id	sid	tid	token	lemma	pos
ejpam-4703	1	1	european	european	PROPN
ejpam-4703	1	2	journal	journal	PROPN
ejpam-4703	1	3	of	of	ADP
ejpam-4703	1	4	pure	pure	ADJ
ejpam-4703	1	5	and	and	CCONJ
ejpam-4703	1	6	applied	apply	VERB
ejpam-4703	1	7	mathematics	mathematic	NOUN
ejpam-4703	1	8	vol	vol	NOUN
ejpam-4703	1	9	.	.	PUNCT
ejpam-4703	2	1	16	16	NUM
ejpam-4703	2	2	,	,	PUNCT
ejpam-4703	2	3	no	no	INTJ
ejpam-4703	2	4	.	.	NOUN
ejpam-4703	2	5	2	2	NUM
ejpam-4703	2	6	,	,	PUNCT
ejpam-4703	2	7	2023	2023	NUM
ejpam-4703	2	8	,	,	PUNCT
ejpam-4703	2	9	791	791	NUM
ejpam-4703	2	10	-	-	SYM
ejpam-4703	2	11	805	805	NUM
ejpam-4703	2	12	issn	issn	PROPN
ejpam-4703	2	13	1307	1307	NUM
ejpam-4703	2	14	-	-	SYM
ejpam-4703	2	15	5543	5543	NUM
ejpam-4703	2	16	–	–	PUNCT
ejpam-4703	2	17	ejpam.com	ejpam.com	X
ejpam-4703	2	18	published	publish	VERB
ejpam-4703	2	19	by	by	ADP
ejpam-4703	2	20	new	new	PROPN
ejpam-4703	2	21	york	york	PROPN
ejpam-4703	2	22	business	business	PROPN
ejpam-4703	2	23	global	global	ADJ
ejpam-4703	2	24	asymptotic	asymptotic	ADJ
ejpam-4703	2	25	approximations	approximation	NOUN
ejpam-4703	2	26	for	for	ADP
ejpam-4703	2	27	generalized	generalized	ADJ
ejpam-4703	2	28	apostol	apostol	NOUN
ejpam-4703	2	29	-	-	PUNCT
ejpam-4703	2	30	bernoulli	bernoulli	NOUN
ejpam-4703	2	31	,	,	PUNCT
ejpam-4703	2	32	apostol	apostol	NOUN
ejpam-4703	2	33	-	-	PUNCT
ejpam-4703	2	34	euler	euler	NOUN
ejpam-4703	2	35	and	and	CCONJ
ejpam-4703	2	36	apostol	apostol	NOUN
ejpam-4703	2	37	-	-	PUNCT
ejpam-4703	2	38	genocchi	genocchi	PROPN
ejpam-4703	2	39	polynomials	polynomial	NOUN
ejpam-4703	2	40	in	in	ADP
ejpam-4703	2	41	terms	term	NOUN
ejpam-4703	2	42	of	of	ADP
ejpam-4703	2	43	hyperbolic	hyperbolic	ADJ
ejpam-4703	2	44	functions	function	NOUN
ejpam-4703	2	45	cristina	cristina	PROPN
ejpam-4703	2	46	b.	b.	PROPN
ejpam-4703	3	1	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-4703	3	2	,	,	PUNCT
ejpam-4703	3	3	roberto	roberto	PROPN
ejpam-4703	3	4	b.	b.	PROPN
ejpam-4703	3	5	corcino1,2	corcino1,2	PROPN
ejpam-4703	3	6	1	1	NUM
ejpam-4703	3	7	research	research	NOUN
ejpam-4703	3	8	institute	institute	NOUN
ejpam-4703	3	9	for	for	ADP
ejpam-4703	3	10	computational	computational	ADJ
ejpam-4703	3	11	mathematics	mathematic	NOUN
ejpam-4703	3	12	and	and	CCONJ
ejpam-4703	3	13	physics	physics	NOUN
ejpam-4703	3	14	,	,	PUNCT
ejpam-4703	3	15	cebu	cebu	NOUN
ejpam-4703	3	16	normal	normal	ADJ
ejpam-4703	3	17	university	university	NOUN
ejpam-4703	3	18	,	,	PUNCT
ejpam-4703	3	19	6000	6000	NUM
ejpam-4703	3	20	cebu	cebu	NOUN
ejpam-4703	3	21	city	city	NOUN
ejpam-4703	3	22	,	,	PUNCT
ejpam-4703	3	23	philippines	philippine	NOUN
ejpam-4703	3	24	2	2	NUM
ejpam-4703	3	25	mathematics	mathematics	NOUN
ejpam-4703	3	26	department	department	NOUN
ejpam-4703	3	27	,	,	PUNCT
ejpam-4703	3	28	cebu	cebu	NOUN
ejpam-4703	3	29	normal	normal	ADJ
ejpam-4703	3	30	university	university	NOUN
ejpam-4703	3	31	,	,	PUNCT
ejpam-4703	3	32	6000	6000	NUM
ejpam-4703	3	33	cebu	cebu	NOUN
ejpam-4703	3	34	city	city	NOUN
ejpam-4703	3	35	,	,	PUNCT
ejpam-4703	3	36	philippines	philippine	NOUN
ejpam-4703	3	37	abstract	abstract	ADJ
ejpam-4703	3	38	.	.	PUNCT
ejpam-4703	4	1	asymptotic	asymptotic	ADJ
ejpam-4703	4	2	approximation	approximation	NOUN
ejpam-4703	4	3	formulas	formula	NOUN
ejpam-4703	4	4	for	for	ADP
ejpam-4703	4	5	polynomials	polynomial	NOUN
ejpam-4703	4	6	of	of	ADP
ejpam-4703	4	7	the	the	DET
ejpam-4703	4	8	type	type	NOUN
ejpam-4703	4	9	apostol	apostol	NOUN
ejpam-4703	4	10	-	-	PUNCT
ejpam-4703	4	11	bernoulli	bernoulli	NOUN
ejpam-4703	4	12	,	,	PUNCT
ejpam-4703	4	13	apostol	apostol	NOUN
ejpam-4703	4	14	-	-	PUNCT
ejpam-4703	4	15	euler	euler	NOUN
ejpam-4703	4	16	and	and	CCONJ
ejpam-4703	4	17	apostol	apostol	NOUN
ejpam-4703	4	18	-	-	PUNCT
ejpam-4703	4	19	genocchi	genocchi	PROPN
ejpam-4703	4	20	with	with	ADP
ejpam-4703	4	21	integer	integer	NOUN
ejpam-4703	4	22	order	order	NOUN
ejpam-4703	4	23	and	and	CCONJ
ejpam-4703	4	24	real	real	ADJ
ejpam-4703	4	25	parameters	parameter	NOUN
ejpam-4703	4	26	are	be	AUX
ejpam-4703	4	27	obtained	obtain	VERB
ejpam-4703	4	28	via	via	ADP
ejpam-4703	4	29	hyperbolic	hyperbolic	ADJ
ejpam-4703	4	30	functions	function	NOUN
ejpam-4703	4	31	.	.	PUNCT
ejpam-4703	5	1	the	the	DET
ejpam-4703	5	2	derivation	derivation	NOUN
ejpam-4703	5	3	of	of	ADP
ejpam-4703	5	4	the	the	DET
ejpam-4703	5	5	formulas	formula	NOUN
ejpam-4703	5	6	is	be	AUX
ejpam-4703	5	7	done	do	VERB
ejpam-4703	5	8	using	use	VERB
ejpam-4703	5	9	the	the	DET
ejpam-4703	5	10	principle	principle	NOUN
ejpam-4703	5	11	of	of	ADP
ejpam-4703	5	12	saddle	saddle	NOUN
ejpam-4703	5	13	point	point	NOUN
ejpam-4703	5	14	and	and	CCONJ
ejpam-4703	5	15	expansion	expansion	NOUN
ejpam-4703	5	16	of	of	ADP
ejpam-4703	5	17	appropriate	appropriate	ADJ
ejpam-4703	5	18	hyperbolic	hyperbolic	ADJ
ejpam-4703	5	19	function	function	NOUN
ejpam-4703	5	20	about	about	ADP
ejpam-4703	5	21	a	a	DET
ejpam-4703	5	22	saddle	saddle	NOUN
ejpam-4703	5	23	point	point	NOUN
ejpam-4703	5	24	.	.	PUNCT
ejpam-4703	6	1	2020	2020	NUM
ejpam-4703	6	2	mathematics	mathematic	NOUN
ejpam-4703	6	3	subject	subject	NOUN
ejpam-4703	6	4	classifications	classification	NOUN
ejpam-4703	6	5	:	:	PUNCT
ejpam-4703	6	6	11b68	11b68	NUM
ejpam-4703	6	7	,	,	PUNCT
ejpam-4703	6	8	42a16	42a16	NUM
ejpam-4703	6	9	,	,	PUNCT
ejpam-4703	6	10	11m35	11m35	NUM
ejpam-4703	6	11	key	key	ADJ
ejpam-4703	6	12	words	word	NOUN
ejpam-4703	6	13	and	and	CCONJ
ejpam-4703	6	14	phrases	phrase	NOUN
ejpam-4703	6	15	:	:	PUNCT
ejpam-4703	6	16	approximations	approximation	NOUN
ejpam-4703	6	17	,	,	PUNCT
ejpam-4703	6	18	bernoulli	bernoulli	NOUN
ejpam-4703	6	19	polynomials	polynomial	NOUN
ejpam-4703	6	20	,	,	PUNCT
ejpam-4703	6	21	euler	euler	NOUN
ejpam-4703	6	22	polynomials	polynomial	NOUN
ejpam-4703	6	23	,	,	PUNCT
ejpam-4703	6	24	genocchi	genocchi	PROPN
ejpam-4703	6	25	polynomials	polynomial	VERB
ejpam-4703	6	26	1	1	NUM
ejpam-4703	6	27	.	.	PUNCT
ejpam-4703	7	1	introduction	introduction	NOUN
ejpam-4703	7	2	let	let	VERB
ejpam-4703	7	3	α	α	PRON
ejpam-4703	7	4	∈	∈	PROPN
ejpam-4703	7	5	z+	z+	X
ejpam-4703	7	6	,	,	PUNCT
ejpam-4703	7	7	λ	λ	PROPN
ejpam-4703	7	8	∈	∈	PROPN
ejpam-4703	7	9	c\{0	c\{0	PROPN
ejpam-4703	7	10	}	}	PUNCT
ejpam-4703	7	11	,	,	PUNCT
ejpam-4703	7	12	a	a	DET
ejpam-4703	7	13	,	,	PUNCT
ejpam-4703	7	14	b	b	NOUN
ejpam-4703	7	15	,	,	PUNCT
ejpam-4703	7	16	c	c	PROPN
ejpam-4703	7	17	∈	∈	PROPN
ejpam-4703	7	18	r+	r+	X
ejpam-4703	7	19	,	,	PUNCT
ejpam-4703	7	20	b	b	PROPN
ejpam-4703	7	21	̸=	̸=	PROPN
ejpam-4703	7	22	1	1	NUM
ejpam-4703	7	23	,	,	PUNCT
ejpam-4703	7	24	c	c	PROPN
ejpam-4703	7	25	̸=	̸=	PROPN
ejpam-4703	7	26	1	1	NUM
ejpam-4703	7	27	,	,	PUNCT
ejpam-4703	7	28	a	a	DET
ejpam-4703	7	29	̸=	̸=	PROPN
ejpam-4703	7	30	b	b	PROPN
ejpam-4703	7	31	and	and	CCONJ
ejpam-4703	7	32	x	x	PROPN
ejpam-4703	7	33	∈	∈	PROPN
ejpam-4703	7	34	r.	r.	NOUN
ejpam-4703	7	35	the	the	DET
ejpam-4703	7	36	generalized	generalize	VERB
ejpam-4703	7	37	apostol	apostol	NOUN
ejpam-4703	7	38	-	-	PUNCT
ejpam-4703	7	39	bernoulli	bernoulli	PROPN
ejpam-4703	7	40	,	,	PUNCT
ejpam-4703	7	41	euler	euler	NOUN
ejpam-4703	7	42	and	and	CCONJ
ejpam-4703	7	43	genocchi	genocchi	PROPN
ejpam-4703	7	44	polynomials	polynomial	VERB
ejpam-4703	7	45	with	with	ADP
ejpam-4703	7	46	parameters	parameter	NOUN
ejpam-4703	7	47	α	α	NOUN
ejpam-4703	7	48	,	,	PUNCT
ejpam-4703	7	49	λ	λ	PROPN
ejpam-4703	7	50	,	,	PUNCT
ejpam-4703	7	51	a	a	PRON
ejpam-4703	7	52	,	,	PUNCT
ejpam-4703	7	53	b	b	NOUN
ejpam-4703	7	54	,	,	PUNCT
ejpam-4703	7	55	c	c	NOUN
ejpam-4703	7	56	,	,	PUNCT
ejpam-4703	7	57	are	be	AUX
ejpam-4703	7	58	given	give	VERB
ejpam-4703	7	59	by	by	ADP
ejpam-4703	7	60	means	mean	NOUN
ejpam-4703	7	61	of	of	ADP
ejpam-4703	7	62	the	the	DET
ejpam-4703	7	63	following	follow	VERB
ejpam-4703	7	64	generating	generating	NOUN
ejpam-4703	7	65	functions	function	NOUN
ejpam-4703	7	66	(	(	PUNCT
ejpam-4703	7	67	see	see	VERB
ejpam-4703	7	68	[	[	X
ejpam-4703	7	69	1	1	NUM
ejpam-4703	7	70	]	]	NUM
ejpam-4703	7	71	)	)	PUNCT
ejpam-4703	7	72	.	.	PUNCT
ejpam-4703	8	1	(	(	PUNCT
ejpam-4703	8	2	t	t	NOUN
ejpam-4703	8	3	λbt	λbt	VERB
ejpam-4703	8	4	−	−	NOUN
ejpam-4703	8	5	at	at	ADP
ejpam-4703	8	6	)	)	PUNCT
ejpam-4703	8	7	α	α	NOUN
ejpam-4703	8	8	cxt	cxt	NOUN
ejpam-4703	8	9	=	=	PUNCT
ejpam-4703	8	10	∞∑	∞∑	PROPN
ejpam-4703	8	11	n=0	n=0	NUM
ejpam-4703	8	12	b(α	b(α	NOUN
ejpam-4703	8	13	)	)	PUNCT
ejpam-4703	8	14	n	n	CCONJ
ejpam-4703	8	15	(	(	PUNCT
ejpam-4703	8	16	x;λ	x;λ	NUM
ejpam-4703	8	17	;	;	PUNCT
ejpam-4703	8	18	a	a	DET
ejpam-4703	8	19	,	,	PUNCT
ejpam-4703	8	20	b	b	NOUN
ejpam-4703	8	21	,	,	PUNCT
ejpam-4703	8	22	c	c	NOUN
ejpam-4703	8	23	)	)	PUNCT
ejpam-4703	8	24	tn	tn	PROPN
ejpam-4703	8	25	n	n	CCONJ
ejpam-4703	8	26	!	!	PROPN
ejpam-4703	8	27	,	,	PUNCT
ejpam-4703	8	28	∣∣∣∣t	∣∣∣∣t	PROPN
ejpam-4703	8	29	ln	ln	PROPN
ejpam-4703	8	30	b	b	PROPN
ejpam-4703	8	31	a	a	DET
ejpam-4703	8	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4703	8	33	<	<	X
ejpam-4703	8	34	2π	2π	NOUN
ejpam-4703	8	35	,	,	PUNCT
ejpam-4703	8	36	(	(	PUNCT
ejpam-4703	8	37	1.1	1.1	NUM
ejpam-4703	8	38	)	)	PUNCT
ejpam-4703	8	39	(	(	PUNCT
ejpam-4703	8	40	2	2	NUM
ejpam-4703	8	41	λbt	λbt	NOUN
ejpam-4703	8	42	+	+	X
ejpam-4703	8	43	at	at	ADP
ejpam-4703	8	44	)	)	PUNCT
ejpam-4703	8	45	α	α	NOUN
ejpam-4703	8	46	cxt	cxt	NOUN
ejpam-4703	8	47	=	=	PUNCT
ejpam-4703	8	48	∞∑	∞∑	NUM
ejpam-4703	8	49	n=0	n=0	NUM
ejpam-4703	8	50	e(α	e(α	NOUN
ejpam-4703	8	51	)	)	PUNCT
ejpam-4703	8	52	n	n	CCONJ
ejpam-4703	8	53	(	(	PUNCT
ejpam-4703	8	54	x;λ	x;λ	NUM
ejpam-4703	8	55	;	;	PUNCT
ejpam-4703	8	56	a	a	DET
ejpam-4703	8	57	,	,	PUNCT
ejpam-4703	8	58	b	b	NOUN
ejpam-4703	8	59	,	,	PUNCT
ejpam-4703	8	60	c	c	NOUN
ejpam-4703	8	61	)	)	PUNCT
ejpam-4703	8	62	tn	tn	PROPN
ejpam-4703	8	63	n	n	CCONJ
ejpam-4703	8	64	!	!	PROPN
ejpam-4703	8	65	,	,	PUNCT
ejpam-4703	8	66	∣∣∣∣t	∣∣∣∣t	PROPN
ejpam-4703	8	67	ln	ln	PROPN
ejpam-4703	8	68	b	b	PROPN
ejpam-4703	8	69	a	a	DET
ejpam-4703	8	70	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4703	8	71	<	<	X
ejpam-4703	8	72	π	π	PROPN
ejpam-4703	8	73	,	,	PUNCT
ejpam-4703	8	74	(	(	PUNCT
ejpam-4703	8	75	1.2	1.2	NUM
ejpam-4703	8	76	)	)	PUNCT
ejpam-4703	8	77	and	and	CCONJ
ejpam-4703	8	78	(	(	PUNCT
ejpam-4703	8	79	2	2	NUM
ejpam-4703	8	80	t	t	NOUN
ejpam-4703	8	81	λbt	λbt	X
ejpam-4703	8	82	+	+	X
ejpam-4703	8	83	at	at	ADP
ejpam-4703	8	84	)	)	PUNCT
ejpam-4703	8	85	α	α	NOUN
ejpam-4703	8	86	cxt	cxt	NOUN
ejpam-4703	8	87	=	=	PUNCT
ejpam-4703	8	88	∞∑	∞∑	PROPN
ejpam-4703	8	89	n=0	n=0	NUM
ejpam-4703	8	90	g(α	g(α	PROPN
ejpam-4703	8	91	)	)	PUNCT
ejpam-4703	8	92	n	n	CCONJ
ejpam-4703	8	93	(	(	PUNCT
ejpam-4703	8	94	x;λ	x;λ	NUM
ejpam-4703	8	95	;	;	PUNCT
ejpam-4703	8	96	a	a	DET
ejpam-4703	8	97	,	,	PUNCT
ejpam-4703	8	98	b	b	NOUN
ejpam-4703	8	99	,	,	PUNCT
ejpam-4703	8	100	c	c	NOUN
ejpam-4703	8	101	)	)	PUNCT
ejpam-4703	8	102	tn	tn	PROPN
ejpam-4703	8	103	n	n	CCONJ
ejpam-4703	8	104	!	!	PROPN
ejpam-4703	8	105	,	,	PUNCT
ejpam-4703	9	1	∣∣∣∣t	∣∣∣∣t	PROPN
ejpam-4703	9	2	ln	ln	PROPN
ejpam-4703	9	3	b	b	PROPN
ejpam-4703	9	4	a	a	DET
ejpam-4703	9	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4703	9	6	<	<	X
ejpam-4703	9	7	π	π	PROPN
ejpam-4703	9	8	.	.	PUNCT
ejpam-4703	10	1	(	(	PUNCT
ejpam-4703	10	2	1.3	1.3	NUM
ejpam-4703	10	3	)	)	PUNCT
ejpam-4703	10	4	∗corresponding	∗corresponde	VERB
ejpam-4703	10	5	author	author	NOUN
ejpam-4703	10	6	.	.	PUNCT
ejpam-4703	11	1	doi	doi	NOUN
ejpam-4703	11	2	:	:	PUNCT
ejpam-4703	11	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4703	https://doi.org/10.29020/nybg.ejpam.v16i2.4703	DET
ejpam-4703	11	4	email	email	NOUN
ejpam-4703	11	5	addresses	address	NOUN
ejpam-4703	11	6	:	:	PUNCT
ejpam-4703	11	7	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-4703	11	8	(	(	PUNCT
ejpam-4703	11	9	c.	c.	PROPN
ejpam-4703	11	10	corcino	corcino	PROPN
ejpam-4703	11	11	)	)	PUNCT
ejpam-4703	11	12	,	,	PUNCT
ejpam-4703	11	13	corcinor@cnu.edu.ph	corcinor@cnu.edu.ph	PROPN
ejpam-4703	11	14	(	(	PUNCT
ejpam-4703	11	15	r.	r.	PROPN
ejpam-4703	11	16	corcino	corcino	PROPN
ejpam-4703	11	17	)	)	PUNCT
ejpam-4703	11	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4703	11	19	791	791	NUM
ejpam-4703	12	1	©	©	ADP
ejpam-4703	12	2	2023	2023	NUM
ejpam-4703	12	3	ejpam	ejpam	NOUN
ejpam-4703	12	4	all	all	DET
ejpam-4703	12	5	rights	right	NOUN
ejpam-4703	12	6	reserved	reserve	VERB
ejpam-4703	12	7	.	.	PUNCT
ejpam-4703	13	1	c.	c.	PROPN
ejpam-4703	13	2	corcino	corcino	PROPN
ejpam-4703	13	3	,	,	PUNCT
ejpam-4703	13	4	r.	r.	PROPN
ejpam-4703	13	5	corcino	corcino	PROPN
ejpam-4703	13	6	/	/	SYM
ejpam-4703	13	7	eur	eur	PROPN
ejpam-4703	13	8	.	.	PUNCT
ejpam-4703	14	1	j.	j.	PROPN
ejpam-4703	14	2	pure	pure	PROPN
ejpam-4703	14	3	appl	appl	PROPN
ejpam-4703	14	4	.	.	PROPN
ejpam-4703	14	5	math	math	PROPN
ejpam-4703	14	6	,	,	PUNCT
ejpam-4703	14	7	16	16	NUM
ejpam-4703	14	8	(	(	PUNCT
ejpam-4703	14	9	2	2	NUM
ejpam-4703	14	10	)	)	PUNCT
ejpam-4703	14	11	(	(	PUNCT
ejpam-4703	14	12	2023	2023	NUM
ejpam-4703	14	13	)	)	PUNCT
ejpam-4703	14	14	,	,	PUNCT
ejpam-4703	14	15	791	791	NUM
ejpam-4703	14	16	-	-	SYM
ejpam-4703	14	17	805	805	NUM
ejpam-4703	14	18	792	792	NUM
ejpam-4703	14	19	the	the	DET
ejpam-4703	14	20	polynomials	polynomial	NOUN
ejpam-4703	14	21	defined	define	VERB
ejpam-4703	14	22	above	above	ADV
ejpam-4703	14	23	will	will	AUX
ejpam-4703	14	24	also	also	ADV
ejpam-4703	14	25	be	be	AUX
ejpam-4703	14	26	referred	refer	VERB
ejpam-4703	14	27	to	to	ADP
ejpam-4703	14	28	as	as	ADP
ejpam-4703	14	29	apostol	apostol	NOUN
ejpam-4703	14	30	-	-	PUNCT
ejpam-4703	14	31	bernoulli	bernoulli	NOUN
ejpam-4703	14	32	type	type	NOUN
ejpam-4703	14	33	,	,	PUNCT
ejpam-4703	14	34	apostoleuler	apostoleuler	NOUN
ejpam-4703	14	35	type	type	NOUN
ejpam-4703	14	36	and	and	CCONJ
ejpam-4703	14	37	apostol	apostol	NOUN
ejpam-4703	14	38	-	-	PUNCT
ejpam-4703	14	39	genocchi	genocchi	PROPN
ejpam-4703	14	40	type	type	NOUN
ejpam-4703	14	41	polynomials	polynomial	NOUN
ejpam-4703	14	42	in	in	ADP
ejpam-4703	14	43	the	the	DET
ejpam-4703	14	44	discussion	discussion	NOUN
ejpam-4703	14	45	below	below	ADP
ejpam-4703	14	46	.	.	PUNCT
ejpam-4703	15	1	when	when	SCONJ
ejpam-4703	15	2	α	α	PRON
ejpam-4703	15	3	=	=	SYM
ejpam-4703	15	4	1	1	NUM
ejpam-4703	15	5	,	,	PUNCT
ejpam-4703	15	6	λ	λ	NOUN
ejpam-4703	15	7	=	=	SYM
ejpam-4703	15	8	1	1	NUM
ejpam-4703	15	9	,	,	PUNCT
ejpam-4703	15	10	b	b	NOUN
ejpam-4703	15	11	=	=	SYM
ejpam-4703	15	12	c	c	NOUN
ejpam-4703	15	13	=	=	SYM
ejpam-4703	15	14	e	e	PROPN
ejpam-4703	15	15	and	and	CCONJ
ejpam-4703	15	16	a	a	DET
ejpam-4703	15	17	=	=	ADJ
ejpam-4703	15	18	1	1	NUM
ejpam-4703	15	19	,	,	PUNCT
ejpam-4703	15	20	these	these	DET
ejpam-4703	15	21	polynomials	polynomial	NOUN
ejpam-4703	15	22	will	will	AUX
ejpam-4703	15	23	reduce	reduce	VERB
ejpam-4703	15	24	to	to	ADP
ejpam-4703	15	25	the	the	DET
ejpam-4703	15	26	classical	classical	ADJ
ejpam-4703	15	27	bernoulli	bernoulli	NOUN
ejpam-4703	15	28	,	,	PUNCT
ejpam-4703	15	29	euler	euler	VERB
ejpam-4703	15	30	and	and	CCONJ
ejpam-4703	15	31	genocchi	genocchi	PROPN
ejpam-4703	15	32	polynomials	polynomial	NOUN
ejpam-4703	15	33	.	.	PUNCT
ejpam-4703	16	1	asymptotic	asymptotic	ADJ
ejpam-4703	16	2	approximations	approximation	NOUN
ejpam-4703	16	3	for	for	ADP
ejpam-4703	16	4	higher	high	ADJ
ejpam-4703	16	5	order	order	NOUN
ejpam-4703	16	6	genocchi	genocchi	NOUN
ejpam-4703	16	7	polynomials	polynomial	NOUN
ejpam-4703	16	8	using	use	VERB
ejpam-4703	16	9	residues	residue	NOUN
ejpam-4703	16	10	were	be	AUX
ejpam-4703	16	11	done	do	VERB
ejpam-4703	16	12	in	in	ADP
ejpam-4703	16	13	[	[	X
ejpam-4703	16	14	2	2	NUM
ejpam-4703	16	15	]	]	PUNCT
ejpam-4703	16	16	and	and	CCONJ
ejpam-4703	16	17	[	[	X
ejpam-4703	16	18	3	3	NUM
ejpam-4703	16	19	]	]	PUNCT
ejpam-4703	16	20	.	.	PUNCT
ejpam-4703	17	1	approximations	approximation	NOUN
ejpam-4703	17	2	for	for	ADP
ejpam-4703	17	3	the	the	DET
ejpam-4703	17	4	bernoulli	bernoulli	PROPN
ejpam-4703	17	5	and	and	CCONJ
ejpam-4703	17	6	euler	euler	NOUN
ejpam-4703	17	7	polynomials	polynomial	NOUN
ejpam-4703	17	8	using	use	VERB
ejpam-4703	17	9	hyperbolic	hyperbolic	ADJ
ejpam-4703	17	10	functions	function	NOUN
ejpam-4703	17	11	were	be	AUX
ejpam-4703	17	12	obtained	obtain	VERB
ejpam-4703	17	13	in	in	ADP
ejpam-4703	17	14	[	[	X
ejpam-4703	17	15	4	4	NUM
ejpam-4703	17	16	]	]	PUNCT
ejpam-4703	17	17	and	and	CCONJ
ejpam-4703	17	18	approximations	approximation	NOUN
ejpam-4703	17	19	for	for	ADP
ejpam-4703	17	20	genocchi	genocchi	PROPN
ejpam-4703	17	21	polynomials	polynomial	NOUN
ejpam-4703	17	22	in	in	ADP
ejpam-4703	17	23	terms	term	NOUN
ejpam-4703	17	24	of	of	ADP
ejpam-4703	17	25	hyperbolic	hyperbolic	ADJ
ejpam-4703	17	26	functions	function	NOUN
ejpam-4703	17	27	were	be	AUX
ejpam-4703	17	28	obtained	obtain	VERB
ejpam-4703	17	29	in	in	ADP
ejpam-4703	17	30	[	[	X
ejpam-4703	17	31	5	5	NUM
ejpam-4703	17	32	]	]	PUNCT
ejpam-4703	17	33	.	.	PUNCT
ejpam-4703	18	1	at	at	ADP
ejpam-4703	18	2	the	the	DET
ejpam-4703	18	3	time	time	NOUN
ejpam-4703	18	4	of	of	ADP
ejpam-4703	18	5	the	the	DET
ejpam-4703	18	6	search	search	NOUN
ejpam-4703	18	7	,	,	PUNCT
ejpam-4703	18	8	there	there	PRON
ejpam-4703	18	9	were	be	VERB
ejpam-4703	18	10	no	no	DET
ejpam-4703	18	11	approximations	approximation	NOUN
ejpam-4703	18	12	for	for	SCONJ
ejpam-4703	18	13	the	the	DET
ejpam-4703	18	14	generalized	generalize	VERB
ejpam-4703	18	15	apostol	apostol	NOUN
ejpam-4703	18	16	-	-	PUNCT
ejpam-4703	18	17	bernoulli	bernoulli	NOUN
ejpam-4703	18	18	,	,	PUNCT
ejpam-4703	18	19	apostol	apostol	NOUN
ejpam-4703	18	20	-	-	PUNCT
ejpam-4703	18	21	euler	euler	NOUN
ejpam-4703	18	22	and	and	CCONJ
ejpam-4703	18	23	apostol	apostol	NOUN
ejpam-4703	18	24	-	-	PUNCT
ejpam-4703	18	25	genocchi	genocchi	PROPN
ejpam-4703	18	26	polynomials	polynomial	NOUN
ejpam-4703	18	27	found	find	VERB
ejpam-4703	18	28	in	in	ADP
ejpam-4703	18	29	the	the	DET
ejpam-4703	18	30	literature	literature	NOUN
ejpam-4703	18	31	.	.	PUNCT
ejpam-4703	19	1	in	in	ADP
ejpam-4703	19	2	this	this	DET
ejpam-4703	19	3	paper	paper	NOUN
ejpam-4703	19	4	asymptotic	asymptotic	ADJ
ejpam-4703	19	5	approximations	approximation	NOUN
ejpam-4703	19	6	for	for	ADP
ejpam-4703	19	7	these	these	DET
ejpam-4703	19	8	polynomials	polynomial	NOUN
ejpam-4703	19	9	will	will	AUX
ejpam-4703	19	10	be	be	AUX
ejpam-4703	19	11	derived	derive	VERB
ejpam-4703	19	12	using	use	VERB
ejpam-4703	19	13	the	the	DET
ejpam-4703	19	14	method	method	NOUN
ejpam-4703	19	15	of	of	ADP
ejpam-4703	19	16	[	[	X
ejpam-4703	19	17	4	4	NUM
ejpam-4703	19	18	]	]	PUNCT
ejpam-4703	19	19	.	.	PUNCT
ejpam-4703	20	1	in	in	ADP
ejpam-4703	20	2	particular	particular	ADJ
ejpam-4703	20	3	,	,	PUNCT
ejpam-4703	20	4	the	the	DET
ejpam-4703	20	5	following	following	ADJ
ejpam-4703	20	6	results	result	NOUN
ejpam-4703	20	7	in	in	ADP
ejpam-4703	20	8	[	[	X
ejpam-4703	20	9	4	4	NUM
ejpam-4703	20	10	]	]	PUNCT
ejpam-4703	20	11	will	will	AUX
ejpam-4703	20	12	be	be	AUX
ejpam-4703	20	13	utilized	utilize	VERB
ejpam-4703	20	14	.	.	PUNCT
ejpam-4703	21	1	lemma	lemma	PROPN
ejpam-4703	21	2	1.1	1.1	NUM
ejpam-4703	21	3	.	.	PUNCT
ejpam-4703	22	1	for	for	ADP
ejpam-4703	22	2	z	z	PROPN
ejpam-4703	22	3	∈	∈	PROPN
ejpam-4703	22	4	c\{0	c\{0	PROPN
ejpam-4703	22	5	}	}	PUNCT
ejpam-4703	22	6	,	,	PUNCT
ejpam-4703	22	7	the	the	DET
ejpam-4703	22	8	function	function	NOUN
ejpam-4703	22	9	φk(n	φk(n	NUM
ejpam-4703	22	10	,	,	PUNCT
ejpam-4703	22	11	z	z	NOUN
ejpam-4703	22	12	)	)	PUNCT
ejpam-4703	22	13	defined	define	VERB
ejpam-4703	22	14	by	by	ADP
ejpam-4703	22	15	φk(n	φk(n	NUM
ejpam-4703	22	16	,	,	PUNCT
ejpam-4703	22	17	z	z	NOUN
ejpam-4703	22	18	)	)	PUNCT
ejpam-4703	22	19	=	=	SYM
ejpam-4703	22	20	n	n	X
ejpam-4703	22	21	!	!	PUNCT
ejpam-4703	22	22	(	(	PUNCT
ejpam-4703	22	23	nz)n	nz)n	PROPN
ejpam-4703	22	24	1	1	NUM
ejpam-4703	22	25	2πi	2πi	NOUN
ejpam-4703	22	26	∫	∫	PROPN
ejpam-4703	22	27	c	c	X
ejpam-4703	22	28	(	(	PUNCT
ejpam-4703	22	29	w	w	PROPN
ejpam-4703	22	30	−	−	PROPN
ejpam-4703	22	31	z−1)kenzw	z−1)kenzw	NUM
ejpam-4703	22	32	dw	dw	PROPN
ejpam-4703	22	33	wn+1	wn+1	VERB
ejpam-4703	22	34	,	,	PUNCT
ejpam-4703	22	35	(	(	PUNCT
ejpam-4703	22	36	1.4	1.4	NUM
ejpam-4703	22	37	)	)	PUNCT
ejpam-4703	22	38	where	where	SCONJ
ejpam-4703	22	39	c	c	NOUN
ejpam-4703	22	40	is	be	AUX
ejpam-4703	22	41	a	a	DET
ejpam-4703	22	42	circle	circle	NOUN
ejpam-4703	22	43	with	with	ADP
ejpam-4703	22	44	center	center	NOUN
ejpam-4703	22	45	at	at	ADP
ejpam-4703	22	46	the	the	DET
ejpam-4703	22	47	origin	origin	NOUN
ejpam-4703	22	48	and	and	CCONJ
ejpam-4703	22	49	radius	radius	NOUN
ejpam-4703	22	50	ϵ1	ϵ1	NOUN
ejpam-4703	22	51	,	,	PUNCT
ejpam-4703	22	52	can	can	AUX
ejpam-4703	22	53	be	be	AUX
ejpam-4703	22	54	represented	represent	VERB
ejpam-4703	22	55	in	in	ADP
ejpam-4703	22	56	the	the	DET
ejpam-4703	22	57	form	form	NOUN
ejpam-4703	22	58	φk(n	φk(n	NOUN
ejpam-4703	22	59	,	,	PUNCT
ejpam-4703	22	60	z	z	NOUN
ejpam-4703	22	61	)	)	PUNCT
ejpam-4703	22	62	=	=	SYM
ejpam-4703	22	63	pk(n	pk(n	X
ejpam-4703	22	64	)	)	PUNCT
ejpam-4703	22	65	(	(	PUNCT
ejpam-4703	22	66	nz)k	nz)k	X
ejpam-4703	22	67	(	(	PUNCT
ejpam-4703	22	68	1.5	1.5	NUM
ejpam-4703	22	69	)	)	PUNCT
ejpam-4703	22	70	with	with	ADP
ejpam-4703	22	71	p0(n	p0(n	NOUN
ejpam-4703	22	72	)	)	PUNCT
ejpam-4703	22	73	=	=	SYM
ejpam-4703	22	74	1	1	NUM
ejpam-4703	22	75	,	,	PUNCT
ejpam-4703	22	76	p1(n	p1(n	PROPN
ejpam-4703	22	77	)	)	PUNCT
ejpam-4703	22	78	=	=	SYM
ejpam-4703	22	79	0	0	NUM
ejpam-4703	22	80	,	,	PUNCT
ejpam-4703	22	81	p2(n	p2(n	NOUN
ejpam-4703	22	82	)	)	PUNCT
ejpam-4703	22	83	=	=	SYM
ejpam-4703	23	1	−n	−n	NOUN
ejpam-4703	23	2	,	,	PUNCT
ejpam-4703	23	3	p3(n	p3(n	NOUN
ejpam-4703	23	4	)	)	PUNCT
ejpam-4703	23	5	=	=	SYM
ejpam-4703	23	6	2n	2n	NUM
ejpam-4703	23	7	,	,	PUNCT
ejpam-4703	23	8	(	(	PUNCT
ejpam-4703	23	9	1.6	1.6	NUM
ejpam-4703	23	10	)	)	PUNCT
ejpam-4703	23	11	and	and	CCONJ
ejpam-4703	23	12	the	the	DET
ejpam-4703	23	13	remaining	remain	VERB
ejpam-4703	23	14	polynomials	polynomial	NOUN
ejpam-4703	23	15	are	be	AUX
ejpam-4703	23	16	given	give	VERB
ejpam-4703	23	17	by	by	ADP
ejpam-4703	23	18	the	the	DET
ejpam-4703	23	19	recurrence	recurrence	NOUN
ejpam-4703	23	20	pk(n	pk(n	X
ejpam-4703	23	21	)	)	PUNCT
ejpam-4703	23	22	=	=	SYM
ejpam-4703	23	23	(	(	PUNCT
