id	sid	tid	token	lemma	pos
ejpam-5275	1	1	european	european	PROPN
ejpam-5275	1	2	journal	journal	PROPN
ejpam-5275	1	3	of	of	ADP
ejpam-5275	1	4	pure	pure	ADJ
ejpam-5275	1	5	and	and	CCONJ
ejpam-5275	1	6	applied	apply	VERB
ejpam-5275	1	7	mathematics	mathematic	NOUN
ejpam-5275	1	8	vol	vol	NOUN
ejpam-5275	1	9	.	.	PROPN
ejpam-5275	2	1	17	17	NUM
ejpam-5275	2	2	,	,	PUNCT
ejpam-5275	2	3	no	no	INTJ
ejpam-5275	2	4	.	.	NOUN
ejpam-5275	2	5	3	3	NUM
ejpam-5275	2	6	,	,	PUNCT
ejpam-5275	2	7	2024	2024	NUM
ejpam-5275	2	8	,	,	PUNCT
ejpam-5275	2	9	2336	2336	NUM
ejpam-5275	2	10	-	-	SYM
ejpam-5275	2	11	2348	2348	NUM
ejpam-5275	2	12	issn	issn	PROPN
ejpam-5275	2	13	1307	1307	NUM
ejpam-5275	2	14	-	-	SYM
ejpam-5275	2	15	5543	5543	NUM
ejpam-5275	2	16	–	–	PUNCT
ejpam-5275	2	17	ejpam.com	ejpam.com	X
ejpam-5275	2	18	published	publish	VERB
ejpam-5275	2	19	by	by	ADP
ejpam-5275	2	20	new	new	PROPN
ejpam-5275	2	21	york	york	PROPN
ejpam-5275	2	22	business	business	PROPN
ejpam-5275	2	23	global	global	ADJ
ejpam-5275	2	24	probabilistic	probabilistic	ADJ
ejpam-5275	2	25	type	type	NOUN
ejpam-5275	2	26	2	2	NUM
ejpam-5275	2	27	poly	poly	ADJ
ejpam-5275	2	28	-	-	PUNCT
ejpam-5275	2	29	bernoulli	bernoulli	NOUN
ejpam-5275	2	30	polynomials	polynomial	NOUN
ejpam-5275	2	31	si	si	PROPN
ejpam-5275	2	32	hyeon	hyeon	PROPN
ejpam-5275	2	33	lee1	lee1	PROPN
ejpam-5275	2	34	,	,	PUNCT
ejpam-5275	2	35	∗	∗	NOUN
ejpam-5275	2	36	,	,	PUNCT
ejpam-5275	2	37	li	li	PROPN
ejpam-5275	2	38	chen2	chen2	PROPN
ejpam-5275	2	39	,	,	PUNCT
ejpam-5275	2	40	wonjoo	wonjoo	PROPN
ejpam-5275	2	41	kim3	kim3	PROPN
ejpam-5275	2	42	1	1	NUM
ejpam-5275	2	43	kwangwoon	kwangwoon	NOUN
ejpam-5275	2	44	university	university	NOUN
ejpam-5275	2	45	,	,	PUNCT
ejpam-5275	2	46	seoul	seoul	PROPN
ejpam-5275	2	47	139	139	NUM
ejpam-5275	2	48	-	-	SYM
ejpam-5275	2	49	701	701	NUM
ejpam-5275	2	50	,	,	PUNCT
ejpam-5275	2	51	republic	republic	NOUN
ejpam-5275	2	52	of	of	ADP
ejpam-5275	2	53	korea	korea	PROPN
ejpam-5275	2	54	2	2	NUM
ejpam-5275	2	55	school	school	NOUN
ejpam-5275	2	56	of	of	ADP
ejpam-5275	2	57	mathematics	mathematic	NOUN
ejpam-5275	2	58	,	,	PUNCT
ejpam-5275	2	59	xi’an	xi’an	PROPN
ejpam-5275	2	60	university	university	PROPN
ejpam-5275	2	61	of	of	ADP
ejpam-5275	2	62	finance	finance	NOUN
ejpam-5275	2	63	and	and	CCONJ
ejpam-5275	2	64	economics	economic	NOUN
ejpam-5275	2	65	,	,	PUNCT
ejpam-5275	2	66	xi’an	xi’an	PROPN
ejpam-5275	2	67	710100	710100	NUM
ejpam-5275	2	68	,	,	PUNCT
ejpam-5275	2	69	china	china	PROPN
ejpam-5275	2	70	3	3	NUM
ejpam-5275	2	71	department	department	NOUN
ejpam-5275	2	72	of	of	ADP
ejpam-5275	2	73	applied	apply	VERB
ejpam-5275	2	74	mathematics	mathematic	NOUN
ejpam-5275	2	75	,	,	PUNCT
ejpam-5275	2	76	kyunghee	kyunghee	PROPN
ejpam-5275	2	77	university	university	PROPN
ejpam-5275	2	78	,	,	PUNCT
ejpam-5275	2	79	seoul	seoul	PROPN
ejpam-5275	2	80	,	,	PUNCT
ejpam-5275	2	81	republic	republic	NOUN
ejpam-5275	2	82	of	of	ADP
ejpam-5275	2	83	korea	korea	PROPN
ejpam-5275	2	84	abstract	abstract	PROPN
ejpam-5275	2	85	.	.	PUNCT
ejpam-5275	3	1	the	the	DET
ejpam-5275	3	2	main	main	ADJ
ejpam-5275	3	3	purpose	purpose	NOUN
ejpam-5275	3	4	of	of	ADP
ejpam-5275	3	5	this	this	DET
ejpam-5275	3	6	article	article	NOUN
ejpam-5275	3	7	is	be	AUX
ejpam-5275	3	8	to	to	PART
ejpam-5275	3	9	introduce	introduce	VERB
ejpam-5275	3	10	the	the	DET
ejpam-5275	3	11	probabilistic	probabilistic	ADJ
ejpam-5275	3	12	type	type	NOUN
ejpam-5275	3	13	2	2	NUM
ejpam-5275	3	14	poly	poly	ADJ
ejpam-5275	3	15	-	-	PUNCT
ejpam-5275	3	16	bernoulli	bernoulli	NOUN
ejpam-5275	3	17	polynomials	polynomial	NOUN
ejpam-5275	3	18	under	under	ADP
ejpam-5275	3	19	the	the	DET
ejpam-5275	3	20	condition	condition	NOUN
ejpam-5275	3	21	that	that	SCONJ
ejpam-5275	3	22	y	y	PROPN
ejpam-5275	3	23	is	be	AUX
ejpam-5275	3	24	a	a	DET
ejpam-5275	3	25	random	random	ADJ
ejpam-5275	3	26	variable	variable	NOUN
ejpam-5275	3	27	.	.	PUNCT
ejpam-5275	4	1	this	this	PRON
ejpam-5275	4	2	means	mean	VERB
ejpam-5275	4	3	that	that	SCONJ
ejpam-5275	4	4	we	we	PRON
ejpam-5275	4	5	will	will	AUX
ejpam-5275	4	6	consider	consider	VERB
ejpam-5275	4	7	the	the	DET
ejpam-5275	4	8	probabilistic	probabilistic	ADJ
ejpam-5275	4	9	extension	extension	NOUN
ejpam-5275	4	10	of	of	ADP
ejpam-5275	4	11	the	the	DET
ejpam-5275	4	12	type	type	NOUN
ejpam-5275	4	13	2	2	NUM
ejpam-5275	4	14	poly	poly	ADJ
ejpam-5275	4	15	-	-	PUNCT
ejpam-5275	4	16	bernoulli	bernoulli	NOUN
ejpam-5275	4	17	polynomials	polynomial	NOUN
ejpam-5275	4	18	and	and	CCONJ
ejpam-5275	4	19	study	study	VERB
ejpam-5275	4	20	to	to	PART
ejpam-5275	4	21	obtain	obtain	VERB
ejpam-5275	4	22	some	some	DET
ejpam-5275	4	23	new	new	ADJ
ejpam-5275	4	24	results	result	NOUN
ejpam-5275	4	25	.	.	PUNCT
ejpam-5275	5	1	furthermore	furthermore	ADV
ejpam-5275	5	2	,	,	PUNCT
ejpam-5275	5	3	we	we	PRON
ejpam-5275	5	4	also	also	ADV
ejpam-5275	5	5	define	define	VERB
ejpam-5275	5	6	the	the	DET
ejpam-5275	5	7	probabilistic	probabilistic	ADJ
ejpam-5275	5	8	unipoly	unipoly	ADJ
ejpam-5275	5	9	-	-	PUNCT
ejpam-5275	5	10	bernoulli	bernoulli	NOUN
ejpam-5275	5	11	polynomials	polynomial	NOUN
ejpam-5275	5	12	and	and	CCONJ
ejpam-5275	5	13	numbers	number	NOUN
ejpam-5275	5	14	attached	attach	VERB
ejpam-5275	5	15	to	to	ADP
ejpam-5275	5	16	p	p	PRON
ejpam-5275	5	17	,	,	PUNCT
ejpam-5275	5	18	and	and	CCONJ
ejpam-5275	5	19	investigate	investigate	VERB
ejpam-5275	5	20	their	their	PRON
ejpam-5275	5	21	interesting	interesting	ADJ
ejpam-5275	5	22	basic	basic	ADJ
ejpam-5275	5	23	properties	property	NOUN
ejpam-5275	5	24	.	.	PUNCT
ejpam-5275	6	1	based	base	VERB
ejpam-5275	6	2	on	on	ADP
ejpam-5275	6	3	these	these	DET
ejpam-5275	6	4	new	new	ADJ
ejpam-5275	6	5	definition	definition	NOUN
ejpam-5275	6	6	,	,	PUNCT
ejpam-5275	6	7	we	we	PRON
ejpam-5275	6	8	derive	derive	VERB
ejpam-5275	6	9	some	some	DET
ejpam-5275	6	10	meaningful	meaningful	ADJ
ejpam-5275	6	11	formulae	formulae	NOUN
ejpam-5275	6	12	of	of	ADP
ejpam-5275	6	13	probabilistic	probabilistic	ADJ
ejpam-5275	6	14	type	type	NOUN
ejpam-5275	6	15	2	2	NUM
ejpam-5275	6	16	poly	poly	ADJ
ejpam-5275	6	17	-	-	PUNCT
ejpam-5275	6	18	bernoulli	bernoulli	NOUN
ejpam-5275	6	19	polynomials	polynomial	NOUN
ejpam-5275	6	20	and	and	CCONJ
ejpam-5275	6	21	probabilistic	probabilistic	ADJ
ejpam-5275	6	22	unipoly	unipoly	ADJ
ejpam-5275	6	23	-	-	PUNCT
ejpam-5275	6	24	bernoulli	bernoulli	NOUN
ejpam-5275	6	25	polynomials	polynomial	NOUN
ejpam-5275	6	26	and	and	CCONJ
ejpam-5275	6	27	numbers	number	NOUN
ejpam-5275	6	28	attached	attach	VERB
ejpam-5275	6	29	to	to	ADP
ejpam-5275	6	30	p.	p.	NOUN
ejpam-5275	6	31	2020	2020	NUM
ejpam-5275	6	32	mathematics	mathematic	NOUN
ejpam-5275	6	33	subject	subject	NOUN
ejpam-5275	6	34	classifications	classification	NOUN
ejpam-5275	6	35	:	:	PUNCT
ejpam-5275	6	36	11b68	11b68	NUM
ejpam-5275	6	37	key	key	ADJ
ejpam-5275	6	38	words	word	NOUN
ejpam-5275	6	39	and	and	CCONJ
ejpam-5275	6	40	phrases	phrase	NOUN
ejpam-5275	6	41	:	:	PUNCT
ejpam-5275	6	42	bernoulli	bernoulli	NOUN
ejpam-5275	6	43	polynomials	polynomial	NOUN
ejpam-5275	6	44	,	,	PUNCT
ejpam-5275	6	45	stirling	stirling	NOUN
ejpam-5275	6	46	numbers	number	NOUN
ejpam-5275	6	47	,	,	PUNCT
ejpam-5275	6	48	probabilistic	probabilistic	ADJ
ejpam-5275	6	49	type	type	NOUN
ejpam-5275	6	50	2	2	NUM
ejpam-5275	6	51	polybernoulli	polybernoulli	NOUN
ejpam-5275	6	52	polynomials	polynomial	NOUN
ejpam-5275	6	53	,	,	PUNCT
ejpam-5275	6	54	probabilistic	probabilistic	ADJ
ejpam-5275	6	55	unipoly	unipoly	ADJ
ejpam-5275	6	56	-	-	PUNCT
ejpam-5275	6	57	bernoulli	bernoulli	NOUN
ejpam-5275	6	58	polynomials	polynomial	NOUN
ejpam-5275	6	59	.	.	PUNCT
ejpam-5275	7	1	1	1	X
ejpam-5275	7	2	.	.	X
ejpam-5275	7	3	introduction	introduction	NOUN
ejpam-5275	7	4	the	the	DET
ejpam-5275	7	5	bernoulli	bernoulli	NOUN
ejpam-5275	7	6	polynomials	polynomial	NOUN
ejpam-5275	7	7	are	be	AUX
ejpam-5275	7	8	defined	define	VERB
ejpam-5275	7	9	by	by	ADP
ejpam-5275	7	10	t	t	PROPN
ejpam-5275	7	11	et	et	NOUN
ejpam-5275	7	12	−	−	PROPN
ejpam-5275	7	13	1	1	NUM
ejpam-5275	7	14	ext	ext	NOUN
ejpam-5275	7	15	=	=	NOUN
ejpam-5275	8	1	∞∑	∞∑	PRON
ejpam-5275	8	2	n=0	n=0	NUM
ejpam-5275	8	3	bn(x	bn(x	NUM
ejpam-5275	8	4	)	)	PUNCT
ejpam-5275	8	5	tn	tn	PROPN
ejpam-5275	8	6	n	n	PROPN
ejpam-5275	8	7	!	!	PROPN
ejpam-5275	8	8	,	,	PUNCT
ejpam-5275	8	9	(	(	PUNCT
ejpam-5275	8	10	see[1	see[1	X
ejpam-5275	8	11	,	,	PUNCT
ejpam-5275	8	12	2	2	NUM
ejpam-5275	8	13	,	,	PUNCT
ejpam-5275	8	14	7	7	NUM
ejpam-5275	8	15	,	,	PUNCT
ejpam-5275	8	16	15	15	NUM
ejpam-5275	8	17	,	,	PUNCT
ejpam-5275	8	18	27	27	NUM
ejpam-5275	8	19	,	,	PUNCT
ejpam-5275	8	20	30	30	NUM
ejpam-5275	8	21	]	]	PUNCT
ejpam-5275	8	22	,	,	PUNCT
ejpam-5275	8	23	[	[	X
ejpam-5275	8	24	12	12	NUM
ejpam-5275	8	25	,	,	PUNCT
ejpam-5275	8	26	19	19	NUM
ejpam-5275	8	27	,	,	PUNCT
ejpam-5275	8	28	20	20	NUM
ejpam-5275	8	29	,	,	PUNCT
ejpam-5275	8	30	28	28	NUM
ejpam-5275	8	31	]	]	PUNCT
ejpam-5275	8	32	)	)	PUNCT
ejpam-5275	8	33	.	.	PUNCT
ejpam-5275	9	1	(	(	PUNCT
ejpam-5275	9	2	1	1	X
ejpam-5275	9	3	)	)	PUNCT
ejpam-5275	9	4	for	for	ADP
ejpam-5275	9	5	k	k	PROPN
ejpam-5275	9	6	∈	∈	PROPN
ejpam-5275	9	7	z	z	PROPN
ejpam-5275	9	8	,	,	PUNCT
ejpam-5275	9	9	the	the	DET
ejpam-5275	9	10	polylogarithm	polylogarithm	PROPN
ejpam-5275	9	11	function	function	NOUN
ejpam-5275	9	12	is	be	AUX
ejpam-5275	9	13	defined	define	VERB
ejpam-5275	9	14	by	by	ADP
ejpam-5275	9	15	lik(x	lik(x	NOUN
ejpam-5275	9	16	)	)	PUNCT
ejpam-5275	9	17	=	=	PROPN
ejpam-5275	10	1	∞∑	∞∑	NUM
ejpam-5275	10	2	n=1	n=1	PROPN
ejpam-5275	10	3	xn	xn	PROPN
ejpam-5275	10	4	nk	nk	PROPN
ejpam-5275	10	5	,	,	PUNCT
ejpam-5275	10	6	(	(	PUNCT
ejpam-5275	10	7	|x|	|x|	X
ejpam-5275	10	8	<	<	X
ejpam-5275	10	9	1	1	NUM
ejpam-5275	10	10	)	)	PUNCT
ejpam-5275	10	11	,	,	PUNCT
ejpam-5275	10	12	(	(	PUNCT
ejpam-5275	10	13	see[4	see[4	NOUN
ejpam-5275	10	14	,	,	PUNCT
ejpam-5275	10	15	5	5	NUM
ejpam-5275	10	16	,	,	PUNCT
ejpam-5275	10	17	24	24	NUM
ejpam-5275	10	18	]	]	PUNCT
ejpam-5275	10	19	,	,	PUNCT
ejpam-5275	10	20	[	[	X
ejpam-5275	10	21	23	23	NUM
ejpam-5275	10	22	]	]	PUNCT
ejpam-5275	10	23	)	)	PUNCT
ejpam-5275	10	24	.	.	PUNCT
ejpam-5275	11	1	(	(	PUNCT
ejpam-5275	11	2	2	2	X
ejpam-5275	11	3	)	)	PUNCT
ejpam-5275	11	4	for	for	ADP
ejpam-5275	11	5	k	k	PROPN
ejpam-5275	11	6	∈	∈	PROPN
ejpam-5275	11	7	z	z	PROPN
ejpam-5275	11	8	,	,	PUNCT
ejpam-5275	11	9	kim	kim	PROPN
ejpam-5275	11	10	defined	define	VERB
ejpam-5275	11	11	the	the	DET
ejpam-5275	11	12	polyexponential	polyexponential	ADJ
ejpam-5275	11	13	function	function	NOUN
ejpam-5275	11	14	ek(x	ek(x	NOUN
ejpam-5275	11	15	)	)	PUNCT
ejpam-5275	11	16	,	,	PUNCT
ejpam-5275	11	17	which	which	PRON
ejpam-5275	11	18	is	be	AUX
ejpam-5275	11	19	given	give	VERB
ejpam-5275	11	20	by	by	ADP
ejpam-5275	11	21	ek(x	ek(x	NOUN
ejpam-5275	11	22	)	)	PUNCT
ejpam-5275	12	1	=	=	NOUN
ejpam-5275	13	1	∞∑	∞∑	NUM
ejpam-5275	13	2	n=1	n=1	PROPN
ejpam-5275	13	3	xn	xn	PROPN
ejpam-5275	13	4	(	(	PUNCT
ejpam-5275	13	5	n−	n−	NOUN
ejpam-5275	13	6	1)!nk	1)!nk	NUM
ejpam-5275	13	7	,	,	PUNCT
ejpam-5275	13	8	(	(	PUNCT
ejpam-5275	13	9	see[6	see[6	X
ejpam-5275	13	10	]	]	PUNCT
ejpam-5275	13	11	)	)	PUNCT
ejpam-5275	13	12	.	.	PUNCT
ejpam-5275	14	1	(	(	PUNCT
ejpam-5275	14	2	3	3	X
ejpam-5275	14	3	)	)	PUNCT
ejpam-5275	14	4	∗corresponding	∗corresponde	VERB
ejpam-5275	14	5	author	author	NOUN
ejpam-5275	14	6	.	.	PUNCT
ejpam-5275	15	1	doi	doi	NOUN
ejpam-5275	15	2	:	:	PUNCT
ejpam-5275	15	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5275	https://doi.org/10.29020/nybg.ejpam.v17i3.5275	ADJ
ejpam-5275	15	4	email	email	NOUN
ejpam-5275	15	5	addresses	address	VERB
ejpam-5275	15	6	:	:	PUNCT
ejpam-5275	15	7	ugug11@naver.com	ugug11@naver.com	PROPN
ejpam-5275	15	8	(	(	PUNCT
ejpam-5275	15	9	s.	s.	PROPN
ejpam-5275	15	10	h.	h.	PROPN
ejpam-5275	15	11	lee	lee	PROPN
ejpam-5275	15	12	)	)	PUNCT
ejpam-5275	15	13	,	,	PUNCT
ejpam-5275	15	14	chenli	chenli	NOUN
ejpam-5275	15	15	0928@xaufe.edu.cn	0928@xaufe.edu.cn	NUM
ejpam-5275	15	16	(	(	PUNCT
ejpam-5275	15	17	l.	l.	PROPN
ejpam-5275	15	18	chen	chen	PROPN
ejpam-5275	15	19	)	)	PUNCT
ejpam-5275	15	20	,	,	PUNCT
ejpam-5275	15	21	ugug11@naver.com	ugug11@naver.com	PROPN
ejpam-5275	15	22	(	(	PUNCT
ejpam-5275	15	23	w.	w.	PROPN
ejpam-5275	15	24	kim	kim	PROPN
ejpam-5275	15	25	)	)	PUNCT
ejpam-5275	15	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5275	15	27	2336	2336	NUM
ejpam-5275	16	1	©	©	ADP
ejpam-5275	16	2	2024	2024	NUM
ejpam-5275	16	3	ejpam	ejpam	NOUN
ejpam-5275	16	4	all	all	DET
ejpam-5275	16	5	rights	right	NOUN
ejpam-5275	16	6	reserved	reserve	VERB
ejpam-5275	16	7	.	.	PUNCT
ejpam-5275	17	1	s.	s.	PROPN
ejpam-5275	17	2	h.	h.	PROPN
ejpam-5275	17	3	lee	lee	PROPN
ejpam-5275	17	4	,	,	PUNCT
ejpam-5275	17	5	l.	l.	PROPN
ejpam-5275	17	6	chen	chen	PROPN
ejpam-5275	17	7	,	,	PUNCT
ejpam-5275	17	8	w.	w.	PROPN
ejpam-5275	17	9	kim	kim	PROPN
ejpam-5275	17	10	/	/	SYM
ejpam-5275	17	11	eur	eur	PROPN
ejpam-5275	17	12	.	.	PUNCT
ejpam-5275	18	1	j.	j.	PROPN
ejpam-5275	18	2	pure	pure	PROPN
ejpam-5275	18	3	appl	appl	PROPN
ejpam-5275	18	4	.	.	PROPN
ejpam-5275	18	5	math	math	PROPN
ejpam-5275	18	6	,	,	PUNCT
ejpam-5275	18	7	17	17	NUM
ejpam-5275	18	8	(	(	PUNCT
ejpam-5275	18	9	3	3	NUM
ejpam-5275	18	10	)	)	PUNCT
ejpam-5275	18	11	(	(	PUNCT
ejpam-5275	18	12	2024	2024	NUM
ejpam-5275	18	13	)	)	PUNCT
ejpam-5275	18	14	,	,	PUNCT
ejpam-5275	18	15	2336	2336	NUM
ejpam-5275	18	16	-	-	SYM
ejpam-5275	18	17	2348	2348	NUM
ejpam-5275	18	18	2337	2337	NUM
ejpam-5275	18	19	when	when	SCONJ
ejpam-5275	18	20	k	k	PROPN
ejpam-5275	18	21	=	=	SYM
ejpam-5275	18	22	1	1	NUM
ejpam-5275	19	1	,	,	PUNCT
ejpam-5275	19	2	we	we	PRON
ejpam-5275	19	3	note	note	VERB
ejpam-5275	19	4	that	that	PRON
ejpam-5275	19	5	e1(x	e1(x	NOUN
ejpam-5275	19	6	)	)	PUNCT
ejpam-5275	19	7	=	=	PUNCT
ejpam-5275	20	1	∞∑	∞∑	NUM
ejpam-5275	20	2	n=1	n=1	PROPN
ejpam-5275	20	3	xn	xn	PROPN
ejpam-5275	20	4	n	n	CCONJ
ejpam-5275	20	5	!	!	PUNCT
ejpam-5275	20	6	=	=	PRON
ejpam-5275	21	1	ex	ex	X
ejpam-5275	22	1	−	−	NOUN
ejpam-5275	22	2	1	1	NUM
ejpam-5275	22	3	.	.	PUNCT
ejpam-5275	22	4	(	(	PUNCT
ejpam-5275	22	5	4	4	NUM
ejpam-5275	22	6	)	)	PUNCT
ejpam-5275	22	7	as	as	SCONJ
ejpam-5275	22	8	we	we	PRON
ejpam-5275	22	9	all	all	PRON
ejpam-5275	22	10	know	know	VERB
ejpam-5275	22	11	,	,	PUNCT
ejpam-5275	22	12	the	the	DET
ejpam-5275	22	13	poly	poly	ADJ
ejpam-5275	22	14	-	-	PUNCT
ejpam-5275	22	15	bernoulli	bernoulli	NOUN
ejpam-5275	22	16	polynomials	polynomial	NOUN
ejpam-5275	22	17	are	be	AUX
ejpam-5275	22	18	defined	define	VERB
ejpam-5275	22	19	by	by	ADP
ejpam-5275	22	20	kaneko	kaneko	PROPN
ejpam-5275	22	21	.	.	PUNCT
ejpam-5275	23	1	it	it	PRON
ejpam-5275	23	2	is	be	AUX
ejpam-5275	23	3	given	give	VERB
ejpam-5275	23	4	by	by	ADP
ejpam-5275	23	5	lik(1−	lik(1−	ADJ
ejpam-5275	23	6	e−t	e−t	NOUN
ejpam-5275	23	7	)	)	PUNCT
ejpam-5275	23	8	1−	1−	NUM
ejpam-5275	23	9	e−t	e−t	NOUN
ejpam-5275	23	10	ext	ext	NOUN
ejpam-5275	23	11	=	=	PUNCT
ejpam-5275	24	1	∞∑	∞∑	PRON
ejpam-5275	24	2	n=0	n=0	NUM
ejpam-5275	24	3	pb(k	pb(k	NOUN
ejpam-5275	24	4	)	)	PUNCT
ejpam-5275	24	5	n	n	CCONJ
ejpam-5275	24	6	(	(	PUNCT
ejpam-5275	24	7	x	x	X
ejpam-5275	24	8	)	)	PUNCT
ejpam-5275	24	9	tn	tn	PROPN
ejpam-5275	24	10	n	n	CCONJ
ejpam-5275	24	11	!	!	PROPN
ejpam-5275	24	12	,	,	PUNCT
ejpam-5275	24	13	(	(	PUNCT
ejpam-5275	24	14	see[5	see[5	NOUN
ejpam-5275	24	15	]	]	PUNCT
ejpam-5275	24	16	)	)	PUNCT
ejpam-5275	24	17	.	.	PUNCT
ejpam-5275	25	1	(	(	PUNCT
ejpam-5275	25	2	5	5	X
ejpam-5275	25	3	)	)	PUNCT
ejpam-5275	25	4	when	when	SCONJ
ejpam-5275	25	5	x	x	X
ejpam-5275	25	6	=	=	SYM
ejpam-5275	25	7	0	0	NUM
ejpam-5275	25	8	,	,	PUNCT
ejpam-5275	25	9	we	we	PRON
ejpam-5275	25	10	note	note	VERB
ejpam-5275	25	11	that	that	SCONJ
ejpam-5275	25	12	pb	pb	ADP
ejpam-5275	25	13	(	(	PUNCT
ejpam-5275	25	14	k	k	NOUN
ejpam-5275	25	15	)	)	PUNCT
ejpam-5275	25	16	n	n	NOUN
ejpam-5275	25	17	=	=	SYM
ejpam-5275	25	18	pb	pb	X
ejpam-5275	25	19	(	(	PUNCT
ejpam-5275	25	20	k	k	NOUN
ejpam-5275	25	21	)	)	PUNCT
ejpam-5275	25	22	n	n	CCONJ
ejpam-5275	25	23	(	(	PUNCT
ejpam-5275	25	24	0	0	NUM
ejpam-5275	25	25	)	)	PUNCT
ejpam-5275	25	26	are	be	AUX
ejpam-5275	25	27	called	call	VERB
ejpam-5275	25	28	the	the	DET
ejpam-5275	25	29	poly	poly	ADJ
ejpam-5275	25	30	-	-	PUNCT
ejpam-5275	25	31	bernoulli	bernoulli	NOUN
ejpam-5275	25	32	numbers	number	NOUN
ejpam-5275	25	33	.	.	PUNCT
ejpam-5275	26	1	in	in	ADP
ejpam-5275	26	2	2019	2019	NUM
ejpam-5275	26	3	,	,	PUNCT
ejpam-5275	26	4	kim	kim	PROPN
ejpam-5275	26	5	considered	consider	VERB
ejpam-5275	26	6	the	the	DET
ejpam-5275	26	7	definition	definition	NOUN
ejpam-5275	26	8	of	of	ADP
ejpam-5275	26	9	type	type	NOUN
ejpam-5275	26	10	2	2	NUM
ejpam-5275	26	11	poly	poly	ADJ
ejpam-5275	26	12	-	-	PUNCT
ejpam-5275	26	13	bernoulli	bernoulli	NOUN
ejpam-5275	26	14	polynomials	polynomial	NOUN
ejpam-5275	26	15	.	.	PUNCT
ejpam-5275	27	1	it	it	PRON
ejpam-5275	27	2	is	be	AUX
ejpam-5275	27	3	given	give	VERB
ejpam-5275	27	4	by	by	ADP
ejpam-5275	27	5	ek(log(1	ek(log(1	NOUN
ejpam-5275	27	6	+	+	CCONJ
ejpam-5275	27	7	t	t	PROPN
ejpam-5275	27	8	)	)	PUNCT
ejpam-5275	27	9	)	)	PUNCT
ejpam-5275	27	10	et	et	NOUN
ejpam-5275	27	11	−	−	NOUN
ejpam-5275	27	12	1	1	NUM
ejpam-5275	27	13	ext	ext	NOUN
ejpam-5275	27	14	=	=	NOUN
ejpam-5275	27	15	∞∑	∞∑	NUM
ejpam-5275	27	16	n=0	n=0	NUM
ejpam-5275	27	17	β(k	β(k	X
ejpam-5275	27	18	)	)	PUNCT
ejpam-5275	27	19	n	n	CCONJ
ejpam-5275	27	20	(	(	PUNCT
ejpam-5275	27	21	x	x	X
ejpam-5275	27	22	)	)	PUNCT
ejpam-5275	27	23	tn	tn	PROPN
ejpam-5275	27	24	n	n	CCONJ
ejpam-5275	27	25	!	!	PROPN
ejpam-5275	27	26	,	,	PUNCT
ejpam-5275	27	27	(	(	PUNCT
ejpam-5275	27	28	see[6	see[6	X
ejpam-5275	27	29	,	,	PUNCT
ejpam-5275	27	30	22	22	NUM
ejpam-5275	27	31	]	]	PUNCT
ejpam-5275	27	32	)	)	PUNCT
ejpam-5275	27	33	.	.	PUNCT
ejpam-5275	28	1	(	(	PUNCT
ejpam-5275	28	2	6	6	NUM
ejpam-5275	28	3	)	)	PUNCT
ejpam-5275	28	4	when	when	SCONJ
ejpam-5275	28	5	x	x	X
ejpam-5275	28	6	=	=	SYM
ejpam-5275	28	7	0	0	NUM
ejpam-5275	28	8	,	,	PUNCT
ejpam-5275	28	9	we	we	PRON
ejpam-5275	28	10	note	note	VERB
ejpam-5275	28	11	that	that	SCONJ
ejpam-5275	28	12	β	β	X
ejpam-5275	28	13	(	(	PUNCT
ejpam-5275	28	14	k	k	NOUN
ejpam-5275	28	15	)	)	PUNCT
ejpam-5275	28	16	n	n	NOUN
ejpam-5275	28	17	=	=	SYM
ejpam-5275	28	18	β	β	X
ejpam-5275	28	19	(	(	PUNCT
ejpam-5275	28	20	k	k	NOUN
ejpam-5275	28	21	)	)	PUNCT
ejpam-5275	28	22	n	n	CCONJ
ejpam-5275	28	23	(	(	PUNCT
ejpam-5275	28	24	0	0	NUM
ejpam-5275	28	25	)	)	PUNCT
ejpam-5275	28	26	are	be	AUX
ejpam-5275	28	27	called	call	VERB
ejpam-5275	28	28	the	the	DET
ejpam-5275	28	29	type	type	NOUN
ejpam-5275	28	30	2	2	NUM
ejpam-5275	28	31	poly	poly	ADJ
ejpam-5275	28	32	-	-	PUNCT
ejpam-5275	28	33	bernoulli	bernoulli	NOUN
ejpam-5275	28	34	numbers	number	NOUN
ejpam-5275	28	35	.	.	PUNCT
ejpam-5275	29	1	kim	kim	PROPN
ejpam-5275	29	2	also	also	ADV
ejpam-5275	29	3	studied	study	VERB
ejpam-5275	29	4	the	the	DET
ejpam-5275	29	5	unipoly	unipoly	ADJ
ejpam-5275	29	6	function	function	NOUN
ejpam-5275	29	7	attached	attach	VERB
ejpam-5275	29	8	to	to	ADP
ejpam-5275	29	9	p.	p.	VERB
ejpam-5275	29	10	its	its	PRON
ejpam-5275	29	11	definition	definition	NOUN
ejpam-5275	29	12	as	as	SCONJ
ejpam-5275	29	13	follows	follow	VERB
ejpam-5275	29	14	.	.	PUNCT
ejpam-5275	30	1	uk(x|p	uk(x|p	NOUN
ejpam-5275	30	2	)	)	PUNCT
ejpam-5275	31	1	=	=	PUNCT
ejpam-5275	32	1	∞∑	∞∑	NUM
ejpam-5275	32	2	n=1	n=1	PROPN
ejpam-5275	32	3	p(n	p(n	PROPN
ejpam-5275	32	4	)	)	PUNCT
ejpam-5275	32	5	nk	nk	PROPN
ejpam-5275	32	6	xn	xn	PROPN
ejpam-5275	32	7	,	,	PUNCT
