id	sid	tid	token	lemma	pos
ejpam-5702	1	1	european	european	PROPN
ejpam-5702	1	2	journal	journal	PROPN
ejpam-5702	1	3	of	of	ADP
ejpam-5702	1	4	pure	pure	ADJ
ejpam-5702	1	5	and	and	CCONJ
ejpam-5702	1	6	applied	applied	ADJ
ejpam-5702	1	7	mathematics	mathematic	NOUN
ejpam-5702	1	8	2025	2025	NUM
ejpam-5702	1	9	,	,	PUNCT
ejpam-5702	1	10	vol	vol	NOUN
ejpam-5702	1	11	.	.	PROPN
ejpam-5702	1	12	18	18	NUM
ejpam-5702	1	13	,	,	PUNCT
ejpam-5702	1	14	issue	issue	NOUN
ejpam-5702	1	15	1	1	NUM
ejpam-5702	1	16	,	,	PUNCT
ejpam-5702	1	17	article	article	NOUN
ejpam-5702	1	18	number	number	NOUN
ejpam-5702	1	19	5702	5702	NUM
ejpam-5702	1	20	issn	issn	PROPN
ejpam-5702	1	21	1307	1307	NUM
ejpam-5702	1	22	-	-	SYM
ejpam-5702	1	23	5543	5543	NUM
ejpam-5702	1	24	–	–	PUNCT
ejpam-5702	1	25	ejpam.com	ejpam.com	X
ejpam-5702	1	26	published	publish	VERB
ejpam-5702	1	27	by	by	ADP
ejpam-5702	1	28	new	new	PROPN
ejpam-5702	1	29	york	york	PROPN
ejpam-5702	1	30	business	business	PROPN
ejpam-5702	1	31	global	global	PROPN
ejpam-5702	1	32	probabilistic	probabilistic	ADJ
ejpam-5702	1	33	multiple	multiple	ADJ
ejpam-5702	1	34	poly	poly	ADJ
ejpam-5702	1	35	bernoulli	bernoulli	NOUN
ejpam-5702	1	36	polynomials	polynomial	NOUN
ejpam-5702	1	37	of	of	ADP
ejpam-5702	1	38	the	the	DET
ejpam-5702	1	39	second	second	ADJ
ejpam-5702	1	40	kind	kind	NOUN
ejpam-5702	1	41	si	si	PROPN
ejpam-5702	1	42	hyeon	hyeon	PROPN
ejpam-5702	1	43	lee1,∗	lee1,∗	PROPN
ejpam-5702	1	44	,	,	PUNCT
ejpam-5702	1	45	li	li	PROPN
ejpam-5702	1	46	chen2	chen2	PROPN
ejpam-5702	1	47	1	1	NUM
ejpam-5702	1	48	kwangwoon	kwangwoon	NOUN
ejpam-5702	1	49	university	university	NOUN
ejpam-5702	1	50	,	,	PUNCT
ejpam-5702	1	51	seoul	seoul	PROPN
ejpam-5702	1	52	139	139	NUM
ejpam-5702	1	53	-	-	SYM
ejpam-5702	1	54	701	701	NUM
ejpam-5702	1	55	,	,	PUNCT
ejpam-5702	1	56	republic	republic	NOUN
ejpam-5702	1	57	of	of	ADP
ejpam-5702	1	58	korea	korea	PROPN
ejpam-5702	1	59	2	2	NUM
ejpam-5702	1	60	school	school	NOUN
ejpam-5702	1	61	of	of	ADP
ejpam-5702	1	62	mathematics	mathematic	NOUN
ejpam-5702	1	63	,	,	PUNCT
ejpam-5702	1	64	xi’an	xi’an	PROPN
ejpam-5702	1	65	university	university	PROPN
ejpam-5702	1	66	of	of	ADP
ejpam-5702	1	67	finance	finance	NOUN
ejpam-5702	1	68	and	and	CCONJ
ejpam-5702	1	69	economics	economic	NOUN
ejpam-5702	1	70	,	,	PUNCT
ejpam-5702	1	71	xi’an	xi’an	PROPN
ejpam-5702	1	72	710100	710100	NUM
ejpam-5702	1	73	,	,	PUNCT
ejpam-5702	1	74	china	china	PROPN
ejpam-5702	1	75	abstract	abstract	PROPN
ejpam-5702	1	76	.	.	PUNCT
ejpam-5702	2	1	the	the	DET
ejpam-5702	2	2	purpose	purpose	NOUN
ejpam-5702	2	3	of	of	ADP
ejpam-5702	2	4	this	this	DET
ejpam-5702	2	5	paper	paper	NOUN
ejpam-5702	2	6	is	be	AUX
ejpam-5702	2	7	to	to	PART
ejpam-5702	2	8	introduce	introduce	VERB
ejpam-5702	2	9	the	the	DET
ejpam-5702	2	10	probabilistic	probabilistic	ADJ
ejpam-5702	2	11	multiple	multiple	ADJ
ejpam-5702	2	12	poly	poly	ADJ
ejpam-5702	2	13	bernoulli	bernoulli	NOUN
ejpam-5702	2	14	polynomials	polynomial	NOUN
ejpam-5702	2	15	of	of	ADP
ejpam-5702	2	16	the	the	DET
ejpam-5702	2	17	second	second	ADJ
ejpam-5702	2	18	kind	kind	NOUN
ejpam-5702	2	19	under	under	ADP
ejpam-5702	2	20	the	the	DET
ejpam-5702	2	21	condition	condition	NOUN
ejpam-5702	2	22	that	that	SCONJ
ejpam-5702	2	23	y	y	PROPN
ejpam-5702	2	24	is	be	AUX
ejpam-5702	2	25	a	a	DET
ejpam-5702	2	26	random	random	ADJ
ejpam-5702	2	27	variable	variable	NOUN
ejpam-5702	2	28	.	.	PUNCT
ejpam-5702	3	1	this	this	PRON
ejpam-5702	3	2	means	mean	VERB
ejpam-5702	3	3	that	that	SCONJ
ejpam-5702	3	4	we	we	PRON
ejpam-5702	3	5	will	will	AUX
ejpam-5702	3	6	consider	consider	VERB
ejpam-5702	3	7	the	the	DET
ejpam-5702	3	8	probabilistic	probabilistic	ADJ
ejpam-5702	3	9	extension	extension	NOUN
ejpam-5702	3	10	of	of	ADP
ejpam-5702	3	11	the	the	DET
ejpam-5702	3	12	multiple	multiple	ADJ
ejpam-5702	3	13	poly	poly	ADJ
ejpam-5702	3	14	bernoulli	bernoulli	NOUN
ejpam-5702	3	15	polynomials	polynomial	NOUN
ejpam-5702	3	16	of	of	ADP
ejpam-5702	3	17	the	the	DET
ejpam-5702	3	18	second	second	ADJ
ejpam-5702	3	19	kind	kind	NOUN
ejpam-5702	3	20	and	and	CCONJ
ejpam-5702	3	21	study	study	VERB
ejpam-5702	3	22	to	to	PART
ejpam-5702	3	23	obtain	obtain	VERB
ejpam-5702	3	24	some	some	DET
ejpam-5702	3	25	new	new	ADJ
ejpam-5702	3	26	results	result	NOUN
ejpam-5702	3	27	.	.	PUNCT
ejpam-5702	4	1	furthermore	furthermore	ADV
ejpam-5702	4	2	,	,	PUNCT
ejpam-5702	4	3	we	we	PRON
ejpam-5702	4	4	investigate	investigate	VERB
ejpam-5702	4	5	their	their	PRON
ejpam-5702	4	6	interesting	interesting	ADJ
ejpam-5702	4	7	properties	property	NOUN
ejpam-5702	4	8	.	.	PUNCT
ejpam-5702	5	1	2020	2020	NUM
ejpam-5702	5	2	mathematics	mathematic	NOUN
ejpam-5702	5	3	subject	subject	NOUN
ejpam-5702	5	4	classifications	classification	NOUN
ejpam-5702	5	5	:	:	PUNCT
ejpam-5702	5	6	11b68	11b68	NUM
ejpam-5702	5	7	,	,	PUNCT
ejpam-5702	5	8	11b73	11b73	NUM
ejpam-5702	5	9	key	key	ADJ
ejpam-5702	5	10	words	word	NOUN
ejpam-5702	5	11	and	and	CCONJ
ejpam-5702	5	12	phrases	phrase	NOUN
ejpam-5702	5	13	:	:	PUNCT
ejpam-5702	5	14	poly	poly	ADJ
ejpam-5702	5	15	bernoulli	bernoulli	NOUN
ejpam-5702	5	16	polynomials	polynomial	NOUN
ejpam-5702	5	17	of	of	ADP
ejpam-5702	5	18	the	the	DET
ejpam-5702	5	19	second	second	ADJ
ejpam-5702	5	20	kind	kind	NOUN
ejpam-5702	5	21	,	,	PUNCT
ejpam-5702	5	22	stirling	stirling	NOUN
ejpam-5702	5	23	numbers	number	NOUN
ejpam-5702	5	24	,	,	PUNCT
ejpam-5702	5	25	probabilistic	probabilistic	ADJ
ejpam-5702	5	26	poly	poly	ADJ
ejpam-5702	5	27	-	-	PUNCT
ejpam-5702	5	28	bernoulli	bernoulli	NOUN
ejpam-5702	5	29	polynomials	polynomial	NOUN
ejpam-5702	5	30	,	,	PUNCT
ejpam-5702	5	31	probabilistic	probabilistic	ADJ
ejpam-5702	5	32	bernoulli	bernoulli	NOUN
ejpam-5702	5	33	polynomials	polynomial	NOUN
ejpam-5702	5	34	.	.	PUNCT
ejpam-5702	6	1	1	1	X
ejpam-5702	6	2	.	.	X
ejpam-5702	6	3	introduction	introduction	NOUN
ejpam-5702	6	4	many	many	ADJ
ejpam-5702	6	5	years	year	NOUN
ejpam-5702	6	6	ago	ago	ADV
ejpam-5702	6	7	qi	qi	PROPN
ejpam-5702	6	8	-	-	PUNCT
ejpam-5702	6	9	kim	kim	PROPN
ejpam-5702	6	10	-	-	PUNCT
ejpam-5702	6	11	kim	kim	PROPN
ejpam-5702	6	12	-	-	PUNCT
ejpam-5702	6	13	dolgy	dolgy	ADJ
ejpam-5702	6	14	considered	consider	VERB
ejpam-5702	6	15	poly	poly	ADJ
ejpam-5702	6	16	bernoulli	bernoulli	NOUN
ejpam-5702	6	17	polynomials	polynomial	NOUN
ejpam-5702	6	18	of	of	ADP
ejpam-5702	6	19	the	the	DET
ejpam-5702	6	20	second	second	ADJ
ejpam-5702	6	21	kind	kind	NOUN
ejpam-5702	6	22	and	and	CCONJ
ejpam-5702	6	23	multiple	multiple	ADJ
ejpam-5702	6	24	poly	poly	ADJ
ejpam-5702	6	25	bernoulli	bernoulli	NOUN
ejpam-5702	6	26	polynomials	polynomial	NOUN
ejpam-5702	6	27	of	of	ADP
ejpam-5702	6	28	the	the	DET
ejpam-5702	6	29	secon	secon	ADJ
ejpam-5702	6	30	kind	kind	NOUN
ejpam-5702	6	31	in	in	ADV
ejpam-5702	6	32	[	[	X
ejpam-5702	6	33	28	28	NUM
ejpam-5702	6	34	]	]	PUNCT
ejpam-5702	6	35	.	.	PUNCT
ejpam-5702	7	1	recently	recently	ADV
ejpam-5702	7	2	,	,	PUNCT
ejpam-5702	7	3	researchers	researcher	NOUN
ejpam-5702	7	4	considered	consider	VERB
ejpam-5702	7	5	probabilistic	probabilistic	ADJ
ejpam-5702	7	6	stirling	stirling	NOUN
ejpam-5702	7	7	numbers	number	NOUN
ejpam-5702	7	8	,	,	PUNCT
ejpam-5702	7	9	bell	bell	NOUN
ejpam-5702	7	10	numbers	number	NOUN
ejpam-5702	7	11	,	,	PUNCT
ejpam-5702	7	12	bernoulli	bernoulli	NOUN
ejpam-5702	7	13	polynomials	polynomial	NOUN
ejpam-5702	7	14	and	and	CCONJ
ejpam-5702	7	15	euler	euler	NOUN
ejpam-5702	7	16	polynomials	polynomial	NOUN
ejpam-5702	7	17	.	.	PUNCT
ejpam-5702	8	1	the	the	DET
ejpam-5702	8	2	aim	aim	NOUN
ejpam-5702	8	3	of	of	ADP
ejpam-5702	8	4	this	this	DET
ejpam-5702	8	5	paper	paper	NOUN
ejpam-5702	8	6	is	be	AUX
ejpam-5702	8	7	to	to	PART
ejpam-5702	8	8	study	study	VERB
ejpam-5702	8	9	probabilistic	probabilistic	ADJ
ejpam-5702	8	10	multiple	multiple	ADJ
ejpam-5702	8	11	poly	poly	ADJ
ejpam-5702	8	12	bernoulli	bernoulli	NOUN
ejpam-5702	8	13	polynomials	polynomial	NOUN
ejpam-5702	8	14	of	of	ADP
ejpam-5702	8	15	the	the	DET
ejpam-5702	8	16	second	second	ADJ
ejpam-5702	8	17	kind	kind	NOUN
ejpam-5702	8	18	.	.	PUNCT
ejpam-5702	9	1	specifically	specifically	ADV
ejpam-5702	9	2	speaking	speak	VERB
ejpam-5702	9	3	,	,	PUNCT
ejpam-5702	9	4	we	we	PRON
ejpam-5702	9	5	assume	assume	VERB
ejpam-5702	9	6	that	that	SCONJ
ejpam-5702	9	7	y	y	PROPN
ejpam-5702	9	8	is	be	AUX
ejpam-5702	9	9	a	a	DET
ejpam-5702	9	10	random	random	ADJ
ejpam-5702	9	11	variable	variable	NOUN
ejpam-5702	9	12	in	in	ADP
ejpam-5702	9	13	section	section	NOUN
ejpam-5702	9	14	1	1	NUM
ejpam-5702	9	15	,	,	PUNCT
ejpam-5702	9	16	firstly	firstly	ADV
ejpam-5702	9	17	we	we	PRON
ejpam-5702	9	18	recall	recall	VERB
ejpam-5702	9	19	polylogarithm	polylogarithm	PROPN
ejpam-5702	9	20	lik(t	lik(t	PROPN
ejpam-5702	9	21	)	)	PUNCT
ejpam-5702	9	22	,	,	PUNCT
ejpam-5702	9	23	multiple	multiple	ADJ
ejpam-5702	9	24	polylogarithm	polylogarithm	PROPN
ejpam-5702	9	25	lik1,	lik1,	PROPN
ejpam-5702	9	26	...	...	PUNCT
ejpam-5702	9	27	,kr(t	,kr(t	NUM
ejpam-5702	9	28	)	)	PUNCT
ejpam-5702	9	29	.	.	PUNCT
ejpam-5702	10	1	we	we	PRON
ejpam-5702	10	2	remind	remind	VERB
ejpam-5702	10	3	poly	poly	ADJ
ejpam-5702	10	4	bernoulli	bernoulli	NOUN
ejpam-5702	10	5	polynomials	polynomial	NOUN
ejpam-5702	10	6	of	of	ADP
ejpam-5702	10	7	the	the	DET
ejpam-5702	10	8	second	second	ADJ
ejpam-5702	10	9	kind	kind	NOUN
ejpam-5702	10	10	and	and	CCONJ
ejpam-5702	10	11	bernoulli	bernoulli	NOUN
ejpam-5702	10	12	polynomials	polynomial	NOUN
ejpam-5702	10	13	of	of	ADP
ejpam-5702	10	14	order	order	NOUN
ejpam-5702	10	15	α	α	NOUN
ejpam-5702	10	16	.	.	PUNCT
ejpam-5702	11	1	we	we	PRON
ejpam-5702	11	2	recall	recall	VERB
ejpam-5702	11	3	that	that	DET
ejpam-5702	11	4	probabilistic	probabilistic	ADJ
ejpam-5702	11	5	stirling	stirling	NOUN
ejpam-5702	11	6	numbers	number	NOUN
ejpam-5702	11	7	of	of	ADP
ejpam-5702	11	8	the	the	DET
ejpam-5702	11	9	second	second	ADJ
ejpam-5702	11	10	kind	kind	NOUN
ejpam-5702	11	11	and	and	CCONJ
ejpam-5702	11	12	lah	lah	NOUN
ejpam-5702	11	13	numbers	number	NOUN
ejpam-5702	11	14	.	.	PUNCT
ejpam-5702	12	1	in	in	ADP
ejpam-5702	12	2	section	section	NOUN
ejpam-5702	12	3	2	2	NUM
ejpam-5702	12	4	,	,	PUNCT
ejpam-5702	12	5	we	we	PRON
ejpam-5702	12	6	define	define	VERB
ejpam-5702	12	7	probabilistic	probabilistic	ADJ
ejpam-5702	12	8	poly	poly	ADJ
ejpam-5702	12	9	bernoulli	bernoulli	NOUN
ejpam-5702	12	10	polynomials	polynomial	NOUN
ejpam-5702	12	11	of	of	ADP
ejpam-5702	12	12	the	the	DET
ejpam-5702	12	13	second	second	ADJ
ejpam-5702	12	14	kind	kind	NOUN
ejpam-5702	12	15	b	b	PROPN
ejpam-5702	12	16	(	(	PUNCT
ejpam-5702	12	17	k	k	NOUN
ejpam-5702	12	18	)	)	PUNCT
ejpam-5702	12	19	n	n	CCONJ
ejpam-5702	12	20	,	,	PUNCT
ejpam-5702	12	21	y	y	PROPN
ejpam-5702	12	22	and	and	CCONJ
ejpam-5702	12	23	probabilistic	probabilistic	ADJ
ejpam-5702	12	24	multiple	multiple	ADJ
ejpam-5702	12	25	poly	poly	ADJ
ejpam-5702	12	26	bernoulli	bernoulli	NOUN
ejpam-5702	12	27	polynomials	polynomial	NOUN
ejpam-5702	12	28	of	of	ADP
ejpam-5702	12	29	the	the	DET
ejpam-5702	12	30	second	second	ADJ
ejpam-5702	12	31	kind	kind	NOUN
ejpam-5702	12	32	b	b	PROPN
ejpam-5702	12	33	(	(	PUNCT
ejpam-5702	12	34	k1,	k1,	NOUN
ejpam-5702	12	35	...	...	SYM
ejpam-5702	12	36	,kr	,kr	SYM
ejpam-5702	12	37	)	)	PUNCT
ejpam-5702	12	38	n	n	CCONJ
ejpam-5702	12	39	,	,	PUNCT
ejpam-5702	12	40	y	y	PROPN
ejpam-5702	12	41	associated	associate	VERB
ejpam-5702	12	42	with	with	ADP
ejpam-5702	12	43	y	y	PROPN
ejpam-5702	12	44	.	.	PUNCT
ejpam-5702	13	1	in	in	ADP
ejpam-5702	13	2	theorem	theorem	NOUN
ejpam-5702	13	3	2.1	2.1	NUM
ejpam-5702	13	4	,	,	PUNCT
ejpam-5702	13	5	we	we	PRON
ejpam-5702	13	6	derive	derive	VERB
ejpam-5702	13	7	an	an	DET
ejpam-5702	13	8	expression	expression	NOUN
ejpam-5702	13	9	for	for	ADP
ejpam-5702	13	10	nb	nb	PROPN
ejpam-5702	13	11	(	(	PUNCT
ejpam-5702	13	12	k	k	PROPN
ejpam-5702	13	13	)	)	PUNCT
ejpam-5702	13	14	n−1,y	n−1,y	PROPN
ejpam-5702	13	15	(	(	PUNCT
ejpam-5702	13	16	x	x	NOUN
ejpam-5702	13	17	)	)	PUNCT
ejpam-5702	13	18	.	.	PUNCT
ejpam-5702	14	1	when	when	SCONJ
ejpam-5702	14	2	y	y	PROPN
ejpam-5702	14	3	∼	∼	NOUN
ejpam-5702	14	4	γ(1	γ(1	PROPN
ejpam-5702	14	5	,	,	PUNCT
ejpam-5702	14	6	1	1	NUM
ejpam-5702	14	7	)	)	PUNCT
ejpam-5702	14	8	in	in	ADP
ejpam-5702	14	9	theorem	theorem	NOUN
ejpam-5702	14	10	2.2	2.2	NUM
ejpam-5702	14	11	,	,	PUNCT
ejpam-5702	14	12	we	we	PRON
ejpam-5702	14	13	get	get	VERB
ejpam-5702	14	14	an	an	DET
ejpam-5702	14	15	expression	expression	NOUN
ejpam-5702	14	16	for	for	ADP
ejpam-5702	14	17	b	b	PROPN
ejpam-5702	14	18	(	(	PUNCT
ejpam-5702	14	19	k	k	NOUN
ejpam-5702	14	20	)	)	PUNCT
ejpam-5702	14	21	n	n	CCONJ
ejpam-5702	14	22	,	,	PUNCT
ejpam-5702	14	23	y	y	PROPN
ejpam-5702	14	24	(	(	PUNCT
ejpam-5702	14	25	x	x	NOUN
ejpam-5702	14	26	)	)	PUNCT
ejpam-5702	14	27	as	as	ADP
ejpam-5702	14	28	sum	sum	NOUN
ejpam-5702	14	29	of	of	ADP
ejpam-5702	14	30	the	the	DET
ejpam-5702	14	31	products	product	NOUN
ejpam-5702	14	32	.	.	PUNCT
ejpam-5702	15	1	when	when	SCONJ
ejpam-5702	15	2	y	y	PROPN
ejpam-5702	15	3	is	be	AUX
ejpam-5702	15	4	the	the	DET
ejpam-5702	15	5	bernoulli	bernoulli	NOUN
ejpam-5702	15	6	random	random	ADJ
ejpam-5702	15	7	variable	variable	NOUN
ejpam-5702	15	8	,	,	PUNCT
ejpam-5702	15	9	in	in	ADP
ejpam-5702	15	10	theorem	theorem	NOUN
ejpam-5702	15	11	2.3	2.3	NUM
ejpam-5702	15	12	we	we	PRON
ejpam-5702	15	13	get	get	VERB
ejpam-5702	15	14	expression	expression	NOUN
ejpam-5702	15	15	for	for	ADP
ejpam-5702	15	16	b	b	PROPN
ejpam-5702	15	17	(	(	PUNCT
ejpam-5702	15	18	k	k	NOUN
ejpam-5702	15	19	)	)	PUNCT
ejpam-5702	15	20	n	n	CCONJ
ejpam-5702	15	21	,	,	PUNCT
ejpam-5702	15	22	y	y	PROPN
ejpam-5702	15	23	(	(	PUNCT
ejpam-5702	15	24	x	x	NOUN
ejpam-5702	15	25	)	)	PUNCT
ejpam-5702	15	26	.	.	PUNCT
ejpam-5702	16	1	in	in	ADP
ejpam-5702	16	2	theorem	theorem	ADJ
ejpam-5702	16	3	2.4	2.4	NUM
ejpam-5702	16	4	,	,	PUNCT
ejpam-5702	16	5	we	we	PRON
ejpam-5702	16	6	obtain	obtain	VERB
ejpam-5702	16	7	an	an	DET
ejpam-5702	16	8	expression	expression	NOUN
ejpam-5702	16	9	for	for	ADP
ejpam-5702	16	10	b	b	PROPN
ejpam-5702	16	11	(	(	PUNCT
ejpam-5702	16	12	k1,	k1,	NOUN
ejpam-5702	16	13	...	...	SYM
ejpam-5702	16	14	,kr	,kr	SYM
ejpam-5702	16	15	)	)	PUNCT
ejpam-5702	16	16	n	n	CCONJ
ejpam-5702	16	17	,	,	PUNCT
ejpam-5702	16	18	y	y	PROPN
ejpam-5702	16	19	(	(	PUNCT
ejpam-5702	16	20	x	x	NOUN
ejpam-5702	16	21	)	)	PUNCT
ejpam-5702	16	22	.	.	PUNCT
ejpam-5702	17	1	in	in	ADP
ejpam-5702	17	2	theorem	theorem	ADJ
ejpam-5702	17	3	2.5	2.5	NUM
ejpam-5702	17	4	,	,	PUNCT
ejpam-5702	17	5	we	we	PRON
ejpam-5702	17	6	∗corresponding	∗corresponde	VERB
ejpam-5702	17	7	author	author	NOUN
ejpam-5702	17	8	.	.	PUNCT
ejpam-5702	18	1	doi	doi	NOUN
ejpam-5702	18	2	:	:	PUNCT
ejpam-5702	18	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5702	https://doi.org/10.29020/nybg.ejpam.v18i1.5702	PROPN
ejpam-5702	18	4	email	email	NOUN
ejpam-5702	18	5	addresses	address	NOUN
ejpam-5702	18	6	:	:	PUNCT
ejpam-5702	18	7	ugug11@naver.com	ugug11@naver.com	PROPN
ejpam-5702	18	8	(	(	PUNCT
ejpam-5702	18	9	s.	s.	PROPN
ejpam-5702	18	10	h.	h.	PROPN
ejpam-5702	18	11	lee	lee	PROPN
ejpam-5702	18	12	)	)	PUNCT
ejpam-5702	18	13	,	,	PUNCT
ejpam-5702	18	14	chenli	chenli	NOUN
ejpam-5702	18	15	0928@xaufe.edu.cn	0928@xaufe.edu.cn	NUM
ejpam-5702	18	16	(	(	PUNCT
ejpam-5702	18	17	l.	l.	PROPN
ejpam-5702	18	18	chen	chen	PROPN
ejpam-5702	18	19	)	)	PUNCT
ejpam-5702	18	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5702	19	1	1	1	NUM
ejpam-5702	19	2	copyright	copyright	NOUN
ejpam-5702	19	3	:	:	PUNCT
ejpam-5702	19	4	©	©	PROPN
ejpam-5702	19	5	2025	2025	NUM
ejpam-5702	19	6	the	the	DET
ejpam-5702	19	7	author(s	author(s	NOUN
ejpam-5702	19	8	)	)	PUNCT
ejpam-5702	19	9	.	.	PUNCT
ejpam-5702	20	1	(	(	PUNCT
ejpam-5702	20	2	cc	cc	NOUN
ejpam-5702	20	3	by	by	ADP
ejpam-5702	20	4	-	-	PUNCT
ejpam-5702	20	5	nc	nc	PROPN
ejpam-5702	20	6	4.0	4.0	NUM
ejpam-5702	20	7	)	)	PUNCT
ejpam-5702	20	8	s.	s.	PROPN
ejpam-5702	20	9	h.	h.	PROPN
ejpam-5702	20	10	lee	lee	PROPN
ejpam-5702	20	11	,	,	PUNCT
ejpam-5702	20	12	l.	l.	PROPN
ejpam-5702	20	13	chen	chen	PROPN
ejpam-5702	20	14	/	/	SYM
ejpam-5702	20	15	eur	eur	PROPN
ejpam-5702	20	16	.	.	PUNCT
ejpam-5702	21	1	j.	j.	PROPN
ejpam-5702	21	2	pure	pure	PROPN
ejpam-5702	21	3	appl	appl	PROPN
ejpam-5702	21	4	.	.	PROPN
ejpam-5702	21	5	math	math	PROPN
ejpam-5702	21	6	,	,	PUNCT
ejpam-5702	21	7	18	18	NUM
ejpam-5702	21	8	(	(	PUNCT
ejpam-5702	21	9	1	1	NUM
ejpam-5702	21	10	)	)	PUNCT
ejpam-5702	21	11	(	(	PUNCT
ejpam-5702	21	12	2025	2025	NUM
ejpam-5702	21	13	)	)	PUNCT
ejpam-5702	21	14	,	,	PUNCT
ejpam-5702	21	15	5702	5702	NUM
ejpam-5702	21	16	2	2	NUM
ejpam-5702	21	17	of	of	ADP
ejpam-5702	21	18	13	13	NUM
ejpam-5702	21	19	find	find	VERB
ejpam-5702	21	20	an	an	DET
ejpam-5702	21	21	expression	expression	NOUN
ejpam-5702	21	22	of	of	ADP
ejpam-5702	21	23	b	b	PROPN
ejpam-5702	21	24	(	(	PUNCT
ejpam-5702	21	25	k1,	k1,	NOUN
ejpam-5702	21	26	...	...	PUNCT
ejpam-5702	21	27	,kr	,kr	SYM
ejpam-5702	21	28	)	)	PUNCT
ejpam-5702	22	1	n+1,y	n+1,y	PROPN
ejpam-5702	22	2	(	(	PUNCT
ejpam-5702	22	3	x+1)−b	x+1)−b	PROPN
ejpam-5702	22	4	k1,	k1,	NOUN
ejpam-5702	22	5	...	...	PUNCT
ejpam-5702	22	6	,kr	,kr	PUNCT
ejpam-5702	22	7	n+1,y	n+1,y	INTJ
ejpam-5702	22	8	(	(	PUNCT
ejpam-5702	22	9	x	x	X
ejpam-5702	22	10	)	)	PUNCT
ejpam-5702	22	11	n+1	n+1	PROPN
ejpam-5702	22	12	.	.	PUNCT
ejpam-5702	23	1	in	in	ADP
ejpam-5702	23	2	theorem	theorem	NOUN
ejpam-5702	23	3	2.6	2.6	NUM
ejpam-5702	23	4	,	,	PUNCT
ejpam-5702	23	5	we	we	PRON
ejpam-5702	23	6	derive	derive	VERB
ejpam-5702	23	7	an	an	DET
ejpam-5702	23	8	expression	expression	NOUN
ejpam-5702	23	9	of	of	ADP
ejpam-5702	23	10	b	b	PROPN
ejpam-5702	23	11	(	(	PUNCT
ejpam-5702	23	12	k1,	k1,	NOUN
ejpam-5702	23	13	...	...	SYM
ejpam-5702	23	14	,kr	,kr	SYM
ejpam-5702	23	15	)	)	PUNCT
ejpam-5702	23	16	n	n	CCONJ
ejpam-5702	23	17	,	,	PUNCT
ejpam-5702	23	18	y	y	PROPN
ejpam-5702	23	19	(	(	PUNCT
ejpam-5702	23	20	x	x	NOUN
ejpam-5702	23	21	)	)	PUNCT
ejpam-5702	23	22	between	between	ADP
ejpam-5702	23	23	probabilistic	probabilistic	ADJ
ejpam-5702	23	24	multi	multi	ADJ
ejpam-5702	23	25	-	-	ADJ
ejpam-5702	23	26	poly	poly	ADJ
ejpam-5702	23	27	-	-	PUNCT
ejpam-5702	23	28	bernoulli	bernoulli	NOUN
ejpam-5702	23	29	polynomials	polynomial	NOUN
ejpam-5702	23	30	,	,	PUNCT
ejpam-5702	23	31	bernoulli	bernoulli	NOUN
ejpam-5702	23	32	polynomials	polynomial	NOUN
ejpam-5702	23	33	of	of	ADP
ejpam-5702	23	34	the	the	DET
ejpam-5702	23	35	second	second	ADJ
ejpam-5702	23	36	kind	kind	NOUN
ejpam-5702	23	37	of	of	ADP
ejpam-5702	23	38	order	order	NOUN
ejpam-5702	23	39	r	r	NOUN
ejpam-5702	23	40	and	and	CCONJ
ejpam-5702	23	41	probabilistic	probabilistic	VERB
ejpam-5702	23	42	the	the	DET
ejpam-5702	23	43	stirling	stirling	NOUN
ejpam-5702	23	44	numbers	number	NOUN
ejpam-5702	23	45	of	of	ADP
ejpam-5702	23	46	the	the	DET
ejpam-5702	23	47	second	second	ADJ
ejpam-5702	23	48	kind	kind	NOUN
ejpam-5702	23	49	.	.	PUNCT
ejpam-5702	24	1	in	in	ADP
ejpam-5702	24	2	theorem	theorem	ADJ
ejpam-5702	24	3	2.7	2.7	NUM
ejpam-5702	24	4	we	we	PRON
ejpam-5702	24	5	get	get	VERB
ejpam-5702	24	6	an	an	DET
ejpam-5702	24	7	expression	expression	NOUN
ejpam-5702	24	8	of	of	ADP
ejpam-5702	24	9	b	b	PROPN
ejpam-5702	24	10	(	(	PUNCT
ejpam-5702	24	11	k1,	k1,	NOUN
ejpam-5702	24	12	...	...	SYM
ejpam-5702	24	13	,kr	,kr	SYM
ejpam-5702	24	14	)	)	PUNCT
ejpam-5702	24	15	n	n	CCONJ
ejpam-5702	24	16	,	,	PUNCT
ejpam-5702	24	17	y	y	PROPN
ejpam-5702	24	18	(	(	PUNCT
ejpam-5702	24	19	x+	x+	PROPN
ejpam-5702	24	20	y	y	NOUN
ejpam-5702	24	21	)	)	PUNCT
ejpam-5702	24	22	.	.	PUNCT
ejpam-5702	25	1	now	now	ADV
ejpam-5702	25	2	we	we	PRON
ejpam-5702	25	3	recall	recall	VERB
ejpam-5702	25	4	that	that	SCONJ
ejpam-5702	25	5	the	the	DET
ejpam-5702	25	6	bernoulli	bernoulli	NOUN
ejpam-5702	25	7	polynomials	polynomial	NOUN
ejpam-5702	25	8	of	of	ADP
ejpam-5702	25	9	the	the	DET
ejpam-5702	25	10	second	second	ADJ
ejpam-5702	25	11	kind	kind	NOUN
ejpam-5702	25	12	are	be	AUX
ejpam-5702	25	13	defined	define	VERB
ejpam-5702	25	14	by	by	ADP
ejpam-5702	25	15	t	t	NOUN
ejpam-5702	25	16	log(1	log(1	NOUN
ejpam-5702	25	17	+	+	CCONJ
ejpam-5702	25	18	t	t	X
ejpam-5702	25	19	)	)	PUNCT
ejpam-5702	25	20	(	(	PUNCT
ejpam-5702	25	21	1	1	NUM
ejpam-5702	25	22	+	+	CCONJ
ejpam-5702	25	23	t)x	t)x	PUNCT
ejpam-5702	25	24	=	=	PUNCT
ejpam-5702	25	25	∞∑	∞∑	NUM
ejpam-5702	25	26	n=0	n=0	NUM
ejpam-5702	25	27	bn(x	bn(x	NUM
ejpam-5702	25	28	)	)	PUNCT
ejpam-5702	25	29	tn	tn	PROPN
ejpam-5702	25	30	n	n	PROPN
ejpam-5702	25	31	!	!	PROPN
ejpam-5702	25	32	,	,	PUNCT
ejpam-5702	25	33	(	(	PUNCT
ejpam-5702	25	34	see[12	see[12	X
ejpam-5702	25	35	]	]	X
ejpam-5702	25	36	,	,	PUNCT
ejpam-5702	25	37	[	[	X
ejpam-5702	25	38	13	13	NUM
ejpam-5702	25	39	]	]	PUNCT
ejpam-5702	25	40	,	,	PUNCT
ejpam-5702	25	41	[	[	X
ejpam-5702	25	42	25	25	NUM
ejpam-5702	25	43	]	]	PUNCT
ejpam-5702	25	44	,	,	PUNCT
ejpam-5702	25	45	[	[	X
ejpam-5702	25	46	29	29	NUM
ejpam-5702	25	47	]	]	PUNCT
ejpam-5702	25	48	)	)	PUNCT
ejpam-5702	25	49	.	.	PUNCT
ejpam-5702	26	1	(	(	PUNCT
ejpam-5702	26	2	1	1	X
ejpam-5702	26	3	)	)	PUNCT
ejpam-5702	26	4	the	the	DET
ejpam-5702	26	5	bernoulli	bernoulli	PROPN
ejpam-5702	26	6	polynomials	polynomial	NOUN
ejpam-5702	26	7	of	of	ADP
ejpam-5702	26	8	the	the	DET
ejpam-5702	26	9	second	second	ADJ
ejpam-5702	26	10	kind	kind	NOUN
ejpam-5702	26	11	with	with	ADP
ejpam-5702	26	12	order	order	NOUN
ejpam-5702	26	13	r	r	NOUN
ejpam-5702	26	14	are	be	AUX
ejpam-5702	26	15	defined	define	VERB
ejpam-5702	26	16	by	by	ADP
ejpam-5702	26	17	the	the	DET
ejpam-5702	26	18	generating	generate	VERB
ejpam-5702	26	19	function	function	NOUN
ejpam-5702	26	20	(	(	PUNCT
ejpam-5702	26	21	t	t	NOUN
ejpam-5702	26	22	log(1	log(1	NOUN
ejpam-5702	26	23	+	+	CCONJ
ejpam-5702	26	24	t	t	NOUN
ejpam-5702	26	25	)	)	PUNCT
ejpam-5702	26	26	)	)	PUNCT
ejpam-5702	27	1	r	r	NOUN
ejpam-5702	27	2	(	(	PUNCT
ejpam-5702	27	3	1	1	NUM
ejpam-5702	27	4	+	+	CCONJ
ejpam-5702	27	5	t)x	t)x	PUNCT
ejpam-5702	27	6	=	=	PUNCT
ejpam-5702	27	7	∞∑	∞∑	NUM
ejpam-5702	27	8	n=0	n=0	NUM
ejpam-5702	27	9	brn(x	brn(x	PROPN
ejpam-5702	27	10	)	)	PUNCT
ejpam-5702	27	11	tn	tn	PROPN
ejpam-5702	27	12	n	n	PROPN
ejpam-5702	27	13	!	!	PROPN
ejpam-5702	27	14	,	,	PUNCT
ejpam-5702	27	15	(	(	PUNCT
ejpam-5702	27	16	r	r	NOUN
ejpam-5702	27	17	∈	∈	PROPN
ejpam-5702	27	18	z	z	PROPN
ejpam-5702	27	19	)	)	PUNCT
ejpam-5702	27	20	,	,	PUNCT
ejpam-5702	27	21	(	(	PUNCT
ejpam-5702	27	22	see[17	see[17	PROPN
ejpam-5702	27	23	]	]	PUNCT
ejpam-5702	27	24	)	)	PUNCT
ejpam-5702	27	25	.	.	PUNCT
ejpam-5702	28	1	(	(	PUNCT
ejpam-5702	28	2	2	2	X
ejpam-5702	28	3	)	)	PUNCT
ejpam-5702	28	4	it	it	PRON
ejpam-5702	28	5	is	be	AUX
ejpam-5702	28	6	well	well	ADV
ejpam-5702	28	7	known	know	VERB
ejpam-5702	28	8	that	that	SCONJ
ejpam-5702	28	9	t(1	t(1	NOUN
ejpam-5702	28	10	+	+	CCONJ
ejpam-5702	28	11	t)x−1	t)x−1	ADP
ejpam-5702	28	12	log(1	log(1	NOUN
ejpam-5702	28	13	+	+	CCONJ
ejpam-5702	28	14	t	t	X
ejpam-5702	28	15	)	)	PUNCT
ejpam-5702	28	16	=	=	PUNCT
ejpam-5702	29	1	∞∑	∞∑	PRON
ejpam-5702	29	2	n=0	n=0	NUM
ejpam-5702	29	3	b(n	b(n	NOUN
ejpam-5702	29	4	)	)	PUNCT
ejpam-5702	29	5	n	n	CCONJ
ejpam-5702	29	6	(	(	PUNCT
ejpam-5702	29	7	x	x	X
ejpam-5702	29	8	)	)	PUNCT
ejpam-5702	29	9	tn	tn	PROPN
ejpam-5702	29	10	n	n	CCONJ
ejpam-5702	29	11	!	!	NUM
ejpam-5702	29	12	,	,	PUNCT
ejpam-5702	29	13	(	(	PUNCT
ejpam-5702	29	14	see[9	see[9	NOUN
ejpam-5702	29	15	]	]	PUNCT
ejpam-5702	29	16	,	,	PUNCT
ejpam-5702	29	17	[	[	X
ejpam-5702	29	18	22	22	NUM
ejpam-5702	29	19	]	]	PUNCT
ejpam-5702	29	20	,	,	PUNCT
ejpam-5702	30	1	[	[	X
ejpam-5702	30	2	5].[7	5].[7	NUM
ejpam-5702	30	3	]	]	PUNCT
ejpam-5702	30	4	)	)	PUNCT
ejpam-5702	30	5	.	.	PUNCT
ejpam-5702	31	1	(	(	PUNCT
