id	sid	tid	token	lemma	pos
ejpam-6743	1	1	european	european	PROPN
ejpam-6743	1	2	journal	journal	PROPN
ejpam-6743	1	3	of	of	ADP
ejpam-6743	1	4	pure	pure	ADJ
ejpam-6743	1	5	and	and	CCONJ
ejpam-6743	1	6	applied	applied	ADJ
ejpam-6743	1	7	mathematics	mathematic	NOUN
ejpam-6743	1	8	2025	2025	NUM
ejpam-6743	1	9	,	,	PUNCT
ejpam-6743	1	10	vol	vol	NOUN
ejpam-6743	1	11	.	.	PROPN
ejpam-6743	1	12	18	18	NUM
ejpam-6743	1	13	,	,	PUNCT
ejpam-6743	1	14	issue	issue	NOUN
ejpam-6743	1	15	4	4	NUM
ejpam-6743	1	16	,	,	PUNCT
ejpam-6743	1	17	article	article	NOUN
ejpam-6743	1	18	number	number	NOUN
ejpam-6743	1	19	6743	6743	NUM
ejpam-6743	1	20	issn	issn	PROPN
ejpam-6743	1	21	1307	1307	NUM
ejpam-6743	1	22	-	-	SYM
ejpam-6743	1	23	5543	5543	NUM
ejpam-6743	1	24	–	–	PUNCT
ejpam-6743	1	25	ejpam.com	ejpam.com	X
ejpam-6743	1	26	published	publish	VERB
ejpam-6743	1	27	by	by	ADP
ejpam-6743	1	28	new	new	PROPN
ejpam-6743	1	29	york	york	PROPN
ejpam-6743	1	30	business	business	PROPN
ejpam-6743	1	31	global	global	ADJ
ejpam-6743	1	32	integral	integral	ADJ
ejpam-6743	1	33	formulas	formula	NOUN
ejpam-6743	1	34	for	for	ADP
ejpam-6743	1	35	the	the	DET
ejpam-6743	1	36	noncentral	noncentral	ADJ
ejpam-6743	1	37	tanny	tanny	PROPN
ejpam-6743	1	38	-	-	PUNCT
ejpam-6743	1	39	dowling	dowle	VERB
ejpam-6743	1	40	polynomials	polynomial	NOUN
ejpam-6743	1	41	mahid	mahid	PROPN
ejpam-6743	1	42	m.	m.	PROPN
ejpam-6743	1	43	mangontarum1,2,∗	mangontarum1,2,∗	PROPN
ejpam-6743	1	44	,	,	PUNCT
ejpam-6743	1	45	norlailah	norlailah	PROPN
ejpam-6743	1	46	m.	m.	PROPN
ejpam-6743	1	47	madid1	madid1	PROPN
ejpam-6743	1	48	,	,	PUNCT
ejpam-6743	1	49	asnawi	asnawi	PROPN
ejpam-6743	1	50	a.	a.	PROPN
ejpam-6743	1	51	campong1	campong1	PROPN
ejpam-6743	2	1	1	1	NUM
ejpam-6743	2	2	department	department	NOUN
ejpam-6743	2	3	of	of	ADP
ejpam-6743	2	4	mathematics	mathematic	NOUN
ejpam-6743	2	5	,	,	PUNCT
ejpam-6743	2	6	mindanao	mindanao	PROPN
ejpam-6743	2	7	state	state	PROPN
ejpam-6743	2	8	university	university	NOUN
ejpam-6743	2	9	-	-	PUNCT
ejpam-6743	2	10	main	main	ADJ
ejpam-6743	2	11	campus	campus	NOUN
ejpam-6743	2	12	,	,	PUNCT
ejpam-6743	2	13	marawi	marawi	PROPN
ejpam-6743	2	14	city	city	PROPN
ejpam-6743	2	15	9700	9700	NUM
ejpam-6743	2	16	,	,	PUNCT
ejpam-6743	2	17	philippines	philippine	NOUN
ejpam-6743	2	18	2	2	NUM
ejpam-6743	2	19	mamitua	mamitua	PROPN
ejpam-6743	2	20	saber	saber	PROPN
ejpam-6743	2	21	institute	institute	PROPN
ejpam-6743	2	22	of	of	ADP
ejpam-6743	2	23	research	research	NOUN
ejpam-6743	2	24	and	and	CCONJ
ejpam-6743	2	25	creation	creation	NOUN
ejpam-6743	2	26	,	,	PUNCT
ejpam-6743	2	27	mindanao	mindanao	PROPN
ejpam-6743	2	28	state	state	PROPN
ejpam-6743	2	29	university	university	PROPN
ejpam-6743	2	30	main	main	ADJ
ejpam-6743	2	31	campus	campus	NOUN
ejpam-6743	2	32	,	,	PUNCT
ejpam-6743	2	33	marawi	marawi	PROPN
ejpam-6743	2	34	city	city	PROPN
ejpam-6743	2	35	9700	9700	NUM
ejpam-6743	2	36	,	,	PUNCT
ejpam-6743	2	37	philippines	philippine	NOUN
ejpam-6743	2	38	abstract	abstract	ADJ
ejpam-6743	2	39	.	.	PUNCT
ejpam-6743	3	1	in	in	ADP
ejpam-6743	3	2	this	this	DET
ejpam-6743	3	3	paper	paper	NOUN
ejpam-6743	3	4	,	,	PUNCT
ejpam-6743	3	5	the	the	DET
ejpam-6743	3	6	authors	author	NOUN
ejpam-6743	3	7	established	establish	VERB
ejpam-6743	3	8	some	some	DET
ejpam-6743	3	9	integral	integral	ADJ
ejpam-6743	3	10	formulas	formula	NOUN
ejpam-6743	3	11	for	for	ADP
ejpam-6743	3	12	the	the	DET
ejpam-6743	3	13	noncentral	noncentral	ADJ
ejpam-6743	3	14	tannydowling	tannydowling	NOUN
ejpam-6743	3	15	polynomials	polynomial	NOUN
ejpam-6743	3	16	.	.	PUNCT
ejpam-6743	4	1	these	these	DET
ejpam-6743	4	2	formulas	formula	NOUN
ejpam-6743	4	3	are	be	AUX
ejpam-6743	4	4	shown	show	VERB
ejpam-6743	4	5	to	to	PART
ejpam-6743	4	6	be	be	AUX
ejpam-6743	4	7	generalizations	generalization	NOUN
ejpam-6743	4	8	of	of	ADP
ejpam-6743	4	9	some	some	DET
ejpam-6743	4	10	known	know	VERB
ejpam-6743	4	11	results	result	NOUN
ejpam-6743	4	12	on	on	ADP
ejpam-6743	4	13	the	the	DET
ejpam-6743	4	14	classical	classical	ADJ
ejpam-6743	4	15	geometric	geometric	ADJ
ejpam-6743	4	16	polynomials	polynomial	NOUN
ejpam-6743	4	17	.	.	PUNCT
ejpam-6743	5	1	2020	2020	NUM
ejpam-6743	5	2	mathematics	mathematic	NOUN
ejpam-6743	5	3	subject	subject	NOUN
ejpam-6743	5	4	classifications	classification	NOUN
ejpam-6743	5	5	:	:	PUNCT
ejpam-6743	5	6	11b83	11b83	NUM
ejpam-6743	5	7	,	,	PUNCT
ejpam-6743	5	8	11b73	11b73	NUM
ejpam-6743	5	9	key	key	ADJ
ejpam-6743	5	10	words	word	NOUN
ejpam-6743	5	11	and	and	CCONJ
ejpam-6743	5	12	phrases	phrase	NOUN
ejpam-6743	5	13	:	:	PUNCT
ejpam-6743	5	14	geometric	geometric	ADJ
ejpam-6743	5	15	polynomial	polynomial	ADJ
ejpam-6743	5	16	,	,	PUNCT
ejpam-6743	5	17	exponential	exponential	ADJ
ejpam-6743	5	18	polynomial	polynomial	ADJ
ejpam-6743	5	19	,	,	PUNCT
ejpam-6743	5	20	noncentral	noncentral	ADJ
ejpam-6743	5	21	tannydowling	tannydowling	NOUN
ejpam-6743	5	22	polynomial	polynomial	ADJ
ejpam-6743	5	23	,	,	PUNCT
ejpam-6743	5	24	noncentral	noncentral	ADJ
ejpam-6743	5	25	dowling	dowling	NOUN
ejpam-6743	5	26	polynomial	polynomial	ADJ
ejpam-6743	5	27	1	1	NUM
ejpam-6743	5	28	.	.	PUNCT
ejpam-6743	6	1	introduction	introduction	NOUN
ejpam-6743	6	2	let	let	VERB
ejpam-6743	6	3	{	{	PUNCT
ejpam-6743	6	4	n	n	X
ejpam-6743	6	5	k	k	PROPN
ejpam-6743	6	6	}	}	PUNCT
ejpam-6743	6	7	denote	denote	VERB
ejpam-6743	6	8	the	the	DET
ejpam-6743	6	9	stirling	stirling	NOUN
ejpam-6743	6	10	numbers	number	NOUN
ejpam-6743	6	11	of	of	ADP
ejpam-6743	6	12	the	the	DET
ejpam-6743	6	13	second	second	ADJ
ejpam-6743	6	14	kind	kind	NOUN
ejpam-6743	6	15	,	,	PUNCT
ejpam-6743	6	16	see	see	VERB
ejpam-6743	6	17	[	[	X
ejpam-6743	6	18	1	1	NUM
ejpam-6743	6	19	]	]	PUNCT
ejpam-6743	6	20	.	.	PUNCT
ejpam-6743	7	1	in	in	ADP
ejpam-6743	7	2	the	the	DET
ejpam-6743	7	3	classical	classical	ADJ
ejpam-6743	7	4	distribution	distribution	NOUN
ejpam-6743	7	5	problems	problem	NOUN
ejpam-6743	7	6	,	,	PUNCT
ejpam-6743	7	7	{	{	PUNCT
ejpam-6743	7	8	n	n	CCONJ
ejpam-6743	7	9	k	k	PROPN
ejpam-6743	7	10	}	}	PUNCT
ejpam-6743	7	11	count	count	VERB
ejpam-6743	7	12	the	the	DET
ejpam-6743	7	13	number	number	NOUN
ejpam-6743	7	14	of	of	ADP
ejpam-6743	7	15	ways	way	NOUN
ejpam-6743	7	16	to	to	PART
ejpam-6743	7	17	distribute	distribute	VERB
ejpam-6743	7	18	n	n	PRON
ejpam-6743	7	19	distinct	distinct	ADJ
ejpam-6743	7	20	objects	object	NOUN
ejpam-6743	7	21	into	into	ADP
ejpam-6743	7	22	k	k	PROPN
ejpam-6743	7	23	identical	identical	ADJ
ejpam-6743	7	24	boxes	box	NOUN
ejpam-6743	7	25	such	such	ADJ
ejpam-6743	7	26	that	that	SCONJ
ejpam-6743	7	27	no	no	DET
ejpam-6743	7	28	box	box	NOUN
ejpam-6743	7	29	is	be	AUX
ejpam-6743	7	30	empty	empty	ADJ
ejpam-6743	7	31	,	,	PUNCT
ejpam-6743	7	32	see	see	VERB
ejpam-6743	7	33	page	page	NOUN
ejpam-6743	7	34	47	47	NUM
ejpam-6743	7	35	of	of	ADP
ejpam-6743	7	36	[	[	X
ejpam-6743	7	37	2	2	NUM
ejpam-6743	7	38	]	]	PUNCT
ejpam-6743	7	39	.	.	PUNCT
ejpam-6743	8	1	these	these	DET
ejpam-6743	8	2	numbers	number	NOUN
ejpam-6743	8	3	also	also	ADV
ejpam-6743	8	4	appear	appear	VERB
ejpam-6743	8	5	as	as	ADP
ejpam-6743	8	6	coefficients	coefficient	NOUN
ejpam-6743	8	7	in	in	ADP
ejpam-6743	8	8	the	the	DET
ejpam-6743	8	9	expansion	expansion	NOUN
ejpam-6743	8	10	of	of	ADP
ejpam-6743	8	11	xn	xn	PROPN
ejpam-6743	8	12	=	=	SYM
ejpam-6743	8	13	n∑	n∑	PROPN
ejpam-6743	8	14	k=0	k=0	PROPN
ejpam-6743	8	15	{	{	PUNCT
ejpam-6743	8	16	n	n	NOUN
ejpam-6743	8	17	k	k	NOUN
ejpam-6743	8	18	}	}	PUNCT
ejpam-6743	8	19	(	(	PUNCT
ejpam-6743	8	20	x)k	x)k	X
ejpam-6743	8	21	,	,	PUNCT
ejpam-6743	8	22	(	(	PUNCT
ejpam-6743	8	23	1	1	X
ejpam-6743	8	24	)	)	PUNCT
ejpam-6743	9	1	where	where	SCONJ
ejpam-6743	9	2	(	(	PUNCT
ejpam-6743	9	3	x)k	x)k	SYM
ejpam-6743	9	4	=	=	SYM
ejpam-6743	9	5	x(x−	x(x−	PROPN
ejpam-6743	9	6	1)(x−	1)(x−	NUM
ejpam-6743	9	7	2	2	NUM
ejpam-6743	9	8	)	)	PUNCT
ejpam-6743	9	9	·	·	PUNCT
ejpam-6743	9	10	·	·	PUNCT
ejpam-6743	9	11	·	·	PUNCT
ejpam-6743	9	12	(	(	PUNCT
ejpam-6743	9	13	x−	x−	PROPN
ejpam-6743	9	14	k	k	PROPN
ejpam-6743	9	15	+	+	PROPN
ejpam-6743	9	16	1	1	X
ejpam-6743	9	17	)	)	PUNCT
ejpam-6743	9	18	is	be	AUX
ejpam-6743	9	19	the	the	DET
ejpam-6743	9	20	pochhammer	pochhammer	NOUN
ejpam-6743	9	21	symbol	symbol	NOUN
ejpam-6743	9	22	,	,	PUNCT
ejpam-6743	9	23	see	see	VERB
ejpam-6743	9	24	[	[	X
ejpam-6743	9	25	3	3	NUM
ejpam-6743	9	26	]	]	PUNCT
ejpam-6743	9	27	.	.	PUNCT
ejpam-6743	10	1	it	it	PRON
ejpam-6743	10	2	is	be	AUX
ejpam-6743	10	3	easy	easy	ADJ
ejpam-6743	10	4	to	to	PART
ejpam-6743	10	5	see	see	VERB
ejpam-6743	10	6	that	that	PRON
ejpam-6743	10	7	k	k	PROPN
ejpam-6743	10	8	!	!	PUNCT
ejpam-6743	10	9	{	{	PUNCT
ejpam-6743	11	1	n	n	PROPN
ejpam-6743	11	2	k	k	NOUN
ejpam-6743	11	3	}	}	PUNCT
ejpam-6743	11	4	i.e.	i.e.	X
ejpam-6743	11	5	,	,	PUNCT
ejpam-6743	11	6	the	the	DET
ejpam-6743	11	7	stirling	stirling	NOUN
ejpam-6743	11	8	numbers	number	NOUN
ejpam-6743	11	9	of	of	ADP
ejpam-6743	11	10	the	the	DET
ejpam-6743	11	11	second	second	ADJ
ejpam-6743	11	12	kind	kind	NOUN
ejpam-6743	11	13	multiplied	multiply	VERB
ejpam-6743	11	14	by	by	ADP
ejpam-6743	11	15	k	k	PROPN
ejpam-6743	11	16	!	!	PROPN
ejpam-6743	11	17	,	,	PUNCT
ejpam-6743	11	18	counts	count	VERB
ejpam-6743	11	19	the	the	DET
ejpam-6743	11	20	number	number	NOUN
ejpam-6743	11	21	of	of	ADP
ejpam-6743	11	22	ways	way	NOUN
ejpam-6743	11	23	to	to	PART
ejpam-6743	11	24	distribute	distribute	VERB
ejpam-6743	11	25	n	n	PRON
ejpam-6743	11	26	distinct	distinct	ADJ
ejpam-6743	11	27	objects	object	NOUN
ejpam-6743	11	28	to	to	ADP
ejpam-6743	11	29	k	k	X
ejpam-6743	11	30	distinct	distinct	ADJ
ejpam-6743	11	31	boxes	box	NOUN
ejpam-6743	11	32	such	such	ADJ
ejpam-6743	11	33	that	that	SCONJ
ejpam-6743	11	34	no	no	DET
ejpam-6743	11	35	box	box	NOUN
ejpam-6743	11	36	is	be	AUX
ejpam-6743	11	37	empty	empty	ADJ
ejpam-6743	11	38	.	.	PUNCT
ejpam-6743	12	1	∗corresponding	∗corresponde	VERB
ejpam-6743	12	2	author	author	NOUN
ejpam-6743	12	3	.	.	PUNCT
ejpam-6743	13	1	doi	doi	NOUN
ejpam-6743	13	2	:	:	PUNCT
ejpam-6743	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6743	https://doi.org/10.29020/nybg.ejpam.v18i4.6743	PROPN
ejpam-6743	13	4	email	email	NOUN
ejpam-6743	13	5	addresses	address	VERB
ejpam-6743	13	6	:	:	PUNCT
ejpam-6743	14	1	mangontarum.mahid@msumain.edu.ph	mangontarum.mahid@msumain.edu.ph	PROPN
ejpam-6743	14	2	(	(	PUNCT
ejpam-6743	14	3	m.	m.	NOUN
ejpam-6743	14	4	m.	m.	NOUN
ejpam-6743	14	5	mangontarum	mangontarum	PROPN
ejpam-6743	14	6	)	)	PUNCT
ejpam-6743	14	7	,	,	PUNCT
ejpam-6743	14	8	norlailah.madid@msumain.edu.ph	norlailah.madid@msumain.edu.ph	PROPN
ejpam-6743	14	9	(	(	PUNCT
ejpam-6743	14	10	n.	n.	PROPN
ejpam-6743	14	11	m.	m.	PROPN
ejpam-6743	14	12	madid	madid	VERB
ejpam-6743	14	13	)	)	PUNCT
ejpam-6743	14	14	,	,	PUNCT
ejpam-6743	14	15	campong.aa82@s.msumain.edu.ph	campong.aa82@s.msumain.edu.ph	NUM
ejpam-6743	14	16	(	(	PUNCT
ejpam-6743	14	17	a.	a.	NOUN
ejpam-6743	14	18	a.	a.	NOUN
ejpam-6743	14	19	campong	campong	PROPN
ejpam-6743	14	20	)	)	PUNCT
ejpam-6743	14	21	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6743	15	1	1	1	NUM
ejpam-6743	15	2	copyright	copyright	NOUN
ejpam-6743	15	3	:	:	PUNCT
ejpam-6743	15	4	©	©	PROPN
ejpam-6743	15	5	2025	2025	NUM
ejpam-6743	15	6	the	the	DET
