id	sid	tid	token	lemma	pos
ejpam-6069	1	1	european	european	PROPN
ejpam-6069	1	2	journal	journal	PROPN
ejpam-6069	1	3	of	of	ADP
ejpam-6069	1	4	pure	pure	ADJ
ejpam-6069	1	5	and	and	CCONJ
ejpam-6069	1	6	applied	applied	ADJ
ejpam-6069	1	7	mathematics	mathematic	NOUN
ejpam-6069	1	8	2025	2025	NUM
ejpam-6069	1	9	,	,	PUNCT
ejpam-6069	1	10	vol	vol	NOUN
ejpam-6069	1	11	.	.	PROPN
ejpam-6069	1	12	18	18	NUM
ejpam-6069	1	13	,	,	PUNCT
ejpam-6069	1	14	issue	issue	NOUN
ejpam-6069	1	15	2	2	NUM
ejpam-6069	1	16	,	,	PUNCT
ejpam-6069	1	17	article	article	NOUN
ejpam-6069	1	18	number	number	NOUN
ejpam-6069	1	19	6069	6069	NUM
ejpam-6069	1	20	issn	issn	VERB
ejpam-6069	1	21	1307	1307	NUM
ejpam-6069	1	22	-	-	SYM
ejpam-6069	1	23	5543	5543	NUM
ejpam-6069	1	24	–	–	PUNCT
ejpam-6069	1	25	ejpam.com	ejpam.com	X
ejpam-6069	1	26	published	publish	VERB
ejpam-6069	1	27	by	by	ADP
ejpam-6069	1	28	new	new	PROPN
ejpam-6069	1	29	york	york	PROPN
ejpam-6069	1	30	business	business	PROPN
ejpam-6069	1	31	global	global	VERB
ejpam-6069	1	32	some	some	DET
ejpam-6069	1	33	properties	property	NOUN
ejpam-6069	1	34	of	of	ADP
ejpam-6069	1	35	the	the	DET
ejpam-6069	1	36	non	non	ADJ
ejpam-6069	1	37	-	-	ADJ
ejpam-6069	1	38	central	central	ADJ
ejpam-6069	1	39	stirling	stirling	NOUN
ejpam-6069	1	40	numbers	number	NOUN
ejpam-6069	1	41	of	of	ADP
ejpam-6069	1	42	the	the	DET
ejpam-6069	1	43	second	second	ADJ
ejpam-6069	1	44	kind	kind	NOUN
ejpam-6069	1	45	with	with	ADP
ejpam-6069	1	46	complex	complex	ADJ
ejpam-6069	1	47	parameters	parameter	NOUN
ejpam-6069	1	48	erwin	erwin	PROPN
ejpam-6069	1	49	n.	n.	PROPN
ejpam-6069	1	50	arlan1∗	arlan1∗	PROPN
ejpam-6069	1	51	,	,	PUNCT
ejpam-6069	1	52	maribeth	maribeth	PROPN
ejpam-6069	1	53	b.	b.	PROPN
ejpam-6069	1	54	montero2	montero2	PROPN
ejpam-6069	1	55	1	1	NUM
ejpam-6069	1	56	mathematics	mathematics	PROPN
ejpam-6069	1	57	department	department	NOUN
ejpam-6069	1	58	,	,	PUNCT
ejpam-6069	1	59	caraga	caraga	PROPN
ejpam-6069	1	60	state	state	PROPN
ejpam-6069	1	61	university	university	PROPN
ejpam-6069	1	62	,	,	PUNCT
ejpam-6069	1	63	butuan	butuan	PROPN
ejpam-6069	1	64	city	city	PROPN
ejpam-6069	1	65	,	,	PUNCT
ejpam-6069	1	66	philippines	philippine	NOUN
ejpam-6069	1	67	2	2	NUM
ejpam-6069	1	68	mathematics	mathematics	NOUN
ejpam-6069	1	69	department	department	NOUN
ejpam-6069	1	70	,	,	PUNCT
ejpam-6069	1	71	mindanao	mindanao	PROPN
ejpam-6069	1	72	state	state	PROPN
ejpam-6069	1	73	university	university	PROPN
ejpam-6069	1	74	,	,	PUNCT
ejpam-6069	1	75	marawi	marawi	PROPN
ejpam-6069	1	76	city	city	PROPN
ejpam-6069	1	77	,	,	PUNCT
ejpam-6069	1	78	philippines	philippine	NOUN
ejpam-6069	1	79	abstract	abstract	ADJ
ejpam-6069	1	80	.	.	PUNCT
ejpam-6069	2	1	this	this	DET
ejpam-6069	2	2	work	work	NOUN
ejpam-6069	2	3	extends	extend	VERB
ejpam-6069	2	4	the	the	DET
ejpam-6069	2	5	non	non	ADJ
ejpam-6069	2	6	-	-	ADJ
ejpam-6069	2	7	central	central	ADJ
ejpam-6069	2	8	stirling	stirling	NOUN
ejpam-6069	2	9	numbers	number	NOUN
ejpam-6069	2	10	of	of	ADP
ejpam-6069	2	11	the	the	DET
ejpam-6069	2	12	second	second	ADJ
ejpam-6069	2	13	kind	kind	NOUN
ejpam-6069	2	14	to	to	ADP
ejpam-6069	2	15	complex	complex	ADJ
ejpam-6069	2	16	arguments	argument	NOUN
ejpam-6069	2	17	.	.	PUNCT
ejpam-6069	3	1	this	this	DET
ejpam-6069	3	2	extension	extension	NOUN
ejpam-6069	3	3	is	be	AUX
ejpam-6069	3	4	achieved	achieve	VERB
ejpam-6069	3	5	through	through	ADP
ejpam-6069	3	6	an	an	DET
ejpam-6069	3	7	integral	integral	ADJ
ejpam-6069	3	8	representation	representation	NOUN
ejpam-6069	3	9	employing	employ	VERB
ejpam-6069	3	10	a	a	DET
ejpam-6069	3	11	hankel	hankel	NOUN
ejpam-6069	3	12	contour	contour	NOUN
ejpam-6069	3	13	.	.	PUNCT
ejpam-6069	4	1	furthermore	furthermore	ADV
ejpam-6069	4	2	,	,	PUNCT
ejpam-6069	4	3	we	we	PRON
ejpam-6069	4	4	investigate	investigate	VERB
ejpam-6069	4	5	the	the	DET
ejpam-6069	4	6	extent	extent	NOUN
ejpam-6069	4	7	to	to	PART
ejpam-6069	4	8	which	which	PRON
ejpam-6069	4	9	key	key	ADJ
ejpam-6069	4	10	properties	property	NOUN
ejpam-6069	4	11	,	,	PUNCT
ejpam-6069	4	12	including	include	VERB
ejpam-6069	4	13	the	the	DET
ejpam-6069	4	14	recurrence	recurrence	NOUN
ejpam-6069	4	15	relations	relation	NOUN
ejpam-6069	4	16	,	,	PUNCT
ejpam-6069	4	17	of	of	ADP
ejpam-6069	4	18	the	the	DET
ejpam-6069	4	19	classical	classical	ADJ
ejpam-6069	4	20	stirling	stirling	NOUN
ejpam-6069	4	21	numbers	number	NOUN
ejpam-6069	4	22	are	be	AUX
ejpam-6069	4	23	preserved	preserve	VERB
ejpam-6069	4	24	under	under	ADP
ejpam-6069	4	25	this	this	DET
ejpam-6069	4	26	complex	complex	ADJ
ejpam-6069	4	27	generalization	generalization	NOUN
ejpam-6069	4	28	.	.	PUNCT
ejpam-6069	5	1	2020	2020	NUM
ejpam-6069	5	2	mathematics	mathematic	NOUN
ejpam-6069	5	3	subject	subject	NOUN
ejpam-6069	5	4	classifications	classification	NOUN
ejpam-6069	5	5	:	:	PUNCT
ejpam-6069	5	6	05a15	05a15	NUM
ejpam-6069	5	7	,	,	PUNCT
ejpam-6069	5	8	05a18	05a18	NUM
ejpam-6069	5	9	,	,	PUNCT
ejpam-6069	5	10	30c15	30c15	NUM
ejpam-6069	5	11	key	key	ADJ
ejpam-6069	5	12	words	word	NOUN
ejpam-6069	5	13	and	and	CCONJ
ejpam-6069	5	14	phrases	phrase	NOUN
ejpam-6069	5	15	:	:	PUNCT
ejpam-6069	5	16	classical	classical	ADJ
ejpam-6069	5	17	stirling	stirling	NOUN
ejpam-6069	5	18	numbers	number	NOUN
ejpam-6069	5	19	,	,	PUNCT
ejpam-6069	5	20	non	non	ADJ
ejpam-6069	5	21	-	-	ADJ
ejpam-6069	5	22	central	central	ADJ
ejpam-6069	5	23	stirling	stirling	NOUN
ejpam-6069	5	24	numbers	number	NOUN
ejpam-6069	5	25	,	,	PUNCT
ejpam-6069	5	26	complex	complex	ADJ
ejpam-6069	5	27	numbers	number	NOUN
ejpam-6069	5	28	1	1	NUM
ejpam-6069	5	29	.	.	PUNCT
ejpam-6069	6	1	introduction	introduction	NOUN
ejpam-6069	6	2	stirling	stirling	NOUN
ejpam-6069	6	3	numbers	number	NOUN
ejpam-6069	6	4	have	have	AUX
ejpam-6069	6	5	long	long	ADV
ejpam-6069	6	6	been	be	AUX
ejpam-6069	6	7	a	a	DET
ejpam-6069	6	8	fundamental	fundamental	ADJ
ejpam-6069	6	9	concept	concept	NOUN
ejpam-6069	6	10	in	in	ADP
ejpam-6069	6	11	combinatorics	combinatoric	NOUN
ejpam-6069	6	12	,	,	PUNCT
ejpam-6069	6	13	originally	originally	ADV
ejpam-6069	6	14	defined	define	VERB
ejpam-6069	6	15	for	for	ADP
ejpam-6069	6	16	non	non	ADJ
ejpam-6069	6	17	-	-	ADJ
ejpam-6069	6	18	negative	negative	ADJ
ejpam-6069	6	19	integers	integer	NOUN
ejpam-6069	6	20	.	.	PUNCT
ejpam-6069	7	1	these	these	DET
ejpam-6069	7	2	numbers	number	NOUN
ejpam-6069	7	3	play	play	VERB
ejpam-6069	7	4	a	a	DET
ejpam-6069	7	5	crucial	crucial	ADJ
ejpam-6069	7	6	role	role	NOUN
ejpam-6069	7	7	in	in	ADP
ejpam-6069	7	8	counting	count	VERB
ejpam-6069	7	9	permutations	permutation	NOUN
ejpam-6069	7	10	,	,	PUNCT
ejpam-6069	7	11	partitions	partition	NOUN
ejpam-6069	7	12	,	,	PUNCT
ejpam-6069	7	13	and	and	CCONJ
ejpam-6069	7	14	other	other	ADJ
ejpam-6069	7	15	combinatorial	combinatorial	ADJ
ejpam-6069	7	16	structures	structure	NOUN
ejpam-6069	7	17	.	.	PUNCT
ejpam-6069	8	1	however	however	ADV
ejpam-6069	8	2	,	,	PUNCT
ejpam-6069	8	3	their	their	PRON
ejpam-6069	8	4	application	application	NOUN
ejpam-6069	8	5	has	have	AUX
ejpam-6069	8	6	typically	typically	ADV
ejpam-6069	8	7	been	be	AUX
ejpam-6069	8	8	limited	limit	VERB
ejpam-6069	8	9	to	to	PART
ejpam-6069	8	10	discrete	discrete	VERB
ejpam-6069	8	11	contexts	contexts	NOUN
ejpam-6069	8	12	.	.	PUNCT
ejpam-6069	9	1	extending	extend	VERB
ejpam-6069	9	2	stirling	stirling	NOUN
ejpam-6069	9	3	numbers	number	NOUN
ejpam-6069	9	4	to	to	ADP
ejpam-6069	9	5	real	real	ADJ
ejpam-6069	9	6	and	and	CCONJ
ejpam-6069	9	7	complex	complex	ADJ
ejpam-6069	9	8	arguments	argument	NOUN
ejpam-6069	9	9	not	not	PART
ejpam-6069	9	10	only	only	ADV
ejpam-6069	9	11	generalizes	generalize	VERB
ejpam-6069	9	12	many	many	ADJ
ejpam-6069	9	13	well	well	ADV
ejpam-6069	9	14	-	-	PUNCT
ejpam-6069	9	15	known	know	VERB
ejpam-6069	9	16	combinatorial	combinatorial	ADJ
ejpam-6069	9	17	identities	identity	NOUN
ejpam-6069	9	18	but	but	CCONJ
ejpam-6069	9	19	also	also	ADV
ejpam-6069	9	20	significantly	significantly	ADV
ejpam-6069	9	21	broadens	broaden	VERB
ejpam-6069	9	22	their	their	PRON
ejpam-6069	9	23	applicability	applicability	NOUN
ejpam-6069	9	24	across	across	ADP
ejpam-6069	9	25	a	a	DET
ejpam-6069	9	26	wide	wide	ADJ
ejpam-6069	9	27	array	array	NOUN
ejpam-6069	9	28	of	of	ADP
ejpam-6069	9	29	mathematical	mathematical	ADJ
ejpam-6069	9	30	fields	field	NOUN
ejpam-6069	9	31	.	.	PUNCT
ejpam-6069	10	1	in	in	ADP
ejpam-6069	10	2	[	[	X
ejpam-6069	10	3	1	1	NUM
ejpam-6069	10	4	]	]	PUNCT
ejpam-6069	10	5	,	,	PUNCT
ejpam-6069	10	6	koutras	koutra	NOUN
ejpam-6069	10	7	introduced	introduce	VERB
ejpam-6069	10	8	the	the	DET
ejpam-6069	10	9	non	non	ADJ
ejpam-6069	10	10	-	-	ADJ
ejpam-6069	10	11	central	central	ADJ
ejpam-6069	10	12	stirling	stirling	NOUN
ejpam-6069	10	13	numbers	number	NOUN
ejpam-6069	10	14	of	of	ADP
ejpam-6069	10	15	the	the	DET
ejpam-6069	10	16	second	second	ADJ
ejpam-6069	10	17	kind	kind	NOUN
ejpam-6069	10	18	by	by	ADP
ejpam-6069	10	19	a	a	DET
ejpam-6069	10	20	natural	natural	ADJ
ejpam-6069	10	21	extension	extension	NOUN
ejpam-6069	10	22	of	of	ADP
ejpam-6069	10	23	the	the	DET
ejpam-6069	10	24	definition	definition	NOUN
ejpam-6069	10	25	of	of	ADP
ejpam-6069	10	26	the	the	DET
ejpam-6069	10	27	classical	classical	ADJ
ejpam-6069	10	28	stirling	stirling	NOUN
ejpam-6069	10	29	numbers	number	NOUN
ejpam-6069	10	30	of	of	ADP
ejpam-6069	10	31	the	the	DET
ejpam-6069	10	32	second	second	ADJ
ejpam-6069	10	33	kind	kind	NOUN
ejpam-6069	10	34	,	,	PUNCT
ejpam-6069	10	35	s(n	s(n	PROPN
ejpam-6069	10	36	,	,	PUNCT
ejpam-6069	10	37	k	k	NOUN
ejpam-6069	10	38	)	)	PUNCT
ejpam-6069	10	39	.	.	PUNCT
ejpam-6069	11	1	the	the	DET
ejpam-6069	11	2	non	non	ADJ
ejpam-6069	11	3	-	-	ADJ
ejpam-6069	11	4	central	central	ADJ
ejpam-6069	11	5	stirling	stirling	NOUN
ejpam-6069	11	6	numbers	number	NOUN
ejpam-6069	11	7	of	of	ADP
ejpam-6069	11	8	the	the	DET
ejpam-6069	11	9	second	second	ADJ
ejpam-6069	11	10	kind	kind	NOUN
ejpam-6069	11	11	,	,	PUNCT
ejpam-6069	11	12	denoted	denote	VERB
ejpam-6069	11	13	by	by	ADP
ejpam-6069	11	14	sa(n	sa(n	PROPN
ejpam-6069	11	15	,	,	PUNCT
ejpam-6069	11	16	k	k	NOUN
ejpam-6069	11	17	)	)	PUNCT
ejpam-6069	11	18	are	be	AUX
ejpam-6069	11	19	defined	define	VERB
ejpam-6069	11	20	as	as	ADP
ejpam-6069	11	21	the	the	DET
ejpam-6069	11	22	coefficients	coefficient	NOUN
ejpam-6069	11	23	of	of	ADP
ejpam-6069	11	24	the	the	DET
ejpam-6069	11	25	following	follow	VERB
ejpam-6069	11	26	expansion	expansion	NOUN
ejpam-6069	11	27	with	with	ADP
ejpam-6069	11	28	parameter	parameter	PROPN
ejpam-6069	11	29	a	a	PROPN
ejpam-6069	11	30	,	,	PUNCT
ejpam-6069	11	31	(	(	PUNCT
ejpam-6069	11	32	t−	t−	PROPN
ejpam-6069	11	33	a)n	a)n	NOUN
ejpam-6069	11	34	=	=	SYM
ejpam-6069	11	35	n∑	n∑	PROPN
ejpam-6069	11	36	k=0	k=0	PROPN
ejpam-6069	11	37	sa(n	sa(n	PROPN
ejpam-6069	11	38	,	,	PUNCT
ejpam-6069	11	39	k)(t)n	k)(t)n	PUNCT
ejpam-6069	11	40	∗corresponding	∗corresponde	VERB
ejpam-6069	11	41	author	author	NOUN
ejpam-6069	11	42	.	.	PUNCT
ejpam-6069	12	1	doi	doi	NOUN
ejpam-6069	12	2	:	:	PUNCT
ejpam-6069	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6069	https://doi.org/10.29020/nybg.ejpam.v18i2.6069	PROPN
ejpam-6069	12	4	email	email	NOUN
ejpam-6069	12	5	addresses	address	NOUN
ejpam-6069	12	6	:	:	PUNCT
ejpam-6069	12	7	enarlan@carsu.edu.ph	enarlan@carsu.edu.ph	PROPN
ejpam-6069	12	8	(	(	PUNCT
ejpam-6069	12	9	e.	e.	PROPN
ejpam-6069	12	10	n.	n.	PROPN
ejpam-6069	12	11	arlan	arlan	PROPN
ejpam-6069	12	12	)	)	PUNCT
ejpam-6069	12	13	,	,	PUNCT
ejpam-6069	12	14	maribeth.montero@msumain.edu.ph	maribeth.montero@msumain.edu.ph	PROPN
ejpam-6069	12	15	(	(	PUNCT
ejpam-6069	12	16	m.	m.	PROPN
ejpam-6069	12	17	b.	b.	PROPN
ejpam-6069	12	18	montero	montero	PROPN
ejpam-6069	12	19	)	)	PUNCT
ejpam-6069	12	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6069	13	1	1	1	NUM
ejpam-6069	13	2	copyright	copyright	NOUN
ejpam-6069	13	3	:	:	PUNCT
ejpam-6069	13	4	©	©	PROPN
ejpam-6069	13	5	2025	2025	NUM
ejpam-6069	13	6	the	the	DET
ejpam-6069	13	7	author(s	author(s	NOUN
ejpam-6069	13	8	)	)	PUNCT
ejpam-6069	13	9	.	.	PUNCT
ejpam-6069	14	1	(	(	PUNCT
ejpam-6069	14	2	cc	cc	NOUN
ejpam-6069	14	3	by	by	ADP
ejpam-6069	14	4	-	-	PUNCT
ejpam-6069	14	5	nc	nc	PROPN
ejpam-6069	14	6	4.0	4.0	NUM
ejpam-6069	14	7	)	)	PUNCT
ejpam-6069	14	8	e.n	e.n	PROPN
ejpam-6069	14	9	.	.	PROPN
ejpam-6069	14	10	arlan	arlan	PROPN
ejpam-6069	14	11	,	,	PUNCT
ejpam-6069	14	12	m.b	m.b	PROPN
ejpam-6069	14	13	.	.	PROPN
ejpam-6069	14	14	montero	montero	PROPN
ejpam-6069	14	15	/	/	SYM
ejpam-6069	14	16	eur	eur	PROPN
ejpam-6069	14	17	.	.	PUNCT
ejpam-6069	15	1	j.	j.	PROPN
ejpam-6069	15	2	pure	pure	PROPN
ejpam-6069	15	3	appl	appl	PROPN
ejpam-6069	15	4	.	.	PROPN
ejpam-6069	15	5	math	math	PROPN
ejpam-6069	15	6	,	,	PUNCT
ejpam-6069	15	7	18	18	NUM
ejpam-6069	15	8	(	(	PUNCT
ejpam-6069	15	9	2	2	NUM
ejpam-6069	15	10	)	)	PUNCT
ejpam-6069	15	11	(	(	PUNCT
ejpam-6069	15	12	2025	2025	NUM
ejpam-6069	15	13	)	)	PUNCT
ejpam-6069	15	14	,	,	PUNCT
ejpam-6069	15	15	6069	6069	NUM
ejpam-6069	15	16	2	2	NUM
ejpam-6069	15	17	of	of	ADP
ejpam-6069	15	18	10	10	NUM
ejpam-6069	15	19	where	where	SCONJ
ejpam-6069	15	20	(	(	PUNCT
ejpam-6069	15	21	t)n	t)n	NOUN
ejpam-6069	15	22	is	be	AUX
ejpam-6069	15	23	the	the	DET
ejpam-6069	15	24	falling	fall	VERB
ejpam-6069	15	25	factorial	factorial	NOUN
ejpam-6069	15	26	of	of	ADP
ejpam-6069	15	27	t	t	NOUN
ejpam-6069	15	28	of	of	ADP
ejpam-6069	15	29	order	order	NOUN
ejpam-6069	15	30	n	n	CCONJ
ejpam-6069	15	31	given	give	VERB
ejpam-6069	15	32	by	by	ADP
ejpam-6069	15	33	(	(	PUNCT
ejpam-6069	15	34	t)n	t)n	NOUN
ejpam-6069	15	35	=	=	PUNCT
ejpam-6069	15	36	n∏	n∏	PROPN
ejpam-6069	15	37	i=1	i=1	PROPN
ejpam-6069	15	38	(	(	PUNCT
ejpam-6069	15	39	t−	t−	PROPN
ejpam-6069	15	40	i+	i+	NOUN
ejpam-6069	15	41	1	1	NUM
ejpam-6069	15	42	)	)	PUNCT
ejpam-6069	15	43	=	=	SYM
ejpam-6069	16	1	t(t−	t(t−	PROPN
ejpam-6069	16	2	1)(t−	1)(t−	NUM
ejpam-6069	16	3	2	2	NUM
ejpam-6069	16	4	)	)	PUNCT
ejpam-6069	16	5	·	·	PUNCT
ejpam-6069	16	6	·	·	PUNCT
ejpam-6069	16	7	·	·	PUNCT
ejpam-6069	17	1	(	(	PUNCT
ejpam-6069	17	2	t−	t−	PROPN
ejpam-6069	17	3	n+	n+	PUNCT
ejpam-6069	17	4	1	1	NUM
ejpam-6069	17	5	)	)	PUNCT
ejpam-6069	17	6	,	,	PUNCT
ejpam-6069	17	7	for	for	ADP
ejpam-6069	17	8	n	n	PRON
ejpam-6069	17	9	≥	≥	NOUN
ejpam-6069	17	10	1	1	NUM
ejpam-6069	17	11	;	;	PUNCT
ejpam-6069	17	12	(	(	PUNCT
ejpam-6069	17	13	t)0	t)0	X
ejpam-6069	17	14	=	=	SYM
ejpam-6069	17	15	1	1	NUM
ejpam-6069	17	16	and	and	CCONJ
