id	sid	tid	token	lemma	pos
ejpam-4825	1	1	european	european	PROPN
ejpam-4825	1	2	journal	journal	PROPN
ejpam-4825	1	3	of	of	ADP
ejpam-4825	1	4	pure	pure	ADJ
ejpam-4825	1	5	and	and	CCONJ
ejpam-4825	1	6	applied	apply	VERB
ejpam-4825	1	7	mathematics	mathematic	NOUN
ejpam-4825	1	8	vol	vol	NOUN
ejpam-4825	1	9	.	.	PUNCT
ejpam-4825	2	1	16	16	NUM
ejpam-4825	2	2	,	,	PUNCT
ejpam-4825	2	3	no	no	INTJ
ejpam-4825	2	4	.	.	NOUN
ejpam-4825	2	5	3	3	NUM
ejpam-4825	2	6	,	,	PUNCT
ejpam-4825	2	7	2023	2023	NUM
ejpam-4825	2	8	,	,	PUNCT
ejpam-4825	2	9	1747	1747	NUM
ejpam-4825	2	10	-	-	SYM
ejpam-4825	2	11	1761	1761	NUM
ejpam-4825	3	1	issn	issn	PROPN
ejpam-4825	3	2	1307	1307	NUM
ejpam-4825	3	3	-	-	SYM
ejpam-4825	3	4	5543	5543	NUM
ejpam-4825	3	5	–	–	PUNCT
ejpam-4825	3	6	ejpam.com	ejpam.com	X
ejpam-4825	3	7	published	publish	VERB
ejpam-4825	3	8	by	by	ADP
ejpam-4825	3	9	new	new	PROPN
ejpam-4825	3	10	york	york	PROPN
ejpam-4825	3	11	business	business	NOUN
ejpam-4825	3	12	global	global	PROPN
ejpam-4825	3	13	some	some	DET
ejpam-4825	3	14	explicit	explicit	ADJ
ejpam-4825	3	15	formulas	formula	NOUN
ejpam-4825	3	16	of	of	ADP
ejpam-4825	3	17	hurwitz	hurwitz	PROPN
ejpam-4825	3	18	lerch	lerch	PROPN
ejpam-4825	3	19	type	type	PROPN
ejpam-4825	3	20	poly	poly	ADJ
ejpam-4825	3	21	-	-	PUNCT
ejpam-4825	3	22	cauchy	cauchy	NOUN
ejpam-4825	3	23	polynomials	polynomial	NOUN
ejpam-4825	3	24	and	and	CCONJ
ejpam-4825	3	25	poly	poly	ADJ
ejpam-4825	3	26	-	-	PUNCT
ejpam-4825	3	27	bernoulli	bernoulli	NOUN
ejpam-4825	3	28	polynomials	polynomial	NOUN
ejpam-4825	3	29	noel	noel	PROPN
ejpam-4825	3	30	b.	b.	PROPN
ejpam-4825	3	31	lacpao	lacpao	PROPN
ejpam-4825	3	32	department	department	PROPN
ejpam-4825	3	33	of	of	ADP
ejpam-4825	3	34	mathematics	mathematics	PROPN
ejpam-4825	3	35	,	,	PUNCT
ejpam-4825	3	36	college	college	NOUN
ejpam-4825	3	37	of	of	ADP
ejpam-4825	3	38	arts	art	NOUN
ejpam-4825	3	39	and	and	CCONJ
ejpam-4825	3	40	sciences	sciences	PROPN
ejpam-4825	3	41	,	,	PUNCT
ejpam-4825	3	42	bukidnon	bukidnon	NOUN
ejpam-4825	3	43	state	state	PROPN
ejpam-4825	3	44	university	university	PROPN
ejpam-4825	3	45	,	,	PUNCT
ejpam-4825	3	46	malaybalay	malaybalay	NOUN
ejpam-4825	3	47	city	city	NOUN
ejpam-4825	3	48	,	,	PUNCT
ejpam-4825	3	49	8700	8700	NUM
ejpam-4825	3	50	,	,	PUNCT
ejpam-4825	3	51	philippines	philippine	NOUN
ejpam-4825	3	52	abstract	abstract	ADJ
ejpam-4825	3	53	.	.	PUNCT
ejpam-4825	4	1	in	in	ADP
ejpam-4825	4	2	this	this	DET
ejpam-4825	4	3	paper	paper	NOUN
ejpam-4825	4	4	,	,	PUNCT
ejpam-4825	4	5	the	the	DET
ejpam-4825	4	6	hurwitz	hurwitz	PROPN
ejpam-4825	4	7	-	-	PUNCT
ejpam-4825	4	8	lerch	lerch	PROPN
ejpam-4825	4	9	poly	poly	ADJ
ejpam-4825	4	10	-	-	PUNCT
ejpam-4825	4	11	cauchy	cauchy	ADJ
ejpam-4825	4	12	and	and	CCONJ
ejpam-4825	4	13	poly	poly	ADJ
ejpam-4825	4	14	-	-	PUNCT
ejpam-4825	4	15	bernoulli	bernoulli	NOUN
ejpam-4825	4	16	polynomials	polynomial	NOUN
ejpam-4825	4	17	are	be	AUX
ejpam-4825	4	18	defined	define	VERB
ejpam-4825	4	19	using	use	VERB
ejpam-4825	4	20	polylogarithm	polylogarithm	PROPN
ejpam-4825	4	21	factorial	factorial	ADJ
ejpam-4825	4	22	function	function	NOUN
ejpam-4825	4	23	.	.	PUNCT
ejpam-4825	5	1	some	some	DET
ejpam-4825	5	2	properties	property	NOUN
ejpam-4825	5	3	of	of	ADP
ejpam-4825	5	4	these	these	DET
ejpam-4825	5	5	types	type	NOUN
ejpam-4825	5	6	of	of	ADP
ejpam-4825	5	7	polynomials	polynomial	NOUN
ejpam-4825	5	8	were	be	AUX
ejpam-4825	5	9	also	also	ADV
ejpam-4825	5	10	established	establish	VERB
ejpam-4825	5	11	.	.	PUNCT
ejpam-4825	6	1	specifically	specifically	ADV
ejpam-4825	6	2	,	,	PUNCT
ejpam-4825	6	3	two	two	NUM
ejpam-4825	6	4	different	different	ADJ
ejpam-4825	6	5	forms	form	NOUN
ejpam-4825	6	6	of	of	ADP
ejpam-4825	6	7	explicit	explicit	ADJ
ejpam-4825	6	8	formula	formula	NOUN
ejpam-4825	6	9	of	of	ADP
ejpam-4825	6	10	hurwitz	hurwitz	PROPN
ejpam-4825	6	11	-	-	PUNCT
ejpam-4825	6	12	lerch	lerch	PROPN
ejpam-4825	6	13	type	type	NOUN
ejpam-4825	6	14	polycauchy	polycauchy	NOUN
ejpam-4825	6	15	polynomials	polynomial	NOUN
ejpam-4825	6	16	were	be	AUX
ejpam-4825	6	17	obtained	obtain	VERB
ejpam-4825	6	18	using	use	VERB
ejpam-4825	6	19	stirling	stirling	NOUN
ejpam-4825	6	20	numbers	number	NOUN
ejpam-4825	6	21	of	of	ADP
ejpam-4825	6	22	the	the	DET
ejpam-4825	6	23	first	first	ADJ
ejpam-4825	6	24	and	and	CCONJ
ejpam-4825	6	25	second	second	ADJ
ejpam-4825	6	26	kind	kind	NOUN
ejpam-4825	6	27	and	and	CCONJ
ejpam-4825	6	28	an	an	DET
ejpam-4825	6	29	explicit	explicit	ADJ
ejpam-4825	6	30	formula	formula	NOUN
ejpam-4825	6	31	of	of	ADP
ejpam-4825	6	32	hurwitz	hurwitz	PROPN
ejpam-4825	6	33	-	-	PUNCT
ejpam-4825	6	34	lerch	lerch	PROPN
ejpam-4825	6	35	type	type	NOUN
ejpam-4825	6	36	poly	poly	ADJ
ejpam-4825	6	37	-	-	PUNCT
ejpam-4825	6	38	bernoulli	bernoulli	NOUN
ejpam-4825	6	39	polynomials	polynomial	NOUN
ejpam-4825	6	40	was	be	AUX
ejpam-4825	6	41	established	establish	VERB
ejpam-4825	6	42	using	use	VERB
ejpam-4825	6	43	the	the	DET
ejpam-4825	6	44	stirling	stirling	NOUN
ejpam-4825	6	45	numbers	number	NOUN
ejpam-4825	6	46	of	of	ADP
ejpam-4825	6	47	the	the	DET
ejpam-4825	6	48	first	first	ADJ
ejpam-4825	6	49	kind	kind	NOUN
ejpam-4825	6	50	.	.	PUNCT
ejpam-4825	7	1	2020	2020	NUM
ejpam-4825	7	2	mathematics	mathematic	NOUN
ejpam-4825	7	3	subject	subject	NOUN
ejpam-4825	7	4	classifications	classification	NOUN
ejpam-4825	7	5	:	:	PUNCT
ejpam-4825	7	6	11m35	11m35	NUM
ejpam-4825	7	7	,	,	PUNCT
ejpam-4825	7	8	11b83	11b83	NUM
ejpam-4825	7	9	,	,	PUNCT
ejpam-4825	7	10	11b68	11b68	NUM
ejpam-4825	7	11	,	,	PUNCT
ejpam-4825	7	12	11b73	11b73	NUM
ejpam-4825	7	13	,	,	PUNCT
ejpam-4825	7	14	05a19	05a19	NUM
ejpam-4825	7	15	key	key	ADJ
ejpam-4825	7	16	words	word	NOUN
ejpam-4825	7	17	and	and	CCONJ
ejpam-4825	7	18	phrases	phrase	NOUN
ejpam-4825	7	19	:	:	PUNCT
ejpam-4825	7	20	polylogarithm	polylogarithm	PROPN
ejpam-4825	7	21	factorial	factorial	NOUN
ejpam-4825	7	22	functions	function	NOUN
ejpam-4825	7	23	,	,	PUNCT
ejpam-4825	7	24	poly	poly	ADJ
ejpam-4825	7	25	-	-	PUNCT
ejpam-4825	7	26	cauchy	cauchy	ADJ
ejpam-4825	7	27	numbers	number	NOUN
ejpam-4825	7	28	of	of	ADP
ejpam-4825	7	29	the	the	DET
ejpam-4825	7	30	first	first	ADJ
ejpam-4825	7	31	and	and	CCONJ
ejpam-4825	7	32	second	second	ADJ
ejpam-4825	7	33	kind	kind	NOUN
ejpam-4825	7	34	,	,	PUNCT
ejpam-4825	7	35	poly	poly	ADJ
ejpam-4825	7	36	-	-	PUNCT
ejpam-4825	7	37	bernoulli	bernoulli	NOUN
ejpam-4825	7	38	numbers	number	NOUN
ejpam-4825	7	39	,	,	PUNCT
ejpam-4825	7	40	hurwitz	hurwitz	PROPN
ejpam-4825	7	41	–	–	PUNCT
ejpam-4825	7	42	lerch	lerch	PROPN
ejpam-4825	7	43	factorial	factorial	PROPN
ejpam-4825	7	44	zeta	zeta	PROPN
ejpam-4825	7	45	function	function	PROPN
ejpam-4825	7	46	,	,	PUNCT
ejpam-4825	7	47	generating	generate	VERB
ejpam-4825	7	48	function	function	NOUN
ejpam-4825	7	49	1	1	NUM
ejpam-4825	7	50	.	.	PUNCT
ejpam-4825	8	1	introduction	introduction	NOUN
ejpam-4825	8	2	it	it	PRON
ejpam-4825	8	3	is	be	AUX
ejpam-4825	8	4	known	know	VERB
ejpam-4825	8	5	that	that	PRON
ejpam-4825	8	6	euler	euler	NOUN
ejpam-4825	8	7	’s	’s	PART
ejpam-4825	8	8	constant	constant	PROPN
ejpam-4825	8	9	appeared	appear	VERB
ejpam-4825	8	10	many	many	ADJ
ejpam-4825	8	11	times	time	NOUN
ejpam-4825	8	12	in	in	ADP
ejpam-4825	8	13	different	different	ADJ
ejpam-4825	8	14	well	well	ADV
ejpam-4825	8	15	-	-	PUNCT
ejpam-4825	8	16	known	know	VERB
ejpam-4825	8	17	expressions	expression	NOUN
ejpam-4825	8	18	or	or	CCONJ
ejpam-4825	8	19	formulas	formula	NOUN
ejpam-4825	8	20	such	such	ADJ
ejpam-4825	8	21	as	as	ADP
ejpam-4825	8	22	in	in	ADP
ejpam-4825	8	23	exponential	exponential	ADJ
ejpam-4825	8	24	integral	integral	NOUN
ejpam-4825	8	25	,	,	PUNCT
ejpam-4825	8	26	the	the	DET
ejpam-4825	8	27	laplace	laplace	NOUN
ejpam-4825	8	28	transform	transform	NOUN
ejpam-4825	8	29	of	of	ADP
ejpam-4825	8	30	the	the	DET
ejpam-4825	8	31	natural	natural	ADJ
ejpam-4825	8	32	logarithm	logarithm	NOUN
ejpam-4825	8	33	,	,	PUNCT
ejpam-4825	8	34	the	the	DET
ejpam-4825	8	35	first	first	ADJ
ejpam-4825	8	36	of	of	ADP
ejpam-4825	8	37	the	the	DET
ejpam-4825	8	38	laurent	laurent	PROPN
ejpam-4825	8	39	series	series	PROPN
ejpam-4825	8	40	expansion	expansion	NOUN
ejpam-4825	8	41	for	for	ADP
ejpam-4825	8	42	the	the	DET
ejpam-4825	8	43	riemann	riemann	PROPN
ejpam-4825	8	44	zeta	zeta	PROPN
ejpam-4825	8	45	function	function	PROPN
ejpam-4825	8	46	,	,	PUNCT
ejpam-4825	8	47	solution	solution	NOUN
ejpam-4825	8	48	of	of	ADP
ejpam-4825	8	49	the	the	DET
ejpam-4825	8	50	second	second	ADJ
ejpam-4825	8	51	kind	kind	NOUN
ejpam-4825	8	52	to	to	PART
ejpam-4825	8	53	bessel	bessel	VERB
ejpam-4825	8	54	’s	’s	PART
ejpam-4825	8	55	equation	equation	NOUN
ejpam-4825	8	56	and	and	CCONJ
ejpam-4825	8	57	many	many	ADJ
ejpam-4825	8	58	more	more	ADJ
ejpam-4825	8	59	.	.	PUNCT
ejpam-4825	9	1	surprisingly	surprisingly	ADV
ejpam-4825	9	2	,	,	PUNCT
ejpam-4825	9	3	the	the	DET
ejpam-4825	9	4	cauchy	cauchy	ADJ
ejpam-4825	9	5	numbers	number	NOUN
ejpam-4825	9	6	have	have	AUX
ejpam-4825	9	7	appeared	appear	VERB
ejpam-4825	9	8	in	in	ADP
ejpam-4825	9	9	the	the	DET
ejpam-4825	9	10	formula	formula	NOUN
ejpam-4825	9	11	involving	involve	VERB
ejpam-4825	9	12	euler	euler	PROPN
ejpam-4825	9	13	’s	’s	PART
ejpam-4825	9	14	constant	constant	ADJ
ejpam-4825	10	1	[	[	X
ejpam-4825	10	2	16	16	NUM
ejpam-4825	10	3	]	]	PUNCT
ejpam-4825	10	4	.	.	PUNCT
ejpam-4825	11	1	this	this	DET
ejpam-4825	11	2	fact	fact	NOUN
ejpam-4825	11	3	has	have	AUX
ejpam-4825	11	4	attracted	attract	VERB
ejpam-4825	11	5	several	several	ADJ
ejpam-4825	11	6	researchers	researcher	NOUN
ejpam-4825	11	7	to	to	PART
ejpam-4825	11	8	work	work	VERB
ejpam-4825	11	9	further	far	ADV
ejpam-4825	11	10	on	on	ADP
ejpam-4825	11	11	cauchy	cauchy	ADJ
ejpam-4825	11	12	numbers	number	NOUN
ejpam-4825	11	13	.	.	PUNCT
ejpam-4825	12	1	the	the	DET
ejpam-4825	12	2	cauchy	cauchy	ADJ
ejpam-4825	12	3	numbers	number	NOUN
ejpam-4825	12	4	[	[	X
ejpam-4825	12	5	6	6	NUM
ejpam-4825	12	6	,	,	PUNCT
ejpam-4825	12	7	12	12	NUM
ejpam-4825	12	8	,	,	PUNCT
ejpam-4825	12	9	15	15	NUM
ejpam-4825	12	10	]	]	PUNCT
ejpam-4825	12	11	of	of	ADP
ejpam-4825	12	12	the	the	DET
ejpam-4825	12	13	first	first	ADJ
ejpam-4825	12	14	and	and	CCONJ
ejpam-4825	12	15	second	second	ADJ
ejpam-4825	12	16	kind	kind	NOUN
ejpam-4825	12	17	,	,	PUNCT
ejpam-4825	12	18	respectively	respectively	ADV
ejpam-4825	12	19	denoted	denote	VERB
ejpam-4825	12	20	by	by	ADP
ejpam-4825	12	21	cn	cn	PROPN
ejpam-4825	12	22	and	and	CCONJ
ejpam-4825	12	23	ĉn	ĉn	NOUN
ejpam-4825	12	24	,	,	PUNCT
ejpam-4825	12	25	are	be	AUX
ejpam-4825	12	26	usually	usually	ADV
ejpam-4825	12	27	defined	define	VERB
ejpam-4825	12	28	by	by	ADP
ejpam-4825	12	29	its	its	PRON
ejpam-4825	12	30	generating	generating	NOUN
ejpam-4825	12	31	functions	function	NOUN
ejpam-4825	12	32	:	:	PUNCT
ejpam-4825	12	33	t	t	PROPN
