id	sid	tid	token	lemma	pos
ejpam-5193	1	1	european	european	PROPN
ejpam-5193	1	2	journal	journal	PROPN
ejpam-5193	1	3	of	of	ADP
ejpam-5193	1	4	pure	pure	ADJ
ejpam-5193	1	5	and	and	CCONJ
ejpam-5193	1	6	applied	apply	VERB
ejpam-5193	1	7	mathematics	mathematic	NOUN
ejpam-5193	1	8	vol	vol	NOUN
ejpam-5193	1	9	.	.	PROPN
ejpam-5193	2	1	17	17	NUM
ejpam-5193	2	2	,	,	PUNCT
ejpam-5193	2	3	no	no	INTJ
ejpam-5193	2	4	.	.	NOUN
ejpam-5193	2	5	3	3	NUM
ejpam-5193	2	6	,	,	PUNCT
ejpam-5193	2	7	2024	2024	NUM
ejpam-5193	2	8	,	,	PUNCT
ejpam-5193	2	9	1471	1471	NUM
ejpam-5193	2	10	-	-	SYM
ejpam-5193	2	11	1489	1489	NUM
ejpam-5193	2	12	issn	issn	PROPN
ejpam-5193	2	13	1307	1307	NUM
ejpam-5193	2	14	-	-	SYM
ejpam-5193	2	15	5543	5543	NUM
ejpam-5193	2	16	–	–	PUNCT
ejpam-5193	3	1	ejpam.com	ejpam.com	X
ejpam-5193	3	2	published	publish	VERB
ejpam-5193	3	3	by	by	ADP
ejpam-5193	3	4	new	new	PROPN
ejpam-5193	3	5	york	york	PROPN
ejpam-5193	3	6	business	business	PROPN
ejpam-5193	3	7	global	global	ADJ
ejpam-5193	3	8	higher	high	ADJ
ejpam-5193	3	9	order	order	NOUN
ejpam-5193	3	10	bivariate	bivariate	ADJ
ejpam-5193	3	11	bell	bell	NOUN
ejpam-5193	3	12	-	-	PUNCT
ejpam-5193	3	13	based	base	VERB
ejpam-5193	3	14	apostol	apostol	NOUN
ejpam-5193	3	15	-	-	PUNCT
ejpam-5193	3	16	frobenius	frobenius	NOUN
ejpam-5193	3	17	-	-	PUNCT
ejpam-5193	3	18	type	type	NOUN
ejpam-5193	3	19	poly	poly	ADJ
ejpam-5193	3	20	-	-	PUNCT
ejpam-5193	3	21	genocchi	genocchi	NOUN
ejpam-5193	3	22	polynomials	polynomial	NOUN
ejpam-5193	3	23	with	with	ADP
ejpam-5193	3	24	parameters	parameter	NOUN
ejpam-5193	3	25	a	a	DET
ejpam-5193	3	26	and	and	CCONJ
ejpam-5193	3	27	b	b	PROPN
ejpam-5193	3	28	roberto	roberto	PROPN
ejpam-5193	3	29	b.	b.	PROPN
ejpam-5193	3	30	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-5193	3	31	,	,	PUNCT
ejpam-5193	3	32	cristina	cristina	PROPN
ejpam-5193	3	33	b.	b.	PROPN
ejpam-5193	4	1	corcino1,2	corcino1,2	PROPN
ejpam-5193	4	2	1	1	NUM
ejpam-5193	4	3	research	research	NOUN
ejpam-5193	4	4	institute	institute	NOUN
ejpam-5193	4	5	for	for	ADP
ejpam-5193	4	6	computational	computational	ADJ
ejpam-5193	4	7	mathematics	mathematic	NOUN
ejpam-5193	4	8	and	and	CCONJ
ejpam-5193	4	9	physics	physics	NOUN
ejpam-5193	4	10	,	,	PUNCT
ejpam-5193	4	11	cebu	cebu	NOUN
ejpam-5193	4	12	normal	normal	ADJ
ejpam-5193	4	13	university	university	NOUN
ejpam-5193	4	14	,	,	PUNCT
ejpam-5193	4	15	6000	6000	NUM
ejpam-5193	4	16	cebu	cebu	NOUN
ejpam-5193	4	17	city	city	NOUN
ejpam-5193	4	18	,	,	PUNCT
ejpam-5193	4	19	philippines	philippine	NOUN
ejpam-5193	4	20	2	2	NUM
ejpam-5193	4	21	mathematics	mathematics	NOUN
ejpam-5193	4	22	department	department	NOUN
ejpam-5193	4	23	,	,	PUNCT
ejpam-5193	4	24	cebu	cebu	NOUN
ejpam-5193	4	25	normal	normal	ADJ
ejpam-5193	4	26	university	university	NOUN
ejpam-5193	4	27	,	,	PUNCT
ejpam-5193	4	28	6000	6000	NUM
ejpam-5193	4	29	cebu	cebu	NOUN
ejpam-5193	4	30	city	city	NOUN
ejpam-5193	4	31	,	,	PUNCT
ejpam-5193	4	32	philippines	philippine	NOUN
ejpam-5193	4	33	abstract	abstract	ADJ
ejpam-5193	4	34	.	.	PUNCT
ejpam-5193	5	1	in	in	ADP
ejpam-5193	5	2	this	this	DET
ejpam-5193	5	3	paper	paper	NOUN
ejpam-5193	5	4	,	,	PUNCT
ejpam-5193	5	5	we	we	PRON
ejpam-5193	5	6	unveil	unveil	VERB
ejpam-5193	5	7	a	a	DET
ejpam-5193	5	8	novel	novel	ADJ
ejpam-5193	5	9	category	category	NOUN
ejpam-5193	5	10	of	of	ADP
ejpam-5193	5	11	frobenius	frobenius	NOUN
ejpam-5193	5	12	-	-	PUNCT
ejpam-5193	5	13	genocchi	genocchi	NOUN
ejpam-5193	5	14	polynomials	polynomial	NOUN
ejpam-5193	5	15	,	,	PUNCT
ejpam-5193	5	16	grounded	ground	VERB
ejpam-5193	5	17	in	in	ADP
ejpam-5193	5	18	the	the	DET
ejpam-5193	5	19	bell	bell	NOUN
ejpam-5193	5	20	numbers	number	NOUN
ejpam-5193	5	21	and	and	CCONJ
ejpam-5193	5	22	apostol	apostol	NOUN
ejpam-5193	5	23	-	-	PUNCT
ejpam-5193	5	24	type	type	NOUN
ejpam-5193	5	25	functions	function	NOUN
ejpam-5193	5	26	.	.	PUNCT
ejpam-5193	6	1	our	our	PRON
ejpam-5193	6	2	exploration	exploration	NOUN
ejpam-5193	6	3	delves	delf	NOUN
ejpam-5193	6	4	into	into	ADP
ejpam-5193	6	5	a	a	DET
ejpam-5193	6	6	comprehensive	comprehensive	ADJ
ejpam-5193	6	7	examination	examination	NOUN
ejpam-5193	6	8	of	of	ADP
ejpam-5193	6	9	these	these	DET
ejpam-5193	6	10	polynomials	polynomial	NOUN
ejpam-5193	6	11	,	,	PUNCT
ejpam-5193	6	12	elucidating	elucidate	VERB
ejpam-5193	6	13	various	various	ADJ
ejpam-5193	6	14	properties	property	NOUN
ejpam-5193	6	15	.	.	PUNCT
ejpam-5193	7	1	employing	employ	VERB
ejpam-5193	7	2	diverse	diverse	ADJ
ejpam-5193	7	3	analytical	analytical	ADJ
ejpam-5193	7	4	methods	method	NOUN
ejpam-5193	7	5	and	and	CCONJ
ejpam-5193	7	6	leveraging	leverage	VERB
ejpam-5193	7	7	generating	generating	NOUN
ejpam-5193	7	8	functions	function	NOUN
ejpam-5193	7	9	for	for	ADP
ejpam-5193	7	10	bell	bell	NOUN
ejpam-5193	7	11	-	-	PUNCT
ejpam-5193	7	12	based	base	VERB
ejpam-5193	7	13	apostol	apostol	NOUN
ejpam-5193	7	14	-	-	PUNCT
ejpam-5193	7	15	frobenius	frobenius	NOUN
ejpam-5193	7	16	-	-	PUNCT
ejpam-5193	7	17	type	type	NOUN
ejpam-5193	7	18	poly	poly	ADJ
ejpam-5193	7	19	-	-	PUNCT
ejpam-5193	7	20	genocchi	genocchi	NOUN
ejpam-5193	7	21	polynomials	polynomial	NOUN
ejpam-5193	7	22	of	of	ADP
ejpam-5193	7	23	higher	high	ADJ
ejpam-5193	7	24	order	order	NOUN
ejpam-5193	7	25	,	,	PUNCT
ejpam-5193	7	26	we	we	PRON
ejpam-5193	7	27	derive	derive	VERB
ejpam-5193	7	28	explicit	explicit	ADJ
ejpam-5193	7	29	and	and	CCONJ
ejpam-5193	7	30	implicit	implicit	ADJ
ejpam-5193	7	31	summation	summation	NOUN
ejpam-5193	7	32	formulas	formula	NOUN
ejpam-5193	7	33	,	,	PUNCT
ejpam-5193	7	34	complemented	complement	VERB
ejpam-5193	7	35	by	by	ADP
ejpam-5193	7	36	their	their	PRON
ejpam-5193	7	37	symmetric	symmetric	ADJ
ejpam-5193	7	38	identities	identity	NOUN
ejpam-5193	7	39	.	.	PUNCT
ejpam-5193	8	1	2020	2020	NUM
ejpam-5193	8	2	mathematics	mathematic	NOUN
ejpam-5193	8	3	subject	subject	NOUN
ejpam-5193	8	4	classifications	classification	NOUN
ejpam-5193	8	5	:	:	PUNCT
ejpam-5193	8	6	05a15	05a15	NUM
ejpam-5193	8	7	,	,	PUNCT
ejpam-5193	8	8	11b68	11b68	NUM
ejpam-5193	8	9	,	,	PUNCT
ejpam-5193	8	10	11b73	11b73	NUM
ejpam-5193	8	11	,	,	PUNCT
ejpam-5193	8	12	26c05	26c05	NUM
ejpam-5193	8	13	,	,	PUNCT
ejpam-5193	8	14	33b10	33b10	NUM
ejpam-5193	8	15	key	key	ADJ
ejpam-5193	8	16	words	word	NOUN
ejpam-5193	8	17	and	and	CCONJ
ejpam-5193	8	18	phrases	phrase	NOUN
ejpam-5193	8	19	:	:	PUNCT
ejpam-5193	8	20	genocchi	genocchi	PROPN
ejpam-5193	8	21	polynomials	polynomial	NOUN
ejpam-5193	8	22	,	,	PUNCT
ejpam-5193	8	23	bell	bell	NOUN
ejpam-5193	8	24	polynomials	polynomial	NOUN
ejpam-5193	8	25	,	,	PUNCT
ejpam-5193	8	26	apostol	apostol	NOUN
ejpam-5193	8	27	-	-	PUNCT
ejpam-5193	8	28	frobenius	frobenius	NOUN
ejpam-5193	8	29	-	-	PUNCT
ejpam-5193	8	30	type	type	NOUN
ejpam-5193	8	31	poly	poly	ADJ
ejpam-5193	8	32	-	-	PUNCT
ejpam-5193	8	33	genocchi	genocchi	NOUN
ejpam-5193	8	34	polynomials	polynomial	NOUN
ejpam-5193	8	35	,	,	PUNCT
ejpam-5193	8	36	bell	bell	NOUN
ejpam-5193	8	37	-	-	PUNCT
ejpam-5193	8	38	based	base	VERB
ejpam-5193	8	39	apostol	apostol	NOUN
ejpam-5193	8	40	-	-	PUNCT
ejpam-5193	8	41	frobenius	frobenius	NOUN
ejpam-5193	8	42	-	-	PUNCT
ejpam-5193	8	43	type	type	NOUN
ejpam-5193	8	44	poly	poly	ADJ
ejpam-5193	8	45	-	-	PUNCT
ejpam-5193	8	46	genocchi	genocchi	NOUN
ejpam-5193	8	47	polynomials	polynomial	NOUN
ejpam-5193	8	48	,	,	PUNCT
ejpam-5193	8	49	stirling	stirling	NOUN
ejpam-5193	8	50	numbers	number	NOUN
ejpam-5193	8	51	1	1	NUM
ejpam-5193	8	52	.	.	PUNCT
ejpam-5193	8	53	introduction	introduction	NOUN
ejpam-5193	8	54	similar	similar	ADJ
ejpam-5193	8	55	to	to	ADP
ejpam-5193	8	56	the	the	DET
ejpam-5193	8	57	bernoulli	bernoulli	PROPN
ejpam-5193	8	58	and	and	CCONJ
ejpam-5193	8	59	euler	euler	NOUN
ejpam-5193	8	60	numbers	number	NOUN
ejpam-5193	8	61	[	[	X
ejpam-5193	8	62	1	1	NUM
ejpam-5193	8	63	]	]	PUNCT
ejpam-5193	8	64	,	,	PUNCT
ejpam-5193	8	65	the	the	DET
ejpam-5193	8	66	genocchi	genocchi	PROPN
ejpam-5193	8	67	numbers	number	NOUN
ejpam-5193	8	68	,	,	PUNCT
ejpam-5193	8	69	denoted	denote	VERB
ejpam-5193	8	70	as	as	ADP
ejpam-5193	8	71	gn	gn	PROPN
ejpam-5193	8	72	,	,	PUNCT
ejpam-5193	8	73	are	be	AUX
ejpam-5193	8	74	established	establish	VERB
ejpam-5193	8	75	by	by	ADP
ejpam-5193	8	76	means	mean	NOUN
ejpam-5193	8	77	of	of	ADP
ejpam-5193	8	78	the	the	DET
ejpam-5193	8	79	subsequent	subsequent	ADJ
ejpam-5193	8	80	generating	generating	NOUN
ejpam-5193	8	81	function	function	NOUN
ejpam-5193	8	82	:	:	PUNCT
ejpam-5193	8	83	∞∑	∞∑	NUM
ejpam-5193	8	84	n=0	n=0	NUM
ejpam-5193	8	85	gn	gn	PROPN
ejpam-5193	8	86	tn	tn	PROPN
ejpam-5193	8	87	n	n	PROPN
ejpam-5193	8	88	!	!	PUNCT
ejpam-5193	9	1	=	=	PUNCT
ejpam-5193	10	1	2	2	NUM
ejpam-5193	10	2	t	t	NOUN
ejpam-5193	10	3	et	et	NOUN
ejpam-5193	10	4	+	+	CCONJ
ejpam-5193	10	5	1	1	NUM
ejpam-5193	10	6	,	,	PUNCT
ejpam-5193	10	7	|t|	|t|	VERB
ejpam-5193	10	8	<	<	X
ejpam-5193	10	9	π	π	PROPN
ejpam-5193	10	10	.	.	PUNCT
ejpam-5193	11	1	some	some	DET
ejpam-5193	11	2	novel	novel	ADJ
ejpam-5193	11	3	identities	identity	NOUN
ejpam-5193	11	4	involving	involve	VERB
ejpam-5193	11	5	these	these	DET
ejpam-5193	11	6	numbers	number	NOUN
ejpam-5193	11	7	can	can	AUX
ejpam-5193	11	8	be	be	AUX
ejpam-5193	11	9	found	find	VERB
ejpam-5193	11	10	in	in	ADP
ejpam-5193	11	11	[	[	X
ejpam-5193	11	12	5	5	NUM
ejpam-5193	11	13	,	,	PUNCT
ejpam-5193	11	14	19	19	NUM
ejpam-5193	11	15	,	,	PUNCT
ejpam-5193	11	16	27	27	NUM
ejpam-5193	11	17	]	]	PUNCT
ejpam-5193	11	18	.	.	PUNCT
ejpam-5193	12	1	these	these	DET
ejpam-5193	12	2	numbers	number	NOUN
ejpam-5193	12	3	have	have	AUX
ejpam-5193	12	4	undergone	undergo	VERB
ejpam-5193	12	5	diverse	diverse	ADJ
ejpam-5193	12	6	generalizations	generalization	NOUN
ejpam-5193	12	7	,	,	PUNCT
ejpam-5193	12	8	often	often	ADV
ejpam-5193	12	9	achieved	achieve	VERB
ejpam-5193	12	10	by	by	ADP
ejpam-5193	12	11	combining	combine	VERB
ejpam-5193	12	12	them	they	PRON
ejpam-5193	12	13	with	with	ADP
ejpam-5193	12	14	the	the	DET
ejpam-5193	12	15	principles	principle	NOUN
ejpam-5193	12	16	of	of	ADP
ejpam-5193	12	17	well	well	ADV
ejpam-5193	12	18	-	-	PUNCT
ejpam-5193	12	19	known	know	VERB
ejpam-5193	12	20	polynomials	polynomial	NOUN
ejpam-5193	12	21	.	.	PUNCT
ejpam-5193	13	1	a	a	DET
ejpam-5193	13	2	specific	specific	ADJ
ejpam-5193	13	3	example	example	NOUN
ejpam-5193	13	4	is	be	AUX
ejpam-5193	13	5	the	the	DET
ejpam-5193	13	6	integration	integration	NOUN
ejpam-5193	13	7	with	with	ADP
ejpam-5193	13	8	exponential	exponential	NOUN
ejpam-5193	13	9	∗corresponding	∗corresponde	VERB
ejpam-5193	13	10	author	author	NOUN
ejpam-5193	13	11	.	.	PUNCT
ejpam-5193	14	1	doi	doi	NOUN
ejpam-5193	14	2	:	:	PUNCT
ejpam-5193	14	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5193	https://doi.org/10.29020/nybg.ejpam.v17i3.5193	ADP
ejpam-5193	14	4	email	email	NOUN
ejpam-5193	14	5	addresses	address	VERB
ejpam-5193	14	6	:	:	PUNCT
ejpam-5193	15	1	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-5193	15	2	(	(	PUNCT
ejpam-5193	15	3	r.	r.	PROPN
ejpam-5193	15	4	corcino	corcino	PROPN
ejpam-5193	15	5	)	)	PUNCT
ejpam-5193	15	6	,	,	PUNCT
ejpam-5193	15	7	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-5193	15	8	(	(	PUNCT
ejpam-5193	15	9	c.	c.	PROPN
ejpam-5193	15	10	corcino	corcino	PROPN
ejpam-5193	15	11	)	)	PUNCT
ejpam-5193	15	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5193	15	13	1471	1471	NUM
ejpam-5193	15	14	©	©	ADP
ejpam-5193	15	15	2024	2024	NUM
ejpam-5193	15	16	ejpam	ejpam	NOUN
ejpam-5193	15	17	all	all	DET
ejpam-5193	15	18	rights	right	NOUN
ejpam-5193	15	19	reserved	reserve	VERB
ejpam-5193	15	20	.	.	PUNCT
ejpam-5193	16	1	1472	1472	NUM
ejpam-5193	16	2	polynomials	polynomial	NOUN
ejpam-5193	16	3	,	,	PUNCT
ejpam-5193	16	4	leading	lead	VERB
ejpam-5193	16	5	to	to	ADP
ejpam-5193	16	6	the	the	DET
ejpam-5193	16	7	formation	formation	NOUN
ejpam-5193	16	8	of	of	ADP
ejpam-5193	16	9	genocchi	genocchi	PROPN
ejpam-5193	16	10	polynomials	polynomial	NOUN
ejpam-5193	16	11	and	and	CCONJ
ejpam-5193	16	12	higher	high	ADJ
ejpam-5193	16	13	-	-	PUNCT
ejpam-5193	16	14	order	order	NOUN
ejpam-5193	16	15	genocchi	genocchi	NOUN
ejpam-5193	16	16	polynomials	polynomial	NOUN
ejpam-5193	16	17	(	(	PUNCT
ejpam-5193	16	18	see	see	VERB
ejpam-5193	16	19	[	[	X
ejpam-5193	16	20	18	18	NUM
ejpam-5193	16	21	]	]	NUM
ejpam-5193	16	22	)	)	PUNCT
ejpam-5193	16	23	,	,	PUNCT
ejpam-5193	16	24	outlined	outline	VERB
ejpam-5193	16	25	as	as	SCONJ
ejpam-5193	16	26	follows	follow	VERB
ejpam-5193	16	27	:	:	PUNCT
ejpam-5193	16	28	∞∑	∞∑	NUM
ejpam-5193	16	29	n=0	n=0	NUM
ejpam-5193	16	30	gn(x	gn(x	NUM
ejpam-5193	16	31	)	)	PUNCT
ejpam-5193	16	32	tn	tn	NOUN
ejpam-5193	16	33	n	n	NOUN
ejpam-5193	16	34	!	!	PUNCT
ejpam-5193	17	1	=	=	PUNCT
ejpam-5193	18	1	2	2	NUM
ejpam-5193	18	2	t	t	NOUN
ejpam-5193	18	3	et	et	NOUN
ejpam-5193	18	4	+	+	CCONJ
ejpam-5193	18	5	1	1	NUM
ejpam-5193	18	6	ext	ext	NOUN
ejpam-5193	18	7	,	,	PUNCT
ejpam-5193	18	8	|t|	|t|	VERB
ejpam-5193	18	9	<	<	X
ejpam-5193	18	10	π	π	PROPN
ejpam-5193	18	11	,	,	PUNCT
ejpam-5193	18	12	(	(	PUNCT
ejpam-5193	18	13	1.1	1.1	NUM
ejpam-5193	18	14	)	)	PUNCT
ejpam-5193	18	15	∞∑	∞∑	PRON
ejpam-5193	18	16	n=0	n=0	PUNCT
ejpam-5193	18	17	g(k	g(k	NOUN
ejpam-5193	18	18	)	)	PUNCT
ejpam-5193	18	19	n	n	CCONJ
ejpam-5193	18	20	(	(	PUNCT
ejpam-5193	18	21	x	x	X
ejpam-5193	18	22	)	)	PUNCT
ejpam-5193	18	23	tn	tn	PROPN
ejpam-5193	18	24	n	n	NOUN
ejpam-5193	18	25	!	!	PUNCT
ejpam-5193	19	1	=	=	PUNCT
ejpam-5193	19	2	(	(	PUNCT
ejpam-5193	19	3	2	2	NUM
ejpam-5193	19	4	t	t	NOUN
ejpam-5193	19	5	et	et	NOUN
ejpam-5193	19	6	+	+	CCONJ
ejpam-5193	19	7	1	1	X
ejpam-5193	19	8	)	)	PUNCT
ejpam-5193	19	9	k	k	PROPN
ejpam-5193	19	10	ext	ext	NOUN
ejpam-5193	19	11	.	.	PUNCT
ejpam-5193	20	1	(	(	PUNCT
ejpam-5193	20	2	1.2	1.2	NUM
ejpam-5193	20	3	)	)	PUNCT
ejpam-5193	20	4	mixing	mix	VERB
ejpam-5193	20	5	with	with	ADP
ejpam-5193	20	6	the	the	DET
ejpam-5193	20	7	apostol	apostol	NOUN
ejpam-5193	20	8	polynomials	polynomial	NOUN
ejpam-5193	20	9	yields	yield	VERB
ejpam-5193	20	10	the	the	DET
ejpam-5193	20	11	apostol	apostol	NOUN
ejpam-5193	20	12	-	-	PUNCT
ejpam-5193	20	13	genocchi	genocchi	PROPN
ejpam-5193	20	14	polynomials	polynomial	NOUN
ejpam-5193	20	15	,	,	PUNCT
ejpam-5193	20	16	and	and	CCONJ
ejpam-5193	20	17	apostolgenocchi	apostolgenocchi	NOUN
ejpam-5193	20	18	polynomials	polynomial	NOUN
ejpam-5193	20	19	of	of	ADP
ejpam-5193	20	20	higher	high	ADJ
ejpam-5193	20	21	order	order	NOUN
ejpam-5193	20	22	,	,	PUNCT
ejpam-5193	20	23	which	which	PRON
ejpam-5193	20	24	are	be	AUX
ejpam-5193	20	25	respectively	respectively	ADV
ejpam-5193	20	26	defined	define	VERB
ejpam-5193	20	27	as	as	SCONJ
ejpam-5193	20	28	follows	follow	VERB
ejpam-5193	20	29	:	:	PUNCT
ejpam-5193	20	30	∞∑	∞∑	NUM
ejpam-5193	20	31	n=0	n=0	NUM
ejpam-5193	20	32	gn(x	gn(x	X
ejpam-5193	20	33	,	,	PUNCT
ejpam-5193	20	34	λ	λ	NOUN
ejpam-5193	20	35	)	)	PUNCT
ejpam-5193	20	36	tn	tn	PROPN
ejpam-5193	20	37	n	n	NOUN
ejpam-5193	20	38	!	!	PUNCT
ejpam-5193	21	1	=	=	PUNCT
ejpam-5193	22	1	2	2	NUM
ejpam-5193	22	2	t	t	NOUN
ejpam-5193	22	3	λet	λet	NOUN
ejpam-5193	23	1	+	+	CCONJ
ejpam-5193	23	2	1	1	NUM
ejpam-5193	23	3	ext	ext	NOUN
ejpam-5193	23	4	,	,	PUNCT
ejpam-5193	23	5	(	(	PUNCT
ejpam-5193	23	6	1.3	1.3	NUM
ejpam-5193	23	7	)	)	PUNCT
ejpam-5193	23	8	∞∑	∞∑	PRON
ejpam-5193	23	9	n=0	n=0	PUNCT
ejpam-5193	23	10	g(k	g(k	NOUN
ejpam-5193	23	11	)	)	PUNCT
ejpam-5193	23	12	n	n	CCONJ
ejpam-5193	23	13	(	(	PUNCT
ejpam-5193	23	14	x	x	NOUN
ejpam-5193	23	15	,	,	PUNCT
ejpam-5193	23	16	λ	λ	NOUN
ejpam-5193	23	17	)	)	PUNCT
ejpam-5193	23	18	tn	tn	PROPN
ejpam-5193	23	19	n	n	PROPN
ejpam-5193	23	20	!	!	PUNCT
ejpam-5193	23	21	=	=	PUNCT
ejpam-5193	24	1	(	(	PUNCT
ejpam-5193	24	2	2	2	NUM
ejpam-5193	24	3	t	t	NOUN
ejpam-5193	24	4	λet	λet	NOUN
ejpam-5193	25	1	+	+	CCONJ
ejpam-5193	25	2	1	1	X
ejpam-5193	25	3	)	)	PUNCT
ejpam-5193	25	4	k	k	PROPN
ejpam-5193	25	5	ext	ext	PROPN
ejpam-5193	25	6	,	,	PUNCT
ejpam-5193	25	7	(	(	PUNCT
ejpam-5193	25	8	1.4	1.4	NUM
ejpam-5193	25	9	)	)	PUNCT
ejpam-5193	25	10	where	where	SCONJ
ejpam-5193	25	11	|t|	|t|	ADP
ejpam-5193	25	12	<	<	X
ejpam-5193	25	13	π	π	PROPN
ejpam-5193	25	14	when	when	SCONJ
ejpam-5193	25	15	λ	λ	X
ejpam-5193	25	16	=	=	SYM
ejpam-5193	25	17	1	1	NUM
ejpam-5193	25	18	and	and	CCONJ
ejpam-5193	25	19	|t|	|t|	VERB
ejpam-5193	25	20	<	<	X
ejpam-5193	25	21	log(−λ	log(−λ	PROPN
ejpam-5193	25	22	)	)	PUNCT
ejpam-5193	25	23	when	when	SCONJ
ejpam-5193	25	24	λ	λ	X
ejpam-5193	25	25	̸=	̸=	PROPN
ejpam-5193	25	26	1	1	NUM
ejpam-5193	25	27	,	,	PUNCT
ejpam-5193	25	28	λ	λ	PROPN
ejpam-5193	25	29	∈	∈	PROPN
ejpam-5193	25	30	c.	c.	NOUN
ejpam-5193	25	31	also	also	ADV
ejpam-5193	25	32	,	,	PUNCT
ejpam-5193	25	33	mixing	mix	VERB
ejpam-5193	25	34	with	with	ADP
ejpam-5193	25	35	frobenius	frobenius	ADJ
ejpam-5193	25	36	polynomials	polynomial	NOUN
ejpam-5193	25	37	yields	yield	VERB
ejpam-5193	25	38	the	the	DET
ejpam-5193	25	39	so	so	ADV
ejpam-5193	25	40	-	-	PUNCT
ejpam-5193	25	41	called	call	VERB
ejpam-5193	25	42	frobenius	frobenius	NOUN
ejpam-5193	25	43	-	-	PUNCT
ejpam-5193	25	44	genocchi	genocchi	NOUN
ejpam-5193	25	45	polynomials	polynomial	NOUN
ejpam-5193	25	46	,	,	PUNCT
ejpam-5193	25	47	which	which	PRON
ejpam-5193	25	48	are	be	AUX
ejpam-5193	25	49	given	give	VERB
ejpam-5193	25	50	by	by	ADP
ejpam-5193	25	51	∞∑	∞∑	DET
ejpam-5193	25	52	n=0	n=0	NUM
ejpam-5193	25	53	gf	gf	NOUN
ejpam-5193	25	54	n	n	PROPN
ejpam-5193	25	55	(	(	PUNCT
ejpam-5193	25	56	x;u	x;u	PROPN
ejpam-5193	25	57	)	)	PUNCT
ejpam-5193	25	58	tn	tn	PROPN
ejpam-5193	25	59	n	n	PROPN
ejpam-5193	25	60	!	!	PUNCT
ejpam-5193	25	61	=	=	PUNCT
ejpam-5193	26	1	(	(	PUNCT
ejpam-5193	26	2	1−	1−	NUM
ejpam-5193	26	3	u)t	u)t	X
ejpam-5193	26	4	et	et	NOUN
ejpam-5193	26	5	−	−	PROPN
ejpam-5193	26	6	u	u	PROPN
ejpam-5193	26	7	ext	ext	NOUN
ejpam-5193	26	8	,	,	PUNCT
ejpam-5193	26	9	(	(	PUNCT
ejpam-5193	26	10	1.5	1.5	NUM
ejpam-5193	26	11	)	)	PUNCT
ejpam-5193	26	12	and	and	CCONJ
ejpam-5193	26	13	further	far	ADV
ejpam-5193	26	14	gives	give	VERB
ejpam-5193	26	15	∞∑	∞∑	PRON
ejpam-5193	26	16	n=0	n=0	NUM
ejpam-5193	26	17	gf	gf	NOUN
ejpam-5193	26	18	n	n	PROPN
ejpam-5193	26	19	(	(	PUNCT
ejpam-5193	26	20	x;u	x;u	PROPN
ejpam-5193	26	21	,	,	PUNCT
ejpam-5193	26	22	λ	λ	NOUN
ejpam-5193	26	23	)	)	PUNCT
ejpam-5193	26	24	tn	tn	PROPN
ejpam-5193	26	25	n	n	PROPN
ejpam-5193	26	26	!	!	PUNCT
ejpam-5193	26	27	=	=	PUNCT
ejpam-5193	27	1	(	(	PUNCT
ejpam-5193	27	2	1−	1−	NUM
ejpam-5193	27	3	u)t	u)t	AUX
ejpam-5193	27	4	λet	λet	ADP
ejpam-5193	27	5	−	−	NUM
ejpam-5193	27	6	u	u	NOUN
ejpam-5193	27	7	ext	ext	NOUN
ejpam-5193	27	8	,	,	PUNCT
ejpam-5193	27	9	(	(	PUNCT
ejpam-5193	27	10	1.6	1.6	NUM
ejpam-5193	27	11	)	)	PUNCT
ejpam-5193	27	12	the	the	DET
ejpam-5193	27	13	apostol	apostol	NOUN
ejpam-5193	27	14	-	-	PUNCT
ejpam-5193	27	15	frobenius	frobenius	NOUN
ejpam-5193	27	16	-	-	PUNCT
ejpam-5193	27	17	genocchi	genocchi	NOUN
ejpam-5193	27	18	polynomials	polynomial	NOUN
ejpam-5193	27	19	by	by	ADP
ejpam-5193	27	20	mixing	mix	VERB
ejpam-5193	27	21	with	with	ADP
ejpam-5193	27	22	apostol	apostol	NOUN
ejpam-5193	27	23	-	-	PUNCT
ejpam-5193	27	24	genocchi	genocchi	PROPN
ejpam-5193	27	25	polynomials	polynomial	NOUN
ejpam-5193	27	26	(	(	PUNCT
ejpam-5193	27	27	see	see	VERB
ejpam-5193	27	28	[	[	X
ejpam-5193	27	29	6	6	NUM
ejpam-5193	27	30	,	,	PUNCT
ejpam-5193	27	31	15–17	15–17	NUM
ejpam-5193	27	32	,	,	PUNCT
ejpam-5193	27	33	22	22	NUM
ejpam-5193	27	34	,	,	PUNCT
ejpam-5193	27	35	23	23	NUM
ejpam-5193	27	36	,	,	PUNCT
ejpam-5193	27	37	28	28	NUM
ejpam-5193	27	38	,	,	PUNCT
ejpam-5193	27	39	30	30	NUM
ejpam-5193	27	40	,	,	PUNCT
ejpam-5193	27	41	32	32	NUM
ejpam-5193	27	42	,	,	PUNCT
ejpam-5193	27	43	33	33	NUM
ejpam-5193	27	44	]	]	PUNCT
ejpam-5193	27	45	)	)	PUNCT
ejpam-5193	27	46	.	.	PUNCT
ejpam-5193	28	1	further	further	ADJ
ejpam-5193	28	2	generalization	generalization	NOUN
ejpam-5193	28	3	and	and	CCONJ
ejpam-5193	28	4	other	other	ADJ
ejpam-5193	28	5	variation	variation	NOUN
ejpam-5193	28	6	of	of	ADP
ejpam-5193	28	7	frobenius	frobenius	NOUN
ejpam-5193	28	8	-	-	PUNCT
ejpam-5193	28	9	genocchi	genocchi	NOUN
ejpam-5193	28	10	polynomials	polynomial	NOUN
ejpam-5193	28	11	,	,	PUNCT
ejpam-5193	28	12	specifically	specifically	ADV
ejpam-5193	28	13	,	,	PUNCT
ejpam-5193	28	14	the	the	DET
ejpam-5193	28	15	generalized	generalize	VERB
ejpam-5193	28	16	apostol	apostol	NOUN
ejpam-5193	28	17	-	-	PUNCT
ejpam-5193	28	18	frobenius	frobenius	NOUN
ejpam-5193	28	19	-	-	PUNCT
ejpam-5193	28	20	genocchi	genocchi	NOUN
ejpam-5193	28	21	polynomials	polynomial	NOUN
ejpam-5193	28	22	and	and	CCONJ
ejpam-5193	28	23	frobenius	frobenius	NOUN
ejpam-5193	28	24	-	-	PUNCT
ejpam-5193	28	25	euler	euler	NOUN
ejpam-5193	28	26	-	-	PUNCT
ejpam-5193	28	27	genocchi	genocchi	PROPN
ejpam-5193	28	28	polynomials	polynomial	NOUN
ejpam-5193	28	29	,	,	PUNCT
ejpam-5193	28	30	are	be	AUX
ejpam-5193	28	31	introduced	introduce	VERB
ejpam-5193	28	32	in	in	ADP
ejpam-5193	28	33	[	[	X
ejpam-5193	28	34	34	34	NUM
ejpam-5193	28	35	]	]	PUNCT
ejpam-5193	28	36	and	and	CCONJ
ejpam-5193	28	37	[	[	X
ejpam-5193	28	38	3	3	NUM
ejpam-5193	28	39	]	]	PUNCT
ejpam-5193	28	40	respectively	respectively	ADV
ejpam-5193	28	41	,	,	PUNCT
ejpam-5193	28	42	and	and	CCONJ
ejpam-5193	28	43	defined	define	VERB
ejpam-5193	28	44	as	as	SCONJ
ejpam-5193	28	45	follows	follow	VERB
ejpam-5193	28	46	:	:	PUNCT
ejpam-5193	28	47	∞∑	∞∑	NUM
ejpam-5193	28	48	n=0	n=0	NUM
ejpam-5193	28	49	hr	hr	NOUN
ejpam-5193	28	50	n(x;u	n(x;u	PROPN
ejpam-5193	28	51	,	,	PUNCT
ejpam-5193	28	52	a	a	DET
ejpam-5193	28	53	,	,	PUNCT
ejpam-5193	28	54	b	b	NOUN
ejpam-5193	28	55	,	,	PUNCT
ejpam-5193	28	56	c	c	X
ejpam-5193	28	57	,	,	PUNCT
ejpam-5193	28	58	λ	λ	PROPN
ejpam-5193	28	59	,	,	PUNCT
ejpam-5193	28	60	)	)	PUNCT
ejpam-5193	28	61	tn	tn	PROPN
ejpam-5193	28	62	n	n	PROPN
ejpam-5193	28	63	!	!	PUNCT
ejpam-5193	29	1	=	=	PUNCT
ejpam-5193	29	2	(	(	PUNCT
ejpam-5193	29	3	(	(	PUNCT
ejpam-5193	29	4	at	at	ADP
ejpam-5193	29	5	−	−	PROPN
ejpam-5193	29	6	u)t	u)t	X
ejpam-5193	29	7	λbt	λbt	VERB
ejpam-5193	29	8	−	−	PROPN
ejpam-5193	29	9	u	u	NOUN
ejpam-5193	29	10	)	)	PUNCT
ejpam-5193	29	11	r	r	NOUN
ejpam-5193	29	12	cxt	cxt	NOUN
ejpam-5193	29	13	,	,	PUNCT
ejpam-5193	29	14	(	(	PUNCT
ejpam-5193	29	15	1.7	1.7	NUM
ejpam-5193	29	16	)	)	PUNCT
ejpam-5193	29	17	∞∑	∞∑	PROPN
ejpam-5193	29	18	n=0	n=0	PRON
ejpam-5193	29	19	ar	ar	NOUN
ejpam-5193	29	20	n(x;u	n(x;u	NOUN
ejpam-5193	29	21	)	)	PUNCT
ejpam-5193	29	22	tn	tn	PROPN
ejpam-5193	29	23	n	n	PROPN
ejpam-5193	29	24	!	!	PUNCT
ejpam-5193	29	25	=	=	PUNCT
ejpam-5193	30	1	(	(	PUNCT
ejpam-5193	30	2	1−	1−	NUM
ejpam-5193	30	3	u)tr	u)tr	NOUN
ejpam-5193	30	4	et	et	NOUN
ejpam-5193	30	5	−	−	NOUN
ejpam-5193	30	6	u	u	PROPN
ejpam-5193	30	7	ext	ext	NOUN
ejpam-5193	30	8	.	.	PUNCT
ejpam-5193	31	1	(	(	PUNCT
ejpam-5193	31	2	1.8	1.8	NUM
ejpam-5193	31	3	)	)	PUNCT
ejpam-5193	31	4	it	it	PRON
ejpam-5193	31	5	is	be	AUX
ejpam-5193	31	6	worth	worth	ADJ
ejpam-5193	31	7	-	-	PUNCT
ejpam-5193	31	8	mentioning	mention	VERB
ejpam-5193	31	9	that	that	SCONJ
ejpam-5193	31	10	(	(	PUNCT
ejpam-5193	31	11	1.7	1.7	NUM
ejpam-5193	31	12	)	)	PUNCT
ejpam-5193	31	13	is	be	AUX
ejpam-5193	31	14	parallel	parallel	ADJ
ejpam-5193	31	15	to	to	ADP
ejpam-5193	31	16	the	the	DET
ejpam-5193	31	17	generalized	generalize	VERB
ejpam-5193	31	18	apostol	apostol	NOUN
ejpam-5193	31	19	type	type	NOUN
ejpam-5193	31	20	frobeniuseuler	frobeniuseuler	NOUN
ejpam-5193	31	21	polynomials	polynomial	NOUN
ejpam-5193	31	22	of	of	ADP
ejpam-5193	31	23	kurt	kurt	NOUN
ejpam-5193	31	24	and	and	CCONJ
ejpam-5193	31	25	simsek	simsek	NOUN
ejpam-5193	31	26	[	[	X
ejpam-5193	31	27	24	24	NUM
ejpam-5193	31	28	]	]	PUNCT
ejpam-5193	31	29	.	.	PUNCT
ejpam-5193	32	1	moreover	moreover	ADV
ejpam-5193	32	2	,	,	PUNCT
ejpam-5193	32	3	mixing	mix	VERB
ejpam-5193	32	4	the	the	DET
ejpam-5193	32	5	genocchi	genocchi	PROPN
ejpam-5193	32	6	numbers	number	NOUN
ejpam-5193	32	7	with	with	ADP
ejpam-5193	32	8	the	the	DET
ejpam-5193	32	9	concept	concept	NOUN
ejpam-5193	32	10	of	of	ADP
ejpam-5193	32	11	polylogarithm	polylogarithm	PROPN
ejpam-5193	32	12	lik(z	lik(z	PROPN
ejpam-5193	32	13	)	)	PUNCT
ejpam-5193	33	1	[	[	X
ejpam-5193	33	2	9	9	NUM
ejpam-5193	33	3	]	]	SYM
ejpam-5193	33	4	lik(z	lik(z	NOUN
ejpam-5193	33	5	)	)	PUNCT
ejpam-5193	34	1	=	=	PUNCT
ejpam-5193	35	1	∞∑	∞∑	NUM
ejpam-5193	35	2	n=0	n=0	NUM
ejpam-5193	35	3	zn	zn	PROPN
ejpam-5193	35	4	nk	nk	PROPN
ejpam-5193	35	5	,	,	PUNCT
ejpam-5193	35	6	k	k	PROPN
ejpam-5193	35	7	∈	∈	PROPN
ejpam-5193	35	8	z	z	PROPN
ejpam-5193	35	9	,	,	PUNCT
ejpam-5193	35	10	(	(	PUNCT
ejpam-5193	35	11	1.9	1.9	NUM
ejpam-5193	35	12	)	)	PUNCT
ejpam-5193	35	13	1473	1473	NUM
ejpam-5193	35	14	yields	yield	VERB
ejpam-5193	35	15	the	the	DET
ejpam-5193	35	16	poly	poly	ADJ
ejpam-5193	35	17	-	-	PUNCT
ejpam-5193	35	18	genocchi	genocchi	NOUN
ejpam-5193	35	19	polynomials	polynomial	NOUN
ejpam-5193	35	20	,	,	PUNCT
ejpam-5193	35	21	which	which	PRON
ejpam-5193	35	22	are	be	AUX
ejpam-5193	35	23	defined	define	VERB
ejpam-5193	35	24	as	as	SCONJ
ejpam-5193	35	25	follows	follow	VERB
ejpam-5193	35	26	∞∑	∞∑	NUM
ejpam-5193	35	27	n=0	n=0	NUM
ejpam-5193	35	28	g(k	g(k	NOUN
ejpam-5193	35	29	)	)	PUNCT
ejpam-5193	35	30	n	n	CCONJ
ejpam-5193	35	31	(	(	PUNCT
ejpam-5193	35	32	x	x	X
ejpam-5193	35	33	)	)	PUNCT
ejpam-5193	35	34	xn	xn	PROPN
ejpam-5193	35	35	n	n	X
ejpam-5193	35	36	!	!	PUNCT
ejpam-5193	36	1	=	=	SYM
ejpam-5193	36	2	2lik(1−	2lik(1−	NUM
ejpam-5193	36	3	et	et	NOUN
ejpam-5193	36	4	)	)	PUNCT
ejpam-5193	36	5	et	et	NOUN
ejpam-5193	37	1	+	+	NOUN
ejpam-5193	37	2	1	1	NUM
ejpam-5193	37	3	ext	ext	NOUN
ejpam-5193	37	4	,	,	PUNCT
ejpam-5193	37	5	(	(	PUNCT
ejpam-5193	37	6	1.10	1.10	NUM
ejpam-5193	37	7	)	)	PUNCT
ejpam-5193	37	8	such	such	ADJ
ejpam-5193	37	9	that	that	SCONJ
ejpam-5193	37	10	when	when	SCONJ
ejpam-5193	37	11	k	k	PROPN
ejpam-5193	37	12	=	=	SYM
ejpam-5193	37	13	1	1	NUM
ejpam-5193	37	14	,	,	PUNCT
ejpam-5193	37	15	li1(1−	li1(1−	X
ejpam-5193	37	16	et	et	NOUN
ejpam-5193	37	17	)	)	PUNCT
ejpam-5193	37	18	=	=	SYM
ejpam-5193	38	1	ln(1−	ln(1−	PROPN
ejpam-5193	38	2	(	(	PUNCT
ejpam-5193	38	3	1−	1−	NUM
ejpam-5193	38	4	et	et	NOUN
ejpam-5193	38	5	)	)	PUNCT
ejpam-5193	38	6	)	)	PUNCT
ejpam-5193	39	1	=	=	PUNCT
ejpam-5193	39	2	ln(et	ln(et	PROPN
ejpam-5193	39	3	)	)	PUNCT
ejpam-5193	39	4	=	=	SYM
ejpam-5193	39	5	t	t	PROPN
ejpam-5193	39	6	and	and	CCONJ
ejpam-5193	39	7	so	so	ADV
ejpam-5193	39	8	(	(	PUNCT
ejpam-5193	39	9	1.10	1.10	NUM
ejpam-5193	39	10	)	)	PUNCT
ejpam-5193	39	11	gives	give	VERB
ejpam-5193	39	12	(	(	PUNCT
ejpam-5193	39	13	1.1	1.1	NUM
ejpam-5193	39	14	)	)	PUNCT
ejpam-5193	39	15	.	.	PUNCT
ejpam-5193	40	1	furthermore	furthermore	ADV
ejpam-5193	40	2	,	,	PUNCT
ejpam-5193	40	3	with	with	ADP
ejpam-5193	40	4	a	a	DET
ejpam-5193	40	5	slight	slight	ADJ
ejpam-5193	40	6	modification	modification	NOUN
ejpam-5193	40	7	of	of	ADP
ejpam-5193	40	8	the	the	DET
ejpam-5193	40	9	generating	generate	VERB
ejpam-5193	40	10	function	function	NOUN
ejpam-5193	40	11	,	,	PUNCT
ejpam-5193	40	12	another	another	DET
ejpam-5193	40	13	generalization	generalization	NOUN
ejpam-5193	40	14	,	,	PUNCT
ejpam-5193	40	15	denoted	denote	VERB
ejpam-5193	40	16	by	by	ADP
ejpam-5193	40	17	g	g	PROPN
ejpam-5193	40	18	(	(	PUNCT
ejpam-5193	40	19	k	k	NOUN
ejpam-5193	40	20	)	)	PUNCT
ejpam-5193	40	21	n,2(x	n,2(x	NOUN
ejpam-5193	40	22	)	)	PUNCT
ejpam-5193	40	23	,	,	PUNCT
ejpam-5193	40	24	was	be	AUX
ejpam-5193	40	25	defined	define	VERB
ejpam-5193	40	26	by	by	ADP
ejpam-5193	40	27	kim	kim	PROPN
ejpam-5193	40	28	et	et	PROPN
ejpam-5193	40	29	al	al	PROPN
ejpam-5193	40	30	.	.	PUNCT
ejpam-5193	41	1	[	[	X
ejpam-5193	41	2	31	31	NUM
ejpam-5193	41	3	]	]	PUNCT
ejpam-5193	41	4	as	as	SCONJ
ejpam-5193	41	5	follows	follow	VERB
ejpam-5193	41	6	∞∑	∞∑	NUM
ejpam-5193	41	7	n=0	n=0	ADJ
ejpam-5193	41	8	g	g	NOUN
ejpam-5193	41	9	(	(	PUNCT
ejpam-5193	41	10	k	k	NOUN
ejpam-5193	41	11	)	)	PUNCT
ejpam-5193	41	12	n,2(x	n,2(x	NOUN
ejpam-5193	41	13	)	)	PUNCT
ejpam-5193	41	14	xn	xn	PROPN
ejpam-5193	41	15	n	n	X
ejpam-5193	41	16	!	!	PUNCT
ejpam-5193	41	17	=	=	PRON
ejpam-5193	41	18	lik(1−	lik(1−	PROPN
ejpam-5193	41	19	e−2	e−2	PROPN
ejpam-5193	41	20	t	t	PROPN
ejpam-5193	41	21	)	)	PUNCT
ejpam-5193	41	22	et	et	NOUN
ejpam-5193	42	1	+	+	NOUN
ejpam-5193	42	2	1	1	NUM
ejpam-5193	42	3	ext	ext	NOUN
ejpam-5193	42	4	.	.	PUNCT
ejpam-5193	43	1	(	(	PUNCT
ejpam-5193	43	2	1.11	1.11	NUM
ejpam-5193	43	3	)	)	PUNCT
ejpam-5193	43	4	these	these	DET
ejpam-5193	43	5	polynomials	polynomial	NOUN
ejpam-5193	43	6	are	be	AUX
ejpam-5193	43	7	called	call	VERB
ejpam-5193	43	8	modified	modified	ADJ
ejpam-5193	43	9	poly	poly	ADJ
ejpam-5193	43	10	-	-	PUNCT
ejpam-5193	43	11	genocchi	genocchi	NOUN
ejpam-5193	43	12	polynomials	polynomial	NOUN
ejpam-5193	43	13	.	.	PUNCT
ejpam-5193	44	1	note	note	VERB
ejpam-5193	44	2	that	that	SCONJ
ejpam-5193	44	3	,	,	PUNCT
ejpam-5193	44	4	when	when	SCONJ
ejpam-5193	44	5	k	k	PROPN
ejpam-5193	44	6	=	=	SYM
ejpam-5193	44	7	1	1	NUM
ejpam-5193	44	8	,	,	PUNCT
ejpam-5193	44	9	equations	equation	NOUN
ejpam-5193	44	10	(	(	PUNCT
ejpam-5193	44	11	1.10	1.10	NUM
ejpam-5193	44	12	)	)	PUNCT
ejpam-5193	44	13	and	and	CCONJ
ejpam-5193	44	14	(	(	PUNCT
ejpam-5193	44	15	1.11	1.11	NUM
ejpam-5193	44	16	)	)	PUNCT
ejpam-5193	44	17	give	give	VERB
ejpam-5193	44	18	the	the	DET
ejpam-5193	44	19	genocchi	genocchi	NOUN
ejpam-5193	44	20	polynomials	polynomial	NOUN
ejpam-5193	44	21	in	in	ADP
ejpam-5193	44	22	(	(	PUNCT
ejpam-5193	44	23	1.1	1.1	NUM
ejpam-5193	44	24	)	)	PUNCT
ejpam-5193	44	25	.	.	PUNCT
ejpam-5193	45	1	that	that	PRON
ejpam-5193	45	2	is	be	AUX
ejpam-5193	45	3	,	,	PUNCT
ejpam-5193	45	4	g(1	g(1	NOUN
ejpam-5193	45	5	)	)	PUNCT
ejpam-5193	45	6	n	n	CCONJ
ejpam-5193	45	7	(	(	PUNCT
ejpam-5193	45	8	x	x	X
ejpam-5193	45	9	)	)	PUNCT
ejpam-5193	45	10	=	=	SYM
ejpam-5193	45	11	g	g	PROPN
ejpam-5193	45	12	(	(	PUNCT
ejpam-5193	45	13	1	1	NUM
ejpam-5193	45	14	)	)	PUNCT
ejpam-5193	45	15	n,2(x	n,2(x	NOUN
ejpam-5193	45	16	)	)	PUNCT
ejpam-5193	45	17	=	=	SYM
ejpam-5193	45	18	gn(x	gn(x	NUM
ejpam-5193	45	19	)	)	PUNCT
ejpam-5193	45	20	.	.	PUNCT
ejpam-5193	46	1	kim	kim	PROPN
ejpam-5193	46	2	et	et	PROPN
ejpam-5193	46	3	.	.	PUNCT
ejpam-5193	47	1	al	al	PROPN
ejpam-5193	48	1	[	[	X
ejpam-5193	48	2	31	31	NUM
ejpam-5193	48	3	]	]	PUNCT
ejpam-5193	48	4	obtained	obtain	VERB
ejpam-5193	48	5	several	several	ADJ
ejpam-5193	48	6	properties	property	NOUN
ejpam-5193	48	7	of	of	ADP
ejpam-5193	48	8	these	these	DET
ejpam-5193	48	9	polynomials	polynomial	NOUN
ejpam-5193	48	10	.	.	PUNCT
ejpam-5193	49	1	the	the	DET
ejpam-5193	49	2	higher	high	ADJ
ejpam-5193	49	3	order	order	NOUN
ejpam-5193	49	4	apostol	apostol	NOUN
ejpam-5193	49	5	-	-	PUNCT
ejpam-5193	49	6	type	type	NOUN
ejpam-5193	49	7	poly	poly	ADJ
ejpam-5193	49	8	-	-	PUNCT
ejpam-5193	49	9	genocchi	genocchi	NOUN
ejpam-5193	49	10	polynomials	polynomial	NOUN
ejpam-5193	49	11	g(k	g(k	VERB
ejpam-5193	49	12	,	,	PUNCT
ejpam-5193	49	13	α	α	NOUN
ejpam-5193	49	14	)	)	PUNCT
ejpam-5193	49	15	n	n	CCONJ
ejpam-5193	49	16	(	(	PUNCT
ejpam-5193	49	17	x;λ	x;λ	PROPN
ejpam-5193	49	18	,	,	PUNCT
ejpam-5193	49	19	a	a	DET
ejpam-5193	49	20	,	,	PUNCT
ejpam-5193	49	21	b	b	NOUN
ejpam-5193	49	22	,	,	PUNCT
ejpam-5193	49	23	c	c	NOUN
ejpam-5193	49	24	)	)	PUNCT
ejpam-5193	49	25	and	and	CCONJ
ejpam-5193	49	26	apostolfrobenius	apostolfrobenius	NOUN
ejpam-5193	49	27	-	-	PUNCT
ejpam-5193	49	28	type	type	NOUN
ejpam-5193	49	29	poly	poly	ADJ
ejpam-5193	49	30	-	-	PUNCT
ejpam-5193	49	31	genocchi	genocchi	NOUN
ejpam-5193	49	32	polynomials	polynomial	NOUN
ejpam-5193	49	33	g(k	g(k	VERB
ejpam-5193	49	34	,	,	PUNCT
ejpam-5193	49	35	α	α	NOUN
ejpam-5193	49	36	)	)	PUNCT
ejpam-5193	49	37	n	n	CCONJ
ejpam-5193	49	38	(	(	PUNCT
ejpam-5193	49	39	x;λ	x;λ	PROPN
ejpam-5193	49	40	,	,	PUNCT
ejpam-5193	49	41	u	u	NOUN
ejpam-5193	49	42	,	,	PUNCT
ejpam-5193	49	43	a	a	DET
ejpam-5193	49	44	,	,	PUNCT
ejpam-5193	49	45	b	b	NOUN
ejpam-5193	49	46	,	,	PUNCT
ejpam-5193	49	47	c	c	NOUN
ejpam-5193	49	48	)	)	PUNCT
ejpam-5193	49	49	and	and	CCONJ
ejpam-5193	49	50	are	be	AUX
ejpam-5193	49	51	respectively	respectively	ADV
ejpam-5193	49	52	defined	define	VERB
ejpam-5193	49	53	by	by	ADP
ejpam-5193	49	54	(	(	PUNCT
ejpam-5193	49	55	see	see	VERB
ejpam-5193	49	56	[	[	X
ejpam-5193	49	57	11	11	NUM
ejpam-5193	49	58	,	,	PUNCT
ejpam-5193	49	59	12	12	NUM
ejpam-5193	49	60	]	]	PUNCT
ejpam-5193	49	61	)	)	PUNCT