ejpam-6069	17	17	sa(0	sa(0	PROPN
ejpam-6069	17	18	,	,	PUNCT
ejpam-6069	17	19	0	0	NUM
ejpam-6069	17	20	)	)	PUNCT
ejpam-6069	17	21	=	=	SYM
ejpam-6069	17	22	1	1	NUM
ejpam-6069	17	23	,	,	PUNCT
ejpam-6069	17	24	sa(n	sa(n	ADV
ejpam-6069	17	25	,	,	PUNCT
ejpam-6069	17	26	0	0	NUM
ejpam-6069	17	27	)	)	PUNCT
ejpam-6069	17	28	=	=	SYM
ejpam-6069	17	29	(	(	PUNCT
ejpam-6069	17	30	−a)n	−a)n	NOUN
ejpam-6069	17	31	and	and	CCONJ
ejpam-6069	17	32	sa(0	sa(0	PROPN
ejpam-6069	17	33	,	,	PUNCT
ejpam-6069	17	34	k	k	NOUN
ejpam-6069	17	35	)	)	PUNCT
ejpam-6069	17	36	=	=	SYM
ejpam-6069	17	37	0	0	NUM
ejpam-6069	17	38	,	,	PUNCT
ejpam-6069	17	39	n	n	CCONJ
ejpam-6069	17	40	,	,	PUNCT
ejpam-6069	17	41	k	k	PROPN
ejpam-6069	17	42	̸=	̸=	PROPN
ejpam-6069	17	43	0	0	NUM
ejpam-6069	17	44	.	.	PUNCT
ejpam-6069	17	45	note	note	VERB
ejpam-6069	17	46	that	that	SCONJ
ejpam-6069	17	47	if	if	SCONJ
ejpam-6069	17	48	a	a	DET
ejpam-6069	17	49	=	=	SYM
ejpam-6069	17	50	0	0	NUM
ejpam-6069	17	51	,	,	PUNCT
ejpam-6069	17	52	the	the	DET
ejpam-6069	17	53	classical	classical	ADJ
ejpam-6069	17	54	stirling	stirling	NOUN
ejpam-6069	17	55	numbers	number	NOUN
ejpam-6069	17	56	,	,	PUNCT
ejpam-6069	17	57	s(n	s(n	PROPN
ejpam-6069	17	58	,	,	PUNCT
ejpam-6069	17	59	k	k	NOUN
ejpam-6069	17	60	)	)	PUNCT
ejpam-6069	17	61	,	,	PUNCT
ejpam-6069	17	62	are	be	AUX
ejpam-6069	17	63	obtained	obtain	VERB
ejpam-6069	17	64	.	.	PUNCT
ejpam-6069	18	1	this	this	DET
ejpam-6069	18	2	definition	definition	NOUN
ejpam-6069	18	3	leads	lead	VERB
ejpam-6069	18	4	to	to	ADP
ejpam-6069	18	5	an	an	DET
ejpam-6069	18	6	alternative	alternative	ADJ
ejpam-6069	18	7	definition	definition	NOUN
ejpam-6069	18	8	in	in	ADP
ejpam-6069	18	9	terms	term	NOUN
ejpam-6069	18	10	of	of	ADP
ejpam-6069	18	11	exponential	exponential	ADJ
ejpam-6069	18	12	generating	generating	NOUN
ejpam-6069	18	13	functions	function	NOUN
ejpam-6069	18	14	which	which	PRON
ejpam-6069	18	15	allows	allow	VERB
ejpam-6069	18	16	for	for	ADP
ejpam-6069	18	17	further	further	ADJ
ejpam-6069	18	18	extensions	extension	NOUN
ejpam-6069	18	19	to	to	ADP
ejpam-6069	18	20	generalized	generalize	VERB
ejpam-6069	18	21	non	non	ADJ
ejpam-6069	18	22	-	-	ADJ
ejpam-6069	18	23	central	central	ADJ
ejpam-6069	18	24	stirling	stirling	NOUN
ejpam-6069	18	25	numbers	number	NOUN
ejpam-6069	18	26	.	.	PUNCT
ejpam-6069	19	1	motivated	motivate	VERB
ejpam-6069	19	2	by	by	ADP
ejpam-6069	19	3	the	the	DET
ejpam-6069	19	4	problem	problem	NOUN
ejpam-6069	19	5	of	of	ADP
ejpam-6069	19	6	graham	graham	PROPN
ejpam-6069	19	7	,	,	PUNCT
ejpam-6069	19	8	knuth	knuth	PROPN
ejpam-6069	19	9	,	,	PUNCT
ejpam-6069	19	10	and	and	CCONJ
ejpam-6069	19	11	patashnik	patashnik	ADJ
ejpam-6069	19	12	,	,	PUNCT
ejpam-6069	19	13	in	in	ADP
ejpam-6069	19	14	[	[	PUNCT
ejpam-6069	19	15	2	2	NUM
ejpam-6069	19	16	]	]	PUNCT
ejpam-6069	19	17	,	,	PUNCT
ejpam-6069	19	18	that	that	ADV
ejpam-6069	19	19	is	is	ADV
ejpam-6069	19	20	,	,	PUNCT
ejpam-6069	19	21	to	to	PART
ejpam-6069	19	22	generalize	generalize	VERB
ejpam-6069	19	23	stirling	stirling	NOUN
ejpam-6069	19	24	numbers	number	NOUN
ejpam-6069	19	25	of	of	ADP
ejpam-6069	19	26	the	the	DET
ejpam-6069	19	27	second	second	ADJ
ejpam-6069	19	28	kind	kind	NOUN
ejpam-6069	19	29	s(n	s(n	PROPN
ejpam-6069	19	30	,	,	PUNCT
ejpam-6069	19	31	k	k	NOUN
ejpam-6069	19	32	)	)	PUNCT
ejpam-6069	19	33	by	by	ADP
ejpam-6069	19	34	extending	extend	VERB
ejpam-6069	19	35	the	the	DET
ejpam-6069	19	36	range	range	NOUN
ejpam-6069	19	37	values	value	NOUN
ejpam-6069	19	38	of	of	ADP
ejpam-6069	19	39	parameters	parameter	NOUN
ejpam-6069	19	40	n	n	CCONJ
ejpam-6069	19	41	and	and	CCONJ
ejpam-6069	19	42	k	k	X
ejpam-6069	19	43	to	to	ADP
ejpam-6069	19	44	complex	complex	ADJ
ejpam-6069	19	45	numbers	number	NOUN
ejpam-6069	19	46	,	,	PUNCT
ejpam-6069	19	47	flajolet	flajolet	NOUN
ejpam-6069	19	48	and	and	CCONJ
ejpam-6069	19	49	prodinger	prodinger	NOUN
ejpam-6069	19	50	,	,	PUNCT
ejpam-6069	19	51	in	in	ADP
ejpam-6069	19	52	[	[	X
ejpam-6069	19	53	3	3	NUM
ejpam-6069	19	54	]	]	PUNCT
ejpam-6069	19	55	,	,	PUNCT
ejpam-6069	19	56	defined	define	VERB
ejpam-6069	19	57	an	an	DET
ejpam-6069	19	58	extension	extension	NOUN
ejpam-6069	19	59	of	of	ADP
ejpam-6069	19	60	the	the	DET
ejpam-6069	19	61	classical	classical	ADJ
ejpam-6069	19	62	stirling	stirling	NOUN
ejpam-6069	19	63	numbers	number	NOUN
ejpam-6069	19	64	s(n	s(n	PROPN
ejpam-6069	19	65	,	,	PUNCT
ejpam-6069	19	66	k	k	NOUN
ejpam-6069	19	67	)	)	PUNCT
ejpam-6069	19	68	of	of	ADP
ejpam-6069	19	69	the	the	DET
ejpam-6069	19	70	second	second	ADJ
ejpam-6069	19	71	kind	kind	NOUN
ejpam-6069	19	72	to	to	ADP
ejpam-6069	19	73	complex	complex	ADJ
ejpam-6069	19	74	arguments	argument	NOUN
ejpam-6069	19	75	.	.	PUNCT
ejpam-6069	20	1	they	they	PRON
ejpam-6069	20	2	established	establish	VERB
ejpam-6069	20	3	an	an	DET
ejpam-6069	20	4	alternative	alternative	ADJ
ejpam-6069	20	5	and	and	CCONJ
ejpam-6069	20	6	more	more	ADV
ejpam-6069	20	7	natural	natural	ADJ
ejpam-6069	20	8	extension	extension	NOUN
ejpam-6069	20	9	of	of	ADP
ejpam-6069	20	10	stirling	stirling	NOUN
ejpam-6069	20	11	numbers	number	NOUN
ejpam-6069	20	12	of	of	ADP
ejpam-6069	20	13	complex	complex	ADJ
ejpam-6069	20	14	arguments	argument	NOUN
ejpam-6069	20	15	for	for	ADP
ejpam-6069	20	16	which	which	PRON
ejpam-6069	20	17	most	most	ADJ
ejpam-6069	20	18	classical	classical	ADJ
ejpam-6069	20	19	identities	identity	NOUN
ejpam-6069	20	20	are	be	AUX
ejpam-6069	20	21	still	still	ADV
ejpam-6069	20	22	satisfied	satisfied	ADJ
ejpam-6069	20	23	.	.	PUNCT
ejpam-6069	21	1	some	some	PRON
ejpam-6069	21	2	of	of	ADP
ejpam-6069	21	3	these	these	DET
ejpam-6069	21	4	properties	property	NOUN
ejpam-6069	21	5	are	be	AUX
ejpam-6069	21	6	listed	list	VERB
ejpam-6069	21	7	here	here	ADV
ejpam-6069	21	8	.	.	PUNCT
ejpam-6069	22	1	i	i	PRON
ejpam-6069	22	2	)	)	PUNCT
ejpam-6069	22	3	the	the	DET
ejpam-6069	22	4	stirling	stirling	PROPN
ejpam-6069	22	5	numbers	number	NOUN
ejpam-6069	22	6	s(x	s(x	PROPN
ejpam-6069	22	7	,	,	PUNCT
ejpam-6069	22	8	y	y	PROPN
ejpam-6069	22	9	)	)	PUNCT
ejpam-6069	22	10	of	of	ADP
ejpam-6069	22	11	the	the	DET
ejpam-6069	22	12	second	second	ADJ
ejpam-6069	22	13	kind	kind	NOUN
ejpam-6069	22	14	for	for	ADP
ejpam-6069	22	15	complex	complex	ADJ
ejpam-6069	22	16	arguments	argument	NOUN
ejpam-6069	22	17	satisfy	satisfy	VERB
ejpam-6069	22	18	the	the	DET
ejpam-6069	22	19	following	follow	VERB
ejpam-6069	22	20	recurrence	recurrence	NOUN
ejpam-6069	22	21	relation	relation	NOUN
ejpam-6069	22	22	s(x	s(x	PROPN
ejpam-6069	22	23	,	,	PUNCT
ejpam-6069	22	24	y	y	NOUN
ejpam-6069	22	25	)	)	PUNCT
ejpam-6069	22	26	=	=	SYM
ejpam-6069	23	1	s(x−	s(x−	X
ejpam-6069	23	2	1	1	NUM
ejpam-6069	23	3	,	,	PUNCT
ejpam-6069	23	4	y	y	PROPN
ejpam-6069	23	5	−	−	PROPN
ejpam-6069	23	6	1	1	NUM
ejpam-6069	23	7	)	)	PUNCT
ejpam-6069	23	8	+	+	NUM
ejpam-6069	23	9	ys(x−	ys(x−	NOUN
ejpam-6069	23	10	1	1	NUM
ejpam-6069	23	11	,	,	PUNCT
ejpam-6069	23	12	y	y	PROPN
ejpam-6069	23	13	)	)	PUNCT
ejpam-6069	23	14	.	.	PUNCT
ejpam-6069	24	1	ii	ii	PROPN
ejpam-6069	24	2	)	)	PUNCT
ejpam-6069	24	3	for	for	ADP
ejpam-6069	24	4	any	any	DET
ejpam-6069	24	5	complex	complex	ADJ
ejpam-6069	24	6	x	x	X
ejpam-6069	24	7	and	and	CCONJ
ejpam-6069	24	8	n	n	CCONJ
ejpam-6069	24	9	∈	∈	PROPN
ejpam-6069	24	10	n	n	CCONJ
ejpam-6069	24	11	,	,	PUNCT
ejpam-6069	24	12	we	we	PRON
ejpam-6069	24	13	have	have	VERB
ejpam-6069	24	14	the	the	DET
ejpam-6069	24	15	following	follow	VERB
ejpam-6069	24	16	formula	formula	NOUN
ejpam-6069	24	17	s(x	s(x	PROPN
ejpam-6069	24	18	,	,	PUNCT
ejpam-6069	24	19	k	k	X
ejpam-6069	24	20	)	)	PUNCT
ejpam-6069	24	21	=	=	SYM
ejpam-6069	24	22	1	1	NUM
ejpam-6069	24	23	k	k	X
ejpam-6069	24	24	!	!	PUNCT
ejpam-6069	24	25	k∑	k∑	PROPN
ejpam-6069	25	1	j=1	j=1	NOUN
ejpam-6069	25	2	(	(	PUNCT
ejpam-6069	25	3	k	k	PROPN
ejpam-6069	25	4	j	j	PROPN
ejpam-6069	25	5	)	)	PUNCT
ejpam-6069	25	6	(	(	PUNCT
ejpam-6069	25	7	−1)k−jjx	−1)k−jjx	X
ejpam-6069	25	8	.	.	PUNCT
ejpam-6069	25	9	thus	thus	ADV
ejpam-6069	25	10	,	,	PUNCT
ejpam-6069	25	11	following	follow	VERB
ejpam-6069	25	12	the	the	DET
ejpam-6069	25	13	work	work	NOUN
ejpam-6069	25	14	of	of	ADP
ejpam-6069	25	15	flajolet	flajolet	NOUN
ejpam-6069	25	16	and	and	CCONJ
ejpam-6069	25	17	prodinger	prodinger	NOUN
ejpam-6069	25	18	,	,	PUNCT
ejpam-6069	25	19	it	it	PRON
ejpam-6069	25	20	is	be	AUX
ejpam-6069	25	21	interesting	interesting	ADJ
ejpam-6069	25	22	if	if	SCONJ
ejpam-6069	25	23	we	we	PRON
ejpam-6069	25	24	could	could	AUX
ejpam-6069	25	25	extend	extend	VERB
ejpam-6069	25	26	non	non	ADJ
ejpam-6069	25	27	-	-	ADJ
ejpam-6069	25	28	central	central	ADJ
ejpam-6069	25	29	stirling	stirling	NOUN
ejpam-6069	25	30	numbers	number	NOUN
ejpam-6069	25	31	of	of	ADP
ejpam-6069	25	32	the	the	DET
ejpam-6069	25	33	second	second	ADJ
ejpam-6069	25	34	kind	kind	NOUN
ejpam-6069	25	35	to	to	ADP
ejpam-6069	25	36	complex	complex	ADJ
ejpam-6069	25	37	arguments	argument	NOUN
ejpam-6069	25	38	.	.	PUNCT
ejpam-6069	26	1	2	2	X
ejpam-6069	26	2	.	.	X
ejpam-6069	26	3	preliminaries	preliminary	NOUN
ejpam-6069	26	4	this	this	DET
ejpam-6069	26	5	section	section	NOUN
ejpam-6069	26	6	covers	cover	VERB
ejpam-6069	26	7	fundamental	fundamental	ADJ
ejpam-6069	26	8	concepts	concept	NOUN
ejpam-6069	26	9	and	and	CCONJ
ejpam-6069	26	10	results	result	NOUN
ejpam-6069	26	11	in	in	ADP
ejpam-6069	26	12	complex	complex	ADJ
ejpam-6069	26	13	analysis	analysis	NOUN
ejpam-6069	26	14	and	and	CCONJ
ejpam-6069	26	15	combinatorics	combinatoric	NOUN
ejpam-6069	26	16	,	,	PUNCT
ejpam-6069	26	17	including	include	VERB
ejpam-6069	26	18	the	the	DET
ejpam-6069	26	19	binomial	binomial	ADJ
ejpam-6069	26	20	theorem	theorem	NOUN
ejpam-6069	26	21	,	,	PUNCT
ejpam-6069	26	22	which	which	PRON
ejpam-6069	26	23	will	will	AUX
ejpam-6069	26	24	be	be	AUX
ejpam-6069	26	25	applied	apply	VERB
ejpam-6069	26	26	in	in	ADP
ejpam-6069	26	27	the	the	DET
ejpam-6069	26	28	later	later	ADJ
ejpam-6069	26	29	section	section	NOUN
ejpam-6069	26	30	.	.	PUNCT
ejpam-6069	27	1	these	these	DET
ejpam-6069	27	2	results	result	NOUN
ejpam-6069	27	3	can	can	AUX
ejpam-6069	27	4	be	be	AUX
ejpam-6069	27	5	found	find	VERB
ejpam-6069	27	6	in	in	ADP
ejpam-6069	27	7	[	[	X
ejpam-6069	27	8	4	4	NUM
ejpam-6069	27	9	]	]	PUNCT
ejpam-6069	27	10	,	,	PUNCT
ejpam-6069	27	11	[	[	X
ejpam-6069	27	12	5	5	NUM
ejpam-6069	27	13	]	]	PUNCT
ejpam-6069	27	14	,	,	PUNCT
ejpam-6069	27	15	[	[	X
ejpam-6069	27	16	6	6	NUM
ejpam-6069	27	17	]	]	PUNCT
ejpam-6069	27	18	,	,	PUNCT
ejpam-6069	27	19	[	[	X
ejpam-6069	27	20	7	7	NUM
ejpam-6069	27	21	]	]	PUNCT
ejpam-6069	27	22	,	,	PUNCT
ejpam-6069	27	23	and	and	CCONJ
ejpam-6069	27	24	[	[	X
ejpam-6069	27	25	8	8	NUM
ejpam-6069	27	26	]	]	PUNCT
ejpam-6069	27	27	.	.	PUNCT
ejpam-6069	28	1	lemma	lemma	PROPN
ejpam-6069	28	2	1	1	NUM
ejpam-6069	28	3	.	.	PUNCT
ejpam-6069	29	1	[	[	X
ejpam-6069	29	2	4	4	X
ejpam-6069	29	3	]	]	PUNCT
ejpam-6069	29	4	for	for	ADP
ejpam-6069	29	5	any	any	DET
ejpam-6069	29	6	integer	integer	NOUN
ejpam-6069	29	7	n	n	PRON
ejpam-6069	29	8	≥	≥	NOUN
ejpam-6069	29	9	0	0	NUM
ejpam-6069	29	10	,	,	PUNCT
ejpam-6069	29	11	we	we	PRON
ejpam-6069	29	12	have	have	VERB
ejpam-6069	29	13	(	(	PUNCT
ejpam-6069	29	14	x+	x+	X
ejpam-6069	29	15	y)n	y)n	VERB
ejpam-6069	30	1	=	=	SYM
ejpam-6069	30	2	n∑	n∑	NOUN
ejpam-6069	30	3	r=0	r=0	PROPN
ejpam-6069	30	4	(	(	PUNCT
ejpam-6069	30	5	n	n	NOUN
ejpam-6069	30	6	r	r	NOUN
ejpam-6069	30	7	)	)	PUNCT
ejpam-6069	30	8	xn−ryr	xn−ryr	INTJ
ejpam-6069	30	9	.	.	PUNCT
ejpam-6069	31	1	e.n	e.n	PROPN
ejpam-6069	31	2	.	.	PROPN
ejpam-6069	31	3	arlan	arlan	PROPN
ejpam-6069	31	4	,	,	PUNCT
ejpam-6069	31	5	m.b	m.b	PROPN
ejpam-6069	31	6	.	.	PROPN
ejpam-6069	31	7	montero	montero	PROPN
ejpam-6069	31	8	/	/	SYM
ejpam-6069	31	9	eur	eur	PROPN
ejpam-6069	31	10	.	.	PUNCT
ejpam-6069	32	1	j.	j.	PROPN
ejpam-6069	32	2	pure	pure	PROPN
ejpam-6069	32	3	appl	appl	PROPN
ejpam-6069	32	4	.	.	PROPN
ejpam-6069	32	5	math	math	PROPN
ejpam-6069	32	6	,	,	PUNCT
ejpam-6069	32	7	18	18	NUM
ejpam-6069	32	8	(	(	PUNCT
ejpam-6069	32	9	2	2	NUM
ejpam-6069	32	10	)	)	PUNCT
ejpam-6069	32	11	(	(	PUNCT
ejpam-6069	32	12	2025	2025	NUM
ejpam-6069	32	13	)	)	PUNCT
ejpam-6069	32	14	,	,	PUNCT
ejpam-6069	32	15	6069	6069	NUM
ejpam-6069	32	16	3	3	NUM
ejpam-6069	32	17	of	of	ADP
ejpam-6069	32	18	10	10	NUM
ejpam-6069	32	19	the	the	DET
ejpam-6069	32	20	number	number	NOUN
ejpam-6069	32	21	(	(	PUNCT
ejpam-6069	32	22	n	n	NOUN
ejpam-6069	32	23	r	r	NOUN
ejpam-6069	32	24	)	)	PUNCT
ejpam-6069	32	25	is	be	AUX
ejpam-6069	32	26	called	call	VERB
ejpam-6069	32	27	a	a	DET
ejpam-6069	32	28	binomial	binomial	ADJ
ejpam-6069	32	29	coefficient	coefficient	NOUN
ejpam-6069	32	30	and	and	CCONJ
ejpam-6069	32	31	satisfies	satisfy	VERB
ejpam-6069	32	32	the	the	DET
ejpam-6069	32	33	following	follow	VERB
ejpam-6069	32	34	recurrence	recurrence	NOUN
ejpam-6069	32	35	relation	relation	NOUN
ejpam-6069	32	36	(	(	PUNCT
ejpam-6069	32	37	n	n	NOUN
ejpam-6069	32	38	r	r	NOUN
ejpam-6069	32	39	)	)	PUNCT
ejpam-6069	33	1	=	=	PUNCT
ejpam-6069	33	2	(	(	PUNCT
ejpam-6069	33	3	n−	n−	NOUN
ejpam-6069	33	4	1	1	NUM
ejpam-6069	33	5	r	r	NOUN
ejpam-6069	33	6	)	)	PUNCT
ejpam-6069	34	1	+	+	CCONJ
ejpam-6069	34	2	(	(	PUNCT
ejpam-6069	34	3	n−	n−	NOUN
ejpam-6069	34	4	1	1	NUM
ejpam-6069	34	5	r	r	NOUN
ejpam-6069	34	6	−	−	NOUN
ejpam-6069	34	7	1	1	NUM
ejpam-6069	34	8	)	)	PUNCT
ejpam-6069	34	9	.	.	PUNCT
ejpam-6069	35	1	the	the	DET
ejpam-6069	35	2	following	follow	VERB
ejpam-6069	35	3	is	be	AUX
ejpam-6069	35	4	the	the	DET
ejpam-6069	35	5	generalized	generalized	ADJ
ejpam-6069	35	6	binomial	binomial	ADJ
ejpam-6069	35	7	theorem	theorem	NOUN
ejpam-6069	35	8	due	due	ADP
ejpam-6069	35	9	to	to	ADP
ejpam-6069	35	10	newton	newton	PROPN
ejpam-6069	35	11	.	.	PUNCT
ejpam-6069	36	1	lemma	lemma	PROPN
ejpam-6069	36	2	2	2	NUM
ejpam-6069	36	3	.	.	PUNCT
ejpam-6069	37	1	[	[	X
ejpam-6069	37	2	4	4	X
ejpam-6069	37	3	]	]	X
ejpam-6069	37	4	for	for	ADP
ejpam-6069	37	5	complex	complex	ADJ
ejpam-6069	37	6	numbers	number	NOUN
ejpam-6069	37	7	x	x	NOUN
ejpam-6069	37	8	,	,	PUNCT
ejpam-6069	37	9	y	y	PROPN
ejpam-6069	37	10	,	,	PUNCT
ejpam-6069	37	11	and	and	CCONJ
ejpam-6069	37	12	s	s	X
ejpam-6069	37	13	,	,	PUNCT
ejpam-6069	37	14	we	we	PRON
ejpam-6069	37	15	have	have	VERB
ejpam-6069	37	16	(	(	PUNCT
ejpam-6069	37	17	x+	x+	X
ejpam-6069	37	18	y)s	y)s	X
ejpam-6069	37	19	=	=	SYM
ejpam-6069	37	20	∞∑	∞∑	NUM
ejpam-6069	37	21	r=0	r=0	PROPN
ejpam-6069	37	22	(	(	PUNCT
ejpam-6069	37	23	s	s	NOUN
ejpam-6069	37	24	r	r	NOUN