ejpam-4825	12	34	ln(1	ln(1	PROPN
ejpam-4825	12	35	+	+	PROPN
ejpam-4825	12	36	t	t	PROPN
ejpam-4825	12	37	)	)	PUNCT
ejpam-4825	13	1	=	=	PUNCT
ejpam-4825	14	1	∞∑	∞∑	PROPN
ejpam-4825	14	2	n=0	n=0	PROPN
ejpam-4825	14	3	cn	cn	PROPN
ejpam-4825	14	4	tn	tn	PROPN
ejpam-4825	14	5	n	n	PROPN
ejpam-4825	14	6	!	!	PROPN
ejpam-4825	14	7	,	,	PUNCT
ejpam-4825	14	8	(	(	PUNCT
ejpam-4825	14	9	|t|	|t|	ADP
ejpam-4825	14	10	<	<	X
ejpam-4825	14	11	1	1	NUM
ejpam-4825	14	12	)	)	PUNCT
ejpam-4825	14	13	doi	doi	NOUN
ejpam-4825	14	14	:	:	PUNCT
ejpam-4825	14	15	https://doi.org/10.29020/nybg.ejpam.v16i3.4825	https://doi.org/10.29020/nybg.ejpam.v16i3.4825	PROPN
ejpam-4825	14	16	email	email	NOUN
ejpam-4825	14	17	address	address	NOUN
ejpam-4825	14	18	:	:	PUNCT
ejpam-4825	14	19	noel.lacpao@buksu.edu.ph	noel.lacpao@buksu.edu.ph	PROPN
ejpam-4825	14	20	(	(	PUNCT
ejpam-4825	14	21	n.	n.	PROPN
ejpam-4825	14	22	lacpao	lacpao	PROPN
ejpam-4825	14	23	)	)	PUNCT
ejpam-4825	14	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4825	14	25	1747	1747	NUM
ejpam-4825	15	1	©	©	ADP
ejpam-4825	15	2	2023	2023	NUM
ejpam-4825	15	3	ejpam	ejpam	NOUN
ejpam-4825	15	4	all	all	DET
ejpam-4825	15	5	rights	right	NOUN
ejpam-4825	15	6	reserved	reserve	VERB
ejpam-4825	15	7	.	.	PUNCT
ejpam-4825	16	1	n.	n.	PROPN
ejpam-4825	16	2	b.	b.	PROPN
ejpam-4825	17	1	lacpao	lacpao	PROPN
ejpam-4825	17	2	/	/	SYM
ejpam-4825	17	3	eur	eur	PROPN
ejpam-4825	17	4	.	.	PUNCT
ejpam-4825	18	1	j.	j.	PROPN
ejpam-4825	18	2	pure	pure	PROPN
ejpam-4825	18	3	appl	appl	PROPN
ejpam-4825	18	4	.	.	PROPN
ejpam-4825	18	5	math	math	PROPN
ejpam-4825	18	6	,	,	PUNCT
ejpam-4825	18	7	16	16	NUM
ejpam-4825	18	8	(	(	PUNCT
ejpam-4825	18	9	3	3	NUM
ejpam-4825	18	10	)	)	PUNCT
ejpam-4825	18	11	(	(	PUNCT
ejpam-4825	18	12	2023	2023	NUM
ejpam-4825	18	13	)	)	PUNCT
ejpam-4825	18	14	,	,	PUNCT
ejpam-4825	18	15	1747	1747	NUM
ejpam-4825	18	16	-	-	SYM
ejpam-4825	18	17	1761	1761	NUM
ejpam-4825	18	18	1748	1748	NUM
ejpam-4825	18	19	and	and	CCONJ
ejpam-4825	18	20	t	t	PROPN
ejpam-4825	18	21	(	(	PUNCT
ejpam-4825	18	22	1	1	NUM
ejpam-4825	18	23	+	+	NUM
ejpam-4825	18	24	t	t	NOUN
ejpam-4825	18	25	)	)	PUNCT
ejpam-4825	19	1	ln(1	ln(1	PROPN
ejpam-4825	19	2	+	+	NUM
ejpam-4825	19	3	t	t	NOUN
ejpam-4825	19	4	)	)	PUNCT
ejpam-4825	20	1	=	=	PUNCT
ejpam-4825	21	1	∞∑	∞∑	NUM
ejpam-4825	21	2	n=0	n=0	NUM
ejpam-4825	21	3	ĉn	ĉn	NUM
ejpam-4825	21	4	tn	tn	NOUN
ejpam-4825	21	5	n	n	CCONJ
ejpam-4825	21	6	!	!	PUNCT
ejpam-4825	21	7	,	,	PUNCT
ejpam-4825	21	8	(	(	PUNCT
ejpam-4825	21	9	|t|	|t|	ADP
ejpam-4825	21	10	<	<	X
ejpam-4825	21	11	1	1	NUM
ejpam-4825	21	12	)	)	PUNCT
ejpam-4825	21	13	.	.	PUNCT
ejpam-4825	22	1	the	the	DET
ejpam-4825	22	2	bernoulli	bernoulli	PROPN
ejpam-4825	22	3	numbers	number	NOUN
ejpam-4825	22	4	[	[	X
ejpam-4825	22	5	1	1	X
ejpam-4825	22	6	]	]	PUNCT
ejpam-4825	22	7	denoted	denote	VERB
ejpam-4825	22	8	by	by	ADP
ejpam-4825	22	9	bn	bn	INTJ
ejpam-4825	22	10	are	be	AUX
ejpam-4825	22	11	defined	define	VERB
ejpam-4825	22	12	by	by	ADP
ejpam-4825	22	13	the	the	DET
ejpam-4825	22	14	generating	generate	VERB
ejpam-4825	22	15	function	function	NOUN
ejpam-4825	22	16	t	t	NOUN
ejpam-4825	22	17	et	et	NOUN
ejpam-4825	23	1	−	−	NOUN
ejpam-4825	23	2	1	1	NUM
ejpam-4825	23	3	=	=	PUNCT
ejpam-4825	23	4	∞∑	∞∑	NUM
ejpam-4825	23	5	n=0	n=0	NUM
ejpam-4825	23	6	bn	bn	NUM
ejpam-4825	23	7	tn	tn	NOUN
ejpam-4825	23	8	n	n	CCONJ
ejpam-4825	23	9	!	!	PROPN
ejpam-4825	23	10	,	,	PUNCT
ejpam-4825	23	11	(	(	PUNCT
ejpam-4825	23	12	|t|	|t|	ADP
ejpam-4825	23	13	<	<	X
ejpam-4825	23	14	2π	2π	NOUN
ejpam-4825	23	15	)	)	PUNCT
ejpam-4825	23	16	.	.	PUNCT
ejpam-4825	24	1	one	one	NUM
ejpam-4825	24	2	of	of	ADP
ejpam-4825	24	3	its	its	PRON
ejpam-4825	24	4	combinatorial	combinatorial	ADJ
ejpam-4825	24	5	relations	relation	NOUN
ejpam-4825	24	6	is	be	AUX
ejpam-4825	24	7	given	give	VERB
ejpam-4825	24	8	by	by	ADP
ejpam-4825	24	9	bn	bn	NOUN
ejpam-4825	24	10	=	=	SYM
ejpam-4825	24	11	(	(	PUNCT
ejpam-4825	24	12	−1)n	−1)n	PROPN
ejpam-4825	24	13	n∑	n∑	X
ejpam-4825	24	14	m=0	m=0	PROPN
ejpam-4825	25	1	[	[	PUNCT
ejpam-4825	25	2	n	n	NOUN
ejpam-4825	25	3	m	m	VERB
ejpam-4825	25	4	]	]	PUNCT
ejpam-4825	25	5	(	(	PUNCT
ejpam-4825	25	6	−1)mm	−1)mm	PROPN
ejpam-4825	25	7	!	!	NOUN
ejpam-4825	25	8	m+	m+	NOUN
ejpam-4825	25	9	1	1	NUM
ejpam-4825	25	10	.	.	PUNCT
ejpam-4825	26	1	the	the	DET
ejpam-4825	26	2	cauchy	cauchy	PROPN
ejpam-4825	26	3	numbers	number	NOUN
ejpam-4825	26	4	appear	appear	VERB
ejpam-4825	26	5	in	in	ADP
ejpam-4825	26	6	the	the	DET
ejpam-4825	26	7	laplace	laplace	NOUN
ejpam-4825	26	8	summation	summation	NOUN
ejpam-4825	26	9	formula	formula	NOUN
ejpam-4825	26	10	[	[	X
ejpam-4825	26	11	15	15	NUM
ejpam-4825	26	12	]	]	PUNCT
ejpam-4825	26	13	as	as	ADP
ejpam-4825	26	14	a	a	DET
ejpam-4825	26	15	coefficient	coefficient	NOUN
ejpam-4825	26	16	and	and	CCONJ
ejpam-4825	26	17	are	be	AUX
ejpam-4825	26	18	also	also	ADV
ejpam-4825	26	19	called	call	VERB
ejpam-4825	26	20	the	the	DET
ejpam-4825	26	21	cauchy	cauchy	ADJ
ejpam-4825	26	22	numbers	number	NOUN
ejpam-4825	26	23	of	of	ADP
ejpam-4825	26	24	the	the	DET
ejpam-4825	26	25	first	first	ADJ
ejpam-4825	26	26	kind	kind	NOUN
ejpam-4825	26	27	.	.	PUNCT
ejpam-4825	27	1	in	in	ADP
ejpam-4825	27	2	this	this	DET
ejpam-4825	27	3	formula	formula	NOUN
ejpam-4825	27	4	,	,	PUNCT
ejpam-4825	27	5	the	the	DET
ejpam-4825	27	6	cauchy	cauchy	ADJ
ejpam-4825	27	7	numbers	number	NOUN
ejpam-4825	27	8	are	be	AUX
ejpam-4825	27	9	expressed	express	VERB
ejpam-4825	27	10	in	in	ADP
ejpam-4825	27	11	terms	term	NOUN
ejpam-4825	27	12	of	of	ADP
ejpam-4825	27	13	stirling	stirling	NOUN
ejpam-4825	27	14	numbers	number	NOUN
ejpam-4825	27	15	as	as	ADP
ejpam-4825	27	16	follows,∫	follows,∫	NOUN
ejpam-4825	27	17	f(t)dt	f(t)dt	NOUN
ejpam-4825	27	18	=	=	SYM
ejpam-4825	27	19	∆−1	∆−1	PROPN
ejpam-4825	28	1	∞∑	∞∑	NUM
ejpam-4825	28	2	k=0	k=0	PROPN
ejpam-4825	28	3	ck	ck	PROPN
ejpam-4825	28	4	k	k	X
ejpam-4825	28	5	!	!	PUNCT
ejpam-4825	28	6	∆k	∆k	PROPN
ejpam-4825	28	7	where	where	SCONJ
ejpam-4825	28	8	∆	∆	PROPN
ejpam-4825	28	9	is	be	AUX
ejpam-4825	28	10	the	the	DET
ejpam-4825	28	11	forward	forward	ADJ
ejpam-4825	28	12	difference	difference	NOUN
ejpam-4825	28	13	operator	operator	NOUN
ejpam-4825	28	14	.	.	PUNCT
ejpam-4825	29	1	this	this	PRON
ejpam-4825	29	2	is	be	AUX
ejpam-4825	29	3	analogous	analogous	ADJ
ejpam-4825	29	4	to	to	PART
ejpam-4825	29	5	euler	euler	VERB
ejpam-4825	29	6	mclaurin	mclaurin	ADJ
ejpam-4825	29	7	summation	summation	NOUN
ejpam-4825	29	8	formula	formula	NOUN
ejpam-4825	29	9	where	where	SCONJ
ejpam-4825	29	10	bernoulli	bernoulli	NOUN
ejpam-4825	29	11	numbers	number	NOUN
ejpam-4825	29	12	are	be	AUX
ejpam-4825	29	13	expressed	express	VERB
ejpam-4825	29	14	in	in	ADP
ejpam-4825	29	15	terms	term	NOUN
ejpam-4825	29	16	of	of	ADP
ejpam-4825	29	17	stirling	stirling	NOUN
ejpam-4825	29	18	numbers	number	NOUN
ejpam-4825	29	19	,	,	PUNCT
ejpam-4825	29	20	however	however	ADV
ejpam-4825	29	21	,	,	PUNCT
ejpam-4825	29	22	differentiation	differentiation	NOUN
ejpam-4825	29	23	is	be	AUX
ejpam-4825	29	24	being	be	AUX
ejpam-4825	29	25	used	use	VERB
ejpam-4825	29	26	instead	instead	ADV
ejpam-4825	29	27	of	of	ADP
ejpam-4825	29	28	the	the	DET
ejpam-4825	29	29	difference	difference	NOUN
ejpam-4825	29	30	operators	operator	NOUN
ejpam-4825	29	31	as	as	SCONJ
ejpam-4825	29	32	shown	show	VERB
ejpam-4825	29	33	below	below	ADV
ejpam-4825	29	34	:	:	PUNCT
ejpam-4825	29	35	b−1∑	b−1∑	VERB
ejpam-4825	29	36	k	k	X
ejpam-4825	29	37	=	=	DET
ejpam-4825	29	38	a	a	DET
ejpam-4825	29	39	f(k	f(k	NOUN
ejpam-4825	29	40	)	)	PUNCT
ejpam-4825	29	41	=	=	SYM
ejpam-4825	30	1	∫	∫	PROPN
ejpam-4825	30	2	b	b	PROPN
ejpam-4825	30	3	a	a	DET
ejpam-4825	30	4	f(x)dx+	f(x)dx+	ADJ
ejpam-4825	30	5	n∑	n∑	NOUN
ejpam-4825	30	6	v=1	v=1	ADP
ejpam-4825	30	7	v	v	NOUN
ejpam-4825	30	8	!	!	PUNCT
ejpam-4825	31	1	bv	bv	PROPN
ejpam-4825	31	2	f	f	PROPN
ejpam-4825	31	3	(	(	PUNCT
ejpam-4825	31	4	v−1)(x	v−1)(x	PROPN
ejpam-4825	31	5	)	)	PUNCT
ejpam-4825	31	6	∣∣∣b	∣∣∣b	VERB
ejpam-4825	31	7	a	a	DET
ejpam-4825	31	8	−rn[f	−rn[f	PROPN
ejpam-4825	31	9	]	]	PUNCT
ejpam-4825	31	10	.	.	PUNCT
ejpam-4825	32	1	a	a	DET
ejpam-4825	32	2	variation	variation	NOUN
ejpam-4825	32	3	of	of	ADP
ejpam-4825	32	4	cauchy	cauchy	ADJ
ejpam-4825	32	5	numbers	number	NOUN
ejpam-4825	32	6	of	of	ADP
ejpam-4825	32	7	the	the	DET
ejpam-4825	32	8	first	first	ADJ
ejpam-4825	32	9	kind	kind	NOUN
ejpam-4825	32	10	was	be	AUX
ejpam-4825	32	11	introduced	introduce	VERB
ejpam-4825	32	12	by	by	ADP
ejpam-4825	32	13	komatsu	komatsu	NOUN
ejpam-4825	33	1	[	[	X
ejpam-4825	33	2	12	12	NUM
ejpam-4825	33	3	]	]	PUNCT
ejpam-4825	33	4	inspired	inspire	VERB
ejpam-4825	33	5	by	by	ADP
ejpam-4825	33	6	the	the	DET
ejpam-4825	33	7	polylogarithm	polylogarithm	PROPN
ejpam-4825	33	8	factorial	factorial	PROPN
ejpam-4825	33	9	functions	function	NOUN
ejpam-4825	33	10	lifk(z	lifk(z	VERB
ejpam-4825	33	11	)	)	PUNCT
ejpam-4825	33	12	=	=	PUNCT
ejpam-4825	34	1	∞∑	∞∑	NUM
ejpam-4825	34	2	m=0	m=0	PROPN
ejpam-4825	34	3	zm	zm	PROPN
ejpam-4825	34	4	m!(m+	m!(m+	VERB
ejpam-4825	34	5	1)k	1)k	NUM
ejpam-4825	34	6	.	.	PUNCT
ejpam-4825	35	1	these	these	DET
ejpam-4825	35	2	numbers	number	NOUN
ejpam-4825	35	3	are	be	AUX
ejpam-4825	35	4	called	call	VERB
ejpam-4825	35	5	poly	poly	ADJ
ejpam-4825	35	6	-	-	PUNCT
ejpam-4825	35	7	cauchy	cauchy	NOUN
ejpam-4825	35	8	numbers	number	NOUN
ejpam-4825	35	9	of	of	ADP
ejpam-4825	35	10	the	the	DET
ejpam-4825	35	11	first	first	ADJ
ejpam-4825	35	12	and	and	CCONJ
ejpam-4825	35	13	second	second	ADJ
ejpam-4825	35	14	kind	kind	NOUN
ejpam-4825	35	15	,	,	PUNCT
ejpam-4825	35	16	denoted	denote	VERB
ejpam-4825	35	17	by	by	ADP
ejpam-4825	35	18	c	c	PROPN
ejpam-4825	35	19	(	(	PUNCT
ejpam-4825	35	20	k	k	NOUN
ejpam-4825	35	21	)	)	PUNCT
ejpam-4825	35	22	n	n	NOUN
ejpam-4825	35	23	and	and	CCONJ
ejpam-4825	35	24	ĉ	ĉ	ADV
ejpam-4825	35	25	(	(	PUNCT
ejpam-4825	35	26	k	k	NOUN
ejpam-4825	35	27	)	)	PUNCT
ejpam-4825	35	28	n	n	CCONJ
ejpam-4825	35	29	,	,	PUNCT
ejpam-4825	35	30	respectively	respectively	ADV
ejpam-4825	35	31	.	.	PUNCT
ejpam-4825	36	1	more	more	ADV
ejpam-4825	36	2	precisely	precisely	ADV
ejpam-4825	36	3	,	,	PUNCT
ejpam-4825	36	4	these	these	DET
ejpam-4825	36	5	numbers	number	NOUN
ejpam-4825	36	6	are	be	AUX
ejpam-4825	36	7	defined	define	VERB
ejpam-4825	36	8	by	by	ADP
ejpam-4825	36	9	means	mean	NOUN
ejpam-4825	36	10	of	of	ADP
ejpam-4825	36	11	integrals	integral	NOUN
ejpam-4825	36	12	as	as	SCONJ
ejpam-4825	36	13	follows	follow	VERB
ejpam-4825	36	14	:	:	PUNCT
ejpam-4825	37	1	c(k)n	c(k)n	X
ejpam-4825	37	2	=	=	PUNCT
ejpam-4825	37	3	n	n	X
ejpam-4825	37	4	!	!	PUNCT
ejpam-4825	37	5	∫	∫	PROPN
ejpam-4825	37	6	1	1	NUM
ejpam-4825	37	7	0	0	NUM
ejpam-4825	37	8	·	·	PUNCT
ejpam-4825	37	9	·	·	PUNCT
ejpam-4825	37	10	·	·	PUNCT
ejpam-4825	38	1	∫	∫	PROPN