ejpam-5193	49	62	∞∑	∞∑	PRON
ejpam-5193	49	63	n=0	n=0	PUNCT
ejpam-5193	49	64	g(k	g(k	NOUN
ejpam-5193	49	65	,	,	PUNCT
ejpam-5193	49	66	α	α	NOUN
ejpam-5193	49	67	)	)	PUNCT
ejpam-5193	49	68	n	n	CCONJ
ejpam-5193	49	69	(	(	PUNCT
ejpam-5193	49	70	x;λ	x;λ	PROPN
ejpam-5193	49	71	,	,	PUNCT
ejpam-5193	49	72	a	a	DET
ejpam-5193	49	73	,	,	PUNCT
ejpam-5193	49	74	b	b	NOUN
ejpam-5193	49	75	,	,	PUNCT
ejpam-5193	49	76	c	c	NOUN
ejpam-5193	49	77	)	)	PUNCT
ejpam-5193	49	78	tn	tn	PROPN
ejpam-5193	49	79	n	n	CCONJ
ejpam-5193	49	80	!	!	PUNCT
ejpam-5193	50	1	=	=	PUNCT
ejpam-5193	50	2	(	(	PUNCT
ejpam-5193	50	3	lik(1−	lik(1−	X
ejpam-5193	50	4	(	(	PUNCT
ejpam-5193	50	5	ab)−2	ab)−2	NOUN
ejpam-5193	50	6	t	t	PROPN
ejpam-5193	50	7	)	)	PUNCT
ejpam-5193	50	8	a−t	a−t	NOUN
ejpam-5193	51	1	+	+	CCONJ
ejpam-5193	51	2	λbt	λbt	NOUN
ejpam-5193	51	3	)	)	PUNCT
ejpam-5193	51	4	α	α	PROPN
ejpam-5193	51	5	cxt	cxt	PROPN
ejpam-5193	51	6	,	,	PUNCT
ejpam-5193	51	7	(	(	PUNCT
ejpam-5193	51	8	1.12	1.12	NUM
ejpam-5193	51	9	)	)	PUNCT
ejpam-5193	51	10	∞∑	∞∑	PRON
ejpam-5193	51	11	n=0	n=0	PUNCT
ejpam-5193	51	12	g(k	g(k	NOUN
ejpam-5193	51	13	,	,	PUNCT
ejpam-5193	51	14	α	α	NOUN
ejpam-5193	51	15	)	)	PUNCT
ejpam-5193	51	16	n	n	CCONJ
ejpam-5193	51	17	(	(	PUNCT
ejpam-5193	51	18	x;λ	x;λ	PROPN
ejpam-5193	51	19	,	,	PUNCT
ejpam-5193	51	20	u	u	NOUN
ejpam-5193	51	21	,	,	PUNCT
ejpam-5193	51	22	a	a	DET
ejpam-5193	51	23	,	,	PUNCT
ejpam-5193	51	24	b	b	NOUN
ejpam-5193	51	25	,	,	PUNCT
ejpam-5193	51	26	c	c	NOUN
ejpam-5193	51	27	)	)	PUNCT
ejpam-5193	51	28	tn	tn	PROPN
ejpam-5193	51	29	n	n	CCONJ
ejpam-5193	51	30	!	!	PUNCT
ejpam-5193	51	31	=	=	PUNCT
ejpam-5193	52	1	(	(	PUNCT
ejpam-5193	52	2	lik(1−	lik(1−	X
ejpam-5193	52	3	(	(	PUNCT
ejpam-5193	52	4	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	52	5	)	)	PUNCT
ejpam-5193	52	6	λbt	λbt	VERB
ejpam-5193	52	7	−	−	PROPN
ejpam-5193	52	8	ua−t	ua−t	ADJ
ejpam-5193	52	9	)	)	PUNCT
ejpam-5193	52	10	α	α	PROPN
ejpam-5193	52	11	cxt	cxt	PROPN
ejpam-5193	52	12	.	.	PUNCT
ejpam-5193	53	1	(	(	PUNCT
ejpam-5193	53	2	1.13	1.13	NUM
ejpam-5193	53	3	)	)	PUNCT
ejpam-5193	53	4	further	further	ADJ
ejpam-5193	53	5	extension	extension	NOUN
ejpam-5193	53	6	and	and	CCONJ
ejpam-5193	53	7	variation	variation	NOUN
ejpam-5193	53	8	of	of	ADP
ejpam-5193	53	9	these	these	DET
ejpam-5193	53	10	polynomials	polynomial	NOUN
ejpam-5193	53	11	can	can	AUX
ejpam-5193	53	12	be	be	AUX
ejpam-5193	53	13	found	find	VERB
ejpam-5193	53	14	in	in	ADP
ejpam-5193	53	15	[	[	NOUN
ejpam-5193	53	16	13	13	NUM
ejpam-5193	53	17	,	,	PUNCT
ejpam-5193	53	18	14	14	NUM
ejpam-5193	53	19	]	]	PUNCT
ejpam-5193	53	20	.	.	PUNCT
ejpam-5193	54	1	the	the	DET
ejpam-5193	54	2	bell	bell	PROPN
ejpam-5193	54	3	polynomials	polynomial	NOUN
ejpam-5193	54	4	,	,	PUNCT
ejpam-5193	54	5	represented	represent	VERB
ejpam-5193	54	6	as	as	ADP
ejpam-5193	54	7	bn(x	bn(x	NOUN
ejpam-5193	54	8	)	)	PUNCT
ejpam-5193	54	9	,	,	PUNCT
ejpam-5193	54	10	are	be	AUX
ejpam-5193	54	11	defined	define	VERB
ejpam-5193	54	12	as	as	ADP
ejpam-5193	54	13	polynomials	polynomial	NOUN
ejpam-5193	54	14	with	with	ADP
ejpam-5193	54	15	coefficients	coefficient	NOUN
ejpam-5193	54	16	corresponding	correspond	VERB
ejpam-5193	54	17	to	to	ADP
ejpam-5193	54	18	the	the	DET
ejpam-5193	54	19	stirling	stirling	NOUN
ejpam-5193	54	20	numbers	number	NOUN
ejpam-5193	54	21	of	of	ADP
ejpam-5193	54	22	the	the	DET
ejpam-5193	54	23	second	second	ADJ
ejpam-5193	54	24	kind	kind	NOUN
ejpam-5193	54	25	.	.	PUNCT
ejpam-5193	55	1	to	to	PART
ejpam-5193	55	2	be	be	AUX
ejpam-5193	55	3	more	more	ADV
ejpam-5193	55	4	precise	precise	ADJ
ejpam-5193	55	5	,	,	PUNCT
ejpam-5193	55	6	bn(x	bn(x	NUM
ejpam-5193	55	7	)	)	PUNCT
ejpam-5193	56	1	=	=	SYM
ejpam-5193	56	2	n∑	n∑	X
ejpam-5193	56	3	k=0	k=0	PROPN
ejpam-5193	56	4	s(n	s(n	PROPN
ejpam-5193	56	5	,	,	PUNCT
ejpam-5193	56	6	k)xk	k)xk	PROPN
ejpam-5193	56	7	,	,	PUNCT
ejpam-5193	56	8	(	(	PUNCT
ejpam-5193	56	9	1.14	1.14	NUM
ejpam-5193	56	10	)	)	PUNCT
ejpam-5193	56	11	where	where	SCONJ
ejpam-5193	56	12	s(n	s(n	PROPN
ejpam-5193	56	13	,	,	PUNCT
ejpam-5193	56	14	k	k	NOUN
ejpam-5193	56	15	)	)	PUNCT
ejpam-5193	56	16	denotes	denote	VERB
ejpam-5193	56	17	the	the	DET
ejpam-5193	56	18	stirling	stirling	NOUN
ejpam-5193	56	19	numbers	number	NOUN
ejpam-5193	56	20	of	of	ADP
ejpam-5193	56	21	the	the	DET
ejpam-5193	56	22	second	second	ADJ
ejpam-5193	56	23	kind	kind	NOUN
ejpam-5193	56	24	.	.	PUNCT
ejpam-5193	57	1	these	these	DET
ejpam-5193	57	2	numbers	number	NOUN
ejpam-5193	57	3	adhere	adhere	VERB
ejpam-5193	57	4	to	to	ADP
ejpam-5193	57	5	the	the	DET
ejpam-5193	57	6	following	follow	VERB
ejpam-5193	57	7	exponential	exponential	ADJ
ejpam-5193	57	8	generating	generating	NOUN
ejpam-5193	57	9	function	function	NOUN
ejpam-5193	57	10	∞∑	∞∑	PRON
ejpam-5193	57	11	n=0	n=0	X
ejpam-5193	57	12	s(n	s(n	PROPN
ejpam-5193	57	13	,	,	PUNCT
ejpam-5193	57	14	j	j	NOUN
ejpam-5193	57	15	)	)	PUNCT
ejpam-5193	57	16	tn	tn	PROPN
ejpam-5193	57	17	n	n	PROPN
ejpam-5193	57	18	!	!	PUNCT
ejpam-5193	58	1	=	=	PUNCT
ejpam-5193	58	2	(	(	PUNCT
ejpam-5193	58	3	et	et	NOUN
ejpam-5193	58	4	−	−	PROPN
ejpam-5193	58	5	1)j	1)j	NUM
ejpam-5193	59	1	j	j	PROPN
ejpam-5193	59	2	!	!	PROPN
ejpam-5193	59	3	,	,	PUNCT
ejpam-5193	59	4	(	(	PUNCT
ejpam-5193	59	5	1.15	1.15	NUM
ejpam-5193	59	6	)	)	PUNCT
ejpam-5193	59	7	(	(	PUNCT
ejpam-5193	59	8	see	see	VERB
ejpam-5193	59	9	[	[	X
ejpam-5193	59	10	10	10	NUM
ejpam-5193	59	11	,	,	PUNCT
ejpam-5193	59	12	26	26	NUM
ejpam-5193	59	13	]	]	PUNCT
ejpam-5193	59	14	)	)	PUNCT
ejpam-5193	59	15	.	.	PUNCT
ejpam-5193	60	1	by	by	ADP
ejpam-5193	60	2	mixing	mix	VERB
ejpam-5193	60	3	the	the	DET
ejpam-5193	60	4	concept	concept	NOUN
ejpam-5193	60	5	of	of	ADP
ejpam-5193	60	6	bell	bell	NOUN
ejpam-5193	60	7	polynomials	polynomial	NOUN
ejpam-5193	60	8	with	with	ADP
ejpam-5193	60	9	partially	partially	ADV
ejpam-5193	60	10	degenerate	degenerate	ADJ
ejpam-5193	60	11	bernoulli	bernoulli	NOUN
ejpam-5193	60	12	polynomials	polynomial	NOUN
ejpam-5193	60	13	of	of	ADP
ejpam-5193	60	14	the	the	DET
ejpam-5193	60	15	first	first	ADJ
ejpam-5193	60	16	kind	kind	NOUN
ejpam-5193	60	17	defined	define	VERB
ejpam-5193	60	18	by	by	ADP
ejpam-5193	60	19	the	the	DET
ejpam-5193	60	20	generating	generate	VERB
ejpam-5193	60	21	function	function	NOUN
ejpam-5193	60	22	log(1	log(1	NOUN
ejpam-5193	60	23	+	+	CCONJ
ejpam-5193	61	1	λt)1	λt)1	NOUN
ejpam-5193	61	2	/	/	SYM
ejpam-5193	61	3	λ	λ	PROPN
ejpam-5193	61	4	et	et	NOUN
ejpam-5193	61	5	−	−	NUM
ejpam-5193	61	6	1	1	NUM
ejpam-5193	61	7	ext	ext	NOUN
ejpam-5193	61	8	=	=	NOUN
ejpam-5193	61	9	∞∑	∞∑	DET
ejpam-5193	61	10	n=0	n=0	PROPN
ejpam-5193	61	11	bn	bn	NOUN
ejpam-5193	61	12	,	,	PUNCT
ejpam-5193	61	13	λ(x	λ(x	PROPN
ejpam-5193	61	14	)	)	PUNCT
ejpam-5193	61	15	tn	tn	PROPN
ejpam-5193	61	16	n	n	PROPN
ejpam-5193	61	17	!	!	PROPN
ejpam-5193	61	18	,	,	PUNCT
ejpam-5193	61	19	1474	1474	NUM
ejpam-5193	61	20	the	the	DET
ejpam-5193	61	21	partially	partially	ADV
ejpam-5193	61	22	degenerate	degenerate	ADJ
ejpam-5193	61	23	bell	bell	ADJ
ejpam-5193	61	24	-	-	PUNCT
ejpam-5193	61	25	bernoulli	bernoulli	NOUN
ejpam-5193	61	26	polynomials	polynomial	NOUN
ejpam-5193	61	27	of	of	ADP
ejpam-5193	61	28	the	the	DET
ejpam-5193	61	29	first	first	ADJ
ejpam-5193	61	30	kind	kind	NOUN
ejpam-5193	61	31	are	be	AUX
ejpam-5193	61	32	defined	define	VERB
ejpam-5193	61	33	in	in	ADP
ejpam-5193	61	34	[	[	X
ejpam-5193	61	35	20	20	NUM
ejpam-5193	61	36	]	]	PUNCT
ejpam-5193	61	37	by	by	ADP
ejpam-5193	61	38	the	the	DET
ejpam-5193	61	39	generating	generate	VERB
ejpam-5193	61	40	function	function	NOUN
ejpam-5193	61	41	log(1	log(1	NOUN
ejpam-5193	61	42	+	+	CCONJ
ejpam-5193	62	1	λt)1	λt)1	NOUN
ejpam-5193	62	2	/	/	SYM
ejpam-5193	62	3	λ	λ	PROPN
ejpam-5193	62	4	et	et	NOUN
ejpam-5193	62	5	−	−	NUM
ejpam-5193	62	6	1	1	NUM
ejpam-5193	62	7	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	62	8	)	)	PUNCT
ejpam-5193	63	1	=	=	PUNCT
ejpam-5193	63	2	∞∑	∞∑	ADJ
ejpam-5193	63	3	n=0	n=0	NUM
ejpam-5193	63	4	belbn	belbn	NOUN
ejpam-5193	63	5	,	,	PUNCT
ejpam-5193	63	6	λ(x	λ(x	PROPN
ejpam-5193	63	7	,	,	PUNCT
ejpam-5193	63	8	y	y	PROPN
ejpam-5193	63	9	)	)	PUNCT
ejpam-5193	63	10	tn	tn	PROPN
ejpam-5193	63	11	n	n	PROPN
ejpam-5193	63	12	!	!	PUNCT
ejpam-5193	63	13	.	.	PUNCT
ejpam-5193	64	1	further	further	ADJ
ejpam-5193	64	2	generalization	generalization	NOUN
ejpam-5193	64	3	is	be	AUX
ejpam-5193	64	4	introduced	introduce	VERB
ejpam-5193	64	5	in	in	ADP
ejpam-5193	64	6	[	[	X
ejpam-5193	64	7	20	20	NUM
ejpam-5193	64	8	]	]	PUNCT
ejpam-5193	64	9	by	by	ADP
ejpam-5193	64	10	incorporating	incorporate	VERB
ejpam-5193	64	11	the	the	DET
ejpam-5193	64	12	concept	concept	NOUN
ejpam-5193	64	13	of	of	ADP
ejpam-5193	64	14	dirichlet	dirichlet	PROPN
ejpam-5193	64	15	character	character	NOUN
ejpam-5193	64	16	with	with	ADP
ejpam-5193	64	17	conductor	conductor	PROPN
ejpam-5193	64	18	d.	d.	PROPN
ejpam-5193	64	19	also	also	ADV
ejpam-5193	64	20	,	,	PUNCT
ejpam-5193	64	21	by	by	ADP
ejpam-5193	64	22	mixing	mix	VERB
ejpam-5193	64	23	the	the	DET
ejpam-5193	64	24	concept	concept	NOUN
ejpam-5193	64	25	of	of	ADP
ejpam-5193	64	26	bell	bell	NOUN
ejpam-5193	64	27	polynomials	polynomial	NOUN
ejpam-5193	64	28	,	,	PUNCT
ejpam-5193	64	29	alam	alam	PROPN
ejpam-5193	64	30	et	et	PROPN
ejpam-5193	64	31	al	al	PROPN
ejpam-5193	64	32	.	.	PUNCT
ejpam-5193	65	1	[	[	X
ejpam-5193	65	2	2	2	NUM
ejpam-5193	65	3	]	]	PUNCT
ejpam-5193	65	4	developed	develop	VERB
ejpam-5193	65	5	generating	generating	NOUN
ejpam-5193	65	6	functions	function	NOUN
ejpam-5193	65	7	for	for	ADP
ejpam-5193	65	8	new	new	ADJ
ejpam-5193	65	9	families	family	NOUN
ejpam-5193	65	10	of	of	ADP
ejpam-5193	65	11	special	special	ADJ
ejpam-5193	65	12	polynomials	polynomial	NOUN
ejpam-5193	65	13	,	,	PUNCT
ejpam-5193	65	14	including	include	VERB
ejpam-5193	65	15	two	two	NUM
ejpam-5193	65	16	parametric	parametric	ADJ
ejpam-5193	65	17	types	type	NOUN
ejpam-5193	65	18	of	of	ADP
ejpam-5193	65	19	bellbased	bellbased	ADJ
ejpam-5193	65	20	bernoulli	bernoulli	PROPN
ejpam-5193	65	21	and	and	CCONJ
ejpam-5193	65	22	euler	euler	NOUN
ejpam-5193	65	23	polynomials	polynomial	NOUN
ejpam-5193	65	24	,	,	PUNCT
ejpam-5193	65	25	defined	define	VERB
ejpam-5193	65	26	as	as	SCONJ
ejpam-5193	65	27	follows	follow	VERB
ejpam-5193	65	28	:	:	PUNCT
ejpam-5193	65	29	∞∑	∞∑	NUM
ejpam-5193	65	30	n=0	n=0	NUM
ejpam-5193	65	31	bellbr	bellbr	NOUN
ejpam-5193	65	32	n(ξ	n(ξ	PROPN
ejpam-5193	65	33	+	+	CCONJ
ejpam-5193	65	34	iη	iη	PROPN
ejpam-5193	65	35	,	,	PUNCT
ejpam-5193	65	36	x;u	x;u	PROPN
ejpam-5193	65	37	,	,	PUNCT
ejpam-5193	65	38	λ	λ	PROPN
ejpam-5193	65	39	)	)	PUNCT
ejpam-5193	65	40	tn	tn	PROPN
ejpam-5193	65	41	n	n	PROPN
ejpam-5193	65	42	!	!	PUNCT
ejpam-5193	66	1	=	=	PUNCT
ejpam-5193	66	2	(	(	PUNCT
ejpam-5193	66	3	1	1	NUM
ejpam-5193	66	4	et	et	NOUN
ejpam-5193	66	5	−	−	NOUN
ejpam-5193	66	6	1	1	X
ejpam-5193	66	7	)	)	PUNCT
ejpam-5193	66	8	r	r	NOUN
ejpam-5193	66	9	e(ξ+iη)teζ(e	e(ξ+iη)teζ(e	PROPN
ejpam-5193	66	10	x−1	x−1	PROPN
ejpam-5193	66	11	)	)	PUNCT
ejpam-5193	66	12	,	,	PUNCT
ejpam-5193	66	13	∞∑	∞∑	PROPN
ejpam-5193	66	14	n=0	n=0	NUM
ejpam-5193	66	15	bellhr	bellhr	VERB
ejpam-5193	66	16	n(ξ	n(ξ	PROPN
ejpam-5193	66	17	+	+	CCONJ
ejpam-5193	66	18	iη	iη	PROPN
ejpam-5193	66	19	,	,	PUNCT
ejpam-5193	66	20	x;u	x;u	PROPN
ejpam-5193	66	21	,	,	PUNCT
ejpam-5193	66	22	λ	λ	PROPN
ejpam-5193	66	23	)	)	PUNCT
ejpam-5193	66	24	tn	tn	PROPN
ejpam-5193	66	25	n	n	PROPN
ejpam-5193	66	26	!	!	PUNCT
ejpam-5193	66	27	=	=	PUNCT
ejpam-5193	67	1	(	(	PUNCT
ejpam-5193	67	2	2	2	NUM
ejpam-5193	67	3	et	et	NOUN
ejpam-5193	67	4	+	+	NOUN
ejpam-5193	67	5	1	1	X
ejpam-5193	67	6	)	)	PUNCT
ejpam-5193	67	7	r	r	NOUN
ejpam-5193	67	8	e(ξ+iη)teζ(e	e(ξ+iη)teζ(e	PROPN
ejpam-5193	67	9	x−1	x−1	PROPN
ejpam-5193	67	10	)	)	PUNCT
ejpam-5193	67	11	.	.	PUNCT
ejpam-5193	68	1	they	they	PRON
ejpam-5193	68	2	investigated	investigate	VERB
ejpam-5193	68	3	fundamental	fundamental	ADJ
ejpam-5193	68	4	properties	property	NOUN
ejpam-5193	68	5	of	of	ADP
ejpam-5193	68	6	these	these	DET
ejpam-5193	68	7	generating	generate	VERB
ejpam-5193	68	8	functions	function	NOUN
ejpam-5193	68	9	and	and	CCONJ
ejpam-5193	68	10	used	use	VERB
ejpam-5193	68	11	them	they	PRON
ejpam-5193	68	12	,	,	PUNCT
ejpam-5193	68	13	along	along	ADP
ejpam-5193	68	14	with	with	ADP
ejpam-5193	68	15	certain	certain	ADJ
ejpam-5193	68	16	identities	identity	NOUN
ejpam-5193	68	17	,	,	PUNCT
ejpam-5193	68	18	to	to	PART
ejpam-5193	68	19	present	present	VERB
ejpam-5193	68	20	relations	relation	NOUN
ejpam-5193	68	21	among	among	ADP
ejpam-5193	68	22	trigonometric	trigonometric	ADJ
ejpam-5193	68	23	functions	function	NOUN
ejpam-5193	68	24	,	,	PUNCT
ejpam-5193	68	25	two	two	NUM
ejpam-5193	68	26	parametric	parametric	ADJ
ejpam-5193	68	27	types	type	NOUN
ejpam-5193	68	28	of	of	ADP
ejpam-5193	68	29	bell	bell	NOUN
ejpam-5193	68	30	-	-	PUNCT
ejpam-5193	68	31	based	base	VERB
ejpam-5193	68	32	bernoulli	bernoulli	PROPN
ejpam-5193	68	33	and	and	CCONJ
ejpam-5193	68	34	euler	euler	NOUN
ejpam-5193	68	35	polynomials	polynomial	NOUN
ejpam-5193	68	36	,	,	PUNCT
ejpam-5193	68	37	and	and	CCONJ
ejpam-5193	68	38	stirling	stirling	NOUN
ejpam-5193	68	39	numbers	number	NOUN
ejpam-5193	68	40	.	.	PUNCT
ejpam-5193	69	1	they	they	PRON
ejpam-5193	69	2	also	also	ADV
ejpam-5193	69	3	derived	derive	VERB
ejpam-5193	69	4	computational	computational	ADJ
ejpam-5193	69	5	formulae	formulae	NOUN
ejpam-5193	69	6	for	for	ADP
ejpam-5193	69	7	these	these	DET
ejpam-5193	69	8	polynomials	polynomial	NOUN
ejpam-5193	69	9	.	.	PUNCT
ejpam-5193	70	1	by	by	ADP
ejpam-5193	70	2	applying	apply	VERB
ejpam-5193	70	3	a	a	DET
ejpam-5193	70	4	partial	partial	ADJ
ejpam-5193	70	5	derivative	derivative	ADJ
ejpam-5193	70	6	operator	operator	NOUN
ejpam-5193	70	7	to	to	ADP
ejpam-5193	70	8	these	these	DET
ejpam-5193	70	9	generating	generating	NOUN
ejpam-5193	70	10	functions	function	NOUN
ejpam-5193	70	11	,	,	PUNCT
ejpam-5193	70	12	they	they	PRON
ejpam-5193	70	13	obtained	obtain	VERB
ejpam-5193	70	14	various	various	ADJ
ejpam-5193	70	15	derivative	derivative	ADJ
ejpam-5193	70	16	formulae	formulae	NOUN
ejpam-5193	70	17	and	and	CCONJ
ejpam-5193	70	18	finite	finite	ADJ
ejpam-5193	70	19	combinatorial	combinatorial	ADJ
ejpam-5193	70	20	sums	sum	NOUN
ejpam-5193	70	21	involving	involve	VERB
ejpam-5193	70	22	the	the	DET
ejpam-5193	70	23	aforementioned	aforementioned	ADJ
ejpam-5193	70	24	polynomials	polynomial	NOUN
ejpam-5193	70	25	and	and	CCONJ
ejpam-5193	70	26	numbers	number	NOUN
ejpam-5193	70	27	.	.	PUNCT
ejpam-5193	71	1	in	in	ADP
ejpam-5193	71	2	separate	separate	ADJ
ejpam-5193	71	3	papers	paper	NOUN
ejpam-5193	71	4	,	,	PUNCT
ejpam-5193	71	5	alam	alam	PROPN
ejpam-5193	71	6	et	et	PROPN
ejpam-5193	71	7	al	al	PROPN
ejpam-5193	71	8	.	.	PUNCT
ejpam-5193	72	1	[	[	X
ejpam-5193	72	2	4	4	X
ejpam-5193	72	3	]	]	PUNCT
ejpam-5193	72	4	and	and	CCONJ
ejpam-5193	72	5	ayed	aye	VERB
ejpam-5193	72	6	et	et	PROPN
ejpam-5193	72	7	al	al	PROPN
ejpam-5193	72	8	.	.	PUNCT
ejpam-5193	73	1	[	[	X
ejpam-5193	73	2	8	8	NUM
ejpam-5193	73	3	]	]	PUNCT
ejpam-5193	73	4	introduced	introduce	VERB
ejpam-5193	73	5	a	a	DET
ejpam-5193	73	6	novel	novel	ADJ
ejpam-5193	73	7	class	class	NOUN
ejpam-5193	73	8	of	of	ADP
ejpam-5193	73	9	bellbased	bellbase	VERB
ejpam-5193	73	10	apostol	apostol	NOUN
ejpam-5193	73	11	-	-	PUNCT
ejpam-5193	73	12	type	type	NOUN
ejpam-5193	73	13	frobenius	frobenius	NOUN
ejpam-5193	73	14	-	-	PUNCT
ejpam-5193	73	15	euler	euler	NOUN
ejpam-5193	73	16	polynomials	polynomial	NOUN
ejpam-5193	73	17	and	and	CCONJ
ejpam-5193	73	18	bell	bell	NOUN
ejpam-5193	73	19	-	-	PUNCT
ejpam-5193	73	20	based	base	VERB
ejpam-5193	73	21	apostol	apostol	NOUN
ejpam-5193	73	22	-	-	PUNCT
ejpam-5193	73	23	type	type	NOUN
ejpam-5193	73	24	frobeniusgenocchi	frobeniusgenocchi	ADJ
ejpam-5193	73	25	polynomials	polynomial	NOUN
ejpam-5193	73	26	,	,	PUNCT
ejpam-5193	73	27	respectively	respectively	ADV
ejpam-5193	73	28	.	.	PUNCT
ejpam-5193	74	1	these	these	PRON
ejpam-5193	74	2	are	be	AUX
ejpam-5193	74	3	defined	define	VERB
ejpam-5193	74	4	as	as	SCONJ
ejpam-5193	74	5	follows	follow	VERB
ejpam-5193	74	6	:	:	PUNCT
ejpam-5193	74	7	∞∑	∞∑	NUM
ejpam-5193	74	8	n=0	n=0	NUM
ejpam-5193	74	9	bellhr	bellhr	VERB
ejpam-5193	74	10	n(x;u	n(x;u	NOUN
ejpam-5193	74	11	,	,	PUNCT
ejpam-5193	74	12	λ	λ	PROPN
ejpam-5193	74	13	)	)	PUNCT
ejpam-5193	74	14	tn	tn	PROPN
ejpam-5193	74	15	n	n	PROPN
ejpam-5193	74	16	!	!	PUNCT
ejpam-5193	75	1	=	=	PUNCT
ejpam-5193	76	1	(	(	PUNCT
ejpam-5193	76	2	1−	1−	NUM
ejpam-5193	76	3	u	u	NOUN
ejpam-5193	76	4	λet	λet	ADP
ejpam-5193	76	5	−	−	NUM
ejpam-5193	76	6	u	u	NOUN
ejpam-5193	76	7	)	)	PUNCT
ejpam-5193	76	8	r	r	NOUN
ejpam-5193	76	9	eζ(e	eζ(e	X
ejpam-5193	76	10	x−1	x−1	NOUN
ejpam-5193	76	11	)	)	PUNCT
ejpam-5193	76	12	,	,	PUNCT
ejpam-5193	76	13	(	(	PUNCT
ejpam-5193	76	14	1.16	1.16	NUM
ejpam-5193	76	15	)	)	PUNCT
ejpam-5193	76	16	∞∑	∞∑	PRON
ejpam-5193	76	17	n=0	n=0	X
ejpam-5193	76	18	bellgr	bellgr	NOUN
ejpam-5193	76	19	n(ξ	n(ξ	PROPN
ejpam-5193	76	20	+	+	CCONJ
ejpam-5193	76	21	iη	iη	PROPN
ejpam-5193	76	22	,	,	PUNCT
ejpam-5193	76	23	x;u	x;u	PROPN
ejpam-5193	76	24	,	,	PUNCT
ejpam-5193	76	25	λ	λ	PROPN
ejpam-5193	76	26	)	)	PUNCT
ejpam-5193	76	27	tn	tn	PROPN
ejpam-5193	76	28	n	n	PROPN
ejpam-5193	76	29	!	!	PUNCT
ejpam-5193	77	1	=	=	PUNCT
ejpam-5193	77	2	(	(	PUNCT
ejpam-5193	77	3	(	(	PUNCT
ejpam-5193	77	4	1−	1−	NUM
ejpam-5193	77	5	u)t	u)t	X
ejpam-5193	77	6	λet	λet	ADP
ejpam-5193	77	7	−	−	NUM
ejpam-5193	77	8	u	u	NOUN
ejpam-5193	77	9	)	)	PUNCT
ejpam-5193	77	10	r	r	NOUN
ejpam-5193	77	11	e(ξ+iη)teζ(e	e(ξ+iη)teζ(e	PROPN
ejpam-5193	77	12	x−1	x−1	PROPN
ejpam-5193	77	13	)	)	PUNCT
ejpam-5193	77	14	.	.	PUNCT
ejpam-5193	78	1	(	(	PUNCT
ejpam-5193	78	2	1.17	1.17	X
ejpam-5193	78	3	)	)	PUNCT
ejpam-5193	78	4	their	their	PRON
ejpam-5193	78	5	research	research	NOUN
ejpam-5193	78	6	explored	explore	VERB
ejpam-5193	78	7	various	various	ADJ
ejpam-5193	78	8	properties	property	NOUN
ejpam-5193	78	9	of	of	ADP
ejpam-5193	78	10	these	these	DET
ejpam-5193	78	11	polynomials	polynomial	NOUN
ejpam-5193	78	12	and	and	CCONJ
ejpam-5193	78	13	numbers	number	NOUN
ejpam-5193	78	14	,	,	PUNCT
ejpam-5193	78	15	deriving	derive	VERB
ejpam-5193	78	16	summation	summation	NOUN
ejpam-5193	78	17	formulas	formula	NOUN
ejpam-5193	78	18	in	in	ADP
ejpam-5193	78	19	terms	term	NOUN
ejpam-5193	78	20	of	of	ADP
ejpam-5193	78	21	apostol	apostol	NOUN
ejpam-5193	78	22	-	-	PUNCT
ejpam-5193	78	23	type	type	NOUN
ejpam-5193	78	24	bernoulli	bernoulli	PROPN
ejpam-5193	78	25	,	,	PUNCT
ejpam-5193	78	26	euler	euler	NOUN
ejpam-5193	78	27	,	,	PUNCT
ejpam-5193	78	28	and	and	CCONJ
ejpam-5193	78	29	genocchi	genocchi	PROPN
ejpam-5193	78	30	polynomials	polynomial	VERB
ejpam-5193	78	31	[	[	X
ejpam-5193	78	32	4	4	NUM
ejpam-5193	78	33	]	]	PUNCT
ejpam-5193	78	34	.	.	PUNCT
ejpam-5193	79	1	they	they	PRON
ejpam-5193	79	2	established	establish	VERB
ejpam-5193	79	3	numerous	numerous	ADJ
ejpam-5193	79	4	identities	identity	NOUN
ejpam-5193	79	5	using	use	VERB
ejpam-5193	79	6	diverse	diverse	ADJ
ejpam-5193	79	7	analytical	analytical	ADJ
ejpam-5193	79	8	methods	method	NOUN
ejpam-5193	79	9	and	and	CCONJ
ejpam-5193	79	10	the	the	DET
ejpam-5193	79	11	generating	generate	VERB
ejpam-5193	79	12	function	function	NOUN
ejpam-5193	79	13	technique	technique	NOUN
ejpam-5193	79	14	,	,	PUNCT
ejpam-5193	79	15	and	and	CCONJ
ejpam-5193	79	16	introduced	introduce	VERB
ejpam-5193	79	17	parametric	parametric	ADJ
ejpam-5193	79	18	variations	variation	NOUN
ejpam-5193	79	19	that	that	PRON
ejpam-5193	79	20	unveiled	unveil	VERB
ejpam-5193	79	21	specific	specific	ADJ
ejpam-5193	79	22	polynomial	polynomial	ADJ
ejpam-5193	79	23	identities	identity	NOUN
ejpam-5193	79	24	[	[	X
ejpam-5193	79	25	4	4	NUM
ejpam-5193	79	26	]	]	PUNCT
ejpam-5193	79	27	.	.	PUNCT
ejpam-5193	80	1	additionally	additionally	ADV
ejpam-5193	80	2	,	,	PUNCT
ejpam-5193	80	3	they	they	PRON
ejpam-5193	80	4	investigated	investigate	VERB
ejpam-5193	80	5	various	various	ADJ
ejpam-5193	80	6	formulas	formula	NOUN
ejpam-5193	80	7	and	and	CCONJ
ejpam-5193	80	8	properties	property	NOUN
ejpam-5193	80	9	,	,	PUNCT
ejpam-5193	80	10	including	include	VERB
ejpam-5193	80	11	differentiation	differentiation	NOUN
ejpam-5193	80	12	rules	rule	NOUN
ejpam-5193	80	13	,	,	PUNCT
ejpam-5193	80	14	addition	addition	NOUN
ejpam-5193	80	15	formulas	formula	NOUN
ejpam-5193	80	16	,	,	PUNCT
ejpam-5193	80	17	relations	relation	NOUN
ejpam-5193	80	18	,	,	PUNCT
ejpam-5193	80	19	and	and	CCONJ
ejpam-5193	80	20	summation	summation	NOUN
ejpam-5193	80	21	formulas	formula	NOUN
ejpam-5193	80	22	.	.	PUNCT
ejpam-5193	81	1	moreover	moreover	ADV
ejpam-5193	81	2	,	,	PUNCT
ejpam-5193	81	3	they	they	PRON
ejpam-5193	81	4	identified	identify	VERB
ejpam-5193	81	5	the	the	DET
ejpam-5193	81	6	first	first	ADJ
ejpam-5193	81	7	few	few	ADJ
ejpam-5193	81	8	zero	zero	NUM
ejpam-5193	81	9	values	value	NOUN
ejpam-5193	81	10	of	of	ADP
ejpam-5193	81	11	the	the	DET
ejpam-5193	81	12	apostol	apostol	NOUN
ejpam-5193	81	13	-	-	PUNCT
ejpam-5193	81	14	type	type	NOUN
ejpam-5193	81	15	frobenius	frobenius	NOUN
ejpam-5193	81	16	-	-	PUNCT
ejpam-5193	81	17	genocchi	genocchi	NOUN
ejpam-5193	81	18	polynomials	polynomial	NOUN
ejpam-5193	81	19	and	and	CCONJ
ejpam-5193	81	20	provided	provide	VERB
ejpam-5193	81	21	graphical	graphical	ADJ
ejpam-5193	81	22	representations	representation	NOUN
ejpam-5193	81	23	of	of	ADP
ejpam-5193	81	24	these	these	DET
ejpam-5193	81	25	zero	zero	NUM
ejpam-5193	81	26	values	value	NOUN
ejpam-5193	81	27	[	[	X
ejpam-5193	81	28	7	7	NUM
ejpam-5193	81	29	,	,	PUNCT
ejpam-5193	81	30	8	8	NUM
ejpam-5193	81	31	]	]	PUNCT
ejpam-5193	81	32	.	.	PUNCT
ejpam-5193	82	1	it	it	PRON
ejpam-5193	82	2	is	be	AUX
ejpam-5193	82	3	noteworthy	noteworthy	ADJ
ejpam-5193	82	4	that	that	SCONJ
ejpam-5193	82	5	an	an	DET
ejpam-5193	82	6	alternative	alternative	ADJ
ejpam-5193	82	7	method	method	NOUN
ejpam-5193	82	8	for	for	ADP
ejpam-5193	82	9	introducing	introduce	VERB
ejpam-5193	82	10	bell	bell	NOUN
ejpam-5193	82	11	-	-	PUNCT
ejpam-5193	82	12	based	base	VERB
ejpam-5193	82	13	frobenius	frobenius	NOUN
ejpam-5193	82	14	-	-	PUNCT
ejpam-5193	82	15	euler	euler	NOUN
ejpam-5193	82	16	polynomials	polynomial	NOUN
ejpam-5193	82	17	has	have	AUX
ejpam-5193	82	18	been	be	AUX
ejpam-5193	82	19	established	establish	VERB
ejpam-5193	82	20	in	in	ADP
ejpam-5193	82	21	[	[	X
ejpam-5193	82	22	21	21	NUM
ejpam-5193	82	23	]	]	PUNCT
ejpam-5193	82	24	.	.	PUNCT
ejpam-5193	83	1	this	this	DET
ejpam-5193	83	2	variation	variation	NOUN
ejpam-5193	83	3	,	,	PUNCT
ejpam-5193	83	4	known	know	VERB
ejpam-5193	83	5	as	as	ADP
ejpam-5193	83	6	bell	bell	NOUN
ejpam-5193	83	7	-	-	PUNCT
ejpam-5193	83	8	based	base	VERB
ejpam-5193	83	9	frobenius	frobenius	NOUN
ejpam-5193	83	10	-	-	PUNCT
ejpam-5193	83	11	type	type	NOUN
ejpam-5193	83	12	eulerian	eulerian	ADJ
ejpam-5193	83	13	1475	1475	NUM
ejpam-5193	83	14	polynomials	polynomial	NOUN
ejpam-5193	83	15	,	,	PUNCT
ejpam-5193	83	16	is	be	AUX
ejpam-5193	83	17	defined	define	VERB
ejpam-5193	83	18	as	as	SCONJ
ejpam-5193	83	19	follows	follow	VERB
ejpam-5193	83	20	:	:	PUNCT
ejpam-5193	83	21	∞∑	∞∑	PRON
ejpam-5193	83	22	n=0	n=0	NUM
ejpam-5193	83	23	bellar	bellar	ADJ
ejpam-5193	83	24	n(ξ	n(ξ	PROPN
ejpam-5193	83	25	,	,	PUNCT
ejpam-5193	83	26	ζ|u	ζ|u	NUM
ejpam-5193	83	27	)	)	PUNCT
ejpam-5193	83	28	tn	tn	PROPN
ejpam-5193	84	1	n	n	PROPN
ejpam-5193	84	2	!	!	PUNCT
ejpam-5193	85	1	=	=	PUNCT
ejpam-5193	85	2	(	(	PUNCT
ejpam-5193	85	3	1−	1−	NUM
ejpam-5193	85	4	u	u	PROPN
ejpam-5193	85	5	et(u−1	et(u−1	PROPN
ejpam-5193	85	6	)	)	PUNCT
ejpam-5193	85	7	−	−	PROPN
ejpam-5193	85	8	u	u	NOUN
ejpam-5193	85	9	)	)	PUNCT
ejpam-5193	85	10	r	r	NOUN
ejpam-5193	85	11	eξteζ(e	eξteζ(e	PROPN
ejpam-5193	85	12	x−1	x−1	PROPN
ejpam-5193	85	13	)	)	PUNCT
ejpam-5193	85	14	in	in	ADP
ejpam-5193	85	15	line	line	NOUN
ejpam-5193	85	16	with	with	ADP
ejpam-5193	85	17	the	the	DET
ejpam-5193	85	18	polynomial	polynomial	ADJ
ejpam-5193	85	19	exploration	exploration	NOUN
ejpam-5193	85	20	in	in	ADP
ejpam-5193	85	21	[	[	X
ejpam-5193	85	22	12	12	NUM
ejpam-5193	85	23	]	]	PUNCT
ejpam-5193	85	24	,	,	PUNCT
ejpam-5193	85	25	it	it	PRON
ejpam-5193	85	26	is	be	AUX
ejpam-5193	85	27	equally	equally	ADV
ejpam-5193	85	28	compelling	compelling	ADJ
ejpam-5193	85	29	to	to	PART
ejpam-5193	85	30	investigate	investigate	VERB
ejpam-5193	85	31	bell	bell	NOUN
ejpam-5193	85	32	-	-	PUNCT
ejpam-5193	85	33	based	base	VERB
ejpam-5193	85	34	apostol	apostol	NOUN
ejpam-5193	85	35	-	-	PUNCT
ejpam-5193	85	36	frobenius	frobenius	NOUN
ejpam-5193	85	37	-	-	PUNCT
ejpam-5193	85	38	type	type	NOUN
ejpam-5193	85	39	poly	poly	ADJ
ejpam-5193	85	40	-	-	PUNCT
ejpam-5193	85	41	genocchi	genocchi	NOUN
ejpam-5193	85	42	polynomials	polynomial	NOUN
ejpam-5193	85	43	.	.	PUNCT
ejpam-5193	86	1	2	2	X
ejpam-5193	86	2	.	.	X
ejpam-5193	86	3	higher	high	ADJ
ejpam-5193	86	4	order	order	NOUN
ejpam-5193	86	5	bivariate	bivariate	ADJ
ejpam-5193	86	6	bell	bell	NOUN
ejpam-5193	86	7	-	-	PUNCT
ejpam-5193	86	8	based	base	VERB
ejpam-5193	86	9	apostol	apostol	NOUN
ejpam-5193	86	10	-	-	PUNCT
ejpam-5193	86	11	frobenius	frobenius	NOUN
ejpam-5193	86	12	-	-	PUNCT
ejpam-5193	86	13	type	type	NOUN
ejpam-5193	86	14	poly	poly	ADJ
ejpam-5193	86	15	-	-	PUNCT
ejpam-5193	86	16	genocchi	genocchi	NOUN
ejpam-5193	86	17	polynomials	polynomial	NOUN
ejpam-5193	86	18	in	in	ADP
ejpam-5193	86	19	this	this	DET
ejpam-5193	86	20	section	section	NOUN
ejpam-5193	86	21	,	,	PUNCT
ejpam-5193	86	22	we	we	PRON
ejpam-5193	86	23	introduce	introduce	VERB
ejpam-5193	86	24	higher	high	ADJ
ejpam-5193	86	25	-	-	PUNCT
ejpam-5193	86	26	order	order	NOUN
ejpam-5193	86	27	bivariate	bivariate	ADJ
ejpam-5193	86	28	bell	bell	NOUN
ejpam-5193	86	29	-	-	PUNCT
ejpam-5193	86	30	based	base	VERB
ejpam-5193	86	31	apostol	apostol	NOUN
ejpam-5193	86	32	-	-	PUNCT
ejpam-5193	86	33	frobenius	frobenius	NOUN
ejpam-5193	86	34	-	-	PUNCT
ejpam-5193	86	35	type	type	NOUN
ejpam-5193	86	36	poly	poly	ADJ
ejpam-5193	86	37	-	-	PUNCT
ejpam-5193	86	38	genocchi	genocchi	NOUN
ejpam-5193	86	39	polynomials	polynomial	NOUN
ejpam-5193	86	40	,	,	PUNCT
ejpam-5193	86	41	aligning	align	VERB
ejpam-5193	86	42	them	they	PRON
ejpam-5193	86	43	with	with	ADP
ejpam-5193	86	44	the	the	DET
ejpam-5193	86	45	bell	bell	NOUN
ejpam-5193	86	46	-	-	PUNCT
ejpam-5193	86	47	based	base	VERB
ejpam-5193	86	48	apostol	apostol	NOUN
ejpam-5193	86	49	-	-	PUNCT
ejpam-5193	86	50	type	type	NOUN
ejpam-5193	86	51	frobeniuseuler	frobeniuseuler	NOUN
ejpam-5193	86	52	polynomials	polynomial	NOUN
ejpam-5193	86	53	as	as	SCONJ
ejpam-5193	86	54	defined	define	VERB
ejpam-5193	86	55	by	by	ADP
ejpam-5193	86	56	alam	alam	PROPN
ejpam-5193	86	57	et	et	PROPN
ejpam-5193	86	58	al	al	PROPN
ejpam-5193	86	59	.	.	PUNCT
ejpam-5193	87	1	[	[	X
ejpam-5193	87	2	4	4	X
ejpam-5193	87	3	]	]	PUNCT
ejpam-5193	87	4	and	and	CCONJ
ejpam-5193	87	5	the	the	DET
ejpam-5193	87	6	generalized	generalize	VERB
ejpam-5193	87	7	apostol	apostol	NOUN
ejpam-5193	87	8	-	-	PUNCT
ejpam-5193	87	9	frobeniustype	frobeniustype	NOUN
ejpam-5193	87	10	poly	poly	ADJ
ejpam-5193	87	11	-	-	PUNCT
ejpam-5193	87	12	genocchi	genocchi	NOUN
ejpam-5193	87	13	polynomials	polynomial	NOUN
ejpam-5193	87	14	by	by	ADP
ejpam-5193	87	15	khan	khan	PROPN
ejpam-5193	87	16	[	[	X
ejpam-5193	87	17	34	34	NUM
ejpam-5193	87	18	]	]	PUNCT
ejpam-5193	87	19	.	.	PUNCT
ejpam-5193	88	1	the	the	DET
ejpam-5193	88	2	following	follow	VERB
ejpam-5193	88	3	definition	definition	NOUN
ejpam-5193	88	4	formally	formally	ADV
ejpam-5193	88	5	presents	present	VERB
ejpam-5193	88	6	the	the	DET
ejpam-5193	88	7	higher	high	ADJ
ejpam-5193	88	8	-	-	PUNCT
ejpam-5193	88	9	order	order	NOUN
ejpam-5193	88	10	bell	bell	NOUN
ejpam-5193	88	11	-	-	PUNCT
ejpam-5193	88	12	based	base	VERB
ejpam-5193	88	13	apostol	apostol	NOUN
ejpam-5193	88	14	-	-	PUNCT
ejpam-5193	88	15	frobenius	frobenius	NOUN
ejpam-5193	88	16	-	-	PUNCT
ejpam-5193	88	17	type	type	NOUN
ejpam-5193	88	18	poly	poly	ADJ
ejpam-5193	88	19	-	-	PUNCT
ejpam-5193	88	20	genocchi	genocchi	NOUN
ejpam-5193	88	21	polynomials	polynomial	NOUN
ejpam-5193	88	22	.	.	PUNCT
ejpam-5193	89	1	definition	definition	NOUN
ejpam-5193	89	2	2.1	2.1	NUM
ejpam-5193	89	3	.	.	PUNCT
ejpam-5193	90	1	the	the	DET
ejpam-5193	90	2	bivariate	bivariate	ADJ
ejpam-5193	90	3	bell	bell	NOUN
ejpam-5193	90	4	-	-	PUNCT
ejpam-5193	90	5	based	base	VERB
ejpam-5193	90	6	apostol	apostol	NOUN
ejpam-5193	90	7	-	-	PUNCT
ejpam-5193	90	8	frobenius	frobenius	NOUN
ejpam-5193	90	9	-	-	PUNCT
ejpam-5193	90	10	type	type	NOUN
ejpam-5193	90	11	poly	poly	ADJ
ejpam-5193	90	12	-	-	PUNCT
ejpam-5193	90	13	genocchi	genocchi	NOUN
ejpam-5193	90	14	polynomials	polynomial	NOUN
ejpam-5193	90	15	of	of	ADP
ejpam-5193	90	16	higher	high	ADJ
ejpam-5193	90	17	order	order	NOUN
ejpam-5193	90	18	with	with	ADP
ejpam-5193	90	19	parameters	parameter	NOUN
ejpam-5193	90	20	a	a	PRON
ejpam-5193	90	21	and	and	CCONJ
ejpam-5193	90	22	b	b	NOUN
ejpam-5193	90	23	,	,	PUNCT
ejpam-5193	90	24	denoted	denote	VERB
ejpam-5193	90	25	by	by	ADP
ejpam-5193	90	26	bg	bg	PROPN
ejpam-5193	90	27	(	(	PUNCT
ejpam-5193	90	28	r	r	NOUN
ejpam-5193	90	29	)	)	PUNCT
ejpam-5193	90	30	n	n	NOUN
ejpam-5193	90	31	(	(	PUNCT
ejpam-5193	90	32	x	x	X
ejpam-5193	90	33	,	,	PUNCT
ejpam-5193	90	34	y;u	y;u	PROPN
ejpam-5193	90	35	,	,	PUNCT
ejpam-5193	90	36	λ	λ	PROPN
ejpam-5193	90	37	,	,	PUNCT
ejpam-5193	90	38	a	a	DET
ejpam-5193	90	39	,	,	PUNCT
ejpam-5193	90	40	b	b	NOUN
ejpam-5193	90	41	)	)	PUNCT
ejpam-5193	90	42	are	be	AUX
ejpam-5193	90	43	defined	define	VERB
ejpam-5193	90	44	by	by	ADP
ejpam-5193	90	45	∞∑	∞∑	NUM
ejpam-5193	90	46	n=0	n=0	PROPN
ejpam-5193	90	47	bg	bg	NOUN
ejpam-5193	90	48	(	(	PUNCT
ejpam-5193	90	49	r	r	NOUN
ejpam-5193	90	50	)	)	PUNCT
ejpam-5193	90	51	n	n	CCONJ
ejpam-5193	90	52	,	,	PUNCT
ejpam-5193	90	53	k(x	k(x	PROPN
ejpam-5193	90	54	,	,	PUNCT
ejpam-5193	90	55	y;u	y;u	PROPN
ejpam-5193	90	56	,	,	PUNCT
ejpam-5193	90	57	λ	λ	PROPN
ejpam-5193	90	58	,	,	PUNCT
ejpam-5193	90	59	a	a	DET
ejpam-5193	90	60	,	,	PUNCT
ejpam-5193	90	61	b	b	NOUN
ejpam-5193	90	62	)	)	PUNCT
ejpam-5193	90	63	tn	tn	NOUN
ejpam-5193	90	64	n	n	CCONJ
ejpam-5193	90	65	!	!	PUNCT
ejpam-5193	91	1	=	=	PUNCT
ejpam-5193	91	2	(	(	PUNCT
ejpam-5193	91	3	lik(1−	lik(1−	X
ejpam-5193	91	4	(	(	PUNCT
ejpam-5193	91	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	91	6	)	)	PUNCT
ejpam-5193	91	7	λbt	λbt	VERB
ejpam-5193	91	8	−	−	PROPN
ejpam-5193	91	9	ua−t	ua−t	ADJ
ejpam-5193	91	10	)	)	PUNCT
ejpam-5193	91	11	r	r	NOUN
ejpam-5193	91	12	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	91	13	)	)	PUNCT
ejpam-5193	91	14	.	.	PUNCT
ejpam-5193	92	1	(	(	PUNCT
ejpam-5193	92	2	2.1	2.1	NUM
ejpam-5193	92	3	)	)	PUNCT
ejpam-5193	92	4	when	when	SCONJ
ejpam-5193	92	5	x	x	X
ejpam-5193	92	6	=	=	SYM
ejpam-5193	92	7	0	0	NUM
ejpam-5193	92	8	,	,	PUNCT
ejpam-5193	92	9	the	the	DET
ejpam-5193	92	10	bell	bell	NOUN
ejpam-5193	92	11	-	-	PUNCT
ejpam-5193	92	12	based	base	VERB
ejpam-5193	92	13	apostol	apostol	NOUN
ejpam-5193	92	14	-	-	PUNCT
ejpam-5193	92	15	frobenius	frobenius	NOUN
ejpam-5193	92	16	-	-	PUNCT
ejpam-5193	92	17	type	type	NOUN
ejpam-5193	92	18	poly	poly	ADJ
ejpam-5193	92	19	-	-	PUNCT
ejpam-5193	92	20	genocchi	genocchi	NOUN
ejpam-5193	92	21	polynomials	polynomial	NOUN
ejpam-5193	92	22	of	of	ADP
ejpam-5193	92	23	higher	high	ADJ
ejpam-5193	92	24	order	order	NOUN
ejpam-5193	92	25	bg	bg	NOUN
ejpam-5193	92	26	(	(	PUNCT
ejpam-5193	92	27	r	r	NOUN
ejpam-5193	92	28	)	)	PUNCT
ejpam-5193	92	29	n	n	CCONJ
ejpam-5193	92	30	,	,	PUNCT
ejpam-5193	92	31	k(y;u	k(y;u	PROPN
ejpam-5193	92	32	,	,	PUNCT
ejpam-5193	92	33	λ	λ	NOUN
ejpam-5193	92	34	)	)	PUNCT
ejpam-5193	92	35	are	be	AUX
ejpam-5193	92	36	defined	define	VERB
ejpam-5193	92	37	by	by	ADP
ejpam-5193	92	38	∞∑	∞∑	NUM
ejpam-5193	92	39	n=0	n=0	PROPN
ejpam-5193	92	40	bg	bg	NOUN
ejpam-5193	92	41	(	(	PUNCT
ejpam-5193	92	42	r	r	NOUN
ejpam-5193	92	43	)	)	PUNCT
ejpam-5193	92	44	n	n	CCONJ
ejpam-5193	92	45	,	,	PUNCT
ejpam-5193	92	46	k(y;u	k(y;u	PROPN
ejpam-5193	92	47	,	,	PUNCT
ejpam-5193	92	48	λ	λ	PROPN
ejpam-5193	92	49	,	,	PUNCT
ejpam-5193	92	50	a	a	DET
ejpam-5193	92	51	,	,	PUNCT
ejpam-5193	92	52	b	b	NOUN
ejpam-5193	92	53	)	)	PUNCT
ejpam-5193	92	54	tn	tn	NOUN
ejpam-5193	92	55	n	n	CCONJ
ejpam-5193	92	56	!	!	PUNCT
