id	sid	tid	token	lemma	pos
ejpam-6165	1	1	european	european	PROPN
ejpam-6165	1	2	journal	journal	PROPN
ejpam-6165	1	3	of	of	ADP
ejpam-6165	1	4	pure	pure	ADJ
ejpam-6165	1	5	and	and	CCONJ
ejpam-6165	1	6	applied	applied	ADJ
ejpam-6165	1	7	mathematics	mathematic	NOUN
ejpam-6165	1	8	2025	2025	NUM
ejpam-6165	1	9	,	,	PUNCT
ejpam-6165	1	10	vol	vol	NOUN
ejpam-6165	1	11	.	.	PROPN
ejpam-6165	1	12	18	18	NUM
ejpam-6165	1	13	,	,	PUNCT
ejpam-6165	1	14	issue	issue	NOUN
ejpam-6165	1	15	3	3	NUM
ejpam-6165	1	16	,	,	PUNCT
ejpam-6165	1	17	article	article	NOUN
ejpam-6165	1	18	number	number	NOUN
ejpam-6165	1	19	6165	6165	NUM
ejpam-6165	1	20	issn	issn	PROPN
ejpam-6165	1	21	1307	1307	NUM
ejpam-6165	1	22	-	-	SYM
ejpam-6165	1	23	5543	5543	NUM
ejpam-6165	1	24	–	–	PUNCT
ejpam-6165	1	25	ejpam.com	ejpam.com	X
ejpam-6165	1	26	published	publish	VERB
ejpam-6165	1	27	by	by	ADP
ejpam-6165	1	28	new	new	PROPN
ejpam-6165	1	29	york	york	PROPN
ejpam-6165	1	30	business	business	PROPN
ejpam-6165	1	31	global	global	PROPN
ejpam-6165	1	32	on	on	ADP
ejpam-6165	1	33	r	r	NOUN
ejpam-6165	1	34	-	-	PUNCT
ejpam-6165	1	35	bell	bell	NOUN
ejpam-6165	1	36	-	-	PUNCT
ejpam-6165	1	37	based	base	VERB
ejpam-6165	1	38	apostol	apostol	NOUN
ejpam-6165	1	39	-	-	PUNCT
ejpam-6165	1	40	frobenius	frobenius	NOUN
ejpam-6165	1	41	-	-	PUNCT
ejpam-6165	1	42	type	type	NOUN
ejpam-6165	1	43	poly	poly	ADJ
ejpam-6165	1	44	-	-	PUNCT
ejpam-6165	1	45	euler	euler	NOUN
ejpam-6165	1	46	polynomials	polynomial	NOUN
ejpam-6165	1	47	roberto	roberto	PROPN
ejpam-6165	1	48	b.	b.	PROPN
ejpam-6165	1	49	corcino1,2	corcino1,2	PROPN
ejpam-6165	1	50	,	,	PUNCT
ejpam-6165	1	51	cristina	cristina	PROPN
ejpam-6165	1	52	b.	b.	PROPN
ejpam-6165	1	53	corcino1,2	corcino1,2	PROPN
ejpam-6165	1	54	,	,	PUNCT
ejpam-6165	1	55	rodin	rodin	VERB
ejpam-6165	1	56	paspasan1,2	paspasan1,2	PROPN
ejpam-6165	1	57	,	,	PUNCT
ejpam-6165	1	58	ronald	ronald	PROPN
ejpam-6165	1	59	alambra1,2	alambra1,2	PROPN
ejpam-6165	1	60	1	1	NUM
ejpam-6165	1	61	research	research	NOUN
ejpam-6165	1	62	institute	institute	NOUN
ejpam-6165	1	63	for	for	ADP
ejpam-6165	1	64	computational	computational	ADJ
ejpam-6165	1	65	mathematics	mathematic	NOUN
ejpam-6165	1	66	and	and	CCONJ
ejpam-6165	1	67	physics	physics	NOUN
ejpam-6165	1	68	,	,	PUNCT
ejpam-6165	1	69	cebu	cebu	NOUN
ejpam-6165	1	70	normal	normal	ADJ
ejpam-6165	1	71	university	university	NOUN
ejpam-6165	1	72	,	,	PUNCT
ejpam-6165	1	73	6000	6000	NUM
ejpam-6165	1	74	cebu	cebu	NOUN
ejpam-6165	1	75	city	city	NOUN
ejpam-6165	1	76	,	,	PUNCT
ejpam-6165	1	77	philippines	philippine	NOUN
ejpam-6165	1	78	2	2	NUM
ejpam-6165	1	79	mathematics	mathematics	NOUN
ejpam-6165	1	80	department	department	NOUN
ejpam-6165	1	81	,	,	PUNCT
ejpam-6165	1	82	cebu	cebu	NOUN
ejpam-6165	1	83	normal	normal	ADJ
ejpam-6165	1	84	university	university	NOUN
ejpam-6165	1	85	,	,	PUNCT
ejpam-6165	1	86	6000	6000	NUM
ejpam-6165	1	87	cebu	cebu	NOUN
ejpam-6165	1	88	city	city	NOUN
ejpam-6165	1	89	,	,	PUNCT
ejpam-6165	1	90	philippines	philippine	NOUN
ejpam-6165	1	91	abstract	abstract	ADJ
ejpam-6165	1	92	.	.	PUNCT
ejpam-6165	2	1	this	this	DET
ejpam-6165	2	2	paper	paper	NOUN
ejpam-6165	2	3	introduces	introduce	VERB
ejpam-6165	2	4	a	a	DET
ejpam-6165	2	5	novel	novel	ADJ
ejpam-6165	2	6	variation	variation	NOUN
ejpam-6165	2	7	of	of	ADP
ejpam-6165	2	8	frobenius	frobenius	NOUN
ejpam-6165	2	9	-	-	PUNCT
ejpam-6165	2	10	euler	euler	NOUN
ejpam-6165	2	11	polynomials	polynomial	NOUN
ejpam-6165	2	12	derived	derive	VERB
ejpam-6165	2	13	from	from	ADP
ejpam-6165	2	14	bell	bell	NOUN
ejpam-6165	2	15	numbers	number	NOUN
ejpam-6165	2	16	and	and	CCONJ
ejpam-6165	2	17	apostol	apostol	NOUN
ejpam-6165	2	18	-	-	PUNCT
ejpam-6165	2	19	type	type	NOUN
ejpam-6165	2	20	functions	function	NOUN
ejpam-6165	2	21	,	,	PUNCT
ejpam-6165	2	22	incorporating	incorporate	VERB
ejpam-6165	2	23	the	the	DET
ejpam-6165	2	24	polylogarithm	polylogarithm	PROPN
ejpam-6165	2	25	concept	concept	NOUN
ejpam-6165	2	26	.	.	PUNCT
ejpam-6165	3	1	we	we	PRON
ejpam-6165	3	2	explore	explore	VERB
ejpam-6165	3	3	their	their	PRON
ejpam-6165	3	4	structure	structure	NOUN
ejpam-6165	3	5	and	and	CCONJ
ejpam-6165	3	6	properties	property	NOUN
ejpam-6165	3	7	through	through	ADP
ejpam-6165	3	8	various	various	ADJ
ejpam-6165	3	9	analytical	analytical	ADJ
ejpam-6165	3	10	methods	method	NOUN
ejpam-6165	3	11	,	,	PUNCT
ejpam-6165	3	12	with	with	ADP
ejpam-6165	3	13	a	a	DET
ejpam-6165	3	14	particular	particular	ADJ
ejpam-6165	3	15	emphasis	emphasis	NOUN
ejpam-6165	3	16	on	on	ADP
ejpam-6165	3	17	generating	generating	NOUN
ejpam-6165	3	18	functions	function	NOUN
ejpam-6165	3	19	designed	design	VERB
ejpam-6165	3	20	for	for	ADP
ejpam-6165	3	21	higher	high	ADJ
ejpam-6165	3	22	-	-	PUNCT
ejpam-6165	3	23	order	order	NOUN
ejpam-6165	3	24	apostol	apostol	NOUN
ejpam-6165	3	25	-	-	PUNCT
ejpam-6165	3	26	frobenius	frobenius	NOUN
ejpam-6165	3	27	-	-	PUNCT
ejpam-6165	3	28	type	type	NOUN
ejpam-6165	3	29	poly	poly	ADJ
ejpam-6165	3	30	-	-	PUNCT
ejpam-6165	3	31	euler	euler	NOUN
ejpam-6165	3	32	polynomials	polynomial	NOUN
ejpam-6165	3	33	based	base	VERB
ejpam-6165	3	34	on	on	ADP
ejpam-6165	3	35	bell	bell	NOUN
ejpam-6165	3	36	numbers	number	NOUN
ejpam-6165	3	37	.	.	PUNCT
ejpam-6165	4	1	these	these	DET
ejpam-6165	4	2	functions	function	NOUN
ejpam-6165	4	3	facilitate	facilitate	VERB
ejpam-6165	4	4	the	the	DET
ejpam-6165	4	5	derivation	derivation	NOUN
ejpam-6165	4	6	of	of	ADP
ejpam-6165	4	7	both	both	CCONJ
ejpam-6165	4	8	explicit	explicit	ADJ
ejpam-6165	4	9	and	and	CCONJ
ejpam-6165	4	10	implicit	implicit	ADJ
ejpam-6165	4	11	summation	summation	NOUN
ejpam-6165	4	12	formulas	formula	NOUN
ejpam-6165	4	13	.	.	PUNCT
ejpam-6165	5	1	furthermore	furthermore	ADV
ejpam-6165	5	2	,	,	PUNCT
ejpam-6165	5	3	we	we	PRON
ejpam-6165	5	4	establish	establish	VERB
ejpam-6165	5	5	symmetric	symmetric	ADJ
ejpam-6165	5	6	identities	identity	NOUN
ejpam-6165	5	7	that	that	PRON
ejpam-6165	5	8	unveil	unveil	VERB
ejpam-6165	5	9	intricate	intricate	ADJ
ejpam-6165	5	10	polynomial	polynomial	ADJ
ejpam-6165	5	11	relationships	relationship	NOUN
ejpam-6165	5	12	.	.	PUNCT
ejpam-6165	6	1	this	this	DET
ejpam-6165	6	2	integration	integration	NOUN
ejpam-6165	6	3	provides	provide	VERB
ejpam-6165	6	4	a	a	DET
ejpam-6165	6	5	new	new	ADJ
ejpam-6165	6	6	framework	framework	NOUN
ejpam-6165	6	7	that	that	PRON
ejpam-6165	6	8	deepens	deepen	VERB
ejpam-6165	6	9	the	the	DET
ejpam-6165	6	10	understanding	understanding	NOUN
ejpam-6165	6	11	and	and	CCONJ
ejpam-6165	6	12	expands	expand	VERB
ejpam-6165	6	13	the	the	DET
ejpam-6165	6	14	applicability	applicability	NOUN
ejpam-6165	6	15	of	of	ADP
ejpam-6165	6	16	poly	poly	ADJ
ejpam-6165	6	17	-	-	PUNCT
ejpam-6165	6	18	euler	euler	NOUN
ejpam-6165	6	19	polynomials	polynomial	NOUN
ejpam-6165	6	20	.	.	PUNCT
ejpam-6165	7	1	our	our	PRON
ejpam-6165	7	2	findings	finding	NOUN
ejpam-6165	7	3	contribute	contribute	VERB
ejpam-6165	7	4	to	to	ADP
ejpam-6165	7	5	combinatorial	combinatorial	ADJ
ejpam-6165	7	6	and	and	CCONJ
ejpam-6165	7	7	algebraic	algebraic	ADJ
ejpam-6165	7	8	mathematics	mathematic	NOUN
ejpam-6165	7	9	,	,	PUNCT
ejpam-6165	7	10	fostering	foster	VERB
ejpam-6165	7	11	further	further	ADJ
ejpam-6165	7	12	research	research	NOUN
ejpam-6165	7	13	in	in	ADP
ejpam-6165	7	14	related	related	ADJ
ejpam-6165	7	15	areas	area	NOUN
ejpam-6165	7	16	.	.	PUNCT
ejpam-6165	8	1	2020	2020	NUM
ejpam-6165	8	2	mathematics	mathematic	NOUN
ejpam-6165	8	3	subject	subject	NOUN
ejpam-6165	8	4	classifications	classification	NOUN
ejpam-6165	8	5	:	:	PUNCT
ejpam-6165	8	6	05a15	05a15	NUM
ejpam-6165	8	7	,	,	PUNCT
ejpam-6165	8	8	11b68	11b68	NUM
ejpam-6165	8	9	;	;	PUNCT
ejpam-6165	8	10	11b73	11b73	NUM
ejpam-6165	8	11	,	,	PUNCT
ejpam-6165	8	12	26c05	26c05	NUM
ejpam-6165	8	13	,	,	PUNCT
ejpam-6165	8	14	33b10	33b10	NUM
ejpam-6165	8	15	key	key	ADJ
ejpam-6165	8	16	words	word	NOUN
ejpam-6165	8	17	and	and	CCONJ
ejpam-6165	8	18	phrases	phrase	NOUN
ejpam-6165	8	19	:	:	PUNCT
ejpam-6165	8	20	bell	bell	NOUN
ejpam-6165	8	21	polynomials	polynomial	NOUN
ejpam-6165	8	22	,	,	PUNCT
ejpam-6165	8	23	apostol	apostol	NOUN
ejpam-6165	8	24	-	-	PUNCT
ejpam-6165	8	25	type	type	NOUN
ejpam-6165	8	26	frobenius	frobenius	NOUN
ejpam-6165	8	27	-	-	PUNCT
ejpam-6165	8	28	euler	euler	NOUN
ejpam-6165	8	29	polynomials	polynomial	NOUN
ejpam-6165	8	30	,	,	PUNCT
ejpam-6165	8	31	bellbased	bellbase	VERB
ejpam-6165	8	32	apostol	apostol	NOUN
ejpam-6165	8	33	-	-	PUNCT
ejpam-6165	8	34	type	type	NOUN
ejpam-6165	8	35	frobenius	frobenius	NOUN
ejpam-6165	8	36	-	-	PUNCT
ejpam-6165	8	37	euler	euler	NOUN
ejpam-6165	8	38	polynomials	polynomial	NOUN
ejpam-6165	8	39	,	,	PUNCT
ejpam-6165	8	40	stirling	stirling	NOUN
ejpam-6165	8	41	numbers	number	NOUN
ejpam-6165	8	42	,	,	PUNCT
ejpam-6165	8	43	polylogarithm	polylogarithm	PROPN
ejpam-6165	8	44	1	1	NUM
ejpam-6165	8	45	.	.	PUNCT
ejpam-6165	8	46	introduction	introduction	NOUN
ejpam-6165	8	47	in	in	ADP
ejpam-6165	8	48	recent	recent	ADJ
ejpam-6165	8	49	years	year	NOUN
ejpam-6165	8	50	,	,	PUNCT
ejpam-6165	8	51	a	a	DET
ejpam-6165	8	52	growing	grow	VERB
ejpam-6165	8	53	number	number	NOUN
ejpam-6165	8	54	of	of	ADP
ejpam-6165	8	55	authors	author	NOUN
ejpam-6165	8	56	[	[	X
ejpam-6165	8	57	1	1	NUM
ejpam-6165	8	58	-	-	SYM
ejpam-6165	8	59	4	4	NUM
ejpam-6165	8	60	]	]	PUNCT
ejpam-6165	8	61	have	have	AUX
ejpam-6165	8	62	explored	explore	VERB
ejpam-6165	8	63	the	the	DET
ejpam-6165	8	64	use	use	NOUN
ejpam-6165	8	65	of	of	ADP
ejpam-6165	8	66	generating	generating	NOUN
ejpam-6165	8	67	functions	function	NOUN
ejpam-6165	8	68	to	to	PART
ejpam-6165	8	69	introduce	introduce	VERB
ejpam-6165	8	70	new	new	ADJ
ejpam-6165	8	71	families	family	NOUN
ejpam-6165	8	72	of	of	ADP
ejpam-6165	8	73	special	special	ADJ
ejpam-6165	8	74	polynomials	polynomial	NOUN
ejpam-6165	8	75	,	,	PUNCT
ejpam-6165	8	76	including	include	VERB
ejpam-6165	8	77	two	two	NUM
ejpam-6165	8	78	-	-	PUNCT
ejpam-6165	8	79	parameter	parameter	NOUN
ejpam-6165	8	80	versions	version	NOUN
ejpam-6165	8	81	of	of	ADP
ejpam-6165	8	82	well	well	ADV
ejpam-6165	8	83	-	-	PUNCT
ejpam-6165	8	84	known	know	VERB
ejpam-6165	8	85	polynomials	polynomial	NOUN
ejpam-6165	8	86	such	such	ADJ
ejpam-6165	8	87	as	as	ADP
ejpam-6165	8	88	bernoulli	bernoulli	PROPN
ejpam-6165	8	89	,	,	PUNCT
ejpam-6165	8	90	euler	euler	NOUN
ejpam-6165	8	91	,	,	PUNCT
ejpam-6165	8	92	and	and	CCONJ
ejpam-6165	8	93	genocchi	genocchi	PROPN
ejpam-6165	8	94	polynomials	polynomial	NOUN
ejpam-6165	8	95	.	.	PUNCT
ejpam-6165	9	1	this	this	DET
ejpam-6165	9	2	approach	approach	NOUN
ejpam-6165	9	3	enables	enable	VERB
ejpam-6165	9	4	researchers	researcher	NOUN
ejpam-6165	9	5	to	to	PART
ejpam-6165	9	6	uncover	uncover	VERB
ejpam-6165	9	7	new	new	ADJ
ejpam-6165	9	8	properties	property	NOUN
ejpam-6165	9	9	for	for	ADP
ejpam-6165	9	10	these	these	DET
ejpam-6165	9	11	polynomial	polynomial	ADJ
ejpam-6165	9	12	families	family	NOUN
ejpam-6165	9	13	,	,	PUNCT
ejpam-6165	9	14	which	which	PRON
ejpam-6165	9	15	often	often	ADV
ejpam-6165	9	16	involve	involve	VERB
ejpam-6165	9	17	relationships	relationship	NOUN
ejpam-6165	9	18	between	between	ADP
ejpam-6165	9	19	trigonometric	trigonometric	ADJ
ejpam-6165	9	20	functions	function	NOUN
ejpam-6165	9	21	and	and	CCONJ
ejpam-6165	9	22	other	other	ADJ
ejpam-6165	9	23	parametric	parametric	ADJ
ejpam-6165	9	24	forms	form	NOUN
ejpam-6165	9	25	of	of	ADP
ejpam-6165	9	26	special	special	ADJ
ejpam-6165	9	27	polynomials	polynomial	NOUN
ejpam-6165	9	28	.	.	PUNCT
ejpam-6165	10	1	by	by	ADP
ejpam-6165	10	2	applying	apply	VERB
ejpam-6165	10	3	partial	partial	ADJ
ejpam-6165	10	4	differentiation	differentiation	NOUN
ejpam-6165	10	5	to	to	ADP
ejpam-6165	10	6	these	these	DET
ejpam-6165	10	7	generating	generating	NOUN
ejpam-6165	10	8	functions	function	NOUN
ejpam-6165	10	9	,	,	PUNCT
ejpam-6165	10	10	additional	additional	ADJ
ejpam-6165	10	11	derivative	derivative	ADJ
ejpam-6165	10	12	formulas	formula	NOUN
ejpam-6165	10	13	can	can	AUX
ejpam-6165	10	14	be	be	AUX
ejpam-6165	10	15	derived	derive	VERB
ejpam-6165	10	16	,	,	PUNCT
ejpam-6165	10	17	as	as	ADV
ejpam-6165	10	18	well	well	ADV
ejpam-6165	10	19	as	as	ADP
ejpam-6165	10	20	finite	finite	ADJ
ejpam-6165	10	21	combinatorial	combinatorial	ADJ
ejpam-6165	10	22	sums	sum	NOUN
ejpam-6165	10	23	associated	associate	VERB
ejpam-6165	10	24	with	with	ADP
ejpam-6165	10	25	these	these	DET
ejpam-6165	10	26	polynomials	polynomial	NOUN
ejpam-6165	10	27	and	and	CCONJ
ejpam-6165	10	28	their	their	PRON
ejpam-6165	10	29	related	relate	VERB
ejpam-6165	10	30	numerical	numerical	ADJ
ejpam-6165	10	31	sequences	sequence	NOUN
ejpam-6165	10	32	.	.	PUNCT
ejpam-6165	11	1	furthermore	furthermore	ADV
ejpam-6165	11	2	,	,	PUNCT
ejpam-6165	11	3	these	these	DET
ejpam-6165	11	4	special	special	ADJ
ejpam-6165	11	5	polynomials	polynomial	NOUN
ejpam-6165	11	6	provide	provide	VERB
ejpam-6165	11	7	an	an	DET
ejpam-6165	11	8	accessible	accessible	ADJ
ejpam-6165	11	9	means	mean	NOUN
ejpam-6165	11	10	to	to	PART
ejpam-6165	11	11	derive	derive	VERB
ejpam-6165	11	12	various	various	ADJ
ejpam-6165	11	13	useful	useful	ADJ
ejpam-6165	11	14	mathematical	mathematical	ADJ
ejpam-6165	11	15	identities	identity	NOUN
ejpam-6165	11	16	.	.	PUNCT
ejpam-6165	12	1	doi	doi	NOUN
ejpam-6165	12	2	:	:	PUNCT
ejpam-6165	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6165	https://doi.org/10.29020/nybg.ejpam.v18i3.6165	NUM
ejpam-6165	12	4	email	email	NOUN
ejpam-6165	12	5	addresses	address	NOUN
ejpam-6165	12	6	:	:	PUNCT
ejpam-6165	12	7	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-6165	12	8	(	(	PUNCT
ejpam-6165	12	9	r.	r.	PROPN
ejpam-6165	12	10	corcino	corcino	PROPN
ejpam-6165	12	11	)	)	PUNCT
ejpam-6165	12	12	,	,	PUNCT
ejpam-6165	12	13	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-6165	12	14	(	(	PUNCT
ejpam-6165	12	15	c.	c.	PROPN
ejpam-6165	12	16	corcino	corcino	PROPN
ejpam-6165	12	17	)	)	PUNCT
ejpam-6165	12	18	,	,	PUNCT
ejpam-6165	12	19	paspasanr@cnu.edu.ph	paspasanr@cnu.edu.ph	NOUN
ejpam-6165	12	20	(	(	PUNCT
ejpam-6165	12	21	r.	r.	NOUN
ejpam-6165	12	22	paspasan	paspasan	NOUN
ejpam-6165	12	23	)	)	PUNCT
ejpam-6165	12	24	,	,	PUNCT
ejpam-6165	12	25	alamrar@cnu.edu.ph	alamrar@cnu.edu.ph	PROPN
ejpam-6165	12	26	(	(	PUNCT
ejpam-6165	12	27	r.	r.	PROPN
ejpam-6165	12	28	alambra	alambra	PROPN
ejpam-6165	12	29	)	)	PUNCT
ejpam-6165	12	30	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6165	13	1	1	1	NUM
ejpam-6165	13	2	copyright	copyright	NOUN
ejpam-6165	13	3	:	:	PUNCT
ejpam-6165	13	4	©	©	PROPN
ejpam-6165	13	5	2025	2025	NUM
ejpam-6165	13	6	the	the	DET
ejpam-6165	13	7	author(s	author(s	NOUN
ejpam-6165	13	8	)	)	PUNCT
ejpam-6165	13	9	.	.	PUNCT
ejpam-6165	14	1	(	(	PUNCT
ejpam-6165	14	2	cc	cc	NOUN
ejpam-6165	14	3	by	by	ADP
ejpam-6165	14	4	-	-	PUNCT
ejpam-6165	14	5	nc	nc	PROPN
ejpam-6165	14	6	4.0	4.0	NUM
ejpam-6165	14	7	)	)	PUNCT
ejpam-6165	14	8	2	2	NUM
ejpam-6165	14	9	of	of	ADP
ejpam-6165	14	10	15	15	NUM
ejpam-6165	14	11	a	a	DET
ejpam-6165	14	12	notable	notable	ADJ
ejpam-6165	14	13	example	example	NOUN
ejpam-6165	14	14	is	be	AUX
ejpam-6165	14	15	the	the	DET
ejpam-6165	14	16	apostol	apostol	NOUN
ejpam-6165	14	17	-	-	PUNCT
ejpam-6165	14	18	type	type	NOUN
ejpam-6165	14	19	frobenius	frobenius	NOUN
ejpam-6165	14	20	-	-	PUNCT
ejpam-6165	14	21	euler	euler	NOUN
ejpam-6165	14	22	polynomials	polynomial	NOUN
ejpam-6165	14	23	,	,	PUNCT
ejpam-6165	14	24	which	which	PRON
ejpam-6165	14	25	are	be	AUX
ejpam-6165	14	26	significant	significant	ADJ
ejpam-6165	14	27	in	in	ADP
ejpam-6165	14	28	combinatorial	combinatorial	ADJ
ejpam-6165	14	29	mathematics	mathematic	NOUN
ejpam-6165	14	30	and	and	CCONJ
ejpam-6165	14	31	hold	hold	VERB
ejpam-6165	14	32	an	an	DET
ejpam-6165	14	33	essential	essential	ADJ
ejpam-6165	14	34	place	place	NOUN
ejpam-6165	14	35	in	in	ADP
ejpam-6165	14	36	mathematical	mathematical	ADJ
ejpam-6165	14	37	theory	theory	NOUN
ejpam-6165	14	38	and	and	CCONJ
ejpam-6165	14	39	applications	application	NOUN
ejpam-6165	14	40	.	.	PUNCT
ejpam-6165	15	1	these	these	DET
ejpam-6165	15	2	polynomials	polynomial	NOUN
ejpam-6165	15	3	have	have	AUX
ejpam-6165	15	4	inspired	inspire	VERB
ejpam-6165	15	5	a	a	DET
ejpam-6165	15	6	wide	wide	ADJ
ejpam-6165	15	7	range	range	NOUN
ejpam-6165	15	8	of	of	ADP
ejpam-6165	15	9	theoretical	theoretical	ADJ
ejpam-6165	15	10	developments	development	NOUN
ejpam-6165	15	11	and	and	CCONJ
ejpam-6165	15	12	are	be	AUX
ejpam-6165	15	13	the	the	DET
ejpam-6165	15	14	subject	subject	NOUN
ejpam-6165	15	15	of	of	ADP
ejpam-6165	15	16	extensive	extensive	ADJ
ejpam-6165	15	17	research	research	NOUN
ejpam-6165	15	18	in	in	ADP
ejpam-6165	15	19	combinatorics	combinatoric	NOUN
ejpam-6165	15	20	,	,	PUNCT
ejpam-6165	15	21	yielding	yield	VERB
ejpam-6165	15	22	numerous	numerous	ADJ
ejpam-6165	15	23	intriguing	intriguing	ADJ
ejpam-6165	15	24	findings	finding	NOUN
ejpam-6165	15	25	(	(	PUNCT
ejpam-6165	15	26	see	see	VERB
ejpam-6165	15	27	,	,	PUNCT
ejpam-6165	15	28	for	for	ADP
ejpam-6165	15	29	example	example	NOUN
ejpam-6165	15	30	,	,	PUNCT
ejpam-6165	15	31	[	[	X
ejpam-6165	15	32	5	5	NUM
ejpam-6165	15	33	-	-	SYM
ejpam-6165	15	34	10	10	NUM
ejpam-6165	15	35	]	]	PUNCT
ejpam-6165	15	36	and	and	CCONJ
ejpam-6165	15	37	references	reference	NOUN
ejpam-6165	15	38	therein	therein	ADV
ejpam-6165	15	39	)	)	PUNCT
ejpam-6165	15	40	.	.	PUNCT
ejpam-6165	16	1	the	the	DET
ejpam-6165	16	2	apostol	apostol	NOUN
ejpam-6165	16	3	-	-	PUNCT
ejpam-6165	16	4	type	type	NOUN
ejpam-6165	16	5	frobenius	frobenius	NOUN
ejpam-6165	16	6	-	-	PUNCT
ejpam-6165	16	7	euler	euler	NOUN
ejpam-6165	16	8	polynomials	polynomial	NOUN
ejpam-6165	16	9	e	e	X
ejpam-6165	16	10	(	(	PUNCT
ejpam-6165	16	11	α	α	NOUN
ejpam-6165	16	12	)	)	PUNCT
ejpam-6165	16	13	j	j	PROPN
ejpam-6165	16	14	(	(	PUNCT
ejpam-6165	16	15	ξ;u;λ	ξ;u;λ	PROPN
ejpam-6165	16	16	)	)	PUNCT
ejpam-6165	16	17	of	of	ADP
ejpam-6165	16	18	order	order	NOUN
ejpam-6165	16	19	α	α	NOUN
ejpam-6165	16	20	are	be	AUX
ejpam-6165	16	21	defined	define	VERB
ejpam-6165	16	22	by	by	ADP
ejpam-6165	16	23	(	(	PUNCT
ejpam-6165	16	24	see[7	see[7	NOUN
ejpam-6165	16	25	,	,	PUNCT
ejpam-6165	16	26	8	8	NUM
ejpam-6165	16	27	]	]	PUNCT
ejpam-6165	16	28	):	):	PUNCT
ejpam-6165	16	29	(	(	PUNCT
ejpam-6165	16	30	1−	1−	NUM
ejpam-6165	16	31	u	u	NOUN
ejpam-6165	16	32	λez	λez	NOUN
ejpam-6165	16	33	−	−	PROPN
ejpam-6165	16	34	u	u	NOUN
ejpam-6165	16	35	)	)	PUNCT
ejpam-6165	16	36	α	α	PROPN
ejpam-6165	16	37	eξz	eξz	NOUN
ejpam-6165	17	1	=	=	PRON
ejpam-6165	17	2	∞∑	∞∑	NUM
ejpam-6165	17	3	j=0	j=0	PROPN
ejpam-6165	17	4	e	e	X
ejpam-6165	17	5	(	(	PUNCT
ejpam-6165	17	6	α	α	NOUN
ejpam-6165	17	7	)	)	PUNCT
ejpam-6165	17	8	j	j	PROPN
ejpam-6165	17	9	(	(	PUNCT
ejpam-6165	17	10	ξ;u;λ	ξ;u;λ	PROPN
ejpam-6165	17	11	)	)	PUNCT
ejpam-6165	17	12	zj	zj	PROPN
ejpam-6165	17	13	j	j	PROPN
ejpam-6165	17	14	!	!	PROPN
ejpam-6165	17	15	,	,	PUNCT
ejpam-6165	17	16	(	(	PUNCT
ejpam-6165	17	17	1.1	1.1	NUM
ejpam-6165	17	18	)	)	PUNCT
ejpam-6165	17	19	(	(	PUNCT
ejpam-6165	17	20	α	α	X
ejpam-6165	17	21	,	,	PUNCT
ejpam-6165	17	22	ξ	ξ	PROPN
ejpam-6165	17	23	,	,	PUNCT
ejpam-6165	17	24	λ	λ	X
ejpam-6165	17	25	∈	∈	PROPN
ejpam-6165	17	26	c	c	NOUN
ejpam-6165	17	27	,	,	PUNCT
ejpam-6165	17	28	u	u	PROPN
ejpam-6165	17	29	∈	∈	PROPN
ejpam-6165	17	30	c	c	NOUN
ejpam-6165	17	31	\{1	\{1	NOUN
ejpam-6165	17	32	}	}	PUNCT
ejpam-6165	17	33	,	,	PUNCT
ejpam-6165	17	34	λ	λ	PROPN
ejpam-6165	17	35	̸=	̸=	PROPN
ejpam-6165	17	36	u	u	NOUN
ejpam-6165	17	37	,	,	PUNCT
ejpam-6165	17	38	|z|	|z|	VERB
ejpam-6165	17	39	<	<	X
ejpam-6165	17	40	∣∣∣log(u	∣∣∣log(u	PROPN
ejpam-6165	17	41	λ	λ	PROPN
ejpam-6165	17	42	)	)	PUNCT
ejpam-6165	17	43	∣∣∣	∣∣∣	ADJ
ejpam-6165	17	44	)	)	PUNCT
ejpam-6165	17	45	and	and	CCONJ
ejpam-6165	17	46	eξz	eξz	PROPN
ejpam-6165	17	47	is	be	AUX
ejpam-6165	17	48	an	an	DET
ejpam-6165	17	49	entire	entire	ADJ
ejpam-6165	17	50	function	function	NOUN
ejpam-6165	17	51	of	of	ADP
ejpam-6165	17	52	z	z	NOUN
ejpam-6165	17	53	for	for	ADP
ejpam-6165	17	54	any	any	DET
ejpam-6165	17	55	ξ	ξ	PROPN
ejpam-6165	17	56	∈	∈	PROPN
ejpam-6165	17	57	c.	c.	NOUN
ejpam-6165	17	58	at	at	ADP
ejpam-6165	17	59	the	the	DET
ejpam-6165	17	60	point	point	NOUN
ejpam-6165	17	61	ξ	ξ	X
ejpam-6165	17	62	=	=	SYM
ejpam-6165	17	63	0	0	NUM
ejpam-6165	17	64	,	,	PUNCT
ejpam-6165	17	65	e	e	X
ejpam-6165	17	66	(	(	PUNCT
ejpam-6165	17	67	α	α	NOUN
ejpam-6165	17	68	)	)	PUNCT
ejpam-6165	17	69	j	j	PROPN
ejpam-6165	17	70	(	(	PUNCT
ejpam-6165	17	71	u;λ	u;λ	NOUN
ejpam-6165	17	72	)	)	PUNCT
ejpam-6165	18	1	=	=	SYM
ejpam-6165	18	2	e	e	X
ejpam-6165	18	3	(	(	PUNCT
ejpam-6165	18	4	α	α	NOUN
ejpam-6165	18	5	)	)	PUNCT
ejpam-6165	18	6	j	j	PROPN
ejpam-6165	18	7	(	(	PUNCT
ejpam-6165	18	8	0;u;λ	0;u;λ	NUM
ejpam-6165	18	9	)	)	PUNCT
ejpam-6165	18	10	are	be	AUX
ejpam-6165	18	11	called	call	VERB
ejpam-6165	18	12	the	the	DET
ejpam-6165	18	13	apostol	apostol	NOUN
ejpam-6165	18	14	-	-	PUNCT
ejpam-6165	18	15	type	type	NOUN
ejpam-6165	18	16	frobenius	frobenius	NOUN
ejpam-6165	18	17	-	-	PUNCT
ejpam-6165	18	18	euler	euler	NOUN
ejpam-6165	18	19	numbers	number	NOUN
ejpam-6165	18	20	of	of	ADP
ejpam-6165	18	21	order	order	NOUN
ejpam-6165	18	22	α	α	NOUN
ejpam-6165	18	23	.	.	PUNCT
ejpam-6165	19	1	from	from	ADP
ejpam-6165	19	2	(	(	PUNCT
ejpam-6165	19	3	1	1	NUM
ejpam-6165	19	4	)	)	PUNCT
ejpam-6165	19	5	,	,	PUNCT
ejpam-6165	19	6	we	we	PRON
ejpam-6165	19	7	find	find	VERB
ejpam-6165	19	8	e	e	NOUN
ejpam-6165	19	9	(	(	PUNCT
ejpam-6165	19	10	α	α	NOUN
ejpam-6165	19	11	)	)	PUNCT
ejpam-6165	19	12	j	j	PROPN
ejpam-6165	19	13	(	(	PUNCT
ejpam-6165	19	14	ξ;u;λ	ξ;u;λ	NUM
ejpam-6165	19	15	)	)	PUNCT
ejpam-6165	19	16	=	=	SYM
ejpam-6165	20	1	j∑	j∑	ADJ
ejpam-6165	20	2	v=0	v=0	X
ejpam-6165	20	3	(	(	PUNCT
ejpam-6165	20	4	j	j	PROPN
ejpam-6165	20	5	v	v	NOUN
ejpam-6165	20	6	)	)	PUNCT
ejpam-6165	20	7	e(α	e(α	PROPN
ejpam-6165	20	8	)	)	PUNCT
ejpam-6165	20	9	v	v	NOUN
ejpam-6165	20	10	(	(	PUNCT
ejpam-6165	20	11	u;λ)ξj−v	u;λ)ξj−v	X
ejpam-6165	20	12	(	(	PUNCT
ejpam-6165	20	13	2	2	NUM
ejpam-6165	20	14	)	)	PUNCT
ejpam-6165	20	15	and	and	CCONJ
ejpam-6165	20	16	eα	eα	PRON
ejpam-6165	20	17	j	j	PROPN
ejpam-6165	20	18	(	(	PUNCT
ejpam-6165	20	19	ξ;−1;λ	ξ;−1;λ	PROPN
ejpam-6165	20	20	)	)	PUNCT
ejpam-6165	20	21	=	=	SYM
ejpam-6165	20	22	e	e	X
ejpam-6165	20	23	(	(	PUNCT
ejpam-6165	20	24	α	α	NOUN
ejpam-6165	20	25	)	)	PUNCT
ejpam-6165	20	26	j	j	PROPN
ejpam-6165	20	27	(	(	PUNCT
ejpam-6165	20	28	ξ;λ	ξ;λ	PROPN
ejpam-6165	20	29	)	)	PUNCT
ejpam-6165	20	30	(	(	PUNCT
ejpam-6165	20	31	3	3	X
ejpam-6165	20	32	)	)	PUNCT
ejpam-6165	20	33	where	where	SCONJ
ejpam-6165	20	34	e	e	X
ejpam-6165	20	35	(	(	PUNCT
ejpam-6165	20	36	α	α	NOUN
ejpam-6165	20	37	)	)	PUNCT
ejpam-6165	20	38	j	j	PROPN
ejpam-6165	20	39	(	(	PUNCT
ejpam-6165	20	40	ξ;λ	ξ;λ	NOUN
ejpam-6165	20	41	)	)	PUNCT
ejpam-6165	20	42	are	be	AUX
ejpam-6165	20	43	the	the	DET
ejpam-6165	20	44	jth	jth	PROPN
ejpam-6165	20	45	apostol	apostol	PROPN
ejpam-6165	20	46	-	-	PUNCT
ejpam-6165	20	47	euler	euler	NOUN
ejpam-6165	20	48	polynomials	polynomial	NOUN
ejpam-6165	20	49	of	of	ADP
ejpam-6165	20	50	order	order	NOUN
ejpam-6165	20	51	α	α	NOUN
ejpam-6165	20	52	.	.	PUNCT
ejpam-6165	21	1	when	when	SCONJ
ejpam-6165	21	2	u	u	PROPN
ejpam-6165	21	3	=	=	PROPN
ejpam-6165	21	4	−1	−1	PROPN
ejpam-6165	21	5	,	,	PUNCT
ejpam-6165	21	6	(	(	PUNCT
ejpam-6165	21	7	1.1	1.1	NUM
ejpam-6165	21	8	)	)	PUNCT
ejpam-6165	21	9	will	will	AUX
ejpam-6165	21	10	reduce	reduce	VERB
ejpam-6165	21	11	to	to	ADP
ejpam-6165	21	12	the	the	DET
ejpam-6165	21	13	apostol	apostol	NOUN
ejpam-6165	21	14	-	-	PUNCT
ejpam-6165	21	15	type	type	NOUN
ejpam-6165	21	16	euler	euler	NOUN
ejpam-6165	21	17	polynomials	polynomial	NOUN
ejpam-6165	21	18	:(	:(	X
ejpam-6165	21	19	2	2	NUM
ejpam-6165	21	20	λez	λez	NOUN
ejpam-6165	21	21	+	+	NOUN
ejpam-6165	21	22	1	1	X
ejpam-6165	21	23	)	)	PUNCT
ejpam-6165	21	24	α	α	PRON
ejpam-6165	21	25	eξz	eξz	NOUN
ejpam-6165	22	1	=	=	PRON
ejpam-6165	22	2	∞∑	∞∑	NUM
ejpam-6165	22	3	j=0	j=0	PROPN
ejpam-6165	22	4	e	e	X
ejpam-6165	22	5	(	(	PUNCT
ejpam-6165	22	6	α	α	NOUN
ejpam-6165	22	7	)	)	PUNCT
ejpam-6165	22	8	j	j	PROPN
ejpam-6165	22	9	(	(	PUNCT
ejpam-6165	22	10	ξ;λ	ξ;λ	PROPN
ejpam-6165	22	11	)	)	PUNCT
ejpam-6165	22	12	zj	zj	PROPN
ejpam-6165	22	13	j	j	PROPN
ejpam-6165	22	14	!	!	PROPN
ejpam-6165	22	15	,	,	PUNCT
ejpam-6165	22	16	(	(	PUNCT
ejpam-6165	22	17	1.2	1.2	NUM
ejpam-6165	22	18	)	)	PUNCT
ejpam-6165	22	19	it	it	PRON
ejpam-6165	22	20	is	be	AUX
ejpam-6165	22	21	worth	worth	ADJ
ejpam-6165	22	22	-	-	PUNCT
ejpam-6165	22	23	mentioning	mention	VERB
ejpam-6165	22	24	that	that	SCONJ
ejpam-6165	22	25	(	(	PUNCT
ejpam-6165	22	26	1.1	1.1	NUM
ejpam-6165	22	27	)	)	PUNCT
ejpam-6165	22	28	is	be	AUX
ejpam-6165	22	29	a	a	DET
ejpam-6165	22	30	special	special	ADJ
ejpam-6165	22	31	case	case	NOUN
ejpam-6165	22	32	of	of	ADP
ejpam-6165	22	33	the	the	DET
ejpam-6165	22	34	generalized	generalize	VERB
ejpam-6165	22	35	apostol	apostol	NOUN
ejpam-6165	22	36	type	type	NOUN
ejpam-6165	22	37	frobenius	frobenius	NOUN
ejpam-6165	22	38	-	-	PUNCT
ejpam-6165	22	39	euler	euler	NOUN
ejpam-6165	22	40	polynomials	polynomial	NOUN
ejpam-6165	22	41	of	of	ADP
ejpam-6165	22	42	kurt	kurt	NOUN
ejpam-6165	22	43	and	and	CCONJ
ejpam-6165	22	44	simsek	simsek	VERB
ejpam-6165	22	45	[	[	X
ejpam-6165	22	46	35	35	NUM
ejpam-6165	22	47	]	]	PUNCT
ejpam-6165	22	48	.	.	PUNCT
ejpam-6165	23	1	moreover	moreover	ADV
ejpam-6165	23	2	,	,	PUNCT
ejpam-6165	23	3	mixing	mix	VERB
ejpam-6165	23	4	the	the	DET
ejpam-6165	23	5	frobeniuseuler	frobeniuseuler	NOUN
ejpam-6165	23	6	polynomials	polynomial	NOUN
ejpam-6165	23	7	with	with	ADP
ejpam-6165	23	8	the	the	DET
ejpam-6165	23	9	concept	concept	NOUN
ejpam-6165	23	10	of	of	ADP
ejpam-6165	23	11	polylogarithm	polylogarithm	PROPN
ejpam-6165	23	12	lik(z	lik(z	PROPN
ejpam-6165	23	13	)	)	PUNCT
ejpam-6165	24	1	[	[	X
ejpam-6165	24	2	14	14	NUM
ejpam-6165	24	3	]	]	X
ejpam-6165	24	4	lik(z	lik(z	PROPN
ejpam-6165	24	5	)	)	PUNCT
ejpam-6165	25	1	=	=	PUNCT
ejpam-6165	26	1	∞∑	∞∑	NUM
ejpam-6165	26	2	n=0	n=0	NUM
ejpam-6165	26	3	zn	zn	PROPN
ejpam-6165	26	4	nk	nk	PROPN
ejpam-6165	26	5	,	,	PUNCT
ejpam-6165	26	6	k	k	PROPN
ejpam-6165	26	7	∈	∈	PROPN
ejpam-6165	26	8	z	z	PROPN
ejpam-6165	26	9	,	,	PUNCT
