id	sid	tid	token	lemma	pos
ejpam-4694	1	1	european	european	PROPN
ejpam-4694	1	2	journal	journal	PROPN
ejpam-4694	1	3	of	of	ADP
ejpam-4694	1	4	pure	pure	ADJ
ejpam-4694	1	5	and	and	CCONJ
ejpam-4694	1	6	applied	apply	VERB
ejpam-4694	1	7	mathematics	mathematic	NOUN
ejpam-4694	1	8	vol	vol	NOUN
ejpam-4694	1	9	.	.	PUNCT
ejpam-4694	2	1	16	16	NUM
ejpam-4694	2	2	,	,	PUNCT
ejpam-4694	2	3	no	no	INTJ
ejpam-4694	2	4	.	.	NOUN
ejpam-4694	2	5	2	2	NUM
ejpam-4694	2	6	,	,	PUNCT
ejpam-4694	2	7	2023	2023	NUM
ejpam-4694	2	8	,	,	PUNCT
ejpam-4694	2	9	687	687	NUM
ejpam-4694	2	10	-	-	SYM
ejpam-4694	2	11	712	712	NUM
ejpam-4694	2	12	issn	issn	PROPN
ejpam-4694	2	13	1307	1307	NUM
ejpam-4694	2	14	-	-	SYM
ejpam-4694	2	15	5543	5543	NUM
ejpam-4694	2	16	–	–	PUNCT
ejpam-4694	3	1	ejpam.com	ejpam.com	X
ejpam-4694	3	2	published	publish	VERB
ejpam-4694	3	3	by	by	ADP
ejpam-4694	3	4	new	new	PROPN
ejpam-4694	3	5	york	york	PROPN
ejpam-4694	3	6	business	business	PROPN
ejpam-4694	3	7	global	global	ADJ
ejpam-4694	3	8	degenerate	degenerate	ADJ
ejpam-4694	3	9	apostol	apostol	NOUN
ejpam-4694	3	10	-	-	PUNCT
ejpam-4694	3	11	frobenius	frobenius	NOUN
ejpam-4694	3	12	-	-	PUNCT
ejpam-4694	3	13	type	type	NOUN
ejpam-4694	3	14	poly	poly	ADJ
ejpam-4694	3	15	-	-	PUNCT
ejpam-4694	3	16	genocchi	genocchi	NOUN
ejpam-4694	3	17	polynomials	polynomial	NOUN
ejpam-4694	3	18	of	of	ADP
ejpam-4694	3	19	higher	high	ADJ
ejpam-4694	3	20	order	order	NOUN
ejpam-4694	3	21	with	with	ADP
ejpam-4694	3	22	parameters	parameter	NOUN
ejpam-4694	3	23	a	a	PRON
ejpam-4694	3	24	and	and	CCONJ
ejpam-4694	3	25	b	b	PROPN
ejpam-4694	3	26	roberto	roberto	PROPN
ejpam-4694	3	27	b.	b.	PROPN
ejpam-4694	3	28	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-4694	3	29	,	,	PUNCT
ejpam-4694	3	30	cristina	cristina	PROPN
ejpam-4694	3	31	b.	b.	PROPN
ejpam-4694	4	1	corcino1,2	corcino1,2	PROPN
ejpam-4694	4	2	1	1	NUM
ejpam-4694	4	3	research	research	NOUN
ejpam-4694	4	4	institute	institute	NOUN
ejpam-4694	4	5	for	for	ADP
ejpam-4694	4	6	computational	computational	ADJ
ejpam-4694	4	7	mathematics	mathematic	NOUN
ejpam-4694	4	8	and	and	CCONJ
ejpam-4694	4	9	physics	physics	NOUN
ejpam-4694	4	10	,	,	PUNCT
ejpam-4694	4	11	cebu	cebu	NOUN
ejpam-4694	4	12	normal	normal	ADJ
ejpam-4694	4	13	university	university	NOUN
ejpam-4694	4	14	,	,	PUNCT
ejpam-4694	4	15	6000	6000	NUM
ejpam-4694	4	16	cebu	cebu	NOUN
ejpam-4694	4	17	city	city	NOUN
ejpam-4694	4	18	,	,	PUNCT
ejpam-4694	4	19	philippines	philippine	NOUN
ejpam-4694	4	20	2	2	NUM
ejpam-4694	4	21	mathematics	mathematics	NOUN
ejpam-4694	4	22	department	department	NOUN
ejpam-4694	4	23	,	,	PUNCT
ejpam-4694	4	24	cebu	cebu	NOUN
ejpam-4694	4	25	normal	normal	ADJ
ejpam-4694	4	26	university	university	NOUN
ejpam-4694	4	27	,	,	PUNCT
ejpam-4694	4	28	6000	6000	NUM
ejpam-4694	4	29	cebu	cebu	NOUN
ejpam-4694	4	30	city	city	NOUN
ejpam-4694	4	31	,	,	PUNCT
ejpam-4694	4	32	philippines	philippine	NOUN
ejpam-4694	4	33	abstract	abstract	ADJ
ejpam-4694	4	34	.	.	PUNCT
ejpam-4694	5	1	this	this	DET
ejpam-4694	5	2	paper	paper	NOUN
ejpam-4694	5	3	introduces	introduce	VERB
ejpam-4694	5	4	another	another	DET
ejpam-4694	5	5	variation	variation	NOUN
ejpam-4694	5	6	of	of	ADP
ejpam-4694	5	7	poly	poly	ADJ
ejpam-4694	5	8	-	-	PUNCT
ejpam-4694	5	9	genocchi	genocchi	NOUN
ejpam-4694	5	10	polynomials	polynomial	NOUN
ejpam-4694	5	11	by	by	ADP
ejpam-4694	5	12	mixing	mix	VERB
ejpam-4694	5	13	the	the	DET
ejpam-4694	5	14	concept	concept	NOUN
ejpam-4694	5	15	of	of	ADP
ejpam-4694	5	16	modified	modified	ADJ
ejpam-4694	5	17	degenerate	degenerate	ADJ
ejpam-4694	5	18	polyexponential	polyexponential	ADJ
ejpam-4694	5	19	function	function	NOUN
ejpam-4694	5	20	,	,	PUNCT
ejpam-4694	5	21	apostol	apostol	NOUN
ejpam-4694	5	22	-	-	PUNCT
ejpam-4694	5	23	genocchi	genocchi	PROPN
ejpam-4694	5	24	polynomials	polynomial	NOUN
ejpam-4694	5	25	and	and	CCONJ
ejpam-4694	5	26	frobenius	frobenius	ADJ
ejpam-4694	5	27	polynomials	polynomial	NOUN
ejpam-4694	5	28	.	.	PUNCT
ejpam-4694	6	1	these	these	DET
ejpam-4694	6	2	polynomials	polynomial	NOUN
ejpam-4694	6	3	are	be	AUX
ejpam-4694	6	4	called	call	VERB
ejpam-4694	6	5	the	the	DET
ejpam-4694	6	6	degenerate	degenerate	ADJ
ejpam-4694	6	7	apostol	apostol	NOUN
ejpam-4694	6	8	-	-	PUNCT
ejpam-4694	6	9	frobenius	frobenius	NOUN
ejpam-4694	6	10	-	-	PUNCT
ejpam-4694	6	11	type	type	NOUN
ejpam-4694	6	12	polygenocchi	polygenocchi	NOUN
ejpam-4694	6	13	polynomials	polynomial	NOUN
ejpam-4694	6	14	with	with	ADP
ejpam-4694	6	15	parameters	parameter	NOUN
ejpam-4694	6	16	a	a	PRON
ejpam-4694	6	17	and	and	CCONJ
ejpam-4694	6	18	b.	b.	NOUN
ejpam-4694	6	19	several	several	ADJ
ejpam-4694	6	20	identities	identity	NOUN
ejpam-4694	6	21	and	and	CCONJ
ejpam-4694	6	22	formulas	formula	NOUN
ejpam-4694	6	23	are	be	AUX
ejpam-4694	6	24	derived	derive	VERB
ejpam-4694	6	25	including	include	VERB
ejpam-4694	6	26	recurrence	recurrence	NOUN
ejpam-4694	6	27	relations	relation	NOUN
ejpam-4694	6	28	,	,	PUNCT
ejpam-4694	6	29	explicit	explicit	ADJ
ejpam-4694	6	30	formulas	formula	NOUN
ejpam-4694	6	31	and	and	CCONJ
ejpam-4694	6	32	certain	certain	ADJ
ejpam-4694	6	33	differential	differential	ADJ
ejpam-4694	6	34	identity	identity	NOUN
ejpam-4694	6	35	.	.	PUNCT
ejpam-4694	7	1	moreover	moreover	ADV
ejpam-4694	7	2	,	,	PUNCT
ejpam-4694	7	3	some	some	DET
ejpam-4694	7	4	relations	relation	NOUN
ejpam-4694	7	5	are	be	AUX
ejpam-4694	7	6	established	establish	VERB
ejpam-4694	7	7	connecting	connect	VERB
ejpam-4694	7	8	these	these	DET
ejpam-4694	7	9	polynomials	polynomial	NOUN
ejpam-4694	7	10	to	to	PART
ejpam-4694	7	11	degenerate	degenerate	VERB
ejpam-4694	7	12	stirling	stirling	NOUN
ejpam-4694	7	13	numbers	number	NOUN
ejpam-4694	7	14	of	of	ADP
ejpam-4694	7	15	the	the	DET
ejpam-4694	7	16	first	first	ADJ
ejpam-4694	7	17	and	and	CCONJ
ejpam-4694	7	18	second	second	ADJ
ejpam-4694	7	19	kind	kind	NOUN
ejpam-4694	7	20	,	,	PUNCT
ejpam-4694	7	21	higher	high	ADJ
ejpam-4694	7	22	order	order	NOUN
ejpam-4694	7	23	degenerate	degenerate	ADJ
ejpam-4694	7	24	bernoulli	bernoulli	NOUN
ejpam-4694	7	25	polynomials	polynomial	NOUN
ejpam-4694	7	26	,	,	PUNCT
ejpam-4694	7	27	and	and	CCONJ
ejpam-4694	7	28	higher	high	ADJ
ejpam-4694	7	29	order	order	NOUN
ejpam-4694	7	30	degenerate	degenerate	ADJ
ejpam-4694	7	31	frobenius	frobenius	NOUN
ejpam-4694	7	32	-	-	PUNCT
ejpam-4694	7	33	euler	euler	NOUN
ejpam-4694	7	34	polynomials	polynomial	NOUN
ejpam-4694	7	35	.	.	PUNCT
ejpam-4694	8	1	2020	2020	NUM
ejpam-4694	8	2	mathematics	mathematic	NOUN
ejpam-4694	8	3	subject	subject	NOUN
ejpam-4694	8	4	classifications	classification	NOUN
ejpam-4694	8	5	:	:	PUNCT
ejpam-4694	8	6	11b68	11b68	NUM
ejpam-4694	8	7	,	,	PUNCT
ejpam-4694	8	8	11b73	11b73	NUM
ejpam-4694	8	9	,	,	PUNCT
ejpam-4694	8	10	05a15	05a15	NOUN
ejpam-4694	8	11	key	key	ADJ
ejpam-4694	8	12	words	word	NOUN
ejpam-4694	8	13	and	and	CCONJ
ejpam-4694	8	14	phrases	phrase	NOUN
ejpam-4694	8	15	:	:	PUNCT
ejpam-4694	8	16	poly	poly	ADJ
ejpam-4694	8	17	-	-	PUNCT
ejpam-4694	8	18	genocchi	genocchi	PROPN
ejpam-4694	8	19	polynomials	polynomial	NOUN
ejpam-4694	8	20	,	,	PUNCT
ejpam-4694	8	21	degenerate	degenerate	ADJ
ejpam-4694	8	22	exponential	exponential	ADJ
ejpam-4694	8	23	function	function	NOUN
ejpam-4694	8	24	,	,	PUNCT
ejpam-4694	8	25	polyexponential	polyexponential	ADJ
ejpam-4694	8	26	function	function	NOUN
ejpam-4694	8	27	,	,	PUNCT
ejpam-4694	8	28	polylogarithm	polylogarithm	PROPN
ejpam-4694	8	29	,	,	PUNCT
ejpam-4694	8	30	frobenius	frobenius	NOUN
ejpam-4694	8	31	polynomials	polynomial	NOUN
ejpam-4694	8	32	,	,	PUNCT
ejpam-4694	8	33	appell	appell	NOUN
ejpam-4694	8	34	polynomials	polynomial	NOUN
ejpam-4694	8	35	,	,	PUNCT
ejpam-4694	8	36	euler	euler	NOUN
ejpam-4694	8	37	polynomials	polynomial	NOUN
ejpam-4694	8	38	,	,	PUNCT
ejpam-4694	8	39	bernoulli	bernoulli	NOUN
ejpam-4694	8	40	polynomials	polynomial	VERB
ejpam-4694	8	41	1	1	NUM
ejpam-4694	8	42	.	.	PUNCT
ejpam-4694	9	1	introduction	introduction	NOUN
ejpam-4694	9	2	there	there	PRON
ejpam-4694	9	3	are	be	VERB
ejpam-4694	9	4	many	many	ADJ
ejpam-4694	9	5	ways	way	NOUN
ejpam-4694	9	6	of	of	ADP
ejpam-4694	9	7	constructing	construct	VERB
ejpam-4694	9	8	a	a	DET
ejpam-4694	9	9	generalization	generalization	NOUN
ejpam-4694	9	10	of	of	ADP
ejpam-4694	9	11	certain	certain	ADJ
ejpam-4694	9	12	special	special	ADJ
ejpam-4694	9	13	function	function	NOUN
ejpam-4694	9	14	,	,	PUNCT
ejpam-4694	9	15	polynomial	polynomial	ADJ
ejpam-4694	9	16	or	or	CCONJ
ejpam-4694	9	17	number	number	NOUN
ejpam-4694	9	18	.	.	PUNCT
ejpam-4694	10	1	one	one	NUM
ejpam-4694	10	2	of	of	ADP
ejpam-4694	10	3	these	these	PRON
ejpam-4694	10	4	is	be	AUX
ejpam-4694	10	5	by	by	ADP
ejpam-4694	10	6	mixing	mix	VERB
ejpam-4694	10	7	it	it	PRON
ejpam-4694	10	8	with	with	ADP
ejpam-4694	10	9	the	the	DET
ejpam-4694	10	10	concept	concept	NOUN
ejpam-4694	10	11	of	of	ADP
ejpam-4694	10	12	some	some	DET
ejpam-4694	10	13	other	other	ADJ
ejpam-4694	10	14	known	know	VERB
ejpam-4694	10	15	functions	function	NOUN
ejpam-4694	10	16	and	and	CCONJ
ejpam-4694	10	17	polynomials	polynomial	NOUN
ejpam-4694	10	18	.	.	PUNCT
ejpam-4694	11	1	for	for	ADP
ejpam-4694	11	2	instance	instance	NOUN
ejpam-4694	11	3	,	,	PUNCT
ejpam-4694	11	4	multiplying	multiply	VERB
ejpam-4694	11	5	the	the	DET
ejpam-4694	11	6	generating	generate	VERB
ejpam-4694	11	7	function	function	NOUN
ejpam-4694	11	8	of	of	ADP
ejpam-4694	11	9	the	the	DET
ejpam-4694	11	10	genocchi	genocchi	PROPN
ejpam-4694	11	11	numbers	number	NOUN
ejpam-4694	11	12	gn	gn	PROPN
ejpam-4694	11	13	(	(	PUNCT
ejpam-4694	11	14	see	see	VERB
ejpam-4694	11	15	[	[	X
ejpam-4694	11	16	12	12	NUM
ejpam-4694	11	17	]	]	PUNCT
ejpam-4694	11	18	)	)	PUNCT
ejpam-4694	12	1	∞∑	∞∑	PROPN
ejpam-4694	12	2	n=0	n=0	NUM
ejpam-4694	12	3	gn	gn	PROPN
ejpam-4694	12	4	tn	tn	PROPN
ejpam-4694	12	5	n	n	PROPN
ejpam-4694	12	6	!	!	PUNCT
ejpam-4694	13	1	=	=	PUNCT
ejpam-4694	14	1	2	2	NUM
ejpam-4694	14	2	t	t	NOUN
ejpam-4694	14	3	et	et	NOUN
ejpam-4694	14	4	+	+	CCONJ
ejpam-4694	14	5	1	1	NUM
ejpam-4694	14	6	,	,	PUNCT
ejpam-4694	14	7	|t|	|t|	VERB
ejpam-4694	14	8	<	<	X
ejpam-4694	14	9	π	π	PROPN
ejpam-4694	14	10	,	,	PUNCT
ejpam-4694	14	11	and	and	CCONJ
ejpam-4694	14	12	its	its	PRON
ejpam-4694	14	13	variations	variation	NOUN
ejpam-4694	14	14	with	with	ADP
ejpam-4694	14	15	exponential	exponential	ADJ
ejpam-4694	14	16	polynomials	polynomial	NOUN
ejpam-4694	14	17	yields	yield	VERB
ejpam-4694	14	18	the	the	DET
ejpam-4694	14	19	genocchi	genocchi	PROPN
ejpam-4694	14	20	polynomials	polynomial	VERB
ejpam-4694	14	21	,	,	PUNCT
ejpam-4694	14	22	the	the	DET
ejpam-4694	14	23	genocchi	genocchi	PROPN
ejpam-4694	14	24	polynomials	polynomial	VERB
ejpam-4694	14	25	of	of	ADP
ejpam-4694	14	26	higher	high	ADJ
ejpam-4694	14	27	order	order	NOUN
ejpam-4694	14	28	,	,	PUNCT
ejpam-4694	14	29	the	the	DET
ejpam-4694	14	30	apostol	apostol	NOUN
ejpam-4694	14	31	-	-	PUNCT
ejpam-4694	14	32	genocchi	genocchi	PROPN
ejpam-4694	14	33	polynomials	polynomial	NOUN
ejpam-4694	14	34	,	,	PUNCT
ejpam-4694	14	35	and	and	CCONJ
ejpam-4694	14	36	apostolgenocchi	apostolgenocchi	NOUN
ejpam-4694	14	37	polynomials	polynomial	NOUN
ejpam-4694	14	38	of	of	ADP
ejpam-4694	14	39	higher	high	ADJ
ejpam-4694	14	40	order	order	NOUN
ejpam-4694	14	41	,	,	PUNCT
ejpam-4694	14	42	which	which	PRON
ejpam-4694	14	43	are	be	AUX
ejpam-4694	14	44	respectively	respectively	ADV
ejpam-4694	14	45	defined	define	VERB
ejpam-4694	14	46	as	as	SCONJ
ejpam-4694	14	47	follows	follow	VERB
ejpam-4694	14	48	:	:	PUNCT
ejpam-4694	14	49	∞∑	∞∑	NUM
ejpam-4694	14	50	n=0	n=0	NUM
ejpam-4694	14	51	gn(x	gn(x	NUM
ejpam-4694	14	52	)	)	PUNCT
ejpam-4694	14	53	tn	tn	NOUN
ejpam-4694	15	1	n	n	NOUN
ejpam-4694	15	2	!	!	PUNCT
ejpam-4694	16	1	=	=	PUNCT
ejpam-4694	17	1	2	2	NUM
ejpam-4694	17	2	t	t	NOUN
ejpam-4694	17	3	et	et	NOUN
ejpam-4694	17	4	+	+	CCONJ
ejpam-4694	17	5	1	1	NUM
ejpam-4694	17	6	ext	ext	NOUN
ejpam-4694	17	7	,	,	PUNCT
ejpam-4694	17	8	|t|	|t|	VERB
ejpam-4694	17	9	<	<	X
ejpam-4694	17	10	π	π	PROPN
ejpam-4694	17	11	,	,	PUNCT
ejpam-4694	17	12	(	(	PUNCT
ejpam-4694	17	13	1	1	X
ejpam-4694	17	14	)	)	PUNCT
ejpam-4694	17	15	∗corresponding	∗corresponde	VERB
ejpam-4694	17	16	author	author	NOUN
ejpam-4694	17	17	.	.	PUNCT
ejpam-4694	18	1	doi	doi	NOUN
ejpam-4694	18	2	:	:	PUNCT
ejpam-4694	18	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4694	https://doi.org/10.29020/nybg.ejpam.v16i2.4694	DET
ejpam-4694	18	4	email	email	NOUN
ejpam-4694	18	5	addresses	address	VERB
ejpam-4694	18	6	:	:	PUNCT
ejpam-4694	19	1	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-4694	19	2	(	(	PUNCT
ejpam-4694	19	3	r.	r.	PROPN
ejpam-4694	19	4	corcino	corcino	PROPN
ejpam-4694	19	5	)	)	PUNCT
ejpam-4694	19	6	,	,	PUNCT
ejpam-4694	19	7	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-4694	19	8	(	(	PUNCT
ejpam-4694	19	9	c.	c.	PROPN
ejpam-4694	19	10	corcino	corcino	PROPN
ejpam-4694	19	11	)	)	PUNCT
ejpam-4694	19	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4694	20	1	687	687	NUM
ejpam-4694	20	2	©	©	ADP
ejpam-4694	20	3	2023	2023	NUM
ejpam-4694	20	4	ejpam	ejpam	NOUN
ejpam-4694	20	5	all	all	DET
ejpam-4694	20	6	rights	right	NOUN
ejpam-4694	20	7	reserved	reserve	VERB
ejpam-4694	20	8	.	.	PUNCT
ejpam-4694	21	1	r.	r.	PROPN
ejpam-4694	21	2	corcino	corcino	PROPN
ejpam-4694	21	3	,	,	PUNCT
ejpam-4694	21	4	c.	c.	PROPN
ejpam-4694	21	5	corcino	corcino	PROPN
ejpam-4694	21	6	/	/	SYM
ejpam-4694	21	7	eur	eur	PROPN
ejpam-4694	21	8	.	.	PUNCT
ejpam-4694	22	1	j.	j.	PROPN
ejpam-4694	22	2	pure	pure	PROPN
ejpam-4694	22	3	appl	appl	PROPN
ejpam-4694	22	4	.	.	PROPN
ejpam-4694	22	5	math	math	PROPN
ejpam-4694	22	6	,	,	PUNCT
ejpam-4694	22	7	16	16	NUM
ejpam-4694	22	8	(	(	PUNCT
ejpam-4694	22	9	2	2	NUM
ejpam-4694	22	10	)	)	PUNCT
ejpam-4694	22	11	(	(	PUNCT
ejpam-4694	22	12	2023	2023	NUM
ejpam-4694	22	13	)	)	PUNCT
ejpam-4694	22	14	,	,	PUNCT
ejpam-4694	22	15	687	687	NUM
ejpam-4694	22	16	-	-	SYM
ejpam-4694	22	17	712	712	NUM
ejpam-4694	22	18	688	688	NUM
ejpam-4694	22	19	∞∑	∞∑	NUM
ejpam-4694	22	20	n=0	n=0	PUNCT
ejpam-4694	22	21	g(k	g(k	NOUN
ejpam-4694	22	22	)	)	PUNCT
ejpam-4694	22	23	n	n	CCONJ
ejpam-4694	22	24	(	(	PUNCT
ejpam-4694	22	25	x	x	X
ejpam-4694	22	26	)	)	PUNCT
ejpam-4694	22	27	tn	tn	PROPN
ejpam-4694	22	28	n	n	NOUN
ejpam-4694	22	29	!	!	PUNCT
ejpam-4694	23	1	=	=	PUNCT
ejpam-4694	23	2	(	(	PUNCT
ejpam-4694	23	3	2	2	NUM
ejpam-4694	23	4	t	t	NOUN
ejpam-4694	23	5	et	et	NOUN
ejpam-4694	23	6	+	+	CCONJ
ejpam-4694	23	7	1	1	X
ejpam-4694	23	8	)	)	PUNCT
ejpam-4694	23	9	k	k	PROPN
ejpam-4694	23	10	ext	ext	PROPN
ejpam-4694	23	11	,	,	PUNCT
ejpam-4694	23	12	(	(	PUNCT
ejpam-4694	23	13	2	2	X
ejpam-4694	23	14	)	)	PUNCT
ejpam-4694	23	15	∞∑	∞∑	NUM
ejpam-4694	23	16	n=0	n=0	NUM
ejpam-4694	23	17	gn(x	gn(x	X
ejpam-4694	23	18	,	,	PUNCT
ejpam-4694	23	19	λ	λ	NOUN
ejpam-4694	23	20	)	)	PUNCT
ejpam-4694	23	21	tn	tn	PROPN
ejpam-4694	23	22	n	n	NOUN
ejpam-4694	23	23	!	!	PUNCT
ejpam-4694	23	24	=	=	PUNCT
ejpam-4694	24	1	2	2	NUM
ejpam-4694	24	2	t	t	NOUN
ejpam-4694	24	3	λet	λet	NOUN
ejpam-4694	25	1	+	+	CCONJ
ejpam-4694	25	2	1	1	NUM
ejpam-4694	25	3	ext	ext	NOUN
ejpam-4694	25	4	,	,	PUNCT
ejpam-4694	25	5	(	(	PUNCT
ejpam-4694	25	6	3	3	X
ejpam-4694	25	7	)	)	PUNCT
ejpam-4694	25	8	∞∑	∞∑	PRON
ejpam-4694	25	9	n=0	n=0	PUNCT
ejpam-4694	25	10	g(k	g(k	NOUN
ejpam-4694	25	11	)	)	PUNCT
ejpam-4694	25	12	n	n	CCONJ
ejpam-4694	25	13	(	(	PUNCT
ejpam-4694	25	14	x	x	NOUN
ejpam-4694	25	15	,	,	PUNCT
ejpam-4694	25	16	λ	λ	NOUN
ejpam-4694	25	17	)	)	PUNCT
ejpam-4694	25	18	tn	tn	PROPN
ejpam-4694	25	19	n	n	PROPN
ejpam-4694	25	20	!	!	PUNCT
ejpam-4694	25	21	=	=	PUNCT
ejpam-4694	26	1	(	(	PUNCT
ejpam-4694	26	2	2	2	NUM
ejpam-4694	26	3	t	t	NOUN
ejpam-4694	26	4	λet	λet	NOUN
ejpam-4694	27	1	+	+	CCONJ
ejpam-4694	27	2	1	1	X
ejpam-4694	27	3	)	)	PUNCT
ejpam-4694	27	4	k	k	PROPN
ejpam-4694	27	5	ext	ext	PROPN
ejpam-4694	27	6	,	,	PUNCT
ejpam-4694	27	7	(	(	PUNCT
ejpam-4694	27	8	4	4	X
ejpam-4694	27	9	)	)	PUNCT
ejpam-4694	27	10	where	where	SCONJ
ejpam-4694	27	11	|t|	|t|	ADP
ejpam-4694	27	12	<	<	X
ejpam-4694	27	13	π	π	PROPN
ejpam-4694	27	14	when	when	SCONJ
ejpam-4694	27	15	λ	λ	X
ejpam-4694	27	16	=	=	SYM
ejpam-4694	27	17	1	1	NUM
ejpam-4694	27	18	and	and	CCONJ
ejpam-4694	27	19	|t|	|t|	VERB
ejpam-4694	27	20	<	<	X
ejpam-4694	27	21	log(−λ	log(−λ	PROPN
ejpam-4694	27	22	)	)	PUNCT
ejpam-4694	28	1	when	when	SCONJ
ejpam-4694	28	2	λ	λ	X
ejpam-4694	28	3	̸=	̸=	PROPN
ejpam-4694	28	4	1	1	NUM
ejpam-4694	28	5	,	,	PUNCT
ejpam-4694	28	6	λ	λ	PROPN
ejpam-4694	28	7	∈	∈	PROPN
ejpam-4694	28	8	c	c	NOUN
ejpam-4694	28	9	(	(	PUNCT
ejpam-4694	28	10	see	see	VERB
ejpam-4694	28	11	[	[	X
ejpam-4694	28	12	1–3	1–3	NOUN
ejpam-4694	28	13	,	,	PUNCT
ejpam-4694	28	14	5	5	NUM
ejpam-4694	28	15	,	,	PUNCT
ejpam-4694	28	16	6	6	NUM
ejpam-4694	28	17	,	,	PUNCT
ejpam-4694	28	18	40	40	NUM
ejpam-4694	28	19	]	]	PUNCT
ejpam-4694	28	20	)	)	PUNCT
ejpam-4694	28	21	.	.	PUNCT
ejpam-4694	29	1	the	the	DET
ejpam-4694	29	2	first	first	ADJ
ejpam-4694	29	3	two	two	NUM
ejpam-4694	29	4	polynomials	polynomial	NOUN
ejpam-4694	29	5	are	be	AUX
ejpam-4694	29	6	well	well	ADV
ejpam-4694	29	7	-	-	PUNCT
ejpam-4694	29	8	studied	study	VERB
ejpam-4694	29	9	and	and	CCONJ
ejpam-4694	29	10	two	two	NUM
ejpam-4694	29	11	of	of	ADP
ejpam-4694	29	12	the	the	DET
ejpam-4694	29	13	most	most	ADV
ejpam-4694	29	14	recent	recent	ADJ
ejpam-4694	29	15	studies	study	NOUN
ejpam-4694	29	16	are	be	AUX
ejpam-4694	29	17	the	the	DET
ejpam-4694	29	18	works	work	NOUN
ejpam-4694	29	19	of	of	ADP
ejpam-4694	29	20	corcino	corcino	NOUN
ejpam-4694	29	21	-	-	PUNCT
ejpam-4694	29	22	corcino	corcino	NOUN
ejpam-4694	29	23	[	[	X
ejpam-4694	29	24	14	14	NUM
ejpam-4694	29	25	,	,	PUNCT
ejpam-4694	29	26	15	15	NUM
ejpam-4694	29	27	]	]	PUNCT
ejpam-4694	29	28	on	on	ADP
ejpam-4694	29	29	asymptotic	asymptotic	ADJ
ejpam-4694	29	30	approximations	approximation	NOUN
ejpam-4694	29	31	,	,	PUNCT
ejpam-4694	29	32	while	while	SCONJ
ejpam-4694	29	33	the	the	DET
ejpam-4694	29	34	last	last	ADJ
ejpam-4694	29	35	two	two	NUM
ejpam-4694	29	36	were	be	AUX
ejpam-4694	29	37	given	give	VERB
ejpam-4694	29	38	asymptotic	asymptotic	ADJ
ejpam-4694	29	39	approximation	approximation	NOUN
ejpam-4694	29	40	and	and	CCONJ
ejpam-4694	29	41	fourier	fourier	NOUN
ejpam-4694	29	42	series	series	NOUN
ejpam-4694	29	43	expansion	expansion	NOUN
ejpam-4694	29	44	in	in	ADP
ejpam-4694	29	45	[	[	X
ejpam-4694	29	46	13	13	NUM
ejpam-4694	29	47	,	,	PUNCT
ejpam-4694	29	48	16	16	NUM
ejpam-4694	29	49	,	,	PUNCT
ejpam-4694	29	50	20	20	NUM
ejpam-4694	29	51	]	]	PUNCT
ejpam-4694	29	52	.	.	PUNCT
ejpam-4694	30	1	also	also	ADV
ejpam-4694	30	2	,	,	PUNCT
ejpam-4694	30	3	incorporating	incorporate	VERB
ejpam-4694	30	4	the	the	DET
ejpam-4694	30	5	concept	concept	NOUN
ejpam-4694	30	6	of	of	ADP
ejpam-4694	30	7	frobenius	frobenius	ADJ
ejpam-4694	30	8	polynomials	polynomial	NOUN
ejpam-4694	30	9	yields	yield	VERB
ejpam-4694	30	10	the	the	DET
ejpam-4694	30	11	so	so	ADV
ejpam-4694	30	12	-	-	PUNCT
ejpam-4694	30	13	called	call	VERB
ejpam-4694	30	14	frobeniusgenocchi	frobeniusgenocchi	ADJ
ejpam-4694	30	15	polynomials	polynomial	NOUN
ejpam-4694	30	16	,	,	PUNCT
ejpam-4694	30	17	which	which	PRON
ejpam-4694	30	18	are	be	AUX
ejpam-4694	30	19	given	give	VERB
ejpam-4694	30	20	by	by	ADP
ejpam-4694	30	21	∞∑	∞∑	DET
ejpam-4694	30	22	n=0	n=0	NUM
ejpam-4694	30	23	gf	gf	NOUN
ejpam-4694	30	24	n	n	PROPN
ejpam-4694	30	25	(	(	PUNCT
ejpam-4694	30	26	x;u	x;u	PROPN
ejpam-4694	30	27	)	)	PUNCT
ejpam-4694	30	28	tn	tn	PROPN
ejpam-4694	30	29	n	n	PROPN
ejpam-4694	30	30	!	!	PUNCT
ejpam-4694	31	1	=	=	PUNCT
ejpam-4694	31	2	(	(	PUNCT
ejpam-4694	31	3	1−	1−	NUM
ejpam-4694	31	4	u)t	u)t	X
ejpam-4694	31	5	et	et	NOUN
ejpam-4694	31	6	−	−	PROPN
ejpam-4694	31	7	u	u	PROPN
ejpam-4694	31	8	ext	ext	NOUN
ejpam-4694	31	9	,	,	PUNCT
ejpam-4694	31	10	(	(	PUNCT
ejpam-4694	31	11	5	5	NUM
ejpam-4694	31	12	)	)	PUNCT
ejpam-4694	31	13	(	(	PUNCT
ejpam-4694	31	14	see	see	VERB
ejpam-4694	31	15	[	[	X
ejpam-4694	31	16	4	4	NUM
ejpam-4694	31	17	,	,	PUNCT
ejpam-4694	31	18	6	6	NUM
ejpam-4694	31	19	,	,	PUNCT
ejpam-4694	31	20	7	7	NUM
ejpam-4694	31	21	,	,	PUNCT
ejpam-4694	31	22	19	19	NUM
ejpam-4694	31	23	,	,	PUNCT
ejpam-4694	31	24	21	21	NUM
ejpam-4694	31	25	,	,	PUNCT
ejpam-4694	31	26	24	24	NUM
ejpam-4694	31	27	,	,	PUNCT
ejpam-4694	31	28	32	32	NUM
ejpam-4694	31	29	,	,	PUNCT
ejpam-4694	31	30	43	43	NUM
ejpam-4694	31	31	,	,	PUNCT
ejpam-4694	31	32	44	44	NUM
ejpam-4694	31	33	]	]	PUNCT
ejpam-4694	31	34	for	for	ADP
ejpam-4694	31	35	other	other	ADJ
ejpam-4694	31	36	interesting	interesting	ADJ
ejpam-4694	31	37	studies	study	NOUN
ejpam-4694	31	38	related	relate	VERB
ejpam-4694	31	39	to	to	ADP
ejpam-4694	31	40	these	these	DET
ejpam-4694	31	41	polynomials	polynomial	NOUN
ejpam-4694	31	42	)	)	PUNCT
ejpam-4694	31	43	.	.	PUNCT
ejpam-4694	32	1	moreover	moreover	ADV
ejpam-4694	32	2	,	,	PUNCT
ejpam-4694	32	3	mixing	mix	VERB
ejpam-4694	32	4	the	the	DET
ejpam-4694	32	5	genocchi	genocchi	PROPN
ejpam-4694	32	6	numbers	number	NOUN
ejpam-4694	32	7	with	with	ADP
ejpam-4694	32	8	the	the	DET
ejpam-4694	32	9	concept	concept	NOUN
ejpam-4694	32	10	of	of	ADP
ejpam-4694	32	11	polylogarithm	polylogarithm	PROPN
ejpam-4694	32	12	lik(z	lik(z	PROPN
ejpam-4694	32	13	)	)	PUNCT
ejpam-4694	32	14	lik(z	lik(z	PROPN
ejpam-4694	32	15	)	)	PUNCT
ejpam-4694	33	1	=	=	PUNCT
ejpam-4694	34	1	∞∑	∞∑	NUM
ejpam-4694	34	2	n=0	n=0	NUM
ejpam-4694	34	3	zn	zn	PROPN
ejpam-4694	34	4	nk	nk	PROPN
ejpam-4694	34	5	,	,	PUNCT
ejpam-4694	34	6	k	k	PROPN
ejpam-4694	34	7	∈	∈	PROPN
ejpam-4694	34	8	z	z	PROPN
ejpam-4694	34	9	,	,	PUNCT
ejpam-4694	34	10	(	(	PUNCT
ejpam-4694	34	11	6	6	X
ejpam-4694	34	12	)	)	PUNCT
ejpam-4694	34	13	yields	yield	VERB
ejpam-4694	34	14	the	the	DET
ejpam-4694	34	15	poly	poly	ADJ
ejpam-4694	34	16	-	-	PUNCT
ejpam-4694	34	17	genocchi	genocchi	NOUN
ejpam-4694	34	18	polynomials	polynomial	NOUN
ejpam-4694	34	19	,	,	PUNCT
ejpam-4694	34	20	which	which	PRON
ejpam-4694	34	21	are	be	AUX
ejpam-4694	34	22	defined	define	VERB
ejpam-4694	34	23	as	as	SCONJ
ejpam-4694	34	24	follows	follow	VERB
ejpam-4694	34	25	∞∑	∞∑	NUM
ejpam-4694	34	26	n=0	n=0	NUM
ejpam-4694	34	27	g(k	g(k	NOUN
ejpam-4694	34	28	)	)	PUNCT
ejpam-4694	34	29	n	n	CCONJ
ejpam-4694	34	30	(	(	PUNCT
ejpam-4694	34	31	x	x	X
ejpam-4694	34	32	)	)	PUNCT
ejpam-4694	34	33	xn	xn	PROPN
ejpam-4694	34	34	n	n	X
ejpam-4694	34	35	!	!	PUNCT
ejpam-4694	35	1	=	=	SYM
ejpam-4694	35	2	2lik(1−	2lik(1−	NUM
ejpam-4694	35	3	et	et	NOUN
ejpam-4694	35	4	)	)	PUNCT
ejpam-4694	35	5	et	et	NOUN
ejpam-4694	36	1	+	+	NOUN
ejpam-4694	36	2	1	1	NUM
ejpam-4694	36	3	ext	ext	NOUN
ejpam-4694	36	4	.	.	PUNCT
ejpam-4694	37	1	(	(	PUNCT
ejpam-4694	37	2	7	7	X
ejpam-4694	37	3	)	)	PUNCT
ejpam-4694	37	4	furthermore	furthermore	ADV
ejpam-4694	37	5	,	,	PUNCT
ejpam-4694	37	6	with	with	ADP
ejpam-4694	37	7	a	a	DET
ejpam-4694	37	8	slight	slight	ADJ
ejpam-4694	37	9	modification	modification	NOUN
ejpam-4694	37	10	of	of	ADP
ejpam-4694	37	11	the	the	DET
ejpam-4694	37	12	generating	generate	VERB
ejpam-4694	37	13	function	function	NOUN
ejpam-4694	37	14	,	,	PUNCT
ejpam-4694	37	15	another	another	DET
ejpam-4694	37	16	generalization	generalization	NOUN
ejpam-4694	37	17	,	,	PUNCT
ejpam-4694	37	18	denoted	denote	VERB
ejpam-4694	37	19	by	by	ADP
ejpam-4694	37	20	g	g	PROPN
ejpam-4694	37	21	(	(	PUNCT
ejpam-4694	37	22	k	k	NOUN
ejpam-4694	37	23	)	)	PUNCT
ejpam-4694	37	24	n,2(x	n,2(x	NOUN
ejpam-4694	37	25	)	)	PUNCT
ejpam-4694	37	26	,	,	PUNCT
ejpam-4694	37	27	was	be	AUX
ejpam-4694	37	28	defined	define	VERB
ejpam-4694	37	29	by	by	ADP
ejpam-4694	37	30	kim	kim	PROPN
ejpam-4694	37	31	et	et	PROPN
ejpam-4694	37	32	al	al	PROPN
ejpam-4694	37	33	.	.	PUNCT
ejpam-4694	38	1	[	[	X
ejpam-4694	38	2	9	9	NUM
ejpam-4694	38	3	,	,	PUNCT
ejpam-4694	38	4	25	25	NUM
ejpam-4694	38	5	,	,	PUNCT
ejpam-4694	38	6	34	34	NUM
ejpam-4694	38	7	]	]	PUNCT
ejpam-4694	38	8	as	as	SCONJ
ejpam-4694	38	9	follows	follow	VERB
ejpam-4694	38	10	∞∑	∞∑	NUM
ejpam-4694	38	11	n=0	n=0	ADJ
ejpam-4694	38	12	g	g	NOUN
ejpam-4694	38	13	(	(	PUNCT
ejpam-4694	38	14	k	k	NOUN
ejpam-4694	38	15	)	)	PUNCT
ejpam-4694	38	16	n,2(x	n,2(x	NOUN
ejpam-4694	38	17	)	)	PUNCT
ejpam-4694	38	18	xn	xn	PROPN
ejpam-4694	39	1	n	n	X
ejpam-4694	39	2	!	!	PUNCT
ejpam-4694	40	1	=	=	PRON
ejpam-4694	40	2	lik(1−	lik(1−	PROPN
ejpam-4694	40	3	e−2	e−2	PROPN
ejpam-4694	40	4	t	t	PROPN
ejpam-4694	40	5	)	)	PUNCT
ejpam-4694	40	6	et	et	NOUN
ejpam-4694	41	1	+	+	NOUN
ejpam-4694	41	2	1	1	NUM
ejpam-4694	41	3	ext	ext	NOUN
ejpam-4694	41	4	.	.	PUNCT
ejpam-4694	42	1	(	(	PUNCT
ejpam-4694	42	2	8)	8)	NUM
ejpam-4694	42	3	these	these	DET
ejpam-4694	42	4	polynomials	polynomial	NOUN
ejpam-4694	42	5	are	be	AUX
ejpam-4694	42	6	called	call	VERB
ejpam-4694	42	7	modified	modified	ADJ
ejpam-4694	42	8	poly	poly	ADJ
ejpam-4694	42	9	-	-	PUNCT
ejpam-4694	42	10	genocchi	genocchi	NOUN
ejpam-4694	42	11	polynomials	polynomial	NOUN
ejpam-4694	42	12	.	.	PUNCT
ejpam-4694	43	1	note	note	VERB
ejpam-4694	43	2	that	that	SCONJ
ejpam-4694	43	3	,	,	PUNCT
ejpam-4694	43	4	when	when	SCONJ
ejpam-4694	43	5	k	k	PROPN
ejpam-4694	43	6	=	=	SYM
ejpam-4694	43	7	1	1	NUM
ejpam-4694	43	8	,	,	PUNCT
ejpam-4694	43	9	equations	equation	NOUN
ejpam-4694	43	10	(	(	PUNCT
ejpam-4694	43	11	7	7	NUM
ejpam-4694	43	12	)	)	PUNCT
ejpam-4694	43	13	and	and	CCONJ
ejpam-4694	43	14	(	(	PUNCT
ejpam-4694	43	15	8)	8)	NUM
ejpam-4694	43	16	give	give	VERB
ejpam-4694	43	17	the	the	DET
ejpam-4694	43	18	genocchi	genocchi	NOUN
ejpam-4694	43	19	polynomials	polynomial	NOUN
ejpam-4694	43	20	in	in	ADP
ejpam-4694	43	21	(	(	PUNCT
ejpam-4694	43	22	1	1	NUM
ejpam-4694	43	23	)	)	PUNCT
ejpam-4694	43	24	.	.	PUNCT
ejpam-4694	44	1	that	that	PRON
ejpam-4694	44	2	is	be	AUX
ejpam-4694	44	3	,	,	PUNCT
ejpam-4694	44	4	g(1	g(1	NOUN
ejpam-4694	44	5	)	)	PUNCT
ejpam-4694	44	6	n	n	CCONJ
ejpam-4694	44	7	(	(	PUNCT
ejpam-4694	44	8	x	x	X
ejpam-4694	44	9	)	)	PUNCT
ejpam-4694	44	10	=	=	SYM
ejpam-4694	44	11	g	g	PROPN
ejpam-4694	44	12	(	(	PUNCT
ejpam-4694	44	13	1	1	NUM
ejpam-4694	44	14	)	)	PUNCT
ejpam-4694	44	15	n,2(x	n,2(x	NOUN
ejpam-4694	44	16	)	)	PUNCT
ejpam-4694	44	17	=	=	SYM
ejpam-4694	44	18	gn(x	gn(x	NUM
ejpam-4694	44	19	)	)	PUNCT
ejpam-4694	44	20	.	.	PUNCT
ejpam-4694	45	1	kim	kim	PROPN
ejpam-4694	45	2	et	et	PROPN
ejpam-4694	45	3	.	.	PUNCT
ejpam-4694	46	1	al	al	PROPN
ejpam-4694	47	1	[	[	X
ejpam-4694	47	2	25	25	NUM
ejpam-4694	47	3	]	]	PUNCT
ejpam-4694	47	4	obtained	obtain	VERB
ejpam-4694	47	5	several	several	ADJ
ejpam-4694	47	6	properties	property	NOUN
ejpam-4694	47	7	of	of	ADP
ejpam-4694	47	8	these	these	DET
ejpam-4694	47	9	polynomials	polynomial	NOUN
ejpam-4694	47	10	.	.	PUNCT
ejpam-4694	48	1	by	by	ADP
ejpam-4694	48	2	introducing	introduce	VERB
ejpam-4694	48	3	additional	additional	ADJ
ejpam-4694	48	4	three	three	NUM
ejpam-4694	48	5	parameters	parameter	NOUN
ejpam-4694	48	6	a	a	DET
ejpam-4694	48	7	,	,	PUNCT
ejpam-4694	48	8	b	b	NOUN
ejpam-4694	48	9	,	,	PUNCT
ejpam-4694	48	10	and	and	CCONJ
ejpam-4694	48	11	c	c	X
ejpam-4694	48	12	,	,	PUNCT
ejpam-4694	48	13	kurt	kurt	PROPN
ejpam-4694	48	14	[	[	X
ejpam-4694	48	15	33	33	NUM
ejpam-4694	48	16	]	]	PUNCT
ejpam-4694	48	17	defined	define	VERB
ejpam-4694	48	18	two	two	NUM
ejpam-4694	48	19	forms	form	NOUN
ejpam-4694	48	20	of	of	ADP
ejpam-4694	48	21	generalized	generalized	ADJ
ejpam-4694	48	22	poly	poly	ADJ
ejpam-4694	48	23	-	-	PUNCT
ejpam-4694	48	24	genocchi	genocchi	NOUN
ejpam-4694	48	25	polynomials	polynomial	NOUN
ejpam-4694	48	26	as	as	SCONJ
ejpam-4694	48	27	follows	follow	VERB
ejpam-4694	48	28	2lik(1−	2lik(1−	NUM
ejpam-4694	48	29	(	(	PUNCT
ejpam-4694	48	30	ab)−t	ab)−t	PROPN
ejpam-4694	48	31	)	)	PUNCT
ejpam-4694	48	32	a−t	a−t	VERB
ejpam-4694	49	1	+	+	CCONJ
ejpam-4694	49	2	bt	bt	X
ejpam-4694	49	3	ext	ext	NOUN
ejpam-4694	49	4	=	=	PUNCT
ejpam-4694	49	5	∞∑	∞∑	NUM
ejpam-4694	49	6	n=0	n=0	NUM
ejpam-4694	49	7	g(k	g(k	NOUN
ejpam-4694	49	8	)	)	PUNCT
ejpam-4694	49	9	n	n	CCONJ
ejpam-4694	49	10	(	(	PUNCT
ejpam-4694	49	11	x	x	X
ejpam-4694	49	12	;	;	PUNCT
ejpam-4694	49	13	a	a	DET
ejpam-4694	49	14	,	,	PUNCT
ejpam-4694	49	15	b	b	NOUN
ejpam-4694	49	16	,	,	PUNCT
ejpam-4694	49	17	c	c	NOUN
ejpam-4694	49	18	)	)	PUNCT
ejpam-4694	49	19	xn	xn	PROPN
ejpam-4694	49	20	n	n	X
ejpam-4694	49	21	!	!	PUNCT
ejpam-4694	50	1	(	(	PUNCT
ejpam-4694	50	2	9	9	X
ejpam-4694	50	3	)	)	PUNCT
ejpam-4694	50	4	r.	r.	NOUN
ejpam-4694	50	5	corcino	corcino	PROPN
ejpam-4694	50	6	,	,	PUNCT
ejpam-4694	50	7	c.	c.	PROPN
ejpam-4694	50	8	corcino	corcino	PROPN
ejpam-4694	50	9	/	/	SYM
ejpam-4694	50	10	eur	eur	PROPN
ejpam-4694	50	11	.	.	PUNCT
ejpam-4694	51	1	j.	j.	PROPN
ejpam-4694	51	2	pure	pure	PROPN
ejpam-4694	51	3	appl	appl	PROPN
ejpam-4694	51	4	.	.	PROPN
ejpam-4694	51	5	math	math	PROPN
ejpam-4694	51	6	,	,	PUNCT
ejpam-4694	51	7	16	16	NUM
ejpam-4694	51	8	(	(	PUNCT
ejpam-4694	51	9	2	2	NUM
ejpam-4694	51	10	)	)	PUNCT
ejpam-4694	51	11	(	(	PUNCT
ejpam-4694	51	12	2023	2023	NUM
ejpam-4694	51	13	)	)	PUNCT
ejpam-4694	51	14	,	,	PUNCT
ejpam-4694	51	15	687	687	NUM
ejpam-4694	51	16	-	-	SYM
ejpam-4694	51	17	712	712	NUM
ejpam-4694	51	18	689	689	NUM
ejpam-4694	51	19	2lik(1−	2lik(1−	NUM
ejpam-4694	51	20	(	(	PUNCT
ejpam-4694	51	21	ab)−2	ab)−2	NOUN
ejpam-4694	51	22	t	t	PROPN
ejpam-4694	51	23	)	)	PUNCT
ejpam-4694	51	24	a−t	a−t	PROPN
ejpam-4694	52	1	+	+	CCONJ
ejpam-4694	52	2	bt	bt	X
ejpam-4694	52	3	ext	ext	NOUN
ejpam-4694	52	4	=	=	PUNCT
ejpam-4694	52	5	∞∑	∞∑	NUM
ejpam-4694	52	6	n=0	n=0	NUM
ejpam-4694	52	7	g	g	NOUN
ejpam-4694	52	8	(	(	PUNCT
ejpam-4694	52	9	k	k	NOUN
ejpam-4694	52	10	)	)	PUNCT
ejpam-4694	52	11	n,2(x	n,2(x	PROPN
ejpam-4694	52	12	;	;	PUNCT
ejpam-4694	52	13	a	a	DET
ejpam-4694	52	14	,	,	PUNCT
ejpam-4694	52	15	b	b	NOUN
ejpam-4694	52	16	,	,	PUNCT
ejpam-4694	52	17	c	c	NOUN
ejpam-4694	52	18	)	)	PUNCT
ejpam-4694	52	19	xn	xn	PROPN
ejpam-4694	53	1	n	n	NUM
ejpam-4694	53	2	!	!	PUNCT
ejpam-4694	53	3	.	.	PUNCT
ejpam-4694	54	1	(	(	PUNCT
ejpam-4694	54	2	10	10	NUM
ejpam-4694	54	3	)	)	PUNCT
ejpam-4694	54	4	these	these	PRON
ejpam-4694	54	5	were	be	AUX
ejpam-4694	54	6	motivated	motivate	VERB
ejpam-4694	54	7	by	by	ADP
ejpam-4694	54	8	the	the	DET
ejpam-4694	54	9	generalizations	generalization	NOUN
ejpam-4694	54	10	introduced	introduce	VERB
ejpam-4694	54	11	in	in	ADP
ejpam-4694	54	12	(	(	PUNCT
ejpam-4694	54	13	7	7	NUM
ejpam-4694	54	14	)	)	PUNCT
ejpam-4694	54	15	and	and	CCONJ
ejpam-4694	54	16	(	(	PUNCT
ejpam-4694	54	17	8)	8)	NUM
ejpam-4694	54	18	,	,	PUNCT
ejpam-4694	54	19	respectively	respectively	ADV
ejpam-4694	54	20	.	.	PUNCT
ejpam-4694	55	1	note	note	VERB
ejpam-4694	55	2	that	that	SCONJ
ejpam-4694	55	3	,	,	PUNCT
ejpam-4694	55	4	when	when	SCONJ
ejpam-4694	55	5	x	x	X
ejpam-4694	55	6	=	=	SYM
ejpam-4694	55	7	0	0	NUM
ejpam-4694	55	8	,	,	PUNCT
ejpam-4694	55	9	(	(	PUNCT
ejpam-4694	55	10	7	7	X
ejpam-4694	55	11	)	)	PUNCT
ejpam-4694	55	12	reduces	reduce	VERB
ejpam-4694	55	13	to	to	ADP
ejpam-4694	55	14	2lik(1−	2lik(1−	NUM
ejpam-4694	55	15	et	et	NOUN
ejpam-4694	55	16	)	)	PUNCT
ejpam-4694	55	17	et	et	NOUN
ejpam-4694	56	1	+	+	NOUN
ejpam-4694	56	2	1	1	X
ejpam-4694	56	3	=	=	VERB
ejpam-4694	56	4	∞∑	∞∑	PRON
ejpam-4694	56	5	n=0	n=0	NUM
ejpam-4694	56	6	g(k	g(k	NOUN
ejpam-4694	56	7	)	)	PUNCT
ejpam-4694	56	8	n	n	NOUN
ejpam-4694	56	9	xn	xn	NUM
ejpam-4694	56	10	n	n	CCONJ
ejpam-4694	56	11	!	!	NUM
ejpam-4694	56	12	,	,	PUNCT
ejpam-4694	56	13	(	(	PUNCT
ejpam-4694	56	14	11	11	NUM
ejpam-4694	56	15	)	)	PUNCT
ejpam-4694	56	16	where	where	SCONJ
ejpam-4694	56	17	g	g	PROPN
ejpam-4694	56	18	(	(	PUNCT
ejpam-4694	56	19	k	k	NOUN
ejpam-4694	56	20	)	)	PUNCT
ejpam-4694	56	21	n	n	CCONJ
ejpam-4694	56	22	are	be	AUX
ejpam-4694	56	23	called	call	VERB
ejpam-4694	56	24	the	the	DET
ejpam-4694	56	25	poly	poly	ADJ
ejpam-4694	56	26	-	-	PUNCT
ejpam-4694	56	27	genocchi	genocchi	NOUN
ejpam-4694	56	28	numbers	number	NOUN
ejpam-4694	56	29	.	.	PUNCT
ejpam-4694	57	1	it	it	PRON
ejpam-4694	57	2	is	be	AUX
ejpam-4694	57	3	worth	worth	ADJ
ejpam-4694	57	4	-	-	PUNCT
ejpam-4694	57	5	mentioning	mention	VERB
ejpam-4694	57	6	that	that	SCONJ
ejpam-4694	57	7	,	,	PUNCT
ejpam-4694	57	8	using	use	VERB
ejpam-4694	57	9	multi	multi	NOUN
ejpam-4694	57	10	-	-	ADJ
ejpam-4694	57	11	polylogarithm	polylogarithm	ADJ
ejpam-4694	57	12	,	,	PUNCT
ejpam-4694	57	13	the	the	DET
ejpam-4694	57	14	generalized	generalize	VERB
ejpam-4694	57	15	poly	poly	ADJ
ejpam-4694	57	16	-	-	PUNCT
ejpam-4694	57	17	genocchi	genocchi	NOUN
ejpam-4694	57	18	polynomials	polynomial	NOUN
ejpam-4694	57	19	in	in	ADP
ejpam-4694	57	20	(	(	PUNCT
ejpam-4694	57	21	9	9	NUM
ejpam-4694	57	22	)	)	PUNCT
ejpam-4694	57	23	and	and	CCONJ
ejpam-4694	57	24	(	(	PUNCT
ejpam-4694	57	25	10	10	NUM
ejpam-4694	57	26	)	)	PUNCT
ejpam-4694	57	27	have	have	AUX
ejpam-4694	57	28	been	be	AUX
ejpam-4694	57	29	extended	extend	VERB
ejpam-4694	57	30	further	far	ADV
ejpam-4694	57	31	in	in	ADP
ejpam-4694	57	32	[	[	X
ejpam-4694	57	33	39	39	NUM
ejpam-4694	57	34	]	]	PUNCT
ejpam-4694	57	35	.	.	PUNCT
ejpam-4694	58	1	recently	recently	ADV
ejpam-4694	58	2	,	,	PUNCT
ejpam-4694	58	3	a	a	DET
ejpam-4694	58	4	new	new	ADJ
ejpam-4694	58	5	variation	variation	NOUN
ejpam-4694	58	6	of	of	ADP
ejpam-4694	58	7	poly	poly	ADJ
ejpam-4694	58	8	-	-	PUNCT
ejpam-4694	58	9	genocchi	genocchi	NOUN
ejpam-4694	58	10	polynomials	polynomial	NOUN
ejpam-4694	58	11	with	with	ADP
ejpam-4694	58	12	parameters	parameter	NOUN
ejpam-4694	58	13	a	a	DET
ejpam-4694	58	14	,	,	PUNCT
ejpam-4694	58	15	b	b	PROPN
ejpam-4694	58	16	and	and	CCONJ
ejpam-4694	58	17	c	c	PROPN
ejpam-4694	58	18	was	be	AUX
ejpam-4694	58	19	defined	define	VERB
ejpam-4694	58	20	in	in	ADP
ejpam-4694	58	21	[	[	X
ejpam-4694	58	22	17	17	NUM
ejpam-4694	58	23	]	]	PUNCT
ejpam-4694	58	24	by	by	ADP
ejpam-4694	58	25	mixing	mix	VERB
ejpam-4694	58	26	the	the	DET
ejpam-4694	58	27	definitions	definition	NOUN
ejpam-4694	58	28	of	of	ADP
ejpam-4694	58	29	polylogarithm	polylogarithm	NOUN
ejpam-4694	58	30	,	,	PUNCT
ejpam-4694	58	31	apostolgenocchi	apostolgenocchi	NOUN
ejpam-4694	58	32	polynomials	polynomial	NOUN
ejpam-4694	58	33	and	and	CCONJ
ejpam-4694	58	34	frobenius	frobenius	ADJ
ejpam-4694	58	35	polynomials	polynomial	NOUN
ejpam-4694	58	36	,	,	PUNCT
ejpam-4694	58	37	namely	namely	ADV
ejpam-4694	58	38	,	,	PUNCT
ejpam-4694	58	39	the	the	DET
ejpam-4694	58	40	apostol	apostol	NOUN
ejpam-4694	58	41	-	-	PUNCT
ejpam-4694	58	42	frobenius	frobenius	NOUN
ejpam-4694	58	43	-	-	PUNCT
ejpam-4694	58	44	type	type	NOUN
ejpam-4694	58	45	poly	poly	ADJ
ejpam-4694	58	46	-	-	PUNCT
ejpam-4694	58	47	genocchi	genocchi	NOUN
ejpam-4694	58	48	polynomials	polynomial	NOUN
ejpam-4694	58	49	of	of	ADP
ejpam-4694	58	50	higher	high	ADJ
ejpam-4694	58	51	order	order	NOUN
ejpam-4694	58	52	with	with	ADP
ejpam-4694	58	53	parameters	parameter	NOUN
ejpam-4694	58	54	a	a	DET
ejpam-4694	58	55	,	,	PUNCT
ejpam-4694	58	56	b	b	PROPN
ejpam-4694	58	57	and	and	CCONJ
ejpam-4694	58	58	c.	c.	PROPN
ejpam-4694	58	59	more	more	ADV
ejpam-4694	58	60	precisely	precisely	ADV
ejpam-4694	58	61	,	,	PUNCT
ejpam-4694	58	62	the	the	DET
ejpam-4694	58	63	said	say	VERB
ejpam-4694	58	64	polynomials	polynomial	NOUN
ejpam-4694	58	65	,	,	PUNCT
ejpam-4694	58	66	denoted	denote	VERB
ejpam-4694	58	67	by	by	ADP
ejpam-4694	58	68	ĝ(k	ĝ(k	PRON
ejpam-4694	58	69	,	,	PUNCT
ejpam-4694	58	70	α	α	NOUN
ejpam-4694	58	71	)	)	PUNCT
ejpam-4694	58	72	n	n	CCONJ
ejpam-4694	58	73	(	(	PUNCT
ejpam-4694	58	74	x;λ	x;λ	PROPN
ejpam-4694	58	75	,	,	PUNCT
ejpam-4694	58	76	ρ	ρ	PROPN
ejpam-4694	58	77	,	,	PUNCT
ejpam-4694	58	78	u	u	NOUN
ejpam-4694	58	79	,	,	PUNCT
ejpam-4694	58	80	a	a	DET
ejpam-4694	58	81	,	,	PUNCT
ejpam-4694	58	82	b	b	NOUN
ejpam-4694	58	83	)	)	PUNCT
ejpam-4694	58	84	,	,	PUNCT
ejpam-4694	58	85	are	be	AUX
ejpam-4694	58	86	defined	define	VERB
ejpam-4694	58	87	as	as	ADP
ejpam-4694	58	88	coefficients	coefficient	NOUN
ejpam-4694	58	89	of	of	ADP
ejpam-4694	58	90	the	the	DET
ejpam-4694	58	91	following	follow	VERB
ejpam-4694	58	92	generating	generate	VERB
ejpam-4694	58	93	function	function	NOUN
ejpam-4694	58	94	∞∑	∞∑	PROPN
ejpam-4694	58	95	n=0	n=0	NUM
ejpam-4694	58	96	ĝ(k	ĝ(k	PROPN
ejpam-4694	58	97	,	,	PUNCT
ejpam-4694	58	98	α	α	NOUN
ejpam-4694	58	99	)	)	PUNCT
ejpam-4694	58	100	n	n	CCONJ
ejpam-4694	58	101	(	(	PUNCT
ejpam-4694	58	102	x;λ	x;λ	PROPN
ejpam-4694	58	103	,	,	PUNCT
ejpam-4694	58	104	ρ	ρ	PROPN
ejpam-4694	58	105	,	,	PUNCT
ejpam-4694	58	106	u	u	NOUN
ejpam-4694	58	107	,	,	PUNCT
ejpam-4694	58	108	a	a	DET
ejpam-4694	58	109	,	,	PUNCT
ejpam-4694	58	110	b	b	NOUN
ejpam-4694	58	111	)	)	PUNCT
ejpam-4694	58	112	tn	tn	NOUN
ejpam-4694	58	113	n	n	CCONJ
ejpam-4694	58	114	!	!	PUNCT
ejpam-4694	59	1	=	=	PUNCT
ejpam-4694	59	2	(	(	PUNCT
ejpam-4694	59	3	lik	lik	PROPN
ejpam-4694	59	4	,	,	PUNCT
ejpam-4694	59	5	ρ(1−	ρ(1−	PROPN
ejpam-4694	59	6	(	(	PUNCT
ejpam-4694	59	7	ab)−(1−u)t	ab)−(1−u)t	PROPN
ejpam-4694	59	8	)	)	PUNCT
ejpam-4694	59	9	λbt	λbt	VERB
ejpam-4694	59	10	−	−	PROPN
ejpam-4694	59	11	ua−t	ua−t	ADJ
ejpam-4694	59	12	)	)	PUNCT
ejpam-4694	59	13	α	α	PROPN
ejpam-4694	59	14	cxt	cxt	PROPN
ejpam-4694	59	15	.	.	PUNCT
ejpam-4694	60	1	(	(	PUNCT
ejpam-4694	60	2	12	12	NUM
ejpam-4694	60	3	)	)	PUNCT
ejpam-4694	60	4	it	it	PRON
ejpam-4694	60	5	is	be	AUX
ejpam-4694	60	6	worth	worth	ADJ
ejpam-4694	60	7	-	-	PUNCT
ejpam-4694	60	8	mentioning	mention	VERB
ejpam-4694	60	9	the	the	DET
ejpam-4694	60	10	following	follow	VERB
ejpam-4694	60	11	interesting	interesting	ADJ
ejpam-4694	60	12	applications	application	NOUN
ejpam-4694	60	13	of	of	ADP
ejpam-4694	60	14	genocchi	genocchi	PROPN
ejpam-4694	60	15	numbers	number	NOUN
ejpam-4694	60	16	,	,	PUNCT
ejpam-4694	60	17	genocchi	genocchi	PROPN
ejpam-4694	60	18	polynomials	polynomial	NOUN
ejpam-4694	60	19	and	and	CCONJ
ejpam-4694	60	20	poly	poly	ADJ
ejpam-4694	60	21	-	-	PUNCT
ejpam-4694	60	22	genocchi	genocchi	NOUN
ejpam-4694	60	23	polynomials	polynomial	NOUN
ejpam-4694	60	24	:	:	PUNCT
ejpam-4694	60	25	(	(	PUNCT
ejpam-4694	60	26	i	i	NOUN
ejpam-4694	60	27	)	)	PUNCT
ejpam-4694	60	28	the	the	DET
ejpam-4694	60	29	genocchi	genocchi	PROPN
ejpam-4694	60	30	numbers	number	NOUN
ejpam-4694	60	31	were	be	AUX
ejpam-4694	60	32	used	use	VERB
ejpam-4694	60	33	to	to	PART
ejpam-4694	60	34	bound	bind	VERB
ejpam-4694	60	35	the	the	DET
ejpam-4694	60	36	number	number	NOUN
ejpam-4694	60	37	of	of	ADP
ejpam-4694	60	38	finite	finite	ADJ
ejpam-4694	60	39	languages	language	NOUN
ejpam-4694	60	40	over	over	ADP
ejpam-4694	60	41	a	a	DET
ejpam-4694	60	42	two	two	NUM
ejpam-4694	60	43	-	-	PUNCT
ejpam-4694	60	44	letter	letter	NOUN
ejpam-4694	60	45	alphabet	alphabet	NOUN
ejpam-4694	60	46	accepted	accept	VERB
ejpam-4694	60	47	by	by	ADP
ejpam-4694	60	48	a	a	DET
ejpam-4694	60	49	deterministic	deterministic	ADJ
ejpam-4694	60	50	finite	finite	ADJ
ejpam-4694	60	51	automation	automation	NOUN
ejpam-4694	60	52	(	(	PUNCT
ejpam-4694	60	53	dfa	dfa	PROPN
ejpam-4694	60	54	)	)	PUNCT
ejpam-4694	60	55	with	with	ADP
ejpam-4694	60	56	n	n	PROPN
ejpam-4694	60	57	states	state	NOUN
ejpam-4694	60	58	(	(	PUNCT
ejpam-4694	60	59	see	see	VERB
ejpam-4694	60	60	[	[	X
ejpam-4694	60	61	18	18	NUM
ejpam-4694	60	62	]	]	NUM
ejpam-4694	60	63	)	)	PUNCT
ejpam-4694	60	64	;	;	PUNCT
ejpam-4694	60	65	(	(	PUNCT
ejpam-4694	60	66	ii	ii	X
ejpam-4694	60	67	)	)	PUNCT
ejpam-4694	60	68	certain	certain	ADJ
ejpam-4694	60	69	wavelets	wavelet	NOUN
ejpam-4694	60	70	method	method	NOUN
ejpam-4694	60	71	was	be	AUX
ejpam-4694	60	72	constructed	construct	VERB
ejpam-4694	60	73	using	use	VERB
ejpam-4694	60	74	genocchi	genocchi	PROPN
ejpam-4694	60	75	polynomials	polynomial	NOUN
ejpam-4694	60	76	which	which	PRON
ejpam-4694	60	77	has	have	AUX
ejpam-4694	60	78	been	be	AUX
ejpam-4694	60	79	used	use	VERB
ejpam-4694	60	80	to	to	PART
ejpam-4694	60	81	obtain	obtain	VERB
ejpam-4694	60	82	a	a	DET
ejpam-4694	60	83	numerical	numerical	ADJ
ejpam-4694	60	84	solution	solution	NOUN
ejpam-4694	60	85	for	for	ADP
ejpam-4694	60	86	the	the	DET
ejpam-4694	60	87	classical	classical	ADJ
ejpam-4694	60	88	and	and	CCONJ
ejpam-4694	60	89	time	time	NOUN
ejpam-4694	60	90	-	-	PUNCT
ejpam-4694	60	91	fractional	fractional	ADJ
ejpam-4694	60	92	rosenauhyman	rosenauhyman	NOUN
ejpam-4694	60	93	equation	equation	NOUN
ejpam-4694	60	94	arising	arise	VERB
ejpam-4694	60	95	in	in	ADP
ejpam-4694	60	96	the	the	DET
ejpam-4694	60	97	formation	formation	NOUN
ejpam-4694	60	98	of	of	ADP
ejpam-4694	60	99	patterns	pattern	NOUN
ejpam-4694	60	100	in	in	ADP
ejpam-4694	60	101	liquid	liquid	ADJ
ejpam-4694	60	102	drops	drop	NOUN
ejpam-4694	60	103	(	(	PUNCT
ejpam-4694	60	104	see	see	VERB
ejpam-4694	60	105	[	[	X
ejpam-4694	60	106	37	37	NUM
ejpam-4694	60	107	]	]	NUM
ejpam-4694	60	108	)	)	PUNCT
ejpam-4694	60	109	;	;	PUNCT
ejpam-4694	60	110	(	(	PUNCT
ejpam-4694	60	111	iii	iii	X
ejpam-4694	60	112	)	)	PUNCT
ejpam-4694	60	113	the	the	DET
ejpam-4694	60	114	orthogonal	orthogonal	ADJ
ejpam-4694	60	115	version	version	NOUN
ejpam-4694	60	116	of	of	ADP
ejpam-4694	60	117	poly	poly	ADJ
ejpam-4694	60	118	-	-	PUNCT
ejpam-4694	60	119	genocchi	genocchi	NOUN
ejpam-4694	60	120	polynomials	polynomial	NOUN
ejpam-4694	60	121	coincides	coincide	VERB
ejpam-4694	60	122	with	with	ADP
ejpam-4694	60	123	the	the	DET
ejpam-4694	60	124	shifted	shift	VERB
ejpam-4694	60	125	legendre	legendre	PROPN
ejpam-4694	60	126	polynomials	polynomial	NOUN
ejpam-4694	60	127	.	.	PUNCT
ejpam-4694	61	1	also	also	ADV
ejpam-4694	61	2	,	,	PUNCT
ejpam-4694	61	3	the	the	DET
ejpam-4694	61	4	poly	poly	ADJ
ejpam-4694	61	5	-	-	PUNCT
ejpam-4694	61	6	genocchi	genocchi	NOUN
ejpam-4694	61	7	polynomials	polynomial	NOUN
ejpam-4694	61	8	were	be	AUX
ejpam-4694	61	9	used	use	VERB
ejpam-4694	61	10	to	to	PART
ejpam-4694	61	11	solve	solve	VERB
ejpam-4694	61	12	the	the	DET
ejpam-4694	61	13	fractional	fractional	ADJ
ejpam-4694	61	14	differential	differential	NOUN
ejpam-4694	61	15	equation	equation	NOUN
ejpam-4694	61	16	,	,	PUNCT
ejpam-4694	61	17	including	include	VERB
ejpam-4694	61	18	the	the	DET
ejpam-4694	61	19	delay	delay	NOUN
ejpam-4694	61	20	fractional	fractional	ADJ
ejpam-4694	61	21	differential	differential	NOUN
ejpam-4694	61	22	equation	equation	NOUN
ejpam-4694	61	23	via	via	ADP
ejpam-4694	61	24	the	the	DET
ejpam-4694	61	25	operational	operational	ADJ
ejpam-4694	61	26	matrix	matrix	NOUN
ejpam-4694	61	27	method	method	NOUN
ejpam-4694	61	28	with	with	ADP
ejpam-4694	61	29	a	a	DET
ejpam-4694	61	30	collocation	collocation	NOUN
ejpam-4694	61	31	scheme	scheme	NOUN
ejpam-4694	61	32	(	(	PUNCT
ejpam-4694	61	33	see	see	VERB
ejpam-4694	61	34	[	[	X
ejpam-4694	61	35	8	8	NUM
ejpam-4694	61	36	]	]	NUM
ejpam-4694	61	37	)	)	PUNCT
ejpam-4694	61	38	.	.	PUNCT
ejpam-4694	62	1	the	the	DET
ejpam-4694	62	2	degenerate	degenerate	ADJ
ejpam-4694	62	3	exponential	exponential	ADJ
ejpam-4694	62	4	function	function	NOUN
ejpam-4694	62	5	,	,	PUNCT
ejpam-4694	62	6	denoted	denote	VERB
ejpam-4694	62	7	by	by	ADP
ejpam-4694	62	8	exλ(t	exλ(t	NOUN
ejpam-4694	62	9	)	)	PUNCT
ejpam-4694	62	10	,	,	PUNCT
ejpam-4694	62	11	was	be	AUX
ejpam-4694	62	12	defined	define	VERB
ejpam-4694	62	13	in	in	ADP
ejpam-4694	62	14	[	[	X
ejpam-4694	62	15	10	10	NUM
ejpam-4694	62	16	,	,	PUNCT
ejpam-4694	62	17	11	11	NUM
ejpam-4694	62	18	]	]	PUNCT
ejpam-4694	62	19	)	)	PUNCT
ejpam-4694	62	20	exλ(t	exλ(t	PROPN
ejpam-4694	62	21	)	)	PUNCT
ejpam-4694	62	22	=	=	PUNCT
ejpam-4694	63	1	(	(	PUNCT
ejpam-4694	63	2	1	1	NUM
ejpam-4694	63	3	+	+	CCONJ
ejpam-4694	63	4	λt)x	λt)x	PROPN
ejpam-4694	63	5	/	/	SYM
ejpam-4694	63	6	λ	λ	NOUN
ejpam-4694	63	7	=	=	SYM
ejpam-4694	63	8	∞∑	∞∑	PROPN
ejpam-4694	63	9	n=0	n=0	NUM
ejpam-4694	63	10	(	(	PUNCT
ejpam-4694	63	11	x)n	x)n	PROPN
ejpam-4694	63	12	,	,	PUNCT
ejpam-4694	63	13	λ	λ	PROPN
ejpam-4694	63	14	tn	tn	NOUN
ejpam-4694	63	15	n	n	X
ejpam-4694	63	16	!	!	PUNCT
ejpam-4694	63	17	,	,	PUNCT
ejpam-4694	64	1	λ	λ	PROPN
ejpam-4694	64	2	∈	∈	PROPN
ejpam-4694	64	3	r+	r+	NOUN
ejpam-4694	64	4	∪	∪	X
ejpam-4694	64	5	{	{	PUNCT
ejpam-4694	64	6	0	0	NUM
ejpam-4694	64	7	}	}	PUNCT
ejpam-4694	64	8	,	,	PUNCT
ejpam-4694	64	9	(	(	PUNCT
ejpam-4694	64	10	13	13	NUM
ejpam-4694	64	11	)	)	PUNCT
ejpam-4694	64	12	where	where	SCONJ
ejpam-4694	64	13	eλ(t	eλ(t	NOUN
ejpam-4694	64	14	)	)	PUNCT
ejpam-4694	64	15	=	=	SYM
ejpam-4694	64	16	e1λ(t	e1λ(t	NOUN
ejpam-4694	64	17	)	)	PUNCT
ejpam-4694	64	18	=	=	PUNCT
ejpam-4694	64	19	(	(	PUNCT
ejpam-4694	64	20	1	1	NUM
ejpam-4694	64	21	+	+	CCONJ
ejpam-4694	64	22	λt)1	λt)1	PROPN
ejpam-4694	64	23	/	/	SYM
ejpam-4694	64	24	λ	λ	PROPN
ejpam-4694	64	25	and	and	CCONJ
ejpam-4694	64	26	(	(	PUNCT
ejpam-4694	64	27	x)0,λ	x)0,λ	NOUN
ejpam-4694	64	28	=	=	SYM
ejpam-4694	64	29	1	1	NUM
ejpam-4694	64	30	,	,	PUNCT
ejpam-4694	64	31	(	(	PUNCT
ejpam-4694	64	32	x)n	x)n	PROPN
ejpam-4694	64	33	,	,	PUNCT
ejpam-4694	64	34	λ	λ	PROPN
ejpam-4694	64	35	=	=	SYM
ejpam-4694	64	36	x(x−	x(x−	PROPN
ejpam-4694	64	37	λ)(x−	λ)(x−	PROPN
ejpam-4694	64	38	2λ	2λ	NUM
ejpam-4694	64	39	)	)	PUNCT
ejpam-4694	64	40	.	.	PUNCT
ejpam-4694	64	41	.	.	PUNCT
ejpam-4694	64	42	.	.	PUNCT
ejpam-4694	65	1	(	(	PUNCT
ejpam-4694	65	2	x−	x−	PROPN
ejpam-4694	65	3	(	(	PUNCT
ejpam-4694	65	4	n−	n−	NOUN
ejpam-4694	65	5	1)λ	1)λ	NUM
ejpam-4694	65	6	)	)	PUNCT
ejpam-4694	65	7	,	,	PUNCT
ejpam-4694	65	8	n	n	PRON
ejpam-4694	65	9	≥	≥	NOUN
ejpam-4694	65	10	1	1	NUM
ejpam-4694	65	11	.	.	PUNCT
ejpam-4694	65	12	r.	r.	PROPN
ejpam-4694	65	13	corcino	corcino	PROPN
ejpam-4694	65	14	,	,	PUNCT
ejpam-4694	65	15	c.	c.	PROPN
ejpam-4694	65	16	corcino	corcino	PROPN
ejpam-4694	65	17	/	/	SYM
ejpam-4694	65	18	eur	eur	PROPN
ejpam-4694	65	19	.	.	PUNCT
ejpam-4694	66	1	j.	j.	PROPN
ejpam-4694	66	2	pure	pure	PROPN
ejpam-4694	66	3	appl	appl	PROPN
ejpam-4694	66	4	.	.	PROPN
ejpam-4694	66	5	math	math	PROPN
ejpam-4694	66	6	,	,	PUNCT
ejpam-4694	66	7	16	16	NUM
ejpam-4694	66	8	(	(	PUNCT
ejpam-4694	66	9	2	2	NUM
ejpam-4694	66	10	)	)	PUNCT
ejpam-4694	66	11	(	(	PUNCT
ejpam-4694	66	12	2023	2023	NUM
ejpam-4694	66	13	)	)	PUNCT
ejpam-4694	66	14	,	,	PUNCT
ejpam-4694	66	15	687	687	NUM
ejpam-4694	66	16	-	-	SYM
ejpam-4694	66	17	712	712	NUM
ejpam-4694	66	18	690	690	NUM
ejpam-4694	66	19	it	it	PRON
ejpam-4694	66	20	can	can	AUX
ejpam-4694	66	21	easily	easily	ADV
ejpam-4694	66	22	be	be	AUX
ejpam-4694	66	23	seen	see	VERB
ejpam-4694	66	24	that	that	SCONJ
ejpam-4694	66	25	ex+y	ex+y	PROPN
ejpam-4694	66	26	λ	λ	PROPN
ejpam-4694	66	27	(	(	PUNCT
ejpam-4694	66	28	t	t	PROPN
ejpam-4694	66	29	)	)	PUNCT
ejpam-4694	66	30	=	=	PUNCT
ejpam-4694	67	1	(	(	PUNCT
ejpam-4694	67	2	1	1	NUM
ejpam-4694	67	3	+	+	NUM
ejpam-4694	67	4	λt)(x+y)/λ	λt)(x+y)/λ	X
ejpam-4694	67	5	=	=	PUNCT
ejpam-4694	67	6	(	(	PUNCT
ejpam-4694	67	7	1	1	NUM
ejpam-4694	67	8	+	+	NUM
ejpam-4694	67	9	λt)(x	λt)(x	PROPN
ejpam-4694	67	10	/	/	SYM
ejpam-4694	67	11	λ)+(y	λ)+(y	NOUN
ejpam-4694	67	12	/	/	SYM
ejpam-4694	67	13	λ	λ	NOUN
ejpam-4694	67	14	)	)	PUNCT
ejpam-4694	67	15	=	=	SYM
ejpam-4694	67	16	(	(	PUNCT
ejpam-4694	67	17	1	1	NUM