ejpam-5193	93	1	=	=	PUNCT
ejpam-5193	93	2	(	(	PUNCT
ejpam-5193	93	3	lik(1−	lik(1−	X
ejpam-5193	93	4	(	(	PUNCT
ejpam-5193	93	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	93	6	)	)	PUNCT
ejpam-5193	93	7	λbt	λbt	VERB
ejpam-5193	93	8	−	−	PROPN
ejpam-5193	93	9	ua−t	ua−t	ADJ
ejpam-5193	93	10	)	)	PUNCT
ejpam-5193	93	11	r	r	NOUN
ejpam-5193	93	12	ey(e	ey(e	X
ejpam-5193	93	13	t−1	t−1	PROPN
ejpam-5193	93	14	)	)	PUNCT
ejpam-5193	93	15	(	(	PUNCT
ejpam-5193	93	16	2.2	2.2	NUM
ejpam-5193	93	17	)	)	PUNCT
ejpam-5193	93	18	remark	remark	NOUN
ejpam-5193	93	19	2.2	2.2	NUM
ejpam-5193	93	20	.	.	PUNCT
ejpam-5193	94	1	using	use	VERB
ejpam-5193	94	2	the	the	DET
ejpam-5193	94	3	fact	fact	NOUN
ejpam-5193	94	4	that	that	SCONJ
ejpam-5193	94	5	li1(z	li1(z	PROPN
ejpam-5193	94	6	)	)	PUNCT
ejpam-5193	94	7	=	=	PUNCT
ejpam-5193	95	1	−	−	PROPN
ejpam-5193	95	2	ln(1−	ln(1−	PROPN
ejpam-5193	95	3	z	z	PROPN
ejpam-5193	95	4	)	)	PUNCT
ejpam-5193	95	5	,	,	PUNCT
ejpam-5193	95	6	we	we	PRON
ejpam-5193	95	7	get	get	VERB
ejpam-5193	95	8	li1(1−	li1(1−	X
ejpam-5193	95	9	(	(	PUNCT
ejpam-5193	95	10	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	95	11	)	)	PUNCT
ejpam-5193	95	12	=	=	PUNCT
ejpam-5193	96	1	−	−	PROPN
ejpam-5193	96	2	ln(1−	ln(1−	PROPN
ejpam-5193	96	3	(	(	PUNCT
ejpam-5193	96	4	1−	1−	NUM
ejpam-5193	96	5	(	(	PUNCT
ejpam-5193	96	6	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	96	7	)	)	PUNCT
ejpam-5193	96	8	)	)	PUNCT
ejpam-5193	97	1	=	=	PUNCT
ejpam-5193	97	2	(	(	PUNCT
ejpam-5193	97	3	1−	1−	NUM
ejpam-5193	97	4	u)t	u)t	X
ejpam-5193	97	5	ln	ln	PROPN
ejpam-5193	97	6	ab	ab	PROPN
ejpam-5193	97	7	.	.	PUNCT
ejpam-5193	98	1	hence	hence	ADV
ejpam-5193	98	2	,	,	PUNCT
ejpam-5193	98	3	when	when	SCONJ
ejpam-5193	98	4	k	k	PROPN
ejpam-5193	98	5	=	=	SYM
ejpam-5193	98	6	1	1	NUM
ejpam-5193	98	7	,	,	PUNCT
ejpam-5193	98	8	the	the	DET
ejpam-5193	98	9	bell	bell	NOUN
ejpam-5193	98	10	-	-	PUNCT
ejpam-5193	98	11	based	base	VERB
ejpam-5193	98	12	apostol	apostol	NOUN
ejpam-5193	98	13	-	-	PUNCT
ejpam-5193	98	14	frobenius	frobenius	NOUN
ejpam-5193	98	15	-	-	PUNCT
ejpam-5193	98	16	type	type	NOUN
ejpam-5193	98	17	poly	poly	ADJ
ejpam-5193	98	18	-	-	PUNCT
ejpam-5193	98	19	genocchi	genocchi	NOUN
ejpam-5193	98	20	polynomials	polynomial	NOUN
ejpam-5193	98	21	of	of	ADP
ejpam-5193	98	22	higher	high	ADJ
ejpam-5193	98	23	order	order	NOUN
ejpam-5193	98	24	bg	bg	NOUN
ejpam-5193	98	25	(	(	PUNCT
ejpam-5193	98	26	r	r	NOUN
ejpam-5193	98	27	)	)	PUNCT
ejpam-5193	98	28	n	n	CCONJ
ejpam-5193	98	29	,	,	PUNCT
ejpam-5193	98	30	k(y;u	k(y;u	PROPN
ejpam-5193	98	31	,	,	PUNCT
ejpam-5193	98	32	λ	λ	NOUN
ejpam-5193	98	33	)	)	PUNCT
ejpam-5193	98	34	in	in	ADP
ejpam-5193	98	35	(	(	PUNCT
ejpam-5193	98	36	2.2	2.2	NUM
ejpam-5193	98	37	)	)	PUNCT
ejpam-5193	98	38	can	can	AUX
ejpam-5193	98	39	further	far	ADV
ejpam-5193	98	40	be	be	AUX
ejpam-5193	98	41	reduced	reduce	VERB
ejpam-5193	98	42	to	to	ADP
ejpam-5193	98	43	∞∑	∞∑	NUM
ejpam-5193	98	44	n=0	n=0	ADJ
ejpam-5193	98	45	bg	bg	NOUN
ejpam-5193	98	46	(	(	PUNCT
ejpam-5193	98	47	r	r	NOUN
ejpam-5193	98	48	)	)	PUNCT
ejpam-5193	98	49	n	n	NOUN
ejpam-5193	98	50	(	(	PUNCT
ejpam-5193	98	51	x	x	X
ejpam-5193	98	52	,	,	PUNCT
ejpam-5193	98	53	y;u	y;u	PROPN
ejpam-5193	98	54	,	,	PUNCT
ejpam-5193	98	55	λ	λ	PROPN
ejpam-5193	98	56	,	,	PUNCT
ejpam-5193	98	57	a	a	DET
ejpam-5193	98	58	,	,	PUNCT
ejpam-5193	98	59	b	b	NOUN
ejpam-5193	98	60	)	)	PUNCT
ejpam-5193	98	61	tn	tn	NOUN
ejpam-5193	98	62	n	n	NOUN
ejpam-5193	98	63	!	!	PUNCT
ejpam-5193	99	1	=	=	PUNCT
ejpam-5193	99	2	(	(	PUNCT
ejpam-5193	99	3	(	(	PUNCT
ejpam-5193	99	4	1−	1−	NUM
ejpam-5193	99	5	u)t	u)t	X
ejpam-5193	99	6	ln	ln	PROPN
ejpam-5193	99	7	ab	ab	PROPN
ejpam-5193	99	8	λbt	λbt	VERB
ejpam-5193	99	9	−	−	PROPN
ejpam-5193	99	10	ua−t	ua−t	ADJ
ejpam-5193	99	11	)	)	PUNCT
ejpam-5193	99	12	r	r	NOUN
ejpam-5193	99	13	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	99	14	)	)	PUNCT
ejpam-5193	99	15	,	,	PUNCT
ejpam-5193	99	16	(	(	PUNCT
ejpam-5193	99	17	2.3	2.3	NUM
ejpam-5193	99	18	)	)	PUNCT
ejpam-5193	99	19	the	the	DET
ejpam-5193	99	20	higher	high	ADJ
ejpam-5193	99	21	order	order	NOUN
ejpam-5193	99	22	bivariate	bivariate	ADJ
ejpam-5193	99	23	bell	bell	NOUN
ejpam-5193	99	24	-	-	PUNCT
ejpam-5193	99	25	based	base	VERB
ejpam-5193	99	26	apostol	apostol	NOUN
ejpam-5193	99	27	-	-	PUNCT
ejpam-5193	99	28	frobenius	frobenius	NOUN
ejpam-5193	99	29	-	-	PUNCT
ejpam-5193	99	30	type	type	NOUN
ejpam-5193	99	31	genocchi	genocchi	NOUN
ejpam-5193	99	32	numbers	number	NOUN
ejpam-5193	99	33	with	with	ADP
ejpam-5193	99	34	parameters	parameter	NOUN
ejpam-5193	99	35	a	a	PRON
ejpam-5193	99	36	and	and	CCONJ
ejpam-5193	99	37	b.	b.	PROPN
ejpam-5193	99	38	1476	1476	NUM
ejpam-5193	99	39	remark	remark	NOUN
ejpam-5193	99	40	2.3	2.3	NUM
ejpam-5193	99	41	.	.	PUNCT
ejpam-5193	100	1	when	when	SCONJ
ejpam-5193	100	2	y	y	PROPN
ejpam-5193	100	3	=	=	SYM
ejpam-5193	100	4	1	1	NUM
ejpam-5193	100	5	,	,	PUNCT
ejpam-5193	100	6	the	the	DET
ejpam-5193	100	7	bell	bell	NOUN
ejpam-5193	100	8	-	-	PUNCT
ejpam-5193	100	9	based	base	VERB
ejpam-5193	100	10	apostol	apostol	NOUN
ejpam-5193	100	11	-	-	PUNCT
ejpam-5193	100	12	frobenius	frobenius	NOUN
ejpam-5193	100	13	-	-	PUNCT
ejpam-5193	100	14	type	type	NOUN
ejpam-5193	100	15	poly	poly	ADJ
ejpam-5193	100	16	-	-	PUNCT
ejpam-5193	100	17	genocchi	genocchi	NOUN
ejpam-5193	100	18	polynomials	polynomial	NOUN
ejpam-5193	100	19	of	of	ADP
ejpam-5193	100	20	higher	high	ADJ
ejpam-5193	100	21	order	order	NOUN
ejpam-5193	100	22	bg	bg	NOUN
ejpam-5193	100	23	(	(	PUNCT
ejpam-5193	100	24	r	r	NOUN
ejpam-5193	100	25	)	)	PUNCT
ejpam-5193	100	26	n	n	CCONJ
ejpam-5193	100	27	,	,	PUNCT
ejpam-5193	100	28	k(y;u	k(y;u	PROPN
ejpam-5193	100	29	,	,	PUNCT
ejpam-5193	100	30	λ	λ	NOUN
ejpam-5193	100	31	)	)	PUNCT
ejpam-5193	100	32	in	in	ADP
ejpam-5193	100	33	(	(	PUNCT
ejpam-5193	100	34	2.2	2.2	NUM
ejpam-5193	100	35	)	)	PUNCT
ejpam-5193	100	36	can	can	AUX
ejpam-5193	100	37	further	far	ADV
ejpam-5193	100	38	be	be	AUX
ejpam-5193	100	39	reduced	reduce	VERB
ejpam-5193	100	40	to	to	ADP
ejpam-5193	100	41	∞∑	∞∑	NUM
ejpam-5193	100	42	n=0	n=0	ADJ
ejpam-5193	100	43	bg	bg	NOUN
ejpam-5193	100	44	(	(	PUNCT
ejpam-5193	100	45	r	r	NOUN
ejpam-5193	100	46	)	)	PUNCT
ejpam-5193	100	47	n	n	CCONJ
ejpam-5193	100	48	,	,	PUNCT
ejpam-5193	100	49	k(1;u	k(1;u	PROPN
ejpam-5193	100	50	,	,	PUNCT
ejpam-5193	100	51	λ	λ	PROPN
ejpam-5193	100	52	,	,	PUNCT
ejpam-5193	100	53	a	a	PRON
ejpam-5193	100	54	,	,	PUNCT
ejpam-5193	100	55	b	b	NOUN
ejpam-5193	100	56	)	)	PUNCT
ejpam-5193	100	57	tn	tn	NOUN
ejpam-5193	100	58	n	n	CCONJ
ejpam-5193	100	59	!	!	PUNCT
ejpam-5193	101	1	=	=	PUNCT
ejpam-5193	101	2	(	(	PUNCT
ejpam-5193	101	3	lik(1−	lik(1−	X
ejpam-5193	101	4	(	(	PUNCT
ejpam-5193	101	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	101	6	)	)	PUNCT
ejpam-5193	101	7	λbt	λbt	VERB
ejpam-5193	101	8	−	−	PROPN
ejpam-5193	101	9	ua−t	ua−t	ADJ
ejpam-5193	101	10	)	)	PUNCT
ejpam-5193	101	11	r	r	NOUN
ejpam-5193	101	12	ee	ee	PROPN
ejpam-5193	101	13	t−1	t−1	PROPN
ejpam-5193	101	14	,	,	PUNCT
ejpam-5193	101	15	the	the	DET
ejpam-5193	101	16	bell	bell	NOUN
ejpam-5193	101	17	-	-	PUNCT
ejpam-5193	101	18	based	base	VERB
ejpam-5193	101	19	apostol	apostol	NOUN
ejpam-5193	101	20	-	-	PUNCT
ejpam-5193	101	21	frobenius	frobenius	NOUN
ejpam-5193	101	22	-	-	PUNCT
ejpam-5193	101	23	type	type	NOUN
ejpam-5193	101	24	poly	poly	ADJ
ejpam-5193	101	25	-	-	PUNCT
ejpam-5193	101	26	genocchi	genocchi	NOUN
ejpam-5193	101	27	numbers	number	NOUN
ejpam-5193	101	28	of	of	ADP
ejpam-5193	101	29	higher	high	ADJ
ejpam-5193	101	30	order	order	NOUN
ejpam-5193	101	31	.	.	PUNCT
ejpam-5193	102	1	remark	remark	PROPN
ejpam-5193	102	2	2.4	2.4	NUM
ejpam-5193	102	3	.	.	PUNCT
ejpam-5193	103	1	the	the	DET
ejpam-5193	103	2	bell	bell	NOUN
ejpam-5193	103	3	-	-	PUNCT
ejpam-5193	103	4	based	base	VERB
ejpam-5193	103	5	apostol	apostol	NOUN
ejpam-5193	103	6	-	-	PUNCT
ejpam-5193	103	7	frobenius	frobenius	NOUN
ejpam-5193	103	8	-	-	PUNCT
ejpam-5193	103	9	type	type	NOUN
ejpam-5193	103	10	poly	poly	ADJ
ejpam-5193	103	11	-	-	PUNCT
ejpam-5193	103	12	genocchi	genocchi	NOUN
ejpam-5193	103	13	polynomials	polynomial	NOUN
ejpam-5193	103	14	of	of	ADP
ejpam-5193	103	15	higher	high	ADJ
ejpam-5193	103	16	order	order	NOUN
ejpam-5193	103	17	bg	bg	NOUN
ejpam-5193	103	18	(	(	PUNCT
ejpam-5193	103	19	r	r	NOUN
ejpam-5193	103	20	)	)	PUNCT
ejpam-5193	103	21	n	n	CCONJ
ejpam-5193	103	22	,	,	PUNCT
ejpam-5193	103	23	k(y;u	k(y;u	PROPN
ejpam-5193	103	24	,	,	PUNCT
ejpam-5193	103	25	λ	λ	NOUN
ejpam-5193	103	26	)	)	PUNCT
ejpam-5193	103	27	in	in	ADP
ejpam-5193	103	28	(	(	PUNCT
ejpam-5193	103	29	2.2	2.2	NUM
ejpam-5193	103	30	)	)	PUNCT
ejpam-5193	103	31	can	can	AUX
ejpam-5193	103	32	further	far	ADV
ejpam-5193	103	33	be	be	AUX
ejpam-5193	103	34	reduced	reduce	VERB
ejpam-5193	103	35	as	as	SCONJ
ejpam-5193	103	36	follows	follow	VERB
ejpam-5193	103	37	:	:	PUNCT
ejpam-5193	103	38	(	(	PUNCT
ejpam-5193	103	39	i	i	NOUN
ejpam-5193	103	40	)	)	PUNCT
ejpam-5193	103	41	when	when	SCONJ
ejpam-5193	103	42	k	k	PROPN
ejpam-5193	103	43	=	=	SYM
ejpam-5193	103	44	1	1	NUM
ejpam-5193	103	45	,	,	PUNCT
ejpam-5193	103	46	a	a	DET
ejpam-5193	103	47	=	=	SYM
ejpam-5193	103	48	1	1	NUM
ejpam-5193	103	49	,	,	PUNCT
ejpam-5193	103	50	b	b	NOUN
ejpam-5193	103	51	=	=	SYM
ejpam-5193	103	52	e	e	NOUN
ejpam-5193	103	53	,	,	PUNCT
ejpam-5193	103	54	∞∑	∞∑	ADJ
ejpam-5193	103	55	n=0	n=0	ADJ
ejpam-5193	103	56	bg	bg	NOUN
ejpam-5193	103	57	(	(	PUNCT
ejpam-5193	103	58	r	r	NOUN
ejpam-5193	103	59	)	)	PUNCT
ejpam-5193	103	60	n	n	NOUN
ejpam-5193	103	61	(	(	PUNCT
ejpam-5193	103	62	x	x	X
ejpam-5193	103	63	,	,	PUNCT
ejpam-5193	103	64	y;u	y;u	PROPN
ejpam-5193	103	65	,	,	PUNCT
ejpam-5193	103	66	λ	λ	PROPN
ejpam-5193	103	67	)	)	PUNCT
ejpam-5193	103	68	tn	tn	PROPN
ejpam-5193	103	69	n	n	PROPN
ejpam-5193	103	70	!	!	PUNCT
ejpam-5193	104	1	=	=	PUNCT
ejpam-5193	104	2	(	(	PUNCT
ejpam-5193	104	3	(	(	PUNCT
ejpam-5193	104	4	1−	1−	NUM
ejpam-5193	104	5	u)t	u)t	X
ejpam-5193	104	6	λet	λet	ADP
ejpam-5193	104	7	−	−	PROPN
ejpam-5193	104	8	u	u	NOUN
ejpam-5193	104	9	)	)	PUNCT
ejpam-5193	104	10	r	r	NOUN
ejpam-5193	104	11	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	104	12	)	)	PUNCT
ejpam-5193	104	13	,	,	PUNCT
ejpam-5193	104	14	(	(	PUNCT
ejpam-5193	104	15	2.4	2.4	NUM
ejpam-5193	104	16	)	)	PUNCT
ejpam-5193	104	17	the	the	DET
ejpam-5193	104	18	higher	high	ADJ
ejpam-5193	104	19	order	order	NOUN
ejpam-5193	104	20	bivariate	bivariate	ADJ
ejpam-5193	104	21	bell	bell	NOUN
ejpam-5193	104	22	-	-	PUNCT
ejpam-5193	104	23	based	base	VERB
ejpam-5193	104	24	apostol	apostol	NOUN
ejpam-5193	104	25	-	-	PUNCT
ejpam-5193	104	26	frobenius	frobenius	NOUN
ejpam-5193	104	27	-	-	PUNCT
ejpam-5193	104	28	type	type	NOUN
ejpam-5193	104	29	genocchi	genocchi	NOUN
ejpam-5193	104	30	polynomials	polynomial	NOUN
ejpam-5193	104	31	,	,	PUNCT
ejpam-5193	104	32	where	where	SCONJ
ejpam-5193	104	33	bgn(x	bgn(x	NOUN
ejpam-5193	104	34	,	,	PUNCT
ejpam-5193	104	35	y;u	y;u	PROPN
ejpam-5193	104	36	,	,	PUNCT
ejpam-5193	104	37	λ	λ	NOUN
ejpam-5193	104	38	)	)	PUNCT
ejpam-5193	104	39	=	=	SYM
ejpam-5193	104	40	bg	bg	PROPN
ejpam-5193	104	41	(	(	PUNCT
ejpam-5193	104	42	1	1	NUM
ejpam-5193	104	43	)	)	PUNCT
ejpam-5193	104	44	n	n	CCONJ
ejpam-5193	104	45	(	(	PUNCT
ejpam-5193	104	46	x	x	X
ejpam-5193	104	47	,	,	PUNCT
ejpam-5193	104	48	y;u	y;u	PROPN
ejpam-5193	104	49	,	,	PUNCT
ejpam-5193	104	50	λ	λ	PROPN
ejpam-5193	104	51	,	,	PUNCT
ejpam-5193	104	52	1	1	NUM
ejpam-5193	104	53	,	,	PUNCT
ejpam-5193	104	54	e	e	NOUN
ejpam-5193	104	55	)	)	PUNCT
ejpam-5193	104	56	.	.	PUNCT
ejpam-5193	105	1	(	(	PUNCT
ejpam-5193	105	2	ii	ii	NOUN
ejpam-5193	105	3	)	)	PUNCT
ejpam-5193	105	4	when	when	SCONJ
ejpam-5193	105	5	r	r	NOUN
ejpam-5193	105	6	=	=	SYM
ejpam-5193	105	7	1	1	NUM
ejpam-5193	105	8	,	,	PUNCT
ejpam-5193	105	9	(	(	PUNCT
ejpam-5193	105	10	2.4	2.4	NUM
ejpam-5193	105	11	)	)	PUNCT
ejpam-5193	105	12	gives	give	VERB
ejpam-5193	105	13	∞∑	∞∑	DET
ejpam-5193	105	14	n=0	n=0	NUM
ejpam-5193	105	15	bgn(x	bgn(x	NOUN
ejpam-5193	105	16	,	,	PUNCT
ejpam-5193	105	17	y;u	y;u	PROPN
ejpam-5193	105	18	,	,	PUNCT
ejpam-5193	105	19	λ	λ	PROPN
ejpam-5193	105	20	)	)	PUNCT
ejpam-5193	105	21	tn	tn	PROPN
ejpam-5193	105	22	n	n	PROPN
ejpam-5193	105	23	!	!	PUNCT
ejpam-5193	106	1	=	=	PUNCT
ejpam-5193	106	2	(	(	PUNCT
ejpam-5193	106	3	1−	1−	NUM
ejpam-5193	106	4	u)t	u)t	X
ejpam-5193	106	5	λet	λet	CCONJ
ejpam-5193	106	6	−	−	NUM
ejpam-5193	106	7	u	u	NOUN
ejpam-5193	106	8	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	106	9	)	)	PUNCT
ejpam-5193	106	10	,	,	PUNCT
ejpam-5193	106	11	(	(	PUNCT
ejpam-5193	106	12	2.5	2.5	NUM
ejpam-5193	106	13	)	)	PUNCT
ejpam-5193	106	14	the	the	DET
ejpam-5193	106	15	bivariate	bivariate	ADJ
ejpam-5193	106	16	bell	bell	NOUN
ejpam-5193	106	17	-	-	PUNCT
ejpam-5193	106	18	based	base	VERB
ejpam-5193	106	19	apostol	apostol	NOUN
ejpam-5193	106	20	-	-	PUNCT
ejpam-5193	106	21	frobenius	frobenius	NOUN
ejpam-5193	106	22	-	-	PUNCT
ejpam-5193	106	23	type	type	NOUN
ejpam-5193	106	24	genocchi	genocchi	NOUN
ejpam-5193	106	25	polynomials	polynomial	NOUN
ejpam-5193	106	26	,	,	PUNCT
ejpam-5193	106	27	where	where	SCONJ
ejpam-5193	106	28	bgn(x	bgn(x	NOUN
ejpam-5193	106	29	,	,	PUNCT
ejpam-5193	106	30	y;u	y;u	PROPN
ejpam-5193	106	31	,	,	PUNCT
ejpam-5193	106	32	λ	λ	NOUN
ejpam-5193	106	33	)	)	PUNCT
ejpam-5193	106	34	=	=	SYM
ejpam-5193	106	35	bg	bg	PROPN
ejpam-5193	106	36	(	(	PUNCT
ejpam-5193	106	37	1	1	NUM
ejpam-5193	106	38	)	)	PUNCT
ejpam-5193	106	39	n	n	CCONJ
ejpam-5193	106	40	(	(	PUNCT
ejpam-5193	106	41	x	x	X
ejpam-5193	106	42	,	,	PUNCT
ejpam-5193	106	43	y;u	y;u	PROPN
ejpam-5193	106	44	,	,	PUNCT
ejpam-5193	106	45	λ	λ	PROPN
ejpam-5193	106	46	,	,	PUNCT
ejpam-5193	106	47	1	1	NUM
ejpam-5193	106	48	,	,	PUNCT
ejpam-5193	106	49	e	e	NOUN
ejpam-5193	106	50	)	)	PUNCT
ejpam-5193	106	51	.	.	PUNCT
ejpam-5193	107	1	remark	remark	VERB
ejpam-5193	107	2	2.5	2.5	NUM
ejpam-5193	107	3	.	.	PUNCT
ejpam-5193	108	1	when	when	SCONJ
ejpam-5193	108	2	r	r	NOUN
ejpam-5193	108	3	=	=	SYM
ejpam-5193	108	4	0	0	NUM
ejpam-5193	108	5	,	,	PUNCT
ejpam-5193	108	6	the	the	DET
ejpam-5193	108	7	bivariate	bivariate	ADJ
ejpam-5193	108	8	bell	bell	NOUN
ejpam-5193	108	9	-	-	PUNCT
ejpam-5193	108	10	based	base	VERB
ejpam-5193	108	11	apostol	apostol	NOUN
ejpam-5193	108	12	-	-	PUNCT
ejpam-5193	108	13	frobenius	frobenius	NOUN
ejpam-5193	108	14	-	-	PUNCT
ejpam-5193	108	15	type	type	NOUN
ejpam-5193	108	16	poly	poly	ADJ
ejpam-5193	108	17	-	-	PUNCT
ejpam-5193	108	18	genocchi	genocchi	NOUN
ejpam-5193	108	19	polynomials	polynomial	NOUN
ejpam-5193	108	20	of	of	ADP
ejpam-5193	108	21	higher	high	ADJ
ejpam-5193	108	22	order	order	NOUN
ejpam-5193	108	23	bg	bg	NOUN
ejpam-5193	108	24	(	(	PUNCT
ejpam-5193	108	25	r	r	NOUN
ejpam-5193	108	26	)	)	PUNCT
ejpam-5193	108	27	n	n	CCONJ
ejpam-5193	108	28	,	,	PUNCT
ejpam-5193	108	29	k(y;u	k(y;u	PROPN
ejpam-5193	108	30	,	,	PUNCT
ejpam-5193	108	31	λ	λ	NOUN
ejpam-5193	108	32	)	)	PUNCT
ejpam-5193	108	33	in	in	ADP
ejpam-5193	108	34	(	(	PUNCT
ejpam-5193	108	35	2.1	2.1	NUM
ejpam-5193	108	36	)	)	PUNCT
ejpam-5193	108	37	can	can	AUX
ejpam-5193	108	38	be	be	AUX
ejpam-5193	108	39	reduced	reduce	VERB
ejpam-5193	108	40	to	to	ADP
ejpam-5193	108	41	∞∑	∞∑	NUM
ejpam-5193	108	42	n=0	n=0	ADJ
ejpam-5193	108	43	bg	bg	PROPN
ejpam-5193	108	44	(	(	PUNCT
ejpam-5193	108	45	0	0	NUM
ejpam-5193	108	46	)	)	PUNCT
ejpam-5193	108	47	n	n	NOUN
ejpam-5193	108	48	(	(	PUNCT
ejpam-5193	108	49	x	x	X
ejpam-5193	108	50	,	,	PUNCT
ejpam-5193	108	51	y;u	y;u	PROPN
ejpam-5193	108	52	,	,	PUNCT
ejpam-5193	108	53	λ	λ	PROPN
ejpam-5193	108	54	)	)	PUNCT
ejpam-5193	108	55	tn	tn	PROPN
ejpam-5193	108	56	n	n	PROPN
ejpam-5193	108	57	!	!	PUNCT
ejpam-5193	109	1	=	=	SYM
ejpam-5193	109	2	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	109	3	)	)	PUNCT
ejpam-5193	109	4	,	,	PUNCT
ejpam-5193	109	5	bn(x	bn(x	NUM
ejpam-5193	109	6	,	,	PUNCT
ejpam-5193	109	7	y	y	PROPN
ejpam-5193	109	8	)	)	PUNCT
ejpam-5193	110	1	=	=	SYM
ejpam-5193	110	2	bg	bg	PROPN
ejpam-5193	110	3	(	(	PUNCT
ejpam-5193	110	4	0	0	NUM
ejpam-5193	110	5	)	)	PUNCT
ejpam-5193	110	6	n	n	NOUN
ejpam-5193	110	7	(	(	PUNCT
ejpam-5193	110	8	x	x	X
ejpam-5193	110	9	,	,	PUNCT
ejpam-5193	110	10	y;u	y;u	PROPN
ejpam-5193	110	11	,	,	PUNCT
ejpam-5193	110	12	λ	λ	PROPN
ejpam-5193	110	13	)	)	PUNCT
ejpam-5193	110	14	(	(	PUNCT
ejpam-5193	110	15	2.6	2.6	NUM
ejpam-5193	110	16	)	)	PUNCT
ejpam-5193	110	17	the	the	DET
ejpam-5193	110	18	bivariate	bivariate	ADJ
ejpam-5193	110	19	bell	bell	NOUN
ejpam-5193	110	20	polynomial	polynomial	NOUN
ejpam-5193	110	21	.	.	PUNCT
ejpam-5193	111	1	the	the	DET
ejpam-5193	111	2	following	follow	VERB
ejpam-5193	111	3	theorem	theorem	NOUN
ejpam-5193	111	4	contains	contain	VERB
ejpam-5193	111	5	the	the	DET
ejpam-5193	111	6	first	first	ADJ
ejpam-5193	111	7	identity	identity	NOUN
ejpam-5193	111	8	for	for	ADP
ejpam-5193	111	9	the	the	DET
ejpam-5193	111	10	bivariate	bivariate	ADJ
ejpam-5193	111	11	bell	bell	NOUN
ejpam-5193	111	12	-	-	PUNCT
ejpam-5193	111	13	based	base	VERB
ejpam-5193	111	14	apostolfrobenius	apostolfrobenius	NOUN
ejpam-5193	111	15	-	-	PUNCT
ejpam-5193	111	16	type	type	NOUN
ejpam-5193	111	17	poly	poly	ADJ
ejpam-5193	111	18	-	-	PUNCT
ejpam-5193	111	19	genocchi	genocchi	NOUN
ejpam-5193	111	20	polynomials	polynomial	NOUN
ejpam-5193	111	21	of	of	ADP
ejpam-5193	111	22	higher	high	ADJ
ejpam-5193	111	23	order	order	NOUN
ejpam-5193	111	24	expressed	express	VERB
ejpam-5193	111	25	in	in	ADP
ejpam-5193	111	26	terms	term	NOUN
ejpam-5193	111	27	bell	bell	NOUN
ejpam-5193	111	28	-	-	PUNCT
ejpam-5193	111	29	based	base	VERB
ejpam-5193	111	30	apostol	apostol	NOUN
ejpam-5193	111	31	-	-	PUNCT
ejpam-5193	111	32	frobenius	frobenius	NOUN
ejpam-5193	111	33	-	-	PUNCT
ejpam-5193	111	34	type	type	NOUN
ejpam-5193	111	35	poly	poly	ADJ
ejpam-5193	111	36	-	-	PUNCT
ejpam-5193	111	37	genocchi	genocchi	NOUN
ejpam-5193	111	38	polynomials	polynomial	NOUN
ejpam-5193	111	39	of	of	ADP
ejpam-5193	111	40	higher	high	ADJ
ejpam-5193	111	41	order	order	NOUN
ejpam-5193	111	42	and	and	CCONJ
ejpam-5193	111	43	the	the	DET
ejpam-5193	111	44	bell	bell	NOUN
ejpam-5193	111	45	polyomials	polyomial	NOUN
ejpam-5193	111	46	.	.	PUNCT
ejpam-5193	112	1	theorem	theorem	VERB
ejpam-5193	112	2	2.6	2.6	NUM
ejpam-5193	112	3	.	.	PUNCT
ejpam-5193	113	1	the	the	DET
ejpam-5193	113	2	bivariate	bivariate	ADJ
ejpam-5193	113	3	bell	bell	NOUN
ejpam-5193	113	4	-	-	PUNCT
ejpam-5193	113	5	based	base	VERB
ejpam-5193	113	6	apostol	apostol	NOUN
ejpam-5193	113	7	-	-	PUNCT
ejpam-5193	113	8	frobenius	frobenius	NOUN
ejpam-5193	113	9	-	-	PUNCT
ejpam-5193	113	10	type	type	NOUN
ejpam-5193	113	11	poly	poly	ADJ
ejpam-5193	113	12	-	-	PUNCT
ejpam-5193	113	13	genocchi	genocchi	NOUN
ejpam-5193	113	14	polynomials	polynomial	NOUN
ejpam-5193	113	15	of	of	ADP
ejpam-5193	113	16	higher	high	ADJ
ejpam-5193	113	17	order	order	NOUN
ejpam-5193	113	18	with	with	ADP
ejpam-5193	113	19	parameters	parameter	NOUN
ejpam-5193	113	20	a	a	DET
ejpam-5193	113	21	and	and	CCONJ
ejpam-5193	113	22	b	b	NOUN
ejpam-5193	113	23	,	,	PUNCT
ejpam-5193	113	24	bg	bg	PROPN
ejpam-5193	113	25	(	(	PUNCT
ejpam-5193	113	26	r	r	NOUN
ejpam-5193	113	27	)	)	PUNCT
ejpam-5193	113	28	n	n	CCONJ
ejpam-5193	113	29	,	,	PUNCT
ejpam-5193	113	30	k(x	k(x	PROPN
ejpam-5193	113	31	,	,	PUNCT
ejpam-5193	113	32	y;u	y;u	PROPN
ejpam-5193	113	33	,	,	PUNCT
ejpam-5193	113	34	λ	λ	PROPN
ejpam-5193	113	35	,	,	PUNCT
ejpam-5193	113	36	a	a	DET
ejpam-5193	113	37	,	,	PUNCT
ejpam-5193	113	38	b	b	NOUN
ejpam-5193	113	39	)	)	PUNCT
ejpam-5193	113	40	,	,	PUNCT
ejpam-5193	113	41	are	be	AUX
ejpam-5193	113	42	equal	equal	ADJ
ejpam-5193	113	43	to	to	ADP
ejpam-5193	113	44	bg	bg	PROPN
ejpam-5193	113	45	(	(	PUNCT
ejpam-5193	113	46	r	r	NOUN
ejpam-5193	113	47	)	)	PUNCT
ejpam-5193	113	48	n	n	CCONJ
ejpam-5193	113	49	,	,	PUNCT
ejpam-5193	113	50	k(x	k(x	PROPN
ejpam-5193	113	51	,	,	PUNCT
ejpam-5193	113	52	y;u	y;u	PROPN
ejpam-5193	113	53	,	,	PUNCT
ejpam-5193	113	54	λ	λ	PROPN
ejpam-5193	113	55	,	,	PUNCT
ejpam-5193	113	56	a	a	DET
ejpam-5193	113	57	,	,	PUNCT
ejpam-5193	113	58	b	b	NOUN
ejpam-5193	113	59	)	)	PUNCT
ejpam-5193	113	60	=	=	SYM
ejpam-5193	114	1	n∑	n∑	NOUN
ejpam-5193	114	2	k=0	k=0	PROPN
ejpam-5193	114	3	(	(	PUNCT
ejpam-5193	114	4	n	n	X
ejpam-5193	114	5	k	k	NOUN
ejpam-5193	114	6	)	)	PUNCT
ejpam-5193	114	7	g	g	NOUN
ejpam-5193	114	8	(	(	PUNCT
ejpam-5193	114	9	r	r	NOUN
ejpam-5193	114	10	)	)	PUNCT
ejpam-5193	114	11	k	k	NOUN
ejpam-5193	114	12	(	(	PUNCT
ejpam-5193	114	13	x;u	x;u	PROPN
ejpam-5193	114	14	,	,	PUNCT
ejpam-5193	114	15	λ	λ	PROPN
ejpam-5193	114	16	,	,	PUNCT
ejpam-5193	114	17	a	a	PRON
ejpam-5193	114	18	,	,	PUNCT
ejpam-5193	114	19	b)bn−k(y	b)bn−k(y	PROPN
ejpam-5193	114	20	)	)	PUNCT
ejpam-5193	114	21	.	.	PUNCT
ejpam-5193	115	1	(	(	PUNCT
ejpam-5193	115	2	2.7	2.7	NUM
ejpam-5193	115	3	)	)	PUNCT
ejpam-5193	115	4	1477	1477	NUM
ejpam-5193	115	5	proof	proof	NOUN
ejpam-5193	115	6	.	.	PUNCT
ejpam-5193	116	1	using	use	VERB
ejpam-5193	116	2	definition	definition	NOUN
ejpam-5193	116	3	2.1	2.1	NUM
ejpam-5193	116	4	,	,	PUNCT
ejpam-5193	116	5	we	we	PRON
ejpam-5193	116	6	have	have	VERB
ejpam-5193	116	7	∞∑	∞∑	NUM
ejpam-5193	116	8	n=0	n=0	ADJ
ejpam-5193	116	9	bg	bg	NOUN
ejpam-5193	116	10	(	(	PUNCT
ejpam-5193	116	11	r	r	NOUN
ejpam-5193	116	12	)	)	PUNCT
ejpam-5193	116	13	n	n	CCONJ
ejpam-5193	116	14	,	,	PUNCT
ejpam-5193	116	15	k(x	k(x	PROPN
ejpam-5193	116	16	,	,	PUNCT
ejpam-5193	116	17	y;u	y;u	PROPN
ejpam-5193	116	18	,	,	PUNCT
ejpam-5193	116	19	λ	λ	PROPN
ejpam-5193	116	20	,	,	PUNCT
ejpam-5193	116	21	a	a	DET
ejpam-5193	116	22	,	,	PUNCT
ejpam-5193	116	23	b	b	NOUN
ejpam-5193	116	24	)	)	PUNCT
ejpam-5193	116	25	tn	tn	NOUN
ejpam-5193	116	26	n	n	CCONJ
ejpam-5193	116	27	!	!	PUNCT
ejpam-5193	117	1	=	=	PUNCT
ejpam-5193	117	2	(	(	PUNCT
ejpam-5193	117	3	lik(1−	lik(1−	X
ejpam-5193	117	4	(	(	PUNCT
ejpam-5193	117	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	117	6	)	)	PUNCT
ejpam-5193	117	7	λbt	λbt	VERB
ejpam-5193	117	8	−	−	PROPN
ejpam-5193	117	9	ua−t	ua−t	ADJ
ejpam-5193	117	10	)	)	PUNCT
ejpam-5193	117	11	r	r	NOUN
ejpam-5193	117	12	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	117	13	)	)	PUNCT
ejpam-5193	117	14	=	=	PRON
ejpam-5193	118	1	{	{	PUNCT
ejpam-5193	118	2	(	(	PUNCT
ejpam-5193	118	3	lik(1−	lik(1−	PROPN
ejpam-5193	118	4	(	(	PUNCT
ejpam-5193	118	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	118	6	)	)	PUNCT
ejpam-5193	118	7	λbt	λbt	VERB
ejpam-5193	118	8	−	−	PROPN
ejpam-5193	118	9	ua−t	ua−t	ADJ
ejpam-5193	118	10	)	)	PUNCT
ejpam-5193	118	11	r	r	NOUN
ejpam-5193	118	12	ext	ext	NOUN
ejpam-5193	118	13	}	}	PUNCT
ejpam-5193	118	14	ey(e	ey(e	X
ejpam-5193	118	15	t−1	t−1	PROPN
ejpam-5193	118	16	)	)	PUNCT
ejpam-5193	118	17	=	=	NOUN
ejpam-5193	119	1	(	(	PUNCT
ejpam-5193	119	2	∞∑	∞∑	NUM
ejpam-5193	119	3	n=0	n=0	NUM
ejpam-5193	119	4	g	g	NOUN
ejpam-5193	119	5	(	(	PUNCT
ejpam-5193	119	6	r	r	NOUN
ejpam-5193	119	7	)	)	PUNCT
ejpam-5193	119	8	n	n	CCONJ
ejpam-5193	119	9	,	,	PUNCT
ejpam-5193	119	10	k(x;u	k(x;u	PROPN
ejpam-5193	119	11	,	,	PUNCT
ejpam-5193	119	12	λ	λ	PROPN
ejpam-5193	119	13	,	,	PUNCT
ejpam-5193	119	14	a	a	DET
ejpam-5193	119	15	,	,	PUNCT
ejpam-5193	119	16	b	b	NOUN
ejpam-5193	119	17	)	)	PUNCT
ejpam-5193	119	18	tn	tn	PROPN
ejpam-5193	119	19	n	n	CCONJ
ejpam-5193	119	20	!	!	PUNCT
ejpam-5193	119	21	)	)	PUNCT
ejpam-5193	120	1	(	(	PUNCT
ejpam-5193	120	2	∞∑	∞∑	NUM
ejpam-5193	120	3	n=0	n=0	NUM
ejpam-5193	120	4	bn(y	bn(y	NUM
ejpam-5193	120	5	)	)	PUNCT
ejpam-5193	120	6	tn	tn	PROPN
ejpam-5193	120	7	n	n	PROPN
ejpam-5193	120	8	!	!	PUNCT
ejpam-5193	120	9	)	)	PUNCT
ejpam-5193	121	1	=	=	PUNCT
ejpam-5193	122	1	∞∑	∞∑	NUM
ejpam-5193	122	2	n=0	n=0	NUM
ejpam-5193	122	3	{	{	PUNCT
ejpam-5193	122	4	n∑	n∑	NOUN
ejpam-5193	122	5	k=0	k=0	PROPN
ejpam-5193	122	6	(	(	PUNCT
ejpam-5193	122	7	n	n	X
ejpam-5193	122	8	k	k	NOUN
ejpam-5193	122	9	)	)	PUNCT
ejpam-5193	122	10	g	g	NOUN
ejpam-5193	122	11	(	(	PUNCT
ejpam-5193	122	12	r	r	NOUN
ejpam-5193	122	13	)	)	PUNCT
ejpam-5193	122	14	k	k	NOUN
ejpam-5193	122	15	(	(	PUNCT
ejpam-5193	122	16	x;u	x;u	PROPN
ejpam-5193	122	17	,	,	PUNCT
ejpam-5193	122	18	λ	λ	PROPN
ejpam-5193	122	19	,	,	PUNCT
ejpam-5193	122	20	a	a	PRON
ejpam-5193	122	21	,	,	PUNCT
ejpam-5193	122	22	b)bn−k(y	b)bn−k(y	PROPN
ejpam-5193	122	23	)	)	PUNCT
ejpam-5193	122	24	}	}	PUNCT
ejpam-5193	122	25	tn	tn	PROPN
ejpam-5193	122	26	n	n	X
ejpam-5193	122	27	!	!	PUNCT
ejpam-5193	122	28	.	.	PUNCT
ejpam-5193	123	1	comparing	compare	VERB
ejpam-5193	123	2	the	the	DET
ejpam-5193	123	3	coefficients	coefficient	NOUN
ejpam-5193	123	4	of	of	ADP
ejpam-5193	123	5	tn	tn	NOUN
ejpam-5193	123	6	n	n	X
ejpam-5193	123	7	!	!	PUNCT
ejpam-5193	124	1	yields	yield	VERB
ejpam-5193	124	2	the	the	DET
ejpam-5193	124	3	desired	desire	VERB
ejpam-5193	124	4	identity	identity	NOUN
ejpam-5193	124	5	in	in	ADP
ejpam-5193	124	6	(	(	PUNCT
ejpam-5193	124	7	2.7	2.7	NUM
ejpam-5193	124	8	)	)	PUNCT
ejpam-5193	124	9	.	.	PUNCT
ejpam-5193	125	1	the	the	DET
ejpam-5193	125	2	next	next	ADJ
ejpam-5193	125	3	theorem	theorem	NOUN
ejpam-5193	125	4	expresses	express	VERB
ejpam-5193	125	5	the	the	DET
ejpam-5193	125	6	bivariate	bivariate	ADJ
ejpam-5193	125	7	bell	bell	NOUN
ejpam-5193	125	8	-	-	PUNCT
ejpam-5193	125	9	based	base	VERB
ejpam-5193	125	10	apostol	apostol	NOUN
ejpam-5193	125	11	-	-	PUNCT
ejpam-5193	125	12	frobenius	frobenius	NOUN
ejpam-5193	125	13	-	-	PUNCT
ejpam-5193	125	14	type	type	NOUN
ejpam-5193	125	15	polygenocchi	polygenocchi	ADJ
ejpam-5193	125	16	polynomials	polynomial	NOUN
ejpam-5193	125	17	of	of	ADP
ejpam-5193	125	18	higher	high	ADJ
ejpam-5193	125	19	order	order	NOUN
ejpam-5193	125	20	as	as	ADP
ejpam-5193	125	21	polynomial	polynomial	ADJ
ejpam-5193	125	22	in	in	ADP
ejpam-5193	125	23	x	x	PUNCT
ejpam-5193	125	24	with	with	ADP
ejpam-5193	125	25	bell	bell	NOUN
ejpam-5193	125	26	-	-	PUNCT
ejpam-5193	125	27	based	base	VERB
ejpam-5193	125	28	apostol	apostol	NOUN
ejpam-5193	125	29	-	-	PUNCT
ejpam-5193	125	30	frobeniustype	frobeniustype	NOUN
ejpam-5193	125	31	poly	poly	ADJ
ejpam-5193	125	32	-	-	PUNCT
ejpam-5193	125	33	genocchi	genocchi	NOUN
ejpam-5193	125	34	polynomials	polynomial	NOUN
ejpam-5193	125	35	of	of	ADP
ejpam-5193	125	36	higher	high	ADJ
ejpam-5193	125	37	order	order	NOUN
ejpam-5193	125	38	as	as	ADP
ejpam-5193	125	39	the	the	DET
ejpam-5193	125	40	coefficients	coefficient	NOUN
ejpam-5193	125	41	.	.	PUNCT
ejpam-5193	126	1	theorem	theorem	VERB
ejpam-5193	126	2	2.7	2.7	NUM
ejpam-5193	126	3	.	.	PUNCT
ejpam-5193	127	1	the	the	DET
ejpam-5193	127	2	bivariate	bivariate	ADJ
ejpam-5193	127	3	bell	bell	NOUN
ejpam-5193	127	4	-	-	PUNCT
ejpam-5193	127	5	based	base	VERB
ejpam-5193	127	6	apostol	apostol	NOUN
ejpam-5193	127	7	-	-	PUNCT
ejpam-5193	127	8	frobenius	frobenius	NOUN
ejpam-5193	127	9	-	-	PUNCT
ejpam-5193	127	10	type	type	NOUN
ejpam-5193	127	11	poly	poly	ADJ
ejpam-5193	127	12	-	-	PUNCT
ejpam-5193	127	13	genocchi	genocchi	NOUN
ejpam-5193	127	14	polynomials	polynomial	NOUN
ejpam-5193	127	15	of	of	ADP
ejpam-5193	127	16	higher	high	ADJ
ejpam-5193	127	17	order	order	NOUN
ejpam-5193	127	18	bg	bg	NOUN
ejpam-5193	127	19	(	(	PUNCT
ejpam-5193	127	20	r	r	NOUN
ejpam-5193	127	21	)	)	PUNCT
ejpam-5193	127	22	n	n	CCONJ
ejpam-5193	127	23	,	,	PUNCT
ejpam-5193	127	24	k(x	k(x	PROPN
ejpam-5193	127	25	,	,	PUNCT
ejpam-5193	127	26	y;u	y;u	PROPN
ejpam-5193	127	27	,	,	PUNCT
ejpam-5193	127	28	λ	λ	PROPN
ejpam-5193	127	29	,	,	PUNCT
ejpam-5193	127	30	a	a	DET
ejpam-5193	127	31	,	,	PUNCT
ejpam-5193	127	32	b	b	NOUN
ejpam-5193	127	33	)	)	PUNCT
ejpam-5193	127	34	are	be	AUX
ejpam-5193	127	35	equal	equal	ADJ
ejpam-5193	127	36	to	to	ADP
ejpam-5193	127	37	bg	bg	PROPN
ejpam-5193	127	38	(	(	PUNCT
ejpam-5193	127	39	r	r	NOUN
ejpam-5193	127	40	)	)	PUNCT
ejpam-5193	127	41	n	n	CCONJ
ejpam-5193	127	42	,	,	PUNCT
ejpam-5193	127	43	k(x	k(x	PROPN
ejpam-5193	127	44	,	,	PUNCT
ejpam-5193	127	45	y;u	y;u	PROPN
ejpam-5193	127	46	,	,	PUNCT
ejpam-5193	127	47	λ	λ	PROPN
ejpam-5193	127	48	,	,	PUNCT
ejpam-5193	127	49	a	a	DET
ejpam-5193	127	50	,	,	PUNCT
ejpam-5193	127	51	b	b	NOUN
ejpam-5193	127	52	)	)	PUNCT
ejpam-5193	127	53	=	=	SYM
ejpam-5193	127	54	n∑	n∑	NOUN
ejpam-5193	127	55	j=0	j=0	PROPN
ejpam-5193	127	56	(	(	PUNCT
ejpam-5193	127	57	n	n	X
ejpam-5193	127	58	k	k	PROPN
ejpam-5193	127	59	)	)	PUNCT
ejpam-5193	127	60	bg	bg	PROPN
ejpam-5193	127	61	(	(	PUNCT
ejpam-5193	127	62	r	r	NOUN
ejpam-5193	127	63	)	)	PUNCT
ejpam-5193	127	64	n−j	n−j	ADV
ejpam-5193	127	65	,	,	PUNCT
ejpam-5193	127	66	k(y;u	k(y;u	PROPN
ejpam-5193	127	67	,	,	PUNCT
ejpam-5193	127	68	λ	λ	PROPN
ejpam-5193	127	69	,	,	PUNCT
ejpam-5193	127	70	a	a	PRON
ejpam-5193	127	71	,	,	PUNCT
ejpam-5193	127	72	b)x	b)x	X
ejpam-5193	127	73	j	j	PROPN
ejpam-5193	127	74	.	.	PUNCT
ejpam-5193	128	1	(	(	PUNCT
ejpam-5193	128	2	2.8	2.8	NUM
ejpam-5193	128	3	)	)	PUNCT
ejpam-5193	128	4	proof	proof	NOUN
ejpam-5193	128	5	.	.	PUNCT
ejpam-5193	129	1	using	use	VERB
ejpam-5193	129	2	definition	definition	NOUN
ejpam-5193	129	3	2.1	2.1	NUM
ejpam-5193	129	4	,	,	PUNCT
ejpam-5193	129	5	we	we	PRON
ejpam-5193	129	6	have	have	VERB
ejpam-5193	129	7	∞∑	∞∑	NUM
ejpam-5193	129	8	n=0	n=0	ADJ
ejpam-5193	129	9	bg	bg	NOUN
ejpam-5193	129	10	(	(	PUNCT
ejpam-5193	129	11	r	r	NOUN
ejpam-5193	129	12	)	)	PUNCT
ejpam-5193	129	13	n	n	CCONJ
ejpam-5193	129	14	,	,	PUNCT
ejpam-5193	129	15	k(x	k(x	PROPN
ejpam-5193	129	16	,	,	PUNCT
ejpam-5193	129	17	y;u	y;u	PROPN
ejpam-5193	129	18	,	,	PUNCT
ejpam-5193	129	19	λ	λ	PROPN
ejpam-5193	129	20	,	,	PUNCT
ejpam-5193	129	21	a	a	DET
ejpam-5193	129	22	,	,	PUNCT
ejpam-5193	129	23	b	b	NOUN
ejpam-5193	129	24	)	)	PUNCT
ejpam-5193	129	25	tn	tn	NOUN
ejpam-5193	129	26	n	n	CCONJ
ejpam-5193	129	27	!	!	PUNCT
ejpam-5193	130	1	=	=	PUNCT
ejpam-5193	130	2	(	(	PUNCT
ejpam-5193	130	3	lik(1−	lik(1−	X
ejpam-5193	130	4	(	(	PUNCT
ejpam-5193	130	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	130	6	)	)	PUNCT
ejpam-5193	130	7	λbt	λbt	VERB
ejpam-5193	130	8	−	−	PROPN
ejpam-5193	130	9	ua−t	ua−t	ADJ
ejpam-5193	130	10	)	)	PUNCT
ejpam-5193	130	11	r	r	NOUN
ejpam-5193	130	12	ey(e	ey(e	X
ejpam-5193	130	13	t−1)ext	t−1)ext	NOUN
ejpam-5193	131	1	=	=	PUNCT
ejpam-5193	131	2	(	(	PUNCT
ejpam-5193	131	3	∞∑	∞∑	PROPN
ejpam-5193	131	4	n=0	n=0	PROPN
ejpam-5193	131	5	bg	bg	NOUN
ejpam-5193	131	6	(	(	PUNCT
ejpam-5193	131	7	r	r	NOUN
ejpam-5193	131	8	)	)	PUNCT
ejpam-5193	131	9	n	n	CCONJ
ejpam-5193	131	10	,	,	PUNCT
ejpam-5193	131	11	k(y;u	k(y;u	PROPN
ejpam-5193	131	12	,	,	PUNCT
ejpam-5193	131	13	λ	λ	PROPN
ejpam-5193	131	14	,	,	PUNCT
ejpam-5193	131	15	a	a	DET
ejpam-5193	131	16	,	,	PUNCT
ejpam-5193	131	17	b	b	NOUN
ejpam-5193	131	18	)	)	PUNCT
ejpam-5193	131	19	tn	tn	PROPN
ejpam-5193	131	20	n	n	CCONJ
ejpam-5193	131	21	!	!	PUNCT
ejpam-5193	131	22	)	)	PUNCT
ejpam-5193	132	1	(	(	PUNCT
ejpam-5193	132	2	∞∑	∞∑	NUM
ejpam-5193	132	3	n=0	n=0	NUM
ejpam-5193	132	4	(	(	PUNCT
ejpam-5193	132	5	xt)n	xt)n	PROPN
ejpam-5193	132	6	n	n	CCONJ
ejpam-5193	132	7	!	!	PUNCT
ejpam-5193	132	8	)	)	PUNCT
ejpam-5193	133	1	=	=	PUNCT
ejpam-5193	134	1	∞∑	∞∑	NUM
ejpam-5193	134	2	n=0	n=0	NUM
ejpam-5193	134	3			PUNCT
ejpam-5193	134	4	n∑	n∑	NOUN
ejpam-5193	134	5	j=0	j=0	PROPN
ejpam-5193	134	6	(	(	PUNCT
ejpam-5193	134	7	n	n	X
ejpam-5193	134	8	j	j	PROPN
ejpam-5193	134	9	)	)	PUNCT
ejpam-5193	134	10	bg	bg	PROPN
ejpam-5193	134	11	(	(	PUNCT
ejpam-5193	134	12	r	r	NOUN
ejpam-5193	134	13	)	)	PUNCT
ejpam-5193	134	14	j	j	PROPN
ejpam-5193	134	15	,	,	PUNCT
ejpam-5193	134	16	k(y;u	k(y;u	PROPN
ejpam-5193	134	17	,	,	PUNCT
ejpam-5193	134	18	λ	λ	PROPN
ejpam-5193	134	19	,	,	PUNCT
ejpam-5193	134	20	a	a	PRON
ejpam-5193	134	21	,	,	PUNCT
ejpam-5193	134	22	b)x	b)x	X
ejpam-5193	134	23	n−j	n−j	X
ejpam-5193	134	24			PROPN
ejpam-5193	134	25	tn	tn	PROPN
ejpam-5193	134	26	n	n	X
ejpam-5193	134	27	!	!	PUNCT
ejpam-5193	134	28	comparing	compare	VERB
ejpam-5193	134	29	the	the	DET
ejpam-5193	134	30	coefficients	coefficient	NOUN
ejpam-5193	134	31	of	of	ADP
ejpam-5193	134	32	tn	tn	NOUN
ejpam-5193	134	33	n	n	ADP
ejpam-5193	134	34	!	!	PUNCT
ejpam-5193	135	1	yields	yield	NOUN
ejpam-5193	135	2	bg	bg	PROPN
ejpam-5193	135	3	(	(	PUNCT
ejpam-5193	135	4	r	r	NOUN
ejpam-5193	135	5	)	)	PUNCT
ejpam-5193	135	6	n	n	CCONJ
ejpam-5193	135	7	,	,	PUNCT
ejpam-5193	135	8	k(x	k(x	PROPN
ejpam-5193	135	9	,	,	PUNCT