ejpam-4703	23	24	1−	1−	NUM
ejpam-4703	23	25	k)pk−1(n	k)pk−1(n	PROPN
ejpam-4703	23	26	)	)	PUNCT
ejpam-4703	24	1	+	+	NUM
ejpam-4703	24	2	npk−2(n	npk−2(n	ADJ
ejpam-4703	24	3	)	)	PUNCT
ejpam-4703	24	4	.	.	PUNCT
ejpam-4703	25	1	(	(	PUNCT
ejpam-4703	25	2	1.7	1.7	NUM
ejpam-4703	25	3	)	)	PUNCT
ejpam-4703	25	4	lemma	lemma	PROPN
ejpam-4703	25	5	1.2	1.2	NUM
ejpam-4703	25	6	.	.	PUNCT
ejpam-4703	26	1	for	for	ADP
ejpam-4703	26	2	fixed	fixed	ADJ
ejpam-4703	26	3	z	z	PROPN
ejpam-4703	26	4	̸=	̸=	PROPN
ejpam-4703	26	5	0	0	NUM
ejpam-4703	26	6	,	,	PUNCT
ejpam-4703	26	7	the	the	DET
ejpam-4703	26	8	sequence	sequence	NOUN
ejpam-4703	26	9	φk(n	φk(n	NUM
ejpam-4703	26	10	,	,	PUNCT
ejpam-4703	26	11	z	z	NOUN
ejpam-4703	26	12	)	)	PUNCT
ejpam-4703	26	13	is	be	AUX
ejpam-4703	26	14	an	an	DET
ejpam-4703	26	15	asymptotic	asymptotic	ADJ
ejpam-4703	26	16	sequence	sequence	NOUN
ejpam-4703	26	17	for	for	ADP
ejpam-4703	26	18	n	n	NOUN
ejpam-4703	26	19	→	→	SYM
ejpam-4703	26	20	+	+	NUM
ejpam-4703	26	21	∞	∞	PROPN
ejpam-4703	26	22	that	that	PRON
ejpam-4703	26	23	satisfies	satisfy	VERB
ejpam-4703	26	24	φk(n	φk(n	NUM
ejpam-4703	26	25	,	,	PUNCT
ejpam-4703	26	26	z	z	NOUN
ejpam-4703	26	27	)	)	PUNCT
ejpam-4703	27	1	=	=	SYM
ejpam-4703	27	2	o(n	o(n	PROPN
ejpam-4703	27	3	[	[	PUNCT
ejpam-4703	27	4	k	k	NOUN
ejpam-4703	27	5	2	2	NUM
ejpam-4703	27	6	]	]	PUNCT
ejpam-4703	27	7	−k	−k	ADJ
ejpam-4703	27	8	)	)	PUNCT
ejpam-4703	27	9	.	.	PUNCT
ejpam-4703	28	1	theorem	theorem	VERB
ejpam-4703	28	2	1.3	1.3	NUM
ejpam-4703	28	3	.	.	PUNCT
ejpam-4703	29	1	let	let	AUX
ejpam-4703	29	2	f(w	f(w	PROPN
ejpam-4703	29	3	)	)	PUNCT
ejpam-4703	29	4	be	be	AUX
ejpam-4703	29	5	a	a	DET
ejpam-4703	29	6	meromorphic	meromorphic	ADJ
ejpam-4703	29	7	function	function	NOUN
ejpam-4703	29	8	with	with	ADP
ejpam-4703	29	9	simple	simple	ADJ
ejpam-4703	29	10	poles	pole	NOUN
ejpam-4703	29	11	w1	w1	NOUN
ejpam-4703	29	12	,	,	PUNCT
ejpam-4703	29	13	w2	w2	NOUN
ejpam-4703	29	14	,	,	PUNCT
ejpam-4703	29	15	...	...	PUNCT
ejpam-4703	29	16	and	and	CCONJ
ejpam-4703	29	17	analytic	analytic	ADJ
ejpam-4703	29	18	at	at	ADP
ejpam-4703	29	19	the	the	DET
ejpam-4703	29	20	origin	origin	NOUN
ejpam-4703	29	21	.	.	PUNCT
ejpam-4703	30	1	let	let	VERB
ejpam-4703	30	2	the	the	DET
ejpam-4703	30	3	contour	contour	NOUN
ejpam-4703	30	4	c	c	AUX
ejpam-4703	30	5	be	be	AUX
ejpam-4703	30	6	a	a	DET
ejpam-4703	30	7	circle	circle	NOUN
ejpam-4703	30	8	whose	whose	DET
ejpam-4703	30	9	center	center	NOUN
ejpam-4703	30	10	is	be	AUX
ejpam-4703	30	11	at	at	ADP
ejpam-4703	30	12	the	the	DET
ejpam-4703	30	13	origin	origin	NOUN
ejpam-4703	30	14	and	and	CCONJ
ejpam-4703	30	15	which	which	PRON
ejpam-4703	30	16	contains	contain	VERB
ejpam-4703	30	17	no	no	DET
ejpam-4703	30	18	poles	pole	NOUN
ejpam-4703	30	19	of	of	ADP
ejpam-4703	30	20	f(w	f(w	NOUN
ejpam-4703	30	21	)	)	PUNCT
ejpam-4703	30	22	inside	inside	ADV
ejpam-4703	30	23	.	.	PUNCT
ejpam-4703	31	1	the	the	DET
ejpam-4703	31	2	polynomials	polynomial	NOUN
ejpam-4703	31	3	pn(nz	pn(nz	NOUN
ejpam-4703	31	4	)	)	PUNCT
ejpam-4703	31	5	defined	define	VERB
ejpam-4703	31	6	by	by	ADP
ejpam-4703	31	7	pn(nz	pn(nz	NOUN
ejpam-4703	31	8	)	)	PUNCT
ejpam-4703	31	9	=	=	SYM
ejpam-4703	31	10	n	n	X
ejpam-4703	31	11	!	!	PUNCT
ejpam-4703	31	12	2πi	2πi	NOUN
ejpam-4703	32	1	∫	∫	PROPN
ejpam-4703	32	2	c	c	PROPN
ejpam-4703	32	3	f(w)enwz	f(w)enwz	PROPN
ejpam-4703	32	4	dw	dw	PROPN
ejpam-4703	32	5	wn+1	wn+1	VERB
ejpam-4703	32	6	(	(	PUNCT
ejpam-4703	32	7	1.8	1.8	NUM
ejpam-4703	32	8	)	)	PUNCT
ejpam-4703	32	9	may	may	AUX
ejpam-4703	32	10	be	be	AUX
ejpam-4703	32	11	expanded	expand	VERB
ejpam-4703	32	12	as	as	ADP
ejpam-4703	32	13	the	the	DET
ejpam-4703	32	14	infinite	infinite	ADJ
ejpam-4703	32	15	sum	sum	NOUN
ejpam-4703	32	16	pn(nz	pn(nz	NOUN
ejpam-4703	32	17	)	)	PUNCT
ejpam-4703	32	18	=	=	SYM
ejpam-4703	32	19	(	(	PUNCT
ejpam-4703	33	1	nz)n	nz)n	PROPN
ejpam-4703	33	2	∞∑	∞∑	PROPN
ejpam-4703	33	3	k=0	k=0	PROPN
ejpam-4703	33	4	f	f	X
ejpam-4703	33	5	(	(	PUNCT
ejpam-4703	33	6	k)(z−1	k)(z−1	PROPN
ejpam-4703	33	7	)	)	PUNCT
ejpam-4703	34	1	k	k	NOUN
ejpam-4703	34	2	!	!	PROPN
ejpam-4703	34	3	pk(n	pk(n	X
ejpam-4703	34	4	)	)	PUNCT
ejpam-4703	34	5	(	(	PUNCT
ejpam-4703	34	6	nz)k	nz)k	NUM
ejpam-4703	34	7	,	,	PUNCT
ejpam-4703	34	8	(	(	PUNCT
ejpam-4703	34	9	1.9	1.9	NUM
ejpam-4703	34	10	)	)	PUNCT
ejpam-4703	34	11	valid	valid	NOUN
ejpam-4703	34	12	for	for	ADP
ejpam-4703	34	13	z	z	PROPN
ejpam-4703	34	14	∈	∈	PROPN
ejpam-4703	34	15	c\{0	c\{0	PROPN
ejpam-4703	34	16	}	}	PUNCT
ejpam-4703	34	17	such	such	ADJ
ejpam-4703	34	18	that	that	SCONJ
ejpam-4703	34	19	|z−1|	|z−1|	NOUN
ejpam-4703	34	20	<	<	X
ejpam-4703	34	21	|z−1	|z−1	PROPN
ejpam-4703	34	22	−	−	PROPN
ejpam-4703	34	23	wk|	wk|	NOUN
ejpam-4703	34	24	for	for	ADP
ejpam-4703	34	25	all	all	PRON
ejpam-4703	34	26	k	k	NOUN
ejpam-4703	34	27	=	=	SYM
ejpam-4703	34	28	1	1	NUM
ejpam-4703	34	29	,	,	PUNCT
ejpam-4703	34	30	2	2	NUM
ejpam-4703	34	31	,	,	PUNCT
ejpam-4703	34	32	...	...	PUNCT
ejpam-4703	34	33	where	where	SCONJ
ejpam-4703	34	34	pk(n	pk(n	X
ejpam-4703	34	35	)	)	PUNCT
ejpam-4703	34	36	are	be	AUX
ejpam-4703	34	37	the	the	DET
ejpam-4703	34	38	polynomials	polynomial	NOUN
ejpam-4703	34	39	given	give	VERB
ejpam-4703	34	40	in	in	ADP
ejpam-4703	34	41	lemma	lemma	PROPN
ejpam-4703	34	42	1.1	1.1	NUM
ejpam-4703	34	43	.	.	PUNCT
ejpam-4703	35	1	c.	c.	PROPN
ejpam-4703	35	2	corcino	corcino	PROPN
ejpam-4703	35	3	,	,	PUNCT
ejpam-4703	35	4	r.	r.	PROPN
ejpam-4703	35	5	corcino	corcino	PROPN
ejpam-4703	35	6	/	/	SYM
ejpam-4703	35	7	eur	eur	PROPN
ejpam-4703	35	8	.	.	PUNCT
ejpam-4703	36	1	j.	j.	PROPN
ejpam-4703	36	2	pure	pure	PROPN
ejpam-4703	36	3	appl	appl	PROPN
ejpam-4703	36	4	.	.	PROPN
ejpam-4703	36	5	math	math	PROPN
ejpam-4703	36	6	,	,	PUNCT
ejpam-4703	36	7	16	16	NUM
ejpam-4703	36	8	(	(	PUNCT
ejpam-4703	36	9	2	2	NUM
ejpam-4703	36	10	)	)	PUNCT
ejpam-4703	36	11	(	(	PUNCT
ejpam-4703	36	12	2023	2023	NUM
ejpam-4703	36	13	)	)	PUNCT
ejpam-4703	36	14	,	,	PUNCT
ejpam-4703	36	15	791	791	NUM
ejpam-4703	36	16	-	-	SYM
ejpam-4703	36	17	805	805	NUM
ejpam-4703	36	18	793	793	NUM
ejpam-4703	36	19	2	2	NUM
ejpam-4703	36	20	.	.	PUNCT
ejpam-4703	36	21	proof	proof	NOUN
ejpam-4703	36	22	of	of	ADP
ejpam-4703	36	23	theorem	theorem	ADJ
ejpam-4703	36	24	1.3	1.3	NUM
ejpam-4703	36	25	the	the	DET
ejpam-4703	36	26	following	follow	VERB
ejpam-4703	36	27	proof	proof	NOUN
ejpam-4703	36	28	of	of	ADP
ejpam-4703	36	29	theorem	theorem	ADJ
ejpam-4703	36	30	1.3	1.3	NUM
ejpam-4703	36	31	is	be	AUX
ejpam-4703	36	32	an	an	DET
ejpam-4703	36	33	expository	expository	NOUN
ejpam-4703	36	34	of	of	ADP
ejpam-4703	36	35	the	the	DET
ejpam-4703	36	36	proof	proof	NOUN
ejpam-4703	36	37	presented	present	VERB
ejpam-4703	36	38	in	in	ADP
ejpam-4703	36	39	[	[	X
ejpam-4703	36	40	4	4	NUM
ejpam-4703	36	41	]	]	PUNCT
ejpam-4703	36	42	.	.	PUNCT
ejpam-4703	37	1	this	this	PRON
ejpam-4703	37	2	is	be	AUX
ejpam-4703	37	3	being	be	AUX
ejpam-4703	37	4	provided	provide	VERB
ejpam-4703	37	5	to	to	PART
ejpam-4703	37	6	aid	aid	VERB
ejpam-4703	37	7	the	the	DET
ejpam-4703	37	8	derivation	derivation	NOUN
ejpam-4703	37	9	of	of	ADP
ejpam-4703	37	10	the	the	DET
ejpam-4703	37	11	asymptotic	asymptotic	ADJ
ejpam-4703	37	12	formulas	formula	NOUN
ejpam-4703	37	13	in	in	ADP
ejpam-4703	37	14	section	section	NOUN
ejpam-4703	37	15	3	3	NUM
ejpam-4703	37	16	.	.	PUNCT
ejpam-4703	38	1	proof	proof	NOUN
ejpam-4703	38	2	.	.	PUNCT
ejpam-4703	39	1	write	write	VERB
ejpam-4703	39	2	pn(nz	pn(nz	NOUN
ejpam-4703	39	3	)	)	PUNCT
ejpam-4703	39	4	=	=	SYM
ejpam-4703	39	5	n	n	X
ejpam-4703	39	6	!	!	PUNCT
ejpam-4703	40	1	2πi	2πi	NOUN
ejpam-4703	40	2	∫	∫	PROPN
ejpam-4703	40	3	c	c	PROPN
ejpam-4703	41	1	f(w)enwz−n	f(w)enwz−n	PROPN
ejpam-4703	41	2	logw	logw	PROPN
ejpam-4703	41	3	dw	dw	PROPN
ejpam-4703	41	4	w	w	PROPN
ejpam-4703	41	5	.	.	PUNCT
ejpam-4703	42	1	(	(	PUNCT
ejpam-4703	42	2	2.1	2.1	NUM
ejpam-4703	42	3	)	)	PUNCT
ejpam-4703	42	4	the	the	DET
ejpam-4703	42	5	key	key	ADJ
ejpam-4703	42	6	observation	observation	NOUN
ejpam-4703	42	7	used	use	VERB
ejpam-4703	42	8	for	for	ADP
ejpam-4703	42	9	obtaining	obtain	VERB
ejpam-4703	42	10	approximations	approximation	NOUN
ejpam-4703	42	11	of	of	ADP
ejpam-4703	42	12	pn(nz	pn(nz	NOUN
ejpam-4703	42	13	)	)	PUNCT
ejpam-4703	42	14	for	for	ADP
ejpam-4703	42	15	large	large	ADJ
ejpam-4703	42	16	n	n	NOUN
ejpam-4703	42	17	and	and	CCONJ
ejpam-4703	42	18	fixed	fix	VERB
ejpam-4703	42	19	z	z	NOUN
ejpam-4703	42	20	is	be	AUX
ejpam-4703	42	21	that	that	SCONJ
ejpam-4703	42	22	the	the	DET
ejpam-4703	42	23	main	main	ADJ
ejpam-4703	42	24	contribution	contribution	NOUN
ejpam-4703	42	25	of	of	ADP
ejpam-4703	42	26	the	the	DET
ejpam-4703	42	27	integrand	integrand	NOUN
ejpam-4703	42	28	to	to	ADP
ejpam-4703	42	29	the	the	DET
ejpam-4703	42	30	integral	integral	ADJ
ejpam-4703	42	31	originates	originate	NOUN
ejpam-4703	42	32	at	at	ADP
ejpam-4703	42	33	the	the	DET
ejpam-4703	42	34	saddle	saddle	NOUN
ejpam-4703	42	35	point	point	NOUN
ejpam-4703	42	36	of	of	ADP
ejpam-4703	42	37	the	the	DET
ejpam-4703	42	38	argument	argument	NOUN
ejpam-4703	42	39	of	of	ADP
ejpam-4703	42	40	the	the	DET
ejpam-4703	42	41	exponential	exponential	NOUN
ejpam-4703	42	42	(	(	PUNCT
ejpam-4703	42	43	for	for	ADP
ejpam-4703	42	44	a	a	DET
ejpam-4703	42	45	discussion	discussion	NOUN
ejpam-4703	42	46	of	of	ADP
ejpam-4703	42	47	saddle	saddle	NOUN
ejpam-4703	42	48	point	point	NOUN
ejpam-4703	42	49	method	method	NOUN
ejpam-4703	42	50	see	see	VERB
ejpam-4703	42	51	[	[	X
ejpam-4703	42	52	6	6	NUM
ejpam-4703	42	53	]	]	NUM
ejpam-4703	42	54	)	)	PUNCT
ejpam-4703	42	55	,	,	PUNCT
ejpam-4703	42	56	that	that	ADV
ejpam-4703	42	57	is	is	ADV
ejpam-4703	42	58	,	,	PUNCT
ejpam-4703	42	59	at	at	ADP
ejpam-4703	42	60	w	w	NOUN
ejpam-4703	42	61	=	=	SYM
ejpam-4703	42	62	z−1	z−1	PROPN
ejpam-4703	42	63	.	.	PUNCT
ejpam-4703	43	1	if	if	SCONJ
ejpam-4703	43	2	z−1	z−1	PROPN
ejpam-4703	43	3	is	be	AUX
ejpam-4703	43	4	not	not	PART
ejpam-4703	43	5	a	a	DET
ejpam-4703	43	6	pole	pole	NOUN
ejpam-4703	43	7	of	of	ADP
ejpam-4703	43	8	f(w	f(w	PROPN
ejpam-4703	43	9	)	)	PUNCT
ejpam-4703	43	10	,	,	PUNCT
ejpam-4703	43	11	then	then	ADV
ejpam-4703	43	12	f(w	f(w	PROPN
ejpam-4703	43	13	)	)	PUNCT
ejpam-4703	43	14	can	can	AUX
ejpam-4703	43	15	be	be	AUX
ejpam-4703	43	16	expanded	expand	VERB
ejpam-4703	43	17	around	around	ADP
ejpam-4703	43	18	z−1	z−1	PROPN
ejpam-4703	43	19	as	as	SCONJ
ejpam-4703	43	20	follows	follow	VERB
ejpam-4703	43	21	:	:	PUNCT
ejpam-4703	43	22	f(w	f(w	NUM
ejpam-4703	43	23	)	)	PUNCT
ejpam-4703	43	24	=	=	PUNCT
ejpam-4703	44	1	∞∑	∞∑	NUM
ejpam-4703	44	2	k=0	k=0	PROPN
ejpam-4703	44	3	f	f	X
ejpam-4703	44	4	(	(	PUNCT
ejpam-4703	44	5	k)(z−1	k)(z−1	PROPN
ejpam-4703	44	6	)	)	PUNCT
ejpam-4703	44	7	k	k	NOUN
ejpam-4703	44	8	!	!	PUNCT
ejpam-4703	44	9	(	(	PUNCT
ejpam-4703	44	10	w	w	ADP
ejpam-4703	44	11	−	−	PROPN
ejpam-4703	44	12	z−1)k	z−1)k	NUM
ejpam-4703	44	13	,	,	PUNCT
ejpam-4703	44	14	∣∣w	∣∣w	ADV
ejpam-4703	44	15	−	−	X
ejpam-4703	44	16	z−1	z−1	X
ejpam-4703	44	17	∣∣	∣∣	X
ejpam-4703	44	18	<	<	X
ejpam-4703	44	19	r	r	NOUN
ejpam-4703	44	20	,	,	PUNCT
ejpam-4703	44	21	(	(	PUNCT
ejpam-4703	44	22	2.2	2.2	NUM
ejpam-4703	44	23	)	)	PUNCT
ejpam-4703	44	24	where	where	SCONJ
ejpam-4703	44	25	r	r	NOUN
ejpam-4703	44	26	is	be	AUX
ejpam-4703	44	27	the	the	DET
ejpam-4703	44	28	distance	distance	NOUN
ejpam-4703	44	29	from	from	ADP
ejpam-4703	44	30	the	the	DET
ejpam-4703	44	31	z−1	z−1	PROPN
ejpam-4703	44	32	to	to	ADP
ejpam-4703	44	33	the	the	DET
ejpam-4703	44	34	nearest	near	ADJ
ejpam-4703	44	35	singularity	singularity	NOUN
ejpam-4703	44	36	of	of	ADP
ejpam-4703	44	37	f(w	f(w	PROPN
ejpam-4703	44	38	)	)	PUNCT
ejpam-4703	44	39	.	.	PUNCT
ejpam-4703	45	1	the	the	DET
ejpam-4703	45	2	radius	radius	NOUN
ejpam-4703	45	3	ϵ1	ϵ1	NOUN
ejpam-4703	45	4	of	of	ADP
ejpam-4703	45	5	the	the	DET
ejpam-4703	45	6	contour	contour	NOUN
ejpam-4703	45	7	c	c	NOUN
ejpam-4703	45	8	in	in	ADP
ejpam-4703	45	9	the	the	DET
ejpam-4703	45	10	definition	definition	NOUN
ejpam-4703	45	11	of	of	ADP
ejpam-4703	45	12	pn(z	pn(z	NOUN
ejpam-4703	45	13	)	)	PUNCT
ejpam-4703	45	14	can	can	AUX
ejpam-4703	45	15	be	be	AUX
ejpam-4703	45	16	chosen	choose	VERB
ejpam-4703	45	17	as	as	ADP
ejpam-4703	45	18	close	close	ADV
ejpam-4703	45	19	to	to	ADP
ejpam-4703	45	20	0	0	NUM
ejpam-4703	45	21	as	as	ADP
ejpam-4703	45	22	necessary	necessary	ADJ
ejpam-4703	45	23	.	.	PUNCT
ejpam-4703	46	1	then	then	ADV
ejpam-4703	46	2	for	for	ADP
ejpam-4703	46	3	w	w	PROPN
ejpam-4703	46	4	∈	∈	PROPN
ejpam-4703	46	5	c(c	c(c	PROPN
ejpam-4703	46	6	:	:	PUNCT
ejpam-4703	46	7	|w|	|w|	ADJ
ejpam-4703	46	8	=	=	PUNCT
ejpam-4703	46	9	ϵ1	ϵ1	NOUN
ejpam-4703	46	10	)	)	PUNCT
ejpam-4703	46	11	,	,	PUNCT
ejpam-4703	46	12	the	the	DET
ejpam-4703	46	13	above	above	ADJ
ejpam-4703	46	14	series	series	NOUN
ejpam-4703	46	15	is	be	AUX
ejpam-4703	46	16	absolutely	absolutely	ADV
ejpam-4703	46	17	convergent	convergent	ADJ
ejpam-4703	46	18	if	if	SCONJ
ejpam-4703	46	19	∣∣z−1	∣∣z−1	NOUN
ejpam-4703	46	20	∣∣	∣∣	X
ejpam-4703	46	21	<	<	X
ejpam-4703	46	22	∣∣z−1	∣∣z−1	NOUN
ejpam-4703	46	23	−	−	X
ejpam-4703	46	24	wk	wk	NOUN
ejpam-4703	46	25	∣∣	∣∣	X
ejpam-4703	46	26	for	for	ADP
ejpam-4703	46	27	all	all	PRON
ejpam-4703	46	28	k	k	NOUN
ejpam-4703	46	29	=	=	SYM
ejpam-4703	46	30	1	1	NUM
ejpam-4703	46	31	,	,	PUNCT
ejpam-4703	46	32	2	2	NUM
ejpam-4703	46	33	,	,	PUNCT
ejpam-4703	46	34	·	·	PUNCT
ejpam-4703	46	35	·	·	PUNCT
ejpam-4703	46	36	·	·	PUNCT
ejpam-4703	46	37	.	.	PUNCT
ejpam-4703	47	1	substituting	substitute	VERB
ejpam-4703	47	2	the	the	DET
ejpam-4703	47	3	expansion	expansion	NOUN
ejpam-4703	47	4	to	to	ADP
ejpam-4703	47	5	f(w	f(w	PROPN
ejpam-4703	47	6	)	)	PUNCT
ejpam-4703	47	7	yields	yield	VERB
ejpam-4703	47	8	pn(nz	pn(nz	NOUN
ejpam-4703	47	9	)	)	PUNCT
ejpam-4703	47	10	=	=	SYM
ejpam-4703	47	11	n	n	X
ejpam-4703	47	12	!	!	PUNCT
ejpam-4703	47	13	2πi	2πi	NOUN
ejpam-4703	47	14	∫	∫	PROPN
ejpam-4703	48	1	c	c	NOUN
ejpam-4703	48	2	∞∑	∞∑	ADJ
ejpam-4703	48	3	k=0	k=0	PROPN
ejpam-4703	48	4	f	f	X
ejpam-4703	48	5	(	(	PUNCT
ejpam-4703	48	6	k)(z−1	k)(z−1	PROPN
ejpam-4703	48	7	)	)	PUNCT
ejpam-4703	48	8	k	k	NOUN
ejpam-4703	48	9	!	!	PUNCT
ejpam-4703	49	1	(	(	PUNCT
ejpam-4703	49	2	w	w	NOUN
ejpam-4703	49	3	−	−	PROPN
ejpam-4703	49	4	z−1)kenwz	z−1)kenwz	NOUN
ejpam-4703	49	5	dw	dw	PROPN
ejpam-4703	49	6	wn+1	wn+1	VERB
ejpam-4703	49	7	,	,	PUNCT
ejpam-4703	49	8	(	(	PUNCT
ejpam-4703	49	9	2.3	2.3	NUM
ejpam-4703	49	10	)	)	PUNCT
ejpam-4703	49	11	where	where	SCONJ
ejpam-4703	49	12	f	f	PROPN
ejpam-4703	49	13	(	(	PUNCT
ejpam-4703	49	14	k)(z−1	k)(z−1	PROPN
ejpam-4703	49	15	)	)	PUNCT
ejpam-4703	49	16	=	=	SYM
ejpam-4703	50	1	k	k	X
ejpam-4703	50	2	!	!	PUNCT
ejpam-4703	51	1	2π	2π	PROPN
ejpam-4703	51	2	∫	∫	PROPN
ejpam-4703	51	3	c′	c′	NOUN
ejpam-4703	51	4	f(t)dt	f(t)dt	PROPN
ejpam-4703	51	5	(	(	PUNCT
ejpam-4703	51	6	t−	t−	PROPN
ejpam-4703	51	7	z−1)k+1	z−1)k+1	NUM
ejpam-4703	51	8	,	,	PUNCT
ejpam-4703	51	9	(	(	PUNCT
ejpam-4703	51	10	2.4	2.4	NUM
ejpam-4703	51	11	)	)	PUNCT
ejpam-4703	51	12	and	and	CCONJ
ejpam-4703	51	13	c	c	NOUN
ejpam-4703	51	14	′	′	NOUN
ejpam-4703	51	15	is	be	AUX
ejpam-4703	51	16	a	a	DET
ejpam-4703	51	17	circle	circle	NOUN
ejpam-4703	51	18	around	around	ADP
ejpam-4703	51	19	z−1	z−1	PROPN
ejpam-4703	51	20	whose	whose	DET
ejpam-4703	51	21	radius	radius	NOUN
ejpam-4703	51	22	r	r	PROPN
ejpam-4703	51	23	≡	≡	PROPN
ejpam-4703	51	24	∣∣t−	∣∣t−	VERB
ejpam-4703	51	25	z−1	z−1	PROPN
ejpam-4703	51	26	∣∣	∣∣	X
ejpam-4703	51	27	<	<	X
ejpam-4703	51	28	∣∣z−1	∣∣z−1	NOUN
ejpam-4703	51	29	−	−	X
ejpam-4703	51	30	wk	wk	NOUN
ejpam-4703	51	31	∣∣	∣∣	X
ejpam-4703	51	32	for	for	ADP
ejpam-4703	51	33	all	all	DET
ejpam-4703	51	34	k.	k.	PROPN
ejpam-4703	51	35	that	that	PRON
ejpam-4703	51	36	is	be	AUX
ejpam-4703	51	37	,	,	PUNCT
ejpam-4703	51	38	r	r	PROPN
ejpam-4703	51	39	≡	≡	PROPN
ejpam-4703	51	40	min	min	PROPN
ejpam-4703	51	41	∣∣z−1	∣∣z−1	PROPN
ejpam-4703	51	42	−	−	PROPN
ejpam-4703	51	43	wk	wk	INTJ
ejpam-4703	51	44	∣∣−	∣∣−	PROPN
ejpam-4703	51	45	ϵ2	ϵ2	PROPN
ejpam-4703	51	46	for	for	ADP
ejpam-4703	51	47	some	some	DET
ejpam-4703	51	48	ϵ2	ϵ2	NOUN
ejpam-4703	51	49	>	>	X
ejpam-4703	51	50	0	0	X
ejpam-4703	51	51	.	.	PUNCT
ejpam-4703	52	1	since	since	SCONJ
ejpam-4703	52	2	f(t	f(t	PROPN
ejpam-4703	52	3	)	)	PUNCT
ejpam-4703	52	4	is	be	AUX
ejpam-4703	52	5	bounded	bound	VERB
ejpam-4703	52	6	on	on	ADP
ejpam-4703	52	7	c	c	NOUN
ejpam-4703	52	8	′	′	NOUN
ejpam-4703	52	9	there	there	PRON
ejpam-4703	52	10	exists	exist	VERB
ejpam-4703	52	11	m1	m1	NOUN
ejpam-4703	52	12	such	such	ADJ
ejpam-4703	52	13	that	that	SCONJ
ejpam-4703	52	14	|f(t)|	|f(t)|	PROPN
ejpam-4703	52	15	<	<	X
ejpam-4703	52	16	m1	m1	PROPN
ejpam-4703	52	17	for	for	ADP
ejpam-4703	52	18	t	t	PROPN
ejpam-4703	52	19	∈	∈	PROPN
ejpam-4703	52	20	c	c	PROPN
ejpam-4703	52	21	′.	′.	NOUN
ejpam-4703	52	22	therefore,∣∣∣f	therefore,∣∣∣f	NOUN
ejpam-4703	52	23	(	(	PUNCT
ejpam-4703	52	24	k)(z−1	k)(z−1	PROPN
ejpam-4703	52	25	)	)	PUNCT
ejpam-4703	52	26	∣∣∣	∣∣∣	NOUN
ejpam-4703	52	27	≤	≤	NUM
ejpam-4703	52	28	k	k	X
ejpam-4703	52	29	!	!	PUNCT
ejpam-4703	53	1	2π	2π	PROPN
ejpam-4703	53	2	∫	∫	PROPN
ejpam-4703	53	3	c′	c′	NOUN
ejpam-4703	54	1	|f(t)|	|f(t)|	PROPN
ejpam-4703	54	2	|t−	|t−	PROPN
ejpam-4703	54	3	z−1|k+1	z−1|k+1	NUM
ejpam-4703	54	4	|dt|	|dt|	PROPN
ejpam-4703	54	5	≤	≤	PUNCT
ejpam-4703	55	1	k	k	X
ejpam-4703	55	2	!	!	PUNCT
ejpam-4703	56	1	2π	2π	PROPN
ejpam-4703	56	2	m1	m1	PROPN
ejpam-4703	56	3	rk+1	rk+1	ADP
ejpam-4703	56	4	2πr	2πr	NOUN
ejpam-4703	56	5	=	=	SYM
ejpam-4703	57	1	m1	m1	PROPN
ejpam-4703	57	2	k	k	X
ejpam-4703	57	3	!	!	PUNCT
ejpam-4703	57	4	rk	rk	PROPN
ejpam-4703	57	5	.	.	PUNCT
ejpam-4703	58	1	(	(	PUNCT
ejpam-4703	58	2	2.5	2.5	NUM
ejpam-4703	58	3	)	)	PUNCT
ejpam-4703	58	4	let	let	VERB
ejpam-4703	58	5	a	a	DET
ejpam-4703	58	6	=	=	SYM
ejpam-4703	58	7	max	max	PROPN
ejpam-4703	58	8	w∈c	w∈c	X
ejpam-4703	59	1	|w−z−1|	|w−z−1|	X
ejpam-4703	59	2	r	r	NOUN
ejpam-4703	59	3	.	.	PUNCT
ejpam-4703	60	1	note	note	VERB
ejpam-4703	60	2	that	that	SCONJ
ejpam-4703	60	3	a	a	PRON
ejpam-4703	60	4	depends	depend	VERB
ejpam-4703	60	5	only	only	ADV
ejpam-4703	60	6	on	on	ADP
ejpam-4703	60	7	z	z	PROPN
ejpam-4703	60	8	,	,	PUNCT
ejpam-4703	60	9	ϵ	ϵ	X
ejpam-4703	60	10	,	,	PUNCT
ejpam-4703	60	11	and	and	CCONJ
ejpam-4703	60	12	r	r	AUX
ejpam-4703	60	13	and	and	CCONJ
ejpam-4703	60	14	we	we	PRON
ejpam-4703	60	15	can	can	AUX
ejpam-4703	60	16	make	make	VERB
ejpam-4703	60	17	a	a	DET
ejpam-4703	60	18	<	<	X
ejpam-4703	60	19	1	1	NUM
ejpam-4703	60	20	.	.	PUNCT
ejpam-4703	60	21	then	then	ADV
ejpam-4703	60	22	|pn(nz)|	|pn(nz)|	VERB
ejpam-4703	60	23	≤	≤	ADJ
ejpam-4703	60	24	m1	m1	PROPN
ejpam-4703	60	25	∞∑	∞∑	PROPN
ejpam-4703	60	26	k=0	k=0	PROPN
ejpam-4703	60	27	n	n	CCONJ
ejpam-4703	60	28	!	!	PUNCT
ejpam-4703	61	1	2π	2π	PROPN
ejpam-4703	61	2	∫	∫	PROPN
ejpam-4703	62	1	c	c	X
ejpam-4703	62	2	(	(	PUNCT
ejpam-4703	62	3	∣∣w	∣∣w	ADV
ejpam-4703	62	4	−	−	X
ejpam-4703	62	5	z−1	z−1	PROPN
ejpam-4703	62	6	∣∣	∣∣	PROPN
ejpam-4703	62	7	r	r	NOUN
ejpam-4703	62	8	)	)	PUNCT
ejpam-4703	62	9	k	k	NOUN
ejpam-4703	62	10	|enwz|	|enwz|	NOUN
ejpam-4703	62	11	|dw|	|dw|	NUM
ejpam-4703	62	12	|wn+1|	|wn+1|	NOUN
ejpam-4703	62	13	(	(	PUNCT
ejpam-4703	62	14	2.6	2.6	NUM
ejpam-4703	62	15	)	)	PUNCT
ejpam-4703	62	16	c.	c.	NOUN
ejpam-4703	62	17	corcino	corcino	PROPN
ejpam-4703	62	18	,	,	PUNCT
ejpam-4703	62	19	r.	r.	PROPN
ejpam-4703	62	20	corcino	corcino	PROPN
ejpam-4703	62	21	/	/	SYM
ejpam-4703	62	22	eur	eur	PROPN
ejpam-4703	62	23	.	.	PUNCT
ejpam-4703	63	1	j.	j.	PROPN
ejpam-4703	63	2	pure	pure	PROPN
ejpam-4703	63	3	appl	appl	PROPN
ejpam-4703	63	4	.	.	PROPN
ejpam-4703	63	5	math	math	PROPN
ejpam-4703	63	6	,	,	PUNCT
ejpam-4703	63	7	16	16	NUM
ejpam-4703	63	8	(	(	PUNCT
ejpam-4703	63	9	2	2	NUM
ejpam-4703	63	10	)	)	PUNCT
ejpam-4703	63	11	(	(	PUNCT
ejpam-4703	63	12	2023	2023	NUM
ejpam-4703	63	13	)	)	PUNCT
ejpam-4703	63	14	,	,	PUNCT
ejpam-4703	63	15	791	791	NUM
ejpam-4703	63	16	-	-	SYM
ejpam-4703	63	17	805	805	NUM
ejpam-4703	63	18	794	794	NUM
ejpam-4703	63	19	the	the	DET
ejpam-4703	63	20	function	function	NOUN
ejpam-4703	63	21	enwz	enwz	NOUN
ejpam-4703	63	22	is	be	AUX
ejpam-4703	63	23	bounded	bound	VERB
ejpam-4703	63	24	on	on	ADP
ejpam-4703	63	25	c	c	PROPN
ejpam-4703	63	26	for	for	ADP
ejpam-4703	63	27	finite	finite	NOUN
ejpam-4703	63	28	n	n	CCONJ
ejpam-4703	63	29	and	and	CCONJ
ejpam-4703	63	30	fixed	fix	VERB
ejpam-4703	63	31	z.	z.	PROPN
ejpam-4703	64	1	thus	thus	ADV
ejpam-4703	64	2	,	,	PUNCT
ejpam-4703	64	3	there	there	PRON
ejpam-4703	64	4	exists	exist	VERB
ejpam-4703	64	5	m2	m2	PROPN
ejpam-4703	64	6	such	such	ADJ
ejpam-4703	64	7	that	that	SCONJ
ejpam-4703	64	8	|enwz|	|enwz|	PROPN
ejpam-4703	64	9	≤	≤	PROPN
ejpam-4703	64	10	m2	m2	PROPN
ejpam-4703	64	11	,	,	PUNCT
ejpam-4703	64	12	for	for	ADP
ejpam-4703	64	13	w	w	PROPN
ejpam-4703	64	14	∈	∈	PROPN
ejpam-4703	64	15	c.	c.	NOUN
ejpam-4703	64	16	hence	hence	ADV
ejpam-4703	64	17	,	,	PUNCT
ejpam-4703	64	18	|pn(nz)|	|pn(nz)|	VERB
ejpam-4703	64	19	≤	≤	NOUN
ejpam-4703	65	1	m1m2	m1m2	PROPN
ejpam-4703	65	2	∞∑	∞∑	ADJ
ejpam-4703	65	3	k=0	k=0	PROPN
ejpam-4703	65	4	n	n	CCONJ
ejpam-4703	65	5	!	!	PUNCT
ejpam-4703	66	1	2π	2π	PROPN
ejpam-4703	66	2	∫	∫	PROPN
ejpam-4703	66	3	c	c	PROPN
ejpam-4703	66	4	ak	ak	PROPN
ejpam-4703	66	5	|dw|	|dw|	PROPN
ejpam-4703	66	6	|wn+1|	|wn+1|	NOUN
ejpam-4703	66	7	=	=	PUNCT
ejpam-4703	66	8	m1m2	m1m2	PROPN
ejpam-4703	66	9	∞∑	∞∑	DET
ejpam-4703	66	10	k=0	k=0	PROPN
ejpam-4703	66	11	ak	ak	PROPN
ejpam-4703	66	12	n	n	X
ejpam-4703	66	13	!	!	PUNCT
ejpam-4703	67	1	2π	2π	NOUN
ejpam-4703	67	2	1	1	NUM
ejpam-4703	67	3	ϵn+1	ϵn+1	NUM
ejpam-4703	67	4	1	1	NUM
ejpam-4703	67	5	2π	2π	NOUN
ejpam-4703	67	6	ϵ1	ϵ1	VERB
ejpam-4703	67	7	=	=	SYM
ejpam-4703	67	8	m1m2	m1m2	X
ejpam-4703	67	9	n	n	X
ejpam-4703	67	10	!	!	PUNCT
ejpam-4703	68	1	ϵn1	ϵn1	NOUN
ejpam-4703	69	1	∞∑	∞∑	DET
ejpam-4703	69	2	k=0	k=0	PROPN
ejpam-4703	69	3	ak	ak	PROPN
ejpam-4703	69	4	<	<	X
ejpam-4703	69	5	∞	∞	PROPN
ejpam-4703	69	6	.	.	PUNCT
ejpam-4703	70	1	(	(	PUNCT
ejpam-4703	70	2	2.7	2.7	NUM
ejpam-4703	70	3	)	)	PUNCT
ejpam-4703	70	4	evaluating	evaluate	VERB
ejpam-4703	70	5	the	the	DET
ejpam-4703	70	6	integral	integral	ADJ
ejpam-4703	70	7	in	in	ADP
ejpam-4703	70	8	(	(	PUNCT