ejpam-6069	37	25	)	)	PUNCT
ejpam-6069	37	26	xs−ryr	xs−ryr	PROPN
ejpam-6069	37	27	,	,	PUNCT
ejpam-6069	38	1	where	where	SCONJ
ejpam-6069	38	2	(	(	PUNCT
ejpam-6069	38	3	s	s	NOUN
ejpam-6069	38	4	r	r	NOUN
ejpam-6069	38	5	)	)	PUNCT
ejpam-6069	38	6	=	=	PUNCT
ejpam-6069	38	7			PROPN
ejpam-6069	38	8	1	1	NUM
ejpam-6069	38	9	,	,	PUNCT
ejpam-6069	38	10	r	r	NOUN
ejpam-6069	38	11	=	=	SYM
ejpam-6069	38	12	0	0	SYM
ejpam-6069	38	13	s(s−	s(s−	PROPN
ejpam-6069	38	14	1)(s−	1)(s−	NUM
ejpam-6069	38	15	2	2	NUM
ejpam-6069	38	16	)	)	PUNCT
ejpam-6069	38	17	·	·	PUNCT
ejpam-6069	38	18	·	·	PUNCT
ejpam-6069	38	19	·	·	PUNCT
ejpam-6069	38	20	(	(	PUNCT
ejpam-6069	38	21	s−	s−	NOUN
ejpam-6069	38	22	r	r	NOUN
ejpam-6069	38	23	+	+	NOUN
ejpam-6069	38	24	1	1	NUM
ejpam-6069	38	25	)	)	PUNCT
ejpam-6069	38	26	r	r	NOUN
ejpam-6069	38	27	!	!	NOUN
ejpam-6069	38	28	,	,	PUNCT
ejpam-6069	38	29	r	r	NOUN
ejpam-6069	38	30	>	>	X
ejpam-6069	38	31	0	0	NUM
ejpam-6069	38	32	.	.	PUNCT
ejpam-6069	39	1	moreover	moreover	ADV
ejpam-6069	39	2	,	,	PUNCT
ejpam-6069	39	3	the	the	DET
ejpam-6069	39	4	gamma	gamma	NOUN
ejpam-6069	39	5	function	function	NOUN
ejpam-6069	39	6	is	be	AUX
ejpam-6069	39	7	being	be	AUX
ejpam-6069	39	8	considered	consider	VERB
ejpam-6069	39	9	.	.	PUNCT
ejpam-6069	40	1	this	this	DET
ejpam-6069	40	2	function	function	NOUN
ejpam-6069	40	3	is	be	AUX
ejpam-6069	40	4	known	know	VERB
ejpam-6069	40	5	to	to	PART
ejpam-6069	40	6	be	be	AUX
ejpam-6069	40	7	related	relate	VERB
ejpam-6069	40	8	to	to	ADP
ejpam-6069	40	9	stirling	stirling	NOUN
ejpam-6069	40	10	-	-	PUNCT
ejpam-6069	40	11	type	type	NOUN
ejpam-6069	40	12	numbers	number	NOUN
ejpam-6069	40	13	.	.	PUNCT
ejpam-6069	41	1	the	the	DET
ejpam-6069	41	2	gamma	gamma	PROPN
ejpam-6069	41	3	function	function	NOUN
ejpam-6069	41	4	[	[	X
ejpam-6069	41	5	7	7	NUM
ejpam-6069	41	6	]	]	PUNCT
ejpam-6069	41	7	,	,	PUNCT
ejpam-6069	41	8	denoted	denote	VERB
ejpam-6069	41	9	by	by	ADP
ejpam-6069	41	10	γ	γ	NOUN
ejpam-6069	41	11	,	,	PUNCT
ejpam-6069	41	12	is	be	AUX
ejpam-6069	41	13	an	an	DET
ejpam-6069	41	14	extension	extension	NOUN
ejpam-6069	41	15	of	of	ADP
ejpam-6069	41	16	the	the	DET
ejpam-6069	41	17	factorial	factorial	ADJ
ejpam-6069	41	18	function	function	NOUN
ejpam-6069	41	19	to	to	ADP
ejpam-6069	41	20	real	real	ADJ
ejpam-6069	41	21	and	and	CCONJ
ejpam-6069	41	22	complex	complex	ADJ
ejpam-6069	41	23	numbers	number	NOUN
ejpam-6069	41	24	defined	define	VERB
ejpam-6069	41	25	via	via	ADP
ejpam-6069	41	26	improper	improper	ADJ
ejpam-6069	41	27	integral	integral	NOUN
ejpam-6069	41	28	that	that	SCONJ
ejpam-6069	41	29	converges	converge	VERB
ejpam-6069	41	30	only	only	ADV
ejpam-6069	41	31	for	for	ADP
ejpam-6069	41	32	complex	complex	ADJ
ejpam-6069	41	33	numbers	number	NOUN
ejpam-6069	41	34	with	with	ADP
ejpam-6069	41	35	a	a	DET
ejpam-6069	41	36	positive	positive	ADJ
ejpam-6069	41	37	real	real	ADJ
ejpam-6069	41	38	part	part	NOUN
ejpam-6069	41	39	.	.	PUNCT
ejpam-6069	42	1	that	that	PRON
ejpam-6069	42	2	is	be	AUX
ejpam-6069	42	3	,	,	PUNCT
ejpam-6069	42	4	γ(z	γ(z	ADJ
ejpam-6069	42	5	)	)	PUNCT
ejpam-6069	42	6	=	=	SYM
ejpam-6069	43	1	∫	∫	PROPN
ejpam-6069	43	2	∞	∞	PROPN
ejpam-6069	43	3	0	0	NUM
ejpam-6069	44	1	tz−1e−tdt	tz−1e−tdt	ADJ
ejpam-6069	44	2	,	,	PUNCT
ejpam-6069	44	3	where	where	SCONJ
ejpam-6069	44	4	re(z	re(z	NOUN
ejpam-6069	44	5	)	)	PUNCT
ejpam-6069	44	6	>	>	X
ejpam-6069	45	1	0	0	X
ejpam-6069	45	2	.	.	PUNCT
ejpam-6069	46	1	when	when	SCONJ
ejpam-6069	46	2	z	z	NOUN
ejpam-6069	46	3	=	=	SYM
ejpam-6069	46	4	1	1	NUM
ejpam-6069	46	5	,	,	PUNCT
ejpam-6069	46	6	γ(1	γ(1	PROPN
ejpam-6069	46	7	)	)	PUNCT
ejpam-6069	46	8	=	=	SYM
ejpam-6069	46	9	∫	∫	PROPN
ejpam-6069	46	10	∞	∞	PROPN
ejpam-6069	46	11	0	0	NUM
ejpam-6069	46	12	e−tdt	e−tdt	NOUN
ejpam-6069	46	13	=	=	NOUN
ejpam-6069	46	14	1	1	X
ejpam-6069	46	15	.	.	PUNCT
ejpam-6069	46	16	when	when	SCONJ
ejpam-6069	46	17	z	z	NOUN
ejpam-6069	46	18	=	=	SYM
ejpam-6069	46	19	n	n	SYM
ejpam-6069	46	20	∈	∈	PROPN
ejpam-6069	46	21	z+	z+	NUM
ejpam-6069	46	22	,	,	PUNCT
ejpam-6069	46	23	we	we	PRON
ejpam-6069	46	24	use	use	VERB
ejpam-6069	46	25	integraton	integraton	NOUN
ejpam-6069	46	26	by	by	ADP
ejpam-6069	46	27	parts	part	NOUN
ejpam-6069	46	28	and	and	CCONJ
ejpam-6069	46	29	get	get	VERB
ejpam-6069	46	30	γ(n	γ(n	NUM
ejpam-6069	46	31	)	)	PUNCT
ejpam-6069	47	1	=	=	SYM
ejpam-6069	47	2	(	(	PUNCT
ejpam-6069	47	3	n−	n−	NOUN
ejpam-6069	47	4	1	1	NUM
ejpam-6069	47	5	)	)	PUNCT
ejpam-6069	47	6	∫	∫	PROPN
ejpam-6069	47	7	∞	∞	PROPN
ejpam-6069	47	8	0	0	NUM
ejpam-6069	47	9	tn−2e−tdt	tn−2e−tdt	NOUN
ejpam-6069	47	10	.	.	PUNCT
ejpam-6069	48	1	consequently	consequently	ADV
ejpam-6069	48	2	,	,	PUNCT
ejpam-6069	48	3	after	after	ADP
ejpam-6069	48	4	applying	apply	VERB
ejpam-6069	48	5	integration	integration	NOUN
ejpam-6069	48	6	by	by	ADP
ejpam-6069	48	7	parts	part	NOUN
ejpam-6069	48	8	(	(	PUNCT
ejpam-6069	48	9	n−	n−	NOUN
ejpam-6069	48	10	1	1	NUM
ejpam-6069	48	11	)	)	PUNCT
ejpam-6069	48	12	times	time	NOUN
ejpam-6069	48	13	,	,	PUNCT
ejpam-6069	48	14	we	we	PRON
ejpam-6069	48	15	obtain	obtain	VERB
ejpam-6069	48	16	γ(n	γ(n	X
ejpam-6069	48	17	)	)	PUNCT
ejpam-6069	49	1	=	=	PUNCT
ejpam-6069	49	2	(	(	PUNCT
ejpam-6069	49	3	n−	n−	NOUN
ejpam-6069	49	4	1)(n−	1)(n−	NOUN
ejpam-6069	49	5	2	2	NUM
ejpam-6069	49	6	)	)	PUNCT
ejpam-6069	49	7	·	·	PUNCT
ejpam-6069	49	8	·	·	PUNCT
ejpam-6069	49	9	·	·	PUNCT
ejpam-6069	49	10	(	(	PUNCT
ejpam-6069	49	11	1	1	X
ejpam-6069	49	12	)	)	PUNCT
ejpam-6069	49	13	∫	∫	PROPN
ejpam-6069	50	1	∞	∞	PROPN
ejpam-6069	50	2	0	0	NUM
ejpam-6069	50	3	e−tdt	e−tdt	NOUN
ejpam-6069	50	4	=	=	PUNCT
ejpam-6069	50	5	(	(	PUNCT
ejpam-6069	50	6	n−	n−	NOUN
ejpam-6069	50	7	1	1	NUM
ejpam-6069	50	8	)	)	PUNCT
ejpam-6069	50	9	!	!	PUNCT
ejpam-6069	50	10	.	.	PUNCT
ejpam-6069	51	1	this	this	PRON
ejpam-6069	51	2	shows	show	VERB
ejpam-6069	51	3	that	that	SCONJ
ejpam-6069	51	4	γ(z	γ(z	PROPN
ejpam-6069	51	5	)	)	PUNCT
ejpam-6069	51	6	is	be	AUX
ejpam-6069	51	7	indeed	indeed	ADV
ejpam-6069	51	8	an	an	DET
ejpam-6069	51	9	extension	extension	NOUN
ejpam-6069	51	10	of	of	ADP
ejpam-6069	51	11	the	the	DET
ejpam-6069	51	12	factorial	factorial	ADJ
ejpam-6069	51	13	function	function	NOUN
ejpam-6069	51	14	with	with	ADP
ejpam-6069	51	15	its	its	PRON
ejpam-6069	51	16	argument	argument	NOUN
ejpam-6069	51	17	shifted	shift	VERB
ejpam-6069	51	18	down	down	ADP
ejpam-6069	51	19	by	by	ADP
ejpam-6069	51	20	1	1	NUM
ejpam-6069	51	21	.	.	PUNCT
ejpam-6069	52	1	the	the	DET
ejpam-6069	52	2	following	follow	VERB
ejpam-6069	52	3	theorem	theorem	NOUN
ejpam-6069	52	4	is	be	AUX
ejpam-6069	52	5	a	a	DET
ejpam-6069	52	6	property	property	NOUN
ejpam-6069	52	7	of	of	ADP
ejpam-6069	52	8	the	the	DET
ejpam-6069	52	9	gamma	gamma	NOUN
ejpam-6069	52	10	function	function	NOUN
ejpam-6069	52	11	.	.	PUNCT
ejpam-6069	53	1	e.n	e.n	PROPN
ejpam-6069	53	2	.	.	PROPN
ejpam-6069	53	3	arlan	arlan	PROPN
ejpam-6069	53	4	,	,	PUNCT
ejpam-6069	53	5	m.b	m.b	PROPN
ejpam-6069	53	6	.	.	PROPN
ejpam-6069	53	7	montero	montero	PROPN
ejpam-6069	53	8	/	/	SYM
ejpam-6069	53	9	eur	eur	PROPN
ejpam-6069	53	10	.	.	PUNCT
ejpam-6069	54	1	j.	j.	PROPN
ejpam-6069	54	2	pure	pure	PROPN
ejpam-6069	54	3	appl	appl	PROPN
ejpam-6069	54	4	.	.	PROPN
ejpam-6069	54	5	math	math	PROPN
ejpam-6069	54	6	,	,	PUNCT
ejpam-6069	54	7	18	18	NUM
ejpam-6069	54	8	(	(	PUNCT
ejpam-6069	54	9	2	2	NUM
ejpam-6069	54	10	)	)	PUNCT
ejpam-6069	54	11	(	(	PUNCT
ejpam-6069	54	12	2025	2025	NUM
ejpam-6069	54	13	)	)	PUNCT
ejpam-6069	54	14	,	,	PUNCT
ejpam-6069	54	15	6069	6069	NUM
ejpam-6069	54	16	4	4	NUM
ejpam-6069	54	17	of	of	ADP
ejpam-6069	54	18	10	10	NUM
ejpam-6069	54	19	lemma	lemma	PROPN
ejpam-6069	54	20	3	3	NUM
ejpam-6069	54	21	.	.	PUNCT
ejpam-6069	55	1	[	[	X
ejpam-6069	55	2	9	9	NUM
ejpam-6069	55	3	]	]	PUNCT
ejpam-6069	55	4	the	the	DET
ejpam-6069	55	5	gamma	gamma	PROPN
ejpam-6069	55	6	function	function	PROPN
ejpam-6069	55	7	γ(z	γ(z	PROPN
ejpam-6069	55	8	)	)	PUNCT
ejpam-6069	55	9	has	have	VERB
ejpam-6069	55	10	an	an	DET
ejpam-6069	55	11	integral	integral	ADJ
ejpam-6069	55	12	representation	representation	NOUN
ejpam-6069	55	13	1	1	NUM
ejpam-6069	55	14	γ(z	γ(z	PROPN
ejpam-6069	55	15	)	)	PUNCT
ejpam-6069	55	16	=	=	SYM
ejpam-6069	55	17	1	1	NUM
ejpam-6069	55	18	2πi	2πi	ADJ
ejpam-6069	55	19	∫	∫	PROPN
ejpam-6069	55	20	γ	γ	X
ejpam-6069	55	21	ett−zdt	ett−zdt	PROPN
ejpam-6069	55	22	,	,	PUNCT
ejpam-6069	55	23	where	where	SCONJ
ejpam-6069	55	24	γ	γ	PROPN
ejpam-6069	55	25	is	be	AUX
ejpam-6069	55	26	a	a	DET
ejpam-6069	55	27	hankel	hankel	NOUN
ejpam-6069	55	28	contour	contour	NOUN
ejpam-6069	55	29	.	.	PUNCT
ejpam-6069	56	1	the	the	DET
ejpam-6069	56	2	preceding	precede	VERB
ejpam-6069	56	3	formula	formula	NOUN
ejpam-6069	56	4	is	be	AUX
ejpam-6069	56	5	known	know	VERB
ejpam-6069	56	6	as	as	ADP
ejpam-6069	56	7	hankel	hankel	NOUN
ejpam-6069	56	8	’s	’s	PART
ejpam-6069	56	9	contour	contour	NOUN
ejpam-6069	56	10	integral	integral	NOUN
ejpam-6069	56	11	.	.	PUNCT
ejpam-6069	57	1	the	the	DET
ejpam-6069	57	2	path	path	NOUN
ejpam-6069	57	3	of	of	ADP
ejpam-6069	57	4	integration	integration	NOUN
ejpam-6069	57	5	γ	γ	PROPN
ejpam-6069	57	6	starts	start	VERB
ejpam-6069	57	7	at	at	ADP
ejpam-6069	57	8	−∞	−∞	X
ejpam-6069	57	9	−	−	PROPN
ejpam-6069	57	10	i0	i0	PROPN
ejpam-6069	57	11	on	on	ADP
ejpam-6069	57	12	the	the	DET
ejpam-6069	57	13	real	real	ADJ
ejpam-6069	57	14	axis	axis	NOUN
ejpam-6069	57	15	,	,	PUNCT
ejpam-6069	57	16	goes	go	VERB
ejpam-6069	57	17	to	to	ADP
ejpam-6069	57	18	−ϵ	−ϵ	PROPN
ejpam-6069	57	19	−	−	PROPN
ejpam-6069	57	20	i0	i0	PROPN
ejpam-6069	57	21	,	,	PUNCT
ejpam-6069	57	22	circles	circle	VERB
ejpam-6069	57	23	the	the	DET
ejpam-6069	57	24	origin	origin	NOUN
ejpam-6069	57	25	in	in	ADP
ejpam-6069	57	26	the	the	DET
ejpam-6069	57	27	counterclockwise	counterclockwise	NOUN
ejpam-6069	57	28	direction	direction	NOUN
ejpam-6069	57	29	with	with	ADP
ejpam-6069	57	30	the	the	DET
ejpam-6069	57	31	radius	radius	NOUN
ejpam-6069	57	32	ϵ	ϵ	X
ejpam-6069	57	33	to	to	ADP
ejpam-6069	57	34	the	the	DET
ejpam-6069	57	35	point	point	NOUN
ejpam-6069	57	36	−ϵ+i0	−ϵ+i0	PUNCT
ejpam-6069	57	37	and	and	CCONJ
ejpam-6069	57	38	returns	return	VERB
ejpam-6069	57	39	to	to	ADP
ejpam-6069	57	40	the	the	DET
ejpam-6069	57	41	point	point	NOUN
ejpam-6069	57	42	−∞+i0	−∞+i0	PROPN
ejpam-6069	57	43	.	.	PUNCT
ejpam-6069	58	1	before	before	ADP
ejpam-6069	58	2	presenting	present	VERB
ejpam-6069	58	3	the	the	DET
ejpam-6069	58	4	main	main	ADJ
ejpam-6069	58	5	result	result	NOUN
ejpam-6069	58	6	,	,	PUNCT
ejpam-6069	58	7	we	we	PRON
ejpam-6069	58	8	introduce	introduce	VERB
ejpam-6069	58	9	the	the	DET
ejpam-6069	58	10	following	follow	VERB
ejpam-6069	58	11	lemma	lemma	PROPN
ejpam-6069	58	12	,	,	PUNCT
ejpam-6069	58	13	an	an	DET
ejpam-6069	58	14	original	original	ADJ
ejpam-6069	58	15	contribution	contribution	NOUN
ejpam-6069	58	16	by	by	ADP
ejpam-6069	58	17	the	the	DET
ejpam-6069	58	18	author	author	NOUN
ejpam-6069	58	19	,	,	PUNCT
ejpam-6069	58	20	which	which	PRON
ejpam-6069	58	21	plays	play	VERB
ejpam-6069	58	22	an	an	DET
ejpam-6069	58	23	important	important	ADJ
ejpam-6069	58	24	role	role	NOUN
ejpam-6069	58	25	in	in	ADP
ejpam-6069	58	26	establishing	establish	VERB
ejpam-6069	58	27	several	several	ADJ
ejpam-6069	58	28	fundamental	fundamental	ADJ
ejpam-6069	58	29	properties	property	NOUN
ejpam-6069	58	30	of	of	ADP
ejpam-6069	58	31	non	non	ADJ
ejpam-6069	58	32	-	-	ADJ
ejpam-6069	58	33	central	central	ADJ
ejpam-6069	58	34	stirling	stirling	NOUN
ejpam-6069	58	35	numbers	number	NOUN
ejpam-6069	58	36	with	with	ADP
ejpam-6069	58	37	complex	complex	ADJ
ejpam-6069	58	38	indices	index	NOUN
ejpam-6069	58	39	.	.	PUNCT
ejpam-6069	59	1	lemma	lemma	PROPN
ejpam-6069	59	2	4	4	NUM
ejpam-6069	59	3	.	.	X
ejpam-6069	59	4	for	for	ADP
ejpam-6069	59	5	complex	complex	ADJ
ejpam-6069	59	6	numbers	number	NOUN
ejpam-6069	59	7	x	x	PUNCT
ejpam-6069	59	8	and	and	CCONJ
ejpam-6069	59	9	a	a	PRON
ejpam-6069	59	10	with	with	ADP
ejpam-6069	59	11	re(a	re(a	NOUN
ejpam-6069	59	12	)	)	PUNCT
ejpam-6069	59	13	<	<	X
ejpam-6069	59	14	0	0	NUM
ejpam-6069	59	15	,	,	PUNCT
ejpam-6069	59	16	we	we	PRON
ejpam-6069	59	17	have	have	AUX
ejpam-6069	59	18	x	x	NOUN
ejpam-6069	60	1	!	!	PUNCT
ejpam-6069	60	2	2πi	2πi	ADJ
ejpam-6069	60	3	∫	∫	PROPN
ejpam-6069	61	1	h	h	PROPN
ejpam-6069	61	2	e(j−a)u	e(j−a)u	NOUN
ejpam-6069	61	3	du	du	PROPN
ejpam-6069	61	4	ux+1	ux+1	PROPN
ejpam-6069	61	5	=	=	PUNCT
ejpam-6069	61	6	(	(	PUNCT
ejpam-6069	61	7	j	j	PROPN
ejpam-6069	61	8	−	−	PROPN
ejpam-6069	61	9	a)x	a)x	PUNCT
ejpam-6069	61	10	.	.	PUNCT
ejpam-6069	62	1	proof	proof	NOUN
ejpam-6069	62	2	.	.	PUNCT
ejpam-6069	63	1	let	let	VERB
ejpam-6069	63	2	s	s	VERB
ejpam-6069	63	3	=	=	PUNCT
ejpam-6069	63	4	x+	x+	SYM
ejpam-6069	63	5	1	1	NUM
ejpam-6069	63	6	and	and	CCONJ
ejpam-6069	63	7	t	t	NOUN
ejpam-6069	63	8	=	=	SYM
ejpam-6069	63	9	(	(	PUNCT
ejpam-6069	63	10	j	j	PROPN
ejpam-6069	63	11	−	−	PROPN
ejpam-6069	63	12	a)u	a)u	VERB
ejpam-6069	63	13	.	.	PUNCT
ejpam-6069	64	1	then	then	ADV
ejpam-6069	64	2	u	u	X
ejpam-6069	64	3	=	=	PUNCT
ejpam-6069	64	4	(	(	PUNCT
ejpam-6069	64	5	j	j	PROPN
ejpam-6069	64	6	−	−	PROPN
ejpam-6069	64	7	a)−1	a)−1	NOUN
ejpam-6069	64	8	t	t	PROPN
ejpam-6069	64	9	and	and	CCONJ
ejpam-6069	64	10	du	du	PROPN
ejpam-6069	64	11	=	=	SYM
ejpam-6069	64	12	(	(	PUNCT
ejpam-6069	64	13	j	j	PROPN
ejpam-6069	64	14	−	−	PROPN
ejpam-6069	64	15	a)−1dt	a)−1dt	NOUN
ejpam-6069	64	16	.	.	PUNCT
ejpam-6069	65	1	hence	hence	ADV
ejpam-6069	65	2	,	,	PUNCT
ejpam-6069	65	3	x	x	X
ejpam-6069	65	4	!	!	PUNCT
ejpam-6069	65	5	2πi	2πi	ADJ
ejpam-6069	65	6	∫	∫	PROPN
ejpam-6069	65	7	h	h	PROPN
ejpam-6069	65	8	e(j−a)u	e(j−a)u	NOUN
ejpam-6069	65	9	du	du	PROPN
ejpam-6069	65	10	ux+1	ux+1	PROPN
ejpam-6069	65	11	=	=	PUNCT
ejpam-6069	65	12	(	(	PUNCT
ejpam-6069	65	13	j	j	NOUN
ejpam-6069	65	14	−	−	PROPN
ejpam-6069	65	15	a)s−1	a)s−1	NOUN
ejpam-6069	65	16	(	(	PUNCT
ejpam-6069	65	17	s−	s−	PROPN
ejpam-6069	65	18	1	1	NUM
ejpam-6069	65	19	)	)	PUNCT
ejpam-6069	65	20	!	!	PUNCT
ejpam-6069	66	1	2πi	2πi	ADJ
ejpam-6069	66	2	∫	∫	PROPN
ejpam-6069	66	3	h	h	NOUN
ejpam-6069	66	4	t−setdt	t−setdt	X
ejpam-6069	67	1	=	=	PUNCT
ejpam-6069	67	2	(	(	PUNCT
ejpam-6069	67	3	j	j	NOUN
ejpam-6069	67	4	−	−	PROPN
ejpam-6069	67	5	a)s−1γ(s	a)s−1γ(	NOUN
ejpam-6069	67	6	)	)	PUNCT
ejpam-6069	68	1	2πi	2πi	NOUN
ejpam-6069	68	2	∫	∫	PROPN
ejpam-6069	68	3	h	h	PROPN
ejpam-6069	69	1	t−setdt	t−setdt	PROPN
ejpam-6069	69	2	.	.	PUNCT
ejpam-6069	70	1	however	however	ADV
