam-4507	229	16	,	,	PUNCT
ejpam-4507	229	17	(	(	PUNCT
ejpam-4507	229	18	t−	t−	PROPN
ejpam-4507	229	19	tk	tk	PROPN
ejpam-4507	229	20	)	)	PUNCT
ejpam-4507	229	21	α	α	PROPN
ejpam-4507	229	22	(	(	PUNCT
ejpam-4507	229	23	e(t−tk	e(t−tk	NOUN
ejpam-4507	229	24	)	)	PUNCT
ejpam-4507	229	25	ln	ln	PROPN
ejpam-4507	229	26	b	b	NOUN
ejpam-4507	229	27	−	−	NOUN
ejpam-4507	229	28	e(t−tk	e(t−tk	NOUN
ejpam-4507	229	29	)	)	PUNCT
ejpam-4507	229	30	ln	ln	ADJ
ejpam-4507	229	31	a)α	a)α	NOUN
ejpam-4507	230	1	=	=	SYM
ejpam-4507	230	2	∞∑	∞∑	NUM
ejpam-4507	230	3	n=0	n=0	NUM
ejpam-4507	230	4	b(α	b(α	NOUN
ejpam-4507	230	5	)	)	PUNCT
ejpam-4507	230	6	n	n	CCONJ
ejpam-4507	230	7	(	(	PUNCT
ejpam-4507	230	8	0	0	NUM
ejpam-4507	230	9	;	;	PUNCT
ejpam-4507	230	10	a	a	DET
ejpam-4507	230	11	,	,	PUNCT
ejpam-4507	230	12	b	b	NOUN
ejpam-4507	230	13	,	,	PUNCT
ejpam-4507	230	14	c	c	NOUN
ejpam-4507	230	15	)	)	PUNCT
ejpam-4507	230	16	(	(	PUNCT
ejpam-4507	230	17	t−	t−	PROPN
ejpam-4507	230	18	tk	tk	PROPN
ejpam-4507	230	19	)	)	PUNCT
ejpam-4507	230	20	n	n	PRON
ejpam-4507	230	21	n	n	CCONJ
ejpam-4507	230	22	!	!	PUNCT
ejpam-4507	230	23	.	.	PUNCT
ejpam-4507	231	1	(	(	PUNCT
ejpam-4507	231	2	6	6	X
ejpam-4507	231	3	)	)	PUNCT
ejpam-4507	231	4	multiplying	multiply	VERB
ejpam-4507	231	5	and	and	CCONJ
ejpam-4507	231	6	dividing	divide	VERB
ejpam-4507	231	7	the	the	DET
ejpam-4507	231	8	left	left	ADJ
ejpam-4507	231	9	hand	hand	NOUN
ejpam-4507	231	10	side	side	NOUN
ejpam-4507	231	11	of	of	ADP
ejpam-4507	231	12	(	(	PUNCT
ejpam-4507	231	13	6	6	NUM
ejpam-4507	231	14	)	)	PUNCT
ejpam-4507	231	15	by	by	ADP
ejpam-4507	231	16	eαtk	eαtk	PROPN
ejpam-4507	231	17	ln	ln	PROPN
ejpam-4507	231	18	b	b	PROPN
ejpam-4507	231	19	gives	give	VERB
ejpam-4507	231	20	(	(	PUNCT
ejpam-4507	231	21	t−	t−	PROPN
ejpam-4507	231	22	tk	tk	PROPN
ejpam-4507	231	23	)	)	PUNCT
ejpam-4507	231	24	αeαtk	αeαtk	NOUN
ejpam-4507	231	25	ln	ln	PROPN
ejpam-4507	231	26	b	b	PROPN
ejpam-4507	231	27	(	(	PUNCT
ejpam-4507	231	28	et	et	PROPN
ejpam-4507	231	29	ln	ln	PROPN
ejpam-4507	231	30	b	b	PROPN
ejpam-4507	232	1	−	−	X
ejpam-4507	232	2	et	et	NOUN
ejpam-4507	232	3	ln	ln	NOUN
ejpam-4507	232	4	aetkb)α	aetkb)α	PROPN
ejpam-4507	232	5	=	=	PROPN
ejpam-4507	233	1	∞∑	∞∑	NUM
ejpam-4507	233	2	n=0	n=0	NUM
ejpam-4507	233	3	b(α	b(α	NOUN
ejpam-4507	233	4	)	)	PUNCT
ejpam-4507	233	5	n	n	CCONJ
ejpam-4507	233	6	(	(	PUNCT
ejpam-4507	233	7	0	0	NUM
ejpam-4507	233	8	;	;	PUNCT
ejpam-4507	233	9	a	a	DET
ejpam-4507	233	10	,	,	PUNCT
ejpam-4507	233	11	b	b	NOUN
ejpam-4507	233	12	,	,	PUNCT
ejpam-4507	233	13	c	c	NOUN
ejpam-4507	233	14	)	)	PUNCT
ejpam-4507	233	15	(	(	PUNCT
ejpam-4507	233	16	t−	t−	PROPN
ejpam-4507	233	17	tk	tk	PROPN
ejpam-4507	233	18	)	)	PUNCT
ejpam-4507	233	19	n	n	PRON
ejpam-4507	233	20	n	n	CCONJ
ejpam-4507	233	21	!	!	PUNCT
ejpam-4507	233	22	.	.	PUNCT
ejpam-4507	234	1	(	(	PUNCT
ejpam-4507	234	2	7	7	X
ejpam-4507	234	3	)	)	PUNCT
ejpam-4507	234	4	with	with	ADP
ejpam-4507	234	5	tk	tk	PROPN
ejpam-4507	234	6	=	=	SYM
ejpam-4507	234	7	(	(	PUNCT
ejpam-4507	234	8	2kπi)/b	2kπi)/b	NUM
ejpam-4507	234	9	,	,	PUNCT
ejpam-4507	234	10	we	we	PRON
ejpam-4507	234	11	have	have	VERB
ejpam-4507	234	12	etkb	etkb	NOUN
ejpam-4507	234	13	=	=	SYM
ejpam-4507	235	1	e2kπi	e2kπi	NOUN
ejpam-4507	235	2	=	=	SYM
ejpam-4507	235	3	1	1	X
ejpam-4507	235	4	.	.	PUNCT
ejpam-4507	235	5	thus	thus	ADV
ejpam-4507	235	6	,	,	PUNCT
ejpam-4507	235	7	(	(	PUNCT
ejpam-4507	235	8	7	7	X
ejpam-4507	235	9	)	)	PUNCT
ejpam-4507	235	10	becomes	become	VERB
ejpam-4507	235	11	(	(	PUNCT
ejpam-4507	235	12	t−	t−	PROPN
ejpam-4507	235	13	tk	tk	PROPN
ejpam-4507	235	14	)	)	PUNCT
ejpam-4507	235	15	αeαtk	αeαtk	NOUN
ejpam-4507	235	16	ln	ln	PROPN
ejpam-4507	235	17	b	b	PROPN
ejpam-4507	235	18	(	(	PUNCT
ejpam-4507	235	19	bt	bt	NOUN
ejpam-4507	235	20	−	−	PROPN
ejpam-4507	235	21	at)α	at)α	PROPN
ejpam-4507	235	22	=	=	X
ejpam-4507	235	23	∞∑	∞∑	NUM
ejpam-4507	235	24	n=0	n=0	NUM
ejpam-4507	235	25	b(α	b(α	NOUN
ejpam-4507	235	26	)	)	PUNCT
ejpam-4507	235	27	n	n	CCONJ
ejpam-4507	235	28	(	(	PUNCT
ejpam-4507	235	29	0	0	NUM
ejpam-4507	235	30	;	;	PUNCT
ejpam-4507	235	31	a	a	DET
ejpam-4507	235	32	,	,	PUNCT
ejpam-4507	235	33	b	b	NOUN
ejpam-4507	235	34	,	,	PUNCT
ejpam-4507	235	35	c	c	NOUN
ejpam-4507	235	36	)	)	PUNCT
ejpam-4507	235	37	(	(	PUNCT
ejpam-4507	235	38	t−	t−	PROPN
ejpam-4507	235	39	tk	tk	PROPN
ejpam-4507	235	40	)	)	PUNCT
ejpam-4507	235	41	n	n	PRON
ejpam-4507	235	42	n	n	CCONJ
ejpam-4507	235	43	!	!	PUNCT
ejpam-4507	236	1	(	(	PUNCT
ejpam-4507	236	2	t−	t−	PROPN
ejpam-4507	236	3	tk	tk	PROPN
ejpam-4507	236	4	)	)	PUNCT
ejpam-4507	236	5	α	α	PROPN
ejpam-4507	236	6	(	(	PUNCT
ejpam-4507	236	7	bt	bt	NOUN
ejpam-4507	236	8	−	−	PROPN
ejpam-4507	236	9	at)α	at)α	PROPN
ejpam-4507	236	10	=	=	SYM
ejpam-4507	236	11	e−αtk	e−αtk	PROPN
ejpam-4507	236	12	ln	ln	PROPN
ejpam-4507	236	13	b	b	PROPN
ejpam-4507	237	1	∞∑	∞∑	PROPN
ejpam-4507	237	2	n=0	n=0	NUM
ejpam-4507	237	3	b(α	b(α	NOUN
ejpam-4507	237	4	)	)	PUNCT
ejpam-4507	237	5	n	n	CCONJ
ejpam-4507	237	6	(	(	PUNCT
ejpam-4507	237	7	0	0	NUM
ejpam-4507	237	8	;	;	PUNCT
ejpam-4507	237	9	a	a	DET
ejpam-4507	237	10	,	,	PUNCT
ejpam-4507	237	11	b	b	NOUN
ejpam-4507	237	12	,	,	PUNCT
ejpam-4507	237	13	c	c	NOUN
ejpam-4507	237	14	)	)	PUNCT
ejpam-4507	237	15	(	(	PUNCT
ejpam-4507	237	16	t−	t−	PROPN
ejpam-4507	237	17	tk	tk	PROPN
ejpam-4507	237	18	)	)	PUNCT
ejpam-4507	237	19	n	n	PRON
ejpam-4507	237	20	n	n	CCONJ
ejpam-4507	237	21	!	!	PUNCT
ejpam-4507	237	22	.	.	PUNCT
ejpam-4507	238	1	(	(	PUNCT
ejpam-4507	238	2	8)	8)	NUM
ejpam-4507	238	3	substituting	substituting	NOUN
ejpam-4507	238	4	(	(	PUNCT
ejpam-4507	238	5	8)	8)	NUM
ejpam-4507	238	6	to	to	PART
ejpam-4507	238	7	(	(	PUNCT
ejpam-4507	238	8	5	5	NUM
ejpam-4507	238	9	)	)	PUNCT
ejpam-4507	238	10	gives	give	VERB
ejpam-4507	238	11	,	,	PUNCT
ejpam-4507	238	12	res(fα(t	res(fα(t	PROPN
ejpam-4507	238	13	)	)	PUNCT
ejpam-4507	238	14	,	,	PUNCT
ejpam-4507	238	15	t	t	PROPN
ejpam-4507	238	16	=	=	SYM
ejpam-4507	238	17	tk	tk	PROPN
ejpam-4507	238	18	)	)	PUNCT
ejpam-4507	238	19	=	=	SYM
ejpam-4507	239	1	e−αtk	e−αtk	PROPN
ejpam-4507	239	2	ln	ln	PROPN
ejpam-4507	239	3	b	b	PROPN
ejpam-4507	239	4	(	(	PUNCT
ejpam-4507	239	5	α−	α−	ADP
ejpam-4507	239	6	1	1	NUM
ejpam-4507	239	7	)	)	PUNCT
ejpam-4507	239	8	!	!	PUNCT
ejpam-4507	240	1	lim	lim	PROPN
ejpam-4507	240	2	t→tk	t→tk	PROPN
ejpam-4507	240	3	dα−1	dα−1	PROPN
ejpam-4507	240	4	dtα−1	dtα−1	PROPN
ejpam-4507	240	5	(	(	PUNCT
ejpam-4507	240	6	ext	ext	PROPN
ejpam-4507	240	7	ln	ln	NOUN
ejpam-4507	240	8	c	c	NOUN
ejpam-4507	240	9	tn−α+1	tn−α+1	PROPN
ejpam-4507	240	10	∞∑	∞∑	PROPN
ejpam-4507	240	11	n=0	n=0	PROPN
ejpam-4507	240	12	bn(0	bn(0	NOUN
ejpam-4507	240	13	;	;	PUNCT
ejpam-4507	240	14	a	a	DET
ejpam-4507	240	15	,	,	PUNCT
ejpam-4507	240	16	b	b	NOUN
ejpam-4507	240	17	,	,	PUNCT
ejpam-4507	240	18	c	c	NOUN
ejpam-4507	240	19	)	)	PUNCT
ejpam-4507	240	20	(	(	PUNCT
ejpam-4507	240	21	t−	t−	PROPN
ejpam-4507	240	22	tk	tk	PROPN
ejpam-4507	240	23	)	)	PUNCT
ejpam-4507	240	24	n	n	PRON
ejpam-4507	240	25	n	n	CCONJ
ejpam-4507	240	26	!	!	PUNCT
ejpam-4507	240	27	)	)	PUNCT
ejpam-4507	240	28	.	.	PUNCT
ejpam-4507	241	1	the	the	DET
ejpam-4507	241	2	derivatives	derivative	NOUN
ejpam-4507	241	3	will	will	AUX
ejpam-4507	241	4	be	be	AUX
ejpam-4507	241	5	obtained	obtain	VERB
ejpam-4507	241	6	using	use	VERB
ejpam-4507	241	7	leibniz	leibniz	PROPN
ejpam-4507	241	8	rule	rule	NOUN
ejpam-4507	241	9	.	.	PUNCT
ejpam-4507	242	1	this	this	PRON
ejpam-4507	242	2	is	be	AUX
ejpam-4507	242	3	done	do	VERB
ejpam-4507	242	4	as	as	SCONJ
ejpam-4507	242	5	follows	follow	VERB
ejpam-4507	242	6	.	.	PUNCT
ejpam-4507	243	1	recalling	recall	VERB
ejpam-4507	243	2	the	the	DET
ejpam-4507	243	3	leibniz	leibniz	PROPN
ejpam-4507	243	4	rule	rule	NOUN
ejpam-4507	243	5	for	for	ADP
ejpam-4507	243	6	derivatives	derivative	NOUN
ejpam-4507	243	7	,	,	PUNCT
ejpam-4507	243	8	dn	dn	PROPN
ejpam-4507	243	9	dtn	dtn	PROPN
ejpam-4507	243	10	(	(	PUNCT
ejpam-4507	243	11	fg	fg	PROPN
ejpam-4507	243	12	)	)	PUNCT
ejpam-4507	243	13	=	=	SYM
ejpam-4507	244	1	n∑	n∑	NOUN
ejpam-4507	244	2	k=0	k=0	PROPN
ejpam-4507	244	3	(	(	PUNCT
ejpam-4507	244	4	n	n	X
ejpam-4507	244	5	k	k	NOUN
ejpam-4507	244	6	)	)	PUNCT
ejpam-4507	244	7	(	(	PUNCT
ejpam-4507	244	8	dn−k	dn−k	PROPN
ejpam-4507	244	9	dtn−k	dtn−k	NOUN
ejpam-4507	244	10	f	f	PROPN
ejpam-4507	244	11	)	)	PUNCT
ejpam-4507	244	12	(	(	PUNCT
ejpam-4507	244	13	dk	dk	PROPN
ejpam-4507	244	14	dtk	dtk	PROPN
ejpam-4507	244	15	g	g	PROPN
ejpam-4507	244	16	)	)	PUNCT
ejpam-4507	244	17	.	.	PUNCT
ejpam-4507	245	1	let	let	VERB
ejpam-4507	245	2	f	f	NOUN
ejpam-4507	245	3	=	=	PUNCT
ejpam-4507	245	4	tα−n−1	tα−n−1	PROPN
ejpam-4507	245	5	,	,	PUNCT
ejpam-4507	245	6	g	g	NOUN
ejpam-4507	245	7	=	=	PUNCT
ejpam-4507	245	8	ext	ext	NOUN
ejpam-4507	246	1	ln	ln	PROPN
ejpam-4507	246	2	c	c	NOUN
ejpam-4507	246	3	∑∞	∑∞	NOUN
ejpam-4507	246	4	n=0b	n=0b	NOUN
ejpam-4507	246	5	(	(	PUNCT
ejpam-4507	246	6	α	α	NOUN
ejpam-4507	246	7	)	)	PUNCT
ejpam-4507	246	8	n	n	CCONJ
ejpam-4507	246	9	(	(	PUNCT
ejpam-4507	246	10	0	0	NUM
ejpam-4507	246	11	;	;	PUNCT
ejpam-4507	246	12	a	a	DET
ejpam-4507	246	13	,	,	PUNCT
ejpam-4507	246	14	b	b	NOUN
ejpam-4507	246	15	,	,	PUNCT
ejpam-4507	246	16	c	c	NOUN
ejpam-4507	246	17	)	)	PUNCT
ejpam-4507	246	18	(	(	PUNCT
ejpam-4507	246	19	t−	t−	PROPN
ejpam-4507	246	20	tk	tk	PROPN
ejpam-4507	246	21	)	)	PUNCT
ejpam-4507	246	22	n	n	PRON
ejpam-4507	246	23	n	n	CCONJ
ejpam-4507	246	24	!	!	PUNCT
ejpam-4507	246	25	.	.	PUNCT
ejpam-4507	247	1	then	then	ADV
ejpam-4507	247	2	dα−1	dα−1	PROPN
ejpam-4507	247	3	dtα−1	dtα−1	PROPN
ejpam-4507	247	4	(	(	PUNCT
ejpam-4507	247	5	fg	fg	PROPN
ejpam-4507	247	6	)	)	PUNCT
ejpam-4507	247	7	=	=	PRON
ejpam-4507	247	8	α−1∑	α−1∑	NUM
ejpam-4507	247	9	ν=0	ν=0	PROPN
ejpam-4507	247	10	(	(	PUNCT
ejpam-4507	247	11	α−	α−	ADP
ejpam-4507	247	12	1	1	NUM
ejpam-4507	247	13	ν	ν	NOUN
ejpam-4507	247	14	)	)	PUNCT
ejpam-4507	247	15	(	(	PUNCT
ejpam-4507	247	16	dd−1−ν	dd−1−ν	NOUN
ejpam-4507	247	17	dtd−1−ν	dtd−1−ν	NOUN
ejpam-4507	247	18	f	f	NOUN
ejpam-4507	247	19	)	)	PUNCT
ejpam-4507	247	20	(	(	PUNCT
ejpam-4507	247	21	dν	dν	ADP
ejpam-4507	247	22	dtν	dtν	NOUN
ejpam-4507	247	23	g	g	NOUN
ejpam-4507	247	24	)	)	PUNCT
ejpam-4507	247	25	c.	c.	PROPN
ejpam-4507	247	26	corcino	corcino	PROPN
ejpam-4507	247	27	,	,	PUNCT
ejpam-4507	247	28	r.	r.	PROPN
ejpam-4507	247	29	corcino	corcino	PROPN
ejpam-4507	247	30	/	/	SYM
ejpam-4507	247	31	eur	eur	PROPN
ejpam-4507	247	32	.	.	PUNCT
ejpam-4507	248	1	j.	j.	PROPN
ejpam-4507	248	2	pure	pure	PROPN
ejpam-4507	248	3	appl	appl	PROPN
ejpam-4507	248	4	.	.	PROPN
ejpam-4507	248	5	math	math	PROPN
ejpam-4507	248	6	,	,	PUNCT
ejpam-4507	248	7	15	15	NUM
ejpam-4507	248	8	(	(	PUNCT
ejpam-4507	248	9	4	4	NUM
ejpam-4507	248	10	)	)	PUNCT
ejpam-4507	248	11	(	(	PUNCT
ejpam-4507	248	12	2022	2022	NUM
ejpam-4507	248	13	)	)	PUNCT
ejpam-4507	248	14	,	,	PUNCT
ejpam-4507	248	15	1662	1662	NUM
ejpam-4507	248	16	-	-	SYM
ejpam-4507	248	17	1682	1682	NUM
ejpam-4507	248	18	1675	1675	NUM
ejpam-4507	248	19	=	=	SYM
ejpam-4507	248	20	α−1∑	α−1∑	NUM
ejpam-4507	248	21	ν=0	ν=0	PROPN
ejpam-4507	248	22	(	(	PUNCT
ejpam-4507	248	23	α−	α−	ADP
ejpam-4507	248	24	1	1	NUM
ejpam-4507	248	25	ν	ν	NOUN
ejpam-4507	248	26	)	)	PUNCT
ejpam-4507	248	27	(	(	PUNCT
ejpam-4507	248	28	α−	α−	ADP
ejpam-4507	248	29	n−	n−	VERB
ejpam-4507	248	30	1)α−1−νt	1)α−1−νt	NOUN
ejpam-4507	248	31	α−n−1−(α−1−ν	α−n−1−(α−1−ν	NUM
ejpam-4507	248	32	)	)	PUNCT
ejpam-4507	248	33	(	(	PUNCT
ejpam-4507	248	34	dν	dν	VERB
ejpam-4507	248	35	dtν	dtν	NOUN
ejpam-4507	248	36	g	g	NOUN
ejpam-4507	248	37	)	)	PUNCT
ejpam-4507	248	38	=	=	SYM
ejpam-4507	248	39	α−1∑	α−1∑	NUM
ejpam-4507	248	40	ν=0	ν=0	PROPN
ejpam-4507	248	41	(	(	PUNCT
ejpam-4507	248	42	α−	α−	ADP
ejpam-4507	248	43	1	1	NUM
ejpam-4507	248	44	ν	ν	NOUN
ejpam-4507	248	45	)	)	PUNCT
ejpam-4507	248	46	(	(	PUNCT
ejpam-4507	248	47	α−	α−	ADP
ejpam-4507	248	48	n−	n−	NOUN
ejpam-4507	248	49	1)α−1−νt	1)α−1−νt	NOUN
ejpam-4507	248	50	−n+ν	−n+ν	PROPN
ejpam-4507	248	51	(	(	PUNCT
ejpam-4507	248	52	dν	dν	VERB
ejpam-4507	248	53	dtν	dtν	NOUN
ejpam-4507	248	54	g	g	NOUN
ejpam-4507	248	55	)	)	PUNCT
ejpam-4507	248	56	,	,	PUNCT
ejpam-4507	248	57	(	(	PUNCT
ejpam-4507	248	58	9	9	X
ejpam-4507	248	59	)	)	PUNCT
ejpam-4507	248	60	where	where	SCONJ
ejpam-4507	248	61	the	the	DET
ejpam-4507	248	62	notation	notation	NOUN
ejpam-4507	248	63	(	(	PUNCT
ejpam-4507	248	64	n)k	n)k	ADV
ejpam-4507	248	65	is	be	AUX
ejpam-4507	248	66	designed	design	VERB
ejpam-4507	248	67	as	as	ADP
ejpam-4507	248	68	(	(	PUNCT
ejpam-4507	248	69	n)k	n)k	ADV
ejpam-4507	248	70	=	=	SYM
ejpam-4507	248	71	n(n−	n(n−	NUM
ejpam-4507	248	72	1)(n−	1)(n−	PROPN
ejpam-4507	248	73	2)	2)	NUM
ejpam-4507	248	74	...	...	PUNCT
ejpam-4507	248	75	(n−	(n−	PUNCT
ejpam-4507	248	76	k	k	X
ejpam-4507	249	1	+	+	PROPN
ejpam-4507	249	2	1	1	NUM
ejpam-4507	249	3	)	)	PUNCT
ejpam-4507	249	4	.	.	PUNCT
ejpam-4507	250	1	also	also	ADV
ejpam-4507	250	2	,	,	PUNCT
ejpam-4507	250	3	(	(	PUNCT
ejpam-4507	250	4	α−	α−	ADP
ejpam-4507	250	5	n−	n−	NOUN
ejpam-4507	250	6	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	250	7	=	=	SYM
ejpam-4507	250	8	(	(	PUNCT
ejpam-4507	250	9	−1)α−1−ν(n−	−1)α−1−ν(n−	NOUN
ejpam-4507	250	10	α+	α+	PUNCT
ejpam-4507	250	11	1)(n−	1)(n−	NUM
ejpam-4507	250	12	α+	α+	PUNCT
ejpam-4507	250	13	2)(n−	2)(n−	NUM
ejpam-4507	250	14	α+	α+	PUNCT
ejpam-4507	250	15	3	3	NUM
ejpam-4507	250	16	)	)	PUNCT
ejpam-4507	250	17	...	...	PUNCT
ejpam-4507	250	18	(	(	PUNCT
ejpam-4507	250	19	(	(	PUNCT
ejpam-4507	250	20	n−	n−	NOUN
ejpam-4507	250	21	α	α	X
ejpam-4507	250	22	)	)	PUNCT
ejpam-4507	250	23	+	+	CCONJ
ejpam-4507	250	24	α−	α−	ADP
ejpam-4507	250	25	ν	ν	X
ejpam-4507	250	26	−	−	PROPN
ejpam-4507	250	27	1	1	NUM
ejpam-4507	250	28	)	)	PUNCT
ejpam-4507	250	29	=	=	NOUN
ejpam-4507	250	30	(	(	PUNCT
ejpam-4507	250	31	−1)α−1−ν	−1)α−1−ν	NOUN
ejpam-4507	250	32	⟨n−	⟨n−	VERB
ejpam-4507	250	33	α+	α+	X
ejpam-4507	250	34	1⟩α−ν−1	1⟩α−ν−1	NOUN
ejpam-4507	250	35	.	.	PUNCT
ejpam-4507	251	1	on	on	ADP
ejpam-4507	251	2	the	the	DET
ejpam-4507	251	3	other	other	ADJ
ejpam-4507	251	4	hand	hand	NOUN
ejpam-4507	251	5	,	,	PUNCT
ejpam-4507	251	6	dν	dν	VERB
ejpam-4507	251	7	dtν	dtν	VERB
ejpam-4507	251	8	g	g	PROPN
ejpam-4507	251	9	=	=	PUNCT
ejpam-4507	251	10	dν	dν	ADV
ejpam-4507	251	11	dtν	dtν	ADV