ejpam-4703	70	9	2.3	2.3	NUM
ejpam-4703	70	10	)	)	PUNCT
ejpam-4703	70	11	,	,	PUNCT
ejpam-4703	70	12	pn(nz	pn(nz	PROPN
ejpam-4703	70	13	)	)	PUNCT
ejpam-4703	70	14	=	=	NOUN
ejpam-4703	71	1	∞∑	∞∑	NUM
ejpam-4703	71	2	k=0	k=0	PROPN
ejpam-4703	71	3	f	f	X
ejpam-4703	71	4	(	(	PUNCT
ejpam-4703	71	5	k)(z−1	k)(z−1	PROPN
ejpam-4703	71	6	)	)	PUNCT
ejpam-4703	71	7	k	k	NOUN
ejpam-4703	71	8	!	!	PUNCT
ejpam-4703	71	9	n	n	CCONJ
ejpam-4703	71	10	!	!	PUNCT
ejpam-4703	72	1	2πi	2πi	NOUN
ejpam-4703	73	1	∫	∫	PROPN
ejpam-4703	73	2	c	c	X
ejpam-4703	73	3	(	(	PUNCT
ejpam-4703	73	4	w	w	NOUN
ejpam-4703	73	5	−	−	PROPN
ejpam-4703	73	6	z−1)kenwz	z−1)kenwz	NOUN
ejpam-4703	73	7	dw	dw	PROPN
ejpam-4703	73	8	wn+1	wn+1	AUX
ejpam-4703	73	9	=	=	SYM
ejpam-4703	73	10	(	(	PUNCT
ejpam-4703	73	11	nz)n	nz)n	PROPN
ejpam-4703	73	12	∞∑	∞∑	PROPN
ejpam-4703	73	13	k=0	k=0	PROPN
ejpam-4703	73	14	f	f	X
ejpam-4703	73	15	(	(	PUNCT
ejpam-4703	73	16	k)(z−1	k)(z−1	PROPN
ejpam-4703	73	17	)	)	PUNCT
ejpam-4703	73	18	k	k	NOUN
ejpam-4703	73	19	!	!	PUNCT
ejpam-4703	73	20	n	n	X
ejpam-4703	73	21	!	!	PUNCT
ejpam-4703	74	1	(	(	PUNCT
ejpam-4703	74	2	nz)n	nz)n	PROPN
ejpam-4703	74	3	1	1	NUM
ejpam-4703	74	4	2πi	2πi	NOUN
ejpam-4703	74	5	∫	∫	PROPN
ejpam-4703	74	6	c	c	X
ejpam-4703	74	7	(	(	PUNCT
ejpam-4703	74	8	w	w	NOUN
ejpam-4703	74	9	−	−	PROPN
ejpam-4703	74	10	z−1)kenwz	z−1)kenwz	NOUN
ejpam-4703	74	11	dw	dw	PROPN
ejpam-4703	74	12	wn+1	wn+1	AUX
ejpam-4703	74	13	=	=	SYM
ejpam-4703	74	14	(	(	PUNCT
ejpam-4703	74	15	nz)n	nz)n	PROPN
ejpam-4703	74	16	∞∑	∞∑	PROPN
ejpam-4703	74	17	k=0	k=0	PROPN
ejpam-4703	74	18	f	f	X
ejpam-4703	74	19	(	(	PUNCT
ejpam-4703	74	20	k)(z−1	k)(z−1	PROPN
ejpam-4703	74	21	)	)	PUNCT
ejpam-4703	75	1	k	k	PROPN
ejpam-4703	75	2	!	!	PROPN
ejpam-4703	75	3	φk(n	φk(n	PROPN
ejpam-4703	75	4	,	,	PUNCT
ejpam-4703	75	5	z	z	NOUN
ejpam-4703	75	6	)	)	PUNCT
ejpam-4703	75	7	,	,	PUNCT
ejpam-4703	75	8	(	(	PUNCT
ejpam-4703	75	9	2.8	2.8	NUM
ejpam-4703	75	10	)	)	PUNCT
ejpam-4703	76	1	where	where	SCONJ
ejpam-4703	76	2	φk(n	φk(n	NUM
ejpam-4703	76	3	,	,	PUNCT
ejpam-4703	76	4	z	z	NOUN
ejpam-4703	76	5	)	)	PUNCT
ejpam-4703	76	6	=	=	SYM
ejpam-4703	76	7	n	n	X
ejpam-4703	76	8	!	!	PUNCT
ejpam-4703	76	9	(	(	PUNCT
ejpam-4703	76	10	nz)n	nz)n	PROPN
ejpam-4703	76	11	1	1	NUM
ejpam-4703	76	12	2πi	2πi	NOUN
ejpam-4703	76	13	∫	∫	PROPN
ejpam-4703	76	14	c	c	X
ejpam-4703	76	15	(	(	PUNCT
ejpam-4703	76	16	w	w	NOUN
ejpam-4703	76	17	−	−	PROPN
ejpam-4703	76	18	z−1)kenwz	z−1)kenwz	NOUN
ejpam-4703	76	19	dw	dw	PROPN
ejpam-4703	76	20	wn+1	wn+1	AUX
ejpam-4703	76	21	.	.	PUNCT
ejpam-4703	77	1	(	(	PUNCT
ejpam-4703	77	2	2.9	2.9	NUM
ejpam-4703	77	3	)	)	PUNCT
ejpam-4703	77	4	from	from	ADP
ejpam-4703	77	5	lemma	lemma	PROPN
ejpam-4703	77	6	1.1	1.1	NUM
ejpam-4703	77	7	and	and	CCONJ
ejpam-4703	77	8	lemma	lemma	PROPN
ejpam-4703	77	9	1.2	1.2	NUM
ejpam-4703	77	10	,	,	PUNCT
ejpam-4703	77	11	the	the	DET
ejpam-4703	77	12	functions	function	NOUN
ejpam-4703	77	13	φk(n	φk(n	NUM
ejpam-4703	77	14	,	,	PUNCT
ejpam-4703	77	15	z	z	NOUN
ejpam-4703	77	16	)	)	PUNCT
ejpam-4703	77	17	are	be	AUX
ejpam-4703	77	18	polynomials	polynomial	NOUN
ejpam-4703	77	19	in	in	ADP
ejpam-4703	77	20	n	n	CCONJ
ejpam-4703	77	21	divided	divide	VERB
ejpam-4703	77	22	by	by	ADP
ejpam-4703	77	23	powers	power	NOUN
ejpam-4703	77	24	of	of	ADP
ejpam-4703	77	25	nz	nz	PROPN
ejpam-4703	77	26	and	and	CCONJ
ejpam-4703	77	27	constitute	constitute	VERB
ejpam-4703	77	28	an	an	DET
ejpam-4703	77	29	asymptotic	asymptotic	ADJ
ejpam-4703	77	30	sequence	sequence	NOUN
ejpam-4703	77	31	for	for	ADP
ejpam-4703	77	32	n	n	PRON
ejpam-4703	77	33	→	→	PUNCT
ejpam-4703	77	34	+	+	PROPN
ejpam-4703	77	35	∞.	∞.	PROPN
ejpam-4703	77	36	the	the	DET
ejpam-4703	77	37	desired	desire	VERB
ejpam-4703	77	38	asymptotic	asymptotic	ADJ
ejpam-4703	77	39	sequence	sequence	NOUN
ejpam-4703	77	40	is	be	AUX
ejpam-4703	77	41	pn(nz	pn(nz	NOUN
ejpam-4703	77	42	)	)	PUNCT
ejpam-4703	78	1	=	=	SYM
ejpam-4703	78	2	(	(	PUNCT
ejpam-4703	78	3	nz)n	nz)n	PROPN
ejpam-4703	78	4	∞∑	∞∑	PROPN
ejpam-4703	78	5	k=0	k=0	PROPN
ejpam-4703	78	6	f	f	X
ejpam-4703	78	7	(	(	PUNCT
ejpam-4703	78	8	k)(z−1	k)(z−1	PROPN
ejpam-4703	78	9	)	)	PUNCT
ejpam-4703	79	1	k	k	NOUN
ejpam-4703	79	2	!	!	PROPN
ejpam-4703	79	3	pk(n	pk(n	X
ejpam-4703	79	4	)	)	PUNCT
ejpam-4703	79	5	(	(	PUNCT
ejpam-4703	79	6	nz)k	nz)k	NUM
ejpam-4703	79	7	,	,	PUNCT
ejpam-4703	79	8	(	(	PUNCT
ejpam-4703	79	9	2.10	2.10	NUM
ejpam-4703	79	10	)	)	PUNCT
ejpam-4703	80	1	where	where	SCONJ
ejpam-4703	80	2	pk(n	pk(n	NOUN
ejpam-4703	80	3	)	)	PUNCT
ejpam-4703	80	4	are	be	AUX
ejpam-4703	80	5	defined	define	VERB
ejpam-4703	80	6	in	in	ADP
ejpam-4703	80	7	lemma	lemma	PROPN
ejpam-4703	80	8	1.1	1.1	NUM
ejpam-4703	80	9	.	.	PUNCT
ejpam-4703	81	1	remark	remark	VERB
ejpam-4703	81	2	2.1	2.1	NUM
ejpam-4703	81	3	.	.	PUNCT
ejpam-4703	82	1	as	as	SCONJ
ejpam-4703	82	2	can	can	AUX
ejpam-4703	82	3	be	be	AUX
ejpam-4703	82	4	seen	see	VERB
ejpam-4703	82	5	in	in	ADP
ejpam-4703	82	6	the	the	DET
ejpam-4703	82	7	proof	proof	NOUN
ejpam-4703	82	8	of	of	ADP
ejpam-4703	82	9	theorem	theorem	ADJ
ejpam-4703	82	10	1.3	1.3	NUM
ejpam-4703	82	11	,	,	PUNCT
ejpam-4703	82	12	the	the	DET
ejpam-4703	82	13	results	result	NOUN
ejpam-4703	82	14	of	of	ADP
ejpam-4703	82	15	the	the	DET
ejpam-4703	82	16	theorem	theorem	NOUN
ejpam-4703	82	17	still	still	ADV
ejpam-4703	82	18	hold	hold	VERB
ejpam-4703	82	19	for	for	ADP
ejpam-4703	82	20	f(t	f(t	NOUN
ejpam-4703	82	21	)	)	PUNCT
ejpam-4703	82	22	having	have	VERB
ejpam-4703	82	23	poles	pole	NOUN
ejpam-4703	82	24	w1	w1	NOUN
ejpam-4703	82	25	,	,	PUNCT
ejpam-4703	82	26	w2	w2	NOUN
ejpam-4703	82	27	,	,	PUNCT
ejpam-4703	82	28	.	.	PUNCT
ejpam-4703	82	29	.	.	PUNCT
ejpam-4703	82	30	.	.	PUNCT
ejpam-4703	83	1	of	of	ADP
ejpam-4703	83	2	order	order	NOUN
ejpam-4703	83	3	greater	great	ADJ
ejpam-4703	83	4	than	than	ADP
ejpam-4703	83	5	1	1	NUM
ejpam-4703	83	6	.	.	NOUN
ejpam-4703	83	7	3	3	NUM
ejpam-4703	83	8	.	.	PUNCT
ejpam-4703	84	1	the	the	DET
ejpam-4703	84	2	asymptotic	asymptotic	ADJ
ejpam-4703	84	3	approximations	approximation	NOUN
ejpam-4703	84	4	the	the	DET
ejpam-4703	84	5	following	follow	VERB
ejpam-4703	84	6	are	be	AUX
ejpam-4703	84	7	the	the	DET
ejpam-4703	84	8	main	main	ADJ
ejpam-4703	84	9	results	result	NOUN
ejpam-4703	84	10	of	of	ADP
ejpam-4703	84	11	the	the	DET
ejpam-4703	84	12	study	study	NOUN
ejpam-4703	84	13	.	.	PUNCT
ejpam-4703	85	1	in	in	ADP
ejpam-4703	85	2	the	the	DET
ejpam-4703	85	3	discussion	discussion	NOUN
ejpam-4703	85	4	below	below	ADV
ejpam-4703	85	5	,	,	PUNCT
ejpam-4703	85	6	δ	δ	PROPN
ejpam-4703	85	7	=	=	PRON
ejpam-4703	85	8	log	log	PROPN
ejpam-4703	85	9	λ	λ	NOUN
ejpam-4703	85	10	,	,	PUNCT
ejpam-4703	85	11	λ	λ	PROPN
ejpam-4703	85	12	∈	∈	PROPN
ejpam-4703	85	13	c\{0	c\{0	PROPN
ejpam-4703	85	14	}	}	PUNCT
ejpam-4703	85	15	where	where	SCONJ
ejpam-4703	85	16	the	the	DET
ejpam-4703	85	17	logarithm	logarithm	NOUN
ejpam-4703	85	18	is	be	AUX
ejpam-4703	85	19	taken	take	VERB
ejpam-4703	85	20	to	to	PART
ejpam-4703	85	21	be	be	AUX
ejpam-4703	85	22	the	the	DET
ejpam-4703	85	23	principal	principal	ADJ
ejpam-4703	85	24	branch	branch	NOUN
ejpam-4703	85	25	and	and	CCONJ
ejpam-4703	85	26	ρ	ρ	NUM
ejpam-4703	85	27	=	=	SYM
ejpam-4703	85	28	(	(	PUNCT
ejpam-4703	85	29	δ+µ	δ+µ	PROPN
ejpam-4703	85	30	ln(ba−1))/2	ln(ba−1))/2	PROPN
ejpam-4703	85	31	.	.	PUNCT
ejpam-4703	85	32	theorem	theorem	VERB
ejpam-4703	85	33	3.1	3.1	NUM
ejpam-4703	85	34	.	.	PUNCT
ejpam-4703	86	1	(	(	PUNCT
ejpam-4703	86	2	apostol	apostol	NOUN
ejpam-4703	86	3	-	-	PUNCT
ejpam-4703	86	4	bernoulli	bernoulli	NOUN
ejpam-4703	86	5	type	type	NOUN
ejpam-4703	86	6	polynomials	polynomial	NOUN
ejpam-4703	86	7	of	of	ADP
ejpam-4703	86	8	order	order	NOUN
ejpam-4703	86	9	1	1	X
ejpam-4703	86	10	)	)	PUNCT
ejpam-4703	86	11	let	let	VERB
ejpam-4703	86	12	a	a	DET
ejpam-4703	86	13	,	,	PUNCT
ejpam-4703	86	14	b	b	NOUN
ejpam-4703	86	15	,	,	PUNCT
ejpam-4703	86	16	c	c	PROPN
ejpam-4703	86	17	∈	∈	PROPN
ejpam-4703	86	18	r+\{1	r+\{1	PROPN
ejpam-4703	86	19	}	}	PUNCT
ejpam-4703	86	20	,	,	PUNCT
ejpam-4703	86	21	a	a	DET
ejpam-4703	86	22	̸=	̸=	PROPN
ejpam-4703	86	23	b	b	PROPN
ejpam-4703	86	24	and	and	CCONJ
ejpam-4703	86	25	µ	µ	X
ejpam-4703	86	26	=	=	PUNCT
ejpam-4703	86	27	(	(	PUNCT
ejpam-4703	86	28	x	x	X
ejpam-4703	86	29	ln	ln	PROPN
ejpam-4703	86	30	c)−1	c)−1	PROPN
ejpam-4703	86	31	.	.	PUNCT
ejpam-4703	87	1	for	for	ADP
ejpam-4703	87	2	x	x	PROPN
ejpam-4703	87	3	∈	∈	PROPN
ejpam-4703	87	4	c\{0	c\{0	PROPN
ejpam-4703	87	5	}	}	PUNCT
ejpam-4703	87	6	,	,	PUNCT
ejpam-4703	87	7	such	such	ADJ
ejpam-4703	87	8	that	that	SCONJ
ejpam-4703	87	9	|µ|	|µ|	PROPN
ejpam-4703	87	10	<	<	X
ejpam-4703	87	11	|µ±	|µ±	PROPN
ejpam-4703	87	12	δ	δ	PROPN
ejpam-4703	87	13	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	87	14	)	)	PUNCT
ejpam-4703	87	15	|	|	ADV
ejpam-4703	87	16	,	,	PUNCT
ejpam-4703	87	17	c.	c.	PROPN
ejpam-4703	87	18	corcino	corcino	PROPN
ejpam-4703	87	19	,	,	PUNCT
ejpam-4703	87	20	r.	r.	PROPN
ejpam-4703	87	21	corcino	corcino	PROPN
ejpam-4703	87	22	/	/	SYM
ejpam-4703	87	23	eur	eur	PROPN
ejpam-4703	87	24	.	.	PUNCT
ejpam-4703	88	1	j.	j.	PROPN
ejpam-4703	88	2	pure	pure	PROPN
ejpam-4703	88	3	appl	appl	PROPN
ejpam-4703	88	4	.	.	PROPN
ejpam-4703	88	5	math	math	PROPN
ejpam-4703	88	6	,	,	PUNCT
ejpam-4703	88	7	16	16	NUM
ejpam-4703	88	8	(	(	PUNCT
ejpam-4703	88	9	2	2	NUM
ejpam-4703	88	10	)	)	PUNCT
ejpam-4703	88	11	(	(	PUNCT
ejpam-4703	88	12	2023	2023	NUM
ejpam-4703	88	13	)	)	PUNCT
ejpam-4703	88	14	,	,	PUNCT
ejpam-4703	88	15	791	791	NUM
ejpam-4703	88	16	-	-	SYM
ejpam-4703	88	17	805	805	NUM
ejpam-4703	88	18	795	795	NUM
ejpam-4703	88	19	the	the	DET
ejpam-4703	88	20	following	follow	VERB
ejpam-4703	88	21	formula	formula	NOUN
ejpam-4703	88	22	holds	hold	VERB
ejpam-4703	88	23	,	,	PUNCT
ejpam-4703	88	24	bn(nx;λ	bn(nx;λ	VERB
ejpam-4703	88	25	;	;	PUNCT
ejpam-4703	88	26	a	a	DET
ejpam-4703	88	27	,	,	PUNCT
ejpam-4703	88	28	b	b	NOUN
ejpam-4703	88	29	,	,	PUNCT
ejpam-4703	88	30	c	c	NOUN
ejpam-4703	88	31	)	)	PUNCT
ejpam-4703	88	32	=	=	SYM
ejpam-4703	89	1	(	(	PUNCT
ejpam-4703	89	2	nx	nx	X
ejpam-4703	89	3	ln	ln	NOUN
ejpam-4703	89	4	c)n	c)n	NOUN
ejpam-4703	89	5	2	2	NUM
ejpam-4703	89	6	√	√	PROPN
ejpam-4703	89	7	λ	λ	NOUN
ejpam-4703	89	8	µ(ab	µ(ab	PROPN
ejpam-4703	89	9	)	)	PUNCT
ejpam-4703	89	10	−µ	−µ	ADJ
ejpam-4703	89	11	2	2	NUM
ejpam-4703	89	12	sinh	sinh	NOUN
ejpam-4703	89	13	ρ	ρ	NOUN
ejpam-4703	89	14	{	{	PUNCT
ejpam-4703	89	15	1−	1−	NUM
ejpam-4703	89	16	a	a	DET
ejpam-4703	89	17	2n(x	2n(x	NUM
ejpam-4703	89	18	ln	ln	ADJ
ejpam-4703	89	19	c)2	c)2	NOUN
ejpam-4703	89	20	+	+	PROPN
ejpam-4703	89	21	o(n−2	o(n−2	PROPN
ejpam-4703	89	22	)	)	PUNCT
ejpam-4703	89	23	}	}	PUNCT
ejpam-4703	89	24	,	,	PUNCT
ejpam-4703	89	25	(	(	PUNCT
ejpam-4703	89	26	3.1	3.1	NUM
ejpam-4703	89	27	)	)	PUNCT
ejpam-4703	89	28	where	where	SCONJ
ejpam-4703	89	29	,	,	PUNCT
ejpam-4703	89	30	a	a	DET
ejpam-4703	89	31	=	=	X
ejpam-4703	89	32	(	(	PUNCT
ejpam-4703	89	33	ln(ab	ln(ab	PROPN
ejpam-4703	89	34	)	)	PUNCT
ejpam-4703	89	35	2	2	NUM
ejpam-4703	89	36	−	−	PROPN
ejpam-4703	89	37	1	1	NUM
ejpam-4703	89	38	µ	µ	X
ejpam-4703	89	39	+	+	X
ejpam-4703	89	40	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	89	41	)	)	PUNCT
ejpam-4703	89	42	2	2	NUM
ejpam-4703	89	43	coth	coth	NOUN
ejpam-4703	89	44	ρ	ρ	PROPN
ejpam-4703	89	45	)	)	PUNCT
ejpam-4703	89	46	(	(	PUNCT
ejpam-4703	89	47	ln(ab	ln(ab	PROPN
ejpam-4703	89	48	)	)	PUNCT
ejpam-4703	89	49	2	2	NUM
ejpam-4703	89	50	+	+	SYM
ejpam-4703	89	51	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	89	52	)	)	PUNCT
ejpam-4703	89	53	2	2	NUM
ejpam-4703	89	54	coth	coth	NOUN
ejpam-4703	89	55	ρ	ρ	NOUN
ejpam-4703	89	56	)	)	PUNCT
ejpam-4703	89	57	−	−	PROPN
ejpam-4703	89	58	ln(ab	ln(ab	PROPN
ejpam-4703	89	59	)	)	PUNCT
ejpam-4703	89	60	2µ	2µ	VERB
ejpam-4703	90	1	+	+	PUNCT
ejpam-4703	90	2	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	90	3	)	)	PUNCT
ejpam-4703	90	4	2	2	NUM
ejpam-4703	90	5	(	(	PUNCT
ejpam-4703	90	6	csch2ρ	csch2ρ	PROPN
ejpam-4703	90	7	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	90	8	)	)	PUNCT
ejpam-4703	90	9	2	2	NUM
ejpam-4703	90	10	−	−	NOUN
ejpam-4703	90	11	coth	coth	PROPN
ejpam-4703	90	12	ρ	ρ	PROPN
ejpam-4703	90	13	µ	µ	NOUN
ejpam-4703	90	14	)	)	PUNCT
ejpam-4703	90	15	.	.	PUNCT
ejpam-4703	91	1	(	(	PUNCT
ejpam-4703	91	2	3.2	3.2	NUM
ejpam-4703	91	3	)	)	PUNCT
ejpam-4703	91	4	proof	proof	NOUN
ejpam-4703	91	5	.	.	PUNCT
ejpam-4703	92	1	taking	take	VERB
ejpam-4703	92	2	α	α	NOUN
ejpam-4703	92	3	=	=	SYM
ejpam-4703	92	4	1	1	NUM
ejpam-4703	92	5	,	,	PUNCT
ejpam-4703	92	6	(	(	PUNCT
ejpam-4703	92	7	1.1	1.1	NUM
ejpam-4703	92	8	)	)	PUNCT
ejpam-4703	92	9	reduces	reduce	VERB
ejpam-4703	92	10	to	to	ADP
ejpam-4703	92	11	(	(	PUNCT
ejpam-4703	92	12	t	t	NOUN
ejpam-4703	92	13	λbt	λbt	VERB
ejpam-4703	92	14	−	−	NOUN
ejpam-4703	92	15	at	at	ADP
ejpam-4703	92	16	)	)	PUNCT
ejpam-4703	92	17	cxt	cxt	NOUN
ejpam-4703	92	18	=	=	PUNCT
ejpam-4703	93	1	∞∑	∞∑	ADJ
ejpam-4703	93	2	n=0	n=0	NUM
ejpam-4703	93	3	bn(x;λ	bn(x;λ	NOUN
ejpam-4703	93	4	;	;	PUNCT
ejpam-4703	93	5	a	a	DET
ejpam-4703	93	6	,	,	PUNCT
ejpam-4703	93	7	b	b	NOUN
ejpam-4703	93	8	,	,	PUNCT
ejpam-4703	93	9	c	c	NOUN
ejpam-4703	93	10	)	)	PUNCT
ejpam-4703	93	11	tn	tn	PROPN
ejpam-4703	93	12	n	n	CCONJ
ejpam-4703	93	13	!	!	PUNCT
ejpam-4703	93	14	.	.	PUNCT
ejpam-4703	94	1	applying	apply	VERB
ejpam-4703	94	2	the	the	DET
ejpam-4703	94	3	cauchy	cauchy	ADJ
ejpam-4703	94	4	integral	integral	ADJ
ejpam-4703	94	5	formula	formula	NOUN
ejpam-4703	94	6	(	(	PUNCT
ejpam-4703	94	7	for	for	ADP
ejpam-4703	94	8	a	a	DET
ejpam-4703	94	9	discussion	discussion	NOUN
ejpam-4703	94	10	about	about	ADP
ejpam-4703	94	11	cauchy	cauchy	ADJ
ejpam-4703	94	12	integral	integral	ADJ
ejpam-4703	94	13	formula	formula	NOUN
ejpam-4703	94	14	,	,	PUNCT
ejpam-4703	94	15	see	see	VERB
ejpam-4703	94	16	[	[	X
ejpam-4703	94	17	7	7	NUM
ejpam-4703	94	18	]	]	PUNCT
ejpam-4703	94	19	,	,	PUNCT
ejpam-4703	94	20	[	[	X
ejpam-4703	94	21	8	8	NUM
ejpam-4703	94	22	]	]	NUM
ejpam-4703	94	23	)	)	PUNCT
ejpam-4703	94	24	,	,	PUNCT
ejpam-4703	94	25	bn(x;λ	bn(x;λ	NOUN
ejpam-4703	94	26	;	;	PUNCT
ejpam-4703	94	27	a	a	DET
ejpam-4703	94	28	,	,	PUNCT
ejpam-4703	94	29	b	b	NOUN
ejpam-4703	94	30	,	,	PUNCT
ejpam-4703	94	31	c	c	NOUN
ejpam-4703	94	32	)	)	PUNCT
ejpam-4703	94	33	n	n	CCONJ
ejpam-4703	94	34	!	!	PUNCT
ejpam-4703	95	1	=	=	SYM
ejpam-4703	95	2	1	1	NUM
ejpam-4703	95	3	2πi	2πi	ADJ
ejpam-4703	95	4	∫	∫	PROPN
ejpam-4703	95	5	c	c	PROPN
ejpam-4703	95	6	tcxt	tcxt	NOUN
ejpam-4703	95	7	λbt	λbt	VERB
ejpam-4703	95	8	−	−	PROPN
ejpam-4703	95	9	at	at	ADP
ejpam-4703	95	10	dt	dt	PROPN
ejpam-4703	95	11	tn+1	tn+1	PROPN
ejpam-4703	95	12	,	,	PUNCT
ejpam-4703	95	13	(	(	PUNCT
ejpam-4703	95	14	3.3	3.3	NUM
ejpam-4703	95	15	)	)	PUNCT
ejpam-4703	95	16	where	where	SCONJ
ejpam-4703	95	17	c	c	NOUN
ejpam-4703	95	18	is	be	AUX
ejpam-4703	95	19	a	a	DET
ejpam-4703	95	20	circle	circle	NOUN
ejpam-4703	95	21	with	with	ADP
ejpam-4703	95	22	center	center	NOUN
ejpam-4703	95	23	at	at	ADP
ejpam-4703	95	24	the	the	DET
ejpam-4703	95	25	origin	origin	NOUN
ejpam-4703	95	26	and	and	CCONJ
ejpam-4703	95	27	radius	radius	NOUN
ejpam-4703	95	28	<	<	X
ejpam-4703	95	29	∣∣∣	∣∣∣	PROPN
ejpam-4703	95	30	δ	δ	PROPN
ejpam-4703	95	31	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	95	32	)	)	PUNCT
ejpam-4703	96	1	∣∣∣.	∣∣∣.	PROPN
ejpam-4703	96	2	note	note	VERB
ejpam-4703	96	3	that	that	SCONJ
ejpam-4703	96	4	−δ/	−δ/	PUNCT
ejpam-4703	96	5	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	96	6	)	)	PUNCT
ejpam-4703	96	7	is	be	AUX
ejpam-4703	96	8	the	the	DET
ejpam-4703	96	9	simple	simple	ADJ
ejpam-4703	96	10	pole	pole	NOUN
ejpam-4703	96	11	of	of	ADP
ejpam-4703	96	12	the	the	DET
ejpam-4703	96	13	integrand	integrand	NOUN
ejpam-4703	96	14	of	of	ADP
ejpam-4703	96	15	(	(	PUNCT
ejpam-4703	96	16	3.3	3.3	NUM
ejpam-4703	96	17	)	)	PUNCT
ejpam-4703	96	18	different	different	ADJ
ejpam-4703	96	19	from	from	ADP
ejpam-4703	96	20	zero	zero	NUM
ejpam-4703	96	21	and	and	CCONJ
ejpam-4703	96	22	nearest	near	ADJ
ejpam-4703	96	23	to	to	ADP
ejpam-4703	96	24	the	the	DET
ejpam-4703	96	25	origin	origin	NOUN
ejpam-4703	96	26	as	as	SCONJ
ejpam-4703	96	27	can	can	AUX
ejpam-4703	96	28	be	be	AUX
ejpam-4703	96	29	seen	see	VERB
ejpam-4703	96	30	in	in	ADP
ejpam-4703	96	31	the	the	DET
ejpam-4703	96	32	computation	computation	NOUN
ejpam-4703	96	33	of	of	ADP
ejpam-4703	96	34	the	the	DET
ejpam-4703	96	35	singularities	singularity	NOUN
ejpam-4703	96	36	below	below	ADV
ejpam-4703	96	37	.	.	PUNCT
ejpam-4703	97	1	rewriting	rewrite	VERB
ejpam-4703	97	2	λbt	λbt	NOUN
ejpam-4703	97	3	−	−	NOUN
ejpam-4703	97	4	at	at	ADP
ejpam-4703	97	5	=	=	PUNCT
ejpam-4703	97	6	eδet	eδet	PROPN
ejpam-4703	97	7	ln	ln	PROPN
ejpam-4703	97	8	b	b	PROPN
ejpam-4703	97	9	−	−	X
ejpam-4703	97	10	et	et	NOUN
ejpam-4703	97	11	ln	ln	NOUN
ejpam-4703	97	12	a	a	NOUN
ejpam-4703	97	13	=	=	X
ejpam-4703	97	14	(	(	PUNCT
ejpam-4703	97	15	eδ+t	eδ+t	PROPN
ejpam-4703	97	16	ln	ln	PROPN
ejpam-4703	97	17	b	b	PROPN
ejpam-4703	97	18	−	−	X
ejpam-4703	97	19	et	et	NOUN
ejpam-4703	97	20	ln	ln	NOUN
ejpam-4703	97	21	a	a	NOUN
ejpam-4703	97	22	)	)	PUNCT
ejpam-4703	97	23	e−t	e−t	NOUN
ejpam-4703	97	24	ln	ln	NOUN
ejpam-4703	97	25	a	a	DET
ejpam-4703	97	26	e−t	e−t	NOUN
ejpam-4703	97	27	ln	ln	NOUN
ejpam-4703	97	28	a	a	DET
ejpam-4703	97	29	=	=	SYM
ejpam-4703	97	30	(	(	PUNCT
ejpam-4703	97	31	eδ+t(ln	eδ+t(ln	PROPN
ejpam-4703	97	32	ba−1	ba−1	NOUN
ejpam-4703	97	33	)	)	PUNCT
ejpam-4703	97	34	−	−	PROPN
ejpam-4703	97	35	1	1	X
ejpam-4703	97	36	)	)	PUNCT
ejpam-4703	97	37	et	et	NOUN
ejpam-4703	97	38	ln	ln	NOUN
ejpam-4703	98	1	a	a	NOUN
ejpam-4703	99	1	=	=	X
ejpam-4703	100	1	[	[	PUNCT
ejpam-4703	100	2	2e	2e	NUM
ejpam-4703	100	3	δ+t	δ+t	NOUN
ejpam-4703	100	4	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	100	5	)	)	PUNCT
ejpam-4703	100	6	2	2	NUM
ejpam-4703	100	7	sinh	sinh	NOUN
ejpam-4703	100	8	(	(	PUNCT
ejpam-4703	100	9	δ	δ	PROPN
ejpam-4703	100	10	+	+	PROPN
ejpam-4703	100	11	t	t	PROPN
ejpam-4703	100	12	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	100	13	)	)	PUNCT
ejpam-4703	100	14	2	2	NUM
ejpam-4703	100	15	)	)	PUNCT
ejpam-4703	100	16	]	]	PUNCT
ejpam-4703	100	17	et	et	PROPN
ejpam-4703	100	18	ln	ln	PROPN
ejpam-4703	100	19	a.	a.	NOUN
ejpam-4703	100	20	then	then	ADV
ejpam-4703	100	21	(	(	PUNCT
ejpam-4703	100	22	3.3	3.3	NUM
ejpam-4703	100	23	)	)	PUNCT
ejpam-4703	100	24	becomes	become	VERB
ejpam-4703	100	25	bn(x;λ	bn(x;λ	NOUN
ejpam-4703	100	26	;	;	PUNCT
ejpam-4703	100	27	a	a	DET
ejpam-4703	100	28	,	,	PUNCT
ejpam-4703	100	29	b	b	NOUN
ejpam-4703	100	30	,	,	PUNCT
ejpam-4703	100	31	c	c	NOUN
ejpam-4703	100	32	)	)	PUNCT
ejpam-4703	100	33	n	n	CCONJ
ejpam-4703	100	34	!	!	PUNCT
ejpam-4703	101	1	=	=	SYM
ejpam-4703	101	2	1	1	NUM
ejpam-4703	101	3	2λ	2λ	NUM
ejpam-4703	101	4	−1/2	−1/2	ADJ
ejpam-4703	101	5	2πi	2πi	ADJ
ejpam-4703	101	6	∫	∫	PROPN
ejpam-4703	101	7	c	c	NOUN
ejpam-4703	101	8	t(ab	t(ab	PROPN
ejpam-4703	101	9	)	)	PUNCT
ejpam-4703	101	10	−t	−t	NOUN
ejpam-4703	101	11	2	2	NUM
ejpam-4703	101	12	sinh	sinh	NOUN
ejpam-4703	101	13	(	(	PUNCT
ejpam-4703	101	14	δ+t	δ+t	NOUN
ejpam-4703	101	15	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	101	16	)	)	PUNCT
ejpam-4703	101	17	2	2	NUM
ejpam-4703	101	18	)	)	PUNCT
ejpam-4703	101	19	cxt	cxt	PROPN
ejpam-4703	101	20	dt	dt	X
ejpam-4703	101	21	tn+1	tn+1	PROPN
ejpam-4703	101	22	,	,	PUNCT
ejpam-4703	101	23	c.	c.	PROPN
ejpam-4703	101	24	corcino	corcino	PROPN
ejpam-4703	101	25	,	,	PUNCT
ejpam-4703	101	26	r.	r.	PROPN
ejpam-4703	101	27	corcino	corcino	PROPN
ejpam-4703	101	28	/	/	SYM
ejpam-4703	101	29	eur	eur	PROPN
ejpam-4703	101	30	.	.	PUNCT
ejpam-4703	102	1	j.	j.	PROPN
ejpam-4703	102	2	pure	pure	PROPN
ejpam-4703	102	3	appl	appl	PROPN
ejpam-4703	102	4	.	.	PROPN
ejpam-4703	102	5	math	math	PROPN
ejpam-4703	102	6	,	,	PUNCT
ejpam-4703	102	7	16	16	NUM
ejpam-4703	102	8	(	(	PUNCT
ejpam-4703	102	9	2	2	NUM
ejpam-4703	102	10	)	)	PUNCT
ejpam-4703	102	11	(	(	PUNCT
ejpam-4703	102	12	2023	2023	NUM
ejpam-4703	102	13	)	)	PUNCT
ejpam-4703	102	14	,	,	PUNCT
ejpam-4703	102	15	791	791	NUM
ejpam-4703	102	16	-	-	SYM
ejpam-4703	102	17	805	805	NUM
ejpam-4703	102	18	796	796	NUM
ejpam-4703	102	19	from	from	ADP
ejpam-4703	102	20	which	which	PRON
ejpam-4703	102	21	,	,	PUNCT
ejpam-4703	102	22	bn(nx;λ	bn(nx;λ	NOUN
ejpam-4703	102	23	;	;	PUNCT
ejpam-4703	102	24	a	a	DET
ejpam-4703	102	25	,	,	PUNCT
ejpam-4703	102	26	b	b	NOUN
ejpam-4703	102	27	,	,	PUNCT
ejpam-4703	102	28	c	c	NOUN
ejpam-4703	102	29	)	)	PUNCT
ejpam-4703	102	30	n	n	CCONJ
ejpam-4703	102	31	!	!	PUNCT
ejpam-4703	103	1	=	=	SYM
ejpam-4703	103	2	1	1	NUM
ejpam-4703	103	3	2λ	2λ	NOUN
ejpam-4703	103	4	−	−	NOUN
ejpam-4703	103	5	1	1	NUM
ejpam-4703	103	6	2	2	NUM
ejpam-4703	103	7	2πi	2πi	NOUN
ejpam-4703	103	8	∫	∫	PROPN
ejpam-4703	103	9	c	c	PROPN
ejpam-4703	103	10	g(t)etnx	g(t)etnx	VERB
ejpam-4703	103	11	ln	ln	ADJ
ejpam-4703	103	12	c−n	c−n	X
ejpam-4703	103	13	log	log	VERB
ejpam-4703	103	14	tdt	tdt	PROPN
ejpam-4703	103	15	t	t	PROPN
ejpam-4703	103	16	,	,	PUNCT
ejpam-4703	103	17	(	(	PUNCT
ejpam-4703	103	18	3.4	3.4	NUM
ejpam-4703	103	19	)	)	PUNCT
ejpam-4703	103	20	where	where	SCONJ
ejpam-4703	103	21	g(t	g(t	NOUN
ejpam-4703	103	22	)	)	PUNCT
ejpam-4703	103	23	=	=	PUNCT
ejpam-4703	103	24	t(ab	t(ab	PROPN
ejpam-4703	103	25	)	)	PUNCT
ejpam-4703	103	26	−t	−t	NOUN
ejpam-4703	103	27	2	2	NUM
ejpam-4703	103	28	sinh	sinh	NOUN
ejpam-4703	103	29	(	(	PUNCT
ejpam-4703	103	30	δ+t	δ+t	NOUN
ejpam-4703	103	31	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	103	32	)	)	PUNCT
ejpam-4703	103	33	2	2	NUM
ejpam-4703	103	34	)	)	PUNCT
ejpam-4703	103	35	.	.	PUNCT
ejpam-4703	104	1	(	(	PUNCT
ejpam-4703	104	2	3.5	3.5	NUM
ejpam-4703	104	3	)	)	PUNCT
ejpam-4703	104	4	the	the	DET
ejpam-4703	104	5	saddle	saddle	NOUN
ejpam-4703	104	6	-	-	PUNCT
ejpam-4703	104	7	point	point	NOUN
ejpam-4703	104	8	at	at	ADP
ejpam-4703	104	9	which	which	PRON
ejpam-4703	104	10	the	the	DET
ejpam-4703	104	11	major	major	ADJ
ejpam-4703	104	12	contribution	contribution	NOUN
ejpam-4703	104	13	to	to	ADP
ejpam-4703	104	14	the	the	DET
ejpam-4703	104	15	integral	integral	ADJ
ejpam-4703	104	16	in	in	ADP
ejpam-4703	104	17	(	(	PUNCT