ejpam-4694	67	18	+	+	CCONJ
ejpam-4694	67	19	λt)(x	λt)(x	PROPN
ejpam-4694	67	20	/	/	SYM
ejpam-4694	67	21	λ)(1	λ)(1	X
ejpam-4694	67	22	+	+	ADJ
ejpam-4694	67	23	λt)(y	λt)(y	NOUN
ejpam-4694	67	24	/	/	SYM
ejpam-4694	67	25	λ	λ	NOUN
ejpam-4694	67	26	)	)	PUNCT
ejpam-4694	67	27	=	=	PUNCT
ejpam-4694	67	28	exλ(t)e	exλ(t)e	PROPN
ejpam-4694	67	29	y	y	PROPN
ejpam-4694	67	30	λ(t	λ(t	PROPN
ejpam-4694	67	31	)	)	PUNCT
ejpam-4694	67	32	,	,	PUNCT
ejpam-4694	67	33	(	(	PUNCT
ejpam-4694	67	34	14	14	NUM
ejpam-4694	67	35	)	)	PUNCT
ejpam-4694	67	36	and	and	CCONJ
ejpam-4694	67	37	d	d	X
ejpam-4694	67	38	dx	dx	PROPN
ejpam-4694	67	39	exλ(t	exλ(t	PROPN
ejpam-4694	67	40	)	)	PUNCT
ejpam-4694	67	41	=	=	SYM
ejpam-4694	67	42	log(1	log(1	NOUN
ejpam-4694	68	1	+	+	CCONJ
ejpam-4694	68	2	λt)1	λt)1	PROPN
ejpam-4694	68	3	/	/	SYM
ejpam-4694	68	4	λexλ(t	λexλ(t	PROPN
ejpam-4694	68	5	)	)	PUNCT
ejpam-4694	68	6	.	.	PUNCT
ejpam-4694	69	1	(	(	PUNCT
ejpam-4694	69	2	15	15	NUM
ejpam-4694	69	3	)	)	PUNCT
ejpam-4694	69	4	the	the	DET
ejpam-4694	69	5	degenerate	degenerate	ADJ
ejpam-4694	69	6	bernoulli	bernoulli	NOUN
ejpam-4694	69	7	polynomials	polynomial	NOUN
ejpam-4694	69	8	bn	bn	ADP
ejpam-4694	69	9	,	,	PUNCT
ejpam-4694	69	10	λ(x	λ(x	PROPN
ejpam-4694	69	11	)	)	PUNCT
ejpam-4694	69	12	and	and	CCONJ
ejpam-4694	69	13	degenerate	degenerate	ADJ
ejpam-4694	69	14	euler	euler	NOUN
ejpam-4694	69	15	polynomials	polynomial	NOUN
ejpam-4694	69	16	en	en	ADP
ejpam-4694	69	17	,	,	PUNCT
ejpam-4694	69	18	λ(x	λ(x	PROPN
ejpam-4694	69	19	)	)	PUNCT
ejpam-4694	69	20	were	be	AUX
ejpam-4694	69	21	defined	define	VERB
ejpam-4694	69	22	by	by	ADP
ejpam-4694	69	23	carlitz	carlitz	NOUN
ejpam-4694	69	24	[	[	X
ejpam-4694	69	25	11	11	NUM
ejpam-4694	69	26	]	]	PUNCT
ejpam-4694	69	27	by	by	ADP
ejpam-4694	69	28	means	mean	NOUN
ejpam-4694	69	29	of	of	ADP
ejpam-4694	69	30	the	the	DET
ejpam-4694	69	31	following	follow	VERB
ejpam-4694	69	32	generating	generating	NOUN
ejpam-4694	69	33	functions	function	NOUN
ejpam-4694	69	34	t	t	NOUN
ejpam-4694	69	35	eλ(t	eλ(t	NOUN
ejpam-4694	69	36	)	)	PUNCT
ejpam-4694	70	1	+	+	CCONJ
ejpam-4694	70	2	1	1	NUM
ejpam-4694	70	3	exλ(t	exλ(t	NOUN
ejpam-4694	70	4	)	)	PUNCT
ejpam-4694	71	1	=	=	SYM
ejpam-4694	71	2	t	t	PROPN
ejpam-4694	71	3	(	(	PUNCT
ejpam-4694	71	4	1	1	NUM
ejpam-4694	71	5	+	+	CCONJ
ejpam-4694	71	6	λt)1	λt)1	PROPN
ejpam-4694	71	7	/	/	SYM
ejpam-4694	71	8	λ	λ	PROPN
ejpam-4694	71	9	+	+	NOUN
ejpam-4694	71	10	1	1	NUM
ejpam-4694	71	11	(	(	PUNCT
ejpam-4694	71	12	1	1	NUM
ejpam-4694	71	13	+	+	CCONJ
ejpam-4694	71	14	λt)x	λt)x	PROPN
ejpam-4694	71	15	/	/	SYM
ejpam-4694	71	16	λ	λ	NOUN
ejpam-4694	71	17	=	=	SYM
ejpam-4694	71	18	∞∑	∞∑	PRON
ejpam-4694	71	19	n=0	n=0	NUM
ejpam-4694	71	20	bn	bn	NOUN
ejpam-4694	71	21	,	,	PUNCT
ejpam-4694	71	22	λ(x	λ(x	PROPN
ejpam-4694	71	23	)	)	PUNCT
ejpam-4694	71	24	tn	tn	PROPN
ejpam-4694	71	25	n	n	CCONJ
ejpam-4694	71	26	!	!	X
ejpam-4694	71	27	2	2	NUM
ejpam-4694	71	28	eλ(t	eλ(t	NUM
ejpam-4694	71	29	)	)	PUNCT
ejpam-4694	72	1	+	+	CCONJ
ejpam-4694	72	2	1	1	NUM
ejpam-4694	72	3	exλ(t	exλ(t	NOUN
ejpam-4694	72	4	)	)	PUNCT
ejpam-4694	72	5	=	=	SYM
ejpam-4694	72	6	2	2	NUM
ejpam-4694	72	7	(	(	PUNCT
ejpam-4694	72	8	1	1	NUM
ejpam-4694	72	9	+	+	CCONJ
ejpam-4694	72	10	λt)1	λt)1	PROPN
ejpam-4694	72	11	/	/	SYM
ejpam-4694	72	12	λ	λ	PROPN
ejpam-4694	72	13	+	+	NOUN
ejpam-4694	72	14	1	1	NUM
ejpam-4694	72	15	(	(	PUNCT
ejpam-4694	72	16	1	1	NUM
ejpam-4694	72	17	+	+	CCONJ
ejpam-4694	72	18	λt)x	λt)x	PROPN
ejpam-4694	72	19	/	/	SYM
ejpam-4694	72	20	λ	λ	NOUN
ejpam-4694	72	21	=	=	SYM
ejpam-4694	72	22	∞∑	∞∑	PRON
ejpam-4694	72	23	n=0	n=0	NUM
ejpam-4694	72	24	en	en	X
ejpam-4694	72	25	,	,	PUNCT
ejpam-4694	72	26	λ(x	λ(x	PROPN
ejpam-4694	72	27	)	)	PUNCT
ejpam-4694	72	28	tn	tn	PROPN
ejpam-4694	72	29	n	n	PROPN
ejpam-4694	72	30	!	!	PUNCT
ejpam-4694	72	31	.	.	PUNCT
ejpam-4694	73	1	parallel	parallel	ADJ
ejpam-4694	73	2	to	to	ADP
ejpam-4694	73	3	these	these	PRON
ejpam-4694	73	4	,	,	PUNCT
ejpam-4694	73	5	lim	lim	PROPN
ejpam-4694	74	1	[	[	X
ejpam-4694	74	2	36	36	NUM
ejpam-4694	74	3	]	]	PUNCT
ejpam-4694	74	4	defined	define	VERB
ejpam-4694	74	5	the	the	DET
ejpam-4694	74	6	degenerate	degenerate	ADJ
ejpam-4694	74	7	genocchi	genocchi	NOUN
ejpam-4694	74	8	polynomials	polynomial	NOUN
ejpam-4694	74	9	as	as	SCONJ
ejpam-4694	74	10	follows	follow	VERB
ejpam-4694	74	11	2	2	NUM
ejpam-4694	74	12	t	t	NOUN
ejpam-4694	74	13	eλ(t	eλ(t	NUM
ejpam-4694	74	14	)	)	PUNCT
ejpam-4694	75	1	+	+	CCONJ
ejpam-4694	75	2	1	1	NUM
ejpam-4694	75	3	exλ(t	exλ(t	NOUN
ejpam-4694	75	4	)	)	PUNCT
ejpam-4694	75	5	=	=	PUNCT
ejpam-4694	75	6	2	2	NUM
ejpam-4694	75	7	t	t	NOUN
ejpam-4694	75	8	(	(	PUNCT
ejpam-4694	75	9	1	1	NUM
ejpam-4694	75	10	+	+	CCONJ
ejpam-4694	75	11	λt)1	λt)1	PROPN
ejpam-4694	75	12	/	/	SYM
ejpam-4694	75	13	λ	λ	PROPN
ejpam-4694	75	14	+	+	NOUN
ejpam-4694	75	15	1	1	NUM
ejpam-4694	75	16	(	(	PUNCT
ejpam-4694	75	17	1	1	NUM
ejpam-4694	75	18	+	+	CCONJ
ejpam-4694	75	19	λt)x	λt)x	PROPN
ejpam-4694	75	20	/	/	SYM
ejpam-4694	75	21	λ	λ	NOUN
ejpam-4694	75	22	=	=	SYM
ejpam-4694	75	23	∞∑	∞∑	PROPN
ejpam-4694	75	24	n=0	n=0	PROPN
ejpam-4694	75	25	gn	gn	PROPN
ejpam-4694	75	26	,	,	PUNCT
ejpam-4694	75	27	λ(x	λ(x	PROPN
ejpam-4694	75	28	)	)	PUNCT
ejpam-4694	75	29	tn	tn	PROPN
ejpam-4694	75	30	n	n	PROPN
ejpam-4694	75	31	!	!	PUNCT
ejpam-4694	75	32	.	.	PUNCT
ejpam-4694	76	1	(	(	PUNCT
ejpam-4694	76	2	16	16	NUM
ejpam-4694	76	3	)	)	PUNCT
ejpam-4694	76	4	kim	kim	PROPN
ejpam-4694	76	5	and	and	CCONJ
ejpam-4694	76	6	kim	kim	PROPN
ejpam-4694	77	1	[	[	X
ejpam-4694	77	2	42	42	NUM
ejpam-4694	77	3	]	]	PUNCT
ejpam-4694	77	4	introduced	introduce	VERB
ejpam-4694	77	5	the	the	DET
ejpam-4694	77	6	degenerate	degenerate	ADJ
ejpam-4694	77	7	frobenius	frobenius	NOUN
ejpam-4694	77	8	-	-	PUNCT
ejpam-4694	77	9	euler	euler	NOUN
ejpam-4694	77	10	polynomials	polynomial	NOUN
ejpam-4694	77	11	as	as	ADP
ejpam-4694	77	12	coefficients	coefficient	NOUN
ejpam-4694	77	13	of	of	ADP
ejpam-4694	77	14	the	the	DET
ejpam-4694	77	15	following	follow	VERB
ejpam-4694	77	16	generating	generate	VERB
ejpam-4694	77	17	function	function	NOUN
ejpam-4694	77	18	1−	1−	NUM
ejpam-4694	77	19	u	u	NOUN
ejpam-4694	77	20	eλ(t)−	eλ(t)−	PROPN
ejpam-4694	77	21	u	u	NOUN
ejpam-4694	77	22	exλ(t	exλ(t	PROPN
ejpam-4694	77	23	)	)	PUNCT
ejpam-4694	77	24	=	=	PUNCT
ejpam-4694	78	1	∞∑	∞∑	NUM
ejpam-4694	78	2	n=0	n=0	PUNCT
ejpam-4694	78	3	hn	hn	PROPN
ejpam-4694	78	4	,	,	PUNCT
ejpam-4694	78	5	λ(x|u	λ(x|u	NUM
ejpam-4694	78	6	)	)	PUNCT
ejpam-4694	78	7	tn	tn	PROPN
ejpam-4694	78	8	n	n	PROPN
ejpam-4694	78	9	!	!	PUNCT
ejpam-4694	79	1	(	(	PUNCT
ejpam-4694	79	2	17	17	NUM
ejpam-4694	79	3	)	)	PUNCT
ejpam-4694	79	4	and	and	CCONJ
ejpam-4694	79	5	kim	kim	PROPN
ejpam-4694	79	6	et	et	PROPN
ejpam-4694	79	7	al	al	PROPN
ejpam-4694	79	8	.	.	PUNCT
ejpam-4694	80	1	[	[	X
ejpam-4694	80	2	26	26	NUM
ejpam-4694	80	3	]	]	PUNCT
ejpam-4694	80	4	derived	derive	VERB
ejpam-4694	80	5	formulas	formula	NOUN
ejpam-4694	80	6	that	that	PRON
ejpam-4694	80	7	express	express	VERB
ejpam-4694	80	8	any	any	DET
ejpam-4694	80	9	polynomial	polynomial	NOUN
ejpam-4694	80	10	in	in	ADP
ejpam-4694	80	11	terms	term	NOUN
ejpam-4694	80	12	of	of	ADP
ejpam-4694	80	13	hn	hn	PROPN
ejpam-4694	80	14	,	,	PUNCT
ejpam-4694	80	15	λ(x|u	λ(x|u	NUM
ejpam-4694	80	16	)	)	PUNCT
ejpam-4694	80	17	.	.	PUNCT
ejpam-4694	81	1	in	in	ADP
ejpam-4694	81	2	their	their	PRON
ejpam-4694	81	3	separate	separate	ADJ
ejpam-4694	81	4	paper	paper	NOUN
ejpam-4694	81	5	,	,	PUNCT
ejpam-4694	81	6	kim	kim	PROPN
ejpam-4694	81	7	and	and	CCONJ
ejpam-4694	81	8	kim	kim	PROPN
ejpam-4694	81	9	[	[	X
ejpam-4694	81	10	27	27	NUM
ejpam-4694	81	11	]	]	PUNCT
ejpam-4694	81	12	defined	define	VERB
ejpam-4694	81	13	the	the	DET
ejpam-4694	81	14	generalized	generalize	VERB
ejpam-4694	81	15	degenerate	degenerate	ADJ
ejpam-4694	81	16	euler	euler	VERB
ejpam-4694	81	17	-	-	PUNCT
ejpam-4694	81	18	genocchi	genocchi	PROPN
ejpam-4694	81	19	polynomials	polynomial	NOUN
ejpam-4694	81	20	,	,	PUNCT
ejpam-4694	81	21	denoted	denote	VERB
ejpam-4694	81	22	by	by	ADP
ejpam-4694	81	23	a	a	DET
ejpam-4694	81	24	(	(	PUNCT
ejpam-4694	81	25	r	r	NOUN
ejpam-4694	81	26	)	)	PUNCT
ejpam-4694	81	27	n	n	CCONJ
ejpam-4694	81	28	,	,	PUNCT
ejpam-4694	81	29	λ(x	λ(x	PROPN
ejpam-4694	81	30	)	)	PUNCT
ejpam-4694	81	31	,	,	PUNCT
ejpam-4694	81	32	as	as	ADP
ejpam-4694	81	33	coefficients	coefficient	NOUN
ejpam-4694	81	34	of	of	ADP
ejpam-4694	81	35	the	the	DET
ejpam-4694	81	36	following	follow	VERB
ejpam-4694	81	37	generating	generate	VERB
ejpam-4694	81	38	function	function	NOUN
ejpam-4694	81	39	2tr	2tr	NOUN
ejpam-4694	81	40	eλ(t	eλ(t	PUNCT
ejpam-4694	81	41	)	)	PUNCT
ejpam-4694	82	1	+	+	CCONJ
ejpam-4694	82	2	1	1	NUM
ejpam-4694	82	3	exλ(t	exλ(t	NOUN
ejpam-4694	82	4	)	)	PUNCT
ejpam-4694	82	5	=	=	PUNCT
ejpam-4694	83	1	∞∑	∞∑	ADJ
ejpam-4694	83	2	n=0	n=0	NUM
ejpam-4694	83	3	a	a	DET
ejpam-4694	83	4	(	(	PUNCT
ejpam-4694	83	5	r	r	NOUN
ejpam-4694	83	6	)	)	PUNCT
ejpam-4694	83	7	n	n	CCONJ
ejpam-4694	83	8	,	,	PUNCT
ejpam-4694	83	9	λ(x	λ(x	PROPN
ejpam-4694	83	10	)	)	PUNCT
ejpam-4694	83	11	tn	tn	PROPN
ejpam-4694	83	12	n	n	PROPN
ejpam-4694	83	13	!	!	PROPN
ejpam-4694	83	14	,	,	PUNCT
ejpam-4694	83	15	which	which	PRON
ejpam-4694	83	16	reduce	reduce	VERB
ejpam-4694	83	17	to	to	ADP
ejpam-4694	83	18	the	the	DET
ejpam-4694	83	19	degenerate	degenerate	ADJ
ejpam-4694	83	20	genocchi	genocchi	NOUN
ejpam-4694	83	21	polynomials	polynomial	VERB
ejpam-4694	83	22	in	in	ADP
ejpam-4694	83	23	(	(	PUNCT
ejpam-4694	83	24	26	26	NUM
ejpam-4694	83	25	)	)	PUNCT
ejpam-4694	83	26	when	when	SCONJ
ejpam-4694	83	27	r	r	NOUN
ejpam-4694	83	28	=	=	SYM
ejpam-4694	83	29	1	1	X
ejpam-4694	83	30	.	.	PUNCT
ejpam-4694	84	1	that	that	PRON
ejpam-4694	84	2	is	is	ADV
ejpam-4694	84	3	,	,	PUNCT
ejpam-4694	84	4	a	a	DET
ejpam-4694	84	5	(	(	PUNCT
ejpam-4694	84	6	1	1	NUM
ejpam-4694	84	7	)	)	PUNCT
ejpam-4694	84	8	n	n	CCONJ
ejpam-4694	84	9	,	,	PUNCT
ejpam-4694	84	10	λ(x	λ(x	PROPN
ejpam-4694	84	11	)	)	PUNCT
ejpam-4694	84	12	=	=	SYM
ejpam-4694	84	13	gn	gn	PROPN
ejpam-4694	84	14	,	,	PUNCT
ejpam-4694	84	15	λ(x	λ(x	PROPN
ejpam-4694	84	16	)	)	PUNCT
ejpam-4694	84	17	.	.	PUNCT
ejpam-4694	85	1	the	the	DET
ejpam-4694	85	2	degenerate	degenerate	ADJ
ejpam-4694	85	3	stirling	stirling	NOUN
ejpam-4694	85	4	numbers	number	NOUN
ejpam-4694	85	5	of	of	ADP
ejpam-4694	85	6	the	the	DET
ejpam-4694	85	7	first	first	ADJ
ejpam-4694	85	8	and	and	CCONJ
ejpam-4694	85	9	second	second	ADJ
ejpam-4694	85	10	kind	kind	NOUN
ejpam-4694	85	11	,	,	PUNCT
ejpam-4694	85	12	denoted	denote	VERB
ejpam-4694	85	13	by	by	ADP
ejpam-4694	85	14	s1,ρ(n	s1,ρ(n	NOUN
ejpam-4694	85	15	,	,	PUNCT
ejpam-4694	85	16	k	k	NOUN
ejpam-4694	85	17	)	)	PUNCT
ejpam-4694	85	18	and	and	CCONJ
ejpam-4694	85	19	s2,ρ(n	s2,ρ(n	PRON
ejpam-4694	85	20	,	,	PUNCT
ejpam-4694	85	21	k	k	PROPN
ejpam-4694	85	22	)	)	PUNCT
ejpam-4694	85	23	,	,	PUNCT
ejpam-4694	85	24	were	be	AUX
ejpam-4694	85	25	defined	define	VERB
ejpam-4694	85	26	in	in	ADP
ejpam-4694	85	27	(	(	PUNCT
ejpam-4694	85	28	[	[	X
ejpam-4694	85	29	23	23	NUM
ejpam-4694	85	30	,	,	PUNCT
ejpam-4694	85	31	29	29	NUM
ejpam-4694	85	32	,	,	PUNCT
ejpam-4694	85	33	31	31	NUM
ejpam-4694	85	34	]	]	PUNCT
ejpam-4694	85	35	)	)	PUNCT
ejpam-4694	86	1	(	(	PUNCT
ejpam-4694	86	2	logρ(1	logρ(1	PROPN
ejpam-4694	86	3	+	+	NUM
ejpam-4694	86	4	t))k	t))k	PROPN
ejpam-4694	86	5	k	k	NOUN
ejpam-4694	86	6	!	!	PUNCT
ejpam-4694	86	7	=	=	PUNCT
ejpam-4694	87	1	∞∑	∞∑	DET
ejpam-4694	87	2	n=0	n=0	NUM
ejpam-4694	87	3	s1,ρ(n	s1,ρ(n	X
ejpam-4694	87	4	,	,	PUNCT
ejpam-4694	87	5	k	k	NOUN
ejpam-4694	87	6	)	)	PUNCT
ejpam-4694	87	7	tn	tn	PROPN
ejpam-4694	87	8	n	n	PROPN
ejpam-4694	87	9	!	!	PROPN
ejpam-4694	87	10	,	,	PUNCT
ejpam-4694	87	11	(	(	PUNCT
ejpam-4694	87	12	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	87	13	1)k	1)k	NUM
ejpam-4694	87	14	k	k	X
ejpam-4694	87	15	!	!	PUNCT
ejpam-4694	87	16	=	=	PUNCT
ejpam-4694	88	1	∞∑	∞∑	PRON
ejpam-4694	88	2	n=0	n=0	ADV
ejpam-4694	88	3	s2,ρ(n	s2,ρ(n	ADV
ejpam-4694	88	4	,	,	PUNCT
ejpam-4694	88	5	k	k	NOUN
ejpam-4694	88	6	)	)	PUNCT
ejpam-4694	88	7	tn	tn	PROPN
ejpam-4694	88	8	n	n	PROPN
ejpam-4694	88	9	!	!	PROPN
ejpam-4694	88	10	,	,	PUNCT
ejpam-4694	88	11	(	(	PUNCT
ejpam-4694	88	12	18	18	NUM
ejpam-4694	88	13	)	)	PUNCT
ejpam-4694	88	14	r.	r.	PROPN
ejpam-4694	88	15	corcino	corcino	PROPN
ejpam-4694	88	16	,	,	PUNCT
ejpam-4694	88	17	c.	c.	PROPN
ejpam-4694	88	18	corcino	corcino	PROPN
ejpam-4694	88	19	/	/	SYM
ejpam-4694	88	20	eur	eur	PROPN
ejpam-4694	88	21	.	.	PUNCT
ejpam-4694	89	1	j.	j.	PROPN
ejpam-4694	89	2	pure	pure	PROPN
ejpam-4694	89	3	appl	appl	PROPN
ejpam-4694	89	4	.	.	PROPN
ejpam-4694	89	5	math	math	PROPN
ejpam-4694	89	6	,	,	PUNCT
ejpam-4694	89	7	16	16	NUM
ejpam-4694	89	8	(	(	PUNCT
ejpam-4694	89	9	2	2	NUM
ejpam-4694	89	10	)	)	PUNCT
ejpam-4694	89	11	(	(	PUNCT
ejpam-4694	89	12	2023	2023	NUM
ejpam-4694	89	13	)	)	PUNCT
ejpam-4694	89	14	,	,	PUNCT
ejpam-4694	89	15	687	687	NUM
ejpam-4694	89	16	-	-	SYM
ejpam-4694	89	17	712	712	NUM
ejpam-4694	89	18	691	691	NUM
ejpam-4694	89	19	where	where	SCONJ
ejpam-4694	89	20	logρ(eρ(t	logρ(eρ(t	ADV
ejpam-4694	89	21	)	)	PUNCT
ejpam-4694	89	22	)	)	PUNCT
ejpam-4694	90	1	=	=	PUNCT
ejpam-4694	90	2	eρ(logρ(t	eρ(logρ(t	NUM
ejpam-4694	90	3	)	)	PUNCT
ejpam-4694	90	4	)	)	PUNCT
ejpam-4694	91	1	=	=	SYM
ejpam-4694	92	1	t.	t.	NOUN
ejpam-4694	92	2	(	(	PUNCT
ejpam-4694	92	3	19	19	NUM
ejpam-4694	92	4	)	)	PUNCT
ejpam-4694	93	1	when	when	SCONJ
ejpam-4694	93	2	ρ	ρ	PROPN
ejpam-4694	93	3	→	→	SYM
ejpam-4694	93	4	0	0	PROPN
ejpam-4694	93	5	,	,	PUNCT
ejpam-4694	93	6	lim	lim	PROPN
ejpam-4694	93	7	ρ→0	ρ→0	X
ejpam-4694	93	8	s1,ρ(n	s1,ρ(n	PROPN
ejpam-4694	93	9	,	,	PUNCT
ejpam-4694	93	10	k	k	NOUN
ejpam-4694	93	11	)	)	PUNCT
ejpam-4694	93	12	=	=	SYM
ejpam-4694	93	13	s1(n	s1(n	PROPN
ejpam-4694	93	14	,	,	PUNCT
ejpam-4694	93	15	k	k	NOUN
ejpam-4694	93	16	)	)	PUNCT
ejpam-4694	93	17	,	,	PUNCT
ejpam-4694	93	18	lim	lim	PROPN
ejpam-4694	93	19	ρ→0	ρ→0	X
ejpam-4694	93	20	s2,ρ(n	s2,ρ(n	PROPN
ejpam-4694	93	21	,	,	PUNCT
ejpam-4694	93	22	k	k	NOUN
ejpam-4694	93	23	)	)	PUNCT
ejpam-4694	93	24	=	=	SYM
ejpam-4694	93	25	s2(n	s2(n	PROPN
ejpam-4694	93	26	,	,	PUNCT
ejpam-4694	93	27	k	k	NOUN
ejpam-4694	93	28	)	)	PUNCT
ejpam-4694	93	29	where	where	SCONJ
ejpam-4694	93	30	s1(n	s1(n	ADP
ejpam-4694	93	31	,	,	PUNCT
ejpam-4694	93	32	k	k	NOUN
ejpam-4694	93	33	)	)	PUNCT
ejpam-4694	93	34	and	and	CCONJ
ejpam-4694	93	35	s2(n	s2(n	PROPN
ejpam-4694	93	36	,	,	PUNCT
ejpam-4694	93	37	k	k	NOUN
ejpam-4694	93	38	)	)	PUNCT
ejpam-4694	93	39	are	be	AUX
ejpam-4694	93	40	the	the	DET
ejpam-4694	93	41	classical	classical	ADJ
ejpam-4694	93	42	stirling	stirling	NOUN
ejpam-4694	93	43	numbers	number	NOUN
ejpam-4694	93	44	of	of	ADP
ejpam-4694	93	45	the	the	DET
ejpam-4694	93	46	first	first	ADJ
ejpam-4694	93	47	and	and	CCONJ
ejpam-4694	93	48	second	second	ADJ
ejpam-4694	93	49	kind	kind	NOUN
ejpam-4694	93	50	.	.	PUNCT
ejpam-4694	94	1	also	also	ADV
ejpam-4694	94	2	,	,	PUNCT
ejpam-4694	94	3	the	the	DET
ejpam-4694	94	4	degenerate	degenerate	ADJ
ejpam-4694	94	5	bernoulli	bernoulli	NOUN
ejpam-4694	94	6	polynomials	polynomial	NOUN
ejpam-4694	94	7	of	of	ADP
ejpam-4694	94	8	the	the	DET
ejpam-4694	94	9	second	second	ADJ
ejpam-4694	94	10	kind	kind	NOUN
ejpam-4694	94	11	are	be	AUX
ejpam-4694	94	12	defined	define	VERB
ejpam-4694	94	13	by	by	ADP
ejpam-4694	94	14	(	(	PUNCT
ejpam-4694	94	15	1	1	NUM
ejpam-4694	94	16	+	+	CCONJ
ejpam-4694	94	17	t)x	t)x	VERB
ejpam-4694	94	18	logρ(1	logρ(1	PROPN
ejpam-4694	94	19	+	+	SYM
ejpam-4694	94	20	t	t	PROPN
ejpam-4694	94	21	)	)	PUNCT
ejpam-4694	94	22	t	t	NOUN
ejpam-4694	94	23	=	=	PUNCT
ejpam-4694	95	1	∞∑	∞∑	PRON
ejpam-4694	95	2	n=0	n=0	NUM
ejpam-4694	95	3	bn	bn	NOUN
ejpam-4694	95	4	,	,	PUNCT
ejpam-4694	95	5	ρ(x	ρ(x	PROPN
ejpam-4694	95	6	)	)	PUNCT
ejpam-4694	95	7	tn	tn	NOUN
ejpam-4694	95	8	n	n	PROPN
ejpam-4694	95	9	!	!	PUNCT
ejpam-4694	95	10	.	.	PUNCT
ejpam-4694	96	1	(	(	PUNCT
ejpam-4694	96	2	20	20	NUM
ejpam-4694	96	3	)	)	PUNCT
ejpam-4694	96	4	the	the	DET
ejpam-4694	96	5	degenerate	degenerate	ADJ
ejpam-4694	96	6	stirling	stirling	NOUN
ejpam-4694	96	7	numbers	number	NOUN
ejpam-4694	96	8	of	of	ADP
ejpam-4694	96	9	the	the	DET
ejpam-4694	96	10	second	second	ADJ
ejpam-4694	96	11	kind	kind	NOUN
ejpam-4694	96	12	appeared	appear	VERB
ejpam-4694	96	13	in	in	ADP
ejpam-4694	96	14	the	the	DET
ejpam-4694	96	15	probability	probability	NOUN
ejpam-4694	96	16	distribution	distribution	NOUN
ejpam-4694	96	17	of	of	ADP
ejpam-4694	96	18	the	the	DET
ejpam-4694	96	19	random	random	ADJ
ejpam-4694	96	20	variable	variable	NOUN
ejpam-4694	96	21	given	give	VERB
ejpam-4694	96	22	as	as	ADP
ejpam-4694	96	23	the	the	DET
ejpam-4694	96	24	sum	sum	NOUN
ejpam-4694	96	25	of	of	ADP
ejpam-4694	96	26	a	a	DET
ejpam-4694	96	27	finite	finite	ADJ
ejpam-4694	96	28	number	number	NOUN
ejpam-4694	96	29	of	of	ADP
ejpam-4694	96	30	random	random	ADJ
ejpam-4694	96	31	variables	variable	NOUN
ejpam-4694	96	32	with	with	ADP
ejpam-4694	96	33	degenerate	degenerate	ADJ
ejpam-4694	96	34	zero	zero	NUM
ejpam-4694	96	35	-	-	PUNCT
ejpam-4694	96	36	truncated	truncate	VERB
ejpam-4694	96	37	poisson	poisson	NOUN
ejpam-4694	96	38	distributions	distribution	NOUN
ejpam-4694	96	39	and	and	CCONJ
ejpam-4694	96	40	a	a	DET
ejpam-4694	96	41	random	random	ADJ
ejpam-4694	96	42	variable	variable	NOUN
ejpam-4694	96	43	with	with	ADP
ejpam-4694	96	44	degenerate	degenerate	ADJ
ejpam-4694	96	45	poisson	poisson	NOUN
ejpam-4694	96	46	distribution	distribution	NOUN
ejpam-4694	96	47	,	,	PUNCT
ejpam-4694	96	48	all	all	PRON
ejpam-4694	96	49	having	have	VERB
ejpam-4694	96	50	the	the	DET
ejpam-4694	96	51	same	same	ADJ
ejpam-4694	96	52	parameter	parameter	NOUN
ejpam-4694	96	53	(	(	PUNCT
ejpam-4694	96	54	see	see	VERB
ejpam-4694	96	55	[	[	X
ejpam-4694	96	56	31	31	NUM
ejpam-4694	96	57	]	]	NUM
ejpam-4694	96	58	)	)	PUNCT
ejpam-4694	96	59	.	.	PUNCT
ejpam-4694	97	1	the	the	DET
ejpam-4694	97	2	polyexponential	polyexponential	ADJ
ejpam-4694	97	3	functions	function	NOUN
ejpam-4694	97	4	are	be	AUX
ejpam-4694	97	5	defined	define	VERB
ejpam-4694	97	6	by	by	ADP
ejpam-4694	97	7	the	the	DET
ejpam-4694	97	8	following	follow	VERB
ejpam-4694	97	9	generating	generating	NOUN
ejpam-4694	97	10	functions	function	NOUN
ejpam-4694	97	11	[	[	X
ejpam-4694	97	12	22	22	NUM
ejpam-4694	97	13	,	,	PUNCT
ejpam-4694	97	14	23	23	NUM
ejpam-4694	97	15	,	,	PUNCT
ejpam-4694	97	16	28	28	NUM
ejpam-4694	97	17	,	,	PUNCT
ejpam-4694	97	18	30	30	NUM
ejpam-4694	97	19	]	]	PUNCT
ejpam-4694	97	20	eik(x	eik(x	PROPN
ejpam-4694	97	21	)	)	PUNCT
ejpam-4694	97	22	=	=	PUNCT
ejpam-4694	98	1	∞∑	∞∑	NUM
ejpam-4694	98	2	n=1	n=1	PROPN
ejpam-4694	98	3	xn	xn	PROPN
ejpam-4694	98	4	nk(n−	nk(n−	PROPN
ejpam-4694	98	5	1	1	NUM
ejpam-4694	98	6	)	)	PUNCT
ejpam-4694	98	7	!	!	PUNCT
ejpam-4694	98	8	,	,	PUNCT
ejpam-4694	99	1	k	k	PROPN
ejpam-4694	99	2	∈	∈	PROPN
ejpam-4694	99	3	z.	z.	PROPN
ejpam-4694	99	4	(	(	PUNCT
ejpam-4694	99	5	21	21	NUM
ejpam-4694	99	6	)	)	PUNCT
ejpam-4694	99	7	for	for	ADP
ejpam-4694	99	8	k	k	PROPN
ejpam-4694	99	9	=	=	SYM
ejpam-4694	99	10	1	1	NUM
ejpam-4694	99	11	,	,	PUNCT
ejpam-4694	99	12	ei1(x	ei1(x	PROPN
ejpam-4694	99	13	)	)	PUNCT
ejpam-4694	99	14	=	=	SYM
ejpam-4694	100	1	ex	ex	PRON
ejpam-4694	101	1	−	−	NOUN
ejpam-4694	101	2	1	1	NUM
ejpam-4694	101	3	.	.	PUNCT
ejpam-4694	102	1	the	the	DET
ejpam-4694	102	2	modified	modify	VERB
ejpam-4694	102	3	degenerate	degenerate	ADJ
ejpam-4694	102	4	polyexponential	polyexponential	ADJ
ejpam-4694	102	5	function	function	NOUN
ejpam-4694	102	6	are	be	AUX
ejpam-4694	102	7	given	give	VERB
ejpam-4694	102	8	by	by	ADP
ejpam-4694	102	9	(	(	PUNCT
ejpam-4694	102	10	[	[	X
ejpam-4694	102	11	22	22	NUM
ejpam-4694	102	12	,	,	PUNCT
ejpam-4694	102	13	23	23	NUM
ejpam-4694	102	14	,	,	PUNCT
ejpam-4694	102	15	28	28	NUM
ejpam-4694	102	16	,	,	PUNCT
ejpam-4694	102	17	30	30	NUM
ejpam-4694	102	18	]	]	PUNCT
ejpam-4694	102	19	)	)	PUNCT
ejpam-4694	102	20	eik	eik	PROPN
ejpam-4694	102	21	,	,	PUNCT
ejpam-4694	102	22	ρ(x	ρ(x	PROPN
ejpam-4694	102	23	)	)	PUNCT
ejpam-4694	102	24	=	=	NOUN
ejpam-4694	103	1	∞∑	∞∑	NUM
ejpam-4694	103	2	n=1	n=1	PROPN
ejpam-4694	103	3	(	(	PUNCT
ejpam-4694	103	4	1)n	1)n	X
ejpam-4694	103	5	,	,	PUNCT
ejpam-4694	103	6	ρx	ρx	VERB
ejpam-4694	103	7	n	n	CCONJ
ejpam-4694	103	8	nk(n−	nk(n−	PROPN
ejpam-4694	103	9	1	1	NUM
ejpam-4694	103	10	)	)	PUNCT
ejpam-4694	103	11	!	!	PUNCT
ejpam-4694	103	12	,	,	PUNCT
ejpam-4694	103	13	ρ	ρ	PROPN
ejpam-4694	103	14	∈	∈	PROPN
ejpam-4694	103	15	r.	r.	PROPN
ejpam-4694	103	16	(	(	PUNCT
ejpam-4694	103	17	22	22	NUM
ejpam-4694	103	18	)	)	PUNCT
ejpam-4694	103	19	note	note	VERB
ejpam-4694	103	20	that	that	SCONJ
ejpam-4694	103	21	ei1,ρ(x	ei1,ρ(x	NUM
ejpam-4694	103	22	)	)	PUNCT
ejpam-4694	104	1	=	=	PUNCT
ejpam-4694	105	1	∞∑	∞∑	NUM
ejpam-4694	105	2	n=1	n=1	PROPN
ejpam-4694	105	3	(	(	PUNCT
ejpam-4694	105	4	1)n	1)n	X
ejpam-4694	105	5	,	,	PUNCT
ejpam-4694	105	6	ρ	ρ	PROPN
ejpam-4694	105	7	xn	xn	PROPN
ejpam-4694	105	8	n	n	X
ejpam-4694	105	9	!	!	PUNCT
ejpam-4694	106	1	=	=	PRON
ejpam-4694	106	2	eρ(x)−	eρ(x)−	NOUN
ejpam-4694	106	3	1	1	NUM
ejpam-4694	106	4	,	,	PUNCT
ejpam-4694	106	5	ρ	ρ	PROPN
ejpam-4694	106	6	∈	∈	PROPN
ejpam-4694	106	7	r.	r.	PROPN
ejpam-4694	106	8	(	(	PUNCT
ejpam-4694	106	9	23	23	NUM
ejpam-4694	106	10	)	)	PUNCT
ejpam-4694	106	11	also	also	ADV
ejpam-4694	106	12	,	,	PUNCT
ejpam-4694	106	13	we	we	PRON
ejpam-4694	106	14	have	have	VERB
ejpam-4694	106	15	d	d	PROPN
ejpam-4694	106	16	dx	dx	PROPN
ejpam-4694	106	17	eik	eik	PROPN
ejpam-4694	106	18	,	,	PUNCT
ejpam-4694	106	19	ρ(logρ(1	ρ(logρ(1	PROPN
ejpam-4694	106	20	+	+	CCONJ
ejpam-4694	106	21	x	x	X
ejpam-4694	106	22	)	)	PUNCT
ejpam-4694	106	23	)	)	PUNCT
ejpam-4694	107	1	=	=	PUNCT
ejpam-4694	107	2	(	(	PUNCT
ejpam-4694	107	3	1	1	NUM
ejpam-4694	107	4	+	+	NUM
ejpam-4694	107	5	x)ρ−1	x)ρ−1	NOUN
ejpam-4694	107	6	logρ(1	logρ(1	PROPN
ejpam-4694	107	7	+	+	CCONJ
ejpam-4694	107	8	x	x	X
ejpam-4694	107	9	)	)	PUNCT
ejpam-4694	107	10	eik−1,ρ(logρ(1	eik−1,ρ(logρ(1	PROPN
ejpam-4694	107	11	+	+	NUM
ejpam-4694	107	12	x	x	X
ejpam-4694	107	13	)	)	PUNCT
ejpam-4694	107	14	)	)	PUNCT
ejpam-4694	107	15	,	,	PUNCT
ejpam-4694	107	16	(	(	PUNCT
ejpam-4694	107	17	24	24	NUM
ejpam-4694	107	18	)	)	PUNCT
ejpam-4694	107	19	which	which	PRON
ejpam-4694	107	20	implies	imply	VERB
ejpam-4694	107	21	eik	eik	PROPN
ejpam-4694	107	22	,	,	PUNCT
ejpam-4694	107	23	ρ(logρ(1	ρ(logρ(1	PROPN
ejpam-4694	107	24	+	+	CCONJ
ejpam-4694	107	25	x	x	X
ejpam-4694	107	26	)	)	PUNCT
ejpam-4694	107	27	)	)	PUNCT
ejpam-4694	108	1	=	=	SYM
ejpam-4694	108	2	∫	∫	PUNCT
ejpam-4694	109	1	x	x	SYM
ejpam-4694	109	2	0	0	PUNCT
ejpam-4694	109	3	(	(	PUNCT
ejpam-4694	109	4	1	1	NUM
ejpam-4694	109	5	+	+	CCONJ
ejpam-4694	109	6	t)ρ−1	t)ρ−1	NOUN
ejpam-4694	109	7	logρ(1	logρ(1	PROPN
ejpam-4694	109	8	+	+	CCONJ
ejpam-4694	109	9	t	t	X
ejpam-4694	109	10	)	)	PUNCT
ejpam-4694	109	11	∫	∫	PROPN
ejpam-4694	110	1	y	y	PROPN
ejpam-4694	110	2	0	0	PROPN
ejpam-4694	110	3	.	.	PUNCT
ejpam-4694	110	4	.	.	PUNCT
ejpam-4694	110	5	.	.	PUNCT
ejpam-4694	111	1	(	(	PUNCT
ejpam-4694	111	2	1	1	NUM
ejpam-4694	111	3	+	+	NUM
ejpam-4694	111	4	x)ρ−1	x)ρ−1	NOUN
ejpam-4694	111	5	logρ(1	logρ(1	PROPN
ejpam-4694	111	6	+	+	CCONJ
ejpam-4694	111	7	x	x	X
ejpam-4694	111	8	)	)	PUNCT
ejpam-4694	111	9	∫	∫	PROPN
ejpam-4694	111	10	y	y	PROPN
ejpam-4694	111	11	0	0	NUM
ejpam-4694	111	12	(	(	PUNCT
ejpam-4694	111	13	1	1	NUM
ejpam-4694	111	14	+	+	NUM
ejpam-4694	111	15	x)ρ−1	x)ρ−1	NOUN
ejpam-4694	111	16	logρ(1	logρ(1	PROPN
ejpam-4694	111	17	+	+	CCONJ
ejpam-4694	111	18	x	x	X
ejpam-4694	111	19	)	)	PUNCT
ejpam-4694	111	20	xdx	xdx	PROPN
ejpam-4694	111	21	.	.	PUNCT
ejpam-4694	111	22	.	.	PUNCT
ejpam-4694	111	23	.	.	PUNCT
ejpam-4694	112	1	dx	dx	PROPN
ejpam-4694	113	1	=	=	PROPN
ejpam-4694	113	2	∞∑	∞∑	NUM
ejpam-4694	113	3	m=0	m=0	PROPN
ejpam-4694	113	4	∑	∑	PUNCT
ejpam-4694	113	5	m1+m2+	m1+m2+	PROPN
ejpam-4694	113	6	...	...	PUNCT
ejpam-4694	113	7	+mk−1	+mk−1	PROPN
ejpam-4694	113	8	=	=	NOUN
ejpam-4694	113	9	m	m	PROPN
ejpam-4694	113	10	(	(	PUNCT
ejpam-4694	113	11	m	m	PROPN
ejpam-4694	113	12	m1	m1	NOUN
ejpam-4694	113	13	,	,	PUNCT
ejpam-4694	113	14	.	.	PUNCT
ejpam-4694	113	15	.	.	PUNCT
ejpam-4694	114	1	.	.	PUNCT
ejpam-4694	115	1	,	,	PUNCT
ejpam-4694	115	2	mk−1	mk−1	PROPN
ejpam-4694	115	3	)	)	PUNCT
ejpam-4694	115	4	×	×	PROPN
ejpam-4694	115	5	bm1,ρ(ρ−	bm1,ρ(ρ−	PROPN
ejpam-4694	115	6	1	1	NUM
ejpam-4694	115	7	)	)	PUNCT
ejpam-4694	115	8	m1	m1	NOUN
ejpam-4694	115	9	+	+	CCONJ
ejpam-4694	115	10	1	1	NUM
ejpam-4694	115	11	bm2,ρ(ρ−	bm2,ρ(ρ−	NOUN
ejpam-4694	115	12	1	1	NUM
ejpam-4694	115	13	)	)	PUNCT
ejpam-4694	115	14	m1	m1	PROPN
ejpam-4694	116	1	+	+	PROPN
ejpam-4694	116	2	m2	m2	PROPN
ejpam-4694	116	3	+	+	X
ejpam-4694	116	4	1	1	NUM
ejpam-4694	116	5	.	.	PUNCT
ejpam-4694	116	6	.	.	PUNCT
ejpam-4694	116	7	.	.	PUNCT
ejpam-4694	117	1	bmk−1,ρ(ρ−	bmk−1,ρ(ρ−	NOUN
ejpam-4694	117	2	1	1	NUM
ejpam-4694	117	3	)	)	PUNCT
ejpam-4694	117	4	m1	m1	NOUN
ejpam-4694	117	5	+	+	CCONJ
ejpam-4694	117	6	.	.	PUNCT
ejpam-4694	117	7	.	.	PUNCT
ejpam-4694	118	1	.+mk−1	.+mk−1	PROPN
ejpam-4694	119	1	+	+	CCONJ
ejpam-4694	119	2	1	1	NUM
ejpam-4694	119	3	xm+1	xm+1	NUM
ejpam-4694	119	4	m	m	NOUN
ejpam-4694	119	5	!	!	PUNCT
ejpam-4694	119	6	.	.	PUNCT
ejpam-4694	120	1	(	(	PUNCT
ejpam-4694	120	2	25	25	NUM
ejpam-4694	120	3	)	)	PUNCT
ejpam-4694	120	4	r.	r.	PROPN
ejpam-4694	120	5	corcino	corcino	PROPN
ejpam-4694	120	6	,	,	PUNCT
ejpam-4694	120	7	c.	c.	PROPN
ejpam-4694	120	8	corcino	corcino	PROPN
ejpam-4694	120	9	/	/	SYM
ejpam-4694	120	10	eur	eur	PROPN
ejpam-4694	120	11	.	.	PUNCT
ejpam-4694	121	1	j.	j.	PROPN
ejpam-4694	121	2	pure	pure	PROPN
ejpam-4694	121	3	appl	appl	PROPN
ejpam-4694	121	4	.	.	PROPN
ejpam-4694	121	5	math	math	PROPN
ejpam-4694	121	6	,	,	PUNCT
ejpam-4694	121	7	16	16	NUM
ejpam-4694	121	8	(	(	PUNCT
ejpam-4694	121	9	2	2	NUM
ejpam-4694	121	10	)	)	PUNCT
ejpam-4694	121	11	(	(	PUNCT
ejpam-4694	121	12	2023	2023	NUM
ejpam-4694	121	13	)	)	PUNCT
ejpam-4694	121	14	,	,	PUNCT
ejpam-4694	121	15	687	687	NUM
ejpam-4694	121	16	-	-	SYM
ejpam-4694	121	17	712	712	NUM
ejpam-4694	121	18	692	692	NUM
ejpam-4694	121	19	the	the	DET
ejpam-4694	121	20	degenerate	degenerate	ADJ
ejpam-4694	121	21	poly	poly	ADJ
ejpam-4694	121	22	-	-	PUNCT
ejpam-4694	121	23	euler	euler	NOUN
ejpam-4694	121	24	polynomials	polynomial	NOUN
ejpam-4694	121	25	were	be	AUX
ejpam-4694	121	26	defined	define	VERB
ejpam-4694	121	27	in	in	ADP
ejpam-4694	121	28	[	[	X
ejpam-4694	121	29	35	35	NUM
ejpam-4694	121	30	]	]	PUNCT
ejpam-4694	121	31	by	by	ADP
ejpam-4694	121	32	means	mean	NOUN
ejpam-4694	121	33	of	of	ADP
ejpam-4694	121	34	the	the	DET
ejpam-4694	121	35	following	follow	VERB
ejpam-4694	121	36	generating	generate	VERB
ejpam-4694	121	37	function	function	NOUN
ejpam-4694	121	38	2	2	NUM
ejpam-4694	121	39	eik	eik	NOUN
ejpam-4694	121	40	,	,	PUNCT
ejpam-4694	121	41	ρ(logρ(1	ρ(logρ(1	PROPN
ejpam-4694	121	42	+	+	X
ejpam-4694	121	43	t	t	PROPN
ejpam-4694	121	44	)	)	PUNCT
ejpam-4694	121	45	)	)	PUNCT
ejpam-4694	122	1	teρ(t	teρ(t	X
ejpam-4694	122	2	)	)	PUNCT
ejpam-4694	122	3	+	+	CCONJ
ejpam-4694	122	4	1	1	NUM
ejpam-4694	122	5	exρ(t	exρ(t	NUM
ejpam-4694	122	6	)	)	PUNCT
ejpam-4694	122	7	=	=	PUNCT
ejpam-4694	123	1	∞∑	∞∑	PRON
ejpam-4694	123	2	n=0	n=0	NUM
ejpam-4694	123	3	e(k	e(k	NOUN
ejpam-4694	123	4	)	)	PUNCT
ejpam-4694	123	5	n	n	CCONJ
ejpam-4694	123	6	,	,	PUNCT
ejpam-4694	123	7	ρ(x	ρ(x	PROPN
ejpam-4694	123	8	)	)	PUNCT
ejpam-4694	123	9	tn	tn	NOUN
ejpam-4694	123	10	n	n	PROPN
ejpam-4694	123	11	!	!	PROPN
ejpam-4694	123	12	,	,	PUNCT
ejpam-4694	123	13	(	(	PUNCT
ejpam-4694	123	14	26	26	NUM
ejpam-4694	123	15	)	)	PUNCT
ejpam-4694	123	16	where	where	SCONJ
ejpam-4694	123	17	k	k	PROPN
ejpam-4694	123	18	∈	∈	PROPN
ejpam-4694	123	19	z.	z.	PROPN
ejpam-4694	123	20	in	in	ADP
ejpam-4694	123	21	this	this	DET
ejpam-4694	123	22	paper	paper	NOUN
ejpam-4694	123	23	,	,	PUNCT
ejpam-4694	123	24	a	a	DET
ejpam-4694	123	25	new	new	ADJ
ejpam-4694	123	26	variation	variation	NOUN
ejpam-4694	123	27	of	of	ADP
ejpam-4694	123	28	poly	poly	ADJ
ejpam-4694	123	29	-	-	PUNCT
ejpam-4694	123	30	genocchi	genocchi	NOUN
ejpam-4694	123	31	polynomials	polynomial	NOUN
ejpam-4694	123	32	is	be	AUX
ejpam-4694	123	33	constructed	construct	VERB
ejpam-4694	123	34	by	by	ADP
ejpam-4694	123	35	mixing	mix	VERB
ejpam-4694	123	36	the	the	DET
ejpam-4694	123	37	concepts	concept	NOUN
ejpam-4694	123	38	of	of	ADP
ejpam-4694	123	39	modified	modified	ADJ
ejpam-4694	123	40	degenerate	degenerate	ADJ
ejpam-4694	123	41	polyexponential	polyexponential	ADJ
ejpam-4694	123	42	function	function	NOUN
ejpam-4694	123	43	,	,	PUNCT
ejpam-4694	123	44	apostol	apostol	NOUN
ejpam-4694	123	45	-	-	PUNCT
ejpam-4694	123	46	genocchi	genocchi	PROPN
ejpam-4694	123	47	polynomials	polynomial	NOUN
ejpam-4694	123	48	and	and	CCONJ
ejpam-4694	123	49	frobenius	frobenius	ADJ
ejpam-4694	123	50	polynomials	polynomial	NOUN
ejpam-4694	123	51	.	.	PUNCT
ejpam-4694	124	1	these	these	DET
ejpam-4694	124	2	polynomials	polynomial	NOUN
ejpam-4694	124	3	are	be	AUX
ejpam-4694	124	4	called	call	VERB
ejpam-4694	124	5	the	the	DET
ejpam-4694	124	6	degenerate	degenerate	ADJ
ejpam-4694	124	7	apostolfrobenius	apostolfrobenius	NOUN
ejpam-4694	124	8	-	-	PUNCT
ejpam-4694	124	9	type	type	NOUN
ejpam-4694	124	10	poly	poly	ADJ
ejpam-4694	124	11	-	-	PUNCT
ejpam-4694	124	12	genocchi	genocchi	NOUN
ejpam-4694	124	13	polynomials	polynomial	NOUN
ejpam-4694	124	14	of	of	ADP
ejpam-4694	124	15	higher	high	ADJ
ejpam-4694	124	16	order	order	NOUN
ejpam-4694	124	17	with	with	ADP
ejpam-4694	124	18	parameters	parameter	NOUN
ejpam-4694	124	19	a	a	PRON
ejpam-4694	124	20	and	and	CCONJ
ejpam-4694	124	21	b.	b.	NOUN
ejpam-4694	124	22	some	some	DET
ejpam-4694	124	23	special	special	ADJ
ejpam-4694	124	24	cases	case	NOUN
ejpam-4694	124	25	of	of	ADP
ejpam-4694	124	26	these	these	DET
ejpam-4694	124	27	polynomials	polynomial	NOUN
ejpam-4694	124	28	are	be	AUX
ejpam-4694	124	29	enumerated	enumerate	VERB
ejpam-4694	124	30	and	and	CCONJ
ejpam-4694	124	31	some	some	DET
ejpam-4694	124	32	identities	identity	NOUN
ejpam-4694	124	33	that	that	PRON
ejpam-4694	124	34	contain	contain	VERB
ejpam-4694	124	35	a	a	DET
ejpam-4694	124	36	number	number	NOUN
ejpam-4694	124	37	of	of	ADP
ejpam-4694	124	38	relations	relation	NOUN
ejpam-4694	124	39	of	of	ADP
ejpam-4694	124	40	this	this	DET
ejpam-4694	124	41	new	new	ADJ
ejpam-4694	124	42	variation	variation	NOUN
ejpam-4694	124	43	with	with	ADP
ejpam-4694	124	44	some	some	DET
ejpam-4694	124	45	genocchi	genocchi	NOUN
ejpam-4694	124	46	-	-	PUNCT
ejpam-4694	124	47	type	type	NOUN
ejpam-4694	124	48	polynomials	polynomial	NOUN
ejpam-4694	124	49	are	be	AUX
ejpam-4694	124	50	provided	provide	VERB
ejpam-4694	124	51	.	.	PUNCT
ejpam-4694	125	1	finally	finally	ADV
ejpam-4694	125	2	,	,	PUNCT
ejpam-4694	125	3	some	some	DET
ejpam-4694	125	4	connections	connection	NOUN
ejpam-4694	125	5	of	of	ADP
ejpam-4694	125	6	these	these	DET
ejpam-4694	125	7	degenerate	degenerate	ADJ
ejpam-4694	125	8	apostol	apostol	NOUN
ejpam-4694	125	9	-	-	PUNCT
ejpam-4694	125	10	frobenius	frobenius	NOUN
ejpam-4694	125	11	-	-	PUNCT
ejpam-4694	125	12	type	type	NOUN
ejpam-4694	125	13	poly	poly	ADJ
ejpam-4694	125	14	-	-	PUNCT
ejpam-4694	125	15	genocchi	genocchi	NOUN
ejpam-4694	125	16	polynomials	polynomial	NOUN
ejpam-4694	125	17	to	to	PART
ejpam-4694	125	18	degenerate	degenerate	VERB
ejpam-4694	125	19	stirling	stirling	NOUN
ejpam-4694	125	20	numbers	number	NOUN
ejpam-4694	125	21	of	of	ADP
ejpam-4694	125	22	the	the	DET
ejpam-4694	125	23	first	first	ADJ
ejpam-4694	125	24	and	and	CCONJ
ejpam-4694	125	25	second	second	ADJ
ejpam-4694	125	26	kind	kind	NOUN
ejpam-4694	125	27	,	,	PUNCT
ejpam-4694	125	28	higher	high	ADJ
ejpam-4694	125	29	order	order	NOUN
ejpam-4694	125	30	degenerate	degenerate	ADJ
ejpam-4694	125	31	bernoulli	bernoulli	NOUN
ejpam-4694	125	32	polynomials	polynomial	NOUN
ejpam-4694	125	33	,	,	PUNCT
ejpam-4694	125	34	and	and	CCONJ
ejpam-4694	125	35	higher	high	ADJ
ejpam-4694	125	36	order	order	NOUN
ejpam-4694	125	37	degenerate	degenerate	ADJ
ejpam-4694	125	38	frobenius	frobenius	NOUN
ejpam-4694	125	39	-	-	PUNCT
ejpam-4694	125	40	euler	euler	NOUN
ejpam-4694	125	41	polynomials	polynomial	NOUN
ejpam-4694	125	42	are	be	AUX
ejpam-4694	125	43	discussed	discuss	VERB
ejpam-4694	125	44	.	.	PUNCT
ejpam-4694	126	1	2	2	X
ejpam-4694	126	2	.	.	X
ejpam-4694	126	3	definition	definition	NOUN
ejpam-4694	126	4	and	and	CCONJ
ejpam-4694	126	5	some	some	DET
ejpam-4694	126	6	explicit	explicit	ADJ
ejpam-4694	126	7	formulas	formula	NOUN
ejpam-4694	126	8	analogous	analogous	ADJ
ejpam-4694	126	9	to	to	ADP
ejpam-4694	126	10	the	the	DET
ejpam-4694	126	11	definition	definition	NOUN
ejpam-4694	126	12	of	of	ADP
ejpam-4694	126	13	degenerate	degenerate	ADJ
ejpam-4694	126	14	poly	poly	ADJ
ejpam-4694	126	15	-	-	PUNCT
ejpam-4694	126	16	euler	euler	NOUN
ejpam-4694	126	17	polynomials	polynomial	NOUN
ejpam-4694	126	18	in	in	ADP
ejpam-4694	126	19	(	(	PUNCT
ejpam-4694	126	20	26	26	NUM
ejpam-4694	126	21	)	)	PUNCT
ejpam-4694	126	22	,	,	PUNCT
ejpam-4694	126	23	the	the	DET
ejpam-4694	126	24	desired	desire	VERB
ejpam-4694	126	25	variation	variation	NOUN
ejpam-4694	126	26	of	of	ADP
ejpam-4694	126	27	apostol	apostol	NOUN
ejpam-4694	126	28	-	-	PUNCT
ejpam-4694	126	29	type	type	NOUN
ejpam-4694	126	30	poly	poly	ADJ
ejpam-4694	126	31	-	-	PUNCT
ejpam-4694	126	32	genocchi	genocchi	NOUN
ejpam-4694	126	33	polynomials	polynomial	NOUN
ejpam-4694	126	34	can	can	AUX
ejpam-4694	126	35	be	be	AUX
ejpam-4694	126	36	constructed	construct	VERB
ejpam-4694	126	37	by	by	ADP
ejpam-4694	126	38	introducing	introduce	VERB
ejpam-4694	126	39	the	the	DET
ejpam-4694	126	40	parameter	parameter	NOUN
ejpam-4694	126	41	u	u	NOUN
ejpam-4694	126	42	to	to	PART
ejpam-4694	126	43	incorporate	incorporate	VERB
ejpam-4694	126	44	the	the	DET
ejpam-4694	126	45	concept	concept	NOUN
ejpam-4694	126	46	of	of	ADP
ejpam-4694	126	47	frobenius	frobenius	ADJ
ejpam-4694	126	48	polynomials	polynomial	NOUN
ejpam-4694	126	49	as	as	ADV
ejpam-4694	126	50	well	well	ADV
ejpam-4694	126	51	as	as	ADP
ejpam-4694	126	52	the	the	DET
ejpam-4694	126	53	parameters	parameter	NOUN
ejpam-4694	126	54	a	a	PRON
ejpam-4694	126	55	and	and	CCONJ
ejpam-4694	126	56	b.	b.	PROPN
ejpam-4694	126	57	the	the	DET
ejpam-4694	126	58	following	following	NOUN
ejpam-4694	126	59	contains	contain	VERB
ejpam-4694	126	60	the	the	DET
ejpam-4694	126	61	formal	formal	ADJ
ejpam-4694	126	62	definition	definition	NOUN
ejpam-4694	126	63	of	of	ADP
ejpam-4694	126	64	the	the	DET
ejpam-4694	126	65	desired	desire	VERB
ejpam-4694	126	66	polynomials	polynomial	NOUN
ejpam-4694	126	67	.	.	PUNCT
ejpam-4694	127	1	definition	definition	NOUN
ejpam-4694	127	2	2.1	2.1	NUM
ejpam-4694	127	3	.	.	PUNCT
ejpam-4694	128	1	the	the	DET
ejpam-4694	128	2	degenerate	degenerate	ADJ
ejpam-4694	128	3	apostol	apostol	NOUN
ejpam-4694	128	4	-	-	PUNCT
ejpam-4694	128	5	frobenius	frobenius	NOUN
ejpam-4694	128	6	-	-	PUNCT
ejpam-4694	128	7	type	type	NOUN
ejpam-4694	128	8	poly	poly	ADJ
ejpam-4694	128	9	-	-	PUNCT
ejpam-4694	128	10	genocchi	genocchi	NOUN
ejpam-4694	128	11	polynomials	polynomial	NOUN
ejpam-4694	128	12	of	of	ADP
ejpam-4694	128	13	higher	high	ADJ
ejpam-4694	128	14	order	order	NOUN
ejpam-4694	128	15	with	with	ADP
ejpam-4694	128	16	parameters	parameter	NOUN
ejpam-4694	128	17	a	a	PRON
ejpam-4694	128	18	and	and	CCONJ
ejpam-4694	128	19	b	b	NOUN
ejpam-4694	128	20	,	,	PUNCT
ejpam-4694	128	21	denoted	denote	VERB
ejpam-4694	128	22	by	by	ADP
ejpam-4694	128	23	ĝ(k	ĝ(k	PRON
ejpam-4694	128	24	,	,	PUNCT
ejpam-4694	128	25	α	α	NOUN
ejpam-4694	128	26	)	)	PUNCT
ejpam-4694	128	27	n	n	CCONJ
ejpam-4694	128	28	(	(	PUNCT
ejpam-4694	128	29	x;λ	x;λ	PROPN
ejpam-4694	128	30	,	,	PUNCT
ejpam-4694	128	31	ρ	ρ	PROPN
ejpam-4694	128	32	,	,	PUNCT
ejpam-4694	128	33	u	u	NOUN
ejpam-4694	128	34	,	,	PUNCT
ejpam-4694	128	35	a	a	DET
ejpam-4694	128	36	,	,	PUNCT
ejpam-4694	128	37	b	b	NOUN
ejpam-4694	128	38	)	)	PUNCT
ejpam-4694	128	39	,	,	PUNCT
ejpam-4694	128	40	are	be	AUX
ejpam-4694	128	41	defined	define	VERB
ejpam-4694	128	42	as	as	ADP
ejpam-4694	128	43	coefficients	coefficient	NOUN
ejpam-4694	128	44	of	of	ADP
ejpam-4694	128	45	the	the	DET
ejpam-4694	128	46	following	follow	VERB
ejpam-4694	128	47	generating	generate	VERB
ejpam-4694	128	48	function	function	NOUN
ejpam-4694	128	49	:	:	PUNCT
ejpam-4694	128	50	∞∑	∞∑	NUM
ejpam-4694	128	51	n=0	n=0	NUM
ejpam-4694	128	52	ĝ(k	ĝ(k	PROPN
ejpam-4694	128	53	,	,	PUNCT
ejpam-4694	128	54	α	α	NOUN
ejpam-4694	128	55	)	)	PUNCT
ejpam-4694	128	56	n	n	CCONJ
ejpam-4694	128	57	(	(	PUNCT
ejpam-4694	128	58	x;λ	x;λ	PROPN
ejpam-4694	128	59	,	,	PUNCT
ejpam-4694	128	60	ρ	ρ	PROPN
ejpam-4694	128	61	,	,	PUNCT
ejpam-4694	128	62	u	u	NOUN
ejpam-4694	128	63	,	,	PUNCT
ejpam-4694	128	64	a	a	DET
ejpam-4694	128	65	,	,	PUNCT
ejpam-4694	128	66	b	b	NOUN
ejpam-4694	128	67	)	)	PUNCT
ejpam-4694	128	68	tn	tn	NOUN
ejpam-4694	128	69	n	n	NOUN
ejpam-4694	128	70	!	!	PUNCT
ejpam-4694	129	1	=	=	PRON
ejpam-4694	129	2	(	(	PUNCT
ejpam-4694	129	3	eik	eik	PROPN
ejpam-4694	129	4	,	,	PUNCT
ejpam-4694	129	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	129	6	+	+	CCONJ
ejpam-4694	129	7	(	(	PUNCT
ejpam-4694	129	8	1−	1−	NUM
ejpam-4694	129	9	u)t	u)t	X
ejpam-4694	129	10	ln	ln	PROPN
ejpam-4694	129	11	ab	ab	PROPN
ejpam-4694	129	12	)	)	PUNCT
ejpam-4694	129	13	)	)	PUNCT
ejpam-4694	130	1	λbt	λbt	VERB
ejpam-4694	130	2	−	−	PROPN
ejpam-4694	130	3	ua−t	ua−t	ADJ
ejpam-4694	130	4	)	)	PUNCT
ejpam-4694	130	5	α	α	PROPN
ejpam-4694	130	6	exρ(t	exρ(t	NOUN
ejpam-4694	130	7	)	)	PUNCT
ejpam-4694	130	8	,	,	PUNCT
ejpam-4694	130	9	(	(	PUNCT
ejpam-4694	130	10	27	27	NUM
ejpam-4694	130	11	)	)	PUNCT
ejpam-4694	130	12	where	where	SCONJ
ejpam-4694	130	13	|t|	|t|	VERB
ejpam-4694	130	14	<	<	X
ejpam-4694	130	15	√	√	X
ejpam-4694	130	16	(	(	PUNCT
ejpam-4694	130	17	ln(λ	ln(λ	X
ejpam-4694	130	18	u))2	u))2	X
ejpam-4694	131	1	+	+	NOUN
ejpam-4694	131	2	4π2	4π2	NOUN
ejpam-4694	131	3	|	|	ADV
ejpam-4694	131	4	ln	ln	ADJ
ejpam-4694	131	5	a+ln	a+ln	NOUN
ejpam-4694	131	6	b|	b|	PROPN
ejpam-4694	131	7	.	.	PUNCT
ejpam-4694	132	1	when	when	SCONJ
ejpam-4694	132	2	α	α	PRON
ejpam-4694	132	3	=	=	SYM
ejpam-4694	132	4	1	1	NUM
ejpam-4694	132	5	,	,	PUNCT
ejpam-4694	132	6	(	(	PUNCT
ejpam-4694	132	7	27	27	NUM
ejpam-4694	132	8	)	)	PUNCT
ejpam-4694	132	9	yields	yield	VERB
ejpam-4694	132	10	∞∑	∞∑	PRON
ejpam-4694	132	11	n=0	n=0	NUM
ejpam-4694	132	12	ĝ(k	ĝ(k	NOUN
ejpam-4694	132	13	)	)	PUNCT
ejpam-4694	132	14	n	n	CCONJ
ejpam-4694	132	15	(	(	PUNCT
ejpam-4694	132	16	x;λ	x;λ	PROPN
ejpam-4694	132	17	,	,	PUNCT
ejpam-4694	132	18	ρ	ρ	PROPN
ejpam-4694	132	19	,	,	PUNCT
ejpam-4694	132	20	u	u	NOUN
ejpam-4694	132	21	,	,	PUNCT
ejpam-4694	132	22	a	a	DET
ejpam-4694	132	23	,	,	PUNCT
ejpam-4694	132	24	b	b	NOUN
ejpam-4694	132	25	)	)	PUNCT
ejpam-4694	132	26	tn	tn	PROPN
ejpam-4694	132	27	n	n	NOUN
ejpam-4694	132	28	!	!	PUNCT
ejpam-4694	133	1	=	=	PUNCT
ejpam-4694	133	2	eik	eik	PROPN
ejpam-4694	133	3	,	,	PUNCT
ejpam-4694	133	4	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	133	5	+	+	CCONJ
ejpam-4694	133	6	(	(	PUNCT
ejpam-4694	133	7	1−	1−	NUM
ejpam-4694	133	8	u)t	u)t	X
ejpam-4694	133	9	ln	ln	PROPN
ejpam-4694	133	10	ab	ab	PROPN
ejpam-4694	133	11	)	)	PUNCT
ejpam-4694	133	12	)	)	PUNCT
ejpam-4694	134	1	λbt	λbt	VERB
ejpam-4694	134	2	−	−	PROPN
ejpam-4694	134	3	ua−t	ua−t	PROPN
ejpam-4694	134	4	exρ(t	exρ(t	PROPN
ejpam-4694	134	5	)	)	PUNCT
ejpam-4694	134	6	.	.	PUNCT
ejpam-4694	135	1	(	(	PUNCT
ejpam-4694	135	2	28	28	NUM
ejpam-4694	135	3	)	)	PUNCT
ejpam-4694	135	4	where	where	SCONJ
ejpam-4694	135	5	ĝ(k	ĝ(k	NOUN
ejpam-4694	135	6	)	)	PUNCT
ejpam-4694	135	7	n	n	CCONJ
ejpam-4694	135	8	(	(	PUNCT
ejpam-4694	135	9	x;λ	x;λ	PROPN
ejpam-4694	135	10	,	,	PUNCT
ejpam-4694	135	11	ρ	ρ	PROPN
ejpam-4694	135	12	,	,	PUNCT
ejpam-4694	135	13	u	u	NOUN
ejpam-4694	135	14	,	,	PUNCT
ejpam-4694	135	15	a	a	DET
ejpam-4694	135	16	,	,	PUNCT
ejpam-4694	135	17	b	b	NOUN
ejpam-4694	135	18	)	)	PUNCT
ejpam-4694	135	19	=	=	SYM
ejpam-4694	135	20	ĝ(k,1	ĝ(k,1	NOUN
ejpam-4694	135	21	)	)	PUNCT
ejpam-4694	135	22	n	n	CCONJ
ejpam-4694	135	23	(	(	PUNCT
ejpam-4694	135	24	x;λ	x;λ	PROPN
ejpam-4694	135	25	,	,	PUNCT
ejpam-4694	135	26	ρ	ρ	PROPN
ejpam-4694	135	27	,	,	PUNCT
ejpam-4694	135	28	u	u	NOUN
ejpam-4694	135	29	,	,	PUNCT
ejpam-4694	135	30	a	a	DET
ejpam-4694	135	31	,	,	PUNCT
ejpam-4694	135	32	b	b	NOUN
ejpam-4694	135	33	)	)	PUNCT
ejpam-4694	135	34	denotes	denote	VERB
ejpam-4694	135	35	the	the	DET
ejpam-4694	135	36	degenerate	degenerate	ADJ
ejpam-4694	135	37	apostol	apostol	NOUN
ejpam-4694	135	38	-	-	PUNCT
ejpam-4694	135	39	frobeniustype	frobeniustype	NOUN
ejpam-4694	135	40	poly	poly	ADJ
ejpam-4694	135	41	-	-	PUNCT
ejpam-4694	135	42	genocchi	genocchi	NOUN
ejpam-4694	135	43	polynomials	polynomial	NOUN
ejpam-4694	135	44	with	with	ADP
ejpam-4694	135	45	parameters	parameter	NOUN
ejpam-4694	135	46	a	a	PRON
ejpam-4694	135	47	and	and	CCONJ
ejpam-4694	135	48	b.	b.	PROPN
ejpam-4694	136	1	now	now	ADV
ejpam-4694	136	2	,	,	PUNCT
ejpam-4694	136	3	if	if	SCONJ
ejpam-4694	136	4	x	x	X
ejpam-4694	136	5	=	=	SYM
ejpam-4694	136	6	(	(	PUNCT
ejpam-4694	136	7	1−	1−	NUM
ejpam-4694	136	8	u)t	u)t	X
ejpam-4694	136	9	ln	ln	PROPN
ejpam-4694	136	10	ab	ab	PROPN
ejpam-4694	136	11	,	,	PUNCT
ejpam-4694	136	12	then	then	ADV
ejpam-4694	136	13	(	(	PUNCT
ejpam-4694	136	14	25	25	NUM
ejpam-4694	136	15	)	)	PUNCT
ejpam-4694	136	16	yields	yield	NOUN
ejpam-4694	136	17	eik	eik	PROPN
ejpam-4694	136	18	,	,	PUNCT
ejpam-4694	136	19	ρ(logρ(1	ρ(logρ(1	PROPN
ejpam-4694	136	20	+	+	CCONJ
ejpam-4694	136	21	(	(	PUNCT
ejpam-4694	136	22	1−	1−	NUM
ejpam-4694	136	23	u)t	u)t	X
ejpam-4694	136	24	ln	ln	PROPN
ejpam-4694	136	25	ab	ab	PROPN
ejpam-4694	136	26	)	)	PUNCT
ejpam-4694	136	27	)	)	PUNCT
ejpam-4694	136	28	r.	r.	PROPN
ejpam-4694	136	29	corcino	corcino	PROPN
ejpam-4694	136	30	,	,	PUNCT
ejpam-4694	136	31	c.	c.	PROPN
ejpam-4694	136	32	corcino	corcino	PROPN
ejpam-4694	136	33	/	/	SYM
ejpam-4694	136	34	eur	eur	PROPN
ejpam-4694	136	35	.	.	PUNCT
ejpam-4694	137	1	j.	j.	PROPN
ejpam-4694	137	2	pure	pure	PROPN
ejpam-4694	137	3	appl	appl	PROPN
ejpam-4694	137	4	.	.	PROPN
ejpam-4694	137	5	math	math	PROPN
ejpam-4694	137	6	,	,	PUNCT
ejpam-4694	137	7	16	16	NUM
ejpam-4694	137	8	(	(	PUNCT
ejpam-4694	137	9	2	2	NUM
ejpam-4694	137	10	)	)	PUNCT
ejpam-4694	137	11	(	(	PUNCT
ejpam-4694	137	12	2023	2023	NUM
ejpam-4694	137	13	)	)	PUNCT
ejpam-4694	137	14	,	,	PUNCT
ejpam-4694	137	15	687	687	NUM
ejpam-4694	137	16	-	-	SYM
ejpam-4694	137	17	712	712	NUM
ejpam-4694	137	18	693	693	NUM
ejpam-4694	137	19	=	=	SYM
ejpam-4694	137	20	t	t	PROPN
ejpam-4694	137	21	∞∑	∞∑	PROPN
ejpam-4694	137	22	m=0	m=0	PROPN
ejpam-4694	137	23	(	(	PUNCT
ejpam-4694	137	24	(	(	PUNCT
ejpam-4694	137	25	1−	1−	NUM
ejpam-4694	137	26	u	u	NOUN
ejpam-4694	137	27	)	)	PUNCT
ejpam-4694	137	28	ln	ln	ADJ
ejpam-4694	137	29	ab)m+1	ab)m+1	NOUN
ejpam-4694	137	30	∑	∑	ADV
ejpam-4694	137	31	m1+m2+	m1+m2+	ADJ
ejpam-4694	137	32	...	...	PUNCT
ejpam-4694	137	33	+mk−1	+mk−1	PROPN
ejpam-4694	137	34	=	=	NOUN
ejpam-4694	137	35	m	m	PROPN
ejpam-4694	137	36	(	(	PUNCT
ejpam-4694	137	37	m	m	PROPN
ejpam-4694	137	38	m1	m1	NOUN
ejpam-4694	137	39	,	,	PUNCT
ejpam-4694	137	40	.	.	PUNCT
ejpam-4694	137	41	.	.	PUNCT
ejpam-4694	138	1	.	.	PUNCT
ejpam-4694	139	1	,	,	PUNCT
ejpam-4694	139	2	mk−1	mk−1	PROPN
ejpam-4694	139	3	)	)	PUNCT
ejpam-4694	139	4	×	×	PROPN
ejpam-4694	139	5	bm1,ρ(ρ−	bm1,ρ(ρ−	PROPN
ejpam-4694	139	6	1	1	NUM
ejpam-4694	139	7	)	)	PUNCT
ejpam-4694	139	8	m1	m1	NOUN
ejpam-4694	139	9	+	+	CCONJ
ejpam-4694	139	10	1	1	NUM
ejpam-4694	139	11	bm2,ρ(ρ−	bm2,ρ(ρ−	NOUN
ejpam-4694	139	12	1	1	NUM
ejpam-4694	139	13	)	)	PUNCT
ejpam-4694	139	14	m1	m1	PROPN
ejpam-4694	140	1	+	+	PROPN
ejpam-4694	140	2	m2	m2	PROPN
ejpam-4694	140	3	+	+	X
ejpam-4694	140	4	1	1	NUM
ejpam-4694	140	5	.	.	PUNCT
ejpam-4694	140	6	.	.	PUNCT
ejpam-4694	140	7	.	.	PUNCT
ejpam-4694	141	1	bmk−1,ρ(ρ−	bmk−1,ρ(ρ−	NOUN
ejpam-4694	141	2	1	1	NUM
ejpam-4694	141	3	)	)	PUNCT
ejpam-4694	141	4	m1	m1	NOUN
ejpam-4694	141	5	+	+	CCONJ
ejpam-4694	141	6	.	.	PUNCT
ejpam-4694	141	7	.	.	PUNCT
ejpam-4694	142	1	.+mk−1	.+mk−1	PROPN
ejpam-4694	143	1	+	+	CCONJ
ejpam-4694	143	2	1	1	NUM
ejpam-4694	143	3	tm	tm	NOUN
ejpam-4694	143	4	m	m	PROPN
ejpam-4694	143	5	!	!	PUNCT
ejpam-4694	143	6	.	.	PUNCT
ejpam-4694	144	1	also	also	ADV
ejpam-4694	144	2	,	,	PUNCT
ejpam-4694	144	3	exρ(t	exρ(t	ADV
ejpam-4694	144	4	)	)	PUNCT
ejpam-4694	144	5	λbt	λbt	VERB
ejpam-4694	144	6	−	−	PROPN
ejpam-4694	144	7	ua−t	ua−t	NOUN
ejpam-4694	144	8	=	=	PUNCT
ejpam-4694	145	1	∞∑	∞∑	NUM
ejpam-4694	145	2	m=0	m=0	PROPN
ejpam-4694	145	3	m∑	m∑	VERB
ejpam-4694	145	4	j=0	j=0	VERB
ejpam-4694	145	5	∞∑	∞∑	NUM
ejpam-4694	145	6	n=0	n=0	NUM
ejpam-4694	145	7	(	(	PUNCT
ejpam-4694	145	8	m	m	NOUN
ejpam-4694	145	9	j	j	NOUN
ejpam-4694	145	10	)	)	PUNCT
ejpam-4694	145	11	(	(	PUNCT
ejpam-4694	145	12	x)j	x)j	NUM
ejpam-4694	145	13	,	,	PUNCT
ejpam-4694	145	14	ρ	ρ	PROPN
ejpam-4694	145	15	(	(	PUNCT
ejpam-4694	145	16	u	u	NOUN
ejpam-4694	145	17	λ	λ	PROPN
ejpam-4694	145	18	)	)	PUNCT
ejpam-4694	145	19	n	n	CCONJ
ejpam-4694	145	20	(	(	PUNCT
ejpam-4694	145	21	−n	−n	ADV
ejpam-4694	145	22	log	log	NOUN
ejpam-4694	145	23	ab)m−j	ab)m−j	PROPN
ejpam-4694	145	24	t	t	PROPN
ejpam-4694	145	25	m	m	NOUN
ejpam-4694	145	26	m	m	PROPN
ejpam-4694	145	27	!	!	PUNCT
ejpam-4694	145	28	.	.	PUNCT
ejpam-4694	146	1	with	with	ADP
ejpam-4694	146	2	bm1,m2,	bm1,m2,	ADJ
ejpam-4694	146	3	...	...	PUNCT
ejpam-4694	146	4	,mk−1	,mk−1	PUNCT
ejpam-4694	146	5	(	(	PUNCT
ejpam-4694	146	6	m	m	PROPN
ejpam-4694	146	7	,	,	PUNCT
ejpam-4694	146	8	ρ−	ρ−	NOUN
ejpam-4694	146	9	1	1	NUM
ejpam-4694	146	10	)	)	PUNCT
ejpam-4694	146	11	=	=	SYM
ejpam-4694	146	12	(	(	PUNCT
ejpam-4694	146	13	(	(	PUNCT
ejpam-4694	146	14	1−	1−	NUM
ejpam-4694	146	15	u	u	NOUN
ejpam-4694	146	16	)	)	PUNCT
ejpam-4694	146	17	ln	ln	ADJ
ejpam-4694	146	18	ab)m+1	ab)m+1	NOUN
ejpam-4694	146	19	∑	∑	ADV
ejpam-4694	146	20	m1+m2+	m1+m2+	ADJ
ejpam-4694	146	21	...	...	PUNCT
ejpam-4694	146	22	+mk−1	+mk−1	PROPN
ejpam-4694	146	23	=	=	NOUN
ejpam-4694	146	24	m	m	PROPN
ejpam-4694	146	25	(	(	PUNCT
ejpam-4694	146	26	m	m	PROPN
ejpam-4694	146	27	m1	m1	NOUN
ejpam-4694	146	28	,	,	PUNCT
ejpam-4694	146	29	.	.	PUNCT
ejpam-4694	146	30	.	.	PUNCT
ejpam-4694	146	31	.	.	PUNCT
ejpam-4694	147	1	,	,	PUNCT
ejpam-4694	147	2	mk−1	mk−1	PROPN
ejpam-4694	147	3	)	)	PUNCT
ejpam-4694	147	4	×	×	PROPN
ejpam-4694	147	5	bm1,ρ(ρ−	bm1,ρ(ρ−	PROPN
ejpam-4694	147	6	1	1	NUM
ejpam-4694	147	7	)	)	PUNCT
ejpam-4694	147	8	m1	m1	NOUN
ejpam-4694	147	9	+	+	CCONJ
ejpam-4694	147	10	1	1	NUM
ejpam-4694	147	11	bm2,ρ(ρ−	bm2,ρ(ρ−	NOUN
ejpam-4694	147	12	1	1	NUM
ejpam-4694	147	13	)	)	PUNCT
ejpam-4694	147	14	m1	m1	PROPN
ejpam-4694	148	1	+	+	PROPN
ejpam-4694	148	2	m2	m2	PROPN