ejpam-5275	32	8	(	(	PUNCT
ejpam-5275	32	9	k	k	PROPN
ejpam-5275	32	10	∈	∈	PROPN
ejpam-5275	32	11	z	z	PROPN
ejpam-5275	32	12	)	)	PUNCT
ejpam-5275	32	13	,	,	PUNCT
ejpam-5275	32	14	(	(	PUNCT
ejpam-5275	32	15	see[6	see[6	X
ejpam-5275	32	16	]	]	PUNCT
ejpam-5275	32	17	)	)	PUNCT
ejpam-5275	32	18	.	.	PUNCT
ejpam-5275	33	1	(	(	PUNCT
ejpam-5275	33	2	7	7	X
ejpam-5275	33	3	)	)	PUNCT
ejpam-5275	33	4	later	later	ADV
ejpam-5275	33	5	,	,	PUNCT
ejpam-5275	33	6	he	he	PRON
ejpam-5275	33	7	defined	define	VERB
ejpam-5275	33	8	the	the	DET
ejpam-5275	33	9	unipoly	unipoly	ADJ
ejpam-5275	33	10	-	-	PUNCT
ejpam-5275	33	11	bernoulli	bernoulli	NOUN
ejpam-5275	33	12	polynomials	polynomial	NOUN
ejpam-5275	33	13	attached	attach	VERB
ejpam-5275	33	14	to	to	ADP
ejpam-5275	33	15	p	p	NOUN
ejpam-5275	33	16	by	by	ADP
ejpam-5275	33	17	1	1	NUM
ejpam-5275	33	18	1−	1−	NUM
ejpam-5275	33	19	e−t	e−t	NOUN
ejpam-5275	33	20	uk(1−	uk(1−	PROPN
ejpam-5275	33	21	e−t|p)ext	e−t|p)ext	NOUN
ejpam-5275	33	22	=	=	SYM
ejpam-5275	33	23	∞∑	∞∑	PROPN
ejpam-5275	33	24	n=0	n=0	PROPN
ejpam-5275	33	25	b(k	b(k	PROPN
ejpam-5275	33	26	)	)	PUNCT
ejpam-5275	33	27	n	n	CCONJ
ejpam-5275	33	28	,	,	PUNCT
ejpam-5275	33	29	p(x	p(x	PROPN
ejpam-5275	33	30	)	)	PUNCT
ejpam-5275	33	31	tn	tn	PROPN
ejpam-5275	33	32	n	n	PROPN
ejpam-5275	33	33	!	!	PROPN
ejpam-5275	33	34	,	,	PUNCT
ejpam-5275	33	35	(	(	PUNCT
ejpam-5275	33	36	see[6	see[6	X
ejpam-5275	33	37	]	]	PUNCT
ejpam-5275	33	38	)	)	PUNCT
ejpam-5275	33	39	.	.	PUNCT
ejpam-5275	34	1	(	(	PUNCT
ejpam-5275	34	2	8)	8)	NUM
ejpam-5275	34	3	recently	recently	ADV
ejpam-5275	34	4	,	,	PUNCT
ejpam-5275	34	5	kim	kim	PROPN
ejpam-5275	34	6	studied	study	VERB
ejpam-5275	34	7	the	the	DET
ejpam-5275	34	8	probabilistic	probabilistic	ADJ
ejpam-5275	34	9	poly	poly	ADJ
ejpam-5275	34	10	-	-	PUNCT
ejpam-5275	34	11	bernoulli	bernoulli	NOUN
ejpam-5275	34	12	polynomials	polynomial	NOUN
ejpam-5275	34	13	associated	associate	VERB
ejpam-5275	34	14	with	with	ADP
ejpam-5275	34	15	y	y	PROPN
ejpam-5275	34	16	.	.	PUNCT
ejpam-5275	35	1	assume	assume	VERB
ejpam-5275	35	2	that	that	SCONJ
ejpam-5275	35	3	y	y	PROPN
ejpam-5275	35	4	is	be	AUX
ejpam-5275	35	5	a	a	DET
ejpam-5275	35	6	random	random	ADJ
ejpam-5275	35	7	variable	variable	NOUN
ejpam-5275	35	8	such	such	ADJ
ejpam-5275	35	9	that	that	SCONJ
ejpam-5275	35	10	the	the	DET
ejpam-5275	35	11	moment	moment	NOUN
ejpam-5275	35	12	generating	generate	VERB
ejpam-5275	35	13	function	function	NOUN
ejpam-5275	35	14	of	of	ADP
ejpam-5275	35	15	y	y	PROPN
ejpam-5275	35	16	given	give	VERB
ejpam-5275	35	17	by	by	ADP
ejpam-5275	35	18	e[ey	e[ey	PROPN
ejpam-5275	35	19	t	t	PROPN
ejpam-5275	35	20	]	]	X
ejpam-5275	35	21	=	=	PUNCT
ejpam-5275	36	1	∞∑	∞∑	NUM
ejpam-5275	36	2	n=0	n=0	NUM
ejpam-5275	36	3	e[y	e[y	ADJ
ejpam-5275	36	4	n	n	X
ejpam-5275	36	5	]	]	PUNCT
ejpam-5275	36	6	tn	tn	PROPN
ejpam-5275	36	7	n	n	CCONJ
ejpam-5275	36	8	!	!	PROPN
ejpam-5275	36	9	,	,	PUNCT
ejpam-5275	36	10	(	(	PUNCT
ejpam-5275	36	11	|t|	|t|	ADP
ejpam-5275	36	12	<	<	X
ejpam-5275	36	13	r	r	NOUN
ejpam-5275	36	14	)	)	PUNCT
ejpam-5275	36	15	,	,	PUNCT
ejpam-5275	36	16	(	(	PUNCT
ejpam-5275	36	17	[	[	X
ejpam-5275	36	18	6	6	NUM
ejpam-5275	36	19	,	,	PUNCT
ejpam-5275	36	20	14	14	NUM
ejpam-5275	36	21	,	,	PUNCT
ejpam-5275	36	22	16	16	NUM
ejpam-5275	36	23	]	]	PUNCT
ejpam-5275	36	24	)	)	PUNCT
ejpam-5275	36	25	.	.	PUNCT
ejpam-5275	37	1	(	(	PUNCT
ejpam-5275	37	2	9	9	X
ejpam-5275	37	3	)	)	PUNCT
ejpam-5275	37	4	exist	exist	VERB
ejpam-5275	37	5	for	for	ADP
ejpam-5275	37	6	some	some	DET
ejpam-5275	37	7	r	r	NOUN
ejpam-5275	37	8	≥	≥	NOUN
ejpam-5275	37	9	0	0	NUM
ejpam-5275	37	10	.	.	PUNCT
ejpam-5275	38	1	then	then	ADV
ejpam-5275	38	2	the	the	DET
ejpam-5275	38	3	definition	definition	NOUN
ejpam-5275	38	4	of	of	ADP
ejpam-5275	38	5	the	the	DET
ejpam-5275	38	6	probabilistic	probabilistic	ADJ
ejpam-5275	38	7	poly	poly	ADJ
ejpam-5275	38	8	-	-	PUNCT
ejpam-5275	38	9	bernoulli	bernoulli	NOUN
ejpam-5275	38	10	polynomials	polynomial	NOUN
ejpam-5275	38	11	are	be	AUX
ejpam-5275	38	12	given	give	VERB
ejpam-5275	38	13	by	by	ADP
ejpam-5275	38	14	lik(1−	lik(1−	ADJ
ejpam-5275	38	15	e−t	e−t	NOUN
ejpam-5275	38	16	)	)	PUNCT
ejpam-5275	38	17	1−	1−	NUM
ejpam-5275	38	18	e[e−y	e[e−y	PROPN
ejpam-5275	38	19	t	t	PROPN
ejpam-5275	38	20	]	]	PUNCT
ejpam-5275	38	21	(	(	PUNCT
ejpam-5275	38	22	e[e−y	e[e−y	PROPN
ejpam-5275	38	23	t])x	t])x	NOUN
ejpam-5275	38	24	=	=	PUNCT
ejpam-5275	38	25	∞∑	∞∑	NUM
ejpam-5275	38	26	n=0	n=0	PROPN
ejpam-5275	38	27	b(k	b(k	PROPN
ejpam-5275	38	28	,	,	PUNCT
ejpam-5275	38	29	y	y	PROPN
ejpam-5275	38	30	)	)	PUNCT
ejpam-5275	38	31	n	n	CCONJ
ejpam-5275	38	32	(	(	PUNCT
ejpam-5275	38	33	x	x	X
ejpam-5275	38	34	)	)	PUNCT
ejpam-5275	38	35	tn	tn	PROPN
ejpam-5275	38	36	n	n	CCONJ
ejpam-5275	38	37	!	!	NUM
ejpam-5275	38	38	,	,	PUNCT
ejpam-5275	38	39	(	(	PUNCT
ejpam-5275	38	40	see[3	see[3	ADJ
ejpam-5275	38	41	,	,	PUNCT
ejpam-5275	38	42	8	8	NUM
ejpam-5275	38	43	,	,	PUNCT
ejpam-5275	38	44	9	9	NUM
ejpam-5275	38	45	,	,	PUNCT
ejpam-5275	38	46	18	18	NUM
ejpam-5275	38	47	,	,	PUNCT
ejpam-5275	38	48	31	31	NUM
ejpam-5275	38	49	,	,	PUNCT
ejpam-5275	38	50	32	32	NUM
ejpam-5275	38	51	]	]	PUNCT
ejpam-5275	38	52	)	)	PUNCT
ejpam-5275	38	53	.	.	PUNCT
ejpam-5275	39	1	(	(	PUNCT
ejpam-5275	39	2	10	10	NUM
ejpam-5275	39	3	)	)	PUNCT
ejpam-5275	39	4	when	when	SCONJ
ejpam-5275	39	5	k	k	PROPN
ejpam-5275	39	6	=	=	SYM
ejpam-5275	39	7	1	1	NUM
ejpam-5275	39	8	,	,	PUNCT
ejpam-5275	39	9	it	it	PRON
ejpam-5275	39	10	is	be	AUX
ejpam-5275	39	11	obvious	obvious	ADJ
ejpam-5275	39	12	that	that	SCONJ
ejpam-5275	39	13	b	b	X
ejpam-5275	39	14	(	(	PUNCT
ejpam-5275	39	15	1,y	1,y	NUM
ejpam-5275	39	16	)	)	PUNCT
ejpam-5275	40	1	n	n	PROPN
ejpam-5275	40	2	=	=	SYM
ejpam-5275	40	3	(	(	PUNCT
ejpam-5275	40	4	−1)nby	−1)nby	PROPN
ejpam-5275	40	5	n	n	PART
ejpam-5275	40	6	(	(	PUNCT
ejpam-5275	40	7	x	x	NOUN
ejpam-5275	40	8	)	)	PUNCT
ejpam-5275	40	9	.	.	PUNCT
ejpam-5275	41	1	this	this	DET
ejpam-5275	41	2	type	type	NOUN
ejpam-5275	41	3	of	of	ADP
ejpam-5275	41	4	polynomials	polynomial	NOUN
ejpam-5275	41	5	is	be	AUX
ejpam-5275	41	6	a	a	DET
ejpam-5275	41	7	new	new	ADJ
ejpam-5275	41	8	extension	extension	NOUN
ejpam-5275	41	9	.	.	PUNCT
ejpam-5275	42	1	inspired	inspire	VERB
ejpam-5275	42	2	by	by	ADP
ejpam-5275	42	3	this	this	PRON
ejpam-5275	42	4	,	,	PUNCT
ejpam-5275	42	5	the	the	DET
ejpam-5275	42	6	aim	aim	NOUN
ejpam-5275	42	7	of	of	ADP
ejpam-5275	42	8	our	our	PRON
ejpam-5275	42	9	paper	paper	NOUN
ejpam-5275	42	10	is	be	AUX
ejpam-5275	42	11	to	to	PART
ejpam-5275	42	12	explore	explore	VERB
ejpam-5275	42	13	the	the	DET
ejpam-5275	42	14	probabilistic	probabilistic	ADJ
ejpam-5275	42	15	type	type	NOUN
ejpam-5275	42	16	2	2	NUM
ejpam-5275	42	17	poly	poly	ADJ
ejpam-5275	42	18	-	-	PUNCT
ejpam-5275	42	19	bernoulli	bernoulli	NOUN
ejpam-5275	42	20	polynomials	polynomial	NOUN
ejpam-5275	42	21	and	and	CCONJ
ejpam-5275	42	22	obtain	obtain	VERB
ejpam-5275	42	23	some	some	DET
ejpam-5275	42	24	new	new	ADJ
ejpam-5275	42	25	results	result	NOUN
ejpam-5275	42	26	.	.	PUNCT
ejpam-5275	43	1	meanwhile	meanwhile	ADV
ejpam-5275	43	2	,	,	PUNCT
ejpam-5275	43	3	the	the	DET
ejpam-5275	43	4	probabilistic	probabilistic	ADJ
ejpam-5275	43	5	unipoly	unipoly	ADJ
ejpam-5275	43	6	-	-	PUNCT
ejpam-5275	43	7	bernoulli	bernoulli	NOUN
ejpam-5275	43	8	polynomials	polynomial	NOUN
ejpam-5275	43	9	are	be	AUX
ejpam-5275	43	10	also	also	ADV
ejpam-5275	43	11	another	another	DET
ejpam-5275	43	12	research	research	NOUN
ejpam-5275	43	13	.	.	PUNCT
ejpam-5275	44	1	s.	s.	PROPN
ejpam-5275	44	2	h.	h.	PROPN
ejpam-5275	44	3	lee	lee	PROPN
ejpam-5275	44	4	,	,	PUNCT
ejpam-5275	44	5	l.	l.	PROPN
ejpam-5275	44	6	chen	chen	PROPN
ejpam-5275	44	7	,	,	PUNCT
ejpam-5275	44	8	w.	w.	PROPN
ejpam-5275	44	9	kim	kim	PROPN
ejpam-5275	44	10	/	/	SYM
ejpam-5275	44	11	eur	eur	PROPN
ejpam-5275	44	12	.	.	PUNCT
ejpam-5275	45	1	j.	j.	PROPN
ejpam-5275	45	2	pure	pure	PROPN
ejpam-5275	45	3	appl	appl	PROPN
ejpam-5275	45	4	.	.	PROPN
ejpam-5275	45	5	math	math	PROPN
ejpam-5275	45	6	,	,	PUNCT
ejpam-5275	45	7	17	17	NUM
ejpam-5275	45	8	(	(	PUNCT
ejpam-5275	45	9	3	3	NUM
ejpam-5275	45	10	)	)	PUNCT
ejpam-5275	45	11	(	(	PUNCT
ejpam-5275	45	12	2024	2024	NUM
ejpam-5275	45	13	)	)	PUNCT
ejpam-5275	45	14	,	,	PUNCT
ejpam-5275	45	15	2336	2336	NUM
ejpam-5275	45	16	-	-	SYM
ejpam-5275	45	17	2348	2348	NUM
ejpam-5275	45	18	2338	2338	NUM
ejpam-5275	45	19	the	the	DET
ejpam-5275	45	20	stirling	stirling	NOUN
ejpam-5275	45	21	number	number	NOUN
ejpam-5275	45	22	of	of	ADP
ejpam-5275	45	23	the	the	DET
ejpam-5275	45	24	first	first	ADJ
ejpam-5275	45	25	kind	kind	NOUN
ejpam-5275	45	26	are	be	AUX
ejpam-5275	45	27	defined	define	VERB
ejpam-5275	45	28	by	by	ADP
ejpam-5275	45	29	(	(	PUNCT
ejpam-5275	45	30	x)n	x)n	PUNCT
ejpam-5275	45	31	=	=	PUNCT
ejpam-5275	45	32	n∑	n∑	DET
ejpam-5275	45	33	k=0	k=0	PROPN
ejpam-5275	45	34	s1(n	s1(n	PROPN
ejpam-5275	45	35	,	,	PUNCT
ejpam-5275	45	36	k)x	k)x	X
ejpam-5275	45	37	k	k	X
ejpam-5275	45	38	,	,	PUNCT
ejpam-5275	45	39	(	(	PUNCT
ejpam-5275	45	40	see[10	see[10	PROPN
ejpam-5275	45	41	,	,	PUNCT
ejpam-5275	45	42	28	28	NUM
ejpam-5275	45	43	,	,	PUNCT
ejpam-5275	45	44	29	29	NUM
ejpam-5275	45	45	]	]	PUNCT
ejpam-5275	45	46	)	)	PUNCT
ejpam-5275	45	47	.	.	PUNCT
ejpam-5275	46	1	(	(	PUNCT
ejpam-5275	46	2	11	11	NUM
ejpam-5275	46	3	)	)	PUNCT
ejpam-5275	46	4	where	where	SCONJ
ejpam-5275	46	5	(	(	PUNCT
ejpam-5275	46	6	x)0	x)0	X
ejpam-5275	46	7	=	=	SYM
ejpam-5275	46	8	1	1	NUM
ejpam-5275	46	9	,	,	PUNCT
ejpam-5275	46	10	(	(	PUNCT
ejpam-5275	46	11	x)n	x)n	PUNCT
ejpam-5275	46	12	=	=	SYM
ejpam-5275	46	13	x(x−	x(x−	PROPN
ejpam-5275	46	14	1	1	NUM
ejpam-5275	46	15	)	)	PUNCT
ejpam-5275	46	16	·	·	PUNCT
ejpam-5275	46	17	·	·	PUNCT
ejpam-5275	46	18	·	·	PUNCT
ejpam-5275	47	1	(	(	PUNCT
ejpam-5275	47	2	x−	x−	PROPN
ejpam-5275	47	3	n+	n+	PROPN
ejpam-5275	47	4	1	1	NUM
ejpam-5275	47	5	)	)	PUNCT
ejpam-5275	47	6	,	,	PUNCT
ejpam-5275	47	7	(	(	PUNCT
ejpam-5275	47	8	n	n	X
ejpam-5275	47	9	≥	≥	NOUN
ejpam-5275	47	10	1	1	NUM
ejpam-5275	47	11	)	)	PUNCT
ejpam-5275	47	12	.	.	PUNCT
ejpam-5275	48	1	from	from	ADP
ejpam-5275	48	2	(	(	PUNCT
ejpam-5275	48	3	11	11	NUM
ejpam-5275	48	4	)	)	PUNCT
ejpam-5275	48	5	,	,	PUNCT
ejpam-5275	48	6	we	we	PRON
ejpam-5275	48	7	can	can	AUX
ejpam-5275	48	8	easily	easily	ADV
ejpam-5275	48	9	know	know	VERB
ejpam-5275	48	10	1	1	NUM
ejpam-5275	48	11	k	k	NOUN
ejpam-5275	48	12	!	!	PUNCT
ejpam-5275	49	1	(	(	PUNCT
ejpam-5275	49	2	log(1	log(1	NOUN
ejpam-5275	49	3	+	+	CCONJ
ejpam-5275	49	4	t))k	t))k	NOUN
ejpam-5275	49	5	=	=	SYM
ejpam-5275	50	1	∞∑	∞∑	NUM
ejpam-5275	50	2	n	n	X
ejpam-5275	50	3	=	=	X
ejpam-5275	50	4	k	k	NOUN
ejpam-5275	50	5	s1(n	s1(n	PROPN
ejpam-5275	50	6	,	,	PUNCT
ejpam-5275	50	7	k	k	NOUN
ejpam-5275	50	8	)	)	PUNCT
ejpam-5275	50	9	tn	tn	PROPN
ejpam-5275	50	10	n	n	PROPN
ejpam-5275	50	11	!	!	PROPN
ejpam-5275	50	12	,	,	PUNCT
ejpam-5275	50	13	(	(	PUNCT
ejpam-5275	50	14	see[10	see[10	PROPN
ejpam-5275	50	15	,	,	PUNCT
ejpam-5275	50	16	11	11	NUM
ejpam-5275	50	17	,	,	PUNCT
ejpam-5275	50	18	29	29	NUM
ejpam-5275	50	19	]	]	PUNCT
ejpam-5275	50	20	)	)	PUNCT
ejpam-5275	50	21	.	.	PUNCT
ejpam-5275	51	1	(	(	PUNCT
ejpam-5275	51	2	12	12	NUM
ejpam-5275	51	3	)	)	PUNCT
ejpam-5275	51	4	the	the	DET
ejpam-5275	51	5	stirling	stirling	NOUN
ejpam-5275	51	6	number	number	NOUN
ejpam-5275	51	7	of	of	ADP
ejpam-5275	51	8	the	the	DET
ejpam-5275	51	9	second	second	ADJ
ejpam-5275	51	10	kind	kind	NOUN
ejpam-5275	51	11	are	be	AUX
ejpam-5275	51	12	defined	define	VERB
ejpam-5275	51	13	by	by	ADP
ejpam-5275	51	14	xn	xn	PROPN
ejpam-5275	51	15	=	=	SYM
ejpam-5275	51	16	n∑	n∑	PROPN
ejpam-5275	51	17	k=0	k=0	PROPN
ejpam-5275	51	18	s2(n	s2(n	PROPN
ejpam-5275	51	19	,	,	PUNCT
ejpam-5275	51	20	k)(x)k	k)(x)k	PRON
ejpam-5275	51	21	,	,	PUNCT
ejpam-5275	51	22	(	(	PUNCT
ejpam-5275	51	23	see[17	see[17	PROPN
ejpam-5275	51	24	,	,	PUNCT
ejpam-5275	51	25	21	21	NUM
ejpam-5275	51	26	,	,	PUNCT
ejpam-5275	51	27	26	26	NUM
ejpam-5275	51	28	]	]	PUNCT
ejpam-5275	51	29	)	)	PUNCT
ejpam-5275	51	30	.	.	PUNCT
ejpam-5275	52	1	(	(	PUNCT
ejpam-5275	52	2	13	13	NUM
ejpam-5275	52	3	)	)	PUNCT
ejpam-5275	52	4	from	from	ADP
ejpam-5275	52	5	(	(	PUNCT
ejpam-5275	52	6	13	13	NUM
ejpam-5275	52	7	)	)	PUNCT
ejpam-5275	52	8	,	,	PUNCT
ejpam-5275	52	9	we	we	PRON
ejpam-5275	52	10	also	also	ADV
ejpam-5275	52	11	derive	derive	VERB
ejpam-5275	52	12	the	the	DET
ejpam-5275	52	13	generating	generate	VERB
ejpam-5275	52	14	function	function	NOUN
ejpam-5275	52	15	as	as	SCONJ
ejpam-5275	52	16	follows	follow	VERB
ejpam-5275	52	17	.	.	PUNCT
ejpam-5275	53	1	1	1	NUM
ejpam-5275	53	2	k	k	X
ejpam-5275	53	3	!	!	PUNCT
ejpam-5275	54	1	(	(	PUNCT
ejpam-5275	54	2	et	et	X
ejpam-5275	54	3	−	−	PROPN
ejpam-5275	54	4	1)k	1)k	NUM
ejpam-5275	54	5	=	=	PUNCT
ejpam-5275	55	1	∞∑	∞∑	NUM
ejpam-5275	55	2	n	n	CCONJ
ejpam-5275	55	3	=	=	SYM
ejpam-5275	55	4	k	k	PROPN
ejpam-5275	55	5	s2(n	s2(n	PROPN
ejpam-5275	55	6	,	,	PUNCT
ejpam-5275	55	7	k	k	NOUN
ejpam-5275	55	8	)	)	PUNCT
ejpam-5275	55	9	tn	tn	PROPN
ejpam-5275	55	10	n	n	PROPN
ejpam-5275	55	11	!	!	PROPN
ejpam-5275	55	12	,	,	PUNCT
ejpam-5275	55	13	(	(	PUNCT
ejpam-5275	55	14	see[21	see[21	PROPN
ejpam-5275	55	15	,	,	PUNCT
ejpam-5275	55	16	26	26	NUM
ejpam-5275	55	17	]	]	PUNCT
ejpam-5275	55	18	)	)	PUNCT
ejpam-5275	55	19	.	.	PUNCT
ejpam-5275	56	1	(	(	PUNCT
ejpam-5275	56	2	14	14	NUM
ejpam-5275	56	3	)	)	PUNCT
ejpam-5275	56	4	in	in	ADP
ejpam-5275	56	5	2024	2024	NUM
ejpam-5275	56	6	,	,	PUNCT
ejpam-5275	56	7	kim	kim	PROPN
ejpam-5275	56	8	defined	define	VERB
ejpam-5275	56	9	the	the	DET
ejpam-5275	56	10	probabilistic	probabilistic	ADJ
ejpam-5275	56	11	stirling	stirling	NOUN
ejpam-5275	56	12	number	number	NOUN
ejpam-5275	56	13	of	of	ADP
ejpam-5275	56	14	the	the	DET
ejpam-5275	56	15	second	second	ADJ
ejpam-5275	56	16	kind	kind	NOUN
ejpam-5275	56	17	associated	associate	VERB
ejpam-5275	56	18	with	with	ADP
ejpam-5275	56	19	y	y	PROPN
ejpam-5275	56	20	are	be	AUX
ejpam-5275	56	21	given	give	VERB
ejpam-5275	56	22	by	by	ADP
ejpam-5275	56	23	1	1	NUM
ejpam-5275	56	24	k	k	NOUN
ejpam-5275	56	25	!	!	PUNCT
ejpam-5275	57	1	(	(	PUNCT
ejpam-5275	57	2	e[ey	e[ey	INTJ
ejpam-5275	57	3	t]−	t]−	NOUN
ejpam-5275	57	4	1)k	1)k	NUM
ejpam-5275	57	5	=	=	SYM
ejpam-5275	58	1	∞∑	∞∑	NUM
ejpam-5275	58	2	n	n	CCONJ
ejpam-5275	58	3	=	=	SYM
ejpam-5275	58	4	k	k	X
ejpam-5275	58	5	{	{	PUNCT
ejpam-5275	58	6	n	n	NOUN
ejpam-5275	58	7	k	k	PROPN
ejpam-5275	58	8	}	}	PUNCT
ejpam-5275	58	9	y	y	PROPN
ejpam-5275	58	10	tn	tn	PROPN
ejpam-5275	58	11	n	n	CCONJ
ejpam-5275	58	12	!	!	PROPN
ejpam-5275	58	13	,	,	PUNCT
ejpam-5275	58	14	(	(	PUNCT
ejpam-5275	58	15	see[3	see[3	ADJ
ejpam-5275	58	16	,	,	PUNCT
ejpam-5275	58	17	9	9	NUM
ejpam-5275	58	18	,	,	PUNCT
ejpam-5275	58	19	18	18	NUM
ejpam-5275	58	20	]	]	PUNCT
ejpam-5275	58	21	,	,	PUNCT
ejpam-5275	58	22	[	[	X
ejpam-5275	58	23	14	14	NUM
ejpam-5275	58	24	]	]	PUNCT
ejpam-5275	58	25	)	)	PUNCT
ejpam-5275	58	26	.	.	PUNCT
ejpam-5275	59	1	(	(	PUNCT
ejpam-5275	59	2	15	15	X
ejpam-5275	59	3	)	)	PUNCT
ejpam-5275	59	4	the	the	DET
ejpam-5275	59	5	bell	bell	NOUN
ejpam-5275	59	6	polynomials	polynomial	NOUN
ejpam-5275	59	7	are	be	AUX
ejpam-5275	59	8	defined	define	VERB
ejpam-5275	59	9	by	by	ADP
ejpam-5275	59	10	ex(e	ex(e	NOUN
ejpam-5275	59	11	t−1	t−1	NOUN
ejpam-5275	59	12	)	)	PUNCT
ejpam-5275	59	13	=	=	PUNCT
ejpam-5275	60	1	∞∑	∞∑	ADJ
ejpam-5275	60	2	n=0	n=0	NUM
ejpam-5275	60	3	beln(x	beln(x	NOUN
ejpam-5275	60	4	)	)	PUNCT
ejpam-5275	60	5	tn	tn	PROPN
ejpam-5275	60	6	n	n	PROPN
ejpam-5275	60	7	!	!	PROPN
ejpam-5275	60	8	,	,	PUNCT
ejpam-5275	60	9	(	(	PUNCT
ejpam-5275	60	10	see[13	see[13	PROPN
ejpam-5275	60	11	,	,	PUNCT
ejpam-5275	60	12	16	16	NUM
ejpam-5275	60	13	,	,	PUNCT
ejpam-5275	60	14	22	22	NUM
ejpam-5275	60	15	,	,	PUNCT
ejpam-5275	60	16	23	23	NUM
ejpam-5275	60	17	,	,	PUNCT
ejpam-5275	60	18	25	25	NUM
ejpam-5275	60	19	]	]	PUNCT
ejpam-5275	60	20	)	)	PUNCT
ejpam-5275	60	21	.	.	PUNCT
ejpam-5275	61	1	(	(	PUNCT
ejpam-5275	61	2	16	16	NUM
ejpam-5275	61	3	)	)	PUNCT
ejpam-5275	61	4	2	2	NUM
ejpam-5275	61	5	.	.	PUNCT
ejpam-5275	61	6	probabilistic	probabilistic	ADJ
ejpam-5275	61	7	type	type	NOUN
ejpam-5275	61	8	2	2	NUM
ejpam-5275	61	9	poly	poly	ADJ
ejpam-5275	61	10	-	-	PUNCT
ejpam-5275	61	11	bernoulli	bernoulli	NOUN
ejpam-5275	61	12	polynomials	polynomial	NOUN
ejpam-5275	61	13	let	let	VERB
ejpam-5275	61	14	(	(	PUNCT
ejpam-5275	61	15	yj)j≥1	yj)j≥1	NOUN
ejpam-5275	61	16	be	be	AUX
ejpam-5275	61	17	a	a	DET
ejpam-5275	61	18	sequence	sequence	NOUN
ejpam-5275	61	19	of	of	ADP
ejpam-5275	61	20	mutually	mutually	ADV
ejpam-5275	61	21	independent	independent	ADJ
ejpam-5275	61	22	copies	copy	NOUN
ejpam-5275	61	23	of	of	ADP
ejpam-5275	61	24	the	the	DET
ejpam-5275	61	25	random	random	ADJ
ejpam-5275	61	26	variable	variable	NOUN
ejpam-5275	61	27	y	y	PROPN
ejpam-5275	61	28	,	,	PUNCT
ejpam-5275	61	29	and	and	CCONJ
ejpam-5275	61	30	let	let	VERB
ejpam-5275	61	31	s0	s0	PROPN
ejpam-5275	61	32	=	=	SYM
ejpam-5275	61	33	0	0	NUM
ejpam-5275	61	34	,	,	PUNCT
ejpam-5275	61	35	sk	sk	ADP
ejpam-5275	61	36	=	=	PUNCT
ejpam-5275	61	37	y1	y1	PROPN
ejpam-5275	62	1	+	+	CCONJ
ejpam-5275	62	2	y2	y2	PROPN
ejpam-5275	62	3	+	+	SYM
ejpam-5275	62	4	·	·	PUNCT
ejpam-5275	62	5	·	·	PUNCT
ejpam-5275	62	6	·	·	PUNCT
ejpam-5275	63	1	+	+	NUM
ejpam-5275	63	2	yk	yk	PROPN
ejpam-5275	63	3	,	,	PUNCT
ejpam-5275	63	4	(	(	PUNCT
ejpam-5275	63	5	k	k	PROPN
ejpam-5275	63	6	∈	∈	PROPN
ejpam-5275	63	7	n	n	CCONJ
ejpam-5275	63	8	)	)	PUNCT
ejpam-5275	63	9	.	.	PUNCT
ejpam-5275	64	1	(	(	PUNCT
ejpam-5275	64	2	17	17	NUM
ejpam-5275	64	3	)	)	PUNCT
ejpam-5275	64	4	in	in	ADP
ejpam-5275	64	5	this	this	DET
ejpam-5275	64	6	section	section	NOUN
ejpam-5275	64	7	we	we	PRON
ejpam-5275	64	8	consider	consider	VERB
ejpam-5275	64	9	probabilistic	probabilistic	ADJ
ejpam-5275	64	10	type	type	NOUN
ejpam-5275	64	11	2	2	NUM
ejpam-5275	64	12	poly	poly	ADJ
ejpam-5275	64	13	-	-	PUNCT
ejpam-5275	64	14	bernoulli	bernoulli	NOUN
ejpam-5275	64	15	polynomials	polynomial	NOUN
ejpam-5275	64	16	.	.	PUNCT
ejpam-5275	65	1	ek(log(1	ek(log(1	PROPN
ejpam-5275	65	2	+	+	NUM
ejpam-5275	65	3	t	t	PROPN
ejpam-5275	65	4	)	)	PUNCT
ejpam-5275	65	5	)	)	PUNCT
ejpam-5275	66	1	e[ey	e[ey	ADP
ejpam-5275	66	2	t]−	t]−	NOUN
ejpam-5275	66	3	1	1	NUM
ejpam-5275	66	4	(	(	PUNCT
ejpam-5275	66	5	e[ey	e[ey	ADJ
ejpam-5275	66	6	t])x	t])x	NOUN
ejpam-5275	66	7	=	=	SYM
ejpam-5275	66	8	∞∑	∞∑	NUM
ejpam-5275	66	9	n=0	n=0	NUM
ejpam-5275	66	10	β(k	β(k	PROPN
ejpam-5275	66	11	,	,	PUNCT
ejpam-5275	66	12	y	y	PROPN
ejpam-5275	66	13	)	)	PUNCT
ejpam-5275	66	14	n	n	CCONJ
ejpam-5275	66	15	(	(	PUNCT
ejpam-5275	66	16	x	x	X
ejpam-5275	66	17	)	)	PUNCT
ejpam-5275	66	18	tn	tn	PROPN
ejpam-5275	66	19	n	n	NUM
ejpam-5275	66	20	!	!	PUNCT
ejpam-5275	66	21	.	.	PUNCT
ejpam-5275	67	1	(	(	PUNCT
ejpam-5275	67	2	18	18	NUM
ejpam-5275	67	3	)	)	PUNCT
ejpam-5275	67	4	s.	s.	PROPN
ejpam-5275	67	5	h.	h.	PROPN
ejpam-5275	67	6	lee	lee	PROPN
ejpam-5275	67	7	,	,	PUNCT
ejpam-5275	67	8	l.	l.	PROPN
ejpam-5275	67	9	chen	chen	PROPN
ejpam-5275	67	10	,	,	PUNCT
ejpam-5275	67	11	w.	w.	PROPN
ejpam-5275	67	12	kim	kim	PROPN
ejpam-5275	67	13	/	/	SYM
ejpam-5275	67	14	eur	eur	PROPN
ejpam-5275	67	15	.	.	PUNCT
ejpam-5275	68	1	j.	j.	PROPN
ejpam-5275	68	2	pure	pure	PROPN
ejpam-5275	68	3	appl	appl	PROPN
ejpam-5275	68	4	.	.	PROPN
ejpam-5275	68	5	math	math	PROPN
ejpam-5275	68	6	,	,	PUNCT
ejpam-5275	68	7	17	17	NUM
ejpam-5275	68	8	(	(	PUNCT
ejpam-5275	68	9	3	3	NUM
ejpam-5275	68	10	)	)	PUNCT
ejpam-5275	68	11	(	(	PUNCT
ejpam-5275	68	12	2024	2024	NUM