ejpam-6069	70	2	,	,	PUNCT
ejpam-6069	70	3	by	by	ADP
ejpam-6069	70	4	lemma	lemma	PROPN
ejpam-6069	70	5	3	3	NUM
ejpam-6069	70	6	,	,	PUNCT
ejpam-6069	70	7	γ(s	γ(s	PROPN
ejpam-6069	70	8	)	)	PUNCT
ejpam-6069	70	9	2πi	2πi	NOUN
ejpam-6069	70	10	∫	∫	PROPN
ejpam-6069	70	11	h	h	NOUN
ejpam-6069	71	1	t−setdt	t−setdt	X
ejpam-6069	71	2	=	=	PUNCT
ejpam-6069	71	3	1	1	X
ejpam-6069	71	4	.	.	PUNCT
ejpam-6069	71	5	thus	thus	ADV
ejpam-6069	71	6	,	,	PUNCT
ejpam-6069	71	7	x	x	X
ejpam-6069	71	8	!	!	PUNCT
ejpam-6069	71	9	2πi	2πi	ADJ
ejpam-6069	71	10	∫	∫	PROPN
ejpam-6069	71	11	h	h	PROPN
ejpam-6069	71	12	e(j−a)u	e(j−a)u	NOUN
ejpam-6069	71	13	du	du	PROPN
ejpam-6069	71	14	ux+1	ux+1	PROPN
ejpam-6069	71	15	=	=	PUNCT
ejpam-6069	71	16	(	(	PUNCT
ejpam-6069	71	17	j	j	PROPN
ejpam-6069	71	18	−	−	PROPN
ejpam-6069	71	19	a)x	a)x	NOUN
ejpam-6069	71	20	.	.	PUNCT
ejpam-6069	72	1	in	in	ADP
ejpam-6069	72	2	the	the	DET
ejpam-6069	72	3	following	following	ADJ
ejpam-6069	72	4	section	section	NOUN
ejpam-6069	72	5	,	,	PUNCT
ejpam-6069	72	6	we	we	PRON
ejpam-6069	72	7	begin	begin	VERB
ejpam-6069	72	8	by	by	ADP
ejpam-6069	72	9	presenting	present	VERB
ejpam-6069	72	10	the	the	DET
ejpam-6069	72	11	definition	definition	NOUN
ejpam-6069	72	12	of	of	ADP
ejpam-6069	72	13	the	the	DET
ejpam-6069	72	14	non	non	ADJ
ejpam-6069	72	15	-	-	ADJ
ejpam-6069	72	16	central	central	ADJ
ejpam-6069	72	17	stirling	stirling	NOUN
ejpam-6069	72	18	numbers	number	NOUN
ejpam-6069	72	19	of	of	ADP
ejpam-6069	72	20	the	the	DET
ejpam-6069	72	21	second	second	ADJ
ejpam-6069	72	22	kind	kind	NOUN
ejpam-6069	72	23	for	for	ADP
ejpam-6069	72	24	complex	complex	ADJ
ejpam-6069	72	25	arguments	argument	NOUN
ejpam-6069	72	26	and	and	CCONJ
ejpam-6069	72	27	establish	establish	VERB
ejpam-6069	72	28	several	several	ADJ
ejpam-6069	72	29	key	key	ADJ
ejpam-6069	72	30	properties	property	NOUN
ejpam-6069	72	31	.	.	PUNCT
ejpam-6069	73	1	this	this	DET
ejpam-6069	73	2	section	section	NOUN
ejpam-6069	73	3	presents	present	VERB
ejpam-6069	73	4	the	the	DET
ejpam-6069	73	5	central	central	ADJ
ejpam-6069	73	6	result	result	NOUN
ejpam-6069	73	7	of	of	ADP
ejpam-6069	73	8	our	our	PRON
ejpam-6069	73	9	work	work	NOUN
ejpam-6069	73	10	,	,	PUNCT
ejpam-6069	73	11	which	which	PRON
ejpam-6069	73	12	we	we	PRON
ejpam-6069	73	13	hope	hope	VERB
ejpam-6069	73	14	will	will	AUX
ejpam-6069	73	15	serve	serve	VERB
ejpam-6069	73	16	as	as	ADP
ejpam-6069	73	17	a	a	DET
ejpam-6069	73	18	foundation	foundation	NOUN
ejpam-6069	73	19	for	for	ADP
ejpam-6069	73	20	further	further	ADJ
ejpam-6069	73	21	analysis	analysis	NOUN
ejpam-6069	73	22	and	and	CCONJ
ejpam-6069	73	23	potential	potential	ADJ
ejpam-6069	73	24	applications	application	NOUN
ejpam-6069	73	25	.	.	PUNCT
ejpam-6069	74	1	e.n	e.n	PROPN
ejpam-6069	74	2	.	.	PROPN
ejpam-6069	74	3	arlan	arlan	PROPN
ejpam-6069	74	4	,	,	PUNCT
ejpam-6069	74	5	m.b	m.b	PROPN
ejpam-6069	74	6	.	.	PROPN
ejpam-6069	74	7	montero	montero	PROPN
ejpam-6069	74	8	/	/	SYM
ejpam-6069	74	9	eur	eur	PROPN
ejpam-6069	74	10	.	.	PUNCT
ejpam-6069	75	1	j.	j.	PROPN
ejpam-6069	75	2	pure	pure	PROPN
ejpam-6069	75	3	appl	appl	PROPN
ejpam-6069	75	4	.	.	PROPN
ejpam-6069	75	5	math	math	PROPN
ejpam-6069	75	6	,	,	PUNCT
ejpam-6069	75	7	18	18	NUM
ejpam-6069	75	8	(	(	PUNCT
ejpam-6069	75	9	2	2	NUM
ejpam-6069	75	10	)	)	PUNCT
ejpam-6069	75	11	(	(	PUNCT
ejpam-6069	75	12	2025	2025	NUM
ejpam-6069	75	13	)	)	PUNCT
ejpam-6069	75	14	,	,	PUNCT
ejpam-6069	75	15	6069	6069	NUM
ejpam-6069	75	16	5	5	NUM
ejpam-6069	75	17	of	of	ADP
ejpam-6069	75	18	10	10	NUM
ejpam-6069	75	19	3	3	NUM
ejpam-6069	75	20	.	.	PUNCT
ejpam-6069	76	1	the	the	DET
ejpam-6069	76	2	non	non	ADJ
ejpam-6069	76	3	-	-	ADJ
ejpam-6069	76	4	central	central	ADJ
ejpam-6069	76	5	stirling	stirling	NOUN
ejpam-6069	76	6	numbers	number	NOUN
ejpam-6069	76	7	with	with	ADP
ejpam-6069	76	8	complex	complex	ADJ
ejpam-6069	76	9	indices	index	NOUN
ejpam-6069	76	10	the	the	DET
ejpam-6069	76	11	exponential	exponential	ADJ
ejpam-6069	76	12	generating	generating	NOUN
ejpam-6069	76	13	funcion	funcion	NOUN
ejpam-6069	76	14	for	for	ADP
ejpam-6069	76	15	sa(n	sa(n	PROPN
ejpam-6069	76	16	,	,	PUNCT
ejpam-6069	76	17	k	k	NOUN
ejpam-6069	76	18	)	)	PUNCT
ejpam-6069	76	19	is	be	AUX
ejpam-6069	76	20	given	give	VERB
ejpam-6069	76	21	by	by	ADP
ejpam-6069	76	22	∞∑	∞∑	NUM
ejpam-6069	76	23	n	n	X
ejpam-6069	76	24	=	=	SYM
ejpam-6069	76	25	k	k	PROPN
ejpam-6069	76	26	sa(n	sa(n	PROPN
ejpam-6069	76	27	,	,	PUNCT
ejpam-6069	76	28	k	k	X
ejpam-6069	76	29	)	)	PUNCT
ejpam-6069	76	30	un	un	PROPN
ejpam-6069	76	31	n	n	PROPN
ejpam-6069	76	32	!	!	PUNCT
ejpam-6069	77	1	=	=	PRON
ejpam-6069	77	2	e−au	e−au	NOUN
ejpam-6069	77	3	1	1	NUM
ejpam-6069	77	4	k	k	X
ejpam-6069	77	5	!	!	PUNCT
ejpam-6069	78	1	(	(	PUNCT
ejpam-6069	78	2	eu	eu	PROPN
ejpam-6069	78	3	−	−	PROPN
ejpam-6069	78	4	1)k	1)k	NUM
ejpam-6069	78	5	.	.	PUNCT
ejpam-6069	79	1	that	that	PRON
ejpam-6069	79	2	is	be	AUX
ejpam-6069	79	3	,	,	PUNCT
ejpam-6069	79	4	∑	∑	ADV
ejpam-6069	79	5	n≥0	n≥0	ADJ
ejpam-6069	79	6	sa(n	sa(n	ADJ
ejpam-6069	79	7	,	,	PUNCT
ejpam-6069	79	8	k	k	NOUN
ejpam-6069	79	9	)	)	PUNCT
ejpam-6069	79	10	k	k	NOUN
ejpam-6069	79	11	!	!	PUNCT
ejpam-6069	80	1	n	n	PROPN
ejpam-6069	80	2	!	!	PROPN
ejpam-6069	80	3	un	un	PROPN
ejpam-6069	81	1	=	=	SYM
ejpam-6069	81	2	e−au(eu	e−au(eu	PROPN
ejpam-6069	81	3	−	−	NOUN
ejpam-6069	81	4	1)k	1)k	NUM
ejpam-6069	81	5	.	.	PUNCT
ejpam-6069	82	1	hence	hence	ADV
ejpam-6069	82	2	,	,	PUNCT
ejpam-6069	82	3	by	by	ADP
ejpam-6069	82	4	cauchy	cauchy	ADJ
ejpam-6069	82	5	integral	integral	ADJ
ejpam-6069	82	6	formula	formula	NOUN
ejpam-6069	82	7	,	,	PUNCT
ejpam-6069	82	8	we	we	PRON
ejpam-6069	82	9	have	have	VERB
ejpam-6069	82	10	sa(n	sa(n	ADV
ejpam-6069	82	11	,	,	PUNCT
ejpam-6069	82	12	k	k	NOUN
ejpam-6069	82	13	)	)	PUNCT
ejpam-6069	82	14	=	=	SYM
ejpam-6069	82	15	1	1	NUM
ejpam-6069	82	16	2πi	2πi	NOUN
ejpam-6069	82	17	n	n	CCONJ
ejpam-6069	82	18	!	!	PUNCT
ejpam-6069	83	1	k	k	AUX
ejpam-6069	83	2	!	!	PUNCT
ejpam-6069	83	3	∫	∫	PROPN
ejpam-6069	83	4	γ	γ	X
ejpam-6069	83	5	e−au(eu	e−au(eu	PROPN
ejpam-6069	83	6	−	−	PROPN
ejpam-6069	84	1	1)kdu	1)kdu	NUM
ejpam-6069	84	2	un+1	un+1	NOUN
ejpam-6069	84	3	,	,	PUNCT
ejpam-6069	84	4	where	where	SCONJ
ejpam-6069	84	5	γ	γ	PROPN
ejpam-6069	84	6	is	be	AUX
ejpam-6069	84	7	a	a	DET
ejpam-6069	84	8	small	small	ADJ
ejpam-6069	84	9	contour	contour	NOUN
ejpam-6069	84	10	encircling	encircle	VERB
ejpam-6069	84	11	the	the	DET
ejpam-6069	84	12	origin	origin	NOUN
ejpam-6069	84	13	.	.	PUNCT
ejpam-6069	85	1	we	we	PRON
ejpam-6069	85	2	can	can	AUX
ejpam-6069	85	3	deform	deform	VERB
ejpam-6069	85	4	γ	γ	NOUN
ejpam-6069	85	5	into	into	ADP
ejpam-6069	85	6	a	a	DET
ejpam-6069	85	7	hankel	hankel	NOUN
ejpam-6069	85	8	contour	contour	NOUN
ejpam-6069	85	9	which	which	PRON
ejpam-6069	85	10	starts	start	VERB
ejpam-6069	85	11	from	from	ADP
ejpam-6069	85	12	−∞	−∞	X
ejpam-6069	85	13	below	below	ADP
ejpam-6069	85	14	the	the	DET
ejpam-6069	85	15	negative	negative	ADJ
ejpam-6069	85	16	x	x	NOUN
ejpam-6069	85	17	−	−	NOUN
ejpam-6069	85	18	axis	axis	NOUN
ejpam-6069	85	19	surrounding	surround	VERB
ejpam-6069	85	20	the	the	DET
ejpam-6069	85	21	origin	origin	NOUN
ejpam-6069	85	22	couterclockwise	couterclockwise	NOUN
ejpam-6069	85	23	and	and	CCONJ
ejpam-6069	85	24	returns	return	VERB
ejpam-6069	85	25	to	to	ADP
ejpam-6069	85	26	−∞	−∞	PUNCT
ejpam-6069	85	27	above	above	ADP
ejpam-6069	85	28	the	the	DET
ejpam-6069	85	29	negative	negative	ADJ
ejpam-6069	85	30	x	x	NOUN
ejpam-6069	85	31	−	−	NOUN
ejpam-6069	85	32	axis	axis	NOUN
ejpam-6069	85	33	.	.	PUNCT
ejpam-6069	86	1	this	this	PRON
ejpam-6069	86	2	suggest	suggest	VERB
ejpam-6069	86	3	the	the	DET
ejpam-6069	86	4	following	follow	VERB
ejpam-6069	86	5	definition	definition	NOUN
ejpam-6069	86	6	.	.	PUNCT
ejpam-6069	87	1	here	here	ADV
ejpam-6069	87	2	,	,	PUNCT
ejpam-6069	87	3	we	we	PRON
ejpam-6069	87	4	assume	assume	VERB
ejpam-6069	87	5	that	that	SCONJ
ejpam-6069	87	6	h	h	NOUN
ejpam-6069	87	7	is	be	AUX
ejpam-6069	87	8	at	at	ADP
ejpam-6069	87	9	a	a	DET
ejpam-6069	87	10	distance	distance	NOUN
ejpam-6069	87	11	≤	≤	NUM
ejpam-6069	87	12	1	1	NUM
ejpam-6069	87	13	from	from	ADP
ejpam-6069	87	14	the	the	DET
ejpam-6069	87	15	real	real	ADJ
ejpam-6069	87	16	axis	axis	NOUN
ejpam-6069	87	17	.	.	PUNCT
ejpam-6069	88	1	definition	definition	NOUN
ejpam-6069	88	2	3.1	3.1	NUM
ejpam-6069	88	3	.	.	PUNCT
ejpam-6069	89	1	the	the	DET
ejpam-6069	89	2	non	non	ADJ
ejpam-6069	89	3	-	-	ADJ
ejpam-6069	89	4	central	central	ADJ
ejpam-6069	89	5	stirling	stirling	NOUN
ejpam-6069	89	6	numbers	number	NOUN
ejpam-6069	89	7	of	of	ADP
ejpam-6069	89	8	the	the	DET
ejpam-6069	89	9	second	second	ADJ
ejpam-6069	89	10	kind	kind	NOUN
ejpam-6069	89	11	with	with	ADP
ejpam-6069	89	12	complex	complex	ADJ
ejpam-6069	89	13	arguments	argument	NOUN
ejpam-6069	89	14	x	x	PUNCT
ejpam-6069	89	15	and	and	CCONJ
ejpam-6069	89	16	y	y	PROPN
ejpam-6069	89	17	,	,	PUNCT
ejpam-6069	89	18	denoted	denote	VERB
ejpam-6069	89	19	by	by	ADP
ejpam-6069	89	20	sa(x	sa(x	NOUN
ejpam-6069	89	21	,	,	PUNCT
ejpam-6069	89	22	y	y	PROPN
ejpam-6069	89	23	)	)	PUNCT
ejpam-6069	89	24	,	,	PUNCT
ejpam-6069	89	25	are	be	AUX
ejpam-6069	89	26	defined	define	VERB
ejpam-6069	89	27	by	by	ADP
ejpam-6069	89	28	sa(x	sa(x	NOUN
ejpam-6069	89	29	,	,	PUNCT
ejpam-6069	89	30	y	y	NOUN
ejpam-6069	89	31	)	)	PUNCT
ejpam-6069	89	32	=	=	SYM
ejpam-6069	90	1	1	1	NUM
ejpam-6069	90	2	2πi	2πi	NOUN
ejpam-6069	90	3	x	x	X
ejpam-6069	90	4	!	!	PUNCT
ejpam-6069	90	5	y	y	PROPN
ejpam-6069	90	6	!	!	PUNCT
ejpam-6069	90	7	∫	∫	PROPN
ejpam-6069	91	1	h	h	PROPN
ejpam-6069	91	2	e−au(eu	e−au(eu	PROPN
ejpam-6069	91	3	−	−	NUM
ejpam-6069	91	4	1)ydu	1)ydu	NUM
ejpam-6069	91	5	ux+1	ux+1	PROPN
ejpam-6069	91	6	,	,	PUNCT
ejpam-6069	91	7	where	where	SCONJ
ejpam-6069	91	8	a	a	PRON
ejpam-6069	91	9	is	be	AUX
ejpam-6069	91	10	a	a	DET
ejpam-6069	91	11	complex	complex	ADJ
ejpam-6069	91	12	number	number	NOUN
ejpam-6069	91	13	with	with	ADP
ejpam-6069	91	14	re(a	re(a	NOUN
ejpam-6069	91	15	)	)	PUNCT
ejpam-6069	91	16	<	<	X
ejpam-6069	91	17	0	0	NUM
ejpam-6069	91	18	,	,	PUNCT
ejpam-6069	91	19	x	x	X
ejpam-6069	91	20	!	!	PUNCT
ejpam-6069	91	21	=	=	PUNCT
ejpam-6069	91	22	γ(x+1	γ(x+1	NOUN
ejpam-6069	91	23	)	)	PUNCT
ejpam-6069	91	24	and	and	CCONJ
ejpam-6069	91	25	the	the	DET
ejpam-6069	91	26	logarithm	logarithm	NOUN
ejpam-6069	91	27	involved	involve	VERB
ejpam-6069	91	28	in	in	ADP
ejpam-6069	91	29	the	the	DET
ejpam-6069	91	30	functions	function	NOUN
ejpam-6069	91	31	(	(	PUNCT
ejpam-6069	91	32	eu	eu	PROPN
ejpam-6069	91	33	−	−	PROPN
ejpam-6069	91	34	1)y	1)y	NUM
ejpam-6069	91	35	and	and	CCONJ
ejpam-6069	91	36	ux+1	ux+1	PROPN
ejpam-6069	91	37	is	be	AUX
ejpam-6069	91	38	taken	take	VERB
ejpam-6069	91	39	to	to	PART
ejpam-6069	91	40	be	be	AUX
ejpam-6069	91	41	the	the	DET
ejpam-6069	91	42	principal	principal	ADJ
ejpam-6069	91	43	branch	branch	NOUN
ejpam-6069	91	44	.	.	PUNCT
ejpam-6069	92	1	following	follow	VERB
ejpam-6069	92	2	this	this	DET
ejpam-6069	92	3	definition	definition	NOUN
ejpam-6069	92	4	,	,	PUNCT
ejpam-6069	92	5	we	we	PRON
ejpam-6069	92	6	explore	explore	VERB
ejpam-6069	92	7	a	a	DET
ejpam-6069	92	8	fundamental	fundamental	ADJ
ejpam-6069	92	9	relationship	relationship	NOUN
ejpam-6069	92	10	that	that	PRON
ejpam-6069	92	11	is	be	AUX
ejpam-6069	92	12	essential	essential	ADJ
ejpam-6069	92	13	to	to	ADP
ejpam-6069	92	14	the	the	DET
ejpam-6069	92	15	theory	theory	NOUN
ejpam-6069	92	16	of	of	ADP
ejpam-6069	92	17	stirling	stirling	NOUN
ejpam-6069	92	18	-	-	PUNCT
ejpam-6069	92	19	type	type	NOUN
ejpam-6069	92	20	numbers	number	NOUN
ejpam-6069	92	21	.	.	PUNCT
ejpam-6069	93	1	the	the	DET
ejpam-6069	93	2	first	first	ADJ
ejpam-6069	93	3	theorem	theorem	NOUN
ejpam-6069	93	4	we	we	PRON
ejpam-6069	93	5	present	present	VERB
ejpam-6069	93	6	establishes	establish	VERB
ejpam-6069	93	7	a	a	DET
ejpam-6069	93	8	relation	relation	NOUN
ejpam-6069	93	9	commonly	commonly	ADV
ejpam-6069	93	10	employed	employ	VERB
ejpam-6069	93	11	to	to	PART
ejpam-6069	93	12	define	define	VERB
ejpam-6069	93	13	these	these	DET
ejpam-6069	93	14	numbers	number	NOUN
ejpam-6069	93	15	.	.	PUNCT
ejpam-6069	94	1	theorem	theorem	VERB
ejpam-6069	94	2	3.1	3.1	NUM
ejpam-6069	94	3	.	.	PUNCT
ejpam-6069	95	1	for	for	ADP
ejpam-6069	95	2	complex	complex	ADJ
ejpam-6069	95	3	numbers	number	NOUN
ejpam-6069	95	4	x	x	PUNCT
ejpam-6069	95	5	and	and	CCONJ
ejpam-6069	95	6	a	a	PRON
ejpam-6069	95	7	with	with	ADP
ejpam-6069	95	8	re(a	re(a	NOUN
ejpam-6069	95	9	)	)	PUNCT
ejpam-6069	95	10	<	<	X
ejpam-6069	95	11	0	0	PROPN
ejpam-6069	95	12	,	,	PUNCT
ejpam-6069	95	13	the	the	DET
ejpam-6069	95	14	non	non	ADJ
ejpam-6069	95	15	-	-	ADJ
ejpam-6069	95	16	central	central	ADJ
ejpam-6069	95	17	stirling	stirling	NOUN
ejpam-6069	95	18	numbers	number	NOUN
ejpam-6069	95	19	for	for	ADP
ejpam-6069	95	20	complex	complex	ADJ
ejpam-6069	95	21	arguments	argument	NOUN
ejpam-6069	95	22	satisfy	satisfy	VERB
ejpam-6069	95	23	the	the	DET
ejpam-6069	95	24	following	follow	VERB
ejpam-6069	95	25	relation	relation	NOUN
ejpam-6069	95	26	:	:	PUNCT
ejpam-6069	95	27	(	(	PUNCT
ejpam-6069	95	28	t−	t−	PROPN
ejpam-6069	95	29	a)x	a)x	PUNCT
ejpam-6069	95	30	=	=	PUNCT
ejpam-6069	96	1	∞∑	∞∑	NUM
ejpam-6069	96	2	k=0	k=0	PROPN
ejpam-6069	96	3	sa(x	sa(x	NOUN
ejpam-6069	96	4	,	,	PUNCT
ejpam-6069	96	5	k)(t)k	k)(t)k	PUNCT
ejpam-6069	96	6	.	.	PUNCT
ejpam-6069	97	1	proof	proof	NOUN
ejpam-6069	97	2	.	.	PUNCT
ejpam-6069	98	1	first	first	ADV
ejpam-6069	98	2	,	,	PUNCT
ejpam-6069	98	3	observe	observe	VERB
ejpam-6069	98	4	that	that	SCONJ
ejpam-6069	98	5	(	(	PUNCT
ejpam-6069	98	6	t)k	t)k	X
ejpam-6069	98	7	=	=	PUNCT
ejpam-6069	99	1	[	[	X
ejpam-6069	99	2	t(t−	t(t−	NUM
ejpam-6069	99	3	1)(t−	1)(t−	NUM
ejpam-6069	99	4	2	2	NUM
ejpam-6069	99	5	)	)	PUNCT
ejpam-6069	99	6	·	·	PUNCT
ejpam-6069	99	7	·	·	PUNCT
ejpam-6069	99	8	·	·	PUNCT
ejpam-6069	99	9	(	(	PUNCT
ejpam-6069	99	10	t−	t−	PROPN
ejpam-6069	99	11	k	k	PROPN
ejpam-6069	99	12	+	+	PROPN
ejpam-6069	99	13	1	1	NUM
ejpam-6069	99	14	)	)	PUNCT
ejpam-6069	99	15	]	]	PUNCT
ejpam-6069	100	1	k	k	X
ejpam-6069	100	2	!	!	PUNCT
ejpam-6069	101	1	k	k	X
ejpam-6069	101	2	!	!	PUNCT
ejpam-6069	102	1	(	(	PUNCT
ejpam-6069	102	2	t−	t−	PROPN
ejpam-6069	102	3	k	k	NOUN
ejpam-6069	102	4	)	)	PUNCT
ejpam-6069	102	5	!	!	PUNCT
ejpam-6069	103	1	(	(	PUNCT
ejpam-6069	103	2	t−	t−	PROPN
ejpam-6069	103	3	k	k	NOUN
ejpam-6069	103	4	)	)	PUNCT
ejpam-6069	103	5	!	!	PUNCT
ejpam-6069	104	1	=	=	PUNCT