ejpam-4694	148	3	+	+	X
ejpam-4694	148	4	1	1	NUM
ejpam-4694	148	5	.	.	PUNCT
ejpam-4694	148	6	.	.	PUNCT
ejpam-4694	148	7	.	.	PUNCT
ejpam-4694	149	1	bmk−1,ρ(ρ−	bmk−1,ρ(ρ−	NOUN
ejpam-4694	149	2	1	1	NUM
ejpam-4694	149	3	)	)	PUNCT
ejpam-4694	149	4	m1	m1	NOUN
ejpam-4694	149	5	+	+	CCONJ
ejpam-4694	149	6	.	.	PUNCT
ejpam-4694	149	7	.	.	PUNCT
ejpam-4694	150	1	.+mk−1	.+mk−1	PROPN
ejpam-4694	151	1	+	+	CCONJ
ejpam-4694	151	2	1	1	NUM
ejpam-4694	151	3	,	,	PUNCT
ejpam-4694	151	4	(	(	PUNCT
ejpam-4694	151	5	29	29	NUM
ejpam-4694	151	6	)	)	PUNCT
ejpam-4694	151	7	we	we	PRON
ejpam-4694	151	8	have	have	VERB
ejpam-4694	151	9	∞∑	∞∑	NUM
ejpam-4694	151	10	m=0	m=0	PROPN
ejpam-4694	151	11	ĝ(k	ĝ(k	NOUN
ejpam-4694	151	12	)	)	PUNCT
ejpam-4694	151	13	m	m	VERB
ejpam-4694	151	14	(	(	PUNCT
ejpam-4694	151	15	x;λ	x;λ	PROPN
ejpam-4694	151	16	,	,	PUNCT
ejpam-4694	151	17	ρ	ρ	PROPN
ejpam-4694	151	18	,	,	PUNCT
ejpam-4694	151	19	u	u	NOUN
ejpam-4694	151	20	,	,	PUNCT
ejpam-4694	151	21	a	a	DET
ejpam-4694	151	22	,	,	PUNCT
ejpam-4694	151	23	b	b	NOUN
ejpam-4694	151	24	)	)	PUNCT
ejpam-4694	151	25	tm	tm	PROPN
ejpam-4694	151	26	m	m	PROPN
ejpam-4694	151	27	!	!	PUNCT
ejpam-4694	152	1	=	=	SYM
ejpam-4694	152	2	eik	eik	PROPN
ejpam-4694	152	3	,	,	PUNCT
ejpam-4694	152	4	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	152	5	+	+	CCONJ
ejpam-4694	152	6	(	(	PUNCT
ejpam-4694	152	7	1−	1−	NUM
ejpam-4694	152	8	u)t	u)t	X
ejpam-4694	152	9	ln	ln	PROPN
ejpam-4694	152	10	ab	ab	PROPN
ejpam-4694	152	11	)	)	PUNCT
ejpam-4694	152	12	)	)	PUNCT
ejpam-4694	153	1	λbt	λbt	VERB
ejpam-4694	153	2	−	−	PROPN
ejpam-4694	153	3	ua−t	ua−t	NOUN
ejpam-4694	153	4	exρ(t	exρ(t	NOUN
ejpam-4694	153	5	)	)	PUNCT
ejpam-4694	153	6	=	=	PUNCT
ejpam-4694	154	1	t	t	PROPN
ejpam-4694	155	1	∞∑	∞∑	PROPN
ejpam-4694	155	2	m=0	m=0	PROPN
ejpam-4694	155	3	m∑	m∑	VERB
ejpam-4694	155	4	i=0	i=0	PROPN
ejpam-4694	155	5	m−i∑	m−i∑	NOUN
ejpam-4694	155	6	j=0	j=0	PROPN
ejpam-4694	155	7	∞∑	∞∑	PRON
ejpam-4694	155	8	n=0	n=0	ADV
ejpam-4694	155	9	bm1,m2,	bm1,m2,	ADJ
ejpam-4694	155	10	...	...	PUNCT
ejpam-4694	155	11	,mk−1	,mk−1	PUNCT
ejpam-4694	155	12	(	(	PUNCT
ejpam-4694	155	13	i	i	NOUN
ejpam-4694	155	14	,	,	PUNCT
ejpam-4694	155	15	ρ−	ρ−	NOUN
ejpam-4694	155	16	1	1	NUM
ejpam-4694	155	17	)	)	PUNCT
ejpam-4694	155	18	(	(	PUNCT
ejpam-4694	155	19	m−	m−	PROPN
ejpam-4694	155	20	i	i	PRON
ejpam-4694	155	21	j	j	PROPN
ejpam-4694	155	22	)	)	PUNCT
ejpam-4694	155	23	(	(	PUNCT
ejpam-4694	155	24	m	m	VERB
ejpam-4694	155	25	i	i	NOUN
ejpam-4694	155	26	)	)	PUNCT
ejpam-4694	155	27	(	(	PUNCT
ejpam-4694	155	28	x)j	x)j	NUM
ejpam-4694	155	29	,	,	PUNCT
ejpam-4694	155	30	ρ	ρ	PROPN
ejpam-4694	155	31	(	(	PUNCT
ejpam-4694	155	32	u	u	NOUN
ejpam-4694	155	33	λ	λ	PROPN
ejpam-4694	155	34	)	)	PUNCT
ejpam-4694	155	35	n	n	CCONJ
ejpam-4694	155	36	(	(	PUNCT
ejpam-4694	155	37	−n	−n	ADV
ejpam-4694	155	38	log	log	NOUN
ejpam-4694	155	39	ab)m−i−j	ab)m−i−j	PROPN
ejpam-4694	155	40	t	t	PROPN
ejpam-4694	155	41	m	m	PROPN
ejpam-4694	155	42	m	m	PROPN
ejpam-4694	155	43	!	!	PUNCT
ejpam-4694	155	44	.	.	PUNCT
ejpam-4694	156	1	note	note	VERB
ejpam-4694	156	2	that	that	SCONJ
ejpam-4694	156	3	the	the	DET
ejpam-4694	156	4	right	right	ADJ
ejpam-4694	156	5	-	-	PUNCT
ejpam-4694	156	6	hand	hand	NOUN
ejpam-4694	156	7	side	side	NOUN
ejpam-4694	156	8	of	of	ADP
ejpam-4694	156	9	the	the	DET
ejpam-4694	156	10	preceding	precede	VERB
ejpam-4694	156	11	equation	equation	NOUN
ejpam-4694	156	12	has	have	VERB
ejpam-4694	156	13	no	no	DET
ejpam-4694	156	14	constant	constant	ADJ
ejpam-4694	156	15	term	term	NOUN
ejpam-4694	156	16	.	.	PUNCT
ejpam-4694	157	1	hence	hence	ADV
ejpam-4694	157	2	,	,	PUNCT
ejpam-4694	157	3	when	when	SCONJ
ejpam-4694	157	4	m	m	VERB
ejpam-4694	157	5	=	=	SYM
ejpam-4694	157	6	0	0	NUM
ejpam-4694	157	7	,	,	PUNCT
ejpam-4694	157	8	ĝ(k	ĝ(k	NOUN
ejpam-4694	157	9	)	)	PUNCT
ejpam-4694	157	10	0	0	NUM
ejpam-4694	158	1	(	(	PUNCT
ejpam-4694	158	2	x;λ	x;λ	PROPN
ejpam-4694	158	3	,	,	PUNCT
ejpam-4694	158	4	ρ	ρ	PROPN
ejpam-4694	158	5	,	,	PUNCT
ejpam-4694	158	6	u	u	NOUN
ejpam-4694	158	7	,	,	PUNCT
ejpam-4694	158	8	a	a	DET
ejpam-4694	158	9	,	,	PUNCT
ejpam-4694	158	10	b	b	NOUN
ejpam-4694	158	11	)	)	PUNCT
ejpam-4694	158	12	=	=	SYM
ejpam-4694	159	1	0	0	X
ejpam-4694	159	2	.	.	PUNCT
ejpam-4694	160	1	moreover	moreover	ADV
ejpam-4694	160	2	,	,	PUNCT
ejpam-4694	160	3	∞∑	∞∑	PROPN
ejpam-4694	160	4	m=0	m=0	PROPN
ejpam-4694	160	5	1	1	NUM
ejpam-4694	160	6	m	m	NOUN
ejpam-4694	160	7	ĝ(k	ĝ(k	NOUN
ejpam-4694	160	8	)	)	PUNCT
ejpam-4694	160	9	m	m	VERB
ejpam-4694	160	10	(	(	PUNCT
ejpam-4694	160	11	x;λ	x;λ	PROPN
ejpam-4694	160	12	,	,	PUNCT
ejpam-4694	160	13	ρ	ρ	PROPN
ejpam-4694	160	14	,	,	PUNCT
ejpam-4694	160	15	u	u	NOUN
ejpam-4694	160	16	,	,	PUNCT
ejpam-4694	160	17	a	a	DET
ejpam-4694	160	18	,	,	PUNCT
ejpam-4694	160	19	b	b	NOUN
ejpam-4694	160	20	)	)	PUNCT
ejpam-4694	160	21	tm−1	tm−1	NOUN
ejpam-4694	160	22	(	(	PUNCT
ejpam-4694	160	23	m−	m−	PROPN
ejpam-4694	160	24	1	1	NUM
ejpam-4694	160	25	)	)	PUNCT
ejpam-4694	160	26	!	!	PUNCT
ejpam-4694	161	1	=	=	PUNCT
ejpam-4694	162	1	∞∑	∞∑	NUM
ejpam-4694	162	2	m=0	m=0	PROPN
ejpam-4694	162	3	m∑	m∑	VERB
ejpam-4694	162	4	i=0	i=0	PROPN
ejpam-4694	162	5	m−i∑	m−i∑	NOUN
ejpam-4694	162	6	j=0	j=0	PROPN
ejpam-4694	162	7	∞∑	∞∑	PRON
ejpam-4694	162	8	n=0	n=0	ADV
ejpam-4694	162	9	bm1,m2,	bm1,m2,	ADJ
ejpam-4694	162	10	...	...	PUNCT
ejpam-4694	162	11	,mk−1	,mk−1	PUNCT
ejpam-4694	162	12	(	(	PUNCT
ejpam-4694	162	13	i	i	NOUN
ejpam-4694	162	14	,	,	PUNCT
ejpam-4694	162	15	ρ−	ρ−	NOUN
ejpam-4694	162	16	1	1	NUM
ejpam-4694	162	17	)	)	PUNCT
ejpam-4694	162	18	(	(	PUNCT
ejpam-4694	162	19	m−	m−	PROPN
ejpam-4694	162	20	i	i	PRON
ejpam-4694	162	21	j	j	PROPN
ejpam-4694	162	22	)	)	PUNCT
ejpam-4694	162	23	(	(	PUNCT
ejpam-4694	162	24	m	m	VERB
ejpam-4694	162	25	i	i	NOUN
ejpam-4694	162	26	)	)	PUNCT
ejpam-4694	162	27	(	(	PUNCT
ejpam-4694	162	28	x)j	x)j	NUM
ejpam-4694	162	29	,	,	PUNCT
ejpam-4694	162	30	ρ	ρ	PROPN
ejpam-4694	162	31	(	(	PUNCT
ejpam-4694	162	32	u	u	NOUN
ejpam-4694	162	33	λ	λ	PROPN
ejpam-4694	162	34	)	)	PUNCT
ejpam-4694	162	35	n	n	CCONJ
ejpam-4694	162	36	(	(	PUNCT
ejpam-4694	162	37	−n	−n	ADV
ejpam-4694	162	38	log	log	NOUN
ejpam-4694	162	39	ab)m−i−j	ab)m−i−j	PROPN
ejpam-4694	162	40	t	t	PROPN
ejpam-4694	162	41	m	m	PROPN
ejpam-4694	162	42	m	m	PROPN
ejpam-4694	162	43	!	!	PUNCT
ejpam-4694	162	44	.	.	PUNCT
ejpam-4694	163	1	by	by	ADP
ejpam-4694	163	2	comparing	compare	VERB
ejpam-4694	163	3	the	the	DET
ejpam-4694	163	4	coefficients	coefficient	NOUN
ejpam-4694	163	5	of	of	ADP
ejpam-4694	163	6	tm	tm	PROPN
ejpam-4694	163	7	m	m	PROPN
ejpam-4694	163	8	!	!	PROPN
ejpam-4694	163	9	,	,	PUNCT
ejpam-4694	163	10	we	we	PRON
ejpam-4694	163	11	obtain	obtain	VERB
ejpam-4694	163	12	the	the	DET
ejpam-4694	163	13	following	follow	VERB
ejpam-4694	163	14	explicit	explicit	ADJ
ejpam-4694	163	15	formula	formula	NOUN
ejpam-4694	163	16	:	:	PUNCT
ejpam-4694	163	17	1	1	NUM
ejpam-4694	163	18	m+	m+	NUM
ejpam-4694	163	19	1	1	NUM
ejpam-4694	163	20	ĝ(k	ĝ(k	NOUN
ejpam-4694	163	21	)	)	PUNCT
ejpam-4694	163	22	m+1(x;λ	m+1(x;λ	PROPN
ejpam-4694	163	23	,	,	PUNCT
ejpam-4694	163	24	ρ	ρ	PROPN
ejpam-4694	163	25	,	,	PUNCT
ejpam-4694	163	26	u	u	NOUN
ejpam-4694	163	27	,	,	PUNCT
ejpam-4694	163	28	a	a	DET
ejpam-4694	163	29	,	,	PUNCT
ejpam-4694	163	30	b	b	NOUN
ejpam-4694	163	31	)	)	PUNCT
ejpam-4694	163	32	=	=	PUNCT
ejpam-4694	163	33	m∑	m∑	CCONJ
ejpam-4694	163	34	i=0	i=0	PROPN
ejpam-4694	163	35	m−i∑	m−i∑	ADJ
ejpam-4694	163	36	j=0	j=0	PROPN
ejpam-4694	163	37	∞∑	∞∑	PRON
ejpam-4694	163	38	n=0	n=0	ADV
ejpam-4694	163	39	bm1,m2,	bm1,m2,	ADJ
ejpam-4694	163	40	...	...	PUNCT
ejpam-4694	163	41	,mk−1	,mk−1	PUNCT
ejpam-4694	163	42	(	(	PUNCT
ejpam-4694	163	43	i	i	NOUN
ejpam-4694	163	44	,	,	PUNCT
ejpam-4694	163	45	ρ−	ρ−	NOUN
ejpam-4694	163	46	1	1	NUM
ejpam-4694	163	47	)	)	PUNCT
ejpam-4694	163	48	(	(	PUNCT
ejpam-4694	163	49	m−	m−	PROPN
ejpam-4694	163	50	i	i	PRON
ejpam-4694	163	51	j	j	PROPN
ejpam-4694	163	52	)	)	PUNCT
ejpam-4694	163	53	(	(	PUNCT
ejpam-4694	163	54	m	m	VERB
ejpam-4694	163	55	i	i	NOUN
ejpam-4694	163	56	)	)	PUNCT
ejpam-4694	163	57	(	(	PUNCT
ejpam-4694	163	58	x)j	x)j	NUM
ejpam-4694	163	59	,	,	PUNCT
ejpam-4694	163	60	ρ	ρ	PROPN
ejpam-4694	163	61	(	(	PUNCT
ejpam-4694	163	62	u	u	NOUN
ejpam-4694	163	63	λ	λ	PROPN
ejpam-4694	163	64	)	)	PUNCT
ejpam-4694	163	65	n	n	CCONJ
ejpam-4694	163	66	(	(	PUNCT
ejpam-4694	163	67	−n	−n	ADV
ejpam-4694	163	68	log	log	NOUN
ejpam-4694	163	69	ab)m−i−j	ab)m−i−j	PROPN
ejpam-4694	163	70	.	.	PUNCT
ejpam-4694	164	1	r.	r.	PROPN
ejpam-4694	164	2	corcino	corcino	PROPN
ejpam-4694	164	3	,	,	PUNCT
ejpam-4694	164	4	c.	c.	PROPN
ejpam-4694	164	5	corcino	corcino	PROPN
ejpam-4694	164	6	/	/	SYM
ejpam-4694	164	7	eur	eur	PROPN
ejpam-4694	164	8	.	.	PUNCT
ejpam-4694	165	1	j.	j.	PROPN
ejpam-4694	165	2	pure	pure	PROPN
ejpam-4694	165	3	appl	appl	PROPN
ejpam-4694	165	4	.	.	PROPN
ejpam-4694	165	5	math	math	PROPN
ejpam-4694	165	6	,	,	PUNCT
ejpam-4694	165	7	16	16	NUM
ejpam-4694	165	8	(	(	PUNCT
ejpam-4694	165	9	2	2	NUM
ejpam-4694	165	10	)	)	PUNCT
ejpam-4694	165	11	(	(	PUNCT
ejpam-4694	165	12	2023	2023	NUM
ejpam-4694	165	13	)	)	PUNCT
ejpam-4694	165	14	,	,	PUNCT
ejpam-4694	165	15	687	687	NUM
ejpam-4694	165	16	-	-	SYM
ejpam-4694	165	17	712	712	NUM
ejpam-4694	165	18	694	694	NUM
ejpam-4694	165	19	furthermore	furthermore	ADV
ejpam-4694	165	20	,	,	PUNCT
ejpam-4694	165	21	using	use	VERB
ejpam-4694	165	22	the	the	DET
ejpam-4694	165	23	arithmetic	arithmetic	ADJ
ejpam-4694	165	24	-	-	PUNCT
ejpam-4694	165	25	geometric	geometric	ADJ
ejpam-4694	165	26	series	series	NOUN
ejpam-4694	165	27	formula	formula	NOUN
ejpam-4694	165	28	in	in	ADP
ejpam-4694	165	29	[	[	X
ejpam-4694	165	30	12	12	NUM
ejpam-4694	165	31	,	,	PUNCT
ejpam-4694	165	32	p.245	p.245	NOUN
ejpam-4694	165	33	]	]	PUNCT
ejpam-4694	165	34	,	,	PUNCT
ejpam-4694	165	35	we	we	PRON
ejpam-4694	165	36	can	can	AUX
ejpam-4694	165	37	write	write	VERB
ejpam-4694	165	38	∞∑	∞∑	NUM
ejpam-4694	165	39	n=0	n=0	PROPN
ejpam-4694	165	40	(	(	PUNCT
ejpam-4694	165	41	u	u	NOUN
ejpam-4694	165	42	λ	λ	PROPN
ejpam-4694	165	43	)	)	PUNCT
ejpam-4694	165	44	n	n	CCONJ
ejpam-4694	165	45	nm−i−j	nm−i−j	NOUN
ejpam-4694	165	46	=	=	SYM
ejpam-4694	165	47	am−i−j	am−i−j	PROPN
ejpam-4694	165	48	(	(	PUNCT
ejpam-4694	165	49	u	u	NOUN
ejpam-4694	165	50	λ	λ	PROPN
ejpam-4694	165	51	)	)	PUNCT
ejpam-4694	165	52	(	(	PUNCT
ejpam-4694	165	53	1−	1−	NUM
ejpam-4694	165	54	u	u	NOUN
ejpam-4694	165	55	λ	λ	NOUN
ejpam-4694	165	56	)	)	PUNCT
ejpam-4694	165	57	m−i−j+1	m−i−j+1	NOUN
ejpam-4694	165	58	,	,	PUNCT
ejpam-4694	165	59	where	where	SCONJ
ejpam-4694	165	60	an(u	an(u	PUNCT
ejpam-4694	165	61	)	)	PUNCT
ejpam-4694	165	62	is	be	AUX
ejpam-4694	165	63	the	the	DET
ejpam-4694	165	64	eulerian	eulerian	ADJ
ejpam-4694	165	65	polynomial	polynomial	ADJ
ejpam-4694	165	66	an(u	an(u	NOUN
ejpam-4694	165	67	)	)	PUNCT
ejpam-4694	166	1	=	=	SYM
ejpam-4694	166	2	n∑	n∑	PROPN
ejpam-4694	166	3	k=0	k=0	PROPN
ejpam-4694	166	4	a(n	a(n	PROPN
ejpam-4694	166	5	,	,	PUNCT
ejpam-4694	166	6	k)uk	k)uk	PROPN
ejpam-4694	166	7	(	(	PUNCT
ejpam-4694	166	8	30	30	NUM
ejpam-4694	166	9	)	)	PUNCT
ejpam-4694	166	10	with	with	ADP
ejpam-4694	166	11	a(n	a(n	NOUN
ejpam-4694	166	12	,	,	PUNCT
ejpam-4694	166	13	k	k	NOUN
ejpam-4694	166	14	)	)	PUNCT
ejpam-4694	166	15	,	,	PUNCT
ejpam-4694	166	16	the	the	DET
ejpam-4694	166	17	eulerian	eulerian	ADJ
ejpam-4694	166	18	number	number	NOUN
ejpam-4694	166	19	,	,	PUNCT
ejpam-4694	166	20	satisfying	satisfy	VERB
ejpam-4694	166	21	a(n	a(n	NOUN
ejpam-4694	166	22	,	,	PUNCT
ejpam-4694	166	23	k	k	NOUN
ejpam-4694	166	24	)	)	PUNCT
ejpam-4694	166	25	=	=	SYM
ejpam-4694	167	1	(	(	PUNCT
ejpam-4694	167	2	n−	n−	NOUN
ejpam-4694	167	3	k	k	NOUN
ejpam-4694	167	4	+	+	CCONJ
ejpam-4694	167	5	1)a(n−	1)a(n−	NUM
ejpam-4694	167	6	1	1	NUM
ejpam-4694	167	7	,	,	PUNCT
ejpam-4694	167	8	k	k	PROPN
ejpam-4694	167	9	−	−	PROPN
ejpam-4694	167	10	1	1	NUM
ejpam-4694	167	11	)	)	PUNCT
ejpam-4694	168	1	+	+	CCONJ
ejpam-4694	168	2	ka(n−	ka(n−	PROPN
ejpam-4694	168	3	1	1	NUM
ejpam-4694	168	4	,	,	PUNCT
ejpam-4694	168	5	k	k	NOUN
ejpam-4694	168	6	)	)	PUNCT
ejpam-4694	168	7	.	.	PUNCT
ejpam-4694	169	1	thus	thus	ADV
ejpam-4694	169	2	,	,	PUNCT
ejpam-4694	169	3	1	1	NUM
ejpam-4694	169	4	m+	m+	NUM
ejpam-4694	169	5	1	1	NUM
ejpam-4694	169	6	ĝ(k	ĝ(k	NOUN
ejpam-4694	169	7	)	)	PUNCT
ejpam-4694	169	8	m+1(x;λ	m+1(x;λ	PROPN
ejpam-4694	169	9	,	,	PUNCT
ejpam-4694	169	10	ρ	ρ	PROPN
ejpam-4694	169	11	,	,	PUNCT
ejpam-4694	169	12	u	u	NOUN
ejpam-4694	169	13	,	,	PUNCT
ejpam-4694	169	14	a	a	DET
ejpam-4694	169	15	,	,	PUNCT
ejpam-4694	169	16	b	b	NOUN
ejpam-4694	169	17	)	)	PUNCT
ejpam-4694	169	18	=	=	PUNCT
ejpam-4694	169	19	m∑	m∑	CCONJ
ejpam-4694	169	20	i=0	i=0	PROPN
ejpam-4694	169	21	m−i∑	m−i∑	X
ejpam-4694	169	22	j=0	j=0	PROPN
ejpam-4694	169	23	bm1,m2,	bm1,m2,	PROPN
ejpam-4694	169	24	...	...	PUNCT
ejpam-4694	169	25	,mk−1	,mk−1	PUNCT
ejpam-4694	169	26	(	(	PUNCT
ejpam-4694	169	27	i	i	NOUN
ejpam-4694	169	28	,	,	PUNCT
ejpam-4694	169	29	ρ−	ρ−	PROPN
ejpam-4694	169	30	1)am−i−j	1)am−i−j	NUM
ejpam-4694	169	31	(	(	PUNCT
ejpam-4694	169	32	u	u	NOUN
ejpam-4694	169	33	λ	λ	PROPN
ejpam-4694	169	34	)	)	PUNCT
ejpam-4694	169	35	(	(	PUNCT
ejpam-4694	169	36	m−	m−	PROPN
ejpam-4694	169	37	i	i	PRON
ejpam-4694	169	38	j	j	PROPN
ejpam-4694	169	39	)	)	PUNCT
ejpam-4694	169	40	(	(	PUNCT
ejpam-4694	169	41	m	m	VERB
ejpam-4694	169	42	i	i	NOUN
ejpam-4694	169	43	)	)	PUNCT
ejpam-4694	169	44	(	(	PUNCT
ejpam-4694	169	45	x)j	x)j	PROPN
ejpam-4694	169	46	,	,	PUNCT
ejpam-4694	169	47	ρ(−	ρ(−	PROPN
ejpam-4694	169	48	log	log	PROPN
ejpam-4694	169	49	ab)m−i−j	ab)m−i−j	PROPN
ejpam-4694	169	50	(	(	PUNCT
ejpam-4694	169	51	1−	1−	NUM
ejpam-4694	169	52	u	u	NOUN
ejpam-4694	169	53	λ	λ	NOUN
ejpam-4694	169	54	)	)	PUNCT
ejpam-4694	169	55	m−i−j+1	m−i−j+1	PROPN
ejpam-4694	169	56	.	.	PUNCT
ejpam-4694	170	1	to	to	PART
ejpam-4694	170	2	state	state	VERB
ejpam-4694	170	3	formally	formally	ADV
ejpam-4694	170	4	this	this	DET
ejpam-4694	170	5	result	result	NOUN
ejpam-4694	170	6	,	,	PUNCT
ejpam-4694	170	7	we	we	PRON
ejpam-4694	170	8	have	have	VERB
ejpam-4694	170	9	the	the	DET
ejpam-4694	170	10	following	follow	VERB
ejpam-4694	170	11	theorem	theorem	VERB
ejpam-4694	170	12	.	.	PUNCT
ejpam-4694	170	13	theorem	theorem	VERB
ejpam-4694	170	14	2.2	2.2	NUM
ejpam-4694	170	15	.	.	PUNCT
ejpam-4694	171	1	the	the	DET
ejpam-4694	171	2	degenerate	degenerate	ADJ
ejpam-4694	171	3	apostol	apostol	NOUN
ejpam-4694	171	4	-	-	PUNCT
ejpam-4694	171	5	frobenius	frobenius	NOUN
ejpam-4694	171	6	-	-	PUNCT
ejpam-4694	171	7	type	type	NOUN
ejpam-4694	171	8	poly	poly	ADJ
ejpam-4694	171	9	-	-	PUNCT
ejpam-4694	171	10	genocchi	genocchi	NOUN
ejpam-4694	171	11	polynomials	polynomial	NOUN
ejpam-4694	171	12	with	with	ADP
ejpam-4694	171	13	parameters	parameter	NOUN
ejpam-4694	171	14	a	a	PRON
ejpam-4694	171	15	and	and	CCONJ
ejpam-4694	171	16	b	b	NOUN
ejpam-4694	171	17	are	be	AUX
ejpam-4694	171	18	equal	equal	ADJ
ejpam-4694	171	19	to	to	ADP
ejpam-4694	171	20	1	1	NUM
ejpam-4694	171	21	m+	m+	NUM
ejpam-4694	171	22	1	1	NUM
ejpam-4694	171	23	ĝ(k	ĝ(k	NOUN
ejpam-4694	171	24	)	)	PUNCT
ejpam-4694	171	25	m+1(x;λ	m+1(x;λ	PROPN
ejpam-4694	171	26	,	,	PUNCT
ejpam-4694	171	27	ρ	ρ	PROPN
ejpam-4694	171	28	,	,	PUNCT
ejpam-4694	171	29	u	u	NOUN
ejpam-4694	171	30	,	,	PUNCT
ejpam-4694	171	31	a	a	DET
ejpam-4694	171	32	,	,	PUNCT
ejpam-4694	171	33	b	b	NOUN
ejpam-4694	171	34	)	)	PUNCT
ejpam-4694	171	35	=	=	PUNCT
ejpam-4694	171	36	m∑	m∑	CCONJ
ejpam-4694	171	37	i=0	i=0	PROPN
ejpam-4694	171	38	m−i∑	m−i∑	X
ejpam-4694	171	39	j=0	j=0	PROPN
ejpam-4694	171	40	bm1,m2,	bm1,m2,	PROPN
ejpam-4694	171	41	...	...	PUNCT
ejpam-4694	171	42	,mk−1	,mk−1	PUNCT
ejpam-4694	171	43	(	(	PUNCT
ejpam-4694	171	44	i	i	NOUN
ejpam-4694	171	45	,	,	PUNCT
ejpam-4694	171	46	ρ−	ρ−	PROPN
ejpam-4694	171	47	1)am−i−j	1)am−i−j	NUM
ejpam-4694	171	48	(	(	PUNCT
ejpam-4694	171	49	u	u	NOUN
ejpam-4694	171	50	λ	λ	PROPN
ejpam-4694	171	51	)	)	PUNCT
ejpam-4694	171	52	(	(	PUNCT
ejpam-4694	171	53	m−	m−	PROPN
ejpam-4694	171	54	i	i	PRON
ejpam-4694	171	55	j	j	PROPN
ejpam-4694	171	56	)	)	PUNCT
ejpam-4694	171	57	(	(	PUNCT
ejpam-4694	171	58	m	m	VERB
ejpam-4694	171	59	i	i	NOUN
ejpam-4694	171	60	)	)	PUNCT
ejpam-4694	171	61	(	(	PUNCT
ejpam-4694	171	62	x)j	x)j	PROPN
ejpam-4694	171	63	,	,	PUNCT
ejpam-4694	171	64	ρ(−	ρ(−	PROPN
ejpam-4694	171	65	log	log	PROPN
ejpam-4694	171	66	ab)m−i−j	ab)m−i−j	PROPN
ejpam-4694	171	67	(	(	PUNCT
ejpam-4694	171	68	1−	1−	NUM
ejpam-4694	171	69	u	u	NOUN
ejpam-4694	171	70	λ	λ	NOUN
ejpam-4694	171	71	)	)	PUNCT
ejpam-4694	171	72	m−i−j+1	m−i−j+1	NOUN
ejpam-4694	171	73	,	,	PUNCT
ejpam-4694	171	74	where	where	SCONJ
ejpam-4694	171	75	ĝ(k	ĝ(k	X
ejpam-4694	171	76	,	,	PUNCT
ejpam-4694	171	77	α	α	NOUN
ejpam-4694	171	78	)	)	PUNCT
ejpam-4694	171	79	0	0	NUM
ejpam-4694	172	1	(	(	PUNCT
ejpam-4694	172	2	x;λ	x;λ	PROPN
ejpam-4694	172	3	,	,	PUNCT
ejpam-4694	172	4	ρ	ρ	PROPN
ejpam-4694	172	5	,	,	PUNCT
ejpam-4694	172	6	u	u	NOUN
ejpam-4694	172	7	,	,	PUNCT
ejpam-4694	172	8	a	a	DET
ejpam-4694	172	9	,	,	PUNCT
ejpam-4694	172	10	b	b	NOUN
ejpam-4694	172	11	)	)	PUNCT
ejpam-4694	172	12	=	=	SYM
ejpam-4694	172	13	0	0	NUM
ejpam-4694	172	14	,	,	PUNCT
ejpam-4694	172	15	an(u	an(u	ADJ
ejpam-4694	172	16	)	)	PUNCT
ejpam-4694	172	17	is	be	AUX
ejpam-4694	172	18	the	the	DET
ejpam-4694	172	19	eulerian	eulerian	ADJ
ejpam-4694	172	20	polynomial	polynomial	ADJ
ejpam-4694	172	21	and	and	CCONJ
ejpam-4694	172	22	bm1,m2,	bm1,m2,	ADJ
ejpam-4694	172	23	...	...	PUNCT
ejpam-4694	172	24	,mk−1	,mk−1	PUNCT
ejpam-4694	172	25	(	(	PUNCT
ejpam-4694	172	26	i	i	NOUN
ejpam-4694	172	27	,	,	PUNCT
ejpam-4694	172	28	ρ−	ρ−	NOUN
ejpam-4694	172	29	1	1	NUM
ejpam-4694	172	30	)	)	PUNCT
ejpam-4694	172	31	satisfies	satisfie	NOUN
ejpam-4694	172	32	(	(	PUNCT
ejpam-4694	172	33	29	29	NUM
ejpam-4694	172	34	)	)	PUNCT
ejpam-4694	172	35	.	.	PUNCT
ejpam-4694	173	1	now	now	ADV
ejpam-4694	173	2	,	,	PUNCT
ejpam-4694	173	3	let	let	VERB
ejpam-4694	173	4	us	we	PRON
ejpam-4694	173	5	extend	extend	VERB
ejpam-4694	173	6	the	the	DET
ejpam-4694	173	7	explicit	explicit	ADJ
ejpam-4694	173	8	formula	formula	NOUN
ejpam-4694	173	9	to	to	ADP
ejpam-4694	173	10	higher	high	ADJ
ejpam-4694	173	11	order	order	NOUN
ejpam-4694	173	12	degenerate	degenerate	ADJ
ejpam-4694	173	13	apostol	apostol	NOUN
ejpam-4694	173	14	-	-	PUNCT
ejpam-4694	173	15	frobeniustype	frobeniustype	NOUN
ejpam-4694	173	16	poly	poly	ADJ
ejpam-4694	173	17	-	-	PUNCT
ejpam-4694	173	18	genocchi	genocchi	NOUN
ejpam-4694	173	19	polynomials	polynomial	NOUN
ejpam-4694	173	20	with	with	ADP
ejpam-4694	173	21	parameters	parameter	NOUN
ejpam-4694	173	22	a	a	PRON
ejpam-4694	173	23	and	and	CCONJ
ejpam-4694	173	24	b.	b.	PROPN
ejpam-4694	173	25	first	first	ADV
ejpam-4694	173	26	,	,	PUNCT
ejpam-4694	173	27	we	we	PRON
ejpam-4694	173	28	have	have	VERB
ejpam-4694	173	29	to	to	PART
ejpam-4694	173	30	find	find	VERB
ejpam-4694	173	31	the	the	DET
ejpam-4694	173	32	expansion	expansion	NOUN
ejpam-4694	173	33	of	of	ADP
ejpam-4694	173	34	the	the	DET
ejpam-4694	173	35	following	follow	VERB
ejpam-4694	173	36	function	function	NOUN
ejpam-4694	173	37	:	:	PUNCT
ejpam-4694	173	38	eik	eik	PROPN
ejpam-4694	173	39	,	,	PUNCT
ejpam-4694	173	40	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	173	41	+	+	CCONJ
ejpam-4694	173	42	(	(	PUNCT
ejpam-4694	173	43	1−	1−	NUM
ejpam-4694	173	44	u)t	u)t	X
ejpam-4694	173	45	ln	ln	PROPN
ejpam-4694	173	46	ab	ab	PROPN
ejpam-4694	173	47	)	)	PUNCT
ejpam-4694	173	48	)	)	PUNCT
ejpam-4694	174	1	λbt	λbt	VERB
ejpam-4694	174	2	−	−	PROPN
ejpam-4694	174	3	ua−t	ua−t	NOUN
ejpam-4694	174	4	=	=	PUNCT
ejpam-4694	174	5	t	t	PROPN
ejpam-4694	174	6	∞∑	∞∑	PROPN
ejpam-4694	174	7	m=0	m=0	PROPN
ejpam-4694	174	8			PUNCT
ejpam-4694	174	9	m∑	m∑	CCONJ
ejpam-4694	174	10	j=0	j=0	VERB
ejpam-4694	174	11	∞∑	∞∑	PRON
ejpam-4694	174	12	n=0	n=0	NUM
ejpam-4694	174	13	1	1	NUM
ejpam-4694	174	14	m	m	NOUN
ejpam-4694	174	15	!	!	PUNCT
ejpam-4694	175	1	(	(	PUNCT
ejpam-4694	175	2	m	m	PROPN
ejpam-4694	175	3	j	j	NOUN
ejpam-4694	175	4	)	)	PUNCT
ejpam-4694	175	5	bm1,m2,	bm1,m2,	PROPN
ejpam-4694	175	6	...	...	PUNCT
ejpam-4694	175	7	,mk−1	,mk−1	PUNCT
ejpam-4694	175	8	(	(	PUNCT
ejpam-4694	175	9	j	j	NOUN
ejpam-4694	175	10	,	,	PUNCT
ejpam-4694	175	11	ρ−	ρ−	NOUN
ejpam-4694	175	12	1	1	NUM
ejpam-4694	175	13	)	)	PUNCT
ejpam-4694	175	14	(	(	PUNCT
ejpam-4694	175	15	u	u	NOUN
ejpam-4694	175	16	λ	λ	PROPN
ejpam-4694	175	17	)	)	PUNCT
ejpam-4694	175	18	n	n	CCONJ
ejpam-4694	175	19	(	(	PUNCT
ejpam-4694	175	20	−n	−n	ADV
ejpam-4694	175	21	log	log	NOUN
ejpam-4694	175	22	ab)m−j	ab)m−j	ADV
ejpam-4694	175	23			PROPN
ejpam-4694	175	24	tm	tm	PROPN
ejpam-4694	175	25	.	.	PROPN
ejpam-4694	175	26	r.	r.	PROPN
ejpam-4694	175	27	corcino	corcino	PROPN
ejpam-4694	175	28	,	,	PUNCT
ejpam-4694	175	29	c.	c.	PROPN
ejpam-4694	175	30	corcino	corcino	PROPN
ejpam-4694	175	31	/	/	SYM
ejpam-4694	175	32	eur	eur	PROPN
ejpam-4694	175	33	.	.	PUNCT
ejpam-4694	176	1	j.	j.	PROPN
ejpam-4694	176	2	pure	pure	PROPN
ejpam-4694	176	3	appl	appl	PROPN
ejpam-4694	176	4	.	.	PROPN
ejpam-4694	176	5	math	math	PROPN
ejpam-4694	176	6	,	,	PUNCT
ejpam-4694	176	7	16	16	NUM
ejpam-4694	176	8	(	(	PUNCT
ejpam-4694	176	9	2	2	NUM
ejpam-4694	176	10	)	)	PUNCT
ejpam-4694	176	11	(	(	PUNCT
ejpam-4694	176	12	2023	2023	NUM
ejpam-4694	176	13	)	)	PUNCT
ejpam-4694	176	14	,	,	PUNCT
ejpam-4694	176	15	687	687	NUM
ejpam-4694	176	16	-	-	SYM
ejpam-4694	176	17	712	712	NUM
ejpam-4694	176	18	695	695	NUM
ejpam-4694	176	19	raising	raise	VERB
ejpam-4694	176	20	this	this	PRON
ejpam-4694	176	21	to	to	ADP
ejpam-4694	176	22	power	power	NOUN
ejpam-4694	176	23	α	α	PROPN
ejpam-4694	176	24	gives	give	VERB
ejpam-4694	176	25	(	(	PUNCT
ejpam-4694	176	26	eik	eik	PROPN
ejpam-4694	176	27	,	,	PUNCT
ejpam-4694	176	28	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	176	29	+	+	CCONJ
ejpam-4694	176	30	(	(	PUNCT
ejpam-4694	176	31	1−	1−	NUM
ejpam-4694	176	32	u)t	u)t	X
ejpam-4694	176	33	ln	ln	PROPN
ejpam-4694	176	34	ab	ab	PROPN
ejpam-4694	176	35	)	)	PUNCT
ejpam-4694	176	36	)	)	PUNCT
ejpam-4694	177	1	λbt	λbt	VERB
ejpam-4694	177	2	−	−	PROPN
ejpam-4694	177	3	ua−t	ua−t	ADJ
ejpam-4694	177	4	)	)	PUNCT
ejpam-4694	177	5	α	α	X
ejpam-4694	177	6	=	=	PUNCT
ejpam-4694	177	7	tα	tα	PROPN
ejpam-4694	177	8	∞∑	∞∑	PROPN
ejpam-4694	177	9	m=0	m=0	PROPN
ejpam-4694	177	10	∑	∑	PUNCT
ejpam-4694	177	11	k1+k2+	k1+k2+	PROPN
ejpam-4694	177	12	...	...	PUNCT
ejpam-4694	177	13	+kα	+kα	X
ejpam-4694	177	14	=	=	NOUN
ejpam-4694	177	15	m	m	PROPN
ejpam-4694	177	16	α∏	α∏	ADJ
ejpam-4694	177	17	i=1	i=1	PROPN
ejpam-4694	177	18			PUNCT
ejpam-4694	177	19	ki∑	ki∑	PROPN
ejpam-4694	177	20	j=0	j=0	VERB
ejpam-4694	177	21	∞∑	∞∑	PRON
ejpam-4694	177	22	n=0	n=0	NUM
ejpam-4694	177	23	1	1	NUM
ejpam-4694	177	24	ki	ki	INTJ
ejpam-4694	177	25	!	!	PUNCT
ejpam-4694	178	1	(	(	PUNCT
ejpam-4694	178	2	ki	ki	PROPN
ejpam-4694	178	3	j	j	PROPN
ejpam-4694	178	4	)	)	PUNCT
ejpam-4694	179	1	bm1,m2,	bm1,m2,	PROPN
ejpam-4694	179	2	...	...	PUNCT
ejpam-4694	179	3	,mk−1	,mk−1	PUNCT
ejpam-4694	179	4	(	(	PUNCT
ejpam-4694	179	5	j	j	NOUN
ejpam-4694	179	6	,	,	PUNCT
ejpam-4694	179	7	ρ−	ρ−	NOUN
ejpam-4694	179	8	1	1	NUM
ejpam-4694	179	9	)	)	PUNCT
ejpam-4694	179	10	(	(	PUNCT
ejpam-4694	179	11	u	u	NOUN
ejpam-4694	179	12	λ	λ	PROPN
ejpam-4694	179	13	)	)	PUNCT
ejpam-4694	179	14	n	n	CCONJ
ejpam-4694	179	15	(	(	PUNCT
ejpam-4694	179	16	−n	−n	INTJ
ejpam-4694	179	17	log	log	NOUN
ejpam-4694	179	18	ab)ki−j	ab)ki−j	PROPN
ejpam-4694	179	19			PROPN
ejpam-4694	179	20	tm	tm	PROPN
ejpam-4694	179	21	.	.	PROPN
ejpam-4694	180	1	hence	hence	ADV
ejpam-4694	180	2	,	,	PUNCT
ejpam-4694	180	3	∞∑	∞∑	PROPN
ejpam-4694	180	4	m=0	m=0	PROPN
ejpam-4694	180	5	ĝ(k	ĝ(k	PROPN
ejpam-4694	180	6	,	,	PUNCT
ejpam-4694	180	7	α	α	NOUN
ejpam-4694	180	8	)	)	PUNCT
ejpam-4694	180	9	m	m	VERB
ejpam-4694	180	10	(	(	PUNCT
ejpam-4694	180	11	x;λ	x;λ	PROPN
ejpam-4694	180	12	,	,	PUNCT
ejpam-4694	180	13	ρ	ρ	PROPN
ejpam-4694	180	14	,	,	PUNCT
ejpam-4694	180	15	u	u	NOUN
ejpam-4694	180	16	,	,	PUNCT
ejpam-4694	180	17	a	a	DET
ejpam-4694	180	18	,	,	PUNCT
ejpam-4694	180	19	b	b	NOUN
ejpam-4694	180	20	)	)	PUNCT
ejpam-4694	180	21	tm	tm	PROPN
ejpam-4694	180	22	m	m	PROPN
ejpam-4694	180	23	!	!	PUNCT
ejpam-4694	181	1	=	=	PRON
ejpam-4694	181	2	(	(	PUNCT
ejpam-4694	181	3	eik	eik	PROPN
ejpam-4694	181	4	,	,	PUNCT
ejpam-4694	181	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	181	6	+	+	CCONJ
ejpam-4694	181	7	(	(	PUNCT
ejpam-4694	181	8	1−	1−	NUM
ejpam-4694	181	9	u)t	u)t	X
ejpam-4694	181	10	ln	ln	PROPN
ejpam-4694	181	11	ab	ab	PROPN
ejpam-4694	181	12	)	)	PUNCT
ejpam-4694	181	13	)	)	PUNCT
ejpam-4694	182	1	λbt	λbt	VERB
ejpam-4694	182	2	−	−	PROPN
ejpam-4694	182	3	ua−t	ua−t	ADJ
ejpam-4694	182	4	)	)	PUNCT
ejpam-4694	182	5	α	α	PROPN
ejpam-4694	182	6	exρ(t	exρ(t	NOUN
ejpam-4694	182	7	)	)	PUNCT
ejpam-4694	182	8	=	=	SYM
ejpam-4694	183	1	tα	tα	PROPN
ejpam-4694	183	2	∞∑	∞∑	NUM
ejpam-4694	183	3	m=0	m=0	PROPN
ejpam-4694	183	4	m∑	m∑	VERB
ejpam-4694	183	5	q=0	q=0	PROPN
ejpam-4694	184	1	(	(	PUNCT
ejpam-4694	184	2	m	m	NOUN
ejpam-4694	184	3	q	q	NOUN
ejpam-4694	184	4	)	)	PUNCT
ejpam-4694	184	5	(	(	PUNCT
ejpam-4694	184	6	x)q	x)q	PROPN
ejpam-4694	184	7	,	,	PUNCT
ejpam-4694	184	8	ρ(m−	ρ(m−	PROPN
ejpam-4694	184	9	q	q	NOUN
ejpam-4694	184	10	)	)	PUNCT
ejpam-4694	184	11	!	!	PUNCT
ejpam-4694	185	1	×	×	NOUN
ejpam-4694	185	2	∑	∑	PUNCT
ejpam-4694	185	3	k1+k2+	k1+k2+	NOUN
ejpam-4694	185	4	...	...	PUNCT
ejpam-4694	186	1	+kα	+kα	PRON
ejpam-4694	186	2	=	=	NOUN
ejpam-4694	186	3	m−q	m−q	PROPN
ejpam-4694	186	4	α∏	α∏	PROPN
ejpam-4694	186	5	i=1	i=1	PROPN
ejpam-4694	186	6			PUNCT
ejpam-4694	186	7	ki∑	ki∑	PROPN
ejpam-4694	186	8	j=0	j=0	VERB
ejpam-4694	186	9	∞∑	∞∑	PRON
ejpam-4694	186	10	n=0	n=0	NUM
ejpam-4694	186	11	1	1	NUM
ejpam-4694	186	12	ki	ki	INTJ
ejpam-4694	186	13	!	!	PUNCT
ejpam-4694	187	1	(	(	PUNCT
ejpam-4694	187	2	ki	ki	PROPN
ejpam-4694	187	3	j	j	PROPN
ejpam-4694	187	4	)	)	PUNCT
ejpam-4694	188	1	bm1,m2,	bm1,m2,	PROPN
ejpam-4694	188	2	...	...	PUNCT
ejpam-4694	188	3	,mk−1	,mk−1	PUNCT
ejpam-4694	188	4	(	(	PUNCT
ejpam-4694	188	5	j	j	NOUN
ejpam-4694	188	6	,	,	PUNCT
ejpam-4694	188	7	ρ−	ρ−	NOUN
ejpam-4694	188	8	1	1	NUM
ejpam-4694	188	9	)	)	PUNCT
ejpam-4694	188	10	(	(	PUNCT
ejpam-4694	188	11	u	u	NOUN
ejpam-4694	188	12	λ	λ	PROPN
ejpam-4694	188	13	)	)	PUNCT
ejpam-4694	188	14	n	n	CCONJ
ejpam-4694	188	15	(	(	PUNCT
ejpam-4694	188	16	−n	−n	INTJ
ejpam-4694	188	17	log	log	NOUN
ejpam-4694	188	18	ab)ki−j	ab)ki−j	PROPN
ejpam-4694	188	19			PROPN
ejpam-4694	188	20	tm	tm	NOUN
ejpam-4694	188	21	m	m	PROPN
ejpam-4694	188	22	!	!	PUNCT
ejpam-4694	188	23	.	.	PUNCT
ejpam-4694	189	1	note	note	VERB
ejpam-4694	189	2	that	that	SCONJ
ejpam-4694	189	3	,	,	PUNCT
ejpam-4694	189	4	when	when	SCONJ
ejpam-4694	189	5	0	0	NUM
ejpam-4694	189	6	≤	≤	NUM
ejpam-4694	189	7	m	m	VERB
ejpam-4694	189	8	≤	≤	NOUN
ejpam-4694	189	9	α	α	PRON
ejpam-4694	189	10	−	−	NOUN
ejpam-4694	189	11	1	1	NUM
ejpam-4694	189	12	,	,	PUNCT
ejpam-4694	189	13	ĝ(k	ĝ(k	PRON
ejpam-4694	189	14	,	,	PUNCT
ejpam-4694	189	15	α	α	NOUN
ejpam-4694	189	16	)	)	PUNCT
ejpam-4694	189	17	m	m	VERB
ejpam-4694	189	18	(	(	PUNCT
ejpam-4694	189	19	x;λ	x;λ	PROPN
ejpam-4694	189	20	,	,	PUNCT
ejpam-4694	189	21	ρ	ρ	PROPN
ejpam-4694	189	22	,	,	PUNCT
ejpam-4694	189	23	u	u	NOUN
ejpam-4694	189	24	,	,	PUNCT
ejpam-4694	189	25	a	a	DET
ejpam-4694	189	26	,	,	PUNCT
ejpam-4694	189	27	b	b	NOUN
ejpam-4694	189	28	)	)	PUNCT
ejpam-4694	189	29	=	=	SYM
ejpam-4694	190	1	0	0	X
ejpam-4694	190	2	.	.	PUNCT
ejpam-4694	191	1	now	now	ADV
ejpam-4694	191	2	,	,	PUNCT
ejpam-4694	191	3	we	we	PRON
ejpam-4694	191	4	can	can	AUX
ejpam-4694	191	5	further	far	ADV
ejpam-4694	191	6	rewrite	rewrite	VERB
ejpam-4694	191	7	the	the	DET
ejpam-4694	191	8	preceding	precede	VERB
ejpam-4694	191	9	equation	equation	NOUN
ejpam-4694	191	10	as	as	SCONJ
ejpam-4694	191	11	follows	follow	VERB
ejpam-4694	191	12	:	:	PUNCT
ejpam-4694	191	13	∞∑	∞∑	NUM
ejpam-4694	191	14	m=−α	m=−α	NOUN
ejpam-4694	191	15	ĝ(k	ĝ(k	X
ejpam-4694	191	16	,	,	PUNCT
ejpam-4694	191	17	α	α	NOUN
ejpam-4694	191	18	)	)	PUNCT
ejpam-4694	191	19	m+α(x;λ	m+α(x;λ	PROPN
ejpam-4694	191	20	,	,	PUNCT
ejpam-4694	191	21	ρ	ρ	PROPN
ejpam-4694	191	22	,	,	PUNCT
ejpam-4694	191	23	u	u	NOUN
ejpam-4694	191	24	,	,	PUNCT
ejpam-4694	191	25	a	a	DET
ejpam-4694	191	26	,	,	PUNCT
ejpam-4694	191	27	b	b	NOUN
ejpam-4694	191	28	)	)	PUNCT
ejpam-4694	191	29	tm	tm	NOUN
ejpam-4694	191	30	(	(	PUNCT
ejpam-4694	191	31	m+	m+	NOUN
ejpam-4694	191	32	α	α	NOUN
ejpam-4694	191	33	)	)	PUNCT
ejpam-4694	191	34	!	!	PUNCT
ejpam-4694	192	1	=	=	PRON
ejpam-4694	192	2	(	(	PUNCT
ejpam-4694	192	3	eik	eik	PROPN
ejpam-4694	192	4	,	,	PUNCT
ejpam-4694	192	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	192	6	+	+	CCONJ
ejpam-4694	192	7	(	(	PUNCT
ejpam-4694	192	8	1−	1−	NUM
ejpam-4694	192	9	u)t	u)t	X
ejpam-4694	192	10	ln	ln	PROPN
ejpam-4694	192	11	ab	ab	PROPN
ejpam-4694	192	12	)	)	PUNCT
ejpam-4694	192	13	)	)	PUNCT
ejpam-4694	193	1	λbt	λbt	VERB
ejpam-4694	193	2	−	−	PROPN
ejpam-4694	193	3	ua−t	ua−t	ADJ
ejpam-4694	193	4	)	)	PUNCT
ejpam-4694	193	5	α	α	PROPN
ejpam-4694	193	6	exρ(t	exρ(t	NOUN
ejpam-4694	193	7	)	)	PUNCT
ejpam-4694	193	8	=	=	PUNCT
ejpam-4694	194	1	∞∑	∞∑	NUM
ejpam-4694	194	2	m=0	m=0	PROPN
ejpam-4694	194	3	m∑	m∑	VERB
ejpam-4694	194	4	q=0	q=0	PROPN
ejpam-4694	194	5	(	(	PUNCT
ejpam-4694	194	6	m	m	NOUN
ejpam-4694	194	7	q	q	NOUN
ejpam-4694	194	8	)	)	PUNCT
ejpam-4694	194	9	(	(	PUNCT
ejpam-4694	194	10	x)q	x)q	PROPN
ejpam-4694	194	11	,	,	PUNCT
ejpam-4694	194	12	ρ(m−	ρ(m−	PROPN
ejpam-4694	194	13	q	q	NOUN
ejpam-4694	194	14	)	)	PUNCT
ejpam-4694	194	15	!	!	PUNCT
ejpam-4694	195	1	×	×	NOUN
ejpam-4694	195	2	∑	∑	PUNCT
ejpam-4694	195	3	k1+k2+	k1+k2+	NOUN
ejpam-4694	195	4	...	...	PUNCT
ejpam-4694	196	1	+kα	+kα	PRON
ejpam-4694	196	2	=	=	NOUN
ejpam-4694	196	3	m−q	m−q	PROPN
ejpam-4694	196	4	α∏	α∏	PROPN
ejpam-4694	196	5	i=1	i=1	PROPN
ejpam-4694	196	6			PUNCT
ejpam-4694	196	7	ki∑	ki∑	PROPN
ejpam-4694	196	8	j=0	j=0	VERB
ejpam-4694	196	9	∞∑	∞∑	PRON
ejpam-4694	196	10	n=0	n=0	NUM
ejpam-4694	196	11	1	1	NUM
ejpam-4694	196	12	ki	ki	INTJ
ejpam-4694	196	13	!	!	PUNCT
ejpam-4694	197	1	(	(	PUNCT
ejpam-4694	197	2	ki	ki	PROPN
ejpam-4694	197	3	j	j	PROPN
ejpam-4694	197	4	)	)	PUNCT
ejpam-4694	198	1	bm1,m2,	bm1,m2,	PROPN
ejpam-4694	198	2	...	...	PUNCT
ejpam-4694	198	3	,mk−1	,mk−1	PUNCT
ejpam-4694	198	4	(	(	PUNCT
ejpam-4694	198	5	j	j	NOUN
ejpam-4694	198	6	,	,	PUNCT
ejpam-4694	198	7	ρ−	ρ−	NOUN
ejpam-4694	198	8	1	1	NUM
ejpam-4694	198	9	)	)	PUNCT
ejpam-4694	198	10	(	(	PUNCT
ejpam-4694	198	11	u	u	NOUN
ejpam-4694	198	12	λ	λ	PROPN
ejpam-4694	198	13	)	)	PUNCT
ejpam-4694	198	14	n	n	CCONJ
ejpam-4694	198	15	(	(	PUNCT
ejpam-4694	198	16	−n	−n	INTJ
ejpam-4694	198	17	log	log	NOUN
ejpam-4694	198	18	ab)ki−j	ab)ki−j	PROPN
ejpam-4694	198	19			PROPN
ejpam-4694	198	20	tm	tm	NOUN
ejpam-4694	198	21	m	m	PROPN
ejpam-4694	198	22	!	!	PUNCT
ejpam-4694	198	23	.	.	PUNCT
ejpam-4694	199	1	comparing	compare	VERB
ejpam-4694	199	2	the	the	DET
ejpam-4694	199	3	coefficients	coefficient	NOUN
ejpam-4694	199	4	of	of	ADP
ejpam-4694	199	5	tm	tm	PROPN
ejpam-4694	199	6	m	m	PROPN
ejpam-4694	199	7	!	!	PUNCT
ejpam-4694	200	1	and	and	CCONJ
ejpam-4694	200	2	using	use	VERB
ejpam-4694	200	3	the	the	DET
ejpam-4694	200	4	arithmetic	arithmetic	ADJ
ejpam-4694	200	5	-	-	PUNCT
ejpam-4694	200	6	geometric	geometric	ADJ
ejpam-4694	200	7	formula	formula	NOUN
ejpam-4694	200	8	yield	yield	VERB
ejpam-4694	200	9	the	the	DET
ejpam-4694	200	10	following	follow	VERB
ejpam-4694	200	11	explicit	explicit	ADJ
ejpam-4694	200	12	formula	formula	NOUN
ejpam-4694	200	13	.	.	PUNCT
ejpam-4694	201	1	theorem	theorem	VERB
ejpam-4694	201	2	2.3	2.3	NUM
ejpam-4694	201	3	.	.	PUNCT
ejpam-4694	202	1	the	the	DET
ejpam-4694	202	2	degenerate	degenerate	ADJ
ejpam-4694	202	3	apostol	apostol	NOUN
ejpam-4694	202	4	-	-	PUNCT
ejpam-4694	202	5	frobenius	frobenius	NOUN
ejpam-4694	202	6	-	-	PUNCT
ejpam-4694	202	7	type	type	NOUN
ejpam-4694	202	8	poly	poly	ADJ
ejpam-4694	202	9	-	-	PUNCT
ejpam-4694	202	10	genocchi	genocchi	NOUN
ejpam-4694	202	11	polynomials	polynomial	NOUN
ejpam-4694	202	12	of	of	ADP
ejpam-4694	202	13	higher	high	ADJ
ejpam-4694	202	14	order	order	NOUN
ejpam-4694	202	15	with	with	ADP
ejpam-4694	202	16	parameters	parameter	NOUN
ejpam-4694	202	17	a	a	PRON
ejpam-4694	202	18	and	and	CCONJ
ejpam-4694	202	19	b	b	NOUN
ejpam-4694	202	20	are	be	AUX
ejpam-4694	202	21	equal	equal	ADJ
ejpam-4694	202	22	to	to	ADP
ejpam-4694	202	23	1	1	NUM
ejpam-4694	202	24	(	(	PUNCT
ejpam-4694	202	25	m+	m+	NOUN
ejpam-4694	202	26	α)α	α)α	VERB
ejpam-4694	202	27	ĝ(k	ĝ(k	PRON
ejpam-4694	202	28	,	,	PUNCT
ejpam-4694	202	29	α	α	NOUN
ejpam-4694	202	30	)	)	PUNCT
ejpam-4694	202	31	m+α(x;λ	m+α(x;λ	PROPN
ejpam-4694	202	32	,	,	PUNCT
ejpam-4694	202	33	ρ	ρ	PROPN
ejpam-4694	202	34	,	,	PUNCT
ejpam-4694	202	35	u	u	NOUN
ejpam-4694	202	36	,	,	PUNCT
ejpam-4694	202	37	a	a	DET
ejpam-4694	202	38	,	,	PUNCT
ejpam-4694	202	39	b	b	NOUN
ejpam-4694	202	40	)	)	PUNCT
ejpam-4694	202	41	=	=	PUNCT
ejpam-4694	203	1	m∑	m∑	INTJ
ejpam-4694	203	2	q=0	q=0	NOUN
ejpam-4694	204	1	(	(	PUNCT
ejpam-4694	204	2	m	m	NOUN
ejpam-4694	204	3	q	q	NOUN
ejpam-4694	204	4	)	)	PUNCT
ejpam-4694	204	5	(	(	PUNCT
ejpam-4694	204	6	x)q	x)q	PROPN
ejpam-4694	204	7	,	,	PUNCT
ejpam-4694	204	8	ρ(m−	ρ(m−	PROPN
ejpam-4694	204	9	q	q	NOUN
ejpam-4694	204	10	)	)	PUNCT
ejpam-4694	204	11	!	!	PUNCT
ejpam-4694	205	1	∑	∑	PUNCT
ejpam-4694	205	2	k1+k2+	k1+k2+	PROPN
ejpam-4694	205	3	...	...	PUNCT
ejpam-4694	205	4	+kα	+kα	PRON
ejpam-4694	205	5	=	=	NOUN
ejpam-4694	205	6	m−q	m−q	NOUN
ejpam-4694	205	7	α∏	α∏	PROPN
ejpam-4694	205	8	i=1	i=1	PROPN
ejpam-4694	206	1	ki∑	ki∑	PROPN
ejpam-4694	206	2	j=0	j=0	PROPN
ejpam-4694	206	3	1	1	NUM
ejpam-4694	206	4	ki	ki	PROPN
ejpam-4694	206	5	!	!	PUNCT
ejpam-4694	207	1	(	(	PUNCT
ejpam-4694	207	2	ki	ki	PROPN
ejpam-4694	207	3	j	j	PROPN
ejpam-4694	207	4	)	)	PUNCT
ejpam-4694	207	5	×	×	PROPN
ejpam-4694	207	6	bm1,m2,	bm1,m2,	NOUN
ejpam-4694	207	7	...	...	PUNCT
ejpam-4694	207	8	,mk−1	,mk−1	PUNCT
ejpam-4694	207	9	(	(	PUNCT
ejpam-4694	207	10	j	j	NOUN
ejpam-4694	207	11	,	,	PUNCT
ejpam-4694	207	12	ρ−	ρ−	PROPN
ejpam-4694	207	13	1)aki−j	1)aki−j	NUM
ejpam-4694	207	14	(	(	PUNCT
ejpam-4694	207	15	u	u	NOUN
ejpam-4694	207	16	λ	λ	PROPN
ejpam-4694	207	17	)	)	PUNCT
ejpam-4694	207	18	(	(	PUNCT
ejpam-4694	207	19	−	−	NOUN
ejpam-4694	207	20	log	log	NOUN
ejpam-4694	207	21	ab)ki−j	ab)ki−j	PROPN
ejpam-4694	207	22	(	(	PUNCT
ejpam-4694	207	23	1−	1−	NUM
ejpam-4694	207	24	u	u	NOUN
ejpam-4694	207	25	λ	λ	PROPN
ejpam-4694	207	26	)	)	PUNCT
ejpam-4694	207	27	ki−j+1	ki−j+1	PROPN
ejpam-4694	207	28	.	.	PUNCT
ejpam-4694	208	1	where	where	SCONJ
ejpam-4694	208	2	ĝ(k	ĝ(k	X
ejpam-4694	208	3	,	,	PUNCT
ejpam-4694	208	4	α	α	NOUN
ejpam-4694	208	5	)	)	PUNCT
ejpam-4694	208	6	m	m	VERB
ejpam-4694	208	7	(	(	PUNCT
ejpam-4694	208	8	x;λ	x;λ	PROPN
ejpam-4694	208	9	,	,	PUNCT
ejpam-4694	208	10	ρ	ρ	PROPN
ejpam-4694	208	11	,	,	PUNCT
ejpam-4694	208	12	u	u	NOUN
ejpam-4694	208	13	,	,	PUNCT
ejpam-4694	208	14	a	a	DET
ejpam-4694	208	15	,	,	PUNCT
ejpam-4694	208	16	b	b	NOUN
ejpam-4694	208	17	)	)	PUNCT
ejpam-4694	208	18	=	=	SYM
ejpam-4694	208	19	0	0	NUM
ejpam-4694	208	20	for	for	ADP
ejpam-4694	208	21	m	m	PROPN
ejpam-4694	208	22	=	=	SYM
ejpam-4694	208	23	0	0	NUM
ejpam-4694	208	24	,	,	PUNCT
ejpam-4694	208	25	1	1	NUM
ejpam-4694	208	26	,	,	PUNCT
ejpam-4694	208	27	.	.	PUNCT
ejpam-4694	208	28	.	.	PUNCT
ejpam-4694	209	1	.	.	PUNCT
ejpam-4694	210	1	,	,	PUNCT
ejpam-4694	211	1	α	α	PRON
ejpam-4694	211	2	−	−	PROPN
ejpam-4694	211	3	1	1	NUM
ejpam-4694	211	4	,	,	PUNCT
ejpam-4694	211	5	an(u	an(u	ADJ
ejpam-4694	211	6	)	)	PUNCT
ejpam-4694	211	7	is	be	AUX
ejpam-4694	211	8	the	the	DET
ejpam-4694	211	9	eulerian	eulerian	ADJ
ejpam-4694	211	10	polynomial	polynomial	NOUN
ejpam-4694	211	11	defined	define	VERB
ejpam-4694	211	12	in	in	ADP
ejpam-4694	211	13	(	(	PUNCT
ejpam-4694	211	14	30	30	NUM
ejpam-4694	211	15	)	)	PUNCT
ejpam-4694	211	16	and	and	CCONJ
ejpam-4694	211	17	bm1,m2,	bm1,m2,	ADJ
ejpam-4694	211	18	...	...	PUNCT
ejpam-4694	211	19	,mk−1	,mk−1	PUNCT
ejpam-4694	211	20	(	(	PUNCT
ejpam-4694	211	21	i	i	NOUN
ejpam-4694	211	22	,	,	PUNCT
ejpam-4694	211	23	ρ−	ρ−	NOUN
ejpam-4694	211	24	1	1	NUM
ejpam-4694	211	25	)	)	PUNCT
ejpam-4694	211	26	satisfies	satisfie	NOUN
ejpam-4694	211	27	(	(	PUNCT
ejpam-4694	211	28	29	29	NUM
ejpam-4694	211	29	)	)	PUNCT
ejpam-4694	211	30	.	.	PUNCT
ejpam-4694	212	1	r.	r.	PROPN
ejpam-4694	212	2	corcino	corcino	PROPN
ejpam-4694	212	3	,	,	PUNCT
ejpam-4694	212	4	c.	c.	PROPN
ejpam-4694	212	5	corcino	corcino	PROPN
ejpam-4694	212	6	/	/	SYM
ejpam-4694	212	7	eur	eur	PROPN
ejpam-4694	212	8	.	.	PUNCT
ejpam-4694	213	1	j.	j.	PROPN
ejpam-4694	213	2	pure	pure	PROPN
ejpam-4694	213	3	appl	appl	PROPN
ejpam-4694	213	4	.	.	PROPN
ejpam-4694	213	5	math	math	PROPN
ejpam-4694	213	6	,	,	PUNCT
ejpam-4694	213	7	16	16	NUM
ejpam-4694	213	8	(	(	PUNCT
ejpam-4694	213	9	2	2	NUM
ejpam-4694	213	10	)	)	PUNCT
ejpam-4694	213	11	(	(	PUNCT
ejpam-4694	213	12	2023	2023	NUM
ejpam-4694	213	13	)	)	PUNCT
ejpam-4694	213	14	,	,	PUNCT
ejpam-4694	213	15	687	687	NUM
ejpam-4694	213	16	-	-	SYM
ejpam-4694	213	17	712	712	NUM
ejpam-4694	213	18	696	696	NUM
ejpam-4694	213	19	remark	remark	NOUN
ejpam-4694	213	20	2.4	2.4	NUM
ejpam-4694	213	21	.	.	PUNCT
ejpam-4694	214	1	it	it	PRON
ejpam-4694	214	2	can	can	AUX
ejpam-4694	214	3	easily	easily	ADV
ejpam-4694	214	4	be	be	AUX
ejpam-4694	214	5	seen	see	VERB
ejpam-4694	214	6	that	that	SCONJ
ejpam-4694	214	7	,	,	PUNCT
ejpam-4694	214	8	when	when	SCONJ
ejpam-4694	214	9	α	α	PROPN
ejpam-4694	214	10	=	=	SYM
ejpam-4694	214	11	1	1	NUM
ejpam-4694	214	12	,	,	PUNCT
ejpam-4694	214	13	the	the	DET
ejpam-4694	214	14	explicit	explicit	ADJ
ejpam-4694	214	15	formula	formula	NOUN
ejpam-4694	214	16	in	in	ADP
ejpam-4694	214	17	theorem	theorem	ADJ
ejpam-4694	214	18	2.3	2.3	NUM
ejpam-4694	214	19	reduces	reduce	VERB
ejpam-4694	214	20	to	to	ADP
ejpam-4694	214	21	that	that	PRON
ejpam-4694	214	22	in	in	ADP
ejpam-4694	214	23	theorem	theorem	NOUN
ejpam-4694	214	24	2.2	2.2	NUM
ejpam-4694	214	25	.	.	PUNCT
ejpam-4694	215	1	3	3	X
ejpam-4694	215	2	.	.	X
ejpam-4694	215	3	relation	relation	NOUN
ejpam-4694	215	4	with	with	ADP
ejpam-4694	215	5	some	some	DET
ejpam-4694	215	6	genocchi	genocchi	NOUN
ejpam-4694	215	7	-	-	PUNCT
ejpam-4694	215	8	type	type	NOUN
ejpam-4694	215	9	polynomials	polynomial	NOUN
ejpam-4694	215	10	by	by	ADP
ejpam-4694	215	11	giving	give	VERB
ejpam-4694	215	12	special	special	ADJ
ejpam-4694	215	13	values	value	NOUN
ejpam-4694	215	14	to	to	ADP
ejpam-4694	215	15	the	the	DET
ejpam-4694	215	16	parameters	parameter	NOUN
ejpam-4694	215	17	involved	involve	VERB
ejpam-4694	215	18	,	,	PUNCT
ejpam-4694	215	19	ĝ(k	ĝ(k	INTJ
ejpam-4694	215	20	,	,	PUNCT
ejpam-4694	215	21	α	α	NOUN
ejpam-4694	215	22	)	)	PUNCT
ejpam-4694	215	23	n	n	CCONJ
ejpam-4694	215	24	(	(	PUNCT
ejpam-4694	215	25	x;λ	x;λ	PROPN
ejpam-4694	215	26	,	,	PUNCT
ejpam-4694	215	27	ρ	ρ	PROPN
ejpam-4694	215	28	,	,	PUNCT
ejpam-4694	215	29	u	u	NOUN
ejpam-4694	215	30	,	,	PUNCT
ejpam-4694	215	31	a	a	DET
ejpam-4694	215	32	,	,	PUNCT
ejpam-4694	215	33	b	b	NOUN
ejpam-4694	215	34	)	)	PUNCT
ejpam-4694	215	35	reduces	reduce	VERB
ejpam-4694	215	36	to	to	ADP
ejpam-4694	215	37	some	some	DET
ejpam-4694	215	38	interesting	interesting	ADJ
ejpam-4694	215	39	genocchi	genocchi	NOUN
ejpam-4694	215	40	-	-	PUNCT
ejpam-4694	215	41	type	type	NOUN
ejpam-4694	215	42	polynomials	polynomial	NOUN
ejpam-4694	215	43	.	.	PUNCT
ejpam-4694	216	1	(	(	PUNCT
ejpam-4694	216	2	i	i	NOUN
ejpam-4694	216	3	)	)	PUNCT
ejpam-4694	216	4	using	use	VERB
ejpam-4694	216	5	(	(	PUNCT
ejpam-4694	216	6	23	23	NUM
ejpam-4694	216	7	)	)	PUNCT
ejpam-4694	216	8	,	,	PUNCT
ejpam-4694	216	9	when	when	SCONJ
ejpam-4694	216	10	k	k	PROPN
ejpam-4694	216	11	=	=	SYM
ejpam-4694	216	12	1	1	NUM
ejpam-4694	216	13	,	,	PUNCT
ejpam-4694	216	14	(	(	PUNCT
ejpam-4694	216	15	27	27	NUM
ejpam-4694	216	16	)	)	PUNCT
ejpam-4694	216	17	yields	yield	VERB
ejpam-4694	216	18	∞∑	∞∑	PRON
ejpam-4694	216	19	n=0	n=0	NUM
ejpam-4694	216	20	ĝ(α	ĝ(α	NOUN
ejpam-4694	216	21	)	)	PUNCT
ejpam-4694	216	22	n	n	CCONJ
ejpam-4694	216	23	(	(	PUNCT
ejpam-4694	216	24	x;λ	x;λ	PROPN
ejpam-4694	216	25	,	,	PUNCT
ejpam-4694	216	26	ρ	ρ	PROPN
ejpam-4694	216	27	,	,	PUNCT
ejpam-4694	216	28	u	u	NOUN
ejpam-4694	216	29	,	,	PUNCT
ejpam-4694	216	30	a	a	DET
ejpam-4694	216	31	,	,	PUNCT
ejpam-4694	216	32	b	b	NOUN
ejpam-4694	216	33	)	)	PUNCT
ejpam-4694	216	34	tn	tn	NOUN
ejpam-4694	216	35	n	n	NOUN
ejpam-4694	216	36	!	!	PUNCT
ejpam-4694	217	1	=	=	PUNCT
ejpam-4694	217	2	(	(	PUNCT
ejpam-4694	217	3	(	(	PUNCT
ejpam-4694	217	4	1−	1−	NUM
ejpam-4694	217	5	u)t	u)t	X
ejpam-4694	217	6	ln	ln	PROPN
ejpam-4694	217	7	ab	ab	PROPN
ejpam-4694	217	8	λbt	λbt	VERB
ejpam-4694	217	9	−	−	PROPN
ejpam-4694	217	10	ua−t	ua−t	PROPN
ejpam-4694	217	11	)	)	PUNCT
ejpam-4694	217	12	α	α	PROPN
ejpam-4694	217	13	exρ(t	exρ(t	NOUN
ejpam-4694	217	14	)	)	PUNCT
ejpam-4694	217	15	,	,	PUNCT
ejpam-4694	217	16	(	(	PUNCT
ejpam-4694	217	17	31	31	NUM
ejpam-4694	217	18	)	)	PUNCT
ejpam-4694	217	19	where	where	SCONJ
ejpam-4694	217	20	the	the	DET
ejpam-4694	217	21	polynomials	polynomial	NOUN
ejpam-4694	217	22	ĝ(α	ĝ(α	NOUN
ejpam-4694	217	23	)	)	PUNCT
ejpam-4694	217	24	n	n	CCONJ
ejpam-4694	217	25	(	(	PUNCT
ejpam-4694	217	26	x;λ	x;λ	PROPN
ejpam-4694	217	27	,	,	PUNCT
ejpam-4694	217	28	ρ	ρ	PROPN
ejpam-4694	217	29	,	,	PUNCT
ejpam-4694	217	30	u	u	NOUN
ejpam-4694	217	31	,	,	PUNCT
ejpam-4694	217	32	a	a	PRON
ejpam-4694	217	33	,	,	PUNCT
ejpam-4694	217	34	b	b	NOUN
ejpam-4694	217	35	)	)	PUNCT
ejpam-4694	217	36	=	=	SYM
ejpam-4694	217	37	ĝ(1,α	ĝ(1,α	NOUN
ejpam-4694	217	38	)	)	PUNCT
ejpam-4694	217	39	n	n	CCONJ
ejpam-4694	217	40	(	(	PUNCT
ejpam-4694	217	41	x;λ	x;λ	PROPN
ejpam-4694	217	42	,	,	PUNCT
ejpam-4694	217	43	ρ	ρ	PROPN
ejpam-4694	217	44	,	,	PUNCT
ejpam-4694	217	45	u	u	NOUN
ejpam-4694	217	46	,	,	PUNCT
ejpam-4694	217	47	a	a	DET
ejpam-4694	217	48	,	,	PUNCT
ejpam-4694	217	49	b	b	NOUN
ejpam-4694	217	50	)	)	PUNCT
ejpam-4694	217	51	are	be	AUX
ejpam-4694	217	52	called	call	VERB
ejpam-4694	217	53	the	the	DET
ejpam-4694	217	54	degenerate	degenerate	ADJ
ejpam-4694	217	55	apostol	apostol	NOUN
ejpam-4694	217	56	-	-	PUNCT
ejpam-4694	217	57	frobenius	frobenius	NOUN
ejpam-4694	217	58	-	-	PUNCT
ejpam-4694	217	59	type	type	NOUN
ejpam-4694	217	60	genocchi	genocchi	NOUN
ejpam-4694	217	61	polynomials	polynomial	NOUN
ejpam-4694	217	62	of	of	ADP
ejpam-4694	217	63	higher	high	ADJ
ejpam-4694	217	64	order	order	NOUN
ejpam-4694	217	65	with	with	ADP
ejpam-4694	217	66	parameters	parameter	NOUN
ejpam-4694	217	67	a	a	DET
ejpam-4694	217	68	,	,	PUNCT
ejpam-4694	217	69	b	b	NOUN
ejpam-4694	217	70	and	and	CCONJ
ejpam-4694	217	71	c.	c.	NOUN
ejpam-4694	217	72	when	when	SCONJ
ejpam-4694	217	73	α	α	PROPN
ejpam-4694	217	74	=	=	SYM
ejpam-4694	217	75	1	1	NUM
ejpam-4694	217	76	,	,	PUNCT
ejpam-4694	217	77	(	(	PUNCT
ejpam-4694	217	78	31	31	NUM
ejpam-4694	217	79	)	)	PUNCT
ejpam-4694	217	80	yields	yield	VERB
ejpam-4694	217	81	∞∑	∞∑	NUM
ejpam-4694	217	82	n=0	n=0	NUM
ejpam-4694	217	83	ĝ(1	ĝ(1	NOUN
ejpam-4694	217	84	)	)	PUNCT
ejpam-4694	217	85	n	n	CCONJ
ejpam-4694	217	86	(	(	PUNCT
ejpam-4694	217	87	x;λ	x;λ	PROPN
ejpam-4694	217	88	,	,	PUNCT
ejpam-4694	217	89	ρ	ρ	PROPN
ejpam-4694	217	90	,	,	PUNCT
ejpam-4694	217	91	u	u	NOUN
ejpam-4694	217	92	,	,	PUNCT
ejpam-4694	217	93	a	a	DET
ejpam-4694	217	94	,	,	PUNCT
ejpam-4694	217	95	b	b	NOUN
ejpam-4694	217	96	)	)	PUNCT
ejpam-4694	217	97	tn	tn	NOUN
ejpam-4694	217	98	n	n	NOUN
ejpam-4694	217	99	!	!	PUNCT
ejpam-4694	218	1	=	=	PUNCT
ejpam-4694	218	2	(	(	PUNCT
ejpam-4694	218	3	1−	1−	NUM
ejpam-4694	218	4	u)t	u)t	X
ejpam-4694	218	5	ln	ln	PROPN
ejpam-4694	218	6	ab	ab	PROPN
ejpam-4694	218	7	λbt	λbt	VERB
ejpam-4694	218	8	−	−	PROPN
ejpam-4694	218	9	ua−t	ua−t	PROPN
ejpam-4694	218	10	exρ(t	exρ(t	PROPN
ejpam-4694	218	11	)	)	PUNCT
ejpam-4694	218	12	,	,	PUNCT
ejpam-4694	218	13	(	(	PUNCT
ejpam-4694	218	14	32	32	NUM
ejpam-4694	218	15	)	)	PUNCT
ejpam-4694	218	16	where	where	SCONJ
ejpam-4694	218	17	the	the	DET
ejpam-4694	218	18	polynomials	polynomial	NOUN
ejpam-4694	218	19	ĝ(1	ĝ(1	NOUN
ejpam-4694	218	20	)	)	PUNCT
ejpam-4694	218	21	n	n	CCONJ
ejpam-4694	218	22	(	(	PUNCT
ejpam-4694	218	23	x;λ	x;λ	PROPN
ejpam-4694	218	24	,	,	PUNCT
ejpam-4694	218	25	ρ	ρ	PROPN
ejpam-4694	218	26	,	,	PUNCT
ejpam-4694	218	27	u	u	NOUN
ejpam-4694	218	28	,	,	PUNCT
ejpam-4694	218	29	a	a	DET
ejpam-4694	218	30	,	,	PUNCT
ejpam-4694	218	31	b	b	NOUN
ejpam-4694	218	32	)	)	PUNCT
ejpam-4694	218	33	are	be	AUX
ejpam-4694	218	34	called	call	VERB
ejpam-4694	218	35	the	the	DET
ejpam-4694	218	36	degenerate	degenerate	ADJ
ejpam-4694	218	37	apostol	apostol	NOUN
ejpam-4694	218	38	-	-	PUNCT
ejpam-4694	218	39	frobeniustype	frobeniustype	NOUN
ejpam-4694	218	40	genocchi	genocchi	NOUN
ejpam-4694	218	41	polynomials	polynomial	NOUN
ejpam-4694	218	42	with	with	ADP
ejpam-4694	218	43	parameters	parameter	NOUN
ejpam-4694	218	44	a	a	PRON
ejpam-4694	218	45	and	and	CCONJ
ejpam-4694	218	46	b.	b.	PROPN
ejpam-4694	218	47	(	(	PUNCT
ejpam-4694	218	48	ii	ii	PROPN
ejpam-4694	218	49	)	)	PUNCT
ejpam-4694	218	50	when	when	SCONJ
ejpam-4694	218	51	x	x	X
ejpam-4694	218	52	=	=	SYM
ejpam-4694	218	53	0	0	NUM
ejpam-4694	218	54	,	,	PUNCT
ejpam-4694	218	55	equation	equation	NOUN
ejpam-4694	218	56	(	(	PUNCT
ejpam-4694	218	57	27	27	NUM
ejpam-4694	218	58	)	)	PUNCT
ejpam-4694	218	59	reduces	reduce	VERB
ejpam-4694	218	60	to	to	ADP
ejpam-4694	218	61	∞∑	∞∑	NUM
ejpam-4694	218	62	n=0	n=0	NUM
ejpam-4694	218	63	ĝ(k	ĝ(k	PROPN
ejpam-4694	218	64	,	,	PUNCT
ejpam-4694	218	65	α	α	NOUN
ejpam-4694	218	66	)	)	PUNCT
ejpam-4694	218	67	n	n	PROPN
ejpam-4694	218	68	(	(	PUNCT
ejpam-4694	218	69	λ	λ	PROPN
ejpam-4694	218	70	,	,	PUNCT
ejpam-4694	218	71	ρ	ρ	PROPN
ejpam-4694	218	72	,	,	PUNCT
ejpam-4694	218	73	u	u	NOUN
ejpam-4694	218	74	,	,	PUNCT
ejpam-4694	218	75	a	a	DET
ejpam-4694	218	76	,	,	PUNCT
ejpam-4694	218	77	b	b	NOUN
ejpam-4694	218	78	)	)	PUNCT
ejpam-4694	218	79	tn	tn	NOUN
ejpam-4694	218	80	n	n	NOUN
ejpam-4694	218	81	!	!	PUNCT
ejpam-4694	219	1	=	=	PRON
ejpam-4694	219	2	(	(	PUNCT
ejpam-4694	219	3	eik	eik	PROPN
ejpam-4694	219	4	,	,	PUNCT
ejpam-4694	219	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	219	6	+	+	CCONJ
ejpam-4694	219	7	(	(	PUNCT
ejpam-4694	219	8	1−	1−	NUM
ejpam-4694	219	9	u)t	u)t	X
ejpam-4694	219	10	ln	ln	PROPN
ejpam-4694	219	11	ab	ab	PROPN
ejpam-4694	219	12	)	)	PUNCT
ejpam-4694	219	13	)	)	PUNCT
ejpam-4694	220	1	λbt	λbt	VERB
ejpam-4694	220	2	−	−	PROPN
ejpam-4694	220	3	ua−t	ua−t	ADJ
ejpam-4694	220	4	)	)	PUNCT
ejpam-4694	220	5	α	α	PROPN
ejpam-4694	220	6	,	,	PUNCT
ejpam-4694	220	7	(	(	PUNCT
ejpam-4694	220	8	33	33	NUM
ejpam-4694	220	9	)	)	PUNCT
ejpam-4694	220	10	the	the	DET