ejpam-4825	38	2	1	1	NUM
ejpam-4825	38	3	0	0	NUM
ejpam-4825	38	4	(	(	PUNCT
ejpam-4825	38	5	t1t2	t1t2	PROPN
ejpam-4825	38	6	·	·	PUNCT
ejpam-4825	38	7	·	·	PUNCT
ejpam-4825	38	8	·	·	PUNCT
ejpam-4825	38	9	tk	tk	PROPN
ejpam-4825	38	10	n	n	PROPN
ejpam-4825	38	11	)	)	PUNCT
ejpam-4825	38	12	dt1dt2	dt1dt2	ADP
ejpam-4825	38	13	·	·	PUNCT
ejpam-4825	38	14	·	·	PUNCT
ejpam-4825	38	15	·	·	PUNCT
ejpam-4825	38	16	dtk	dtk	PROPN
ejpam-4825	38	17	and	and	CCONJ
ejpam-4825	38	18	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	38	19	=	=	SYM
ejpam-4825	38	20	n	n	X
ejpam-4825	38	21	!	!	PUNCT
ejpam-4825	38	22	∫	∫	PROPN
ejpam-4825	39	1	1	1	NUM
ejpam-4825	39	2	0	0	NUM
ejpam-4825	39	3	·	·	PUNCT
ejpam-4825	39	4	·	·	PUNCT
ejpam-4825	39	5	·	·	PUNCT
ejpam-4825	40	1	∫	∫	PROPN
ejpam-4825	40	2	1	1	NUM
ejpam-4825	40	3	0	0	NUM
ejpam-4825	40	4	(	(	PUNCT
ejpam-4825	40	5	−t1t2	−t1t2	PROPN
ejpam-4825	40	6	·	·	PUNCT
ejpam-4825	40	7	·	·	PUNCT
ejpam-4825	40	8	·	·	PUNCT
ejpam-4825	40	9	tk	tk	PROPN
ejpam-4825	40	10	n	n	PROPN
ejpam-4825	40	11	)	)	PUNCT
ejpam-4825	40	12	dt1dt2	dt1dt2	ADP
ejpam-4825	40	13	·	·	PUNCT
ejpam-4825	40	14	·	·	PUNCT
ejpam-4825	40	15	·	·	PUNCT
ejpam-4825	40	16	dtk	dtk	PROPN
ejpam-4825	40	17	.	.	PUNCT
ejpam-4825	41	1	these	these	DET
ejpam-4825	41	2	numbers	number	NOUN
ejpam-4825	41	3	have	have	VERB
ejpam-4825	41	4	combinatorial	combinatorial	ADJ
ejpam-4825	41	5	relations	relation	NOUN
ejpam-4825	41	6	with	with	ADP
ejpam-4825	41	7	stirling	stirling	NOUN
ejpam-4825	41	8	numbers	number	NOUN
ejpam-4825	41	9	of	of	ADP
ejpam-4825	41	10	the	the	DET
ejpam-4825	41	11	first	first	ADJ
ejpam-4825	41	12	and	and	CCONJ
ejpam-4825	41	13	second	second	ADJ
ejpam-4825	41	14	kind	kind	NOUN
ejpam-4825	41	15	as	as	SCONJ
ejpam-4825	41	16	follows	follow	VERB
ejpam-4825	41	17	n.	n.	PROPN
ejpam-4825	41	18	b.	b.	PROPN
ejpam-4825	41	19	lacpao	lacpao	PROPN
ejpam-4825	41	20	/	/	SYM
ejpam-4825	41	21	eur	eur	PROPN
ejpam-4825	41	22	.	.	PUNCT
ejpam-4825	42	1	j.	j.	PROPN
ejpam-4825	42	2	pure	pure	PROPN
ejpam-4825	42	3	appl	appl	PROPN
ejpam-4825	42	4	.	.	PROPN
ejpam-4825	42	5	math	math	PROPN
ejpam-4825	42	6	,	,	PUNCT
ejpam-4825	42	7	16	16	NUM
ejpam-4825	42	8	(	(	PUNCT
ejpam-4825	42	9	3	3	NUM
ejpam-4825	42	10	)	)	PUNCT
ejpam-4825	42	11	(	(	PUNCT
ejpam-4825	42	12	2023	2023	NUM
ejpam-4825	42	13	)	)	PUNCT
ejpam-4825	42	14	,	,	PUNCT
ejpam-4825	42	15	1747	1747	NUM
ejpam-4825	42	16	-	-	SYM
ejpam-4825	42	17	1761	1761	NUM
ejpam-4825	42	18	1749	1749	NUM
ejpam-4825	42	19	n∑	n∑	PROPN
ejpam-4825	42	20	m=0	m=0	PROPN
ejpam-4825	42	21	{	{	PUNCT
ejpam-4825	42	22	n	n	NOUN
ejpam-4825	42	23	m	m	VERB
ejpam-4825	42	24	}	}	PUNCT
ejpam-4825	42	25	c(k)m	c(k)m	NOUN
ejpam-4825	42	26	=	=	SYM
ejpam-4825	42	27	1	1	NUM
ejpam-4825	42	28	(	(	PUNCT
ejpam-4825	42	29	n+	n+	NUM
ejpam-4825	42	30	1)k	1)k	NUM
ejpam-4825	42	31	,	,	PUNCT
ejpam-4825	42	32	n∑	n∑	PROPN
ejpam-4825	42	33	m=0	m=0	PROPN
ejpam-4825	42	34	{	{	PUNCT
ejpam-4825	42	35	n	n	NOUN
ejpam-4825	42	36	m	m	VERB
ejpam-4825	42	37	}	}	PUNCT
ejpam-4825	42	38	ĉ(k)m	ĉ(k)m	PROPN
ejpam-4825	42	39	=	=	SYM
ejpam-4825	42	40	(	(	PUNCT
ejpam-4825	42	41	−1)n	−1)n	X
ejpam-4825	42	42	(	(	PUNCT
ejpam-4825	42	43	n+	n+	NUM
ejpam-4825	42	44	1)k	1)k	NUM
ejpam-4825	42	45	and	and	CCONJ
ejpam-4825	42	46	explicit	explicit	ADJ
ejpam-4825	42	47	formulas	formula	NOUN
ejpam-4825	42	48	c(k)n	c(k)n	X
ejpam-4825	42	49	=	=	PUNCT
ejpam-4825	42	50	(	(	PUNCT
ejpam-4825	42	51	−1)n	−1)n	PROPN
ejpam-4825	42	52	n∑	n∑	X
ejpam-4825	42	53	m=0	m=0	PROPN
ejpam-4825	42	54	[	[	PUNCT
ejpam-4825	42	55	n	n	NOUN
ejpam-4825	42	56	m	m	VERB
ejpam-4825	42	57	]	]	PUNCT
ejpam-4825	42	58	(	(	PUNCT
ejpam-4825	42	59	−1)m	−1)m	PROPN
ejpam-4825	42	60	(	(	PUNCT
ejpam-4825	42	61	m+	m+	NOUN
ejpam-4825	42	62	1)k	1)k	NUM
ejpam-4825	42	63	,	,	PUNCT
ejpam-4825	43	1	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	43	2	=	=	SYM
ejpam-4825	43	3	(	(	PUNCT
ejpam-4825	43	4	−1)n	−1)n	PROPN
ejpam-4825	43	5	n∑	n∑	X
ejpam-4825	43	6	m=0	m=0	PROPN
ejpam-4825	43	7	[	[	PUNCT
ejpam-4825	43	8	n	n	X
ejpam-4825	43	9	m	m	VERB
ejpam-4825	43	10	]	]	X
ejpam-4825	43	11	1	1	NUM
ejpam-4825	43	12	(	(	PUNCT
ejpam-4825	43	13	m+	m+	NOUN
ejpam-4825	43	14	1)k	1)k	NUM
ejpam-4825	43	15	where	where	SCONJ
ejpam-4825	43	16	[	[	PUNCT
ejpam-4825	43	17	n	n	X
ejpam-4825	43	18	m	m	VERB
ejpam-4825	43	19	]	]	PUNCT
ejpam-4825	43	20	and	and	CCONJ
ejpam-4825	43	21	{	{	PUNCT
ejpam-4825	43	22	n	n	ADV
ejpam-4825	43	23	m	m	VERB
ejpam-4825	43	24	}	}	PUNCT
ejpam-4825	43	25	are	be	AUX
ejpam-4825	43	26	the	the	DET
ejpam-4825	43	27	stirling	stirling	NOUN
ejpam-4825	43	28	numbers	number	NOUN
ejpam-4825	43	29	of	of	ADP
ejpam-4825	43	30	the	the	DET
ejpam-4825	43	31	first	first	ADJ
ejpam-4825	43	32	and	and	CCONJ
ejpam-4825	43	33	second	second	ADJ
ejpam-4825	43	34	kind	kind	NOUN
ejpam-4825	43	35	,	,	PUNCT
ejpam-4825	43	36	respectively	respectively	ADV
ejpam-4825	43	37	,	,	PUNCT
ejpam-4825	43	38	with	with	ADP
ejpam-4825	43	39	generating	generate	VERB
ejpam-4825	43	40	functions	function	NOUN
ejpam-4825	43	41	:	:	PUNCT
ejpam-4825	44	1	[	[	X
ejpam-4825	44	2	ln(1	ln(1	NOUN
ejpam-4825	44	3	+	+	NUM
ejpam-4825	44	4	t)]m	t)]m	NOUN
ejpam-4825	44	5	m	m	NOUN
ejpam-4825	44	6	!	!	PUNCT
ejpam-4825	44	7	=	=	NOUN
ejpam-4825	45	1	∞∑	∞∑	NUM
ejpam-4825	45	2	n	n	NOUN
ejpam-4825	45	3	=	=	NOUN
ejpam-4825	45	4	m	m	PROPN
ejpam-4825	45	5	(	(	PUNCT
ejpam-4825	45	6	−1)n−m	−1)n−m	PUNCT
ejpam-4825	45	7	[	[	PUNCT
ejpam-4825	45	8	n	n	X
ejpam-4825	45	9	m	m	PROPN
ejpam-4825	45	10	]	]	PUNCT
ejpam-4825	45	11	tn	tn	PROPN
ejpam-4825	45	12	n	n	X
ejpam-4825	45	13	!	!	PROPN
ejpam-4825	45	14	,	,	PUNCT
ejpam-4825	45	15	(	(	PUNCT
ejpam-4825	45	16	|t|	|t|	ADP
ejpam-4825	45	17	<	<	X
ejpam-4825	45	18	1	1	NUM
ejpam-4825	45	19	)	)	PUNCT
ejpam-4825	45	20	and	and	CCONJ
ejpam-4825	45	21	(	(	PUNCT
ejpam-4825	45	22	et	et	NOUN
ejpam-4825	45	23	−	−	PROPN
ejpam-4825	45	24	1)m	1)m	NUM
ejpam-4825	45	25	m	m	NOUN
ejpam-4825	45	26	!	!	PUNCT
ejpam-4825	46	1	=	=	NOUN
ejpam-4825	47	1	∞∑	∞∑	NUM
ejpam-4825	47	2	n	n	NOUN
ejpam-4825	47	3	=	=	NOUN
ejpam-4825	47	4	m	m	PROPN
ejpam-4825	47	5	{	{	PUNCT
ejpam-4825	47	6	n	n	NOUN
ejpam-4825	47	7	m	m	PROPN
ejpam-4825	47	8	}	}	PUNCT
ejpam-4825	47	9	tn	tn	PROPN
ejpam-4825	47	10	n	n	CCONJ
ejpam-4825	47	11	!	!	PROPN
ejpam-4825	47	12	,	,	PUNCT
ejpam-4825	47	13	(	(	PUNCT
ejpam-4825	47	14	|t|	|t|	ADP
ejpam-4825	47	15	<	<	X
ejpam-4825	47	16	1	1	NUM
ejpam-4825	47	17	)	)	PUNCT
ejpam-4825	47	18	such	such	ADJ
ejpam-4825	47	19	that	that	SCONJ
ejpam-4825	47	20	[	[	PUNCT
ejpam-4825	47	21	n	n	X
ejpam-4825	47	22	m	m	VERB
ejpam-4825	47	23	]	]	PUNCT
ejpam-4825	48	1	=	=	SYM
ejpam-4825	48	2	0	0	PUNCT
ejpam-4825	48	3	and	and	CCONJ
ejpam-4825	48	4	{	{	PUNCT
ejpam-4825	48	5	n	n	NOUN
ejpam-4825	48	6	m	m	VERB
ejpam-4825	48	7	}	}	PUNCT
ejpam-4825	48	8	=	=	SYM
ejpam-4825	48	9	0	0	NUM
ejpam-4825	48	10	for	for	ADP
ejpam-4825	48	11	n	n	NOUN
ejpam-4825	48	12	<	<	X
ejpam-4825	48	13	m.	m.	NOUN
ejpam-4825	48	14	parallel	parallel	NOUN
ejpam-4825	48	15	to	to	ADP
ejpam-4825	48	16	this	this	PRON
ejpam-4825	48	17	,	,	PUNCT
ejpam-4825	48	18	kaneko	kaneko	PROPN
ejpam-4825	48	19	[	[	X
ejpam-4825	48	20	11	11	NUM
ejpam-4825	48	21	]	]	PUNCT
ejpam-4825	48	22	defined	define	VERB
ejpam-4825	48	23	certain	certain	ADJ
ejpam-4825	48	24	variation	variation	NOUN
ejpam-4825	48	25	of	of	ADP
ejpam-4825	48	26	bernoulli	bernoulli	NOUN
ejpam-4825	48	27	numbers	number	NOUN
ejpam-4825	48	28	in	in	ADP
ejpam-4825	48	29	terms	term	NOUN
ejpam-4825	48	30	of	of	ADP
ejpam-4825	48	31	polylogarithm	polylogarithm	PROPN
ejpam-4825	48	32	function	function	PROPN
ejpam-4825	48	33	lik(z	lik(z	PROPN
ejpam-4825	48	34	)	)	PUNCT
ejpam-4825	49	1	=	=	PUNCT
ejpam-4825	50	1	∞∑	∞∑	NUM
ejpam-4825	50	2	n=1	n=1	PROPN
ejpam-4825	50	3	zn	zn	PROPN
ejpam-4825	50	4	nk	nk	PROPN
ejpam-4825	50	5	,	,	PUNCT
ejpam-4825	50	6	(	(	PUNCT
ejpam-4825	50	7	|z|	|z|	NOUN
ejpam-4825	50	8	<	<	X
ejpam-4825	50	9	1	1	NUM
ejpam-4825	50	10	)	)	PUNCT
ejpam-4825	50	11	which	which	PRON
ejpam-4825	50	12	are	be	AUX
ejpam-4825	50	13	called	call	VERB
ejpam-4825	50	14	poly	poly	ADJ
ejpam-4825	50	15	-	-	PUNCT
ejpam-4825	50	16	bernoulli	bernoulli	NOUN
ejpam-4825	50	17	numbers	number	NOUN
ejpam-4825	50	18	denoted	denote	VERB
ejpam-4825	50	19	by	by	ADP
ejpam-4825	50	20	b	b	PROPN
ejpam-4825	50	21	(	(	PUNCT
ejpam-4825	50	22	k	k	NOUN
ejpam-4825	50	23	)	)	PUNCT
ejpam-4825	50	24	n	n	NOUN
ejpam-4825	50	25	.	.	PUNCT
ejpam-4825	51	1	these	these	DET
ejpam-4825	51	2	types	type	NOUN
ejpam-4825	51	3	of	of	ADP
ejpam-4825	51	4	numbers	number	NOUN
ejpam-4825	51	5	are	be	AUX
ejpam-4825	51	6	defined	define	VERB
ejpam-4825	51	7	by	by	ADP
ejpam-4825	51	8	lik(1−	lik(1−	NOUN
ejpam-4825	51	9	e−t	e−t	NOUN
ejpam-4825	51	10	)	)	PUNCT
ejpam-4825	51	11	1−	1−	NUM
ejpam-4825	51	12	e−t	e−t	NOUN
ejpam-4825	51	13	=	=	NOUN
ejpam-4825	51	14	∞∑	∞∑	NUM
ejpam-4825	51	15	n=0	n=0	NUM
ejpam-4825	51	16	b(k	b(k	PROPN
ejpam-4825	51	17	)	)	PUNCT
ejpam-4825	51	18	n	n	PROPN
ejpam-4825	51	19	tn	tn	PROPN
ejpam-4825	51	20	n	n	X
ejpam-4825	51	21	!	!	PUNCT
ejpam-4825	51	22	.	.	PUNCT
ejpam-4825	52	1	certain	certain	ADJ
ejpam-4825	52	2	generalization	generalization	NOUN
ejpam-4825	52	3	of	of	ADP
ejpam-4825	52	4	poly	poly	ADJ
ejpam-4825	52	5	-	-	PUNCT
ejpam-4825	52	6	cauchy	cauchy	ADJ
ejpam-4825	52	7	numbers	number	NOUN
ejpam-4825	52	8	of	of	ADP
ejpam-4825	52	9	the	the	DET
ejpam-4825	52	10	first	first	ADJ
ejpam-4825	52	11	and	and	CCONJ
ejpam-4825	52	12	second	second	ADJ
ejpam-4825	52	13	kind	kind	NOUN
ejpam-4825	52	14	was	be	AUX
ejpam-4825	52	15	introduced	introduce	VERB
ejpam-4825	52	16	by	by	ADP
ejpam-4825	52	17	cenkci	cenkci	NOUN
ejpam-4825	52	18	and	and	CCONJ
ejpam-4825	52	19	young	young	ADJ
ejpam-4825	52	20	[	[	X
ejpam-4825	52	21	4	4	NUM
ejpam-4825	52	22	]	]	PUNCT
ejpam-4825	52	23	.	.	PUNCT
ejpam-4825	53	1	this	this	DET
ejpam-4825	53	2	generalization	generalization	NOUN
ejpam-4825	53	3	was	be	AUX
ejpam-4825	53	4	motivated	motivate	VERB
ejpam-4825	53	5	by	by	ADP
ejpam-4825	53	6	the	the	DET
ejpam-4825	53	7	concept	concept	NOUN
ejpam-4825	53	8	of	of	ADP
ejpam-4825	53	9	hurwitz	hurwitz	PROPN
ejpam-4825	53	10	-	-	PUNCT
ejpam-4825	53	11	lerch	lerch	PROPN
ejpam-4825	53	12	factorial	factorial	PROPN
ejpam-4825	53	13	zeta	zeta	PROPN
ejpam-4825	53	14	function	function	NOUN
ejpam-4825	53	15	defined	define	VERB
ejpam-4825	53	16	by	by	ADP
ejpam-4825	53	17	φf(z	φf(z	NUM
ejpam-4825	53	18	,	,	PUNCT
ejpam-4825	53	19	s	s	X
ejpam-4825	53	20	,	,	PUNCT
ejpam-4825	53	21	a	a	PRON
ejpam-4825	53	22	)	)	PUNCT
ejpam-4825	53	23	=	=	SYM
ejpam-4825	54	1	∞∑	∞∑	NUM
ejpam-4825	54	2	n=0	n=0	NUM
ejpam-4825	54	3	zn	zn	PROPN
ejpam-4825	54	4	n!(n+	n!(n+	NOUN
ejpam-4825	54	5	a)s	a)s	NOUN
ejpam-4825	54	6	for	for	ADP
ejpam-4825	54	7	s	s	NOUN
ejpam-4825	54	8	∈	∈	PROPN