ejpam-5193	135	10	y;u	y;u	PROPN
ejpam-5193	135	11	,	,	PUNCT
ejpam-5193	135	12	λ	λ	PROPN
ejpam-5193	135	13	,	,	PUNCT
ejpam-5193	135	14	a	a	DET
ejpam-5193	135	15	,	,	PUNCT
ejpam-5193	135	16	b	b	NOUN
ejpam-5193	135	17	)	)	PUNCT
ejpam-5193	136	1	=	=	SYM
ejpam-5193	136	2	n∑	n∑	NOUN
ejpam-5193	136	3	j=0	j=0	PROPN
ejpam-5193	136	4	(	(	PUNCT
ejpam-5193	136	5	n	n	X
ejpam-5193	136	6	j	j	PROPN
ejpam-5193	136	7	)	)	PUNCT
ejpam-5193	136	8	bg	bg	PROPN
ejpam-5193	136	9	(	(	PUNCT
ejpam-5193	136	10	r	r	NOUN
ejpam-5193	136	11	)	)	PUNCT
ejpam-5193	136	12	j	j	PROPN
ejpam-5193	136	13	,	,	PUNCT
ejpam-5193	136	14	k(y;u	k(y;u	PROPN
ejpam-5193	136	15	,	,	PUNCT
ejpam-5193	136	16	λ	λ	PROPN
ejpam-5193	136	17	,	,	PUNCT
ejpam-5193	136	18	a	a	PRON
ejpam-5193	136	19	,	,	PUNCT
ejpam-5193	136	20	b)x	b)x	X
ejpam-5193	136	21	n−j	n−j	PROPN
ejpam-5193	136	22	,	,	PUNCT
ejpam-5193	136	23	which	which	PRON
ejpam-5193	136	24	is	be	AUX
ejpam-5193	136	25	equivalent	equivalent	ADJ
ejpam-5193	136	26	to	to	ADP
ejpam-5193	136	27	the	the	DET
ejpam-5193	136	28	desired	desire	VERB
ejpam-5193	136	29	identity	identity	NOUN
ejpam-5193	136	30	in	in	ADP
ejpam-5193	136	31	(	(	PUNCT
ejpam-5193	136	32	2.8	2.8	NUM
ejpam-5193	136	33	)	)	PUNCT
ejpam-5193	136	34	.	.	PUNCT
ejpam-5193	137	1	1478	1478	NUM
ejpam-5193	138	1	the	the	DET
ejpam-5193	138	2	next	next	ADJ
ejpam-5193	138	3	theorem	theorem	NOUN
ejpam-5193	138	4	contains	contain	VERB
ejpam-5193	138	5	the	the	DET
ejpam-5193	138	6	addition	addition	NOUN
ejpam-5193	138	7	formula	formula	NOUN
ejpam-5193	138	8	for	for	ADP
ejpam-5193	138	9	bivariate	bivariate	ADJ
ejpam-5193	138	10	bell	bell	NOUN
ejpam-5193	138	11	-	-	PUNCT
ejpam-5193	138	12	based	base	VERB
ejpam-5193	138	13	apostolfrobenius	apostolfrobenius	NOUN
ejpam-5193	138	14	-	-	PUNCT
ejpam-5193	138	15	type	type	NOUN
ejpam-5193	138	16	poly	poly	ADJ
ejpam-5193	138	17	-	-	PUNCT
ejpam-5193	138	18	genocchi	genocchi	NOUN
ejpam-5193	138	19	polynomials	polynomial	NOUN
ejpam-5193	138	20	of	of	ADP
ejpam-5193	138	21	higher	high	ADJ
ejpam-5193	138	22	order	order	NOUN
ejpam-5193	138	23	.	.	PUNCT
ejpam-5193	139	1	theorem	theorem	VERB
ejpam-5193	139	2	2.8	2.8	NUM
ejpam-5193	139	3	.	.	PUNCT
ejpam-5193	140	1	the	the	DET
ejpam-5193	140	2	bivariate	bivariate	ADJ
ejpam-5193	140	3	bell	bell	NOUN
ejpam-5193	140	4	-	-	PUNCT
ejpam-5193	140	5	based	base	VERB
ejpam-5193	140	6	apostol	apostol	NOUN
ejpam-5193	140	7	-	-	PUNCT
ejpam-5193	140	8	frobenius	frobenius	NOUN
ejpam-5193	140	9	-	-	PUNCT
ejpam-5193	140	10	type	type	NOUN
ejpam-5193	140	11	poly	poly	ADJ
ejpam-5193	140	12	-	-	PUNCT
ejpam-5193	140	13	genocchi	genocchi	NOUN
ejpam-5193	140	14	polynomials	polynomial	NOUN
ejpam-5193	140	15	of	of	ADP
ejpam-5193	140	16	higher	high	ADJ
ejpam-5193	140	17	order	order	NOUN
ejpam-5193	140	18	bg	bg	NOUN
ejpam-5193	140	19	(	(	PUNCT
ejpam-5193	140	20	r	r	NOUN
ejpam-5193	140	21	)	)	PUNCT
ejpam-5193	140	22	n	n	CCONJ
ejpam-5193	140	23	,	,	PUNCT
ejpam-5193	140	24	k(x	k(x	PROPN
ejpam-5193	140	25	,	,	PUNCT
ejpam-5193	140	26	y;u	y;u	PROPN
ejpam-5193	140	27	,	,	PUNCT
ejpam-5193	140	28	λ	λ	PROPN
ejpam-5193	140	29	,	,	PUNCT
ejpam-5193	140	30	a	a	DET
ejpam-5193	140	31	,	,	PUNCT
ejpam-5193	140	32	b	b	NOUN
ejpam-5193	140	33	)	)	PUNCT
ejpam-5193	140	34	are	be	AUX
ejpam-5193	140	35	equal	equal	ADJ
ejpam-5193	140	36	to	to	ADP
ejpam-5193	140	37	bg	bg	PROPN
ejpam-5193	140	38	(	(	PUNCT
ejpam-5193	140	39	r	r	NOUN
ejpam-5193	140	40	)	)	PUNCT
ejpam-5193	140	41	n	n	CCONJ
ejpam-5193	140	42	,	,	PUNCT
ejpam-5193	140	43	k(x+	k(x+	PROPN
ejpam-5193	140	44	y	y	PROPN
ejpam-5193	140	45	,	,	PUNCT
ejpam-5193	140	46	z;u	z;u	PROPN
ejpam-5193	140	47	,	,	PUNCT
ejpam-5193	140	48	λ	λ	PROPN
ejpam-5193	140	49	,	,	PUNCT
ejpam-5193	140	50	a	a	DET
ejpam-5193	140	51	,	,	PUNCT
ejpam-5193	140	52	b	b	NOUN
ejpam-5193	140	53	)	)	PUNCT
ejpam-5193	140	54	=	=	SYM
ejpam-5193	140	55	n∑	n∑	NOUN
ejpam-5193	140	56	j=0	j=0	PROPN
ejpam-5193	140	57	(	(	PUNCT
ejpam-5193	140	58	n	n	X
ejpam-5193	140	59	j	j	PROPN
ejpam-5193	140	60	)	)	PUNCT
ejpam-5193	140	61	g	g	NOUN
ejpam-5193	140	62	(	(	PUNCT
ejpam-5193	140	63	r	r	NOUN
ejpam-5193	140	64	)	)	PUNCT
ejpam-5193	140	65	j	j	PROPN
ejpam-5193	140	66	,	,	PUNCT
ejpam-5193	140	67	k(x;u	k(x;u	PROPN
ejpam-5193	140	68	,	,	PUNCT
ejpam-5193	140	69	λ	λ	PROPN
ejpam-5193	140	70	,	,	PUNCT
ejpam-5193	140	71	a	a	PRON
ejpam-5193	140	72	,	,	PUNCT
ejpam-5193	140	73	b)bn−j(y	b)bn−j(y	PROPN
ejpam-5193	140	74	,	,	PUNCT
ejpam-5193	140	75	z	z	NOUN
ejpam-5193	140	76	)	)	PUNCT
ejpam-5193	140	77	.	.	PUNCT
ejpam-5193	141	1	(	(	PUNCT
ejpam-5193	141	2	2.9	2.9	NUM
ejpam-5193	141	3	)	)	PUNCT
ejpam-5193	141	4	proof	proof	NOUN
ejpam-5193	141	5	.	.	PUNCT
ejpam-5193	142	1	using	use	VERB
ejpam-5193	142	2	definition	definition	NOUN
ejpam-5193	142	3	2.1	2.1	NUM
ejpam-5193	142	4	,	,	PUNCT
ejpam-5193	142	5	we	we	PRON
ejpam-5193	142	6	have	have	VERB
ejpam-5193	142	7	∞∑	∞∑	NUM
ejpam-5193	142	8	n=0	n=0	ADJ
ejpam-5193	142	9	bg	bg	NOUN
ejpam-5193	142	10	(	(	PUNCT
ejpam-5193	142	11	r	r	NOUN
ejpam-5193	142	12	)	)	PUNCT
ejpam-5193	142	13	n	n	CCONJ
ejpam-5193	142	14	,	,	PUNCT
ejpam-5193	142	15	k(x+	k(x+	PROPN
ejpam-5193	142	16	y	y	PROPN
ejpam-5193	142	17	,	,	PUNCT
ejpam-5193	142	18	z;u	z;u	PROPN
ejpam-5193	142	19	,	,	PUNCT
ejpam-5193	142	20	λ	λ	PROPN
ejpam-5193	142	21	,	,	PUNCT
ejpam-5193	142	22	a	a	DET
ejpam-5193	142	23	,	,	PUNCT
ejpam-5193	142	24	b	b	NOUN
ejpam-5193	142	25	)	)	PUNCT
ejpam-5193	142	26	tn	tn	NOUN
ejpam-5193	142	27	n	n	CCONJ
ejpam-5193	142	28	!	!	PUNCT
ejpam-5193	143	1	=	=	PUNCT
ejpam-5193	143	2	(	(	PUNCT
ejpam-5193	143	3	lik(1−	lik(1−	X
ejpam-5193	143	4	(	(	PUNCT
ejpam-5193	143	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	143	6	)	)	PUNCT
ejpam-5193	143	7	λbt	λbt	VERB
ejpam-5193	143	8	−	−	PROPN
ejpam-5193	143	9	ua−t	ua−t	ADJ
ejpam-5193	143	10	)	)	PUNCT
ejpam-5193	143	11	r	r	NOUN
ejpam-5193	143	12	e(x+y)t+z(et−1	e(x+y)t+z(et−1	NOUN
ejpam-5193	143	13	)	)	PUNCT
ejpam-5193	143	14	=	=	SYM
ejpam-5193	144	1	{	{	PUNCT
ejpam-5193	144	2	(	(	PUNCT
ejpam-5193	144	3	lik(1−	lik(1−	PROPN
ejpam-5193	144	4	(	(	PUNCT
ejpam-5193	144	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	144	6	)	)	PUNCT
ejpam-5193	144	7	λbt	λbt	VERB
ejpam-5193	144	8	−	−	PROPN
ejpam-5193	144	9	ua−t	ua−t	ADJ
ejpam-5193	144	10	)	)	PUNCT
ejpam-5193	144	11	r	r	NOUN
ejpam-5193	144	12	ext	ext	NOUN
ejpam-5193	144	13	}	}	PUNCT
ejpam-5193	144	14	eyt+z(et−1	eyt+z(et−1	PROPN
ejpam-5193	144	15	)	)	PUNCT
ejpam-5193	144	16	=	=	NOUN
ejpam-5193	145	1	(	(	PUNCT
ejpam-5193	145	2	∞∑	∞∑	NUM
ejpam-5193	145	3	n=0	n=0	NUM
ejpam-5193	145	4	g	g	NOUN
ejpam-5193	145	5	(	(	PUNCT
ejpam-5193	145	6	r	r	NOUN
ejpam-5193	145	7	)	)	PUNCT
ejpam-5193	145	8	n	n	CCONJ
ejpam-5193	145	9	,	,	PUNCT
ejpam-5193	145	10	k(x;u	k(x;u	PROPN
ejpam-5193	145	11	,	,	PUNCT
ejpam-5193	145	12	λ	λ	PROPN
ejpam-5193	145	13	,	,	PUNCT
ejpam-5193	145	14	a	a	DET
ejpam-5193	145	15	,	,	PUNCT
ejpam-5193	145	16	b	b	NOUN
ejpam-5193	145	17	)	)	PUNCT
ejpam-5193	145	18	tn	tn	PROPN
ejpam-5193	145	19	n	n	CCONJ
ejpam-5193	145	20	!	!	PUNCT
ejpam-5193	145	21	)	)	PUNCT
ejpam-5193	146	1	(	(	PUNCT
ejpam-5193	146	2	∞∑	∞∑	NUM
ejpam-5193	146	3	n=0	n=0	PROPN
ejpam-5193	146	4	bn(y	bn(y	NUM
ejpam-5193	146	5	,	,	PUNCT
ejpam-5193	146	6	z	z	NOUN
ejpam-5193	146	7	)	)	PUNCT
ejpam-5193	146	8	tn	tn	PROPN
ejpam-5193	146	9	n	n	CCONJ
ejpam-5193	146	10	!	!	PUNCT
ejpam-5193	146	11	)	)	PUNCT
ejpam-5193	147	1	=	=	PUNCT
ejpam-5193	148	1	∞∑	∞∑	NUM
ejpam-5193	148	2	n=0	n=0	NUM
ejpam-5193	148	3			PUNCT
ejpam-5193	148	4	n∑	n∑	NOUN
ejpam-5193	148	5	j=0	j=0	PROPN
ejpam-5193	148	6	(	(	PUNCT
ejpam-5193	148	7	n	n	NOUN
ejpam-5193	148	8	k	k	NOUN
ejpam-5193	148	9	)	)	PUNCT
ejpam-5193	148	10	g	g	NOUN
ejpam-5193	148	11	(	(	PUNCT
ejpam-5193	148	12	r	r	NOUN
ejpam-5193	148	13	)	)	PUNCT
ejpam-5193	148	14	j	j	PROPN
ejpam-5193	148	15	,	,	PUNCT
ejpam-5193	148	16	k(x;u	k(x;u	PROPN
ejpam-5193	148	17	,	,	PUNCT
ejpam-5193	148	18	λ	λ	PROPN
ejpam-5193	148	19	,	,	PUNCT
ejpam-5193	148	20	a	a	PRON
ejpam-5193	148	21	,	,	PUNCT
ejpam-5193	148	22	b)bn−j(y	b)bn−j(y	PROPN
ejpam-5193	148	23	,	,	PUNCT
ejpam-5193	148	24	z	z	NOUN
ejpam-5193	148	25	)	)	PUNCT
ejpam-5193	148	26			PROPN
ejpam-5193	148	27	tn	tn	NOUN
ejpam-5193	148	28	n	n	CCONJ
ejpam-5193	148	29	!	!	PUNCT
ejpam-5193	148	30	.	.	PUNCT
ejpam-5193	149	1	comparing	compare	VERB
ejpam-5193	149	2	the	the	DET
ejpam-5193	149	3	coefficients	coefficient	NOUN
ejpam-5193	149	4	of	of	ADP
ejpam-5193	149	5	tn	tn	NOUN
ejpam-5193	149	6	n	n	X
ejpam-5193	149	7	!	!	PUNCT
ejpam-5193	150	1	yields	yield	VERB
ejpam-5193	150	2	the	the	DET
ejpam-5193	150	3	desired	desire	VERB
ejpam-5193	150	4	identity	identity	NOUN
ejpam-5193	150	5	in	in	ADP
ejpam-5193	150	6	(	(	PUNCT
ejpam-5193	150	7	2.9	2.9	NUM
ejpam-5193	150	8	)	)	PUNCT
ejpam-5193	150	9	.	.	PUNCT
ejpam-5193	151	1	3	3	X
ejpam-5193	151	2	.	.	X
ejpam-5193	151	3	implicit	implicit	ADJ
ejpam-5193	151	4	summation	summation	NOUN
ejpam-5193	151	5	formula	formula	NOUN
ejpam-5193	151	6	within	within	ADP
ejpam-5193	151	7	this	this	DET
ejpam-5193	151	8	section	section	NOUN
ejpam-5193	151	9	,	,	PUNCT
ejpam-5193	151	10	we	we	PRON
ejpam-5193	151	11	will	will	AUX
ejpam-5193	151	12	derive	derive	VERB
ejpam-5193	151	13	different	different	ADJ
ejpam-5193	151	14	summation	summation	NOUN
ejpam-5193	151	15	formulas	formula	NOUN
ejpam-5193	151	16	for	for	ADP
ejpam-5193	151	17	bg	bg	PROPN
ejpam-5193	151	18	(	(	PUNCT
ejpam-5193	151	19	r	r	NOUN
ejpam-5193	151	20	)	)	PUNCT
ejpam-5193	151	21	n	n	CCONJ
ejpam-5193	151	22	(	(	PUNCT
ejpam-5193	151	23	x+y	x+y	NUM
ejpam-5193	151	24	,	,	PUNCT
ejpam-5193	151	25	z;u	z;u	PROPN
ejpam-5193	151	26	,	,	PUNCT
ejpam-5193	151	27	λ	λ	PROPN
ejpam-5193	151	28	)	)	PUNCT
ejpam-5193	151	29	,	,	PUNCT
ejpam-5193	151	30	establishing	establish	VERB
ejpam-5193	151	31	implicit	implicit	ADJ
ejpam-5193	151	32	connections	connection	NOUN
ejpam-5193	151	33	among	among	ADP
ejpam-5193	151	34	the	the	DET
ejpam-5193	151	35	variables	variable	NOUN
ejpam-5193	151	36	by	by	ADP
ejpam-5193	151	37	considering	consider	VERB
ejpam-5193	151	38	them	they	PRON
ejpam-5193	151	39	as	as	ADP
ejpam-5193	151	40	arguments	argument	NOUN
ejpam-5193	151	41	.	.	PUNCT
ejpam-5193	152	1	the	the	DET
ejpam-5193	152	2	subsequent	subsequent	ADJ
ejpam-5193	152	3	theorem	theorem	NOUN
ejpam-5193	152	4	encapsulates	encapsulate	VERB
ejpam-5193	152	5	a	a	DET
ejpam-5193	152	6	particular	particular	ADJ
ejpam-5193	152	7	expression	expression	NOUN
ejpam-5193	152	8	of	of	ADP
ejpam-5193	152	9	these	these	DET
ejpam-5193	152	10	summation	summation	NOUN
ejpam-5193	152	11	formulas	formula	NOUN
ejpam-5193	152	12	.	.	PUNCT
ejpam-5193	153	1	theorem	theorem	VERB
ejpam-5193	153	2	3.1	3.1	NUM
ejpam-5193	153	3	.	.	PUNCT
ejpam-5193	154	1	the	the	DET
ejpam-5193	154	2	bivariate	bivariate	ADJ
ejpam-5193	154	3	bell	bell	NOUN
ejpam-5193	154	4	-	-	PUNCT
ejpam-5193	154	5	based	base	VERB
ejpam-5193	154	6	apostol	apostol	NOUN
ejpam-5193	154	7	-	-	PUNCT
ejpam-5193	154	8	frobenius	frobenius	NOUN
ejpam-5193	154	9	-	-	PUNCT
ejpam-5193	154	10	type	type	NOUN
ejpam-5193	154	11	poly	poly	ADJ
ejpam-5193	154	12	-	-	PUNCT
ejpam-5193	154	13	genocchi	genocchi	NOUN
ejpam-5193	154	14	polynomials	polynomial	NOUN
ejpam-5193	154	15	of	of	ADP
ejpam-5193	154	16	higher	high	ADJ
ejpam-5193	154	17	order	order	NOUN
ejpam-5193	154	18	bg	bg	NOUN
ejpam-5193	154	19	(	(	PUNCT
ejpam-5193	154	20	r	r	NOUN
ejpam-5193	154	21	)	)	PUNCT
ejpam-5193	154	22	n	n	NOUN
ejpam-5193	154	23	(	(	PUNCT
ejpam-5193	154	24	x	x	X
ejpam-5193	154	25	,	,	PUNCT
ejpam-5193	154	26	y;u	y;u	PROPN
ejpam-5193	154	27	,	,	PUNCT
ejpam-5193	154	28	λ	λ	NOUN
ejpam-5193	154	29	)	)	PUNCT
ejpam-5193	154	30	satisfy	satisfy	VERB
ejpam-5193	154	31	the	the	DET
ejpam-5193	154	32	following	follow	VERB
ejpam-5193	154	33	summation	summation	NOUN
ejpam-5193	154	34	formula	formula	NOUN
ejpam-5193	154	35	:	:	PUNCT
ejpam-5193	154	36	bg	bg	PROPN
ejpam-5193	154	37	(	(	PUNCT
ejpam-5193	154	38	r1+r2	r1+r2	PROPN
ejpam-5193	154	39	)	)	PUNCT
ejpam-5193	154	40	n	n	CCONJ
ejpam-5193	154	41	,	,	PUNCT
ejpam-5193	154	42	k	k	PROPN
ejpam-5193	154	43	(	(	PUNCT
ejpam-5193	154	44	x1	x1	PROPN
ejpam-5193	154	45	+	+	NUM
ejpam-5193	154	46	x2	x2	PROPN
ejpam-5193	154	47	,	,	PUNCT
ejpam-5193	154	48	y2	y2	PROPN
ejpam-5193	155	1	+	+	CCONJ
ejpam-5193	155	2	y2;u	y2;u	PROPN
ejpam-5193	155	3	,	,	PUNCT
ejpam-5193	155	4	λ	λ	PROPN
ejpam-5193	155	5	,	,	PUNCT
ejpam-5193	155	6	a	a	PRON
ejpam-5193	155	7	,	,	PUNCT
ejpam-5193	155	8	b	b	NOUN
ejpam-5193	155	9	)	)	PUNCT
ejpam-5193	155	10	=	=	SYM
ejpam-5193	155	11	n∑	n∑	NOUN
ejpam-5193	155	12	j=0	j=0	PROPN
ejpam-5193	155	13	(	(	PUNCT
ejpam-5193	155	14	n	n	X
ejpam-5193	155	15	j	j	PROPN
ejpam-5193	155	16	)	)	PUNCT
ejpam-5193	155	17	bg	bg	PROPN
ejpam-5193	155	18	(	(	PUNCT
ejpam-5193	155	19	r1	r1	PROPN
ejpam-5193	155	20	)	)	PUNCT
ejpam-5193	155	21	j	j	PROPN
ejpam-5193	155	22	,	,	PUNCT
ejpam-5193	155	23	k	k	PROPN
ejpam-5193	155	24	(	(	PUNCT
ejpam-5193	155	25	x1	x1	PROPN
ejpam-5193	155	26	,	,	PUNCT
ejpam-5193	155	27	y1;u	y1;u	PROPN
ejpam-5193	155	28	,	,	PUNCT
ejpam-5193	155	29	λ	λ	PROPN
ejpam-5193	155	30	,	,	PUNCT
ejpam-5193	155	31	a	a	PRON
ejpam-5193	155	32	,	,	PUNCT
ejpam-5193	155	33	b)bg	b)bg	PROPN
ejpam-5193	155	34	(	(	PUNCT
ejpam-5193	155	35	r2	r2	PROPN
ejpam-5193	155	36	)	)	PUNCT
ejpam-5193	155	37	n−j	n−j	ADV
ejpam-5193	155	38	,	,	PUNCT
ejpam-5193	155	39	k(x2	k(x2	NOUN
ejpam-5193	155	40	,	,	PUNCT
ejpam-5193	155	41	y2;u	y2;u	PROPN
ejpam-5193	155	42	,	,	PUNCT
ejpam-5193	155	43	λ	λ	NOUN
ejpam-5193	155	44	)	)	PUNCT
ejpam-5193	155	45	.	.	PUNCT
ejpam-5193	156	1	(	(	PUNCT
ejpam-5193	156	2	3.1	3.1	NUM
ejpam-5193	156	3	)	)	PUNCT
ejpam-5193	156	4	proof	proof	NOUN
ejpam-5193	156	5	.	.	PUNCT
ejpam-5193	157	1	note	note	VERB
ejpam-5193	157	2	that	that	SCONJ
ejpam-5193	157	3	we	we	PRON
ejpam-5193	157	4	can	can	AUX
ejpam-5193	157	5	express	express	VERB
ejpam-5193	157	6	the	the	DET
ejpam-5193	157	7	right	right	ADJ
ejpam-5193	157	8	hand	hand	NOUN
ejpam-5193	157	9	side	side	NOUN
ejpam-5193	157	10	of	of	ADP
ejpam-5193	157	11	(	(	PUNCT
ejpam-5193	157	12	2.1	2.1	NUM
ejpam-5193	157	13	)	)	PUNCT
ejpam-5193	157	14	as	as	SCONJ
ejpam-5193	157	15	follows	follow	VERB
ejpam-5193	157	16	:(	:(	X
ejpam-5193	158	1	lik(1−	lik(1−	PROPN
ejpam-5193	158	2	(	(	PUNCT
ejpam-5193	158	3	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	158	4	)	)	PUNCT
ejpam-5193	158	5	λbt	λbt	VERB
ejpam-5193	158	6	−	−	PROPN
ejpam-5193	158	7	ua−t	ua−t	PROPN
ejpam-5193	158	8	)	)	PUNCT
ejpam-5193	158	9	r1+r2	r1+r2	PROPN
ejpam-5193	158	10	e(x1+x2)t+(y1+y2)(et−1	e(x1+x2)t+(y1+y2)(et−1	PROPN
ejpam-5193	158	11	)	)	PUNCT
ejpam-5193	158	12	1479	1479	NUM
ejpam-5193	158	13	=	=	SYM
ejpam-5193	158	14	{	{	PUNCT
ejpam-5193	158	15	(	(	PUNCT
ejpam-5193	158	16	lik(1−	lik(1−	PROPN
ejpam-5193	158	17	(	(	PUNCT
ejpam-5193	158	18	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	158	19	)	)	PUNCT
ejpam-5193	158	20	λbt	λbt	VERB
ejpam-5193	158	21	−	−	PROPN
ejpam-5193	158	22	ua−t	ua−t	PROPN
ejpam-5193	158	23	)	)	PUNCT
ejpam-5193	158	24	r1	r1	PROPN
ejpam-5193	158	25	ex1t+y1(et−1	ex1t+y1(et−1	NOUN
ejpam-5193	158	26	)	)	PUNCT
ejpam-5193	158	27	}	}	PUNCT
ejpam-5193	159	1	{	{	PUNCT
ejpam-5193	159	2	(	(	PUNCT
ejpam-5193	159	3	lik(1−	lik(1−	PROPN
ejpam-5193	159	4	(	(	PUNCT
ejpam-5193	159	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	159	6	)	)	PUNCT
ejpam-5193	159	7	λbt	λbt	VERB
ejpam-5193	159	8	−	−	PROPN
ejpam-5193	159	9	ua−t	ua−t	ADJ
ejpam-5193	159	10	)	)	PUNCT
ejpam-5193	159	11	r2	r2	PROPN
ejpam-5193	159	12	ex2t+y2(et−1	ex2t+y2(et−1	NOUN
ejpam-5193	159	13	)	)	PUNCT
ejpam-5193	159	14	}	}	PUNCT
ejpam-5193	159	15	.	.	PUNCT
ejpam-5193	160	1	applying	apply	VERB
ejpam-5193	160	2	(	(	PUNCT
ejpam-5193	160	3	2.1	2.1	NUM
ejpam-5193	160	4	)	)	PUNCT
ejpam-5193	160	5	yields	yield	VERB
ejpam-5193	160	6	∞∑	∞∑	NUM
ejpam-5193	160	7	n=0	n=0	ADJ
ejpam-5193	160	8	bg	bg	NOUN
ejpam-5193	160	9	(	(	PUNCT
ejpam-5193	160	10	r1+r2	r1+r2	PROPN
ejpam-5193	160	11	)	)	PUNCT
ejpam-5193	160	12	n	n	CCONJ
ejpam-5193	160	13	,	,	PUNCT
ejpam-5193	160	14	k	k	PROPN
ejpam-5193	160	15	(	(	PUNCT
ejpam-5193	160	16	x1	x1	PROPN
ejpam-5193	160	17	+	+	NUM
ejpam-5193	160	18	x2	x2	PROPN
ejpam-5193	160	19	,	,	PUNCT
ejpam-5193	160	20	y2	y2	PROPN
ejpam-5193	161	1	+	+	CCONJ
ejpam-5193	162	1	y2;u	y2;u	PROPN
ejpam-5193	162	2	,	,	PUNCT
ejpam-5193	162	3	λ	λ	PROPN
ejpam-5193	162	4	,	,	PUNCT
ejpam-5193	162	5	a	a	DET
ejpam-5193	162	6	,	,	PUNCT
ejpam-5193	162	7	b	b	NOUN
ejpam-5193	162	8	)	)	PUNCT
ejpam-5193	162	9	tn	tn	NOUN
ejpam-5193	162	10	n	n	NOUN
ejpam-5193	162	11	!	!	PUNCT
ejpam-5193	162	12	=	=	PUNCT
ejpam-5193	163	1	(	(	PUNCT
ejpam-5193	163	2	∞∑	∞∑	NUM
ejpam-5193	163	3	n=0	n=0	PROPN
ejpam-5193	163	4	bg	bg	PROPN
ejpam-5193	163	5	(	(	PUNCT
ejpam-5193	163	6	r1	r1	PROPN
ejpam-5193	163	7	)	)	PUNCT
ejpam-5193	163	8	n	n	CCONJ
ejpam-5193	163	9	,	,	PUNCT
ejpam-5193	163	10	k	k	PROPN
ejpam-5193	163	11	(	(	PUNCT
ejpam-5193	163	12	x1	x1	PROPN
ejpam-5193	163	13	,	,	PUNCT
ejpam-5193	163	14	y1;u	y1;u	PROPN
ejpam-5193	163	15	,	,	PUNCT
ejpam-5193	163	16	λ	λ	PROPN
ejpam-5193	163	17	,	,	PUNCT
ejpam-5193	163	18	a	a	DET
ejpam-5193	163	19	,	,	PUNCT
ejpam-5193	163	20	b	b	NOUN
ejpam-5193	163	21	)	)	PUNCT
ejpam-5193	163	22	tn	tn	PROPN
ejpam-5193	163	23	n	n	CCONJ
ejpam-5193	163	24	!	!	PUNCT
ejpam-5193	163	25	)	)	PUNCT
ejpam-5193	164	1	(	(	PUNCT
ejpam-5193	164	2	∞∑	∞∑	NUM
ejpam-5193	164	3	n=0	n=0	PROPN
ejpam-5193	164	4	bg	bg	PROPN
ejpam-5193	164	5	(	(	PUNCT
ejpam-5193	164	6	r2	r2	PROPN
ejpam-5193	164	7	)	)	PUNCT
ejpam-5193	164	8	n	n	CCONJ
ejpam-5193	164	9	,	,	PUNCT
ejpam-5193	164	10	k	k	PROPN
ejpam-5193	164	11	(	(	PUNCT
ejpam-5193	164	12	x2	x2	PROPN
ejpam-5193	164	13	,	,	PUNCT
ejpam-5193	164	14	y2;u	y2;u	PROPN
ejpam-5193	164	15	,	,	PUNCT
ejpam-5193	164	16	λ	λ	PROPN
ejpam-5193	164	17	,	,	PUNCT
ejpam-5193	164	18	a	a	DET
ejpam-5193	164	19	,	,	PUNCT
ejpam-5193	164	20	b	b	NOUN
ejpam-5193	164	21	)	)	PUNCT
ejpam-5193	164	22	tn	tn	PROPN
ejpam-5193	164	23	n	n	NOUN
ejpam-5193	164	24	!	!	PUNCT
ejpam-5193	164	25	)	)	PUNCT
ejpam-5193	165	1	=	=	PUNCT
ejpam-5193	166	1	∞∑	∞∑	NUM
ejpam-5193	166	2	n=0	n=0	NUM
ejpam-5193	166	3	n∑	n∑	PRON
ejpam-5193	166	4	j=0	j=0	PROPN
ejpam-5193	166	5	bg	bg	PROPN
ejpam-5193	166	6	(	(	PUNCT
ejpam-5193	166	7	r1	r1	PROPN
ejpam-5193	166	8	)	)	PUNCT
ejpam-5193	166	9	j	j	PROPN
ejpam-5193	166	10	,	,	PUNCT
ejpam-5193	166	11	k	k	PROPN
ejpam-5193	166	12	(	(	PUNCT
ejpam-5193	166	13	x1	x1	PROPN
ejpam-5193	166	14	,	,	PUNCT
ejpam-5193	166	15	y1;u	y1;u	PROPN
ejpam-5193	166	16	,	,	PUNCT
ejpam-5193	166	17	λ	λ	PROPN
ejpam-5193	166	18	,	,	PUNCT
ejpam-5193	166	19	a	a	PRON
ejpam-5193	166	20	,	,	PUNCT
ejpam-5193	166	21	b)bg	b)bg	PROPN
ejpam-5193	166	22	(	(	PUNCT
ejpam-5193	166	23	r2	r2	PROPN
ejpam-5193	166	24	)	)	PUNCT
ejpam-5193	166	25	n−j	n−j	ADV
ejpam-5193	166	26	,	,	PUNCT
ejpam-5193	166	27	k(x2	k(x2	NOUN
ejpam-5193	166	28	,	,	PUNCT
ejpam-5193	166	29	y2;u	y2;u	PROPN
ejpam-5193	166	30	,	,	PUNCT
ejpam-5193	166	31	λ	λ	PROPN
ejpam-5193	166	32	,	,	PUNCT
ejpam-5193	166	33	a	a	DET
ejpam-5193	166	34	,	,	PUNCT
ejpam-5193	166	35	b	b	NOUN
ejpam-5193	166	36	)	)	PUNCT
ejpam-5193	166	37	(	(	PUNCT
ejpam-5193	166	38	n	n	X
ejpam-5193	166	39	j	j	PROPN
ejpam-5193	166	40	)	)	PUNCT
ejpam-5193	166	41	.	.	PUNCT
ejpam-5193	167	1	by	by	ADP
ejpam-5193	167	2	comparing	compare	VERB
ejpam-5193	167	3	the	the	DET
ejpam-5193	167	4	coefficients	coefficient	NOUN
ejpam-5193	167	5	of	of	ADP
ejpam-5193	167	6	tn	tn	NOUN
ejpam-5193	167	7	n	n	CCONJ
ejpam-5193	167	8	!	!	PROPN
ejpam-5193	167	9	,	,	PUNCT
ejpam-5193	167	10	we	we	PRON
ejpam-5193	167	11	obtain	obtain	VERB
ejpam-5193	167	12	bg	bg	PROPN
ejpam-5193	167	13	(	(	PUNCT
ejpam-5193	167	14	r1+r2	r1+r2	PROPN
ejpam-5193	167	15	)	)	PUNCT
ejpam-5193	167	16	n	n	CCONJ
ejpam-5193	167	17	,	,	PUNCT
ejpam-5193	167	18	k	k	PROPN
ejpam-5193	167	19	(	(	PUNCT
ejpam-5193	167	20	x1	x1	PROPN
ejpam-5193	167	21	+	+	NUM
ejpam-5193	167	22	x2	x2	PROPN
ejpam-5193	167	23	,	,	PUNCT
ejpam-5193	167	24	y2	y2	PROPN
ejpam-5193	167	25	+	+	CCONJ
ejpam-5193	167	26	y2;u	y2;u	PROPN
ejpam-5193	167	27	,	,	PUNCT
ejpam-5193	167	28	λ	λ	PROPN
ejpam-5193	167	29	,	,	PUNCT
ejpam-5193	167	30	a	a	PRON
ejpam-5193	167	31	,	,	PUNCT
ejpam-5193	167	32	b	b	NOUN
ejpam-5193	167	33	)	)	PUNCT
ejpam-5193	167	34	=	=	SYM
ejpam-5193	168	1	n∑	n∑	NOUN
ejpam-5193	168	2	j=0	j=0	PROPN
ejpam-5193	168	3	(	(	PUNCT
ejpam-5193	168	4	n	n	X
ejpam-5193	168	5	k	k	PROPN
ejpam-5193	168	6	)	)	PUNCT
ejpam-5193	168	7	bg	bg	PROPN
ejpam-5193	168	8	(	(	PUNCT
ejpam-5193	168	9	r1	r1	PROPN
ejpam-5193	168	10	)	)	PUNCT
ejpam-5193	168	11	j	j	PROPN
ejpam-5193	168	12	,	,	PUNCT
ejpam-5193	168	13	k	k	PROPN
ejpam-5193	168	14	(	(	PUNCT
ejpam-5193	168	15	x1	x1	PROPN
ejpam-5193	168	16	,	,	PUNCT
ejpam-5193	168	17	y1;u	y1;u	PROPN
ejpam-5193	168	18	,	,	PUNCT
ejpam-5193	168	19	λ	λ	PROPN
ejpam-5193	168	20	,	,	PUNCT
ejpam-5193	168	21	a	a	PRON
ejpam-5193	168	22	,	,	PUNCT
ejpam-5193	168	23	b)bg	b)bg	PROPN
ejpam-5193	168	24	(	(	PUNCT
ejpam-5193	168	25	r2	r2	PROPN
ejpam-5193	168	26	)	)	PUNCT
ejpam-5193	168	27	n−j	n−j	ADV
ejpam-5193	168	28	,	,	PUNCT
ejpam-5193	168	29	k(x2	k(x2	NOUN
ejpam-5193	168	30	,	,	PUNCT
ejpam-5193	168	31	y2;u	y2;u	PROPN
ejpam-5193	168	32	,	,	PUNCT
ejpam-5193	168	33	λ	λ	NOUN
ejpam-5193	168	34	)	)	PUNCT
ejpam-5193	168	35	,	,	PUNCT
ejpam-5193	168	36	which	which	PRON
ejpam-5193	168	37	is	be	AUX
ejpam-5193	168	38	exactly	exactly	ADV
ejpam-5193	168	39	the	the	DET
ejpam-5193	168	40	desired	desire	VERB
ejpam-5193	168	41	summation	summation	NOUN
ejpam-5193	168	42	formula	formula	NOUN
ejpam-5193	168	43	in	in	ADP
ejpam-5193	168	44	(	(	PUNCT
ejpam-5193	168	45	3.5	3.5	NUM
ejpam-5193	168	46	)	)	PUNCT
ejpam-5193	168	47	.	.	PUNCT
ejpam-5193	169	1	remark	remark	PROPN
ejpam-5193	169	2	3.2	3.2	NUM
ejpam-5193	169	3	.	.	PUNCT
ejpam-5193	170	1	when	when	SCONJ
ejpam-5193	170	2	r1	r1	PROPN
ejpam-5193	170	3	=	=	SYM
ejpam-5193	170	4	r	r	PROPN
ejpam-5193	170	5	,	,	PUNCT
ejpam-5193	170	6	r2	r2	NOUN
ejpam-5193	170	7	=	=	PUNCT
ejpam-5193	170	8	0,x1	0,x1	PUNCT
ejpam-5193	171	1	=	=	SYM
ejpam-5193	171	2	x	x	X
ejpam-5193	171	3	,	,	PUNCT
ejpam-5193	171	4	x2	x2	PROPN
ejpam-5193	171	5	=	=	SYM
ejpam-5193	171	6	1,y1	1,y1	NUM
ejpam-5193	171	7	=	=	SYM
ejpam-5193	171	8	y	y	PROPN
ejpam-5193	171	9	,	,	PUNCT
ejpam-5193	171	10	y2	y2	PROPN
ejpam-5193	171	11	=	=	SYM
ejpam-5193	171	12	0	0	PROPN
ejpam-5193	171	13	,	,	PUNCT
ejpam-5193	171	14	the	the	DET
ejpam-5193	171	15	summation	summation	NOUN
ejpam-5193	171	16	formula	formula	NOUN
ejpam-5193	171	17	in	in	ADP
ejpam-5193	171	18	(	(	PUNCT
ejpam-5193	171	19	3.5	3.5	NUM
ejpam-5193	171	20	)	)	PUNCT
ejpam-5193	171	21	reduces	reduce	VERB
ejpam-5193	171	22	to	to	ADP
ejpam-5193	171	23	bg	bg	PROPN
ejpam-5193	171	24	(	(	PUNCT
ejpam-5193	171	25	r	r	NOUN
ejpam-5193	171	26	)	)	PUNCT
ejpam-5193	171	27	n	n	CCONJ
ejpam-5193	171	28	,	,	PUNCT
ejpam-5193	171	29	k(x+	k(x+	PROPN
ejpam-5193	171	30	1	1	NUM
ejpam-5193	171	31	,	,	PUNCT
ejpam-5193	171	32	y;u	y;u	PROPN
ejpam-5193	171	33	,	,	PUNCT
ejpam-5193	171	34	λ	λ	PROPN
ejpam-5193	171	35	,	,	PUNCT
ejpam-5193	171	36	a	a	DET
ejpam-5193	171	37	,	,	PUNCT
ejpam-5193	171	38	b	b	NOUN
ejpam-5193	171	39	)	)	PUNCT
ejpam-5193	171	40	=	=	SYM
ejpam-5193	172	1	n∑	n∑	NOUN
ejpam-5193	172	2	j=0	j=0	PROPN
ejpam-5193	172	3	(	(	PUNCT
ejpam-5193	172	4	n	n	X
ejpam-5193	172	5	j	j	PROPN
ejpam-5193	172	6	)	)	PUNCT
ejpam-5193	172	7	bg	bg	PROPN
ejpam-5193	172	8	(	(	PUNCT
ejpam-5193	172	9	r	r	NOUN
ejpam-5193	172	10	)	)	PUNCT
ejpam-5193	172	11	j	j	PROPN
ejpam-5193	172	12	,	,	PUNCT
ejpam-5193	172	13	k(x	k(x	PROPN
ejpam-5193	172	14	,	,	PUNCT
ejpam-5193	172	15	y;u	y;u	PROPN
ejpam-5193	172	16	,	,	PUNCT
ejpam-5193	172	17	λ	λ	PROPN
ejpam-5193	172	18	,	,	PUNCT
ejpam-5193	172	19	a	a	PRON
ejpam-5193	172	20	,	,	PUNCT
ejpam-5193	172	21	b)bn−k(1	b)bn−k(1	NOUN
ejpam-5193	172	22	,	,	PUNCT
ejpam-5193	172	23	0	0	NUM
ejpam-5193	172	24	)	)	PUNCT
ejpam-5193	172	25	=	=	SYM
ejpam-5193	172	26	n∑	n∑	X
ejpam-5193	172	27	j=0	j=0	PROPN
ejpam-5193	172	28	(	(	PUNCT
ejpam-5193	172	29	n	n	X
ejpam-5193	172	30	j	j	PROPN
ejpam-5193	172	31	)	)	PUNCT
ejpam-5193	172	32	bg	bg	PROPN
ejpam-5193	172	33	(	(	PUNCT
ejpam-5193	172	34	r	r	NOUN
ejpam-5193	172	35	)	)	PUNCT
ejpam-5193	172	36	j	j	PROPN
ejpam-5193	172	37	,	,	PUNCT
ejpam-5193	172	38	k(x	k(x	PROPN
ejpam-5193	172	39	,	,	PUNCT
ejpam-5193	172	40	y;u	y;u	PROPN
ejpam-5193	172	41	,	,	PUNCT
ejpam-5193	172	42	λ	λ	PROPN
ejpam-5193	172	43	,	,	PUNCT
ejpam-5193	172	44	a	a	DET
ejpam-5193	172	45	,	,	PUNCT
ejpam-5193	172	46	b	b	NOUN
ejpam-5193	172	47	)	)	PUNCT
ejpam-5193	172	48	.	.	PUNCT
ejpam-5193	173	1	(	(	PUNCT
ejpam-5193	173	2	3.2	3.2	NUM
ejpam-5193	173	3	)	)	PUNCT
ejpam-5193	173	4	on	on	ADP
ejpam-5193	173	5	the	the	DET
ejpam-5193	173	6	other	other	ADJ
ejpam-5193	173	7	hand	hand	NOUN
ejpam-5193	173	8	,	,	PUNCT
ejpam-5193	173	9	when	when	SCONJ
ejpam-5193	173	10	y	y	PROPN
ejpam-5193	173	11	=	=	SYM
ejpam-5193	173	12	1	1	NUM
ejpam-5193	173	13	,	,	PUNCT
ejpam-5193	173	14	(	(	PUNCT
ejpam-5193	173	15	2.9	2.9	NUM
ejpam-5193	173	16	)	)	PUNCT
ejpam-5193	173	17	gives	give	VERB
ejpam-5193	173	18	bg	bg	PROPN
ejpam-5193	173	19	(	(	PUNCT
ejpam-5193	173	20	r	r	NOUN
ejpam-5193	173	21	)	)	PUNCT
ejpam-5193	173	22	n	n	CCONJ
ejpam-5193	173	23	,	,	PUNCT
ejpam-5193	173	24	k(x+	k(x+	PROPN
ejpam-5193	173	25	1	1	NUM
ejpam-5193	173	26	,	,	PUNCT
ejpam-5193	173	27	z;u	z;u	PROPN
ejpam-5193	173	28	,	,	PUNCT
ejpam-5193	173	29	λ	λ	PROPN
ejpam-5193	173	30	,	,	PUNCT
ejpam-5193	173	31	a	a	PRON
ejpam-5193	173	32	,	,	PUNCT
ejpam-5193	173	33	b	b	NOUN
ejpam-5193	173	34	)	)	PUNCT
ejpam-5193	174	1	=	=	SYM
ejpam-5193	174	2	n∑	n∑	NOUN
ejpam-5193	174	3	j=0	j=0	PROPN
ejpam-5193	174	4	(	(	PUNCT
ejpam-5193	174	5	n	n	X
ejpam-5193	174	6	j	j	PROPN
ejpam-5193	174	7	)	)	PUNCT
ejpam-5193	174	8	g	g	NOUN
ejpam-5193	174	9	(	(	PUNCT
ejpam-5193	174	10	r	r	NOUN
ejpam-5193	174	11	)	)	PUNCT
ejpam-5193	174	12	j	j	PROPN
ejpam-5193	174	13	,	,	PUNCT
ejpam-5193	174	14	k(x;u	k(x;u	PROPN
ejpam-5193	174	15	,	,	PUNCT
ejpam-5193	174	16	λ	λ	PROPN
ejpam-5193	174	17	,	,	PUNCT
ejpam-5193	174	18	a	a	PRON
ejpam-5193	174	19	,	,	PUNCT
ejpam-5193	174	20	b)bn−j(1	b)bn−j(1	NOUN
ejpam-5193	174	21	,	,	PUNCT
ejpam-5193	174	22	z	z	NOUN
ejpam-5193	174	23	)	)	PUNCT
ejpam-5193	174	24	.	.	PUNCT
ejpam-5193	175	1	(	(	PUNCT
ejpam-5193	175	2	3.3	3.3	NUM
ejpam-5193	175	3	)	)	PUNCT
ejpam-5193	175	4	replacing	replace	VERB
ejpam-5193	175	5	z	z	NOUN
ejpam-5193	175	6	with	with	ADP
ejpam-5193	175	7	y	y	PROPN
ejpam-5193	175	8	in	in	ADP
ejpam-5193	175	9	(	(	PUNCT
ejpam-5193	175	10	3.3	3.3	NUM
ejpam-5193	175	11	)	)	PUNCT
ejpam-5193	175	12	and	and	CCONJ
ejpam-5193	175	13	subtract	subtract	VERB
ejpam-5193	175	14	it	it	PRON
ejpam-5193	175	15	from	from	ADP
ejpam-5193	175	16	(	(	PUNCT
ejpam-5193	175	17	3.2	3.2	NUM
ejpam-5193	175	18	)	)	PUNCT
ejpam-5193	175	19	yields	yield	NOUN
ejpam-5193	175	20	n∑	n∑	CCONJ
ejpam-5193	175	21	j=0	j=0	PROPN
ejpam-5193	175	22	(	(	PUNCT
ejpam-5193	175	23	n	n	X
ejpam-5193	175	24	j	j	PROPN
ejpam-5193	175	25	)	)	PUNCT
ejpam-5193	175	26	g	g	NOUN
ejpam-5193	175	27	(	(	PUNCT
ejpam-5193	175	28	r	r	NOUN
ejpam-5193	175	29	)	)	PUNCT
ejpam-5193	175	30	j	j	PROPN
ejpam-5193	175	31	,	,	PUNCT
ejpam-5193	175	32	k(x;u	k(x;u	PROPN
ejpam-5193	175	33	,	,	PUNCT
ejpam-5193	175	34	λ	λ	PROPN
ejpam-5193	175	35	,	,	PUNCT
ejpam-5193	175	36	a	a	PRON
ejpam-5193	175	37	,	,	PUNCT
ejpam-5193	175	38	b)bn−j(1	b)bn−j(1	NOUN
ejpam-5193	175	39	,	,	PUNCT
ejpam-5193	175	40	z	z	NOUN
ejpam-5193	175	41	)	)	PUNCT
ejpam-5193	175	42	=	=	SYM
ejpam-5193	176	1	n∑	n∑	X
ejpam-5193	176	2	j=0	j=0	PROPN
ejpam-5193	176	3	(	(	PUNCT
ejpam-5193	176	4	n	n	X
ejpam-5193	176	5	j	j	PROPN
ejpam-5193	176	6	)	)	PUNCT
ejpam-5193	176	7	bg	bg	PROPN
ejpam-5193	176	8	(	(	PUNCT
ejpam-5193	176	9	r	r	NOUN
ejpam-5193	176	10	)	)	PUNCT
ejpam-5193	176	11	j	j	PROPN
ejpam-5193	176	12	,	,	PUNCT
ejpam-5193	176	13	k(x	k(x	PROPN
ejpam-5193	176	14	,	,	PUNCT
ejpam-5193	176	15	y;u	y;u	PROPN
ejpam-5193	176	16	,	,	PUNCT
ejpam-5193	176	17	λ	λ	PROPN
ejpam-5193	176	18	,	,	PUNCT
ejpam-5193	176	19	a	a	DET
ejpam-5193	176	20	,	,	PUNCT
ejpam-5193	176	21	b	b	NOUN
ejpam-5193	176	22	)	)	PUNCT
ejpam-5193	176	23	.	.	PUNCT
ejpam-5193	176	24	1480	1480	NUM
ejpam-5193	177	1	we	we	PRON
ejpam-5193	177	2	recall	recall	VERB
ejpam-5193	177	3	the	the	DET
ejpam-5193	177	4	following	follow	VERB
ejpam-5193	177	5	series	series	NOUN
ejpam-5193	177	6	manipulation	manipulation	NOUN
ejpam-5193	177	7	formula	formula	NOUN
ejpam-5193	177	8	:	:	PUNCT
ejpam-5193	177	9	∞∑	∞∑	NUM
ejpam-5193	177	10	n=0	n=0	NUM
ejpam-5193	177	11	f(n	f(n	PROPN
ejpam-5193	177	12	)	)	PUNCT
ejpam-5193	177	13	(	(	PUNCT
ejpam-5193	177	14	x+	x+	X
ejpam-5193	177	15	y)n	y)n	NUM
ejpam-5193	177	16	n	n	NOUN
ejpam-5193	177	17	!	!	PUNCT
ejpam-5193	177	18	=	=	PUNCT
ejpam-5193	178	1	∞∑	∞∑	PRON
ejpam-5193	178	2	n=0	n=0	NUM
ejpam-5193	178	3	∞∑	∞∑	NUM
ejpam-5193	178	4	m=0	m=0	PROPN
ejpam-5193	178	5	f(n+m	f(n+m	PROPN
ejpam-5193	178	6	)	)	PUNCT
ejpam-5193	178	7	xn	xn	PROPN
ejpam-5193	178	8	n	n	X
ejpam-5193	178	9	!	!	PUNCT
ejpam-5193	179	1	yn	yn	PRON
ejpam-5193	179	2	m	m	PROPN
ejpam-5193	179	3	!	!	PUNCT
ejpam-5193	179	4	.	.	PUNCT
ejpam-5193	180	1	(	(	PUNCT
ejpam-5193	180	2	3.4	3.4	NUM
ejpam-5193	180	3	)	)	PUNCT
ejpam-5193	180	4	applying	apply	VERB
ejpam-5193	180	5	(	(	PUNCT
ejpam-5193	180	6	3.4	3.4	NUM
ejpam-5193	180	7	)	)	PUNCT
ejpam-5193	180	8	obtains	obtain	VERB
ejpam-5193	180	9	(	(	PUNCT
ejpam-5193	180	10	lik(1−	lik(1−	X
ejpam-5193	180	11	(	(	PUNCT
ejpam-5193	180	12	ab)−(1−u)(t+v	ab)−(1−u)(t+v	NOUN
ejpam-5193	180	13	)	)	PUNCT
ejpam-5193	180	14	)	)	PUNCT
ejpam-5193	181	1	λbt+v	λbt+v	PUNCT
ejpam-5193	181	2	−	−	PROPN
ejpam-5193	181	3	ua−(t+v	ua−(t+v	PROPN
ejpam-5193	181	4	)	)	PUNCT
ejpam-5193	181	5	)	)	PUNCT
ejpam-5193	182	1	r	r	NOUN
ejpam-5193	182	2	ey(e	ey(e	X
ejpam-5193	182	3	t+v−1	t+v−1	PROPN
ejpam-5193	182	4	)	)	PUNCT
ejpam-5193	182	5	=	=	SYM
ejpam-5193	182	6	e−x(t+v	e−x(t+v	PROPN
ejpam-5193	182	7	)	)	PUNCT
ejpam-5193	182	8	∞∑	∞∑	PRON
ejpam-5193	182	9	n=0	n=0	ADJ
ejpam-5193	182	10	bg	bg	NOUN
ejpam-5193	182	11	(	(	PUNCT
ejpam-5193	182	12	r	r	NOUN
ejpam-5193	182	13	)	)	PUNCT
ejpam-5193	182	14	n	n	CCONJ
ejpam-5193	182	15	,	,	PUNCT
ejpam-5193	182	16	k(x	k(x	PROPN
ejpam-5193	182	17	,	,	PUNCT
ejpam-5193	182	18	y;u	y;u	PROPN
ejpam-5193	182	19	,	,	PUNCT
ejpam-5193	182	20	λ	λ	PROPN
ejpam-5193	182	21	,	,	PUNCT
ejpam-5193	182	22	a	a	DET
ejpam-5193	182	23	,	,	PUNCT
ejpam-5193	182	24	b	b	NOUN
ejpam-5193	182	25	)	)	PUNCT
ejpam-5193	182	26	(	(	PUNCT
ejpam-5193	182	27	t+	t+	NOUN
ejpam-5193	182	28	v)n	v)n	NOUN
ejpam-5193	182	29	n	n	CCONJ
ejpam-5193	182	30	!	!	PUNCT
ejpam-5193	183	1	=	=	SYM
ejpam-5193	183	2	e−x(t+v	e−x(t+v	PROPN
ejpam-5193	183	3	)	)	PUNCT
ejpam-5193	184	1	∞∑	∞∑	NUM
ejpam-5193	184	2	j=0	j=0	PROPN
ejpam-5193	184	3	∞∑	∞∑	NUM
ejpam-5193	184	4	l=0	l=0	PROPN
ejpam-5193	184	5	bg	bg	NOUN
ejpam-5193	184	6	(	(	PUNCT
ejpam-5193	184	7	r	r	NOUN
ejpam-5193	184	8	)	)	PUNCT
ejpam-5193	184	9	j+l	j+l	PROPN
ejpam-5193	184	10	,	,	PUNCT
ejpam-5193	184	11	k(x	k(x	PROPN
ejpam-5193	184	12	,	,	PUNCT
ejpam-5193	184	13	y;u	y;u	PROPN
ejpam-5193	184	14	,	,	PUNCT
ejpam-5193	184	15	λ	λ	PROPN
ejpam-5193	184	16	,	,	PUNCT
ejpam-5193	184	17	a	a	PRON
ejpam-5193	184	18	,	,	PUNCT
ejpam-5193	184	19	b	b	NOUN
ejpam-5193	184	20	)	)	PUNCT
ejpam-5193	184	21	tj	tj	PROPN
ejpam-5193	184	22	j	j	PROPN
ejpam-5193	184	23	!	!	PUNCT
ejpam-5193	184	24	vl	vl	PROPN
ejpam-5193	184	25	l	l	PROPN
ejpam-5193	184	26	!	!	PUNCT
ejpam-5193	184	27	.	.	PUNCT
ejpam-5193	185	1	replacing	replace	VERB
ejpam-5193	185	2	x	x	PUNCT
ejpam-5193	185	3	with	with	ADP
ejpam-5193	185	4	z	z	NOUN
ejpam-5193	185	5	yields	yield	NOUN
ejpam-5193	185	6	(	(	PUNCT
ejpam-5193	185	7	lik(1−	lik(1−	X
ejpam-5193	185	8	(	(	PUNCT
ejpam-5193	185	9	ab)−(1−u)(t+v	ab)−(1−u)(t+v	NOUN
ejpam-5193	185	10	)	)	PUNCT
ejpam-5193	185	11	)	)	PUNCT
ejpam-5193	186	1	λbt+v	λbt+v	PUNCT
ejpam-5193	186	2	−	−	PROPN
ejpam-5193	186	3	ua−(t+v	ua−(t+v	PROPN
ejpam-5193	186	4	)	)	PUNCT
ejpam-5193	186	5	)	)	PUNCT
ejpam-5193	187	1	r	r	NOUN
ejpam-5193	187	2	ey(e	ey(e	X
ejpam-5193	187	3	t+v−1	t+v−1	PROPN
ejpam-5193	187	4	)	)	PUNCT