ejpam-4694	220	11	degenerate	degenerate	ADJ
ejpam-4694	220	12	apostol	apostol	NOUN
ejpam-4694	220	13	-	-	PUNCT
ejpam-4694	220	14	frobenius	frobenius	NOUN
ejpam-4694	220	15	-	-	PUNCT
ejpam-4694	220	16	type	type	NOUN
ejpam-4694	220	17	poly	poly	ADJ
ejpam-4694	220	18	-	-	PUNCT
ejpam-4694	220	19	genocchi	genocchi	NOUN
ejpam-4694	220	20	numbers	number	NOUN
ejpam-4694	220	21	with	with	ADP
ejpam-4694	220	22	parameters	parameter	NOUN
ejpam-4694	220	23	a	a	PRON
ejpam-4694	220	24	and	and	CCONJ
ejpam-4694	220	25	b.	b.	PROPN
ejpam-4694	220	26	(	(	PUNCT
ejpam-4694	220	27	iii	iii	NOUN
ejpam-4694	220	28	)	)	PUNCT
ejpam-4694	220	29	when	when	SCONJ
ejpam-4694	220	30	a	a	DET
ejpam-4694	220	31	=	=	SYM
ejpam-4694	220	32	1	1	NUM
ejpam-4694	220	33	,	,	PUNCT
ejpam-4694	220	34	b	b	NOUN
ejpam-4694	220	35	=	=	SYM
ejpam-4694	220	36	e	e	NOUN
ejpam-4694	220	37	,	,	PUNCT
ejpam-4694	220	38	(	(	PUNCT
ejpam-4694	220	39	27	27	NUM
ejpam-4694	220	40	)	)	PUNCT
ejpam-4694	220	41	will	will	AUX
ejpam-4694	220	42	reduce	reduce	VERB
ejpam-4694	220	43	to	to	ADP
ejpam-4694	220	44	∞∑	∞∑	NUM
ejpam-4694	220	45	n=0	n=0	NUM
ejpam-4694	220	46	ĝ(k	ĝ(k	PROPN
ejpam-4694	220	47	,	,	PUNCT
ejpam-4694	220	48	α	α	NOUN
ejpam-4694	220	49	)	)	PUNCT
ejpam-4694	220	50	n	n	CCONJ
ejpam-4694	220	51	(	(	PUNCT
ejpam-4694	220	52	x;λ	x;λ	PROPN
ejpam-4694	220	53	,	,	PUNCT
ejpam-4694	220	54	ρ	ρ	PROPN
ejpam-4694	220	55	,	,	PUNCT
ejpam-4694	220	56	u	u	NOUN
ejpam-4694	220	57	)	)	PUNCT
ejpam-4694	220	58	tn	tn	PROPN
ejpam-4694	220	59	n	n	PROPN
ejpam-4694	220	60	!	!	PUNCT
ejpam-4694	221	1	=	=	PRON
ejpam-4694	221	2	(	(	PUNCT
ejpam-4694	221	3	eik	eik	PROPN
ejpam-4694	221	4	,	,	PUNCT
ejpam-4694	221	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	221	6	+	+	CCONJ
ejpam-4694	221	7	(	(	PUNCT
ejpam-4694	221	8	1−	1−	NUM
ejpam-4694	221	9	u)t	u)t	NOUN
ejpam-4694	221	10	)	)	PUNCT
ejpam-4694	221	11	)	)	PUNCT
ejpam-4694	222	1	λet	λet	CCONJ
ejpam-4694	222	2	−	−	PROPN
ejpam-4694	222	3	u	u	NOUN
ejpam-4694	222	4	)	)	PUNCT
ejpam-4694	222	5	α	α	PROPN
ejpam-4694	222	6	exρ(t	exρ(t	NOUN
ejpam-4694	222	7	)	)	PUNCT
ejpam-4694	222	8	,	,	PUNCT
ejpam-4694	222	9	(	(	PUNCT
ejpam-4694	222	10	34	34	NUM
ejpam-4694	222	11	)	)	PUNCT
ejpam-4694	222	12	and	and	CCONJ
ejpam-4694	222	13	call	call	VERB
ejpam-4694	222	14	ĝ(k	ĝ(k	PRON
ejpam-4694	222	15	,	,	PUNCT
ejpam-4694	222	16	α	α	NOUN
ejpam-4694	222	17	)	)	PUNCT
ejpam-4694	222	18	n	n	CCONJ
ejpam-4694	222	19	(	(	PUNCT
ejpam-4694	222	20	x;λ	x;λ	PROPN
ejpam-4694	222	21	,	,	PUNCT
ejpam-4694	222	22	ρ	ρ	PROPN
ejpam-4694	222	23	,	,	PUNCT
ejpam-4694	222	24	u	u	NOUN
ejpam-4694	222	25	)	)	PUNCT
ejpam-4694	222	26	,	,	PUNCT
ejpam-4694	222	27	the	the	DET
ejpam-4694	222	28	degenerate	degenerate	ADJ
ejpam-4694	222	29	apostol	apostol	NOUN
ejpam-4694	222	30	-	-	PUNCT
ejpam-4694	222	31	frobenius	frobenius	NOUN
ejpam-4694	222	32	-	-	PUNCT
ejpam-4694	222	33	type	type	NOUN
ejpam-4694	222	34	poly	poly	ADJ
ejpam-4694	222	35	-	-	PUNCT
ejpam-4694	222	36	genocchi	genocchi	NOUN
ejpam-4694	222	37	polynomials	polynomial	NOUN
ejpam-4694	222	38	of	of	ADP
ejpam-4694	222	39	higher	high	ADJ
ejpam-4694	222	40	order	order	NOUN
ejpam-4694	222	41	.	.	PUNCT
ejpam-4694	223	1	when	when	SCONJ
ejpam-4694	223	2	x	x	X
ejpam-4694	223	3	=	=	SYM
ejpam-4694	223	4	0	0	NUM
ejpam-4694	223	5	,	,	PUNCT
ejpam-4694	223	6	we	we	PRON
ejpam-4694	223	7	get	get	VERB
ejpam-4694	223	8	∞∑	∞∑	NUM
ejpam-4694	223	9	n=0	n=0	NUM
ejpam-4694	223	10	ĝ(k	ĝ(k	PROPN
ejpam-4694	223	11	,	,	PUNCT
ejpam-4694	223	12	α	α	NOUN
ejpam-4694	223	13	)	)	PUNCT
ejpam-4694	223	14	n	n	PROPN
ejpam-4694	223	15	(	(	PUNCT
ejpam-4694	223	16	λ	λ	PROPN
ejpam-4694	223	17	,	,	PUNCT
ejpam-4694	223	18	ρ	ρ	PROPN
ejpam-4694	223	19	,	,	PUNCT
ejpam-4694	223	20	u	u	NOUN
ejpam-4694	223	21	)	)	PUNCT
ejpam-4694	223	22	tn	tn	PROPN
ejpam-4694	223	23	n	n	PROPN
ejpam-4694	223	24	!	!	PUNCT
ejpam-4694	224	1	=	=	PRON
ejpam-4694	224	2	(	(	PUNCT
ejpam-4694	224	3	eik	eik	PROPN
ejpam-4694	224	4	,	,	PUNCT
ejpam-4694	224	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	224	6	+	+	CCONJ
ejpam-4694	224	7	(	(	PUNCT
ejpam-4694	224	8	1−	1−	NUM
ejpam-4694	224	9	u)t	u)t	NOUN
ejpam-4694	224	10	)	)	PUNCT
ejpam-4694	224	11	λet	λet	ADP
ejpam-4694	224	12	−	−	PROPN
ejpam-4694	224	13	u	u	NOUN
ejpam-4694	224	14	)	)	PUNCT
ejpam-4694	224	15	α	α	PROPN
ejpam-4694	224	16	,	,	PUNCT
ejpam-4694	224	17	(	(	PUNCT
ejpam-4694	224	18	35	35	NUM
ejpam-4694	224	19	)	)	PUNCT
ejpam-4694	224	20	the	the	DET
ejpam-4694	224	21	degenerate	degenerate	ADJ
ejpam-4694	224	22	apostol	apostol	NOUN
ejpam-4694	224	23	-	-	PUNCT
ejpam-4694	224	24	frobenius	frobenius	NOUN
ejpam-4694	224	25	-	-	PUNCT
ejpam-4694	224	26	type	type	NOUN
ejpam-4694	224	27	genocchi	genocchi	NOUN
ejpam-4694	224	28	numbers	number	NOUN
ejpam-4694	224	29	of	of	ADP
ejpam-4694	224	30	higher	high	ADJ
ejpam-4694	224	31	order	order	NOUN
ejpam-4694	224	32	.	.	PUNCT
ejpam-4694	225	1	r.	r.	PROPN
ejpam-4694	225	2	corcino	corcino	PROPN
ejpam-4694	225	3	,	,	PUNCT
ejpam-4694	225	4	c.	c.	PROPN
ejpam-4694	225	5	corcino	corcino	PROPN
ejpam-4694	225	6	/	/	SYM
ejpam-4694	225	7	eur	eur	PROPN
ejpam-4694	225	8	.	.	PUNCT
ejpam-4694	226	1	j.	j.	PROPN
ejpam-4694	226	2	pure	pure	PROPN
ejpam-4694	226	3	appl	appl	PROPN
ejpam-4694	226	4	.	.	PROPN
ejpam-4694	226	5	math	math	PROPN
ejpam-4694	226	6	,	,	PUNCT
ejpam-4694	226	7	16	16	NUM
ejpam-4694	226	8	(	(	PUNCT
ejpam-4694	226	9	2	2	NUM
ejpam-4694	226	10	)	)	PUNCT
ejpam-4694	226	11	(	(	PUNCT
ejpam-4694	226	12	2023	2023	NUM
ejpam-4694	226	13	)	)	PUNCT
ejpam-4694	226	14	,	,	PUNCT
ejpam-4694	226	15	687	687	NUM
ejpam-4694	226	16	-	-	SYM
ejpam-4694	226	17	712	712	NUM
ejpam-4694	226	18	697	697	NUM
ejpam-4694	226	19	(	(	PUNCT
ejpam-4694	226	20	iv	iv	X
ejpam-4694	226	21	)	)	PUNCT
ejpam-4694	226	22	when	when	SCONJ
ejpam-4694	226	23	ρ	ρ	PROPN
ejpam-4694	226	24	→	→	SYM
ejpam-4694	226	25	0	0	NUM
ejpam-4694	226	26	,	,	PUNCT
ejpam-4694	226	27	equation	equation	NOUN
ejpam-4694	226	28	(	(	PUNCT
ejpam-4694	226	29	27	27	NUM
ejpam-4694	226	30	)	)	PUNCT
ejpam-4694	226	31	reduces	reduce	VERB
ejpam-4694	226	32	to	to	ADP
ejpam-4694	226	33	∞∑	∞∑	NUM
ejpam-4694	226	34	n=0	n=0	NUM
ejpam-4694	226	35	ĝ(k	ĝ(k	PROPN
ejpam-4694	226	36	,	,	PUNCT
ejpam-4694	226	37	α	α	NOUN
ejpam-4694	226	38	)	)	PUNCT
ejpam-4694	226	39	n	n	CCONJ
ejpam-4694	226	40	(	(	PUNCT
ejpam-4694	226	41	x;λ	x;λ	PROPN
ejpam-4694	226	42	,	,	PUNCT
ejpam-4694	226	43	0	0	NUM
ejpam-4694	226	44	,	,	PUNCT
ejpam-4694	226	45	u	u	NOUN
ejpam-4694	226	46	,	,	PUNCT
ejpam-4694	226	47	a	a	DET
ejpam-4694	226	48	,	,	PUNCT
ejpam-4694	226	49	b	b	NOUN
ejpam-4694	226	50	)	)	PUNCT
ejpam-4694	226	51	tn	tn	NOUN
ejpam-4694	226	52	n	n	NOUN
ejpam-4694	226	53	!	!	PUNCT
ejpam-4694	227	1	=	=	PUNCT
ejpam-4694	227	2	(	(	PUNCT
ejpam-4694	227	3	eik,0(log0(1	eik,0(log0(1	NOUN
ejpam-4694	227	4	+	+	CCONJ
ejpam-4694	227	5	(	(	PUNCT
ejpam-4694	227	6	1−	1−	NUM
ejpam-4694	227	7	u)t	u)t	X
ejpam-4694	227	8	ln	ln	PROPN
ejpam-4694	227	9	ab	ab	PROPN
ejpam-4694	227	10	)	)	PUNCT
ejpam-4694	227	11	)	)	PUNCT
ejpam-4694	227	12	λbt	λbt	VERB
ejpam-4694	227	13	−	−	PROPN
ejpam-4694	227	14	ua−t	ua−t	PROPN
ejpam-4694	227	15	)	)	PUNCT
ejpam-4694	227	16	α	α	PROPN
ejpam-4694	227	17	ex0(t	ex0(t	PROPN
ejpam-4694	227	18	)	)	PUNCT
ejpam-4694	228	1	∞∑	∞∑	PRON
ejpam-4694	228	2	n=0	n=0	PUNCT
ejpam-4694	228	3	ĝ(k	ĝ(k	NOUN
ejpam-4694	228	4	,	,	PUNCT
ejpam-4694	228	5	α	α	NOUN
ejpam-4694	228	6	)	)	PUNCT
ejpam-4694	228	7	n	n	CCONJ
ejpam-4694	228	8	(	(	PUNCT
ejpam-4694	228	9	x;λ	x;λ	PROPN
ejpam-4694	228	10	,	,	PUNCT
ejpam-4694	228	11	u	u	NOUN
ejpam-4694	228	12	,	,	PUNCT
ejpam-4694	228	13	a	a	DET
ejpam-4694	228	14	,	,	PUNCT
ejpam-4694	228	15	b	b	NOUN
ejpam-4694	228	16	)	)	PUNCT
ejpam-4694	228	17	tn	tn	NOUN
ejpam-4694	228	18	n	n	CCONJ
ejpam-4694	228	19	!	!	PUNCT
ejpam-4694	229	1	=	=	PUNCT
ejpam-4694	229	2	(	(	PUNCT
ejpam-4694	229	3	eik(log(1	eik(log(1	VERB
ejpam-4694	229	4	+	+	CCONJ
ejpam-4694	229	5	(	(	PUNCT
ejpam-4694	229	6	1−	1−	NUM
ejpam-4694	229	7	u)t	u)t	X
ejpam-4694	229	8	ln	ln	PROPN
ejpam-4694	229	9	ab	ab	PROPN
ejpam-4694	229	10	)	)	PUNCT
ejpam-4694	229	11	)	)	PUNCT
ejpam-4694	230	1	λbt	λbt	VERB
ejpam-4694	230	2	−	−	PROPN
ejpam-4694	230	3	ua−t	ua−t	NOUN
ejpam-4694	230	4	)	)	PUNCT
ejpam-4694	230	5	α	α	PROPN
ejpam-4694	230	6	ext	ext	NOUN
ejpam-4694	230	7	,	,	PUNCT
ejpam-4694	230	8	(	(	PUNCT
ejpam-4694	230	9	36	36	NUM
ejpam-4694	230	10	)	)	PUNCT
ejpam-4694	230	11	where	where	SCONJ
ejpam-4694	230	12	the	the	DET
ejpam-4694	230	13	polynomials	polynomial	NOUN
ejpam-4694	230	14	g(k	g(k	VERB
ejpam-4694	230	15	,	,	PUNCT
ejpam-4694	230	16	α	α	NOUN
ejpam-4694	230	17	)	)	PUNCT
ejpam-4694	230	18	n	n	CCONJ
ejpam-4694	230	19	(	(	PUNCT
ejpam-4694	230	20	x;λ	x;λ	PROPN
ejpam-4694	230	21	,	,	PUNCT
ejpam-4694	230	22	u	u	NOUN
ejpam-4694	230	23	,	,	PUNCT
ejpam-4694	230	24	a	a	DET
ejpam-4694	230	25	,	,	PUNCT
ejpam-4694	230	26	b	b	NOUN
ejpam-4694	230	27	)	)	PUNCT
ejpam-4694	230	28	are	be	AUX
ejpam-4694	230	29	the	the	DET
ejpam-4694	230	30	type	type	NOUN
ejpam-4694	230	31	2	2	NUM
ejpam-4694	230	32	apostol	apostol	NOUN
ejpam-4694	230	33	-	-	PUNCT
ejpam-4694	230	34	frobenius	frobenius	NOUN
ejpam-4694	230	35	-	-	PUNCT
ejpam-4694	230	36	type	type	NOUN
ejpam-4694	230	37	polygenocchi	polygenocchi	ADJ
ejpam-4694	230	38	polynomials	polynomial	NOUN
ejpam-4694	230	39	of	of	ADP
ejpam-4694	230	40	higher	high	ADJ
ejpam-4694	230	41	order	order	NOUN
ejpam-4694	230	42	with	with	ADP
ejpam-4694	230	43	parameters	parameter	NOUN
ejpam-4694	230	44	a	a	DET
ejpam-4694	230	45	,	,	PUNCT
ejpam-4694	230	46	b	b	PROPN
ejpam-4694	230	47	and	and	CCONJ
ejpam-4694	230	48	c	c	NOUN
ejpam-4694	230	49	with	with	ADP
ejpam-4694	230	50	c	c	NOUN
ejpam-4694	230	51	=	=	SYM
ejpam-4694	230	52	e	e	NOUN
ejpam-4694	230	53	in	in	ADP
ejpam-4694	230	54	[	[	X
ejpam-4694	230	55	17	17	NUM
ejpam-4694	230	56	]	]	PUNCT
ejpam-4694	230	57	.	.	PUNCT
ejpam-4694	231	1	(	(	PUNCT
ejpam-4694	231	2	v	v	NOUN
ejpam-4694	231	3	)	)	PUNCT
ejpam-4694	231	4	when	when	SCONJ
ejpam-4694	231	5	λ	λ	X
ejpam-4694	231	6	=	=	SYM
ejpam-4694	231	7	1	1	NUM
ejpam-4694	231	8	,	,	PUNCT
ejpam-4694	231	9	(	(	PUNCT
ejpam-4694	231	10	34	34	NUM
ejpam-4694	231	11	)	)	PUNCT
ejpam-4694	231	12	gives	give	VERB
ejpam-4694	231	13	∞∑	∞∑	PRON
ejpam-4694	231	14	n=0	n=0	NUM
ejpam-4694	231	15	ĝ(k	ĝ(k	PROPN
ejpam-4694	231	16	,	,	PUNCT
ejpam-4694	231	17	α	α	NOUN
ejpam-4694	231	18	)	)	PUNCT
ejpam-4694	231	19	n	n	PROPN
ejpam-4694	231	20	(	(	PUNCT
ejpam-4694	231	21	x;u	x;u	PROPN
ejpam-4694	231	22	,	,	PUNCT
ejpam-4694	231	23	1	1	NUM
ejpam-4694	231	24	,	,	PUNCT
ejpam-4694	231	25	e	e	NOUN
ejpam-4694	231	26	)	)	PUNCT
ejpam-4694	231	27	tn	tn	PROPN
ejpam-4694	231	28	n	n	NOUN
ejpam-4694	231	29	!	!	PUNCT
ejpam-4694	232	1	=	=	PRON
ejpam-4694	232	2	(	(	PUNCT
ejpam-4694	232	3	eik	eik	PROPN
ejpam-4694	232	4	,	,	PUNCT
ejpam-4694	232	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	232	6	+	+	CCONJ
ejpam-4694	232	7	(	(	PUNCT
ejpam-4694	232	8	1−	1−	NUM
ejpam-4694	232	9	u)t	u)t	NOUN
ejpam-4694	232	10	)	)	PUNCT
ejpam-4694	232	11	)	)	PUNCT
ejpam-4694	232	12	et	et	NOUN
ejpam-4694	232	13	−	−	PROPN
ejpam-4694	232	14	u	u	PROPN
ejpam-4694	232	15	)	)	PUNCT
ejpam-4694	232	16	α	α	PROPN
ejpam-4694	232	17	ext	ext	NOUN
ejpam-4694	232	18	.	.	PUNCT
ejpam-4694	233	1	(	(	PUNCT
ejpam-4694	233	2	37	37	NUM
ejpam-4694	233	3	)	)	PUNCT
ejpam-4694	233	4	which	which	PRON
ejpam-4694	233	5	is	be	AUX
ejpam-4694	233	6	the	the	DET
ejpam-4694	233	7	higher	high	ADJ
ejpam-4694	233	8	order	order	NOUN
ejpam-4694	233	9	version	version	NOUN
ejpam-4694	233	10	of	of	ADP
ejpam-4694	233	11	equation	equation	NOUN
ejpam-4694	233	12	(	(	PUNCT
ejpam-4694	233	13	8)	8)	NUM
ejpam-4694	233	14	and	and	CCONJ
ejpam-4694	233	15	are	be	AUX
ejpam-4694	233	16	called	call	VERB
ejpam-4694	233	17	the	the	DET
ejpam-4694	233	18	higher	high	ADJ
ejpam-4694	233	19	order	order	NOUN
ejpam-4694	233	20	poly	poly	ADJ
ejpam-4694	233	21	-	-	PUNCT
ejpam-4694	233	22	genocchi	genocchi	NOUN
ejpam-4694	233	23	polynomials	polynomial	NOUN
ejpam-4694	233	24	.	.	PUNCT
ejpam-4694	234	1	we	we	PRON
ejpam-4694	234	2	may	may	AUX
ejpam-4694	234	3	use	use	VERB
ejpam-4694	234	4	ĝ(k	ĝ(k	PRON
ejpam-4694	234	5	,	,	PUNCT
ejpam-4694	234	6	α	α	NOUN
ejpam-4694	234	7	)	)	PUNCT
ejpam-4694	234	8	n	n	PROPN
ejpam-4694	234	9	(	(	PUNCT
ejpam-4694	234	10	x;u	x;u	PROPN
ejpam-4694	234	11	)	)	PUNCT
ejpam-4694	234	12	to	to	PART
ejpam-4694	234	13	denote	denote	VERB
ejpam-4694	234	14	ĝ(k	ĝ(k	PROPN
ejpam-4694	234	15	,	,	PUNCT
ejpam-4694	234	16	α	α	NOUN
ejpam-4694	234	17	)	)	PUNCT
ejpam-4694	234	18	n	n	PROPN
ejpam-4694	234	19	(	(	PUNCT
ejpam-4694	234	20	x;u	x;u	PROPN
ejpam-4694	234	21	,	,	PUNCT
ejpam-4694	234	22	1	1	NUM
ejpam-4694	234	23	,	,	PUNCT
ejpam-4694	234	24	e	e	NOUN
ejpam-4694	234	25	)	)	PUNCT
ejpam-4694	234	26	.	.	PUNCT
ejpam-4694	235	1	(	(	PUNCT
ejpam-4694	235	2	vi	vi	NOUN
ejpam-4694	235	3	)	)	PUNCT
ejpam-4694	235	4	when	when	SCONJ
ejpam-4694	235	5	k	k	PROPN
ejpam-4694	235	6	=	=	SYM
ejpam-4694	235	7	1	1	NUM
ejpam-4694	235	8	,	,	PUNCT
ejpam-4694	235	9	a	a	PRON
ejpam-4694	235	10	=	=	SYM
ejpam-4694	235	11	1	1	NUM
ejpam-4694	235	12	and	and	CCONJ
ejpam-4694	235	13	b	b	NOUN
ejpam-4694	235	14	=	=	SYM
ejpam-4694	235	15	e	e	NOUN
ejpam-4694	235	16	,	,	PUNCT
ejpam-4694	235	17	(	(	PUNCT
ejpam-4694	235	18	36	36	NUM
ejpam-4694	235	19	)	)	PUNCT
ejpam-4694	235	20	gives	give	VERB
ejpam-4694	235	21	∞∑	∞∑	DET
ejpam-4694	235	22	n=0	n=0	NUM
ejpam-4694	235	23	ĝ(1,α	ĝ(1,α	NOUN
ejpam-4694	235	24	)	)	PUNCT
ejpam-4694	235	25	n	n	CCONJ
ejpam-4694	235	26	(	(	PUNCT
ejpam-4694	235	27	x;λ	x;λ	PROPN
ejpam-4694	235	28	,	,	PUNCT
ejpam-4694	235	29	u	u	NOUN
ejpam-4694	235	30	)	)	PUNCT
ejpam-4694	235	31	tn	tn	PROPN
ejpam-4694	235	32	n	n	PROPN
ejpam-4694	235	33	!	!	PUNCT
ejpam-4694	236	1	=	=	PUNCT
ejpam-4694	236	2	(	(	PUNCT
ejpam-4694	236	3	(	(	PUNCT
ejpam-4694	236	4	1−	1−	NUM
ejpam-4694	236	5	u)t	u)t	X
ejpam-4694	236	6	λet	λet	ADP
ejpam-4694	236	7	−	−	PROPN
ejpam-4694	236	8	u	u	NOUN
ejpam-4694	236	9	)	)	PUNCT
ejpam-4694	236	10	α	α	PROPN
ejpam-4694	236	11	ext	ext	NOUN
ejpam-4694	236	12	,	,	PUNCT
ejpam-4694	236	13	(	(	PUNCT
ejpam-4694	236	14	38	38	NUM
ejpam-4694	236	15	)	)	PUNCT
ejpam-4694	236	16	and	and	CCONJ
ejpam-4694	236	17	when	when	SCONJ
ejpam-4694	236	18	λ	λ	X
ejpam-4694	236	19	=	=	SYM
ejpam-4694	236	20	1	1	NUM
ejpam-4694	236	21	,	,	PUNCT
ejpam-4694	236	22	(	(	PUNCT
ejpam-4694	236	23	38	38	NUM
ejpam-4694	236	24	)	)	PUNCT
ejpam-4694	236	25	gives	give	VERB
ejpam-4694	236	26	∞∑	∞∑	DET
ejpam-4694	236	27	n=0	n=0	NUM
ejpam-4694	236	28	ĝ(1,α	ĝ(1,α	NOUN
ejpam-4694	236	29	)	)	PUNCT
ejpam-4694	236	30	n	n	CCONJ
ejpam-4694	236	31	(	(	PUNCT
ejpam-4694	236	32	x	x	NOUN
ejpam-4694	236	33	;	;	PUNCT
ejpam-4694	236	34	1	1	NUM
ejpam-4694	236	35	,	,	PUNCT
ejpam-4694	236	36	u	u	NOUN
ejpam-4694	236	37	)	)	PUNCT
ejpam-4694	236	38	tn	tn	PROPN
ejpam-4694	236	39	n	n	PROPN
ejpam-4694	236	40	!	!	PUNCT
ejpam-4694	237	1	=	=	PUNCT
ejpam-4694	237	2	(	(	PUNCT
ejpam-4694	237	3	(	(	PUNCT
ejpam-4694	237	4	1−	1−	NUM
ejpam-4694	237	5	u)t	u)t	X
ejpam-4694	237	6	et	et	NOUN
ejpam-4694	237	7	−	−	PROPN
ejpam-4694	237	8	u	u	PROPN
ejpam-4694	237	9	)	)	PUNCT
ejpam-4694	237	10	α	α	PROPN
ejpam-4694	237	11	ext	ext	NOUN
ejpam-4694	237	12	,	,	PUNCT
ejpam-4694	237	13	where	where	SCONJ
ejpam-4694	237	14	ĝ(1,α	ĝ(1,α	NOUN
ejpam-4694	237	15	)	)	PUNCT
ejpam-4694	237	16	n	n	CCONJ
ejpam-4694	237	17	(	(	PUNCT
ejpam-4694	237	18	x;λ	x;λ	PROPN
ejpam-4694	237	19	,	,	PUNCT
ejpam-4694	237	20	u	u	NOUN
ejpam-4694	237	21	)	)	PUNCT
ejpam-4694	237	22	=	=	SYM
ejpam-4694	237	23	ĝ(α	ĝ(α	PROPN
ejpam-4694	237	24	)	)	PUNCT
ejpam-4694	237	25	n	n	CCONJ
ejpam-4694	237	26	(	(	PUNCT
ejpam-4694	237	27	x;λ	x;λ	PROPN
ejpam-4694	237	28	,	,	PUNCT
ejpam-4694	237	29	u	u	NOUN
ejpam-4694	237	30	)	)	PUNCT
ejpam-4694	237	31	and	and	CCONJ
ejpam-4694	237	32	ĝ(1,α	ĝ(1,α	NOUN
ejpam-4694	237	33	)	)	PUNCT
ejpam-4694	237	34	n	n	CCONJ
ejpam-4694	237	35	(	(	PUNCT
ejpam-4694	237	36	x	x	NOUN
ejpam-4694	237	37	;	;	PUNCT
ejpam-4694	237	38	1	1	NUM
ejpam-4694	237	39	,	,	PUNCT
ejpam-4694	237	40	u	u	NOUN
ejpam-4694	237	41	)	)	PUNCT
ejpam-4694	237	42	=	=	SYM
ejpam-4694	237	43	ĝ(α	ĝ(α	PROPN
ejpam-4694	237	44	)	)	PUNCT
ejpam-4694	237	45	n	n	CCONJ
ejpam-4694	237	46	(	(	PUNCT
ejpam-4694	237	47	x;u	x;u	PROPN
ejpam-4694	237	48	)	)	PUNCT
ejpam-4694	237	49	are	be	AUX
ejpam-4694	237	50	called	call	VERB
ejpam-4694	237	51	the	the	DET
ejpam-4694	237	52	degenerate	degenerate	ADJ
ejpam-4694	237	53	apostol	apostol	NOUN
ejpam-4694	237	54	-	-	PUNCT
ejpam-4694	237	55	frobenius	frobenius	NOUN
ejpam-4694	237	56	-	-	PUNCT
ejpam-4694	237	57	type	type	NOUN
ejpam-4694	237	58	genocchi	genocchi	NOUN
ejpam-4694	237	59	polynomials	polynomial	NOUN
ejpam-4694	237	60	and	and	CCONJ
ejpam-4694	237	61	frobenius	frobenius	ADJ
ejpam-4694	237	62	-	-	PUNCT
ejpam-4694	237	63	genocchi	genocchi	NOUN
ejpam-4694	237	64	polynomials	polynomial	NOUN
ejpam-4694	237	65	of	of	ADP
ejpam-4694	237	66	higher	high	ADJ
ejpam-4694	237	67	order	order	NOUN
ejpam-4694	237	68	in	in	ADP
ejpam-4694	237	69	(	(	PUNCT
ejpam-4694	237	70	4	4	NUM
ejpam-4694	237	71	)	)	PUNCT
ejpam-4694	237	72	and	and	CCONJ
ejpam-4694	237	73	(	(	PUNCT
ejpam-4694	237	74	2	2	NUM
ejpam-4694	237	75	)	)	PUNCT
ejpam-4694	237	76	,	,	PUNCT
ejpam-4694	237	77	respectively	respectively	ADV
ejpam-4694	237	78	.	.	PUNCT
ejpam-4694	238	1	furthermore	furthermore	ADV
ejpam-4694	238	2	,	,	PUNCT
ejpam-4694	238	3	when	when	SCONJ
ejpam-4694	238	4	α	α	PROPN
ejpam-4694	238	5	=	=	SYM
ejpam-4694	238	6	1	1	NUM
ejpam-4694	238	7	,	,	PUNCT
ejpam-4694	238	8	we	we	PRON
ejpam-4694	238	9	have	have	VERB
ejpam-4694	238	10	∞∑	∞∑	NUM
ejpam-4694	238	11	n=0	n=0	NUM
ejpam-4694	238	12	ĝn(x;λ	ĝn(x;λ	NOUN
ejpam-4694	238	13	,	,	PUNCT
ejpam-4694	238	14	u	u	NOUN
ejpam-4694	238	15	)	)	PUNCT
ejpam-4694	238	16	tn	tn	PROPN
ejpam-4694	238	17	n	n	PROPN
ejpam-4694	238	18	!	!	PUNCT
ejpam-4694	239	1	=	=	PUNCT
ejpam-4694	239	2	(	(	PUNCT
ejpam-4694	239	3	1−	1−	NUM
ejpam-4694	239	4	u)t	u)t	X
ejpam-4694	239	5	λet	λet	ADP
ejpam-4694	239	6	−	−	NUM
ejpam-4694	239	7	u	u	NOUN
ejpam-4694	239	8	ext	ext	NOUN
ejpam-4694	239	9	,	,	PUNCT
ejpam-4694	239	10	(	(	PUNCT
ejpam-4694	239	11	39	39	NUM
ejpam-4694	239	12	)	)	PUNCT
ejpam-4694	239	13	and	and	CCONJ
ejpam-4694	239	14	∞∑	∞∑	ADJ
ejpam-4694	239	15	n=0	n=0	PROPN
ejpam-4694	239	16	ĝn(x;u	ĝn(x;u	NOUN
ejpam-4694	239	17	)	)	PUNCT
ejpam-4694	239	18	tn	tn	PROPN
ejpam-4694	239	19	n	n	PROPN
ejpam-4694	239	20	!	!	PUNCT
ejpam-4694	240	1	=	=	PUNCT
ejpam-4694	240	2	(	(	PUNCT
ejpam-4694	240	3	1−	1−	NUM
ejpam-4694	240	4	u)t	u)t	X
ejpam-4694	240	5	et	et	NOUN
ejpam-4694	240	6	−	−	PROPN
ejpam-4694	240	7	u	u	PROPN
ejpam-4694	240	8	ext	ext	NOUN
ejpam-4694	240	9	,	,	PUNCT
ejpam-4694	240	10	where	where	SCONJ
ejpam-4694	240	11	ĝn(x;λ	ĝn(x;λ	NOUN
ejpam-4694	240	12	,	,	PUNCT
ejpam-4694	240	13	u	u	NOUN
ejpam-4694	240	14	)	)	PUNCT
ejpam-4694	240	15	and	and	CCONJ
ejpam-4694	240	16	ĝn(x;u	ĝn(x;u	PROPN
ejpam-4694	240	17	)	)	PUNCT
ejpam-4694	240	18	are	be	AUX
ejpam-4694	240	19	called	call	VERB
ejpam-4694	240	20	the	the	DET
ejpam-4694	240	21	degenerate	degenerate	ADJ
ejpam-4694	240	22	apostol	apostol	NOUN
ejpam-4694	240	23	-	-	PUNCT
ejpam-4694	240	24	frobenius	frobenius	NOUN
ejpam-4694	240	25	-	-	PUNCT
ejpam-4694	240	26	type	type	NOUN
ejpam-4694	240	27	genocchi	genocchi	NOUN
ejpam-4694	240	28	polynomials	polynomial	NOUN
ejpam-4694	240	29	and	and	CCONJ
ejpam-4694	240	30	frobenius	frobenius	ADJ
ejpam-4694	240	31	-	-	PUNCT
ejpam-4694	240	32	genocchi	genocchi	NOUN
ejpam-4694	240	33	polynomials	polynomial	NOUN
ejpam-4694	240	34	in	in	ADP
ejpam-4694	240	35	(	(	PUNCT
ejpam-4694	240	36	4	4	NUM
ejpam-4694	240	37	)	)	PUNCT
ejpam-4694	240	38	and	and	CCONJ
ejpam-4694	240	39	(	(	PUNCT
ejpam-4694	240	40	2	2	NUM
ejpam-4694	240	41	)	)	PUNCT
ejpam-4694	240	42	,	,	PUNCT
ejpam-4694	240	43	respectively	respectively	ADV
ejpam-4694	240	44	.	.	PUNCT
ejpam-4694	241	1	r.	r.	PROPN
ejpam-4694	241	2	corcino	corcino	PROPN
ejpam-4694	241	3	,	,	PUNCT
ejpam-4694	241	4	c.	c.	PROPN
ejpam-4694	241	5	corcino	corcino	PROPN
ejpam-4694	241	6	/	/	SYM
ejpam-4694	241	7	eur	eur	PROPN
ejpam-4694	241	8	.	.	PUNCT
ejpam-4694	242	1	j.	j.	PROPN
ejpam-4694	242	2	pure	pure	PROPN
ejpam-4694	242	3	appl	appl	PROPN
ejpam-4694	242	4	.	.	PROPN
ejpam-4694	242	5	math	math	PROPN
ejpam-4694	242	6	,	,	PUNCT
ejpam-4694	242	7	16	16	NUM
ejpam-4694	242	8	(	(	PUNCT
ejpam-4694	242	9	2	2	NUM
ejpam-4694	242	10	)	)	PUNCT
ejpam-4694	242	11	(	(	PUNCT
ejpam-4694	242	12	2023	2023	NUM
ejpam-4694	242	13	)	)	PUNCT
ejpam-4694	242	14	,	,	PUNCT
ejpam-4694	242	15	687	687	NUM
ejpam-4694	242	16	-	-	SYM
ejpam-4694	242	17	712	712	NUM
ejpam-4694	242	18	698	698	NUM
ejpam-4694	242	19	now	now	ADV
ejpam-4694	242	20	,	,	PUNCT
ejpam-4694	242	21	let	let	VERB
ejpam-4694	242	22	us	we	PRON
ejpam-4694	242	23	consider	consider	VERB
ejpam-4694	242	24	some	some	DET
ejpam-4694	242	25	some	some	DET
ejpam-4694	242	26	relations	relation	NOUN
ejpam-4694	242	27	of	of	ADP
ejpam-4694	242	28	ĝ(k	ĝ(k	PRON
ejpam-4694	242	29	,	,	PUNCT
ejpam-4694	242	30	α	α	NOUN
ejpam-4694	242	31	)	)	PUNCT
ejpam-4694	242	32	n	n	CCONJ
ejpam-4694	242	33	(	(	PUNCT
ejpam-4694	242	34	x;λ	x;λ	PROPN
ejpam-4694	242	35	,	,	PUNCT
ejpam-4694	242	36	ρ	ρ	PROPN
ejpam-4694	242	37	,	,	PUNCT
ejpam-4694	242	38	u	u	NOUN
ejpam-4694	242	39	,	,	PUNCT
ejpam-4694	242	40	a	a	DET
ejpam-4694	242	41	,	,	PUNCT
ejpam-4694	242	42	b	b	NOUN
ejpam-4694	242	43	)	)	PUNCT
ejpam-4694	242	44	with	with	ADP
ejpam-4694	242	45	other	other	ADJ
ejpam-4694	242	46	genocchitype	genocchitype	NOUN
ejpam-4694	242	47	polynomials	polynomial	NOUN
ejpam-4694	242	48	.	.	PUNCT
ejpam-4694	243	1	first	first	ADV
ejpam-4694	243	2	is	be	AUX
ejpam-4694	243	3	to	to	PART
ejpam-4694	243	4	establish	establish	VERB
ejpam-4694	243	5	a	a	DET
ejpam-4694	243	6	kind	kind	NOUN
ejpam-4694	243	7	of	of	ADP
ejpam-4694	243	8	addition	addition	NOUN
ejpam-4694	243	9	formula	formula	NOUN
ejpam-4694	243	10	for	for	ADP
ejpam-4694	243	11	ĝ(k	ĝ(k	PRON
ejpam-4694	243	12	,	,	PUNCT
ejpam-4694	243	13	α	α	NOUN
ejpam-4694	243	14	)	)	PUNCT
ejpam-4694	243	15	n	n	CCONJ
ejpam-4694	243	16	(	(	PUNCT
ejpam-4694	243	17	x;λ	x;λ	PROPN
ejpam-4694	243	18	,	,	PUNCT
ejpam-4694	243	19	ρ	ρ	PROPN
ejpam-4694	243	20	,	,	PUNCT
ejpam-4694	243	21	u	u	NOUN
ejpam-4694	243	22	,	,	PUNCT
ejpam-4694	243	23	a	a	DET
ejpam-4694	243	24	,	,	PUNCT
ejpam-4694	243	25	b	b	NOUN
ejpam-4694	243	26	)	)	PUNCT
ejpam-4694	243	27	expressing	express	VERB
ejpam-4694	243	28	them	they	PRON
ejpam-4694	243	29	as	as	SCONJ
ejpam-4694	243	30	polynomials	polynomial	NOUN
ejpam-4694	243	31	in	in	ADP
ejpam-4694	243	32	x.	x.	NOUN
ejpam-4694	243	33	theorem	theorem	VERB
ejpam-4694	243	34	3.1	3.1	NUM
ejpam-4694	243	35	.	.	PUNCT
ejpam-4694	244	1	the	the	DET
ejpam-4694	244	2	degenerate	degenerate	ADJ
ejpam-4694	244	3	apostol	apostol	NOUN
ejpam-4694	244	4	-	-	PUNCT
ejpam-4694	244	5	frobenius	frobenius	NOUN
ejpam-4694	244	6	-	-	PUNCT
ejpam-4694	244	7	type	type	NOUN
ejpam-4694	244	8	poly	poly	ADJ
ejpam-4694	244	9	-	-	PUNCT
ejpam-4694	244	10	genocchi	genocchi	NOUN
ejpam-4694	244	11	polynomials	polynomial	NOUN
ejpam-4694	244	12	of	of	ADP
ejpam-4694	244	13	higher	high	ADJ
ejpam-4694	244	14	order	order	NOUN
ejpam-4694	244	15	with	with	ADP
ejpam-4694	244	16	parameters	parameter	NOUN
ejpam-4694	244	17	a	a	PRON
ejpam-4694	244	18	and	and	CCONJ
ejpam-4694	244	19	b	b	NOUN
ejpam-4694	244	20	satisfy	satisfy	VERB
ejpam-4694	244	21	the	the	DET
ejpam-4694	244	22	relation	relation	NOUN
ejpam-4694	244	23	ĝ(k	ĝ(k	PROPN
ejpam-4694	244	24	,	,	PUNCT
ejpam-4694	244	25	α	α	NOUN
ejpam-4694	244	26	)	)	PUNCT
ejpam-4694	244	27	n	n	CCONJ
ejpam-4694	244	28	(	(	PUNCT
ejpam-4694	244	29	x;λ	x;λ	PROPN
ejpam-4694	244	30	,	,	PUNCT
ejpam-4694	244	31	ρ	ρ	PROPN
ejpam-4694	244	32	,	,	PUNCT
ejpam-4694	244	33	u	u	NOUN
ejpam-4694	244	34	,	,	PUNCT
ejpam-4694	244	35	a	a	DET
ejpam-4694	244	36	,	,	PUNCT
ejpam-4694	244	37	b	b	NOUN
ejpam-4694	244	38	)	)	PUNCT
ejpam-4694	244	39	=	=	SYM
ejpam-4694	245	1	n∑	n∑	PROPN
ejpam-4694	245	2	m=0	m=0	PROPN
ejpam-4694	245	3	(	(	PUNCT
ejpam-4694	245	4	n	n	NOUN
ejpam-4694	245	5	m	m	VERB
ejpam-4694	245	6	)	)	PUNCT
ejpam-4694	245	7	ĝ(k	ĝ(k	X
ejpam-4694	245	8	,	,	PUNCT
ejpam-4694	245	9	α	α	NOUN
ejpam-4694	245	10	)	)	PUNCT
ejpam-4694	245	11	n−m(λ	n−m(λ	NOUN
ejpam-4694	245	12	,	,	PUNCT
ejpam-4694	245	13	ρ	ρ	PROPN
ejpam-4694	245	14	,	,	PUNCT
ejpam-4694	245	15	u	u	NOUN
ejpam-4694	245	16	,	,	PUNCT
ejpam-4694	245	17	a	a	PRON
ejpam-4694	245	18	,	,	PUNCT
ejpam-4694	245	19	b)(x)m	b)(x)m	X
ejpam-4694	245	20	,	,	PUNCT
ejpam-4694	245	21	ρ	ρ	PROPN
ejpam-4694	245	22	.	.	PUNCT
ejpam-4694	246	1	(	(	PUNCT
ejpam-4694	246	2	40	40	NUM
ejpam-4694	246	3	)	)	PUNCT
ejpam-4694	246	4	moreover	moreover	ADV
ejpam-4694	246	5	,	,	PUNCT
ejpam-4694	246	6	the	the	DET
ejpam-4694	246	7	expression	expression	NOUN
ejpam-4694	246	8	of	of	ADP
ejpam-4694	246	9	ĝ(k	ĝ(k	PRON
ejpam-4694	246	10	,	,	PUNCT
ejpam-4694	246	11	α	α	NOUN
ejpam-4694	246	12	)	)	PUNCT
ejpam-4694	246	13	n	n	CCONJ
ejpam-4694	246	14	(	(	PUNCT
ejpam-4694	246	15	x;λ	x;λ	PROPN
ejpam-4694	246	16	,	,	PUNCT
ejpam-4694	246	17	ρ	ρ	PROPN
ejpam-4694	246	18	,	,	PUNCT
ejpam-4694	246	19	u	u	NOUN
ejpam-4694	246	20	,	,	PUNCT
ejpam-4694	246	21	a	a	DET
ejpam-4694	246	22	,	,	PUNCT
ejpam-4694	246	23	b	b	NOUN
ejpam-4694	246	24	)	)	PUNCT
ejpam-4694	246	25	as	as	ADV
ejpam-4694	246	26	polynomial	polynomial	ADJ
ejpam-4694	246	27	in	in	ADP
ejpam-4694	246	28	x	x	PROPN
ejpam-4694	246	29	is	be	AUX
ejpam-4694	246	30	given	give	VERB
ejpam-4694	246	31	by	by	ADP
ejpam-4694	246	32	ĝ(k	ĝ(k	PRON
ejpam-4694	246	33	,	,	PUNCT
ejpam-4694	246	34	α	α	NOUN
ejpam-4694	246	35	)	)	PUNCT
ejpam-4694	246	36	n	n	CCONJ
ejpam-4694	246	37	(	(	PUNCT
ejpam-4694	246	38	x;λ	x;λ	PROPN
ejpam-4694	246	39	,	,	PUNCT
ejpam-4694	246	40	ρ	ρ	PROPN
ejpam-4694	246	41	,	,	PUNCT
ejpam-4694	246	42	u	u	NOUN
ejpam-4694	246	43	,	,	PUNCT
ejpam-4694	246	44	a	a	DET
ejpam-4694	246	45	,	,	PUNCT
ejpam-4694	246	46	b	b	NOUN
ejpam-4694	246	47	)	)	PUNCT
ejpam-4694	246	48	=	=	SYM
ejpam-4694	246	49	n∑	n∑	NOUN
ejpam-4694	246	50	j=0	j=0	PROPN
ejpam-4694	246	51	ĝ(k	ĝ(k	PROPN
ejpam-4694	246	52	,	,	PUNCT
ejpam-4694	246	53	α	α	NOUN
ejpam-4694	246	54	)	)	PUNCT
ejpam-4694	246	55	n	n	CCONJ
ejpam-4694	246	56	,	,	PUNCT
ejpam-4694	246	57	j	j	PROPN
ejpam-4694	246	58	,	,	PUNCT
ejpam-4694	246	59	w̃(λ	w̃(λ	PROPN
ejpam-4694	246	60	,	,	PUNCT
ejpam-4694	246	61	ρ	ρ	PROPN
ejpam-4694	246	62	,	,	PUNCT
ejpam-4694	246	63	u	u	NOUN
ejpam-4694	246	64	,	,	PUNCT
ejpam-4694	246	65	a	a	PRON
ejpam-4694	246	66	,	,	PUNCT
ejpam-4694	246	67	b)x	b)x	X
ejpam-4694	246	68	j	j	PROPN
ejpam-4694	246	69	,	,	PUNCT
ejpam-4694	246	70	(	(	PUNCT
ejpam-4694	246	71	41	41	NUM
ejpam-4694	246	72	)	)	PUNCT
ejpam-4694	246	73	where	where	SCONJ
ejpam-4694	246	74	ĝ(k	ĝ(k	X
ejpam-4694	246	75	,	,	PUNCT
ejpam-4694	246	76	α	α	NOUN
ejpam-4694	246	77	)	)	PUNCT
ejpam-4694	246	78	n	n	CCONJ
ejpam-4694	246	79	,	,	PUNCT
ejpam-4694	246	80	j	j	PROPN
ejpam-4694	246	81	,	,	PUNCT
ejpam-4694	246	82	w̃(λ	w̃(λ	PROPN
ejpam-4694	246	83	,	,	PUNCT
ejpam-4694	246	84	ρ	ρ	PROPN
ejpam-4694	246	85	,	,	PUNCT
ejpam-4694	246	86	u	u	NOUN
ejpam-4694	246	87	,	,	PUNCT
ejpam-4694	246	88	a	a	PRON
ejpam-4694	246	89	,	,	PUNCT
ejpam-4694	246	90	b	b	NOUN
ejpam-4694	246	91	)	)	PUNCT
ejpam-4694	246	92	=	=	PUNCT
ejpam-4694	247	1	n∑	n∑	NOUN
ejpam-4694	247	2	m	m	PROPN
ejpam-4694	247	3	=	=	PROPN
ejpam-4694	247	4	j	j	PROPN
ejpam-4694	247	5	(	(	PUNCT
ejpam-4694	247	6	n	n	NOUN
ejpam-4694	247	7	m	m	VERB
ejpam-4694	247	8	)	)	PUNCT
ejpam-4694	247	9	ĝ(k	ĝ(k	X
ejpam-4694	247	10	,	,	PUNCT
ejpam-4694	247	11	α	α	NOUN
ejpam-4694	247	12	)	)	PUNCT
ejpam-4694	247	13	n−m(λ	n−m(λ	NOUN
ejpam-4694	247	14	,	,	PUNCT
ejpam-4694	247	15	ρ	ρ	PROPN
ejpam-4694	247	16	,	,	PUNCT
ejpam-4694	247	17	u	u	NOUN
ejpam-4694	247	18	,	,	PUNCT
ejpam-4694	247	19	a	a	PRON
ejpam-4694	247	20	,	,	PUNCT
ejpam-4694	247	21	b)w̃ρ(m	b)w̃ρ(m	PROPN
ejpam-4694	247	22	,	,	PUNCT
ejpam-4694	247	23	j	j	NOUN
ejpam-4694	247	24	)	)	PUNCT
ejpam-4694	247	25	,	,	PUNCT
ejpam-4694	247	26	proof	proof	NOUN
ejpam-4694	247	27	.	.	PUNCT
ejpam-4694	248	1	using	use	VERB
ejpam-4694	248	2	(	(	PUNCT
ejpam-4694	248	3	33	33	NUM
ejpam-4694	248	4	)	)	PUNCT
ejpam-4694	248	5	,	,	PUNCT
ejpam-4694	248	6	we	we	PRON
ejpam-4694	248	7	can	can	AUX
ejpam-4694	248	8	write	write	VERB
ejpam-4694	248	9	(	(	PUNCT
ejpam-4694	248	10	27	27	NUM
ejpam-4694	248	11	)	)	PUNCT
ejpam-4694	248	12	as	as	SCONJ
ejpam-4694	248	13	follows	follow	VERB
ejpam-4694	248	14	:	:	PUNCT
ejpam-4694	248	15	∞∑	∞∑	NUM
ejpam-4694	248	16	n=0	n=0	NUM
ejpam-4694	248	17	ĝ(k	ĝ(k	PROPN
ejpam-4694	248	18	,	,	PUNCT
ejpam-4694	248	19	α	α	NOUN
ejpam-4694	248	20	)	)	PUNCT
ejpam-4694	248	21	n	n	CCONJ
ejpam-4694	248	22	(	(	PUNCT
ejpam-4694	248	23	x;λ	x;λ	PROPN
ejpam-4694	248	24	,	,	PUNCT
ejpam-4694	248	25	ρ	ρ	PROPN
ejpam-4694	248	26	,	,	PUNCT
ejpam-4694	248	27	u	u	NOUN
ejpam-4694	248	28	,	,	PUNCT
ejpam-4694	248	29	a	a	DET
ejpam-4694	248	30	,	,	PUNCT
ejpam-4694	248	31	b	b	NOUN
ejpam-4694	248	32	)	)	PUNCT
ejpam-4694	248	33	tn	tn	NOUN
ejpam-4694	248	34	n	n	NOUN
ejpam-4694	248	35	!	!	PUNCT
ejpam-4694	249	1	=	=	PRON
ejpam-4694	249	2	(	(	PUNCT
ejpam-4694	249	3	eik	eik	PROPN
ejpam-4694	249	4	,	,	PUNCT
ejpam-4694	249	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	249	6	+	+	CCONJ
ejpam-4694	249	7	(	(	PUNCT
ejpam-4694	249	8	1−	1−	NUM
ejpam-4694	249	9	u)t	u)t	X
ejpam-4694	249	10	ln	ln	PROPN
ejpam-4694	249	11	ab	ab	PROPN
ejpam-4694	249	12	)	)	PUNCT
ejpam-4694	249	13	)	)	PUNCT
ejpam-4694	250	1	λbt	λbt	VERB
ejpam-4694	250	2	−	−	PROPN
ejpam-4694	250	3	ua−t	ua−t	ADJ
ejpam-4694	250	4	)	)	PUNCT
ejpam-4694	250	5	α	α	PROPN
ejpam-4694	250	6	exρ(t	exρ(t	NOUN
ejpam-4694	250	7	)	)	PUNCT
ejpam-4694	250	8	=	=	NOUN
ejpam-4694	251	1	(	(	PUNCT
ejpam-4694	251	2	∞∑	∞∑	PRON
ejpam-4694	251	3	n=0	n=0	NUM
ejpam-4694	251	4	ĝ(k	ĝ(k	PROPN
ejpam-4694	251	5	,	,	PUNCT
ejpam-4694	251	6	α	α	NOUN
ejpam-4694	251	7	)	)	PUNCT
ejpam-4694	251	8	n	n	PROPN
ejpam-4694	251	9	(	(	PUNCT
ejpam-4694	251	10	λ	λ	PROPN
ejpam-4694	251	11	,	,	PUNCT
ejpam-4694	251	12	ρ	ρ	PROPN
ejpam-4694	251	13	,	,	PUNCT
ejpam-4694	251	14	u	u	NOUN
ejpam-4694	251	15	,	,	PUNCT
ejpam-4694	251	16	a	a	DET
ejpam-4694	251	17	,	,	PUNCT
ejpam-4694	251	18	b	b	NOUN
ejpam-4694	251	19	)	)	PUNCT
ejpam-4694	251	20	tn	tn	PROPN
ejpam-4694	251	21	n	n	CCONJ
ejpam-4694	251	22	!	!	PUNCT
ejpam-4694	251	23	)	)	PUNCT
ejpam-4694	252	1	(	(	PUNCT
ejpam-4694	252	2	∞∑	∞∑	NUM
ejpam-4694	252	3	n=0	n=0	NUM
ejpam-4694	252	4	(	(	PUNCT
ejpam-4694	252	5	x)n	x)n	PROPN
ejpam-4694	252	6	,	,	PUNCT
ejpam-4694	252	7	ρ	ρ	PROPN
ejpam-4694	252	8	tn	tn	PROPN
ejpam-4694	252	9	n	n	X
ejpam-4694	252	10	!	!	PUNCT
ejpam-4694	252	11	)	)	PUNCT
ejpam-4694	253	1	=	=	PUNCT
ejpam-4694	254	1	∞∑	∞∑	NUM
ejpam-4694	254	2	n=0	n=0	NUM
ejpam-4694	254	3	(	(	PUNCT
ejpam-4694	254	4	n∑	n∑	PROPN
ejpam-4694	254	5	m=0	m=0	PROPN
ejpam-4694	254	6	(	(	PUNCT
ejpam-4694	254	7	n	n	NOUN
ejpam-4694	254	8	m	m	VERB
ejpam-4694	254	9	)	)	PUNCT
ejpam-4694	255	1	ĝ(k	ĝ(k	X
ejpam-4694	255	2	,	,	PUNCT
ejpam-4694	255	3	α	α	NOUN
ejpam-4694	255	4	)	)	PUNCT
ejpam-4694	255	5	n−m(λ	n−m(λ	NOUN
ejpam-4694	255	6	,	,	PUNCT
ejpam-4694	255	7	ρ	ρ	PROPN
ejpam-4694	255	8	,	,	PUNCT
ejpam-4694	255	9	u	u	NOUN
ejpam-4694	255	10	,	,	PUNCT
ejpam-4694	255	11	a	a	PRON
ejpam-4694	255	12	,	,	PUNCT
ejpam-4694	255	13	b)(x)m	b)(x)m	X
ejpam-4694	255	14	,	,	PUNCT
ejpam-4694	255	15	ρ	ρ	PROPN
ejpam-4694	255	16	)	)	PUNCT
ejpam-4694	255	17	tn	tn	PROPN
ejpam-4694	255	18	n	n	PROPN
ejpam-4694	255	19	!	!	PUNCT
ejpam-4694	256	1	comparing	compare	VERB
ejpam-4694	256	2	the	the	DET
ejpam-4694	256	3	coefficients	coefficient	NOUN
ejpam-4694	256	4	of	of	ADP
ejpam-4694	256	5	tn	tn	NOUN
ejpam-4694	256	6	n	n	X
ejpam-4694	256	7	!	!	PUNCT
ejpam-4694	257	1	yields	yield	NOUN
ejpam-4694	257	2	(	(	PUNCT
ejpam-4694	257	3	40	40	NUM
ejpam-4694	257	4	)	)	PUNCT
ejpam-4694	257	5	.	.	PUNCT
ejpam-4694	258	1	to	to	PART
ejpam-4694	258	2	prove	prove	VERB
ejpam-4694	258	3	(	(	PUNCT
ejpam-4694	258	4	41	41	NUM
ejpam-4694	258	5	)	)	PUNCT
ejpam-4694	258	6	,	,	PUNCT
ejpam-4694	258	7	we	we	PRON
ejpam-4694	258	8	first	first	ADV
ejpam-4694	258	9	recall	recall	VERB
ejpam-4694	258	10	that	that	SCONJ
ejpam-4694	258	11	the	the	DET
ejpam-4694	258	12	rwhitney	rwhitney	NOUN
ejpam-4694	258	13	numbers	number	NOUN
ejpam-4694	258	14	of	of	ADP
ejpam-4694	258	15	the	the	DET
ejpam-4694	258	16	first	first	ADJ
ejpam-4694	258	17	kind	kind	NOUN
ejpam-4694	258	18	,	,	PUNCT
ejpam-4694	258	19	denoted	denote	VERB
ejpam-4694	258	20	by	by	ADP
ejpam-4694	258	21	wm	wm	PROPN
ejpam-4694	258	22	,	,	PUNCT
ejpam-4694	258	23	r(n	r(n	PROPN
ejpam-4694	258	24	,	,	PUNCT
ejpam-4694	258	25	k	k	NOUN
ejpam-4694	258	26	)	)	PUNCT
ejpam-4694	258	27	were	be	AUX
ejpam-4694	258	28	defined	define	VERB
ejpam-4694	258	29	by	by	ADP
ejpam-4694	258	30	mező	mező	PROPN
ejpam-4694	259	1	[	[	X
ejpam-4694	259	2	38	38	NUM
ejpam-4694	259	3	]	]	PUNCT
ejpam-4694	259	4	by	by	ADP
ejpam-4694	259	5	means	mean	NOUN
ejpam-4694	259	6	of	of	ADP
ejpam-4694	259	7	the	the	DET
ejpam-4694	259	8	following	follow	VERB
ejpam-4694	259	9	horizontal	horizontal	ADJ
ejpam-4694	259	10	generating	generating	NOUN
ejpam-4694	259	11	function	function	NOUN
ejpam-4694	259	12	:	:	PUNCT
ejpam-4694	259	13	mn(x)n	mn(x)n	PROPN
ejpam-4694	259	14	=	=	SYM
ejpam-4694	259	15	n∑	n∑	PROPN
ejpam-4694	259	16	j=0	j=0	PROPN
ejpam-4694	259	17	wm	wm	PROPN
ejpam-4694	259	18	,	,	PUNCT
ejpam-4694	259	19	r(n	r(n	PROPN
ejpam-4694	259	20	,	,	PUNCT
ejpam-4694	259	21	j)(mx+	j)(mx+	NOUN
ejpam-4694	259	22	r)j	r)j	NOUN
ejpam-4694	259	23	,	,	PUNCT
ejpam-4694	259	24	(	(	PUNCT
ejpam-4694	259	25	42	42	NUM
ejpam-4694	259	26	)	)	PUNCT
ejpam-4694	260	1	where	where	SCONJ
ejpam-4694	260	2	(	(	PUNCT
ejpam-4694	260	3	x)n	x)n	PUNCT
ejpam-4694	260	4	=	=	SYM
ejpam-4694	260	5	x(x−	x(x−	PROPN
ejpam-4694	260	6	1)(x−	1)(x−	NUM
ejpam-4694	260	7	2	2	NUM
ejpam-4694	260	8	)	)	PUNCT
ejpam-4694	260	9	.	.	PUNCT
ejpam-4694	260	10	.	.	PUNCT
ejpam-4694	261	1	.	.	PUNCT
ejpam-4694	262	1	(	(	PUNCT
ejpam-4694	262	2	x−n+1	x−n+1	PROPN
ejpam-4694	262	3	)	)	PUNCT
ejpam-4694	262	4	.	.	PUNCT
ejpam-4694	263	1	replacing	replace	VERB
ejpam-4694	263	2	x	x	PUNCT
ejpam-4694	263	3	with	with	ADP
ejpam-4694	263	4	x	x	X
ejpam-4694	263	5	/	/	SYM
ejpam-4694	263	6	m	m	VERB
ejpam-4694	263	7	and	and	CCONJ
ejpam-4694	263	8	letting	let	VERB
ejpam-4694	263	9	r	r	NOUN
ejpam-4694	263	10	=	=	SYM
ejpam-4694	263	11	0	0	NUM
ejpam-4694	263	12	yield	yield	NOUN
ejpam-4694	263	13	(	(	PUNCT
ejpam-4694	263	14	x)n	x)n	PROPN
ejpam-4694	263	15	,	,	PUNCT
ejpam-4694	263	16	m	m	VERB
ejpam-4694	263	17	=	=	SYM
ejpam-4694	263	18	n∑	n∑	PRON
ejpam-4694	263	19	j=0	j=0	PROPN
ejpam-4694	263	20	w̃m(n	w̃m(n	NOUN
ejpam-4694	263	21	,	,	PUNCT
ejpam-4694	263	22	j)xj	j)xj	PROPN
ejpam-4694	263	23	,	,	PUNCT
ejpam-4694	263	24	r.	r.	PROPN
ejpam-4694	263	25	corcino	corcino	PROPN
ejpam-4694	263	26	,	,	PUNCT
ejpam-4694	263	27	c.	c.	PROPN
ejpam-4694	263	28	corcino	corcino	PROPN
ejpam-4694	263	29	/	/	SYM
ejpam-4694	263	30	eur	eur	PROPN
ejpam-4694	263	31	.	.	PUNCT
ejpam-4694	264	1	j.	j.	PROPN
ejpam-4694	264	2	pure	pure	PROPN
ejpam-4694	264	3	appl	appl	PROPN
ejpam-4694	264	4	.	.	PROPN
ejpam-4694	264	5	math	math	PROPN
ejpam-4694	264	6	,	,	PUNCT
ejpam-4694	264	7	16	16	NUM
ejpam-4694	264	8	(	(	PUNCT
ejpam-4694	264	9	2	2	NUM
ejpam-4694	264	10	)	)	PUNCT
ejpam-4694	264	11	(	(	PUNCT
ejpam-4694	264	12	2023	2023	NUM
ejpam-4694	264	13	)	)	PUNCT
ejpam-4694	264	14	,	,	PUNCT
ejpam-4694	264	15	687	687	NUM
ejpam-4694	264	16	-	-	SYM
ejpam-4694	264	17	712	712	NUM
ejpam-4694	264	18	699	699	NUM
ejpam-4694	264	19	where	where	SCONJ
ejpam-4694	264	20	w̃m(n	w̃m(n	PROPN
ejpam-4694	264	21	,	,	PUNCT
ejpam-4694	264	22	j	j	PROPN
ejpam-4694	264	23	)	)	PUNCT
ejpam-4694	264	24	=	=	SYM
ejpam-4694	264	25	wm,0(n	wm,0(n	PROPN
ejpam-4694	264	26	,	,	PUNCT
ejpam-4694	264	27	j	j	PROPN
ejpam-4694	264	28	)	)	PUNCT
ejpam-4694	264	29	,	,	PUNCT
ejpam-4694	264	30	a	a	DET
ejpam-4694	264	31	certain	certain	NOUN
ejpam-4694	264	32	of	of	ADP
ejpam-4694	264	33	generalization	generalization	NOUN
ejpam-4694	264	34	of	of	ADP
ejpam-4694	264	35	stirling	stirling	NOUN
ejpam-4694	264	36	numbers	number	NOUN
ejpam-4694	264	37	of	of	ADP
ejpam-4694	264	38	the	the	DET
ejpam-4694	264	39	first	first	ADJ
ejpam-4694	264	40	kind	kind	NOUN
ejpam-4694	264	41	,	,	PUNCT
ejpam-4694	264	42	i.e.	i.e.	X
ejpam-4694	264	43	s1(n	s1(n	PROPN
ejpam-4694	264	44	,	,	PUNCT
ejpam-4694	264	45	j	j	NOUN
ejpam-4694	264	46	)	)	PUNCT
ejpam-4694	264	47	=	=	SYM
ejpam-4694	264	48	w̃0(n	w̃0(n	PROPN
ejpam-4694	264	49	,	,	PUNCT
ejpam-4694	264	50	j	j	PROPN
ejpam-4694	264	51	)	)	PUNCT
ejpam-4694	264	52	.	.	PUNCT
ejpam-4694	265	1	using	use	VERB
ejpam-4694	265	2	(	(	PUNCT
ejpam-4694	265	3	42	42	NUM
ejpam-4694	265	4	)	)	PUNCT
ejpam-4694	265	5	,	,	PUNCT
ejpam-4694	265	6	equation	equation	NOUN
ejpam-4694	265	7	(	(	PUNCT
ejpam-4694	265	8	40	40	NUM
ejpam-4694	265	9	)	)	PUNCT
ejpam-4694	265	10	can	can	AUX
ejpam-4694	265	11	further	far	ADV
ejpam-4694	265	12	be	be	AUX
ejpam-4694	265	13	written	write	VERB
ejpam-4694	265	14	as	as	ADP
ejpam-4694	265	15	polynomial	polynomial	ADJ
ejpam-4694	265	16	in	in	ADP
ejpam-4694	265	17	x	x	PART
ejpam-4694	265	18	ĝ(k	ĝ(k	X
ejpam-4694	265	19	,	,	PUNCT
ejpam-4694	265	20	α	α	NOUN
ejpam-4694	265	21	)	)	PUNCT
ejpam-4694	265	22	n	n	CCONJ
ejpam-4694	265	23	(	(	PUNCT
ejpam-4694	265	24	x;λ	x;λ	PROPN
ejpam-4694	265	25	,	,	PUNCT
ejpam-4694	265	26	ρ	ρ	PROPN
ejpam-4694	265	27	,	,	PUNCT
ejpam-4694	265	28	u	u	NOUN
ejpam-4694	265	29	,	,	PUNCT
ejpam-4694	265	30	a	a	DET
ejpam-4694	265	31	,	,	PUNCT
ejpam-4694	265	32	b	b	NOUN
ejpam-4694	265	33	)	)	PUNCT
ejpam-4694	266	1	=	=	SYM
ejpam-4694	266	2	n∑	n∑	X
ejpam-4694	266	3	j=0	j=0	PROPN
ejpam-4694	266	4			PUNCT
ejpam-4694	266	5	n∑	n∑	PROPN
ejpam-4694	266	6	m	m	PROPN
ejpam-4694	266	7	=	=	PROPN
ejpam-4694	266	8	j	j	PROPN
ejpam-4694	266	9	(	(	PUNCT
ejpam-4694	266	10	n	n	NOUN
ejpam-4694	266	11	m	m	VERB
ejpam-4694	266	12	)	)	PUNCT
ejpam-4694	266	13	ĝ(k	ĝ(k	X
ejpam-4694	266	14	,	,	PUNCT
ejpam-4694	266	15	α	α	NOUN
ejpam-4694	266	16	)	)	PUNCT
ejpam-4694	266	17	n−m(λ	n−m(λ	NOUN
ejpam-4694	266	18	,	,	PUNCT
ejpam-4694	266	19	ρ	ρ	PROPN
ejpam-4694	266	20	,	,	PUNCT
ejpam-4694	266	21	u	u	NOUN
ejpam-4694	266	22	,	,	PUNCT
ejpam-4694	266	23	a	a	PRON
ejpam-4694	266	24	,	,	PUNCT
ejpam-4694	266	25	b)w̃ρ(m	b)w̃ρ(m	PROPN
ejpam-4694	266	26	,	,	PUNCT
ejpam-4694	266	27	j	j	NOUN
ejpam-4694	266	28	)	)	PUNCT
ejpam-4694	266	29	xj	xj	NOUN
ejpam-4694	266	30	,	,	PUNCT
ejpam-4694	266	31	with	with	ADP
ejpam-4694	266	32	coefficients	coefficient	NOUN
ejpam-4694	266	33	ĝ(k	ĝ(k	PRON
ejpam-4694	266	34	,	,	PUNCT
ejpam-4694	266	35	α	α	NOUN
ejpam-4694	266	36	)	)	PUNCT
ejpam-4694	266	37	n	n	CCONJ
ejpam-4694	266	38	,	,	PUNCT
ejpam-4694	266	39	j	j	PROPN
ejpam-4694	266	40	,	,	PUNCT
ejpam-4694	266	41	w̃(λ	w̃(λ	PROPN
ejpam-4694	266	42	,	,	PUNCT
ejpam-4694	266	43	ρ	ρ	PROPN
ejpam-4694	266	44	,	,	PUNCT
ejpam-4694	266	45	u	u	NOUN
ejpam-4694	266	46	,	,	PUNCT
ejpam-4694	266	47	a	a	DET
ejpam-4694	266	48	,	,	PUNCT
ejpam-4694	266	49	b	b	NOUN
ejpam-4694	266	50	)	)	PUNCT
ejpam-4694	266	51	=	=	PUNCT
ejpam-4694	266	52	n∑	n∑	NOUN
ejpam-4694	266	53	m	m	PROPN
ejpam-4694	266	54	=	=	PROPN
ejpam-4694	266	55	j	j	PROPN
ejpam-4694	266	56	(	(	PUNCT
ejpam-4694	266	57	n	n	NOUN
ejpam-4694	266	58	m	m	VERB
ejpam-4694	266	59	)	)	PUNCT
ejpam-4694	266	60	ĝ(k	ĝ(k	X
ejpam-4694	266	61	,	,	PUNCT
ejpam-4694	266	62	α	α	NOUN
ejpam-4694	266	63	)	)	PUNCT
ejpam-4694	266	64	n−m(λ	n−m(λ	NOUN
ejpam-4694	266	65	,	,	PUNCT
ejpam-4694	266	66	ρ	ρ	PROPN
ejpam-4694	266	67	,	,	PUNCT
ejpam-4694	266	68	u	u	NOUN
ejpam-4694	266	69	,	,	PUNCT
ejpam-4694	266	70	a	a	PRON
ejpam-4694	266	71	,	,	PUNCT
ejpam-4694	266	72	b)w̃ρ(m	b)w̃ρ(m	PROPN
ejpam-4694	266	73	,	,	PUNCT
ejpam-4694	266	74	j	j	PROPN
ejpam-4694	266	75	)	)	PUNCT
ejpam-4694	266	76	,	,	PUNCT
ejpam-4694	266	77	the	the	DET
ejpam-4694	266	78	convolution	convolution	NOUN
ejpam-4694	266	79	of	of	ADP
ejpam-4694	266	80	ĝ(k	ĝ(k	PRON
ejpam-4694	266	81	,	,	PUNCT
ejpam-4694	266	82	α	α	NOUN
ejpam-4694	266	83	)	)	PUNCT
ejpam-4694	266	84	n	n	PROPN
ejpam-4694	266	85	(	(	PUNCT
ejpam-4694	266	86	λ	λ	PROPN
ejpam-4694	266	87	,	,	PUNCT
ejpam-4694	266	88	ρ	ρ	PROPN
ejpam-4694	266	89	,	,	PUNCT
ejpam-4694	266	90	u	u	NOUN
ejpam-4694	266	91	,	,	PUNCT
ejpam-4694	266	92	a	a	DET
ejpam-4694	266	93	,	,	PUNCT
ejpam-4694	266	94	b	b	NOUN
ejpam-4694	266	95	)	)	PUNCT
ejpam-4694	266	96	and	and	CCONJ
ejpam-4694	266	97	w̃ρ(n	w̃ρ(n	PRON
ejpam-4694	266	98	,	,	PUNCT
ejpam-4694	266	99	k	k	NOUN
ejpam-4694	266	100	)	)	PUNCT
ejpam-4694	266	101	.	.	PUNCT
ejpam-4694	267	1	the	the	DET
ejpam-4694	267	2	relation	relation	NOUN
ejpam-4694	267	3	in	in	ADP
ejpam-4694	267	4	(	(	PUNCT
ejpam-4694	267	5	41	41	NUM
ejpam-4694	267	6	)	)	PUNCT
ejpam-4694	267	7	is	be	AUX
ejpam-4694	267	8	useful	useful	ADJ
ejpam-4694	267	9	in	in	ADP
ejpam-4694	267	10	constructing	construct	VERB
ejpam-4694	267	11	the	the	DET
ejpam-4694	267	12	orthogonal	orthogonal	ADJ
ejpam-4694	267	13	version	version	NOUN
ejpam-4694	267	14	of	of	ADP
ejpam-4694	267	15	ĝ(k	ĝ(k	PRON
ejpam-4694	267	16	,	,	PUNCT
ejpam-4694	267	17	α	α	NOUN
ejpam-4694	267	18	)	)	PUNCT
ejpam-4694	267	19	n	n	CCONJ
ejpam-4694	267	20	(	(	PUNCT
ejpam-4694	267	21	x;λ	x;λ	PROPN
ejpam-4694	267	22	,	,	PUNCT
ejpam-4694	267	23	ρ	ρ	PROPN
ejpam-4694	267	24	,	,	PUNCT
ejpam-4694	267	25	u	u	NOUN
ejpam-4694	267	26	,	,	PUNCT
ejpam-4694	267	27	a	a	DET
ejpam-4694	267	28	,	,	PUNCT
ejpam-4694	267	29	b	b	NOUN
ejpam-4694	267	30	)	)	PUNCT
ejpam-4694	267	31	using	use	VERB
ejpam-4694	267	32	gram	gram	NOUN
ejpam-4694	267	33	-	-	PUNCT
ejpam-4694	267	34	schmidt	schmidt	NOUN
ejpam-4694	267	35	process	process	NOUN
ejpam-4694	267	36	.	.	PUNCT
ejpam-4694	268	1	it	it	PRON
ejpam-4694	268	2	can	can	AUX
ejpam-4694	268	3	easily	easily	ADV
ejpam-4694	268	4	be	be	AUX
ejpam-4694	268	5	verified	verify	VERB
ejpam-4694	268	6	from	from	ADP
ejpam-4694	268	7	theorem	theorem	ADJ
ejpam-4694	268	8	2.3	2.3	NUM
ejpam-4694	268	9	that	that	PRON
ejpam-4694	268	10	ĝ(k	ĝ(k	X
ejpam-4694	268	11	,	,	PUNCT
ejpam-4694	268	12	α	α	NOUN
ejpam-4694	268	13	)	)	PUNCT
ejpam-4694	268	14	m	m	VERB
ejpam-4694	268	15	(	(	PUNCT
ejpam-4694	268	16	x;λ	x;λ	PROPN
ejpam-4694	268	17	,	,	PUNCT
ejpam-4694	268	18	ρ	ρ	PROPN
ejpam-4694	268	19	,	,	PUNCT
ejpam-4694	268	20	u	u	NOUN
ejpam-4694	268	21	,	,	PUNCT
ejpam-4694	268	22	a	a	DET
ejpam-4694	268	23	,	,	PUNCT
ejpam-4694	268	24	b	b	NOUN
ejpam-4694	268	25	)	)	PUNCT
ejpam-4694	268	26	=	=	SYM
ejpam-4694	268	27	0,m	0,m	PUNCT
ejpam-4694	269	1	=	=	SYM
ejpam-4694	269	2	0	0	NUM
ejpam-4694	269	3	,	,	PUNCT
ejpam-4694	269	4	1	1	NUM
ejpam-4694	269	5	,	,	PUNCT
ejpam-4694	269	6	.	.	PUNCT
ejpam-4694	269	7	.	.	PUNCT
ejpam-4694	270	1	.	.	PUNCT
ejpam-4694	271	1	,	,	PUNCT
ejpam-4694	271	2	α−	α−	ADP
ejpam-4694	271	3	1	1	NUM
ejpam-4694	271	4	,	,	PUNCT
ejpam-4694	271	5	ĝ(k	ĝ(k	PRON
ejpam-4694	271	6	,	,	PUNCT
ejpam-4694	271	7	α	α	NOUN
ejpam-4694	271	8	)	)	PUNCT
ejpam-4694	271	9	α	α	NOUN
ejpam-4694	271	10	(	(	PUNCT
ejpam-4694	271	11	x;λ	x;λ	PROPN
ejpam-4694	271	12	,	,	PUNCT
ejpam-4694	271	13	ρ	ρ	PROPN
ejpam-4694	271	14	,	,	PUNCT
ejpam-4694	271	15	u	u	NOUN
ejpam-4694	271	16	,	,	PUNCT
ejpam-4694	271	17	a	a	DET
ejpam-4694	271	18	,	,	PUNCT
ejpam-4694	271	19	b	b	NOUN
ejpam-4694	271	20	)	)	PUNCT
ejpam-4694	271	21	=	=	SYM
ejpam-4694	271	22	1	1	X
ejpam-4694	271	23	.	.	PUNCT
ejpam-4694	271	24	let	let	VERB
ejpam-4694	271	25	ϕα(x	ϕα(x	NOUN
ejpam-4694	271	26	)	)	PUNCT
ejpam-4694	271	27	,	,	PUNCT
ejpam-4694	271	28	ϕα+1(x	ϕα+1(x	PROPN
ejpam-4694	271	29	)	)	PUNCT
ejpam-4694	271	30	,	,	PUNCT
ejpam-4694	271	31	.	.	PUNCT
ejpam-4694	271	32	.	.	PUNCT
ejpam-4694	271	33	.	.	PUNCT
ejpam-4694	272	1	,	,	PUNCT
ejpam-4694	272	2	ϕs(x	ϕs(x	PUNCT
ejpam-4694	272	3	)	)	PUNCT
ejpam-4694	272	4	be	be	VERB
ejpam-4694	272	5	the	the	DET
ejpam-4694	272	6	orthogonal	orthogonal	ADJ
ejpam-4694	272	7	version	version	NOUN
ejpam-4694	272	8	of	of	ADP
ejpam-4694	272	9	of	of	ADP
ejpam-4694	272	10	poly	poly	ADJ
ejpam-4694	272	11	-	-	PUNCT
ejpam-4694	272	12	genocchi	genocchi	NOUN
ejpam-4694	272	13	polynomials	polynomial	NOUN
ejpam-4694	272	14	obtained	obtain	VERB
ejpam-4694	272	15	from	from	ADP
ejpam-4694	272	16	gram	gram	NOUN
ejpam-4694	272	17	-	-	PUNCT
ejpam-4694	272	18	schmidt	schmidt	NOUN
ejpam-4694	272	19	process	process	NOUN
ejpam-4694	272	20	in	in	ADP
ejpam-4694	272	21	which	which	PRON
ejpam-4694	272	22	the	the	DET
ejpam-4694	272	23	polynomial	polynomial	NOUN
ejpam-4694	272	24	is	be	AUX
ejpam-4694	272	25	orthogonal	orthogonal	ADJ
ejpam-4694	272	26	with	with	ADP
ejpam-4694	272	27	respect	respect	NOUN
ejpam-4694	272	28	to	to	ADP
ejpam-4694	272	29	the	the	DET
ejpam-4694	272	30	inner	inner	ADJ
ejpam-4694	272	31	product	product	NOUN
ejpam-4694	272	32	<	<	X
ejpam-4694	272	33	f	f	X
ejpam-4694	272	34	,	,	PUNCT
ejpam-4694	272	35	g	g	PROPN
ejpam-4694	272	36	>	>	X
ejpam-4694	272	37	=	=	PUNCT
ejpam-4694	273	1	∫	∫	PROPN
ejpam-4694	273	2	1	1	NUM
ejpam-4694	273	3	0	0	NUM
ejpam-4694	273	4	w(x)f(x)g(x)dx	w(x)f(x)g(x)dx	NOUN
ejpam-4694	273	5	.	.	PUNCT
ejpam-4694	274	1	then	then	ADV
ejpam-4694	274	2	ϕs+1	ϕs+1	NOUN
ejpam-4694	274	3	=	=	SYM
ejpam-4694	274	4	ĝ(k	ĝ(k	X
ejpam-4694	274	5	,	,	PUNCT
ejpam-4694	274	6	α	α	NOUN
ejpam-4694	274	7	)	)	PUNCT
ejpam-4694	274	8	s+1	s+1	NOUN
ejpam-4694	274	9	(	(	PUNCT
ejpam-4694	274	10	x;λ	x;λ	PROPN
ejpam-4694	274	11	,	,	PUNCT
ejpam-4694	274	12	ρ	ρ	PROPN
ejpam-4694	274	13	,	,	PUNCT
ejpam-4694	274	14	u	u	NOUN
ejpam-4694	274	15	,	,	PUNCT
ejpam-4694	274	16	a	a	PRON
ejpam-4694	274	17	,	,	PUNCT
ejpam-4694	274	18	b)−	b)−	PROPN
ejpam-4694	274	19	s∑	s∑	PROPN
ejpam-4694	274	20	i=1	i=1	PROPN
ejpam-4694	274	21	λiϕi(x	λiϕi(x	PROPN
ejpam-4694	274	22	)	)	PUNCT
ejpam-4694	274	23	(	(	PUNCT
ejpam-4694	274	24	43	43	NUM
ejpam-4694	274	25	)	)	PUNCT
ejpam-4694	274	26	satisfies	satisfy	VERB
ejpam-4694	274	27	<	<	X
ejpam-4694	274	28	ϕs+1	ϕs+1	NOUN
ejpam-4694	274	29	,	,	PUNCT
ejpam-4694	274	30	ϕj	ϕj	INTJ
ejpam-4694	274	31	>	>	X
ejpam-4694	274	32	=	=	PUNCT
ejpam-4694	275	1	∫	∫	PROPN
ejpam-4694	275	2	1	1	NUM
ejpam-4694	275	3	0	0	NUM
ejpam-4694	275	4	w(x)ϕs+1(x)ϕjdx	w(x)ϕs+1(x)ϕjdx	PROPN
ejpam-4694	275	5	=	=	SYM
ejpam-4694	275	6	0	0	PROPN
ejpam-4694	275	7	,	,	PUNCT
ejpam-4694	275	8	j	j	PROPN
ejpam-4694	275	9	=	=	SYM
ejpam-4694	275	10	0	0	NUM
ejpam-4694	275	11	,	,	PUNCT
ejpam-4694	275	12	1	1	NUM
ejpam-4694	275	13	,	,	PUNCT
ejpam-4694	275	14	.	.	PUNCT
ejpam-4694	275	15	.	.	PUNCT
ejpam-4694	276	1	.	.	PUNCT
ejpam-4694	277	1	,	,	PUNCT
ejpam-4694	277	2	s	s	VERB