ejpam-4825	54	9	c	c	NOUN
ejpam-4825	54	10	when	when	SCONJ
ejpam-4825	54	11	|z|	|z|	NOUN
ejpam-4825	54	12	<	<	X
ejpam-4825	54	13	1	1	NUM
ejpam-4825	54	14	,	,	PUNCT
ejpam-4825	54	15	re	re	X
ejpam-4825	54	16	s	s	VERB
ejpam-4825	54	17	>	>	X
ejpam-4825	54	18	1	1	NUM
ejpam-4825	54	19	when	when	SCONJ
ejpam-4825	54	20	|z|	|z|	NOUN
ejpam-4825	54	21	=	=	SYM
ejpam-4825	54	22	1	1	NUM
ejpam-4825	54	23	and	and	CCONJ
ejpam-4825	54	24	a	a	PRON
ejpam-4825	54	25	/∈	/∈	PUNCT
ejpam-4825	54	26	{	{	PUNCT
ejpam-4825	54	27	0,−1,−2	0,−1,−2	NUM
ejpam-4825	54	28	,	,	PUNCT
ejpam-4825	54	29	·	·	PUNCT
ejpam-4825	54	30	·	·	PUNCT
ejpam-4825	54	31	·	·	PUNCT
ejpam-4825	54	32	}	}	PUNCT
ejpam-4825	54	33	.	.	PUNCT
ejpam-4825	55	1	these	these	DET
ejpam-4825	55	2	numbers	number	NOUN
ejpam-4825	55	3	were	be	AUX
ejpam-4825	55	4	called	call	VERB
ejpam-4825	55	5	hurwitz	hurwitz	PROPN
ejpam-4825	55	6	type	type	NOUN
ejpam-4825	55	7	poly	poly	ADJ
ejpam-4825	55	8	-	-	PUNCT
ejpam-4825	55	9	cauchy	cauchy	NOUN
ejpam-4825	55	10	numbers	number	NOUN
ejpam-4825	55	11	of	of	ADP
ejpam-4825	55	12	the	the	DET
ejpam-4825	55	13	first	first	ADJ
ejpam-4825	55	14	and	and	CCONJ
ejpam-4825	55	15	second	second	ADJ
ejpam-4825	55	16	kind	kind	NOUN
ejpam-4825	55	17	,	,	PUNCT
ejpam-4825	55	18	denoted	denote	VERB
ejpam-4825	55	19	by	by	ADP
ejpam-4825	55	20	n.	n.	PROPN
ejpam-4825	55	21	b.	b.	PROPN
ejpam-4825	55	22	lacpao	lacpao	PROPN
ejpam-4825	55	23	/	/	SYM
ejpam-4825	55	24	eur	eur	PROPN
ejpam-4825	55	25	.	.	PUNCT
ejpam-4825	56	1	j.	j.	PROPN
ejpam-4825	56	2	pure	pure	PROPN
ejpam-4825	56	3	appl	appl	PROPN
ejpam-4825	56	4	.	.	PROPN
ejpam-4825	56	5	math	math	PROPN
ejpam-4825	56	6	,	,	PUNCT
ejpam-4825	56	7	16	16	NUM
ejpam-4825	56	8	(	(	PUNCT
ejpam-4825	56	9	3	3	NUM
ejpam-4825	56	10	)	)	PUNCT
ejpam-4825	56	11	(	(	PUNCT
ejpam-4825	56	12	2023	2023	NUM
ejpam-4825	56	13	)	)	PUNCT
ejpam-4825	56	14	,	,	PUNCT
ejpam-4825	56	15	1747	1747	NUM
ejpam-4825	56	16	-	-	SYM
ejpam-4825	56	17	1761	1761	NUM
ejpam-4825	56	18	1750	1750	NUM
ejpam-4825	56	19	c	c	X
ejpam-4825	56	20	(	(	PUNCT
ejpam-4825	56	21	k	k	NOUN
ejpam-4825	56	22	)	)	PUNCT
ejpam-4825	56	23	n	n	CCONJ
ejpam-4825	56	24	(	(	PUNCT
ejpam-4825	56	25	a	a	NOUN
ejpam-4825	56	26	)	)	PUNCT
ejpam-4825	56	27	and	and	CCONJ
ejpam-4825	56	28	ĉ	ĉ	X
ejpam-4825	56	29	(	(	PUNCT
ejpam-4825	56	30	k	k	NOUN
ejpam-4825	56	31	)	)	PUNCT
ejpam-4825	56	32	n	n	CCONJ
ejpam-4825	56	33	(	(	PUNCT
ejpam-4825	56	34	a	a	NOUN
ejpam-4825	56	35	)	)	PUNCT
ejpam-4825	56	36	,	,	PUNCT
ejpam-4825	56	37	which	which	PRON
ejpam-4825	56	38	are	be	AUX
ejpam-4825	56	39	respectively	respectively	ADV
ejpam-4825	56	40	defined	define	VERB
ejpam-4825	56	41	by	by	ADP
ejpam-4825	56	42	φf(log(1	φf(log(1	PROPN
ejpam-4825	56	43	+	+	PROPN
ejpam-4825	56	44	t	t	PROPN
ejpam-4825	56	45	)	)	PUNCT
ejpam-4825	56	46	,	,	PUNCT
ejpam-4825	56	47	k	k	PROPN
ejpam-4825	56	48	,	,	PUNCT
ejpam-4825	56	49	a	a	PRON
ejpam-4825	56	50	)	)	PUNCT
ejpam-4825	56	51	=	=	SYM
ejpam-4825	57	1	∞∑	∞∑	NUM
ejpam-4825	57	2	n=0	n=0	NUM
ejpam-4825	57	3	c(k)n	c(k)n	PROPN
ejpam-4825	57	4	(	(	PUNCT
ejpam-4825	57	5	a	a	NOUN
ejpam-4825	57	6	)	)	PUNCT
ejpam-4825	57	7	tn	tn	NOUN
ejpam-4825	57	8	n	n	CCONJ
ejpam-4825	57	9	!	!	PUNCT
ejpam-4825	58	1	and	and	CCONJ
ejpam-4825	58	2	φf(−	φf(−	ADV
ejpam-4825	58	3	log(1	log(1	NOUN
ejpam-4825	58	4	+	+	CCONJ
ejpam-4825	59	1	t	t	NOUN
ejpam-4825	59	2	)	)	PUNCT
ejpam-4825	59	3	,	,	PUNCT
ejpam-4825	60	1	k	k	PROPN
ejpam-4825	60	2	,	,	PUNCT
ejpam-4825	60	3	a	a	PRON
ejpam-4825	60	4	)	)	PUNCT
ejpam-4825	60	5	=	=	SYM
ejpam-4825	60	6	∞∑	∞∑	PRON
ejpam-4825	60	7	n=0	n=0	NUM
ejpam-4825	60	8	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	60	9	(	(	PUNCT
ejpam-4825	60	10	a	a	NOUN
ejpam-4825	60	11	)	)	PUNCT
ejpam-4825	60	12	tn	tn	NOUN
ejpam-4825	60	13	n	n	NUM
ejpam-4825	60	14	!	!	PUNCT
ejpam-4825	60	15	.	.	PUNCT
ejpam-4825	61	1	these	these	DET
ejpam-4825	61	2	numbers	number	NOUN
ejpam-4825	61	3	possessed	possess	VERB
ejpam-4825	61	4	the	the	DET
ejpam-4825	61	5	following	follow	VERB
ejpam-4825	61	6	properties	property	NOUN
ejpam-4825	61	7	which	which	PRON
ejpam-4825	61	8	are	be	AUX
ejpam-4825	61	9	analogous	analogous	ADJ
ejpam-4825	61	10	to	to	ADP
ejpam-4825	61	11	those	those	PRON
ejpam-4825	61	12	of	of	ADP
ejpam-4825	61	13	polycauchy	polycauchy	ADJ
ejpam-4825	61	14	numbers	number	NOUN
ejpam-4825	61	15	:	:	PUNCT
ejpam-4825	61	16	explicit	explicit	ADJ
ejpam-4825	61	17	formulas	formula	NOUN
ejpam-4825	61	18	c(k)n	c(k)n	PROPN
ejpam-4825	61	19	(	(	PUNCT
ejpam-4825	61	20	a	a	X
ejpam-4825	61	21	)	)	PUNCT
ejpam-4825	61	22	=	=	SYM
ejpam-4825	61	23	(	(	PUNCT
ejpam-4825	61	24	−1)n	−1)n	PROPN
ejpam-4825	61	25	n∑	n∑	PROPN
ejpam-4825	61	26	m=0	m=0	PROPN
ejpam-4825	61	27	(	(	PUNCT
ejpam-4825	61	28	−1)ms1(n	−1)ms1(n	NOUN
ejpam-4825	61	29	,	,	PUNCT
ejpam-4825	61	30	m	m	NOUN
ejpam-4825	61	31	)	)	PUNCT
ejpam-4825	61	32	(	(	PUNCT
ejpam-4825	61	33	m+	m+	NUM
ejpam-4825	61	34	a)k	a)k	ADJ
ejpam-4825	61	35	,	,	PUNCT
ejpam-4825	61	36	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	61	37	(	(	PUNCT
ejpam-4825	61	38	a	a	X
ejpam-4825	61	39	)	)	PUNCT
ejpam-4825	61	40	=	=	SYM
ejpam-4825	61	41	(	(	PUNCT
ejpam-4825	61	42	−1)n	−1)n	PROPN
ejpam-4825	61	43	n∑	n∑	X
ejpam-4825	61	44	m=0	m=0	PROPN
ejpam-4825	61	45	s1(n	s1(n	PROPN
ejpam-4825	61	46	,	,	PUNCT
ejpam-4825	61	47	m	m	NOUN
ejpam-4825	61	48	)	)	PUNCT
ejpam-4825	61	49	(	(	PUNCT
ejpam-4825	61	50	m+	m+	NUM
ejpam-4825	61	51	a)k	a)k	ADJ
ejpam-4825	62	1	,	,	PUNCT
ejpam-4825	62	2	relations	relation	NOUN
ejpam-4825	62	3	with	with	ADP
ejpam-4825	62	4	stirling	stirling	NOUN
ejpam-4825	62	5	numbers	number	NOUN
ejpam-4825	62	6	of	of	ADP
ejpam-4825	62	7	the	the	DET
ejpam-4825	62	8	second	second	ADJ
ejpam-4825	62	9	kind	kind	NOUN
ejpam-4825	62	10	n∑	n∑	PROPN
ejpam-4825	62	11	m=0	m=0	PROPN
ejpam-4825	62	12	s2(n	s2(n	PROPN
ejpam-4825	62	13	,	,	PUNCT
ejpam-4825	62	14	m)c(k)m	m)c(k)m	PROPN
ejpam-4825	62	15	(	(	PUNCT
ejpam-4825	62	16	a	a	NOUN
ejpam-4825	62	17	)	)	PUNCT
ejpam-4825	62	18	=	=	SYM
ejpam-4825	62	19	1	1	NUM
ejpam-4825	62	20	(	(	PUNCT
ejpam-4825	62	21	n+	n+	X
ejpam-4825	62	22	a)k	a)k	ADJ
ejpam-4825	62	23	,	,	PUNCT
ejpam-4825	62	24	n∑	n∑	PROPN
ejpam-4825	62	25	m=0	m=0	PROPN
ejpam-4825	62	26	s2(n	s2(n	PROPN
ejpam-4825	62	27	,	,	PUNCT
ejpam-4825	62	28	m)ĉ(k)m	m)ĉ(k)m	PROPN
ejpam-4825	62	29	(	(	PUNCT
ejpam-4825	62	30	a	a	X
ejpam-4825	62	31	)	)	PUNCT
ejpam-4825	62	32	=	=	SYM
ejpam-4825	62	33	(	(	PUNCT
ejpam-4825	62	34	−1)n	−1)n	X
ejpam-4825	62	35	(	(	PUNCT
ejpam-4825	62	36	n+	n+	X
ejpam-4825	62	37	a)k	a)k	ADJ
ejpam-4825	62	38	,	,	PUNCT
ejpam-4825	62	39	and	and	CCONJ
ejpam-4825	62	40	expressions	expression	NOUN
ejpam-4825	62	41	of	of	ADP
ejpam-4825	62	42	hurwitz	hurwitz	PROPN
ejpam-4825	62	43	type	type	NOUN
ejpam-4825	62	44	poly	poly	ADJ
ejpam-4825	62	45	-	-	PUNCT
ejpam-4825	62	46	bernoulli	bernoulli	NOUN
ejpam-4825	62	47	numbers	number	NOUN
ejpam-4825	62	48	in	in	ADP
ejpam-4825	62	49	terms	term	NOUN
ejpam-4825	62	50	of	of	ADP
ejpam-4825	62	51	hurwitz	hurwitz	PROPN
ejpam-4825	62	52	type	type	NOUN
ejpam-4825	62	53	polycauchy	polycauchy	ADJ
ejpam-4825	62	54	numbers	number	NOUN
ejpam-4825	62	55	b(k	b(k	PROPN
ejpam-4825	62	56	)	)	PUNCT
ejpam-4825	62	57	n	n	CCONJ
ejpam-4825	62	58	(	(	PUNCT
ejpam-4825	62	59	a	a	X
ejpam-4825	62	60	)	)	PUNCT
ejpam-4825	62	61	=	=	SYM
ejpam-4825	62	62	n∑	n∑	PROPN
ejpam-4825	62	63	l=0	l=0	PROPN
ejpam-4825	62	64	n∑	n∑	PROPN
ejpam-4825	62	65	m=0	m=0	PROPN
ejpam-4825	62	66	(	(	PUNCT
ejpam-4825	62	67	−1)m+nm!s2(n	−1)m+nm!s2(n	PROPN
ejpam-4825	62	68	,	,	PUNCT
ejpam-4825	62	69	m)s2(m	m)s2(m	NOUN
ejpam-4825	62	70	,	,	PUNCT
ejpam-4825	62	71	l)c	l)c	X
ejpam-4825	62	72	(	(	PUNCT
ejpam-4825	62	73	k	k	NOUN
ejpam-4825	62	74	)	)	PUNCT
ejpam-4825	62	75	l	l	NOUN
ejpam-4825	62	76	(	(	PUNCT
ejpam-4825	62	77	a	a	NOUN
ejpam-4825	62	78	)	)	PUNCT
ejpam-4825	62	79	,	,	PUNCT
ejpam-4825	62	80	b(k	b(k	PROPN
ejpam-4825	62	81	)	)	PUNCT
ejpam-4825	62	82	n	n	CCONJ
ejpam-4825	62	83	(	(	PUNCT
ejpam-4825	62	84	a	a	X
ejpam-4825	62	85	)	)	PUNCT
ejpam-4825	62	86	=	=	SYM
ejpam-4825	62	87	n∑	n∑	PROPN
ejpam-4825	62	88	l=0	l=0	PROPN
ejpam-4825	62	89	n∑	n∑	PROPN
ejpam-4825	62	90	m=0	m=0	PROPN
ejpam-4825	62	91	(	(	PUNCT
ejpam-4825	62	92	−1)mm!s2(n	−1)mm!s2(n	PROPN
ejpam-4825	62	93	,	,	PUNCT
ejpam-4825	62	94	m)s2(m	m)s2(m	NOUN
ejpam-4825	62	95	,	,	PUNCT
ejpam-4825	62	96	l)ĉ	l)ĉ	NOUN
ejpam-4825	62	97	(	(	PUNCT
ejpam-4825	62	98	k	k	NOUN
ejpam-4825	62	99	)	)	PUNCT
ejpam-4825	62	100	l	l	NOUN
ejpam-4825	62	101	(	(	PUNCT
ejpam-4825	62	102	a	a	NOUN
ejpam-4825	62	103	)	)	PUNCT
ejpam-4825	62	104	,	,	PUNCT
ejpam-4825	62	105	c(k)n	c(k)n	PROPN
ejpam-4825	62	106	(	(	PUNCT
ejpam-4825	62	107	a	a	X
ejpam-4825	62	108	)	)	PUNCT
ejpam-4825	62	109	=	=	SYM
ejpam-4825	62	110	n∑	n∑	PROPN
ejpam-4825	62	111	l=0	l=0	PROPN
ejpam-4825	62	112	n∑	n∑	PROPN
ejpam-4825	62	113	m=0	m=0	PROPN
ejpam-4825	62	114	(	(	PUNCT
ejpam-4825	62	115	−1)m+n	−1)m+n	NUM
ejpam-4825	62	116	m	m	NOUN
ejpam-4825	62	117	!	!	PUNCT
ejpam-4825	63	1	s1(n	s1(n	ADJ
ejpam-4825	63	2	,	,	PUNCT
ejpam-4825	63	3	m)s1(m	m)s1(m	NOUN
ejpam-4825	63	4	,	,	PUNCT
ejpam-4825	63	5	l)b	l)b	ADJ
ejpam-4825	63	6	(	(	PUNCT
ejpam-4825	63	7	k	k	NOUN
ejpam-4825	63	8	)	)	PUNCT
ejpam-4825	63	9	l	l	NOUN
ejpam-4825	63	10	(	(	PUNCT
ejpam-4825	63	11	a	a	NOUN
ejpam-4825	63	12	)	)	PUNCT
ejpam-4825	63	13	,	,	PUNCT
ejpam-4825	63	14	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	63	15	(	(	PUNCT
ejpam-4825	63	16	a	a	X
ejpam-4825	63	17	)	)	PUNCT
ejpam-4825	63	18	=	=	SYM
ejpam-4825	64	1	n∑	n∑	PROPN
ejpam-4825	64	2	l=0	l=0	PROPN
ejpam-4825	64	3	n∑	n∑	PROPN
ejpam-4825	64	4	m=0	m=0	PROPN
ejpam-4825	64	5	(	(	PUNCT
ejpam-4825	64	6	−1)n	−1)n	PROPN
ejpam-4825	64	7	m	m	PROPN
ejpam-4825	64	8	!	!	PUNCT
ejpam-4825	65	1	s1(n	s1(n	ADJ
ejpam-4825	65	2	,	,	PUNCT
ejpam-4825	65	3	m)s1(m	m)s1(m	NOUN
ejpam-4825	65	4	,	,	PUNCT
ejpam-4825	65	5	l)b	l)b	ADJ
ejpam-4825	65	6	(	(	PUNCT
ejpam-4825	65	7	k	k	NOUN
ejpam-4825	65	8	)	)	PUNCT
ejpam-4825	65	9	l	l	NOUN
ejpam-4825	65	10	(	(	PUNCT
ejpam-4825	65	11	a	a	NOUN
ejpam-4825	65	12	)	)	PUNCT
ejpam-4825	65	13	.	.	PUNCT
ejpam-4825	66	1	recently	recently	ADV
ejpam-4825	66	2	,	,	PUNCT
ejpam-4825	66	3	several	several	ADJ
ejpam-4825	66	4	generalizations	generalization	NOUN
ejpam-4825	66	5	of	of	ADP
ejpam-4825	66	6	these	these	DET
ejpam-4825	66	7	numbers	number	NOUN
ejpam-4825	66	8	have	have	AUX
ejpam-4825	66	9	been	be	AUX
ejpam-4825	66	10	introduced	introduce	VERB
ejpam-4825	66	11	relating	relate	VERB
ejpam-4825	66	12	to	to	ADP
ejpam-4825	66	13	some	some	DET
ejpam-4825	66	14	well	well	ADV
ejpam-4825	66	15	-	-	PUNCT
ejpam-4825	66	16	known	know	VERB
ejpam-4825	66	17	special	special	ADJ
ejpam-4825	66	18	numbers	number	NOUN
ejpam-4825	66	19	.	.	PUNCT
ejpam-4825	67	1	for	for	ADP