ejpam-4703	104	18	3.4	3.4	NUM
ejpam-4703	104	19	)	)	PUNCT
ejpam-4703	104	20	occurs	occur	VERB
ejpam-4703	104	21	is	be	AUX
ejpam-4703	104	22	µ	µ	X
ejpam-4703	104	23	=	=	PUNCT
ejpam-4703	104	24	(	(	PUNCT
ejpam-4703	104	25	x	x	X
ejpam-4703	104	26	ln	ln	PROPN
ejpam-4703	104	27	c)−1	c)−1	PROPN
ejpam-4703	104	28	.	.	PUNCT
ejpam-4703	105	1	the	the	DET
ejpam-4703	105	2	singularities	singularity	NOUN
ejpam-4703	105	3	of	of	ADP
ejpam-4703	105	4	g(t	g(t	PROPN
ejpam-4703	105	5	)	)	PUNCT
ejpam-4703	105	6	are	be	AUX
ejpam-4703	105	7	computed	compute	VERB
ejpam-4703	105	8	as	as	SCONJ
ejpam-4703	105	9	follows	follow	VERB
ejpam-4703	105	10	:	:	PUNCT
ejpam-4703	105	11	sinh	sinh	NOUN
ejpam-4703	105	12	(	(	PUNCT
ejpam-4703	105	13	δ	δ	PROPN
ejpam-4703	105	14	+	+	PROPN
ejpam-4703	105	15	t	t	PROPN
ejpam-4703	105	16	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	105	17	)	)	PUNCT
ejpam-4703	105	18	2	2	NUM
ejpam-4703	105	19	)	)	PUNCT
ejpam-4703	105	20	⇔	⇔	PROPN
ejpam-4703	105	21	δ	δ	PROPN
ejpam-4703	105	22	+	+	PROPN
ejpam-4703	105	23	t	t	PROPN
ejpam-4703	105	24	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	105	25	)	)	PUNCT
ejpam-4703	105	26	2	2	NUM
ejpam-4703	105	27	=	=	SYM
ejpam-4703	105	28	kπi	kπi	PROPN
ejpam-4703	105	29	,	,	PUNCT
ejpam-4703	105	30	k	k	PROPN
ejpam-4703	105	31	∈	∈	PROPN
ejpam-4703	105	32	z	z	PROPN
ejpam-4703	105	33	δ	δ	PROPN
ejpam-4703	105	34	+	+	PROPN
ejpam-4703	105	35	t	t	PROPN
ejpam-4703	105	36	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	105	37	)	)	PUNCT
ejpam-4703	105	38	=	=	PUNCT
ejpam-4703	106	1	2kπi	2kπi	NUM
ejpam-4703	106	2	t	t	PROPN
ejpam-4703	106	3	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	106	4	)	)	PUNCT
ejpam-4703	106	5	=	=	SYM
ejpam-4703	107	1	2kπi−	2kπi−	PUNCT
ejpam-4703	107	2	δ	δ	INTJ
ejpam-4703	107	3	tk	tk	NOUN
ejpam-4703	107	4	:	:	PUNCT
ejpam-4703	108	1	=	=	SYM
ejpam-4703	108	2	t	t	PROPN
ejpam-4703	108	3	=	=	SYM
ejpam-4703	108	4	2kπi−	2kπi−	NUM
ejpam-4703	108	5	δ	δ	PROPN
ejpam-4703	108	6	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	108	7	)	)	PUNCT
ejpam-4703	109	1	,	,	PUNCT
ejpam-4703	109	2	k	k	PROPN
ejpam-4703	109	3	∈	∈	PROPN
ejpam-4703	109	4	z.	z.	PROPN
ejpam-4703	109	5	assume	assume	VERB
ejpam-4703	109	6	that	that	SCONJ
ejpam-4703	109	7	µ	µ	X
ejpam-4703	109	8	=	=	SYM
ejpam-4703	109	9	(	(	PUNCT
ejpam-4703	109	10	x	x	X
ejpam-4703	109	11	ln	ln	ADJ
ejpam-4703	109	12	c)−1	c)−1	NOUN
ejpam-4703	109	13	is	be	AUX
ejpam-4703	109	14	not	not	PART
ejpam-4703	109	15	a	a	DET
ejpam-4703	109	16	singularity	singularity	NOUN
ejpam-4703	109	17	of	of	ADP
ejpam-4703	109	18	g.	g.	PROPN
ejpam-4703	109	19	then	then	ADV
ejpam-4703	109	20	g(t	g(t	PROPN
ejpam-4703	109	21	)	)	PUNCT
ejpam-4703	109	22	can	can	AUX
ejpam-4703	109	23	be	be	AUX
ejpam-4703	109	24	expanded	expand	VERB
ejpam-4703	109	25	about	about	ADP
ejpam-4703	109	26	µ.	µ.	NOUN
ejpam-4703	109	27	that	that	PRON
ejpam-4703	109	28	is	be	AUX
ejpam-4703	109	29	,	,	PUNCT
ejpam-4703	109	30	g(t	g(t	PROPN
ejpam-4703	109	31	)	)	PUNCT
ejpam-4703	110	1	=	=	PUNCT
ejpam-4703	110	2	∞∑	∞∑	NUM
ejpam-4703	110	3	k=0	k=0	PROPN
ejpam-4703	110	4	g(k)(µ	g(k)(µ	PROPN
ejpam-4703	110	5	)	)	PUNCT
ejpam-4703	110	6	k	k	NOUN
ejpam-4703	110	7	!	!	PUNCT
ejpam-4703	111	1	(	(	PUNCT
ejpam-4703	111	2	t−	t−	PROPN
ejpam-4703	111	3	µ)k	µ)k	NOUN
ejpam-4703	111	4	,	,	PUNCT
ejpam-4703	111	5	|t−	|t−	PROPN
ejpam-4703	111	6	µ|	µ|	PROPN
ejpam-4703	111	7	<	<	X
ejpam-4703	111	8	r	r	NOUN
ejpam-4703	111	9	where	where	SCONJ
ejpam-4703	111	10	r	r	NOUN
ejpam-4703	111	11	is	be	AUX
ejpam-4703	111	12	the	the	DET
ejpam-4703	111	13	distance	distance	NOUN
ejpam-4703	111	14	from	from	ADP
ejpam-4703	111	15	µ	µ	PRON
ejpam-4703	111	16	to	to	ADP
ejpam-4703	111	17	the	the	DET
ejpam-4703	111	18	nearest	near	ADJ
ejpam-4703	111	19	singularity	singularity	NOUN
ejpam-4703	111	20	of	of	ADP
ejpam-4703	111	21	g(t	g(t	PROPN
ejpam-4703	111	22	)	)	PUNCT
ejpam-4703	111	23	.	.	PUNCT
ejpam-4703	112	1	the	the	DET
ejpam-4703	112	2	derivatives	derivative	NOUN
ejpam-4703	112	3	of	of	ADP
ejpam-4703	112	4	g(t	g(t	PROPN
ejpam-4703	112	5	)	)	PUNCT
ejpam-4703	112	6	for	for	ADP
ejpam-4703	112	7	k	k	PROPN
ejpam-4703	112	8	=	=	SYM
ejpam-4703	112	9	1	1	NUM
ejpam-4703	112	10	,	,	PUNCT
ejpam-4703	112	11	2	2	NUM
ejpam-4703	112	12	evaluated	evaluate	VERB
ejpam-4703	112	13	at	at	ADP
ejpam-4703	112	14	t	t	NOUN
ejpam-4703	112	15	=	=	SYM
ejpam-4703	112	16	µ	µ	X
ejpam-4703	112	17	are	be	AUX
ejpam-4703	112	18	given	give	VERB
ejpam-4703	112	19	below	below	ADP
ejpam-4703	112	20	:	:	PUNCT
ejpam-4703	112	21	g′(µ	g′(µ	NOUN
ejpam-4703	112	22	)	)	PUNCT
ejpam-4703	112	23	=	=	PUNCT
ejpam-4703	112	24	(	(	PUNCT
ejpam-4703	112	25	1	1	NUM
ejpam-4703	112	26	+	+	NUM
ejpam-4703	112	27	−µ	−µ	ADJ
ejpam-4703	112	28	ln(ab	ln(ab	PROPN
ejpam-4703	112	29	)	)	PUNCT
ejpam-4703	112	30	2	2	NUM
ejpam-4703	112	31	−	−	PROPN
ejpam-4703	112	32	µ	µ	X
ejpam-4703	112	33	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	112	34	)	)	PUNCT
ejpam-4703	112	35	2	2	NUM
ejpam-4703	112	36	coth	coth	NOUN
ejpam-4703	112	37	ρ	ρ	NOUN
ejpam-4703	112	38	)	)	PUNCT
ejpam-4703	112	39	e	e	NOUN
ejpam-4703	112	40	−µ	−µ	ADJ
ejpam-4703	112	41	2	2	NUM
ejpam-4703	112	42	ln(ab	ln(ab	PROPN
ejpam-4703	112	43	)	)	PUNCT
ejpam-4703	112	44	sinh	sinh	NOUN
ejpam-4703	112	45	ρ	ρ	PROPN
ejpam-4703	112	46	,	,	PUNCT
ejpam-4703	112	47	(	(	PUNCT
ejpam-4703	112	48	3.6	3.6	NUM
ejpam-4703	112	49	)	)	PUNCT
ejpam-4703	112	50	g′′(µ	g′′(µ	NOUN
ejpam-4703	112	51	)	)	PUNCT
ejpam-4703	112	52	=	=	PRON
ejpam-4703	113	1	{	{	PUNCT
ejpam-4703	113	2	(	(	PUNCT
ejpam-4703	113	3	ln(ab	ln(ab	PROPN
ejpam-4703	113	4	)	)	PUNCT
ejpam-4703	113	5	2	2	NUM
ejpam-4703	113	6	−	−	PROPN
ejpam-4703	113	7	1	1	NUM
ejpam-4703	113	8	µ	µ	X
ejpam-4703	113	9	+	+	X
ejpam-4703	113	10	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	113	11	)	)	PUNCT
ejpam-4703	113	12	2	2	NUM
ejpam-4703	113	13	coth	coth	NOUN
ejpam-4703	113	14	ρ	ρ	PROPN
ejpam-4703	113	15	)	)	PUNCT
ejpam-4703	113	16	(	(	PUNCT
ejpam-4703	113	17	ln(ab	ln(ab	PROPN
ejpam-4703	113	18	)	)	PUNCT
ejpam-4703	113	19	2	2	NUM
ejpam-4703	113	20	+	+	SYM
ejpam-4703	113	21	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	113	22	)	)	PUNCT
ejpam-4703	113	23	2	2	NUM
ejpam-4703	113	24	coth	coth	NOUN
ejpam-4703	113	25	ρ	ρ	NOUN
ejpam-4703	113	26	)	)	PUNCT
ejpam-4703	113	27	−	−	PROPN
ejpam-4703	113	28	ln(ab	ln(ab	PROPN
ejpam-4703	113	29	)	)	PUNCT
ejpam-4703	113	30	2µ	2µ	PUNCT
ejpam-4703	114	1	+	+	PUNCT
ejpam-4703	114	2	[	[	X
ejpam-4703	114	3	ln(ba−1)]2	ln(ba−1)]2	PROPN
ejpam-4703	114	4	4	4	NUM
ejpam-4703	114	5	csch2ρ−	csch2ρ−	PROPN
ejpam-4703	114	6	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	114	7	)	)	PUNCT
ejpam-4703	114	8	2µ	2µ	NUM
ejpam-4703	114	9	coth	coth	PROPN
ejpam-4703	114	10	ρ	ρ	PROPN
ejpam-4703	114	11	}	}	PUNCT
ejpam-4703	114	12	×	×	PROPN
ejpam-4703	114	13	µ	µ	PROPN
ejpam-4703	114	14	e	e	NOUN
ejpam-4703	114	15	−µ	−µ	ADJ
ejpam-4703	114	16	2	2	NUM
ejpam-4703	114	17	ln(ab	ln(ab	PROPN
ejpam-4703	114	18	)	)	PUNCT
ejpam-4703	114	19	sinh	sinh	NOUN
ejpam-4703	114	20	ρ	ρ	PROPN
ejpam-4703	114	21	.	.	PUNCT
ejpam-4703	115	1	(	(	PUNCT
ejpam-4703	115	2	3.7	3.7	NUM
ejpam-4703	115	3	)	)	PUNCT
ejpam-4703	115	4	using	use	VERB
ejpam-4703	115	5	(	(	PUNCT
ejpam-4703	115	6	3.4	3.4	NUM
ejpam-4703	115	7	)	)	PUNCT
ejpam-4703	115	8	and	and	CCONJ
ejpam-4703	115	9	applying	apply	VERB
ejpam-4703	115	10	theorem	theorem	NOUN
ejpam-4703	115	11	1.3	1.3	NUM
ejpam-4703	115	12	,	,	PUNCT
ejpam-4703	115	13	bn(nx;λ	bn(nx;λ	NOUN
ejpam-4703	115	14	;	;	PUNCT
ejpam-4703	115	15	a	a	DET
ejpam-4703	115	16	,	,	PUNCT
ejpam-4703	115	17	b	b	NOUN
ejpam-4703	115	18	,	,	PUNCT
ejpam-4703	115	19	c	c	NOUN
ejpam-4703	115	20	)	)	PUNCT
ejpam-4703	115	21	=	=	SYM
ejpam-4703	116	1	(	(	PUNCT
ejpam-4703	116	2	nx	nx	X
ejpam-4703	116	3	ln	ln	NOUN
ejpam-4703	116	4	c)n	c)n	NOUN
ejpam-4703	116	5	2	2	NUM
ejpam-4703	116	6	√	√	NOUN
ejpam-4703	116	7	λ	λ	PROPN
ejpam-4703	116	8	{	{	PUNCT
ejpam-4703	116	9	g(µ)−	g(µ)−	PROPN
ejpam-4703	116	10	g′′(µ	g′′(µ	PROPN
ejpam-4703	116	11	)	)	PUNCT
ejpam-4703	116	12	2n(x	2n(x	NUM
ejpam-4703	116	13	ln	ln	ADJ
ejpam-4703	116	14	c)2	c)2	NOUN
ejpam-4703	116	15	+	+	SYM
ejpam-4703	116	16	o(n−2	o(n−2	PROPN
ejpam-4703	116	17	)	)	PUNCT
ejpam-4703	116	18	}	}	PUNCT
ejpam-4703	116	19	=	=	SYM
ejpam-4703	117	1	(	(	PUNCT
ejpam-4703	117	2	nx	nx	X
ejpam-4703	117	3	ln	ln	NOUN
ejpam-4703	117	4	c)n	c)n	NOUN
ejpam-4703	117	5	2	2	NUM
ejpam-4703	117	6	√	√	NOUN
ejpam-4703	117	7	λ	λ	PROPN
ejpam-4703	117	8	{	{	PUNCT
ejpam-4703	117	9	µ(ab	µ(ab	NOUN
ejpam-4703	117	10	)	)	PUNCT
ejpam-4703	117	11	−µ	−µ	ADJ
ejpam-4703	117	12	2	2	NUM
ejpam-4703	117	13	sinh	sinh	NOUN
ejpam-4703	117	14	ρ	ρ	PROPN
ejpam-4703	117	15	−	−	NOUN
ejpam-4703	117	16	µ(ab	µ(ab	NOUN
ejpam-4703	117	17	)	)	PUNCT
ejpam-4703	117	18	−µ	−µ	ADJ
ejpam-4703	117	19	2	2	NUM
ejpam-4703	117	20	sinh	sinh	NOUN
ejpam-4703	117	21	ρ	ρ	NOUN
ejpam-4703	117	22	a	a	DET
ejpam-4703	117	23	2n(x	2n(x	NUM
ejpam-4703	117	24	ln	ln	ADJ
ejpam-4703	117	25	c)2	c)2	NOUN
ejpam-4703	117	26	+	+	PROPN
ejpam-4703	117	27	o(n−2	o(n−2	PROPN
ejpam-4703	117	28	)	)	PUNCT
ejpam-4703	117	29	}	}	PUNCT
ejpam-4703	117	30	c.	c.	PROPN
ejpam-4703	117	31	corcino	corcino	PROPN
ejpam-4703	117	32	,	,	PUNCT
ejpam-4703	117	33	r.	r.	PROPN
ejpam-4703	117	34	corcino	corcino	PROPN
ejpam-4703	117	35	/	/	SYM
ejpam-4703	117	36	eur	eur	PROPN
ejpam-4703	117	37	.	.	PUNCT
ejpam-4703	118	1	j.	j.	PROPN
ejpam-4703	118	2	pure	pure	PROPN
ejpam-4703	118	3	appl	appl	PROPN
ejpam-4703	118	4	.	.	PROPN
ejpam-4703	118	5	math	math	PROPN
ejpam-4703	118	6	,	,	PUNCT
ejpam-4703	118	7	16	16	NUM
ejpam-4703	118	8	(	(	PUNCT
ejpam-4703	118	9	2	2	NUM
ejpam-4703	118	10	)	)	PUNCT
ejpam-4703	118	11	(	(	PUNCT
ejpam-4703	118	12	2023	2023	NUM
ejpam-4703	118	13	)	)	PUNCT
ejpam-4703	118	14	,	,	PUNCT
ejpam-4703	118	15	791	791	NUM
ejpam-4703	118	16	-	-	SYM
ejpam-4703	118	17	805	805	NUM
ejpam-4703	118	18	797	797	NUM
ejpam-4703	118	19	=	=	SYM
ejpam-4703	118	20	(	(	PUNCT
ejpam-4703	118	21	nx	nx	X
ejpam-4703	118	22	ln	ln	NOUN
ejpam-4703	118	23	c)n	c)n	NOUN
ejpam-4703	118	24	2	2	NUM
ejpam-4703	118	25	√	√	PROPN
ejpam-4703	118	26	λ	λ	NOUN
ejpam-4703	118	27	µ(ab	µ(ab	PROPN
ejpam-4703	118	28	)	)	PUNCT
ejpam-4703	118	29	−µ	−µ	ADJ
ejpam-4703	118	30	2	2	NUM
ejpam-4703	118	31	sinh	sinh	NOUN
ejpam-4703	118	32	ρ	ρ	NOUN
ejpam-4703	118	33	{	{	PUNCT
ejpam-4703	118	34	1−	1−	NUM
ejpam-4703	118	35	a	a	DET
ejpam-4703	118	36	2n(x	2n(x	NUM
ejpam-4703	118	37	ln	ln	ADJ
ejpam-4703	118	38	c)2	c)2	NOUN
ejpam-4703	118	39	+	+	PROPN
ejpam-4703	118	40	o(n−2	o(n−2	PROPN
ejpam-4703	118	41	)	)	PUNCT
ejpam-4703	118	42	}	}	PUNCT
ejpam-4703	118	43	,	,	PUNCT
ejpam-4703	118	44	where	where	SCONJ
ejpam-4703	118	45	a	a	PRON
ejpam-4703	118	46	is	be	AUX
ejpam-4703	118	47	as	as	SCONJ
ejpam-4703	118	48	given	give	VERB
ejpam-4703	118	49	in	in	ADP
ejpam-4703	118	50	(	(	PUNCT
ejpam-4703	118	51	3.2	3.2	NUM
ejpam-4703	118	52	)	)	PUNCT
ejpam-4703	118	53	.	.	PUNCT
ejpam-4703	119	1	asymptotic	asymptotic	ADJ
ejpam-4703	119	2	formula	formula	NOUN
ejpam-4703	119	3	for	for	ADP
ejpam-4703	119	4	the	the	DET
ejpam-4703	119	5	apostol	apostol	NOUN
ejpam-4703	119	6	-	-	PUNCT
ejpam-4703	119	7	bernoulli	bernoulli	NOUN
ejpam-4703	119	8	type	type	NOUN
ejpam-4703	119	9	polynomials	polynomial	NOUN
ejpam-4703	119	10	of	of	ADP
ejpam-4703	119	11	order	order	NOUN
ejpam-4703	119	12	α	α	X
ejpam-4703	119	13	>	>	X
ejpam-4703	119	14	1	1	NUM
ejpam-4703	119	15	is	be	AUX
ejpam-4703	119	16	given	give	VERB
ejpam-4703	119	17	in	in	ADP
ejpam-4703	119	18	the	the	DET
ejpam-4703	119	19	next	next	ADJ
ejpam-4703	119	20	theorem	theorem	PROPN
ejpam-4703	119	21	.	.	PUNCT
ejpam-4703	119	22	theorem	theorem	VERB
ejpam-4703	119	23	3.2	3.2	NUM
ejpam-4703	119	24	.	.	PUNCT
ejpam-4703	120	1	(	(	PUNCT
ejpam-4703	120	2	apostol	apostol	NOUN
ejpam-4703	120	3	-	-	PUNCT
ejpam-4703	120	4	bernoulli	bernoulli	NOUN
ejpam-4703	120	5	type	type	NOUN
ejpam-4703	120	6	polynomials	polynomial	NOUN
ejpam-4703	120	7	of	of	ADP
ejpam-4703	120	8	order	order	NOUN
ejpam-4703	120	9	α	α	PRON
ejpam-4703	120	10	≥	≥	NUM
ejpam-4703	120	11	2	2	NUM
ejpam-4703	120	12	)	)	PUNCT
ejpam-4703	120	13	let	let	VERB
ejpam-4703	120	14	a	a	DET
ejpam-4703	120	15	,	,	PUNCT
ejpam-4703	120	16	b	b	NOUN
ejpam-4703	120	17	,	,	PUNCT
ejpam-4703	120	18	c	c	PROPN
ejpam-4703	120	19	∈	∈	PROPN
ejpam-4703	120	20	r+\{1	r+\{1	PROPN
ejpam-4703	120	21	}	}	PUNCT
ejpam-4703	120	22	,	,	PUNCT
ejpam-4703	120	23	a	a	DET
ejpam-4703	120	24	̸=	̸=	PROPN
ejpam-4703	120	25	b	b	PROPN
ejpam-4703	120	26	and	and	CCONJ
ejpam-4703	120	27	µ	µ	X
ejpam-4703	120	28	=	=	PUNCT
ejpam-4703	120	29	(	(	PUNCT
ejpam-4703	120	30	x	x	X
ejpam-4703	120	31	ln	ln	PROPN
ejpam-4703	120	32	c)−1	c)−1	PROPN
ejpam-4703	120	33	.	.	PUNCT
ejpam-4703	121	1	for	for	ADP
ejpam-4703	121	2	x	x	PROPN
ejpam-4703	121	3	∈	∈	PROPN
ejpam-4703	121	4	c\{0	c\{0	PROPN
ejpam-4703	121	5	}	}	PUNCT
ejpam-4703	121	6	such	such	ADJ
ejpam-4703	121	7	that	that	SCONJ
ejpam-4703	121	8	|µ|	|µ|	PROPN
ejpam-4703	121	9	<	<	X
ejpam-4703	121	10	∣∣µ±	∣∣µ±	PROPN
ejpam-4703	121	11	δ	δ	PROPN
ejpam-4703	121	12	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	121	13	)	)	PUNCT
ejpam-4703	121	14	∣∣	∣∣	PROPN
ejpam-4703	121	15	,	,	PUNCT
ejpam-4703	121	16	δ	δ	PROPN
ejpam-4703	121	17	=	=	PROPN
ejpam-4703	121	18	log	log	PROPN
ejpam-4703	121	19	λ	λ	PROPN
ejpam-4703	121	20	,	,	PUNCT
ejpam-4703	121	21	n	n	PRON
ejpam-4703	121	22	≥	≥	NOUN
ejpam-4703	121	23	α	α	NOUN
ejpam-4703	121	24	,	,	PUNCT
ejpam-4703	121	25	the	the	DET
ejpam-4703	121	26	following	follow	VERB
ejpam-4703	121	27	holds	hold	NOUN
ejpam-4703	121	28	,	,	PUNCT
ejpam-4703	121	29	b(α	b(α	NOUN
ejpam-4703	121	30	)	)	PUNCT
ejpam-4703	121	31	n	n	CCONJ
ejpam-4703	121	32	(	(	PUNCT
ejpam-4703	121	33	nx;λ	nx;λ	NUM
ejpam-4703	121	34	;	;	PUNCT
ejpam-4703	121	35	a	a	DET
ejpam-4703	121	36	,	,	PUNCT
ejpam-4703	121	37	b	b	NOUN
ejpam-4703	121	38	,	,	PUNCT
ejpam-4703	121	39	c	c	NOUN
ejpam-4703	121	40	)	)	PUNCT
ejpam-4703	121	41	=	=	SYM
ejpam-4703	121	42	(	(	PUNCT
ejpam-4703	121	43	nx	nx	INTJ
ejpam-4703	121	44	ln	ln	NOUN
ejpam-4703	122	1	c)n	c)n	NOUN
ejpam-4703	122	2	2αλ	2αλ	NOUN
ejpam-4703	123	1	α	α	PRON
ejpam-4703	123	2	2	2	NUM
ejpam-4703	123	3	(	(	PUNCT
ejpam-4703	123	4	µ(ab)−	µ(ab)−	X
ejpam-4703	123	5	µ	µ	X
ejpam-4703	123	6	2	2	NUM
ejpam-4703	123	7	sinh	sinh	NOUN
ejpam-4703	123	8	ρ	ρ	PROPN
ejpam-4703	123	9	)	)	PUNCT
ejpam-4703	123	10	α	α	PROPN
ejpam-4703	123	11	{	{	PUNCT
ejpam-4703	123	12	1−	1−	NUM
ejpam-4703	123	13	α(a+	α(a+	NOUN
ejpam-4703	123	14	(	(	PUNCT
ejpam-4703	123	15	α−	α−	ADP
ejpam-4703	123	16	1)j2	1)j2	NUM
ejpam-4703	123	17	)	)	PUNCT
ejpam-4703	123	18	2n(x	2n(x	NUM
ejpam-4703	123	19	ln	ln	ADJ
ejpam-4703	123	20	c)2	c)2	NOUN
ejpam-4703	123	21	+	+	SYM
ejpam-4703	123	22	o(n−2	o(n−2	PROPN
ejpam-4703	123	23	)	)	PUNCT
ejpam-4703	123	24	}	}	PUNCT
ejpam-4703	123	25	,	,	PUNCT
ejpam-4703	123	26	(	(	PUNCT
ejpam-4703	123	27	3.8	3.8	NUM
ejpam-4703	123	28	)	)	PUNCT
ejpam-4703	123	29	where	where	SCONJ
ejpam-4703	123	30	a	a	PRON
ejpam-4703	123	31	is	be	AUX
ejpam-4703	123	32	given	give	VERB
ejpam-4703	123	33	in	in	ADP
ejpam-4703	123	34	(	(	PUNCT
ejpam-4703	123	35	3.2	3.2	NUM
ejpam-4703	123	36	)	)	PUNCT
ejpam-4703	123	37	and	and	CCONJ
ejpam-4703	123	38	j	j	PROPN
ejpam-4703	123	39	is	be	AUX
ejpam-4703	123	40	given	give	VERB
ejpam-4703	123	41	by	by	ADP
ejpam-4703	123	42	j	j	PROPN
ejpam-4703	123	43	=	=	SYM
ejpam-4703	123	44	−	−	PROPN
ejpam-4703	123	45	ln(ab	ln(ab	PROPN
ejpam-4703	123	46	)	)	PUNCT
ejpam-4703	123	47	2	2	NUM
ejpam-4703	123	48	+	+	SYM
ejpam-4703	123	49	1	1	NUM
ejpam-4703	123	50	µ	µ	PRON
ejpam-4703	123	51	−	−	PROPN
ejpam-4703	123	52	coth	coth	PROPN
ejpam-4703	123	53	ρ	ρ	PROPN
ejpam-4703	123	54	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	123	55	)	)	PUNCT
ejpam-4703	123	56	2	2	NUM
ejpam-4703	123	57	.	.	PUNCT
ejpam-4703	124	1	(	(	PUNCT
ejpam-4703	124	2	3.9	3.9	NUM
ejpam-4703	124	3	)	)	PUNCT
ejpam-4703	124	4	proof	proof	NOUN
ejpam-4703	124	5	.	.	PUNCT
ejpam-4703	125	1	applying	apply	VERB
ejpam-4703	125	2	the	the	DET
ejpam-4703	125	3	cauchy	cauchy	ADJ
ejpam-4703	125	4	integral	integral	ADJ
ejpam-4703	125	5	formula	formula	NOUN
ejpam-4703	125	6	to	to	ADP
ejpam-4703	125	7	(	(	PUNCT
ejpam-4703	125	8	1.1	1.1	NUM
ejpam-4703	125	9	)	)	PUNCT
ejpam-4703	125	10	yields	yield	NOUN
ejpam-4703	125	11	b	b	PROPN
ejpam-4703	125	12	(	(	PUNCT
ejpam-4703	125	13	α	α	NOUN
ejpam-4703	125	14	)	)	PUNCT
ejpam-4703	125	15	n	n	CCONJ
ejpam-4703	125	16	(	(	PUNCT
ejpam-4703	125	17	x;λ	x;λ	NUM
ejpam-4703	125	18	;	;	PUNCT
ejpam-4703	125	19	a	a	DET
ejpam-4703	125	20	,	,	PUNCT
ejpam-4703	125	21	b	b	NOUN
ejpam-4703	125	22	,	,	PUNCT
ejpam-4703	125	23	c	c	NOUN
ejpam-4703	125	24	)	)	PUNCT
ejpam-4703	125	25	n	n	CCONJ
ejpam-4703	125	26	!	!	PUNCT
ejpam-4703	126	1	=	=	SYM
ejpam-4703	126	2	1	1	NUM
ejpam-4703	126	3	2πi	2πi	NOUN
ejpam-4703	126	4	∫	∫	PROPN
ejpam-4703	126	5	c	c	PROPN
ejpam-4703	126	6	(	(	PUNCT
ejpam-4703	126	7	t	t	NOUN
ejpam-4703	126	8	λbt	λbt	VERB
ejpam-4703	126	9	−	−	NOUN
ejpam-4703	126	10	at	at	ADP
ejpam-4703	126	11	)	)	PUNCT
ejpam-4703	126	12	α	α	PROPN
ejpam-4703	126	13	cxt	cxt	NOUN
ejpam-4703	126	14	dt	dt	X
ejpam-4703	126	15	tn+1	tn+1	PROPN
ejpam-4703	126	16	,	,	PUNCT
ejpam-4703	126	17	where	where	SCONJ
ejpam-4703	126	18	c	c	PROPN
ejpam-4703	126	19	is	be	AUX
ejpam-4703	126	20	a	a	DET
ejpam-4703	126	21	circle	circle	NOUN
ejpam-4703	126	22	around	around	ADP
ejpam-4703	126	23	the	the	DET
ejpam-4703	126	24	origin	origin	NOUN
ejpam-4703	126	25	with	with	ADP
ejpam-4703	126	26	radius	radius	NOUN
ejpam-4703	126	27	<	<	X
ejpam-4703	126	28	∣∣	∣∣	NUM
ejpam-4703	126	29	δ	δ	PROPN
ejpam-4703	126	30	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	126	31	)	)	PUNCT
ejpam-4703	126	32	∣∣.	∣∣.	PROPN
ejpam-4703	126	33	writing	writing	NOUN
ejpam-4703	126	34	(	(	PUNCT
ejpam-4703	126	35	t	t	NOUN
ejpam-4703	126	36	λbt	λbt	VERB
ejpam-4703	126	37	−	−	NOUN
ejpam-4703	126	38	at	at	ADP
ejpam-4703	126	39	)	)	PUNCT
ejpam-4703	126	40	α	α	NOUN
ejpam-4703	126	41	=	=	PUNCT
ejpam-4703	126	42	tαa−αt	tαa−αt	NOUN
ejpam-4703	126	43	(	(	PUNCT
ejpam-4703	126	44	eδ(ba−1)t	eδ(ba−1)t	NOUN
ejpam-4703	126	45	−	−	PROPN
ejpam-4703	126	46	1)α	1)α	NUM
ejpam-4703	127	1	=	=	NOUN
ejpam-4703	127	2	tαa−αt	tαa−αt	NOUN
ejpam-4703	128	1	[	[	X
ejpam-4703	128	2	exp	exp	X
ejpam-4703	128	3	(	(	PUNCT
ejpam-4703	128	4	t	t	PROPN
ejpam-4703	128	5	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	128	6	)	)	PUNCT
ejpam-4703	128	7	+	+	CCONJ
ejpam-4703	128	8	δ)−	δ)−	PROPN
ejpam-4703	128	9	1]α	1]α	NUM
ejpam-4703	128	10	=	=	SYM
ejpam-4703	128	11	tαa−αt	tαa−αt	NOUN
ejpam-4703	128	12	[	[	PUNCT
ejpam-4703	128	13	2	2	NUM
ejpam-4703	128	14	exp	exp	NOUN
ejpam-4703	128	15	(	(	PUNCT
ejpam-4703	128	16	t	t	NOUN
ejpam-4703	128	17	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	128	18	2	2	NUM
ejpam-4703	128	19	)	)	PUNCT
ejpam-4703	128	20	sinh	sinh	NOUN
ejpam-4703	128	21	(	(	PUNCT
ejpam-4703	128	22	t	t	PROPN
ejpam-4703	128	23	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	128	24	2	2	NUM
ejpam-4703	128	25	)	)	PUNCT
ejpam-4703	128	26	]	]	PUNCT
ejpam-4703	128	27	α	α	X
ejpam-4703	128	28	=	=	SYM
ejpam-4703	128	29	tα(ab	tα(ab	PROPN
ejpam-4703	128	30	)	)	PUNCT
ejpam-4703	128	31	−α	−α	NOUN
ejpam-4703	128	32	2	2	NUM
ejpam-4703	128	33	t	t	NOUN
ejpam-4703	128	34	2αλ	2αλ	NOUN
ejpam-4703	128	35	α	α	DET
ejpam-4703	128	36	2	2	NUM
ejpam-4703	128	37	sinhα	sinhα	NOUN
ejpam-4703	128	38	(	(	PUNCT
ejpam-4703	128	39	t	t	NOUN
ejpam-4703	128	40	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	128	41	2	2	NUM
ejpam-4703	128	42	)	)	PUNCT
ejpam-4703	128	43	thus	thus	ADV
ejpam-4703	128	44	,	,	PUNCT
ejpam-4703	128	45	b	b	X
ejpam-4703	128	46	(	(	PUNCT
ejpam-4703	128	47	α	α	NOUN
ejpam-4703	128	48	)	)	PUNCT
ejpam-4703	128	49	n	n	CCONJ
ejpam-4703	128	50	(	(	PUNCT
ejpam-4703	128	51	nx;λ	nx;λ	NUM
ejpam-4703	128	52	;	;	PUNCT
ejpam-4703	128	53	a	a	DET
ejpam-4703	128	54	,	,	PUNCT
ejpam-4703	128	55	b	b	NOUN
ejpam-4703	128	56	,	,	PUNCT
ejpam-4703	128	57	c	c	NOUN
ejpam-4703	128	58	)	)	PUNCT
ejpam-4703	128	59	n	n	CCONJ
ejpam-4703	128	60	!	!	PUNCT
ejpam-4703	128	61	=	=	PUNCT
ejpam-4703	129	1	(	(	PUNCT
ejpam-4703	129	2	2−αλ	2−αλ	NUM
ejpam-4703	129	3	−α	−α	NOUN
ejpam-4703	129	4	2	2	NUM
ejpam-4703	129	5	)	)	PUNCT
ejpam-4703	129	6	1	1	NUM
ejpam-4703	129	7	2πi	2πi	NOUN
ejpam-4703	129	8	∫	∫	PROPN
ejpam-4703	130	1	c	c	NOUN
ejpam-4703	130	2	tα(ab)−	tα(ab)−	VERB
ejpam-4703	130	3	α	α	NOUN
ejpam-4703	130	4	2	2	NUM
ejpam-4703	130	5	tcnxt	tcnxt	NOUN
ejpam-4703	130	6	sinhα	sinhα	NOUN
ejpam-4703	130	7	(	(	PUNCT
ejpam-4703	130	8	t	t	NOUN
ejpam-4703	130	9	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	130	10	2	2	NUM
ejpam-4703	130	11	)	)	PUNCT
ejpam-4703	130	12	dt	dt	X
ejpam-4703	130	13	tn+1	tn+1	NOUN
ejpam-4703	131	1	=	=	SYM
ejpam-4703	132	1	2−αλ	2−αλ	NUM
ejpam-4703	132	2	−α	−α	NOUN
ejpam-4703	132	3	2	2	NUM
ejpam-4703	132	4	1	1	NUM
ejpam-4703	132	5	2πi	2πi	ADJ
ejpam-4703	132	6	∫	∫	PROPN
ejpam-4703	133	1	c	c	NOUN
ejpam-4703	133	2	gα(t)c	gα(t)c	PROPN
ejpam-4703	133	3	nxt	nxt	PROPN
ejpam-4703	133	4	dt	dt	PROPN
ejpam-4703	133	5	tn+1	tn+1	PROPN
ejpam-4703	133	6	,	,	PUNCT
ejpam-4703	133	7	c.	c.	PROPN
ejpam-4703	133	8	corcino	corcino	PROPN
ejpam-4703	133	9	,	,	PUNCT
ejpam-4703	133	10	r.	r.	PROPN
ejpam-4703	133	11	corcino	corcino	PROPN
ejpam-4703	133	12	/	/	SYM
ejpam-4703	133	13	eur	eur	PROPN
ejpam-4703	133	14	.	.	PUNCT
ejpam-4703	134	1	j.	j.	PROPN
ejpam-4703	134	2	pure	pure	PROPN
ejpam-4703	134	3	appl	appl	PROPN
ejpam-4703	134	4	.	.	PROPN
ejpam-4703	134	5	math	math	PROPN
ejpam-4703	134	6	,	,	PUNCT
ejpam-4703	134	7	16	16	NUM
ejpam-4703	134	8	(	(	PUNCT
ejpam-4703	134	9	2	2	NUM
ejpam-4703	134	10	)	)	PUNCT
ejpam-4703	134	11	(	(	PUNCT
ejpam-4703	134	12	2023	2023	NUM
ejpam-4703	134	13	)	)	PUNCT
ejpam-4703	134	14	,	,	PUNCT
ejpam-4703	134	15	791	791	NUM
ejpam-4703	134	16	-	-	SYM
ejpam-4703	134	17	805	805	NUM
ejpam-4703	134	18	798	798	NUM
ejpam-4703	134	19	where	where	SCONJ
ejpam-4703	134	20	,	,	PUNCT
ejpam-4703	134	21	gα(t	gα(t	NOUN
ejpam-4703	134	22	)	)	PUNCT