ejpam-5275	68	13	)	)	PUNCT
ejpam-5275	68	14	,	,	PUNCT
ejpam-5275	68	15	2336	2336	NUM
ejpam-5275	68	16	-	-	SYM
ejpam-5275	68	17	2348	2348	NUM
ejpam-5275	68	18	2339	2339	NUM
ejpam-5275	69	1	when	when	SCONJ
ejpam-5275	69	2	x	x	X
ejpam-5275	69	3	=	=	SYM
ejpam-5275	69	4	0	0	NUM
ejpam-5275	69	5	,	,	PUNCT
ejpam-5275	69	6	β	β	X
ejpam-5275	69	7	(	(	PUNCT
ejpam-5275	69	8	k	k	X
ejpam-5275	69	9	,	,	PUNCT
ejpam-5275	69	10	y	y	PROPN
ejpam-5275	69	11	)	)	PUNCT
ejpam-5275	69	12	n	n	CCONJ
ejpam-5275	69	13	(	(	PUNCT
ejpam-5275	69	14	0	0	NUM
ejpam-5275	69	15	)	)	PUNCT
ejpam-5275	69	16	=	=	SYM
ejpam-5275	69	17	β	β	X
ejpam-5275	69	18	(	(	PUNCT
ejpam-5275	69	19	k	k	X
ejpam-5275	69	20	,	,	PUNCT
ejpam-5275	69	21	y	y	PROPN
ejpam-5275	69	22	)	)	PUNCT
ejpam-5275	69	23	n	n	CCONJ
ejpam-5275	69	24	are	be	AUX
ejpam-5275	69	25	called	call	VERB
ejpam-5275	69	26	probabilistic	probabilistic	ADJ
ejpam-5275	69	27	type	type	NOUN
ejpam-5275	69	28	2	2	NUM
ejpam-5275	69	29	poly	poly	ADJ
ejpam-5275	69	30	-	-	PUNCT
ejpam-5275	69	31	bernoulli	bernoulli	NOUN
ejpam-5275	69	32	numbers	number	NOUN
ejpam-5275	69	33	.	.	PUNCT
ejpam-5275	70	1	from	from	ADP
ejpam-5275	70	2	(	(	PUNCT
ejpam-5275	70	3	18	18	NUM
ejpam-5275	70	4	)	)	PUNCT
ejpam-5275	70	5	,	,	PUNCT
ejpam-5275	70	6	we	we	PRON
ejpam-5275	70	7	get	get	VERB
ejpam-5275	70	8	∞∑	∞∑	NUM
ejpam-5275	70	9	n=0	n=0	NUM
ejpam-5275	70	10	β(k	β(k	PROPN
ejpam-5275	70	11	,	,	PUNCT
ejpam-5275	70	12	y	y	PROPN
ejpam-5275	70	13	)	)	PUNCT
ejpam-5275	70	14	n	n	CCONJ
ejpam-5275	70	15	(	(	PUNCT
ejpam-5275	70	16	x	x	X
ejpam-5275	70	17	)	)	PUNCT
ejpam-5275	70	18	tn	tn	PROPN
ejpam-5275	70	19	n	n	NOUN
ejpam-5275	70	20	!	!	PUNCT
ejpam-5275	71	1	=	=	PUNCT
ejpam-5275	71	2	ek(log(1	ek(log(1	PROPN
ejpam-5275	71	3	+	+	NUM
ejpam-5275	71	4	t	t	PROPN
ejpam-5275	71	5	)	)	PUNCT
ejpam-5275	71	6	)	)	PUNCT
ejpam-5275	72	1	e[ey	e[ey	ADP
ejpam-5275	72	2	t]−	t]−	NOUN
ejpam-5275	72	3	1	1	NUM
ejpam-5275	72	4	(	(	PUNCT
ejpam-5275	72	5	e[ey	e[ey	PROPN
ejpam-5275	72	6	t])x	t])x	PROPN
ejpam-5275	72	7	(	(	PUNCT
ejpam-5275	72	8	19	19	NUM
ejpam-5275	72	9	)	)	PUNCT
ejpam-5275	72	10	=	=	NOUN
ejpam-5275	72	11	∞∑	∞∑	NUM
ejpam-5275	72	12	j=0	j=0	PROPN
ejpam-5275	72	13	β	β	X
ejpam-5275	72	14	(	(	PUNCT
ejpam-5275	72	15	k	k	X
ejpam-5275	72	16	,	,	PUNCT
ejpam-5275	72	17	y	y	PROPN
ejpam-5275	72	18	)	)	PUNCT
ejpam-5275	72	19	j	j	PROPN
ejpam-5275	72	20	tj	tj	PROPN
ejpam-5275	72	21	j	j	PROPN
ejpam-5275	72	22	!	!	PUNCT
ejpam-5275	73	1	∞∑	∞∑	ADJ
ejpam-5275	73	2	k=0	k=0	PROPN
ejpam-5275	73	3	(	(	PUNCT
ejpam-5275	73	4	x	x	SYM
ejpam-5275	73	5	k	k	X
ejpam-5275	73	6	)	)	PUNCT
ejpam-5275	74	1	k	k	X
ejpam-5275	74	2	!	!	PUNCT
ejpam-5275	75	1	∞∑	∞∑	NUM
ejpam-5275	75	2	m	m	NOUN
ejpam-5275	75	3	=	=	VERB
ejpam-5275	75	4	k	k	X
ejpam-5275	75	5	{	{	PUNCT
ejpam-5275	75	6	m	m	PROPN
ejpam-5275	75	7	k	k	X
ejpam-5275	75	8	}	}	PUNCT
ejpam-5275	75	9	y	y	PROPN
ejpam-5275	75	10	tm	tm	NOUN
ejpam-5275	75	11	m	m	PROPN
ejpam-5275	75	12	!	!	PUNCT
ejpam-5275	75	13	=	=	NOUN
ejpam-5275	76	1	∞∑	∞∑	PRON
ejpam-5275	76	2	n=0	n=0	NUM
ejpam-5275	76	3	n∑	n∑	NOUN
ejpam-5275	76	4	m=0	m=0	PROPN
ejpam-5275	76	5	m∑	m∑	AUX
ejpam-5275	76	6	k=0	k=0	PROPN
ejpam-5275	76	7	(	(	PUNCT
ejpam-5275	76	8	n	n	X
ejpam-5275	76	9	m	m	VERB
ejpam-5275	76	10	)	)	PUNCT
ejpam-5275	76	11	β	β	X
ejpam-5275	76	12	(	(	PUNCT
ejpam-5275	76	13	k	k	X
ejpam-5275	76	14	,	,	PUNCT
ejpam-5275	76	15	y	y	PROPN
ejpam-5275	76	16	)	)	PUNCT
ejpam-5275	76	17	n−m	n−m	PROPN
ejpam-5275	76	18	(	(	PUNCT
ejpam-5275	76	19	x)k	x)k	X
ejpam-5275	76	20	{	{	PUNCT
ejpam-5275	76	21	m	m	VERB
ejpam-5275	76	22	k	k	X
ejpam-5275	76	23	}	}	PUNCT
ejpam-5275	76	24	y	y	PROPN
ejpam-5275	76	25	tn	tn	PROPN
ejpam-5275	76	26	n	n	PROPN
ejpam-5275	76	27	!	!	PUNCT
ejpam-5275	76	28	.	.	PUNCT
ejpam-5275	77	1	therefore	therefore	ADV
ejpam-5275	77	2	,	,	PUNCT
ejpam-5275	77	3	by	by	ADP
ejpam-5275	77	4	comparing	compare	VERB
ejpam-5275	77	5	the	the	DET
ejpam-5275	77	6	coefficients	coefficient	NOUN
ejpam-5275	77	7	on	on	ADP
ejpam-5275	77	8	both	both	DET
ejpam-5275	77	9	sides	side	NOUN
ejpam-5275	77	10	of	of	ADP
ejpam-5275	77	11	(	(	PUNCT
ejpam-5275	77	12	19	19	NUM
ejpam-5275	77	13	)	)	PUNCT
ejpam-5275	77	14	,	,	PUNCT
ejpam-5275	77	15	we	we	PRON
ejpam-5275	77	16	have	have	VERB
ejpam-5275	77	17	the	the	DET
ejpam-5275	77	18	following	follow	VERB
ejpam-5275	77	19	theorem	theorem	VERB
ejpam-5275	77	20	.	.	PUNCT
ejpam-5275	77	21	theorem	theorem	NOUN
ejpam-5275	77	22	1	1	NUM
ejpam-5275	77	23	.	.	PUNCT
ejpam-5275	77	24	for	for	ADP
ejpam-5275	77	25	n	n	PRON
ejpam-5275	77	26	,	,	PUNCT
ejpam-5275	77	27	k	k	PROPN
ejpam-5275	77	28	≥	≥	PROPN
ejpam-5275	77	29	0	0	NUM
ejpam-5275	77	30	,	,	PUNCT
ejpam-5275	77	31	we	we	PRON
ejpam-5275	77	32	have	have	VERB
ejpam-5275	77	33	β(k	β(k	PROPN
ejpam-5275	77	34	,	,	PUNCT
ejpam-5275	77	35	y	y	PROPN
ejpam-5275	77	36	)	)	PUNCT
ejpam-5275	78	1	n	n	PROPN
ejpam-5275	78	2	=	=	SYM
ejpam-5275	78	3	n∑	n∑	PROPN
ejpam-5275	78	4	m=0	m=0	PROPN
ejpam-5275	78	5	m∑	m∑	AUX
ejpam-5275	78	6	k=0	k=0	PROPN
ejpam-5275	78	7	(	(	PUNCT
ejpam-5275	78	8	n	n	X
ejpam-5275	78	9	m	m	VERB
ejpam-5275	78	10	)	)	PUNCT
ejpam-5275	79	1	β	β	X
ejpam-5275	79	2	(	(	PUNCT
ejpam-5275	79	3	k	k	X
ejpam-5275	79	4	,	,	PUNCT
ejpam-5275	79	5	y	y	PROPN
ejpam-5275	79	6	)	)	PUNCT
ejpam-5275	79	7	n−m	n−m	PROPN
ejpam-5275	79	8	(	(	PUNCT
ejpam-5275	79	9	x)k	x)k	X
ejpam-5275	79	10	{	{	PUNCT
ejpam-5275	79	11	m	m	VERB
ejpam-5275	79	12	k	k	X
ejpam-5275	79	13	}	}	PUNCT
ejpam-5275	79	14	y	y	PROPN
ejpam-5275	79	15	.	.	PUNCT
ejpam-5275	80	1	from	from	ADP
ejpam-5275	80	2	(	(	PUNCT
ejpam-5275	80	3	18	18	NUM
ejpam-5275	80	4	)	)	PUNCT
ejpam-5275	80	5	,	,	PUNCT
ejpam-5275	80	6	we	we	PRON
ejpam-5275	80	7	have	have	VERB
ejpam-5275	80	8	∞∑	∞∑	NUM
ejpam-5275	80	9	n=0	n=0	NUM
ejpam-5275	80	10	β(k	β(k	PROPN
ejpam-5275	80	11	,	,	PUNCT
ejpam-5275	80	12	y	y	PROPN
ejpam-5275	80	13	)	)	PUNCT
ejpam-5275	80	14	n	n	CCONJ
ejpam-5275	80	15	(	(	PUNCT
ejpam-5275	80	16	x	x	X
ejpam-5275	80	17	)	)	PUNCT
ejpam-5275	80	18	tn	tn	PROPN
ejpam-5275	80	19	n	n	NOUN
ejpam-5275	80	20	!	!	PUNCT
ejpam-5275	81	1	=	=	PUNCT
ejpam-5275	81	2	ek(log(1	ek(log(1	PROPN
ejpam-5275	81	3	+	+	NUM
ejpam-5275	81	4	t	t	PROPN
ejpam-5275	81	5	)	)	PUNCT
ejpam-5275	81	6	)	)	PUNCT
ejpam-5275	82	1	t	t	PROPN
ejpam-5275	82	2	t	t	PROPN
ejpam-5275	82	3	e[ey	e[ey	PROPN
ejpam-5275	82	4	t]−	t]−	PROPN
ejpam-5275	82	5	1	1	NUM
ejpam-5275	82	6	(	(	PUNCT
ejpam-5275	82	7	e[ey	e[ey	PROPN
ejpam-5275	82	8	t])x	t])x	PROPN
ejpam-5275	82	9	(	(	PUNCT
ejpam-5275	82	10	20	20	NUM
ejpam-5275	82	11	)	)	PUNCT
ejpam-5275	82	12	=	=	NOUN
ejpam-5275	83	1	∞∑	∞∑	NUM
ejpam-5275	83	2	l=0	l=0	PROPN
ejpam-5275	83	3	by	by	ADP
ejpam-5275	83	4	l	l	PROPN
ejpam-5275	83	5	(	(	PUNCT
ejpam-5275	83	6	x	x	X
ejpam-5275	83	7	)	)	PUNCT
ejpam-5275	83	8	tl	tl	PROPN
ejpam-5275	83	9	l	l	NOUN
ejpam-5275	83	10	!	!	PUNCT
ejpam-5275	84	1	∞∑	∞∑	NUM
ejpam-5275	84	2	i=1	i=1	PRON
ejpam-5275	84	3	(	(	PUNCT
ejpam-5275	84	4	log(1	log(1	NOUN
ejpam-5275	84	5	+	+	CCONJ
ejpam-5275	84	6	t))i	t))i	NOUN
ejpam-5275	84	7	(	(	PUNCT
ejpam-5275	84	8	i−	i−	PROPN
ejpam-5275	84	9	1)!ik	1)!ik	NUM
ejpam-5275	84	10	=	=	SYM
ejpam-5275	85	1	∞∑	∞∑	NUM
ejpam-5275	85	2	l=0	l=0	PROPN
ejpam-5275	85	3	by	by	ADP
ejpam-5275	85	4	l	l	PROPN
ejpam-5275	85	5	(	(	PUNCT
ejpam-5275	85	6	x	x	X
ejpam-5275	85	7	)	)	PUNCT
ejpam-5275	85	8	tl	tl	PROPN
ejpam-5275	85	9	l	l	NOUN
ejpam-5275	85	10	!	!	NOUN
ejpam-5275	86	1	1	1	NUM
ejpam-5275	86	2	t	t	NOUN
ejpam-5275	86	3	∞∑	∞∑	NUM
ejpam-5275	86	4	i=1	i=1	PROPN
ejpam-5275	86	5	1	1	NUM
ejpam-5275	86	6	ik−1	ik−1	PROPN
ejpam-5275	86	7	∞∑	∞∑	PROPN
ejpam-5275	86	8	j	j	PROPN
ejpam-5275	86	9	=	=	PROPN
ejpam-5275	86	10	i	i	PROPN
ejpam-5275	86	11	s1(j	s1(j	PROPN
ejpam-5275	86	12	,	,	PUNCT
ejpam-5275	86	13	i	i	NOUN
ejpam-5275	86	14	)	)	PUNCT
ejpam-5275	86	15	tj	tj	PROPN
ejpam-5275	86	16	j	j	PROPN
ejpam-5275	86	17	!	!	PUNCT
ejpam-5275	86	18	=	=	PUNCT
ejpam-5275	87	1	∞∑	∞∑	NUM
ejpam-5275	87	2	l=0	l=0	PROPN
ejpam-5275	87	3	by	by	ADP
ejpam-5275	87	4	l	l	PROPN
ejpam-5275	87	5	(	(	PUNCT
ejpam-5275	87	6	x	x	X
ejpam-5275	87	7	)	)	PUNCT
ejpam-5275	87	8	tl	tl	PROPN
ejpam-5275	87	9	l	l	NOUN
ejpam-5275	87	10	!	!	PUNCT
ejpam-5275	88	1	∞∑	∞∑	NUM
ejpam-5275	88	2	j=0	j=0	PROPN
ejpam-5275	88	3	j+1∑	j+1∑	PROPN
ejpam-5275	88	4	i=1	i=1	PROPN
ejpam-5275	88	5	1	1	NUM
ejpam-5275	88	6	ik−1	ik−1	PROPN
ejpam-5275	88	7	s1(j	s1(j	PROPN
ejpam-5275	88	8	+	+	NOUN
ejpam-5275	88	9	1	1	NUM
ejpam-5275	88	10	,	,	PUNCT
ejpam-5275	88	11	i	i	NOUN
ejpam-5275	88	12	)	)	PUNCT
ejpam-5275	88	13	j	j	PROPN
ejpam-5275	89	1	+	+	CCONJ
ejpam-5275	89	2	1	1	NUM
ejpam-5275	89	3	tj	tj	X
ejpam-5275	89	4	j	j	PROPN
ejpam-5275	89	5	!	!	PUNCT
ejpam-5275	89	6	=	=	PUNCT
ejpam-5275	90	1	∞∑	∞∑	PRON
ejpam-5275	90	2	n=0	n=0	PUNCT
ejpam-5275	90	3			PROPN
ejpam-5275	90	4	n∑	n∑	PROPN
ejpam-5275	90	5	j=0	j=0	PROPN
ejpam-5275	90	6	j+1∑	j+1∑	PROPN
ejpam-5275	90	7	i=1	i=1	PROPN
ejpam-5275	91	1	(	(	PUNCT
ejpam-5275	91	2	n	n	X
ejpam-5275	91	3	j	j	PROPN
ejpam-5275	91	4	)	)	PUNCT
ejpam-5275	92	1	s1(j	s1(j	PROPN
ejpam-5275	93	1	+	+	NUM
ejpam-5275	93	2	1	1	NUM
ejpam-5275	93	3	,	,	PUNCT
ejpam-5275	93	4	i	i	NOUN
ejpam-5275	93	5	)	)	PUNCT
ejpam-5275	93	6	ik−1(j	ik−1(j	NOUN
ejpam-5275	93	7	+	+	CCONJ
ejpam-5275	93	8	1	1	X
ejpam-5275	93	9	)	)	PUNCT
ejpam-5275	93	10	by	by	ADP
ejpam-5275	93	11	n−j(x	n−j(x	NOUN
ejpam-5275	93	12	)	)	PUNCT
ejpam-5275	93	13			PROPN
ejpam-5275	93	14	tn	tn	PROPN
ejpam-5275	93	15	n	n	NOUN
ejpam-5275	93	16	!	!	PUNCT
ejpam-5275	93	17	.	.	PUNCT
ejpam-5275	94	1	thus	thus	ADV
ejpam-5275	94	2	,	,	PUNCT
ejpam-5275	94	3	by	by	ADP
ejpam-5275	94	4	comparing	compare	VERB
ejpam-5275	94	5	the	the	DET
ejpam-5275	94	6	coefficients	coefficient	NOUN
ejpam-5275	94	7	on	on	ADP
ejpam-5275	94	8	both	both	DET
ejpam-5275	94	9	sides	side	NOUN
ejpam-5275	94	10	of	of	ADP
ejpam-5275	94	11	(	(	PUNCT
ejpam-5275	94	12	20	20	NUM
ejpam-5275	94	13	)	)	PUNCT
ejpam-5275	94	14	,	,	PUNCT
ejpam-5275	94	15	we	we	PRON
ejpam-5275	94	16	have	have	VERB
ejpam-5275	94	17	the	the	DET
ejpam-5275	94	18	following	follow	VERB
ejpam-5275	94	19	theorem	theorem	VERB
ejpam-5275	94	20	.	.	PUNCT
ejpam-5275	94	21	theorem	theorem	NOUN
ejpam-5275	94	22	2	2	NUM
ejpam-5275	94	23	.	.	NOUN
ejpam-5275	94	24	for	for	ADP
ejpam-5275	94	25	n	n	PRON
ejpam-5275	94	26	,	,	PUNCT
ejpam-5275	94	27	j	j	PROPN
ejpam-5275	94	28	≥	≥	NUM
ejpam-5275	94	29	0	0	NUM
ejpam-5275	94	30	,	,	PUNCT
ejpam-5275	94	31	we	we	PRON
ejpam-5275	94	32	have	have	VERB
ejpam-5275	94	33	β(k	β(k	PROPN
ejpam-5275	94	34	,	,	PUNCT
ejpam-5275	94	35	y	y	PROPN
ejpam-5275	94	36	)	)	PUNCT
ejpam-5275	95	1	n	n	CCONJ
ejpam-5275	95	2	(	(	PUNCT
ejpam-5275	95	3	x	x	X
ejpam-5275	95	4	)	)	PUNCT
ejpam-5275	95	5	=	=	SYM
ejpam-5275	96	1	n∑	n∑	PROPN
ejpam-5275	96	2	j=0	j=0	PROPN
ejpam-5275	96	3	j+1∑	j+1∑	PROPN
ejpam-5275	96	4	i=1	i=1	PROPN
ejpam-5275	97	1	(	(	PUNCT
ejpam-5275	97	2	n	n	X
ejpam-5275	97	3	j	j	PROPN
ejpam-5275	97	4	)	)	PUNCT
ejpam-5275	98	1	s1(j	s1(j	PROPN
ejpam-5275	99	1	+	+	NUM
ejpam-5275	99	2	1	1	NUM
ejpam-5275	99	3	,	,	PUNCT
ejpam-5275	99	4	i	i	NOUN
ejpam-5275	99	5	)	)	PUNCT
ejpam-5275	99	6	ik−1(j	ik−1(j	NOUN
ejpam-5275	99	7	+	+	CCONJ
ejpam-5275	99	8	1	1	X
ejpam-5275	99	9	)	)	PUNCT
ejpam-5275	99	10	by	by	ADP
ejpam-5275	99	11	n−j(x	n−j(x	NOUN
ejpam-5275	99	12	)	)	PUNCT
ejpam-5275	99	13	.	.	PUNCT
ejpam-5275	100	1	s.	s.	PROPN
ejpam-5275	100	2	h.	h.	PROPN
ejpam-5275	100	3	lee	lee	PROPN
ejpam-5275	100	4	,	,	PUNCT
ejpam-5275	100	5	l.	l.	PROPN
ejpam-5275	100	6	chen	chen	PROPN
ejpam-5275	100	7	,	,	PUNCT
ejpam-5275	100	8	w.	w.	PROPN
ejpam-5275	100	9	kim	kim	PROPN
ejpam-5275	100	10	/	/	SYM
ejpam-5275	100	11	eur	eur	PROPN
ejpam-5275	100	12	.	.	PUNCT
ejpam-5275	101	1	j.	j.	PROPN
ejpam-5275	101	2	pure	pure	PROPN
ejpam-5275	101	3	appl	appl	PROPN
ejpam-5275	101	4	.	.	PROPN
ejpam-5275	101	5	math	math	PROPN
ejpam-5275	101	6	,	,	PUNCT
ejpam-5275	101	7	17	17	NUM
ejpam-5275	101	8	(	(	PUNCT
ejpam-5275	101	9	3	3	NUM
ejpam-5275	101	10	)	)	PUNCT
ejpam-5275	101	11	(	(	PUNCT
ejpam-5275	101	12	2024	2024	NUM
ejpam-5275	101	13	)	)	PUNCT
ejpam-5275	101	14	,	,	PUNCT
ejpam-5275	101	15	2336	2336	NUM
ejpam-5275	101	16	-	-	SYM
ejpam-5275	101	17	2348	2348	NUM
ejpam-5275	101	18	2340	2340	NUM
ejpam-5275	101	19	now	now	ADV
ejpam-5275	101	20	,	,	PUNCT
ejpam-5275	101	21	we	we	PRON
ejpam-5275	101	22	observe	observe	VERB
ejpam-5275	101	23	that	that	SCONJ
ejpam-5275	101	24	n∑	n∑	PROPN
ejpam-5275	101	25	m=0	m=0	PROPN
ejpam-5275	101	26	(	(	PUNCT
ejpam-5275	101	27	e[ey	e[ey	PROPN
ejpam-5275	101	28	t	t	PROPN
ejpam-5275	101	29	]	]	PUNCT
ejpam-5275	101	30	)	)	PUNCT
ejpam-5275	101	31	m	m	VERB
ejpam-5275	101	32	=	=	SYM
ejpam-5275	101	33	e[ey	e[ey	ADJ
ejpam-5275	101	34	t]n+1	t]n+1	NOUN
ejpam-5275	101	35	−	−	NOUN
ejpam-5275	101	36	1	1	NUM
ejpam-5275	101	37	e[ey	e[ey	PUNCT
ejpam-5275	101	38	t]−	t]−	NOUN
ejpam-5275	101	39	1	1	NUM
ejpam-5275	101	40	.	.	PUNCT
ejpam-5275	102	1	(	(	PUNCT
ejpam-5275	102	2	21	21	NUM
ejpam-5275	102	3	)	)	PUNCT
ejpam-5275	102	4	from	from	ADP
ejpam-5275	102	5	(	(	PUNCT
ejpam-5275	102	6	21	21	NUM
ejpam-5275	102	7	)	)	PUNCT
ejpam-5275	102	8	,	,	PUNCT
ejpam-5275	102	9	we	we	PRON
ejpam-5275	102	10	have	have	VERB
ejpam-5275	102	11	n∑	n∑	PROPN
ejpam-5275	102	12	m=0	m=0	PROPN
ejpam-5275	102	13	e[ey	e[ey	PROPN
ejpam-5275	102	14	t	t	PROPN
ejpam-5275	102	15	]	]	X
ejpam-5275	102	16	=	=	SYM
ejpam-5275	103	1	1	1	NUM
ejpam-5275	103	2	e1(log(1	e1(log(1	PROPN
ejpam-5275	103	3	+	+	PROPN
ejpam-5275	103	4	t	t	PROPN
ejpam-5275	103	5	)	)	PUNCT
ejpam-5275	103	6	)	)	PUNCT
ejpam-5275	104	1	e1(log(1	e1(log(1	PROPN
ejpam-5275	104	2	+	+	NUM
ejpam-5275	104	3	t	t	PROPN
ejpam-5275	104	4	)	)	PUNCT
ejpam-5275	104	5	)	)	PUNCT
ejpam-5275	105	1	e[ey	e[ey	ADP
ejpam-5275	105	2	t]−	t]−	NOUN
ejpam-5275	105	3	1	1	NUM
ejpam-5275	105	4	(	(	PUNCT
ejpam-5275	105	5	e[ey	e[ey	PROPN
ejpam-5275	105	6	t]n+1	t]n+1	NOUN
ejpam-5275	105	7	−	−	NOUN
ejpam-5275	105	8	1	1	NUM
ejpam-5275	105	9	)	)	PUNCT
ejpam-5275	105	10	(	(	PUNCT
ejpam-5275	105	11	22	22	NUM
ejpam-5275	105	12	)	)	PUNCT
ejpam-5275	105	13	=	=	SYM
ejpam-5275	105	14	1	1	NUM
ejpam-5275	105	15	t	t	NOUN
ejpam-5275	105	16	t	t	NOUN
ejpam-5275	105	17	e[ey	e[ey	PROPN
ejpam-5275	105	18	t]−	t]−	PROPN
ejpam-5275	105	19	1	1	NUM
ejpam-5275	105	20	(	(	PUNCT
ejpam-5275	105	21	e[ey	e[ey	PROPN
ejpam-5275	105	22	t]n+1	t]n+1	NOUN
ejpam-5275	105	23	−	−	NOUN
ejpam-5275	105	24	1	1	NUM
ejpam-5275	105	25	)	)	PUNCT
ejpam-5275	105	26	=	=	SYM
ejpam-5275	105	27	1	1	NUM
ejpam-5275	105	28	t	t	NOUN
ejpam-5275	105	29	(	(	PUNCT
ejpam-5275	105	30	∞∑	∞∑	NUM
ejpam-5275	105	31	l=0	l=0	PROPN
ejpam-5275	105	32	β	β	X
ejpam-5275	105	33	(	(	PUNCT
ejpam-5275	105	34	1,y	1,y	NUM
ejpam-5275	105	35	)	)	PUNCT
ejpam-5275	105	36	l	l	NOUN
ejpam-5275	106	1	−	−	PROPN
ejpam-5275	106	2	∞∑	∞∑	NUM
ejpam-5275	106	3	l=0	l=0	PROPN
ejpam-5275	106	4	β	β	X
ejpam-5275	106	5	(	(	PUNCT
ejpam-5275	106	6	1,y	1,y	PROPN
ejpam-5275	106	7	)	)	PUNCT
ejpam-5275	107	1	l	l	NOUN
ejpam-5275	107	2	tl	tl	PROPN
ejpam-5275	107	3	l	l	NOUN
ejpam-5275	107	4	!	!	PUNCT
ejpam-5275	107	5	)	)	PUNCT
ejpam-5275	108	1	=	=	PUNCT
ejpam-5275	109	1	∞∑	∞∑	NUM
ejpam-5275	109	2	l=0	l=0	PROPN
ejpam-5275	109	3	β	β	X
ejpam-5275	109	4	(	(	PUNCT
ejpam-5275	109	5	1,y	1,y	NUM
ejpam-5275	109	6	)	)	PUNCT
ejpam-5275	109	7	l+1	l+1	X
ejpam-5275	109	8	(	(	PUNCT
ejpam-5275	109	9	n+	n+	NUM
ejpam-5275	109	10	1)−	1)−	NUM
ejpam-5275	109	11	β	β	X
ejpam-5275	109	12	(	(	PUNCT
ejpam-5275	109	13	1,y	1,y	NUM
ejpam-5275	109	14	)	)	PUNCT
ejpam-5275	109	15	l+1	l+1	X
ejpam-5275	110	1	l	l	NOUN
ejpam-5275	111	1	+	+	CCONJ
ejpam-5275	111	2	1	1	NUM
ejpam-5275	111	3	tl	tl	PROPN
ejpam-5275	111	4	l	l	NOUN
ejpam-5275	111	5	!	!	PUNCT
ejpam-5275	111	6	.	.	PUNCT
ejpam-5275	112	1	on	on	ADP
ejpam-5275	112	2	the	the	DET
ejpam-5275	112	3	other	other	ADJ
ejpam-5275	112	4	hand	hand	NOUN
ejpam-5275	112	5	,	,	PUNCT
ejpam-5275	112	6	n∑	n∑	PROPN
ejpam-5275	112	7	m=0	m=0	PROPN
ejpam-5275	112	8	(	(	PUNCT
ejpam-5275	112	9	e[ey	e[ey	PROPN
ejpam-5275	112	10	t	t	PROPN
ejpam-5275	112	11	]	]	PUNCT
ejpam-5275	112	12	)	)	PUNCT
ejpam-5275	112	13	m	m	PROPN
ejpam-5275	112	14	=	=	SYM
ejpam-5275	112	15	n∑	n∑	PROPN
ejpam-5275	112	16	m=0	m=0	PROPN
ejpam-5275	112	17	e[e(y1+y2+···+ym)t	e[e(y1+y2+···+ym)t	PROPN
ejpam-5275	112	18	]	]	X
ejpam-5275	112	19	(	(	PUNCT
ejpam-5275	112	20	23	23	NUM
ejpam-5275	112	21	)	)	PUNCT
ejpam-5275	112	22	=	=	SYM
ejpam-5275	112	23	n∑	n∑	NOUN
ejpam-5275	112	24	m=0	m=0	PROPN
ejpam-5275	113	1	∞∑	∞∑	NUM
ejpam-5275	113	2	l=0	l=0	PROPN
ejpam-5275	113	3	e[sl	e[sl	PROPN
ejpam-5275	113	4	m	m	PROPN
ejpam-5275	113	5	]	]	X
ejpam-5275	113	6	tl	tl	PROPN
ejpam-5275	113	7	l	l	NOUN
ejpam-5275	113	8	!	!	PUNCT
ejpam-5275	114	1	=	=	PUNCT
ejpam-5275	115	1	∞∑	∞∑	NUM
ejpam-5275	115	2	l=0	l=0	PROPN
ejpam-5275	115	3	n∑	n∑	X
ejpam-5275	115	4	m=0	m=0	PROPN
ejpam-5275	115	5	e[sl	e[sl	PROPN
ejpam-5275	115	6	m	m	PROPN
ejpam-5275	115	7	]	]	X
ejpam-5275	115	8	tl	tl	PROPN
ejpam-5275	115	9	l	l	NOUN
ejpam-5275	115	10	!	!	PUNCT
ejpam-5275	115	11	.	.	PUNCT
ejpam-5275	116	1	hence	hence	ADV
ejpam-5275	116	2	,	,	PUNCT
ejpam-5275	116	3	comparing	compare	VERB
ejpam-5275	116	4	the	the	DET
ejpam-5275	116	5	coefficients	coefficient	NOUN
ejpam-5275	116	6	on	on	ADP
ejpam-5275	116	7	both	both	DET
ejpam-5275	116	8	sides	side	NOUN
ejpam-5275	116	9	of	of	ADP
ejpam-5275	116	10	(	(	PUNCT
ejpam-5275	116	11	22	22	NUM
ejpam-5275	116	12	)	)	PUNCT
ejpam-5275	116	13	and	and	CCONJ
ejpam-5275	116	14	(	(	PUNCT
ejpam-5275	116	15	23	23	NUM
ejpam-5275	116	16	)	)	PUNCT
ejpam-5275	116	17	,	,	PUNCT
ejpam-5275	116	18	we	we	PRON
ejpam-5275	116	19	have	have	VERB
ejpam-5275	116	20	the	the	DET
ejpam-5275	116	21	following	follow	VERB
ejpam-5275	116	22	theorem	theorem	VERB
ejpam-5275	116	23	.	.	PUNCT
ejpam-5275	116	24	theorem	theorem	NOUN
ejpam-5275	116	25	3	3	NUM
ejpam-5275	116	26	.	.	X
ejpam-5275	116	27	for	for	ADP
ejpam-5275	116	28	n	n	PRON
ejpam-5275	116	29	≥	≥	NOUN
ejpam-5275	116	30	0	0	NUM
ejpam-5275	116	31	,	,	PUNCT
ejpam-5275	116	32	we	we	PRON
ejpam-5275	116	33	have	have	VERB
ejpam-5275	116	34	n∑	n∑	PROPN
ejpam-5275	116	35	m=0	m=0	PROPN
ejpam-5275	116	36	e[sm	e[sm	PROPN
ejpam-5275	116	37	]	]	X
ejpam-5275	117	1	=	=	X
ejpam-5275	117	2	β	β	X
ejpam-5275	117	3	(	(	PUNCT
ejpam-5275	117	4	1,y	1,y	NUM
ejpam-5275	117	5	)	)	PUNCT
ejpam-5275	117	6	l+1	l+1	X
ejpam-5275	117	7	(	(	PUNCT
ejpam-5275	117	8	n+	n+	NUM
ejpam-5275	117	9	1)−	1)−	NUM
ejpam-5275	117	10	β	β	X
ejpam-5275	117	11	(	(	PUNCT
ejpam-5275	117	12	1,y	1,y	NUM
ejpam-5275	117	13	)	)	PUNCT
ejpam-5275	117	14	l+1	l+1	X
ejpam-5275	118	1	l	l	NOUN
ejpam-5275	119	1	+	+	CCONJ
ejpam-5275	119	2	1	1	NUM
ejpam-5275	119	3	.	.	PUNCT
ejpam-5275	120	1	from	from	ADP
ejpam-5275	120	2	(	(	PUNCT
ejpam-5275	120	3	3	3	NUM
ejpam-5275	120	4	)	)	PUNCT
ejpam-5275	120	5	,	,	PUNCT
ejpam-5275	120	6	we	we	PRON
ejpam-5275	120	7	have	have	VERB
ejpam-5275	120	8	em(log(1	em(log(1	NOUN
ejpam-5275	121	1	+	+	X
ejpam-5275	121	2	t	t	NOUN
ejpam-5275	121	3	)	)	PUNCT
ejpam-5275	121	4	)	)	PUNCT
ejpam-5275	122	1	=	=	PUNCT
ejpam-5275	123	1	∞∑	∞∑	NUM
ejpam-5275	123	2	k=1	k=1	X
ejpam-5275	123	3	(	(	PUNCT
ejpam-5275	123	4	log(1	log(1	NOUN
ejpam-5275	123	5	+	+	CCONJ
ejpam-5275	123	6	t))k	t))k	PROPN
ejpam-5275	123	7	(	(	PUNCT
ejpam-5275	123	8	k	k	PROPN
ejpam-5275	123	9	−	−	PROPN
ejpam-5275	124	1	1)!km	1)!km	PROPN
ejpam-5275	124	2	(	(	PUNCT
ejpam-5275	124	3	24	24	NUM
ejpam-5275	124	4	)	)	PUNCT
ejpam-5275	124	5	=	=	NOUN
ejpam-5275	125	1	∞∑	∞∑	NUM