ejpam-5193	187	5	=	=	SYM
ejpam-5193	188	1	e−z(t+v	e−z(t+v	NOUN
ejpam-5193	188	2	)	)	PUNCT
ejpam-5193	188	3	∞∑	∞∑	NUM
ejpam-5193	188	4	j=0	j=0	PROPN
ejpam-5193	188	5	∞∑	∞∑	NUM
ejpam-5193	188	6	l=0	l=0	PROPN
ejpam-5193	188	7	bg	bg	NOUN
ejpam-5193	188	8	(	(	PUNCT
ejpam-5193	188	9	r	r	NOUN
ejpam-5193	188	10	)	)	PUNCT
ejpam-5193	188	11	j+l	j+l	PROPN
ejpam-5193	188	12	,	,	PUNCT
ejpam-5193	188	13	k(z	k(z	PROPN
ejpam-5193	188	14	,	,	PUNCT
ejpam-5193	188	15	y;u	y;u	PROPN
ejpam-5193	188	16	,	,	PUNCT
ejpam-5193	188	17	λ	λ	PROPN
ejpam-5193	188	18	,	,	PUNCT
ejpam-5193	188	19	a	a	PRON
ejpam-5193	188	20	,	,	PUNCT
ejpam-5193	188	21	b	b	NOUN
ejpam-5193	188	22	)	)	PUNCT
ejpam-5193	188	23	tj	tj	PROPN
ejpam-5193	188	24	j	j	PROPN
ejpam-5193	188	25	!	!	PUNCT
ejpam-5193	188	26	vl	vl	PROPN
ejpam-5193	189	1	l	l	PROPN
ejpam-5193	189	2	!	!	PUNCT
ejpam-5193	189	3	.	.	PUNCT
ejpam-5193	190	1	thus	thus	ADV
ejpam-5193	190	2	,	,	PUNCT
ejpam-5193	190	3	by	by	ADP
ejpam-5193	190	4	using	use	VERB
ejpam-5193	190	5	(	(	PUNCT
ejpam-5193	190	6	3.4	3.4	NUM
ejpam-5193	190	7	)	)	PUNCT
ejpam-5193	190	8	again	again	ADV
ejpam-5193	190	9	,	,	PUNCT
ejpam-5193	190	10	we	we	PRON
ejpam-5193	190	11	have	have	VERB
ejpam-5193	190	12	∞∑	∞∑	NUM
ejpam-5193	190	13	j=0	j=0	PROPN
ejpam-5193	190	14	∞∑	∞∑	NUM
ejpam-5193	190	15	l=0	l=0	PROPN
ejpam-5193	190	16	bg	bg	NOUN
ejpam-5193	190	17	(	(	PUNCT
ejpam-5193	190	18	r	r	NOUN
ejpam-5193	190	19	)	)	PUNCT
ejpam-5193	190	20	j+l	j+l	PROPN
ejpam-5193	190	21	,	,	PUNCT
ejpam-5193	190	22	k(x	k(x	PROPN
ejpam-5193	190	23	,	,	PUNCT
ejpam-5193	190	24	y;u	y;u	PROPN
ejpam-5193	190	25	,	,	PUNCT
ejpam-5193	190	26	λ	λ	PROPN
ejpam-5193	190	27	,	,	PUNCT
ejpam-5193	190	28	a	a	PRON
ejpam-5193	190	29	,	,	PUNCT
ejpam-5193	190	30	b	b	NOUN
ejpam-5193	190	31	)	)	PUNCT
ejpam-5193	190	32	tj	tj	PROPN
ejpam-5193	190	33	j	j	PROPN
ejpam-5193	190	34	!	!	PUNCT
ejpam-5193	191	1	vl	vl	PROPN
ejpam-5193	192	1	l	l	NOUN
ejpam-5193	192	2	!	!	PUNCT
ejpam-5193	193	1	=	=	SYM
ejpam-5193	193	2	e(x−z)(t+v	e(x−z)(t+v	PROPN
ejpam-5193	193	3	)	)	PUNCT
ejpam-5193	193	4	∑	∑	PROPN
ejpam-5193	193	5	j	j	PROPN
ejpam-5193	193	6	,	,	PUNCT
ejpam-5193	193	7	l≥0	l≥0	PROPN
ejpam-5193	193	8	bg	bg	PROPN
ejpam-5193	193	9	(	(	PUNCT
ejpam-5193	193	10	r	r	NOUN
ejpam-5193	193	11	)	)	PUNCT
ejpam-5193	193	12	j+l	j+l	PROPN
ejpam-5193	193	13	,	,	PUNCT
ejpam-5193	193	14	k(z	k(z	PROPN
ejpam-5193	193	15	,	,	PUNCT
ejpam-5193	193	16	y;u	y;u	PROPN
ejpam-5193	193	17	,	,	PUNCT
ejpam-5193	193	18	λ	λ	PROPN
ejpam-5193	193	19	,	,	PUNCT
ejpam-5193	193	20	a	a	PRON
ejpam-5193	193	21	,	,	PUNCT
ejpam-5193	193	22	b	b	NOUN
ejpam-5193	193	23	)	)	PUNCT
ejpam-5193	193	24	tj	tj	PROPN
ejpam-5193	193	25	j	j	PROPN
ejpam-5193	193	26	!	!	PUNCT
ejpam-5193	194	1	vl	vl	PROPN
ejpam-5193	194	2	l	l	NOUN
ejpam-5193	194	3	!	!	PUNCT
ejpam-5193	195	1	=	=	PUNCT
ejpam-5193	195	2	(	(	PUNCT
ejpam-5193	195	3	∞∑	∞∑	NUM
ejpam-5193	195	4	n=0	n=0	NUM
ejpam-5193	195	5	(	(	PUNCT
ejpam-5193	195	6	x−	x−	PROPN
ejpam-5193	195	7	z)n	z)n	X
ejpam-5193	195	8	(	(	PUNCT
ejpam-5193	195	9	t+	t+	X
ejpam-5193	195	10	v)n	v)n	NOUN
ejpam-5193	195	11	n	n	X
ejpam-5193	195	12	!	!	PUNCT
ejpam-5193	195	13	)	)	PUNCT
ejpam-5193	196	1	∑	∑	NOUN
ejpam-5193	196	2	j	j	NOUN
ejpam-5193	196	3	,	,	PUNCT
ejpam-5193	196	4	l≥0	l≥0	PROPN
ejpam-5193	196	5	bg	bg	PROPN
ejpam-5193	196	6	(	(	PUNCT
ejpam-5193	196	7	r	r	NOUN
ejpam-5193	196	8	)	)	PUNCT
ejpam-5193	196	9	j+l	j+l	PROPN
ejpam-5193	196	10	,	,	PUNCT
ejpam-5193	196	11	k(z	k(z	PROPN
ejpam-5193	196	12	,	,	PUNCT
ejpam-5193	196	13	y;u	y;u	PROPN
ejpam-5193	196	14	,	,	PUNCT
ejpam-5193	196	15	λ	λ	PROPN
ejpam-5193	196	16	,	,	PUNCT
ejpam-5193	196	17	a	a	PRON
ejpam-5193	196	18	,	,	PUNCT
ejpam-5193	196	19	b	b	NOUN
ejpam-5193	196	20	)	)	PUNCT
ejpam-5193	196	21	tj	tj	PROPN
ejpam-5193	196	22	j	j	PROPN
ejpam-5193	196	23	!	!	PUNCT
ejpam-5193	197	1	vl	vl	PROPN
ejpam-5193	197	2	l	l	NOUN
ejpam-5193	197	3	!	!	PUNCT
ejpam-5193	198	1			PROPN
ejpam-5193	198	2	=	=	SYM
ejpam-5193	198	3			PROPN
ejpam-5193	198	4	∑	∑	PUNCT
ejpam-5193	198	5	n	n	CCONJ
ejpam-5193	198	6	,	,	PUNCT
ejpam-5193	198	7	m≥0	m≥0	PROPN
ejpam-5193	198	8	(	(	PUNCT
ejpam-5193	198	9	x−	x−	PROPN
ejpam-5193	198	10	z)n+m	z)n+m	PROPN
ejpam-5193	198	11	tn	tn	PROPN
ejpam-5193	198	12	n	n	PROPN
ejpam-5193	198	13	!	!	PUNCT
ejpam-5193	198	14	vm	vm	PROPN
ejpam-5193	198	15	m	m	PROPN
ejpam-5193	198	16	!	!	PUNCT
ejpam-5193	198	17	∑	∑	PROPN
ejpam-5193	199	1	j	j	NOUN
ejpam-5193	199	2	,	,	PUNCT
ejpam-5193	199	3	l≥0	l≥0	PROPN
ejpam-5193	199	4	bg	bg	PROPN
ejpam-5193	199	5	(	(	PUNCT
ejpam-5193	199	6	r	r	NOUN
ejpam-5193	199	7	)	)	PUNCT
ejpam-5193	199	8	j+l	j+l	PROPN
ejpam-5193	199	9	,	,	PUNCT
ejpam-5193	199	10	k(z	k(z	PROPN
ejpam-5193	199	11	,	,	PUNCT
ejpam-5193	199	12	y;u	y;u	PROPN
ejpam-5193	199	13	,	,	PUNCT
ejpam-5193	199	14	λ	λ	PROPN
ejpam-5193	199	15	,	,	PUNCT
ejpam-5193	199	16	a	a	PRON
ejpam-5193	199	17	,	,	PUNCT
ejpam-5193	199	18	b	b	NOUN
ejpam-5193	199	19	)	)	PUNCT
ejpam-5193	199	20	tj	tj	PROPN
ejpam-5193	199	21	j	j	PROPN
ejpam-5193	199	22	!	!	PUNCT
ejpam-5193	199	23	vl	vl	PROPN
ejpam-5193	200	1	l	l	NOUN
ejpam-5193	200	2	!	!	PUNCT
ejpam-5193	201	1			PROPN
ejpam-5193	201	2	=	=	SYM
ejpam-5193	201	3	∑	∑	PUNCT
ejpam-5193	201	4	j	j	PROPN
ejpam-5193	201	5	,	,	PUNCT
ejpam-5193	201	6	l≥0	l≥0	PROPN
ejpam-5193	201	7			PUNCT
ejpam-5193	201	8	j	j	PROPN
ejpam-5193	201	9	,	,	PUNCT
ejpam-5193	201	10	l∑	l∑	PROPN
ejpam-5193	201	11	n	n	CCONJ
ejpam-5193	201	12	,	,	PUNCT
ejpam-5193	201	13	m=0	m=0	PROPN
ejpam-5193	201	14	(	(	PUNCT
ejpam-5193	201	15	j	j	PROPN
ejpam-5193	201	16	n	n	CCONJ
ejpam-5193	201	17	)	)	PUNCT
ejpam-5193	201	18	(	(	PUNCT
ejpam-5193	201	19	l	l	NOUN
ejpam-5193	201	20	m	m	VERB
ejpam-5193	201	21	)	)	PUNCT
ejpam-5193	202	1	(	(	PUNCT
ejpam-5193	202	2	x−	x−	PROPN
ejpam-5193	202	3	z)n+m	z)n+m	PROPN
ejpam-5193	202	4	bg	bg	PROPN
ejpam-5193	202	5	(	(	PUNCT
ejpam-5193	202	6	r	r	NOUN
ejpam-5193	202	7	)	)	PUNCT
ejpam-5193	202	8	j+l	j+l	PROPN
ejpam-5193	202	9	,	,	PUNCT
ejpam-5193	202	10	k(z	k(z	PROPN
ejpam-5193	202	11	,	,	PUNCT
ejpam-5193	202	12	y;u	y;u	PROPN
ejpam-5193	202	13	,	,	PUNCT
ejpam-5193	202	14	λ	λ	PROPN
ejpam-5193	202	15	,	,	PUNCT
ejpam-5193	202	16	a	a	DET
ejpam-5193	202	17	,	,	PUNCT
ejpam-5193	202	18	b	b	NOUN
ejpam-5193	202	19	)	)	PUNCT
ejpam-5193	202	20			PROPN
ejpam-5193	202	21	tj	tj	PROPN
ejpam-5193	202	22	j	j	PROPN
ejpam-5193	202	23	!	!	PUNCT
ejpam-5193	202	24	vl	vl	PROPN
ejpam-5193	202	25	l	l	PROPN
ejpam-5193	202	26	!	!	PUNCT
ejpam-5193	202	27	.	.	PUNCT
ejpam-5193	203	1	comparing	compare	VERB
ejpam-5193	203	2	the	the	DET
ejpam-5193	203	3	coefficients	coefficient	NOUN
ejpam-5193	203	4	of	of	ADP
ejpam-5193	203	5	tj	tj	PROPN
ejpam-5193	203	6	j	j	PROPN
ejpam-5193	203	7	!	!	PUNCT
ejpam-5193	204	1	vl	vl	PROPN
ejpam-5193	204	2	l	l	PROPN
ejpam-5193	204	3	!	!	PROPN
ejpam-5193	204	4	completes	complete	VERB
ejpam-5193	204	5	the	the	DET
ejpam-5193	204	6	proof	proof	NOUN
ejpam-5193	204	7	of	of	ADP
ejpam-5193	204	8	the	the	DET
ejpam-5193	204	9	following	follow	VERB
ejpam-5193	204	10	theorem	theorem	VERB
ejpam-5193	204	11	.	.	PROPN
ejpam-5193	204	12	1481	1481	NUM
ejpam-5193	204	13	theorem	theorem	VERB
ejpam-5193	204	14	3.3	3.3	NUM
ejpam-5193	204	15	.	.	PUNCT
ejpam-5193	205	1	the	the	DET
ejpam-5193	205	2	bivariate	bivariate	ADJ
ejpam-5193	205	3	bell	bell	NOUN
ejpam-5193	205	4	-	-	PUNCT
ejpam-5193	205	5	based	base	VERB
ejpam-5193	205	6	apostol	apostol	NOUN
ejpam-5193	205	7	-	-	PUNCT
ejpam-5193	205	8	frobenius	frobenius	NOUN
ejpam-5193	205	9	-	-	PUNCT
ejpam-5193	205	10	type	type	NOUN
ejpam-5193	205	11	poly	poly	ADJ
ejpam-5193	205	12	-	-	PUNCT
ejpam-5193	205	13	genocchi	genocchi	NOUN
ejpam-5193	205	14	polynomials	polynomial	NOUN
ejpam-5193	205	15	of	of	ADP
ejpam-5193	205	16	higher	high	ADJ
ejpam-5193	205	17	order	order	NOUN
ejpam-5193	205	18	bg	bg	NOUN
ejpam-5193	205	19	(	(	PUNCT
ejpam-5193	205	20	r	r	NOUN
ejpam-5193	205	21	)	)	PUNCT
ejpam-5193	205	22	n	n	CCONJ
ejpam-5193	205	23	,	,	PUNCT
ejpam-5193	205	24	k(x	k(x	PROPN
ejpam-5193	205	25	,	,	PUNCT
ejpam-5193	205	26	y;u	y;u	PROPN
ejpam-5193	205	27	,	,	PUNCT
ejpam-5193	205	28	λ	λ	PROPN
ejpam-5193	205	29	,	,	PUNCT
ejpam-5193	205	30	a	a	DET
ejpam-5193	205	31	,	,	PUNCT
ejpam-5193	205	32	b	b	NOUN
ejpam-5193	205	33	)	)	PUNCT
ejpam-5193	205	34	satisfy	satisfy	VERB
ejpam-5193	205	35	the	the	DET
ejpam-5193	205	36	following	follow	VERB
ejpam-5193	205	37	summation	summation	NOUN
ejpam-5193	205	38	formula	formula	NOUN
ejpam-5193	205	39	:	:	PUNCT
ejpam-5193	205	40	bg	bg	PROPN
ejpam-5193	205	41	(	(	PUNCT
ejpam-5193	205	42	r	r	NOUN
ejpam-5193	205	43	)	)	PUNCT
ejpam-5193	205	44	j+l	j+l	PROPN
ejpam-5193	205	45	,	,	PUNCT
ejpam-5193	205	46	k(x	k(x	PROPN
ejpam-5193	205	47	,	,	PUNCT
ejpam-5193	205	48	y;u	y;u	PROPN
ejpam-5193	205	49	,	,	PUNCT
ejpam-5193	205	50	λ	λ	PROPN
ejpam-5193	205	51	,	,	PUNCT
ejpam-5193	205	52	a	a	DET
ejpam-5193	205	53	,	,	PUNCT
ejpam-5193	205	54	b	b	NOUN
ejpam-5193	205	55	)	)	PUNCT
ejpam-5193	205	56	=	=	SYM
ejpam-5193	205	57	j	j	PROPN
ejpam-5193	205	58	,	,	PUNCT
ejpam-5193	205	59	l∑	l∑	PROPN
ejpam-5193	205	60	n	n	CCONJ
ejpam-5193	205	61	,	,	PUNCT
ejpam-5193	205	62	m=0	m=0	PROPN
ejpam-5193	205	63	(	(	PUNCT
ejpam-5193	205	64	k	k	NOUN
ejpam-5193	205	65	n	n	PROPN
ejpam-5193	205	66	)	)	PUNCT
ejpam-5193	205	67	(	(	PUNCT
ejpam-5193	205	68	l	l	NOUN
ejpam-5193	205	69	m	m	VERB
ejpam-5193	205	70	)	)	PUNCT
ejpam-5193	205	71	(	(	PUNCT
ejpam-5193	205	72	x−	x−	PROPN
ejpam-5193	205	73	z)n+m	z)n+m	PROPN
ejpam-5193	205	74	bgk+l−n−m(z	bgk+l−n−m(z	PROPN
ejpam-5193	205	75	,	,	PUNCT
ejpam-5193	205	76	y;u	y;u	PROPN
ejpam-5193	205	77	,	,	PUNCT
ejpam-5193	205	78	λ	λ	PROPN
ejpam-5193	205	79	,	,	PUNCT
ejpam-5193	205	80	a	a	DET
ejpam-5193	205	81	,	,	PUNCT
ejpam-5193	205	82	b	b	NOUN
ejpam-5193	205	83	)	)	PUNCT
ejpam-5193	205	84	.	.	PUNCT
ejpam-5193	206	1	(	(	PUNCT
ejpam-5193	206	2	3.5	3.5	NUM
ejpam-5193	206	3	)	)	PUNCT
ejpam-5193	206	4	the	the	DET
ejpam-5193	206	5	next	next	ADJ
ejpam-5193	206	6	theorem	theorem	NOUN
ejpam-5193	206	7	gives	give	VERB
ejpam-5193	206	8	the	the	DET
ejpam-5193	206	9	difference	difference	NOUN
ejpam-5193	206	10	when	when	SCONJ
ejpam-5193	206	11	the	the	DET
ejpam-5193	206	12	variable	variable	NOUN
ejpam-5193	206	13	x	x	NOUN
ejpam-5193	206	14	in	in	ADP
ejpam-5193	206	15	bg	bg	PROPN
ejpam-5193	206	16	(	(	PUNCT
ejpam-5193	206	17	r	r	NOUN
ejpam-5193	206	18	)	)	PUNCT
ejpam-5193	206	19	n	n	CCONJ
ejpam-5193	206	20	,	,	PUNCT
ejpam-5193	206	21	k(x	k(x	PROPN
ejpam-5193	206	22	,	,	PUNCT
ejpam-5193	206	23	y;u	y;u	PROPN
ejpam-5193	206	24	,	,	PUNCT
ejpam-5193	206	25	λ	λ	PROPN
ejpam-5193	206	26	,	,	PUNCT
ejpam-5193	206	27	a	a	DET
ejpam-5193	206	28	,	,	PUNCT
ejpam-5193	206	29	b	b	NOUN
ejpam-5193	206	30	)	)	PUNCT
ejpam-5193	206	31	is	be	AUX
ejpam-5193	206	32	shifted	shift	VERB
ejpam-5193	206	33	by	by	ADP
ejpam-5193	206	34	1	1	NUM
ejpam-5193	206	35	.	.	PUNCT
ejpam-5193	206	36	theorem	theorem	VERB
ejpam-5193	206	37	3.4	3.4	NUM
ejpam-5193	206	38	.	.	PUNCT
ejpam-5193	207	1	for	for	ADP
ejpam-5193	207	2	n	n	PRON
ejpam-5193	207	3	≥	≥	NUM
ejpam-5193	207	4	1	1	NUM
ejpam-5193	207	5	,	,	PUNCT
ejpam-5193	207	6	the	the	DET
ejpam-5193	207	7	difference	difference	NOUN
ejpam-5193	207	8	bg	bg	PROPN
ejpam-5193	207	9	(	(	PUNCT
ejpam-5193	207	10	r	r	NOUN
ejpam-5193	207	11	)	)	PUNCT
ejpam-5193	207	12	n	n	CCONJ
ejpam-5193	207	13	,	,	PUNCT
ejpam-5193	207	14	k(x+1	k(x+1	PROPN
ejpam-5193	207	15	,	,	PUNCT
ejpam-5193	207	16	y;u	y;u	PROPN
ejpam-5193	207	17	,	,	PUNCT
ejpam-5193	207	18	λ)−bg	λ)−bg	X
ejpam-5193	207	19	(	(	PUNCT
ejpam-5193	207	20	r	r	NOUN
ejpam-5193	207	21	)	)	PUNCT
ejpam-5193	207	22	n	n	CCONJ
ejpam-5193	207	23	,	,	PUNCT
ejpam-5193	207	24	k(x	k(x	PROPN
ejpam-5193	207	25	,	,	PUNCT
ejpam-5193	207	26	y;u	y;u	PROPN
ejpam-5193	207	27	,	,	PUNCT
ejpam-5193	207	28	λ	λ	PROPN
ejpam-5193	207	29	,	,	PUNCT
ejpam-5193	207	30	a	a	DET
ejpam-5193	207	31	,	,	PUNCT
ejpam-5193	207	32	b	b	NOUN
ejpam-5193	207	33	)	)	PUNCT
ejpam-5193	207	34	equals	equal	VERB
ejpam-5193	207	35	bg	bg	PROPN
ejpam-5193	207	36	(	(	PUNCT
ejpam-5193	207	37	r	r	NOUN
ejpam-5193	207	38	)	)	PUNCT
ejpam-5193	207	39	n	n	CCONJ
ejpam-5193	207	40	,	,	PUNCT
ejpam-5193	207	41	k(x+	k(x+	PROPN
ejpam-5193	207	42	1	1	NUM
ejpam-5193	207	43	,	,	PUNCT
ejpam-5193	207	44	y;u	y;u	PROPN
ejpam-5193	207	45	,	,	PUNCT
ejpam-5193	207	46	λ	λ	PROPN
ejpam-5193	207	47	,	,	PUNCT
ejpam-5193	207	48	a	a	PRON
ejpam-5193	207	49	,	,	PUNCT
ejpam-5193	207	50	b)−	b)−	PROPN
ejpam-5193	207	51	bg	bg	PROPN
ejpam-5193	207	52	(	(	PUNCT
ejpam-5193	207	53	r	r	NOUN
ejpam-5193	207	54	)	)	PUNCT
ejpam-5193	207	55	n	n	CCONJ
ejpam-5193	207	56	,	,	PUNCT
ejpam-5193	207	57	k(x	k(x	PROPN
ejpam-5193	207	58	,	,	PUNCT
ejpam-5193	207	59	y;u	y;u	PROPN
ejpam-5193	207	60	,	,	PUNCT
ejpam-5193	207	61	λ	λ	PROPN
ejpam-5193	207	62	,	,	PUNCT
ejpam-5193	207	63	a	a	DET
ejpam-5193	207	64	,	,	PUNCT
ejpam-5193	207	65	b	b	NOUN
ejpam-5193	207	66	)	)	PUNCT
ejpam-5193	208	1	=	=	SYM
ejpam-5193	208	2	n−1∑	n−1∑	PROPN
ejpam-5193	208	3	j=0	j=0	PROPN
ejpam-5193	208	4	(	(	PUNCT
ejpam-5193	208	5	n	n	X
ejpam-5193	208	6	k	k	PROPN
ejpam-5193	208	7	)	)	PUNCT
ejpam-5193	208	8	bg	bg	PROPN
ejpam-5193	208	9	(	(	PUNCT
ejpam-5193	208	10	r	r	NOUN
ejpam-5193	208	11	)	)	PUNCT
ejpam-5193	208	12	j	j	PROPN
ejpam-5193	208	13	,	,	PUNCT
ejpam-5193	208	14	k(x	k(x	PROPN
ejpam-5193	208	15	,	,	PUNCT
ejpam-5193	208	16	y;u	y;u	PROPN
ejpam-5193	208	17	,	,	PUNCT
ejpam-5193	208	18	λ	λ	PROPN
ejpam-5193	208	19	,	,	PUNCT
ejpam-5193	208	20	a	a	DET
ejpam-5193	208	21	,	,	PUNCT
ejpam-5193	208	22	b	b	NOUN
ejpam-5193	208	23	)	)	PUNCT
ejpam-5193	208	24	.	.	PUNCT
ejpam-5193	209	1	(	(	PUNCT
ejpam-5193	209	2	3.6	3.6	NUM
ejpam-5193	209	3	)	)	PUNCT
ejpam-5193	209	4	proof	proof	NOUN
ejpam-5193	209	5	.	.	PUNCT
ejpam-5193	210	1	using	use	VERB
ejpam-5193	210	2	definition	definition	NOUN
ejpam-5193	210	3	2.1	2.1	NUM
ejpam-5193	210	4	,	,	PUNCT
ejpam-5193	210	5	we	we	PRON
ejpam-5193	210	6	have	have	VERB
ejpam-5193	210	7	∞∑	∞∑	NUM
ejpam-5193	210	8	n=0	n=0	ADJ
ejpam-5193	210	9	bg	bg	NOUN
ejpam-5193	210	10	(	(	PUNCT
ejpam-5193	210	11	r	r	NOUN
ejpam-5193	210	12	)	)	PUNCT
ejpam-5193	210	13	n	n	CCONJ
ejpam-5193	210	14	,	,	PUNCT
ejpam-5193	210	15	k(x+	k(x+	PROPN
ejpam-5193	210	16	1	1	NUM
ejpam-5193	210	17	,	,	PUNCT
ejpam-5193	210	18	y;u	y;u	PROPN
ejpam-5193	210	19	,	,	PUNCT
ejpam-5193	210	20	λ	λ	PROPN
ejpam-5193	210	21	,	,	PUNCT
ejpam-5193	210	22	a	a	DET
ejpam-5193	210	23	,	,	PUNCT
ejpam-5193	210	24	b	b	NOUN
ejpam-5193	210	25	)	)	PUNCT
ejpam-5193	210	26	tn	tn	PROPN
ejpam-5193	210	27	n	n	NOUN
ejpam-5193	210	28	!	!	PUNCT
ejpam-5193	211	1	−	−	PROPN
ejpam-5193	212	1	∞∑	∞∑	PRON
ejpam-5193	212	2	n=0	n=0	ADJ
ejpam-5193	212	3	bg	bg	NOUN
ejpam-5193	212	4	(	(	PUNCT
ejpam-5193	212	5	r	r	NOUN
ejpam-5193	212	6	)	)	PUNCT
ejpam-5193	212	7	n	n	CCONJ
ejpam-5193	212	8	,	,	PUNCT
ejpam-5193	212	9	k(x	k(x	PROPN
ejpam-5193	212	10	,	,	PUNCT
ejpam-5193	212	11	y;u	y;u	PROPN
ejpam-5193	212	12	,	,	PUNCT
ejpam-5193	212	13	λ	λ	PROPN
ejpam-5193	212	14	,	,	PUNCT
ejpam-5193	212	15	a	a	DET
ejpam-5193	212	16	,	,	PUNCT
ejpam-5193	212	17	b	b	NOUN
ejpam-5193	212	18	)	)	PUNCT
ejpam-5193	212	19	tn	tn	NOUN
ejpam-5193	212	20	n	n	CCONJ
ejpam-5193	212	21	!	!	PUNCT
ejpam-5193	212	22	=	=	PUNCT
ejpam-5193	213	1	(	(	PUNCT
ejpam-5193	213	2	lik(1−	lik(1−	X
ejpam-5193	213	3	(	(	PUNCT
ejpam-5193	213	4	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	213	5	)	)	PUNCT
ejpam-5193	213	6	λbt	λbt	VERB
ejpam-5193	213	7	−	−	PROPN
ejpam-5193	213	8	ua−t	ua−t	ADJ
ejpam-5193	213	9	)	)	PUNCT
ejpam-5193	213	10	r	r	NOUN
ejpam-5193	213	11	e(x+1)t+y(et−1	e(x+1)t+y(et−1	NOUN
ejpam-5193	213	12	)	)	PUNCT
ejpam-5193	213	13	−	−	PROPN
ejpam-5193	214	1	(	(	PUNCT
ejpam-5193	214	2	lik(1−	lik(1−	PROPN
ejpam-5193	214	3	(	(	PUNCT
ejpam-5193	214	4	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	214	5	)	)	PUNCT
ejpam-5193	214	6	λbt	λbt	VERB
ejpam-5193	214	7	−	−	PROPN
ejpam-5193	214	8	ua−t	ua−t	ADJ
ejpam-5193	214	9	)	)	PUNCT
ejpam-5193	214	10	r	r	NOUN
ejpam-5193	214	11	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	214	12	)	)	PUNCT
ejpam-5193	214	13	=	=	PRON
ejpam-5193	215	1	(	(	PUNCT
ejpam-5193	215	2	lik(1−	lik(1−	X
ejpam-5193	215	3	(	(	PUNCT
ejpam-5193	215	4	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	215	5	)	)	PUNCT
ejpam-5193	215	6	λbt	λbt	VERB
ejpam-5193	215	7	−	−	PROPN
ejpam-5193	215	8	ua−t	ua−t	ADJ
ejpam-5193	215	9	)	)	PUNCT
ejpam-5193	215	10	r	r	NOUN
ejpam-5193	215	11	ext+y(et−1)(et	ext+y(et−1)(et	NOUN
ejpam-5193	215	12	−	−	ADP
ejpam-5193	215	13	1	1	NUM
ejpam-5193	215	14	)	)	PUNCT
ejpam-5193	215	15	=	=	NOUN
ejpam-5193	215	16	(	(	PUNCT
ejpam-5193	215	17	∞∑	∞∑	PROPN
ejpam-5193	215	18	n=0	n=0	PROPN
ejpam-5193	215	19	bg	bg	NOUN
ejpam-5193	215	20	(	(	PUNCT
ejpam-5193	215	21	r	r	NOUN
ejpam-5193	215	22	)	)	PUNCT
ejpam-5193	215	23	n	n	CCONJ
ejpam-5193	215	24	,	,	PUNCT
ejpam-5193	215	25	k(x	k(x	PROPN
ejpam-5193	215	26	,	,	PUNCT
ejpam-5193	215	27	y;u	y;u	PROPN
ejpam-5193	215	28	,	,	PUNCT
ejpam-5193	215	29	λ	λ	PROPN
ejpam-5193	215	30	,	,	PUNCT
ejpam-5193	215	31	a	a	DET
ejpam-5193	215	32	,	,	PUNCT
ejpam-5193	215	33	b	b	NOUN
ejpam-5193	215	34	)	)	PUNCT
ejpam-5193	215	35	tn	tn	PROPN
ejpam-5193	216	1	n	n	PROPN
ejpam-5193	216	2	!	!	PUNCT
ejpam-5193	216	3	)	)	PUNCT
ejpam-5193	217	1	∑	∑	NOUN
ejpam-5193	217	2	n≥0	n≥0	PROPN
ejpam-5193	217	3	tn+1	tn+1	NOUN
ejpam-5193	217	4	(	(	PUNCT
ejpam-5193	217	5	n+	n+	NOUN
ejpam-5193	217	6	1	1	NUM
ejpam-5193	217	7	)	)	PUNCT
ejpam-5193	217	8	!	!	PUNCT
ejpam-5193	218	1			PROPN
ejpam-5193	219	1	=	=	PUNCT
ejpam-5193	220	1	∞∑	∞∑	NUM
ejpam-5193	220	2	n=0	n=0	NUM
ejpam-5193	220	3			PUNCT
ejpam-5193	220	4	n∑	n∑	NOUN
ejpam-5193	220	5	j=0	j=0	PROPN
ejpam-5193	220	6	(	(	PUNCT
ejpam-5193	220	7	n+	n+	NUM
ejpam-5193	220	8	1	1	NUM
ejpam-5193	220	9	j	j	NOUN
ejpam-5193	220	10	)	)	PUNCT
ejpam-5193	220	11	bg	bg	PROPN
ejpam-5193	220	12	(	(	PUNCT
ejpam-5193	220	13	r	r	NOUN
ejpam-5193	220	14	)	)	PUNCT
ejpam-5193	220	15	j	j	PROPN
ejpam-5193	220	16	,	,	PUNCT
ejpam-5193	220	17	k(x	k(x	PROPN
ejpam-5193	220	18	,	,	PUNCT
ejpam-5193	220	19	y;u	y;u	PROPN
ejpam-5193	220	20	,	,	PUNCT
ejpam-5193	220	21	λ	λ	PROPN
ejpam-5193	220	22	,	,	PUNCT
ejpam-5193	220	23	a	a	DET
ejpam-5193	220	24	,	,	PUNCT
ejpam-5193	220	25	b	b	NOUN
ejpam-5193	220	26	)	)	PUNCT
ejpam-5193	220	27			PROPN
ejpam-5193	220	28	tn	tn	PROPN
ejpam-5193	220	29	n	n	CCONJ
ejpam-5193	220	30	!	!	PUNCT
ejpam-5193	220	31	.	.	PUNCT
ejpam-5193	221	1	thus	thus	ADV
ejpam-5193	221	2	,	,	PUNCT
ejpam-5193	221	3	we	we	PRON
ejpam-5193	221	4	have	have	VERB
ejpam-5193	221	5	∞∑	∞∑	NUM
ejpam-5193	221	6	n=0	n=0	NUM
ejpam-5193	221	7	(	(	PUNCT
ejpam-5193	221	8	bg	bg	PROPN
ejpam-5193	221	9	(	(	PUNCT
ejpam-5193	221	10	r	r	NOUN
ejpam-5193	221	11	)	)	PUNCT
ejpam-5193	221	12	n	n	CCONJ
ejpam-5193	221	13	,	,	PUNCT
ejpam-5193	221	14	k(x+	k(x+	PROPN
ejpam-5193	221	15	1	1	NUM
ejpam-5193	221	16	,	,	PUNCT
ejpam-5193	221	17	y;u	y;u	PROPN
ejpam-5193	221	18	,	,	PUNCT
ejpam-5193	221	19	λ	λ	PROPN
ejpam-5193	221	20	,	,	PUNCT
ejpam-5193	221	21	a	a	PRON
ejpam-5193	221	22	,	,	PUNCT
ejpam-5193	221	23	b)−	b)−	PROPN
ejpam-5193	221	24	bg	bg	PROPN
ejpam-5193	221	25	(	(	PUNCT
ejpam-5193	221	26	r	r	NOUN
ejpam-5193	221	27	)	)	PUNCT
ejpam-5193	221	28	n	n	CCONJ
ejpam-5193	221	29	,	,	PUNCT
ejpam-5193	221	30	k(x	k(x	PROPN
ejpam-5193	221	31	,	,	PUNCT
ejpam-5193	221	32	y;u	y;u	PROPN
ejpam-5193	221	33	,	,	PUNCT
ejpam-5193	221	34	λ	λ	PROPN
ejpam-5193	221	35	,	,	PUNCT
ejpam-5193	221	36	a	a	DET
ejpam-5193	221	37	,	,	PUNCT
ejpam-5193	221	38	b	b	NOUN
ejpam-5193	221	39	)	)	PUNCT
ejpam-5193	221	40	)	)	PUNCT
ejpam-5193	221	41	tn	tn	PROPN
ejpam-5193	221	42	n	n	CCONJ
ejpam-5193	221	43	!	!	PUNCT
ejpam-5193	221	44	=	=	PUNCT
ejpam-5193	222	1	∞∑	∞∑	PRON
ejpam-5193	222	2	n=0	n=0	NUM
ejpam-5193	222	3			PUNCT
ejpam-5193	222	4	n∑	n∑	NOUN
ejpam-5193	222	5	j=0	j=0	PROPN
ejpam-5193	222	6	(	(	PUNCT
ejpam-5193	222	7	n+	n+	NUM
ejpam-5193	222	8	1	1	NUM
ejpam-5193	222	9	j	j	NOUN
ejpam-5193	222	10	)	)	PUNCT
ejpam-5193	222	11	bg	bg	PROPN
ejpam-5193	222	12	(	(	PUNCT
ejpam-5193	222	13	r	r	NOUN
ejpam-5193	222	14	)	)	PUNCT
ejpam-5193	222	15	j	j	PROPN
ejpam-5193	222	16	,	,	PUNCT
ejpam-5193	222	17	k(x	k(x	PROPN
ejpam-5193	222	18	,	,	PUNCT
ejpam-5193	222	19	y;u	y;u	PROPN
ejpam-5193	222	20	,	,	PUNCT
ejpam-5193	222	21	λ	λ	PROPN
ejpam-5193	222	22	,	,	PUNCT
ejpam-5193	222	23	a	a	DET
ejpam-5193	222	24	,	,	PUNCT
ejpam-5193	222	25	b	b	NOUN
ejpam-5193	222	26	)	)	PUNCT
ejpam-5193	222	27			NOUN
ejpam-5193	222	28	tn+1	tn+1	NOUN
ejpam-5193	222	29	(	(	PUNCT
ejpam-5193	222	30	n+	n+	NOUN
ejpam-5193	222	31	1	1	NUM
ejpam-5193	222	32	)	)	PUNCT
ejpam-5193	222	33	!	!	PUNCT
ejpam-5193	223	1	=	=	PUNCT
ejpam-5193	224	1	∞∑	∞∑	NUM
ejpam-5193	224	2	n=1	n=1	PUNCT
ejpam-5193	224	3			PUNCT
ejpam-5193	224	4	n−1∑	n−1∑	PROPN
ejpam-5193	224	5	j=0	j=0	PROPN
ejpam-5193	224	6	(	(	PUNCT
ejpam-5193	224	7	n	n	X
ejpam-5193	224	8	j	j	PROPN
ejpam-5193	224	9	)	)	PUNCT
ejpam-5193	224	10	bg	bg	PROPN
ejpam-5193	224	11	(	(	PUNCT
ejpam-5193	224	12	r	r	NOUN
ejpam-5193	224	13	)	)	PUNCT
ejpam-5193	224	14	j	j	PROPN
ejpam-5193	224	15	,	,	PUNCT
ejpam-5193	224	16	k(x	k(x	PROPN
ejpam-5193	224	17	,	,	PUNCT
ejpam-5193	224	18	y;u	y;u	PROPN
ejpam-5193	224	19	,	,	PUNCT
ejpam-5193	224	20	λ	λ	PROPN
ejpam-5193	224	21	,	,	PUNCT
ejpam-5193	224	22	a	a	DET
ejpam-5193	224	23	,	,	PUNCT
ejpam-5193	224	24	b	b	NOUN
ejpam-5193	224	25	)	)	PUNCT
ejpam-5193	224	26			PROPN
ejpam-5193	224	27	tn	tn	NOUN
ejpam-5193	224	28	n	n	CCONJ
ejpam-5193	224	29	!	!	PUNCT
ejpam-5193	224	30	.	.	PUNCT
ejpam-5193	225	1	this	this	PRON
ejpam-5193	225	2	immediately	immediately	ADV
ejpam-5193	225	3	gives	give	VERB
ejpam-5193	225	4	bg	bg	PROPN
ejpam-5193	225	5	(	(	PUNCT
ejpam-5193	225	6	r	r	NOUN
ejpam-5193	225	7	)	)	PUNCT
ejpam-5193	225	8	n	n	CCONJ
ejpam-5193	225	9	,	,	PUNCT
ejpam-5193	225	10	k(x+	k(x+	PROPN
ejpam-5193	225	11	1	1	NUM
ejpam-5193	225	12	,	,	PUNCT
ejpam-5193	225	13	y;u	y;u	PROPN
ejpam-5193	225	14	,	,	PUNCT
ejpam-5193	225	15	λ	λ	PROPN
ejpam-5193	225	16	,	,	PUNCT
ejpam-5193	225	17	a	a	PRON
ejpam-5193	225	18	,	,	PUNCT
ejpam-5193	225	19	b)−	b)−	PROPN
ejpam-5193	225	20	bg	bg	PROPN
ejpam-5193	225	21	(	(	PUNCT
ejpam-5193	225	22	r	r	NOUN
ejpam-5193	225	23	)	)	PUNCT
ejpam-5193	225	24	n	n	CCONJ
ejpam-5193	225	25	,	,	PUNCT
ejpam-5193	225	26	k(x	k(x	PROPN
ejpam-5193	225	27	,	,	PUNCT
ejpam-5193	225	28	y;u	y;u	PROPN
ejpam-5193	225	29	,	,	PUNCT
ejpam-5193	225	30	λ	λ	PROPN
ejpam-5193	225	31	,	,	PUNCT
ejpam-5193	225	32	a	a	DET
ejpam-5193	225	33	,	,	PUNCT
ejpam-5193	225	34	b	b	NOUN
ejpam-5193	225	35	)	)	PUNCT
ejpam-5193	225	36	=	=	SYM
ejpam-5193	226	1	n−1∑	n−1∑	PROPN
ejpam-5193	226	2	j=0	j=0	PROPN
ejpam-5193	226	3	(	(	PUNCT
ejpam-5193	226	4	n	n	X
ejpam-5193	226	5	j	j	PROPN
ejpam-5193	226	6	)	)	PUNCT
ejpam-5193	226	7	bg	bg	PROPN
ejpam-5193	226	8	(	(	PUNCT
ejpam-5193	226	9	r	r	NOUN
ejpam-5193	226	10	)	)	PUNCT
ejpam-5193	226	11	j	j	PROPN
ejpam-5193	226	12	,	,	PUNCT
ejpam-5193	226	13	k(x	k(x	PROPN
ejpam-5193	226	14	,	,	PUNCT
ejpam-5193	226	15	y;u	y;u	PROPN
ejpam-5193	226	16	,	,	PUNCT
ejpam-5193	226	17	λ	λ	PROPN
ejpam-5193	226	18	,	,	PUNCT
ejpam-5193	226	19	a	a	DET
ejpam-5193	226	20	,	,	PUNCT
ejpam-5193	226	21	b	b	NOUN
ejpam-5193	226	22	)	)	PUNCT
ejpam-5193	226	23	.	.	PUNCT
ejpam-5193	227	1	1482	1482	NUM
ejpam-5193	228	1	4	4	X
ejpam-5193	228	2	.	.	PUNCT
ejpam-5193	228	3	connection	connection	NOUN
ejpam-5193	228	4	with	with	ADP
ejpam-5193	228	5	second	second	ADJ
ejpam-5193	228	6	kind	kind	ADJ
ejpam-5193	228	7	stirling	stirling	NOUN
ejpam-5193	228	8	numbers	number	NOUN
ejpam-5193	228	9	and	and	CCONJ
ejpam-5193	228	10	bivariate	bivariate	ADJ
ejpam-5193	228	11	bell	bell	NOUN
ejpam-5193	228	12	polynomials	polynomial	NOUN
ejpam-5193	228	13	in	in	ADP
ejpam-5193	228	14	this	this	DET
ejpam-5193	228	15	section	section	NOUN
ejpam-5193	228	16	,	,	PUNCT
ejpam-5193	228	17	we	we	PRON
ejpam-5193	228	18	derive	derive	VERB
ejpam-5193	228	19	some	some	DET
ejpam-5193	228	20	formulas	formula	NOUN
ejpam-5193	228	21	connecting	connect	VERB
ejpam-5193	228	22	bg	bg	PROPN
ejpam-5193	228	23	(	(	PUNCT
ejpam-5193	228	24	r	r	NOUN
ejpam-5193	228	25	)	)	PUNCT
ejpam-5193	228	26	n	n	NOUN
ejpam-5193	228	27	(	(	PUNCT
ejpam-5193	228	28	x	x	X
ejpam-5193	228	29	,	,	PUNCT
ejpam-5193	228	30	y;u	y;u	PROPN
ejpam-5193	228	31	,	,	PUNCT
ejpam-5193	228	32	λ	λ	PROPN
ejpam-5193	228	33	)	)	PUNCT
ejpam-5193	228	34	with	with	ADP
ejpam-5193	228	35	stirling	stirling	NOUN
ejpam-5193	228	36	numbers	number	NOUN
ejpam-5193	228	37	of	of	ADP
ejpam-5193	228	38	the	the	DET
ejpam-5193	228	39	second	second	ADJ
ejpam-5193	228	40	kind	kind	NOUN
ejpam-5193	228	41	given	give	VERB
ejpam-5193	228	42	in	in	ADP
ejpam-5193	228	43	(	(	PUNCT
ejpam-5193	228	44	1.15	1.15	NUM
ejpam-5193	228	45	)	)	PUNCT
ejpam-5193	228	46	and	and	CCONJ
ejpam-5193	228	47	bivariate	bivariate	ADJ
ejpam-5193	228	48	bell	bell	NOUN
ejpam-5193	228	49	polynomials	polynomial	NOUN
ejpam-5193	228	50	in	in	ADP
ejpam-5193	228	51	(	(	PUNCT
ejpam-5193	228	52	2.6	2.6	NUM
ejpam-5193	228	53	)	)	PUNCT
ejpam-5193	228	54	.	.	PUNCT
ejpam-5193	229	1	theorem	theorem	VERB
ejpam-5193	229	2	4.1	4.1	NUM
ejpam-5193	229	3	.	.	PUNCT
ejpam-5193	230	1	the	the	DET
ejpam-5193	230	2	bivariate	bivariate	ADJ
ejpam-5193	230	3	bell	bell	NOUN
ejpam-5193	230	4	-	-	PUNCT
ejpam-5193	230	5	based	base	VERB
ejpam-5193	230	6	apostol	apostol	NOUN
ejpam-5193	230	7	-	-	PUNCT
ejpam-5193	230	8	frobenius	frobenius	NOUN
ejpam-5193	230	9	-	-	PUNCT
ejpam-5193	230	10	type	type	NOUN
ejpam-5193	230	11	poly	poly	ADJ
ejpam-5193	230	12	-	-	PUNCT
ejpam-5193	230	13	genocchi	genocchi	NOUN
ejpam-5193	230	14	polynomials	polynomial	NOUN
ejpam-5193	230	15	of	of	ADP
ejpam-5193	230	16	higher	high	ADJ
ejpam-5193	230	17	order	order	NOUN
ejpam-5193	230	18	bg	bg	NOUN
ejpam-5193	230	19	(	(	PUNCT
ejpam-5193	230	20	r	r	NOUN
ejpam-5193	230	21	)	)	PUNCT
ejpam-5193	230	22	n	n	NOUN
ejpam-5193	230	23	(	(	PUNCT
ejpam-5193	230	24	x	x	X
ejpam-5193	230	25	,	,	PUNCT
ejpam-5193	230	26	y;u	y;u	PROPN
ejpam-5193	230	27	,	,	PUNCT
ejpam-5193	230	28	λ	λ	NOUN
ejpam-5193	230	29	)	)	PUNCT
ejpam-5193	230	30	satisfy	satisfy	VERB
ejpam-5193	230	31	the	the	DET
ejpam-5193	230	32	following	follow	VERB
ejpam-5193	230	33	summation	summation	NOUN
ejpam-5193	230	34	formula	formula	NOUN
ejpam-5193	230	35	bg	bg	PROPN
ejpam-5193	230	36	(	(	PUNCT
ejpam-5193	230	37	r	r	NOUN
ejpam-5193	230	38	)	)	PUNCT
ejpam-5193	230	39	n	n	CCONJ
ejpam-5193	230	40	,	,	PUNCT
ejpam-5193	230	41	k(x	k(x	PROPN
ejpam-5193	230	42	,	,	PUNCT
ejpam-5193	230	43	y;u	y;u	PROPN
ejpam-5193	230	44	,	,	PUNCT
ejpam-5193	230	45	λ	λ	PROPN
ejpam-5193	230	46	)	)	PUNCT
ejpam-5193	230	47	=	=	SYM
ejpam-5193	230	48	n∑	n∑	PROPN
ejpam-5193	230	49	i=0	i=0	PROPN
ejpam-5193	230	50	i∑	i∑	PROPN
ejpam-5193	230	51	j=0	j=0	PROPN
ejpam-5193	230	52	(	(	PUNCT
ejpam-5193	230	53	n	n	NOUN
ejpam-5193	230	54	i	i	PRON
ejpam-5193	230	55	)	)	PUNCT
ejpam-5193	230	56	(	(	PUNCT
ejpam-5193	230	57	x)js(i	x)js(i	ADV
ejpam-5193	230	58	,	,	PUNCT
ejpam-5193	230	59	j)bg	j)bg	PROPN
ejpam-5193	230	60	(	(	PUNCT
ejpam-5193	230	61	r	r	NOUN
ejpam-5193	230	62	)	)	PUNCT
ejpam-5193	230	63	n−i	n−i	NOUN
ejpam-5193	230	64	,	,	PUNCT
ejpam-5193	230	65	k(y;u	k(y;u	PROPN
ejpam-5193	230	66	,	,	PUNCT
ejpam-5193	230	67	λ	λ	NOUN
ejpam-5193	230	68	)	)	PUNCT
ejpam-5193	230	69	.	.	PUNCT
ejpam-5193	231	1	(	(	PUNCT
ejpam-5193	231	2	4.1	4.1	NUM
ejpam-5193	231	3	)	)	PUNCT
ejpam-5193	231	4	proof	proof	NOUN
ejpam-5193	231	5	.	.	PUNCT
ejpam-5193	232	1	using	use	VERB
ejpam-5193	232	2	definition	definition	NOUN
ejpam-5193	232	3	2.1	2.1	NUM
ejpam-5193	232	4	,	,	PUNCT
ejpam-5193	232	5	we	we	PRON
ejpam-5193	232	6	have	have	VERB
ejpam-5193	232	7	∞∑	∞∑	NUM
ejpam-5193	232	8	n=0	n=0	ADJ
ejpam-5193	232	9	bg	bg	NOUN
ejpam-5193	232	10	(	(	PUNCT
ejpam-5193	232	11	r	r	NOUN
ejpam-5193	232	12	)	)	PUNCT
ejpam-5193	232	13	n	n	CCONJ
ejpam-5193	232	14	,	,	PUNCT
ejpam-5193	232	15	k(x	k(x	PROPN
ejpam-5193	232	16	,	,	PUNCT
ejpam-5193	232	17	y;u	y;u	PROPN
ejpam-5193	232	18	,	,	PUNCT
ejpam-5193	232	19	λ	λ	PROPN
ejpam-5193	232	20	,	,	PUNCT
ejpam-5193	232	21	a	a	DET
ejpam-5193	232	22	,	,	PUNCT
ejpam-5193	232	23	b	b	NOUN
ejpam-5193	232	24	)	)	PUNCT
ejpam-5193	232	25	tn	tn	NOUN
ejpam-5193	232	26	n	n	CCONJ
ejpam-5193	232	27	!	!	PUNCT
ejpam-5193	233	1	=	=	PUNCT
ejpam-5193	233	2	(	(	PUNCT
ejpam-5193	233	3	lik(1−	lik(1−	X
ejpam-5193	233	4	(	(	PUNCT
ejpam-5193	233	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	233	6	)	)	PUNCT
ejpam-5193	233	7	λbt	λbt	VERB
ejpam-5193	233	8	−	−	PROPN
ejpam-5193	233	9	ua−t	ua−t	ADJ
ejpam-5193	233	10	)	)	PUNCT
ejpam-5193	233	11	r	r	NOUN
ejpam-5193	233	12	ey(e	ey(e	PUNCT
ejpam-5193	233	13	t−1)(1	t−1)(1	PROPN
ejpam-5193	234	1	+	+	CCONJ
ejpam-5193	234	2	et	et	NOUN
ejpam-5193	234	3	−	−	NOUN
ejpam-5193	234	4	1)x	1)x	NUM
ejpam-5193	234	5	=	=	SYM
ejpam-5193	234	6	(	(	PUNCT
ejpam-5193	234	7	∞∑	∞∑	PROPN
ejpam-5193	234	8	n=0	n=0	PROPN
ejpam-5193	234	9	bg	bg	NOUN
ejpam-5193	234	10	(	(	PUNCT
ejpam-5193	234	11	r	r	NOUN
ejpam-5193	234	12	)	)	PUNCT
ejpam-5193	234	13	n	n	CCONJ
ejpam-5193	234	14	,	,	PUNCT
ejpam-5193	234	15	k(y;u	k(y;u	PROPN
ejpam-5193	234	16	,	,	PUNCT
ejpam-5193	234	17	λ	λ	PROPN
ejpam-5193	234	18	,	,	PUNCT
ejpam-5193	234	19	a	a	DET
ejpam-5193	234	20	,	,	PUNCT
ejpam-5193	234	21	b	b	NOUN
ejpam-5193	234	22	)	)	PUNCT
ejpam-5193	234	23	tn	tn	PROPN
ejpam-5193	234	24	n	n	PROPN
ejpam-5193	234	25	!	!	PUNCT
ejpam-5193	234	26	)	)	PUNCT
ejpam-5193	235	1			PROPN
ejpam-5193	235	2	∞∑	∞∑	NUM
ejpam-5193	235	3	j=0	j=0	PROPN
ejpam-5193	235	4	(	(	PUNCT
ejpam-5193	235	5	x	x	NOUN
ejpam-5193	235	6	n	n	X
ejpam-5193	235	7	)	)	PUNCT
ejpam-5193	235	8	(	(	PUNCT
ejpam-5193	235	9	et	et	X
ejpam-5193	235	10	−	−	PROPN
ejpam-5193	235	11	1)n	1)n	X
ejpam-5193	235	12			PROPN
ejpam-5193	235	13	=	=	PUNCT
ejpam-5193	235	14	(	(	PUNCT
ejpam-5193	235	15	∞∑	∞∑	PROPN
ejpam-5193	235	16	n=0	n=0	PROPN
ejpam-5193	235	17	bg	bg	NOUN
ejpam-5193	235	18	(	(	PUNCT
ejpam-5193	235	19	r	r	NOUN
ejpam-5193	235	20	)	)	PUNCT
ejpam-5193	235	21	n	n	CCONJ
ejpam-5193	235	22	,	,	PUNCT
ejpam-5193	235	23	k(y;u	k(y;u	PROPN
ejpam-5193	235	24	,	,	PUNCT
ejpam-5193	235	25	λ	λ	PROPN
ejpam-5193	235	26	,	,	PUNCT
ejpam-5193	235	27	a	a	DET
ejpam-5193	235	28	,	,	PUNCT
ejpam-5193	235	29	b	b	NOUN
ejpam-5193	235	30	)	)	PUNCT
ejpam-5193	235	31	tn	tn	PROPN
ejpam-5193	235	32	n	n	PROPN
ejpam-5193	235	33	!	!	PUNCT
ejpam-5193	235	34	)	)	PUNCT
ejpam-5193	236	1			PROPN
ejpam-5193	236	2	∞∑	∞∑	NUM
ejpam-5193	236	3	j=0	j=0	PROPN
ejpam-5193	236	4	(	(	PUNCT
ejpam-5193	236	5	x)j	x)j	X
ejpam-5193	236	6	(	(	PUNCT
ejpam-5193	236	7	et	et	NOUN
ejpam-5193	236	8	−	−	PROPN
ejpam-5193	236	9	1)j	1)j	NUM
ejpam-5193	236	10	j	j	PROPN
ejpam-5193	236	11	!	!	PUNCT
ejpam-5193	237	1			PROPN
ejpam-5193	238	1	=	=	PUNCT
ejpam-5193	239	1	(	(	PUNCT
ejpam-5193	239	2	∞∑	∞∑	PROPN
ejpam-5193	239	3	n=0	n=0	PROPN
ejpam-5193	239	4	bg	bg	NOUN
ejpam-5193	239	5	(	(	PUNCT
ejpam-5193	239	6	r	r	NOUN
ejpam-5193	239	7	)	)	PUNCT
ejpam-5193	239	8	n	n	CCONJ
ejpam-5193	239	9	,	,	PUNCT
ejpam-5193	239	10	k(y;u	k(y;u	PROPN
ejpam-5193	239	11	,	,	PUNCT
ejpam-5193	239	12	λ	λ	PROPN
ejpam-5193	239	13	,	,	PUNCT
ejpam-5193	239	14	a	a	DET
ejpam-5193	239	15	,	,	PUNCT
ejpam-5193	239	16	b	b	NOUN
ejpam-5193	239	17	)	)	PUNCT
ejpam-5193	239	18	tn	tn	PROPN
ejpam-5193	239	19	n	n	PROPN
ejpam-5193	239	20	!	!	PUNCT
ejpam-5193	239	21	)	)	PUNCT
ejpam-5193	240	1			PROPN
ejpam-5193	240	2	∞∑	∞∑	NUM
ejpam-5193	240	3	j=0	j=0	PROPN
ejpam-5193	240	4	(	(	PUNCT
ejpam-5193	240	5	x)j	x)j	X
ejpam-5193	240	6	∞∑	∞∑	NUM
ejpam-5193	240	7	n=0	n=0	PUNCT
ejpam-5193	240	8	s(n	s(n	PROPN
ejpam-5193	240	9	,	,	PUNCT
ejpam-5193	240	10	j	j	NOUN
ejpam-5193	240	11	)	)	PUNCT
ejpam-5193	240	12	tn	tn	PROPN
ejpam-5193	240	13	n	n	NOUN
ejpam-5193	240	14	!	!	PUNCT
ejpam-5193	241	1			PROPN
ejpam-5193	241	2	=	=	PUNCT
ejpam-5193	242	1	(	(	PUNCT
ejpam-5193	242	2	∞∑	∞∑	PROPN
ejpam-5193	242	3	n=0	n=0	PROPN
ejpam-5193	242	4	bg	bg	NOUN
ejpam-5193	242	5	(	(	PUNCT
ejpam-5193	242	6	r	r	NOUN
ejpam-5193	242	7	)	)	PUNCT
ejpam-5193	242	8	n	n	CCONJ
ejpam-5193	242	9	,	,	PUNCT
ejpam-5193	242	10	k(y;u	k(y;u	PROPN
ejpam-5193	242	11	,	,	PUNCT