ejpam-6069	105	1	k	k	X
ejpam-6069	105	2	!	!	PUNCT
ejpam-6069	106	1	(	(	PUNCT
ejpam-6069	106	2	t	t	PROPN
ejpam-6069	106	3	k	k	PROPN
ejpam-6069	106	4	)	)	PUNCT
ejpam-6069	106	5	.	.	PUNCT
ejpam-6069	107	1	e.n	e.n	PROPN
ejpam-6069	107	2	.	.	PROPN
ejpam-6069	107	3	arlan	arlan	PROPN
ejpam-6069	107	4	,	,	PUNCT
ejpam-6069	107	5	m.b	m.b	PROPN
ejpam-6069	107	6	.	.	PROPN
ejpam-6069	107	7	montero	montero	PROPN
ejpam-6069	107	8	/	/	SYM
ejpam-6069	107	9	eur	eur	PROPN
ejpam-6069	107	10	.	.	PUNCT
ejpam-6069	108	1	j.	j.	PROPN
ejpam-6069	108	2	pure	pure	PROPN
ejpam-6069	108	3	appl	appl	PROPN
ejpam-6069	108	4	.	.	PROPN
ejpam-6069	108	5	math	math	PROPN
ejpam-6069	108	6	,	,	PUNCT
ejpam-6069	108	7	18	18	NUM
ejpam-6069	108	8	(	(	PUNCT
ejpam-6069	108	9	2	2	NUM
ejpam-6069	108	10	)	)	PUNCT
ejpam-6069	108	11	(	(	PUNCT
ejpam-6069	108	12	2025	2025	NUM
ejpam-6069	108	13	)	)	PUNCT
ejpam-6069	108	14	,	,	PUNCT
ejpam-6069	108	15	6069	6069	NUM
ejpam-6069	108	16	6	6	NUM
ejpam-6069	108	17	of	of	ADP
ejpam-6069	108	18	10	10	NUM
ejpam-6069	108	19	now	now	ADV
ejpam-6069	108	20	,	,	PUNCT
ejpam-6069	108	21	applying	apply	VERB
ejpam-6069	108	22	definition	definition	NOUN
ejpam-6069	108	23	3.1	3.1	NUM
ejpam-6069	108	24	,	,	PUNCT
ejpam-6069	108	25	we	we	PRON
ejpam-6069	108	26	get	get	VERB
ejpam-6069	108	27	∞∑	∞∑	NUM
ejpam-6069	108	28	k=0	k=0	PROPN
ejpam-6069	108	29	sa(x	sa(x	NOUN
ejpam-6069	108	30	,	,	PUNCT
ejpam-6069	108	31	k)(t)k	k)(t)k	PUNCT
ejpam-6069	108	32	=	=	SYM
ejpam-6069	108	33	∞∑	∞∑	NUM
ejpam-6069	108	34	k=0	k=0	PROPN
ejpam-6069	108	35	{	{	PUNCT
ejpam-6069	108	36	1	1	NUM
ejpam-6069	108	37	2πi	2πi	NOUN
ejpam-6069	108	38	x	x	X
ejpam-6069	108	39	!	!	PUNCT
ejpam-6069	109	1	k	k	X
ejpam-6069	109	2	!	!	PUNCT
ejpam-6069	109	3	∫	∫	PROPN
ejpam-6069	110	1	h	h	PROPN
ejpam-6069	110	2	e−au(eu	e−au(eu	PROPN
ejpam-6069	111	1	−	−	ADP
ejpam-6069	111	2	1)kdu	1)kdu	NUM
ejpam-6069	111	3	ux+1	ux+1	PROPN
ejpam-6069	111	4	}	}	PUNCT
ejpam-6069	111	5	(	(	PUNCT
ejpam-6069	111	6	t)k	t)k	X
ejpam-6069	111	7	=	=	SYM
ejpam-6069	111	8	x	x	X
ejpam-6069	111	9	!	!	PUNCT
ejpam-6069	111	10	2πi	2πi	ADJ
ejpam-6069	111	11	∫	∫	PROPN
ejpam-6069	112	1	h	h	NOUN
ejpam-6069	112	2	e−au	e−au	NOUN
ejpam-6069	112	3	{	{	PUNCT
ejpam-6069	112	4	∞∑	∞∑	NUM
ejpam-6069	112	5	k=0	k=0	PROPN
ejpam-6069	112	6	(	(	PUNCT
ejpam-6069	112	7	eu	eu	PROPN
ejpam-6069	112	8	−	−	PROPN
ejpam-6069	112	9	1)k	1)k	NUM
ejpam-6069	112	10	k	k	X
ejpam-6069	112	11	!	!	PUNCT
ejpam-6069	112	12	(	(	PUNCT
ejpam-6069	112	13	t)k	t)k	X
ejpam-6069	112	14	}	}	PUNCT
ejpam-6069	112	15	du	du	PROPN
ejpam-6069	112	16	ux+1	ux+1	PROPN
ejpam-6069	112	17	.	.	PUNCT
ejpam-6069	113	1	then	then	ADV
ejpam-6069	113	2	by	by	ADP
ejpam-6069	113	3	the	the	DET
ejpam-6069	113	4	generalized	generalize	VERB
ejpam-6069	113	5	binomial	binomial	ADJ
ejpam-6069	113	6	theorem	theorem	NOUN
ejpam-6069	113	7	due	due	ADP
ejpam-6069	113	8	to	to	ADP
ejpam-6069	113	9	newton	newton	PROPN
ejpam-6069	113	10	,	,	PUNCT
ejpam-6069	113	11	∞∑	∞∑	PROPN
ejpam-6069	113	12	k=0	k=0	PROPN
ejpam-6069	113	13	(	(	PUNCT
ejpam-6069	113	14	eu	eu	PROPN
ejpam-6069	113	15	−	−	PROPN
ejpam-6069	113	16	1)k	1)k	NUM
ejpam-6069	113	17	k	k	X
ejpam-6069	113	18	!	!	PUNCT
ejpam-6069	114	1	(	(	PUNCT
ejpam-6069	114	2	t)k	t)k	X
ejpam-6069	114	3	=	=	PUNCT
ejpam-6069	114	4	∞∑	∞∑	NUM
ejpam-6069	114	5	k=0	k=0	PROPN
ejpam-6069	114	6	(	(	PUNCT
ejpam-6069	114	7	t	t	NOUN
ejpam-6069	114	8	k	k	PROPN
ejpam-6069	114	9	)	)	PUNCT
ejpam-6069	115	1	(	(	PUNCT
ejpam-6069	115	2	eu	eu	PROPN
ejpam-6069	115	3	−	−	PROPN
ejpam-6069	115	4	1)k	1)k	NUM
ejpam-6069	116	1	=	=	SYM
ejpam-6069	117	1	[	[	X
ejpam-6069	117	2	(	(	PUNCT
ejpam-6069	117	3	eu	eu	PROPN
ejpam-6069	117	4	−	−	PROPN
ejpam-6069	117	5	1	1	NUM
ejpam-6069	117	6	)	)	PUNCT
ejpam-6069	117	7	+	+	CCONJ
ejpam-6069	117	8	1]t	1]t	NUM
ejpam-6069	117	9	=	=	SYM
ejpam-6069	117	10	eut	eut	NOUN
ejpam-6069	117	11	.	.	PUNCT
ejpam-6069	117	12	therefore	therefore	ADV
ejpam-6069	117	13	,	,	PUNCT
ejpam-6069	117	14	by	by	ADP
ejpam-6069	117	15	lemma	lemma	PROPN
ejpam-6069	117	16	4	4	NUM
ejpam-6069	117	17	,	,	PUNCT
ejpam-6069	117	18	∞∑	∞∑	PRON
ejpam-6069	117	19	k=0	k=0	PROPN
ejpam-6069	117	20	sa(x	sa(x	NOUN
ejpam-6069	117	21	,	,	PUNCT
ejpam-6069	117	22	k)(t)k	k)(t)k	PUNCT
ejpam-6069	117	23	=	=	SYM
ejpam-6069	117	24	x	x	X
ejpam-6069	117	25	!	!	PUNCT
ejpam-6069	118	1	2πi	2πi	ADJ
ejpam-6069	118	2	∫	∫	PROPN
ejpam-6069	118	3	h	h	PROPN
ejpam-6069	118	4	e−aueut	e−aueut	X
ejpam-6069	118	5	du	du	PROPN
ejpam-6069	118	6	ux+1	ux+1	PROPN
ejpam-6069	118	7	=	=	PUNCT
ejpam-6069	118	8	(	(	PUNCT
ejpam-6069	118	9	t−	t−	PROPN
ejpam-6069	118	10	a)x	a)x	ADJ
ejpam-6069	118	11	.	.	PUNCT
ejpam-6069	119	1	theorem	theorem	VERB
ejpam-6069	119	2	3.2	3.2	NUM
ejpam-6069	119	3	.	.	PUNCT
ejpam-6069	120	1	for	for	ADP
ejpam-6069	120	2	complex	complex	ADJ
ejpam-6069	120	3	numbers	number	NOUN
ejpam-6069	120	4	x	x	PUNCT
ejpam-6069	120	5	and	and	CCONJ
ejpam-6069	120	6	a	a	PRON
ejpam-6069	120	7	with	with	ADP
ejpam-6069	120	8	re(a	re(a	NOUN
ejpam-6069	120	9	)	)	PUNCT
ejpam-6069	120	10	<	<	X
ejpam-6069	120	11	0	0	NUM
ejpam-6069	120	12	,	,	PUNCT
ejpam-6069	120	13	re(x	re(x	X
ejpam-6069	120	14	)	)	PUNCT
ejpam-6069	120	15	>	>	X
ejpam-6069	120	16	0	0	NUM
ejpam-6069	120	17	,	,	PUNCT
ejpam-6069	120	18	the	the	DET
ejpam-6069	120	19	non	non	ADJ
ejpam-6069	120	20	-	-	ADJ
ejpam-6069	120	21	central	central	ADJ
ejpam-6069	120	22	stirling	stirling	NOUN
ejpam-6069	120	23	numbers	number	NOUN
ejpam-6069	120	24	sa(x	sa(x	NOUN
ejpam-6069	120	25	,	,	PUNCT
ejpam-6069	120	26	y	y	NOUN
ejpam-6069	120	27	)	)	PUNCT
ejpam-6069	120	28	satisfy	satisfy	VERB
ejpam-6069	120	29	the	the	DET
ejpam-6069	120	30	following	follow	VERB
ejpam-6069	120	31	recurrence	recurrence	NOUN
ejpam-6069	120	32	relation	relation	NOUN
ejpam-6069	120	33	:	:	PUNCT
ejpam-6069	120	34	sa(x	sa(x	NOUN
ejpam-6069	120	35	,	,	PUNCT
ejpam-6069	120	36	y	y	NOUN
ejpam-6069	120	37	)	)	PUNCT
ejpam-6069	120	38	=	=	SYM
ejpam-6069	120	39	sa(x−	sa(x−	NUM
ejpam-6069	121	1	1	1	NUM
ejpam-6069	121	2	,	,	PUNCT
ejpam-6069	121	3	y	y	PROPN
ejpam-6069	121	4	−	−	PROPN
ejpam-6069	121	5	1	1	NUM
ejpam-6069	121	6	)	)	PUNCT
ejpam-6069	121	7	+	+	CCONJ
ejpam-6069	121	8	(	(	PUNCT
ejpam-6069	121	9	y	y	PROPN
ejpam-6069	121	10	−	−	PROPN
ejpam-6069	121	11	a)sa(x−	a)sa(x−	ADP
ejpam-6069	121	12	1	1	NUM
ejpam-6069	121	13	,	,	PUNCT
ejpam-6069	121	14	y	y	NOUN
ejpam-6069	121	15	)	)	PUNCT
ejpam-6069	121	16	.	.	PUNCT
ejpam-6069	122	1	proof	proof	NOUN
ejpam-6069	122	2	.	.	PUNCT
ejpam-6069	123	1	by	by	ADP
ejpam-6069	123	2	definition	definition	NOUN
ejpam-6069	123	3	3.1	3.1	NUM
ejpam-6069	123	4	,	,	PUNCT
ejpam-6069	123	5	sa(x	sa(x	NOUN
ejpam-6069	123	6	,	,	PUNCT
ejpam-6069	123	7	y	y	NOUN
ejpam-6069	123	8	)	)	PUNCT
ejpam-6069	123	9	=	=	SYM
ejpam-6069	123	10	1	1	NUM
ejpam-6069	123	11	2πi	2πi	NOUN
ejpam-6069	123	12	x	x	X
ejpam-6069	123	13	!	!	PUNCT
ejpam-6069	123	14	y	y	PROPN
ejpam-6069	123	15	!	!	PUNCT
ejpam-6069	123	16	∫	∫	PROPN
ejpam-6069	124	1	h	h	PROPN
ejpam-6069	124	2	e−au(eu	e−au(eu	PROPN
ejpam-6069	124	3	−	−	NUM
ejpam-6069	124	4	1)ydu	1)ydu	NUM
ejpam-6069	124	5	ux+1	ux+1	PROPN
ejpam-6069	124	6	.	.	PUNCT
ejpam-6069	125	1	now	now	ADV
ejpam-6069	125	2	let	let	VERB
ejpam-6069	125	3	s	s	NOUN
ejpam-6069	125	4	=	=	PUNCT
ejpam-6069	125	5	e−au(eu	e−au(eu	PROPN
ejpam-6069	125	6	−	−	NOUN
ejpam-6069	125	7	1)y	1)y	NUM
ejpam-6069	125	8	and	and	CCONJ
ejpam-6069	125	9	dt	dt	NOUN
ejpam-6069	125	10	=	=	SYM
ejpam-6069	125	11	du	du	PROPN
ejpam-6069	125	12	ux+1	ux+1	PROPN
ejpam-6069	125	13	.	.	PUNCT
ejpam-6069	126	1	then	then	ADV
ejpam-6069	126	2	,	,	PUNCT
ejpam-6069	126	3	ds	ds	ADJ
ejpam-6069	126	4	=	=	SYM
ejpam-6069	126	5	(	(	PUNCT
ejpam-6069	126	6	eue−auy(eu	eue−auy(eu	PROPN
ejpam-6069	126	7	−	−	PROPN
ejpam-6069	126	8	1)y−1	1)y−1	NUM
ejpam-6069	126	9	−	−	PROPN
ejpam-6069	126	10	ae−au(eu	ae−au(eu	PROPN
ejpam-6069	126	11	−	−	PROPN
ejpam-6069	126	12	1)y	1)y	NUM
ejpam-6069	126	13	)	)	PUNCT
ejpam-6069	126	14	du	du	PROPN
ejpam-6069	126	15	and	and	CCONJ
ejpam-6069	126	16	t	t	NOUN
ejpam-6069	126	17	=	=	SYM
ejpam-6069	126	18	1	1	NUM
ejpam-6069	126	19	−xux	−xux	X
ejpam-6069	126	20	.	.	PUNCT
ejpam-6069	127	1	thus	thus	ADV
ejpam-6069	127	2	,	,	PUNCT
ejpam-6069	127	3	integration	integration	NOUN
ejpam-6069	127	4	by	by	ADP
ejpam-6069	127	5	parts	part	NOUN
ejpam-6069	127	6	yields	yield	NOUN
ejpam-6069	127	7	sa(x	sa(x	NOUN
ejpam-6069	127	8	,	,	PUNCT
ejpam-6069	127	9	y	y	NOUN
ejpam-6069	127	10	)	)	PUNCT
ejpam-6069	127	11	=	=	SYM
ejpam-6069	128	1	1	1	NUM
ejpam-6069	128	2	2πi	2πi	NOUN
ejpam-6069	128	3	x	x	X
ejpam-6069	128	4	!	!	PUNCT
ejpam-6069	128	5	y	y	X
ejpam-6069	128	6	!	!	PUNCT
ejpam-6069	128	7	{	{	PUNCT
ejpam-6069	129	1	[	[	X
ejpam-6069	129	2	e−au(eu	e−au(eu	ADP
ejpam-6069	129	3	−	−	NUM
ejpam-6069	129	4	1)y	1)y	NOUN
ejpam-6069	129	5	−xux	−xux	X
ejpam-6069	129	6	]	]	PUNCT
ejpam-6069	130	1	h	h	NOUN
ejpam-6069	131	1	−	−	PROPN
ejpam-6069	131	2	∫	∫	PROPN
ejpam-6069	131	3	h	h	PROPN
ejpam-6069	131	4	1	1	NUM
ejpam-6069	131	5	−xux	−xux	X
ejpam-6069	131	6	(	(	PUNCT
ejpam-6069	131	7	eue−auy(eu−1)y−1−ae−au(eu−1)y	eue−auy(eu−1)y−1−ae−au(eu−1)y	X
ejpam-6069	131	8	)	)	PUNCT
ejpam-6069	131	9	du	du	NOUN
ejpam-6069	131	10	}	}	PUNCT
ejpam-6069	131	11	.	.	PUNCT
ejpam-6069	132	1	however	however	ADV
ejpam-6069	132	2	,	,	PUNCT
ejpam-6069	132	3	as	as	ADP
ejpam-6069	132	4	u	u	PROPN
ejpam-6069	132	5	→	→	SYM
ejpam-6069	132	6	−∞	−∞	NOUN
ejpam-6069	132	7	,	,	PUNCT
ejpam-6069	132	8	1	1	NUM
ejpam-6069	132	9	−xux	−xux	X
ejpam-6069	132	10	→	→	X
ejpam-6069	132	11	0	0	X
ejpam-6069	132	12	.	.	PUNCT
ejpam-6069	132	13	hence	hence	ADV
ejpam-6069	132	14	,	,	PUNCT
ejpam-6069	132	15	sa(x	sa(x	NOUN
ejpam-6069	132	16	,	,	PUNCT
ejpam-6069	132	17	y	y	NOUN
ejpam-6069	132	18	)	)	PUNCT
ejpam-6069	132	19	=	=	SYM
ejpam-6069	132	20	1	1	NUM
ejpam-6069	132	21	2πi	2πi	NOUN
ejpam-6069	132	22	x	x	X
ejpam-6069	132	23	!	!	PUNCT
ejpam-6069	132	24	y	y	PROPN
ejpam-6069	132	25	!	!	PUNCT
ejpam-6069	133	1	[	[	PUNCT
ejpam-6069	133	2	−	−	NUM
ejpam-6069	133	3	∫	∫	PROPN
ejpam-6069	133	4	h	h	PROPN
ejpam-6069	133	5	1	1	NUM
ejpam-6069	133	6	−xux	−xux	VERB
ejpam-6069	133	7	e−au(eu	e−au(eu	PROPN
ejpam-6069	134	1	−	−	PROPN
ejpam-6069	134	2	1)y−1	1)y−1	NUM
ejpam-6069	134	3	(	(	PUNCT
ejpam-6069	134	4	euy	euy	PROPN
ejpam-6069	134	5	−	−	PROPN
ejpam-6069	134	6	a(eu	a(eu	NOUN
ejpam-6069	134	7	−	−	PROPN
ejpam-6069	134	8	1	1	NUM
ejpam-6069	134	9	)	)	PUNCT
ejpam-6069	134	10	)	)	PUNCT
ejpam-6069	134	11	du	du	X
ejpam-6069	134	12	]	]	PUNCT
ejpam-6069	135	1	=	=	SYM
ejpam-6069	136	1	1	1	NUM
ejpam-6069	136	2	2πi	2πi	NOUN
ejpam-6069	136	3	(	(	PUNCT
ejpam-6069	136	4	x−	x−	PROPN
ejpam-6069	136	5	1	1	NUM
ejpam-6069	136	6	)	)	PUNCT
ejpam-6069	136	7	!	!	PUNCT
ejpam-6069	137	1	y	y	X
ejpam-6069	137	2	!	!	PUNCT
ejpam-6069	138	1	∫	∫	PROPN
ejpam-6069	138	2	h	h	PROPN
ejpam-6069	139	1	(	(	PUNCT
ejpam-6069	139	2	ye−au(eu	ye−au(eu	ADV
ejpam-6069	139	3	−	−	PROPN
ejpam-6069	139	4	1)y−1	1)y−1	NUM
ejpam-6069	139	5	ux	ux	PROPN
ejpam-6069	139	6	+	+	CCONJ
ejpam-6069	139	7	(	(	PUNCT
ejpam-6069	139	8	y	y	PROPN
ejpam-6069	139	9	−	−	PROPN
ejpam-6069	139	10	a)e−au(eu	a)e−au(eu	ADV
ejpam-6069	139	11	−	−	NUM
ejpam-6069	139	12	1)y	1)y	NUM
ejpam-6069	139	13	ux	ux	PROPN
ejpam-6069	139	14	)	)	PUNCT
ejpam-6069	139	15	du	du	PROPN
ejpam-6069	139	16	=	=	SYM
ejpam-6069	139	17	1	1	NUM
ejpam-6069	139	18	2πi	2πi	NOUN
ejpam-6069	139	19	(	(	PUNCT
ejpam-6069	139	20	x−	x−	PROPN
ejpam-6069	139	21	1	1	NUM
ejpam-6069	139	22	)	)	PUNCT
ejpam-6069	139	23	!	!	PUNCT
ejpam-6069	140	1	(	(	PUNCT
ejpam-6069	140	2	y	y	NOUN
ejpam-6069	140	3	−	−	PROPN
ejpam-6069	140	4	1	1	NUM
ejpam-6069	140	5	)	)	PUNCT
ejpam-6069	140	6	!	!	PUNCT
ejpam-6069	141	1	∫	∫	PROPN
ejpam-6069	142	1	h	h	PROPN
ejpam-6069	142	2	e−au(eu	e−au(eu	PROPN
ejpam-6069	142	3	−	−	NUM
ejpam-6069	142	4	1)y−1du	1)y−1du	NUM
ejpam-6069	142	5	u(x−1)+1	u(x−1)+1	NOUN
ejpam-6069	143	1	+	+	CCONJ
ejpam-6069	143	2	(	(	PUNCT
ejpam-6069	143	3	y	y	PROPN
ejpam-6069	143	4	−	−	PROPN
ejpam-6069	143	5	a	a	X
ejpam-6069	143	6	)	)	PUNCT
ejpam-6069	143	7	1	1	NUM
ejpam-6069	143	8	2πi	2πi	NOUN
ejpam-6069	143	9	(	(	PUNCT
ejpam-6069	143	10	x−	x−	PROPN
ejpam-6069	143	11	1	1	NUM
ejpam-6069	143	12	)	)	PUNCT
ejpam-6069	143	13	!	!	PUNCT
ejpam-6069	144	1	y	y	X
ejpam-6069	144	2	!	!	PUNCT
ejpam-6069	145	1	∫	∫	PROPN
ejpam-6069	146	1	h	h	PROPN
ejpam-6069	146	2	e−au(eu	e−au(eu	PROPN
ejpam-6069	146	3	−	−	NUM
ejpam-6069	146	4	1)ydu	1)ydu	NUM
ejpam-6069	146	5	u(x−1)+1	u(x−1)+1	NOUN
ejpam-6069	146	6	.	.	PUNCT
ejpam-6069	147	1	e.n	e.n	PROPN
ejpam-6069	147	2	.	.	PROPN
ejpam-6069	147	3	arlan	arlan	PROPN
ejpam-6069	147	4	,	,	PUNCT
ejpam-6069	147	5	m.b	m.b	PROPN
ejpam-6069	147	6	.	.	PROPN
ejpam-6069	147	7	montero	montero	PROPN
ejpam-6069	147	8	/	/	SYM
ejpam-6069	147	9	eur	eur	PROPN
ejpam-6069	147	10	.	.	PUNCT
ejpam-6069	148	1	j.	j.	PROPN
ejpam-6069	148	2	pure	pure	PROPN
ejpam-6069	148	3	appl	appl	PROPN
ejpam-6069	148	4	.	.	PROPN
ejpam-6069	148	5	math	math	PROPN
ejpam-6069	148	6	,	,	PUNCT
ejpam-6069	148	7	18	18	NUM
ejpam-6069	148	8	(	(	PUNCT
ejpam-6069	148	9	2	2	NUM
ejpam-6069	148	10	)	)	PUNCT
ejpam-6069	148	11	(	(	PUNCT
ejpam-6069	148	12	2025	2025	NUM
ejpam-6069	148	13	)	)	PUNCT
ejpam-6069	148	14	,	,	PUNCT
ejpam-6069	148	15	6069	6069	NUM
ejpam-6069	148	16	7	7	NUM
ejpam-6069	148	17	of	of	ADP
ejpam-6069	148	18	10	10	NUM
ejpam-6069	148	19	thus	thus	ADV
ejpam-6069	148	20	,	,	PUNCT
ejpam-6069	148	21	by	by	ADP
ejpam-6069	148	22	definition	definition	NOUN
ejpam-6069	148	23	3.1	3.1	NUM
ejpam-6069	148	24	,	,	PUNCT
ejpam-6069	148	25	sa(x	sa(x	NOUN
ejpam-6069	148	26	,	,	PUNCT
ejpam-6069	148	27	y	y	NOUN
ejpam-6069	148	28	)	)	PUNCT
ejpam-6069	148	29	=	=	SYM
ejpam-6069	148	30	sa(x−	sa(x−	NUM
ejpam-6069	148	31	1	1	NUM
ejpam-6069	148	32	,	,	PUNCT
ejpam-6069	148	33	y	y	PROPN
ejpam-6069	148	34	−	−	PROPN
ejpam-6069	148	35	1	1	NUM
ejpam-6069	148	36	)	)	PUNCT
ejpam-6069	148	37	+	+	CCONJ
ejpam-6069	148	38	(	(	PUNCT
ejpam-6069	148	39	y	y	PROPN
ejpam-6069	148	40	−	−	PROPN
ejpam-6069	148	41	a)sa(x−	a)sa(x−	ADP
ejpam-6069	148	42	1	1	NUM
ejpam-6069	148	43	,	,	PUNCT
ejpam-6069	148	44	y	y	PROPN
ejpam-6069	148	45	)	)	PUNCT
ejpam-6069	148	46	.	.	PUNCT
ejpam-6069	149	1	the	the	DET
ejpam-6069	149	2	next	next	ADJ
ejpam-6069	149	3	result	result	NOUN
ejpam-6069	149	4	is	be	AUX
ejpam-6069	149	5	an	an	DET
ejpam-6069	149	6	explicit	explicit	ADJ