ejpam-6743	15	7	author(s	author(s	NOUN
ejpam-6743	15	8	)	)	PUNCT
ejpam-6743	15	9	.	.	PUNCT
ejpam-6743	16	1	(	(	PUNCT
ejpam-6743	16	2	cc	cc	NOUN
ejpam-6743	16	3	by	by	ADP
ejpam-6743	16	4	-	-	PUNCT
ejpam-6743	16	5	nc	nc	PROPN
ejpam-6743	16	6	4.0	4.0	NUM
ejpam-6743	16	7	)	)	PUNCT
ejpam-6743	16	8	m.	m.	NOUN
ejpam-6743	16	9	m.	m.	NOUN
ejpam-6743	16	10	mangontarum	mangontarum	PROPN
ejpam-6743	16	11	et	et	PROPN
ejpam-6743	16	12	al	al	PROPN
ejpam-6743	16	13	.	.	PUNCT
ejpam-6743	16	14	/	/	SYM
ejpam-6743	16	15	eur	eur	PROPN
ejpam-6743	16	16	.	.	PUNCT
ejpam-6743	17	1	j.	j.	PROPN
ejpam-6743	17	2	pure	pure	PROPN
ejpam-6743	17	3	appl	appl	PROPN
ejpam-6743	17	4	.	.	PROPN
ejpam-6743	17	5	math	math	PROPN
ejpam-6743	17	6	,	,	PUNCT
ejpam-6743	17	7	18	18	NUM
ejpam-6743	17	8	(	(	PUNCT
ejpam-6743	17	9	4	4	NUM
ejpam-6743	17	10	)	)	PUNCT
ejpam-6743	17	11	(	(	PUNCT
ejpam-6743	17	12	2025	2025	NUM
ejpam-6743	17	13	)	)	PUNCT
ejpam-6743	17	14	,	,	PUNCT
ejpam-6743	17	15	6743	6743	NUM
ejpam-6743	17	16	2	2	NUM
ejpam-6743	17	17	of	of	ADP
ejpam-6743	17	18	8	8	NUM
ejpam-6743	17	19	the	the	DET
ejpam-6743	17	20	geometric	geometric	ADJ
ejpam-6743	17	21	polynomials	polynomial	NOUN
ejpam-6743	17	22	,	,	PUNCT
ejpam-6743	17	23	also	also	ADV
ejpam-6743	17	24	known	know	VERB
ejpam-6743	17	25	as	as	ADP
ejpam-6743	17	26	fubini	fubini	ADJ
ejpam-6743	17	27	polynomials	polynomial	NOUN
ejpam-6743	17	28	,	,	PUNCT
ejpam-6743	17	29	see	see	VERB
ejpam-6743	17	30	[	[	X
ejpam-6743	17	31	4	4	NUM
ejpam-6743	17	32	]	]	PUNCT
ejpam-6743	17	33	,	,	PUNCT
ejpam-6743	17	34	are	be	AUX
ejpam-6743	17	35	defined	define	VERB
ejpam-6743	17	36	by	by	ADP
ejpam-6743	17	37	wn(x	wn(x	NOUN
ejpam-6743	17	38	)	)	PUNCT
ejpam-6743	17	39	=	=	SYM
ejpam-6743	18	1	n∑	n∑	PROPN
ejpam-6743	18	2	k=0	k=0	PROPN
ejpam-6743	18	3	k	k	PROPN
ejpam-6743	18	4	!	!	PUNCT
ejpam-6743	18	5	{	{	PUNCT
ejpam-6743	19	1	n	n	NOUN
ejpam-6743	19	2	k	k	X
ejpam-6743	19	3	}	}	PUNCT
ejpam-6743	19	4	xk	xk	PROPN
ejpam-6743	19	5	.	.	PROPN
ejpam-6743	20	1	(	(	PUNCT
ejpam-6743	20	2	2	2	X
ejpam-6743	20	3	)	)	PUNCT
ejpam-6743	20	4	these	these	DET
ejpam-6743	20	5	polynomials	polynomial	NOUN
ejpam-6743	20	6	are	be	AUX
ejpam-6743	20	7	known	know	VERB
ejpam-6743	20	8	to	to	PART
ejpam-6743	20	9	satisfy	satisfy	VERB
ejpam-6743	20	10	the	the	DET
ejpam-6743	20	11	exponential	exponential	ADJ
ejpam-6743	20	12	generating	generating	NOUN
ejpam-6743	20	13	function	function	NOUN
ejpam-6743	20	14	given	give	VERB
ejpam-6743	20	15	by	by	ADP
ejpam-6743	20	16	[	[	X
ejpam-6743	20	17	5	5	NUM
ejpam-6743	20	18	,	,	PUNCT
ejpam-6743	20	19	eq	eq	NOUN
ejpam-6743	20	20	.	.	PUNCT
ejpam-6743	21	1	(	(	PUNCT
ejpam-6743	21	2	3.14	3.14	NUM
ejpam-6743	21	3	)	)	PUNCT
ejpam-6743	21	4	]	]	PUNCT
ejpam-6743	22	1	∞∑	∞∑	PRON
ejpam-6743	22	2	n=0	n=0	NUM
ejpam-6743	22	3	wn(x	wn(x	X
ejpam-6743	22	4	)	)	PUNCT
ejpam-6743	22	5	zn	zn	NOUN
ejpam-6743	22	6	n	n	X
ejpam-6743	22	7	!	!	PUNCT
ejpam-6743	23	1	=	=	PUNCT
ejpam-6743	23	2	1	1	NUM
ejpam-6743	23	3	1−	1−	NUM
ejpam-6743	23	4	x(ez	x(ez	PROPN
ejpam-6743	23	5	−	−	PROPN
ejpam-6743	23	6	1	1	NUM
ejpam-6743	23	7	)	)	PUNCT
ejpam-6743	23	8	.	.	PUNCT
ejpam-6743	24	1	(	(	PUNCT
ejpam-6743	24	2	3	3	X
ejpam-6743	24	3	)	)	PUNCT
ejpam-6743	24	4	these	these	DET
ejpam-6743	24	5	polynomials	polynomial	NOUN
ejpam-6743	24	6	have	have	VERB
ejpam-6743	24	7	strong	strong	ADJ
ejpam-6743	24	8	links	link	NOUN
ejpam-6743	24	9	to	to	ADP
ejpam-6743	24	10	combinatorics	combinatoric	NOUN
ejpam-6743	24	11	,	,	PUNCT
ejpam-6743	24	12	exponential	exponential	ADJ
ejpam-6743	24	13	generating	generating	NOUN
ejpam-6743	24	14	functions	function	NOUN
ejpam-6743	24	15	,	,	PUNCT
ejpam-6743	24	16	and	and	CCONJ
ejpam-6743	24	17	classical	classical	ADJ
ejpam-6743	24	18	sequences	sequence	NOUN
ejpam-6743	24	19	such	such	ADJ
ejpam-6743	24	20	as	as	ADP
ejpam-6743	24	21	the	the	DET
ejpam-6743	24	22	bernoulli	bernoulli	NOUN
ejpam-6743	24	23	numbers	number	NOUN
ejpam-6743	24	24	.	.	PUNCT
ejpam-6743	25	1	the	the	DET
ejpam-6743	25	2	case	case	NOUN
ejpam-6743	25	3	when	when	SCONJ
ejpam-6743	25	4	x	x	PRON
ejpam-6743	25	5	=	=	NOUN
ejpam-6743	25	6	1	1	NUM
ejpam-6743	25	7	given	give	VERB
ejpam-6743	25	8	by	by	ADP
ejpam-6743	25	9	wn	wn	PROPN
ejpam-6743	25	10	:	:	PUNCT
ejpam-6743	25	11	=	=	SYM
ejpam-6743	25	12	wn(1	wn(1	PROPN
ejpam-6743	25	13	)	)	PUNCT
ejpam-6743	25	14	=	=	SYM
ejpam-6743	25	15	n∑	n∑	NOUN
ejpam-6743	25	16	k=0	k=0	PROPN
ejpam-6743	25	17	k	k	PROPN
ejpam-6743	25	18	!	!	PUNCT
ejpam-6743	25	19	{	{	PUNCT
ejpam-6743	26	1	n	n	NOUN
ejpam-6743	26	2	k	k	NOUN
ejpam-6743	26	3	}	}	PUNCT
ejpam-6743	26	4	(	(	PUNCT
ejpam-6743	26	5	4	4	X
ejpam-6743	26	6	)	)	PUNCT
ejpam-6743	26	7	is	be	AUX
ejpam-6743	26	8	called	call	VERB
ejpam-6743	26	9	geometric	geometric	ADJ
ejpam-6743	26	10	numbers	number	NOUN
ejpam-6743	26	11	or	or	CCONJ
ejpam-6743	26	12	fubini	fubini	ADJ
ejpam-6743	26	13	numbers	number	NOUN
ejpam-6743	26	14	.	.	PUNCT
ejpam-6743	27	1	these	these	PRON
ejpam-6743	27	2	count	count	VERB
ejpam-6743	27	3	all	all	DET
ejpam-6743	27	4	the	the	DET
ejpam-6743	27	5	possible	possible	ADJ
ejpam-6743	27	6	set	set	ADJ
ejpam-6743	27	7	partitions	partition	NOUN
ejpam-6743	27	8	of	of	ADP
ejpam-6743	27	9	an	an	DET
ejpam-6743	27	10	n	n	DET
ejpam-6743	27	11	element	element	NOUN
ejpam-6743	27	12	set	set	VERB
ejpam-6743	27	13	such	such	ADJ
ejpam-6743	27	14	that	that	SCONJ
ejpam-6743	27	15	the	the	DET
ejpam-6743	27	16	order	order	NOUN
ejpam-6743	27	17	of	of	ADP
ejpam-6743	27	18	the	the	DET
ejpam-6743	27	19	blocks	block	NOUN
ejpam-6743	27	20	matters	matter	NOUN
ejpam-6743	27	21	.	.	PUNCT
ejpam-6743	28	1	the	the	DET
ejpam-6743	28	2	exponential	exponential	ADJ
ejpam-6743	28	3	generating	generating	NOUN
ejpam-6743	28	4	function	function	NOUN
ejpam-6743	28	5	of	of	ADP
ejpam-6743	28	6	wn	wn	PROPN
ejpam-6743	28	7	can	can	AUX
ejpam-6743	28	8	be	be	AUX
ejpam-6743	28	9	easily	easily	ADV
ejpam-6743	28	10	by	by	ADP
ejpam-6743	28	11	setting	set	VERB
ejpam-6743	28	12	x	x	PUNCT
ejpam-6743	28	13	=	=	SYM
ejpam-6743	28	14	1	1	NUM
ejpam-6743	28	15	in	in	ADP
ejpam-6743	28	16	(	(	PUNCT
ejpam-6743	28	17	3	3	NUM
ejpam-6743	28	18	)	)	PUNCT
ejpam-6743	28	19	.	.	PUNCT
ejpam-6743	29	1	that	that	PRON
ejpam-6743	29	2	is	be	AUX
ejpam-6743	29	3	,	,	PUNCT
ejpam-6743	29	4	∞∑	∞∑	PROPN
ejpam-6743	29	5	n=0	n=0	NUM
ejpam-6743	29	6	wn(1	wn(1	PROPN
ejpam-6743	29	7	)	)	PUNCT
ejpam-6743	29	8	zn	zn	PROPN
ejpam-6743	29	9	n	n	NUM
ejpam-6743	29	10	!	!	PUNCT
ejpam-6743	30	1	:	:	PUNCT
ejpam-6743	31	1	=	=	NOUN
ejpam-6743	31	2	∞∑	∞∑	NUM
ejpam-6743	31	3	n=0	n=0	NUM
ejpam-6743	31	4	wn	wn	PROPN
ejpam-6743	31	5	zn	zn	PROPN
ejpam-6743	31	6	n	n	X
ejpam-6743	31	7	!	!	PUNCT
ejpam-6743	31	8	=	=	SYM
ejpam-6743	32	1	1	1	NUM
ejpam-6743	32	2	2−	2−	NUM
ejpam-6743	32	3	ez	ez	X
ejpam-6743	32	4	.	.	PUNCT
ejpam-6743	33	1	(	(	PUNCT
ejpam-6743	33	2	5	5	X
ejpam-6743	33	3	)	)	PUNCT
ejpam-6743	33	4	the	the	DET
ejpam-6743	33	5	study	study	NOUN
ejpam-6743	33	6	of	of	ADP
ejpam-6743	33	7	geometric	geometric	ADJ
ejpam-6743	33	8	polynomials	polynomial	NOUN
ejpam-6743	33	9	has	have	AUX
ejpam-6743	33	10	remained	remain	VERB
ejpam-6743	33	11	a	a	DET
ejpam-6743	33	12	thrend	thrend	NOUN
ejpam-6743	33	13	for	for	ADP
ejpam-6743	33	14	among	among	ADP
ejpam-6743	33	15	mathematicians	mathematician	NOUN
ejpam-6743	33	16	to	to	ADP
ejpam-6743	33	17	this	this	DET
ejpam-6743	33	18	date	date	NOUN
ejpam-6743	33	19	.	.	PUNCT
ejpam-6743	34	1	for	for	ADP
ejpam-6743	34	2	instance	instance	NOUN
ejpam-6743	34	3	,	,	PUNCT
ejpam-6743	34	4	kellner	kellner	PROPN
ejpam-6743	35	1	[	[	X
ejpam-6743	35	2	6	6	NUM
ejpam-6743	35	3	]	]	PUNCT
ejpam-6743	35	4	established	establish	VERB
ejpam-6743	35	5	several	several	ADJ
ejpam-6743	35	6	identities	identity	NOUN
ejpam-6743	35	7	involving	involve	VERB
ejpam-6743	35	8	the	the	DET
ejpam-6743	35	9	polynomials	polynomial	NOUN
ejpam-6743	35	10	wn(x	wn(x	NOUN
ejpam-6743	35	11	)	)	PUNCT
ejpam-6743	35	12	.	.	PUNCT
ejpam-6743	36	1	among	among	ADP
ejpam-6743	36	2	these	these	DET
ejpam-6743	36	3	identities	identity	NOUN
ejpam-6743	36	4	is	be	AUX
ejpam-6743	36	5	the	the	DET
ejpam-6743	36	6	integral	integral	ADJ
ejpam-6743	36	7	identity	identity	NOUN
ejpam-6743	36	8	over	over	ADP
ejpam-6743	36	9	the	the	DET
ejpam-6743	36	10	interval	interval	NOUN
ejpam-6743	36	11	[	[	X
ejpam-6743	36	12	−1	−1	NOUN
ejpam-6743	36	13	,	,	PUNCT
ejpam-6743	36	14	0	0	NUM
ejpam-6743	36	15	]	]	PUNCT
ejpam-6743	36	16	given	give	VERB
ejpam-6743	36	17	by	by	ADP
ejpam-6743	36	18	∫	∫	PROPN
ejpam-6743	36	19	0	0	NUM
ejpam-6743	36	20	−1	−1	NOUN
ejpam-6743	36	21	wn(x)dx	wn(x)dx	PROPN
ejpam-6743	36	22	=	=	X
ejpam-6743	36	23	bn	bn	NOUN
ejpam-6743	36	24	.	.	PUNCT
ejpam-6743	37	1	(	(	PUNCT
ejpam-6743	37	2	6	6	NUM
ejpam-6743	37	3	)	)	PUNCT
ejpam-6743	37	4	here	here	ADV
ejpam-6743	37	5	,	,	PUNCT
ejpam-6743	37	6	bn	bn	NOUN
ejpam-6743	37	7	denotes	denote	VERB
ejpam-6743	37	8	the	the	DET
ejpam-6743	37	9	nth	nth	NOUN
ejpam-6743	37	10	bernoulli	bernoulli	NOUN
ejpam-6743	37	11	number	number	NOUN
ejpam-6743	37	12	defined	define	VERB
ejpam-6743	37	13	by	by	ADP
ejpam-6743	37	14	the	the	DET
ejpam-6743	37	15	exponential	exponential	ADJ
ejpam-6743	37	16	generating	generating	NOUN
ejpam-6743	37	17	function	function	NOUN
ejpam-6743	38	1	∞∑	∞∑	PROPN
ejpam-6743	38	2	n=0	n=0	NUM
ejpam-6743	38	3	bn	bn	NUM
ejpam-6743	38	4	xk	xk	PROPN
ejpam-6743	38	5	n	n	X
ejpam-6743	38	6	!	!	PUNCT
ejpam-6743	39	1	=	=	PUNCT
ejpam-6743	40	1	x	x	X
ejpam-6743	40	2	ex	ex	NOUN
ejpam-6743	40	3	−	−	NOUN
ejpam-6743	40	4	1	1	NUM
ejpam-6743	40	5	.	.	PUNCT
ejpam-6743	41	1	(	(	PUNCT
ejpam-6743	41	2	7	7	X
ejpam-6743	41	3	)	)	PUNCT
ejpam-6743	41	4	the	the	DET
ejpam-6743	41	5	proof	proof	NOUN
ejpam-6743	41	6	of	of	ADP
ejpam-6743	41	7	(	(	PUNCT
ejpam-6743	41	8	6	6	NUM
ejpam-6743	41	9	)	)	PUNCT
ejpam-6743	41	10	uses	use	VERB
ejpam-6743	41	11	worpitzky	worpitzky	ADJ
ejpam-6743	41	12	’s	’s	PART
ejpam-6743	41	13	identity	identity	NOUN
ejpam-6743	42	1	[	[	X
ejpam-6743	42	2	7	7	NUM
ejpam-6743	42	3	,	,	PUNCT
ejpam-6743	42	4	pg	pg	INTJ
ejpam-6743	42	5	.	.	PROPN
ejpam-6743	42	6	215	215	NUM
ejpam-6743	42	7	(	(	PUNCT
ejpam-6743	42	8	36	36	NUM
ejpam-6743	42	9	)	)	PUNCT
ejpam-6743	42	10	]	]	PUNCT
ejpam-6743	42	11	given	give	VERB
ejpam-6743	42	12	by	by	ADP
ejpam-6743	42	13	bn	bn	PROPN
ejpam-6743	42	14	=	=	SYM
ejpam-6743	42	15	n∑	n∑	PROPN
ejpam-6743	42	16	k=0	k=0	PROPN
ejpam-6743	42	17	k∑	k∑	PROPN
ejpam-6743	42	18	j=0	j=0	PROPN
ejpam-6743	42	19	(	(	PUNCT
ejpam-6743	42	20	−1)j	−1)j	X
ejpam-6743	42	21	(	(	PUNCT
ejpam-6743	42	22	k	k	PROPN
ejpam-6743	42	23	j	j	PROPN
ejpam-6743	42	24	)	)	PUNCT
ejpam-6743	43	1	jn	jn	PROPN
ejpam-6743	44	1	k	k	PROPN
ejpam-6743	45	1	+	+	CCONJ
ejpam-6743	45	2	1	1	NUM
ejpam-6743	45	3	(	(	PUNCT
ejpam-6743	45	4	8)	8)	NUM
ejpam-6743	45	5	and	and	CCONJ
ejpam-6743	45	6	its	its	PRON
ejpam-6743	45	7	equivalent	equivalent	ADJ
ejpam-6743	45	8	form	form	NOUN
ejpam-6743	45	9	bn	bn	NOUN
ejpam-6743	45	10	=	=	SYM
ejpam-6743	45	11	n∑	n∑	NOUN
ejpam-6743	45	12	k=1	k=1	PROPN
ejpam-6743	45	13	(	(	PUNCT
ejpam-6743	45	14	−1)k	−1)k	PROPN
ejpam-6743	45	15	k	k	X
ejpam-6743	45	16	!	!	PUNCT
ejpam-6743	46	1	k	k	PROPN
ejpam-6743	47	1	+	+	CCONJ
ejpam-6743	47	2	1	1	NUM