ejpam-5275	125	2	k=0	k=0	PROPN
ejpam-5275	125	3	(	(	PUNCT
ejpam-5275	125	4	log(1	log(1	NOUN
ejpam-5275	125	5	+	+	CCONJ
ejpam-5275	125	6	t))k+1	t))k+1	NOUN
ejpam-5275	125	7	k!(k	k!(k	NUM
ejpam-5275	125	8	+	+	CCONJ
ejpam-5275	125	9	1)m	1)m	NUM
ejpam-5275	125	10	s.	s.	PROPN
ejpam-5275	125	11	h.	h.	PROPN
ejpam-5275	125	12	lee	lee	PROPN
ejpam-5275	125	13	,	,	PUNCT
ejpam-5275	125	14	l.	l.	PROPN
ejpam-5275	125	15	chen	chen	PROPN
ejpam-5275	125	16	,	,	PUNCT
ejpam-5275	125	17	w.	w.	PROPN
ejpam-5275	125	18	kim	kim	PROPN
ejpam-5275	125	19	/	/	SYM
ejpam-5275	125	20	eur	eur	PROPN
ejpam-5275	125	21	.	.	PUNCT
ejpam-5275	126	1	j.	j.	PROPN
ejpam-5275	126	2	pure	pure	PROPN
ejpam-5275	126	3	appl	appl	PROPN
ejpam-5275	126	4	.	.	PROPN
ejpam-5275	126	5	math	math	PROPN
ejpam-5275	126	6	,	,	PUNCT
ejpam-5275	126	7	17	17	NUM
ejpam-5275	126	8	(	(	PUNCT
ejpam-5275	126	9	3	3	NUM
ejpam-5275	126	10	)	)	PUNCT
ejpam-5275	126	11	(	(	PUNCT
ejpam-5275	126	12	2024	2024	NUM
ejpam-5275	126	13	)	)	PUNCT
ejpam-5275	126	14	,	,	PUNCT
ejpam-5275	126	15	2336	2336	NUM
ejpam-5275	126	16	-	-	SYM
ejpam-5275	126	17	2348	2348	NUM
ejpam-5275	126	18	2341	2341	NUM
ejpam-5275	126	19	=	=	NOUN
ejpam-5275	127	1	∞∑	∞∑	NUM
ejpam-5275	127	2	k=0	k=0	PROPN
ejpam-5275	127	3	1	1	NUM
ejpam-5275	127	4	(	(	PUNCT
ejpam-5275	127	5	k	k	PROPN
ejpam-5275	127	6	+	+	NUM
ejpam-5275	127	7	1)m−1	1)m−1	NUM
ejpam-5275	127	8	∞∑	∞∑	NUM
ejpam-5275	127	9	n	n	X
ejpam-5275	127	10	=	=	NOUN
ejpam-5275	127	11	k+1	k+1	X
ejpam-5275	127	12	s1(n	s1(n	PROPN
ejpam-5275	127	13	,	,	PUNCT
ejpam-5275	127	14	k	k	PROPN
ejpam-5275	127	15	+	+	PROPN
ejpam-5275	127	16	1	1	X
ejpam-5275	127	17	)	)	PUNCT
ejpam-5275	127	18	tn	tn	NOUN
ejpam-5275	127	19	n	n	NOUN
ejpam-5275	127	20	!	!	PUNCT
ejpam-5275	127	21	=	=	NOUN
ejpam-5275	128	1	∞∑	∞∑	NUM
ejpam-5275	128	2	n	n	NOUN
ejpam-5275	128	3	=	=	SYM
ejpam-5275	128	4	k+1	k+1	NOUN
ejpam-5275	128	5	n−1∑	n−1∑	NUM
ejpam-5275	128	6	k=0	k=0	PROPN
ejpam-5275	128	7	s1(n	s1(n	PROPN
ejpam-5275	128	8	,	,	PUNCT
ejpam-5275	128	9	k	k	X
ejpam-5275	128	10	+	+	PROPN
ejpam-5275	128	11	1	1	X
ejpam-5275	128	12	)	)	PUNCT
ejpam-5275	128	13	(	(	PUNCT
ejpam-5275	128	14	k	k	PROPN
ejpam-5275	128	15	+	+	PROPN
ejpam-5275	128	16	1)m−1	1)m−1	NUM
ejpam-5275	128	17	tn	tn	NOUN
ejpam-5275	128	18	n	n	CCONJ
ejpam-5275	128	19	!	!	PUNCT
ejpam-5275	128	20	.	.	PUNCT
ejpam-5275	129	1	on	on	ADP
ejpam-5275	129	2	the	the	DET
ejpam-5275	129	3	other	other	ADJ
ejpam-5275	129	4	hand	hand	NOUN
ejpam-5275	129	5	,	,	PUNCT
ejpam-5275	129	6	em(log(1	em(log(1	NOUN
ejpam-5275	130	1	+	+	X
ejpam-5275	130	2	t	t	NOUN
ejpam-5275	130	3	)	)	PUNCT
ejpam-5275	130	4	)	)	PUNCT
ejpam-5275	131	1	=	=	NOUN
ejpam-5275	132	1	∞∑	∞∑	NUM
ejpam-5275	132	2	l=0	l=0	PROPN
ejpam-5275	132	3	β	β	X
ejpam-5275	132	4	(	(	PUNCT
ejpam-5275	132	5	m	m	PROPN
ejpam-5275	132	6	,	,	PUNCT
ejpam-5275	132	7	y	y	PROPN
ejpam-5275	132	8	)	)	PUNCT
ejpam-5275	132	9	l	l	NOUN
ejpam-5275	132	10	tl	tl	PROPN
ejpam-5275	132	11	l	l	NOUN
ejpam-5275	132	12	!	!	PUNCT
ejpam-5275	133	1	(	(	PUNCT
ejpam-5275	133	2	e[ey	e[ey	PROPN
ejpam-5275	133	3	t	t	NOUN
ejpam-5275	133	4	−	−	PROPN
ejpam-5275	133	5	1	1	NUM
ejpam-5275	133	6	]	]	PUNCT
ejpam-5275	133	7	)	)	PUNCT
ejpam-5275	133	8	(	(	PUNCT
ejpam-5275	133	9	25	25	NUM
ejpam-5275	133	10	)	)	PUNCT
ejpam-5275	133	11	=	=	NOUN
ejpam-5275	134	1	∞∑	∞∑	NUM
ejpam-5275	134	2	l=0	l=0	PROPN
ejpam-5275	134	3	β	β	X
ejpam-5275	134	4	(	(	PUNCT
ejpam-5275	134	5	m	m	PROPN
ejpam-5275	134	6	,	,	PUNCT
ejpam-5275	134	7	y	y	PROPN
ejpam-5275	134	8	)	)	PUNCT
ejpam-5275	134	9	l	l	NOUN
ejpam-5275	134	10	tl	tl	PROPN
ejpam-5275	134	11	l	l	NOUN
ejpam-5275	134	12	!	!	PUNCT
ejpam-5275	135	1			PROPN
ejpam-5275	135	2	∞∑	∞∑	NUM
ejpam-5275	135	3	j=0	j=0	PROPN
ejpam-5275	135	4	e[y	e[y	PUNCT
ejpam-5275	135	5	j	j	PROPN
ejpam-5275	135	6	]	]	PUNCT
ejpam-5275	135	7	tj	tj	PROPN
ejpam-5275	135	8	j	j	PROPN
ejpam-5275	135	9	!	!	PUNCT
ejpam-5275	135	10	−	−	PROPN
ejpam-5275	136	1	1	1	NUM
ejpam-5275	136	2			PROPN
ejpam-5275	136	3	=	=	X
ejpam-5275	137	1	∞∑	∞∑	NUM
ejpam-5275	137	2	n=0	n=0	NUM
ejpam-5275	137	3	(	(	PUNCT
ejpam-5275	137	4	n∑	n∑	NOUN
ejpam-5275	137	5	l=0	l=0	PROPN
ejpam-5275	137	6	(	(	PUNCT
ejpam-5275	137	7	n	n	X
ejpam-5275	137	8	l	l	NOUN
ejpam-5275	137	9	)	)	PUNCT
ejpam-5275	137	10	β	β	X
ejpam-5275	137	11	(	(	PUNCT
ejpam-5275	137	12	m	m	PROPN
ejpam-5275	137	13	,	,	PUNCT
ejpam-5275	137	14	y	y	PROPN
ejpam-5275	137	15	)	)	PUNCT
ejpam-5275	137	16	l	l	NOUN
ejpam-5275	137	17	e[y	e[y	ADJ
ejpam-5275	137	18	n−l]−	n−l]−	NOUN
ejpam-5275	137	19	β(m	β(m	PROPN
ejpam-5275	137	20	,	,	PUNCT
ejpam-5275	137	21	y	y	PROPN
ejpam-5275	137	22	)	)	PUNCT
ejpam-5275	137	23	n	n	CCONJ
ejpam-5275	137	24	)	)	PUNCT
ejpam-5275	137	25	tn	tn	PROPN
ejpam-5275	137	26	n	n	PROPN
ejpam-5275	137	27	!	!	PUNCT
ejpam-5275	137	28	.	.	PUNCT
ejpam-5275	138	1	therefore	therefore	ADV
ejpam-5275	138	2	,	,	PUNCT
ejpam-5275	138	3	by	by	ADP
ejpam-5275	138	4	comparing	compare	VERB
ejpam-5275	138	5	the	the	DET
ejpam-5275	138	6	coefficients	coefficient	NOUN
ejpam-5275	138	7	on	on	ADP
ejpam-5275	138	8	both	both	DET
ejpam-5275	138	9	sides	side	NOUN
ejpam-5275	138	10	of	of	ADP
ejpam-5275	138	11	(	(	PUNCT
ejpam-5275	138	12	24	24	NUM
ejpam-5275	138	13	)	)	PUNCT
ejpam-5275	138	14	and	and	CCONJ
ejpam-5275	138	15	(	(	PUNCT
ejpam-5275	138	16	25	25	NUM
ejpam-5275	138	17	)	)	PUNCT
ejpam-5275	138	18	,	,	PUNCT
ejpam-5275	138	19	we	we	PRON
ejpam-5275	138	20	have	have	VERB
ejpam-5275	138	21	the	the	DET
ejpam-5275	138	22	following	follow	VERB
ejpam-5275	138	23	theorem	theorem	VERB
ejpam-5275	138	24	.	.	PUNCT
ejpam-5275	138	25	theorem	theorem	NOUN
ejpam-5275	138	26	4	4	NUM
ejpam-5275	138	27	.	.	NOUN
ejpam-5275	138	28	for	for	ADP
ejpam-5275	138	29	n	n	PRON
ejpam-5275	138	30	,	,	PUNCT
ejpam-5275	138	31	k	k	PROPN
ejpam-5275	138	32	≥	≥	PROPN
ejpam-5275	138	33	0	0	NUM
ejpam-5275	138	34	,	,	PUNCT
ejpam-5275	138	35	we	we	PRON
ejpam-5275	138	36	have	have	VERB
ejpam-5275	138	37	n−1∑	n−1∑	NUM
ejpam-5275	138	38	k=0	k=0	PROPN
ejpam-5275	138	39	s1(n	s1(n	PROPN
ejpam-5275	138	40	,	,	PUNCT
ejpam-5275	138	41	k	k	X
ejpam-5275	139	1	+	+	PROPN
ejpam-5275	139	2	1	1	X
ejpam-5275	139	3	)	)	PUNCT
ejpam-5275	139	4	(	(	PUNCT
ejpam-5275	139	5	k	k	PROPN
ejpam-5275	139	6	+	+	PUNCT
ejpam-5275	139	7	1)m−1	1)m−1	NUM
ejpam-5275	139	8	=	=	SYM
ejpam-5275	139	9	{	{	PUNCT
ejpam-5275	139	10	∑n	∑n	PROPN
ejpam-5275	139	11	l=0	l=0	PROPN
ejpam-5275	139	12	(	(	PUNCT
ejpam-5275	139	13	(	(	PUNCT
ejpam-5275	139	14	n	n	X
ejpam-5275	139	15	l	l	NOUN
ejpam-5275	139	16	)	)	PUNCT
ejpam-5275	140	1	β	β	X
ejpam-5275	140	2	(	(	PUNCT
ejpam-5275	140	3	m	m	PROPN
ejpam-5275	140	4	,	,	PUNCT
ejpam-5275	140	5	y	y	PROPN
ejpam-5275	140	6	)	)	PUNCT
ejpam-5275	140	7	l	l	NOUN
ejpam-5275	140	8	e[y	e[y	ADJ
ejpam-5275	140	9	n−l]−	n−l]−	NOUN
ejpam-5275	140	10	β	β	X
ejpam-5275	140	11	(	(	PUNCT
ejpam-5275	140	12	m	m	PROPN
ejpam-5275	140	13	,	,	PUNCT
ejpam-5275	140	14	y	y	PROPN
ejpam-5275	140	15	)	)	PUNCT
ejpam-5275	140	16	n	n	CCONJ
ejpam-5275	140	17	)	)	PUNCT
ejpam-5275	140	18	,	,	PUNCT
ejpam-5275	140	19	if	if	SCONJ
ejpam-5275	140	20	n	n	PRON
ejpam-5275	140	21	≥	≥	NOUN
ejpam-5275	140	22	k	k	NOUN
ejpam-5275	141	1	+	+	CCONJ
ejpam-5275	141	2	1	1	NUM
ejpam-5275	141	3	,	,	PUNCT
ejpam-5275	141	4	0	0	NUM
ejpam-5275	141	5	,	,	PUNCT
ejpam-5275	141	6	if	if	SCONJ
ejpam-5275	141	7	n	n	ADV
ejpam-5275	141	8	<	<	X
ejpam-5275	141	9	k	k	X
ejpam-5275	142	1	+	+	NOUN
ejpam-5275	142	2	1	1	X
ejpam-5275	142	3	.	.	PUNCT
ejpam-5275	143	1	let	let	VERB
ejpam-5275	143	2	y	y	PRON
ejpam-5275	143	3	be	be	AUX
ejpam-5275	143	4	the	the	DET
ejpam-5275	143	5	poisson	poisson	NOUN
ejpam-5275	143	6	random	random	ADJ
ejpam-5275	143	7	variable	variable	NOUN
ejpam-5275	143	8	with	with	ADP
ejpam-5275	143	9	parameter	parameter	PROPN
ejpam-5275	143	10	α	α	PROPN
ejpam-5275	143	11	>	>	X
ejpam-5275	143	12	0	0	PROPN
ejpam-5275	143	13	,	,	PUNCT
ejpam-5275	143	14	then	then	ADV
ejpam-5275	143	15	we	we	PRON
ejpam-5275	143	16	have	have	VERB
ejpam-5275	143	17	ek(log(1	ek(log(1	NOUN
ejpam-5275	143	18	+	+	PROPN
ejpam-5275	143	19	t	t	PROPN
ejpam-5275	143	20	)	)	PUNCT
ejpam-5275	143	21	)	)	PUNCT
ejpam-5275	144	1	e[ey	e[ey	ADP
ejpam-5275	144	2	t]−	t]−	NOUN
ejpam-5275	144	3	1	1	NUM
ejpam-5275	144	4	(	(	PUNCT
ejpam-5275	144	5	e[ey	e[ey	PROPN
ejpam-5275	144	6	t	t	PROPN
ejpam-5275	144	7	]	]	PUNCT
ejpam-5275	144	8	)	)	PUNCT
ejpam-5275	144	9	x	x	X
ejpam-5275	144	10	=	=	PUNCT
ejpam-5275	144	11	ek(log(1	ek(log(1	PROPN
ejpam-5275	144	12	+	+	NUM
ejpam-5275	144	13	t	t	PROPN
ejpam-5275	144	14	)	)	PUNCT
ejpam-5275	144	15	)	)	PUNCT
ejpam-5275	144	16	eα(et−1	eα(et−1	PUNCT
ejpam-5275	144	17	)	)	PUNCT
ejpam-5275	144	18	−	−	PROPN
ejpam-5275	144	19	1	1	NUM
ejpam-5275	144	20	eαx(e	eαx(e	PROPN
ejpam-5275	144	21	t−1	t−1	PROPN
ejpam-5275	144	22	)	)	PUNCT
ejpam-5275	144	23	(	(	PUNCT
ejpam-5275	144	24	26	26	NUM
ejpam-5275	144	25	)	)	PUNCT
ejpam-5275	144	26	=	=	NOUN
ejpam-5275	144	27	α(et	α(et	NOUN
ejpam-5275	144	28	−	−	PROPN
ejpam-5275	144	29	1	1	NUM
ejpam-5275	144	30	)	)	PUNCT
ejpam-5275	144	31	α(et	α(et	NOUN
ejpam-5275	144	32	−	−	PROPN
ejpam-5275	144	33	1	1	NUM
ejpam-5275	144	34	)	)	PUNCT
ejpam-5275	144	35	ek(log(1	ek(log(1	NOUN
ejpam-5275	144	36	+	+	CCONJ
ejpam-5275	144	37	t	t	PROPN
ejpam-5275	144	38	)	)	PUNCT
ejpam-5275	144	39	)	)	PUNCT
ejpam-5275	144	40	eα(et−1)−1	eα(et−1)−1	PROPN
ejpam-5275	144	41	eαx(e	eαx(e	PROPN
ejpam-5275	144	42	t−1	t−1	PROPN
ejpam-5275	144	43	)	)	PUNCT
ejpam-5275	144	44	=	=	SYM
ejpam-5275	145	1	1	1	NUM
ejpam-5275	145	2	α	α	NOUN
ejpam-5275	145	3	∞∑	∞∑	NUM
ejpam-5275	145	4	j=0	j=0	PROPN
ejpam-5275	145	5	β	β	X
ejpam-5275	145	6	(	(	PUNCT
ejpam-5275	145	7	k	k	NOUN
ejpam-5275	145	8	)	)	PUNCT
ejpam-5275	145	9	j	j	PROPN
ejpam-5275	145	10	tj	tj	PROPN
ejpam-5275	145	11	j	j	PROPN
ejpam-5275	145	12	!	!	PUNCT
ejpam-5275	145	13	α(et	α(et	NOUN
ejpam-5275	145	14	−	−	PROPN
ejpam-5275	145	15	1	1	NUM
ejpam-5275	145	16	)	)	PUNCT
ejpam-5275	145	17	eα(et−1	eα(et−1	NOUN
ejpam-5275	145	18	)	)	PUNCT
ejpam-5275	146	1	−	−	PROPN
ejpam-5275	146	2	1	1	NUM
ejpam-5275	146	3	eαx(e	eαx(e	PROPN
ejpam-5275	146	4	x−1	x−1	PROPN
ejpam-5275	146	5	)	)	PUNCT
ejpam-5275	146	6	=	=	SYM
ejpam-5275	147	1	1	1	NUM
ejpam-5275	147	2	α	α	NOUN
ejpam-5275	147	3	∞∑	∞∑	NUM
ejpam-5275	147	4	j=0	j=0	PROPN
ejpam-5275	147	5	β	β	X
ejpam-5275	147	6	(	(	PUNCT
ejpam-5275	147	7	k	k	NOUN
ejpam-5275	147	8	)	)	PUNCT
ejpam-5275	147	9	j	j	PROPN
ejpam-5275	147	10	tj	tj	PROPN
ejpam-5275	147	11	j	j	PROPN
ejpam-5275	147	12	!	!	PUNCT
ejpam-5275	148	1	∞∑	∞∑	ADJ
ejpam-5275	148	2	l=0	l=0	PROPN
ejpam-5275	148	3	αlbl(x	αlbl(x	PROPN
ejpam-5275	148	4	)	)	PUNCT
ejpam-5275	148	5	(	(	PUNCT
ejpam-5275	148	6	ex	ex	NOUN
ejpam-5275	148	7	−	−	PROPN
ejpam-5275	148	8	1)l	1)l	NUM
ejpam-5275	148	9	l	l	NOUN
ejpam-5275	148	10	!	!	PUNCT
ejpam-5275	148	11	=	=	NOUN
ejpam-5275	149	1	∞∑	∞∑	NUM
ejpam-5275	149	2	j=0	j=0	PROPN
ejpam-5275	149	3	β	β	X
ejpam-5275	149	4	(	(	PUNCT
ejpam-5275	149	5	k	k	NOUN
ejpam-5275	149	6	)	)	PUNCT
ejpam-5275	149	7	j	j	PROPN
ejpam-5275	149	8	tj	tj	PROPN
ejpam-5275	149	9	j	j	PROPN
ejpam-5275	149	10	!	!	PUNCT
ejpam-5275	150	1	∞∑	∞∑	NUM
ejpam-5275	150	2	m=0	m=0	PROPN
ejpam-5275	150	3	m∑	m∑	CCONJ
ejpam-5275	150	4	l=0	l=0	PROPN
ejpam-5275	150	5	αl−1bl(x)s2(m	αl−1bl(x)s2(m	NOUN
ejpam-5275	150	6	,	,	PUNCT
ejpam-5275	150	7	l	l	NOUN
ejpam-5275	150	8	)	)	PUNCT
ejpam-5275	150	9	tm	tm	PROPN
ejpam-5275	150	10	m	m	PROPN
ejpam-5275	150	11	!	!	PUNCT
ejpam-5275	151	1	=	=	NOUN
ejpam-5275	152	1	∞∑	∞∑	DET
ejpam-5275	152	2	n=0	n=0	NUM
ejpam-5275	152	3	n∑	n∑	NOUN
ejpam-5275	152	4	m=0	m=0	PROPN
ejpam-5275	152	5	m∑	m∑	PRON
ejpam-5275	152	6	l=0	l=0	PROPN
ejpam-5275	152	7	(	(	PUNCT
ejpam-5275	152	8	n	n	NOUN
ejpam-5275	152	9	m	m	VERB
ejpam-5275	152	10	)	)	PUNCT
ejpam-5275	152	11	β	β	X
ejpam-5275	152	12	(	(	PUNCT
ejpam-5275	152	13	k	k	X
ejpam-5275	152	14	)	)	PUNCT
ejpam-5275	152	15	n−mαl−1bl(x)s2(m	n−mαl−1bl(x)s2(m	PROPN
ejpam-5275	152	16	,	,	PUNCT
ejpam-5275	152	17	l	l	NOUN
ejpam-5275	152	18	)	)	PUNCT
ejpam-5275	152	19	tn	tn	PROPN
ejpam-5275	152	20	m	m	PROPN
ejpam-5275	152	21	.	.	PUNCT
ejpam-5275	153	1	s.	s.	PROPN
ejpam-5275	153	2	h.	h.	PROPN
ejpam-5275	153	3	lee	lee	PROPN
ejpam-5275	153	4	,	,	PUNCT
ejpam-5275	153	5	l.	l.	PROPN
ejpam-5275	153	6	chen	chen	PROPN
ejpam-5275	153	7	,	,	PUNCT
ejpam-5275	153	8	w.	w.	PROPN
ejpam-5275	153	9	kim	kim	PROPN
ejpam-5275	153	10	/	/	SYM
ejpam-5275	153	11	eur	eur	PROPN
ejpam-5275	153	12	.	.	PUNCT
ejpam-5275	154	1	j.	j.	PROPN
ejpam-5275	154	2	pure	pure	PROPN
ejpam-5275	154	3	appl	appl	PROPN
ejpam-5275	154	4	.	.	PROPN
ejpam-5275	154	5	math	math	PROPN
ejpam-5275	154	6	,	,	PUNCT
ejpam-5275	154	7	17	17	NUM
ejpam-5275	154	8	(	(	PUNCT
ejpam-5275	154	9	3	3	NUM
ejpam-5275	154	10	)	)	PUNCT
ejpam-5275	154	11	(	(	PUNCT
ejpam-5275	154	12	2024	2024	NUM
ejpam-5275	154	13	)	)	PUNCT
ejpam-5275	154	14	,	,	PUNCT
ejpam-5275	154	15	2336	2336	NUM
ejpam-5275	154	16	-	-	SYM
ejpam-5275	154	17	2348	2348	NUM
ejpam-5275	154	18	2342	2342	NUM
ejpam-5275	154	19	from	from	ADP
ejpam-5275	154	20	(	(	PUNCT
ejpam-5275	154	21	18	18	NUM
ejpam-5275	154	22	)	)	PUNCT
ejpam-5275	154	23	and	and	CCONJ
ejpam-5275	154	24	(	(	PUNCT
ejpam-5275	154	25	26	26	NUM
ejpam-5275	154	26	)	)	PUNCT
ejpam-5275	154	27	,	,	PUNCT
ejpam-5275	154	28	we	we	PRON
ejpam-5275	154	29	have	have	VERB
ejpam-5275	154	30	the	the	DET
ejpam-5275	154	31	following	follow	VERB
ejpam-5275	154	32	theorem	theorem	VERB
ejpam-5275	154	33	.	.	PUNCT
ejpam-5275	155	1	theorem	theorem	NOUN
ejpam-5275	155	2	5	5	NUM
ejpam-5275	155	3	.	.	PUNCT
ejpam-5275	156	1	let	let	VERB
ejpam-5275	156	2	y	y	PRON
ejpam-5275	156	3	be	be	AUX
ejpam-5275	156	4	the	the	DET
ejpam-5275	156	5	poisson	poisson	NOUN
ejpam-5275	156	6	random	random	ADJ
ejpam-5275	156	7	variable	variable	NOUN
ejpam-5275	156	8	with	with	ADP
ejpam-5275	156	9	parameter	parameter	PROPN
ejpam-5275	156	10	α	α	NOUN
ejpam-5275	156	11	,	,	PUNCT
ejpam-5275	156	12	we	we	PRON
ejpam-5275	156	13	have	have	VERB
ejpam-5275	156	14	β(k	β(k	PROPN
ejpam-5275	156	15	,	,	PUNCT
ejpam-5275	156	16	y	y	PROPN
ejpam-5275	156	17	)	)	PUNCT
ejpam-5275	157	1	n	n	CCONJ
ejpam-5275	157	2	(	(	PUNCT
ejpam-5275	157	3	x	x	X
ejpam-5275	157	4	)	)	PUNCT
ejpam-5275	157	5	=	=	SYM
ejpam-5275	158	1	n∑	n∑	PROPN
ejpam-5275	158	2	m=0	m=0	PROPN
ejpam-5275	158	3	m∑	m∑	PRON
ejpam-5275	158	4	l=0	l=0	PROPN
ejpam-5275	158	5	(	(	PUNCT
ejpam-5275	158	6	n	n	NOUN
ejpam-5275	158	7	m	m	VERB
ejpam-5275	158	8	)	)	PUNCT
ejpam-5275	159	1	β	β	X
ejpam-5275	159	2	(	(	PUNCT
ejpam-5275	159	3	k	k	X
ejpam-5275	159	4	)	)	PUNCT
ejpam-5275	159	5	n−mαl−1bl(x)s2(m	n−mαl−1bl(x)s2(m	PROPN
ejpam-5275	159	6	,	,	PUNCT
ejpam-5275	159	7	l	l	NOUN
ejpam-5275	159	8	)	)	PUNCT
ejpam-5275	159	9	.	.	PUNCT
ejpam-5275	160	1	from	from	ADP
ejpam-5275	160	2	(	(	PUNCT
ejpam-5275	160	3	18	18	NUM
ejpam-5275	160	4	)	)	PUNCT
ejpam-5275	160	5	,	,	PUNCT
ejpam-5275	160	6	we	we	PRON
ejpam-5275	160	7	have	have	VERB
ejpam-5275	160	8	∞∑	∞∑	NUM
ejpam-5275	160	9	n=0	n=0	PROPN
ejpam-5275	160	10	b(k	b(k	PROPN
ejpam-5275	160	11	,	,	PUNCT
ejpam-5275	160	12	y	y	PROPN
ejpam-5275	160	13	)	)	PUNCT
ejpam-5275	160	14	n	n	CCONJ
ejpam-5275	160	15	(	(	PUNCT
ejpam-5275	160	16	α+	α+	NOUN
ejpam-5275	160	17	1	1	NUM
ejpam-5275	160	18	)	)	PUNCT
ejpam-5275	160	19	=	=	SYM
ejpam-5275	160	20	ek(log(1	ek(log(1	PROPN
ejpam-5275	160	21	+	+	NUM
ejpam-5275	160	22	t	t	PROPN
ejpam-5275	160	23	)	)	PUNCT
ejpam-5275	160	24	)	)	PUNCT
ejpam-5275	161	1	e[ey	e[ey	ADP
ejpam-5275	161	2	t]−	t]−	NOUN
ejpam-5275	161	3	1	1	NUM
ejpam-5275	161	4	(	(	PUNCT
ejpam-5275	161	5	e[ey	e[ey	PROPN
ejpam-5275	161	6	t	t	PROPN
ejpam-5275	161	7	]	]	PUNCT
ejpam-5275	161	8	)	)	PUNCT
ejpam-5275	161	9	α	α	PROPN
ejpam-5275	161	10	e[ey	e[ey	PROPN
ejpam-5275	161	11	t	t	PROPN
ejpam-5275	161	12	]	]	PUNCT
ejpam-5275	161	13	(	(	PUNCT
ejpam-5275	161	14	27	27	NUM
ejpam-5275	161	15	)	)	PUNCT
ejpam-5275	161	16	=	=	NOUN
ejpam-5275	162	1	∞∑	∞∑	NUM
ejpam-5275	162	2	l=0	l=0	PROPN
ejpam-5275	162	3	b	b	PROPN
ejpam-5275	162	4	(	(	PUNCT
ejpam-5275	162	5	k	k	X
ejpam-5275	162	6	,	,	PUNCT
ejpam-5275	162	7	y	y	PROPN
ejpam-5275	162	8	)	)	PUNCT
ejpam-5275	162	9	l	l	NOUN
ejpam-5275	162	10	(	(	PUNCT
ejpam-5275	162	11	α	α	NOUN
ejpam-5275	162	12	)	)	PUNCT
ejpam-5275	162	13	tl	tl	PROPN
ejpam-5275	162	14	l	l	NOUN
ejpam-5275	162	15	!	!	PUNCT
ejpam-5275	163	1	∞∑	∞∑	NUM
ejpam-5275	163	2	m=0	m=0	PROPN
ejpam-5275	163	3	e[y	e[y	ADJ
ejpam-5275	163	4	m	m	PROPN
ejpam-5275	163	5	]	]	X
ejpam-5275	163	6	tm	tm	PROPN
ejpam-5275	163	7	m	m	PROPN
ejpam-5275	163	8	!	!	PUNCT
ejpam-5275	163	9	=	=	NOUN
ejpam-5275	164	1	∞∑	∞∑	PRON
ejpam-5275	164	2	n=0	n=0	NUM
ejpam-5275	164	3	n∑	n∑	X
ejpam-5275	164	4	l=0	l=0	PROPN
ejpam-5275	164	5	(	(	PUNCT
ejpam-5275	164	6	n	n	X
ejpam-5275	164	7	l	l	NOUN
ejpam-5275	164	8	)	)	PUNCT
ejpam-5275	164	9	b	b	NOUN
ejpam-5275	164	10	(	(	PUNCT
ejpam-5275	164	11	k	k	X
ejpam-5275	164	12	,	,	PUNCT
ejpam-5275	164	13	y	y	PROPN
ejpam-5275	164	14	)	)	PUNCT
ejpam-5275	164	15	l	l	NOUN
ejpam-5275	164	16	(	(	PUNCT
ejpam-5275	164	17	α)e[y	α)e[y	PROPN
ejpam-5275	164	18	n−l	n−l	PROPN
ejpam-5275	164	19	]	]	PUNCT
ejpam-5275	164	20	tn	tn	PROPN
ejpam-5275	164	21	n	n	X
ejpam-5275	164	22	!	!	PUNCT
ejpam-5275	164	23	.	.	PUNCT
ejpam-5275	165	1	from	from	ADP
ejpam-5275	165	2	(	(	PUNCT
ejpam-5275	165	3	18	18	NUM
ejpam-5275	165	4	)	)	PUNCT
ejpam-5275	165	5	,	,	PUNCT
ejpam-5275	165	6	we	we	PRON
ejpam-5275	165	7	also	also	ADV
ejpam-5275	165	8	have	have	VERB
ejpam-5275	165	9	∞∑	∞∑	NUM
ejpam-5275	165	10	n=0	n=0	NUM
ejpam-5275	165	11	b(k	b(k	PROPN
ejpam-5275	165	12	,	,	PUNCT
ejpam-5275	165	13	y	y	PROPN
ejpam-5275	165	14	)	)	PUNCT
ejpam-5275	165	15	n	n	CCONJ
ejpam-5275	165	16	(	(	PUNCT
ejpam-5275	165	17	α	α	NOUN
ejpam-5275	165	18	)	)	PUNCT
ejpam-5275	165	19	tn	tn	PROPN
ejpam-5275	165	20	n	n	NOUN
ejpam-5275	165	21	!	!	PUNCT
ejpam-5275	165	22	=	=	NOUN
ejpam-5275	166	1	∞∑	∞∑	PRON
ejpam-5275	166	2	n=0	n=0	PROPN
ejpam-5275	166	3	by	by	ADP
ejpam-5275	166	4	n	n	PROPN
ejpam-5275	166	5	tn	tn	PROPN
ejpam-5275	166	6	n	n	X
ejpam-5275	166	7	!	!	PUNCT
ejpam-5275	167	1	e[e(y1+y2+···+yα)t	e[e(y1+y2+···+yα)t	PROPN
ejpam-5275	167	2	]	]	PUNCT
ejpam-5275	167	3	(	(	PUNCT
ejpam-5275	167	4	28	28	NUM
ejpam-5275	167	5	)	)	PUNCT
ejpam-5275	167	6	=	=	NOUN
ejpam-5275	168	1	∞∑	∞∑	NUM
ejpam-5275	168	2	l=0	l=0	PROPN
ejpam-5275	168	3	b	b	PROPN
ejpam-5275	168	4	(	(	PUNCT
ejpam-5275	168	5	k	k	X
ejpam-5275	168	6	,	,	PUNCT
ejpam-5275	168	7	y	y	PROPN
ejpam-5275	168	8	)	)	PUNCT
ejpam-5275	168	9	l	l	PROPN
ejpam-5275	168	10	tn	tn	PROPN
ejpam-5275	168	11	n	n	CCONJ
ejpam-5275	168	12	!	!	PUNCT
ejpam-5275	169	1	∞∑	∞∑	NUM
ejpam-5275	169	2	m=0	m=0	PROPN
ejpam-5275	169	3	e[sm	e[sm	PROPN
ejpam-5275	169	4	α	α	PROPN
ejpam-5275	169	5	]	]	PUNCT
ejpam-5275	169	6	tm	tm	PROPN
ejpam-5275	169	7	m	m	PROPN
ejpam-5275	169	8	!	!	PUNCT
ejpam-5275	169	9	=	=	NOUN
ejpam-5275	170	1	∞∑	∞∑	PRON
ejpam-5275	170	2	n=0	n=0	NUM
ejpam-5275	170	3	n∑	n∑	X
ejpam-5275	170	4	l=0	l=0	PROPN
ejpam-5275	170	5	(	(	PUNCT
ejpam-5275	170	6	n	n	X
ejpam-5275	170	7	l	l	NOUN
ejpam-5275	170	8	)	)	PUNCT
ejpam-5275	170	9	b	b	NOUN
ejpam-5275	170	10	(	(	PUNCT
ejpam-5275	170	11	k	k	X
ejpam-5275	170	12	,	,	PUNCT
ejpam-5275	170	13	y	y	PROPN
ejpam-5275	170	14	)	)	PUNCT
ejpam-5275	170	15	l	l	NOUN
ejpam-5275	170	16	e[sm	e[sm	PROPN
ejpam-5275	170	17	α	α	X
ejpam-5275	170	18	]	]	PUNCT
ejpam-5275	170	19	tn	tn	PROPN
ejpam-5275	170	20	n	n	X
ejpam-5275	170	21	!	!	PUNCT
ejpam-5275	170	22	.	.	PUNCT