ejpam-6069	149	7	formula	formula	NOUN
ejpam-6069	149	8	for	for	ADP
ejpam-6069	149	9	sa(x	sa(x	NOUN
ejpam-6069	149	10	,	,	PUNCT
ejpam-6069	149	11	k	k	NOUN
ejpam-6069	149	12	)	)	PUNCT
ejpam-6069	149	13	.	.	PUNCT
ejpam-6069	150	1	theorem	theorem	VERB
ejpam-6069	150	2	3.3	3.3	NUM
ejpam-6069	150	3	.	.	PUNCT
ejpam-6069	151	1	for	for	ADP
ejpam-6069	151	2	complex	complex	ADJ
ejpam-6069	151	3	numbers	number	NOUN
ejpam-6069	151	4	x	x	PUNCT
ejpam-6069	151	5	and	and	CCONJ
ejpam-6069	151	6	a	a	PRON
ejpam-6069	151	7	with	with	ADP
ejpam-6069	151	8	re(a	re(a	NOUN
ejpam-6069	151	9	)	)	PUNCT
ejpam-6069	151	10	<	<	X
ejpam-6069	151	11	0	0	NUM
ejpam-6069	151	12	,	,	PUNCT
ejpam-6069	151	13	and	and	CCONJ
ejpam-6069	151	14	a	a	DET
ejpam-6069	151	15	nonnegative	nonnegative	ADJ
ejpam-6069	151	16	integer	integer	NOUN
ejpam-6069	151	17	k	k	NOUN
ejpam-6069	151	18	,	,	PUNCT
ejpam-6069	151	19	we	we	PRON
ejpam-6069	151	20	have	have	VERB
ejpam-6069	151	21	sa(x	sa(x	NOUN
ejpam-6069	151	22	,	,	PUNCT
ejpam-6069	151	23	k	k	NOUN
ejpam-6069	151	24	)	)	PUNCT
ejpam-6069	151	25	=	=	SYM
ejpam-6069	152	1	1	1	NUM
ejpam-6069	152	2	k	k	X
ejpam-6069	152	3	!	!	PUNCT
ejpam-6069	152	4	k∑	k∑	PROPN
ejpam-6069	152	5	j=0	j=0	PROPN
ejpam-6069	152	6	(	(	PUNCT
ejpam-6069	152	7	−1)k−j	−1)k−j	X
ejpam-6069	152	8	(	(	PUNCT
ejpam-6069	152	9	k	k	PROPN
ejpam-6069	152	10	j	j	PROPN
ejpam-6069	152	11	)	)	PUNCT
ejpam-6069	152	12	(	(	PUNCT
ejpam-6069	152	13	j	j	PROPN
ejpam-6069	152	14	−	−	PROPN
ejpam-6069	152	15	a)x	a)x	PUNCT
ejpam-6069	152	16	.	.	PUNCT
ejpam-6069	153	1	proof	proof	NOUN
ejpam-6069	153	2	.	.	PUNCT
ejpam-6069	154	1	by	by	ADP
ejpam-6069	154	2	definition	definition	NOUN
ejpam-6069	154	3	3.1	3.1	NUM
ejpam-6069	154	4	,	,	PUNCT
ejpam-6069	154	5	we	we	PRON
ejpam-6069	154	6	have	have	VERB
ejpam-6069	154	7	sa(x	sa(x	NOUN
ejpam-6069	154	8	,	,	PUNCT
ejpam-6069	154	9	k	k	NOUN
ejpam-6069	154	10	)	)	PUNCT
ejpam-6069	154	11	=	=	SYM
ejpam-6069	154	12	1	1	NUM
ejpam-6069	154	13	2πi	2πi	NOUN
ejpam-6069	154	14	x	x	X
ejpam-6069	154	15	!	!	PUNCT
ejpam-6069	155	1	k	k	X
ejpam-6069	155	2	!	!	PUNCT
ejpam-6069	155	3	∫	∫	PROPN
ejpam-6069	156	1	h	h	PROPN
ejpam-6069	156	2	e−au(eu	e−au(eu	PROPN
ejpam-6069	157	1	−	−	ADP
ejpam-6069	157	2	1)kdu	1)kdu	NUM
ejpam-6069	157	3	ux+1	ux+1	PROPN
ejpam-6069	157	4	.	.	PUNCT
ejpam-6069	158	1	applying	apply	VERB
ejpam-6069	158	2	the	the	DET
ejpam-6069	158	3	binomial	binomial	ADJ
ejpam-6069	158	4	theorem	theorem	NOUN
ejpam-6069	158	5	,	,	PUNCT
ejpam-6069	158	6	(	(	PUNCT
ejpam-6069	158	7	eu	eu	PROPN
ejpam-6069	158	8	−	−	PROPN
ejpam-6069	158	9	1)k	1)k	NUM
ejpam-6069	158	10	=	=	SYM
ejpam-6069	158	11	k∑	k∑	PROPN
ejpam-6069	158	12	j=0	j=0	PROPN
ejpam-6069	158	13	(	(	PUNCT
ejpam-6069	158	14	k	k	PROPN
ejpam-6069	158	15	j	j	PROPN
ejpam-6069	158	16	)	)	PUNCT
ejpam-6069	158	17	(	(	PUNCT
ejpam-6069	158	18	−1)k−j(eu)j	−1)k−j(eu)j	NOUN
ejpam-6069	158	19	=	=	SYM
ejpam-6069	158	20	k∑	k∑	NOUN
ejpam-6069	158	21	j=0	j=0	PROPN
ejpam-6069	158	22	(	(	PUNCT
ejpam-6069	158	23	−1)k−j(e)uj	−1)k−j(e)uj	PROPN
ejpam-6069	158	24	(	(	PUNCT
ejpam-6069	158	25	k	k	PROPN
ejpam-6069	158	26	j	j	PROPN
ejpam-6069	158	27	)	)	PUNCT
ejpam-6069	158	28	.	.	PUNCT
ejpam-6069	159	1	thus	thus	ADV
ejpam-6069	159	2	,	,	PUNCT
ejpam-6069	159	3	sa(x	sa(x	NOUN
ejpam-6069	159	4	,	,	PUNCT
ejpam-6069	159	5	k	k	NOUN
ejpam-6069	159	6	)	)	PUNCT
ejpam-6069	159	7	=	=	SYM
ejpam-6069	159	8	1	1	NUM
ejpam-6069	159	9	2πi	2πi	NOUN
ejpam-6069	159	10	x	x	X
ejpam-6069	159	11	!	!	PUNCT
ejpam-6069	160	1	k	k	X
ejpam-6069	160	2	!	!	PUNCT
ejpam-6069	160	3	∫	∫	PROPN
ejpam-6069	161	1	h	h	PROPN
ejpam-6069	161	2	e−au	e−au	PROPN
ejpam-6069	162	1	(	(	PUNCT
ejpam-6069	162	2	k∑	k∑	NOUN
ejpam-6069	162	3	j=0	j=0	PROPN
ejpam-6069	162	4	(	(	PUNCT
ejpam-6069	162	5	−1)k−jeuj	−1)k−jeuj	NOUN
ejpam-6069	162	6	(	(	PUNCT
ejpam-6069	162	7	k	k	PROPN
ejpam-6069	162	8	j	j	PROPN
ejpam-6069	162	9	)	)	PUNCT
ejpam-6069	162	10	)	)	PUNCT
ejpam-6069	162	11	du	du	PROPN
ejpam-6069	162	12	ux+1	ux+1	PROPN
ejpam-6069	162	13	=	=	SYM
ejpam-6069	162	14	1	1	NUM
ejpam-6069	162	15	k	k	X
ejpam-6069	162	16	!	!	PUNCT
ejpam-6069	162	17	k∑	k∑	PROPN
ejpam-6069	162	18	j=0	j=0	PROPN
ejpam-6069	162	19	[	[	PUNCT
ejpam-6069	162	20	(	(	PUNCT
ejpam-6069	162	21	−1)k−j	−1)k−j	X
ejpam-6069	162	22	(	(	PUNCT
ejpam-6069	162	23	k	k	PROPN
ejpam-6069	162	24	j	j	PROPN
ejpam-6069	162	25	)	)	PUNCT
ejpam-6069	162	26	·	·	PUNCT
ejpam-6069	163	1	x	x	X
ejpam-6069	163	2	!	!	PUNCT
ejpam-6069	163	3	2πi	2πi	ADJ
ejpam-6069	164	1	∫	∫	PROPN
ejpam-6069	164	2	h	h	NOUN
ejpam-6069	164	3	e−aueuj	e−aueuj	PROPN
ejpam-6069	164	4	du	du	PROPN
ejpam-6069	164	5	ux+1	ux+1	PROPN
ejpam-6069	164	6	]	]	PUNCT
ejpam-6069	164	7	.	.	PUNCT
ejpam-6069	165	1	moreover	moreover	ADV
ejpam-6069	165	2	,	,	PUNCT
ejpam-6069	165	3	by	by	ADP
ejpam-6069	165	4	lemma	lemma	PROPN
ejpam-6069	165	5	4	4	NUM
ejpam-6069	165	6	,	,	PUNCT
ejpam-6069	165	7	sa(x	sa(x	NOUN
ejpam-6069	165	8	,	,	PUNCT
ejpam-6069	165	9	k	k	NOUN
ejpam-6069	165	10	)	)	PUNCT
ejpam-6069	165	11	=	=	SYM
ejpam-6069	165	12	1	1	NUM
ejpam-6069	165	13	k	k	X
ejpam-6069	165	14	!	!	PUNCT
ejpam-6069	165	15	k∑	k∑	PROPN
ejpam-6069	166	1	j=0	j=0	PROPN
ejpam-6069	167	1	(	(	PUNCT
ejpam-6069	167	2	−1)k−j	−1)k−j	X
ejpam-6069	167	3	(	(	PUNCT
ejpam-6069	167	4	k	k	PROPN
ejpam-6069	167	5	j	j	PROPN
ejpam-6069	167	6	)	)	PUNCT
ejpam-6069	167	7	(	(	PUNCT
ejpam-6069	167	8	j	j	PROPN
ejpam-6069	167	9	−	−	PROPN
ejpam-6069	167	10	a)x	a)x	NOUN
ejpam-6069	167	11	.	.	PUNCT
ejpam-6069	168	1	to	to	PART
ejpam-6069	168	2	illustrate	illustrate	VERB
ejpam-6069	168	3	this	this	PRON
ejpam-6069	168	4	,	,	PUNCT
ejpam-6069	168	5	let	let	VERB
ejpam-6069	168	6	us	we	PRON
ejpam-6069	168	7	consider	consider	VERB
ejpam-6069	168	8	the	the	DET
ejpam-6069	168	9	case	case	NOUN
ejpam-6069	168	10	where	where	SCONJ
ejpam-6069	168	11	a	a	DET
ejpam-6069	168	12	=	=	NOUN
ejpam-6069	168	13	−1	−1	NOUN
ejpam-6069	168	14	.	.	PUNCT
ejpam-6069	169	1	using	use	VERB
ejpam-6069	169	2	the	the	DET
ejpam-6069	169	3	explicit	explicit	ADJ
ejpam-6069	169	4	formula	formula	NOUN
ejpam-6069	169	5	above	above	ADV
ejpam-6069	169	6	,	,	PUNCT
ejpam-6069	169	7	we	we	PRON
ejpam-6069	169	8	compute	compute	VERB
ejpam-6069	169	9	the	the	DET
ejpam-6069	169	10	values	value	NOUN
ejpam-6069	169	11	of	of	ADP
ejpam-6069	169	12	s−1(i	s−1(i	PROPN
ejpam-6069	169	13	,	,	PUNCT
ejpam-6069	169	14	0	0	NUM
ejpam-6069	169	15	)	)	PUNCT
ejpam-6069	169	16	,	,	PUNCT
ejpam-6069	169	17	s−1(i	s−1(i	PROPN
ejpam-6069	169	18	,	,	PUNCT
ejpam-6069	169	19	1	1	NUM
ejpam-6069	169	20	)	)	PUNCT
ejpam-6069	169	21	,	,	PUNCT
ejpam-6069	169	22	and	and	CCONJ
ejpam-6069	169	23	s−1(1	s−1(1	X
ejpam-6069	169	24	+	+	CCONJ
ejpam-6069	169	25	i	i	NOUN
ejpam-6069	169	26	,	,	PUNCT
ejpam-6069	169	27	1	1	NUM
ejpam-6069	169	28	)	)	PUNCT
ejpam-6069	169	29	as	as	SCONJ
ejpam-6069	169	30	follows	follow	VERB
ejpam-6069	169	31	:	:	PUNCT
ejpam-6069	169	32	s−1	s−1	PROPN
ejpam-6069	169	33	(	(	PUNCT
ejpam-6069	169	34	i	i	NOUN
ejpam-6069	169	35	,	,	PUNCT
ejpam-6069	169	36	0	0	NUM
ejpam-6069	169	37	)	)	PUNCT
ejpam-6069	169	38	=	=	SYM
ejpam-6069	170	1	1	1	NUM
ejpam-6069	170	2	0	0	NUM
ejpam-6069	170	3	!	!	PUNCT
ejpam-6069	171	1	0∑	0∑	PROPN
ejpam-6069	171	2	j=0	j=0	PROPN
ejpam-6069	171	3	(	(	PUNCT
ejpam-6069	171	4	−1)0−j	−1)0−j	NOUN
ejpam-6069	171	5	(	(	PUNCT
ejpam-6069	171	6	0	0	NUM
ejpam-6069	171	7	j	j	NOUN
ejpam-6069	171	8	)	)	PUNCT
ejpam-6069	171	9	(	(	PUNCT
ejpam-6069	171	10	j	j	PROPN
ejpam-6069	171	11	+	+	CCONJ
ejpam-6069	171	12	1)i	1)i	NUM
ejpam-6069	171	13	=	=	SYM
ejpam-6069	171	14	1(−1)0	1(−1)0	NUM
ejpam-6069	171	15	(	(	PUNCT
ejpam-6069	171	16	0	0	NUM
ejpam-6069	171	17	0	0	NUM
ejpam-6069	171	18	)	)	PUNCT
ejpam-6069	171	19	(	(	PUNCT
ejpam-6069	171	20	0	0	NUM
ejpam-6069	171	21	+	+	NUM
ejpam-6069	171	22	1)i	1)i	NUM
ejpam-6069	171	23	=	=	SYM
ejpam-6069	171	24	1i	1i	NOUN
ejpam-6069	171	25	=	=	SYM
ejpam-6069	171	26	1	1	NUM
ejpam-6069	171	27	;	;	PUNCT
ejpam-6069	171	28	e.n	e.n	PROPN
ejpam-6069	171	29	.	.	PROPN
ejpam-6069	171	30	arlan	arlan	PROPN
ejpam-6069	171	31	,	,	PUNCT
ejpam-6069	171	32	m.b	m.b	PROPN
ejpam-6069	171	33	.	.	PROPN
ejpam-6069	171	34	montero	montero	PROPN
ejpam-6069	171	35	/	/	SYM
ejpam-6069	171	36	eur	eur	PROPN
ejpam-6069	171	37	.	.	PUNCT
ejpam-6069	172	1	j.	j.	PROPN
ejpam-6069	172	2	pure	pure	PROPN
ejpam-6069	172	3	appl	appl	PROPN
ejpam-6069	172	4	.	.	PROPN
ejpam-6069	172	5	math	math	PROPN
ejpam-6069	172	6	,	,	PUNCT
ejpam-6069	172	7	18	18	NUM
ejpam-6069	172	8	(	(	PUNCT
ejpam-6069	172	9	2	2	NUM
ejpam-6069	172	10	)	)	PUNCT
ejpam-6069	172	11	(	(	PUNCT
ejpam-6069	172	12	2025	2025	NUM
ejpam-6069	172	13	)	)	PUNCT
ejpam-6069	172	14	,	,	PUNCT
ejpam-6069	172	15	6069	6069	NUM
ejpam-6069	172	16	8	8	NUM
ejpam-6069	172	17	of	of	ADP
ejpam-6069	172	18	10	10	NUM
ejpam-6069	172	19	s−1	s−1	PROPN
ejpam-6069	172	20	(	(	PUNCT
ejpam-6069	172	21	i	i	NOUN
ejpam-6069	172	22	,	,	PUNCT
ejpam-6069	172	23	1	1	X
ejpam-6069	172	24	)	)	PUNCT
ejpam-6069	172	25	=	=	SYM
ejpam-6069	172	26	1	1	NUM
ejpam-6069	172	27	1	1	NUM
ejpam-6069	172	28	!	!	X
ejpam-6069	173	1	1∑	1∑	PROPN
ejpam-6069	173	2	j=0	j=0	PROPN
ejpam-6069	173	3	(	(	PUNCT
ejpam-6069	173	4	−1)1−j	−1)1−j	NOUN
ejpam-6069	173	5	(	(	PUNCT
ejpam-6069	173	6	1	1	NUM
ejpam-6069	173	7	j	j	NOUN
ejpam-6069	173	8	)	)	PUNCT
ejpam-6069	173	9	(	(	PUNCT
ejpam-6069	173	10	j	j	PROPN
ejpam-6069	173	11	+	+	CCONJ
ejpam-6069	173	12	1)i	1)i	NUM
ejpam-6069	173	13	=	=	SYM
ejpam-6069	173	14	1	1	NUM
ejpam-6069	173	15	[	[	PUNCT
ejpam-6069	173	16	(	(	PUNCT
ejpam-6069	173	17	−1)1	−1)1	X
ejpam-6069	173	18	(	(	PUNCT
ejpam-6069	173	19	1	1	NUM
ejpam-6069	173	20	0	0	NUM
ejpam-6069	173	21	)	)	PUNCT
ejpam-6069	173	22	(	(	PUNCT
ejpam-6069	173	23	0	0	NUM
ejpam-6069	173	24	+	+	NUM
ejpam-6069	173	25	1)i	1)i	NUM
ejpam-6069	173	26	+	+	CCONJ
ejpam-6069	173	27	(	(	PUNCT
ejpam-6069	173	28	−1)0	−1)0	X
ejpam-6069	173	29	(	(	PUNCT
ejpam-6069	173	30	1	1	NUM
ejpam-6069	173	31	1	1	NUM
ejpam-6069	173	32	)	)	PUNCT
ejpam-6069	173	33	(	(	PUNCT
ejpam-6069	173	34	1	1	NUM
ejpam-6069	173	35	+	+	NUM
ejpam-6069	173	36	1)i	1)i	NUM
ejpam-6069	173	37	]	]	PUNCT
ejpam-6069	173	38	=	=	PUNCT
ejpam-6069	173	39	−1	−1	NOUN
ejpam-6069	173	40	+	+	X
ejpam-6069	173	41	cos	cos	X
ejpam-6069	173	42	(	(	PUNCT
ejpam-6069	173	43	ln	ln	NOUN
ejpam-6069	173	44	2	2	NUM
ejpam-6069	173	45	)	)	PUNCT
ejpam-6069	173	46	+	+	CCONJ
ejpam-6069	173	47	i	i	PRON
ejpam-6069	173	48	sin	sin	VERB
ejpam-6069	173	49	(	(	PUNCT
ejpam-6069	173	50	ln	ln	NOUN
ejpam-6069	173	51	2	2	NUM
ejpam-6069	173	52	)	)	PUNCT
ejpam-6069	173	53	;	;	PUNCT
ejpam-6069	173	54	s−1	s−1	PROPN
ejpam-6069	173	55	(	(	PUNCT
ejpam-6069	173	56	1	1	NUM
ejpam-6069	174	1	+	+	CCONJ
ejpam-6069	174	2	i	i	PRON
ejpam-6069	174	3	,	,	PUNCT
ejpam-6069	174	4	1	1	X
ejpam-6069	174	5	)	)	PUNCT
ejpam-6069	174	6	=	=	SYM
ejpam-6069	174	7	1	1	NUM
ejpam-6069	174	8	1	1	NUM
ejpam-6069	174	9	!	!	X
ejpam-6069	175	1	1∑	1∑	PROPN
ejpam-6069	175	2	j=0	j=0	PROPN
ejpam-6069	175	3	(	(	PUNCT
ejpam-6069	175	4	−1)1−j	−1)1−j	NOUN
ejpam-6069	175	5	(	(	PUNCT
ejpam-6069	175	6	1	1	NUM
ejpam-6069	175	7	j	j	NOUN
ejpam-6069	175	8	)	)	PUNCT
ejpam-6069	175	9	(	(	PUNCT
ejpam-6069	175	10	j	j	PROPN
ejpam-6069	175	11	+	+	CCONJ
ejpam-6069	175	12	1)1+i	1)1+i	NUM
ejpam-6069	175	13	=	=	SYM
ejpam-6069	175	14	1	1	NUM
ejpam-6069	175	15	[	[	PUNCT
ejpam-6069	175	16	(	(	PUNCT
ejpam-6069	175	17	−1)1	−1)1	X
ejpam-6069	175	18	(	(	PUNCT
ejpam-6069	175	19	1	1	NUM
ejpam-6069	175	20	0	0	NUM
ejpam-6069	175	21	)	)	PUNCT
ejpam-6069	175	22	(	(	PUNCT
ejpam-6069	175	23	0	0	NUM
ejpam-6069	175	24	+	+	NUM
ejpam-6069	175	25	1)1+i	1)1+i	NUM
ejpam-6069	175	26	+	+	CCONJ
ejpam-6069	175	27	(	(	PUNCT
ejpam-6069	175	28	−1)0	−1)0	X
ejpam-6069	175	29	(	(	PUNCT
ejpam-6069	175	30	1	1	NUM
ejpam-6069	175	31	1	1	NUM
ejpam-6069	175	32	)	)	PUNCT
ejpam-6069	175	33	(	(	PUNCT
ejpam-6069	175	34	1	1	NUM
ejpam-6069	175	35	+	+	NUM
ejpam-6069	175	36	1)1+i	1)1+i	NOUN
ejpam-6069	175	37	]	]	PUNCT
ejpam-6069	175	38	=	=	PUNCT
ejpam-6069	175	39	−1	−1	NOUN
ejpam-6069	175	40	+	+	CCONJ
ejpam-6069	175	41	2	2	NUM
ejpam-6069	175	42	cos	cos	X
ejpam-6069	175	43	(	(	PUNCT
ejpam-6069	175	44	ln	ln	NOUN
ejpam-6069	175	45	2	2	NUM
ejpam-6069	175	46	)	)	PUNCT
ejpam-6069	175	47	+	+	NUM
ejpam-6069	175	48	2i	2i	NUM
ejpam-6069	175	49	sin	sin	NOUN
ejpam-6069	175	50	(	(	PUNCT
ejpam-6069	175	51	ln	ln	NOUN
ejpam-6069	175	52	2	2	NUM
ejpam-6069	175	53	)	)	PUNCT
ejpam-6069	175	54	.	.	PUNCT
ejpam-6069	176	1	the	the	DET
ejpam-6069	176	2	same	same	ADJ
ejpam-6069	176	3	value	value	NOUN
ejpam-6069	176	4	is	be	AUX
ejpam-6069	176	5	obtained	obtain	VERB
ejpam-6069	176	6	for	for	ADP
ejpam-6069	176	7	s−1(1	s−1(1	ADJ
ejpam-6069	176	8	+	+	X
ejpam-6069	176	9	i	i	PROPN
ejpam-6069	176	10	,	,	PUNCT
ejpam-6069	176	11	1	1	X
ejpam-6069	176	12	)	)	PUNCT
ejpam-6069	176	13	using	use	VERB
ejpam-6069	176	14	the	the	DET
ejpam-6069	176	15	recurrence	recurrence	NOUN
ejpam-6069	176	16	relation	relation	NOUN
ejpam-6069	176	17	in	in	ADP
ejpam-6069	176	18	theorem	theorem	ADJ
ejpam-6069	176	19	3.2	3.2	NUM
ejpam-6069	176	20	as	as	SCONJ
ejpam-6069	176	21	shown	show	VERB
ejpam-6069	176	22	below	below	ADV
ejpam-6069	176	23	:	:	PUNCT
ejpam-6069	176	24	s−1	s−1	PROPN
ejpam-6069	176	25	(	(	PUNCT
ejpam-6069	176	26	1	1	NUM
ejpam-6069	176	27	+	+	CCONJ
ejpam-6069	176	28	i	i	PRON
ejpam-6069	176	29	,	,	PUNCT
ejpam-6069	176	30	1	1	X
ejpam-6069	176	31	)	)	PUNCT
ejpam-6069	176	32	=	=	SYM
ejpam-6069	176	33	s−1	s−1	NOUN
ejpam-6069	176	34	(	(	PUNCT
ejpam-6069	176	35	(	(	PUNCT
ejpam-6069	176	36	1	1	NUM
ejpam-6069	176	37	+	+	CCONJ
ejpam-6069	176	38	i)−	i)−	PROPN
ejpam-6069	176	39	1	1	NUM
ejpam-6069	176	40	,	,	PUNCT
ejpam-6069	176	41	(	(	PUNCT
ejpam-6069	176	42	1−	1−	NUM
ejpam-6069	176	43	1	1	NUM
ejpam-6069	176	44	)	)	PUNCT
ejpam-6069	176	45	)	)	PUNCT
ejpam-6069	177	1	+	+	CCONJ
ejpam-6069	177	2	(	(	PUNCT
ejpam-6069	177	3	1−	1−	NUM
ejpam-6069	177	4	(	(	PUNCT
ejpam-6069	177	5	−1	−1	NOUN
ejpam-6069	177	6	)	)	PUNCT
ejpam-6069	177	7	)	)	PUNCT
ejpam-6069	178	1	s−1	s−1	PROPN
ejpam-6069	178	2	(	(	PUNCT
ejpam-6069	178	3	(	(	PUNCT
ejpam-6069	178	4	1	1	NUM
ejpam-6069	178	5	+	+	CCONJ
ejpam-6069	178	6	i)−	i)−	PROPN
ejpam-6069	178	7	1	1	NUM
ejpam-6069	178	8	,	,	PUNCT
ejpam-6069	178	9	1	1	NUM
ejpam-6069	178	10	)	)	PUNCT
ejpam-6069	178	11	=	=	SYM
ejpam-6069	178	12	s−1	s−1	NOUN
ejpam-6069	178	13	(	(	PUNCT
ejpam-6069	178	14	i	i	NOUN
ejpam-6069	178	15	,	,	PUNCT
ejpam-6069	178	16	0	0	NUM