ejpam-6743	47	3	{	{	PUNCT
ejpam-6743	47	4	n	n	NOUN
ejpam-6743	47	5	k	k	PROPN
ejpam-6743	47	6	}	}	PUNCT
ejpam-6743	47	7	.	.	PUNCT
ejpam-6743	48	1	(	(	PUNCT
ejpam-6743	48	2	9	9	X
ejpam-6743	48	3	)	)	PUNCT
ejpam-6743	48	4	m.	m.	NOUN
ejpam-6743	48	5	m.	m.	NOUN
ejpam-6743	48	6	mangontarum	mangontarum	PROPN
ejpam-6743	48	7	et	et	PROPN
ejpam-6743	48	8	al	al	PROPN
ejpam-6743	48	9	.	.	PUNCT
ejpam-6743	48	10	/	/	SYM
ejpam-6743	48	11	eur	eur	PROPN
ejpam-6743	48	12	.	.	PUNCT
ejpam-6743	49	1	j.	j.	PROPN
ejpam-6743	49	2	pure	pure	PROPN
ejpam-6743	49	3	appl	appl	PROPN
ejpam-6743	49	4	.	.	PROPN
ejpam-6743	49	5	math	math	PROPN
ejpam-6743	49	6	,	,	PUNCT
ejpam-6743	49	7	18	18	NUM
ejpam-6743	49	8	(	(	PUNCT
ejpam-6743	49	9	4	4	NUM
ejpam-6743	49	10	)	)	PUNCT
ejpam-6743	49	11	(	(	PUNCT
ejpam-6743	49	12	2025	2025	NUM
ejpam-6743	49	13	)	)	PUNCT
ejpam-6743	49	14	,	,	PUNCT
ejpam-6743	49	15	6743	6743	NUM
ejpam-6743	49	16	3	3	NUM
ejpam-6743	49	17	of	of	ADP
ejpam-6743	49	18	8	8	NUM
ejpam-6743	49	19	boyadzhiev	boyadzhiev	NOUN
ejpam-6743	50	1	[	[	X
ejpam-6743	50	2	5	5	NUM
ejpam-6743	50	3	]	]	PUNCT
ejpam-6743	50	4	established	establish	VERB
ejpam-6743	50	5	transformation	transformation	NOUN
ejpam-6743	50	6	formulas	formula	NOUN
ejpam-6743	50	7	for	for	ADP
ejpam-6743	50	8	the	the	DET
ejpam-6743	50	9	geometric	geometric	ADJ
ejpam-6743	50	10	polynomials	polynomial	NOUN
ejpam-6743	50	11	.	.	PUNCT
ejpam-6743	51	1	in	in	ADP
ejpam-6743	51	2	his	his	PRON
ejpam-6743	51	3	paper	paper	NOUN
ejpam-6743	51	4	,	,	PUNCT
ejpam-6743	51	5	given	give	VERB
ejpam-6743	51	6	the	the	DET
ejpam-6743	51	7	exponential	exponential	ADJ
ejpam-6743	51	8	polynomials	polynomial	NOUN
ejpam-6743	51	9	or	or	CCONJ
ejpam-6743	51	10	bell	bell	NOUN
ejpam-6743	51	11	polynomials	polynomial	NOUN
ejpam-6743	51	12	ϕn(x	ϕn(x	PRON
ejpam-6743	51	13	)	)	PUNCT
ejpam-6743	51	14	defined	define	VERB
ejpam-6743	51	15	by	by	ADP
ejpam-6743	51	16	ϕn(x	ϕn(x	PRON
ejpam-6743	51	17	)	)	PUNCT
ejpam-6743	51	18	=	=	SYM
ejpam-6743	51	19	n∑	n∑	NOUN
ejpam-6743	51	20	k=0	k=0	PROPN
ejpam-6743	51	21	{	{	PUNCT
ejpam-6743	51	22	n	n	NOUN
ejpam-6743	51	23	k	k	PROPN
ejpam-6743	51	24	}	}	PUNCT
ejpam-6743	51	25	xk	xk	PROPN
ejpam-6743	51	26	,	,	PUNCT
ejpam-6743	51	27	(	(	PUNCT
ejpam-6743	51	28	10	10	NUM
ejpam-6743	51	29	)	)	PUNCT
ejpam-6743	51	30	boyadzhiev	boyadzhiev	NOUN
ejpam-6743	51	31	[	[	X
ejpam-6743	51	32	5	5	NUM
ejpam-6743	51	33	]	]	PUNCT
ejpam-6743	51	34	expressed	express	VERB
ejpam-6743	51	35	the	the	DET
ejpam-6743	51	36	geometric	geometric	ADJ
ejpam-6743	51	37	polynomials	polynomial	NOUN
ejpam-6743	51	38	wn(x	wn(x	NOUN
ejpam-6743	51	39	)	)	PUNCT
ejpam-6743	51	40	in	in	ADP
ejpam-6743	51	41	terms	term	NOUN
ejpam-6743	51	42	of	of	ADP
ejpam-6743	51	43	the	the	DET
ejpam-6743	51	44	exponential	exponential	ADJ
ejpam-6743	51	45	polynomials	polynomial	NOUN
ejpam-6743	51	46	,	,	PUNCT
ejpam-6743	51	47	as	as	SCONJ
ejpam-6743	51	48	follows	follow	VERB
ejpam-6743	51	49	wn(x	wn(x	NOUN
ejpam-6743	51	50	)	)	PUNCT
ejpam-6743	51	51	=	=	SYM
ejpam-6743	52	1	∫	∫	PROPN
ejpam-6743	52	2	∞	∞	PROPN
ejpam-6743	52	3	0	0	NUM
ejpam-6743	52	4	ϕn(xλ)e	ϕn(xλ)e	PROPN
ejpam-6743	52	5	−λdλ	−λdλ	NOUN
ejpam-6743	52	6	.	.	PUNCT
ejpam-6743	53	1	(	(	PUNCT
ejpam-6743	53	2	11	11	NUM
ejpam-6743	53	3	)	)	PUNCT
ejpam-6743	53	4	this	this	PRON
ejpam-6743	53	5	was	be	AUX
ejpam-6743	53	6	used	use	VERB
ejpam-6743	53	7	to	to	PART
ejpam-6743	53	8	derive	derive	VERB
ejpam-6743	53	9	more	more	ADJ
ejpam-6743	53	10	properties	property	NOUN
ejpam-6743	53	11	for	for	ADP
ejpam-6743	53	12	wn(x	wn(x	NOUN
ejpam-6743	53	13	)	)	PUNCT
ejpam-6743	53	14	including	include	VERB
ejpam-6743	53	15	the	the	DET
ejpam-6743	53	16	exponential	exponential	ADJ
ejpam-6743	53	17	generating	generating	NOUN
ejpam-6743	53	18	function	function	NOUN
ejpam-6743	53	19	[	[	X
ejpam-6743	53	20	5	5	NUM
ejpam-6743	53	21	,	,	PUNCT
ejpam-6743	53	22	eq	eq	NOUN
ejpam-6743	53	23	.	.	PUNCT
ejpam-6743	54	1	(	(	PUNCT
ejpam-6743	54	2	3.13	3.13	NUM
ejpam-6743	54	3	)	)	PUNCT
ejpam-6743	54	4	]	]	PUNCT
ejpam-6743	55	1	∫	∫	PROPN
ejpam-6743	56	1	∞	∞	NUM
ejpam-6743	56	2	0	0	NUM
ejpam-6743	57	1	e−λ(1−x(ex−1))dλ	e−λ(1−x(ex−1))dλ	PROPN
ejpam-6743	57	2	=	=	PUNCT
ejpam-6743	58	1	∞∑	∞∑	ADJ
ejpam-6743	58	2	n=0	n=0	NUM
ejpam-6743	58	3	wn(x	wn(x	X
ejpam-6743	58	4	)	)	PUNCT
ejpam-6743	58	5	zn	zn	PROPN
ejpam-6743	58	6	n	n	PRON
ejpam-6743	58	7	!	!	PUNCT
ejpam-6743	58	8	.	.	PUNCT
ejpam-6743	59	1	(	(	PUNCT
ejpam-6743	59	2	12	12	NUM
ejpam-6743	59	3	)	)	PUNCT
ejpam-6743	59	4	additional	additional	ADJ
ejpam-6743	59	5	important	important	ADJ
ejpam-6743	59	6	works	work	NOUN
ejpam-6743	59	7	are	be	AUX
ejpam-6743	59	8	due	due	ADJ
ejpam-6743	59	9	to	to	AUX
ejpam-6743	59	10	kargın	kargın	PROPN
ejpam-6743	59	11	[	[	X
ejpam-6743	59	12	8	8	NUM
ejpam-6743	59	13	]	]	PUNCT
ejpam-6743	59	14	,	,	PUNCT
ejpam-6743	59	15	dil	dil	NOUN
ejpam-6743	59	16	and	and	CCONJ
ejpam-6743	59	17	kurt	kurt	NOUN
ejpam-6743	60	1	[	[	X
ejpam-6743	60	2	9	9	NUM
ejpam-6743	60	3	]	]	PUNCT
ejpam-6743	60	4	,	,	PUNCT
ejpam-6743	60	5	boyadzhiev	boyadzhiev	NOUN
ejpam-6743	60	6	and	and	CCONJ
ejpam-6743	60	7	dil	dil	X
ejpam-6743	61	1	[	[	X
ejpam-6743	61	2	10	10	NUM
ejpam-6743	61	3	]	]	PUNCT
ejpam-6743	61	4	,	,	PUNCT
ejpam-6743	61	5	kargın	kargın	PROPN
ejpam-6743	61	6	and	and	CCONJ
ejpam-6743	61	7	çekim	çekim	PROPN
ejpam-6743	62	1	[	[	X
ejpam-6743	62	2	11	11	NUM
ejpam-6743	62	3	]	]	PUNCT
ejpam-6743	62	4	,	,	PUNCT
ejpam-6743	62	5	ramı́rez	ramı́rez	NOUN
ejpam-6743	62	6	and	and	CCONJ
ejpam-6743	62	7	cesarano	cesarano	PROPN
ejpam-6743	63	1	[	[	X
ejpam-6743	63	2	12	12	NUM
ejpam-6743	63	3	]	]	PUNCT
ejpam-6743	63	4	,	,	PUNCT
ejpam-6743	63	5	among	among	ADP
ejpam-6743	63	6	others	other	NOUN
ejpam-6743	63	7	.	.	PUNCT
ejpam-6743	64	1	in	in	ADP
ejpam-6743	64	2	2016	2016	NUM
ejpam-6743	64	3	,	,	PUNCT
ejpam-6743	64	4	mangontarum	mangontarum	NOUN
ejpam-6743	64	5	et	et	NOUN
ejpam-6743	64	6	al	al	PROPN
ejpam-6743	64	7	.	.	PUNCT
ejpam-6743	65	1	[	[	X
ejpam-6743	65	2	13	13	NUM
ejpam-6743	65	3	]	]	PUNCT
ejpam-6743	65	4	introduced	introduce	VERB
ejpam-6743	65	5	the	the	DET
ejpam-6743	65	6	noncentral	noncentral	ADJ
ejpam-6743	65	7	tanny	tanny	PROPN
ejpam-6743	65	8	-	-	PUNCT
ejpam-6743	65	9	dowling	dowle	VERB
ejpam-6743	65	10	polynomials	polynomial	NOUN
ejpam-6743	65	11	f̃m	f̃m	NOUN
ejpam-6743	65	12	,	,	PUNCT
ejpam-6743	65	13	a(n;x	a(n;x	PROPN
ejpam-6743	65	14	)	)	PUNCT
ejpam-6743	65	15	defined	define	VERB
ejpam-6743	65	16	by	by	ADP
ejpam-6743	65	17	f̃m	f̃m	PROPN
ejpam-6743	65	18	,	,	PUNCT
ejpam-6743	65	19	a(n;x	a(n;x	PROPN
ejpam-6743	65	20	)	)	PUNCT
ejpam-6743	65	21	=	=	SYM
ejpam-6743	65	22	n∑	n∑	PROPN
ejpam-6743	65	23	k=0	k=0	PROPN
ejpam-6743	65	24	k!w̃m	k!w̃m	PROPN
ejpam-6743	65	25	,	,	PUNCT
ejpam-6743	65	26	a(n	a(n	ADV
ejpam-6743	65	27	,	,	PUNCT
ejpam-6743	65	28	k)x	k)x	X
ejpam-6743	65	29	k	k	X
ejpam-6743	65	30	(	(	PUNCT
ejpam-6743	65	31	13	13	NUM
ejpam-6743	65	32	)	)	PUNCT
ejpam-6743	65	33	and	and	CCONJ
ejpam-6743	65	34	satisfying	satisfy	VERB
ejpam-6743	65	35	the	the	DET
ejpam-6743	65	36	exponential	exponential	ADJ
ejpam-6743	65	37	generating	generating	NOUN
ejpam-6743	65	38	function	function	NOUN
ejpam-6743	65	39	∞∑	∞∑	PROPN
ejpam-6743	65	40	n	n	CCONJ
ejpam-6743	65	41	=	=	SYM
ejpam-6743	65	42	k	k	PROPN
ejpam-6743	65	43	f̃m	f̃m	PROPN
ejpam-6743	65	44	,	,	PUNCT
ejpam-6743	65	45	a(n;x	a(n;x	PROPN
ejpam-6743	65	46	)	)	PUNCT
ejpam-6743	65	47	zn	zn	PROPN
ejpam-6743	65	48	n	n	X
ejpam-6743	65	49	!	!	PUNCT
ejpam-6743	66	1	=	=	NOUN
ejpam-6743	67	1	me−az	me−az	NOUN
ejpam-6743	67	2	m−	m−	PROPN
ejpam-6743	67	3	x(emz	x(emz	PROPN
ejpam-6743	68	1	−	−	PROPN
ejpam-6743	68	2	1	1	NUM
ejpam-6743	68	3	)	)	PUNCT
ejpam-6743	68	4	,	,	PUNCT
ejpam-6743	68	5	(	(	PUNCT
ejpam-6743	68	6	14	14	NUM
ejpam-6743	68	7	)	)	PUNCT
ejpam-6743	68	8	where	where	SCONJ
ejpam-6743	68	9	the	the	DET
ejpam-6743	68	10	numbers	number	NOUN
ejpam-6743	68	11	w̃m	w̃m	PROPN
ejpam-6743	68	12	,	,	PUNCT
ejpam-6743	68	13	a(n	a(n	ADV
ejpam-6743	68	14	,	,	PUNCT
ejpam-6743	68	15	k	k	NOUN
ejpam-6743	68	16	)	)	PUNCT
ejpam-6743	68	17	are	be	AUX
ejpam-6743	68	18	the	the	DET
ejpam-6743	68	19	noncentral	noncentral	ADJ
ejpam-6743	68	20	whitney	whitney	NOUN
ejpam-6743	68	21	numbers	number	NOUN
ejpam-6743	68	22	of	of	ADP
ejpam-6743	68	23	the	the	DET
ejpam-6743	68	24	second	second	ADJ
ejpam-6743	68	25	kind	kind	NOUN
ejpam-6743	68	26	,	,	PUNCT
ejpam-6743	68	27	a	a	DET
ejpam-6743	68	28	generalization	generalization	NOUN
ejpam-6743	68	29	of	of	ADP
ejpam-6743	68	30	{	{	PUNCT
ejpam-6743	68	31	n	n	PROPN
ejpam-6743	68	32	k	k	PROPN
ejpam-6743	68	33	}	}	PUNCT
ejpam-6743	68	34	.	.	PUNCT
ejpam-6743	69	1	the	the	DET
ejpam-6743	69	2	parameters	parameter	NOUN
ejpam-6743	69	3	(	(	PUNCT
ejpam-6743	69	4	m	m	PROPN
ejpam-6743	69	5	,	,	PUNCT
ejpam-6743	69	6	a	a	PRON
ejpam-6743	69	7	)	)	PUNCT
ejpam-6743	69	8	deform	deform	VERB
ejpam-6743	69	9	the	the	DET
ejpam-6743	69	10	classical	classical	ADJ
ejpam-6743	69	11	structure	structure	NOUN
ejpam-6743	69	12	:	:	PUNCT
ejpam-6743	69	13	f̃1,0(n;x	f̃1,0(n;x	PROPN
ejpam-6743	69	14	)	)	PUNCT
ejpam-6743	69	15	=	=	SYM
ejpam-6743	69	16	wn(x	wn(x	X
ejpam-6743	69	17	)	)	PUNCT
ejpam-6743	69	18	.	.	PUNCT
ejpam-6743	70	1	further	far	ADV
ejpam-6743	70	2	,	,	PUNCT
ejpam-6743	70	3	in	in	ADP
ejpam-6743	70	4	a	a	DET
ejpam-6743	70	5	recent	recent	ADJ
ejpam-6743	70	6	paper	paper	NOUN
ejpam-6743	70	7	by	by	ADP
ejpam-6743	70	8	mangontarum	mangontarum	NOUN
ejpam-6743	70	9	and	and	CCONJ
ejpam-6743	70	10	madid	madid	VERB
ejpam-6743	70	11	[	[	X
ejpam-6743	70	12	14	14	NUM
ejpam-6743	70	13	]	]	PUNCT
ejpam-6743	70	14	,	,	PUNCT
ejpam-6743	70	15	a	a	DET
ejpam-6743	70	16	number	number	NOUN
ejpam-6743	70	17	of	of	ADP
ejpam-6743	70	18	identities	identity	NOUN
ejpam-6743	70	19	for	for	ADP
ejpam-6743	70	20	f̃m	f̃m	NOUN
ejpam-6743	70	21	,	,	PUNCT
ejpam-6743	70	22	a(n;x	a(n;x	PROPN
ejpam-6743	70	23	)	)	PUNCT
ejpam-6743	70	24	are	be	AUX
ejpam-6743	70	25	established	establish	VERB
ejpam-6743	70	26	.	.	PUNCT
ejpam-6743	71	1	such	such	ADJ
ejpam-6743	71	2	identities	identity	NOUN
ejpam-6743	71	3	are	be	AUX
ejpam-6743	71	4	shown	show	VERB
ejpam-6743	71	5	to	to	PART
ejpam-6743	71	6	generalize	generalize	VERB
ejpam-6743	71	7	some	some	DET
ejpam-6743	71	8	known	know	VERB
ejpam-6743	71	9	results	result	NOUN
ejpam-6743	71	10	on	on	ADP
ejpam-6743	71	11	the	the	DET
ejpam-6743	71	12	geometric	geometric	ADJ
ejpam-6743	71	13	polynomials	polynomial	NOUN
ejpam-6743	71	14	,	,	PUNCT
ejpam-6743	71	15	including	include	VERB
ejpam-6743	71	16	the	the	DET
ejpam-6743	71	17	ones	one	NOUN
ejpam-6743	71	18	in	in	ADP
ejpam-6743	71	19	the	the	DET
ejpam-6743	71	20	paper	paper	NOUN
ejpam-6743	71	21	of	of	ADP
ejpam-6743	71	22	kargın	kargın	PROPN
ejpam-6743	72	1	[	[	X
ejpam-6743	72	2	8	8	NUM
ejpam-6743	72	3	]	]	PUNCT
ejpam-6743	72	4	.	.	PUNCT
ejpam-6743	73	1	in	in	ADP
ejpam-6743	73	2	the	the	DET
ejpam-6743	73	3	present	present	ADJ
ejpam-6743	73	4	paper	paper	NOUN
ejpam-6743	73	5	,	,	PUNCT
ejpam-6743	73	6	the	the	DET
ejpam-6743	73	7	authors	author	NOUN
ejpam-6743	73	8	establish	establish	VERB
ejpam-6743	73	9	integral	integral	ADJ
ejpam-6743	73	10	formulas	formula	NOUN