ejpam-6165	26	10	(	(	PUNCT
ejpam-6165	26	11	1.3	1.3	NUM
ejpam-6165	26	12	)	)	PUNCT
ejpam-6165	26	13	yields	yield	VERB
ejpam-6165	26	14	the	the	DET
ejpam-6165	26	15	frobenius	frobenius	ADJ
ejpam-6165	26	16	-	-	PUNCT
ejpam-6165	26	17	type	type	NOUN
ejpam-6165	26	18	poly	poly	ADJ
ejpam-6165	26	19	-	-	PUNCT
ejpam-6165	26	20	euler	euler	NOUN
ejpam-6165	26	21	polynomials	polynomial	NOUN
ejpam-6165	26	22	,	,	PUNCT
ejpam-6165	26	23	which	which	PRON
ejpam-6165	26	24	are	be	AUX
ejpam-6165	26	25	defined	define	VERB
ejpam-6165	26	26	as	as	SCONJ
ejpam-6165	26	27	follows	follow	VERB
ejpam-6165	26	28	∞∑	∞∑	NUM
ejpam-6165	26	29	n=0	n=0	NUM
ejpam-6165	26	30	e(k	e(k	NOUN
ejpam-6165	26	31	)	)	PUNCT
ejpam-6165	26	32	n	n	CCONJ
ejpam-6165	26	33	(	(	PUNCT
ejpam-6165	26	34	x;u	x;u	PROPN
ejpam-6165	26	35	,	,	PUNCT
ejpam-6165	26	36	λ	λ	NOUN
ejpam-6165	26	37	)	)	PUNCT
ejpam-6165	26	38	tn	tn	PROPN
ejpam-6165	26	39	n	n	ADV
ejpam-6165	26	40	!	!	PUNCT
ejpam-6165	27	1	=	=	PRON
ejpam-6165	27	2	lik(1−	lik(1−	VERB
ejpam-6165	27	3	e(1−u	e(1−u	ADJ
ejpam-6165	27	4	)	)	PUNCT
ejpam-6165	27	5	)	)	PUNCT
ejpam-6165	28	1	λet	λet	CCONJ
ejpam-6165	28	2	−	−	PUNCT
ejpam-6165	28	3	u	u	PROPN
ejpam-6165	28	4	ext	ext	NOUN
ejpam-6165	28	5	,	,	PUNCT
ejpam-6165	28	6	(	(	PUNCT
ejpam-6165	28	7	1.4	1.4	NUM
ejpam-6165	28	8	)	)	PUNCT
ejpam-6165	28	9	such	such	ADJ
ejpam-6165	28	10	that	that	SCONJ
ejpam-6165	28	11	when	when	SCONJ
ejpam-6165	28	12	k	k	PROPN
ejpam-6165	28	13	=	=	SYM
ejpam-6165	28	14	1	1	NUM
ejpam-6165	28	15	,	,	PUNCT
ejpam-6165	28	16	li1(1	li1(1	NOUN
ejpam-6165	28	17	−	−	PROPN
ejpam-6165	28	18	e(1−u	e(1−u	ADJ
ejpam-6165	28	19	)	)	PUNCT
ejpam-6165	28	20	)	)	PUNCT
ejpam-6165	29	1	=	=	PUNCT
ejpam-6165	30	1	−ln(1	−ln(1	NUM
ejpam-6165	30	2	−	−	NOUN
ejpam-6165	30	3	(	(	PUNCT
ejpam-6165	30	4	1	1	NUM
ejpam-6165	30	5	−	−	NOUN
ejpam-6165	30	6	e−(1−u	e−(1−u	NOUN
ejpam-6165	30	7	)	)	PUNCT
ejpam-6165	30	8	)	)	PUNCT
ejpam-6165	30	9	)	)	PUNCT
ejpam-6165	31	1	=	=	SYM
ejpam-6165	31	2	−ln(e−(1−u	−ln(e−(1−u	VERB
ejpam-6165	31	3	)	)	PUNCT
ejpam-6165	31	4	)	)	PUNCT
ejpam-6165	31	5	=	=	SYM
ejpam-6165	32	1	1	1	NUM
ejpam-6165	32	2	−	−	NOUN
ejpam-6165	32	3	u	u	NOUN
ejpam-6165	32	4	and	and	CCONJ
ejpam-6165	32	5	so	so	ADV
ejpam-6165	32	6	(	(	PUNCT
ejpam-6165	32	7	1.4	1.4	NUM
ejpam-6165	32	8	)	)	PUNCT
ejpam-6165	32	9	gives	give	VERB
ejpam-6165	32	10	(	(	PUNCT
ejpam-6165	32	11	1.1	1.1	NUM
ejpam-6165	32	12	)	)	PUNCT
ejpam-6165	32	13	.	.	PUNCT
ejpam-6165	33	1	3	3	NUM
ejpam-6165	33	2	of	of	ADP
ejpam-6165	33	3	15	15	NUM
ejpam-6165	33	4	for	for	ADP
ejpam-6165	33	5	j	j	PROPN
ejpam-6165	33	6	≥	≥	PROPN
ejpam-6165	33	7	0	0	NUM
ejpam-6165	33	8	,	,	PUNCT
ejpam-6165	33	9	the	the	DET
ejpam-6165	33	10	stirling	stirling	NOUN
ejpam-6165	33	11	numbers	number	NOUN
ejpam-6165	33	12	of	of	ADP
ejpam-6165	33	13	the	the	DET
ejpam-6165	33	14	first	first	ADJ
ejpam-6165	33	15	kind	kind	NOUN
ejpam-6165	33	16	are	be	AUX
ejpam-6165	33	17	defined	define	VERB
ejpam-6165	33	18	by	by	ADP
ejpam-6165	33	19	(	(	PUNCT
ejpam-6165	33	20	ξ)j	ξ)j	NOUN
ejpam-6165	33	21	=	=	SYM
ejpam-6165	33	22	j∑	j∑	PROPN
ejpam-6165	33	23	p=0	p=0	PROPN
ejpam-6165	33	24	s1(j	s1(j	PROPN
ejpam-6165	33	25	,	,	PUNCT
ejpam-6165	33	26	p)ξ	p)ξ	NOUN
ejpam-6165	33	27	p	p	X
ejpam-6165	33	28	,	,	PUNCT
ejpam-6165	33	29	(	(	PUNCT
ejpam-6165	33	30	4	4	NUM
ejpam-6165	33	31	)	)	PUNCT
ejpam-6165	34	1	where	where	SCONJ
ejpam-6165	34	2	(	(	PUNCT
ejpam-6165	34	3	ξ)0	ξ)0	X
ejpam-6165	34	4	=	=	SYM
ejpam-6165	34	5	1	1	NUM
ejpam-6165	34	6	,	,	PUNCT
ejpam-6165	34	7	and	and	CCONJ
ejpam-6165	34	8	(	(	PUNCT
ejpam-6165	34	9	ξ)j	ξ)j	NOUN
ejpam-6165	34	10	=	=	SYM
ejpam-6165	34	11	ξ(ξ	ξ(ξ	NOUN
ejpam-6165	34	12	−	−	NOUN
ejpam-6165	34	13	1	1	NUM
ejpam-6165	34	14	)	)	PUNCT
ejpam-6165	34	15	·	·	PUNCT
ejpam-6165	34	16	·	·	PUNCT
ejpam-6165	34	17	·	·	PUNCT
ejpam-6165	34	18	(	(	PUNCT
ejpam-6165	34	19	ξ	ξ	X
ejpam-6165	34	20	−	−	PROPN
ejpam-6165	34	21	j	j	PROPN
ejpam-6165	34	22	+	+	NOUN
ejpam-6165	34	23	1),(j	1),(j	NUM
ejpam-6165	34	24	≥	≥	NOUN
ejpam-6165	34	25	1	1	NUM
ejpam-6165	34	26	)	)	PUNCT
ejpam-6165	34	27	.	.	PUNCT
ejpam-6165	35	1	from	from	ADP
ejpam-6165	35	2	(	(	PUNCT
ejpam-6165	35	3	4	4	NUM
ejpam-6165	35	4	)	)	PUNCT
ejpam-6165	35	5	,	,	PUNCT
ejpam-6165	35	6	we	we	PRON
ejpam-6165	35	7	obtain	obtain	VERB
ejpam-6165	35	8	1	1	NUM
ejpam-6165	35	9	r	r	NOUN
ejpam-6165	35	10	!	!	PUNCT
ejpam-6165	36	1	(	(	PUNCT
ejpam-6165	36	2	log(1	log(1	NOUN
ejpam-6165	36	3	+	+	CCONJ
ejpam-6165	37	1	z))r	z))r	NOUN
ejpam-6165	38	1	=	=	PUNCT
ejpam-6165	39	1	∞∑	∞∑	NUM
ejpam-6165	39	2	j	j	NOUN
ejpam-6165	39	3	=	=	NOUN
ejpam-6165	39	4	r	r	NOUN
ejpam-6165	39	5	s1(j	s1(j	PROPN
ejpam-6165	39	6	,	,	PUNCT
ejpam-6165	39	7	r	r	NOUN
ejpam-6165	39	8	)	)	PUNCT
ejpam-6165	39	9	zj	zj	PROPN
ejpam-6165	39	10	j	j	PROPN
ejpam-6165	39	11	!	!	PROPN
ejpam-6165	39	12	,	,	PUNCT
ejpam-6165	39	13	(	(	PUNCT
ejpam-6165	39	14	r	r	NOUN
ejpam-6165	39	15	≥	≥	NOUN
ejpam-6165	39	16	0	0	NUM
ejpam-6165	39	17	)	)	PUNCT
ejpam-6165	39	18	.	.	PUNCT
ejpam-6165	40	1	(	(	PUNCT
ejpam-6165	40	2	5	5	NUM
ejpam-6165	40	3	)	)	PUNCT
ejpam-6165	40	4	for	for	ADP
ejpam-6165	40	5	j	j	PROPN
ejpam-6165	40	6	≥	≥	PROPN
ejpam-6165	40	7	0	0	NUM
ejpam-6165	40	8	,	,	PUNCT
ejpam-6165	40	9	the	the	DET
ejpam-6165	40	10	stirling	stirling	NOUN
ejpam-6165	40	11	numbers	number	NOUN
ejpam-6165	40	12	of	of	ADP
ejpam-6165	40	13	the	the	DET
ejpam-6165	40	14	second	second	ADJ
ejpam-6165	40	15	kind	kind	NOUN
ejpam-6165	40	16	are	be	AUX
ejpam-6165	40	17	defined	define	VERB
ejpam-6165	40	18	by	by	ADP
ejpam-6165	40	19	ξj	ξj	NOUN
ejpam-6165	40	20	=	=	SYM
ejpam-6165	40	21	j∑	j∑	PROPN
ejpam-6165	40	22	q=0	q=0	PUNCT
ejpam-6165	41	1	s2(j	s2(j	PROPN
ejpam-6165	41	2	,	,	PUNCT
ejpam-6165	41	3	q)(ξ)q	q)(ξ)q	PUNCT
ejpam-6165	41	4	(	(	PUNCT
ejpam-6165	41	5	6	6	NUM
ejpam-6165	41	6	)	)	PUNCT
ejpam-6165	41	7	from	from	ADP
ejpam-6165	41	8	(	(	PUNCT
ejpam-6165	41	9	6	6	NUM
ejpam-6165	41	10	)	)	PUNCT
ejpam-6165	41	11	,	,	PUNCT
ejpam-6165	41	12	we	we	PRON
ejpam-6165	41	13	see	see	VERB
ejpam-6165	41	14	that	that	SCONJ
ejpam-6165	41	15	1	1	NUM
ejpam-6165	41	16	r	r	NOUN
ejpam-6165	41	17	!	!	PUNCT
ejpam-6165	42	1	(	(	PUNCT
ejpam-6165	42	2	ez	ez	PROPN
ejpam-6165	42	3	−	−	PROPN
ejpam-6165	42	4	1)r	1)r	NUM
ejpam-6165	42	5	=	=	PUNCT
ejpam-6165	43	1	∞∑	∞∑	NUM
ejpam-6165	43	2	j	j	X
ejpam-6165	43	3	=	=	NOUN
ejpam-6165	43	4	r	r	NOUN
ejpam-6165	43	5	s2(j	s2(j	PROPN
ejpam-6165	43	6	,	,	PUNCT
ejpam-6165	43	7	r	r	NOUN
ejpam-6165	43	8	)	)	PUNCT
ejpam-6165	43	9	zj	zj	PROPN
ejpam-6165	43	10	j	j	PROPN
ejpam-6165	43	11	!	!	PUNCT
ejpam-6165	44	1	(	(	PUNCT
ejpam-6165	45	1	7	7	X
ejpam-6165	45	2	)	)	PUNCT
ejpam-6165	45	3	for	for	ADP
ejpam-6165	45	4	any	any	DET
ejpam-6165	45	5	nonnegative	nonnegative	ADJ
ejpam-6165	45	6	integerr	integerr	NOUN
ejpam-6165	45	7	,	,	PUNCT
ejpam-6165	45	8	the	the	DET
ejpam-6165	45	9	r	r	NOUN
ejpam-6165	45	10	-	-	PUNCT
ejpam-6165	45	11	stirling	stirling	NOUN
ejpam-6165	45	12	numbers	number	NOUN
ejpam-6165	45	13	sr(j	sr(j	X
ejpam-6165	45	14	,	,	PUNCT
ejpam-6165	45	15	k	k	NOUN
ejpam-6165	45	16	)	)	PUNCT
ejpam-6165	45	17	of	of	ADP
ejpam-6165	45	18	the	the	DET
ejpam-6165	45	19	second	second	ADJ
ejpam-6165	45	20	kind	kind	NOUN
ejpam-6165	45	21	are	be	AUX
ejpam-6165	45	22	defined	define	VERB
ejpam-6165	45	23	by	by	ADP
ejpam-6165	45	24	(	(	PUNCT
ejpam-6165	45	25	see[11	see[11	PROPN
ejpam-6165	45	26	]	]	PUNCT
ejpam-6165	45	27	)	)	PUNCT
ejpam-6165	45	28	1	1	NUM
ejpam-6165	46	1	k	k	X
ejpam-6165	46	2	!	!	PROPN
ejpam-6165	46	3	erz(ez	erz(ez	PROPN
ejpam-6165	47	1	−	−	PROPN
ejpam-6165	47	2	1)k	1)k	NUM
ejpam-6165	47	3	=	=	PUNCT
ejpam-6165	48	1	∞∑	∞∑	NUM
ejpam-6165	48	2	j	j	PROPN
ejpam-6165	48	3	=	=	SYM
ejpam-6165	48	4	k	k	X
ejpam-6165	48	5	sr(j	sr(j	X
ejpam-6165	48	6	+	+	X
ejpam-6165	48	7	r	r	X
ejpam-6165	48	8	,	,	PUNCT
ejpam-6165	48	9	k	k	PROPN
ejpam-6165	48	10	+	+	CCONJ
ejpam-6165	48	11	r	r	X
ejpam-6165	48	12	)	)	PUNCT
ejpam-6165	48	13	zj	zj	PROPN
ejpam-6165	48	14	j	j	PROPN
ejpam-6165	48	15	!	!	PUNCT
ejpam-6165	48	16	.	.	PUNCT
ejpam-6165	49	1	(	(	PUNCT
ejpam-6165	49	2	8)	8)	NUM
ejpam-6165	49	3	for	for	ADP
ejpam-6165	49	4	any	any	DET
ejpam-6165	49	5	positive	positive	ADJ
ejpam-6165	49	6	integer	integer	NOUN
ejpam-6165	49	7	m	m	NOUN
ejpam-6165	49	8	,	,	PUNCT
ejpam-6165	49	9	the	the	DET
ejpam-6165	49	10	r	r	PROPN
ejpam-6165	49	11	-	-	PUNCT
ejpam-6165	49	12	whitney	whitney	NOUN
ejpam-6165	49	13	numbers	number	NOUN
ejpam-6165	49	14	wm	wm	PROPN
ejpam-6165	49	15	,	,	PUNCT
ejpam-6165	49	16	r(j	r(j	PROPN
ejpam-6165	49	17	,	,	PUNCT
ejpam-6165	49	18	k	k	NOUN
ejpam-6165	49	19	)	)	PUNCT
ejpam-6165	49	20	of	of	ADP
ejpam-6165	49	21	the	the	DET
ejpam-6165	49	22	second	second	ADJ
ejpam-6165	49	23	kind	kind	NOUN
ejpam-6165	49	24	are	be	AUX
ejpam-6165	49	25	defined	define	VERB
ejpam-6165	49	26	by	by	ADP
ejpam-6165	49	27	(	(	PUNCT
ejpam-6165	49	28	see[12	see[12	PROPN
ejpam-6165	49	29	,	,	PUNCT
ejpam-6165	49	30	12	12	NUM
ejpam-6165	49	31	]	]	PUNCT
ejpam-6165	49	32	)	)	PUNCT
ejpam-6165	49	33	1	1	NUM
ejpam-6165	49	34	mkk	mkk	PROPN
ejpam-6165	49	35	!	!	PUNCT
ejpam-6165	49	36	erz(emz	erz(emz	PUNCT
ejpam-6165	50	1	−	−	NOUN
ejpam-6165	50	2	1)k	1)k	NUM
ejpam-6165	50	3	=	=	PUNCT
ejpam-6165	51	1	∞∑	∞∑	NUM
ejpam-6165	51	2	j	j	PROPN
ejpam-6165	51	3	=	=	PROPN
ejpam-6165	51	4	k	k	PROPN
ejpam-6165	51	5	wm	wm	PROPN
ejpam-6165	51	6	,	,	PUNCT
ejpam-6165	51	7	r(j	r(j	PROPN
ejpam-6165	51	8	,	,	PUNCT
ejpam-6165	51	9	k	k	X
ejpam-6165	51	10	)	)	PUNCT
ejpam-6165	51	11	zj	zj	PROPN
ejpam-6165	51	12	j	j	PROPN
ejpam-6165	51	13	!	!	PUNCT
ejpam-6165	51	14	.	.	PUNCT
ejpam-6165	52	1	(	(	PUNCT
ejpam-6165	52	2	9	9	X
ejpam-6165	52	3	)	)	PUNCT
ejpam-6165	52	4	the	the	DET
ejpam-6165	52	5	bell	bell	NOUN
ejpam-6165	52	6	polynomials	polynomial	VERB
ejpam-6165	52	7	bj(ξ	bj(ξ	NOUN
ejpam-6165	52	8	)	)	PUNCT
ejpam-6165	52	9	are	be	AUX
ejpam-6165	52	10	defined	define	VERB
ejpam-6165	52	11	by	by	ADP
ejpam-6165	52	12	the	the	DET
ejpam-6165	52	13	generating	generating	NOUN
ejpam-6165	52	14	function(see[14,15	function(see[14,15	NOUN
ejpam-6165	52	15	]	]	PUNCT
ejpam-6165	52	16	)	)	PUNCT
ejpam-6165	53	1	eξ(e	eξ(e	ADV
ejpam-6165	53	2	z−1	z−1	X
ejpam-6165	53	3	)	)	PUNCT
ejpam-6165	53	4	=	=	SYM
ejpam-6165	54	1	j∑	j∑	NOUN
ejpam-6165	54	2	k=0	k=0	ADJ
ejpam-6165	54	3	bj(ξ	bj(ξ	NOUN
ejpam-6165	54	4	)	)	PUNCT
ejpam-6165	54	5	zj	zj	PROPN
ejpam-6165	54	6	j	j	PROPN
ejpam-6165	54	7	!	!	PUNCT
ejpam-6165	54	8	.	.	PUNCT
ejpam-6165	55	1	(	(	PUNCT
ejpam-6165	55	2	13	13	NUM
ejpam-6165	55	3	)	)	PUNCT
ejpam-6165	55	4	when	when	SCONJ
ejpam-6165	55	5	ξ	ξ	X
ejpam-6165	55	6	=	=	SYM
ejpam-6165	55	7	1	1	NUM
ejpam-6165	55	8	,	,	PUNCT
ejpam-6165	55	9	bj	bj	ADP
ejpam-6165	55	10	=	=	SYM
ejpam-6165	55	11	bj(1	bj(1	PROPN
ejpam-6165	55	12	)	)	PUNCT
ejpam-6165	55	13	,	,	PUNCT
ejpam-6165	55	14	(	(	PUNCT
ejpam-6165	55	15	j	j	X
ejpam-6165	55	16	≥	≥	NOUN
ejpam-6165	55	17	0	0	NUM
ejpam-6165	55	18	)	)	PUNCT
ejpam-6165	55	19	are	be	AUX
ejpam-6165	55	20	called	call	VERB
ejpam-6165	55	21	the	the	DET
ejpam-6165	55	22	bell	bell	NOUN
ejpam-6165	55	23	numbers	number	NOUN
ejpam-6165	55	24	.	.	PUNCT
ejpam-6165	56	1	from	from	ADP
ejpam-6165	56	2	(	(	PUNCT
ejpam-6165	56	3	7	7	NUM
ejpam-6165	56	4	)	)	PUNCT
ejpam-6165	56	5	and	and	CCONJ
ejpam-6165	56	6	(	(	PUNCT
ejpam-6165	56	7	13	13	NUM
ejpam-6165	56	8	)	)	PUNCT
ejpam-6165	56	9	,	,	PUNCT
ejpam-6165	56	10	we	we	PRON
ejpam-6165	56	11	note	note	VERB
ejpam-6165	56	12	that	that	DET
ejpam-6165	56	13	bj(ξ	bj(ξ	NOUN
ejpam-6165	56	14	)	)	PUNCT
ejpam-6165	56	15	=	=	SYM
ejpam-6165	57	1	j∑	j∑	PROPN
ejpam-6165	57	2	k=1	k=1	PUNCT
ejpam-6165	58	1	s2(j	s2(j	NOUN
ejpam-6165	58	2	,	,	PUNCT
ejpam-6165	58	3	k)ξ	k)ξ	NOUN
ejpam-6165	58	4	k(j	k(j	PROPN
ejpam-6165	58	5	≥	≥	NUM
ejpam-6165	58	6	0	0	NUM
ejpam-6165	58	7	)	)	PUNCT
ejpam-6165	58	8	(	(	PUNCT
ejpam-6165	58	9	14	14	NUM
ejpam-6165	58	10	)	)	PUNCT
ejpam-6165	58	11	recently	recently	ADV
ejpam-6165	58	12	,	,	PUNCT
ejpam-6165	58	13	duran	duran	PROPN
ejpam-6165	58	14	et	et	PROPN
ejpam-6165	58	15	al	al	PROPN
ejpam-6165	58	16	.	.	PUNCT
ejpam-6165	59	1	[	[	X
ejpam-6165	59	2	12	12	NUM
ejpam-6165	59	3	]	]	PUNCT
ejpam-6165	59	4	,	,	PUNCT
ejpam-6165	59	5	introduced	introduce	VERB
ejpam-6165	59	6	the	the	DET
ejpam-6165	59	7	bell	bell	NOUN
ejpam-6165	59	8	polynomials	polynomial	NOUN
ejpam-6165	59	9	bj(ξ	bj(ξ	NOUN
ejpam-6165	59	10	;	;	PUNCT
ejpam-6165	59	11	η	η	PROPN
ejpam-6165	59	12	)	)	PUNCT
ejpam-6165	59	13	of	of	ADP
ejpam-6165	59	14	two	two	NUM
ejpam-6165	59	15	variable	variable	NOUN
ejpam-6165	59	16	defined	define	VERB
ejpam-6165	59	17	by	by	ADP
ejpam-6165	59	18	the	the	DET
ejpam-6165	59	19	generating	generate	VERB
ejpam-6165	59	20	function	function	NOUN
ejpam-6165	59	21	eξz+η(ez−1	eξz+η(ez−1	NOUN
ejpam-6165	59	22	)	)	PUNCT
ejpam-6165	59	23	=	=	NOUN
ejpam-6165	60	1	∞∑	∞∑	NUM
ejpam-6165	60	2	j=0	j=0	PROPN
ejpam-6165	60	3	bj(ξ	bj(ξ	NOUN
ejpam-6165	60	4	;	;	PUNCT
ejpam-6165	60	5	η	η	PROPN
ejpam-6165	60	6	)	)	PUNCT
ejpam-6165	60	7	zj	zj	PROPN
ejpam-6165	60	8	j	j	PROPN
ejpam-6165	60	9	!	!	PUNCT
ejpam-6165	60	10	.	.	PUNCT
ejpam-6165	61	1	(	(	PUNCT
ejpam-6165	61	2	1.5	1.5	NUM
ejpam-6165	61	3	)	)	PUNCT
ejpam-6165	61	4	4	4	NUM
ejpam-6165	61	5	of	of	ADP
ejpam-6165	61	6	15	15	NUM
ejpam-6165	61	7	this	this	PRON
ejpam-6165	61	8	is	be	AUX
ejpam-6165	61	9	exactly	exactly	ADV
ejpam-6165	61	10	the	the	DET
ejpam-6165	61	11	exponential	exponential	ADJ
ejpam-6165	61	12	generating	generating	NOUN
ejpam-6165	61	13	of	of	ADP
ejpam-6165	61	14	r	r	NOUN
ejpam-6165	61	15	-	-	PUNCT
ejpam-6165	61	16	bell	bell	NOUN
ejpam-6165	61	17	polynomials	polynomial	NOUN
ejpam-6165	61	18	of	of	ADP
ejpam-6165	61	19	mezo	mezo	PROPN
ejpam-6165	62	1	[	[	X
ejpam-6165	62	2	25	25	NUM
ejpam-6165	62	3	,	,	PUNCT
ejpam-6165	62	4	26	26	NUM
ejpam-6165	62	5	]	]	PUNCT
ejpam-6165	62	6	,	,	PUNCT
ejpam-6165	62	7	which	which	PRON
ejpam-6165	62	8	is	be	AUX
ejpam-6165	62	9	given	give	VERB
ejpam-6165	62	10	by	by	ADP
ejpam-6165	62	11	erz+x(ez−1	erz+x(ez−1	NOUN
ejpam-6165	62	12	)	)	PUNCT
ejpam-6165	62	13	=	=	PUNCT
ejpam-6165	62	14	∞∑	∞∑	DET
ejpam-6165	62	15	n=0	n=0	NUM
ejpam-6165	62	16	bn	bn	NOUN
ejpam-6165	62	17	,	,	PUNCT
ejpam-6165	62	18	r(x	r(x	PROPN
ejpam-6165	62	19	)	)	PUNCT
ejpam-6165	62	20	zn	zn	PROPN
ejpam-6165	62	21	n	n	CCONJ
ejpam-6165	62	22	!	!	PROPN
ejpam-6165	62	23	,	,	PUNCT
ejpam-6165	62	24	where	where	SCONJ
ejpam-6165	62	25	bn	bn	NOUN
ejpam-6165	62	26	,	,	PUNCT
ejpam-6165	62	27	r(x	r(x	PROPN
ejpam-6165	62	28	)	)	PUNCT
ejpam-6165	62	29	=	=	SYM
ejpam-6165	62	30	n∑	n∑	X
ejpam-6165	62	31	j=0	j=0	PROPN
ejpam-6165	62	32	bn	bn	PROPN
ejpam-6165	62	33	,	,	PUNCT
ejpam-6165	62	34	rx	rx	ADP
ejpam-6165	62	35	j	j	PROPN
ejpam-6165	62	36	,	,	PUNCT
ejpam-6165	62	37	bn	bn	PROPN
ejpam-6165	62	38	,	,	PUNCT
ejpam-6165	62	39	r	r	NOUN
ejpam-6165	62	40	=	=	SYM
ejpam-6165	62	41	n∑	n∑	PROPN
ejpam-6165	62	42	i=0	i=0	PROPN
ejpam-6165	62	43	{	{	PUNCT
ejpam-6165	62	44	n	n	NOUN
ejpam-6165	62	45	i	i	PRON
ejpam-6165	62	46	}	}	PUNCT
ejpam-6165	62	47	r	r	NOUN
ejpam-6165	62	48	,	,	PUNCT
ejpam-6165	62	49	with	with	ADP
ejpam-6165	62	50	bn	bn	NOUN
ejpam-6165	62	51	,	,	PUNCT
ejpam-6165	62	52	r	r	NOUN
ejpam-6165	62	53	and	and	CCONJ
ejpam-6165	62	54	{	{	PUNCT
ejpam-6165	62	55	n	n	NOUN
ejpam-6165	62	56	i	i	PRON
ejpam-6165	62	57	}	}	PUNCT
ejpam-6165	62	58	r	r	NOUN
ejpam-6165	62	59	are	be	AUX
ejpam-6165	62	60	called	call	VERB
ejpam-6165	62	61	the	the	DET
ejpam-6165	62	62	r	r	NOUN
ejpam-6165	62	63	-	-	PUNCT
ejpam-6165	62	64	bell	bell	NOUN
ejpam-6165	62	65	numbers	number	NOUN
ejpam-6165	62	66	and	and	CCONJ
ejpam-6165	62	67	r	r	NOUN
ejpam-6165	62	68	-	-	PUNCT
ejpam-6165	62	69	stirling	stirling	NOUN
ejpam-6165	62	70	numbers	number	NOUN
ejpam-6165	62	71	of	of	ADP
ejpam-6165	62	72	the	the	DET
ejpam-6165	62	73	second	second	ADJ
ejpam-6165	62	74	kind	kind	NOUN
ejpam-6165	62	75	,	,	PUNCT
ejpam-6165	62	76	respectively	respectively	ADV
ejpam-6165	62	77	.	.	PUNCT
ejpam-6165	63	1	by	by	ADP
ejpam-6165	63	2	taking	take	VERB
ejpam-6165	63	3	ξ	ξ	PROPN
ejpam-6165	63	4	=	=	SYM
ejpam-6165	63	5	r	r	NOUN
ejpam-6165	63	6	,	,	PUNCT
ejpam-6165	63	7	we	we	PRON
ejpam-6165	63	8	have	have	VERB
ejpam-6165	63	9	bn(r	bn(r	NUM
ejpam-6165	63	10	;	;	PUNCT
ejpam-6165	63	11	η	η	NOUN
ejpam-6165	63	12	)	)	PUNCT
ejpam-6165	63	13	=	=	SYM
ejpam-6165	63	14	bn	bn	PROPN
ejpam-6165	63	15	,	,	PUNCT
ejpam-6165	63	16	r(η	r(η	NUM
ejpam-6165	63	17	)	)	PUNCT
ejpam-6165	63	18	.	.	PUNCT
ejpam-6165	64	1	from	from	ADP
ejpam-6165	64	2	(	(	PUNCT
ejpam-6165	64	3	1.5	1.5	NUM
ejpam-6165	64	4	)	)	PUNCT
ejpam-6165	64	5	,	,	PUNCT
ejpam-6165	64	6	alam	alam	PROPN
ejpam-6165	64	7	et	et	PROPN
ejpam-6165	64	8	al	al	PROPN
ejpam-6165	64	9	.	.	PUNCT
ejpam-6165	65	1	[	[	X
ejpam-6165	65	2	3	3	NUM
ejpam-6165	65	3	]	]	X
ejpam-6165	65	4	defined	define	VERB
ejpam-6165	65	5	bivariate	bivariate	ADJ
ejpam-6165	65	6	bell	bell	NOUN
ejpam-6165	65	7	-	-	PUNCT
ejpam-6165	65	8	based	base	VERB
ejpam-6165	65	9	apostol	apostol	NOUN
ejpam-6165	65	10	-	-	PUNCT
ejpam-6165	65	11	frobenius	frobenius	NOUN
ejpam-6165	65	12	-	-	PUNCT
ejpam-6165	65	13	type	type	NOUN
ejpam-6165	65	14	euler	euler	NOUN
ejpam-6165	65	15	polynomials	polynomial	NOUN
ejpam-6165	65	16	denoted	denote	VERB
ejpam-6165	65	17	by	by	ADP
ejpam-6165	65	18	bellhn(x	bellhn(x	PROPN
ejpam-6165	65	19	,	,	PUNCT
ejpam-6165	65	20	y;µ	y;µ	PROPN
ejpam-6165	65	21	,	,	PUNCT
ejpam-6165	65	22	λ	λ	PROPN
ejpam-6165	65	23	)	)	PUNCT
ejpam-6165	65	24	as	as	SCONJ
ejpam-6165	65	25	follows	follow	VERB
ejpam-6165	65	26	∞∑	∞∑	NUM
ejpam-6165	65	27	n=0	n=0	NUM
ejpam-6165	65	28	bellhn(x	bellhn(x	NUM
ejpam-6165	65	29	,	,	PUNCT
ejpam-6165	65	30	y;u	y;u	PROPN
ejpam-6165	65	31	,	,	PUNCT
ejpam-6165	65	32	λ	λ	PROPN
ejpam-6165	65	33	)	)	PUNCT
ejpam-6165	65	34	tn	tn	PROPN
ejpam-6165	65	35	n	n	PROPN
ejpam-6165	65	36	!	!	PUNCT
ejpam-6165	66	1	=	=	PUNCT
ejpam-6165	67	1	(	(	PUNCT
ejpam-6165	67	2	1−	1−	NUM
ejpam-6165	67	3	u	u	NOUN
ejpam-6165	67	4	λet	λet	ADP
ejpam-6165	67	5	−	−	PROPN
ejpam-6165	67	6	u	u	NOUN
ejpam-6165	67	7	)	)	PUNCT
ejpam-6165	67	8	α	α	PROPN
ejpam-6165	67	9	ext+y(et−1	ext+y(et−1	NOUN
ejpam-6165	67	10	)	)	PUNCT
ejpam-6165	67	11	(	(	PUNCT
ejpam-6165	67	12	1.6	1.6	NUM
ejpam-6165	67	13	)	)	PUNCT
ejpam-6165	67	14	the	the	DET
ejpam-6165	67	15	manuscript	manuscript	NOUN
ejpam-6165	67	16	of	of	ADP
ejpam-6165	67	17	this	this	DET
ejpam-6165	67	18	paper	paper	NOUN
ejpam-6165	67	19	is	be	AUX
ejpam-6165	67	20	arranged	arrange	VERB
ejpam-6165	67	21	as	as	SCONJ
ejpam-6165	67	22	follows	follow	VERB
ejpam-6165	67	23	:	:	PUNCT
ejpam-6165	67	24	in	in	ADP
ejpam-6165	67	25	section	section	NOUN
ejpam-6165	67	26	2	2	NUM
ejpam-6165	67	27	,	,	PUNCT
ejpam-6165	67	28	we	we	PRON
ejpam-6165	67	29	introduce	introduce	VERB
ejpam-6165	67	30	rbell	rbell	NOUN
ejpam-6165	67	31	-	-	PUNCT
ejpam-6165	67	32	based	base	VERB
ejpam-6165	67	33	apostol	apostol	NOUN
ejpam-6165	67	34	-	-	PUNCT
ejpam-6165	67	35	type	type	NOUN
ejpam-6165	67	36	frobenius	frobenius	NOUN
ejpam-6165	67	37	-	-	PUNCT
ejpam-6165	67	38	euler	euler	NOUN
ejpam-6165	67	39	numbers	number	NOUN
ejpam-6165	67	40	and	and	CCONJ
ejpam-6165	67	41	polynomials	polynomial	NOUN
ejpam-6165	67	42	and	and	CCONJ
ejpam-6165	67	43	investigate	investigate	VERB
ejpam-6165	67	44	some	some	DET
ejpam-6165	67	45	properties	property	NOUN
ejpam-6165	67	46	of	of	ADP
ejpam-6165	67	47	these	these	DET
ejpam-6165	67	48	numbers	number	NOUN
ejpam-6165	67	49	and	and	CCONJ
ejpam-6165	67	50	polynomials	polynomial	NOUN
ejpam-6165	67	51	.	.	PUNCT
ejpam-6165	68	1	in	in	ADP
ejpam-6165	68	2	section	section	NOUN
ejpam-6165	68	3	3	3	NUM
ejpam-6165	68	4	,	,	PUNCT
ejpam-6165	68	5	we	we	PRON
ejpam-6165	68	6	derive	derive	VERB
ejpam-6165	68	7	summation	summation	NOUN
ejpam-6165	68	8	formulas	formula	NOUN
ejpam-6165	68	9	of	of	ADP
ejpam-6165	68	10	apostol	apostol	NOUN
ejpam-6165	68	11	-	-	PUNCT
ejpam-6165	68	12	type	type	NOUN
ejpam-6165	68	13	frobenius	frobenius	NOUN
ejpam-6165	68	14	-	-	PUNCT
ejpam-6165	68	15	euler	euler	NOUN
ejpam-6165	68	16	numbers	number	NOUN
ejpam-6165	68	17	and	and	CCONJ
ejpam-6165	68	18	polynomials	polynomial	NOUN
ejpam-6165	68	19	,	,	PUNCT
ejpam-6165	68	20	connected	connect	VERB
ejpam-6165	68	21	with	with	ADP
ejpam-6165	68	22	apostol	apostol	NOUN
ejpam-6165	68	23	-	-	PUNCT
ejpam-6165	68	24	type	type	NOUN
ejpam-6165	68	25	bernoulli	bernoulli	PROPN
ejpam-6165	68	26	,	,	PUNCT
ejpam-6165	68	27	euler	euler	NOUN
ejpam-6165	68	28	,	,	PUNCT
ejpam-6165	68	29	and	and	CCONJ
ejpam-6165	68	30	genocchi	genocchi	PROPN
ejpam-6165	68	31	polynomials	polynomial	NOUN
ejpam-6165	68	32	.	.	PUNCT
ejpam-6165	69	1	in	in	ADP
ejpam-6165	69	2	section	section	NOUN
ejpam-6165	69	3	4	4	NUM
ejpam-6165	69	4	,	,	PUNCT
ejpam-6165	69	5	we	we	PRON
ejpam-6165	69	6	prove	prove	VERB
ejpam-6165	69	7	several	several	ADJ
ejpam-6165	69	8	identities	identity	NOUN
ejpam-6165	69	9	of	of	ADP
ejpam-6165	69	10	apostol	apostol	NOUN
ejpam-6165	69	11	-	-	PUNCT
ejpam-6165	69	12	type	type	NOUN
ejpam-6165	69	13	frobenius	frobenius	NOUN
ejpam-6165	69	14	-	-	PUNCT
ejpam-6165	69	15	euler	euler	NOUN
ejpam-6165	69	16	polynomials	polynomial	NOUN
ejpam-6165	69	17	by	by	ADP
ejpam-6165	69	18	using	use	VERB
ejpam-6165	69	19	different	different	ADJ
ejpam-6165	69	20	analytical	analytical	ADJ
ejpam-6165	69	21	means	mean	NOUN
ejpam-6165	69	22	and	and	CCONJ
ejpam-6165	69	23	applying	apply	VERB
ejpam-6165	69	24	generating	generating	NOUN
ejpam-6165	69	25	functions	function	NOUN
ejpam-6165	69	26	.	.	PUNCT
ejpam-6165	70	1	2	2	NUM
ejpam-6165	70	2	.	.	X
ejpam-6165	70	3	r	r	X
ejpam-6165	70	4	-	-	PUNCT
ejpam-6165	70	5	bell	bell	NOUN
ejpam-6165	70	6	-	-	PUNCT
ejpam-6165	70	7	based	base	VERB
ejpam-6165	70	8	apostol	apostol	NOUN
ejpam-6165	70	9	-	-	PUNCT
ejpam-6165	70	10	frobenius	frobenius	NOUN
ejpam-6165	70	11	-	-	PUNCT
ejpam-6165	70	12	type	type	NOUN
ejpam-6165	70	13	poly	poly	ADJ
ejpam-6165	70	14	-	-	PUNCT
ejpam-6165	70	15	euler	euler	NOUN
ejpam-6165	70	16	polynomials	polynomial	NOUN
ejpam-6165	70	17	be	be	AUX
ejpam-6165	70	18	(	(	PUNCT
ejpam-6165	70	19	α	α	NOUN
ejpam-6165	70	20	)	)	PUNCT
ejpam-6165	70	21	j	j	NOUN
ejpam-6165	70	22	(	(	PUNCT
ejpam-6165	70	23	r	r	NOUN
ejpam-6165	70	24	,	,	PUNCT
ejpam-6165	70	25	y;u;λ	y;u;λ	NOUN
ejpam-6165	70	26	)	)	PUNCT
ejpam-6165	70	27	in	in	ADP
ejpam-6165	70	28	this	this	DET
ejpam-6165	70	29	section	section	NOUN
ejpam-6165	70	30	,	,	PUNCT
ejpam-6165	70	31	we	we	PRON
ejpam-6165	70	32	introduce	introduce	VERB
ejpam-6165	70	33	the	the	DET
ejpam-6165	70	34	r	r	NOUN
ejpam-6165	70	35	-	-	PUNCT
ejpam-6165	70	36	bell	bell	NOUN
ejpam-6165	70	37	-	-	PUNCT
ejpam-6165	70	38	based	base	VERB
ejpam-6165	70	39	apostol	apostol	NOUN
ejpam-6165	70	40	-	-	PUNCT
ejpam-6165	70	41	type	type	NOUN
ejpam-6165	70	42	frobenius	frobenius	NOUN
ejpam-6165	70	43	-	-	PUNCT
ejpam-6165	70	44	euler	euler	NOUN
ejpam-6165	70	45	polynomials	polynomial	NOUN
ejpam-6165	70	46	,	,	PUNCT
ejpam-6165	70	47	denoted	denote	VERB
ejpam-6165	70	48	as	as	ADP
ejpam-6165	70	49	be	be	AUX
ejpam-6165	70	50	(	(	PUNCT
ejpam-6165	70	51	α	α	NOUN
ejpam-6165	70	52	)	)	PUNCT
ejpam-6165	70	53	j	j	NOUN
ejpam-6165	70	54	(	(	PUNCT
ejpam-6165	70	55	r	r	NOUN
ejpam-6165	70	56	,	,	PUNCT
ejpam-6165	70	57	y;u;λ	y;u;λ	NOUN
ejpam-6165	70	58	)	)	PUNCT
ejpam-6165	70	59	,	,	PUNCT
ejpam-6165	70	60	and	and	CCONJ
ejpam-6165	70	61	present	present	VERB
ejpam-6165	70	62	an	an	DET
ejpam-6165	70	63	explicit	explicit	ADJ
ejpam-6165	70	64	formula	formula	NOUN
ejpam-6165	70	65	for	for	ADP
ejpam-6165	70	66	these	these	DET
ejpam-6165	70	67	polynomials	polynomial	NOUN
ejpam-6165	70	68	.	.	PUNCT
ejpam-6165	71	1	additionally	additionally	ADV
ejpam-6165	71	2	,	,	PUNCT
ejpam-6165	71	3	we	we	PRON
ejpam-6165	71	4	explore	explore	VERB
ejpam-6165	71	5	their	their	PRON
ejpam-6165	71	6	fundamental	fundamental	ADJ
ejpam-6165	71	7	properties	property	NOUN
ejpam-6165	71	8	.	.	PUNCT
ejpam-6165	72	1	we	we	PRON
ejpam-6165	72	2	begin	begin	VERB
ejpam-6165	72	3	with	with	ADP
ejpam-6165	72	4	the	the	DET
ejpam-6165	72	5	following	follow	VERB
ejpam-6165	72	6	definition	definition	NOUN
ejpam-6165	72	7	.	.	PUNCT
ejpam-6165	73	1	definition	definition	NOUN
ejpam-6165	73	2	2.1	2.1	NUM
ejpam-6165	73	3	.	.	PUNCT
ejpam-6165	74	1	the	the	DET
ejpam-6165	74	2	r	r	NOUN
ejpam-6165	74	3	-	-	PUNCT
ejpam-6165	74	4	bell	bell	NOUN
ejpam-6165	74	5	-	-	PUNCT
ejpam-6165	74	6	based	base	VERB
ejpam-6165	74	7	apostol	apostol	NOUN
ejpam-6165	74	8	-	-	PUNCT
ejpam-6165	74	9	frobenius	frobenius	NOUN
ejpam-6165	74	10	-	-	PUNCT
ejpam-6165	74	11	type	type	NOUN
ejpam-6165	74	12	poly	poly	ADJ
ejpam-6165	74	13	-	-	PUNCT
ejpam-6165	74	14	euler	euler	NOUN
ejpam-6165	74	15	polynomials	polynomial	NOUN
ejpam-6165	74	16	be	be	AUX
ejpam-6165	74	17	(	(	PUNCT
ejpam-6165	74	18	k	k	X
ejpam-6165	74	19	,	,	PUNCT
ejpam-6165	74	20	α	α	NOUN
ejpam-6165	74	21	)	)	PUNCT
ejpam-6165	74	22	j	j	NOUN
ejpam-6165	74	23	(	(	PUNCT
ejpam-6165	74	24	r	r	NOUN
ejpam-6165	74	25	,	,	PUNCT
ejpam-6165	74	26	y;u;λ	y;u;λ	NOUN
ejpam-6165	74	27	)	)	PUNCT
ejpam-6165	74	28	of	of	ADP
ejpam-6165	74	29	order	order	NOUN
ejpam-6165	74	30	α	α	NOUN
ejpam-6165	74	31	are	be	AUX
ejpam-6165	74	32	defined	define	VERB
ejpam-6165	74	33	by	by	ADP
ejpam-6165	74	34	means	mean	NOUN
ejpam-6165	74	35	of	of	ADP
ejpam-6165	74	36	the	the	DET
ejpam-6165	74	37	following	follow	VERB
ejpam-6165	74	38	generating	generate	VERB
ejpam-6165	74	39	function	function	NOUN
ejpam-6165	74	40	:(	:(	PUNCT
ejpam-6165	74	41	lik(1−	lik(1−	NOUN
ejpam-6165	74	42	e−(1−u	e−(1−u	NOUN
ejpam-6165	74	43	)	)	PUNCT
ejpam-6165	74	44	)	)	PUNCT
ejpam-6165	75	1	λet	λet	CCONJ
ejpam-6165	75	2	−	−	PROPN
ejpam-6165	75	3	u	u	NOUN
ejpam-6165	75	4	)	)	PUNCT
ejpam-6165	75	5	α	α	PROPN
ejpam-6165	75	6	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	75	7	)	)	PUNCT
ejpam-6165	75	8	=	=	NOUN
ejpam-6165	76	1	∞∑	∞∑	NUM
ejpam-6165	76	2	j=0	j=0	ADJ
ejpam-6165	76	3	be	be	VERB
ejpam-6165	76	4	(	(	PUNCT
ejpam-6165	76	5	k	k	X
ejpam-6165	76	6	,	,	PUNCT
ejpam-6165	76	7	α	α	NOUN
ejpam-6165	76	8	)	)	PUNCT
ejpam-6165	76	9	j	j	NOUN
ejpam-6165	76	10	(	(	PUNCT
ejpam-6165	76	11	r	r	NOUN
ejpam-6165	76	12	,	,	PUNCT