ejpam-5193	242	12	λ	λ	PROPN
ejpam-5193	242	13	,	,	PUNCT
ejpam-5193	242	14	a	a	DET
ejpam-5193	242	15	,	,	PUNCT
ejpam-5193	242	16	b	b	NOUN
ejpam-5193	242	17	)	)	PUNCT
ejpam-5193	242	18	tn	tn	PROPN
ejpam-5193	242	19	n	n	PROPN
ejpam-5193	242	20	!	!	PUNCT
ejpam-5193	242	21	)	)	PUNCT
ejpam-5193	243	1			PROPN
ejpam-5193	243	2	∞∑	∞∑	PROPN
ejpam-5193	243	3	n=0	n=0	NUM
ejpam-5193	243	4			PUNCT
ejpam-5193	243	5	∞∑	∞∑	NUM
ejpam-5193	243	6	j=0	j=0	PROPN
ejpam-5193	243	7	(	(	PUNCT
ejpam-5193	243	8	x)js(n	x)js(n	PROPN
ejpam-5193	243	9	,	,	PUNCT
ejpam-5193	243	10	j	j	NOUN
ejpam-5193	243	11	)	)	PUNCT
ejpam-5193	243	12			PROPN
ejpam-5193	243	13	tn	tn	NOUN
ejpam-5193	243	14	n	n	ADV
ejpam-5193	243	15	!	!	PUNCT
ejpam-5193	244	1			PROPN
ejpam-5193	244	2	=	=	PUNCT
ejpam-5193	245	1	∞∑	∞∑	NUM
ejpam-5193	245	2	n=0	n=0	NUM
ejpam-5193	245	3	n∑	n∑	NOUN
ejpam-5193	245	4	i=0	i=0	PROPN
ejpam-5193	245	5	(	(	PUNCT
ejpam-5193	245	6	n	n	NOUN
ejpam-5193	245	7	i	i	PRON
ejpam-5193	245	8	)	)	PUNCT
ejpam-5193	245	9			PUNCT
ejpam-5193	245	10	∞∑	∞∑	NUM
ejpam-5193	245	11	j=0	j=0	PROPN
ejpam-5193	245	12	(	(	PUNCT
ejpam-5193	245	13	x)js(i	x)js(i	NUM
ejpam-5193	245	14	,	,	PUNCT
ejpam-5193	245	15	j)bg	j)bg	PROPN
ejpam-5193	245	16	(	(	PUNCT
ejpam-5193	245	17	r	r	NOUN
ejpam-5193	245	18	)	)	PUNCT
ejpam-5193	245	19	n−i	n−i	NOUN
ejpam-5193	245	20	,	,	PUNCT
ejpam-5193	245	21	k(y;u	k(y;u	PROPN
ejpam-5193	245	22	,	,	PUNCT
ejpam-5193	245	23	λ	λ	PROPN
ejpam-5193	245	24	,	,	PUNCT
ejpam-5193	245	25	a	a	DET
ejpam-5193	245	26	,	,	PUNCT
ejpam-5193	245	27	b	b	NOUN
ejpam-5193	245	28	)	)	PUNCT
ejpam-5193	245	29			PROPN
ejpam-5193	245	30	tn	tn	NOUN
ejpam-5193	245	31	n	n	CCONJ
ejpam-5193	245	32	!	!	PUNCT
ejpam-5193	245	33	=	=	PUNCT
ejpam-5193	246	1	∞∑	∞∑	PRON
ejpam-5193	246	2	n=0	n=0	NUM
ejpam-5193	246	3			PUNCT
ejpam-5193	246	4	n∑	n∑	PROPN
ejpam-5193	246	5	i=0	i=0	PROPN
ejpam-5193	246	6	(	(	PUNCT
ejpam-5193	246	7	n	n	X
ejpam-5193	246	8	i	i	PRON
ejpam-5193	246	9	)	)	PUNCT
ejpam-5193	247	1	∞∑	∞∑	NUM
ejpam-5193	247	2	j=0	j=0	PROPN
ejpam-5193	247	3	(	(	PUNCT
ejpam-5193	247	4	x)js(i	x)js(i	NUM
ejpam-5193	247	5	,	,	PUNCT
ejpam-5193	247	6	j)bg	j)bg	PROPN
ejpam-5193	247	7	(	(	PUNCT
ejpam-5193	247	8	r	r	NOUN
ejpam-5193	247	9	)	)	PUNCT
ejpam-5193	247	10	n−i	n−i	NOUN
ejpam-5193	247	11	,	,	PUNCT
ejpam-5193	247	12	k(y;u	k(y;u	PROPN
ejpam-5193	247	13	,	,	PUNCT
ejpam-5193	247	14	λ	λ	PROPN
ejpam-5193	247	15	,	,	PUNCT
ejpam-5193	247	16	a	a	DET
ejpam-5193	247	17	,	,	PUNCT
ejpam-5193	247	18	b	b	NOUN
ejpam-5193	247	19	)	)	PUNCT
ejpam-5193	247	20			PROPN
ejpam-5193	247	21	tn	tn	PROPN
ejpam-5193	247	22	n	n	PROPN
ejpam-5193	247	23	!	!	PUNCT
ejpam-5193	247	24	bg	bg	PROPN
ejpam-5193	247	25	(	(	PUNCT
ejpam-5193	247	26	r	r	NOUN
ejpam-5193	247	27	)	)	PUNCT
ejpam-5193	247	28	n	n	CCONJ
ejpam-5193	247	29	,	,	PUNCT
ejpam-5193	247	30	k(x	k(x	PROPN
ejpam-5193	247	31	,	,	PUNCT
ejpam-5193	247	32	y;u	y;u	PROPN
ejpam-5193	247	33	,	,	PUNCT
ejpam-5193	247	34	λ	λ	PROPN
ejpam-5193	247	35	,	,	PUNCT
ejpam-5193	247	36	a	a	DET
ejpam-5193	247	37	,	,	PUNCT
ejpam-5193	247	38	b	b	NOUN
ejpam-5193	247	39	)	)	PUNCT
ejpam-5193	247	40	=	=	SYM
ejpam-5193	247	41	n∑	n∑	PROPN
ejpam-5193	247	42	i=0	i=0	PROPN
ejpam-5193	247	43	∞∑	∞∑	NUM
ejpam-5193	247	44	j=0	j=0	PROPN
ejpam-5193	247	45	(	(	PUNCT
ejpam-5193	247	46	n	n	NOUN
ejpam-5193	247	47	i	i	PRON
ejpam-5193	247	48	)	)	PUNCT
ejpam-5193	247	49	(	(	PUNCT
ejpam-5193	247	50	x)js(i	x)js(i	ADV
ejpam-5193	247	51	,	,	PUNCT
ejpam-5193	247	52	j)bg	j)bg	PROPN
ejpam-5193	247	53	(	(	PUNCT
ejpam-5193	247	54	r	r	NOUN
ejpam-5193	247	55	)	)	PUNCT
ejpam-5193	247	56	n−i	n−i	NOUN
ejpam-5193	247	57	,	,	PUNCT
ejpam-5193	247	58	k(y;u	k(y;u	PROPN
ejpam-5193	247	59	,	,	PUNCT
ejpam-5193	247	60	λ	λ	PROPN
ejpam-5193	247	61	,	,	PUNCT
ejpam-5193	247	62	a	a	DET
ejpam-5193	247	63	,	,	PUNCT
ejpam-5193	247	64	b	b	NOUN
ejpam-5193	247	65	)	)	PUNCT
ejpam-5193	247	66	=	=	SYM
ejpam-5193	247	67	n∑	n∑	PROPN
ejpam-5193	247	68	i=0	i=0	PROPN
ejpam-5193	247	69	i∑	i∑	PROPN
ejpam-5193	247	70	j=0	j=0	PROPN
ejpam-5193	247	71	(	(	PUNCT
ejpam-5193	247	72	n	n	NOUN
ejpam-5193	247	73	i	i	PRON
ejpam-5193	247	74	)	)	PUNCT
ejpam-5193	247	75	(	(	PUNCT
ejpam-5193	247	76	x)js(i	x)js(i	ADV
ejpam-5193	247	77	,	,	PUNCT
ejpam-5193	247	78	j)bg	j)bg	PROPN
ejpam-5193	247	79	(	(	PUNCT
ejpam-5193	247	80	r	r	NOUN
ejpam-5193	247	81	)	)	PUNCT
ejpam-5193	247	82	n−i	n−i	NOUN
ejpam-5193	247	83	,	,	PUNCT
ejpam-5193	247	84	k(y;u	k(y;u	PROPN
ejpam-5193	247	85	,	,	PUNCT
ejpam-5193	247	86	λ	λ	PROPN
ejpam-5193	247	87	,	,	PUNCT
ejpam-5193	247	88	a	a	DET
ejpam-5193	247	89	,	,	PUNCT
ejpam-5193	247	90	b	b	NOUN
ejpam-5193	247	91	)	)	PUNCT
ejpam-5193	247	92	.	.	PUNCT
ejpam-5193	248	1	the	the	DET
ejpam-5193	248	2	subsequent	subsequent	ADJ
ejpam-5193	248	3	theorem	theorem	NOUN
ejpam-5193	248	4	is	be	AUX
ejpam-5193	248	5	another	another	DET
ejpam-5193	248	6	relation	relation	NOUN
ejpam-5193	248	7	for	for	ADP
ejpam-5193	248	8	bg	bg	PROPN
ejpam-5193	248	9	(	(	PUNCT
ejpam-5193	248	10	r	r	NOUN
ejpam-5193	248	11	)	)	PUNCT
ejpam-5193	248	12	n	n	CCONJ
ejpam-5193	248	13	,	,	PUNCT
ejpam-5193	248	14	k(x	k(x	PROPN
ejpam-5193	248	15	,	,	PUNCT
ejpam-5193	248	16	y;u	y;u	PROPN
ejpam-5193	248	17	,	,	PUNCT
ejpam-5193	248	18	λ	λ	PROPN
ejpam-5193	248	19	,	,	PUNCT
ejpam-5193	248	20	a	a	DET
ejpam-5193	248	21	,	,	PUNCT
ejpam-5193	248	22	b	b	NOUN
ejpam-5193	248	23	)	)	PUNCT
ejpam-5193	248	24	in	in	ADP
ejpam-5193	248	25	connection	connection	NOUN
ejpam-5193	248	26	with	with	ADP
ejpam-5193	248	27	stirling	stirling	NOUN
ejpam-5193	248	28	numbers	number	NOUN
ejpam-5193	248	29	of	of	ADP
ejpam-5193	248	30	the	the	DET
ejpam-5193	248	31	second	second	ADJ
ejpam-5193	248	32	kind	kind	NOUN
ejpam-5193	248	33	.	.	PUNCT
ejpam-5193	249	1	1483	1483	NUM
ejpam-5193	249	2	theorem	theorem	VERB
ejpam-5193	249	3	4.2	4.2	NUM
ejpam-5193	249	4	.	.	PUNCT
ejpam-5193	250	1	the	the	DET
ejpam-5193	250	2	higher	high	ADJ
ejpam-5193	250	3	order	order	NOUN
ejpam-5193	250	4	bivariate	bivariate	ADJ
ejpam-5193	250	5	bell	bell	NOUN
ejpam-5193	250	6	-	-	PUNCT
ejpam-5193	250	7	based	base	VERB
ejpam-5193	250	8	apostol	apostol	NOUN
ejpam-5193	250	9	-	-	PUNCT
ejpam-5193	250	10	frobenius	frobenius	NOUN
ejpam-5193	250	11	-	-	PUNCT
ejpam-5193	250	12	type	type	NOUN
ejpam-5193	250	13	poly	poly	ADJ
ejpam-5193	250	14	-	-	PUNCT
ejpam-5193	250	15	genocchi	genocchi	NOUN
ejpam-5193	250	16	polynomials	polynomial	NOUN
ejpam-5193	250	17	with	with	ADP
ejpam-5193	250	18	parameters	parameter	NOUN
ejpam-5193	250	19	a	a	PRON
ejpam-5193	250	20	,	,	PUNCT
ejpam-5193	250	21	b	b	X
ejpam-5193	250	22	satisfy	satisfy	VERB
ejpam-5193	250	23	the	the	DET
ejpam-5193	250	24	relation	relation	NOUN
ejpam-5193	250	25	,	,	PUNCT
ejpam-5193	250	26	bg	bg	PROPN
ejpam-5193	250	27	(	(	PUNCT
ejpam-5193	250	28	r	r	NOUN
ejpam-5193	250	29	)	)	PUNCT
ejpam-5193	250	30	n	n	CCONJ
ejpam-5193	250	31	,	,	PUNCT
ejpam-5193	250	32	k(x	k(x	PROPN
ejpam-5193	250	33	,	,	PUNCT
ejpam-5193	250	34	y;u	y;u	PROPN
ejpam-5193	250	35	,	,	PUNCT
ejpam-5193	250	36	λ	λ	PROPN
ejpam-5193	250	37	,	,	PUNCT
ejpam-5193	250	38	a	a	DET
ejpam-5193	250	39	,	,	PUNCT
ejpam-5193	250	40	b	b	NOUN
ejpam-5193	250	41	)	)	PUNCT
ejpam-5193	250	42	=	=	SYM
ejpam-5193	250	43	n∑	n∑	NOUN
ejpam-5193	250	44	j=0	j=0	PROPN
ejpam-5193	250	45	(	(	PUNCT
ejpam-5193	250	46	n	n	X
ejpam-5193	250	47	j	j	NOUN
ejpam-5193	250	48	)	)	PUNCT
ejpam-5193	250	49	(	(	PUNCT
ejpam-5193	250	50	−1)rbg	−1)rbg	PROPN
ejpam-5193	250	51	(	(	PUNCT
ejpam-5193	250	52	r	r	NOUN
ejpam-5193	250	53	)	)	PUNCT
ejpam-5193	250	54	n−j(x	n−j(x	NOUN
ejpam-5193	250	55	,	,	PUNCT
ejpam-5193	250	56	y;u	y;u	PROPN
ejpam-5193	250	57	,	,	PUNCT
ejpam-5193	250	58	λ	λ	PROPN
ejpam-5193	250	59	,	,	PUNCT
ejpam-5193	250	60	a	a	PRON
ejpam-5193	250	61	,	,	PUNCT
ejpam-5193	250	62	b)dj	b)dj	PROPN
ejpam-5193	250	63	(	(	PUNCT
ejpam-5193	250	64	4.2	4.2	NUM
ejpam-5193	250	65	)	)	PUNCT
ejpam-5193	250	66	where	where	SCONJ
ejpam-5193	250	67	dj	dj	NOUN
ejpam-5193	250	68	=	=	SYM
ejpam-5193	250	69	∑	∑	NOUN
ejpam-5193	250	70	n1+n2+	n1+n2+	NOUN
ejpam-5193	250	71	...	...	PUNCT
ejpam-5193	250	72	+nr	+nr	PROPN
ejpam-5193	251	1	=	=	ADJ
ejpam-5193	252	1	j	j	PROPN
ejpam-5193	252	2	r∏	r∏	PROPN
ejpam-5193	252	3	i=1	i=1	PROPN
ejpam-5193	253	1	cni	cni	PROPN
ejpam-5193	253	2	(	(	PUNCT
ejpam-5193	253	3	j	j	PROPN
ejpam-5193	253	4	n1	n1	PROPN
ejpam-5193	253	5	,	,	PUNCT
ejpam-5193	253	6	n2	n2	NOUN
ejpam-5193	253	7	,	,	PUNCT
ejpam-5193	253	8	.	.	PUNCT
ejpam-5193	253	9	.	.	PUNCT
ejpam-5193	253	10	.	.	PUNCT
ejpam-5193	254	1	,	,	PUNCT
ejpam-5193	254	2	nr	nr	PROPN
ejpam-5193	254	3	)	)	PUNCT
ejpam-5193	254	4	cj	cj	VERB
ejpam-5193	255	1	=	=	SYM
ejpam-5193	255	2	j∑	j∑	PROPN
ejpam-5193	255	3	m=0	m=0	PROPN
ejpam-5193	255	4	(	(	PUNCT
ejpam-5193	255	5	−1)m+j+1	−1)m+j+1	NOUN
ejpam-5193	255	6	(	(	PUNCT
ejpam-5193	255	7	(	(	PUNCT
ejpam-5193	255	8	1−	1−	NUM
ejpam-5193	255	9	u	u	NOUN
ejpam-5193	255	10	)	)	PUNCT
ejpam-5193	255	11	ln	ln	ADJ
ejpam-5193	255	12	ab)jm!s(j	ab)jm!s(j	PROPN
ejpam-5193	255	13	+	+	CCONJ
ejpam-5193	255	14	1,m+	1,m+	NUM
ejpam-5193	255	15	1	1	NUM
ejpam-5193	255	16	)	)	PUNCT
ejpam-5193	255	17	(	(	PUNCT
ejpam-5193	255	18	j	j	PROPN
ejpam-5193	255	19	+	+	CCONJ
ejpam-5193	255	20	1)(m+	1)(m+	NUM
ejpam-5193	255	21	1)k−1	1)k−1	NUM
ejpam-5193	255	22	.	.	PUNCT
ejpam-5193	256	1	proof	proof	NOUN
ejpam-5193	256	2	.	.	PUNCT
ejpam-5193	257	1	now	now	ADV
ejpam-5193	257	2	,	,	PUNCT
ejpam-5193	257	3	(	(	PUNCT
ejpam-5193	257	4	2.1	2.1	NUM
ejpam-5193	257	5	)	)	PUNCT
ejpam-5193	257	6	can	can	AUX
ejpam-5193	257	7	be	be	AUX
ejpam-5193	257	8	written	write	VERB
ejpam-5193	257	9	as	as	ADP
ejpam-5193	257	10	∞∑	∞∑	NUM
ejpam-5193	257	11	n=0	n=0	ADJ
ejpam-5193	257	12	bg	bg	NOUN
ejpam-5193	257	13	(	(	PUNCT
ejpam-5193	257	14	r	r	NOUN
ejpam-5193	257	15	)	)	PUNCT
ejpam-5193	257	16	n	n	CCONJ
ejpam-5193	257	17	,	,	PUNCT
ejpam-5193	257	18	k(x	k(x	PROPN
ejpam-5193	257	19	,	,	PUNCT
ejpam-5193	257	20	y;u	y;u	PROPN
ejpam-5193	257	21	,	,	PUNCT
ejpam-5193	257	22	λ	λ	PROPN
ejpam-5193	257	23	,	,	PUNCT
ejpam-5193	257	24	a	a	DET
ejpam-5193	257	25	,	,	PUNCT
ejpam-5193	257	26	b	b	NOUN
ejpam-5193	257	27	)	)	PUNCT
ejpam-5193	257	28	tn	tn	PROPN
ejpam-5193	257	29	n	n	NOUN
ejpam-5193	257	30	!	!	PUNCT
ejpam-5193	258	1	=	=	SYM
ejpam-5193	258	2	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	258	3	)	)	PUNCT
ejpam-5193	258	4	(	(	PUNCT
ejpam-5193	258	5	λbt	λbt	VERB
ejpam-5193	258	6	−	−	X
ejpam-5193	258	7	ua−t)r	ua−t)r	NOUN
ejpam-5193	258	8	(	(	PUNCT
ejpam-5193	258	9	∞∑	∞∑	PROPN
ejpam-5193	258	10	m=1	m=1	X
ejpam-5193	258	11	(	(	PUNCT
ejpam-5193	258	12	1−	1−	NUM
ejpam-5193	258	13	e−(1−u)t	e−(1−u)t	PROPN
ejpam-5193	258	14	ln	ln	X
ejpam-5193	258	15	ab)m	ab)m	PROPN
ejpam-5193	258	16	mk	mk	NOUN
ejpam-5193	258	17	)	)	PUNCT
ejpam-5193	258	18	r	r	NOUN
ejpam-5193	258	19	=	=	SYM
ejpam-5193	258	20	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	258	21	)	)	PUNCT
ejpam-5193	258	22	(	(	PUNCT
ejpam-5193	258	23	λbt	λbt	VERB
ejpam-5193	258	24	−	−	X
ejpam-5193	258	25	ua−t)r	ua−t)r	PROPN
ejpam-5193	258	26	(	(	PUNCT
ejpam-5193	258	27	∞∑	∞∑	NUM
ejpam-5193	258	28	m=0	m=0	PROPN
ejpam-5193	258	29	(	(	PUNCT
ejpam-5193	258	30	1−	1−	NUM
ejpam-5193	258	31	e−(1−u)t	e−(1−u)t	NOUN
ejpam-5193	258	32	ln	ln	ADJ
ejpam-5193	258	33	ab)m+1	ab)m+1	PROPN
ejpam-5193	258	34	(	(	PUNCT
ejpam-5193	258	35	m+	m+	NOUN
ejpam-5193	258	36	1)k	1)k	NUM
ejpam-5193	258	37	)	)	PUNCT
ejpam-5193	258	38	r	r	NOUN
ejpam-5193	258	39	=	=	SYM
ejpam-5193	258	40	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	258	41	)	)	PUNCT
ejpam-5193	258	42	(	(	PUNCT
ejpam-5193	258	43	λbt	λbt	VERB
ejpam-5193	258	44	−	−	X
ejpam-5193	258	45	ua−t)r	ua−t)r	PROPN
ejpam-5193	258	46	(	(	PUNCT
ejpam-5193	258	47	∞∑	∞∑	NUM
ejpam-5193	258	48	m=0	m=0	PROPN
ejpam-5193	258	49	m	m	PROPN
ejpam-5193	258	50	!	!	PUNCT
ejpam-5193	259	1	(	(	PUNCT
ejpam-5193	259	2	m+	m+	NUM
ejpam-5193	259	3	1)k−1	1)k−1	NUM
ejpam-5193	259	4	(	(	PUNCT
ejpam-5193	259	5	1−	1−	NUM
ejpam-5193	259	6	e−(1−u)t	e−(1−u)t	NOUN
ejpam-5193	259	7	ln	ln	ADJ
ejpam-5193	259	8	ab)m+1	ab)m+1	PROPN
ejpam-5193	259	9	(	(	PUNCT
ejpam-5193	259	10	m+	m+	NOUN
ejpam-5193	259	11	1	1	NUM
ejpam-5193	259	12	)	)	PUNCT
ejpam-5193	259	13	!	!	PUNCT
ejpam-5193	259	14	)	)	PUNCT
ejpam-5193	260	1	r	r	NOUN
ejpam-5193	260	2	=	=	SYM
ejpam-5193	260	3	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	260	4	)	)	PUNCT
ejpam-5193	260	5	(	(	PUNCT
ejpam-5193	260	6	λbt	λbt	VERB
ejpam-5193	260	7	−	−	X
ejpam-5193	260	8	ua−t)r	ua−t)r	ADJ
ejpam-5193	260	9			PROPN
ejpam-5193	260	10	∞∑	∞∑	PROPN
ejpam-5193	260	11	m=0	m=0	PROPN
ejpam-5193	260	12	(	(	PUNCT
ejpam-5193	260	13	−1)m+1	−1)m+1	PROPN
ejpam-5193	260	14	m	m	PRON
ejpam-5193	260	15	!	!	PUNCT
ejpam-5193	261	1	(	(	PUNCT
ejpam-5193	261	2	m+	m+	NUM
ejpam-5193	261	3	1)k−1	1)k−1	NUM
ejpam-5193	261	4	∞∑	∞∑	PROPN
ejpam-5193	261	5	j	j	X
ejpam-5193	261	6	=	=	NOUN
ejpam-5193	261	7	m+1	m+1	PROPN
ejpam-5193	261	8	s(j	s(j	PROPN
ejpam-5193	261	9	,	,	PUNCT
ejpam-5193	261	10	m+	m+	NOUN
ejpam-5193	261	11	1	1	NUM
ejpam-5193	261	12	)	)	PUNCT
ejpam-5193	261	13	(	(	PUNCT
ejpam-5193	261	14	−(1−	−(1−	VERB
ejpam-5193	261	15	u)t	u)t	X
ejpam-5193	261	16	ln	ln	PROPN
ejpam-5193	261	17	ab)j	ab)j	PROPN
ejpam-5193	261	18	j	j	PROPN
ejpam-5193	261	19	!	!	PUNCT
ejpam-5193	261	20	r	r	PUNCT
ejpam-5193	262	1	=	=	PRON
ejpam-5193	262	2	(	(	PUNCT
ejpam-5193	262	3	−1)rext+y(et−1	−1)rext+y(et−1	NOUN
ejpam-5193	262	4	)	)	PUNCT
ejpam-5193	262	5	(	(	PUNCT
ejpam-5193	262	6	(	(	PUNCT
ejpam-5193	262	7	1−	1−	NUM
ejpam-5193	262	8	u)t	u)t	X
ejpam-5193	262	9	ln	ln	PROPN
ejpam-5193	262	10	ab	ab	PROPN
ejpam-5193	262	11	λbt	λbt	VERB
ejpam-5193	262	12	−	−	PROPN
ejpam-5193	262	13	ua−t	ua−t	ADJ
ejpam-5193	262	14	)	)	PUNCT
ejpam-5193	262	15	r	r	NOUN
ejpam-5193	262	16			PROPN
ejpam-5193	262	17	∞∑	∞∑	NUM
ejpam-5193	262	18	j=0	j=0	PROPN
ejpam-5193	262	19	cj	cj	PROPN
ejpam-5193	262	20	tj	tj	PROPN
ejpam-5193	262	21	j	j	PROPN
ejpam-5193	262	22	!	!	PROPN
ejpam-5193	262	23	r	r	PROPN
ejpam-5193	262	24	,	,	PUNCT
ejpam-5193	262	25	where	where	SCONJ
ejpam-5193	262	26	cj	cj	VERB
ejpam-5193	262	27	=	=	SYM
ejpam-5193	262	28	j∑	j∑	PROPN
ejpam-5193	262	29	m=0	m=0	PROPN
ejpam-5193	262	30	(	(	PUNCT
ejpam-5193	262	31	−1)m+j+1	−1)m+j+1	NOUN
ejpam-5193	262	32	(	(	PUNCT
ejpam-5193	262	33	(	(	PUNCT
ejpam-5193	262	34	1−	1−	NUM
ejpam-5193	262	35	u	u	NOUN
ejpam-5193	262	36	)	)	PUNCT
ejpam-5193	262	37	ln	ln	ADJ
ejpam-5193	262	38	ab)jm!s(j	ab)jm!s(j	PROPN
ejpam-5193	262	39	+	+	CCONJ
ejpam-5193	262	40	1,m+	1,m+	NUM
ejpam-5193	262	41	1	1	NUM
ejpam-5193	262	42	)	)	PUNCT
ejpam-5193	262	43	(	(	PUNCT
ejpam-5193	262	44	j	j	PROPN
ejpam-5193	262	45	+	+	CCONJ
ejpam-5193	262	46	1)(m+	1)(m+	NUM
ejpam-5193	262	47	1)k−1	1)k−1	NUM
ejpam-5193	262	48	.	.	PUNCT
ejpam-5193	263	1	note	note	VERB
ejpam-5193	263	2	that	that	SCONJ
ejpam-5193	263	3	the	the	DET
ejpam-5193	263	4	power	power	NOUN
ejpam-5193	263	5	series	series	PROPN
ejpam-5193	263	6	(	(	PUNCT
ejpam-5193	263	7	∑∞	∑∞	X
ejpam-5193	263	8	j=0	j=0	PROPN
ejpam-5193	263	9	cj	cj	PROPN
ejpam-5193	263	10	tj	tj	PROPN
ejpam-5193	263	11	j	j	PROPN
ejpam-5193	263	12	!	!	PUNCT
ejpam-5193	263	13	)	)	PUNCT
ejpam-5193	263	14	r	r	NOUN
ejpam-5193	263	15	can	can	AUX
ejpam-5193	263	16	be	be	AUX
ejpam-5193	263	17	expressed	express	VERB
ejpam-5193	263	18	as	as	ADJ
ejpam-5193	263	19	∞∑	∞∑	PROPN
ejpam-5193	263	20	j=0	j=0	PROPN
ejpam-5193	263	21	cj	cj	PROPN
ejpam-5193	263	22	tj	tj	PROPN
ejpam-5193	263	23	j	j	PROPN
ejpam-5193	263	24	!	!	PUNCT
ejpam-5193	263	25	r	r	PUNCT
ejpam-5193	264	1	=	=	PRON
ejpam-5193	265	1	∞∑	∞∑	PRON
ejpam-5193	265	2	n=0	n=0	NUM
ejpam-5193	265	3	dn	dn	PROPN
ejpam-5193	265	4	tn	tn	PROPN
ejpam-5193	265	5	n	n	CCONJ
ejpam-5193	265	6	!	!	PROPN
ejpam-5193	265	7	,	,	PUNCT
ejpam-5193	265	8	where	where	SCONJ
ejpam-5193	265	9	dn	dn	PROPN
ejpam-5193	265	10	=	=	SYM
ejpam-5193	265	11	∑	∑	PUNCT
ejpam-5193	265	12	n1+n2+	n1+n2+	NOUN
ejpam-5193	265	13	...	...	PUNCT
ejpam-5193	265	14	+nr	+nr	PROPN
ejpam-5193	265	15	=	=	SYM
ejpam-5193	265	16	n	n	PRON
ejpam-5193	266	1	r∏	r∏	NOUN
ejpam-5193	266	2	i=1	i=1	PROPN
ejpam-5193	267	1	cni	cni	PROPN
ejpam-5193	267	2	(	(	PUNCT
ejpam-5193	267	3	n	n	CCONJ
ejpam-5193	267	4	n1	n1	NOUN
ejpam-5193	267	5	,	,	PUNCT
ejpam-5193	267	6	n2	n2	NOUN
ejpam-5193	267	7	,	,	PUNCT
ejpam-5193	267	8	.	.	PUNCT
ejpam-5193	267	9	.	.	PUNCT
ejpam-5193	267	10	.	.	PUNCT
ejpam-5193	268	1	,	,	PUNCT
ejpam-5193	268	2	nr	nr	PROPN
ejpam-5193	268	3	)	)	PUNCT
ejpam-5193	268	4	,	,	PUNCT
ejpam-5193	268	5	1484	1484	NUM
ejpam-5193	268	6	(	(	PUNCT
ejpam-5193	268	7	see	see	VERB
ejpam-5193	268	8	[	[	X
ejpam-5193	268	9	10	10	NUM
ejpam-5193	268	10	]	]	NUM
ejpam-5193	268	11	)	)	PUNCT
ejpam-5193	268	12	.	.	PUNCT
ejpam-5193	269	1	it	it	PRON
ejpam-5193	269	2	follows	follow	VERB
ejpam-5193	269	3	that	that	SCONJ
ejpam-5193	269	4	∞∑	∞∑	NUM
ejpam-5193	269	5	n=0	n=0	ADJ
ejpam-5193	269	6	bg	bg	NOUN
ejpam-5193	269	7	(	(	PUNCT
ejpam-5193	269	8	r	r	NOUN
ejpam-5193	269	9	)	)	PUNCT
ejpam-5193	269	10	n	n	CCONJ
ejpam-5193	269	11	,	,	PUNCT
ejpam-5193	269	12	k(x	k(x	PROPN
ejpam-5193	269	13	,	,	PUNCT
ejpam-5193	269	14	y;u	y;u	PROPN
ejpam-5193	269	15	,	,	PUNCT
ejpam-5193	269	16	λ	λ	PROPN
ejpam-5193	269	17	,	,	PUNCT
ejpam-5193	269	18	a	a	DET
ejpam-5193	269	19	,	,	PUNCT
ejpam-5193	269	20	b	b	NOUN
ejpam-5193	269	21	)	)	PUNCT
ejpam-5193	269	22	tn	tn	NOUN
ejpam-5193	269	23	n	n	NOUN
ejpam-5193	269	24	!	!	PUNCT
ejpam-5193	270	1	=	=	PUNCT
ejpam-5193	270	2	(	(	PUNCT
ejpam-5193	270	3	−1)r	−1)r	X
ejpam-5193	270	4	(	(	PUNCT
ejpam-5193	270	5	∞∑	∞∑	PROPN
ejpam-5193	270	6	n=0	n=0	PROPN
ejpam-5193	270	7	bg	bg	NOUN
ejpam-5193	270	8	(	(	PUNCT
ejpam-5193	270	9	r	r	NOUN
ejpam-5193	270	10	)	)	PUNCT
ejpam-5193	270	11	n	n	NOUN
ejpam-5193	270	12	(	(	PUNCT
ejpam-5193	270	13	x	x	X
ejpam-5193	270	14	,	,	PUNCT
ejpam-5193	270	15	y;u	y;u	PROPN
ejpam-5193	270	16	,	,	PUNCT
ejpam-5193	270	17	λ	λ	PROPN
ejpam-5193	270	18	,	,	PUNCT
ejpam-5193	270	19	a	a	DET
ejpam-5193	270	20	,	,	PUNCT
ejpam-5193	270	21	b	b	NOUN
ejpam-5193	270	22	)	)	PUNCT
ejpam-5193	270	23	tn	tn	PROPN
ejpam-5193	270	24	n	n	CCONJ
ejpam-5193	270	25	!	!	PUNCT
ejpam-5193	270	26	)	)	PUNCT
ejpam-5193	271	1	(	(	PUNCT
ejpam-5193	271	2	∞∑	∞∑	PROPN
ejpam-5193	271	3	n=0	n=0	NUM
ejpam-5193	271	4	dn	dn	PROPN
ejpam-5193	271	5	tn	tn	PROPN
ejpam-5193	271	6	n	n	CCONJ
ejpam-5193	271	7	!	!	PUNCT
ejpam-5193	271	8	)	)	PUNCT
ejpam-5193	272	1	=	=	PUNCT
ejpam-5193	273	1	∞∑	∞∑	NUM
ejpam-5193	273	2	n=0	n=0	NUM
ejpam-5193	273	3			PUNCT
ejpam-5193	273	4	n∑	n∑	NOUN
ejpam-5193	273	5	j=0	j=0	PROPN
ejpam-5193	273	6	(	(	PUNCT
ejpam-5193	273	7	n	n	X
ejpam-5193	273	8	j	j	NOUN
ejpam-5193	273	9	)	)	PUNCT
ejpam-5193	273	10	(	(	PUNCT
ejpam-5193	273	11	−1)rbg	−1)rbg	PROPN
ejpam-5193	273	12	(	(	PUNCT
ejpam-5193	273	13	r	r	NOUN
ejpam-5193	273	14	)	)	PUNCT
ejpam-5193	273	15	n−j(x	n−j(x	NOUN
ejpam-5193	273	16	,	,	PUNCT
ejpam-5193	273	17	y;u	y;u	PROPN
ejpam-5193	273	18	,	,	PUNCT
ejpam-5193	273	19	λ	λ	PROPN
ejpam-5193	273	20	,	,	PUNCT
ejpam-5193	273	21	a	a	PRON
ejpam-5193	273	22	,	,	PUNCT
ejpam-5193	273	23	b)dj	b)dj	PROPN
ejpam-5193	273	24			PROPN
ejpam-5193	273	25	tn	tn	PROPN
ejpam-5193	273	26	n	n	CCONJ
ejpam-5193	273	27	!	!	PUNCT
ejpam-5193	273	28	comparing	compare	VERB
ejpam-5193	273	29	the	the	DET
ejpam-5193	273	30	coefficients	coefficient	NOUN
ejpam-5193	273	31	completes	complete	VERB
ejpam-5193	273	32	the	the	DET
ejpam-5193	273	33	proof	proof	NOUN
ejpam-5193	273	34	of	of	ADP
ejpam-5193	273	35	the	the	DET
ejpam-5193	273	36	theorem	theorem	NOUN
ejpam-5193	273	37	.	.	PUNCT
ejpam-5193	274	1	the	the	DET
ejpam-5193	274	2	next	next	ADJ
ejpam-5193	274	3	theorem	theorem	NOUN
ejpam-5193	274	4	contains	contain	VERB
ejpam-5193	274	5	a	a	DET
ejpam-5193	274	6	relation	relation	NOUN
ejpam-5193	274	7	that	that	PRON
ejpam-5193	274	8	expresses	express	VERB
ejpam-5193	274	9	the	the	DET
ejpam-5193	274	10	bivariate	bivariate	ADJ
ejpam-5193	274	11	bell	bell	NOUN
ejpam-5193	274	12	polynomials	polynomial	NOUN
ejpam-5193	274	13	in	in	ADP
ejpam-5193	274	14	terms	term	NOUN
ejpam-5193	274	15	of	of	ADP
ejpam-5193	274	16	bivariate	bivariate	ADJ
ejpam-5193	274	17	bell	bell	NOUN
ejpam-5193	274	18	-	-	PUNCT
ejpam-5193	274	19	based	base	VERB
ejpam-5193	274	20	apostol	apostol	NOUN
ejpam-5193	274	21	-	-	PUNCT
ejpam-5193	274	22	frobenius	frobenius	NOUN
ejpam-5193	274	23	-	-	PUNCT
ejpam-5193	274	24	type	type	NOUN
ejpam-5193	274	25	poly	poly	ADJ
ejpam-5193	274	26	-	-	PUNCT
ejpam-5193	274	27	genocchi	genocchi	NOUN
ejpam-5193	274	28	polynomials	polynomial	NOUN
ejpam-5193	274	29	.	.	PUNCT
ejpam-5193	275	1	theorem	theorem	VERB
ejpam-5193	275	2	4.3	4.3	NUM
ejpam-5193	275	3	.	.	PUNCT
ejpam-5193	276	1	the	the	DET
ejpam-5193	276	2	following	follow	VERB
ejpam-5193	276	3	relation	relation	NOUN
ejpam-5193	276	4	holds	hold	VERB
ejpam-5193	276	5	bn(x	bn(x	NOUN
ejpam-5193	276	6	,	,	PUNCT
ejpam-5193	276	7	y	y	NOUN
ejpam-5193	276	8	)	)	PUNCT
ejpam-5193	277	1	=	=	PUNCT
ejpam-5193	277	2	λ	λ	X
ejpam-5193	277	3	bgn+1(x+	bgn+1(x+	PROPN
ejpam-5193	277	4	1	1	NUM
ejpam-5193	277	5	,	,	PUNCT
ejpam-5193	277	6	y;u	y;u	PROPN
ejpam-5193	277	7	,	,	PUNCT
ejpam-5193	277	8	λ)−	λ)−	PROPN
ejpam-5193	277	9	u	u	NOUN
ejpam-5193	277	10	bgn+1(x	bgn+1(x	NOUN
ejpam-5193	277	11	,	,	PUNCT
ejpam-5193	277	12	y;u	y;u	PROPN
ejpam-5193	277	13	,	,	PUNCT
ejpam-5193	277	14	λ	λ	PROPN
ejpam-5193	277	15	)	)	PUNCT
ejpam-5193	277	16	(	(	PUNCT
ejpam-5193	277	17	1−	1−	NUM
ejpam-5193	277	18	u)(n+	u)(n+	NOUN
ejpam-5193	277	19	1	1	NUM
ejpam-5193	277	20	)	)	PUNCT
ejpam-5193	277	21	.	.	PUNCT
ejpam-5193	278	1	(	(	PUNCT
ejpam-5193	278	2	4.3	4.3	NUM
ejpam-5193	278	3	)	)	PUNCT
ejpam-5193	278	4	proof	proof	NOUN
ejpam-5193	278	5	.	.	PUNCT
ejpam-5193	279	1	using	use	VERB
ejpam-5193	279	2	equation	equation	NOUN
ejpam-5193	279	3	(	(	PUNCT
ejpam-5193	279	4	2.6	2.6	NUM
ejpam-5193	279	5	)	)	PUNCT
ejpam-5193	279	6	,	,	PUNCT
ejpam-5193	279	7	we	we	PRON
ejpam-5193	279	8	have	have	VERB
ejpam-5193	279	9	∞∑	∞∑	NUM
ejpam-5193	279	10	n=0	n=0	NUM
ejpam-5193	279	11	bn(x	bn(x	NUM
ejpam-5193	279	12	,	,	PUNCT
ejpam-5193	279	13	y	y	NOUN
ejpam-5193	279	14	)	)	PUNCT
ejpam-5193	279	15	tn	tn	PROPN
ejpam-5193	279	16	n	n	PROPN
ejpam-5193	279	17	!	!	PUNCT
ejpam-5193	280	1	=	=	PUNCT
ejpam-5193	281	1	(	(	PUNCT
ejpam-5193	281	2	λet	λet	X
ejpam-5193	281	3	−	−	NUM
ejpam-5193	281	4	u	u	NOUN
ejpam-5193	281	5	(	(	PUNCT
ejpam-5193	281	6	1−	1−	NUM
ejpam-5193	281	7	u)t	u)t	X
ejpam-5193	281	8	)	)	PUNCT
ejpam-5193	281	9	(	(	PUNCT
ejpam-5193	281	10	(	(	PUNCT
ejpam-5193	281	11	1−	1−	NUM
ejpam-5193	281	12	u	u	NOUN
ejpam-5193	281	13	)	)	PUNCT
ejpam-5193	281	14	t	t	PROPN
ejpam-5193	281	15	λet	λet	CCONJ
ejpam-5193	281	16	−	−	PROPN
ejpam-5193	281	17	u	u	NOUN
ejpam-5193	281	18	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	281	19	)	)	PUNCT
ejpam-5193	281	20	)	)	PUNCT
ejpam-5193	282	1	=	=	SYM
ejpam-5193	282	2	1	1	NUM
ejpam-5193	282	3	(	(	PUNCT
ejpam-5193	282	4	1−	1−	NUM
ejpam-5193	282	5	u)t	u)t	X
ejpam-5193	282	6	(	(	PUNCT
ejpam-5193	282	7	λ	λ	X
ejpam-5193	282	8	(	(	PUNCT
ejpam-5193	282	9	(	(	PUNCT
ejpam-5193	282	10	1−	1−	NUM
ejpam-5193	282	11	u	u	NOUN
ejpam-5193	282	12	)	)	PUNCT
ejpam-5193	282	13	t	t	PROPN
ejpam-5193	282	14	λet	λet	CCONJ
ejpam-5193	282	15	−	−	PROPN
ejpam-5193	282	16	u	u	PROPN
ejpam-5193	282	17	e(x+1)t+y(et−1	e(x+1)t+y(et−1	NOUN
ejpam-5193	282	18	)	)	PUNCT
ejpam-5193	282	19	)	)	PUNCT
ejpam-5193	283	1	−	−	PROPN
ejpam-5193	283	2	u	u	NOUN
ejpam-5193	283	3	(	(	PUNCT
ejpam-5193	283	4	(	(	PUNCT
ejpam-5193	283	5	1−	1−	NUM
ejpam-5193	283	6	u	u	NOUN
ejpam-5193	283	7	)	)	PUNCT
ejpam-5193	283	8	t	t	PROPN
ejpam-5193	283	9	λet	λet	CCONJ
ejpam-5193	283	10	−	−	PROPN
ejpam-5193	283	11	u	u	NOUN
ejpam-5193	283	12	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	283	13	)	)	PUNCT
ejpam-5193	283	14	)	)	PUNCT
ejpam-5193	283	15	)	)	PUNCT
ejpam-5193	284	1	=	=	SYM
ejpam-5193	284	2	1	1	NUM
ejpam-5193	284	3	(	(	PUNCT
ejpam-5193	284	4	1−	1−	NUM
ejpam-5193	284	5	u	u	NOUN
ejpam-5193	284	6	)	)	PUNCT
ejpam-5193	284	7	(	(	PUNCT
ejpam-5193	284	8	λ	λ	X
ejpam-5193	284	9	∞∑	∞∑	VERB
ejpam-5193	284	10	n=0	n=0	PUNCT
ejpam-5193	284	11	bgn(x+	bgn(x+	ADV
ejpam-5193	284	12	1	1	NUM
ejpam-5193	284	13	,	,	PUNCT
ejpam-5193	284	14	y;u	y;u	PROPN
ejpam-5193	284	15	,	,	PUNCT
ejpam-5193	284	16	λ	λ	PROPN
ejpam-5193	284	17	)	)	PUNCT
ejpam-5193	284	18	tn−1	tn−1	PROPN
ejpam-5193	284	19	n	n	CCONJ
ejpam-5193	284	20	!	!	PUNCT
ejpam-5193	284	21	−	−	PROPN
ejpam-5193	285	1	u	u	PRON
ejpam-5193	285	2	∞∑	∞∑	PROPN
ejpam-5193	285	3	n=0	n=0	PROPN
ejpam-5193	285	4	bg	bg	NOUN
ejpam-5193	285	5	(	(	PUNCT
ejpam-5193	285	6	r	r	NOUN
ejpam-5193	285	7	)	)	PUNCT
ejpam-5193	285	8	n	n	NOUN
ejpam-5193	285	9	(	(	PUNCT
ejpam-5193	285	10	x	x	X
ejpam-5193	285	11	,	,	PUNCT
ejpam-5193	285	12	y;u	y;u	PROPN
ejpam-5193	285	13	,	,	PUNCT
ejpam-5193	285	14	λ	λ	PROPN
ejpam-5193	285	15	)	)	PUNCT
ejpam-5193	285	16	tn−1	tn−1	PROPN
ejpam-5193	285	17	n	n	CCONJ
ejpam-5193	285	18	!	!	PUNCT
ejpam-5193	285	19	)	)	PUNCT
ejpam-5193	286	1	=	=	PUNCT
ejpam-5193	286	2	1	1	NUM
ejpam-5193	286	3	1−	1−	NUM
ejpam-5193	286	4	u	u	NOUN
ejpam-5193	286	5	(	(	PUNCT
ejpam-5193	286	6	λ	λ	PROPN
ejpam-5193	286	7	∞∑	∞∑	NOUN
ejpam-5193	286	8	n=−1	n=−1	ADV
ejpam-5193	286	9	bgn(x+	bgn(x+	ADV
ejpam-5193	286	10	1	1	NUM
ejpam-5193	286	11	,	,	PUNCT
ejpam-5193	286	12	y;u	y;u	PROPN
ejpam-5193	286	13	,	,	PUNCT
ejpam-5193	286	14	λ	λ	PROPN
ejpam-5193	286	15	)	)	PUNCT
ejpam-5193	286	16	tn	tn	PROPN
ejpam-5193	286	17	(	(	PUNCT
ejpam-5193	286	18	n+	n+	NOUN
ejpam-5193	286	19	1	1	NUM
ejpam-5193	286	20	)	)	PUNCT
ejpam-5193	286	21	!	!	PUNCT
ejpam-5193	287	1	−	−	PROPN
ejpam-5193	288	1	u	u	PRON
ejpam-5193	289	1	∞∑	∞∑	PRON
ejpam-5193	289	2	n=−1	n=−1	ADV
ejpam-5193	289	3	bg	bg	NOUN
ejpam-5193	289	4	(	(	PUNCT
ejpam-5193	289	5	r	r	NOUN
ejpam-5193	289	6	)	)	PUNCT
ejpam-5193	289	7	n	n	NOUN
ejpam-5193	289	8	(	(	PUNCT
ejpam-5193	289	9	x	x	X
ejpam-5193	289	10	,	,	PUNCT
ejpam-5193	289	11	y;u	y;u	PROPN
ejpam-5193	289	12	,	,	PUNCT
ejpam-5193	289	13	λ	λ	PROPN
ejpam-5193	289	14	)	)	PUNCT
ejpam-5193	289	15	tn	tn	PROPN
ejpam-5193	289	16	(	(	PUNCT
ejpam-5193	289	17	n+	n+	NOUN
ejpam-5193	289	18	1	1	NUM
ejpam-5193	289	19	)	)	PUNCT
ejpam-5193	289	20	!	!	PUNCT
ejpam-5193	289	21	)	)	PUNCT
ejpam-5193	290	1	=	=	PUNCT
ejpam-5193	291	1	∞∑	∞∑	NUM
ejpam-5193	291	2	n=−1	n=−1	ADV
ejpam-5193	291	3	(	(	PUNCT
ejpam-5193	291	4	λ	λ	X
ejpam-5193	291	5	bgn+1(x+	bgn+1(x+	PROPN
ejpam-5193	291	6	1	1	NUM
ejpam-5193	291	7	,	,	PUNCT
ejpam-5193	291	8	y;u	y;u	PROPN
ejpam-5193	291	9	,	,	PUNCT
ejpam-5193	291	10	λ)−	λ)−	PROPN
ejpam-5193	291	11	u	u	NOUN
ejpam-5193	291	12	bgn+1(x	bgn+1(x	NOUN
ejpam-5193	291	13	,	,	PUNCT
ejpam-5193	291	14	y;u	y;u	PROPN
ejpam-5193	291	15	,	,	PUNCT
ejpam-5193	291	16	λ	λ	PROPN
ejpam-5193	291	17	)	)	PUNCT
ejpam-5193	291	18	(	(	PUNCT
ejpam-5193	291	19	1−	1−	NUM
ejpam-5193	291	20	u)(n+	u)(n+	NOUN
ejpam-5193	291	21	1	1	NUM
ejpam-5193	291	22	)	)	PUNCT
ejpam-5193	291	23	)	)	PUNCT
ejpam-5193	291	24	tn	tn	PROPN
ejpam-5193	291	25	n	n	PROPN
ejpam-5193	291	26	!	!	PUNCT
ejpam-5193	291	27	comparing	compare	VERB
ejpam-5193	291	28	the	the	DET
ejpam-5193	291	29	coefficients	coefficient	NOUN
ejpam-5193	291	30	of	of	ADP
ejpam-5193	291	31	tn	tn	NOUN
ejpam-5193	291	32	n	n	ADP
ejpam-5193	291	33	!	!	PUNCT
ejpam-5193	292	1	yields	yield	NOUN
ejpam-5193	292	2	bn(x	bn(x	X
ejpam-5193	292	3	,	,	PUNCT
ejpam-5193	292	4	y	y	NOUN
ejpam-5193	292	5	)	)	PUNCT
ejpam-5193	293	1	=	=	PUNCT
ejpam-5193	293	2	λ	λ	X
ejpam-5193	293	3	bgn+1(x+	bgn+1(x+	PROPN
ejpam-5193	293	4	1	1	NUM
ejpam-5193	293	5	,	,	PUNCT
ejpam-5193	293	6	y;u	y;u	PROPN
ejpam-5193	293	7	,	,	PUNCT
ejpam-5193	293	8	λ)−	λ)−	PROPN
ejpam-5193	293	9	u	u	NOUN
ejpam-5193	293	10	bgn+1(x	bgn+1(x	NOUN
ejpam-5193	293	11	,	,	PUNCT
ejpam-5193	293	12	y;u	y;u	PROPN
ejpam-5193	293	13	,	,	PUNCT
ejpam-5193	293	14	λ	λ	PROPN
ejpam-5193	293	15	)	)	PUNCT
ejpam-5193	293	16	(	(	PUNCT
ejpam-5193	293	17	1−	1−	NUM
ejpam-5193	293	18	u)(n+	u)(n+	NOUN
ejpam-5193	293	19	1	1	NUM
ejpam-5193	293	20	)	)	PUNCT
ejpam-5193	293	21	.	.	PUNCT
ejpam-5193	294	1	5	5	X
ejpam-5193	294	2	.	.	X
ejpam-5193	294	3	derivative	derivative	ADJ
ejpam-5193	294	4	formulas	formula	NOUN
ejpam-5193	294	5	the	the	DET
ejpam-5193	294	6	derivative	derivative	ADJ
ejpam-5193	294	7	formulas	formula	NOUN
ejpam-5193	294	8	for	for	ADP
ejpam-5193	294	9	special	special	ADJ
ejpam-5193	294	10	polynomials	polynomial	NOUN
ejpam-5193	294	11	play	play	VERB
ejpam-5193	294	12	a	a	DET
ejpam-5193	294	13	crucial	crucial	ADJ
ejpam-5193	294	14	role	role	NOUN
ejpam-5193	294	15	in	in	ADP
ejpam-5193	294	16	various	various	ADJ
ejpam-5193	294	17	areas	area	NOUN
ejpam-5193	294	18	of	of	ADP
ejpam-5193	294	19	mathematics	mathematic	NOUN
ejpam-5193	294	20	,	,	PUNCT
ejpam-5193	294	21	physics	physics	NOUN
ejpam-5193	294	22	,	,	PUNCT
ejpam-5193	294	23	engineering	engineering	NOUN
ejpam-5193	294	24	,	,	PUNCT
ejpam-5193	294	25	and	and	CCONJ
ejpam-5193	294	26	other	other	ADJ
ejpam-5193	294	27	scientific	scientific	ADJ
ejpam-5193	294	28	disciplines	discipline	NOUN
ejpam-5193	294	29	.	.	PUNCT
ejpam-5193	295	1	for	for	ADP
ejpam-5193	295	2	instance	instance	NOUN
ejpam-5193	295	3	,	,	PUNCT
ejpam-5193	295	4	derivative	derivative	ADJ
ejpam-5193	295	5	formulas	formula	NOUN
ejpam-5193	295	6	allow	allow	VERB
ejpam-5193	295	7	for	for	ADP
ejpam-5193	295	8	the	the	DET
ejpam-5193	295	9	analysis	analysis	NOUN
ejpam-5193	295	10	of	of	ADP
ejpam-5193	295	11	the	the	DET
ejpam-5193	295	12	behavior	behavior	NOUN
ejpam-5193	295	13	and	and	CCONJ
ejpam-5193	295	14	properties	property	NOUN
ejpam-5193	295	15	of	of	ADP
ejpam-5193	295	16	special	special	ADJ
ejpam-5193	295	17	polynomials	polynomial	NOUN
ejpam-5193	295	18	in	in	ADP
ejpam-5193	295	19	terms	term	NOUN
ejpam-5193	295	20	of	of	ADP
ejpam-5193	295	21	their	their	PRON
ejpam-5193	295	22	rates	rate	NOUN
ejpam-5193	295	23	of	of	ADP
ejpam-5193	295	24	change	change	NOUN
ejpam-5193	295	25	.	.	PUNCT
ejpam-5193	296	1	this	this	PRON
ejpam-5193	296	2	is	be	AUX
ejpam-5193	296	3	fundamental	fundamental	ADJ
ejpam-5193	296	4	in	in	ADP
ejpam-5193	296	5	calculus	calculus	NOUN
ejpam-5193	296	6	and	and	CCONJ
ejpam-5193	296	7	mathematical	mathematical	ADJ
ejpam-5193	296	8	analysis	analysis	NOUN
ejpam-5193	296	9	1485	1485	NUM
ejpam-5193	296	10	for	for	ADP
ejpam-5193	296	11	understanding	understanding	NOUN
ejpam-5193	296	12	functions	function	NOUN
ejpam-5193	296	13	and	and	CCONJ
ejpam-5193	296	14	their	their	PRON
ejpam-5193	296	15	behavior	behavior	NOUN
ejpam-5193	296	16	.	.	PUNCT
ejpam-5193	297	1	they	they	PRON
ejpam-5193	297	2	are	be	AUX
ejpam-5193	297	3	also	also	ADV
ejpam-5193	297	4	essential	essential	ADJ
ejpam-5193	297	5	for	for	ADP
ejpam-5193	297	6	manipulating	manipulate	VERB
ejpam-5193	297	7	generating	generating	NOUN
ejpam-5193	297	8	functions	function	NOUN
ejpam-5193	297	9	,	,	PUNCT
ejpam-5193	297	10	which	which	PRON
ejpam-5193	297	11	represent	represent	VERB
ejpam-5193	297	12	sequences	sequence	NOUN
ejpam-5193	297	13	of	of	ADP
ejpam-5193	297	14	coefficients	coefficient	NOUN
ejpam-5193	297	15	of	of	ADP
ejpam-5193	297	16	special	special	ADJ
ejpam-5193	297	17	polynomials	polynomial	NOUN
ejpam-5193	297	18	.	.	PUNCT
ejpam-5193	298	1	these	these	DET
ejpam-5193	298	2	functions	function	NOUN
ejpam-5193	298	3	are	be	AUX
ejpam-5193	298	4	widely	widely	ADV
ejpam-5193	298	5	used	use	VERB
ejpam-5193	298	6	in	in	ADP
ejpam-5193	298	7	combinatorics	combinatoric	NOUN
ejpam-5193	298	8	,	,	PUNCT
ejpam-5193	298	9	number	number	NOUN
ejpam-5193	298	10	theory	theory	NOUN
ejpam-5193	298	11	,	,	PUNCT
ejpam-5193	298	12	and	and	CCONJ
ejpam-5193	298	13	discrete	discrete	ADJ
ejpam-5193	298	14	mathematics	mathematic	NOUN
ejpam-5193	298	15	for	for	ADP
ejpam-5193	298	16	counting	counting	NOUN
ejpam-5193	298	17	and	and	CCONJ
ejpam-5193	298	18	enumerative	enumerative	ADJ
ejpam-5193	298	19	purposes	purpose	NOUN
ejpam-5193	298	20	.	.	PUNCT
ejpam-5193	299	1	the	the	DET
ejpam-5193	299	2	following	follow	VERB
ejpam-5193	299	3	theorem	theorem	NOUN
ejpam-5193	299	4	contains	contain	VERB
ejpam-5193	299	5	the	the	DET
ejpam-5193	299	6	derivative	derivative	ADJ
ejpam-5193	299	7	formula	formula	NOUN