ejpam-6743	73	11	for	for	ADP
ejpam-6743	73	12	and	and	CCONJ
ejpam-6743	73	13	involving	involve	VERB
ejpam-6743	73	14	the	the	DET
ejpam-6743	73	15	noncentral	noncentral	ADJ
ejpam-6743	73	16	tanny	tanny	PROPN
ejpam-6743	73	17	-	-	PUNCT
ejpam-6743	73	18	dowling	dowle	VERB
ejpam-6743	73	19	polynomials	polynomial	NOUN
ejpam-6743	73	20	.	.	PUNCT
ejpam-6743	74	1	in	in	ADP
ejpam-6743	74	2	particulay	particulay	PROPN
ejpam-6743	74	3	,	,	PUNCT
ejpam-6743	74	4	we	we	PRON
ejpam-6743	74	5	will	will	AUX
ejpam-6743	74	6	derive	derive	VERB
ejpam-6743	74	7	a	a	DET
ejpam-6743	74	8	generalization	generalization	NOUN
ejpam-6743	74	9	of	of	ADP
ejpam-6743	74	10	kellner	kellner	PROPN
ejpam-6743	74	11	’s	’s	PART
ejpam-6743	74	12	[	[	X
ejpam-6743	74	13	6	6	NUM
ejpam-6743	74	14	]	]	X
ejpam-6743	74	15	integral	integral	ADJ
ejpam-6743	74	16	formula	formula	NOUN
ejpam-6743	74	17	relating	relate	VERB
ejpam-6743	74	18	the	the	DET
ejpam-6743	74	19	noncentral	noncentral	ADJ
ejpam-6743	74	20	tanny	tanny	PROPN
ejpam-6743	74	21	-	-	PUNCT
ejpam-6743	74	22	dowling	dowle	VERB
ejpam-6743	74	23	polynomials	polynomial	NOUN
ejpam-6743	74	24	with	with	ADP
ejpam-6743	74	25	the	the	DET
ejpam-6743	74	26	bernoulli	bernoulli	NOUN
ejpam-6743	74	27	polynomials	polynomial	NOUN
ejpam-6743	74	28	,	,	PUNCT
ejpam-6743	74	29	obtain	obtain	VERB
ejpam-6743	74	30	generalizations	generalization	NOUN
ejpam-6743	74	31	of	of	ADP
ejpam-6743	74	32	the	the	DET
ejpam-6743	74	33	worpitzky	worpitzky	NOUN
ejpam-6743	74	34	’s	’s	PART
ejpam-6743	75	1	[	[	X
ejpam-6743	75	2	7	7	NUM
ejpam-6743	75	3	]	]	ADV
ejpam-6743	75	4	explicit	explicit	ADJ
ejpam-6743	75	5	formulas	formula	NOUN
ejpam-6743	75	6	in	in	ADP
ejpam-6743	75	7	terms	term	NOUN
ejpam-6743	75	8	of	of	ADP
ejpam-6743	75	9	noncentral	noncentral	ADJ
ejpam-6743	75	10	whitney	whitney	NOUN
ejpam-6743	75	11	numbers	number	NOUN
ejpam-6743	75	12	of	of	ADP
ejpam-6743	75	13	the	the	DET
ejpam-6743	75	14	second	second	ADJ
ejpam-6743	75	15	kind	kind	NOUN
ejpam-6743	75	16	,	,	PUNCT
ejpam-6743	75	17	and	and	CCONJ
ejpam-6743	75	18	derive	derive	VERB
ejpam-6743	75	19	a	a	DET
ejpam-6743	75	20	generalizations	generalization	NOUN
ejpam-6743	75	21	of	of	ADP
ejpam-6743	75	22	boyadzhiev	boyadzhiev	NOUN
ejpam-6743	75	23	’s	’s	PART
ejpam-6743	76	1	[	[	X
ejpam-6743	76	2	5	5	NUM
ejpam-6743	76	3	]	]	PUNCT
ejpam-6743	76	4	identities	identity	NOUN
ejpam-6743	76	5	for	for	ADP
ejpam-6743	76	6	the	the	DET
ejpam-6743	76	7	noncentral	noncentral	ADJ
ejpam-6743	76	8	tanny	tanny	PROPN
ejpam-6743	76	9	-	-	PUNCT
ejpam-6743	76	10	dowling	dowle	VERB
ejpam-6743	76	11	polynomials	polynomial	NOUN
ejpam-6743	76	12	.	.	PUNCT
ejpam-6743	77	1	m.	m.	NOUN
ejpam-6743	77	2	m.	m.	NOUN
ejpam-6743	77	3	mangontarum	mangontarum	PROPN
ejpam-6743	77	4	et	et	PROPN
ejpam-6743	77	5	al	al	PROPN
ejpam-6743	77	6	.	.	PUNCT
ejpam-6743	77	7	/	/	SYM
ejpam-6743	77	8	eur	eur	PROPN
ejpam-6743	77	9	.	.	PUNCT
ejpam-6743	78	1	j.	j.	PROPN
ejpam-6743	78	2	pure	pure	PROPN
ejpam-6743	78	3	appl	appl	PROPN
ejpam-6743	78	4	.	.	PROPN
ejpam-6743	78	5	math	math	PROPN
ejpam-6743	78	6	,	,	PUNCT
ejpam-6743	78	7	18	18	NUM
ejpam-6743	78	8	(	(	PUNCT
ejpam-6743	78	9	4	4	NUM
ejpam-6743	78	10	)	)	PUNCT
ejpam-6743	78	11	(	(	PUNCT
ejpam-6743	78	12	2025	2025	NUM
ejpam-6743	78	13	)	)	PUNCT
ejpam-6743	78	14	,	,	PUNCT
ejpam-6743	78	15	6743	6743	NUM
ejpam-6743	78	16	4	4	NUM
ejpam-6743	78	17	of	of	ADP
ejpam-6743	78	18	8	8	NUM
ejpam-6743	78	19	2	2	NUM
ejpam-6743	78	20	.	.	PUNCT
ejpam-6743	78	21	results	result	NOUN
ejpam-6743	78	22	and	and	CCONJ
ejpam-6743	78	23	discussions	discussion	NOUN
ejpam-6743	78	24	the	the	DET
ejpam-6743	78	25	first	first	ADJ
ejpam-6743	78	26	theorem	theorem	NOUN
ejpam-6743	78	27	establishes	establish	VERB
ejpam-6743	78	28	a	a	DET
ejpam-6743	78	29	relationship	relationship	NOUN
ejpam-6743	78	30	between	between	ADP
ejpam-6743	78	31	the	the	DET
ejpam-6743	78	32	noncentral	noncentral	PROPN
ejpam-6743	78	33	tanny	tanny	PROPN
ejpam-6743	78	34	-	-	PUNCT
ejpam-6743	78	35	dowling	dowle	VERB
ejpam-6743	78	36	polynomials	polynomial	NOUN
ejpam-6743	78	37	and	and	CCONJ
ejpam-6743	78	38	the	the	DET
ejpam-6743	78	39	bernoulli	bernoulli	NOUN
ejpam-6743	78	40	polynomials	polynomial	NOUN
ejpam-6743	78	41	,	,	PUNCT
ejpam-6743	78	42	and	and	CCONJ
ejpam-6743	78	43	extends	extend	VERB
ejpam-6743	78	44	the	the	DET
ejpam-6743	78	45	result	result	NOUN
ejpam-6743	78	46	of	of	ADP
ejpam-6743	78	47	kellner	kellner	PROPN
ejpam-6743	78	48	[	[	X
ejpam-6743	78	49	6	6	NUM
ejpam-6743	78	50	]	]	PUNCT
ejpam-6743	78	51	presented	present	VERB
ejpam-6743	78	52	in	in	ADP
ejpam-6743	78	53	(	(	PUNCT
ejpam-6743	78	54	6	6	NUM
ejpam-6743	78	55	)	)	PUNCT
ejpam-6743	78	56	.	.	PUNCT
ejpam-6743	79	1	theorem	theorem	NOUN
ejpam-6743	79	2	1	1	NUM
ejpam-6743	79	3	.	.	X
ejpam-6743	80	1	for	for	ADP
ejpam-6743	80	2	any	any	DET
ejpam-6743	80	3	real	real	ADJ
ejpam-6743	80	4	number	number	NOUN
ejpam-6743	80	5	a	a	PRON
ejpam-6743	80	6	and	and	CCONJ
ejpam-6743	80	7	positive	positive	ADJ
ejpam-6743	80	8	integer	integer	NOUN
ejpam-6743	80	9	m	m	PROPN
ejpam-6743	80	10	,	,	PUNCT
ejpam-6743	80	11	the	the	DET
ejpam-6743	80	12	following	follow	VERB
ejpam-6743	80	13	integral	integral	ADJ
ejpam-6743	80	14	formula	formula	NOUN
ejpam-6743	80	15	over	over	ADP
ejpam-6743	80	16	the	the	DET
ejpam-6743	80	17	interval	interval	NOUN
ejpam-6743	80	18	[	[	X
ejpam-6743	80	19	−1	−1	NOUN
ejpam-6743	80	20	,	,	PUNCT
ejpam-6743	80	21	0	0	NUM
ejpam-6743	80	22	]	]	X
ejpam-6743	80	23	holds:∫	holds:∫	NOUN
ejpam-6743	80	24	0	0	NUM
ejpam-6743	80	25	−1	−1	NOUN
ejpam-6743	80	26	f̃m	f̃m	NOUN
ejpam-6743	80	27	,	,	PUNCT
ejpam-6743	80	28	a(n;mx)dx	a(n;mx)dx	VERB
ejpam-6743	80	29	=	=	PUNCT
ejpam-6743	80	30	mnbn	mnbn	X
ejpam-6743	80	31	(	(	PUNCT
ejpam-6743	80	32	−a	−a	NOUN
ejpam-6743	80	33	m	m	PROPN
ejpam-6743	80	34	)	)	PUNCT
ejpam-6743	80	35	.	.	PUNCT
ejpam-6743	81	1	(	(	PUNCT
ejpam-6743	81	2	15	15	X
ejpam-6743	81	3	)	)	PUNCT
ejpam-6743	81	4	proof	proof	NOUN
ejpam-6743	81	5	.	.	PUNCT
ejpam-6743	82	1	note	note	VERB
ejpam-6743	82	2	that	that	SCONJ
ejpam-6743	82	3	from	from	ADP
ejpam-6743	82	4	(	(	PUNCT
ejpam-6743	82	5	14	14	NUM
ejpam-6743	82	6	)	)	PUNCT
ejpam-6743	82	7	,	,	PUNCT
ejpam-6743	82	8	we	we	PRON
ejpam-6743	82	9	have	have	VERB
ejpam-6743	82	10	∞∑	∞∑	NUM
ejpam-6743	82	11	n=0	n=0	NUM
ejpam-6743	82	12	∫	∫	NOUN
ejpam-6743	82	13	0	0	NUM
ejpam-6743	82	14	−1	−1	NOUN
ejpam-6743	82	15	f̃m	f̃m	PROPN
ejpam-6743	82	16	,	,	PUNCT
ejpam-6743	82	17	a(n;mx	a(n;mx	ADJ
ejpam-6743	82	18	)	)	PUNCT
ejpam-6743	82	19	zn	zn	PROPN
ejpam-6743	82	20	n	n	X
ejpam-6743	82	21	!	!	PUNCT
ejpam-6743	82	22	dx	dx	PROPN
ejpam-6743	83	1	=	=	SYM
ejpam-6743	83	2	∫	∫	PROPN
ejpam-6743	83	3	0	0	NUM
ejpam-6743	83	4	−1	−1	NOUN
ejpam-6743	83	5	e−az	e−az	NOUN
ejpam-6743	83	6	1−	1−	NUM
ejpam-6743	83	7	xemz	xemz	NOUN
ejpam-6743	84	1	+	+	CCONJ
ejpam-6743	84	2	x	x	SYM
ejpam-6743	84	3	dx	dx	PROPN
ejpam-6743	84	4	.	.	PUNCT
ejpam-6743	85	1	(	(	PUNCT
ejpam-6743	85	2	16	16	X
ejpam-6743	85	3	)	)	PUNCT
ejpam-6743	85	4	evaluating	evaluate	VERB
ejpam-6743	85	5	the	the	DET
ejpam-6743	85	6	integral	integral	ADJ
ejpam-6743	85	7	and	and	CCONJ
ejpam-6743	85	8	by	by	ADP
ejpam-6743	85	9	(	(	PUNCT
ejpam-6743	85	10	7	7	NUM
ejpam-6743	85	11	)	)	PUNCT
ejpam-6743	85	12	,	,	PUNCT
ejpam-6743	85	13	we	we	PRON
ejpam-6743	85	14	get	get	VERB
ejpam-6743	85	15	∞∑	∞∑	NUM
ejpam-6743	85	16	n=0	n=0	NUM
ejpam-6743	85	17	∫	∫	NOUN
ejpam-6743	85	18	0	0	NUM
ejpam-6743	85	19	−1	−1	NOUN
ejpam-6743	85	20	f̃m	f̃m	PROPN
ejpam-6743	85	21	,	,	PUNCT
ejpam-6743	85	22	a(n;mx	a(n;mx	ADJ
ejpam-6743	85	23	)	)	PUNCT
ejpam-6743	85	24	zn	zn	PROPN
ejpam-6743	85	25	n	n	X
ejpam-6743	85	26	!	!	PUNCT
ejpam-6743	85	27	dx	dx	PROPN
ejpam-6743	86	1	=	=	SYM
ejpam-6743	86	2	−e−az	−e−az	PROPN
ejpam-6743	86	3	emz	emz	PROPN
ejpam-6743	86	4	−	−	PROPN
ejpam-6743	86	5	1	1	NUM
ejpam-6743	86	6	ln	ln	NOUN
ejpam-6743	86	7	|1−	|1−	NOUN
ejpam-6743	86	8	xemz	xemz	NOUN
ejpam-6743	86	9	+	+	CCONJ
ejpam-6743	86	10	x|	x|	PROPN
ejpam-6743	86	11	∣∣∣∣0	∣∣∣∣0	X
ejpam-6743	86	12	−1	−1	NOUN
ejpam-6743	86	13	=	=	SYM
ejpam-6743	86	14	−e−az	−e−az	NUM
ejpam-6743	86	15	emz	emz	PROPN
ejpam-6743	86	16	−	−	PROPN
ejpam-6743	86	17	1	1	NUM
ejpam-6743	86	18	(	(	PUNCT
ejpam-6743	86	19	−	−	PROPN
ejpam-6743	86	20	ln	ln	ADJ
ejpam-6743	86	21	|emz|	|emz|	NOUN
ejpam-6743	86	22	)	)	PUNCT
ejpam-6743	86	23	=	=	NOUN
ejpam-6743	86	24	mze−az	mze−az	NOUN
ejpam-6743	86	25	emz	emz	NOUN
ejpam-6743	86	26	−	−	NOUN
ejpam-6743	86	27	1	1	NUM
ejpam-6743	86	28	=	=	PUNCT
ejpam-6743	86	29	∞∑	∞∑	NUM
ejpam-6743	86	30	n=0	n=0	NUM
ejpam-6743	86	31	mnbn	mnbn	NOUN
ejpam-6743	86	32	(	(	PUNCT
ejpam-6743	86	33	−a	−a	NOUN
ejpam-6743	86	34	m	m	PROPN
ejpam-6743	86	35	)	)	PUNCT
ejpam-6743	86	36	zn	zn	PROPN
ejpam-6743	86	37	n	n	PRON
ejpam-6743	86	38	!	!	PUNCT
ejpam-6743	86	39	.	.	PUNCT
ejpam-6743	87	1	comparing	compare	VERB
ejpam-6743	87	2	the	the	DET
ejpam-6743	87	3	coefficients	coefficient	NOUN
ejpam-6743	87	4	of	of	ADP
ejpam-6743	87	5	zn	zn	PROPN
ejpam-6743	87	6	n	n	CCONJ
ejpam-6743	87	7	!	!	PROPN
ejpam-6743	87	8	completes	complete	VERB
ejpam-6743	87	9	the	the	DET
ejpam-6743	87	10	proof	proof	NOUN
ejpam-6743	87	11	.	.	PUNCT
ejpam-6743	88	1	remark	remark	NOUN
ejpam-6743	88	2	1	1	NUM
ejpam-6743	88	3	.	.	PUNCT
ejpam-6743	89	1	since	since	SCONJ
ejpam-6743	89	2	f̃1,0(n;x	f̃1,0(n;x	NOUN
ejpam-6743	89	3	)	)	PUNCT
ejpam-6743	89	4	=	=	SYM
ejpam-6743	89	5	wn(x	wn(x	X
ejpam-6743	89	6	)	)	PUNCT
ejpam-6743	89	7	,	,	PUNCT
ejpam-6743	89	8	then	then	ADV
ejpam-6743	89	9	by	by	ADP
ejpam-6743	89	10	setting	set	VERB
ejpam-6743	89	11	m	m	NOUN
ejpam-6743	89	12	=	=	SYM
ejpam-6743	89	13	1	1	NUM
ejpam-6743	89	14	and	and	CCONJ
ejpam-6743	89	15	a	a	DET
ejpam-6743	89	16	=	=	NOUN
ejpam-6743	89	17	0	0	NUM
ejpam-6743	89	18	in	in	ADP
ejpam-6743	89	19	theorem	theorem	NOUN
ejpam-6743	89	20	1	1	NUM
ejpam-6743	89	21	,	,	PUNCT
ejpam-6743	89	22	we	we	PRON
ejpam-6743	89	23	get	get	VERB
ejpam-6743	89	24	the	the	DET
ejpam-6743	89	25	integral	integral	ADJ
ejpam-6743	89	26	∫	∫	PROPN
ejpam-6743	89	27	0	0	NUM
ejpam-6743	89	28	−1	−1	NOUN
ejpam-6743	89	29	f̃1,0(n;x)dx	f̃1,0(n;x)dx	PROPN
ejpam-6743	89	30	=	=	SYM
ejpam-6743	89	31	bn(0	bn(0	PROPN
ejpam-6743	89	32	)	)	PUNCT
ejpam-6743	89	33	which	which	PRON
ejpam-6743	89	34	is	be	AUX
ejpam-6743	89	35	kellner	kellner	PROPN
ejpam-6743	89	36	’s	’s	PART
ejpam-6743	89	37	[	[	X
ejpam-6743	89	38	6	6	NUM
ejpam-6743	89	39	]	]	PUNCT
ejpam-6743	89	40	identity	identity	NOUN
ejpam-6743	89	41	in	in	ADP
ejpam-6743	89	42	(	(	PUNCT
ejpam-6743	89	43	6	6	NUM
ejpam-6743	89	44	)	)	PUNCT
ejpam-6743	89	45	.	.	PUNCT
ejpam-6743	90	1	now	now	ADV
ejpam-6743	90	2	,	,	PUNCT
ejpam-6743	90	3	observe	observe	VERB
ejpam-6743	90	4	that	that	SCONJ
ejpam-6743	90	5	from	from	ADP
ejpam-6743	90	6	(	(	PUNCT
ejpam-6743	90	7	13	13	NUM
ejpam-6743	90	8	)	)	PUNCT
ejpam-6743	90	9	,	,	PUNCT
ejpam-6743	90	10	mnbn	mnbn	X
ejpam-6743	90	11	(	(	PUNCT
ejpam-6743	90	12	−a	−a	NOUN
ejpam-6743	90	13	m	m	PROPN
ejpam-6743	90	14	)	)	PUNCT
ejpam-6743	91	1	=	=	SYM
ejpam-6743	91	2	∫	∫	PROPN
ejpam-6743	91	3	0	0	NUM
ejpam-6743	92	1	−1	−1	NOUN
ejpam-6743	92	2	(	(	PUNCT
ejpam-6743	92	3	n∑	n∑	PROPN