ejpam-4694	277	3	with	with	ADP
ejpam-4694	277	4	λj	λj	PROPN
ejpam-4694	277	5	=	=	X
ejpam-4694	277	6	<	<	X
ejpam-4694	277	7	ĝ(k	ĝ(k	X
ejpam-4694	277	8	,	,	PUNCT
ejpam-4694	277	9	α	α	NOUN
ejpam-4694	277	10	)	)	PUNCT
ejpam-4694	277	11	s+1	s+1	NOUN
ejpam-4694	277	12	(	(	PUNCT
ejpam-4694	277	13	x;λ	x;λ	PROPN
ejpam-4694	277	14	,	,	PUNCT
ejpam-4694	277	15	ρ	ρ	PROPN
ejpam-4694	277	16	,	,	PUNCT
ejpam-4694	277	17	u	u	NOUN
ejpam-4694	277	18	,	,	PUNCT
ejpam-4694	277	19	a	a	DET
ejpam-4694	277	20	,	,	PUNCT
ejpam-4694	277	21	b	b	NOUN
ejpam-4694	277	22	)	)	PUNCT
ejpam-4694	277	23	,	,	PUNCT
ejpam-4694	277	24	ϕj	ϕj	ADP
ejpam-4694	277	25	>	>	X
ejpam-4694	277	26	<	<	X
ejpam-4694	277	27	ϕj	ϕj	INTJ
ejpam-4694	277	28	,	,	PUNCT
ejpam-4694	277	29	ϕj	ϕj	INTJ
ejpam-4694	277	30	>	>	X
ejpam-4694	277	31	.	.	PUNCT
ejpam-4694	278	1	clearly	clearly	ADV
ejpam-4694	278	2	,	,	PUNCT
ejpam-4694	278	3	ϕi(x	ϕi(x	PROPN
ejpam-4694	278	4	)	)	PUNCT
ejpam-4694	278	5	=	=	PUNCT
ejpam-4694	278	6	0	0	PUNCT
ejpam-4694	278	7	when	when	SCONJ
ejpam-4694	278	8	0	0	NUM
ejpam-4694	278	9	≤	≤	NUM
ejpam-4694	278	10	i	i	PRON
ejpam-4694	278	11	≤	≤	NOUN
ejpam-4694	278	12	α−	α−	ADP
ejpam-4694	278	13	1	1	NUM
ejpam-4694	278	14	and	and	CCONJ
ejpam-4694	278	15	ϕα(x	ϕα(x	PUNCT
ejpam-4694	278	16	)	)	PUNCT
ejpam-4694	278	17	=	=	SYM
ejpam-4694	279	1	1	1	X
ejpam-4694	279	2	.	.	PUNCT
ejpam-4694	279	3	then	then	ADV
ejpam-4694	279	4	,	,	PUNCT
ejpam-4694	279	5	ϕα+1(x	ϕα+1(x	PROPN
ejpam-4694	279	6	)	)	PUNCT
ejpam-4694	279	7	=	=	PUNCT
ejpam-4694	279	8	ĝ(k	ĝ(k	X
ejpam-4694	279	9	,	,	PUNCT
ejpam-4694	279	10	α	α	NOUN
ejpam-4694	279	11	)	)	PUNCT
ejpam-4694	279	12	α+1	α+1	NUM
ejpam-4694	279	13	(	(	PUNCT
ejpam-4694	279	14	x;λ	x;λ	PROPN
ejpam-4694	279	15	,	,	PUNCT
ejpam-4694	279	16	ρ	ρ	PROPN
ejpam-4694	279	17	,	,	PUNCT
ejpam-4694	279	18	u	u	NOUN
ejpam-4694	279	19	,	,	PUNCT
ejpam-4694	279	20	a	a	PRON
ejpam-4694	279	21	,	,	PUNCT
ejpam-4694	279	22	b)−	b)−	PROPN
ejpam-4694	279	23	α∑	α∑	NUM
ejpam-4694	279	24	i=1	i=1	NUM
ejpam-4694	279	25	λiϕi(x	λiϕi(x	PROPN
ejpam-4694	279	26	)	)	PUNCT
ejpam-4694	279	27	=	=	SYM
ejpam-4694	279	28	α+1∑	α+1∑	PROPN
ejpam-4694	279	29	j=0	j=0	PROPN
ejpam-4694	279	30	ĝ(k	ĝ(k	PROPN
ejpam-4694	279	31	,	,	PUNCT
ejpam-4694	279	32	α	α	NOUN
ejpam-4694	279	33	)	)	PUNCT
ejpam-4694	279	34	α+1,j	α+1,j	NOUN
ejpam-4694	279	35	,	,	PUNCT
ejpam-4694	279	36	w̃(λ	w̃(λ	PROPN
ejpam-4694	279	37	,	,	PUNCT
ejpam-4694	279	38	ρ	ρ	PROPN
ejpam-4694	279	39	,	,	PUNCT
ejpam-4694	279	40	u	u	NOUN
ejpam-4694	279	41	,	,	PUNCT
ejpam-4694	279	42	a	a	PRON
ejpam-4694	279	43	,	,	PUNCT
ejpam-4694	279	44	b)x	b)x	X
ejpam-4694	279	45	j	j	PROPN
ejpam-4694	279	46	−	−	PROPN
ejpam-4694	279	47	∫	∫	PROPN
ejpam-4694	279	48	1	1	NUM
ejpam-4694	279	49	0	0	X
ejpam-4694	279	50	∑α+1	∑α+1	PRON
ejpam-4694	279	51	j=0	j=0	PROPN
ejpam-4694	279	52	ĝ(k	ĝ(k	PROPN
ejpam-4694	279	53	,	,	PUNCT
ejpam-4694	279	54	α	α	NOUN
ejpam-4694	279	55	)	)	PUNCT
ejpam-4694	279	56	α+1,j	α+1,j	NOUN
ejpam-4694	279	57	,	,	PUNCT
ejpam-4694	279	58	w̃(λ	w̃(λ	PROPN
ejpam-4694	279	59	,	,	PUNCT
ejpam-4694	279	60	ρ	ρ	PROPN
ejpam-4694	279	61	,	,	PUNCT
ejpam-4694	279	62	u	u	NOUN
ejpam-4694	279	63	,	,	PUNCT
ejpam-4694	279	64	a	a	PRON
ejpam-4694	279	65	,	,	PUNCT
ejpam-4694	279	66	b)x	b)x	X
ejpam-4694	279	67	jϕα(x)dx∫	jϕα(x)dx∫	PROPN
ejpam-4694	279	68	1	1	NUM
ejpam-4694	279	69	0	0	NUM
ejpam-4694	279	70	(	(	PUNCT
ejpam-4694	279	71	ϕα(x))2dx	ϕα(x))2dx	PROPN
ejpam-4694	279	72	ϕα(x	ϕα(x	PUNCT
ejpam-4694	279	73	)	)	PUNCT
ejpam-4694	280	1	=	=	SYM
ejpam-4694	280	2	α+1∑	α+1∑	PROPN
ejpam-4694	280	3	j=0	j=0	PROPN
ejpam-4694	280	4	ĝ(k	ĝ(k	PROPN
ejpam-4694	280	5	,	,	PUNCT
ejpam-4694	280	6	α	α	NOUN
ejpam-4694	280	7	)	)	PUNCT
ejpam-4694	280	8	α+1,j	α+1,j	NOUN
ejpam-4694	280	9	,	,	PUNCT
ejpam-4694	280	10	w̃(λ	w̃(λ	PROPN
ejpam-4694	280	11	,	,	PUNCT
ejpam-4694	280	12	ρ	ρ	PROPN
ejpam-4694	280	13	,	,	PUNCT
ejpam-4694	280	14	u	u	NOUN
ejpam-4694	280	15	,	,	PUNCT
ejpam-4694	280	16	a	a	DET
ejpam-4694	280	17	,	,	PUNCT
ejpam-4694	280	18	b	b	NOUN
ejpam-4694	280	19	)	)	PUNCT
ejpam-4694	280	20	(	(	PUNCT
ejpam-4694	280	21	xj	xj	PROPN
ejpam-4694	280	22	−	−	PROPN
ejpam-4694	280	23	1	1	NUM
ejpam-4694	280	24	j	j	PROPN
ejpam-4694	280	25	+	+	CCONJ
ejpam-4694	280	26	1	1	X
ejpam-4694	280	27	)	)	PUNCT
ejpam-4694	280	28	r.	r.	PROPN
ejpam-4694	280	29	corcino	corcino	PROPN
ejpam-4694	280	30	,	,	PUNCT
ejpam-4694	280	31	c.	c.	PROPN
ejpam-4694	280	32	corcino	corcino	PROPN
ejpam-4694	280	33	/	/	SYM
ejpam-4694	280	34	eur	eur	PROPN
ejpam-4694	280	35	.	.	PUNCT
ejpam-4694	281	1	j.	j.	PROPN
ejpam-4694	281	2	pure	pure	PROPN
ejpam-4694	281	3	appl	appl	PROPN
ejpam-4694	281	4	.	.	PROPN
ejpam-4694	281	5	math	math	PROPN
ejpam-4694	281	6	,	,	PUNCT
ejpam-4694	281	7	16	16	NUM
ejpam-4694	281	8	(	(	PUNCT
ejpam-4694	281	9	2	2	NUM
ejpam-4694	281	10	)	)	PUNCT
ejpam-4694	281	11	(	(	PUNCT
ejpam-4694	281	12	2023	2023	NUM
ejpam-4694	281	13	)	)	PUNCT
ejpam-4694	281	14	,	,	PUNCT
ejpam-4694	281	15	687	687	NUM
ejpam-4694	281	16	-	-	SYM
ejpam-4694	281	17	712	712	NUM
ejpam-4694	281	18	700	700	NUM
ejpam-4694	281	19	=	=	SYM
ejpam-4694	281	20	ĝ(k	ĝ(k	X
ejpam-4694	281	21	,	,	PUNCT
ejpam-4694	281	22	α	α	NOUN
ejpam-4694	281	23	)	)	PUNCT
ejpam-4694	281	24	α+1,0,w̃(λ	α+1,0,w̃(λ	NOUN
ejpam-4694	281	25	,	,	PUNCT
ejpam-4694	281	26	ρ	ρ	PROPN
ejpam-4694	281	27	,	,	PUNCT
ejpam-4694	281	28	u	u	NOUN
ejpam-4694	281	29	,	,	PUNCT
ejpam-4694	281	30	a	a	DET
ejpam-4694	281	31	,	,	PUNCT
ejpam-4694	281	32	b	b	NOUN
ejpam-4694	281	33	)	)	PUNCT
ejpam-4694	281	34	(	(	PUNCT
ejpam-4694	281	35	x−	x−	PROPN
ejpam-4694	281	36	1	1	NUM
ejpam-4694	281	37	2	2	NUM
ejpam-4694	281	38	)	)	PUNCT
ejpam-4694	281	39	+	+	CCONJ
ejpam-4694	281	40	ĝ(k	ĝ(k	PRON
ejpam-4694	281	41	,	,	PUNCT
ejpam-4694	281	42	α	α	NOUN
ejpam-4694	281	43	)	)	PUNCT
ejpam-4694	281	44	α+1,1,w̃(λ	α+1,1,w̃(λ	NOUN
ejpam-4694	281	45	,	,	PUNCT
ejpam-4694	281	46	ρ	ρ	PROPN
ejpam-4694	281	47	,	,	PUNCT
ejpam-4694	281	48	u	u	NOUN
ejpam-4694	281	49	,	,	PUNCT
ejpam-4694	281	50	a	a	DET
ejpam-4694	281	51	,	,	PUNCT
ejpam-4694	281	52	b	b	NOUN
ejpam-4694	281	53	)	)	PUNCT
ejpam-4694	281	54	(	(	PUNCT
ejpam-4694	282	1	x2	x2	INTJ
ejpam-4694	282	2	−	−	PROPN
ejpam-4694	282	3	1	1	NUM
ejpam-4694	282	4	3	3	NUM
ejpam-4694	282	5	)	)	PUNCT
ejpam-4694	282	6	=	=	SYM
ejpam-4694	282	7	2	2	NUM
ejpam-4694	282	8	(	(	PUNCT
ejpam-4694	282	9	x−	x−	PROPN
ejpam-4694	282	10	1	1	NUM
ejpam-4694	282	11	2	2	NUM
ejpam-4694	282	12	)	)	PUNCT
ejpam-4694	282	13	.	.	PUNCT
ejpam-4694	283	1	ϕ3(x	ϕ3(x	X
ejpam-4694	283	2	)	)	PUNCT
ejpam-4694	283	3	=	=	SYM
ejpam-4694	283	4	ĝ(k	ĝ(k	X
ejpam-4694	283	5	,	,	PUNCT
ejpam-4694	283	6	α	α	NOUN
ejpam-4694	283	7	)	)	PUNCT
ejpam-4694	283	8	3	3	NUM
ejpam-4694	283	9	(	(	PUNCT
ejpam-4694	283	10	x;λ	x;λ	PROPN
ejpam-4694	283	11	,	,	PUNCT
ejpam-4694	283	12	ρ	ρ	PROPN
ejpam-4694	283	13	,	,	PUNCT
ejpam-4694	283	14	u	u	NOUN
ejpam-4694	283	15	,	,	PUNCT
ejpam-4694	283	16	a	a	PRON
ejpam-4694	283	17	,	,	PUNCT
ejpam-4694	283	18	b)−	b)−	PROPN
ejpam-4694	283	19	2∑	2∑	NUM
ejpam-4694	283	20	i=1	i=1	NUM
ejpam-4694	283	21	λiϕi(x	λiϕi(x	NOUN
ejpam-4694	283	22	)	)	PUNCT
ejpam-4694	283	23	=	=	PUNCT
ejpam-4694	284	1	3∑	3∑	NUM
ejpam-4694	284	2	j=0	j=0	PROPN
ejpam-4694	284	3	ĝ(k	ĝ(k	PRON
ejpam-4694	284	4	,	,	PUNCT
ejpam-4694	284	5	α	α	NOUN
ejpam-4694	284	6	)	)	PUNCT
ejpam-4694	284	7	3,j	3,j	NUM
ejpam-4694	284	8	,	,	PUNCT
ejpam-4694	284	9	w̃	w̃	PROPN
ejpam-4694	284	10	(	(	PUNCT
ejpam-4694	284	11	λ	λ	PROPN
ejpam-4694	284	12	,	,	PUNCT
ejpam-4694	284	13	ρ	ρ	PROPN
ejpam-4694	284	14	,	,	PUNCT
ejpam-4694	284	15	u	u	NOUN
ejpam-4694	284	16	,	,	PUNCT
ejpam-4694	284	17	a	a	PRON
ejpam-4694	284	18	,	,	PUNCT
ejpam-4694	284	19	b)x	b)x	X
ejpam-4694	284	20	j	j	PROPN
ejpam-4694	285	1	−	−	PROPN
ejpam-4694	285	2	∫	∫	PROPN
ejpam-4694	285	3	1	1	NUM
ejpam-4694	285	4	0	0	NUM
ejpam-4694	285	5	∑3	∑3	PROPN
ejpam-4694	285	6	j=0	j=0	X
ejpam-4694	285	7	ĝ	ĝ	X
ejpam-4694	285	8	(	(	PUNCT
ejpam-4694	285	9	k	k	X
ejpam-4694	285	10	,	,	PUNCT
ejpam-4694	285	11	α	α	NOUN
ejpam-4694	285	12	)	)	PUNCT
ejpam-4694	285	13	3,j	3,j	NUM
ejpam-4694	285	14	,	,	PUNCT
ejpam-4694	285	15	w̃	w̃	PROPN
ejpam-4694	285	16	(	(	PUNCT
ejpam-4694	285	17	λ	λ	PROPN
ejpam-4694	285	18	,	,	PUNCT
ejpam-4694	285	19	ρ	ρ	PROPN
ejpam-4694	285	20	,	,	PUNCT
ejpam-4694	285	21	u	u	NOUN
ejpam-4694	285	22	,	,	PUNCT
ejpam-4694	285	23	a	a	PRON
ejpam-4694	285	24	,	,	PUNCT
ejpam-4694	285	25	b)x	b)x	X
ejpam-4694	285	26	jϕ2(x)dx∫	jϕ2(x)dx∫	PROPN
ejpam-4694	285	27	1	1	NUM
ejpam-4694	285	28	0	0	NUM
ejpam-4694	285	29	(	(	PUNCT
ejpam-4694	285	30	ϕ2(x))2dx	ϕ2(x))2dx	PROPN
ejpam-4694	285	31	ϕ2(x	ϕ2(x	PROPN
ejpam-4694	285	32	)	)	PUNCT
ejpam-4694	286	1	−	−	NOUN
ejpam-4694	287	1	∫	∫	PROPN
ejpam-4694	287	2	1	1	NUM
ejpam-4694	287	3	0	0	NUM
ejpam-4694	287	4	∑3	∑3	PROPN
ejpam-4694	287	5	j=0	j=0	X
ejpam-4694	287	6	ĝ	ĝ	X
ejpam-4694	287	7	(	(	PUNCT
ejpam-4694	287	8	k	k	X
ejpam-4694	287	9	,	,	PUNCT
ejpam-4694	287	10	α	α	NOUN
ejpam-4694	287	11	)	)	PUNCT
ejpam-4694	287	12	3,j	3,j	NUM
ejpam-4694	287	13	,	,	PUNCT
ejpam-4694	287	14	w̃	w̃	PROPN
ejpam-4694	287	15	(	(	PUNCT
ejpam-4694	287	16	λ	λ	PROPN
ejpam-4694	287	17	,	,	PUNCT
ejpam-4694	287	18	ρ	ρ	PROPN
ejpam-4694	287	19	,	,	PUNCT
ejpam-4694	287	20	u	u	NOUN
ejpam-4694	287	21	,	,	PUNCT
ejpam-4694	287	22	a	a	PRON
ejpam-4694	287	23	,	,	PUNCT
ejpam-4694	287	24	b)x	b)x	X
ejpam-4694	287	25	jϕ1(x)dx∫	jϕ1(x)dx∫	PROPN
ejpam-4694	287	26	1	1	NUM
ejpam-4694	287	27	0	0	NUM
ejpam-4694	287	28	(	(	PUNCT
ejpam-4694	287	29	ϕ1(x))2dx	ϕ1(x))2dx	NOUN
ejpam-4694	287	30	ϕ1(x	ϕ1(x	NOUN
ejpam-4694	287	31	)	)	PUNCT
ejpam-4694	287	32	=	=	SYM
ejpam-4694	288	1	3∑	3∑	NUM
ejpam-4694	288	2	j=0	j=0	PROPN
ejpam-4694	288	3	ĝ(k	ĝ(k	PRON
ejpam-4694	288	4	,	,	PUNCT
ejpam-4694	288	5	α	α	NOUN
ejpam-4694	288	6	)	)	PUNCT
ejpam-4694	288	7	3,j	3,j	NUM
ejpam-4694	288	8	,	,	PUNCT
ejpam-4694	288	9	w̃	w̃	PROPN
ejpam-4694	288	10	(	(	PUNCT
ejpam-4694	288	11	λ	λ	PROPN
ejpam-4694	288	12	,	,	PUNCT
ejpam-4694	288	13	ρ	ρ	PROPN
ejpam-4694	288	14	,	,	PUNCT
ejpam-4694	288	15	u	u	NOUN
ejpam-4694	288	16	,	,	PUNCT
ejpam-4694	288	17	a	a	DET
ejpam-4694	288	18	,	,	PUNCT
ejpam-4694	288	19	b	b	NOUN
ejpam-4694	288	20	)	)	PUNCT
ejpam-4694	288	21	(	(	PUNCT
ejpam-4694	288	22	xj	xj	PROPN
ejpam-4694	288	23	−	−	PROPN
ejpam-4694	288	24	3j(2x−	3j(2x−	NUM
ejpam-4694	288	25	1	1	NUM
ejpam-4694	288	26	)	)	PUNCT
ejpam-4694	288	27	(	(	PUNCT
ejpam-4694	288	28	j	j	PROPN
ejpam-4694	288	29	+	+	NOUN
ejpam-4694	288	30	2)(j	2)(j	NUM
ejpam-4694	288	31	+	+	CCONJ
ejpam-4694	288	32	1	1	NUM
ejpam-4694	288	33	)	)	PUNCT
ejpam-4694	288	34	−	−	PROPN
ejpam-4694	288	35	1	1	NUM
ejpam-4694	288	36	j	j	NOUN
ejpam-4694	288	37	+	+	NOUN
ejpam-4694	288	38	1	1	NUM
ejpam-4694	288	39	)	)	PUNCT
ejpam-4694	288	40	=	=	SYM
ejpam-4694	288	41	ĝ(k	ĝ(k	X
ejpam-4694	288	42	,	,	PUNCT
ejpam-4694	288	43	α	α	NOUN
ejpam-4694	288	44	)	)	PUNCT
ejpam-4694	288	45	3,1,w̃(λ	3,1,w̃(λ	NUM
ejpam-4694	288	46	,	,	PUNCT
ejpam-4694	288	47	ρ	ρ	PROPN
ejpam-4694	288	48	,	,	PUNCT
ejpam-4694	288	49	u	u	NOUN
ejpam-4694	288	50	,	,	PUNCT
ejpam-4694	288	51	a	a	DET
ejpam-4694	288	52	,	,	PUNCT
ejpam-4694	288	53	b	b	NOUN
ejpam-4694	288	54	)	)	PUNCT
ejpam-4694	288	55	(	(	PUNCT
ejpam-4694	288	56	x−	x−	PROPN
ejpam-4694	288	57	2x−	2x−	NUM
ejpam-4694	288	58	1	1	NUM
ejpam-4694	288	59	2	2	NUM
ejpam-4694	288	60	−	−	NUM
ejpam-4694	288	61	1	1	NUM
ejpam-4694	288	62	2	2	NUM
ejpam-4694	288	63	)	)	PUNCT
ejpam-4694	288	64	+	+	CCONJ
ejpam-4694	288	65	ĝ(k	ĝ(k	X
ejpam-4694	288	66	,	,	PUNCT
ejpam-4694	288	67	α	α	NOUN
ejpam-4694	288	68	)	)	PUNCT
ejpam-4694	288	69	3,2,w̃(λ	3,2,w̃(λ	NUM
ejpam-4694	288	70	,	,	PUNCT
ejpam-4694	288	71	ρ	ρ	PROPN
ejpam-4694	288	72	,	,	PUNCT
ejpam-4694	288	73	u	u	NOUN
ejpam-4694	288	74	,	,	PUNCT
ejpam-4694	288	75	a	a	DET
ejpam-4694	288	76	,	,	PUNCT
ejpam-4694	288	77	b	b	NOUN
ejpam-4694	288	78	)	)	PUNCT
ejpam-4694	288	79	(	(	PUNCT
ejpam-4694	289	1	x2	x2	INTJ
ejpam-4694	289	2	−	−	PROPN
ejpam-4694	289	3	2x−	2x−	NUM
ejpam-4694	289	4	1	1	NUM
ejpam-4694	289	5	2	2	NUM
ejpam-4694	289	6	−	−	NUM
ejpam-4694	289	7	1	1	NUM
ejpam-4694	289	8	3	3	NUM
ejpam-4694	289	9	)	)	PUNCT
ejpam-4694	289	10	=	=	SYM
ejpam-4694	289	11	ĝ(k	ĝ(k	X
ejpam-4694	289	12	,	,	PUNCT
ejpam-4694	289	13	α	α	NOUN
ejpam-4694	289	14	)	)	PUNCT
ejpam-4694	289	15	3,2,w̃(λ	3,2,w̃(λ	NUM
ejpam-4694	289	16	,	,	PUNCT
ejpam-4694	289	17	ρ	ρ	PROPN
ejpam-4694	289	18	,	,	PUNCT
ejpam-4694	289	19	u	u	NOUN
ejpam-4694	289	20	,	,	PUNCT
ejpam-4694	289	21	a	a	DET
ejpam-4694	289	22	,	,	PUNCT
ejpam-4694	289	23	b	b	NOUN
ejpam-4694	289	24	)	)	PUNCT
ejpam-4694	289	25	(	(	PUNCT
ejpam-4694	289	26	x2	x2	INTJ
ejpam-4694	289	27	−	−	PROPN
ejpam-4694	289	28	x+	x+	PUNCT
ejpam-4694	289	29	1	1	NUM
ejpam-4694	289	30	6	6	NUM
ejpam-4694	289	31	)	)	PUNCT
ejpam-4694	289	32	=	=	SYM
ejpam-4694	289	33	3x2	3x2	NUM
ejpam-4694	289	34	−	−	NOUN
ejpam-4694	289	35	3x+	3x+	NUM
ejpam-4694	289	36	1	1	NUM
ejpam-4694	289	37	2	2	NUM
ejpam-4694	289	38	ϕ4(x	ϕ4(x	NUM
ejpam-4694	289	39	)	)	PUNCT
ejpam-4694	289	40	=	=	SYM
ejpam-4694	289	41	ĝ(k	ĝ(k	X
ejpam-4694	289	42	,	,	PUNCT
ejpam-4694	289	43	α	α	NOUN
ejpam-4694	289	44	)	)	PUNCT
ejpam-4694	289	45	4	4	NUM
ejpam-4694	289	46	(	(	PUNCT
ejpam-4694	289	47	x;λ	x;λ	PROPN
ejpam-4694	289	48	,	,	PUNCT
ejpam-4694	289	49	ρ	ρ	PROPN
ejpam-4694	289	50	,	,	PUNCT
ejpam-4694	289	51	u	u	NOUN
ejpam-4694	289	52	,	,	PUNCT
ejpam-4694	289	53	a	a	PRON
ejpam-4694	289	54	,	,	PUNCT
ejpam-4694	289	55	b)−	b)−	PROPN
ejpam-4694	289	56	3∑	3∑	NUM
ejpam-4694	289	57	i=1	i=1	NUM
ejpam-4694	289	58	λiϕi(x	λiϕi(x	PROPN
ejpam-4694	289	59	)	)	PUNCT
ejpam-4694	289	60	=	=	SYM
ejpam-4694	289	61	4∑	4∑	NUM
ejpam-4694	289	62	j=0	j=0	PROPN
ejpam-4694	289	63	ĝ(k	ĝ(k	PROPN
ejpam-4694	289	64	,	,	PUNCT
ejpam-4694	289	65	α	α	NOUN
ejpam-4694	289	66	)	)	PUNCT
ejpam-4694	289	67	4,j	4,j	NUM
ejpam-4694	289	68	,	,	PUNCT
ejpam-4694	289	69	w̃	w̃	PROPN
ejpam-4694	289	70	(	(	PUNCT
ejpam-4694	289	71	λ	λ	PROPN
ejpam-4694	289	72	,	,	PUNCT
ejpam-4694	289	73	ρ	ρ	PROPN
ejpam-4694	289	74	,	,	PUNCT
ejpam-4694	289	75	u	u	NOUN
ejpam-4694	289	76	,	,	PUNCT
ejpam-4694	289	77	a	a	PRON
ejpam-4694	289	78	,	,	PUNCT
ejpam-4694	289	79	b)x	b)x	X
ejpam-4694	289	80	j	j	PROPN
ejpam-4694	290	1	−	−	PROPN
ejpam-4694	290	2	∫	∫	PROPN
ejpam-4694	290	3	1	1	NUM
ejpam-4694	290	4	0	0	NUM
ejpam-4694	290	5	∑4	∑4	PROPN
ejpam-4694	290	6	j=0	j=0	PROPN
ejpam-4694	290	7	ĝ	ĝ	X
ejpam-4694	290	8	(	(	PUNCT
ejpam-4694	290	9	k	k	X
ejpam-4694	290	10	,	,	PUNCT
ejpam-4694	290	11	α	α	NOUN
ejpam-4694	290	12	)	)	PUNCT
ejpam-4694	290	13	4,j	4,j	NUM
ejpam-4694	290	14	,	,	PUNCT
ejpam-4694	290	15	w̃	w̃	PROPN
ejpam-4694	290	16	(	(	PUNCT
ejpam-4694	290	17	λ	λ	PROPN
ejpam-4694	290	18	,	,	PUNCT
ejpam-4694	290	19	ρ	ρ	PROPN
ejpam-4694	290	20	,	,	PUNCT
ejpam-4694	290	21	u	u	NOUN
ejpam-4694	290	22	,	,	PUNCT
ejpam-4694	290	23	a	a	PRON
ejpam-4694	290	24	,	,	PUNCT
ejpam-4694	290	25	b)x	b)x	X
ejpam-4694	290	26	jϕ3(x)dx∫	jϕ3(x)dx∫	PROPN
ejpam-4694	291	1	1	1	NUM
ejpam-4694	291	2	0	0	NUM
ejpam-4694	291	3	(	(	PUNCT
ejpam-4694	291	4	ϕ3(x))2dx	ϕ3(x))2dx	PROPN
ejpam-4694	291	5	ϕ3(x	ϕ3(x	PROPN
ejpam-4694	291	6	)	)	PUNCT
ejpam-4694	291	7	−	−	PROPN
ejpam-4694	291	8	∫	∫	PROPN
ejpam-4694	291	9	2	2	NUM
ejpam-4694	291	10	0	0	NUM
ejpam-4694	291	11	∑4	∑4	PROPN
ejpam-4694	291	12	j=0	j=0	PROPN
ejpam-4694	291	13	ĝ	ĝ	X
ejpam-4694	291	14	(	(	PUNCT
ejpam-4694	291	15	k	k	X
ejpam-4694	291	16	,	,	PUNCT
ejpam-4694	291	17	α	α	NOUN
ejpam-4694	291	18	)	)	PUNCT
ejpam-4694	291	19	4,j	4,j	NUM
ejpam-4694	291	20	,	,	PUNCT
ejpam-4694	291	21	w̃	w̃	PROPN
ejpam-4694	291	22	(	(	PUNCT
ejpam-4694	291	23	λ	λ	PROPN
ejpam-4694	291	24	,	,	PUNCT
ejpam-4694	291	25	ρ	ρ	PROPN
ejpam-4694	291	26	,	,	PUNCT
ejpam-4694	291	27	u	u	NOUN
ejpam-4694	291	28	,	,	PUNCT
ejpam-4694	291	29	a	a	PRON
ejpam-4694	291	30	,	,	PUNCT
ejpam-4694	291	31	b)x	b)x	X
ejpam-4694	291	32	jϕ2(x)dx∫	jϕ2(x)dx∫	PROPN
ejpam-4694	291	33	1	1	NUM
ejpam-4694	291	34	0	0	NUM
ejpam-4694	292	1	(	(	PUNCT
ejpam-4694	292	2	ϕ2(x))2dx	ϕ2(x))2dx	PROPN
ejpam-4694	292	3	ϕ2(x)−	ϕ2(x)−	PROPN
ejpam-4694	292	4	∫	∫	PROPN
ejpam-4694	292	5	2	2	NUM
ejpam-4694	292	6	0	0	NUM
ejpam-4694	292	7	∑4	∑4	PROPN
ejpam-4694	292	8	j=0	j=0	PROPN
ejpam-4694	292	9	ĝ	ĝ	X
ejpam-4694	292	10	(	(	PUNCT
ejpam-4694	292	11	k	k	X
ejpam-4694	292	12	,	,	PUNCT
ejpam-4694	292	13	α	α	NOUN
ejpam-4694	292	14	)	)	PUNCT
ejpam-4694	292	15	4,j	4,j	NUM
ejpam-4694	292	16	,	,	PUNCT
ejpam-4694	292	17	w̃	w̃	PROPN
ejpam-4694	292	18	(	(	PUNCT
ejpam-4694	292	19	λ	λ	PROPN
ejpam-4694	292	20	,	,	PUNCT
ejpam-4694	292	21	ρ	ρ	PROPN
ejpam-4694	292	22	,	,	PUNCT
ejpam-4694	292	23	u	u	NOUN
ejpam-4694	292	24	,	,	PUNCT
ejpam-4694	292	25	a	a	PRON
ejpam-4694	292	26	,	,	PUNCT
ejpam-4694	292	27	b)x	b)x	X
ejpam-4694	292	28	jϕ1(x)dx∫	jϕ1(x)dx∫	PROPN
ejpam-4694	293	1	1	1	NUM
ejpam-4694	293	2	0	0	NUM
ejpam-4694	293	3	(	(	PUNCT
ejpam-4694	293	4	ϕ1(x))2dx	ϕ1(x))2dx	NOUN
ejpam-4694	293	5	ϕ1(x	ϕ1(x	NOUN
ejpam-4694	293	6	)	)	PUNCT
ejpam-4694	293	7	=	=	SYM
ejpam-4694	293	8	4∑	4∑	NUM
ejpam-4694	293	9	j=0	j=0	PROPN
ejpam-4694	293	10	ĝ(k	ĝ(k	PROPN
ejpam-4694	293	11	,	,	PUNCT
ejpam-4694	293	12	α	α	NOUN
ejpam-4694	293	13	)	)	PUNCT
ejpam-4694	293	14	4,j	4,j	NUM
ejpam-4694	293	15	,	,	PUNCT
ejpam-4694	293	16	w̃	w̃	PROPN
ejpam-4694	293	17	(	(	PUNCT
ejpam-4694	293	18	λ	λ	PROPN
ejpam-4694	293	19	,	,	PUNCT
ejpam-4694	293	20	ρ	ρ	PROPN
ejpam-4694	293	21	,	,	PUNCT
ejpam-4694	293	22	u	u	NOUN
ejpam-4694	293	23	,	,	PUNCT
ejpam-4694	293	24	a	a	DET
ejpam-4694	293	25	,	,	PUNCT
ejpam-4694	293	26	b	b	NOUN
ejpam-4694	293	27	)	)	PUNCT
ejpam-4694	293	28	(	(	PUNCT
ejpam-4694	293	29	xj	xj	PROPN
ejpam-4694	293	30	−	−	PROPN
ejpam-4694	293	31	9(20)j(j	9(20)j(j	NUM
ejpam-4694	294	1	−	−	NOUN
ejpam-4694	294	2	1	1	NUM
ejpam-4694	294	3	)	)	PUNCT
ejpam-4694	294	4	(	(	PUNCT
ejpam-4694	294	5	x2	x2	INTJ
ejpam-4694	294	6	−	−	PROPN
ejpam-4694	294	7	x+	x+	PUNCT
ejpam-4694	294	8	1	1	NUM
ejpam-4694	294	9	6	6	NUM
ejpam-4694	294	10	)	)	PUNCT
ejpam-4694	294	11	6(j	6(j	NUM
ejpam-4694	295	1	+	+	CCONJ
ejpam-4694	295	2	3)(j	3)(j	NUM
ejpam-4694	295	3	+	+	NUM
ejpam-4694	295	4	2)(j	2)(j	NUM
ejpam-4694	295	5	+	+	CCONJ
ejpam-4694	295	6	1	1	NUM
ejpam-4694	295	7	)	)	PUNCT
ejpam-4694	295	8	−	−	PROPN
ejpam-4694	295	9	3j(2x−	3j(2x−	NUM
ejpam-4694	295	10	1	1	NUM
ejpam-4694	295	11	)	)	PUNCT
ejpam-4694	295	12	(	(	PUNCT
ejpam-4694	295	13	j	j	PROPN
ejpam-4694	296	1	+	+	NOUN
ejpam-4694	296	2	2)(j	2)(j	NUM
ejpam-4694	296	3	+	+	CCONJ
ejpam-4694	296	4	1	1	NUM
ejpam-4694	296	5	)	)	PUNCT
ejpam-4694	296	6	−	−	PROPN
ejpam-4694	296	7	1	1	NUM
ejpam-4694	296	8	j	j	NOUN
ejpam-4694	296	9	+	+	NOUN
ejpam-4694	296	10	1	1	NUM
ejpam-4694	296	11	)	)	PUNCT
ejpam-4694	296	12	=	=	SYM
ejpam-4694	296	13	ĝ(k	ĝ(k	X
ejpam-4694	296	14	,	,	PUNCT
ejpam-4694	296	15	α	α	NOUN
ejpam-4694	296	16	)	)	PUNCT
ejpam-4694	296	17	4,3,w̃(λ	4,3,w̃(λ	NUM
ejpam-4694	296	18	,	,	PUNCT
ejpam-4694	296	19	ρ	ρ	PROPN
ejpam-4694	296	20	,	,	PUNCT
ejpam-4694	296	21	u	u	NOUN
ejpam-4694	296	22	,	,	PUNCT
ejpam-4694	296	23	a	a	DET
ejpam-4694	296	24	,	,	PUNCT
ejpam-4694	296	25	b	b	NOUN
ejpam-4694	296	26	)	)	PUNCT
ejpam-4694	296	27	(	(	PUNCT
ejpam-4694	296	28	x3	x3	ADV
ejpam-4694	296	29	−	−	PROPN
ejpam-4694	296	30	3	3	NUM
ejpam-4694	296	31	2	2	NUM
ejpam-4694	296	32	x2	x2	NOUN
ejpam-4694	296	33	+	+	CCONJ
ejpam-4694	296	34	3	3	NUM
ejpam-4694	296	35	5	5	NUM
ejpam-4694	296	36	x−	x−	PROPN
ejpam-4694	296	37	1	1	NUM
ejpam-4694	296	38	20	20	NUM
ejpam-4694	296	39	)	)	PUNCT
ejpam-4694	296	40	=	=	SYM
ejpam-4694	296	41	4x3	4x3	NUM
ejpam-4694	296	42	−	−	NUM
ejpam-4694	296	43	6x2	6x2	NUM
ejpam-4694	296	44	+	+	CCONJ
ejpam-4694	296	45	12	12	NUM
ejpam-4694	296	46	5	5	NUM
ejpam-4694	296	47	x−	x−	PROPN
ejpam-4694	296	48	1	1	NUM
ejpam-4694	296	49	5	5	NUM
ejpam-4694	296	50	the	the	DET
ejpam-4694	296	51	next	next	ADJ
ejpam-4694	296	52	identity	identity	NOUN
ejpam-4694	296	53	gives	give	VERB
ejpam-4694	296	54	the	the	DET
ejpam-4694	296	55	relation	relation	NOUN
ejpam-4694	296	56	between	between	ADP
ejpam-4694	296	57	ĝ(k	ĝ(k	PROPN
ejpam-4694	296	58	,	,	PUNCT
ejpam-4694	296	59	α	α	NOUN
ejpam-4694	296	60	)	)	PUNCT
ejpam-4694	296	61	n	n	CCONJ
ejpam-4694	296	62	(	(	PUNCT
ejpam-4694	296	63	x;λ	x;λ	PROPN
ejpam-4694	296	64	,	,	PUNCT
ejpam-4694	296	65	ρ	ρ	PROPN
ejpam-4694	296	66	,	,	PUNCT
ejpam-4694	296	67	u	u	NOUN
ejpam-4694	296	68	,	,	PUNCT
ejpam-4694	296	69	a	a	DET
ejpam-4694	296	70	,	,	PUNCT
ejpam-4694	296	71	b	b	NOUN
ejpam-4694	296	72	)	)	PUNCT
ejpam-4694	296	73	and	and	CCONJ
ejpam-4694	296	74	ĝ(k	ĝ(k	PRON
ejpam-4694	296	75	,	,	PUNCT
ejpam-4694	296	76	α	α	NOUN
ejpam-4694	296	77	)	)	PUNCT
ejpam-4694	296	78	n	n	CCONJ
ejpam-4694	296	79	(	(	PUNCT
ejpam-4694	296	80	x;λ	x;λ	PROPN
ejpam-4694	296	81	,	,	PUNCT
ejpam-4694	296	82	ρ	ρ	PROPN
ejpam-4694	296	83	,	,	PUNCT
ejpam-4694	296	84	u	u	NOUN
ejpam-4694	296	85	)	)	PUNCT
ejpam-4694	296	86	.	.	PUNCT
ejpam-4694	297	1	r.	r.	PROPN
ejpam-4694	297	2	corcino	corcino	PROPN
ejpam-4694	297	3	,	,	PUNCT
ejpam-4694	297	4	c.	c.	PROPN
ejpam-4694	297	5	corcino	corcino	PROPN
ejpam-4694	297	6	/	/	SYM
ejpam-4694	297	7	eur	eur	PROPN
ejpam-4694	297	8	.	.	PUNCT
ejpam-4694	298	1	j.	j.	PROPN
ejpam-4694	298	2	pure	pure	PROPN
ejpam-4694	298	3	appl	appl	PROPN
ejpam-4694	298	4	.	.	PROPN
ejpam-4694	298	5	math	math	PROPN
ejpam-4694	298	6	,	,	PUNCT
ejpam-4694	298	7	16	16	NUM
ejpam-4694	298	8	(	(	PUNCT
ejpam-4694	298	9	2	2	NUM
ejpam-4694	298	10	)	)	PUNCT
ejpam-4694	298	11	(	(	PUNCT
ejpam-4694	298	12	2023	2023	NUM
ejpam-4694	298	13	)	)	PUNCT
ejpam-4694	298	14	,	,	PUNCT
ejpam-4694	298	15	687	687	NUM
ejpam-4694	298	16	-	-	SYM
ejpam-4694	298	17	712	712	NUM
ejpam-4694	298	18	701	701	NUM
ejpam-4694	298	19	theorem	theorem	NOUN
ejpam-4694	298	20	3.2	3.2	NUM
ejpam-4694	298	21	.	.	PUNCT
ejpam-4694	299	1	the	the	DET
ejpam-4694	299	2	degenerate	degenerate	ADJ
ejpam-4694	299	3	apostol	apostol	NOUN
ejpam-4694	299	4	-	-	PUNCT
ejpam-4694	299	5	frobenius	frobenius	NOUN
ejpam-4694	299	6	-	-	PUNCT
ejpam-4694	299	7	type	type	NOUN
ejpam-4694	299	8	poly	poly	ADJ
ejpam-4694	299	9	-	-	PUNCT
ejpam-4694	299	10	genocchi	genocchi	NOUN
ejpam-4694	299	11	polynomials	polynomial	NOUN
ejpam-4694	299	12	of	of	ADP
ejpam-4694	299	13	higher	high	ADJ
ejpam-4694	299	14	order	order	NOUN
ejpam-4694	299	15	with	with	ADP
ejpam-4694	299	16	parameters	parameter	NOUN
ejpam-4694	299	17	a	a	PRON
ejpam-4694	299	18	and	and	CCONJ
ejpam-4694	299	19	b	b	NOUN
ejpam-4694	299	20	satisfy	satisfy	VERB
ejpam-4694	299	21	the	the	DET
ejpam-4694	299	22	relation	relation	NOUN
ejpam-4694	299	23	,	,	PUNCT
ejpam-4694	299	24	ĝ(k	ĝ(k	PRON
ejpam-4694	299	25	,	,	PUNCT
ejpam-4694	299	26	α	α	NOUN
ejpam-4694	299	27	)	)	PUNCT
ejpam-4694	299	28	n	n	CCONJ
ejpam-4694	299	29	(	(	PUNCT
ejpam-4694	299	30	x;λ	x;λ	PROPN
ejpam-4694	299	31	,	,	PUNCT
ejpam-4694	299	32	ρ	ρ	PROPN
ejpam-4694	299	33	,	,	PUNCT
ejpam-4694	299	34	u	u	NOUN
ejpam-4694	299	35	,	,	PUNCT
ejpam-4694	299	36	a	a	DET
ejpam-4694	299	37	,	,	PUNCT
ejpam-4694	299	38	b	b	NOUN
ejpam-4694	299	39	)	)	PUNCT
ejpam-4694	299	40	=	=	SYM
ejpam-4694	300	1	n∑	n∑	PROPN
ejpam-4694	300	2	m=0	m=0	PROPN
ejpam-4694	300	3	(	(	PUNCT
ejpam-4694	300	4	n	n	NOUN
ejpam-4694	300	5	m	m	VERB
ejpam-4694	300	6	)	)	PUNCT
ejpam-4694	300	7	(	(	PUNCT
ejpam-4694	300	8	ln	ln	ADJ
ejpam-4694	300	9	a)m(ln	a)m(ln	PROPN
ejpam-4694	300	10	ab)n−mĝ(k	ab)n−mĝ(k	PROPN
ejpam-4694	300	11	,	,	PUNCT
ejpam-4694	300	12	α	α	NOUN
ejpam-4694	300	13	)	)	PUNCT
ejpam-4694	300	14	n−m	n−m	PROPN
ejpam-4694	300	15	(	(	PUNCT
ejpam-4694	300	16	x	x	X
ejpam-4694	300	17	ln	ln	NOUN
ejpam-4694	300	18	ab	ab	PROPN
ejpam-4694	300	19	;	;	PUNCT
ejpam-4694	300	20	λ	λ	PROPN
ejpam-4694	300	21	,	,	PUNCT
ejpam-4694	300	22	ρ	ρ	PROPN
ejpam-4694	300	23	,	,	PUNCT
ejpam-4694	300	24	u	u	NOUN
ejpam-4694	300	25	)	)	PUNCT
ejpam-4694	300	26	.	.	PUNCT
ejpam-4694	301	1	(	(	PUNCT
ejpam-4694	301	2	44	44	NUM
ejpam-4694	301	3	)	)	PUNCT
ejpam-4694	301	4	proof	proof	NOUN
ejpam-4694	301	5	.	.	PUNCT
ejpam-4694	302	1	using	use	VERB
ejpam-4694	302	2	(	(	PUNCT
ejpam-4694	302	3	34	34	NUM
ejpam-4694	302	4	)	)	PUNCT
ejpam-4694	302	5	,	,	PUNCT
ejpam-4694	302	6	we	we	PRON
ejpam-4694	302	7	can	can	AUX
ejpam-4694	302	8	rewrite	rewrite	VERB
ejpam-4694	302	9	(	(	PUNCT
ejpam-4694	302	10	27	27	NUM
ejpam-4694	302	11	)	)	PUNCT
ejpam-4694	302	12	as	as	SCONJ
ejpam-4694	302	13	follows	follow	VERB
ejpam-4694	302	14	∞∑	∞∑	NUM
ejpam-4694	302	15	n=0	n=0	NUM
ejpam-4694	302	16	ĝ(k	ĝ(k	PROPN
ejpam-4694	302	17	,	,	PUNCT
ejpam-4694	302	18	α	α	NOUN
ejpam-4694	302	19	)	)	PUNCT
ejpam-4694	302	20	n	n	CCONJ
ejpam-4694	302	21	(	(	PUNCT
ejpam-4694	302	22	x;λ	x;λ	PROPN
ejpam-4694	302	23	,	,	PUNCT
ejpam-4694	302	24	ρ	ρ	PROPN
ejpam-4694	302	25	,	,	PUNCT
ejpam-4694	302	26	u	u	NOUN
ejpam-4694	302	27	,	,	PUNCT
ejpam-4694	302	28	a	a	DET
ejpam-4694	302	29	,	,	PUNCT
ejpam-4694	302	30	b	b	NOUN
ejpam-4694	302	31	)	)	PUNCT
ejpam-4694	302	32	tn	tn	NOUN
ejpam-4694	302	33	n	n	NOUN
ejpam-4694	302	34	!	!	PUNCT
ejpam-4694	303	1	=	=	PRON
ejpam-4694	303	2	(	(	PUNCT
ejpam-4694	303	3	eik	eik	PROPN
ejpam-4694	303	4	,	,	PUNCT
ejpam-4694	303	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	303	6	+	+	CCONJ
ejpam-4694	303	7	(	(	PUNCT
ejpam-4694	303	8	1−	1−	NUM
ejpam-4694	303	9	u)t	u)t	X
ejpam-4694	303	10	ln	ln	PROPN
ejpam-4694	303	11	ab	ab	PROPN
ejpam-4694	303	12	)	)	PUNCT
ejpam-4694	303	13	)	)	PUNCT
ejpam-4694	303	14	a−t(λ(ab)t	a−t(λ(ab)t	PROPN
ejpam-4694	303	15	−	−	PROPN
ejpam-4694	303	16	u	u	NOUN
ejpam-4694	303	17	)	)	PUNCT
ejpam-4694	303	18	)	)	PUNCT
ejpam-4694	304	1	α	α	PRON
ejpam-4694	304	2	ex	ex	X
ejpam-4694	304	3	ln	ln	NOUN
ejpam-4694	304	4	ab	ab	PROPN
ejpam-4694	304	5	ρ	ρ	PROPN
ejpam-4694	304	6	ln	ln	X
ejpam-4694	304	7	ab(t	ab(t	X
ejpam-4694	304	8	ln	ln	PROPN
ejpam-4694	304	9	ab	ab	PROPN
ejpam-4694	304	10	)	)	PUNCT
ejpam-4694	304	11	=	=	SYM
ejpam-4694	304	12	aαt	aαt	PROPN
ejpam-4694	304	13	(	(	PUNCT
ejpam-4694	304	14	eik	eik	PROPN
ejpam-4694	304	15	,	,	PUNCT
ejpam-4694	304	16	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	305	1	+	+	CCONJ
ejpam-4694	306	1	(	(	PUNCT
ejpam-4694	306	2	1−	1−	NUM
ejpam-4694	306	3	u)t	u)t	X
ejpam-4694	306	4	ln	ln	PROPN
ejpam-4694	306	5	ab	ab	PROPN
ejpam-4694	306	6	)	)	PUNCT
ejpam-4694	306	7	)	)	PUNCT
ejpam-4694	307	1	λet	λet	PRON
ejpam-4694	307	2	ln	ln	INTJ
ejpam-4694	307	3	ab	ab	PROPN
ejpam-4694	307	4	−	−	PROPN
ejpam-4694	307	5	u	u	PROPN
ejpam-4694	307	6	)	)	PUNCT
ejpam-4694	307	7	α	α	PROPN
ejpam-4694	307	8	ex	ex	X
ejpam-4694	307	9	ln	ln	NOUN
ejpam-4694	307	10	ab	ab	PROPN
ejpam-4694	307	11	ρ	ρ	PROPN
ejpam-4694	307	12	ln	ln	X
ejpam-4694	307	13	ab(t	ab(t	X
ejpam-4694	307	14	ln	ln	PROPN
ejpam-4694	307	15	ab	ab	PROPN
ejpam-4694	307	16	)	)	PUNCT
ejpam-4694	307	17	=	=	PUNCT
ejpam-4694	308	1	(	(	PUNCT
ejpam-4694	308	2	∞∑	∞∑	NUM
ejpam-4694	308	3	n=0	n=0	NUM
ejpam-4694	308	4	(	(	PUNCT
ejpam-4694	308	5	ln	ln	ADJ
ejpam-4694	308	6	ab)nĝ(k	ab)nĝ(k	PROPN
ejpam-4694	308	7	,	,	PUNCT
ejpam-4694	308	8	α	α	NOUN
ejpam-4694	308	9	)	)	PUNCT
ejpam-4694	308	10	n	n	PROPN
ejpam-4694	308	11	(	(	PUNCT
ejpam-4694	308	12	x	x	X
ejpam-4694	308	13	ln	ln	NOUN
ejpam-4694	308	14	ab	ab	PROPN
ejpam-4694	308	15	;	;	PUNCT
ejpam-4694	308	16	λ	λ	PROPN
ejpam-4694	308	17	,	,	PUNCT
ejpam-4694	308	18	ρ	ρ	PROPN
ejpam-4694	308	19	,	,	PUNCT
ejpam-4694	308	20	u	u	NOUN
ejpam-4694	308	21	)	)	PUNCT
ejpam-4694	308	22	tn	tn	PROPN
ejpam-4694	308	23	n	n	PROPN
ejpam-4694	308	24	!	!	PUNCT
ejpam-4694	308	25	)	)	PUNCT
ejpam-4694	309	1	(	(	PUNCT
ejpam-4694	309	2	∞∑	∞∑	NUM
ejpam-4694	309	3	n=0	n=0	NUM
ejpam-4694	309	4	(	(	PUNCT
ejpam-4694	309	5	t	t	PROPN
ejpam-4694	309	6	ln	ln	PROPN
ejpam-4694	309	7	a)n	a)n	PROPN
ejpam-4694	309	8	n	n	CCONJ
ejpam-4694	309	9	!	!	PUNCT
ejpam-4694	309	10	)	)	PUNCT
ejpam-4694	310	1	=	=	PUNCT
ejpam-4694	311	1	∞∑	∞∑	NUM
ejpam-4694	311	2	n=0	n=0	NUM
ejpam-4694	311	3	n∑	n∑	NOUN
ejpam-4694	311	4	m=0	m=0	PROPN
ejpam-4694	311	5	(	(	PUNCT
ejpam-4694	311	6	n	n	NOUN
ejpam-4694	311	7	m	m	VERB
ejpam-4694	311	8	)	)	PUNCT
ejpam-4694	311	9	(	(	PUNCT
ejpam-4694	311	10	ln	ln	ADJ
ejpam-4694	311	11	a)m(ln	a)m(ln	PROPN
ejpam-4694	311	12	ab)n−mĝ(k	ab)n−mĝ(k	PROPN
ejpam-4694	311	13	,	,	PUNCT
ejpam-4694	311	14	α	α	NOUN
ejpam-4694	311	15	)	)	PUNCT
ejpam-4694	311	16	n−m	n−m	PROPN
ejpam-4694	311	17	(	(	PUNCT
ejpam-4694	311	18	x	x	X
ejpam-4694	311	19	ln	ln	NOUN
ejpam-4694	311	20	ab	ab	PROPN
ejpam-4694	311	21	;	;	PUNCT
ejpam-4694	311	22	λ	λ	PROPN
ejpam-4694	311	23	,	,	PUNCT
ejpam-4694	311	24	ρ	ρ	PROPN
ejpam-4694	311	25	,	,	PUNCT
ejpam-4694	311	26	u	u	NOUN
ejpam-4694	311	27	)	)	PUNCT
ejpam-4694	311	28	tn	tn	PROPN
ejpam-4694	311	29	n	n	PROPN
ejpam-4694	311	30	!	!	PUNCT
ejpam-4694	311	31	comparing	compare	VERB
ejpam-4694	311	32	the	the	DET
ejpam-4694	311	33	coefficients	coefficient	NOUN
ejpam-4694	311	34	of	of	ADP
ejpam-4694	311	35	tn	tn	NOUN
ejpam-4694	311	36	n	n	CCONJ
ejpam-4694	311	37	!	!	PROPN
ejpam-4694	312	1	,	,	PUNCT
ejpam-4694	312	2	we	we	PRON
ejpam-4694	312	3	obtain	obtain	VERB
ejpam-4694	312	4	the	the	DET
ejpam-4694	312	5	desired	desire	VERB
ejpam-4694	312	6	result	result	NOUN
ejpam-4694	312	7	.	.	PUNCT
ejpam-4694	313	1	the	the	DET
ejpam-4694	313	2	next	next	ADJ
ejpam-4694	313	3	result	result	NOUN
ejpam-4694	313	4	is	be	AUX
ejpam-4694	313	5	another	another	DET
ejpam-4694	313	6	form	form	NOUN
ejpam-4694	313	7	of	of	ADP
ejpam-4694	313	8	addition	addition	NOUN
ejpam-4694	313	9	formula	formula	NOUN
ejpam-4694	313	10	for	for	ADP
ejpam-4694	313	11	ĝ(k	ĝ(k	PRON
ejpam-4694	313	12	,	,	PUNCT
ejpam-4694	313	13	α	α	NOUN
ejpam-4694	313	14	)	)	PUNCT
ejpam-4694	313	15	n	n	CCONJ
ejpam-4694	313	16	(	(	PUNCT
ejpam-4694	313	17	x;λ	x;λ	PROPN
ejpam-4694	313	18	,	,	PUNCT
ejpam-4694	313	19	ρ	ρ	PROPN
ejpam-4694	313	20	,	,	PUNCT
ejpam-4694	313	21	u	u	NOUN
ejpam-4694	313	22	,	,	PUNCT
ejpam-4694	313	23	a	a	DET
ejpam-4694	313	24	,	,	PUNCT
ejpam-4694	313	25	b	b	NOUN
ejpam-4694	313	26	)	)	PUNCT
ejpam-4694	313	27	.	.	PUNCT
ejpam-4694	314	1	theorem	theorem	VERB
ejpam-4694	314	2	3.3	3.3	NUM
ejpam-4694	314	3	.	.	PUNCT
ejpam-4694	315	1	the	the	DET
ejpam-4694	315	2	degenerate	degenerate	ADJ
ejpam-4694	315	3	apostol	apostol	NOUN
ejpam-4694	315	4	-	-	PUNCT
ejpam-4694	315	5	frobenius	frobenius	NOUN
ejpam-4694	315	6	-	-	PUNCT
ejpam-4694	315	7	type	type	NOUN
ejpam-4694	315	8	poly	poly	ADJ
ejpam-4694	315	9	-	-	PUNCT
ejpam-4694	315	10	genocchi	genocchi	NOUN
ejpam-4694	315	11	polynomials	polynomial	NOUN
ejpam-4694	315	12	of	of	ADP
ejpam-4694	315	13	higher	high	ADJ
ejpam-4694	315	14	order	order	NOUN
ejpam-4694	315	15	with	with	ADP
ejpam-4694	315	16	parameters	parameter	NOUN
ejpam-4694	315	17	a	a	PRON
ejpam-4694	315	18	and	and	CCONJ
ejpam-4694	315	19	b	b	NOUN
ejpam-4694	315	20	satisfy	satisfy	VERB
ejpam-4694	315	21	the	the	DET
ejpam-4694	315	22	relation	relation	NOUN
ejpam-4694	315	23	ĝ(k	ĝ(k	PROPN
ejpam-4694	315	24	,	,	PUNCT
ejpam-4694	315	25	α	α	NOUN
ejpam-4694	315	26	)	)	PUNCT
ejpam-4694	315	27	n	n	CCONJ
ejpam-4694	315	28	(	(	PUNCT
ejpam-4694	315	29	x+	x+	PROPN
ejpam-4694	315	30	y;λ	y;λ	PROPN
ejpam-4694	315	31	,	,	PUNCT
ejpam-4694	315	32	ρ	ρ	PROPN
ejpam-4694	315	33	,	,	PUNCT
ejpam-4694	315	34	u	u	NOUN
ejpam-4694	315	35	,	,	PUNCT
ejpam-4694	315	36	a	a	DET
ejpam-4694	315	37	,	,	PUNCT
ejpam-4694	315	38	b	b	NOUN
ejpam-4694	315	39	)	)	PUNCT
ejpam-4694	315	40	=	=	SYM
ejpam-4694	316	1	n∑	n∑	PROPN
ejpam-4694	316	2	m=0	m=0	PROPN
ejpam-4694	316	3	(	(	PUNCT
ejpam-4694	316	4	n	n	NOUN
ejpam-4694	316	5	m	m	VERB
ejpam-4694	316	6	)	)	PUNCT
ejpam-4694	316	7	ĝ(k	ĝ(k	X
ejpam-4694	316	8	,	,	PUNCT
ejpam-4694	316	9	α	α	NOUN
ejpam-4694	316	10	)	)	PUNCT
ejpam-4694	316	11	n−m(x;λ	n−m(x;λ	PROPN
ejpam-4694	316	12	,	,	PUNCT
ejpam-4694	316	13	ρ	ρ	PROPN
ejpam-4694	316	14	,	,	PUNCT
ejpam-4694	316	15	u	u	NOUN
ejpam-4694	316	16	,	,	PUNCT
ejpam-4694	316	17	a	a	PRON
ejpam-4694	316	18	,	,	PUNCT
ejpam-4694	316	19	b)(y)m	b)(y)m	PROPN
ejpam-4694	316	20	,	,	PUNCT
ejpam-4694	316	21	ρ	ρ	NOUN
ejpam-4694	316	22	.	.	PUNCT
ejpam-4694	316	23	proof	proof	NOUN
ejpam-4694	316	24	.	.	PUNCT
ejpam-4694	317	1	we	we	PRON
ejpam-4694	317	2	can	can	AUX
ejpam-4694	317	3	write	write	VERB
ejpam-4694	317	4	(	(	PUNCT
ejpam-4694	317	5	27	27	NUM
ejpam-4694	317	6	)	)	PUNCT
ejpam-4694	317	7	as	as	SCONJ
ejpam-4694	317	8	follows	follow	VERB
ejpam-4694	317	9	:	:	PUNCT
ejpam-4694	317	10	∞∑	∞∑	NUM
ejpam-4694	317	11	n=0	n=0	NUM
ejpam-4694	317	12	ĝ(k	ĝ(k	PROPN
ejpam-4694	317	13	,	,	PUNCT
ejpam-4694	317	14	α	α	NOUN
ejpam-4694	317	15	)	)	PUNCT
ejpam-4694	317	16	n	n	CCONJ
ejpam-4694	317	17	(	(	PUNCT
ejpam-4694	317	18	x+	x+	PROPN
ejpam-4694	317	19	y;λ	y;λ	PROPN
ejpam-4694	317	20	,	,	PUNCT
ejpam-4694	317	21	ρ	ρ	PROPN
ejpam-4694	317	22	,	,	PUNCT
ejpam-4694	317	23	u	u	NOUN
ejpam-4694	317	24	,	,	PUNCT
ejpam-4694	317	25	a	a	DET
ejpam-4694	317	26	,	,	PUNCT
ejpam-4694	317	27	b	b	NOUN
ejpam-4694	317	28	)	)	PUNCT
ejpam-4694	317	29	tn	tn	NOUN
ejpam-4694	317	30	n	n	NOUN
ejpam-4694	317	31	!	!	PUNCT
ejpam-4694	318	1	=	=	PRON
ejpam-4694	318	2	(	(	PUNCT
ejpam-4694	318	3	eik	eik	PROPN
ejpam-4694	318	4	,	,	PUNCT
ejpam-4694	318	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	318	6	+	+	CCONJ
ejpam-4694	318	7	(	(	PUNCT
ejpam-4694	318	8	1−	1−	NUM
ejpam-4694	318	9	u)t	u)t	X
ejpam-4694	318	10	ln	ln	PROPN
ejpam-4694	318	11	ab	ab	PROPN
ejpam-4694	318	12	)	)	PUNCT
ejpam-4694	318	13	)	)	PUNCT
ejpam-4694	319	1	λbt	λbt	VERB
ejpam-4694	319	2	−	−	PROPN
ejpam-4694	319	3	ua−t	ua−t	NOUN
ejpam-4694	319	4	)	)	PUNCT
ejpam-4694	319	5	α	α	PROPN
ejpam-4694	319	6	ex+y	ex+y	PROPN
ejpam-4694	319	7	ρ	ρ	PROPN
ejpam-4694	319	8	(	(	PUNCT
ejpam-4694	319	9	t	t	PROPN
ejpam-4694	319	10	)	)	PUNCT
ejpam-4694	319	11	=	=	PRON
ejpam-4694	319	12	(	(	PUNCT
ejpam-4694	319	13	eik	eik	PROPN
ejpam-4694	319	14	,	,	PUNCT
ejpam-4694	319	15	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	320	1	+	+	CCONJ
ejpam-4694	321	1	(	(	PUNCT
ejpam-4694	321	2	1−	1−	NUM
ejpam-4694	321	3	u)t	u)t	X
ejpam-4694	321	4	ln	ln	PROPN
ejpam-4694	321	5	ab	ab	PROPN
ejpam-4694	321	6	)	)	PUNCT
ejpam-4694	321	7	)	)	PUNCT
ejpam-4694	322	1	λbt	λbt	VERB
ejpam-4694	322	2	−	−	PROPN
ejpam-4694	322	3	ua−t	ua−t	INTJ
ejpam-4694	322	4	)	)	PUNCT
ejpam-4694	322	5	α	α	PRON
ejpam-4694	322	6	exρ(t)e	exρ(t)e	NOUN
ejpam-4694	322	7	y	y	PROPN
ejpam-4694	322	8	ρ(t	ρ(t	NUM
ejpam-4694	322	9	)	)	PUNCT
ejpam-4694	323	1	=	=	PRON
ejpam-4694	323	2	(	(	PUNCT
ejpam-4694	323	3	∞∑	∞∑	PRON
ejpam-4694	323	4	n=0	n=0	NUM
ejpam-4694	323	5	ĝ(k	ĝ(k	PROPN
ejpam-4694	323	6	,	,	PUNCT
ejpam-4694	323	7	α	α	NOUN
ejpam-4694	323	8	)	)	PUNCT
ejpam-4694	323	9	n	n	CCONJ
ejpam-4694	323	10	(	(	PUNCT
ejpam-4694	323	11	x;λ	x;λ	PROPN
ejpam-4694	323	12	,	,	PUNCT
ejpam-4694	323	13	ρ	ρ	PROPN
ejpam-4694	323	14	,	,	PUNCT
ejpam-4694	323	15	u	u	NOUN
ejpam-4694	323	16	,	,	PUNCT
ejpam-4694	323	17	a	a	DET
ejpam-4694	323	18	,	,	PUNCT
ejpam-4694	323	19	b	b	NOUN
ejpam-4694	323	20	)	)	PUNCT
ejpam-4694	323	21	tn	tn	PROPN
ejpam-4694	323	22	n	n	CCONJ
ejpam-4694	323	23	!	!	PUNCT
ejpam-4694	323	24	)	)	PUNCT
ejpam-4694	324	1	(	(	PUNCT
ejpam-4694	324	2	∞∑	∞∑	NUM
ejpam-4694	324	3	n=0	n=0	NUM
ejpam-4694	324	4	(	(	PUNCT
ejpam-4694	324	5	y)n	y)n	NUM
ejpam-4694	324	6	,	,	PUNCT
ejpam-4694	324	7	ρ	ρ	PROPN
ejpam-4694	324	8	tn	tn	PROPN
ejpam-4694	324	9	n	n	X
ejpam-4694	324	10	!	!	PUNCT
ejpam-4694	324	11	)	)	PUNCT
ejpam-4694	325	1	=	=	PUNCT
ejpam-4694	326	1	∞∑	∞∑	NUM
ejpam-4694	326	2	n=0	n=0	NUM
ejpam-4694	326	3	(	(	PUNCT
ejpam-4694	326	4	n∑	n∑	PROPN
ejpam-4694	326	5	m=0	m=0	PROPN
ejpam-4694	326	6	(	(	PUNCT
ejpam-4694	326	7	n	n	NOUN
ejpam-4694	326	8	m	m	VERB
ejpam-4694	326	9	)	)	PUNCT
ejpam-4694	327	1	ĝ(k	ĝ(k	X
ejpam-4694	327	2	,	,	PUNCT
ejpam-4694	327	3	α	α	NOUN
ejpam-4694	327	4	)	)	PUNCT
ejpam-4694	327	5	n−m(x;λ	n−m(x;λ	PROPN
ejpam-4694	327	6	,	,	PUNCT
ejpam-4694	327	7	ρ	ρ	PROPN
ejpam-4694	327	8	,	,	PUNCT
ejpam-4694	327	9	u	u	NOUN
ejpam-4694	327	10	,	,	PUNCT
ejpam-4694	327	11	a	a	PRON
ejpam-4694	327	12	,	,	PUNCT
ejpam-4694	327	13	b)(y)m	b)(y)m	PROPN
ejpam-4694	327	14	,	,	PUNCT
ejpam-4694	327	15	ρ	ρ	PROPN
ejpam-4694	327	16	)	)	PUNCT
ejpam-4694	327	17	tn	tn	PROPN
ejpam-4694	327	18	n	n	PROPN
ejpam-4694	327	19	!	!	PUNCT
ejpam-4694	327	20	.	.	PUNCT
ejpam-4694	328	1	comparing	compare	VERB
ejpam-4694	328	2	the	the	DET
ejpam-4694	328	3	coefficients	coefficient	NOUN
ejpam-4694	328	4	of	of	ADP
ejpam-4694	328	5	tn	tn	NOUN
ejpam-4694	328	6	n	n	ADP
ejpam-4694	328	7	!	!	PROPN
ejpam-4694	328	8	completes	complete	VERB
ejpam-4694	328	9	the	the	DET
ejpam-4694	328	10	proof	proof	NOUN
ejpam-4694	328	11	of	of	ADP
ejpam-4694	328	12	the	the	DET
ejpam-4694	328	13	theorem	theorem	PROPN
ejpam-4694	328	14	.	.	PROPN
ejpam-4694	328	15	r.	r.	PROPN
ejpam-4694	328	16	corcino	corcino	PROPN
ejpam-4694	328	17	,	,	PUNCT
ejpam-4694	328	18	c.	c.	PROPN
ejpam-4694	328	19	corcino	corcino	PROPN
ejpam-4694	328	20	/	/	SYM
ejpam-4694	328	21	eur	eur	PROPN
ejpam-4694	328	22	.	.	PUNCT
ejpam-4694	329	1	j.	j.	PROPN
ejpam-4694	329	2	pure	pure	PROPN
ejpam-4694	329	3	appl	appl	PROPN
ejpam-4694	329	4	.	.	PROPN
ejpam-4694	329	5	math	math	PROPN
ejpam-4694	329	6	,	,	PUNCT
ejpam-4694	329	7	16	16	NUM
ejpam-4694	329	8	(	(	PUNCT
ejpam-4694	329	9	2	2	NUM
ejpam-4694	329	10	)	)	PUNCT
ejpam-4694	329	11	(	(	PUNCT
ejpam-4694	329	12	2023	2023	NUM
ejpam-4694	329	13	)	)	PUNCT
ejpam-4694	329	14	,	,	PUNCT
ejpam-4694	329	15	687	687	NUM
ejpam-4694	329	16	-	-	SYM
ejpam-4694	329	17	712	712	NUM
ejpam-4694	329	18	702	702	NUM
ejpam-4694	329	19	4	4	NUM
ejpam-4694	329	20	.	.	PUNCT
ejpam-4694	329	21	differential	differential	ADJ
ejpam-4694	329	22	and	and	CCONJ
ejpam-4694	329	23	integral	integral	ADJ
ejpam-4694	329	24	formulas	formula	NOUN
ejpam-4694	329	25	in	in	ADP
ejpam-4694	329	26	the	the	DET
ejpam-4694	329	27	following	following	NOUN
ejpam-4694	329	28	theorem	theorem	ADJ
ejpam-4694	329	29	,	,	PUNCT
ejpam-4694	329	30	certain	certain	ADJ
ejpam-4694	329	31	differential	differential	ADJ
ejpam-4694	329	32	equation	equation	NOUN
ejpam-4694	329	33	will	will	AUX
ejpam-4694	329	34	be	be	AUX
ejpam-4694	329	35	established	establish	VERB
ejpam-4694	329	36	containing	contain	VERB
ejpam-4694	329	37	the	the	DET
ejpam-4694	329	38	degenerate	degenerate	ADJ
ejpam-4694	329	39	apostol	apostol	NOUN
ejpam-4694	329	40	-	-	PUNCT
ejpam-4694	329	41	type	type	NOUN
ejpam-4694	329	42	poly	poly	ADJ
ejpam-4694	329	43	-	-	PUNCT
ejpam-4694	329	44	genocchi	genocchi	NOUN
ejpam-4694	329	45	polynomials	polynomial	NOUN
ejpam-4694	329	46	of	of	ADP
ejpam-4694	329	47	higher	high	ADJ
ejpam-4694	329	48	order	order	NOUN
ejpam-4694	329	49	with	with	ADP
ejpam-4694	329	50	parameters	parameter	NOUN
ejpam-4694	329	51	a	a	PRON
ejpam-4694	329	52	and	and	CCONJ
ejpam-4694	329	53	b.	b.	PROPN
ejpam-4694	329	54	here	here	ADV
ejpam-4694	329	55	,	,	PUNCT
ejpam-4694	329	56	we	we	PRON
ejpam-4694	329	57	consider	consider	VERB
ejpam-4694	329	58	ĝ(k	ĝ(k	PRON
ejpam-4694	329	59	,	,	PUNCT
ejpam-4694	329	60	α	α	NOUN
ejpam-4694	329	61	)	)	PUNCT
ejpam-4694	329	62	n	n	CCONJ
ejpam-4694	329	63	(	(	PUNCT
ejpam-4694	329	64	x;λ	x;λ	PROPN
ejpam-4694	329	65	,	,	PUNCT
ejpam-4694	329	66	ρ	ρ	PROPN
ejpam-4694	329	67	,	,	PUNCT
ejpam-4694	329	68	u	u	NOUN
ejpam-4694	329	69	,	,	PUNCT
ejpam-4694	329	70	a	a	DET
ejpam-4694	329	71	,	,	PUNCT
ejpam-4694	329	72	b	b	NOUN
ejpam-4694	329	73	)	)	PUNCT
ejpam-4694	329	74	as	as	ADV
ejpam-4694	329	75	polynomial	polynomial	ADJ
ejpam-4694	329	76	in	in	ADP
ejpam-4694	329	77	x.	x.	PROPN
ejpam-4694	329	78	theorem	theorem	VERB
ejpam-4694	329	79	4.1	4.1	NUM
ejpam-4694	329	80	.	.	PUNCT
ejpam-4694	330	1	the	the	DET
ejpam-4694	330	2	degenerate	degenerate	ADJ
ejpam-4694	330	3	apostol	apostol	NOUN
ejpam-4694	330	4	-	-	PUNCT
ejpam-4694	330	5	frobenius	frobenius	NOUN
ejpam-4694	330	6	-	-	PUNCT
ejpam-4694	330	7	type	type	NOUN
ejpam-4694	330	8	poly	poly	ADJ
ejpam-4694	330	9	-	-	PUNCT
ejpam-4694	330	10	genocchi	genocchi	NOUN
ejpam-4694	330	11	polynomials	polynomial	NOUN
ejpam-4694	330	12	with	with	ADP
ejpam-4694	330	13	parameters	parameter	NOUN
ejpam-4694	330	14	a	a	PRON
ejpam-4694	330	15	and	and	CCONJ
ejpam-4694	330	16	b	b	NOUN
ejpam-4694	330	17	satisfy	satisfy	VERB
ejpam-4694	330	18	the	the	DET
ejpam-4694	330	19	relation	relation	NOUN
ejpam-4694	330	20	,	,	PUNCT
ejpam-4694	330	21	d	d	X
ejpam-4694	330	22	dx	dx	PROPN
ejpam-4694	330	23	ĝ(k	ĝ(k	X
ejpam-4694	330	24	,	,	PUNCT
ejpam-4694	330	25	α	α	X
ejpam-4694	330	26	)	)	PUNCT
ejpam-4694	330	27	n+1	n+1	PROPN
ejpam-4694	330	28	(	(	PUNCT
ejpam-4694	330	29	x;λ	x;λ	PROPN
ejpam-4694	330	30	,	,	PUNCT
ejpam-4694	330	31	ρ	ρ	PROPN
ejpam-4694	330	32	,	,	PUNCT
ejpam-4694	330	33	u	u	NOUN
ejpam-4694	330	34	,	,	PUNCT
ejpam-4694	330	35	a	a	DET
ejpam-4694	330	36	,	,	PUNCT
ejpam-4694	330	37	b	b	NOUN
ejpam-4694	330	38	)	)	PUNCT
ejpam-4694	330	39	=	=	SYM
ejpam-4694	330	40	n∑	n∑	NOUN
ejpam-4694	330	41	j=0	j=0	PROPN
ejpam-4694	330	42	(	(	PUNCT
ejpam-4694	330	43	n	n	X
ejpam-4694	330	44	j	j	NOUN
ejpam-4694	330	45	)	)	PUNCT
ejpam-4694	330	46	(	(	PUNCT
ejpam-4694	330	47	−1)n−j	−1)n−j	CCONJ
ejpam-4694	330	48	n−	n−	NOUN
ejpam-4694	330	49	j	j	NOUN
ejpam-4694	330	50	+	+	CCONJ
ejpam-4694	330	51	1	1	NUM
ejpam-4694	330	52	ρn−jĝ(k	ρn−jĝ(k	PROPN
ejpam-4694	330	53	,	,	PUNCT
ejpam-4694	330	54	α	α	NOUN
ejpam-4694	330	55	)	)	PUNCT
ejpam-4694	330	56	j	j	PROPN
ejpam-4694	330	57	(	(	PUNCT
ejpam-4694	330	58	x;λ	x;λ	PROPN
ejpam-4694	330	59	,	,	PUNCT
ejpam-4694	330	60	ρ	ρ	PROPN
ejpam-4694	330	61	,	,	PUNCT
ejpam-4694	330	62	u	u	NOUN
ejpam-4694	330	63	,	,	PUNCT
ejpam-4694	330	64	a	a	DET
ejpam-4694	330	65	,	,	PUNCT
ejpam-4694	330	66	b	b	NOUN
ejpam-4694	330	67	)	)	PUNCT
ejpam-4694	330	68	.	.	PUNCT
ejpam-4694	331	1	(	(	PUNCT
ejpam-4694	331	2	45	45	NUM
ejpam-4694	331	3	)	)	PUNCT
ejpam-4694	331	4	proof	proof	NOUN
ejpam-4694	331	5	.	.	PUNCT
ejpam-4694	332	1	applying	apply	VERB
ejpam-4694	332	2	the	the	DET
ejpam-4694	332	3	first	first	ADJ
ejpam-4694	332	4	derivative	derivative	NOUN
ejpam-4694	332	5	to	to	ADP
ejpam-4694	332	6	equation	equation	NOUN
ejpam-4694	332	7	(	(	PUNCT
ejpam-4694	332	8	27	27	NUM
ejpam-4694	332	9	)	)	PUNCT
ejpam-4694	332	10	with	with	ADP
ejpam-4694	332	11	respect	respect	NOUN
ejpam-4694	332	12	to	to	ADP
ejpam-4694	332	13	x	x	PUNCT
ejpam-4694	332	14	and	and	CCONJ
ejpam-4694	332	15	using	use	VERB
ejpam-4694	332	16	(	(	PUNCT
ejpam-4694	332	17	15	15	NUM
ejpam-4694	332	18	)	)	PUNCT
ejpam-4694	332	19	yield	yield	VERB
ejpam-4694	332	20	∞∑	∞∑	PRON
ejpam-4694	332	21	n=0	n=0	NUM
ejpam-4694	332	22	d	d	NOUN
ejpam-4694	332	23	dx	dx	PROPN
ejpam-4694	332	24	ĝ(k	ĝ(k	X
ejpam-4694	332	25	,	,	PUNCT
ejpam-4694	332	26	α	α	NOUN
ejpam-4694	332	27	)	)	PUNCT
ejpam-4694	332	28	n	n	CCONJ
ejpam-4694	332	29	(	(	PUNCT
ejpam-4694	332	30	x;λ	x;λ	PROPN
ejpam-4694	332	31	,	,	PUNCT
ejpam-4694	332	32	ρ	ρ	PROPN
ejpam-4694	332	33	,	,	PUNCT
ejpam-4694	332	34	u	u	NOUN
ejpam-4694	332	35	,	,	PUNCT
ejpam-4694	332	36	a	a	DET
ejpam-4694	332	37	,	,	PUNCT
ejpam-4694	332	38	b	b	NOUN
ejpam-4694	332	39	)	)	PUNCT
ejpam-4694	332	40	tn	tn	NOUN
ejpam-4694	332	41	n	n	NOUN
ejpam-4694	332	42	!	!	PUNCT
ejpam-4694	333	1	=	=	PRON
ejpam-4694	333	2	(	(	PUNCT
ejpam-4694	333	3	eik	eik	PROPN
ejpam-4694	333	4	,	,	PUNCT
ejpam-4694	333	5	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	333	6	+	+	CCONJ
ejpam-4694	333	7	(	(	PUNCT
ejpam-4694	333	8	1−	1−	NUM
ejpam-4694	333	9	u)t	u)t	X
ejpam-4694	333	10	ln	ln	PROPN
ejpam-4694	333	11	ab	ab	PROPN
ejpam-4694	333	12	)	)	PUNCT
ejpam-4694	333	13	)	)	PUNCT
ejpam-4694	334	1	(	(	PUNCT
ejpam-4694	334	2	λbt	λbt	VERB
ejpam-4694	334	3	−	−	PROPN
ejpam-4694	334	4	ua−t	ua−t	PROPN
ejpam-4694	334	5	)	)	PUNCT
ejpam-4694	334	6	)	)	PUNCT
ejpam-4694	334	7	α	α	PROPN
ejpam-4694	334	8	exρ(t	exρ(t	NOUN
ejpam-4694	334	9	)	)	PUNCT
ejpam-4694	334	10	log(1	log(1	NOUN
ejpam-4694	335	1	+	+	CCONJ
ejpam-4694	335	2	ρt)1	ρt)1	PROPN
ejpam-4694	335	3	/	/	SYM
ejpam-4694	335	4	ρ	ρ	PROPN
ejpam-4694	335	5	=	=	SYM
ejpam-4694	335	6	t	t	PROPN
ejpam-4694	335	7	(	(	PUNCT
ejpam-4694	335	8	∞∑	∞∑	PROPN
ejpam-4694	335	9	n=0	n=0	NUM
ejpam-4694	335	10	ĝ(k	ĝ(k	PROPN
ejpam-4694	335	11	,	,	PUNCT
ejpam-4694	335	12	α	α	NOUN
ejpam-4694	335	13	)	)	PUNCT
ejpam-4694	335	14	n	n	CCONJ
ejpam-4694	335	15	(	(	PUNCT
ejpam-4694	335	16	x;λ	x;λ	PROPN
ejpam-4694	335	17	,	,	PUNCT
ejpam-4694	335	18	ρ	ρ	PROPN
ejpam-4694	335	19	,	,	PUNCT
ejpam-4694	335	20	u	u	NOUN
ejpam-4694	335	21	,	,	PUNCT
ejpam-4694	335	22	a	a	DET
ejpam-4694	335	23	,	,	PUNCT
ejpam-4694	335	24	b	b	NOUN
ejpam-4694	335	25	)	)	PUNCT
ejpam-4694	335	26	tn	tn	PROPN
ejpam-4694	335	27	n	n	CCONJ
ejpam-4694	335	28	!	!	PUNCT
ejpam-4694	335	29	)	)	PUNCT
ejpam-4694	336	1	(	(	PUNCT
ejpam-4694	336	2	∞∑	∞∑	NUM
ejpam-4694	336	3	n=0	n=0	NUM
ejpam-4694	336	4	(	(	PUNCT
ejpam-4694	336	5	−1)n	−1)n	PROPN
ejpam-4694	336	6	1	1	NUM
ejpam-4694	336	7	n+	n+	SYM
ejpam-4694	336	8	1	1	NUM
ejpam-4694	336	9	(	(	PUNCT
ejpam-4694	336	10	ρt)n	ρt)n	NUM
ejpam-4694	336	11	n	n	CCONJ
ejpam-4694	336	12	!	!	PUNCT
ejpam-4694	336	13	)	)	PUNCT
ejpam-4694	336	14	,	,	PUNCT
ejpam-4694	336	15	∞∑	∞∑	NUM
ejpam-4694	336	16	n=0	n=0	NUM
ejpam-4694	336	17	d	d	PROPN
ejpam-4694	336	18	dx	dx	PROPN
ejpam-4694	336	19	ĝ(k	ĝ(k	X
ejpam-4694	336	20	,	,	PUNCT
ejpam-4694	336	21	α	α	NOUN
ejpam-4694	336	22	)	)	PUNCT
ejpam-4694	336	23	n	n	CCONJ
ejpam-4694	336	24	(	(	PUNCT
ejpam-4694	336	25	x;λ	x;λ	PROPN
ejpam-4694	336	26	,	,	PUNCT
ejpam-4694	336	27	ρ	ρ	PROPN
ejpam-4694	336	28	,	,	PUNCT
ejpam-4694	336	29	u	u	NOUN
ejpam-4694	336	30	,	,	PUNCT
ejpam-4694	336	31	a	a	DET
ejpam-4694	336	32	,	,	PUNCT
ejpam-4694	336	33	b	b	NOUN
ejpam-4694	336	34	)	)	PUNCT
ejpam-4694	336	35	tn	tn	NOUN
ejpam-4694	336	36	n	n	NOUN
ejpam-4694	336	37	!	!	PUNCT
ejpam-4694	336	38	=	=	PUNCT
ejpam-4694	337	1	t	t	PROPN
ejpam-4694	337	2	∞∑	∞∑	PROPN
ejpam-4694	337	3	n=0	n=0	PROPN
ejpam-4694	337	4	n∑	n∑	PUNCT
ejpam-4694	337	5	j=0	j=0	PROPN
ejpam-4694	337	6	(	(	PUNCT
ejpam-4694	337	7	n	n	CCONJ
ejpam-4694	337	8	j	j	PROPN
ejpam-4694	337	9	)	)	PUNCT
ejpam-4694	338	1	ĝ(k	ĝ(k	PROPN
ejpam-4694	338	2	,	,	PUNCT
ejpam-4694	338	3	α	α	NOUN
ejpam-4694	338	4	)	)	PUNCT
ejpam-4694	338	5	j	j	PROPN
ejpam-4694	338	6	(	(	PUNCT
ejpam-4694	338	7	x;λ	x;λ	PROPN
ejpam-4694	338	8	,	,	PUNCT
ejpam-4694	338	9	ρ	ρ	PROPN
ejpam-4694	338	10	,	,	PUNCT
ejpam-4694	338	11	u	u	NOUN
ejpam-4694	338	12	,	,	PUNCT
ejpam-4694	338	13	a	a	DET
ejpam-4694	338	14	,	,	PUNCT
ejpam-4694	338	15	b	b	NOUN
ejpam-4694	338	16	)	)	PUNCT
ejpam-4694	338	17	(	(	PUNCT
ejpam-4694	338	18	−1)n−j	−1)n−j	CCONJ
ejpam-4694	338	19	n−	n−	NOUN
ejpam-4694	338	20	j	j	NOUN
ejpam-4694	338	21	+	+	CCONJ
ejpam-4694	338	22	1	1	NUM
ejpam-4694	338	23	ρn−j	ρn−j	PROPN
ejpam-4694	338	24	t	t	NOUN
ejpam-4694	338	25	n	n	NOUN
ejpam-4694	338	26	n	n	CCONJ
ejpam-4694	338	27	!	!	PUNCT
ejpam-4694	338	28	.	.	PUNCT
ejpam-4694	339	1	it	it	PRON