ejpam-4507	251	12	(	(	PUNCT
ejpam-4507	251	13	∞∑	∞∑	NUM
ejpam-4507	251	14	n=0	n=0	NUM
ejpam-4507	251	15	b(α	b(α	NOUN
ejpam-4507	251	16	)	)	PUNCT
ejpam-4507	251	17	n	n	CCONJ
ejpam-4507	251	18	(	(	PUNCT
ejpam-4507	251	19	0	0	NUM
ejpam-4507	251	20	;	;	PUNCT
ejpam-4507	251	21	a	a	DET
ejpam-4507	251	22	,	,	PUNCT
ejpam-4507	251	23	b	b	NOUN
ejpam-4507	251	24	,	,	PUNCT
ejpam-4507	251	25	c	c	NOUN
ejpam-4507	251	26	)	)	PUNCT
ejpam-4507	251	27	(	(	PUNCT
ejpam-4507	251	28	t−	t−	PROPN
ejpam-4507	251	29	tk	tk	PROPN
ejpam-4507	251	30	)	)	PUNCT
ejpam-4507	251	31	n	n	PRON
ejpam-4507	251	32	n	n	CCONJ
ejpam-4507	251	33	!	!	PUNCT
ejpam-4507	251	34	·	·	PUNCT
ejpam-4507	252	1	ext	ext	NOUN
ejpam-4507	252	2	ln	ln	NOUN
ejpam-4507	252	3	c	c	NOUN
ejpam-4507	252	4	)	)	PUNCT
ejpam-4507	253	1	=	=	SYM
ejpam-4507	253	2	ν∑	ν∑	PROPN
ejpam-4507	254	1	l=0	l=0	PROPN
ejpam-4507	254	2	(	(	PUNCT
ejpam-4507	254	3	ν	ν	NOUN
ejpam-4507	254	4	l	l	NOUN
ejpam-4507	254	5	)	)	PUNCT
ejpam-4507	254	6	dν−l	dν−l	ADV
ejpam-4507	254	7	dtv−l	dtv−l	NOUN
ejpam-4507	254	8	et(x	et(x	PUNCT
ejpam-4507	254	9	ln	ln	PROPN
ejpam-4507	254	10	c	c	NOUN
ejpam-4507	254	11	)	)	PUNCT
ejpam-4507	254	12	·	·	PUNCT
ejpam-4507	254	13	dl	dl	PROPN
ejpam-4507	254	14	dtl	dtl	PROPN
ejpam-4507	254	15	(	(	PUNCT
ejpam-4507	254	16	∞∑	∞∑	NUM
ejpam-4507	254	17	n=0	n=0	NUM
ejpam-4507	254	18	b(α	b(α	NOUN
ejpam-4507	254	19	)	)	PUNCT
ejpam-4507	254	20	n	n	CCONJ
ejpam-4507	254	21	(	(	PUNCT
ejpam-4507	254	22	0	0	NUM
ejpam-4507	254	23	;	;	PUNCT
ejpam-4507	254	24	a	a	DET
ejpam-4507	254	25	,	,	PUNCT
ejpam-4507	254	26	b	b	NOUN
ejpam-4507	254	27	,	,	PUNCT
ejpam-4507	254	28	c	c	NOUN
ejpam-4507	254	29	)	)	PUNCT
ejpam-4507	254	30	(	(	PUNCT
ejpam-4507	254	31	t−	t−	PROPN
ejpam-4507	254	32	tk	tk	PROPN
ejpam-4507	254	33	)	)	PUNCT
ejpam-4507	254	34	n	n	PRON
ejpam-4507	254	35	n	n	CCONJ
ejpam-4507	254	36	!	!	PUNCT
ejpam-4507	254	37	)	)	PUNCT
ejpam-4507	255	1	=	=	PUNCT
ejpam-4507	255	2	ν∑	ν∑	PROPN
ejpam-4507	256	1	l=0	l=0	PROPN
ejpam-4507	256	2	(	(	PUNCT
ejpam-4507	256	3	ν	ν	X
ejpam-4507	256	4	l	l	NOUN
ejpam-4507	256	5	)	)	PUNCT
ejpam-4507	256	6	(	(	PUNCT
ejpam-4507	256	7	x	x	X
ejpam-4507	256	8	ln	ln	PROPN
ejpam-4507	256	9	c)ν−lext	c)ν−lext	PROPN
ejpam-4507	256	10	ln	ln	NOUN
ejpam-4507	256	11	c	c	PROPN
ejpam-4507	256	12	∑	∑	PROPN
ejpam-4507	256	13	n≥l	n≥l	PROPN
ejpam-4507	256	14	b(α	b(α	NOUN
ejpam-4507	256	15	)	)	PUNCT
ejpam-4507	256	16	n	n	CCONJ
ejpam-4507	256	17	(	(	PUNCT
ejpam-4507	256	18	0	0	NUM
ejpam-4507	256	19	;	;	PUNCT
ejpam-4507	256	20	a	a	DET
ejpam-4507	256	21	,	,	PUNCT
ejpam-4507	256	22	b	b	NOUN
ejpam-4507	256	23	,	,	PUNCT
ejpam-4507	256	24	c)(n)l	c)(n)l	PUNCT
ejpam-4507	256	25	(	(	PUNCT
ejpam-4507	256	26	t−	t−	PROPN
ejpam-4507	256	27	tk	tk	PROPN
ejpam-4507	256	28	)	)	PUNCT
ejpam-4507	256	29	n−l	n−l	NOUN
ejpam-4507	256	30	n	n	X
ejpam-4507	256	31	!	!	PUNCT
ejpam-4507	256	32	.	.	PUNCT
ejpam-4507	257	1	now	now	ADV
ejpam-4507	257	2	take	take	VERB
ejpam-4507	257	3	the	the	DET
ejpam-4507	257	4	limit	limit	NOUN
ejpam-4507	257	5	as	as	ADP
ejpam-4507	257	6	t	t	PROPN
ejpam-4507	257	7	→	→	SYM
ejpam-4507	257	8	tk	tk	PROPN
ejpam-4507	257	9	.	.	PROPN
ejpam-4507	257	10	then	then	ADV
ejpam-4507	257	11	lim	lim	PROPN
ejpam-4507	257	12	t→tk	t→tk	PROPN
ejpam-4507	258	1	dν	dν	VERB
ejpam-4507	258	2	dtν	dtν	PROPN
ejpam-4507	258	3	g	g	PROPN
ejpam-4507	258	4	=	=	PUNCT
ejpam-4507	258	5	ν∑	ν∑	PROPN
ejpam-4507	259	1	l=0	l=0	PROPN
ejpam-4507	259	2	(	(	PUNCT
ejpam-4507	259	3	ν	ν	X
ejpam-4507	259	4	l	l	NOUN
ejpam-4507	259	5	)	)	PUNCT
ejpam-4507	260	1	(	(	PUNCT
ejpam-4507	260	2	x	x	X
ejpam-4507	260	3	ln	ln	ADP
ejpam-4507	260	4	c)v−letkx	c)v−letkx	PROPN
ejpam-4507	260	5	ln	ln	PROPN
ejpam-4507	260	6	cb	cb	PROPN
ejpam-4507	260	7	(	(	PUNCT
ejpam-4507	260	8	α	α	NOUN
ejpam-4507	260	9	)	)	PUNCT
ejpam-4507	260	10	l	l	NOUN
ejpam-4507	260	11	(	(	PUNCT
ejpam-4507	260	12	0	0	NUM
ejpam-4507	260	13	;	;	PUNCT
ejpam-4507	260	14	a	a	DET
ejpam-4507	260	15	,	,	PUNCT
ejpam-4507	260	16	b	b	NOUN
ejpam-4507	260	17	,	,	PUNCT
ejpam-4507	260	18	c	c	NOUN
ejpam-4507	260	19	)	)	PUNCT
ejpam-4507	260	20	.	.	PUNCT
ejpam-4507	261	1	substituting	substitute	VERB
ejpam-4507	261	2	to	to	ADP
ejpam-4507	261	3	(	(	PUNCT
ejpam-4507	261	4	9	9	NUM
ejpam-4507	261	5	)	)	PUNCT
ejpam-4507	261	6	and	and	CCONJ
ejpam-4507	261	7	taking	take	VERB
ejpam-4507	261	8	the	the	DET
ejpam-4507	261	9	limit	limit	NOUN
ejpam-4507	261	10	as	as	ADP
ejpam-4507	261	11	t	t	PROPN
ejpam-4507	261	12	→	→	SYM
ejpam-4507	261	13	tk	tk	PROPN
ejpam-4507	261	14	will	will	AUX
ejpam-4507	261	15	yield	yield	VERB
ejpam-4507	261	16	lim	lim	PROPN
ejpam-4507	261	17	t→k	t→k	ADP
ejpam-4507	261	18	dα−1	dα−1	PROPN
ejpam-4507	261	19	dtα−1	dtα−1	PROPN
ejpam-4507	261	20	(	(	PUNCT
ejpam-4507	261	21	fg	fg	PROPN
ejpam-4507	261	22	)	)	PUNCT
ejpam-4507	261	23	=	=	PRON
ejpam-4507	261	24	α−1∑	α−1∑	NUM
ejpam-4507	261	25	ν=0	ν=0	PROPN
ejpam-4507	261	26	(	(	PUNCT
ejpam-4507	261	27	α−	α−	ADP
ejpam-4507	261	28	1	1	NUM
ejpam-4507	261	29	ν	ν	NOUN
ejpam-4507	261	30	)	)	PUNCT
ejpam-4507	261	31	(	(	PUNCT
ejpam-4507	261	32	α−	α−	ADP
ejpam-4507	261	33	n−	n−	NOUN
ejpam-4507	261	34	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	261	35	t−n+ν	t−n+ν	PUNCT
ejpam-4507	261	36	k	k	X
ejpam-4507	261	37	ν∑	ν∑	PROPN
ejpam-4507	262	1	l=0	l=0	PROPN
ejpam-4507	262	2	(	(	PUNCT
ejpam-4507	262	3	ν	ν	X
ejpam-4507	262	4	l	l	NOUN
ejpam-4507	262	5	)	)	PUNCT
ejpam-4507	263	1	(	(	PUNCT
ejpam-4507	263	2	x	x	X
ejpam-4507	263	3	ln	ln	PROPN
ejpam-4507	263	4	c)ν−letk	c)ν−letk	PROPN
ejpam-4507	263	5	ln	ln	PROPN
ejpam-4507	263	6	cb	cb	PROPN
ejpam-4507	263	7	(	(	PUNCT
ejpam-4507	263	8	α	α	NOUN
ejpam-4507	263	9	)	)	PUNCT
ejpam-4507	263	10	l	l	NOUN
ejpam-4507	263	11	(	(	PUNCT
ejpam-4507	263	12	0	0	NUM
ejpam-4507	263	13	;	;	PUNCT
ejpam-4507	263	14	a	a	DET
ejpam-4507	263	15	,	,	PUNCT
ejpam-4507	263	16	b	b	NOUN
ejpam-4507	263	17	,	,	PUNCT
ejpam-4507	263	18	c	c	NOUN
ejpam-4507	263	19	)	)	PUNCT
ejpam-4507	263	20	=	=	SYM
ejpam-4507	264	1	α−1∑	α−1∑	NUM
ejpam-4507	264	2	ν=0	ν=0	PROPN
ejpam-4507	264	3	(	(	PUNCT
ejpam-4507	264	4	α−	α−	ADP
ejpam-4507	264	5	1	1	NUM
ejpam-4507	264	6	ν	ν	NOUN
ejpam-4507	264	7	)	)	PUNCT
ejpam-4507	264	8	(	(	PUNCT
ejpam-4507	264	9	α−	α−	ADP
ejpam-4507	264	10	n−	n−	NOUN
ejpam-4507	264	11	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	264	12	t−n+ν	t−n+ν	PUNCT
ejpam-4507	264	13	k	k	PROPN
ejpam-4507	264	14	etk	etk	PROPN
ejpam-4507	264	15	ln	ln	PROPN
ejpam-4507	264	16	c	c	PROPN
ejpam-4507	264	17	(	(	PUNCT
ejpam-4507	264	18	ν∑	ν∑	X
ejpam-4507	264	19	l=0	l=0	PROPN
ejpam-4507	264	20	(	(	PUNCT
ejpam-4507	264	21	ν	ν	X
ejpam-4507	264	22	l	l	NOUN
ejpam-4507	264	23	)	)	PUNCT
ejpam-4507	264	24	(	(	PUNCT
ejpam-4507	264	25	x	x	X
ejpam-4507	264	26	ln	ln	ADJ
ejpam-4507	264	27	c)v−lb	c)v−lb	NOUN
ejpam-4507	264	28	(	(	PUNCT
ejpam-4507	264	29	α	α	NOUN
ejpam-4507	264	30	)	)	PUNCT
ejpam-4507	264	31	l	l	NOUN
ejpam-4507	264	32	(	(	PUNCT
ejpam-4507	264	33	0	0	NUM
ejpam-4507	264	34	;	;	PUNCT
ejpam-4507	264	35	a	a	DET
ejpam-4507	264	36	,	,	PUNCT
ejpam-4507	264	37	b	b	NOUN
ejpam-4507	264	38	,	,	PUNCT
ejpam-4507	264	39	c	c	NOUN
ejpam-4507	264	40	)	)	PUNCT
ejpam-4507	264	41	)	)	PUNCT
ejpam-4507	264	42	.	.	PUNCT
ejpam-4507	265	1	(	(	PUNCT
ejpam-4507	265	2	10	10	NUM
ejpam-4507	265	3	)	)	PUNCT
ejpam-4507	265	4	c.	c.	NOUN
ejpam-4507	265	5	corcino	corcino	PROPN
ejpam-4507	265	6	,	,	PUNCT
ejpam-4507	265	7	r.	r.	PROPN
ejpam-4507	265	8	corcino	corcino	PROPN
ejpam-4507	265	9	/	/	SYM
ejpam-4507	265	10	eur	eur	PROPN
ejpam-4507	265	11	.	.	PUNCT
ejpam-4507	266	1	j.	j.	PROPN
ejpam-4507	266	2	pure	pure	PROPN
ejpam-4507	266	3	appl	appl	PROPN
ejpam-4507	266	4	.	.	PROPN
ejpam-4507	266	5	math	math	PROPN
ejpam-4507	266	6	,	,	PUNCT
ejpam-4507	266	7	15	15	NUM
ejpam-4507	266	8	(	(	PUNCT
ejpam-4507	266	9	4	4	NUM
ejpam-4507	266	10	)	)	PUNCT
ejpam-4507	266	11	(	(	PUNCT
ejpam-4507	266	12	2022	2022	NUM
ejpam-4507	266	13	)	)	PUNCT
ejpam-4507	266	14	,	,	PUNCT
ejpam-4507	266	15	1662	1662	NUM
ejpam-4507	266	16	-	-	SYM
ejpam-4507	266	17	1682	1682	NUM
ejpam-4507	266	18	1676	1676	NUM
ejpam-4507	266	19	applying	apply	VERB
ejpam-4507	266	20	lemma	lemma	PROPN
ejpam-4507	266	21	3.2	3.2	NUM
ejpam-4507	266	22	to	to	PART
ejpam-4507	266	23	(	(	PUNCT
ejpam-4507	266	24	10	10	NUM
ejpam-4507	266	25	)	)	PUNCT
ejpam-4507	266	26	,	,	PUNCT
ejpam-4507	266	27	lim	lim	PROPN
ejpam-4507	266	28	t→k	t→k	ADP
ejpam-4507	266	29	dα−1	dα−1	PROPN
ejpam-4507	266	30	dtα−1	dtα−1	PROPN
ejpam-4507	266	31	(	(	PUNCT
ejpam-4507	266	32	fg	fg	PROPN
ejpam-4507	266	33	)	)	PUNCT
ejpam-4507	266	34	=	=	PRON
ejpam-4507	266	35	α−1∑	α−1∑	NUM
ejpam-4507	266	36	ν=0	ν=0	PROPN
ejpam-4507	266	37	(	(	PUNCT
ejpam-4507	266	38	α−	α−	ADP
ejpam-4507	266	39	1	1	NUM
ejpam-4507	266	40	ν	ν	NOUN
ejpam-4507	266	41	)	)	PUNCT
ejpam-4507	266	42	(	(	PUNCT
ejpam-4507	266	43	α−	α−	ADP
ejpam-4507	266	44	n−	n−	NOUN
ejpam-4507	266	45	1)α−1−νt	1)α−1−νt	NOUN
ejpam-4507	266	46	−n+ν	−n+ν	PROPN
ejpam-4507	266	47	k	k	PROPN
ejpam-4507	266	48	etk	etk	PROPN
ejpam-4507	266	49	ln	ln	ADJ
ejpam-4507	266	50	cb(α	cb(α	NOUN
ejpam-4507	266	51	)	)	PUNCT
ejpam-4507	266	52	ν	ν	NOUN
ejpam-4507	266	53	(	(	PUNCT
ejpam-4507	266	54	x	x	NOUN
ejpam-4507	266	55	;	;	PUNCT
ejpam-4507	266	56	a	a	DET
ejpam-4507	266	57	,	,	PUNCT
ejpam-4507	266	58	b	b	NOUN
ejpam-4507	266	59	,	,	PUNCT
ejpam-4507	266	60	c	c	NOUN
ejpam-4507	266	61	)	)	PUNCT
ejpam-4507	266	62	.	.	PUNCT
ejpam-4507	267	1	thus	thus	ADV
ejpam-4507	267	2	,	,	PUNCT
ejpam-4507	267	3	res(fα(t	res(fα(t	ADJ
ejpam-4507	267	4	)	)	PUNCT
ejpam-4507	267	5	,	,	PUNCT
ejpam-4507	267	6	t	t	PROPN
ejpam-4507	267	7	=	=	SYM
ejpam-4507	267	8	tk	tk	PROPN
ejpam-4507	267	9	)	)	PUNCT
ejpam-4507	267	10	=	=	SYM
ejpam-4507	267	11	etk(x	etk(x	PROPN
ejpam-4507	267	12	ln	ln	ADJ
ejpam-4507	267	13	c−α	c−α	PROPN
ejpam-4507	267	14	ln	ln	PROPN
ejpam-4507	267	15	b	b	X
ejpam-4507	267	16	)	)	PUNCT
ejpam-4507	267	17	tnk	tnk	PROPN
ejpam-4507	267	18	α−1∑	α−1∑	NUM
ejpam-4507	267	19	ν=0	ν=0	PROPN
ejpam-4507	267	20	(	(	PUNCT
ejpam-4507	267	21	α−	α−	ADP
ejpam-4507	267	22	n−	n−	NOUN
ejpam-4507	267	23	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	267	24	ν!(α−	ν!(α−	VERB
ejpam-4507	267	25	1−	1−	NUM
ejpam-4507	267	26	ν	ν	NOUN
ejpam-4507	267	27	)	)	PUNCT
ejpam-4507	267	28	!	!	PUNCT
ejpam-4507	268	1	tνkb	tνkb	NOUN
ejpam-4507	268	2	(	(	PUNCT
ejpam-4507	268	3	α	α	NOUN
ejpam-4507	268	4	)	)	PUNCT
ejpam-4507	268	5	ν	ν	NOUN
ejpam-4507	268	6	(	(	PUNCT
ejpam-4507	268	7	x	x	NOUN
ejpam-4507	268	8	;	;	PUNCT
ejpam-4507	268	9	a	a	DET
ejpam-4507	268	10	,	,	PUNCT
ejpam-4507	268	11	b	b	NOUN
ejpam-4507	268	12	,	,	PUNCT
ejpam-4507	268	13	c	c	NOUN
ejpam-4507	268	14	)	)	PUNCT
ejpam-4507	268	15	.	.	PUNCT
ejpam-4507	269	1	(	(	PUNCT
ejpam-4507	269	2	11	11	NUM
ejpam-4507	269	3	)	)	PUNCT
ejpam-4507	269	4	the	the	DET
ejpam-4507	269	5	desired	desire	VERB
ejpam-4507	269	6	fourier	fourier	NOUN
ejpam-4507	269	7	series	series	NOUN
ejpam-4507	269	8	is	be	AUX
ejpam-4507	269	9	obtained	obtain	VERB
ejpam-4507	269	10	by	by	ADP
ejpam-4507	269	11	substituting	substitute	VERB
ejpam-4507	269	12	(	(	PUNCT
ejpam-4507	269	13	11	11	NUM
ejpam-4507	269	14	)	)	PUNCT
ejpam-4507	269	15	to	to	ADP
ejpam-4507	269	16	(	(	PUNCT
ejpam-4507	269	17	4	4	NUM
ejpam-4507	269	18	)	)	PUNCT
ejpam-4507	269	19	.	.	PUNCT
ejpam-4507	270	1	taking	take	VERB
ejpam-4507	270	2	α	α	NOUN
ejpam-4507	270	3	=	=	SYM
ejpam-4507	270	4	1	1	NUM
ejpam-4507	270	5	,	,	PUNCT
ejpam-4507	270	6	the	the	DET
ejpam-4507	270	7	fourier	fourier	ADJ
ejpam-4507	270	8	series	series	NOUN
ejpam-4507	270	9	in	in	ADP
ejpam-4507	270	10	theorem	theorem	ADJ
ejpam-4507	270	11	3.3	3.3	NUM
ejpam-4507	270	12	reduces	reduce	VERB
ejpam-4507	270	13	to	to	ADP
ejpam-4507	270	14	that	that	PRON
ejpam-4507	270	15	in	in	ADP
ejpam-4507	270	16	theorem	theorem	NOUN
ejpam-4507	270	17	2.2	2.2	NUM
ejpam-4507	270	18	.	.	PUNCT
ejpam-4507	271	1	for	for	ADP
ejpam-4507	271	2	α	α	NOUN
ejpam-4507	271	3	=	=	SYM
ejpam-4507	271	4	2	2	NUM
ejpam-4507	271	5	,	,	PUNCT
ejpam-4507	271	6	theorem	theorem	VERB
ejpam-4507	271	7	3.3	3.3	NUM
ejpam-4507	271	8	gives	give	VERB
ejpam-4507	271	9	the	the	DET
ejpam-4507	271	10	fourier	fourier	ADJ
ejpam-4507	271	11	series	series	NOUN
ejpam-4507	271	12	of	of	ADP
ejpam-4507	271	13	the	the	DET
ejpam-4507	271	14	bernoulli	bernoulli	NOUN
ejpam-4507	271	15	-	-	PUNCT
ejpam-4507	271	16	type	type	NOUN
ejpam-4507	271	17	polynomials	polynomial	NOUN
ejpam-4507	271	18	of	of	ADP
ejpam-4507	271	19	order	order	NOUN
ejpam-4507	271	20	2	2	X
ejpam-4507	271	21	.	.	PUNCT
ejpam-4507	272	1	this	this	PRON
ejpam-4507	272	2	is	be	AUX
ejpam-4507	272	3	given	give	VERB
ejpam-4507	272	4	by	by	ADP
ejpam-4507	272	5	b	b	PROPN
ejpam-4507	272	6	(	(	PUNCT
ejpam-4507	272	7	2	2	NUM
ejpam-4507	272	8	)	)	PUNCT
ejpam-4507	272	9	n	n	NOUN
ejpam-4507	272	10	(	(	PUNCT
ejpam-4507	272	11	x	x	X
ejpam-4507	272	12	;	;	PUNCT
ejpam-4507	272	13	a	a	DET
ejpam-4507	272	14	,	,	PUNCT
ejpam-4507	272	15	b	b	NOUN
ejpam-4507	272	16	,	,	PUNCT
ejpam-4507	272	17	c	c	NOUN
ejpam-4507	272	18	)	)	PUNCT
ejpam-4507	272	19	n	n	CCONJ
ejpam-4507	272	20	!	!	PUNCT
ejpam-4507	273	1	=	=	SYM
ejpam-4507	273	2	−1	−1	NOUN
ejpam-4507	273	3	b2	b2	NOUN
ejpam-4507	273	4	∑	∑	ADP
ejpam-4507	273	5	k∈z	k∈z	PROPN
ejpam-4507	273	6	,	,	PUNCT
ejpam-4507	273	7	k	k	PROPN
ejpam-4507	273	8	̸=0	̸=0	ADJ
ejpam-4507	273	9	(	(	PUNCT
ejpam-4507	273	10	−n+	−n+	NOUN
ejpam-4507	273	11	1	1	NUM
ejpam-4507	274	1	+	+	CCONJ
ejpam-4507	274	2	x	x	SYM
ejpam-4507	274	3	ln	ln	PROPN
ejpam-4507	274	4	c	c	NOUN
ejpam-4507	274	5	)	)	PUNCT
ejpam-4507	274	6	e2kπi(x	e2kπi(x	PROPN
ejpam-4507	275	1	ln	ln	INTJ
ejpam-4507	275	2	c−2	c−2	PROPN
ejpam-4507	275	3	ln	ln	PROPN
ejpam-4507	275	4	b	b	PROPN
ejpam-4507	275	5	)	)	PUNCT
ejpam-4507	275	6	(	(	PUNCT
ejpam-4507	275	7	2kπi)n	2kπi)n	NUM
ejpam-4507	275	8	,	,	PUNCT
ejpam-4507	275	9	valid	valid	ADJ
ejpam-4507	275	10	under	under	ADP
ejpam-4507	275	11	the	the	DET
ejpam-4507	275	12	conditions	condition	NOUN
ejpam-4507	275	13	in	in	ADP
ejpam-4507	275	14	theorem	theorem	ADJ
ejpam-4507	275	15	3.3	3.3	NUM
ejpam-4507	275	16	.	.	PUNCT
ejpam-4507	276	1	lemma	lemma	PROPN
ejpam-4507	276	2	3.4	3.4	NUM
ejpam-4507	276	3	.	.	PUNCT
ejpam-4507	277	1	let	let	VERB
ejpam-4507	277	2	a	a	DET