ejpam-6165	76	13	y;u;λ	y;u;λ	NOUN
ejpam-6165	76	14	)	)	PUNCT
ejpam-6165	76	15	tj	tj	PROPN
ejpam-6165	76	16	j	j	PROPN
ejpam-6165	76	17	!	!	PROPN
ejpam-6165	76	18	,	,	PUNCT
ejpam-6165	76	19	(	(	PUNCT
ejpam-6165	76	20	2.1	2.1	NUM
ejpam-6165	76	21	)	)	PUNCT
ejpam-6165	77	1	where	where	SCONJ
ejpam-6165	77	2	(	(	PUNCT
ejpam-6165	77	3	α	α	NOUN
ejpam-6165	77	4	,	,	PUNCT
ejpam-6165	77	5	r	r	NOUN
ejpam-6165	77	6	,	,	PUNCT
ejpam-6165	77	7	y	y	PROPN
ejpam-6165	77	8	,	,	PUNCT
ejpam-6165	77	9	λ	λ	X
ejpam-6165	77	10	∈	∈	NOUN
ejpam-6165	77	11	c	c	X
ejpam-6165	77	12	\	\	X
ejpam-6165	77	13	{	{	PUNCT
ejpam-6165	77	14	1	1	NUM
ejpam-6165	77	15	}	}	PUNCT
ejpam-6165	77	16	,	,	PUNCT
ejpam-6165	77	17	λ	λ	PROPN
ejpam-6165	77	18	̸=	̸=	PROPN
ejpam-6165	77	19	u	u	NOUN
ejpam-6165	77	20	,	,	PUNCT
ejpam-6165	77	21	|t|	|t|	NOUN
ejpam-6165	77	22	)	)	PUNCT
ejpam-6165	77	23	∣∣∣log	∣∣∣log	NOUN
ejpam-6165	77	24	(	(	PUNCT
ejpam-6165	77	25	u	u	NOUN
ejpam-6165	77	26	λ	λ	PROPN
ejpam-6165	77	27	)	)	PUNCT
ejpam-6165	77	28	∣∣∣	∣∣∣	NOUN
ejpam-6165	77	29	.	.	PUNCT
ejpam-6165	78	1	5	5	NUM
ejpam-6165	78	2	of	of	ADP
ejpam-6165	78	3	15	15	NUM
ejpam-6165	78	4	remark	remark	NOUN
ejpam-6165	78	5	2.2	2.2	NUM
ejpam-6165	78	6	.	.	PUNCT
ejpam-6165	79	1	when	when	SCONJ
ejpam-6165	79	2	k	k	PROPN
ejpam-6165	79	3	=	=	SYM
ejpam-6165	79	4	1	1	NUM
ejpam-6165	79	5	,	,	PUNCT
ejpam-6165	79	6	(	(	PUNCT
ejpam-6165	79	7	2.1	2.1	NUM
ejpam-6165	79	8	)	)	PUNCT
ejpam-6165	79	9	reduces	reduce	VERB
ejpam-6165	79	10	to	to	ADP
ejpam-6165	79	11	∞∑	∞∑	NUM
ejpam-6165	79	12	j=0	j=0	VERB
ejpam-6165	79	13	be	be	AUX
ejpam-6165	79	14	(	(	PUNCT
ejpam-6165	79	15	k	k	X
ejpam-6165	79	16	,	,	PUNCT
ejpam-6165	79	17	α	α	NOUN
ejpam-6165	79	18	)	)	PUNCT
ejpam-6165	79	19	j	j	NOUN
ejpam-6165	79	20	(	(	PUNCT
ejpam-6165	79	21	r	r	NOUN
ejpam-6165	79	22	,	,	PUNCT
ejpam-6165	79	23	y;u;λ	y;u;λ	NOUN
ejpam-6165	79	24	)	)	PUNCT
ejpam-6165	79	25	tj	tj	PROPN
ejpam-6165	79	26	j	j	PROPN
ejpam-6165	79	27	!	!	PUNCT
ejpam-6165	79	28	=	=	PUNCT
ejpam-6165	80	1	(	(	PUNCT
ejpam-6165	80	2	li1(1−	li1(1−	X
ejpam-6165	80	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	80	4	)	)	PUNCT
ejpam-6165	80	5	)	)	PUNCT
ejpam-6165	81	1	λet	λet	CCONJ
ejpam-6165	81	2	−	−	PROPN
ejpam-6165	81	3	u	u	NOUN
ejpam-6165	81	4	)	)	PUNCT
ejpam-6165	81	5	α	α	PROPN
ejpam-6165	81	6	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	81	7	)	)	PUNCT
ejpam-6165	81	8	=	=	PUNCT
ejpam-6165	81	9	(	(	PUNCT
ejpam-6165	81	10	−ln(1−	−ln(1−	NOUN
ejpam-6165	81	11	(	(	PUNCT
ejpam-6165	81	12	1−	1−	NUM
ejpam-6165	81	13	e−(1−u	e−(1−u	NOUN
ejpam-6165	81	14	)	)	PUNCT
ejpam-6165	81	15	)	)	PUNCT
ejpam-6165	81	16	)	)	PUNCT
ejpam-6165	82	1	λet	λet	CCONJ
ejpam-6165	82	2	−	−	PROPN
ejpam-6165	82	3	u	u	NOUN
ejpam-6165	82	4	)	)	PUNCT
ejpam-6165	82	5	α	α	PROPN
ejpam-6165	82	6	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	82	7	)	)	PUNCT
ejpam-6165	82	8	=	=	PUNCT
ejpam-6165	83	1	(	(	PUNCT
ejpam-6165	83	2	1−	1−	NUM
ejpam-6165	83	3	u	u	NOUN
ejpam-6165	83	4	λet	λet	ADP
ejpam-6165	83	5	−	−	PROPN
ejpam-6165	83	6	u	u	NOUN
ejpam-6165	83	7	)	)	PUNCT
ejpam-6165	83	8	α	α	PROPN
ejpam-6165	83	9	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	83	10	)	)	PUNCT
ejpam-6165	83	11	.	.	PUNCT
ejpam-6165	84	1	this	this	PRON
ejpam-6165	84	2	is	be	AUX
ejpam-6165	84	3	exactly	exactly	ADV
ejpam-6165	84	4	the	the	DET
ejpam-6165	84	5	bivariate	bivariate	ADJ
ejpam-6165	84	6	bell	bell	NOUN
ejpam-6165	84	7	-	-	PUNCT
ejpam-6165	84	8	based	base	VERB
ejpam-6165	84	9	apostol	apostol	NOUN
ejpam-6165	84	10	-	-	PUNCT
ejpam-6165	84	11	frobenius	frobenius	NOUN
ejpam-6165	84	12	-	-	PUNCT
ejpam-6165	84	13	type	type	NOUN
ejpam-6165	84	14	poly	poly	ADJ
ejpam-6165	84	15	-	-	PUNCT
ejpam-6165	84	16	euler	euler	NOUN
ejpam-6165	84	17	polynomials	polynomial	NOUN
ejpam-6165	84	18	introduced	introduce	VERB
ejpam-6165	84	19	by	by	ADP
ejpam-6165	84	20	alam	alam	PROPN
ejpam-6165	84	21	et	et	PROPN
ejpam-6165	84	22	al	al	PROPN
ejpam-6165	84	23	.	.	PUNCT
ejpam-6165	85	1	[	[	X
ejpam-6165	85	2	3	3	NUM
ejpam-6165	85	3	]	]	PUNCT
ejpam-6165	85	4	.	.	PUNCT
ejpam-6165	86	1	that	that	PRON
ejpam-6165	86	2	is	be	AUX
ejpam-6165	86	3	,	,	PUNCT
ejpam-6165	86	4	by	by	ADP
ejpam-6165	86	5	(	(	PUNCT
ejpam-6165	86	6	1.6	1.6	NUM
ejpam-6165	86	7	)	)	PUNCT
ejpam-6165	86	8	bellhn(r	bellhn(r	NOUN
ejpam-6165	86	9	,	,	PUNCT
ejpam-6165	86	10	y;u	y;u	PROPN
ejpam-6165	86	11	,	,	PUNCT
ejpam-6165	86	12	λ	λ	NOUN
ejpam-6165	86	13	)	)	PUNCT
ejpam-6165	86	14	=	=	PRON
ejpam-6165	86	15	be	be	AUX
ejpam-6165	86	16	(	(	PUNCT
ejpam-6165	86	17	1,α	1,α	NOUN
ejpam-6165	86	18	)	)	PUNCT
ejpam-6165	86	19	j	j	NOUN
ejpam-6165	87	1	(	(	PUNCT
ejpam-6165	87	2	r	r	NOUN
ejpam-6165	87	3	,	,	PUNCT
ejpam-6165	87	4	y;u;λ	y;u;λ	NOUN
ejpam-6165	87	5	)	)	PUNCT
ejpam-6165	87	6	.	.	PUNCT
ejpam-6165	88	1	remark	remark	VERB
ejpam-6165	88	2	2.3	2.3	NUM
ejpam-6165	88	3	.	.	PUNCT
ejpam-6165	89	1	on	on	ADP
ejpam-6165	89	2	taking	take	VERB
ejpam-6165	89	3	r	r	NOUN
ejpam-6165	89	4	=	=	SYM
ejpam-6165	89	5	0	0	NUM
ejpam-6165	89	6	in	in	ADP
ejpam-6165	89	7	(	(	PUNCT
ejpam-6165	89	8	2.1	2.1	NUM
ejpam-6165	89	9	)	)	PUNCT
ejpam-6165	89	10	,	,	PUNCT
ejpam-6165	89	11	we	we	PRON
ejpam-6165	89	12	obtain	obtain	VERB
ejpam-6165	89	13	new	new	ADJ
ejpam-6165	89	14	type	type	NOUN
ejpam-6165	89	15	bell	bell	NOUN
ejpam-6165	89	16	-	-	PUNCT
ejpam-6165	89	17	based	base	VERB
ejpam-6165	89	18	apostol	apostol	NOUN
ejpam-6165	89	19	-	-	PUNCT
ejpam-6165	89	20	frobeniustype	frobeniustype	NOUN
ejpam-6165	89	21	poly	poly	ADJ
ejpam-6165	89	22	-	-	PUNCT
ejpam-6165	89	23	euler	euler	NOUN
ejpam-6165	89	24	polynomials	polynomial	NOUN
ejpam-6165	89	25	be	be	AUX
ejpam-6165	89	26	(	(	PUNCT
ejpam-6165	89	27	k	k	X
ejpam-6165	89	28	,	,	PUNCT
ejpam-6165	89	29	α	α	NOUN
ejpam-6165	89	30	)	)	PUNCT
ejpam-6165	89	31	j	j	PROPN
ejpam-6165	89	32	(	(	PUNCT
ejpam-6165	89	33	y;u;λ	y;u;λ	PROPN
ejpam-6165	89	34	)	)	PUNCT
ejpam-6165	89	35	(	(	PUNCT
ejpam-6165	89	36	lik(1−	lik(1−	PROPN
ejpam-6165	89	37	e−(1−u	e−(1−u	NOUN
ejpam-6165	89	38	)	)	PUNCT
ejpam-6165	89	39	)	)	PUNCT
ejpam-6165	90	1	λet	λet	CCONJ
ejpam-6165	90	2	−	−	PROPN
ejpam-6165	90	3	u	u	NOUN
ejpam-6165	90	4	)	)	PUNCT
ejpam-6165	90	5	α	α	PROPN
ejpam-6165	90	6	ey(e	ey(e	X
ejpam-6165	90	7	t−1	t−1	PROPN
ejpam-6165	90	8	)	)	PUNCT
ejpam-6165	90	9	=	=	SYM
ejpam-6165	91	1	∞∑	∞∑	NUM
ejpam-6165	91	2	j=0	j=0	ADJ
ejpam-6165	91	3	be	be	VERB
ejpam-6165	91	4	(	(	PUNCT
ejpam-6165	91	5	k	k	X
ejpam-6165	91	6	,	,	PUNCT
ejpam-6165	91	7	α	α	NOUN
ejpam-6165	91	8	)	)	PUNCT
ejpam-6165	91	9	j	j	PROPN
ejpam-6165	91	10	(	(	PUNCT
ejpam-6165	91	11	y;u;λ	y;u;λ	PROPN
ejpam-6165	91	12	)	)	PUNCT
ejpam-6165	91	13	tj	tj	PROPN
ejpam-6165	91	14	j	j	PROPN
ejpam-6165	91	15	!	!	PUNCT
ejpam-6165	91	16	.	.	PUNCT
ejpam-6165	92	1	(	(	PUNCT
ejpam-6165	92	2	2.2	2.2	NUM
ejpam-6165	92	3	)	)	PUNCT
ejpam-6165	92	4	we	we	PRON
ejpam-6165	92	5	call	call	VERB
ejpam-6165	92	6	e	e	NOUN
ejpam-6165	92	7	(	(	PUNCT
ejpam-6165	92	8	k	k	X
ejpam-6165	92	9	,	,	PUNCT
ejpam-6165	92	10	α	α	NOUN
ejpam-6165	92	11	)	)	PUNCT
ejpam-6165	92	12	j	j	PROPN
ejpam-6165	92	13	(	(	PUNCT
ejpam-6165	92	14	y;u;λ	y;u;λ	PROPN
ejpam-6165	92	15	)	)	PUNCT
ejpam-6165	92	16	the	the	DET
ejpam-6165	92	17	bell	bell	NOUN
ejpam-6165	92	18	-	-	PUNCT
ejpam-6165	92	19	based	base	VERB
ejpam-6165	92	20	apostol	apostol	NOUN
ejpam-6165	92	21	-	-	PUNCT
ejpam-6165	92	22	frobenius	frobenius	NOUN
ejpam-6165	92	23	-	-	PUNCT
ejpam-6165	92	24	type	type	NOUN
ejpam-6165	92	25	poly	poly	ADJ
ejpam-6165	92	26	-	-	PUNCT
ejpam-6165	92	27	euler	euler	NOUN
ejpam-6165	92	28	polynomials	polynomial	NOUN
ejpam-6165	92	29	.	.	PUNCT
ejpam-6165	93	1	moreover	moreover	ADV
ejpam-6165	93	2	,	,	PUNCT
ejpam-6165	93	3	when	when	SCONJ
ejpam-6165	93	4	k	k	PROPN
ejpam-6165	93	5	=	=	SYM
ejpam-6165	93	6	1	1	NUM
ejpam-6165	93	7	,	,	PUNCT
ejpam-6165	93	8	we	we	PRON
ejpam-6165	93	9	have	have	VERB
ejpam-6165	93	10	∞∑	∞∑	NUM
ejpam-6165	93	11	j=0	j=0	VERB
ejpam-6165	93	12	be	be	AUX
ejpam-6165	93	13	(	(	PUNCT
ejpam-6165	93	14	k	k	X
ejpam-6165	93	15	,	,	PUNCT
ejpam-6165	93	16	α	α	NOUN
ejpam-6165	93	17	)	)	PUNCT
ejpam-6165	93	18	j	j	PROPN
ejpam-6165	93	19	(	(	PUNCT
ejpam-6165	93	20	y;u;λ	y;u;λ	PROPN
ejpam-6165	93	21	)	)	PUNCT
ejpam-6165	93	22	tj	tj	PROPN
ejpam-6165	93	23	j	j	PROPN
ejpam-6165	93	24	!	!	PUNCT
ejpam-6165	94	1	=	=	PUNCT
ejpam-6165	95	1	(	(	PUNCT
ejpam-6165	95	2	li1(1−	li1(1−	X
ejpam-6165	95	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	95	4	)	)	PUNCT
ejpam-6165	95	5	)	)	PUNCT
ejpam-6165	96	1	λet	λet	CCONJ
ejpam-6165	96	2	−	−	PROPN
ejpam-6165	96	3	u	u	NOUN
ejpam-6165	96	4	)	)	PUNCT
ejpam-6165	96	5	α	α	PROPN
ejpam-6165	96	6	ey(e	ey(e	X
ejpam-6165	96	7	z−1	z−1	PROPN
ejpam-6165	96	8	)	)	PUNCT
ejpam-6165	96	9	=	=	NOUN
ejpam-6165	96	10	(	(	PUNCT
ejpam-6165	96	11	−ln(1−	−ln(1−	NOUN
ejpam-6165	96	12	(	(	PUNCT
ejpam-6165	96	13	1−	1−	NUM
ejpam-6165	96	14	e−(1−u	e−(1−u	NOUN
ejpam-6165	96	15	)	)	PUNCT
ejpam-6165	96	16	)	)	PUNCT
ejpam-6165	96	17	)	)	PUNCT
ejpam-6165	97	1	λet	λet	CCONJ
ejpam-6165	97	2	−	−	PROPN
ejpam-6165	97	3	u	u	NOUN
ejpam-6165	97	4	)	)	PUNCT
ejpam-6165	97	5	α	α	PROPN
ejpam-6165	97	6	ey(e	ey(e	X
ejpam-6165	97	7	z−1	z−1	PROPN
ejpam-6165	97	8	)	)	PUNCT
ejpam-6165	97	9	=	=	PUNCT
ejpam-6165	97	10	(	(	PUNCT
ejpam-6165	97	11	1−	1−	NUM
ejpam-6165	97	12	u	u	NOUN
ejpam-6165	97	13	λet	λet	ADP
ejpam-6165	97	14	−	−	PROPN
ejpam-6165	97	15	u	u	NOUN
ejpam-6165	97	16	)	)	PUNCT
ejpam-6165	97	17	α	α	PROPN
ejpam-6165	97	18	ey(e	ey(e	X
ejpam-6165	97	19	z−1	z−1	PROPN
ejpam-6165	97	20	)	)	PUNCT
ejpam-6165	97	21	,	,	PUNCT
ejpam-6165	97	22	where	where	SCONJ
ejpam-6165	97	23	bellhn(y;u	bellhn(y;u	NOUN
ejpam-6165	97	24	,	,	PUNCT
ejpam-6165	97	25	λ	λ	NOUN
ejpam-6165	97	26	)	)	PUNCT
ejpam-6165	97	27	=	=	PRON
ejpam-6165	97	28	be	be	AUX
ejpam-6165	97	29	(	(	PUNCT
ejpam-6165	97	30	1,α	1,α	NOUN
ejpam-6165	97	31	)	)	PUNCT
ejpam-6165	97	32	j	j	PROPN
ejpam-6165	97	33	(	(	PUNCT
ejpam-6165	97	34	y;u;λ	y;u;λ	PROPN
ejpam-6165	97	35	)	)	PUNCT
ejpam-6165	97	36	,	,	PUNCT
ejpam-6165	97	37	the	the	DET
ejpam-6165	97	38	bell	bell	NOUN
ejpam-6165	97	39	-	-	PUNCT
ejpam-6165	97	40	based	base	VERB
ejpam-6165	97	41	apostol	apostol	NOUN
ejpam-6165	97	42	-	-	PUNCT
ejpam-6165	97	43	frobenius	frobenius	NOUN
ejpam-6165	97	44	-	-	PUNCT
ejpam-6165	97	45	type	type	NOUN
ejpam-6165	97	46	euler	euler	NOUN
ejpam-6165	97	47	polynomials	polynomial	NOUN
ejpam-6165	97	48	.	.	PUNCT
ejpam-6165	98	1	remark	remark	PROPN
ejpam-6165	98	2	2.4	2.4	NUM
ejpam-6165	98	3	.	.	PUNCT
ejpam-6165	99	1	upon	upon	SCONJ
ejpam-6165	99	2	setting	set	VERB
ejpam-6165	99	3	y	y	NOUN
ejpam-6165	99	4	=	=	PUNCT
ejpam-6165	99	5	0	0	NUM
ejpam-6165	99	6	in	in	ADP
ejpam-6165	99	7	(	(	PUNCT
ejpam-6165	99	8	2.1	2.1	NUM
ejpam-6165	99	9	)	)	PUNCT
ejpam-6165	99	10	,	,	PUNCT
ejpam-6165	99	11	the	the	DET
ejpam-6165	99	12	r	r	NOUN
ejpam-6165	99	13	-	-	PUNCT
ejpam-6165	99	14	bell	bell	NOUN
ejpam-6165	99	15	-	-	PUNCT
ejpam-6165	99	16	based	base	VERB
ejpam-6165	99	17	apostol	apostol	NOUN
ejpam-6165	99	18	-	-	PUNCT
ejpam-6165	99	19	frobenius	frobenius	NOUN
ejpam-6165	99	20	-	-	PUNCT
ejpam-6165	99	21	type	type	NOUN
ejpam-6165	99	22	polyeuler	polyeuler	NOUN
ejpam-6165	99	23	polynomials	polynomial	NOUN
ejpam-6165	99	24	be	be	AUX
ejpam-6165	99	25	(	(	PUNCT
ejpam-6165	99	26	k	k	X
ejpam-6165	99	27	,	,	PUNCT
ejpam-6165	99	28	α	α	NOUN
ejpam-6165	99	29	)	)	PUNCT
ejpam-6165	99	30	j	j	NOUN
ejpam-6165	99	31	(	(	PUNCT
ejpam-6165	99	32	r	r	NOUN
ejpam-6165	99	33	,	,	PUNCT
ejpam-6165	99	34	y;u;λ	y;u;λ	NOUN
ejpam-6165	99	35	)	)	PUNCT
ejpam-6165	99	36	of	of	ADP
ejpam-6165	99	37	order	order	NOUN
ejpam-6165	99	38	α	α	NOUN
ejpam-6165	99	39	reduces	reduce	VERB
ejpam-6165	99	40	to	to	ADP
ejpam-6165	99	41	familiar	familiar	ADJ
ejpam-6165	99	42	apostol	apostol	NOUN
ejpam-6165	99	43	-	-	PUNCT
ejpam-6165	99	44	frobenius	frobenius	NOUN
ejpam-6165	99	45	-	-	PUNCT
ejpam-6165	99	46	type	type	NOUN
ejpam-6165	99	47	poly	poly	ADJ
ejpam-6165	99	48	-	-	PUNCT
ejpam-6165	99	49	euler	euler	NOUN
ejpam-6165	99	50	polynomials	polynomial	NOUN
ejpam-6165	99	51	be	be	AUX
ejpam-6165	99	52	(	(	PUNCT
ejpam-6165	99	53	k	k	X
ejpam-6165	99	54	,	,	PUNCT
ejpam-6165	99	55	α	α	NOUN
ejpam-6165	99	56	)	)	PUNCT
ejpam-6165	99	57	j	j	PROPN
ejpam-6165	99	58	(	(	PUNCT
ejpam-6165	99	59	r;u;λ	r;u;λ	NOUN
ejpam-6165	99	60	)	)	PUNCT
ejpam-6165	99	61	of	of	ADP
ejpam-6165	99	62	order	order	NOUN
ejpam-6165	99	63	α	α	PRON
ejpam-6165	99	64	remark	remark	VERB
ejpam-6165	99	65	2.5	2.5	NUM
ejpam-6165	99	66	.	.	PUNCT
ejpam-6165	100	1	when	when	SCONJ
ejpam-6165	100	2	y	y	PROPN
ejpam-6165	100	3	=	=	PROPN
ejpam-6165	100	4	0	0	PROPN
ejpam-6165	100	5	and	and	CCONJ
ejpam-6165	100	6	α	α	NOUN
ejpam-6165	100	7	=	=	SYM
ejpam-6165	100	8	1	1	NUM
ejpam-6165	100	9	,	,	PUNCT
ejpam-6165	100	10	r	r	NOUN
ejpam-6165	100	11	-	-	PUNCT
ejpam-6165	100	12	bell	bell	NOUN
ejpam-6165	100	13	-	-	PUNCT
ejpam-6165	100	14	based	base	VERB
ejpam-6165	100	15	apostol	apostol	NOUN
ejpam-6165	100	16	-	-	PUNCT
ejpam-6165	100	17	frobenius	frobenius	NOUN
ejpam-6165	100	18	-	-	PUNCT
ejpam-6165	100	19	type	type	NOUN
ejpam-6165	100	20	poly	poly	ADJ
ejpam-6165	100	21	-	-	PUNCT
ejpam-6165	100	22	euler	euler	NOUN
ejpam-6165	100	23	polynomials	polynomial	NOUN
ejpam-6165	100	24	be	be	AUX
ejpam-6165	100	25	(	(	PUNCT
ejpam-6165	100	26	k	k	X
ejpam-6165	100	27	,	,	PUNCT
ejpam-6165	100	28	α	α	NOUN
ejpam-6165	100	29	)	)	PUNCT
ejpam-6165	100	30	j	j	NOUN
ejpam-6165	100	31	(	(	PUNCT
ejpam-6165	100	32	r	r	NOUN
ejpam-6165	100	33	,	,	PUNCT
ejpam-6165	100	34	y;u;λ	y;u;λ	NOUN
ejpam-6165	100	35	)	)	PUNCT
ejpam-6165	100	36	of	of	ADP
ejpam-6165	100	37	order	order	NOUN
ejpam-6165	100	38	α	α	PRON
ejpam-6165	100	39	reduce	reduce	VERB
ejpam-6165	100	40	to	to	ADP
ejpam-6165	100	41	the	the	DET
ejpam-6165	100	42	usual	usual	ADJ
ejpam-6165	100	43	frobenius	frobenius	NOUN
ejpam-6165	100	44	-	-	PUNCT
ejpam-6165	100	45	euler	euler	NOUN
ejpam-6165	100	46	polynomials	polynomial	NOUN
ejpam-6165	100	47	ej(r;u;λ	ej(r;u;λ	PROPN
ejpam-6165	100	48	)	)	PUNCT
ejpam-6165	100	49	.	.	PUNCT
ejpam-6165	101	1	we	we	PRON
ejpam-6165	101	2	note	note	VERB
ejpam-6165	101	3	that	that	PRON
ejpam-6165	101	4	be	be	AUX
ejpam-6165	101	5	(	(	PUNCT
ejpam-6165	101	6	k,1	k,1	PROPN
ejpam-6165	101	7	)	)	PUNCT
ejpam-6165	101	8	j	j	PROPN
ejpam-6165	101	9	(	(	PUNCT
ejpam-6165	101	10	r	r	NOUN
ejpam-6165	101	11	,	,	PUNCT
ejpam-6165	101	12	0;u;λ	0;u;λ	PUNCT
ejpam-6165	101	13	)	)	PUNCT
ejpam-6165	102	1	=	=	PRON
ejpam-6165	102	2	be	be	AUX
ejpam-6165	102	3	(	(	PUNCT
ejpam-6165	102	4	k	k	NOUN
ejpam-6165	102	5	)	)	PUNCT
ejpam-6165	102	6	j	j	PROPN
ejpam-6165	102	7	(	(	PUNCT
ejpam-6165	102	8	r;u;λ	r;u;λ	PROPN
ejpam-6165	102	9	)	)	PUNCT
ejpam-6165	102	10	.	.	PUNCT
ejpam-6165	103	1	(	(	PUNCT
ejpam-6165	103	2	2.3	2.3	NUM
ejpam-6165	103	3	)	)	PUNCT
ejpam-6165	103	4	6	6	NUM
ejpam-6165	103	5	of	of	ADP
ejpam-6165	103	6	15	15	NUM
ejpam-6165	103	7	the	the	DET
ejpam-6165	103	8	following	follow	VERB
ejpam-6165	103	9	theorem	theorem	NOUN
ejpam-6165	103	10	contains	contain	VERB
ejpam-6165	103	11	a	a	DET
ejpam-6165	103	12	summation	summation	NOUN
ejpam-6165	103	13	formula	formula	NOUN
ejpam-6165	103	14	relating	relate	VERB
ejpam-6165	103	15	be	be	AUX
ejpam-6165	103	16	(	(	PUNCT
ejpam-6165	103	17	r	r	NOUN
ejpam-6165	103	18	)	)	PUNCT
ejpam-6165	103	19	n	n	NOUN
ejpam-6165	103	20	(	(	PUNCT
ejpam-6165	103	21	r	r	NOUN
ejpam-6165	103	22	,	,	PUNCT
ejpam-6165	103	23	y;u	y;u	PROPN
ejpam-6165	103	24	,	,	PUNCT
ejpam-6165	103	25	λ	λ	NOUN
ejpam-6165	103	26	)	)	PUNCT
ejpam-6165	103	27	with	with	ADP
ejpam-6165	103	28	e	e	X
ejpam-6165	103	29	(	(	PUNCT
ejpam-6165	103	30	r	r	NOUN
ejpam-6165	103	31	)	)	PUNCT
ejpam-6165	103	32	k	k	NOUN
ejpam-6165	103	33	(	(	PUNCT
ejpam-6165	103	34	r;u	r;u	NOUN
ejpam-6165	103	35	,	,	PUNCT
ejpam-6165	103	36	λ	λ	NOUN
ejpam-6165	103	37	)	)	PUNCT
ejpam-6165	103	38	and	and	CCONJ
ejpam-6165	103	39	bn(y	bn(y	NUM
ejpam-6165	103	40	)	)	PUNCT
ejpam-6165	103	41	theorem	theorem	VERB
ejpam-6165	103	42	2.6	2.6	NUM
ejpam-6165	103	43	.	.	PUNCT
ejpam-6165	104	1	the	the	DET
ejpam-6165	104	2	r	r	NOUN
ejpam-6165	104	3	-	-	PUNCT
ejpam-6165	104	4	bell	bell	NOUN
ejpam-6165	104	5	-	-	PUNCT
ejpam-6165	104	6	based	base	VERB
ejpam-6165	104	7	apostol	apostol	NOUN
ejpam-6165	104	8	-	-	PUNCT
ejpam-6165	104	9	frobenius	frobenius	NOUN
ejpam-6165	104	10	-	-	PUNCT
ejpam-6165	104	11	type	type	NOUN
ejpam-6165	104	12	poly	poly	ADJ
ejpam-6165	104	13	-	-	PUNCT
ejpam-6165	104	14	euler	euler	NOUN
ejpam-6165	104	15	polynomials	polynomial	NOUN
ejpam-6165	104	16	be	be	AUX
ejpam-6165	104	17	(	(	PUNCT
ejpam-6165	104	18	α	α	NOUN
ejpam-6165	104	19	)	)	PUNCT
ejpam-6165	104	20	j	j	NOUN
ejpam-6165	104	21	(	(	PUNCT
ejpam-6165	104	22	r	r	NOUN
ejpam-6165	104	23	,	,	PUNCT
ejpam-6165	104	24	y;u;λ	y;u;λ	NOUN
ejpam-6165	104	25	)	)	PUNCT
ejpam-6165	104	26	of	of	ADP
ejpam-6165	104	27	order	order	NOUN
ejpam-6165	104	28	α	α	PRON
ejpam-6165	104	29	satisfy	satisfy	VERB
ejpam-6165	104	30	the	the	DET
ejpam-6165	104	31	following	follow	VERB
ejpam-6165	104	32	summation	summation	NOUN
ejpam-6165	104	33	identity	identity	NOUN
ejpam-6165	104	34	be	be	AUX
ejpam-6165	104	35	(	(	PUNCT
ejpam-6165	104	36	k	k	X
ejpam-6165	104	37	,	,	PUNCT
ejpam-6165	104	38	α	α	NOUN
ejpam-6165	104	39	)	)	PUNCT
ejpam-6165	104	40	j	j	NOUN
ejpam-6165	104	41	(	(	PUNCT
ejpam-6165	104	42	r	r	NOUN
ejpam-6165	104	43	,	,	PUNCT
ejpam-6165	104	44	y;u;λ	y;u;λ	NOUN
ejpam-6165	104	45	)	)	PUNCT
ejpam-6165	104	46	=	=	SYM
ejpam-6165	105	1	n∑	n∑	NOUN
ejpam-6165	105	2	j=0	j=0	PROPN
ejpam-6165	105	3	(	(	PUNCT
ejpam-6165	105	4	n	n	X
ejpam-6165	105	5	k	k	NOUN
ejpam-6165	105	6	)	)	PUNCT
ejpam-6165	105	7	e	e	X
ejpam-6165	105	8	(	(	PUNCT
ejpam-6165	105	9	k	k	X
ejpam-6165	105	10	,	,	PUNCT
ejpam-6165	105	11	α	α	NOUN
ejpam-6165	105	12	)	)	PUNCT
ejpam-6165	105	13	j	j	PROPN
ejpam-6165	105	14	(	(	PUNCT
ejpam-6165	105	15	r;u;λ)bn−j(y	r;u;λ)bn−j(y	PROPN
ejpam-6165	105	16	)	)	PUNCT
ejpam-6165	105	17	.	.	PUNCT
ejpam-6165	106	1	proof	proof	NOUN
ejpam-6165	106	2	.	.	PUNCT
ejpam-6165	107	1	using	use	VERB
ejpam-6165	107	2	(	(	PUNCT
ejpam-6165	107	3	2.1	2.1	NUM
ejpam-6165	107	4	)	)	PUNCT
ejpam-6165	107	5	,	,	PUNCT
ejpam-6165	107	6	we	we	PRON
ejpam-6165	107	7	have	have	VERB
ejpam-6165	107	8	∞∑	∞∑	NUM
ejpam-6165	107	9	j=0	j=0	VERB
ejpam-6165	107	10	be	be	AUX
ejpam-6165	107	11	(	(	PUNCT
ejpam-6165	107	12	k	k	X
ejpam-6165	107	13	,	,	PUNCT
ejpam-6165	107	14	α	α	NOUN
ejpam-6165	107	15	)	)	PUNCT
ejpam-6165	107	16	j	j	NOUN
ejpam-6165	107	17	(	(	PUNCT
ejpam-6165	107	18	r	r	NOUN
ejpam-6165	107	19	,	,	PUNCT
ejpam-6165	107	20	y;u;λ	y;u;λ	NOUN
ejpam-6165	107	21	)	)	PUNCT
ejpam-6165	107	22	tj	tj	PROPN
ejpam-6165	107	23	j	j	PROPN
ejpam-6165	107	24	!	!	PUNCT
ejpam-6165	108	1	=	=	PRON
ejpam-6165	108	2	{	{	PUNCT
ejpam-6165	108	3	(	(	PUNCT
ejpam-6165	108	4	lik(1−	lik(1−	PROPN
ejpam-6165	108	5	e−(1−u	e−(1−u	NOUN
ejpam-6165	108	6	)	)	PUNCT
ejpam-6165	108	7	)	)	PUNCT
ejpam-6165	109	1	λet	λet	CCONJ
ejpam-6165	109	2	−	−	PROPN
ejpam-6165	109	3	u	u	NOUN
ejpam-6165	109	4	)	)	PUNCT
ejpam-6165	109	5	α	α	PROPN
ejpam-6165	109	6	ert	ert	NOUN
ejpam-6165	109	7	}	}	PUNCT
ejpam-6165	109	8	ey(e	ey(e	X
ejpam-6165	109	9	t−1	t−1	PROPN
ejpam-6165	109	10	)	)	PUNCT
ejpam-6165	109	11	=	=	NOUN
ejpam-6165	110	1	(	(	PUNCT
ejpam-6165	110	2	∞∑	∞∑	NUM
ejpam-6165	110	3	n=0	n=0	NUM
ejpam-6165	110	4	e	e	NOUN
ejpam-6165	110	5	(	(	PUNCT
ejpam-6165	110	6	k	k	X
ejpam-6165	110	7	,	,	PUNCT
ejpam-6165	110	8	α	α	NOUN
ejpam-6165	110	9	)	)	PUNCT
ejpam-6165	110	10	j	j	PROPN
ejpam-6165	110	11	(	(	PUNCT
ejpam-6165	110	12	r;u;λ	r;u;λ	PROPN
ejpam-6165	110	13	)	)	PUNCT
ejpam-6165	110	14	tn	tn	PROPN
ejpam-6165	110	15	n	n	PROPN
ejpam-6165	110	16	!	!	PUNCT
ejpam-6165	110	17	)	)	PUNCT
ejpam-6165	111	1	(	(	PUNCT
ejpam-6165	111	2	∞∑	∞∑	NUM
ejpam-6165	111	3	n=0	n=0	NUM
ejpam-6165	111	4	bn(y	bn(y	NUM
ejpam-6165	111	5	)	)	PUNCT
ejpam-6165	111	6	tn	tn	PROPN
ejpam-6165	111	7	n	n	PROPN
ejpam-6165	111	8	!	!	PUNCT
ejpam-6165	111	9	)	)	PUNCT
ejpam-6165	112	1	=	=	PUNCT
ejpam-6165	113	1	∞∑	∞∑	NUM
ejpam-6165	113	2	n=0	n=0	NUM
ejpam-6165	113	3			PUNCT
ejpam-6165	113	4	n∑	n∑	NOUN
ejpam-6165	113	5	j=0	j=0	PROPN
ejpam-6165	113	6	(	(	PUNCT
ejpam-6165	113	7	n	n	X
ejpam-6165	113	8	k	k	NOUN
ejpam-6165	113	9	)	)	PUNCT
ejpam-6165	113	10	e	e	X
ejpam-6165	113	11	(	(	PUNCT
ejpam-6165	113	12	k	k	X
ejpam-6165	113	13	,	,	PUNCT
ejpam-6165	113	14	α	α	NOUN
ejpam-6165	113	15	)	)	PUNCT
ejpam-6165	113	16	j	j	PROPN
ejpam-6165	113	17	(	(	PUNCT
ejpam-6165	113	18	r;u;λ)bn−j(y	r;u;λ)bn−j(y	PROPN
ejpam-6165	113	19	)	)	PUNCT
ejpam-6165	113	20			PROPN
ejpam-6165	113	21	tn	tn	PROPN
ejpam-6165	113	22	n	n	CCONJ
ejpam-6165	113	23	!	!	PUNCT
ejpam-6165	113	24	.	.	PUNCT
ejpam-6165	114	1	comparing	compare	VERB
ejpam-6165	114	2	the	the	DET
ejpam-6165	114	3	coefficients	coefficient	NOUN
ejpam-6165	114	4	of	of	ADP
ejpam-6165	114	5	tn	tn	NOUN
ejpam-6165	114	6	/	/	SYM
ejpam-6165	114	7	n	n	CCONJ
ejpam-6165	114	8	!	!	X
ejpam-6165	114	9	completes	complete	VERB
ejpam-6165	114	10	the	the	DET
ejpam-6165	114	11	proof	proof	NOUN
ejpam-6165	114	12	of	of	ADP
ejpam-6165	114	13	the	the	DET
ejpam-6165	114	14	theorem	theorem	NOUN
ejpam-6165	114	15	.	.	PUNCT
ejpam-6165	115	1	the	the	DET
ejpam-6165	115	2	next	next	ADJ
ejpam-6165	115	3	theorem	theorem	NOUN
ejpam-6165	115	4	expresses	expresses	AUX
ejpam-6165	115	5	be	be	AUX
ejpam-6165	115	6	(	(	PUNCT
ejpam-6165	115	7	k	k	X
ejpam-6165	115	8	,	,	PUNCT
ejpam-6165	115	9	α	α	NOUN
ejpam-6165	115	10	)	)	PUNCT
ejpam-6165	115	11	n	n	CCONJ
ejpam-6165	115	12	(	(	PUNCT
ejpam-6165	115	13	r	r	NOUN
ejpam-6165	115	14	,	,	PUNCT
ejpam-6165	115	15	y;u	y;u	PROPN
ejpam-6165	115	16	,	,	PUNCT
ejpam-6165	115	17	λ	λ	NOUN
ejpam-6165	115	18	)	)	PUNCT
ejpam-6165	115	19	as	as	ADV
ejpam-6165	115	20	polynomial	polynomial	ADJ
ejpam-6165	115	21	in	in	ADP
ejpam-6165	115	22	r	r	NOUN
ejpam-6165	115	23	with	with	ADP
ejpam-6165	115	24	be	be	AUX
ejpam-6165	115	25	(	(	PUNCT
ejpam-6165	115	26	k	k	X
ejpam-6165	115	27	,	,	PUNCT
ejpam-6165	115	28	α	α	NOUN
ejpam-6165	115	29	)	)	PUNCT
ejpam-6165	115	30	n−k	n−k	NOUN
ejpam-6165	115	31	(	(	PUNCT
ejpam-6165	115	32	y;u	y;u	PROPN
ejpam-6165	115	33	,	,	PUNCT
ejpam-6165	115	34	λ	λ	NOUN
ejpam-6165	115	35	)	)	PUNCT
ejpam-6165	115	36	as	as	ADP
ejpam-6165	115	37	coefficients	coefficient	NOUN
ejpam-6165	115	38	.	.	PUNCT
ejpam-6165	116	1	theorem	theorem	VERB
ejpam-6165	116	2	2.7	2.7	NUM
ejpam-6165	116	3	.	.	PUNCT
ejpam-6165	117	1	the	the	DET
ejpam-6165	117	2	r	r	NOUN
ejpam-6165	117	3	-	-	PUNCT
ejpam-6165	117	4	bell	bell	NOUN
ejpam-6165	117	5	-	-	PUNCT
ejpam-6165	117	6	based	base	VERB
ejpam-6165	117	7	apostol	apostol	NOUN
ejpam-6165	117	8	-	-	PUNCT
ejpam-6165	117	9	frobenius	frobenius	NOUN
ejpam-6165	117	10	-	-	PUNCT
ejpam-6165	117	11	type	type	NOUN
ejpam-6165	117	12	poly	poly	ADJ
ejpam-6165	117	13	-	-	PUNCT
ejpam-6165	117	14	euler	euler	NOUN
ejpam-6165	117	15	polynomials	polynomial	NOUN
ejpam-6165	117	16	be	be	AUX
ejpam-6165	117	17	(	(	PUNCT
ejpam-6165	117	18	α	α	NOUN
ejpam-6165	117	19	)	)	PUNCT
ejpam-6165	117	20	j	j	NOUN
ejpam-6165	117	21	(	(	PUNCT
ejpam-6165	117	22	r	r	NOUN
ejpam-6165	117	23	,	,	PUNCT
ejpam-6165	117	24	y;u;λ	y;u;λ	NOUN
ejpam-6165	117	25	)	)	PUNCT
ejpam-6165	117	26	of	of	ADP
ejpam-6165	117	27	order	order	NOUN
ejpam-6165	117	28	α	α	PRON
ejpam-6165	117	29	satisfy	satisfy	VERB
ejpam-6165	117	30	the	the	DET
ejpam-6165	117	31	following	follow	VERB
ejpam-6165	117	32	summation	summation	NOUN
ejpam-6165	117	33	identity	identity	NOUN
ejpam-6165	117	34	be	be	AUX
ejpam-6165	117	35	(	(	PUNCT
ejpam-6165	117	36	k	k	X
ejpam-6165	117	37	,	,	PUNCT
ejpam-6165	117	38	α	α	NOUN
ejpam-6165	117	39	)	)	PUNCT
ejpam-6165	117	40	n	n	CCONJ
ejpam-6165	117	41	(	(	PUNCT
ejpam-6165	117	42	r	r	NOUN
ejpam-6165	117	43	,	,	PUNCT
ejpam-6165	117	44	y;u	y;u	PROPN
ejpam-6165	117	45	,	,	PUNCT
ejpam-6165	117	46	λ	λ	NOUN
ejpam-6165	117	47	)	)	PUNCT
ejpam-6165	117	48	=	=	SYM
ejpam-6165	117	49	n∑	n∑	X
ejpam-6165	117	50	j=0	j=0	PROPN
ejpam-6165	117	51	(	(	PUNCT
ejpam-6165	117	52	n	n	CCONJ
ejpam-6165	117	53	j	j	PROPN
ejpam-6165	117	54	)	)	PUNCT
ejpam-6165	117	55	be	be	AUX
ejpam-6165	117	56	(	(	PUNCT
ejpam-6165	117	57	k	k	X
ejpam-6165	117	58	,	,	PUNCT
ejpam-6165	117	59	α	α	NOUN
ejpam-6165	117	60	)	)	PUNCT
ejpam-6165	117	61	n−j	n−j	ADV
ejpam-6165	117	62	(	(	PUNCT
ejpam-6165	117	63	y;u;λ)rj	y;u;λ)rj	ADP
ejpam-6165	117	64	proof	proof	NOUN
ejpam-6165	117	65	.	.	PUNCT
ejpam-6165	118	1	using	use	VERB
ejpam-6165	118	2	(	(	PUNCT
ejpam-6165	118	3	2.1	2.1	NUM
ejpam-6165	118	4	)	)	PUNCT
ejpam-6165	118	5	,	,	PUNCT
ejpam-6165	118	6	we	we	PRON
ejpam-6165	118	7	have	have	VERB
ejpam-6165	118	8	∞∑	∞∑	NUM
ejpam-6165	118	9	j=0	j=0	VERB
ejpam-6165	118	10	be	be	AUX
ejpam-6165	118	11	(	(	PUNCT
ejpam-6165	118	12	k	k	X
ejpam-6165	118	13	,	,	PUNCT
ejpam-6165	118	14	α	α	NOUN
ejpam-6165	118	15	)	)	PUNCT
ejpam-6165	118	16	j	j	NOUN
ejpam-6165	118	17	(	(	PUNCT
ejpam-6165	118	18	r	r	NOUN
ejpam-6165	118	19	,	,	PUNCT
ejpam-6165	118	20	y;u;λ	y;u;λ	NOUN
ejpam-6165	118	21	)	)	PUNCT
ejpam-6165	118	22	tj	tj	PROPN
ejpam-6165	118	23	j	j	PROPN
ejpam-6165	118	24	!	!	PUNCT
ejpam-6165	119	1	=	=	PRON
ejpam-6165	119	2	{	{	PUNCT
ejpam-6165	119	3	(	(	PUNCT
ejpam-6165	119	4	lik(1−	lik(1−	PROPN
ejpam-6165	119	5	e−(1−u	e−(1−u	NOUN
ejpam-6165	119	6	)	)	PUNCT
ejpam-6165	119	7	)	)	PUNCT
ejpam-6165	120	1	λet	λet	CCONJ
ejpam-6165	120	2	−	−	PROPN
ejpam-6165	120	3	u	u	NOUN
ejpam-6165	120	4	)	)	PUNCT
ejpam-6165	120	5	α	α	PROPN
ejpam-6165	120	6	ey(e	ey(e	X
ejpam-6165	120	7	t−1	t−1	PROPN
ejpam-6165	120	8	)	)	PUNCT
ejpam-6165	120	9	}	}	PUNCT
ejpam-6165	120	10	ert	ert	NOUN
ejpam-6165	120	11	=	=	X
ejpam-6165	120	12	(	(	PUNCT
ejpam-6165	120	13	∞∑	∞∑	PROPN
ejpam-6165	120	14	n=0	n=0	X
ejpam-6165	120	15	be	be	AUX
ejpam-6165	120	16	(	(	PUNCT
ejpam-6165	120	17	k	k	X
ejpam-6165	120	18	,	,	PUNCT
ejpam-6165	120	19	α	α	NOUN
ejpam-6165	120	20	)	)	PUNCT
ejpam-6165	120	21	j	j	PROPN
ejpam-6165	120	22	(	(	PUNCT
ejpam-6165	120	23	y;u;λ	y;u;λ	PROPN
ejpam-6165	120	24	)	)	PUNCT
ejpam-6165	120	25	tn	tn	PROPN
ejpam-6165	120	26	n	n	PROPN
ejpam-6165	120	27	!	!	PUNCT