ejpam-5193	299	8	for	for	ADP
ejpam-5193	299	9	bg	bg	PROPN
ejpam-5193	299	10	(	(	PUNCT
ejpam-5193	299	11	r	r	NOUN
ejpam-5193	299	12	)	)	PUNCT
ejpam-5193	299	13	n	n	CCONJ
ejpam-5193	299	14	,	,	PUNCT
ejpam-5193	299	15	k(x	k(x	PROPN
ejpam-5193	299	16	,	,	PUNCT
ejpam-5193	299	17	y;u	y;u	PROPN
ejpam-5193	299	18	,	,	PUNCT
ejpam-5193	299	19	λ	λ	PROPN
ejpam-5193	299	20	)	)	PUNCT
ejpam-5193	299	21	with	with	ADP
ejpam-5193	299	22	respect	respect	NOUN
ejpam-5193	299	23	to	to	ADP
ejpam-5193	299	24	the	the	DET
ejpam-5193	299	25	variable	variable	ADJ
ejpam-5193	299	26	x.	x.	NOUN
ejpam-5193	299	27	theorem	theorem	VERB
ejpam-5193	299	28	5.1	5.1	NUM
ejpam-5193	299	29	.	.	PUNCT
ejpam-5193	300	1	the	the	DET
ejpam-5193	300	2	following	follow	VERB
ejpam-5193	300	3	derivative	derivative	ADJ
ejpam-5193	300	4	formula	formula	NOUN
ejpam-5193	300	5	holds	hold	VERB
ejpam-5193	300	6	∂	∂	ADJ
ejpam-5193	300	7	∂x	∂x	PROPN
ejpam-5193	300	8	bg	bg	NOUN
ejpam-5193	300	9	(	(	PUNCT
ejpam-5193	300	10	r	r	NOUN
ejpam-5193	300	11	)	)	PUNCT
ejpam-5193	300	12	n	n	CCONJ
ejpam-5193	300	13	,	,	PUNCT
ejpam-5193	300	14	k(x	k(x	PROPN
ejpam-5193	300	15	,	,	PUNCT
ejpam-5193	300	16	y;u	y;u	PROPN
ejpam-5193	300	17	,	,	PUNCT
ejpam-5193	300	18	λ	λ	NOUN
ejpam-5193	300	19	)	)	PUNCT
ejpam-5193	300	20	=	=	SYM
ejpam-5193	300	21	nbg	nbg	PROPN
ejpam-5193	300	22	(	(	PUNCT
ejpam-5193	300	23	r	r	NOUN
ejpam-5193	300	24	)	)	PUNCT
ejpam-5193	300	25	n−1,k(x	n−1,k(x	PROPN
ejpam-5193	300	26	,	,	PUNCT
ejpam-5193	300	27	y;u	y;u	PROPN
ejpam-5193	300	28	,	,	PUNCT
ejpam-5193	300	29	λ	λ	PROPN
ejpam-5193	300	30	)	)	PUNCT
ejpam-5193	300	31	.	.	PUNCT
ejpam-5193	301	1	(	(	PUNCT
ejpam-5193	301	2	5.1	5.1	NUM
ejpam-5193	301	3	)	)	PUNCT
ejpam-5193	301	4	proof	proof	NOUN
ejpam-5193	301	5	.	.	PUNCT
ejpam-5193	302	1	using	use	VERB
ejpam-5193	302	2	definition	definition	NOUN
ejpam-5193	302	3	2.1	2.1	NUM
ejpam-5193	302	4	,	,	PUNCT
ejpam-5193	302	5	we	we	PRON
ejpam-5193	302	6	have	have	VERB
ejpam-5193	302	7	∂	∂	NUM
ejpam-5193	302	8	∂x	∂x	PROPN
ejpam-5193	302	9	∞∑	∞∑	PROPN
ejpam-5193	302	10	n=0	n=0	ADJ
ejpam-5193	302	11	bg	bg	NOUN
ejpam-5193	302	12	(	(	PUNCT
ejpam-5193	302	13	r	r	NOUN
ejpam-5193	302	14	)	)	PUNCT
ejpam-5193	302	15	n	n	CCONJ
ejpam-5193	302	16	,	,	PUNCT
ejpam-5193	302	17	k(x	k(x	PROPN
ejpam-5193	302	18	,	,	PUNCT
ejpam-5193	302	19	y;u	y;u	PROPN
ejpam-5193	302	20	,	,	PUNCT
ejpam-5193	302	21	λ	λ	PROPN
ejpam-5193	302	22	,	,	PUNCT
ejpam-5193	302	23	a	a	DET
ejpam-5193	302	24	,	,	PUNCT
ejpam-5193	302	25	b	b	NOUN
ejpam-5193	302	26	)	)	PUNCT
ejpam-5193	302	27	tn	tn	PROPN
ejpam-5193	302	28	n	n	NOUN
ejpam-5193	302	29	!	!	PUNCT
ejpam-5193	303	1	=	=	SYM
ejpam-5193	303	2	∂	∂	NUM
ejpam-5193	303	3	∂x	∂x	PROPN
ejpam-5193	303	4	(	(	PUNCT
ejpam-5193	303	5	lik(1−	lik(1−	PROPN
ejpam-5193	303	6	(	(	PUNCT
ejpam-5193	303	7	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	303	8	)	)	PUNCT
ejpam-5193	303	9	λbt	λbt	VERB
ejpam-5193	303	10	−	−	PROPN
ejpam-5193	303	11	ua−t	ua−t	ADJ
ejpam-5193	303	12	)	)	PUNCT
ejpam-5193	303	13	r	r	NOUN
ejpam-5193	303	14	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	303	15	)	)	PUNCT
ejpam-5193	303	16	∞∑	∞∑	PRON
ejpam-5193	303	17	n=0	n=0	NUM
ejpam-5193	303	18	∂	∂	NUM
ejpam-5193	303	19	∂x	∂x	PROPN
ejpam-5193	303	20	bg	bg	NOUN
ejpam-5193	303	21	(	(	PUNCT
ejpam-5193	303	22	r	r	NOUN
ejpam-5193	303	23	)	)	PUNCT
ejpam-5193	303	24	n	n	CCONJ
ejpam-5193	303	25	,	,	PUNCT
ejpam-5193	303	26	k(x	k(x	PROPN
ejpam-5193	303	27	,	,	PUNCT
ejpam-5193	303	28	y;u	y;u	PROPN
ejpam-5193	303	29	,	,	PUNCT
ejpam-5193	303	30	λ	λ	PROPN
ejpam-5193	303	31	,	,	PUNCT
ejpam-5193	303	32	a	a	DET
ejpam-5193	303	33	,	,	PUNCT
ejpam-5193	303	34	b	b	NOUN
ejpam-5193	303	35	)	)	PUNCT
ejpam-5193	303	36	tn	tn	NOUN
ejpam-5193	303	37	n	n	CCONJ
ejpam-5193	303	38	!	!	PUNCT
ejpam-5193	304	1	=	=	PUNCT
ejpam-5193	304	2	(	(	PUNCT
ejpam-5193	304	3	lik(1−	lik(1−	X
ejpam-5193	304	4	(	(	PUNCT
ejpam-5193	304	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	304	6	)	)	PUNCT
ejpam-5193	304	7	λbt	λbt	VERB
ejpam-5193	304	8	−	−	PROPN
ejpam-5193	304	9	ua−t	ua−t	ADJ
ejpam-5193	304	10	)	)	PUNCT
ejpam-5193	304	11	r	r	NOUN
ejpam-5193	304	12	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	304	13	)	)	PUNCT
ejpam-5193	304	14	t	t	PROPN
ejpam-5193	305	1	=	=	SYM
ejpam-5193	305	2	t	t	PROPN
ejpam-5193	305	3	∞∑	∞∑	PROPN
ejpam-5193	305	4	n=0	n=0	PROPN
ejpam-5193	305	5	bg	bg	NOUN
ejpam-5193	305	6	(	(	PUNCT
ejpam-5193	305	7	r	r	NOUN
ejpam-5193	305	8	)	)	PUNCT
ejpam-5193	305	9	n	n	CCONJ
ejpam-5193	305	10	,	,	PUNCT
ejpam-5193	305	11	k(x	k(x	PROPN
ejpam-5193	305	12	,	,	PUNCT
ejpam-5193	305	13	y;u	y;u	PROPN
ejpam-5193	305	14	,	,	PUNCT
ejpam-5193	305	15	λ	λ	PROPN
ejpam-5193	305	16	,	,	PUNCT
ejpam-5193	305	17	a	a	DET
ejpam-5193	305	18	,	,	PUNCT
ejpam-5193	305	19	b	b	NOUN
ejpam-5193	305	20	)	)	PUNCT
ejpam-5193	305	21	tn	tn	NOUN
ejpam-5193	305	22	n	n	NOUN
ejpam-5193	305	23	!	!	PUNCT
ejpam-5193	306	1	=	=	NOUN
ejpam-5193	307	1	∞∑	∞∑	PRON
ejpam-5193	307	2	n=0	n=0	ADJ
ejpam-5193	307	3	bg	bg	NOUN
ejpam-5193	307	4	(	(	PUNCT
ejpam-5193	307	5	r	r	NOUN
ejpam-5193	307	6	)	)	PUNCT
ejpam-5193	307	7	n	n	CCONJ
ejpam-5193	307	8	,	,	PUNCT
ejpam-5193	307	9	k(x	k(x	PROPN
ejpam-5193	307	10	,	,	PUNCT
ejpam-5193	307	11	y;u	y;u	PROPN
ejpam-5193	307	12	,	,	PUNCT
ejpam-5193	307	13	λ	λ	PROPN
ejpam-5193	307	14	,	,	PUNCT
ejpam-5193	307	15	a	a	PRON
ejpam-5193	307	16	,	,	PUNCT
ejpam-5193	307	17	b	b	NOUN
ejpam-5193	307	18	)	)	PUNCT
ejpam-5193	307	19	tn+1	tn+1	NOUN
ejpam-5193	307	20	n	n	X
ejpam-5193	307	21	!	!	PUNCT
ejpam-5193	307	22	=	=	NOUN
ejpam-5193	308	1	∞∑	∞∑	NUM
ejpam-5193	308	2	n=1	n=1	PROPN
ejpam-5193	308	3	nbg	nbg	PROPN
ejpam-5193	308	4	(	(	PUNCT
ejpam-5193	308	5	r	r	NOUN
ejpam-5193	308	6	)	)	PUNCT
ejpam-5193	308	7	n−1,k(x	n−1,k(x	PROPN
ejpam-5193	308	8	,	,	PUNCT
ejpam-5193	308	9	y;u	y;u	PROPN
ejpam-5193	308	10	,	,	PUNCT
ejpam-5193	308	11	λ	λ	PROPN
ejpam-5193	308	12	,	,	PUNCT
ejpam-5193	308	13	a	a	DET
ejpam-5193	308	14	,	,	PUNCT
ejpam-5193	308	15	b	b	NOUN
ejpam-5193	308	16	)	)	PUNCT
ejpam-5193	308	17	tn	tn	PROPN
ejpam-5193	308	18	n	n	CCONJ
ejpam-5193	308	19	!	!	PUNCT
ejpam-5193	308	20	.	.	PUNCT
ejpam-5193	309	1	comparing	compare	VERB
ejpam-5193	309	2	the	the	DET
ejpam-5193	309	3	coefficients	coefficient	NOUN
ejpam-5193	309	4	of	of	ADP
ejpam-5193	309	5	tn	tn	NOUN
ejpam-5193	309	6	n	n	NOUN
ejpam-5193	309	7	!	!	PUNCT
ejpam-5193	310	1	yields	yield	NOUN
ejpam-5193	310	2	∂	∂	NUM
ejpam-5193	311	1	∂x	∂x	PROPN
ejpam-5193	311	2	bg	bg	PROPN
ejpam-5193	311	3	(	(	PUNCT
ejpam-5193	311	4	r	r	NOUN
ejpam-5193	311	5	)	)	PUNCT
ejpam-5193	311	6	n	n	CCONJ
ejpam-5193	311	7	,	,	PUNCT
ejpam-5193	311	8	k(x	k(x	PROPN
ejpam-5193	311	9	,	,	PUNCT
ejpam-5193	311	10	y;u	y;u	PROPN
ejpam-5193	311	11	,	,	PUNCT
ejpam-5193	311	12	λ	λ	PROPN
ejpam-5193	311	13	,	,	PUNCT
ejpam-5193	311	14	a	a	DET
ejpam-5193	311	15	,	,	PUNCT
ejpam-5193	311	16	b	b	NOUN
ejpam-5193	311	17	)	)	PUNCT
ejpam-5193	311	18	=	=	SYM
ejpam-5193	311	19	nbg	nbg	PROPN
ejpam-5193	311	20	(	(	PUNCT
ejpam-5193	311	21	r	r	NOUN
ejpam-5193	311	22	)	)	PUNCT
ejpam-5193	311	23	n−1,k(x	n−1,k(x	PROPN
ejpam-5193	311	24	,	,	PUNCT
ejpam-5193	311	25	y;u	y;u	PROPN
ejpam-5193	311	26	,	,	PUNCT
ejpam-5193	311	27	λ	λ	PROPN
ejpam-5193	311	28	,	,	PUNCT
ejpam-5193	311	29	a	a	DET
ejpam-5193	311	30	,	,	PUNCT
ejpam-5193	311	31	b	b	NOUN
ejpam-5193	311	32	)	)	PUNCT
ejpam-5193	311	33	.	.	PUNCT
ejpam-5193	312	1	remark	remark	VERB
ejpam-5193	312	2	5.2	5.2	NUM
ejpam-5193	312	3	.	.	PUNCT
ejpam-5193	313	1	this	this	DET
ejpam-5193	313	2	relation	relation	NOUN
ejpam-5193	313	3	shows	show	VERB
ejpam-5193	313	4	that	that	SCONJ
ejpam-5193	313	5	bg	bg	PROPN
ejpam-5193	313	6	(	(	PUNCT
ejpam-5193	313	7	r	r	NOUN
ejpam-5193	313	8	)	)	PUNCT
ejpam-5193	313	9	n	n	CCONJ
ejpam-5193	313	10	,	,	PUNCT
ejpam-5193	313	11	k(x	k(x	PROPN
ejpam-5193	313	12	,	,	PUNCT
ejpam-5193	313	13	y;u	y;u	PROPN
ejpam-5193	313	14	,	,	PUNCT
ejpam-5193	313	15	λ	λ	PROPN
ejpam-5193	313	16	,	,	PUNCT
ejpam-5193	313	17	a	a	DET
ejpam-5193	313	18	,	,	PUNCT
ejpam-5193	313	19	b	b	NOUN
ejpam-5193	313	20	)	)	PUNCT
ejpam-5193	313	21	is	be	AUX
ejpam-5193	313	22	an	an	DET
ejpam-5193	313	23	apell	apell	ADJ
ejpam-5193	313	24	polynomial	polynomial	NOUN
ejpam-5193	313	25	(	(	PUNCT
ejpam-5193	313	26	see	see	VERB
ejpam-5193	313	27	[	[	X
ejpam-5193	313	28	25	25	NUM
ejpam-5193	313	29	,	,	PUNCT
ejpam-5193	313	30	29	29	NUM
ejpam-5193	313	31	]	]	PUNCT
ejpam-5193	313	32	)	)	PUNCT
ejpam-5193	313	33	.	.	PUNCT
ejpam-5193	314	1	belonging	belong	VERB
ejpam-5193	314	2	to	to	ADP
ejpam-5193	314	3	the	the	DET
ejpam-5193	314	4	category	category	NOUN
ejpam-5193	314	5	of	of	ADP
ejpam-5193	314	6	appell	appell	PROPN
ejpam-5193	314	7	polynomials	polynomial	NOUN
ejpam-5193	314	8	,	,	PUNCT
ejpam-5193	314	9	the	the	DET
ejpam-5193	314	10	polynomials	polynomial	NOUN
ejpam-5193	314	11	bg	bg	PROPN
ejpam-5193	314	12	(	(	PUNCT
ejpam-5193	314	13	r	r	NOUN
ejpam-5193	314	14	)	)	PUNCT
ejpam-5193	314	15	n	n	CCONJ
ejpam-5193	314	16	,	,	PUNCT
ejpam-5193	314	17	k(x	k(x	PROPN
ejpam-5193	314	18	,	,	PUNCT
ejpam-5193	314	19	y;u	y;u	PROPN
ejpam-5193	314	20	,	,	PUNCT
ejpam-5193	314	21	λ	λ	PROPN
ejpam-5193	314	22	,	,	PUNCT
ejpam-5193	314	23	a	a	DET
ejpam-5193	314	24	,	,	PUNCT
ejpam-5193	314	25	b	b	NOUN
ejpam-5193	314	26	)	)	PUNCT
ejpam-5193	314	27	are	be	AUX
ejpam-5193	314	28	expected	expect	VERB
ejpam-5193	314	29	to	to	PART
ejpam-5193	314	30	demonstrate	demonstrate	VERB
ejpam-5193	314	31	the	the	DET
ejpam-5193	314	32	following	following	ADJ
ejpam-5193	314	33	characteristics	characteristic	NOUN
ejpam-5193	314	34	:	:	PUNCT
ejpam-5193	314	35	bg	bg	PROPN
ejpam-5193	314	36	(	(	PUNCT
ejpam-5193	314	37	r	r	NOUN
ejpam-5193	314	38	)	)	PUNCT
ejpam-5193	314	39	n	n	CCONJ
ejpam-5193	314	40	,	,	PUNCT
ejpam-5193	314	41	k(x	k(x	PROPN
ejpam-5193	314	42	,	,	PUNCT
ejpam-5193	314	43	y;u	y;u	PROPN
ejpam-5193	314	44	,	,	PUNCT
ejpam-5193	314	45	λ	λ	PROPN
ejpam-5193	314	46	,	,	PUNCT
ejpam-5193	314	47	a	a	DET
ejpam-5193	314	48	,	,	PUNCT
ejpam-5193	314	49	b	b	NOUN
ejpam-5193	314	50	)	)	PUNCT
ejpam-5193	315	1	=	=	SYM
ejpam-5193	315	2	n∑	n∑	NOUN
ejpam-5193	315	3	j=0	j=0	PROPN
ejpam-5193	315	4	(	(	PUNCT
ejpam-5193	315	5	n	n	CCONJ
ejpam-5193	315	6	j	j	NOUN
ejpam-5193	315	7	)	)	PUNCT
ejpam-5193	315	8	cjx	cjx	ADJ
ejpam-5193	315	9	n−j	n−j	ADV
ejpam-5193	315	10	bg	bg	NOUN
ejpam-5193	315	11	(	(	PUNCT
ejpam-5193	315	12	r	r	NOUN
ejpam-5193	315	13	)	)	PUNCT
ejpam-5193	315	14	n	n	CCONJ
ejpam-5193	315	15	,	,	PUNCT
ejpam-5193	315	16	k(x	k(x	PROPN
ejpam-5193	315	17	,	,	PUNCT
ejpam-5193	315	18	y;u	y;u	PROPN
ejpam-5193	315	19	,	,	PUNCT
ejpam-5193	315	20	λ	λ	PROPN
ejpam-5193	315	21	,	,	PUNCT
ejpam-5193	315	22	a	a	DET
ejpam-5193	315	23	,	,	PUNCT
ejpam-5193	315	24	b	b	NOUN
ejpam-5193	315	25	)	)	PUNCT
ejpam-5193	315	26	=	=	SYM
ejpam-5193	316	1			PROPN
ejpam-5193	316	2	n∑	n∑	PROPN
ejpam-5193	316	3	j=0	j=0	PROPN
ejpam-5193	316	4	cj	cj	PROPN
ejpam-5193	316	5	j	j	PROPN
ejpam-5193	316	6	!	!	PUNCT
ejpam-5193	316	7	dj	dj	PROPN
ejpam-5193	316	8	xn	xn	PUNCT
ejpam-5193	317	1	for	for	ADP
ejpam-5193	317	2	some	some	DET
ejpam-5193	317	3	scalar	scalar	NOUN
ejpam-5193	317	4	ck	ck	PROPN
ejpam-5193	317	5	̸=	̸=	PROPN
ejpam-5193	317	6	0	0	NUM
ejpam-5193	317	7	.	.	PUNCT
ejpam-5193	318	1	clearly	clearly	ADV
ejpam-5193	318	2	,	,	PUNCT
ejpam-5193	318	3	using	use	VERB
ejpam-5193	318	4	(	(	PUNCT
ejpam-5193	318	5	2.8	2.8	NUM
ejpam-5193	318	6	)	)	PUNCT
ejpam-5193	318	7	,	,	PUNCT
ejpam-5193	318	8	cj	cj	NOUN
ejpam-5193	318	9	=	=	SYM
ejpam-5193	318	10	bg	bg	PROPN
ejpam-5193	318	11	(	(	PUNCT
ejpam-5193	318	12	r	r	NOUN
ejpam-5193	318	13	)	)	PUNCT
ejpam-5193	318	14	j	j	PROPN
ejpam-5193	318	15	,	,	PUNCT
ejpam-5193	318	16	k(y;u	k(y;u	PROPN
ejpam-5193	318	17	,	,	PUNCT
ejpam-5193	318	18	λ	λ	PROPN
ejpam-5193	318	19	,	,	PUNCT
ejpam-5193	318	20	a	a	DET
ejpam-5193	318	21	,	,	PUNCT
ejpam-5193	318	22	b	b	NOUN
ejpam-5193	318	23	)	)	PUNCT
ejpam-5193	318	24	.	.	PUNCT
ejpam-5193	319	1	hence	hence	ADV
ejpam-5193	319	2	,	,	PUNCT
ejpam-5193	319	3	bg	bg	PROPN
ejpam-5193	319	4	(	(	PUNCT
ejpam-5193	319	5	r	r	NOUN
ejpam-5193	319	6	)	)	PUNCT
ejpam-5193	319	7	n	n	CCONJ
ejpam-5193	319	8	,	,	PUNCT
ejpam-5193	319	9	k(x	k(x	PROPN
ejpam-5193	319	10	,	,	PUNCT
ejpam-5193	319	11	y;u	y;u	PROPN
ejpam-5193	319	12	,	,	PUNCT
ejpam-5193	319	13	λ	λ	PROPN
ejpam-5193	319	14	,	,	PUNCT
ejpam-5193	319	15	a	a	DET
ejpam-5193	319	16	,	,	PUNCT
ejpam-5193	319	17	b	b	NOUN
ejpam-5193	319	18	)	)	PUNCT
ejpam-5193	319	19	=	=	SYM
ejpam-5193	319	20			PROPN
ejpam-5193	319	21	n∑	n∑	PROPN
ejpam-5193	319	22	j=0	j=0	PROPN
ejpam-5193	319	23	bg	bg	PROPN
ejpam-5193	319	24	(	(	PUNCT
ejpam-5193	319	25	r	r	NOUN
ejpam-5193	319	26	)	)	PUNCT
ejpam-5193	319	27	j	j	PROPN
ejpam-5193	319	28	,	,	PUNCT
ejpam-5193	319	29	k(y;u	k(y;u	PROPN
ejpam-5193	319	30	,	,	PUNCT
ejpam-5193	319	31	λ	λ	PROPN
ejpam-5193	319	32	,	,	PUNCT
ejpam-5193	319	33	a	a	PRON
ejpam-5193	319	34	,	,	PUNCT
ejpam-5193	319	35	b	b	NOUN
ejpam-5193	319	36	)	)	PUNCT
ejpam-5193	319	37	j	j	PROPN
ejpam-5193	319	38	!	!	PUNCT
ejpam-5193	319	39	dj	dj	PROPN
ejpam-5193	319	40	xn	xn	PROPN
ejpam-5193	319	41	.	.	PUNCT
ejpam-5193	320	1	(	(	PUNCT
ejpam-5193	320	2	5.2	5.2	NUM
ejpam-5193	320	3	)	)	PUNCT
ejpam-5193	320	4	references	reference	NOUN
ejpam-5193	320	5	1486	1486	NUM
ejpam-5193	320	6	the	the	DET
ejpam-5193	320	7	next	next	ADJ
ejpam-5193	320	8	theorem	theorem	NOUN
ejpam-5193	320	9	contains	contain	VERB
ejpam-5193	320	10	the	the	DET
ejpam-5193	320	11	derivative	derivative	ADJ
ejpam-5193	320	12	formula	formula	NOUN
ejpam-5193	320	13	for	for	ADP
ejpam-5193	320	14	bg	bg	PROPN
ejpam-5193	320	15	(	(	PUNCT
ejpam-5193	320	16	r	r	NOUN
ejpam-5193	320	17	)	)	PUNCT
ejpam-5193	320	18	n	n	CCONJ
ejpam-5193	320	19	,	,	PUNCT
ejpam-5193	320	20	k(x	k(x	PROPN
ejpam-5193	320	21	,	,	PUNCT
ejpam-5193	320	22	y;u	y;u	PROPN
ejpam-5193	320	23	,	,	PUNCT
ejpam-5193	320	24	λ	λ	PROPN
ejpam-5193	320	25	,	,	PUNCT
ejpam-5193	320	26	a	a	DET
ejpam-5193	320	27	,	,	PUNCT
ejpam-5193	320	28	b	b	NOUN
ejpam-5193	320	29	)	)	PUNCT
ejpam-5193	320	30	with	with	ADP
ejpam-5193	320	31	respect	respect	NOUN
ejpam-5193	320	32	to	to	ADP
ejpam-5193	320	33	the	the	DET
ejpam-5193	320	34	variable	variable	ADJ
ejpam-5193	320	35	y.	y.	PROPN
ejpam-5193	320	36	theorem	theorem	VERB
ejpam-5193	320	37	5.3	5.3	NUM
ejpam-5193	320	38	.	.	PUNCT
ejpam-5193	321	1	the	the	DET
ejpam-5193	321	2	following	follow	VERB
ejpam-5193	321	3	derivative	derivative	ADJ
ejpam-5193	321	4	formula	formula	NOUN
ejpam-5193	321	5	holds	hold	VERB
ejpam-5193	321	6	∂	∂	ADJ
ejpam-5193	321	7	∂y	∂y	PROPN
ejpam-5193	321	8	bg	bg	PROPN
ejpam-5193	321	9	(	(	PUNCT
ejpam-5193	321	10	r	r	NOUN
ejpam-5193	321	11	)	)	PUNCT
ejpam-5193	321	12	n	n	CCONJ
ejpam-5193	321	13	,	,	PUNCT
ejpam-5193	321	14	k(x	k(x	PROPN
ejpam-5193	321	15	,	,	PUNCT
ejpam-5193	321	16	y;u	y;u	PROPN
ejpam-5193	321	17	,	,	PUNCT
ejpam-5193	321	18	λ	λ	PROPN
ejpam-5193	321	19	,	,	PUNCT
ejpam-5193	321	20	a	a	DET
ejpam-5193	321	21	,	,	PUNCT
ejpam-5193	321	22	b	b	NOUN
ejpam-5193	321	23	)	)	PUNCT
ejpam-5193	321	24	=	=	SYM
ejpam-5193	321	25	bg	bg	PROPN
ejpam-5193	321	26	(	(	PUNCT
ejpam-5193	321	27	r	r	NOUN
ejpam-5193	321	28	)	)	PUNCT
ejpam-5193	321	29	n	n	CCONJ
ejpam-5193	321	30	,	,	PUNCT
ejpam-5193	321	31	k(x+	k(x+	PROPN
ejpam-5193	321	32	1	1	NUM
ejpam-5193	321	33	,	,	PUNCT
ejpam-5193	321	34	y;u	y;u	PROPN
ejpam-5193	321	35	,	,	PUNCT
ejpam-5193	321	36	λ	λ	PROPN
ejpam-5193	321	37	,	,	PUNCT
ejpam-5193	321	38	a	a	PRON
ejpam-5193	321	39	,	,	PUNCT
ejpam-5193	321	40	b)−	b)−	PROPN
ejpam-5193	321	41	bg	bg	PROPN
ejpam-5193	321	42	(	(	PUNCT
ejpam-5193	321	43	r	r	NOUN
ejpam-5193	321	44	)	)	PUNCT
ejpam-5193	321	45	n	n	CCONJ
ejpam-5193	321	46	,	,	PUNCT
ejpam-5193	321	47	k(x	k(x	PROPN
ejpam-5193	321	48	,	,	PUNCT
ejpam-5193	321	49	y;u	y;u	PROPN
ejpam-5193	321	50	,	,	PUNCT
ejpam-5193	321	51	λ	λ	PROPN
ejpam-5193	321	52	,	,	PUNCT
ejpam-5193	321	53	a	a	DET
ejpam-5193	321	54	,	,	PUNCT
ejpam-5193	321	55	b	b	NOUN
ejpam-5193	321	56	)	)	PUNCT
ejpam-5193	321	57	.	.	PUNCT
ejpam-5193	322	1	(	(	PUNCT
ejpam-5193	322	2	5.3	5.3	NUM
ejpam-5193	322	3	)	)	PUNCT
ejpam-5193	322	4	proof	proof	NOUN
ejpam-5193	322	5	.	.	PUNCT
ejpam-5193	323	1	using	use	VERB
ejpam-5193	323	2	definition	definition	NOUN
ejpam-5193	323	3	2.1	2.1	NUM
ejpam-5193	323	4	,	,	PUNCT
ejpam-5193	323	5	we	we	PRON
ejpam-5193	323	6	have	have	VERB
ejpam-5193	323	7	∞∑	∞∑	NUM
ejpam-5193	323	8	n=0	n=0	NUM
ejpam-5193	323	9	∂	∂	NOUN
ejpam-5193	323	10	∂y	∂y	PROPN
ejpam-5193	323	11	bg	bg	PROPN
ejpam-5193	323	12	(	(	PUNCT
ejpam-5193	323	13	r	r	NOUN
ejpam-5193	323	14	)	)	PUNCT
ejpam-5193	323	15	n	n	CCONJ
ejpam-5193	323	16	,	,	PUNCT
ejpam-5193	323	17	k(x	k(x	PROPN
ejpam-5193	323	18	,	,	PUNCT
ejpam-5193	323	19	y;u	y;u	PROPN
ejpam-5193	323	20	,	,	PUNCT
ejpam-5193	323	21	λ	λ	PROPN
ejpam-5193	323	22	,	,	PUNCT
ejpam-5193	323	23	a	a	DET
ejpam-5193	323	24	,	,	PUNCT
ejpam-5193	323	25	b	b	NOUN
ejpam-5193	323	26	)	)	PUNCT
ejpam-5193	323	27	tn	tn	NOUN
ejpam-5193	323	28	n	n	CCONJ
ejpam-5193	323	29	!	!	PUNCT
ejpam-5193	324	1	=	=	PUNCT
ejpam-5193	324	2	(	(	PUNCT
ejpam-5193	324	3	lik(1−	lik(1−	X
ejpam-5193	324	4	(	(	PUNCT
ejpam-5193	324	5	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	324	6	)	)	PUNCT
ejpam-5193	324	7	λbt	λbt	VERB
ejpam-5193	324	8	−	−	PROPN
ejpam-5193	324	9	ua−t	ua−t	ADJ
ejpam-5193	324	10	)	)	PUNCT
ejpam-5193	324	11	r	r	NOUN
ejpam-5193	324	12	ext+y(et−1)(et	ext+y(et−1)(et	NOUN
ejpam-5193	324	13	−	−	ADP
ejpam-5193	324	14	1	1	NUM
ejpam-5193	324	15	)	)	PUNCT
ejpam-5193	324	16	=	=	SYM
ejpam-5193	324	17	(	(	PUNCT
ejpam-5193	324	18	lik(1−	lik(1−	X
ejpam-5193	324	19	(	(	PUNCT
ejpam-5193	324	20	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	324	21	)	)	PUNCT
ejpam-5193	324	22	λbt	λbt	VERB
ejpam-5193	324	23	−	−	PROPN
ejpam-5193	324	24	ua−t	ua−t	ADJ
ejpam-5193	324	25	)	)	PUNCT
ejpam-5193	324	26	r	r	NOUN
ejpam-5193	324	27	e(x+1)t+y(et−1	e(x+1)t+y(et−1	NOUN
ejpam-5193	324	28	)	)	PUNCT
ejpam-5193	325	1	−	−	PROPN
ejpam-5193	326	1	(	(	PUNCT
ejpam-5193	326	2	lik(1−	lik(1−	PROPN
ejpam-5193	326	3	(	(	PUNCT
ejpam-5193	326	4	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-5193	326	5	)	)	PUNCT
ejpam-5193	326	6	λbt	λbt	VERB
ejpam-5193	326	7	−	−	PROPN
ejpam-5193	326	8	ua−t	ua−t	ADJ
ejpam-5193	326	9	)	)	PUNCT
ejpam-5193	326	10	r	r	NOUN
ejpam-5193	326	11	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5193	326	12	)	)	PUNCT
ejpam-5193	326	13	=	=	PUNCT
ejpam-5193	327	1	∞∑	∞∑	NUM
ejpam-5193	327	2	n=0	n=0	ADJ
ejpam-5193	327	3	bg	bg	NOUN
ejpam-5193	327	4	(	(	PUNCT
ejpam-5193	327	5	r	r	NOUN
ejpam-5193	327	6	)	)	PUNCT
ejpam-5193	327	7	n	n	CCONJ
ejpam-5193	327	8	,	,	PUNCT
ejpam-5193	327	9	k(x+	k(x+	PROPN
ejpam-5193	327	10	1	1	NUM
ejpam-5193	327	11	,	,	PUNCT
ejpam-5193	327	12	y;u	y;u	PROPN
ejpam-5193	327	13	,	,	PUNCT
ejpam-5193	327	14	λ	λ	PROPN
ejpam-5193	327	15	)	)	PUNCT
ejpam-5193	327	16	tn	tn	PROPN
ejpam-5193	327	17	n	n	PROPN
ejpam-5193	327	18	!	!	PUNCT
ejpam-5193	327	19	−	−	PROPN
ejpam-5193	328	1	∞∑	∞∑	PRON
ejpam-5193	328	2	n=0	n=0	ADJ
ejpam-5193	328	3	bg	bg	NOUN
ejpam-5193	328	4	(	(	PUNCT
ejpam-5193	328	5	r	r	NOUN
ejpam-5193	328	6	)	)	PUNCT
ejpam-5193	328	7	n	n	CCONJ
ejpam-5193	328	8	,	,	PUNCT
ejpam-5193	328	9	k(x	k(x	PROPN
ejpam-5193	328	10	,	,	PUNCT
ejpam-5193	328	11	y;u	y;u	PROPN
ejpam-5193	328	12	,	,	PUNCT
ejpam-5193	328	13	λ	λ	PROPN
ejpam-5193	328	14	)	)	PUNCT
ejpam-5193	328	15	tn	tn	PROPN
ejpam-5193	328	16	n	n	NOUN
ejpam-5193	328	17	!	!	PUNCT
ejpam-5193	328	18	=	=	NOUN
ejpam-5193	329	1	∞∑	∞∑	PRON
ejpam-5193	329	2	n=0	n=0	NUM
ejpam-5193	329	3	{	{	PUNCT
ejpam-5193	329	4	bg	bg	PROPN
ejpam-5193	329	5	(	(	PUNCT
ejpam-5193	329	6	r	r	NOUN
ejpam-5193	329	7	)	)	PUNCT
ejpam-5193	329	8	n	n	CCONJ
ejpam-5193	329	9	,	,	PUNCT
ejpam-5193	329	10	k(x+	k(x+	PROPN
ejpam-5193	329	11	1	1	NUM
ejpam-5193	329	12	,	,	PUNCT
ejpam-5193	329	13	y;u	y;u	PROPN
ejpam-5193	329	14	,	,	PUNCT
ejpam-5193	329	15	λ	λ	PROPN
ejpam-5193	329	16	,	,	PUNCT
ejpam-5193	329	17	a	a	PRON
ejpam-5193	329	18	,	,	PUNCT
ejpam-5193	329	19	b)−	b)−	PROPN
ejpam-5193	329	20	bg	bg	PROPN
ejpam-5193	329	21	(	(	PUNCT
ejpam-5193	329	22	r	r	NOUN
ejpam-5193	329	23	)	)	PUNCT
ejpam-5193	329	24	n	n	CCONJ
ejpam-5193	329	25	,	,	PUNCT
ejpam-5193	329	26	k(x	k(x	PROPN
ejpam-5193	329	27	,	,	PUNCT
ejpam-5193	329	28	y;u	y;u	PROPN
ejpam-5193	329	29	,	,	PUNCT
ejpam-5193	329	30	λ	λ	PROPN
ejpam-5193	329	31	,	,	PUNCT
ejpam-5193	329	32	a	a	DET
ejpam-5193	329	33	,	,	PUNCT
ejpam-5193	329	34	b	b	NOUN
ejpam-5193	329	35	)	)	PUNCT
ejpam-5193	329	36	}	}	PUNCT
ejpam-5193	329	37	tn	tn	PROPN
ejpam-5193	329	38	n	n	X
ejpam-5193	329	39	!	!	PUNCT
ejpam-5193	329	40	.	.	PUNCT
ejpam-5193	330	1	comparing	compare	VERB
ejpam-5193	330	2	the	the	DET
ejpam-5193	330	3	coefficients	coefficient	NOUN
ejpam-5193	330	4	of	of	ADP
ejpam-5193	330	5	tn	tn	NOUN
ejpam-5193	330	6	n	n	NOUN
ejpam-5193	330	7	!	!	PUNCT
ejpam-5193	331	1	yields	yield	NOUN
ejpam-5193	331	2	∂	∂	NOUN
ejpam-5193	331	3	∂y	∂y	PROPN
ejpam-5193	331	4	bg	bg	PROPN
ejpam-5193	331	5	(	(	PUNCT
ejpam-5193	331	6	r	r	NOUN
ejpam-5193	331	7	)	)	PUNCT
ejpam-5193	331	8	n	n	CCONJ
ejpam-5193	331	9	,	,	PUNCT
ejpam-5193	331	10	k(x	k(x	PROPN
ejpam-5193	331	11	,	,	PUNCT
ejpam-5193	331	12	y;u	y;u	PROPN
ejpam-5193	331	13	,	,	PUNCT
ejpam-5193	331	14	λ	λ	PROPN
ejpam-5193	331	15	,	,	PUNCT
ejpam-5193	331	16	a	a	DET
ejpam-5193	331	17	,	,	PUNCT
ejpam-5193	331	18	b	b	NOUN
ejpam-5193	331	19	)	)	PUNCT
ejpam-5193	331	20	=	=	SYM
ejpam-5193	331	21	bg	bg	PROPN
ejpam-5193	331	22	(	(	PUNCT
ejpam-5193	331	23	r	r	NOUN
ejpam-5193	331	24	)	)	PUNCT
ejpam-5193	331	25	n	n	CCONJ
ejpam-5193	331	26	,	,	PUNCT
ejpam-5193	331	27	k(x+	k(x+	PROPN
ejpam-5193	331	28	1	1	NUM
ejpam-5193	331	29	,	,	PUNCT
ejpam-5193	331	30	y;u	y;u	PROPN
ejpam-5193	331	31	,	,	PUNCT
ejpam-5193	331	32	λ	λ	PROPN
ejpam-5193	331	33	,	,	PUNCT
ejpam-5193	331	34	a	a	PRON
ejpam-5193	331	35	,	,	PUNCT
ejpam-5193	331	36	b)−	b)−	PROPN
ejpam-5193	331	37	bg	bg	PROPN
ejpam-5193	331	38	(	(	PUNCT
ejpam-5193	331	39	r	r	NOUN
ejpam-5193	331	40	)	)	PUNCT
ejpam-5193	331	41	n	n	CCONJ
ejpam-5193	331	42	,	,	PUNCT
ejpam-5193	331	43	k(x	k(x	PROPN
ejpam-5193	331	44	,	,	PUNCT
ejpam-5193	331	45	y;u	y;u	PROPN
ejpam-5193	331	46	,	,	PUNCT
ejpam-5193	331	47	λ	λ	PROPN
ejpam-5193	331	48	,	,	PUNCT
ejpam-5193	331	49	a	a	DET
ejpam-5193	331	50	,	,	PUNCT
ejpam-5193	331	51	b	b	NOUN
ejpam-5193	331	52	)	)	PUNCT
ejpam-5193	331	53	.	.	PUNCT
ejpam-5193	332	1	acknowledgement	acknowledgement	NOUN
ejpam-5193	332	2	.	.	PUNCT
ejpam-5193	333	1	this	this	DET
ejpam-5193	333	2	research	research	NOUN
ejpam-5193	333	3	has	have	AUX
ejpam-5193	333	4	been	be	AUX
ejpam-5193	333	5	funded	fund	VERB
ejpam-5193	333	6	by	by	ADP
ejpam-5193	333	7	cebu	cebu	PROPN
ejpam-5193	333	8	normal	normal	ADJ
ejpam-5193	333	9	university	university	PROPN
ejpam-5193	333	10	(	(	PUNCT
ejpam-5193	333	11	cnu	cnu	PROPN
ejpam-5193	333	12	)	)	PUNCT
ejpam-5193	333	13	through	through	ADP
ejpam-5193	333	14	its	its	PRON
ejpam-5193	333	15	center	center	NOUN
ejpam-5193	333	16	for	for	ADP
ejpam-5193	333	17	research	research	NOUN
ejpam-5193	333	18	and	and	CCONJ
ejpam-5193	333	19	development	development	NOUN
ejpam-5193	333	20	(	(	PUNCT
ejpam-5193	333	21	crd	crd	NOUN
ejpam-5193	333	22	)	)	PUNCT
ejpam-5193	333	23	.	.	PUNCT
ejpam-5193	334	1	references	reference	NOUN
ejpam-5193	334	2	[	[	X
ejpam-5193	334	3	1	1	NUM
ejpam-5193	334	4	]	]	PUNCT
ejpam-5193	334	5	m.	m.	NOUN
ejpam-5193	334	6	abramowitz	abramowitz	PROPN
ejpam-5193	334	7	and	and	CCONJ
ejpam-5193	334	8	i.a	i.a	PROPN
ejpam-5193	334	9	.	.	PROPN
ejpam-5193	334	10	stegun	stegun	PROPN
ejpam-5193	334	11	.	.	PUNCT
ejpam-5193	335	1	handbook	handbook	NOUN
ejpam-5193	335	2	of	of	ADP
ejpam-5193	335	3	mathematical	mathematical	ADJ
ejpam-5193	335	4	functions	function	NOUN
ejpam-5193	335	5	,	,	PUNCT
ejpam-5193	335	6	volume	volume	NOUN
ejpam-5193	335	7	48	48	NUM
ejpam-5193	335	8	.	.	PUNCT
ejpam-5193	336	1	dover	dover	PROPN
ejpam-5193	336	2	,	,	PUNCT
ejpam-5193	336	3	new	new	PROPN
ejpam-5193	336	4	york	york	PROPN
ejpam-5193	336	5	,	,	PUNCT
ejpam-5193	336	6	1970	1970	NUM
ejpam-5193	336	7	.	.	PUNCT
ejpam-5193	337	1	[	[	X
ejpam-5193	337	2	2	2	NUM
ejpam-5193	337	3	]	]	X
ejpam-5193	337	4	n.	n.	PROPN
ejpam-5193	337	5	alam	alam	PROPN
ejpam-5193	337	6	,	,	PUNCT
ejpam-5193	337	7	w.	w.	PROPN
ejpam-5193	337	8	a.	a.	PROPN
ejpam-5193	337	9	khan	khan	PROPN
ejpam-5193	337	10	,	,	PUNCT
ejpam-5193	337	11	s.	s.	PROPN
ejpam-5193	337	12	obeidat	obeidat	PROPN
ejpam-5193	337	13	,	,	PUNCT
ejpam-5193	337	14	g.	g.	PROPN
ejpam-5193	337	15	muhiuddin	muhiuddin	PROPN
ejpam-5193	337	16	,	,	PUNCT
ejpam-5193	337	17	n.s	n.s	PROPN
ejpam-5193	337	18	.	.	PROPN
ejpam-5193	337	19	diab	diab	PROPN
ejpam-5193	337	20	,	,	PUNCT
ejpam-5193	337	21	h.n	h.n	PROPN
ejpam-5193	337	22	.	.	PROPN
ejpam-5193	337	23	zaidi	zaidi	PROPN
ejpam-5193	337	24	,	,	PUNCT
ejpam-5193	337	25	a.	a.	NOUN
ejpam-5193	337	26	altaleb	altaleb	PROPN
ejpam-5193	337	27	,	,	PUNCT
ejpam-5193	337	28	and	and	CCONJ
ejpam-5193	337	29	l.	l.	PROPN
ejpam-5193	337	30	bachioua	bachioua	PROPN
ejpam-5193	337	31	.	.	PUNCT
ejpam-5193	338	1	a	a	DET
ejpam-5193	338	2	note	note	NOUN
ejpam-5193	338	3	on	on	ADP
ejpam-5193	338	4	bell	bell	NOUN
ejpam-5193	338	5	-	-	PUNCT
ejpam-5193	338	6	based	base	VERB
ejpam-5193	338	7	bernoulli	bernoulli	NOUN
ejpam-5193	338	8	and	and	CCONJ
ejpam-5193	338	9	euler	euler	NOUN
ejpam-5193	338	10	polynomials	polynomial	NOUN
ejpam-5193	338	11	of	of	ADP
ejpam-5193	338	12	complex	complex	ADJ
ejpam-5193	338	13	variable	variable	NOUN
ejpam-5193	338	14	.	.	PUNCT
ejpam-5193	339	1	computer	computer	NOUN
ejpam-5193	339	2	modelling	modelling	NOUN
ejpam-5193	339	3	in	in	ADP
ejpam-5193	339	4	engineering	engineering	NOUN
ejpam-5193	339	5	and	and	CCONJ
ejpam-5193	339	6	sciences	science	NOUN
ejpam-5193	339	7	,	,	PUNCT
ejpam-5193	339	8	153(1):187–209	153(1):187–209	NUM
ejpam-5193	339	9	,	,	PUNCT
ejpam-5193	339	10	2023	2023	NUM
ejpam-5193	339	11	.	.	PUNCT
ejpam-5193	340	1	references	reference	NOUN
ejpam-5193	340	2	1487	1487	NUM
ejpam-5193	340	3	[	[	X
ejpam-5193	340	4	3	3	NUM
ejpam-5193	340	5	]	]	X
ejpam-5193	340	6	n.	n.	PROPN
ejpam-5193	340	7	alam	alam	PROPN
ejpam-5193	340	8	,	,	PUNCT
ejpam-5193	340	9	w.a	w.a	PROPN
ejpam-5193	340	10	.	.	PROPN
ejpam-5193	340	11	khan	khan	PROPN
ejpam-5193	340	12	,	,	PUNCT
ejpam-5193	340	13	c.	c.	PROPN
ejpam-5193	340	14	kizilates	kizilates	PROPN
ejpam-5193	340	15	,	,	PUNCT
ejpam-5193	340	16	s.	s.	PROPN
ejpam-5193	340	17	obeidat	obeidat	PROPN
ejpam-5193	340	18	,	,	PUNCT
ejpam-5193	340	19	c.s	c.s	PROPN
ejpam-5193	340	20	.	.	PROPN
ejpam-5193	340	21	ryoo	ryoo	PROPN
ejpam-5193	340	22	,	,	PUNCT
ejpam-5193	340	23	and	and	CCONJ
ejpam-5193	340	24	n.s	n.s	PROPN
ejpam-5193	340	25	.	.	PROPN
ejpam-5193	340	26	diab	diab	PROPN
ejpam-5193	340	27	.	.	PUNCT
ejpam-5193	341	1	some	some	DET
ejpam-5193	341	2	explicit	explicit	ADJ
ejpam-5193	341	3	properties	property	NOUN
ejpam-5193	341	4	of	of	ADP
ejpam-5193	341	5	frobenius	frobenius	NOUN
ejpam-5193	341	6	-	-	PUNCT
ejpam-5193	341	7	euler	euler	NOUN
ejpam-5193	341	8	-	-	PUNCT
ejpam-5193	341	9	genocchi	genocchi	PROPN
ejpam-5193	341	10	polynomials	polynomial	VERB
ejpam-5193	341	11	with	with	ADP
ejpam-5193	341	12	applications	application	NOUN
ejpam-5193	341	13	in	in	ADP
ejpam-5193	341	14	computer	computer	NOUN
ejpam-5193	341	15	modeling	modeling	NOUN
ejpam-5193	341	16	.	.	PUNCT
ejpam-5193	342	1	symmetry	symmetry	NOUN
ejpam-5193	342	2	,	,	PUNCT
ejpam-5193	342	3	15(1358):1–20	15(1358):1–20	NUM
ejpam-5193	342	4	,	,	PUNCT
ejpam-5193	342	5	2023	2023	NUM
ejpam-5193	342	6	.	.	PUNCT
ejpam-5193	343	1	[	[	X
ejpam-5193	343	2	4	4	NUM
ejpam-5193	343	3	]	]	X
ejpam-5193	343	4	n.	n.	PROPN
ejpam-5193	343	5	alam	alam	PROPN
ejpam-5193	343	6	,	,	PUNCT
ejpam-5193	343	7	w.a	w.a	PROPN
ejpam-5193	343	8	.	.	PROPN
ejpam-5193	343	9	khan	khan	PROPN
ejpam-5193	343	10	,	,	PUNCT
ejpam-5193	343	11	and	and	CCONJ
ejpam-5193	343	12	c.s	c.s	PROPN
ejpam-5193	343	13	.	.	PROPN
ejpam-5193	343	14	ryoo	ryoo	PROPN
ejpam-5193	343	15	.	.	PUNCT
ejpam-5193	344	1	a	a	DET
ejpam-5193	344	2	note	note	NOUN
ejpam-5193	344	3	on	on	ADP
ejpam-5193	344	4	bell	bell	NOUN
ejpam-5193	344	5	-	-	PUNCT
ejpam-5193	344	6	based	base	VERB
ejpam-5193	344	7	apostol	apostol	NOUN
ejpam-5193	344	8	-	-	PUNCT
ejpam-5193	344	9	type	type	NOUN
ejpam-5193	344	10	frobeniuseuler	frobeniuseuler	NOUN
ejpam-5193	344	11	polynomials	polynomial	NOUN
ejpam-5193	344	12	of	of	ADP
ejpam-5193	344	13	complex	complex	ADJ
ejpam-5193	344	14	variable	variable	NOUN
ejpam-5193	344	15	with	with	ADP
ejpam-5193	344	16	its	its	PRON
ejpam-5193	344	17	certain	certain	ADJ
ejpam-5193	344	18	applications	application	NOUN
ejpam-5193	344	19	.	.	PUNCT
ejpam-5193	345	1	mathematics	mathematic	NOUN
ejpam-5193	345	2	,	,	PUNCT
ejpam-5193	345	3	2022(12):2109	2022(12):2109	NUM
ejpam-5193	345	4	,	,	PUNCT
ejpam-5193	345	5	10	10	NUM
ejpam-5193	345	6	.	.	PUNCT
ejpam-5193	346	1	[	[	X
ejpam-5193	346	2	5	5	X
ejpam-5193	346	3	]	]	PUNCT
ejpam-5193	346	4	s.	s.	PROPN
ejpam-5193	346	5	araci	araci	PROPN
ejpam-5193	346	6	.	.	PUNCT
ejpam-5193	347	1	novel	novel	ADJ
ejpam-5193	347	2	identities	identity	NOUN
ejpam-5193	347	3	involving	involve	VERB
ejpam-5193	347	4	genocchi	genocchi	PROPN
ejpam-5193	347	5	numbers	number	NOUN
ejpam-5193	347	6	and	and	CCONJ
ejpam-5193	347	7	polynomials	polynomial	NOUN
ejpam-5193	347	8	arising	arise	VERB
ejpam-5193	347	9	from	from	ADP
ejpam-5193	347	10	application	application	NOUN
ejpam-5193	347	11	of	of	ADP
ejpam-5193	347	12	umbral	umbral	ADJ
ejpam-5193	347	13	calculus	calculus	NOUN
ejpam-5193	347	14	.	.	PUNCT
ejpam-5193	348	1	appl	appl	PROPN
ejpam-5193	348	2	.	.	PROPN
ejpam-5193	348	3	math	math	PROPN
ejpam-5193	348	4	.	.	PUNCT
ejpam-5193	349	1	comput	comput	NOUN
ejpam-5193	349	2	.	.	PUNCT
ejpam-5193	349	3	,	,	PUNCT
ejpam-5193	349	4	233:599–607	233:599–607	NUM
ejpam-5193	349	5	.	.	PUNCT
ejpam-5193	349	6	,	,	PUNCT
ejpam-5193	349	7	2014	2014	NUM
ejpam-5193	349	8	.	.	PUNCT
ejpam-5193	350	1	[	[	X
ejpam-5193	350	2	6	6	NUM
ejpam-5193	350	3	]	]	PUNCT
ejpam-5193	350	4	s.	s.	PROPN
ejpam-5193	350	5	araci	araci	PROPN
ejpam-5193	350	6	,	,	PUNCT
ejpam-5193	350	7	e.	e.	PROPN
ejpam-5193	350	8	sen	sen	PROPN
ejpam-5193	350	9	,	,	PUNCT
ejpam-5193	350	10	and	and	CCONJ
ejpam-5193	350	11	m.	m.	NOUN
ejpam-5193	350	12	acikgoz	acikgoz	VERB
ejpam-5193	350	13	.	.	PUNCT
ejpam-5193	351	1	theorems	theorem	NOUN
ejpam-5193	351	2	on	on	ADP
ejpam-5193	351	3	genocchi	genocchi	PROPN
ejpam-5193	351	4	polynomials	polynomial	NOUN
ejpam-5193	351	5	of	of	ADP
ejpam-5193	351	6	higher	high	ADJ
ejpam-5193	351	7	order	order	NOUN
ejpam-5193	351	8	arising	arise	VERB
ejpam-5193	351	9	from	from	ADP
ejpam-5193	351	10	genocchi	genocchi	PROPN
ejpam-5193	351	11	basis	basis	NOUN
ejpam-5193	351	12	.	.	PUNCT
ejpam-5193	352	1	taiwanese	taiwanese	ADJ
ejpam-5193	352	2	j.	j.	PROPN
ejpam-5193	352	3	math	math	PROPN
ejpam-5193	352	4	.	.	PUNCT
ejpam-5193	353	1	math	math	NOUN
ejpam-5193	353	2	.	.	PUNCT
ejpam-5193	354	1	sci	sci	PROPN
ejpam-5193	354	2	.	.	PROPN
ejpam-5193	354	3	,	,	PUNCT
ejpam-5193	354	4	18(2):473–482	18(2):473–482	PROPN
ejpam-5193	354	5	,	,	PUNCT
ejpam-5193	354	6	2014	2014	NUM
ejpam-5193	354	7	.	.	PUNCT
ejpam-5193	355	1	[	[	X
ejpam-5193	355	2	7	7	NUM
ejpam-5193	355	3	]	]	PUNCT
ejpam-5193	355	4	a.	a.	NOUN
ejpam-5193	355	5	ayed	aye	VERB
ejpam-5193	355	6	,	,	PUNCT
ejpam-5193	355	7	w.a	w.a	PROPN
ejpam-5193	355	8	.	.	PROPN
ejpam-5193	355	9	khan	khan	PROPN
ejpam-5193	355	10	,	,	PUNCT
ejpam-5193	355	11	and	and	CCONJ
ejpam-5193	355	12	c.s	c.s	PROPN
ejpam-5193	355	13	.	.	PROPN
ejpam-5193	355	14	ryoo	ryoo	NOUN
ejpam-5193	355	15	.	.	PUNCT
ejpam-5193	356	1	certain	certain	ADJ
ejpam-5193	356	2	properties	property	NOUN
ejpam-5193	356	3	on	on	ADP
ejpam-5193	356	4	bell	bell	NOUN
ejpam-5193	356	5	-	-	PUNCT
ejpam-5193	356	6	based	base	VERB
ejpam-5193	356	7	apostol	apostol	NOUN
ejpam-5193	356	8	-	-	PUNCT
ejpam-5193	356	9	type	type	NOUN
ejpam-5193	356	10	frobenius	frobenius	NOUN
ejpam-5193	356	11	-	-	PUNCT
ejpam-5193	356	12	genocchi	genocchi	NOUN
ejpam-5193	356	13	polynomials	polynomial	NOUN
ejpam-5193	356	14	and	and	CCONJ
ejpam-5193	356	15	its	its	PRON