ejpam-4825	67	2	instance	instance	NOUN
ejpam-4825	67	3	,	,	PUNCT
ejpam-4825	67	4	the	the	DET
ejpam-4825	67	5	poly	poly	ADJ
ejpam-4825	67	6	-	-	PUNCT
ejpam-4825	67	7	cauchy	cauchy	NOUN
ejpam-4825	67	8	polynomials	polynomial	NOUN
ejpam-4825	67	9	are	be	AUX
ejpam-4825	67	10	expressed	express	VERB
ejpam-4825	67	11	in	in	ADP
ejpam-4825	67	12	terms	term	NOUN
ejpam-4825	67	13	of	of	ADP
ejpam-4825	67	14	polylogarithm	polylogarithm	PROPN
ejpam-4825	67	15	factorial	factorial	PROPN
ejpam-4825	67	16	function	function	NOUN
ejpam-4825	67	17	and	and	CCONJ
ejpam-4825	67	18	multi	multi	ADJ
ejpam-4825	67	19	poly	poly	ADJ
ejpam-4825	67	20	-	-	PUNCT
ejpam-4825	67	21	cauchy	cauchy	NOUN
ejpam-4825	67	22	polynomials	polynomial	NOUN
ejpam-4825	67	23	,	,	PUNCT
ejpam-4825	67	24	multi	multi	ADJ
ejpam-4825	67	25	poly	poly	ADJ
ejpam-4825	67	26	-	-	PUNCT
ejpam-4825	67	27	bernoulli	bernoulli	NOUN
ejpam-4825	67	28	and	and	CCONJ
ejpam-4825	67	29	multi	multi	ADJ
ejpam-4825	67	30	poly	poly	ADJ
ejpam-4825	67	31	-	-	PUNCT
ejpam-4825	67	32	euler	euler	NOUN
ejpam-4825	67	33	numbers	number	NOUN
ejpam-4825	67	34	and	and	CCONJ
ejpam-4825	67	35	polynomials	polynomial	NOUN
ejpam-4825	67	36	are	be	AUX
ejpam-4825	67	37	expressed	express	VERB
ejpam-4825	67	38	in	in	ADP
ejpam-4825	67	39	terms	term	NOUN
ejpam-4825	67	40	n.	n.	PROPN
ejpam-4825	67	41	b.	b.	PROPN
ejpam-4825	67	42	lacpao	lacpao	PROPN
ejpam-4825	67	43	/	/	SYM
ejpam-4825	67	44	eur	eur	PROPN
ejpam-4825	67	45	.	.	PUNCT
ejpam-4825	68	1	j.	j.	PROPN
ejpam-4825	68	2	pure	pure	PROPN
ejpam-4825	68	3	appl	appl	PROPN
ejpam-4825	68	4	.	.	PROPN
ejpam-4825	68	5	math	math	PROPN
ejpam-4825	68	6	,	,	PUNCT
ejpam-4825	68	7	16	16	NUM
ejpam-4825	68	8	(	(	PUNCT
ejpam-4825	68	9	3	3	NUM
ejpam-4825	68	10	)	)	PUNCT
ejpam-4825	68	11	(	(	PUNCT
ejpam-4825	68	12	2023	2023	NUM
ejpam-4825	68	13	)	)	PUNCT
ejpam-4825	68	14	,	,	PUNCT
ejpam-4825	68	15	1747	1747	NUM
ejpam-4825	68	16	-	-	SYM
ejpam-4825	68	17	1761	1761	NUM
ejpam-4825	68	18	1751	1751	NUM
ejpam-4825	68	19	of	of	ADP
ejpam-4825	68	20	multiple	multiple	ADJ
ejpam-4825	68	21	polylogarithm	polylogarithm	PROPN
ejpam-4825	68	22	factorial	factorial	NOUN
ejpam-4825	68	23	function	function	NOUN
ejpam-4825	68	24	[	[	X
ejpam-4825	68	25	7	7	NUM
ejpam-4825	68	26	,	,	PUNCT
ejpam-4825	68	27	8	8	NUM
ejpam-4825	68	28	,	,	PUNCT
ejpam-4825	68	29	10	10	NUM
ejpam-4825	68	30	]	]	PUNCT
ejpam-4825	68	31	.	.	PUNCT
ejpam-4825	69	1	moreover	moreover	ADV
ejpam-4825	69	2	,	,	PUNCT
ejpam-4825	69	3	other	other	ADJ
ejpam-4825	69	4	well	well	ADV
ejpam-4825	69	5	known	know	VERB
ejpam-4825	69	6	families	family	NOUN
ejpam-4825	69	7	of	of	ADP
ejpam-4825	69	8	polynomials	polynomial	NOUN
ejpam-4825	69	9	such	such	ADJ
ejpam-4825	69	10	as	as	ADP
ejpam-4825	69	11	the	the	DET
ejpam-4825	69	12	apell	apell	NOUN
ejpam-4825	69	13	-	-	PUNCT
ejpam-4825	69	14	type	type	NOUN
ejpam-4825	69	15	classical	classical	ADJ
ejpam-4825	69	16	polynomials	polynomial	NOUN
ejpam-4825	69	17	and	and	CCONJ
ejpam-4825	69	18	apostol	apostol	NOUN
ejpam-4825	69	19	-	-	PUNCT
ejpam-4825	69	20	type	type	NOUN
ejpam-4825	69	21	polynomials	polynomial	NOUN
ejpam-4825	69	22	have	have	AUX
ejpam-4825	69	23	attracted	attract	VERB
ejpam-4825	69	24	research	research	NOUN
ejpam-4825	69	25	attention	attention	NOUN
ejpam-4825	69	26	due	due	ADP
ejpam-4825	69	27	to	to	ADP
ejpam-4825	69	28	their	their	PRON
ejpam-4825	69	29	important	important	ADJ
ejpam-4825	69	30	applications	application	NOUN
ejpam-4825	69	31	in	in	ADP
ejpam-4825	69	32	the	the	DET
ejpam-4825	69	33	areas	area	NOUN
ejpam-4825	69	34	of	of	ADP
ejpam-4825	69	35	applied	applied	ADJ
ejpam-4825	69	36	mathematics	mathematic	NOUN
ejpam-4825	69	37	,	,	PUNCT
ejpam-4825	69	38	physics	physics	NOUN
ejpam-4825	69	39	and	and	CCONJ
ejpam-4825	69	40	engineering	engineering	NOUN
ejpam-4825	69	41	[	[	X
ejpam-4825	69	42	3	3	NUM
ejpam-4825	69	43	,	,	PUNCT
ejpam-4825	69	44	5	5	NUM
ejpam-4825	69	45	]	]	PUNCT
ejpam-4825	69	46	.	.	PUNCT
ejpam-4825	70	1	this	this	DET
ejpam-4825	70	2	present	present	ADJ
ejpam-4825	70	3	study	study	NOUN
ejpam-4825	70	4	aims	aim	VERB
ejpam-4825	70	5	to	to	PART
ejpam-4825	70	6	establish	establish	VERB
ejpam-4825	70	7	other	other	ADJ
ejpam-4825	70	8	variation	variation	NOUN
ejpam-4825	70	9	of	of	ADP
ejpam-4825	70	10	generalizing	generalize	VERB
ejpam-4825	70	11	cauchy	cauchy	NOUN
ejpam-4825	70	12	and	and	CCONJ
ejpam-4825	70	13	bernoulli	bernoulli	NOUN
ejpam-4825	70	14	polynomials	polynomial	NOUN
ejpam-4825	70	15	that	that	PRON
ejpam-4825	70	16	can	can	AUX
ejpam-4825	70	17	be	be	AUX
ejpam-4825	70	18	related	relate	VERB
ejpam-4825	70	19	to	to	ADP
ejpam-4825	70	20	the	the	DET
ejpam-4825	70	21	well	well	ADV
ejpam-4825	70	22	-	-	PUNCT
ejpam-4825	70	23	known	know	VERB
ejpam-4825	70	24	hurwitz	hurwitz	PROPN
ejpam-4825	70	25	-	-	PUNCT
ejpam-4825	70	26	lerch	lerch	PROPN
ejpam-4825	70	27	factorial	factorial	PROPN
ejpam-4825	70	28	zeta	zeta	PROPN
ejpam-4825	70	29	function	function	NOUN
ejpam-4825	70	30	.	.	PUNCT
ejpam-4825	71	1	the	the	DET
ejpam-4825	71	2	generalization	generalization	NOUN
ejpam-4825	71	3	may	may	AUX
ejpam-4825	71	4	contribute	contribute	VERB
ejpam-4825	71	5	to	to	ADP
ejpam-4825	71	6	the	the	DET
ejpam-4825	71	7	development	development	NOUN
ejpam-4825	71	8	of	of	ADP
ejpam-4825	71	9	numerous	numerous	ADJ
ejpam-4825	71	10	applications	application	NOUN
ejpam-4825	71	11	in	in	ADP
ejpam-4825	71	12	number	number	NOUN
ejpam-4825	71	13	theory	theory	NOUN
ejpam-4825	71	14	,	,	PUNCT
ejpam-4825	71	15	numerical	numerical	ADJ
ejpam-4825	71	16	analysis	analysis	NOUN
ejpam-4825	71	17	and	and	CCONJ
ejpam-4825	71	18	difference	difference	NOUN
ejpam-4825	71	19	-	-	PUNCT
ejpam-4825	71	20	differential	differential	NOUN
ejpam-4825	71	21	equations	equation	NOUN
ejpam-4825	71	22	.	.	PUNCT
ejpam-4825	72	1	2	2	X
ejpam-4825	72	2	.	.	X
ejpam-4825	72	3	hurwitz	hurwitz	PROPN
ejpam-4825	72	4	-	-	PUNCT
ejpam-4825	72	5	lerch	lerch	PROPN
ejpam-4825	72	6	type	type	NOUN
ejpam-4825	72	7	poly	poly	ADJ
ejpam-4825	72	8	-	-	PUNCT
ejpam-4825	72	9	cauchy	cauchy	ADJ
ejpam-4825	72	10	and	and	CCONJ
ejpam-4825	72	11	poly	poly	ADJ
ejpam-4825	72	12	-	-	PUNCT
ejpam-4825	72	13	bernoulli	bernoulli	NOUN
ejpam-4825	72	14	polynomials	polynomial	NOUN
ejpam-4825	72	15	kamano	kamano	ADJ
ejpam-4825	72	16	and	and	CCONJ
ejpam-4825	72	17	komatsu	komatsu	NOUN
ejpam-4825	73	1	[	[	X
ejpam-4825	73	2	13	13	NUM
ejpam-4825	73	3	]	]	PUNCT
ejpam-4825	73	4	defined	define	VERB
ejpam-4825	73	5	the	the	DET
ejpam-4825	73	6	poly	poly	ADJ
ejpam-4825	73	7	-	-	PUNCT
ejpam-4825	73	8	cauchy	cauchy	ADJ
ejpam-4825	73	9	polynomials	polynomial	NOUN
ejpam-4825	73	10	of	of	ADP
ejpam-4825	73	11	the	the	DET
ejpam-4825	73	12	first	first	ADJ
ejpam-4825	73	13	and	and	CCONJ
ejpam-4825	73	14	second	second	ADJ
ejpam-4825	73	15	kind	kind	NOUN
ejpam-4825	73	16	,	,	PUNCT
ejpam-4825	73	17	c	c	PROPN
ejpam-4825	73	18	(	(	PUNCT
ejpam-4825	73	19	k	k	NOUN
ejpam-4825	73	20	)	)	PUNCT
ejpam-4825	73	21	n	n	PROPN
ejpam-4825	73	22	(	(	PUNCT
ejpam-4825	73	23	x	x	X
ejpam-4825	73	24	)	)	PUNCT
ejpam-4825	73	25	and	and	CCONJ
ejpam-4825	73	26	ĉ	ĉ	X
ejpam-4825	73	27	(	(	PUNCT
ejpam-4825	73	28	k	k	NOUN
ejpam-4825	73	29	)	)	PUNCT
ejpam-4825	73	30	n	n	PROPN
ejpam-4825	73	31	(	(	PUNCT
ejpam-4825	73	32	x	x	NOUN
ejpam-4825	73	33	)	)	PUNCT
ejpam-4825	73	34	,	,	PUNCT
ejpam-4825	73	35	respectively	respectively	ADV
ejpam-4825	73	36	,	,	PUNCT
ejpam-4825	73	37	as	as	SCONJ
ejpam-4825	73	38	follows	follow	VERB
ejpam-4825	73	39	:	:	PUNCT
ejpam-4825	73	40	c(k)n	c(k)n	PROPN
ejpam-4825	73	41	(	(	PUNCT
ejpam-4825	73	42	x	x	NOUN
ejpam-4825	73	43	)	)	PUNCT
ejpam-4825	73	44	=	=	SYM
ejpam-4825	73	45	n	n	X
ejpam-4825	73	46	!	!	PUNCT
ejpam-4825	73	47	∫	∫	PROPN
ejpam-4825	74	1	1	1	NUM
ejpam-4825	74	2	0	0	NUM
ejpam-4825	74	3	·	·	PUNCT
ejpam-4825	74	4	·	·	PUNCT
ejpam-4825	74	5	·	·	PUNCT
ejpam-4825	75	1	∫	∫	PROPN
ejpam-4825	75	2	1	1	NUM
ejpam-4825	75	3	0	0	NUM
ejpam-4825	75	4	(	(	PUNCT
ejpam-4825	75	5	t1t2	t1t2	PROPN
ejpam-4825	75	6	·	·	PUNCT
ejpam-4825	76	1	·	·	PUNCT
ejpam-4825	76	2	·	·	PUNCT
ejpam-4825	76	3	tk	tk	PROPN
ejpam-4825	77	1	+	+	CCONJ
ejpam-4825	77	2	x	x	PROPN
ejpam-4825	77	3	n	n	X
ejpam-4825	77	4	)	)	PUNCT
ejpam-4825	77	5	dt1dt2	dt1dt2	ADP
ejpam-4825	77	6	·	·	PUNCT
ejpam-4825	77	7	·	·	PUNCT
ejpam-4825	77	8	·	·	PUNCT
ejpam-4825	77	9	dtk	dtk	PROPN
ejpam-4825	77	10	,	,	PUNCT
ejpam-4825	77	11	(	(	PUNCT
ejpam-4825	77	12	k	k	X
ejpam-4825	77	13	≥	≥	NUM
ejpam-4825	77	14	1	1	NUM
ejpam-4825	77	15	)	)	PUNCT
ejpam-4825	77	16	and	and	CCONJ
ejpam-4825	77	17	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	77	18	(	(	PUNCT
ejpam-4825	77	19	x	x	NOUN
ejpam-4825	77	20	)	)	PUNCT
ejpam-4825	77	21	=	=	SYM
ejpam-4825	77	22	n	n	X
ejpam-4825	77	23	!	!	PUNCT
ejpam-4825	77	24	∫	∫	PROPN
ejpam-4825	78	1	1	1	NUM
ejpam-4825	78	2	0	0	NUM
ejpam-4825	78	3	·	·	PUNCT
ejpam-4825	78	4	·	·	PUNCT
ejpam-4825	78	5	·	·	PUNCT
ejpam-4825	79	1	∫	∫	PROPN
ejpam-4825	79	2	1	1	NUM
ejpam-4825	79	3	0	0	NUM
ejpam-4825	79	4	(	(	PUNCT
ejpam-4825	79	5	−t1t2	−t1t2	PROPN
ejpam-4825	80	1	·	·	PUNCT
ejpam-4825	80	2	·	·	PUNCT
ejpam-4825	80	3	·	·	PUNCT
ejpam-4825	80	4	tk	tk	NOUN
ejpam-4825	80	5	−	−	NOUN
ejpam-4825	80	6	x	x	SYM
ejpam-4825	80	7	n	n	PROPN
ejpam-4825	80	8	)	)	PUNCT
ejpam-4825	81	1	dt1dt2	dt1dt2	ADP
ejpam-4825	81	2	·	·	PUNCT
ejpam-4825	81	3	·	·	PUNCT
ejpam-4825	81	4	·	·	PUNCT
ejpam-4825	81	5	dtk	dtk	PROPN
ejpam-4825	81	6	,	,	PUNCT
ejpam-4825	81	7	(	(	PUNCT
ejpam-4825	81	8	k	k	X
ejpam-4825	81	9	≥	≥	NUM
ejpam-4825	81	10	1	1	NUM
ejpam-4825	81	11	)	)	PUNCT
ejpam-4825	81	12	with	with	ADP
ejpam-4825	81	13	generating	generating	NOUN
ejpam-4825	81	14	functions	function	NOUN
ejpam-4825	81	15	(	(	PUNCT
ejpam-4825	81	16	1	1	NUM
ejpam-4825	81	17	+	+	NUM
ejpam-4825	81	18	t)xlifk(ln(1	t)xlifk(ln(1	NOUN
ejpam-4825	81	19	+	+	CCONJ
ejpam-4825	81	20	t	t	NOUN
ejpam-4825	81	21	)	)	PUNCT
ejpam-4825	81	22	)	)	PUNCT
ejpam-4825	82	1	=	=	PUNCT
ejpam-4825	83	1	∞∑	∞∑	NUM
ejpam-4825	83	2	n=0	n=0	NUM
ejpam-4825	83	3	c(k)n	c(k)n	PROPN
ejpam-4825	83	4	(	(	PUNCT
ejpam-4825	83	5	x	x	NOUN
ejpam-4825	83	6	)	)	PUNCT
ejpam-4825	83	7	tn	tn	PROPN
ejpam-4825	83	8	n	n	PROPN
ejpam-4825	83	9	!	!	PUNCT
ejpam-4825	84	1	(	(	PUNCT
ejpam-4825	84	2	1	1	X
ejpam-4825	84	3	)	)	PUNCT
ejpam-4825	84	4	lifk(−	lifk(−	PROPN
ejpam-4825	84	5	ln(1	ln(1	PROPN
ejpam-4825	84	6	+	+	PROPN
ejpam-4825	84	7	t	t	PROPN
ejpam-4825	84	8	)	)	PUNCT
ejpam-4825	84	9	)	)	PUNCT
ejpam-4825	85	1	(	(	PUNCT
ejpam-4825	85	2	1	1	NUM
ejpam-4825	85	3	+	+	CCONJ
ejpam-4825	85	4	t)x	t)x	PUNCT
ejpam-4825	85	5	=	=	PUNCT
ejpam-4825	85	6	∞∑	∞∑	PRON
ejpam-4825	85	7	n=0	n=0	NUM
ejpam-4825	85	8	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	85	9	(	(	PUNCT
ejpam-4825	85	10	x	x	NOUN
ejpam-4825	85	11	)	)	PUNCT