ejpam-6165	120	28	)	)	PUNCT
ejpam-6165	121	1	(	(	PUNCT
ejpam-6165	121	2	∞∑	∞∑	NUM
ejpam-6165	121	3	n=0	n=0	NUM
ejpam-6165	121	4	(	(	PUNCT
ejpam-6165	121	5	rt)n	rt)n	PROPN
ejpam-6165	121	6	n	n	NUM
ejpam-6165	121	7	!	!	PUNCT
ejpam-6165	121	8	)	)	PUNCT
ejpam-6165	122	1	=	=	PUNCT
ejpam-6165	123	1	∞∑	∞∑	NUM
ejpam-6165	123	2	n=0	n=0	NUM
ejpam-6165	123	3			PUNCT
ejpam-6165	123	4	n∑	n∑	NOUN
ejpam-6165	123	5	j=0	j=0	PROPN
ejpam-6165	123	6	(	(	PUNCT
ejpam-6165	123	7	n	n	CCONJ
ejpam-6165	123	8	j	j	PROPN
ejpam-6165	123	9	)	)	PUNCT
ejpam-6165	123	10	be	be	AUX
ejpam-6165	123	11	(	(	PUNCT
ejpam-6165	123	12	k	k	X
ejpam-6165	123	13	,	,	PUNCT
ejpam-6165	123	14	α	α	NOUN
ejpam-6165	123	15	)	)	PUNCT
ejpam-6165	123	16	j	j	PROPN
ejpam-6165	123	17	(	(	PUNCT
ejpam-6165	123	18	y;u;λ)rn−j	y;u;λ)rn−j	PROPN
ejpam-6165	123	19			PROPN
ejpam-6165	123	20	tn	tn	NOUN
ejpam-6165	123	21	n	n	CCONJ
ejpam-6165	123	22	!	!	PUNCT
ejpam-6165	123	23	.	.	PUNCT
ejpam-6165	124	1	comparing	compare	VERB
ejpam-6165	124	2	the	the	DET
ejpam-6165	124	3	coefficients	coefficient	NOUN
ejpam-6165	124	4	of	of	ADP
ejpam-6165	124	5	tn	tn	NOUN
ejpam-6165	124	6	/	/	SYM
ejpam-6165	124	7	n	n	CCONJ
ejpam-6165	124	8	!	!	X
ejpam-6165	124	9	completes	complete	VERB
ejpam-6165	124	10	the	the	DET
ejpam-6165	124	11	proof	proof	NOUN
ejpam-6165	124	12	of	of	ADP
ejpam-6165	124	13	the	the	DET
ejpam-6165	124	14	theorem	theorem	NOUN
ejpam-6165	124	15	.	.	PUNCT
ejpam-6165	125	1	the	the	DET
ejpam-6165	125	2	following	follow	VERB
ejpam-6165	125	3	theorem	theorem	NOUN
ejpam-6165	125	4	contains	contain	VERB
ejpam-6165	125	5	the	the	DET
ejpam-6165	125	6	summation	summation	NOUN
ejpam-6165	125	7	formula	formula	NOUN
ejpam-6165	125	8	for	for	ADP
ejpam-6165	125	9	be	be	AUX
ejpam-6165	125	10	(	(	PUNCT
ejpam-6165	125	11	k	k	X
ejpam-6165	125	12	,	,	PUNCT
ejpam-6165	125	13	α	α	NOUN
ejpam-6165	125	14	)	)	PUNCT
ejpam-6165	125	15	n	n	CCONJ
ejpam-6165	125	16	(	(	PUNCT
ejpam-6165	125	17	r	r	NOUN
ejpam-6165	125	18	,	,	PUNCT
ejpam-6165	125	19	y;u;λ	y;u;λ	PROPN
ejpam-6165	125	20	)	)	PUNCT
ejpam-6165	125	21	.	.	PUNCT
ejpam-6165	126	1	7	7	NUM
ejpam-6165	126	2	of	of	ADP
ejpam-6165	126	3	15	15	NUM
ejpam-6165	126	4	theorem	theorem	VERB
ejpam-6165	126	5	2.8	2.8	NUM
ejpam-6165	126	6	.	.	PUNCT
ejpam-6165	127	1	the	the	DET
ejpam-6165	127	2	r	r	NOUN
ejpam-6165	127	3	-	-	PUNCT
ejpam-6165	127	4	bell	bell	NOUN
ejpam-6165	127	5	-	-	PUNCT
ejpam-6165	127	6	based	base	VERB
ejpam-6165	127	7	apostol	apostol	NOUN
ejpam-6165	127	8	-	-	PUNCT
ejpam-6165	127	9	frobenius	frobenius	NOUN
ejpam-6165	127	10	-	-	PUNCT
ejpam-6165	127	11	type	type	NOUN
ejpam-6165	127	12	poly	poly	ADJ
ejpam-6165	127	13	-	-	PUNCT
ejpam-6165	127	14	euler	euler	NOUN
ejpam-6165	127	15	polynomials	polynomial	NOUN
ejpam-6165	127	16	be	be	AUX
ejpam-6165	127	17	(	(	PUNCT
ejpam-6165	127	18	k	k	X
ejpam-6165	127	19	,	,	PUNCT
ejpam-6165	127	20	α	α	NOUN
ejpam-6165	127	21	)	)	PUNCT
ejpam-6165	127	22	n	n	CCONJ
ejpam-6165	127	23	(	(	PUNCT
ejpam-6165	127	24	r	r	NOUN
ejpam-6165	127	25	,	,	PUNCT
ejpam-6165	127	26	y;u;λ	y;u;λ	NOUN
ejpam-6165	127	27	)	)	PUNCT
ejpam-6165	127	28	of	of	ADP
ejpam-6165	127	29	order	order	NOUN
ejpam-6165	127	30	α	α	PRON
ejpam-6165	127	31	satisfy	satisfy	VERB
ejpam-6165	127	32	the	the	DET
ejpam-6165	127	33	following	follow	VERB
ejpam-6165	127	34	summation	summation	NOUN
ejpam-6165	127	35	identity	identity	NOUN
ejpam-6165	127	36	be	be	AUX
ejpam-6165	127	37	(	(	PUNCT
ejpam-6165	127	38	r	r	NOUN
ejpam-6165	127	39	)	)	PUNCT
ejpam-6165	127	40	n	n	NOUN
ejpam-6165	127	41	(	(	PUNCT
ejpam-6165	128	1	r	r	NOUN
ejpam-6165	128	2	+	+	PROPN
ejpam-6165	128	3	y	y	PROPN
ejpam-6165	128	4	,	,	PUNCT
ejpam-6165	128	5	z;u	z;u	PROPN
ejpam-6165	128	6	,	,	PUNCT
ejpam-6165	128	7	λ	λ	NOUN
ejpam-6165	128	8	)	)	PUNCT
ejpam-6165	128	9	=	=	SYM
ejpam-6165	128	10	n∑	n∑	X
ejpam-6165	128	11	j=0	j=0	PROPN
ejpam-6165	128	12	(	(	PUNCT
ejpam-6165	128	13	n	n	X
ejpam-6165	128	14	j	j	PROPN
ejpam-6165	128	15	)	)	PUNCT
ejpam-6165	129	1	e	e	X
ejpam-6165	129	2	(	(	PUNCT
ejpam-6165	129	3	k	k	X
ejpam-6165	129	4	,	,	PUNCT
ejpam-6165	129	5	α	α	NOUN
ejpam-6165	129	6	)	)	PUNCT
ejpam-6165	129	7	j	j	PROPN
ejpam-6165	129	8	(	(	PUNCT
ejpam-6165	129	9	y;u;λ)bn−j(y	y;u;λ)bn−j(y	PROPN
ejpam-6165	129	10	,	,	PUNCT
ejpam-6165	129	11	z	z	NOUN
ejpam-6165	129	12	)	)	PUNCT
ejpam-6165	129	13	proof	proof	NOUN
ejpam-6165	129	14	.	.	PUNCT
ejpam-6165	130	1	using	use	VERB
ejpam-6165	130	2	(	(	PUNCT
ejpam-6165	130	3	2.1	2.1	NUM
ejpam-6165	130	4	)	)	PUNCT
ejpam-6165	130	5	,	,	PUNCT
ejpam-6165	130	6	we	we	PRON
ejpam-6165	130	7	have	have	VERB
ejpam-6165	130	8	∞∑	∞∑	NUM
ejpam-6165	130	9	j=0	j=0	VERB
ejpam-6165	130	10	be	be	AUX
ejpam-6165	130	11	(	(	PUNCT
ejpam-6165	130	12	k	k	X
ejpam-6165	130	13	,	,	PUNCT
ejpam-6165	130	14	α	α	NOUN
ejpam-6165	130	15	)	)	PUNCT
ejpam-6165	130	16	j	j	NOUN
ejpam-6165	130	17	(	(	PUNCT
ejpam-6165	130	18	r	r	NOUN
ejpam-6165	130	19	+	+	NUM
ejpam-6165	130	20	y	y	PROPN
ejpam-6165	130	21	,	,	PUNCT
ejpam-6165	130	22	z;u;λ	z;u;λ	NUM
ejpam-6165	130	23	)	)	PUNCT
ejpam-6165	130	24	tj	tj	PROPN
ejpam-6165	130	25	j	j	PROPN
ejpam-6165	130	26	!	!	PUNCT
ejpam-6165	131	1	=	=	PRON
ejpam-6165	131	2	{	{	PUNCT
ejpam-6165	131	3	(	(	PUNCT
ejpam-6165	131	4	lik(1−	lik(1−	PROPN
ejpam-6165	131	5	e−(1−u	e−(1−u	NOUN
ejpam-6165	131	6	)	)	PUNCT
ejpam-6165	131	7	)	)	PUNCT
ejpam-6165	132	1	λet	λet	CCONJ
ejpam-6165	132	2	−	−	PROPN
ejpam-6165	132	3	u	u	NOUN
ejpam-6165	132	4	)	)	PUNCT
ejpam-6165	132	5	α	α	PROPN
ejpam-6165	132	6	ert	ert	NOUN
ejpam-6165	132	7	}	}	PUNCT
ejpam-6165	132	8	eyt+z(et−1	eyt+z(et−1	PROPN
ejpam-6165	132	9	)	)	PUNCT
ejpam-6165	132	10	=	=	NOUN
ejpam-6165	132	11	(	(	PUNCT
ejpam-6165	132	12	∞∑	∞∑	NUM
ejpam-6165	132	13	n=0	n=0	NUM
ejpam-6165	132	14	e	e	NOUN
ejpam-6165	132	15	(	(	PUNCT
ejpam-6165	132	16	k	k	X
ejpam-6165	132	17	,	,	PUNCT
ejpam-6165	132	18	α	α	NOUN
ejpam-6165	132	19	)	)	PUNCT
ejpam-6165	132	20	j	j	PROPN
ejpam-6165	132	21	(	(	PUNCT
ejpam-6165	132	22	r;u;λ	r;u;λ	PROPN
ejpam-6165	132	23	)	)	PUNCT
ejpam-6165	132	24	tn	tn	PROPN
ejpam-6165	132	25	n	n	PROPN
ejpam-6165	132	26	!	!	PUNCT
ejpam-6165	132	27	)	)	PUNCT
ejpam-6165	133	1	(	(	PUNCT
ejpam-6165	133	2	∞∑	∞∑	NUM
ejpam-6165	133	3	n=0	n=0	PROPN
ejpam-6165	133	4	bn(y	bn(y	NUM
ejpam-6165	133	5	,	,	PUNCT
ejpam-6165	133	6	z	z	NOUN
ejpam-6165	133	7	)	)	PUNCT
ejpam-6165	133	8	tn	tn	PROPN
ejpam-6165	133	9	n	n	CCONJ
ejpam-6165	133	10	!	!	PUNCT
ejpam-6165	133	11	)	)	PUNCT
ejpam-6165	134	1	=	=	PUNCT
ejpam-6165	135	1	∞∑	∞∑	NUM
ejpam-6165	135	2	n=0	n=0	NUM
ejpam-6165	135	3			PUNCT
ejpam-6165	135	4	n∑	n∑	NOUN
ejpam-6165	135	5	j=0	j=0	PROPN
ejpam-6165	135	6	(	(	PUNCT
ejpam-6165	135	7	n	n	X
ejpam-6165	135	8	j	j	PROPN
ejpam-6165	135	9	)	)	PUNCT
ejpam-6165	135	10	e	e	X
ejpam-6165	135	11	(	(	PUNCT
ejpam-6165	135	12	k	k	X
ejpam-6165	135	13	,	,	PUNCT
ejpam-6165	135	14	α	α	NOUN
ejpam-6165	135	15	)	)	PUNCT
ejpam-6165	135	16	j	j	PROPN
ejpam-6165	135	17	(	(	PUNCT
ejpam-6165	135	18	y;u;λ)bn−j(y	y;u;λ)bn−j(y	PROPN
ejpam-6165	135	19	,	,	PUNCT
ejpam-6165	135	20	z	z	NOUN
ejpam-6165	135	21	)	)	PUNCT
ejpam-6165	135	22			PROPN
ejpam-6165	135	23	tn	tn	NOUN
ejpam-6165	135	24	n	n	CCONJ
ejpam-6165	135	25	!	!	PUNCT
ejpam-6165	135	26	.	.	PUNCT
ejpam-6165	136	1	comparing	compare	VERB
ejpam-6165	136	2	the	the	DET
ejpam-6165	136	3	coefficients	coefficient	NOUN
ejpam-6165	136	4	of	of	ADP
ejpam-6165	136	5	tn	tn	NOUN
ejpam-6165	136	6	/	/	SYM
ejpam-6165	136	7	n	n	CCONJ
ejpam-6165	136	8	!	!	X
ejpam-6165	136	9	completes	complete	VERB
ejpam-6165	136	10	the	the	DET
ejpam-6165	136	11	proof	proof	NOUN
ejpam-6165	136	12	of	of	ADP
ejpam-6165	136	13	the	the	DET
ejpam-6165	136	14	theorem	theorem	NOUN
ejpam-6165	136	15	.	.	PROPN
ejpam-6165	137	1	3	3	X
ejpam-6165	137	2	.	.	X
ejpam-6165	137	3	implicit	implicit	ADJ
ejpam-6165	137	4	summation	summation	NOUN
ejpam-6165	137	5	formula	formula	NOUN
ejpam-6165	137	6	theorem	theorem	VERB
ejpam-6165	137	7	3.1	3.1	NUM
ejpam-6165	137	8	.	.	PUNCT
ejpam-6165	138	1	the	the	DET
ejpam-6165	138	2	r	r	NOUN
ejpam-6165	138	3	-	-	PUNCT
ejpam-6165	138	4	bell	bell	NOUN
ejpam-6165	138	5	-	-	PUNCT
ejpam-6165	138	6	based	base	VERB
ejpam-6165	138	7	apostol	apostol	NOUN
ejpam-6165	138	8	-	-	PUNCT
ejpam-6165	138	9	frobenius	frobenius	NOUN
ejpam-6165	138	10	-	-	PUNCT
ejpam-6165	138	11	type	type	NOUN
ejpam-6165	138	12	poly	poly	ADJ
ejpam-6165	138	13	-	-	PUNCT
ejpam-6165	138	14	euler	euler	NOUN
ejpam-6165	138	15	polynomials	polynomial	NOUN
ejpam-6165	138	16	be	be	AUX
ejpam-6165	138	17	(	(	PUNCT
ejpam-6165	138	18	α	α	NOUN
ejpam-6165	138	19	)	)	PUNCT
ejpam-6165	138	20	j	j	NOUN
ejpam-6165	138	21	(	(	PUNCT
ejpam-6165	138	22	r	r	NOUN
ejpam-6165	138	23	,	,	PUNCT
ejpam-6165	138	24	y;u;λ	y;u;λ	NOUN
ejpam-6165	138	25	)	)	PUNCT
ejpam-6165	138	26	of	of	ADP
ejpam-6165	138	27	order	order	NOUN
ejpam-6165	138	28	α	α	PRON
ejpam-6165	138	29	satisfy	satisfy	VERB
ejpam-6165	138	30	the	the	DET
ejpam-6165	138	31	following	follow	VERB
ejpam-6165	138	32	summation	summation	NOUN
ejpam-6165	138	33	identity	identity	NOUN
ejpam-6165	138	34	be	be	AUX
ejpam-6165	138	35	(	(	PUNCT
ejpam-6165	138	36	k	k	X
ejpam-6165	138	37	,	,	PUNCT
ejpam-6165	138	38	α1+α2	α1+α2	PROPN
ejpam-6165	138	39	)	)	PUNCT
ejpam-6165	138	40	n	n	CCONJ
ejpam-6165	138	41	(	(	PUNCT
ejpam-6165	138	42	r1	r1	PROPN
ejpam-6165	138	43	+	+	CCONJ
ejpam-6165	138	44	r2	r2	PROPN
ejpam-6165	138	45	,	,	PUNCT
ejpam-6165	138	46	y2	y2	PROPN
ejpam-6165	138	47	+	+	CCONJ
ejpam-6165	139	1	y2;u	y2;u	PROPN
ejpam-6165	139	2	,	,	PUNCT
ejpam-6165	139	3	λ	λ	NOUN
ejpam-6165	139	4	)	)	PUNCT
ejpam-6165	139	5	=	=	SYM
ejpam-6165	139	6	n∑	n∑	X
ejpam-6165	139	7	j=0	j=0	PROPN
ejpam-6165	139	8	(	(	PUNCT
ejpam-6165	139	9	n	n	CCONJ
ejpam-6165	139	10	j	j	PROPN
ejpam-6165	139	11	)	)	PUNCT
ejpam-6165	139	12	be	be	AUX
ejpam-6165	139	13	(	(	PUNCT
ejpam-6165	139	14	k	k	X
ejpam-6165	139	15	,	,	PUNCT
ejpam-6165	139	16	α1	α1	PROPN
ejpam-6165	139	17	)	)	PUNCT
ejpam-6165	139	18	j	j	PROPN
ejpam-6165	139	19	(	(	PUNCT
ejpam-6165	139	20	r1	r1	PROPN
ejpam-6165	139	21	,	,	PUNCT
ejpam-6165	139	22	y1;u	y1;u	PROPN
ejpam-6165	139	23	,	,	PUNCT
ejpam-6165	139	24	λ)be	λ)be	PROPN
ejpam-6165	139	25	(	(	PUNCT
ejpam-6165	139	26	k	k	NOUN
ejpam-6165	139	27	,	,	PUNCT
ejpam-6165	139	28	α2	α2	ADJ
ejpam-6165	139	29	)	)	PUNCT
ejpam-6165	139	30	n−j	n−j	ADV
ejpam-6165	139	31	(	(	PUNCT
ejpam-6165	139	32	r2	r2	PROPN
ejpam-6165	139	33	,	,	PUNCT
ejpam-6165	139	34	y2;u	y2;u	PROPN
ejpam-6165	139	35	,	,	PUNCT
ejpam-6165	139	36	λ	λ	NOUN
ejpam-6165	139	37	)	)	PUNCT
ejpam-6165	139	38	proof	proof	NOUN
ejpam-6165	139	39	.	.	PUNCT
ejpam-6165	140	1	replacing	replace	VERB
ejpam-6165	140	2	the	the	DET
ejpam-6165	140	3	parameters	parameter	NOUN
ejpam-6165	140	4	α	α	NOUN
ejpam-6165	140	5	,	,	PUNCT
ejpam-6165	140	6	r	r	NOUN
ejpam-6165	140	7	and	and	CCONJ
ejpam-6165	140	8	y	y	PROPN
ejpam-6165	140	9	at	at	ADP
ejpam-6165	140	10	the	the	DET
ejpam-6165	140	11	left	left	ADJ
ejpam-6165	140	12	-	-	PUNCT
ejpam-6165	140	13	hand	hand	NOUN
ejpam-6165	140	14	side	side	NOUN
ejpam-6165	140	15	of	of	ADP
ejpam-6165	140	16	equation	equation	NOUN
ejpam-6165	140	17	(	(	PUNCT
ejpam-6165	140	18	2.1	2.1	NUM
ejpam-6165	140	19	)	)	PUNCT
ejpam-6165	140	20	in	in	ADP
ejpam-6165	140	21	definition	definition	NOUN
ejpam-6165	140	22	2.1	2.1	NUM
ejpam-6165	140	23	,	,	PUNCT
ejpam-6165	140	24	with	with	ADP
ejpam-6165	140	25	α1	α1	PROPN
ejpam-6165	140	26	+	+	CCONJ
ejpam-6165	140	27	α2	α2	ADJ
ejpam-6165	140	28	,	,	PUNCT
ejpam-6165	140	29	r1	r1	NOUN
ejpam-6165	140	30	+	+	CCONJ
ejpam-6165	140	31	r2	r2	PROPN
ejpam-6165	140	32	and	and	CCONJ
ejpam-6165	140	33	y1	y1	NOUN
ejpam-6165	140	34	+	+	CCONJ
ejpam-6165	140	35	y2	y2	PROPN
ejpam-6165	140	36	,	,	PUNCT
ejpam-6165	140	37	respectively	respectively	ADV
ejpam-6165	140	38	,	,	PUNCT
ejpam-6165	140	39	we	we	PRON
ejpam-6165	140	40	obtain	obtain	AUX
ejpam-6165	140	41	(	(	PUNCT
ejpam-6165	140	42	lik(1−	lik(1−	NOUN
ejpam-6165	140	43	e−(1−u	e−(1−u	NOUN
ejpam-6165	140	44	)	)	PUNCT
ejpam-6165	140	45	)	)	PUNCT
ejpam-6165	141	1	λet	λet	CCONJ
ejpam-6165	141	2	−	−	PROPN
ejpam-6165	141	3	u	u	NOUN
ejpam-6165	141	4	)	)	PUNCT
ejpam-6165	141	5	α1+α2	α1+α2	PROPN
ejpam-6165	141	6	e(r1+r2)t+(y1+y2)(et−1	e(r1+r2)t+(y1+y2)(et−1	NOUN
ejpam-6165	141	7	)	)	PUNCT
ejpam-6165	141	8	=	=	SYM
ejpam-6165	142	1	(	(	PUNCT
ejpam-6165	142	2	lik(1−	lik(1−	PROPN
ejpam-6165	142	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	142	4	)	)	PUNCT
ejpam-6165	142	5	)	)	PUNCT
ejpam-6165	143	1	λet	λet	CCONJ
ejpam-6165	143	2	−	−	PROPN
ejpam-6165	143	3	u	u	PROPN
ejpam-6165	143	4	)	)	PUNCT
ejpam-6165	143	5	α1	α1	PROPN
ejpam-6165	143	6	e(r1)t+(y1)(et−1	e(r1)t+(y1)(et−1	NOUN
ejpam-6165	143	7	)	)	PUNCT
ejpam-6165	143	8	(	(	PUNCT
ejpam-6165	143	9	lik(1−	lik(1−	PROPN
ejpam-6165	143	10	e−(1−u	e−(1−u	NOUN
ejpam-6165	143	11	)	)	PUNCT
ejpam-6165	143	12	)	)	PUNCT
ejpam-6165	144	1	λet	λet	CCONJ
ejpam-6165	144	2	−	−	PROPN
ejpam-6165	144	3	u	u	NOUN
ejpam-6165	144	4	)	)	PUNCT
ejpam-6165	144	5	α2	α2	PROPN
ejpam-6165	144	6	e(r2)t+(y2)(et−1	e(r2)t+(y2)(et−1	NOUN
ejpam-6165	144	7	)	)	PUNCT
ejpam-6165	145	1	∞∑	∞∑	PROPN
ejpam-6165	145	2	n=0	n=0	NUM
ejpam-6165	145	3	be	be	AUX
ejpam-6165	145	4	(	(	PUNCT
ejpam-6165	145	5	k	k	X
ejpam-6165	145	6	,	,	PUNCT
ejpam-6165	145	7	α1+α2	α1+α2	PROPN
ejpam-6165	145	8	)	)	PUNCT
ejpam-6165	145	9	n	n	CCONJ
ejpam-6165	145	10	(	(	PUNCT
ejpam-6165	145	11	r1	r1	PROPN
ejpam-6165	145	12	+	+	CCONJ
ejpam-6165	145	13	r2	r2	PROPN
ejpam-6165	145	14	,	,	PUNCT
ejpam-6165	145	15	y2	y2	PROPN
ejpam-6165	145	16	+	+	CCONJ
ejpam-6165	145	17	y2;u	y2;u	PROPN
ejpam-6165	145	18	,	,	PUNCT
ejpam-6165	145	19	λ	λ	NOUN
ejpam-6165	145	20	)	)	PUNCT
ejpam-6165	145	21	tn	tn	PROPN
ejpam-6165	145	22	n	n	PROPN
ejpam-6165	145	23	!	!	PUNCT
ejpam-6165	145	24	=	=	PUNCT
ejpam-6165	146	1	(	(	PUNCT
ejpam-6165	146	2	∞∑	∞∑	PRON
ejpam-6165	146	3	n=0	n=0	X
ejpam-6165	146	4	be	be	AUX
ejpam-6165	146	5	(	(	PUNCT
ejpam-6165	146	6	k	k	X
ejpam-6165	146	7	,	,	PUNCT
ejpam-6165	146	8	α1	α1	PROPN
ejpam-6165	146	9	)	)	PUNCT
ejpam-6165	146	10	n	n	CCONJ
ejpam-6165	146	11	(	(	PUNCT
ejpam-6165	146	12	r1	r1	PROPN
ejpam-6165	146	13	,	,	PUNCT
ejpam-6165	146	14	y1;u	y1;u	PROPN
ejpam-6165	146	15	,	,	PUNCT
ejpam-6165	146	16	λ	λ	NOUN
ejpam-6165	146	17	)	)	PUNCT
ejpam-6165	146	18	tn	tn	PROPN
ejpam-6165	146	19	n	n	PROPN
ejpam-6165	146	20	!	!	PUNCT
ejpam-6165	146	21	)	)	PUNCT
ejpam-6165	147	1	(	(	PUNCT
ejpam-6165	147	2	∞∑	∞∑	PRON
ejpam-6165	147	3	n=0	n=0	PRON
ejpam-6165	147	4	be	be	AUX
ejpam-6165	147	5	(	(	PUNCT
ejpam-6165	147	6	k	k	NOUN
ejpam-6165	147	7	,	,	PUNCT
ejpam-6165	147	8	α2	α2	ADJ
ejpam-6165	147	9	)	)	PUNCT
ejpam-6165	147	10	n	n	CCONJ
ejpam-6165	147	11	(	(	PUNCT
ejpam-6165	147	12	r2	r2	PROPN
ejpam-6165	147	13	,	,	PUNCT
ejpam-6165	147	14	y2;u	y2;u	PROPN
ejpam-6165	147	15	,	,	PUNCT
ejpam-6165	147	16	λ	λ	NOUN
ejpam-6165	147	17	)	)	PUNCT
ejpam-6165	147	18	tn	tn	PROPN
ejpam-6165	147	19	n	n	PROPN
ejpam-6165	147	20	!	!	PUNCT
ejpam-6165	147	21	)	)	PUNCT
ejpam-6165	148	1	8	8	NUM
ejpam-6165	148	2	of	of	ADP
ejpam-6165	148	3	15	15	NUM
ejpam-6165	148	4	=	=	NOUN
ejpam-6165	149	1	∞∑	∞∑	NUM
ejpam-6165	149	2	n=0	n=0	PROPN
ejpam-6165	149	3	n∑	n∑	PRON
ejpam-6165	149	4	j=0	j=0	PROPN
ejpam-6165	149	5	(	(	PUNCT
ejpam-6165	149	6	n	n	X
ejpam-6165	149	7	j	j	PROPN
ejpam-6165	149	8	)	)	PUNCT
ejpam-6165	149	9	be	be	AUX
ejpam-6165	149	10	(	(	PUNCT
ejpam-6165	149	11	k	k	X
ejpam-6165	149	12	,	,	PUNCT
ejpam-6165	149	13	α1	α1	PROPN
ejpam-6165	149	14	)	)	PUNCT
ejpam-6165	149	15	j	j	PROPN
ejpam-6165	149	16	(	(	PUNCT
ejpam-6165	149	17	r1	r1	PROPN
ejpam-6165	149	18	,	,	PUNCT
ejpam-6165	149	19	y1;u	y1;u	PROPN
ejpam-6165	149	20	,	,	PUNCT
ejpam-6165	149	21	λ)be	λ)be	PROPN
ejpam-6165	149	22	(	(	PUNCT
ejpam-6165	149	23	k	k	NOUN
ejpam-6165	149	24	,	,	PUNCT
ejpam-6165	149	25	α2	α2	ADJ
ejpam-6165	149	26	)	)	PUNCT
ejpam-6165	149	27	n−j	n−j	ADV
ejpam-6165	149	28	(	(	PUNCT
ejpam-6165	149	29	r2	r2	PROPN
ejpam-6165	149	30	,	,	PUNCT
ejpam-6165	149	31	y2;u	y2;u	PROPN
ejpam-6165	149	32	,	,	PUNCT
ejpam-6165	149	33	λ	λ	NOUN
ejpam-6165	149	34	)	)	PUNCT
ejpam-6165	149	35	tn	tn	PROPN
ejpam-6165	149	36	n	n	NUM
ejpam-6165	149	37	!	!	PUNCT
ejpam-6165	149	38	.	.	PUNCT
ejpam-6165	150	1	comparing	compare	VERB
ejpam-6165	150	2	the	the	DET
ejpam-6165	150	3	coefficients	coefficient	NOUN
ejpam-6165	150	4	of	of	ADP
ejpam-6165	150	5	tn	tn	NOUN
ejpam-6165	150	6	n	n	ADP
ejpam-6165	150	7	!	!	PROPN
ejpam-6165	150	8	completes	complete	VERB
ejpam-6165	150	9	the	the	DET
ejpam-6165	150	10	proof	proof	NOUN
ejpam-6165	150	11	of	of	ADP
ejpam-6165	150	12	the	the	DET
ejpam-6165	150	13	theorem	theorem	NOUN
ejpam-6165	150	14	.	.	PUNCT
ejpam-6165	151	1	taking	take	VERB
ejpam-6165	151	2	α1	α1	PROPN
ejpam-6165	151	3	=	=	SYM
ejpam-6165	151	4	α	α	NOUN
ejpam-6165	151	5	,	,	PUNCT
ejpam-6165	151	6	α2	α2	NOUN
ejpam-6165	151	7	=	=	SYM
ejpam-6165	152	1	0,r1	0,r1	NUM
ejpam-6165	152	2	=	=	SYM
ejpam-6165	152	3	r	r	NOUN
ejpam-6165	152	4	,	,	PUNCT
ejpam-6165	152	5	r2	r2	NOUN
ejpam-6165	152	6	=	=	SYM
ejpam-6165	152	7	1,y1	1,y1	NUM
ejpam-6165	152	8	=	=	SYM
ejpam-6165	152	9	y	y	PROPN
ejpam-6165	152	10	,	,	PUNCT
ejpam-6165	152	11	y2	y2	PROPN
ejpam-6165	152	12	=	=	SYM
ejpam-6165	152	13	0	0	NUM
ejpam-6165	152	14	,	,	PUNCT
ejpam-6165	152	15	theorem	theorem	VERB
ejpam-6165	152	16	3.1	3.1	NUM
ejpam-6165	152	17	yields	yield	NOUN
ejpam-6165	152	18	be	be	VERB
ejpam-6165	152	19	(	(	PUNCT
ejpam-6165	152	20	k	k	X
ejpam-6165	152	21	,	,	PUNCT
ejpam-6165	152	22	α	α	NOUN
ejpam-6165	152	23	)	)	PUNCT
ejpam-6165	152	24	n	n	CCONJ
ejpam-6165	152	25	(	(	PUNCT
ejpam-6165	152	26	r	r	NOUN
ejpam-6165	152	27	+	+	NOUN
ejpam-6165	152	28	1	1	NUM
ejpam-6165	152	29	,	,	PUNCT
ejpam-6165	152	30	y;u	y;u	PROPN
ejpam-6165	152	31	,	,	PUNCT
ejpam-6165	152	32	λ	λ	PROPN
ejpam-6165	152	33	)	)	PUNCT
ejpam-6165	153	1	=	=	SYM
ejpam-6165	153	2	n∑	n∑	X
ejpam-6165	153	3	j=0	j=0	PROPN
ejpam-6165	153	4	(	(	PUNCT
ejpam-6165	153	5	n	n	CCONJ
ejpam-6165	153	6	j	j	PROPN
ejpam-6165	153	7	)	)	PUNCT
ejpam-6165	153	8	be	be	AUX
ejpam-6165	153	9	(	(	PUNCT
ejpam-6165	153	10	k	k	X
ejpam-6165	153	11	,	,	PUNCT
ejpam-6165	153	12	α	α	NOUN
ejpam-6165	153	13	)	)	PUNCT
ejpam-6165	153	14	j	j	NOUN
ejpam-6165	153	15	(	(	PUNCT
ejpam-6165	153	16	r	r	NOUN
ejpam-6165	153	17	,	,	PUNCT
ejpam-6165	153	18	y;u	y;u	PROPN
ejpam-6165	153	19	,	,	PUNCT
ejpam-6165	153	20	λ)bn−j(1	λ)bn−j(1	NOUN
ejpam-6165	153	21	,	,	PUNCT
ejpam-6165	153	22	0	0	NUM
ejpam-6165	153	23	)	)	PUNCT
ejpam-6165	153	24	=	=	SYM
ejpam-6165	153	25	n∑	n∑	X
ejpam-6165	153	26	j=0	j=0	PROPN
ejpam-6165	153	27	(	(	PUNCT
ejpam-6165	153	28	n	n	CCONJ
ejpam-6165	153	29	j	j	PROPN
ejpam-6165	153	30	)	)	PUNCT
ejpam-6165	153	31	be	be	AUX
ejpam-6165	153	32	(	(	PUNCT
ejpam-6165	153	33	kα	kα	PROPN
ejpam-6165	153	34	)	)	PUNCT
ejpam-6165	153	35	j	j	NOUN
ejpam-6165	153	36	(	(	PUNCT
ejpam-6165	153	37	r	r	NOUN
ejpam-6165	153	38	,	,	PUNCT
ejpam-6165	153	39	y;u	y;u	PROPN
ejpam-6165	153	40	,	,	PUNCT
ejpam-6165	153	41	λ	λ	NOUN
ejpam-6165	153	42	)	)	PUNCT
ejpam-6165	153	43	.	.	PUNCT
ejpam-6165	154	1	theorem	theorem	VERB
ejpam-6165	154	2	3.2	3.2	NUM
ejpam-6165	154	3	.	.	PUNCT
ejpam-6165	155	1	the	the	DET
ejpam-6165	155	2	r	r	NOUN
ejpam-6165	155	3	-	-	PUNCT
ejpam-6165	155	4	bell	bell	NOUN
ejpam-6165	155	5	-	-	PUNCT
ejpam-6165	155	6	based	base	VERB
ejpam-6165	155	7	apostol	apostol	NOUN
ejpam-6165	155	8	-	-	PUNCT
ejpam-6165	155	9	frobenius	frobenius	NOUN
ejpam-6165	155	10	-	-	PUNCT
ejpam-6165	155	11	type	type	NOUN
ejpam-6165	155	12	poly	poly	ADJ
ejpam-6165	155	13	-	-	PUNCT
ejpam-6165	155	14	euler	euler	NOUN
ejpam-6165	155	15	polynomials	polynomial	NOUN
ejpam-6165	155	16	be	be	AUX
ejpam-6165	155	17	(	(	PUNCT
ejpam-6165	155	18	α	α	NOUN
ejpam-6165	155	19	)	)	PUNCT
ejpam-6165	155	20	j	j	NOUN
ejpam-6165	155	21	(	(	PUNCT
ejpam-6165	155	22	r	r	NOUN
ejpam-6165	155	23	,	,	PUNCT
ejpam-6165	155	24	y;u;λ	y;u;λ	NOUN
ejpam-6165	155	25	)	)	PUNCT
ejpam-6165	155	26	of	of	ADP
ejpam-6165	155	27	order	order	NOUN
ejpam-6165	155	28	α	α	PRON
ejpam-6165	155	29	satisfy	satisfy	VERB
ejpam-6165	155	30	the	the	DET
ejpam-6165	155	31	following	follow	VERB
ejpam-6165	155	32	implicit	implicit	ADJ
ejpam-6165	155	33	summation	summation	NOUN
ejpam-6165	155	34	identity	identity	NOUN
ejpam-6165	155	35	be	be	AUX
ejpam-6165	155	36	(	(	PUNCT
ejpam-6165	155	37	k	k	X
ejpam-6165	155	38	,	,	PUNCT
ejpam-6165	155	39	α	α	NOUN
ejpam-6165	155	40	)	)	PUNCT
ejpam-6165	155	41	q+l	q+l	NUM
ejpam-6165	155	42	(	(	PUNCT
ejpam-6165	155	43	r	r	NOUN
ejpam-6165	155	44	,	,	PUNCT
ejpam-6165	155	45	y;u	y;u	PROPN
ejpam-6165	155	46	,	,	PUNCT
ejpam-6165	155	47	λ	λ	NOUN
ejpam-6165	155	48	)	)	PUNCT
ejpam-6165	155	49	=	=	SYM
ejpam-6165	156	1	q	q	X
ejpam-6165	156	2	,	,	PUNCT
ejpam-6165	156	3	l∑	l∑	PROPN
ejpam-6165	156	4	j	j	PROPN
ejpam-6165	156	5	,	,	PUNCT
ejpam-6165	156	6	m=0	m=0	PROPN
ejpam-6165	156	7	(	(	PUNCT
ejpam-6165	156	8	q	q	PROPN
ejpam-6165	156	9	j	j	PROPN
ejpam-6165	156	10	)	)	PUNCT
ejpam-6165	156	11	(	(	PUNCT
ejpam-6165	156	12	l	l	NOUN
ejpam-6165	156	13	m	m	VERB
ejpam-6165	156	14	)	)	PUNCT
ejpam-6165	157	1	(	(	PUNCT
ejpam-6165	157	2	r	r	NOUN
ejpam-6165	157	3	−	−	NOUN
ejpam-6165	157	4	z)q−j+i−m	z)q−j+i−m	AUX
ejpam-6165	157	5	be	be	AUX
ejpam-6165	157	6	(	(	PUNCT
ejpam-6165	157	7	k	k	X
ejpam-6165	157	8	,	,	PUNCT
ejpam-6165	157	9	α	α	NOUN
ejpam-6165	157	10	)	)	PUNCT
ejpam-6165	157	11	q+l	q+l	NUM
ejpam-6165	157	12	(	(	PUNCT
ejpam-6165	157	13	z	z	NOUN
ejpam-6165	157	14	,	,	PUNCT
ejpam-6165	157	15	y;u	y;u	PROPN
ejpam-6165	157	16	,	,	PUNCT
ejpam-6165	157	17	λ	λ	NOUN
ejpam-6165	157	18	)	)	PUNCT
ejpam-6165	157	19	proof	proof	NOUN
ejpam-6165	157	20	.	.	PUNCT
ejpam-6165	158	1	let	let	VERB
ejpam-6165	158	2	us	we	PRON
ejpam-6165	158	3	recall	recall	VERB
ejpam-6165	158	4	the	the	DET
ejpam-6165	158	5	following	follow	VERB
ejpam-6165	158	6	series	series	NOUN
ejpam-6165	158	7	manipulation	manipulation	NOUN
ejpam-6165	158	8	formula	formula	NOUN
ejpam-6165	158	9	:	:	PUNCT
ejpam-6165	158	10	∞∑	∞∑	NUM
ejpam-6165	158	11	n=0	n=0	NUM
ejpam-6165	158	12	f(n	f(n	PROPN
ejpam-6165	158	13	)	)	PUNCT
ejpam-6165	158	14	(	(	PUNCT
ejpam-6165	158	15	r	r	NOUN
ejpam-6165	158	16	+	+	X
ejpam-6165	158	17	y)n	y)n	NUM
ejpam-6165	158	18	n	n	ADV
ejpam-6165	158	19	!	!	PUNCT
ejpam-6165	159	1	=	=	PUNCT
ejpam-6165	160	1	∞∑	∞∑	PRON
ejpam-6165	160	2	n=0	n=0	NUM
ejpam-6165	160	3	∞∑	∞∑	NUM
ejpam-6165	160	4	m=0	m=0	PROPN
ejpam-6165	160	5	f(n+m	f(n+m	PROPN
ejpam-6165	160	6	)	)	PUNCT
ejpam-6165	160	7	rn	rn	PROPN
ejpam-6165	160	8	n	n	PROPN
ejpam-6165	160	9	!	!	PUNCT
ejpam-6165	161	1	yn	yn	PROPN
ejpam-6165	161	2	m	m	PROPN
ejpam-6165	161	3	!	!	PUNCT
ejpam-6165	162	1	note	note	VERB
ejpam-6165	162	2	that	that	SCONJ
ejpam-6165	162	3	we	we	PRON
ejpam-6165	162	4	can	can	AUX
ejpam-6165	162	5	rewrite	rewrite	VERB
ejpam-6165	162	6	(	(	PUNCT
ejpam-6165	162	7	2.1	2.1	NUM
ejpam-6165	162	8	)	)	PUNCT
ejpam-6165	162	9	as	as	SCONJ
ejpam-6165	162	10	follows	follow	VERB
ejpam-6165	162	11	:(	:(	PUNCT
ejpam-6165	162	12	lik(1−	lik(1−	PROPN
ejpam-6165	162	13	e−(1−u	e−(1−u	NOUN
ejpam-6165	162	14	)	)	PUNCT
ejpam-6165	162	15	λet+v	λet+v	PROPN
ejpam-6165	162	16	−	−	PROPN
ejpam-6165	162	17	u	u	NOUN
ejpam-6165	162	18	)	)	PUNCT
ejpam-6165	162	19	α	α	PROPN
ejpam-6165	162	20	ey(e	ey(e	X
ejpam-6165	162	21	t+v−1	t+v−1	PROPN
ejpam-6165	162	22	)	)	PUNCT
ejpam-6165	162	23	=	=	SYM
ejpam-6165	163	1	e−r(t+v	e−r(t+v	NOUN
ejpam-6165	163	2	)	)	PUNCT
ejpam-6165	164	1	∞∑	∞∑	PROPN
ejpam-6165	164	2	n=0	n=0	NUM
ejpam-6165	164	3	be	be	AUX
ejpam-6165	164	4	(	(	PUNCT
ejpam-6165	164	5	k	k	X
ejpam-6165	164	6	,	,	PUNCT
ejpam-6165	164	7	α	α	NOUN
ejpam-6165	164	8	)	)	PUNCT
ejpam-6165	164	9	n	n	CCONJ
ejpam-6165	164	10	(	(	PUNCT
ejpam-6165	164	11	r	r	NOUN
ejpam-6165	164	12	,	,	PUNCT
ejpam-6165	164	13	y;u	y;u	PROPN
ejpam-6165	164	14	,	,	PUNCT
ejpam-6165	164	15	λ	λ	NOUN
ejpam-6165	164	16	)	)	PUNCT
ejpam-6165	164	17	(	(	PUNCT
ejpam-6165	164	18	t+	t+	NOUN
ejpam-6165	164	19	v)n	v)n	NOUN
ejpam-6165	164	20	n	n	CCONJ
ejpam-6165	164	21	!	!	PUNCT
ejpam-6165	164	22	.	.	PUNCT
ejpam-6165	165	1	applying	apply	VERB
ejpam-6165	165	2	the	the	DET
ejpam-6165	165	3	above	above	ADJ
ejpam-6165	165	4	series	series	NOUN
ejpam-6165	165	5	manipulation	manipulation	NOUN
ejpam-6165	165	6	formula	formula	NOUN
ejpam-6165	165	7	yields	yield	NOUN
ejpam-6165	165	8	(	(	PUNCT
ejpam-6165	165	9	lik(1−	lik(1−	NOUN
ejpam-6165	165	10	e−(1−u	e−(1−u	NOUN
ejpam-6165	165	11	)	)	PUNCT
ejpam-6165	165	12	λet+v	λet+v	PROPN
ejpam-6165	165	13	−	−	PROPN
ejpam-6165	165	14	u	u	NOUN
ejpam-6165	165	15	)	)	PUNCT
ejpam-6165	165	16	α	α	PROPN
ejpam-6165	165	17	ey(e	ey(e	X
ejpam-6165	165	18	t+v−1	t+v−1	PROPN
ejpam-6165	165	19	)	)	PUNCT
ejpam-6165	166	1	=	=	SYM
ejpam-6165	166	2	e−r(t+v	e−r(t+v	X
ejpam-6165	166	3	)	)	PUNCT
ejpam-6165	167	1	∞∑	∞∑	NUM
ejpam-6165	167	2	j=0	j=0	ADJ
ejpam-6165	167	3	∞∑	∞∑	NUM
ejpam-6165	167	4	l=0	l=0	PROPN
ejpam-6165	167	5	be	be	AUX
ejpam-6165	167	6	(	(	PUNCT
ejpam-6165	167	7	k	k	X
ejpam-6165	167	8	,	,	PUNCT
ejpam-6165	167	9	α	α	NOUN
ejpam-6165	167	10	)	)	PUNCT
ejpam-6165	167	11	j+l	j+l	PROPN
ejpam-6165	167	12	(	(	PUNCT
ejpam-6165	167	13	r	r	NOUN
ejpam-6165	167	14	,	,	PUNCT
ejpam-6165	167	15	y;u	y;u	PROPN
ejpam-6165	167	16	,	,	PUNCT
ejpam-6165	167	17	λ	λ	NOUN
ejpam-6165	167	18	)	)	PUNCT
ejpam-6165	167	19	tj	tj	NOUN
ejpam-6165	167	20	n	n	NOUN
ejpam-6165	167	21	!	!	PUNCT
ejpam-6165	167	22	vl	vl	PROPN
ejpam-6165	167	23	l	l	NOUN
ejpam-6165	167	24	!	!	PUNCT
ejpam-6165	167	25	=	=	PUNCT
ejpam-6165	167	26	e−z(t+v	e−z(t+v	NOUN
ejpam-6165	167	27	)	)	PUNCT
ejpam-6165	167	28	∞∑	∞∑	NUM
ejpam-6165	167	29	j=0	j=0	ADJ
ejpam-6165	167	30	∞∑	∞∑	NUM
ejpam-6165	167	31	l=0	l=0	PROPN
ejpam-6165	167	32	be	be	AUX
ejpam-6165	167	33	(	(	PUNCT
ejpam-6165	167	34	k	k	X
ejpam-6165	167	35	,	,	PUNCT
ejpam-6165	167	36	α	α	NOUN
ejpam-6165	167	37	)	)	PUNCT
ejpam-6165	167	38	j+l	j+l	PROPN
ejpam-6165	167	39	(	(	PUNCT
ejpam-6165	167	40	z	z	NOUN
ejpam-6165	167	41	,	,	PUNCT
ejpam-6165	167	42	y;u	y;u	PROPN
ejpam-6165	167	43	,	,	PUNCT
ejpam-6165	167	44	λ	λ	NOUN
ejpam-6165	167	45	)	)	PUNCT
ejpam-6165	167	46	tj	tj	PROPN
ejpam-6165	167	47	j	j	PROPN
ejpam-6165	167	48	!	!	PUNCT