ejpam-4694	339	2	follows	follow	VERB
ejpam-4694	339	3	that	that	SCONJ
ejpam-4694	339	4	∞∑	∞∑	NUM
ejpam-4694	339	5	n=0	n=0	SYM
ejpam-4694	339	6	1	1	NUM
ejpam-4694	339	7	n+	n+	ADP
ejpam-4694	339	8	1	1	NUM
ejpam-4694	339	9	d	d	NOUN
ejpam-4694	339	10	dx	dx	PROPN
ejpam-4694	339	11	ĝ(k	ĝ(k	X
ejpam-4694	339	12	,	,	PUNCT
ejpam-4694	339	13	α	α	X
ejpam-4694	339	14	)	)	PUNCT
ejpam-4694	339	15	n+1	n+1	PROPN
ejpam-4694	339	16	(	(	PUNCT
ejpam-4694	339	17	x;λ	x;λ	PROPN
ejpam-4694	339	18	,	,	PUNCT
ejpam-4694	339	19	ρ	ρ	PROPN
ejpam-4694	339	20	,	,	PUNCT
ejpam-4694	339	21	u	u	NOUN
ejpam-4694	339	22	,	,	PUNCT
ejpam-4694	339	23	a	a	DET
ejpam-4694	339	24	,	,	PUNCT
ejpam-4694	339	25	b	b	NOUN
ejpam-4694	339	26	)	)	PUNCT
ejpam-4694	339	27	tn	tn	NOUN
ejpam-4694	339	28	n	n	NOUN
ejpam-4694	339	29	!	!	PUNCT
ejpam-4694	339	30	=	=	NOUN
ejpam-4694	340	1	∞∑	∞∑	PRON
ejpam-4694	340	2	n=0	n=0	PROPN
ejpam-4694	340	3	n∑	n∑	PRON
ejpam-4694	340	4	j=0	j=0	PROPN
ejpam-4694	340	5	(	(	PUNCT
ejpam-4694	340	6	n	n	CCONJ
ejpam-4694	340	7	j	j	PROPN
ejpam-4694	340	8	)	)	PUNCT
ejpam-4694	340	9	ĝ(k	ĝ(k	PROPN
ejpam-4694	340	10	,	,	PUNCT
ejpam-4694	340	11	α	α	NOUN
ejpam-4694	340	12	)	)	PUNCT
ejpam-4694	340	13	j	j	PROPN
ejpam-4694	340	14	(	(	PUNCT
ejpam-4694	340	15	x;λ	x;λ	PROPN
ejpam-4694	340	16	,	,	PUNCT
ejpam-4694	340	17	ρ	ρ	PROPN
ejpam-4694	340	18	,	,	PUNCT
ejpam-4694	340	19	u	u	NOUN
ejpam-4694	340	20	,	,	PUNCT
ejpam-4694	340	21	a	a	DET
ejpam-4694	340	22	,	,	PUNCT
ejpam-4694	340	23	b	b	NOUN
ejpam-4694	340	24	)	)	PUNCT
ejpam-4694	340	25	(	(	PUNCT
ejpam-4694	340	26	−1)n−j	−1)n−j	CCONJ
ejpam-4694	340	27	n−	n−	NOUN
ejpam-4694	340	28	j	j	NOUN
ejpam-4694	340	29	+	+	CCONJ
ejpam-4694	340	30	1	1	NUM
ejpam-4694	340	31	ρn−j	ρn−j	PROPN
ejpam-4694	340	32	t	t	NOUN
ejpam-4694	340	33	n	n	NOUN
ejpam-4694	340	34	n	n	CCONJ
ejpam-4694	340	35	!	!	PUNCT
ejpam-4694	340	36	.	.	PUNCT
ejpam-4694	341	1	comparing	compare	VERB
ejpam-4694	341	2	the	the	DET
ejpam-4694	341	3	coefficients	coefficient	NOUN
ejpam-4694	341	4	of	of	ADP
ejpam-4694	341	5	tn	tn	NOUN
ejpam-4694	341	6	n	n	X
ejpam-4694	341	7	!	!	PUNCT
ejpam-4694	342	1	yields	yield	VERB
ejpam-4694	342	2	the	the	DET
ejpam-4694	342	3	desired	desire	VERB
ejpam-4694	342	4	differential	differential	NOUN
ejpam-4694	342	5	identity	identity	NOUN
ejpam-4694	342	6	.	.	PUNCT
ejpam-4694	343	1	remark	remark	NOUN
ejpam-4694	343	2	4.2	4.2	NUM
ejpam-4694	343	3	.	.	PUNCT
ejpam-4694	344	1	when	when	SCONJ
ejpam-4694	344	2	ρ	ρ	PROPN
ejpam-4694	344	3	→	→	SYM
ejpam-4694	344	4	0	0	NUM
ejpam-4694	344	5	,	,	PUNCT
ejpam-4694	344	6	equation	equation	NOUN
ejpam-4694	344	7	(	(	PUNCT
ejpam-4694	344	8	45	45	NUM
ejpam-4694	344	9	)	)	PUNCT
ejpam-4694	344	10	reduces	reduce	VERB
ejpam-4694	344	11	to	to	ADP
ejpam-4694	344	12	the	the	DET
ejpam-4694	344	13	following	follow	VERB
ejpam-4694	344	14	differential	differential	ADJ
ejpam-4694	344	15	identity	identity	NOUN
ejpam-4694	344	16	d	d	X
ejpam-4694	344	17	dx	dx	PROPN
ejpam-4694	344	18	ĝ(k	ĝ(k	X
ejpam-4694	344	19	,	,	PUNCT
ejpam-4694	344	20	α	α	X
ejpam-4694	344	21	)	)	PUNCT
ejpam-4694	344	22	n+1	n+1	PROPN
ejpam-4694	344	23	(	(	PUNCT
ejpam-4694	344	24	x;λ	x;λ	PROPN
ejpam-4694	344	25	,	,	PUNCT
ejpam-4694	344	26	u	u	NOUN
ejpam-4694	344	27	,	,	PUNCT
ejpam-4694	344	28	a	a	DET
ejpam-4694	344	29	,	,	PUNCT
ejpam-4694	344	30	b	b	NOUN
ejpam-4694	344	31	)	)	PUNCT
ejpam-4694	344	32	=	=	SYM
ejpam-4694	344	33	(	(	PUNCT
ejpam-4694	344	34	n+	n+	NUM
ejpam-4694	344	35	1)ĝ(k	1)ĝ(k	NUM
ejpam-4694	344	36	,	,	PUNCT
ejpam-4694	344	37	α	α	NOUN
ejpam-4694	344	38	)	)	PUNCT
ejpam-4694	344	39	n	n	CCONJ
ejpam-4694	344	40	(	(	PUNCT
ejpam-4694	344	41	x;λ	x;λ	PROPN
ejpam-4694	344	42	,	,	PUNCT
ejpam-4694	344	43	u	u	NOUN
ejpam-4694	344	44	,	,	PUNCT
ejpam-4694	344	45	a	a	DET
ejpam-4694	344	46	,	,	PUNCT
ejpam-4694	344	47	b	b	NOUN
ejpam-4694	344	48	)	)	PUNCT
ejpam-4694	344	49	,	,	PUNCT
ejpam-4694	344	50	(	(	PUNCT
ejpam-4694	344	51	46	46	NUM
ejpam-4694	344	52	)	)	PUNCT
ejpam-4694	344	53	where	where	SCONJ
ejpam-4694	344	54	ĝ(k	ĝ(k	X
ejpam-4694	344	55	,	,	PUNCT
ejpam-4694	344	56	α	α	NOUN
ejpam-4694	344	57	)	)	PUNCT
ejpam-4694	344	58	n	n	CCONJ
ejpam-4694	344	59	(	(	PUNCT
ejpam-4694	344	60	x;λ	x;λ	PROPN
ejpam-4694	344	61	,	,	PUNCT
ejpam-4694	344	62	u	u	NOUN
ejpam-4694	344	63	,	,	PUNCT
ejpam-4694	344	64	a	a	DET
ejpam-4694	344	65	,	,	PUNCT
ejpam-4694	344	66	b	b	NOUN
ejpam-4694	344	67	)	)	PUNCT
ejpam-4694	344	68	is	be	AUX
ejpam-4694	344	69	the	the	DET
ejpam-4694	344	70	type	type	NOUN
ejpam-4694	344	71	2	2	NUM
ejpam-4694	344	72	apostol	apostol	NOUN
ejpam-4694	344	73	-	-	PUNCT
ejpam-4694	344	74	frobenius	frobenius	NOUN
ejpam-4694	344	75	-	-	PUNCT
ejpam-4694	344	76	type	type	NOUN
ejpam-4694	344	77	poly	poly	ADJ
ejpam-4694	344	78	-	-	PUNCT
ejpam-4694	344	79	genocchi	genocchi	NOUN
ejpam-4694	344	80	polynomials	polynomial	NOUN
ejpam-4694	344	81	in	in	ADP
ejpam-4694	344	82	(	(	PUNCT
ejpam-4694	344	83	36	36	NUM
ejpam-4694	344	84	)	)	PUNCT
ejpam-4694	344	85	.	.	PUNCT
ejpam-4694	345	1	equation	equation	NOUN
ejpam-4694	345	2	(	(	PUNCT
ejpam-4694	345	3	46	46	NUM
ejpam-4694	345	4	)	)	PUNCT
ejpam-4694	345	5	was	be	AUX
ejpam-4694	345	6	used	use	VERB
ejpam-4694	345	7	to	to	PART
ejpam-4694	345	8	classify	classify	VERB
ejpam-4694	345	9	ĝ(k	ĝ(k	PRON
ejpam-4694	345	10	,	,	PUNCT
ejpam-4694	345	11	α	α	NOUN
ejpam-4694	345	12	)	)	PUNCT
ejpam-4694	345	13	n	n	CCONJ
ejpam-4694	345	14	(	(	PUNCT
ejpam-4694	345	15	x;λ	x;λ	PROPN
ejpam-4694	345	16	,	,	PUNCT
ejpam-4694	345	17	u	u	NOUN
ejpam-4694	345	18	,	,	PUNCT
ejpam-4694	345	19	a	a	DET
ejpam-4694	345	20	,	,	PUNCT
ejpam-4694	345	21	b	b	NOUN
ejpam-4694	345	22	)	)	PUNCT
ejpam-4694	345	23	as	as	ADP
ejpam-4694	345	24	an	an	DET
ejpam-4694	345	25	appell	appell	ADJ
ejpam-4694	345	26	polynomial	polynomial	NOUN
ejpam-4694	345	27	.	.	PUNCT
ejpam-4694	346	1	r.	r.	PROPN
ejpam-4694	346	2	corcino	corcino	PROPN
ejpam-4694	346	3	,	,	PUNCT
ejpam-4694	346	4	c.	c.	PROPN
ejpam-4694	346	5	corcino	corcino	PROPN
ejpam-4694	346	6	/	/	SYM
ejpam-4694	346	7	eur	eur	PROPN
ejpam-4694	346	8	.	.	PUNCT
ejpam-4694	347	1	j.	j.	PROPN
ejpam-4694	347	2	pure	pure	PROPN
ejpam-4694	347	3	appl	appl	PROPN
ejpam-4694	347	4	.	.	PROPN
ejpam-4694	347	5	math	math	PROPN
ejpam-4694	347	6	,	,	PUNCT
ejpam-4694	347	7	16	16	NUM
ejpam-4694	347	8	(	(	PUNCT
ejpam-4694	347	9	2	2	NUM
ejpam-4694	347	10	)	)	PUNCT
ejpam-4694	347	11	(	(	PUNCT
ejpam-4694	347	12	2023	2023	NUM
ejpam-4694	347	13	)	)	PUNCT
ejpam-4694	347	14	,	,	PUNCT
ejpam-4694	347	15	687	687	NUM
ejpam-4694	347	16	-	-	SYM
ejpam-4694	347	17	712	712	NUM
ejpam-4694	347	18	703	703	NUM
ejpam-4694	347	19	to	to	PART
ejpam-4694	347	20	derive	derive	VERB
ejpam-4694	347	21	the	the	DET
ejpam-4694	347	22	integral	integral	ADJ
ejpam-4694	347	23	formula	formula	NOUN
ejpam-4694	347	24	gin	gin	NOUN
ejpam-4694	347	25	=	=	PUNCT
ejpam-4694	347	26	∫	∫	PROPN
ejpam-4694	347	27	ĝ(k	ĝ(k	X
ejpam-4694	347	28	,	,	PUNCT
ejpam-4694	347	29	α	α	NOUN
ejpam-4694	347	30	)	)	PUNCT
ejpam-4694	347	31	n	n	CCONJ
ejpam-4694	347	32	(	(	PUNCT
ejpam-4694	347	33	x;λ	x;λ	PROPN
ejpam-4694	347	34	,	,	PUNCT
ejpam-4694	347	35	u	u	NOUN
ejpam-4694	347	36	,	,	PUNCT
ejpam-4694	347	37	a	a	PRON
ejpam-4694	347	38	,	,	PUNCT
ejpam-4694	347	39	b)dx	b)dx	PROPN
ejpam-4694	347	40	,	,	PUNCT
ejpam-4694	347	41	we	we	PRON
ejpam-4694	347	42	need	need	VERB
ejpam-4694	347	43	to	to	PART
ejpam-4694	347	44	consider	consider	VERB
ejpam-4694	347	45	the	the	DET
ejpam-4694	347	46	following	follow	VERB
ejpam-4694	347	47	lemma	lemma	PROPN
ejpam-4694	347	48	.	.	PUNCT
ejpam-4694	348	1	lemma	lemma	PROPN
ejpam-4694	348	2	4.3	4.3	NUM
ejpam-4694	348	3	.	.	PUNCT
ejpam-4694	349	1	if	if	SCONJ
ejpam-4694	349	2	an	an	DET
ejpam-4694	349	3	=	=	SYM
ejpam-4694	349	4	n∑	n∑	NOUN
ejpam-4694	349	5	j=0	j=0	PROPN
ejpam-4694	349	6	(	(	PUNCT
ejpam-4694	349	7	−1)n−j	−1)n−j	X
ejpam-4694	349	8	(	(	PUNCT
ejpam-4694	349	9	n	n	X
ejpam-4694	349	10	j	j	NOUN
ejpam-4694	349	11	)	)	PUNCT
ejpam-4694	349	12	1	1	NUM
ejpam-4694	349	13	n−	n−	NOUN
ejpam-4694	349	14	j	j	NOUN
ejpam-4694	349	15	+	+	CCONJ
ejpam-4694	349	16	1	1	NUM
ejpam-4694	349	17	bj	bj	NOUN
ejpam-4694	349	18	,	,	PUNCT
ejpam-4694	349	19	then	then	ADV
ejpam-4694	349	20	bn	bn	ADP
ejpam-4694	349	21	−	−	PROPN
ejpam-4694	349	22	nan−1	nan−1	PROPN
ejpam-4694	349	23	=	=	SYM
ejpam-4694	349	24	n∑	n∑	NOUN
ejpam-4694	349	25	j=0	j=0	PROPN
ejpam-4694	349	26	(	(	PUNCT
ejpam-4694	349	27	−1)n−j	−1)n−j	X
ejpam-4694	349	28	(	(	PUNCT
ejpam-4694	349	29	n	n	X
ejpam-4694	349	30	j	j	NOUN
ejpam-4694	349	31	)	)	PUNCT
ejpam-4694	349	32	bj	bj	VERB
ejpam-4694	349	33	.	.	PUNCT
ejpam-4694	350	1	(	(	PUNCT
ejpam-4694	350	2	47	47	NUM
ejpam-4694	350	3	)	)	PUNCT
ejpam-4694	350	4	proof	proof	NOUN
ejpam-4694	350	5	.	.	PUNCT
ejpam-4694	351	1	using	use	VERB
ejpam-4694	351	2	the	the	DET
ejpam-4694	351	3	fact	fact	NOUN
ejpam-4694	351	4	that	that	SCONJ
ejpam-4694	351	5	(	(	PUNCT
ejpam-4694	351	6	n+	n+	NUM
ejpam-4694	351	7	1	1	NUM
ejpam-4694	351	8	j	j	NOUN
ejpam-4694	351	9	)	)	PUNCT
ejpam-4694	351	10	1	1	NUM
ejpam-4694	351	11	n+	n+	SYM
ejpam-4694	351	12	1	1	NUM
ejpam-4694	351	13	=	=	SYM
ejpam-4694	351	14	(	(	PUNCT
ejpam-4694	351	15	n	n	X
ejpam-4694	351	16	j	j	NOUN
ejpam-4694	351	17	)	)	PUNCT
ejpam-4694	351	18	1	1	NUM
ejpam-4694	351	19	n−	n−	PROPN
ejpam-4694	351	20	j	j	NOUN
ejpam-4694	352	1	+	+	CCONJ
ejpam-4694	352	2	1	1	NUM
ejpam-4694	352	3	,	,	PUNCT
ejpam-4694	352	4	we	we	PRON
ejpam-4694	352	5	have	have	VERB
ejpam-4694	352	6	−(n+	−(n+	PRON
ejpam-4694	353	1	1)an	1)an	PROPN
ejpam-4694	353	2	=	=	SYM
ejpam-4694	353	3	n∑	n∑	X
ejpam-4694	353	4	j=0	j=0	PROPN
ejpam-4694	353	5	(	(	PUNCT
ejpam-4694	353	6	−1)n+1−j	−1)n+1−j	PROPN
ejpam-4694	353	7	(	(	PUNCT
ejpam-4694	353	8	n+	n+	NUM
ejpam-4694	353	9	1	1	NUM
ejpam-4694	353	10	j	j	NOUN
ejpam-4694	353	11	)	)	PUNCT
ejpam-4694	353	12	1	1	NUM
ejpam-4694	353	13	n−	n−	NOUN
ejpam-4694	353	14	j	j	NOUN
ejpam-4694	353	15	+	+	CCONJ
ejpam-4694	353	16	1	1	NUM
ejpam-4694	353	17	bj	bj	NOUN
ejpam-4694	353	18	,	,	PUNCT
ejpam-4694	353	19	which	which	PRON
ejpam-4694	353	20	is	be	AUX
ejpam-4694	353	21	equivalent	equivalent	ADJ
ejpam-4694	353	22	to	to	ADP
ejpam-4694	353	23	(	(	PUNCT
ejpam-4694	353	24	47	47	NUM
ejpam-4694	353	25	)	)	PUNCT
ejpam-4694	353	26	.	.	PUNCT
ejpam-4694	354	1	to	to	PART
ejpam-4694	354	2	compute	compute	VERB
ejpam-4694	354	3	the	the	DET
ejpam-4694	354	4	value	value	NOUN
ejpam-4694	354	5	of	of	ADP
ejpam-4694	354	6	the	the	DET
ejpam-4694	354	7	integral	integral	ADJ
ejpam-4694	354	8	gin	gin	NOUN
ejpam-4694	354	9	,	,	PUNCT
ejpam-4694	354	10	we	we	PRON
ejpam-4694	354	11	can	can	AUX
ejpam-4694	354	12	use	use	VERB
ejpam-4694	354	13	the	the	DET
ejpam-4694	354	14	following	follow	VERB
ejpam-4694	354	15	recurrence	recurrence	NOUN
ejpam-4694	354	16	relation	relation	NOUN
ejpam-4694	354	17	.	.	PUNCT
ejpam-4694	355	1	theorem	theorem	VERB
ejpam-4694	355	2	4.4	4.4	NUM
ejpam-4694	355	3	.	.	PUNCT
ejpam-4694	356	1	the	the	DET
ejpam-4694	356	2	integral	integral	ADJ
ejpam-4694	356	3	gin	gin	NOUN
ejpam-4694	356	4	satisfies	satisfy	VERB
ejpam-4694	356	5	the	the	DET
ejpam-4694	356	6	following	follow	VERB
ejpam-4694	356	7	recurrence	recurrence	NOUN
ejpam-4694	356	8	relation	relation	NOUN
ejpam-4694	356	9	gin	gin	NOUN
ejpam-4694	356	10	=	=	PUNCT
ejpam-4694	357	1	−	−	PROPN
ejpam-4694	357	2	ρn	ρn	INTJ
ejpam-4694	357	3	n+	n+	NUM
ejpam-4694	357	4	1	1	NUM
ejpam-4694	357	5			VERB
ejpam-4694	357	6	n−1∑	n−1∑	PROPN
ejpam-4694	357	7	j=0	j=0	PROPN
ejpam-4694	357	8	(	(	PUNCT
ejpam-4694	357	9	n+	n+	ADP
ejpam-4694	357	10	1	1	NUM
ejpam-4694	357	11	j	j	NOUN
ejpam-4694	357	12	)	)	PUNCT
ejpam-4694	357	13	1	1	NUM
ejpam-4694	358	1	ρj	ρj	X
ejpam-4694	358	2	gij	gij	PROPN
ejpam-4694	358	3	−	−	PROPN
ejpam-4694	358	4	n+1∑	n+1∑	PROPN
ejpam-4694	358	5	j=0	j=0	PROPN
ejpam-4694	358	6	(	(	PUNCT
ejpam-4694	358	7	n+	n+	ADP
ejpam-4694	358	8	1	1	NUM
ejpam-4694	358	9	j	j	NOUN
ejpam-4694	358	10	)	)	PUNCT
ejpam-4694	359	1	j	j	PROPN
ejpam-4694	360	1	ρj−1	ρj−1	PROPN
ejpam-4694	360	2	ĝ(k	ĝ(k	PROPN
ejpam-4694	360	3	,	,	PUNCT
ejpam-4694	360	4	α	α	NOUN
ejpam-4694	360	5	)	)	PUNCT
ejpam-4694	360	6	j	j	PROPN
ejpam-4694	360	7	(	(	PUNCT
ejpam-4694	360	8	x;λ	x;λ	PROPN
ejpam-4694	360	9	,	,	PUNCT
ejpam-4694	360	10	ρ	ρ	PROPN
ejpam-4694	360	11	,	,	PUNCT
ejpam-4694	360	12	u	u	NOUN
ejpam-4694	360	13	,	,	PUNCT
ejpam-4694	360	14	a	a	DET
ejpam-4694	360	15	,	,	PUNCT
ejpam-4694	360	16	b	b	NOUN
ejpam-4694	360	17	)	)	PUNCT
ejpam-4694	360	18			NOUN
ejpam-4694	360	19	.	.	PUNCT
ejpam-4694	361	1	proof	proof	NOUN
ejpam-4694	361	2	.	.	PUNCT
ejpam-4694	362	1	integrating	integrate	VERB
ejpam-4694	362	2	both	both	DET
ejpam-4694	362	3	sides	side	NOUN
ejpam-4694	362	4	of	of	ADP
ejpam-4694	362	5	(	(	PUNCT
ejpam-4694	362	6	45	45	NUM
ejpam-4694	362	7	)	)	PUNCT
ejpam-4694	362	8	gives	give	VERB
ejpam-4694	362	9	1	1	NUM
ejpam-4694	362	10	ρn	ρn	ADP
ejpam-4694	362	11	ĝ(k	ĝ(k	PRON
ejpam-4694	362	12	,	,	PUNCT
ejpam-4694	362	13	α	α	X
ejpam-4694	362	14	)	)	PUNCT
ejpam-4694	362	15	n+1	n+1	PROPN
ejpam-4694	362	16	(	(	PUNCT
ejpam-4694	362	17	x;λ	x;λ	PROPN
ejpam-4694	362	18	,	,	PUNCT
ejpam-4694	362	19	ρ	ρ	PROPN
ejpam-4694	362	20	,	,	PUNCT
ejpam-4694	362	21	u	u	NOUN
ejpam-4694	362	22	,	,	PUNCT
ejpam-4694	362	23	a	a	DET
ejpam-4694	362	24	,	,	PUNCT
ejpam-4694	362	25	b	b	NOUN
ejpam-4694	362	26	)	)	PUNCT
ejpam-4694	363	1	=	=	SYM
ejpam-4694	363	2	n∑	n∑	NOUN
ejpam-4694	363	3	j=0	j=0	PROPN
ejpam-4694	363	4	(	(	PUNCT
ejpam-4694	363	5	−1)n−j	−1)n−j	X
ejpam-4694	363	6	(	(	PUNCT
ejpam-4694	363	7	n	n	X
ejpam-4694	363	8	j	j	NOUN
ejpam-4694	363	9	)	)	PUNCT
ejpam-4694	363	10	1	1	NUM
ejpam-4694	363	11	n−	n−	NOUN
ejpam-4694	363	12	j	j	NOUN
ejpam-4694	363	13	+	+	CCONJ
ejpam-4694	363	14	1	1	NUM
ejpam-4694	363	15	1	1	NUM
ejpam-4694	363	16	ρj	ρj	NOUN
ejpam-4694	363	17	∫	∫	PROPN
ejpam-4694	363	18	ĝ(k	ĝ(k	X
ejpam-4694	363	19	,	,	PUNCT
ejpam-4694	363	20	α	α	NOUN
ejpam-4694	363	21	)	)	PUNCT
ejpam-4694	363	22	j	j	PROPN
ejpam-4694	363	23	(	(	PUNCT
ejpam-4694	363	24	x;λ	x;λ	PROPN
ejpam-4694	363	25	,	,	PUNCT
ejpam-4694	363	26	ρ	ρ	PROPN
ejpam-4694	363	27	,	,	PUNCT
ejpam-4694	363	28	u	u	NOUN
ejpam-4694	363	29	,	,	PUNCT
ejpam-4694	363	30	a	a	PRON
ejpam-4694	363	31	,	,	PUNCT
ejpam-4694	363	32	b)dx	b)dx	PROPN
ejpam-4694	363	33	.	.	PUNCT
ejpam-4694	363	34	applying	apply	VERB
ejpam-4694	363	35	lemma	lemma	PROPN
ejpam-4694	363	36	4.3	4.3	NUM
ejpam-4694	363	37	yields	yield	NOUN
ejpam-4694	363	38	1	1	NUM
ejpam-4694	363	39	ρn	ρn	ADP
ejpam-4694	363	40	gin	gin	NOUN
ejpam-4694	363	41	−	−	PROPN
ejpam-4694	363	42	n	n	CCONJ
ejpam-4694	363	43	1	1	NUM
ejpam-4694	363	44	ρn−1	ρn−1	PROPN
ejpam-4694	363	45	ĝ(k	ĝ(k	PROPN
ejpam-4694	363	46	,	,	PUNCT
ejpam-4694	363	47	α	α	NOUN
ejpam-4694	363	48	)	)	PUNCT
ejpam-4694	363	49	n	n	CCONJ
ejpam-4694	363	50	(	(	PUNCT
ejpam-4694	363	51	x;λ	x;λ	PROPN
ejpam-4694	363	52	,	,	PUNCT
ejpam-4694	363	53	ρ	ρ	PROPN
ejpam-4694	363	54	,	,	PUNCT
ejpam-4694	363	55	u	u	NOUN
ejpam-4694	363	56	,	,	PUNCT
ejpam-4694	363	57	a	a	DET
ejpam-4694	363	58	,	,	PUNCT
ejpam-4694	363	59	b	b	NOUN
ejpam-4694	363	60	)	)	PUNCT
ejpam-4694	363	61	=	=	SYM
ejpam-4694	363	62	n∑	n∑	NOUN
ejpam-4694	363	63	j=0	j=0	PROPN
ejpam-4694	363	64	(	(	PUNCT
ejpam-4694	363	65	−1)n−j	−1)n−j	X
ejpam-4694	363	66	(	(	PUNCT
ejpam-4694	363	67	n	n	X
ejpam-4694	363	68	j	j	NOUN
ejpam-4694	363	69	)	)	PUNCT
ejpam-4694	363	70	1	1	NUM
ejpam-4694	363	71	ρj	ρj	NOUN
ejpam-4694	363	72	gij	gij	ADJ
ejpam-4694	363	73	.	.	PUNCT
ejpam-4694	364	1	using	use	VERB
ejpam-4694	364	2	the	the	DET
ejpam-4694	364	3	inversion	inversion	NOUN
ejpam-4694	364	4	formula	formula	NOUN
ejpam-4694	364	5	an	an	DET
ejpam-4694	364	6	=	=	SYM
ejpam-4694	364	7	n∑	n∑	NOUN
ejpam-4694	364	8	j=0	j=0	PROPN
ejpam-4694	364	9	(	(	PUNCT
ejpam-4694	364	10	−1)n−j	−1)n−j	X
ejpam-4694	364	11	(	(	PUNCT
ejpam-4694	364	12	n	n	X
ejpam-4694	364	13	j	j	NOUN
ejpam-4694	364	14	)	)	PUNCT
ejpam-4694	364	15	bj	bj	VERB
ejpam-4694	364	16	⇐	⇐	ADJ
ejpam-4694	364	17	⇒	⇒	NOUN
ejpam-4694	364	18	bn	bn	PROPN
ejpam-4694	365	1	=	=	SYM
ejpam-4694	365	2	n∑	n∑	PROPN
ejpam-4694	365	3	j=0	j=0	PROPN
ejpam-4694	365	4	(	(	PUNCT
ejpam-4694	365	5	n	n	CCONJ
ejpam-4694	365	6	j	j	PROPN
ejpam-4694	365	7	)	)	PUNCT
ejpam-4694	365	8	aj	aj	PROPN
ejpam-4694	365	9	,	,	PUNCT
ejpam-4694	365	10	r.	r.	PROPN
ejpam-4694	365	11	corcino	corcino	PROPN
ejpam-4694	365	12	,	,	PUNCT
ejpam-4694	365	13	c.	c.	PROPN
ejpam-4694	365	14	corcino	corcino	PROPN
ejpam-4694	365	15	/	/	SYM
ejpam-4694	365	16	eur	eur	PROPN
ejpam-4694	365	17	.	.	PUNCT
ejpam-4694	366	1	j.	j.	PROPN
ejpam-4694	366	2	pure	pure	PROPN
ejpam-4694	366	3	appl	appl	PROPN
ejpam-4694	366	4	.	.	PROPN
ejpam-4694	366	5	math	math	PROPN
ejpam-4694	366	6	,	,	PUNCT
ejpam-4694	366	7	16	16	NUM
ejpam-4694	366	8	(	(	PUNCT
ejpam-4694	366	9	2	2	NUM
ejpam-4694	366	10	)	)	PUNCT
ejpam-4694	366	11	(	(	PUNCT
ejpam-4694	366	12	2023	2023	NUM
ejpam-4694	366	13	)	)	PUNCT
ejpam-4694	366	14	,	,	PUNCT
ejpam-4694	366	15	687	687	NUM
ejpam-4694	366	16	-	-	SYM
ejpam-4694	366	17	712	712	NUM
ejpam-4694	366	18	704	704	NUM
ejpam-4694	366	19	we	we	PRON
ejpam-4694	366	20	have	have	AUX
ejpam-4694	366	21	1	1	NUM
ejpam-4694	366	22	ρn	ρn	ADP
ejpam-4694	367	1	gin	gin	NOUN
ejpam-4694	367	2	=	=	PROPN
ejpam-4694	367	3	n∑	n∑	NOUN
ejpam-4694	367	4	j=0	j=0	PROPN
ejpam-4694	367	5	(	(	PUNCT
ejpam-4694	367	6	n	n	X
ejpam-4694	367	7	j	j	NOUN
ejpam-4694	367	8	)	)	PUNCT
ejpam-4694	367	9	{	{	PUNCT
ejpam-4694	367	10	1	1	NUM
ejpam-4694	367	11	ρj	ρj	NOUN
ejpam-4694	367	12	gij	gij	PROPN
ejpam-4694	367	13	−	−	PROPN
ejpam-4694	367	14	j	j	PROPN
ejpam-4694	367	15	1	1	NUM
ejpam-4694	367	16	ρj−1	ρj−1	PROPN
ejpam-4694	367	17	ĝ(k	ĝ(k	PROPN
ejpam-4694	367	18	,	,	PUNCT
ejpam-4694	367	19	α	α	NOUN
ejpam-4694	367	20	)	)	PUNCT
ejpam-4694	367	21	j	j	PROPN
ejpam-4694	367	22	(	(	PUNCT
ejpam-4694	367	23	x;λ	x;λ	PROPN
ejpam-4694	367	24	,	,	PUNCT
ejpam-4694	367	25	ρ	ρ	PROPN
ejpam-4694	367	26	,	,	PUNCT
ejpam-4694	367	27	u	u	NOUN
ejpam-4694	367	28	,	,	PUNCT
ejpam-4694	367	29	a	a	DET
ejpam-4694	367	30	,	,	PUNCT
ejpam-4694	367	31	b	b	NOUN
ejpam-4694	367	32	)	)	PUNCT
ejpam-4694	367	33	}	}	PUNCT
ejpam-4694	367	34	.	.	PUNCT
ejpam-4694	368	1	thus	thus	ADV
ejpam-4694	368	2	,	,	PUNCT
ejpam-4694	368	3	n−1∑	n−1∑	PROPN
ejpam-4694	368	4	j=0	j=0	PROPN
ejpam-4694	368	5	(	(	PUNCT
ejpam-4694	368	6	n	n	CCONJ
ejpam-4694	368	7	j	j	PROPN
ejpam-4694	368	8	)	)	PUNCT
ejpam-4694	368	9	1	1	NUM
ejpam-4694	368	10	ρj	ρj	NOUN
ejpam-4694	368	11	gij	gij	NOUN
ejpam-4694	368	12	=	=	SYM
ejpam-4694	368	13	n∑	n∑	X
ejpam-4694	368	14	j=0	j=0	PROPN
ejpam-4694	368	15	(	(	PUNCT
ejpam-4694	368	16	n	n	X
ejpam-4694	368	17	j	j	PROPN
ejpam-4694	368	18	)	)	PUNCT
ejpam-4694	368	19	j	j	PROPN
ejpam-4694	368	20	ρj−1	ρj−1	PROPN
ejpam-4694	368	21	ĝ(k	ĝ(k	PROPN
ejpam-4694	368	22	,	,	PUNCT
ejpam-4694	368	23	α	α	NOUN
ejpam-4694	368	24	)	)	PUNCT
ejpam-4694	368	25	j	j	PROPN
ejpam-4694	368	26	(	(	PUNCT
ejpam-4694	368	27	x;λ	x;λ	PROPN
ejpam-4694	368	28	,	,	PUNCT
ejpam-4694	368	29	ρ	ρ	PROPN
ejpam-4694	368	30	,	,	PUNCT
ejpam-4694	368	31	u	u	NOUN
ejpam-4694	368	32	,	,	PUNCT
ejpam-4694	368	33	a	a	DET
ejpam-4694	368	34	,	,	PUNCT
ejpam-4694	368	35	b	b	NOUN
ejpam-4694	368	36	)	)	PUNCT
ejpam-4694	368	37	.	.	PUNCT
ejpam-4694	369	1	n	n	CCONJ
ejpam-4694	369	2	1	1	NUM
ejpam-4694	369	3	ρn−1	ρn−1	PROPN
ejpam-4694	369	4	gin−1	gin−1	PROPN
ejpam-4694	369	5	=	=	PUNCT
ejpam-4694	370	1	−	−	PROPN
ejpam-4694	370	2	n−2∑	n−2∑	NUM
ejpam-4694	370	3	j=0	j=0	PROPN
ejpam-4694	370	4	(	(	PUNCT
ejpam-4694	370	5	n	n	X
ejpam-4694	370	6	j	j	PROPN
ejpam-4694	370	7	)	)	PUNCT
ejpam-4694	370	8	1	1	NUM
ejpam-4694	371	1	ρj	ρj	X
ejpam-4694	371	2	gij	gij	NOUN
ejpam-4694	371	3	+	+	CCONJ
ejpam-4694	371	4	n∑	n∑	ADJ
ejpam-4694	371	5	j=0	j=0	PROPN
ejpam-4694	371	6	(	(	PUNCT
ejpam-4694	371	7	n	n	X
ejpam-4694	371	8	j	j	PROPN
ejpam-4694	371	9	)	)	PUNCT
ejpam-4694	372	1	j	j	PROPN
ejpam-4694	373	1	ρj−1	ρj−1	PROPN
ejpam-4694	373	2	ĝ(k	ĝ(k	PROPN
ejpam-4694	373	3	,	,	PUNCT
ejpam-4694	373	4	α	α	NOUN
ejpam-4694	373	5	)	)	PUNCT
ejpam-4694	373	6	j	j	PROPN
ejpam-4694	373	7	(	(	PUNCT
ejpam-4694	373	8	x;λ	x;λ	PROPN
ejpam-4694	373	9	,	,	PUNCT
ejpam-4694	373	10	ρ	ρ	PROPN
ejpam-4694	373	11	,	,	PUNCT
ejpam-4694	373	12	u	u	NOUN
ejpam-4694	373	13	,	,	PUNCT
ejpam-4694	373	14	a	a	DET
ejpam-4694	373	15	,	,	PUNCT
ejpam-4694	373	16	b	b	NOUN
ejpam-4694	373	17	)	)	PUNCT
ejpam-4694	373	18	.	.	PUNCT
ejpam-4694	374	1	this	this	PRON
ejpam-4694	374	2	completes	complete	VERB
ejpam-4694	374	3	the	the	DET
ejpam-4694	374	4	proof	proof	NOUN
ejpam-4694	374	5	of	of	ADP
ejpam-4694	374	6	the	the	DET
ejpam-4694	374	7	theorem	theorem	PROPN
ejpam-4694	374	8	.	.	PROPN
ejpam-4694	374	9	remark	remark	PROPN
ejpam-4694	374	10	4.5	4.5	NUM
ejpam-4694	374	11	.	.	PUNCT
ejpam-4694	375	1	with	with	ADP
ejpam-4694	375	2	the	the	DET
ejpam-4694	375	3	aid	aid	NOUN
ejpam-4694	375	4	of	of	ADP
ejpam-4694	375	5	the	the	DET
ejpam-4694	375	6	explicit	explicit	ADJ
ejpam-4694	375	7	formula	formula	NOUN
ejpam-4694	375	8	in	in	ADP
ejpam-4694	375	9	theorem	theorem	ADJ
ejpam-4694	375	10	2.3	2.3	NUM
ejpam-4694	375	11	,	,	PUNCT
ejpam-4694	375	12	one	one	PRON
ejpam-4694	375	13	can	can	AUX
ejpam-4694	375	14	easily	easily	ADV
ejpam-4694	375	15	compute	compute	VERB
ejpam-4694	375	16	the	the	DET
ejpam-4694	375	17	value	value	NOUN
ejpam-4694	375	18	of	of	ADP
ejpam-4694	375	19	gin	gin	NOUN
ejpam-4694	375	20	recursively	recursively	NOUN
ejpam-4694	375	21	.	.	PUNCT
ejpam-4694	376	1	5	5	X
ejpam-4694	376	2	.	.	X
ejpam-4694	376	3	connections	connection	NOUN
ejpam-4694	376	4	with	with	ADP
ejpam-4694	376	5	some	some	DET
ejpam-4694	376	6	special	special	ADJ
ejpam-4694	376	7	polynomials	polynomial	NOUN
ejpam-4694	376	8	here	here	ADV
ejpam-4694	376	9	,	,	PUNCT
ejpam-4694	376	10	some	some	DET
ejpam-4694	376	11	connections	connection	NOUN
ejpam-4694	376	12	of	of	ADP
ejpam-4694	376	13	the	the	DET
ejpam-4694	376	14	higher	high	ADJ
ejpam-4694	376	15	order	order	NOUN
ejpam-4694	376	16	degenerate	degenerate	ADJ
ejpam-4694	376	17	apostol	apostol	NOUN
ejpam-4694	376	18	-	-	PUNCT
ejpam-4694	376	19	type	type	NOUN
ejpam-4694	376	20	poly	poly	ADJ
ejpam-4694	376	21	-	-	PUNCT
ejpam-4694	376	22	genocchi	genocchi	NOUN
ejpam-4694	376	23	polynomials	polynomial	VERB
ejpam-4694	376	24	ĝ(k	ĝ(k	PRON
ejpam-4694	376	25	,	,	PUNCT
ejpam-4694	376	26	α	α	NOUN
ejpam-4694	376	27	)	)	PUNCT
ejpam-4694	376	28	n	n	CCONJ
ejpam-4694	376	29	(	(	PUNCT
ejpam-4694	376	30	x;λ	x;λ	PROPN
ejpam-4694	376	31	,	,	PUNCT
ejpam-4694	376	32	ρ	ρ	PROPN
ejpam-4694	376	33	,	,	PUNCT
ejpam-4694	376	34	u	u	NOUN
ejpam-4694	376	35	,	,	PUNCT
ejpam-4694	376	36	a	a	DET
ejpam-4694	376	37	,	,	PUNCT
ejpam-4694	376	38	b	b	NOUN
ejpam-4694	376	39	)	)	PUNCT
ejpam-4694	376	40	with	with	ADP
ejpam-4694	376	41	other	other	ADJ
ejpam-4694	376	42	well	well	ADV
ejpam-4694	376	43	-	-	PUNCT
ejpam-4694	376	44	known	know	VERB
ejpam-4694	376	45	special	special	ADJ
ejpam-4694	376	46	numbers	number	NOUN
ejpam-4694	376	47	and	and	CCONJ
ejpam-4694	376	48	polynomials	polynomial	NOUN
ejpam-4694	376	49	will	will	AUX
ejpam-4694	376	50	be	be	AUX
ejpam-4694	376	51	established	establish	VERB
ejpam-4694	376	52	.	.	PUNCT
ejpam-4694	377	1	carlitz	carlitz	PROPN
ejpam-4694	378	1	[	[	X
ejpam-4694	378	2	10	10	NUM
ejpam-4694	378	3	,	,	PUNCT
ejpam-4694	378	4	11	11	NUM
ejpam-4694	378	5	]	]	PUNCT
ejpam-4694	378	6	defined	define	VERB
ejpam-4694	378	7	the	the	DET
ejpam-4694	378	8	degenerate	degenerate	ADJ
ejpam-4694	378	9	bernoulli	bernoulli	NOUN
ejpam-4694	378	10	polynomials	polynomial	NOUN
ejpam-4694	378	11	,	,	PUNCT
ejpam-4694	378	12	denoted	denote	VERB
ejpam-4694	378	13	by	by	ADP
ejpam-4694	378	14	βn	βn	NOUN
ejpam-4694	378	15	,	,	PUNCT
ejpam-4694	378	16	ρ(x	ρ(x	PROPN
ejpam-4694	378	17	)	)	PUNCT
ejpam-4694	378	18	,	,	PUNCT
ejpam-4694	378	19	as	as	SCONJ
ejpam-4694	378	20	follows	follow	VERB
ejpam-4694	378	21	:	:	PUNCT
ejpam-4694	378	22	t	t	PROPN
ejpam-4694	378	23	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	378	24	1	1	NUM
ejpam-4694	378	25	exρ(t	exρ(t	NUM
ejpam-4694	378	26	)	)	PUNCT
ejpam-4694	378	27	=	=	PUNCT
ejpam-4694	379	1	∞∑	∞∑	PRON
ejpam-4694	379	2	n=0	n=0	NUM
ejpam-4694	379	3	βn	βn	NOUN
ejpam-4694	379	4	,	,	PUNCT
ejpam-4694	379	5	ρ(x	ρ(x	PROPN
ejpam-4694	379	6	)	)	PUNCT
ejpam-4694	379	7	tn	tn	NOUN
ejpam-4694	379	8	n	n	PROPN
ejpam-4694	379	9	!	!	PUNCT
ejpam-4694	379	10	.	.	PUNCT
ejpam-4694	380	1	(	(	PUNCT
ejpam-4694	380	2	48	48	NUM
ejpam-4694	380	3	)	)	PUNCT
ejpam-4694	380	4	one	one	NOUN
ejpam-4694	380	5	may	may	AUX
ejpam-4694	380	6	extend	extend	VERB
ejpam-4694	380	7	this	this	PRON
ejpam-4694	380	8	to	to	ADP
ejpam-4694	380	9	higher	high	ADJ
ejpam-4694	380	10	order	order	NOUN
ejpam-4694	380	11	degenerate	degenerate	ADJ
ejpam-4694	380	12	bernoulli	bernoulli	NOUN
ejpam-4694	380	13	polynomials	polynomial	NOUN
ejpam-4694	380	14	,	,	PUNCT
ejpam-4694	380	15	which	which	PRON
ejpam-4694	380	16	can	can	AUX
ejpam-4694	380	17	be	be	AUX
ejpam-4694	380	18	defined	define	VERB
ejpam-4694	380	19	as	as	ADP
ejpam-4694	380	20	follows	follow	VERB
ejpam-4694	380	21	(	(	PUNCT
ejpam-4694	380	22	t	t	NOUN
ejpam-4694	380	23	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	380	24	1	1	NUM
ejpam-4694	380	25	)	)	PUNCT
ejpam-4694	380	26	s	s	PART
ejpam-4694	380	27	exρ(t	exρ(t	NOUN
ejpam-4694	380	28	)	)	PUNCT
ejpam-4694	380	29	=	=	PUNCT
ejpam-4694	381	1	∞∑	∞∑	NUM
ejpam-4694	381	2	n=0	n=0	NUM
ejpam-4694	381	3	β(s	β(	NOUN
ejpam-4694	381	4	)	)	PUNCT
ejpam-4694	381	5	n	n	CCONJ
ejpam-4694	381	6	,	,	PUNCT
ejpam-4694	381	7	ρ(x	ρ(x	PROPN
ejpam-4694	381	8	)	)	PUNCT
ejpam-4694	381	9	tn	tn	NOUN
ejpam-4694	381	10	n	n	PROPN
ejpam-4694	381	11	!	!	PUNCT
ejpam-4694	381	12	.	.	PUNCT
ejpam-4694	382	1	(	(	PUNCT
ejpam-4694	382	2	49	49	NUM
ejpam-4694	382	3	)	)	PUNCT
ejpam-4694	382	4	the	the	DET
ejpam-4694	382	5	degenerate	degenerate	ADJ
ejpam-4694	382	6	frobenius	frobenius	NOUN
ejpam-4694	382	7	-	-	PUNCT
ejpam-4694	382	8	euler	euler	NOUN
ejpam-4694	382	9	polynomials	polynomial	NOUN
ejpam-4694	382	10	of	of	ADP
ejpam-4694	382	11	higher	high	ADJ
ejpam-4694	382	12	order	order	NOUN
ejpam-4694	382	13	,	,	PUNCT
ejpam-4694	382	14	denoted	denote	VERB
ejpam-4694	382	15	by	by	ADP
ejpam-4694	382	16	h	h	PROPN
ejpam-4694	382	17	(	(	PUNCT
ejpam-4694	382	18	s	s	NOUN
ejpam-4694	382	19	)	)	PUNCT
ejpam-4694	382	20	n	n	CCONJ
ejpam-4694	382	21	,	,	PUNCT
ejpam-4694	382	22	ρ(x;µ	ρ(x;µ	NUM
ejpam-4694	382	23	)	)	PUNCT
ejpam-4694	382	24	,	,	PUNCT
ejpam-4694	382	25	are	be	AUX
ejpam-4694	382	26	defined	define	VERB
ejpam-4694	382	27	in	in	ADP
ejpam-4694	382	28	[	[	X
ejpam-4694	382	29	42	42	NUM
ejpam-4694	382	30	]	]	PUNCT
ejpam-4694	382	31	as	as	SCONJ
ejpam-4694	382	32	follows	follow	VERB
ejpam-4694	382	33	(	(	PUNCT
ejpam-4694	382	34	1−	1−	NUM
ejpam-4694	382	35	µ	µ	NUM
ejpam-4694	382	36	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	382	37	µ	µ	X
ejpam-4694	382	38	)	)	PUNCT
ejpam-4694	382	39	s	s	PART
ejpam-4694	382	40	exρ(t	exρ(t	NOUN
ejpam-4694	382	41	)	)	PUNCT
ejpam-4694	382	42	=	=	PUNCT
ejpam-4694	383	1	∞∑	∞∑	NUM
ejpam-4694	383	2	n=0	n=0	NUM
ejpam-4694	383	3	h(s	h(	NOUN
ejpam-4694	383	4	)	)	PUNCT
ejpam-4694	383	5	n	n	CCONJ
ejpam-4694	383	6	,	,	PUNCT
ejpam-4694	383	7	ρ(x;µ	ρ(x;µ	NUM
ejpam-4694	383	8	)	)	PUNCT
ejpam-4694	383	9	tn	tn	PROPN
ejpam-4694	383	10	n	n	PROPN
ejpam-4694	383	11	!	!	PUNCT
ejpam-4694	383	12	.	.	PUNCT
ejpam-4694	384	1	(	(	PUNCT
ejpam-4694	384	2	50	50	NUM
ejpam-4694	384	3	)	)	PUNCT
ejpam-4694	384	4	when	when	SCONJ
ejpam-4694	384	5	s	s	VERB
ejpam-4694	384	6	=	=	SYM
ejpam-4694	384	7	1	1	NUM
ejpam-4694	384	8	,	,	PUNCT
ejpam-4694	384	9	w	w	NOUN
ejpam-4694	384	10	=	=	SYM
ejpam-4694	384	11	0	0	NUM
ejpam-4694	384	12	,	,	PUNCT
ejpam-4694	384	13	(	(	PUNCT
ejpam-4694	384	14	50	50	NUM
ejpam-4694	384	15	)	)	PUNCT
ejpam-4694	384	16	gives	give	VERB
ejpam-4694	384	17	e	e	NOUN
ejpam-4694	384	18	(	(	PUNCT
ejpam-4694	384	19	s	s	NOUN
ejpam-4694	384	20	)	)	PUNCT
ejpam-4694	384	21	n	n	PROPN
ejpam-4694	384	22	(	(	PUNCT
ejpam-4694	384	23	x;µ	x;µ	PROPN
ejpam-4694	384	24	,	,	PUNCT
ejpam-4694	384	25	λ	λ	PROPN
ejpam-4694	384	26	)	)	PUNCT
ejpam-4694	384	27	,	,	PUNCT
ejpam-4694	384	28	the	the	DET
ejpam-4694	384	29	apostol	apostol	NOUN
ejpam-4694	384	30	-	-	PUNCT
ejpam-4694	384	31	type	type	NOUN
ejpam-4694	384	32	frobenius	frobenius	NOUN
ejpam-4694	384	33	-	-	PUNCT
ejpam-4694	384	34	euler	euler	NOUN
ejpam-4694	384	35	polynomials	polynomial	NOUN
ejpam-4694	384	36	in	in	ADP
ejpam-4694	384	37	[	[	X
ejpam-4694	384	38	41	41	NUM
ejpam-4694	384	39	]	]	PUNCT
ejpam-4694	384	40	.	.	PUNCT
ejpam-4694	385	1	now	now	ADV
ejpam-4694	385	2	,	,	PUNCT
ejpam-4694	385	3	if	if	SCONJ
ejpam-4694	385	4	λ	λ	PROPN
ejpam-4694	385	5	=	=	SYM
ejpam-4694	385	6	0	0	NUM
ejpam-4694	385	7	,	,	PUNCT
ejpam-4694	385	8	we	we	PRON
ejpam-4694	385	9	can	can	AUX
ejpam-4694	385	10	define	define	VERB
ejpam-4694	385	11	the	the	DET
ejpam-4694	385	12	frobenius	frobenius	NOUN
ejpam-4694	385	13	-	-	PUNCT
ejpam-4694	385	14	euler	euler	NOUN
ejpam-4694	385	15	polynomials	polynomial	NOUN
ejpam-4694	385	16	,	,	PUNCT
ejpam-4694	385	17	denoted	denote	VERB
ejpam-4694	385	18	by	by	ADP
ejpam-4694	385	19	e	e	PROPN
ejpam-4694	385	20	(	(	PUNCT
ejpam-4694	385	21	s	s	NOUN
ejpam-4694	385	22	)	)	PUNCT
ejpam-4694	385	23	n	n	CCONJ
ejpam-4694	385	24	,	,	PUNCT
ejpam-4694	385	25	h(x;µ	h(x;µ	PROPN
ejpam-4694	385	26	)	)	PUNCT
ejpam-4694	385	27	,	,	PUNCT
ejpam-4694	385	28	as	as	SCONJ
ejpam-4694	385	29	follows	follow	VERB
ejpam-4694	385	30	:	:	PUNCT
ejpam-4694	385	31	(	(	PUNCT
ejpam-4694	385	32	1−	1−	NUM
ejpam-4694	385	33	µ	µ	X
ejpam-4694	385	34	et	et	NOUN
ejpam-4694	385	35	−	−	PROPN
ejpam-4694	385	36	µ	µ	X
ejpam-4694	385	37	)	)	PUNCT
ejpam-4694	385	38	s	s	PART
ejpam-4694	385	39	ext	ext	NOUN
ejpam-4694	385	40	=	=	NOUN
ejpam-4694	386	1	∞∑	∞∑	NUM
ejpam-4694	386	2	n=0	n=0	PROPN
ejpam-4694	386	3	e(s	e(s	PROPN
ejpam-4694	386	4	)	)	PUNCT
ejpam-4694	386	5	n	n	CCONJ
ejpam-4694	386	6	(	(	PUNCT
ejpam-4694	386	7	x;µ	x;µ	NUM
ejpam-4694	386	8	)	)	PUNCT
ejpam-4694	386	9	tn	tn	PROPN
ejpam-4694	386	10	n	n	PROPN
ejpam-4694	386	11	!	!	PUNCT
ejpam-4694	386	12	.	.	PUNCT
ejpam-4694	387	1	(	(	PUNCT
ejpam-4694	387	2	51	51	NUM
ejpam-4694	387	3	)	)	PUNCT
ejpam-4694	387	4	r.	r.	PROPN
ejpam-4694	387	5	corcino	corcino	PROPN
ejpam-4694	387	6	,	,	PUNCT
ejpam-4694	387	7	c.	c.	PROPN
ejpam-4694	387	8	corcino	corcino	PROPN
ejpam-4694	387	9	/	/	SYM
ejpam-4694	387	10	eur	eur	PROPN
ejpam-4694	387	11	.	.	PUNCT
ejpam-4694	388	1	j.	j.	PROPN
ejpam-4694	388	2	pure	pure	PROPN
ejpam-4694	388	3	appl	appl	PROPN
ejpam-4694	388	4	.	.	PROPN
ejpam-4694	388	5	math	math	PROPN
ejpam-4694	388	6	,	,	PUNCT
ejpam-4694	388	7	16	16	NUM
ejpam-4694	388	8	(	(	PUNCT
ejpam-4694	388	9	2	2	NUM
ejpam-4694	388	10	)	)	PUNCT
ejpam-4694	388	11	(	(	PUNCT
ejpam-4694	388	12	2023	2023	NUM
ejpam-4694	388	13	)	)	PUNCT
ejpam-4694	388	14	,	,	PUNCT
ejpam-4694	388	15	687	687	NUM
ejpam-4694	388	16	-	-	SYM
ejpam-4694	388	17	712	712	NUM
ejpam-4694	388	18	705	705	NUM
ejpam-4694	388	19	the	the	DET
ejpam-4694	388	20	following	follow	VERB
ejpam-4694	388	21	theorem	theorem	NOUN
ejpam-4694	388	22	contains	contain	VERB
ejpam-4694	388	23	an	an	DET
ejpam-4694	388	24	identity	identity	NOUN
ejpam-4694	388	25	that	that	PRON
ejpam-4694	388	26	relates	relate	VERB
ejpam-4694	388	27	the	the	DET
ejpam-4694	388	28	degenerate	degenerate	ADJ
ejpam-4694	388	29	apostol	apostol	NOUN
ejpam-4694	388	30	-	-	PUNCT
ejpam-4694	388	31	frobeniustype	frobeniustype	NOUN
ejpam-4694	388	32	poly	poly	ADJ
ejpam-4694	388	33	-	-	PUNCT
ejpam-4694	388	34	genocchi	genocchi	NOUN
ejpam-4694	388	35	polynomials	polynomial	NOUN
ejpam-4694	388	36	of	of	ADP
ejpam-4694	388	37	higher	high	ADJ
ejpam-4694	388	38	order	order	NOUN
ejpam-4694	388	39	with	with	ADP
ejpam-4694	388	40	parameters	parameter	NOUN
ejpam-4694	388	41	a	a	DET
ejpam-4694	388	42	,	,	PUNCT
ejpam-4694	388	43	b	b	PROPN
ejpam-4694	388	44	and	and	CCONJ
ejpam-4694	388	45	c	c	NOUN
ejpam-4694	388	46	to	to	ADP
ejpam-4694	388	47	the	the	DET
ejpam-4694	388	48	degenerate	degenerate	ADJ
ejpam-4694	388	49	stirling	stirling	NOUN
ejpam-4694	388	50	numbers	number	NOUN
ejpam-4694	388	51	of	of	ADP
ejpam-4694	388	52	the	the	DET
ejpam-4694	388	53	first	first	ADJ
ejpam-4694	388	54	kind	kind	NOUN
ejpam-4694	388	55	s1,ρ(n	s1,ρ(n	NOUN
ejpam-4694	388	56	,	,	PUNCT
ejpam-4694	388	57	k	k	NOUN
ejpam-4694	388	58	)	)	PUNCT
ejpam-4694	388	59	in	in	ADP
ejpam-4694	388	60	(	(	PUNCT
ejpam-4694	388	61	18	18	NUM
ejpam-4694	388	62	)	)	PUNCT
ejpam-4694	388	63	.	.	PUNCT
ejpam-4694	389	1	here	here	ADV
ejpam-4694	389	2	,	,	PUNCT
ejpam-4694	389	3	it	it	PRON
ejpam-4694	389	4	is	be	AUX
ejpam-4694	389	5	important	important	ADJ
ejpam-4694	389	6	to	to	PART
ejpam-4694	389	7	note	note	VERB
ejpam-4694	389	8	that	that	SCONJ
ejpam-4694	389	9	if	if	SCONJ
ejpam-4694	389	10	(	(	PUNCT
ejpam-4694	389	11	c0	c0	NOUN
ejpam-4694	389	12	,	,	PUNCT
ejpam-4694	389	13	c1	c1	PROPN
ejpam-4694	389	14	,	,	PUNCT
ejpam-4694	389	15	.	.	PUNCT
ejpam-4694	389	16	.	.	PUNCT
ejpam-4694	390	1	.	.	PUNCT
ejpam-4694	391	1	,	,	PUNCT
ejpam-4694	391	2	cj	cj	INTJ
ejpam-4694	391	3	,	,	PUNCT
ejpam-4694	391	4	.	.	PUNCT
ejpam-4694	391	5	.	.	PUNCT
ejpam-4694	391	6	.	.	PUNCT
ejpam-4694	391	7	)	)	PUNCT
ejpam-4694	391	8	is	be	AUX
ejpam-4694	391	9	any	any	DET
ejpam-4694	391	10	sequence	sequence	NOUN
ejpam-4694	391	11	of	of	ADP
ejpam-4694	391	12	numbers	number	NOUN
ejpam-4694	391	13	and	and	CCONJ
ejpam-4694	391	14	l	l	NOUN
ejpam-4694	391	15	is	be	AUX
ejpam-4694	391	16	a	a	DET
ejpam-4694	391	17	positive	positive	ADJ
ejpam-4694	391	18	integer	integer	NOUN
ejpam-4694	391	19	,	,	PUNCT
ejpam-4694	391	20	then	then	PROPN
ejpam-4694	391	21	∞∑	∞∑	NUM
ejpam-4694	391	22	j=0	j=0	PROPN
ejpam-4694	391	23	cj	cj	PROPN
ejpam-4694	391	24	tj	tj	PROPN
ejpam-4694	391	25	j	j	PROPN
ejpam-4694	391	26	!	!	PUNCT
ejpam-4694	391	27	l	l	X
ejpam-4694	392	1	=	=	PUNCT
ejpam-4694	393	1	l∏	l∏	NOUN
ejpam-4694	393	2	i=1	i=1	X
ejpam-4694	394	1	(	(	PUNCT
ejpam-4694	394	2	∞∑	∞∑	NUM
ejpam-4694	394	3	ni=0	ni=0	PROPN
ejpam-4694	394	4	cni	cni	PROPN
ejpam-4694	394	5	ni	ni	PROPN
ejpam-4694	394	6	!	!	PROPN
ejpam-4694	394	7	tni	tni	NOUN
ejpam-4694	394	8	)	)	PUNCT
ejpam-4694	395	1	=	=	PUNCT
ejpam-4694	396	1	∞∑	∞∑	NUM
ejpam-4694	396	2	n=0	n=0	NUM
ejpam-4694	396	3	{	{	PUNCT
ejpam-4694	396	4	∑	∑	ADV
ejpam-4694	396	5	n1+n2+	n1+n2+	NOUN
ejpam-4694	396	6	...	...	PUNCT
ejpam-4694	396	7	+nα	+nα	PUNCT
ejpam-4694	396	8	=	=	PROPN
ejpam-4694	396	9	n	n	PROPN
ejpam-4694	396	10	l∏	l∏	PROPN
ejpam-4694	396	11	i=1	i=1	PROPN
ejpam-4694	397	1	cni	cni	PROPN
ejpam-4694	397	2	(	(	PUNCT
ejpam-4694	397	3	n	n	CCONJ
ejpam-4694	397	4	n1	n1	NOUN
ejpam-4694	397	5	,	,	PUNCT
ejpam-4694	397	6	n2	n2	NOUN
ejpam-4694	397	7	,	,	PUNCT
ejpam-4694	397	8	.	.	PUNCT
ejpam-4694	397	9	.	.	PUNCT
ejpam-4694	398	1	.	.	PUNCT
ejpam-4694	398	2	,	,	PUNCT
ejpam-4694	398	3	nα	nα	NOUN
ejpam-4694	398	4	)	)	PUNCT
ejpam-4694	398	5	}	}	PUNCT
ejpam-4694	398	6	tn	tn	PROPN
ejpam-4694	398	7	n	n	X
ejpam-4694	398	8	!	!	PUNCT
ejpam-4694	398	9	.	.	PUNCT
ejpam-4694	399	1	(	(	PUNCT
ejpam-4694	399	2	52	52	NUM
ejpam-4694	399	3	)	)	PUNCT
ejpam-4694	399	4	(	(	PUNCT
ejpam-4694	399	5	see	see	VERB
ejpam-4694	399	6	[	[	X
ejpam-4694	399	7	12	12	NUM
ejpam-4694	399	8	]	]	PUNCT
ejpam-4694	399	9	)	)	PUNCT
ejpam-4694	399	10	.	.	PUNCT
ejpam-4694	400	1	now	now	ADV
ejpam-4694	400	2	,	,	PUNCT
ejpam-4694	400	3	we	we	PRON
ejpam-4694	400	4	are	be	AUX
ejpam-4694	400	5	ready	ready	ADJ
ejpam-4694	400	6	to	to	PART
ejpam-4694	400	7	introduce	introduce	VERB
ejpam-4694	400	8	the	the	DET
ejpam-4694	400	9	following	follow	VERB
ejpam-4694	400	10	theorem	theorem	NOUN
ejpam-4694	400	11	.	.	PUNCT
ejpam-4694	400	12	theorem	theorem	VERB
ejpam-4694	400	13	5.1	5.1	NUM
ejpam-4694	400	14	.	.	PUNCT
ejpam-4694	401	1	the	the	DET
ejpam-4694	401	2	degenerate	degenerate	ADJ
ejpam-4694	401	3	apostol	apostol	NOUN
ejpam-4694	401	4	-	-	PUNCT
ejpam-4694	401	5	frobenius	frobenius	NOUN
ejpam-4694	401	6	-	-	PUNCT
ejpam-4694	401	7	type	type	NOUN
ejpam-4694	401	8	poly	poly	ADJ
ejpam-4694	401	9	-	-	PUNCT
ejpam-4694	401	10	genocchi	genocchi	NOUN
ejpam-4694	401	11	polynomials	polynomial	NOUN
ejpam-4694	401	12	of	of	ADP
ejpam-4694	401	13	higher	high	ADJ
ejpam-4694	401	14	order	order	NOUN
ejpam-4694	401	15	with	with	ADP
ejpam-4694	401	16	parameters	parameter	NOUN
ejpam-4694	401	17	a	a	DET
ejpam-4694	401	18	,	,	PUNCT
ejpam-4694	401	19	b	b	NOUN
ejpam-4694	401	20	and	and	CCONJ
ejpam-4694	401	21	c	c	NOUN
ejpam-4694	401	22	satisfies	satisfy	VERB
ejpam-4694	401	23	the	the	DET
ejpam-4694	401	24	relation	relation	NOUN
ejpam-4694	401	25	,	,	PUNCT
ejpam-4694	401	26	ĝ(k	ĝ(k	PRON
ejpam-4694	401	27	,	,	PUNCT
ejpam-4694	401	28	α	α	NOUN
ejpam-4694	401	29	)	)	PUNCT
ejpam-4694	401	30	n	n	CCONJ
ejpam-4694	401	31	(	(	PUNCT
ejpam-4694	401	32	x;λ	x;λ	PROPN
ejpam-4694	401	33	,	,	PUNCT
ejpam-4694	401	34	ρ	ρ	PROPN
ejpam-4694	401	35	,	,	PUNCT
ejpam-4694	401	36	u	u	NOUN
ejpam-4694	401	37	,	,	PUNCT
ejpam-4694	401	38	a	a	DET
ejpam-4694	401	39	,	,	PUNCT
ejpam-4694	401	40	b	b	NOUN
ejpam-4694	401	41	)	)	PUNCT
ejpam-4694	402	1	=	=	SYM
ejpam-4694	402	2	n∑	n∑	NOUN
ejpam-4694	402	3	j=0	j=0	PROPN
ejpam-4694	402	4	(	(	PUNCT
ejpam-4694	402	5	n	n	X
ejpam-4694	402	6	j	j	NOUN
ejpam-4694	402	7	)	)	PUNCT
ejpam-4694	402	8	(	(	PUNCT
ejpam-4694	402	9	ln	ln	PROPN
ejpam-4694	402	10	ab)n−jĝ(α	ab)n−jĝ(α	PROPN
ejpam-4694	402	11	)	)	PUNCT
ejpam-4694	402	12	n−j	n−j	ADV
ejpam-4694	402	13	(	(	PUNCT
ejpam-4694	402	14	x	x	X
ejpam-4694	402	15	ln	ln	NOUN
ejpam-4694	402	16	ab	ab	PROPN
ejpam-4694	402	17	;	;	PUNCT
ejpam-4694	402	18	λ	λ	PROPN
ejpam-4694	402	19	,	,	PUNCT
ejpam-4694	402	20	ρ	ρ	PROPN
ejpam-4694	402	21	,	,	PUNCT
ejpam-4694	402	22	u	u	NOUN
ejpam-4694	402	23	)	)	PUNCT
ejpam-4694	402	24	dj	dj	NOUN
ejpam-4694	402	25	(	(	PUNCT
ejpam-4694	402	26	53	53	NUM
ejpam-4694	402	27	)	)	PUNCT
ejpam-4694	402	28	where	where	SCONJ
ejpam-4694	402	29	dj	dj	NOUN
ejpam-4694	402	30	=	=	SYM
ejpam-4694	402	31	∑	∑	NOUN
ejpam-4694	402	32	n1+n2+	n1+n2+	NOUN
ejpam-4694	402	33	...	...	PUNCT
ejpam-4694	402	34	+nα	+nα	PUNCT
ejpam-4694	402	35	=	=	PROPN
ejpam-4694	402	36	j	j	PROPN
ejpam-4694	402	37	α∏	α∏	PROPN
ejpam-4694	402	38	i=1	i=1	PROPN
ejpam-4694	402	39	cni	cni	PROPN
ejpam-4694	402	40	(	(	PUNCT
ejpam-4694	402	41	j	j	PROPN
ejpam-4694	402	42	n1	n1	PROPN
ejpam-4694	402	43	,	,	PUNCT
ejpam-4694	402	44	n2	n2	NOUN
ejpam-4694	402	45	,	,	PUNCT
ejpam-4694	402	46	.	.	PUNCT
ejpam-4694	402	47	.	.	PUNCT
ejpam-4694	403	1	.	.	PUNCT
ejpam-4694	403	2	,	,	PUNCT
ejpam-4694	403	3	nα	nα	NOUN
ejpam-4694	403	4	)	)	PUNCT
ejpam-4694	403	5	cj	cj	NOUN
ejpam-4694	404	1	=	=	SYM
ejpam-4694	404	2	j∑	j∑	PROPN
ejpam-4694	404	3	m=0	m=0	PROPN
ejpam-4694	404	4	(	(	PUNCT
ejpam-4694	404	5	−1)m+j+1	−1)m+j+1	NOUN
ejpam-4694	404	6	(	(	PUNCT
ejpam-4694	404	7	(	(	PUNCT
ejpam-4694	404	8	1−	1−	NUM
ejpam-4694	404	9	u	u	NOUN
ejpam-4694	404	10	)	)	PUNCT
ejpam-4694	404	11	ln	ln	PROPN
ejpam-4694	404	12	ab)j(1)m+1,ρs1,ρ(j	ab)j(1)m+1,ρs1,ρ(j	PROPN
ejpam-4694	404	13	+	+	CCONJ
ejpam-4694	404	14	1,m+	1,m+	NUM
ejpam-4694	404	15	1	1	NUM
ejpam-4694	404	16	)	)	PUNCT
ejpam-4694	404	17	(	(	PUNCT
ejpam-4694	404	18	j	j	PROPN
ejpam-4694	404	19	+	+	CCONJ
ejpam-4694	404	20	1)(m+	1)(m+	NUM
ejpam-4694	404	21	1)k−1	1)k−1	NUM
ejpam-4694	404	22	.	.	PUNCT
ejpam-4694	405	1	proof	proof	NOUN
ejpam-4694	405	2	.	.	PUNCT
ejpam-4694	406	1	now	now	ADV
ejpam-4694	406	2	,	,	PUNCT
ejpam-4694	406	3	(	(	PUNCT
ejpam-4694	406	4	27	27	NUM
ejpam-4694	406	5	)	)	PUNCT
ejpam-4694	406	6	can	can	AUX
ejpam-4694	406	7	be	be	AUX
ejpam-4694	406	8	written	write	VERB
ejpam-4694	406	9	as	as	ADP
ejpam-4694	406	10	∞∑	∞∑	NUM
ejpam-4694	406	11	n=0	n=0	NUM
ejpam-4694	406	12	ĝ(k	ĝ(k	PROPN
ejpam-4694	406	13	,	,	PUNCT
ejpam-4694	406	14	α	α	NOUN
ejpam-4694	406	15	)	)	PUNCT
ejpam-4694	406	16	n	n	CCONJ
ejpam-4694	406	17	(	(	PUNCT
ejpam-4694	406	18	x;λ	x;λ	PROPN
ejpam-4694	406	19	,	,	PUNCT
ejpam-4694	406	20	ρ	ρ	PROPN
ejpam-4694	406	21	,	,	PUNCT
ejpam-4694	406	22	u	u	NOUN
ejpam-4694	406	23	,	,	PUNCT
ejpam-4694	406	24	a	a	DET
ejpam-4694	406	25	,	,	PUNCT
ejpam-4694	406	26	b	b	NOUN
ejpam-4694	406	27	)	)	PUNCT
ejpam-4694	406	28	tn	tn	NOUN
ejpam-4694	406	29	n	n	NOUN
ejpam-4694	406	30	!	!	PUNCT
ejpam-4694	407	1	=	=	PUNCT
ejpam-4694	407	2	exρ(t	exρ(t	X
ejpam-4694	407	3	)	)	PUNCT
ejpam-4694	407	4	(	(	PUNCT
ejpam-4694	407	5	λbt	λbt	VERB
ejpam-4694	407	6	−	−	NOUN
ejpam-4694	407	7	ua−t)α	ua−t)α	NUM
ejpam-4694	407	8	(	(	PUNCT
ejpam-4694	407	9	∞∑	∞∑	PROPN
ejpam-4694	407	10	m=1	m=1	X
ejpam-4694	407	11	(	(	PUNCT
ejpam-4694	407	12	1)m	1)m	NUM
ejpam-4694	407	13	,	,	PUNCT
ejpam-4694	407	14	ρ	ρ	PROPN
ejpam-4694	407	15	mk−1	mk−1	PROPN
ejpam-4694	407	16	(	(	PUNCT
ejpam-4694	407	17	logρ(1	logρ(1	PROPN
ejpam-4694	407	18	+	+	CCONJ
ejpam-4694	407	19	(	(	PUNCT
ejpam-4694	407	20	1−	1−	NUM
ejpam-4694	407	21	u)t	u)t	X
ejpam-4694	407	22	ln	ln	PROPN
ejpam-4694	407	23	ab))m	ab))m	PROPN
ejpam-4694	407	24	m	m	PROPN
ejpam-4694	407	25	!	!	PUNCT
ejpam-4694	407	26	)	)	PUNCT
ejpam-4694	408	1	α	α	X
ejpam-4694	408	2	=	=	PUNCT
ejpam-4694	408	3	exρ(t	exρ(t	PROPN
ejpam-4694	408	4	)	)	PUNCT
ejpam-4694	408	5	(	(	PUNCT
ejpam-4694	408	6	λbt	λbt	VERB
ejpam-4694	408	7	−	−	NOUN
ejpam-4694	408	8	ua−t)α	ua−t)α	NUM
ejpam-4694	408	9	(	(	PUNCT
ejpam-4694	408	10	∞∑	∞∑	NUM
ejpam-4694	408	11	m=0	m=0	PROPN
ejpam-4694	408	12	(	(	PUNCT
ejpam-4694	408	13	1)m+1,ρ	1)m+1,ρ	NUM
ejpam-4694	408	14	(	(	PUNCT
ejpam-4694	408	15	m+	m+	NUM
ejpam-4694	408	16	1)k−1	1)k−1	NUM
ejpam-4694	408	17	(	(	PUNCT
ejpam-4694	408	18	logρ(1	logρ(1	PROPN
ejpam-4694	408	19	+	+	CCONJ
ejpam-4694	408	20	(	(	PUNCT
ejpam-4694	408	21	1−	1−	NUM
ejpam-4694	408	22	u)t	u)t	X
ejpam-4694	408	23	ln	ln	ADV
ejpam-4694	408	24	ab))m+1	ab))m+1	PROPN
ejpam-4694	408	25	(	(	PUNCT
ejpam-4694	408	26	m+	m+	NOUN
ejpam-4694	408	27	1	1	NUM
ejpam-4694	408	28	)	)	PUNCT
ejpam-4694	408	29	!	!	PUNCT
ejpam-4694	408	30	)	)	PUNCT
ejpam-4694	409	1	α	α	X
ejpam-4694	409	2	=	=	PUNCT
ejpam-4694	409	3	exρ(t	exρ(t	PROPN
ejpam-4694	409	4	)	)	PUNCT
ejpam-4694	409	5	(	(	PUNCT
ejpam-4694	409	6	λbt	λbt	VERB
ejpam-4694	409	7	−	−	NOUN
ejpam-4694	409	8	ua−t)α	ua−t)α	ADV
ejpam-4694	409	9			PROPN
ejpam-4694	409	10	∞∑	∞∑	PROPN
ejpam-4694	409	11	m=0	m=0	PROPN
ejpam-4694	409	12	(	(	PUNCT
ejpam-4694	409	13	1)m+1,ρ	1)m+1,ρ	NUM
ejpam-4694	409	14	(	(	PUNCT
ejpam-4694	409	15	m+	m+	NUM
ejpam-4694	409	16	1)k−1	1)k−1	NUM
ejpam-4694	409	17	∞∑	∞∑	PROPN
ejpam-4694	409	18	j	j	PROPN
ejpam-4694	409	19	=	=	ADJ
ejpam-4694	409	20	m+1	m+1	NUM
ejpam-4694	409	21	s1,ρ(j	s1,ρ(j	NOUN
ejpam-4694	409	22	,	,	PUNCT
ejpam-4694	409	23	m+	m+	NOUN
ejpam-4694	409	24	1	1	NUM
ejpam-4694	409	25	)	)	PUNCT
ejpam-4694	409	26	(	(	PUNCT
ejpam-4694	409	27	(	(	PUNCT
ejpam-4694	409	28	1−	1−	NUM
ejpam-4694	409	29	u)t	u)t	X
ejpam-4694	409	30	ln	ln	PROPN
ejpam-4694	409	31	ab)j	ab)j	PROPN
ejpam-4694	409	32	j	j	PROPN
ejpam-4694	409	33	!	!	PUNCT
ejpam-4694	409	34	α	α	PRON
ejpam-4694	410	1	=	=	PUNCT
ejpam-4694	410	2	exρ(t	exρ(t	PROPN
ejpam-4694	410	3	)	)	PUNCT
ejpam-4694	410	4	(	(	PUNCT
ejpam-4694	410	5	λbt	λbt	VERB
ejpam-4694	410	6	−	−	NOUN
ejpam-4694	410	7	ua−t)α	ua−t)α	ADV
ejpam-4694	410	8			PROPN
ejpam-4694	410	9	∞∑	∞∑	PROPN
ejpam-4694	410	10	m=0	m=0	PROPN
ejpam-4694	410	11	(	(	PUNCT
ejpam-4694	410	12	1)m+1,ρ	1)m+1,ρ	NUM
ejpam-4694	410	13	(	(	PUNCT
ejpam-4694	410	14	m+	m+	NUM
ejpam-4694	410	15	1)k−1	1)k−1	NUM
ejpam-4694	410	16	∞∑	∞∑	PROPN
ejpam-4694	410	17	j	j	PROPN
ejpam-4694	410	18	=	=	NOUN
ejpam-4694	410	19	m	m	PROPN
ejpam-4694	410	20	s1,ρ(j	s1,ρ(j	NOUN
ejpam-4694	410	21	+	+	CCONJ
ejpam-4694	410	22	1,m+	1,m+	NUM
ejpam-4694	410	23	1	1	NUM
ejpam-4694	410	24	)	)	PUNCT
ejpam-4694	410	25	(	(	PUNCT
ejpam-4694	410	26	(	(	PUNCT
ejpam-4694	410	27	1−	1−	NUM
ejpam-4694	410	28	u)t	u)t	X
ejpam-4694	410	29	ln	ln	ADJ
ejpam-4694	410	30	ab)j+1	ab)j+1	NOUN
ejpam-4694	410	31	(	(	PUNCT
ejpam-4694	410	32	j	j	NOUN
ejpam-4694	410	33	+	+	NOUN
ejpam-4694	410	34	1	1	NUM
ejpam-4694	410	35	)	)	PUNCT
ejpam-4694	410	36	!	!	PUNCT
ejpam-4694	411	1	α	α	PROPN
ejpam-4694	411	2	r.	r.	PROPN
ejpam-4694	411	3	corcino	corcino	PROPN
ejpam-4694	411	4	,	,	PUNCT
ejpam-4694	411	5	c.	c.	PROPN
ejpam-4694	411	6	corcino	corcino	PROPN
ejpam-4694	411	7	/	/	SYM
ejpam-4694	411	8	eur	eur	PROPN
ejpam-4694	411	9	.	.	PUNCT
ejpam-4694	412	1	j.	j.	PROPN
ejpam-4694	412	2	pure	pure	PROPN
ejpam-4694	412	3	appl	appl	PROPN
ejpam-4694	412	4	.	.	PROPN
ejpam-4694	412	5	math	math	PROPN
ejpam-4694	412	6	,	,	PUNCT
ejpam-4694	412	7	16	16	NUM
ejpam-4694	412	8	(	(	PUNCT
ejpam-4694	412	9	2	2	NUM
ejpam-4694	412	10	)	)	PUNCT
ejpam-4694	412	11	(	(	PUNCT
ejpam-4694	412	12	2023	2023	NUM
ejpam-4694	412	13	)	)	PUNCT
ejpam-4694	412	14	,	,	PUNCT
ejpam-4694	412	15	687	687	NUM
ejpam-4694	412	16	-	-	SYM
ejpam-4694	412	17	712	712	NUM
ejpam-4694	412	18	706	706	NUM
ejpam-4694	412	19	=	=	SYM
ejpam-4694	412	20	exρ(t	exρ(t	PROPN
ejpam-4694	412	21	)	)	PUNCT
ejpam-4694	412	22	(	(	PUNCT
ejpam-4694	412	23	λbt	λbt	VERB
ejpam-4694	412	24	−	−	NOUN
ejpam-4694	412	25	ua−t)α	ua−t)α	ADV
ejpam-4694	412	26			PROPN
ejpam-4694	412	27	∞∑	∞∑	NUM
ejpam-4694	412	28	j=0	j=0	PROPN
ejpam-4694	412	29	j∑	j∑	PROPN
ejpam-4694	412	30	m=0	m=0	PROPN
ejpam-4694	412	31	(	(	PUNCT
ejpam-4694	412	32	1)m+1,ρ	1)m+1,ρ	NUM
ejpam-4694	412	33	(	(	PUNCT
ejpam-4694	412	34	m+	m+	NUM
ejpam-4694	412	35	1)k−1	1)k−1	NUM
ejpam-4694	412	36	s1,ρ(j	s1,ρ(j	NOUN
ejpam-4694	412	37	+	+	CCONJ
ejpam-4694	412	38	1,m+	1,m+	NUM
ejpam-4694	412	39	1	1	NUM
ejpam-4694	412	40	)	)	PUNCT
ejpam-4694	412	41	(	(	PUNCT
ejpam-4694	412	42	(	(	PUNCT
ejpam-4694	412	43	1−	1−	NUM
ejpam-4694	412	44	u)t	u)t	X
ejpam-4694	412	45	ln	ln	ADJ
ejpam-4694	412	46	ab)j+1	ab)j+1	NOUN
ejpam-4694	412	47	(	(	PUNCT
ejpam-4694	412	48	j	j	NOUN
ejpam-4694	412	49	+	+	NOUN
ejpam-4694	412	50	1	1	NUM
ejpam-4694	412	51	)	)	PUNCT
ejpam-4694	412	52	!	!	PUNCT
ejpam-4694	413	1	α	α	PRON
ejpam-4694	413	2	=	=	PUNCT
ejpam-4694	414	1	exρ(t	exρ(t	PROPN
ejpam-4694	414	2	)	)	PUNCT
ejpam-4694	414	3	(	(	PUNCT
ejpam-4694	414	4	(	(	PUNCT
ejpam-4694	414	5	1−	1−	NUM
ejpam-4694	414	6	u)t	u)t	X
ejpam-4694	414	7	ln	ln	PROPN
ejpam-4694	414	8	ab	ab	PROPN
ejpam-4694	414	9	λbt	λbt	VERB
ejpam-4694	414	10	−	−	PROPN
ejpam-4694	414	11	ua−t	ua−t	PROPN
ejpam-4694	414	12	)	)	PUNCT
ejpam-4694	414	13	α	α	PROPN
ejpam-4694	415	1			PROPN
ejpam-4694	415	2	∞∑	∞∑	NUM
ejpam-4694	415	3	j=0	j=0	PROPN
ejpam-4694	415	4	cj	cj	PROPN
ejpam-4694	415	5	tj	tj	PROPN
ejpam-4694	415	6	j	j	PROPN
ejpam-4694	415	7	!	!	PUNCT
ejpam-4694	416	1	α	α	PROPN
ejpam-4694	416	2	,	,	PUNCT
ejpam-4694	416	3	where	where	SCONJ
ejpam-4694	416	4	cj	cj	NOUN
ejpam-4694	417	1	=	=	SYM
ejpam-4694	417	2	j∑	j∑	PROPN
ejpam-4694	417	3	m=0	m=0	PROPN