ejpam-6743	92	4	k=0	k=0	PROPN
ejpam-6743	92	5	mkk!w̃m	mkk!w̃m	PROPN
ejpam-6743	92	6	,	,	PUNCT
ejpam-6743	92	7	a(n	a(n	ADV
ejpam-6743	92	8	,	,	PUNCT
ejpam-6743	92	9	k)x	k)x	X
ejpam-6743	92	10	k	k	X
ejpam-6743	92	11	)	)	PUNCT
ejpam-6743	92	12	dx	dx	PROPN
ejpam-6743	93	1	=	=	SYM
ejpam-6743	93	2	n∑	n∑	PROPN
ejpam-6743	93	3	k=0	k=0	PROPN
ejpam-6743	93	4	mkk!w̃m	mkk!w̃m	PROPN
ejpam-6743	93	5	,	,	PUNCT
ejpam-6743	93	6	a(n	a(n	ADV
ejpam-6743	93	7	,	,	PUNCT
ejpam-6743	93	8	k	k	NOUN
ejpam-6743	93	9	)	)	PUNCT
ejpam-6743	93	10	∫	∫	PROPN
ejpam-6743	93	11	0	0	NUM
ejpam-6743	93	12	−1	−1	PROPN
ejpam-6743	93	13	xkdx	xkdx	PROPN
ejpam-6743	93	14	m.	m.	PROPN
ejpam-6743	93	15	m.	m.	NOUN
ejpam-6743	93	16	mangontarum	mangontarum	PROPN
ejpam-6743	93	17	et	et	PROPN
ejpam-6743	93	18	al	al	PROPN
ejpam-6743	93	19	.	.	PUNCT
ejpam-6743	93	20	/	/	SYM
ejpam-6743	93	21	eur	eur	PROPN
ejpam-6743	93	22	.	.	PUNCT
ejpam-6743	94	1	j.	j.	PROPN
ejpam-6743	94	2	pure	pure	PROPN
ejpam-6743	94	3	appl	appl	PROPN
ejpam-6743	94	4	.	.	PROPN
ejpam-6743	94	5	math	math	PROPN
ejpam-6743	94	6	,	,	PUNCT
ejpam-6743	94	7	18	18	NUM
ejpam-6743	94	8	(	(	PUNCT
ejpam-6743	94	9	4	4	NUM
ejpam-6743	94	10	)	)	PUNCT
ejpam-6743	94	11	(	(	PUNCT
ejpam-6743	94	12	2025	2025	NUM
ejpam-6743	94	13	)	)	PUNCT
ejpam-6743	94	14	,	,	PUNCT
ejpam-6743	94	15	6743	6743	NUM
ejpam-6743	94	16	5	5	NUM
ejpam-6743	94	17	of	of	ADP
ejpam-6743	94	18	8	8	NUM
ejpam-6743	94	19	=	=	SYM
ejpam-6743	94	20	n∑	n∑	PRON
ejpam-6743	94	21	k=0	k=0	PROPN
ejpam-6743	94	22	mkk!w̃m	mkk!w̃m	PROPN
ejpam-6743	94	23	,	,	PUNCT
ejpam-6743	94	24	a(n	a(n	ADV
ejpam-6743	94	25	,	,	PUNCT
ejpam-6743	94	26	k	k	NOUN
ejpam-6743	94	27	)	)	PUNCT
ejpam-6743	94	28	(	(	PUNCT
ejpam-6743	94	29	−1)k	−1)k	PROPN
ejpam-6743	94	30	k	k	PROPN
ejpam-6743	95	1	+	+	PROPN
ejpam-6743	95	2	1	1	NUM
ejpam-6743	95	3	.	.	PUNCT
ejpam-6743	96	1	thus	thus	ADV
ejpam-6743	96	2	,	,	PUNCT
ejpam-6743	96	3	we	we	PRON
ejpam-6743	96	4	have	have	VERB
ejpam-6743	96	5	the	the	DET
ejpam-6743	96	6	following	follow	VERB
ejpam-6743	96	7	corollary	corollary	ADJ
ejpam-6743	96	8	:	:	PUNCT
ejpam-6743	96	9	corollary	corollary	ADJ
ejpam-6743	96	10	1	1	NUM
ejpam-6743	96	11	.	.	PUNCT
ejpam-6743	97	1	the	the	DET
ejpam-6743	97	2	nth	nth	PROPN
ejpam-6743	97	3	bernoulli	bernoulli	PROPN
ejpam-6743	97	4	polynomial	polynomial	PROPN
ejpam-6743	97	5	bn	bn	PROPN
ejpam-6743	97	6	(	(	PUNCT
ejpam-6743	97	7	−a	−a	NOUN
ejpam-6743	97	8	m	m	NOUN
ejpam-6743	97	9	)	)	PUNCT
ejpam-6743	97	10	satisfies	satisfy	VERB
ejpam-6743	97	11	the	the	DET
ejpam-6743	97	12	following	follow	VERB
ejpam-6743	97	13	explicit	explicit	ADJ
ejpam-6743	97	14	formula	formula	NOUN
ejpam-6743	97	15	:	:	PUNCT
ejpam-6743	97	16	bn	bn	INTJ
ejpam-6743	97	17	(	(	PUNCT
ejpam-6743	97	18	−a	−a	NOUN
ejpam-6743	97	19	m	m	NOUN
ejpam-6743	97	20	)	)	PUNCT
ejpam-6743	98	1	=	=	PUNCT
ejpam-6743	98	2	n∑	n∑	PRON
ejpam-6743	98	3	k=0	k=0	PROPN
ejpam-6743	98	4	k!w̃m	k!w̃m	PROPN
ejpam-6743	98	5	,	,	PUNCT
ejpam-6743	98	6	a(n	a(n	NOUN
ejpam-6743	98	7	,	,	PUNCT
ejpam-6743	98	8	k	k	NOUN
ejpam-6743	98	9	)	)	PUNCT
ejpam-6743	98	10	(	(	PUNCT
ejpam-6743	98	11	−1)k	−1)k	PROPN
ejpam-6743	98	12	mn−k(k	mn−k(k	PROPN
ejpam-6743	98	13	+	+	CCONJ
ejpam-6743	98	14	1	1	NUM
ejpam-6743	98	15	)	)	PUNCT
ejpam-6743	98	16	.	.	PUNCT
ejpam-6743	99	1	(	(	PUNCT
ejpam-6743	99	2	17	17	NUM
ejpam-6743	99	3	)	)	PUNCT
ejpam-6743	99	4	remark	remark	NOUN
ejpam-6743	99	5	2	2	NUM
ejpam-6743	99	6	.	.	PUNCT
ejpam-6743	100	1	since	since	SCONJ
ejpam-6743	100	2	w̃1,0(n	w̃1,0(n	NOUN
ejpam-6743	100	3	,	,	PUNCT
ejpam-6743	100	4	k	k	NOUN
ejpam-6743	100	5	)	)	PUNCT
ejpam-6743	100	6	=	=	SYM
ejpam-6743	100	7	{	{	PUNCT
ejpam-6743	100	8	n	n	X
ejpam-6743	100	9	k	k	PROPN
ejpam-6743	100	10	}	}	PUNCT
ejpam-6743	100	11	,	,	PUNCT
ejpam-6743	100	12	then	then	ADV
ejpam-6743	100	13	when	when	SCONJ
ejpam-6743	100	14	m	m	VERB
ejpam-6743	100	15	=	=	SYM
ejpam-6743	100	16	1	1	NUM
ejpam-6743	100	17	and	and	CCONJ
ejpam-6743	100	18	a	a	DET
ejpam-6743	100	19	=	=	NOUN
ejpam-6743	100	20	0	0	NUM
ejpam-6743	100	21	in	in	ADP
ejpam-6743	100	22	corollary	corollary	ADJ
ejpam-6743	100	23	1	1	NUM
ejpam-6743	100	24	,	,	PUNCT
ejpam-6743	100	25	we	we	PRON
ejpam-6743	100	26	recover	recover	VERB
ejpam-6743	100	27	the	the	DET
ejpam-6743	100	28	bernoulli	bernoulli	NOUN
ejpam-6743	100	29	formula	formula	NOUN
ejpam-6743	100	30	in	in	ADP
ejpam-6743	100	31	(	(	PUNCT
ejpam-6743	100	32	9	9	NUM
ejpam-6743	100	33	)	)	PUNCT
ejpam-6743	100	34	.	.	PUNCT
ejpam-6743	101	1	moreover	moreover	ADV
ejpam-6743	101	2	,	,	PUNCT
ejpam-6743	101	3	using	use	VERB
ejpam-6743	101	4	the	the	DET
ejpam-6743	101	5	explicit	explicit	ADJ
ejpam-6743	101	6	formula	formula	NOUN
ejpam-6743	101	7	of	of	ADP
ejpam-6743	101	8	w̃m	w̃m	PROPN
ejpam-6743	101	9	,	,	PUNCT
ejpam-6743	101	10	a(n	a(n	ADV
ejpam-6743	101	11	,	,	PUNCT
ejpam-6743	101	12	k	k	NOUN
ejpam-6743	101	13	)	)	PUNCT
ejpam-6743	102	1	[	[	X
ejpam-6743	102	2	13	13	NUM
ejpam-6743	102	3	,	,	PUNCT
ejpam-6743	102	4	eq	eq	NOUN
ejpam-6743	102	5	.	.	PUNCT
ejpam-6743	103	1	(	(	PUNCT
ejpam-6743	103	2	38	38	NUM
ejpam-6743	103	3	)	)	PUNCT
ejpam-6743	103	4	]	]	PUNCT
ejpam-6743	103	5	given	give	VERB
ejpam-6743	103	6	by	by	ADP
ejpam-6743	103	7	w̃m	w̃m	PROPN
ejpam-6743	103	8	,	,	PUNCT
ejpam-6743	103	9	a(n	a(n	ADV
ejpam-6743	103	10	,	,	PUNCT
ejpam-6743	103	11	k	k	NOUN
ejpam-6743	103	12	)	)	PUNCT
ejpam-6743	103	13	=	=	SYM
ejpam-6743	103	14	1	1	NUM
ejpam-6743	103	15	mkk	mkk	PROPN
ejpam-6743	103	16	!	!	PUNCT
ejpam-6743	103	17	k∑	k∑	PROPN
ejpam-6743	104	1	j=0	j=0	PROPN
ejpam-6743	104	2	(	(	PUNCT
ejpam-6743	104	3	k	k	PROPN
ejpam-6743	104	4	j	j	PROPN
ejpam-6743	104	5	)	)	PUNCT
ejpam-6743	104	6	(	(	PUNCT
ejpam-6743	104	7	−1)k−j(mj	−1)k−j(mj	NOUN
ejpam-6743	104	8	−	−	PROPN
ejpam-6743	104	9	a)n	a)n	ADJ
ejpam-6743	104	10	,	,	PUNCT
ejpam-6743	104	11	equation	equation	NOUN
ejpam-6743	104	12	(	(	PUNCT
ejpam-6743	104	13	17	17	NUM
ejpam-6743	104	14	)	)	PUNCT
ejpam-6743	104	15	can	can	AUX
ejpam-6743	104	16	be	be	AUX
ejpam-6743	104	17	written	write	VERB
ejpam-6743	104	18	as	as	ADP
ejpam-6743	104	19	bn	bn	PROPN
ejpam-6743	104	20	(	(	PUNCT
ejpam-6743	104	21	−a	−a	NOUN
ejpam-6743	104	22	m	m	NOUN
ejpam-6743	104	23	)	)	PUNCT
ejpam-6743	105	1	=	=	SYM
ejpam-6743	105	2	n∑	n∑	PROPN
ejpam-6743	105	3	k=0	k=0	PROPN
ejpam-6743	105	4	k∑	k∑	PROPN
ejpam-6743	105	5	j=0	j=0	PROPN
ejpam-6743	105	6	(	(	PUNCT
ejpam-6743	105	7	k	k	PROPN
ejpam-6743	105	8	j	j	PROPN
ejpam-6743	105	9	)	)	PUNCT
ejpam-6743	105	10	(	(	PUNCT
ejpam-6743	105	11	mj	mj	PROPN
ejpam-6743	105	12	−	−	PROPN
ejpam-6743	105	13	a)n	a)n	NOUN
ejpam-6743	105	14	(	(	PUNCT
ejpam-6743	105	15	−1)j	−1)j	NOUN
ejpam-6743	105	16	mn(k	mn(k	NOUN
ejpam-6743	105	17	+	+	CCONJ
ejpam-6743	105	18	1	1	NUM
ejpam-6743	105	19	)	)	PUNCT
ejpam-6743	105	20	.	.	PUNCT
ejpam-6743	106	1	(	(	PUNCT
ejpam-6743	106	2	18	18	NUM
ejpam-6743	106	3	)	)	PUNCT
ejpam-6743	106	4	this	this	PRON
ejpam-6743	106	5	is	be	AUX
ejpam-6743	106	6	a	a	DET
ejpam-6743	106	7	generalization	generalization	NOUN
ejpam-6743	106	8	of	of	ADP
ejpam-6743	106	9	worpitzky	worpitzky	ADJ
ejpam-6743	106	10	’s	’s	PART
ejpam-6743	106	11	[	[	X
ejpam-6743	106	12	7	7	NUM
ejpam-6743	106	13	]	]	ADJ
ejpam-6743	106	14	identity	identity	NOUN
ejpam-6743	106	15	in	in	ADP
ejpam-6743	106	16	(	(	PUNCT
ejpam-6743	106	17	8)	8)	NUM
ejpam-6743	106	18	.	.	PUNCT
ejpam-6743	106	19	before	before	ADP
ejpam-6743	106	20	proceeding	proceeding	NOUN
ejpam-6743	106	21	,	,	PUNCT
ejpam-6743	106	22	note	note	VERB
ejpam-6743	106	23	that	that	SCONJ
ejpam-6743	106	24	by	by	ADP
ejpam-6743	106	25	induction	induction	NOUN
ejpam-6743	106	26	on	on	ADP
ejpam-6743	106	27	k	k	PROPN
ejpam-6743	106	28	,	,	PUNCT
ejpam-6743	106	29	it	it	PRON
ejpam-6743	106	30	is	be	AUX
ejpam-6743	106	31	easy	easy	ADJ
ejpam-6743	106	32	to	to	PART
ejpam-6743	106	33	show	show	VERB
ejpam-6743	106	34	that∫	that∫	NOUN
ejpam-6743	106	35	∞	∞	PROPN
ejpam-6743	106	36	0	0	PUNCT
ejpam-6743	107	1	xke−xdx	xke−xdx	PROPN
ejpam-6743	108	1	=	=	SYM
ejpam-6743	108	2	k	k	PROPN
ejpam-6743	108	3	!	!	PUNCT
ejpam-6743	108	4	.	.	PUNCT
ejpam-6743	109	1	(	(	PUNCT
ejpam-6743	109	2	19	19	NUM
ejpam-6743	109	3	)	)	PUNCT
ejpam-6743	109	4	also	also	ADV
ejpam-6743	109	5	,	,	PUNCT
ejpam-6743	109	6	the	the	DET
ejpam-6743	109	7	noncentral	noncentral	ADJ
ejpam-6743	109	8	dowling	dowling	NOUN
ejpam-6743	109	9	polynomials	polynomial	NOUN
ejpam-6743	109	10	[	[	X
ejpam-6743	109	11	13	13	NUM
ejpam-6743	109	12	,	,	PUNCT
ejpam-6743	109	13	eq	eq	NOUN
ejpam-6743	109	14	.	.	PUNCT
ejpam-6743	110	1	(	(	PUNCT
ejpam-6743	110	2	89	89	NUM
ejpam-6743	110	3	)	)	PUNCT
ejpam-6743	110	4	]	]	PUNCT
ejpam-6743	110	5	defined	define	VERB
ejpam-6743	110	6	by	by	ADP
ejpam-6743	110	7	d̃m	d̃m	PROPN
ejpam-6743	110	8	,	,	PUNCT
ejpam-6743	110	9	a(n;x	a(n;x	PROPN
ejpam-6743	110	10	)	)	PUNCT
ejpam-6743	111	1	=	=	SYM
ejpam-6743	111	2	n∑	n∑	PROPN
ejpam-6743	111	3	k=0	k=0	PROPN
ejpam-6743	111	4	w̃m	w̃m	PROPN
ejpam-6743	111	5	,	,	PUNCT
ejpam-6743	111	6	a(n	a(n	ADV
ejpam-6743	111	7	,	,	PUNCT
ejpam-6743	111	8	k)x	k)x	NOUN
ejpam-6743	111	9	k	k	X
ejpam-6743	111	10	satisfies	satisfy	VERB
ejpam-6743	111	11	the	the	DET
ejpam-6743	111	12	exponential	exponential	ADJ
ejpam-6743	111	13	generating	generating	NOUN
ejpam-6743	111	14	function	function	NOUN
ejpam-6743	111	15	[	[	X
ejpam-6743	111	16	13	13	NUM
ejpam-6743	111	17	,	,	PUNCT
ejpam-6743	111	18	eq	eq	NOUN
ejpam-6743	111	19	.	.	PUNCT
ejpam-6743	112	1	(	(	PUNCT
ejpam-6743	112	2	91	91	NUM
ejpam-6743	112	3	)	)	PUNCT
ejpam-6743	112	4	]	]	PUNCT
ejpam-6743	113	1	∞∑	∞∑	PRON
ejpam-6743	113	2	n=0	n=0	NUM
ejpam-6743	113	3	d̃m	d̃m	NOUN
ejpam-6743	113	4	,	,	PUNCT
ejpam-6743	113	5	a(n;x	a(n;x	PROPN
ejpam-6743	113	6	)	)	PUNCT
ejpam-6743	113	7	zn	zn	PROPN
ejpam-6743	113	8	n	n	X
ejpam-6743	113	9	!	!	PUNCT
ejpam-6743	113	10	=	=	PUNCT
ejpam-6743	114	1	e−az+(emz−a)(x	e−az+(emz−a)(x	PROPN
ejpam-6743	114	2	/	/	SYM
ejpam-6743	114	3	m	m	PROPN
ejpam-6743	114	4	)	)	PUNCT
ejpam-6743	114	5	.	.	PUNCT
ejpam-6743	115	1	(	(	PUNCT
ejpam-6743	115	2	20	20	NUM
ejpam-6743	115	3	)	)	PUNCT
ejpam-6743	115	4	the	the	DET
ejpam-6743	115	5	next	next	ADJ
ejpam-6743	115	6	theorem	theorem	NOUN
ejpam-6743	115	7	provides	provide	VERB
ejpam-6743	115	8	an	an	DET
ejpam-6743	115	9	integral	integral	ADJ
ejpam-6743	115	10	representation	representation	NOUN
ejpam-6743	115	11	of	of	ADP
ejpam-6743	115	12	the	the	DET
ejpam-6743	115	13	noncentral	noncentral	PROPN
ejpam-6743	115	14	tanny	tanny	PROPN
ejpam-6743	115	15	-	-	PUNCT
ejpam-6743	115	16	dowling	dowle	VERB
ejpam-6743	115	17	polynomials	polynomial	NOUN
ejpam-6743	115	18	in	in	ADP
ejpam-6743	115	19	terms	term	NOUN
ejpam-6743	115	20	of	of	ADP
ejpam-6743	115	21	noncentral	noncentral	ADJ
ejpam-6743	115	22	dowling	dowling	NOUN
ejpam-6743	115	23	polynomials	polynomial	NOUN
ejpam-6743	115	24	.	.	PUNCT
ejpam-6743	116	1	this	this	PRON
ejpam-6743	116	2	extends	extend	VERB
ejpam-6743	116	3	boyadzhiev	boyadzhiev	PROPN
ejpam-6743	116	4	’s	’s	PART
ejpam-6743	116	5	[	[	X
ejpam-6743	116	6	5	5	NUM
ejpam-6743	116	7	]	]	PUNCT
ejpam-6743	116	8	identity	identity	NOUN
ejpam-6743	116	9	for	for	ADP
ejpam-6743	116	10	geometric	geometric	ADJ
ejpam-6743	116	11	polynomials	polynomial	NOUN