ejpam-6165	167	49	vl	vl	PROPN
ejpam-6165	168	1	l	l	PROPN
ejpam-6165	168	2	!	!	PUNCT
ejpam-6165	169	1	∑	∑	PROPN
ejpam-6165	169	2	j	j	PROPN
ejpam-6165	169	3	,	,	PUNCT
ejpam-6165	169	4	l≥0	l≥0	NOUN
ejpam-6165	169	5	be	be	AUX
ejpam-6165	169	6	(	(	PUNCT
ejpam-6165	169	7	k	k	X
ejpam-6165	169	8	,	,	PUNCT
ejpam-6165	169	9	α	α	NOUN
ejpam-6165	169	10	)	)	PUNCT
ejpam-6165	169	11	j+l	j+l	PROPN
ejpam-6165	169	12	(	(	PUNCT
ejpam-6165	169	13	r	r	NOUN
ejpam-6165	169	14	,	,	PUNCT
ejpam-6165	169	15	y;u	y;u	PROPN
ejpam-6165	169	16	,	,	PUNCT
ejpam-6165	169	17	λ	λ	NOUN
ejpam-6165	169	18	)	)	PUNCT
ejpam-6165	169	19	tj	tj	PROPN
ejpam-6165	169	20	j	j	PROPN
ejpam-6165	169	21	!	!	PUNCT
ejpam-6165	169	22	vl	vl	PROPN
ejpam-6165	170	1	l	l	NOUN
ejpam-6165	170	2	!	!	PUNCT
ejpam-6165	171	1	=	=	PUNCT
ejpam-6165	171	2	e(r−z)(t+v	e(r−z)(t+v	PROPN
ejpam-6165	171	3	)	)	PUNCT
ejpam-6165	171	4	∑	∑	PROPN
ejpam-6165	171	5	j	j	PROPN
ejpam-6165	171	6	,	,	PUNCT
ejpam-6165	171	7	l≥0	l≥0	NOUN
ejpam-6165	171	8	be	be	AUX
ejpam-6165	171	9	(	(	PUNCT
ejpam-6165	171	10	k	k	X
ejpam-6165	171	11	,	,	PUNCT
ejpam-6165	171	12	α	α	NOUN
ejpam-6165	171	13	)	)	PUNCT
ejpam-6165	171	14	j+l	j+l	PROPN
ejpam-6165	171	15	(	(	PUNCT
ejpam-6165	171	16	z	z	NOUN
ejpam-6165	171	17	,	,	PUNCT
ejpam-6165	171	18	y;u	y;u	PROPN
ejpam-6165	171	19	,	,	PUNCT
ejpam-6165	171	20	λ	λ	NOUN
ejpam-6165	171	21	)	)	PUNCT
ejpam-6165	171	22	tj	tj	PROPN
ejpam-6165	171	23	j	j	PROPN
ejpam-6165	171	24	!	!	PUNCT
ejpam-6165	172	1	vl	vl	PROPN
ejpam-6165	172	2	l	l	NOUN
ejpam-6165	172	3	!	!	PUNCT
ejpam-6165	173	1	=	=	PUNCT
ejpam-6165	173	2	(	(	PUNCT
ejpam-6165	173	3	∞∑	∞∑	NUM
ejpam-6165	173	4	n=0	n=0	NUM
ejpam-6165	173	5	(	(	PUNCT
ejpam-6165	173	6	r	r	NOUN
ejpam-6165	173	7	−	−	PROPN
ejpam-6165	173	8	z)n	z)n	X
ejpam-6165	173	9	(	(	PUNCT
ejpam-6165	173	10	t+	t+	NOUN
ejpam-6165	173	11	v)n	v)n	NOUN
ejpam-6165	173	12	n	n	X
ejpam-6165	173	13	!	!	PUNCT
ejpam-6165	173	14	)	)	PUNCT
ejpam-6165	174	1	∑	∑	NOUN
ejpam-6165	174	2	j	j	NOUN
ejpam-6165	174	3	,	,	PUNCT
ejpam-6165	174	4	l≥0	l≥0	NOUN
ejpam-6165	174	5	be	be	AUX
ejpam-6165	174	6	(	(	PUNCT
ejpam-6165	174	7	k	k	X
ejpam-6165	174	8	,	,	PUNCT
ejpam-6165	174	9	α	α	NOUN
ejpam-6165	174	10	)	)	PUNCT
ejpam-6165	174	11	j+l	j+l	PROPN
ejpam-6165	174	12	(	(	PUNCT
ejpam-6165	174	13	z	z	NOUN
ejpam-6165	174	14	,	,	PUNCT
ejpam-6165	174	15	y;u	y;u	PROPN
ejpam-6165	174	16	,	,	PUNCT
ejpam-6165	174	17	λ	λ	NOUN
ejpam-6165	174	18	)	)	PUNCT
ejpam-6165	174	19	tj	tj	PROPN
ejpam-6165	174	20	j	j	PROPN
ejpam-6165	174	21	!	!	PUNCT
ejpam-6165	175	1	vl	vl	PROPN
ejpam-6165	175	2	l	l	NOUN
ejpam-6165	175	3	!	!	PUNCT
ejpam-6165	176	1			PROPN
ejpam-6165	176	2	9	9	NUM
ejpam-6165	176	3	of	of	ADP
ejpam-6165	176	4	15	15	NUM
ejpam-6165	176	5	=	=	SYM
ejpam-6165	176	6			PROPN
ejpam-6165	176	7	∑	∑	PUNCT
ejpam-6165	176	8	n	n	CCONJ
ejpam-6165	176	9	,	,	PUNCT
ejpam-6165	176	10	m≥0	m≥0	PROPN
ejpam-6165	176	11	(	(	PUNCT
ejpam-6165	176	12	r	r	NOUN
ejpam-6165	176	13	−	−	PROPN
ejpam-6165	176	14	z)n+m	z)n+m	PROPN
ejpam-6165	176	15	tn	tn	PROPN
ejpam-6165	176	16	n	n	PROPN
ejpam-6165	176	17	!	!	PUNCT
ejpam-6165	176	18	vm	vm	PROPN
ejpam-6165	176	19	m	m	PROPN
ejpam-6165	176	20	!	!	PUNCT
ejpam-6165	176	21	∑	∑	PROPN
ejpam-6165	177	1	j	j	NOUN
ejpam-6165	177	2	,	,	PUNCT
ejpam-6165	177	3	l≥0	l≥0	NOUN
ejpam-6165	177	4	be	be	AUX
ejpam-6165	177	5	(	(	PUNCT
ejpam-6165	177	6	k	k	X
ejpam-6165	177	7	,	,	PUNCT
ejpam-6165	177	8	α	α	NOUN
ejpam-6165	177	9	)	)	PUNCT
ejpam-6165	177	10	j+l	j+l	PROPN
ejpam-6165	177	11	(	(	PUNCT
ejpam-6165	177	12	z	z	NOUN
ejpam-6165	177	13	,	,	PUNCT
ejpam-6165	177	14	y;u	y;u	PROPN
ejpam-6165	177	15	,	,	PUNCT
ejpam-6165	177	16	λ	λ	NOUN
ejpam-6165	177	17	)	)	PUNCT
ejpam-6165	177	18	tj	tj	PROPN
ejpam-6165	177	19	j	j	PROPN
ejpam-6165	177	20	!	!	PUNCT
ejpam-6165	178	1	vl	vl	PROPN
ejpam-6165	178	2	l	l	NOUN
ejpam-6165	178	3	!	!	PUNCT
ejpam-6165	179	1			PROPN
ejpam-6165	179	2	=	=	PUNCT
ejpam-6165	179	3	∑	∑	PUNCT
ejpam-6165	179	4	q	q	X
ejpam-6165	179	5	,	,	PUNCT
ejpam-6165	179	6	l≥0	l≥0	NOUN
ejpam-6165	179	7			PUNCT
ejpam-6165	179	8	q	q	NOUN
ejpam-6165	179	9	,	,	PUNCT
ejpam-6165	179	10	l∑	l∑	PROPN
ejpam-6165	179	11	j	j	PROPN
ejpam-6165	179	12	,	,	PUNCT
ejpam-6165	179	13	m=0	m=0	PROPN
ejpam-6165	179	14	(	(	PUNCT
ejpam-6165	179	15	q	q	PROPN
ejpam-6165	179	16	j	j	PROPN
ejpam-6165	179	17	)	)	PUNCT
ejpam-6165	179	18	(	(	PUNCT
ejpam-6165	179	19	l	l	NOUN
ejpam-6165	179	20	m	m	VERB
ejpam-6165	179	21	)	)	PUNCT
ejpam-6165	180	1	(	(	PUNCT
ejpam-6165	180	2	r	r	NOUN
ejpam-6165	180	3	−	−	NOUN
ejpam-6165	180	4	z)q−j+i−m	z)q−j+i−m	AUX
ejpam-6165	180	5	be	be	AUX
ejpam-6165	180	6	(	(	PUNCT
ejpam-6165	180	7	k	k	X
ejpam-6165	180	8	,	,	PUNCT
ejpam-6165	180	9	α	α	NOUN
ejpam-6165	180	10	)	)	PUNCT
ejpam-6165	180	11	q+l	q+l	NUM
ejpam-6165	180	12	(	(	PUNCT
ejpam-6165	180	13	z	z	NOUN
ejpam-6165	180	14	,	,	PUNCT
ejpam-6165	180	15	y;u	y;u	PROPN
ejpam-6165	180	16	,	,	PUNCT
ejpam-6165	180	17	λ	λ	NOUN
ejpam-6165	180	18	)	)	PUNCT
ejpam-6165	180	19			NOUN
ejpam-6165	180	20	tq	tq	ADP
ejpam-6165	180	21	q	q	NOUN
ejpam-6165	180	22	!	!	PUNCT
ejpam-6165	181	1	vl	vl	PROPN
ejpam-6165	181	2	l	l	NOUN
ejpam-6165	181	3	!	!	PUNCT
ejpam-6165	181	4	.	.	PUNCT
ejpam-6165	182	1	comparing	compare	VERB
ejpam-6165	182	2	the	the	DET
ejpam-6165	182	3	coefficients	coefficient	NOUN
ejpam-6165	182	4	of	of	ADP
ejpam-6165	182	5	tq	tq	ADV
ejpam-6165	182	6	q	q	NOUN
ejpam-6165	182	7	!	!	PUNCT
ejpam-6165	183	1	vl	vl	PROPN
ejpam-6165	183	2	l	l	PROPN
ejpam-6165	183	3	!	!	PROPN
ejpam-6165	183	4	completes	complete	VERB
ejpam-6165	183	5	the	the	DET
ejpam-6165	183	6	proof	proof	NOUN
ejpam-6165	183	7	of	of	ADP
ejpam-6165	183	8	the	the	DET
ejpam-6165	183	9	theorem	theorem	PROPN
ejpam-6165	183	10	.	.	PUNCT
ejpam-6165	183	11	theorem	theorem	VERB
ejpam-6165	183	12	3.3	3.3	NUM
ejpam-6165	183	13	.	.	PUNCT
ejpam-6165	184	1	the	the	DET
ejpam-6165	184	2	r	r	NOUN
ejpam-6165	184	3	-	-	PUNCT
ejpam-6165	184	4	bell	bell	NOUN
ejpam-6165	184	5	-	-	PUNCT
ejpam-6165	184	6	based	base	VERB
ejpam-6165	184	7	apostol	apostol	NOUN
ejpam-6165	184	8	-	-	PUNCT
ejpam-6165	184	9	frobenius	frobenius	NOUN
ejpam-6165	184	10	-	-	PUNCT
ejpam-6165	184	11	type	type	NOUN
ejpam-6165	184	12	poly	poly	ADJ
ejpam-6165	184	13	-	-	PUNCT
ejpam-6165	184	14	euler	euler	NOUN
ejpam-6165	184	15	polynomials	polynomial	NOUN
ejpam-6165	184	16	be	be	AUX
ejpam-6165	184	17	(	(	PUNCT
ejpam-6165	184	18	α	α	NOUN
ejpam-6165	184	19	)	)	PUNCT
ejpam-6165	184	20	j	j	NOUN
ejpam-6165	184	21	(	(	PUNCT
ejpam-6165	184	22	r	r	NOUN
ejpam-6165	184	23	,	,	PUNCT
ejpam-6165	184	24	y;u;λ	y;u;λ	NOUN
ejpam-6165	184	25	)	)	PUNCT
ejpam-6165	184	26	of	of	ADP
ejpam-6165	184	27	order	order	NOUN
ejpam-6165	184	28	α	α	PRON
ejpam-6165	184	29	satisfy	satisfy	VERB
ejpam-6165	184	30	the	the	DET
ejpam-6165	184	31	following	follow	VERB
ejpam-6165	184	32	summation	summation	NOUN
ejpam-6165	184	33	identity	identity	NOUN
ejpam-6165	184	34	be	be	AUX
ejpam-6165	184	35	(	(	PUNCT
ejpam-6165	184	36	k	k	X
ejpam-6165	184	37	,	,	PUNCT
ejpam-6165	184	38	α	α	NOUN
ejpam-6165	184	39	)	)	PUNCT
ejpam-6165	184	40	n	n	CCONJ
ejpam-6165	184	41	(	(	PUNCT
ejpam-6165	184	42	r	r	NOUN
ejpam-6165	184	43	,	,	PUNCT
ejpam-6165	184	44	y;u	y;u	PROPN
ejpam-6165	184	45	,	,	PUNCT
ejpam-6165	184	46	λ	λ	NOUN
ejpam-6165	184	47	)	)	PUNCT
ejpam-6165	184	48	=	=	SYM
ejpam-6165	185	1	n∑	n∑	PROPN
ejpam-6165	185	2	k=0	k=0	PROPN
ejpam-6165	185	3	∞∑	∞∑	NUM
ejpam-6165	185	4	j=0	j=0	PROPN
ejpam-6165	185	5	(	(	PUNCT
ejpam-6165	185	6	n	n	X
ejpam-6165	185	7	k	k	NOUN
ejpam-6165	185	8	)	)	PUNCT
ejpam-6165	185	9	(	(	PUNCT
ejpam-6165	185	10	r)js(k	r)js(k	ADP
ejpam-6165	185	11	,	,	PUNCT
ejpam-6165	185	12	j)be	j)be	PROPN
ejpam-6165	185	13	(	(	PUNCT
ejpam-6165	185	14	k	k	X
ejpam-6165	185	15	,	,	PUNCT
ejpam-6165	185	16	α	α	NOUN
ejpam-6165	185	17	)	)	PUNCT
ejpam-6165	185	18	n−k	n−k	NOUN
ejpam-6165	185	19	(	(	PUNCT
ejpam-6165	185	20	y;u	y;u	PROPN
ejpam-6165	185	21	,	,	PUNCT
ejpam-6165	185	22	λ	λ	NOUN
ejpam-6165	185	23	)	)	PUNCT
ejpam-6165	185	24	.	.	PUNCT
ejpam-6165	186	1	proof	proof	NOUN
ejpam-6165	186	2	.	.	PUNCT
ejpam-6165	187	1	∞∑	∞∑	PRON
ejpam-6165	187	2	n=0	n=0	X
ejpam-6165	187	3	be	be	AUX
ejpam-6165	187	4	(	(	PUNCT
ejpam-6165	187	5	k	k	X
ejpam-6165	187	6	,	,	PUNCT
ejpam-6165	187	7	α	α	NOUN
ejpam-6165	187	8	)	)	PUNCT
ejpam-6165	187	9	n	n	CCONJ
ejpam-6165	187	10	(	(	PUNCT
ejpam-6165	187	11	r	r	NOUN
ejpam-6165	187	12	,	,	PUNCT
ejpam-6165	187	13	y;u	y;u	PROPN
ejpam-6165	187	14	,	,	PUNCT
ejpam-6165	187	15	λ	λ	PROPN
ejpam-6165	187	16	)	)	PUNCT
ejpam-6165	187	17	tn	tn	PROPN
ejpam-6165	187	18	n	n	PROPN
ejpam-6165	187	19	!	!	PUNCT
ejpam-6165	187	20	=	=	PUNCT
ejpam-6165	188	1	(	(	PUNCT
ejpam-6165	188	2	lik(1−	lik(1−	PROPN
ejpam-6165	188	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	188	4	)	)	PUNCT
ejpam-6165	188	5	λet	λet	ADP
ejpam-6165	188	6	−	−	PROPN
ejpam-6165	188	7	u	u	NOUN
ejpam-6165	188	8	)	)	PUNCT
ejpam-6165	188	9	r	r	NOUN
ejpam-6165	188	10	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	188	11	)	)	PUNCT
ejpam-6165	189	1	=	=	PUNCT
ejpam-6165	189	2	(	(	PUNCT
ejpam-6165	189	3	lik(1−	lik(1−	PROPN
ejpam-6165	189	4	e−(1−u	e−(1−u	NOUN
ejpam-6165	189	5	)	)	PUNCT
ejpam-6165	189	6	λet	λet	ADP
ejpam-6165	189	7	−	−	PROPN
ejpam-6165	189	8	u	u	NOUN
ejpam-6165	189	9	)	)	PUNCT
ejpam-6165	189	10	α	α	PROPN
ejpam-6165	189	11	ey(e	ey(e	PUNCT
ejpam-6165	189	12	t−1)ert	t−1)ert	NOUN
ejpam-6165	190	1	=	=	PUNCT
ejpam-6165	190	2	(	(	PUNCT
ejpam-6165	190	3	lik(1−	lik(1−	PROPN
ejpam-6165	190	4	e−(1−u	e−(1−u	NOUN
ejpam-6165	190	5	)	)	PUNCT
ejpam-6165	190	6	λet	λet	ADP
ejpam-6165	190	7	−	−	PROPN
ejpam-6165	190	8	u	u	NOUN
ejpam-6165	190	9	)	)	PUNCT
ejpam-6165	190	10	α	α	PROPN
ejpam-6165	190	11	ey(e	ey(e	PUNCT
ejpam-6165	190	12	t−1)(1	t−1)(1	PROPN
ejpam-6165	191	1	+	+	CCONJ
ejpam-6165	191	2	et	et	NOUN
ejpam-6165	191	3	−	−	PROPN
ejpam-6165	191	4	1)r	1)r	NUM
ejpam-6165	191	5	=	=	PUNCT
ejpam-6165	191	6	(	(	PUNCT
ejpam-6165	191	7	∞∑	∞∑	PROPN
ejpam-6165	191	8	n=0	n=0	X
ejpam-6165	191	9	be	be	AUX
ejpam-6165	191	10	(	(	PUNCT
ejpam-6165	191	11	k	k	X
ejpam-6165	191	12	,	,	PUNCT
ejpam-6165	191	13	α	α	NOUN
ejpam-6165	191	14	)	)	PUNCT
ejpam-6165	191	15	n	n	PROPN
ejpam-6165	191	16	(	(	PUNCT
ejpam-6165	191	17	y;u	y;u	PROPN
ejpam-6165	191	18	,	,	PUNCT
ejpam-6165	191	19	λ	λ	PROPN
ejpam-6165	191	20	)	)	PUNCT
ejpam-6165	191	21	tn	tn	PROPN
ejpam-6165	191	22	n	n	PROPN
ejpam-6165	191	23	!	!	PUNCT
ejpam-6165	191	24	)	)	PUNCT
ejpam-6165	192	1			PROPN
ejpam-6165	192	2	∞∑	∞∑	NUM
ejpam-6165	192	3	j=0	j=0	PROPN
ejpam-6165	192	4	(	(	PUNCT
ejpam-6165	192	5	r	r	NOUN
ejpam-6165	192	6	j	j	PROPN
ejpam-6165	192	7	)	)	PUNCT
ejpam-6165	192	8	(	(	PUNCT
ejpam-6165	192	9	et	et	NOUN
ejpam-6165	192	10	−	−	PROPN
ejpam-6165	192	11	1)j	1)j	NUM
ejpam-6165	192	12			PROPN
ejpam-6165	193	1	=	=	PUNCT
ejpam-6165	194	1	(	(	PUNCT
ejpam-6165	194	2	∞∑	∞∑	PROPN
ejpam-6165	194	3	n=0	n=0	X
ejpam-6165	194	4	be	be	AUX
ejpam-6165	194	5	(	(	PUNCT
ejpam-6165	194	6	k	k	X
ejpam-6165	194	7	,	,	PUNCT
ejpam-6165	194	8	α	α	NOUN
ejpam-6165	194	9	)	)	PUNCT
ejpam-6165	194	10	n	n	PROPN
ejpam-6165	194	11	(	(	PUNCT
ejpam-6165	194	12	y;u	y;u	PROPN
ejpam-6165	194	13	,	,	PUNCT
ejpam-6165	194	14	λ	λ	PROPN
ejpam-6165	194	15	)	)	PUNCT
ejpam-6165	194	16	tn	tn	PROPN
ejpam-6165	194	17	n	n	PROPN
ejpam-6165	194	18	!	!	PUNCT
ejpam-6165	194	19	)	)	PUNCT
ejpam-6165	195	1			PROPN
ejpam-6165	195	2	∞∑	∞∑	NUM
ejpam-6165	195	3	j=0	j=0	PROPN
ejpam-6165	195	4	(	(	PUNCT
ejpam-6165	195	5	r)j	r)j	X
ejpam-6165	195	6	(	(	PUNCT
ejpam-6165	195	7	et	et	NOUN
ejpam-6165	195	8	−	−	PROPN
ejpam-6165	195	9	1)j	1)j	NUM
ejpam-6165	195	10	j	j	PROPN
ejpam-6165	195	11	!	!	PUNCT
ejpam-6165	196	1			PROPN
ejpam-6165	197	1	=	=	PUNCT
ejpam-6165	198	1	(	(	PUNCT
ejpam-6165	198	2	∞∑	∞∑	PROPN
ejpam-6165	198	3	n=0	n=0	X
ejpam-6165	198	4	be	be	AUX
ejpam-6165	198	5	(	(	PUNCT
ejpam-6165	198	6	k	k	X
ejpam-6165	198	7	,	,	PUNCT
ejpam-6165	198	8	α	α	NOUN
ejpam-6165	198	9	)	)	PUNCT
ejpam-6165	198	10	n	n	PROPN
ejpam-6165	198	11	(	(	PUNCT
ejpam-6165	198	12	y;u	y;u	PROPN
ejpam-6165	198	13	,	,	PUNCT
ejpam-6165	198	14	λ	λ	PROPN
ejpam-6165	198	15	)	)	PUNCT
ejpam-6165	198	16	tn	tn	PROPN
ejpam-6165	198	17	n	n	PROPN
ejpam-6165	198	18	!	!	PUNCT
ejpam-6165	198	19	)	)	PUNCT
ejpam-6165	199	1			PROPN
ejpam-6165	199	2	∞∑	∞∑	NUM
ejpam-6165	199	3	j=0	j=0	PROPN
ejpam-6165	199	4	(	(	PUNCT
ejpam-6165	199	5	r)j	r)j	NOUN
ejpam-6165	199	6	∞∑	∞∑	PRON
ejpam-6165	199	7	n=0	n=0	PUNCT
ejpam-6165	199	8	s(n	s(n	PROPN
ejpam-6165	199	9	,	,	PUNCT
ejpam-6165	199	10	j	j	NOUN
ejpam-6165	199	11	)	)	PUNCT
ejpam-6165	199	12	tn	tn	PROPN
ejpam-6165	199	13	n	n	NOUN
ejpam-6165	199	14	!	!	PUNCT
ejpam-6165	200	1			PROPN
ejpam-6165	201	1	=	=	PUNCT
ejpam-6165	202	1	(	(	PUNCT
ejpam-6165	202	2	∞∑	∞∑	PROPN
ejpam-6165	202	3	n=0	n=0	X
ejpam-6165	202	4	be	be	AUX
ejpam-6165	202	5	(	(	PUNCT
ejpam-6165	202	6	k	k	X
ejpam-6165	202	7	,	,	PUNCT
ejpam-6165	202	8	α	α	NOUN
ejpam-6165	202	9	)	)	PUNCT
ejpam-6165	202	10	n	n	PROPN
ejpam-6165	202	11	(	(	PUNCT
ejpam-6165	202	12	y;u	y;u	PROPN
ejpam-6165	202	13	,	,	PUNCT
ejpam-6165	202	14	λ	λ	PROPN
ejpam-6165	202	15	)	)	PUNCT
ejpam-6165	202	16	tn	tn	PROPN
ejpam-6165	202	17	n	n	PROPN
ejpam-6165	202	18	!	!	PUNCT
ejpam-6165	202	19	)	)	PUNCT
ejpam-6165	203	1			PROPN
ejpam-6165	203	2	∞∑	∞∑	PROPN
ejpam-6165	203	3	n=0	n=0	NUM
ejpam-6165	203	4			PUNCT
ejpam-6165	203	5	∞∑	∞∑	NUM
ejpam-6165	203	6	j=0	j=0	PROPN
ejpam-6165	203	7	(	(	PUNCT
ejpam-6165	203	8	r)js(n	r)js(n	PROPN
ejpam-6165	203	9	,	,	PUNCT
ejpam-6165	203	10	j	j	NOUN
ejpam-6165	203	11	)	)	PUNCT
ejpam-6165	203	12			PROPN
ejpam-6165	203	13	tn	tn	NOUN
ejpam-6165	203	14	n	n	ADV
ejpam-6165	203	15	!	!	PUNCT
ejpam-6165	204	1			PROPN
ejpam-6165	204	2	=	=	PUNCT
ejpam-6165	205	1	∞∑	∞∑	NUM
ejpam-6165	205	2	n=0	n=0	NUM
ejpam-6165	205	3	n∑	n∑	NOUN
ejpam-6165	205	4	k=0	k=0	PROPN
ejpam-6165	205	5	(	(	PUNCT
ejpam-6165	205	6	n	n	X
ejpam-6165	205	7	k	k	NOUN
ejpam-6165	205	8	)	)	PUNCT
ejpam-6165	205	9			PUNCT
ejpam-6165	205	10	∞∑	∞∑	NUM
ejpam-6165	205	11	j=0	j=0	PROPN
ejpam-6165	205	12	(	(	PUNCT
ejpam-6165	205	13	r)js(k	r)js(k	PROPN
ejpam-6165	205	14	,	,	PUNCT
ejpam-6165	205	15	j)be	j)be	PROPN
ejpam-6165	205	16	(	(	PUNCT
ejpam-6165	205	17	k	k	X
ejpam-6165	205	18	,	,	PUNCT
ejpam-6165	205	19	α	α	NOUN
ejpam-6165	205	20	)	)	PUNCT
ejpam-6165	205	21	n−k	n−k	NOUN
ejpam-6165	205	22	(	(	PUNCT
ejpam-6165	205	23	y;u	y;u	PROPN
ejpam-6165	205	24	,	,	PUNCT
ejpam-6165	205	25	λ	λ	NOUN
ejpam-6165	205	26	)	)	PUNCT
ejpam-6165	206	1			PROPN
ejpam-6165	206	2	tn	tn	PROPN
ejpam-6165	206	3	n	n	CCONJ
ejpam-6165	206	4	!	!	PROPN
ejpam-6165	206	5	10	10	NUM
ejpam-6165	206	6	of	of	ADP
ejpam-6165	206	7	15	15	NUM
ejpam-6165	206	8	=	=	NOUN
ejpam-6165	206	9	∞∑	∞∑	NUM
ejpam-6165	206	10	n=0	n=0	NUM
ejpam-6165	206	11			PUNCT
ejpam-6165	206	12	n∑	n∑	NOUN
ejpam-6165	206	13	k=0	k=0	PROPN
ejpam-6165	206	14	(	(	PUNCT
ejpam-6165	206	15	n	n	X
ejpam-6165	206	16	k	k	NOUN
ejpam-6165	206	17	)	)	PUNCT
ejpam-6165	207	1	∞∑	∞∑	NUM
ejpam-6165	207	2	j=0	j=0	PROPN
ejpam-6165	207	3	(	(	PUNCT
ejpam-6165	207	4	r)js(k	r)js(k	PROPN
ejpam-6165	207	5	,	,	PUNCT
ejpam-6165	207	6	j)be	j)be	PROPN
ejpam-6165	207	7	(	(	PUNCT
ejpam-6165	207	8	k	k	X
ejpam-6165	207	9	,	,	PUNCT
ejpam-6165	207	10	α	α	NOUN
ejpam-6165	207	11	)	)	PUNCT
ejpam-6165	207	12	n−k	n−k	NOUN
ejpam-6165	207	13	(	(	PUNCT
ejpam-6165	207	14	y;u	y;u	PROPN
ejpam-6165	207	15	,	,	PUNCT
ejpam-6165	207	16	λ	λ	NOUN
ejpam-6165	207	17	)	)	PUNCT
ejpam-6165	207	18			PROPN
ejpam-6165	207	19	tn	tn	PROPN
ejpam-6165	207	20	n	n	CCONJ
ejpam-6165	207	21	!	!	PUNCT
ejpam-6165	207	22	.	.	PUNCT
ejpam-6165	208	1	comparing	compare	VERB
ejpam-6165	208	2	the	the	DET
ejpam-6165	208	3	coefficients	coefficient	NOUN
ejpam-6165	208	4	of	of	ADP
ejpam-6165	208	5	tn	tn	NOUN
ejpam-6165	208	6	/	/	SYM
ejpam-6165	208	7	n	n	CCONJ
ejpam-6165	208	8	!	!	X
ejpam-6165	208	9	completes	complete	VERB
ejpam-6165	208	10	the	the	DET
ejpam-6165	208	11	proof	proof	NOUN
ejpam-6165	208	12	of	of	ADP
ejpam-6165	208	13	the	the	DET
ejpam-6165	208	14	theorem	theorem	NOUN
ejpam-6165	208	15	.	.	PUNCT
ejpam-6165	209	1	the	the	DET
ejpam-6165	209	2	next	next	ADJ
ejpam-6165	209	3	result	result	NOUN
ejpam-6165	209	4	that	that	SCONJ
ejpam-6165	209	5	we	we	PRON
ejpam-6165	209	6	are	be	AUX
ejpam-6165	209	7	going	go	VERB
ejpam-6165	209	8	to	to	PART
ejpam-6165	209	9	obtain	obtain	VERB
ejpam-6165	209	10	is	be	AUX
ejpam-6165	209	11	to	to	PART
ejpam-6165	209	12	express	express	VERB
ejpam-6165	209	13	the	the	DET
ejpam-6165	209	14	r	r	NOUN
ejpam-6165	209	15	-	-	PUNCT
ejpam-6165	209	16	bell	bell	NOUN
ejpam-6165	209	17	polynomials	polynomial	NOUN
ejpam-6165	209	18	in	in	ADP
ejpam-6165	209	19	terms	term	NOUN
ejpam-6165	209	20	of	of	ADP
ejpam-6165	209	21	the	the	DET
ejpam-6165	209	22	difference	difference	NOUN
ejpam-6165	209	23	of	of	ADP
ejpam-6165	209	24	r	r	NOUN
ejpam-6165	209	25	-	-	PUNCT
ejpam-6165	209	26	bell	bell	NOUN
ejpam-6165	209	27	-	-	PUNCT
ejpam-6165	209	28	based	base	VERB
ejpam-6165	209	29	apostol	apostol	NOUN
ejpam-6165	209	30	-	-	PUNCT
ejpam-6165	209	31	frobenius	frobenius	NOUN
ejpam-6165	209	32	-	-	PUNCT
ejpam-6165	209	33	type	type	NOUN
ejpam-6165	209	34	poly	poly	ADJ
ejpam-6165	209	35	-	-	PUNCT
ejpam-6165	209	36	euler	euler	NOUN
ejpam-6165	209	37	polynomials	polynomial	NOUN
ejpam-6165	209	38	be	be	AUX
ejpam-6165	209	39	(	(	PUNCT
ejpam-6165	209	40	α	α	NOUN
ejpam-6165	209	41	)	)	PUNCT
ejpam-6165	209	42	j	j	NOUN
ejpam-6165	209	43	(	(	PUNCT
ejpam-6165	209	44	r	r	NOUN
ejpam-6165	209	45	,	,	PUNCT
ejpam-6165	209	46	y;u;λ	y;u;λ	NOUN
ejpam-6165	209	47	)	)	PUNCT
ejpam-6165	209	48	of	of	ADP
ejpam-6165	209	49	order	order	NOUN
ejpam-6165	209	50	α	α	X
ejpam-6165	209	51	.	.	PUNCT
ejpam-6165	209	52	theorem	theorem	VERB
ejpam-6165	209	53	3.4	3.4	NUM
ejpam-6165	209	54	.	.	PUNCT
ejpam-6165	210	1	the	the	DET
ejpam-6165	210	2	r	r	NOUN
ejpam-6165	210	3	-	-	PUNCT
ejpam-6165	210	4	bell	bell	NOUN
ejpam-6165	210	5	-	-	PUNCT
ejpam-6165	210	6	based	base	VERB
ejpam-6165	210	7	apostol	apostol	NOUN
ejpam-6165	210	8	-	-	PUNCT
ejpam-6165	210	9	frobenius	frobenius	NOUN
ejpam-6165	210	10	-	-	PUNCT
ejpam-6165	210	11	type	type	NOUN
ejpam-6165	210	12	poly	poly	ADJ
ejpam-6165	210	13	-	-	PUNCT
ejpam-6165	210	14	euler	euler	NOUN
ejpam-6165	210	15	polynomials	polynomial	NOUN
ejpam-6165	210	16	be	be	AUX
ejpam-6165	210	17	(	(	PUNCT
ejpam-6165	210	18	k,1	k,1	PROPN
ejpam-6165	210	19	)	)	PUNCT
ejpam-6165	210	20	j	j	PROPN
ejpam-6165	210	21	(	(	PUNCT
ejpam-6165	210	22	r	r	NOUN
ejpam-6165	210	23	,	,	PUNCT
ejpam-6165	210	24	y;u;λ	y;u;λ	NOUN
ejpam-6165	210	25	)	)	PUNCT
ejpam-6165	210	26	satisfy	satisfy	VERB
ejpam-6165	210	27	the	the	DET
ejpam-6165	210	28	following	follow	VERB
ejpam-6165	210	29	relation	relation	NOUN
ejpam-6165	210	30	bn(r	bn(r	NOUN
ejpam-6165	210	31	,	,	PUNCT
ejpam-6165	210	32	y	y	NOUN
ejpam-6165	210	33	)	)	PUNCT
ejpam-6165	210	34	=	=	SYM
ejpam-6165	210	35	λ	λ	PART
ejpam-6165	210	36	·	·	PUNCT
ejpam-6165	210	37	be(k,1	be(k,1	NOUN
ejpam-6165	210	38	)	)	PUNCT
ejpam-6165	210	39	n+1	n+1	PROPN
ejpam-6165	211	1	(	(	PUNCT
ejpam-6165	211	2	r	r	NOUN
ejpam-6165	211	3	+	+	NOUN
ejpam-6165	211	4	1	1	NUM
ejpam-6165	211	5	,	,	PUNCT
ejpam-6165	211	6	y;u	y;u	PROPN
ejpam-6165	211	7	,	,	PUNCT
ejpam-6165	211	8	λ)−	λ)−	PROPN
ejpam-6165	211	9	u	u	NOUN
ejpam-6165	211	10	·	·	PUNCT
ejpam-6165	211	11	be(k,1	be(k,1	NOUN
ejpam-6165	211	12	)	)	PUNCT
ejpam-6165	211	13	n+1	n+1	PROPN
ejpam-6165	212	1	(	(	PUNCT
ejpam-6165	212	2	r	r	NOUN
ejpam-6165	212	3	,	,	PUNCT
ejpam-6165	212	4	y;u	y;u	PROPN
ejpam-6165	212	5	,	,	PUNCT
ejpam-6165	212	6	λ	λ	NOUN
ejpam-6165	212	7	)	)	PUNCT
ejpam-6165	212	8	lik(1−	lik(1−	VERB
ejpam-6165	212	9	e−(1−u))(n+	e−(1−u))(n+	NOUN
ejpam-6165	212	10	1	1	NUM
ejpam-6165	212	11	)	)	PUNCT
ejpam-6165	212	12	proof	proof	NOUN
ejpam-6165	212	13	.	.	PUNCT
ejpam-6165	213	1	by	by	ADP
ejpam-6165	213	2	rewriting	rewrite	VERB
ejpam-6165	213	3	the	the	DET
ejpam-6165	213	4	definition	definition	NOUN
ejpam-6165	213	5	of	of	ADP
ejpam-6165	213	6	r	r	NOUN
ejpam-6165	213	7	-	-	PUNCT
ejpam-6165	213	8	bell	bell	NOUN
ejpam-6165	213	9	polynomials	polynomial	NOUN
ejpam-6165	213	10	,	,	PUNCT
ejpam-6165	213	11	we	we	PRON
ejpam-6165	213	12	obtain	obtain	VERB
ejpam-6165	213	13	∞∑	∞∑	NUM
ejpam-6165	213	14	n=0	n=0	NUM
ejpam-6165	213	15	bn(r	bn(r	NOUN
ejpam-6165	213	16	,	,	PUNCT
ejpam-6165	213	17	y	y	NOUN
ejpam-6165	213	18	)	)	PUNCT
ejpam-6165	213	19	tn	tn	PROPN
ejpam-6165	213	20	n	n	PROPN
ejpam-6165	213	21	!	!	PUNCT
ejpam-6165	214	1	=	=	SYM
ejpam-6165	214	2	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	214	3	)	)	PUNCT
ejpam-6165	215	1	=	=	PRON
ejpam-6165	216	1	(	(	PUNCT
ejpam-6165	216	2	λet	λet	X
ejpam-6165	216	3	−	−	PUNCT
ejpam-6165	216	4	u	u	PRON
ejpam-6165	216	5	lik(1−	lik(1−	VERB
ejpam-6165	216	6	e−(1−u	e−(1−u	NOUN
ejpam-6165	216	7	)	)	PUNCT
ejpam-6165	216	8	)	)	PUNCT
ejpam-6165	216	9	)	)	PUNCT
ejpam-6165	217	1	(	(	PUNCT
ejpam-6165	217	2	lik(1−	lik(1−	PROPN
ejpam-6165	217	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	217	4	)	)	PUNCT
ejpam-6165	217	5	)	)	PUNCT
ejpam-6165	218	1	λet	λet	CCONJ
ejpam-6165	218	2	−	−	PROPN
ejpam-6165	218	3	u	u	NOUN
ejpam-6165	218	4	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	218	5	)	)	PUNCT
ejpam-6165	218	6	)	)	PUNCT
ejpam-6165	219	1	=	=	SYM
ejpam-6165	219	2	1	1	NUM
ejpam-6165	219	3	lik(1−	lik(1−	ADJ
ejpam-6165	219	4	e−(1−u	e−(1−u	NOUN
ejpam-6165	219	5	)	)	PUNCT
ejpam-6165	219	6	)	)	PUNCT
ejpam-6165	220	1	(	(	PUNCT
ejpam-6165	220	2	λ	λ	X
ejpam-6165	220	3	(	(	PUNCT
ejpam-6165	220	4	lik(1−	lik(1−	PROPN
ejpam-6165	220	5	e−(1−u	e−(1−u	NOUN
ejpam-6165	220	6	)	)	PUNCT
ejpam-6165	220	7	)	)	PUNCT
ejpam-6165	221	1	λet	λet	CCONJ
ejpam-6165	221	2	−	−	PROPN
ejpam-6165	221	3	u	u	PROPN
ejpam-6165	221	4	e(r+1)t+y(et−1	e(r+1)t+y(et−1	NOUN
ejpam-6165	221	5	)	)	PUNCT
ejpam-6165	221	6	)	)	PUNCT
ejpam-6165	222	1	−u	−u	NOUN
ejpam-6165	222	2	(	(	PUNCT
ejpam-6165	222	3	lik(1−	lik(1−	PROPN
ejpam-6165	222	4	e−(1−u	e−(1−u	NOUN
ejpam-6165	222	5	)	)	PUNCT
ejpam-6165	222	6	)	)	PUNCT
ejpam-6165	223	1	λet	λet	CCONJ
ejpam-6165	223	2	−	−	PROPN
ejpam-6165	223	3	u	u	NOUN
ejpam-6165	223	4	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	223	5	)	)	PUNCT
ejpam-6165	223	6	)	)	PUNCT
ejpam-6165	223	7	)	)	PUNCT
ejpam-6165	224	1	=	=	SYM
ejpam-6165	224	2	1	1	NUM
ejpam-6165	224	3	lik(1−	lik(1−	ADJ
ejpam-6165	224	4	e−(1−u	e−(1−u	NOUN
ejpam-6165	224	5	)	)	PUNCT
ejpam-6165	224	6	)	)	PUNCT
ejpam-6165	225	1	(	(	PUNCT
ejpam-6165	225	2	λ	λ	X
ejpam-6165	225	3	∞∑	∞∑	PROPN
ejpam-6165	225	4	n=0	n=0	X
ejpam-6165	225	5	be	be	AUX
ejpam-6165	225	6	(	(	PUNCT
ejpam-6165	225	7	r	r	NOUN
ejpam-6165	225	8	)	)	PUNCT
ejpam-6165	225	9	n	n	NOUN
ejpam-6165	225	10	(	(	PUNCT
ejpam-6165	225	11	r	r	NOUN
ejpam-6165	225	12	+	+	NOUN
ejpam-6165	225	13	1	1	NUM
ejpam-6165	225	14	,	,	PUNCT
ejpam-6165	225	15	y;u	y;u	PROPN
ejpam-6165	225	16	,	,	PUNCT
ejpam-6165	225	17	λ	λ	PROPN
ejpam-6165	225	18	)	)	PUNCT
ejpam-6165	225	19	tn	tn	PROPN
ejpam-6165	225	20	n	n	NOUN
ejpam-6165	225	21	!	!	PUNCT
ejpam-6165	226	1	−u	−u	PRON
ejpam-6165	226	2	∞∑	∞∑	PROPN
ejpam-6165	226	3	n=0	n=0	PROPN
ejpam-6165	226	4	be	be	AUX
ejpam-6165	226	5	(	(	PUNCT
ejpam-6165	226	6	k,1	k,1	NOUN
ejpam-6165	226	7	)	)	PUNCT
ejpam-6165	226	8	n	n	CCONJ
ejpam-6165	226	9	(	(	PUNCT
ejpam-6165	226	10	r	r	NOUN
ejpam-6165	226	11	,	,	PUNCT
ejpam-6165	226	12	y;u	y;u	PROPN
ejpam-6165	226	13	,	,	PUNCT
ejpam-6165	226	14	λ	λ	PROPN
ejpam-6165	226	15	)	)	PUNCT
ejpam-6165	226	16	tn	tn	PROPN
ejpam-6165	226	17	n	n	PROPN
ejpam-6165	226	18	!	!	PUNCT
ejpam-6165	226	19	)	)	PUNCT
ejpam-6165	227	1	=	=	SYM
ejpam-6165	227	2	1	1	NUM
ejpam-6165	227	3	lik(1−	lik(1−	ADJ
ejpam-6165	227	4	e−(1−u	e−(1−u	NOUN
ejpam-6165	227	5	)	)	PUNCT
ejpam-6165	227	6	)	)	PUNCT
ejpam-6165	228	1	(	(	PUNCT
ejpam-6165	228	2	λ	λ	X
ejpam-6165	228	3	∞∑	∞∑	PROPN
ejpam-6165	228	4	n=0	n=0	NUM
ejpam-6165	228	5	be	be	AUX
ejpam-6165	228	6	(	(	PUNCT
ejpam-6165	228	7	k,1	k,1	NOUN
ejpam-6165	228	8	)	)	PUNCT
ejpam-6165	228	9	n	n	CCONJ
ejpam-6165	228	10	(	(	PUNCT
ejpam-6165	228	11	r	r	NOUN
ejpam-6165	228	12	+	+	NOUN
ejpam-6165	228	13	1	1	NUM
ejpam-6165	228	14	,	,	PUNCT
ejpam-6165	228	15	y;u	y;u	PROPN
ejpam-6165	228	16	,	,	PUNCT
ejpam-6165	228	17	λ	λ	PROPN
ejpam-6165	228	18	)	)	PUNCT
ejpam-6165	228	19	tn−1	tn−1	PROPN
ejpam-6165	228	20	n	n	CCONJ
ejpam-6165	228	21	!	!	PUNCT
ejpam-6165	229	1	−u	−u	PRON
ejpam-6165	229	2	∞∑	∞∑	PROPN
ejpam-6165	229	3	n=0	n=0	PROPN
ejpam-6165	229	4	be	be	AUX
ejpam-6165	229	5	(	(	PUNCT
ejpam-6165	229	6	k,1	k,1	NOUN
ejpam-6165	229	7	)	)	PUNCT
ejpam-6165	229	8	n	n	CCONJ
ejpam-6165	229	9	(	(	PUNCT
ejpam-6165	229	10	r	r	NOUN
ejpam-6165	229	11	,	,	PUNCT
ejpam-6165	229	12	y;u	y;u	PROPN
ejpam-6165	229	13	,	,	PUNCT
ejpam-6165	229	14	λ	λ	PROPN
ejpam-6165	229	15	)	)	PUNCT
ejpam-6165	229	16	tn−1	tn−1	PROPN
ejpam-6165	229	17	n	n	CCONJ
ejpam-6165	229	18	!	!	PUNCT
ejpam-6165	229	19	)	)	PUNCT
ejpam-6165	230	1	=	=	PUNCT
ejpam-6165	231	1	λ	λ	NOUN
ejpam-6165	231	2	lik(1−	lik(1−	ADJ
ejpam-6165	231	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	231	4	)	)	PUNCT
ejpam-6165	231	5	)	)	PUNCT
ejpam-6165	232	1	∞∑	∞∑	DET
ejpam-6165	232	2	n=−1	n=−1	ADV
ejpam-6165	232	3	1	1	NUM
ejpam-6165	232	4	n+	n+	NUM
ejpam-6165	232	5	1	1	NUM
ejpam-6165	232	6	be	be	AUX
ejpam-6165	232	7	(	(	PUNCT
ejpam-6165	232	8	k,1	k,1	PROPN
ejpam-6165	232	9	)	)	PUNCT
ejpam-6165	232	10	n+1	n+1	PROPN
ejpam-6165	233	1	(	(	PUNCT
ejpam-6165	233	2	r	r	NOUN
ejpam-6165	233	3	+	+	NOUN
ejpam-6165	233	4	1	1	NUM
ejpam-6165	233	5	,	,	PUNCT
ejpam-6165	233	6	y;u	y;u	PROPN
ejpam-6165	233	7	,	,	PUNCT
ejpam-6165	233	8	λ	λ	PROPN
ejpam-6165	233	9	)	)	PUNCT
ejpam-6165	233	10	tn	tn	PROPN
ejpam-6165	233	11	n	n	PROPN
ejpam-6165	233	12	!	!	PUNCT
ejpam-6165	233	13	−	−	PUNCT
ejpam-6165	234	1	u	u	PRON
ejpam-6165	234	2	lik(1−	lik(1−	VERB
ejpam-6165	234	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	234	4	)	)	PUNCT
ejpam-6165	234	5	)	)	PUNCT
ejpam-6165	235	1	∞∑	∞∑	DET
ejpam-6165	235	2	n=−1	n=−1	ADV
ejpam-6165	235	3	1	1	NUM
ejpam-6165	235	4	n+	n+	NUM
ejpam-6165	235	5	1	1	NUM
ejpam-6165	235	6	be	be	AUX