ejpam-4694	417	4	(	(	PUNCT
ejpam-4694	417	5	−1)m+j+1	−1)m+j+1	NOUN
ejpam-4694	417	6	(	(	PUNCT
ejpam-4694	417	7	(	(	PUNCT
ejpam-4694	417	8	1−	1−	NUM
ejpam-4694	417	9	u	u	NOUN
ejpam-4694	417	10	)	)	PUNCT
ejpam-4694	417	11	ln	ln	PROPN
ejpam-4694	417	12	ab)j(1)m+1,ρs1,ρ(j	ab)j(1)m+1,ρs1,ρ(j	PROPN
ejpam-4694	417	13	+	+	CCONJ
ejpam-4694	417	14	1,m+	1,m+	NUM
ejpam-4694	417	15	1	1	NUM
ejpam-4694	417	16	)	)	PUNCT
ejpam-4694	417	17	(	(	PUNCT
ejpam-4694	417	18	j	j	PROPN
ejpam-4694	417	19	+	+	CCONJ
ejpam-4694	417	20	1)(m+	1)(m+	NUM
ejpam-4694	417	21	1)k−1	1)k−1	NUM
ejpam-4694	417	22	.	.	PUNCT
ejpam-4694	418	1	using	use	VERB
ejpam-4694	418	2	(	(	PUNCT
ejpam-4694	418	3	31	31	NUM
ejpam-4694	418	4	)	)	PUNCT
ejpam-4694	418	5	,	,	PUNCT
ejpam-4694	418	6	we	we	PRON
ejpam-4694	418	7	get	get	VERB
ejpam-4694	418	8	∞∑	∞∑	NUM
ejpam-4694	418	9	n=0	n=0	NUM
ejpam-4694	418	10	ĝ(k	ĝ(k	PROPN
ejpam-4694	418	11	,	,	PUNCT
ejpam-4694	418	12	α	α	NOUN
ejpam-4694	418	13	)	)	PUNCT
ejpam-4694	418	14	n	n	CCONJ
ejpam-4694	418	15	(	(	PUNCT
ejpam-4694	418	16	x;λ	x;λ	PROPN
ejpam-4694	418	17	,	,	PUNCT
ejpam-4694	418	18	ρ	ρ	PROPN
ejpam-4694	418	19	,	,	PUNCT
ejpam-4694	418	20	u	u	NOUN
ejpam-4694	418	21	,	,	PUNCT
ejpam-4694	418	22	a	a	DET
ejpam-4694	418	23	,	,	PUNCT
ejpam-4694	418	24	b	b	NOUN
ejpam-4694	418	25	)	)	PUNCT
ejpam-4694	418	26	tn	tn	NOUN
ejpam-4694	418	27	n	n	NOUN
ejpam-4694	418	28	!	!	PUNCT
ejpam-4694	419	1	=	=	PUNCT
ejpam-4694	420	1	(	(	PUNCT
ejpam-4694	420	2	∞∑	∞∑	NUM
ejpam-4694	420	3	n=0	n=0	NUM
ejpam-4694	420	4	ĝ(α	ĝ(α	NOUN
ejpam-4694	420	5	)	)	PUNCT
ejpam-4694	420	6	n	n	CCONJ
ejpam-4694	420	7	(	(	PUNCT
ejpam-4694	420	8	x;λ	x;λ	PROPN
ejpam-4694	420	9	,	,	PUNCT
ejpam-4694	420	10	ρ	ρ	PROPN
ejpam-4694	420	11	,	,	PUNCT
ejpam-4694	420	12	u	u	NOUN
ejpam-4694	420	13	,	,	PUNCT
ejpam-4694	420	14	a	a	DET
ejpam-4694	420	15	,	,	PUNCT
ejpam-4694	420	16	b	b	NOUN
ejpam-4694	420	17	)	)	PUNCT
ejpam-4694	420	18	tn	tn	PROPN
ejpam-4694	420	19	n	n	PROPN
ejpam-4694	420	20	!	!	PUNCT
ejpam-4694	420	21	)	)	PUNCT
ejpam-4694	421	1			PROPN
ejpam-4694	421	2	∞∑	∞∑	NUM
ejpam-4694	421	3	j=0	j=0	PROPN
ejpam-4694	421	4	cj	cj	PROPN
ejpam-4694	421	5	tj	tj	PROPN
ejpam-4694	421	6	j	j	PROPN
ejpam-4694	421	7	!	!	PUNCT
ejpam-4694	421	8	α	α	PROPN
ejpam-4694	421	9	.	.	PUNCT
ejpam-4694	422	1	note	note	VERB
ejpam-4694	422	2	that	that	SCONJ
ejpam-4694	422	3	,	,	PUNCT
ejpam-4694	422	4	using	use	VERB
ejpam-4694	422	5	(	(	PUNCT
ejpam-4694	422	6	52	52	NUM
ejpam-4694	422	7	)	)	PUNCT
ejpam-4694	422	8	,	,	PUNCT
ejpam-4694	422	9	(	(	PUNCT
ejpam-4694	422	10	∑∞	∑∞	X
ejpam-4694	422	11	j=0	j=0	PROPN
ejpam-4694	422	12	cj	cj	PROPN
ejpam-4694	422	13	tj	tj	PROPN
ejpam-4694	422	14	j	j	PROPN
ejpam-4694	422	15	!	!	PUNCT
ejpam-4694	422	16	)	)	PUNCT
ejpam-4694	423	1	α	α	PRON
ejpam-4694	423	2	can	can	AUX
ejpam-4694	423	3	be	be	AUX
ejpam-4694	423	4	expressed	express	VERB
ejpam-4694	423	5	as	as	ADJ
ejpam-4694	423	6	∞∑	∞∑	PROPN
ejpam-4694	423	7	j=0	j=0	PROPN
ejpam-4694	423	8	cj	cj	PROPN
ejpam-4694	423	9	tj	tj	PROPN
ejpam-4694	423	10	j	j	PROPN
ejpam-4694	423	11	!	!	PUNCT
ejpam-4694	423	12	α	α	PUNCT
ejpam-4694	424	1	=	=	PUNCT
ejpam-4694	425	1	∞∑	∞∑	PROPN
ejpam-4694	425	2	n=0	n=0	NUM
ejpam-4694	425	3	dn	dn	PROPN
ejpam-4694	425	4	tn	tn	PROPN
ejpam-4694	425	5	n	n	CCONJ
ejpam-4694	425	6	!	!	PROPN
ejpam-4694	425	7	,	,	PUNCT
ejpam-4694	425	8	where	where	SCONJ
ejpam-4694	425	9	dn	dn	PROPN
ejpam-4694	425	10	=	=	SYM
ejpam-4694	425	11	∑	∑	PUNCT
ejpam-4694	425	12	n1+n2+	n1+n2+	NOUN
ejpam-4694	425	13	...	...	PUNCT
ejpam-4694	425	14	+nα	+nα	PUNCT
ejpam-4694	425	15	=	=	PROPN
ejpam-4694	425	16	n	n	PRON
ejpam-4694	425	17	α∏	α∏	PROPN
ejpam-4694	425	18	i=1	i=1	PROPN
ejpam-4694	425	19	cni	cni	PROPN
ejpam-4694	425	20	(	(	PUNCT
ejpam-4694	425	21	n	n	CCONJ
ejpam-4694	425	22	n1	n1	NOUN
ejpam-4694	425	23	,	,	PUNCT
ejpam-4694	425	24	n2	n2	NOUN
ejpam-4694	425	25	,	,	PUNCT
ejpam-4694	425	26	.	.	PUNCT
ejpam-4694	425	27	.	.	PUNCT
ejpam-4694	426	1	.	.	PUNCT
ejpam-4694	426	2	,	,	PUNCT
ejpam-4694	426	3	nα	nα	VERB
ejpam-4694	426	4	)	)	PUNCT
ejpam-4694	426	5	.	.	PUNCT
ejpam-4694	427	1	it	it	PRON
ejpam-4694	427	2	follows	follow	VERB
ejpam-4694	427	3	that	that	SCONJ
ejpam-4694	427	4	∞∑	∞∑	NUM
ejpam-4694	427	5	n=0	n=0	NUM
ejpam-4694	427	6	ĝ(k	ĝ(k	PROPN
ejpam-4694	427	7	,	,	PUNCT
ejpam-4694	427	8	α	α	NOUN
ejpam-4694	427	9	)	)	PUNCT
ejpam-4694	427	10	n	n	CCONJ
ejpam-4694	427	11	(	(	PUNCT
ejpam-4694	427	12	x;λ	x;λ	PROPN
ejpam-4694	427	13	,	,	PUNCT
ejpam-4694	427	14	ρ	ρ	PROPN
ejpam-4694	427	15	,	,	PUNCT
ejpam-4694	427	16	u	u	NOUN
ejpam-4694	427	17	,	,	PUNCT
ejpam-4694	427	18	a	a	DET
ejpam-4694	427	19	,	,	PUNCT
ejpam-4694	427	20	b	b	NOUN
ejpam-4694	427	21	)	)	PUNCT
ejpam-4694	427	22	tn	tn	NOUN
ejpam-4694	427	23	n	n	NOUN
ejpam-4694	427	24	!	!	PUNCT
ejpam-4694	427	25	=	=	PUNCT
ejpam-4694	428	1	∞∑	∞∑	PRON
ejpam-4694	428	2	n=0	n=0	NUM
ejpam-4694	428	3			PUNCT
ejpam-4694	428	4	n∑	n∑	NOUN
ejpam-4694	428	5	j=0	j=0	PROPN
ejpam-4694	428	6	(	(	PUNCT
ejpam-4694	428	7	n	n	CCONJ
ejpam-4694	428	8	j	j	PROPN
ejpam-4694	428	9	)	)	PUNCT
ejpam-4694	428	10	ĝ(α	ĝ(α	PROPN
ejpam-4694	428	11	)	)	PUNCT
ejpam-4694	428	12	n−j(x;λ	n−j(x;λ	PROPN
ejpam-4694	428	13	,	,	PUNCT
ejpam-4694	428	14	ρ	ρ	PROPN
ejpam-4694	428	15	,	,	PUNCT
ejpam-4694	428	16	u	u	NOUN
ejpam-4694	428	17	,	,	PUNCT
ejpam-4694	428	18	a	a	PRON
ejpam-4694	428	19	,	,	PUNCT
ejpam-4694	428	20	b)dj	b)dj	PROPN
ejpam-4694	428	21			PROPN
ejpam-4694	428	22	tn	tn	NOUN
ejpam-4694	428	23	n	n	CCONJ
ejpam-4694	428	24	!	!	PUNCT
ejpam-4694	428	25	.	.	PUNCT
ejpam-4694	429	1	comparing	compare	VERB
ejpam-4694	429	2	the	the	DET
ejpam-4694	429	3	coefficients	coefficient	NOUN
ejpam-4694	429	4	and	and	CCONJ
ejpam-4694	429	5	using	use	VERB
ejpam-4694	429	6	equation	equation	NOUN
ejpam-4694	429	7	(	(	PUNCT
ejpam-4694	429	8	44	44	NUM
ejpam-4694	429	9	)	)	PUNCT
ejpam-4694	429	10	complete	complete	VERB
ejpam-4694	429	11	the	the	DET
ejpam-4694	429	12	proof	proof	NOUN
ejpam-4694	429	13	of	of	ADP
ejpam-4694	429	14	the	the	DET
ejpam-4694	429	15	theorem	theorem	PROPN
ejpam-4694	429	16	.	.	PROPN
ejpam-4694	429	17	remark	remark	PROPN
ejpam-4694	429	18	5.2	5.2	NUM
ejpam-4694	429	19	.	.	PUNCT
ejpam-4694	430	1	when	when	SCONJ
ejpam-4694	430	2	α	α	PRON
ejpam-4694	430	3	=	=	SYM
ejpam-4694	430	4	1	1	NUM
ejpam-4694	430	5	,	,	PUNCT
ejpam-4694	430	6	dj	dj	NOUN
ejpam-4694	430	7	=	=	SYM
ejpam-4694	430	8	cj	cj	NOUN
ejpam-4694	430	9	.	.	PUNCT
ejpam-4694	431	1	the	the	DET
ejpam-4694	431	2	identities	identity	NOUN
ejpam-4694	431	3	in	in	ADP
ejpam-4694	431	4	the	the	DET
ejpam-4694	431	5	following	following	ADJ
ejpam-4694	431	6	theorem	theorem	NOUN
ejpam-4694	431	7	are	be	AUX
ejpam-4694	431	8	derived	derive	VERB
ejpam-4694	431	9	using	use	VERB
ejpam-4694	431	10	the	the	DET
ejpam-4694	431	11	fact	fact	NOUN
ejpam-4694	431	12	that	that	SCONJ
ejpam-4694	431	13	the	the	DET
ejpam-4694	431	14	polynomials	polynomial	NOUN
ejpam-4694	431	15	ĝ(k	ĝ(k	VERB
ejpam-4694	431	16	,	,	PUNCT
ejpam-4694	431	17	α	α	NOUN
ejpam-4694	431	18	)	)	PUNCT
ejpam-4694	431	19	n	n	CCONJ
ejpam-4694	431	20	(	(	PUNCT
ejpam-4694	431	21	x;λ	x;λ	PROPN
ejpam-4694	431	22	,	,	PUNCT
ejpam-4694	431	23	ρ	ρ	PROPN
ejpam-4694	431	24	,	,	PUNCT
ejpam-4694	431	25	u	u	NOUN
ejpam-4694	431	26	,	,	PUNCT
ejpam-4694	431	27	a	a	DET
ejpam-4694	431	28	,	,	PUNCT
ejpam-4694	431	29	b	b	NOUN
ejpam-4694	431	30	,	,	PUNCT
ejpam-4694	431	31	)	)	PUNCT
ejpam-4694	431	32	with	with	ADP
ejpam-4694	431	33	parameters	parameter	NOUN
ejpam-4694	431	34	a	a	PRON
ejpam-4694	431	35	and	and	CCONJ
ejpam-4694	431	36	b	b	NOUN
ejpam-4694	431	37	satisfy	satisfy	VERB
ejpam-4694	431	38	the	the	DET
ejpam-4694	431	39	relation	relation	NOUN
ejpam-4694	431	40	in	in	ADP
ejpam-4694	431	41	(	(	PUNCT
ejpam-4694	431	42	27	27	NUM
ejpam-4694	431	43	)	)	PUNCT
ejpam-4694	431	44	.	.	PUNCT
ejpam-4694	432	1	theorem	theorem	VERB
ejpam-4694	432	2	5.3	5.3	NUM
ejpam-4694	432	3	.	.	PUNCT
ejpam-4694	433	1	the	the	DET
ejpam-4694	433	2	degenerate	degenerate	ADJ
ejpam-4694	433	3	apostol	apostol	NOUN
ejpam-4694	433	4	-	-	PUNCT
ejpam-4694	433	5	type	type	NOUN
ejpam-4694	433	6	poly	poly	ADJ
ejpam-4694	433	7	-	-	PUNCT
ejpam-4694	433	8	genocchi	genocchi	NOUN
ejpam-4694	433	9	polynomials	polynomial	NOUN
ejpam-4694	433	10	of	of	ADP
ejpam-4694	433	11	higher	high	ADJ
ejpam-4694	433	12	order	order	NOUN
ejpam-4694	433	13	with	with	ADP
ejpam-4694	433	14	parameters	parameter	NOUN
ejpam-4694	433	15	a	a	PRON
ejpam-4694	433	16	,	,	PUNCT
ejpam-4694	433	17	b	b	X
ejpam-4694	433	18	satisfy	satisfy	VERB
ejpam-4694	433	19	the	the	DET
ejpam-4694	433	20	following	follow	VERB
ejpam-4694	433	21	explicit	explicit	ADJ
ejpam-4694	433	22	formulas	formula	NOUN
ejpam-4694	433	23	:	:	PUNCT
ejpam-4694	433	24	ĝ(k	ĝ(k	NUM
ejpam-4694	433	25	,	,	PUNCT
ejpam-4694	433	26	α	α	NOUN
ejpam-4694	433	27	)	)	PUNCT
ejpam-4694	433	28	n	n	CCONJ
ejpam-4694	433	29	(	(	PUNCT
ejpam-4694	433	30	x;λ	x;λ	PROPN
ejpam-4694	433	31	,	,	PUNCT
ejpam-4694	433	32	ρ	ρ	PROPN
ejpam-4694	433	33	,	,	PUNCT
ejpam-4694	433	34	u	u	NOUN
ejpam-4694	433	35	,	,	PUNCT
ejpam-4694	433	36	a	a	DET
ejpam-4694	433	37	,	,	PUNCT
ejpam-4694	433	38	b	b	NOUN
ejpam-4694	433	39	)	)	PUNCT
ejpam-4694	433	40	=	=	SYM
ejpam-4694	433	41	n∑	n∑	PROPN
ejpam-4694	433	42	l=0	l=0	PROPN
ejpam-4694	433	43	n−l∑	n−l∑	X
ejpam-4694	433	44	m=0	m=0	PROPN
ejpam-4694	433	45	(	(	PUNCT
ejpam-4694	433	46	n	n	X
ejpam-4694	433	47	l	l	NOUN
ejpam-4694	433	48	)	)	PUNCT
ejpam-4694	433	49	s2,ρ(l	s2,ρ(l	PROPN
ejpam-4694	434	1	+	+	NUM
ejpam-4694	434	2	s	s	PROPN
ejpam-4694	434	3	,	,	PUNCT
ejpam-4694	434	4	s	s	AUX
ejpam-4694	434	5	)	)	PUNCT
ejpam-4694	434	6	(	(	PUNCT
ejpam-4694	434	7	n−l	n−l	NOUN
ejpam-4694	434	8	m	m	VERB
ejpam-4694	434	9	)	)	PUNCT
ejpam-4694	434	10	(	(	PUNCT
ejpam-4694	434	11	l+s	l+s	PROPN
ejpam-4694	434	12	s	s	PART
ejpam-4694	434	13	)	)	PUNCT
ejpam-4694	434	14	β(s	β(s	PROPN
ejpam-4694	434	15	)	)	PUNCT
ejpam-4694	434	16	m	m	PROPN
ejpam-4694	434	17	,	,	PUNCT
ejpam-4694	434	18	ρ(x)ĝ	ρ(x)ĝ	X
ejpam-4694	434	19	(	(	PUNCT
ejpam-4694	434	20	k	k	X
ejpam-4694	434	21	,	,	PUNCT
ejpam-4694	434	22	α	α	NOUN
ejpam-4694	434	23	)	)	PUNCT
ejpam-4694	434	24	n−l−m(λ	n−l−m(λ	PROPN
ejpam-4694	434	25	,	,	PUNCT
ejpam-4694	434	26	ρ	ρ	PROPN
ejpam-4694	434	27	,	,	PUNCT
ejpam-4694	434	28	u	u	NOUN
ejpam-4694	434	29	,	,	PUNCT
ejpam-4694	434	30	a	a	DET
ejpam-4694	434	31	,	,	PUNCT
ejpam-4694	434	32	b	b	NOUN
ejpam-4694	434	33	)	)	PUNCT
ejpam-4694	434	34	,	,	PUNCT
ejpam-4694	434	35	(	(	PUNCT
ejpam-4694	434	36	54	54	NUM
ejpam-4694	434	37	)	)	PUNCT
ejpam-4694	434	38	r.	r.	NOUN
ejpam-4694	434	39	corcino	corcino	PROPN
ejpam-4694	434	40	,	,	PUNCT
ejpam-4694	434	41	c.	c.	PROPN
ejpam-4694	434	42	corcino	corcino	PROPN
ejpam-4694	434	43	/	/	SYM
ejpam-4694	434	44	eur	eur	PROPN
ejpam-4694	434	45	.	.	PUNCT
ejpam-4694	435	1	j.	j.	PROPN
ejpam-4694	435	2	pure	pure	PROPN
ejpam-4694	435	3	appl	appl	PROPN
ejpam-4694	435	4	.	.	PROPN
ejpam-4694	435	5	math	math	PROPN
ejpam-4694	435	6	,	,	PUNCT
ejpam-4694	435	7	16	16	NUM
ejpam-4694	435	8	(	(	PUNCT
ejpam-4694	435	9	2	2	NUM
ejpam-4694	435	10	)	)	PUNCT
ejpam-4694	435	11	(	(	PUNCT
ejpam-4694	435	12	2023	2023	NUM
ejpam-4694	435	13	)	)	PUNCT
ejpam-4694	435	14	,	,	PUNCT
ejpam-4694	435	15	687	687	NUM
ejpam-4694	435	16	-	-	SYM
ejpam-4694	435	17	712	712	NUM
ejpam-4694	435	18	707	707	NUM
ejpam-4694	435	19	ĝ(k	ĝ(k	NOUN
ejpam-4694	435	20	,	,	PUNCT
ejpam-4694	435	21	α	α	NOUN
ejpam-4694	435	22	)	)	PUNCT
ejpam-4694	435	23	n	n	CCONJ
ejpam-4694	435	24	(	(	PUNCT
ejpam-4694	435	25	x;λ	x;λ	PROPN
ejpam-4694	435	26	,	,	PUNCT
ejpam-4694	435	27	ρ	ρ	PROPN
ejpam-4694	435	28	,	,	PUNCT
ejpam-4694	435	29	u	u	NOUN
ejpam-4694	435	30	,	,	PUNCT
ejpam-4694	435	31	a	a	DET
ejpam-4694	435	32	,	,	PUNCT
ejpam-4694	435	33	b	b	NOUN
ejpam-4694	435	34	)	)	PUNCT
ejpam-4694	435	35	=	=	SYM
ejpam-4694	436	1	n∑	n∑	PROPN
ejpam-4694	436	2	m=0	m=0	PROPN
ejpam-4694	436	3	(	(	PUNCT
ejpam-4694	436	4	n	n	NOUN
ejpam-4694	436	5	m	m	VERB
ejpam-4694	436	6	)	)	PUNCT
ejpam-4694	437	1	(	(	PUNCT
ejpam-4694	437	2	1−	1−	NUM
ejpam-4694	437	3	µ)s	µ)s	NOUN
ejpam-4694	437	4	s∑	s∑	PROPN
ejpam-4694	437	5	j=0	j=0	PROPN
ejpam-4694	437	6	(	(	PUNCT
ejpam-4694	437	7	s	s	PROPN
ejpam-4694	437	8	j	j	PROPN
ejpam-4694	437	9	)	)	PUNCT
ejpam-4694	437	10	(	(	PUNCT
ejpam-4694	437	11	−µ)s−jĝ(k	−µ)s−jĝ(k	PROPN
ejpam-4694	437	12	,	,	PUNCT
ejpam-4694	437	13	α	α	NOUN
ejpam-4694	437	14	)	)	PUNCT
ejpam-4694	437	15	n−m(λ	n−m(λ	NOUN
ejpam-4694	437	16	,	,	PUNCT
ejpam-4694	437	17	ρ	ρ	PROPN
ejpam-4694	437	18	,	,	PUNCT
ejpam-4694	437	19	u	u	PROPN
ejpam-4694	437	20	,	,	PUNCT
ejpam-4694	437	21	j	j	PROPN
ejpam-4694	437	22	,	,	PUNCT
ejpam-4694	437	23	a	a	DET
ejpam-4694	437	24	,	,	PUNCT
ejpam-4694	437	25	b)e(s	b)e(s	NOUN
ejpam-4694	437	26	)	)	PUNCT
ejpam-4694	437	27	n	n	CCONJ
ejpam-4694	437	28	(	(	PUNCT
ejpam-4694	437	29	x	x	PROPN
ejpam-4694	437	30	ln	ln	PROPN
ejpam-4694	437	31	c;µ	c;µ	PROPN
ejpam-4694	437	32	)	)	PUNCT
ejpam-4694	437	33	.	.	PUNCT
ejpam-4694	438	1	(	(	PUNCT
ejpam-4694	438	2	55	55	NUM
ejpam-4694	438	3	)	)	PUNCT
ejpam-4694	438	4	proof	proof	NOUN
ejpam-4694	438	5	.	.	PUNCT
ejpam-4694	439	1	using	use	VERB
ejpam-4694	439	2	(	(	PUNCT
ejpam-4694	439	3	49	49	NUM
ejpam-4694	439	4	)	)	PUNCT
ejpam-4694	439	5	,	,	PUNCT
ejpam-4694	439	6	(	(	PUNCT
ejpam-4694	439	7	27	27	NUM
ejpam-4694	439	8	)	)	PUNCT
ejpam-4694	439	9	may	may	AUX
ejpam-4694	439	10	be	be	AUX
ejpam-4694	439	11	expressed	express	VERB
ejpam-4694	439	12	as	as	ADP
ejpam-4694	439	13	∞∑	∞∑	NUM
ejpam-4694	439	14	n=0	n=0	NUM
ejpam-4694	439	15	ĝ(k	ĝ(k	PROPN
ejpam-4694	439	16	,	,	PUNCT
ejpam-4694	439	17	α	α	NOUN
ejpam-4694	439	18	)	)	PUNCT
ejpam-4694	439	19	n	n	CCONJ
ejpam-4694	439	20	(	(	PUNCT
ejpam-4694	439	21	x;λ	x;λ	PROPN
ejpam-4694	439	22	,	,	PUNCT
ejpam-4694	439	23	ρ	ρ	PROPN
ejpam-4694	439	24	,	,	PUNCT
ejpam-4694	439	25	u	u	NOUN
ejpam-4694	439	26	,	,	PUNCT
ejpam-4694	439	27	a	a	DET
ejpam-4694	439	28	,	,	PUNCT
ejpam-4694	439	29	b	b	NOUN
ejpam-4694	439	30	)	)	PUNCT
ejpam-4694	439	31	tn	tn	NOUN
ejpam-4694	439	32	n	n	NOUN
ejpam-4694	439	33	!	!	PUNCT
ejpam-4694	440	1	=	=	PUNCT
ejpam-4694	440	2	(	(	PUNCT
ejpam-4694	440	3	(	(	PUNCT
ejpam-4694	440	4	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	440	5	1)s	1)s	NUM
ejpam-4694	440	6	s	s	NOUN
ejpam-4694	440	7	!	!	PUNCT
ejpam-4694	440	8	)	)	PUNCT
ejpam-4694	440	9	(	(	PUNCT
ejpam-4694	440	10	tsexρ(t	tsexρ(t	NOUN
ejpam-4694	440	11	)	)	PUNCT
ejpam-4694	440	12	(	(	PUNCT
ejpam-4694	440	13	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	440	14	1)s	1)s	NUM
ejpam-4694	440	15	)	)	PUNCT
ejpam-4694	440	16	(	(	PUNCT
ejpam-4694	440	17	eik	eik	PROPN
ejpam-4694	440	18	,	,	PUNCT
ejpam-4694	440	19	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	440	20	+	+	CCONJ
ejpam-4694	440	21	(	(	PUNCT
ejpam-4694	440	22	1−	1−	NUM
ejpam-4694	440	23	u)t	u)t	X
ejpam-4694	440	24	ln	ln	PROPN
ejpam-4694	440	25	ab	ab	PROPN
ejpam-4694	440	26	)	)	PUNCT
ejpam-4694	440	27	)	)	PUNCT
ejpam-4694	441	1	λbt	λbt	VERB
ejpam-4694	441	2	−	−	PROPN
ejpam-4694	441	3	ua−t	ua−t	PROPN
ejpam-4694	441	4	)	)	PUNCT
ejpam-4694	441	5	α	α	PROPN
ejpam-4694	441	6	s	s	X
ejpam-4694	441	7	!	!	NOUN
ejpam-4694	441	8	ts	ts	X
ejpam-4694	442	1	=	=	PUNCT
ejpam-4694	443	1	(	(	PUNCT
ejpam-4694	443	2	∞∑	∞∑	NUM
ejpam-4694	443	3	n=0	n=0	NUM
ejpam-4694	443	4	s2,ρ(n+	s2,ρ(n+	NOUN
ejpam-4694	443	5	s	s	PART
ejpam-4694	443	6	,	,	PUNCT
ejpam-4694	443	7	s	s	PART
ejpam-4694	443	8	)	)	PUNCT
ejpam-4694	443	9	tn+s	tn+s	PROPN
ejpam-4694	443	10	(	(	PUNCT
ejpam-4694	443	11	n+	n+	X
ejpam-4694	443	12	s	s	X
ejpam-4694	443	13	)	)	PUNCT
ejpam-4694	443	14	!	!	PUNCT
ejpam-4694	443	15	)	)	PUNCT
ejpam-4694	444	1	(	(	PUNCT
ejpam-4694	444	2	∞∑	∞∑	NUM
ejpam-4694	444	3	m=0	m=0	PROPN
ejpam-4694	444	4	β(s	β(s	PROPN
ejpam-4694	444	5	)	)	PUNCT
ejpam-4694	444	6	m	m	PROPN
ejpam-4694	444	7	,	,	PUNCT
ejpam-4694	444	8	ρ(x	ρ(x	PROPN
ejpam-4694	444	9	)	)	PUNCT
ejpam-4694	444	10	tm	tm	PROPN
ejpam-4694	444	11	m	m	PROPN
ejpam-4694	444	12	!	!	PUNCT
ejpam-4694	444	13	)	)	PUNCT
ejpam-4694	445	1	(	(	PUNCT
ejpam-4694	445	2	∞∑	∞∑	NUM
ejpam-4694	445	3	n=0	n=0	NUM
ejpam-4694	445	4	ĝ(k	ĝ(k	PROPN
ejpam-4694	445	5	,	,	PUNCT
ejpam-4694	445	6	α	α	NOUN
ejpam-4694	445	7	)	)	PUNCT
ejpam-4694	445	8	n	n	PROPN
ejpam-4694	445	9	(	(	PUNCT
ejpam-4694	445	10	λ	λ	PROPN
ejpam-4694	445	11	,	,	PUNCT
ejpam-4694	445	12	ρ	ρ	PROPN
ejpam-4694	445	13	,	,	PUNCT
ejpam-4694	445	14	u	u	NOUN
ejpam-4694	445	15	,	,	PUNCT
ejpam-4694	445	16	a	a	DET
ejpam-4694	445	17	,	,	PUNCT
ejpam-4694	445	18	b	b	NOUN
ejpam-4694	445	19	)	)	PUNCT
ejpam-4694	445	20	tm	tm	PROPN
ejpam-4694	445	21	m	m	PROPN
ejpam-4694	445	22	!	!	PUNCT
ejpam-4694	445	23	)	)	PUNCT
ejpam-4694	446	1	s	s	X
ejpam-4694	446	2	!	!	NOUN
ejpam-4694	446	3	ts	ts	X
ejpam-4694	446	4	=	=	PUNCT
ejpam-4694	447	1	(	(	PUNCT
ejpam-4694	447	2	∞∑	∞∑	NUM
ejpam-4694	447	3	n=0	n=0	NUM
ejpam-4694	447	4	s2,ρ(n+	s2,ρ(n+	NOUN
ejpam-4694	447	5	s	s	PART
ejpam-4694	447	6	,	,	PUNCT
ejpam-4694	447	7	s	s	PART
ejpam-4694	447	8	)	)	PUNCT
ejpam-4694	447	9	tn+s	tn+s	PROPN
ejpam-4694	447	10	(	(	PUNCT
ejpam-4694	447	11	n+	n+	X
ejpam-4694	447	12	s	s	X
ejpam-4694	447	13	)	)	PUNCT
ejpam-4694	447	14	!	!	PUNCT
ejpam-4694	447	15	)	)	PUNCT
ejpam-4694	448	1	(	(	PUNCT
ejpam-4694	448	2	∞∑	∞∑	NUM
ejpam-4694	448	3	n=0	n=0	PROPN
ejpam-4694	448	4	n∑	n∑	NOUN
ejpam-4694	448	5	m=0	m=0	PROPN
ejpam-4694	448	6	(	(	PUNCT
ejpam-4694	448	7	n	n	NOUN
ejpam-4694	448	8	m	m	PROPN
ejpam-4694	448	9	)	)	PUNCT
ejpam-4694	448	10	β(s	β(s	PROPN
ejpam-4694	448	11	)	)	PUNCT
ejpam-4694	448	12	m	m	PROPN
ejpam-4694	448	13	,	,	PUNCT
ejpam-4694	448	14	ρ(x	ρ(x	PROPN
ejpam-4694	448	15	ln	ln	ADJ
ejpam-4694	448	16	c)ĝ	c)ĝ	NOUN
ejpam-4694	448	17	(	(	PUNCT
ejpam-4694	448	18	k	k	X
ejpam-4694	448	19	,	,	PUNCT
ejpam-4694	448	20	α	α	NOUN
ejpam-4694	448	21	)	)	PUNCT
ejpam-4694	448	22	n−m(λ	n−m(λ	NOUN
ejpam-4694	448	23	,	,	PUNCT
ejpam-4694	448	24	ρ	ρ	PROPN
ejpam-4694	448	25	,	,	PUNCT
ejpam-4694	448	26	u	u	NOUN
ejpam-4694	448	27	,	,	PUNCT
ejpam-4694	448	28	a	a	DET
ejpam-4694	448	29	,	,	PUNCT
ejpam-4694	448	30	b	b	NOUN
ejpam-4694	448	31	)	)	PUNCT
ejpam-4694	448	32	tn	tn	PROPN
ejpam-4694	448	33	n	n	PROPN
ejpam-4694	448	34	!	!	PUNCT
ejpam-4694	448	35	)	)	PUNCT
ejpam-4694	449	1	s	s	X
ejpam-4694	449	2	!	!	NOUN
ejpam-4694	449	3	ts	ts	X
ejpam-4694	449	4	=	=	PUNCT
ejpam-4694	450	1	(	(	PUNCT
ejpam-4694	450	2	∞∑	∞∑	NUM
ejpam-4694	450	3	n=0	n=0	NUM
ejpam-4694	450	4	n∑	n∑	X
ejpam-4694	450	5	l=0	l=0	PROPN
ejpam-4694	450	6	s2,ρ(l	s2,ρ(l	PROPN
ejpam-4694	450	7	+	+	CCONJ
ejpam-4694	451	1	s	s	PROPN
ejpam-4694	451	2	,	,	PUNCT
ejpam-4694	451	3	s	s	NOUN
ejpam-4694	451	4	)	)	PUNCT
ejpam-4694	451	5	tl+s	tl+s	PROPN
ejpam-4694	451	6	(	(	PUNCT
ejpam-4694	452	1	l	l	NOUN
ejpam-4694	452	2	+	+	X
ejpam-4694	452	3	s	s	NOUN
ejpam-4694	452	4	)	)	PUNCT
ejpam-4694	452	5	!	!	PUNCT
ejpam-4694	453	1	n−l∑	n−l∑	INTJ
ejpam-4694	453	2	m=0	m=0	PROPN
ejpam-4694	454	1	(	(	PUNCT
ejpam-4694	454	2	n−	n−	NOUN
ejpam-4694	454	3	l	l	NOUN
ejpam-4694	454	4	m	m	NOUN
ejpam-4694	454	5	)	)	PUNCT
ejpam-4694	454	6	β(s	β(s	PROPN
ejpam-4694	454	7	)	)	PUNCT
ejpam-4694	454	8	m	m	PROPN
ejpam-4694	454	9	,	,	PUNCT
ejpam-4694	454	10	ρ(x)ĝ	ρ(x)ĝ	X
ejpam-4694	454	11	(	(	PUNCT
ejpam-4694	454	12	k	k	X
ejpam-4694	454	13	,	,	PUNCT
ejpam-4694	454	14	α	α	NOUN
ejpam-4694	454	15	)	)	PUNCT
ejpam-4694	454	16	n−l−m(λ	n−l−m(λ	PROPN
ejpam-4694	454	17	,	,	PUNCT
ejpam-4694	454	18	ρ	ρ	PROPN
ejpam-4694	454	19	,	,	PUNCT
ejpam-4694	454	20	u	u	NOUN
ejpam-4694	454	21	,	,	PUNCT
ejpam-4694	454	22	a	a	DET
ejpam-4694	454	23	,	,	PUNCT
ejpam-4694	454	24	b	b	NOUN
ejpam-4694	454	25	)	)	PUNCT
ejpam-4694	454	26	tn−l	tn−l	PROPN
ejpam-4694	454	27	(	(	PUNCT
ejpam-4694	454	28	n−	n−	NOUN
ejpam-4694	454	29	l	l	NOUN
ejpam-4694	454	30	)	)	PUNCT
ejpam-4694	454	31	!	!	PUNCT
ejpam-4694	454	32	)	)	PUNCT
ejpam-4694	455	1	s	s	X
ejpam-4694	455	2	!	!	NOUN
ejpam-4694	455	3	ts	ts	ADJ
ejpam-4694	455	4	.	.	PUNCT
ejpam-4694	456	1	this	this	PRON
ejpam-4694	456	2	can	can	AUX
ejpam-4694	456	3	further	far	ADV
ejpam-4694	456	4	be	be	AUX
ejpam-4694	456	5	written	write	VERB
ejpam-4694	456	6	as	as	ADP
ejpam-4694	456	7	∞∑	∞∑	NUM
ejpam-4694	456	8	n=0	n=0	NUM
ejpam-4694	456	9	ĝ(k	ĝ(k	PROPN
ejpam-4694	456	10	,	,	PUNCT
ejpam-4694	456	11	α	α	NOUN
ejpam-4694	456	12	)	)	PUNCT
ejpam-4694	456	13	n	n	CCONJ
ejpam-4694	456	14	(	(	PUNCT
ejpam-4694	456	15	x;λ	x;λ	PROPN
ejpam-4694	456	16	,	,	PUNCT
ejpam-4694	456	17	ρ	ρ	PROPN
ejpam-4694	456	18	,	,	PUNCT
ejpam-4694	456	19	u	u	NOUN
ejpam-4694	456	20	,	,	PUNCT
ejpam-4694	456	21	a	a	DET
ejpam-4694	456	22	,	,	PUNCT
ejpam-4694	456	23	b	b	NOUN
ejpam-4694	456	24	)	)	PUNCT
ejpam-4694	456	25	tn	tn	NOUN
ejpam-4694	456	26	n	n	NOUN
ejpam-4694	456	27	!	!	PUNCT
ejpam-4694	457	1	=	=	PUNCT
ejpam-4694	458	1	(	(	PUNCT
ejpam-4694	458	2	∞∑	∞∑	NUM
ejpam-4694	458	3	l=0	l=0	PROPN
ejpam-4694	458	4	∞∑	∞∑	NUM
ejpam-4694	458	5	n	n	CCONJ
ejpam-4694	458	6	=	=	SYM
ejpam-4694	458	7	l	l	NOUN
ejpam-4694	458	8	n−l∑	n−l∑	X
ejpam-4694	458	9	m=0	m=0	PROPN
ejpam-4694	458	10	{	{	PUNCT
ejpam-4694	458	11	l	l	PROPN
ejpam-4694	459	1	+	+	SYM
ejpam-4694	459	2	s	s	X
ejpam-4694	459	3	s	s	X
ejpam-4694	459	4	}	}	PUNCT
ejpam-4694	459	5	l!s	l!s	PROPN
ejpam-4694	459	6	!	!	PUNCT
ejpam-4694	460	1	(	(	PUNCT
ejpam-4694	460	2	l	l	NOUN
ejpam-4694	460	3	+	+	X
ejpam-4694	460	4	s	s	NOUN
ejpam-4694	460	5	)	)	PUNCT
ejpam-4694	460	6	!	!	PUNCT
ejpam-4694	461	1	(	(	PUNCT
ejpam-4694	461	2	n−	n−	NOUN
ejpam-4694	461	3	l	l	NOUN
ejpam-4694	461	4	m	m	NOUN
ejpam-4694	461	5	)	)	PUNCT
ejpam-4694	461	6	b(s	b(	NOUN
ejpam-4694	461	7	)	)	PUNCT
ejpam-4694	462	1	m	m	VERB
ejpam-4694	462	2	(	(	PUNCT
ejpam-4694	462	3	x	x	PROPN
ejpam-4694	462	4	ln	ln	PROPN
ejpam-4694	462	5	c)ĝ(k	c)ĝ(k	PROPN
ejpam-4694	462	6	,	,	PUNCT
ejpam-4694	462	7	α	α	NOUN
ejpam-4694	462	8	)	)	PUNCT
ejpam-4694	462	9	n−l−m(x;λ	n−l−m(x;λ	PROPN
ejpam-4694	462	10	,	,	PUNCT
ejpam-4694	462	11	ρ	ρ	PROPN
ejpam-4694	462	12	,	,	PUNCT
ejpam-4694	462	13	u	u	NOUN
ejpam-4694	462	14	,	,	PUNCT
ejpam-4694	462	15	a	a	DET
ejpam-4694	462	16	,	,	PUNCT
ejpam-4694	462	17	b	b	NOUN
ejpam-4694	462	18	)	)	PUNCT
ejpam-4694	462	19	n	n	CCONJ
ejpam-4694	462	20	!	!	PUNCT
ejpam-4694	463	1	(	(	PUNCT
ejpam-4694	463	2	n−	n−	NOUN
ejpam-4694	463	3	l)!l	l)!l	VERB
ejpam-4694	463	4	!	!	PUNCT
ejpam-4694	463	5	tn	tn	PROPN
ejpam-4694	464	1	n	n	PROPN
ejpam-4694	464	2	!	!	PUNCT
ejpam-4694	464	3	)	)	PUNCT
ejpam-4694	465	1	=	=	PUNCT
ejpam-4694	466	1	∞∑	∞∑	NUM
ejpam-4694	466	2	n=0	n=0	NUM
ejpam-4694	466	3	(	(	PUNCT
ejpam-4694	466	4	n∑	n∑	PROPN
ejpam-4694	466	5	l=0	l=0	PROPN
ejpam-4694	466	6	n−l∑	n−l∑	X
ejpam-4694	466	7	m=0	m=0	PROPN
ejpam-4694	466	8	(	(	PUNCT
ejpam-4694	466	9	n	n	X
ejpam-4694	466	10	l	l	NOUN
ejpam-4694	466	11	)	)	PUNCT
ejpam-4694	466	12	s2,ρ(l	s2,ρ(l	PROPN
ejpam-4694	466	13	+	+	NUM
ejpam-4694	467	1	s	s	PROPN
ejpam-4694	467	2	,	,	PUNCT
ejpam-4694	467	3	s	s	AUX
ejpam-4694	467	4	)	)	PUNCT
ejpam-4694	467	5	(	(	PUNCT
ejpam-4694	467	6	n−l	n−l	NOUN
ejpam-4694	467	7	m	m	VERB
ejpam-4694	467	8	)	)	PUNCT
ejpam-4694	467	9	(	(	PUNCT
ejpam-4694	467	10	l+s	l+s	PROPN
ejpam-4694	467	11	s	s	PART
ejpam-4694	467	12	)	)	PUNCT
ejpam-4694	467	13	β(s	β(s	PROPN
ejpam-4694	467	14	)	)	PUNCT
ejpam-4694	467	15	m	m	PROPN
ejpam-4694	467	16	,	,	PUNCT
ejpam-4694	467	17	ρ(x)ĝ	ρ(x)ĝ	X
ejpam-4694	467	18	(	(	PUNCT
ejpam-4694	467	19	k	k	X
ejpam-4694	467	20	,	,	PUNCT
ejpam-4694	467	21	α	α	NOUN
ejpam-4694	467	22	)	)	PUNCT
ejpam-4694	467	23	n−l−m(λ	n−l−m(λ	PROPN
ejpam-4694	467	24	,	,	PUNCT
ejpam-4694	467	25	ρ	ρ	PROPN
ejpam-4694	467	26	,	,	PUNCT
ejpam-4694	467	27	u	u	NOUN
ejpam-4694	467	28	,	,	PUNCT
ejpam-4694	467	29	a	a	DET
ejpam-4694	467	30	,	,	PUNCT
ejpam-4694	467	31	b	b	NOUN
ejpam-4694	467	32	)	)	PUNCT
ejpam-4694	467	33	)	)	PUNCT
ejpam-4694	467	34	tn	tn	PROPN
ejpam-4694	468	1	n	n	PROPN
ejpam-4694	468	2	!	!	PUNCT
ejpam-4694	468	3	.	.	PUNCT
ejpam-4694	469	1	comparing	compare	VERB
ejpam-4694	469	2	the	the	DET
ejpam-4694	469	3	coefficients	coefficient	NOUN
ejpam-4694	469	4	of	of	ADP
ejpam-4694	469	5	tn	tn	NOUN
ejpam-4694	469	6	n	n	ADP
ejpam-4694	469	7	!	!	PROPN
ejpam-4694	470	1	gives	give	VERB
ejpam-4694	470	2	(	(	PUNCT
ejpam-4694	470	3	54	54	NUM
ejpam-4694	470	4	)	)	PUNCT
ejpam-4694	470	5	.	.	PUNCT
ejpam-4694	471	1	now	now	ADV
ejpam-4694	471	2	,	,	PUNCT
ejpam-4694	471	3	to	to	PART
ejpam-4694	471	4	prove	prove	VERB
ejpam-4694	471	5	relation	relation	NOUN
ejpam-4694	471	6	(	(	PUNCT
ejpam-4694	471	7	55	55	NUM
ejpam-4694	471	8	)	)	PUNCT
ejpam-4694	471	9	,	,	PUNCT
ejpam-4694	471	10	(	(	PUNCT
ejpam-4694	471	11	27	27	NUM
ejpam-4694	471	12	)	)	PUNCT
ejpam-4694	471	13	may	may	AUX
ejpam-4694	471	14	be	be	AUX
ejpam-4694	471	15	expressed	express	VERB
ejpam-4694	471	16	as	as	ADP
ejpam-4694	471	17	∞∑	∞∑	NUM
ejpam-4694	471	18	n=0	n=0	NUM
ejpam-4694	471	19	ĝ(k	ĝ(k	PROPN
ejpam-4694	471	20	,	,	PUNCT
ejpam-4694	471	21	α	α	NOUN
ejpam-4694	471	22	)	)	PUNCT
ejpam-4694	471	23	n	n	CCONJ
ejpam-4694	471	24	(	(	PUNCT
ejpam-4694	471	25	x;λ	x;λ	PROPN
ejpam-4694	471	26	,	,	PUNCT
ejpam-4694	471	27	ρ	ρ	PROPN
ejpam-4694	471	28	,	,	PUNCT
ejpam-4694	471	29	u	u	NOUN
ejpam-4694	471	30	,	,	PUNCT
ejpam-4694	471	31	a	a	DET
ejpam-4694	471	32	,	,	PUNCT
ejpam-4694	471	33	b	b	NOUN
ejpam-4694	471	34	)	)	PUNCT
ejpam-4694	471	35	tn	tn	NOUN
ejpam-4694	471	36	n	n	NOUN
ejpam-4694	471	37	!	!	PUNCT
ejpam-4694	472	1	=	=	PUNCT
ejpam-4694	472	2	(	(	PUNCT
ejpam-4694	472	3	(	(	PUNCT
ejpam-4694	472	4	1−	1−	NUM
ejpam-4694	472	5	µ)s	µ)s	NOUN
ejpam-4694	472	6	(	(	PUNCT
ejpam-4694	472	7	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	472	8	µ)s	µ)s	NOUN
ejpam-4694	472	9	exρ(t	exρ(t	NOUN
ejpam-4694	472	10	)	)	PUNCT
ejpam-4694	472	11	)	)	PUNCT
ejpam-4694	472	12	(	(	PUNCT
ejpam-4694	472	13	(	(	PUNCT
ejpam-4694	472	14	eρ(t)−	eρ(t)−	PROPN
ejpam-4694	472	15	µ)s	µ)s	NOUN
ejpam-4694	472	16	(	(	PUNCT
ejpam-4694	472	17	1−	1−	NUM
ejpam-4694	472	18	µ)s	µ)s	NOUN
ejpam-4694	472	19	)	)	PUNCT
ejpam-4694	472	20	(	(	PUNCT
ejpam-4694	472	21	eik	eik	PROPN
ejpam-4694	472	22	,	,	PUNCT
ejpam-4694	472	23	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	472	24	+	+	CCONJ
ejpam-4694	472	25	(	(	PUNCT
ejpam-4694	472	26	1−	1−	NUM
ejpam-4694	472	27	u)t	u)t	X
ejpam-4694	472	28	ln	ln	PROPN
ejpam-4694	472	29	ab	ab	PROPN
ejpam-4694	472	30	)	)	PUNCT
ejpam-4694	472	31	)	)	PUNCT
ejpam-4694	473	1	λbt	λbt	VERB
ejpam-4694	473	2	−	−	PROPN
ejpam-4694	473	3	ua−t	ua−t	ADJ
ejpam-4694	473	4	)	)	PUNCT
ejpam-4694	473	5	α	α	NOUN
ejpam-4694	473	6	=	=	SYM
ejpam-4694	473	7	1	1	NUM
ejpam-4694	473	8	(	(	PUNCT
ejpam-4694	473	9	1−	1−	NUM
ejpam-4694	473	10	µ)s	µ)s	NOUN
ejpam-4694	473	11	(	(	PUNCT
ejpam-4694	473	12	∞∑	∞∑	NUM
ejpam-4694	473	13	n=0	n=0	NUM
ejpam-4694	473	14	h(s	h(	NOUN
ejpam-4694	473	15	)	)	PUNCT
ejpam-4694	473	16	n	n	CCONJ
ejpam-4694	473	17	,	,	PUNCT
ejpam-4694	473	18	ρ(x;µ	ρ(x;µ	NUM
ejpam-4694	473	19	)	)	PUNCT
ejpam-4694	473	20	tn	tn	PROPN
ejpam-4694	473	21	n	n	PROPN
ejpam-4694	473	22	!	!	PUNCT
ejpam-4694	473	23	)	)	PUNCT
ejpam-4694	474	1			PROPN
ejpam-4694	474	2	s∑	s∑	PROPN
ejpam-4694	474	3	j=0	j=0	PROPN
ejpam-4694	474	4	(	(	PUNCT
ejpam-4694	474	5	s	s	PROPN
ejpam-4694	474	6	j	j	PROPN
ejpam-4694	474	7	)	)	PUNCT
ejpam-4694	474	8	(	(	PUNCT
ejpam-4694	474	9	−µ)s−j×	−µ)s−j×	X
ejpam-4694	474	10	×	×	NOUN
ejpam-4694	474	11	(	(	PUNCT
ejpam-4694	474	12	eik	eik	PROPN
ejpam-4694	474	13	,	,	PUNCT
ejpam-4694	474	14	ρ(logρ(1	ρ(logρ(1	X
ejpam-4694	474	15	+	+	CCONJ
ejpam-4694	474	16	(	(	PUNCT
ejpam-4694	474	17	1−	1−	NUM
ejpam-4694	474	18	u)t	u)t	X
ejpam-4694	474	19	ln	ln	PROPN
ejpam-4694	474	20	ab	ab	PROPN
ejpam-4694	474	21	)	)	PUNCT
ejpam-4694	474	22	)	)	PUNCT
ejpam-4694	475	1	λbt	λbt	VERB
ejpam-4694	475	2	−	−	PROPN
ejpam-4694	475	3	ua−t	ua−t	ADJ
ejpam-4694	475	4	)	)	PUNCT
ejpam-4694	475	5	α	α	PROPN
ejpam-4694	475	6	(	(	PUNCT
ejpam-4694	475	7	eρ(t	eρ(t	NUM
ejpam-4694	475	8	)	)	PUNCT
ejpam-4694	475	9	)	)	PUNCT
ejpam-4694	476	1	j	j	PROPN
ejpam-4694	476	2	)	)	PUNCT
ejpam-4694	476	3	r.	r.	PROPN
ejpam-4694	476	4	corcino	corcino	PROPN
ejpam-4694	476	5	,	,	PUNCT
ejpam-4694	476	6	c.	c.	PROPN
ejpam-4694	476	7	corcino	corcino	PROPN
ejpam-4694	476	8	/	/	SYM
ejpam-4694	476	9	eur	eur	PROPN
ejpam-4694	476	10	.	.	PUNCT
ejpam-4694	477	1	j.	j.	PROPN
ejpam-4694	477	2	pure	pure	PROPN
ejpam-4694	477	3	appl	appl	PROPN
ejpam-4694	477	4	.	.	PROPN
ejpam-4694	477	5	math	math	PROPN
ejpam-4694	477	6	,	,	PUNCT
ejpam-4694	477	7	16	16	NUM
ejpam-4694	477	8	(	(	PUNCT
ejpam-4694	477	9	2	2	NUM
ejpam-4694	477	10	)	)	PUNCT
ejpam-4694	477	11	(	(	PUNCT
ejpam-4694	477	12	2023	2023	NUM
ejpam-4694	477	13	)	)	PUNCT
ejpam-4694	477	14	,	,	PUNCT
ejpam-4694	477	15	687	687	NUM
ejpam-4694	477	16	-	-	SYM
ejpam-4694	477	17	712	712	NUM
ejpam-4694	477	18	708	708	NUM
ejpam-4694	477	19	=	=	SYM
ejpam-4694	477	20	1	1	NUM
ejpam-4694	477	21	(	(	PUNCT
ejpam-4694	477	22	1−	1−	NUM
ejpam-4694	477	23	µ)s	µ)s	NOUN
ejpam-4694	477	24	s∑	s∑	PROPN
ejpam-4694	477	25	j=0	j=0	PROPN
ejpam-4694	477	26	(	(	PUNCT
ejpam-4694	477	27	s	s	PROPN
ejpam-4694	477	28	j	j	PROPN
ejpam-4694	477	29	)	)	PUNCT
ejpam-4694	477	30	(	(	PUNCT
ejpam-4694	477	31	−µ)s−j	−µ)s−j	NOUN
ejpam-4694	477	32	(	(	PUNCT
ejpam-4694	477	33	∞∑	∞∑	NUM
ejpam-4694	477	34	n=0	n=0	NUM
ejpam-4694	477	35	h(s	h(	NOUN
ejpam-4694	477	36	)	)	PUNCT
ejpam-4694	477	37	n	n	CCONJ
ejpam-4694	477	38	,	,	PUNCT
ejpam-4694	477	39	ρ(x	ρ(x	PROPN
ejpam-4694	477	40	ln	ln	NOUN
ejpam-4694	477	41	c;µ	c;µ	PROPN
ejpam-4694	477	42	)	)	PUNCT
ejpam-4694	477	43	tn	tn	PROPN
ejpam-4694	477	44	n	n	PROPN
ejpam-4694	477	45	!	!	PUNCT
ejpam-4694	477	46	)	)	PUNCT
ejpam-4694	478	1	×	×	NOUN
ejpam-4694	478	2	×	×	NOUN
ejpam-4694	478	3	(	(	PUNCT
ejpam-4694	478	4	∞∑	∞∑	PROPN
ejpam-4694	478	5	n=0	n=0	NUM
ejpam-4694	478	6	ĝ(k	ĝ(k	PROPN
ejpam-4694	478	7	,	,	PUNCT
ejpam-4694	478	8	α	α	NOUN
ejpam-4694	478	9	)	)	PUNCT
ejpam-4694	478	10	n	n	PROPN
ejpam-4694	478	11	(	(	PUNCT
ejpam-4694	478	12	λ	λ	PROPN
ejpam-4694	478	13	,	,	PUNCT
ejpam-4694	478	14	ρ	ρ	PROPN
ejpam-4694	478	15	,	,	PUNCT
ejpam-4694	478	16	u	u	PROPN
ejpam-4694	478	17	,	,	PUNCT
ejpam-4694	478	18	j	j	PROPN
ejpam-4694	478	19	,	,	PUNCT
ejpam-4694	478	20	a	a	DET
ejpam-4694	478	21	,	,	PUNCT
ejpam-4694	478	22	b	b	NOUN
ejpam-4694	478	23	)	)	PUNCT
ejpam-4694	478	24	tn	tn	PROPN
ejpam-4694	478	25	n	n	NOUN
ejpam-4694	478	26	!	!	PUNCT
ejpam-4694	478	27	)	)	PUNCT
ejpam-4694	479	1	=	=	SYM
ejpam-4694	479	2	1	1	NUM
ejpam-4694	479	3	(	(	PUNCT
ejpam-4694	479	4	1−	1−	NUM
ejpam-4694	479	5	µ)s	µ)s	NOUN
ejpam-4694	479	6	s∑	s∑	PROPN
ejpam-4694	479	7	j=0	j=0	PROPN
ejpam-4694	479	8	(	(	PUNCT
ejpam-4694	479	9	s	s	PROPN
ejpam-4694	479	10	j	j	PROPN
ejpam-4694	479	11	)	)	PUNCT
ejpam-4694	479	12	(	(	PUNCT
ejpam-4694	479	13	−µ)s−j	−µ)s−j	VERB
ejpam-4694	479	14	∞∑	∞∑	NUM
ejpam-4694	479	15	n=0	n=0	PRON
ejpam-4694	479	16	(	(	PUNCT
ejpam-4694	479	17	n∑	n∑	PROPN
ejpam-4694	479	18	m=0	m=0	PROPN
ejpam-4694	480	1	(	(	PUNCT
ejpam-4694	480	2	n	n	NOUN
ejpam-4694	480	3	m	m	VERB
ejpam-4694	480	4	)	)	PUNCT
ejpam-4694	480	5	ĝ(k	ĝ(k	X
ejpam-4694	480	6	,	,	PUNCT
ejpam-4694	480	7	α	α	NOUN
ejpam-4694	480	8	)	)	PUNCT
ejpam-4694	480	9	n−m(λ	n−m(λ	NOUN
ejpam-4694	480	10	,	,	PUNCT
ejpam-4694	480	11	ρ	ρ	PROPN
ejpam-4694	480	12	,	,	PUNCT
ejpam-4694	480	13	u	u	PROPN
ejpam-4694	480	14	,	,	PUNCT
ejpam-4694	480	15	j	j	PROPN
ejpam-4694	480	16	,	,	PUNCT
ejpam-4694	480	17	a	a	PRON
ejpam-4694	480	18	,	,	PUNCT
ejpam-4694	480	19	b)×	b)×	ADV
ejpam-4694	480	20	×h(s	×h(s	PROPN
ejpam-4694	480	21	)	)	PUNCT
ejpam-4694	481	1	n	n	CCONJ
ejpam-4694	481	2	,	,	PUNCT
ejpam-4694	481	3	ρ(x	ρ(x	PROPN
ejpam-4694	481	4	ln	ln	NOUN
ejpam-4694	481	5	c;µ	c;µ	PROPN
ejpam-4694	481	6	)	)	PUNCT
ejpam-4694	481	7	)	)	PUNCT
ejpam-4694	481	8	tn	tn	PROPN
ejpam-4694	481	9	n	n	CCONJ
ejpam-4694	481	10	!	!	PUNCT
ejpam-4694	482	1	=	=	NOUN
ejpam-4694	483	1	∞∑	∞∑	PRON
ejpam-4694	483	2	n=0	n=0	PUNCT
ejpam-4694	483	3			PROPN
ejpam-4694	483	4	n∑	n∑	PROPN
ejpam-4694	483	5	m=0	m=0	PROPN
ejpam-4694	483	6	(	(	PUNCT
ejpam-4694	483	7	n	n	NOUN
ejpam-4694	483	8	m	m	VERB
ejpam-4694	483	9	)	)	PUNCT
ejpam-4694	483	10	(	(	PUNCT
ejpam-4694	483	11	1−	1−	NUM
ejpam-4694	483	12	µ)s	µ)s	NOUN
ejpam-4694	483	13	s∑	s∑	PROPN
ejpam-4694	483	14	j=0	j=0	PROPN
ejpam-4694	483	15	(	(	PUNCT
ejpam-4694	483	16	s	s	PROPN
ejpam-4694	483	17	j	j	PROPN
ejpam-4694	483	18	)	)	PUNCT
ejpam-4694	483	19	(	(	PUNCT
ejpam-4694	483	20	−µ)s−jĝ(k	−µ)s−jĝ(k	PROPN
ejpam-4694	483	21	,	,	PUNCT
ejpam-4694	483	22	α	α	NOUN
ejpam-4694	483	23	)	)	PUNCT
ejpam-4694	483	24	n−m(λ	n−m(λ	NOUN
ejpam-4694	483	25	,	,	PUNCT
ejpam-4694	483	26	ρ	ρ	PROPN
ejpam-4694	483	27	,	,	PUNCT
ejpam-4694	483	28	u	u	PROPN
ejpam-4694	483	29	,	,	PUNCT
ejpam-4694	483	30	j	j	PROPN
ejpam-4694	483	31	,	,	PUNCT
ejpam-4694	483	32	a	a	PRON
ejpam-4694	483	33	,	,	PUNCT
ejpam-4694	483	34	b)×	b)×	ADV
ejpam-4694	483	35	×h(s	×h(s	PROPN
ejpam-4694	483	36	)	)	PUNCT
ejpam-4694	483	37	n	n	CCONJ
ejpam-4694	483	38	,	,	PUNCT
ejpam-4694	483	39	ρ(x	ρ(x	PROPN
ejpam-4694	483	40	ln	ln	NOUN
ejpam-4694	483	41	c;µ	c;µ	PROPN
ejpam-4694	483	42	)	)	PUNCT
ejpam-4694	483	43	)	)	PUNCT
ejpam-4694	483	44	tn	tn	PROPN
ejpam-4694	483	45	n	n	PROPN
ejpam-4694	483	46	!	!	PUNCT
ejpam-4694	483	47	.	.	PUNCT
ejpam-4694	484	1	comparing	compare	VERB
ejpam-4694	484	2	the	the	DET
ejpam-4694	484	3	coefficients	coefficient	NOUN
ejpam-4694	484	4	of	of	ADP
ejpam-4694	484	5	tn	tn	NOUN
ejpam-4694	484	6	n	n	ADP
ejpam-4694	484	7	!	!	PROPN
ejpam-4694	485	1	gives	give	VERB
ejpam-4694	485	2	(	(	PUNCT
ejpam-4694	485	3	55	55	NUM
ejpam-4694	485	4	)	)	PUNCT
ejpam-4694	485	5	.	.	PUNCT
ejpam-4694	486	1	6	6	X
ejpam-4694	486	2	.	.	X
ejpam-4694	486	3	conclusion	conclusion	NOUN
ejpam-4694	486	4	and	and	CCONJ
ejpam-4694	486	5	recommendations	recommendation	NOUN
ejpam-4694	486	6	in	in	ADP
ejpam-4694	486	7	this	this	DET
ejpam-4694	486	8	paper	paper	NOUN
ejpam-4694	486	9	,	,	PUNCT
ejpam-4694	486	10	a	a	DET
ejpam-4694	486	11	certain	certain	ADJ
ejpam-4694	486	12	variation	variation	NOUN
ejpam-4694	486	13	of	of	ADP
ejpam-4694	486	14	poly	poly	ADJ
ejpam-4694	486	15	-	-	PUNCT
ejpam-4694	486	16	genocchi	genocchi	NOUN
ejpam-4694	486	17	polynomials	polynomial	NOUN
ejpam-4694	486	18	,	,	PUNCT
ejpam-4694	486	19	called	call	VERB
ejpam-4694	486	20	the	the	DET
ejpam-4694	486	21	degenerate	degenerate	ADJ
ejpam-4694	486	22	apostol	apostol	NOUN
ejpam-4694	486	23	-	-	PUNCT
ejpam-4694	486	24	frobenius	frobenius	NOUN
ejpam-4694	486	25	-	-	PUNCT
ejpam-4694	486	26	type	type	NOUN
ejpam-4694	486	27	poly	poly	ADJ
ejpam-4694	486	28	-	-	PUNCT
ejpam-4694	486	29	genocchi	genocchi	NOUN
ejpam-4694	486	30	polynomials	polynomial	NOUN
ejpam-4694	486	31	of	of	ADP
ejpam-4694	486	32	higher	high	ADJ
ejpam-4694	486	33	order	order	NOUN
ejpam-4694	486	34	with	with	ADP
ejpam-4694	486	35	parameter	parameter	PROPN
ejpam-4694	486	36	a	a	DET
ejpam-4694	486	37	,	,	PUNCT
ejpam-4694	486	38	b	b	PROPN
ejpam-4694	486	39	and	and	CCONJ
ejpam-4694	486	40	c	c	PROPN
ejpam-4694	486	41	was	be	AUX
ejpam-4694	486	42	constructed	construct	VERB
ejpam-4694	486	43	using	use	VERB
ejpam-4694	486	44	the	the	DET
ejpam-4694	486	45	concept	concept	NOUN
ejpam-4694	486	46	of	of	ADP
ejpam-4694	486	47	modified	modified	ADJ
ejpam-4694	486	48	degenerate	degenerate	ADJ
ejpam-4694	486	49	polylexponential	polylexponential	ADJ
ejpam-4694	486	50	function	function	NOUN
ejpam-4694	486	51	,	,	PUNCT
ejpam-4694	486	52	apostol	apostol	NOUN
ejpam-4694	486	53	-	-	PUNCT
ejpam-4694	486	54	genocchi	genocchi	PROPN
ejpam-4694	486	55	polynomials	polynomial	NOUN
ejpam-4694	486	56	and	and	CCONJ
ejpam-4694	486	57	frobenius	frobenius	ADJ
ejpam-4694	486	58	polynomials	polynomial	NOUN
ejpam-4694	486	59	.	.	PUNCT
ejpam-4694	487	1	some	some	DET
ejpam-4694	487	2	interesting	interesting	ADJ
ejpam-4694	487	3	properties	property	NOUN
ejpam-4694	487	4	and	and	CCONJ
ejpam-4694	487	5	identities	identity	NOUN
ejpam-4694	487	6	of	of	ADP
ejpam-4694	487	7	these	these	DET
ejpam-4694	487	8	polynomials	polynomial	NOUN
ejpam-4694	487	9	were	be	AUX
ejpam-4694	487	10	explored	explore	VERB
ejpam-4694	487	11	parallel	parallel	NOUN
ejpam-4694	487	12	to	to	ADP
ejpam-4694	487	13	those	those	PRON
ejpam-4694	487	14	of	of	ADP
ejpam-4694	487	15	the	the	DET
ejpam-4694	487	16	poly	poly	ADJ
ejpam-4694	487	17	-	-	PUNCT
ejpam-4694	487	18	genocchi	genocchi	NOUN
ejpam-4694	487	19	,	,	PUNCT
ejpam-4694	487	20	poly	poly	NOUN
ejpam-4694	487	21	-	-	PUNCT
ejpam-4694	487	22	euler	euler	NOUN
ejpam-4694	487	23	and	and	CCONJ
ejpam-4694	487	24	poly	poly	ADJ
ejpam-4694	487	25	-	-	PUNCT
ejpam-4694	487	26	bernoulli	bernoulli	NOUN
ejpam-4694	487	27	polynomials	polynomial	NOUN
ejpam-4694	487	28	.	.	PUNCT
ejpam-4694	488	1	the	the	DET
ejpam-4694	488	2	paper	paper	NOUN
ejpam-4694	488	3	was	be	AUX
ejpam-4694	488	4	concluded	conclude	VERB
ejpam-4694	488	5	by	by	ADP
ejpam-4694	488	6	expressing	express	VERB
ejpam-4694	488	7	these	these	DET
ejpam-4694	488	8	degenerate	degenerate	ADJ
ejpam-4694	488	9	apostol	apostol	NOUN
ejpam-4694	488	10	-	-	PUNCT
ejpam-4694	488	11	frobenius	frobenius	NOUN
ejpam-4694	488	12	-	-	PUNCT
ejpam-4694	488	13	type	type	NOUN
ejpam-4694	488	14	poly	poly	ADJ
ejpam-4694	488	15	-	-	PUNCT
ejpam-4694	488	16	genocchi	genocchi	NOUN
ejpam-4694	488	17	polynomials	polynomial	NOUN
ejpam-4694	488	18	of	of	ADP
ejpam-4694	488	19	higher	high	ADJ
ejpam-4694	488	20	order	order	NOUN
ejpam-4694	488	21	in	in	ADP
ejpam-4694	488	22	terms	term	NOUN
ejpam-4694	488	23	of	of	ADP
ejpam-4694	488	24	degenerate	degenerate	ADJ
ejpam-4694	488	25	stirling	stirling	NOUN
ejpam-4694	488	26	numbers	number	NOUN
ejpam-4694	488	27	of	of	ADP
ejpam-4694	488	28	the	the	DET
ejpam-4694	488	29	first	first	ADJ
ejpam-4694	488	30	and	and	CCONJ
ejpam-4694	488	31	second	second	ADJ
ejpam-4694	488	32	kind	kind	NOUN
ejpam-4694	488	33	,	,	PUNCT
ejpam-4694	488	34	higher	high	ADJ
ejpam-4694	488	35	order	order	NOUN
ejpam-4694	488	36	degenerate	degenerate	ADJ
ejpam-4694	488	37	bernoulli	bernoulli	NOUN
ejpam-4694	488	38	polynomials	polynomial	NOUN
ejpam-4694	488	39	,	,	PUNCT
ejpam-4694	488	40	and	and	CCONJ
ejpam-4694	488	41	higher	high	ADJ
ejpam-4694	488	42	order	order	NOUN
ejpam-4694	488	43	degenerate	degenerate	ADJ
ejpam-4694	488	44	frobenius	frobenius	NOUN
ejpam-4694	488	45	-	-	PUNCT
ejpam-4694	488	46	euler	euler	NOUN
ejpam-4694	488	47	polynomials	polynomial	NOUN
ejpam-4694	488	48	.	.	PUNCT
ejpam-4694	489	1	for	for	ADP
ejpam-4694	489	2	future	future	ADJ
ejpam-4694	489	3	research	research	NOUN
ejpam-4694	489	4	work	work	NOUN
ejpam-4694	489	5	,	,	PUNCT
ejpam-4694	489	6	one	one	PRON
ejpam-4694	489	7	may	may	AUX
ejpam-4694	489	8	try	try	VERB
ejpam-4694	489	9	investigate	investigate	VERB
ejpam-4694	489	10	more	more	ADJ
ejpam-4694	489	11	identities	identity	NOUN
ejpam-4694	489	12	and	and	CCONJ
ejpam-4694	489	13	properties	property	NOUN
ejpam-4694	489	14	for	for	ADP
ejpam-4694	489	15	ĝ(k	ĝ(k	PRON
ejpam-4694	489	16	,	,	PUNCT
ejpam-4694	489	17	α	α	NOUN
ejpam-4694	489	18	)	)	PUNCT
ejpam-4694	489	19	n	n	CCONJ
ejpam-4694	489	20	(	(	PUNCT
ejpam-4694	489	21	x;λ	x;λ	PROPN
ejpam-4694	489	22	,	,	PUNCT
ejpam-4694	489	23	ρ	ρ	PROPN
ejpam-4694	489	24	,	,	PUNCT
ejpam-4694	489	25	u	u	NOUN
ejpam-4694	489	26	,	,	PUNCT
ejpam-4694	489	27	a	a	DET
ejpam-4694	489	28	,	,	PUNCT
ejpam-4694	489	29	b	b	NOUN
ejpam-4694	489	30	)	)	PUNCT
ejpam-4694	489	31	to	to	PART
ejpam-4694	489	32	describe	describe	VERB
ejpam-4694	489	33	further	far	ADV
ejpam-4694	489	34	the	the	DET
ejpam-4694	489	35	structure	structure	NOUN
ejpam-4694	489	36	of	of	ADP
ejpam-4694	489	37	these	these	DET
ejpam-4694	489	38	polynomials	polynomial	NOUN
ejpam-4694	489	39	that	that	PRON
ejpam-4694	489	40	may	may	AUX
ejpam-4694	489	41	eventually	eventually	ADV
ejpam-4694	489	42	be	be	AUX
ejpam-4694	489	43	used	use	VERB
ejpam-4694	489	44	to	to	PART
ejpam-4694	489	45	find	find	VERB
ejpam-4694	489	46	some	some	DET
ejpam-4694	489	47	applications	application	NOUN
ejpam-4694	489	48	of	of	ADP
ejpam-4694	489	49	these	these	DET
ejpam-4694	489	50	polynomials	polynomial	NOUN
ejpam-4694	489	51	to	to	ADP
ejpam-4694	489	52	other	other	ADJ
ejpam-4694	489	53	areas	area	NOUN
ejpam-4694	489	54	in	in	ADP
ejpam-4694	489	55	mathematics	mathematic	NOUN
ejpam-4694	489	56	.	.	PUNCT
ejpam-4694	490	1	for	for	ADP
ejpam-4694	490	2	instance	instance	NOUN
ejpam-4694	490	3	,	,	PUNCT
ejpam-4694	490	4	it	it	PRON
ejpam-4694	490	5	would	would	AUX
ejpam-4694	490	6	be	be	AUX
ejpam-4694	490	7	interesting	interesting	ADJ
ejpam-4694	490	8	to	to	PART
ejpam-4694	490	9	establish	establish	VERB
ejpam-4694	490	10	the	the	DET
ejpam-4694	490	11	orthogonal	orthogonal	ADJ
ejpam-4694	490	12	version	version	NOUN
ejpam-4694	490	13	of	of	ADP
ejpam-4694	490	14	ĝ(k	ĝ(k	PRON
ejpam-4694	490	15	,	,	PUNCT
ejpam-4694	490	16	α	α	NOUN
ejpam-4694	490	17	)	)	PUNCT
ejpam-4694	490	18	n	n	CCONJ
ejpam-4694	490	19	(	(	PUNCT
ejpam-4694	490	20	x;λ	x;λ	PROPN
ejpam-4694	490	21	,	,	PUNCT
ejpam-4694	490	22	ρ	ρ	PROPN
ejpam-4694	490	23	,	,	PUNCT
ejpam-4694	490	24	u	u	NOUN
ejpam-4694	490	25	,	,	PUNCT
ejpam-4694	490	26	a	a	DET
ejpam-4694	490	27	,	,	PUNCT
ejpam-4694	490	28	b	b	NOUN
ejpam-4694	490	29	)	)	PUNCT
ejpam-4694	490	30	as	as	ADV
ejpam-4694	490	31	well	well	ADV
ejpam-4694	490	32	as	as	ADP
ejpam-4694	490	33	to	to	PART
ejpam-4694	490	34	derive	derive	VERB
ejpam-4694	490	35	new	new	ADJ
ejpam-4694	490	36	operational	operational	ADJ
ejpam-4694	490	37	matrix	matrix	NOUN
ejpam-4694	490	38	based	base	VERB
ejpam-4694	490	39	on	on	ADP
ejpam-4694	490	40	these	these	DET
ejpam-4694	490	41	polynomials	polynomial	NOUN
ejpam-4694	490	42	in	in	ADP
ejpam-4694	490	43	order	order	NOUN
ejpam-4694	490	44	to	to	PART
ejpam-4694	490	45	provide	provide	VERB
ejpam-4694	490	46	possible	possible	ADJ
ejpam-4694	490	47	application	application	NOUN
ejpam-4694	490	48	to	to	PART
ejpam-4694	490	49	solve	solve	VERB
ejpam-4694	490	50	some	some	DET
ejpam-4694	490	51	fractional	fractional	ADJ
ejpam-4694	490	52	differential	differential	NOUN
ejpam-4694	490	53	equation	equation	NOUN
ejpam-4694	490	54	(	(	PUNCT
ejpam-4694	490	55	see	see	VERB
ejpam-4694	490	56	[	[	X
ejpam-4694	490	57	8	8	NUM
ejpam-4694	490	58	]	]	NUM
ejpam-4694	490	59	)	)	PUNCT
ejpam-4694	490	60	.	.	PUNCT
ejpam-4694	491	1	lastly	lastly	ADV
ejpam-4694	491	2	,	,	PUNCT
ejpam-4694	491	3	it	it	PRON
ejpam-4694	491	4	would	would	AUX
ejpam-4694	491	5	also	also	ADV
ejpam-4694	491	6	be	be	AUX
ejpam-4694	491	7	interesting	interesting	ADJ
ejpam-4694	491	8	to	to	PART
ejpam-4694	491	9	construct	construct	VERB
ejpam-4694	491	10	other	other	ADJ
ejpam-4694	491	11	variations	variation	NOUN
ejpam-4694	491	12	of	of	ADP
ejpam-4694	491	13	poly	poly	ADJ
ejpam-4694	491	14	-	-	PUNCT
ejpam-4694	491	15	genocchi	genocchi	NOUN
ejpam-4694	491	16	polynomials	polynomial	NOUN
ejpam-4694	491	17	by	by	ADP
ejpam-4694	491	18	mixing	mix	VERB
ejpam-4694	491	19	ĝ(k	ĝ(k	PROPN
ejpam-4694	491	20	,	,	PUNCT
ejpam-4694	491	21	α	α	NOUN
ejpam-4694	491	22	)	)	PUNCT
ejpam-4694	491	23	n	n	CCONJ
ejpam-4694	491	24	(	(	PUNCT
ejpam-4694	491	25	x;λ	x;λ	PROPN
ejpam-4694	491	26	,	,	PUNCT
ejpam-4694	491	27	ρ	ρ	PROPN
ejpam-4694	491	28	,	,	PUNCT
ejpam-4694	491	29	u	u	NOUN
ejpam-4694	491	30	,	,	PUNCT
ejpam-4694	491	31	a	a	DET
ejpam-4694	491	32	,	,	PUNCT
ejpam-4694	491	33	b	b	NOUN
ejpam-4694	491	34	)	)	PUNCT
ejpam-4694	491	35	with	with	ADP
ejpam-4694	491	36	2	2	NUM
ejpam-4694	491	37	-	-	PUNCT
ejpam-4694	491	38	variable	variable	ADJ
ejpam-4694	491	39	generalization	generalization	NOUN
ejpam-4694	491	40	of	of	ADP
ejpam-4694	491	41	hermite	hermite	ADJ
ejpam-4694	491	42	polynomials	polynomial	NOUN
ejpam-4694	491	43	.	.	PUNCT
ejpam-4694	492	1	references	reference	NOUN
ejpam-4694	492	2	709	709	NUM
ejpam-4694	492	3	acknowledgements	acknowledgement	NOUN
ejpam-4694	492	4	the	the	DET
ejpam-4694	492	5	authors	author	NOUN
ejpam-4694	492	6	are	be	AUX
ejpam-4694	492	7	grateful	grateful	ADJ
ejpam-4694	492	8	to	to	PART
ejpam-4694	492	9	cebu	cebu	VERB
ejpam-4694	492	10	normal	normal	ADJ
ejpam-4694	492	11	university	university	NOUN
ejpam-4694	492	12	(	(	PUNCT
ejpam-4694	492	13	cnu	cnu	PROPN
ejpam-4694	492	14	)	)	PUNCT
ejpam-4694	492	15	for	for	ADP
ejpam-4694	492	16	funding	fund	VERB
ejpam-4694	492	17	this	this	DET
ejpam-4694	492	18	research	research	NOUN
ejpam-4694	492	19	project	project	NOUN
ejpam-4694	492	20	through	through	ADP
ejpam-4694	492	21	its	its	PRON
ejpam-4694	492	22	research	research	NOUN
ejpam-4694	492	23	institute	institute	NOUN
ejpam-4694	492	24	for	for	ADP
ejpam-4694	492	25	computational	computational	ADJ
ejpam-4694	492	26	mathematics	mathematic	NOUN
ejpam-4694	492	27	and	and	CCONJ
ejpam-4694	492	28	physics	physics	PROPN
ejpam-4694	492	29	(	(	PUNCT
ejpam-4694	492	30	ricmp	ricmp	PROPN
ejpam-4694	492	31	)	)	PUNCT
ejpam-4694	492	32	.	.	PUNCT
ejpam-4694	493	1	they	they	PRON
ejpam-4694	493	2	are	be	AUX
ejpam-4694	493	3	also	also	ADV
ejpam-4694	493	4	grateful	grateful	ADJ
ejpam-4694	493	5	to	to	ADP
ejpam-4694	493	6	the	the	DET
ejpam-4694	493	7	two	two	NUM
ejpam-4694	493	8	referees	referee	NOUN
ejpam-4694	493	9	for	for	ADP
ejpam-4694	493	10	their	their	PRON
ejpam-4694	493	11	valuable	valuable	ADJ
ejpam-4694	493	12	time	time	NOUN
ejpam-4694	493	13	in	in	ADP
ejpam-4694	493	14	reviewing	review	VERB
ejpam-4694	493	15	the	the	DET
ejpam-4694	493	16	paper	paper	NOUN
ejpam-4694	493	17	.	.	PUNCT
ejpam-4694	494	1	references	reference	NOUN
ejpam-4694	494	2	[	[	X
ejpam-4694	494	3	1	1	X
ejpam-4694	494	4	]	]	PUNCT
ejpam-4694	494	5	t.	t.	NOUN
ejpam-4694	494	6	agoh	agoh	PROPN
ejpam-4694	494	7	.	.	PUNCT
ejpam-4694	495	1	convolution	convolution	NOUN
ejpam-4694	495	2	identities	identity	NOUN
ejpam-4694	495	3	for	for	ADP
ejpam-4694	495	4	bernoulli	bernoulli	PROPN
ejpam-4694	495	5	and	and	CCONJ
ejpam-4694	495	6	genocchi	genocchi	PROPN
ejpam-4694	495	7	polynomials	polynomial	NOUN
ejpam-4694	495	8	.	.	PUNCT
ejpam-4694	496	1	electronic	electronic	ADJ
ejpam-4694	496	2	j.	j.	PROPN
ejpam-4694	496	3	combin	combin	PROPN
ejpam-4694	496	4	.	.	PROPN
ejpam-4694	496	5	,	,	PUNCT
ejpam-4694	496	6	21	21	NUM
ejpam-4694	496	7	:	:	PUNCT
ejpam-4694	496	8	article	article	NOUN
ejpam-4694	496	9	i	i	PROPN
ejpam-4694	496	10	d	d	PROPN
ejpam-4694	496	11	p1.65	p1.65	PROPN
ejpam-4694	496	12	,	,	PUNCT
ejpam-4694	496	13	2014	2014	NUM
ejpam-4694	496	14	.	.	PUNCT
ejpam-4694	497	1	[	[	X
ejpam-4694	497	2	2	2	X
ejpam-4694	497	3	]	]	PUNCT
ejpam-4694	497	4	s.	s.	PROPN
ejpam-4694	497	5	araci	araci	PROPN
ejpam-4694	497	6	.	.	PUNCT
ejpam-4694	498	1	novel	novel	ADJ
ejpam-4694	498	2	identities	identity	NOUN
ejpam-4694	498	3	for	for	ADP
ejpam-4694	498	4	q	q	ADJ
ejpam-4694	498	5	-	-	ADJ
ejpam-4694	498	6	genocchi	genocchi	ADJ