ejpam-6743	116	12	in	in	ADP
ejpam-6743	116	13	(	(	PUNCT
ejpam-6743	116	14	11	11	NUM
ejpam-6743	116	15	)	)	PUNCT
ejpam-6743	116	16	.	.	PUNCT
ejpam-6743	117	1	m.	m.	NOUN
ejpam-6743	117	2	m.	m.	NOUN
ejpam-6743	117	3	mangontarum	mangontarum	PROPN
ejpam-6743	117	4	et	et	PROPN
ejpam-6743	117	5	al	al	PROPN
ejpam-6743	117	6	.	.	PUNCT
ejpam-6743	117	7	/	/	SYM
ejpam-6743	117	8	eur	eur	PROPN
ejpam-6743	117	9	.	.	PUNCT
ejpam-6743	118	1	j.	j.	PROPN
ejpam-6743	118	2	pure	pure	PROPN
ejpam-6743	118	3	appl	appl	PROPN
ejpam-6743	118	4	.	.	PROPN
ejpam-6743	118	5	math	math	PROPN
ejpam-6743	118	6	,	,	PUNCT
ejpam-6743	118	7	18	18	NUM
ejpam-6743	118	8	(	(	PUNCT
ejpam-6743	118	9	4	4	NUM
ejpam-6743	118	10	)	)	PUNCT
ejpam-6743	118	11	(	(	PUNCT
ejpam-6743	118	12	2025	2025	NUM
ejpam-6743	118	13	)	)	PUNCT
ejpam-6743	118	14	,	,	PUNCT
ejpam-6743	118	15	6743	6743	NUM
ejpam-6743	118	16	6	6	NUM
ejpam-6743	118	17	of	of	ADP
ejpam-6743	118	18	8	8	NUM
ejpam-6743	118	19	theorem	theorem	NOUN
ejpam-6743	118	20	2	2	NUM
ejpam-6743	118	21	.	.	PUNCT
ejpam-6743	119	1	the	the	DET
ejpam-6743	119	2	noncentral	noncentral	PROPN
ejpam-6743	119	3	tanny	tanny	PROPN
ejpam-6743	119	4	-	-	PUNCT
ejpam-6743	119	5	dowling	dowle	VERB
ejpam-6743	119	6	polynomials	polynomial	NOUN
ejpam-6743	119	7	satisfy	satisfy	VERB
ejpam-6743	119	8	the	the	DET
ejpam-6743	119	9	following	follow	VERB
ejpam-6743	119	10	relation	relation	NOUN
ejpam-6743	119	11	:	:	PUNCT
ejpam-6743	119	12	f̃m	f̃m	PROPN
ejpam-6743	119	13	,	,	PUNCT
ejpam-6743	119	14	a(n;x	a(n;x	PROPN
ejpam-6743	119	15	)	)	PUNCT
ejpam-6743	119	16	=	=	SYM
ejpam-6743	120	1	∫	∫	PROPN
ejpam-6743	120	2	∞	∞	PROPN
ejpam-6743	120	3	0	0	NUM
ejpam-6743	121	1	d̃m	d̃m	PROPN
ejpam-6743	121	2	,	,	PUNCT
ejpam-6743	121	3	a(n;xλ)e	a(n;xλ)e	PROPN
ejpam-6743	121	4	−λ	−λ	PROPN
ejpam-6743	121	5	dλ	dλ	PROPN
ejpam-6743	121	6	.	.	PUNCT
ejpam-6743	122	1	(	(	PUNCT
ejpam-6743	122	2	21	21	NUM
ejpam-6743	122	3	)	)	PUNCT
ejpam-6743	122	4	proof	proof	NOUN
ejpam-6743	122	5	.	.	PUNCT
ejpam-6743	123	1	by	by	ADP
ejpam-6743	123	2	definition,∫	definition,∫	X
ejpam-6743	123	3	∞	∞	PROPN
ejpam-6743	123	4	0	0	NUM
ejpam-6743	123	5	d̃m	d̃m	PROPN
ejpam-6743	123	6	,	,	PUNCT
ejpam-6743	123	7	a(n;xλ)e	a(n;xλ)e	PROPN
ejpam-6743	123	8	−λdλ	−λdλ	NOUN
ejpam-6743	124	1	=	=	SYM
ejpam-6743	125	1	∫	∫	PROPN
ejpam-6743	126	1	∞	∞	NUM
ejpam-6743	126	2	0	0	PUNCT
ejpam-6743	127	1	[	[	PUNCT
ejpam-6743	127	2	n∑	n∑	PROPN
ejpam-6743	127	3	k=0	k=0	PROPN
ejpam-6743	127	4	w̃m	w̃m	PROPN
ejpam-6743	127	5	,	,	PUNCT
ejpam-6743	127	6	a(n	a(n	ADV
ejpam-6743	127	7	,	,	PUNCT
ejpam-6743	127	8	k)x	k)x	X
ejpam-6743	127	9	kλk	kλk	X
ejpam-6743	127	10	]	]	PUNCT
ejpam-6743	127	11	e−λdλ	e−λdλ	NOUN
ejpam-6743	128	1	=	=	SYM
ejpam-6743	128	2	n∑	n∑	PROPN
ejpam-6743	128	3	k=0	k=0	PROPN
ejpam-6743	128	4	w̃m	w̃m	PROPN
ejpam-6743	128	5	,	,	PUNCT
ejpam-6743	128	6	a(n	a(n	ADV
ejpam-6743	128	7	,	,	PUNCT
ejpam-6743	128	8	k)x	k)x	X
ejpam-6743	128	9	k	k	X
ejpam-6743	128	10	∫	∫	PROPN
ejpam-6743	129	1	∞	∞	NUM
ejpam-6743	129	2	0	0	NUM
ejpam-6743	130	1	λke−λdλ	λke−λdλ	NOUN
ejpam-6743	130	2	.	.	PUNCT
ejpam-6743	131	1	using	use	VERB
ejpam-6743	131	2	(	(	PUNCT
ejpam-6743	131	3	19	19	NUM
ejpam-6743	131	4	)	)	PUNCT
ejpam-6743	131	5	and	and	CCONJ
ejpam-6743	131	6	then	then	ADV
ejpam-6743	131	7	(	(	PUNCT
ejpam-6743	131	8	13	13	NUM
ejpam-6743	131	9	)	)	PUNCT
ejpam-6743	131	10	yield∫	yield∫	NOUN
ejpam-6743	131	11	∞	∞	PROPN
ejpam-6743	131	12	0	0	NUM
ejpam-6743	132	1	d̃m	d̃m	PROPN
ejpam-6743	132	2	,	,	PUNCT
ejpam-6743	132	3	a(n;xλ)e	a(n;xλ)e	PROPN
ejpam-6743	132	4	−λdλ	−λdλ	NOUN
ejpam-6743	133	1	=	=	PUNCT
ejpam-6743	133	2	n∑	n∑	PROPN
ejpam-6743	133	3	k=0	k=0	PROPN
ejpam-6743	133	4	k!w̃m	k!w̃m	PROPN
ejpam-6743	133	5	,	,	PUNCT
ejpam-6743	133	6	a(n	a(n	ADV
ejpam-6743	133	7	,	,	PUNCT
ejpam-6743	133	8	k)x	k)x	X
ejpam-6743	133	9	k	k	X
ejpam-6743	133	10	=	=	SYM
ejpam-6743	133	11	f̃m	f̃m	PROPN
ejpam-6743	133	12	,	,	PUNCT
ejpam-6743	133	13	a(n;x	a(n;x	PROPN
ejpam-6743	133	14	)	)	PUNCT
ejpam-6743	133	15	which	which	PRON
ejpam-6743	133	16	is	be	AUX
ejpam-6743	133	17	the	the	DET
ejpam-6743	133	18	desired	desire	VERB
ejpam-6743	133	19	result	result	NOUN
ejpam-6743	133	20	.	.	PUNCT
ejpam-6743	134	1	remark	remark	VERB
ejpam-6743	134	2	3	3	NUM
ejpam-6743	134	3	.	.	PUNCT
ejpam-6743	135	1	since	since	SCONJ
ejpam-6743	135	2	d̃1,0(n;xλ	d̃1,0(n;xλ	VERB
ejpam-6743	135	3	)	)	PUNCT
ejpam-6743	135	4	=	=	SYM
ejpam-6743	135	5	ϕn(xλ	ϕn(xλ	PROPN
ejpam-6743	135	6	)	)	PUNCT
ejpam-6743	135	7	,	,	PUNCT
ejpam-6743	135	8	then	then	ADV
ejpam-6743	135	9	when	when	SCONJ
ejpam-6743	135	10	m	m	VERB
ejpam-6743	135	11	=	=	SYM
ejpam-6743	135	12	1	1	NUM
ejpam-6743	135	13	and	and	CCONJ
ejpam-6743	135	14	a	a	DET
ejpam-6743	135	15	=	=	SYM
ejpam-6743	135	16	0	0	NUM
ejpam-6743	135	17	,	,	PUNCT
ejpam-6743	135	18	the	the	DET
ejpam-6743	135	19	following	follow	VERB
ejpam-6743	135	20	relation	relation	NOUN
ejpam-6743	135	21	∫	∫	PROPN
ejpam-6743	135	22	∞	∞	PROPN
ejpam-6743	135	23	0	0	NUM
ejpam-6743	135	24	d̃1,0(n;xλ)e	d̃1,0(n;xλ)e	NOUN
ejpam-6743	135	25	−λ	−λ	PROPN
ejpam-6743	135	26	dλ	dλ	PROPN
ejpam-6743	135	27	=	=	SYM
ejpam-6743	135	28	f̃1,0(n;x	f̃1,0(n;x	PROPN
ejpam-6743	135	29	)	)	PUNCT
ejpam-6743	135	30	(	(	PUNCT
ejpam-6743	135	31	22	22	NUM
ejpam-6743	135	32	)	)	PUNCT
ejpam-6743	135	33	is	be	AUX
ejpam-6743	135	34	precisely	precisely	ADV
ejpam-6743	135	35	boyadzhiev	boyadzhiev	NOUN
ejpam-6743	135	36	’s	’s	PART
ejpam-6743	135	37	[	[	X
ejpam-6743	135	38	5	5	NUM
ejpam-6743	135	39	]	]	PUNCT
ejpam-6743	135	40	formula	formula	NOUN
ejpam-6743	135	41	in	in	ADP
ejpam-6743	135	42	(	(	PUNCT
ejpam-6743	135	43	11	11	NUM
ejpam-6743	135	44	)	)	PUNCT
ejpam-6743	135	45	.	.	PUNCT
ejpam-6743	136	1	finally	finally	ADV
ejpam-6743	136	2	,	,	PUNCT
ejpam-6743	136	3	the	the	DET
ejpam-6743	136	4	next	next	ADJ
ejpam-6743	136	5	theorem	theorem	NOUN
ejpam-6743	136	6	presents	present	VERB
ejpam-6743	136	7	another	another	DET
ejpam-6743	136	8	form	form	NOUN
ejpam-6743	136	9	of	of	ADP
ejpam-6743	136	10	exponential	exponential	ADJ
ejpam-6743	136	11	generating	generating	NOUN
ejpam-6743	136	12	function	function	NOUN
ejpam-6743	136	13	for	for	ADP
ejpam-6743	136	14	the	the	DET
ejpam-6743	136	15	polynomials	polynomial	NOUN
ejpam-6743	136	16	f̃m	f̃m	NOUN
ejpam-6743	136	17	,	,	PUNCT
ejpam-6743	136	18	a(n;x	a(n;x	PROPN
ejpam-6743	136	19	)	)	PUNCT
ejpam-6743	136	20	.	.	PUNCT
ejpam-6743	137	1	theorem	theorem	NOUN
ejpam-6743	137	2	3	3	NUM
ejpam-6743	137	3	.	.	PUNCT
ejpam-6743	138	1	the	the	DET
ejpam-6743	138	2	exponential	exponential	ADJ
ejpam-6743	138	3	generating	generating	NOUN
ejpam-6743	138	4	function	function	NOUN
ejpam-6743	138	5	of	of	ADP
ejpam-6743	138	6	the	the	DET
ejpam-6743	138	7	noncentral	noncentral	PROPN
ejpam-6743	138	8	tanny	tanny	PROPN
ejpam-6743	138	9	-	-	PUNCT
ejpam-6743	138	10	dowling	dowle	VERB
ejpam-6743	138	11	polynomial	polynomial	ADJ
ejpam-6743	138	12	satisfies	satisfie	NOUN
ejpam-6743	138	13	the	the	DET
ejpam-6743	138	14	following	follow	VERB
ejpam-6743	138	15	integral	integral	ADJ
ejpam-6743	138	16	formula	formula	NOUN
ejpam-6743	138	17	:	:	PUNCT
ejpam-6743	138	18	∞∑	∞∑	NUM
ejpam-6743	138	19	n=0	n=0	NUM
ejpam-6743	138	20	f̃m	f̃m	NOUN
ejpam-6743	138	21	,	,	PUNCT
ejpam-6743	138	22	a(n;x	a(n;x	PROPN
ejpam-6743	138	23	)	)	PUNCT
ejpam-6743	138	24	zn	zn	PROPN
ejpam-6743	138	25	n	n	X
ejpam-6743	138	26	!	!	PUNCT
ejpam-6743	139	1	=	=	SYM
ejpam-6743	139	2	∫	∫	PROPN
ejpam-6743	140	1	∞	∞	PROPN
ejpam-6743	140	2	0	0	NUM
ejpam-6743	140	3	exp	exp	NOUN
ejpam-6743	140	4	[	[	PUNCT
ejpam-6743	140	5	−az	−az	NOUN
ejpam-6743	140	6	−	−	PROPN
ejpam-6743	140	7	λ	λ	PROPN
ejpam-6743	140	8	(	(	PUNCT
ejpam-6743	140	9	1−	1−	NUM
ejpam-6743	140	10	x	x	SYM
ejpam-6743	140	11	m	m	PROPN
ejpam-6743	140	12	(	(	PUNCT
ejpam-6743	140	13	emz	emz	PROPN
ejpam-6743	140	14	−	−	PROPN
ejpam-6743	140	15	1	1	NUM
ejpam-6743	140	16	)	)	PUNCT
ejpam-6743	140	17	)	)	PUNCT
ejpam-6743	140	18	]	]	PUNCT
ejpam-6743	141	1	dλ	dλ	INTJ
ejpam-6743	141	2	.	.	PUNCT
ejpam-6743	142	1	(	(	PUNCT
ejpam-6743	142	2	23	23	X
ejpam-6743	142	3	)	)	PUNCT
ejpam-6743	142	4	proof	proof	NOUN
ejpam-6743	142	5	.	.	PUNCT
ejpam-6743	143	1	multiplying	multiply	VERB
ejpam-6743	143	2	both	both	DET
ejpam-6743	143	3	sides	side	NOUN
ejpam-6743	143	4	of	of	ADP
ejpam-6743	143	5	(	(	PUNCT
ejpam-6743	143	6	21	21	NUM
ejpam-6743	143	7	)	)	PUNCT
ejpam-6743	143	8	by	by	ADP
ejpam-6743	143	9	zn	zn	PROPN
ejpam-6743	143	10	n	n	CCONJ
ejpam-6743	143	11	!	!	PUNCT
ejpam-6743	143	12	and	and	CCONJ
ejpam-6743	143	13	summing	sum	VERB
ejpam-6743	143	14	over	over	ADP
ejpam-6743	143	15	n	n	PROPN
ejpam-6743	143	16	gives	give	VERB
ejpam-6743	143	17	∞∑	∞∑	PRON
ejpam-6743	143	18	n=0	n=0	NUM
ejpam-6743	143	19	f̃m	f̃m	NOUN
ejpam-6743	143	20	,	,	PUNCT
ejpam-6743	143	21	a(n;x	a(n;x	PROPN
ejpam-6743	143	22	)	)	PUNCT
ejpam-6743	143	23	zn	zn	PROPN
ejpam-6743	143	24	n	n	X
ejpam-6743	143	25	!	!	PUNCT
ejpam-6743	144	1	=	=	SYM
ejpam-6743	145	1	∫	∫	PROPN
ejpam-6743	146	1	∞	∞	NUM
ejpam-6743	146	2	0	0	NUM
ejpam-6743	146	3	(	(	PUNCT
ejpam-6743	146	4	e−λ	e−λ	NOUN
ejpam-6743	146	5	∞∑	∞∑	NUM
ejpam-6743	146	6	n=0	n=0	NUM
ejpam-6743	146	7	d̃m	d̃m	NOUN
ejpam-6743	146	8	,	,	PUNCT
ejpam-6743	146	9	a(n;xλ	a(n;xλ	PROPN
ejpam-6743	146	10	)	)	PUNCT
ejpam-6743	146	11	zn	zn	NOUN
ejpam-6743	146	12	n	n	PROPN
ejpam-6743	146	13	!	!	PUNCT
ejpam-6743	146	14	)	)	PUNCT
ejpam-6743	147	1	dλ	dλ	INTJ
ejpam-6743	147	2	.	.	PUNCT
ejpam-6743	148	1	by	by	ADP
ejpam-6743	148	2	apply	apply	VERB
ejpam-6743	148	3	(	(	PUNCT
ejpam-6743	148	4	20	20	NUM
ejpam-6743	148	5	)	)	PUNCT
ejpam-6743	148	6	in	in	ADP
ejpam-6743	148	7	the	the	DET
ejpam-6743	148	8	right	right	ADJ
ejpam-6743	148	9	-	-	PUNCT
ejpam-6743	148	10	hand	hand	NOUN
ejpam-6743	148	11	side	side	NOUN
ejpam-6743	148	12	,	,	PUNCT
ejpam-6743	148	13	∞∑	∞∑	ADJ
ejpam-6743	148	14	n=0	n=0	NUM
ejpam-6743	148	15	f̃m	f̃m	NOUN
ejpam-6743	148	16	,	,	PUNCT
ejpam-6743	148	17	a(n;x	a(n;x	PROPN
ejpam-6743	148	18	)	)	PUNCT
ejpam-6743	148	19	zn	zn	PROPN
ejpam-6743	148	20	n	n	X
ejpam-6743	148	21	!	!	PUNCT
ejpam-6743	149	1	=	=	SYM
ejpam-6743	149	2	∫	∫	PROPN
ejpam-6743	150	1	∞	∞	PROPN
ejpam-6743	150	2	0	0	NUM
ejpam-6743	150	3	e−az−λ(1−	e−az−λ(1−	PROPN
ejpam-6743	150	4	x	x	PUNCT
ejpam-6743	150	5	m	m	VERB
ejpam-6743	150	6	(	(	PUNCT
ejpam-6743	150	7	emz−1))dλ	emz−1))dλ	PROPN
ejpam-6743	150	8	.	.	PUNCT
ejpam-6743	151	1	m.	m.	NOUN
ejpam-6743	151	2	m.	m.	NOUN
ejpam-6743	151	3	mangontarum	mangontarum	PROPN
ejpam-6743	151	4	et	et	PROPN
ejpam-6743	151	5	al	al	PROPN
ejpam-6743	151	6	.	.	PUNCT
ejpam-6743	151	7	/	/	SYM
ejpam-6743	151	8	eur	eur	PROPN
ejpam-6743	151	9	.	.	PUNCT
ejpam-6743	152	1	j.	j.	PROPN
ejpam-6743	152	2	pure	pure	PROPN
ejpam-6743	152	3	appl	appl	PROPN
ejpam-6743	152	4	.	.	PROPN
ejpam-6743	152	5	math	math	PROPN
ejpam-6743	152	6	,	,	PUNCT
ejpam-6743	152	7	18	18	NUM
ejpam-6743	152	8	(	(	PUNCT
ejpam-6743	152	9	4	4	NUM
ejpam-6743	152	10	)	)	PUNCT
ejpam-6743	152	11	(	(	PUNCT
ejpam-6743	152	12	2025	2025	NUM
ejpam-6743	152	13	)	)	PUNCT
ejpam-6743	152	14	,	,	PUNCT
ejpam-6743	152	15	6743	6743	NUM
ejpam-6743	152	16	7	7	NUM
ejpam-6743	152	17	of	of	ADP
ejpam-6743	152	18	8	8	NUM