ejpam-6165	235	7	(	(	PUNCT
ejpam-6165	235	8	k,1	k,1	PROPN
ejpam-6165	235	9	)	)	PUNCT
ejpam-6165	235	10	n+1	n+1	PROPN
ejpam-6165	235	11	(	(	PUNCT
ejpam-6165	235	12	r	r	NOUN
ejpam-6165	235	13	,	,	PUNCT
ejpam-6165	235	14	y;u	y;u	PROPN
ejpam-6165	235	15	,	,	PUNCT
ejpam-6165	235	16	λ	λ	PROPN
ejpam-6165	235	17	)	)	PUNCT
ejpam-6165	235	18	tn	tn	PROPN
ejpam-6165	235	19	n	n	PROPN
ejpam-6165	235	20	!	!	PUNCT
ejpam-6165	235	21	.	.	PUNCT
ejpam-6165	236	1	11	11	NUM
ejpam-6165	236	2	of	of	ADP
ejpam-6165	236	3	15	15	NUM
ejpam-6165	236	4	comparing	compare	VERB
ejpam-6165	236	5	the	the	DET
ejpam-6165	236	6	coefficients	coefficient	NOUN
ejpam-6165	236	7	of	of	ADP
ejpam-6165	236	8	tn	tn	NOUN
ejpam-6165	236	9	n	n	X
ejpam-6165	236	10	!	!	PUNCT
ejpam-6165	237	1	yields	yield	VERB
ejpam-6165	237	2	the	the	DET
ejpam-6165	237	3	theorem	theorem	PROPN
ejpam-6165	237	4	.	.	PUNCT
ejpam-6165	238	1	the	the	DET
ejpam-6165	238	2	next	next	ADJ
ejpam-6165	238	3	theorem	theorem	NOUN
ejpam-6165	238	4	contains	contain	VERB
ejpam-6165	238	5	the	the	DET
ejpam-6165	238	6	derivative	derivative	ADJ
ejpam-6165	238	7	formula	formula	NOUN
ejpam-6165	238	8	for	for	ADP
ejpam-6165	238	9	be	be	AUX
ejpam-6165	238	10	(	(	PUNCT
ejpam-6165	238	11	α	α	NOUN
ejpam-6165	238	12	)	)	PUNCT
ejpam-6165	238	13	j	j	NOUN
ejpam-6165	238	14	(	(	PUNCT
ejpam-6165	238	15	r	r	NOUN
ejpam-6165	238	16	,	,	PUNCT
ejpam-6165	238	17	y;u;λ	y;u;λ	NOUN
ejpam-6165	238	18	)	)	PUNCT
ejpam-6165	238	19	of	of	ADP
ejpam-6165	238	20	order	order	NOUN
ejpam-6165	238	21	α	α	PRON
ejpam-6165	238	22	wit	wit	ADJ
ejpam-6165	238	23	respect	respect	NOUN
ejpam-6165	238	24	to	to	ADP
ejpam-6165	238	25	r.	r.	PROPN
ejpam-6165	238	26	theorem	theorem	VERB
ejpam-6165	238	27	3.5	3.5	NUM
ejpam-6165	238	28	.	.	PUNCT
ejpam-6165	239	1	the	the	DET
ejpam-6165	239	2	r	r	NOUN
ejpam-6165	239	3	-	-	PUNCT
ejpam-6165	239	4	bell	bell	NOUN
ejpam-6165	239	5	-	-	PUNCT
ejpam-6165	239	6	based	base	VERB
ejpam-6165	239	7	apostol	apostol	NOUN
ejpam-6165	239	8	-	-	PUNCT
ejpam-6165	239	9	frobenius	frobenius	NOUN
ejpam-6165	239	10	-	-	PUNCT
ejpam-6165	239	11	type	type	NOUN
ejpam-6165	239	12	poly	poly	ADJ
ejpam-6165	239	13	-	-	PUNCT
ejpam-6165	239	14	euler	euler	NOUN
ejpam-6165	239	15	polynomials	polynomial	NOUN
ejpam-6165	239	16	be	be	AUX
ejpam-6165	239	17	(	(	PUNCT
ejpam-6165	239	18	k	k	X
ejpam-6165	239	19	,	,	PUNCT
ejpam-6165	239	20	α	α	NOUN
ejpam-6165	239	21	)	)	PUNCT
ejpam-6165	239	22	j	j	NOUN
ejpam-6165	239	23	(	(	PUNCT
ejpam-6165	239	24	r	r	NOUN
ejpam-6165	239	25	,	,	PUNCT
ejpam-6165	239	26	y;u;λ	y;u;λ	NOUN
ejpam-6165	239	27	)	)	PUNCT
ejpam-6165	239	28	of	of	ADP
ejpam-6165	239	29	order	order	NOUN
ejpam-6165	239	30	α	α	PRON
ejpam-6165	239	31	satisfy	satisfy	VERB
ejpam-6165	239	32	the	the	DET
ejpam-6165	239	33	derivative	derivative	ADJ
ejpam-6165	239	34	formula	formula	NOUN
ejpam-6165	239	35	∂	∂	NOUN
ejpam-6165	240	1	∂r	∂r	NOUN
ejpam-6165	240	2	be	be	AUX
ejpam-6165	240	3	(	(	PUNCT
ejpam-6165	240	4	k	k	X
ejpam-6165	240	5	,	,	PUNCT
ejpam-6165	240	6	α	α	NOUN
ejpam-6165	240	7	)	)	PUNCT
ejpam-6165	240	8	n	n	CCONJ
ejpam-6165	240	9	(	(	PUNCT
ejpam-6165	240	10	r	r	NOUN
ejpam-6165	240	11	,	,	PUNCT
ejpam-6165	240	12	y;u	y;u	PROPN
ejpam-6165	240	13	,	,	PUNCT
ejpam-6165	240	14	λ	λ	NOUN
ejpam-6165	240	15	)	)	PUNCT
ejpam-6165	240	16	=	=	SYM
ejpam-6165	241	1	nbe	nbe	PROPN
ejpam-6165	241	2	(	(	PUNCT
ejpam-6165	241	3	k	k	X
ejpam-6165	241	4	,	,	PUNCT
ejpam-6165	241	5	α	α	NOUN
ejpam-6165	241	6	)	)	PUNCT
ejpam-6165	241	7	n−1	n−1	PROPN
ejpam-6165	241	8	(	(	PUNCT
ejpam-6165	241	9	r	r	NOUN
ejpam-6165	241	10	,	,	PUNCT
ejpam-6165	241	11	y;u	y;u	PROPN
ejpam-6165	241	12	,	,	PUNCT
ejpam-6165	241	13	λ	λ	NOUN
ejpam-6165	241	14	)	)	PUNCT
ejpam-6165	241	15	.	.	PUNCT
ejpam-6165	242	1	proof	proof	NOUN
ejpam-6165	242	2	.	.	PUNCT
ejpam-6165	242	3	.	.	PUNCT
ejpam-6165	243	1	by	by	ADP
ejpam-6165	243	2	applying	apply	VERB
ejpam-6165	243	3	the	the	DET
ejpam-6165	243	4	first	first	ADJ
ejpam-6165	243	5	derivative	derivative	NOUN
ejpam-6165	243	6	to	to	ADP
ejpam-6165	243	7	both	both	DET
ejpam-6165	243	8	sides	side	NOUN
ejpam-6165	243	9	of	of	ADP
ejpam-6165	243	10	(	(	PUNCT
ejpam-6165	243	11	2.1	2.1	NUM
ejpam-6165	243	12	)	)	PUNCT
ejpam-6165	243	13	with	with	ADP
ejpam-6165	243	14	respect	respect	NOUN
ejpam-6165	243	15	to	to	ADP
ejpam-6165	243	16	r	r	NOUN
ejpam-6165	243	17	,	,	PUNCT
ejpam-6165	243	18	we	we	PRON
ejpam-6165	243	19	have	have	VERB
ejpam-6165	243	20	∂	∂	NUM
ejpam-6165	244	1	∂r	∂r	PROPN
ejpam-6165	245	1	∞∑	∞∑	NOUN
ejpam-6165	245	2	n=0	n=0	NUM
ejpam-6165	245	3	be	be	AUX
ejpam-6165	245	4	(	(	PUNCT
ejpam-6165	245	5	k	k	X
ejpam-6165	245	6	,	,	PUNCT
ejpam-6165	245	7	α	α	NOUN
ejpam-6165	245	8	)	)	PUNCT
ejpam-6165	245	9	n	n	CCONJ
ejpam-6165	245	10	(	(	PUNCT
ejpam-6165	245	11	r	r	NOUN
ejpam-6165	245	12	,	,	PUNCT
ejpam-6165	245	13	y;u	y;u	PROPN
ejpam-6165	245	14	,	,	PUNCT
ejpam-6165	245	15	λ	λ	PROPN
ejpam-6165	245	16	)	)	PUNCT
ejpam-6165	245	17	tn	tn	PROPN
ejpam-6165	245	18	n	n	NOUN
ejpam-6165	245	19	!	!	PUNCT
ejpam-6165	246	1	=	=	SYM
ejpam-6165	246	2	∂	∂	NUM
ejpam-6165	247	1	∂r	∂r	NOUN
ejpam-6165	247	2	(	(	PUNCT
ejpam-6165	247	3	lik(1−	lik(1−	PROPN
ejpam-6165	247	4	e−(1−u	e−(1−u	NOUN
ejpam-6165	247	5	)	)	PUNCT
ejpam-6165	247	6	)	)	PUNCT
ejpam-6165	248	1	λet	λet	CCONJ
ejpam-6165	248	2	−	−	PROPN
ejpam-6165	248	3	u	u	NOUN
ejpam-6165	248	4	)	)	PUNCT
ejpam-6165	248	5	α	α	PROPN
ejpam-6165	248	6	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	248	7	)	)	PUNCT
ejpam-6165	248	8	∞∑	∞∑	PRON
ejpam-6165	248	9	n=0	n=0	NUM
ejpam-6165	248	10	∂	∂	PUNCT
ejpam-6165	249	1	∂r	∂r	NOUN
ejpam-6165	249	2	be	be	AUX
ejpam-6165	249	3	(	(	PUNCT
ejpam-6165	249	4	k	k	X
ejpam-6165	249	5	,	,	PUNCT
ejpam-6165	249	6	α	α	NOUN
ejpam-6165	249	7	)	)	PUNCT
ejpam-6165	249	8	n	n	CCONJ
ejpam-6165	249	9	(	(	PUNCT
ejpam-6165	249	10	r	r	NOUN
ejpam-6165	249	11	,	,	PUNCT
ejpam-6165	249	12	y;u	y;u	PROPN
ejpam-6165	249	13	,	,	PUNCT
ejpam-6165	249	14	λ	λ	PROPN
ejpam-6165	249	15	)	)	PUNCT
ejpam-6165	249	16	tn	tn	PROPN
ejpam-6165	249	17	n	n	PROPN
ejpam-6165	249	18	!	!	PUNCT
ejpam-6165	250	1	=	=	PUNCT
ejpam-6165	251	1	(	(	PUNCT
ejpam-6165	251	2	lik(1−	lik(1−	PROPN
ejpam-6165	251	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	251	4	)	)	PUNCT
ejpam-6165	251	5	)	)	PUNCT
ejpam-6165	252	1	λet	λet	CCONJ
ejpam-6165	252	2	−	−	PROPN
ejpam-6165	252	3	u	u	NOUN
ejpam-6165	252	4	)	)	PUNCT
ejpam-6165	252	5	α	α	PROPN
ejpam-6165	252	6	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	252	7	)	)	PUNCT
ejpam-6165	252	8	t	t	NOUN
ejpam-6165	252	9	=	=	PUNCT
ejpam-6165	252	10	t	t	PROPN
ejpam-6165	252	11	∞∑	∞∑	PROPN
ejpam-6165	252	12	n=0	n=0	X
ejpam-6165	252	13	be	be	AUX
ejpam-6165	252	14	(	(	PUNCT
ejpam-6165	252	15	k	k	X
ejpam-6165	252	16	,	,	PUNCT
ejpam-6165	252	17	α	α	NOUN
ejpam-6165	252	18	)	)	PUNCT
ejpam-6165	252	19	n	n	CCONJ
ejpam-6165	252	20	(	(	PUNCT
ejpam-6165	252	21	r	r	NOUN
ejpam-6165	252	22	,	,	PUNCT
ejpam-6165	252	23	y;u	y;u	PROPN
ejpam-6165	252	24	,	,	PUNCT
ejpam-6165	252	25	λ	λ	PROPN
ejpam-6165	252	26	)	)	PUNCT
ejpam-6165	252	27	tn	tn	PROPN
ejpam-6165	252	28	n	n	NOUN
ejpam-6165	252	29	!	!	PUNCT
ejpam-6165	252	30	=	=	NOUN
ejpam-6165	253	1	∞∑	∞∑	NOUN
ejpam-6165	253	2	n=0	n=0	NUM
ejpam-6165	253	3	be	be	AUX
ejpam-6165	253	4	(	(	PUNCT
ejpam-6165	253	5	k	k	X
ejpam-6165	253	6	,	,	PUNCT
ejpam-6165	253	7	α	α	NOUN
ejpam-6165	253	8	)	)	PUNCT
ejpam-6165	253	9	n	n	CCONJ
ejpam-6165	253	10	(	(	PUNCT
ejpam-6165	253	11	r	r	NOUN
ejpam-6165	253	12	,	,	PUNCT
ejpam-6165	253	13	y;u	y;u	PROPN
ejpam-6165	253	14	,	,	PUNCT
ejpam-6165	253	15	λ	λ	NOUN
ejpam-6165	253	16	)	)	PUNCT
ejpam-6165	253	17	tn+1	tn+1	NOUN
ejpam-6165	253	18	n	n	X
ejpam-6165	253	19	!	!	PUNCT
ejpam-6165	253	20	=	=	NOUN
ejpam-6165	254	1	∞∑	∞∑	NUM
ejpam-6165	254	2	n=1	n=1	PROPN
ejpam-6165	254	3	nbe	nbe	PROPN
ejpam-6165	254	4	(	(	PUNCT
ejpam-6165	254	5	k	k	X
ejpam-6165	254	6	,	,	PUNCT
ejpam-6165	254	7	α	α	NOUN
ejpam-6165	254	8	)	)	PUNCT
ejpam-6165	254	9	n−1	n−1	PROPN
ejpam-6165	254	10	(	(	PUNCT
ejpam-6165	254	11	r	r	NOUN
ejpam-6165	254	12	,	,	PUNCT
ejpam-6165	254	13	y;u	y;u	PROPN
ejpam-6165	254	14	,	,	PUNCT
ejpam-6165	254	15	λ	λ	PROPN
ejpam-6165	254	16	)	)	PUNCT
ejpam-6165	254	17	tn	tn	PROPN
ejpam-6165	254	18	n	n	NUM
ejpam-6165	254	19	!	!	PUNCT
ejpam-6165	254	20	.	.	PUNCT
ejpam-6165	255	1	comparing	compare	VERB
ejpam-6165	255	2	the	the	DET
ejpam-6165	255	3	coefficients	coefficient	NOUN
ejpam-6165	255	4	of	of	ADP
ejpam-6165	255	5	tn	tn	NOUN
ejpam-6165	255	6	n	n	ADP
ejpam-6165	255	7	!	!	PROPN
ejpam-6165	255	8	completes	complete	VERB
ejpam-6165	255	9	the	the	DET
ejpam-6165	255	10	proof	proof	NOUN
ejpam-6165	255	11	of	of	ADP
ejpam-6165	255	12	the	the	DET
ejpam-6165	255	13	theorem	theorem	PROPN
ejpam-6165	255	14	.	.	PROPN
ejpam-6165	255	15	remark	remark	PROPN
ejpam-6165	255	16	3.6	3.6	NUM
ejpam-6165	255	17	.	.	PUNCT
ejpam-6165	256	1	this	this	DET
ejpam-6165	256	2	relation	relation	NOUN
ejpam-6165	256	3	shows	show	VERB
ejpam-6165	256	4	that	that	PRON
ejpam-6165	256	5	be	be	AUX
ejpam-6165	256	6	(	(	PUNCT
ejpam-6165	256	7	k	k	X
ejpam-6165	256	8	,	,	PUNCT
ejpam-6165	256	9	α	α	NOUN
ejpam-6165	256	10	)	)	PUNCT
ejpam-6165	256	11	n	n	CCONJ
ejpam-6165	256	12	(	(	PUNCT
ejpam-6165	256	13	r	r	NOUN
ejpam-6165	256	14	,	,	PUNCT
ejpam-6165	256	15	y;u	y;u	PROPN
ejpam-6165	256	16	,	,	PUNCT
ejpam-6165	256	17	λ	λ	NOUN
ejpam-6165	256	18	)	)	PUNCT
ejpam-6165	256	19	can	can	AUX
ejpam-6165	256	20	be	be	AUX
ejpam-6165	256	21	classified	classify	VERB
ejpam-6165	256	22	as	as	ADP
ejpam-6165	256	23	an	an	DET
ejpam-6165	256	24	apell	apell	NOUN
ejpam-6165	256	25	polynomial	polynomial	NOUN
ejpam-6165	256	26	.	.	PUNCT
ejpam-6165	257	1	the	the	DET
ejpam-6165	257	2	next	next	ADJ
ejpam-6165	257	3	theorem	theorem	NOUN
ejpam-6165	257	4	contains	contain	VERB
ejpam-6165	257	5	the	the	DET
ejpam-6165	257	6	derivative	derivative	ADJ
ejpam-6165	257	7	formula	formula	NOUN
ejpam-6165	257	8	for	for	ADP
ejpam-6165	257	9	be	be	AUX
ejpam-6165	257	10	(	(	PUNCT
ejpam-6165	257	11	k	k	X
ejpam-6165	257	12	,	,	PUNCT
ejpam-6165	257	13	α	α	NOUN
ejpam-6165	257	14	)	)	PUNCT
ejpam-6165	257	15	j	j	NOUN
ejpam-6165	257	16	(	(	PUNCT
ejpam-6165	257	17	r	r	NOUN
ejpam-6165	257	18	,	,	PUNCT
ejpam-6165	257	19	y;u;λ	y;u;λ	NOUN
ejpam-6165	257	20	)	)	PUNCT
ejpam-6165	257	21	of	of	ADP
ejpam-6165	257	22	order	order	NOUN
ejpam-6165	257	23	α	α	NOUN
ejpam-6165	257	24	with	with	ADP
ejpam-6165	257	25	respect	respect	NOUN
ejpam-6165	257	26	to	to	ADP
ejpam-6165	257	27	y.	y.	PROPN
ejpam-6165	257	28	theorem	theorem	VERB
ejpam-6165	257	29	3.7	3.7	NUM
ejpam-6165	257	30	.	.	PUNCT
ejpam-6165	258	1	the	the	DET
ejpam-6165	258	2	r	r	NOUN
ejpam-6165	258	3	-	-	PUNCT
ejpam-6165	258	4	bell	bell	NOUN
ejpam-6165	258	5	-	-	PUNCT
ejpam-6165	258	6	based	base	VERB
ejpam-6165	258	7	apostol	apostol	NOUN
ejpam-6165	258	8	-	-	PUNCT
ejpam-6165	258	9	frobenius	frobenius	NOUN
ejpam-6165	258	10	-	-	PUNCT
ejpam-6165	258	11	type	type	NOUN
ejpam-6165	258	12	poly	poly	ADJ
ejpam-6165	258	13	-	-	PUNCT
ejpam-6165	258	14	euler	euler	NOUN
ejpam-6165	258	15	polynomials	polynomial	NOUN
ejpam-6165	258	16	be	be	AUX
ejpam-6165	258	17	(	(	PUNCT
ejpam-6165	258	18	k	k	X
ejpam-6165	258	19	,	,	PUNCT
ejpam-6165	258	20	α	α	NOUN
ejpam-6165	258	21	)	)	PUNCT
ejpam-6165	258	22	j	j	NOUN
ejpam-6165	258	23	(	(	PUNCT
ejpam-6165	258	24	r	r	NOUN
ejpam-6165	258	25	,	,	PUNCT
ejpam-6165	258	26	y;u;λ	y;u;λ	NOUN
ejpam-6165	258	27	)	)	PUNCT
ejpam-6165	258	28	of	of	ADP
ejpam-6165	258	29	order	order	NOUN
ejpam-6165	258	30	α	α	PRON
ejpam-6165	258	31	satisfy	satisfy	VERB
ejpam-6165	258	32	the	the	DET
ejpam-6165	258	33	derivative	derivative	ADJ
ejpam-6165	258	34	formula	formula	NOUN
ejpam-6165	258	35	∂	∂	NOUN
ejpam-6165	258	36	∂y	∂y	PRON
ejpam-6165	258	37	be	be	AUX
ejpam-6165	258	38	(	(	PUNCT
ejpam-6165	258	39	k	k	X
ejpam-6165	258	40	,	,	PUNCT
ejpam-6165	258	41	α	α	NOUN
ejpam-6165	258	42	)	)	PUNCT
ejpam-6165	258	43	n	n	CCONJ
ejpam-6165	258	44	(	(	PUNCT
ejpam-6165	258	45	r	r	NOUN
ejpam-6165	258	46	,	,	PUNCT
ejpam-6165	258	47	y;u	y;u	PROPN
ejpam-6165	258	48	,	,	PUNCT
ejpam-6165	258	49	λ	λ	NOUN
ejpam-6165	258	50	)	)	PUNCT
ejpam-6165	258	51	=	=	SYM
ejpam-6165	258	52	n	n	CCONJ
ejpam-6165	258	53	(	(	PUNCT
ejpam-6165	258	54	be	be	AUX
ejpam-6165	258	55	(	(	PUNCT
ejpam-6165	258	56	k	k	X
ejpam-6165	258	57	,	,	PUNCT
ejpam-6165	258	58	α	α	NOUN
ejpam-6165	258	59	)	)	PUNCT
ejpam-6165	258	60	n−1	n−1	PROPN
ejpam-6165	258	61	(	(	PUNCT
ejpam-6165	258	62	r	r	NOUN
ejpam-6165	258	63	+	+	NOUN
ejpam-6165	258	64	1	1	NUM
ejpam-6165	258	65	,	,	PUNCT
ejpam-6165	258	66	y;u	y;u	PROPN
ejpam-6165	258	67	,	,	PUNCT
ejpam-6165	258	68	λ)−	λ)−	X
ejpam-6165	258	69	be	be	AUX
ejpam-6165	258	70	(	(	PUNCT
ejpam-6165	258	71	k	k	X
ejpam-6165	258	72	,	,	PUNCT
ejpam-6165	258	73	α	α	NOUN
ejpam-6165	258	74	)	)	PUNCT
ejpam-6165	258	75	n−1	n−1	PROPN
ejpam-6165	258	76	(	(	PUNCT
ejpam-6165	258	77	r	r	NOUN
ejpam-6165	258	78	,	,	PUNCT
ejpam-6165	258	79	y;u	y;u	PROPN
ejpam-6165	258	80	,	,	PUNCT
ejpam-6165	258	81	λ	λ	NOUN
ejpam-6165	258	82	)	)	PUNCT
ejpam-6165	258	83	)	)	PUNCT
ejpam-6165	258	84	.	.	PUNCT
ejpam-6165	259	1	proof	proof	NOUN
ejpam-6165	259	2	.	.	PUNCT
ejpam-6165	260	1	by	by	ADP
ejpam-6165	260	2	applying	apply	VERB
ejpam-6165	260	3	the	the	DET
ejpam-6165	260	4	first	first	ADJ
ejpam-6165	260	5	derivative	derivative	NOUN
ejpam-6165	260	6	to	to	ADP
ejpam-6165	260	7	both	both	DET
ejpam-6165	260	8	sides	side	NOUN
ejpam-6165	260	9	of	of	ADP
ejpam-6165	260	10	(	(	PUNCT
ejpam-6165	260	11	2.1	2.1	NUM
ejpam-6165	260	12	)	)	PUNCT
ejpam-6165	260	13	with	with	ADP
ejpam-6165	260	14	respect	respect	NOUN
ejpam-6165	260	15	to	to	ADP
ejpam-6165	260	16	y	y	PROPN
ejpam-6165	260	17	,	,	PUNCT
ejpam-6165	260	18	we	we	PRON
ejpam-6165	260	19	have	have	VERB
ejpam-6165	260	20	∞∑	∞∑	NUM
ejpam-6165	260	21	n=0	n=0	NUM
ejpam-6165	260	22	∂	∂	NOUN
ejpam-6165	260	23	∂y	∂y	PRON
ejpam-6165	260	24	be	be	AUX
ejpam-6165	260	25	(	(	PUNCT
ejpam-6165	260	26	k	k	X
ejpam-6165	260	27	,	,	PUNCT
ejpam-6165	260	28	α	α	NOUN
ejpam-6165	260	29	)	)	PUNCT
ejpam-6165	260	30	n	n	CCONJ
ejpam-6165	260	31	(	(	PUNCT
ejpam-6165	260	32	r	r	NOUN
ejpam-6165	260	33	,	,	PUNCT
ejpam-6165	260	34	y;u	y;u	PROPN
ejpam-6165	260	35	,	,	PUNCT
ejpam-6165	260	36	λ	λ	PROPN
ejpam-6165	260	37	)	)	PUNCT
ejpam-6165	260	38	tn	tn	PROPN
ejpam-6165	260	39	n	n	PROPN
ejpam-6165	260	40	!	!	PUNCT
ejpam-6165	261	1	=	=	PUNCT
ejpam-6165	262	1	(	(	PUNCT
ejpam-6165	262	2	lik(1−	lik(1−	PROPN
ejpam-6165	262	3	e−(1−u	e−(1−u	NOUN
ejpam-6165	262	4	)	)	PUNCT
ejpam-6165	262	5	)	)	PUNCT
ejpam-6165	263	1	λet	λet	CCONJ
ejpam-6165	263	2	−	−	PROPN
ejpam-6165	263	3	u	u	NOUN
ejpam-6165	263	4	)	)	PUNCT
ejpam-6165	263	5	α	α	PRON
ejpam-6165	263	6	ert+y(et−1)(et	ert+y(et−1)(et	X
ejpam-6165	263	7	−	−	NOUN
ejpam-6165	263	8	1	1	NUM
ejpam-6165	263	9	)	)	PUNCT
ejpam-6165	263	10	12	12	NUM
ejpam-6165	263	11	of	of	ADP
ejpam-6165	263	12	15	15	NUM
ejpam-6165	263	13	=	=	SYM
ejpam-6165	263	14	(	(	PUNCT
ejpam-6165	263	15	lik(1−	lik(1−	PROPN
ejpam-6165	263	16	e−(1−u	e−(1−u	NOUN
ejpam-6165	263	17	)	)	PUNCT
ejpam-6165	263	18	)	)	PUNCT
ejpam-6165	264	1	λet	λet	CCONJ
ejpam-6165	264	2	−	−	PROPN
ejpam-6165	264	3	u	u	NOUN
ejpam-6165	264	4	)	)	PUNCT
ejpam-6165	264	5	α	α	PROPN
ejpam-6165	264	6	e(r+1)t+y(et−1	e(r+1)t+y(et−1	NOUN
ejpam-6165	264	7	)	)	PUNCT
ejpam-6165	264	8	−	−	PROPN
ejpam-6165	264	9	(	(	PUNCT
ejpam-6165	264	10	lik(1−	lik(1−	PROPN
ejpam-6165	264	11	e−(1−u	e−(1−u	NOUN
ejpam-6165	264	12	)	)	PUNCT
ejpam-6165	264	13	)	)	PUNCT
ejpam-6165	265	1	λet	λet	CCONJ
ejpam-6165	265	2	−	−	PROPN
ejpam-6165	265	3	u	u	NOUN
ejpam-6165	265	4	)	)	PUNCT
ejpam-6165	265	5	α	α	PROPN
ejpam-6165	265	6	ert+y(et−1	ert+y(et−1	NOUN
ejpam-6165	265	7	)	)	PUNCT
ejpam-6165	265	8	=	=	PUNCT
ejpam-6165	266	1	∞∑	∞∑	NOUN
ejpam-6165	266	2	n=0	n=0	NUM
ejpam-6165	266	3	be	be	AUX
ejpam-6165	266	4	(	(	PUNCT
ejpam-6165	266	5	k	k	X
ejpam-6165	266	6	,	,	PUNCT
ejpam-6165	266	7	α	α	NOUN
ejpam-6165	266	8	)	)	PUNCT
ejpam-6165	266	9	n	n	CCONJ
ejpam-6165	266	10	(	(	PUNCT
ejpam-6165	266	11	r	r	NOUN
ejpam-6165	266	12	+	+	NOUN
ejpam-6165	266	13	1	1	NUM
ejpam-6165	266	14	,	,	PUNCT
ejpam-6165	266	15	y;u	y;u	PROPN
ejpam-6165	266	16	,	,	PUNCT
ejpam-6165	266	17	λ	λ	PROPN
ejpam-6165	266	18	)	)	PUNCT
ejpam-6165	266	19	tn	tn	PROPN
ejpam-6165	266	20	n	n	PROPN
ejpam-6165	266	21	!	!	PUNCT
ejpam-6165	266	22	−	−	ADP
ejpam-6165	267	1	∞∑	∞∑	PRON
ejpam-6165	267	2	n=0	n=0	X
ejpam-6165	267	3	be	be	AUX
ejpam-6165	267	4	(	(	PUNCT
ejpam-6165	267	5	k	k	X
ejpam-6165	267	6	,	,	PUNCT
ejpam-6165	267	7	α	α	NOUN
ejpam-6165	267	8	)	)	PUNCT
ejpam-6165	267	9	n	n	CCONJ
ejpam-6165	267	10	(	(	PUNCT
ejpam-6165	267	11	r	r	NOUN
ejpam-6165	267	12	,	,	PUNCT
ejpam-6165	267	13	y;u	y;u	PROPN
ejpam-6165	267	14	,	,	PUNCT
ejpam-6165	267	15	λ	λ	PROPN
ejpam-6165	267	16	)	)	PUNCT
ejpam-6165	267	17	tn	tn	PROPN
ejpam-6165	267	18	n	n	NOUN
ejpam-6165	267	19	!	!	PUNCT
ejpam-6165	267	20	=	=	NOUN
ejpam-6165	268	1	∞∑	∞∑	PRON
ejpam-6165	268	2	n=0	n=0	PUNCT
ejpam-6165	268	3	{	{	PUNCT
ejpam-6165	268	4	be	be	AUX
ejpam-6165	268	5	(	(	PUNCT
ejpam-6165	268	6	k	k	X
ejpam-6165	268	7	,	,	PUNCT
ejpam-6165	268	8	α	α	NOUN
ejpam-6165	268	9	)	)	PUNCT
ejpam-6165	268	10	n	n	CCONJ
ejpam-6165	268	11	(	(	PUNCT
ejpam-6165	268	12	r	r	NOUN
ejpam-6165	268	13	+	+	NOUN
ejpam-6165	268	14	1	1	NUM
ejpam-6165	268	15	,	,	PUNCT
ejpam-6165	268	16	y;u	y;u	PROPN
ejpam-6165	268	17	,	,	PUNCT
ejpam-6165	268	18	λ)−	λ)−	X
ejpam-6165	268	19	be	be	AUX
ejpam-6165	268	20	(	(	PUNCT
ejpam-6165	268	21	k	k	X
ejpam-6165	268	22	,	,	PUNCT
ejpam-6165	268	23	α	α	NOUN
ejpam-6165	268	24	)	)	PUNCT
ejpam-6165	268	25	n	n	CCONJ
ejpam-6165	268	26	(	(	PUNCT
ejpam-6165	268	27	r	r	NOUN
ejpam-6165	268	28	,	,	PUNCT
ejpam-6165	268	29	y;u	y;u	PROPN
ejpam-6165	268	30	,	,	PUNCT
ejpam-6165	268	31	λ	λ	NOUN
ejpam-6165	268	32	)	)	PUNCT
ejpam-6165	268	33	}	}	PUNCT
ejpam-6165	268	34	tn+1	tn+1	NOUN
ejpam-6165	268	35	n	n	CCONJ
ejpam-6165	268	36	!	!	PUNCT
ejpam-6165	268	37	=	=	NOUN
ejpam-6165	269	1	∞∑	∞∑	NUM
ejpam-6165	269	2	n=1	n=1	PROPN
ejpam-6165	269	3	n	n	PROPN
ejpam-6165	269	4	(	(	PUNCT
ejpam-6165	269	5	be	be	AUX
ejpam-6165	269	6	(	(	PUNCT
ejpam-6165	269	7	k	k	X
ejpam-6165	269	8	,	,	PUNCT
ejpam-6165	269	9	α	α	NOUN
ejpam-6165	269	10	)	)	PUNCT
ejpam-6165	269	11	n−1	n−1	PROPN
ejpam-6165	269	12	(	(	PUNCT
ejpam-6165	269	13	r	r	NOUN
ejpam-6165	269	14	+	+	NOUN
ejpam-6165	269	15	1	1	NUM
ejpam-6165	269	16	,	,	PUNCT
ejpam-6165	269	17	y;u	y;u	PROPN
ejpam-6165	269	18	,	,	PUNCT
ejpam-6165	269	19	λ)−	λ)−	X
ejpam-6165	269	20	be	be	AUX
ejpam-6165	269	21	(	(	PUNCT
ejpam-6165	269	22	k	k	X
ejpam-6165	269	23	,	,	PUNCT
ejpam-6165	269	24	α	α	NOUN
ejpam-6165	269	25	)	)	PUNCT
ejpam-6165	269	26	n−1	n−1	PROPN
ejpam-6165	269	27	(	(	PUNCT
ejpam-6165	269	28	r	r	NOUN
ejpam-6165	269	29	,	,	PUNCT
ejpam-6165	269	30	y;u	y;u	PROPN
ejpam-6165	269	31	,	,	PUNCT
ejpam-6165	269	32	λ	λ	NOUN
ejpam-6165	269	33	)	)	PUNCT
ejpam-6165	269	34	)	)	PUNCT
ejpam-6165	269	35	tn	tn	PROPN
ejpam-6165	269	36	n	n	PROPN
ejpam-6165	269	37	!	!	PUNCT
ejpam-6165	269	38	.	.	PUNCT
ejpam-6165	270	1	comparing	compare	VERB
ejpam-6165	270	2	the	the	DET
ejpam-6165	270	3	coefficients	coefficient	NOUN
ejpam-6165	270	4	of	of	ADP
ejpam-6165	270	5	tn	tn	NOUN
ejpam-6165	270	6	n	n	ADP
ejpam-6165	270	7	!	!	PROPN
ejpam-6165	270	8	completes	complete	VERB
ejpam-6165	270	9	the	the	DET
ejpam-6165	270	10	proof	proof	NOUN
ejpam-6165	270	11	of	of	ADP
ejpam-6165	270	12	the	the	DET
ejpam-6165	270	13	theorem	theorem	NOUN
ejpam-6165	270	14	.	.	PROPN
ejpam-6165	270	15	4	4	X
ejpam-6165	270	16	.	.	X
ejpam-6165	270	17	conclusion	conclusion	NOUN
ejpam-6165	270	18	this	this	DET
ejpam-6165	270	19	study	study	NOUN
ejpam-6165	270	20	introduces	introduce	VERB
ejpam-6165	270	21	a	a	DET
ejpam-6165	270	22	novel	novel	ADJ
ejpam-6165	270	23	class	class	NOUN
ejpam-6165	270	24	of	of	ADP
ejpam-6165	270	25	frobenius	frobenius	NOUN
ejpam-6165	270	26	-	-	PUNCT
ejpam-6165	270	27	euler	euler	NOUN
ejpam-6165	270	28	polynomials	polynomial	NOUN
ejpam-6165	270	29	by	by	ADP
ejpam-6165	270	30	leveraging	leverage	VERB
ejpam-6165	270	31	the	the	DET
ejpam-6165	270	32	mathematical	mathematical	ADJ
ejpam-6165	270	33	structures	structure	NOUN
ejpam-6165	270	34	of	of	ADP
ejpam-6165	270	35	bell	bell	NOUN
ejpam-6165	270	36	numbers	number	NOUN
ejpam-6165	270	37	,	,	PUNCT
ejpam-6165	270	38	apostol	apostol	NOUN
ejpam-6165	270	39	-	-	PUNCT
ejpam-6165	270	40	type	type	NOUN
ejpam-6165	270	41	functions	function	NOUN
ejpam-6165	270	42	,	,	PUNCT
ejpam-6165	270	43	and	and	CCONJ
ejpam-6165	270	44	the	the	DET
ejpam-6165	270	45	polylogarithm	polylogarithm	PROPN
ejpam-6165	270	46	concept	concept	NOUN
ejpam-6165	270	47	.	.	PUNCT
ejpam-6165	271	1	through	through	ADP
ejpam-6165	271	2	rigorous	rigorous	ADJ
ejpam-6165	271	3	analytical	analytical	ADJ
ejpam-6165	271	4	methods	method	NOUN
ejpam-6165	271	5	,	,	PUNCT
ejpam-6165	271	6	we	we	PRON
ejpam-6165	271	7	have	have	AUX
ejpam-6165	271	8	successfully	successfully	ADV
ejpam-6165	271	9	derived	derive	VERB
ejpam-6165	271	10	generating	generating	NOUN
ejpam-6165	271	11	functions	function	NOUN
ejpam-6165	271	12	that	that	PRON
ejpam-6165	271	13	serve	serve	VERB
ejpam-6165	271	14	as	as	ADP
ejpam-6165	271	15	powerful	powerful	ADJ
ejpam-6165	271	16	tools	tool	NOUN
ejpam-6165	271	17	in	in	ADP
ejpam-6165	271	18	understanding	understand	VERB
ejpam-6165	271	19	higher	high	ADJ
ejpam-6165	271	20	-	-	PUNCT
ejpam-6165	271	21	order	order	NOUN
ejpam-6165	271	22	apostol	apostol	NOUN
ejpam-6165	271	23	-	-	PUNCT
ejpam-6165	271	24	frobeniustype	frobeniustype	NOUN
ejpam-6165	271	25	poly	poly	ADJ
ejpam-6165	271	26	-	-	PUNCT
ejpam-6165	271	27	euler	euler	NOUN
ejpam-6165	271	28	polynomials	polynomial	NOUN
ejpam-6165	271	29	.	.	PUNCT
ejpam-6165	272	1	these	these	DET
ejpam-6165	272	2	generating	generate	VERB
ejpam-6165	272	3	functions	function	NOUN
ejpam-6165	272	4	facilitate	facilitate	VERB
ejpam-6165	272	5	the	the	DET
ejpam-6165	272	6	formulation	formulation	NOUN
ejpam-6165	272	7	of	of	ADP
ejpam-6165	272	8	both	both	CCONJ
ejpam-6165	272	9	explicit	explicit	ADJ
ejpam-6165	272	10	and	and	CCONJ
ejpam-6165	272	11	implicit	implicit	ADJ
ejpam-6165	272	12	summation	summation	NOUN
ejpam-6165	272	13	formulas	formula	NOUN
ejpam-6165	272	14	,	,	PUNCT
ejpam-6165	272	15	which	which	PRON
ejpam-6165	272	16	further	far	ADV
ejpam-6165	272	17	contribute	contribute	VERB
ejpam-6165	272	18	to	to	ADP
ejpam-6165	272	19	the	the	DET
ejpam-6165	272	20	mathematical	mathematical	ADJ
ejpam-6165	272	21	characterization	characterization	NOUN
ejpam-6165	272	22	of	of	ADP
ejpam-6165	272	23	these	these	DET
ejpam-6165	272	24	polynomials	polynomial	NOUN
ejpam-6165	272	25	.	.	PUNCT
ejpam-6165	273	1	additionally	additionally	ADV
ejpam-6165	273	2	,	,	PUNCT
ejpam-6165	273	3	the	the	DET
ejpam-6165	273	4	study	study	NOUN
ejpam-6165	273	5	establishes	establish	VERB
ejpam-6165	273	6	symmetric	symmetric	ADJ
ejpam-6165	273	7	identities	identity	NOUN
ejpam-6165	273	8	that	that	PRON
ejpam-6165	273	9	reveal	reveal	VERB
ejpam-6165	273	10	deep	deep	ADJ
ejpam-6165	273	11	interconnections	interconnection	NOUN
ejpam-6165	273	12	among	among	ADP
ejpam-6165	273	13	these	these	DET
ejpam-6165	273	14	polynomials	polynomial	NOUN
ejpam-6165	273	15	,	,	PUNCT
ejpam-6165	273	16	highlighting	highlight	VERB
ejpam-6165	273	17	their	their	PRON
ejpam-6165	273	18	structural	structural	ADJ
ejpam-6165	273	19	complexity	complexity	NOUN
ejpam-6165	273	20	and	and	CCONJ
ejpam-6165	273	21	mathematical	mathematical	ADJ
ejpam-6165	273	22	significance	significance	NOUN
ejpam-6165	273	23	.	.	PUNCT
ejpam-6165	274	1	these	these	DET
ejpam-6165	274	2	identities	identity	NOUN
ejpam-6165	274	3	not	not	PART
ejpam-6165	274	4	only	only	ADV
ejpam-6165	274	5	enhance	enhance	VERB
ejpam-6165	274	6	the	the	DET
ejpam-6165	274	7	understanding	understanding	NOUN
ejpam-6165	274	8	of	of	ADP
ejpam-6165	274	9	polynomial	polynomial	ADJ
ejpam-6165	274	10	relationships	relationship	NOUN
ejpam-6165	274	11	but	but	CCONJ
ejpam-6165	274	12	also	also	ADV
ejpam-6165	274	13	provide	provide	VERB
ejpam-6165	274	14	a	a	DET
ejpam-6165	274	15	unified	unified	ADJ
ejpam-6165	274	16	framework	framework	NOUN
ejpam-6165	274	17	for	for	ADP
ejpam-6165	274	18	exploring	explore	VERB
ejpam-6165	274	19	new	new	ADJ
ejpam-6165	274	20	properties	property	NOUN
ejpam-6165	274	21	and	and	CCONJ
ejpam-6165	274	22	potential	potential	ADJ
ejpam-6165	274	23	generalizations	generalization	NOUN
ejpam-6165	274	24	.	.	PUNCT
ejpam-6165	275	1	the	the	DET
ejpam-6165	275	2	integration	integration	NOUN
ejpam-6165	275	3	of	of	ADP
ejpam-6165	275	4	these	these	DET
ejpam-6165	275	5	mathematical	mathematical	ADJ
ejpam-6165	275	6	components	component	NOUN
ejpam-6165	275	7	offers	offer	VERB
ejpam-6165	275	8	fresh	fresh	ADJ
ejpam-6165	275	9	insights	insight	NOUN
ejpam-6165	275	10	into	into	ADP
ejpam-6165	275	11	combinatorial	combinatorial	ADJ
ejpam-6165	275	12	and	and	CCONJ
ejpam-6165	275	13	algebraic	algebraic	ADJ
ejpam-6165	275	14	mathematics	mathematic	NOUN
ejpam-6165	275	15	,	,	PUNCT
ejpam-6165	275	16	broadening	broaden	VERB
ejpam-6165	275	17	the	the	DET
ejpam-6165	275	18	scope	scope	NOUN
ejpam-6165	275	19	of	of	ADP
ejpam-6165	275	20	applications	application	NOUN
ejpam-6165	275	21	for	for	ADP
ejpam-6165	275	22	poly	poly	ADJ
ejpam-6165	275	23	-	-	PUNCT
ejpam-6165	275	24	euler	euler	NOUN
ejpam-6165	275	25	polynomials	polynomial	NOUN
ejpam-6165	275	26	in	in	ADP
ejpam-6165	275	27	various	various	ADJ
ejpam-6165	275	28	domains	domain	NOUN
ejpam-6165	275	29	,	,	PUNCT
ejpam-6165	275	30	such	such	ADJ
ejpam-6165	275	31	as	as	ADP
ejpam-6165	275	32	number	number	NOUN
ejpam-6165	275	33	theory	theory	NOUN
ejpam-6165	275	34	,	,	PUNCT
ejpam-6165	275	35	discrete	discrete	ADJ
ejpam-6165	275	36	mathematics	mathematic	NOUN
ejpam-6165	275	37	,	,	PUNCT
ejpam-6165	275	38	and	and	CCONJ
ejpam-6165	275	39	computational	computational	ADJ
ejpam-6165	275	40	algebra	algebra	NOUN
ejpam-6165	275	41	.	.	PUNCT
ejpam-6165	276	1	the	the	DET
ejpam-6165	276	2	results	result	NOUN
ejpam-6165	276	3	of	of	ADP