ejpam-5702	31	2	3	3	X
ejpam-5702	31	3	)	)	PUNCT
ejpam-5702	31	4	where	where	SCONJ
ejpam-5702	31	5	the	the	DET
ejpam-5702	31	6	bernoulli	bernoulli	NOUN
ejpam-5702	31	7	polynomials	polynomial	NOUN
ejpam-5702	31	8	of	of	ADP
ejpam-5702	31	9	order	order	NOUN
ejpam-5702	31	10	α	α	PRON
ejpam-5702	31	11	which	which	PRON
ejpam-5702	31	12	are	be	AUX
ejpam-5702	31	13	given	give	VERB
ejpam-5702	31	14	by	by	ADP
ejpam-5702	31	15	(	(	PUNCT
ejpam-5702	31	16	t	t	NOUN
ejpam-5702	31	17	et	et	NOUN
ejpam-5702	31	18	−	−	NOUN
ejpam-5702	31	19	1	1	X
ejpam-5702	31	20	)	)	PUNCT
ejpam-5702	31	21	α	α	PRON
ejpam-5702	31	22	ext	ext	NOUN
ejpam-5702	31	23	=	=	PUNCT
ejpam-5702	32	1	∞∑	∞∑	NUM
ejpam-5702	32	2	n=0	n=0	NUM
ejpam-5702	32	3	bα	bα	NOUN
ejpam-5702	32	4	n	n	CCONJ
ejpam-5702	32	5	(	(	PUNCT
ejpam-5702	32	6	x	x	NOUN
ejpam-5702	32	7	)	)	PUNCT
ejpam-5702	32	8	tn	tn	PROPN
ejpam-5702	32	9	n	n	CCONJ
ejpam-5702	32	10	!	!	NUM
ejpam-5702	32	11	,	,	PUNCT
ejpam-5702	32	12	(	(	PUNCT
ejpam-5702	32	13	see[9	see[9	NOUN
ejpam-5702	32	14	]	]	PUNCT
ejpam-5702	32	15	,	,	PUNCT
ejpam-5702	32	16	[	[	X
ejpam-5702	32	17	22	22	NUM
ejpam-5702	32	18	]	]	PUNCT
ejpam-5702	32	19	,	,	PUNCT
ejpam-5702	32	20	[	[	X
ejpam-5702	32	21	5	5	NUM
ejpam-5702	32	22	]	]	PUNCT
ejpam-5702	32	23	,	,	PUNCT
ejpam-5702	32	24	[	[	X
ejpam-5702	32	25	29	29	NUM
ejpam-5702	32	26	]	]	PUNCT
ejpam-5702	32	27	,	,	PUNCT
ejpam-5702	32	28	[	[	X
ejpam-5702	32	29	8].[7	8].[7	NUM
ejpam-5702	32	30	]	]	X
ejpam-5702	32	31	)	)	PUNCT
ejpam-5702	32	32	.	.	PUNCT
ejpam-5702	33	1	(	(	PUNCT
ejpam-5702	33	2	4	4	X
ejpam-5702	33	3	)	)	PUNCT
ejpam-5702	33	4	from	from	ADP
ejpam-5702	33	5	(	(	PUNCT
ejpam-5702	33	6	1	1	NUM
ejpam-5702	33	7	)	)	PUNCT
ejpam-5702	33	8	and	and	CCONJ
ejpam-5702	33	9	(	(	PUNCT
ejpam-5702	33	10	3	3	NUM
ejpam-5702	33	11	)	)	PUNCT
ejpam-5702	33	12	,	,	PUNCT
ejpam-5702	33	13	we	we	PRON
ejpam-5702	33	14	note	note	VERB
ejpam-5702	33	15	that	that	SCONJ
ejpam-5702	33	16	bn(x	bn(x	NOUN
ejpam-5702	33	17	)	)	PUNCT
ejpam-5702	33	18	=	=	SYM
ejpam-5702	33	19	b(n	b(n	NOUN
ejpam-5702	33	20	)	)	PUNCT
ejpam-5702	33	21	n	n	CCONJ
ejpam-5702	33	22	(	(	PUNCT
ejpam-5702	33	23	x+	x+	PROPN
ejpam-5702	33	24	1	1	NUM
ejpam-5702	33	25	)	)	PUNCT
ejpam-5702	33	26	,	,	PUNCT
ejpam-5702	33	27	(	(	PUNCT
ejpam-5702	33	28	n	n	X
ejpam-5702	33	29	≥	≥	NOUN
ejpam-5702	33	30	0	0	NUM
ejpam-5702	33	31	)	)	PUNCT
ejpam-5702	33	32	,	,	PUNCT
ejpam-5702	33	33	(	(	PUNCT
ejpam-5702	33	34	see[9	see[9	NOUN
ejpam-5702	33	35	]	]	PUNCT
ejpam-5702	33	36	,	,	PUNCT
ejpam-5702	34	1	[	[	X
ejpam-5702	34	2	22	22	NUM
ejpam-5702	34	3	]	]	PUNCT
ejpam-5702	34	4	)	)	PUNCT
ejpam-5702	34	5	.	.	PUNCT
ejpam-5702	35	1	(	(	PUNCT
ejpam-5702	35	2	5	5	NUM
ejpam-5702	35	3	)	)	PUNCT
ejpam-5702	35	4	for	for	ADP
ejpam-5702	35	5	k	k	PROPN
ejpam-5702	35	6	∈	∈	PROPN
ejpam-5702	35	7	z	z	PROPN
ejpam-5702	35	8	,	,	PUNCT
ejpam-5702	35	9	the	the	DET
ejpam-5702	35	10	polylogarithm	polylogarithm	PROPN
ejpam-5702	35	11	function	function	NOUN
ejpam-5702	35	12	is	be	AUX
ejpam-5702	35	13	defined	define	VERB
ejpam-5702	35	14	by	by	ADP
ejpam-5702	35	15	lik(x	lik(x	NOUN
ejpam-5702	35	16	)	)	PUNCT
ejpam-5702	35	17	=	=	PROPN
ejpam-5702	36	1	∞∑	∞∑	NUM
ejpam-5702	36	2	n=1	n=1	PROPN
ejpam-5702	36	3	xn	xn	PROPN
ejpam-5702	36	4	nk	nk	PROPN
ejpam-5702	36	5	,	,	PUNCT
ejpam-5702	36	6	(	(	PUNCT
ejpam-5702	36	7	see[4	see[4	X
ejpam-5702	36	8	]	]	PUNCT
ejpam-5702	36	9	,	,	PUNCT
ejpam-5702	36	10	[	[	X
ejpam-5702	36	11	13	13	NUM
ejpam-5702	36	12	]	]	PUNCT
ejpam-5702	36	13	,	,	PUNCT
ejpam-5702	37	1	[	[	X
ejpam-5702	37	2	9	9	NUM
ejpam-5702	37	3	]	]	PUNCT
ejpam-5702	37	4	,	,	PUNCT
ejpam-5702	38	1	[	[	X
ejpam-5702	38	2	22	22	NUM
ejpam-5702	38	3	]	]	PUNCT
ejpam-5702	38	4	,	,	PUNCT
ejpam-5702	39	1	[	[	X
ejpam-5702	39	2	11	11	NUM
ejpam-5702	39	3	]	]	PUNCT
ejpam-5702	39	4	,	,	PUNCT
ejpam-5702	39	5	[	[	X
ejpam-5702	39	6	16	16	NUM
ejpam-5702	39	7	]	]	PUNCT
ejpam-5702	39	8	,	,	PUNCT
ejpam-5702	39	9	[	[	X
ejpam-5702	39	10	21	21	NUM
ejpam-5702	39	11	]	]	PUNCT
ejpam-5702	39	12	)	)	PUNCT
ejpam-5702	39	13	.	.	PUNCT
ejpam-5702	40	1	(	(	PUNCT
ejpam-5702	40	2	6	6	X
ejpam-5702	40	3	)	)	PUNCT
ejpam-5702	40	4	the	the	DET
ejpam-5702	40	5	poly	poly	ADJ
ejpam-5702	40	6	bernoulli	bernoulli	NOUN
ejpam-5702	40	7	polynomials	polynomial	NOUN
ejpam-5702	40	8	of	of	ADP
ejpam-5702	40	9	the	the	DET
ejpam-5702	40	10	second	second	ADJ
ejpam-5702	40	11	kind	kind	NOUN
ejpam-5702	40	12	are	be	AUX
ejpam-5702	40	13	defined	define	VERB
ejpam-5702	40	14	by	by	ADP
ejpam-5702	40	15	lik(1−	lik(1−	NOUN
ejpam-5702	40	16	e−t	e−t	NOUN
ejpam-5702	40	17	)	)	PUNCT
ejpam-5702	40	18	log(1	log(1	NOUN
ejpam-5702	41	1	+	+	CCONJ
ejpam-5702	41	2	t	t	X
ejpam-5702	41	3	)	)	PUNCT
ejpam-5702	41	4	(	(	PUNCT
ejpam-5702	41	5	1	1	NUM
ejpam-5702	41	6	+	+	CCONJ
ejpam-5702	41	7	t)x	t)x	PUNCT
ejpam-5702	41	8	=	=	PUNCT
ejpam-5702	41	9	∞∑	∞∑	PRON
ejpam-5702	41	10	n=0	n=0	NUM
ejpam-5702	41	11	b(k)n	b(k)n	NOUN
ejpam-5702	41	12	(	(	PUNCT
ejpam-5702	41	13	x	x	NOUN
ejpam-5702	41	14	)	)	PUNCT
ejpam-5702	41	15	tn	tn	PROPN
ejpam-5702	41	16	n	n	CCONJ
ejpam-5702	41	17	!	!	NUM
ejpam-5702	41	18	,	,	PUNCT
ejpam-5702	41	19	(	(	PUNCT
ejpam-5702	41	20	see[9	see[9	NOUN
ejpam-5702	41	21	]	]	PUNCT
ejpam-5702	41	22	,	,	PUNCT
ejpam-5702	41	23	[	[	X
ejpam-5702	41	24	23	23	NUM
ejpam-5702	41	25	]	]	PUNCT
ejpam-5702	41	26	)	)	PUNCT
ejpam-5702	41	27	.	.	PUNCT
ejpam-5702	42	1	(	(	PUNCT
ejpam-5702	42	2	7	7	X
ejpam-5702	42	3	)	)	PUNCT
ejpam-5702	42	4	for	for	ADP
ejpam-5702	42	5	k1	k1	NOUN
ejpam-5702	42	6	,	,	PUNCT
ejpam-5702	42	7	k2	k2	NOUN
ejpam-5702	42	8	,	,	PUNCT
ejpam-5702	42	9	.	.	PUNCT
ejpam-5702	42	10	.	.	PUNCT
ejpam-5702	42	11	.	.	PUNCT
ejpam-5702	43	1	,	,	PUNCT
ejpam-5702	43	2	kr	kr	PROPN
ejpam-5702	43	3	∈	∈	PROPN
ejpam-5702	43	4	z	z	PROPN
ejpam-5702	43	5	,	,	PUNCT
ejpam-5702	43	6	the	the	DET
ejpam-5702	43	7	multiple	multiple	ADJ
ejpam-5702	43	8	polylogarithm	polylogarithm	NOUN
ejpam-5702	43	9	is	be	AUX
ejpam-5702	43	10	defined	define	VERB
ejpam-5702	43	11	by	by	ADP
ejpam-5702	43	12	lik1,	lik1,	PROPN
ejpam-5702	43	13	...	...	PUNCT
ejpam-5702	43	14	,kr(z	,kr(z	PUNCT
ejpam-5702	43	15	)	)	PUNCT
ejpam-5702	44	1	=	=	PUNCT
ejpam-5702	44	2	∑	∑	PUNCT
ejpam-5702	44	3	0	0	NUM
ejpam-5702	44	4	<	<	X
ejpam-5702	44	5	n1<···<nr	n1<···<nr	PROPN
ejpam-5702	44	6	znr	znr	PROPN
ejpam-5702	44	7	nk1	nk1	PROPN
ejpam-5702	44	8	1	1	NUM
ejpam-5702	44	9	·	·	PUNCT
ejpam-5702	44	10	·	·	PUNCT
ejpam-5702	44	11	·	·	PUNCT
ejpam-5702	44	12	nkr	nkr	NUM
ejpam-5702	44	13	r	r	NOUN
ejpam-5702	44	14	,	,	PUNCT
ejpam-5702	44	15	(	(	PUNCT
ejpam-5702	44	16	|t|	|t|	ADP
ejpam-5702	44	17	<	<	X
ejpam-5702	44	18	1	1	NUM
ejpam-5702	44	19	)	)	PUNCT
ejpam-5702	44	20	,	,	PUNCT
ejpam-5702	44	21	(	(	PUNCT
ejpam-5702	44	22	see[9	see[9	NOUN
ejpam-5702	44	23	]	]	PUNCT
ejpam-5702	44	24	,	,	PUNCT
ejpam-5702	44	25	[	[	X
ejpam-5702	44	26	21	21	NUM
ejpam-5702	44	27	]	]	PUNCT
ejpam-5702	44	28	,	,	PUNCT
ejpam-5702	44	29	[	[	X
ejpam-5702	44	30	18	18	NUM
ejpam-5702	44	31	]	]	PUNCT
ejpam-5702	44	32	,	,	PUNCT
ejpam-5702	44	33	[	[	X
ejpam-5702	44	34	24	24	NUM
ejpam-5702	44	35	]	]	PUNCT
ejpam-5702	44	36	,	,	PUNCT
ejpam-5702	44	37	[	[	X
ejpam-5702	44	38	25	25	NUM
ejpam-5702	44	39	]	]	PUNCT
ejpam-5702	44	40	,	,	PUNCT
ejpam-5702	44	41	[	[	X
ejpam-5702	44	42	27	27	NUM
ejpam-5702	44	43	]	]	PUNCT
ejpam-5702	44	44	,	,	PUNCT
ejpam-5702	44	45	[	[	X
ejpam-5702	44	46	28	28	NUM
ejpam-5702	44	47	]	]	PUNCT
ejpam-5702	44	48	,	,	PUNCT
ejpam-5702	44	49	[	[	X
ejpam-5702	44	50	26	26	NUM
ejpam-5702	44	51	]	]	PUNCT
ejpam-5702	44	52	)	)	PUNCT
ejpam-5702	44	53	.	.	PUNCT
ejpam-5702	45	1	(	(	PUNCT
ejpam-5702	45	2	8)	8)	NUM
ejpam-5702	45	3	s.	s.	PROPN
ejpam-5702	45	4	h.	h.	PROPN
ejpam-5702	45	5	lee	lee	PROPN
ejpam-5702	45	6	,	,	PUNCT
ejpam-5702	45	7	l.	l.	PROPN
ejpam-5702	45	8	chen	chen	PROPN
ejpam-5702	45	9	/	/	SYM
ejpam-5702	45	10	eur	eur	PROPN
ejpam-5702	45	11	.	.	PUNCT
ejpam-5702	46	1	j.	j.	PROPN
ejpam-5702	46	2	pure	pure	PROPN
ejpam-5702	46	3	appl	appl	PROPN
ejpam-5702	46	4	.	.	PROPN
ejpam-5702	46	5	math	math	PROPN
ejpam-5702	46	6	,	,	PUNCT
ejpam-5702	46	7	18	18	NUM
ejpam-5702	46	8	(	(	PUNCT
ejpam-5702	46	9	1	1	NUM
ejpam-5702	46	10	)	)	PUNCT
ejpam-5702	46	11	(	(	PUNCT
ejpam-5702	46	12	2025	2025	NUM
ejpam-5702	46	13	)	)	PUNCT
ejpam-5702	46	14	,	,	PUNCT
ejpam-5702	46	15	5702	5702	NUM
ejpam-5702	46	16	3	3	NUM
ejpam-5702	46	17	of	of	ADP
ejpam-5702	46	18	13	13	NUM
ejpam-5702	46	19	by	by	ADP
ejpam-5702	46	20	(	(	PUNCT
ejpam-5702	46	21	8)	8)	NUM
ejpam-5702	46	22	,	,	PUNCT
ejpam-5702	46	23	we	we	PRON
ejpam-5702	46	24	note	note	VERB
ejpam-5702	46	25	that	that	SCONJ
ejpam-5702	46	26	d	d	PROPN
ejpam-5702	46	27	dt	dt	NOUN
ejpam-5702	46	28	lik,1(t	lik,1(t	PUNCT
ejpam-5702	46	29	)	)	PUNCT
ejpam-5702	46	30	=	=	SYM
ejpam-5702	46	31	1	1	NUM
ejpam-5702	46	32	1−	1−	NUM
ejpam-5702	46	33	t	t	PROPN
ejpam-5702	46	34	lik(t	lik(t	PROPN
ejpam-5702	46	35	)	)	PUNCT
ejpam-5702	46	36	,	,	PUNCT
ejpam-5702	46	37	(	(	PUNCT
ejpam-5702	46	38	see[9	see[9	NOUN
ejpam-5702	46	39	]	]	PUNCT
ejpam-5702	46	40	,	,	PUNCT
ejpam-5702	46	41	[	[	X
ejpam-5702	46	42	21	21	NUM
ejpam-5702	46	43	]	]	PUNCT
ejpam-5702	46	44	,	,	PUNCT
ejpam-5702	46	45	[	[	X
ejpam-5702	46	46	24	24	NUM
ejpam-5702	46	47	]	]	PUNCT
ejpam-5702	46	48	,	,	PUNCT
ejpam-5702	46	49	[	[	X
ejpam-5702	46	50	25	25	NUM
ejpam-5702	46	51	]	]	PUNCT
ejpam-5702	46	52	,	,	PUNCT
ejpam-5702	46	53	[	[	X
ejpam-5702	46	54	27	27	NUM
ejpam-5702	46	55	]	]	PUNCT
ejpam-5702	46	56	,	,	PUNCT
ejpam-5702	46	57	[	[	X
ejpam-5702	46	58	28	28	NUM
ejpam-5702	46	59	]	]	NUM
ejpam-5702	46	60	)	)	PUNCT
ejpam-5702	46	61	.	.	PUNCT
ejpam-5702	47	1	(	(	PUNCT
ejpam-5702	47	2	9	9	X
ejpam-5702	47	3	)	)	PUNCT
ejpam-5702	47	4	it	it	PRON
ejpam-5702	47	5	is	be	AUX
ejpam-5702	47	6	obvious	obvious	ADJ
ejpam-5702	47	7	that	that	SCONJ
ejpam-5702	47	8	li1,1(t	li1,1(t	PROPN
ejpam-5702	47	9	)	)	PUNCT
ejpam-5702	48	1	=	=	SYM
ejpam-5702	49	1	∫	∫	PROPN
ejpam-5702	49	2	t	t	NOUN
ejpam-5702	49	3	0	0	NUM
ejpam-5702	50	1	d	d	NOUN
ejpam-5702	50	2	dt	dt	NOUN
ejpam-5702	50	3	li1,1(t)dt	li1,1(t)dt	PROPN
ejpam-5702	50	4	=	=	SYM
ejpam-5702	50	5	∫	∫	PROPN
ejpam-5702	50	6	t	t	NOUN
ejpam-5702	50	7	0	0	NUM
ejpam-5702	50	8	1	1	NUM
ejpam-5702	50	9	1−	1−	NUM
ejpam-5702	50	10	t	t	NOUN
ejpam-5702	50	11	(	(	PUNCT
ejpam-5702	50	12	−log(1−	−log(1−	NOUN
ejpam-5702	50	13	t))dt	t))dt	NOUN
ejpam-5702	50	14	=	=	SYM
ejpam-5702	50	15	1	1	NUM
ejpam-5702	50	16	2	2	NUM
ejpam-5702	50	17	!	!	PUNCT
ejpam-5702	51	1	(	(	PUNCT
ejpam-5702	51	2	−log(1−	−log(1−	NOUN
ejpam-5702	51	3	t))2	t))2	NOUN
ejpam-5702	51	4	.	.	PUNCT
ejpam-5702	52	1	(	(	PUNCT
ejpam-5702	52	2	10	10	NUM
ejpam-5702	52	3	)	)	PUNCT
ejpam-5702	52	4	continuing	continue	VERB
ejpam-5702	52	5	this	this	DET
ejpam-5702	52	6	process	process	NOUN
ejpam-5702	52	7	in	in	ADP
ejpam-5702	52	8	(	(	PUNCT
ejpam-5702	52	9	10	10	NUM
ejpam-5702	52	10	)	)	PUNCT
ejpam-5702	52	11	,	,	PUNCT
ejpam-5702	52	12	we	we	PRON
ejpam-5702	52	13	have	have	VERB
ejpam-5702	52	14	li1,	li1,	X
ejpam-5702	52	15	...	...	PUNCT
ejpam-5702	52	16	,1(t	,1(t	PUNCT
ejpam-5702	52	17	)	)	PUNCT
ejpam-5702	53	1	=	=	SYM
ejpam-5702	53	2	1	1	NUM
ejpam-5702	53	3	r	r	NOUN
ejpam-5702	53	4	!	!	PUNCT
ejpam-5702	54	1	(	(	PUNCT
ejpam-5702	54	2	−log(1−	−log(1−	NOUN
ejpam-5702	54	3	t))r	t))r	NOUN
ejpam-5702	54	4	,	,	PUNCT
ejpam-5702	54	5	(	(	PUNCT
ejpam-5702	54	6	r	r	NOUN
ejpam-5702	54	7	∈	∈	PROPN
ejpam-5702	54	8	n	n	CCONJ
ejpam-5702	54	9	)	)	PUNCT
ejpam-5702	54	10	,	,	PUNCT
ejpam-5702	54	11	(	(	PUNCT
ejpam-5702	54	12	see[3	see[3	X
ejpam-5702	54	13	]	]	PUNCT
ejpam-5702	54	14	,	,	PUNCT
ejpam-5702	54	15	[	[	X
ejpam-5702	54	16	9	9	NUM
ejpam-5702	54	17	]	]	PUNCT
ejpam-5702	54	18	,	,	PUNCT
ejpam-5702	54	19	[	[	X
ejpam-5702	54	20	21	21	NUM
ejpam-5702	54	21	]	]	PUNCT
ejpam-5702	54	22	,	,	PUNCT
ejpam-5702	54	23	[	[	X
ejpam-5702	54	24	24	24	NUM
ejpam-5702	54	25	]	]	PUNCT
ejpam-5702	54	26	,	,	PUNCT
ejpam-5702	54	27	[	[	X
ejpam-5702	54	28	25	25	NUM
ejpam-5702	54	29	]	]	PUNCT
ejpam-5702	54	30	,	,	PUNCT
ejpam-5702	54	31	[	[	X
ejpam-5702	54	32	27	27	NUM
ejpam-5702	54	33	]	]	PUNCT
ejpam-5702	54	34	,	,	PUNCT
ejpam-5702	54	35	[	[	X
ejpam-5702	54	36	28	28	NUM
ejpam-5702	54	37	]	]	NUM
ejpam-5702	54	38	)	)	PUNCT
ejpam-5702	54	39	.	.	PUNCT
ejpam-5702	55	1	(	(	PUNCT
ejpam-5702	55	2	11	11	NUM
ejpam-5702	55	3	)	)	PUNCT
ejpam-5702	55	4	throught	throught	NOUN
ejpam-5702	55	5	this	this	DET
ejpam-5702	55	6	paper	paper	NOUN
ejpam-5702	55	7	,	,	PUNCT
ejpam-5702	55	8	we	we	PRON
ejpam-5702	55	9	assume	assume	VERB
ejpam-5702	55	10	that	that	SCONJ
ejpam-5702	55	11	y	y	PROPN
ejpam-5702	55	12	is	be	AUX
ejpam-5702	55	13	a	a	DET
ejpam-5702	55	14	random	random	ADJ
ejpam-5702	55	15	variable	variable	NOUN
ejpam-5702	55	16	such	such	ADJ
ejpam-5702	55	17	that	that	SCONJ
ejpam-5702	55	18	the	the	DET
ejpam-5702	55	19	moment	moment	NOUN
ejpam-5702	55	20	generating	generate	VERB
ejpam-5702	55	21	function	function	NOUN
ejpam-5702	55	22	of	of	ADP
ejpam-5702	55	23	y	y	PROPN
ejpam-5702	55	24	given	give	VERB
ejpam-5702	55	25	by	by	ADP
ejpam-5702	55	26	e[ey	e[ey	PROPN
ejpam-5702	55	27	t	t	PROPN
ejpam-5702	55	28	]	]	X
ejpam-5702	55	29	=	=	PUNCT
ejpam-5702	56	1	∞∑	∞∑	NUM
ejpam-5702	56	2	n=0	n=0	NUM
ejpam-5702	56	3	e[y	e[y	ADJ
ejpam-5702	56	4	n	n	X
ejpam-5702	56	5	]	]	PUNCT
ejpam-5702	56	6	tn	tn	PROPN
ejpam-5702	56	7	n	n	CCONJ
ejpam-5702	56	8	!	!	PROPN
ejpam-5702	56	9	,	,	PUNCT
ejpam-5702	56	10	(	(	PUNCT
ejpam-5702	56	11	|t|	|t|	ADP
ejpam-5702	56	12	<	<	X
ejpam-5702	56	13	r	r	NOUN
ejpam-5702	56	14	)	)	PUNCT
ejpam-5702	56	15	,	,	PUNCT
ejpam-5702	56	16	(	(	PUNCT
ejpam-5702	56	17	see[15	see[15	PROPN
ejpam-5702	56	18	]	]	PUNCT
ejpam-5702	56	19	,	,	PUNCT
ejpam-5702	56	20	[	[	X
ejpam-5702	56	21	12	12	NUM
ejpam-5702	56	22	]	]	PUNCT
ejpam-5702	56	23	,	,	PUNCT
ejpam-5702	56	24	[	[	X
ejpam-5702	56	25	13	13	NUM
ejpam-5702	56	26	]	]	PUNCT
ejpam-5702	56	27	,	,	PUNCT
ejpam-5702	56	28	[	[	X
ejpam-5702	56	29	19	19	NUM
ejpam-5702	56	30	]	]	PUNCT
ejpam-5702	56	31	,	,	PUNCT
ejpam-5702	56	32	[	[	X
ejpam-5702	56	33	10	10	NUM
ejpam-5702	56	34	]	]	PUNCT
ejpam-5702	56	35	,	,	PUNCT
ejpam-5702	56	36	[	[	X
ejpam-5702	56	37	30	30	NUM
ejpam-5702	56	38	]	]	PUNCT
ejpam-5702	56	39	)	)	PUNCT
ejpam-5702	56	40	.	.	PUNCT
ejpam-5702	57	1	(	(	PUNCT
ejpam-5702	57	2	12	12	NUM
ejpam-5702	57	3	)	)	PUNCT
ejpam-5702	57	4	exists	exist	VERB
ejpam-5702	57	5	for	for	ADP
ejpam-5702	57	6	some	some	DET
ejpam-5702	57	7	r	r	NOUN
ejpam-5702	57	8	>	>	X
ejpam-5702	57	9	0	0	X
ejpam-5702	57	10	.	.	PUNCT
ejpam-5702	58	1	let	let	VERB
ejpam-5702	58	2	(	(	PUNCT
ejpam-5702	58	3	yi)i≥1	yi)i≥1	NOUN
ejpam-5702	58	4	be	be	AUX
ejpam-5702	58	5	a	a	DET
ejpam-5702	58	6	sequence	sequence	NOUN
ejpam-5702	58	7	of	of	ADP
ejpam-5702	58	8	mutually	mutually	ADV
ejpam-5702	58	9	independent	independent	ADJ
ejpam-5702	58	10	copies	copy	NOUN
ejpam-5702	58	11	of	of	ADP
ejpam-5702	58	12	random	random	ADJ
ejpam-5702	58	13	variable	variable	ADJ
ejpam-5702	58	14	y	y	NOUN
ejpam-5702	58	15	,	,	PUNCT
ejpam-5702	58	16	and	and	CCONJ
ejpam-5702	58	17	let	let	VERB
ejpam-5702	58	18	sn	sn	PROPN
ejpam-5702	58	19	=	=	PUNCT
ejpam-5702	58	20	y1	y1	PROPN
ejpam-5702	58	21	+	+	NUM
ejpam-5702	58	22	·	·	PUNCT
ejpam-5702	58	23	·	·	PUNCT
ejpam-5702	58	24	·	·	PUNCT
ejpam-5702	59	1	+	+	CCONJ
ejpam-5702	59	2	yn	yn	PROPN
ejpam-5702	59	3	,	,	PUNCT
ejpam-5702	59	4	(	(	PUNCT
ejpam-5702	59	5	n	n	CCONJ
ejpam-5702	59	6	≥	≥	NOUN
ejpam-5702	59	7	1	1	NUM
ejpam-5702	59	8	)	)	PUNCT
ejpam-5702	59	9	,	,	PUNCT
ejpam-5702	59	10	with	with	ADP
ejpam-5702	59	11	s0	s0	PROPN
ejpam-5702	59	12	=	=	PUNCT
ejpam-5702	59	13	0	0	PROPN
ejpam-5702	59	14	.	.	PUNCT
ejpam-5702	60	1	a	a	DET
ejpam-5702	60	2	continuous	continuous	ADJ
ejpam-5702	60	3	random	random	ADJ
ejpam-5702	60	4	variable	variable	NOUN
ejpam-5702	60	5	y	y	PROPN
ejpam-5702	60	6	whose	whose	DET
ejpam-5702	60	7	density	density	NOUN
ejpam-5702	60	8	function	function	NOUN
ejpam-5702	60	9	is	be	AUX
ejpam-5702	60	10	given	give	VERB
ejpam-5702	60	11	by	by	ADP
ejpam-5702	60	12	f(y	f(y	NOUN
ejpam-5702	60	13	)	)	PUNCT
ejpam-5702	60	14	=	=	PRON
ejpam-5702	60	15	{	{	PUNCT
ejpam-5702	60	16	βe−βy	βe−βy	X
ejpam-5702	60	17	(	(	PUNCT
ejpam-5702	60	18	βy)α−1	βy)α−1	X
ejpam-5702	60	19	γ(α	γ(α	NOUN
ejpam-5702	60	20	)	)	PUNCT
ejpam-5702	60	21	,	,	PUNCT
ejpam-5702	60	22	if	if	SCONJ
ejpam-5702	60	23	y	y	PROPN
ejpam-5702	60	24	>	>	X
ejpam-5702	60	25	0	0	PROPN
ejpam-5702	60	26	,	,	PUNCT
ejpam-5702	60	27	0	0	NUM
ejpam-5702	60	28	,	,	PUNCT
ejpam-5702	60	29	if	if	SCONJ
ejpam-5702	60	30	y	y	PROPN
ejpam-5702	60	31	≤	≤	PROPN
ejpam-5702	60	32	0	0	NUM
ejpam-5702	60	33	,	,	PUNCT
ejpam-5702	60	34	(	(	PUNCT
ejpam-5702	60	35	see[13	see[13	PROPN
ejpam-5702	60	36	]	]	PUNCT
ejpam-5702	60	37	,	,	PUNCT
ejpam-5702	60	38	[	[	X
ejpam-5702	60	39	16	16	NUM
ejpam-5702	60	40	]	]	PUNCT
ejpam-5702	60	41	,	,	PUNCT
ejpam-5702	60	42	[	[	X
ejpam-5702	60	43	20	20	NUM
ejpam-5702	60	44	]	]	NUM
ejpam-5702	60	45	)	)	PUNCT
ejpam-5702	60	46	,	,	PUNCT
ejpam-5702	60	47	(	(	PUNCT
ejpam-5702	60	48	13	13	NUM
ejpam-5702	60	49	)	)	PUNCT
ejpam-5702	60	50	for	for	ADP
ejpam-5702	60	51	some	some	DET
ejpam-5702	60	52	α	α	NOUN
ejpam-5702	60	53	,	,	PUNCT
ejpam-5702	60	54	β	β	X
ejpam-5702	60	55	>	>	X
ejpam-5702	60	56	0	0	NUM
ejpam-5702	60	57	is	be	AUX
ejpam-5702	60	58	said	say	VERB
ejpam-5702	60	59	to	to	PART
ejpam-5702	60	60	be	be	AUX
ejpam-5702	60	61	the	the	DET
ejpam-5702	60	62	gamma	gamma	NOUN
ejpam-5702	60	63	random	random	ADJ
ejpam-5702	60	64	variable	variable	NOUN
ejpam-5702	60	65	with	with	ADP
ejpam-5702	60	66	parameters	parameter	NOUN
ejpam-5702	60	67	α	α	NOUN
ejpam-5702	60	68	,	,	PUNCT
ejpam-5702	60	69	β	β	PROPN
ejpam-5702	60	70	,	,	PUNCT
ejpam-5702	60	71	which	which	PRON
ejpam-5702	60	72	is	be	AUX
ejpam-5702	60	73	denoted	denote	VERB
ejpam-5702	60	74	by	by	ADP
ejpam-5702	60	75	y	y	PROPN
ejpam-5702	60	76	∼	∼	NOUN
ejpam-5702	60	77	γ(α	γ(α	NOUN
ejpam-5702	60	78	,	,	PUNCT
ejpam-5702	60	79	β	β	NOUN
ejpam-5702	60	80	)	)	PUNCT
ejpam-5702	60	81	.	.	PUNCT
ejpam-5702	61	1	the	the	DET
ejpam-5702	61	2	stirling	stirling	NOUN
ejpam-5702	61	3	number	number	NOUN
ejpam-5702	61	4	of	of	ADP
ejpam-5702	61	5	the	the	DET
ejpam-5702	61	6	second	second	ADJ
ejpam-5702	61	7	kind	kind	NOUN
ejpam-5702	61	8	are	be	AUX
ejpam-5702	61	9	defined	define	VERB
ejpam-5702	61	10	by	by	ADP
ejpam-5702	61	11	xn	xn	PROPN
ejpam-5702	61	12	=	=	SYM
ejpam-5702	61	13	n∑	n∑	PROPN
ejpam-5702	61	14	k=0	k=0	PROPN
ejpam-5702	61	15	s2(n	s2(n	PROPN
ejpam-5702	61	16	,	,	PUNCT
ejpam-5702	61	17	k)(x)k	k)(x)k	NOUN
ejpam-5702	61	18	,	,	PUNCT
ejpam-5702	61	19	(	(	PUNCT
ejpam-5702	61	20	see[2	see[2	X
ejpam-5702	61	21	]	]	PUNCT
ejpam-5702	61	22	,	,	PUNCT
ejpam-5702	61	23	[	[	X
ejpam-5702	61	24	19	19	NUM
ejpam-5702	61	25	]	]	PUNCT
ejpam-5702	61	26	,	,	PUNCT
ejpam-5702	62	1	[	[	X
ejpam-5702	62	2	6	6	NUM
ejpam-5702	62	3	]	]	PUNCT
ejpam-5702	62	4	,	,	PUNCT
ejpam-5702	62	5	[	[	X
ejpam-5702	62	6	14	14	NUM
ejpam-5702	62	7	]	]	PUNCT
ejpam-5702	62	8	,	,	PUNCT
ejpam-5702	62	9	[	[	X
ejpam-5702	62	10	29	29	NUM
ejpam-5702	62	11	]	]	PUNCT
ejpam-5702	62	12	)	)	PUNCT
ejpam-5702	62	13	.	.	PUNCT
ejpam-5702	63	1	(	(	PUNCT
ejpam-5702	63	2	14	14	NUM
ejpam-5702	63	3	)	)	PUNCT
ejpam-5702	63	4	from	from	ADP
ejpam-5702	63	5	(	(	PUNCT
ejpam-5702	63	6	14	14	NUM
ejpam-5702	63	7	)	)	PUNCT
ejpam-5702	63	8	,	,	PUNCT
ejpam-5702	63	9	we	we	PRON
ejpam-5702	63	10	also	also	ADV
ejpam-5702	63	11	derive	derive	VERB
ejpam-5702	63	12	the	the	DET
ejpam-5702	63	13	generating	generate	VERB
ejpam-5702	63	14	function	function	NOUN
ejpam-5702	63	15	as	as	SCONJ
ejpam-5702	63	16	follows	follow	VERB
ejpam-5702	63	17	.	.	PUNCT
ejpam-5702	64	1	1	1	NUM
ejpam-5702	64	2	k	k	X
ejpam-5702	64	3	!	!	PUNCT
ejpam-5702	65	1	(	(	PUNCT
ejpam-5702	65	2	et	et	X
ejpam-5702	65	3	−	−	PROPN
ejpam-5702	65	4	1)k	1)k	NUM
ejpam-5702	65	5	=	=	PUNCT
ejpam-5702	66	1	∞∑	∞∑	NUM
ejpam-5702	66	2	n	n	CCONJ
ejpam-5702	66	3	=	=	SYM
ejpam-5702	66	4	k	k	PROPN
ejpam-5702	66	5	s2(n	s2(n	PROPN
ejpam-5702	66	6	,	,	PUNCT
ejpam-5702	66	7	k	k	NOUN
ejpam-5702	66	8	)	)	PUNCT
ejpam-5702	66	9	tn	tn	PROPN
ejpam-5702	66	10	n	n	PROPN
ejpam-5702	66	11	!	!	PROPN
ejpam-5702	66	12	,	,	PUNCT
ejpam-5702	66	13	(	(	PUNCT
ejpam-5702	66	14	see[2	see[2	NOUN
ejpam-5702	66	15	]	]	PUNCT
ejpam-5702	66	16	,	,	PUNCT
ejpam-5702	66	17	[	[	X
ejpam-5702	66	18	19	19	NUM
ejpam-5702	66	19	]	]	PUNCT
ejpam-5702	66	20	,	,	PUNCT
ejpam-5702	66	21	[	[	X
ejpam-5702	66	22	6	6	NUM
ejpam-5702	66	23	]	]	PUNCT
ejpam-5702	66	24	,	,	PUNCT
ejpam-5702	66	25	[	[	X
ejpam-5702	66	26	14	14	NUM
ejpam-5702	66	27	]	]	PUNCT
ejpam-5702	66	28	)	)	PUNCT
ejpam-5702	66	29	.	.	PUNCT
ejpam-5702	67	1	(	(	PUNCT
ejpam-5702	67	2	15	15	X
ejpam-5702	67	3	)	)	PUNCT
ejpam-5702	67	4	it	it	PRON
ejpam-5702	67	5	is	be	AUX
ejpam-5702	67	6	well	well	ADV
ejpam-5702	67	7	known	know	VERB
ejpam-5702	67	8	that	that	SCONJ
ejpam-5702	67	9	the	the	DET
ejpam-5702	67	10	lah	lah	PROPN
ejpam-5702	67	11	numbers	number	NOUN
ejpam-5702	67	12	are	be	AUX
ejpam-5702	67	13	defined	define	VERB
ejpam-5702	67	14	by	by	ADP
ejpam-5702	67	15	1	1	NUM
ejpam-5702	67	16	k	k	NOUN
ejpam-5702	67	17	!	!	PUNCT
ejpam-5702	68	1	(	(	PUNCT
ejpam-5702	68	2	t	t	PROPN
ejpam-5702	68	3	1−	1−	NUM
ejpam-5702	68	4	t	t	NOUN
ejpam-5702	68	5	)	)	PUNCT
ejpam-5702	68	6	k	k	X
ejpam-5702	69	1	=	=	PUNCT
ejpam-5702	69	2	∞∑	∞∑	NUM
ejpam-5702	69	3	n	n	CCONJ
ejpam-5702	69	4	=	=	SYM
ejpam-5702	69	5	k	k	PROPN
ejpam-5702	69	6	l(n	l(n	PROPN
ejpam-5702	69	7	,	,	PUNCT
ejpam-5702	69	8	k	k	NOUN
ejpam-5702	69	9	)	)	PUNCT
ejpam-5702	69	10	tn	tn	PROPN
ejpam-5702	69	11	n	n	PROPN
ejpam-5702	69	12	!	!	PROPN
ejpam-5702	69	13	,	,	PUNCT
ejpam-5702	69	14	(	(	PUNCT
ejpam-5702	69	15	r	r	NOUN
ejpam-5702	69	16	≥	≥	NOUN
ejpam-5702	69	17	0	0	NUM
ejpam-5702	69	18	)	)	PUNCT
ejpam-5702	69	19	,	,	PUNCT
ejpam-5702	69	20	(	(	PUNCT
ejpam-5702	69	21	see[13	see[13	PROPN
ejpam-5702	69	22	]	]	PUNCT
ejpam-5702	69	23	,	,	PUNCT
ejpam-5702	69	24	[	[	X
ejpam-5702	69	25	6	6	NUM
ejpam-5702	69	26	]	]	PUNCT
ejpam-5702	69	27	)	)	PUNCT
ejpam-5702	69	28	.	.	PUNCT
ejpam-5702	70	1	(	(	PUNCT
ejpam-5702	70	2	16	16	NUM
ejpam-5702	70	3	)	)	PUNCT
ejpam-5702	70	4	the	the	DET
ejpam-5702	70	5	probabilistic	probabilistic	ADJ
ejpam-5702	70	6	stirling	stirling	NOUN
ejpam-5702	70	7	number	number	NOUN
ejpam-5702	70	8	of	of	ADP
ejpam-5702	70	9	the	the	DET
ejpam-5702	70	10	second	second	ADJ
ejpam-5702	70	11	kind	kind	NOUN
ejpam-5702	70	12	associated	associate	VERB
ejpam-5702	70	13	with	with	ADP
ejpam-5702	70	14	y	y	PROPN
ejpam-5702	70	15	are	be	AUX
ejpam-5702	70	16	defined	define	VERB
ejpam-5702	70	17	by	by	ADP
ejpam-5702	70	18	1	1	NUM
ejpam-5702	70	19	k	k	NOUN
ejpam-5702	70	20	!	!	PUNCT
ejpam-5702	71	1	(	(	PUNCT
ejpam-5702	71	2	e[ey	e[ey	INTJ
ejpam-5702	71	3	t]−	t]−	NOUN
ejpam-5702	71	4	1)k	1)k	NUM
ejpam-5702	71	5	=	=	SYM
ejpam-5702	72	1	∞∑	∞∑	NUM
ejpam-5702	72	2	n	n	CCONJ
ejpam-5702	72	3	=	=	SYM
ejpam-5702	72	4	k	k	X
ejpam-5702	72	5	{	{	PUNCT
ejpam-5702	72	6	n	n	NOUN
ejpam-5702	72	7	k	k	PROPN
ejpam-5702	72	8	}	}	PUNCT
ejpam-5702	72	9	y	y	PROPN
ejpam-5702	72	10	tn	tn	PROPN
ejpam-5702	72	11	n	n	CCONJ
ejpam-5702	72	12	!	!	PROPN
ejpam-5702	72	13	,	,	PUNCT
ejpam-5702	72	14	(	(	PUNCT
ejpam-5702	72	15	see[1	see[1	X
ejpam-5702	72	16	]	]	PUNCT
ejpam-5702	72	17	,	,	PUNCT
ejpam-5702	72	18	[	[	X
ejpam-5702	72	19	13	13	NUM
ejpam-5702	72	20	]	]	PUNCT
ejpam-5702	72	21	,	,	PUNCT
ejpam-5702	72	22	[	[	X
ejpam-5702	72	23	19	19	NUM
ejpam-5702	72	24	]	]	NUM
ejpam-5702	72	25	)	)	PUNCT
ejpam-5702	72	26	.	.	PUNCT
ejpam-5702	73	1	(	(	PUNCT
ejpam-5702	73	2	17	17	NUM
ejpam-5702	73	3	)	)	PUNCT