ejpam-5275	171	1	therefore	therefore	ADV
ejpam-5275	171	2	,	,	PUNCT
ejpam-5275	171	3	by	by	ADP
ejpam-5275	171	4	(	(	PUNCT
ejpam-5275	171	5	27	27	NUM
ejpam-5275	171	6	)	)	PUNCT
ejpam-5275	171	7	and	and	CCONJ
ejpam-5275	171	8	(	(	PUNCT
ejpam-5275	171	9	28	28	NUM
ejpam-5275	171	10	)	)	PUNCT
ejpam-5275	171	11	,	,	PUNCT
ejpam-5275	171	12	we	we	PRON
ejpam-5275	171	13	have	have	VERB
ejpam-5275	171	14	the	the	DET
ejpam-5275	171	15	following	follow	VERB
ejpam-5275	171	16	theorem	theorem	VERB
ejpam-5275	171	17	.	.	PUNCT
ejpam-5275	171	18	theorem	theorem	PROPN
ejpam-5275	171	19	6	6	NUM
ejpam-5275	171	20	.	.	X
ejpam-5275	172	1	for	for	ADP
ejpam-5275	172	2	any	any	DET
ejpam-5275	172	3	α	α	NOUN
ejpam-5275	172	4	∈	∈	PROPN
ejpam-5275	172	5	z	z	PROPN
ejpam-5275	172	6	and	and	CCONJ
ejpam-5275	172	7	n	n	CCONJ
ejpam-5275	172	8	,	,	PUNCT
ejpam-5275	172	9	α	α	PRON
ejpam-5275	172	10	≥	≥	NOUN
ejpam-5275	172	11	0	0	NUM
ejpam-5275	172	12	,	,	PUNCT
ejpam-5275	172	13	we	we	PRON
ejpam-5275	172	14	have	have	VERB
ejpam-5275	172	15	b(k	b(k	PROPN
ejpam-5275	172	16	,	,	PUNCT
ejpam-5275	172	17	y	y	PROPN
ejpam-5275	172	18	)	)	PUNCT
ejpam-5275	172	19	n	n	CCONJ
ejpam-5275	172	20	(	(	PUNCT
ejpam-5275	172	21	α+	α+	PROPN
ejpam-5275	172	22	1)−b(k	1)−b(k	NUM
ejpam-5275	172	23	,	,	PUNCT
ejpam-5275	172	24	y	y	PROPN
ejpam-5275	172	25	)	)	PUNCT
ejpam-5275	172	26	n	n	CCONJ
ejpam-5275	172	27	(	(	PUNCT
ejpam-5275	172	28	α	α	NOUN
ejpam-5275	172	29	)	)	PUNCT
ejpam-5275	173	1	=	=	SYM
ejpam-5275	173	2	n∑	n∑	NOUN
ejpam-5275	173	3	l=0	l=0	PROPN
ejpam-5275	173	4	(	(	PUNCT
ejpam-5275	173	5	n	n	NOUN
ejpam-5275	173	6	l	l	NOUN
ejpam-5275	173	7	)	)	PUNCT
ejpam-5275	173	8	(	(	PUNCT
ejpam-5275	173	9	b	b	X
ejpam-5275	173	10	(	(	PUNCT
ejpam-5275	173	11	k	k	X
ejpam-5275	173	12	,	,	PUNCT
ejpam-5275	173	13	y	y	PROPN
ejpam-5275	173	14	)	)	PUNCT
ejpam-5275	173	15	l	l	NOUN
ejpam-5275	173	16	(	(	PUNCT
ejpam-5275	173	17	α)e[y	α)e[y	PROPN
ejpam-5275	173	18	n−l]−b	n−l]−b	NOUN
ejpam-5275	173	19	(	(	PUNCT
ejpam-5275	173	20	k	k	X
ejpam-5275	173	21	,	,	PUNCT
ejpam-5275	173	22	y	y	PROPN
ejpam-5275	173	23	)	)	PUNCT
ejpam-5275	174	1	l	l	NOUN
ejpam-5275	174	2	e[sm	e[sm	PROPN
ejpam-5275	174	3	α	α	X
ejpam-5275	174	4	]	]	PUNCT
ejpam-5275	174	5	)	)	PUNCT
ejpam-5275	174	6	.	.	PUNCT
ejpam-5275	175	1	3	3	X
ejpam-5275	175	2	.	.	X
ejpam-5275	175	3	the	the	DET
ejpam-5275	175	4	probabilistic	probabilistic	ADJ
ejpam-5275	175	5	unipoly	unipoly	ADJ
ejpam-5275	175	6	-	-	PUNCT
ejpam-5275	175	7	bernoulli	bernoulli	NOUN
ejpam-5275	175	8	polynomials	polynomial	NOUN
ejpam-5275	175	9	in	in	ADP
ejpam-5275	175	10	this	this	DET
ejpam-5275	175	11	section	section	NOUN
ejpam-5275	175	12	,	,	PUNCT
ejpam-5275	175	13	we	we	PRON
ejpam-5275	175	14	give	give	VERB
ejpam-5275	175	15	the	the	DET
ejpam-5275	175	16	definition	definition	NOUN
ejpam-5275	175	17	of	of	ADP
ejpam-5275	175	18	the	the	DET
ejpam-5275	175	19	probabilistic	probabilistic	ADJ
ejpam-5275	175	20	unipoly	unipoly	ADJ
ejpam-5275	175	21	-	-	PUNCT
ejpam-5275	175	22	bernoulli	bernoulli	NOUN
ejpam-5275	175	23	polynomials	polynomial	NOUN
ejpam-5275	175	24	attached	attach	VERB
ejpam-5275	175	25	to	to	ADP
ejpam-5275	175	26	p	p	PROPN
ejpam-5275	175	27	as	as	SCONJ
ejpam-5275	175	28	follows	follow	VERB
ejpam-5275	175	29	.	.	PUNCT
ejpam-5275	176	1	1	1	NUM
ejpam-5275	176	2	1−	1−	NUM
ejpam-5275	176	3	e[e−y	e[e−y	PROPN
ejpam-5275	176	4	t	t	X
ejpam-5275	176	5	]	]	PUNCT
ejpam-5275	176	6	uk(1−	uk(1−	ADJ
ejpam-5275	176	7	e−t|p)(e[e−y	e−t|p)(e[e−y	DET
ejpam-5275	176	8	t])x	t])x	NOUN
ejpam-5275	176	9	=	=	PUNCT
ejpam-5275	176	10	∞∑	∞∑	NUM
ejpam-5275	176	11	n=0	n=0	PROPN
ejpam-5275	176	12	b(k	b(k	PROPN
ejpam-5275	176	13	,	,	PUNCT
ejpam-5275	176	14	y	y	PROPN
ejpam-5275	176	15	)	)	PUNCT
ejpam-5275	176	16	n	n	CCONJ
ejpam-5275	176	17	,	,	PUNCT
ejpam-5275	176	18	p	p	X
ejpam-5275	176	19	(	(	PUNCT
ejpam-5275	176	20	x	x	NOUN
ejpam-5275	176	21	)	)	PUNCT
ejpam-5275	176	22	tn	tn	PROPN
ejpam-5275	176	23	n	n	NUM
ejpam-5275	176	24	!	!	PUNCT
ejpam-5275	176	25	.	.	PUNCT
ejpam-5275	177	1	(	(	PUNCT
ejpam-5275	177	2	29	29	NUM
ejpam-5275	177	3	)	)	PUNCT
ejpam-5275	177	4	s.	s.	PROPN
ejpam-5275	177	5	h.	h.	PROPN
ejpam-5275	177	6	lee	lee	PROPN
ejpam-5275	177	7	,	,	PUNCT
ejpam-5275	177	8	l.	l.	PROPN
ejpam-5275	177	9	chen	chen	PROPN
ejpam-5275	177	10	,	,	PUNCT
ejpam-5275	177	11	w.	w.	PROPN
ejpam-5275	177	12	kim	kim	PROPN
ejpam-5275	177	13	/	/	SYM
ejpam-5275	177	14	eur	eur	PROPN
ejpam-5275	177	15	.	.	PUNCT
ejpam-5275	178	1	j.	j.	PROPN
ejpam-5275	178	2	pure	pure	PROPN
ejpam-5275	178	3	appl	appl	PROPN
ejpam-5275	178	4	.	.	PROPN
ejpam-5275	178	5	math	math	PROPN
ejpam-5275	178	6	,	,	PUNCT
ejpam-5275	178	7	17	17	NUM
ejpam-5275	178	8	(	(	PUNCT
ejpam-5275	178	9	3	3	NUM
ejpam-5275	178	10	)	)	PUNCT
ejpam-5275	178	11	(	(	PUNCT
ejpam-5275	178	12	2024	2024	NUM
ejpam-5275	178	13	)	)	PUNCT
ejpam-5275	178	14	,	,	PUNCT
ejpam-5275	178	15	2336	2336	NUM
ejpam-5275	178	16	-	-	SYM
ejpam-5275	178	17	2348	2348	NUM
ejpam-5275	178	18	2343	2343	NUM
ejpam-5275	178	19	if	if	SCONJ
ejpam-5275	178	20	x	x	NOUN
ejpam-5275	178	21	=	=	SYM
ejpam-5275	178	22	0	0	NUM
ejpam-5275	178	23	,	,	PUNCT
ejpam-5275	178	24	b	b	PROPN
ejpam-5275	178	25	(	(	PUNCT
ejpam-5275	178	26	k	k	X
ejpam-5275	178	27	,	,	PUNCT
ejpam-5275	178	28	y	y	PROPN
ejpam-5275	178	29	)	)	PUNCT
ejpam-5275	178	30	n	n	CCONJ
ejpam-5275	178	31	,	,	PUNCT
ejpam-5275	178	32	p	p	NOUN
ejpam-5275	178	33	=	=	SYM
ejpam-5275	178	34	b	b	PROPN
ejpam-5275	178	35	(	(	PUNCT
ejpam-5275	178	36	k	k	X
ejpam-5275	178	37	,	,	PUNCT
ejpam-5275	178	38	y	y	PROPN
ejpam-5275	178	39	)	)	PUNCT
ejpam-5275	178	40	n	n	CCONJ
ejpam-5275	178	41	,	,	PUNCT
ejpam-5275	178	42	p	p	X
ejpam-5275	178	43	(	(	PUNCT
ejpam-5275	178	44	0	0	NUM
ejpam-5275	178	45	)	)	PUNCT
ejpam-5275	178	46	are	be	AUX
ejpam-5275	178	47	called	call	VERB
ejpam-5275	178	48	the	the	DET
ejpam-5275	178	49	probabilistic	probabilistic	ADJ
ejpam-5275	178	50	unipoly	unipoly	ADJ
ejpam-5275	178	51	-	-	PUNCT
ejpam-5275	178	52	bernoulli	bernoulli	NOUN
ejpam-5275	178	53	numbers	number	NOUN
ejpam-5275	178	54	.	.	PUNCT
ejpam-5275	179	1	particularly	particularly	ADV
ejpam-5275	179	2	,	,	PUNCT
ejpam-5275	179	3	if	if	SCONJ
ejpam-5275	179	4	p(n	p(n	VERB
ejpam-5275	179	5	)	)	PUNCT
ejpam-5275	179	6	=	=	SYM
ejpam-5275	180	1	1	1	NUM
ejpam-5275	180	2	,	,	PUNCT
ejpam-5275	180	3	then	then	ADV
ejpam-5275	180	4	b	b	X
ejpam-5275	180	5	(	(	PUNCT
ejpam-5275	180	6	k	k	X
ejpam-5275	180	7	,	,	PUNCT
ejpam-5275	180	8	y	y	PROPN
ejpam-5275	180	9	)	)	PUNCT
ejpam-5275	180	10	n,1	n,1	X
ejpam-5275	181	1	=	=	SYM
ejpam-5275	181	2	b	b	PROPN
ejpam-5275	181	3	(	(	PUNCT
ejpam-5275	181	4	k	k	X
ejpam-5275	181	5	,	,	PUNCT
ejpam-5275	181	6	y	y	PROPN
ejpam-5275	181	7	)	)	PUNCT
ejpam-5275	181	8	n	n	CCONJ
ejpam-5275	181	9	(	(	PUNCT
ejpam-5275	181	10	x	x	NOUN
ejpam-5275	181	11	)	)	PUNCT
ejpam-5275	181	12	.	.	PUNCT
ejpam-5275	182	1	from	from	ADP
ejpam-5275	182	2	(	(	PUNCT
ejpam-5275	182	3	29	29	NUM
ejpam-5275	182	4	)	)	SYM
ejpam-5275	182	5	1	1	NUM
ejpam-5275	182	6	1−	1−	NUM
ejpam-5275	182	7	e[e−y	e[e−y	PROPN
ejpam-5275	182	8	t	t	PROPN
ejpam-5275	182	9	]	]	PUNCT
ejpam-5275	182	10	uk(1−	uk(1−	PROPN
ejpam-5275	182	11	e−t|p	e−t|p	PROPN
ejpam-5275	182	12	)	)	PUNCT
ejpam-5275	182	13	=	=	SYM
ejpam-5275	182	14	1	1	NUM
ejpam-5275	182	15	1−	1−	NUM
ejpam-5275	182	16	e[e−y	e[e−y	PROPN
ejpam-5275	182	17	t	t	X
ejpam-5275	182	18	]	]	X
ejpam-5275	182	19	∞∑	∞∑	NUM
ejpam-5275	182	20	m=1	m=1	X
ejpam-5275	182	21	p	p	X
ejpam-5275	182	22	(	(	PUNCT
ejpam-5275	182	23	m)(1−	m)(1−	PROPN
ejpam-5275	182	24	e−t)m	e−t)m	PROPN
ejpam-5275	182	25	mk	mk	PROPN
ejpam-5275	182	26	(	(	PUNCT
ejpam-5275	182	27	30	30	NUM
ejpam-5275	182	28	)	)	PUNCT
ejpam-5275	182	29	=	=	SYM
ejpam-5275	182	30	t	t	PROPN
ejpam-5275	182	31	1−	1−	NUM
ejpam-5275	182	32	e[e−y	e[e−y	PROPN
ejpam-5275	182	33	t	t	PROPN
ejpam-5275	182	34	]	]	PUNCT
ejpam-5275	182	35	1	1	NUM
ejpam-5275	182	36	t	t	NOUN
ejpam-5275	182	37	∞∑	∞∑	NUM
ejpam-5275	182	38	m=1	m=1	PROPN
ejpam-5275	182	39	p(m	p(m	NOUN
ejpam-5275	182	40	)	)	PUNCT
ejpam-5275	182	41	mk	mk	NOUN
ejpam-5275	182	42	(	(	PUNCT
ejpam-5275	182	43	1−	1−	NUM
ejpam-5275	182	44	e−t)m	e−t)m	PROPN
ejpam-5275	182	45	m	m	PROPN
ejpam-5275	182	46	!	!	PUNCT
ejpam-5275	182	47	m	m	X
ejpam-5275	182	48	!	!	PUNCT
ejpam-5275	182	49	=	=	NOUN
ejpam-5275	183	1	∞∑	∞∑	NUM
ejpam-5275	183	2	j=0	j=0	PROPN
ejpam-5275	183	3	by	by	ADP
ejpam-5275	183	4	j	j	PROPN
ejpam-5275	183	5	(	(	PUNCT
ejpam-5275	183	6	−1)j	−1)j	NOUN
ejpam-5275	183	7	tj	tj	PROPN
ejpam-5275	183	8	j	j	PROPN
ejpam-5275	183	9	!	!	PROPN
ejpam-5275	183	10	1	1	NUM
ejpam-5275	183	11	t	t	PROPN
ejpam-5275	183	12	∞∑	∞∑	PROPN
ejpam-5275	183	13	m=1	m=1	PROPN
ejpam-5275	183	14	p(m)m	p(m)m	PROPN
ejpam-5275	183	15	!	!	PUNCT
ejpam-5275	183	16	mk	mk	PROPN
ejpam-5275	183	17	∞∑	∞∑	PROPN
ejpam-5275	183	18	l	l	NOUN
ejpam-5275	183	19	=	=	PROPN
ejpam-5275	183	20	m	m	PROPN
ejpam-5275	183	21	s2(l	s2(l	PROPN
ejpam-5275	183	22	,	,	PUNCT
ejpam-5275	183	23	m)(−1)l−m	m)(−1)l−m	PROPN
ejpam-5275	183	24	tl	tl	PROPN
ejpam-5275	183	25	l	l	NOUN
ejpam-5275	183	26	!	!	PUNCT
ejpam-5275	184	1	=	=	NOUN
ejpam-5275	185	1	∞∑	∞∑	NUM
ejpam-5275	185	2	j=0	j=0	PROPN
ejpam-5275	185	3	by	by	ADP
ejpam-5275	185	4	j	j	PROPN
ejpam-5275	185	5	(	(	PUNCT
ejpam-5275	185	6	−1)j	−1)j	NOUN
ejpam-5275	185	7	tj	tj	PROPN
ejpam-5275	185	8	j	j	PROPN
ejpam-5275	185	9	!	!	PUNCT
ejpam-5275	186	1	∞∑	∞∑	NUM
ejpam-5275	186	2	l=0	l=0	PROPN
ejpam-5275	186	3	l+1∑	l+1∑	PROPN
ejpam-5275	186	4	m=1	m=1	PROPN
ejpam-5275	186	5	p(m)m	p(m)m	PROPN
ejpam-5275	186	6	!	!	PUNCT
ejpam-5275	187	1	mk	mk	PROPN
ejpam-5275	187	2	s2(l	s2(l	X
ejpam-5275	188	1	+	+	CCONJ
ejpam-5275	188	2	1,m)(−1)l+1−m	1,m)(−1)l+1−m	NUM
ejpam-5275	188	3	l	l	NOUN
ejpam-5275	188	4	+	+	CCONJ
ejpam-5275	188	5	1	1	NUM
ejpam-5275	188	6	tl	tl	PROPN
ejpam-5275	188	7	l	l	NOUN
ejpam-5275	188	8	!	!	PUNCT
ejpam-5275	189	1	=	=	PUNCT
ejpam-5275	190	1	∞∑	∞∑	PRON
ejpam-5275	190	2	n=0	n=0	NUM
ejpam-5275	190	3	n∑	n∑	NOUN
ejpam-5275	190	4	l=0	l=0	PROPN
ejpam-5275	190	5	l+1∑	l+1∑	PROPN
ejpam-5275	190	6	m=1	m=1	X
ejpam-5275	190	7	(	(	PUNCT
ejpam-5275	190	8	n	n	X
ejpam-5275	190	9	l	l	NOUN
ejpam-5275	190	10	)	)	PUNCT
ejpam-5275	190	11	p(m)(m−	p(m)(m−	ADP
ejpam-5275	190	12	1	1	NUM
ejpam-5275	190	13	)	)	PUNCT
ejpam-5275	190	14	!	!	PUNCT
ejpam-5275	191	1	mk−1	mk−1	NOUN
ejpam-5275	191	2	(	(	PUNCT
ejpam-5275	191	3	−1)n−m+1s2(l	−1)n−m+1s2(l	PRON
ejpam-5275	191	4	+	+	CCONJ
ejpam-5275	191	5	1,m	1,m	X
ejpam-5275	191	6	)	)	PUNCT
ejpam-5275	191	7	l	l	NOUN
ejpam-5275	192	1	+	+	CCONJ
ejpam-5275	192	2	1	1	NUM
ejpam-5275	192	3	by	by	ADP
ejpam-5275	192	4	n−l	n−l	PROPN
ejpam-5275	192	5	tn	tn	PROPN
ejpam-5275	192	6	n	n	X
ejpam-5275	192	7	!	!	PUNCT
ejpam-5275	192	8	.	.	PUNCT
ejpam-5275	193	1	therefore	therefore	ADV
ejpam-5275	193	2	,	,	PUNCT
ejpam-5275	193	3	by	by	ADP
ejpam-5275	193	4	compring	compre	VERB
ejpam-5275	193	5	the	the	DET
ejpam-5275	193	6	coefficients	coefficient	NOUN
ejpam-5275	193	7	on	on	ADP
ejpam-5275	193	8	both	both	DET
ejpam-5275	193	9	sides	side	NOUN
ejpam-5275	193	10	of	of	ADP
ejpam-5275	193	11	(	(	PUNCT
ejpam-5275	193	12	29	29	NUM
ejpam-5275	193	13	)	)	PUNCT
ejpam-5275	193	14	and	and	CCONJ
ejpam-5275	193	15	(	(	PUNCT
ejpam-5275	193	16	30	30	NUM
ejpam-5275	193	17	)	)	PUNCT
ejpam-5275	193	18	,	,	PUNCT
ejpam-5275	193	19	we	we	PRON
ejpam-5275	193	20	have	have	VERB
ejpam-5275	193	21	the	the	DET
ejpam-5275	193	22	following	follow	VERB
ejpam-5275	193	23	theorem	theorem	VERB
ejpam-5275	193	24	.	.	PUNCT
ejpam-5275	193	25	theorem	theorem	PROPN
ejpam-5275	193	26	7	7	NUM
ejpam-5275	193	27	.	.	NOUN
ejpam-5275	193	28	for	for	ADP
ejpam-5275	193	29	n	n	PRON
ejpam-5275	193	30	,	,	PUNCT
ejpam-5275	193	31	k	k	PROPN
ejpam-5275	193	32	≥	≥	PROPN
ejpam-5275	193	33	0	0	NUM
ejpam-5275	193	34	,	,	PUNCT
ejpam-5275	193	35	we	we	PRON
ejpam-5275	193	36	have	have	VERB
ejpam-5275	193	37	b(k	b(k	PROPN
ejpam-5275	193	38	,	,	PUNCT
ejpam-5275	193	39	y	y	PROPN
ejpam-5275	193	40	)	)	PUNCT
ejpam-5275	193	41	n	n	CCONJ
ejpam-5275	193	42	,	,	PUNCT
ejpam-5275	194	1	p	p	X
ejpam-5275	194	2	=	=	PUNCT
ejpam-5275	194	3	n∑	n∑	PROPN
ejpam-5275	194	4	l=0	l=0	PROPN
ejpam-5275	194	5	l+1∑	l+1∑	PROPN
ejpam-5275	194	6	m=1	m=1	X
ejpam-5275	194	7	(	(	PUNCT
ejpam-5275	194	8	n	n	X
ejpam-5275	194	9	l	l	NOUN
ejpam-5275	194	10	)	)	PUNCT
ejpam-5275	194	11	p(m)(m−	p(m)(m−	ADP
ejpam-5275	194	12	1	1	NUM
ejpam-5275	194	13	)	)	PUNCT
ejpam-5275	194	14	!	!	PUNCT
ejpam-5275	195	1	mk−1	mk−1	NOUN
ejpam-5275	195	2	(	(	PUNCT
ejpam-5275	195	3	−1)n−m+1s2(l	−1)n−m+1s2(l	PRON
ejpam-5275	195	4	+	+	CCONJ
ejpam-5275	195	5	1,m	1,m	X
ejpam-5275	195	6	)	)	PUNCT
ejpam-5275	195	7	l	l	NOUN
ejpam-5275	196	1	+	+	CCONJ
ejpam-5275	196	2	1	1	NUM
ejpam-5275	196	3	by	by	ADP
ejpam-5275	196	4	n−l	n−l	NOUN
ejpam-5275	196	5	.	.	PUNCT
ejpam-5275	197	1	let	let	VERB
ejpam-5275	197	2	y	y	PRON
ejpam-5275	197	3	be	be	AUX
ejpam-5275	197	4	the	the	DET
ejpam-5275	197	5	poisson	poisson	NOUN
ejpam-5275	197	6	random	random	ADJ
ejpam-5275	197	7	variable	variable	NOUN
ejpam-5275	197	8	with	with	ADP
ejpam-5275	197	9	parameter	parameter	PROPN
ejpam-5275	197	10	α	α	PROPN
ejpam-5275	197	11	>	>	X
ejpam-5275	197	12	0	0	PROPN
ejpam-5275	197	13	.	.	PUNCT
ejpam-5275	198	1	then	then	ADV
ejpam-5275	198	2	we	we	PRON
ejpam-5275	198	3	have	have	VERB
ejpam-5275	198	4	uk(1−	uk(1−	ADJ
ejpam-5275	198	5	e−t|p)exα(et−1	e−t|p)exα(et−1	NOUN
ejpam-5275	198	6	)	)	PUNCT
ejpam-5275	198	7	=	=	PUNCT
ejpam-5275	199	1	∞∑	∞∑	NUM
ejpam-5275	199	2	n=0	n=0	NUM
ejpam-5275	199	3	b(k	b(k	PROPN
ejpam-5275	199	4	,	,	PUNCT
ejpam-5275	199	5	y	y	PROPN
ejpam-5275	199	6	)	)	PUNCT
ejpam-5275	199	7	n	n	CCONJ
ejpam-5275	199	8	,	,	PUNCT
ejpam-5275	199	9	p	p	X
ejpam-5275	199	10	(	(	PUNCT
ejpam-5275	199	11	x	x	NOUN
ejpam-5275	199	12	)	)	PUNCT
ejpam-5275	199	13	tn	tn	PROPN
ejpam-5275	199	14	n	n	PROPN
ejpam-5275	199	15	!	!	PUNCT
ejpam-5275	199	16	(	(	PUNCT
ejpam-5275	199	17	1−	1−	NUM
ejpam-5275	199	18	eα(e	eα(e	NUM
ejpam-5275	199	19	−t−1	−t−1	NUM
ejpam-5275	199	20	)	)	PUNCT
ejpam-5275	199	21	)	)	PUNCT
ejpam-5275	199	22	(	(	PUNCT
ejpam-5275	199	23	31	31	NUM
ejpam-5275	199	24	)	)	PUNCT
ejpam-5275	199	25	=	=	NOUN
ejpam-5275	200	1	∞∑	∞∑	NUM
ejpam-5275	200	2	n=0	n=0	NUM
ejpam-5275	200	3	b(k	b(k	PROPN
ejpam-5275	200	4	,	,	PUNCT
ejpam-5275	200	5	y	y	PROPN
ejpam-5275	200	6	)	)	PUNCT
ejpam-5275	200	7	n	n	CCONJ
ejpam-5275	200	8	,	,	PUNCT
ejpam-5275	200	9	p	p	X
ejpam-5275	200	10	(	(	PUNCT
ejpam-5275	200	11	x	x	NOUN
ejpam-5275	200	12	)	)	PUNCT
ejpam-5275	200	13	tn	tn	PROPN
ejpam-5275	200	14	n	n	NOUN
ejpam-5275	200	15	!	!	PUNCT
ejpam-5275	201	1	−	−	PROPN
ejpam-5275	202	1	∞∑	∞∑	NUM
ejpam-5275	202	2	m=0	m=0	PROPN
ejpam-5275	202	3	b(k	b(k	PROPN
ejpam-5275	202	4	,	,	PUNCT
ejpam-5275	202	5	y	y	PROPN
ejpam-5275	202	6	)	)	PUNCT
ejpam-5275	202	7	m	m	VERB
ejpam-5275	202	8	(	(	PUNCT
ejpam-5275	202	9	x	x	NOUN
ejpam-5275	202	10	)	)	PUNCT
ejpam-5275	202	11	tm	tm	PROPN
ejpam-5275	202	12	m	m	PROPN
ejpam-5275	202	13	!	!	PUNCT
ejpam-5275	203	1	∞∑	∞∑	NUM
ejpam-5275	203	2	l=0	l=0	PROPN
ejpam-5275	203	3	αl(e−t	αl(e−t	PROPN
ejpam-5275	204	1	−	−	PROPN
ejpam-5275	204	2	1)l	1)l	NUM
ejpam-5275	204	3	l	l	NOUN
ejpam-5275	204	4	!	!	PUNCT
ejpam-5275	205	1	=	=	PUNCT
ejpam-5275	206	1	∞∑	∞∑	PRON
ejpam-5275	206	2	n=0	n=0	NUM
ejpam-5275	206	3	b(k	b(k	PROPN
ejpam-5275	206	4	,	,	PUNCT
ejpam-5275	206	5	y	y	PROPN
ejpam-5275	206	6	)	)	PUNCT
ejpam-5275	206	7	n	n	CCONJ
ejpam-5275	206	8	,	,	PUNCT
ejpam-5275	206	9	p	p	X
ejpam-5275	206	10	(	(	PUNCT
ejpam-5275	206	11	x	x	NOUN
ejpam-5275	206	12	)	)	PUNCT
ejpam-5275	206	13	tn	tn	PROPN
ejpam-5275	206	14	n	n	NOUN
ejpam-5275	206	15	!	!	PUNCT
ejpam-5275	206	16	−	−	PROPN
ejpam-5275	207	1	∞∑	∞∑	NUM
ejpam-5275	207	2	m=0	m=0	PROPN
ejpam-5275	207	3	b(k	b(k	PROPN
ejpam-5275	207	4	,	,	PUNCT
ejpam-5275	207	5	y	y	PROPN
ejpam-5275	207	6	)	)	PUNCT
ejpam-5275	207	7	m	m	VERB
ejpam-5275	207	8	(	(	PUNCT
ejpam-5275	207	9	x	x	NOUN
ejpam-5275	207	10	)	)	PUNCT
ejpam-5275	207	11	tm	tm	PROPN
ejpam-5275	207	12	m	m	PROPN
ejpam-5275	207	13	!	!	PUNCT
ejpam-5275	208	1	∞∑	∞∑	NUM
ejpam-5275	208	2	l=0	l=0	PROPN
ejpam-5275	208	3	αl	αl	ADP
ejpam-5275	208	4	∞∑	∞∑	NUM
ejpam-5275	208	5	i	i	PROPN
ejpam-5275	208	6	=	=	NOUN
ejpam-5275	208	7	l	l	NOUN
ejpam-5275	208	8	s2(i	s2(i	PROPN
ejpam-5275	208	9	,	,	PUNCT
ejpam-5275	208	10	l)(−1)i	l)(−1)i	PROPN
ejpam-5275	208	11	ti	ti	NOUN
ejpam-5275	208	12	i	i	PRON
ejpam-5275	208	13	!	!	PUNCT
ejpam-5275	209	1	=	=	PUNCT
ejpam-5275	210	1	∞∑	∞∑	PRON
ejpam-5275	210	2	n=0	n=0	NUM
ejpam-5275	210	3	b(k	b(k	PROPN
ejpam-5275	210	4	,	,	PUNCT
ejpam-5275	210	5	y	y	PROPN
ejpam-5275	210	6	)	)	PUNCT
ejpam-5275	210	7	n	n	CCONJ
ejpam-5275	210	8	,	,	PUNCT
ejpam-5275	210	9	p	p	X
ejpam-5275	210	10	(	(	PUNCT
ejpam-5275	210	11	x	x	NOUN
ejpam-5275	210	12	)	)	PUNCT
ejpam-5275	210	13	tn	tn	PROPN
ejpam-5275	210	14	n	n	NOUN
ejpam-5275	210	15	!	!	PUNCT
ejpam-5275	211	1	−	−	PROPN
ejpam-5275	212	1	∞∑	∞∑	NUM
ejpam-5275	212	2	n=0	n=0	PROPN
ejpam-5275	212	3	n∑	n∑	ADP
ejpam-5275	212	4	i=0	i=0	PROPN
ejpam-5275	212	5	i∑	i∑	PROPN
ejpam-5275	212	6	l=0	l=0	PROPN
ejpam-5275	212	7	(	(	PUNCT
ejpam-5275	212	8	n	n	NOUN
ejpam-5275	212	9	i	i	PRON
ejpam-5275	212	10	)	)	PUNCT
ejpam-5275	212	11	(	(	PUNCT
ejpam-5275	212	12	−1)iαls2(i	−1)iαls2(i	PROPN
ejpam-5275	212	13	,	,	PUNCT
ejpam-5275	212	14	l)b	l)b	X
ejpam-5275	212	15	(	(	PUNCT
ejpam-5275	212	16	k	k	X
ejpam-5275	212	17	,	,	PUNCT
ejpam-5275	212	18	y	y	PROPN
ejpam-5275	212	19	)	)	PUNCT
ejpam-5275	212	20	n−i	n−i	PROPN
ejpam-5275	212	21	(	(	PUNCT
ejpam-5275	212	22	x	x	NOUN
ejpam-5275	212	23	)	)	PUNCT
ejpam-5275	212	24	tn	tn	PROPN
ejpam-5275	212	25	n	n	NOUN
ejpam-5275	212	26	!	!	PUNCT
ejpam-5275	212	27	=	=	PUNCT
ejpam-5275	213	1	∞∑	∞∑	PRON
ejpam-5275	213	2	n=0	n=0	NUM
ejpam-5275	213	3	(	(	PUNCT
ejpam-5275	213	4	b(k	b(k	PROPN
ejpam-5275	213	5	,	,	PUNCT
ejpam-5275	213	6	y	y	PROPN
ejpam-5275	213	7	)	)	PUNCT
ejpam-5275	213	8	n	n	CCONJ
ejpam-5275	213	9	,	,	PUNCT
ejpam-5275	213	10	p	p	X
ejpam-5275	213	11	(	(	PUNCT
ejpam-5275	213	12	x)−	x)−	PROPN
ejpam-5275	213	13	n∑	n∑	PROPN
ejpam-5275	213	14	i=0	i=0	PROPN
ejpam-5275	213	15	i∑	i∑	PROPN
ejpam-5275	213	16	l=0	l=0	PROPN
ejpam-5275	213	17	(	(	PUNCT
ejpam-5275	213	18	n	n	NOUN
ejpam-5275	213	19	i	i	PRON
ejpam-5275	213	20	)	)	PUNCT
ejpam-5275	213	21	(	(	PUNCT
ejpam-5275	213	22	−1)iαls2(i	−1)iαls2(i	PROPN
ejpam-5275	213	23	,	,	PUNCT
ejpam-5275	213	24	l)b	l)b	X
ejpam-5275	213	25	(	(	PUNCT
ejpam-5275	213	26	k	k	X
ejpam-5275	213	27	,	,	PUNCT
ejpam-5275	213	28	y	y	PROPN
ejpam-5275	213	29	)	)	PUNCT
ejpam-5275	213	30	n−i	n−i	PROPN
ejpam-5275	213	31	(	(	PUNCT
ejpam-5275	213	32	x	x	NOUN
ejpam-5275	213	33	)	)	PUNCT
ejpam-5275	213	34	)	)	PUNCT
ejpam-5275	213	35	tn	tn	PROPN
ejpam-5275	213	36	n	n	PROPN
ejpam-5275	213	37	!	!	PUNCT
ejpam-5275	213	38	.	.	PUNCT
ejpam-5275	214	1	s.	s.	PROPN
ejpam-5275	214	2	h.	h.	PROPN
ejpam-5275	214	3	lee	lee	PROPN
ejpam-5275	214	4	,	,	PUNCT
ejpam-5275	214	5	l.	l.	PROPN
ejpam-5275	214	6	chen	chen	PROPN
ejpam-5275	214	7	,	,	PUNCT
ejpam-5275	214	8	w.	w.	PROPN
ejpam-5275	214	9	kim	kim	PROPN
ejpam-5275	214	10	/	/	SYM
ejpam-5275	214	11	eur	eur	PROPN
ejpam-5275	214	12	.	.	PUNCT
ejpam-5275	215	1	j.	j.	PROPN
ejpam-5275	215	2	pure	pure	PROPN
ejpam-5275	215	3	appl	appl	PROPN
ejpam-5275	215	4	.	.	PROPN
ejpam-5275	215	5	math	math	PROPN
ejpam-5275	215	6	,	,	PUNCT
ejpam-5275	215	7	17	17	NUM
ejpam-5275	215	8	(	(	PUNCT
ejpam-5275	215	9	3	3	NUM