ejpam-4507	277	3	,	,	PUNCT
ejpam-4507	277	4	b	b	NOUN
ejpam-4507	277	5	,	,	PUNCT
ejpam-4507	277	6	c	c	AUX
ejpam-4507	277	7	be	be	AUX
ejpam-4507	277	8	positive	positive	ADJ
ejpam-4507	277	9	real	real	ADJ
ejpam-4507	277	10	numbers	number	NOUN
ejpam-4507	277	11	with	with	ADP
ejpam-4507	277	12	b	b	PROPN
ejpam-4507	277	13	>	>	X
ejpam-4507	277	14	a	a	PROPN
ejpam-4507	277	15	,	,	PUNCT
ejpam-4507	277	16	n	n	CCONJ
ejpam-4507	277	17	,	,	PUNCT
ejpam-4507	277	18	α	α	PROPN
ejpam-4507	277	19	∈	∈	PROPN
ejpam-4507	277	20	z+	z+	NUM
ejpam-4507	277	21	with	with	ADP
ejpam-4507	277	22	n	n	PRON
ejpam-4507	277	23	≥	≥	NOUN
ejpam-4507	277	24	α	α	NOUN
ejpam-4507	277	25	,	,	PUNCT
ejpam-4507	277	26	n	n	PROPN
ejpam-4507	277	27	>	>	ADP
ejpam-4507	277	28	1	1	NUM
ejpam-4507	277	29	and	and	CCONJ
ejpam-4507	277	30	cn	cn	PROPN
ejpam-4507	277	31	be	be	AUX
ejpam-4507	277	32	the	the	DET
ejpam-4507	277	33	circle	circle	NOUN
ejpam-4507	277	34	about	about	ADP
ejpam-4507	277	35	zero	zero	NUM
ejpam-4507	277	36	of	of	ADP
ejpam-4507	277	37	radius	radius	NOUN
ejpam-4507	277	38	r	r	NOUN
ejpam-4507	277	39	=	=	SYM
ejpam-4507	278	1	(	(	PUNCT
ejpam-4507	278	2	(	(	PUNCT
ejpam-4507	278	3	2n	2n	NUM
ejpam-4507	278	4	+	+	CCONJ
ejpam-4507	278	5	1)π	1)π	NUM
ejpam-4507	278	6	−	−	NOUN
ejpam-4507	278	7	ε)/b	ε)/b	NOUN
ejpam-4507	278	8	,	,	PUNCT
ejpam-4507	278	9	where	where	SCONJ
ejpam-4507	278	10	0	0	X
ejpam-4507	278	11	<	<	X
ejpam-4507	278	12	ε	ε	X
ejpam-4507	278	13	<	<	X
ejpam-4507	278	14	1	1	NUM
ejpam-4507	278	15	and	and	CCONJ
ejpam-4507	278	16	b	b	NOUN
ejpam-4507	278	17	=	=	SYM
ejpam-4507	278	18	ln	ln	PROPN
ejpam-4507	278	19	b−	b−	PROPN
ejpam-4507	278	20	ln	ln	ADJ
ejpam-4507	278	21	a.	a.	NOUN
ejpam-4507	278	22	for	for	ADP
ejpam-4507	278	23	ln	ln	PROPN
ejpam-4507	278	24	c	c	PROPN
ejpam-4507	278	25	>	>	PUNCT
ejpam-4507	278	26	0	0	PUNCT
ejpam-4507	278	27	and	and	CCONJ
ejpam-4507	278	28	0	0	NUM
ejpam-4507	278	29	<	<	X
ejpam-4507	278	30	x	x	X
ejpam-4507	278	31	<	<	X
ejpam-4507	278	32	(	(	PUNCT
ejpam-4507	278	33	α	α	X
ejpam-4507	278	34	ln	ln	PROPN
ejpam-4507	278	35	a−	a−	PROPN
ejpam-4507	278	36	b	b	PROPN
ejpam-4507	278	37	π	π	NOUN
ejpam-4507	278	38	−	−	PROPN
ejpam-4507	278	39	ε	ε	PROPN
ejpam-4507	278	40	)	)	PUNCT
ejpam-4507	278	41	/	/	SYM
ejpam-4507	278	42	ln	ln	NOUN
ejpam-4507	278	43	c	c	NOUN
ejpam-4507	278	44	(	(	PUNCT
ejpam-4507	278	45	12	12	NUM
ejpam-4507	278	46	)	)	PUNCT
ejpam-4507	278	47	we	we	PRON
ejpam-4507	278	48	have	have	VERB
ejpam-4507	278	49	lim	lim	PROPN
ejpam-4507	278	50	n→+∞	n→+∞	PROPN
ejpam-4507	278	51	∫	∫	PROPN
ejpam-4507	278	52	cn	cn	PROPN
ejpam-4507	278	53	cxt	cxt	PROPN
ejpam-4507	278	54	(	(	PUNCT
ejpam-4507	278	55	bt	bt	NOUN
ejpam-4507	278	56	+	+	CCONJ
ejpam-4507	278	57	at)α	at)α	PROPN
ejpam-4507	278	58	dt	dt	X
ejpam-4507	278	59	tn+1	tn+1	NOUN
ejpam-4507	278	60	=	=	SYM
ejpam-4507	278	61	0	0	NUM
ejpam-4507	278	62	.	.	PUNCT
ejpam-4507	279	1	proof	proof	NOUN
ejpam-4507	279	2	.	.	PUNCT
ejpam-4507	280	1	from	from	ADP
ejpam-4507	280	2	the	the	DET
ejpam-4507	280	3	proof	proof	NOUN
ejpam-4507	280	4	of	of	ADP
ejpam-4507	280	5	lemma	lemma	PROPN
ejpam-4507	280	6	3.2	3.2	NUM
ejpam-4507	280	7	,	,	PUNCT
ejpam-4507	280	8	|bt	|bt	NUM
ejpam-4507	280	9	+	+	NUM
ejpam-4507	280	10	at|α	at|α	NOUN
ejpam-4507	280	11	=	=	PUNCT
ejpam-4507	280	12	eαγ	eαγ	PROPN
ejpam-4507	280	13	ln	ln	NOUN
ejpam-4507	280	14	a[e2γb	a[e2γb	PROPN
ejpam-4507	280	15	+	+	CCONJ
ejpam-4507	280	16	2eγb	2eγb	NUM
ejpam-4507	280	17	cos	cos	NOUN
ejpam-4507	280	18	ρb	ρb	PROPN
ejpam-4507	280	19	+	+	NOUN
ejpam-4507	280	20	1	1	NUM
ejpam-4507	280	21	]	]	PUNCT
ejpam-4507	280	22	α	α	PRON
ejpam-4507	280	23	2	2	NUM
ejpam-4507	280	24	,	,	PUNCT
ejpam-4507	280	25	t	t	PROPN
ejpam-4507	280	26	∈	∈	PROPN
ejpam-4507	280	27	cn	cn	PROPN
ejpam-4507	280	28	where	where	SCONJ
ejpam-4507	280	29	t	t	NOUN
ejpam-4507	280	30	=	=	SYM
ejpam-4507	280	31	γ	γ	X
ejpam-4507	280	32	+	+	X
ejpam-4507	280	33	iρ	iρ	NOUN
ejpam-4507	280	34	=	=	SYM
ejpam-4507	280	35	(	(	PUNCT
ejpam-4507	280	36	2n	2n	NUM
ejpam-4507	280	37	+	+	CCONJ
ejpam-4507	280	38	1)π	1)π	NUM
ejpam-4507	280	39	−	−	PROPN
ejpam-4507	280	40	ε	ε	PROPN
ejpam-4507	280	41	b	b	PROPN
ejpam-4507	280	42	(	(	PUNCT
ejpam-4507	280	43	cos	cos	PROPN
ejpam-4507	280	44	θ	θ	PROPN
ejpam-4507	280	45	+	+	CCONJ
ejpam-4507	280	46	i	i	PRON
ejpam-4507	280	47	sin	sin	VERB
ejpam-4507	280	48	θ	θ	PROPN
ejpam-4507	280	49	)	)	PUNCT
ejpam-4507	280	50	,	,	PUNCT
ejpam-4507	280	51	0	0	NUM
ejpam-4507	280	52	≤	≤	NUM
ejpam-4507	280	53	θ	θ	NOUN
ejpam-4507	280	54	≤	≤	ADJ
ejpam-4507	280	55	2π	2π	NOUN
ejpam-4507	280	56	.	.	PUNCT
ejpam-4507	281	1	thus	thus	ADV
ejpam-4507	281	2	,	,	PUNCT
ejpam-4507	281	3	γ	γ	X
ejpam-4507	281	4	=	=	SYM
ejpam-4507	281	5	(	(	PUNCT
ejpam-4507	281	6	2n	2n	NUM
ejpam-4507	281	7	+	+	CCONJ
ejpam-4507	281	8	1)π	1)π	NUM
ejpam-4507	281	9	−	−	PROPN
ejpam-4507	281	10	ε	ε	PROPN
ejpam-4507	281	11	b	b	PROPN
ejpam-4507	281	12	cos	cos	PROPN
ejpam-4507	281	13	θ	θ	PROPN
ejpam-4507	281	14	,	,	PUNCT
ejpam-4507	281	15	ρ	ρ	NOUN
ejpam-4507	281	16	=	=	SYM
ejpam-4507	281	17	(	(	PUNCT
ejpam-4507	281	18	2n	2n	NUM
ejpam-4507	281	19	+	+	CCONJ
ejpam-4507	281	20	1)π	1)π	NUM
ejpam-4507	281	21	−	−	PROPN
ejpam-4507	281	22	ε	ε	PROPN
ejpam-4507	281	23	b	b	PROPN
ejpam-4507	281	24	sin	sin	PROPN
ejpam-4507	281	25	θ	θ	PROPN
ejpam-4507	281	26	.	.	PUNCT
ejpam-4507	281	27	c.	c.	PROPN
ejpam-4507	281	28	corcino	corcino	PROPN
ejpam-4507	281	29	,	,	PUNCT
ejpam-4507	281	30	r.	r.	PROPN
ejpam-4507	281	31	corcino	corcino	PROPN
ejpam-4507	281	32	/	/	SYM
ejpam-4507	281	33	eur	eur	PROPN
ejpam-4507	281	34	.	.	PUNCT
ejpam-4507	282	1	j.	j.	PROPN
ejpam-4507	282	2	pure	pure	PROPN
ejpam-4507	282	3	appl	appl	PROPN
ejpam-4507	282	4	.	.	PROPN
ejpam-4507	282	5	math	math	PROPN
ejpam-4507	282	6	,	,	PUNCT
ejpam-4507	282	7	15	15	NUM
ejpam-4507	282	8	(	(	PUNCT
ejpam-4507	282	9	4	4	NUM
ejpam-4507	282	10	)	)	PUNCT
ejpam-4507	282	11	(	(	PUNCT
ejpam-4507	282	12	2022	2022	NUM
ejpam-4507	282	13	)	)	PUNCT
ejpam-4507	282	14	,	,	PUNCT
ejpam-4507	282	15	1662	1662	NUM
ejpam-4507	282	16	-	-	SYM
ejpam-4507	282	17	1682	1682	NUM
ejpam-4507	282	18	1677	1677	NUM
ejpam-4507	282	19	for	for	ADP
ejpam-4507	282	20	x	x	SYM
ejpam-4507	282	21	satisfying	satisfy	VERB
ejpam-4507	282	22	(	(	PUNCT
ejpam-4507	282	23	12	12	NUM
ejpam-4507	282	24	)	)	PUNCT
ejpam-4507	283	1	,	,	PUNCT
ejpam-4507	283	2	it	it	PRON
ejpam-4507	283	3	follows	follow	VERB
ejpam-4507	283	4	that	that	SCONJ
ejpam-4507	283	5	α	α	PRON
ejpam-4507	283	6	ln	ln	X
ejpam-4507	283	7	a−	a−	PROPN
ejpam-4507	283	8	x	x	X
ejpam-4507	284	1	ln	ln	PROPN
ejpam-4507	284	2	c	c	X
ejpam-4507	284	3	>	>	X
ejpam-4507	284	4	b	b	PROPN
ejpam-4507	284	5	π	π	X
ejpam-4507	284	6	−	−	PROPN
ejpam-4507	284	7	ε	ε	PROPN
ejpam-4507	284	8	≥	≥	PROPN
ejpam-4507	284	9	b	b	PROPN
ejpam-4507	284	10	(	(	PUNCT
ejpam-4507	284	11	2n	2n	NUM
ejpam-4507	284	12	+	+	CCONJ
ejpam-4507	284	13	1)π	1)π	NUM
ejpam-4507	284	14	−	−	PROPN
ejpam-4507	284	15	ε	ε	PROPN
ejpam-4507	284	16	,	,	PUNCT
ejpam-4507	284	17	∀n	∀n	NUM
ejpam-4507	284	18	≥	≥	NOUN
ejpam-4507	284	19	1	1	NUM
ejpam-4507	284	20	.	.	PUNCT
ejpam-4507	285	1	then	then	ADV
ejpam-4507	285	2	1	1	NUM
ejpam-4507	285	3	eγ[α	eγ[α	NOUN
ejpam-4507	285	4	ln	ln	ADJ
ejpam-4507	285	5	a−x	a−x	NOUN
ejpam-4507	285	6	ln	ln	NOUN
ejpam-4507	285	7	c	c	NOUN
ejpam-4507	285	8	]	]	X
ejpam-4507	285	9	=	=	SYM
ejpam-4507	285	10	1	1	NUM
ejpam-4507	285	11	e	e	X
ejpam-4507	285	12	(	(	PUNCT
ejpam-4507	285	13	2n+1)−ε	2n+1)−ε	PROPN
ejpam-4507	285	14	b	b	X
ejpam-4507	285	15	cos	cos	X
ejpam-4507	285	16	θ[α	θ[α	ADJ
ejpam-4507	285	17	ln	ln	ADJ
ejpam-4507	285	18	a−x	a−x	NOUN
ejpam-4507	285	19	ln	ln	NOUN
ejpam-4507	285	20	c	c	NOUN
ejpam-4507	285	21	]	]	X
ejpam-4507	285	22	<	<	X
ejpam-4507	285	23	1	1	NUM
ejpam-4507	285	24	ecos	ecos	X
ejpam-4507	285	25	θ	θ	X
ejpam-4507	285	26	<	<	X
ejpam-4507	285	27	e.	e.	PROPN
ejpam-4507	285	28	consequently,∣∣∣∣	consequently,∣∣∣∣	PROPN
ejpam-4507	285	29	cxt	cxt	PROPN
ejpam-4507	285	30	(	(	PUNCT
ejpam-4507	285	31	bt	bt	NOUN
ejpam-4507	285	32	+	+	CCONJ
ejpam-4507	285	33	at)α	at)α	PROPN
ejpam-4507	285	34	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4507	285	35	=	=	SYM
ejpam-4507	285	36	|cxt|	|cxt|	NOUN
ejpam-4507	285	37	|bt	|bt	NUM
ejpam-4507	285	38	+	+	NUM
ejpam-4507	285	39	at|α	at|α	NOUN
ejpam-4507	285	40	=	=	SYM
ejpam-4507	285	41	1	1	NUM
ejpam-4507	285	42	eγ[α	eγ[α	NOUN
ejpam-4507	285	43	ln	ln	ADJ
ejpam-4507	285	44	a−x	a−x	NOUN
ejpam-4507	285	45	ln	ln	NOUN
ejpam-4507	285	46	c][e2γb	c][e2γb	X
ejpam-4507	285	47	+	+	CCONJ
ejpam-4507	285	48	2eγb	2eγb	NUM
ejpam-4507	285	49	cos	cos	NOUN
ejpam-4507	285	50	ρb	ρb	PROPN
ejpam-4507	285	51	+	+	NOUN
ejpam-4507	285	52	1	1	NUM
ejpam-4507	285	53	]	]	PUNCT
ejpam-4507	285	54	α	α	PRON
ejpam-4507	285	55	2	2	NUM
ejpam-4507	285	56	<	<	X
ejpam-4507	285	57	e	e	X
ejpam-4507	285	58	(	(	PUNCT
ejpam-4507	285	59	e2γb	e2γb	PUNCT
ejpam-4507	285	60	+	+	CCONJ
ejpam-4507	285	61	2eγb	2eγb	NUM
ejpam-4507	285	62	cos	cos	NOUN
ejpam-4507	285	63	ρb	ρb	PROPN
ejpam-4507	285	64	+	+	NOUN
ejpam-4507	285	65	1	1	X
ejpam-4507	285	66	)	)	PUNCT
ejpam-4507	285	67	α	α	NOUN
ejpam-4507	285	68	2	2	NUM
ejpam-4507	285	69	.	.	PUNCT
ejpam-4507	286	1	the	the	DET
ejpam-4507	286	2	expression	expression	NOUN
ejpam-4507	286	3	e2γb	e2γb	PUNCT
ejpam-4507	287	1	+	+	CCONJ
ejpam-4507	287	2	2eγb	2eγb	NUM
ejpam-4507	287	3	cos	cos	NOUN
ejpam-4507	287	4	ρb	ρb	PROPN
ejpam-4507	287	5	+	+	SYM
ejpam-4507	287	6	1	1	NUM
ejpam-4507	287	7	̸=	̸=	PROPN
ejpam-4507	287	8	0	0	NUM
ejpam-4507	287	9	∀t	∀t	PROPN
ejpam-4507	287	10	∈	∈	PROPN
ejpam-4507	287	11	cn	cn	PROPN
ejpam-4507	287	12	as	as	SCONJ
ejpam-4507	287	13	discussed	discuss	VERB
ejpam-4507	287	14	in	in	ADP
ejpam-4507	287	15	lemma	lemma	PROPN
ejpam-4507	287	16	2.3	2.3	NUM
ejpam-4507	287	17	.	.	PUNCT
ejpam-4507	288	1	thus	thus	ADV
ejpam-4507	288	2	,	,	PUNCT
ejpam-4507	288	3	∃	∃	PROPN
ejpam-4507	288	4	an	an	DET
ejpam-4507	288	5	integer	integer	NOUN
ejpam-4507	288	6	m	m	VERB
ejpam-4507	288	7	s.t	s.t	PROPN
ejpam-4507	288	8	.	.	PUNCT
ejpam-4507	288	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	288	10	cxt	cxt	PROPN
ejpam-4507	288	11	(	(	PUNCT
ejpam-4507	288	12	bt	bt	NOUN
ejpam-4507	288	13	+	+	CCONJ
ejpam-4507	288	14	at)α	at)α	PROPN
ejpam-4507	288	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4507	288	16	<	<	X
ejpam-4507	288	17	m	m	PROPN
ejpam-4507	288	18	,	,	PUNCT
ejpam-4507	288	19	∀t	∀t	PROPN
ejpam-4507	288	20	∈	∈	PROPN
ejpam-4507	288	21	cn	cn	PROPN
ejpam-4507	288	22	.	.	PUNCT
ejpam-4507	289	1	hence	hence	ADV
ejpam-4507	289	2	,	,	PUNCT
ejpam-4507	289	3	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-4507	289	4	cn	cn	PROPN
ejpam-4507	289	5	cxt	cxt	PROPN
ejpam-4507	289	6	(	(	PUNCT
ejpam-4507	289	7	bt	bt	NOUN
ejpam-4507	289	8	+	+	CCONJ
ejpam-4507	289	9	at)α	at)α	PROPN
ejpam-4507	289	10	dt	dt	PUNCT
ejpam-4507	289	11	tn+1	tn+1	NOUN
ejpam-4507	289	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4507	289	13	≤	≤	NUM
ejpam-4507	289	14	m	m	VERB
ejpam-4507	289	15	∫	∫	PROPN
ejpam-4507	289	16	cn	cn	PROPN
ejpam-4507	289	17	|dt|	|dt|	PROPN
ejpam-4507	289	18	|tn+1|	|tn+1|	PROPN
ejpam-4507	289	19	=	=	PUNCT
ejpam-4507	289	20	m	m	NOUN
ejpam-4507	289	21	·	·	PUNCT
ejpam-4507	289	22	(	(	PUNCT
ejpam-4507	289	23	2n	2n	NUM
ejpam-4507	289	24	+	+	CCONJ
ejpam-4507	289	25	1)π	1)π	NUM
ejpam-4507	289	26	−	−	PROPN
ejpam-4507	289	27	ε	ε	PROPN
ejpam-4507	289	28	b	b	PROPN
ejpam-4507	289	29	·	·	PUNCT
ejpam-4507	289	30	2π	2π	NOUN
ejpam-4507	289	31	(	(	PUNCT
ejpam-4507	289	32	(	(	PUNCT
ejpam-4507	289	33	2n	2n	NUM
ejpam-4507	289	34	+	+	CCONJ
ejpam-4507	289	35	1)π	1)π	NUM
ejpam-4507	289	36	−	−	PROPN
ejpam-4507	289	37	ε	ε	PROPN
ejpam-4507	289	38	b	b	PROPN
ejpam-4507	289	39	)	)	PUNCT
ejpam-4507	289	40	n+1	n+1	PROPN
ejpam-4507	289	41	=	=	SYM
ejpam-4507	289	42	2πmbn	2πmbn	NUM
ejpam-4507	289	43	(	(	PUNCT
ejpam-4507	289	44	(	(	PUNCT
ejpam-4507	289	45	2n	2n	NUM
ejpam-4507	289	46	+	+	CCONJ
ejpam-4507	289	47	1)π	1)π	NUM
ejpam-4507	289	48	−	−	ADP
ejpam-4507	289	49	ε)n+1	ε)n+1	PROPN
ejpam-4507	289	50	,	,	PUNCT
ejpam-4507	289	51	n	n	CCONJ
ejpam-4507	289	52	>	>	X
ejpam-4507	289	53	1	1	X
ejpam-4507	289	54	.	.	X
ejpam-4507	290	1	−→	−→	NOUN
ejpam-4507	290	2	0	0	NUM
ejpam-4507	291	1	as	as	ADP
ejpam-4507	291	2	n	n	PRON
ejpam-4507	291	3	→	→	PUNCT
ejpam-4507	291	4	+	+	NUM
ejpam-4507	291	5	∞.	∞.	PROPN
ejpam-4507	291	6	lemma	lemma	PROPN
ejpam-4507	291	7	3.5	3.5	NUM
ejpam-4507	291	8	.	.	PUNCT
ejpam-4507	292	1	for	for	ADP
ejpam-4507	292	2	a	a	DET
ejpam-4507	292	3	,	,	PUNCT
ejpam-4507	292	4	b	b	NOUN
ejpam-4507	292	5	,	,	PUNCT
ejpam-4507	292	6	c	c	PROPN
ejpam-4507	292	7	∈	∈	PROPN
ejpam-4507	292	8	r+	r+	X
ejpam-4507	292	9	,	,	PUNCT
ejpam-4507	292	10	x	x	PUNCT
ejpam-4507	292	11	∈	∈	PROPN
ejpam-4507	292	12	r	r	NOUN
ejpam-4507	292	13	,	,	PUNCT
ejpam-4507	292	14	ν	ν	PROPN
ejpam-4507	292	15	,	,	PUNCT
ejpam-4507	292	16	α	α	PROPN
ejpam-4507	292	17	∈	∈	PROPN
ejpam-4507	292	18	z+	z+	NUM
ejpam-4507	292	19	with	with	ADP
ejpam-4507	292	20	fixed	fix	VERB
ejpam-4507	292	21	ν	ν	NOUN
ejpam-4507	292	22	≥	≥	PROPN
ejpam-4507	292	23	α	α	PRON
ejpam-4507	292	24	≥	≥	NUM
ejpam-4507	292	25	2	2	NUM
ejpam-4507	292	26	,	,	PUNCT
ejpam-4507	292	27	e(α	e(α	NUM
ejpam-4507	292	28	)	)	PUNCT
ejpam-4507	292	29	ν	ν	NOUN
ejpam-4507	292	30	(	(	PUNCT
ejpam-4507	292	31	x	x	NOUN
ejpam-4507	292	32	;	;	PUNCT
ejpam-4507	292	33	a	a	DET
ejpam-4507	292	34	,	,	PUNCT
ejpam-4507	292	35	b	b	NOUN
ejpam-4507	292	36	,	,	PUNCT
ejpam-4507	292	37	c	c	NOUN
ejpam-4507	292	38	)	)	PUNCT
ejpam-4507	292	39	=	=	SYM
ejpam-4507	292	40	ν∑	ν∑	PROPN
ejpam-4507	293	1	l=0	l=0	PROPN
ejpam-4507	293	2	(	(	PUNCT
ejpam-4507	293	3	ν	ν	X
ejpam-4507	293	4	l	l	NOUN
ejpam-4507	293	5	)	)	PUNCT
ejpam-4507	294	1	e	e	NOUN
ejpam-4507	294	2	(	(	PUNCT
ejpam-4507	294	3	α	α	NOUN
ejpam-4507	294	4	)	)	PUNCT
ejpam-4507	294	5	l	l	NOUN
ejpam-4507	294	6	(	(	PUNCT
ejpam-4507	294	7	0	0	NUM
ejpam-4507	294	8	;	;	PUNCT
ejpam-4507	294	9	a	a	DET
ejpam-4507	294	10	,	,	PUNCT
ejpam-4507	294	11	b	b	NOUN
ejpam-4507	294	12	,	,	PUNCT
ejpam-4507	294	13	c)(x	c)(x	PROPN
ejpam-4507	294	14	ln	ln	ADV
ejpam-4507	294	15	c)v−l	c)v−l	PROPN
ejpam-4507	294	16	.	.	PUNCT
ejpam-4507	295	1	proof	proof	NOUN
ejpam-4507	295	2	.	.	PUNCT