ejpam-5702	73	4	s.	s.	PROPN
ejpam-5702	73	5	h.	h.	PROPN
ejpam-5702	73	6	lee	lee	PROPN
ejpam-5702	73	7	,	,	PUNCT
ejpam-5702	73	8	l.	l.	PROPN
ejpam-5702	73	9	chen	chen	PROPN
ejpam-5702	73	10	/	/	SYM
ejpam-5702	73	11	eur	eur	PROPN
ejpam-5702	73	12	.	.	PUNCT
ejpam-5702	74	1	j.	j.	PROPN
ejpam-5702	74	2	pure	pure	PROPN
ejpam-5702	74	3	appl	appl	PROPN
ejpam-5702	74	4	.	.	PROPN
ejpam-5702	74	5	math	math	PROPN
ejpam-5702	74	6	,	,	PUNCT
ejpam-5702	74	7	18	18	NUM
ejpam-5702	74	8	(	(	PUNCT
ejpam-5702	74	9	1	1	NUM
ejpam-5702	74	10	)	)	PUNCT
ejpam-5702	74	11	(	(	PUNCT
ejpam-5702	74	12	2025	2025	NUM
ejpam-5702	74	13	)	)	PUNCT
ejpam-5702	74	14	,	,	PUNCT
ejpam-5702	74	15	5702	5702	NUM
ejpam-5702	74	16	4	4	NUM
ejpam-5702	74	17	of	of	ADP
ejpam-5702	74	18	13	13	NUM
ejpam-5702	74	19	in	in	ADP
ejpam-5702	74	20	[	[	X
ejpam-5702	74	21	13	13	NUM
ejpam-5702	74	22	]	]	PUNCT
ejpam-5702	74	23	.	.	PUNCT
ejpam-5702	75	1	kim	kim	PROPN
ejpam-5702	75	2	also	also	ADV
ejpam-5702	75	3	considered	consider	VERB
ejpam-5702	75	4	the	the	DET
ejpam-5702	75	5	probabilistic	probabilistic	ADJ
ejpam-5702	75	6	multi	multi	ADJ
ejpam-5702	75	7	-	-	ADJ
ejpam-5702	75	8	poly	poly	ADJ
ejpam-5702	75	9	-	-	PUNCT
ejpam-5702	75	10	bernoulli	bernoulli	NOUN
ejpam-5702	75	11	polynomials	polynomial	NOUN
ejpam-5702	75	12	associated	associate	VERB
ejpam-5702	75	13	with	with	ADP
ejpam-5702	75	14	y	y	PROPN
ejpam-5702	75	15	by	by	ADP
ejpam-5702	75	16	lik1,	lik1,	PROPN
ejpam-5702	75	17	...	...	PUNCT
ejpam-5702	75	18	,kr	,kr	PUNCT
ejpam-5702	75	19	(	(	PUNCT
ejpam-5702	75	20	1−	1−	NUM
ejpam-5702	75	21	e[e−y	e[e−y	PROPN
ejpam-5702	75	22	t	t	PROPN
ejpam-5702	75	23	]	]	PUNCT
ejpam-5702	75	24	)	)	PUNCT
ejpam-5702	76	1	(	(	PUNCT
ejpam-5702	76	2	1−	1−	NUM
ejpam-5702	76	3	e[e−y	e[e−y	PROPN
ejpam-5702	76	4	t])r	t])r	PROPN
ejpam-5702	76	5	(	(	PUNCT
ejpam-5702	76	6	e[e−y	e[e−y	PROPN
ejpam-5702	76	7	t	t	PROPN
ejpam-5702	76	8	]	]	PUNCT
ejpam-5702	76	9	)	)	PUNCT
ejpam-5702	76	10	x	x	PUNCT
ejpam-5702	77	1	=	=	PUNCT
ejpam-5702	77	2	∞∑	∞∑	NUM
ejpam-5702	77	3	n=0	n=0	PROPN
ejpam-5702	77	4	b	b	NOUN
ejpam-5702	77	5	(	(	PUNCT
ejpam-5702	77	6	k1,	k1,	NOUN
ejpam-5702	77	7	...	...	SYM
ejpam-5702	77	8	,kr	,kr	SYM
ejpam-5702	77	9	)	)	PUNCT
ejpam-5702	77	10	n	n	CCONJ
ejpam-5702	77	11	,	,	PUNCT
ejpam-5702	77	12	y	y	PROPN
ejpam-5702	77	13	(	(	PUNCT
ejpam-5702	77	14	x	x	NOUN
ejpam-5702	77	15	)	)	PUNCT
ejpam-5702	77	16	tn	tn	PROPN
ejpam-5702	77	17	n	n	CCONJ
ejpam-5702	77	18	!	!	PROPN
ejpam-5702	77	19	,	,	PUNCT
ejpam-5702	77	20	(	(	PUNCT
ejpam-5702	77	21	see[13	see[13	PROPN
ejpam-5702	77	22	]	]	PUNCT
ejpam-5702	77	23	)	)	PUNCT
ejpam-5702	77	24	.	.	PUNCT
ejpam-5702	78	1	(	(	PUNCT
ejpam-5702	78	2	18	18	NUM
ejpam-5702	78	3	)	)	SYM
ejpam-5702	78	4	2	2	NUM
ejpam-5702	78	5	.	.	PUNCT
ejpam-5702	78	6	probabilistic	probabilistic	ADJ
ejpam-5702	78	7	poly	poly	ADJ
ejpam-5702	78	8	and	and	CCONJ
ejpam-5702	78	9	multiple	multiple	ADJ
ejpam-5702	78	10	poly	poly	ADJ
ejpam-5702	78	11	bernoulli	bernoulli	NOUN
ejpam-5702	78	12	polynomials	polynomial	NOUN
ejpam-5702	78	13	of	of	ADP
ejpam-5702	78	14	the	the	DET
ejpam-5702	78	15	second	second	ADJ
ejpam-5702	78	16	kind	kind	NOUN
ejpam-5702	78	17	in	in	ADP
ejpam-5702	78	18	this	this	DET
ejpam-5702	78	19	section	section	NOUN
ejpam-5702	79	1	,	,	PUNCT
ejpam-5702	79	2	we	we	PRON
ejpam-5702	79	3	consider	consider	VERB
ejpam-5702	79	4	probabilistic	probabilistic	ADJ
ejpam-5702	79	5	poly	poly	ADJ
ejpam-5702	79	6	bernoulli	bernoulli	NOUN
ejpam-5702	79	7	polynomials	polynomial	NOUN
ejpam-5702	79	8	of	of	ADP
ejpam-5702	79	9	the	the	DET
ejpam-5702	79	10	second	second	ADJ
ejpam-5702	79	11	kind	kind	NOUN
ejpam-5702	79	12	associated	associate	VERB
ejpam-5702	79	13	with	with	ADP
ejpam-5702	79	14	y	y	PRON
ejpam-5702	79	15	which	which	PRON
ejpam-5702	79	16	are	be	AUX
ejpam-5702	79	17	given	give	VERB
ejpam-5702	79	18	by	by	ADP
ejpam-5702	79	19	lik(1−	lik(1−	PROPN
ejpam-5702	79	20	e[e−y	e[e−y	PROPN
ejpam-5702	79	21	t	t	PROPN
ejpam-5702	79	22	]	]	PUNCT
ejpam-5702	79	23	)	)	PUNCT
ejpam-5702	79	24	log(1	log(1	NOUN
ejpam-5702	80	1	+	+	CCONJ
ejpam-5702	80	2	t	t	X
ejpam-5702	80	3	)	)	PUNCT
ejpam-5702	80	4	(	(	PUNCT
ejpam-5702	80	5	1	1	NUM
ejpam-5702	80	6	+	+	CCONJ
ejpam-5702	80	7	t)x	t)x	PUNCT
ejpam-5702	80	8	=	=	PUNCT
ejpam-5702	80	9	∞∑	∞∑	NUM
ejpam-5702	80	10	n=0	n=0	NUM
ejpam-5702	80	11	b	b	NOUN
ejpam-5702	80	12	(	(	PUNCT
ejpam-5702	80	13	k	k	NOUN
ejpam-5702	80	14	)	)	PUNCT
ejpam-5702	80	15	n	n	CCONJ
ejpam-5702	80	16	,	,	PUNCT
ejpam-5702	80	17	y	y	PROPN
ejpam-5702	80	18	(	(	PUNCT
ejpam-5702	80	19	x	x	NOUN
ejpam-5702	80	20	)	)	PUNCT
ejpam-5702	80	21	tn	tn	PROPN
ejpam-5702	80	22	n	n	NUM
ejpam-5702	80	23	!	!	PUNCT
ejpam-5702	80	24	.	.	PUNCT
ejpam-5702	81	1	(	(	PUNCT
ejpam-5702	81	2	19	19	NUM
ejpam-5702	81	3	)	)	PUNCT
ejpam-5702	81	4	when	when	SCONJ
ejpam-5702	81	5	x	x	X
ejpam-5702	81	6	=	=	SYM
ejpam-5702	81	7	0	0	NUM
ejpam-5702	81	8	,	,	PUNCT
ejpam-5702	81	9	b	b	PROPN
ejpam-5702	81	10	(	(	PUNCT
ejpam-5702	81	11	k	k	NOUN
ejpam-5702	81	12	)	)	PUNCT
ejpam-5702	81	13	n	n	CCONJ
ejpam-5702	81	14	,	,	PUNCT
ejpam-5702	81	15	y	y	PROPN
ejpam-5702	81	16	(	(	PUNCT
ejpam-5702	81	17	0	0	NUM
ejpam-5702	81	18	)	)	PUNCT
ejpam-5702	81	19	=	=	SYM
ejpam-5702	81	20	b	b	X
ejpam-5702	81	21	(	(	PUNCT
ejpam-5702	81	22	k	k	NOUN
ejpam-5702	81	23	)	)	PUNCT
ejpam-5702	81	24	n	n	CCONJ
ejpam-5702	81	25	,	,	PUNCT
ejpam-5702	81	26	y	y	PROPN
ejpam-5702	81	27	are	be	AUX
ejpam-5702	81	28	called	call	VERB
ejpam-5702	81	29	probabilistic	probabilistic	ADJ
ejpam-5702	81	30	multiple	multiple	ADJ
ejpam-5702	81	31	poly	poly	ADJ
ejpam-5702	81	32	bernoulli	bernoulli	NOUN
ejpam-5702	81	33	numbers	number	NOUN
ejpam-5702	81	34	of	of	ADP
ejpam-5702	81	35	the	the	DET
ejpam-5702	81	36	second	second	ADJ
ejpam-5702	81	37	kind	kind	NOUN
ejpam-5702	81	38	.	.	PUNCT
ejpam-5702	82	1	from	from	ADP
ejpam-5702	82	2	(	(	PUNCT
ejpam-5702	82	3	19	19	NUM
ejpam-5702	82	4	)	)	PUNCT
ejpam-5702	82	5	,	,	PUNCT
ejpam-5702	82	6	we	we	PRON
ejpam-5702	82	7	have	have	VERB
ejpam-5702	82	8	proof	proof	NOUN
ejpam-5702	82	9	.	.	PUNCT
ejpam-5702	83	1	theorem	theorem	NOUN
ejpam-5702	83	2	1	1	NUM
ejpam-5702	83	3	.	.	PUNCT
ejpam-5702	83	4	t	t	PROPN
ejpam-5702	83	5	∞∑	∞∑	PROPN
ejpam-5702	83	6	n=0	n=0	PROPN
ejpam-5702	83	7	b	b	PROPN
ejpam-5702	83	8	(	(	PUNCT
ejpam-5702	83	9	k	k	NOUN
ejpam-5702	83	10	)	)	PUNCT
ejpam-5702	83	11	n	n	CCONJ
ejpam-5702	83	12	,	,	PUNCT
ejpam-5702	83	13	y	y	PROPN
ejpam-5702	83	14	(	(	PUNCT
ejpam-5702	83	15	x	x	NOUN
ejpam-5702	83	16	)	)	PUNCT
ejpam-5702	83	17	tn	tn	PROPN
ejpam-5702	84	1	n	n	NOUN
ejpam-5702	84	2	!	!	PUNCT
ejpam-5702	85	1	=	=	SYM
ejpam-5702	86	1	t	t	NOUN
ejpam-5702	86	2	log(1	log(1	NOUN
ejpam-5702	86	3	+	+	CCONJ
ejpam-5702	86	4	t	t	X
ejpam-5702	86	5	)	)	PUNCT
ejpam-5702	86	6	(	(	PUNCT
ejpam-5702	86	7	1	1	NUM
ejpam-5702	86	8	+	+	CCONJ
ejpam-5702	86	9	t)xlik(1−	t)xlik(1−	NUM
ejpam-5702	86	10	e[e−y	e[e−y	PROPN
ejpam-5702	86	11	t	t	PROPN
ejpam-5702	86	12	]	]	PUNCT
ejpam-5702	86	13	)	)	PUNCT
ejpam-5702	86	14	(	(	PUNCT
ejpam-5702	86	15	20	20	NUM
ejpam-5702	86	16	)	)	PUNCT
ejpam-5702	86	17	=	=	NOUN
ejpam-5702	87	1	∞∑	∞∑	NUM
ejpam-5702	87	2	l=0	l=0	PROPN
ejpam-5702	87	3	b	b	PROPN
ejpam-5702	87	4	(	(	PUNCT
ejpam-5702	87	5	l	l	NOUN
ejpam-5702	87	6	)	)	PUNCT
ejpam-5702	87	7	l	l	NOUN
ejpam-5702	87	8	(	(	PUNCT
ejpam-5702	87	9	x+	x+	X
ejpam-5702	87	10	1	1	X
ejpam-5702	87	11	)	)	PUNCT
ejpam-5702	87	12	tl	tl	PROPN
ejpam-5702	87	13	l	l	NOUN
ejpam-5702	87	14	!	!	PUNCT
ejpam-5702	88	1	∞∑	∞∑	PRON
ejpam-5702	88	2	m=1	m=1	X
ejpam-5702	88	3	(	(	PUNCT
ejpam-5702	88	4	1−	1−	NUM
ejpam-5702	88	5	e[e−y	e[e−y	PROPN
ejpam-5702	88	6	t])m	t])m	PROPN
ejpam-5702	88	7	mk	mk	NOUN
ejpam-5702	88	8	=	=	PUNCT
ejpam-5702	89	1	∞∑	∞∑	NUM
ejpam-5702	89	2	l=0	l=0	PROPN
ejpam-5702	89	3	b	b	PROPN
ejpam-5702	89	4	(	(	PUNCT
ejpam-5702	89	5	l	l	NOUN
ejpam-5702	89	6	)	)	PUNCT
ejpam-5702	89	7	l	l	NOUN
ejpam-5702	89	8	(	(	PUNCT
ejpam-5702	89	9	x+	x+	X
ejpam-5702	89	10	1	1	X
ejpam-5702	89	11	)	)	PUNCT
ejpam-5702	89	12	tl	tl	PROPN
ejpam-5702	89	13	l	l	NOUN
ejpam-5702	89	14	!	!	PUNCT
ejpam-5702	90	1	∞∑	∞∑	PRON
ejpam-5702	90	2	m=1	m=1	X
ejpam-5702	90	3	(	(	PUNCT
ejpam-5702	90	4	−1)mm	−1)mm	PROPN
ejpam-5702	90	5	!	!	PROPN
ejpam-5702	90	6	mk	mk	NOUN
ejpam-5702	90	7	∞∑	∞∑	NUM
ejpam-5702	90	8	j	j	PROPN
ejpam-5702	90	9	=	=	NOUN
ejpam-5702	90	10	m	m	PROPN
ejpam-5702	90	11	(	(	PUNCT
ejpam-5702	90	12	−1)j	−1)j	X
ejpam-5702	90	13	{	{	PUNCT
ejpam-5702	90	14	j	j	NOUN
ejpam-5702	90	15	m	m	VERB
ejpam-5702	90	16	}	}	PUNCT
ejpam-5702	90	17	y	y	PROPN
ejpam-5702	90	18	tj	tj	PROPN
ejpam-5702	90	19	j	j	PROPN
ejpam-5702	90	20	!	!	PUNCT
ejpam-5702	91	1	=	=	PUNCT
ejpam-5702	92	1	∞∑	∞∑	NUM
ejpam-5702	92	2	l=0	l=0	PROPN
ejpam-5702	92	3	b	b	PROPN
ejpam-5702	92	4	(	(	PUNCT
ejpam-5702	92	5	l	l	NOUN
ejpam-5702	92	6	)	)	PUNCT
ejpam-5702	92	7	l	l	NOUN
ejpam-5702	92	8	(	(	PUNCT
ejpam-5702	92	9	x+	x+	X
ejpam-5702	92	10	1	1	X
ejpam-5702	92	11	)	)	PUNCT
ejpam-5702	92	12	tl	tl	PROPN
ejpam-5702	92	13	l	l	NOUN
ejpam-5702	92	14	!	!	PUNCT
ejpam-5702	93	1	∞∑	∞∑	NUM
ejpam-5702	93	2	j=1	j=1	NOUN
ejpam-5702	93	3	j∑	j∑	PROPN
ejpam-5702	93	4	m=1	m=1	X
ejpam-5702	93	5	(	(	PUNCT
ejpam-5702	93	6	−1)m+jm	−1)m+jm	ADV
ejpam-5702	93	7	!	!	PUNCT
ejpam-5702	94	1	mk	mk	PROPN
ejpam-5702	95	1	{	{	PUNCT
ejpam-5702	96	1	j	j	PROPN
ejpam-5702	96	2	m	m	VERB
ejpam-5702	96	3	}	}	PUNCT
ejpam-5702	96	4	y	y	PROPN
ejpam-5702	96	5	tj	tj	PROPN
ejpam-5702	96	6	j	j	PROPN
ejpam-5702	96	7	!	!	PUNCT
ejpam-5702	97	1	=	=	PUNCT
ejpam-5702	98	1	∞∑	∞∑	NUM
ejpam-5702	98	2	n=1	n=1	PROPN
ejpam-5702	98	3	n∑	n∑	PROPN
ejpam-5702	98	4	j=1	j=1	PROPN
ejpam-5702	98	5	j∑	j∑	PROPN
ejpam-5702	98	6	m=1	m=1	X
ejpam-5702	98	7	(	(	PUNCT
ejpam-5702	98	8	−1)m+jm	−1)m+jm	ADV
ejpam-5702	98	9	!	!	PUNCT
ejpam-5702	99	1	mk	mk	PROPN
ejpam-5702	99	2	(	(	PUNCT
ejpam-5702	99	3	n	n	X
ejpam-5702	99	4	j	j	NOUN
ejpam-5702	99	5	)	)	PUNCT
ejpam-5702	99	6	{	{	PUNCT
ejpam-5702	100	1	j	j	NOUN
ejpam-5702	100	2	m	m	VERB
ejpam-5702	100	3	}	}	PUNCT
ejpam-5702	100	4	y	y	PROPN
ejpam-5702	100	5	b	b	PROPN
ejpam-5702	100	6	(	(	PUNCT
ejpam-5702	100	7	n−j	n−j	ADV
ejpam-5702	100	8	)	)	PUNCT
ejpam-5702	100	9	n−j	n−j	X
ejpam-5702	100	10	(	(	PUNCT
ejpam-5702	100	11	x+	x+	X
ejpam-5702	100	12	1	1	NUM
ejpam-5702	100	13	)	)	PUNCT
ejpam-5702	100	14	tn	tn	NOUN
ejpam-5702	100	15	n	n	NUM
ejpam-5702	100	16	!	!	PUNCT
ejpam-5702	100	17	.	.	PUNCT
ejpam-5702	101	1	on	on	ADP
ejpam-5702	101	2	the	the	DET
ejpam-5702	101	3	other	other	ADJ
ejpam-5702	101	4	hand	hand	NOUN
ejpam-5702	101	5	,	,	PUNCT
ejpam-5702	101	6	in	in	ADP
ejpam-5702	101	7	(	(	PUNCT
ejpam-5702	101	8	20	20	NUM
ejpam-5702	101	9	)	)	PUNCT
ejpam-5702	101	10	t	t	NOUN
ejpam-5702	101	11	∞∑	∞∑	PROPN
ejpam-5702	101	12	n=0	n=0	PROPN
ejpam-5702	101	13	b	b	PROPN
ejpam-5702	101	14	(	(	PUNCT
ejpam-5702	101	15	k	k	NOUN
ejpam-5702	101	16	)	)	PUNCT
ejpam-5702	101	17	n	n	CCONJ
ejpam-5702	101	18	,	,	PUNCT
ejpam-5702	101	19	y	y	PROPN
ejpam-5702	101	20	(	(	PUNCT
ejpam-5702	101	21	x	x	NOUN
ejpam-5702	101	22	)	)	PUNCT
ejpam-5702	101	23	tn	tn	PROPN
ejpam-5702	101	24	n	n	NOUN
ejpam-5702	101	25	!	!	PUNCT
ejpam-5702	102	1	=	=	NOUN
ejpam-5702	103	1	∞∑	∞∑	NUM
ejpam-5702	103	2	n=1	n=1	PROPN
ejpam-5702	103	3	nb	nb	PROPN
ejpam-5702	103	4	(	(	PUNCT
ejpam-5702	103	5	k	k	PROPN
ejpam-5702	103	6	)	)	PUNCT
ejpam-5702	103	7	n−1,y	n−1,y	PROPN
ejpam-5702	103	8	(	(	PUNCT
ejpam-5702	103	9	x	x	NOUN
ejpam-5702	103	10	)	)	PUNCT
ejpam-5702	103	11	tn	tn	PROPN
ejpam-5702	103	12	n	n	NUM
ejpam-5702	103	13	!	!	PUNCT
ejpam-5702	103	14	.	.	PUNCT
ejpam-5702	104	1	(	(	PUNCT
ejpam-5702	104	2	21	21	NUM
ejpam-5702	104	3	)	)	PUNCT
ejpam-5702	104	4	thus	thus	ADV
ejpam-5702	104	5	,	,	PUNCT
ejpam-5702	104	6	by	by	ADP
ejpam-5702	104	7	comparing	compare	VERB
ejpam-5702	104	8	the	the	DET
ejpam-5702	104	9	coefficients	coefficient	NOUN
ejpam-5702	104	10	on	on	ADP
ejpam-5702	104	11	both	both	DET
ejpam-5702	104	12	sides	side	NOUN
ejpam-5702	104	13	of	of	ADP
ejpam-5702	104	14	(	(	PUNCT
ejpam-5702	104	15	20	20	NUM
ejpam-5702	104	16	)	)	PUNCT
ejpam-5702	104	17	and	and	CCONJ
ejpam-5702	104	18	(	(	PUNCT
ejpam-5702	104	19	21	21	NUM
ejpam-5702	104	20	)	)	PUNCT
ejpam-5702	104	21	,	,	PUNCT
ejpam-5702	104	22	we	we	PRON
ejpam-5702	104	23	have	have	VERB
ejpam-5702	104	24	the	the	DET
ejpam-5702	104	25	following	follow	VERB
ejpam-5702	104	26	theorem	theorem	VERB
ejpam-5702	104	27	.	.	PUNCT
ejpam-5702	105	1	s.	s.	PROPN
ejpam-5702	105	2	h.	h.	PROPN
ejpam-5702	105	3	lee	lee	PROPN
ejpam-5702	105	4	,	,	PUNCT
ejpam-5702	105	5	l.	l.	PROPN
ejpam-5702	105	6	chen	chen	PROPN
ejpam-5702	105	7	/	/	SYM
ejpam-5702	105	8	eur	eur	PROPN
ejpam-5702	105	9	.	.	PUNCT
ejpam-5702	106	1	j.	j.	PROPN
ejpam-5702	106	2	pure	pure	PROPN
ejpam-5702	106	3	appl	appl	PROPN
ejpam-5702	106	4	.	.	PROPN
ejpam-5702	106	5	math	math	PROPN
ejpam-5702	106	6	,	,	PUNCT
ejpam-5702	106	7	18	18	NUM
ejpam-5702	106	8	(	(	PUNCT
ejpam-5702	106	9	1	1	NUM
ejpam-5702	106	10	)	)	PUNCT
ejpam-5702	106	11	(	(	PUNCT
ejpam-5702	106	12	2025	2025	NUM
ejpam-5702	106	13	)	)	PUNCT
ejpam-5702	106	14	,	,	PUNCT
ejpam-5702	106	15	5702	5702	NUM
ejpam-5702	106	16	5	5	NUM
ejpam-5702	106	17	of	of	ADP
ejpam-5702	106	18	13	13	NUM
ejpam-5702	106	19	theorem	theorem	NOUN
ejpam-5702	106	20	1	1	NUM
ejpam-5702	106	21	.	.	PUNCT
ejpam-5702	106	22	for	for	ADP
ejpam-5702	106	23	n	n	PRON
ejpam-5702	106	24	≥	≥	NUM
ejpam-5702	106	25	1	1	NUM
ejpam-5702	106	26	,	,	PUNCT
ejpam-5702	106	27	we	we	PRON
ejpam-5702	106	28	have	have	AUX
ejpam-5702	106	29	nb	nb	INTJ
ejpam-5702	106	30	(	(	PUNCT
ejpam-5702	106	31	k	k	NOUN
ejpam-5702	106	32	)	)	PUNCT
ejpam-5702	106	33	n−1,y	n−1,y	PROPN
ejpam-5702	106	34	(	(	PUNCT
ejpam-5702	106	35	x	x	X
ejpam-5702	106	36	)	)	PUNCT
ejpam-5702	107	1	=	=	SYM
ejpam-5702	107	2	n∑	n∑	NOUN
ejpam-5702	107	3	j=1	j=1	PROPN
ejpam-5702	107	4	j∑	j∑	PROPN
ejpam-5702	108	1	m=1	m=1	X
ejpam-5702	108	2	(	(	PUNCT
ejpam-5702	108	3	−1)m+jm	−1)m+jm	ADV
ejpam-5702	108	4	!	!	PUNCT
ejpam-5702	108	5	mk	mk	PROPN
ejpam-5702	109	1	(	(	PUNCT
ejpam-5702	109	2	n	n	X
ejpam-5702	109	3	j	j	NOUN
ejpam-5702	109	4	)	)	PUNCT
ejpam-5702	109	5	{	{	PUNCT
ejpam-5702	110	1	j	j	NOUN
ejpam-5702	110	2	m	m	VERB
ejpam-5702	110	3	}	}	PUNCT
ejpam-5702	110	4	y	y	PROPN
ejpam-5702	110	5	b	b	PROPN
ejpam-5702	110	6	(	(	PUNCT
ejpam-5702	110	7	n−j	n−j	ADV
ejpam-5702	110	8	)	)	PUNCT
ejpam-5702	110	9	n−j	n−j	X
ejpam-5702	110	10	(	(	PUNCT
ejpam-5702	110	11	x+	x+	X
ejpam-5702	110	12	1	1	NUM
ejpam-5702	110	13	)	)	PUNCT
ejpam-5702	110	14	.	.	PUNCT
ejpam-5702	111	1	let	let	VERB
ejpam-5702	111	2	y	y	PRON
ejpam-5702	111	3	∼	∼	VERB
ejpam-5702	111	4	γ(1	γ(1	PROPN
ejpam-5702	111	5	,	,	PUNCT
ejpam-5702	111	6	1	1	NUM
ejpam-5702	111	7	)	)	PUNCT
ejpam-5702	111	8	,	,	PUNCT
ejpam-5702	111	9	then	then	ADV
ejpam-5702	111	10	we	we	PRON
ejpam-5702	111	11	note	note	VERB
ejpam-5702	111	12	that	that	SCONJ
ejpam-5702	111	13	e[ey	e[ey	PROPN
ejpam-5702	111	14	t	t	PROPN
ejpam-5702	111	15	]	]	X
ejpam-5702	111	16	=	=	SYM
ejpam-5702	111	17	1	1	NUM
ejpam-5702	111	18	1−	1−	NUM
ejpam-5702	111	19	t	t	NOUN
ejpam-5702	111	20	.	.	PUNCT
ejpam-5702	112	1	(	(	PUNCT
ejpam-5702	112	2	22	22	NUM
ejpam-5702	112	3	)	)	PUNCT
ejpam-5702	112	4	from	from	ADP
ejpam-5702	112	5	(	(	PUNCT
ejpam-5702	112	6	19	19	NUM
ejpam-5702	112	7	)	)	PUNCT
ejpam-5702	112	8	and	and	CCONJ
ejpam-5702	112	9	(	(	PUNCT
ejpam-5702	112	10	22	22	NUM
ejpam-5702	112	11	)	)	PUNCT
ejpam-5702	112	12	,	,	PUNCT
ejpam-5702	112	13	we	we	PRON
ejpam-5702	112	14	have	have	VERB
ejpam-5702	112	15	proof	proof	NOUN
ejpam-5702	112	16	.	.	PUNCT
ejpam-5702	113	1	theorem	theorem	NOUN
ejpam-5702	113	2	2	2	NUM
ejpam-5702	113	3	.	.	PUNCT
ejpam-5702	114	1	∞∑	∞∑	NUM
ejpam-5702	114	2	n=0	n=0	PROPN
ejpam-5702	114	3	b	b	NOUN
ejpam-5702	114	4	(	(	PUNCT
ejpam-5702	114	5	k	k	NOUN
ejpam-5702	114	6	)	)	PUNCT
ejpam-5702	114	7	n	n	CCONJ
ejpam-5702	114	8	,	,	PUNCT
ejpam-5702	114	9	y	y	PROPN
ejpam-5702	114	10	(	(	PUNCT
ejpam-5702	114	11	x	x	NOUN
ejpam-5702	114	12	)	)	PUNCT
ejpam-5702	114	13	tn	tn	PROPN
ejpam-5702	114	14	n	n	NOUN
ejpam-5702	114	15	!	!	PUNCT
ejpam-5702	115	1	=	=	PUNCT
ejpam-5702	116	1	t(1	t(1	NOUN
ejpam-5702	116	2	+	+	CCONJ
ejpam-5702	116	3	t)x	t)x	NOUN
ejpam-5702	116	4	tlog(1	tlog(1	PROPN
ejpam-5702	116	5	+	+	CCONJ
ejpam-5702	116	6	t	t	X
ejpam-5702	116	7	)	)	PUNCT
ejpam-5702	116	8	∑	∑	PUNCT
ejpam-5702	116	9	m=1	m=1	PROPN
ejpam-5702	116	10	(	(	PUNCT
ejpam-5702	116	11	1−	1−	NUM
ejpam-5702	116	12	1	1	NUM
ejpam-5702	116	13	1−t	1−t	NUM
ejpam-5702	116	14	)	)	PUNCT
ejpam-5702	116	15	m	m	PROPN
ejpam-5702	116	16	mk	mk	NOUN
ejpam-5702	116	17	(	(	PUNCT
ejpam-5702	116	18	23	23	NUM
ejpam-5702	116	19	)	)	PUNCT
ejpam-5702	116	20	=	=	SYM
ejpam-5702	116	21	1	1	NUM
ejpam-5702	116	22	t	t	PROPN
ejpam-5702	116	23	∞∑	∞∑	PROPN
ejpam-5702	116	24	i=0	i=0	PROPN
ejpam-5702	116	25	bi(x	bi(x	NUM
ejpam-5702	116	26	)	)	PUNCT
ejpam-5702	116	27	ti	ti	NOUN
ejpam-5702	116	28	i	i	PRON
ejpam-5702	116	29	!	!	PUNCT
ejpam-5702	117	1	∞∑	∞∑	PRON
ejpam-5702	117	2	m=1	m=1	X
ejpam-5702	117	3	(	(	PUNCT
ejpam-5702	117	4	−1)mm	−1)mm	PROPN
ejpam-5702	117	5	!	!	SYM
ejpam-5702	117	6	mk	mk	PROPN
ejpam-5702	117	7	1	1	NUM
ejpam-5702	117	8	m	m	NOUN
ejpam-5702	117	9	!	!	PUNCT
ejpam-5702	118	1	(	(	PUNCT
ejpam-5702	118	2	t	t	PROPN
ejpam-5702	118	3	1−	1−	NUM
ejpam-5702	118	4	t	t	NOUN
ejpam-5702	118	5	)	)	PUNCT
ejpam-5702	118	6	m	m	VERB
ejpam-5702	118	7	=	=	SYM
ejpam-5702	118	8	1	1	NUM
ejpam-5702	118	9	t	t	PROPN
ejpam-5702	118	10	∞∑	∞∑	PROPN
ejpam-5702	118	11	i=0	i=0	PROPN
ejpam-5702	118	12	bi(x	bi(x	NUM
ejpam-5702	118	13	)	)	PUNCT
ejpam-5702	118	14	ti	ti	NOUN
ejpam-5702	119	1	i	i	PRON
ejpam-5702	119	2	!	!	PUNCT
ejpam-5702	120	1	∞∑	∞∑	PRON
ejpam-5702	120	2	m=1	m=1	X
ejpam-5702	120	3	(	(	PUNCT
ejpam-5702	120	4	−1)mm	−1)mm	PROPN
ejpam-5702	120	5	!	!	PROPN
ejpam-5702	120	6	mk	mk	NOUN
ejpam-5702	120	7	∞∑	∞∑	PROPN
ejpam-5702	120	8	l	l	NOUN
ejpam-5702	120	9	=	=	NOUN
ejpam-5702	120	10	m	m	NOUN
ejpam-5702	120	11	l(l	l(l	PROPN
ejpam-5702	120	12	,	,	PUNCT
ejpam-5702	120	13	m	m	NOUN
ejpam-5702	120	14	)	)	PUNCT
ejpam-5702	120	15	tl	tl	PROPN
ejpam-5702	120	16	l	l	NOUN
ejpam-5702	120	17	!	!	PUNCT
ejpam-5702	121	1	=	=	SYM
ejpam-5702	121	2	1	1	NUM
ejpam-5702	121	3	t	t	PROPN
ejpam-5702	121	4	∞∑	∞∑	PROPN
ejpam-5702	121	5	i=0	i=0	PROPN
ejpam-5702	121	6	bi(x	bi(x	NUM
ejpam-5702	121	7	)	)	PUNCT
ejpam-5702	121	8	ti	ti	NOUN
ejpam-5702	122	1	i	i	PRON
ejpam-5702	122	2	!	!	PUNCT
ejpam-5702	123	1	∞∑	∞∑	PRON
ejpam-5702	123	2	l=1	l=1	NOUN
ejpam-5702	123	3	l∑	l∑	PROPN
ejpam-5702	124	1	m=1	m=1	X
ejpam-5702	124	2	(	(	PUNCT
ejpam-5702	124	3	−1)mm	−1)mm	PROPN
ejpam-5702	124	4	!	!	PROPN
ejpam-5702	124	5	mk	mk	PROPN
ejpam-5702	124	6	l(l	l(l	PROPN
ejpam-5702	124	7	,	,	PUNCT
ejpam-5702	124	8	m	m	NOUN
ejpam-5702	124	9	)	)	PUNCT
ejpam-5702	124	10	tl	tl	PROPN
ejpam-5702	124	11	l	l	NOUN
ejpam-5702	124	12	!	!	PUNCT
ejpam-5702	125	1	=	=	PUNCT
ejpam-5702	126	1	∞∑	∞∑	NUM
ejpam-5702	126	2	n=1	n=1	PUNCT
ejpam-5702	126	3	n∑	n∑	PROPN
ejpam-5702	126	4	l=1	l=1	PROPN
ejpam-5702	126	5	l∑	l∑	PUNCT
ejpam-5702	127	1	m=1	m=1	X
ejpam-5702	127	2	(	(	PUNCT
ejpam-5702	127	3	n	n	X
ejpam-5702	127	4	l	l	NOUN
ejpam-5702	127	5	)	)	PUNCT
ejpam-5702	127	6	(	(	PUNCT
ejpam-5702	127	7	−1)mm	−1)mm	PROPN
ejpam-5702	127	8	!	!	PROPN
ejpam-5702	127	9	mk	mk	PROPN
ejpam-5702	127	10	l(l	l(l	PROPN
ejpam-5702	127	11	,	,	PUNCT
ejpam-5702	127	12	m)bn−l(x	m)bn−l(x	PROPN
ejpam-5702	127	13	)	)	PUNCT
ejpam-5702	127	14	tn−1	tn−1	PROPN
ejpam-5702	127	15	n	n	CCONJ
ejpam-5702	127	16	!	!	PUNCT
ejpam-5702	127	17	=	=	NOUN
ejpam-5702	128	1	∞∑	∞∑	PRON
ejpam-5702	128	2	n=0	n=0	PROPN
ejpam-5702	128	3	n+1∑	n+1∑	ADP
ejpam-5702	128	4	l=1	l=1	PROPN
ejpam-5702	128	5	l∑	l∑	PROPN
ejpam-5702	129	1	m=1	m=1	X
ejpam-5702	129	2	(	(	PUNCT
ejpam-5702	129	3	n+	n+	NUM
ejpam-5702	129	4	1	1	NUM
ejpam-5702	129	5	l	l	NOUN
ejpam-5702	129	6	)	)	PUNCT
ejpam-5702	129	7	(	(	PUNCT
ejpam-5702	129	8	−1)mm	−1)mm	PROPN
ejpam-5702	129	9	!	!	PROPN
ejpam-5702	129	10	mk	mk	PROPN
ejpam-5702	129	11	l(l	l(l	PROPN
ejpam-5702	129	12	,	,	PUNCT
ejpam-5702	129	13	m	m	NOUN
ejpam-5702	129	14	)	)	PUNCT
ejpam-5702	129	15	bn−l+1(x	bn−l+1(x	NOUN
ejpam-5702	129	16	)	)	PUNCT
ejpam-5702	129	17	n+	n+	PUNCT
ejpam-5702	129	18	1	1	NUM
ejpam-5702	129	19	tn	tn	NOUN
ejpam-5702	129	20	n	n	X
ejpam-5702	129	21	!	!	PUNCT
ejpam-5702	129	22	.	.	PUNCT
ejpam-5702	130	1	thus	thus	ADV
ejpam-5702	130	2	,	,	PUNCT
ejpam-5702	130	3	we	we	PRON
ejpam-5702	130	4	have	have	VERB
ejpam-5702	130	5	the	the	DET
ejpam-5702	130	6	following	follow	VERB
ejpam-5702	130	7	theorem	theorem	VERB
ejpam-5702	130	8	.	.	PUNCT
ejpam-5702	130	9	theorem	theorem	NOUN
ejpam-5702	130	10	2	2	NUM
ejpam-5702	130	11	.	.	PUNCT
ejpam-5702	131	1	let	let	VERB
ejpam-5702	131	2	y	y	NOUN
ejpam-5702	131	3	∼	∼	VERB
ejpam-5702	131	4	γ(1	γ(1	PROPN
ejpam-5702	131	5	,	,	PUNCT
ejpam-5702	131	6	1	1	NUM
ejpam-5702	131	7	)	)	PUNCT
ejpam-5702	131	8	.	.	PUNCT
ejpam-5702	132	1	for	for	ADP
ejpam-5702	132	2	n	n	PRON
ejpam-5702	132	3	≥	≥	NOUN
ejpam-5702	132	4	0	0	NUM
ejpam-5702	132	5	,	,	PUNCT
ejpam-5702	132	6	we	we	PRON
ejpam-5702	132	7	have	have	VERB
ejpam-5702	132	8	b	b	NUM
ejpam-5702	132	9	(	(	PUNCT
ejpam-5702	132	10	k	k	NOUN
ejpam-5702	132	11	)	)	PUNCT
ejpam-5702	132	12	n	n	CCONJ
ejpam-5702	132	13	,	,	PUNCT
ejpam-5702	132	14	y	y	PROPN
ejpam-5702	132	15	(	(	PUNCT
ejpam-5702	132	16	x	x	NOUN
ejpam-5702	132	17	)	)	PUNCT
ejpam-5702	133	1	=	=	SYM
ejpam-5702	133	2	n+1∑	n+1∑	PROPN
ejpam-5702	134	1	l=1	l=1	X
ejpam-5702	134	2	l∑	l∑	PROPN
ejpam-5702	135	1	m=1	m=1	X
ejpam-5702	135	2	(	(	PUNCT
ejpam-5702	135	3	n+	n+	NUM
ejpam-5702	135	4	1	1	NUM
ejpam-5702	135	5	l	l	NOUN
ejpam-5702	135	6	)	)	PUNCT
ejpam-5702	135	7	(	(	PUNCT
ejpam-5702	135	8	−1)mm	−1)mm	PROPN
ejpam-5702	135	9	!	!	PROPN
ejpam-5702	135	10	mk	mk	PROPN
ejpam-5702	135	11	l(l	l(l	PROPN
ejpam-5702	135	12	,	,	PUNCT
ejpam-5702	135	13	m	m	NOUN
ejpam-5702	135	14	)	)	PUNCT
ejpam-5702	135	15	bn−l+1(x	bn−l+1(x	NOUN
ejpam-5702	135	16	)	)	PUNCT
ejpam-5702	135	17	n+	n+	PUNCT
ejpam-5702	136	1	1	1	X
ejpam-5702	136	2	.	.	PUNCT
ejpam-5702	137	1	let	let	VERB
ejpam-5702	137	2	y	y	PRON
ejpam-5702	137	3	be	be	AUX
ejpam-5702	137	4	the	the	DET
ejpam-5702	137	5	bernoulli	bernoulli	NOUN
ejpam-5702	137	6	random	random	ADJ
ejpam-5702	137	7	variable	variable	NOUN
ejpam-5702	137	8	with	with	ADP
ejpam-5702	137	9	probability	probability	NOUN
ejpam-5702	137	10	of	of	ADP
ejpam-5702	137	11	success	success	NOUN
ejpam-5702	138	1	p.	p.	NOUN
ejpam-5702	138	2	then	then	ADV
ejpam-5702	138	3	we	we	PRON
ejpam-5702	138	4	have	have	VERB
ejpam-5702	138	5	e[ey	e[ey	PROPN
ejpam-5702	138	6	t	t	NOUN
ejpam-5702	138	7	]	]	X
ejpam-5702	138	8	=	=	PUNCT
ejpam-5702	138	9	p(et	p(et	NOUN
ejpam-5702	138	10	−	−	NOUN
ejpam-5702	138	11	1	1	NUM
ejpam-5702	138	12	)	)	PUNCT
ejpam-5702	138	13	+	+	NUM
ejpam-5702	139	1	1	1	X
ejpam-5702	139	2	.	.	PUNCT
ejpam-5702	139	3	(	(	PUNCT
ejpam-5702	139	4	24	24	NUM
ejpam-5702	139	5	)	)	PUNCT
ejpam-5702	139	6	by	by	ADP
ejpam-5702	139	7	(	(	PUNCT
ejpam-5702	139	8	19	19	NUM
ejpam-5702	139	9	)	)	PUNCT
ejpam-5702	139	10	and	and	CCONJ
ejpam-5702	139	11	(	(	PUNCT
ejpam-5702	139	12	24	24	NUM
ejpam-5702	139	13	)	)	PUNCT
ejpam-5702	139	14	,	,	PUNCT
ejpam-5702	139	15	we	we	PRON
ejpam-5702	139	16	have	have	VERB
ejpam-5702	139	17	s.	s.	PROPN
ejpam-5702	139	18	h.	h.	PROPN
ejpam-5702	139	19	lee	lee	PROPN
ejpam-5702	139	20	,	,	PUNCT
ejpam-5702	139	21	l.	l.	PROPN
ejpam-5702	139	22	chen	chen	PROPN
ejpam-5702	139	23	/	/	SYM
ejpam-5702	139	24	eur	eur	PROPN
ejpam-5702	139	25	.	.	PUNCT
ejpam-5702	140	1	j.	j.	PROPN
ejpam-5702	140	2	pure	pure	PROPN