ejpam-4703	134	23	=	=	VERB
ejpam-4703	135	1	[	[	X
ejpam-4703	135	2	g(t)]α	g(t)]α	X
ejpam-4703	135	3	=	=	SYM
ejpam-4703	135	4			PROPN
ejpam-4703	135	5	t(ab	t(ab	PROPN
ejpam-4703	135	6	)	)	PUNCT
ejpam-4703	135	7	−t	−t	NOUN
ejpam-4703	135	8	2	2	NUM
ejpam-4703	135	9	sinh	sinh	NOUN
ejpam-4703	135	10	(	(	PUNCT
ejpam-4703	135	11	t	t	NOUN
ejpam-4703	135	12	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	135	13	2	2	NUM
ejpam-4703	135	14	)	)	PUNCT
ejpam-4703	135	15	α	α	PRON
ejpam-4703	135	16	.	.	PUNCT
ejpam-4703	136	1	(	(	PUNCT
ejpam-4703	136	2	3.10	3.10	NUM
ejpam-4703	136	3	)	)	PUNCT
ejpam-4703	136	4	the	the	DET
ejpam-4703	136	5	saddle	saddle	NOUN
ejpam-4703	136	6	-	-	PUNCT
ejpam-4703	136	7	point	point	NOUN
ejpam-4703	136	8	is	be	AUX
ejpam-4703	136	9	still	still	ADV
ejpam-4703	136	10	µ	µ	X
ejpam-4703	136	11	=	=	PUNCT
ejpam-4703	136	12	(	(	PUNCT
ejpam-4703	136	13	x	x	X
ejpam-4703	136	14	ln	ln	PROPN
ejpam-4703	136	15	c)−1	c)−1	PROPN
ejpam-4703	136	16	.	.	PUNCT
ejpam-4703	137	1	the	the	DET
ejpam-4703	137	2	function	function	NOUN
ejpam-4703	137	3	gα(t	gα(t	NOUN
ejpam-4703	137	4	)	)	PUNCT
ejpam-4703	137	5	has	have	VERB
ejpam-4703	137	6	poles	pole	NOUN
ejpam-4703	137	7	of	of	ADP
ejpam-4703	137	8	order	order	NOUN
ejpam-4703	137	9	α	α	NOUN
ejpam-4703	137	10	at	at	ADP
ejpam-4703	137	11	tk	tk	PROPN
ejpam-4703	137	12	=	=	SYM
ejpam-4703	137	13	2kπi−δ	2kπi−δ	NUM
ejpam-4703	137	14	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	137	15	)	)	PUNCT
ejpam-4703	137	16	,	,	PUNCT
ejpam-4703	137	17	k	k	PROPN
ejpam-4703	137	18	∈	∈	PROPN
ejpam-4703	137	19	z.	z.	PROPN
ejpam-4703	137	20	assuming	assume	VERB
ejpam-4703	137	21	that	that	SCONJ
ejpam-4703	137	22	µ	µ	NOUN
ejpam-4703	137	23	=	=	SYM
ejpam-4703	137	24	(	(	PUNCT
ejpam-4703	137	25	x	x	X
ejpam-4703	137	26	ln	ln	ADJ
ejpam-4703	137	27	c)−1	c)−1	NOUN
ejpam-4703	137	28	is	be	AUX
ejpam-4703	137	29	not	not	PART
ejpam-4703	137	30	a	a	DET
ejpam-4703	137	31	singularity	singularity	NOUN
ejpam-4703	137	32	of	of	ADP
ejpam-4703	137	33	gα(t	gα(t	NOUN
ejpam-4703	137	34	)	)	PUNCT
ejpam-4703	137	35	.	.	PUNCT
ejpam-4703	138	1	then	then	ADV
ejpam-4703	138	2	gα(t	gα(t	X
ejpam-4703	138	3	)	)	PUNCT
ejpam-4703	138	4	can	can	AUX
ejpam-4703	138	5	be	be	AUX
ejpam-4703	138	6	expanded	expand	VERB
ejpam-4703	138	7	about	about	ADP
ejpam-4703	138	8	µ.	µ.	NOUN
ejpam-4703	138	9	that	that	PRON
ejpam-4703	138	10	is	be	AUX
ejpam-4703	138	11	,	,	PUNCT
ejpam-4703	138	12	gα(t	gα(t	ADJ
ejpam-4703	138	13	)	)	PUNCT
ejpam-4703	138	14	=	=	SYM
ejpam-4703	139	1	∞∑	∞∑	NUM
ejpam-4703	139	2	k=0	k=0	PUNCT
ejpam-4703	139	3	g	g	PROPN
ejpam-4703	139	4	(	(	PUNCT
ejpam-4703	139	5	k	k	NOUN
ejpam-4703	139	6	)	)	PUNCT
ejpam-4703	139	7	α	α	PROPN
ejpam-4703	139	8	(	(	PUNCT
ejpam-4703	139	9	µ	µ	NOUN
ejpam-4703	139	10	)	)	PUNCT
ejpam-4703	139	11	k	k	NOUN
ejpam-4703	139	12	!	!	PUNCT
ejpam-4703	139	13	(	(	PUNCT
ejpam-4703	139	14	t−	t−	PROPN
ejpam-4703	139	15	µ)k	µ)k	NOUN
ejpam-4703	139	16	,	,	PUNCT
ejpam-4703	139	17	|t−	|t−	PROPN
ejpam-4703	139	18	µ|	µ|	PROPN
ejpam-4703	139	19	<	<	X
ejpam-4703	139	20	r	r	NOUN
ejpam-4703	139	21	where	where	SCONJ
ejpam-4703	139	22	r	r	NOUN
ejpam-4703	139	23	is	be	AUX
ejpam-4703	139	24	the	the	DET
ejpam-4703	139	25	distance	distance	NOUN
ejpam-4703	139	26	from	from	ADP
ejpam-4703	139	27	µ	µ	PRON
ejpam-4703	139	28	to	to	ADP
ejpam-4703	139	29	the	the	DET
ejpam-4703	139	30	nearest	near	ADJ
ejpam-4703	139	31	singularity	singularity	NOUN
ejpam-4703	139	32	of	of	ADP
ejpam-4703	139	33	gα(t	gα(t	NOUN
ejpam-4703	139	34	)	)	PUNCT
ejpam-4703	139	35	.	.	PUNCT
ejpam-4703	140	1	the	the	DET
ejpam-4703	140	2	derivatives	derivative	NOUN
ejpam-4703	140	3	for	for	ADP
ejpam-4703	140	4	k	k	PROPN
ejpam-4703	140	5	=	=	SYM
ejpam-4703	140	6	1	1	NUM
ejpam-4703	140	7	,	,	PUNCT
ejpam-4703	140	8	2	2	NUM
ejpam-4703	140	9	are	be	AUX
ejpam-4703	140	10	g′α(t	g′α(t	NOUN
ejpam-4703	140	11	)	)	PUNCT
ejpam-4703	140	12	=	=	SYM
ejpam-4703	140	13	α[g(t)]α−1g′(t	α[g(t)]α−1g′(t	NOUN
ejpam-4703	140	14	)	)	PUNCT
ejpam-4703	140	15	,	,	PUNCT
ejpam-4703	140	16	(	(	PUNCT
ejpam-4703	140	17	3.11	3.11	NUM
ejpam-4703	140	18	)	)	PUNCT
ejpam-4703	140	19	g′′α(t	g′′α(t	PROPN
ejpam-4703	140	20	)	)	PUNCT
ejpam-4703	140	21	=	=	SYM
ejpam-4703	140	22	α	α	PROPN
ejpam-4703	140	23	{	{	PUNCT
ejpam-4703	140	24	g(t)α−1g′′(t	g(t)α−1g′′(t	VERB
ejpam-4703	140	25	)	)	PUNCT
ejpam-4703	141	1	+	+	CCONJ
ejpam-4703	141	2	(	(	PUNCT
ejpam-4703	141	3	α−	α−	ADP
ejpam-4703	141	4	1)g(t)α−2[g′(t)]2	1)g(t)α−2[g′(t)]2	NUM
ejpam-4703	141	5	}	}	PUNCT
ejpam-4703	141	6	,	,	PUNCT
ejpam-4703	141	7	(	(	PUNCT
ejpam-4703	141	8	3.12	3.12	NUM
ejpam-4703	141	9	)	)	PUNCT
ejpam-4703	141	10	where	where	SCONJ
ejpam-4703	141	11	g(t	g(t	PROPN
ejpam-4703	141	12	)	)	PUNCT
ejpam-4703	141	13	is	be	AUX
ejpam-4703	141	14	defined	define	VERB
ejpam-4703	141	15	in	in	ADP
ejpam-4703	141	16	(	(	PUNCT
ejpam-4703	141	17	3.5	3.5	NUM
ejpam-4703	141	18	)	)	PUNCT
ejpam-4703	141	19	.	.	PUNCT
ejpam-4703	142	1	evaluating	evaluate	VERB
ejpam-4703	142	2	at	at	ADP
ejpam-4703	142	3	t	t	PROPN
ejpam-4703	142	4	=	=	SYM
ejpam-4703	142	5	µ	µ	PROPN
ejpam-4703	142	6	,	,	PUNCT
ejpam-4703	142	7	g′α(µ	g′α(µ	NOUN
ejpam-4703	142	8	)	)	PUNCT
ejpam-4703	143	1	=	=	SYM
ejpam-4703	143	2	α	α	PROPN
ejpam-4703	143	3	(	(	PUNCT
ejpam-4703	143	4	µ(ab)−	µ(ab)−	X
ejpam-4703	143	5	µ	µ	X
ejpam-4703	143	6	2	2	NUM
ejpam-4703	143	7	sinh	sinh	NOUN
ejpam-4703	143	8	ρ	ρ	NOUN
ejpam-4703	143	9	)	)	PUNCT
ejpam-4703	143	10	α	α	PROPN
ejpam-4703	143	11	(	(	PUNCT
ejpam-4703	143	12	−	−	PROPN
ejpam-4703	143	13	ln(ab	ln(ab	PROPN
ejpam-4703	143	14	)	)	PUNCT
ejpam-4703	143	15	2	2	NUM
ejpam-4703	144	1	+	+	SYM
ejpam-4703	144	2	1	1	NUM
ejpam-4703	144	3	µ	µ	PRON
ejpam-4703	144	4	−	−	PROPN
ejpam-4703	144	5	coth	coth	PROPN
ejpam-4703	144	6	ρ	ρ	PROPN
ejpam-4703	144	7	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	144	8	)	)	PUNCT
ejpam-4703	144	9	2	2	NUM
ejpam-4703	144	10	)	)	PUNCT
ejpam-4703	144	11	,	,	PUNCT
ejpam-4703	144	12	(	(	PUNCT
ejpam-4703	144	13	3.13	3.13	NUM
ejpam-4703	144	14	)	)	PUNCT
ejpam-4703	144	15	g′′α(µ	g′′α(µ	PROPN
ejpam-4703	144	16	)	)	PUNCT
ejpam-4703	145	1	=	=	SYM
ejpam-4703	145	2	α	α	PROPN
ejpam-4703	145	3			PUNCT
ejpam-4703	145	4	(	(	PUNCT
ejpam-4703	145	5	µ(ab)−	µ(ab)−	X
ejpam-4703	145	6	µ	µ	X
ejpam-4703	145	7	2	2	NUM
ejpam-4703	145	8	sinh	sinh	NOUN
ejpam-4703	145	9	ρ	ρ	NOUN
ejpam-4703	145	10	)	)	PUNCT
ejpam-4703	145	11	α−1	α−1	PROPN
ejpam-4703	145	12	µe−	µe−	PROPN
ejpam-4703	145	13	µ	µ	PRON
ejpam-4703	145	14	ln(ab	ln(ab	PROPN
ejpam-4703	145	15	)	)	PUNCT
ejpam-4703	145	16	2	2	NUM
ejpam-4703	145	17	sinh	sinh	NOUN
ejpam-4703	145	18	ρ	ρ	NOUN
ejpam-4703	145	19	a+	a+	PUNCT
ejpam-4703	145	20	(	(	PUNCT
ejpam-4703	145	21	α−	α−	ADP
ejpam-4703	145	22	1	1	NUM
ejpam-4703	145	23	)	)	PUNCT
ejpam-4703	145	24	(	(	PUNCT
ejpam-4703	145	25	µ(ab)−	µ(ab)−	X
ejpam-4703	145	26	µ	µ	X
ejpam-4703	145	27	2	2	NUM
ejpam-4703	145	28	sinh	sinh	NOUN
ejpam-4703	145	29	ρ	ρ	NOUN
ejpam-4703	145	30	)	)	PUNCT
ejpam-4703	145	31	α−2	α−2	PROPN
ejpam-4703	145	32	(	(	PUNCT
ejpam-4703	145	33	µe−	µe−	X
ejpam-4703	145	34	µ	µ	X
ejpam-4703	145	35	ln(ab	ln(ab	PROPN
ejpam-4703	145	36	)	)	PUNCT
ejpam-4703	145	37	2	2	NUM
ejpam-4703	145	38	sinh	sinh	NOUN
ejpam-4703	145	39	ρ	ρ	PROPN
ejpam-4703	145	40	j	j	PROPN
ejpam-4703	145	41	)	)	PUNCT
ejpam-4703	145	42	2	2	NUM
ejpam-4703	145	43			NOUN
ejpam-4703	145	44	(	(	PUNCT
ejpam-4703	145	45	3.14	3.14	NUM
ejpam-4703	145	46	)	)	PUNCT
ejpam-4703	145	47	=	=	SYM
ejpam-4703	145	48	α	α	PROPN
ejpam-4703	145	49	(	(	PUNCT
ejpam-4703	145	50	µ(ab)−	µ(ab)−	X
ejpam-4703	145	51	µ	µ	X
ejpam-4703	145	52	2	2	NUM
ejpam-4703	145	53	sinh	sinh	NOUN
ejpam-4703	145	54	ρ	ρ	PROPN
ejpam-4703	145	55	)	)	PUNCT
ejpam-4703	145	56	α	α	PROPN
ejpam-4703	145	57	{	{	PUNCT
ejpam-4703	145	58	a+	a+	PUNCT
ejpam-4703	145	59	(	(	PUNCT
ejpam-4703	145	60	α−	α−	ADP
ejpam-4703	145	61	1	1	NUM
ejpam-4703	145	62	)	)	PUNCT
ejpam-4703	145	63	(	(	PUNCT
ejpam-4703	145	64	−	−	PROPN
ejpam-4703	145	65	ln(ab	ln(ab	PROPN
ejpam-4703	145	66	)	)	PUNCT
ejpam-4703	145	67	2	2	NUM
ejpam-4703	146	1	+	+	SYM
ejpam-4703	146	2	1	1	NUM
ejpam-4703	146	3	µ	µ	PRON
ejpam-4703	146	4	−	−	PROPN
ejpam-4703	146	5	coth	coth	PROPN
ejpam-4703	146	6	ρ	ρ	PROPN
ejpam-4703	146	7	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	146	8	)	)	PUNCT
ejpam-4703	146	9	2	2	NUM
ejpam-4703	146	10	)	)	PUNCT
ejpam-4703	146	11	2	2	NUM
ejpam-4703	146	12	}	}	PUNCT
ejpam-4703	146	13	.	.	PUNCT
ejpam-4703	147	1	(	(	PUNCT
ejpam-4703	147	2	3.15	3.15	NUM
ejpam-4703	147	3	)	)	PUNCT
ejpam-4703	147	4	it	it	PRON
ejpam-4703	147	5	follows	follow	VERB
ejpam-4703	147	6	from	from	ADP
ejpam-4703	147	7	theorem	theorem	ADJ
ejpam-4703	147	8	1.3	1.3	NUM
ejpam-4703	147	9	that	that	DET
ejpam-4703	147	10	b	b	X
ejpam-4703	147	11	(	(	PUNCT
ejpam-4703	147	12	α	α	NOUN
ejpam-4703	147	13	)	)	PUNCT
ejpam-4703	147	14	n	n	CCONJ
ejpam-4703	147	15	(	(	PUNCT
ejpam-4703	147	16	nx;λ	nx;λ	NUM
ejpam-4703	147	17	;	;	PUNCT
ejpam-4703	147	18	a	a	DET
ejpam-4703	147	19	,	,	PUNCT
ejpam-4703	147	20	b	b	NOUN
ejpam-4703	147	21	,	,	PUNCT
ejpam-4703	147	22	c	c	NOUN
ejpam-4703	147	23	)	)	PUNCT
ejpam-4703	147	24	2−αλ	2−αλ	NUM
ejpam-4703	147	25	−α	−α	NOUN
ejpam-4703	147	26	2	2	NUM
ejpam-4703	147	27	=	=	SYM
ejpam-4703	147	28	(	(	PUNCT
ejpam-4703	147	29	nx	nx	X
ejpam-4703	147	30	ln	ln	NOUN
ejpam-4703	147	31	c)n	c)n	NOUN
ejpam-4703	148	1	∞∑	∞∑	PRON
ejpam-4703	148	2	k=0	k=0	PROPN
ejpam-4703	148	3	g	g	PROPN
ejpam-4703	148	4	(	(	PUNCT
ejpam-4703	148	5	k	k	NOUN
ejpam-4703	148	6	)	)	PUNCT
ejpam-4703	148	7	α	α	PROPN
ejpam-4703	148	8	(	(	PUNCT
ejpam-4703	148	9	n	n	CCONJ
ejpam-4703	148	10	)	)	PUNCT
ejpam-4703	148	11	k	k	NOUN
ejpam-4703	148	12	!	!	NOUN
ejpam-4703	148	13	pk(n	pk(n	X
ejpam-4703	148	14	)	)	PUNCT
ejpam-4703	149	1	(	(	PUNCT
ejpam-4703	149	2	nx	nx	NUM
ejpam-4703	149	3	ln	ln	ADJ
ejpam-4703	149	4	c)k	c)k	NOUN
ejpam-4703	149	5	=	=	PUNCT
ejpam-4703	149	6	(	(	PUNCT
ejpam-4703	149	7	nx	nx	X
ejpam-4703	149	8	ln	ln	PROPN
ejpam-4703	149	9	c)n	c)n	NOUN
ejpam-4703	149	10	{	{	PUNCT
ejpam-4703	149	11	gα(µ	gα(µ	PROPN
ejpam-4703	149	12	)	)	PUNCT
ejpam-4703	150	1	+	+	CCONJ
ejpam-4703	150	2	g′′α(µ	g′′α(µ	PROPN
ejpam-4703	150	3	)	)	PUNCT
ejpam-4703	150	4	2(nx	2(nx	NUM
ejpam-4703	150	5	ln	ln	ADJ
ejpam-4703	150	6	c)2	c)2	PROPN
ejpam-4703	150	7	p2(n	p2(n	NOUN
ejpam-4703	150	8	)	)	PUNCT
ejpam-4703	150	9	+	+	PROPN
ejpam-4703	150	10	o(n−2	o(n−2	X
ejpam-4703	150	11	)	)	PUNCT
ejpam-4703	150	12	}	}	PUNCT
ejpam-4703	150	13	.	.	PUNCT
ejpam-4703	151	1	then	then	ADV
ejpam-4703	151	2	,	,	PUNCT
ejpam-4703	151	3	b(α	b(α	PROPN
ejpam-4703	151	4	)	)	PUNCT
ejpam-4703	151	5	n	n	CCONJ
ejpam-4703	151	6	(	(	PUNCT
ejpam-4703	151	7	nx;λ	nx;λ	NUM
ejpam-4703	151	8	;	;	PUNCT
ejpam-4703	151	9	a	a	DET
ejpam-4703	151	10	,	,	PUNCT
ejpam-4703	151	11	b	b	NOUN
ejpam-4703	151	12	,	,	PUNCT
ejpam-4703	151	13	c	c	NOUN
ejpam-4703	151	14	)	)	PUNCT
ejpam-4703	151	15	=	=	SYM
ejpam-4703	151	16	2−αλ−α	2−αλ−α	NUM
ejpam-4703	151	17	2	2	NUM
ejpam-4703	151	18	(	(	PUNCT
ejpam-4703	151	19	nx	nx	PROPN
ejpam-4703	151	20	ln	ln	NOUN
ejpam-4703	151	21	c)n	c)n	NOUN
ejpam-4703	151	22	{	{	PUNCT
ejpam-4703	151	23	(	(	PUNCT
ejpam-4703	151	24	µ(ab	µ(ab	NOUN
ejpam-4703	151	25	)	)	PUNCT
ejpam-4703	151	26	−µ	−µ	ADJ
ejpam-4703	151	27	2	2	NUM
ejpam-4703	151	28	sinh	sinh	NOUN
ejpam-4703	151	29	ρ	ρ	NOUN
ejpam-4703	151	30	)	)	PUNCT
ejpam-4703	152	1	α	α	PROPN
ejpam-4703	152	2	+	+	X
ejpam-4703	152	3	g′′α(µ	g′′α(µ	PROPN
ejpam-4703	152	4	)	)	PUNCT
ejpam-4703	152	5	2n(x	2n(x	NUM
ejpam-4703	152	6	ln	ln	ADJ
ejpam-4703	152	7	c)2	c)2	NOUN
ejpam-4703	152	8	+	+	PROPN
ejpam-4703	152	9	o(n−2	o(n−2	PROPN
ejpam-4703	152	10	)	)	PUNCT
ejpam-4703	152	11	}	}	PUNCT
ejpam-4703	152	12	c.	c.	PROPN
ejpam-4703	152	13	corcino	corcino	PROPN
ejpam-4703	152	14	,	,	PUNCT
ejpam-4703	152	15	r.	r.	PROPN
ejpam-4703	152	16	corcino	corcino	PROPN
ejpam-4703	152	17	/	/	SYM
ejpam-4703	152	18	eur	eur	PROPN
ejpam-4703	152	19	.	.	PUNCT
ejpam-4703	153	1	j.	j.	PROPN
ejpam-4703	153	2	pure	pure	PROPN
ejpam-4703	153	3	appl	appl	PROPN
ejpam-4703	153	4	.	.	PROPN
ejpam-4703	153	5	math	math	PROPN
ejpam-4703	153	6	,	,	PUNCT
ejpam-4703	153	7	16	16	NUM
ejpam-4703	153	8	(	(	PUNCT
ejpam-4703	153	9	2	2	NUM
ejpam-4703	153	10	)	)	PUNCT
ejpam-4703	153	11	(	(	PUNCT
ejpam-4703	153	12	2023	2023	NUM
ejpam-4703	153	13	)	)	PUNCT
ejpam-4703	153	14	,	,	PUNCT
ejpam-4703	153	15	791	791	NUM
ejpam-4703	153	16	-	-	SYM
ejpam-4703	153	17	805	805	NUM
ejpam-4703	153	18	799	799	NUM
ejpam-4703	153	19	=	=	SYM
ejpam-4703	153	20	2−αλ−α	2−αλ−α	NUM
ejpam-4703	153	21	2	2	NUM
ejpam-4703	153	22	(	(	PUNCT
ejpam-4703	153	23	nx	nx	X
ejpam-4703	153	24	ln	ln	PROPN
ejpam-4703	153	25	c)n	c)n	NOUN
ejpam-4703	153	26	(	(	PUNCT
ejpam-4703	153	27	µ(ab	µ(ab	NOUN
ejpam-4703	153	28	)	)	PUNCT
ejpam-4703	153	29	−µ	−µ	ADJ
ejpam-4703	153	30	2	2	NUM
ejpam-4703	153	31	sinh	sinh	NOUN
ejpam-4703	153	32	ρ	ρ	PROPN
ejpam-4703	153	33	)	)	PUNCT
ejpam-4703	153	34	α	α	PROPN
ejpam-4703	153	35	{	{	PUNCT
ejpam-4703	153	36	1−	1−	NUM
ejpam-4703	153	37	αa+	αa+	ADJ
ejpam-4703	153	38	α(α−	α(α−	NOUN
ejpam-4703	154	1	1)j2	1)j2	NUM
ejpam-4703	154	2	2n(x	2n(x	NUM
ejpam-4703	154	3	ln	ln	ADJ
ejpam-4703	154	4	c)2	c)2	NOUN
ejpam-4703	154	5	+	+	PROPN
ejpam-4703	154	6	o(n−2	o(n−2	PROPN
ejpam-4703	154	7	)	)	PUNCT
ejpam-4703	154	8	}	}	PUNCT
ejpam-4703	154	9	,	,	PUNCT
ejpam-4703	154	10	where	where	SCONJ
ejpam-4703	154	11	a	a	PRON
ejpam-4703	154	12	is	be	AUX
ejpam-4703	154	13	given	give	VERB
ejpam-4703	154	14	in(3.2	in(3.2	NOUN
ejpam-4703	154	15	)	)	PUNCT
ejpam-4703	154	16	and	and	CCONJ
ejpam-4703	154	17	j	j	PROPN
ejpam-4703	154	18	=	=	SYM
ejpam-4703	154	19	−	−	PROPN
ejpam-4703	154	20	ln(ab	ln(ab	PROPN
ejpam-4703	154	21	)	)	PUNCT
ejpam-4703	154	22	2	2	NUM
ejpam-4703	154	23	+	+	SYM
ejpam-4703	154	24	1	1	NUM
ejpam-4703	154	25	µ	µ	PRON
ejpam-4703	154	26	−	−	PROPN
ejpam-4703	154	27	coth	coth	PROPN
ejpam-4703	154	28	ρ	ρ	PROPN
ejpam-4703	154	29	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	154	30	)	)	PUNCT
ejpam-4703	154	31	2	2	NUM
ejpam-4703	154	32	.	.	PUNCT
ejpam-4703	154	33	theorem	theorem	VERB
ejpam-4703	154	34	3.3	3.3	NUM
ejpam-4703	154	35	.	.	PUNCT
ejpam-4703	155	1	(	(	PUNCT
ejpam-4703	155	2	apostol	apostol	NOUN
ejpam-4703	155	3	-	-	PUNCT
ejpam-4703	155	4	euler	euler	NOUN
ejpam-4703	155	5	type	type	NOUN
ejpam-4703	155	6	polynomials	polynomial	NOUN
ejpam-4703	155	7	of	of	ADP
ejpam-4703	155	8	order	order	NOUN
ejpam-4703	155	9	1	1	X
ejpam-4703	155	10	)	)	PUNCT
ejpam-4703	155	11	let	let	VERB
ejpam-4703	155	12	a	a	DET
ejpam-4703	155	13	,	,	PUNCT
ejpam-4703	155	14	b	b	NOUN
ejpam-4703	155	15	,	,	PUNCT
ejpam-4703	155	16	c	c	PROPN
ejpam-4703	155	17	∈	∈	PROPN
ejpam-4703	155	18	r+\{1	r+\{1	PROPN
ejpam-4703	155	19	}	}	PUNCT
ejpam-4703	155	20	,	,	PUNCT
ejpam-4703	155	21	a	a	DET
ejpam-4703	155	22	̸=	̸=	PROPN
ejpam-4703	155	23	b	b	PROPN
ejpam-4703	155	24	and	and	CCONJ
ejpam-4703	155	25	µ	µ	X
ejpam-4703	155	26	=	=	PUNCT
ejpam-4703	155	27	(	(	PUNCT
ejpam-4703	155	28	x	x	X
ejpam-4703	155	29	ln	ln	PROPN
ejpam-4703	155	30	c)−1	c)−1	PROPN
ejpam-4703	155	31	.	.	PUNCT
ejpam-4703	156	1	for	for	ADP
ejpam-4703	156	2	x	x	PROPN
ejpam-4703	156	3	∈	∈	PROPN
ejpam-4703	156	4	c\{0	c\{0	PROPN
ejpam-4703	156	5	}	}	PUNCT
ejpam-4703	156	6	such	such	ADJ
ejpam-4703	156	7	that	that	SCONJ
ejpam-4703	156	8	|µ|	|µ|	PROPN
ejpam-4703	156	9	<	<	X
ejpam-4703	156	10	|µ±	|µ±	PROPN
ejpam-4703	156	11	πi−δ	πi−δ	PROPN
ejpam-4703	156	12	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	156	13	)	)	PUNCT
ejpam-4703	156	14	|	|	ADV
ejpam-4703	156	15	,	,	PUNCT
ejpam-4703	156	16	the	the	DET
ejpam-4703	156	17	following	follow	VERB
ejpam-4703	156	18	holds	hold	NOUN
ejpam-4703	156	19	,	,	PUNCT
ejpam-4703	156	20	en(nx;λ	en(nx;λ	ADP
ejpam-4703	156	21	;	;	PUNCT
ejpam-4703	156	22	a	a	DET
ejpam-4703	156	23	,	,	PUNCT
ejpam-4703	156	24	b	b	NOUN
ejpam-4703	156	25	,	,	PUNCT
ejpam-4703	156	26	c	c	NOUN
ejpam-4703	156	27	)	)	PUNCT
ejpam-4703	156	28	=	=	SYM
ejpam-4703	157	1	(	(	PUNCT
ejpam-4703	157	2	nx	nx	X
ejpam-4703	157	3	ln	ln	NOUN
ejpam-4703	157	4	c)n(ab	c)n(ab	NOUN
ejpam-4703	157	5	)	)	PUNCT
ejpam-4703	157	6	−µ	−µ	NOUN
ejpam-4703	157	7	2	2	NUM
ejpam-4703	157	8	λ	λ	NOUN
ejpam-4703	157	9	−1	−1	NOUN
ejpam-4703	157	10	2	2	NUM
ejpam-4703	157	11	cosh	cosh	NOUN
ejpam-4703	157	12	ρ	ρ	NOUN
ejpam-4703	157	13	{	{	PUNCT
ejpam-4703	157	14	1−	1−	NUM
ejpam-4703	157	15	f	f	PROPN
ejpam-4703	157	16	2n(x	2n(x	NUM
ejpam-4703	157	17	ln	ln	ADJ
ejpam-4703	157	18	c)2	c)2	NOUN
ejpam-4703	157	19	+	+	PROPN
ejpam-4703	157	20	o(n−2	o(n−2	PROPN
ejpam-4703	157	21	)	)	PUNCT
ejpam-4703	157	22	}	}	PUNCT
ejpam-4703	157	23	(	(	PUNCT
ejpam-4703	157	24	3.16	3.16	NUM
ejpam-4703	157	25	)	)	PUNCT
ejpam-4703	157	26	where	where	SCONJ
ejpam-4703	157	27	f	f	AUX
ejpam-4703	157	28	=	=	PRON
ejpam-4703	157	29	(	(	PUNCT
ejpam-4703	157	30	ln(ab	ln(ab	PROPN
ejpam-4703	157	31	)	)	PUNCT
ejpam-4703	157	32	2	2	NUM
ejpam-4703	157	33	+	+	SYM
ejpam-4703	157	34	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	157	35	)	)	PUNCT
ejpam-4703	157	36	2	2	NUM
ejpam-4703	157	37	tanh	tanh	PROPN
ejpam-4703	157	38	ρ	ρ	PROPN
ejpam-4703	157	39	)	)	PUNCT
ejpam-4703	157	40	2	2	NUM
ejpam-4703	157	41	−	−	PROPN
ejpam-4703	157	42	ln2(ba−1	ln2(ba−1	NOUN
ejpam-4703	157	43	)	)	PUNCT
ejpam-4703	157	44	4	4	NUM
ejpam-4703	157	45	sech2	sech2	NOUN
ejpam-4703	157	46	ρ	ρ	PROPN
ejpam-4703	157	47	.	.	PUNCT
ejpam-4703	158	1	(	(	PUNCT
ejpam-4703	158	2	3.17	3.17	NUM
ejpam-4703	158	3	)	)	PUNCT
ejpam-4703	158	4	proof	proof	NOUN
ejpam-4703	158	5	.	.	PUNCT
ejpam-4703	159	1	taking	take	VERB
ejpam-4703	159	2	α	α	NOUN
ejpam-4703	159	3	=	=	SYM
ejpam-4703	159	4	1	1	NUM
ejpam-4703	159	5	,	,	PUNCT
ejpam-4703	159	6	(	(	PUNCT
ejpam-4703	159	7	1.2	1.2	NUM
ejpam-4703	159	8	)	)	PUNCT
ejpam-4703	159	9	reduces	reduce	VERB
ejpam-4703	159	10	to	to	PART
ejpam-4703	159	11	(	(	PUNCT
ejpam-4703	159	12	2	2	NUM
ejpam-4703	159	13	λbt	λbt	NOUN
ejpam-4703	159	14	+	+	CCONJ
ejpam-4703	159	15	at	at	ADP
ejpam-4703	159	16	)	)	PUNCT
ejpam-4703	159	17	cxt	cxt	NOUN
ejpam-4703	159	18	=	=	PUNCT
ejpam-4703	160	1	∞∑	∞∑	ADJ
ejpam-4703	160	2	n=0	n=0	SYM
ejpam-4703	160	3	en(x;λ	en(x;λ	NOUN
ejpam-4703	160	4	;	;	PUNCT
ejpam-4703	160	5	a	a	DET
ejpam-4703	160	6	,	,	PUNCT
ejpam-4703	160	7	b	b	NOUN
ejpam-4703	160	8	,	,	PUNCT
ejpam-4703	160	9	c	c	NOUN
ejpam-4703	160	10	)	)	PUNCT
ejpam-4703	160	11	tn	tn	PROPN
ejpam-4703	160	12	n	n	CCONJ
ejpam-4703	160	13	!	!	PROPN
ejpam-4703	160	14	,	,	PUNCT
ejpam-4703	160	15	∣∣∣∣t	∣∣∣∣t	PROPN
ejpam-4703	160	16	ln	ln	PROPN
ejpam-4703	161	1	b	b	PROPN
ejpam-4703	161	2	a	a	DET
ejpam-4703	161	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4703	161	4	<	<	X
ejpam-4703	161	5	π	π	PROPN
ejpam-4703	161	6	.	.	PUNCT
ejpam-4703	161	7	applying	apply	VERB
ejpam-4703	161	8	the	the	DET
ejpam-4703	161	9	cauchy	cauchy	ADJ
ejpam-4703	161	10	integral	integral	ADJ
ejpam-4703	161	11	formula	formula	NOUN
ejpam-4703	161	12	,	,	PUNCT
ejpam-4703	161	13	en(x;λ	en(x;λ	NOUN
ejpam-4703	161	14	;	;	PUNCT
ejpam-4703	161	15	a	a	DET
ejpam-4703	161	16	,	,	PUNCT
ejpam-4703	161	17	b	b	NOUN
ejpam-4703	161	18	,	,	PUNCT
ejpam-4703	161	19	c	c	NOUN
ejpam-4703	161	20	)	)	PUNCT
ejpam-4703	161	21	n	n	CCONJ
ejpam-4703	161	22	!	!	PUNCT
ejpam-4703	162	1	=	=	SYM
ejpam-4703	162	2	1	1	NUM
ejpam-4703	162	3	2πi	2πi	ADJ
ejpam-4703	162	4	∫	∫	PROPN
ejpam-4703	163	1	c	c	NOUN
ejpam-4703	163	2	2cxt	2cxt	NUM
ejpam-4703	163	3	[	[	X
ejpam-4703	163	4	λbt	λbt	X
ejpam-4703	164	1	+	+	X
ejpam-4703	164	2	at	at	ADP
ejpam-4703	164	3	]	]	X
ejpam-4703	164	4	dt	dt	X
ejpam-4703	164	5	tn+1	tn+1	PROPN
ejpam-4703	164	6	,	,	PUNCT
ejpam-4703	164	7	where	where	SCONJ
ejpam-4703	164	8	c	c	PROPN
ejpam-4703	164	9	is	be	AUX
ejpam-4703	164	10	a	a	DET
ejpam-4703	164	11	circle	circle	NOUN
ejpam-4703	164	12	around	around	ADP
ejpam-4703	164	13	the	the	DET
ejpam-4703	164	14	origin	origin	NOUN
ejpam-4703	164	15	with	with	ADP
ejpam-4703	164	16	radius	radius	NOUN
ejpam-4703	164	17	<	<	X
ejpam-4703	164	18	∣∣∣	∣∣∣	PROPN
ejpam-4703	164	19	πi−δ	πi−δ	PROPN
ejpam-4703	164	20	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	164	21	)	)	PUNCT
ejpam-4703	164	22	∣∣∣.	∣∣∣.	PROPN
ejpam-4703	164	23	writing	write	VERB
ejpam-4703	164	24	1	1	NUM
ejpam-4703	164	25	λbt	λbt	NOUN
ejpam-4703	164	26	+	+	X
ejpam-4703	164	27	at	at	ADP
ejpam-4703	164	28	=	=	NOUN
ejpam-4703	164	29	a−t	a−t	NOUN
ejpam-4703	164	30	eδ(ba−1)t	eδ(ba−1)t	NOUN
ejpam-4703	165	1	+	+	CCONJ
ejpam-4703	165	2	1	1	NUM
ejpam-4703	165	3	,	,	PUNCT
ejpam-4703	165	4	then	then	ADV
ejpam-4703	165	5	en(x;λ	en(x;λ	VERB
ejpam-4703	165	6	;	;	PUNCT
ejpam-4703	165	7	a	a	DET
ejpam-4703	165	8	,	,	PUNCT
ejpam-4703	165	9	b	b	NOUN
ejpam-4703	165	10	,	,	PUNCT
ejpam-4703	165	11	c	c	NOUN
ejpam-4703	165	12	)	)	PUNCT
ejpam-4703	165	13	n	n	CCONJ
ejpam-4703	165	14	!	!	PUNCT
ejpam-4703	166	1	=	=	SYM
ejpam-4703	166	2	1	1	NUM
ejpam-4703	166	3	2πi	2πi	ADJ
ejpam-4703	166	4	∫	∫	PROPN
ejpam-4703	166	5	c	c	NOUN
ejpam-4703	166	6	2(a−1cx)t	2(a−1cx)t	NUM
ejpam-4703	166	7	[	[	X
ejpam-4703	166	8	eδ(ba−1)t	eδ(ba−1)t	NOUN
ejpam-4703	167	1	+	+	X
ejpam-4703	167	2	1	1	X
ejpam-4703	167	3	]	]	PUNCT
ejpam-4703	167	4	dt	dt	X
ejpam-4703	167	5	tn+1	tn+1	PROPN
ejpam-4703	167	6	.	.	PUNCT
ejpam-4703	168	1	with	with	ADP
ejpam-4703	168	2	c.	c.	PROPN
ejpam-4703	168	3	corcino	corcino	PROPN
ejpam-4703	168	4	,	,	PUNCT
ejpam-4703	168	5	r.	r.	PROPN
ejpam-4703	168	6	corcino	corcino	PROPN
ejpam-4703	168	7	/	/	SYM
ejpam-4703	168	8	eur	eur	PROPN
ejpam-4703	168	9	.	.	PUNCT
ejpam-4703	169	1	j.	j.	PROPN
ejpam-4703	169	2	pure	pure	PROPN
ejpam-4703	169	3	appl	appl	PROPN
ejpam-4703	169	4	.	.	PROPN
ejpam-4703	169	5	math	math	PROPN
ejpam-4703	169	6	,	,	PUNCT
ejpam-4703	169	7	16	16	NUM
ejpam-4703	169	8	(	(	PUNCT
ejpam-4703	169	9	2	2	NUM
ejpam-4703	169	10	)	)	PUNCT
ejpam-4703	169	11	(	(	PUNCT
ejpam-4703	169	12	2023	2023	NUM
ejpam-4703	169	13	)	)	PUNCT
ejpam-4703	169	14	,	,	PUNCT
ejpam-4703	169	15	791	791	NUM
ejpam-4703	169	16	-	-	SYM
ejpam-4703	169	17	805	805	NUM
ejpam-4703	169	18	800	800	NUM
ejpam-4703	169	19	eδ(ba−1)t	eδ(ba−1)t	NOUN
ejpam-4703	170	1	+	+	CCONJ