ejpam-4507	296	1	the	the	DET
ejpam-4507	296	2	proof	proof	NOUN
ejpam-4507	296	3	is	be	AUX
ejpam-4507	296	4	done	do	VERB
ejpam-4507	296	5	similarly	similarly	ADV
ejpam-4507	296	6	as	as	ADP
ejpam-4507	296	7	that	that	PRON
ejpam-4507	296	8	of	of	ADP
ejpam-4507	296	9	lemma	lemma	PROPN
ejpam-4507	296	10	3.2	3.2	NUM
ejpam-4507	296	11	.	.	PUNCT
ejpam-4507	297	1	theorem	theorem	VERB
ejpam-4507	297	2	3.6	3.6	NUM
ejpam-4507	297	3	.	.	PUNCT
ejpam-4507	298	1	let	let	VERB
ejpam-4507	298	2	a	a	DET
ejpam-4507	298	3	,	,	PUNCT
ejpam-4507	298	4	b	b	NOUN
ejpam-4507	298	5	,	,	PUNCT
ejpam-4507	298	6	c	c	AUX
ejpam-4507	298	7	be	be	AUX
ejpam-4507	298	8	positive	positive	ADJ
ejpam-4507	298	9	real	real	ADJ
ejpam-4507	298	10	numbers	number	NOUN
ejpam-4507	298	11	with	with	ADP
ejpam-4507	298	12	b	b	PROPN
ejpam-4507	298	13	>	>	X
ejpam-4507	298	14	a	a	PROPN
ejpam-4507	298	15	,	,	PUNCT
ejpam-4507	298	16	n	n	NOUN
ejpam-4507	298	17	,	,	PUNCT
ejpam-4507	298	18	n	n	CCONJ
ejpam-4507	298	19	,	,	PUNCT
ejpam-4507	298	20	α	α	PROPN
ejpam-4507	298	21	∈	∈	PROPN
ejpam-4507	298	22	z+	z+	X
ejpam-4507	298	23	,	,	PUNCT
ejpam-4507	298	24	n	n	PRON
ejpam-4507	298	25	≥	≥	NOUN
ejpam-4507	298	26	α	α	PRON
ejpam-4507	298	27	≥	≥	NUM
ejpam-4507	298	28	2	2	NUM
ejpam-4507	298	29	,	,	PUNCT
ejpam-4507	298	30	n	n	CCONJ
ejpam-4507	298	31	>	>	SYM
ejpam-4507	298	32	1	1	NUM
ejpam-4507	298	33	and	and	CCONJ
ejpam-4507	298	34	cn	cn	PROPN
ejpam-4507	298	35	be	be	AUX
ejpam-4507	298	36	the	the	DET
ejpam-4507	298	37	circle	circle	NOUN
ejpam-4507	298	38	about	about	ADP
ejpam-4507	298	39	zero	zero	NUM
ejpam-4507	298	40	of	of	ADP
ejpam-4507	298	41	radius	radius	NOUN
ejpam-4507	298	42	r	r	NOUN
ejpam-4507	298	43	=	=	SYM
ejpam-4507	298	44	(	(	PUNCT
ejpam-4507	298	45	(	(	PUNCT
ejpam-4507	298	46	2n	2n	NUM
ejpam-4507	298	47	+1)π−	+1)π−	ADJ
ejpam-4507	298	48	ε)/b	ε)/b	NOUN
ejpam-4507	298	49	,	,	PUNCT
ejpam-4507	298	50	where	where	SCONJ
ejpam-4507	298	51	0	0	X
ejpam-4507	298	52	<	<	X
ejpam-4507	298	53	ε	ε	X
ejpam-4507	298	54	<	<	X
ejpam-4507	298	55	1	1	NUM
ejpam-4507	298	56	c.	c.	PROPN
ejpam-4507	298	57	corcino	corcino	PROPN
ejpam-4507	298	58	,	,	PUNCT
ejpam-4507	298	59	r.	r.	PROPN
ejpam-4507	298	60	corcino	corcino	PROPN
ejpam-4507	298	61	/	/	SYM
ejpam-4507	298	62	eur	eur	PROPN
ejpam-4507	298	63	.	.	PUNCT
ejpam-4507	299	1	j.	j.	PROPN
ejpam-4507	299	2	pure	pure	PROPN
ejpam-4507	299	3	appl	appl	PROPN
ejpam-4507	299	4	.	.	PROPN
ejpam-4507	299	5	math	math	PROPN
ejpam-4507	299	6	,	,	PUNCT
ejpam-4507	299	7	15	15	NUM
ejpam-4507	299	8	(	(	PUNCT
ejpam-4507	299	9	4	4	NUM
ejpam-4507	299	10	)	)	PUNCT
ejpam-4507	299	11	(	(	PUNCT
ejpam-4507	299	12	2022	2022	NUM
ejpam-4507	299	13	)	)	PUNCT
ejpam-4507	299	14	,	,	PUNCT
ejpam-4507	299	15	1662	1662	NUM
ejpam-4507	299	16	-	-	SYM
ejpam-4507	299	17	1682	1682	NUM
ejpam-4507	299	18	1678	1678	NUM
ejpam-4507	299	19	and	and	CCONJ
ejpam-4507	299	20	b	b	X
ejpam-4507	299	21	=	=	SYM
ejpam-4507	299	22	ln	ln	PROPN
ejpam-4507	299	23	b	b	PROPN
ejpam-4507	299	24	−	−	NOUN
ejpam-4507	299	25	ln	ln	ADJ
ejpam-4507	299	26	a.	a.	NOUN
ejpam-4507	300	1	the	the	DET
ejpam-4507	300	2	fourier	fourier	ADJ
ejpam-4507	300	3	series	series	NOUN
ejpam-4507	300	4	of	of	ADP
ejpam-4507	300	5	the	the	DET
ejpam-4507	300	6	euler	euler	NOUN
ejpam-4507	300	7	-	-	PUNCT
ejpam-4507	300	8	type	type	NOUN
ejpam-4507	300	9	polynomials	polynomial	NOUN
ejpam-4507	300	10	e	e	X
ejpam-4507	300	11	(	(	PUNCT
ejpam-4507	300	12	α	α	NOUN
ejpam-4507	300	13	)	)	PUNCT
ejpam-4507	300	14	n	n	PROPN
ejpam-4507	300	15	(	(	PUNCT
ejpam-4507	300	16	x	x	X
ejpam-4507	300	17	;	;	PUNCT
ejpam-4507	300	18	a	a	DET
ejpam-4507	300	19	,	,	PUNCT
ejpam-4507	300	20	b	b	NOUN
ejpam-4507	300	21	,	,	PUNCT
ejpam-4507	300	22	c	c	NOUN
ejpam-4507	300	23	)	)	PUNCT
ejpam-4507	300	24	of	of	ADP
ejpam-4507	300	25	order	order	NOUN
ejpam-4507	300	26	α	α	NOUN
ejpam-4507	300	27	is	be	AUX
ejpam-4507	300	28	given	give	VERB
ejpam-4507	300	29	by	by	ADP
ejpam-4507	300	30	e	e	PROPN
ejpam-4507	300	31	(	(	PUNCT
ejpam-4507	300	32	α	α	NOUN
ejpam-4507	300	33	)	)	PUNCT
ejpam-4507	300	34	n	n	PROPN
ejpam-4507	300	35	(	(	PUNCT
ejpam-4507	300	36	x	x	X
ejpam-4507	300	37	;	;	PUNCT
ejpam-4507	300	38	a	a	DET
ejpam-4507	300	39	,	,	PUNCT
ejpam-4507	300	40	b	b	NOUN
ejpam-4507	300	41	,	,	PUNCT
ejpam-4507	300	42	c	c	NOUN
ejpam-4507	300	43	)	)	PUNCT
ejpam-4507	300	44	n	n	CCONJ
ejpam-4507	300	45	!	!	PUNCT
ejpam-4507	301	1	=	=	SYM
ejpam-4507	302	1	−2α	−2α	PROPN
ejpam-4507	302	2	(	(	PUNCT
ejpam-4507	302	3	α−	α−	ADP
ejpam-4507	302	4	1	1	NUM
ejpam-4507	302	5	)	)	PUNCT
ejpam-4507	302	6	!	!	PUNCT
ejpam-4507	303	1	∑	∑	PUNCT
ejpam-4507	303	2	k∈z	k∈z	PROPN
ejpam-4507	303	3	α−1∑	α−1∑	NUM
ejpam-4507	304	1	ν=0	ν=0	PROPN
ejpam-4507	304	2	(	(	PUNCT
ejpam-4507	304	3	α−	α−	ADP
ejpam-4507	304	4	1	1	NUM
ejpam-4507	304	5	ν	ν	NOUN
ejpam-4507	304	6	)	)	PUNCT
ejpam-4507	304	7	(	(	PUNCT
ejpam-4507	304	8	−n−	−n−	NOUN
ejpam-4507	304	9	1)α−1−νb	1)α−1−νb	NOUN
ejpam-4507	304	10	(	(	PUNCT
ejpam-4507	304	11	α	α	NOUN
ejpam-4507	304	12	)	)	PUNCT
ejpam-4507	304	13	ν	ν	NOUN
ejpam-4507	304	14	(	(	PUNCT
ejpam-4507	304	15	x	x	NOUN
ejpam-4507	304	16	;	;	PUNCT
ejpam-4507	304	17	a	a	PRON
ejpam-4507	304	18	,	,	PUNCT
ejpam-4507	304	19	b	b	NOUN
ejpam-4507	304	20	,	,	PUNCT
ejpam-4507	304	21	c	c	NOUN
ejpam-4507	304	22	)	)	PUNCT
ejpam-4507	304	23	etk(x	etk(x	PROPN
ejpam-4507	304	24	ln	ln	NOUN
ejpam-4507	304	25	c−α	c−α	PROPN
ejpam-4507	304	26	ln	ln	PROPN
ejpam-4507	304	27	b	b	PROPN
ejpam-4507	304	28	)	)	PUNCT
ejpam-4507	304	29	tn+α−ν	tn+α−ν	PROPN
ejpam-4507	304	30	k	k	PROPN
ejpam-4507	304	31	,	,	PUNCT
ejpam-4507	304	32	valid	valid	ADJ
ejpam-4507	304	33	for	for	ADP
ejpam-4507	304	34	0	0	NUM
ejpam-4507	304	35	<	<	X
ejpam-4507	304	36	x	x	X
ejpam-4507	304	37	<	<	X
ejpam-4507	304	38	(	(	PUNCT
ejpam-4507	304	39	α	α	X
ejpam-4507	304	40	ln	ln	PROPN
ejpam-4507	304	41	a−	a−	PROPN
ejpam-4507	304	42	b	b	PROPN
ejpam-4507	304	43	π	π	NOUN
ejpam-4507	304	44	−	−	PROPN
ejpam-4507	304	45	ε	ε	PROPN
ejpam-4507	304	46	)	)	PUNCT
ejpam-4507	304	47	/	/	SYM
ejpam-4507	304	48	ln	ln	NOUN
ejpam-4507	304	49	c	c	NOUN
ejpam-4507	304	50	,	,	PUNCT
ejpam-4507	304	51	ln	ln	NOUN
ejpam-4507	304	52	c	c	NOUN
ejpam-4507	304	53	>	>	X
ejpam-4507	304	54	0	0	X
ejpam-4507	304	55	.	.	PUNCT
ejpam-4507	304	56	proof	proof	NOUN
ejpam-4507	304	57	.	.	PUNCT
ejpam-4507	305	1	applying	apply	VERB
ejpam-4507	305	2	the	the	DET
ejpam-4507	305	3	cauchy	cauchy	NOUN
ejpam-4507	305	4	-	-	PUNCT
ejpam-4507	305	5	integral	integral	ADJ
ejpam-4507	305	6	formula	formula	NOUN
ejpam-4507	305	7	to	to	ADP
ejpam-4507	305	8	(	(	PUNCT
ejpam-4507	305	9	2	2	NUM
ejpam-4507	305	10	)	)	PUNCT
ejpam-4507	305	11	,	,	PUNCT
ejpam-4507	305	12	e	e	X
ejpam-4507	305	13	(	(	PUNCT
ejpam-4507	305	14	α	α	NOUN
ejpam-4507	305	15	)	)	PUNCT
ejpam-4507	305	16	n	n	PROPN
ejpam-4507	305	17	(	(	PUNCT
ejpam-4507	305	18	x	x	X
ejpam-4507	305	19	;	;	PUNCT
ejpam-4507	305	20	a	a	DET
ejpam-4507	305	21	,	,	PUNCT
ejpam-4507	305	22	b	b	NOUN
ejpam-4507	305	23	,	,	PUNCT
ejpam-4507	305	24	c	c	NOUN
ejpam-4507	305	25	)	)	PUNCT
ejpam-4507	305	26	n	n	CCONJ
ejpam-4507	305	27	!	!	PUNCT
ejpam-4507	306	1	=	=	SYM
ejpam-4507	306	2	1	1	NUM
ejpam-4507	306	3	2πi	2πi	ADJ
ejpam-4507	306	4	∫	∫	PROPN
ejpam-4507	307	1	c	c	PROPN
ejpam-4507	307	2	2αcxt	2αcxt	PROPN
ejpam-4507	307	3	(	(	PUNCT
ejpam-4507	307	4	bt	bt	X
ejpam-4507	307	5	+	+	CCONJ
ejpam-4507	307	6	at)α	at)α	PROPN
ejpam-4507	307	7	dt	dt	X
ejpam-4507	307	8	tn+1	tn+1	NOUN
ejpam-4507	307	9	,	,	PUNCT
ejpam-4507	307	10	where	where	SCONJ
ejpam-4507	307	11	c	c	PROPN
ejpam-4507	307	12	is	be	AUX
ejpam-4507	307	13	a	a	DET
ejpam-4507	307	14	circle	circle	NOUN
ejpam-4507	307	15	about	about	ADP
ejpam-4507	307	16	zero	zero	NUM
ejpam-4507	307	17	of	of	ADP
ejpam-4507	307	18	radius	radius	NOUN
ejpam-4507	307	19	less	less	ADJ
ejpam-4507	307	20	than	than	ADP
ejpam-4507	307	21	π	π	PROPN
ejpam-4507	307	22	b	b	X
ejpam-4507	307	23	.	.	PUNCT
ejpam-4507	308	1	let	let	VERB
ejpam-4507	308	2	gα(t	gα(t	NOUN
ejpam-4507	308	3	)	)	PUNCT
ejpam-4507	308	4	=	=	SYM
ejpam-4507	308	5	cxt	cxt	X
ejpam-4507	308	6	(	(	PUNCT
ejpam-4507	308	7	bt	bt	X
ejpam-4507	308	8	+	+	CCONJ
ejpam-4507	308	9	at)αtn+1	at)αtn+1	ADJ
ejpam-4507	308	10	.	.	PUNCT
ejpam-4507	309	1	then	then	ADV
ejpam-4507	309	2	e	e	X
ejpam-4507	309	3	(	(	PUNCT
ejpam-4507	309	4	α	α	NOUN
ejpam-4507	309	5	)	)	PUNCT
ejpam-4507	309	6	n	n	PROPN
ejpam-4507	309	7	(	(	PUNCT
ejpam-4507	309	8	x	x	X
ejpam-4507	309	9	;	;	PUNCT
ejpam-4507	309	10	a	a	DET
ejpam-4507	309	11	,	,	PUNCT
ejpam-4507	309	12	b	b	NOUN
ejpam-4507	309	13	,	,	PUNCT
ejpam-4507	309	14	c	c	NOUN
ejpam-4507	309	15	)	)	PUNCT
ejpam-4507	309	16	2α(n	2α(n	NUM
ejpam-4507	309	17	!	!	PUNCT
ejpam-4507	309	18	)	)	PUNCT
ejpam-4507	310	1	=	=	SYM
ejpam-4507	310	2	1	1	NUM
ejpam-4507	310	3	2πi	2πi	ADJ
ejpam-4507	310	4	∫	∫	PROPN
ejpam-4507	310	5	c	c	PROPN
ejpam-4507	310	6	gα(t)dt	gα(t)dt	PROPN
ejpam-4507	310	7	.	.	PUNCT
ejpam-4507	311	1	the	the	DET
ejpam-4507	311	2	function	function	NOUN
ejpam-4507	311	3	gα(t	gα(t	NOUN
ejpam-4507	311	4	)	)	PUNCT
ejpam-4507	311	5	has	have	VERB
ejpam-4507	311	6	a	a	DET
ejpam-4507	311	7	pole	pole	NOUN
ejpam-4507	311	8	of	of	ADP
ejpam-4507	311	9	order	order	NOUN
ejpam-4507	311	10	n	n	NOUN
ejpam-4507	311	11	+	+	NOUN
ejpam-4507	311	12	1	1	NUM
ejpam-4507	311	13	at	at	ADP
ejpam-4507	311	14	t	t	NOUN
ejpam-4507	311	15	=	=	SYM
ejpam-4507	311	16	0	0	PROPN
ejpam-4507	311	17	and	and	CCONJ
ejpam-4507	311	18	a	a	DET
ejpam-4507	311	19	pole	pole	NOUN
ejpam-4507	311	20	of	of	ADP
ejpam-4507	311	21	order	order	NOUN
ejpam-4507	311	22	α	α	NOUN
ejpam-4507	311	23	at	at	ADP
ejpam-4507	311	24	the	the	DET
ejpam-4507	311	25	zeros	zero	NOUN
ejpam-4507	311	26	of	of	ADP
ejpam-4507	311	27	bt	bt	NOUN
ejpam-4507	311	28	+	+	CCONJ
ejpam-4507	311	29	at	at	ADP
ejpam-4507	311	30	which	which	PRON
ejpam-4507	311	31	are	be	AUX
ejpam-4507	311	32	given	give	VERB
ejpam-4507	311	33	by	by	ADP
ejpam-4507	311	34	tk	tk	PROPN
ejpam-4507	311	35	=	=	SYM
ejpam-4507	311	36	(	(	PUNCT
ejpam-4507	311	37	(	(	PUNCT
ejpam-4507	311	38	2k	2k	NUM
ejpam-4507	311	39	+	+	CCONJ
ejpam-4507	311	40	1)πi)/b	1)πi)/b	NUM
ejpam-4507	311	41	,	,	PUNCT
ejpam-4507	311	42	k	k	PROPN
ejpam-4507	311	43	∈	∈	PROPN
ejpam-4507	311	44	z.	z.	NOUN
ejpam-4507	311	45	applying	apply	VERB
ejpam-4507	311	46	the	the	DET
ejpam-4507	311	47	residue	residue	NOUN
ejpam-4507	311	48	theorem	theorem	NOUN
ejpam-4507	311	49	and	and	CCONJ
ejpam-4507	311	50	taking	take	VERB
ejpam-4507	311	51	the	the	DET
ejpam-4507	311	52	limit	limit	NOUN
ejpam-4507	311	53	as	as	ADP
ejpam-4507	311	54	n	n	PROPN
ejpam-4507	311	55	→	→	SYM
ejpam-4507	311	56	+	+	PROPN
ejpam-4507	311	57	∞	∞	PROPN
ejpam-4507	311	58	,	,	PUNCT
ejpam-4507	311	59	lim	lim	PROPN
ejpam-4507	311	60	n→+∞	n→+∞	VERB
ejpam-4507	311	61	1	1	NUM
ejpam-4507	311	62	2πi	2πi	NOUN
ejpam-4507	311	63	∫	∫	PROPN
ejpam-4507	311	64	c	c	PROPN
ejpam-4507	311	65	gα(t)dt	gα(t)dt	PROPN
ejpam-4507	311	66	=	=	SYM
ejpam-4507	311	67	res(gα(t	res(gα(t	PROPN
ejpam-4507	311	68	)	)	PUNCT
ejpam-4507	311	69	,	,	PUNCT
ejpam-4507	311	70	t	t	PROPN
ejpam-4507	311	71	=	=	SYM
ejpam-4507	311	72	0	0	NUM
ejpam-4507	311	73	)	)	PUNCT
ejpam-4507	312	1	+	+	CCONJ
ejpam-4507	312	2	∑	∑	ADP
ejpam-4507	312	3	k∈z	k∈z	NOUN
ejpam-4507	312	4	res(gα(t	res(gα(t	PROPN
ejpam-4507	312	5	)	)	PUNCT
ejpam-4507	312	6	,	,	PUNCT
ejpam-4507	312	7	t	t	PROPN
ejpam-4507	312	8	=	=	SYM
ejpam-4507	312	9	tk	tk	PROPN
ejpam-4507	312	10	)	)	PUNCT
ejpam-4507	312	11	.	.	PUNCT
ejpam-4507	313	1	it	it	PRON
ejpam-4507	313	2	follows	follow	VERB
ejpam-4507	313	3	from	from	ADP
ejpam-4507	313	4	lemma	lemma	PROPN
ejpam-4507	313	5	3.4	3.4	NUM
ejpam-4507	313	6	that	that	DET
ejpam-4507	313	7	e	e	PROPN
ejpam-4507	313	8	(	(	PUNCT
ejpam-4507	313	9	α	α	NOUN
ejpam-4507	313	10	)	)	PUNCT
ejpam-4507	313	11	n	n	PROPN
ejpam-4507	313	12	(	(	PUNCT
ejpam-4507	313	13	x	x	X
ejpam-4507	313	14	;	;	PUNCT
ejpam-4507	313	15	a	a	DET
ejpam-4507	313	16	,	,	PUNCT
ejpam-4507	313	17	b	b	NOUN
ejpam-4507	313	18	,	,	PUNCT
ejpam-4507	313	19	c	c	NOUN
ejpam-4507	313	20	)	)	PUNCT
ejpam-4507	313	21	2α(n	2α(n	NUM
ejpam-4507	313	22	!	!	PUNCT
ejpam-4507	313	23	)	)	PUNCT
ejpam-4507	314	1	=	=	PUNCT
ejpam-4507	315	1	−	−	PROPN
ejpam-4507	315	2	∑	∑	PUNCT
ejpam-4507	315	3	k∈z	k∈z	NOUN
ejpam-4507	315	4	res(gα(t	res(gα(t	PROPN
ejpam-4507	315	5	)	)	PUNCT
ejpam-4507	315	6	,	,	PUNCT
ejpam-4507	315	7	t	t	PROPN
ejpam-4507	315	8	=	=	SYM
ejpam-4507	315	9	tk	tk	PROPN
ejpam-4507	315	10	)	)	PUNCT
ejpam-4507	315	11	.	.	PUNCT
ejpam-4507	316	1	computing	compute	VERB
ejpam-4507	316	2	the	the	DET
ejpam-4507	316	3	residues	residue	NOUN
ejpam-4507	316	4	at	at	ADP
ejpam-4507	316	5	tk	tk	NOUN
ejpam-4507	316	6	:	:	PUNCT
ejpam-4507	316	7	res(gα(t	res(gα(t	PROPN
ejpam-4507	316	8	)	)	PUNCT
ejpam-4507	316	9	,	,	PUNCT
ejpam-4507	316	10	t	t	PROPN
ejpam-4507	316	11	=	=	SYM
ejpam-4507	316	12	tk	tk	PROPN
ejpam-4507	316	13	)	)	PUNCT
ejpam-4507	316	14	=	=	SYM
ejpam-4507	316	15	1	1	NUM
ejpam-4507	316	16	(	(	PUNCT
ejpam-4507	316	17	α−	α−	ADP
ejpam-4507	316	18	1	1	NUM
ejpam-4507	316	19	)	)	PUNCT
ejpam-4507	316	20	!	!	PUNCT
ejpam-4507	317	1	lim	lim	PROPN
ejpam-4507	317	2	t→tk	t→tk	PROPN
ejpam-4507	317	3	dα−1	dα−1	PROPN
ejpam-4507	317	4	dtα−1	dtα−1	PROPN
ejpam-4507	317	5	(	(	PUNCT
ejpam-4507	317	6	(	(	PUNCT
ejpam-4507	317	7	t−	t−	PROPN
ejpam-4507	317	8	tk	tk	PROPN
ejpam-4507	317	9	)	)	PUNCT
ejpam-4507	317	10	α	α	PROPN
ejpam-4507	317	11	cxt	cxt	NOUN
ejpam-4507	317	12	(	(	PUNCT
ejpam-4507	317	13	bt	bt	X
ejpam-4507	317	14	+	+	X
ejpam-4507	317	15	at)α	at)α	PROPN
ejpam-4507	317	16	·	·	PUNCT
ejpam-4507	317	17	1	1	NUM
ejpam-4507	317	18	tn+1	tn+1	NOUN
ejpam-4507	317	19	)	)	PUNCT
ejpam-4507	317	20	.	.	PUNCT
ejpam-4507	318	1	(	(	PUNCT
ejpam-4507	318	2	13	13	NUM
ejpam-4507	318	3	)	)	PUNCT
ejpam-4507	318	4	now	now	ADV
ejpam-4507	318	5	use	use	VERB
ejpam-4507	318	6	(	(	PUNCT
ejpam-4507	318	7	7	7	NUM
ejpam-4507	318	8	)	)	PUNCT
ejpam-4507	318	9	.	.	PUNCT
ejpam-4507	319	1	with	with	ADP
ejpam-4507	319	2	tk	tk	PROPN
ejpam-4507	319	3	=	=	SYM
ejpam-4507	319	4	(	(	PUNCT
ejpam-4507	319	5	2k	2k	NOUN
ejpam-4507	319	6	+	+	CCONJ
ejpam-4507	319	7	1)πi	1)πi	NUM
ejpam-4507	319	8	/	/	SYM
ejpam-4507	319	9	b	b	NOUN
ejpam-4507	319	10	,	,	PUNCT
ejpam-4507	319	11	etkb	etkb	X