ejpam-5702	140	3	appl	appl	PROPN
ejpam-5702	140	4	.	.	PROPN
ejpam-5702	140	5	math	math	PROPN
ejpam-5702	140	6	,	,	PUNCT
ejpam-5702	140	7	18	18	NUM
ejpam-5702	140	8	(	(	PUNCT
ejpam-5702	140	9	1	1	NUM
ejpam-5702	140	10	)	)	PUNCT
ejpam-5702	140	11	(	(	PUNCT
ejpam-5702	140	12	2025	2025	NUM
ejpam-5702	140	13	)	)	PUNCT
ejpam-5702	140	14	,	,	PUNCT
ejpam-5702	140	15	5702	5702	NUM
ejpam-5702	140	16	6	6	NUM
ejpam-5702	140	17	of	of	ADP
ejpam-5702	140	18	13	13	NUM
ejpam-5702	140	19	proof	proof	NOUN
ejpam-5702	140	20	.	.	PUNCT
ejpam-5702	141	1	theorem	theorem	VERB
ejpam-5702	141	2	3	3	NUM
ejpam-5702	141	3	.	.	PUNCT
ejpam-5702	142	1	∞∑	∞∑	NUM
ejpam-5702	142	2	n=0	n=0	PROPN
ejpam-5702	142	3	b	b	NOUN
ejpam-5702	142	4	(	(	PUNCT
ejpam-5702	142	5	k	k	NOUN
ejpam-5702	142	6	)	)	PUNCT
ejpam-5702	142	7	n	n	CCONJ
ejpam-5702	142	8	,	,	PUNCT
ejpam-5702	142	9	y	y	PROPN
ejpam-5702	142	10	tn	tn	PROPN
ejpam-5702	142	11	n	n	PROPN
ejpam-5702	142	12	!	!	PUNCT
ejpam-5702	142	13	=	=	PUNCT
ejpam-5702	143	1	(	(	PUNCT
ejpam-5702	143	2	1	1	NUM
ejpam-5702	143	3	+	+	CCONJ
ejpam-5702	143	4	t)x	t)x	NOUN
ejpam-5702	143	5	log(1	log(1	NOUN
ejpam-5702	143	6	+	+	CCONJ
ejpam-5702	143	7	t	t	X
ejpam-5702	143	8	)	)	PUNCT
ejpam-5702	144	1	∞∑	∞∑	PROPN
ejpam-5702	144	2	m=1	m=1	X
ejpam-5702	144	3	(	(	PUNCT
ejpam-5702	144	4	1−	1−	NUM
ejpam-5702	144	5	e[e−y	e[e−y	PROPN
ejpam-5702	144	6	t])m	t])m	PROPN
ejpam-5702	144	7	mk	mk	PROPN
ejpam-5702	144	8	(	(	PUNCT
ejpam-5702	144	9	25	25	NUM
ejpam-5702	144	10	)	)	PUNCT
ejpam-5702	144	11	=	=	NOUN
ejpam-5702	144	12	(	(	PUNCT
ejpam-5702	144	13	1	1	NUM
ejpam-5702	144	14	+	+	CCONJ
ejpam-5702	144	15	t)x	t)x	NOUN
ejpam-5702	144	16	log(1	log(1	NOUN
ejpam-5702	144	17	+	+	CCONJ
ejpam-5702	144	18	t	t	X
ejpam-5702	144	19	)	)	PUNCT
ejpam-5702	144	20	∞∑	∞∑	PROPN
ejpam-5702	144	21	m=1	m=1	X
ejpam-5702	144	22	(	(	PUNCT
ejpam-5702	144	23	−1)mpm(et	−1)mpm(et	NOUN
ejpam-5702	144	24	−	−	NOUN
ejpam-5702	144	25	1)m	1)m	NUM
ejpam-5702	144	26	mk	mk	NOUN
ejpam-5702	144	27	=	=	PROPN
ejpam-5702	144	28	t(1	t(1	PROPN
ejpam-5702	144	29	+	+	CCONJ
ejpam-5702	144	30	t)x	t)x	NOUN
ejpam-5702	144	31	tlog(1	tlog(1	PROPN
ejpam-5702	144	32	+	+	CCONJ
ejpam-5702	144	33	t	t	X
ejpam-5702	144	34	)	)	PUNCT
ejpam-5702	145	1	∞∑	∞∑	PROPN
ejpam-5702	145	2	m=1	m=1	X
ejpam-5702	145	3	(	(	PUNCT
ejpam-5702	145	4	−1)mpmm	−1)mpmm	PROPN
ejpam-5702	145	5	!	!	PUNCT
ejpam-5702	146	1	mk	mk	PROPN
ejpam-5702	146	2	(	(	PUNCT
ejpam-5702	146	3	et	et	NOUN
ejpam-5702	146	4	−	−	PROPN
ejpam-5702	146	5	1)m	1)m	NUM
ejpam-5702	146	6	m	m	NOUN
ejpam-5702	146	7	!	!	PUNCT
ejpam-5702	147	1	=	=	SYM
ejpam-5702	147	2	1	1	NUM
ejpam-5702	147	3	t	t	NOUN
ejpam-5702	147	4	∞∑	∞∑	NUM
ejpam-5702	147	5	l=0	l=0	PROPN
ejpam-5702	147	6	bl(x	bl(x	PUNCT
ejpam-5702	147	7	)	)	PUNCT
ejpam-5702	147	8	tl	tl	PROPN
ejpam-5702	147	9	l	l	NOUN
ejpam-5702	147	10	!	!	PUNCT
ejpam-5702	148	1	∞∑	∞∑	PRON
ejpam-5702	148	2	m=1	m=1	X
ejpam-5702	148	3	(	(	PUNCT
ejpam-5702	148	4	−1)mpmm	−1)mpmm	PROPN
ejpam-5702	148	5	!	!	PUNCT
ejpam-5702	149	1	mk	mk	PROPN
ejpam-5702	150	1	∞∑	∞∑	NUM
ejpam-5702	150	2	i	i	PROPN
ejpam-5702	150	3	=	=	NOUN
ejpam-5702	150	4	m	m	VERB
ejpam-5702	150	5	s2(i	s2(i	PROPN
ejpam-5702	150	6	,	,	PUNCT
ejpam-5702	150	7	m	m	NOUN
ejpam-5702	150	8	)	)	PUNCT
ejpam-5702	150	9	ti	ti	X
ejpam-5702	150	10	i	i	PRON
ejpam-5702	150	11	!	!	PUNCT
ejpam-5702	151	1	=	=	SYM
ejpam-5702	151	2	1	1	NUM
ejpam-5702	151	3	t	t	NOUN
ejpam-5702	151	4	∞∑	∞∑	NUM
ejpam-5702	151	5	l=0	l=0	PROPN
ejpam-5702	151	6	bl(x	bl(x	PUNCT
ejpam-5702	151	7	)	)	PUNCT
ejpam-5702	151	8	tl	tl	PROPN
ejpam-5702	151	9	l	l	NOUN
ejpam-5702	151	10	!	!	PUNCT
ejpam-5702	152	1	∞∑	∞∑	NUM
ejpam-5702	152	2	i=1	i=1	ADP
ejpam-5702	152	3	i∑	i∑	PROPN
ejpam-5702	152	4	m=1	m=1	X
ejpam-5702	152	5	(	(	PUNCT
ejpam-5702	152	6	−1)mpmm	−1)mpmm	PROPN
ejpam-5702	152	7	!	!	PUNCT
ejpam-5702	153	1	mk	mk	PROPN
ejpam-5702	154	1	s2(i	s2(i	PROPN
ejpam-5702	154	2	,	,	PUNCT
ejpam-5702	154	3	m	m	NOUN
ejpam-5702	154	4	)	)	PUNCT
ejpam-5702	154	5	ti	ti	X
ejpam-5702	154	6	i	i	PRON
ejpam-5702	154	7	!	!	PUNCT
ejpam-5702	155	1	=	=	PUNCT
ejpam-5702	156	1	∞∑	∞∑	NUM
ejpam-5702	156	2	n=1	n=1	PROPN
ejpam-5702	156	3	n∑	n∑	PROPN
ejpam-5702	156	4	i=1	i=1	PROPN
ejpam-5702	157	1	i∑	i∑	PROPN
ejpam-5702	158	1	m=1	m=1	X
ejpam-5702	159	1	(	(	PUNCT
ejpam-5702	159	2	n	n	NOUN
ejpam-5702	159	3	i	i	PRON
ejpam-5702	159	4	)	)	PUNCT
ejpam-5702	159	5	(	(	PUNCT
ejpam-5702	159	6	−1)mpmm	−1)mpmm	PROPN
ejpam-5702	159	7	!	!	PUNCT
ejpam-5702	160	1	mk	mk	PROPN
ejpam-5702	160	2	s2(i	s2(i	PROPN
ejpam-5702	160	3	,	,	PUNCT
ejpam-5702	160	4	m)bn−i(x	m)bn−i(x	NOUN
ejpam-5702	160	5	)	)	PUNCT
ejpam-5702	160	6	tn−1	tn−1	PROPN
ejpam-5702	160	7	n	n	X
ejpam-5702	160	8	!	!	PUNCT
ejpam-5702	160	9	=	=	NOUN
ejpam-5702	161	1	∞∑	∞∑	PRON
ejpam-5702	161	2	n=0	n=0	NUM
ejpam-5702	161	3	n+1∑	n+1∑	ADP
ejpam-5702	161	4	i=1	i=1	PROPN
ejpam-5702	161	5	i∑	i∑	PROPN
ejpam-5702	161	6	m=1	m=1	X
ejpam-5702	161	7	(	(	PUNCT
ejpam-5702	161	8	n+	n+	ADP
ejpam-5702	161	9	1	1	NUM
ejpam-5702	161	10	i	i	NOUN
ejpam-5702	161	11	)	)	PUNCT
ejpam-5702	161	12	(	(	PUNCT
ejpam-5702	161	13	−1)mpmm	−1)mpmm	PROPN
ejpam-5702	161	14	!	!	PUNCT
ejpam-5702	161	15	mk	mk	PROPN
ejpam-5702	161	16	s2(i	s2(i	PROPN
ejpam-5702	161	17	,	,	PUNCT
ejpam-5702	161	18	m	m	NOUN
ejpam-5702	161	19	)	)	PUNCT
ejpam-5702	161	20	bn−i+1(x	bn−i+1(x	NOUN
ejpam-5702	161	21	)	)	PUNCT
ejpam-5702	161	22	n+	n+	PUNCT
ejpam-5702	161	23	1	1	NUM
ejpam-5702	161	24	tn	tn	NOUN
ejpam-5702	161	25	n	n	X
ejpam-5702	161	26	!	!	PUNCT
ejpam-5702	161	27	.	.	PUNCT
ejpam-5702	162	1	thus	thus	ADV
ejpam-5702	162	2	,	,	PUNCT
ejpam-5702	162	3	we	we	PRON
ejpam-5702	162	4	have	have	VERB
ejpam-5702	162	5	the	the	DET
ejpam-5702	162	6	following	follow	VERB
ejpam-5702	162	7	theorem	theorem	VERB
ejpam-5702	162	8	.	.	PUNCT
ejpam-5702	162	9	theorem	theorem	NOUN
ejpam-5702	162	10	3	3	X
ejpam-5702	162	11	.	.	PUNCT
ejpam-5702	163	1	let	let	VERB
ejpam-5702	163	2	y	y	PRON
ejpam-5702	163	3	be	be	AUX
ejpam-5702	163	4	the	the	DET
ejpam-5702	163	5	bernoulli	bernoulli	NOUN
ejpam-5702	163	6	random	random	ADJ
ejpam-5702	163	7	variable	variable	NOUN
ejpam-5702	163	8	with	with	ADP
ejpam-5702	163	9	probability	probability	NOUN
ejpam-5702	163	10	of	of	ADP
ejpam-5702	163	11	success	success	NOUN
ejpam-5702	163	12	p.	p.	NOUN
ejpam-5702	163	13	for	for	ADP
ejpam-5702	163	14	n	n	PROPN
ejpam-5702	163	15	≥	≥	NOUN
ejpam-5702	163	16	0	0	NUM
ejpam-5702	163	17	,	,	PUNCT
ejpam-5702	163	18	we	we	PRON
ejpam-5702	163	19	have	have	VERB
ejpam-5702	163	20	b	b	NUM
ejpam-5702	163	21	(	(	PUNCT
ejpam-5702	163	22	k	k	NOUN
ejpam-5702	163	23	)	)	PUNCT
ejpam-5702	163	24	n	n	CCONJ
ejpam-5702	163	25	,	,	PUNCT
ejpam-5702	163	26	y	y	PROPN
ejpam-5702	163	27	=	=	PUNCT
ejpam-5702	163	28	n+1∑	n+1∑	PROPN
ejpam-5702	163	29	i=1	i=1	PROPN
ejpam-5702	163	30	i∑	i∑	PROPN
ejpam-5702	163	31	m=1	m=1	X
ejpam-5702	163	32	(	(	PUNCT
ejpam-5702	163	33	n+	n+	ADP
ejpam-5702	163	34	1	1	NUM
ejpam-5702	163	35	i	i	NOUN
ejpam-5702	163	36	)	)	PUNCT
ejpam-5702	163	37	(	(	PUNCT
ejpam-5702	163	38	−1)mpmm	−1)mpmm	PROPN
ejpam-5702	163	39	!	!	PUNCT
ejpam-5702	164	1	mk	mk	PROPN
ejpam-5702	164	2	s2(i	s2(i	PROPN
ejpam-5702	164	3	,	,	PUNCT
ejpam-5702	164	4	m	m	NOUN
ejpam-5702	164	5	)	)	PUNCT
ejpam-5702	164	6	bn−i+1(x	bn−i+1(x	NOUN
ejpam-5702	164	7	)	)	PUNCT
ejpam-5702	164	8	n+	n+	PUNCT
ejpam-5702	165	1	1	1	X
ejpam-5702	165	2	.	.	PUNCT
ejpam-5702	166	1	now	now	ADV
ejpam-5702	166	2	,	,	PUNCT
ejpam-5702	166	3	we	we	PRON
ejpam-5702	166	4	consider	consider	VERB
ejpam-5702	166	5	probabilistic	probabilistic	ADJ
ejpam-5702	166	6	multiple	multiple	ADJ
ejpam-5702	166	7	poly	poly	ADJ
ejpam-5702	166	8	bernoulli	bernoulli	NOUN
ejpam-5702	166	9	polynomials	polynomial	NOUN
ejpam-5702	166	10	of	of	ADP
ejpam-5702	166	11	the	the	DET
ejpam-5702	166	12	second	second	ADJ
ejpam-5702	166	13	kind	kind	NOUN
ejpam-5702	166	14	which	which	PRON
ejpam-5702	166	15	are	be	AUX
ejpam-5702	166	16	given	give	VERB
ejpam-5702	166	17	by	by	ADP
ejpam-5702	166	18	r!lik1,	r!lik1,	NOUN
ejpam-5702	166	19	...	...	PUNCT
ejpam-5702	166	20	,kr(1−	,kr(1−	PROPN
ejpam-5702	166	21	e[e−y	e[e−y	PROPN
ejpam-5702	166	22	t	t	PROPN
ejpam-5702	166	23	]	]	PUNCT
ejpam-5702	166	24	)	)	PUNCT
ejpam-5702	166	25	(	(	PUNCT
ejpam-5702	166	26	log(1	log(1	NOUN
ejpam-5702	166	27	+	+	CCONJ
ejpam-5702	167	1	t))r	t))r	ADJ
ejpam-5702	168	1	(	(	PUNCT
ejpam-5702	168	2	1	1	NUM
ejpam-5702	168	3	+	+	CCONJ
ejpam-5702	168	4	t)x	t)x	PUNCT
ejpam-5702	168	5	=	=	PUNCT
ejpam-5702	168	6	∞∑	∞∑	NUM
ejpam-5702	168	7	n=0	n=0	PROPN
ejpam-5702	168	8	b	b	NOUN
ejpam-5702	168	9	(	(	PUNCT
ejpam-5702	168	10	k1,	k1,	NOUN
ejpam-5702	168	11	...	...	SYM
ejpam-5702	168	12	,kr	,kr	SYM
ejpam-5702	168	13	)	)	PUNCT
ejpam-5702	168	14	n	n	CCONJ
ejpam-5702	168	15	,	,	PUNCT
ejpam-5702	168	16	y	y	PROPN
ejpam-5702	168	17	(	(	PUNCT
ejpam-5702	168	18	x	x	NOUN
ejpam-5702	168	19	)	)	PUNCT
ejpam-5702	168	20	tn	tn	PROPN
ejpam-5702	168	21	n	n	NUM
ejpam-5702	168	22	!	!	PUNCT
ejpam-5702	168	23	.	.	PUNCT
ejpam-5702	169	1	(	(	PUNCT
ejpam-5702	169	2	26	26	NUM
ejpam-5702	169	3	)	)	PUNCT
ejpam-5702	169	4	when	when	SCONJ
ejpam-5702	169	5	k1	k1	X
ejpam-5702	169	6	=	=	SYM
ejpam-5702	169	7	·	·	PUNCT
ejpam-5702	169	8	·	·	PUNCT
ejpam-5702	169	9	·	·	PUNCT
ejpam-5702	170	1	=	=	SYM
ejpam-5702	170	2	kr	kr	PROPN
ejpam-5702	170	3	=	=	SYM
ejpam-5702	170	4	1	1	NUM
ejpam-5702	170	5	and	and	CCONJ
ejpam-5702	170	6	y	y	NOUN
ejpam-5702	170	7	=	=	SYM
ejpam-5702	170	8	1	1	NUM
ejpam-5702	170	9	,	,	PUNCT
ejpam-5702	170	10	we	we	PRON
ejpam-5702	170	11	note	note	VERB
ejpam-5702	170	12	that	that	SCONJ
ejpam-5702	170	13	∞∑	∞∑	NUM
ejpam-5702	170	14	n=0	n=0	PROPN
ejpam-5702	170	15	b	b	NOUN
ejpam-5702	170	16	(	(	PUNCT
ejpam-5702	170	17	1,	1,	NUM
ejpam-5702	170	18	...	...	PUNCT
ejpam-5702	170	19	,1	,1	NOUN
ejpam-5702	170	20	)	)	PUNCT
ejpam-5702	170	21	n	n	CCONJ
ejpam-5702	170	22	,	,	PUNCT
ejpam-5702	170	23	y	y	PROPN
ejpam-5702	170	24	(	(	PUNCT
ejpam-5702	170	25	x	x	NOUN
ejpam-5702	170	26	)	)	PUNCT
ejpam-5702	170	27	=	=	SYM
ejpam-5702	170	28	(	(	PUNCT
ejpam-5702	170	29	t	t	NOUN
ejpam-5702	170	30	log(1	log(1	NOUN
ejpam-5702	170	31	+	+	CCONJ
ejpam-5702	170	32	t	t	NOUN
ejpam-5702	170	33	)	)	PUNCT
ejpam-5702	170	34	)	)	PUNCT
ejpam-5702	171	1	r	r	NOUN
ejpam-5702	171	2	(	(	PUNCT
ejpam-5702	171	3	1	1	NUM
ejpam-5702	171	4	+	+	CCONJ
ejpam-5702	171	5	t)x	t)x	PUNCT
ejpam-5702	171	6	=	=	PUNCT
ejpam-5702	171	7	∞∑	∞∑	NUM
ejpam-5702	171	8	n=0	n=0	NUM
ejpam-5702	171	9	brn(x	brn(x	PROPN
ejpam-5702	171	10	)	)	PUNCT
ejpam-5702	171	11	tn	tn	PROPN
ejpam-5702	171	12	n	n	PROPN
ejpam-5702	171	13	!	!	PUNCT
ejpam-5702	171	14	.	.	PUNCT
ejpam-5702	172	1	(	(	PUNCT
ejpam-5702	172	2	27	27	NUM
ejpam-5702	172	3	)	)	PUNCT
ejpam-5702	172	4	from	from	ADP
ejpam-5702	172	5	(	(	PUNCT
ejpam-5702	172	6	26	26	NUM
ejpam-5702	172	7	)	)	PUNCT
ejpam-5702	172	8	,	,	PUNCT
ejpam-5702	172	9	we	we	PRON
ejpam-5702	172	10	have	have	VERB
ejpam-5702	172	11	s.	s.	PROPN
ejpam-5702	172	12	h.	h.	PROPN
ejpam-5702	172	13	lee	lee	PROPN
ejpam-5702	172	14	,	,	PUNCT
ejpam-5702	172	15	l.	l.	PROPN
ejpam-5702	172	16	chen	chen	PROPN
ejpam-5702	172	17	/	/	SYM
ejpam-5702	172	18	eur	eur	PROPN
ejpam-5702	172	19	.	.	PUNCT
ejpam-5702	173	1	j.	j.	PROPN
ejpam-5702	173	2	pure	pure	PROPN
ejpam-5702	173	3	appl	appl	PROPN
ejpam-5702	173	4	.	.	PROPN
ejpam-5702	173	5	math	math	PROPN
ejpam-5702	173	6	,	,	PUNCT
ejpam-5702	173	7	18	18	NUM
ejpam-5702	173	8	(	(	PUNCT
ejpam-5702	173	9	1	1	NUM
ejpam-5702	173	10	)	)	PUNCT
ejpam-5702	173	11	(	(	PUNCT
ejpam-5702	173	12	2025	2025	NUM
ejpam-5702	173	13	)	)	PUNCT
ejpam-5702	173	14	,	,	PUNCT
ejpam-5702	173	15	5702	5702	NUM
ejpam-5702	173	16	7	7	NUM
ejpam-5702	173	17	of	of	ADP
ejpam-5702	173	18	13	13	NUM
ejpam-5702	173	19	proof	proof	NOUN
ejpam-5702	173	20	.	.	PUNCT
ejpam-5702	174	1	theorem	theorem	VERB
ejpam-5702	174	2	4	4	NUM
ejpam-5702	174	3	.	.	PUNCT
ejpam-5702	175	1	∞∑	∞∑	NUM
ejpam-5702	175	2	n=0	n=0	PROPN
ejpam-5702	175	3	b	b	NOUN
ejpam-5702	175	4	(	(	PUNCT
ejpam-5702	175	5	k1,	k1,	NOUN
ejpam-5702	175	6	...	...	SYM
ejpam-5702	175	7	,kr	,kr	SYM
ejpam-5702	175	8	)	)	PUNCT
ejpam-5702	175	9	n	n	CCONJ
ejpam-5702	175	10	,	,	PUNCT
ejpam-5702	175	11	y	y	PROPN
ejpam-5702	175	12	(	(	PUNCT
ejpam-5702	175	13	x	x	NOUN
ejpam-5702	175	14	)	)	PUNCT
ejpam-5702	175	15	tn	tn	PROPN
ejpam-5702	175	16	n	n	NOUN
ejpam-5702	175	17	!	!	PUNCT
ejpam-5702	175	18	=	=	PUNCT
ejpam-5702	175	19	r!(1	r!(1	VERB
ejpam-5702	175	20	+	+	CCONJ
ejpam-5702	175	21	t)x	t)x	PUNCT
ejpam-5702	175	22	(	(	PUNCT
ejpam-5702	175	23	log(1	log(1	NOUN
ejpam-5702	175	24	+	+	CCONJ
ejpam-5702	175	25	t))r	t))r	ADJ
ejpam-5702	175	26	lik1,	lik1,	PROPN
ejpam-5702	175	27	...	...	PUNCT
ejpam-5702	175	28	,kr(1−	,kr(1−	PROPN
ejpam-5702	175	29	e[e−y	e[e−y	PROPN
ejpam-5702	175	30	t	t	PROPN
ejpam-5702	175	31	]	]	PUNCT
ejpam-5702	175	32	)	)	PUNCT
ejpam-5702	175	33	(	(	PUNCT
ejpam-5702	175	34	28	28	NUM
ejpam-5702	175	35	)	)	PUNCT
ejpam-5702	175	36	=	=	VERB
ejpam-5702	175	37	r!(1	r!(1	VERB
ejpam-5702	175	38	+	+	CCONJ
ejpam-5702	175	39	t)x	t)x	PUNCT
ejpam-5702	175	40	(	(	PUNCT
ejpam-5702	175	41	log(1	log(1	NOUN
ejpam-5702	175	42	+	+	CCONJ
ejpam-5702	175	43	t))r	t))r	VERB
ejpam-5702	175	44	∑	∑	PROPN
ejpam-5702	175	45	0	0	NUM
ejpam-5702	175	46	<	<	X
ejpam-5702	175	47	m1<···<mr	m1<···<mr	NOUN
ejpam-5702	175	48	(	(	PUNCT
ejpam-5702	175	49	1−	1−	NUM
ejpam-5702	175	50	e[e−y	e[e−y	PROPN
ejpam-5702	175	51	t	t	PROPN
ejpam-5702	175	52	]	]	PUNCT
ejpam-5702	175	53	)	)	PUNCT
ejpam-5702	176	1	mr	mr	PROPN
ejpam-5702	176	2	mk1	mk1	NOUN
ejpam-5702	176	3	1	1	NUM
ejpam-5702	176	4	·	·	PUNCT
ejpam-5702	176	5	·	·	PUNCT
ejpam-5702	176	6	·	·	PUNCT
ejpam-5702	176	7	mkr	mkr	NOUN
ejpam-5702	176	8	r	r	NOUN
ejpam-5702	176	9	=	=	PUNCT
ejpam-5702	176	10	r!(1	r!(1	VERB
ejpam-5702	176	11	+	+	CCONJ
ejpam-5702	176	12	t)x	t)x	PUNCT
ejpam-5702	176	13	(	(	PUNCT
ejpam-5702	176	14	log(1	log(1	NOUN
ejpam-5702	176	15	+	+	CCONJ
ejpam-5702	176	16	t))r	t))r	VERB
ejpam-5702	176	17	∑	∑	PROPN
ejpam-5702	176	18	0	0	PUNCT
ejpam-5702	176	19	<	<	X
ejpam-5702	176	20	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	176	21	1	1	NUM
ejpam-5702	176	22	mk1	mk1	NOUN
ejpam-5702	176	23	1	1	NUM
ejpam-5702	176	24	·	·	PUNCT
ejpam-5702	176	25	·	·	PUNCT
ejpam-5702	176	26	·	·	PUNCT
ejpam-5702	177	1	mkr−1	mkr−1	PROPN
ejpam-5702	177	2	r−1	r−1	PROPN
ejpam-5702	177	3	∞∑	∞∑	NUM
ejpam-5702	177	4	mr	mr	PROPN
ejpam-5702	177	5	=	=	PROPN
ejpam-5702	177	6	mr−1	mr−1	PROPN
ejpam-5702	177	7	+	+	NOUN
ejpam-5702	177	8	1	1	NUM
ejpam-5702	177	9	(	(	PUNCT
ejpam-5702	177	10	1−	1−	NUM
ejpam-5702	177	11	e[e−y	e[e−y	PROPN
ejpam-5702	177	12	t	t	PROPN
ejpam-5702	177	13	]	]	PUNCT
ejpam-5702	177	14	)	)	PUNCT
ejpam-5702	177	15	mr	mr	PROPN
ejpam-5702	177	16	mkr	mkr	PROPN
ejpam-5702	177	17	r	r	NOUN
ejpam-5702	177	18	=	=	PUNCT
ejpam-5702	177	19	r!(1	r!(1	VERB
ejpam-5702	177	20	+	+	CCONJ
ejpam-5702	177	21	t)x	t)x	PUNCT
ejpam-5702	177	22	(	(	PUNCT
ejpam-5702	177	23	log(1	log(1	NOUN
ejpam-5702	177	24	+	+	CCONJ
ejpam-5702	177	25	t))r	t))r	VERB
ejpam-5702	177	26	∑	∑	PROPN
ejpam-5702	177	27	0	0	PUNCT
ejpam-5702	177	28	<	<	X
ejpam-5702	177	29	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	178	1	(	(	PUNCT
ejpam-5702	178	2	1−	1−	NUM
ejpam-5702	178	3	e[e−y	e[e−y	PROPN
ejpam-5702	178	4	t	t	PROPN
ejpam-5702	178	5	]	]	PUNCT
ejpam-5702	178	6	)	)	PUNCT
ejpam-5702	178	7	mr−1	mr−1	PROPN
ejpam-5702	178	8	mk1	mk1	NOUN
ejpam-5702	178	9	1	1	NUM
ejpam-5702	178	10	·	·	PUNCT
ejpam-5702	178	11	·	·	PUNCT
ejpam-5702	178	12	·	·	PUNCT
ejpam-5702	179	1	mkr−1	mkr−1	INTJ
ejpam-5702	179	2	r−1	r−1	PROPN
ejpam-5702	179	3	×	×	VERB
ejpam-5702	179	4	∞∑	∞∑	ADJ
ejpam-5702	179	5	mr=0	mr=0	NOUN
ejpam-5702	179	6	(	(	PUNCT
ejpam-5702	179	7	−1)mr+1(mr	−1)mr+1(mr	NOUN
ejpam-5702	179	8	+	+	NOUN
ejpam-5702	179	9	1	1	NUM
ejpam-5702	179	10	)	)	PUNCT
ejpam-5702	179	11	!	!	PUNCT
ejpam-5702	180	1	(	(	PUNCT
ejpam-5702	180	2	mr	mr	PROPN
ejpam-5702	180	3	+	+	PROPN
ejpam-5702	180	4	mr−1	mr−1	PROPN
ejpam-5702	180	5	+	+	ADJ
ejpam-5702	180	6	1)kr	1)kr	NUM
ejpam-5702	180	7	(	(	PUNCT
ejpam-5702	180	8	e[e−y	e[e−y	PROPN
ejpam-5702	180	9	t	t	PROPN
ejpam-5702	180	10	−	−	PROPN
ejpam-5702	180	11	1	1	NUM
ejpam-5702	180	12	]	]	PUNCT
ejpam-5702	180	13	)	)	PUNCT
ejpam-5702	180	14	mr+1	mr+1	INTJ
ejpam-5702	180	15	(	(	PUNCT
ejpam-5702	180	16	mr	mr	PROPN
ejpam-5702	180	17	+	+	PROPN
ejpam-5702	180	18	1	1	NUM
ejpam-5702	180	19	)	)	PUNCT
ejpam-5702	180	20	!	!	PUNCT
ejpam-5702	181	1	=	=	PUNCT
ejpam-5702	181	2	r!(1	r!(1	VERB
ejpam-5702	181	3	+	+	CCONJ
ejpam-5702	181	4	t)x	t)x	PUNCT
ejpam-5702	181	5	(	(	PUNCT
ejpam-5702	181	6	log(1	log(1	NOUN
ejpam-5702	181	7	+	+	CCONJ
ejpam-5702	181	8	t))r	t))r	VERB
ejpam-5702	181	9	∑	∑	PROPN
ejpam-5702	181	10	0	0	PUNCT
ejpam-5702	181	11	<	<	X
ejpam-5702	181	12	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	182	1	(	(	PUNCT
ejpam-5702	182	2	1−	1−	NUM
ejpam-5702	182	3	e[e−y	e[e−y	PROPN
ejpam-5702	182	4	t	t	PROPN
ejpam-5702	182	5	]	]	PUNCT
ejpam-5702	182	6	)	)	PUNCT
ejpam-5702	182	7	mr−1	mr−1	PROPN
ejpam-5702	182	8	mk1	mk1	NOUN
ejpam-5702	182	9	1	1	NUM
ejpam-5702	182	10	·	·	PUNCT
ejpam-5702	182	11	·	·	PUNCT
ejpam-5702	182	12	·	·	PUNCT
ejpam-5702	183	1	mkr−1	mkr−1	INTJ
ejpam-5702	183	2	r−1	r−1	PROPN
ejpam-5702	183	3	×	×	VERB
ejpam-5702	183	4	∞∑	∞∑	ADJ
ejpam-5702	183	5	mr=0	mr=0	NOUN
ejpam-5702	183	6	(	(	PUNCT
ejpam-5702	183	7	−1)mr+1(mr	−1)mr+1(mr	NOUN
ejpam-5702	183	8	+	+	NOUN
ejpam-5702	183	9	1	1	NUM
ejpam-5702	183	10	)	)	PUNCT
ejpam-5702	183	11	!	!	PUNCT
ejpam-5702	184	1	(	(	PUNCT
ejpam-5702	184	2	mr	mr	PROPN
ejpam-5702	184	3	+	+	PROPN
ejpam-5702	184	4	mr−1	mr−1	PROPN
ejpam-5702	184	5	+	+	NOUN
ejpam-5702	184	6	1)kr	1)kr	ADJ
ejpam-5702	184	7	∞∑	∞∑	NUM
ejpam-5702	184	8	l	l	NOUN
ejpam-5702	184	9	=	=	X
ejpam-5702	184	10	mr+1	mr+1	ADJ
ejpam-5702	184	11	{	{	PUNCT
ejpam-5702	184	12	l	l	NOUN
ejpam-5702	184	13	mr	mr	PROPN
ejpam-5702	184	14	+	+	PROPN
ejpam-5702	184	15	1	1	NUM
ejpam-5702	184	16	}	}	PUNCT
ejpam-5702	184	17	y	y	PROPN
ejpam-5702	184	18	(	(	PUNCT
ejpam-5702	184	19	−1)ltl	−1)ltl	PROPN
ejpam-5702	184	20	l	l	NOUN
ejpam-5702	184	21	!	!	PUNCT
ejpam-5702	185	1	=	=	PUNCT
ejpam-5702	185	2	r!(1	r!(1	VERB
ejpam-5702	185	3	+	+	CCONJ
ejpam-5702	185	4	t)x	t)x	PUNCT
ejpam-5702	185	5	(	(	PUNCT
ejpam-5702	185	6	log(1	log(1	NOUN
ejpam-5702	185	7	+	+	CCONJ
ejpam-5702	185	8	t))r	t))r	VERB
ejpam-5702	185	9	∑	∑	PROPN
ejpam-5702	185	10	0	0	PUNCT
ejpam-5702	185	11	<	<	X
ejpam-5702	185	12	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	186	1	(	(	PUNCT
ejpam-5702	186	2	1−	1−	NUM
ejpam-5702	186	3	e[e−y	e[e−y	PROPN
ejpam-5702	186	4	t	t	PROPN
ejpam-5702	186	5	]	]	PUNCT
ejpam-5702	186	6	)	)	PUNCT
ejpam-5702	186	7	mr−1	mr−1	PROPN
ejpam-5702	186	8	mk1	mk1	NOUN
ejpam-5702	186	9	1	1	NUM
ejpam-5702	186	10	·	·	PUNCT
ejpam-5702	186	11	·	·	PUNCT
ejpam-5702	186	12	·	·	PUNCT
ejpam-5702	187	1	mkr−1	mkr−1	INTJ
ejpam-5702	187	2	r−1	r−1	PROPN
ejpam-5702	187	3	×	×	NOUN
ejpam-5702	188	1	∞∑	∞∑	NUM
ejpam-5702	188	2	l=1	l=1	PROPN
ejpam-5702	188	3	l−1∑	l−1∑	ADJ
ejpam-5702	188	4	mr=0	mr=0	NOUN
ejpam-5702	188	5	(	(	PUNCT
ejpam-5702	188	6	−1)m	−1)m	NOUN
ejpam-5702	188	7	r+l+1(mr	r+l+1(mr	NOUN
ejpam-5702	188	8	+	+	NOUN
ejpam-5702	188	9	1	1	NUM
ejpam-5702	188	10	)	)	PUNCT
ejpam-5702	188	11	!	!	PUNCT
ejpam-5702	189	1	(	(	PUNCT
ejpam-5702	189	2	mr	mr	PROPN
ejpam-5702	189	3	+	+	PROPN
ejpam-5702	189	4	mr−1	mr−1	PROPN
ejpam-5702	189	5	+	+	ADJ
ejpam-5702	189	6	1)kr	1)kr	ADJ
ejpam-5702	189	7	{	{	PUNCT
ejpam-5702	189	8	l	l	NOUN
ejpam-5702	189	9	mr	mr	PROPN
ejpam-5702	189	10	+	+	PROPN
ejpam-5702	189	11	1	1	NUM
ejpam-5702	189	12	}	}	PUNCT
ejpam-5702	189	13	y	y	PROPN
ejpam-5702	189	14	tl	tl	PROPN
ejpam-5702	189	15	l	l	NOUN
ejpam-5702	189	16	!	!	PUNCT
ejpam-5702	190	1	=	=	PUNCT
ejpam-5702	190	2	r!(1	r!(1	VERB
ejpam-5702	190	3	+	+	CCONJ
ejpam-5702	190	4	t)x	t)x	PUNCT
ejpam-5702	190	5	(	(	PUNCT
ejpam-5702	190	6	log(1	log(1	NOUN
ejpam-5702	190	7	+	+	CCONJ
ejpam-5702	190	8	t))r	t))r	VERB
ejpam-5702	190	9	∑	∑	PROPN
ejpam-5702	190	10	0	0	PUNCT
ejpam-5702	190	11	<	<	X
ejpam-5702	190	12	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	191	1	(	(	PUNCT
ejpam-5702	191	2	1−	1−	NUM
ejpam-5702	191	3	e[e−y	e[e−y	PROPN
ejpam-5702	191	4	t	t	PROPN
ejpam-5702	191	5	]	]	PUNCT
ejpam-5702	191	6	)	)	PUNCT
ejpam-5702	191	7	mr−1	mr−1	PROPN
ejpam-5702	191	8	mk1	mk1	NOUN
ejpam-5702	191	9	1	1	NUM
ejpam-5702	191	10	·	·	PUNCT
ejpam-5702	191	11	·	·	PUNCT
ejpam-5702	191	12	·	·	PUNCT
ejpam-5702	191	13	mkr−1−j	mkr−1−j	NOUN
ejpam-5702	192	1	r−1	r−1	PROPN
ejpam-5702	192	2	×	×	NOUN
ejpam-5702	192	3	∞∑	∞∑	NUM
ejpam-5702	192	4	l=1	l=1	PROPN
ejpam-5702	192	5	l−1∑	l−1∑	ADJ
ejpam-5702	192	6	mr=0	mr=0	NOUN
ejpam-5702	192	7	(	(	PUNCT
ejpam-5702	192	8	−1)m	−1)m	PROPN
ejpam-5702	192	9	r+l+j+1(mr	r+l+j+1(mr	NOUN
ejpam-5702	192	10	+	+	X
ejpam-5702	192	11	1	1	NUM
ejpam-5702	192	12	)	)	PUNCT
ejpam-5702	192	13	!	!	PUNCT
ejpam-5702	193	1	{	{	PUNCT
ejpam-5702	194	1	l	l	NOUN
ejpam-5702	194	2	mr	mr	PROPN
ejpam-5702	194	3	+	+	PROPN
ejpam-5702	194	4	1	1	NUM
ejpam-5702	194	5	}	}	PUNCT
ejpam-5702	194	6	tl	tl	PROPN
ejpam-5702	194	7	l	l	NOUN
ejpam-5702	194	8	!	!	PUNCT
ejpam-5702	195	1	∞∑	∞∑	NUM
ejpam-5702	195	2	j=0	j=0	PROPN
ejpam-5702	195	3	(	(	PUNCT
ejpam-5702	195	4	kr	kr	PROPN
ejpam-5702	195	5	+	+	PROPN
ejpam-5702	195	6	j	j	PROPN
ejpam-5702	195	7	−	−	PROPN
ejpam-5702	195	8	1	1	NUM
ejpam-5702	195	9	j	j	PROPN
ejpam-5702	195	10	)	)	PUNCT
ejpam-5702	196	1	(	(	PUNCT
ejpam-5702	196	2	mr	mr	PROPN
ejpam-5702	196	3	+	+	PROPN
ejpam-5702	196	4	1)−kr−j	1)−kr−j	NUM
ejpam-5702	196	5	t	t	PROPN
ejpam-5702	196	6	j	j	PROPN
ejpam-5702	196	7	j	j	PROPN
ejpam-5702	196	8	!	!	PUNCT
ejpam-5702	196	9	=	=	PUNCT
ejpam-5702	196	10	r!(1	r!(1	VERB
ejpam-5702	196	11	+	+	CCONJ
ejpam-5702	196	12	t)x	t)x	PUNCT
ejpam-5702	196	13	(	(	PUNCT
ejpam-5702	196	14	log(1	log(1	NOUN
ejpam-5702	196	15	+	+	CCONJ
ejpam-5702	196	16	t))r	t))r	VERB
ejpam-5702	196	17	∑	∑	PROPN
ejpam-5702	196	18	0	0	PUNCT
ejpam-5702	196	19	<	<	X
ejpam-5702	196	20	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	197	1	(	(	PUNCT
ejpam-5702	197	2	1−	1−	NUM
ejpam-5702	197	3	e[e−y	e[e−y	PROPN
ejpam-5702	197	4	t	t	PROPN
ejpam-5702	197	5	]	]	PUNCT
ejpam-5702	197	6	)	)	PUNCT
ejpam-5702	197	7	mr−1	mr−1	PROPN
ejpam-5702	197	8	mk1	mk1	NOUN
ejpam-5702	197	9	1	1	NUM
ejpam-5702	197	10	·	·	PUNCT
ejpam-5702	197	11	·	·	PUNCT
ejpam-5702	197	12	·	·	PUNCT
ejpam-5702	197	13	mkr−1−j	mkr−1−j	NOUN
ejpam-5702	198	1	r−1	r−1	PROPN
ejpam-5702	198	2	×	×	NOUN
ejpam-5702	198	3	∞∑	∞∑	NUM
ejpam-5702	198	4	l=1	l=1	NOUN
ejpam-5702	198	5	l−1∑	l−1∑	ADJ
ejpam-5702	198	6	mr=0	mr=0	ADJ
ejpam-5702	198	7	∞∑	∞∑	PROPN
ejpam-5702	198	8	j=0	j=0	PROPN
ejpam-5702	198	9	(	(	PUNCT
ejpam-5702	198	10	−1)mr+l+j+1(mr	−1)mr+l+j+1(mr	NOUN
ejpam-5702	198	11	+	+	NOUN
ejpam-5702	198	12	1)!(mr	1)!(mr	NUM
ejpam-5702	198	13	+	+	NUM
ejpam-5702	198	14	1)−kr−j	1)−kr−j	NUM
ejpam-5702	198	15	{	{	PUNCT
ejpam-5702	198	16	l	l	NOUN
ejpam-5702	198	17	mr	mr	PROPN
ejpam-5702	198	18	+	+	PROPN
ejpam-5702	198	19	1	1	NUM
ejpam-5702	198	20	}	}	PUNCT
ejpam-5702	198	21	y	y	PROPN
ejpam-5702	198	22	(	(	PUNCT
ejpam-5702	198	23	kr	kr	PROPN
ejpam-5702	198	24	+	+	PROPN
ejpam-5702	198	25	j	j	PROPN
ejpam-5702	198	26	−	−	PROPN
ejpam-5702	198	27	1	1	NUM
ejpam-5702	198	28	j	j	PROPN
ejpam-5702	198	29	)	)	PUNCT
ejpam-5702	198	30	tl	tl	PROPN
ejpam-5702	198	31	l	l	NOUN
ejpam-5702	198	32	!	!	PUNCT
ejpam-5702	199	1	=	=	PUNCT
ejpam-5702	199	2	r	r	NOUN
ejpam-5702	199	3	log(1	log(1	NOUN
ejpam-5702	199	4	+	+	CCONJ
ejpam-5702	199	5	t	t	X
ejpam-5702	199	6	)	)	PUNCT