ejpam-4703	170	2	1	1	X
ejpam-4703	170	3	=	=	NOUN
ejpam-4703	170	4	eδet	eδet	NOUN
ejpam-4703	170	5	ln(ba	ln(ba	X
ejpam-4703	170	6	−1	−1	NOUN
ejpam-4703	170	7	)	)	PUNCT
ejpam-4703	171	1	+	+	CCONJ
ejpam-4703	171	2	1	1	NUM
ejpam-4703	171	3	=	=	SYM
ejpam-4703	171	4	2	2	NUM
ejpam-4703	171	5	exp	exp	NOUN
ejpam-4703	171	6	(	(	PUNCT
ejpam-4703	171	7	t	t	PROPN
ejpam-4703	171	8	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	171	9	)	)	PUNCT
ejpam-4703	172	1	+	+	CCONJ
ejpam-4703	172	2	δ	δ	PROPN
ejpam-4703	172	3	2	2	X
ejpam-4703	172	4	)	)	PUNCT
ejpam-4703	172	5	cosh	cosh	NOUN
ejpam-4703	172	6	(	(	PUNCT
ejpam-4703	172	7	t	t	PROPN
ejpam-4703	172	8	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	172	9	)	)	PUNCT
ejpam-4703	173	1	+	+	CCONJ
ejpam-4703	173	2	δ	δ	PROPN
ejpam-4703	173	3	2	2	NUM
ejpam-4703	173	4	)	)	PUNCT
ejpam-4703	173	5	,	,	PUNCT
ejpam-4703	173	6	yields	yield	NOUN
ejpam-4703	173	7	en(x;λ	en(x;λ	NOUN
ejpam-4703	173	8	;	;	PUNCT
ejpam-4703	173	9	a	a	DET
ejpam-4703	173	10	,	,	PUNCT
ejpam-4703	173	11	b	b	NOUN
ejpam-4703	173	12	,	,	PUNCT
ejpam-4703	173	13	c	c	NOUN
ejpam-4703	173	14	)	)	PUNCT
ejpam-4703	173	15	n	n	CCONJ
ejpam-4703	173	16	!	!	PUNCT
ejpam-4703	174	1	=	=	PUNCT
ejpam-4703	175	1	e−	e−	NUM
ejpam-4703	175	2	δ	δ	PROPN
ejpam-4703	175	3	2	2	NUM
ejpam-4703	175	4	2πi	2πi	NOUN
ejpam-4703	175	5	∫	∫	PROPN
ejpam-4703	175	6	c	c	X
ejpam-4703	175	7	(	(	PUNCT
ejpam-4703	175	8	(	(	PUNCT
ejpam-4703	175	9	ab)−	ab)−	ADJ
ejpam-4703	175	10	1	1	NUM
ejpam-4703	175	11	2	2	NUM
ejpam-4703	175	12	cx)t	cx)t	NOUN
ejpam-4703	175	13	cosh	cosh	NOUN
ejpam-4703	175	14	(	(	PUNCT
ejpam-4703	175	15	t	t	PROPN
ejpam-4703	175	16	ln(ba	ln(ba	X
ejpam-4703	175	17	−1)+δ	−1)+δ	NOUN
ejpam-4703	175	18	2	2	X
ejpam-4703	175	19	)	)	PUNCT
ejpam-4703	175	20	dt	dt	X
ejpam-4703	175	21	tn+1	tn+1	NOUN
ejpam-4703	175	22	=	=	SYM
ejpam-4703	175	23	(	(	PUNCT
ejpam-4703	175	24	λ)−	λ)−	ADV
ejpam-4703	175	25	1	1	NUM
ejpam-4703	175	26	2	2	NUM
ejpam-4703	175	27	2πi	2πi	NOUN
ejpam-4703	175	28	∫	∫	PROPN
ejpam-4703	175	29	c	c	PROPN
ejpam-4703	175	30	(	(	PUNCT
ejpam-4703	175	31	ab)−	ab)−	ADJ
ejpam-4703	175	32	1	1	NUM
ejpam-4703	175	33	2	2	NUM
ejpam-4703	175	34	tcxt	tcxt	NOUN
ejpam-4703	175	35	cosh	cosh	NOUN
ejpam-4703	175	36	(	(	PUNCT
ejpam-4703	175	37	t	t	PROPN
ejpam-4703	175	38	ln(ba	ln(ba	X
ejpam-4703	175	39	−1)+δ	−1)+δ	NOUN
ejpam-4703	175	40	2	2	X
ejpam-4703	175	41	)	)	PUNCT
ejpam-4703	175	42	dt	dt	X
ejpam-4703	176	1	tn+1	tn+1	PROPN
ejpam-4703	176	2	=	=	SYM
ejpam-4703	176	3	λ−	λ−	PROPN
ejpam-4703	176	4	1	1	NUM
ejpam-4703	176	5	2	2	NUM
ejpam-4703	176	6	2πi	2πi	NOUN
ejpam-4703	176	7	∫	∫	PROPN
ejpam-4703	177	1	c	c	PROPN
ejpam-4703	177	2	f(t)cxt	f(t)cxt	PROPN
ejpam-4703	177	3	dt	dt	NOUN
ejpam-4703	177	4	tn+1	tn+1	PROPN
ejpam-4703	177	5	(	(	PUNCT
ejpam-4703	177	6	3.18	3.18	NUM
ejpam-4703	177	7	)	)	PUNCT
ejpam-4703	177	8	where	where	SCONJ
ejpam-4703	177	9	f(t	f(t	NOUN
ejpam-4703	177	10	)	)	PUNCT
ejpam-4703	177	11	=	=	SYM
ejpam-4703	177	12	(	(	PUNCT
ejpam-4703	177	13	ab)−	ab)−	NOUN
ejpam-4703	177	14	1	1	NUM
ejpam-4703	177	15	2	2	NUM
ejpam-4703	177	16	t	t	NOUN
ejpam-4703	177	17	cosh	cosh	PROPN
ejpam-4703	177	18	(	(	PUNCT
ejpam-4703	177	19	t	t	PROPN
ejpam-4703	177	20	ln(ba	ln(ba	X
ejpam-4703	177	21	−1)+δ	−1)+δ	NOUN
ejpam-4703	177	22	2	2	NUM
ejpam-4703	177	23	)	)	PUNCT
ejpam-4703	177	24	.	.	PUNCT
ejpam-4703	178	1	(	(	PUNCT
ejpam-4703	178	2	3.19	3.19	NUM
ejpam-4703	178	3	)	)	PUNCT
ejpam-4703	178	4	taking	take	VERB
ejpam-4703	178	5	x	x	PROPN
ejpam-4703	178	6	7→	7→	NUM
ejpam-4703	178	7	nx	nx	NOUN
ejpam-4703	178	8	and	and	CCONJ
ejpam-4703	178	9	writing	write	VERB
ejpam-4703	178	10	cxt	cxt	PROPN
ejpam-4703	178	11	=	=	SYM
ejpam-4703	178	12	etx	etx	PROPN
ejpam-4703	178	13	ln	ln	NOUN
ejpam-4703	178	14	c	c	NOUN
ejpam-4703	178	15	,	,	PUNCT
ejpam-4703	178	16	(	(	PUNCT
ejpam-4703	178	17	3.18	3.18	NUM
ejpam-4703	178	18	)	)	PUNCT
ejpam-4703	178	19	will	will	AUX
ejpam-4703	178	20	take	take	VERB
ejpam-4703	178	21	the	the	DET
ejpam-4703	178	22	form	form	NOUN
ejpam-4703	178	23	en(nx;λ	en(nx;λ	PROPN
ejpam-4703	178	24	,	,	PUNCT
ejpam-4703	178	25	a	a	DET
ejpam-4703	178	26	,	,	PUNCT
ejpam-4703	178	27	b	b	NOUN
ejpam-4703	178	28	,	,	PUNCT
ejpam-4703	178	29	c	c	NOUN
ejpam-4703	178	30	)	)	PUNCT
ejpam-4703	178	31	λ−	λ−	PROPN
ejpam-4703	178	32	1	1	NUM
ejpam-4703	178	33	2	2	NUM
ejpam-4703	178	34	=	=	SYM
ejpam-4703	178	35	n	n	X
ejpam-4703	178	36	!	!	PUNCT
ejpam-4703	179	1	2πi	2πi	NOUN
ejpam-4703	179	2	∫	∫	PROPN
ejpam-4703	179	3	c	c	NOUN
ejpam-4703	179	4	f(t)et(nx	f(t)et(nx	NOUN
ejpam-4703	179	5	ln	ln	NOUN
ejpam-4703	179	6	c	c	NOUN
ejpam-4703	179	7	)	)	PUNCT
ejpam-4703	179	8	dt	dt	NOUN
ejpam-4703	179	9	tn+1	tn+1	PROPN
ejpam-4703	179	10	,	,	PUNCT
ejpam-4703	179	11	which	which	PRON
ejpam-4703	179	12	is	be	AUX
ejpam-4703	179	13	of	of	ADP
ejpam-4703	179	14	the	the	DET
ejpam-4703	179	15	form	form	NOUN
ejpam-4703	179	16	(	(	PUNCT
ejpam-4703	179	17	1.8	1.8	NUM
ejpam-4703	179	18	)	)	PUNCT
ejpam-4703	180	1	where	where	SCONJ
ejpam-4703	180	2	z	z	NOUN
ejpam-4703	180	3	=	=	PUNCT
ejpam-4703	180	4	x	x	SYM
ejpam-4703	180	5	ln	ln	PROPN
ejpam-4703	180	6	c.	c.	NOUN
ejpam-4703	180	7	the	the	DET
ejpam-4703	180	8	saddle	saddle	NOUN
ejpam-4703	180	9	-	-	PUNCT
ejpam-4703	180	10	point	point	NOUN
ejpam-4703	180	11	occurs	occur	VERB
ejpam-4703	180	12	at	at	ADP
ejpam-4703	180	13	d	d	X
ejpam-4703	180	14	dt	dt	X
ejpam-4703	180	15	(	(	PUNCT
ejpam-4703	180	16	nxt	nxt	PROPN
ejpam-4703	180	17	ln	ln	X
ejpam-4703	180	18	c−	c−	NOUN
ejpam-4703	180	19	n	n	CCONJ
ejpam-4703	180	20	log	log	VERB
ejpam-4703	180	21	t	t	PROPN
ejpam-4703	180	22	)	)	PUNCT
ejpam-4703	181	1	=	=	SYM
ejpam-4703	181	2	0	0	PUNCT
ejpam-4703	182	1	x	x	SYM
ejpam-4703	182	2	ln	ln	ADJ
ejpam-4703	182	3	c−	c−	NOUN
ejpam-4703	182	4	n	n	PRON
ejpam-4703	182	5	t	t	NOUN
ejpam-4703	182	6	=	=	SYM
ejpam-4703	182	7	0	0	PROPN
ejpam-4703	182	8	⇔	⇔	PROPN
ejpam-4703	182	9	t	t	PROPN
ejpam-4703	182	10	=	=	SYM
ejpam-4703	182	11	(	(	PUNCT
ejpam-4703	182	12	x	x	SYM
ejpam-4703	182	13	ln	ln	NOUN
ejpam-4703	182	14	c)−1	c)−1	NOUN
ejpam-4703	182	15	=	=	SYM
ejpam-4703	182	16	z−1	z−1	PROPN
ejpam-4703	182	17	:	:	PUNCT
ejpam-4703	182	18	=	=	SYM
ejpam-4703	182	19	µ	µ	VERB
ejpam-4703	182	20	the	the	DET
ejpam-4703	182	21	function	function	NOUN
ejpam-4703	182	22	f(t	f(t	PROPN
ejpam-4703	182	23	)	)	PUNCT
ejpam-4703	182	24	is	be	AUX
ejpam-4703	182	25	defined	define	VERB
ejpam-4703	182	26	at	at	ADP
ejpam-4703	182	27	t	t	NOUN
ejpam-4703	182	28	=	=	SYM
ejpam-4703	182	29	0	0	NUM
ejpam-4703	182	30	with	with	ADP
ejpam-4703	182	31	f(0	f(0	NOUN
ejpam-4703	182	32	)	)	PUNCT
ejpam-4703	182	33	=	=	SYM
ejpam-4703	182	34	1	1	NUM
ejpam-4703	182	35	cosh	cosh	NOUN
ejpam-4703	182	36	δ	δ	PROPN
ejpam-4703	182	37	2	2	NUM
ejpam-4703	182	38	.	.	PUNCT
ejpam-4703	183	1	also	also	ADV
ejpam-4703	183	2	f	f	PROPN
ejpam-4703	183	3	′(0	′(0	NOUN
ejpam-4703	183	4	)	)	PUNCT
ejpam-4703	183	5	is	be	AUX
ejpam-4703	183	6	defined	define	VERB
ejpam-4703	183	7	.	.	PUNCT
ejpam-4703	184	1	the	the	DET
ejpam-4703	184	2	singularities	singularity	NOUN
ejpam-4703	184	3	of	of	ADP
ejpam-4703	184	4	f(t	f(t	NOUN
ejpam-4703	184	5	)	)	PUNCT
ejpam-4703	184	6	are	be	AUX
ejpam-4703	184	7	the	the	DET
ejpam-4703	184	8	zeros	zero	NOUN
ejpam-4703	184	9	of	of	ADP
ejpam-4703	184	10	cosh	cosh	PROPN
ejpam-4703	184	11	t	t	PROPN
ejpam-4703	184	12	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	184	13	2	2	NUM
ejpam-4703	184	14	,	,	PUNCT
ejpam-4703	184	15	which	which	PRON
ejpam-4703	184	16	are	be	AUX
ejpam-4703	184	17	computed	compute	VERB
ejpam-4703	184	18	by	by	ADP
ejpam-4703	184	19	solving	solve	VERB
ejpam-4703	184	20	for	for	ADP
ejpam-4703	184	21	t	t	NOUN
ejpam-4703	184	22	such	such	ADJ
ejpam-4703	184	23	that	that	DET
ejpam-4703	184	24	cosh	cosh	PROPN
ejpam-4703	184	25	(	(	PUNCT
ejpam-4703	184	26	t	t	PROPN
ejpam-4703	184	27	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	184	28	)	)	PUNCT
ejpam-4703	184	29	+	+	CCONJ
ejpam-4703	184	30	δ	δ	PROPN
ejpam-4703	184	31	2	2	X
ejpam-4703	184	32	)	)	PUNCT
ejpam-4703	184	33	=	=	SYM
ejpam-4703	184	34	0	0	X
ejpam-4703	184	35	.	.	PUNCT
ejpam-4703	184	36	c.	c.	PROPN
ejpam-4703	184	37	corcino	corcino	PROPN
ejpam-4703	184	38	,	,	PUNCT
ejpam-4703	184	39	r.	r.	PROPN
ejpam-4703	184	40	corcino	corcino	PROPN
ejpam-4703	184	41	/	/	SYM
ejpam-4703	184	42	eur	eur	PROPN
ejpam-4703	184	43	.	.	PUNCT
ejpam-4703	185	1	j.	j.	PROPN
ejpam-4703	185	2	pure	pure	PROPN
ejpam-4703	185	3	appl	appl	PROPN
ejpam-4703	185	4	.	.	PROPN
ejpam-4703	185	5	math	math	PROPN
ejpam-4703	185	6	,	,	PUNCT
ejpam-4703	185	7	16	16	NUM
ejpam-4703	185	8	(	(	PUNCT
ejpam-4703	185	9	2	2	NUM
ejpam-4703	185	10	)	)	PUNCT
ejpam-4703	185	11	(	(	PUNCT
ejpam-4703	185	12	2023	2023	NUM
ejpam-4703	185	13	)	)	PUNCT
ejpam-4703	185	14	,	,	PUNCT
ejpam-4703	185	15	791	791	NUM
ejpam-4703	185	16	-	-	SYM
ejpam-4703	185	17	805	805	NUM
ejpam-4703	185	18	801	801	NUM
ejpam-4703	185	19	let	let	VERB
ejpam-4703	185	20	w	w	NOUN
ejpam-4703	185	21	=	=	SYM
ejpam-4703	185	22	t	t	PROPN
ejpam-4703	185	23	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	185	24	2	2	NUM
ejpam-4703	185	25	.	.	PUNCT
ejpam-4703	186	1	then	then	ADV
ejpam-4703	186	2	coshw	coshw	NOUN
ejpam-4703	186	3	=	=	SYM
ejpam-4703	186	4	0	0	NUM
ejpam-4703	186	5	⇔	⇔	PROPN
ejpam-4703	186	6	w	w	PROPN
ejpam-4703	187	1	=	=	PRON
ejpam-4703	188	1	(	(	PUNCT
ejpam-4703	188	2	k	k	PROPN
ejpam-4703	188	3	+	+	CCONJ
ejpam-4703	188	4	1	1	NUM
ejpam-4703	188	5	2	2	NUM
ejpam-4703	188	6	)	)	PUNCT
ejpam-4703	188	7	πi	πi	ADV
ejpam-4703	188	8	,	,	PUNCT
ejpam-4703	188	9	(	(	PUNCT
ejpam-4703	188	10	k	k	PROPN
ejpam-4703	188	11	∈	∈	PROPN
ejpam-4703	188	12	z	z	PROPN
ejpam-4703	188	13	)	)	PUNCT
ejpam-4703	188	14	.	.	PUNCT
ejpam-4703	189	1	that	that	PRON
ejpam-4703	189	2	is	be	AUX
ejpam-4703	189	3	,	,	PUNCT
ejpam-4703	189	4	t	t	PROPN
ejpam-4703	189	5	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	189	6	)	)	PUNCT
ejpam-4703	190	1	+	+	CCONJ
ejpam-4703	190	2	δ	δ	PROPN
ejpam-4703	190	3	2	2	X
ejpam-4703	190	4	=	=	SYM
ejpam-4703	190	5	(	(	PUNCT
ejpam-4703	190	6	k	k	X
ejpam-4703	190	7	+	+	PROPN
ejpam-4703	190	8	1	1	NUM
ejpam-4703	190	9	2	2	NUM
ejpam-4703	190	10	)	)	PUNCT
ejpam-4703	190	11	πi	πi	ADP
ejpam-4703	190	12	t	t	PROPN
ejpam-4703	190	13	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	190	14	)	)	PUNCT
ejpam-4703	190	15	=	=	PUNCT
ejpam-4703	191	1	(	(	PUNCT
ejpam-4703	191	2	2k	2k	NOUN
ejpam-4703	191	3	+	+	CCONJ
ejpam-4703	191	4	1)πi−	1)πi−	NUM
ejpam-4703	191	5	δ	δ	NOUN
ejpam-4703	191	6	tk	tk	NOUN
ejpam-4703	191	7	:	:	PUNCT
ejpam-4703	191	8	=	=	SYM
ejpam-4703	191	9	t	t	PROPN
ejpam-4703	191	10	=	=	SYM
ejpam-4703	191	11	(	(	PUNCT
ejpam-4703	191	12	2k	2k	NOUN
ejpam-4703	191	13	+	+	SYM
ejpam-4703	191	14	1)πi−	1)πi−	NUM
ejpam-4703	191	15	δ	δ	PROPN
ejpam-4703	191	16	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	191	17	)	)	PUNCT
ejpam-4703	191	18	,	,	PUNCT
ejpam-4703	191	19	k	k	PROPN
ejpam-4703	191	20	∈	∈	PROPN
ejpam-4703	191	21	z.	z.	PROPN
ejpam-4703	192	1	the	the	DET
ejpam-4703	192	2	tk	tk	PROPN
ejpam-4703	192	3	are	be	AUX
ejpam-4703	192	4	simple	simple	ADJ
ejpam-4703	192	5	poles	pole	NOUN
ejpam-4703	192	6	of	of	ADP
ejpam-4703	192	7	f(t	f(t	NOUN
ejpam-4703	192	8	)	)	PUNCT
ejpam-4703	192	9	.	.	PUNCT
ejpam-4703	193	1	assume	assume	VERB
ejpam-4703	193	2	that	that	SCONJ
ejpam-4703	193	3	µ	µ	X
ejpam-4703	193	4	=	=	SYM
ejpam-4703	193	5	(	(	PUNCT
ejpam-4703	193	6	x	x	X
ejpam-4703	193	7	ln	ln	ADJ
ejpam-4703	193	8	c)−1	c)−1	NOUN
ejpam-4703	193	9	is	be	AUX
ejpam-4703	193	10	not	not	PART
ejpam-4703	193	11	a	a	DET
ejpam-4703	193	12	singularity	singularity	NOUN
ejpam-4703	193	13	of	of	ADP
ejpam-4703	193	14	f(t	f(t	PROPN
ejpam-4703	193	15	)	)	PUNCT
ejpam-4703	193	16	.	.	PUNCT
ejpam-4703	194	1	then	then	ADV
ejpam-4703	194	2	f(t	f(t	NOUN
ejpam-4703	194	3	)	)	PUNCT
ejpam-4703	194	4	can	can	AUX
ejpam-4703	194	5	be	be	AUX
ejpam-4703	194	6	expanded	expand	VERB
ejpam-4703	194	7	about	about	ADP
ejpam-4703	194	8	t	t	NOUN
ejpam-4703	194	9	=	=	SYM
ejpam-4703	194	10	µ	µ	PROPN
ejpam-4703	194	11	as	as	SCONJ
ejpam-4703	194	12	follows	follow	VERB
ejpam-4703	194	13	:	:	PUNCT
ejpam-4703	194	14	f(t	f(t	NOUN
ejpam-4703	194	15	)	)	PUNCT
ejpam-4703	195	1	=	=	NOUN
ejpam-4703	196	1	∞∑	∞∑	NUM
ejpam-4703	196	2	k=0	k=0	PROPN
ejpam-4703	196	3	f	f	PROPN
ejpam-4703	196	4	(	(	PUNCT
ejpam-4703	196	5	k)(µ	k)(µ	NOUN
ejpam-4703	196	6	)	)	PUNCT
ejpam-4703	197	1	k	k	NOUN
ejpam-4703	197	2	!	!	PUNCT
ejpam-4703	198	1	(	(	PUNCT
ejpam-4703	198	2	t−	t−	PROPN
ejpam-4703	198	3	µ)k	µ)k	NOUN
ejpam-4703	198	4	,	,	PUNCT
ejpam-4703	198	5	|t−	|t−	PROPN
ejpam-4703	198	6	µ|	µ|	PROPN
ejpam-4703	198	7	<	<	X
ejpam-4703	198	8	r	r	NOUN
ejpam-4703	198	9	where	where	SCONJ
ejpam-4703	198	10	r	r	NOUN
ejpam-4703	198	11	is	be	AUX
ejpam-4703	198	12	the	the	DET
ejpam-4703	198	13	distance	distance	NOUN
ejpam-4703	198	14	from	from	ADP
ejpam-4703	198	15	µ	µ	PRON
ejpam-4703	198	16	to	to	ADP
ejpam-4703	198	17	the	the	DET
ejpam-4703	198	18	nearest	near	ADJ
ejpam-4703	198	19	singularity	singularity	NOUN
ejpam-4703	198	20	of	of	ADP
ejpam-4703	198	21	f(t	f(t	PROPN
ejpam-4703	198	22	)	)	PUNCT
ejpam-4703	198	23	.	.	PUNCT
ejpam-4703	199	1	the	the	DET
ejpam-4703	199	2	first	first	ADJ
ejpam-4703	199	3	few	few	ADJ
ejpam-4703	199	4	derivatives	derivative	NOUN
ejpam-4703	199	5	of	of	ADP
ejpam-4703	199	6	f	f	PROPN
ejpam-4703	199	7	at	at	ADP
ejpam-4703	199	8	t	t	PROPN
ejpam-4703	199	9	=	=	SYM
ejpam-4703	199	10	µ	µ	X
ejpam-4703	199	11	are	be	AUX
ejpam-4703	199	12	given	give	VERB
ejpam-4703	199	13	below	below	ADP
ejpam-4703	199	14	:	:	PUNCT
ejpam-4703	199	15	f	f	PROPN
ejpam-4703	199	16	′(µ	′(µ	PROPN
ejpam-4703	199	17	)	)	PUNCT
ejpam-4703	200	1	=	=	PRON
ejpam-4703	200	2	(	(	PUNCT
ejpam-4703	200	3	−	−	PROPN
ejpam-4703	200	4	ln(ab	ln(ab	PROPN
ejpam-4703	200	5	)	)	PUNCT
ejpam-4703	200	6	2	2	NUM
ejpam-4703	200	7	−	−	PROPN
ejpam-4703	200	8	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	200	9	)	)	PUNCT
ejpam-4703	200	10	2	2	NUM
ejpam-4703	200	11	tanh	tanh	PROPN
ejpam-4703	200	12	ρ	ρ	PROPN
ejpam-4703	200	13	)	)	PUNCT
ejpam-4703	200	14	(	(	PUNCT
ejpam-4703	200	15	ab)−	ab)−	PROPN
ejpam-4703	200	16	t	t	PROPN
ejpam-4703	200	17	2	2	NUM
ejpam-4703	200	18	cosh	cosh	NOUN
ejpam-4703	200	19	ρ	ρ	PROPN
ejpam-4703	200	20	,	,	PUNCT
ejpam-4703	200	21	(	(	PUNCT
ejpam-4703	200	22	3.20	3.20	NUM
ejpam-4703	200	23	)	)	PUNCT
ejpam-4703	200	24	f	f	PROPN
ejpam-4703	200	25	′′(µ	′′(µ	NOUN
ejpam-4703	200	26	)	)	PUNCT
ejpam-4703	200	27	=	=	PRON
ejpam-4703	201	1	{	{	PUNCT
ejpam-4703	201	2	[	[	PUNCT
ejpam-4703	201	3	ln(ab	ln(ab	PROPN
ejpam-4703	201	4	)	)	PUNCT
ejpam-4703	201	5	2	2	NUM
ejpam-4703	201	6	+	+	SYM
ejpam-4703	201	7	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	201	8	)	)	PUNCT
ejpam-4703	201	9	2	2	NUM
ejpam-4703	201	10	tanh	tanh	PROPN
ejpam-4703	201	11	ρ	ρ	PROPN
ejpam-4703	201	12	]	]	PUNCT
ejpam-4703	201	13	2	2	NUM
ejpam-4703	201	14	−	−	PROPN
ejpam-4703	201	15	ln2(ba−1	ln2(ba−1	NOUN
ejpam-4703	201	16	)	)	PUNCT
ejpam-4703	201	17	4	4	NUM
ejpam-4703	201	18	sech2	sech2	NOUN
ejpam-4703	201	19	ρ	ρ	NOUN
ejpam-4703	201	20	}	}	PUNCT
ejpam-4703	201	21	(	(	PUNCT
ejpam-4703	201	22	ab)−	ab)−	PROPN
ejpam-4703	201	23	t	t	PROPN
ejpam-4703	201	24	2	2	NUM
ejpam-4703	201	25	cosh	cosh	PROPN
ejpam-4703	201	26	ρ	ρ	NOUN
ejpam-4703	201	27	.	.	PUNCT
ejpam-4703	202	1	(	(	PUNCT
ejpam-4703	202	2	3.21	3.21	NUM
ejpam-4703	202	3	)	)	PUNCT
ejpam-4703	202	4	applying	apply	VERB
ejpam-4703	202	5	theorem	theorem	NOUN
ejpam-4703	202	6	1.3	1.3	NUM
ejpam-4703	202	7	,	,	PUNCT
ejpam-4703	202	8	the	the	DET
ejpam-4703	202	9	result	result	NOUN
ejpam-4703	202	10	follows	follow	VERB
ejpam-4703	202	11	.	.	PUNCT
ejpam-4703	203	1	for	for	ADP
ejpam-4703	203	2	the	the	DET
ejpam-4703	203	3	apostol	apostol	NOUN
ejpam-4703	203	4	-	-	PUNCT
ejpam-4703	203	5	euler	euler	NOUN
ejpam-4703	203	6	type	type	NOUN
ejpam-4703	203	7	polynomials	polynomial	NOUN
ejpam-4703	203	8	of	of	ADP
ejpam-4703	203	9	order	order	NOUN
ejpam-4703	203	10	α	α	X
ejpam-4703	203	11	>	>	X
ejpam-4703	203	12	1	1	NUM
ejpam-4703	203	13	see	see	VERB
ejpam-4703	203	14	the	the	DET
ejpam-4703	203	15	following	follow	VERB
ejpam-4703	203	16	theorem	theorem	PROPN
ejpam-4703	203	17	.	.	PUNCT
ejpam-4703	203	18	theorem	theorem	VERB
ejpam-4703	203	19	3.4	3.4	NUM
ejpam-4703	203	20	.	.	PUNCT
ejpam-4703	204	1	(	(	PUNCT
ejpam-4703	204	2	apostol	apostol	NOUN
ejpam-4703	204	3	-	-	PUNCT
ejpam-4703	204	4	euler	euler	NOUN
ejpam-4703	204	5	type	type	NOUN
ejpam-4703	204	6	polynomials	polynomial	NOUN
ejpam-4703	204	7	of	of	ADP
ejpam-4703	204	8	order	order	NOUN
ejpam-4703	204	9	α	α	PRON
ejpam-4703	204	10	≥	≥	NUM
ejpam-4703	204	11	2	2	NUM
ejpam-4703	204	12	)	)	PUNCT
ejpam-4703	204	13	let	let	VERB
ejpam-4703	204	14	a	a	DET
ejpam-4703	204	15	,	,	PUNCT
ejpam-4703	204	16	b	b	NOUN
ejpam-4703	204	17	,	,	PUNCT
ejpam-4703	204	18	c	c	PROPN
ejpam-4703	204	19	∈	∈	PROPN
ejpam-4703	204	20	r+\{1	r+\{1	PROPN
ejpam-4703	204	21	}	}	PUNCT
ejpam-4703	204	22	,	,	PUNCT
ejpam-4703	204	23	α	α	PROPN
ejpam-4703	204	24	∈	∈	PROPN
ejpam-4703	204	25	z+	z+	PRON
ejpam-4703	204	26	,	,	PUNCT
ejpam-4703	204	27	a	a	DET
ejpam-4703	204	28	̸=	̸=	PROPN
ejpam-4703	204	29	b	b	PROPN
ejpam-4703	204	30	and	and	CCONJ
ejpam-4703	204	31	µ	µ	X
ejpam-4703	204	32	=	=	PUNCT
ejpam-4703	204	33	(	(	PUNCT
ejpam-4703	204	34	x	x	X
ejpam-4703	204	35	ln	ln	PROPN
ejpam-4703	204	36	c)−1	c)−1	PROPN
ejpam-4703	204	37	.	.	PUNCT
ejpam-4703	205	1	for	for	ADP
ejpam-4703	205	2	x	x	PROPN
ejpam-4703	205	3	∈	∈	PROPN
ejpam-4703	205	4	c	c	NOUN
ejpam-4703	205	5	such	such	ADJ
ejpam-4703	205	6	that	that	DET
ejpam-4703	205	7	∣∣µ±	∣∣µ±	ADJ
ejpam-4703	205	8	πi−δ	πi−δ	NOUN
ejpam-4703	205	9	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	205	10	)	)	PUNCT
ejpam-4703	205	11	∣∣	∣∣	PROPN
ejpam-4703	205	12	and	and	CCONJ
ejpam-4703	205	13	n	n	PRON
ejpam-4703	205	14	≥	≥	NOUN
ejpam-4703	205	15	α	α	NOUN
ejpam-4703	205	16	,	,	PUNCT
ejpam-4703	205	17	the	the	DET
ejpam-4703	205	18	following	follow	VERB
ejpam-4703	205	19	formula	formula	NOUN
ejpam-4703	205	20	holds	hold	NOUN
ejpam-4703	205	21	,	,	PUNCT
ejpam-4703	205	22	e(α	e(α	NUM
ejpam-4703	205	23	)	)	PUNCT
ejpam-4703	205	24	n	n	CCONJ
ejpam-4703	205	25	(	(	PUNCT
ejpam-4703	205	26	nx;λ	nx;λ	NUM
ejpam-4703	205	27	;	;	PUNCT
ejpam-4703	205	28	a	a	DET
ejpam-4703	205	29	,	,	PUNCT
ejpam-4703	205	30	b	b	NOUN
ejpam-4703	205	31	,	,	PUNCT
ejpam-4703	205	32	c	c	NOUN
ejpam-4703	205	33	)	)	PUNCT
ejpam-4703	205	34	=	=	SYM
ejpam-4703	206	1	(	(	PUNCT
ejpam-4703	206	2	nx	nx	X
ejpam-4703	206	3	ln	ln	ADJ
ejpam-4703	206	4	c)n	c)n	NOUN
ejpam-4703	207	1	λ	λ	INTJ
ejpam-4703	207	2	α	α	NOUN
ejpam-4703	207	3	2	2	NUM
ejpam-4703	207	4	(	(	PUNCT
ejpam-4703	207	5	(	(	PUNCT
ejpam-4703	207	6	ab)−	ab)−	X
ejpam-4703	207	7	µ	µ	X
ejpam-4703	207	8	2	2	NUM
ejpam-4703	207	9	cosh	cosh	NOUN
ejpam-4703	207	10	ρ	ρ	PROPN
ejpam-4703	207	11	)	)	PUNCT
ejpam-4703	207	12	α	α	PROPN
ejpam-4703	207	13	{	{	PUNCT
ejpam-4703	207	14	1−	1−	NUM
ejpam-4703	207	15	αf	αf	ADP
ejpam-4703	207	16	+	+	NOUN
ejpam-4703	207	17	α(α−	α(α−	PROPN
ejpam-4703	207	18	1)h2	1)h2	NUM
ejpam-4703	207	19	2n(x	2n(x	NUM
ejpam-4703	207	20	ln	ln	ADJ
ejpam-4703	207	21	c)2	c)2	NOUN
ejpam-4703	207	22	+	+	PROPN
ejpam-4703	207	23	o(n−2	o(n−2	PROPN
ejpam-4703	207	24	)	)	PUNCT
ejpam-4703	207	25	}	}	PUNCT
ejpam-4703	207	26	,	,	PUNCT
ejpam-4703	207	27	(	(	PUNCT
ejpam-4703	207	28	3.22	3.22	NUM
ejpam-4703	207	29	)	)	PUNCT
ejpam-4703	207	30	where	where	SCONJ
ejpam-4703	207	31	h	h	NOUN
ejpam-4703	207	32	=	=	PUNCT
ejpam-4703	207	33	−	−	PROPN
ejpam-4703	207	34	ln(ab	ln(ab	PROPN
ejpam-4703	207	35	)	)	PUNCT
ejpam-4703	207	36	2	2	NUM
ejpam-4703	207	37	−	−	PROPN
ejpam-4703	207	38	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	207	39	)	)	PUNCT
ejpam-4703	207	40	2	2	NUM
ejpam-4703	207	41	tanh	tanh	PROPN
ejpam-4703	207	42	ρ	ρ	PROPN
ejpam-4703	207	43	,	,	PUNCT
ejpam-4703	207	44	and	and	CCONJ
ejpam-4703	207	45	f	f	PROPN
ejpam-4703	207	46	is	be	AUX
ejpam-4703	207	47	given	give	VERB
ejpam-4703	207	48	in	in	ADP
ejpam-4703	207	49	theorem	theorem	ADJ
ejpam-4703	207	50	3.3	3.3	NUM
ejpam-4703	207	51	.	.	PUNCT
ejpam-4703	208	1	c.	c.	PROPN
ejpam-4703	208	2	corcino	corcino	PROPN
ejpam-4703	208	3	,	,	PUNCT
ejpam-4703	208	4	r.	r.	PROPN
ejpam-4703	208	5	corcino	corcino	PROPN
ejpam-4703	208	6	/	/	SYM
ejpam-4703	208	7	eur	eur	PROPN
ejpam-4703	208	8	.	.	PUNCT
ejpam-4703	209	1	j.	j.	PROPN
ejpam-4703	209	2	pure	pure	PROPN
ejpam-4703	209	3	appl	appl	PROPN
ejpam-4703	209	4	.	.	PROPN
ejpam-4703	209	5	math	math	PROPN
ejpam-4703	209	6	,	,	PUNCT
ejpam-4703	209	7	16	16	NUM
ejpam-4703	209	8	(	(	PUNCT
ejpam-4703	209	9	2	2	NUM
ejpam-4703	209	10	)	)	PUNCT
ejpam-4703	209	11	(	(	PUNCT
ejpam-4703	209	12	2023	2023	NUM
ejpam-4703	209	13	)	)	PUNCT
ejpam-4703	209	14	,	,	PUNCT
ejpam-4703	209	15	791	791	NUM
ejpam-4703	209	16	-	-	SYM
ejpam-4703	209	17	805	805	NUM
ejpam-4703	209	18	802	802	NUM
ejpam-4703	209	19	proof	proof	NOUN
ejpam-4703	209	20	.	.	PUNCT
ejpam-4703	210	1	applying	apply	VERB
ejpam-4703	210	2	the	the	DET
ejpam-4703	210	3	cauchy	cauchy	ADJ
ejpam-4703	210	4	integral	integral	ADJ
ejpam-4703	210	5	formula	formula	NOUN
ejpam-4703	210	6	to	to	ADP
ejpam-4703	210	7	(	(	PUNCT
ejpam-4703	210	8	1.2	1.2	NUM
ejpam-4703	210	9	)	)	PUNCT
ejpam-4703	210	10	yields	yield	NOUN
ejpam-4703	210	11	e	e	X
ejpam-4703	210	12	(	(	PUNCT
ejpam-4703	210	13	α	α	NOUN
ejpam-4703	210	14	)	)	PUNCT
ejpam-4703	210	15	n	n	CCONJ
ejpam-4703	210	16	(	(	PUNCT
ejpam-4703	210	17	x;λ	x;λ	NUM
ejpam-4703	210	18	;	;	PUNCT
ejpam-4703	210	19	a	a	DET
ejpam-4703	210	20	,	,	PUNCT
ejpam-4703	210	21	b	b	NOUN
ejpam-4703	210	22	,	,	PUNCT
ejpam-4703	210	23	c	c	NOUN
ejpam-4703	210	24	)	)	PUNCT
ejpam-4703	210	25	n	n	CCONJ
ejpam-4703	210	26	!	!	PUNCT
ejpam-4703	211	1	=	=	NOUN
ejpam-4703	212	1	2α	2α	NUM
ejpam-4703	212	2	2πi	2πi	NOUN
ejpam-4703	212	3	∫	∫	PROPN
ejpam-4703	212	4	c	c	PROPN
ejpam-4703	212	5	cxt	cxt	PROPN
ejpam-4703	212	6	(	(	PUNCT
ejpam-4703	212	7	λbt	λbt	NOUN
ejpam-4703	212	8	+	+	X
ejpam-4703	212	9	at)α	at)α	NOUN
ejpam-4703	212	10	dt	dt	NOUN