ejpam-6165	276	4	this	this	DET
ejpam-6165	276	5	study	study	NOUN
ejpam-6165	276	6	serve	serve	VERB
ejpam-6165	276	7	as	as	ADP
ejpam-6165	276	8	a	a	DET
ejpam-6165	276	9	foundation	foundation	NOUN
ejpam-6165	276	10	for	for	ADP
ejpam-6165	276	11	further	further	ADJ
ejpam-6165	276	12	theoretical	theoretical	ADJ
ejpam-6165	276	13	developments	development	NOUN
ejpam-6165	276	14	,	,	PUNCT
ejpam-6165	276	15	inviting	invite	VERB
ejpam-6165	276	16	future	future	ADJ
ejpam-6165	276	17	research	research	NOUN
ejpam-6165	276	18	to	to	PART
ejpam-6165	276	19	extend	extend	VERB
ejpam-6165	276	20	these	these	DET
ejpam-6165	276	21	findings	finding	NOUN
ejpam-6165	276	22	into	into	ADP
ejpam-6165	276	23	new	new	ADJ
ejpam-6165	276	24	mathematical	mathematical	ADJ
ejpam-6165	276	25	territories	territory	NOUN
ejpam-6165	276	26	,	,	PUNCT
ejpam-6165	276	27	including	include	VERB
ejpam-6165	276	28	special	special	ADJ
ejpam-6165	276	29	functions	function	NOUN
ejpam-6165	276	30	,	,	PUNCT
ejpam-6165	276	31	recurrence	recurrence	NOUN
ejpam-6165	276	32	relations	relation	NOUN
ejpam-6165	276	33	,	,	PUNCT
ejpam-6165	276	34	and	and	CCONJ
ejpam-6165	276	35	their	their	PRON
ejpam-6165	276	36	computational	computational	ADJ
ejpam-6165	276	37	applications	application	NOUN
ejpam-6165	276	38	.	.	PUNCT
ejpam-6165	277	1	references	reference	NOUN
ejpam-6165	277	2	[	[	X
ejpam-6165	277	3	1	1	NUM
ejpam-6165	277	4	]	]	PUNCT
ejpam-6165	277	5	m.	m.	NOUN
ejpam-6165	277	6	abramowitz	abramowitz	PROPN
ejpam-6165	277	7	and	and	CCONJ
ejpam-6165	277	8	i.a	i.a	PROPN
ejpam-6165	277	9	.	.	PROPN
ejpam-6165	277	10	stegun	stegun	PROPN
ejpam-6165	277	11	,	,	PUNCT
ejpam-6165	277	12	handbook	handbook	NOUN
ejpam-6165	277	13	of	of	ADP
ejpam-6165	277	14	mathematical	mathematical	ADJ
ejpam-6165	277	15	functions	function	NOUN
ejpam-6165	277	16	,	,	PUNCT
ejpam-6165	277	17	dover	dover	PROPN
ejpam-6165	277	18	,	,	PUNCT
ejpam-6165	277	19	new	new	PROPN
ejpam-6165	277	20	york	york	PROPN
ejpam-6165	277	21	,	,	PUNCT
ejpam-6165	277	22	1970	1970	NUM
ejpam-6165	277	23	.	.	PUNCT
ejpam-6165	278	1	[	[	X
ejpam-6165	278	2	2	2	NUM
ejpam-6165	278	3	]	]	X
ejpam-6165	278	4	agoh	agoh	PROPN
ejpam-6165	278	5	t.	t.	PROPN
ejpam-6165	278	6	,	,	PUNCT
ejpam-6165	278	7	convolution	convolution	NOUN
ejpam-6165	278	8	identities	identity	NOUN
ejpam-6165	278	9	for	for	ADP
ejpam-6165	278	10	benoulli	benoulli	NOUN
ejpam-6165	278	11	and	and	CCONJ
ejpam-6165	278	12	genocchi	genocchi	PROPN
ejpam-6165	278	13	polynomials	polynomial	NOUN
ejpam-6165	278	14	,	,	PUNCT
ejpam-6165	278	15	electronic	electronic	ADJ
ejpam-6165	278	16	j.	j.	PROPN
ejpam-6165	278	17	combin	combin	PROPN
ejpam-6165	278	18	.	.	PROPN
ejpam-6165	279	1	21	21	NUM
ejpam-6165	279	2	(	(	PUNCT
ejpam-6165	279	3	2014	2014	NUM
ejpam-6165	279	4	)	)	PUNCT
ejpam-6165	279	5	,	,	PUNCT
ejpam-6165	279	6	article	article	NOUN
ejpam-6165	279	7	i	i	PROPN
ejpam-6165	279	8	d	d	PROPN
ejpam-6165	279	9	p1.65	p1.65	PROPN
ejpam-6165	279	10	.	.	PROPN
ejpam-6165	279	11	13	13	NUM
ejpam-6165	279	12	of	of	ADP
ejpam-6165	279	13	15	15	NUM
ejpam-6165	279	14	[	[	SYM
ejpam-6165	279	15	3	3	NUM
ejpam-6165	279	16	]	]	X
ejpam-6165	279	17	alam	alam	PROPN
ejpam-6165	279	18	,	,	PUNCT
ejpam-6165	279	19	n.	n.	PROPN
ejpam-6165	279	20	,	,	PUNCT
ejpam-6165	279	21	khan	khan	PROPN
ejpam-6165	279	22	,	,	PUNCT
ejpam-6165	279	23	w.a	w.a	PROPN
ejpam-6165	279	24	.	.	PROPN
ejpam-6165	279	25	,	,	PUNCT
ejpam-6165	279	26	and	and	CCONJ
ejpam-6165	279	27	ryoo	ryoo	NOUN
ejpam-6165	279	28	,	,	PUNCT
ejpam-6165	279	29	c.s	c.s	PROPN
ejpam-6165	279	30	.	.	PROPN
ejpam-6165	279	31	,	,	PUNCT
ejpam-6165	279	32	a	a	DET
ejpam-6165	279	33	note	note	NOUN
ejpam-6165	279	34	on	on	ADP
ejpam-6165	279	35	bell	bell	NOUN
ejpam-6165	279	36	-	-	PUNCT
ejpam-6165	279	37	based	base	VERB
ejpam-6165	279	38	apostol	apostol	NOUN
ejpam-6165	279	39	-	-	PUNCT
ejpam-6165	279	40	type	type	NOUN
ejpam-6165	279	41	frobenius	frobenius	NOUN
ejpam-6165	279	42	-	-	PUNCT
ejpam-6165	279	43	euler	euler	NOUN
ejpam-6165	279	44	polynomials	polynomial	NOUN
ejpam-6165	279	45	of	of	ADP
ejpam-6165	279	46	complex	complex	ADJ
ejpam-6165	279	47	variable	variable	NOUN
ejpam-6165	279	48	with	with	ADP
ejpam-6165	279	49	its	its	PRON
ejpam-6165	279	50	certain	certain	ADJ
ejpam-6165	279	51	applications	application	NOUN
ejpam-6165	279	52	,	,	PUNCT
ejpam-6165	279	53	mathematics	mathematic	NOUN
ejpam-6165	279	54	,	,	PUNCT
ejpam-6165	279	55	2022	2022	NUM
ejpam-6165	279	56	,	,	PUNCT
ejpam-6165	279	57	10(12	10(12	NUM
ejpam-6165	279	58	)	)	PUNCT
ejpam-6165	279	59	,	,	PUNCT
ejpam-6165	279	60	2109	2109	NUM
ejpam-6165	279	61	.	.	PUNCT
ejpam-6165	280	1	[	[	X
ejpam-6165	280	2	4	4	NUM
ejpam-6165	280	3	]	]	X
ejpam-6165	280	4	alam	alam	PROPN
ejpam-6165	280	5	,	,	PUNCT
ejpam-6165	280	6	n.	n.	PROPN
ejpam-6165	280	7	,	,	PUNCT
ejpam-6165	280	8	khan	khan	PROPN
ejpam-6165	280	9	,	,	PUNCT
ejpam-6165	280	10	w.	w.	PROPN
ejpam-6165	280	11	a.	a.	PROPN
ejpam-6165	280	12	,	,	PUNCT
ejpam-6165	280	13	obeidat	obeidat	NOUN
ejpam-6165	280	14	,	,	PUNCT
ejpam-6165	280	15	s.	s.	PROPN
ejpam-6165	280	16	,	,	PUNCT
ejpam-6165	280	17	muhiuddin	muhiuddin	PROPN
ejpam-6165	280	18	,	,	PUNCT
ejpam-6165	280	19	g.	g.	PROPN
ejpam-6165	280	20	,	,	PUNCT
ejpam-6165	280	21	diab	diab	PROPN
ejpam-6165	280	22	,	,	PUNCT
ejpam-6165	280	23	n.s	n.s	PROPN
ejpam-6165	280	24	.	.	PROPN
ejpam-6165	280	25	,	,	PUNCT
ejpam-6165	280	26	zaidi	zaidi	PROPN
ejpam-6165	280	27	,	,	PUNCT
ejpam-6165	280	28	h.n	h.n	PROPN
ejpam-6165	280	29	.	.	PROPN
ejpam-6165	280	30	,	,	PUNCT
ejpam-6165	280	31	altaleb	altaleb	PROPN
ejpam-6165	280	32	,	,	PUNCT
ejpam-6165	280	33	a.	a.	NOUN
ejpam-6165	280	34	and	and	CCONJ
ejpam-6165	280	35	bachioua	bachioua	PROPN
ejpam-6165	280	36	,	,	PUNCT
ejpam-6165	280	37	l.	l.	PROPN
ejpam-6165	280	38	,	,	PUNCT
ejpam-6165	280	39	a	a	DET
ejpam-6165	280	40	note	note	NOUN
ejpam-6165	280	41	on	on	ADP
ejpam-6165	280	42	bell	bell	NOUN
ejpam-6165	280	43	-	-	PUNCT
ejpam-6165	280	44	based	base	VERB
ejpam-6165	280	45	bernoulli	bernoulli	NOUN
ejpam-6165	280	46	and	and	CCONJ
ejpam-6165	280	47	euler	euler	NOUN
ejpam-6165	280	48	polynomials	polynomial	NOUN
ejpam-6165	280	49	of	of	ADP
ejpam-6165	280	50	complex	complex	ADJ
ejpam-6165	280	51	variable	variable	NOUN
ejpam-6165	280	52	.	.	PUNCT
ejpam-6165	281	1	computer	computer	NOUN
ejpam-6165	281	2	modelling	modelling	NOUN
ejpam-6165	281	3	in	in	ADP
ejpam-6165	281	4	engineering	engineering	NOUN
ejpam-6165	281	5	and	and	CCONJ
ejpam-6165	281	6	sciences	science	NOUN
ejpam-6165	281	7	.	.	PUNCT
ejpam-6165	282	1	153(1	153(1	NUM
ejpam-6165	282	2	)	)	PUNCT
ejpam-6165	282	3	(	(	PUNCT
ejpam-6165	282	4	2023),187	2023),187	NUM
ejpam-6165	282	5	-	-	SYM
ejpam-6165	282	6	209	209	NUM
ejpam-6165	282	7	.	.	PUNCT
ejpam-6165	283	1	[	[	X
ejpam-6165	283	2	5	5	NUM
ejpam-6165	283	3	]	]	X
ejpam-6165	283	4	alam	alam	PROPN
ejpam-6165	283	5	,	,	PUNCT
ejpam-6165	283	6	n.	n.	PROPN
ejpam-6165	283	7	,	,	PUNCT
ejpam-6165	283	8	khan	khan	PROPN
ejpam-6165	283	9	,	,	PUNCT
ejpam-6165	283	10	w.a	w.a	PROPN
ejpam-6165	283	11	.	.	PROPN
ejpam-6165	283	12	,	,	PUNCT
ejpam-6165	283	13	kizilates	kizilates	PROPN
ejpam-6165	283	14	,	,	PUNCT
ejpam-6165	283	15	c.	c.	PROPN
ejpam-6165	283	16	,	,	PUNCT
ejpam-6165	283	17	obeidat	obeidat	NOUN
ejpam-6165	283	18	,	,	PUNCT
ejpam-6165	283	19	s.	s.	PROPN
ejpam-6165	283	20	,	,	PUNCT
ejpam-6165	283	21	ryoo	ryoo	PROPN
ejpam-6165	283	22	,	,	PUNCT
ejpam-6165	283	23	c.s	c.s	PROPN
ejpam-6165	283	24	.	.	PROPN
ejpam-6165	283	25	and	and	CCONJ
ejpam-6165	283	26	diab	diab	PROPN
ejpam-6165	283	27	,	,	PUNCT
ejpam-6165	283	28	n.s	n.s	PROPN
ejpam-6165	283	29	.	.	PROPN
ejpam-6165	283	30	,	,	PUNCT
ejpam-6165	283	31	some	some	DET
ejpam-6165	283	32	explicit	explicit	ADJ
ejpam-6165	283	33	properties	property	NOUN
ejpam-6165	283	34	of	of	ADP
ejpam-6165	283	35	frobenius	frobenius	NOUN
ejpam-6165	283	36	-	-	PUNCT
ejpam-6165	283	37	euler	euler	NOUN
ejpam-6165	283	38	-	-	PUNCT
ejpam-6165	283	39	genocchi	genocchi	PROPN
ejpam-6165	283	40	polynomials	polynomial	VERB
ejpam-6165	283	41	with	with	ADP
ejpam-6165	283	42	applications	application	NOUN
ejpam-6165	283	43	in	in	ADP
ejpam-6165	283	44	computer	computer	NOUN
ejpam-6165	283	45	modeling	modeling	NOUN
ejpam-6165	283	46	.	.	PUNCT
ejpam-6165	284	1	symmetry	symmetry	NOUN
ejpam-6165	284	2	,	,	PUNCT
ejpam-6165	284	3	(	(	PUNCT
ejpam-6165	284	4	2023	2023	NUM
ejpam-6165	284	5	)	)	PUNCT
ejpam-6165	284	6	,	,	PUNCT
ejpam-6165	284	7	15:1358	15:1358	NUM
ejpam-6165	284	8	,	,	PUNCT
ejpam-6165	284	9	1	1	NUM
ejpam-6165	284	10	-	-	SYM
ejpam-6165	284	11	20	20	NUM
ejpam-6165	284	12	.	.	PUNCT
ejpam-6165	285	1	[	[	X
ejpam-6165	285	2	6	6	NUM
ejpam-6165	285	3	]	]	X
ejpam-6165	285	4	appell	appell	ADV
ejpam-6165	285	5	,	,	PUNCT
ejpam-6165	285	6	p.	p.	NOUN
ejpam-6165	285	7	and	and	CCONJ
ejpam-6165	285	8	kampé	kampé	PROPN
ejpam-6165	285	9	de	de	PROPN
ejpam-6165	285	10	fériet	fériet	PROPN
ejpam-6165	285	11	,	,	PUNCT
ejpam-6165	285	12	j.	j.	PROPN
ejpam-6165	285	13	,	,	PUNCT
ejpam-6165	285	14	polynome	polynome	NOUN
ejpam-6165	285	15	d’hermite	d’hermite	NOUN
ejpam-6165	285	16	,	,	PUNCT
ejpam-6165	285	17	fonctions	fonction	NOUN
ejpam-6165	285	18	hypergéométriques	hypergéométrique	VERB
ejpam-6165	285	19	et	et	NOUN
ejpam-6165	285	20	hyperspheriques	hyperspherique	NOUN
ejpam-6165	285	21	,	,	PUNCT
ejpam-6165	285	22	gauthier	gauthier	NOUN
ejpam-6165	285	23	-	-	PUNCT
ejpam-6165	285	24	villars	villar	NOUN
ejpam-6165	285	25	,	,	PUNCT
ejpam-6165	285	26	paris	paris	PROPN
ejpam-6165	285	27	,	,	PUNCT
ejpam-6165	285	28	1926	1926	NUM
ejpam-6165	285	29	.	.	PUNCT
ejpam-6165	286	1	[	[	X
ejpam-6165	286	2	7	7	X
ejpam-6165	286	3	]	]	PUNCT
ejpam-6165	286	4	apostol	apostol	NOUN
ejpam-6165	286	5	t.m	t.m	PROPN
ejpam-6165	286	6	.	.	PROPN
ejpam-6165	286	7	,	,	PUNCT
ejpam-6165	286	8	on	on	ADP
ejpam-6165	286	9	the	the	DET
ejpam-6165	286	10	lerch	lerch	PROPN
ejpam-6165	286	11	zeta	zeta	PROPN
ejpam-6165	286	12	function	function	PROPN
ejpam-6165	286	13	,	,	PUNCT
ejpam-6165	286	14	pacific	pacific	PROPN
ejpam-6165	286	15	j.	j.	PROPN
ejpam-6165	286	16	math	math	PROPN
ejpam-6165	286	17	.	.	PUNCT
ejpam-6165	287	1	1	1	NUM
ejpam-6165	287	2	(	(	PUNCT
ejpam-6165	287	3	1951	1951	NUM
ejpam-6165	287	4	)	)	PUNCT
ejpam-6165	287	5	,	,	PUNCT
ejpam-6165	287	6	161–167	161–167	NUM
ejpam-6165	287	7	.	.	PUNCT
ejpam-6165	288	1	[	[	X
ejpam-6165	288	2	8	8	NUM
ejpam-6165	288	3	]	]	X
ejpam-6165	288	4	araci	araci	NOUN
ejpam-6165	288	5	,	,	PUNCT
ejpam-6165	288	6	s.	s.	PROPN
ejpam-6165	288	7	,	,	PUNCT
ejpam-6165	288	8	novel	novel	ADJ
ejpam-6165	288	9	identities	identity	NOUN
ejpam-6165	288	10	involving	involve	VERB
ejpam-6165	288	11	genocchi	genocchi	PROPN
ejpam-6165	288	12	numbers	number	NOUN
ejpam-6165	288	13	and	and	CCONJ
ejpam-6165	288	14	polynomials	polynomial	NOUN
ejpam-6165	288	15	arising	arise	VERB
ejpam-6165	288	16	from	from	ADP
ejpam-6165	288	17	application	application	NOUN
ejpam-6165	288	18	of	of	ADP
ejpam-6165	288	19	umbral	umbral	ADJ
ejpam-6165	288	20	calculus	calculus	NOUN
ejpam-6165	288	21	,	,	PUNCT
ejpam-6165	288	22	appl	appl	PROPN
ejpam-6165	288	23	.	.	PROPN
ejpam-6165	288	24	math	math	PROPN
ejpam-6165	288	25	.	.	PUNCT
ejpam-6165	289	1	comput	comput	NOUN
ejpam-6165	289	2	.	.	PUNCT
ejpam-6165	289	3	,	,	PUNCT
ejpam-6165	289	4	233(2014	233(2014	NUM
ejpam-6165	289	5	)	)	PUNCT
ejpam-6165	289	6	,	,	PUNCT
ejpam-6165	289	7	599–607	599–607	NUM
ejpam-6165	289	8	.	.	PUNCT
ejpam-6165	290	1	[	[	X
ejpam-6165	290	2	9	9	NUM
ejpam-6165	290	3	]	]	X
ejpam-6165	290	4	araci	araci	NOUN
ejpam-6165	290	5	,	,	PUNCT
ejpam-6165	290	6	s.	s.	PROPN
ejpam-6165	290	7	,	,	PUNCT
ejpam-6165	290	8	sen	sen	PROPN
ejpam-6165	290	9	,	,	PUNCT
ejpam-6165	290	10	e.	e.	PROPN
ejpam-6165	290	11	,	,	PUNCT
ejpam-6165	290	12	and	and	CCONJ
ejpam-6165	290	13	acikgoz	acikgoz	ADJ
ejpam-6165	290	14	,	,	PUNCT
ejpam-6165	290	15	m.	m.	NOUN
ejpam-6165	290	16	,	,	PUNCT
ejpam-6165	290	17	theorems	theorem	NOUN
ejpam-6165	290	18	on	on	ADP
ejpam-6165	290	19	genocchi	genocchi	PROPN
ejpam-6165	290	20	polynomials	polynomial	NOUN
ejpam-6165	290	21	of	of	ADP
ejpam-6165	290	22	higher	high	ADJ
ejpam-6165	290	23	order	order	NOUN
ejpam-6165	290	24	arising	arise	VERB
ejpam-6165	290	25	from	from	ADP
ejpam-6165	290	26	genocchi	genocchi	PROPN
ejpam-6165	290	27	basis	basis	NOUN
ejpam-6165	290	28	,	,	PUNCT
ejpam-6165	290	29	taiwanese	taiwanese	PROPN
ejpam-6165	290	30	j.	j.	PROPN
ejpam-6165	290	31	math	math	PROPN
ejpam-6165	290	32	.	.	PUNCT
ejpam-6165	291	1	math	math	NOUN
ejpam-6165	291	2	.	.	PUNCT
ejpam-6165	292	1	sci	sci	PROPN
ejpam-6165	292	2	.	.	PROPN
ejpam-6165	292	3	,	,	PUNCT
ejpam-6165	292	4	18(2	18(2	NUM
ejpam-6165	292	5	)	)	PUNCT
ejpam-6165	292	6	(	(	PUNCT
ejpam-6165	292	7	2014	2014	NUM
ejpam-6165	292	8	)	)	PUNCT
ejpam-6165	292	9	,	,	PUNCT
ejpam-6165	292	10	473–482	473–482	NUM
ejpam-6165	292	11	.	.	PUNCT
ejpam-6165	293	1	[	[	X
ejpam-6165	293	2	10	10	NUM
ejpam-6165	293	3	]	]	X
ejpam-6165	293	4	araci	araci	NOUN
ejpam-6165	293	5	,	,	PUNCT
ejpam-6165	293	6	s.	s.	PROPN
ejpam-6165	293	7	,	,	PUNCT
ejpam-6165	293	8	khan	khan	PROPN
ejpam-6165	293	9	,	,	PUNCT
ejpam-6165	293	10	w.a	w.a	PROPN
ejpam-6165	293	11	.	.	PROPN
ejpam-6165	293	12	,	,	PUNCT
ejpam-6165	293	13	acikgoz	acikgoz	ADJ
ejpam-6165	293	14	,	,	PUNCT
ejpam-6165	293	15	m.	m.	NOUN
ejpam-6165	293	16	,	,	PUNCT
ejpam-6165	293	17	ozel	ozel	NOUN
ejpam-6165	293	18	,	,	PUNCT
ejpam-6165	293	19	c.	c.	PROPN
ejpam-6165	293	20	and	and	CCONJ
ejpam-6165	293	21	kumam	kumam	PROPN
ejpam-6165	293	22	,	,	PUNCT
ejpam-6165	293	23	p.	p.	PROPN
ejpam-6165	293	24	,	,	PUNCT
ejpam-6165	293	25	a	a	DET
ejpam-6165	293	26	new	new	ADJ
ejpam-6165	293	27	generaliztion	generaliztion	NOUN
ejpam-6165	293	28	of	of	ADP
ejpam-6165	293	29	apostol	apostol	PROPN
ejpam-6165	293	30	type	type	NOUN
ejpam-6165	293	31	hermite	hermite	PROPN
ejpam-6165	293	32	-	-	PUNCT
ejpam-6165	293	33	genocchi	genocchi	PROPN
ejpam-6165	293	34	polynomials	polynomial	NOUN
ejpam-6165	293	35	and	and	CCONJ
ejpam-6165	293	36	its	its	PRON
ejpam-6165	293	37	applications	application	NOUN
ejpam-6165	293	38	,	,	PUNCT
ejpam-6165	293	39	springerplus	springerplus	NOUN
ejpam-6165	293	40	,	,	PUNCT
ejpam-6165	293	41	5(2016	5(2016	NUM
ejpam-6165	293	42	)	)	PUNCT
ejpam-6165	293	43	,	,	PUNCT
ejpam-6165	293	44	art	art	NOUN
ejpam-6165	293	45	.	.	PUNCT
ejpam-6165	294	1	i	i	PRON
ejpam-6165	294	2	d	d	PROPN
ejpam-6165	294	3	860	860	NUM
ejpam-6165	294	4	.	.	PUNCT
ejpam-6165	295	1	[	[	X
ejpam-6165	295	2	11	11	NUM
ejpam-6165	295	3	]	]	X
ejpam-6165	295	4	araci	araci	NOUN
ejpam-6165	295	5	,	,	PUNCT
ejpam-6165	295	6	s.	s.	PROPN
ejpam-6165	295	7	,	,	PUNCT
ejpam-6165	295	8	acikgoz	acikgoz	ADJ
ejpam-6165	295	9	,	,	PUNCT
ejpam-6165	295	10	m.	m.	NOUN
ejpam-6165	295	11	and	and	CCONJ
ejpam-6165	295	12	sen	sen	PROPN
ejpam-6165	295	13	,	,	PUNCT
ejpam-6165	295	14	e.	e.	PROPN
ejpam-6165	295	15	,	,	PUNCT
ejpam-6165	295	16	some	some	DET
ejpam-6165	295	17	new	new	ADJ
ejpam-6165	295	18	formulae	formulae	NOUN
ejpam-6165	295	19	for	for	ADP
ejpam-6165	295	20	genocchi	genocchi	PROPN
ejpam-6165	295	21	numbers	number	NOUN
ejpam-6165	295	22	and	and	CCONJ
ejpam-6165	295	23	polynomials	polynomial	NOUN
ejpam-6165	295	24	involving	involve	VERB
ejpam-6165	295	25	benoulli	benoulli	NOUN
ejpam-6165	295	26	and	and	CCONJ
ejpam-6165	295	27	euler	euler	NOUN
ejpam-6165	295	28	polynomials	polynomial	NOUN
ejpam-6165	295	29	,	,	PUNCT
ejpam-6165	295	30	int	int	NOUN
ejpam-6165	295	31	.	.	PUNCT
ejpam-6165	296	1	j.	j.	PROPN
ejpam-6165	296	2	math	math	PROPN
ejpam-6165	296	3	.	.	PUNCT
ejpam-6165	297	1	sci	sci	PROPN
ejpam-6165	297	2	.	.	PROPN
ejpam-6165	297	3	,	,	PUNCT
ejpam-6165	297	4	2014(2014	2014(2014	NUM
ejpam-6165	297	5	)	)	PUNCT
ejpam-6165	297	6	,	,	PUNCT
ejpam-6165	297	7	article	article	NOUN
ejpam-6165	297	8	i	i	PROPN
ejpam-6165	297	9	d	d	PROPN
ejpam-6165	297	10	760613	760613	NUM
ejpam-6165	297	11	.	.	PUNCT
ejpam-6165	298	1	[	[	X
ejpam-6165	298	2	12	12	NUM
ejpam-6165	298	3	]	]	PUNCT
ejpam-6165	298	4	ayed	aye	VERB
ejpam-6165	298	5	,	,	PUNCT
ejpam-6165	298	6	a.	a.	PROPN
ejpam-6165	298	7	,	,	PUNCT
ejpam-6165	298	8	khan	khan	PROPN
ejpam-6165	298	9	,	,	PUNCT
ejpam-6165	298	10	w.a	w.a	PROPN
ejpam-6165	298	11	.	.	PROPN
ejpam-6165	298	12	,	,	PUNCT
ejpam-6165	298	13	ryoo	ryoo	NOUN
ejpam-6165	298	14	,	,	PUNCT
ejpam-6165	298	15	c.s	c.s	PROPN
ejpam-6165	298	16	.	.	PROPN
ejpam-6165	298	17	,	,	PUNCT
ejpam-6165	298	18	certain	certain	ADJ
ejpam-6165	298	19	properties	property	NOUN
ejpam-6165	298	20	on	on	ADP
ejpam-6165	298	21	bell	bell	NOUN
ejpam-6165	298	22	-	-	PUNCT
ejpam-6165	298	23	based	base	VERB
ejpam-6165	298	24	apostol	apostol	NOUN
ejpam-6165	298	25	-	-	PUNCT
ejpam-6165	298	26	type	type	NOUN
ejpam-6165	298	27	frobenius	frobenius	NOUN
ejpam-6165	298	28	-	-	PUNCT
ejpam-6165	298	29	genocchi	genocchi	NOUN
ejpam-6165	298	30	polynomials	polynomial	NOUN
ejpam-6165	298	31	and	and	CCONJ
ejpam-6165	298	32	its	its	PRON
ejpam-6165	298	33	applications	application	NOUN
ejpam-6165	298	34	.	.	PUNCT
ejpam-6165	299	1	advanced	advanced	ADJ
ejpam-6165	299	2	mathematical	mathematical	ADJ
ejpam-6165	299	3	models	model	NOUN
ejpam-6165	299	4	and	and	CCONJ
ejpam-6165	299	5	applications	application	NOUN
ejpam-6165	299	6	,	,	PUNCT
ejpam-6165	299	7	1(8	1(8	NUM
ejpam-6165	299	8	)	)	PUNCT
ejpam-6165	299	9	(	(	PUNCT
ejpam-6165	299	10	2023	2023	NUM
ejpam-6165	299	11	)	)	PUNCT
ejpam-6165	299	12	,	,	PUNCT
ejpam-6165	299	13	92	92	NUM
ejpam-6165	299	14	-	-	SYM
ejpam-6165	299	15	107	107	NUM
ejpam-6165	299	16	.	.	PUNCT
ejpam-6165	300	1	[	[	X
ejpam-6165	300	2	13	13	NUM
ejpam-6165	300	3	]	]	PUNCT
ejpam-6165	300	4	ayed	aye	VERB
ejpam-6165	300	5	,	,	PUNCT
ejpam-6165	300	6	a.	a.	PROPN
ejpam-6165	300	7	,	,	PUNCT
ejpam-6165	300	8	khan	khan	PROPN
ejpam-6165	300	9	,	,	PUNCT
ejpam-6165	300	10	w.a	w.a	PROPN
ejpam-6165	300	11	.	.	PROPN
ejpam-6165	300	12	,	,	PUNCT
ejpam-6165	300	13	ryoo	ryoo	NOUN
ejpam-6165	300	14	,	,	PUNCT
ejpam-6165	300	15	c.s	c.s	PROPN
ejpam-6165	300	16	.	.	PROPN
ejpam-6165	300	17	,	,	PUNCT
ejpam-6165	300	18	certain	certain	ADJ
ejpam-6165	300	19	properties	property	NOUN
ejpam-6165	300	20	on	on	ADP
ejpam-6165	300	21	bell	bell	NOUN
ejpam-6165	300	22	based	base	VERB
ejpam-6165	300	23	apostolfrobenius	apostolfrobenius	NOUN
ejpam-6165	300	24	-	-	PUNCT
ejpam-6165	300	25	genocchi	genocchi	PROPN
ejpam-6165	300	26	polynomials	polynomial	NOUN
ejpam-6165	300	27	of	of	ADP
ejpam-6165	300	28	complex	complex	ADJ
ejpam-6165	300	29	variables	variable	NOUN
ejpam-6165	300	30	.	.	PUNCT
ejpam-6165	301	1	journal	journal	NOUN
ejpam-6165	301	2	of	of	ADP
ejpam-6165	301	3	mathematics	mathematic	NOUN
ejpam-6165	301	4	and	and	CCONJ
ejpam-6165	301	5	computer	computer	NOUN
ejpam-6165	301	6	science	science	NOUN
ejpam-6165	301	7	,	,	PUNCT
ejpam-6165	301	8	33(3	33(3	NOUN
ejpam-6165	301	9	)	)	PUNCT
ejpam-6165	301	10	(	(	PUNCT
ejpam-6165	301	11	2024	2024	NUM
ejpam-6165	301	12	)	)	PUNCT
ejpam-6165	301	13	,	,	PUNCT
ejpam-6165	301	14	326	326	NUM
ejpam-6165	301	15	-	-	SYM
ejpam-6165	301	16	338	338	NUM
ejpam-6165	301	17	.	.	PUNCT
ejpam-6165	302	1	[	[	X
ejpam-6165	302	2	14	14	NUM
ejpam-6165	302	3	]	]	X
ejpam-6165	302	4	bayad	bayad	NOUN
ejpam-6165	302	5	,	,	PUNCT
ejpam-6165	302	6	a.	a.	NOUN
ejpam-6165	302	7	and	and	CCONJ
ejpam-6165	302	8	hamahata	hamahata	PROPN
ejpam-6165	302	9	,	,	PUNCT
ejpam-6165	302	10	y.	y.	NOUN
ejpam-6165	302	11	,	,	PUNCT
ejpam-6165	302	12	polylogarithms	polylogarithm	NOUN
ejpam-6165	302	13	and	and	CCONJ
ejpam-6165	302	14	poly	poly	ADJ
ejpam-6165	302	15	-	-	PUNCT
ejpam-6165	302	16	bernoulli	bernoulli	NOUN
ejpam-6165	302	17	polynomials	polynomial	NOUN
ejpam-6165	302	18	,	,	PUNCT
ejpam-6165	302	19	kyushu	kyushu	PROPN
ejpam-6165	302	20	j.	j.	PROPN
ejpam-6165	302	21	math	math	PROPN
ejpam-6165	302	22	,	,	PUNCT
ejpam-6165	302	23	65(2011	65(2011	NUM
ejpam-6165	302	24	)	)	PUNCT
ejpam-6165	302	25	,	,	PUNCT
ejpam-6165	302	26	15–24	15–24	NUM
ejpam-6165	302	27	.	.	PUNCT
ejpam-6165	303	1	[	[	X
ejpam-6165	303	2	15	15	NUM
ejpam-6165	303	3	]	]	X
ejpam-6165	303	4	comtet	comtet	NOUN
ejpam-6165	303	5	,	,	PUNCT
ejpam-6165	303	6	l.	l.	PROPN
ejpam-6165	303	7	(	(	PUNCT
ejpam-6165	303	8	1974	1974	NUM
ejpam-6165	303	9	)	)	PUNCT
ejpam-6165	303	10	.	.	PUNCT
ejpam-6165	304	1	advanced	advanced	ADJ
ejpam-6165	304	2	combinatorics	combinatoric	NOUN
ejpam-6165	304	3	,	,	PUNCT
ejpam-6165	304	4	reidel	reidel	PROPN
ejpam-6165	304	5	,	,	PUNCT
ejpam-6165	304	6	dordrecht	dordrecht	PROPN
ejpam-6165	304	7	,	,	PUNCT
ejpam-6165	304	8	the	the	DET
ejpam-6165	304	9	netherlands	netherlands	PROPN
ejpam-6165	304	10	.	.	PUNCT
ejpam-6165	305	1	[	[	X
ejpam-6165	305	2	16	16	NUM
ejpam-6165	305	3	]	]	X
ejpam-6165	305	4	corcino	corcino	NOUN
ejpam-6165	305	5	,	,	PUNCT
ejpam-6165	305	6	c.	c.	PROPN
ejpam-6165	305	7	and	and	CCONJ
ejpam-6165	305	8	corcino	corcino	PROPN
ejpam-6165	305	9	,	,	PUNCT
ejpam-6165	305	10	r.	r.	PROPN
ejpam-6165	305	11	,	,	PUNCT
ejpam-6165	305	12	higher	high	ADJ
ejpam-6165	305	13	order	order	NOUN
ejpam-6165	305	14	apostol	apostol	NOUN
ejpam-6165	305	15	-	-	PUNCT
ejpam-6165	305	16	type	type	NOUN
ejpam-6165	305	17	poly	poly	ADJ
ejpam-6165	305	18	-	-	PUNCT
ejpam-6165	305	19	genocchi	genocchi	NOUN
ejpam-6165	305	20	polynomials	polynomial	NOUN
ejpam-6165	305	21	with	with	ADP
ejpam-6165	305	22	parameters	parameter	NOUN
ejpam-6165	305	23	a	a	PRON
ejpam-6165	305	24	,	,	PUNCT
ejpam-6165	305	25	b	b	PROPN
ejpam-6165	305	26	and	and	CCONJ
ejpam-6165	305	27	c	c	NOUN
ejpam-6165	305	28	,	,	PUNCT
ejpam-6165	305	29	communication	communication	NOUN
ejpam-6165	305	30	of	of	ADP
ejpam-6165	305	31	the	the	DET
ejpam-6165	305	32	korean	korean	ADJ
ejpam-6165	305	33	mathematical	mathematical	ADJ
ejpam-6165	305	34	society	society	NOUN
ejpam-6165	305	35	,	,	PUNCT
ejpam-6165	305	36	volume	volume	NOUN
ejpam-6165	305	37	36(3	36(3	NUM
ejpam-6165	305	38	)	)	PUNCT
ejpam-6165	305	39	(	(	PUNCT
ejpam-6165	305	40	2021	2021	NUM
ejpam-6165	305	41	)	)	PUNCT
ejpam-6165	305	42	,	,	PUNCT
ejpam-6165	305	43	423	423	NUM
ejpam-6165	305	44	-	-	SYM
ejpam-6165	305	45	445	445	NUM
ejpam-6165	305	46	.	.	PUNCT
ejpam-6165	306	1	[	[	X
ejpam-6165	306	2	17	17	NUM
ejpam-6165	306	3	]	]	X
ejpam-6165	306	4	corcino	corcino	NOUN
ejpam-6165	306	5	,	,	PUNCT
ejpam-6165	306	6	r.	r.	PROPN
ejpam-6165	306	7	and	and	CCONJ
ejpam-6165	306	8	corcino	corcino	PROPN
ejpam-6165	306	9	,	,	PUNCT
ejpam-6165	306	10	c.	c.	PROPN
ejpam-6165	306	11	,	,	PUNCT
ejpam-6165	306	12	generalized	generalize	VERB
ejpam-6165	306	13	laguerre	laguerre	NOUN
ejpam-6165	306	14	-	-	PUNCT
ejpam-6165	306	15	apostol	apostol	NOUN
ejpam-6165	306	16	-	-	PUNCT
ejpam-6165	306	17	frobenius	frobenius	NOUN
ejpam-6165	306	18	-	-	PUNCT
ejpam-6165	306	19	type	type	NOUN
ejpam-6165	306	20	polygenocchi	polygenocchi	ADJ
ejpam-6165	306	21	polynomials	polynomial	NOUN
ejpam-6165	306	22	of	of	ADP
ejpam-6165	306	23	higher	high	ADJ
ejpam-6165	306	24	order	order	NOUN
ejpam-6165	306	25	with	with	ADP
ejpam-6165	306	26	parameters	parameter	NOUN
ejpam-6165	306	27	a	a	PRON
ejpam-6165	306	28	,	,	PUNCT
ejpam-6165	306	29	b	b	PROPN
ejpam-6165	306	30	and	and	CCONJ
ejpam-6165	306	31	c	c	NOUN
ejpam-6165	306	32	,	,	PUNCT
ejpam-6165	306	33	european	european	ADJ
ejpam-6165	306	34	journal	journal	PROPN
ejpam-6165	306	35	of	of	ADP
ejpam-6165	306	36	pure	pure	ADJ
ejpam-6165	306	37	and	and	CCONJ
ejpam-6165	306	38	applied	apply	VERB
ejpam-6165	306	39	mathematics,15(4	mathematics,15(4	PROPN
ejpam-6165	306	40	)	)	PUNCT
ejpam-6165	306	41	(	(	PUNCT
ejpam-6165	306	42	2022	2022	NUM
ejpam-6165	306	43	)	)	PUNCT
ejpam-6165	306	44	,	,	PUNCT
ejpam-6165	306	45	1549	1549	NUM
ejpam-6165	306	46	-	-	SYM
ejpam-6165	306	47	1565	1565	NUM
ejpam-6165	306	48	.	.	PUNCT
ejpam-6165	307	1	[	[	X
ejpam-6165	307	2	18	18	NUM
ejpam-6165	307	3	]	]	X
ejpam-6165	307	4	corcino	corcino	NOUN
ejpam-6165	307	5	,	,	PUNCT
ejpam-6165	307	6	r.	r.	PROPN
ejpam-6165	307	7	and	and	CCONJ
ejpam-6165	307	8	corcino	corcino	PROPN
ejpam-6165	307	9	,	,	PUNCT
ejpam-6165	307	10	c.	c.	NOUN
ejpam-6165	307	11	,	,	PUNCT
ejpam-6165	307	12	degenerate	degenerate	ADJ
ejpam-6165	307	13	apostol	apostol	NOUN
ejpam-6165	307	14	-	-	PUNCT
ejpam-6165	307	15	frobenius	frobenius	NOUN
ejpam-6165	307	16	-	-	PUNCT
ejpam-6165	307	17	type	type	NOUN
ejpam-6165	307	18	poly	poly	ADJ
ejpam-6165	307	19	-	-	PUNCT
ejpam-6165	307	20	genocchi	genocchi	NOUN
ejpam-6165	307	21	polynomials	polynomial	NOUN
ejpam-6165	307	22	of	of	ADP
ejpam-6165	307	23	higher	high	ADJ
ejpam-6165	307	24	order	order	NOUN
ejpam-6165	307	25	with	with	ADP
ejpam-6165	307	26	parameters	parameter	NOUN
ejpam-6165	307	27	a	a	PRON
ejpam-6165	307	28	and	and	CCONJ
ejpam-6165	307	29	b	b	NOUN
ejpam-6165	307	30	,	,	PUNCT
ejpam-6165	307	31	european	european	ADJ
ejpam-6165	307	32	journal	journal	PROPN
ejpam-6165	307	33	of	of	ADP
ejpam-6165	307	34	pure	pure	ADJ
ejpam-6165	307	35	and	and	CCONJ
ejpam-6165	307	36	applied	applied	ADJ
ejpam-6165	307	37	mathematics	mathematic	NOUN
ejpam-6165	307	38	,	,	PUNCT
ejpam-6165	307	39	16(2	16(2	NUM
ejpam-6165	307	40	)	)	PUNCT
ejpam-6165	307	41	(	(	PUNCT
ejpam-6165	307	42	2023	2023	NUM
ejpam-6165	307	43	)	)	PUNCT
ejpam-6165	307	44	,	,	PUNCT
ejpam-6165	307	45	687	687	NUM
ejpam-6165	307	46	-	-	SYM
ejpam-6165	307	47	712	712	NUM
ejpam-6165	307	48	.	.	PUNCT
ejpam-6165	308	1	[	[	X
ejpam-6165	308	2	19	19	NUM
ejpam-6165	308	3	]	]	X
ejpam-6165	308	4	corcino	corcino	NOUN
ejpam-6165	308	5	,	,	PUNCT
ejpam-6165	308	6	r.	r.	PROPN
ejpam-6165	308	7	,	,	PUNCT
ejpam-6165	308	8	corcino	corcino	PROPN
ejpam-6165	308	9	,	,	PUNCT
ejpam-6165	308	10	c.	c.	PROPN
ejpam-6165	308	11	,	,	PUNCT
ejpam-6165	308	12	casas	casas	PROPN
ejpam-6165	308	13	,	,	PUNCT
ejpam-6165	308	14	k.	k.	PROPN
ejpam-6165	308	15	,	,	PUNCT
ejpam-6165	308	16	elnar	elnar	PROPN
ejpam-6165	308	17	,	,	PUNCT
ejpam-6165	308	18	a.	a.	NOUN
ejpam-6165	308	19	,	,	PUNCT
ejpam-6165	308	20	maglasang	maglasang	PROPN
ejpam-6165	308	21	,	,	PUNCT
ejpam-6165	308	22	g.	g.	PROPN
ejpam-6165	308	23	,	,	PUNCT
ejpam-6165	308	24	construction	construction	NOUN
ejpam-6165	308	25	of	of	ADP
ejpam-6165	308	26	fourier	fourier	ADJ
ejpam-6165	308	27	series	series	NOUN