ejpam-5702	200	1	∞∑	∞∑	NUM
ejpam-5702	200	2	l=1	l=1	NOUN
ejpam-5702	200	3	l−1∑	l−1∑	ADJ
ejpam-5702	200	4	mr=0	mr=0	ADJ
ejpam-5702	200	5	∞∑	∞∑	PROPN
ejpam-5702	200	6	j=0	j=0	PROPN
ejpam-5702	200	7	(	(	PUNCT
ejpam-5702	200	8	−1)mr+l+j+1(mr	−1)mr+l+j+1(mr	NOUN
ejpam-5702	200	9	+	+	NOUN
ejpam-5702	200	10	1)!(mr	1)!(mr	NUM
ejpam-5702	200	11	+	+	NUM
ejpam-5702	200	12	1)−kr−j	1)−kr−j	NUM
ejpam-5702	200	13	{	{	PUNCT
ejpam-5702	200	14	l	l	NOUN
ejpam-5702	200	15	mr	mr	PROPN
ejpam-5702	200	16	+	+	PROPN
ejpam-5702	200	17	1	1	NUM
ejpam-5702	200	18	}	}	PUNCT
ejpam-5702	200	19	y	y	PROPN
ejpam-5702	200	20	(	(	PUNCT
ejpam-5702	200	21	kr	kr	PROPN
ejpam-5702	200	22	+	+	PROPN
ejpam-5702	200	23	j	j	PROPN
ejpam-5702	200	24	−	−	PROPN
ejpam-5702	200	25	1	1	NUM
ejpam-5702	200	26	j	j	PROPN
ejpam-5702	200	27	)	)	PUNCT
ejpam-5702	200	28	tl	tl	PROPN
ejpam-5702	200	29	l	l	NOUN
ejpam-5702	200	30	!	!	PUNCT
ejpam-5702	201	1	s.	s.	PROPN
ejpam-5702	201	2	h.	h.	PROPN
ejpam-5702	201	3	lee	lee	PROPN
ejpam-5702	201	4	,	,	PUNCT
ejpam-5702	201	5	l.	l.	PROPN
ejpam-5702	201	6	chen	chen	PROPN
ejpam-5702	201	7	/	/	SYM
ejpam-5702	201	8	eur	eur	PROPN
ejpam-5702	201	9	.	.	PUNCT
ejpam-5702	202	1	j.	j.	PROPN
ejpam-5702	202	2	pure	pure	PROPN
ejpam-5702	202	3	appl	appl	PROPN
ejpam-5702	202	4	.	.	PROPN
ejpam-5702	202	5	math	math	PROPN
ejpam-5702	202	6	,	,	PUNCT
ejpam-5702	202	7	18	18	NUM
ejpam-5702	202	8	(	(	PUNCT
ejpam-5702	202	9	1	1	NUM
ejpam-5702	202	10	)	)	PUNCT
ejpam-5702	202	11	(	(	PUNCT
ejpam-5702	202	12	2025	2025	NUM
ejpam-5702	202	13	)	)	PUNCT
ejpam-5702	202	14	,	,	PUNCT
ejpam-5702	202	15	5702	5702	NUM
ejpam-5702	202	16	8	8	NUM
ejpam-5702	202	17	of	of	ADP
ejpam-5702	202	18	13	13	NUM
ejpam-5702	202	19	×	×	NOUN
ejpam-5702	202	20	∞∑	∞∑	PROPN
ejpam-5702	202	21	i=0	i=0	PROPN
ejpam-5702	202	22	b	b	PROPN
ejpam-5702	202	23	(	(	PUNCT
ejpam-5702	202	24	k1,	k1,	NOUN
ejpam-5702	202	25	...	...	PUNCT
ejpam-5702	202	26	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	202	27	)	)	PUNCT
ejpam-5702	203	1	i	i	PRON
ejpam-5702	203	2	,	,	PUNCT
ejpam-5702	203	3	y	y	PROPN
ejpam-5702	203	4	(	(	PUNCT
ejpam-5702	203	5	x	x	X
ejpam-5702	203	6	)	)	PUNCT
ejpam-5702	203	7	ti	ti	NOUN
ejpam-5702	203	8	i	i	PRON
ejpam-5702	203	9	!	!	PUNCT
ejpam-5702	204	1	=	=	PUNCT
ejpam-5702	204	2	r	r	NOUN
ejpam-5702	204	3	li1(−t	li1(−t	NOUN
ejpam-5702	204	4	)	)	PUNCT
ejpam-5702	204	5	∞∑	∞∑	NUM
ejpam-5702	204	6	n=1	n=1	ADP
ejpam-5702	204	7	n−1∑	n−1∑	NUM
ejpam-5702	204	8	l=0	l=0	PROPN
ejpam-5702	204	9	l−1∑	l−1∑	ADJ
ejpam-5702	204	10	mr=0	mr=0	ADJ
ejpam-5702	204	11	∞∑	∞∑	PROPN
ejpam-5702	204	12	j=0	j=0	PROPN
ejpam-5702	204	13	(	(	PUNCT
ejpam-5702	204	14	−1)mr+l+j	−1)mr+l+j	ADV
ejpam-5702	204	15	(	(	PUNCT
ejpam-5702	204	16	n	n	X
ejpam-5702	204	17	l	l	NOUN
ejpam-5702	205	1	+	+	CCONJ
ejpam-5702	205	2	1	1	NUM
ejpam-5702	205	3	)	)	PUNCT
ejpam-5702	205	4	(	(	PUNCT
ejpam-5702	205	5	kr	kr	PROPN
ejpam-5702	205	6	+	+	PROPN
ejpam-5702	205	7	j	j	PROPN
ejpam-5702	205	8	−	−	PROPN
ejpam-5702	205	9	1	1	NUM
ejpam-5702	205	10	j	j	NOUN
ejpam-5702	205	11	)	)	PUNCT
ejpam-5702	205	12	{	{	PUNCT
ejpam-5702	206	1	l	l	NOUN
ejpam-5702	207	1	+	+	NUM
ejpam-5702	207	2	1	1	NUM
ejpam-5702	207	3	mr	mr	PROPN
ejpam-5702	207	4	+	+	PROPN
ejpam-5702	207	5	1	1	NUM
ejpam-5702	207	6	}	}	PUNCT
ejpam-5702	207	7	y	y	PROPN
ejpam-5702	207	8	×	×	NOUN
ejpam-5702	207	9	(	(	PUNCT
ejpam-5702	207	10	mr	mr	PROPN
ejpam-5702	207	11	+	+	PROPN
ejpam-5702	207	12	1)!(mr	1)!(mr	NUM
ejpam-5702	207	13	+	+	NUM
ejpam-5702	207	14	1)−kr−jb	1)−kr−jb	NUM
ejpam-5702	207	15	(	(	PUNCT
ejpam-5702	207	16	k1,	k1,	NOUN
ejpam-5702	207	17	...	...	PUNCT
ejpam-5702	207	18	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	207	19	)	)	PUNCT
ejpam-5702	207	20	n−l−1,y	n−l−1,y	X
ejpam-5702	207	21	(	(	PUNCT
ejpam-5702	207	22	x	x	X
ejpam-5702	207	23	)	)	PUNCT
ejpam-5702	207	24	tn	tn	PROPN
ejpam-5702	207	25	n	n	NUM
ejpam-5702	207	26	!	!	PUNCT
ejpam-5702	207	27	.	.	PUNCT
ejpam-5702	208	1	therefore	therefore	ADV
ejpam-5702	208	2	,	,	PUNCT
ejpam-5702	208	3	by	by	ADP
ejpam-5702	208	4	(	(	PUNCT
ejpam-5702	208	5	28	28	NUM
ejpam-5702	208	6	)	)	PUNCT
ejpam-5702	208	7	,	,	PUNCT
ejpam-5702	208	8	we	we	PRON
ejpam-5702	208	9	have	have	VERB
ejpam-5702	208	10	the	the	DET
ejpam-5702	208	11	following	follow	VERB
ejpam-5702	208	12	theorem	theorem	VERB
ejpam-5702	208	13	.	.	PUNCT
ejpam-5702	208	14	theorem	theorem	NOUN
ejpam-5702	208	15	4	4	NUM
ejpam-5702	208	16	.	.	PUNCT
ejpam-5702	208	17	for	for	ADP
ejpam-5702	208	18	n	n	PRON
ejpam-5702	208	19	≥	≥	NOUN
ejpam-5702	208	20	0	0	NUM
ejpam-5702	208	21	,	,	PUNCT
ejpam-5702	208	22	t	t	PROPN
ejpam-5702	208	23	̸=	̸=	PROPN
ejpam-5702	208	24	0	0	NUM
ejpam-5702	208	25	,	,	PUNCT
ejpam-5702	208	26	we	we	PRON
ejpam-5702	208	27	have	have	VERB
ejpam-5702	208	28	b	b	NUM
ejpam-5702	208	29	(	(	PUNCT
ejpam-5702	208	30	k1,	k1,	NOUN
ejpam-5702	208	31	...	...	SYM
ejpam-5702	208	32	,kr	,kr	SYM
ejpam-5702	208	33	)	)	PUNCT
ejpam-5702	208	34	n	n	CCONJ
ejpam-5702	208	35	,	,	PUNCT
ejpam-5702	208	36	y	y	PROPN
ejpam-5702	208	37	(	(	PUNCT
ejpam-5702	208	38	x	x	NOUN
ejpam-5702	208	39	)	)	PUNCT
ejpam-5702	208	40	=	=	SYM
ejpam-5702	208	41	r	r	NOUN
ejpam-5702	208	42	lik(−t	lik(−t	PROPN
ejpam-5702	208	43	)	)	PUNCT
ejpam-5702	208	44	n−1∑	n−1∑	PROPN
ejpam-5702	208	45	l=0	l=0	PROPN
ejpam-5702	208	46	l−1∑	l−1∑	ADJ
ejpam-5702	208	47	mr=0	mr=0	ADJ
ejpam-5702	208	48	∞∑	∞∑	PROPN
ejpam-5702	208	49	j=0	j=0	PROPN
ejpam-5702	208	50	(	(	PUNCT
ejpam-5702	208	51	−1)mr+l+j	−1)mr+l+j	ADV
ejpam-5702	208	52	(	(	PUNCT
ejpam-5702	208	53	n	n	X
ejpam-5702	208	54	l	l	NOUN
ejpam-5702	209	1	+	+	CCONJ
ejpam-5702	209	2	1	1	NUM
ejpam-5702	209	3	)	)	PUNCT
ejpam-5702	209	4	(	(	PUNCT
ejpam-5702	209	5	kr	kr	PROPN
ejpam-5702	209	6	+	+	PROPN
ejpam-5702	209	7	j	j	PROPN
ejpam-5702	209	8	−	−	PROPN
ejpam-5702	209	9	1	1	NUM
ejpam-5702	209	10	j	j	NOUN
ejpam-5702	209	11	)	)	PUNCT
ejpam-5702	209	12	{	{	PUNCT
ejpam-5702	210	1	l	l	NOUN
ejpam-5702	211	1	+	+	NUM
ejpam-5702	211	2	1	1	NUM
ejpam-5702	211	3	mr	mr	PROPN
ejpam-5702	211	4	+	+	PROPN
ejpam-5702	211	5	1	1	NUM
ejpam-5702	211	6	}	}	PUNCT
ejpam-5702	211	7	y	y	PROPN
ejpam-5702	211	8	×	×	NOUN
ejpam-5702	211	9	(	(	PUNCT
ejpam-5702	211	10	mr	mr	PROPN
ejpam-5702	211	11	+	+	PROPN
ejpam-5702	211	12	1)!(mr	1)!(mr	NUM
ejpam-5702	211	13	+	+	NUM
ejpam-5702	211	14	1)−kr−jb	1)−kr−jb	NUM
ejpam-5702	211	15	(	(	PUNCT
ejpam-5702	211	16	k1,	k1,	NOUN
ejpam-5702	211	17	...	...	PUNCT
ejpam-5702	211	18	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	211	19	)	)	PUNCT
ejpam-5702	211	20	n−l−1,y	n−l−1,y	PUNCT
ejpam-5702	211	21	(	(	PUNCT
ejpam-5702	211	22	x	x	NOUN
ejpam-5702	211	23	)	)	PUNCT
ejpam-5702	211	24	.	.	PUNCT
ejpam-5702	212	1	from	from	ADP
ejpam-5702	212	2	(	(	PUNCT
ejpam-5702	212	3	26	26	NUM
ejpam-5702	212	4	)	)	PUNCT
ejpam-5702	212	5	,	,	PUNCT
ejpam-5702	212	6	we	we	PRON
ejpam-5702	212	7	obtain	obtain	VERB
ejpam-5702	212	8	proof	proof	NOUN
ejpam-5702	212	9	.	.	PUNCT
ejpam-5702	213	1	theorem	theorem	ADJ
ejpam-5702	213	2	5	5	NUM
ejpam-5702	213	3	.	.	SYM
ejpam-5702	213	4	1	1	NUM
ejpam-5702	213	5	t	t	NOUN
ejpam-5702	213	6	(	(	PUNCT
ejpam-5702	213	7	∞∑	∞∑	PROPN
ejpam-5702	213	8	n=0	n=0	PROPN
ejpam-5702	213	9	b	b	NOUN
ejpam-5702	213	10	(	(	PUNCT
ejpam-5702	213	11	k1,	k1,	NOUN
ejpam-5702	213	12	...	...	SYM
ejpam-5702	213	13	,kr	,kr	SYM
ejpam-5702	213	14	)	)	PUNCT
ejpam-5702	213	15	n	n	CCONJ
ejpam-5702	213	16	,	,	PUNCT
ejpam-5702	213	17	y	y	PROPN
ejpam-5702	213	18	(	(	PUNCT
ejpam-5702	213	19	x+	x+	PROPN
ejpam-5702	213	20	1	1	NUM
ejpam-5702	213	21	)	)	PUNCT
ejpam-5702	213	22	tn	tn	NOUN
ejpam-5702	213	23	n	n	NOUN
ejpam-5702	213	24	!	!	PUNCT
ejpam-5702	214	1	−	−	PROPN
ejpam-5702	215	1	∞∑	∞∑	PRON
ejpam-5702	215	2	n=0	n=0	PROPN
ejpam-5702	215	3	b	b	NOUN
ejpam-5702	215	4	(	(	PUNCT
ejpam-5702	215	5	k1,	k1,	NOUN
ejpam-5702	215	6	...	...	SYM
ejpam-5702	215	7	,kr	,kr	SYM
ejpam-5702	215	8	)	)	PUNCT
ejpam-5702	215	9	n	n	CCONJ
ejpam-5702	215	10	,	,	PUNCT
ejpam-5702	215	11	y	y	PROPN
ejpam-5702	215	12	(	(	PUNCT
ejpam-5702	215	13	x	x	NOUN
ejpam-5702	215	14	)	)	PUNCT
ejpam-5702	215	15	tn	tn	PROPN
ejpam-5702	215	16	n	n	NOUN
ejpam-5702	215	17	!	!	PUNCT
ejpam-5702	215	18	)	)	PUNCT
ejpam-5702	216	1	=	=	PUNCT
ejpam-5702	216	2	r!lik1,	r!lik1,	NOUN
ejpam-5702	216	3	...	...	PUNCT
ejpam-5702	216	4	,kr	,kr	PUNCT
ejpam-5702	216	5	(	(	PUNCT
ejpam-5702	216	6	1−	1−	NUM
ejpam-5702	216	7	e[e−y	e[e−y	PROPN
ejpam-5702	216	8	t	t	PROPN
ejpam-5702	216	9	]	]	PUNCT
ejpam-5702	216	10	)	)	PUNCT
ejpam-5702	216	11	(	(	PUNCT
ejpam-5702	216	12	log(1	log(1	NOUN
ejpam-5702	216	13	+	+	CCONJ
ejpam-5702	216	14	t))r	t))r	ADJ
ejpam-5702	216	15	(	(	PUNCT
ejpam-5702	216	16	1	1	NUM
ejpam-5702	216	17	+	+	CCONJ
ejpam-5702	216	18	t)x	t)x	PUNCT
ejpam-5702	216	19	(	(	PUNCT
ejpam-5702	216	20	29	29	NUM
ejpam-5702	216	21	)	)	PUNCT
ejpam-5702	216	22	=	=	VERB
ejpam-5702	216	23	r!(1	r!(1	VERB
ejpam-5702	216	24	+	+	CCONJ
ejpam-5702	216	25	t)x	t)x	PUNCT
ejpam-5702	216	26	(	(	PUNCT
ejpam-5702	216	27	log(1	log(1	NOUN
ejpam-5702	216	28	+	+	CCONJ
ejpam-5702	216	29	t))r	t))r	VERB
ejpam-5702	216	30	∑	∑	PROPN
ejpam-5702	216	31	0	0	NUM
ejpam-5702	216	32	<	<	X
ejpam-5702	216	33	m1<···<mr	m1<···<mr	NOUN
ejpam-5702	216	34	(	(	PUNCT
ejpam-5702	216	35	1−	1−	NUM
ejpam-5702	216	36	e[e−y	e[e−y	PROPN
ejpam-5702	216	37	t	t	PROPN
ejpam-5702	216	38	]	]	PUNCT
ejpam-5702	216	39	)	)	PUNCT
ejpam-5702	216	40	mr	mr	PROPN
ejpam-5702	216	41	mk1	mk1	NOUN
ejpam-5702	216	42	1	1	NUM
ejpam-5702	216	43	·	·	PUNCT
ejpam-5702	216	44	·	·	PUNCT
ejpam-5702	216	45	·	·	PUNCT
ejpam-5702	216	46	mkr	mkr	NOUN
ejpam-5702	216	47	r	r	NOUN
ejpam-5702	216	48	=	=	PUNCT
ejpam-5702	216	49	r!(1	r!(1	VERB
ejpam-5702	216	50	+	+	CCONJ
ejpam-5702	216	51	t)x	t)x	PUNCT
ejpam-5702	216	52	(	(	PUNCT
ejpam-5702	216	53	log(1	log(1	NOUN
ejpam-5702	216	54	+	+	CCONJ
ejpam-5702	216	55	t))r	t))r	VERB
ejpam-5702	216	56	∑	∑	PROPN
ejpam-5702	216	57	0	0	PUNCT
ejpam-5702	216	58	<	<	X
ejpam-5702	216	59	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	216	60	1	1	NUM
ejpam-5702	216	61	mk1	mk1	NOUN
ejpam-5702	216	62	1	1	NUM
ejpam-5702	216	63	·	·	PUNCT
ejpam-5702	216	64	·	·	PUNCT
ejpam-5702	216	65	·	·	PUNCT
ejpam-5702	217	1	mkr−1	mkr−1	PROPN
ejpam-5702	217	2	r−1	r−1	PROPN
ejpam-5702	217	3	∑	∑	PUNCT
ejpam-5702	217	4	mr	mr	PROPN
ejpam-5702	217	5	=	=	PROPN
ejpam-5702	217	6	mr−1	mr−1	PROPN
ejpam-5702	217	7	+	+	PROPN
ejpam-5702	217	8	1	1	NUM
ejpam-5702	217	9	(	(	PUNCT
ejpam-5702	217	10	1−	1−	NUM
ejpam-5702	217	11	e[e−y	e[e−y	PROPN
ejpam-5702	217	12	t	t	PROPN
ejpam-5702	217	13	]	]	PUNCT
ejpam-5702	217	14	)	)	PUNCT
ejpam-5702	217	15	mr	mr	PROPN
ejpam-5702	217	16	mkr	mkr	PROPN
ejpam-5702	217	17	r	r	NOUN
ejpam-5702	217	18	=	=	PUNCT
ejpam-5702	217	19	r!(1	r!(1	VERB
ejpam-5702	217	20	+	+	CCONJ
ejpam-5702	217	21	t)x	t)x	PUNCT
ejpam-5702	217	22	(	(	PUNCT
ejpam-5702	217	23	log(1	log(1	NOUN
ejpam-5702	217	24	+	+	CCONJ
ejpam-5702	217	25	t))r	t))r	VERB
ejpam-5702	217	26	∑	∑	PROPN
ejpam-5702	217	27	0	0	PUNCT
ejpam-5702	217	28	<	<	X
ejpam-5702	217	29	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	218	1	(	(	PUNCT
ejpam-5702	218	2	1−	1−	NUM
ejpam-5702	218	3	e[ey	e[ey	PROPN
ejpam-5702	218	4	t	t	PROPN
ejpam-5702	218	5	]	]	PUNCT
ejpam-5702	218	6	)	)	PUNCT
ejpam-5702	218	7	mr−1	mr−1	PROPN
ejpam-5702	218	8	mk1	mk1	NOUN
ejpam-5702	218	9	1	1	NUM
ejpam-5702	218	10	·	·	PUNCT
ejpam-5702	218	11	·	·	PUNCT
ejpam-5702	218	12	·	·	PUNCT
ejpam-5702	219	1	mkr−1	mkr−1	PROPN
ejpam-5702	219	2	r−1	r−1	PROPN
ejpam-5702	219	3	∞∑	∞∑	NUM
ejpam-5702	219	4	mr=1	mr=1	PROPN
ejpam-5702	219	5	(	(	PUNCT
ejpam-5702	219	6	−1)mrmr	−1)mrmr	PROPN
ejpam-5702	219	7	!	!	PUNCT
ejpam-5702	220	1	(	(	PUNCT
ejpam-5702	220	2	mr	mr	PROPN
ejpam-5702	220	3	+	+	PROPN
ejpam-5702	220	4	mr−1)kr	mr−1)kr	PROPN
ejpam-5702	220	5	(	(	PUNCT
ejpam-5702	220	6	e[e−y	e[e−y	PROPN
ejpam-5702	220	7	t]−	t]−	NOUN
ejpam-5702	220	8	1	1	NUM
ejpam-5702	220	9	)	)	PUNCT
ejpam-5702	220	10	mr	mr	PROPN
ejpam-5702	220	11	mr	mr	PROPN
ejpam-5702	220	12	!	!	PROPN
ejpam-5702	220	13	=	=	PRON
ejpam-5702	220	14	r!(1	r!(1	VERB
ejpam-5702	220	15	+	+	CCONJ
ejpam-5702	220	16	t)x	t)x	PUNCT
ejpam-5702	220	17	(	(	PUNCT
ejpam-5702	220	18	log(1	log(1	NOUN
ejpam-5702	220	19	+	+	CCONJ
ejpam-5702	220	20	t))r	t))r	VERB
ejpam-5702	220	21	∑	∑	PROPN
ejpam-5702	220	22	0	0	PUNCT
ejpam-5702	220	23	<	<	X
ejpam-5702	220	24	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	221	1	(	(	PUNCT
ejpam-5702	221	2	1−	1−	NUM
ejpam-5702	221	3	e[ey	e[ey	PROPN
ejpam-5702	221	4	t	t	PROPN
ejpam-5702	221	5	]	]	PUNCT
ejpam-5702	221	6	)	)	PUNCT
ejpam-5702	221	7	mr−1	mr−1	PROPN
ejpam-5702	221	8	mk1	mk1	NOUN
ejpam-5702	221	9	1	1	NUM
ejpam-5702	221	10	·	·	PUNCT
ejpam-5702	221	11	·	·	PUNCT
ejpam-5702	221	12	·	·	PUNCT
ejpam-5702	222	1	mkr−1	mkr−1	PROPN
ejpam-5702	222	2	r−1	r−1	PROPN
ejpam-5702	222	3	∞∑	∞∑	NUM
ejpam-5702	222	4	mr=1	mr=1	PROPN
ejpam-5702	222	5	(	(	PUNCT
ejpam-5702	222	6	−1)mr+lmr	−1)mr+lmr	PROPN
ejpam-5702	222	7	!	!	PUNCT
ejpam-5702	223	1	(	(	PUNCT
ejpam-5702	223	2	mr	mr	PROPN
ejpam-5702	223	3	+	+	PROPN
ejpam-5702	223	4	mr−1)kr	mr−1)kr	PROPN
ejpam-5702	223	5	∞∑	∞∑	PROPN
ejpam-5702	223	6	l	l	NOUN
ejpam-5702	223	7	=	=	PRON
ejpam-5702	223	8	mr	mr	PROPN
ejpam-5702	223	9	{	{	PUNCT
ejpam-5702	223	10	l	l	NOUN
ejpam-5702	223	11	mr	mr	PROPN
ejpam-5702	223	12	}	}	PUNCT
ejpam-5702	223	13	y	y	PROPN
ejpam-5702	223	14	tl	tl	PROPN
ejpam-5702	223	15	l	l	NOUN
ejpam-5702	223	16	!	!	PUNCT
ejpam-5702	224	1	=	=	PUNCT
ejpam-5702	224	2	r!(1	r!(1	VERB
ejpam-5702	224	3	+	+	CCONJ
ejpam-5702	224	4	t)x	t)x	PUNCT
ejpam-5702	224	5	(	(	PUNCT
ejpam-5702	224	6	log(1	log(1	NOUN
ejpam-5702	224	7	+	+	CCONJ
ejpam-5702	224	8	t))r	t))r	VERB
ejpam-5702	224	9	∑	∑	PROPN
ejpam-5702	224	10	0	0	PUNCT
ejpam-5702	224	11	<	<	X
ejpam-5702	224	12	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	225	1	(	(	PUNCT
ejpam-5702	225	2	1−	1−	NUM
ejpam-5702	225	3	e[ey	e[ey	PROPN
ejpam-5702	225	4	t	t	PROPN
ejpam-5702	225	5	]	]	PUNCT
ejpam-5702	225	6	)	)	PUNCT
ejpam-5702	225	7	mr−1	mr−1	PROPN
ejpam-5702	225	8	mk1	mk1	NOUN
ejpam-5702	225	9	1	1	NUM
ejpam-5702	225	10	·	·	PUNCT
ejpam-5702	225	11	·	·	PUNCT
ejpam-5702	225	12	·	·	PUNCT
ejpam-5702	226	1	mkr−1	mkr−1	PROPN
ejpam-5702	226	2	r−1	r−1	PROPN
ejpam-5702	226	3	∞∑	∞∑	NUM
ejpam-5702	226	4	l=1	l=1	PROPN
ejpam-5702	226	5	l∑	l∑	PUNCT
ejpam-5702	227	1	mr=1	mr=1	NOUN
ejpam-5702	227	2	(	(	PUNCT
ejpam-5702	227	3	−1)mr+lmr	−1)mr+lmr	PROPN
ejpam-5702	227	4	!	!	PUNCT
ejpam-5702	228	1	(	(	PUNCT
ejpam-5702	228	2	mr	mr	PROPN
ejpam-5702	228	3	+	+	PROPN
ejpam-5702	228	4	mr−1)kr	mr−1)kr	PROPN
ejpam-5702	228	5	{	{	PUNCT
ejpam-5702	228	6	l	l	NOUN
ejpam-5702	228	7	mr	mr	PROPN
ejpam-5702	228	8	}	}	PUNCT
ejpam-5702	228	9	y	y	PROPN
ejpam-5702	228	10	tl	tl	PROPN
ejpam-5702	228	11	l	l	NOUN
ejpam-5702	228	12	!	!	PUNCT
ejpam-5702	229	1	=	=	PUNCT
ejpam-5702	229	2	r!(1	r!(1	VERB
ejpam-5702	229	3	+	+	CCONJ
ejpam-5702	229	4	t)x	t)x	PUNCT
ejpam-5702	229	5	(	(	PUNCT
ejpam-5702	229	6	log(1	log(1	NOUN
ejpam-5702	229	7	+	+	CCONJ
ejpam-5702	229	8	t))r	t))r	VERB
ejpam-5702	229	9	∑	∑	PROPN
ejpam-5702	229	10	0	0	PUNCT
ejpam-5702	229	11	<	<	X
ejpam-5702	229	12	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	230	1	(	(	PUNCT
ejpam-5702	230	2	1−	1−	NUM
ejpam-5702	230	3	e[ey	e[ey	PROPN
ejpam-5702	230	4	t	t	PROPN
ejpam-5702	230	5	]	]	PUNCT
ejpam-5702	230	6	)	)	PUNCT
ejpam-5702	230	7	mr−1	mr−1	PROPN
ejpam-5702	230	8	mk1	mk1	NOUN
ejpam-5702	230	9	1	1	NUM
ejpam-5702	230	10	·	·	PUNCT
ejpam-5702	230	11	·	·	PUNCT
ejpam-5702	230	12	·	·	PUNCT
ejpam-5702	230	13	mkr−1−j	mkr−1−j	NOUN
ejpam-5702	231	1	r−1	r−1	PROPN
ejpam-5702	231	2	×	×	NOUN
ejpam-5702	231	3	∞∑	∞∑	NUM
ejpam-5702	231	4	l=1	l=1	X
ejpam-5702	231	5	l∑	l∑	PUNCT
ejpam-5702	232	1	mr=1	mr=1	NOUN
ejpam-5702	232	2	∞∑	∞∑	PROPN
ejpam-5702	232	3	j=0	j=0	PROPN
ejpam-5702	232	4	(	(	PUNCT
ejpam-5702	232	5	kr	kr	PROPN
ejpam-5702	232	6	+	+	PROPN
ejpam-5702	232	7	j	j	PROPN
ejpam-5702	232	8	−	−	PROPN
ejpam-5702	232	9	1	1	NUM
ejpam-5702	232	10	j	j	NOUN
ejpam-5702	232	11	)	)	PUNCT
ejpam-5702	233	1	(	(	PUNCT
ejpam-5702	233	2	−1)mr+l+jm−kr−j	−1)mr+l+jm−kr−j	PROPN
ejpam-5702	233	3	r	r	PROPN
ejpam-5702	233	4	mr	mr	PROPN
ejpam-5702	233	5	!	!	PROPN
ejpam-5702	233	6	{	{	PUNCT
ejpam-5702	233	7	l	l	NOUN
ejpam-5702	233	8	mr	mr	PROPN
ejpam-5702	233	9	}	}	PUNCT
ejpam-5702	233	10	y	y	PROPN
ejpam-5702	233	11	tl	tl	PROPN
ejpam-5702	233	12	l	l	PROPN
ejpam-5702	233	13	!	!	PUNCT
ejpam-5702	233	14	s.	s.	PROPN
ejpam-5702	233	15	h.	h.	PROPN
ejpam-5702	233	16	lee	lee	PROPN
ejpam-5702	233	17	,	,	PUNCT
ejpam-5702	233	18	l.	l.	PROPN
ejpam-5702	233	19	chen	chen	PROPN
ejpam-5702	233	20	/	/	SYM
ejpam-5702	233	21	eur	eur	PROPN
ejpam-5702	233	22	.	.	PUNCT
ejpam-5702	234	1	j.	j.	PROPN
ejpam-5702	234	2	pure	pure	PROPN
ejpam-5702	234	3	appl	appl	PROPN
ejpam-5702	234	4	.	.	PROPN
ejpam-5702	234	5	math	math	PROPN
ejpam-5702	234	6	,	,	PUNCT
ejpam-5702	234	7	18	18	NUM
ejpam-5702	234	8	(	(	PUNCT
ejpam-5702	234	9	1	1	NUM
ejpam-5702	234	10	)	)	PUNCT
ejpam-5702	234	11	(	(	PUNCT
ejpam-5702	234	12	2025	2025	NUM
ejpam-5702	234	13	)	)	PUNCT
ejpam-5702	234	14	,	,	PUNCT
ejpam-5702	234	15	5702	5702	NUM
ejpam-5702	234	16	9	9	NUM
ejpam-5702	234	17	of	of	ADP
ejpam-5702	234	18	13	13	NUM
ejpam-5702	234	19	=	=	SYM
ejpam-5702	234	20	r	r	NOUN
ejpam-5702	234	21	log(1	log(1	NOUN
ejpam-5702	234	22	+	+	CCONJ
ejpam-5702	234	23	t	t	X
ejpam-5702	234	24	)	)	PUNCT
ejpam-5702	235	1	∞∑	∞∑	NUM
ejpam-5702	235	2	i=0	i=0	PROPN
ejpam-5702	235	3	b	b	PROPN
ejpam-5702	235	4	(	(	PUNCT
ejpam-5702	235	5	k1,	k1,	NOUN
ejpam-5702	235	6	...	...	PUNCT
ejpam-5702	235	7	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	235	8	)	)	PUNCT
ejpam-5702	236	1	i	i	PRON
ejpam-5702	236	2	,	,	PUNCT
ejpam-5702	236	3	y	y	PROPN
ejpam-5702	236	4	(	(	PUNCT
ejpam-5702	236	5	x	x	X
ejpam-5702	236	6	)	)	PUNCT
ejpam-5702	236	7	ti	ti	NOUN
ejpam-5702	236	8	i	i	PRON
ejpam-5702	236	9	!	!	PUNCT
ejpam-5702	237	1	∞∑	∞∑	PRON
ejpam-5702	237	2	l=1	l=1	NOUN
ejpam-5702	237	3	l∑	l∑	PUNCT
ejpam-5702	238	1	mr=1	mr=1	NOUN
ejpam-5702	238	2	∞∑	∞∑	PROPN
ejpam-5702	238	3	j=0	j=0	PROPN
ejpam-5702	238	4	(	(	PUNCT
ejpam-5702	238	5	kr	kr	PROPN
ejpam-5702	238	6	+	+	PROPN
ejpam-5702	238	7	j	j	PROPN
ejpam-5702	238	8	−	−	PROPN
ejpam-5702	238	9	1	1	NUM
ejpam-5702	238	10	j	j	NOUN
ejpam-5702	238	11	)	)	PUNCT
ejpam-5702	239	1	(	(	PUNCT
ejpam-5702	239	2	−1)mr+l+jm−kr−j	−1)mr+l+jm−kr−j	PROPN
ejpam-5702	239	3	r	r	PROPN
ejpam-5702	239	4	mr	mr	PROPN
ejpam-5702	239	5	!	!	PROPN
ejpam-5702	239	6	{	{	PUNCT
ejpam-5702	239	7	l	l	NOUN
ejpam-5702	239	8	mr	mr	PROPN
ejpam-5702	239	9	}	}	PUNCT
ejpam-5702	239	10	y	y	PROPN
ejpam-5702	239	11	tl	tl	PROPN
ejpam-5702	239	12	l	l	NOUN
ejpam-5702	239	13	!	!	PUNCT
ejpam-5702	240	1	=	=	PUNCT
ejpam-5702	240	2	r	r	NOUN
ejpam-5702	240	3	li1(−t	li1(−t	NOUN
ejpam-5702	240	4	)	)	PUNCT
ejpam-5702	240	5	∞∑	∞∑	PROPN
ejpam-5702	240	6	n=1	n=1	PUNCT
ejpam-5702	240	7	n∑	n∑	PROPN
ejpam-5702	240	8	l=1	l=1	PROPN
ejpam-5702	240	9	l∑	l∑	PUNCT
ejpam-5702	241	1	mr=1	mr=1	NOUN
ejpam-5702	241	2	∞∑	∞∑	PROPN
ejpam-5702	241	3	j=0	j=0	PROPN
ejpam-5702	241	4	(	(	PUNCT
ejpam-5702	241	5	kr	kr	PROPN
ejpam-5702	241	6	+	+	PROPN
ejpam-5702	241	7	j	j	PROPN
ejpam-5702	241	8	−	−	PROPN
ejpam-5702	241	9	1	1	NUM
ejpam-5702	241	10	j	j	PROPN
ejpam-5702	241	11	)	)	PUNCT
ejpam-5702	241	12	(	(	PUNCT
ejpam-5702	241	13	n	n	X
ejpam-5702	241	14	l	l	NOUN
ejpam-5702	241	15	)	)	PUNCT
ejpam-5702	242	1	(	(	PUNCT
ejpam-5702	242	2	−1)mr+l+jm−kr−j	−1)mr+l+jm−kr−j	PROPN
ejpam-5702	242	3	r	r	PROPN
ejpam-5702	242	4	mr	mr	PROPN
ejpam-5702	242	5	!	!	PROPN
ejpam-5702	242	6	{	{	PUNCT
ejpam-5702	242	7	l	l	NOUN
ejpam-5702	242	8	mr	mr	PROPN
ejpam-5702	242	9	}	}	PUNCT
ejpam-5702	242	10	y	y	PROPN
ejpam-5702	242	11	b	b	PROPN
ejpam-5702	242	12	(	(	PUNCT
ejpam-5702	242	13	k1,	k1,	NOUN
ejpam-5702	242	14	...	...	PUNCT
ejpam-5702	242	15	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	242	16	)	)	PUNCT
ejpam-5702	242	17	n−l	n−l	PROPN
ejpam-5702	242	18	,	,	PUNCT
ejpam-5702	242	19	y	y	PROPN
ejpam-5702	242	20	(	(	PUNCT
ejpam-5702	242	21	x	x	NOUN
ejpam-5702	242	22	)	)	PUNCT
ejpam-5702	242	23	tn	tn	PROPN
ejpam-5702	242	24	n	n	NUM
ejpam-5702	242	25	!	!	PUNCT
ejpam-5702	242	26	.	.	PUNCT
ejpam-5702	243	1	on	on	ADP
ejpam-5702	243	2	the	the	DET
ejpam-5702	243	3	other	other	ADJ
ejpam-5702	243	4	hand	hand	NOUN
ejpam-5702	243	5	in	in	ADP
ejpam-5702	243	6	(	(	PUNCT
ejpam-5702	243	7	29	29	NUM
ejpam-5702	243	8	)	)	SYM
ejpam-5702	243	9	1	1	NUM
ejpam-5702	243	10	t	t	NOUN
ejpam-5702	243	11	(	(	PUNCT
ejpam-5702	243	12	∞∑	∞∑	PROPN
ejpam-5702	243	13	n=0	n=0	PROPN
ejpam-5702	243	14	b	b	NOUN
ejpam-5702	243	15	(	(	PUNCT
ejpam-5702	243	16	k1,	k1,	NOUN
ejpam-5702	243	17	...	...	SYM
ejpam-5702	243	18	,kr	,kr	SYM
ejpam-5702	243	19	)	)	PUNCT
ejpam-5702	243	20	n	n	CCONJ
ejpam-5702	243	21	,	,	PUNCT
ejpam-5702	243	22	y	y	PROPN
ejpam-5702	243	23	(	(	PUNCT
ejpam-5702	243	24	x+	x+	PROPN
ejpam-5702	243	25	1	1	NUM
ejpam-5702	243	26	)	)	PUNCT
ejpam-5702	243	27	tn	tn	NOUN
ejpam-5702	243	28	n	n	NOUN
ejpam-5702	243	29	!	!	PUNCT
ejpam-5702	243	30	−	−	PROPN
ejpam-5702	244	1	∞∑	∞∑	PRON
ejpam-5702	244	2	n=0	n=0	PROPN
ejpam-5702	244	3	b	b	NOUN
ejpam-5702	244	4	(	(	PUNCT
ejpam-5702	244	5	k1,	k1,	NOUN
ejpam-5702	244	6	...	...	SYM
ejpam-5702	244	7	,kr	,kr	SYM
ejpam-5702	244	8	)	)	PUNCT
ejpam-5702	244	9	n	n	CCONJ
ejpam-5702	244	10	,	,	PUNCT
ejpam-5702	244	11	y	y	PROPN
ejpam-5702	244	12	(	(	PUNCT
ejpam-5702	244	13	x	x	NOUN
ejpam-5702	244	14	)	)	PUNCT
ejpam-5702	244	15	tn	tn	PROPN
ejpam-5702	244	16	n	n	NOUN
ejpam-5702	244	17	!	!	PUNCT
ejpam-5702	244	18	)	)	PUNCT
ejpam-5702	245	1	=	=	PUNCT
ejpam-5702	246	1	∞∑	∞∑	NUM
ejpam-5702	246	2	n=0	n=0	NUM
ejpam-5702	246	3	(	(	PUNCT
ejpam-5702	246	4	b	b	NOUN
ejpam-5702	246	5	k1,	k1,	NOUN
ejpam-5702	246	6	...	...	PUNCT
ejpam-5702	246	7	,kr	,kr	PUNCT
ejpam-5702	246	8	n+1,y	n+1,y	PROPN
ejpam-5702	246	9	(	(	PUNCT
ejpam-5702	246	10	x+	x+	PROPN
ejpam-5702	246	11	1)−	1)−	NUM
ejpam-5702	246	12	bk1,	bk1,	NOUN
ejpam-5702	246	13	...	...	PUNCT
ejpam-5702	246	14	,krn+1,y	,krn+1,y	PUNCT
ejpam-5702	246	15	(	(	PUNCT
ejpam-5702	246	16	x	x	NOUN
ejpam-5702	246	17	)	)	PUNCT
ejpam-5702	246	18	)	)	PUNCT
ejpam-5702	247	1	n+	n+	PUNCT
ejpam-5702	247	2	1	1	NUM
ejpam-5702	247	3	tn	tn	NOUN
ejpam-5702	247	4	n	n	X
ejpam-5702	247	5	!	!	PUNCT
ejpam-5702	247	6	.	.	PUNCT
ejpam-5702	248	1	(	(	PUNCT
ejpam-5702	248	2	30	30	NUM
ejpam-5702	248	3	)	)	PUNCT
ejpam-5702	248	4	by	by	ADP
ejpam-5702	248	5	comparing	compare	VERB
ejpam-5702	248	6	the	the	DET
ejpam-5702	248	7	coefficients	coefficient	NOUN
ejpam-5702	248	8	on	on	ADP
ejpam-5702	248	9	both	both	DET
ejpam-5702	248	10	sides	side	NOUN
ejpam-5702	248	11	of	of	ADP
ejpam-5702	248	12	(	(	PUNCT
ejpam-5702	248	13	29	29	NUM
ejpam-5702	248	14	)	)	PUNCT
ejpam-5702	248	15	and	and	CCONJ
ejpam-5702	248	16	(	(	PUNCT
ejpam-5702	248	17	30	30	NUM
ejpam-5702	248	18	)	)	PUNCT
ejpam-5702	248	19	,	,	PUNCT
ejpam-5702	248	20	we	we	PRON
ejpam-5702	248	21	have	have	VERB
ejpam-5702	248	22	the	the	DET
ejpam-5702	248	23	following	follow	VERB
ejpam-5702	248	24	theorem	theorem	VERB
ejpam-5702	248	25	.	.	PUNCT
ejpam-5702	248	26	theorem	theorem	NOUN
ejpam-5702	248	27	5	5	NUM
ejpam-5702	248	28	.	.	PUNCT
ejpam-5702	248	29	for	for	ADP
ejpam-5702	248	30	n	n	PRON
ejpam-5702	248	31	≥	≥	NUM
ejpam-5702	248	32	1	1	NUM
ejpam-5702	248	33	,	,	PUNCT
ejpam-5702	248	34	t	t	PROPN
ejpam-5702	248	35	̸=	̸=	PROPN
ejpam-5702	248	36	0	0	NUM
ejpam-5702	248	37	,	,	PUNCT
ejpam-5702	248	38	we	we	PRON
ejpam-5702	248	39	have	have	VERB
ejpam-5702	248	40	(	(	PUNCT
ejpam-5702	248	41	b	b	X
ejpam-5702	248	42	(	(	PUNCT