ejpam-4703	212	11	tn+1	tn+1	NOUN
ejpam-4703	212	12	,	,	PUNCT
ejpam-4703	212	13	where	where	SCONJ
ejpam-4703	212	14	c	c	PROPN
ejpam-4703	212	15	is	be	AUX
ejpam-4703	212	16	a	a	DET
ejpam-4703	212	17	circle	circle	NOUN
ejpam-4703	212	18	centered	center	VERB
ejpam-4703	212	19	at	at	ADP
ejpam-4703	212	20	zero	zero	NUM
ejpam-4703	212	21	with	with	ADP
ejpam-4703	212	22	radius	radius	NOUN
ejpam-4703	212	23	<	<	X
ejpam-4703	212	24	∣∣∣	∣∣∣	PROPN
ejpam-4703	212	25	πi−δ	πi−δ	PROPN
ejpam-4703	212	26	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	212	27	)	)	PUNCT
ejpam-4703	212	28	∣∣∣.	∣∣∣.	PROPN
ejpam-4703	212	29	write	write	VERB
ejpam-4703	212	30	1	1	NUM
ejpam-4703	212	31	λbt	λbt	NOUN
ejpam-4703	212	32	+	+	CCONJ
ejpam-4703	212	33	at	at	ADP
ejpam-4703	212	34	=	=	NOUN
ejpam-4703	212	35	a−t	a−t	NOUN
ejpam-4703	212	36	eδ(ba−1)t	eδ(ba−1)t	NOUN
ejpam-4703	213	1	+	+	CCONJ
ejpam-4703	213	2	1	1	NUM
ejpam-4703	213	3	,	,	PUNCT
ejpam-4703	213	4	1	1	NUM
ejpam-4703	213	5	(	(	PUNCT
ejpam-4703	213	6	λbt	λbt	VERB
ejpam-4703	213	7	+	+	X
ejpam-4703	213	8	at)α	at)α	PROPN
ejpam-4703	213	9	=	=	SYM
ejpam-4703	213	10	a−αt	a−αt	PROPN
ejpam-4703	214	1	[	[	X
ejpam-4703	214	2	eδ(ba−1)t	eδ(ba−1)t	NOUN
ejpam-4703	215	1	+	+	CCONJ
ejpam-4703	215	2	1	1	X
ejpam-4703	215	3	]	]	PUNCT
ejpam-4703	215	4	α	α	NOUN
ejpam-4703	215	5	,	,	PUNCT
ejpam-4703	215	6	eδ(ba−1)t	eδ(ba−1)t	NOUN
ejpam-4703	216	1	+	+	CCONJ
ejpam-4703	216	2	1	1	NUM
ejpam-4703	216	3	=	=	SYM
ejpam-4703	216	4	2	2	NUM
ejpam-4703	216	5	exp	exp	NOUN
ejpam-4703	216	6	(	(	PUNCT
ejpam-4703	216	7	t	t	PROPN
ejpam-4703	216	8	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	216	9	)	)	PUNCT
ejpam-4703	217	1	+	+	CCONJ
ejpam-4703	217	2	δ	δ	PROPN
ejpam-4703	217	3	2	2	X
ejpam-4703	217	4	)	)	PUNCT
ejpam-4703	217	5	cosh	cosh	NOUN
ejpam-4703	217	6	(	(	PUNCT
ejpam-4703	217	7	t	t	PROPN
ejpam-4703	217	8	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	217	9	)	)	PUNCT
ejpam-4703	218	1	+	+	CCONJ
ejpam-4703	218	2	δ	δ	PROPN
ejpam-4703	218	3	2	2	NUM
ejpam-4703	218	4	)	)	PUNCT
ejpam-4703	218	5	,	,	PUNCT
ejpam-4703	218	6	[	[	PUNCT
ejpam-4703	218	7	eδ(ba−1)t	eδ(ba−1)t	X
ejpam-4703	219	1	+	+	CCONJ
ejpam-4703	219	2	1	1	NUM
ejpam-4703	219	3	]	]	SYM
ejpam-4703	219	4	α	α	NOUN
ejpam-4703	219	5	=	=	X
ejpam-4703	219	6	[	[	PUNCT
ejpam-4703	219	7	2	2	NUM
ejpam-4703	219	8	exp	exp	NOUN
ejpam-4703	219	9	(	(	PUNCT
ejpam-4703	219	10	t	t	PROPN
ejpam-4703	219	11	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	219	12	)	)	PUNCT
ejpam-4703	220	1	+	+	CCONJ
ejpam-4703	220	2	δ	δ	PROPN
ejpam-4703	220	3	2	2	NUM
ejpam-4703	220	4	)	)	PUNCT
ejpam-4703	220	5	]	]	PUNCT
ejpam-4703	220	6	α	α	X
ejpam-4703	220	7	[	[	PUNCT
ejpam-4703	220	8	cosh	cosh	PROPN
ejpam-4703	220	9	(	(	PUNCT
ejpam-4703	220	10	t	t	PROPN
ejpam-4703	220	11	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	220	12	)	)	PUNCT
ejpam-4703	220	13	+	+	CCONJ
ejpam-4703	220	14	δ	δ	PROPN
ejpam-4703	220	15	2	2	NUM
ejpam-4703	220	16	)	)	PUNCT
ejpam-4703	220	17	]	]	PUNCT
ejpam-4703	221	1	α	α	X
ejpam-4703	221	2	=	=	PUNCT
ejpam-4703	221	3	2αλ	2αλ	NOUN
ejpam-4703	221	4	α	α	ADP
ejpam-4703	221	5	2	2	NUM
ejpam-4703	221	6	et	et	NOUN
ejpam-4703	221	7	α	α	PROPN
ejpam-4703	221	8	2	2	NUM
ejpam-4703	221	9	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	221	10	)	)	PUNCT
ejpam-4703	221	11	[	[	PUNCT
ejpam-4703	221	12	cosh	cosh	PROPN
ejpam-4703	221	13	(	(	PUNCT
ejpam-4703	221	14	t	t	PROPN
ejpam-4703	221	15	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	221	16	)	)	PUNCT
ejpam-4703	221	17	+	+	CCONJ
ejpam-4703	221	18	δ	δ	PROPN
ejpam-4703	221	19	2	2	NUM
ejpam-4703	221	20	)	)	PUNCT
ejpam-4703	221	21	]	]	X
ejpam-4703	222	1	α	α	PROPN
ejpam-4703	222	2	.	.	PUNCT
ejpam-4703	223	1	then	then	ADV
ejpam-4703	223	2	,	,	PUNCT
ejpam-4703	223	3	e	e	X
ejpam-4703	223	4	(	(	PUNCT
ejpam-4703	223	5	α	α	NOUN
ejpam-4703	223	6	)	)	PUNCT
ejpam-4703	223	7	n	n	CCONJ
ejpam-4703	223	8	(	(	PUNCT
ejpam-4703	223	9	x;λ	x;λ	NUM
ejpam-4703	223	10	;	;	PUNCT
ejpam-4703	223	11	a	a	DET
ejpam-4703	223	12	,	,	PUNCT
ejpam-4703	223	13	b	b	NOUN
ejpam-4703	223	14	,	,	PUNCT
ejpam-4703	223	15	c	c	NOUN
ejpam-4703	223	16	)	)	PUNCT
ejpam-4703	223	17	n	n	CCONJ
ejpam-4703	223	18	!	!	PUNCT
ejpam-4703	224	1	=	=	PRON
ejpam-4703	225	1	λ−α	λ−α	NOUN
ejpam-4703	225	2	2	2	NUM
ejpam-4703	225	3	2πi	2πi	NOUN
ejpam-4703	225	4	∫	∫	PROPN
ejpam-4703	225	5	c	c	PROPN
ejpam-4703	225	6	(	(	PUNCT
ejpam-4703	225	7	ab)−	ab)−	PROPN
ejpam-4703	225	8	α	α	PROPN
ejpam-4703	225	9	2	2	NUM
ejpam-4703	225	10	t	t	PROPN
ejpam-4703	225	11	[	[	PUNCT
ejpam-4703	225	12	cosh	cosh	NOUN
ejpam-4703	225	13	(	(	PUNCT
ejpam-4703	225	14	t	t	NOUN
ejpam-4703	225	15	ln(ba−1)+δ	ln(ba−1)+δ	NOUN
ejpam-4703	225	16	2	2	NUM
ejpam-4703	225	17	)	)	PUNCT
ejpam-4703	225	18	]	]	PUNCT
ejpam-4703	225	19	α	α	PROPN
ejpam-4703	225	20	cxt	cxt	PROPN
ejpam-4703	225	21	dt	dt	X
ejpam-4703	225	22	tn+1	tn+1	PROPN
ejpam-4703	225	23	,	,	PUNCT
ejpam-4703	225	24	let	let	VERB
ejpam-4703	225	25	h(t	h(t	PRON
ejpam-4703	225	26	)	)	PUNCT
ejpam-4703	225	27	=	=	SYM
ejpam-4703	225	28	(	(	PUNCT
ejpam-4703	225	29	ab)−	ab)−	NOUN
ejpam-4703	225	30	α	α	PROPN
ejpam-4703	225	31	2	2	NUM
ejpam-4703	225	32	t	t	PROPN
ejpam-4703	225	33	[	[	PUNCT
ejpam-4703	225	34	cosh	cosh	PROPN
ejpam-4703	225	35	(	(	PUNCT
ejpam-4703	225	36	t	t	PROPN
ejpam-4703	225	37	ln(ba	ln(ba	X
ejpam-4703	226	1	−1)+δ	−1)+δ	NOUN
ejpam-4703	226	2	2	2	NUM
ejpam-4703	226	3	)	)	PUNCT
ejpam-4703	227	1	]	]	PUNCT
ejpam-4703	227	2	α	α	X
ejpam-4703	227	3	=	=	X
ejpam-4703	228	1	[	[	X
ejpam-4703	228	2	f(t)]α	f(t)]α	NOUN
ejpam-4703	228	3	.	.	PUNCT
ejpam-4703	229	1	then	then	ADV
ejpam-4703	229	2	e	e	X
ejpam-4703	229	3	(	(	PUNCT
ejpam-4703	229	4	α	α	NOUN
ejpam-4703	229	5	)	)	PUNCT
ejpam-4703	229	6	n	n	CCONJ
ejpam-4703	229	7	(	(	PUNCT
ejpam-4703	229	8	nx;λ	nx;λ	NUM
ejpam-4703	229	9	;	;	PUNCT
ejpam-4703	229	10	a	a	DET
ejpam-4703	229	11	,	,	PUNCT
ejpam-4703	229	12	b	b	NOUN
ejpam-4703	229	13	,	,	PUNCT
ejpam-4703	229	14	c	c	NOUN
ejpam-4703	229	15	)	)	PUNCT
ejpam-4703	229	16	n	n	CCONJ
ejpam-4703	229	17	!	!	PUNCT
ejpam-4703	229	18	=	=	PRON
ejpam-4703	230	1	λ−α	λ−α	NOUN
ejpam-4703	230	2	2	2	NUM
ejpam-4703	230	3	2πi	2πi	NOUN
ejpam-4703	230	4	∫	∫	PROPN
ejpam-4703	230	5	c	c	PROPN
ejpam-4703	230	6	h(t	h(t	PROPN
ejpam-4703	230	7	)	)	PUNCT
ejpam-4703	230	8	cnxt	cnxt	VERB
ejpam-4703	230	9	dt	dt	PROPN
ejpam-4703	230	10	tn+1	tn+1	PROPN
ejpam-4703	230	11	,	,	PUNCT
ejpam-4703	230	12	(	(	PUNCT
ejpam-4703	230	13	3.23	3.23	NUM
ejpam-4703	230	14	)	)	PUNCT
ejpam-4703	230	15	still	still	ADV
ejpam-4703	230	16	with	with	ADP
ejpam-4703	230	17	saddle	saddle	ADJ
ejpam-4703	230	18	point	point	NOUN
ejpam-4703	230	19	at	at	ADP
ejpam-4703	230	20	µ	µ	NOUN
ejpam-4703	230	21	=	=	SYM
ejpam-4703	230	22	(	(	PUNCT
ejpam-4703	230	23	x	x	X
ejpam-4703	230	24	ln	ln	PROPN
ejpam-4703	230	25	c)−1	c)−1	PROPN
ejpam-4703	230	26	.	.	PUNCT
ejpam-4703	231	1	the	the	DET
ejpam-4703	231	2	poles	pole	NOUN
ejpam-4703	231	3	of	of	ADP
ejpam-4703	231	4	h(t	h(t	PROPN
ejpam-4703	231	5	)	)	PUNCT
ejpam-4703	231	6	are	be	AUX
ejpam-4703	231	7	at	at	ADP
ejpam-4703	231	8	t	t	NOUN
ejpam-4703	231	9	=	=	SYM
ejpam-4703	231	10	0	0	NUM
ejpam-4703	231	11	of	of	ADP
ejpam-4703	231	12	order	order	NOUN
ejpam-4703	231	13	n+	n+	ADP
ejpam-4703	231	14	1	1	NUM
ejpam-4703	231	15	and	and	CCONJ
ejpam-4703	231	16	at	at	ADP
ejpam-4703	231	17	tk	tk	PROPN
ejpam-4703	231	18	=	=	SYM
ejpam-4703	231	19	(	(	PUNCT
ejpam-4703	231	20	2k+1)πi−δ	2k+1)πi−δ	NUM
ejpam-4703	231	21	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	231	22	)	)	PUNCT
ejpam-4703	231	23	,	,	PUNCT
ejpam-4703	231	24	k	k	PROPN
ejpam-4703	231	25	∈	∈	PROPN
ejpam-4703	231	26	z	z	NOUN
ejpam-4703	231	27	each	each	PRON
ejpam-4703	231	28	of	of	ADP
ejpam-4703	231	29	order	order	NOUN
ejpam-4703	231	30	α	α	NOUN
ejpam-4703	231	31	.	.	PUNCT
ejpam-4703	232	1	assuming	assume	VERB
ejpam-4703	232	2	that	that	SCONJ
ejpam-4703	232	3	µ	µ	NOUN
ejpam-4703	232	4	is	be	AUX
ejpam-4703	232	5	not	not	PART
ejpam-4703	232	6	a	a	DET
ejpam-4703	232	7	singularity	singularity	NOUN
ejpam-4703	232	8	of	of	ADP
ejpam-4703	232	9	h(t	h(t	PROPN
ejpam-4703	232	10	)	)	PUNCT
ejpam-4703	232	11	,	,	PUNCT
ejpam-4703	232	12	h(t	h(t	PROPN
ejpam-4703	232	13	)	)	PUNCT
ejpam-4703	232	14	can	can	AUX
ejpam-4703	232	15	be	be	AUX
ejpam-4703	232	16	expanded	expand	VERB
ejpam-4703	232	17	about	about	ADP
ejpam-4703	232	18	µ	µ	NOUN
ejpam-4703	232	19	given	give	VERB
ejpam-4703	232	20	by	by	ADP
ejpam-4703	232	21	h(t	h(t	PROPN
ejpam-4703	232	22	)	)	PUNCT
ejpam-4703	233	1	=	=	PUNCT
ejpam-4703	234	1	∞∑	∞∑	NUM
ejpam-4703	234	2	k=0	k=0	PROPN
ejpam-4703	234	3	h(k)(µ	h(k)(µ	PROPN
ejpam-4703	234	4	)	)	PUNCT
ejpam-4703	234	5	k	k	X
ejpam-4703	234	6	!	!	PUNCT
ejpam-4703	235	1	(	(	PUNCT
ejpam-4703	235	2	t−	t−	PRON
ejpam-4703	235	3	µ)k	µ)k	NOUN
ejpam-4703	235	4	.	.	PUNCT
ejpam-4703	236	1	it	it	PRON
ejpam-4703	236	2	follows	follow	VERB
ejpam-4703	236	3	from	from	ADP
ejpam-4703	236	4	theorem	theorem	ADJ
ejpam-4703	236	5	1.3	1.3	NUM
ejpam-4703	236	6	that	that	SCONJ
ejpam-4703	236	7	e	e	X
ejpam-4703	236	8	(	(	PUNCT
ejpam-4703	236	9	α	α	NOUN
ejpam-4703	236	10	)	)	PUNCT
ejpam-4703	236	11	n	n	CCONJ
ejpam-4703	236	12	(	(	PUNCT
ejpam-4703	236	13	nx;λ	nx;λ	NUM
ejpam-4703	236	14	;	;	PUNCT
ejpam-4703	236	15	a	a	DET
ejpam-4703	236	16	,	,	PUNCT
ejpam-4703	236	17	b	b	NOUN
ejpam-4703	236	18	,	,	PUNCT
ejpam-4703	236	19	c	c	NOUN
ejpam-4703	236	20	)	)	PUNCT
ejpam-4703	236	21	λ−α	λ−α	NOUN
ejpam-4703	236	22	2	2	NUM
ejpam-4703	236	23	=	=	SYM
ejpam-4703	236	24	(	(	PUNCT
ejpam-4703	236	25	nx	nx	X
ejpam-4703	236	26	ln	ln	NOUN
ejpam-4703	236	27	c)n	c)n	NOUN
ejpam-4703	237	1	∞∑	∞∑	DET
ejpam-4703	237	2	k=0	k=0	PROPN
ejpam-4703	237	3	h(k)(µ	h(k)(µ	PROPN
ejpam-4703	237	4	)	)	PUNCT
ejpam-4703	237	5	k	k	NOUN
ejpam-4703	237	6	!	!	PUNCT
ejpam-4703	237	7	pk(n	pk(n	X
ejpam-4703	237	8	)	)	PUNCT
ejpam-4703	237	9	(	(	PUNCT
ejpam-4703	237	10	nx	nx	NUM
ejpam-4703	237	11	ln	ln	PROPN
ejpam-4703	237	12	c)k	c)k	PROPN
ejpam-4703	237	13	c.	c.	PROPN
ejpam-4703	237	14	corcino	corcino	PROPN
ejpam-4703	237	15	,	,	PUNCT
ejpam-4703	237	16	r.	r.	PROPN
ejpam-4703	237	17	corcino	corcino	PROPN
ejpam-4703	237	18	/	/	SYM
ejpam-4703	237	19	eur	eur	PROPN
ejpam-4703	237	20	.	.	PUNCT
ejpam-4703	238	1	j.	j.	PROPN
ejpam-4703	238	2	pure	pure	PROPN
ejpam-4703	238	3	appl	appl	PROPN
ejpam-4703	238	4	.	.	PROPN
ejpam-4703	238	5	math	math	PROPN
ejpam-4703	238	6	,	,	PUNCT
ejpam-4703	238	7	16	16	NUM
ejpam-4703	238	8	(	(	PUNCT
ejpam-4703	238	9	2	2	NUM
ejpam-4703	238	10	)	)	PUNCT
ejpam-4703	238	11	(	(	PUNCT
ejpam-4703	238	12	2023	2023	NUM
ejpam-4703	238	13	)	)	PUNCT
ejpam-4703	238	14	,	,	PUNCT
ejpam-4703	238	15	791	791	NUM
ejpam-4703	238	16	-	-	SYM
ejpam-4703	238	17	805	805	NUM
ejpam-4703	238	18	803	803	NUM
ejpam-4703	238	19	=	=	SYM
ejpam-4703	238	20	(	(	PUNCT
ejpam-4703	238	21	nx	nx	X
ejpam-4703	238	22	ln	ln	NOUN
ejpam-4703	238	23	c)n	c)n	NOUN
ejpam-4703	238	24	{	{	PUNCT
ejpam-4703	238	25	h(µ)−	h(µ)−	PRON
ejpam-4703	238	26	h′′(µ	h′′(µ	NOUN
ejpam-4703	238	27	)	)	PUNCT
ejpam-4703	238	28	n(x	n(x	PROPN
ejpam-4703	238	29	ln	ln	ADJ
ejpam-4703	238	30	c)2	c)2	NOUN
ejpam-4703	238	31	+	+	SYM
ejpam-4703	238	32	o(n−2	o(n−2	PROPN
ejpam-4703	238	33	)	)	PUNCT
ejpam-4703	238	34	}	}	PUNCT
ejpam-4703	238	35	.	.	PUNCT
ejpam-4703	239	1	(	(	PUNCT
ejpam-4703	239	2	3.24	3.24	NUM
ejpam-4703	239	3	)	)	PUNCT
ejpam-4703	239	4	computing	compute	VERB
ejpam-4703	239	5	the	the	DET
ejpam-4703	239	6	derivatives	derivative	NOUN
ejpam-4703	239	7	h(k)(t	h(k)(t	NUM
ejpam-4703	239	8	)	)	PUNCT
ejpam-4703	239	9	,	,	PUNCT
ejpam-4703	239	10	k	k	X
ejpam-4703	239	11	=	=	SYM
ejpam-4703	239	12	0	0	NUM
ejpam-4703	239	13	,	,	PUNCT
ejpam-4703	239	14	1	1	NUM
ejpam-4703	239	15	,	,	PUNCT
ejpam-4703	239	16	2	2	NUM
ejpam-4703	239	17	with	with	ADP
ejpam-4703	239	18	h0(t	h0(t	NOUN
ejpam-4703	239	19	)	)	PUNCT
ejpam-4703	239	20	=	=	PUNCT
ejpam-4703	239	21	h(t	h(t	PROPN
ejpam-4703	239	22	)	)	PUNCT
ejpam-4703	239	23	and	and	CCONJ
ejpam-4703	239	24	evaluating	evaluate	VERB
ejpam-4703	239	25	at	at	ADP
ejpam-4703	239	26	t	t	NOUN
ejpam-4703	239	27	=	=	SYM
ejpam-4703	239	28	µ	µ	X
ejpam-4703	239	29	will	will	AUX
ejpam-4703	239	30	give	give	VERB
ejpam-4703	239	31	h(µ	h(µ	PRON
ejpam-4703	239	32	)	)	PUNCT
ejpam-4703	240	1	=	=	PUNCT
ejpam-4703	241	1	[	[	X
ejpam-4703	241	2	f(µ)]α	f(µ)]α	X
ejpam-4703	241	3	=	=	SYM
ejpam-4703	241	4	(	(	PUNCT
ejpam-4703	241	5	ab)−	ab)−	ADJ
ejpam-4703	241	6	α	α	PROPN
ejpam-4703	241	7	2	2	PROPN
ejpam-4703	241	8	µ	µ	PRON
ejpam-4703	241	9	coshα	coshα	PROPN
ejpam-4703	241	10	ρ	ρ	PROPN
ejpam-4703	241	11	h′(µ	h′(µ	PROPN
ejpam-4703	241	12	)	)	PUNCT
ejpam-4703	241	13	=	=	SYM
ejpam-4703	241	14	α	α	PROPN
ejpam-4703	241	15	[	[	X
ejpam-4703	241	16	f(µ)]α−1	f(µ)]α−1	X
ejpam-4703	241	17	f	f	PROPN
ejpam-4703	241	18	′(µ	′(µ	PROPN
ejpam-4703	241	19	)	)	PUNCT
ejpam-4703	241	20	h′′(µ	h′′(µ	NOUN
ejpam-4703	241	21	)	)	PUNCT
ejpam-4703	241	22	=	=	SYM
ejpam-4703	242	1	α	α	NOUN
ejpam-4703	242	2	{	{	PUNCT
ejpam-4703	242	3	[	[	X
ejpam-4703	242	4	f(µ)]α−1f	f(µ)]α−1f	X
ejpam-4703	242	5	′′(µ	′′(µ	NOUN
ejpam-4703	242	6	)	)	PUNCT
ejpam-4703	243	1	+	+	CCONJ
ejpam-4703	243	2	(	(	PUNCT
ejpam-4703	243	3	α−	α−	ADP
ejpam-4703	243	4	1)[f(µ)]α−2[f	1)[f(µ)]α−2[f	NUM
ejpam-4703	243	5	′]2	′]2	NOUN
ejpam-4703	243	6	}	}	PUNCT
ejpam-4703	243	7	,	,	PUNCT
ejpam-4703	243	8	where	where	SCONJ
ejpam-4703	243	9	f(µ	f(µ	NOUN
ejpam-4703	243	10	)	)	PUNCT
ejpam-4703	243	11	is	be	AUX
ejpam-4703	243	12	obtained	obtain	VERB
ejpam-4703	243	13	from	from	ADP
ejpam-4703	243	14	(	(	PUNCT
ejpam-4703	243	15	3.19	3.19	NUM
ejpam-4703	243	16	)	)	PUNCT
ejpam-4703	243	17	,	,	PUNCT
ejpam-4703	243	18	f	f	PROPN
ejpam-4703	243	19	′(µ	′(µ	PROPN
ejpam-4703	243	20	)	)	PUNCT
ejpam-4703	243	21	,	,	PUNCT
ejpam-4703	243	22	and	and	CCONJ
ejpam-4703	243	23	f	f	PROPN
ejpam-4703	243	24	′′(µ	′′(µ	NOUN
ejpam-4703	243	25	)	)	PUNCT
ejpam-4703	243	26	are	be	AUX
ejpam-4703	243	27	given	give	VERB
ejpam-4703	243	28	in	in	ADP
ejpam-4703	243	29	(	(	PUNCT
ejpam-4703	243	30	3.20	3.20	NUM
ejpam-4703	243	31	)	)	PUNCT
ejpam-4703	243	32	,	,	PUNCT
ejpam-4703	243	33	and	and	CCONJ
ejpam-4703	243	34	(	(	PUNCT
ejpam-4703	243	35	3.21	3.21	NUM
ejpam-4703	243	36	)	)	PUNCT
ejpam-4703	243	37	,	,	PUNCT
ejpam-4703	244	1	respectively	respectively	ADV
ejpam-4703	244	2	.	.	PUNCT
ejpam-4703	244	3	substitution	substitution	NOUN
ejpam-4703	244	4	to	to	ADP
ejpam-4703	244	5	(	(	PUNCT
ejpam-4703	244	6	3.24	3.24	NUM
ejpam-4703	244	7	)	)	PUNCT
ejpam-4703	244	8	will	will	AUX
ejpam-4703	244	9	give	give	VERB
ejpam-4703	244	10	the	the	DET
ejpam-4703	244	11	desired	desire	VERB
ejpam-4703	244	12	result	result	NOUN
ejpam-4703	244	13	.	.	PUNCT
ejpam-4703	245	1	to	to	PART
ejpam-4703	245	2	obtain	obtain	VERB
ejpam-4703	245	3	an	an	DET
ejpam-4703	245	4	asymptotic	asymptotic	ADJ
ejpam-4703	245	5	formula	formula	NOUN
ejpam-4703	245	6	for	for	ADP
ejpam-4703	245	7	the	the	DET
ejpam-4703	245	8	apostol	apostol	NOUN
ejpam-4703	245	9	-	-	PUNCT
ejpam-4703	245	10	genocchi	genocchi	PROPN
ejpam-4703	245	11	type	type	NOUN
ejpam-4703	245	12	polynomials	polynomial	VERB
ejpam-4703	245	13	the	the	DET
ejpam-4703	245	14	following	follow	VERB
ejpam-4703	245	15	lemma	lemma	PROPN
ejpam-4703	245	16	will	will	AUX
ejpam-4703	245	17	be	be	AUX
ejpam-4703	245	18	used	use	VERB
ejpam-4703	245	19	.	.	PUNCT
ejpam-4703	246	1	lemma	lemma	PROPN
ejpam-4703	246	2	3.5	3.5	NUM
ejpam-4703	246	3	.	.	PUNCT
ejpam-4703	247	1	let	let	VERB
ejpam-4703	247	2	a	a	DET
ejpam-4703	247	3	,	,	PUNCT
ejpam-4703	247	4	b	b	NOUN
ejpam-4703	247	5	,	,	PUNCT
ejpam-4703	247	6	c	c	PROPN
ejpam-4703	247	7	∈	∈	PROPN
ejpam-4703	247	8	r+\{1	r+\{1	PROPN
ejpam-4703	247	9	}	}	PUNCT
ejpam-4703	247	10	,	,	PUNCT
ejpam-4703	247	11	α	α	PROPN
ejpam-4703	247	12	∈	∈	PROPN
ejpam-4703	247	13	z+	z+	NUM
ejpam-4703	247	14	,	,	PUNCT
ejpam-4703	247	15	λ	λ	PROPN
ejpam-4703	247	16	∈	∈	PROPN
ejpam-4703	247	17	c\{1	c\{1	PROPN
ejpam-4703	247	18	}	}	PUNCT
ejpam-4703	247	19	,	,	PUNCT
ejpam-4703	247	20	a	a	DET
ejpam-4703	247	21	̸=	̸=	PROPN
ejpam-4703	247	22	b.	b.	NOUN
ejpam-4703	247	23	for	for	ADP
ejpam-4703	247	24	x	x	PROPN
ejpam-4703	247	25	∈	∈	PROPN
ejpam-4703	247	26	c	c	X
ejpam-4703	247	27	,	,	PUNCT
ejpam-4703	247	28	g	g	PROPN
ejpam-4703	247	29	(	(	PUNCT
ejpam-4703	247	30	α	α	NOUN
ejpam-4703	247	31	)	)	PUNCT
ejpam-4703	247	32	n+α(x;λ	n+α(x;λ	PROPN
ejpam-4703	247	33	;	;	PUNCT
ejpam-4703	247	34	a	a	DET
ejpam-4703	247	35	,	,	PUNCT
ejpam-4703	247	36	b	b	NOUN
ejpam-4703	247	37	,	,	PUNCT
ejpam-4703	247	38	c	c	NOUN
ejpam-4703	247	39	)	)	PUNCT
ejpam-4703	247	40	=	=	SYM
ejpam-4703	248	1	(	(	PUNCT
ejpam-4703	248	2	n+	n+	X
ejpam-4703	248	3	α)αe	α)αe	NOUN
ejpam-4703	248	4	(	(	PUNCT
ejpam-4703	248	5	α	α	NOUN
ejpam-4703	248	6	)	)	PUNCT
ejpam-4703	248	7	n	n	CCONJ
ejpam-4703	248	8	(	(	PUNCT
ejpam-4703	248	9	x;λ	x;λ	NUM
ejpam-4703	248	10	;	;	PUNCT
ejpam-4703	248	11	a	a	DET
ejpam-4703	248	12	,	,	PUNCT
ejpam-4703	248	13	b	b	NOUN
ejpam-4703	248	14	,	,	PUNCT
ejpam-4703	248	15	c	c	NOUN
ejpam-4703	248	16	)	)	PUNCT
ejpam-4703	248	17	,	,	PUNCT
ejpam-4703	248	18	where	where	SCONJ
ejpam-4703	248	19	(	(	PUNCT
ejpam-4703	248	20	n)α	n)α	PRON
ejpam-4703	248	21	=	=	SYM
ejpam-4703	248	22	n(n−	n(n−	PROPN
ejpam-4703	248	23	1)(n−	1)(n−	PROPN
ejpam-4703	248	24	2)	2)	NUM
ejpam-4703	248	25	....	....	PUNCT
ejpam-4703	248	26	(n−	(n−	PUNCT
ejpam-4703	248	27	(	(	PUNCT
ejpam-4703	248	28	α−	α−	ADP
ejpam-4703	248	29	1	1	NUM
ejpam-4703	248	30	)	)	PUNCT
ejpam-4703	248	31	.	.	PUNCT
ejpam-4703	249	1	proof	proof	NOUN
ejpam-4703	249	2	.	.	PUNCT
ejpam-4703	250	1	dividing	divide	VERB
ejpam-4703	250	2	both	both	DET
ejpam-4703	250	3	sides	side	NOUN
ejpam-4703	250	4	of	of	ADP
ejpam-4703	250	5	(	(	PUNCT
ejpam-4703	250	6	1.3	1.3	NUM
ejpam-4703	250	7	)	)	PUNCT
ejpam-4703	250	8	by	by	ADP
ejpam-4703	250	9	tα	tα	PROPN
ejpam-4703	250	10	yields	yield	NOUN
ejpam-4703	250	11	,	,	PUNCT
ejpam-4703	250	12	(	(	PUNCT
ejpam-4703	250	13	2	2	NUM
ejpam-4703	250	14	λbt	λbt	NOUN
ejpam-4703	250	15	+	+	X
ejpam-4703	250	16	at	at	ADP
ejpam-4703	250	17	)	)	PUNCT
ejpam-4703	250	18	α	α	NOUN
ejpam-4703	250	19	cxt	cxt	NOUN
ejpam-4703	250	20	=	=	PUNCT
ejpam-4703	250	21	∞∑	∞∑	PROPN
ejpam-4703	250	22	n=0	n=0	NUM
ejpam-4703	250	23	g(α	g(α	PROPN
ejpam-4703	250	24	)	)	PUNCT
ejpam-4703	250	25	n	n	CCONJ
ejpam-4703	250	26	(	(	PUNCT
ejpam-4703	250	27	x;λ	x;λ	NUM
ejpam-4703	250	28	;	;	PUNCT
ejpam-4703	250	29	a	a	DET
ejpam-4703	250	30	,	,	PUNCT
ejpam-4703	250	31	b	b	NOUN
ejpam-4703	250	32	,	,	PUNCT
ejpam-4703	250	33	c	c	NOUN
ejpam-4703	250	34	)	)	PUNCT
ejpam-4703	250	35	tn−α	tn−α	NOUN
ejpam-4703	250	36	n	n	NOUN
ejpam-4703	250	37	!	!	PUNCT
ejpam-4703	251	1	=	=	NOUN
ejpam-4703	252	1	∞∑	∞∑	NUM
ejpam-4703	252	2	n	n	NOUN
ejpam-4703	252	3	=	=	SYM
ejpam-4703	252	4	α	α	NOUN
ejpam-4703	252	5	(	(	PUNCT
ejpam-4703	252	6	n−	n−	NOUN
ejpam-4703	252	7	α	α	NOUN
ejpam-4703	252	8	)	)	PUNCT
ejpam-4703	252	9	!	!	PUNCT
ejpam-4703	253	1	n	n	X
ejpam-4703	253	2	!	!	PUNCT
ejpam-4703	253	3	g(α	g(α	NOUN
ejpam-4703	253	4	)	)	PUNCT
ejpam-4703	253	5	n	n	CCONJ
ejpam-4703	253	6	(	(	PUNCT
ejpam-4703	253	7	x;λ	x;λ	NUM
ejpam-4703	253	8	;	;	PUNCT
ejpam-4703	253	9	a	a	DET
ejpam-4703	253	10	,	,	PUNCT
ejpam-4703	253	11	b	b	NOUN
ejpam-4703	253	12	,	,	PUNCT
ejpam-4703	253	13	c	c	NOUN
ejpam-4703	253	14	)	)	PUNCT
ejpam-4703	253	15	tn−α	tn−α	NOUN
ejpam-4703	253	16	(	(	PUNCT
ejpam-4703	253	17	n−	n−	NOUN
ejpam-4703	253	18	α	α	NOUN
ejpam-4703	253	19	)	)	PUNCT
ejpam-4703	253	20	!	!	PUNCT
ejpam-4703	254	1	=	=	PUNCT
ejpam-4703	255	1	∞∑	∞∑	NUM
ejpam-4703	255	2	n	n	NOUN
ejpam-4703	255	3	=	=	NOUN
ejpam-4703	255	4	α	α	NOUN
ejpam-4703	255	5	g	g	PROPN
ejpam-4703	255	6	(	(	PUNCT
ejpam-4703	255	7	α	α	NOUN
ejpam-4703	255	8	)	)	PUNCT
ejpam-4703	255	9	n	n	CCONJ
ejpam-4703	255	10	(	(	PUNCT
ejpam-4703	255	11	x;λ	x;λ	NUM
ejpam-4703	255	12	;	;	PUNCT
ejpam-4703	255	13	a	a	DET
ejpam-4703	255	14	,	,	PUNCT
ejpam-4703	255	15	b	b	NOUN
ejpam-4703	255	16	,	,	PUNCT
ejpam-4703	255	17	c	c	NOUN
ejpam-4703	255	18	)	)	PUNCT
ejpam-4703	255	19	(	(	PUNCT
ejpam-4703	255	20	n)α	n)α	NOUN
ejpam-4703	255	21	tn−α	tn−α	NOUN
ejpam-4703	255	22	(	(	PUNCT
ejpam-4703	255	23	n−	n−	NOUN
ejpam-4703	255	24	α	α	NUM
ejpam-4703	255	25	)	)	PUNCT
ejpam-4703	255	26	!	!	PUNCT
ejpam-4703	256	1	let	let	VERB
ejpam-4703	256	2	s	s	PRON
ejpam-4703	256	3	=	=	VERB
ejpam-4703	256	4	n−	n−	PROPN
ejpam-4703	256	5	α	α	NOUN
ejpam-4703	256	6	.	.	PUNCT
ejpam-4703	257	1	then	then	ADV
ejpam-4703	257	2	n	n	PROPN
ejpam-4703	257	3	=	=	PUNCT
ejpam-4703	257	4	s+	s+	PUNCT
ejpam-4703	257	5	α	α	PROPN
ejpam-4703	257	6	and	and	CCONJ
ejpam-4703	257	7	(	(	PUNCT
ejpam-4703	257	8	2	2	NUM
ejpam-4703	257	9	λbt	λbt	NOUN
ejpam-4703	257	10	+	+	X
ejpam-4703	257	11	at	at	ADP
ejpam-4703	257	12	)	)	PUNCT
ejpam-4703	257	13	α	α	NOUN
ejpam-4703	257	14	cxt	cxt	NOUN
ejpam-4703	257	15	=	=	PUNCT
ejpam-4703	257	16	∞∑	∞∑	NUM
ejpam-4703	257	17	s=0	s=0	X
ejpam-4703	257	18	g	g	PROPN
ejpam-4703	257	19	(	(	PUNCT
ejpam-4703	257	20	α	α	NOUN
ejpam-4703	257	21	)	)	PUNCT
ejpam-4703	257	22	s+α(x;λ	s+α(x;λ	NOUN
ejpam-4703	257	23	;	;	PUNCT
ejpam-4703	257	24	a.b.c	a.b.c	ADJ
ejpam-4703	257	25	)	)	PUNCT
ejpam-4703	257	26	(	(	PUNCT
ejpam-4703	257	27	s+	s+	X
ejpam-4703	257	28	α)α	α)α	VERB
ejpam-4703	257	29	ts	ts	ADP
ejpam-4703	257	30	s	s	PART
ejpam-4703	257	31	!	!	PUNCT
ejpam-4703	257	32	=	=	NOUN
ejpam-4703	258	1	∞∑	∞∑	PRON
ejpam-4703	258	2	n=0	n=0	NUM
ejpam-4703	258	3	g	g	NOUN
ejpam-4703	258	4	(	(	PUNCT
ejpam-4703	258	5	α	α	NOUN
ejpam-4703	258	6	)	)	PUNCT
ejpam-4703	258	7	n+α(x;λ	n+α(x;λ	PROPN
ejpam-4703	258	8	;	;	PUNCT
ejpam-4703	258	9	a.b.c	a.b.c	ADJ
ejpam-4703	258	10	)	)	PUNCT
ejpam-4703	258	11	(	(	PUNCT
ejpam-4703	258	12	n+	n+	NUM
ejpam-4703	258	13	α)α	α)α	NUM
ejpam-4703	258	14	tn	tn	NOUN
ejpam-4703	258	15	n	n	CCONJ
ejpam-4703	258	16	!	!	PUNCT
ejpam-4703	259	1	∞∑	∞∑	PRON
ejpam-4703	259	2	n=0	n=0	NUM
ejpam-4703	259	3	e(α	e(α	NOUN
ejpam-4703	259	4	)	)	PUNCT
ejpam-4703	259	5	n	n	CCONJ
ejpam-4703	259	6	(	(	PUNCT
ejpam-4703	259	7	x;λ	x;λ	NUM
ejpam-4703	259	8	;	;	PUNCT
ejpam-4703	259	9	a	a	DET
ejpam-4703	259	10	,	,	PUNCT