ejpam-6069	178	17	)	)	PUNCT
ejpam-6069	179	1	+	+	CCONJ
ejpam-6069	179	2	(	(	PUNCT
ejpam-6069	179	3	2	2	X
ejpam-6069	179	4	)	)	PUNCT
ejpam-6069	179	5	s−1	s−1	PROPN
ejpam-6069	179	6	(	(	PUNCT
ejpam-6069	179	7	i	i	PRON
ejpam-6069	179	8	,	,	PUNCT
ejpam-6069	179	9	1	1	X
ejpam-6069	179	10	)	)	PUNCT
ejpam-6069	179	11	=	=	SYM
ejpam-6069	179	12	1	1	NUM
ejpam-6069	179	13	+	+	NUM
ejpam-6069	179	14	2	2	NUM
ejpam-6069	179	15	[	[	PUNCT
ejpam-6069	179	16	−	−	PROPN
ejpam-6069	179	17	1	1	NUM
ejpam-6069	179	18	+	+	NUM
ejpam-6069	179	19	cos	cos	X
ejpam-6069	179	20	(	(	PUNCT
ejpam-6069	179	21	ln	ln	NOUN
ejpam-6069	179	22	2	2	NUM
ejpam-6069	179	23	)	)	PUNCT
ejpam-6069	179	24	+	+	CCONJ
ejpam-6069	179	25	i	i	PRON
ejpam-6069	179	26	sin	sin	VERB
ejpam-6069	179	27	(	(	PUNCT
ejpam-6069	179	28	ln	ln	NOUN
ejpam-6069	179	29	2	2	NUM
ejpam-6069	179	30	)	)	PUNCT
ejpam-6069	179	31	]	]	PUNCT
ejpam-6069	180	1	=	=	PUNCT
ejpam-6069	180	2	−1	−1	NOUN
ejpam-6069	180	3	+	+	CCONJ
ejpam-6069	180	4	2	2	NUM
ejpam-6069	180	5	cos	cos	X
ejpam-6069	180	6	(	(	PUNCT
ejpam-6069	180	7	ln	ln	NOUN
ejpam-6069	180	8	2	2	NUM
ejpam-6069	180	9	)	)	PUNCT
ejpam-6069	180	10	+	+	NUM
ejpam-6069	180	11	2i	2i	NUM
ejpam-6069	180	12	sin	sin	NOUN
ejpam-6069	180	13	(	(	PUNCT
ejpam-6069	180	14	ln	ln	NOUN
ejpam-6069	180	15	2	2	NUM
ejpam-6069	180	16	)	)	PUNCT
ejpam-6069	180	17	.	.	PUNCT
ejpam-6069	181	1	theorem	theorem	NOUN
ejpam-6069	181	2	3.3	3.3	NUM
ejpam-6069	181	3	can	can	AUX
ejpam-6069	181	4	be	be	AUX
ejpam-6069	181	5	generalized	generalize	VERB
ejpam-6069	181	6	further	far	ADV
ejpam-6069	181	7	by	by	ADP
ejpam-6069	181	8	substituting	substitute	VERB
ejpam-6069	181	9	k	k	PROPN
ejpam-6069	181	10	with	with	ADP
ejpam-6069	181	11	a	a	DET
ejpam-6069	181	12	complex	complex	ADJ
ejpam-6069	181	13	number	number	NOUN
ejpam-6069	181	14	y	y	PROPN
ejpam-6069	181	15	,	,	PUNCT
ejpam-6069	181	16	as	as	SCONJ
ejpam-6069	181	17	presented	present	VERB
ejpam-6069	181	18	in	in	ADP
ejpam-6069	181	19	the	the	DET
ejpam-6069	181	20	subsequent	subsequent	ADJ
ejpam-6069	181	21	theorem	theorem	PROPN
ejpam-6069	181	22	.	.	PUNCT
ejpam-6069	181	23	theorem	theorem	VERB
ejpam-6069	181	24	3.4	3.4	NUM
ejpam-6069	181	25	.	.	PUNCT
ejpam-6069	182	1	for	for	ADP
ejpam-6069	182	2	complex	complex	ADJ
ejpam-6069	182	3	numbers	number	NOUN
ejpam-6069	182	4	x	x	X
ejpam-6069	182	5	,	,	PUNCT
ejpam-6069	182	6	y	y	PROPN
ejpam-6069	182	7	and	and	CCONJ
ejpam-6069	182	8	a	a	PRON
ejpam-6069	182	9	with	with	ADP
ejpam-6069	182	10	re(a	re(a	NOUN
ejpam-6069	182	11	)	)	PUNCT
ejpam-6069	182	12	<	<	X
ejpam-6069	182	13	0	0	NUM
ejpam-6069	182	14	,	,	PUNCT
ejpam-6069	182	15	we	we	PRON
ejpam-6069	182	16	have	have	VERB
ejpam-6069	182	17	sa(x	sa(x	NOUN
ejpam-6069	182	18	,	,	PUNCT
ejpam-6069	182	19	y	y	NOUN
ejpam-6069	182	20	)	)	PUNCT
ejpam-6069	182	21	=	=	SYM
ejpam-6069	182	22	1	1	NUM
ejpam-6069	182	23	y	y	NOUN
ejpam-6069	182	24	!	!	PUNCT
ejpam-6069	183	1	∞∑	∞∑	NUM
ejpam-6069	183	2	j=0	j=0	PROPN
ejpam-6069	183	3	(	(	PUNCT
ejpam-6069	183	4	−1)y−j	−1)y−j	X
ejpam-6069	183	5	(	(	PUNCT
ejpam-6069	183	6	y	y	PROPN
ejpam-6069	183	7	j	j	PROPN
ejpam-6069	183	8	)	)	PUNCT
ejpam-6069	183	9	(	(	PUNCT
ejpam-6069	183	10	j	j	PROPN
ejpam-6069	183	11	−	−	PROPN
ejpam-6069	183	12	a)x	a)x	PUNCT
ejpam-6069	183	13	.	.	PUNCT
ejpam-6069	184	1	proof	proof	NOUN
ejpam-6069	184	2	.	.	PUNCT
ejpam-6069	185	1	since	since	SCONJ
ejpam-6069	185	2	y	y	PROPN
ejpam-6069	185	3	is	be	AUX
ejpam-6069	185	4	a	a	DET
ejpam-6069	185	5	complex	complex	ADJ
ejpam-6069	185	6	number	number	NOUN
ejpam-6069	185	7	,	,	PUNCT
ejpam-6069	185	8	we	we	PRON
ejpam-6069	185	9	use	use	VERB
ejpam-6069	185	10	the	the	DET
ejpam-6069	185	11	generalized	generalize	VERB
ejpam-6069	185	12	binomial	binomial	ADJ
ejpam-6069	185	13	theorem	theorem	NOUN
ejpam-6069	185	14	due	due	ADP
ejpam-6069	185	15	to	to	ADP
ejpam-6069	185	16	newton	newton	PROPN
ejpam-6069	185	17	to	to	PART
ejpam-6069	185	18	obtain	obtain	VERB
ejpam-6069	185	19	(	(	PUNCT
ejpam-6069	185	20	eu	eu	NOUN
ejpam-6069	185	21	−	−	PROPN
ejpam-6069	185	22	1)y	1)y	NUM
ejpam-6069	185	23	=	=	PUNCT
ejpam-6069	186	1	∞∑	∞∑	NUM
ejpam-6069	186	2	j=0	j=0	PROPN
ejpam-6069	186	3	(	(	PUNCT
ejpam-6069	186	4	y	y	PROPN
ejpam-6069	186	5	j	j	PROPN
ejpam-6069	186	6	)	)	PUNCT
ejpam-6069	186	7	(	(	PUNCT
ejpam-6069	186	8	−1)y−j(eu)j	−1)y−j(eu)j	NOUN
ejpam-6069	186	9	.	.	PUNCT
ejpam-6069	187	1	e.n	e.n	PROPN
ejpam-6069	187	2	.	.	PROPN
ejpam-6069	187	3	arlan	arlan	PROPN
ejpam-6069	187	4	,	,	PUNCT
ejpam-6069	187	5	m.b	m.b	PROPN
ejpam-6069	187	6	.	.	PROPN
ejpam-6069	187	7	montero	montero	PROPN
ejpam-6069	187	8	/	/	SYM
ejpam-6069	187	9	eur	eur	PROPN
ejpam-6069	187	10	.	.	PUNCT
ejpam-6069	188	1	j.	j.	PROPN
ejpam-6069	188	2	pure	pure	PROPN
ejpam-6069	188	3	appl	appl	PROPN
ejpam-6069	188	4	.	.	PROPN
ejpam-6069	188	5	math	math	PROPN
ejpam-6069	188	6	,	,	PUNCT
ejpam-6069	188	7	18	18	NUM
ejpam-6069	188	8	(	(	PUNCT
ejpam-6069	188	9	2	2	NUM
ejpam-6069	188	10	)	)	PUNCT
ejpam-6069	188	11	(	(	PUNCT
ejpam-6069	188	12	2025	2025	NUM
ejpam-6069	188	13	)	)	PUNCT
ejpam-6069	188	14	,	,	PUNCT
ejpam-6069	188	15	6069	6069	NUM
ejpam-6069	188	16	9	9	NUM
ejpam-6069	188	17	of	of	ADP
ejpam-6069	188	18	10	10	NUM
ejpam-6069	188	19	in	in	ADP
ejpam-6069	188	20	effect	effect	NOUN
ejpam-6069	188	21	,	,	PUNCT
ejpam-6069	188	22	using	use	VERB
ejpam-6069	188	23	definition	definition	NOUN
ejpam-6069	188	24	3.1	3.1	NUM
ejpam-6069	188	25	,	,	PUNCT
ejpam-6069	188	26	we	we	PRON
ejpam-6069	188	27	have	have	VERB
ejpam-6069	188	28	sa(x	sa(x	NOUN
ejpam-6069	188	29	,	,	PUNCT
ejpam-6069	188	30	y	y	NOUN
ejpam-6069	188	31	)	)	PUNCT
ejpam-6069	188	32	=	=	SYM
ejpam-6069	189	1	1	1	NUM
ejpam-6069	189	2	2πi	2πi	NOUN
ejpam-6069	189	3	x	x	X
ejpam-6069	189	4	!	!	PUNCT
ejpam-6069	189	5	y	y	PROPN
ejpam-6069	189	6	!	!	PUNCT
ejpam-6069	189	7	∫	∫	PROPN
ejpam-6069	190	1	h	h	PROPN
ejpam-6069	190	2	e−au	e−au	PROPN
ejpam-6069	191	1	(	(	PUNCT
ejpam-6069	191	2	∞∑	∞∑	NUM
ejpam-6069	191	3	j=0	j=0	PROPN
ejpam-6069	191	4	(	(	PUNCT
ejpam-6069	191	5	−1)y−jeuj	−1)y−jeuj	PROPN
ejpam-6069	191	6	(	(	PUNCT
ejpam-6069	191	7	y	y	PROPN
ejpam-6069	191	8	j	j	PROPN
ejpam-6069	191	9	)	)	PUNCT
ejpam-6069	191	10	)	)	PUNCT
ejpam-6069	192	1	du	du	PROPN
ejpam-6069	192	2	ux+1	ux+1	PROPN
ejpam-6069	192	3	=	=	SYM
ejpam-6069	192	4	1	1	NUM
ejpam-6069	192	5	2πi	2πi	NOUN
ejpam-6069	192	6	x	x	X
ejpam-6069	192	7	!	!	PUNCT
ejpam-6069	192	8	y	y	X
ejpam-6069	192	9	!	!	PUNCT
ejpam-6069	193	1	∞∑	∞∑	NUM
ejpam-6069	193	2	k=0	k=0	PROPN
ejpam-6069	193	3	∫	∫	PROPN
ejpam-6069	193	4	h	h	PROPN
ejpam-6069	193	5	e−au(−1)y−jeuj	e−au(−1)y−jeuj	PROPN
ejpam-6069	194	1	(	(	PUNCT
ejpam-6069	194	2	y	y	PROPN
ejpam-6069	194	3	j	j	PROPN
ejpam-6069	194	4	)	)	PUNCT
ejpam-6069	194	5	du	du	PROPN
ejpam-6069	194	6	ux+1	ux+1	PROPN
ejpam-6069	194	7	=	=	SYM
ejpam-6069	194	8	1	1	NUM
ejpam-6069	194	9	y	y	NOUN
ejpam-6069	194	10	!	!	PUNCT
ejpam-6069	195	1	∞∑	∞∑	NUM
ejpam-6069	195	2	k=0	k=0	PROPN
ejpam-6069	195	3	[	[	PUNCT
ejpam-6069	195	4	(	(	PUNCT
ejpam-6069	195	5	−1)y−jeuj	−1)y−jeuj	PROPN
ejpam-6069	195	6	(	(	PUNCT
ejpam-6069	195	7	y	y	PROPN
ejpam-6069	195	8	j	j	PROPN
ejpam-6069	195	9	)	)	PUNCT
ejpam-6069	195	10	·	·	PUNCT
ejpam-6069	195	11	x	x	X
ejpam-6069	195	12	!	!	PUNCT
ejpam-6069	195	13	2πi	2πi	ADJ
ejpam-6069	195	14	∫	∫	PROPN
ejpam-6069	195	15	h	h	PROPN
ejpam-6069	195	16	e(j−a)u	e(j−a)u	NOUN
ejpam-6069	195	17	du	du	PROPN
ejpam-6069	195	18	ux+1	ux+1	PROPN
ejpam-6069	195	19	]	]	PUNCT
ejpam-6069	195	20	.	.	PUNCT
ejpam-6069	196	1	consequently	consequently	ADV
ejpam-6069	196	2	,	,	PUNCT
ejpam-6069	196	3	by	by	ADP
ejpam-6069	196	4	lemma	lemma	PROPN
ejpam-6069	196	5	4	4	NUM
ejpam-6069	196	6	,	,	PUNCT
ejpam-6069	196	7	sa(x	sa(x	NOUN
ejpam-6069	196	8	,	,	PUNCT
ejpam-6069	196	9	y	y	NOUN
ejpam-6069	196	10	)	)	PUNCT
ejpam-6069	196	11	=	=	SYM
ejpam-6069	196	12	1	1	NUM
ejpam-6069	196	13	y	y	NOUN
ejpam-6069	196	14	!	!	PUNCT
ejpam-6069	197	1	∞∑	∞∑	NUM
ejpam-6069	197	2	j=0	j=0	PROPN
ejpam-6069	197	3	(	(	PUNCT
ejpam-6069	197	4	−1)y−j	−1)y−j	X
ejpam-6069	197	5	(	(	PUNCT
ejpam-6069	197	6	y	y	PROPN
ejpam-6069	197	7	j	j	PROPN
ejpam-6069	197	8	)	)	PUNCT
ejpam-6069	197	9	(	(	PUNCT
ejpam-6069	197	10	j	j	PROPN
ejpam-6069	197	11	−	−	PROPN
ejpam-6069	197	12	a)x	a)x	NOUN
ejpam-6069	197	13	.	.	PUNCT
ejpam-6069	198	1	4	4	X
ejpam-6069	198	2	.	.	X
ejpam-6069	198	3	conclusion	conclusion	NOUN
ejpam-6069	198	4	in	in	ADP
ejpam-6069	198	5	this	this	DET
ejpam-6069	198	6	work	work	NOUN
ejpam-6069	198	7	,	,	PUNCT
ejpam-6069	198	8	we	we	PRON
ejpam-6069	198	9	extended	extend	VERB
ejpam-6069	198	10	the	the	DET
ejpam-6069	198	11	non	non	ADJ
ejpam-6069	198	12	-	-	ADJ
ejpam-6069	198	13	central	central	ADJ
ejpam-6069	198	14	stirling	stirling	NOUN
ejpam-6069	198	15	numbers	number	NOUN
ejpam-6069	198	16	of	of	ADP
ejpam-6069	198	17	the	the	DET
ejpam-6069	198	18	second	second	ADJ
ejpam-6069	198	19	kind	kind	NOUN
ejpam-6069	198	20	to	to	ADP
ejpam-6069	198	21	complex	complex	ADJ
ejpam-6069	198	22	arguments	argument	NOUN
ejpam-6069	198	23	using	use	VERB
ejpam-6069	198	24	an	an	DET
ejpam-6069	198	25	integral	integral	ADJ
ejpam-6069	198	26	representation	representation	NOUN
ejpam-6069	198	27	with	with	ADP
ejpam-6069	198	28	a	a	DET
ejpam-6069	198	29	hankel	hankel	NOUN
ejpam-6069	198	30	contour	contour	NOUN
ejpam-6069	198	31	.	.	PUNCT
ejpam-6069	199	1	this	this	DET
ejpam-6069	199	2	extension	extension	NOUN
ejpam-6069	199	3	broadens	broaden	VERB
ejpam-6069	199	4	the	the	DET
ejpam-6069	199	5	use	use	NOUN
ejpam-6069	199	6	of	of	ADP
ejpam-6069	199	7	these	these	DET
ejpam-6069	199	8	numbers	number	NOUN
ejpam-6069	199	9	and	and	CCONJ
ejpam-6069	199	10	offers	offer	VERB
ejpam-6069	199	11	new	new	ADJ
ejpam-6069	199	12	insights	insight	NOUN
ejpam-6069	199	13	into	into	ADP
ejpam-6069	199	14	their	their	PRON
ejpam-6069	199	15	properties	property	NOUN
ejpam-6069	199	16	in	in	ADP
ejpam-6069	199	17	the	the	DET
ejpam-6069	199	18	complex	complex	ADJ
ejpam-6069	199	19	domain	domain	NOUN
ejpam-6069	199	20	.	.	PUNCT
ejpam-6069	200	1	we	we	PRON
ejpam-6069	200	2	also	also	ADV
ejpam-6069	200	3	explored	explore	VERB
ejpam-6069	200	4	how	how	SCONJ
ejpam-6069	200	5	important	important	ADJ
ejpam-6069	200	6	properties	property	NOUN
ejpam-6069	200	7	,	,	PUNCT
ejpam-6069	200	8	such	such	ADJ
ejpam-6069	200	9	as	as	ADP
ejpam-6069	200	10	recurrence	recurrence	NOUN
ejpam-6069	200	11	relations	relation	NOUN
ejpam-6069	200	12	,	,	PUNCT
ejpam-6069	200	13	are	be	AUX
ejpam-6069	200	14	preserved	preserve	VERB
ejpam-6069	200	15	and	and	CCONJ
ejpam-6069	200	16	adapted	adapt	VERB
ejpam-6069	200	17	,	,	PUNCT
ejpam-6069	200	18	showing	show	VERB
ejpam-6069	200	19	the	the	DET
ejpam-6069	200	20	usefulness	usefulness	NOUN
ejpam-6069	200	21	of	of	ADP
ejpam-6069	200	22	this	this	DET
ejpam-6069	200	23	approach	approach	NOUN
ejpam-6069	200	24	for	for	ADP
ejpam-6069	200	25	studying	study	VERB
ejpam-6069	200	26	combinatorial	combinatorial	ADJ
ejpam-6069	200	27	structures	structure	NOUN
ejpam-6069	200	28	.	.	PUNCT
ejpam-6069	201	1	looking	look	VERB
ejpam-6069	201	2	ahead	ahead	ADV
ejpam-6069	201	3	,	,	PUNCT
ejpam-6069	201	4	it	it	PRON
ejpam-6069	201	5	would	would	AUX
ejpam-6069	201	6	be	be	AUX
ejpam-6069	201	7	beneficial	beneficial	ADJ
ejpam-6069	201	8	to	to	PART
ejpam-6069	201	9	extend	extend	VERB
ejpam-6069	201	10	non	non	ADJ
ejpam-6069	201	11	-	-	ADJ
ejpam-6069	201	12	central	central	ADJ
ejpam-6069	201	13	bell	bell	NOUN
ejpam-6069	201	14	numbers	number	NOUN
ejpam-6069	201	15	(	(	PUNCT
ejpam-6069	201	16	as	as	SCONJ
ejpam-6069	201	17	defined	define	VERB
ejpam-6069	201	18	in	in	ADP
ejpam-6069	201	19	[	[	X
ejpam-6069	201	20	10	10	NUM
ejpam-6069	201	21	]	]	PUNCT
ejpam-6069	201	22	)	)	PUNCT
ejpam-6069	201	23	to	to	ADP
ejpam-6069	201	24	complex	complex	ADJ
ejpam-6069	201	25	arguments	argument	NOUN
ejpam-6069	201	26	,	,	PUNCT
ejpam-6069	201	27	building	build	VERB
ejpam-6069	201	28	on	on	ADP
ejpam-6069	201	29	the	the	DET
ejpam-6069	201	30	work	work	NOUN
ejpam-6069	201	31	in	in	ADP
ejpam-6069	201	32	[	[	X
ejpam-6069	201	33	11	11	NUM
ejpam-6069	201	34	]	]	PUNCT
ejpam-6069	201	35	.	.	PUNCT
ejpam-6069	202	1	these	these	DET
ejpam-6069	202	2	bell	bell	NOUN
ejpam-6069	202	3	numbers	number	NOUN
ejpam-6069	202	4	are	be	AUX
ejpam-6069	202	5	important	important	ADJ
ejpam-6069	202	6	for	for	ADP
ejpam-6069	202	7	counting	count	VERB
ejpam-6069	202	8	partitions	partition	NOUN
ejpam-6069	202	9	and	and	CCONJ
ejpam-6069	202	10	other	other	ADJ
ejpam-6069	202	11	combinatorial	combinatorial	ADJ
ejpam-6069	202	12	structures	structure	NOUN
ejpam-6069	202	13	,	,	PUNCT
ejpam-6069	202	14	and	and	CCONJ
ejpam-6069	202	15	extending	extend	VERB
ejpam-6069	202	16	them	they	PRON
ejpam-6069	202	17	could	could	AUX
ejpam-6069	202	18	uncover	uncover	VERB
ejpam-6069	202	19	new	new	ADJ
ejpam-6069	202	20	identities	identity	NOUN
ejpam-6069	202	21	,	,	PUNCT
ejpam-6069	202	22	recurrence	recurrence	NOUN
ejpam-6069	202	23	relations	relation	NOUN
ejpam-6069	202	24	,	,	PUNCT
ejpam-6069	202	25	and	and	CCONJ
ejpam-6069	202	26	lead	lead	VERB
ejpam-6069	202	27	to	to	ADP
ejpam-6069	202	28	deeper	deep	ADJ
ejpam-6069	202	29	insights	insight	NOUN
ejpam-6069	202	30	in	in	ADP
ejpam-6069	202	31	areas	area	NOUN
ejpam-6069	202	32	like	like	ADP
ejpam-6069	202	33	number	number	NOUN
ejpam-6069	202	34	theory	theory	NOUN
ejpam-6069	202	35	,	,	PUNCT
ejpam-6069	202	36	asymptotics	asymptotic	NOUN
ejpam-6069	202	37	,	,	PUNCT
ejpam-6069	202	38	and	and	CCONJ
ejpam-6069	202	39	complex	complex	ADJ
ejpam-6069	202	40	analysis	analysis	NOUN
ejpam-6069	202	41	.	.	PUNCT
ejpam-6069	203	1	additionally	additionally	ADV
ejpam-6069	203	2	,	,	PUNCT
ejpam-6069	203	3	expanding	expand	VERB
ejpam-6069	203	4	the	the	DET
ejpam-6069	203	5	parameters	parameter	NOUN
ejpam-6069	203	6	of	of	ADP
ejpam-6069	203	7	(	(	PUNCT
ejpam-6069	203	8	r1	r1	PROPN
ejpam-6069	203	9	,	,	PUNCT
ejpam-6069	203	10	·	·	PUNCT
ejpam-6069	203	11	·	·	PUNCT
ejpam-6069	203	12	·	·	PUNCT
ejpam-6069	203	13	,	,	PUNCT
ejpam-6069	203	14	rp)-stirling	rp)-stirle	VERB
ejpam-6069	203	15	numbers	number	NOUN
ejpam-6069	203	16	of	of	ADP
ejpam-6069	203	17	the	the	DET
ejpam-6069	203	18	second	second	ADJ
ejpam-6069	203	19	kind	kind	NOUN
ejpam-6069	203	20	from	from	ADP
ejpam-6069	203	21	[	[	X
ejpam-6069	203	22	12	12	NUM
ejpam-6069	203	23	]	]	PUNCT
ejpam-6069	203	24	and	and	CCONJ
ejpam-6069	203	25	the	the	DET