ejpam-5702	248	43	k1,	k1,	NOUN
ejpam-5702	248	44	...	...	PUNCT
ejpam-5702	248	45	,kr	,kr	SYM
ejpam-5702	248	46	)	)	PUNCT
ejpam-5702	249	1	n+1,y	n+1,y	PROPN
ejpam-5702	249	2	(	(	PUNCT
ejpam-5702	249	3	x+	x+	PROPN
ejpam-5702	249	4	1)−	1)−	PROPN
ejpam-5702	249	5	b	b	PROPN
ejpam-5702	249	6	(	(	PUNCT
ejpam-5702	249	7	k1,	k1,	NOUN
ejpam-5702	249	8	...	...	PUNCT
ejpam-5702	249	9	,kr	,kr	SYM
ejpam-5702	249	10	)	)	PUNCT
ejpam-5702	249	11	n+1,y	n+1,y	PROPN
ejpam-5702	249	12	(	(	PUNCT
ejpam-5702	249	13	x	x	NOUN
ejpam-5702	249	14	)	)	PUNCT
ejpam-5702	249	15	)	)	PUNCT
ejpam-5702	250	1	n+	n+	PUNCT
ejpam-5702	250	2	1	1	NUM
ejpam-5702	250	3	=	=	SYM
ejpam-5702	250	4	r	r	NOUN
ejpam-5702	250	5	li1(−t	li1(−t	NOUN
ejpam-5702	250	6	)	)	PUNCT
ejpam-5702	250	7	n∑	n∑	NOUN
ejpam-5702	251	1	l=1	l=1	NOUN
ejpam-5702	251	2	l∑	l∑	PUNCT
ejpam-5702	252	1	mr=1	mr=1	NOUN
ejpam-5702	252	2	∞∑	∞∑	PROPN
ejpam-5702	252	3	j=0	j=0	PROPN
ejpam-5702	252	4	(	(	PUNCT
ejpam-5702	252	5	kr	kr	PROPN
ejpam-5702	252	6	+	+	PROPN
ejpam-5702	252	7	j	j	PROPN
ejpam-5702	252	8	−	−	PROPN
ejpam-5702	252	9	1	1	NUM
ejpam-5702	252	10	j	j	PROPN
ejpam-5702	252	11	)	)	PUNCT
ejpam-5702	252	12	(	(	PUNCT
ejpam-5702	252	13	n	n	X
ejpam-5702	252	14	l	l	NOUN
ejpam-5702	252	15	)	)	PUNCT
ejpam-5702	253	1	(	(	PUNCT
ejpam-5702	253	2	−1)mr+l+jm−kr−j	−1)mr+l+jm−kr−j	PROPN
ejpam-5702	253	3	r	r	PROPN
ejpam-5702	253	4	mr	mr	PROPN
ejpam-5702	253	5	!	!	PROPN
ejpam-5702	253	6	{	{	PUNCT
ejpam-5702	253	7	l	l	NOUN
ejpam-5702	253	8	mr	mr	PROPN
ejpam-5702	253	9	}	}	PUNCT
ejpam-5702	253	10	y	y	PROPN
ejpam-5702	253	11	b	b	PROPN
ejpam-5702	253	12	(	(	PUNCT
ejpam-5702	253	13	k1,	k1,	NOUN
ejpam-5702	253	14	...	...	PUNCT
ejpam-5702	253	15	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	253	16	)	)	PUNCT
ejpam-5702	253	17	n−l	n−l	PROPN
ejpam-5702	253	18	,	,	PUNCT
ejpam-5702	253	19	y	y	PROPN
ejpam-5702	253	20	(	(	PUNCT
ejpam-5702	253	21	x	x	NOUN
ejpam-5702	253	22	)	)	PUNCT
ejpam-5702	253	23	.	.	PUNCT
ejpam-5702	254	1	from	from	ADP
ejpam-5702	254	2	(	(	PUNCT
ejpam-5702	254	3	26	26	NUM
ejpam-5702	254	4	)	)	PUNCT
ejpam-5702	254	5	,	,	PUNCT
ejpam-5702	254	6	we	we	PRON
ejpam-5702	254	7	have	have	VERB
ejpam-5702	254	8	proof	proof	NOUN
ejpam-5702	254	9	.	.	PUNCT
ejpam-5702	255	1	theorem	theorem	VERB
ejpam-5702	255	2	6	6	NUM
ejpam-5702	255	3	.	.	PUNCT
ejpam-5702	256	1	∞∑	∞∑	NUM
ejpam-5702	256	2	n=0	n=0	PROPN
ejpam-5702	256	3	b	b	NOUN
ejpam-5702	256	4	(	(	PUNCT
ejpam-5702	256	5	k1,	k1,	NOUN
ejpam-5702	256	6	...	...	SYM
ejpam-5702	256	7	,kr	,kr	SYM
ejpam-5702	256	8	)	)	PUNCT
ejpam-5702	256	9	n	n	CCONJ
ejpam-5702	256	10	,	,	PUNCT
ejpam-5702	256	11	y	y	PROPN
ejpam-5702	256	12	(	(	PUNCT
ejpam-5702	256	13	x	x	NOUN
ejpam-5702	256	14	)	)	PUNCT
ejpam-5702	256	15	tn	tn	PROPN
ejpam-5702	256	16	n	n	NOUN
ejpam-5702	256	17	!	!	PUNCT
ejpam-5702	257	1	=	=	NOUN
ejpam-5702	257	2	r!lik1,	r!lik1,	NOUN
ejpam-5702	257	3	...	...	PUNCT
ejpam-5702	257	4	,kr	,kr	PUNCT
ejpam-5702	257	5	(	(	PUNCT
ejpam-5702	257	6	1−	1−	NUM
ejpam-5702	257	7	e[e−y	e[e−y	PROPN
ejpam-5702	257	8	t	t	PROPN
ejpam-5702	257	9	]	]	PUNCT
ejpam-5702	257	10	)	)	PUNCT
ejpam-5702	257	11	(	(	PUNCT
ejpam-5702	257	12	log(1	log(1	NOUN
ejpam-5702	257	13	+	+	CCONJ
ejpam-5702	258	1	t))r	t))r	ADJ
ejpam-5702	258	2	(	(	PUNCT
ejpam-5702	258	3	1	1	NUM
ejpam-5702	258	4	+	+	CCONJ
ejpam-5702	258	5	t)x	t)x	PUNCT
ejpam-5702	258	6	(	(	PUNCT
ejpam-5702	258	7	31	31	NUM
ejpam-5702	258	8	)	)	PUNCT
ejpam-5702	258	9	=	=	VERB
ejpam-5702	259	1	trr!(1	trr!(1	VERB
ejpam-5702	259	2	+	+	CCONJ
ejpam-5702	259	3	t)x	t)x	PUNCT
ejpam-5702	259	4	tr((log(1	tr((log(1	NOUN
ejpam-5702	259	5	+	+	CCONJ
ejpam-5702	259	6	t))r	t))r	ADJ
ejpam-5702	259	7	lik1,	lik1,	PROPN
ejpam-5702	259	8	...	...	PUNCT
ejpam-5702	259	9	,kr	,kr	PUNCT
ejpam-5702	259	10	(	(	PUNCT
ejpam-5702	259	11	1−	1−	NUM
ejpam-5702	259	12	e[e−y	e[e−y	PROPN
ejpam-5702	259	13	t	t	PROPN
ejpam-5702	259	14	]	]	PUNCT
ejpam-5702	259	15	)	)	PUNCT
ejpam-5702	260	1	(	(	PUNCT
ejpam-5702	260	2	1−	1−	NUM
ejpam-5702	260	3	e[e−y	e[e−y	PROPN
ejpam-5702	260	4	t])r	t])r	PROPN
ejpam-5702	260	5	(	(	PUNCT
ejpam-5702	260	6	1−	1−	NUM
ejpam-5702	260	7	e[e−y	e[e−y	PROPN
ejpam-5702	260	8	t	t	PROPN
ejpam-5702	260	9	]	]	PUNCT
ejpam-5702	260	10	)	)	PUNCT
ejpam-5702	260	11	r	r	NOUN
ejpam-5702	260	12	=	=	SYM
ejpam-5702	260	13	(	(	PUNCT
ejpam-5702	260	14	r!)2	r!)2	ADP
ejpam-5702	260	15	tr	tr	PUNCT
ejpam-5702	260	16	∞∑	∞∑	NUM
ejpam-5702	260	17	m=0	m=0	PROPN
ejpam-5702	260	18	b	b	PROPN
ejpam-5702	260	19	(	(	PUNCT
ejpam-5702	260	20	k1,	k1,	NOUN
ejpam-5702	260	21	...	...	PUNCT
ejpam-5702	260	22	,kr	,kr	SYM
ejpam-5702	260	23	)	)	PUNCT
ejpam-5702	260	24	m	m	PROPN
ejpam-5702	260	25	,	,	PUNCT
ejpam-5702	260	26	y	y	PROPN
ejpam-5702	260	27	tm	tm	PROPN
ejpam-5702	260	28	m	m	PROPN
ejpam-5702	260	29	!	!	PUNCT
ejpam-5702	261	1	∞∑	∞∑	NUM
ejpam-5702	261	2	l	l	NOUN
ejpam-5702	261	3	=	=	NOUN
ejpam-5702	261	4	r	r	NOUN
ejpam-5702	261	5	{	{	PUNCT
ejpam-5702	261	6	l	l	NOUN
ejpam-5702	261	7	r	r	NOUN
ejpam-5702	261	8	}	}	PUNCT
ejpam-5702	261	9	y	y	PROPN
ejpam-5702	261	10	(	(	PUNCT
ejpam-5702	261	11	−1)l	−1)l	PROPN
ejpam-5702	261	12	tl	tl	PROPN
ejpam-5702	261	13	l	l	NOUN
ejpam-5702	261	14	!	!	PUNCT
ejpam-5702	262	1	∞∑	∞∑	PRON
ejpam-5702	262	2	i=0	i=0	PROPN
ejpam-5702	262	3	bri	bri	NOUN
ejpam-5702	262	4	(	(	PUNCT
ejpam-5702	262	5	x	x	X
ejpam-5702	262	6	)	)	PUNCT
ejpam-5702	262	7	ti	ti	NOUN
ejpam-5702	262	8	i	i	PRON
ejpam-5702	262	9	!	!	PUNCT
ejpam-5702	263	1	=	=	PUNCT
ejpam-5702	264	1	(	(	PUNCT
ejpam-5702	264	2	r!)2	r!)2	ADP
ejpam-5702	264	3	tr	tr	PUNCT
ejpam-5702	264	4	∞∑	∞∑	NUM
ejpam-5702	264	5	j=0	j=0	PROPN
ejpam-5702	264	6	j∑	j∑	PROPN
ejpam-5702	264	7	m=0	m=0	PROPN
ejpam-5702	264	8	(	(	PUNCT
ejpam-5702	264	9	j	j	PROPN
ejpam-5702	264	10	m	m	PROPN
ejpam-5702	264	11	)	)	PUNCT
ejpam-5702	264	12	b	b	PROPN
ejpam-5702	264	13	(	(	PUNCT
ejpam-5702	264	14	k1,	k1,	NOUN
ejpam-5702	264	15	...	...	PUNCT
ejpam-5702	264	16	,kr	,kr	SYM
ejpam-5702	264	17	)	)	PUNCT
ejpam-5702	264	18	m	m	PROPN
ejpam-5702	264	19	,	,	PUNCT
ejpam-5702	264	20	y	y	PROPN
ejpam-5702	264	21	brj−m(x	brj−m(x	PROPN
ejpam-5702	264	22	)	)	PUNCT
ejpam-5702	264	23	tj	tj	PROPN
ejpam-5702	264	24	j	j	PROPN
ejpam-5702	264	25	!	!	PUNCT
ejpam-5702	265	1	∞∑	∞∑	NUM
ejpam-5702	265	2	l	l	NOUN
ejpam-5702	265	3	=	=	NOUN
ejpam-5702	265	4	r	r	NOUN
ejpam-5702	265	5	{	{	PUNCT
ejpam-5702	265	6	l	l	NOUN
ejpam-5702	265	7	r	r	NOUN
ejpam-5702	265	8	}	}	PUNCT
ejpam-5702	265	9	y	y	PROPN
ejpam-5702	265	10	(	(	PUNCT
ejpam-5702	265	11	−1)l	−1)l	PROPN
ejpam-5702	265	12	tl	tl	PROPN
ejpam-5702	265	13	l	l	NOUN
ejpam-5702	265	14	!	!	PUNCT
ejpam-5702	265	15	=	=	PUNCT
ejpam-5702	266	1	(	(	PUNCT
ejpam-5702	266	2	r!)2	r!)2	ADP
ejpam-5702	266	3	tr	tr	PUNCT
ejpam-5702	266	4	∞∑	∞∑	NUM
ejpam-5702	266	5	n	n	CCONJ
ejpam-5702	266	6	=	=	SYM
ejpam-5702	266	7	r	r	NOUN
ejpam-5702	266	8	n∑	n∑	X
ejpam-5702	266	9	l=0	l=0	PROPN
ejpam-5702	266	10	n−l∑	n−l∑	X
ejpam-5702	266	11	m=0	m=0	PROPN
ejpam-5702	266	12	(	(	PUNCT
ejpam-5702	266	13	n−	n−	NOUN
ejpam-5702	266	14	l	l	NOUN
ejpam-5702	266	15	m	m	VERB
ejpam-5702	266	16	)	)	PUNCT
ejpam-5702	266	17	(	(	PUNCT
ejpam-5702	266	18	n	n	X
ejpam-5702	266	19	l	l	NOUN
ejpam-5702	266	20	)	)	PUNCT
ejpam-5702	266	21	(	(	PUNCT
ejpam-5702	266	22	−1)lb	−1)lb	X
ejpam-5702	266	23	(	(	PUNCT
ejpam-5702	266	24	k1,	k1,	NOUN
ejpam-5702	266	25	...	...	PUNCT
ejpam-5702	266	26	,kr	,kr	SYM
ejpam-5702	266	27	)	)	PUNCT
ejpam-5702	266	28	m	m	PROPN
ejpam-5702	266	29	,	,	PUNCT
ejpam-5702	266	30	y	y	PROPN
ejpam-5702	266	31	b	b	PROPN
ejpam-5702	266	32	(	(	PUNCT
ejpam-5702	266	33	r	r	NOUN
ejpam-5702	266	34	)	)	PUNCT
ejpam-5702	266	35	n−l−m(x	n−l−m(x	NOUN
ejpam-5702	266	36	)	)	PUNCT
ejpam-5702	266	37	{	{	PUNCT
ejpam-5702	266	38	l	l	NOUN
ejpam-5702	266	39	r	r	NOUN
ejpam-5702	266	40	}	}	PUNCT
ejpam-5702	266	41	y	y	PROPN
ejpam-5702	266	42	tn	tn	PROPN
ejpam-5702	266	43	n	n	PROPN
ejpam-5702	266	44	!	!	PUNCT
ejpam-5702	267	1	=	=	PUNCT
ejpam-5702	268	1	(	(	PUNCT
ejpam-5702	268	2	r!)2	r!)2	ADP
ejpam-5702	268	3	∞∑	∞∑	NUM
ejpam-5702	268	4	n=0	n=0	NUM
ejpam-5702	268	5	n+r∑	n+r∑	NOUN
ejpam-5702	268	6	l=0	l=0	PROPN
ejpam-5702	268	7	n+r−l∑	n+r−l∑	NUM
ejpam-5702	269	1	m=0	m=0	PROPN
ejpam-5702	270	1	(	(	PUNCT
ejpam-5702	270	2	j	j	PROPN
ejpam-5702	270	3	m	m	VERB
ejpam-5702	270	4	)	)	PUNCT
ejpam-5702	270	5	(	(	PUNCT
ejpam-5702	270	6	n+	n+	ADP
ejpam-5702	271	1	r	r	NOUN
ejpam-5702	271	2	−	−	PROPN
ejpam-5702	271	3	l	l	NOUN
ejpam-5702	271	4	l	l	NOUN
ejpam-5702	271	5	)	)	PUNCT
ejpam-5702	271	6	(	(	PUNCT
ejpam-5702	271	7	−1)l	−1)l	NOUN
ejpam-5702	271	8	b	b	X
ejpam-5702	271	9	(	(	PUNCT
ejpam-5702	271	10	k1,	k1,	NOUN
ejpam-5702	271	11	...	...	PUNCT
ejpam-5702	271	12	,kr	,kr	SYM
ejpam-5702	271	13	)	)	PUNCT
ejpam-5702	272	1	m	m	PROPN
ejpam-5702	272	2	,	,	PUNCT
ejpam-5702	272	3	y	y	PROPN
ejpam-5702	272	4	b	b	PROPN
ejpam-5702	272	5	(	(	PUNCT
ejpam-5702	272	6	r	r	NOUN
ejpam-5702	272	7	)	)	PUNCT
ejpam-5702	272	8	n+r−l−m(x	n+r−l−m(x	NUM
ejpam-5702	272	9	)	)	PUNCT
ejpam-5702	272	10	(	(	PUNCT
ejpam-5702	272	11	n+	n+	X
ejpam-5702	272	12	r)r	r)r	NOUN
ejpam-5702	272	13	{	{	PUNCT
ejpam-5702	272	14	l	l	NOUN
ejpam-5702	272	15	r	r	NOUN
ejpam-5702	272	16	}	}	PUNCT
ejpam-5702	272	17	y	y	PROPN
ejpam-5702	272	18	tn	tn	PROPN
ejpam-5702	272	19	n	n	PROPN
ejpam-5702	272	20	!	!	PUNCT
ejpam-5702	272	21	.	.	PUNCT
ejpam-5702	273	1	s.	s.	PROPN
ejpam-5702	273	2	h.	h.	PROPN
ejpam-5702	273	3	lee	lee	PROPN
ejpam-5702	273	4	,	,	PUNCT
ejpam-5702	273	5	l.	l.	PROPN
ejpam-5702	273	6	chen	chen	PROPN
ejpam-5702	273	7	/	/	SYM
ejpam-5702	273	8	eur	eur	PROPN
ejpam-5702	273	9	.	.	PUNCT
ejpam-5702	274	1	j.	j.	PROPN
ejpam-5702	274	2	pure	pure	PROPN
ejpam-5702	274	3	appl	appl	PROPN
ejpam-5702	274	4	.	.	PROPN
ejpam-5702	274	5	math	math	PROPN
ejpam-5702	274	6	,	,	PUNCT
ejpam-5702	274	7	18	18	NUM
ejpam-5702	274	8	(	(	PUNCT
ejpam-5702	274	9	1	1	NUM
ejpam-5702	274	10	)	)	PUNCT
ejpam-5702	274	11	(	(	PUNCT
ejpam-5702	274	12	2025	2025	NUM
ejpam-5702	274	13	)	)	PUNCT
ejpam-5702	274	14	,	,	PUNCT
ejpam-5702	274	15	5702	5702	NUM
ejpam-5702	274	16	10	10	NUM
ejpam-5702	274	17	of	of	ADP
ejpam-5702	274	18	13	13	NUM
ejpam-5702	274	19	therefore	therefore	ADV
ejpam-5702	274	20	,	,	PUNCT
ejpam-5702	274	21	by	by	ADP
ejpam-5702	274	22	(	(	PUNCT
ejpam-5702	274	23	31	31	NUM
ejpam-5702	274	24	)	)	PUNCT
ejpam-5702	274	25	,	,	PUNCT
ejpam-5702	274	26	we	we	PRON
ejpam-5702	274	27	have	have	VERB
ejpam-5702	274	28	the	the	DET
ejpam-5702	274	29	following	follow	VERB
ejpam-5702	274	30	theorem	theorem	VERB
ejpam-5702	274	31	.	.	PUNCT
ejpam-5702	275	1	theorem	theorem	PROPN
ejpam-5702	275	2	6	6	NUM
ejpam-5702	275	3	.	.	PUNCT
ejpam-5702	275	4	for	for	ADP
ejpam-5702	275	5	n	n	PRON
ejpam-5702	275	6	≥	≥	NOUN
ejpam-5702	275	7	0	0	NUM
ejpam-5702	275	8	,	,	PUNCT
ejpam-5702	275	9	we	we	PRON
ejpam-5702	275	10	have	have	VERB
ejpam-5702	275	11	b	b	NUM
ejpam-5702	275	12	(	(	PUNCT
ejpam-5702	275	13	k1,	k1,	NOUN
ejpam-5702	275	14	...	...	SYM
ejpam-5702	275	15	,kr	,kr	SYM
ejpam-5702	275	16	)	)	PUNCT
ejpam-5702	275	17	n	n	CCONJ
ejpam-5702	275	18	,	,	PUNCT
ejpam-5702	275	19	y	y	PROPN
ejpam-5702	275	20	(	(	PUNCT
ejpam-5702	275	21	x	x	NOUN
ejpam-5702	275	22	)	)	PUNCT
ejpam-5702	275	23	=	=	SYM
ejpam-5702	275	24	(	(	PUNCT
ejpam-5702	275	25	r!)2	r!)2	NOUN
ejpam-5702	275	26	n+r∑	n+r∑	ADJ
ejpam-5702	275	27	l=0	l=0	PROPN
ejpam-5702	275	28	r−l∑	r−l∑	NOUN
ejpam-5702	276	1	m=0	m=0	PROPN
ejpam-5702	276	2	(	(	PUNCT
ejpam-5702	276	3	j	j	PROPN
ejpam-5702	276	4	m	m	VERB
ejpam-5702	276	5	)	)	PUNCT
ejpam-5702	276	6	(	(	PUNCT
ejpam-5702	276	7	n+	n+	ADP
ejpam-5702	276	8	r	r	NOUN
ejpam-5702	276	9	j	j	PROPN
ejpam-5702	276	10	)	)	PUNCT
ejpam-5702	276	11	(	(	PUNCT
ejpam-5702	276	12	−1)l	−1)l	NOUN
ejpam-5702	276	13	b	b	X
ejpam-5702	276	14	(	(	PUNCT
ejpam-5702	276	15	k1,	k1,	NOUN
ejpam-5702	276	16	...	...	PUNCT
ejpam-5702	276	17	,kr	,kr	SYM
ejpam-5702	276	18	)	)	PUNCT
ejpam-5702	276	19	m	m	PROPN
ejpam-5702	276	20	,	,	PUNCT
ejpam-5702	276	21	y	y	PROPN
ejpam-5702	276	22	b	b	PROPN
ejpam-5702	276	23	(	(	PUNCT
ejpam-5702	276	24	r	r	NOUN
ejpam-5702	276	25	)	)	PUNCT
ejpam-5702	276	26	n+r−l−m(x	n+r−l−m(x	NUM
ejpam-5702	276	27	)	)	PUNCT
ejpam-5702	276	28	(	(	PUNCT
ejpam-5702	276	29	n)r	n)r	X
ejpam-5702	276	30	{	{	PUNCT
ejpam-5702	276	31	l	l	NOUN
ejpam-5702	276	32	r	r	NOUN
ejpam-5702	276	33	}	}	PUNCT
ejpam-5702	276	34	y	y	PROPN
ejpam-5702	276	35	.	.	PUNCT
ejpam-5702	277	1	from	from	ADP
ejpam-5702	277	2	(	(	PUNCT
ejpam-5702	277	3	26	26	NUM
ejpam-5702	277	4	)	)	PUNCT
ejpam-5702	277	5	,	,	PUNCT
ejpam-5702	277	6	we	we	PRON
ejpam-5702	277	7	have	have	VERB
ejpam-5702	277	8	proof	proof	NOUN
ejpam-5702	277	9	.	.	PUNCT
ejpam-5702	278	1	theorem	theorem	VERB
ejpam-5702	278	2	7	7	NUM
ejpam-5702	278	3	.	.	PUNCT
ejpam-5702	279	1	∞∑	∞∑	NUM
ejpam-5702	279	2	n=0	n=0	PROPN
ejpam-5702	279	3	b	b	NOUN
ejpam-5702	279	4	(	(	PUNCT
ejpam-5702	279	5	k1,	k1,	NOUN
ejpam-5702	279	6	...	...	SYM
ejpam-5702	279	7	,kr	,kr	SYM
ejpam-5702	279	8	)	)	PUNCT
ejpam-5702	279	9	n	n	CCONJ
ejpam-5702	279	10	,	,	PUNCT
ejpam-5702	279	11	y	y	PROPN
ejpam-5702	279	12	(	(	PUNCT
ejpam-5702	279	13	x+	x+	PROPN
ejpam-5702	279	14	y	y	PROPN
ejpam-5702	279	15	)	)	PUNCT
ejpam-5702	279	16	tn	tn	PROPN
ejpam-5702	279	17	n	n	NOUN
ejpam-5702	279	18	!	!	PUNCT
ejpam-5702	280	1	=	=	NOUN
ejpam-5702	280	2	r!lik1,	r!lik1,	NOUN
ejpam-5702	280	3	...	...	PUNCT
ejpam-5702	280	4	,kr(1−	,kr(1−	PROPN
ejpam-5702	280	5	e[e−y	e[e−y	PROPN
ejpam-5702	280	6	t	t	PROPN
ejpam-5702	280	7	]	]	PUNCT
ejpam-5702	280	8	)	)	PUNCT
ejpam-5702	280	9	(	(	PUNCT
ejpam-5702	280	10	log(1	log(1	NOUN
ejpam-5702	280	11	+	+	CCONJ
ejpam-5702	281	1	t))r	t))r	ADJ
ejpam-5702	281	2	(	(	PUNCT
ejpam-5702	281	3	1	1	NUM
ejpam-5702	281	4	+	+	NUM
ejpam-5702	281	5	t)x+y	t)x+y	PROPN
ejpam-5702	281	6	(	(	PUNCT
ejpam-5702	281	7	32	32	NUM
ejpam-5702	281	8	)	)	PUNCT
ejpam-5702	281	9	=	=	VERB
ejpam-5702	281	10	r!(1	r!(1	VERB
ejpam-5702	281	11	+	+	CCONJ
ejpam-5702	281	12	t)x	t)x	PUNCT
ejpam-5702	281	13	(	(	PUNCT
ejpam-5702	281	14	log(1	log(1	NOUN
ejpam-5702	281	15	+	+	CCONJ
ejpam-5702	281	16	t))r	t))r	VERB
ejpam-5702	281	17	∞∑	∞∑	NUM
ejpam-5702	281	18	l=0	l=0	PROPN
ejpam-5702	281	19	(	(	PUNCT
ejpam-5702	281	20	y)l	y)l	X
ejpam-5702	281	21	tl	tl	PROPN
ejpam-5702	281	22	l	l	NOUN
ejpam-5702	281	23	!	!	PUNCT
ejpam-5702	282	1	∑	∑	PROPN
ejpam-5702	282	2	0	0	PUNCT
ejpam-5702	282	3	<	<	X
ejpam-5702	282	4	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	282	5	1	1	NUM
ejpam-5702	282	6	mk1	mk1	NOUN
ejpam-5702	282	7	1	1	NUM
ejpam-5702	282	8	·	·	PUNCT
ejpam-5702	282	9	·	·	PUNCT
ejpam-5702	282	10	·	·	PUNCT
ejpam-5702	283	1	mkr−1	mkr−1	PROPN
ejpam-5702	283	2	r−1	r−1	PROPN
ejpam-5702	283	3	∞∑	∞∑	NUM
ejpam-5702	283	4	mr	mr	PROPN
ejpam-5702	283	5	=	=	PROPN
ejpam-5702	283	6	mr−1	mr−1	PROPN
ejpam-5702	283	7	+	+	NOUN
ejpam-5702	283	8	1	1	NUM
ejpam-5702	283	9	(	(	PUNCT
ejpam-5702	283	10	1−	1−	NUM
ejpam-5702	283	11	e[e−y	e[e−y	PROPN
ejpam-5702	283	12	t	t	PROPN
ejpam-5702	283	13	]	]	PUNCT
ejpam-5702	283	14	)	)	PUNCT
ejpam-5702	283	15	mr	mr	PROPN
ejpam-5702	283	16	mkr	mkr	PROPN
ejpam-5702	283	17	r	r	NOUN
ejpam-5702	283	18	=	=	PUNCT
ejpam-5702	283	19	r!(1	r!(1	VERB
ejpam-5702	283	20	+	+	CCONJ
ejpam-5702	283	21	t)x	t)x	PUNCT
ejpam-5702	283	22	(	(	PUNCT
ejpam-5702	283	23	log(1	log(1	NOUN
ejpam-5702	283	24	+	+	CCONJ
ejpam-5702	283	25	t))r	t))r	VERB
ejpam-5702	283	26	∞∑	∞∑	NUM
ejpam-5702	283	27	l=0	l=0	PROPN
ejpam-5702	283	28	(	(	PUNCT
ejpam-5702	283	29	y)l	y)l	X
ejpam-5702	283	30	tl	tl	PROPN
ejpam-5702	283	31	l	l	NOUN
ejpam-5702	283	32	!	!	PUNCT
ejpam-5702	284	1	∑	∑	PROPN
ejpam-5702	284	2	0	0	PUNCT
ejpam-5702	284	3	<	<	X
ejpam-5702	284	4	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	284	5	(	(	PUNCT
ejpam-5702	284	6	1−	1−	NUM
ejpam-5702	284	7	e[e−y	e[e−y	PROPN
ejpam-5702	284	8	t	t	PROPN
ejpam-5702	284	9	]	]	PUNCT
ejpam-5702	284	10	)	)	PUNCT
ejpam-5702	284	11	mr−1	mr−1	PROPN
ejpam-5702	284	12	mk1	mk1	NOUN
ejpam-5702	284	13	1	1	NUM
ejpam-5702	284	14	·	·	PUNCT
ejpam-5702	284	15	·	·	PUNCT
ejpam-5702	284	16	·	·	PUNCT
ejpam-5702	285	1	mkr−1	mkr−1	INTJ
ejpam-5702	285	2	r−1	r−1	PROPN
ejpam-5702	285	3	×	×	VERB
ejpam-5702	285	4	∞∑	∞∑	PROPN
ejpam-5702	285	5	mr=1	mr=1	PROPN
ejpam-5702	285	6	(	(	PUNCT
ejpam-5702	285	7	−1)mrmr	−1)mrmr	PROPN
ejpam-5702	285	8	!	!	PUNCT
ejpam-5702	286	1	(	(	PUNCT
ejpam-5702	286	2	mr	mr	PROPN
ejpam-5702	286	3	+	+	PROPN
ejpam-5702	286	4	mr−1)k	mr−1)k	PROPN
ejpam-5702	286	5	(	(	PUNCT
ejpam-5702	286	6	e[e−y	e[e−y	INTJ
ejpam-5702	286	7	t]−	t]−	NOUN
ejpam-5702	286	8	1	1	NUM
ejpam-5702	286	9	)	)	PUNCT
ejpam-5702	286	10	mr	mr	PROPN
ejpam-5702	286	11	mr	mr	PROPN
ejpam-5702	286	12	!	!	PROPN
ejpam-5702	286	13	=	=	PRON
ejpam-5702	286	14	r!(1	r!(1	VERB
ejpam-5702	286	15	+	+	CCONJ
ejpam-5702	286	16	t)x	t)x	PUNCT
ejpam-5702	286	17	(	(	PUNCT
ejpam-5702	286	18	log(1	log(1	NOUN
ejpam-5702	286	19	+	+	CCONJ
ejpam-5702	286	20	t))r	t))r	VERB
ejpam-5702	286	21	∞∑	∞∑	NUM
ejpam-5702	286	22	l=0	l=0	PROPN
ejpam-5702	286	23	(	(	PUNCT
ejpam-5702	286	24	y)l	y)l	X
ejpam-5702	286	25	tl	tl	PROPN
ejpam-5702	286	26	l	l	NOUN
ejpam-5702	286	27	!	!	PUNCT
ejpam-5702	287	1	∑	∑	PROPN
ejpam-5702	287	2	0	0	PUNCT
ejpam-5702	287	3	<	<	X
ejpam-5702	287	4	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	287	5	(	(	PUNCT
ejpam-5702	287	6	1−	1−	NUM
ejpam-5702	287	7	e[e−y	e[e−y	PROPN
ejpam-5702	287	8	t	t	PROPN
ejpam-5702	287	9	]	]	PUNCT
ejpam-5702	287	10	)	)	PUNCT
ejpam-5702	287	11	mr−1	mr−1	PROPN
ejpam-5702	287	12	mk1	mk1	NOUN
ejpam-5702	287	13	1	1	NUM
ejpam-5702	287	14	·	·	PUNCT
ejpam-5702	287	15	·	·	PUNCT
ejpam-5702	287	16	·	·	PUNCT
ejpam-5702	288	1	mkr−1	mkr−1	INTJ
ejpam-5702	288	2	r−1	r−1	PROPN
ejpam-5702	288	3	×	×	VERB
ejpam-5702	288	4	∞∑	∞∑	PROPN
ejpam-5702	288	5	mr=1	mr=1	PROPN
ejpam-5702	288	6	(	(	PUNCT
ejpam-5702	288	7	−1)mrmr	−1)mrmr	PROPN
ejpam-5702	288	8	!	!	PUNCT
ejpam-5702	289	1	(	(	PUNCT
ejpam-5702	289	2	mr	mr	PROPN
ejpam-5702	289	3	+	+	PROPN
ejpam-5702	289	4	mr−1)k	mr−1)k	PROPN
ejpam-5702	289	5	∞∑	∞∑	NUM
ejpam-5702	289	6	i	i	PRON
ejpam-5702	289	7	=	=	NOUN
ejpam-5702	289	8	mr	mr	PROPN
ejpam-5702	289	9	{	{	PUNCT
ejpam-5702	289	10	i	i	PRON
ejpam-5702	289	11	mr	mr	PROPN
ejpam-5702	289	12	}	}	PUNCT
ejpam-5702	289	13	y	y	PROPN
ejpam-5702	289	14	(	(	PUNCT
ejpam-5702	289	15	−1)i	−1)i	X
ejpam-5702	289	16	ti	ti	X
ejpam-5702	289	17	i	i	PRON
ejpam-5702	289	18	!	!	PUNCT
ejpam-5702	290	1	=	=	PUNCT
ejpam-5702	290	2	r!(1	r!(1	VERB
ejpam-5702	290	3	+	+	CCONJ
ejpam-5702	290	4	t)x	t)x	PUNCT
ejpam-5702	290	5	(	(	PUNCT
ejpam-5702	290	6	log(1	log(1	NOUN
ejpam-5702	290	7	+	+	CCONJ
ejpam-5702	290	8	t))r	t))r	VERB
ejpam-5702	290	9	∞∑	∞∑	NUM
ejpam-5702	290	10	l=0	l=0	PROPN
ejpam-5702	290	11	(	(	PUNCT
ejpam-5702	290	12	y)l	y)l	X
ejpam-5702	290	13	tl	tl	PROPN
ejpam-5702	290	14	l	l	NOUN
ejpam-5702	290	15	!	!	PUNCT
ejpam-5702	291	1	∑	∑	PROPN
ejpam-5702	291	2	0	0	PUNCT
ejpam-5702	291	3	<	<	X
ejpam-5702	291	4	m1<···<mr−1	m1<···<mr−1	PROPN
ejpam-5702	291	5	(	(	PUNCT
ejpam-5702	291	6	1−	1−	NUM
ejpam-5702	291	7	e[e−y	e[e−y	PROPN
ejpam-5702	291	8	t	t	PROPN
ejpam-5702	291	9	]	]	PUNCT
ejpam-5702	291	10	)	)	PUNCT
ejpam-5702	291	11	mr−1	mr−1	PROPN
ejpam-5702	291	12	mk1	mk1	NOUN
ejpam-5702	291	13	1	1	NUM
ejpam-5702	291	14	·	·	PUNCT
ejpam-5702	291	15	·	·	PUNCT
ejpam-5702	291	16	·	·	PUNCT
ejpam-5702	292	1	mkr−1	mkr−1	PROPN
ejpam-5702	292	2	r−1	r−1	PROPN
ejpam-5702	292	3	∞∑	∞∑	NUM
ejpam-5702	292	4	i=1	i=1	ADP
ejpam-5702	292	5	i∑	i∑	PROPN
ejpam-5702	292	6	mr=1	mr=1	NOUN
ejpam-5702	292	7	(	(	PUNCT
ejpam-5702	292	8	−1)mr+imr	−1)mr+imr	NOUN
ejpam-5702	292	9	!	!	PUNCT
ejpam-5702	293	1	{	{	PUNCT
ejpam-5702	294	1	i	i	PRON
ejpam-5702	294	2	mr	mr	PROPN
ejpam-5702	294	3	}	}	PUNCT
ejpam-5702	294	4	(	(	PUNCT
ejpam-5702	294	5	mr	mr	PROPN
ejpam-5702	294	6	+	+	PROPN
ejpam-5702	294	7	mr−1)k	mr−1)k	PROPN
ejpam-5702	294	8	ti	ti	X
ejpam-5702	294	9	i	i	PRON
ejpam-5702	294	10	!	!	PUNCT
ejpam-5702	295	1	=	=	PUNCT
ejpam-5702	296	1	∞∑	∞∑	NUM
ejpam-5702	296	2	i=1	i=1	ADP
ejpam-5702	296	3	i∑	i∑	PROPN
ejpam-5702	296	4	mr=1	mr=1	NOUN
ejpam-5702	296	5	∞∑	∞∑	PROPN
ejpam-5702	296	6	j=0	j=0	PROPN
ejpam-5702	296	7	(	(	PUNCT
ejpam-5702	296	8	mr	mr	PROPN
ejpam-5702	296	9	+	+	PROPN
ejpam-5702	296	10	j	j	PROPN
ejpam-5702	296	11	−	−	PROPN
ejpam-5702	296	12	1	1	NUM
ejpam-5702	296	13	j	j	NOUN
ejpam-5702	296	14	)	)	PUNCT
ejpam-5702	296	15	(	(	PUNCT
ejpam-5702	296	16	−1)mr+i−jm−kr−j	−1)mr+i−jm−kr−j	NOUN
ejpam-5702	296	17	r	r	VERB
ejpam-5702	296	18	mr	mr	PROPN
ejpam-5702	296	19	!	!	PROPN
ejpam-5702	296	20	{	{	PUNCT
ejpam-5702	297	1	i	i	PRON
ejpam-5702	297	2	mr	mr	PROPN
ejpam-5702	297	3	}	}	PUNCT
ejpam-5702	297	4	y	y	PROPN
ejpam-5702	297	5	ti	ti	PROPN
ejpam-5702	297	6	i	i	PRON
ejpam-5702	297	7	!	!	PUNCT
ejpam-5702	298	1	×	×	NOUN
ejpam-5702	298	2	r!(1	r!(1	VERB
ejpam-5702	298	3	+	+	CCONJ
ejpam-5702	298	4	t)x	t)x	PUNCT
ejpam-5702	298	5	(	(	PUNCT
ejpam-5702	298	6	log(1	log(1	NOUN
ejpam-5702	298	7	+	+	CCONJ
ejpam-5702	298	8	t))r	t))r	ADJ
ejpam-5702	298	9	lik1,	lik1,	PROPN
ejpam-5702	298	10	...	...	PUNCT
ejpam-5702	298	11	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	298	12	(	(	PUNCT
ejpam-5702	298	13	1−	1−	NUM
ejpam-5702	298	14	e[e−y	e[e−y	PROPN
ejpam-5702	298	15	t	t	PROPN
ejpam-5702	298	16	]	]	PUNCT
ejpam-5702	298	17	)	)	PUNCT
ejpam-5702	299	1	∞∑	∞∑	NUM
ejpam-5702	299	2	l=0	l=0	PROPN
ejpam-5702	299	3	(	(	PUNCT
ejpam-5702	299	4	y)l	y)l	X
ejpam-5702	299	5	tl	tl	PROPN
ejpam-5702	299	6	l	l	NOUN
ejpam-5702	299	7	!	!	PUNCT
ejpam-5702	300	1	=	=	PUNCT
ejpam-5702	300	2	r	r	NOUN
ejpam-5702	300	3	log(1	log(1	NOUN
ejpam-5702	300	4	+	+	CCONJ
ejpam-5702	300	5	t	t	X
ejpam-5702	300	6	)	)	PUNCT
ejpam-5702	300	7	∞∑	∞∑	NUM
ejpam-5702	300	8	i=1	i=1	X
ejpam-5702	300	9	i∑	i∑	PROPN
ejpam-5702	301	1	mr=1	mr=1	NOUN
ejpam-5702	301	2	∞∑	∞∑	PROPN
ejpam-5702	301	3	j=0	j=0	PROPN
ejpam-5702	301	4	(	(	PUNCT
ejpam-5702	301	5	mr	mr	PROPN
ejpam-5702	301	6	+	+	PROPN
ejpam-5702	301	7	j	j	PROPN
ejpam-5702	301	8	−	−	PROPN
ejpam-5702	301	9	1	1	NUM
ejpam-5702	301	10	j	j	NOUN
ejpam-5702	301	11	)	)	PUNCT
ejpam-5702	301	12	(	(	PUNCT
ejpam-5702	301	13	−1)mr+i−jm−kr−j	−1)mr+i−jm−kr−j	NOUN
ejpam-5702	301	14	r	r	VERB
ejpam-5702	301	15	mr	mr	PROPN
ejpam-5702	301	16	!	!	PROPN
ejpam-5702	301	17	{	{	PUNCT
ejpam-5702	302	1	i	i	PRON
ejpam-5702	302	2	mr	mr	PROPN
ejpam-5702	302	3	}	}	PUNCT
ejpam-5702	302	4	y	y	PROPN
ejpam-5702	302	5	ti	ti	PROPN
ejpam-5702	302	6	i	i	PRON
ejpam-5702	302	7	!	!	PUNCT
ejpam-5702	303	1	×	×	NOUN
ejpam-5702	303	2	∞∑	∞∑	PROPN
ejpam-5702	303	3	s=0	s=0	PROPN
ejpam-5702	303	4	b	b	PROPN
ejpam-5702	303	5	(	(	PUNCT
ejpam-5702	303	6	k1,	k1,	NOUN
ejpam-5702	303	7	...	...	PUNCT
ejpam-5702	303	8	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	303	9	)	)	PUNCT
ejpam-5702	303	10	s	s	PROPN
ejpam-5702	303	11	,	,	PUNCT
ejpam-5702	303	12	y	y	PROPN
ejpam-5702	303	13	(	(	PUNCT
ejpam-5702	303	14	x	x	X
ejpam-5702	303	15	)	)	PUNCT
ejpam-5702	303	16	ts	ts	ADP
ejpam-5702	303	17	s	s	PART
ejpam-5702	303	18	!	!	PUNCT
ejpam-5702	304	1	∞∑	∞∑	ADJ
ejpam-5702	304	2	l=0	l=0	PROPN
ejpam-5702	304	3	(	(	PUNCT
ejpam-5702	304	4	y)l	y)l	X
ejpam-5702	304	5	tl	tl	PROPN
ejpam-5702	304	6	l	l	NOUN
ejpam-5702	304	7	!	!	PUNCT
ejpam-5702	305	1	s.	s.	PROPN
ejpam-5702	305	2	h.	h.	PROPN
ejpam-5702	305	3	lee	lee	PROPN
ejpam-5702	305	4	,	,	PUNCT
ejpam-5702	305	5	l.	l.	PROPN
ejpam-5702	305	6	chen	chen	PROPN
ejpam-5702	305	7	/	/	SYM
ejpam-5702	305	8	eur	eur	PROPN
ejpam-5702	305	9	.	.	PUNCT
ejpam-5702	306	1	j.	j.	PROPN
ejpam-5702	306	2	pure	pure	PROPN
ejpam-5702	306	3	appl	appl	PROPN
ejpam-5702	306	4	.	.	PROPN