ejpam-4825	85	12	tn	tn	PROPN
ejpam-4825	85	13	n	n	PROPN
ejpam-4825	85	14	!	!	PUNCT
ejpam-4825	86	1	(	(	PUNCT
ejpam-4825	86	2	2	2	X
ejpam-4825	86	3	)	)	PUNCT
ejpam-4825	86	4	where	where	SCONJ
ejpam-4825	86	5	lifk(z	lifk(z	NOUN
ejpam-4825	86	6	)	)	PUNCT
ejpam-4825	86	7	=	=	PUNCT
ejpam-4825	87	1	∞∑	∞∑	NUM
ejpam-4825	87	2	m=0	m=0	PROPN
ejpam-4825	87	3	zm	zm	PROPN
ejpam-4825	87	4	m!(m+	m!(m+	VERB
ejpam-4825	87	5	1)k	1)k	NUM
ejpam-4825	87	6	.	.	PUNCT
ejpam-4825	88	1	(	(	PUNCT
ejpam-4825	88	2	3	3	X
ejpam-4825	88	3	)	)	PUNCT
ejpam-4825	88	4	observe	observe	VERB
ejpam-4825	88	5	that	that	SCONJ
ejpam-4825	88	6	from	from	ADP
ejpam-4825	88	7	(	(	PUNCT
ejpam-4825	88	8	3	3	NUM
ejpam-4825	88	9	)	)	PUNCT
ejpam-4825	88	10	,	,	PUNCT
ejpam-4825	88	11	we	we	PRON
ejpam-4825	88	12	get	get	VERB
ejpam-4825	88	13	φf(ln(1	φf(ln(1	PROPN
ejpam-4825	88	14	+	+	PROPN
ejpam-4825	88	15	t	t	PROPN
ejpam-4825	88	16	)	)	PUNCT
ejpam-4825	88	17	,	,	PUNCT
ejpam-4825	88	18	k	k	PROPN
ejpam-4825	88	19	,	,	PUNCT
ejpam-4825	88	20	a	a	PRON
ejpam-4825	88	21	)	)	PUNCT
ejpam-4825	88	22	=	=	SYM
ejpam-4825	89	1	∞∑	∞∑	NUM
ejpam-4825	89	2	n=0	n=0	PUNCT
ejpam-4825	89	3	(	(	PUNCT
ejpam-4825	89	4	ln(1	ln(1	NOUN
ejpam-4825	89	5	+	+	NUM
ejpam-4825	89	6	t))n	t))n	NOUN
ejpam-4825	89	7	n!(n+	n!(n+	NOUN
ejpam-4825	89	8	a)k	a)k	NOUN
ejpam-4825	89	9	=	=	PUNCT
ejpam-4825	89	10	lifk(ln(1	lifk(ln(1	NOUN
ejpam-4825	89	11	+	+	CCONJ
ejpam-4825	89	12	t))(a	t))(a	NOUN
ejpam-4825	89	13	)	)	PUNCT
ejpam-4825	89	14	.	.	PUNCT
ejpam-4825	90	1	if	if	SCONJ
ejpam-4825	90	2	a	a	DET
ejpam-4825	90	3	=	=	NOUN
ejpam-4825	90	4	1	1	NUM
ejpam-4825	90	5	,	,	PUNCT
ejpam-4825	90	6	we	we	PRON
ejpam-4825	90	7	get	get	AUX
ejpam-4825	90	8	φf(z	φf(z	VERB
ejpam-4825	90	9	,	,	PUNCT
ejpam-4825	90	10	k	k	NOUN
ejpam-4825	90	11	,	,	PUNCT
ejpam-4825	90	12	1	1	NUM
ejpam-4825	90	13	)	)	PUNCT
ejpam-4825	90	14	=	=	SYM
ejpam-4825	90	15	lifk(z	lifk(z	PROPN
ejpam-4825	90	16	)	)	PUNCT
ejpam-4825	90	17	.	.	PUNCT
ejpam-4825	91	1	comparing	compare	VERB
ejpam-4825	91	2	this	this	PRON
ejpam-4825	91	3	with	with	ADP
ejpam-4825	91	4	the	the	DET
ejpam-4825	91	5	left	left	ADJ
ejpam-4825	91	6	hand	hand	NOUN
ejpam-4825	91	7	side	side	NOUN
ejpam-4825	91	8	of	of	ADP
ejpam-4825	91	9	(	(	PUNCT
ejpam-4825	91	10	1	1	NUM
ejpam-4825	91	11	)	)	PUNCT
ejpam-4825	91	12	and	and	CCONJ
ejpam-4825	91	13	(	(	PUNCT
ejpam-4825	91	14	2	2	NUM
ejpam-4825	91	15	)	)	PUNCT
ejpam-4825	91	16	,	,	PUNCT
ejpam-4825	91	17	it	it	PRON
ejpam-4825	91	18	would	would	AUX
ejpam-4825	91	19	be	be	AUX
ejpam-4825	91	20	logical	logical	ADJ
ejpam-4825	91	21	to	to	PART
ejpam-4825	91	22	define	define	VERB
ejpam-4825	91	23	the	the	DET
ejpam-4825	91	24	hurwitz	hurwitz	PROPN
ejpam-4825	91	25	-	-	PUNCT
ejpam-4825	91	26	lerch	lerch	PROPN
ejpam-4825	91	27	poly	poly	ADJ
ejpam-4825	91	28	-	-	PUNCT
ejpam-4825	91	29	cauchy	cauchy	ADJ
ejpam-4825	91	30	polynomials	polynomial	NOUN
ejpam-4825	91	31	of	of	ADP
ejpam-4825	91	32	the	the	DET
ejpam-4825	91	33	first	first	ADJ
ejpam-4825	91	34	and	and	CCONJ
ejpam-4825	91	35	seconds	second	NOUN
ejpam-4825	91	36	kind	kind	ADV
ejpam-4825	91	37	as	as	SCONJ
ejpam-4825	91	38	follows	follow	VERB
ejpam-4825	91	39	:	:	PUNCT
ejpam-4825	91	40	definition	definition	NOUN
ejpam-4825	91	41	1	1	NUM
ejpam-4825	91	42	.	.	PUNCT
ejpam-4825	92	1	the	the	DET
ejpam-4825	92	2	hurwitz	hurwitz	PROPN
ejpam-4825	92	3	-	-	PUNCT
ejpam-4825	92	4	lerch	lerch	PROPN
ejpam-4825	92	5	type	type	NOUN
ejpam-4825	92	6	poly	poly	ADJ
ejpam-4825	92	7	-	-	PUNCT
ejpam-4825	92	8	cauchy	cauchy	ADJ
ejpam-4825	92	9	polynomials	polynomial	NOUN
ejpam-4825	92	10	of	of	ADP
ejpam-4825	92	11	the	the	DET
ejpam-4825	92	12	first	first	ADJ
ejpam-4825	92	13	kind	kind	NOUN
ejpam-4825	92	14	denoted	denote	VERB
ejpam-4825	92	15	by	by	ADP
ejpam-4825	92	16	c	c	PROPN
ejpam-4825	92	17	(	(	PUNCT
ejpam-4825	92	18	k	k	NOUN
ejpam-4825	92	19	)	)	PUNCT
ejpam-4825	92	20	n	n	CCONJ
ejpam-4825	92	21	,	,	PUNCT
ejpam-4825	92	22	a(x	a(x	NOUN
ejpam-4825	92	23	)	)	PUNCT
ejpam-4825	92	24	are	be	AUX
ejpam-4825	92	25	defined	define	VERB
ejpam-4825	92	26	by	by	ADP
ejpam-4825	92	27	(	(	PUNCT
ejpam-4825	92	28	1	1	NUM
ejpam-4825	92	29	+	+	NUM
ejpam-4825	92	30	t)xφf(ln(1	t)xφf(ln(1	NOUN
ejpam-4825	92	31	+	+	X
ejpam-4825	92	32	t	t	PROPN
ejpam-4825	92	33	)	)	PUNCT
ejpam-4825	92	34	,	,	PUNCT
ejpam-4825	92	35	k	k	PROPN
ejpam-4825	92	36	,	,	PUNCT
ejpam-4825	92	37	a	a	PRON
ejpam-4825	92	38	)	)	PUNCT
ejpam-4825	92	39	=	=	SYM
ejpam-4825	93	1	∞∑	∞∑	NUM
ejpam-4825	93	2	n=0	n=0	NUM
ejpam-4825	93	3	c(k)n	c(k)n	PROPN
ejpam-4825	93	4	,	,	PUNCT
ejpam-4825	93	5	a(x	a(x	PROPN
ejpam-4825	93	6	)	)	PUNCT
ejpam-4825	93	7	tn	tn	NOUN
ejpam-4825	93	8	n	n	NUM
ejpam-4825	93	9	!	!	PUNCT
ejpam-4825	93	10	.	.	PUNCT
ejpam-4825	94	1	n.	n.	PROPN
ejpam-4825	94	2	b.	b.	PROPN
ejpam-4825	95	1	lacpao	lacpao	PROPN
ejpam-4825	95	2	/	/	SYM
ejpam-4825	95	3	eur	eur	PROPN
ejpam-4825	95	4	.	.	PUNCT
ejpam-4825	96	1	j.	j.	PROPN
ejpam-4825	96	2	pure	pure	PROPN
ejpam-4825	96	3	appl	appl	PROPN
ejpam-4825	96	4	.	.	PROPN
ejpam-4825	96	5	math	math	PROPN
ejpam-4825	96	6	,	,	PUNCT
ejpam-4825	96	7	16	16	NUM
ejpam-4825	96	8	(	(	PUNCT
ejpam-4825	96	9	3	3	NUM
ejpam-4825	96	10	)	)	PUNCT
ejpam-4825	96	11	(	(	PUNCT
ejpam-4825	96	12	2023	2023	NUM
ejpam-4825	96	13	)	)	PUNCT
ejpam-4825	96	14	,	,	PUNCT
ejpam-4825	96	15	1747	1747	NUM
ejpam-4825	96	16	-	-	SYM
ejpam-4825	96	17	1761	1761	NUM
ejpam-4825	96	18	1752	1752	NUM
ejpam-4825	96	19	definition	definition	NOUN
ejpam-4825	96	20	2	2	NUM
ejpam-4825	96	21	.	.	PUNCT
ejpam-4825	97	1	the	the	DET
ejpam-4825	97	2	hurwitz	hurwitz	PROPN
ejpam-4825	97	3	-	-	PUNCT
ejpam-4825	97	4	lerch	lerch	PROPN
ejpam-4825	97	5	type	type	NOUN
ejpam-4825	97	6	poly	poly	ADJ
ejpam-4825	97	7	-	-	PUNCT
ejpam-4825	97	8	cauchy	cauchy	ADJ
ejpam-4825	97	9	polynomials	polynomial	NOUN
ejpam-4825	97	10	of	of	ADP
ejpam-4825	97	11	the	the	DET
ejpam-4825	97	12	second	second	ADJ
ejpam-4825	97	13	kind	kind	NOUN
ejpam-4825	97	14	denoted	denote	VERB
ejpam-4825	97	15	by	by	ADP
ejpam-4825	97	16	ĉ	ĉ	NOUN
ejpam-4825	97	17	(	(	PUNCT
ejpam-4825	97	18	k	k	NOUN
ejpam-4825	97	19	)	)	PUNCT
ejpam-4825	97	20	n	n	CCONJ
ejpam-4825	97	21	,	,	PUNCT
ejpam-4825	97	22	a(x	a(x	NOUN
ejpam-4825	97	23	)	)	PUNCT
ejpam-4825	97	24	are	be	AUX
ejpam-4825	97	25	defined	define	VERB
ejpam-4825	97	26	by	by	ADP
ejpam-4825	97	27	φf(−	φf(−	NOUN
ejpam-4825	97	28	ln(1	ln(1	PROPN
ejpam-4825	97	29	+	+	PROPN
ejpam-4825	97	30	t	t	PROPN
ejpam-4825	97	31	)	)	PUNCT
ejpam-4825	97	32	,	,	PUNCT
ejpam-4825	97	33	k	k	PROPN
ejpam-4825	97	34	,	,	PUNCT
ejpam-4825	97	35	a	a	PRON
ejpam-4825	97	36	)	)	PUNCT
ejpam-4825	97	37	(	(	PUNCT
ejpam-4825	97	38	1	1	NUM
ejpam-4825	97	39	+	+	CCONJ
ejpam-4825	97	40	t)x	t)x	PUNCT
ejpam-4825	97	41	=	=	PUNCT
ejpam-4825	97	42	∞∑	∞∑	PRON
ejpam-4825	97	43	n=0	n=0	NUM
ejpam-4825	97	44	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	97	45	,	,	PUNCT
ejpam-4825	97	46	a(x	a(x	PROPN
ejpam-4825	97	47	)	)	PUNCT
ejpam-4825	97	48	tn	tn	NOUN
ejpam-4825	97	49	n	n	NUM
ejpam-4825	97	50	!	!	PUNCT
ejpam-4825	97	51	.	.	PUNCT
ejpam-4825	98	1	these	these	DET
ejpam-4825	98	2	polynomials	polynomial	NOUN
ejpam-4825	98	3	have	have	VERB
ejpam-4825	98	4	an	an	DET
ejpam-4825	98	5	explicit	explicit	ADJ
ejpam-4825	98	6	formula	formula	NOUN
ejpam-4825	98	7	involving	involve	VERB
ejpam-4825	98	8	the	the	DET
ejpam-4825	98	9	stirling	stirling	NOUN
ejpam-4825	98	10	numbers	number	NOUN
ejpam-4825	98	11	of	of	ADP
ejpam-4825	98	12	the	the	DET
ejpam-4825	98	13	first	first	ADJ
ejpam-4825	98	14	and	and	CCONJ
ejpam-4825	98	15	second	second	ADJ
ejpam-4825	98	16	kind	kind	NOUN
ejpam-4825	98	17	.	.	PUNCT
ejpam-4825	99	1	theorem	theorem	NOUN
ejpam-4825	99	2	1	1	NUM
ejpam-4825	99	3	.	.	X
ejpam-4825	100	1	for	for	ADP
ejpam-4825	100	2	k	k	PROPN
ejpam-4825	100	3	∈	∈	PROPN
ejpam-4825	100	4	z	z	PROPN
ejpam-4825	100	5	,	,	PUNCT
ejpam-4825	100	6	n	n	DET
ejpam-4825	100	7	≥	≥	NOUN
ejpam-4825	100	8	0	0	NUM
ejpam-4825	100	9	we	we	PRON
ejpam-4825	100	10	have	have	VERB
ejpam-4825	100	11	c(k)n	c(k)n	PROPN
ejpam-4825	100	12	,	,	PUNCT
ejpam-4825	100	13	a(x	a(x	PROPN
ejpam-4825	100	14	)	)	PUNCT
ejpam-4825	100	15	=	=	SYM
ejpam-4825	100	16	n∑	n∑	NOUN
ejpam-4825	100	17	s=0	s=0	PROPN
ejpam-4825	101	1	x	x	X
ejpam-4825	101	2	!	!	PUNCT
ejpam-4825	101	3	(	(	PUNCT
ejpam-4825	101	4	x−	x−	PROPN
ejpam-4825	101	5	n+	n+	NUM
ejpam-4825	101	6	s	s	PROPN
ejpam-4825	101	7	)	)	PUNCT
ejpam-4825	101	8	!	!	PUNCT
ejpam-4825	102	1	(	(	PUNCT
ejpam-4825	102	2	−1)s−m	−1)s−m	PROPN
ejpam-4825	102	3	(	(	PUNCT
ejpam-4825	102	4	n	n	X
ejpam-4825	102	5	s	s	PART
ejpam-4825	102	6	)	)	PUNCT
ejpam-4825	102	7	s∑	s∑	PROPN
ejpam-4825	102	8	m=0	m=0	PROPN
ejpam-4825	103	1	[	[	PUNCT
ejpam-4825	103	2	s	s	NOUN
ejpam-4825	103	3	m	m	X
ejpam-4825	103	4	]	]	X
ejpam-4825	103	5	(	(	PUNCT
ejpam-4825	103	6	m+	m+	NOUN
ejpam-4825	103	7	a)k	a)k	ADJ
ejpam-4825	103	8	.	.	PUNCT
ejpam-4825	104	1	proof	proof	NOUN
ejpam-4825	104	2	.	.	PUNCT
ejpam-4825	105	1	∞∑	∞∑	PRON
ejpam-4825	105	2	n=0	n=0	NUM
ejpam-4825	105	3	c(k)n	c(k)n	PROPN
ejpam-4825	105	4	,	,	PUNCT
ejpam-4825	105	5	a(x	a(x	PROPN
ejpam-4825	105	6	)	)	PUNCT
ejpam-4825	105	7	tn	tn	NOUN
ejpam-4825	105	8	n	n	NOUN
ejpam-4825	105	9	!	!	PUNCT
ejpam-4825	105	10	=	=	PUNCT
ejpam-4825	106	1	(	(	PUNCT
ejpam-4825	106	2	1	1	NUM
ejpam-4825	106	3	+	+	NUM
ejpam-4825	106	4	t)xφf(ln(1	t)xφf(ln(1	X
ejpam-4825	106	5	+	+	X
ejpam-4825	106	6	t	t	PROPN
ejpam-4825	106	7	)	)	PUNCT
ejpam-4825	106	8	,	,	PUNCT
ejpam-4825	106	9	k	k	PROPN
ejpam-4825	106	10	,	,	PUNCT
ejpam-4825	106	11	a	a	PRON
ejpam-4825	106	12	)	)	PUNCT
ejpam-4825	106	13	.	.	PUNCT
ejpam-4825	107	1	working	work	VERB
ejpam-4825	107	2	on	on	ADP
ejpam-4825	107	3	the	the	DET
ejpam-4825	107	4	right	right	ADJ
ejpam-4825	107	5	hand	hand	NOUN
ejpam-4825	107	6	side	side	NOUN
ejpam-4825	107	7	,	,	PUNCT
ejpam-4825	107	8	we	we	PRON
ejpam-4825	107	9	have	have	VERB
ejpam-4825	107	10	(	(	PUNCT
ejpam-4825	107	11	1	1	NUM
ejpam-4825	107	12	+	+	NUM
ejpam-4825	107	13	t)xφf(ln(1	t)xφf(ln(1	NOUN
ejpam-4825	107	14	+	+	X
ejpam-4825	107	15	t	t	PROPN
ejpam-4825	107	16	)	)	PUNCT
ejpam-4825	107	17	,	,	PUNCT
ejpam-4825	108	1	k	k	PROPN
ejpam-4825	108	2	,	,	PUNCT
ejpam-4825	108	3	a	a	PRON
ejpam-4825	108	4	)	)	PUNCT
ejpam-4825	108	5	=	=	SYM
ejpam-4825	108	6	(	(	PUNCT
ejpam-4825	108	7	∞∑	∞∑	NUM
ejpam-4825	108	8	s=0	s=0	X
ejpam-4825	108	9	(	(	PUNCT
ejpam-4825	108	10	x	x	SYM
ejpam-4825	108	11	s	s	X
ejpam-4825	108	12	)	)	PUNCT
ejpam-4825	108	13	ts	ts	ADP
ejpam-4825	108	14	)	)	PUNCT
ejpam-4825	108	15	(	(	PUNCT
ejpam-4825	108	16	∞∑	∞∑	NUM
ejpam-4825	108	17	m=0	m=0	PROPN
ejpam-4825	108	18	(	(	PUNCT
ejpam-4825	108	19	ln(1	ln(1	NOUN
ejpam-4825	108	20	+	+	CCONJ
ejpam-4825	108	21	t))m	t))m	ADJ
ejpam-4825	108	22	m!(m+	m!(m+	NOUN
ejpam-4825	108	23	a)k	a)k	NOUN