ejpam-6165	308	28	expansion	expansion	NOUN
ejpam-6165	308	29	of	of	ADP
ejpam-6165	308	30	apostol	apostol	NOUN
ejpam-6165	308	31	-	-	PUNCT
ejpam-6165	308	32	frobenius	frobenius	NOUN
ejpam-6165	308	33	-	-	PUNCT
ejpam-6165	308	34	type	type	NOUN
ejpam-6165	308	35	tangent	tangent	NOUN
ejpam-6165	308	36	and	and	CCONJ
ejpam-6165	308	37	genocchi	genocchi	PROPN
ejpam-6165	308	38	polynomials	polynomial	NOUN
ejpam-6165	308	39	of	of	ADP
ejpam-6165	308	40	14	14	NUM
ejpam-6165	308	41	of	of	ADP
ejpam-6165	308	42	15	15	NUM
ejpam-6165	308	43	higher	high	ADJ
ejpam-6165	308	44	-	-	PUNCT
ejpam-6165	308	45	order	order	NOUN
ejpam-6165	308	46	,	,	PUNCT
ejpam-6165	308	47	european	european	ADJ
ejpam-6165	308	48	journal	journal	NOUN
ejpam-6165	308	49	of	of	ADP
ejpam-6165	308	50	pure	pure	ADJ
ejpam-6165	308	51	and	and	CCONJ
ejpam-6165	308	52	applied	applied	ADJ
ejpam-6165	308	53	mathematics	mathematic	NOUN
ejpam-6165	308	54	,	,	PUNCT
ejpam-6165	308	55	16(2	16(2	NUM
ejpam-6165	308	56	)	)	PUNCT
ejpam-6165	308	57	(	(	PUNCT
ejpam-6165	308	58	2023	2023	NUM
ejpam-6165	308	59	)	)	PUNCT
ejpam-6165	308	60	,	,	PUNCT
ejpam-6165	308	61	1005	1005	NUM
ejpam-6165	308	62	-	-	SYM
ejpam-6165	308	63	1023	1023	NUM
ejpam-6165	308	64	.	.	PUNCT
ejpam-6165	309	1	[	[	X
ejpam-6165	309	2	20	20	NUM
ejpam-6165	309	3	]	]	SYM
ejpam-6165	309	4	corcino	corcino	NOUN
ejpam-6165	309	5	,	,	PUNCT
ejpam-6165	309	6	r.	r.	PROPN
ejpam-6165	309	7	and	and	CCONJ
ejpam-6165	309	8	corcino	corcino	PROPN
ejpam-6165	309	9	,	,	PUNCT
ejpam-6165	309	10	c.	c.	NOUN
ejpam-6165	309	11	,	,	PUNCT
ejpam-6165	309	12	higher	high	ADJ
ejpam-6165	309	13	order	order	NOUN
ejpam-6165	309	14	apostol	apostol	NOUN
ejpam-6165	309	15	-	-	PUNCT
ejpam-6165	309	16	frobenius	frobenius	NOUN
ejpam-6165	309	17	-	-	PUNCT
ejpam-6165	309	18	type	type	NOUN
ejpam-6165	309	19	poly	poly	ADJ
ejpam-6165	309	20	-	-	PUNCT
ejpam-6165	309	21	genocchi	genocchi	NOUN
ejpam-6165	309	22	polynomials	polynomial	NOUN
ejpam-6165	309	23	with	with	ADP
ejpam-6165	309	24	parameters	parameter	NOUN
ejpam-6165	309	25	a	a	PRON
ejpam-6165	309	26	,	,	PUNCT
ejpam-6165	309	27	b	b	PROPN
ejpam-6165	309	28	and	and	CCONJ
ejpam-6165	309	29	c	c	NOUN
ejpam-6165	309	30	,	,	PUNCT
ejpam-6165	309	31	journal	journal	NOUN
ejpam-6165	309	32	of	of	ADP
ejpam-6165	309	33	inequalities	inequality	NOUN
ejpam-6165	309	34	and	and	CCONJ
ejpam-6165	309	35	special	special	ADJ
ejpam-6165	309	36	functions	function	NOUN
ejpam-6165	309	37	,	,	PUNCT
ejpam-6165	309	38	12(3	12(3	NUM
ejpam-6165	309	39	)	)	PUNCT
ejpam-6165	309	40	(	(	PUNCT
ejpam-6165	309	41	2021	2021	NUM
ejpam-6165	309	42	)	)	PUNCT
ejpam-6165	309	43	,	,	PUNCT
ejpam-6165	309	44	54–72	54–72	NUM
ejpam-6165	309	45	.	.	PUNCT
ejpam-6165	310	1	[	[	X
ejpam-6165	310	2	21	21	NUM
ejpam-6165	310	3	]	]	X
ejpam-6165	310	4	he	he	PRON
ejpam-6165	310	5	,	,	PUNCT
ejpam-6165	310	6	y.	y.	PROPN
ejpam-6165	310	7	,	,	PUNCT
ejpam-6165	310	8	araci	araci	PROPN
ejpam-6165	310	9	s.	s.	PROPN
ejpam-6165	310	10	,	,	PUNCT
ejpam-6165	310	11	srivastava	srivastava	PROPN
ejpam-6165	310	12	h.m	h.m	PROPN
ejpam-6165	310	13	.	.	PROPN
ejpam-6165	310	14	and	and	CCONJ
ejpam-6165	310	15	acikgoz	acikgoz	ADJ
ejpam-6165	310	16	m.	m.	NOUN
ejpam-6165	310	17	,	,	PUNCT
ejpam-6165	310	18	some	some	DET
ejpam-6165	310	19	new	new	ADJ
ejpam-6165	310	20	identities	identity	NOUN
ejpam-6165	310	21	for	for	ADP
ejpam-6165	310	22	the	the	DET
ejpam-6165	310	23	apostol	apostol	NOUN
ejpam-6165	310	24	-	-	PUNCT
ejpam-6165	310	25	bernoulli	bernoulli	NOUN
ejpam-6165	310	26	polynomials	polynomial	NOUN
ejpam-6165	310	27	and	and	CCONJ
ejpam-6165	310	28	the	the	DET
ejpam-6165	310	29	apostol	apostol	NOUN
ejpam-6165	310	30	-	-	PUNCT
ejpam-6165	310	31	genocchi	genocchi	PROPN
ejpam-6165	310	32	polynomials	polynomial	NOUN
ejpam-6165	310	33	,	,	PUNCT
ejpam-6165	310	34	appl	appl	PROPN
ejpam-6165	310	35	.	.	PROPN
ejpam-6165	310	36	math	math	NOUN
ejpam-6165	310	37	.	.	PUNCT
ejpam-6165	311	1	comput	comput	NOUN
ejpam-6165	311	2	.	.	PUNCT
ejpam-6165	312	1	262	262	NUM
ejpam-6165	312	2	(	(	PUNCT
ejpam-6165	312	3	2015	2015	NUM
ejpam-6165	312	4	)	)	PUNCT
ejpam-6165	312	5	,	,	PUNCT
ejpam-6165	312	6	31	31	NUM
ejpam-6165	312	7	-	-	SYM
ejpam-6165	312	8	41	41	NUM
ejpam-6165	312	9	.	.	PUNCT
ejpam-6165	313	1	[	[	X
ejpam-6165	313	2	22	22	NUM
ejpam-6165	313	3	]	]	PUNCT
ejpam-6165	313	4	he	he	PRON
ejpam-6165	313	5	,	,	PUNCT
ejpam-6165	313	6	y.	y.	PROPN
ejpam-6165	313	7	,	,	PUNCT
ejpam-6165	313	8	some	some	DET
ejpam-6165	313	9	new	new	ADJ
ejpam-6165	313	10	results	result	NOUN
ejpam-6165	313	11	on	on	ADP
ejpam-6165	313	12	products	product	NOUN
ejpam-6165	313	13	of	of	ADP
ejpam-6165	313	14	the	the	DET
ejpam-6165	313	15	apostol	apostol	NOUN
ejpam-6165	313	16	-	-	PUNCT
ejpam-6165	313	17	genocchi	genocchi	PROPN
ejpam-6165	313	18	polynomials	polynomial	NOUN
ejpam-6165	313	19	,	,	PUNCT
ejpam-6165	313	20	j.	j.	PROPN
ejpam-6165	313	21	comput	comput	PROPN
ejpam-6165	313	22	.	.	PUNCT
ejpam-6165	314	1	anal	anal	PROPN
ejpam-6165	314	2	.	.	PUNCT
ejpam-6165	314	3	appl	appl	PROPN
ejpam-6165	314	4	.	.	PUNCT
ejpam-6165	315	1	22	22	NUM
ejpam-6165	315	2	(	(	PUNCT
ejpam-6165	315	3	4	4	NUM
ejpam-6165	315	4	)	)	PUNCT
ejpam-6165	315	5	(	(	PUNCT
ejpam-6165	315	6	2017	2017	NUM
ejpam-6165	315	7	)	)	PUNCT
ejpam-6165	315	8	,	,	PUNCT
ejpam-6165	315	9	591	591	NUM
ejpam-6165	315	10	-	-	SYM
ejpam-6165	315	11	600	600	NUM
ejpam-6165	315	12	.	.	PUNCT
ejpam-6165	316	1	[	[	X
ejpam-6165	316	2	23	23	NUM
ejpam-6165	316	3	]	]	PUNCT
ejpam-6165	316	4	he	he	PRON
ejpam-6165	316	5	,	,	PUNCT
ejpam-6165	316	6	y.	y.	PROPN
ejpam-6165	316	7	and	and	CCONJ
ejpam-6165	316	8	kim	kim	PROPN
ejpam-6165	316	9	,	,	PUNCT
ejpam-6165	316	10	t.	t.	PROPN
ejpam-6165	316	11	,	,	PUNCT
ejpam-6165	316	12	general	general	ADJ
ejpam-6165	316	13	convolution	convolution	NOUN
ejpam-6165	316	14	identities	identity	NOUN
ejpam-6165	316	15	of	of	ADP
ejpam-6165	316	16	apostol	apostol	NOUN
ejpam-6165	316	17	-	-	PUNCT
ejpam-6165	316	18	bernoulli	bernoulli	PROPN
ejpam-6165	316	19	,	,	PUNCT
ejpam-6165	316	20	euler	euler	NOUN
ejpam-6165	316	21	and	and	CCONJ
ejpam-6165	316	22	genocchi	genocchi	PROPN
ejpam-6165	316	23	polynomials	polynomial	NOUN
ejpam-6165	316	24	,	,	PUNCT
ejpam-6165	316	25	j.	j.	PROPN
ejpam-6165	316	26	nonlinear	nonlinear	PROPN
ejpam-6165	316	27	sci	sci	PROPN
ejpam-6165	316	28	.	.	PUNCT
ejpam-6165	316	29	appl	appl	PROPN
ejpam-6165	316	30	.	.	PROPN
ejpam-6165	317	1	9	9	NUM
ejpam-6165	317	2	(	(	PUNCT
ejpam-6165	317	3	2016	2016	NUM
ejpam-6165	317	4	)	)	PUNCT
ejpam-6165	317	5	,	,	PUNCT
ejpam-6165	317	6	4780	4780	NUM
ejpam-6165	317	7	-	-	SYM
ejpam-6165	317	8	4797	4797	NUM
ejpam-6165	317	9	.	.	PUNCT
ejpam-6165	318	1	[	[	X
ejpam-6165	318	2	24	24	NUM
ejpam-6165	318	3	]	]	SYM
ejpam-6165	318	4	hu	hu	PROPN
ejpam-6165	318	5	,	,	PUNCT
ejpam-6165	318	6	s.	s.	PROPN
ejpam-6165	318	7	,	,	PUNCT
ejpam-6165	318	8	kim	kim	PROPN
ejpam-6165	318	9	,	,	PUNCT
ejpam-6165	318	10	d.	d.	PROPN
ejpam-6165	318	11	and	and	CCONJ
ejpam-6165	318	12	kim	kim	PROPN
ejpam-6165	318	13	,	,	PUNCT
ejpam-6165	318	14	m.s	m.s	PROPN
ejpam-6165	318	15	.	.	PROPN
ejpam-6165	318	16	,	,	PUNCT
ejpam-6165	318	17	new	new	ADJ
ejpam-6165	318	18	identities	identity	NOUN
ejpam-6165	318	19	involving	involve	VERB
ejpam-6165	318	20	bernoulli	bernoulli	PROPN
ejpam-6165	318	21	,	,	PUNCT
ejpam-6165	318	22	euler	euler	NOUN
ejpam-6165	318	23	and	and	CCONJ
ejpam-6165	318	24	genocchi	genocchi	PROPN
ejpam-6165	318	25	numbers	number	NOUN
ejpam-6165	318	26	,	,	PUNCT
ejpam-6165	318	27	advances	advance	NOUN
ejpam-6165	318	28	in	in	ADP
ejpam-6165	318	29	difference	difference	NOUN
ejpam-6165	318	30	equations	equation	NOUN
ejpam-6165	318	31	,	,	PUNCT
ejpam-6165	318	32	74	74	NUM
ejpam-6165	318	33	(	(	PUNCT
ejpam-6165	318	34	2013	2013	NUM
ejpam-6165	318	35	)	)	PUNCT
ejpam-6165	318	36	.	.	PUNCT
ejpam-6165	319	1	[	[	X
ejpam-6165	319	2	25	25	NUM
ejpam-6165	319	3	]	]	SYM
ejpam-6165	319	4	mezo	mezo	PROPN
ejpam-6165	319	5	,	,	PUNCT
ejpam-6165	319	6	i.	i.	PROPN
ejpam-6165	319	7	,	,	PUNCT
ejpam-6165	319	8	the	the	DET
ejpam-6165	319	9	r	r	NOUN
ejpam-6165	319	10	-	-	PUNCT
ejpam-6165	319	11	bell	bell	NOUN
ejpam-6165	319	12	numbers	number	NOUN
ejpam-6165	319	13	,	,	PUNCT
ejpam-6165	319	14	journal	journal	NOUN
ejpam-6165	319	15	of	of	ADP
ejpam-6165	319	16	integer	integer	PROPN
ejpam-6165	319	17	sequences	sequence	NOUN
ejpam-6165	319	18	,	,	PUNCT
ejpam-6165	319	19	14	14	NUM
ejpam-6165	319	20	(	(	PUNCT
ejpam-6165	319	21	2011	2011	NUM
ejpam-6165	319	22	)	)	PUNCT
ejpam-6165	319	23	,	,	PUNCT
ejpam-6165	319	24	article	article	NOUN
ejpam-6165	319	25	11.1.1	11.1.1	NUM
ejpam-6165	319	26	.	.	PUNCT
ejpam-6165	320	1	[	[	X
ejpam-6165	320	2	26	26	NUM
ejpam-6165	320	3	]	]	SYM
ejpam-6165	320	4	mezo	mezo	PROPN
ejpam-6165	320	5	,	,	PUNCT
ejpam-6165	320	6	i.	i.	NOUN
ejpam-6165	320	7	and	and	CCONJ
ejpam-6165	320	8	corcino	corcino	PROPN
ejpam-6165	320	9	,	,	PUNCT
ejpam-6165	320	10	r.	r.	PROPN
ejpam-6165	320	11	,the	,the	PUNCT
ejpam-6165	320	12	estimation	estimation	NOUN
ejpam-6165	320	13	of	of	ADP
ejpam-6165	320	14	the	the	DET
ejpam-6165	320	15	zeros	zero	NOUN
ejpam-6165	320	16	of	of	ADP
ejpam-6165	320	17	the	the	DET
ejpam-6165	320	18	bell	bell	NOUN
ejpam-6165	320	19	and	and	CCONJ
ejpam-6165	320	20	r	r	NOUN
ejpam-6165	320	21	-	-	PUNCT
ejpam-6165	320	22	bell	bell	NOUN
ejpam-6165	320	23	polynomials	polynomial	NOUN
ejpam-6165	320	24	,	,	PUNCT
ejpam-6165	320	25	applied	apply	VERB
ejpam-6165	320	26	mathematics	mathematic	NOUN
ejpam-6165	320	27	and	and	CCONJ
ejpam-6165	320	28	computations	computation	NOUN
ejpam-6165	320	29	(	(	PUNCT
ejpam-6165	320	30	elsevier	elsevier	NOUN
ejpam-6165	320	31	)	)	PUNCT
ejpam-6165	320	32	,	,	PUNCT
ejpam-6165	320	33	250	250	NUM
ejpam-6165	320	34	(	(	PUNCT
ejpam-6165	320	35	2015	2015	NUM
ejpam-6165	320	36	)	)	PUNCT
ejpam-6165	320	37	,	,	PUNCT
ejpam-6165	320	38	727	727	NUM
ejpam-6165	320	39	-	-	SYM
ejpam-6165	320	40	732	732	NUM
ejpam-6165	320	41	.	.	PUNCT
ejpam-6165	321	1	[	[	X
ejpam-6165	321	2	27	27	NUM
ejpam-6165	321	3	]	]	X
ejpam-6165	321	4	khan	khan	PROPN
ejpam-6165	321	5	,	,	PUNCT
ejpam-6165	321	6	w.a	w.a	PROPN
ejpam-6165	321	7	.	.	PROPN
ejpam-6165	321	8	,	,	PUNCT
ejpam-6165	321	9	alatawi	alatawi	PROPN
ejpam-6165	321	10	,	,	PUNCT
ejpam-6165	321	11	m.a	m.a	PROPN
ejpam-6165	321	12	.	.	PROPN
ejpam-6165	321	13	,	,	PUNCT
ejpam-6165	321	14	duran	duran	PROPN
ejpam-6165	321	15	,	,	PUNCT
ejpam-6165	321	16	u.	u.	PROPN
ejpam-6165	321	17	,	,	PUNCT
ejpam-6165	321	18	applications	application	NOUN
ejpam-6165	321	19	,	,	PUNCT
ejpam-6165	321	20	and	and	CCONJ
ejpam-6165	321	21	properties	property	NOUN
ejpam-6165	321	22	of	of	ADP
ejpam-6165	321	23	r	r	NOUN
ejpam-6165	321	24	-	-	PUNCT
ejpam-6165	321	25	bell	bell	NOUN
ejpam-6165	321	26	-	-	PUNCT
ejpam-6165	321	27	based	base	VERB
ejpam-6165	321	28	frobenius	frobenius	NOUN
ejpam-6165	321	29	-	-	PUNCT
ejpam-6165	321	30	type	type	NOUN
ejpam-6165	321	31	eulerian	eulerian	ADJ
ejpam-6165	321	32	polynomials	polynomial	NOUN
ejpam-6165	321	33	.	.	PUNCT
ejpam-6165	322	1	journal	journal	NOUN
ejpam-6165	322	2	of	of	ADP
ejpam-6165	322	3	function	function	NOUN
ejpam-6165	322	4	spaces	space	NOUN
ejpam-6165	322	5	.	.	PUNCT
ejpam-6165	323	1	(	(	PUNCT
ejpam-6165	323	2	2023	2023	NUM
ejpam-6165	323	3	)	)	PUNCT
ejpam-6165	323	4	.	.	PUNCT
ejpam-6165	324	1	volume	volume	NOUN
ejpam-6165	324	2	2023	2023	NUM
ejpam-6165	324	3	,	,	PUNCT
ejpam-6165	324	4	article	article	NOUN
ejpam-6165	324	5	i	i	PROPN
ejpam-6165	324	6	d	d	PROPN
ejpam-6165	324	7	5205867	5205867	NUM
ejpam-6165	324	8	,	,	PUNCT
ejpam-6165	324	9	10	10	NUM
ejpam-6165	324	10	pages	page	NOUN
ejpam-6165	324	11	.	.	PUNCT
ejpam-6165	325	1	[	[	X
ejpam-6165	325	2	28	28	NUM
ejpam-6165	325	3	]	]	X
ejpam-6165	325	4	khan	khan	PROPN
ejpam-6165	325	5	,	,	PUNCT
ejpam-6165	325	6	w.	w.	PROPN
ejpam-6165	325	7	a.	a.	PROPN
ejpam-6165	325	8	,	,	PUNCT
ejpam-6165	325	9	younis	younis	PROPN
ejpam-6165	325	10	,	,	PUNCT
ejpam-6165	325	11	j.	j.	PROPN
ejpam-6165	325	12	,	,	PUNCT
ejpam-6165	325	13	nadeem	nadeem	PROPN
ejpam-6165	325	14	,	,	PUNCT
ejpam-6165	325	15	m.	m.	NOUN
ejpam-6165	325	16	,	,	PUNCT
ejpam-6165	325	17	construction	construction	NOUN
ejpam-6165	325	18	of	of	ADP
ejpam-6165	325	19	partially	partially	ADV
ejpam-6165	325	20	degenerate	degenerate	ADJ
ejpam-6165	325	21	bellbernoulli	bellbernoulli	NOUN
ejpam-6165	325	22	polynomials	polynomial	NOUN
ejpam-6165	325	23	of	of	ADP
ejpam-6165	325	24	the	the	DET
ejpam-6165	325	25	first	first	ADJ
ejpam-6165	325	26	kind	kind	NOUN
ejpam-6165	325	27	,	,	PUNCT
ejpam-6165	325	28	analysis	analysis	NOUN
ejpam-6165	325	29	,	,	PUNCT
ejpam-6165	325	30	43(3	43(3	NUM
ejpam-6165	325	31	)	)	PUNCT
ejpam-6165	325	32	(	(	PUNCT
ejpam-6165	325	33	2022	2022	NUM
ejpam-6165	325	34	)	)	PUNCT
ejpam-6165	325	35	,	,	PUNCT
ejpam-6165	325	36	171	171	NUM
ejpam-6165	325	37	-	-	SYM
ejpam-6165	325	38	184	184	NUM
ejpam-6165	325	39	.	.	PUNCT
ejpam-6165	326	1	[	[	X
ejpam-6165	326	2	29	29	NUM
ejpam-6165	326	3	]	]	X
ejpam-6165	326	4	kim	kim	PROPN
ejpam-6165	326	5	t.	t.	PROPN
ejpam-6165	326	6	,	,	PUNCT
ejpam-6165	326	7	jang	jang	PROPN
ejpam-6165	326	8	,	,	PUNCT
ejpam-6165	326	9	y.s	y.s	PROPN
ejpam-6165	326	10	.	.	PROPN
ejpam-6165	326	11	and	and	CCONJ
ejpam-6165	326	12	seo	seo	PROPN
ejpam-6165	326	13	,	,	PUNCT
ejpam-6165	326	14	j.j	j.j	PROPN
ejpam-6165	326	15	.	.	PROPN
ejpam-6165	326	16	,	,	PUNCT
ejpam-6165	326	17	a	a	DET
ejpam-6165	326	18	note	note	NOUN
ejpam-6165	326	19	on	on	ADP
ejpam-6165	326	20	poly	poly	ADJ
ejpam-6165	326	21	-	-	PUNCT
ejpam-6165	326	22	genocchi	genocchi	NOUN
ejpam-6165	326	23	numbers	number	NOUN
ejpam-6165	326	24	and	and	CCONJ
ejpam-6165	326	25	polynomials	polynomial	NOUN
ejpam-6165	326	26	,	,	PUNCT
ejpam-6165	326	27	applied	apply	VERB
ejpam-6165	326	28	mathematical	mathematical	ADJ
ejpam-6165	326	29	sciences	science	NOUN
ejpam-6165	326	30	.	.	PUNCT
ejpam-6165	326	31	8	8	NUM
ejpam-6165	326	32	(	(	PUNCT
ejpam-6165	326	33	2014	2014	NUM
ejpam-6165	326	34	)	)	PUNCT
ejpam-6165	326	35	,	,	PUNCT
ejpam-6165	326	36	4775	4775	NUM
ejpam-6165	326	37	-	-	SYM
ejpam-6165	326	38	4781	4781	NUM
ejpam-6165	326	39	.	.	PUNCT
ejpam-6165	327	1	http://dx.doi.org/10.12988/ams.2014.46465	http://dx.doi.org/10.12988/ams.2014.46465	NOUN
ejpam-6165	327	2	.	.	PUNCT
ejpam-6165	328	1	[	[	X
ejpam-6165	328	2	30	30	NUM
ejpam-6165	328	3	]	]	X
ejpam-6165	328	4	kim	kim	PROPN
ejpam-6165	328	5	,	,	PUNCT
ejpam-6165	328	6	d.s	d.s	PROPN
ejpam-6165	328	7	.	.	PROPN
ejpam-6165	328	8	,	,	PUNCT
ejpam-6165	328	9	dolgy	dolgy	VERB
ejpam-6165	328	10	,	,	PUNCT
ejpam-6165	328	11	d.v	d.v	PROPN
ejpam-6165	328	12	.	.	PROPN
ejpam-6165	328	13	,	,	PUNCT
ejpam-6165	328	14	kim	kim	PROPN
ejpam-6165	328	15	,	,	PUNCT
ejpam-6165	328	16	t.	t.	PROPN
ejpam-6165	328	17	and	and	CCONJ
ejpam-6165	328	18	rim	rim	PROPN
ejpam-6165	328	19	,	,	PUNCT
ejpam-6165	328	20	s.h	s.h	PROPN
ejpam-6165	328	21	.	.	PROPN
ejpam-6165	328	22	,	,	PUNCT
ejpam-6165	328	23	some	some	DET
ejpam-6165	328	24	formula	formula	NOUN
ejpam-6165	328	25	for	for	ADP
ejpam-6165	328	26	the	the	DET
ejpam-6165	328	27	product	product	NOUN
ejpam-6165	328	28	of	of	ADP
ejpam-6165	328	29	two	two	NUM
ejpam-6165	328	30	bernoulli	bernoulli	NOUN
ejpam-6165	328	31	and	and	CCONJ
ejpam-6165	328	32	euler	euler	NOUN
ejpam-6165	328	33	polynomials	polynomial	NOUN
ejpam-6165	328	34	,	,	PUNCT
ejpam-6165	328	35	abstract	abstract	ADJ
ejpam-6165	328	36	and	and	CCONJ
ejpam-6165	328	37	applied	apply	VERB
ejpam-6165	328	38	analysis	analysis	NOUN
ejpam-6165	328	39	.	.	PUNCT
ejpam-6165	329	1	2012	2012	NUM
ejpam-6165	329	2	,	,	PUNCT
ejpam-6165	329	3	article	article	NOUN
ejpam-6165	329	4	i	i	PROPN
ejpam-6165	329	5	d	d	PROPN
ejpam-6165	329	6	784307	784307	NUM
ejpam-6165	329	7	,	,	PUNCT
ejpam-6165	329	8	15	15	NUM
ejpam-6165	329	9	pages	page	NOUN
ejpam-6165	329	10	.	.	PUNCT
ejpam-6165	330	1	[	[	X
ejpam-6165	330	2	31	31	NUM
ejpam-6165	330	3	]	]	X
ejpam-6165	330	4	kim	kim	PROPN
ejpam-6165	330	5	t.	t.	PROPN
ejpam-6165	330	6	,	,	PUNCT
ejpam-6165	330	7	rim	rim	PROPN
ejpam-6165	330	8	.	.	PUNCT
ejpam-6165	331	1	s.h	s.h	PROPN
ejpam-6165	331	2	.	.	PROPN
ejpam-6165	331	3	,	,	PUNCT
ejpam-6165	331	4	dolgy	dolgy	VERB
ejpam-6165	331	5	d.v	d.v	PROPN
ejpam-6165	331	6	.	.	PROPN
ejpam-6165	332	1	and	and	CCONJ
ejpam-6165	332	2	lee	lee	PROPN
ejpam-6165	332	3	s.h	s.h	PROPN
ejpam-6165	332	4	.	.	PROPN
ejpam-6165	332	5	,	,	PUNCT
ejpam-6165	332	6	some	some	DET
ejpam-6165	332	7	identities	identity	NOUN
ejpam-6165	332	8	of	of	ADP
ejpam-6165	332	9	genocchi	genocchi	PROPN
ejpam-6165	332	10	polynomials	polynomial	NOUN
ejpam-6165	332	11	arising	arise	VERB
ejpam-6165	332	12	from	from	ADP
ejpam-6165	332	13	genocchi	genocchi	PROPN
ejpam-6165	332	14	basis	basis	NOUN
ejpam-6165	332	15	,	,	PUNCT
ejpam-6165	332	16	j.	j.	PROPN
ejpam-6165	332	17	ineq	ineq	PROPN
ejpam-6165	332	18	.	.	PUNCT
ejpam-6165	333	1	appl	appl	PROPN
ejpam-6165	333	2	.	.	PUNCT
ejpam-6165	334	1	2013	2013	NUM
ejpam-6165	334	2	(	(	PUNCT
ejpam-6165	334	3	2013	2013	NUM
ejpam-6165	334	4	)	)	PUNCT
ejpam-6165	334	5	,	,	PUNCT
ejpam-6165	334	6	article	article	NOUN
ejpam-6165	334	7	i	i	PROPN
ejpam-6165	334	8	d	d	PROPN
ejpam-6165	334	9	43	43	NUM
ejpam-6165	334	10	.	.	PUNCT
ejpam-6165	335	1	[	[	X
ejpam-6165	335	2	32	32	NUM
ejpam-6165	335	3	]	]	X
ejpam-6165	335	4	kim	kim	PROPN
ejpam-6165	335	5	t.	t.	PROPN
ejpam-6165	335	6	,	,	PUNCT
ejpam-6165	335	7	some	some	DET
ejpam-6165	335	8	identities	identity	NOUN
ejpam-6165	335	9	for	for	ADP
ejpam-6165	335	10	the	the	DET
ejpam-6165	335	11	bernoulli	bernoulli	NOUN
ejpam-6165	335	12	,	,	PUNCT
ejpam-6165	335	13	the	the	DET
ejpam-6165	335	14	euler	euler	NOUN
ejpam-6165	335	15	and	and	CCONJ
ejpam-6165	335	16	the	the	DET
ejpam-6165	335	17	genocchi	genocchi	PROPN
ejpam-6165	335	18	numbers	number	NOUN
ejpam-6165	335	19	and	and	CCONJ
ejpam-6165	335	20	polynomials	polynomial	NOUN
ejpam-6165	335	21	,	,	PUNCT
ejpam-6165	335	22	adv	adv	PROPN
ejpam-6165	335	23	.	.	PUNCT
ejpam-6165	335	24	stud	stud	PROPN
ejpam-6165	335	25	.	.	PUNCT
ejpam-6165	336	1	contemp	contemp	NOUN
ejpam-6165	336	2	.	.	PUNCT
ejpam-6165	337	1	math	math	NOUN
ejpam-6165	337	2	.	.	PUNCT
ejpam-6165	338	1	20	20	NUM
ejpam-6165	338	2	(	(	PUNCT
ejpam-6165	338	3	1	1	NUM
ejpam-6165	338	4	)	)	PUNCT
ejpam-6165	338	5	(	(	PUNCT
ejpam-6165	338	6	2010	2010	NUM
ejpam-6165	338	7	)	)	PUNCT
ejpam-6165	338	8	,	,	PUNCT
ejpam-6165	338	9	23	23	NUM
ejpam-6165	338	10	-	-	SYM
ejpam-6165	338	11	28	28	NUM
ejpam-6165	338	12	.	.	PUNCT
ejpam-6165	339	1	[	[	X
ejpam-6165	339	2	33	33	NUM
ejpam-6165	339	3	]	]	X
ejpam-6165	339	4	kim	kim	PROPN
ejpam-6165	339	5	,	,	PUNCT
ejpam-6165	339	6	d.s	d.s	PROPN
ejpam-6165	339	7	.	.	PROPN
ejpam-6165	339	8	;	;	PUNCT
ejpam-6165	339	9	kim	kim	PROPN
ejpam-6165	339	10	,	,	PUNCT
ejpam-6165	339	11	t.	t.	VERB
ejpam-6165	339	12	some	some	DET
ejpam-6165	339	13	new	new	ADJ
ejpam-6165	339	14	identities	identity	NOUN
ejpam-6165	339	15	of	of	ADP
ejpam-6165	339	16	frobenius	frobenius	NOUN
ejpam-6165	339	17	-	-	PUNCT
ejpam-6165	339	18	euler	euler	NOUN
ejpam-6165	339	19	numbers	number	NOUN
ejpam-6165	339	20	and	and	CCONJ
ejpam-6165	339	21	polynomials	polynomial	NOUN
ejpam-6165	339	22	.	.	PUNCT
ejpam-6165	340	1	j.	j.	PROPN
ejpam-6165	340	2	inequal	inequal	PROPN
ejpam-6165	340	3	.	.	PUNCT
ejpam-6165	341	1	appl	appl	PROPN
ejpam-6165	341	2	.	.	PROPN
ejpam-6165	341	3	2012	2012	NUM
ejpam-6165	341	4	,	,	PUNCT
ejpam-6165	341	5	2012	2012	NUM
ejpam-6165	341	6	,	,	PUNCT
ejpam-6165	341	7	307	307	NUM
ejpam-6165	341	8	.	.	PUNCT
ejpam-6165	342	1	[	[	X
ejpam-6165	342	2	34	34	NUM
ejpam-6165	342	3	]	]	X
ejpam-6165	342	4	khan	khan	PROPN
ejpam-6165	342	5	,	,	PUNCT
ejpam-6165	342	6	w.a	w.a	PROPN
ejpam-6165	342	7	.	.	PROPN
ejpam-6165	342	8	and	and	CCONJ
ejpam-6165	342	9	srivastava	srivastava	PROPN
ejpam-6165	342	10	,	,	PUNCT
ejpam-6165	342	11	d.	d.	PROPN
ejpam-6165	342	12	,	,	PUNCT
ejpam-6165	342	13	on	on	ADP
ejpam-6165	342	14	the	the	DET
ejpam-6165	342	15	generalized	generalize	VERB
ejpam-6165	342	16	apostol	apostol	NOUN
ejpam-6165	342	17	-	-	PUNCT
ejpam-6165	342	18	frobenius	frobenius	NOUN
ejpam-6165	342	19	-	-	PUNCT
ejpam-6165	342	20	type	type	NOUN
ejpam-6165	342	21	polygenocchi	polygenocchi	NOUN
ejpam-6165	342	22	polynomials	polynomial	NOUN
ejpam-6165	342	23	,	,	PUNCT
ejpam-6165	342	24	filomat	filomat	NOUN
ejpam-6165	342	25	,	,	PUNCT
ejpam-6165	342	26	33(7	33(7	NUM
ejpam-6165	342	27	)	)	PUNCT
ejpam-6165	342	28	(	(	PUNCT
ejpam-6165	342	29	2019	2019	NUM
ejpam-6165	342	30	)	)	PUNCT
ejpam-6165	342	31	,	,	PUNCT
ejpam-6165	342	32	1967–1977	1967–1977	NUM
ejpam-6165	342	33	.	.	PUNCT
ejpam-6165	343	1	[	[	X
ejpam-6165	343	2	35	35	NUM
ejpam-6165	343	3	]	]	X
ejpam-6165	343	4	kurt	kurt	PROPN
ejpam-6165	343	5	,	,	PUNCT
ejpam-6165	343	6	b.	b.	PROPN
ejpam-6165	343	7	and	and	CCONJ
ejpam-6165	343	8	symsek	symsek	PROPN
ejpam-6165	343	9	,	,	PUNCT
ejpam-6165	343	10	y.	y.	PROPN
ejpam-6165	343	11	,	,	PUNCT
ejpam-6165	343	12	on	on	ADP
ejpam-6165	343	13	the	the	DET
ejpam-6165	343	14	generalized	generalize	VERB
ejpam-6165	343	15	apostol	apostol	NOUN
ejpam-6165	343	16	type	type	NOUN
ejpam-6165	343	17	frobenius	frobenius	NOUN
ejpam-6165	343	18	-	-	PUNCT
ejpam-6165	343	19	euler	euler	NOUN
ejpam-6165	343	20	polynomials	polynomial	NOUN
ejpam-6165	343	21	,	,	PUNCT
ejpam-6165	343	22	advances	advance	NOUN
ejpam-6165	343	23	in	in	ADP
ejpam-6165	343	24	difference	difference	NOUN
ejpam-6165	343	25	equation	equation	NOUN
ejpam-6165	343	26	,	,	PUNCT
ejpam-6165	343	27	2013	2013	NUM
ejpam-6165	343	28	,	,	PUNCT
ejpam-6165	343	29	1	1	NUM
ejpam-6165	343	30	,	,	PUNCT
ejpam-6165	343	31	(	(	PUNCT
ejpam-6165	343	32	2013	2013	NUM
ejpam-6165	343	33	)	)	PUNCT
ejpam-6165	343	34	,	,	PUNCT
ejpam-6165	343	35	1	1	NUM
ejpam-6165	343	36	-	-	SYM
ejpam-6165	343	37	9	9	NUM
ejpam-6165	343	38	.	.	PUNCT
ejpam-6165	344	1	[	[	X
ejpam-6165	344	2	36	36	NUM
ejpam-6165	344	3	]	]	X
ejpam-6165	344	4	lee	lee	PROPN
ejpam-6165	344	5	,	,	PUNCT
ejpam-6165	344	6	d.w	d.w	PROPN
ejpam-6165	344	7	.	.	PROPN
ejpam-6165	344	8	,	,	PUNCT
ejpam-6165	344	9	on	on	ADP
ejpam-6165	344	10	multiple	multiple	ADJ
ejpam-6165	344	11	appell	appell	ADJ
ejpam-6165	344	12	polynomials	polynomial	NOUN
ejpam-6165	344	13	.	.	PUNCT
ejpam-6165	345	1	proc	proc	NOUN
ejpam-6165	345	2	.	.	PUNCT
ejpam-6165	346	1	amer	amer	PROPN
ejpam-6165	346	2	.	.	PUNCT
ejpam-6165	346	3	math	math	PROPN
ejpam-6165	346	4	.	.	PUNCT
ejpam-6165	347	1	soc	soc	PROPN
ejpam-6165	347	2	,	,	PUNCT
ejpam-6165	347	3	139	139	NUM
ejpam-6165	347	4	(	(	PUNCT
ejpam-6165	347	5	2011	2011	NUM
ejpam-6165	347	6	)	)	PUNCT
ejpam-6165	347	7	,	,	PUNCT
ejpam-6165	347	8	2133	2133	NUM
ejpam-6165	347	9	-	-	SYM
ejpam-6165	347	10	2141	2141	NUM
ejpam-6165	347	11	.	.	PUNCT
ejpam-6165	348	1	[	[	X
ejpam-6165	348	2	37	37	NUM
ejpam-6165	348	3	]	]	X
ejpam-6165	348	4	lou	lou	PROPN
ejpam-6165	348	5	q.m	q.m	PROPN
ejpam-6165	348	6	.	.	PROPN
ejpam-6165	348	7	,	,	PUNCT
ejpam-6165	348	8	guo	guo	PROPN
ejpam-6165	348	9	b.n	b.n	PROPN
ejpam-6165	348	10	.	.	PROPN
ejpam-6165	348	11	,	,	PUNCT
ejpam-6165	348	12	qi	qi	PROPN
ejpam-6165	348	13	f.	f.	PROPN
ejpam-6165	348	14	and	and	CCONJ
ejpam-6165	348	15	debnath	debnath	PROPN
ejpam-6165	348	16	l.	l.	PROPN
ejpam-6165	348	17	,	,	PUNCT
ejpam-6165	348	18	generalizations	generalization	NOUN
ejpam-6165	348	19	of	of	ADP
ejpam-6165	348	20	bernoulli	bernoulli	NOUN
ejpam-6165	348	21	numbers	number	NOUN
ejpam-6165	348	22	and	and	CCONJ
ejpam-6165	348	23	polynomials	polynomial	NOUN
ejpam-6165	348	24	,	,	PUNCT
ejpam-6165	348	25	int	int	NOUN
ejpam-6165	348	26	.	.	PUNCT
ejpam-6165	349	1	j.	j.	PROPN
ejpam-6165	349	2	math	math	PROPN
ejpam-6165	349	3	.	.	PUNCT
ejpam-6165	350	1	math	math	NOUN
ejpam-6165	350	2	.	.	PUNCT
ejpam-6165	351	1	sci	sci	PROPN
ejpam-6165	351	2	.	.	PROPN
ejpam-6165	351	3	,	,	PUNCT
ejpam-6165	351	4	59	59	NUM
ejpam-6165	351	5	(	(	PUNCT
ejpam-6165	351	6	2003	2003	NUM
ejpam-6165	351	7	)	)	PUNCT
ejpam-6165	351	8	,	,	PUNCT
ejpam-6165	351	9	3769–3776	3769–3776	NUM
ejpam-6165	351	10	.	.	PUNCT
ejpam-6165	352	1	[	[	X
ejpam-6165	352	2	38	38	NUM
ejpam-6165	352	3	]	]	PUNCT
ejpam-6165	352	4	shohat	shohat	PROPN
ejpam-6165	352	5	,	,	PUNCT
ejpam-6165	352	6	j.	j.	PROPN
ejpam-6165	352	7	,	,	PUNCT
ejpam-6165	352	8	the	the	DET
ejpam-6165	352	9	relation	relation	NOUN
ejpam-6165	352	10	of	of	ADP
ejpam-6165	352	11	the	the	DET
ejpam-6165	352	12	classical	classical	ADJ
ejpam-6165	352	13	orthogonal	orthogonal	ADJ
ejpam-6165	352	14	polynomials	polynomial	NOUN
ejpam-6165	352	15	to	to	ADP
ejpam-6165	352	16	the	the	DET
ejpam-6165	352	17	polynomials	polynomial	NOUN
ejpam-6165	352	18	15	15	NUM
ejpam-6165	352	19	of	of	ADP
ejpam-6165	352	20	15	15	NUM
ejpam-6165	352	21	of	of	ADP
ejpam-6165	352	22	appell	appell	PROPN
ejpam-6165	352	23	,	,	PUNCT
ejpam-6165	352	24	amer	amer	PROPN
ejpam-6165	352	25	.	.	PUNCT
ejpam-6165	352	26	j.	j.	PROPN
ejpam-6165	352	27	math	math	PROPN
ejpam-6165	352	28	.	.	PUNCT
ejpam-6165	352	29	,	,	PUNCT
ejpam-6165	352	30	58	58	NUM
ejpam-6165	352	31	(	(	PUNCT
ejpam-6165	352	32	1936	1936	NUM
ejpam-6165	352	33	)	)	PUNCT
ejpam-6165	352	34	,	,	PUNCT
ejpam-6165	352	35	453–464	453–464	NUM
ejpam-6165	352	36	.	.	PUNCT
ejpam-6165	353	1	[	[	X
ejpam-6165	353	2	39	39	NUM
ejpam-6165	353	3	]	]	PUNCT
ejpam-6165	353	4	thomas	thomas	PROPN
ejpam-6165	353	5	g.	g.	PROPN
ejpam-6165	353	6	,	,	PUNCT
ejpam-6165	353	7	weir	weir	PROPN
ejpam-6165	353	8	m.	m.	PROPN
ejpam-6165	353	9	,	,	PUNCT
ejpam-6165	353	10	hass	hass	VERB
ejpam-6165	353	11	j.	j.	PROPN
ejpam-6165	353	12	and	and	CCONJ
ejpam-6165	353	13	giordano	giordano	PROPN
ejpam-6165	353	14	f.	f.	PROPN
ejpam-6165	353	15	,	,	PUNCT
ejpam-6165	353	16	thomas	thomas	PROPN
ejpam-6165	353	17	’	'	PUNCT
ejpam-6165	353	18	calculus	calculus	NOUN
ejpam-6165	353	19	,	,	PUNCT
ejpam-6165	353	20	11th	11th	ADJ
ejpam-6165	353	21	edn	edn	NOUN
ejpam-6165	353	22	.	.	PUNCT
ejpam-6165	354	1	pearson	pearson	PROPN
ejpam-6165	354	2	education	education	PROPN
ejpam-6165	354	3	,	,	PUNCT
ejpam-6165	354	4	inc	inc	PROPN
ejpam-6165	354	5	.	.	PROPN
ejpam-6165	354	6	,	,	PUNCT
ejpam-6165	354	7	2005	2005	NUM
ejpam-6165	354	8	.	.	PUNCT