ejpam-4507	319	12	=	=	PUNCT
ejpam-4507	319	13	e(2k+1)πi	e(2k+1)πi	PROPN
ejpam-4507	319	14	=	=	SYM
ejpam-4507	319	15	−1	−1	NOUN
ejpam-4507	319	16	.	.	PUNCT
ejpam-4507	320	1	thus	thus	ADV
ejpam-4507	320	2	,	,	PUNCT
ejpam-4507	320	3	(	(	PUNCT
ejpam-4507	320	4	7	7	X
ejpam-4507	320	5	)	)	PUNCT
ejpam-4507	320	6	becomes	become	VERB
ejpam-4507	320	7	,	,	PUNCT
ejpam-4507	320	8	(	(	PUNCT
ejpam-4507	320	9	t−	t−	PROPN
ejpam-4507	320	10	tk	tk	PROPN
ejpam-4507	320	11	)	)	PUNCT
ejpam-4507	320	12	αeαtk	αeαtk	NOUN
ejpam-4507	320	13	ln	ln	PROPN
ejpam-4507	320	14	b	b	PROPN
ejpam-4507	320	15	(	(	PUNCT
ejpam-4507	320	16	et	et	PROPN
ejpam-4507	320	17	ln	ln	PROPN
ejpam-4507	320	18	b	b	PROPN
ejpam-4507	321	1	+	+	CCONJ
ejpam-4507	321	2	et	et	NOUN
ejpam-4507	321	3	ln	ln	ADJ
ejpam-4507	321	4	a)α	a)α	X
ejpam-4507	321	5	=	=	SYM
ejpam-4507	321	6	∞∑	∞∑	NUM
ejpam-4507	321	7	n=0	n=0	NUM
ejpam-4507	321	8	b(α	b(α	NOUN
ejpam-4507	321	9	)	)	PUNCT
ejpam-4507	321	10	n	n	CCONJ
ejpam-4507	321	11	(	(	PUNCT
ejpam-4507	321	12	0	0	NUM
ejpam-4507	321	13	;	;	PUNCT
ejpam-4507	321	14	a	a	DET
ejpam-4507	321	15	,	,	PUNCT
ejpam-4507	321	16	b	b	NOUN
ejpam-4507	321	17	,	,	PUNCT
ejpam-4507	321	18	c	c	NOUN
ejpam-4507	321	19	)	)	PUNCT
ejpam-4507	321	20	(	(	PUNCT
ejpam-4507	321	21	t−	t−	PROPN
ejpam-4507	321	22	tk	tk	PROPN
ejpam-4507	321	23	)	)	PUNCT
ejpam-4507	321	24	n	n	PRON
ejpam-4507	321	25	n	n	NOUN
ejpam-4507	321	26	!	!	PUNCT
ejpam-4507	322	1	c.	c.	PROPN
ejpam-4507	322	2	corcino	corcino	PROPN
ejpam-4507	322	3	,	,	PUNCT
ejpam-4507	322	4	r.	r.	PROPN
ejpam-4507	322	5	corcino	corcino	PROPN
ejpam-4507	322	6	/	/	SYM
ejpam-4507	322	7	eur	eur	PROPN
ejpam-4507	322	8	.	.	PUNCT
ejpam-4507	323	1	j.	j.	PROPN
ejpam-4507	323	2	pure	pure	PROPN
ejpam-4507	323	3	appl	appl	PROPN
ejpam-4507	323	4	.	.	PROPN
ejpam-4507	323	5	math	math	PROPN
ejpam-4507	323	6	,	,	PUNCT
ejpam-4507	323	7	15	15	NUM
ejpam-4507	323	8	(	(	PUNCT
ejpam-4507	323	9	4	4	NUM
ejpam-4507	323	10	)	)	PUNCT
ejpam-4507	323	11	(	(	PUNCT
ejpam-4507	323	12	2022	2022	NUM
ejpam-4507	323	13	)	)	PUNCT
ejpam-4507	323	14	,	,	PUNCT
ejpam-4507	323	15	1662	1662	NUM
ejpam-4507	323	16	-	-	SYM
ejpam-4507	323	17	1682	1682	NUM
ejpam-4507	323	18	1679	1679	NUM
ejpam-4507	323	19	(	(	PUNCT
ejpam-4507	323	20	t−	t−	PROPN
ejpam-4507	323	21	tk	tk	PROPN
ejpam-4507	323	22	)	)	PUNCT
ejpam-4507	323	23	α	α	PROPN
ejpam-4507	323	24	(	(	PUNCT
ejpam-4507	323	25	bt	bt	NOUN
ejpam-4507	323	26	+	+	CCONJ
ejpam-4507	323	27	at)α	at)α	PROPN
ejpam-4507	323	28	=	=	SYM
ejpam-4507	323	29	e−αtk	e−αtk	PROPN
ejpam-4507	323	30	ln	ln	PROPN
ejpam-4507	323	31	b	b	PROPN
ejpam-4507	324	1	∞∑	∞∑	PROPN
ejpam-4507	324	2	n=0	n=0	NUM
ejpam-4507	324	3	b(α	b(α	NOUN
ejpam-4507	324	4	)	)	PUNCT
ejpam-4507	324	5	n	n	CCONJ
ejpam-4507	324	6	(	(	PUNCT
ejpam-4507	324	7	0	0	NUM
ejpam-4507	324	8	;	;	PUNCT
ejpam-4507	324	9	a	a	DET
ejpam-4507	324	10	,	,	PUNCT
ejpam-4507	324	11	b	b	NOUN
ejpam-4507	324	12	,	,	PUNCT
ejpam-4507	324	13	c	c	NOUN
ejpam-4507	324	14	)	)	PUNCT
ejpam-4507	324	15	(	(	PUNCT
ejpam-4507	324	16	t−	t−	PROPN
ejpam-4507	324	17	tk	tk	PROPN
ejpam-4507	324	18	)	)	PUNCT
ejpam-4507	324	19	n	n	PRON
ejpam-4507	324	20	n	n	CCONJ
ejpam-4507	324	21	!	!	PUNCT
ejpam-4507	324	22	.	.	PUNCT
ejpam-4507	325	1	(	(	PUNCT
ejpam-4507	325	2	14	14	X
ejpam-4507	325	3	)	)	PUNCT
ejpam-4507	325	4	substituting	substituting	NOUN
ejpam-4507	325	5	(	(	PUNCT
ejpam-4507	325	6	14	14	NUM
ejpam-4507	325	7	)	)	PUNCT
ejpam-4507	325	8	to	to	ADP
ejpam-4507	325	9	(	(	PUNCT
ejpam-4507	325	10	13	13	NUM
ejpam-4507	325	11	)	)	PUNCT
ejpam-4507	325	12	,	,	PUNCT
ejpam-4507	325	13	res(gα(t	res(gα(t	PROPN
ejpam-4507	325	14	)	)	PUNCT
ejpam-4507	325	15	,	,	PUNCT
ejpam-4507	325	16	t	t	PROPN
ejpam-4507	325	17	=	=	SYM
ejpam-4507	325	18	tk	tk	PROPN
ejpam-4507	325	19	)	)	PUNCT
ejpam-4507	325	20	=	=	SYM
ejpam-4507	325	21	e−αtk	e−αtk	PROPN
ejpam-4507	325	22	ln	ln	PROPN
ejpam-4507	325	23	b	b	PROPN
ejpam-4507	325	24	(	(	PUNCT
ejpam-4507	325	25	α−	α−	ADP
ejpam-4507	325	26	1	1	NUM
ejpam-4507	325	27	)	)	PUNCT
ejpam-4507	325	28	!	!	PUNCT
ejpam-4507	326	1	lim	lim	PROPN
ejpam-4507	326	2	t→tk	t→tk	PROPN
ejpam-4507	326	3	dα−1	dα−1	PROPN
ejpam-4507	326	4	dtα−1	dtα−1	PROPN
ejpam-4507	326	5	(	(	PUNCT
ejpam-4507	326	6	cxtt−n−1	cxtt−n−1	PROPN
ejpam-4507	326	7	∞∑	∞∑	NUM
ejpam-4507	326	8	n=0	n=0	X
ejpam-4507	326	9	b(α	b(α	NOUN
ejpam-4507	326	10	)	)	PUNCT
ejpam-4507	326	11	n	n	CCONJ
ejpam-4507	326	12	(	(	PUNCT
ejpam-4507	326	13	0	0	NUM
ejpam-4507	326	14	;	;	PUNCT
ejpam-4507	326	15	a	a	DET
ejpam-4507	326	16	,	,	PUNCT
ejpam-4507	326	17	b	b	NOUN
ejpam-4507	326	18	,	,	PUNCT
ejpam-4507	326	19	c	c	NOUN
ejpam-4507	326	20	)	)	PUNCT
ejpam-4507	326	21	(	(	PUNCT
ejpam-4507	326	22	t−	t−	PROPN
ejpam-4507	326	23	tk	tk	PROPN
ejpam-4507	326	24	)	)	PUNCT
ejpam-4507	326	25	n	n	PRON
ejpam-4507	326	26	n	n	CCONJ
ejpam-4507	326	27	!	!	PUNCT
ejpam-4507	326	28	)	)	PUNCT
ejpam-4507	326	29	.	.	PUNCT
ejpam-4507	327	1	applying	apply	VERB
ejpam-4507	327	2	the	the	DET
ejpam-4507	327	3	leibniz	leibniz	NOUN
ejpam-4507	327	4	rule	rule	NOUN
ejpam-4507	327	5	for	for	ADP
ejpam-4507	327	6	differentiation	differentiation	NOUN
ejpam-4507	327	7	,	,	PUNCT
ejpam-4507	327	8	res(gα(t	res(gα(t	PROPN
ejpam-4507	327	9	)	)	PUNCT
ejpam-4507	327	10	,	,	PUNCT
ejpam-4507	327	11	t	t	PROPN
ejpam-4507	327	12	=	=	SYM
ejpam-4507	327	13	tk	tk	PROPN
ejpam-4507	327	14	)	)	PUNCT
ejpam-4507	327	15	=	=	SYM
ejpam-4507	327	16	etk(x	etk(x	PROPN
ejpam-4507	327	17	ln	ln	ADJ
ejpam-4507	327	18	c−α	c−α	PROPN
ejpam-4507	327	19	ln	ln	PROPN
ejpam-4507	327	20	b	b	NOUN
ejpam-4507	327	21	)	)	PUNCT
ejpam-4507	327	22	(	(	PUNCT
ejpam-4507	327	23	α−	α−	ADP
ejpam-4507	327	24	1	1	NUM
ejpam-4507	327	25	)	)	PUNCT
ejpam-4507	327	26	!	!	PUNCT
ejpam-4507	328	1	α−1∑	α−1∑	NUM
ejpam-4507	328	2	ν=0	ν=0	PROPN
ejpam-4507	328	3	(	(	PUNCT
ejpam-4507	328	4	α−	α−	ADP
ejpam-4507	328	5	1	1	NUM
ejpam-4507	328	6	ν	ν	NOUN
ejpam-4507	328	7	)	)	PUNCT
ejpam-4507	328	8	(	(	PUNCT
ejpam-4507	328	9	−n−	−n−	NOUN
ejpam-4507	328	10	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	328	11	t−n−α+ν	t−n−α+ν	ADP
ejpam-4507	328	12	k	k	PROPN
ejpam-4507	328	13	b(α	b(α	PROPN
ejpam-4507	328	14	)	)	PUNCT
ejpam-4507	328	15	ν	ν	NOUN
ejpam-4507	328	16	(	(	PUNCT
ejpam-4507	328	17	x	x	NOUN
ejpam-4507	328	18	;	;	PUNCT
ejpam-4507	328	19	a	a	DET
ejpam-4507	328	20	,	,	PUNCT
ejpam-4507	328	21	b	b	NOUN
ejpam-4507	328	22	,	,	PUNCT
ejpam-4507	328	23	c	c	NOUN
ejpam-4507	328	24	)	)	PUNCT
ejpam-4507	328	25	.	.	PUNCT
ejpam-4507	329	1	thus	thus	ADV
ejpam-4507	329	2	,	,	PUNCT
ejpam-4507	329	3	e	e	X
ejpam-4507	329	4	(	(	PUNCT
ejpam-4507	329	5	α	α	NOUN
ejpam-4507	329	6	)	)	PUNCT
ejpam-4507	329	7	n	n	PROPN
ejpam-4507	329	8	(	(	PUNCT
ejpam-4507	329	9	x	x	X
ejpam-4507	329	10	;	;	PUNCT
ejpam-4507	329	11	a	a	DET
ejpam-4507	329	12	,	,	PUNCT
ejpam-4507	329	13	b	b	NOUN
ejpam-4507	329	14	,	,	PUNCT
ejpam-4507	329	15	c	c	NOUN
ejpam-4507	329	16	)	)	PUNCT
ejpam-4507	329	17	n	n	CCONJ
ejpam-4507	329	18	!	!	PUNCT
ejpam-4507	329	19	=	=	PUNCT
ejpam-4507	329	20	−	−	PROPN
ejpam-4507	329	21	2α	2α	NOUN
ejpam-4507	329	22	(	(	PUNCT
ejpam-4507	329	23	α−	α−	ADP
ejpam-4507	329	24	1	1	NUM
ejpam-4507	329	25	)	)	PUNCT
ejpam-4507	329	26	!	!	PUNCT
ejpam-4507	330	1	∑	∑	PUNCT
ejpam-4507	330	2	k∈z	k∈z	PROPN
ejpam-4507	330	3	etk(x	etk(x	PROPN
ejpam-4507	330	4	ln	ln	PROPN
ejpam-4507	330	5	c−α	c−α	PROPN
ejpam-4507	330	6	ln	ln	PROPN
ejpam-4507	330	7	b	b	NOUN
ejpam-4507	330	8	)	)	PUNCT
ejpam-4507	330	9	α−1∑	α−1∑	NUM
ejpam-4507	331	1	ν=0	ν=0	PROPN
ejpam-4507	331	2	(	(	PUNCT
ejpam-4507	331	3	α−	α−	ADP
ejpam-4507	331	4	1	1	NUM
ejpam-4507	331	5	ν	ν	NOUN
ejpam-4507	331	6	)	)	PUNCT
ejpam-4507	331	7	(	(	PUNCT
ejpam-4507	331	8	−n−	−n−	NOUN
ejpam-4507	331	9	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	331	10	t−n−α+ν	t−n−α+ν	ADP
ejpam-4507	331	11	k	k	PROPN
ejpam-4507	331	12	b(α	b(α	PROPN
ejpam-4507	331	13	)	)	PUNCT
ejpam-4507	331	14	ν	ν	NOUN
ejpam-4507	331	15	(	(	PUNCT
ejpam-4507	331	16	x	x	NOUN
ejpam-4507	331	17	;	;	PUNCT
ejpam-4507	331	18	a	a	DET
ejpam-4507	331	19	,	,	PUNCT
ejpam-4507	331	20	b	b	NOUN
ejpam-4507	331	21	,	,	PUNCT
ejpam-4507	331	22	c	c	NOUN
ejpam-4507	331	23	)	)	PUNCT
ejpam-4507	331	24	=	=	SYM
ejpam-4507	332	1	−	−	PROPN
ejpam-4507	332	2	2α	2α	NOUN
ejpam-4507	332	3	(	(	PUNCT
ejpam-4507	332	4	α−	α−	ADP
ejpam-4507	332	5	1	1	NUM
ejpam-4507	332	6	)	)	PUNCT
ejpam-4507	332	7	!	!	PUNCT
ejpam-4507	333	1	∑	∑	PUNCT
ejpam-4507	333	2	k∈z	k∈z	PROPN
ejpam-4507	333	3	α−1∑	α−1∑	NUM
ejpam-4507	334	1	ν=0	ν=0	PROPN
ejpam-4507	334	2	(	(	PUNCT
ejpam-4507	334	3	α−	α−	ADP
ejpam-4507	334	4	1	1	NUM
ejpam-4507	334	5	ν	ν	NOUN
ejpam-4507	334	6	)	)	PUNCT
ejpam-4507	334	7	(	(	PUNCT
ejpam-4507	334	8	−n−	−n−	NOUN
ejpam-4507	334	9	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	334	10	b(α	b(α	NOUN
ejpam-4507	334	11	)	)	PUNCT
ejpam-4507	334	12	ν	ν	NOUN
ejpam-4507	334	13	(	(	PUNCT
ejpam-4507	334	14	x	x	NOUN
ejpam-4507	334	15	;	;	PUNCT
ejpam-4507	334	16	a	a	DET
ejpam-4507	334	17	,	,	PUNCT
ejpam-4507	334	18	b	b	NOUN
ejpam-4507	334	19	,	,	PUNCT
ejpam-4507	334	20	c	c	NOUN
ejpam-4507	334	21	)	)	PUNCT
ejpam-4507	334	22	etk(x	etk(x	PROPN
ejpam-4507	334	23	ln	ln	NOUN
ejpam-4507	334	24	c−α	c−α	PROPN
ejpam-4507	334	25	ln	ln	PROPN
ejpam-4507	334	26	b	b	PROPN
ejpam-4507	334	27	)	)	PUNCT
ejpam-4507	334	28	tn+α−ν	tn+α−ν	PROPN
ejpam-4507	334	29	k	k	PROPN
ejpam-4507	334	30	,	,	PUNCT
ejpam-4507	334	31	which	which	PRON
ejpam-4507	334	32	is	be	AUX
ejpam-4507	334	33	the	the	DET
ejpam-4507	334	34	desired	desire	VERB
ejpam-4507	334	35	fourier	fourier	NOUN
ejpam-4507	334	36	series	series	NOUN
ejpam-4507	334	37	of	of	ADP
ejpam-4507	334	38	e	e	PROPN
ejpam-4507	334	39	(	(	PUNCT
ejpam-4507	334	40	α	α	NOUN
ejpam-4507	334	41	)	)	PUNCT
ejpam-4507	334	42	n	n	PROPN
ejpam-4507	334	43	(	(	PUNCT
ejpam-4507	334	44	x	x	X
ejpam-4507	334	45	;	;	PUNCT
ejpam-4507	334	46	a	a	DET
ejpam-4507	334	47	,	,	PUNCT
ejpam-4507	334	48	b	b	NOUN
ejpam-4507	334	49	,	,	PUNCT
ejpam-4507	334	50	c	c	NOUN
ejpam-4507	334	51	)	)	PUNCT
ejpam-4507	334	52	.	.	PUNCT
ejpam-4507	335	1	taking	take	VERB
ejpam-4507	335	2	α	α	NOUN
ejpam-4507	335	3	=	=	SYM
ejpam-4507	335	4	1	1	NUM
ejpam-4507	335	5	,	,	PUNCT
ejpam-4507	335	6	the	the	DET
ejpam-4507	335	7	fourier	fourier	ADJ
ejpam-4507	335	8	series	series	NOUN
ejpam-4507	335	9	in	in	ADP
ejpam-4507	335	10	theorem	theorem	ADJ
ejpam-4507	335	11	3.6	3.6	NUM
ejpam-4507	335	12	reduces	reduce	VERB
ejpam-4507	335	13	to	to	ADP
ejpam-4507	335	14	that	that	PRON
ejpam-4507	335	15	in	in	ADP
ejpam-4507	335	16	theorem	theorem	ADJ
ejpam-4507	335	17	2.4	2.4	NUM
ejpam-4507	335	18	.	.	PUNCT
ejpam-4507	336	1	for	for	ADP
ejpam-4507	336	2	α	α	NOUN
ejpam-4507	336	3	=	=	SYM
ejpam-4507	336	4	2	2	NUM
ejpam-4507	336	5	,	,	PUNCT
ejpam-4507	336	6	the	the	DET
ejpam-4507	336	7	fourier	fourier	ADJ
ejpam-4507	336	8	series	series	NOUN
ejpam-4507	336	9	is	be	AUX
ejpam-4507	336	10	given	give	VERB
ejpam-4507	336	11	by	by	ADP
ejpam-4507	336	12	e	e	PROPN
ejpam-4507	336	13	(	(	PUNCT
ejpam-4507	336	14	2	2	NUM
ejpam-4507	336	15	)	)	PUNCT
ejpam-4507	336	16	n	n	NOUN
ejpam-4507	336	17	(	(	PUNCT
ejpam-4507	336	18	x	x	X
ejpam-4507	336	19	;	;	PUNCT
ejpam-4507	336	20	a	a	DET
ejpam-4507	336	21	,	,	PUNCT
ejpam-4507	336	22	b	b	NOUN
ejpam-4507	336	23	,	,	PUNCT
ejpam-4507	336	24	c	c	NOUN
ejpam-4507	336	25	)	)	PUNCT
ejpam-4507	336	26	22(n	22(n	NUM
ejpam-4507	336	27	!	!	PUNCT
ejpam-4507	336	28	)	)	PUNCT
ejpam-4507	337	1	=	=	PUNCT
ejpam-4507	338	1	−	−	PROPN
ejpam-4507	338	2	∑	∑	ADV
ejpam-4507	338	3	k∈z	k∈z	PROPN
ejpam-4507	338	4	(	(	PUNCT
ejpam-4507	338	5	−n−	−n−	NOUN
ejpam-4507	338	6	1)b	1)b	NUM
ejpam-4507	338	7	(	(	PUNCT
ejpam-4507	338	8	2	2	NUM
ejpam-4507	338	9	)	)	PUNCT
ejpam-4507	338	10	0	0	NUM
ejpam-4507	339	1	(	(	PUNCT
ejpam-4507	339	2	x	x	NOUN
ejpam-4507	339	3	;	;	PUNCT
ejpam-4507	339	4	a	a	DET
ejpam-4507	339	5	,	,	PUNCT
ejpam-4507	339	6	b	b	NOUN
ejpam-4507	339	7	,	,	PUNCT
ejpam-4507	339	8	c	c	NOUN
ejpam-4507	339	9	)	)	PUNCT
ejpam-4507	339	10	etk(x	etk(x	PROPN
ejpam-4507	339	11	ln	ln	NOUN
ejpam-4507	339	12	c−2	c−2	PROPN
ejpam-4507	339	13	ln	ln	PROPN
ejpam-4507	339	14	b	b	X
ejpam-4507	339	15	)	)	PUNCT
ejpam-4507	339	16	tn+2	tn+2	AUX
ejpam-4507	339	17	k	k	X
ejpam-4507	340	1	+	+	NOUN
ejpam-4507	340	2	b	b	X
ejpam-4507	340	3	(	(	PUNCT
ejpam-4507	340	4	2	2	NUM
ejpam-4507	340	5	)	)	PUNCT
ejpam-4507	340	6	1	1	NUM
ejpam-4507	340	7	(	(	PUNCT
ejpam-4507	340	8	x	x	NOUN
ejpam-4507	340	9	;	;	PUNCT
ejpam-4507	340	10	a	a	DET
ejpam-4507	340	11	,	,	PUNCT
ejpam-4507	340	12	b	b	NOUN
ejpam-4507	340	13	,	,	PUNCT
ejpam-4507	340	14	c	c	NOUN
ejpam-4507	340	15	)	)	PUNCT
ejpam-4507	340	16	etk(x	etk(x	PROPN
ejpam-4507	340	17	ln	ln	NOUN
ejpam-4507	340	18	c−2	c−2	PROPN
ejpam-4507	340	19	ln	ln	PROPN
ejpam-4507	340	20	b	b	PROPN
ejpam-4507	340	21	)	)	PUNCT
ejpam-4507	340	22	tn+1	tn+1	PROPN
ejpam-4507	340	23	k	k	NOUN
ejpam-4507	340	24	,	,	PUNCT
ejpam-4507	340	25	where	where	SCONJ
ejpam-4507	340	26	b	b	X
ejpam-4507	340	27	(	(	PUNCT
ejpam-4507	340	28	2	2	NUM
ejpam-4507	340	29	)	)	PUNCT
ejpam-4507	340	30	0	0	NUM
ejpam-4507	341	1	(	(	PUNCT
ejpam-4507	341	2	x	x	NOUN
ejpam-4507	341	3	;	;	PUNCT
ejpam-4507	341	4	a	a	DET
ejpam-4507	341	5	,	,	PUNCT
ejpam-4507	341	6	b	b	NOUN
ejpam-4507	341	7	,	,	PUNCT
ejpam-4507	341	8	c	c	NOUN
ejpam-4507	341	9	)	)	PUNCT
ejpam-4507	341	10	=	=	SYM
ejpam-4507	341	11	1	1	NUM
ejpam-4507	341	12	b2	b2	NOUN
ejpam-4507	341	13	,	,	PUNCT
ejpam-4507	341	14	(	(	PUNCT
ejpam-4507	341	15	15	15	NUM
ejpam-4507	341	16	)	)	PUNCT
ejpam-4507	341	17	b	b	NOUN
ejpam-4507	341	18	(	(	PUNCT
ejpam-4507	341	19	2	2	NUM
ejpam-4507	341	20	)	)	PUNCT
ejpam-4507	341	21	1	1	NUM
ejpam-4507	341	22	(	(	PUNCT
ejpam-4507	341	23	x	x	NOUN
ejpam-4507	341	24	;	;	PUNCT
ejpam-4507	341	25	a	a	DET
ejpam-4507	341	26	,	,	PUNCT
ejpam-4507	341	27	b	b	NOUN
ejpam-4507	341	28	,	,	PUNCT
ejpam-4507	341	29	c	c	NOUN
ejpam-4507	341	30	)	)	PUNCT
ejpam-4507	341	31	=	=	PUNCT
ejpam-4507	342	1	x	x	PUNCT
ejpam-4507	342	2	ln	ln	NOUN
ejpam-4507	342	3	c	c	PROPN
ejpam-4507	342	4	b2	b2	NOUN
ejpam-4507	342	5	+	+	CCONJ
ejpam-4507	342	6	ln	ln	ADJ
ejpam-4507	342	7	ab−	ab−	NOUN
ejpam-4507	342	8	(	(	PUNCT
ejpam-4507	342	9	ln	ln	ADJ
ejpam-4507	342	10	b)2	b)2	ADJ
ejpam-4507	342	11	−	−	PROPN