ejpam-4825	108	24	)	)	PUNCT
ejpam-4825	109	1	=	=	PUNCT
ejpam-4825	109	2	(	(	PUNCT
ejpam-4825	109	3	∞∑	∞∑	NUM
ejpam-4825	109	4	s=0	s=0	X
ejpam-4825	109	5	(	(	PUNCT
ejpam-4825	109	6	x	x	SYM
ejpam-4825	109	7	s	s	X
ejpam-4825	109	8	)	)	PUNCT
ejpam-4825	109	9	ts	ts	ADP
ejpam-4825	109	10	)	)	PUNCT
ejpam-4825	109	11	(	(	PUNCT
ejpam-4825	109	12	∞∑	∞∑	NUM
ejpam-4825	109	13	m=0	m=0	PROPN
ejpam-4825	109	14	(	(	PUNCT
ejpam-4825	109	15	∞∑	∞∑	PROPN
ejpam-4825	109	16	n	n	NOUN
ejpam-4825	109	17	=	=	NOUN
ejpam-4825	109	18	m	m	PROPN
ejpam-4825	109	19	(	(	PUNCT
ejpam-4825	109	20	−1)n−m	−1)n−m	PUNCT
ejpam-4825	109	21	[	[	PUNCT
ejpam-4825	109	22	n	n	X
ejpam-4825	109	23	m	m	VERB
ejpam-4825	109	24	]	]	PUNCT
ejpam-4825	109	25	(	(	PUNCT
ejpam-4825	109	26	m+	m+	NOUN
ejpam-4825	109	27	a)k	a)k	ADJ
ejpam-4825	109	28	)	)	PUNCT
ejpam-4825	109	29	)	)	PUNCT
ejpam-4825	110	1	=	=	PUNCT
ejpam-4825	111	1	∞∑	∞∑	NUM
ejpam-4825	111	2	s=0	s=0	NOUN
ejpam-4825	111	3	s∑	s∑	PROPN
ejpam-4825	111	4	n=0	n=0	PUNCT
ejpam-4825	111	5	{	{	PUNCT
ejpam-4825	111	6	(	(	PUNCT
ejpam-4825	111	7	x	x	SYM
ejpam-4825	111	8	s−	s−	PROPN
ejpam-4825	111	9	n	n	PROPN
ejpam-4825	111	10	)	)	PUNCT
ejpam-4825	111	11	(	(	PUNCT
ejpam-4825	111	12	−1)n−mts−n	−1)n−mts−n	PROPN
ejpam-4825	111	13	(	(	PUNCT
ejpam-4825	111	14	n∑	n∑	PROPN
ejpam-4825	111	15	m=0	m=0	PROPN
ejpam-4825	111	16	(	(	PUNCT
ejpam-4825	111	17	[	[	PUNCT
ejpam-4825	111	18	n	n	X
ejpam-4825	111	19	m	m	VERB
ejpam-4825	111	20	]	]	PUNCT
ejpam-4825	111	21	(	(	PUNCT
ejpam-4825	111	22	m+	m+	NUM
ejpam-4825	111	23	a)k	a)k	PROPN
ejpam-4825	111	24	tn	tn	PROPN
ejpam-4825	111	25	n	n	CCONJ
ejpam-4825	111	26	!	!	PUNCT
ejpam-4825	111	27	)	)	PUNCT
ejpam-4825	111	28	)	)	PUNCT
ejpam-4825	111	29	}	}	PUNCT
ejpam-4825	111	30	=	=	SYM
ejpam-4825	112	1	∞∑	∞∑	NUM
ejpam-4825	112	2	s=0	s=0	X
ejpam-4825	112	3	{	{	PUNCT
ejpam-4825	112	4	s∑	s∑	PROPN
ejpam-4825	112	5	n=0	n=0	NUM
ejpam-4825	112	6	x!(−1)n−m	x!(−1)n−m	NOUN
ejpam-4825	112	7	(	(	PUNCT
ejpam-4825	112	8	s−	s−	PROPN
ejpam-4825	112	9	n)!(x−	n)!(x−	PROPN
ejpam-4825	112	10	s+	s+	ADV
ejpam-4825	112	11	n	n	CCONJ
ejpam-4825	112	12	)	)	PUNCT
ejpam-4825	112	13	!	!	PUNCT
ejpam-4825	113	1	(	(	PUNCT
ejpam-4825	113	2	n∑	n∑	NOUN
ejpam-4825	113	3	m=0	m=0	PROPN
ejpam-4825	113	4	(	(	PUNCT
ejpam-4825	113	5	[	[	PUNCT
ejpam-4825	113	6	n	n	X
ejpam-4825	113	7	m	m	VERB
ejpam-4825	113	8	]	]	PUNCT
ejpam-4825	113	9	(	(	PUNCT
ejpam-4825	113	10	m+	m+	NUM
ejpam-4825	113	11	a)k	a)k	NOUN
ejpam-4825	113	12	tss	tss	PROPN
ejpam-4825	113	13	!	!	PUNCT
ejpam-4825	113	14	n!s	n!s	PROPN
ejpam-4825	113	15	!	!	PROPN
ejpam-4825	113	16	)	)	PUNCT
ejpam-4825	113	17	)	)	PUNCT
ejpam-4825	113	18	}	}	PUNCT
ejpam-4825	114	1	=	=	SYM
ejpam-4825	114	2	∞∑	∞∑	NUM
ejpam-4825	114	3	s=0	s=0	X
ejpam-4825	114	4	{	{	PUNCT
ejpam-4825	114	5	s∑	s∑	PROPN
ejpam-4825	114	6	n=0	n=0	NUM
ejpam-4825	114	7	x	x	X
ejpam-4825	114	8	!	!	PUNCT
ejpam-4825	114	9	(	(	PUNCT
ejpam-4825	114	10	x+	x+	PROPN
ejpam-4825	114	11	s−	s−	PROPN
ejpam-4825	114	12	n	n	CCONJ
ejpam-4825	114	13	)	)	PUNCT
ejpam-4825	114	14	!	!	PUNCT
ejpam-4825	115	1	(	(	PUNCT
ejpam-4825	115	2	−1)n−m	−1)n−m	X
ejpam-4825	115	3	(	(	PUNCT
ejpam-4825	115	4	n∑	n∑	NOUN
ejpam-4825	115	5	m=0	m=0	PROPN
ejpam-4825	115	6	(	(	PUNCT
ejpam-4825	115	7	[	[	PUNCT
ejpam-4825	115	8	n	n	X
ejpam-4825	115	9	m	m	VERB
ejpam-4825	115	10	]	]	PUNCT
ejpam-4825	115	11	(	(	PUNCT
ejpam-4825	115	12	m+	m+	NOUN
ejpam-4825	115	13	a)k	a)k	ADJ
ejpam-4825	115	14	)	)	PUNCT
ejpam-4825	116	1	s	s	X
ejpam-4825	116	2	!	!	NOUN
ejpam-4825	116	3	n!(s−	n!(s−	NOUN
ejpam-4825	116	4	n	n	CCONJ
ejpam-4825	116	5	)	)	PUNCT
ejpam-4825	116	6	!	!	PUNCT
ejpam-4825	117	1	ts	ts	ADP
ejpam-4825	117	2	s	s	PROPN
ejpam-4825	117	3	!	!	PUNCT
ejpam-4825	117	4	)	)	PUNCT
ejpam-4825	117	5	}	}	PUNCT
ejpam-4825	118	1	=	=	SYM
ejpam-4825	118	2	∞∑	∞∑	NUM
ejpam-4825	118	3	s=0	s=0	X
ejpam-4825	118	4	{	{	PUNCT
ejpam-4825	118	5	s∑	s∑	PROPN
ejpam-4825	118	6	n=0	n=0	NUM
ejpam-4825	118	7	x	x	X
ejpam-4825	118	8	!	!	PUNCT
ejpam-4825	118	9	(	(	PUNCT
ejpam-4825	118	10	x−	x−	PROPN
ejpam-4825	118	11	s+	s+	NUM
ejpam-4825	118	12	n	n	CCONJ
ejpam-4825	118	13	)	)	PUNCT
ejpam-4825	118	14	!	!	PUNCT
ejpam-4825	119	1	(	(	PUNCT
ejpam-4825	119	2	−1)n−m	−1)n−m	X
ejpam-4825	119	3	(	(	PUNCT
ejpam-4825	119	4	s	s	NOUN
ejpam-4825	119	5	n	n	NOUN
ejpam-4825	119	6	)	)	PUNCT
ejpam-4825	119	7	(	(	PUNCT
ejpam-4825	119	8	n∑	n∑	NOUN
ejpam-4825	119	9	m=0	m=0	PROPN
ejpam-4825	119	10	(	(	PUNCT
ejpam-4825	119	11	[	[	PUNCT
ejpam-4825	119	12	n	n	X
ejpam-4825	119	13	m	m	VERB
ejpam-4825	119	14	]	]	PUNCT
ejpam-4825	119	15	(	(	PUNCT
ejpam-4825	119	16	m+	m+	NOUN
ejpam-4825	119	17	a)k	a)k	ADJ
ejpam-4825	119	18	)	)	PUNCT
ejpam-4825	119	19	)	)	PUNCT
ejpam-4825	119	20	}	}	PUNCT
ejpam-4825	119	21	ts	ts	ADP
ejpam-4825	119	22	s	s	PRON
ejpam-4825	119	23	!	!	PUNCT
ejpam-4825	119	24	=	=	NOUN
ejpam-4825	120	1	∞∑	∞∑	PRON
ejpam-4825	120	2	n=0	n=0	NUM
ejpam-4825	120	3	{	{	PUNCT
ejpam-4825	120	4	n∑	n∑	NOUN
ejpam-4825	120	5	s=0	s=0	PROPN
ejpam-4825	120	6	x	x	X
ejpam-4825	120	7	!	!	PUNCT
ejpam-4825	120	8	(	(	PUNCT
ejpam-4825	120	9	x−	x−	PROPN
ejpam-4825	120	10	n+	n+	NUM
ejpam-4825	120	11	s	s	PROPN
ejpam-4825	120	12	)	)	PUNCT
ejpam-4825	120	13	!	!	PUNCT
ejpam-4825	121	1	(	(	PUNCT
ejpam-4825	121	2	−1)s−m	−1)s−m	PROPN
ejpam-4825	121	3	(	(	PUNCT
ejpam-4825	121	4	n	n	NOUN
ejpam-4825	121	5	s	s	PART
ejpam-4825	121	6	)	)	PUNCT
ejpam-4825	121	7	(	(	PUNCT
ejpam-4825	121	8	s∑	s∑	PROPN
ejpam-4825	121	9	m=0	m=0	PROPN
ejpam-4825	121	10	(	(	PUNCT
ejpam-4825	121	11	[	[	PUNCT
ejpam-4825	121	12	s	s	VERB
ejpam-4825	121	13	m	m	X
ejpam-4825	121	14	]	]	X
ejpam-4825	121	15	(	(	PUNCT
ejpam-4825	121	16	m+	m+	NOUN
ejpam-4825	121	17	a)k	a)k	ADJ
ejpam-4825	121	18	)	)	PUNCT
ejpam-4825	121	19	)	)	PUNCT
ejpam-4825	121	20	}	}	PUNCT
ejpam-4825	121	21	tn	tn	PROPN
ejpam-4825	121	22	n	n	X
ejpam-4825	121	23	!	!	PUNCT
ejpam-4825	121	24	.	.	PUNCT
ejpam-4825	122	1	comparing	compare	VERB
ejpam-4825	122	2	the	the	DET
ejpam-4825	122	3	coefficients	coefficient	NOUN
ejpam-4825	122	4	completes	complete	VERB
ejpam-4825	122	5	the	the	DET
ejpam-4825	122	6	proof	proof	NOUN
ejpam-4825	122	7	.	.	PUNCT
ejpam-4825	123	1	■	■	PUNCT
ejpam-4825	123	2	theorem	theorem	ADJ
ejpam-4825	123	3	2	2	NUM
ejpam-4825	123	4	.	.	X
ejpam-4825	123	5	for	for	ADP
ejpam-4825	123	6	k	k	PROPN
ejpam-4825	123	7	∈	∈	PROPN
ejpam-4825	123	8	z	z	PROPN
ejpam-4825	123	9	,	,	PUNCT
ejpam-4825	123	10	n	n	DET
ejpam-4825	123	11	≥	≥	NOUN
ejpam-4825	123	12	0	0	NUM
ejpam-4825	123	13	we	we	PRON
ejpam-4825	123	14	have	have	VERB
ejpam-4825	123	15	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	123	16	,	,	PUNCT
ejpam-4825	123	17	a(x	a(x	PROPN
ejpam-4825	123	18	)	)	PUNCT
ejpam-4825	123	19	=	=	SYM
ejpam-4825	123	20	n∑	n∑	NOUN
ejpam-4825	123	21	s=0	s=0	PROPN
ejpam-4825	123	22	(	(	PUNCT
ejpam-4825	123	23	x+	x+	X
ejpam-4825	123	24	n−	n−	NOUN
ejpam-4825	123	25	s−	s−	PROPN
ejpam-4825	123	26	1	1	NUM
ejpam-4825	123	27	)	)	PUNCT
ejpam-4825	123	28	!	!	PUNCT
ejpam-4825	124	1	(	(	PUNCT
ejpam-4825	124	2	x−	x−	PROPN
ejpam-4825	124	3	1	1	NUM
ejpam-4825	124	4	)	)	PUNCT
ejpam-4825	124	5	!	!	PUNCT
ejpam-4825	125	1	(	(	PUNCT
ejpam-4825	125	2	−1)n	−1)n	X
ejpam-4825	125	3	(	(	PUNCT
ejpam-4825	125	4	n	n	X
ejpam-4825	125	5	s	s	PART
ejpam-4825	125	6	)	)	PUNCT
ejpam-4825	125	7	s∑	s∑	PROPN
ejpam-4825	125	8	m=0	m=0	PROPN
ejpam-4825	126	1	[	[	PUNCT
ejpam-4825	126	2	s	s	NOUN
ejpam-4825	126	3	m	m	X
ejpam-4825	126	4	]	]	X
ejpam-4825	126	5	(	(	PUNCT
ejpam-4825	126	6	m+	m+	NOUN
ejpam-4825	126	7	a)k	a)k	ADJ
ejpam-4825	126	8	.	.	PUNCT
ejpam-4825	127	1	n.	n.	PROPN
ejpam-4825	127	2	b.	b.	PROPN
ejpam-4825	128	1	lacpao	lacpao	PROPN
ejpam-4825	128	2	/	/	SYM
ejpam-4825	128	3	eur	eur	PROPN
ejpam-4825	128	4	.	.	PUNCT
ejpam-4825	129	1	j.	j.	PROPN
ejpam-4825	129	2	pure	pure	PROPN
ejpam-4825	129	3	appl	appl	PROPN
ejpam-4825	129	4	.	.	PROPN
ejpam-4825	129	5	math	math	PROPN
ejpam-4825	129	6	,	,	PUNCT
ejpam-4825	129	7	16	16	NUM
ejpam-4825	129	8	(	(	PUNCT
ejpam-4825	129	9	3	3	NUM
ejpam-4825	129	10	)	)	PUNCT
ejpam-4825	129	11	(	(	PUNCT
ejpam-4825	129	12	2023	2023	NUM
ejpam-4825	129	13	)	)	PUNCT
ejpam-4825	129	14	,	,	PUNCT
ejpam-4825	129	15	1747	1747	NUM
ejpam-4825	129	16	-	-	SYM
ejpam-4825	129	17	1761	1761	NUM
ejpam-4825	129	18	1753	1753	NUM
ejpam-4825	129	19	proof	proof	NOUN
ejpam-4825	129	20	.	.	PUNCT
ejpam-4825	130	1	∞∑	∞∑	DET
ejpam-4825	130	2	n=0	n=0	NUM
ejpam-4825	130	3	ĉ(k)n	ĉ(k)n	PROPN
ejpam-4825	130	4	,	,	PUNCT
ejpam-4825	130	5	a(x	a(x	PROPN
ejpam-4825	130	6	)	)	PUNCT
ejpam-4825	130	7	tn	tn	NOUN
ejpam-4825	130	8	n	n	NOUN
ejpam-4825	130	9	!	!	PUNCT
ejpam-4825	131	1	=	=	SYM
ejpam-4825	131	2	1	1	NUM
ejpam-4825	131	3	(	(	PUNCT
ejpam-4825	131	4	1	1	NUM
ejpam-4825	131	5	+	+	CCONJ
ejpam-4825	131	6	t)x	t)x	PUNCT
ejpam-4825	131	7	φf(−	φf(−	ADV
ejpam-4825	132	1	ln(1	ln(1	PROPN
ejpam-4825	132	2	+	+	NUM
ejpam-4825	132	3	t	t	PROPN
ejpam-4825	132	4	)	)	PUNCT
ejpam-4825	132	5	,	,	PUNCT
ejpam-4825	133	1	k	k	PROPN
ejpam-4825	133	2	,	,	PUNCT
ejpam-4825	133	3	a	a	PRON
ejpam-4825	133	4	)	)	PUNCT
ejpam-4825	133	5	.	.	PUNCT
ejpam-4825	134	1	working	work	VERB
ejpam-4825	134	2	on	on	ADP
ejpam-4825	134	3	the	the	DET
ejpam-4825	134	4	right	right	ADJ
ejpam-4825	134	5	hand	hand	NOUN
ejpam-4825	134	6	side	side	NOUN
ejpam-4825	134	7	,	,	PUNCT
ejpam-4825	134	8	we	we	PRON
ejpam-4825	134	9	have	have	VERB
ejpam-4825	134	10	1	1	NUM
ejpam-4825	134	11	(	(	PUNCT
ejpam-4825	134	12	1	1	NUM
ejpam-4825	134	13	+	+	CCONJ
ejpam-4825	134	14	t)x	t)x	PUNCT
ejpam-4825	134	15	φf(−	φf(−	ADV
ejpam-4825	135	1	ln(1	ln(1	PROPN
ejpam-4825	135	2	+	+	NUM
ejpam-4825	135	3	t	t	PROPN
ejpam-4825	135	4	)	)	PUNCT
ejpam-4825	135	5	,	,	PUNCT
ejpam-4825	136	1	k	k	PROPN
ejpam-4825	136	2	,	,	PUNCT
ejpam-4825	136	3	a	a	PRON
ejpam-4825	136	4	)	)	PUNCT
ejpam-4825	136	5	=	=	SYM
ejpam-4825	136	6	(	(	PUNCT
ejpam-4825	136	7	∞∑	∞∑	NUM
ejpam-4825	136	8	s=0	s=0	X
ejpam-4825	136	9	(	(	PUNCT
ejpam-4825	136	10	x+	x+	X
ejpam-4825	136	11	s−	s−	PROPN
ejpam-4825	136	12	1	1	NUM
ejpam-4825	136	13	s	s	NOUN
ejpam-4825	136	14	)	)	PUNCT
ejpam-4825	136	15	(	(	PUNCT
ejpam-4825	136	16	−1)sts	−1)st	NOUN
ejpam-4825	136	17	)	)	PUNCT
ejpam-4825	136	18	(	(	PUNCT
ejpam-4825	136	19	∞∑	∞∑	NUM
ejpam-4825	136	20	m=0	m=0	PROPN
ejpam-4825	136	21	(	(	PUNCT
ejpam-4825	136	22	−	−	PROPN
ejpam-4825	136	23	ln(1	ln(1	NOUN
ejpam-4825	136	24	+	+	CCONJ
ejpam-4825	136	25	t))m	t))m	ADJ
ejpam-4825	136	26	m!(m+	m!(m+	NOUN
ejpam-4825	136	27	a)k	a)k	NOUN
ejpam-4825	136	28	)	)	PUNCT
ejpam-4825	137	1	=	=	PUNCT
ejpam-4825	137	2	(	(	PUNCT
ejpam-4825	137	3	∞∑	∞∑	NUM
ejpam-4825	137	4	s=0	s=0	X
ejpam-4825	137	5	(	(	PUNCT
ejpam-4825	137	6	x+	x+	X
ejpam-4825	137	7	s−	s−	PROPN
ejpam-4825	137	8	1	1	NUM
ejpam-4825	137	9	s	s	NOUN
ejpam-4825	137	10	)	)	PUNCT
ejpam-4825	137	11	(	(	PUNCT