ejpam-6743	152	19	remark	remark	NOUN
ejpam-6743	152	20	4	4	NUM
ejpam-6743	152	21	.	.	PUNCT
ejpam-6743	153	1	when	when	SCONJ
ejpam-6743	153	2	m	m	VERB
ejpam-6743	153	3	=	=	SYM
ejpam-6743	153	4	1	1	NUM
ejpam-6743	153	5	and	and	CCONJ
ejpam-6743	153	6	a	a	DET
ejpam-6743	153	7	=	=	SYM
ejpam-6743	153	8	0	0	NUM
ejpam-6743	153	9	,	,	PUNCT
ejpam-6743	153	10	we	we	PRON
ejpam-6743	153	11	obtain∫	obtain∫	VERB
ejpam-6743	153	12	∞	∞	PROPN
ejpam-6743	153	13	0	0	NUM
ejpam-6743	154	1	e−(0)z−λ(1−x	e−(0)z−λ(1−x	PROPN
ejpam-6743	154	2	1	1	NUM
ejpam-6743	154	3	(	(	PUNCT
ejpam-6743	154	4	e(1)z−1)dλ	e(1)z−1)dλ	PROPN
ejpam-6743	154	5	=	=	SYM
ejpam-6743	155	1	∞∑	∞∑	NUM
ejpam-6743	155	2	n=0	n=0	NUM
ejpam-6743	155	3	f̃1,0(n;x	f̃1,0(n;x	PROPN
ejpam-6743	155	4	)	)	PUNCT
ejpam-6743	155	5	zn	zn	PROPN
ejpam-6743	155	6	n	n	CCONJ
ejpam-6743	155	7	!	!	PROPN
ejpam-6743	155	8	,	,	PUNCT
ejpam-6743	155	9	(	(	PUNCT
ejpam-6743	155	10	24	24	NUM
ejpam-6743	155	11	)	)	PUNCT
ejpam-6743	155	12	an	an	DET
ejpam-6743	155	13	equivalent	equivalent	ADJ
ejpam-6743	155	14	representation	representation	NOUN
ejpam-6743	155	15	of	of	ADP
ejpam-6743	155	16	boyadzhiev	boyadzhiev	NOUN
ejpam-6743	155	17	’s	’s	PART
ejpam-6743	155	18	[	[	X
ejpam-6743	155	19	5	5	NUM
ejpam-6743	155	20	]	]	PUNCT
ejpam-6743	155	21	exponential	exponential	ADJ
ejpam-6743	155	22	generating	generating	NOUN
ejpam-6743	155	23	function	function	NOUN
ejpam-6743	155	24	in	in	ADP
ejpam-6743	155	25	(	(	PUNCT
ejpam-6743	155	26	12	12	NUM
ejpam-6743	155	27	)	)	PUNCT
ejpam-6743	155	28	.	.	PUNCT
ejpam-6743	156	1	3	3	X
ejpam-6743	156	2	.	.	X
ejpam-6743	156	3	conclusion	conclusion	NOUN
ejpam-6743	156	4	the	the	DET
ejpam-6743	156	5	results	result	NOUN
ejpam-6743	156	6	of	of	ADP
ejpam-6743	156	7	this	this	DET
ejpam-6743	156	8	study	study	NOUN
ejpam-6743	156	9	demonstrate	demonstrate	VERB
ejpam-6743	156	10	the	the	DET
ejpam-6743	156	11	relationship	relationship	NOUN
ejpam-6743	156	12	between	between	ADP
ejpam-6743	156	13	the	the	DET
ejpam-6743	156	14	noncentral	noncentral	ADJ
ejpam-6743	156	15	tannydowling	tannydowling	NOUN
ejpam-6743	156	16	polynomials	polynomial	NOUN
ejpam-6743	156	17	,	,	PUNCT
ejpam-6743	156	18	a	a	DET
ejpam-6743	156	19	natural	natural	ADJ
ejpam-6743	156	20	generalization	generalization	NOUN
ejpam-6743	156	21	of	of	ADP
ejpam-6743	156	22	the	the	DET
ejpam-6743	156	23	bell	bell	NOUN
ejpam-6743	156	24	polynomials	polynomial	NOUN
ejpam-6743	156	25	,	,	PUNCT
ejpam-6743	156	26	and	and	CCONJ
ejpam-6743	156	27	the	the	DET
ejpam-6743	156	28	bernoulli	bernoulli	NOUN
ejpam-6743	156	29	polynomials	polynomial	NOUN
ejpam-6743	156	30	.	.	PUNCT
ejpam-6743	157	1	it	it	PRON
ejpam-6743	157	2	is	be	AUX
ejpam-6743	157	3	interesting	interesting	ADJ
ejpam-6743	157	4	to	to	PART
ejpam-6743	157	5	explore	explore	VERB
ejpam-6743	157	6	similar	similar	ADJ
ejpam-6743	157	7	connections	connection	NOUN
ejpam-6743	157	8	between	between	ADP
ejpam-6743	157	9	the	the	DET
ejpam-6743	157	10	noncentral	noncentral	ADJ
ejpam-6743	157	11	tannydowling	tannydowling	NOUN
ejpam-6743	157	12	polynomials	polynomial	NOUN
ejpam-6743	157	13	and	and	CCONJ
ejpam-6743	157	14	other	other	ADJ
ejpam-6743	157	15	families	family	NOUN
ejpam-6743	157	16	of	of	ADP
ejpam-6743	157	17	special	special	ADJ
ejpam-6743	157	18	polynomials	polynomial	NOUN
ejpam-6743	157	19	discussed	discuss	VERB
ejpam-6743	157	20	in	in	ADP
ejpam-6743	157	21	[	[	X
ejpam-6743	157	22	12	12	NUM
ejpam-6743	157	23	]	]	X
ejpam-6743	157	24	,	,	PUNCT
ejpam-6743	157	25	such	such	ADJ
ejpam-6743	157	26	as	as	ADP
ejpam-6743	157	27	the	the	DET
ejpam-6743	157	28	apostol	apostol	NOUN
ejpam-6743	157	29	-	-	PUNCT
ejpam-6743	157	30	bernoulli	bernoulli	NOUN
ejpam-6743	157	31	,	,	PUNCT
ejpam-6743	157	32	apostol	apostol	NOUN
ejpam-6743	157	33	-	-	PUNCT
ejpam-6743	157	34	euler	euler	NOUN
ejpam-6743	157	35	,	,	PUNCT
ejpam-6743	157	36	and	and	CCONJ
ejpam-6743	157	37	apostol	apostol	NOUN
ejpam-6743	157	38	-	-	PUNCT
ejpam-6743	157	39	genocchi	genocchi	PROPN
ejpam-6743	157	40	polynomials	polynomial	NOUN
ejpam-6743	157	41	.	.	PUNCT
ejpam-6743	158	1	the	the	DET
ejpam-6743	158	2	work	work	NOUN
ejpam-6743	158	3	of	of	ADP
ejpam-6743	158	4	mangontarum	mangontarum	NOUN
ejpam-6743	158	5	[	[	X
ejpam-6743	158	6	15	15	NUM
ejpam-6743	158	7	]	]	PUNCT
ejpam-6743	158	8	on	on	ADP
ejpam-6743	158	9	the	the	DET
ejpam-6743	158	10	r	r	NOUN
ejpam-6743	158	11	-	-	PUNCT
ejpam-6743	158	12	dowling	dowle	VERB
ejpam-6743	158	13	polynomials	polynomial	NOUN
ejpam-6743	158	14	may	may	AUX
ejpam-6743	158	15	offer	offer	VERB
ejpam-6743	158	16	valuable	valuable	ADJ
ejpam-6743	158	17	insights	insight	NOUN
ejpam-6743	158	18	for	for	ADP
ejpam-6743	158	19	establishing	establish	VERB
ejpam-6743	158	20	these	these	DET
ejpam-6743	158	21	extensions	extension	NOUN
ejpam-6743	158	22	.	.	PUNCT
ejpam-6743	159	1	acknowledgements	acknowledgement	NOUN
ejpam-6743	159	2	the	the	DET
ejpam-6743	159	3	authors	author	NOUN
ejpam-6743	159	4	express	express	VERB
ejpam-6743	159	5	their	their	PRON
ejpam-6743	159	6	sincere	sincere	ADJ
ejpam-6743	159	7	gratitude	gratitude	NOUN
ejpam-6743	159	8	to	to	ADP
ejpam-6743	159	9	the	the	DET
ejpam-6743	159	10	reviewers	reviewer	NOUN
ejpam-6743	159	11	and	and	CCONJ
ejpam-6743	159	12	the	the	DET
ejpam-6743	159	13	editor	editor	NOUN
ejpam-6743	159	14	for	for	ADP
ejpam-6743	159	15	their	their	PRON
ejpam-6743	159	16	comments	comment	NOUN
ejpam-6743	159	17	and	and	CCONJ
ejpam-6743	159	18	suggestions	suggestion	NOUN
ejpam-6743	159	19	,	,	PUNCT
ejpam-6743	159	20	which	which	PRON
ejpam-6743	159	21	have	have	AUX
ejpam-6743	159	22	improved	improve	VERB
ejpam-6743	159	23	the	the	DET
ejpam-6743	159	24	clarity	clarity	NOUN
ejpam-6743	159	25	of	of	ADP
ejpam-6743	159	26	this	this	DET
ejpam-6743	159	27	paper	paper	NOUN
ejpam-6743	159	28	.	.	PUNCT
ejpam-6743	160	1	this	this	DET
ejpam-6743	160	2	research	research	NOUN
ejpam-6743	160	3	was	be	AUX
ejpam-6743	160	4	funded	fund	VERB
ejpam-6743	160	5	by	by	ADP
ejpam-6743	160	6	the	the	DET
ejpam-6743	160	7	mathematical	mathematical	ADJ
ejpam-6743	160	8	society	society	NOUN
ejpam-6743	160	9	of	of	ADP
ejpam-6743	160	10	the	the	DET
ejpam-6743	160	11	philippines	philippine	NOUN
ejpam-6743	160	12	under	under	ADP
ejpam-6743	160	13	the	the	DET
ejpam-6743	160	14	2022	2022	NUM
ejpam-6743	160	15	msp	msp	PROPN
ejpam-6743	160	16	research	research	NOUN
ejpam-6743	160	17	grant	grant	NOUN
ejpam-6743	160	18	and	and	CCONJ
ejpam-6743	160	19	supported	support	VERB
ejpam-6743	160	20	by	by	ADP
ejpam-6743	160	21	the	the	DET
ejpam-6743	160	22	mindanao	mindanao	PROPN
ejpam-6743	160	23	state	state	PROPN
ejpam-6743	160	24	university	university	PROPN
ejpam-6743	160	25	under	under	ADP
ejpam-6743	160	26	special	special	ADJ
ejpam-6743	160	27	order	order	NOUN
ejpam-6743	160	28	no	no	NOUN
ejpam-6743	160	29	.	.	PUNCT
ejpam-6743	160	30	624	624	NUM
ejpam-6743	160	31	-	-	PUNCT
ejpam-6743	160	32	op	op	NOUN
ejpam-6743	160	33	,	,	PUNCT
ejpam-6743	160	34	s.	s.	PROPN
ejpam-6743	160	35	2022	2022	NUM
ejpam-6743	160	36	.	.	PUNCT
ejpam-6743	161	1	references	reference	NOUN
ejpam-6743	161	2	[	[	X
ejpam-6743	161	3	1	1	X
ejpam-6743	161	4	]	]	PUNCT
ejpam-6743	161	5	j.	j.	PROPN
ejpam-6743	161	6	stirling	stirling	PROPN
ejpam-6743	161	7	.	.	PUNCT
ejpam-6743	162	1	methodus	methodus	PROPN
ejpam-6743	162	2	differentialis	differentialis	X
ejpam-6743	162	3	sive	sive	ADJ
ejpam-6743	162	4	tractatus	tractatus	X
ejpam-6743	162	5	de	de	ADP
ejpam-6743	162	6	summatione	summatione	NOUN
ejpam-6743	162	7	et	et	NOUN
ejpam-6743	162	8	interpolatione	interpolatione	NOUN
ejpam-6743	162	9	serierum	serierum	PROPN
ejpam-6743	162	10	infinitarum	infinitarum	PROPN
ejpam-6743	162	11	.	.	PUNCT
ejpam-6743	163	1	london	london	PROPN
ejpam-6743	163	2	,	,	PUNCT
ejpam-6743	163	3	1730	1730	NUM
ejpam-6743	163	4	.	.	PUNCT
ejpam-6743	164	1	[	[	X
ejpam-6743	164	2	2	2	NUM
ejpam-6743	164	3	]	]	PUNCT
ejpam-6743	164	4	c.	c.	PROPN
ejpam-6743	164	5	chen	chen	PROPN
ejpam-6743	164	6	and	and	CCONJ
ejpam-6743	164	7	k.	k.	PROPN
ejpam-6743	164	8	kho	kho	PROPN
ejpam-6743	164	9	.	.	PUNCT
ejpam-6743	165	1	principles	principle	NOUN
ejpam-6743	165	2	and	and	CCONJ
ejpam-6743	165	3	techniques	technique	NOUN
ejpam-6743	165	4	in	in	ADP
ejpam-6743	165	5	combinatorics	combinatoric	NOUN
ejpam-6743	165	6	.	.	PUNCT
ejpam-6743	166	1	world	world	PROPN
ejpam-6743	166	2	scientific	scientific	PROPN
ejpam-6743	166	3	publishing	publishing	PROPN
ejpam-6743	166	4	co.	co.	PROPN
ejpam-6743	166	5	,	,	PUNCT
ejpam-6743	166	6	1992	1992	NUM
ejpam-6743	166	7	.	.	PUNCT
ejpam-6743	167	1	[	[	X
ejpam-6743	167	2	3	3	X
ejpam-6743	167	3	]	]	X
ejpam-6743	167	4	l.	l.	PROPN
ejpam-6743	167	5	comtet	comtet	PROPN
ejpam-6743	167	6	.	.	PUNCT
ejpam-6743	168	1	advanced	advanced	ADJ
ejpam-6743	168	2	combinatorics	combinatoric	NOUN
ejpam-6743	168	3	.	.	PUNCT
ejpam-6743	169	1	d.	d.	PROPN
ejpam-6743	169	2	reidel	reidel	PROPN
ejpam-6743	169	3	publishing	publishing	PROPN
ejpam-6743	169	4	co.	co.	PROPN
ejpam-6743	169	5	,	,	PUNCT
ejpam-6743	169	6	1974	1974	NUM
ejpam-6743	169	7	.	.	PUNCT
ejpam-6743	170	1	[	[	X
ejpam-6743	170	2	4	4	X
ejpam-6743	170	3	]	]	PUNCT
ejpam-6743	170	4	s.	s.	PROPN
ejpam-6743	170	5	m.	m.	PROPN
ejpam-6743	170	6	tanny	tanny	PROPN
ejpam-6743	170	7	.	.	PUNCT
ejpam-6743	171	1	on	on	ADP
ejpam-6743	171	2	some	some	DET
ejpam-6743	171	3	numbers	number	NOUN
ejpam-6743	171	4	related	relate	VERB
ejpam-6743	171	5	to	to	ADP
ejpam-6743	171	6	the	the	DET
ejpam-6743	171	7	bell	bell	NOUN
ejpam-6743	171	8	numbers	number	NOUN
ejpam-6743	171	9	.	.	PUNCT
ejpam-6743	172	1	canadian	canadian	ADJ
ejpam-6743	172	2	mathematical	mathematical	ADJ
ejpam-6743	172	3	bulletin	bulletin	NOUN
ejpam-6743	172	4	,	,	PUNCT
ejpam-6743	172	5	17:733–738	17:733–738	PROPN
ejpam-6743	172	6	,	,	PUNCT
ejpam-6743	172	7	1975	1975	NUM
ejpam-6743	172	8	.	.	PUNCT
ejpam-6743	173	1	[	[	X
ejpam-6743	173	2	5	5	X
ejpam-6743	173	3	]	]	PUNCT
ejpam-6743	173	4	k.	k.	PROPN
ejpam-6743	173	5	n.	n.	PROPN
ejpam-6743	173	6	boyadzhiev	boyadzhiev	PROPN
ejpam-6743	173	7	.	.	PUNCT
ejpam-6743	174	1	a	a	DET
ejpam-6743	174	2	series	series	NOUN
ejpam-6743	174	3	transformation	transformation	NOUN
ejpam-6743	174	4	formula	formula	NOUN
ejpam-6743	174	5	and	and	CCONJ
ejpam-6743	174	6	related	related	ADJ
ejpam-6743	174	7	polynomials	polynomial	NOUN
ejpam-6743	174	8	.	.	PUNCT
ejpam-6743	175	1	international	international	ADJ
ejpam-6743	175	2	journal	journal	PROPN
ejpam-6743	175	3	of	of	ADP
ejpam-6743	175	4	mathematics	mathematics	PROPN
ejpam-6743	175	5	and	and	CCONJ
ejpam-6743	175	6	mathematical	mathematical	ADJ
ejpam-6743	175	7	sciences	sciences	PROPN
ejpam-6743	175	8	,	,	PUNCT
ejpam-6743	175	9	23:3849–3866	23:3849–3866	NUM
ejpam-6743	175	10	,	,	PUNCT
ejpam-6743	175	11	2005	2005	NUM
ejpam-6743	175	12	.	.	PUNCT
ejpam-6743	176	1	[	[	X
ejpam-6743	176	2	6	6	NUM
ejpam-6743	176	3	]	]	PUNCT
ejpam-6743	176	4	b.	b.	PROPN
ejpam-6743	176	5	c.	c.	PROPN
ejpam-6743	176	6	kellner	kellner	PROPN
ejpam-6743	176	7	.	.	PUNCT
ejpam-6743	177	1	identities	identity	NOUN
ejpam-6743	177	2	between	between	ADP
ejpam-6743	177	3	polynomials	polynomial	NOUN
ejpam-6743	177	4	related	relate	VERB
ejpam-6743	177	5	to	to	ADP