ejpam-4507	342	12	ln	ln	PROPN
ejpam-4507	342	13	b	b	PROPN
ejpam-4507	342	14	ln	ln	X
ejpam-4507	342	15	a−	a−	PROPN
ejpam-4507	342	16	(	(	PUNCT
ejpam-4507	342	17	ln	ln	ADJ
ejpam-4507	342	18	a)2	a)2	NOUN
ejpam-4507	342	19	b2	b2	NOUN
ejpam-4507	342	20	.	.	PUNCT
ejpam-4507	343	1	(	(	PUNCT
ejpam-4507	343	2	16	16	X
ejpam-4507	343	3	)	)	PUNCT
ejpam-4507	343	4	lemma	lemma	PROPN
ejpam-4507	343	5	3.7	3.7	NUM
ejpam-4507	343	6	.	.	PUNCT
ejpam-4507	344	1	let	let	VERB
ejpam-4507	344	2	a	a	DET
ejpam-4507	344	3	,	,	PUNCT
ejpam-4507	344	4	b	b	NOUN
ejpam-4507	344	5	,	,	PUNCT
ejpam-4507	344	6	c	c	AUX
ejpam-4507	344	7	be	be	AUX
ejpam-4507	344	8	positive	positive	ADJ
ejpam-4507	344	9	real	real	ADJ
ejpam-4507	344	10	numbers	number	NOUN
ejpam-4507	344	11	with	with	ADP
ejpam-4507	344	12	b	b	PROPN
ejpam-4507	344	13	>	>	X
ejpam-4507	344	14	a.	a.	NOUN
ejpam-4507	344	15	let	let	VERB
ejpam-4507	344	16	n	n	CCONJ
ejpam-4507	344	17	,	,	PUNCT
ejpam-4507	344	18	n	n	CCONJ
ejpam-4507	344	19	,	,	PUNCT
ejpam-4507	344	20	α	α	PROPN
ejpam-4507	344	21	∈	∈	PROPN
ejpam-4507	344	22	z+	z+	NUM
ejpam-4507	344	23	,	,	PUNCT
ejpam-4507	344	24	n	n	CCONJ
ejpam-4507	344	25	>	>	SYM
ejpam-4507	344	26	1	1	NUM
ejpam-4507	344	27	and	and	CCONJ
ejpam-4507	344	28	cn	cn	PROPN
ejpam-4507	344	29	be	be	AUX
ejpam-4507	344	30	the	the	DET
ejpam-4507	344	31	circle	circle	NOUN
ejpam-4507	344	32	about	about	ADP
ejpam-4507	344	33	zero	zero	NUM
ejpam-4507	344	34	with	with	ADP
ejpam-4507	344	35	raidus	raidus	NOUN
ejpam-4507	344	36	r	r	NOUN
ejpam-4507	344	37	=	=	SYM
ejpam-4507	344	38	(	(	PUNCT
ejpam-4507	344	39	2n	2n	NUM
ejpam-4507	344	40	+	+	CCONJ
ejpam-4507	344	41	1)π	1)π	NUM
ejpam-4507	344	42	−	−	PROPN
ejpam-4507	344	43	ε	ε	PROPN
ejpam-4507	344	44	b	b	PROPN
ejpam-4507	344	45	,	,	PUNCT
ejpam-4507	344	46	where	where	SCONJ
ejpam-4507	344	47	0	0	X
ejpam-4507	344	48	<	<	X
ejpam-4507	344	49	ε	ε	X
ejpam-4507	344	50	<	<	X
ejpam-4507	344	51	1	1	NUM
ejpam-4507	344	52	and	and	CCONJ
ejpam-4507	344	53	b	b	NOUN
ejpam-4507	344	54	=	=	SYM
ejpam-4507	344	55	ln	ln	PROPN
ejpam-4507	344	56	b−	b−	PROPN
ejpam-4507	344	57	ln	ln	ADJ
ejpam-4507	344	58	a.	a.	NOUN
ejpam-4507	344	59	for	for	ADP
ejpam-4507	344	60	0	0	NUM
ejpam-4507	344	61	<	<	X
ejpam-4507	344	62	x	x	X
ejpam-4507	344	63	<	<	X
ejpam-4507	344	64	(	(	PUNCT
ejpam-4507	344	65	α	α	X
ejpam-4507	344	66	ln	ln	PROPN
ejpam-4507	344	67	a−	a−	PROPN
ejpam-4507	344	68	b	b	PROPN
ejpam-4507	344	69	π	π	NOUN
ejpam-4507	344	70	−	−	PROPN
ejpam-4507	344	71	ε	ε	PROPN
ejpam-4507	344	72	)	)	PUNCT
ejpam-4507	344	73	/	/	SYM
ejpam-4507	345	1	ln	ln	NOUN
ejpam-4507	345	2	c	c	NOUN
ejpam-4507	345	3	,	,	PUNCT
ejpam-4507	345	4	ln	ln	NOUN
ejpam-4507	345	5	c	c	NOUN
ejpam-4507	345	6	>	>	PUNCT
ejpam-4507	345	7	0	0	NUM
ejpam-4507	346	1	we	we	PRON
ejpam-4507	346	2	have	have	VERB
ejpam-4507	346	3	lim	lim	PROPN
ejpam-4507	346	4	n→+∞	n→+∞	PROPN
ejpam-4507	346	5	∫	∫	PROPN
ejpam-4507	346	6	cn	cn	PROPN
ejpam-4507	346	7	cxt	cxt	PROPN
ejpam-4507	346	8	(	(	PUNCT
ejpam-4507	346	9	bt	bt	NOUN
ejpam-4507	346	10	+	+	CCONJ
ejpam-4507	346	11	at)α	at)α	PROPN
ejpam-4507	346	12	dt	dt	NOUN
ejpam-4507	346	13	tn−α+1	tn−α+1	NOUN
ejpam-4507	346	14	=	=	SYM
ejpam-4507	346	15	0	0	X
ejpam-4507	346	16	.	.	PUNCT
ejpam-4507	347	1	c.	c.	PROPN
ejpam-4507	347	2	corcino	corcino	PROPN
ejpam-4507	347	3	,	,	PUNCT
ejpam-4507	347	4	r.	r.	PROPN
ejpam-4507	347	5	corcino	corcino	PROPN
ejpam-4507	347	6	/	/	SYM
ejpam-4507	347	7	eur	eur	PROPN
ejpam-4507	347	8	.	.	PUNCT
ejpam-4507	348	1	j.	j.	PROPN
ejpam-4507	348	2	pure	pure	PROPN
ejpam-4507	348	3	appl	appl	PROPN
ejpam-4507	348	4	.	.	PROPN
ejpam-4507	348	5	math	math	PROPN
ejpam-4507	348	6	,	,	PUNCT
ejpam-4507	348	7	15	15	NUM
ejpam-4507	348	8	(	(	PUNCT
ejpam-4507	348	9	4	4	NUM
ejpam-4507	348	10	)	)	PUNCT
ejpam-4507	348	11	(	(	PUNCT
ejpam-4507	348	12	2022	2022	NUM
ejpam-4507	348	13	)	)	PUNCT
ejpam-4507	348	14	,	,	PUNCT
ejpam-4507	348	15	1662	1662	NUM
ejpam-4507	348	16	-	-	SYM
ejpam-4507	348	17	1682	1682	NUM
ejpam-4507	348	18	1680	1680	NUM
ejpam-4507	348	19	proof	proof	NOUN
ejpam-4507	348	20	.	.	PUNCT
ejpam-4507	349	1	this	this	PRON
ejpam-4507	349	2	follows	follow	VERB
ejpam-4507	349	3	from	from	ADP
ejpam-4507	349	4	lemma	lemma	PROPN
ejpam-4507	349	5	3.4	3.4	NUM
ejpam-4507	349	6	.	.	PUNCT
ejpam-4507	350	1	lemma	lemma	PROPN
ejpam-4507	350	2	3.8	3.8	NUM
ejpam-4507	350	3	.	.	PUNCT
ejpam-4507	351	1	for	for	ADP
ejpam-4507	351	2	a	a	DET
ejpam-4507	351	3	,	,	PUNCT
ejpam-4507	351	4	b	b	NOUN
ejpam-4507	351	5	,	,	PUNCT
ejpam-4507	351	6	c	c	PROPN
ejpam-4507	351	7	∈	∈	PROPN
ejpam-4507	351	8	r+	r+	X
ejpam-4507	351	9	,	,	PUNCT
ejpam-4507	351	10	x	x	PUNCT
ejpam-4507	351	11	∈	∈	PROPN
ejpam-4507	351	12	r	r	NOUN
ejpam-4507	351	13	,	,	PUNCT
ejpam-4507	351	14	ν	ν	PROPN
ejpam-4507	351	15	,	,	PUNCT
ejpam-4507	351	16	α	α	PROPN
ejpam-4507	351	17	∈	∈	PROPN
ejpam-4507	351	18	z+	z+	NUM
ejpam-4507	351	19	with	with	ADP
ejpam-4507	351	20	fixed	fix	VERB
ejpam-4507	351	21	ν	ν	NOUN
ejpam-4507	351	22	≥	≥	PROPN
ejpam-4507	351	23	α	α	NOUN
ejpam-4507	351	24	,	,	PUNCT
ejpam-4507	351	25	g(α	g(α	PROPN
ejpam-4507	351	26	)	)	PUNCT
ejpam-4507	351	27	ν	ν	NOUN
ejpam-4507	351	28	(	(	PUNCT
ejpam-4507	351	29	x	x	NOUN
ejpam-4507	351	30	;	;	PUNCT
ejpam-4507	351	31	a	a	DET
ejpam-4507	351	32	,	,	PUNCT
ejpam-4507	351	33	b	b	NOUN
ejpam-4507	351	34	,	,	PUNCT
ejpam-4507	351	35	c	c	NOUN
ejpam-4507	351	36	)	)	PUNCT
ejpam-4507	351	37	=	=	SYM
ejpam-4507	351	38	ν∑	ν∑	PROPN
ejpam-4507	352	1	l=0	l=0	PROPN
ejpam-4507	352	2	(	(	PUNCT
ejpam-4507	352	3	ν	ν	X
ejpam-4507	352	4	l	l	NOUN
ejpam-4507	352	5	)	)	PUNCT
ejpam-4507	352	6	g	g	NOUN
ejpam-4507	352	7	(	(	PUNCT
ejpam-4507	352	8	α	α	NOUN
ejpam-4507	352	9	)	)	PUNCT
ejpam-4507	352	10	l	l	NOUN
ejpam-4507	352	11	(	(	PUNCT
ejpam-4507	352	12	0	0	NUM
ejpam-4507	352	13	;	;	PUNCT
ejpam-4507	352	14	a	a	DET
ejpam-4507	352	15	,	,	PUNCT
ejpam-4507	352	16	b	b	NOUN
ejpam-4507	352	17	,	,	PUNCT
ejpam-4507	352	18	c)(x	c)(x	PROPN
ejpam-4507	352	19	ln	ln	PROPN
ejpam-4507	352	20	c)ν−l	c)ν−l	PROPN
ejpam-4507	352	21	.	.	PUNCT
ejpam-4507	353	1	proof	proof	NOUN
ejpam-4507	353	2	.	.	PUNCT
ejpam-4507	354	1	the	the	DET
ejpam-4507	354	2	proof	proof	NOUN
ejpam-4507	354	3	is	be	AUX
ejpam-4507	354	4	done	do	VERB
ejpam-4507	354	5	similarly	similarly	ADV
ejpam-4507	354	6	as	as	ADP
ejpam-4507	354	7	that	that	PRON
ejpam-4507	354	8	of	of	ADP
ejpam-4507	354	9	lemma	lemma	PROPN
ejpam-4507	354	10	3.2	3.2	NUM
ejpam-4507	354	11	.	.	PUNCT
ejpam-4507	355	1	theorem	theorem	VERB
ejpam-4507	355	2	3.9	3.9	NUM
ejpam-4507	355	3	.	.	PUNCT
ejpam-4507	356	1	let	let	VERB
ejpam-4507	356	2	a	a	DET
ejpam-4507	356	3	,	,	PUNCT
ejpam-4507	356	4	b	b	NOUN
ejpam-4507	356	5	,	,	PUNCT
ejpam-4507	356	6	c	c	AUX
ejpam-4507	356	7	be	be	AUX
ejpam-4507	356	8	positive	positive	ADJ
ejpam-4507	356	9	real	real	ADJ
ejpam-4507	356	10	numbers	number	NOUN
ejpam-4507	356	11	with	with	ADP
ejpam-4507	356	12	b	b	PROPN
ejpam-4507	356	13	>	>	X
ejpam-4507	356	14	a.	a.	NOUN
ejpam-4507	356	15	let	let	VERB
ejpam-4507	356	16	n	n	CCONJ
ejpam-4507	356	17	,	,	PUNCT
ejpam-4507	356	18	n	n	CCONJ
ejpam-4507	356	19	,	,	PUNCT
ejpam-4507	356	20	α	α	PROPN
ejpam-4507	356	21	∈	∈	PROPN
ejpam-4507	356	22	z+	z+	NUM
ejpam-4507	356	23	with	with	ADP
ejpam-4507	356	24	n	n	PRON
ejpam-4507	356	25	≥	≥	NOUN
ejpam-4507	356	26	α	α	PRON
ejpam-4507	356	27	≥	≥	NUM
ejpam-4507	356	28	2	2	NUM
ejpam-4507	356	29	,	,	PUNCT
ejpam-4507	356	30	n	n	CCONJ
ejpam-4507	356	31	>	>	SYM
ejpam-4507	356	32	1	1	NUM
ejpam-4507	356	33	and	and	CCONJ
ejpam-4507	356	34	cn	cn	PROPN
ejpam-4507	356	35	be	be	AUX
ejpam-4507	356	36	the	the	DET
ejpam-4507	356	37	circle	circle	NOUN
ejpam-4507	356	38	about	about	ADP
ejpam-4507	356	39	zero	zero	NUM
ejpam-4507	356	40	of	of	ADP
ejpam-4507	356	41	radius	radius	NOUN
ejpam-4507	356	42	r	r	NOUN
ejpam-4507	356	43	=	=	SYM
ejpam-4507	357	1	(	(	PUNCT
ejpam-4507	357	2	(	(	PUNCT
ejpam-4507	357	3	2n	2n	NUM
ejpam-4507	357	4	+	+	CCONJ
ejpam-4507	357	5	1)π	1)π	NUM
ejpam-4507	357	6	−	−	NOUN
ejpam-4507	357	7	ε)/b	ε)/b	NOUN
ejpam-4507	357	8	,	,	PUNCT
ejpam-4507	357	9	where	where	SCONJ
ejpam-4507	357	10	0	0	X
ejpam-4507	357	11	<	<	X
ejpam-4507	357	12	ε	ε	X
ejpam-4507	357	13	<	<	X
ejpam-4507	357	14	1	1	NUM
ejpam-4507	357	15	and	and	CCONJ
ejpam-4507	357	16	b	b	NOUN
ejpam-4507	357	17	=	=	SYM
ejpam-4507	357	18	ln	ln	PROPN
ejpam-4507	357	19	b−	b−	PROPN
ejpam-4507	357	20	ln	ln	ADJ
ejpam-4507	357	21	a.	a.	NOUN
ejpam-4507	358	1	the	the	DET
ejpam-4507	358	2	fourier	fourier	ADJ
ejpam-4507	358	3	series	series	NOUN
ejpam-4507	358	4	of	of	ADP
ejpam-4507	358	5	the	the	DET
ejpam-4507	358	6	genocchi	genocchi	NOUN
ejpam-4507	358	7	-	-	PUNCT
ejpam-4507	358	8	type	type	NOUN
ejpam-4507	358	9	polynomials	polynomial	NOUN
ejpam-4507	358	10	g	g	NOUN
ejpam-4507	358	11	(	(	PUNCT
ejpam-4507	358	12	α	α	NOUN
ejpam-4507	358	13	)	)	PUNCT
ejpam-4507	358	14	n	n	PROPN
ejpam-4507	358	15	(	(	PUNCT
ejpam-4507	358	16	x	x	X
ejpam-4507	358	17	;	;	PUNCT
ejpam-4507	358	18	a	a	DET
ejpam-4507	358	19	,	,	PUNCT
ejpam-4507	358	20	b	b	NOUN
ejpam-4507	358	21	,	,	PUNCT
ejpam-4507	358	22	c	c	NOUN
ejpam-4507	358	23	)	)	PUNCT
ejpam-4507	358	24	of	of	ADP
ejpam-4507	358	25	order	order	NOUN
ejpam-4507	358	26	α	α	NOUN
ejpam-4507	358	27	is	be	AUX
ejpam-4507	358	28	given	give	VERB
ejpam-4507	358	29	by	by	ADP
ejpam-4507	358	30	g	g	PROPN
ejpam-4507	358	31	(	(	PUNCT
ejpam-4507	358	32	α	α	NOUN
ejpam-4507	358	33	)	)	PUNCT
ejpam-4507	358	34	n	n	PROPN
ejpam-4507	358	35	(	(	PUNCT
ejpam-4507	358	36	x	x	X
ejpam-4507	358	37	;	;	PUNCT
ejpam-4507	358	38	a	a	DET
ejpam-4507	358	39	,	,	PUNCT
ejpam-4507	358	40	b	b	NOUN
ejpam-4507	358	41	,	,	PUNCT
ejpam-4507	358	42	c	c	NOUN
ejpam-4507	358	43	)	)	PUNCT
ejpam-4507	358	44	n	n	CCONJ
ejpam-4507	358	45	!	!	PUNCT
ejpam-4507	358	46	=	=	PUNCT
ejpam-4507	359	1	−	−	PROPN
ejpam-4507	359	2	2α	2α	NOUN
ejpam-4507	359	3	(	(	PUNCT
ejpam-4507	359	4	α−	α−	ADP
ejpam-4507	359	5	1	1	NUM
ejpam-4507	359	6	)	)	PUNCT
ejpam-4507	359	7	!	!	PUNCT
ejpam-4507	360	1	∑	∑	PUNCT
ejpam-4507	360	2	k∈z	k∈z	PROPN
ejpam-4507	360	3	α−1∑	α−1∑	NUM
ejpam-4507	361	1	ν=0	ν=0	PROPN
ejpam-4507	361	2	(	(	PUNCT
ejpam-4507	361	3	α−	α−	ADP
ejpam-4507	361	4	1	1	NUM
ejpam-4507	361	5	ν	ν	NOUN
ejpam-4507	361	6	)	)	PUNCT
ejpam-4507	361	7	(	(	PUNCT
ejpam-4507	361	8	α−n−1)α−1−ν	α−n−1)α−1−ν	VERB
ejpam-4507	361	9	b(α	b(α	NOUN
ejpam-4507	361	10	)	)	PUNCT
ejpam-4507	361	11	ν	ν	NOUN
ejpam-4507	361	12	(	(	PUNCT
ejpam-4507	361	13	x	x	NOUN
ejpam-4507	361	14	;	;	PUNCT
ejpam-4507	361	15	a	a	PRON
ejpam-4507	361	16	,	,	PUNCT
ejpam-4507	361	17	b	b	NOUN
ejpam-4507	361	18	,	,	PUNCT
ejpam-4507	361	19	c	c	NOUN
ejpam-4507	361	20	)	)	PUNCT
ejpam-4507	361	21	etk(x	etk(x	PROPN
ejpam-4507	361	22	ln	ln	NOUN
ejpam-4507	361	23	c−α	c−α	PROPN
ejpam-4507	361	24	ln	ln	PROPN
ejpam-4507	361	25	b	b	PROPN
ejpam-4507	361	26	)	)	PUNCT
ejpam-4507	361	27	tn−ν	tn−ν	PROPN
ejpam-4507	361	28	k	k	X
ejpam-4507	361	29	.	.	PUNCT
ejpam-4507	362	1	proof	proof	NOUN
ejpam-4507	362	2	.	.	PUNCT
ejpam-4507	363	1	applying	apply	VERB
ejpam-4507	363	2	the	the	DET
ejpam-4507	363	3	cauchy	cauchy	ADJ
ejpam-4507	363	4	integral	integral	ADJ
ejpam-4507	363	5	formula	formula	NOUN
ejpam-4507	363	6	to	to	ADP
ejpam-4507	363	7	(	(	PUNCT
ejpam-4507	363	8	3	3	NUM
ejpam-4507	363	9	)	)	PUNCT
ejpam-4507	363	10	,	,	PUNCT
ejpam-4507	363	11	g	g	PROPN
ejpam-4507	363	12	(	(	PUNCT
ejpam-4507	363	13	α	α	NOUN
ejpam-4507	363	14	)	)	PUNCT
ejpam-4507	363	15	n	n	PROPN
ejpam-4507	363	16	(	(	PUNCT
ejpam-4507	363	17	x	x	X
ejpam-4507	363	18	;	;	PUNCT
ejpam-4507	363	19	a	a	DET
ejpam-4507	363	20	,	,	PUNCT
ejpam-4507	363	21	b	b	NOUN
ejpam-4507	363	22	,	,	PUNCT
ejpam-4507	363	23	c	c	NOUN
ejpam-4507	363	24	)	)	PUNCT
ejpam-4507	363	25	n	n	CCONJ
ejpam-4507	363	26	!	!	PUNCT
ejpam-4507	364	1	=	=	NOUN
ejpam-4507	365	1	2α	2α	NUM
ejpam-4507	365	2	2πi	2πi	NOUN
ejpam-4507	365	3	∫	∫	PROPN
ejpam-4507	365	4	c	c	PROPN
ejpam-4507	365	5	cxt	cxt	PROPN
ejpam-4507	365	6	(	(	PUNCT
ejpam-4507	365	7	bt	bt	NOUN
ejpam-4507	365	8	+	+	CCONJ
ejpam-4507	365	9	at)α	at)α	PROPN
ejpam-4507	365	10	dt	dt	NOUN
ejpam-4507	365	11	tn−α+1	tn−α+1	NOUN
ejpam-4507	365	12	,	,	PUNCT
ejpam-4507	365	13	where	where	SCONJ
ejpam-4507	365	14	c	c	PROPN
ejpam-4507	365	15	is	be	AUX
ejpam-4507	365	16	a	a	DET
ejpam-4507	365	17	circle	circle	NOUN
ejpam-4507	365	18	about	about	ADP
ejpam-4507	365	19	zero	zero	NUM
ejpam-4507	365	20	of	of	ADP
ejpam-4507	365	21	radius	radius	NOUN
ejpam-4507	365	22	<	<	X
ejpam-4507	365	23	π	π	PROPN
ejpam-4507	365	24	/	/	SYM
ejpam-4507	365	25	b.	b.	PROPN
ejpam-4507	365	26	let	let	VERB
ejpam-4507	365	27	hα(t	hα(t	VERB
ejpam-4507	365	28	)	)	PUNCT
ejpam-4507	365	29	=	=	SYM
ejpam-4507	365	30	cxt	cxt	NOUN
ejpam-4507	365	31	(	(	PUNCT
ejpam-4507	365	32	bt	bt	NOUN
ejpam-4507	365	33	+	+	CCONJ
ejpam-4507	365	34	at)αtn−α+1	at)αtn−α+1	PROPN
ejpam-4507	365	35	.	.	PUNCT
ejpam-4507	366	1	this	this	DET
ejpam-4507	366	2	function	function	NOUN
ejpam-4507	366	3	has	have	VERB
ejpam-4507	366	4	a	a	DET
ejpam-4507	366	5	pole	pole	NOUN
ejpam-4507	366	6	of	of	ADP
ejpam-4507	366	7	order	order	NOUN
ejpam-4507	366	8	n	n	PRON
ejpam-4507	366	9	−	−	PROPN
ejpam-4507	366	10	α	α	NOUN
ejpam-4507	366	11	+	+	NOUN
ejpam-4507	366	12	1	1	NUM
ejpam-4507	366	13	at	at	ADP
ejpam-4507	366	14	t	t	NOUN
ejpam-4507	366	15	=	=	SYM
ejpam-4507	366	16	0	0	PROPN
ejpam-4507	366	17	and	and	CCONJ
ejpam-4507	366	18	a	a	DET
ejpam-4507	366	19	pole	pole	NOUN
ejpam-4507	366	20	of	of	ADP
ejpam-4507	366	21	order	order	NOUN
ejpam-4507	366	22	α	α	NOUN
ejpam-4507	366	23	at	at	ADP
ejpam-4507	366	24	the	the	DET
ejpam-4507	366	25	zeros	zero	NOUN
ejpam-4507	366	26	of	of	ADP
ejpam-4507	366	27	bt	bt	NOUN
ejpam-4507	366	28	+	+	CCONJ
ejpam-4507	366	29	at	at	ADP
ejpam-4507	366	30	.	.	PUNCT
ejpam-4507	367	1	these	these	DET
ejpam-4507	367	2	poles	pole	NOUN
ejpam-4507	367	3	are	be	AUX
ejpam-4507	367	4	given	give	VERB
ejpam-4507	367	5	by	by	ADP
ejpam-4507	367	6	tk	tk	PROPN
ejpam-4507	367	7	=	=	SYM
ejpam-4507	367	8	(	(	PUNCT
ejpam-4507	367	9	2k	2k	NOUN
ejpam-4507	367	10	+	+	CCONJ
ejpam-4507	368	1	1)πi	1)πi	NUM
ejpam-4507	368	2	/	/	SYM
ejpam-4507	368	3	b	b	NOUN
ejpam-4507	368	4	,	,	PUNCT
ejpam-4507	368	5	k	k	PROPN
ejpam-4507	368	6	∈	∈	PROPN
ejpam-4507	368	7	z.	z.	NOUN