ejpam-6069	203	26	generalized	generalize	VERB
ejpam-6069	203	27	apostol	apostol	NOUN
ejpam-6069	203	28	-	-	PUNCT
ejpam-6069	203	29	type	type	NOUN
ejpam-6069	203	30	frobenius	frobenius	NOUN
ejpam-6069	203	31	-	-	PUNCT
ejpam-6069	203	32	euler	euler	NOUN
ejpam-6069	203	33	polynomials	polynomial	NOUN
ejpam-6069	203	34	in	in	ADP
ejpam-6069	203	35	[	[	X
ejpam-6069	203	36	13	13	NUM
ejpam-6069	203	37	]	]	PUNCT
ejpam-6069	203	38	to	to	ADP
ejpam-6069	203	39	complex	complex	ADJ
ejpam-6069	203	40	arguments	argument	NOUN
ejpam-6069	203	41	is	be	AUX
ejpam-6069	203	42	also	also	ADV
ejpam-6069	203	43	an	an	DET
ejpam-6069	203	44	interesting	interesting	ADJ
ejpam-6069	203	45	direction	direction	NOUN
ejpam-6069	203	46	for	for	ADP
ejpam-6069	203	47	future	future	ADJ
ejpam-6069	203	48	research	research	NOUN
ejpam-6069	203	49	.	.	PUNCT
ejpam-6069	204	1	acknowledgements	acknowledgement	NOUN
ejpam-6069	204	2	the	the	DET
ejpam-6069	204	3	authors	author	NOUN
ejpam-6069	204	4	would	would	AUX
ejpam-6069	204	5	like	like	VERB
ejpam-6069	204	6	to	to	PART
ejpam-6069	204	7	express	express	VERB
ejpam-6069	204	8	their	their	PRON
ejpam-6069	204	9	gratitude	gratitude	NOUN
ejpam-6069	204	10	to	to	ADP
ejpam-6069	204	11	dr	dr	PROPN
ejpam-6069	204	12	.	.	PROPN
ejpam-6069	204	13	mary	mary	PROPN
ejpam-6069	204	14	joy	joy	PROPN
ejpam-6069	204	15	d.	d.	PROPN
ejpam-6069	204	16	regidorlatayada	regidorlatayada	PROPN
ejpam-6069	204	17	for	for	ADP
ejpam-6069	204	18	her	her	PRON
ejpam-6069	204	19	valuable	valuable	ADJ
ejpam-6069	204	20	critiques	critique	NOUN
ejpam-6069	204	21	and	and	CCONJ
ejpam-6069	204	22	recommendations	recommendation	NOUN
ejpam-6069	204	23	,	,	PUNCT
ejpam-6069	204	24	which	which	PRON
ejpam-6069	204	25	greatly	greatly	ADV
ejpam-6069	204	26	contributed	contribute	VERB
ejpam-6069	204	27	to	to	ADP
ejpam-6069	204	28	the	the	DET
ejpam-6069	204	29	refinement	refinement	NOUN
ejpam-6069	204	30	and	and	CCONJ
ejpam-6069	204	31	direction	direction	NOUN
ejpam-6069	204	32	of	of	ADP
ejpam-6069	204	33	this	this	DET
ejpam-6069	204	34	research	research	NOUN
ejpam-6069	204	35	.	.	PUNCT
ejpam-6069	205	1	references	reference	NOUN
ejpam-6069	205	2	[	[	X
ejpam-6069	205	3	1	1	NUM
ejpam-6069	205	4	]	]	PUNCT
ejpam-6069	205	5	m.	m.	NOUN
ejpam-6069	205	6	koutras	koutra	NOUN
ejpam-6069	205	7	.	.	PUNCT
ejpam-6069	206	1	non	non	ADJ
ejpam-6069	206	2	-	-	ADJ
ejpam-6069	206	3	central	central	ADJ
ejpam-6069	206	4	stirling	stirling	NOUN
ejpam-6069	206	5	numbers	number	NOUN
ejpam-6069	206	6	and	and	CCONJ
ejpam-6069	206	7	some	some	DET
ejpam-6069	206	8	applications	application	NOUN
ejpam-6069	206	9	.	.	PUNCT
ejpam-6069	207	1	discrete	discrete	ADJ
ejpam-6069	207	2	mathematics	mathematic	NOUN
ejpam-6069	207	3	,	,	PUNCT
ejpam-6069	207	4	42:73–89	42:73–89	NUM
ejpam-6069	207	5	,	,	PUNCT
ejpam-6069	207	6	1982	1982	NUM
ejpam-6069	207	7	.	.	PUNCT
ejpam-6069	208	1	e.n	e.n	PROPN
ejpam-6069	208	2	.	.	PROPN
ejpam-6069	208	3	arlan	arlan	PROPN
ejpam-6069	208	4	,	,	PUNCT
ejpam-6069	208	5	m.b	m.b	PROPN
ejpam-6069	208	6	.	.	PROPN
ejpam-6069	208	7	montero	montero	PROPN
ejpam-6069	208	8	/	/	SYM
ejpam-6069	208	9	eur	eur	PROPN
ejpam-6069	208	10	.	.	PUNCT
ejpam-6069	209	1	j.	j.	PROPN
ejpam-6069	209	2	pure	pure	PROPN
ejpam-6069	209	3	appl	appl	PROPN
ejpam-6069	209	4	.	.	PROPN
ejpam-6069	209	5	math	math	PROPN
ejpam-6069	209	6	,	,	PUNCT
ejpam-6069	209	7	18	18	NUM
ejpam-6069	209	8	(	(	PUNCT
ejpam-6069	209	9	2	2	NUM
ejpam-6069	209	10	)	)	PUNCT
ejpam-6069	209	11	(	(	PUNCT
ejpam-6069	209	12	2025	2025	NUM
ejpam-6069	209	13	)	)	PUNCT
ejpam-6069	209	14	,	,	PUNCT
ejpam-6069	209	15	6069	6069	NUM
ejpam-6069	209	16	10	10	NUM
ejpam-6069	209	17	of	of	ADP
ejpam-6069	209	18	10	10	NUM
ejpam-6069	209	19	[	[	SYM
ejpam-6069	209	20	2	2	NUM
ejpam-6069	209	21	]	]	X
ejpam-6069	209	22	r.l	r.l	PROPN
ejpam-6069	209	23	.	.	PROPN
ejpam-6069	209	24	graham	graham	PROPN
ejpam-6069	209	25	,	,	PUNCT
ejpam-6069	209	26	d.e	d.e	PROPN
ejpam-6069	209	27	.	.	PROPN
ejpam-6069	209	28	knuth	knuth	PROPN
ejpam-6069	209	29	,	,	PUNCT
ejpam-6069	209	30	and	and	CCONJ
ejpam-6069	209	31	o.	o.	PROPN
ejpam-6069	209	32	patashnik	patashnik	PROPN
ejpam-6069	209	33	.	.	PUNCT
ejpam-6069	210	1	discrete	discrete	ADJ
ejpam-6069	210	2	mathematics	mathematic	NOUN
ejpam-6069	210	3	.	.	PUNCT
ejpam-6069	211	1	addison	addison	PROPN
ejpam-6069	211	2	-	-	PUNCT
ejpam-6069	211	3	wesley	wesley	PROPN
ejpam-6069	211	4	,	,	PUNCT
ejpam-6069	211	5	1989	1989	NUM
ejpam-6069	211	6	.	.	PUNCT
ejpam-6069	212	1	[	[	X
ejpam-6069	212	2	3	3	X
ejpam-6069	212	3	]	]	PUNCT
ejpam-6069	212	4	p.	p.	NOUN
ejpam-6069	212	5	flajolet	flajolet	NOUN
ejpam-6069	212	6	and	and	CCONJ
ejpam-6069	212	7	h.	h.	PROPN
ejpam-6069	212	8	prodinger	prodinger	NOUN
ejpam-6069	212	9	.	.	PUNCT
ejpam-6069	213	1	on	on	ADP
ejpam-6069	213	2	stirling	stirling	NOUN
ejpam-6069	213	3	numbers	number	NOUN
ejpam-6069	213	4	for	for	ADP
ejpam-6069	213	5	complex	complex	ADJ
ejpam-6069	213	6	arguments	argument	NOUN
ejpam-6069	213	7	and	and	CCONJ
ejpam-6069	213	8	hankel	hankel	NOUN
ejpam-6069	213	9	contours	contours	PROPN
ejpam-6069	213	10	.	.	PUNCT
ejpam-6069	214	1	siam	siam	PROPN
ejpam-6069	214	2	journal	journal	PROPN
ejpam-6069	214	3	on	on	ADP
ejpam-6069	214	4	discrete	discrete	ADJ
ejpam-6069	214	5	mathematics	mathematic	NOUN
ejpam-6069	214	6	,	,	PUNCT
ejpam-6069	214	7	12(2):155–159	12(2):155–159	PROPN
ejpam-6069	214	8	,	,	PUNCT
ejpam-6069	214	9	1999	1999	NUM
ejpam-6069	214	10	.	.	PUNCT
ejpam-6069	215	1	[	[	X
ejpam-6069	215	2	4	4	NUM
ejpam-6069	215	3	]	]	SYM
ejpam-6069	215	4	c	c	PROPN
ejpam-6069	215	5	-	-	PUNCT
ejpam-6069	215	6	c.	c.	PROPN
ejpam-6069	215	7	chen	chen	PROPN
ejpam-6069	215	8	and	and	CCONJ
ejpam-6069	215	9	k	k	PROPN
ejpam-6069	215	10	-	-	PUNCT
ejpam-6069	215	11	m.	m.	NOUN
ejpam-6069	215	12	koh	koh	PROPN
ejpam-6069	215	13	.	.	PUNCT
ejpam-6069	216	1	principles	principle	NOUN
ejpam-6069	216	2	and	and	CCONJ
ejpam-6069	216	3	techniques	technique	NOUN
ejpam-6069	216	4	in	in	ADP
ejpam-6069	216	5	combinatorics	combinatoric	NOUN
ejpam-6069	216	6	.	.	PUNCT
ejpam-6069	217	1	world	world	PROPN
ejpam-6069	217	2	scientific	scientific	ADJ
ejpam-6069	217	3	,	,	PUNCT
ejpam-6069	217	4	1992	1992	NUM
ejpam-6069	217	5	.	.	PUNCT
ejpam-6069	218	1	[	[	X
ejpam-6069	218	2	5	5	NUM
ejpam-6069	218	3	]	]	PUNCT
ejpam-6069	218	4	l.	l.	PROPN
ejpam-6069	218	5	comtet	comtet	PROPN
ejpam-6069	218	6	.	.	PUNCT
ejpam-6069	219	1	advanced	advanced	ADJ
ejpam-6069	219	2	combinatorics	combinatoric	NOUN
ejpam-6069	219	3	.	.	PUNCT
ejpam-6069	220	1	reidel	reidel	PROPN
ejpam-6069	220	2	,	,	PUNCT
ejpam-6069	220	3	dordrecht	dordrecht	PROPN
ejpam-6069	220	4	,	,	PUNCT
ejpam-6069	220	5	the	the	DET
ejpam-6069	220	6	netherlands	netherlands	PROPN
ejpam-6069	220	7	,	,	PUNCT
ejpam-6069	220	8	1974	1974	NUM
ejpam-6069	220	9	.	.	PUNCT
ejpam-6069	221	1	[	[	X
ejpam-6069	221	2	6	6	NUM
ejpam-6069	221	3	]	]	X
ejpam-6069	221	4	r.v	r.v	PROPN
ejpam-6069	221	5	.	.	PROPN
ejpam-6069	221	6	churchill	churchill	PROPN
ejpam-6069	221	7	and	and	CCONJ
ejpam-6069	221	8	j.w	j.w	PROPN
ejpam-6069	221	9	.	.	PROPN
ejpam-6069	221	10	brown	brown	PROPN
ejpam-6069	221	11	.	.	PUNCT
ejpam-6069	222	1	complex	complex	ADJ
ejpam-6069	222	2	variables	variable	NOUN
ejpam-6069	222	3	and	and	CCONJ
ejpam-6069	222	4	applications	application	NOUN
ejpam-6069	222	5	.	.	PUNCT
ejpam-6069	223	1	mcgraw	mcgraw	PROPN
ejpam-6069	223	2	-	-	PUNCT
ejpam-6069	223	3	hill	hill	PROPN
ejpam-6069	223	4	,	,	PUNCT
ejpam-6069	223	5	inc	inc	PROPN
ejpam-6069	223	6	.	.	PROPN
ejpam-6069	223	7	,	,	PUNCT
ejpam-6069	223	8	5th	5th	ADJ
ejpam-6069	223	9	edition	edition	NOUN
ejpam-6069	223	10	,	,	PUNCT
ejpam-6069	223	11	1990	1990	NUM
ejpam-6069	223	12	.	.	PUNCT
ejpam-6069	224	1	[	[	X
ejpam-6069	224	2	7	7	X
ejpam-6069	224	3	]	]	X
ejpam-6069	224	4	f.w.j	f.w.j	NOUN
ejpam-6069	224	5	.	.	PUNCT
ejpam-6069	224	6	olver	olver	PROPN
ejpam-6069	224	7	.	.	PUNCT
ejpam-6069	225	1	introduction	introduction	NOUN
ejpam-6069	225	2	to	to	ADP
ejpam-6069	225	3	asymptotics	asymptotic	NOUN
ejpam-6069	225	4	and	and	CCONJ
ejpam-6069	225	5	special	special	ADJ
ejpam-6069	225	6	functions	function	NOUN
ejpam-6069	225	7	.	.	PUNCT
ejpam-6069	226	1	academic	academic	ADJ
ejpam-6069	226	2	press	press	NOUN
ejpam-6069	226	3	,	,	PUNCT
ejpam-6069	226	4	1974	1974	NUM
ejpam-6069	226	5	.	.	PUNCT
ejpam-6069	227	1	[	[	X
ejpam-6069	227	2	8	8	NUM
ejpam-6069	227	3	]	]	X
ejpam-6069	227	4	l.l	l.l	PROPN
ejpam-6069	227	5	.	.	PROPN
ejpam-6069	227	6	pennisi	pennisi	PROPN
ejpam-6069	227	7	.	.	PUNCT
ejpam-6069	228	1	elements	element	NOUN
ejpam-6069	228	2	of	of	ADP
ejpam-6069	228	3	complex	complex	ADJ
ejpam-6069	228	4	variables	variable	NOUN
ejpam-6069	228	5	.	.	PUNCT
ejpam-6069	229	1	cacho	cacho	PROPN
ejpam-6069	229	2	hermanos	hermanos	PROPN
ejpam-6069	229	3	,	,	PUNCT
ejpam-6069	229	4	inc	inc	PROPN
ejpam-6069	229	5	.	.	PROPN
ejpam-6069	229	6	,	,	PUNCT
ejpam-6069	229	7	2nd	2nd	PROPN
ejpam-6069	229	8	edition	edition	NOUN
ejpam-6069	229	9	,	,	PUNCT
ejpam-6069	229	10	1976	1976	NUM
ejpam-6069	229	11	.	.	PUNCT
ejpam-6069	230	1	[	[	X
ejpam-6069	230	2	9	9	NUM
ejpam-6069	230	3	]	]	X
ejpam-6069	230	4	f.w.j	f.w.j	NOUN
ejpam-6069	230	5	.	.	PUNCT
ejpam-6069	230	6	olver	olver	PROPN
ejpam-6069	230	7	,	,	PUNCT
ejpam-6069	230	8	d.	d.	PROPN
ejpam-6069	230	9	lozier	lozier	PROPN
ejpam-6069	230	10	,	,	PUNCT
ejpam-6069	230	11	r.	r.	PROPN
ejpam-6069	230	12	boisvert	boisvert	PROPN
ejpam-6069	230	13	,	,	PUNCT
ejpam-6069	230	14	et	et	PROPN
ejpam-6069	230	15	al	al	PROPN
ejpam-6069	230	16	.	.	PROPN
ejpam-6069	230	17	nist	nist	PROPN
ejpam-6069	230	18	handbook	handbook	PROPN
ejpam-6069	230	19	of	of	ADP
ejpam-6069	230	20	mathematical	mathematical	ADJ
ejpam-6069	230	21	functions	function	NOUN
ejpam-6069	230	22	.	.	PUNCT
ejpam-6069	231	1	cambridge	cambridge	PROPN
ejpam-6069	231	2	press	press	PROPN
ejpam-6069	231	3	,	,	PUNCT
ejpam-6069	231	4	2010	2010	NUM
ejpam-6069	231	5	.	.	PUNCT
ejpam-6069	232	1	[	[	X
ejpam-6069	232	2	10	10	NUM
ejpam-6069	232	3	]	]	X
ejpam-6069	232	4	roberto	roberto	PROPN
ejpam-6069	232	5	b.	b.	PROPN
ejpam-6069	232	6	corcino	corcino	PROPN
ejpam-6069	232	7	,	,	PUNCT
ejpam-6069	232	8	harren	harren	PROPN
ejpam-6069	232	9	jaylo	jaylo	PROPN
ejpam-6069	232	10	-	-	PUNCT
ejpam-6069	232	11	campos	campos	PROPN
ejpam-6069	232	12	,	,	PUNCT
ejpam-6069	232	13	and	and	CCONJ
ejpam-6069	232	14	amila	amila	PROPN
ejpam-6069	232	15	p.	p.	NOUN
ejpam-6069	232	16	macodi	macodi	NOUN
ejpam-6069	232	17	-	-	PUNCT
ejpam-6069	232	18	ringia	ringia	NOUN
ejpam-6069	232	19	.	.	PUNCT
ejpam-6069	233	1	on	on	ADP
ejpam-6069	233	2	noncentral	noncentral	ADJ
ejpam-6069	233	3	bell	bell	NOUN
ejpam-6069	233	4	numbers	number	NOUN
ejpam-6069	233	5	and	and	CCONJ
ejpam-6069	233	6	their	their	PRON
ejpam-6069	233	7	hankel	hankel	NOUN
ejpam-6069	233	8	transforms	transform	VERB
ejpam-6069	233	9	.	.	PUNCT
ejpam-6069	234	1	the	the	DET
ejpam-6069	234	2	journal	journal	NOUN
ejpam-6069	234	3	of	of	ADP
ejpam-6069	234	4	algebra	algebra	NOUN
ejpam-6069	234	5	and	and	CCONJ
ejpam-6069	234	6	number	number	NOUN
ejpam-6069	234	7	theory	theory	NOUN
ejpam-6069	234	8	,	,	PUNCT
ejpam-6069	234	9	2(2):1–10	2(2):1–10	NUM
ejpam-6069	234	10	,	,	PUNCT
ejpam-6069	234	11	2014	2014	NUM
ejpam-6069	234	12	.	.	PUNCT
ejpam-6069	235	1	[	[	X
ejpam-6069	235	2	11	11	NUM
ejpam-6069	235	3	]	]	X
ejpam-6069	235	4	roberto	roberto	PROPN
ejpam-6069	235	5	b.	b.	PROPN
ejpam-6069	235	6	corcino	corcino	PROPN
ejpam-6069	235	7	,	,	PUNCT
ejpam-6069	235	8	cristina	cristina	PROPN
ejpam-6069	235	9	b.	b.	PROPN
ejpam-6069	235	10	corcino	corcino	PROPN
ejpam-6069	235	11	,	,	PUNCT
ejpam-6069	235	12	and	and	CCONJ
ejpam-6069	235	13	maribeth	maribeth	PROPN
ejpam-6069	235	14	b.	b.	PROPN
ejpam-6069	235	15	montero	montero	PROPN
ejpam-6069	235	16	.	.	PUNCT
ejpam-6069	236	1	on	on	ADP
ejpam-6069	236	2	generalized	generalized	ADJ
ejpam-6069	236	3	bell	bell	NOUN
ejpam-6069	236	4	numbers	number	NOUN
ejpam-6069	236	5	for	for	ADP
ejpam-6069	236	6	complex	complex	ADJ
ejpam-6069	236	7	argument	argument	NOUN
ejpam-6069	236	8	.	.	PUNCT
ejpam-6069	237	1	journal	journal	NOUN
ejpam-6069	237	2	of	of	ADP
ejpam-6069	237	3	applied	apply	VERB
ejpam-6069	237	4	mathematics	mathematic	NOUN
ejpam-6069	237	5	and	and	CCONJ
ejpam-6069	237	6	computation	computation	NOUN
ejpam-6069	237	7	,	,	PUNCT
ejpam-6069	237	8	270:60–68	270:60–68	NUM
ejpam-6069	237	9	,	,	PUNCT
ejpam-6069	237	10	2015	2015	NUM
ejpam-6069	237	11	.	.	PUNCT
ejpam-6069	238	1	[	[	X
ejpam-6069	238	2	12	12	NUM
ejpam-6069	238	3	]	]	X
ejpam-6069	238	4	miloud	miloud	ADJ
ejpam-6069	238	5	mihoubi	mihoubi	NOUN
ejpam-6069	238	6	and	and	CCONJ
ejpam-6069	238	7	mohammed	mohammed	PROPN
ejpam-6069	238	8	said	say	VERB
ejpam-6069	238	9	maamra	maamra	NOUN
ejpam-6069	238	10	.	.	PUNCT
ejpam-6069	239	1	the	the	DET
ejpam-6069	239	2	(	(	PUNCT
ejpam-6069	239	3	r1	r1	PROPN
ejpam-6069	239	4	,	,	PUNCT
ejpam-6069	239	5	...	...	PUNCT
ejpam-6069	239	6	,	,	PUNCT
ejpam-6069	239	7	rp)-stirling	rp)-stirle	VERB
ejpam-6069	239	8	numbers	number	NOUN
ejpam-6069	239	9	of	of	ADP
ejpam-6069	239	10	the	the	DET
ejpam-6069	239	11	second	second	ADJ
ejpam-6069	239	12	kind	kind	NOUN
ejpam-6069	239	13	.	.	PUNCT
ejpam-6069	240	1	integers	integer	NOUN
ejpam-6069	240	2	,	,	PUNCT
ejpam-6069	240	3	12(5):1047–1059	12(5):1047–1059	NUM
ejpam-6069	240	4	,	,	PUNCT
ejpam-6069	240	5	2012	2012	NUM
ejpam-6069	240	6	.	.	PUNCT
ejpam-6069	241	1	[	[	X
ejpam-6069	241	2	13	13	NUM
ejpam-6069	241	3	]	]	SYM
ejpam-6069	241	4	letelier	letelier	NOUN
ejpam-6069	241	5	castilla	castilla	PROPN
ejpam-6069	241	6	and	and	CCONJ
ejpam-6069	241	7	william	william	PROPN
ejpam-6069	241	8	ramı́rez	ramı́rez	PROPN
ejpam-6069	241	9	.	.	PUNCT
ejpam-6069	242	1	a	a	DET
ejpam-6069	242	2	new	new	ADJ
ejpam-6069	242	3	class	class	NOUN
ejpam-6069	242	4	of	of	ADP
ejpam-6069	242	5	generalized	generalized	ADJ
ejpam-6069	242	6	apostol	apostol	NOUN
ejpam-6069	242	7	–	–	PUNCT
ejpam-6069	242	8	type	type	NOUN
ejpam-6069	242	9	frobenius	frobenius	NOUN
ejpam-6069	242	10	–	–	PUNCT
ejpam-6069	242	11	euler	euler	NOUN
ejpam-6069	242	12	polynomials	polynomial	NOUN
ejpam-6069	242	13	.	.	PUNCT
ejpam-6069	243	1	aims	aim	VERB
ejpam-6069	243	2	mathematics	mathematic	NOUN
ejpam-6069	243	3	,	,	PUNCT
ejpam-6069	243	4	10(2):3623–3641	10(2):3623–3641	NUM
ejpam-6069	243	5	,	,	PUNCT
ejpam-6069	243	6	2025	2025	NUM
ejpam-6069	243	7	.	.	PUNCT