ejpam-5275	215	10	)	)	PUNCT
ejpam-5275	215	11	(	(	PUNCT
ejpam-5275	215	12	2024	2024	NUM
ejpam-5275	215	13	)	)	PUNCT
ejpam-5275	215	14	,	,	PUNCT
ejpam-5275	215	15	2336	2336	NUM
ejpam-5275	215	16	-	-	SYM
ejpam-5275	215	17	2348	2348	NUM
ejpam-5275	215	18	2344	2344	NUM
ejpam-5275	215	19	on	on	ADP
ejpam-5275	215	20	the	the	DET
ejpam-5275	215	21	other	other	ADJ
ejpam-5275	215	22	hand	hand	NOUN
ejpam-5275	215	23	uk(1−	uk(1−	PROPN
ejpam-5275	215	24	e−t|p)exα(et−1	e−t|p)exα(et−1	NOUN
ejpam-5275	215	25	)	)	PUNCT
ejpam-5275	215	26	=	=	PUNCT
ejpam-5275	216	1	∞∑	∞∑	NUM
ejpam-5275	216	2	m=1	m=1	X
ejpam-5275	216	3	p(m	p(m	NOUN
ejpam-5275	216	4	)	)	PUNCT
ejpam-5275	216	5	mk	mk	NOUN
ejpam-5275	216	6	(	(	PUNCT
ejpam-5275	216	7	1−	1−	NUM
ejpam-5275	216	8	e−t)m	e−t)m	PROPN
ejpam-5275	216	9	∞∑	∞∑	NUM
ejpam-5275	216	10	i=0	i=0	PROPN
ejpam-5275	216	11	beli(x	beli(x	NOUN
ejpam-5275	216	12	)	)	PUNCT
ejpam-5275	216	13	αi(e−t	αi(e−t	NUM
ejpam-5275	216	14	−	−	PROPN
ejpam-5275	216	15	1)i	1)i	NUM
ejpam-5275	216	16	i	i	PRON
ejpam-5275	216	17	!	!	PUNCT
ejpam-5275	217	1	(	(	PUNCT
ejpam-5275	217	2	32	32	NUM
ejpam-5275	217	3	)	)	PUNCT
ejpam-5275	217	4	=	=	NOUN
ejpam-5275	218	1	∞∑	∞∑	NUM
ejpam-5275	218	2	j=1	j=1	NOUN
ejpam-5275	218	3	j∑	j∑	PROPN
ejpam-5275	218	4	i=0	i=0	PROPN
ejpam-5275	218	5	p(j	p(j	PROPN
ejpam-5275	218	6	−	−	PROPN
ejpam-5275	218	7	i	i	PROPN
ejpam-5275	218	8	)	)	PUNCT
ejpam-5275	218	9	(	(	PUNCT
ejpam-5275	218	10	j	j	PROPN
ejpam-5275	218	11	−	−	PROPN
ejpam-5275	218	12	i)k	i)k	NOUN
ejpam-5275	218	13	beli(x	beli(x	NOUN
ejpam-5275	218	14	)	)	PUNCT
ejpam-5275	218	15	αi	αi	VERB
ejpam-5275	218	16	i	i	PRON
ejpam-5275	218	17	!	!	PUNCT
ejpam-5275	219	1	(	(	PUNCT
ejpam-5275	219	2	−1)j−i	−1)j−i	PROPN
ejpam-5275	219	3	(	(	PUNCT
ejpam-5275	219	4	e	e	NOUN
ejpam-5275	219	5	−t	−t	NOUN
ejpam-5275	219	6	−	−	PROPN
ejpam-5275	219	7	1)j	1)j	PROPN
ejpam-5275	219	8	j	j	PROPN
ejpam-5275	219	9	!	!	PUNCT
ejpam-5275	219	10	j	j	PROPN
ejpam-5275	219	11	!	!	PUNCT
ejpam-5275	220	1	=	=	PUNCT
ejpam-5275	221	1	∞∑	∞∑	NUM
ejpam-5275	221	2	j=1	j=1	NOUN
ejpam-5275	221	3	j∑	j∑	PROPN
ejpam-5275	221	4	i=0	i=0	PROPN
ejpam-5275	221	5	p(j	p(j	PROPN
ejpam-5275	221	6	−	−	PROPN
ejpam-5275	221	7	i	i	PROPN
ejpam-5275	221	8	)	)	PUNCT
ejpam-5275	221	9	(	(	PUNCT
ejpam-5275	221	10	j	j	PROPN
ejpam-5275	221	11	−	−	PROPN
ejpam-5275	221	12	i)k	i)k	NOUN
ejpam-5275	221	13	beli(x	beli(x	NOUN
ejpam-5275	221	14	)	)	PUNCT
ejpam-5275	221	15	αij	αij	NOUN
ejpam-5275	221	16	!	!	PUNCT
ejpam-5275	222	1	i	i	PRON
ejpam-5275	222	2	!	!	PUNCT
ejpam-5275	223	1	(	(	PUNCT
ejpam-5275	223	2	−1)j−i	−1)j−i	X
ejpam-5275	223	3	∞∑	∞∑	NUM
ejpam-5275	223	4	n	n	CCONJ
ejpam-5275	223	5	=	=	SYM
ejpam-5275	223	6	j	j	PROPN
ejpam-5275	223	7	s2(n	s2(n	PROPN
ejpam-5275	223	8	,	,	PUNCT
ejpam-5275	223	9	j)(−1)n	j)(−1)n	PROPN
ejpam-5275	223	10	tn	tn	PROPN
ejpam-5275	223	11	n	n	PROPN
ejpam-5275	223	12	!	!	PUNCT
ejpam-5275	224	1	=	=	NOUN
ejpam-5275	225	1	∞∑	∞∑	NUM
ejpam-5275	225	2	n=1	n=1	PROPN
ejpam-5275	225	3	n∑	n∑	PROPN
ejpam-5275	225	4	j=1	j=1	PROPN
ejpam-5275	225	5	j∑	j∑	PROPN
ejpam-5275	225	6	i=0	i=0	PROPN
ejpam-5275	225	7	p(j	p(j	PROPN
ejpam-5275	225	8	−	−	PROPN
ejpam-5275	225	9	i	i	PROPN
ejpam-5275	225	10	)	)	PUNCT
ejpam-5275	225	11	(	(	PUNCT
ejpam-5275	225	12	j	j	PROPN
ejpam-5275	225	13	−	−	PROPN
ejpam-5275	225	14	i)k	i)k	NOUN
ejpam-5275	225	15	beli(x	beli(x	NOUN
ejpam-5275	225	16	)	)	PUNCT
ejpam-5275	225	17	αij	αij	NOUN
ejpam-5275	225	18	!	!	PUNCT
ejpam-5275	226	1	i	i	PRON
ejpam-5275	226	2	!	!	PUNCT
ejpam-5275	227	1	(	(	PUNCT
ejpam-5275	227	2	−1)j−i+ns2(n	−1)j−i+ns2(n	PROPN
ejpam-5275	227	3	,	,	PUNCT
ejpam-5275	227	4	j	j	NOUN
ejpam-5275	227	5	)	)	PUNCT
ejpam-5275	227	6	tn	tn	PROPN
ejpam-5275	227	7	n	n	PROPN
ejpam-5275	227	8	!	!	PUNCT
ejpam-5275	227	9	.	.	PUNCT
ejpam-5275	228	1	therefore	therefore	ADV
ejpam-5275	228	2	,	,	PUNCT
ejpam-5275	228	3	by	by	ADP
ejpam-5275	228	4	comparing	compare	VERB
ejpam-5275	228	5	the	the	DET
ejpam-5275	228	6	coefficients	coefficient	NOUN
ejpam-5275	228	7	on	on	ADP
ejpam-5275	228	8	both	both	DET
ejpam-5275	228	9	sides	side	NOUN
ejpam-5275	228	10	of	of	ADP
ejpam-5275	228	11	(	(	PUNCT
ejpam-5275	228	12	31	31	NUM
ejpam-5275	228	13	)	)	PUNCT
ejpam-5275	228	14	and	and	CCONJ
ejpam-5275	228	15	(	(	PUNCT
ejpam-5275	228	16	32	32	NUM
ejpam-5275	228	17	)	)	PUNCT
ejpam-5275	228	18	,	,	PUNCT
ejpam-5275	228	19	we	we	PRON
ejpam-5275	228	20	have	have	VERB
ejpam-5275	228	21	the	the	DET
ejpam-5275	228	22	following	follow	VERB
ejpam-5275	228	23	theorem	theorem	VERB
ejpam-5275	228	24	.	.	PUNCT
ejpam-5275	228	25	theorem	theorem	NOUN
ejpam-5275	228	26	8	8	NUM
ejpam-5275	228	27	.	.	PUNCT
ejpam-5275	229	1	let	let	VERB
ejpam-5275	229	2	y	y	PRON
ejpam-5275	229	3	be	be	AUX
ejpam-5275	229	4	the	the	DET
ejpam-5275	229	5	poisson	poisson	NOUN
ejpam-5275	229	6	random	random	ADJ
ejpam-5275	229	7	variable	variable	NOUN
ejpam-5275	229	8	with	with	ADP
ejpam-5275	229	9	parameter	parameter	PROPN
ejpam-5275	229	10	α	α	PROPN
ejpam-5275	229	11	(	(	PUNCT
ejpam-5275	229	12	>	>	X
ejpam-5275	229	13	0	0	NUM
ejpam-5275	229	14	)	)	PUNCT
ejpam-5275	229	15	.	.	PUNCT
ejpam-5275	230	1	then	then	ADV
ejpam-5275	230	2	we	we	PRON
ejpam-5275	230	3	have	have	VERB
ejpam-5275	230	4	b(k	b(k	PROPN
ejpam-5275	230	5	,	,	PUNCT
ejpam-5275	230	6	y	y	PROPN
ejpam-5275	230	7	)	)	PUNCT
ejpam-5275	230	8	n	n	CCONJ
ejpam-5275	230	9	,	,	PUNCT
ejpam-5275	230	10	p	p	X
ejpam-5275	230	11	(	(	PUNCT
ejpam-5275	230	12	x	x	NOUN
ejpam-5275	230	13	)	)	PUNCT
ejpam-5275	230	14	=	=	SYM
ejpam-5275	231	1	n∑	n∑	NOUN
ejpam-5275	231	2	j=1	j=1	PROPN
ejpam-5275	231	3	j∑	j∑	PROPN
ejpam-5275	231	4	i=0	i=0	PROPN
ejpam-5275	231	5	p(j	p(j	PROPN
ejpam-5275	231	6	−	−	PROPN
ejpam-5275	231	7	i	i	PROPN
ejpam-5275	231	8	)	)	PUNCT
ejpam-5275	231	9	(	(	PUNCT
ejpam-5275	231	10	j	j	PROPN
ejpam-5275	231	11	−	−	PROPN
ejpam-5275	231	12	i)k	i)k	NOUN
ejpam-5275	231	13	beli(x	beli(x	NOUN
ejpam-5275	231	14	)	)	PUNCT
ejpam-5275	231	15	αij	αij	NOUN
ejpam-5275	231	16	!	!	PUNCT
ejpam-5275	232	1	i	i	PRON
ejpam-5275	232	2	!	!	PUNCT
ejpam-5275	233	1	(	(	PUNCT
ejpam-5275	233	2	−1)j−i+ns2(n	−1)j−i+ns2(n	PUNCT
ejpam-5275	233	3	,	,	PUNCT
ejpam-5275	233	4	j)+	j)+	PROPN
ejpam-5275	233	5	n∑	n∑	PROPN
ejpam-5275	233	6	i=0	i=0	PROPN
ejpam-5275	233	7	i∑	i∑	PROPN
ejpam-5275	233	8	l=0	l=0	PROPN
ejpam-5275	233	9	(	(	PUNCT
ejpam-5275	233	10	n	n	NOUN
ejpam-5275	233	11	i	i	PRON
ejpam-5275	233	12	)	)	PUNCT
ejpam-5275	233	13	(	(	PUNCT
ejpam-5275	233	14	−1)iαls2(i	−1)iαls2(i	PROPN
ejpam-5275	233	15	,	,	PUNCT
ejpam-5275	233	16	l)b	l)b	X
ejpam-5275	233	17	(	(	PUNCT
ejpam-5275	233	18	k	k	X
ejpam-5275	233	19	,	,	PUNCT
ejpam-5275	233	20	y	y	PROPN
ejpam-5275	233	21	)	)	PUNCT
ejpam-5275	233	22	n−i	n−i	PROPN
ejpam-5275	233	23	(	(	PUNCT
ejpam-5275	233	24	x	x	NOUN
ejpam-5275	233	25	)	)	PUNCT
ejpam-5275	233	26	.	.	PUNCT
ejpam-5275	234	1	from	from	ADP
ejpam-5275	234	2	(	(	PUNCT
ejpam-5275	234	3	29	29	NUM
ejpam-5275	234	4	)	)	PUNCT
ejpam-5275	234	5	,	,	PUNCT
ejpam-5275	234	6	we	we	PRON
ejpam-5275	234	7	have	have	VERB
ejpam-5275	234	8	∞∑	∞∑	NUM
ejpam-5275	234	9	n=0	n=0	PROPN
ejpam-5275	234	10	b(k	b(k	PROPN
ejpam-5275	234	11	,	,	PUNCT
ejpam-5275	234	12	y	y	PROPN
ejpam-5275	234	13	)	)	PUNCT
ejpam-5275	234	14	n	n	CCONJ
ejpam-5275	234	15	,	,	PUNCT
ejpam-5275	234	16	p	p	X
ejpam-5275	234	17	(	(	PUNCT
ejpam-5275	234	18	α	α	NOUN
ejpam-5275	234	19	)	)	PUNCT
ejpam-5275	234	20	tn	tn	PROPN
ejpam-5275	234	21	n	n	NOUN
ejpam-5275	234	22	!	!	PUNCT
ejpam-5275	234	23	=	=	NOUN
ejpam-5275	235	1	∞∑	∞∑	PRON
ejpam-5275	235	2	n=0	n=0	NUM
ejpam-5275	235	3	b	b	NOUN
ejpam-5275	235	4	(	(	PUNCT
ejpam-5275	235	5	k	k	X
ejpam-5275	235	6	,	,	PUNCT
ejpam-5275	235	7	y	y	PROPN
ejpam-5275	235	8	)	)	PUNCT
ejpam-5275	235	9	l	l	NOUN
ejpam-5275	235	10	,	,	PUNCT
ejpam-5275	235	11	p	p	PROPN
ejpam-5275	235	12	tl	tl	PROPN
ejpam-5275	235	13	l	l	NOUN
ejpam-5275	235	14	!	!	PUNCT
ejpam-5275	236	1	(	(	PUNCT
ejpam-5275	236	2	e[e−y	e[e−y	PROPN
ejpam-5275	236	3	t	t	PROPN
ejpam-5275	236	4	]	]	PUNCT
ejpam-5275	236	5	)	)	PUNCT
ejpam-5275	236	6	α	α	PROPN
ejpam-5275	236	7	(	(	PUNCT
ejpam-5275	236	8	33	33	NUM
ejpam-5275	236	9	)	)	PUNCT
ejpam-5275	236	10	=	=	NOUN
ejpam-5275	237	1	∞∑	∞∑	NUM
ejpam-5275	237	2	l=0	l=0	PROPN
ejpam-5275	237	3	b	b	PROPN
ejpam-5275	237	4	(	(	PUNCT
ejpam-5275	237	5	k	k	X
ejpam-5275	237	6	,	,	PUNCT
ejpam-5275	237	7	y	y	PROPN
ejpam-5275	237	8	)	)	PUNCT
ejpam-5275	237	9	l	l	NOUN
ejpam-5275	237	10	,	,	PUNCT
ejpam-5275	237	11	p	p	PROPN
ejpam-5275	237	12	tl	tl	PROPN
ejpam-5275	237	13	l	l	NOUN
ejpam-5275	237	14	!	!	PUNCT
ejpam-5275	238	1	∞∑	∞∑	ADJ
ejpam-5275	238	2	m=0	m=0	PROPN
ejpam-5275	238	3	(	(	PUNCT
ejpam-5275	238	4	−1)me[y1	−1)me[y1	PROPN
ejpam-5275	238	5	+	+	PUNCT
ejpam-5275	238	6	y2	y2	ADJ
ejpam-5275	238	7	+	+	CCONJ
ejpam-5275	238	8	·	·	PUNCT
ejpam-5275	238	9	·	·	PUNCT
ejpam-5275	238	10	·	·	PUNCT
ejpam-5275	238	11	+	+	NUM
ejpam-5275	238	12	yα	yα	NOUN
ejpam-5275	238	13	]	]	X
ejpam-5275	238	14	tm	tm	PROPN
ejpam-5275	238	15	m	m	PROPN
ejpam-5275	238	16	!	!	PUNCT
ejpam-5275	238	17	=	=	NOUN
ejpam-5275	239	1	∞∑	∞∑	PRON
ejpam-5275	239	2	n=0	n=0	NUM
ejpam-5275	239	3	n∑	n∑	NOUN
ejpam-5275	239	4	m=0	m=0	PROPN
ejpam-5275	239	5	(	(	PUNCT
ejpam-5275	239	6	−1)m	−1)m	PROPN
ejpam-5275	239	7	(	(	PUNCT
ejpam-5275	239	8	n	n	NOUN
ejpam-5275	239	9	m	m	PROPN
ejpam-5275	239	10	)	)	PUNCT
ejpam-5275	239	11	b	b	NOUN
ejpam-5275	239	12	(	(	PUNCT
ejpam-5275	239	13	k	k	X
ejpam-5275	239	14	,	,	PUNCT
ejpam-5275	239	15	y	y	PROPN
ejpam-5275	239	16	)	)	PUNCT
ejpam-5275	239	17	n−m	n−m	PROPN
ejpam-5275	239	18	,	,	PUNCT
ejpam-5275	239	19	pe[sm	pe[sm	PRON
ejpam-5275	239	20	α	α	X
ejpam-5275	239	21	]	]	PUNCT
ejpam-5275	239	22	tn	tn	PROPN
ejpam-5275	239	23	n	n	X
ejpam-5275	239	24	!	!	PUNCT
ejpam-5275	239	25	.	.	PUNCT
ejpam-5275	240	1	therefore	therefore	ADV
ejpam-5275	240	2	,	,	PUNCT
ejpam-5275	240	3	by	by	ADP
ejpam-5275	240	4	compring	compre	VERB
ejpam-5275	240	5	the	the	DET
ejpam-5275	240	6	coefficients	coefficient	NOUN
ejpam-5275	240	7	on	on	ADP
ejpam-5275	240	8	bosides	boside	NOUN
ejpam-5275	240	9	(	(	PUNCT
ejpam-5275	240	10	33	33	NUM
ejpam-5275	240	11	)	)	PUNCT
ejpam-5275	240	12	,	,	PUNCT
ejpam-5275	240	13	we	we	PRON
ejpam-5275	240	14	have	have	VERB
ejpam-5275	240	15	the	the	DET
ejpam-5275	240	16	following	follow	VERB
ejpam-5275	240	17	theorem	theorem	VERB
ejpam-5275	240	18	.	.	PUNCT
ejpam-5275	240	19	theorem	theorem	NOUN
ejpam-5275	240	20	9	9	NUM
ejpam-5275	240	21	.	.	PUNCT
ejpam-5275	241	1	for	for	ADP
ejpam-5275	241	2	α	α	NOUN
ejpam-5275	241	3	,	,	PUNCT
ejpam-5275	241	4	n	n	PRON
ejpam-5275	241	5	≥	≥	NOUN
ejpam-5275	241	6	0	0	NUM
ejpam-5275	241	7	and	and	CCONJ
ejpam-5275	241	8	α	α	PRON
ejpam-5275	241	9	∈	∈	PROPN
ejpam-5275	242	1	z	z	X
ejpam-5275	242	2	,	,	PUNCT
ejpam-5275	242	3	we	we	PRON
ejpam-5275	242	4	have	have	VERB
ejpam-5275	242	5	b(k	b(k	PROPN
ejpam-5275	242	6	,	,	PUNCT
ejpam-5275	242	7	y	y	PROPN
ejpam-5275	242	8	)	)	PUNCT
ejpam-5275	242	9	n	n	CCONJ
ejpam-5275	242	10	,	,	PUNCT
ejpam-5275	242	11	p	p	X
ejpam-5275	242	12	(	(	PUNCT
ejpam-5275	242	13	α	α	NOUN
ejpam-5275	242	14	)	)	PUNCT
ejpam-5275	242	15	=	=	SYM
ejpam-5275	242	16	n∑	n∑	PROPN
ejpam-5275	242	17	m=0	m=0	PROPN
ejpam-5275	243	1	(	(	PUNCT
ejpam-5275	243	2	−1)m	−1)m	PROPN
ejpam-5275	243	3	(	(	PUNCT
ejpam-5275	243	4	n	n	NOUN
ejpam-5275	243	5	m	m	PROPN
ejpam-5275	243	6	)	)	PUNCT
ejpam-5275	243	7	b	b	NOUN
ejpam-5275	243	8	(	(	PUNCT
ejpam-5275	243	9	k	k	X
ejpam-5275	243	10	,	,	PUNCT
ejpam-5275	243	11	y	y	PROPN
ejpam-5275	243	12	)	)	PUNCT
ejpam-5275	243	13	n−m	n−m	PROPN
ejpam-5275	243	14	,	,	PUNCT
ejpam-5275	243	15	pe[sm	pe[sm	PRON
ejpam-5275	243	16	α	α	X
ejpam-5275	243	17	]	]	PUNCT
ejpam-5275	243	18	.	.	PUNCT
ejpam-5275	244	1	let	let	VERB
ejpam-5275	244	2	y	y	PRON
ejpam-5275	244	3	be	be	AUX
ejpam-5275	244	4	the	the	DET
ejpam-5275	244	5	bernoulli	bernoulli	NOUN
ejpam-5275	244	6	random	random	ADJ
ejpam-5275	244	7	variable	variable	NOUN
ejpam-5275	244	8	with	with	ADP
ejpam-5275	244	9	probability	probability	NOUN
ejpam-5275	244	10	of	of	ADP
ejpam-5275	244	11	success	success	NOUN
ejpam-5275	244	12	a.	a.	NOUN
ejpam-5275	244	13	then	then	ADV
ejpam-5275	244	14	we	we	PRON
ejpam-5275	244	15	have	have	VERB
ejpam-5275	244	16	∞∑	∞∑	NUM
ejpam-5275	244	17	n=0	n=0	PROPN
ejpam-5275	244	18	b(k	b(k	PROPN
ejpam-5275	244	19	,	,	PUNCT
ejpam-5275	244	20	y	y	PROPN
ejpam-5275	244	21	)	)	PUNCT
ejpam-5275	244	22	n	n	CCONJ
ejpam-5275	244	23	,	,	PUNCT
ejpam-5275	244	24	p	p	X
ejpam-5275	244	25	(	(	PUNCT
ejpam-5275	244	26	x	x	NOUN
ejpam-5275	244	27	)	)	PUNCT
ejpam-5275	244	28	tn	tn	PROPN
ejpam-5275	244	29	n	n	NOUN
ejpam-5275	244	30	!	!	PUNCT
ejpam-5275	245	1	=	=	SYM
ejpam-5275	245	2	1	1	NUM
ejpam-5275	245	3	a(e−t	a(e−t	NOUN
ejpam-5275	245	4	−	−	NOUN
ejpam-5275	245	5	1	1	NUM
ejpam-5275	245	6	)	)	PUNCT
ejpam-5275	245	7	uk(1−	uk(1−	PROPN
ejpam-5275	245	8	e−t|p	e−t|p	PROPN
ejpam-5275	245	9	)	)	PUNCT
ejpam-5275	245	10	(	(	PUNCT
ejpam-5275	245	11	a(e−t	a(e−t	NOUN
ejpam-5275	245	12	−	−	PROPN
ejpam-5275	245	13	1	1	NUM
ejpam-5275	245	14	)	)	PUNCT
ejpam-5275	245	15	+	+	CCONJ
ejpam-5275	245	16	1	1	NUM
ejpam-5275	245	17	)	)	PUNCT
ejpam-5275	245	18	)	)	PUNCT
ejpam-5275	246	1	x	x	X
ejpam-5275	246	2	(	(	PUNCT
ejpam-5275	246	3	34	34	NUM
ejpam-5275	246	4	)	)	PUNCT
ejpam-5275	246	5	references	reference	NOUN
ejpam-5275	246	6	2345	2345	NUM
ejpam-5275	246	7	=	=	SYM
ejpam-5275	246	8	1	1	NUM
ejpam-5275	246	9	a(e−t	a(e−t	NOUN
ejpam-5275	246	10	−	−	NOUN
ejpam-5275	246	11	1	1	NUM
ejpam-5275	246	12	)	)	PUNCT
ejpam-5275	246	13	∞∑	∞∑	NUM
ejpam-5275	246	14	l=1	l=1	NOUN
ejpam-5275	246	15	p(l	p(l	PROPN
ejpam-5275	246	16	)	)	PUNCT
ejpam-5275	246	17	lk	lk	NOUN
ejpam-5275	246	18	(	(	PUNCT
ejpam-5275	246	19	1−	1−	NUM
ejpam-5275	246	20	e−t)l	e−t)l	PROPN
ejpam-5275	247	1	∞∑	∞∑	PROPN
ejpam-5275	247	2	m=0	m=0	PROPN
ejpam-5275	247	3	(	(	PUNCT
ejpam-5275	247	4	x	x	NOUN
ejpam-5275	247	5	m	m	NOUN
ejpam-5275	247	6	)	)	PUNCT
ejpam-5275	247	7	am(e−t	am(e−t	NOUN
ejpam-5275	248	1	−	−	PROPN
ejpam-5275	248	2	1)m	1)m	NUM
ejpam-5275	248	3	=	=	SYM
ejpam-5275	248	4	1	1	NUM
ejpam-5275	248	5	a(e−t	a(e−t	NOUN
ejpam-5275	248	6	−	−	NOUN
ejpam-5275	248	7	1	1	NUM
ejpam-5275	248	8	)	)	PUNCT
ejpam-5275	248	9	∞∑	∞∑	NUM
ejpam-5275	248	10	i=1	i=1	ADP
ejpam-5275	248	11	i∑	i∑	PROPN
ejpam-5275	249	1	l=1	l=1	PROPN
ejpam-5275	249	2	p(l	p(l	PROPN
ejpam-5275	249	3	)	)	PUNCT
ejpam-5275	249	4	lk	lk	NOUN
ejpam-5275	249	5	(	(	PUNCT
ejpam-5275	249	6	x	x	PROPN
ejpam-5275	249	7	i−	i−	PROPN
ejpam-5275	249	8	l	l	NOUN
ejpam-5275	249	9	)	)	PUNCT
ejpam-5275	249	10	ai−l(e−t	ai−l(e−t	NOUN
ejpam-5275	249	11	−	−	PROPN
ejpam-5275	249	12	1)i	1)i	NOUN
ejpam-5275	249	13	=	=	SYM
ejpam-5275	250	1	∞∑	∞∑	NUM
ejpam-5275	250	2	i=1	i=1	X
ejpam-5275	250	3	i∑	i∑	ADJ
ejpam-5275	250	4	l=1	l=1	PROPN
ejpam-5275	250	5	(	(	PUNCT
ejpam-5275	250	6	−1)l	−1)l	NOUN
ejpam-5275	250	7	p(l	p(l	PROPN
ejpam-5275	250	8	)	)	PUNCT
ejpam-5275	250	9	lk	lk	NOUN
ejpam-5275	250	10	(	(	PUNCT
ejpam-5275	250	11	x	x	PROPN
ejpam-5275	250	12	i−	i−	PROPN
ejpam-5275	250	13	l	l	NOUN
ejpam-5275	250	14	)	)	PUNCT
ejpam-5275	250	15	ai−l−1(e−t	ai−l−1(e−t	NOUN
ejpam-5275	250	16	−	−	PROPN
ejpam-5275	250	17	1)i−1	1)i−1	NUM
ejpam-5275	250	18	=	=	PUNCT
ejpam-5275	250	19	∞∑	∞∑	NUM
ejpam-5275	250	20	i=0	i=0	PROPN
ejpam-5275	250	21	i+1∑	i+1∑	PROPN
ejpam-5275	250	22	l=1	l=1	PROPN
ejpam-5275	250	23	(	(	PUNCT
ejpam-5275	250	24	−1)l	−1)l	ADP
ejpam-5275	250	25	p(l	p(l	PROPN
ejpam-5275	250	26	)	)	PUNCT
ejpam-5275	250	27	lk	lk	NOUN
ejpam-5275	250	28	(	(	PUNCT
ejpam-5275	250	29	x	x	PROPN
ejpam-5275	250	30	i−	i−	PROPN
ejpam-5275	250	31	l	l	NOUN
ejpam-5275	250	32	+	+	CCONJ
ejpam-5275	250	33	1	1	X
ejpam-5275	250	34	)	)	PUNCT
ejpam-5275	250	35	ai−l(e−t	ai−l(e−t	NOUN
ejpam-5275	250	36	−	−	PROPN
ejpam-5275	250	37	1)i	1)i	NOUN
ejpam-5275	250	38	=	=	PUNCT
ejpam-5275	251	1	∞∑	∞∑	NUM
ejpam-5275	251	2	i=0	i=0	PROPN
ejpam-5275	251	3	i+1∑	i+1∑	PROPN
ejpam-5275	251	4	l=1	l=1	PROPN
ejpam-5275	251	5	(	(	PUNCT
ejpam-5275	251	6	−1)l	−1)l	ADP
ejpam-5275	251	7	p(l	p(l	PROPN
ejpam-5275	251	8	)	)	PUNCT
ejpam-5275	251	9	lk	lk	PROPN
ejpam-5275	251	10	i	i	PROPN
ejpam-5275	251	11	!	!	PUNCT
ejpam-5275	252	1	(	(	PUNCT
ejpam-5275	252	2	x	x	X
ejpam-5275	252	3	i−	i−	PROPN
ejpam-5275	252	4	l	l	NOUN
ejpam-5275	252	5	+	+	CCONJ
ejpam-5275	252	6	1	1	X
ejpam-5275	252	7	)	)	PUNCT
ejpam-5275	252	8	ai−l	ai−l	NOUN
ejpam-5275	252	9	∞∑	∞∑	NUM
ejpam-5275	252	10	n	n	NOUN
ejpam-5275	252	11	=	=	ADJ
ejpam-5275	252	12	i	i	PROPN
ejpam-5275	252	13	(	(	PUNCT
ejpam-5275	252	14	−1)ns2(n	−1)ns2(n	PROPN
ejpam-5275	252	15	,	,	PUNCT
ejpam-5275	252	16	i	i	PROPN
ejpam-5275	252	17	)	)	PUNCT
ejpam-5275	252	18	tn	tn	PROPN
ejpam-5275	252	19	n	n	ADV
ejpam-5275	252	20	!	!	PUNCT
ejpam-5275	252	21	=	=	NOUN
ejpam-5275	253	1	∞∑	∞∑	DET
ejpam-5275	253	2	n=0	n=0	NUM
ejpam-5275	253	3	n∑	n∑	NOUN
ejpam-5275	253	4	i=0	i=0	PROPN
ejpam-5275	253	5	i+1∑	i+1∑	PROPN
ejpam-5275	253	6	l=1	l=1	PROPN
ejpam-5275	253	7	(	(	PUNCT
ejpam-5275	253	8	−1)l+n	−1)l+n	PROPN
ejpam-5275	253	9	p(l	p(l	PROPN
ejpam-5275	253	10	)	)	PUNCT
ejpam-5275	253	11	lk	lk	PROPN
ejpam-5275	253	12	(	(	PUNCT
ejpam-5275	253	13	i)l−1(x)i−la	i)l−1(x)i−la	PROPN
ejpam-5275	253	14	i−ls2(n	i−ls2(n	PROPN
ejpam-5275	253	15	,	,	PUNCT
ejpam-5275	253	16	i	i	PROPN
ejpam-5275	253	17	)	)	PUNCT
ejpam-5275	253	18	tn	tn	PROPN
ejpam-5275	253	19	n	n	PROPN
ejpam-5275	253	20	!	!	PUNCT
ejpam-5275	253	21	.	.	PUNCT
ejpam-5275	254	1	therefore	therefore	ADV
ejpam-5275	254	2	,	,	PUNCT
ejpam-5275	254	3	by	by	ADP
ejpam-5275	254	4	compring	compre	VERB
ejpam-5275	254	5	the	the	DET
ejpam-5275	254	6	coefficients	coefficient	NOUN
ejpam-5275	254	7	on	on	ADP
ejpam-5275	254	8	both	both	DET
ejpam-5275	254	9	sides	side	NOUN
ejpam-5275	254	10	of	of	ADP
ejpam-5275	254	11	(	(	PUNCT
ejpam-5275	254	12	34	34	NUM
ejpam-5275	254	13	)	)	PUNCT
ejpam-5275	254	14	,	,	PUNCT
ejpam-5275	254	15	we	we	PRON
ejpam-5275	254	16	have	have	VERB
ejpam-5275	254	17	the	the	DET
ejpam-5275	254	18	following	follow	VERB
ejpam-5275	254	19	theorem	theorem	VERB
ejpam-5275	254	20	.	.	PUNCT
ejpam-5275	254	21	theorem	theorem	PROPN
ejpam-5275	254	22	10	10	NUM
ejpam-5275	254	23	.	.	PUNCT
ejpam-5275	255	1	let	let	VERB
ejpam-5275	255	2	y	y	PRON
ejpam-5275	255	3	be	be	AUX
ejpam-5275	255	4	the	the	DET
ejpam-5275	255	5	bernoulli	bernoulli	NOUN
ejpam-5275	255	6	random	random	ADJ
ejpam-5275	255	7	variable	variable	NOUN
ejpam-5275	255	8	with	with	ADP
ejpam-5275	255	9	probability	probability	NOUN
ejpam-5275	255	10	of	of	ADP
ejpam-5275	255	11	success	success	NOUN
ejpam-5275	255	12	a	a	PRON
ejpam-5275	255	13	,	,	PUNCT
ejpam-5275	255	14	then	then	ADV
ejpam-5275	255	15	we	we	PRON
ejpam-5275	255	16	have	have	VERB
ejpam-5275	255	17	b(k	b(k	PROPN
ejpam-5275	255	18	,	,	PUNCT
ejpam-5275	255	19	y	y	PROPN
ejpam-5275	255	20	)	)	PUNCT
ejpam-5275	255	21	n	n	CCONJ
ejpam-5275	255	22	,	,	PUNCT
ejpam-5275	255	23	p	p	X
ejpam-5275	255	24	(	(	PUNCT
ejpam-5275	255	25	x	x	NOUN
ejpam-5275	255	26	)	)	PUNCT
ejpam-5275	255	27	=	=	SYM
ejpam-5275	255	28	n∑	n∑	PROPN
ejpam-5275	255	29	i=0	i=0	PROPN
ejpam-5275	255	30	i+1∑	i+1∑	PROPN
ejpam-5275	256	1	l=1	l=1	PROPN
ejpam-5275	256	2	(	(	PUNCT
ejpam-5275	256	3	−1)l+n	−1)l+n	PROPN
ejpam-5275	256	4	p(l	p(l	PROPN
ejpam-5275	256	5	)	)	PUNCT
ejpam-5275	256	6	lk	lk	PROPN
ejpam-5275	256	7	(	(	PUNCT
ejpam-5275	256	8	i)l−1(x)i−la	i)l−1(x)i−la	PROPN
ejpam-5275	256	9	i−ls2(n	i−ls2(n	PROPN
ejpam-5275	256	10	,	,	PUNCT