ejpam-4507	368	8	applying	apply	VERB
ejpam-4507	368	9	the	the	DET
ejpam-4507	368	10	residue	residue	NOUN
ejpam-4507	368	11	theorem	theorem	NOUN
ejpam-4507	368	12	and	and	CCONJ
ejpam-4507	368	13	taking	take	VERB
ejpam-4507	368	14	the	the	DET
ejpam-4507	368	15	limit	limit	NOUN
ejpam-4507	368	16	as	as	ADP
ejpam-4507	368	17	n	n	PROPN
ejpam-4507	368	18	→	→	SYM
ejpam-4507	368	19	+	+	PROPN
ejpam-4507	368	20	∞	∞	PROPN
ejpam-4507	368	21	,	,	PUNCT
ejpam-4507	368	22	lim	lim	PROPN
ejpam-4507	368	23	n→+∞	n→+∞	VERB
ejpam-4507	368	24	1	1	NUM
ejpam-4507	368	25	2πi	2πi	NOUN
ejpam-4507	368	26	∫	∫	PROPN
ejpam-4507	368	27	c	c	NOUN
ejpam-4507	368	28	hα(t)dt	hα(t)dt	NOUN
ejpam-4507	368	29	=	=	SYM
ejpam-4507	368	30	res(hα(t	res(hα(t	PROPN
ejpam-4507	368	31	)	)	PUNCT
ejpam-4507	368	32	,	,	PUNCT
ejpam-4507	368	33	t	t	NOUN
ejpam-4507	368	34	=	=	SYM
ejpam-4507	368	35	0	0	NUM
ejpam-4507	368	36	)	)	PUNCT
ejpam-4507	369	1	+	+	CCONJ
ejpam-4507	369	2	∑	∑	ADP
ejpam-4507	369	3	k∈z	k∈z	VERB
ejpam-4507	369	4	res(hα(t	res(hα(t	PROPN
ejpam-4507	369	5	)	)	PUNCT
ejpam-4507	369	6	,	,	PUNCT
ejpam-4507	369	7	t	t	PROPN
ejpam-4507	369	8	=	=	SYM
ejpam-4507	369	9	tk	tk	PROPN
ejpam-4507	369	10	)	)	PUNCT
ejpam-4507	369	11	.	.	PUNCT
ejpam-4507	370	1	it	it	PRON
ejpam-4507	370	2	follows	follow	VERB
ejpam-4507	370	3	from	from	ADP
ejpam-4507	370	4	lemma	lemma	PROPN
ejpam-4507	370	5	3.7	3.7	NUM
ejpam-4507	370	6	that	that	PRON
ejpam-4507	370	7	g	g	PROPN
ejpam-4507	370	8	(	(	PUNCT
ejpam-4507	370	9	α	α	NOUN
ejpam-4507	370	10	)	)	PUNCT
ejpam-4507	370	11	n	n	PROPN
ejpam-4507	370	12	(	(	PUNCT
ejpam-4507	370	13	x	x	X
ejpam-4507	370	14	;	;	PUNCT
ejpam-4507	370	15	a	a	DET
ejpam-4507	370	16	,	,	PUNCT
ejpam-4507	370	17	b	b	NOUN
ejpam-4507	370	18	,	,	PUNCT
ejpam-4507	370	19	c	c	NOUN
ejpam-4507	370	20	)	)	PUNCT
ejpam-4507	370	21	n	n	X
ejpam-4507	370	22	!	!	PUNCT
ejpam-4507	371	1	2α	2α	NOUN
ejpam-4507	371	2	=	=	SYM
ejpam-4507	372	1	−	−	PROPN
ejpam-4507	372	2	∑	∑	PUNCT
ejpam-4507	372	3	k∈z	k∈z	NOUN
ejpam-4507	372	4	res(hα(t	res(hα(t	PROPN
ejpam-4507	372	5	)	)	PUNCT
ejpam-4507	372	6	,	,	PUNCT
ejpam-4507	372	7	t	t	PROPN
ejpam-4507	372	8	=	=	SYM
ejpam-4507	372	9	tk	tk	PROPN
ejpam-4507	372	10	)	)	PUNCT
ejpam-4507	372	11	,	,	PUNCT
ejpam-4507	372	12	(	(	PUNCT
ejpam-4507	372	13	17	17	NUM
ejpam-4507	372	14	)	)	PUNCT
ejpam-4507	372	15	where	where	SCONJ
ejpam-4507	372	16	res(hα(t	res(hα(t	NOUN
ejpam-4507	372	17	)	)	PUNCT
ejpam-4507	372	18	,	,	PUNCT
ejpam-4507	372	19	t	t	PROPN
ejpam-4507	372	20	=	=	SYM
ejpam-4507	372	21	tk	tk	PROPN
ejpam-4507	372	22	)	)	PUNCT
ejpam-4507	372	23	=	=	SYM
ejpam-4507	372	24	1	1	NUM
ejpam-4507	372	25	(	(	PUNCT
ejpam-4507	372	26	α−	α−	ADP
ejpam-4507	372	27	1	1	NUM
ejpam-4507	372	28	)	)	PUNCT
ejpam-4507	372	29	!	!	PUNCT
ejpam-4507	373	1	lim	lim	PROPN
ejpam-4507	373	2	t→tk	t→tk	PROPN
ejpam-4507	373	3	dα−1	dα−1	PROPN
ejpam-4507	373	4	dtα−1	dtα−1	PROPN
ejpam-4507	373	5	(	(	PUNCT
ejpam-4507	373	6	(	(	PUNCT
ejpam-4507	373	7	t−	t−	PROPN
ejpam-4507	373	8	tk	tk	PROPN
ejpam-4507	373	9	)	)	PUNCT
ejpam-4507	373	10	α	α	PROPN
ejpam-4507	373	11	cxt	cxt	NOUN
ejpam-4507	373	12	(	(	PUNCT
ejpam-4507	373	13	bt	bt	X
ejpam-4507	373	14	+	+	X
ejpam-4507	373	15	at)α	at)α	PROPN
ejpam-4507	373	16	·	·	PUNCT
ejpam-4507	373	17	1	1	NUM
ejpam-4507	373	18	tn+1−α	tn+1−α	NOUN
ejpam-4507	373	19	)	)	PUNCT
ejpam-4507	373	20	.	.	PUNCT
ejpam-4507	374	1	from	from	ADP
ejpam-4507	374	2	(	(	PUNCT
ejpam-4507	374	3	14	14	NUM
ejpam-4507	374	4	)	)	PUNCT
ejpam-4507	374	5	,	,	PUNCT
ejpam-4507	374	6	res(hα(t	res(hα(t	PROPN
ejpam-4507	374	7	)	)	PUNCT
ejpam-4507	374	8	,	,	PUNCT
ejpam-4507	374	9	t	t	PROPN
ejpam-4507	374	10	=	=	SYM
ejpam-4507	374	11	tk	tk	AUX
ejpam-4507	374	12	)	)	PUNCT
ejpam-4507	374	13	=	=	SYM
ejpam-4507	374	14	e−αtk	e−αtk	PROPN
ejpam-4507	374	15	ln	ln	PROPN
ejpam-4507	374	16	b	b	PROPN
ejpam-4507	374	17	(	(	PUNCT
ejpam-4507	374	18	α−	α−	ADP
ejpam-4507	374	19	1	1	NUM
ejpam-4507	374	20	)	)	PUNCT
ejpam-4507	374	21	!	!	PUNCT
ejpam-4507	375	1	lim	lim	PROPN
ejpam-4507	375	2	t→tk	t→tk	PROPN
ejpam-4507	375	3	dα−1	dα−1	PROPN
ejpam-4507	375	4	dtα−1	dtα−1	PROPN
ejpam-4507	375	5	(	(	PUNCT
ejpam-4507	375	6	cxtt−n+α−1	cxtt−n+α−1	PROPN
ejpam-4507	375	7	∞∑	∞∑	NUM
ejpam-4507	375	8	n=0	n=0	NUM
ejpam-4507	375	9	b(α	b(α	NOUN
ejpam-4507	375	10	)	)	PUNCT
ejpam-4507	375	11	n	n	CCONJ
ejpam-4507	375	12	(	(	PUNCT
ejpam-4507	375	13	0	0	NUM
ejpam-4507	375	14	;	;	PUNCT
ejpam-4507	375	15	a	a	DET
ejpam-4507	375	16	,	,	PUNCT
ejpam-4507	375	17	b	b	NOUN
ejpam-4507	375	18	,	,	PUNCT
ejpam-4507	375	19	c	c	NOUN
ejpam-4507	375	20	)	)	PUNCT
ejpam-4507	375	21	(	(	PUNCT
ejpam-4507	375	22	t−	t−	PROPN
ejpam-4507	375	23	tk	tk	PROPN
ejpam-4507	375	24	)	)	PUNCT
ejpam-4507	375	25	α	α	PROPN
ejpam-4507	375	26	n	n	NOUN
ejpam-4507	375	27	!	!	PUNCT
ejpam-4507	375	28	)	)	PUNCT
ejpam-4507	375	29	.	.	PUNCT
ejpam-4507	376	1	references	reference	NOUN
ejpam-4507	376	2	1681	1681	NUM
ejpam-4507	376	3	following	follow	VERB
ejpam-4507	376	4	the	the	DET
ejpam-4507	376	5	computation	computation	NOUN
ejpam-4507	376	6	in	in	ADP
ejpam-4507	376	7	the	the	DET
ejpam-4507	376	8	euler	euler	NOUN
ejpam-4507	376	9	-	-	PUNCT
ejpam-4507	376	10	type	type	NOUN
ejpam-4507	376	11	polynomials	polynomial	NOUN
ejpam-4507	376	12	,	,	PUNCT
ejpam-4507	376	13	res(hα(t	res(hα(t	PROPN
ejpam-4507	376	14	)	)	PUNCT
ejpam-4507	376	15	,	,	PUNCT
ejpam-4507	376	16	t	t	PROPN
ejpam-4507	376	17	=	=	SYM
ejpam-4507	376	18	tk	tk	PROPN
ejpam-4507	376	19	)	)	PUNCT
ejpam-4507	376	20	=	=	SYM
ejpam-4507	376	21	etk(x	etk(x	PROPN
ejpam-4507	376	22	ln	ln	ADJ
ejpam-4507	376	23	c−α	c−α	PROPN
ejpam-4507	376	24	ln	ln	PROPN
ejpam-4507	376	25	b	b	NOUN
ejpam-4507	376	26	)	)	PUNCT
ejpam-4507	376	27	(	(	PUNCT
ejpam-4507	376	28	α−	α−	ADP
ejpam-4507	376	29	1	1	NUM
ejpam-4507	376	30	)	)	PUNCT
ejpam-4507	376	31	!	!	PUNCT
ejpam-4507	377	1	α−1∑	α−1∑	NUM
ejpam-4507	378	1	ν=0	ν=0	PROPN
ejpam-4507	378	2	(	(	PUNCT
ejpam-4507	378	3	α−	α−	ADP
ejpam-4507	378	4	1	1	NUM
ejpam-4507	378	5	ν	ν	NOUN
ejpam-4507	378	6	)	)	PUNCT
ejpam-4507	378	7	(	(	PUNCT
ejpam-4507	378	8	α−	α−	ADP
ejpam-4507	378	9	n−	n−	NOUN
ejpam-4507	378	10	1)α−1−ν	1)α−1−ν	NUM
ejpam-4507	378	11	t−n+ν	t−n+ν	SYM
ejpam-4507	378	12	k	k	PROPN
ejpam-4507	378	13	b(α	b(α	NOUN
ejpam-4507	378	14	)	)	PUNCT
ejpam-4507	378	15	ν	ν	NOUN
ejpam-4507	378	16	(	(	PUNCT
ejpam-4507	378	17	x	x	NOUN
ejpam-4507	378	18	;	;	PUNCT
ejpam-4507	378	19	a	a	DET
ejpam-4507	378	20	,	,	PUNCT
ejpam-4507	378	21	b	b	NOUN
ejpam-4507	378	22	,	,	PUNCT
ejpam-4507	378	23	c	c	NOUN
ejpam-4507	378	24	)	)	PUNCT
ejpam-4507	378	25	.	.	PUNCT
ejpam-4507	379	1	(	(	PUNCT
ejpam-4507	379	2	18	18	NUM
ejpam-4507	379	3	)	)	PUNCT
ejpam-4507	379	4	substituting	substituting	NOUN
ejpam-4507	379	5	(	(	PUNCT
ejpam-4507	379	6	18	18	NUM
ejpam-4507	379	7	)	)	PUNCT
ejpam-4507	379	8	to	to	ADP
ejpam-4507	379	9	(	(	PUNCT
ejpam-4507	379	10	17	17	NUM
ejpam-4507	379	11	)	)	PUNCT
ejpam-4507	379	12	gives	give	VERB
ejpam-4507	379	13	the	the	DET
ejpam-4507	379	14	desired	desire	VERB
ejpam-4507	379	15	fourier	fourier	NOUN
ejpam-4507	379	16	series	series	NOUN
ejpam-4507	379	17	.	.	PUNCT
ejpam-4507	380	1	taking	take	VERB
ejpam-4507	380	2	α	α	NOUN
ejpam-4507	380	3	=	=	SYM
ejpam-4507	380	4	1	1	NUM
ejpam-4507	380	5	,	,	PUNCT
ejpam-4507	380	6	the	the	DET
ejpam-4507	380	7	fourier	fourier	ADJ
ejpam-4507	380	8	series	series	NOUN
ejpam-4507	380	9	in	in	ADP
ejpam-4507	380	10	theorem	theorem	ADJ
ejpam-4507	380	11	3.9	3.9	NUM
ejpam-4507	380	12	reduces	reduce	VERB
ejpam-4507	380	13	to	to	ADP
ejpam-4507	380	14	that	that	PRON
ejpam-4507	380	15	in	in	ADP
ejpam-4507	380	16	theorem	theorem	NOUN
ejpam-4507	380	17	2.5	2.5	NUM
ejpam-4507	380	18	.	.	PUNCT
ejpam-4507	381	1	taking	take	VERB
ejpam-4507	381	2	α	α	NOUN
ejpam-4507	381	3	=	=	SYM
ejpam-4507	381	4	2	2	NUM
ejpam-4507	381	5	and	and	CCONJ
ejpam-4507	381	6	n	n	NOUN
ejpam-4507	381	7	=	=	SYM
ejpam-4507	381	8	4	4	NUM
ejpam-4507	381	9	,	,	PUNCT
ejpam-4507	381	10	the	the	DET
ejpam-4507	381	11	series	series	NOUN
ejpam-4507	381	12	gives	give	VERB
ejpam-4507	381	13	g	g	NOUN
ejpam-4507	381	14	(	(	PUNCT
ejpam-4507	381	15	2	2	NUM
ejpam-4507	381	16	)	)	PUNCT
ejpam-4507	381	17	4	4	NUM
ejpam-4507	381	18	(	(	PUNCT
ejpam-4507	381	19	x	x	NOUN
ejpam-4507	381	20	;	;	PUNCT
ejpam-4507	381	21	a	a	DET
ejpam-4507	381	22	,	,	PUNCT
ejpam-4507	381	23	b	b	NOUN
ejpam-4507	381	24	,	,	PUNCT
ejpam-4507	381	25	c	c	NOUN
ejpam-4507	381	26	)	)	PUNCT
ejpam-4507	381	27	22(4	22(4	NUM
ejpam-4507	381	28	!	!	PUNCT
ejpam-4507	381	29	)	)	PUNCT
ejpam-4507	382	1	=	=	PUNCT
ejpam-4507	383	1	−	−	PROPN
ejpam-4507	383	2	∑	∑	ADV
ejpam-4507	383	3	k∈z	k∈z	PROPN
ejpam-4507	383	4	{	{	PUNCT
ejpam-4507	383	5	−3b	−3b	NOUN
ejpam-4507	383	6	(	(	PUNCT
ejpam-4507	383	7	2	2	NUM
ejpam-4507	383	8	)	)	PUNCT
ejpam-4507	383	9	0	0	NUM
ejpam-4507	384	1	(	(	PUNCT
ejpam-4507	384	2	x	x	NOUN
ejpam-4507	384	3	;	;	PUNCT
ejpam-4507	384	4	a	a	DET
ejpam-4507	384	5	,	,	PUNCT
ejpam-4507	384	6	b	b	NOUN
ejpam-4507	384	7	,	,	PUNCT
ejpam-4507	384	8	c	c	NOUN
ejpam-4507	384	9	)	)	PUNCT
ejpam-4507	385	1	e(2k+1)πi(x	e(2k+1)πi(x	PROPN
ejpam-4507	386	1	ln	ln	ADJ
ejpam-4507	386	2	c−2	c−2	PROPN
ejpam-4507	386	3	ln	ln	PROPN
ejpam-4507	386	4	b	b	PROPN
ejpam-4507	386	5	)	)	PUNCT
ejpam-4507	386	6	(	(	PUNCT
ejpam-4507	386	7	(	(	PUNCT
ejpam-4507	386	8	2k	2k	NUM
ejpam-4507	386	9	+	+	CCONJ
ejpam-4507	386	10	1)πi)4	1)πi)4	NUM
ejpam-4507	386	11	+	+	CCONJ
ejpam-4507	386	12	b	b	X
ejpam-4507	386	13	(	(	PUNCT
ejpam-4507	386	14	2	2	NUM
ejpam-4507	386	15	)	)	PUNCT
ejpam-4507	386	16	1	1	NUM
ejpam-4507	386	17	(	(	PUNCT
ejpam-4507	386	18	x	x	NOUN
ejpam-4507	386	19	;	;	PUNCT
ejpam-4507	386	20	a	a	DET
ejpam-4507	386	21	,	,	PUNCT
ejpam-4507	386	22	b	b	NOUN
ejpam-4507	386	23	,	,	PUNCT
ejpam-4507	386	24	c	c	NOUN
ejpam-4507	386	25	)	)	PUNCT
ejpam-4507	387	1	e(2k+1)πi(x	e(2k+1)πi(x	PROPN
ejpam-4507	387	2	ln	ln	ADJ
ejpam-4507	387	3	c−2	c−2	PROPN
ejpam-4507	387	4	ln	ln	PROPN
ejpam-4507	387	5	b	b	PROPN
ejpam-4507	387	6	)	)	PUNCT
ejpam-4507	387	7	(	(	PUNCT
ejpam-4507	387	8	(	(	PUNCT
ejpam-4507	387	9	2k	2k	NUM
ejpam-4507	387	10	+	+	CCONJ
ejpam-4507	387	11	1)πi)3	1)πi)3	NUM
ejpam-4507	387	12	}	}	PUNCT
ejpam-4507	387	13	where	where	SCONJ
ejpam-4507	387	14	b	b	X
ejpam-4507	387	15	(	(	PUNCT
ejpam-4507	387	16	2	2	NUM
ejpam-4507	387	17	)	)	PUNCT
ejpam-4507	387	18	0	0	NUM
ejpam-4507	388	1	(	(	PUNCT
ejpam-4507	388	2	x	x	NOUN
ejpam-4507	388	3	;	;	PUNCT
ejpam-4507	388	4	a	a	DET
ejpam-4507	388	5	,	,	PUNCT
ejpam-4507	388	6	b	b	NOUN
ejpam-4507	388	7	,	,	PUNCT
ejpam-4507	388	8	c	c	NOUN
ejpam-4507	388	9	)	)	PUNCT
ejpam-4507	389	1	and	and	CCONJ
ejpam-4507	389	2	b	b	X
ejpam-4507	389	3	(	(	PUNCT
ejpam-4507	389	4	2	2	NUM
ejpam-4507	389	5	)	)	PUNCT
ejpam-4507	389	6	1	1	NUM
ejpam-4507	389	7	(	(	PUNCT
ejpam-4507	389	8	x	x	NOUN
ejpam-4507	389	9	;	;	PUNCT
ejpam-4507	389	10	a	a	DET
ejpam-4507	389	11	,	,	PUNCT
ejpam-4507	389	12	b	b	NOUN
ejpam-4507	389	13	,	,	PUNCT
ejpam-4507	389	14	c	c	NOUN
ejpam-4507	389	15	)	)	PUNCT
ejpam-4507	389	16	are	be	AUX
ejpam-4507	389	17	given	give	VERB
ejpam-4507	389	18	in	in	ADP
ejpam-4507	389	19	(	(	PUNCT
ejpam-4507	389	20	15	15	NUM
ejpam-4507	389	21	)	)	PUNCT
ejpam-4507	389	22	and	and	CCONJ
ejpam-4507	389	23	(	(	PUNCT
ejpam-4507	389	24	16	16	NUM
ejpam-4507	389	25	)	)	PUNCT
ejpam-4507	389	26	,	,	PUNCT
ejpam-4507	389	27	respectively	respectively	ADV
ejpam-4507	389	28	.	.	PUNCT
ejpam-4507	390	1	4	4	X
ejpam-4507	390	2	.	.	X
ejpam-4507	391	1	some	some	PRON
ejpam-4507	391	2	remarks	remark	VERB
ejpam-4507	391	3	the	the	DET
ejpam-4507	391	4	fourier	fourier	PROPN
ejpam-4507	391	5	series	series	NOUN
ejpam-4507	391	6	expansions	expansion	NOUN
ejpam-4507	391	7	obtained	obtain	VERB
ejpam-4507	391	8	in	in	ADP
ejpam-4507	391	9	this	this	DET
ejpam-4507	391	10	paper	paper	NOUN
ejpam-4507	391	11	for	for	ADP
ejpam-4507	391	12	b	b	PROPN
ejpam-4507	391	13	(	(	PUNCT
ejpam-4507	391	14	α	α	NOUN
ejpam-4507	391	15	)	)	PUNCT
ejpam-4507	391	16	n	n	PROPN
ejpam-4507	391	17	(	(	PUNCT
ejpam-4507	391	18	x	x	X
ejpam-4507	391	19	;	;	PUNCT
ejpam-4507	391	20	a	a	DET
ejpam-4507	391	21	,	,	PUNCT
ejpam-4507	391	22	b	b	NOUN
ejpam-4507	391	23	,	,	PUNCT
ejpam-4507	391	24	c	c	NOUN
ejpam-4507	391	25	)	)	PUNCT
ejpam-4507	391	26	,	,	PUNCT
ejpam-4507	391	27	e	e	X
ejpam-4507	391	28	(	(	PUNCT
ejpam-4507	391	29	α	α	NOUN
ejpam-4507	391	30	)	)	PUNCT
ejpam-4507	391	31	n	n	PROPN
ejpam-4507	391	32	(	(	PUNCT
ejpam-4507	391	33	x	x	X
ejpam-4507	391	34	;	;	PUNCT
ejpam-4507	391	35	a	a	DET
ejpam-4507	391	36	,	,	PUNCT
ejpam-4507	391	37	b	b	NOUN
ejpam-4507	391	38	,	,	PUNCT
ejpam-4507	391	39	c	c	NOUN
ejpam-4507	391	40	)	)	PUNCT
ejpam-4507	391	41	and	and	CCONJ
ejpam-4507	391	42	g	g	PROPN
ejpam-4507	391	43	(	(	PUNCT
ejpam-4507	391	44	α	α	NOUN
ejpam-4507	391	45	)	)	PUNCT
ejpam-4507	391	46	n	n	PROPN
ejpam-4507	391	47	(	(	PUNCT
ejpam-4507	391	48	x	x	X
ejpam-4507	391	49	;	;	PUNCT
ejpam-4507	391	50	a	a	DET
ejpam-4507	391	51	,	,	PUNCT
ejpam-4507	391	52	b	b	NOUN
ejpam-4507	391	53	,	,	PUNCT
ejpam-4507	391	54	c	c	NOUN
ejpam-4507	391	55	)	)	PUNCT
ejpam-4507	391	56	are	be	AUX
ejpam-4507	391	57	useful	useful	ADJ
ejpam-4507	391	58	in	in	ADP
ejpam-4507	391	59	establishing	establish	VERB
ejpam-4507	391	60	the	the	DET
ejpam-4507	391	61	asymptotic	asymptotic	ADJ
ejpam-4507	391	62	formulas	formula	NOUN
ejpam-4507	391	63	of	of	ADP
ejpam-4507	391	64	these	these	DET
ejpam-4507	391	65	polynomials	polynomial	NOUN
ejpam-4507	391	66	.	.	PUNCT
ejpam-4507	392	1	it	it	PRON
ejpam-4507	392	2	would	would	AUX
ejpam-4507	392	3	then	then	ADV
ejpam-4507	392	4	be	be	AUX
ejpam-4507	392	5	interesting	interesting	ADJ
ejpam-4507	392	6	to	to	PART
ejpam-4507	392	7	investigate	investigate	VERB
ejpam-4507	392	8	the	the	DET
ejpam-4507	392	9	asymptotic	asymptotic	ADJ
ejpam-4507	392	10	behavior	behavior	NOUN
ejpam-4507	392	11	of	of	ADP
ejpam-4507	392	12	these	these	DET
ejpam-4507	392	13	polynomials	polynomial	NOUN
ejpam-4507	392	14	.	.	PUNCT
ejpam-4507	393	1	acknowledgements	acknowledgement	NOUN
ejpam-4507	393	2	this	this	DET
ejpam-4507	393	3	research	research	NOUN
ejpam-4507	393	4	is	be	AUX
ejpam-4507	393	5	funded	fund	VERB
ejpam-4507	393	6	by	by	ADP
ejpam-4507	393	7	cebu	cebu	PROPN
ejpam-4507	393	8	normal	normal	ADJ