ejpam-5193	356	16	applications	application	NOUN
ejpam-5193	356	17	.	.	PUNCT
ejpam-5193	357	1	advanced	advanced	ADJ
ejpam-5193	357	2	mathematical	mathematical	ADJ
ejpam-5193	357	3	models	model	NOUN
ejpam-5193	357	4	and	and	CCONJ
ejpam-5193	357	5	applications	application	NOUN
ejpam-5193	357	6	,	,	PUNCT
ejpam-5193	357	7	1(8):92–107	1(8):92–107	NUM
ejpam-5193	357	8	,	,	PUNCT
ejpam-5193	357	9	2023	2023	NUM
ejpam-5193	357	10	.	.	PUNCT
ejpam-5193	358	1	[	[	X
ejpam-5193	358	2	8	8	NUM
ejpam-5193	358	3	]	]	PUNCT
ejpam-5193	358	4	a.	a.	NOUN
ejpam-5193	358	5	ayed	aye	VERB
ejpam-5193	358	6	,	,	PUNCT
ejpam-5193	358	7	w.a	w.a	PROPN
ejpam-5193	358	8	.	.	PROPN
ejpam-5193	358	9	khan	khan	PROPN
ejpam-5193	358	10	,	,	PUNCT
ejpam-5193	358	11	and	and	CCONJ
ejpam-5193	358	12	c.s	c.s	PROPN
ejpam-5193	358	13	.	.	PROPN
ejpam-5193	358	14	ryoo	ryoo	NOUN
ejpam-5193	358	15	.	.	PUNCT
ejpam-5193	359	1	certain	certain	ADJ
ejpam-5193	359	2	properties	property	NOUN
ejpam-5193	359	3	on	on	ADP
ejpam-5193	359	4	bell	bell	NOUN
ejpam-5193	359	5	based	base	VERB
ejpam-5193	359	6	apostolfrobenius	apostolfrobenius	NOUN
ejpam-5193	359	7	-	-	PUNCT
ejpam-5193	359	8	genocchi	genocchi	PROPN
ejpam-5193	359	9	polynomials	polynomial	NOUN
ejpam-5193	359	10	of	of	ADP
ejpam-5193	359	11	complex	complex	ADJ
ejpam-5193	359	12	variables	variable	NOUN
ejpam-5193	359	13	.	.	PUNCT
ejpam-5193	360	1	journal	journal	NOUN
ejpam-5193	360	2	of	of	ADP
ejpam-5193	360	3	mathematics	mathematic	NOUN
ejpam-5193	360	4	and	and	CCONJ
ejpam-5193	360	5	computer	computer	NOUN
ejpam-5193	360	6	science	science	NOUN
ejpam-5193	360	7	,	,	PUNCT
ejpam-5193	360	8	33(3):326–338	33(3):326–338	NOUN
ejpam-5193	360	9	,	,	PUNCT
ejpam-5193	360	10	2024	2024	NUM
ejpam-5193	360	11	.	.	PUNCT
ejpam-5193	361	1	[	[	X
ejpam-5193	361	2	9	9	NUM
ejpam-5193	361	3	]	]	PUNCT
ejpam-5193	361	4	a.	a.	NOUN
ejpam-5193	361	5	bayad	bayad	NOUN
ejpam-5193	361	6	and	and	CCONJ
ejpam-5193	361	7	y.	y.	PROPN
ejpam-5193	361	8	hamahata	hamahata	PROPN
ejpam-5193	361	9	.	.	PUNCT
ejpam-5193	362	1	polylogarithms	polylogarithm	NOUN
ejpam-5193	362	2	and	and	CCONJ
ejpam-5193	362	3	poly	poly	ADJ
ejpam-5193	362	4	-	-	PUNCT
ejpam-5193	362	5	bernoulli	bernoulli	NOUN
ejpam-5193	362	6	polynomials	polynomial	NOUN
ejpam-5193	362	7	.	.	PUNCT
ejpam-5193	363	1	kyushu	kyushu	PROPN
ejpam-5193	363	2	j.	j.	PROPN
ejpam-5193	363	3	math	math	PROPN
ejpam-5193	363	4	,	,	PUNCT
ejpam-5193	363	5	65:15–24	65:15–24	PROPN
ejpam-5193	363	6	,	,	PUNCT
ejpam-5193	363	7	2011	2011	NUM
ejpam-5193	363	8	.	.	PUNCT
ejpam-5193	364	1	[	[	X
ejpam-5193	364	2	10	10	NUM
ejpam-5193	364	3	]	]	X
ejpam-5193	364	4	l.	l.	PROPN
ejpam-5193	364	5	comtet	comtet	PROPN
ejpam-5193	364	6	.	.	PUNCT
ejpam-5193	365	1	advanced	advanced	ADJ
ejpam-5193	365	2	combinatorics	combinatoric	NOUN
ejpam-5193	365	3	.	.	PUNCT
ejpam-5193	366	1	reidel	reidel	PROPN
ejpam-5193	366	2	,	,	PUNCT
ejpam-5193	366	3	dordrecht	dordrecht	PROPN
ejpam-5193	366	4	,	,	PUNCT
ejpam-5193	366	5	the	the	DET
ejpam-5193	366	6	netherlands	netherlands	PROPN
ejpam-5193	366	7	.	.	PUNCT
ejpam-5193	366	8	,	,	PUNCT
ejpam-5193	366	9	1974	1974	NUM
ejpam-5193	366	10	.	.	PUNCT
ejpam-5193	367	1	[	[	X
ejpam-5193	367	2	11	11	NUM
ejpam-5193	367	3	]	]	X
ejpam-5193	367	4	c.	c.	PROPN
ejpam-5193	367	5	corcino	corcino	PROPN
ejpam-5193	367	6	and	and	CCONJ
ejpam-5193	367	7	r.	r.	PROPN
ejpam-5193	367	8	corcino	corcino	PROPN
ejpam-5193	367	9	.	.	PUNCT
ejpam-5193	368	1	higher	high	ADJ
ejpam-5193	368	2	order	order	NOUN
ejpam-5193	368	3	apostol	apostol	NOUN
ejpam-5193	368	4	-	-	PUNCT
ejpam-5193	368	5	type	type	NOUN
ejpam-5193	368	6	poly	poly	ADJ
ejpam-5193	368	7	-	-	PUNCT
ejpam-5193	368	8	genocchi	genocchi	NOUN
ejpam-5193	368	9	polynomials	polynomial	NOUN
ejpam-5193	368	10	with	with	ADP
ejpam-5193	368	11	parameters	parameter	NOUN
ejpam-5193	368	12	a	a	PRON
ejpam-5193	368	13	,	,	PUNCT
ejpam-5193	368	14	b	b	NOUN
ejpam-5193	368	15	and	and	CCONJ
ejpam-5193	368	16	c.	c.	PROPN
ejpam-5193	368	17	communication	communication	NOUN
ejpam-5193	368	18	of	of	ADP
ejpam-5193	368	19	the	the	DET
ejpam-5193	368	20	korean	korean	ADJ
ejpam-5193	368	21	mathematical	mathematical	ADJ
ejpam-5193	368	22	society	society	NOUN
ejpam-5193	368	23	,	,	PUNCT
ejpam-5193	368	24	36(3):423–445	36(3):423–445	NOUN
ejpam-5193	368	25	,	,	PUNCT
ejpam-5193	368	26	2021	2021	NUM
ejpam-5193	368	27	.	.	PUNCT
ejpam-5193	369	1	[	[	X
ejpam-5193	369	2	12	12	NUM
ejpam-5193	369	3	]	]	X
ejpam-5193	369	4	r.	r.	PROPN
ejpam-5193	369	5	corcino	corcino	PROPN
ejpam-5193	369	6	and	and	CCONJ
ejpam-5193	369	7	c.	c.	PROPN
ejpam-5193	369	8	corcino	corcino	PROPN
ejpam-5193	369	9	.	.	PUNCT
ejpam-5193	370	1	higher	high	ADJ
ejpam-5193	370	2	order	order	NOUN
ejpam-5193	370	3	apostol	apostol	NOUN
ejpam-5193	370	4	-	-	PUNCT
ejpam-5193	370	5	frobenius	frobenius	NOUN
ejpam-5193	370	6	-	-	PUNCT
ejpam-5193	370	7	type	type	NOUN
ejpam-5193	370	8	poly	poly	ADJ
ejpam-5193	370	9	-	-	PUNCT
ejpam-5193	370	10	genocchi	genocchi	NOUN
ejpam-5193	370	11	polynomials	polynomial	NOUN
ejpam-5193	370	12	with	with	ADP
ejpam-5193	370	13	parameters	parameter	NOUN
ejpam-5193	370	14	a	a	PRON
ejpam-5193	370	15	,	,	PUNCT
ejpam-5193	370	16	b	b	PROPN
ejpam-5193	370	17	and	and	CCONJ
ejpam-5193	370	18	c.	c.	PROPN
ejpam-5193	370	19	journal	journal	PROPN
ejpam-5193	370	20	of	of	ADP
ejpam-5193	370	21	inequalities	inequality	NOUN
ejpam-5193	370	22	and	and	CCONJ
ejpam-5193	370	23	special	special	ADJ
ejpam-5193	370	24	functions	function	NOUN
ejpam-5193	370	25	,	,	PUNCT
ejpam-5193	370	26	12(3):54–72	12(3):54–72	NUM
ejpam-5193	370	27	,	,	PUNCT
ejpam-5193	370	28	2021	2021	NUM
ejpam-5193	370	29	.	.	PUNCT
ejpam-5193	371	1	[	[	X
ejpam-5193	371	2	13	13	NUM
ejpam-5193	371	3	]	]	X
ejpam-5193	371	4	r.	r.	PROPN
ejpam-5193	371	5	corcino	corcino	PROPN
ejpam-5193	371	6	and	and	CCONJ
ejpam-5193	371	7	c.	c.	PROPN
ejpam-5193	371	8	corcino	corcino	PROPN
ejpam-5193	371	9	.	.	PUNCT
ejpam-5193	372	1	generalized	generalize	VERB
ejpam-5193	372	2	laguerre	laguerre	NOUN
ejpam-5193	372	3	-	-	PUNCT
ejpam-5193	372	4	apostol	apostol	NOUN
ejpam-5193	372	5	-	-	PUNCT
ejpam-5193	372	6	frobenius	frobenius	NOUN
ejpam-5193	372	7	-	-	PUNCT
ejpam-5193	372	8	type	type	NOUN
ejpam-5193	372	9	polygenocchi	polygenocchi	ADJ
ejpam-5193	372	10	polynomials	polynomial	NOUN
ejpam-5193	372	11	of	of	ADP
ejpam-5193	372	12	higher	high	ADJ
ejpam-5193	372	13	order	order	NOUN
ejpam-5193	372	14	with	with	ADP
ejpam-5193	372	15	parameters	parameter	NOUN
ejpam-5193	372	16	a	a	DET
ejpam-5193	372	17	,	,	PUNCT
ejpam-5193	372	18	b	b	PROPN
ejpam-5193	372	19	and	and	CCONJ
ejpam-5193	372	20	c.	c.	PROPN
ejpam-5193	372	21	european	european	PROPN
ejpam-5193	372	22	journal	journal	PROPN
ejpam-5193	372	23	of	of	ADP
ejpam-5193	372	24	pure	pure	ADJ
ejpam-5193	372	25	and	and	CCONJ
ejpam-5193	372	26	applied	applied	ADJ
ejpam-5193	372	27	mathematics	mathematic	NOUN
ejpam-5193	372	28	,	,	PUNCT
ejpam-5193	372	29	15(4):1549–1565	15(4):1549–1565	NUM
ejpam-5193	372	30	,	,	PUNCT
ejpam-5193	372	31	2022	2022	NUM
ejpam-5193	372	32	.	.	PUNCT
ejpam-5193	373	1	[	[	X
ejpam-5193	373	2	14	14	NUM
ejpam-5193	373	3	]	]	X
ejpam-5193	373	4	r.	r.	PROPN
ejpam-5193	373	5	corcino	corcino	PROPN
ejpam-5193	373	6	and	and	CCONJ
ejpam-5193	373	7	c.	c.	PROPN
ejpam-5193	373	8	corcino	corcino	PROPN
ejpam-5193	373	9	.	.	PUNCT
ejpam-5193	373	10	degenerate	degenerate	ADJ
ejpam-5193	373	11	apostol	apostol	NOUN
ejpam-5193	373	12	-	-	PUNCT
ejpam-5193	373	13	frobenius	frobenius	NOUN
ejpam-5193	373	14	-	-	PUNCT
ejpam-5193	373	15	type	type	NOUN
ejpam-5193	373	16	poly	poly	ADJ
ejpam-5193	373	17	-	-	PUNCT
ejpam-5193	373	18	genocchi	genocchi	NOUN
ejpam-5193	373	19	polynomials	polynomial	NOUN
ejpam-5193	373	20	of	of	ADP
ejpam-5193	373	21	higher	high	ADJ
ejpam-5193	373	22	order	order	NOUN
ejpam-5193	373	23	with	with	ADP
ejpam-5193	373	24	parameters	parameter	NOUN
ejpam-5193	373	25	a	a	PRON
ejpam-5193	373	26	and	and	CCONJ
ejpam-5193	373	27	b.	b.	PROPN
ejpam-5193	373	28	european	european	PROPN
ejpam-5193	373	29	journal	journal	PROPN
ejpam-5193	373	30	of	of	ADP
ejpam-5193	373	31	pure	pure	ADJ
ejpam-5193	373	32	and	and	CCONJ
ejpam-5193	373	33	applied	applied	ADJ
ejpam-5193	373	34	mathematics	mathematic	NOUN
ejpam-5193	373	35	,	,	PUNCT
ejpam-5193	373	36	16(2):687–712	16(2):687–712	NOUN
ejpam-5193	373	37	,	,	PUNCT
ejpam-5193	373	38	2023	2023	NUM
ejpam-5193	373	39	.	.	PUNCT
ejpam-5193	374	1	[	[	X
ejpam-5193	374	2	15	15	NUM
ejpam-5193	374	3	]	]	X
ejpam-5193	374	4	r.	r.	PROPN
ejpam-5193	374	5	corcino	corcino	PROPN
ejpam-5193	374	6	,	,	PUNCT
ejpam-5193	374	7	c.	c.	PROPN
ejpam-5193	374	8	corcino	corcino	PROPN
ejpam-5193	374	9	,	,	PUNCT
ejpam-5193	374	10	k.	k.	PROPN
ejpam-5193	374	11	casas	casas	PROPN
ejpam-5193	374	12	,	,	PUNCT
ejpam-5193	374	13	a.	a.	NOUN
ejpam-5193	374	14	elnar	elnar	PROPN
ejpam-5193	374	15	,	,	PUNCT
ejpam-5193	374	16	and	and	CCONJ
ejpam-5193	374	17	g.	g.	PROPN
ejpam-5193	374	18	maglasang	maglasang	PROPN
ejpam-5193	374	19	.	.	PUNCT
ejpam-5193	375	1	construction	construction	NOUN
ejpam-5193	375	2	of	of	ADP
ejpam-5193	375	3	fourier	fourier	ADJ
ejpam-5193	375	4	series	series	NOUN
ejpam-5193	375	5	expansion	expansion	NOUN
ejpam-5193	375	6	of	of	ADP
ejpam-5193	375	7	apostol	apostol	NOUN
ejpam-5193	375	8	-	-	PUNCT
ejpam-5193	375	9	frobenius	frobenius	NOUN
ejpam-5193	375	10	-	-	PUNCT
ejpam-5193	375	11	type	type	NOUN
ejpam-5193	375	12	tangent	tangent	NOUN
ejpam-5193	375	13	and	and	CCONJ
ejpam-5193	375	14	genocchi	genocchi	PROPN
ejpam-5193	375	15	polynomials	polynomial	NOUN
ejpam-5193	375	16	of	of	ADP
ejpam-5193	375	17	higher	high	ADJ
ejpam-5193	375	18	-	-	PUNCT
ejpam-5193	375	19	order	order	NOUN
ejpam-5193	375	20	.	.	PUNCT
ejpam-5193	376	1	european	european	ADJ
ejpam-5193	376	2	journal	journal	PROPN
ejpam-5193	376	3	of	of	ADP
ejpam-5193	376	4	pure	pure	ADJ
ejpam-5193	376	5	and	and	CCONJ
ejpam-5193	376	6	applied	applied	ADJ
ejpam-5193	376	7	mathematics	mathematic	NOUN
ejpam-5193	376	8	,	,	PUNCT
ejpam-5193	376	9	16(2):1005	16(2):1005	NUM
ejpam-5193	376	10	–	–	PUNCT
ejpam-5193	376	11	1023	1023	NUM
ejpam-5193	376	12	,	,	PUNCT
ejpam-5193	376	13	2023	2023	NUM
ejpam-5193	376	14	.	.	PUNCT
ejpam-5193	377	1	references	reference	NOUN
ejpam-5193	377	2	1488	1488	NUM
ejpam-5193	378	1	[	[	X
ejpam-5193	378	2	16	16	NUM
ejpam-5193	378	3	]	]	X
ejpam-5193	378	4	y.	y.	NOUN
ejpam-5193	378	5	he	he	PRON
ejpam-5193	378	6	.	.	PUNCT
ejpam-5193	379	1	some	some	DET
ejpam-5193	379	2	new	new	ADJ
ejpam-5193	379	3	results	result	NOUN
ejpam-5193	379	4	on	on	ADP
ejpam-5193	379	5	products	product	NOUN
ejpam-5193	379	6	of	of	ADP
ejpam-5193	379	7	the	the	DET
ejpam-5193	379	8	apostol	apostol	NOUN
ejpam-5193	379	9	-	-	PUNCT
ejpam-5193	379	10	genocchi	genocchi	PROPN
ejpam-5193	379	11	polynomials	polynomial	NOUN
ejpam-5193	379	12	.	.	PUNCT
ejpam-5193	380	1	j.	j.	PROPN
ejpam-5193	380	2	comput	comput	PROPN
ejpam-5193	380	3	.	.	PUNCT
ejpam-5193	381	1	anal	anal	PROPN
ejpam-5193	381	2	.	.	PUNCT
ejpam-5193	381	3	appl	appl	PROPN
ejpam-5193	381	4	.	.	PROPN
ejpam-5193	381	5	,	,	PUNCT
ejpam-5193	381	6	22(4):591–600	22(4):591–600	PROPN
ejpam-5193	381	7	,	,	PUNCT
ejpam-5193	381	8	2017	2017	NUM
ejpam-5193	381	9	.	.	PUNCT
ejpam-5193	382	1	[	[	X
ejpam-5193	382	2	17	17	NUM
ejpam-5193	382	3	]	]	X
ejpam-5193	382	4	y.	y.	NOUN
ejpam-5193	382	5	he	he	PRON
ejpam-5193	382	6	,	,	PUNCT
ejpam-5193	382	7	s.	s.	PROPN
ejpam-5193	382	8	araci	araci	PROPN
ejpam-5193	382	9	,	,	PUNCT
ejpam-5193	382	10	h.m	h.m	PROPN
ejpam-5193	382	11	.	.	PROPN
ejpam-5193	382	12	srivastava	srivastava	PROPN
ejpam-5193	382	13	,	,	PUNCT
ejpam-5193	382	14	and	and	CCONJ
ejpam-5193	382	15	m.	m.	NOUN
ejpam-5193	382	16	acikgoz	acikgoz	VERB
ejpam-5193	382	17	.	.	PUNCT
ejpam-5193	383	1	some	some	DET
ejpam-5193	383	2	new	new	ADJ
ejpam-5193	383	3	identities	identity	NOUN
ejpam-5193	383	4	for	for	ADP
ejpam-5193	383	5	the	the	DET
ejpam-5193	383	6	apostolbernoulli	apostolbernoulli	NOUN
ejpam-5193	383	7	polynomials	polynomial	NOUN
ejpam-5193	383	8	and	and	CCONJ
ejpam-5193	383	9	the	the	DET
ejpam-5193	383	10	apostol	apostol	NOUN
ejpam-5193	383	11	-	-	PUNCT
ejpam-5193	383	12	genocchi	genocchi	PROPN
ejpam-5193	383	13	polynomials	polynomial	NOUN
ejpam-5193	383	14	.	.	PUNCT
ejpam-5193	384	1	appl	appl	PROPN
ejpam-5193	384	2	.	.	PROPN
ejpam-5193	384	3	math	math	PROPN
ejpam-5193	384	4	.	.	PUNCT
ejpam-5193	385	1	comput	comput	NOUN
ejpam-5193	385	2	.	.	PUNCT
ejpam-5193	385	3	,	,	PUNCT
ejpam-5193	385	4	262:31–41	262:31–41	NUM
ejpam-5193	385	5	,	,	PUNCT
ejpam-5193	385	6	2015	2015	NUM
ejpam-5193	385	7	.	.	PUNCT
ejpam-5193	386	1	[	[	X
ejpam-5193	386	2	18	18	NUM
ejpam-5193	386	3	]	]	X
ejpam-5193	386	4	y.	y.	NOUN
ejpam-5193	386	5	he	he	PRON
ejpam-5193	386	6	and	and	CCONJ
ejpam-5193	386	7	t.	t.	PROPN
ejpam-5193	386	8	kim	kim	PROPN
ejpam-5193	386	9	.	.	PUNCT
ejpam-5193	387	1	general	general	ADJ
ejpam-5193	387	2	convolution	convolution	NOUN
ejpam-5193	387	3	identities	identity	NOUN
ejpam-5193	387	4	of	of	ADP
ejpam-5193	387	5	apostol	apostol	NOUN
ejpam-5193	387	6	-	-	PUNCT
ejpam-5193	387	7	bernoulli	bernoulli	PROPN
ejpam-5193	387	8	,	,	PUNCT
ejpam-5193	387	9	euler	euler	NOUN
ejpam-5193	387	10	and	and	CCONJ
ejpam-5193	387	11	genocchi	genocchi	PROPN
ejpam-5193	387	12	polynomials	polynomial	NOUN
ejpam-5193	387	13	.	.	PUNCT
ejpam-5193	388	1	j.	j.	PROPN
ejpam-5193	388	2	nonlinear	nonlinear	PROPN
ejpam-5193	388	3	sci	sci	PROPN
ejpam-5193	388	4	.	.	PUNCT
ejpam-5193	388	5	appl	appl	PROPN
ejpam-5193	388	6	.	.	PROPN
ejpam-5193	388	7	,	,	PUNCT
ejpam-5193	388	8	9:4780–4797	9:4780–4797	NUM
ejpam-5193	388	9	,	,	PUNCT
ejpam-5193	388	10	2016	2016	NUM
ejpam-5193	388	11	.	.	PUNCT
ejpam-5193	389	1	[	[	X
ejpam-5193	389	2	19	19	NUM
ejpam-5193	389	3	]	]	X
ejpam-5193	389	4	s.	s.	PROPN
ejpam-5193	389	5	hu	hu	PROPN
ejpam-5193	389	6	,	,	PUNCT
ejpam-5193	389	7	d.	d.	PROPN
ejpam-5193	389	8	kim	kim	PROPN
ejpam-5193	389	9	,	,	PUNCT
ejpam-5193	389	10	and	and	CCONJ
ejpam-5193	389	11	m.s	m.s	PROPN
ejpam-5193	389	12	.	.	PROPN
ejpam-5193	389	13	kim	kim	PROPN
ejpam-5193	389	14	.	.	PUNCT
ejpam-5193	390	1	new	new	ADJ
ejpam-5193	390	2	identities	identity	NOUN
ejpam-5193	390	3	involving	involve	VERB
ejpam-5193	390	4	bernoulli	bernoulli	PROPN
ejpam-5193	390	5	,	,	PUNCT
ejpam-5193	390	6	euler	euler	VERB
ejpam-5193	390	7	and	and	CCONJ
ejpam-5193	390	8	genocchi	genocchi	PROPN
ejpam-5193	390	9	numbers	number	NOUN
ejpam-5193	390	10	.	.	PUNCT
ejpam-5193	391	1	advances	advance	NOUN
ejpam-5193	391	2	in	in	ADP
ejpam-5193	391	3	difference	difference	NOUN
ejpam-5193	391	4	equations	equation	NOUN
ejpam-5193	391	5	,	,	PUNCT
ejpam-5193	391	6	2013	2013	NUM
ejpam-5193	391	7	:	:	PUNCT
ejpam-5193	391	8	article	article	NOUN
ejpam-5193	391	9	74	74	NUM
ejpam-5193	391	10	,	,	PUNCT
ejpam-5193	391	11	2013	2013	NUM
ejpam-5193	391	12	.	.	PUNCT
ejpam-5193	392	1	[	[	X
ejpam-5193	392	2	20	20	NUM
ejpam-5193	392	3	]	]	PUNCT
ejpam-5193	392	4	w.	w.	PROPN
ejpam-5193	392	5	a.	a.	PROPN
ejpam-5193	392	6	khan	khan	PROPN
ejpam-5193	392	7	,	,	PUNCT
ejpam-5193	392	8	j.	j.	PROPN
ejpam-5193	392	9	younis	younis	PROPN
ejpam-5193	392	10	,	,	PUNCT
ejpam-5193	392	11	and	and	CCONJ
ejpam-5193	392	12	m.	m.	NOUN
ejpam-5193	392	13	nadeem	nadeem	PROPN
ejpam-5193	392	14	.	.	PUNCT
ejpam-5193	393	1	construction	construction	NOUN
ejpam-5193	393	2	of	of	ADP
ejpam-5193	393	3	partially	partially	ADV
ejpam-5193	393	4	degenerate	degenerate	ADJ
ejpam-5193	393	5	bellbernoulli	bellbernoulli	NOUN
ejpam-5193	393	6	polynomials	polynomial	NOUN
ejpam-5193	393	7	of	of	ADP
ejpam-5193	393	8	the	the	DET
ejpam-5193	393	9	first	first	ADJ
ejpam-5193	393	10	kind	kind	NOUN
ejpam-5193	393	11	.	.	PUNCT
ejpam-5193	394	1	analysis	analysis	NOUN
ejpam-5193	394	2	,	,	PUNCT
ejpam-5193	394	3	43(3):171–184	43(3):171–184	NOUN
ejpam-5193	394	4	,	,	PUNCT
ejpam-5193	394	5	2022	2022	NUM
ejpam-5193	394	6	.	.	PUNCT
ejpam-5193	395	1	[	[	X
ejpam-5193	395	2	21	21	NUM
ejpam-5193	395	3	]	]	X
ejpam-5193	395	4	w.a	w.a	PROPN
ejpam-5193	395	5	.	.	PROPN
ejpam-5193	395	6	khan	khan	PROPN
ejpam-5193	395	7	,	,	PUNCT
ejpam-5193	395	8	m.a	m.a	PROPN
ejpam-5193	395	9	.	.	PROPN
ejpam-5193	395	10	alatawi	alatawi	PROPN
ejpam-5193	395	11	,	,	PUNCT
ejpam-5193	395	12	and	and	CCONJ
ejpam-5193	395	13	u.	u.	PROPN
ejpam-5193	395	14	duran	duran	PROPN
ejpam-5193	395	15	.	.	PUNCT
ejpam-5193	396	1	applications	application	NOUN
ejpam-5193	396	2	,	,	PUNCT
ejpam-5193	396	3	and	and	CCONJ
ejpam-5193	396	4	properties	property	NOUN
ejpam-5193	396	5	of	of	ADP
ejpam-5193	396	6	bivariate	bivariate	ADJ
ejpam-5193	396	7	bell	bell	NOUN
ejpam-5193	396	8	-	-	PUNCT
ejpam-5193	396	9	based	base	VERB
ejpam-5193	396	10	frobenius	frobenius	NOUN
ejpam-5193	396	11	-	-	PUNCT
ejpam-5193	396	12	type	type	NOUN
ejpam-5193	396	13	eulerian	eulerian	ADJ
ejpam-5193	396	14	polynomials	polynomial	NOUN
ejpam-5193	396	15	.	.	PUNCT
ejpam-5193	397	1	journal	journal	NOUN
ejpam-5193	397	2	of	of	ADP
ejpam-5193	397	3	function	function	NOUN
ejpam-5193	397	4	spaces	space	NOUN
ejpam-5193	397	5	,	,	PUNCT
ejpam-5193	397	6	2023	2023	NUM
ejpam-5193	397	7	:	:	PUNCT
ejpam-5193	397	8	article	article	NOUN
ejpam-5193	397	9	i	i	PROPN
ejpam-5193	397	10	d	d	PROPN
ejpam-5193	397	11	5205867	5205867	NUM
ejpam-5193	397	12	,	,	PUNCT
ejpam-5193	397	13	10	10	NUM
ejpam-5193	397	14	pages	page	NOUN
ejpam-5193	397	15	,	,	PUNCT
ejpam-5193	397	16	2023	2023	NUM
ejpam-5193	397	17	.	.	PUNCT
ejpam-5193	398	1	[	[	X
ejpam-5193	398	2	22	22	NUM
ejpam-5193	398	3	]	]	X
ejpam-5193	398	4	d.s	d.s	PROPN
ejpam-5193	398	5	.	.	PROPN
ejpam-5193	398	6	kim	kim	PROPN
ejpam-5193	398	7	,	,	PUNCT
ejpam-5193	398	8	d.v	d.v	PROPN
ejpam-5193	398	9	.	.	PROPN
ejpam-5193	398	10	dolgy	dolgy	PROPN
ejpam-5193	398	11	,	,	PUNCT
ejpam-5193	398	12	t.	t.	PROPN
ejpam-5193	398	13	kim	kim	PROPN
ejpam-5193	398	14	,	,	PUNCT
ejpam-5193	398	15	and	and	CCONJ
ejpam-5193	398	16	s.h	s.h	PROPN
ejpam-5193	398	17	.	.	PROPN
ejpam-5193	398	18	rim	rim	PROPN
ejpam-5193	398	19	.	.	PUNCT
ejpam-5193	399	1	some	some	DET
ejpam-5193	399	2	formula	formula	NOUN
ejpam-5193	399	3	for	for	ADP
ejpam-5193	399	4	the	the	DET
ejpam-5193	399	5	product	product	NOUN
ejpam-5193	399	6	of	of	ADP
ejpam-5193	399	7	two	two	NUM
ejpam-5193	399	8	bernoulli	bernoulli	NOUN
ejpam-5193	399	9	and	and	CCONJ
ejpam-5193	399	10	euler	euler	NOUN
ejpam-5193	399	11	polynomials	polynomial	NOUN
ejpam-5193	399	12	.	.	PUNCT
ejpam-5193	400	1	abstract	abstract	ADJ
ejpam-5193	400	2	and	and	CCONJ
ejpam-5193	400	3	applied	apply	VERB
ejpam-5193	400	4	analysis	analysis	NOUN
ejpam-5193	400	5	,	,	PUNCT
ejpam-5193	400	6	2012	2012	NUM
ejpam-5193	400	7	:	:	PUNCT
ejpam-5193	400	8	article	article	NOUN
ejpam-5193	400	9	i	i	PROPN
ejpam-5193	400	10	d	d	PROPN
ejpam-5193	400	11	784307	784307	NUM
ejpam-5193	400	12	,	,	PUNCT
ejpam-5193	400	13	15	15	NUM
ejpam-5193	400	14	pages	page	NOUN
ejpam-5193	400	15	.	.	PUNCT
ejpam-5193	400	16	,	,	PUNCT
ejpam-5193	400	17	2012	2012	NUM
ejpam-5193	400	18	.	.	PUNCT
ejpam-5193	401	1	[	[	X
ejpam-5193	401	2	23	23	NUM
ejpam-5193	401	3	]	]	X
ejpam-5193	401	4	d.s	d.s	PROPN
ejpam-5193	401	5	.	.	PROPN
ejpam-5193	401	6	kim	kim	PROPN
ejpam-5193	401	7	and	and	CCONJ
ejpam-5193	401	8	t.	t.	PROPN
ejpam-5193	401	9	kim	kim	PROPN
ejpam-5193	401	10	.	.	PUNCT
ejpam-5193	402	1	some	some	DET
ejpam-5193	402	2	new	new	ADJ
ejpam-5193	402	3	identities	identity	NOUN
ejpam-5193	402	4	of	of	ADP
ejpam-5193	402	5	frobenius	frobenius	NOUN
ejpam-5193	402	6	-	-	PUNCT
ejpam-5193	402	7	euler	euler	NOUN
ejpam-5193	402	8	numbers	number	NOUN
ejpam-5193	402	9	and	and	CCONJ
ejpam-5193	402	10	polynomials	polynomial	NOUN
ejpam-5193	402	11	.	.	PUNCT
ejpam-5193	403	1	j.	j.	PROPN
ejpam-5193	403	2	inequal	inequal	PROPN
ejpam-5193	403	3	.	.	PUNCT
ejpam-5193	404	1	appl	appl	PROPN
ejpam-5193	404	2	.	.	PROPN
ejpam-5193	404	3	,	,	PUNCT
ejpam-5193	404	4	2012	2012	NUM
ejpam-5193	404	5	:	:	PUNCT
ejpam-5193	404	6	article	article	NOUN
ejpam-5193	404	7	i	i	PROPN
ejpam-5193	404	8	d	d	PROPN
ejpam-5193	404	9	307	307	NUM
ejpam-5193	404	10	,	,	PUNCT
ejpam-5193	404	11	2012	2012	NUM
ejpam-5193	404	12	.	.	PUNCT
ejpam-5193	405	1	[	[	X
ejpam-5193	405	2	24	24	NUM
ejpam-5193	405	3	]	]	X
ejpam-5193	405	4	b.	b.	PROPN
ejpam-5193	405	5	kurt	kurt	PROPN
ejpam-5193	405	6	and	and	CCONJ
ejpam-5193	405	7	y.	y.	PROPN
ejpam-5193	405	8	symsek	symsek	PROPN
ejpam-5193	405	9	.	.	PUNCT
ejpam-5193	406	1	on	on	ADP
ejpam-5193	406	2	the	the	DET
ejpam-5193	406	3	generalized	generalize	VERB
ejpam-5193	406	4	apostol	apostol	NOUN
ejpam-5193	406	5	type	type	NOUN
ejpam-5193	406	6	frobenius	frobenius	NOUN
ejpam-5193	406	7	-	-	PUNCT
ejpam-5193	406	8	euler	euler	NOUN
ejpam-5193	406	9	polynomials	polynomial	NOUN
ejpam-5193	406	10	.	.	PUNCT
ejpam-5193	407	1	advances	advance	NOUN
ejpam-5193	407	2	in	in	ADP
ejpam-5193	407	3	difference	difference	NOUN
ejpam-5193	407	4	equation	equation	NOUN
ejpam-5193	407	5	,	,	PUNCT
ejpam-5193	407	6	2013(1):1–9	2013(1):1–9	NOUN
ejpam-5193	407	7	,	,	PUNCT
ejpam-5193	407	8	2013	2013	NUM
ejpam-5193	407	9	.	.	PUNCT
ejpam-5193	408	1	[	[	X
ejpam-5193	408	2	25	25	NUM
ejpam-5193	408	3	]	]	X
ejpam-5193	408	4	d.w	d.w	PROPN
ejpam-5193	408	5	.	.	PROPN
ejpam-5193	408	6	lee	lee	PROPN
ejpam-5193	408	7	.	.	PUNCT
ejpam-5193	409	1	on	on	ADP
ejpam-5193	409	2	multiple	multiple	ADJ
ejpam-5193	409	3	appell	appell	ADJ
ejpam-5193	409	4	polynomials	polynomial	NOUN
ejpam-5193	409	5	.	.	PUNCT
ejpam-5193	410	1	proc	proc	NOUN
ejpam-5193	410	2	.	.	PUNCT
ejpam-5193	411	1	amer	amer	PROPN
ejpam-5193	411	2	.	.	PUNCT
ejpam-5193	411	3	math	math	PROPN
ejpam-5193	411	4	.	.	PUNCT
ejpam-5193	412	1	soc	soc	PROPN
ejpam-5193	412	2	.	.	PUNCT
ejpam-5193	412	3	,	,	PUNCT
ejpam-5193	412	4	139:2133–2141	139:2133–2141	NUM
ejpam-5193	412	5	,	,	PUNCT
ejpam-5193	412	6	2011	2011	NUM
ejpam-5193	412	7	.	.	PUNCT
ejpam-5193	413	1	[	[	X
ejpam-5193	413	2	26	26	NUM
ejpam-5193	413	3	]	]	X
ejpam-5193	413	4	i.	i.	NOUN
ejpam-5193	413	5	mezo	mezo	PROPN
ejpam-5193	413	6	and	and	CCONJ
ejpam-5193	413	7	r.	r.	PROPN
ejpam-5193	413	8	corcino	corcino	PROPN
ejpam-5193	413	9	.	.	PUNCT
ejpam-5193	414	1	the	the	DET
ejpam-5193	414	2	estimation	estimation	NOUN
ejpam-5193	414	3	of	of	ADP
ejpam-5193	414	4	the	the	DET
ejpam-5193	414	5	zeros	zero	NOUN
ejpam-5193	414	6	of	of	ADP
ejpam-5193	414	7	the	the	DET
ejpam-5193	414	8	bell	bell	NOUN
ejpam-5193	414	9	and	and	CCONJ
ejpam-5193	414	10	r	r	NOUN
ejpam-5193	414	11	-	-	PUNCT
ejpam-5193	414	12	bell	bell	NOUN
ejpam-5193	414	13	polynomials	polynomial	NOUN
ejpam-5193	414	14	.	.	PUNCT
ejpam-5193	415	1	applied	apply	VERB
ejpam-5193	415	2	mathematics	mathematic	NOUN
ejpam-5193	415	3	and	and	CCONJ
ejpam-5193	415	4	computations	computation	NOUN
ejpam-5193	415	5	,	,	PUNCT
ejpam-5193	415	6	250:727–732	250:727–732	NUM
ejpam-5193	415	7	.	.	PUNCT
ejpam-5193	415	8	,	,	PUNCT
ejpam-5193	415	9	2015	2015	NUM
ejpam-5193	415	10	.	.	PUNCT
ejpam-5193	416	1	[	[	X
ejpam-5193	416	2	27	27	NUM
ejpam-5193	416	3	]	]	X
ejpam-5193	416	4	araci	araci	NOUN
ejpam-5193	416	5	s.	s.	PROPN
ejpam-5193	416	6	,	,	PUNCT
ejpam-5193	416	7	acikgoz	acikgoz	ADJ
ejpam-5193	416	8	m.	m.	NOUN
ejpam-5193	416	9	,	,	PUNCT
ejpam-5193	416	10	and	and	CCONJ
ejpam-5193	416	11	sen	sen	PROPN
ejpam-5193	416	12	e.	e.	PROPN
ejpam-5193	416	13	some	some	DET
ejpam-5193	416	14	new	new	ADJ
ejpam-5193	416	15	formulae	formulae	NOUN
ejpam-5193	416	16	for	for	ADP
ejpam-5193	416	17	genocchi	genocchi	PROPN
ejpam-5193	416	18	numbers	number	NOUN
ejpam-5193	416	19	and	and	CCONJ
ejpam-5193	416	20	polynomials	polynomial	NOUN
ejpam-5193	416	21	involving	involve	VERB
ejpam-5193	416	22	benoulli	benoulli	NOUN
ejpam-5193	416	23	and	and	CCONJ
ejpam-5193	416	24	euler	euler	NOUN
ejpam-5193	416	25	polynomials	polynomial	NOUN
ejpam-5193	416	26	.	.	PUNCT
ejpam-5193	417	1	int	int	NOUN
ejpam-5193	417	2	.	.	PUNCT
ejpam-5193	418	1	j.	j.	PROPN
ejpam-5193	418	2	math	math	PROPN
ejpam-5193	418	3	.	.	PUNCT
ejpam-5193	419	1	sci	sci	PROPN
ejpam-5193	419	2	.	.	PROPN
ejpam-5193	419	3	,	,	PUNCT
ejpam-5193	419	4	2014	2014	NUM
ejpam-5193	419	5	:	:	PUNCT
ejpam-5193	419	6	article	article	NOUN
ejpam-5193	419	7	i	i	PROPN
ejpam-5193	419	8	d	d	PROPN
ejpam-5193	419	9	760613	760613	NUM
ejpam-5193	419	10	,	,	PUNCT
ejpam-5193	419	11	2014	2014	NUM
ejpam-5193	419	12	.	.	PUNCT
ejpam-5193	420	1	[	[	X
ejpam-5193	420	2	28	28	NUM
ejpam-5193	420	3	]	]	X
ejpam-5193	420	4	araci	araci	NOUN
ejpam-5193	420	5	s.	s.	PROPN
ejpam-5193	420	6	,	,	PUNCT
ejpam-5193	420	7	khan	khan	PROPN
ejpam-5193	420	8	w.a	w.a	PROPN
ejpam-5193	420	9	.	.	PROPN
ejpam-5193	420	10	,	,	PUNCT
ejpam-5193	420	11	acikgoz	acikgoz	PROPN
ejpam-5193	420	12	m.	m.	NOUN
ejpam-5193	420	13	,	,	PUNCT
ejpam-5193	420	14	ozel	ozel	PROPN
ejpam-5193	420	15	c.	c.	NOUN
ejpam-5193	420	16	,	,	PUNCT
ejpam-5193	420	17	and	and	CCONJ
ejpam-5193	420	18	kumam	kumam	PROPN
ejpam-5193	420	19	p.	p.	NOUN
ejpam-5193	420	20	a	a	DET
ejpam-5193	420	21	new	new	ADJ
ejpam-5193	420	22	generalization	generalization	NOUN
ejpam-5193	420	23	of	of	ADP
ejpam-5193	420	24	apostol	apostol	PROPN
ejpam-5193	420	25	type	type	NOUN
ejpam-5193	420	26	hermite	hermite	PROPN
ejpam-5193	420	27	-	-	PUNCT
ejpam-5193	420	28	genocchi	genocchi	PROPN
ejpam-5193	420	29	polynomials	polynomial	NOUN
ejpam-5193	420	30	and	and	CCONJ
ejpam-5193	420	31	its	its	PRON
ejpam-5193	420	32	applications	application	NOUN
ejpam-5193	420	33	.	.	PUNCT
ejpam-5193	421	1	springerplus	springerplus	PROPN
ejpam-5193	421	2	,	,	PUNCT
ejpam-5193	421	3	5	5	NUM
ejpam-5193	421	4	:	:	PUNCT
ejpam-5193	421	5	art	art	NOUN
ejpam-5193	421	6	.	.	PUNCT
ejpam-5193	422	1	i	i	PRON
ejpam-5193	422	2	d	d	PROPN
ejpam-5193	422	3	860	860	NUM
ejpam-5193	422	4	,	,	PUNCT
ejpam-5193	422	5	2016	2016	NUM
ejpam-5193	422	6	.	.	PUNCT
ejpam-5193	423	1	[	[	X
ejpam-5193	423	2	29	29	NUM
ejpam-5193	423	3	]	]	PUNCT
ejpam-5193	423	4	j.	j.	PROPN
ejpam-5193	423	5	shohat	shohat	PROPN
ejpam-5193	423	6	.	.	PUNCT
ejpam-5193	424	1	the	the	DET
ejpam-5193	424	2	relation	relation	NOUN
ejpam-5193	424	3	of	of	ADP
ejpam-5193	424	4	the	the	DET
ejpam-5193	424	5	classical	classical	ADJ
ejpam-5193	424	6	orthogonal	orthogonal	ADJ
ejpam-5193	424	7	polynomials	polynomial	NOUN
ejpam-5193	424	8	to	to	ADP
ejpam-5193	424	9	the	the	DET
ejpam-5193	424	10	polynomials	polynomial	NOUN
ejpam-5193	424	11	of	of	ADP
ejpam-5193	424	12	appell	appell	PROPN
ejpam-5193	424	13	.	.	PUNCT
ejpam-5193	425	1	amer	amer	PROPN
ejpam-5193	425	2	.	.	PUNCT
ejpam-5193	426	1	j.	j.	PROPN
ejpam-5193	426	2	math	math	PROPN
ejpam-5193	426	3	.	.	PUNCT
ejpam-5193	426	4	,	,	PUNCT
ejpam-5193	426	5	58:453–464	58:453–464	NUM
ejpam-5193	426	6	,	,	PUNCT
ejpam-5193	426	7	1936	1936	NUM
ejpam-5193	426	8	.	.	PUNCT
ejpam-5193	427	1	references	reference	NOUN
ejpam-5193	427	2	1489	1489	NUM
ejpam-5193	427	3	[	[	X
ejpam-5193	427	4	30	30	NUM
ejpam-5193	427	5	]	]	X
ejpam-5193	427	6	kim	kim	PROPN
ejpam-5193	427	7	t.	t.	PROPN
ejpam-5193	427	8	some	some	DET
ejpam-5193	427	9	identities	identity	NOUN
ejpam-5193	427	10	for	for	ADP
ejpam-5193	427	11	the	the	DET
ejpam-5193	427	12	bernoulli	bernoulli	NOUN
ejpam-5193	427	13	,	,	PUNCT
ejpam-5193	427	14	the	the	DET
ejpam-5193	427	15	euler	euler	NOUN
ejpam-5193	427	16	and	and	CCONJ
ejpam-5193	427	17	the	the	DET
ejpam-5193	427	18	genocchi	genocchi	PROPN
ejpam-5193	427	19	numbers	number	NOUN
ejpam-5193	427	20	and	and	CCONJ
ejpam-5193	427	21	polynomials	polynomial	NOUN
ejpam-5193	427	22	.	.	PUNCT
ejpam-5193	428	1	adv	adv	PROPN
ejpam-5193	428	2	.	.	PUNCT
ejpam-5193	428	3	stud	stud	PROPN
ejpam-5193	428	4	.	.	PUNCT
ejpam-5193	429	1	contemp	contemp	NOUN
ejpam-5193	429	2	.	.	PUNCT
ejpam-5193	430	1	math	math	NOUN
ejpam-5193	430	2	.	.	PUNCT
ejpam-5193	430	3	,	,	PUNCT
ejpam-5193	430	4	20(1):23–28	20(1):23–28	NUM
ejpam-5193	430	5	,	,	PUNCT
ejpam-5193	430	6	2010	2010	NUM
ejpam-5193	430	7	.	.	PUNCT
ejpam-5193	431	1	[	[	X
ejpam-5193	431	2	31	31	NUM
ejpam-5193	431	3	]	]	X
ejpam-5193	431	4	kim	kim	PROPN
ejpam-5193	431	5	t.	t.	PROPN
ejpam-5193	431	6	,	,	PUNCT
ejpam-5193	431	7	y.s	y.s	PROPN
ejpam-5193	431	8	.	.	PROPN
ejpam-5193	431	9	jang	jang	PROPN
ejpam-5193	431	10	,	,	PUNCT
ejpam-5193	431	11	and	and	CCONJ
ejpam-5193	431	12	j.j	j.j	PROPN
ejpam-5193	431	13	.	.	PROPN
ejpam-5193	431	14	seo	seo	PROPN
ejpam-5193	431	15	.	.	PUNCT
ejpam-5193	432	1	a	a	DET
ejpam-5193	432	2	note	note	NOUN
ejpam-5193	432	3	on	on	ADP
ejpam-5193	432	4	poly	poly	ADJ
ejpam-5193	432	5	-	-	PUNCT
ejpam-5193	432	6	genocchi	genocchi	NOUN
ejpam-5193	432	7	numbers	number	NOUN
ejpam-5193	432	8	and	and	CCONJ
ejpam-5193	432	9	polynomials	polynomial	NOUN
ejpam-5193	432	10	.	.	PUNCT
ejpam-5193	433	1	applied	apply	VERB
ejpam-5193	433	2	mathematical	mathematical	ADJ
ejpam-5193	433	3	sciences	science	NOUN
ejpam-5193	433	4	,	,	PUNCT
ejpam-5193	433	5	8:4775–4781	8:4775–4781	NUM
ejpam-5193	433	6	,	,	PUNCT
ejpam-5193	433	7	2014	2014	NUM
ejpam-5193	433	8	.	.	PUNCT
ejpam-5193	434	1	[	[	X
ejpam-5193	434	2	32	32	NUM
ejpam-5193	434	3	]	]	X
ejpam-5193	434	4	kim	kim	PROPN
ejpam-5193	434	5	t.	t.	PROPN
ejpam-5193	434	6	,	,	PUNCT
ejpam-5193	434	7	rim	rim	PROPN
ejpam-5193	434	8	.	.	PUNCT
ejpam-5193	435	1	s.h	s.h	PROPN
ejpam-5193	435	2	.	.	PROPN
ejpam-5193	435	3	,	,	PUNCT
ejpam-5193	435	4	dolgy	dolgy	VERB
ejpam-5193	435	5	d.v	d.v	PROPN
ejpam-5193	435	6	.	.	PROPN
ejpam-5193	435	7	,	,	PUNCT
ejpam-5193	435	8	and	and	CCONJ
ejpam-5193	435	9	lee	lee	PROPN
ejpam-5193	435	10	s.h	s.h	PROPN
ejpam-5193	435	11	.	.	PUNCT
ejpam-5193	436	1	some	some	DET
ejpam-5193	436	2	identities	identity	NOUN
ejpam-5193	436	3	of	of	ADP
ejpam-5193	436	4	genocchi	genocchi	PROPN
ejpam-5193	436	5	polynomials	polynomial	NOUN
ejpam-5193	436	6	arising	arise	VERB
ejpam-5193	436	7	from	from	ADP
ejpam-5193	436	8	genocchi	genocchi	PROPN
ejpam-5193	436	9	basis	basis	NOUN
ejpam-5193	436	10	.	.	PUNCT
ejpam-5193	437	1	j.	j.	PROPN
ejpam-5193	437	2	ineq	ineq	PROPN
ejpam-5193	437	3	.	.	PUNCT
ejpam-5193	438	1	appl	appl	PROPN
ejpam-5193	438	2	.	.	PROPN
ejpam-5193	438	3	,	,	PUNCT
ejpam-5193	438	4	2013	2013	NUM
ejpam-5193	438	5	:	:	PUNCT
ejpam-5193	438	6	article	article	NOUN
ejpam-5193	438	7	i	i	PROPN
ejpam-5193	438	8	d	d	PROPN
ejpam-5193	438	9	43	43	NUM
ejpam-5193	438	10	,	,	PUNCT
ejpam-5193	438	11	2013	2013	NUM
ejpam-5193	438	12	.	.	PUNCT
ejpam-5193	439	1	[	[	X
ejpam-5193	439	2	33	33	NUM
ejpam-5193	439	3	]	]	PUNCT
ejpam-5193	439	4	g.	g.	PROPN
ejpam-5193	439	5	thomas	thomas	PROPN
ejpam-5193	439	6	,	,	PUNCT
ejpam-5193	439	7	m.	m.	PROPN
ejpam-5193	439	8	weir	weir	PROPN
ejpam-5193	439	9	,	,	PUNCT
ejpam-5193	439	10	j.	j.	PROPN
ejpam-5193	439	11	hass	hass	PROPN
ejpam-5193	439	12	,	,	PUNCT
ejpam-5193	439	13	and	and	CCONJ
ejpam-5193	439	14	f.	f.	PROPN
ejpam-5193	439	15	giordano	giordano	PROPN
ejpam-5193	439	16	.	.	PUNCT
ejpam-5193	440	1	thomas	thomas	PROPN
ejpam-5193	440	2	’	'	PUNCT
ejpam-5193	440	3	calculus	calculus	PROPN
ejpam-5193	440	4	.	.	PUNCT
ejpam-5193	441	1	pearson	pearson	PROPN
ejpam-5193	441	2	education	education	PROPN
ejpam-5193	441	3	,	,	PUNCT
ejpam-5193	441	4	inc	inc	PROPN
ejpam-5193	441	5	.	.	PROPN
ejpam-5193	441	6	,	,	PUNCT
ejpam-5193	441	7	11th	11th	ADJ
ejpam-5193	441	8	edn	edn	NOUN
ejpam-5193	441	9	.	.	PUNCT
ejpam-5193	442	1	edition	edition	PROPN
ejpam-5193	442	2	,	,	PUNCT
ejpam-5193	442	3	2005	2005	NUM
ejpam-5193	442	4	.	.	PUNCT
ejpam-5193	443	1	[	[	X
ejpam-5193	443	2	34	34	NUM
ejpam-5193	443	3	]	]	X
ejpam-5193	443	4	khan	khan	PROPN
ejpam-5193	443	5	w.a	w.a	PROPN
ejpam-5193	443	6	.	.	PROPN
ejpam-5193	443	7	and	and	CCONJ
ejpam-5193	443	8	d.	d.	PROPN
ejpam-5193	443	9	srivastava	srivastava	PROPN
ejpam-5193	443	10	.	.	PUNCT
ejpam-5193	444	1	on	on	ADP
ejpam-5193	444	2	the	the	DET
ejpam-5193	444	3	generalized	generalize	VERB
ejpam-5193	444	4	apostol	apostol	NOUN
ejpam-5193	444	5	-	-	PUNCT
ejpam-5193	444	6	frobenius	frobenius	NOUN
ejpam-5193	444	7	-	-	PUNCT
ejpam-5193	444	8	type	type	NOUN
ejpam-5193	444	9	polygenocchi	polygenocchi	NOUN
ejpam-5193	444	10	polynomials	polynomial	NOUN
ejpam-5193	444	11	.	.	PUNCT
ejpam-5193	445	1	filomat	filomat	PROPN
ejpam-5193	445	2	,	,	PUNCT
ejpam-5193	445	3	33(7):1967–1977	33(7):1967–1977	NUM
ejpam-5193	445	4	,	,	PUNCT
ejpam-5193	445	5	2019	2019	NUM
ejpam-5193	445	6	.	.	PUNCT