ejpam-5275	256	11	i	i	NOUN
ejpam-5275	256	12	)	)	PUNCT
ejpam-5275	256	13	.	.	PUNCT
ejpam-5275	257	1	4	4	X
ejpam-5275	257	2	.	.	X
ejpam-5275	257	3	conclusion	conclusion	NOUN
ejpam-5275	257	4	in	in	ADP
ejpam-5275	257	5	this	this	DET
ejpam-5275	257	6	paper	paper	NOUN
ejpam-5275	257	7	,	,	PUNCT
ejpam-5275	257	8	we	we	PRON
ejpam-5275	257	9	present	present	VERB
ejpam-5275	257	10	a	a	DET
ejpam-5275	257	11	probabilistic	probabilistic	ADJ
ejpam-5275	257	12	version	version	NOUN
ejpam-5275	257	13	of	of	ADP
ejpam-5275	257	14	the	the	DET
ejpam-5275	257	15	type	type	NOUN
ejpam-5275	257	16	2	2	NUM
ejpam-5275	257	17	poly	poly	ADJ
ejpam-5275	257	18	-	-	PUNCT
ejpam-5275	257	19	bernoulli	bernoulli	NOUN
ejpam-5275	257	20	polynomials	polynomial	NOUN
ejpam-5275	257	21	associated	associate	VERB
ejpam-5275	257	22	with	with	ADP
ejpam-5275	257	23	a	a	DET
ejpam-5275	257	24	random	random	ADJ
ejpam-5275	257	25	variable	variable	NOUN
ejpam-5275	257	26	y	y	NOUN
ejpam-5275	257	27	satisfying	satisfy	VERB
ejpam-5275	257	28	suitable	suitable	ADJ
ejpam-5275	257	29	moment	moment	NOUN
ejpam-5275	257	30	conditions	condition	NOUN
ejpam-5275	257	31	.	.	PUNCT
ejpam-5275	258	1	we	we	PRON
ejpam-5275	258	2	call	call	VERB
ejpam-5275	258	3	it	it	PRON
ejpam-5275	258	4	probabilistic	probabilistic	ADJ
ejpam-5275	258	5	type	type	NOUN
ejpam-5275	258	6	2	2	NUM
ejpam-5275	258	7	poly	poly	ADJ
ejpam-5275	258	8	-	-	PUNCT
ejpam-5275	258	9	bernoulli	bernoulli	NOUN
ejpam-5275	258	10	polynomials	polynomial	NOUN
ejpam-5275	258	11	.	.	PUNCT
ejpam-5275	259	1	we	we	PRON
ejpam-5275	259	2	study	study	VERB
ejpam-5275	259	3	some	some	DET
ejpam-5275	259	4	properties	property	NOUN
ejpam-5275	259	5	of	of	ADP
ejpam-5275	259	6	such	such	ADJ
ejpam-5275	259	7	polynomials	polynomial	NOUN
ejpam-5275	259	8	and	and	CCONJ
ejpam-5275	259	9	obtain	obtain	VERB
ejpam-5275	259	10	relevant	relevant	ADJ
ejpam-5275	259	11	results	result	NOUN
ejpam-5275	259	12	.	.	PUNCT
ejpam-5275	260	1	more	more	ADV
ejpam-5275	260	2	specifically	specifically	ADV
ejpam-5275	260	3	,	,	PUNCT
ejpam-5275	260	4	we	we	PRON
ejpam-5275	260	5	derived	derive	VERB
ejpam-5275	260	6	an	an	DET
ejpam-5275	260	7	exact	exact	ADJ
ejpam-5275	260	8	expression	expression	NOUN
ejpam-5275	260	9	for	for	ADP
ejpam-5275	260	10	βk	βk	NOUN
ejpam-5275	260	11	,	,	PUNCT
ejpam-5275	260	12	y	y	PROPN
ejpam-5275	260	13	n	n	PROPN
ejpam-5275	260	14	(	(	PUNCT
ejpam-5275	260	15	x	x	NOUN
ejpam-5275	260	16	)	)	PUNCT
ejpam-5275	260	17	,	,	PUNCT
ejpam-5275	260	18	and	and	CCONJ
ejpam-5275	260	19	establish	establish	VERB
ejpam-5275	260	20	a	a	DET
ejpam-5275	260	21	relation	relation	NOUN
ejpam-5275	260	22	between	between	ADP
ejpam-5275	260	23	the	the	DET
ejpam-5275	260	24	type	type	NOUN
ejpam-5275	260	25	2	2	NUM
ejpam-5275	260	26	poly	poly	ADJ
ejpam-5275	260	27	-	-	PUNCT
ejpam-5275	260	28	bernoulli	bernoulli	NOUN
ejpam-5275	260	29	numbers	number	NOUN
ejpam-5275	260	30	and	and	CCONJ
ejpam-5275	260	31	the	the	DET
ejpam-5275	260	32	stirling	stirling	NOUN
ejpam-5275	260	33	number	number	NOUN
ejpam-5275	260	34	of	of	ADP
ejpam-5275	260	35	the	the	DET
ejpam-5275	260	36	first	first	ADJ
ejpam-5275	260	37	kind	kind	NOUN
ejpam-5275	260	38	,	,	PUNCT
ejpam-5275	260	39	and	and	CCONJ
ejpam-5275	260	40	obtain	obtain	VERB
ejpam-5275	260	41	a	a	DET
ejpam-5275	260	42	explicit	explicit	ADJ
ejpam-5275	260	43	formula	formula	NOUN
ejpam-5275	260	44	of	of	ADP
ejpam-5275	260	45	β	β	X
ejpam-5275	260	46	(	(	PUNCT
ejpam-5275	260	47	k	k	X
ejpam-5275	260	48	,	,	PUNCT
ejpam-5275	260	49	y	y	PROPN
ejpam-5275	260	50	)	)	PUNCT
ejpam-5275	260	51	n	n	CCONJ
ejpam-5275	260	52	(	(	PUNCT
ejpam-5275	260	53	x	x	NOUN
ejpam-5275	260	54	)	)	PUNCT
ejpam-5275	260	55	,	,	PUNCT
ejpam-5275	260	56	in	in	ADP
ejpam-5275	260	57	the	the	DET
ejpam-5275	260	58	case	case	NOUN
ejpam-5275	260	59	where	where	SCONJ
ejpam-5275	260	60	y	y	PROPN
ejpam-5275	260	61	is	be	AUX
ejpam-5275	260	62	the	the	DET
ejpam-5275	260	63	poisson	poisson	NOUN
ejpam-5275	260	64	variable	variable	NOUN
ejpam-5275	260	65	with	with	ADP
ejpam-5275	260	66	parameter	parameter	PROPN
ejpam-5275	260	67	α	α	PROPN
ejpam-5275	260	68	.	.	PUNCT
ejpam-5275	261	1	similarly	similarly	ADV
ejpam-5275	261	2	,	,	PUNCT
ejpam-5275	261	3	we	we	PRON
ejpam-5275	261	4	define	define	VERB
ejpam-5275	261	5	the	the	DET
ejpam-5275	261	6	unipoly	unipoly	ADJ
ejpam-5275	261	7	-	-	PUNCT
ejpam-5275	261	8	bernoulli	bernoulli	NOUN
ejpam-5275	261	9	polynomials	polynomial	NOUN
ejpam-5275	261	10	attached	attach	VERB
ejpam-5275	261	11	to	to	ADP
ejpam-5275	261	12	p.	p.	NOUN
ejpam-5275	261	13	then	then	ADV
ejpam-5275	261	14	we	we	PRON
ejpam-5275	261	15	show	show	VERB
ejpam-5275	261	16	the	the	DET
ejpam-5275	261	17	explicit	explicit	ADJ
ejpam-5275	261	18	expression	expression	NOUN
ejpam-5275	261	19	of	of	ADP
ejpam-5275	261	20	bk	bk	PROPN
ejpam-5275	261	21	,	,	PUNCT
ejpam-5275	261	22	y	y	PROPN
ejpam-5275	261	23	n	n	CCONJ
ejpam-5275	261	24	,	,	PUNCT
ejpam-5275	261	25	p	p	X
ejpam-5275	261	26	(	(	PUNCT
ejpam-5275	261	27	x	x	NOUN
ejpam-5275	261	28	)	)	PUNCT
ejpam-5275	261	29	and	and	CCONJ
ejpam-5275	261	30	other	other	ADJ
ejpam-5275	261	31	results	result	NOUN
ejpam-5275	261	32	by	by	ADP
ejpam-5275	261	33	skilful	skilful	ADJ
ejpam-5275	261	34	calculations	calculation	NOUN
ejpam-5275	261	35	.	.	PUNCT
ejpam-5275	262	1	as	as	ADP
ejpam-5275	262	2	a	a	DET
ejpam-5275	262	3	next	next	ADJ
ejpam-5275	262	4	step	step	NOUN
ejpam-5275	262	5	in	in	ADP
ejpam-5275	262	6	our	our	PRON
ejpam-5275	262	7	research	research	NOUN
ejpam-5275	262	8	,	,	PUNCT
ejpam-5275	262	9	we	we	PRON
ejpam-5275	262	10	will	will	AUX
ejpam-5275	262	11	study	study	VERB
ejpam-5275	262	12	this	this	DET
ejpam-5275	262	13	probability	probability	NOUN
ejpam-5275	262	14	type	type	NOUN
ejpam-5275	262	15	of	of	ADP
ejpam-5275	262	16	polynomials	polynomial	NOUN
ejpam-5275	262	17	more	more	ADV
ejpam-5275	262	18	deeply	deeply	ADV
ejpam-5275	262	19	so	so	SCONJ
ejpam-5275	262	20	that	that	PRON
ejpam-5275	262	21	give	give	VERB
ejpam-5275	262	22	better	well	ADJ
ejpam-5275	262	23	and	and	CCONJ
ejpam-5275	262	24	generalizable	generalizable	ADJ
ejpam-5275	262	25	results	result	NOUN
ejpam-5275	262	26	.	.	PUNCT
ejpam-5275	263	1	references	reference	NOUN
ejpam-5275	263	2	[	[	X
ejpam-5275	263	3	1	1	NUM
ejpam-5275	263	4	]	]	PUNCT
ejpam-5275	263	5	l	l	NOUN
ejpam-5275	263	6	carlitz	carlitz	PROPN
ejpam-5275	263	7	.	.	PUNCT
ejpam-5275	264	1	some	some	DET
ejpam-5275	264	2	polynomials	polynomial	NOUN
ejpam-5275	264	3	related	relate	VERB
ejpam-5275	264	4	to	to	ADP
ejpam-5275	264	5	the	the	DET
ejpam-5275	264	6	bernoulli	bernoulli	PROPN
ejpam-5275	264	7	and	and	CCONJ
ejpam-5275	264	8	euler	euler	NOUN
ejpam-5275	264	9	polynomials	polynomial	NOUN
ejpam-5275	264	10	.	.	PUNCT
ejpam-5275	265	1	utilitas	utilitas	PROPN
ejpam-5275	265	2	math	math	NOUN
ejpam-5275	265	3	,	,	PUNCT
ejpam-5275	265	4	19:81–127	19:81–127	NUM
ejpam-5275	265	5	,	,	PUNCT
ejpam-5275	265	6	1981	1981	NUM
ejpam-5275	265	7	.	.	PUNCT
ejpam-5275	266	1	references	reference	NOUN
ejpam-5275	266	2	2346	2346	NUM
ejpam-5275	266	3	[	[	X
ejpam-5275	266	4	2	2	NUM
ejpam-5275	266	5	]	]	PUNCT
ejpam-5275	266	6	l	l	NOUN
ejpam-5275	266	7	catlitz	catlitz	PROPN
ejpam-5275	266	8	.	.	PUNCT
ejpam-5275	267	1	degenerate	degenerate	ADJ
ejpam-5275	267	2	stirling	stirling	PROPN
ejpam-5275	267	3	,	,	PUNCT
ejpam-5275	267	4	bernoulli	bernoulli	PROPN
ejpam-5275	267	5	and	and	CCONJ
ejpam-5275	267	6	eulerian	eulerian	ADJ
ejpam-5275	267	7	numbers	number	NOUN
ejpam-5275	267	8	.	.	PUNCT
ejpam-5275	268	1	util	util	NOUN
ejpam-5275	268	2	.	.	PUNCT
ejpam-5275	269	1	math	math	PROPN
ejpam-5275	269	2	,	,	PUNCT
ejpam-5275	269	3	15:51–88	15:51–88	NUM
ejpam-5275	269	4	,	,	PUNCT
ejpam-5275	269	5	1979	1979	NUM
ejpam-5275	269	6	.	.	PUNCT
ejpam-5275	270	1	[	[	X
ejpam-5275	270	2	3	3	X
ejpam-5275	270	3	]	]	X
ejpam-5275	270	4	li	li	PROPN
ejpam-5275	270	5	chen	chen	PROPN
ejpam-5275	270	6	,	,	PUNCT
ejpam-5275	270	7	dmitry	dmitry	PROPN
ejpam-5275	270	8	v	v	X
ejpam-5275	270	9	dolgy	dolgy	NOUN
ejpam-5275	270	10	,	,	PUNCT
ejpam-5275	270	11	taekyun	taekyun	VERB
ejpam-5275	270	12	kim	kim	PROPN
ejpam-5275	270	13	,	,	PUNCT
ejpam-5275	270	14	dae	dae	VERB
ejpam-5275	270	15	san	san	PROPN
ejpam-5275	270	16	kim	kim	PROPN
ejpam-5275	270	17	,	,	PUNCT
ejpam-5275	270	18	and	and	CCONJ
ejpam-5275	270	19	kwangwoon	kwangwoon	NOUN
ejpam-5275	270	20	global	global	ADJ
ejpam-5275	270	21	education	education	NOUN
ejpam-5275	270	22	center	center	NOUN
ejpam-5275	270	23	.	.	PUNCT
ejpam-5275	271	1	probabilistic	probabilistic	ADJ
ejpam-5275	271	2	type	type	NOUN
ejpam-5275	271	3	2	2	NUM
ejpam-5275	271	4	bernoulli	bernoulli	NOUN
ejpam-5275	271	5	and	and	CCONJ
ejpam-5275	271	6	euler	euler	NOUN
ejpam-5275	271	7	polynomials	polynomial	NOUN
ejpam-5275	271	8	.	.	PUNCT
ejpam-5275	272	1	aims	aim	VERB
ejpam-5275	272	2	mathematics	mathematic	NOUN
ejpam-5275	272	3	,	,	PUNCT
ejpam-5275	272	4	9(6):14312–14324	9(6):14312–14324	NUM
ejpam-5275	272	5	,	,	PUNCT
ejpam-5275	272	6	2024	2024	NUM
ejpam-5275	272	7	.	.	PUNCT
ejpam-5275	273	1	[	[	X
ejpam-5275	273	2	4	4	NUM
ejpam-5275	273	3	]	]	X
ejpam-5275	273	4	msp	msp	PROPN
ejpam-5275	273	5	eastham	eastham	PROPN
ejpam-5275	273	6	.	.	PUNCT
ejpam-5275	274	1	on	on	ADP
ejpam-5275	274	2	polylogarithms	polylogarithm	NOUN
ejpam-5275	274	3	.	.	PUNCT
ejpam-5275	275	1	glasgow	glasgow	PROPN
ejpam-5275	275	2	mathematical	mathematical	ADJ
ejpam-5275	275	3	journal	journal	PROPN
ejpam-5275	275	4	,	,	PUNCT
ejpam-5275	275	5	6(4):169–171	6(4):169–171	NUM
ejpam-5275	275	6	,	,	PUNCT
ejpam-5275	275	7	1964	1964	NUM
ejpam-5275	275	8	.	.	PUNCT
ejpam-5275	276	1	[	[	X
ejpam-5275	276	2	5	5	NUM
ejpam-5275	276	3	]	]	PUNCT
ejpam-5275	276	4	masanobu	masanobu	ADJ
ejpam-5275	276	5	kaneko	kaneko	PROPN
ejpam-5275	276	6	.	.	PUNCT
ejpam-5275	276	7	poly	poly	ADJ
ejpam-5275	276	8	-	-	PUNCT
ejpam-5275	276	9	bernoulli	bernoulli	NOUN
ejpam-5275	276	10	numbers	number	NOUN
ejpam-5275	276	11	.	.	PUNCT
ejpam-5275	277	1	journal	journal	PROPN
ejpam-5275	277	2	de	de	PROPN
ejpam-5275	277	3	théorie	théorie	PROPN
ejpam-5275	277	4	des	des	PROPN
ejpam-5275	277	5	nombres	nombres	PROPN
ejpam-5275	277	6	de	de	X
ejpam-5275	277	7	bordeaux	bordeaux	PROPN
ejpam-5275	277	8	,	,	PUNCT
ejpam-5275	277	9	9(1):221–228	9(1):221–228	NUM
ejpam-5275	277	10	,	,	PUNCT
ejpam-5275	277	11	1997	1997	NUM
ejpam-5275	277	12	.	.	PUNCT
ejpam-5275	278	1	[	[	X
ejpam-5275	278	2	6	6	NUM
ejpam-5275	278	3	]	]	X
ejpam-5275	278	4	ds	ds	PROPN
ejpam-5275	278	5	kim	kim	PROPN
ejpam-5275	278	6	and	and	CCONJ
ejpam-5275	278	7	t	t	PROPN
ejpam-5275	278	8	kim	kim	PROPN
ejpam-5275	278	9	.	.	PUNCT
ejpam-5275	279	1	a	a	DET
ejpam-5275	279	2	note	note	NOUN
ejpam-5275	279	3	on	on	ADP
ejpam-5275	279	4	polyexponential	polyexponential	ADJ
ejpam-5275	279	5	and	and	CCONJ
ejpam-5275	279	6	unipoly	unipoly	ADJ
ejpam-5275	279	7	functions	function	NOUN
ejpam-5275	279	8	.	.	PUNCT
ejpam-5275	280	1	russian	russian	ADJ
ejpam-5275	280	2	journal	journal	PROPN
ejpam-5275	280	3	of	of	ADP
ejpam-5275	280	4	mathematical	mathematical	ADJ
ejpam-5275	280	5	physics	physics	NOUN
ejpam-5275	280	6	,	,	PUNCT
ejpam-5275	280	7	26:40–49	26:40–49	PROPN
ejpam-5275	280	8	,	,	PUNCT
ejpam-5275	280	9	2019	2019	NUM
ejpam-5275	280	10	.	.	PUNCT
ejpam-5275	281	1	[	[	X
ejpam-5275	281	2	7	7	X
ejpam-5275	281	3	]	]	X
ejpam-5275	281	4	ds	ds	PROPN
ejpam-5275	281	5	kim	kim	PROPN
ejpam-5275	281	6	and	and	CCONJ
ejpam-5275	281	7	t	t	PROPN
ejpam-5275	281	8	kim	kim	PROPN
ejpam-5275	281	9	.	.	PUNCT
ejpam-5275	282	1	a	a	DET
ejpam-5275	282	2	note	note	NOUN
ejpam-5275	282	3	on	on	ADP
ejpam-5275	282	4	a	a	DET
ejpam-5275	282	5	new	new	ADJ
ejpam-5275	282	6	type	type	NOUN
ejpam-5275	282	7	of	of	ADP
ejpam-5275	282	8	degenerate	degenerate	ADJ
ejpam-5275	282	9	bernoulli	bernoulli	NOUN
ejpam-5275	282	10	numbers	number	NOUN
ejpam-5275	282	11	.	.	PUNCT
ejpam-5275	283	1	russian	russian	ADJ
ejpam-5275	283	2	journal	journal	PROPN
ejpam-5275	283	3	of	of	ADP
ejpam-5275	283	4	mathematical	mathematical	ADJ
ejpam-5275	283	5	physics	physics	NOUN
ejpam-5275	283	6	,	,	PUNCT
ejpam-5275	283	7	27:227–235	27:227–235	NUM
ejpam-5275	283	8	,	,	PUNCT
ejpam-5275	283	9	2020	2020	NUM
ejpam-5275	283	10	.	.	PUNCT
ejpam-5275	284	1	[	[	X
ejpam-5275	284	2	8	8	NUM
ejpam-5275	284	3	]	]	PUNCT
ejpam-5275	284	4	t	t	PROPN
ejpam-5275	284	5	kim	kim	PROPN
ejpam-5275	284	6	and	and	CCONJ
ejpam-5275	284	7	ds	ds	PROPN
ejpam-5275	284	8	kim	kim	PROPN
ejpam-5275	284	9	.	.	PUNCT
ejpam-5275	285	1	probabilistic	probabilistic	ADJ
ejpam-5275	285	2	degenerate	degenerate	ADJ
ejpam-5275	285	3	bell	bell	NOUN
ejpam-5275	285	4	polynomials	polynomial	NOUN
ejpam-5275	285	5	associated	associate	VERB
ejpam-5275	285	6	with	with	ADP
ejpam-5275	285	7	random	random	ADJ
ejpam-5275	285	8	variables	variable	NOUN
ejpam-5275	285	9	.	.	PUNCT
ejpam-5275	286	1	russian	russian	ADJ
ejpam-5275	286	2	journal	journal	PROPN
ejpam-5275	286	3	of	of	ADP
ejpam-5275	286	4	mathematical	mathematical	ADJ
ejpam-5275	286	5	physics	physics	NOUN
ejpam-5275	286	6	,	,	PUNCT
ejpam-5275	286	7	30(4):528–542	30(4):528–542	NUM
ejpam-5275	286	8	,	,	PUNCT
ejpam-5275	286	9	2023	2023	NUM
ejpam-5275	286	10	.	.	PUNCT
ejpam-5275	287	1	[	[	X
ejpam-5275	287	2	9	9	NUM
ejpam-5275	287	3	]	]	PUNCT
ejpam-5275	287	4	t	t	PROPN
ejpam-5275	287	5	kim	kim	PROPN
ejpam-5275	287	6	and	and	CCONJ
ejpam-5275	287	7	ds	ds	PROPN
ejpam-5275	287	8	kim	kim	PROPN
ejpam-5275	287	9	.	.	PUNCT
ejpam-5275	288	1	probabilistic	probabilistic	ADJ
ejpam-5275	288	2	bernoulli	bernoulli	PROPN
ejpam-5275	288	3	and	and	CCONJ
ejpam-5275	288	4	euler	euler	NOUN
ejpam-5275	288	5	polynomials	polynomial	NOUN
ejpam-5275	288	6	.	.	PUNCT
ejpam-5275	289	1	russian	russian	ADJ
ejpam-5275	289	2	journal	journal	PROPN
ejpam-5275	289	3	of	of	ADP
ejpam-5275	289	4	mathematical	mathematical	ADJ
ejpam-5275	289	5	physics	physics	NOUN
ejpam-5275	289	6	,	,	PUNCT
ejpam-5275	289	7	31(1):94–105	31(1):94–105	NUM
ejpam-5275	289	8	,	,	PUNCT
ejpam-5275	289	9	2024	2024	NUM
ejpam-5275	289	10	.	.	PUNCT
ejpam-5275	290	1	[	[	X
ejpam-5275	290	2	10	10	NUM
ejpam-5275	290	3	]	]	PUNCT
ejpam-5275	290	4	taekyun	taekyun	VERB
ejpam-5275	290	5	kim	kim	PROPN
ejpam-5275	290	6	and	and	CCONJ
ejpam-5275	290	7	dae	dae	VERB
ejpam-5275	290	8	san	san	PROPN
ejpam-5275	290	9	kim	kim	PROPN
ejpam-5275	290	10	.	.	PUNCT
ejpam-5275	291	1	degenerate	degenerate	ADJ
ejpam-5275	291	2	laplace	laplace	NOUN
ejpam-5275	291	3	transform	transform	NOUN
ejpam-5275	291	4	and	and	CCONJ
ejpam-5275	291	5	degenerate	degenerate	ADJ
ejpam-5275	291	6	gamma	gamma	NOUN
ejpam-5275	291	7	function	function	NOUN
ejpam-5275	291	8	.	.	PUNCT
ejpam-5275	292	1	russian	russian	ADJ
ejpam-5275	292	2	journal	journal	PROPN
ejpam-5275	292	3	of	of	ADP
ejpam-5275	292	4	mathematical	mathematical	ADJ
ejpam-5275	292	5	physics	physics	NOUN
ejpam-5275	292	6	,	,	PUNCT
ejpam-5275	292	7	24:241–248	24:241–248	NUM
ejpam-5275	292	8	,	,	PUNCT
ejpam-5275	292	9	2017	2017	NUM
ejpam-5275	292	10	.	.	PUNCT
ejpam-5275	293	1	[	[	X
ejpam-5275	293	2	11	11	NUM
ejpam-5275	293	3	]	]	PUNCT
ejpam-5275	293	4	taekyun	taekyun	VERB
ejpam-5275	293	5	kim	kim	PROPN
ejpam-5275	293	6	and	and	CCONJ
ejpam-5275	293	7	dae	dae	VERB
ejpam-5275	293	8	san	san	PROPN
ejpam-5275	293	9	kim	kim	PROPN
ejpam-5275	293	10	.	.	PUNCT
ejpam-5275	294	1	identities	identity	NOUN
ejpam-5275	294	2	for	for	ADP
ejpam-5275	294	3	degenerate	degenerate	ADJ
ejpam-5275	294	4	bernoulli	bernoulli	NOUN
ejpam-5275	294	5	polynomials	polynomial	NOUN
ejpam-5275	294	6	and	and	CCONJ
ejpam-5275	294	7	korobov	korobov	NOUN
ejpam-5275	294	8	polynomials	polynomial	NOUN
ejpam-5275	294	9	of	of	ADP
ejpam-5275	294	10	the	the	DET
ejpam-5275	294	11	first	first	ADJ
ejpam-5275	294	12	kind	kind	NOUN
ejpam-5275	294	13	.	.	PUNCT
ejpam-5275	295	1	science	science	PROPN
ejpam-5275	295	2	china	china	PROPN
ejpam-5275	295	3	mathematics	mathematics	PROPN
ejpam-5275	295	4	,	,	PUNCT
ejpam-5275	295	5	62:999–1028	62:999–1028	NUM
ejpam-5275	295	6	,	,	PUNCT
ejpam-5275	295	7	2019	2019	NUM
ejpam-5275	295	8	.	.	PUNCT
ejpam-5275	296	1	[	[	X
ejpam-5275	296	2	12	12	NUM
ejpam-5275	296	3	]	]	PUNCT
ejpam-5275	296	4	taekyun	taekyun	VERB
ejpam-5275	296	5	kim	kim	PROPN
ejpam-5275	296	6	and	and	CCONJ
ejpam-5275	296	7	dae	dae	VERB
ejpam-5275	296	8	san	san	PROPN
ejpam-5275	296	9	kim	kim	PROPN
ejpam-5275	296	10	.	.	PUNCT
ejpam-5275	297	1	representation	representation	NOUN
ejpam-5275	297	2	by	by	ADP
ejpam-5275	297	3	degenerate	degenerate	ADJ
ejpam-5275	297	4	frobenius	frobenius	NOUN
ejpam-5275	297	5	–	–	PUNCT
ejpam-5275	297	6	euler	euler	NOUN
ejpam-5275	297	7	polynomials	polynomial	NOUN
ejpam-5275	297	8	.	.	PUNCT
ejpam-5275	298	1	georgian	georgian	PROPN
ejpam-5275	298	2	mathematical	mathematical	PROPN
ejpam-5275	298	3	journal	journal	PROPN
ejpam-5275	298	4	,	,	PUNCT
ejpam-5275	298	5	29(5):741–754	29(5):741–754	NUM
ejpam-5275	298	6	,	,	PUNCT
ejpam-5275	298	7	2022	2022	NUM
ejpam-5275	298	8	.	.	PUNCT
ejpam-5275	299	1	[	[	X
ejpam-5275	299	2	13	13	NUM
ejpam-5275	299	3	]	]	PUNCT
ejpam-5275	299	4	taekyun	taekyun	VERB
ejpam-5275	299	5	kim	kim	PROPN
ejpam-5275	299	6	and	and	CCONJ
ejpam-5275	299	7	dae	dae	VERB
ejpam-5275	299	8	san	san	PROPN
ejpam-5275	299	9	kim	kim	PROPN
ejpam-5275	299	10	.	.	PUNCT
ejpam-5275	300	1	some	some	DET
ejpam-5275	300	2	results	result	NOUN
ejpam-5275	300	3	on	on	ADP
ejpam-5275	300	4	degenerate	degenerate	ADJ
ejpam-5275	300	5	fubini	fubini	ADJ
ejpam-5275	300	6	and	and	CCONJ
ejpam-5275	300	7	degenerate	degenerate	ADJ
ejpam-5275	300	8	bell	bell	NOUN
ejpam-5275	300	9	polynomials	polynomial	NOUN
ejpam-5275	300	10	.	.	PUNCT
ejpam-5275	301	1	applicable	applicable	ADJ
ejpam-5275	301	2	analysis	analysis	NOUN
ejpam-5275	301	3	and	and	CCONJ
ejpam-5275	301	4	discrete	discrete	ADJ
ejpam-5275	301	5	mathematics	mathematic	NOUN
ejpam-5275	301	6	,	,	PUNCT
ejpam-5275	301	7	17(2):548–560	17(2):548–560	PROPN
ejpam-5275	301	8	,	,	PUNCT
ejpam-5275	301	9	2023	2023	NUM
ejpam-5275	301	10	.	.	PUNCT
ejpam-5275	302	1	[	[	X
ejpam-5275	302	2	14	14	NUM
ejpam-5275	302	3	]	]	PUNCT
ejpam-5275	302	4	taekyun	taekyun	VERB
ejpam-5275	302	5	kim	kim	PROPN
ejpam-5275	302	6	and	and	CCONJ
ejpam-5275	302	7	dae	dae	VERB
ejpam-5275	302	8	san	san	PROPN
ejpam-5275	302	9	kim	kim	PROPN
ejpam-5275	302	10	.	.	PUNCT
ejpam-5275	303	1	generalization	generalization	NOUN
ejpam-5275	303	2	of	of	ADP
ejpam-5275	303	3	spivey	spivey	PROPN
ejpam-5275	303	4	’s	’s	PART
ejpam-5275	303	5	recurrence	recurrence	PROPN
ejpam-5275	303	6	relation	relation	PROPN
ejpam-5275	303	7	.	.	PUNCT
ejpam-5275	304	1	russian	russian	ADJ
ejpam-5275	304	2	journal	journal	PROPN
ejpam-5275	304	3	of	of	ADP
ejpam-5275	304	4	mathematical	mathematical	ADJ
ejpam-5275	304	5	physics	physics	NOUN
ejpam-5275	304	6	,	,	PUNCT
ejpam-5275	304	7	31(2):218–226	31(2):218–226	PRON
ejpam-5275	304	8	,	,	PUNCT
ejpam-5275	304	9	2024	2024	NUM
ejpam-5275	304	10	.	.	PUNCT
ejpam-5275	305	1	[	[	X
ejpam-5275	305	2	15	15	NUM
ejpam-5275	305	3	]	]	PUNCT
ejpam-5275	305	4	taekyun	taekyun	NOUN
ejpam-5275	305	5	kim	kim	PROPN
ejpam-5275	305	6	,	,	PUNCT
ejpam-5275	305	7	dae	dae	VERB
ejpam-5275	305	8	san	san	PROPN
ejpam-5275	305	9	kim	kim	PROPN
ejpam-5275	305	10	,	,	PUNCT
ejpam-5275	305	11	and	and	CCONJ
ejpam-5275	305	12	hye	hye	PROPN
ejpam-5275	305	13	kyung	kyung	PROPN
ejpam-5275	305	14	kim	kim	PROPN
ejpam-5275	305	15	.	.	PUNCT
ejpam-5275	306	1	some	some	DET
ejpam-5275	306	2	identities	identity	NOUN