ejpam-4507	393	9	university	university	NOUN
ejpam-4507	393	10	through	through	ADP
ejpam-4507	393	11	its	its	PRON
ejpam-4507	393	12	center	center	NOUN
ejpam-4507	393	13	for	for	ADP
ejpam-4507	393	14	research	research	NOUN
ejpam-4507	393	15	and	and	CCONJ
ejpam-4507	393	16	development	development	NOUN
ejpam-4507	393	17	and	and	CCONJ
ejpam-4507	393	18	the	the	DET
ejpam-4507	393	19	research	research	NOUN
ejpam-4507	393	20	institute	institute	NOUN
ejpam-4507	393	21	for	for	ADP
ejpam-4507	393	22	computational	computational	ADJ
ejpam-4507	393	23	mathematics	mathematic	NOUN
ejpam-4507	393	24	and	and	CCONJ
ejpam-4507	393	25	physics	physic	NOUN
ejpam-4507	393	26	.	.	PUNCT
ejpam-4507	394	1	references	reference	NOUN
ejpam-4507	394	2	[	[	X
ejpam-4507	394	3	1	1	NUM
ejpam-4507	394	4	]	]	X
ejpam-4507	394	5	bedoya	bedoya	PROPN
ejpam-4507	394	6	,	,	PUNCT
ejpam-4507	394	7	d.	d.	PROPN
ejpam-4507	394	8	,	,	PUNCT
ejpam-4507	394	9	ortega	ortega	PROPN
ejpam-4507	394	10	,	,	PUNCT
ejpam-4507	394	11	m.	m.	NOUN
ejpam-4507	394	12	,	,	PUNCT
ejpam-4507	394	13	ramirez	ramirez	PROPN
ejpam-4507	394	14	,	,	PUNCT
ejpam-4507	394	15	w.	w.	PROPN
ejpam-4507	394	16	,	,	PUNCT
ejpam-4507	394	17	urieles	uriele	NOUN
ejpam-4507	394	18	,	,	PUNCT
ejpam-4507	394	19	a.	a.	NOUN
ejpam-4507	394	20	,	,	PUNCT
ejpam-4507	394	21	fourier	fourier	ADJ
ejpam-4507	394	22	expansion	expansion	NOUN
ejpam-4507	394	23	and	and	CCONJ
ejpam-4507	394	24	integral	integral	ADJ
ejpam-4507	394	25	representation	representation	NOUN
ejpam-4507	394	26	generalized	generalize	VERB
ejpam-4507	394	27	apostol	apostol	NOUN
ejpam-4507	394	28	-	-	PUNCT
ejpam-4507	394	29	type	type	NOUN
ejpam-4507	394	30	frobenius	frobenius	NOUN
ejpam-4507	394	31	-	-	PUNCT
ejpam-4507	394	32	euler	euler	NOUN
ejpam-4507	394	33	polynomials	polynomial	NOUN
ejpam-4507	394	34	.	.	PUNCT
ejpam-4507	395	1	adv	adv	PROPN
ejpam-4507	395	2	.	.	PROPN
ejpam-4507	395	3	differ	differ	VERB
ejpam-4507	395	4	.	.	PUNCT
ejpam-4507	396	1	equ	equ	PROPN
ejpam-4507	396	2	.	.	PROPN
ejpam-4507	396	3	2020	2020	NUM
ejpam-4507	396	4	(	(	PUNCT
ejpam-4507	396	5	2020	2020	NUM
ejpam-4507	396	6	)	)	PUNCT
ejpam-4507	396	7	,	,	PUNCT
ejpam-4507	396	8	article	article	NOUN
ejpam-4507	396	9	534	534	NUM
ejpam-4507	396	10	.	.	PUNCT
ejpam-4507	397	1	[	[	X
ejpam-4507	397	2	2	2	NUM
ejpam-4507	397	3	]	]	X
ejpam-4507	397	4	bedoya	bedoya	PROPN
ejpam-4507	397	5	,	,	PUNCT
ejpam-4507	397	6	d.	d.	PROPN
ejpam-4507	397	7	,	,	PUNCT
ejpam-4507	397	8	ortega	ortega	PROPN
ejpam-4507	397	9	,	,	PUNCT
ejpam-4507	397	10	m.	m.	NOUN
ejpam-4507	397	11	,	,	PUNCT
ejpam-4507	397	12	ramirez	ramirez	PROPN
ejpam-4507	397	13	,	,	PUNCT
ejpam-4507	397	14	w.	w.	PROPN
ejpam-4507	397	15	,	,	PUNCT
ejpam-4507	397	16	urieles	uriele	NOUN
ejpam-4507	397	17	.	.	PUNCT
ejpam-4507	398	1	new	new	ADJ
ejpam-4507	398	2	biparametric	biparametric	ADJ
ejpam-4507	398	3	families	family	NOUN
ejpam-4507	398	4	of	of	ADP
ejpam-4507	398	5	apostolfrobenius	apostolfrobenius	NOUN
ejpam-4507	398	6	-	-	PUNCT
ejpam-4507	398	7	euler	euler	NOUN
ejpam-4507	398	8	polynomials	polynomial	NOUN
ejpam-4507	398	9	of	of	ADP
ejpam-4507	398	10	level	level	NOUN
ejpam-4507	398	11	m	m	PROPN
ejpam-4507	398	12	,	,	PUNCT
ejpam-4507	398	13	mat	mat	NOUN
ejpam-4507	398	14	.	.	NOUN
ejpam-4507	398	15	stud	stud	NOUN
ejpam-4507	398	16	.	.	PUNCT
ejpam-4507	399	1	55	55	NUM
ejpam-4507	399	2	(	(	PUNCT
ejpam-4507	399	3	2021	2021	NUM
ejpam-4507	399	4	)	)	PUNCT
ejpam-4507	399	5	,	,	PUNCT
ejpam-4507	399	6	10	10	NUM
ejpam-4507	399	7	-	-	SYM
ejpam-4507	399	8	23	23	NUM
ejpam-4507	399	9	.	.	PUNCT
ejpam-4507	400	1	[	[	X
ejpam-4507	400	2	3	3	NUM
ejpam-4507	400	3	]	]	X
ejpam-4507	400	4	cesarano	cesarano	PROPN
ejpam-4507	400	5	,	,	PUNCT
ejpam-4507	400	6	c.	c.	PROPN
ejpam-4507	400	7	,	,	PUNCT
ejpam-4507	400	8	ramirez	ramirez	PROPN
ejpam-4507	400	9	,	,	PUNCT
ejpam-4507	400	10	w.	w.	PROPN
ejpam-4507	400	11	,	,	PUNCT
ejpam-4507	400	12	khan	khan	PROPN
ejpam-4507	400	13	,	,	PUNCT
ejpam-4507	400	14	s.	s.	PROPN
ejpam-4507	400	15	a	a	DET
ejpam-4507	400	16	new	new	ADJ
ejpam-4507	400	17	class	class	NOUN
ejpam-4507	400	18	of	of	ADP
ejpam-4507	400	19	degenerate	degenerate	ADJ
ejpam-4507	400	20	apostol?type	apostol?type	PROPN
ejpam-4507	400	21	hermite	hermite	ADJ
ejpam-4507	400	22	polynomials	polynomial	NOUN
ejpam-4507	400	23	and	and	CCONJ
ejpam-4507	400	24	applications	application	NOUN
ejpam-4507	400	25	,	,	PUNCT
ejpam-4507	400	26	dolomites	dolomite	NOUN
ejpam-4507	400	27	res	re	NOUN
ejpam-4507	400	28	.	.	PUNCT
ejpam-4507	401	1	notes	notes	PROPN
ejpam-4507	401	2	approx	approx	PROPN
ejpam-4507	401	3	.	.	PUNCT
ejpam-4507	402	1	15	15	NUM
ejpam-4507	402	2	(	(	PUNCT
ejpam-4507	402	3	2022	2022	NUM
ejpam-4507	402	4	)	)	PUNCT
ejpam-4507	402	5	,	,	PUNCT
ejpam-4507	402	6	1	1	NUM
ejpam-4507	402	7	-	-	SYM
ejpam-4507	402	8	10	10	NUM
ejpam-4507	402	9	.	.	PUNCT
ejpam-4507	403	1	[	[	X
ejpam-4507	403	2	4	4	X
ejpam-4507	403	3	]	]	X
ejpam-4507	403	4	cesarano	cesarano	PROPN
ejpam-4507	403	5	,	,	PUNCT
ejpam-4507	403	6	c.	c.	PROPN
ejpam-4507	403	7	,	,	PUNCT
ejpam-4507	403	8	ramirez	ramirez	PROPN
ejpam-4507	403	9	,	,	PUNCT
ejpam-4507	403	10	w.	w.	PROPN
ejpam-4507	403	11	,	,	PUNCT
ejpam-4507	403	12	some	some	DET
ejpam-4507	403	13	new	new	ADJ
ejpam-4507	403	14	classes	class	NOUN
ejpam-4507	403	15	of	of	ADP
ejpam-4507	403	16	degenerated	degenerated	ADJ
ejpam-4507	403	17	generalized	generalized	ADJ
ejpam-4507	403	18	apostolbernoulli	apostolbernoulli	NOUN
ejpam-4507	403	19	,	,	PUNCT
ejpam-4507	403	20	apostol	apostol	NOUN
ejpam-4507	403	21	-	-	PUNCT
ejpam-4507	403	22	euler	euler	NOUN
ejpam-4507	403	23	and	and	CCONJ
ejpam-4507	403	24	apostol	apostol	NOUN
ejpam-4507	403	25	-	-	PUNCT
ejpam-4507	403	26	genocchi	genocchi	PROPN
ejpam-4507	403	27	polynomials	polynomial	NOUN
ejpam-4507	403	28	,	,	PUNCT
ejpam-4507	403	29	carpathian	carpathian	ADJ
ejpam-4507	403	30	math	math	NOUN
ejpam-4507	403	31	.	.	PUNCT
ejpam-4507	404	1	publ	publ	PROPN
ejpam-4507	404	2	.	.	PUNCT
ejpam-4507	405	1	14(2	14(2	NUM
ejpam-4507	405	2	)	)	PUNCT
ejpam-4507	405	3	(	(	PUNCT
ejpam-4507	405	4	2022	2022	NUM
ejpam-4507	405	5	)	)	PUNCT
ejpam-4507	405	6	.	.	PUNCT
ejpam-4507	406	1	references	reference	NOUN
ejpam-4507	406	2	1682	1682	NUM
ejpam-4507	406	3	[	[	X
ejpam-4507	406	4	5	5	NUM
ejpam-4507	406	5	]	]	X
ejpam-4507	406	6	churchill	churchill	PROPN
ejpam-4507	406	7	,	,	PUNCT
ejpam-4507	406	8	r.	r.	PROPN
ejpam-4507	406	9	v.	v.	PROPN
ejpam-4507	406	10	,	,	PUNCT
ejpam-4507	406	11	brown	brown	PROPN
ejpam-4507	406	12	,	,	PUNCT
ejpam-4507	406	13	j.	j.	PROPN
ejpam-4507	406	14	w.	w.	PROPN
ejpam-4507	406	15	complex	complex	PROPN
ejpam-4507	406	16	variable	variable	NOUN
ejpam-4507	406	17	and	and	CCONJ
ejpam-4507	406	18	applications	application	NOUN
ejpam-4507	406	19	,	,	PUNCT
ejpam-4507	406	20	8th	8th	ADJ
ejpam-4507	406	21	ed	ed	NOUN
ejpam-4507	406	22	.	.	PUNCT
ejpam-4507	406	23	;	;	PUNCT
ejpam-4507	406	24	mcgrawhill	mcgrawhill	NOUN
ejpam-4507	406	25	book	book	NOUN
ejpam-4507	406	26	:	:	PUNCT
ejpam-4507	406	27	new	new	PROPN
ejpam-4507	406	28	york	york	PROPN
ejpam-4507	406	29	,	,	PUNCT
ejpam-4507	406	30	ny	ny	PROPN
ejpam-4507	406	31	,	,	PUNCT
ejpam-4507	406	32	usa	usa	PROPN
ejpam-4507	406	33	,	,	PUNCT
ejpam-4507	406	34	2008	2008	NUM
ejpam-4507	406	35	.	.	PUNCT
ejpam-4507	407	1	[	[	X
ejpam-4507	407	2	6	6	NUM
ejpam-4507	407	3	]	]	SYM
ejpam-4507	407	4	corcino	corcino	NOUN
ejpam-4507	407	5	,	,	PUNCT
ejpam-4507	407	6	c.	c.	PROPN
ejpam-4507	407	7	,	,	PUNCT
ejpam-4507	407	8	castañeda	castañeda	NOUN
ejpam-4507	407	9	,	,	PUNCT
ejpam-4507	407	10	w.	w.	PROPN
ejpam-4507	407	11	,	,	PUNCT
ejpam-4507	407	12	corcino	corcino	PROPN
ejpam-4507	407	13	,	,	PUNCT
ejpam-4507	407	14	r.	r.	PROPN
ejpam-4507	407	15	,	,	PUNCT
ejpam-4507	407	16	asymptotic	asymptotic	ADJ
ejpam-4507	407	17	approximations	approximation	NOUN
ejpam-4507	407	18	of	of	ADP
ejpam-4507	407	19	apostoltangent	apostoltangent	ADJ
ejpam-4507	407	20	polynomials	polynomial	NOUN
ejpam-4507	407	21	in	in	ADP
ejpam-4507	407	22	terms	term	NOUN
ejpam-4507	407	23	of	of	ADP
ejpam-4507	407	24	hyperbolic	hyperbolic	ADJ
ejpam-4507	407	25	functions	function	NOUN
ejpam-4507	407	26	,	,	PUNCT
ejpam-4507	407	27	computer	computer	NOUN
ejpam-4507	407	28	modeling	modeling	NOUN
ejpam-4507	407	29	in	in	ADP
ejpam-4507	407	30	engineering	engineering	NOUN
ejpam-4507	407	31	and	and	CCONJ
ejpam-4507	407	32	sciences	science	NOUN
ejpam-4507	407	33	,	,	PUNCT
ejpam-4507	407	34	132(1	132(1	NUM
ejpam-4507	407	35	)	)	PUNCT
ejpam-4507	407	36	(	(	PUNCT
ejpam-4507	407	37	2022	2022	NUM
ejpam-4507	407	38	)	)	PUNCT
ejpam-4507	407	39	,	,	PUNCT
ejpam-4507	407	40	133	133	NUM
ejpam-4507	407	41	-	-	SYM
ejpam-4507	407	42	151	151	NUM
ejpam-4507	407	43	.	.	PUNCT
ejpam-4507	408	1	[	[	X
ejpam-4507	408	2	7	7	NUM
ejpam-4507	408	3	]	]	X
ejpam-4507	408	4	corcino	corcino	NOUN
ejpam-4507	408	5	,	,	PUNCT
ejpam-4507	408	6	c.	c.	PROPN
ejpam-4507	408	7	,	,	PUNCT
ejpam-4507	408	8	corcino	corcino	PROPN
ejpam-4507	408	9	,	,	PUNCT
ejpam-4507	408	10	r.	r.	PROPN
ejpam-4507	408	11	,	,	PUNCT
ejpam-4507	408	12	fourier	fourier	PROPN
ejpam-4507	408	13	series	series	NOUN
ejpam-4507	408	14	for	for	ADP
ejpam-4507	408	15	the	the	DET
ejpam-4507	408	16	tangent	tangent	NOUN
ejpam-4507	408	17	polynomials	polynomial	NOUN
ejpam-4507	408	18	,	,	PUNCT
ejpam-4507	408	19	tangent	tangent	NOUN
ejpam-4507	408	20	-	-	PUNCT
ejpam-4507	408	21	bernoulli	bernoulli	NOUN
ejpam-4507	408	22	and	and	CCONJ
ejpam-4507	408	23	tangent	tangent	NOUN
ejpam-4507	408	24	-	-	PUNCT
ejpam-4507	408	25	genocchi	genocchi	ADJ
ejpam-4507	408	26	polynomials	polynomial	NOUN
ejpam-4507	408	27	of	of	ADP
ejpam-4507	408	28	higher	high	ADJ
ejpam-4507	408	29	order	order	NOUN
ejpam-4507	408	30	,	,	PUNCT
ejpam-4507	408	31	axioms	axiom	VERB
ejpam-4507	408	32	11(3	11(3	NUM
ejpam-4507	408	33	)	)	PUNCT
ejpam-4507	408	34	(	(	PUNCT
ejpam-4507	408	35	2022	2022	NUM
ejpam-4507	408	36	)	)	PUNCT
ejpam-4507	408	37	,	,	PUNCT
ejpam-4507	408	38	article	article	NOUN
ejpam-4507	408	39	86	86	NUM
ejpam-4507	408	40	.	.	PUNCT
ejpam-4507	409	1	[	[	X
ejpam-4507	409	2	8	8	NUM
ejpam-4507	409	3	]	]	X
ejpam-4507	409	4	corcino	corcino	NOUN
ejpam-4507	409	5	,	,	PUNCT
ejpam-4507	409	6	c.	c.	PROPN
ejpam-4507	409	7	,	,	PUNCT
ejpam-4507	409	8	corcino	corcino	PROPN
ejpam-4507	409	9	,	,	PUNCT
ejpam-4507	409	10	r.	r.	PROPN
ejpam-4507	409	11	,	,	PUNCT
ejpam-4507	409	12	casquejo	casquejo	PROPN
ejpam-4507	409	13	,	,	PUNCT
ejpam-4507	409	14	j.	j.	PROPN
ejpam-4507	409	15	;	;	PUNCT
ejpam-4507	409	16	fourier	fourier	ADJ
ejpam-4507	409	17	expansion	expansion	NOUN
ejpam-4507	409	18	,	,	PUNCT
ejpam-4507	409	19	integral	integral	ADJ
ejpam-4507	409	20	representation	representation	NOUN
ejpam-4507	409	21	and	and	CCONJ
ejpam-4507	409	22	explicit	explicit	ADJ
ejpam-4507	409	23	formula	formula	NOUN
ejpam-4507	409	24	at	at	ADP
ejpam-4507	409	25	rational	rational	ADJ
ejpam-4507	409	26	arguments	argument	NOUN
ejpam-4507	409	27	of	of	ADP
ejpam-4507	409	28	the	the	DET
ejpam-4507	409	29	tangent	tangent	ADJ
ejpam-4507	409	30	polynomials	polynomial	NOUN
ejpam-4507	409	31	of	of	ADP
ejpam-4507	409	32	higher	high	ADJ
ejpam-4507	409	33	-	-	PUNCT
ejpam-4507	409	34	order	order	NOUN
ejpam-4507	409	35	,	,	PUNCT
ejpam-4507	409	36	european	european	ADJ
ejpam-4507	409	37	journal	journal	NOUN
ejpam-4507	409	38	of	of	ADP
ejpam-4507	409	39	pure	pure	ADJ
ejpam-4507	409	40	and	and	CCONJ
ejpam-4507	409	41	applied	apply	VERB
ejpam-4507	409	42	mathematics	mathematic	NOUN
ejpam-4507	409	43	14(4	14(4	NUM
ejpam-4507	409	44	)	)	PUNCT
ejpam-4507	409	45	(	(	PUNCT
ejpam-4507	409	46	2021	2021	NUM
ejpam-4507	409	47	)	)	PUNCT
ejpam-4507	409	48	,	,	PUNCT
ejpam-4507	409	49	1457	1457	NUM
ejpam-4507	409	50	-	-	SYM
ejpam-4507	409	51	1466	1466	NUM
ejpam-4507	409	52	.	.	PUNCT
ejpam-4507	410	1	[	[	X
ejpam-4507	410	2	9	9	NUM
ejpam-4507	410	3	]	]	X
ejpam-4507	410	4	khan	khan	PROPN
ejpam-4507	410	5	,	,	PUNCT
ejpam-4507	410	6	w.	w.	PROPN
ejpam-4507	410	7	,	,	PUNCT
ejpam-4507	410	8	srivastava	srivastava	PROPN
ejpam-4507	410	9	,	,	PUNCT
ejpam-4507	410	10	d.	d.	PROPN
ejpam-4507	410	11	,	,	PUNCT
ejpam-4507	410	12	on	on	ADP
ejpam-4507	410	13	the	the	DET
ejpam-4507	410	14	generalized	generalize	VERB
ejpam-4507	410	15	apostol	apostol	NOUN
ejpam-4507	410	16	-	-	PUNCT
ejpam-4507	410	17	type	type	NOUN
ejpam-4507	410	18	frobenius	frobenius	NOUN
ejpam-4507	410	19	-	-	PUNCT
ejpam-4507	410	20	genocchi	genocchi	NOUN
ejpam-4507	410	21	polynomials	polynomial	NOUN
ejpam-4507	410	22	,	,	PUNCT
ejpam-4507	410	23	filomat	filomat	PROPN
ejpam-4507	410	24	33(7	33(7	NUM
ejpam-4507	410	25	)	)	PUNCT
ejpam-4507	410	26	(	(	PUNCT
ejpam-4507	410	27	2019	2019	NUM
ejpam-4507	410	28	)	)	PUNCT
ejpam-4507	410	29	,	,	PUNCT
ejpam-4507	410	30	1967	1967	NUM
ejpam-4507	410	31	-	-	SYM
ejpam-4507	410	32	1977	1977	NUM
ejpam-4507	410	33	.	.	PUNCT
ejpam-4507	411	1	[	[	X
ejpam-4507	411	2	10	10	NUM
ejpam-4507	411	3	]	]	X
ejpam-4507	411	4	corcino	corcino	NOUN
ejpam-4507	411	5	,	,	PUNCT
ejpam-4507	411	6	r.	r.	PROPN
ejpam-4507	411	7	,	,	PUNCT
ejpam-4507	411	8	corcino	corcino	PROPN
ejpam-4507	411	9	,	,	PUNCT
ejpam-4507	411	10	c.	c.	NOUN
ejpam-4507	411	11	higher	high	ADJ
ejpam-4507	411	12	order	order	NOUN
ejpam-4507	411	13	apostol	apostol	NOUN
ejpam-4507	411	14	-	-	PUNCT
ejpam-4507	411	15	frobenius	frobenius	NOUN
ejpam-4507	411	16	-	-	PUNCT
ejpam-4507	411	17	type	type	NOUN
ejpam-4507	411	18	poly	poly	ADJ
ejpam-4507	411	19	-	-	PUNCT
ejpam-4507	411	20	genocchi	genocchi	NOUN
ejpam-4507	411	21	polynomials	polynomial	NOUN
ejpam-4507	411	22	with	with	ADP
ejpam-4507	411	23	parameters	parameter	NOUN
ejpam-4507	411	24	a	a	PRON
ejpam-4507	411	25	,	,	PUNCT
ejpam-4507	411	26	b	b	PROPN
ejpam-4507	411	27	and	and	CCONJ
ejpam-4507	411	28	c.	c.	PROPN
ejpam-4507	411	29	j.	j.	PROPN
ejpam-4507	411	30	inequal	inequal	PROPN
ejpam-4507	411	31	.	.	PUNCT
ejpam-4507	412	1	spec	spec	PROPN
ejpam-4507	412	2	.	.	PUNCT
ejpam-4507	413	1	funct	funct	PROPN
ejpam-4507	413	2	.	.	PUNCT
ejpam-4507	414	1	12	12	NUM
ejpam-4507	414	2	(	(	PUNCT
ejpam-4507	414	3	2021	2021	NUM
ejpam-4507	414	4	)	)	PUNCT
ejpam-4507	414	5	,	,	PUNCT
ejpam-4507	414	6	54	54	NUM
ejpam-4507	414	7	-	-	SYM
ejpam-4507	414	8	72	72	NUM
ejpam-4507	414	9	.	.	PUNCT