ejpam-6743	177	6	stirling	stirling	NOUN
ejpam-6743	177	7	and	and	CCONJ
ejpam-6743	177	8	harmonic	harmonic	ADJ
ejpam-6743	177	9	number	number	NOUN
ejpam-6743	177	10	.	.	PUNCT
ejpam-6743	178	1	integers	integer	NOUN
ejpam-6743	178	2	,	,	PUNCT
ejpam-6743	178	3	14	14	NUM
ejpam-6743	178	4	:	:	PUNCT
ejpam-6743	178	5	a54	a54	PROPN
ejpam-6743	178	6	,	,	PUNCT
ejpam-6743	178	7	2014	2014	NUM
ejpam-6743	178	8	.	.	PUNCT
ejpam-6743	179	1	[	[	X
ejpam-6743	179	2	7	7	X
ejpam-6743	179	3	]	]	X
ejpam-6743	179	4	j.	j.	PROPN
ejpam-6743	179	5	worpitzky	worpitzky	PROPN
ejpam-6743	179	6	.	.	PUNCT
ejpam-6743	180	1	studien	studien	PROPN
ejpam-6743	180	2	über	über	PROPN
ejpam-6743	180	3	die	die	PROPN
ejpam-6743	180	4	bernoullischen	bernoullischen	PROPN
ejpam-6743	180	5	und	und	VERB
ejpam-6743	180	6	eulerschen	eulerschen	PROPN
ejpam-6743	180	7	zahlen	zahlen	PROPN
ejpam-6743	180	8	.	.	PUNCT
ejpam-6743	181	1	journal	journal	PROPN
ejpam-6743	181	2	für	für	AUX
ejpam-6743	181	3	die	die	VERB
ejpam-6743	181	4	reine	reine	PROPN
ejpam-6743	181	5	und	und	PROPN
ejpam-6743	181	6	angewandte	angewandte	PROPN
ejpam-6743	181	7	mathematik	mathematik	PROPN
ejpam-6743	181	8	,	,	PUNCT
ejpam-6743	181	9	94:203–232	94:203–232	PROPN
ejpam-6743	181	10	,	,	PUNCT
ejpam-6743	181	11	1883	1883	NUM
ejpam-6743	181	12	.	.	PUNCT
ejpam-6743	182	1	[	[	X
ejpam-6743	182	2	8	8	NUM
ejpam-6743	182	3	]	]	PUNCT
ejpam-6743	182	4	l.	l.	PROPN
ejpam-6743	182	5	kargın	kargın	PROPN
ejpam-6743	182	6	.	.	PUNCT
ejpam-6743	183	1	some	some	DET
ejpam-6743	183	2	formulae	formulae	NOUN
ejpam-6743	183	3	for	for	ADP
ejpam-6743	183	4	products	product	NOUN
ejpam-6743	183	5	of	of	ADP
ejpam-6743	183	6	geometric	geometric	ADJ
ejpam-6743	183	7	polynomials	polynomial	NOUN
ejpam-6743	183	8	with	with	ADP
ejpam-6743	183	9	applications	application	NOUN
ejpam-6743	183	10	.	.	PUNCT
ejpam-6743	184	1	journal	journal	NOUN
ejpam-6743	184	2	of	of	ADP
ejpam-6743	184	3	integer	integer	PROPN
ejpam-6743	184	4	sequences	sequence	NOUN
ejpam-6743	184	5	,	,	PUNCT
ejpam-6743	184	6	20	20	NUM
ejpam-6743	184	7	:	:	PUNCT
ejpam-6743	184	8	article	article	NOUN
ejpam-6743	184	9	17.4.4	17.4.4	NUM
ejpam-6743	184	10	,	,	PUNCT
ejpam-6743	184	11	2017	2017	NUM
ejpam-6743	184	12	.	.	PUNCT
ejpam-6743	185	1	m.	m.	NOUN
ejpam-6743	185	2	m.	m.	NOUN
ejpam-6743	185	3	mangontarum	mangontarum	PROPN
ejpam-6743	185	4	et	et	PROPN
ejpam-6743	185	5	al	al	PROPN
ejpam-6743	185	6	.	.	PUNCT
ejpam-6743	185	7	/	/	SYM
ejpam-6743	185	8	eur	eur	PROPN
ejpam-6743	185	9	.	.	PUNCT
ejpam-6743	186	1	j.	j.	PROPN
ejpam-6743	186	2	pure	pure	PROPN
ejpam-6743	186	3	appl	appl	PROPN
ejpam-6743	186	4	.	.	PROPN
ejpam-6743	186	5	math	math	PROPN
ejpam-6743	186	6	,	,	PUNCT
ejpam-6743	186	7	18	18	NUM
ejpam-6743	186	8	(	(	PUNCT
ejpam-6743	186	9	4	4	NUM
ejpam-6743	186	10	)	)	PUNCT
ejpam-6743	186	11	(	(	PUNCT
ejpam-6743	186	12	2025	2025	NUM
ejpam-6743	186	13	)	)	PUNCT
ejpam-6743	186	14	,	,	PUNCT
ejpam-6743	186	15	6743	6743	NUM
ejpam-6743	186	16	8	8	NUM
ejpam-6743	186	17	of	of	ADP
ejpam-6743	186	18	8	8	NUM
ejpam-6743	187	1	[	[	X
ejpam-6743	187	2	9	9	NUM
ejpam-6743	187	3	]	]	PUNCT
ejpam-6743	187	4	a.	a.	NOUN
ejpam-6743	187	5	dil	dil	NOUN
ejpam-6743	187	6	and	and	CCONJ
ejpam-6743	187	7	v.	v.	ADP
ejpam-6743	187	8	kurt	kurt	PROPN
ejpam-6743	187	9	.	.	PUNCT
ejpam-6743	188	1	investigating	investigate	VERB
ejpam-6743	188	2	geometric	geometric	ADJ
ejpam-6743	188	3	and	and	CCONJ
ejpam-6743	188	4	exponential	exponential	ADJ
ejpam-6743	188	5	polynomials	polynomial	NOUN
ejpam-6743	188	6	with	with	ADP
ejpam-6743	188	7	eulerseidel	eulerseidel	NOUN
ejpam-6743	188	8	matrices	matrix	NOUN
ejpam-6743	188	9	.	.	PUNCT
ejpam-6743	189	1	journal	journal	NOUN
ejpam-6743	189	2	of	of	ADP
ejpam-6743	189	3	integer	integer	PROPN
ejpam-6743	189	4	sequences	sequence	NOUN
ejpam-6743	189	5	,	,	PUNCT
ejpam-6743	189	6	14	14	NUM
ejpam-6743	189	7	:	:	PUNCT
ejpam-6743	189	8	article	article	NOUN
ejpam-6743	189	9	11.4.6	11.4.6	NUM
ejpam-6743	189	10	,	,	PUNCT
ejpam-6743	189	11	2011	2011	NUM
ejpam-6743	189	12	.	.	PUNCT
ejpam-6743	190	1	[	[	X
ejpam-6743	190	2	10	10	NUM
ejpam-6743	190	3	]	]	PUNCT
ejpam-6743	190	4	k.	k.	PROPN
ejpam-6743	190	5	n.	n.	PROPN
ejpam-6743	190	6	boyadzhiev	boyadzhiev	PROPN
ejpam-6743	190	7	and	and	CCONJ
ejpam-6743	190	8	a.	a.	NOUN
ejpam-6743	190	9	dil	dil	PROPN
ejpam-6743	190	10	.	.	PUNCT
ejpam-6743	191	1	geometric	geometric	ADJ
ejpam-6743	191	2	polynomials	polynomial	NOUN
ejpam-6743	191	3	:	:	PUNCT
ejpam-6743	191	4	properties	property	NOUN
ejpam-6743	191	5	and	and	CCONJ
ejpam-6743	191	6	applications	application	NOUN
ejpam-6743	191	7	to	to	ADP
ejpam-6743	191	8	series	series	NOUN
ejpam-6743	191	9	with	with	ADP
ejpam-6743	191	10	zeta	zeta	PROPN
ejpam-6743	191	11	values	value	NOUN
ejpam-6743	191	12	.	.	PUNCT
ejpam-6743	192	1	analysis	analysis	NOUN
ejpam-6743	192	2	mathematica	mathematica	PROPN
ejpam-6743	192	3	,	,	PUNCT
ejpam-6743	192	4	42:203–224	42:203–224	PROPN
ejpam-6743	192	5	,	,	PUNCT
ejpam-6743	192	6	2016	2016	NUM
ejpam-6743	192	7	.	.	PUNCT
ejpam-6743	193	1	[	[	X
ejpam-6743	193	2	11	11	NUM
ejpam-6743	193	3	]	]	PUNCT
ejpam-6743	193	4	l.	l.	PROPN
ejpam-6743	193	5	kargın	kargın	PROPN
ejpam-6743	193	6	and	and	CCONJ
ejpam-6743	193	7	b.	b.	PROPN
ejpam-6743	193	8	çekim	çekim	PROPN
ejpam-6743	193	9	.	.	PUNCT
ejpam-6743	194	1	higher	high	ADJ
ejpam-6743	194	2	order	order	NOUN
ejpam-6743	194	3	generalized	generalize	VERB
ejpam-6743	194	4	geometric	geometric	ADJ
ejpam-6743	194	5	polynomials	polynomial	NOUN
ejpam-6743	194	6	.	.	PUNCT
ejpam-6743	195	1	turkish	turkish	ADJ
ejpam-6743	195	2	journal	journal	NOUN
ejpam-6743	195	3	of	of	ADP
ejpam-6743	195	4	mathematics	mathematic	NOUN
ejpam-6743	195	5	,	,	PUNCT
ejpam-6743	195	6	42:887–903	42:887–903	PROPN
ejpam-6743	195	7	,	,	PUNCT
ejpam-6743	195	8	2018	2018	NUM
ejpam-6743	195	9	.	.	PUNCT
ejpam-6743	196	1	[	[	X
ejpam-6743	196	2	12	12	NUM
ejpam-6743	196	3	]	]	X
ejpam-6743	196	4	w.	w.	PROPN
ejpam-6743	196	5	ramı́rez	ramı́rez	PROPN
ejpam-6743	196	6	and	and	CCONJ
ejpam-6743	196	7	c.	c.	PROPN
ejpam-6743	196	8	cesarano	cesarano	PROPN
ejpam-6743	196	9	.	.	PUNCT
ejpam-6743	197	1	some	some	DET
ejpam-6743	197	2	new	new	ADJ
ejpam-6743	197	3	classes	class	NOUN
ejpam-6743	197	4	of	of	ADP
ejpam-6743	197	5	degenerated	degenerated	ADJ
ejpam-6743	197	6	generalized	generalized	ADJ
ejpam-6743	197	7	apostolbernoulli	apostolbernoulli	NOUN
ejpam-6743	197	8	,	,	PUNCT
ejpam-6743	197	9	apostol	apostol	NOUN
ejpam-6743	197	10	-	-	PUNCT
ejpam-6743	197	11	euler	euler	NOUN
ejpam-6743	197	12	and	and	CCONJ
ejpam-6743	197	13	apostol	apostol	NOUN
ejpam-6743	197	14	-	-	PUNCT
ejpam-6743	197	15	genocchi	genocchi	PROPN
ejpam-6743	197	16	polynomials	polynomial	NOUN
ejpam-6743	197	17	.	.	PUNCT
ejpam-6743	198	1	carpathian	carpathian	ADJ
ejpam-6743	198	2	mathematical	mathematical	ADJ
ejpam-6743	198	3	publications	publication	NOUN
ejpam-6743	198	4	,	,	PUNCT
ejpam-6743	198	5	14:354–363	14:354–363	NUM
ejpam-6743	198	6	,	,	PUNCT
ejpam-6743	198	7	2022	2022	NUM
ejpam-6743	198	8	.	.	PUNCT
ejpam-6743	199	1	[	[	X
ejpam-6743	199	2	13	13	NUM
ejpam-6743	199	3	]	]	PUNCT
ejpam-6743	199	4	m.	m.	NOUN
ejpam-6743	199	5	m.	m.	NOUN
ejpam-6743	199	6	mangontarum	mangontarum	PROPN
ejpam-6743	199	7	,	,	PUNCT
ejpam-6743	199	8	o.	o.	PROPN
ejpam-6743	199	9	i.	i.	PROPN
ejpam-6743	199	10	cauntongan	cauntongan	PROPN
ejpam-6743	199	11	,	,	PUNCT
ejpam-6743	199	12	and	and	CCONJ
ejpam-6743	199	13	a.	a.	NOUN
ejpam-6743	199	14	p.	p.	NOUN
ejpam-6743	199	15	macodi	macodi	NOUN
ejpam-6743	199	16	-	-	PUNCT
ejpam-6743	199	17	ringia	ringia	ADJ
ejpam-6743	199	18	.	.	PUNCT
ejpam-6743	200	1	the	the	DET
ejpam-6743	200	2	noncentral	noncentral	ADJ
ejpam-6743	200	3	version	version	NOUN
ejpam-6743	200	4	of	of	ADP
ejpam-6743	200	5	the	the	DET
ejpam-6743	200	6	whitney	whitney	NOUN
ejpam-6743	200	7	numbers	number	NOUN
ejpam-6743	200	8	:	:	PUNCT
ejpam-6743	200	9	a	a	DET
ejpam-6743	200	10	comprehensive	comprehensive	ADJ
ejpam-6743	200	11	study	study	NOUN
ejpam-6743	200	12	.	.	PUNCT
ejpam-6743	201	1	international	international	ADJ
ejpam-6743	201	2	journal	journal	PROPN
ejpam-6743	201	3	of	of	ADP
ejpam-6743	201	4	mathematics	mathematics	PROPN
ejpam-6743	201	5	and	and	CCONJ
ejpam-6743	201	6	mathematical	mathematical	ADJ
ejpam-6743	201	7	sciences	science	NOUN
ejpam-6743	201	8	,	,	PUNCT
ejpam-6743	201	9	pages	page	NOUN
ejpam-6743	201	10	article	article	NOUN
ejpam-6743	201	11	i	i	PROPN
ejpam-6743	201	12	d	d	PROPN
ejpam-6743	201	13	6206207	6206207	NUM
ejpam-6743	201	14	,	,	PUNCT
ejpam-6743	201	15	16	16	NUM
ejpam-6743	201	16	pages	page	NOUN
ejpam-6743	201	17	,	,	PUNCT
ejpam-6743	201	18	2016	2016	NUM
ejpam-6743	201	19	.	.	PUNCT
ejpam-6743	202	1	[	[	X
ejpam-6743	202	2	14	14	NUM
ejpam-6743	202	3	]	]	PUNCT
ejpam-6743	202	4	m.	m.	NOUN
ejpam-6743	202	5	m.	m.	NOUN
ejpam-6743	202	6	mangontarum	mangontarum	PROPN
ejpam-6743	202	7	and	and	CCONJ
ejpam-6743	202	8	n.	n.	PROPN
ejpam-6743	202	9	m.	m.	NOUN
ejpam-6743	202	10	madid	madid	VERB
ejpam-6743	202	11	.	.	PUNCT
ejpam-6743	203	1	on	on	ADP
ejpam-6743	203	2	noncentral	noncentral	PROPN
ejpam-6743	203	3	tanny	tanny	PROPN
ejpam-6743	203	4	-	-	PUNCT
ejpam-6743	203	5	dowling	dowle	VERB
ejpam-6743	203	6	polynomials	polynomial	NOUN
ejpam-6743	203	7	and	and	CCONJ
ejpam-6743	203	8	generalizations	generalization	NOUN
ejpam-6743	203	9	of	of	ADP
ejpam-6743	203	10	some	some	DET
ejpam-6743	203	11	formulas	formula	NOUN
ejpam-6743	203	12	for	for	ADP
ejpam-6743	203	13	geometric	geometric	ADJ
ejpam-6743	203	14	polynomials	polynomial	NOUN
ejpam-6743	203	15	.	.	PUNCT
ejpam-6743	204	1	journal	journal	NOUN
ejpam-6743	204	2	of	of	ADP
ejpam-6743	204	3	integer	integer	PROPN
ejpam-6743	204	4	sequences	sequence	NOUN
ejpam-6743	204	5	,	,	PUNCT
ejpam-6743	204	6	24	24	NUM
ejpam-6743	204	7	:	:	PUNCT
ejpam-6743	204	8	article	article	NOUN
ejpam-6743	204	9	21.2.4	21.2.4	NUM
ejpam-6743	204	10	,	,	PUNCT
ejpam-6743	204	11	2021	2021	NUM
ejpam-6743	204	12	.	.	PUNCT
ejpam-6743	205	1	[	[	X
ejpam-6743	205	2	15	15	NUM
ejpam-6743	205	3	]	]	X
ejpam-6743	205	4	m.	m.	NOUN
ejpam-6743	205	5	m.	m.	NOUN
ejpam-6743	205	6	mangontarum	mangontarum	PROPN
ejpam-6743	205	7	.	.	PUNCT
ejpam-6743	206	1	bivariate	bivariate	ADJ
ejpam-6743	206	2	extension	extension	NOUN
ejpam-6743	206	3	of	of	ADP
ejpam-6743	206	4	the	the	DET
ejpam-6743	206	5	r	r	NOUN
ejpam-6743	206	6	-	-	PUNCT
ejpam-6743	206	7	dowling	dowle	VERB
ejpam-6743	206	8	polynomials	polynomial	NOUN
ejpam-6743	206	9	and	and	CCONJ
ejpam-6743	206	10	two	two	NUM
ejpam-6743	206	11	forms	form	NOUN
ejpam-6743	206	12	of	of	ADP
ejpam-6743	206	13	generalized	generalized	ADJ
ejpam-6743	206	14	spivey	spivey	PROPN
ejpam-6743	206	15	’s	’s	PART
ejpam-6743	206	16	formula	formula	NOUN
ejpam-6743	206	17	.	.	PUNCT
ejpam-6743	207	1	indian	indian	ADJ
ejpam-6743	207	2	journal	journal	PROPN
ejpam-6743	207	3	of	of	ADP
ejpam-6743	207	4	pure	pure	ADJ
ejpam-6743	207	5	and	and	CCONJ
ejpam-6743	207	6	applied	applied	ADJ
ejpam-6743	207	7	mathematics	mathematic	NOUN
ejpam-6743	207	8	,	,	PUNCT
ejpam-6743	207	9	54:703–712	54:703–712	PROPN
ejpam-6743	207	10	,	,	PUNCT
ejpam-6743	207	11	2023	2023	NUM
ejpam-6743	207	12	.	.	PUNCT