ejpam-5275	306	3	involving	involve	VERB
ejpam-5275	306	4	bernoulli	bernoulli	PROPN
ejpam-5275	306	5	,	,	PUNCT
ejpam-5275	306	6	euler	euler	NOUN
ejpam-5275	306	7	and	and	CCONJ
ejpam-5275	306	8	degenerate	degenerate	ADJ
ejpam-5275	306	9	bernoulli	bernoulli	NOUN
ejpam-5275	306	10	numbers	number	NOUN
ejpam-5275	306	11	and	and	CCONJ
ejpam-5275	306	12	their	their	PRON
ejpam-5275	306	13	applications	application	NOUN
ejpam-5275	306	14	.	.	PUNCT
ejpam-5275	307	1	applied	apply	VERB
ejpam-5275	307	2	mathematics	mathematic	NOUN
ejpam-5275	307	3	in	in	ADP
ejpam-5275	307	4	science	science	NOUN
ejpam-5275	307	5	and	and	CCONJ
ejpam-5275	307	6	engineering	engineering	NOUN
ejpam-5275	307	7	,	,	PUNCT
ejpam-5275	307	8	31(1):2220873	31(1):2220873	NUM
ejpam-5275	307	9	,	,	PUNCT
ejpam-5275	307	10	2023	2023	NUM
ejpam-5275	307	11	.	.	PUNCT
ejpam-5275	308	1	[	[	X
ejpam-5275	308	2	16	16	NUM
ejpam-5275	308	3	]	]	PUNCT
ejpam-5275	308	4	taekyun	taekyun	NOUN
ejpam-5275	308	5	kim	kim	PROPN
ejpam-5275	308	6	,	,	PUNCT
ejpam-5275	308	7	dae	dae	VERB
ejpam-5275	308	8	san	san	PROPN
ejpam-5275	308	9	kim	kim	PROPN
ejpam-5275	308	10	,	,	PUNCT
ejpam-5275	308	11	and	and	CCONJ
ejpam-5275	308	12	hye	hye	PROPN
ejpam-5275	308	13	kyung	kyung	PROPN
ejpam-5275	308	14	kim	kim	PROPN
ejpam-5275	308	15	.	.	PUNCT
ejpam-5275	309	1	study	study	VERB
ejpam-5275	309	2	on	on	ADP
ejpam-5275	309	3	discrete	discrete	ADJ
ejpam-5275	309	4	degenerate	degenerate	ADJ
ejpam-5275	309	5	bell	bell	NOUN
ejpam-5275	309	6	distributions	distribution	NOUN
ejpam-5275	309	7	with	with	ADP
ejpam-5275	309	8	two	two	NUM
ejpam-5275	309	9	parameters	parameter	NOUN
ejpam-5275	309	10	.	.	PUNCT
ejpam-5275	310	1	georgian	georgian	PROPN
ejpam-5275	310	2	mathematical	mathematical	PROPN
ejpam-5275	310	3	journal	journal	PROPN
ejpam-5275	310	4	,	,	PUNCT
ejpam-5275	310	5	31(3):445–451	31(3):445–451	PROPN
ejpam-5275	310	6	,	,	PUNCT
ejpam-5275	310	7	2024	2024	NUM
ejpam-5275	310	8	.	.	PUNCT
ejpam-5275	311	1	references	reference	NOUN
ejpam-5275	311	2	2347	2347	NUM
ejpam-5275	312	1	[	[	X
ejpam-5275	312	2	17	17	NUM
ejpam-5275	312	3	]	]	PUNCT
ejpam-5275	312	4	taekyun	taekyun	NOUN
ejpam-5275	312	5	kim	kim	PROPN
ejpam-5275	312	6	,	,	PUNCT
ejpam-5275	312	7	dae	dae	VERB
ejpam-5275	312	8	san	san	PROPN
ejpam-5275	312	9	kim	kim	PROPN
ejpam-5275	312	10	,	,	PUNCT
ejpam-5275	312	11	and	and	CCONJ
ejpam-5275	312	12	hyekyung	hyekyung	PROPN
ejpam-5275	312	13	kim	kim	PROPN
ejpam-5275	312	14	.	.	PUNCT
ejpam-5275	313	1	study	study	VERB
ejpam-5275	313	2	on	on	ADP
ejpam-5275	313	3	r	r	NOUN
ejpam-5275	313	4	-	-	PUNCT
ejpam-5275	313	5	truncated	truncate	VERB
ejpam-5275	313	6	degenerate	degenerate	ADJ
ejpam-5275	313	7	stirling	stirling	NOUN
ejpam-5275	313	8	numbers	number	NOUN
ejpam-5275	313	9	of	of	ADP
ejpam-5275	313	10	the	the	DET
ejpam-5275	313	11	second	second	ADJ
ejpam-5275	313	12	kind	kind	NOUN
ejpam-5275	313	13	.	.	PUNCT
ejpam-5275	314	1	open	open	ADJ
ejpam-5275	314	2	mathematics	mathematic	NOUN
ejpam-5275	314	3	,	,	PUNCT
ejpam-5275	314	4	20(1):1685–1695	20(1):1685–1695	NUM
ejpam-5275	314	5	,	,	PUNCT
ejpam-5275	314	6	2022	2022	NUM
ejpam-5275	314	7	.	.	PUNCT
ejpam-5275	315	1	[	[	X
ejpam-5275	315	2	18	18	NUM
ejpam-5275	315	3	]	]	PUNCT
ejpam-5275	315	4	taekyun	taekyun	NOUN
ejpam-5275	315	5	kim	kim	PROPN
ejpam-5275	315	6	,	,	PUNCT
ejpam-5275	315	7	dae	dae	VERB
ejpam-5275	315	8	san	san	PROPN
ejpam-5275	315	9	kim	kim	PROPN
ejpam-5275	315	10	,	,	PUNCT
ejpam-5275	315	11	and	and	CCONJ
ejpam-5275	315	12	jongkyum	jongkyum	PROPN
ejpam-5275	315	13	kwon	kwon	VERB
ejpam-5275	315	14	.	.	PUNCT
ejpam-5275	316	1	probabilistic	probabilistic	ADJ
ejpam-5275	316	2	degenerate	degenerate	ADJ
ejpam-5275	316	3	stirling	stirling	NOUN
ejpam-5275	316	4	polynomials	polynomial	NOUN
ejpam-5275	316	5	of	of	ADP
ejpam-5275	316	6	the	the	DET
ejpam-5275	316	7	second	second	ADJ
ejpam-5275	316	8	kind	kind	NOUN
ejpam-5275	316	9	and	and	CCONJ
ejpam-5275	316	10	their	their	PRON
ejpam-5275	316	11	applications	application	NOUN
ejpam-5275	316	12	.	.	PUNCT
ejpam-5275	317	1	mathematical	mathematical	ADJ
ejpam-5275	317	2	and	and	CCONJ
ejpam-5275	317	3	computer	computer	NOUN
ejpam-5275	317	4	modelling	modelling	NOUN
ejpam-5275	317	5	of	of	ADP
ejpam-5275	317	6	dynamical	dynamical	ADJ
ejpam-5275	317	7	systems	system	NOUN
ejpam-5275	317	8	,	,	PUNCT
ejpam-5275	317	9	30(1):16–30	30(1):16–30	NUM
ejpam-5275	317	10	,	,	PUNCT
ejpam-5275	317	11	2024	2024	NUM
ejpam-5275	317	12	.	.	PUNCT
ejpam-5275	318	1	[	[	X
ejpam-5275	318	2	19	19	NUM
ejpam-5275	318	3	]	]	PUNCT
ejpam-5275	318	4	taekyun	taekyun	NOUN
ejpam-5275	318	5	kim	kim	PROPN
ejpam-5275	318	6	,	,	PUNCT
ejpam-5275	318	7	dae	dae	VERB
ejpam-5275	318	8	san	san	PROPN
ejpam-5275	318	9	kim	kim	PROPN
ejpam-5275	318	10	,	,	PUNCT
ejpam-5275	318	11	hyunseok	hyunseok	PROPN
ejpam-5275	318	12	lee	lee	PROPN
ejpam-5275	318	13	,	,	PUNCT
ejpam-5275	318	14	and	and	CCONJ
ejpam-5275	318	15	jongkyum	jongkyum	PROPN
ejpam-5275	318	16	kwon	kwon	VERB
ejpam-5275	318	17	.	.	PUNCT
ejpam-5275	319	1	representations	representation	NOUN
ejpam-5275	319	2	by	by	ADP
ejpam-5275	319	3	degenerate	degenerate	ADJ
ejpam-5275	319	4	daehee	daehee	NOUN
ejpam-5275	319	5	polynomials	polynomial	NOUN
ejpam-5275	319	6	.	.	PUNCT
ejpam-5275	320	1	open	open	ADJ
ejpam-5275	320	2	mathematics	mathematic	NOUN
ejpam-5275	320	3	,	,	PUNCT
ejpam-5275	320	4	20(1):179–194	20(1):179–194	PROPN
ejpam-5275	320	5	,	,	PUNCT
ejpam-5275	320	6	2022	2022	NUM
ejpam-5275	320	7	.	.	PUNCT
ejpam-5275	321	1	[	[	X
ejpam-5275	321	2	20	20	NUM
ejpam-5275	321	3	]	]	PUNCT
ejpam-5275	321	4	taekyun	taekyun	NOUN
ejpam-5275	321	5	kim	kim	PROPN
ejpam-5275	321	6	,	,	PUNCT
ejpam-5275	321	7	dae	dae	VERB
ejpam-5275	321	8	san	san	PROPN
ejpam-5275	321	9	kim	kim	PROPN
ejpam-5275	321	10	,	,	PUNCT
ejpam-5275	321	11	and	and	CCONJ
ejpam-5275	321	12	jin	jin	NOUN
ejpam-5275	321	13	-	-	PUNCT
ejpam-5275	321	14	woo	woo	NOUN
ejpam-5275	321	15	park	park	NOUN
ejpam-5275	321	16	.	.	PUNCT
ejpam-5275	322	1	fully	fully	ADV
ejpam-5275	322	2	degenerate	degenerate	ADJ
ejpam-5275	322	3	bernoulli	bernoulli	NOUN
ejpam-5275	322	4	numbers	number	NOUN
ejpam-5275	322	5	and	and	CCONJ
ejpam-5275	322	6	polynomials	polynomial	NOUN
ejpam-5275	322	7	.	.	PUNCT
ejpam-5275	323	1	demonstratio	demonstratio	PROPN
ejpam-5275	323	2	mathematica	mathematica	PROPN
ejpam-5275	323	3	,	,	PUNCT
ejpam-5275	323	4	55(1):604–614	55(1):604–614	NUM
ejpam-5275	323	5	,	,	PUNCT
ejpam-5275	323	6	2022	2022	NUM
ejpam-5275	323	7	.	.	PUNCT
ejpam-5275	324	1	[	[	X
ejpam-5275	324	2	21	21	NUM
ejpam-5275	324	3	]	]	PUNCT
ejpam-5275	324	4	taekyun	taekyun	VERB
ejpam-5275	324	5	kim	kim	PROPN
ejpam-5275	324	6	,	,	PUNCT
ejpam-5275	324	7	ds	ds	PROPN
ejpam-5275	324	8	kim	kim	PROPN
ejpam-5275	324	9	,	,	PUNCT
ejpam-5275	324	10	gw	gw	PROPN
ejpam-5275	324	11	jang	jang	PROPN
ejpam-5275	324	12	,	,	PUNCT
ejpam-5275	324	13	and	and	CCONJ
ejpam-5275	324	14	jongkyum	jongkyum	PROPN
ejpam-5275	324	15	kwon	kwon	VERB
ejpam-5275	324	16	.	.	PUNCT
ejpam-5275	325	1	fourier	fourier	PROPN
ejpam-5275	325	2	series	series	NOUN
ejpam-5275	325	3	of	of	ADP
ejpam-5275	325	4	sums	sum	NOUN
ejpam-5275	325	5	of	of	ADP
ejpam-5275	325	6	products	product	NOUN
ejpam-5275	325	7	of	of	ADP
ejpam-5275	325	8	higher	high	ADJ
ejpam-5275	325	9	-	-	PUNCT
ejpam-5275	325	10	order	order	NOUN
ejpam-5275	325	11	euler	euler	NOUN
ejpam-5275	325	12	functions	function	NOUN
ejpam-5275	325	13	.	.	PUNCT
ejpam-5275	326	1	j.	j.	PROPN
ejpam-5275	326	2	comput	comput	PROPN
ejpam-5275	326	3	.	.	PUNCT
ejpam-5275	327	1	anal	anal	PROPN
ejpam-5275	327	2	.	.	PUNCT
ejpam-5275	327	3	appl	appl	PROPN
ejpam-5275	327	4	,	,	PUNCT
ejpam-5275	327	5	27(2):345–360	27(2):345–360	NUM
ejpam-5275	327	6	,	,	PUNCT
ejpam-5275	327	7	2019	2019	NUM
ejpam-5275	327	8	.	.	PUNCT
ejpam-5275	328	1	[	[	X
ejpam-5275	328	2	22	22	NUM
ejpam-5275	328	3	]	]	PUNCT
ejpam-5275	328	4	taekyun	taekyun	VERB
ejpam-5275	328	5	kim	kim	PROPN
ejpam-5275	328	6	and	and	CCONJ
ejpam-5275	328	7	hye	hye	PROPN
ejpam-5275	328	8	kyung	kyung	PROPN
ejpam-5275	328	9	kim	kim	PROPN
ejpam-5275	328	10	.	.	PUNCT
ejpam-5275	329	1	degenerate	degenerate	ADJ
ejpam-5275	329	2	poly	poly	ADJ
ejpam-5275	329	3	-	-	PUNCT
ejpam-5275	329	4	lah	lah	NOUN
ejpam-5275	329	5	-	-	PUNCT
ejpam-5275	329	6	bell	bell	NOUN
ejpam-5275	329	7	polynomials	polynomial	NOUN
ejpam-5275	329	8	and	and	CCONJ
ejpam-5275	329	9	numbers	number	NOUN
ejpam-5275	329	10	.	.	PUNCT
ejpam-5275	330	1	journal	journal	NOUN
ejpam-5275	330	2	of	of	ADP
ejpam-5275	330	3	mathematics	mathematic	NOUN
ejpam-5275	330	4	,	,	PUNCT
ejpam-5275	330	5	2022(1):2917943	2022(1):2917943	NOUN
ejpam-5275	330	6	,	,	PUNCT
ejpam-5275	330	7	2022	2022	NUM
ejpam-5275	330	8	.	.	PUNCT
ejpam-5275	331	1	[	[	X
ejpam-5275	331	2	23	23	NUM
ejpam-5275	331	3	]	]	PUNCT
ejpam-5275	331	4	taekyun	taekyun	VERB
ejpam-5275	331	5	kim	kim	PROPN
ejpam-5275	331	6	,	,	PUNCT
ejpam-5275	331	7	dae	dae	VERB
ejpam-5275	331	8	san	san	PROPN
ejpam-5275	331	9	kim	kim	PROPN
ejpam-5275	331	10	,	,	PUNCT
ejpam-5275	331	11	dmitry	dmitry	PROPN
ejpam-5275	331	12	v	v	X
ejpam-5275	331	13	dolgy	dolgy	NOUN
ejpam-5275	331	14	,	,	PUNCT
ejpam-5275	331	15	hye	hye	PROPN
ejpam-5275	331	16	kyung	kyung	PROPN
ejpam-5275	331	17	kim	kim	PROPN
ejpam-5275	331	18	,	,	PUNCT
ejpam-5275	331	19	and	and	CCONJ
ejpam-5275	331	20	hyunseok	hyunseok	PROPN
ejpam-5275	331	21	lee	lee	PROPN
ejpam-5275	331	22	.	.	PUNCT
ejpam-5275	332	1	a	a	DET
ejpam-5275	332	2	new	new	ADJ
ejpam-5275	332	3	approach	approach	NOUN
ejpam-5275	332	4	to	to	ADP
ejpam-5275	332	5	bell	bell	NOUN
ejpam-5275	332	6	and	and	CCONJ
ejpam-5275	332	7	poly	poly	ADJ
ejpam-5275	332	8	-	-	PUNCT
ejpam-5275	332	9	bell	bell	NOUN
ejpam-5275	332	10	numbers	number	NOUN
ejpam-5275	332	11	and	and	CCONJ
ejpam-5275	332	12	polynomials	polynomial	NOUN
ejpam-5275	332	13	.	.	PUNCT
ejpam-5275	333	1	aims	aim	VERB
ejpam-5275	333	2	math	math	NOUN
ejpam-5275	333	3	,	,	PUNCT
ejpam-5275	333	4	7(3):4004	7(3):4004	NUM
ejpam-5275	333	5	–	–	PUNCT
ejpam-5275	333	6	4016	4016	NUM
ejpam-5275	333	7	,	,	PUNCT
ejpam-5275	333	8	2022	2022	NUM
ejpam-5275	333	9	.	.	PUNCT
ejpam-5275	334	1	[	[	X
ejpam-5275	334	2	24	24	NUM
ejpam-5275	334	3	]	]	PUNCT
ejpam-5275	334	4	taekyun	taekyun	NOUN
ejpam-5275	334	5	kim	kim	PROPN
ejpam-5275	334	6	,	,	PUNCT
ejpam-5275	334	7	dae	dae	VERB
ejpam-5275	334	8	san	san	PROPN
ejpam-5275	334	9	kim	kim	PROPN
ejpam-5275	334	10	,	,	PUNCT
ejpam-5275	334	11	gwan	gwan	PROPN
ejpam-5275	334	12	-	-	PUNCT
ejpam-5275	334	13	woo	woo	PROPN
ejpam-5275	334	14	jang	jang	PROPN
ejpam-5275	334	15	,	,	PUNCT
ejpam-5275	334	16	and	and	CCONJ
ejpam-5275	334	17	jongkyum	jongkyum	PROPN
ejpam-5275	334	18	kwon	kwon	VERB
ejpam-5275	334	19	.	.	PUNCT
ejpam-5275	335	1	fourier	fourier	PROPN
ejpam-5275	335	2	series	series	NOUN
ejpam-5275	335	3	of	of	ADP
ejpam-5275	335	4	sums	sum	NOUN
ejpam-5275	335	5	of	of	ADP
ejpam-5275	335	6	product	product	NOUN
ejpam-5275	335	7	of	of	ADP
ejpam-5275	335	8	poly	poly	ADJ
ejpam-5275	335	9	-	-	PUNCT
ejpam-5275	335	10	bernoulli	bernoulli	NOUN
ejpam-5275	335	11	and	and	CCONJ
ejpam-5275	335	12	euler	euler	NOUN
ejpam-5275	335	13	functions	function	NOUN
ejpam-5275	335	14	and	and	CCONJ
ejpam-5275	335	15	their	their	PRON
ejpam-5275	335	16	applications	application	NOUN
ejpam-5275	335	17	.	.	PUNCT
ejpam-5275	336	1	journal	journal	NOUN
ejpam-5275	336	2	of	of	ADP
ejpam-5275	336	3	computational	computational	ADJ
ejpam-5275	336	4	analysis	analysis	NOUN
ejpam-5275	336	5	&	&	CCONJ
ejpam-5275	336	6	applications	application	NOUN
ejpam-5275	336	7	,	,	PUNCT
ejpam-5275	336	8	26(1	26(1	NUM
ejpam-5275	336	9	)	)	PUNCT
ejpam-5275	336	10	,	,	PUNCT
ejpam-5275	336	11	2019	2019	NUM
ejpam-5275	336	12	.	.	PUNCT
ejpam-5275	337	1	[	[	X
ejpam-5275	337	2	25	25	NUM
ejpam-5275	337	3	]	]	PUNCT
ejpam-5275	337	4	taekyun	taekyun	NOUN
ejpam-5275	337	5	kim	kim	PROPN
ejpam-5275	337	6	,	,	PUNCT
ejpam-5275	337	7	dae	dae	VERB
ejpam-5275	337	8	san	san	PROPN
ejpam-5275	337	9	kim	kim	PROPN
ejpam-5275	337	10	,	,	PUNCT
ejpam-5275	337	11	and	and	CCONJ
ejpam-5275	337	12	jongkyum	jongkyum	PROPN
ejpam-5275	337	13	kwon	kwon	VERB
ejpam-5275	337	14	.	.	PUNCT
ejpam-5275	338	1	some	some	DET
ejpam-5275	338	2	identities	identity	NOUN
ejpam-5275	338	3	related	relate	VERB
ejpam-5275	338	4	to	to	PART
ejpam-5275	338	5	degenerate	degenerate	VERB
ejpam-5275	338	6	r	r	NOUN
ejpam-5275	338	7	-	-	NOUN
ejpam-5275	338	8	bell	bell	NOUN
ejpam-5275	338	9	and	and	CCONJ
ejpam-5275	338	10	degenerate	degenerate	ADJ
ejpam-5275	338	11	fubini	fubini	ADJ
ejpam-5275	338	12	polynomials	polynomial	NOUN
ejpam-5275	338	13	.	.	PUNCT
ejpam-5275	339	1	applied	apply	VERB
ejpam-5275	339	2	mathematics	mathematic	NOUN
ejpam-5275	339	3	in	in	ADP
ejpam-5275	339	4	science	science	NOUN
ejpam-5275	339	5	and	and	CCONJ
ejpam-5275	339	6	engineering	engineering	NOUN
ejpam-5275	339	7	,	,	PUNCT
ejpam-5275	339	8	31(1):2205642	31(1):2205642	NUM
ejpam-5275	339	9	,	,	PUNCT
ejpam-5275	339	10	2023	2023	NUM
ejpam-5275	339	11	.	.	PUNCT
ejpam-5275	340	1	[	[	X
ejpam-5275	340	2	26	26	NUM
ejpam-5275	340	3	]	]	X
ejpam-5275	340	4	tk	tk	PROPN
ejpam-5275	340	5	kim	kim	PROPN
ejpam-5275	340	6	and	and	CCONJ
ejpam-5275	340	7	dae	dae	VERB
ejpam-5275	340	8	san	san	PROPN
ejpam-5275	340	9	kim	kim	PROPN
ejpam-5275	340	10	.	.	PUNCT
ejpam-5275	341	1	some	some	DET
ejpam-5275	341	2	identities	identity	NOUN
ejpam-5275	341	3	involving	involve	VERB
ejpam-5275	341	4	degenerate	degenerate	ADJ
ejpam-5275	341	5	stirling	stirling	NOUN
ejpam-5275	341	6	numbers	number	NOUN
ejpam-5275	341	7	associated	associate	VERB
ejpam-5275	341	8	with	with	ADP
ejpam-5275	341	9	several	several	ADJ
ejpam-5275	341	10	degenerate	degenerate	ADJ
ejpam-5275	341	11	polynomials	polynomial	NOUN
ejpam-5275	341	12	and	and	CCONJ
ejpam-5275	341	13	numbers	number	NOUN
ejpam-5275	341	14	.	.	PUNCT
ejpam-5275	342	1	russian	russian	ADJ
ejpam-5275	342	2	journal	journal	PROPN
ejpam-5275	342	3	of	of	ADP
ejpam-5275	342	4	mathematical	mathematical	ADJ
ejpam-5275	342	5	physics	physics	NOUN
ejpam-5275	342	6	,	,	PUNCT
ejpam-5275	342	7	30(1):62–75	30(1):62–75	NUM
ejpam-5275	342	8	,	,	PUNCT
ejpam-5275	342	9	2023	2023	NUM
ejpam-5275	342	10	.	.	PUNCT
ejpam-5275	343	1	[	[	X
ejpam-5275	343	2	27	27	NUM
ejpam-5275	343	3	]	]	SYM
ejpam-5275	343	4	bf	bf	PROPN
ejpam-5275	343	5	kimball	kimball	PROPN
ejpam-5275	343	6	.	.	PUNCT
ejpam-5275	344	1	a	a	DET
ejpam-5275	344	2	generalization	generalization	NOUN
ejpam-5275	344	3	of	of	ADP
ejpam-5275	344	4	the	the	DET
ejpam-5275	344	5	bernoulli	bernoulli	NOUN
ejpam-5275	344	6	polynomial	polynomial	NOUN
ejpam-5275	344	7	of	of	ADP
ejpam-5275	344	8	order	order	NOUN
ejpam-5275	344	9	one	one	NUM
ejpam-5275	344	10	.	.	PUNCT
ejpam-5275	344	11	1935	1935	NUM
ejpam-5275	344	12	.	.	PUNCT
ejpam-5275	345	1	[	[	X
ejpam-5275	345	2	28	28	NUM
ejpam-5275	345	3	]	]	X
ejpam-5275	345	4	lingling	lingle	VERB
ejpam-5275	345	5	luo	luo	PROPN
ejpam-5275	345	6	,	,	PUNCT
ejpam-5275	345	7	taekyun	taekyun	VERB
ejpam-5275	345	8	kim	kim	PROPN
ejpam-5275	345	9	,	,	PUNCT
ejpam-5275	345	10	dae	dae	VERB
ejpam-5275	345	11	san	san	PROPN
ejpam-5275	345	12	kim	kim	PROPN
ejpam-5275	345	13	,	,	PUNCT
ejpam-5275	345	14	and	and	CCONJ
ejpam-5275	346	1	yuankui	yuankui	PROPN
ejpam-5275	346	2	ma	ma	PROPN
ejpam-5275	346	3	.	.	PROPN
ejpam-5275	346	4	probabilistic	probabilistic	ADJ
ejpam-5275	346	5	degenerate	degenerate	ADJ
ejpam-5275	346	6	bernoulli	bernoulli	NOUN
ejpam-5275	346	7	and	and	CCONJ
ejpam-5275	346	8	degenerate	degenerate	ADJ
ejpam-5275	346	9	euler	euler	NOUN
ejpam-5275	346	10	polynomials	polynomial	NOUN
ejpam-5275	346	11	.	.	PUNCT
ejpam-5275	347	1	mathematical	mathematical	ADJ
ejpam-5275	347	2	and	and	CCONJ
ejpam-5275	347	3	computer	computer	NOUN
ejpam-5275	347	4	modelling	modelling	NOUN
ejpam-5275	347	5	of	of	ADP
ejpam-5275	347	6	dynamical	dynamical	ADJ
ejpam-5275	347	7	systems	system	NOUN
ejpam-5275	347	8	,	,	PUNCT
ejpam-5275	347	9	30(1):342–363	30(1):342–363	NOUN
ejpam-5275	347	10	,	,	PUNCT
ejpam-5275	347	11	2024	2024	NUM
ejpam-5275	347	12	.	.	PUNCT
ejpam-5275	348	1	[	[	X
ejpam-5275	348	2	29	29	NUM
ejpam-5275	348	3	]	]	X
ejpam-5275	348	4	steven	steven	PROPN
ejpam-5275	348	5	roman	roman	PROPN
ejpam-5275	348	6	.	.	PUNCT
ejpam-5275	349	1	the	the	DET
ejpam-5275	349	2	umbral	umbral	ADJ
ejpam-5275	349	3	calculus	calculus	NOUN
ejpam-5275	349	4	,	,	PUNCT
ejpam-5275	349	5	volume	volume	NOUN
ejpam-5275	349	6	111	111	NUM
ejpam-5275	349	7	of	of	ADP
ejpam-5275	349	8	pure	pure	ADJ
ejpam-5275	349	9	and	and	CCONJ
ejpam-5275	349	10	applied	applied	ADJ
ejpam-5275	349	11	mathematics	mathematic	NOUN
ejpam-5275	349	12	,	,	PUNCT
ejpam-5275	349	13	1984	1984	NUM
ejpam-5275	349	14	.	.	PUNCT
ejpam-5275	350	1	[	[	X
ejpam-5275	350	2	30	30	NUM
ejpam-5275	350	3	]	]	X
ejpam-5275	350	4	katsumi	katsumi	PROPN
ejpam-5275	350	5	shiratani	shiratani	PROPN
ejpam-5275	350	6	.	.	PUNCT
ejpam-5275	351	1	kummer	kummer	PROPN
ejpam-5275	351	2	’s	’s	PART
ejpam-5275	351	3	congruence	congruence	NOUN
ejpam-5275	351	4	for	for	ADP
ejpam-5275	351	5	generalized	generalized	ADJ
ejpam-5275	351	6	bernoulli	bernoulli	NOUN
ejpam-5275	351	7	numbers	number	NOUN
ejpam-5275	351	8	and	and	CCONJ
ejpam-5275	351	9	its	its	PRON
ejpam-5275	351	10	application	application	NOUN
ejpam-5275	351	11	.	.	PUNCT
ejpam-5275	352	1	memoirs	memoir	NOUN
ejpam-5275	352	2	of	of	ADP
ejpam-5275	352	3	the	the	DET
ejpam-5275	352	4	faculty	faculty	NOUN
ejpam-5275	352	5	of	of	ADP
ejpam-5275	352	6	science	science	NOUN
ejpam-5275	352	7	,	,	PUNCT
ejpam-5275	352	8	kyushu	kyushu	PROPN
ejpam-5275	352	9	university	university	PROPN
ejpam-5275	352	10	.	.	PUNCT
ejpam-5275	353	1	series	series	PROPN
ejpam-5275	353	2	a	a	PROPN
ejpam-5275	353	3	,	,	PUNCT
ejpam-5275	353	4	mathematics	mathematic	NOUN
ejpam-5275	353	5	,	,	PUNCT
ejpam-5275	353	6	26(1):119–138	26(1):119–138	PROPN
ejpam-5275	353	7	,	,	PUNCT
ejpam-5275	353	8	1972	1972	NUM
ejpam-5275	353	9	.	.	PUNCT
ejpam-5275	354	1	references	reference	NOUN
ejpam-5275	354	2	2348	2348	NUM
ejpam-5275	355	1	[	[	X
ejpam-5275	355	2	31	31	NUM
ejpam-5275	355	3	]	]	X
ejpam-5275	355	4	bao	bao	PROPN
ejpam-5275	355	5	quoc	quoc	PROPN
ejpam-5275	355	6	ta	ta	PROPN
ejpam-5275	355	7	.	.	PUNCT
ejpam-5275	356	1	probabilistic	probabilistic	ADJ
ejpam-5275	356	2	approach	approach	NOUN
ejpam-5275	356	3	to	to	ADP
ejpam-5275	356	4	appell	appell	ADJ
ejpam-5275	356	5	polynomials	polynomial	NOUN
ejpam-5275	356	6	.	.	PUNCT
ejpam-5275	357	1	expositiones	expositione	NOUN
ejpam-5275	357	2	mathematicae	mathematicae	VERB
ejpam-5275	357	3	,	,	PUNCT
ejpam-5275	357	4	33(3):269–294	33(3):269–294	PROPN
ejpam-5275	357	5	,	,	PUNCT
ejpam-5275	357	6	2015	2015	NUM
ejpam-5275	357	7	.	.	PUNCT
ejpam-5275	358	1	[	[	X
ejpam-5275	358	2	32	32	NUM
ejpam-5275	358	3	]	]	PUNCT
ejpam-5275	358	4	henry	henry	PROPN
ejpam-5275	358	5	teicher	teicher	PROPN
ejpam-5275	358	6	.	.	PUNCT
ejpam-5275	359	1	an	an	DET
ejpam-5275	359	2	inequality	inequality	NOUN
ejpam-5275	359	3	on	on	ADP
ejpam-5275	359	4	poisson	poisson	NOUN
ejpam-5275	359	5	probabilities	probability	NOUN
ejpam-5275	359	6	.	.	PUNCT
ejpam-5275	360	1	the	the	DET
ejpam-5275	360	2	annals	annal	NOUN
ejpam-5275	360	3	of	of	ADP
ejpam-5275	360	4	mathematical	mathematical	ADJ
ejpam-5275	360	5	statistics	statistic	NOUN
ejpam-5275	360	6	,	,	PUNCT
ejpam-5275	360	7	26(1):147–149	26(1):147–149	PROPN
ejpam-5275	360	8	,	,	PUNCT
ejpam-5275	360	9	1955	1955	NUM
ejpam-5275	360	10	.	.	PUNCT