ejpam-5702	306	5	math	math	PROPN
ejpam-5702	306	6	,	,	PUNCT
ejpam-5702	306	7	18	18	NUM
ejpam-5702	306	8	(	(	PUNCT
ejpam-5702	306	9	1	1	NUM
ejpam-5702	306	10	)	)	PUNCT
ejpam-5702	306	11	(	(	PUNCT
ejpam-5702	306	12	2025	2025	NUM
ejpam-5702	306	13	)	)	PUNCT
ejpam-5702	306	14	,	,	PUNCT
ejpam-5702	306	15	5702	5702	NUM
ejpam-5702	306	16	11	11	NUM
ejpam-5702	306	17	of	of	ADP
ejpam-5702	306	18	13	13	NUM
ejpam-5702	306	19	=	=	SYM
ejpam-5702	306	20	r	r	NOUN
ejpam-5702	306	21	log(1	log(1	NOUN
ejpam-5702	306	22	+	+	CCONJ
ejpam-5702	306	23	t	t	X
ejpam-5702	306	24	)	)	PUNCT
ejpam-5702	306	25	∞∑	∞∑	PROPN
ejpam-5702	306	26	u=0	u=0	PROPN
ejpam-5702	306	27	u∑	u∑	ADJ
ejpam-5702	306	28	l=0	l=0	PROPN
ejpam-5702	306	29	(	(	PUNCT
ejpam-5702	306	30	u	u	NOUN
ejpam-5702	306	31	l	l	NOUN
ejpam-5702	306	32	)	)	PUNCT
ejpam-5702	306	33	b	b	PROPN
ejpam-5702	306	34	(	(	PUNCT
ejpam-5702	306	35	k1,	k1,	NOUN
ejpam-5702	306	36	...	...	PUNCT
ejpam-5702	306	37	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	306	38	)	)	PUNCT
ejpam-5702	306	39	u−l	u−l	PROPN
ejpam-5702	306	40	,	,	PUNCT
ejpam-5702	306	41	y	y	PROPN
ejpam-5702	306	42	(	(	PUNCT
ejpam-5702	306	43	x	x	X
ejpam-5702	306	44	)	)	PUNCT
ejpam-5702	306	45	tu	tu	PROPN
ejpam-5702	306	46	u	u	PROPN
ejpam-5702	306	47	!	!	PROPN
ejpam-5702	307	1	×	×	PROPN
ejpam-5702	307	2	∞∑	∞∑	NUM
ejpam-5702	307	3	i=1	i=1	X
ejpam-5702	307	4	i∑	i∑	PROPN
ejpam-5702	308	1	mr=1	mr=1	NOUN
ejpam-5702	309	1	∞∑	∞∑	PROPN
ejpam-5702	309	2	j=0	j=0	PROPN
ejpam-5702	309	3	(	(	PUNCT
ejpam-5702	309	4	mr	mr	PROPN
ejpam-5702	309	5	+	+	PROPN
ejpam-5702	309	6	j	j	PROPN
ejpam-5702	309	7	−	−	PROPN
ejpam-5702	309	8	1	1	NUM
ejpam-5702	309	9	j	j	NOUN
ejpam-5702	309	10	)	)	PUNCT
ejpam-5702	309	11	(	(	PUNCT
ejpam-5702	309	12	−1)mr+i+jm−kr−j	−1)mr+i+jm−kr−j	NOUN
ejpam-5702	309	13	r	r	NOUN
ejpam-5702	309	14	mr	mr	PROPN
ejpam-5702	309	15	!	!	PROPN
ejpam-5702	309	16	{	{	PUNCT
ejpam-5702	310	1	i	i	PRON
ejpam-5702	310	2	mr	mr	PROPN
ejpam-5702	310	3	}	}	PUNCT
ejpam-5702	310	4	y	y	PROPN
ejpam-5702	310	5	ti	ti	NOUN
ejpam-5702	310	6	i	i	PRON
ejpam-5702	310	7	!	!	PUNCT
ejpam-5702	311	1	=	=	PUNCT
ejpam-5702	311	2	r	r	NOUN
ejpam-5702	311	3	li1(−t	li1(−t	NOUN
ejpam-5702	311	4	)	)	PUNCT
ejpam-5702	311	5	∞∑	∞∑	PROPN
ejpam-5702	311	6	n=1	n=1	PROPN
ejpam-5702	311	7	n∑	n∑	PROPN
ejpam-5702	311	8	i=1	i=1	PROPN
ejpam-5702	311	9	i∑	i∑	PROPN
ejpam-5702	312	1	mr=1	mr=1	NOUN
ejpam-5702	312	2	∞∑	∞∑	PROPN
ejpam-5702	312	3	j=0	j=0	PROPN
ejpam-5702	312	4	(	(	PUNCT
ejpam-5702	312	5	n−	n−	NOUN
ejpam-5702	312	6	i	i	NOUN
ejpam-5702	312	7	l	l	NOUN
ejpam-5702	312	8	)	)	PUNCT
ejpam-5702	312	9	(	(	PUNCT
ejpam-5702	312	10	n	n	X
ejpam-5702	312	11	i	i	NOUN
ejpam-5702	312	12	)	)	PUNCT
ejpam-5702	312	13	(	(	PUNCT
ejpam-5702	313	1	mr	mr	PROPN
ejpam-5702	313	2	+	+	PROPN
ejpam-5702	313	3	j	j	PROPN
ejpam-5702	313	4	−	−	PROPN
ejpam-5702	313	5	1	1	NUM
ejpam-5702	313	6	j	j	NOUN
ejpam-5702	313	7	)	)	PUNCT
ejpam-5702	313	8	(	(	PUNCT
ejpam-5702	313	9	−1)mr+i+jm−kr−j	−1)mr+i+jm−kr−j	NOUN
ejpam-5702	313	10	r	r	NOUN
ejpam-5702	313	11	mr	mr	PROPN
ejpam-5702	313	12	!	!	PROPN
ejpam-5702	313	13	×	×	PROPN
ejpam-5702	313	14	{	{	PUNCT
ejpam-5702	313	15	i	i	PRON
ejpam-5702	313	16	mr	mr	PROPN
ejpam-5702	313	17	}	}	PUNCT
ejpam-5702	313	18	y	y	PROPN
ejpam-5702	313	19	b	b	PROPN
ejpam-5702	313	20	(	(	PUNCT
ejpam-5702	313	21	k1,	k1,	NOUN
ejpam-5702	313	22	...	...	PUNCT
ejpam-5702	313	23	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	313	24	)	)	PUNCT
ejpam-5702	313	25	n−i−l	n−i−l	PROPN
ejpam-5702	313	26	,	,	PUNCT
ejpam-5702	313	27	y	y	PROPN
ejpam-5702	313	28	(	(	PUNCT
ejpam-5702	313	29	x	x	NOUN
ejpam-5702	313	30	)	)	PUNCT
ejpam-5702	313	31	tn	tn	PROPN
ejpam-5702	313	32	n	n	NUM
ejpam-5702	313	33	!	!	PUNCT
ejpam-5702	313	34	.	.	PUNCT
ejpam-5702	314	1	by	by	ADP
ejpam-5702	314	2	comparing	compare	VERB
ejpam-5702	314	3	the	the	DET
ejpam-5702	314	4	coefficients	coefficient	NOUN
ejpam-5702	314	5	on	on	ADP
ejpam-5702	314	6	both	both	DET
ejpam-5702	314	7	sides	side	NOUN
ejpam-5702	314	8	of	of	ADP
ejpam-5702	314	9	(	(	PUNCT
ejpam-5702	314	10	32	32	NUM
ejpam-5702	314	11	)	)	PUNCT
ejpam-5702	314	12	,	,	PUNCT
ejpam-5702	314	13	we	we	PRON
ejpam-5702	314	14	have	have	AUX
ejpam-5702	314	15	following	follow	VERB
ejpam-5702	314	16	theorem	theorem	VERB
ejpam-5702	314	17	.	.	PUNCT
ejpam-5702	314	18	theorem	theorem	PROPN
ejpam-5702	314	19	7	7	NUM
ejpam-5702	314	20	.	.	NOUN
ejpam-5702	314	21	for	for	ADP
ejpam-5702	314	22	n	n	PRON
ejpam-5702	314	23	≥	≥	NUM
ejpam-5702	314	24	1	1	NUM
ejpam-5702	314	25	,	,	PUNCT
ejpam-5702	314	26	we	we	PRON
ejpam-5702	314	27	have	have	VERB
ejpam-5702	314	28	b	b	NUM
ejpam-5702	314	29	(	(	PUNCT
ejpam-5702	314	30	k1,	k1,	NOUN
ejpam-5702	314	31	...	...	SYM
ejpam-5702	314	32	,kr	,kr	SYM
ejpam-5702	314	33	)	)	PUNCT
ejpam-5702	314	34	n	n	CCONJ
ejpam-5702	314	35	,	,	PUNCT
ejpam-5702	314	36	y	y	PROPN
ejpam-5702	314	37	(	(	PUNCT
ejpam-5702	314	38	x+	x+	PROPN
ejpam-5702	314	39	y	y	NOUN
ejpam-5702	314	40	)	)	PUNCT
ejpam-5702	315	1	=	=	SYM
ejpam-5702	315	2	r	r	NOUN
ejpam-5702	315	3	li1(−t	li1(−t	NOUN
ejpam-5702	315	4	)	)	PUNCT
ejpam-5702	315	5	n∑	n∑	NOUN
ejpam-5702	315	6	i=1	i=1	PROPN
ejpam-5702	315	7	i∑	i∑	PROPN
ejpam-5702	316	1	mr=1	mr=1	NOUN
ejpam-5702	316	2	∞∑	∞∑	PROPN
ejpam-5702	316	3	j=0	j=0	PROPN
ejpam-5702	316	4	(	(	PUNCT
ejpam-5702	316	5	n−	n−	NOUN
ejpam-5702	316	6	i	i	NOUN
ejpam-5702	316	7	l	l	NOUN
ejpam-5702	316	8	)	)	PUNCT
ejpam-5702	316	9	(	(	PUNCT
ejpam-5702	316	10	n	n	X
ejpam-5702	316	11	i	i	NOUN
ejpam-5702	316	12	)	)	PUNCT
ejpam-5702	316	13	(	(	PUNCT
ejpam-5702	317	1	mr	mr	PROPN
ejpam-5702	317	2	+	+	PROPN
ejpam-5702	317	3	j	j	PROPN
ejpam-5702	317	4	−	−	PROPN
ejpam-5702	317	5	1	1	NUM
ejpam-5702	317	6	j	j	NOUN
ejpam-5702	317	7	)	)	PUNCT
ejpam-5702	317	8	(	(	PUNCT
ejpam-5702	317	9	−1)mr+i+jm−kr−j	−1)mr+i+jm−kr−j	NOUN
ejpam-5702	317	10	r	r	NOUN
ejpam-5702	317	11	mr	mr	PROPN
ejpam-5702	317	12	!	!	PROPN
ejpam-5702	317	13	×	×	PROPN
ejpam-5702	317	14	{	{	PUNCT
ejpam-5702	317	15	i	i	PRON
ejpam-5702	317	16	mr	mr	PROPN
ejpam-5702	317	17	}	}	PUNCT
ejpam-5702	317	18	y	y	PROPN
ejpam-5702	317	19	b	b	PROPN
ejpam-5702	317	20	(	(	PUNCT
ejpam-5702	317	21	k1,	k1,	NOUN
ejpam-5702	317	22	...	...	PUNCT
ejpam-5702	317	23	,kr−1−j	,kr−1−j	PUNCT
ejpam-5702	317	24	)	)	PUNCT
ejpam-5702	317	25	n−i−l	n−i−l	PROPN
ejpam-5702	317	26	,	,	PUNCT
ejpam-5702	317	27	y	y	PROPN
ejpam-5702	317	28	(	(	PUNCT
ejpam-5702	317	29	x	x	NOUN
ejpam-5702	317	30	)	)	PUNCT
ejpam-5702	317	31	.	.	PUNCT
ejpam-5702	318	1	3	3	X
ejpam-5702	318	2	.	.	X
ejpam-5702	318	3	conclusion	conclusion	NOUN
ejpam-5702	318	4	an	an	DET
ejpam-5702	318	5	increasing	increase	VERB
ejpam-5702	318	6	number	number	NOUN
ejpam-5702	318	7	of	of	ADP
ejpam-5702	318	8	scholars	scholar	NOUN
ejpam-5702	318	9	have	have	AUX
ejpam-5702	318	10	studied	study	VERB
ejpam-5702	318	11	many	many	ADJ
ejpam-5702	318	12	special	special	ADJ
ejpam-5702	318	13	polynomials	polynomial	NOUN
ejpam-5702	318	14	and	and	CCONJ
ejpam-5702	318	15	numbers	number	NOUN
ejpam-5702	318	16	and	and	CCONJ
ejpam-5702	318	17	have	have	AUX
ejpam-5702	318	18	applied	apply	VERB
ejpam-5702	318	19	the	the	DET
ejpam-5702	318	20	properties	property	NOUN
ejpam-5702	318	21	of	of	ADP
ejpam-5702	318	22	these	these	DET
ejpam-5702	318	23	polynomials	polynomial	NOUN
ejpam-5702	318	24	in	in	ADP
ejpam-5702	318	25	probability	probability	NOUN
ejpam-5702	318	26	theory	theory	NOUN
ejpam-5702	318	27	.	.	PUNCT
ejpam-5702	319	1	in	in	ADP
ejpam-5702	319	2	view	view	NOUN
ejpam-5702	319	3	of	of	ADP
ejpam-5702	319	4	this	this	PRON
ejpam-5702	319	5	,	,	PUNCT
ejpam-5702	319	6	we	we	PRON
ejpam-5702	319	7	explored	explore	VERB
ejpam-5702	319	8	the	the	DET
ejpam-5702	319	9	properties	property	NOUN
ejpam-5702	319	10	of	of	ADP
ejpam-5702	319	11	probabilistic	probabilistic	ADJ
ejpam-5702	319	12	multiple	multiple	ADJ
ejpam-5702	319	13	poly	poly	ADJ
ejpam-5702	319	14	bernoulli	bernoulli	NOUN
ejpam-5702	319	15	polynomials	polynomial	NOUN
ejpam-5702	319	16	of	of	ADP
ejpam-5702	319	17	the	the	DET
ejpam-5702	319	18	second	second	ADJ
ejpam-5702	319	19	kind	kind	NOUN
ejpam-5702	319	20	.	.	PUNCT
ejpam-5702	320	1	that	that	PRON
ejpam-5702	320	2	implies	imply	VERB
ejpam-5702	320	3	that	that	SCONJ
ejpam-5702	320	4	we	we	PRON
ejpam-5702	320	5	have	have	AUX
ejpam-5702	320	6	conducted	conduct	VERB
ejpam-5702	320	7	an	an	DET
ejpam-5702	320	8	in	in	ADP
ejpam-5702	320	9	-	-	PUNCT
ejpam-5702	320	10	depth	depth	NOUN
ejpam-5702	320	11	study	study	NOUN
ejpam-5702	320	12	of	of	ADP
ejpam-5702	320	13	these	these	DET
ejpam-5702	320	14	polynomials	polynomial	NOUN
ejpam-5702	320	15	and	and	CCONJ
ejpam-5702	320	16	numbers	number	NOUN
ejpam-5702	320	17	.	.	PUNCT
ejpam-5702	321	1	we	we	PRON
ejpam-5702	321	2	obtained	obtain	VERB
ejpam-5702	321	3	several	several	ADJ
ejpam-5702	321	4	interesting	interesting	ADJ
ejpam-5702	321	5	results	result	NOUN
ejpam-5702	321	6	and	and	CCONJ
ejpam-5702	321	7	formula	formula	NOUN
ejpam-5702	321	8	when	when	SCONJ
ejpam-5702	321	9	y	y	PROPN
ejpam-5702	321	10	is	be	AUX
ejpam-5702	321	11	the	the	DET
ejpam-5702	321	12	bernoulli	bernoulli	NOUN
ejpam-5702	321	13	random	random	ADJ
ejpam-5702	321	14	variable	variable	NOUN
ejpam-5702	321	15	and	and	CCONJ
ejpam-5702	321	16	gamma	gamma	NOUN
ejpam-5702	321	17	random	random	ADJ
ejpam-5702	321	18	variable	variable	NOUN
ejpam-5702	321	19	.	.	PUNCT
ejpam-5702	322	1	in	in	ADP
ejpam-5702	322	2	the	the	DET
ejpam-5702	322	3	future	future	NOUN
ejpam-5702	322	4	,	,	PUNCT
ejpam-5702	322	5	we	we	PRON
ejpam-5702	322	6	will	will	AUX
ejpam-5702	322	7	consider	consider	VERB
ejpam-5702	322	8	more	more	ADV
ejpam-5702	322	9	valuable	valuable	ADJ
ejpam-5702	322	10	polynomials	polynomial	NOUN
ejpam-5702	322	11	and	and	CCONJ
ejpam-5702	322	12	numbers	number	NOUN
ejpam-5702	322	13	and	and	CCONJ
ejpam-5702	322	14	get	get	VERB
ejpam-5702	322	15	some	some	DET
ejpam-5702	322	16	significant	significant	ADJ
ejpam-5702	322	17	results	result	NOUN
ejpam-5702	322	18	.	.	PUNCT
ejpam-5702	323	1	references	reference	NOUN
ejpam-5702	323	2	[	[	X
ejpam-5702	323	3	1	1	X
ejpam-5702	323	4	]	]	PUNCT
ejpam-5702	323	5	j.	j.	PROPN
ejpam-5702	323	6	a.	a.	PROPN
ejpam-5702	323	7	adell	adell	PROPN
ejpam-5702	323	8	.	.	PUNCT
ejpam-5702	324	1	probabilistic	probabilistic	ADJ
ejpam-5702	324	2	stirling	stirling	NOUN
ejpam-5702	324	3	numbers	number	NOUN
ejpam-5702	324	4	of	of	ADP
ejpam-5702	324	5	the	the	DET
ejpam-5702	324	6	second	second	ADJ
ejpam-5702	324	7	kind	kind	NOUN
ejpam-5702	324	8	and	and	CCONJ
ejpam-5702	324	9	applications	application	NOUN
ejpam-5702	324	10	.	.	PUNCT
ejpam-5702	325	1	journal	journal	NOUN
ejpam-5702	325	2	of	of	ADP
ejpam-5702	325	3	theoretical	theoretical	ADJ
ejpam-5702	325	4	probability	probability	NOUN
ejpam-5702	325	5	,	,	PUNCT
ejpam-5702	325	6	35(1):636–652	35(1):636–652	PROPN
ejpam-5702	325	7	,	,	PUNCT
ejpam-5702	325	8	2022	2022	NUM
ejpam-5702	325	9	.	.	PUNCT
ejpam-5702	326	1	[	[	X
ejpam-5702	326	2	2	2	NUM
ejpam-5702	326	3	]	]	PUNCT
ejpam-5702	326	4	l.	l.	PROPN
ejpam-5702	326	5	comtet	comtet	PROPN
ejpam-5702	326	6	.	.	PUNCT
ejpam-5702	327	1	advanced	advanced	ADJ
ejpam-5702	327	2	combinatorics	combinatoric	NOUN
ejpam-5702	327	3	.	.	PUNCT
ejpam-5702	328	1	the	the	DET
ejpam-5702	328	2	art	art	NOUN
ejpam-5702	328	3	of	of	ADP
ejpam-5702	328	4	finite	finite	NOUN
ejpam-5702	328	5	and	and	CCONJ
ejpam-5702	328	6	infinite	infinite	ADJ
ejpam-5702	328	7	expansions	expansion	NOUN
ejpam-5702	328	8	.	.	PUNCT
ejpam-5702	329	1	revised	revise	VERB
ejpam-5702	329	2	and	and	CCONJ
ejpam-5702	329	3	enlarged	enlarged	ADJ
ejpam-5702	329	4	edition	edition	PROPN
ejpam-5702	329	5	.	.	PUNCT
ejpam-5702	330	1	d.	d.	PROPN
ejpam-5702	330	2	reidel	reidel	PROPN
ejpam-5702	330	3	publishing	publishing	PROPN
ejpam-5702	330	4	co.	co.	PROPN
ejpam-5702	330	5	,	,	PUNCT
ejpam-5702	330	6	dordrecht	dordrecht	PROPN
ejpam-5702	330	7	,	,	PUNCT
ejpam-5702	330	8	1974	1974	NUM
ejpam-5702	330	9	.	.	PUNCT
ejpam-5702	331	1	[	[	X
ejpam-5702	331	2	3	3	X
ejpam-5702	331	3	]	]	X
ejpam-5702	331	4	d.	d.	PROPN
ejpam-5702	331	5	dolgy	dolgy	PROPN
ejpam-5702	331	6	.	.	PUNCT
ejpam-5702	332	1	interval	interval	NOUN
ejpam-5702	332	2	multi	multi	ADJ
ejpam-5702	332	3	-	-	ADJ
ejpam-5702	332	4	criteria	criteria	ADJ
ejpam-5702	332	5	optimization	optimization	NOUN
ejpam-5702	332	6	.	.	PUNCT
ejpam-5702	333	1	adv	adv	PROPN
ejpam-5702	333	2	.	.	PUNCT
ejpam-5702	333	3	stud	stud	PROPN
ejpam-5702	333	4	.	.	PUNCT
ejpam-5702	334	1	contemp	contemp	NOUN
ejpam-5702	334	2	.	.	PUNCT
ejpam-5702	335	1	math	math	NOUN
ejpam-5702	335	2	.	.	PUNCT
ejpam-5702	335	3	,	,	PUNCT
ejpam-5702	336	1	kyungshang	kyungshang	PROPN
ejpam-5702	336	2	,	,	PUNCT
ejpam-5702	336	3	33(4):367–385	33(4):367–385	PROPN
ejpam-5702	336	4	,	,	PUNCT
ejpam-5702	336	5	2023	2023	NUM
ejpam-5702	336	6	.	.	PUNCT
ejpam-5702	337	1	s.	s.	PROPN
ejpam-5702	337	2	h.	h.	PROPN
ejpam-5702	337	3	lee	lee	PROPN
ejpam-5702	337	4	,	,	PUNCT
ejpam-5702	337	5	l.	l.	PROPN
ejpam-5702	337	6	chen	chen	PROPN
ejpam-5702	337	7	/	/	SYM
ejpam-5702	337	8	eur	eur	PROPN
ejpam-5702	337	9	.	.	PUNCT
ejpam-5702	338	1	j.	j.	PROPN
ejpam-5702	338	2	pure	pure	PROPN
ejpam-5702	338	3	appl	appl	PROPN
ejpam-5702	338	4	.	.	PROPN
ejpam-5702	338	5	math	math	PROPN
ejpam-5702	338	6	,	,	PUNCT
ejpam-5702	338	7	18	18	NUM
ejpam-5702	338	8	(	(	PUNCT
ejpam-5702	338	9	1	1	NUM
ejpam-5702	338	10	)	)	PUNCT
ejpam-5702	338	11	(	(	PUNCT
ejpam-5702	338	12	2025	2025	NUM
ejpam-5702	338	13	)	)	PUNCT
ejpam-5702	338	14	,	,	PUNCT
ejpam-5702	338	15	5702	5702	NUM
ejpam-5702	338	16	12	12	NUM
ejpam-5702	338	17	of	of	ADP
ejpam-5702	338	18	13	13	NUM
ejpam-5702	338	19	[	[	SYM
ejpam-5702	338	20	4	4	NUM
ejpam-5702	338	21	]	]	X
ejpam-5702	338	22	l.-c	l.-c	NOUN
ejpam-5702	338	23	.	.	PUNCT
ejpam-5702	339	1	jang	jang	PROPN
ejpam-5702	339	2	.	.	PUNCT
ejpam-5702	340	1	a	a	DET
ejpam-5702	340	2	note	note	NOUN
ejpam-5702	340	3	on	on	ADP
ejpam-5702	340	4	degenerate	degenerate	ADJ
ejpam-5702	340	5	type	type	NOUN
ejpam-5702	340	6	2	2	NUM
ejpam-5702	340	7	multi	multi	ADJ
ejpam-5702	340	8	-	-	ADJ
ejpam-5702	340	9	poly	poly	ADJ
ejpam-5702	340	10	-	-	PUNCT
ejpam-5702	340	11	genocchi	genocchi	NOUN
ejpam-5702	340	12	polynomials	polynomial	NOUN
ejpam-5702	340	13	.	.	PUNCT
ejpam-5702	341	1	adv	adv	PROPN
ejpam-5702	341	2	.	.	PUNCT
ejpam-5702	341	3	stud	stud	PROPN
ejpam-5702	341	4	.	.	PUNCT
ejpam-5702	342	1	contemp	contemp	NOUN
ejpam-5702	342	2	.	.	PUNCT
ejpam-5702	343	1	math	math	NOUN
ejpam-5702	343	2	.	.	PUNCT
ejpam-5702	343	3	,	,	PUNCT
ejpam-5702	344	1	kyungshang	kyungshang	PROPN
ejpam-5702	344	2	,	,	PUNCT
ejpam-5702	344	3	30(4):537–543	30(4):537–543	PROPN
ejpam-5702	344	4	,	,	PUNCT
ejpam-5702	344	5	2020	2020	NUM
ejpam-5702	344	6	.	.	PUNCT
ejpam-5702	345	1	[	[	X
ejpam-5702	345	2	5	5	X
ejpam-5702	345	3	]	]	PUNCT
ejpam-5702	345	4	w.	w.	PROPN
ejpam-5702	345	5	a.	a.	PROPN
ejpam-5702	345	6	khan	khan	PROPN
ejpam-5702	345	7	and	and	CCONJ
ejpam-5702	345	8	m.	m.	NOUN
ejpam-5702	345	9	a.	a.	NOUN
ejpam-5702	345	10	kamarujjama	kamarujjama	PROPN
ejpam-5702	345	11	.	.	PUNCT
ejpam-5702	346	1	a	a	DET
ejpam-5702	346	2	note	note	NOUN
ejpam-5702	346	3	on	on	ADP
ejpam-5702	346	4	type	type	NOUN
ejpam-5702	346	5	2	2	NUM
ejpam-5702	346	6	degenerate	degenerate	ADJ
ejpam-5702	346	7	multi	multi	ADJ
ejpam-5702	346	8	-	-	ADJ
ejpam-5702	346	9	polybernoulli	polybernoulli	ADJ
ejpam-5702	346	10	polynomials	polynomial	NOUN
ejpam-5702	346	11	of	of	ADP
ejpam-5702	346	12	the	the	DET
ejpam-5702	346	13	second	second	ADJ
ejpam-5702	346	14	kind	kind	NOUN
ejpam-5702	346	15	.	.	PUNCT
ejpam-5702	347	1	proc	proc	NOUN
ejpam-5702	347	2	.	.	PUNCT
ejpam-5702	348	1	jangjeon	jangjeon	PROPN
ejpam-5702	348	2	math	math	PROPN
ejpam-5702	348	3	.	.	PUNCT
ejpam-5702	349	1	soc	soc	PROPN
ejpam-5702	349	2	.	.	PUNCT
ejpam-5702	349	3	,	,	PUNCT
ejpam-5702	349	4	25(1):59–68	25(1):59–68	NUM
ejpam-5702	349	5	,	,	PUNCT
ejpam-5702	349	6	2022	2022	NUM
ejpam-5702	349	7	.	.	PUNCT
ejpam-5702	350	1	[	[	X
ejpam-5702	350	2	6	6	NUM
ejpam-5702	350	3	]	]	PUNCT
ejpam-5702	350	4	d.	d.	PROPN
ejpam-5702	350	5	s.	s.	PROPN
ejpam-5702	350	6	kim	kim	PROPN
ejpam-5702	350	7	,	,	PUNCT
ejpam-5702	350	8	h.	h.	PROPN
ejpam-5702	350	9	k.	k.	PROPN
ejpam-5702	350	10	kim	kim	PROPN
ejpam-5702	350	11	,	,	PUNCT
ejpam-5702	350	12	t.	t.	PROPN
ejpam-5702	350	13	kim	kim	PROPN
ejpam-5702	350	14	,	,	PUNCT
ejpam-5702	350	15	h.	h.	PROPN
ejpam-5702	350	16	lee	lee	PROPN
ejpam-5702	350	17	,	,	PUNCT
ejpam-5702	350	18	and	and	CCONJ
ejpam-5702	350	19	s.	s.	PROPN
ejpam-5702	350	20	park	park	PROPN
ejpam-5702	350	21	.	.	PUNCT
ejpam-5702	351	1	multi	multi	ADJ
ejpam-5702	351	2	-	-	ADJ
ejpam-5702	351	3	lah	lah	ADJ
ejpam-5702	351	4	numbers	number	NOUN
ejpam-5702	351	5	and	and	CCONJ
ejpam-5702	351	6	multistirling	multistirle	VERB
ejpam-5702	351	7	numbers	number	NOUN
ejpam-5702	351	8	of	of	ADP
ejpam-5702	351	9	the	the	DET
ejpam-5702	351	10	first	first	ADJ
ejpam-5702	351	11	kind	kind	NOUN
ejpam-5702	351	12	.	.	PUNCT
ejpam-5702	352	1	advances	advance	NOUN
ejpam-5702	352	2	in	in	ADP
ejpam-5702	352	3	difference	difference	NOUN
ejpam-5702	352	4	equations	equation	NOUN
ejpam-5702	352	5	,	,	PUNCT
ejpam-5702	352	6	2021:1–9	2021:1–9	NUM
ejpam-5702	352	7	,	,	PUNCT
ejpam-5702	352	8	2021	2021	NUM
ejpam-5702	352	9	.	.	PUNCT
ejpam-5702	353	1	[	[	X
ejpam-5702	353	2	7	7	X
ejpam-5702	353	3	]	]	X
ejpam-5702	353	4	d.	d.	PROPN
ejpam-5702	353	5	s.	s.	PROPN
ejpam-5702	353	6	kim	kim	PROPN
ejpam-5702	353	7	and	and	CCONJ
ejpam-5702	353	8	t.	t.	PROPN
ejpam-5702	353	9	kim	kim	PROPN
ejpam-5702	353	10	.	.	PUNCT
ejpam-5702	354	1	representations	representation	NOUN
ejpam-5702	354	2	by	by	ADP
ejpam-5702	354	3	degenerate	degenerate	ADJ
ejpam-5702	354	4	bernoulli	bernoulli	NOUN
ejpam-5702	354	5	polynomials	polynomial	NOUN
ejpam-5702	354	6	arising	arise	VERB
ejpam-5702	354	7	from	from	ADP
ejpam-5702	354	8	volkenborn	volkenborn	ADJ
ejpam-5702	354	9	integral	integral	ADJ
ejpam-5702	354	10	.	.	PUNCT
ejpam-5702	355	1	math	math	NOUN
ejpam-5702	355	2	.	.	PUNCT
ejpam-5702	356	1	methods	method	NOUN
ejpam-5702	356	2	appl	appl	PROPN
ejpam-5702	356	3	.	.	PUNCT
ejpam-5702	357	1	sci	sci	PROPN
ejpam-5702	357	2	.	.	PROPN
ejpam-5702	357	3	,	,	PUNCT
ejpam-5702	357	4	45(11):6615–6634	45(11):6615–6634	NOUN
ejpam-5702	357	5	,	,	PUNCT
ejpam-5702	357	6	2022	2022	NUM
ejpam-5702	357	7	.	.	PUNCT
ejpam-5702	358	1	[	[	X
ejpam-5702	358	2	8	8	NUM
ejpam-5702	358	3	]	]	X
ejpam-5702	358	4	d.	d.	PROPN
ejpam-5702	358	5	s.	s.	PROPN
ejpam-5702	358	6	kim	kim	PROPN
ejpam-5702	358	7	and	and	CCONJ
ejpam-5702	358	8	t.	t.	PROPN
ejpam-5702	358	9	kim	kim	PROPN
ejpam-5702	358	10	.	.	PUNCT
ejpam-5702	359	1	representing	represent	VERB
ejpam-5702	359	2	polynomials	polynomial	NOUN
ejpam-5702	359	3	by	by	ADP
ejpam-5702	359	4	degenerate	degenerate	ADJ
ejpam-5702	359	5	bernoulli	bernoulli	NOUN
ejpam-5702	359	6	polynomials	polynomial	NOUN
ejpam-5702	359	7	.	.	PUNCT
ejpam-5702	360	1	quaest	quaest	VERB
ejpam-5702	360	2	.	.	PUNCT
ejpam-5702	361	1	math	math	NOUN
ejpam-5702	361	2	.	.	PUNCT
ejpam-5702	361	3	,	,	PUNCT
ejpam-5702	361	4	46(5):959–998	46(5):959–998	PROPN
ejpam-5702	361	5	,	,	PUNCT
ejpam-5702	361	6	2023	2023	NUM
ejpam-5702	361	7	.	.	PUNCT
ejpam-5702	362	1	[	[	X
ejpam-5702	362	2	9	9	NUM
ejpam-5702	362	3	]	]	X
ejpam-5702	362	4	d.	d.	PROPN
ejpam-5702	362	5	s.	s.	PROPN
ejpam-5702	362	6	kim	kim	PROPN
ejpam-5702	362	7	and	and	CCONJ
ejpam-5702	362	8	t.	t.	PROPN
ejpam-5702	362	9	k.	k.	PROPN
ejpam-5702	362	10	kim	kim	PROPN
ejpam-5702	362	11	.	.	PUNCT
ejpam-5702	363	1	higher	high	ADJ
ejpam-5702	363	2	-	-	PUNCT
ejpam-5702	363	3	order	order	NOUN
ejpam-5702	363	4	cauchy	cauchy	NOUN
ejpam-5702	363	5	of	of	ADP
ejpam-5702	363	6	the	the	DET
ejpam-5702	363	7	second	second	ADJ
ejpam-5702	363	8	kind	kind	NOUN
ejpam-5702	363	9	and	and	CCONJ
ejpam-5702	363	10	poly	poly	ADJ
ejpam-5702	363	11	-	-	PUNCT
ejpam-5702	363	12	cauchy	cauchy	NOUN
ejpam-5702	363	13	of	of	ADP
ejpam-5702	363	14	the	the	DET
ejpam-5702	363	15	second	second	ADJ
ejpam-5702	363	16	kind	kind	ADJ
ejpam-5702	363	17	mixed	mixed	ADJ
ejpam-5702	363	18	type	type	NOUN
ejpam-5702	363	19	polynomials	polynomial	NOUN
ejpam-5702	363	20	.	.	PUNCT
ejpam-5702	364	1	ars	ars	PROPN
ejpam-5702	364	2	combinatoria	combinatoria	PROPN
ejpam-5702	364	3	,	,	PUNCT
ejpam-5702	364	4	115:435–451	115:435–451	NUM
ejpam-5702	364	5	,	,	PUNCT
ejpam-5702	364	6	2014	2014	NUM
ejpam-5702	364	7	.	.	PUNCT
ejpam-5702	365	1	[	[	X
ejpam-5702	365	2	10	10	NUM
ejpam-5702	365	3	]	]	PUNCT
ejpam-5702	365	4	t.	t.	PROPN
ejpam-5702	365	5	kim	kim	PROPN
ejpam-5702	365	6	and	and	CCONJ
ejpam-5702	365	7	d.	d.	PROPN
ejpam-5702	365	8	s.	s.	PROPN
ejpam-5702	365	9	kim	kim	PROPN
ejpam-5702	365	10	.	.	PUNCT
ejpam-5702	366	1	probabilistic	probabilistic	ADJ
ejpam-5702	366	2	degenerate	degenerate	ADJ
ejpam-5702	366	3	dowling	dowling	NOUN
ejpam-5702	366	4	polynomials	polynomial	NOUN
ejpam-5702	366	5	associated	associate	VERB
ejpam-5702	366	6	with	with	ADP
ejpam-5702	366	7	random	random	ADJ
ejpam-5702	366	8	variables	variable	NOUN
ejpam-5702	366	9	.	.	PUNCT
ejpam-5702	367	1	math	math	NOUN
ejpam-5702	367	2	.	.	PUNCT
ejpam-5702	368	1	meth	meth	NOUN
ejpam-5702	368	2	.	.	PUNCT
ejpam-5702	369	1	appl	appl	PROPN
ejpam-5702	369	2	.	.	PUNCT
ejpam-5702	370	1	sci	sci	PROPN
ejpam-5702	370	2	.	.	PROPN
ejpam-5702	370	3	,	,	PUNCT
ejpam-5702	370	4	2024:1–15	2024:1–15	NUM
ejpam-5702	370	5	.	.	PUNCT
ejpam-5702	371	1	[	[	X
ejpam-5702	371	2	11	11	NUM
ejpam-5702	371	3	]	]	PUNCT
ejpam-5702	371	4	t.	t.	PROPN
ejpam-5702	371	5	kim	kim	PROPN
ejpam-5702	371	6	and	and	CCONJ
ejpam-5702	371	7	d.	d.	PROPN
ejpam-5702	371	8	s.	s.	PROPN
ejpam-5702	371	9	kim	kim	PROPN
ejpam-5702	371	10	.	.	PUNCT
ejpam-5702	372	1	a	a	DET
ejpam-5702	372	2	note	note	NOUN
ejpam-5702	372	3	on	on	ADP
ejpam-5702	372	4	degenerate	degenerate	ADJ
ejpam-5702	372	5	multi	multi	ADJ
ejpam-5702	372	6	-	-	ADJ
ejpam-5702	372	7	poly	poly	ADJ
ejpam-5702	372	8	-	-	PUNCT
ejpam-5702	372	9	bernoulli	bernoulli	NOUN
ejpam-5702	372	10	numbers	number	NOUN
ejpam-5702	372	11	and	and	CCONJ
ejpam-5702	372	12	polynomials	polynomial	NOUN
ejpam-5702	372	13	.	.	PUNCT
ejpam-5702	373	1	applicable	applicable	ADJ
ejpam-5702	373	2	analysis	analysis	NOUN
ejpam-5702	373	3	and	and	CCONJ
ejpam-5702	373	4	discrete	discrete	ADJ
ejpam-5702	373	5	mathematics	mathematic	NOUN
ejpam-5702	373	6	,	,	PUNCT
ejpam-5702	373	7	17(1):47–56	17(1):47–56	NUM
ejpam-5702	373	8	,	,	PUNCT
ejpam-5702	373	9	2023	2023	NUM
ejpam-5702	373	10	.	.	PUNCT
ejpam-5702	374	1	[	[	X
ejpam-5702	374	2	12	12	NUM
ejpam-5702	374	3	]	]	PUNCT
ejpam-5702	374	4	t.	t.	PROPN
ejpam-5702	374	5	kim	kim	PROPN
ejpam-5702	374	6	and	and	CCONJ
ejpam-5702	374	7	d.	d.	PROPN
ejpam-5702	374	8	s.	s.	PROPN
ejpam-5702	374	9	kim	kim	PROPN
ejpam-5702	374	10	.	.	PUNCT
ejpam-5702	375	1	probabilistic	probabilistic	ADJ
ejpam-5702	375	2	degenerate	degenerate	ADJ
ejpam-5702	375	3	bell	bell	NOUN
ejpam-5702	375	4	polynomials	polynomial	NOUN
ejpam-5702	375	5	associated	associate	VERB
ejpam-5702	375	6	with	with	ADP
ejpam-5702	375	7	random	random	ADJ
ejpam-5702	375	8	variables	variable	NOUN
ejpam-5702	375	9	.	.	PUNCT
ejpam-5702	376	1	russian	russian	ADJ
ejpam-5702	376	2	journal	journal	PROPN
ejpam-5702	376	3	of	of	ADP
ejpam-5702	376	4	mathematical	mathematical	ADJ
ejpam-5702	376	5	physics	physics	NOUN
ejpam-5702	376	6	,	,	PUNCT
ejpam-5702	376	7	30(4):528–542	30(4):528–542	NUM
ejpam-5702	376	8	,	,	PUNCT
ejpam-5702	376	9	2023	2023	NUM
ejpam-5702	376	10	.	.	PUNCT
ejpam-5702	377	1	[	[	X
ejpam-5702	377	2	13	13	NUM
ejpam-5702	377	3	]	]	PUNCT