ejpam-4694	498	7	numbers	number	NOUN
ejpam-4694	498	8	and	and	CCONJ
ejpam-4694	498	9	polynomials	polynomial	NOUN
ejpam-4694	498	10	.	.	PUNCT
ejpam-4694	499	1	j.	j.	PROPN
ejpam-4694	499	2	funct.spaces	funct.space	NOUN
ejpam-4694	499	3	appl	appl	PROPN
ejpam-4694	499	4	.	.	PUNCT
ejpam-4694	499	5	,	,	PUNCT
ejpam-4694	499	6	2012	2012	NUM
ejpam-4694	499	7	:	:	PUNCT
ejpam-4694	499	8	article	article	NOUN
ejpam-4694	499	9	i	i	PROPN
ejpam-4694	499	10	d	d	PROPN
ejpam-4694	499	11	214961	214961	NUM
ejpam-4694	499	12	,	,	PUNCT
ejpam-4694	499	13	2012	2012	NUM
ejpam-4694	499	14	.	.	PUNCT
ejpam-4694	500	1	[	[	X
ejpam-4694	500	2	3	3	X
ejpam-4694	500	3	]	]	PUNCT
ejpam-4694	500	4	s.	s.	PROPN
ejpam-4694	500	5	araci	araci	PROPN
ejpam-4694	500	6	.	.	PUNCT
ejpam-4694	501	1	novel	novel	ADJ
ejpam-4694	501	2	identities	identity	NOUN
ejpam-4694	501	3	involving	involve	VERB
ejpam-4694	501	4	genocchi	genocchi	PROPN
ejpam-4694	501	5	numbers	number	NOUN
ejpam-4694	501	6	and	and	CCONJ
ejpam-4694	501	7	polynomials	polynomial	NOUN
ejpam-4694	501	8	arising	arise	VERB
ejpam-4694	501	9	from	from	ADP
ejpam-4694	501	10	application	application	NOUN
ejpam-4694	501	11	of	of	ADP
ejpam-4694	501	12	umbral	umbral	ADJ
ejpam-4694	501	13	calculus	calculus	NOUN
ejpam-4694	501	14	.	.	PUNCT
ejpam-4694	502	1	appl	appl	PROPN
ejpam-4694	502	2	.	.	PROPN
ejpam-4694	502	3	math	math	PROPN
ejpam-4694	502	4	.	.	PUNCT
ejpam-4694	503	1	comput	comput	NOUN
ejpam-4694	503	2	.	.	PUNCT
ejpam-4694	503	3	,	,	PUNCT
ejpam-4694	503	4	233:599–607	233:599–607	NUM
ejpam-4694	503	5	,	,	PUNCT
ejpam-4694	503	6	2014	2014	NUM
ejpam-4694	503	7	.	.	PUNCT
ejpam-4694	504	1	[	[	X
ejpam-4694	504	2	4	4	X
ejpam-4694	504	3	]	]	PUNCT
ejpam-4694	504	4	s.	s.	PROPN
ejpam-4694	504	5	araci	araci	PROPN
ejpam-4694	504	6	,	,	PUNCT
ejpam-4694	504	7	w.a	w.a	PROPN
ejpam-4694	504	8	khan	khan	PROPN
ejpam-4694	504	9	,	,	PUNCT
ejpam-4694	504	10	m.	m.	NOUN
ejpam-4694	504	11	acikgoz	acikgoz	PROPN
ejpam-4694	504	12	,	,	PUNCT
ejpam-4694	504	13	c.	c.	PROPN
ejpam-4694	504	14	ozel	ozel	PROPN
ejpam-4694	504	15	,	,	PUNCT
ejpam-4694	504	16	and	and	CCONJ
ejpam-4694	504	17	p.	p.	PROPN
ejpam-4694	504	18	kumam	kumam	PROPN
ejpam-4694	504	19	.	.	PUNCT
ejpam-4694	505	1	a	a	DET
ejpam-4694	505	2	new	new	ADJ
ejpam-4694	505	3	generalization	generalization	NOUN
ejpam-4694	505	4	of	of	ADP
ejpam-4694	505	5	apostol	apostol	PROPN
ejpam-4694	505	6	type	type	NOUN
ejpam-4694	505	7	hermite	hermite	PROPN
ejpam-4694	505	8	-	-	PUNCT
ejpam-4694	505	9	genocchi	genocchi	PROPN
ejpam-4694	505	10	polynomials	polynomial	NOUN
ejpam-4694	505	11	and	and	CCONJ
ejpam-4694	505	12	its	its	PRON
ejpam-4694	505	13	applications	application	NOUN
ejpam-4694	505	14	.	.	PUNCT
ejpam-4694	506	1	springerplus	springerplus	PROPN
ejpam-4694	506	2	,	,	PUNCT
ejpam-4694	506	3	5	5	NUM
ejpam-4694	506	4	:	:	PUNCT
ejpam-4694	506	5	article	article	NOUN
ejpam-4694	506	6	i	i	PROPN
ejpam-4694	506	7	d	d	PROPN
ejpam-4694	506	8	860	860	PROPN
ejpam-4694	506	9	,	,	PUNCT
ejpam-4694	506	10	2016	2016	NUM
ejpam-4694	506	11	.	.	PUNCT
ejpam-4694	507	1	[	[	X
ejpam-4694	507	2	5	5	X
ejpam-4694	507	3	]	]	PUNCT
ejpam-4694	507	4	s.	s.	PROPN
ejpam-4694	507	5	araci	araci	PROPN
ejpam-4694	507	6	,	,	PUNCT
ejpam-4694	507	7	e.	e.	PROPN
ejpam-4694	507	8	sen	sen	PROPN
ejpam-4694	507	9	,	,	PUNCT
ejpam-4694	507	10	and	and	CCONJ
ejpam-4694	507	11	m.	m.	NOUN
ejpam-4694	507	12	acikgoz	acikgoz	VERB
ejpam-4694	507	13	.	.	PUNCT
ejpam-4694	508	1	some	some	DET
ejpam-4694	508	2	new	new	ADJ
ejpam-4694	508	3	formulae	formulae	NOUN
ejpam-4694	508	4	for	for	ADP
ejpam-4694	508	5	genocchi	genocchi	PROPN
ejpam-4694	508	6	numbers	number	NOUN
ejpam-4694	508	7	and	and	CCONJ
ejpam-4694	508	8	polynomials	polynomial	NOUN
ejpam-4694	508	9	involving	involve	VERB
ejpam-4694	508	10	bernoulli	bernoulli	NOUN
ejpam-4694	508	11	and	and	CCONJ
ejpam-4694	508	12	euler	euler	NOUN
ejpam-4694	508	13	polynomials	polynomial	NOUN
ejpam-4694	508	14	.	.	PUNCT
ejpam-4694	509	1	int	int	NOUN
ejpam-4694	509	2	.	.	PUNCT
ejpam-4694	510	1	j.	j.	PROPN
ejpam-4694	510	2	math	math	PROPN
ejpam-4694	510	3	.	.	PUNCT
ejpam-4694	511	1	math	math	NOUN
ejpam-4694	511	2	.	.	PUNCT
ejpam-4694	512	1	sci	sci	PROPN
ejpam-4694	512	2	.	.	PROPN
ejpam-4694	512	3	,	,	PUNCT
ejpam-4694	512	4	2014	2014	NUM
ejpam-4694	512	5	:	:	PUNCT
ejpam-4694	512	6	article	article	NOUN
ejpam-4694	512	7	ic	ic	PROPN
ejpam-4694	512	8	760613	760613	NUM
ejpam-4694	512	9	,	,	PUNCT
ejpam-4694	512	10	7	7	NUM
ejpam-4694	512	11	pages	page	NOUN
ejpam-4694	512	12	,	,	PUNCT
ejpam-4694	512	13	2014	2014	NUM
ejpam-4694	512	14	.	.	PUNCT
ejpam-4694	513	1	[	[	X
ejpam-4694	513	2	6	6	NUM
ejpam-4694	513	3	]	]	PUNCT
ejpam-4694	513	4	s.	s.	PROPN
ejpam-4694	513	5	araci	araci	PROPN
ejpam-4694	513	6	,	,	PUNCT
ejpam-4694	513	7	e.	e.	PROPN
ejpam-4694	513	8	sen	sen	PROPN
ejpam-4694	513	9	,	,	PUNCT
ejpam-4694	513	10	and	and	CCONJ
ejpam-4694	513	11	m.	m.	NOUN
ejpam-4694	513	12	acikgoz	acikgoz	VERB
ejpam-4694	513	13	.	.	PUNCT
ejpam-4694	514	1	theorems	theorem	NOUN
ejpam-4694	514	2	on	on	ADP
ejpam-4694	514	3	genocchi	genocchi	PROPN
ejpam-4694	514	4	polynomials	polynomial	NOUN
ejpam-4694	514	5	of	of	ADP
ejpam-4694	514	6	higher	high	ADJ
ejpam-4694	514	7	order	order	NOUN
ejpam-4694	514	8	arising	arise	VERB
ejpam-4694	514	9	from	from	ADP
ejpam-4694	514	10	genocchi	genocchi	PROPN
ejpam-4694	514	11	basis	basis	NOUN
ejpam-4694	514	12	.	.	PUNCT
ejpam-4694	515	1	taiwanese	taiwanese	ADJ
ejpam-4694	515	2	j.	j.	PROPN
ejpam-4694	515	3	math	math	PROPN
ejpam-4694	515	4	.	.	PROPN
ejpam-4694	515	5	,	,	PUNCT
ejpam-4694	515	6	18(2):473–482	18(2):473–482	PROPN
ejpam-4694	515	7	,	,	PUNCT
ejpam-4694	515	8	2014	2014	NUM
ejpam-4694	515	9	.	.	PUNCT
ejpam-4694	516	1	[	[	X
ejpam-4694	516	2	7	7	X
ejpam-4694	516	3	]	]	PUNCT
ejpam-4694	516	4	a.	a.	NOUN
ejpam-4694	516	5	bayad	bayad	NOUN
ejpam-4694	516	6	and	and	CCONJ
ejpam-4694	516	7	t.	t.	PROPN
ejpam-4694	516	8	kim	kim	PROPN
ejpam-4694	516	9	.	.	PUNCT
ejpam-4694	517	1	identities	identity	NOUN
ejpam-4694	517	2	for	for	ADP
ejpam-4694	517	3	apostol	apostol	NOUN
ejpam-4694	517	4	-	-	PUNCT
ejpam-4694	517	5	type	type	NOUN
ejpam-4694	517	6	frobenius	frobenius	NOUN
ejpam-4694	517	7	-	-	PUNCT
ejpam-4694	517	8	euler	euler	NOUN
ejpam-4694	517	9	polynomials	polynomial	NOUN
ejpam-4694	517	10	resulting	result	VERB
ejpam-4694	517	11	from	from	ADP
ejpam-4694	517	12	the	the	DET
ejpam-4694	517	13	study	study	NOUN
ejpam-4694	517	14	of	of	ADP
ejpam-4694	517	15	a	a	DET
ejpam-4694	517	16	nonlinear	nonlinear	ADJ
ejpam-4694	517	17	operator	operator	NOUN
ejpam-4694	517	18	.	.	PUNCT
ejpam-4694	518	1	russ	russ	PROPN
ejpam-4694	518	2	.	.	PUNCT
ejpam-4694	519	1	j.	j.	PROPN
ejpam-4694	519	2	math	math	PROPN
ejpam-4694	519	3	.	.	PUNCT
ejpam-4694	520	1	phys	phy	NOUN
ejpam-4694	520	2	.	.	PUNCT
ejpam-4694	520	3	,	,	PUNCT
ejpam-4694	520	4	23:164–171	23:164–171	NUM
ejpam-4694	520	5	,	,	PUNCT
ejpam-4694	520	6	2016	2016	NUM
ejpam-4694	520	7	.	.	PUNCT
ejpam-4694	521	1	[	[	X
ejpam-4694	521	2	8	8	NUM
ejpam-4694	521	3	]	]	PUNCT
ejpam-4694	521	4	a.	a.	NOUN
ejpam-4694	521	5	isah	isah	PROPN
ejpam-4694	521	6	c.	c.	PROPN
ejpam-4694	521	7	phang	phang	PROPN
ejpam-4694	521	8	and	and	CCONJ
ejpam-4694	521	9	y.	y.	PROPN
ejpam-4694	521	10	t.	t.	PROPN
ejpam-4694	521	11	toh	toh	PROPN
ejpam-4694	521	12	.	.	PUNCT
ejpam-4694	522	1	poly	poly	ADJ
ejpam-4694	522	2	-	-	PUNCT
ejpam-4694	522	3	genocchi	genocchi	NOUN
ejpam-4694	522	4	polynomials	polynomial	NOUN
ejpam-4694	522	5	and	and	CCONJ
ejpam-4694	522	6	its	its	PRON
ejpam-4694	522	7	applications	application	NOUN
ejpam-4694	522	8	.	.	PUNCT
ejpam-4694	523	1	aims	aim	VERB
ejpam-4694	523	2	mathematics	mathematic	NOUN
ejpam-4694	523	3	,	,	PUNCT
ejpam-4694	523	4	6(8):8221–8238	6(8):8221–8238	NOUN
ejpam-4694	523	5	,	,	PUNCT
ejpam-4694	523	6	2021	2021	NUM
ejpam-4694	523	7	.	.	PUNCT
ejpam-4694	524	1	[	[	X
ejpam-4694	524	2	9	9	NUM
ejpam-4694	524	3	]	]	PUNCT
ejpam-4694	524	4	w.	w.	PROPN
ejpam-4694	524	5	a.	a.	PROPN
ejpam-4694	524	6	khan	khan	PROPN
ejpam-4694	524	7	c.	c.	PROPN
ejpam-4694	524	8	s.	s.	PROPN
ejpam-4694	524	9	ryoo	ryoo	PROPN
ejpam-4694	524	10	.	.	PUNCT
ejpam-4694	525	1	on	on	ADP
ejpam-4694	525	2	two	two	NUM
ejpam-4694	525	3	bivariate	bivariate	ADJ
ejpam-4694	525	4	kinds	kind	NOUN
ejpam-4694	525	5	of	of	ADP
ejpam-4694	525	6	poly	poly	ADJ
ejpam-4694	525	7	-	-	PUNCT
ejpam-4694	525	8	bernoulli	bernoulli	NOUN
ejpam-4694	525	9	and	and	CCONJ
ejpam-4694	525	10	poly	poly	ADJ
ejpam-4694	525	11	-	-	PUNCT
ejpam-4694	525	12	genocchi	genocchi	NOUN
ejpam-4694	525	13	polynomials	polynomial	NOUN
ejpam-4694	525	14	.	.	PUNCT
ejpam-4694	526	1	mathematics	mathematic	NOUN
ejpam-4694	526	2	,	,	PUNCT
ejpam-4694	526	3	8:417	8:417	NUM
ejpam-4694	526	4	,	,	PUNCT
ejpam-4694	526	5	2020	2020	NUM
ejpam-4694	526	6	.	.	PUNCT
ejpam-4694	527	1	[	[	X
ejpam-4694	527	2	10	10	NUM
ejpam-4694	527	3	]	]	X
ejpam-4694	527	4	l.	l.	PROPN
ejpam-4694	527	5	carlitz	carlitz	PROPN
ejpam-4694	527	6	.	.	PUNCT
ejpam-4694	528	1	a	a	DET
ejpam-4694	528	2	note	note	NOUN
ejpam-4694	528	3	on	on	ADP
ejpam-4694	528	4	bernoulli	bernoulli	PROPN
ejpam-4694	528	5	and	and	CCONJ
ejpam-4694	528	6	euler	euler	NOUN
ejpam-4694	528	7	polynomials	polynomial	NOUN
ejpam-4694	528	8	of	of	ADP
ejpam-4694	528	9	the	the	DET
ejpam-4694	528	10	second	second	ADJ
ejpam-4694	528	11	kind	kind	NOUN
ejpam-4694	528	12	.	.	PUNCT
ejpam-4694	529	1	scripta	scripta	PROPN
ejpam-4694	529	2	math	math	PROPN
ejpam-4694	529	3	.	.	PROPN
ejpam-4694	529	4	,	,	PUNCT
ejpam-4694	529	5	25:323–330	25:323–330	NUM
ejpam-4694	529	6	,	,	PUNCT
ejpam-4694	529	7	1961	1961	NUM
ejpam-4694	529	8	.	.	PUNCT
ejpam-4694	530	1	[	[	X
ejpam-4694	530	2	11	11	NUM
ejpam-4694	530	3	]	]	X
ejpam-4694	530	4	l.	l.	PROPN
ejpam-4694	530	5	carlitz	carlitz	PROPN
ejpam-4694	530	6	.	.	PUNCT
ejpam-4694	530	7	degenerate	degenerate	ADJ
ejpam-4694	530	8	stirling	stirling	PROPN
ejpam-4694	530	9	,	,	PUNCT
ejpam-4694	530	10	bernoulli	bernoulli	PROPN
ejpam-4694	530	11	and	and	CCONJ
ejpam-4694	530	12	eulerian	eulerian	ADJ
ejpam-4694	530	13	numbers	number	NOUN
ejpam-4694	530	14	.	.	PUNCT
ejpam-4694	531	1	utilitas	utilitas	PROPN
ejpam-4694	531	2	math	math	NOUN
ejpam-4694	531	3	.	.	PUNCT
ejpam-4694	531	4	,	,	PUNCT
ejpam-4694	531	5	15:51	15:51	NUM
ejpam-4694	531	6	–	–	PUNCT
ejpam-4694	531	7	88	88	NUM
ejpam-4694	531	8	.	.	NUM
ejpam-4694	531	9	,	,	PUNCT
ejpam-4694	531	10	1979	1979	NUM
ejpam-4694	531	11	.	.	PUNCT
ejpam-4694	532	1	[	[	X
ejpam-4694	532	2	12	12	NUM
ejpam-4694	532	3	]	]	PUNCT
ejpam-4694	532	4	l.	l.	PROPN
ejpam-4694	532	5	comtet	comtet	PROPN
ejpam-4694	532	6	.	.	PUNCT
ejpam-4694	533	1	advanced	advanced	ADJ
ejpam-4694	533	2	combinatorics	combinatoric	NOUN
ejpam-4694	533	3	.	.	PUNCT
ejpam-4694	534	1	reidel	reidel	PROPN
ejpam-4694	534	2	,	,	PUNCT
ejpam-4694	534	3	dordrecht	dordrecht	PROPN
ejpam-4694	534	4	,	,	PUNCT
ejpam-4694	534	5	the	the	DET
ejpam-4694	534	6	netherlands	netherlands	PROPN
ejpam-4694	534	7	,	,	PUNCT
ejpam-4694	534	8	1974	1974	NUM
ejpam-4694	534	9	.	.	PUNCT
ejpam-4694	535	1	[	[	X
ejpam-4694	535	2	13	13	NUM
ejpam-4694	535	3	]	]	X
ejpam-4694	535	4	c.	c.	PROPN
ejpam-4694	535	5	corcino	corcino	PROPN
ejpam-4694	535	6	.	.	PUNCT
ejpam-4694	536	1	asymptotic	asymptotic	ADJ
ejpam-4694	536	2	approximations	approximation	NOUN
ejpam-4694	536	3	of	of	ADP
ejpam-4694	536	4	apostol	apostol	NOUN
ejpam-4694	536	5	-	-	PUNCT
ejpam-4694	536	6	genocchi	genocchi	PROPN
ejpam-4694	536	7	numbers	number	NOUN
ejpam-4694	536	8	and	and	CCONJ
ejpam-4694	536	9	polynomials	polynomial	NOUN
ejpam-4694	536	10	.	.	PUNCT
ejpam-4694	537	1	european	european	ADJ
ejpam-4694	537	2	journal	journal	PROPN
ejpam-4694	537	3	of	of	ADP
ejpam-4694	537	4	pure	pure	ADJ
ejpam-4694	537	5	and	and	CCONJ
ejpam-4694	537	6	applied	applied	ADJ
ejpam-4694	537	7	mathematics	mathematic	NOUN
ejpam-4694	537	8	,	,	PUNCT
ejpam-4694	537	9	14(3):666–684	14(3):666–684	NUM
ejpam-4694	537	10	,	,	PUNCT
ejpam-4694	537	11	2021	2021	NUM
ejpam-4694	537	12	.	.	PUNCT
ejpam-4694	538	1	references	reference	NOUN
ejpam-4694	538	2	710	710	NUM
ejpam-4694	538	3	[	[	X
ejpam-4694	538	4	14	14	NUM
ejpam-4694	538	5	]	]	X
ejpam-4694	538	6	c.	c.	PROPN
ejpam-4694	538	7	corcino	corcino	PROPN
ejpam-4694	538	8	and	and	CCONJ
ejpam-4694	538	9	r.	r.	PROPN
ejpam-4694	538	10	corcino	corcino	PROPN
ejpam-4694	538	11	.	.	PUNCT
ejpam-4694	539	1	approximations	approximation	NOUN
ejpam-4694	539	2	of	of	ADP
ejpam-4694	539	3	genocchi	genocchi	PROPN
ejpam-4694	539	4	polynomials	polynomial	NOUN
ejpam-4694	539	5	of	of	ADP
ejpam-4694	539	6	complex	complex	ADJ
ejpam-4694	539	7	order	order	NOUN
ejpam-4694	539	8	.	.	PUNCT
ejpam-4694	540	1	africa	africa	PROPN
ejpam-4694	540	2	matematika	matematika	PROPN
ejpam-4694	540	3	,	,	PUNCT
ejpam-4694	540	4	31:781–792	31:781–792	NUM
ejpam-4694	540	5	,	,	PUNCT
ejpam-4694	540	6	2020	2020	NUM
ejpam-4694	540	7	.	.	PUNCT
ejpam-4694	541	1	[	[	X
ejpam-4694	541	2	15	15	NUM
ejpam-4694	541	3	]	]	X
ejpam-4694	541	4	c.	c.	PROPN
ejpam-4694	541	5	corcino	corcino	PROPN
ejpam-4694	541	6	and	and	CCONJ
ejpam-4694	541	7	r.	r.	PROPN
ejpam-4694	541	8	corcino	corcino	PROPN
ejpam-4694	541	9	.	.	PUNCT
ejpam-4694	542	1	asymptotics	asymptotic	NOUN
ejpam-4694	542	2	of	of	ADP
ejpam-4694	542	3	genocchi	genocchi	PROPN
ejpam-4694	542	4	polynomials	polynomial	NOUN
ejpam-4694	542	5	and	and	CCONJ
ejpam-4694	542	6	higher	high	ADJ
ejpam-4694	542	7	order	order	NOUN
ejpam-4694	542	8	genocchi	genocchi	NOUN
ejpam-4694	542	9	polynomials	polynomial	VERB
ejpam-4694	542	10	using	use	VERB
ejpam-4694	542	11	residues	residue	NOUN
ejpam-4694	542	12	.	.	PUNCT
ejpam-4694	543	1	africa	africa	PROPN
ejpam-4694	543	2	matematika	matematika	PROPN
ejpam-4694	543	3	,	,	PUNCT
ejpam-4694	543	4	31:781–792	31:781–792	NUM
ejpam-4694	543	5	,	,	PUNCT
ejpam-4694	543	6	2020	2020	NUM
ejpam-4694	543	7	.	.	PUNCT
ejpam-4694	544	1	[	[	X
ejpam-4694	544	2	16	16	NUM
ejpam-4694	544	3	]	]	X
ejpam-4694	544	4	c.	c.	PROPN
ejpam-4694	544	5	corcino	corcino	PROPN
ejpam-4694	544	6	and	and	CCONJ
ejpam-4694	544	7	r.	r.	PROPN
ejpam-4694	544	8	corcino	corcino	PROPN
ejpam-4694	544	9	.	.	PUNCT
ejpam-4694	545	1	fourier	fouri	ADJ
ejpam-4694	545	2	expansions	expansion	NOUN
ejpam-4694	545	3	for	for	ADP
ejpam-4694	545	4	higher	high	ADJ
ejpam-4694	545	5	-	-	PUNCT
ejpam-4694	545	6	order	order	NOUN
ejpam-4694	545	7	apostol	apostol	NOUN
ejpam-4694	545	8	-	-	PUNCT
ejpam-4694	545	9	genocchi	genocchi	NOUN
ejpam-4694	545	10	,	,	PUNCT
ejpam-4694	545	11	apostol	apostol	NOUN
ejpam-4694	545	12	-	-	PUNCT
ejpam-4694	545	13	bernoulli	bernoulli	NOUN
ejpam-4694	545	14	and	and	CCONJ
ejpam-4694	545	15	apostol	apostol	NOUN
ejpam-4694	545	16	-	-	PUNCT
ejpam-4694	545	17	euler	euler	NOUN
ejpam-4694	545	18	polynomials	polynomial	NOUN
ejpam-4694	545	19	.	.	PUNCT
ejpam-4694	546	1	adv	adv	PROPN
ejpam-4694	546	2	.	.	PUNCT
ejpam-4694	546	3	difference	difference	PROPN
ejpam-4694	546	4	equ	equ	PROPN
ejpam-4694	546	5	.	.	PROPN
ejpam-4694	546	6	,	,	PUNCT
ejpam-4694	546	7	2020	2020	NUM
ejpam-4694	546	8	:	:	PUNCT
ejpam-4694	546	9	article	article	NOUN
ejpam-4694	546	10	346	346	NUM
ejpam-4694	546	11	,	,	PUNCT
ejpam-4694	546	12	2020	2020	NUM
ejpam-4694	546	13	.	.	PUNCT
ejpam-4694	547	1	[	[	X
ejpam-4694	547	2	17	17	NUM
ejpam-4694	547	3	]	]	X
ejpam-4694	547	4	r.	r.	PROPN
ejpam-4694	547	5	corcino	corcino	PROPN
ejpam-4694	547	6	and	and	CCONJ
ejpam-4694	547	7	c.	c.	PROPN
ejpam-4694	547	8	corcino	corcino	PROPN
ejpam-4694	547	9	.	.	PUNCT
ejpam-4694	548	1	higher	high	ADJ
ejpam-4694	548	2	order	order	NOUN
ejpam-4694	548	3	apostol	apostol	NOUN
ejpam-4694	548	4	-	-	PUNCT
ejpam-4694	548	5	type	type	NOUN
ejpam-4694	548	6	poly	poly	ADJ
ejpam-4694	548	7	-	-	PUNCT
ejpam-4694	548	8	genocchi	genocchi	NOUN
ejpam-4694	548	9	polynomials	polynomial	NOUN
ejpam-4694	548	10	with	with	ADP
ejpam-4694	548	11	parameters	parameter	NOUN
ejpam-4694	548	12	a	a	PRON
ejpam-4694	548	13	,	,	PUNCT
ejpam-4694	548	14	b	b	PROPN
ejpam-4694	548	15	and	and	CCONJ
ejpam-4694	548	16	c.	c.	PROPN
ejpam-4694	548	17	commun	commun	PROPN
ejpam-4694	548	18	.	.	PUNCT
ejpam-4694	549	1	korean	korean	ADJ
ejpam-4694	549	2	math	math	PROPN
ejpam-4694	549	3	.	.	PUNCT
ejpam-4694	550	1	soc	soc	PROPN
ejpam-4694	550	2	,	,	PUNCT
ejpam-4694	550	3	36(3):423–445	36(3):423–445	PROPN
ejpam-4694	550	4	,	,	PUNCT
ejpam-4694	550	5	2021	2021	NUM
ejpam-4694	550	6	.	.	PUNCT
ejpam-4694	551	1	[	[	X
ejpam-4694	551	2	18	18	NUM
ejpam-4694	551	3	]	]	PUNCT
ejpam-4694	551	4	m.	m.	NOUN
ejpam-4694	551	5	domaratzki	domaratzki	NOUN
ejpam-4694	551	6	.	.	PUNCT
ejpam-4694	552	1	combinatorial	combinatorial	ADJ
ejpam-4694	552	2	interpretations	interpretation	NOUN
ejpam-4694	552	3	of	of	ADP
ejpam-4694	552	4	a	a	DET
ejpam-4694	552	5	generalization	generalization	NOUN
ejpam-4694	552	6	of	of	ADP
ejpam-4694	552	7	the	the	DET
ejpam-4694	552	8	genocchi	genocchi	PROPN
ejpam-4694	552	9	numbers	number	NOUN
ejpam-4694	552	10	.	.	PUNCT
ejpam-4694	553	1	j.	j.	PROPN
ejpam-4694	553	2	int	int	PROPN
ejpam-4694	553	3	.	.	PUNCT
ejpam-4694	554	1	seq	seq	PROPN
ejpam-4694	554	2	.	.	PROPN
ejpam-4694	554	3	,	,	PUNCT
ejpam-4694	554	4	7	7	NUM
ejpam-4694	554	5	:	:	PUNCT
ejpam-4694	554	6	article	article	NOUN
ejpam-4694	554	7	04.3.6	04.3.6	ADJ
ejpam-4694	554	8	,	,	PUNCT
ejpam-4694	554	9	2004	2004	NUM
ejpam-4694	554	10	.	.	PUNCT
ejpam-4694	555	1	[	[	X
ejpam-4694	555	2	19	19	NUM
ejpam-4694	555	3	]	]	X
ejpam-4694	555	4	y.	y.	NOUN
ejpam-4694	555	5	he	he	PRON
ejpam-4694	555	6	.	.	PUNCT
ejpam-4694	556	1	some	some	DET
ejpam-4694	556	2	new	new	ADJ
ejpam-4694	556	3	results	result	NOUN
ejpam-4694	556	4	on	on	ADP
ejpam-4694	556	5	products	product	NOUN
ejpam-4694	556	6	of	of	ADP
ejpam-4694	556	7	the	the	DET
ejpam-4694	556	8	apostol	apostol	NOUN
ejpam-4694	556	9	-	-	PUNCT
ejpam-4694	556	10	genocchi	genocchi	PROPN
ejpam-4694	556	11	polynomials	polynomial	NOUN
ejpam-4694	556	12	.	.	PUNCT
ejpam-4694	557	1	j.	j.	PROPN
ejpam-4694	557	2	comput	comput	PROPN
ejpam-4694	557	3	.	.	PUNCT
ejpam-4694	558	1	anal	anal	PROPN
ejpam-4694	558	2	.	.	PUNCT
ejpam-4694	558	3	appl	appl	PROPN
ejpam-4694	558	4	.	.	PROPN
ejpam-4694	558	5	,	,	PUNCT
ejpam-4694	558	6	22(4):591–600	22(4):591–600	PROPN
ejpam-4694	558	7	,	,	PUNCT
ejpam-4694	558	8	2017	2017	NUM
ejpam-4694	558	9	.	.	PUNCT
ejpam-4694	559	1	[	[	X
ejpam-4694	559	2	20	20	NUM
ejpam-4694	559	3	]	]	X
ejpam-4694	559	4	a.f	a.f	PROPN
ejpam-4694	559	5	.	.	PUNCT
ejpam-4694	559	6	horadam	horadam	PROPN
ejpam-4694	559	7	.	.	PUNCT
ejpam-4694	560	1	applications	application	NOUN
ejpam-4694	560	2	of	of	ADP
ejpam-4694	560	3	fibonacci	fibonacci	NOUN
ejpam-4694	560	4	numbers	number	NOUN
ejpam-4694	560	5	,	,	PUNCT
ejpam-4694	560	6	chapter	chapter	NOUN
ejpam-4694	560	7	genocchi	genocchi	PROPN
ejpam-4694	560	8	polynomials	polynomial	VERB
ejpam-4694	560	9	dordrecht	dordrecht	PROPN
ejpam-4694	560	10	.	.	PUNCT
ejpam-4694	560	11	springer	springer	PROPN
ejpam-4694	560	12	,	,	PUNCT
ejpam-4694	560	13	dordrecht	dordrecht	PROPN
ejpam-4694	560	14	,	,	PUNCT
ejpam-4694	560	15	https://doi.org/10.1007/978-94-011-3586-3	https://doi.org/10.1007/978-94-011-3586-3	PROPN
ejpam-4694	560	16	18	18	NUM
ejpam-4694	560	17	.	.	NUM
ejpam-4694	560	18	,	,	PUNCT
ejpam-4694	560	19	1991	1991	NUM
ejpam-4694	560	20	.	.	PUNCT
ejpam-4694	561	1	[	[	X
ejpam-4694	561	2	21	21	NUM
ejpam-4694	561	3	]	]	X
ejpam-4694	561	4	d.s	d.s	PROPN
ejpam-4694	561	5	.	.	PROPN
ejpam-4694	561	6	kim	kim	PROPN
ejpam-4694	561	7	,	,	PUNCT
ejpam-4694	561	8	d.v	d.v	PROPN
ejpam-4694	561	9	.	.	PROPN
ejpam-4694	561	10	dolgy	dolgy	PROPN
ejpam-4694	561	11	,	,	PUNCT
ejpam-4694	561	12	t.	t.	PROPN
ejpam-4694	561	13	kim	kim	PROPN
ejpam-4694	561	14	,	,	PUNCT
ejpam-4694	561	15	and	and	CCONJ
ejpam-4694	561	16	s.h	s.h	PROPN
ejpam-4694	561	17	.	.	PROPN
ejpam-4694	561	18	rim	rim	PROPN
ejpam-4694	561	19	.	.	PUNCT
ejpam-4694	562	1	some	some	DET
ejpam-4694	562	2	formula	formula	NOUN
ejpam-4694	562	3	for	for	ADP
ejpam-4694	562	4	the	the	DET
ejpam-4694	562	5	product	product	NOUN
ejpam-4694	562	6	of	of	ADP
ejpam-4694	562	7	two	two	NUM
ejpam-4694	562	8	bernoulli	bernoulli	NOUN
ejpam-4694	562	9	and	and	CCONJ
ejpam-4694	562	10	euler	euler	NOUN
ejpam-4694	562	11	polynomials	polynomial	NOUN
ejpam-4694	562	12	.	.	PUNCT
ejpam-4694	563	1	abst	abst	PROPN
ejpam-4694	563	2	.	.	PUNCT
ejpam-4694	563	3	appl	appl	PROPN
ejpam-4694	563	4	.	.	PUNCT
ejpam-4694	564	1	anal	anal	PROPN
ejpam-4694	564	2	.	.	PROPN
ejpam-4694	564	3	,	,	PUNCT
ejpam-4694	564	4	2012	2012	NUM
ejpam-4694	564	5	:	:	PUNCT
ejpam-4694	564	6	article	article	NOUN
ejpam-4694	564	7	i	i	PROPN
ejpam-4694	564	8	d	d	PROPN
ejpam-4694	564	9	784307	784307	NUM
ejpam-4694	564	10	,	,	PUNCT
ejpam-4694	564	11	15	15	NUM
ejpam-4694	564	12	pages	page	NOUN
ejpam-4694	564	13	,	,	PUNCT
ejpam-4694	564	14	2012	2012	NUM
ejpam-4694	564	15	.	.	PUNCT
ejpam-4694	565	1	[	[	X
ejpam-4694	565	2	22	22	NUM
ejpam-4694	565	3	]	]	X
ejpam-4694	565	4	d.s	d.s	PROPN
ejpam-4694	565	5	.	.	PROPN
ejpam-4694	565	6	kim	kim	PROPN
ejpam-4694	565	7	and	and	CCONJ
ejpam-4694	565	8	t.	t.	PROPN
ejpam-4694	565	9	kim	kim	PROPN
ejpam-4694	565	10	.	.	PUNCT
ejpam-4694	566	1	a	a	DET
ejpam-4694	566	2	note	note	NOUN
ejpam-4694	566	3	on	on	ADP
ejpam-4694	566	4	polyexponential	polyexponential	ADJ
ejpam-4694	566	5	and	and	CCONJ
ejpam-4694	566	6	unipoly	unipoly	ADJ
ejpam-4694	566	7	functions	function	NOUN
ejpam-4694	566	8	.	.	PUNCT
ejpam-4694	567	1	russ	russ	PROPN
ejpam-4694	567	2	.	.	PUNCT
ejpam-4694	568	1	j.	j.	PROPN
ejpam-4694	568	2	math	math	PROPN
ejpam-4694	568	3	.	.	PUNCT
ejpam-4694	569	1	phys	phy	NOUN
ejpam-4694	569	2	.	.	PUNCT
ejpam-4694	569	3	,	,	PUNCT
ejpam-4694	569	4	26:40–49	26:40–49	PROPN
ejpam-4694	569	5	,	,	PUNCT
ejpam-4694	569	6	2019	2019	NUM
ejpam-4694	569	7	.	.	PUNCT
ejpam-4694	570	1	[	[	X
ejpam-4694	570	2	23	23	NUM
ejpam-4694	570	3	]	]	X
ejpam-4694	570	4	d.s	d.s	PROPN
ejpam-4694	570	5	.	.	PROPN
ejpam-4694	570	6	kim	kim	PROPN
ejpam-4694	570	7	and	and	CCONJ
ejpam-4694	570	8	t.	t.	PROPN
ejpam-4694	570	9	kim	kim	PROPN
ejpam-4694	570	10	.	.	PUNCT
ejpam-4694	571	1	a	a	DET
ejpam-4694	571	2	note	note	NOUN
ejpam-4694	571	3	on	on	ADP
ejpam-4694	571	4	a	a	DET
ejpam-4694	571	5	new	new	ADJ
ejpam-4694	571	6	type	type	NOUN
ejpam-4694	571	7	of	of	ADP
ejpam-4694	571	8	degenerate	degenerate	ADJ
ejpam-4694	571	9	bernoulli	bernoulli	NOUN
ejpam-4694	571	10	numbers	number	NOUN
ejpam-4694	571	11	.	.	PUNCT
ejpam-4694	572	1	russ	russ	PROPN
ejpam-4694	572	2	.	.	PUNCT
ejpam-4694	573	1	j.	j.	PROPN
ejpam-4694	573	2	math	math	PROPN
ejpam-4694	573	3	.	.	PUNCT
ejpam-4694	574	1	phys	phy	NOUN
ejpam-4694	574	2	.	.	PUNCT
ejpam-4694	574	3	,	,	PUNCT
ejpam-4694	574	4	27(2):227–235	27(2):227–235	NUM
ejpam-4694	574	5	,	,	PUNCT
ejpam-4694	574	6	2020	2020	NUM
ejpam-4694	574	7	.	.	PUNCT
ejpam-4694	575	1	[	[	X
ejpam-4694	575	2	24	24	NUM
ejpam-4694	575	3	]	]	PUNCT
ejpam-4694	575	4	t.	t.	PROPN
ejpam-4694	575	5	kim	kim	PROPN
ejpam-4694	575	6	.	.	PUNCT
ejpam-4694	576	1	some	some	DET
ejpam-4694	576	2	identities	identity	NOUN
ejpam-4694	576	3	for	for	ADP
ejpam-4694	576	4	the	the	DET
ejpam-4694	576	5	bernoulli	bernoulli	NOUN
ejpam-4694	576	6	,	,	PUNCT
ejpam-4694	576	7	the	the	DET
ejpam-4694	576	8	euler	euler	NOUN
ejpam-4694	576	9	and	and	CCONJ
ejpam-4694	576	10	the	the	DET
ejpam-4694	576	11	genocchi	genocchi	PROPN
ejpam-4694	576	12	numbers	number	NOUN
ejpam-4694	576	13	and	and	CCONJ
ejpam-4694	576	14	polynomials	polynomial	NOUN
ejpam-4694	576	15	.	.	PUNCT
ejpam-4694	577	1	adv	adv	PROPN
ejpam-4694	577	2	.	.	PUNCT
ejpam-4694	577	3	stud	stud	PROPN
ejpam-4694	577	4	.	.	PUNCT
ejpam-4694	578	1	contemp	contemp	NOUN
ejpam-4694	578	2	.	.	PUNCT
ejpam-4694	579	1	math	math	NOUN
ejpam-4694	579	2	.	.	PUNCT
ejpam-4694	579	3	,	,	PUNCT
ejpam-4694	579	4	20(1):23–28	20(1):23–28	NUM
ejpam-4694	579	5	,	,	PUNCT
ejpam-4694	579	6	2010	2010	NUM
ejpam-4694	579	7	.	.	PUNCT
ejpam-4694	580	1	[	[	X
ejpam-4694	580	2	25	25	NUM
ejpam-4694	580	3	]	]	PUNCT
ejpam-4694	580	4	t.	t.	PROPN
ejpam-4694	580	5	kim	kim	PROPN
ejpam-4694	580	6	,	,	PUNCT
ejpam-4694	580	7	y.s	y.s	PROPN
ejpam-4694	580	8	.	.	PROPN
ejpam-4694	580	9	jang	jang	PROPN
ejpam-4694	580	10	,	,	PUNCT
ejpam-4694	580	11	and	and	CCONJ
ejpam-4694	580	12	j.j	j.j	PROPN
ejpam-4694	580	13	.	.	PROPN
ejpam-4694	580	14	seo	seo	PROPN
ejpam-4694	580	15	.	.	PUNCT
ejpam-4694	581	1	a	a	DET
ejpam-4694	581	2	note	note	NOUN
ejpam-4694	581	3	on	on	ADP
ejpam-4694	581	4	poly	poly	ADJ
ejpam-4694	581	5	-	-	PUNCT
ejpam-4694	581	6	genocchi	genocchi	NOUN
ejpam-4694	581	7	numbers	number	NOUN
ejpam-4694	581	8	and	and	CCONJ
ejpam-4694	581	9	polynomials	polynomial	NOUN
ejpam-4694	581	10	.	.	PUNCT
ejpam-4694	582	1	appl	appl	PROPN
ejpam-4694	582	2	.	.	PROPN
ejpam-4694	582	3	math	math	PROPN
ejpam-4694	582	4	.	.	PUNCT
ejpam-4694	583	1	sci	sci	PROPN
ejpam-4694	583	2	.	.	PROPN
ejpam-4694	583	3	,	,	PUNCT
ejpam-4694	583	4	8:4775–4781	8:4775–4781	NUM
ejpam-4694	583	5	,	,	PUNCT
ejpam-4694	583	6	2014	2014	NUM
ejpam-4694	583	7	.	.	PUNCT
ejpam-4694	584	1	[	[	X
ejpam-4694	584	2	26	26	NUM
ejpam-4694	584	3	]	]	PUNCT
ejpam-4694	584	4	t.	t.	PROPN
ejpam-4694	584	5	kim	kim	PROPN
ejpam-4694	584	6	and	and	CCONJ
ejpam-4694	584	7	d.	d.	PROPN
ejpam-4694	584	8	kim	kim	PROPN
ejpam-4694	584	9	.	.	PUNCT
ejpam-4694	585	1	representation	representation	NOUN
ejpam-4694	585	2	by	by	ADP
ejpam-4694	585	3	degenerate	degenerate	ADJ
ejpam-4694	585	4	frobenius	frobenius	NOUN
ejpam-4694	585	5	-	-	PUNCT
ejpam-4694	585	6	euler	euler	NOUN
ejpam-4694	585	7	polynomials	polynomial	NOUN
ejpam-4694	585	8	.	.	PUNCT
ejpam-4694	586	1	georgian	georgian	ADJ
ejpam-4694	586	2	math	math	PROPN
ejpam-4694	586	3	.	.	PUNCT
ejpam-4694	587	1	j.	j.	PROPN
ejpam-4694	587	2	,	,	PUNCT
ejpam-4694	587	3	29(5):741–754	29(5):741–754	PROPN
ejpam-4694	587	4	,	,	PUNCT
ejpam-4694	587	5	2022	2022	NUM
ejpam-4694	587	6	.	.	PUNCT
ejpam-4694	588	1	[	[	X
ejpam-4694	588	2	27	27	NUM
ejpam-4694	588	3	]	]	PUNCT
ejpam-4694	588	4	t.	t.	PROPN
ejpam-4694	588	5	kim	kim	PROPN
ejpam-4694	588	6	,	,	PUNCT
ejpam-4694	588	7	d.	d.	PROPN
ejpam-4694	588	8	kim	kim	PROPN
ejpam-4694	588	9	,	,	PUNCT
ejpam-4694	588	10	and	and	CCONJ
ejpam-4694	588	11	h.	h.	PROPN
ejpam-4694	588	12	kim	kim	PROPN
ejpam-4694	588	13	.	.	PUNCT
ejpam-4694	589	1	on	on	ADP
ejpam-4694	589	2	generalized	generalized	ADJ
ejpam-4694	589	3	degenerate	degenerate	ADJ
ejpam-4694	589	4	eulerâgenocchi	eulerâgenocchi	PROPN
ejpam-4694	589	5	polynomials	polynomial	NOUN
ejpam-4694	589	6	.	.	PUNCT
ejpam-4694	590	1	appl	appl	PROPN
ejpam-4694	590	2	.	.	PROPN
ejpam-4694	590	3	math	math	PROPN
ejpam-4694	590	4	.	.	PUNCT
ejpam-4694	591	1	sci	sci	PROPN
ejpam-4694	591	2	.	.	PUNCT
ejpam-4694	592	1	eng	eng	PROPN
ejpam-4694	592	2	.	.	PROPN
ejpam-4694	592	3	,	,	PUNCT
ejpam-4694	592	4	31(1):2159958	31(1):2159958	NUM
ejpam-4694	592	5	,	,	PUNCT
ejpam-4694	592	6	15	15	NUM
ejpam-4694	592	7	pp	pp	NOUN
ejpam-4694	592	8	.	.	PUNCT
ejpam-4694	592	9	,	,	PUNCT
ejpam-4694	592	10	2023	2023	NUM
ejpam-4694	592	11	.	.	PUNCT
ejpam-4694	593	1	[	[	X
ejpam-4694	593	2	28	28	NUM
ejpam-4694	593	3	]	]	X
ejpam-4694	593	4	t.	t.	PROPN
ejpam-4694	593	5	kim	kim	PROPN
ejpam-4694	593	6	and	and	CCONJ
ejpam-4694	593	7	d.	d.	PROPN
ejpam-4694	593	8	s.	s.	PROPN
ejpam-4694	593	9	kim	kim	PROPN
ejpam-4694	593	10	.	.	PROPN
ejpam-4694	593	11	degenerate	degenerate	ADJ
ejpam-4694	593	12	polyexponential	polyexponential	ADJ
ejpam-4694	593	13	functions	function	NOUN
ejpam-4694	593	14	and	and	CCONJ
ejpam-4694	593	15	degenerate	degenerate	ADJ
ejpam-4694	593	16	bell	bell	NOUN
ejpam-4694	593	17	polynomials	polynomial	NOUN
ejpam-4694	593	18	.	.	PUNCT
ejpam-4694	594	1	j.	j.	PROPN
ejpam-4694	594	2	math	math	PROPN
ejpam-4694	594	3	.	.	PUNCT
ejpam-4694	595	1	anal	anal	PROPN
ejpam-4694	595	2	.	.	PUNCT
ejpam-4694	595	3	appl	appl	PROPN
ejpam-4694	595	4	.	.	PROPN
ejpam-4694	595	5	,	,	PUNCT
ejpam-4694	595	6	487(2):article	487(2):article	NOUN
ejpam-4694	595	7	124017	124017	NUM
ejpam-4694	595	8	,	,	PUNCT
ejpam-4694	595	9	15	15	NUM
ejpam-4694	595	10	pages	page	NOUN
ejpam-4694	595	11	.	.	PUNCT
ejpam-4694	596	1	https://doi.org/10.1016/j.jmaa.2020.124017	https://doi.org/10.1016/j.jmaa.2020.124017	NOUN
ejpam-4694	596	2	.	.	PUNCT
ejpam-4694	596	3	,	,	PUNCT
ejpam-4694	596	4	2020	2020	NUM
ejpam-4694	596	5	.	.	PUNCT
ejpam-4694	597	1	references	reference	NOUN
ejpam-4694	597	2	711	711	NUM
ejpam-4694	597	3	[	[	X
ejpam-4694	597	4	29	29	NUM
ejpam-4694	597	5	]	]	PUNCT
ejpam-4694	597	6	t.	t.	PROPN
ejpam-4694	597	7	kim	kim	PROPN
ejpam-4694	597	8	,	,	PUNCT
ejpam-4694	597	9	d.	d.	PROPN
ejpam-4694	597	10	s.	s.	PROPN
ejpam-4694	597	11	kim	kim	PROPN
ejpam-4694	597	12	,	,	PUNCT
ejpam-4694	597	13	l.	l.	PROPN
ejpam-4694	597	14	jang	jang	PROPN
ejpam-4694	597	15	,	,	PUNCT
ejpam-4694	597	16	and	and	CCONJ
ejpam-4694	597	17	h.	h.	PROPN
ejpam-4694	597	18	lee	lee	PROPN
ejpam-4694	597	19	.	.	PROPN
ejpam-4694	597	20	jindalrae	jindalrae	PROPN
ejpam-4694	597	21	and	and	CCONJ
ejpam-4694	597	22	gaenari	gaenari	ADJ
ejpam-4694	597	23	numbers	number	NOUN
ejpam-4694	597	24	and	and	CCONJ
ejpam-4694	597	25	polynomials	polynomial	NOUN
ejpam-4694	597	26	in	in	ADP
ejpam-4694	597	27	connection	connection	NOUN
ejpam-4694	597	28	with	with	ADP
ejpam-4694	597	29	jindalrae	jindalrae	NOUN
ejpam-4694	597	30	-	-	PUNCT
ejpam-4694	597	31	stirling	stirling	NOUN
ejpam-4694	597	32	numbers	number	NOUN
ejpam-4694	597	33	.	.	PUNCT
ejpam-4694	598	1	adv	adv	PROPN
ejpam-4694	598	2	.	.	PUNCT
ejpam-4694	598	3	difference	difference	PROPN
ejpam-4694	598	4	equ	equ	PROPN
ejpam-4694	598	5	.	.	PROPN
ejpam-4694	598	6	,	,	PUNCT
ejpam-4694	598	7	2020	2020	NUM
ejpam-4694	598	8	:	:	PUNCT
ejpam-4694	598	9	article	article	NOUN
ejpam-4694	598	10	245	245	NUM
ejpam-4694	598	11	,	,	PUNCT
ejpam-4694	598	12	19	19	NUM
ejpam-4694	598	13	pages	page	NOUN
ejpam-4694	598	14	.	.	PUNCT
ejpam-4694	599	1	https://doi.org/10.1186/s13662–020–02701–1	https://doi.org/10.1186/s13662–020–02701–1	PROPN
ejpam-4694	599	2	,	,	PUNCT
ejpam-4694	599	3	2020	2020	NUM
ejpam-4694	599	4	.	.	PUNCT
ejpam-4694	600	1	[	[	X
ejpam-4694	600	2	30	30	NUM
ejpam-4694	600	3	]	]	PUNCT
ejpam-4694	600	4	t.	t.	PROPN
ejpam-4694	600	5	kim	kim	PROPN
ejpam-4694	600	6	,	,	PUNCT
ejpam-4694	600	7	d.	d.	PROPN
ejpam-4694	600	8	s.	s.	PROPN
ejpam-4694	600	9	kim	kim	PROPN
ejpam-4694	600	10	,	,	PUNCT
ejpam-4694	600	11	h.	h.	PROPN
ejpam-4694	600	12	y.	y.	PROPN
ejpam-4694	600	13	kim	kim	PROPN
ejpam-4694	600	14	,	,	PUNCT
ejpam-4694	600	15	and	and	CCONJ
ejpam-4694	600	16	l.-c	l.-c	PROPN
ejpam-4694	600	17	.	.	PUNCT
ejpam-4694	601	1	jang	jang	PROPN
ejpam-4694	601	2	.	.	PUNCT
ejpam-4694	601	3	degenerate	degenerate	ADJ
ejpam-4694	601	4	poly	poly	ADJ
ejpam-4694	601	5	-	-	PUNCT
ejpam-4694	601	6	bernoulli	bernoulli	NOUN
ejpam-4694	601	7	numbers	number	NOUN
ejpam-4694	601	8	and	and	CCONJ
ejpam-4694	601	9	polynomials	polynomial	NOUN
ejpam-4694	601	10	.	.	PUNCT
ejpam-4694	602	1	informatica	informatica	PROPN
ejpam-4694	602	2	,	,	PUNCT
ejpam-4694	602	3	31:2–8	31:2–8	NUM
ejpam-4694	602	4	,	,	PUNCT
ejpam-4694	602	5	2020	2020	NUM
ejpam-4694	602	6	.	.	PUNCT
ejpam-4694	603	1	[	[	X
ejpam-4694	603	2	31	31	NUM
ejpam-4694	603	3	]	]	PUNCT
ejpam-4694	603	4	t.	t.	PROPN
ejpam-4694	603	5	kim	kim	PROPN
ejpam-4694	603	6	,	,	PUNCT
ejpam-4694	603	7	d.	d.	PROPN
ejpam-4694	603	8	s.	s.	PROPN
ejpam-4694	603	9	kim	kim	PROPN
ejpam-4694	603	10	,	,	PUNCT
ejpam-4694	603	11	y.	y.	PROPN
ejpam-4694	603	12	h.	h.	PROPN
ejpam-4694	603	13	kim	kim	PROPN
ejpam-4694	603	14	,	,	PUNCT
ejpam-4694	603	15	and	and	CCONJ
ejpam-4694	603	16	j.	j.	PROPN
ejpam-4694	603	17	kwon	kwon	PROPN
ejpam-4694	603	18	.	.	PUNCT
ejpam-4694	604	1	degenerate	degenerate	ADJ
ejpam-4694	604	2	stirling	stirling	NOUN
ejpam-4694	604	3	polynomials	polynomial	NOUN
ejpam-4694	604	4	of	of	ADP
ejpam-4694	604	5	the	the	DET
ejpam-4694	604	6	second	second	ADJ
ejpam-4694	604	7	kind	kind	NOUN
ejpam-4694	604	8	and	and	CCONJ
ejpam-4694	604	9	some	some	DET
ejpam-4694	604	10	applications	application	NOUN
ejpam-4694	604	11	.	.	PUNCT
ejpam-4694	605	1	symmetry	symmetry	NOUN
ejpam-4694	605	2	,	,	PUNCT
ejpam-4694	605	3	11:11	11:11	NUM
ejpam-4694	605	4	pages	page	NOUN
ejpam-4694	605	5	,	,	PUNCT
ejpam-4694	605	6	2019	2019	NUM
ejpam-4694	605	7	.	.	PUNCT
ejpam-4694	606	1	[	[	X
ejpam-4694	606	2	32	32	NUM
ejpam-4694	606	3	]	]	PUNCT
ejpam-4694	606	4	t.	t.	PROPN
ejpam-4694	606	5	kim	kim	PROPN
ejpam-4694	606	6	,	,	PUNCT
ejpam-4694	606	7	s.h	s.h	PROPN
ejpam-4694	606	8	.	.	PROPN
ejpam-4694	606	9	rim	rim	PROPN
ejpam-4694	606	10	,	,	PUNCT
ejpam-4694	606	11	d.v	d.v	PROPN
ejpam-4694	606	12	.	.	PROPN
ejpam-4694	606	13	dolgy	dolgy	PROPN
ejpam-4694	606	14	,	,	PUNCT
ejpam-4694	606	15	and	and	CCONJ
ejpam-4694	606	16	s.h	s.h	PROPN
ejpam-4694	606	17	.	.	PROPN
ejpam-4694	606	18	lee	lee	PROPN
ejpam-4694	606	19	.	.	PUNCT
ejpam-4694	607	1	some	some	DET
ejpam-4694	607	2	identities	identity	NOUN
ejpam-4694	607	3	of	of	ADP
ejpam-4694	607	4	genocchi	genocchi	PROPN
ejpam-4694	607	5	polynomials	polynomial	NOUN
ejpam-4694	607	6	arising	arise	VERB
ejpam-4694	607	7	from	from	ADP
ejpam-4694	607	8	genocchi	genocchi	PROPN
ejpam-4694	607	9	basis	basis	NOUN
ejpam-4694	607	10	.	.	PUNCT
ejpam-4694	608	1	j.	j.	PROPN
ejpam-4694	608	2	ineq	ineq	PROPN
ejpam-4694	608	3	.	.	PUNCT
ejpam-4694	609	1	appl	appl	PROPN
ejpam-4694	609	2	.	.	PROPN
ejpam-4694	609	3	,	,	PUNCT
ejpam-4694	609	4	2013	2013	NUM
ejpam-4694	609	5	:	:	PUNCT
ejpam-4694	609	6	article	article	NOUN
ejpam-4694	609	7	i	i	PROPN
ejpam-4694	609	8	d	d	PROPN
ejpam-4694	609	9	43	43	NUM
ejpam-4694	609	10	,	,	PUNCT
ejpam-4694	609	11	2013	2013	NUM
ejpam-4694	609	12	.	.	PUNCT
ejpam-4694	610	1	[	[	X
ejpam-4694	610	2	33	33	NUM
ejpam-4694	610	3	]	]	PUNCT
ejpam-4694	610	4	b.	b.	PROPN
ejpam-4694	610	5	kurt	kurt	PROPN
ejpam-4694	610	6	.	.	PUNCT
ejpam-4694	611	1	some	some	DET
ejpam-4694	611	2	identities	identity	NOUN
ejpam-4694	611	3	for	for	ADP
ejpam-4694	611	4	the	the	DET
ejpam-4694	611	5	generalized	generalize	VERB
ejpam-4694	611	6	poly	poly	ADJ
ejpam-4694	611	7	-	-	PUNCT
ejpam-4694	611	8	genocchi	genocchi	NOUN
ejpam-4694	611	9	polynomials	polynomial	NOUN
ejpam-4694	611	10	with	with	ADP
ejpam-4694	611	11	the	the	DET
ejpam-4694	611	12	parameters	parameter	NOUN
ejpam-4694	611	13	a	a	PRON
ejpam-4694	611	14	,	,	PUNCT
ejpam-4694	611	15	b	b	PROPN
ejpam-4694	611	16	and	and	CCONJ
ejpam-4694	611	17	c.	c.	PROPN
ejpam-4694	611	18	j.	j.	PROPN
ejpam-4694	611	19	math	math	PROPN
ejpam-4694	611	20	.	.	PUNCT
ejpam-4694	612	1	anal	anal	PROPN
ejpam-4694	612	2	.	.	PROPN
ejpam-4694	612	3	,	,	PUNCT
ejpam-4694	612	4	8(1):156–163	8(1):156–163	NUM
ejpam-4694	612	5	,	,	PUNCT
ejpam-4694	612	6	2017	2017	NUM
ejpam-4694	612	7	.	.	PUNCT
ejpam-4694	613	1	[	[	X
ejpam-4694	613	2	34	34	NUM
ejpam-4694	613	3	]	]	X
ejpam-4694	613	4	b.	b.	PROPN
ejpam-4694	613	5	kurt	kurt	PROPN
ejpam-4694	613	6	.	.	PUNCT
ejpam-4694	614	1	identities	identity	NOUN
ejpam-4694	614	2	and	and	CCONJ
ejpam-4694	614	3	relation	relation	NOUN
ejpam-4694	614	4	on	on	ADP
ejpam-4694	614	5	the	the	DET
ejpam-4694	614	6	poly	poly	ADJ
ejpam-4694	614	7	-	-	PUNCT
ejpam-4694	614	8	genocchi	genocchi	NOUN
ejpam-4694	614	9	polynomials	polynomial	VERB
ejpam-4694	614	10	with	with	ADP
ejpam-4694	614	11	a	a	DET
ejpam-4694	614	12	q	q	NOUN
ejpam-4694	614	13	-	-	PUNCT
ejpam-4694	614	14	parameter	parameter	NOUN
ejpam-4694	614	15	.	.	PUNCT
ejpam-4694	615	1	j.	j.	PROPN
ejpam-4694	615	2	inequal	inequal	PROPN
ejpam-4694	615	3	.	.	PUNCT
ejpam-4694	616	1	spec	spec	PROPN
ejpam-4694	616	2	.	.	PUNCT
ejpam-4694	617	1	funct	funct	PROPN
ejpam-4694	617	2	.	.	PROPN
ejpam-4694	617	3	,	,	PUNCT
ejpam-4694	617	4	9:1–8	9:1–8	NUM
ejpam-4694	617	5	,	,	PUNCT
ejpam-4694	617	6	2018	2018	NUM
ejpam-4694	617	7	.	.	PUNCT
ejpam-4694	618	1	[	[	X
ejpam-4694	618	2	35	35	NUM
ejpam-4694	618	3	]	]	X
ejpam-4694	618	4	b.	b.	PROPN
ejpam-4694	618	5	kurt	kurt	PROPN
ejpam-4694	618	6	.	.	PUNCT
ejpam-4694	618	7	degenerate	degenerate	ADJ
ejpam-4694	618	8	polyexponential	polyexponential	ADJ
ejpam-4694	618	9	functions	function	NOUN
ejpam-4694	618	10	and	and	CCONJ
ejpam-4694	618	11	poly	poly	ADJ
ejpam-4694	618	12	-	-	PUNCT
ejpam-4694	618	13	euler	euler	NOUN
ejpam-4694	618	14	polynomials	polynomial	NOUN
ejpam-4694	618	15	.	.	PUNCT
ejpam-4694	619	1	commun	commun	PROPN
ejpam-4694	619	2	.	.	PUNCT
ejpam-4694	620	1	korean	korean	ADJ
ejpam-4694	620	2	math	math	PROPN
ejpam-4694	620	3	.	.	PUNCT
ejpam-4694	621	1	soc	soc	PROPN
ejpam-4694	621	2	.	.	PUNCT
ejpam-4694	621	3	,	,	PUNCT
ejpam-4694	621	4	36(1):19–26	36(1):19–26	NUM
ejpam-4694	621	5	,	,	PUNCT
ejpam-4694	621	6	2021	2021	NUM
ejpam-4694	621	7	.	.	PUNCT
ejpam-4694	622	1	[	[	X
ejpam-4694	622	2	36	36	NUM
ejpam-4694	622	3	]	]	X
ejpam-4694	622	4	d.	d.	PROPN
ejpam-4694	622	5	lim	lim	PROPN
ejpam-4694	622	6	.	.	PUNCT
ejpam-4694	623	1	some	some	DET
ejpam-4694	623	2	identities	identity	NOUN
ejpam-4694	623	3	of	of	ADP
ejpam-4694	623	4	degenerate	degenerate	ADJ
ejpam-4694	623	5	genocchi	genocchi	NOUN
ejpam-4694	623	6	polynomials	polynomial	NOUN
ejpam-4694	623	7	.	.	PUNCT
ejpam-4694	624	1	bull	bull	NOUN
ejpam-4694	624	2	.	.	PUNCT
ejpam-4694	625	1	korean	korean	ADJ
ejpam-4694	625	2	math	math	PROPN
ejpam-4694	625	3	.	.	PUNCT
ejpam-4694	626	1	soc	soc	PROPN
ejpam-4694	626	2	.	.	PUNCT
ejpam-4694	626	3	,	,	PUNCT
ejpam-4694	626	4	53(2):569–579	53(2):569–579	PROPN
ejpam-4694	626	5	,	,	PUNCT
ejpam-4694	626	6	2016	2016	NUM
ejpam-4694	626	7	.	.	PUNCT
ejpam-4694	627	1	[	[	X
ejpam-4694	627	2	37	37	NUM
ejpam-4694	627	3	]	]	PUNCT
ejpam-4694	627	4	a.	a.	NOUN
ejpam-4694	627	5	secer	secer	PROPN
ejpam-4694	627	6	m.	m.	PROPN
ejpam-4694	627	7	cinar	cinar	PROPN
ejpam-4694	627	8	and	and	CCONJ
ejpam-4694	627	9	m.	m.	PROPN
ejpam-4694	627	10	bayram	bayram	PROPN
ejpam-4694	627	11	.	.	PUNCT
ejpam-4694	628	1	an	an	DET
ejpam-4694	628	2	application	application	NOUN
ejpam-4694	628	3	of	of	ADP
ejpam-4694	628	4	genocchi	genocchi	PROPN
ejpam-4694	628	5	wavelets	wavelet	NOUN
ejpam-4694	628	6	for	for	ADP
ejpam-4694	628	7	solving	solve	VERB
ejpam-4694	628	8	the	the	DET
ejpam-4694	628	9	fractional	fractional	ADJ
ejpam-4694	628	10	rosenau	rosenau	NOUN
ejpam-4694	628	11	-	-	PUNCT
ejpam-4694	628	12	hyman	hyman	PROPN
ejpam-4694	628	13	equation	equation	NOUN
ejpam-4694	628	14	.	.	PUNCT
ejpam-4694	629	1	alexandria	alexandria	PROPN
ejpam-4694	629	2	engineering	engineering	PROPN
ejpam-4694	629	3	journal	journal	PROPN
ejpam-4694	629	4	,	,	PUNCT
ejpam-4694	629	5	60:5331–5340	60:5331–5340	NUM
ejpam-4694	629	6	,	,	PUNCT
ejpam-4694	629	7	2021	2021	NUM
ejpam-4694	629	8	.	.	PUNCT
ejpam-4694	630	1	[	[	X
ejpam-4694	630	2	38	38	NUM
ejpam-4694	630	3	]	]	PUNCT
ejpam-4694	630	4	i.	i.	NOUN
ejpam-4694	630	5	mezo	mezo	PROPN
ejpam-4694	630	6	.	.	PUNCT
ejpam-4694	631	1	a	a	DET
ejpam-4694	631	2	new	new	ADJ
ejpam-4694	631	3	formula	formula	NOUN
ejpam-4694	631	4	for	for	ADP
ejpam-4694	631	5	the	the	DET
ejpam-4694	631	6	bernoulli	bernoulli	NOUN
ejpam-4694	631	7	polynomials	polynomial	NOUN
ejpam-4694	631	8	.	.	PUNCT
ejpam-4694	632	1	results	result	NOUN
ejpam-4694	632	2	.	.	PUNCT
ejpam-4694	633	1	math	math	NOUN
ejpam-4694	633	2	.	.	PUNCT
ejpam-4694	633	3	,	,	PUNCT
ejpam-4694	634	1	58:329–335	58:329–335	NUM
ejpam-4694	634	2	,	,	PUNCT
ejpam-4694	634	3	2010	2010	NUM
ejpam-4694	634	4	.	.	PUNCT
ejpam-4694	635	1	[	[	X
ejpam-4694	635	2	39	39	NUM
ejpam-4694	635	3	]	]	PUNCT
ejpam-4694	635	4	m.	m.	NOUN
ejpam-4694	635	5	laurente	laurente	PROPN
ejpam-4694	635	6	r.	r.	PROPN
ejpam-4694	635	7	corcino	corcino	PROPN
ejpam-4694	635	8	and	and	CCONJ
ejpam-4694	635	9	m.a.r.p	m.a.r.p	PROPN
ejpam-4694	635	10	.	.	PUNCT
ejpam-4694	635	11	vega	vega	PROPN
ejpam-4694	635	12	.	.	PUNCT
ejpam-4694	636	1	on	on	ADP
ejpam-4694	636	2	multi	multi	ADJ
ejpam-4694	636	3	poly	poly	ADJ
ejpam-4694	636	4	-	-	PUNCT
ejpam-4694	636	5	genocchi	genocchi	NOUN
ejpam-4694	636	6	polynomials	polynomial	NOUN
ejpam-4694	636	7	with	with	ADP
ejpam-4694	636	8	parameters	parameter	NOUN
ejpam-4694	636	9	a	a	PRON
ejpam-4694	636	10	,	,	PUNCT
ejpam-4694	636	11	b	b	PROPN
ejpam-4694	636	12	and	and	CCONJ
ejpam-4694	636	13	c.	c.	PROPN
ejpam-4694	636	14	european	european	PROPN
ejpam-4694	636	15	journal	journal	PROPN
ejpam-4694	636	16	of	of	ADP
ejpam-4694	636	17	pure	pure	ADJ
ejpam-4694	636	18	and	and	CCONJ
ejpam-4694	636	19	applied	applied	ADJ
ejpam-4694	636	20	mathematics	mathematic	NOUN
ejpam-4694	636	21	,	,	PUNCT
ejpam-4694	636	22	13(3):444–458	13(3):444–458	NUM
ejpam-4694	636	23	,	,	PUNCT
ejpam-4694	636	24	2020	2020	NUM
ejpam-4694	636	25	.	.	PUNCT
ejpam-4694	637	1	[	[	X
ejpam-4694	637	2	40	40	NUM
ejpam-4694	637	3	]	]	PUNCT
ejpam-4694	637	4	h.	h.	PROPN
ejpam-4694	637	5	jolany	jolany	PROPN
ejpam-4694	637	6	s.	s.	PROPN
ejpam-4694	637	7	araci	araci	PROPN
ejpam-4694	637	8	,	,	PUNCT
ejpam-4694	637	9	m.	m.	NOUN
ejpam-4694	637	10	acikgoz	acikgoz	PROPN
ejpam-4694	637	11	and	and	CCONJ
ejpam-4694	637	12	j.j	j.j	PROPN
ejpam-4694	637	13	.	.	PROPN
ejpam-4694	637	14	seo	seo	PROPN
ejpam-4694	637	15	.	.	PUNCT
ejpam-4694	638	1	a	a	DET
ejpam-4694	638	2	unified	unify	VERB
ejpam-4694	638	3	generating	generating	NOUN
ejpam-4694	638	4	function	function	NOUN
ejpam-4694	638	5	of	of	ADP
ejpam-4694	638	6	the	the	DET
ejpam-4694	638	7	q	q	NOUN
ejpam-4694	638	8	-	-	PUNCT
ejpam-4694	638	9	genocchi	genocchi	ADJ
ejpam-4694	638	10	polynomials	polynomial	VERB
ejpam-4694	638	11	with	with	ADP
ejpam-4694	638	12	their	their	PRON
ejpam-4694	638	13	interpolation	interpolation	NOUN
ejpam-4694	638	14	functions	function	NOUN
ejpam-4694	638	15	.	.	PUNCT
ejpam-4694	639	1	proc	proc	NOUN
ejpam-4694	639	2	.	.	PUNCT
ejpam-4694	640	1	jangjeon	jangjeon	PROPN
ejpam-4694	640	2	math.soc	math.soc	PROPN
ejpam-4694	640	3	.	.	PROPN
ejpam-4694	640	4	,	,	PUNCT
ejpam-4694	640	5	15(20):227–233	15(20):227–233	NUM
ejpam-4694	640	6	,	,	PUNCT
ejpam-4694	640	7	2012	2012	NUM
ejpam-4694	640	8	.	.	PUNCT
ejpam-4694	641	1	[	[	X
ejpam-4694	641	2	41	41	NUM
ejpam-4694	641	3	]	]	PUNCT
ejpam-4694	641	4	m.	m.	NOUN
ejpam-4694	641	5	acikgoz	acikgoz	PROPN
ejpam-4694	641	6	s.	s.	PROPN
ejpam-4694	641	7	araci	araci	PROPN
ejpam-4694	641	8	.	.	PUNCT
ejpam-4694	642	1	construction	construction	NOUN
ejpam-4694	642	2	of	of	ADP
ejpam-4694	642	3	fourier	fourier	ADJ
ejpam-4694	642	4	expansion	expansion	NOUN
ejpam-4694	642	5	of	of	ADP
ejpam-4694	642	6	apostol	apostol	NOUN
ejpam-4694	642	7	frobenius	frobenius	NOUN
ejpam-4694	642	8	-	-	PUNCT
ejpam-4694	642	9	euler	euler	NOUN
ejpam-4694	642	10	polynomials	polynomial	NOUN
ejpam-4694	642	11	and	and	CCONJ
ejpam-4694	642	12	its	its	PRON
ejpam-4694	642	13	applications	application	NOUN
ejpam-4694	642	14	.	.	PUNCT
ejpam-4694	643	1	taiwanese	taiwanese	ADJ
ejpam-4694	643	2	j.	j.	PROPN
ejpam-4694	643	3	math	math	PROPN
ejpam-4694	643	4	.	.	PUNCT
ejpam-4694	644	1	math	math	NOUN
ejpam-4694	644	2	.	.	PUNCT
ejpam-4694	645	1	sci	sci	PROPN
ejpam-4694	645	2	.	.	PROPN
ejpam-4694	645	3	,	,	PUNCT
ejpam-4694	645	4	18(2):473–482	18(2):473–482	PROPN
ejpam-4694	645	5	,	,	PUNCT
ejpam-4694	645	6	2014	2014	NUM
ejpam-4694	645	7	.	.	PUNCT
ejpam-4694	646	1	[	[	X
ejpam-4694	646	2	42	42	NUM
ejpam-4694	646	3	]	]	X
ejpam-4694	646	4	d.	d.	PROPN
ejpam-4694	646	5	s.	s.	PROPN
ejpam-4694	646	6	kim	kim	PROPN
ejpam-4694	646	7	t.	t.	PROPN
ejpam-4694	646	8	kim	kim	PROPN
ejpam-4694	646	9	.	.	PUNCT
ejpam-4694	647	1	an	an	DET
ejpam-4694	647	2	identity	identity	NOUN
ejpam-4694	647	3	of	of	ADP
ejpam-4694	647	4	symmetry	symmetry	NOUN
ejpam-4694	647	5	for	for	ADP
ejpam-4694	647	6	the	the	DET
ejpam-4694	647	7	degenerate	degenerate	ADJ
ejpam-4694	647	8	frobenius	frobenius	NOUN
ejpam-4694	647	9	-	-	PUNCT
ejpam-4694	647	10	euler	euler	NOUN
ejpam-4694	647	11	polynomials	polynomial	NOUN
ejpam-4694	647	12	.	.	PUNCT
ejpam-4694	648	1	math	math	NOUN
ejpam-4694	648	2	.	.	PUNCT
ejpam-4694	649	1	slovaca	slovaca	PROPN
ejpam-4694	649	2	,	,	PUNCT
ejpam-4694	649	3	68(1):239–243	68(1):239–243	PROPN
ejpam-4694	649	4	,	,	PUNCT
ejpam-4694	649	5	2018	2018	NUM
ejpam-4694	649	6	.	.	PUNCT
ejpam-4694	650	1	references	reference	NOUN
ejpam-4694	650	2	712	712	NUM
ejpam-4694	651	1	[	[	X
ejpam-4694	651	2	43	43	NUM
ejpam-4694	651	3	]	]	X
ejpam-4694	652	1	y.	y.	NOUN
ejpam-4694	652	2	he	he	PRON
ejpam-4694	653	1	y.	y.	PROPN
ejpam-4694	653	2	,	,	PUNCT
ejpam-4694	653	3	s.	s.	PROPN
ejpam-4694	653	4	araci	araci	PROPN
ejpam-4694	653	5	,	,	PUNCT
ejpam-4694	653	6	h.m	h.m	PROPN
ejpam-4694	653	7	.	.	PROPN
ejpam-4694	653	8	srivastava	srivastava	PROPN
ejpam-4694	653	9	,	,	PUNCT
ejpam-4694	653	10	and	and	CCONJ
ejpam-4694	653	11	m.	m.	NOUN
ejpam-4694	653	12	acikgoz	acikgoz	VERB
ejpam-4694	653	13	.	.	PUNCT
ejpam-4694	654	1	some	some	DET
ejpam-4694	654	2	new	new	ADJ
ejpam-4694	654	3	identities	identity	NOUN
ejpam-4694	654	4	for	for	ADP
ejpam-4694	654	5	the	the	DET
ejpam-4694	654	6	apostol	apostol	NOUN
ejpam-4694	654	7	-	-	PUNCT
ejpam-4694	654	8	bernoulli	bernoulli	NOUN
ejpam-4694	654	9	polynomials	polynomial	NOUN
ejpam-4694	654	10	and	and	CCONJ
ejpam-4694	654	11	the	the	DET
ejpam-4694	654	12	apostol	apostol	NOUN
ejpam-4694	654	13	-	-	PUNCT
ejpam-4694	654	14	genocchi	genocchi	PROPN
ejpam-4694	654	15	polynomials	polynomial	NOUN
ejpam-4694	654	16	.	.	PUNCT
ejpam-4694	655	1	appl	appl	PROPN
ejpam-4694	655	2	.	.	PROPN
ejpam-4694	655	3	math	math	PROPN
ejpam-4694	655	4	.	.	PUNCT
ejpam-4694	656	1	comput	comput	NOUN
ejpam-4694	656	2	.	.	PUNCT
ejpam-4694	656	3	,	,	PUNCT
ejpam-4694	656	4	262:31–41	262:31–41	NUM
ejpam-4694	656	5	,	,	PUNCT
ejpam-4694	656	6	2015	2015	NUM
ejpam-4694	656	7	.	.	PUNCT
ejpam-4694	657	1	[	[	X
ejpam-4694	657	2	44	44	NUM
ejpam-4694	657	3	]	]	X
ejpam-4694	657	4	b.y	b.y	PROPN
ejpam-4694	657	5	.	.	PROPN
ejpam-4694	657	6	yasar	yasar	PROPN
ejpam-4694	657	7	and	and	CCONJ
ejpam-4694	657	8	m.a	m.a	PROPN
ejpam-4694	657	9	ozarslan	ozarslan	PROPN
ejpam-4694	657	10	.	.	PUNCT
ejpam-4694	658	1	frobenius	frobenius	PROPN
ejpam-4694	658	2	-	-	PUNCT
ejpam-4694	658	3	euler	euler	NOUN
ejpam-4694	658	4	and	and	CCONJ
ejpam-4694	658	5	frobenius	frobenius	NOUN
ejpam-4694	658	6	-	-	PUNCT
ejpam-4694	658	7	genocchi	genocchi	NOUN
ejpam-4694	658	8	polynomials	polynomial	NOUN
ejpam-4694	658	9	and	and	CCONJ
ejpam-4694	658	10	their	their	PRON
ejpam-4694	658	11	differential	differential	ADJ
ejpam-4694	658	12	equations	equation	NOUN
ejpam-4694	658	13	.	.	PUNCT
ejpam-4694	659	1	new	new	ADJ
ejpam-4694	659	2	trends	trend	NOUN
ejpam-4694	659	3	in	in	ADP
ejpam-4694	659	4	mathematical	mathematical	ADJ
ejpam-4694	659	5	sciences	science	NOUN
ejpam-4694	659	6	,	,	PUNCT
ejpam-4694	659	7	3(2):172–180	3(2):172–180	NUM
ejpam-4694	659	8	,	,	PUNCT
ejpam-4694	659	9	2015	2015	NUM
ejpam-4694	659	10	.	.	PUNCT