ejpam-4703	259	11	b	b	NOUN
ejpam-4703	259	12	,	,	PUNCT
ejpam-4703	259	13	c	c	NOUN
ejpam-4703	259	14	)	)	PUNCT
ejpam-4703	259	15	tn	tn	PROPN
ejpam-4703	259	16	n	n	CCONJ
ejpam-4703	259	17	!	!	PUNCT
ejpam-4703	259	18	=	=	NOUN
ejpam-4703	260	1	∞∑	∞∑	PRON
ejpam-4703	260	2	n=0	n=0	NUM
ejpam-4703	260	3	g	g	NOUN
ejpam-4703	260	4	(	(	PUNCT
ejpam-4703	260	5	α	α	NOUN
ejpam-4703	260	6	)	)	PUNCT
ejpam-4703	260	7	n+α(x;λ	n+α(x;λ	PROPN
ejpam-4703	260	8	;	;	PUNCT
ejpam-4703	260	9	a.b.c	a.b.c	ADJ
ejpam-4703	260	10	)	)	PUNCT
ejpam-4703	260	11	(	(	PUNCT
ejpam-4703	260	12	n+	n+	NUM
ejpam-4703	260	13	α)α	α)α	NUM
ejpam-4703	260	14	tn	tn	PROPN
ejpam-4703	260	15	n	n	NOUN
ejpam-4703	260	16	!	!	PUNCT
ejpam-4703	261	1	c.	c.	PROPN
ejpam-4703	261	2	corcino	corcino	PROPN
ejpam-4703	261	3	,	,	PUNCT
ejpam-4703	261	4	r.	r.	PROPN
ejpam-4703	261	5	corcino	corcino	PROPN
ejpam-4703	261	6	/	/	SYM
ejpam-4703	261	7	eur	eur	PROPN
ejpam-4703	261	8	.	.	PUNCT
ejpam-4703	262	1	j.	j.	PROPN
ejpam-4703	262	2	pure	pure	PROPN
ejpam-4703	262	3	appl	appl	PROPN
ejpam-4703	262	4	.	.	PROPN
ejpam-4703	262	5	math	math	PROPN
ejpam-4703	262	6	,	,	PUNCT
ejpam-4703	262	7	16	16	NUM
ejpam-4703	262	8	(	(	PUNCT
ejpam-4703	262	9	2	2	NUM
ejpam-4703	262	10	)	)	PUNCT
ejpam-4703	262	11	(	(	PUNCT
ejpam-4703	262	12	2023	2023	NUM
ejpam-4703	262	13	)	)	PUNCT
ejpam-4703	262	14	,	,	PUNCT
ejpam-4703	262	15	791	791	NUM
ejpam-4703	262	16	-	-	SYM
ejpam-4703	262	17	805	805	NUM
ejpam-4703	262	18	804	804	NUM
ejpam-4703	262	19	comparing	compare	VERB
ejpam-4703	262	20	coefficients	coefficient	NOUN
ejpam-4703	262	21	yields	yield	NOUN
ejpam-4703	262	22	g	g	PROPN
ejpam-4703	262	23	(	(	PUNCT
ejpam-4703	262	24	α	α	NOUN
ejpam-4703	262	25	)	)	PUNCT
ejpam-4703	262	26	n+α(x;λ	n+α(x;λ	PROPN
ejpam-4703	262	27	;	;	PUNCT
ejpam-4703	262	28	a.b.c	a.b.c	ADJ
ejpam-4703	262	29	)	)	PUNCT
ejpam-4703	262	30	=	=	PUNCT
ejpam-4703	262	31	(	(	PUNCT
ejpam-4703	262	32	n+	n+	X
ejpam-4703	263	1	α)αe	α)αe	NOUN
ejpam-4703	263	2	(	(	PUNCT
ejpam-4703	263	3	α	α	NOUN
ejpam-4703	263	4	)	)	PUNCT
ejpam-4703	263	5	n	n	CCONJ
ejpam-4703	263	6	(	(	PUNCT
ejpam-4703	263	7	x;λ	x;λ	NUM
ejpam-4703	263	8	;	;	PUNCT
ejpam-4703	263	9	a	a	DET
ejpam-4703	263	10	,	,	PUNCT
ejpam-4703	263	11	b	b	NOUN
ejpam-4703	263	12	,	,	PUNCT
ejpam-4703	263	13	c	c	NOUN
ejpam-4703	263	14	)	)	PUNCT
ejpam-4703	263	15	.	.	PUNCT
ejpam-4703	264	1	(	(	PUNCT
ejpam-4703	264	2	3.25	3.25	NUM
ejpam-4703	264	3	)	)	PUNCT
ejpam-4703	264	4	taking	take	VERB
ejpam-4703	264	5	α	α	NOUN
ejpam-4703	264	6	=	=	SYM
ejpam-4703	264	7	1	1	NUM
ejpam-4703	264	8	,	,	PUNCT
ejpam-4703	264	9	it	it	PRON
ejpam-4703	264	10	follows	follow	VERB
ejpam-4703	264	11	from	from	ADP
ejpam-4703	264	12	lemma	lemma	PROPN
ejpam-4703	264	13	3.5	3.5	NUM
ejpam-4703	264	14	that	that	DET
ejpam-4703	264	15	gn+1(x;λ	gn+1(x;λ	NOUN
ejpam-4703	264	16	;	;	PUNCT
ejpam-4703	264	17	a.b.c	a.b.c	ADJ
ejpam-4703	264	18	)	)	PUNCT
ejpam-4703	264	19	=	=	PUNCT
ejpam-4703	265	1	(	(	PUNCT
ejpam-4703	265	2	n+	n+	NUM
ejpam-4703	265	3	1)en(x;λ	1)en(x;λ	NUM
ejpam-4703	265	4	;	;	PUNCT
ejpam-4703	265	5	a	a	DET
ejpam-4703	265	6	,	,	PUNCT
ejpam-4703	265	7	b	b	NOUN
ejpam-4703	265	8	,	,	PUNCT
ejpam-4703	265	9	c	c	NOUN
ejpam-4703	265	10	)	)	PUNCT
ejpam-4703	265	11	.	.	PUNCT
ejpam-4703	266	1	(	(	PUNCT
ejpam-4703	266	2	3.26	3.26	NUM
ejpam-4703	266	3	)	)	PUNCT
ejpam-4703	266	4	corollary	corollary	ADJ
ejpam-4703	266	5	3.6	3.6	NUM
ejpam-4703	266	6	.	.	PUNCT
ejpam-4703	267	1	let	let	VERB
ejpam-4703	267	2	a	a	DET
ejpam-4703	267	3	,	,	PUNCT
ejpam-4703	267	4	b	b	NOUN
ejpam-4703	267	5	,	,	PUNCT
ejpam-4703	267	6	c	c	PROPN
ejpam-4703	267	7	∈	∈	PROPN
ejpam-4703	267	8	r\{1	r\{1	PROPN
ejpam-4703	267	9	}	}	PUNCT
ejpam-4703	267	10	,	,	PUNCT
ejpam-4703	267	11	a	a	DET
ejpam-4703	267	12	̸=	̸=	PROPN
ejpam-4703	267	13	b	b	PROPN
ejpam-4703	267	14	and	and	CCONJ
ejpam-4703	267	15	µ	µ	X
ejpam-4703	267	16	=	=	PUNCT
ejpam-4703	267	17	(	(	PUNCT
ejpam-4703	267	18	x	x	X
ejpam-4703	267	19	ln	ln	PROPN
ejpam-4703	267	20	c)−1	c)−1	PROPN
ejpam-4703	267	21	.	.	PROPN
ejpam-4703	268	1	for	for	ADP
ejpam-4703	268	2	λ	λ	PROPN
ejpam-4703	268	3	,	,	PUNCT
ejpam-4703	268	4	x	x	SYM
ejpam-4703	268	5	∈	∈	PROPN
ejpam-4703	268	6	c\{0	c\{0	PROPN
ejpam-4703	268	7	}	}	PUNCT
ejpam-4703	268	8	,	,	PUNCT
ejpam-4703	268	9	λ	λ	PROPN
ejpam-4703	268	10	̸=	̸=	PROPN
ejpam-4703	268	11	1	1	NUM
ejpam-4703	268	12	such	such	ADJ
ejpam-4703	268	13	that	that	SCONJ
ejpam-4703	268	14	|µ|	|µ|	PROPN
ejpam-4703	268	15	<	<	X
ejpam-4703	268	16	∣∣∣µ±	∣∣∣µ±	PROPN
ejpam-4703	268	17	πi−δ	πi−δ	PROPN
ejpam-4703	268	18	ln(ba−1	ln(ba−1	PROPN
ejpam-4703	268	19	)	)	PUNCT
ejpam-4703	268	20	∣∣∣	∣∣∣	NOUN
ejpam-4703	268	21	,	,	PUNCT
ejpam-4703	268	22	gn+1(nx;λ	gn+1(nx;λ	PUNCT
ejpam-4703	268	23	;	;	PUNCT
ejpam-4703	268	24	a	a	DET
ejpam-4703	268	25	,	,	PUNCT
ejpam-4703	268	26	b	b	NOUN
ejpam-4703	268	27	,	,	PUNCT
ejpam-4703	268	28	c	c	NOUN
ejpam-4703	268	29	)	)	PUNCT
ejpam-4703	268	30	=	=	SYM
ejpam-4703	269	1	(	(	PUNCT
ejpam-4703	269	2	n+	n+	NOUN
ejpam-4703	269	3	1	1	NUM
ejpam-4703	269	4	)	)	PUNCT
ejpam-4703	269	5	(	(	PUNCT
ejpam-4703	269	6	nx	nx	PROPN
ejpam-4703	269	7	ln	ln	ADJ
ejpam-4703	269	8	c)n(ab	c)n(ab	NOUN
ejpam-4703	269	9	)	)	PUNCT
ejpam-4703	269	10	−µ	−µ	NOUN
ejpam-4703	269	11	2	2	NUM
ejpam-4703	269	12	λ	λ	NOUN
ejpam-4703	269	13	−1	−1	NOUN
ejpam-4703	269	14	2	2	NUM
ejpam-4703	269	15	cosh	cosh	NOUN
ejpam-4703	269	16	ρ	ρ	NOUN
ejpam-4703	269	17	{	{	PUNCT
ejpam-4703	269	18	1−	1−	NUM
ejpam-4703	269	19	f	f	PROPN
ejpam-4703	269	20	2n(x	2n(x	NUM
ejpam-4703	269	21	ln	ln	ADJ
ejpam-4703	269	22	c)2	c)2	NOUN
ejpam-4703	269	23	+	+	PROPN
ejpam-4703	269	24	o(n−2	o(n−2	PROPN
ejpam-4703	269	25	)	)	PUNCT
ejpam-4703	269	26	}	}	PUNCT
ejpam-4703	269	27	,	,	PUNCT
ejpam-4703	269	28	(	(	PUNCT
ejpam-4703	269	29	3.27	3.27	NUM
ejpam-4703	269	30	)	)	PUNCT
ejpam-4703	269	31	where	where	SCONJ
ejpam-4703	269	32	f	f	PROPN
ejpam-4703	269	33	is	be	AUX
ejpam-4703	269	34	given	give	VERB
ejpam-4703	269	35	in	in	ADP
ejpam-4703	269	36	theorem	theorem	ADJ
ejpam-4703	269	37	3.3	3.3	NUM
ejpam-4703	269	38	.	.	PUNCT
ejpam-4703	270	1	proof	proof	NOUN
ejpam-4703	270	2	.	.	PUNCT
ejpam-4703	271	1	this	this	PRON
ejpam-4703	271	2	follows	follow	VERB
ejpam-4703	271	3	from	from	ADP
ejpam-4703	271	4	(	(	PUNCT
ejpam-4703	271	5	3.26	3.26	NUM
ejpam-4703	271	6	)	)	PUNCT
ejpam-4703	271	7	and	and	CCONJ
ejpam-4703	271	8	theorem	theorem	VERB
ejpam-4703	271	9	3.3	3.3	NUM
ejpam-4703	271	10	.	.	PUNCT
ejpam-4703	272	1	corollary	corollary	ADJ
ejpam-4703	272	2	3.7	3.7	NUM
ejpam-4703	272	3	.	.	PUNCT
ejpam-4703	273	1	let	let	VERB
ejpam-4703	273	2	a	a	DET
ejpam-4703	273	3	,	,	PUNCT
ejpam-4703	273	4	b	b	NOUN
ejpam-4703	273	5	,	,	PUNCT
ejpam-4703	273	6	c	c	PROPN
ejpam-4703	273	7	∈	∈	PROPN
ejpam-4703	273	8	r\{1	r\{1	PROPN
ejpam-4703	273	9	}	}	PUNCT
ejpam-4703	273	10	,	,	PUNCT
ejpam-4703	273	11	α	α	PROPN
ejpam-4703	273	12	∈	∈	PROPN
ejpam-4703	273	13	z+	z+	PRON
ejpam-4703	273	14	,	,	PUNCT
ejpam-4703	273	15	a	a	DET
ejpam-4703	273	16	̸=	̸=	PROPN
ejpam-4703	273	17	b	b	PROPN
ejpam-4703	273	18	and	and	CCONJ
ejpam-4703	273	19	µ	µ	X
ejpam-4703	273	20	=	=	PUNCT
ejpam-4703	273	21	(	(	PUNCT
ejpam-4703	273	22	x	x	X
ejpam-4703	273	23	ln	ln	PROPN
ejpam-4703	273	24	c)−1	c)−1	PROPN
ejpam-4703	273	25	.	.	PROPN
ejpam-4703	274	1	for	for	ADP
ejpam-4703	274	2	λ	λ	PROPN
ejpam-4703	274	3	,	,	PUNCT
ejpam-4703	274	4	x	x	SYM
ejpam-4703	274	5	∈	∈	PROPN
ejpam-4703	274	6	c\{0	c\{0	PROPN
ejpam-4703	274	7	}	}	PUNCT
ejpam-4703	274	8	g	g	NOUN
ejpam-4703	274	9	(	(	PUNCT
ejpam-4703	274	10	α	α	NOUN
ejpam-4703	274	11	)	)	PUNCT
ejpam-4703	274	12	n+α(nx;λ	n+α(nx;λ	NOUN
ejpam-4703	274	13	;	;	PUNCT
ejpam-4703	274	14	a	a	DET
ejpam-4703	274	15	,	,	PUNCT
ejpam-4703	274	16	b	b	NOUN
ejpam-4703	274	17	,	,	PUNCT
ejpam-4703	274	18	c	c	NOUN
ejpam-4703	274	19	)	)	PUNCT
ejpam-4703	275	1	=	=	SYM
ejpam-4703	275	2	(	(	PUNCT
ejpam-4703	275	3	n+α)α	n+α)α	PROPN
ejpam-4703	275	4	(	(	PUNCT
ejpam-4703	275	5	nx	nx	X
ejpam-4703	275	6	ln	ln	ADJ
ejpam-4703	275	7	c)n	c)n	NOUN
ejpam-4703	276	1	λ	λ	INTJ
ejpam-4703	276	2	α	α	NOUN
ejpam-4703	276	3	2	2	NUM
ejpam-4703	276	4	(	(	PUNCT
ejpam-4703	276	5	(	(	PUNCT
ejpam-4703	276	6	ab)−	ab)−	X
ejpam-4703	276	7	µ	µ	X
ejpam-4703	276	8	2	2	NUM
ejpam-4703	276	9	cosh	cosh	NOUN
ejpam-4703	276	10	ρ	ρ	PROPN
ejpam-4703	276	11	)	)	PUNCT
ejpam-4703	276	12	α	α	PROPN
ejpam-4703	276	13	{	{	PUNCT
ejpam-4703	276	14	1−	1−	NUM
ejpam-4703	276	15	αf	αf	NOUN
ejpam-4703	276	16	−	−	NOUN
ejpam-4703	276	17	α(α−	α(α−	PROPN
ejpam-4703	276	18	1)h2	1)h2	NUM
ejpam-4703	276	19	2n(x	2n(x	NUM
ejpam-4703	276	20	ln	ln	ADJ
ejpam-4703	276	21	c)2	c)2	NOUN
ejpam-4703	276	22	+	+	PROPN
ejpam-4703	276	23	o(n−2	o(n−2	PROPN
ejpam-4703	276	24	)	)	PUNCT
ejpam-4703	276	25	}	}	PUNCT
ejpam-4703	276	26	,	,	PUNCT
ejpam-4703	276	27	(	(	PUNCT
ejpam-4703	276	28	3.28	3.28	NUM
ejpam-4703	276	29	)	)	PUNCT
ejpam-4703	276	30	where	where	SCONJ
ejpam-4703	276	31	h	h	NOUN
ejpam-4703	276	32	=	=	PUNCT
ejpam-4703	276	33	−	−	PROPN
ejpam-4703	276	34	ln(ab	ln(ab	PROPN
ejpam-4703	276	35	)	)	PUNCT
ejpam-4703	276	36	2	2	NUM
ejpam-4703	276	37	−	−	PROPN
ejpam-4703	276	38	ln(ba−1	ln(ba−1	NOUN
ejpam-4703	276	39	)	)	PUNCT
ejpam-4703	276	40	2	2	NUM
ejpam-4703	276	41	tanh	tanh	PROPN
ejpam-4703	276	42	ρ	ρ	PROPN
ejpam-4703	276	43	,	,	PUNCT
ejpam-4703	276	44	and	and	CCONJ
ejpam-4703	276	45	f	f	PROPN
ejpam-4703	276	46	is	be	AUX
ejpam-4703	276	47	given	give	VERB
ejpam-4703	276	48	in	in	ADP
ejpam-4703	276	49	theorem	theorem	ADJ
ejpam-4703	276	50	3.3	3.3	NUM
ejpam-4703	276	51	.	.	PUNCT
ejpam-4703	277	1	proof	proof	NOUN
ejpam-4703	277	2	.	.	PUNCT
ejpam-4703	278	1	this	this	PRON
ejpam-4703	278	2	follows	follow	VERB
ejpam-4703	278	3	from	from	ADP
ejpam-4703	278	4	lemma	lemma	PROPN
ejpam-4703	278	5	3.5	3.5	NUM
ejpam-4703	278	6	and	and	CCONJ
ejpam-4703	278	7	theorem	theorem	VERB
ejpam-4703	278	8	3.4	3.4	NUM
ejpam-4703	278	9	.	.	NOUN
ejpam-4703	279	1	4	4	NUM
ejpam-4703	279	2	.	.	NOUN
ejpam-4703	279	3	conclusion	conclusion	NOUN
ejpam-4703	279	4	and	and	CCONJ
ejpam-4703	279	5	recommendation	recommendation	NOUN
ejpam-4703	279	6	the	the	DET
ejpam-4703	279	7	formulas	formula	NOUN
ejpam-4703	279	8	obtained	obtain	VERB
ejpam-4703	279	9	in	in	ADP
ejpam-4703	279	10	the	the	DET
ejpam-4703	279	11	paper	paper	NOUN
ejpam-4703	279	12	are	be	AUX
ejpam-4703	279	13	valid	valid	ADJ
ejpam-4703	279	14	for	for	ADP
ejpam-4703	279	15	nonzero	nonzero	ADJ
ejpam-4703	279	16	complex	complex	ADJ
ejpam-4703	279	17	numbers	number	NOUN
ejpam-4703	279	18	x	x	PUNCT
ejpam-4703	279	19	such	such	ADJ
ejpam-4703	279	20	that	that	SCONJ
ejpam-4703	279	21	the	the	DET
ejpam-4703	279	22	distance	distance	NOUN
ejpam-4703	279	23	of	of	ADP
ejpam-4703	279	24	(	(	PUNCT
ejpam-4703	279	25	x	x	X
ejpam-4703	279	26	ln	ln	ADJ
ejpam-4703	279	27	c)−1	c)−1	NOUN
ejpam-4703	279	28	from	from	ADP
ejpam-4703	279	29	the	the	DET
ejpam-4703	279	30	origin	origin	NOUN
ejpam-4703	279	31	is	be	AUX
ejpam-4703	279	32	smaller	small	ADJ
ejpam-4703	279	33	than	than	ADP
ejpam-4703	279	34	its	its	PRON
ejpam-4703	279	35	distance	distance	NOUN
ejpam-4703	279	36	to	to	ADP
ejpam-4703	279	37	the	the	DET
ejpam-4703	279	38	pole	pole	NOUN
ejpam-4703	279	39	of	of	ADP
ejpam-4703	279	40	the	the	DET
ejpam-4703	279	41	generating	generate	VERB
ejpam-4703	279	42	function	function	NOUN
ejpam-4703	279	43	nearest	near	ADV
ejpam-4703	279	44	to	to	ADP
ejpam-4703	279	45	the	the	DET
ejpam-4703	279	46	origin	origin	NOUN
ejpam-4703	279	47	.	.	PUNCT
ejpam-4703	280	1	this	this	DET
ejpam-4703	280	2	validity	validity	NOUN
ejpam-4703	280	3	can	can	AUX
ejpam-4703	280	4	be	be	AUX
ejpam-4703	280	5	enlarged	enlarge	VERB
ejpam-4703	280	6	by	by	ADP
ejpam-4703	280	7	isolating	isolate	VERB
ejpam-4703	280	8	the	the	DET
ejpam-4703	280	9	contribution	contribution	NOUN
ejpam-4703	280	10	of	of	ADP
ejpam-4703	280	11	the	the	DET
ejpam-4703	280	12	poles	pole	NOUN
ejpam-4703	280	13	.	.	PUNCT
ejpam-4703	281	1	this	this	DET
ejpam-4703	281	2	method	method	NOUN
ejpam-4703	281	3	was	be	AUX
ejpam-4703	281	4	done	do	VERB
ejpam-4703	281	5	in	in	ADP
ejpam-4703	281	6	[	[	X
ejpam-4703	281	7	4	4	NUM
ejpam-4703	281	8	]	]	PUNCT
ejpam-4703	281	9	,	,	PUNCT
ejpam-4703	281	10	[	[	X
ejpam-4703	281	11	5	5	NUM
ejpam-4703	281	12	]	]	PUNCT
ejpam-4703	281	13	.	.	PUNCT
ejpam-4703	282	1	the	the	DET
ejpam-4703	282	2	authors	author	NOUN
ejpam-4703	282	3	recommend	recommend	VERB
ejpam-4703	282	4	to	to	PART
ejpam-4703	282	5	obtain	obtain	VERB
ejpam-4703	282	6	approximation	approximation	NOUN
ejpam-4703	282	7	formulas	formula	NOUN
ejpam-4703	282	8	with	with	ADP
ejpam-4703	282	9	enlarged	enlarged	ADJ
ejpam-4703	282	10	region	region	NOUN
ejpam-4703	282	11	of	of	ADP
ejpam-4703	282	12	validity	validity	NOUN
ejpam-4703	282	13	for	for	ADP
ejpam-4703	282	14	the	the	DET
ejpam-4703	282	15	polynomials	polynomial	NOUN
ejpam-4703	282	16	studied	study	VERB
ejpam-4703	282	17	here	here	ADV
ejpam-4703	282	18	.	.	PUNCT
ejpam-4703	283	1	references	reference	NOUN
ejpam-4703	283	2	805	805	NUM
ejpam-4703	283	3	acknowledgements	acknowledgement	NOUN
ejpam-4703	283	4	this	this	DET
ejpam-4703	283	5	research	research	NOUN
ejpam-4703	283	6	is	be	AUX
ejpam-4703	283	7	funded	fund	VERB
ejpam-4703	283	8	by	by	ADP
ejpam-4703	283	9	cebu	cebu	PROPN
ejpam-4703	283	10	normal	normal	ADJ
ejpam-4703	283	11	university	university	NOUN
ejpam-4703	283	12	through	through	ADP
ejpam-4703	283	13	its	its	PRON
ejpam-4703	283	14	center	center	NOUN
ejpam-4703	283	15	for	for	ADP
ejpam-4703	283	16	research	research	NOUN
ejpam-4703	283	17	and	and	CCONJ
ejpam-4703	283	18	development	development	NOUN
ejpam-4703	283	19	(	(	PUNCT
ejpam-4703	283	20	crd	crd	NOUN
ejpam-4703	283	21	)	)	PUNCT
ejpam-4703	283	22	.	.	PUNCT
ejpam-4703	284	1	references	reference	NOUN
ejpam-4703	284	2	[	[	X
ejpam-4703	284	3	1	1	NUM
ejpam-4703	284	4	]	]	X
ejpam-4703	284	5	w.a	w.a	PROPN
ejpam-4703	284	6	.	.	PROPN
ejpam-4703	284	7	khan	khan	PROPN
ejpam-4703	284	8	,	,	PUNCT
ejpam-4703	284	9	d.	d.	PROPN
ejpam-4703	284	10	srivastava	srivastava	PROPN
ejpam-4703	284	11	,	,	PUNCT
ejpam-4703	284	12	on	on	ADP
ejpam-4703	284	13	the	the	DET
ejpam-4703	284	14	generalized	generalize	VERB
ejpam-4703	284	15	apostol	apostol	NOUN
ejpam-4703	284	16	-	-	PUNCT
ejpam-4703	284	17	type	type	NOUN
ejpam-4703	284	18	frobenius	frobenius	NOUN
ejpam-4703	284	19	-	-	PUNCT
ejpam-4703	284	20	genocchi	genocchi	NOUN
ejpam-4703	284	21	polynomials	polynomial	NOUN
ejpam-4703	284	22	,	,	PUNCT
ejpam-4703	284	23	filomat	filomat	NOUN
ejpam-4703	284	24	33	33	NUM
ejpam-4703	284	25	:	:	PUNCT
ejpam-4703	284	26	7(2019	7(2019	NUM
ejpam-4703	284	27	)	)	PUNCT
ejpam-4703	284	28	,	,	PUNCT
ejpam-4703	284	29	1967	1967	NUM
ejpam-4703	284	30	-	-	SYM
ejpam-4703	284	31	1977	1977	NUM
ejpam-4703	284	32	.	.	PUNCT
ejpam-4703	285	1	[	[	X
ejpam-4703	285	2	2	2	NUM
ejpam-4703	285	3	]	]	X
ejpam-4703	285	4	c.b	c.b	PROPN
ejpam-4703	285	5	.	.	PROPN
ejpam-4703	285	6	corcino	corcino	PROPN
ejpam-4703	285	7	,	,	PUNCT
ejpam-4703	285	8	r.b	r.b	PROPN
ejpam-4703	285	9	.	.	PROPN
ejpam-4703	285	10	corcino	corcino	PROPN
ejpam-4703	285	11	,	,	PUNCT
ejpam-4703	285	12	asymptotics	asymptotic	NOUN
ejpam-4703	285	13	of	of	ADP
ejpam-4703	285	14	genocchi	genocchi	PROPN
ejpam-4703	285	15	polynomials	polynomial	NOUN
ejpam-4703	285	16	and	and	CCONJ
ejpam-4703	285	17	higher	high	ADJ
ejpam-4703	285	18	order	order	NOUN
ejpam-4703	285	19	genocchi	genocchi	NOUN
ejpam-4703	285	20	polynomials	polynomial	VERB
ejpam-4703	285	21	using	use	VERB
ejpam-4703	285	22	residues	residue	NOUN
ejpam-4703	285	23	,	,	PUNCT
ejpam-4703	286	1	afr	afr	NOUN
ejpam-4703	286	2	.	.	PUNCT
ejpam-4703	286	3	mat	mat	PROPN
ejpam-4703	286	4	.	.	PROPN
ejpam-4703	286	5	,	,	PUNCT
ejpam-4703	286	6	31	31	NUM
ejpam-4703	286	7	(	(	PUNCT
ejpam-4703	286	8	2020	2020	NUM
ejpam-4703	286	9	)	)	PUNCT
ejpam-4703	286	10	pp	pp	ADV
ejpam-4703	286	11	.	.	PUNCT
ejpam-4703	287	1	781	781	NUM
ejpam-4703	287	2	-	-	SYM
ejpam-4703	287	3	792	792	NUM
ejpam-4703	287	4	.	.	PUNCT
ejpam-4703	288	1	[	[	X
ejpam-4703	288	2	3	3	X
ejpam-4703	288	3	]	]	X
ejpam-4703	288	4	c.b	c.b	PROPN
ejpam-4703	288	5	.	.	PROPN
ejpam-4703	288	6	corcino	corcino	PROPN
ejpam-4703	288	7	,	,	PUNCT
ejpam-4703	288	8	asymptotic	asymptotic	ADJ
ejpam-4703	288	9	approximations	approximation	NOUN
ejpam-4703	288	10	of	of	ADP
ejpam-4703	288	11	apostol	apostol	NOUN
ejpam-4703	288	12	-	-	PUNCT
ejpam-4703	288	13	genocchi	genocchi	PROPN
ejpam-4703	288	14	numbers	number	NOUN
ejpam-4703	288	15	and	and	CCONJ
ejpam-4703	288	16	polynomials	polynomial	NOUN
ejpam-4703	288	17	,	,	PUNCT
ejpam-4703	288	18	eur	eur	PROPN
ejpam-4703	288	19	.	.	PUNCT
ejpam-4703	289	1	j.	j.	PROPN
ejpam-4703	289	2	pure	pure	PROPN
ejpam-4703	289	3	appl	appl	PROPN
ejpam-4703	289	4	.	.	PUNCT
ejpam-4703	289	5	math	math	PROPN
ejpam-4703	289	6	.	.	PUNCT
ejpam-4703	289	7	,	,	PUNCT
ejpam-4703	289	8	14:3	14:3	NUM
ejpam-4703	289	9	(	(	PUNCT
ejpam-4703	289	10	2021	2021	NUM
ejpam-4703	289	11	)	)	PUNCT
ejpam-4703	290	1	pp	pp	ADP
ejpam-4703	290	2	.	.	PUNCT
ejpam-4703	291	1	666	666	NUM
ejpam-4703	291	2	-	-	SYM
ejpam-4703	291	3	684	684	NUM
ejpam-4703	291	4	.	.	PUNCT
ejpam-4703	292	1	[	[	X
ejpam-4703	292	2	4	4	X
ejpam-4703	292	3	]	]	X
ejpam-4703	292	4	j.l	j.l	PROPN
ejpam-4703	292	5	.	.	PROPN
ejpam-4703	292	6	lopez	lopez	PROPN
ejpam-4703	292	7	and	and	CCONJ
ejpam-4703	292	8	n.m	n.m	PROPN
ejpam-4703	292	9	.	.	PROPN
ejpam-4703	292	10	temme	temme	PROPN
ejpam-4703	292	11	,	,	PUNCT
ejpam-4703	292	12	uniform	uniform	ADJ
ejpam-4703	292	13	approximations	approximation	NOUN
ejpam-4703	292	14	of	of	ADP
ejpam-4703	292	15	bernoulli	bernoulli	PROPN
ejpam-4703	292	16	and	and	CCONJ
ejpam-4703	292	17	euler	euler	NOUN
ejpam-4703	292	18	polynomials	polynomial	NOUN
ejpam-4703	292	19	in	in	ADP
ejpam-4703	292	20	terms	term	NOUN
ejpam-4703	292	21	of	of	ADP
ejpam-4703	292	22	hyperbolic	hyperbolic	ADJ
ejpam-4703	292	23	functions	function	NOUN
ejpam-4703	292	24	,	,	PUNCT
ejpam-4703	292	25	stud	stud	NOUN
ejpam-4703	292	26	.	.	PUNCT
ejpam-4703	293	1	appl	appl	PROPN
ejpam-4703	293	2	.	.	PROPN
ejpam-4703	293	3	math	math	NOUN
ejpam-4703	293	4	.	.	PUNCT
ejpam-4703	294	1	103(1999	103(1999	NUM
ejpam-4703	294	2	)	)	PUNCT
ejpam-4703	294	3	,	,	PUNCT
ejpam-4703	294	4	no.3	no.3	PROPN
ejpam-4703	294	5	,	,	PUNCT
ejpam-4703	294	6	241258	241258	NUM
ejpam-4703	294	7	.	.	PUNCT
ejpam-4703	295	1	[	[	X
ejpam-4703	295	2	5	5	X
ejpam-4703	295	3	]	]	X
ejpam-4703	295	4	c.b	c.b	PROPN
ejpam-4703	295	5	.	.	PROPN
ejpam-4703	295	6	corcino	corcino	PROPN
ejpam-4703	295	7	,	,	PUNCT
ejpam-4703	295	8	r.b	r.b	PROPN
ejpam-4703	295	9	.	.	PROPN
ejpam-4703	295	10	corcino	corcino	PROPN
ejpam-4703	295	11	,	,	PUNCT
ejpam-4703	295	12	j.m	j.m	PROPN
ejpam-4703	295	13	.	.	PROPN
ejpam-4703	295	14	ontolan	ontolan	PROPN
ejpam-4703	295	15	,	,	PUNCT
ejpam-4703	295	16	w.d	w.d	PROPN
ejpam-4703	295	17	.	.	PROPN
ejpam-4703	295	18	castaneda	castaneda	PROPN
ejpam-4703	295	19	,	,	PUNCT
ejpam-4703	295	20	approximations	approximation	NOUN
ejpam-4703	295	21	of	of	ADP
ejpam-4703	295	22	genocchi	genocchi	PROPN
ejpam-4703	295	23	polynomials	polynomial	NOUN
ejpam-4703	295	24	in	in	ADP
ejpam-4703	295	25	terms	term	NOUN
ejpam-4703	295	26	of	of	ADP
ejpam-4703	295	27	hyperbolic	hyperbolic	ADJ
ejpam-4703	295	28	functions	function	NOUN
ejpam-4703	295	29	,	,	PUNCT
ejpam-4703	295	30	journal	journal	NOUN
ejpam-4703	295	31	of	of	ADP
ejpam-4703	295	32	mathematical	mathematical	ADJ
ejpam-4703	295	33	analysis	analysis	NOUN
ejpam-4703	295	34	(	(	PUNCT
ejpam-4703	295	35	2019	2019	NUM
ejpam-4703	295	36	)	)	PUNCT
ejpam-4703	295	37	vol	vol	NOUN
ejpam-4703	295	38	.	.	PUNCT
ejpam-4703	295	39	10	10	NUM
ejpam-4703	295	40	issue	issue	NOUN
ejpam-4703	295	41	3	3	NUM
ejpam-4703	295	42	,	,	PUNCT
ejpam-4703	295	43	76	76	NUM
ejpam-4703	295	44	-	-	SYM
ejpam-4703	295	45	88	88	NUM
ejpam-4703	295	46	.	.	PUNCT
ejpam-4703	296	1	[	[	X
ejpam-4703	296	2	6	6	NUM
ejpam-4703	296	3	]	]	PUNCT
ejpam-4703	296	4	r.	r.	PROPN
ejpam-4703	296	5	wong	wong	PROPN
ejpam-4703	296	6	,	,	PUNCT
ejpam-4703	296	7	asymptotic	asymptotic	ADJ
ejpam-4703	296	8	approximations	approximation	NOUN
ejpam-4703	296	9	of	of	ADP
ejpam-4703	296	10	integrals	integral	NOUN
ejpam-4703	296	11	academic	academic	ADJ
ejpam-4703	296	12	press	press	NOUN
ejpam-4703	296	13	,	,	PUNCT
ejpam-4703	296	14	new	new	PROPN
ejpam-4703	296	15	york	york	PROPN
ejpam-4703	296	16	,	,	PUNCT
ejpam-4703	296	17	1989	1989	NUM
ejpam-4703	296	18	.	.	PUNCT
ejpam-4703	297	1	[	[	X
ejpam-4703	297	2	7	7	X
ejpam-4703	297	3	]	]	X
ejpam-4703	297	4	r.v	r.v	PROPN
ejpam-4703	297	5	.	.	PROPN
ejpam-4703	297	6	churchill	churchill	PROPN
ejpam-4703	297	7	and	and	CCONJ
ejpam-4703	297	8	j.w	j.w	PROPN
ejpam-4703	297	9	.	.	PROPN
ejpam-4703	297	10	brown	brown	PROPN
ejpam-4703	297	11	,	,	PUNCT
ejpam-4703	297	12	complex	complex	ADJ
ejpam-4703	297	13	variables	variable	NOUN
ejpam-4703	297	14	and	and	CCONJ
ejpam-4703	297	15	applications	application	NOUN
ejpam-4703	297	16	,	,	PUNCT
ejpam-4703	297	17	mcgraw	mcgraw	PROPN
ejpam-4703	297	18	-	-	PUNCT
ejpam-4703	297	19	hill	hill	NOUN
ejpam-4703	297	20	book	book	NOUN
ejpam-4703	297	21	company	company	NOUN
ejpam-4703	297	22	,	,	PUNCT
ejpam-4703	297	23	4th	4th	ADJ
ejpam-4703	297	24	ed	ed	NOUN
ejpam-4703	297	25	.	.	PROPN
ejpam-4703	297	26	,	,	PUNCT
ejpam-4703	297	27	1984	1984	NUM
ejpam-4703	297	28	.	.	PUNCT
ejpam-4703	298	1	[	[	X
ejpam-4703	298	2	8	8	NUM
ejpam-4703	298	3	]	]	X
ejpam-4703	298	4	l.l	l.l	PROPN
ejpam-4703	298	5	.	.	PROPN
ejpam-4703	298	6	pennisi	pennisi	VERB
ejpam-4703	298	7	,	,	PUNCT
ejpam-4703	298	8	elements	element	NOUN
ejpam-4703	298	9	of	of	ADP
ejpam-4703	298	10	complex	complex	ADJ
ejpam-4703	298	11	variables	variable	NOUN
ejpam-4703	298	12	,	,	PUNCT
ejpam-4703	298	13	holt	holt	PROPN
ejpam-4703	298	14	,	,	PUNCT
ejpam-4703	298	15	rinehart	rinehart	PROPN
ejpam-4703	298	16	and	and	CCONJ
ejpam-4703	298	17	winston	winston	PROPN
ejpam-4703	298	18	,	,	PUNCT
ejpam-4703	298	19	2nd	2nd	PROPN
ejpam-4703	298	20	ed	ed	NOUN
ejpam-4703	298	21	.	.	PROPN
ejpam-4703	298	22	,	,	PUNCT
ejpam-4703	298	23	1976	1976	NUM
ejpam-4703	298	24	.	.	PUNCT