ejpam-5702	377	4	t.	t.	PROPN
ejpam-5702	377	5	kim	kim	PROPN
ejpam-5702	377	6	and	and	CCONJ
ejpam-5702	377	7	d.	d.	PROPN
ejpam-5702	377	8	s.	s.	PROPN
ejpam-5702	377	9	kim	kim	PROPN
ejpam-5702	377	10	.	.	PUNCT
ejpam-5702	378	1	explicit	explicit	ADJ
ejpam-5702	378	2	formulas	formula	NOUN
ejpam-5702	378	3	for	for	ADP
ejpam-5702	378	4	probabilistic	probabilistic	ADJ
ejpam-5702	378	5	multi	multi	ADJ
ejpam-5702	378	6	-	-	ADJ
ejpam-5702	378	7	poly	poly	ADJ
ejpam-5702	378	8	-	-	PUNCT
ejpam-5702	378	9	bernoulli	bernoulli	NOUN
ejpam-5702	378	10	polynomials	polynomial	NOUN
ejpam-5702	378	11	and	and	CCONJ
ejpam-5702	378	12	numbers	number	NOUN
ejpam-5702	378	13	.	.	PUNCT
ejpam-5702	379	1	russian	russian	ADJ
ejpam-5702	379	2	journal	journal	PROPN
ejpam-5702	379	3	of	of	ADP
ejpam-5702	379	4	mathematical	mathematical	ADJ
ejpam-5702	379	5	physics	physics	NOUN
ejpam-5702	379	6	,	,	PUNCT
ejpam-5702	379	7	31(3):450–460	31(3):450–460	NUM
ejpam-5702	379	8	,	,	PUNCT
ejpam-5702	379	9	2024	2024	NUM
ejpam-5702	379	10	.	.	PUNCT
ejpam-5702	380	1	[	[	X
ejpam-5702	380	2	14	14	NUM
ejpam-5702	380	3	]	]	PUNCT
ejpam-5702	380	4	t.	t.	PROPN
ejpam-5702	380	5	kim	kim	PROPN
ejpam-5702	380	6	and	and	CCONJ
ejpam-5702	380	7	d.	d.	PROPN
ejpam-5702	380	8	s.	s.	PROPN
ejpam-5702	380	9	kim	kim	PROPN
ejpam-5702	380	10	.	.	PUNCT
ejpam-5702	381	1	generalization	generalization	NOUN
ejpam-5702	381	2	of	of	ADP
ejpam-5702	381	3	spivey	spivey	PROPN
ejpam-5702	381	4	’s	’s	PART
ejpam-5702	381	5	recurrence	recurrence	PROPN
ejpam-5702	381	6	relation	relation	PROPN
ejpam-5702	381	7	.	.	PUNCT
ejpam-5702	382	1	russ	russ	PROPN
ejpam-5702	382	2	.	.	PUNCT
ejpam-5702	383	1	j.	j.	PROPN
ejpam-5702	383	2	math	math	PROPN
ejpam-5702	383	3	.	.	PUNCT
ejpam-5702	384	1	phys	phy	NOUN
ejpam-5702	384	2	.	.	PUNCT
ejpam-5702	384	3	,	,	PUNCT
ejpam-5702	384	4	31(2):218–226	31(2):218–226	NUM
ejpam-5702	384	5	,	,	PUNCT
ejpam-5702	384	6	2024	2024	NUM
ejpam-5702	384	7	.	.	PUNCT
ejpam-5702	385	1	[	[	X
ejpam-5702	385	2	15	15	X
ejpam-5702	385	3	]	]	PUNCT
ejpam-5702	385	4	t.	t.	PROPN
ejpam-5702	385	5	kim	kim	PROPN
ejpam-5702	385	6	and	and	CCONJ
ejpam-5702	385	7	d.	d.	PROPN
ejpam-5702	385	8	s.	s.	PROPN
ejpam-5702	385	9	kim	kim	PROPN
ejpam-5702	385	10	.	.	PUNCT
ejpam-5702	386	1	probabilistic	probabilistic	ADJ
ejpam-5702	386	2	bernoulli	bernoulli	PROPN
ejpam-5702	386	3	and	and	CCONJ
ejpam-5702	386	4	euler	euler	NOUN
ejpam-5702	386	5	polynomials	polynomial	NOUN
ejpam-5702	386	6	.	.	PUNCT
ejpam-5702	387	1	russian	russian	ADJ
ejpam-5702	387	2	journal	journal	PROPN
ejpam-5702	387	3	of	of	ADP
ejpam-5702	387	4	mathematical	mathematical	ADJ
ejpam-5702	387	5	physics	physics	NOUN
ejpam-5702	387	6	,	,	PUNCT
ejpam-5702	387	7	31(1):94–105	31(1):94–105	NUM
ejpam-5702	387	8	,	,	PUNCT
ejpam-5702	387	9	2024	2024	NUM
ejpam-5702	387	10	.	.	PUNCT
ejpam-5702	388	1	[	[	X
ejpam-5702	388	2	16	16	NUM
ejpam-5702	388	3	]	]	PUNCT
ejpam-5702	388	4	t.	t.	PROPN
ejpam-5702	388	5	kim	kim	PROPN
ejpam-5702	388	6	and	and	CCONJ
ejpam-5702	388	7	d.	d.	PROPN
ejpam-5702	388	8	s.	s.	PROPN
ejpam-5702	388	9	kim	kim	PROPN
ejpam-5702	388	10	.	.	PUNCT
ejpam-5702	389	1	some	some	DET
ejpam-5702	389	2	identities	identity	NOUN
ejpam-5702	389	3	on	on	ADP
ejpam-5702	389	4	degenerate	degenerate	ADJ
ejpam-5702	389	5	harmonic	harmonic	ADJ
ejpam-5702	389	6	and	and	CCONJ
ejpam-5702	389	7	degenerate	degenerate	ADJ
ejpam-5702	389	8	higher	high	ADJ
ejpam-5702	389	9	-	-	PUNCT
ejpam-5702	389	10	order	order	NOUN
ejpam-5702	389	11	harmonic	harmonic	ADJ
ejpam-5702	389	12	numbers	number	NOUN
ejpam-5702	389	13	.	.	PUNCT
ejpam-5702	390	1	appl	appl	PROPN
ejpam-5702	390	2	.	.	PROPN
ejpam-5702	390	3	math	math	PROPN
ejpam-5702	390	4	.	.	PUNCT
ejpam-5702	391	1	comput	comput	NOUN
ejpam-5702	391	2	.	.	PUNCT
ejpam-5702	391	3	,	,	PUNCT
ejpam-5702	391	4	486	486	NUM
ejpam-5702	391	5	:	:	PUNCT
ejpam-5702	391	6	paper	paper	NOUN
ejpam-5702	391	7	no	no	NOUN
ejpam-5702	391	8	.	.	PROPN
ejpam-5702	391	9	129045	129045	NUM
ejpam-5702	391	10	,	,	PUNCT
ejpam-5702	391	11	2025	2025	NUM
ejpam-5702	391	12	.	.	PUNCT
ejpam-5702	392	1	[	[	X
ejpam-5702	392	2	17	17	NUM
ejpam-5702	392	3	]	]	PUNCT
ejpam-5702	392	4	t.	t.	PROPN
ejpam-5702	392	5	kim	kim	PROPN
ejpam-5702	392	6	,	,	PUNCT
ejpam-5702	392	7	d.	d.	PROPN
ejpam-5702	392	8	s.	s.	PROPN
ejpam-5702	392	9	kim	kim	PROPN
ejpam-5702	392	10	,	,	PUNCT
ejpam-5702	392	11	d.	d.	PROPN
ejpam-5702	392	12	v.	v.	PROPN
ejpam-5702	392	13	dolgy	dolgy	PROPN
ejpam-5702	392	14	,	,	PUNCT
ejpam-5702	392	15	s.	s.	PROPN
ejpam-5702	392	16	h.	h.	PROPN
ejpam-5702	392	17	lee	lee	PROPN
ejpam-5702	392	18	,	,	PUNCT
ejpam-5702	392	19	and	and	CCONJ
ejpam-5702	392	20	j.	j.	PROPN
ejpam-5702	392	21	kwon	kwon	PROPN
ejpam-5702	392	22	.	.	PUNCT
ejpam-5702	393	1	some	some	DET
ejpam-5702	393	2	identities	identity	NOUN
ejpam-5702	393	3	of	of	ADP
ejpam-5702	393	4	the	the	DET
ejpam-5702	393	5	higher	high	ADJ
ejpam-5702	393	6	-	-	PUNCT
ejpam-5702	393	7	order	order	NOUN
ejpam-5702	393	8	type	type	NOUN
ejpam-5702	393	9	2	2	NUM
ejpam-5702	393	10	bernoulli	bernoulli	NOUN
ejpam-5702	393	11	numbers	number	NOUN
ejpam-5702	393	12	and	and	CCONJ
ejpam-5702	393	13	polynomials	polynomial	NOUN
ejpam-5702	393	14	of	of	ADP
ejpam-5702	393	15	the	the	DET
ejpam-5702	393	16	second	second	ADJ
ejpam-5702	393	17	kind	kind	NOUN
ejpam-5702	393	18	.	.	PUNCT
ejpam-5702	394	1	comput	comput	NOUN
ejpam-5702	394	2	.	.	PUNCT
ejpam-5702	395	1	model	model	PROPN
ejpam-5702	395	2	.	.	PUNCT
ejpam-5702	396	1	eng	eng	PROPN
ejpam-5702	396	2	.	.	PUNCT
ejpam-5702	397	1	sci	sci	PROPN
ejpam-5702	397	2	,	,	PUNCT
ejpam-5702	397	3	128(3):1121–1132	128(3):1121–1132	PROPN
ejpam-5702	397	4	,	,	PUNCT
ejpam-5702	397	5	2021	2021	NUM
ejpam-5702	397	6	.	.	PUNCT
ejpam-5702	398	1	[	[	X
ejpam-5702	398	2	18	18	NUM
ejpam-5702	398	3	]	]	PUNCT
ejpam-5702	398	4	t.	t.	PROPN
ejpam-5702	398	5	kim	kim	PROPN
ejpam-5702	398	6	,	,	PUNCT
ejpam-5702	398	7	d.	d.	PROPN
ejpam-5702	398	8	s.	s.	PROPN
ejpam-5702	398	9	kim	kim	PROPN
ejpam-5702	398	10	,	,	PUNCT
ejpam-5702	398	11	and	and	CCONJ
ejpam-5702	398	12	h.	h.	PROPN
ejpam-5702	398	13	k.	k.	PROPN
ejpam-5702	398	14	kim	kim	PROPN
ejpam-5702	398	15	.	.	PUNCT
ejpam-5702	399	1	generalized	generalized	ADJ
ejpam-5702	399	2	degenerate	degenerate	ADJ
ejpam-5702	399	3	stirling	stirling	NOUN
ejpam-5702	399	4	numbers	number	NOUN
ejpam-5702	399	5	arising	arise	VERB
ejpam-5702	399	6	from	from	ADP
ejpam-5702	399	7	degenerate	degenerate	ADJ
ejpam-5702	399	8	boson	boson	NOUN
ejpam-5702	399	9	normal	normal	ADJ
ejpam-5702	399	10	ordering	ordering	NOUN
ejpam-5702	399	11	.	.	PUNCT
ejpam-5702	400	1	appl	appl	PROPN
ejpam-5702	400	2	.	.	PROPN
ejpam-5702	400	3	math	math	PROPN
ejpam-5702	400	4	.	.	PUNCT
ejpam-5702	401	1	sci	sci	PROPN
ejpam-5702	401	2	.	.	PUNCT
ejpam-5702	402	1	eng	eng	PROPN
ejpam-5702	402	2	.	.	PROPN
ejpam-5702	402	3	,	,	PUNCT
ejpam-5702	403	1	31(1):paper	31(1):paper	PROPN
ejpam-5702	404	1	no	no	INTJ
ejpam-5702	404	2	.	.	PUNCT
ejpam-5702	405	1	2245540	2245540	NUM
ejpam-5702	405	2	,	,	PUNCT
ejpam-5702	405	3	16	16	NUM
ejpam-5702	406	1	pp	pp	NOUN
ejpam-5702	406	2	.	.	PUNCT
ejpam-5702	406	3	,	,	PUNCT
ejpam-5702	406	4	2023	2023	NUM
ejpam-5702	406	5	.	.	PUNCT
ejpam-5702	407	1	[	[	X
ejpam-5702	407	2	19	19	NUM
ejpam-5702	407	3	]	]	PUNCT
ejpam-5702	407	4	t.	t.	PROPN
ejpam-5702	407	5	kim	kim	PROPN
ejpam-5702	407	6	,	,	PUNCT
ejpam-5702	407	7	d.	d.	PROPN
ejpam-5702	407	8	s.	s.	PROPN
ejpam-5702	407	9	kim	kim	PROPN
ejpam-5702	407	10	,	,	PUNCT
ejpam-5702	407	11	and	and	CCONJ
ejpam-5702	407	12	j.	j.	PROPN
ejpam-5702	407	13	kwon	kwon	PROPN
ejpam-5702	407	14	.	.	PUNCT
ejpam-5702	408	1	probabilistic	probabilistic	ADJ
ejpam-5702	408	2	degenerate	degenerate	ADJ
ejpam-5702	408	3	stirling	stirling	NOUN
ejpam-5702	408	4	polynomials	polynomial	NOUN
ejpam-5702	408	5	of	of	ADP
ejpam-5702	408	6	the	the	DET
ejpam-5702	408	7	second	second	ADJ
ejpam-5702	408	8	kind	kind	NOUN
ejpam-5702	408	9	and	and	CCONJ
ejpam-5702	408	10	their	their	PRON
ejpam-5702	408	11	applications	application	NOUN
ejpam-5702	408	12	.	.	PUNCT
ejpam-5702	409	1	mathematical	mathematical	ADJ
ejpam-5702	409	2	and	and	CCONJ
ejpam-5702	409	3	computer	computer	NOUN
ejpam-5702	409	4	modelling	modelling	NOUN
ejpam-5702	409	5	of	of	ADP
ejpam-5702	409	6	dynamical	dynamical	ADJ
ejpam-5702	409	7	systems	system	NOUN
ejpam-5702	409	8	,	,	PUNCT
ejpam-5702	409	9	30(1):16–30	30(1):16–30	NUM
ejpam-5702	409	10	,	,	PUNCT
ejpam-5702	409	11	2024	2024	NUM
ejpam-5702	409	12	.	.	PUNCT
ejpam-5702	410	1	[	[	X
ejpam-5702	410	2	20	20	NUM
ejpam-5702	410	3	]	]	PUNCT
ejpam-5702	410	4	t.	t.	PROPN
ejpam-5702	410	5	kim	kim	PROPN
ejpam-5702	410	6	,	,	PUNCT
ejpam-5702	410	7	d.	d.	PROPN
ejpam-5702	410	8	s.	s.	PROPN
ejpam-5702	410	9	kim	kim	PROPN
ejpam-5702	410	10	,	,	PUNCT
ejpam-5702	410	11	j.	j.	PROPN
ejpam-5702	410	12	kwon	kwon	PROPN
ejpam-5702	410	13	,	,	PUNCT
ejpam-5702	410	14	and	and	CCONJ
ejpam-5702	410	15	h.	h.	PROPN
ejpam-5702	410	16	lee	lee	PROPN
ejpam-5702	410	17	.	.	PUNCT
ejpam-5702	410	18	lerch	lerch	PROPN
ejpam-5702	410	19	-	-	PUNCT
ejpam-5702	410	20	harmonic	harmonic	ADJ
ejpam-5702	410	21	numbers	number	NOUN
ejpam-5702	410	22	related	relate	VERB
ejpam-5702	410	23	to	to	ADP
ejpam-5702	410	24	lerch	lerch	PROPN
ejpam-5702	410	25	transcendent	transcendent	PROPN
ejpam-5702	410	26	.	.	PUNCT
ejpam-5702	411	1	math	math	NOUN
ejpam-5702	411	2	.	.	PUNCT
ejpam-5702	412	1	comput	comput	PROPN
ejpam-5702	412	2	.	.	PUNCT
ejpam-5702	413	1	model	model	PROPN
ejpam-5702	413	2	.	.	PUNCT
ejpam-5702	414	1	dyn	dyn	PROPN
ejpam-5702	414	2	.	.	PUNCT
ejpam-5702	415	1	syst	syst	PROPN
ejpam-5702	415	2	.	.	PUNCT
ejpam-5702	415	3	,	,	PUNCT
ejpam-5702	416	1	29(1):315–323	29(1):315–323	NUM
ejpam-5702	416	2	,	,	PUNCT
ejpam-5702	416	3	2023	2023	NUM
ejpam-5702	416	4	.	.	PUNCT
ejpam-5702	417	1	[	[	X
ejpam-5702	417	2	21	21	NUM
ejpam-5702	417	3	]	]	PUNCT
ejpam-5702	417	4	t.	t.	PROPN
ejpam-5702	417	5	kim	kim	PROPN
ejpam-5702	417	6	,	,	PUNCT
ejpam-5702	417	7	d.	d.	PROPN
ejpam-5702	417	8	s.	s.	PROPN
ejpam-5702	417	9	kim	kim	PROPN
ejpam-5702	417	10	,	,	PUNCT
ejpam-5702	417	11	j.-w	j.-w	PROPN
ejpam-5702	417	12	.	.	PUNCT
ejpam-5702	418	1	park	park	PROPN
ejpam-5702	418	2	,	,	PUNCT
ejpam-5702	418	3	and	and	CCONJ
ejpam-5702	418	4	j.	j.	PROPN
ejpam-5702	418	5	kwon	kwon	PROPN
ejpam-5702	418	6	.	.	PUNCT
ejpam-5702	419	1	a	a	DET
ejpam-5702	419	2	note	note	NOUN
ejpam-5702	419	3	on	on	ADP
ejpam-5702	419	4	multi	multi	ADJ
ejpam-5702	419	5	-	-	NOUN
ejpam-5702	419	6	euler	euler	VERB
ejpam-5702	419	7	–	–	PUNCT
ejpam-5702	419	8	genocchi	genocchi	PROPN
ejpam-5702	419	9	and	and	CCONJ
ejpam-5702	419	10	degenerate	degenerate	ADJ
ejpam-5702	419	11	multi	multi	NOUN
ejpam-5702	419	12	-	-	NOUN
ejpam-5702	419	13	euler	euler	VERB
ejpam-5702	419	14	–	–	PUNCT
ejpam-5702	419	15	genocchi	genocchi	NOUN
ejpam-5702	419	16	polynomials	polynomial	VERB
ejpam-5702	419	17	.	.	PUNCT
ejpam-5702	420	1	j.	j.	PROPN
ejpam-5702	420	2	math	math	PROPN
ejpam-5702	420	3	.	.	PUNCT
ejpam-5702	420	4	,	,	PUNCT
ejpam-5702	420	5	2023	2023	NUM
ejpam-5702	420	6	:	:	PUNCT
ejpam-5702	420	7	art	art	NOUN
ejpam-5702	420	8	.	.	PUNCT
ejpam-5702	421	1	i	i	PRON
ejpam-5702	421	2	d	d	PROPN
ejpam-5702	421	3	3810046	3810046	NUM
ejpam-5702	421	4	,	,	PUNCT
ejpam-5702	421	5	7	7	NUM
ejpam-5702	421	6	pp	pp	NOUN
ejpam-5702	421	7	.	.	PUNCT
ejpam-5702	421	8	,	,	PUNCT
ejpam-5702	421	9	2023	2023	NUM
ejpam-5702	421	10	.	.	PUNCT
ejpam-5702	422	1	[	[	X
ejpam-5702	422	2	22	22	NUM
ejpam-5702	422	3	]	]	PUNCT
ejpam-5702	422	4	t.	t.	PROPN
ejpam-5702	422	5	kim	kim	PROPN
ejpam-5702	422	6	,	,	PUNCT
ejpam-5702	422	7	h.	h.	PROPN
ejpam-5702	422	8	i.	i.	PROPN
ejpam-5702	422	9	kwon	kwon	PROPN
ejpam-5702	422	10	,	,	PUNCT
ejpam-5702	422	11	s.	s.	PROPN
ejpam-5702	422	12	h.	h.	PROPN
ejpam-5702	422	13	lee	lee	PROPN
ejpam-5702	422	14	,	,	PUNCT
ejpam-5702	422	15	and	and	CCONJ
ejpam-5702	422	16	j.	j.	PROPN
ejpam-5702	422	17	j.	j.	PROPN
ejpam-5702	422	18	seo	seo	PROPN
ejpam-5702	422	19	.	.	PUNCT
ejpam-5702	423	1	a	a	DET
ejpam-5702	423	2	note	note	NOUN
ejpam-5702	423	3	on	on	ADP
ejpam-5702	423	4	poly	poly	ADJ
ejpam-5702	423	5	-	-	PUNCT
ejpam-5702	423	6	bernoulli	bernoulli	NOUN
ejpam-5702	423	7	numbers	number	NOUN
ejpam-5702	423	8	and	and	CCONJ
ejpam-5702	423	9	polynomials	polynomial	NOUN
ejpam-5702	423	10	of	of	ADP
ejpam-5702	423	11	the	the	DET
ejpam-5702	423	12	second	second	ADJ
ejpam-5702	423	13	kind	kind	NOUN
ejpam-5702	423	14	.	.	PUNCT
ejpam-5702	424	1	advances	advance	NOUN
ejpam-5702	424	2	in	in	ADP
ejpam-5702	424	3	difference	difference	NOUN
ejpam-5702	424	4	equations	equation	NOUN
ejpam-5702	424	5	,	,	PUNCT
ejpam-5702	424	6	2014:1–6	2014:1–6	NUM
ejpam-5702	424	7	,	,	PUNCT
ejpam-5702	424	8	2014	2014	NUM
ejpam-5702	424	9	.	.	PUNCT
ejpam-5702	425	1	s.	s.	PROPN
ejpam-5702	425	2	h.	h.	PROPN
ejpam-5702	425	3	lee	lee	PROPN
ejpam-5702	425	4	,	,	PUNCT
ejpam-5702	425	5	l.	l.	PROPN
ejpam-5702	425	6	chen	chen	PROPN
ejpam-5702	425	7	/	/	SYM
ejpam-5702	425	8	eur	eur	PROPN
ejpam-5702	425	9	.	.	PUNCT
ejpam-5702	426	1	j.	j.	PROPN
ejpam-5702	426	2	pure	pure	PROPN
ejpam-5702	426	3	appl	appl	PROPN
ejpam-5702	426	4	.	.	PROPN
ejpam-5702	426	5	math	math	PROPN
ejpam-5702	426	6	,	,	PUNCT
ejpam-5702	426	7	18	18	NUM
ejpam-5702	426	8	(	(	PUNCT
ejpam-5702	426	9	1	1	NUM
ejpam-5702	426	10	)	)	PUNCT
ejpam-5702	426	11	(	(	PUNCT
ejpam-5702	426	12	2025	2025	NUM
ejpam-5702	426	13	)	)	PUNCT
ejpam-5702	426	14	,	,	PUNCT
ejpam-5702	426	15	5702	5702	NUM
ejpam-5702	426	16	13	13	NUM
ejpam-5702	426	17	of	of	ADP
ejpam-5702	426	18	13	13	NUM
ejpam-5702	426	19	[	[	X
ejpam-5702	426	20	23	23	NUM
ejpam-5702	426	21	]	]	PUNCT
ejpam-5702	426	22	h.	h.	PROPN
ejpam-5702	426	23	y.	y.	PROPN
ejpam-5702	426	24	lee	lee	PROPN
ejpam-5702	426	25	,	,	PUNCT
ejpam-5702	426	26	n.	n.	PROPN
ejpam-5702	426	27	s.	s.	PROPN
ejpam-5702	426	28	jung	jung	PROPN
ejpam-5702	426	29	,	,	PUNCT
ejpam-5702	426	30	j.	j.	PROPN
ejpam-5702	426	31	y.	y.	PROPN
ejpam-5702	426	32	kang	kang	PROPN
ejpam-5702	426	33	,	,	PUNCT
ejpam-5702	426	34	and	and	CCONJ
ejpam-5702	426	35	c.	c.	PROPN
ejpam-5702	426	36	s.	s.	PROPN
ejpam-5702	426	37	ryoo	ryoo	PROPN
ejpam-5702	426	38	.	.	PUNCT
ejpam-5702	427	1	extension	extension	NOUN
ejpam-5702	427	2	of	of	ADP
ejpam-5702	427	3	the	the	DET
ejpam-5702	427	4	higher	high	ADJ
ejpam-5702	427	5	-	-	PUNCT
ejpam-5702	427	6	order	order	NOUN
ejpam-5702	427	7	twisted	twisted	ADJ
ejpam-5702	427	8	q	q	ADJ
ejpam-5702	427	9	-	-	PUNCT
ejpam-5702	427	10	euler	euler	NOUN
ejpam-5702	427	11	numbers	number	NOUN
ejpam-5702	427	12	and	and	CCONJ
ejpam-5702	427	13	polynomials	polynomial	NOUN
ejpam-5702	427	14	with	with	ADP
ejpam-5702	427	15	multi	multi	ADJ
ejpam-5702	427	16	weight	weight	NOUN
ejpam-5702	427	17	and	and	CCONJ
ejpam-5702	427	18	higher	high	ADJ
ejpam-5702	427	19	.	.	PUNCT
ejpam-5702	428	1	proc	proc	NOUN
ejpam-5702	428	2	.	.	PUNCT
ejpam-5702	429	1	jangjeon	jangjeon	PROPN
ejpam-5702	429	2	math	math	PROPN
ejpam-5702	429	3	.	.	PUNCT
ejpam-5702	430	1	soc	soc	PROPN
ejpam-5702	430	2	.	.	PROPN
ejpam-5702	430	3	,	,	PUNCT
ejpam-5702	430	4	16(2):203–213	16(2):203–213	NUM
ejpam-5702	430	5	,	,	PUNCT
ejpam-5702	430	6	2013	2013	NUM
ejpam-5702	430	7	.	.	PUNCT
ejpam-5702	431	1	[	[	X
ejpam-5702	431	2	24	24	NUM
ejpam-5702	431	3	]	]	X
ejpam-5702	431	4	l.	l.	PROPN
ejpam-5702	431	5	luo	luo	PROPN
ejpam-5702	431	6	,	,	PUNCT
ejpam-5702	431	7	y.	y.	PROPN
ejpam-5702	431	8	ma	ma	PROPN
ejpam-5702	431	9	,	,	PUNCT
ejpam-5702	431	10	t.	t.	PROPN
ejpam-5702	431	11	kim	kim	PROPN
ejpam-5702	431	12	,	,	PUNCT
ejpam-5702	431	13	and	and	CCONJ
ejpam-5702	431	14	h.	h.	PROPN
ejpam-5702	431	15	li	li	PROPN
ejpam-5702	431	16	.	.	PUNCT
ejpam-5702	432	1	some	some	DET
ejpam-5702	432	2	identities	identity	NOUN
ejpam-5702	432	3	on	on	ADP
ejpam-5702	432	4	degenerate	degenerate	ADJ
ejpam-5702	432	5	poly	poly	ADJ
ejpam-5702	432	6	-	-	PUNCT
ejpam-5702	432	7	euler	euler	NOUN
ejpam-5702	432	8	polynomials	polynomial	NOUN
ejpam-5702	432	9	arising	arise	VERB
ejpam-5702	432	10	from	from	ADP
ejpam-5702	432	11	degenerate	degenerate	ADJ
ejpam-5702	432	12	polylogarithm	polylogarithm	NOUN
ejpam-5702	432	13	functions	function	NOUN
ejpam-5702	432	14	.	.	PUNCT
ejpam-5702	433	1	appl	appl	PROPN
ejpam-5702	433	2	.	.	PROPN
ejpam-5702	433	3	math	math	PROPN
ejpam-5702	433	4	.	.	PUNCT
ejpam-5702	434	1	sci	sci	PROPN
ejpam-5702	434	2	.	.	PUNCT
ejpam-5702	435	1	eng	eng	PROPN
ejpam-5702	435	2	.	.	PROPN
ejpam-5702	435	3	,	,	PUNCT
ejpam-5702	436	1	31(1):paper	31(1):paper	PROPN
ejpam-5702	436	2	no	no	INTJ
ejpam-5702	436	3	.	.	PROPN
ejpam-5702	437	1	2257369	2257369	NUM
ejpam-5702	437	2	,	,	PUNCT
ejpam-5702	437	3	14	14	NUM
ejpam-5702	437	4	pp	pp	NOUN
ejpam-5702	437	5	.	.	PUNCT
ejpam-5702	437	6	,	,	PUNCT
ejpam-5702	437	7	2023	2023	NUM
ejpam-5702	437	8	.	.	PUNCT
ejpam-5702	438	1	[	[	X
ejpam-5702	438	2	25	25	NUM
ejpam-5702	438	3	]	]	PUNCT
ejpam-5702	438	4	m.	m.	NOUN
ejpam-5702	438	5	ma	ma	PROPN
ejpam-5702	438	6	and	and	CCONJ
ejpam-5702	438	7	d.	d.	PROPN
ejpam-5702	438	8	lim	lim	PROPN
ejpam-5702	438	9	.	.	PUNCT
ejpam-5702	439	1	a	a	DET
ejpam-5702	439	2	note	note	NOUN
ejpam-5702	439	3	on	on	ADP
ejpam-5702	439	4	degenerate	degenerate	ADJ
ejpam-5702	439	5	multi	multi	ADJ
ejpam-5702	439	6	-	-	ADJ
ejpam-5702	439	7	poly	poly	ADJ
ejpam-5702	439	8	-	-	PUNCT
ejpam-5702	439	9	bernoulli	bernoulli	NOUN
ejpam-5702	439	10	polynomials	polynomial	NOUN
ejpam-5702	439	11	.	.	PUNCT
ejpam-5702	440	1	adv	adv	PROPN
ejpam-5702	440	2	.	.	PUNCT
ejpam-5702	440	3	stud	stud	PROPN
ejpam-5702	440	4	.	.	PUNCT
ejpam-5702	441	1	contemp	contemp	NOUN
ejpam-5702	441	2	.	.	PUNCT
ejpam-5702	442	1	math	math	PROPN
ejpam-5702	442	2	,	,	PUNCT
ejpam-5702	442	3	kyungshang	kyungshang	PROPN
ejpam-5702	442	4	,	,	PUNCT
ejpam-5702	442	5	30(4):597–606	30(4):597–606	PROPN
ejpam-5702	442	6	,	,	PUNCT
ejpam-5702	442	7	2020	2020	NUM
ejpam-5702	442	8	.	.	PUNCT
ejpam-5702	443	1	[	[	X
ejpam-5702	443	2	26	26	NUM
ejpam-5702	443	3	]	]	X
ejpam-5702	443	4	y.	y.	PROPN
ejpam-5702	443	5	ma	ma	PROPN
ejpam-5702	443	6	,	,	PUNCT
ejpam-5702	443	7	d.	d.	PROPN
ejpam-5702	443	8	s.	s.	PROPN
ejpam-5702	443	9	kim	kim	PROPN
ejpam-5702	443	10	,	,	PUNCT
ejpam-5702	443	11	h.	h.	PROPN
ejpam-5702	443	12	lee	lee	PROPN
ejpam-5702	443	13	,	,	PUNCT
ejpam-5702	443	14	s.	s.	PROPN
ejpam-5702	443	15	park	park	PROPN
ejpam-5702	443	16	,	,	PUNCT
ejpam-5702	443	17	and	and	CCONJ
ejpam-5702	443	18	t.	t.	PROPN
ejpam-5702	443	19	kim	kim	PROPN
ejpam-5702	443	20	.	.	PUNCT
ejpam-5702	444	1	a	a	DET
ejpam-5702	444	2	study	study	NOUN
ejpam-5702	444	3	on	on	ADP
ejpam-5702	444	4	multi	multi	ADJ
ejpam-5702	444	5	-	-	ADJ
ejpam-5702	444	6	stirling	stirling	ADJ
ejpam-5702	444	7	numbers	number	NOUN
ejpam-5702	444	8	of	of	ADP
ejpam-5702	444	9	the	the	DET
ejpam-5702	444	10	first	first	ADJ
ejpam-5702	444	11	kind	kind	NOUN
ejpam-5702	444	12	.	.	PUNCT
ejpam-5702	445	1	fractals	fractal	NOUN
ejpam-5702	445	2	,	,	PUNCT
ejpam-5702	445	3	30(10):2240258	30(10):2240258	NUM
ejpam-5702	445	4	,	,	PUNCT
ejpam-5702	445	5	2022	2022	NUM
ejpam-5702	445	6	.	.	PUNCT
ejpam-5702	446	1	[	[	X
ejpam-5702	446	2	27	27	NUM
ejpam-5702	446	3	]	]	PUNCT
ejpam-5702	446	4	j.-w	j.-w	PROPN
ejpam-5702	446	5	.	.	PUNCT
ejpam-5702	447	1	park	park	NOUN
ejpam-5702	447	2	.	.	PUNCT
ejpam-5702	448	1	on	on	ADP
ejpam-5702	448	2	the	the	DET
ejpam-5702	448	3	degenerate	degenerate	ADJ
ejpam-5702	448	4	multi	multi	ADJ
ejpam-5702	448	5	-	-	ADJ
ejpam-5702	448	6	poly	poly	ADJ
ejpam-5702	448	7	-	-	PUNCT
ejpam-5702	448	8	genocchi	genocchi	NOUN
ejpam-5702	448	9	polynomials	polynomial	NOUN
ejpam-5702	448	10	and	and	CCONJ
ejpam-5702	448	11	numbers	number	NOUN
ejpam-5702	448	12	.	.	PUNCT
ejpam-5702	449	1	adv	adv	PROPN
ejpam-5702	449	2	.	.	PUNCT
ejpam-5702	449	3	stud	stud	PROPN
ejpam-5702	449	4	.	.	PUNCT
ejpam-5702	450	1	contemp	contemp	NOUN
ejpam-5702	450	2	.	.	PUNCT
ejpam-5702	451	1	math	math	NOUN
ejpam-5702	451	2	.	.	PUNCT
ejpam-5702	451	3	,	,	PUNCT
ejpam-5702	452	1	kyungshang	kyungshang	PROPN
ejpam-5702	452	2	,	,	PUNCT
ejpam-5702	452	3	33(2):181–186	33(2):181–186	PROPN
ejpam-5702	452	4	,	,	PUNCT
ejpam-5702	452	5	2023	2023	NUM
ejpam-5702	452	6	.	.	PUNCT
ejpam-5702	453	1	[	[	X
ejpam-5702	453	2	28	28	NUM
ejpam-5702	453	3	]	]	X
ejpam-5702	453	4	f.	f.	PROPN
ejpam-5702	453	5	qi	qi	PROPN
ejpam-5702	453	6	,	,	PUNCT
ejpam-5702	453	7	d.	d.	PROPN
ejpam-5702	453	8	s.	s.	PROPN
ejpam-5702	453	9	kim	kim	PROPN
ejpam-5702	453	10	,	,	PUNCT
ejpam-5702	453	11	t.	t.	PROPN
ejpam-5702	453	12	kim	kim	PROPN
ejpam-5702	453	13	,	,	PUNCT
ejpam-5702	453	14	and	and	CCONJ
ejpam-5702	453	15	d.	d.	PROPN
ejpam-5702	453	16	v.	v.	PROPN
ejpam-5702	453	17	dolgy	dolgy	PROPN
ejpam-5702	453	18	.	.	PUNCT
ejpam-5702	454	1	multiple	multiple	ADJ
ejpam-5702	454	2	-	-	PUNCT
ejpam-5702	454	3	poly	poly	ADJ
ejpam-5702	454	4	-	-	PUNCT
ejpam-5702	454	5	bernoulli	bernoulli	NOUN
ejpam-5702	454	6	polynomials	polynomial	NOUN
ejpam-5702	454	7	of	of	ADP
ejpam-5702	454	8	the	the	DET
ejpam-5702	454	9	second	second	ADJ
ejpam-5702	454	10	kind	kind	NOUN
ejpam-5702	454	11	.	.	PUNCT
ejpam-5702	455	1	advanced	advanced	ADJ
ejpam-5702	455	2	studies	study	NOUN
ejpam-5702	455	3	in	in	ADP
ejpam-5702	455	4	contemporary	contemporary	ADJ
ejpam-5702	455	5	mathematics	mathematics	PROPN
ejpam-5702	455	6	(	(	PUNCT
ejpam-5702	455	7	kyungshang	kyungshang	PROPN
ejpam-5702	455	8	)	)	PUNCT
ejpam-5702	455	9	,	,	PUNCT
ejpam-5702	455	10	25(1):1–7	25(1):1–7	NUM
ejpam-5702	455	11	,	,	PUNCT
ejpam-5702	455	12	2015	2015	NUM
ejpam-5702	455	13	.	.	PUNCT
ejpam-5702	456	1	[	[	X
ejpam-5702	456	2	29	29	NUM
ejpam-5702	456	3	]	]	X
ejpam-5702	456	4	s.	s.	PROPN
ejpam-5702	456	5	roman	roman	PROPN
ejpam-5702	456	6	.	.	PUNCT
ejpam-5702	457	1	the	the	DET
ejpam-5702	457	2	umbral	umbral	ADJ
ejpam-5702	457	3	calculus	calculus	NOUN
ejpam-5702	457	4	,	,	PUNCT
ejpam-5702	457	5	volume	volume	NOUN
ejpam-5702	457	6	111	111	NUM
ejpam-5702	457	7	of	of	ADP
ejpam-5702	457	8	pure	pure	ADJ
ejpam-5702	457	9	and	and	CCONJ
ejpam-5702	457	10	applied	applied	ADJ
ejpam-5702	457	11	mathematics	mathematic	NOUN
ejpam-5702	457	12	.	.	PUNCT
ejpam-5702	458	1	academic	academic	ADJ
ejpam-5702	458	2	press	press	PROPN
ejpam-5702	458	3	,	,	PUNCT
ejpam-5702	458	4	inc	inc	PROPN
ejpam-5702	458	5	.	.	PROPN
ejpam-5702	458	6	,	,	PUNCT
ejpam-5702	458	7	new	new	PROPN
ejpam-5702	458	8	york	york	PROPN
ejpam-5702	458	9	,	,	PUNCT
ejpam-5702	458	10	1984	1984	NUM
ejpam-5702	458	11	.	.	PUNCT
ejpam-5702	459	1	[	[	X
ejpam-5702	459	2	30	30	NUM
ejpam-5702	459	3	]	]	X
ejpam-5702	459	4	d.	d.	PROPN
ejpam-5702	459	5	wang	wang	PROPN
ejpam-5702	459	6	.	.	PUNCT
ejpam-5702	460	1	some	some	PRON
ejpam-5702	460	2	ordering	order	VERB
ejpam-5702	460	3	properties	property	NOUN
ejpam-5702	460	4	of	of	ADP
ejpam-5702	460	5	the	the	DET
ejpam-5702	460	6	expectation	expectation	NOUN
ejpam-5702	460	7	for	for	ADP
ejpam-5702	460	8	multi	multi	ADJ
ejpam-5702	460	9	-	-	ADJ
ejpam-5702	460	10	dimensional	dimensional	ADJ
ejpam-5702	460	11	fuzzy	fuzzy	ADJ
ejpam-5702	460	12	random	random	ADJ
ejpam-5702	460	13	variables	variable	NOUN
ejpam-5702	460	14	.	.	PUNCT
ejpam-5702	461	1	adv	adv	PROPN
ejpam-5702	461	2	.	.	PUNCT
ejpam-5702	461	3	stud	stud	PROPN
ejpam-5702	461	4	.	.	PUNCT
ejpam-5702	462	1	contemp	contemp	NOUN
ejpam-5702	462	2	.	.	PUNCT
ejpam-5702	463	1	math	math	NOUN
ejpam-5702	463	2	.	.	PUNCT
ejpam-5702	463	3	,	,	PUNCT
ejpam-5702	464	1	kyungshang	kyungshang	PROPN
ejpam-5702	464	2	,	,	PUNCT
ejpam-5702	464	3	14(1):29–36	14(1):29–36	NUM
ejpam-5702	464	4	,	,	PUNCT
ejpam-5702	464	5	2007	2007	NUM
ejpam-5702	464	6	.	.	PUNCT