ejpam-4825	137	12	−1)sts	−1)st	NOUN
ejpam-4825	137	13	)	)	PUNCT
ejpam-4825	137	14	(	(	PUNCT
ejpam-4825	137	15	∞∑	∞∑	NUM
ejpam-4825	137	16	m=0	m=0	PROPN
ejpam-4825	137	17	(	(	PUNCT
ejpam-4825	137	18	(	(	PUNCT
ejpam-4825	137	19	ln(1	ln(1	NOUN
ejpam-4825	137	20	+	+	CCONJ
ejpam-4825	137	21	t))m(−1)m	t))m(−1)m	PROPN
ejpam-4825	137	22	m	m	NOUN
ejpam-4825	137	23	!	!	PROPN
ejpam-4825	137	24	1	1	NUM
ejpam-4825	137	25	(	(	PUNCT
ejpam-4825	137	26	m+	m+	NOUN
ejpam-4825	137	27	a)k	a)k	ADJ
ejpam-4825	137	28	)	)	PUNCT
ejpam-4825	138	1	=	=	PUNCT
ejpam-4825	139	1	(	(	PUNCT
ejpam-4825	139	2	∞∑	∞∑	NUM
ejpam-4825	139	3	s=0	s=0	X
ejpam-4825	139	4	(	(	PUNCT
ejpam-4825	139	5	x+	x+	X
ejpam-4825	139	6	s−	s−	PROPN
ejpam-4825	139	7	1	1	NUM
ejpam-4825	139	8	s	s	NOUN
ejpam-4825	139	9	)	)	PUNCT
ejpam-4825	139	10	(	(	PUNCT
ejpam-4825	139	11	−1)sts	−1)st	NOUN
ejpam-4825	139	12	)	)	PUNCT
ejpam-4825	139	13	(	(	PUNCT
ejpam-4825	139	14	∞∑	∞∑	NUM
ejpam-4825	139	15	m=0	m=0	PROPN
ejpam-4825	139	16	(	(	PUNCT
ejpam-4825	139	17	∞∑	∞∑	PROPN
ejpam-4825	139	18	n	n	X
ejpam-4825	139	19	=	=	NOUN
ejpam-4825	139	20	m	m	PROPN
ejpam-4825	139	21	(	(	PUNCT
ejpam-4825	139	22	−1)n	−1)n	X
ejpam-4825	139	23	[	[	PUNCT
ejpam-4825	139	24	n	n	X
ejpam-4825	139	25	m	m	VERB
ejpam-4825	139	26	]	]	PUNCT
ejpam-4825	139	27	(	(	PUNCT
ejpam-4825	139	28	m+	m+	NOUN
ejpam-4825	139	29	a)k	a)k	ADJ
ejpam-4825	139	30	)	)	PUNCT
ejpam-4825	139	31	tn	tn	PROPN
ejpam-4825	139	32	n	n	PROPN
ejpam-4825	139	33	!	!	PUNCT
ejpam-4825	139	34	)	)	PUNCT
ejpam-4825	140	1	=	=	PUNCT
ejpam-4825	141	1	∞∑	∞∑	NUM
ejpam-4825	141	2	s=0	s=0	NOUN
ejpam-4825	141	3	s∑	s∑	PROPN
ejpam-4825	141	4	n=0	n=0	PUNCT
ejpam-4825	141	5	{	{	PUNCT
ejpam-4825	141	6	(	(	PUNCT
ejpam-4825	141	7	x+	x+	ADJ
ejpam-4825	141	8	s−	s−	PROPN
ejpam-4825	141	9	n−	n−	NOUN
ejpam-4825	141	10	1	1	NUM
ejpam-4825	141	11	s−	s−	PROPN
ejpam-4825	141	12	n	n	PROPN
ejpam-4825	141	13	)	)	PUNCT
ejpam-4825	141	14	(	(	PUNCT
ejpam-4825	141	15	−1)sts−n	−1)sts−n	PROPN
ejpam-4825	141	16	(	(	PUNCT
ejpam-4825	141	17	n∑	n∑	NOUN
ejpam-4825	141	18	m=0	m=0	PROPN
ejpam-4825	141	19	(	(	PUNCT
ejpam-4825	141	20	[	[	PUNCT
ejpam-4825	141	21	n	n	X
ejpam-4825	141	22	m	m	VERB
ejpam-4825	141	23	]	]	PUNCT
ejpam-4825	141	24	(	(	PUNCT
ejpam-4825	141	25	m+	m+	NOUN
ejpam-4825	141	26	a)k	a)k	ADJ
ejpam-4825	141	27	)	)	PUNCT
ejpam-4825	141	28	tn	tn	PROPN
ejpam-4825	141	29	n	n	PROPN
ejpam-4825	141	30	!	!	PUNCT
ejpam-4825	141	31	)	)	PUNCT
ejpam-4825	141	32	}	}	PUNCT
ejpam-4825	142	1	=	=	PUNCT
ejpam-4825	142	2	∞∑	∞∑	NUM
ejpam-4825	142	3	s=0	s=0	X
ejpam-4825	142	4	{	{	PUNCT
ejpam-4825	142	5	s∑	s∑	PROPN
ejpam-4825	142	6	n=0	n=0	PUNCT
ejpam-4825	142	7	(	(	PUNCT
ejpam-4825	142	8	x+	x+	X
ejpam-4825	142	9	s−	s−	PROPN
ejpam-4825	142	10	n−	n−	NOUN
ejpam-4825	142	11	1	1	NUM
ejpam-4825	142	12	)	)	PUNCT
ejpam-4825	142	13	!	!	PUNCT
ejpam-4825	143	1	(	(	PUNCT
ejpam-4825	143	2	s−	s−	NOUN
ejpam-4825	143	3	n)!(x−	n)!(x−	ADP
ejpam-4825	143	4	1	1	NUM
ejpam-4825	143	5	)	)	PUNCT
ejpam-4825	143	6	!	!	PUNCT
ejpam-4825	144	1	(	(	PUNCT
ejpam-4825	144	2	−1)s	−1)s	PRON
ejpam-4825	144	3	(	(	PUNCT
ejpam-4825	144	4	n∑	n∑	NOUN
ejpam-4825	144	5	m=0	m=0	PROPN
ejpam-4825	144	6	(	(	PUNCT
ejpam-4825	144	7	[	[	PUNCT
ejpam-4825	144	8	n	n	X
ejpam-4825	144	9	m	m	VERB
ejpam-4825	144	10	]	]	PUNCT
ejpam-4825	144	11	(	(	PUNCT
ejpam-4825	144	12	m+	m+	NUM
ejpam-4825	144	13	a)k	a)k	ADJ
ejpam-4825	144	14	)	)	PUNCT
ejpam-4825	144	15	tss	tss	PROPN
ejpam-4825	144	16	!	!	PUNCT
ejpam-4825	144	17	n!s	n!s	PROPN
ejpam-4825	144	18	!	!	PUNCT
ejpam-4825	144	19	)	)	PUNCT
ejpam-4825	144	20	}	}	PUNCT
ejpam-4825	144	21	=	=	SYM
ejpam-4825	144	22	∞∑	∞∑	NUM
ejpam-4825	144	23	s=0	s=0	X
ejpam-4825	144	24	{	{	PUNCT
ejpam-4825	144	25	s∑	s∑	PROPN
ejpam-4825	144	26	n=0	n=0	PUNCT
ejpam-4825	144	27	(	(	PUNCT
ejpam-4825	144	28	x+	x+	X
ejpam-4825	144	29	s−	s−	PROPN
ejpam-4825	144	30	n−	n−	NOUN
ejpam-4825	144	31	1	1	NUM
ejpam-4825	144	32	)	)	PUNCT
ejpam-4825	144	33	!	!	PUNCT
ejpam-4825	145	1	(	(	PUNCT
ejpam-4825	145	2	x−	x−	PROPN
ejpam-4825	145	3	1	1	NUM
ejpam-4825	145	4	)	)	PUNCT
ejpam-4825	145	5	!	!	PUNCT
ejpam-4825	146	1	(	(	PUNCT
ejpam-4825	146	2	−1)s	−1)s	PRON
ejpam-4825	146	3	(	(	PUNCT
ejpam-4825	146	4	n∑	n∑	NOUN
ejpam-4825	146	5	m=0	m=0	PROPN
ejpam-4825	146	6	(	(	PUNCT
ejpam-4825	146	7	[	[	PUNCT
ejpam-4825	146	8	n	n	X
ejpam-4825	146	9	m	m	VERB
ejpam-4825	146	10	]	]	PUNCT
ejpam-4825	146	11	(	(	PUNCT
ejpam-4825	146	12	m+	m+	NOUN
ejpam-4825	146	13	a)k	a)k	ADJ
ejpam-4825	146	14	)	)	PUNCT
ejpam-4825	146	15	s	s	X
ejpam-4825	146	16	!	!	NOUN
ejpam-4825	146	17	n!(s−	n!(s−	NOUN
ejpam-4825	146	18	n	n	CCONJ
ejpam-4825	146	19	)	)	PUNCT
ejpam-4825	146	20	!	!	PUNCT
ejpam-4825	147	1	ts	ts	ADP
ejpam-4825	147	2	s	s	PROPN
ejpam-4825	147	3	!	!	PUNCT
ejpam-4825	147	4	)	)	PUNCT
ejpam-4825	147	5	}	}	PUNCT
ejpam-4825	148	1	=	=	SYM
ejpam-4825	148	2	∞∑	∞∑	NUM
ejpam-4825	148	3	s=0	s=0	X
ejpam-4825	148	4	{	{	PUNCT
ejpam-4825	148	5	s∑	s∑	PROPN
ejpam-4825	148	6	n=0	n=0	PUNCT
ejpam-4825	148	7	(	(	PUNCT
ejpam-4825	148	8	x+	x+	X
ejpam-4825	148	9	s−	s−	PROPN
ejpam-4825	148	10	n−	n−	NOUN
ejpam-4825	148	11	1	1	NUM
ejpam-4825	148	12	)	)	PUNCT
ejpam-4825	148	13	!	!	PUNCT
ejpam-4825	149	1	(	(	PUNCT
ejpam-4825	149	2	x−	x−	PROPN
ejpam-4825	149	3	1	1	NUM
ejpam-4825	149	4	)	)	PUNCT
ejpam-4825	149	5	!	!	PUNCT
ejpam-4825	150	1	(	(	PUNCT
ejpam-4825	150	2	−1)s	−1)s	PRON
ejpam-4825	150	3	(	(	PUNCT
ejpam-4825	150	4	s	s	NOUN
ejpam-4825	150	5	n	n	NOUN
ejpam-4825	150	6	)	)	PUNCT
ejpam-4825	150	7	(	(	PUNCT
ejpam-4825	150	8	n∑	n∑	NOUN
ejpam-4825	150	9	m=0	m=0	PROPN
ejpam-4825	150	10	(	(	PUNCT
ejpam-4825	150	11	[	[	PUNCT
ejpam-4825	150	12	n	n	X
ejpam-4825	150	13	m	m	VERB
ejpam-4825	150	14	]	]	PUNCT
ejpam-4825	150	15	(	(	PUNCT
ejpam-4825	150	16	m+	m+	NOUN
ejpam-4825	150	17	a)k	a)k	ADJ
ejpam-4825	150	18	)	)	PUNCT
ejpam-4825	150	19	)	)	PUNCT
ejpam-4825	150	20	}	}	PUNCT
ejpam-4825	150	21	ts	ts	ADP
ejpam-4825	150	22	s	s	PRON
ejpam-4825	150	23	!	!	PUNCT
ejpam-4825	151	1	=	=	NOUN
ejpam-4825	152	1	∞∑	∞∑	PRON
ejpam-4825	152	2	n=0	n=0	NUM
ejpam-4825	152	3	{	{	PUNCT
ejpam-4825	152	4	n∑	n∑	PROPN
ejpam-4825	152	5	s=0	s=0	PROPN
ejpam-4825	152	6	(	(	PUNCT
ejpam-4825	152	7	x+	x+	X
ejpam-4825	152	8	n−	n−	NOUN
ejpam-4825	152	9	s−	s−	PROPN
ejpam-4825	152	10	1	1	NUM
ejpam-4825	152	11	)	)	PUNCT
ejpam-4825	152	12	!	!	PUNCT
ejpam-4825	153	1	(	(	PUNCT
ejpam-4825	153	2	x−	x−	PROPN
ejpam-4825	153	3	1	1	NUM
ejpam-4825	153	4	)	)	PUNCT
ejpam-4825	153	5	!	!	PUNCT
ejpam-4825	154	1	(	(	PUNCT
ejpam-4825	154	2	−1)n	−1)n	X
ejpam-4825	154	3	(	(	PUNCT
ejpam-4825	154	4	n	n	X
ejpam-4825	154	5	s	s	NOUN
ejpam-4825	154	6	)	)	PUNCT
ejpam-4825	154	7	(	(	PUNCT
ejpam-4825	154	8	s∑	s∑	PROPN
ejpam-4825	154	9	m=0	m=0	PROPN
ejpam-4825	154	10	(	(	PUNCT
ejpam-4825	154	11	[	[	PUNCT
ejpam-4825	154	12	s	s	VERB
ejpam-4825	154	13	m	m	X
ejpam-4825	154	14	]	]	X
ejpam-4825	154	15	(	(	PUNCT
ejpam-4825	154	16	m+	m+	NOUN
ejpam-4825	154	17	a)k	a)k	ADJ
ejpam-4825	154	18	)	)	PUNCT
ejpam-4825	154	19	)	)	PUNCT
ejpam-4825	154	20	}	}	PUNCT
ejpam-4825	154	21	tn	tn	PROPN
ejpam-4825	154	22	n	n	X
ejpam-4825	154	23	!	!	PUNCT
ejpam-4825	154	24	.	.	PUNCT
ejpam-4825	155	1	comparing	compare	VERB
ejpam-4825	155	2	the	the	DET
ejpam-4825	155	3	coefficients	coefficient	NOUN
ejpam-4825	155	4	yields	yield	VERB
ejpam-4825	155	5	the	the	DET
ejpam-4825	155	6	result	result	NOUN
ejpam-4825	155	7	.	.	PUNCT
ejpam-4825	156	1	■	■	PUNCT
ejpam-4825	156	2	the	the	DET
ejpam-4825	156	3	hurwitz	hurwitz	PROPN
ejpam-4825	156	4	-	-	PUNCT
ejpam-4825	156	5	lerch	lerch	PROPN
ejpam-4825	156	6	type	type	NOUN
ejpam-4825	156	7	poly	poly	ADJ
ejpam-4825	156	8	-	-	PUNCT
ejpam-4825	156	9	bernoulli	bernoulli	NOUN
ejpam-4825	156	10	polynomials	polynomial	NOUN
ejpam-4825	156	11	can	can	AUX
ejpam-4825	156	12	also	also	ADV
ejpam-4825	156	13	be	be	AUX
ejpam-4825	156	14	defined	define	VERB
ejpam-4825	156	15	by	by	ADP
ejpam-4825	156	16	means	mean	NOUN
ejpam-4825	156	17	of	of	ADP
ejpam-4825	156	18	hurwitz	hurwitz	PROPN
ejpam-4825	156	19	-	-	PUNCT
ejpam-4825	156	20	lerch	lerch	PROPN
ejpam-4825	156	21	zeta	zeta	PROPN
ejpam-4825	156	22	function	function	PROPN
ejpam-4825	156	23	φ(z	φ(z	PROPN
ejpam-4825	156	24	,	,	PUNCT
ejpam-4825	156	25	s	s	PROPN
ejpam-4825	156	26	,	,	PUNCT
ejpam-4825	156	27	a	a	PRON
ejpam-4825	156	28	)	)	PUNCT
ejpam-4825	156	29	.	.	PUNCT
ejpam-4825	157	1	definition	definition	NOUN
ejpam-4825	157	2	3	3	NUM
ejpam-4825	157	3	.	.	PUNCT
ejpam-4825	158	1	the	the	DET
ejpam-4825	158	2	hurwitz	hurwitz	PROPN
ejpam-4825	158	3	-	-	PUNCT
ejpam-4825	158	4	lerch	lerch	PROPN
ejpam-4825	158	5	type	type	NOUN
ejpam-4825	158	6	poly	poly	ADJ
ejpam-4825	158	7	-	-	PUNCT
ejpam-4825	158	8	bernoulli	bernoulli	NOUN
ejpam-4825	158	9	polynomials	polynomial	NOUN
ejpam-4825	158	10	denoted	denote	VERB
ejpam-4825	158	11	by	by	ADP
ejpam-4825	158	12	b	b	PROPN
ejpam-4825	158	13	(	(	PUNCT
ejpam-4825	158	14	k	k	NOUN
ejpam-4825	158	15	)	)	PUNCT
ejpam-4825	158	16	n	n	CCONJ
ejpam-4825	158	17	,	,	PUNCT
ejpam-4825	158	18	a(x	a(x	NOUN
ejpam-4825	158	19	)	)	PUNCT
ejpam-4825	158	20	are	be	AUX
ejpam-4825	158	21	defined	define	VERB
ejpam-4825	158	22	by	by	ADP
ejpam-4825	158	23	φ(1−	φ(1−	PROPN
ejpam-4825	158	24	e−t	e−t	PROPN
ejpam-4825	158	25	,	,	PUNCT
ejpam-4825	158	26	k	k	NOUN
ejpam-4825	158	27	,	,	PUNCT
ejpam-4825	158	28	a)etx	a)etx	PROPN
ejpam-4825	158	29	=	=	SYM
ejpam-4825	158	30	∞∑	∞∑	NUM
ejpam-4825	158	31	n=0	n=0	NUM
ejpam-4825	158	32	b(k	b(k	PROPN
ejpam-4825	158	33	)	)	PUNCT
ejpam-4825	158	34	n	n	CCONJ
ejpam-4825	158	35	,	,	PUNCT
ejpam-4825	158	36	a(x	a(x	PROPN
ejpam-4825	158	37	)	)	PUNCT
ejpam-4825	158	38	tn	tn	NOUN
ejpam-4825	158	39	n	n	NUM
ejpam-4825	158	40	!	!	PUNCT
ejpam-4825	158	41	.	.	PUNCT
ejpam-4825	159	1	where	where	SCONJ
ejpam-4825	159	2	etx	etx	NOUN
ejpam-4825	159	3	=	=	PUNCT
ejpam-4825	160	1	∞∑	∞∑	NUM
ejpam-4825	160	2	n=0	n=0	NUM
ejpam-4825	160	3	(	(	PUNCT
ejpam-4825	160	4	tx)n	tx)n	PROPN
ejpam-4825	160	5	n	n	X
ejpam-4825	160	6	!	!	PUNCT
ejpam-4825	160	7	.	.	PUNCT
ejpam-4825	161	1	bayad	bayad	NOUN
ejpam-4825	161	2	and	and	CCONJ
ejpam-4825	161	3	hamahata	hamahata	VERB
ejpam-4825	162	1	[	[	X
ejpam-4825	162	2	2	2	NUM
ejpam-4825	162	3	]	]	PUNCT
ejpam-4825	162	4	established	establish	VERB
ejpam-4825	162	5	an	an	DET
ejpam-4825	162	6	explicit	explicit	ADJ
ejpam-4825	162	7	formula	formula	NOUN
ejpam-4825	162	8	for	for	ADP
ejpam-4825	162	9	poly	poly	ADJ
ejpam-4825	162	10	-	-	PUNCT
ejpam-4825	162	11	bernoulli	bernoulli	NOUN
ejpam-4825	162	12	polynomials	polynomial	NOUN
ejpam-4825	162	13	.	.	PUNCT
ejpam-4825	163	1	analogous	analogous	ADJ
ejpam-4825	163	2	to	to	ADP
ejpam-4825	163	3	this	this	PRON
ejpam-4825	163	4	,	,	PUNCT
ejpam-4825	163	5	the	the	DET
ejpam-4825	163	6	hurwitz	hurwitz	PROPN
ejpam-4825	163	7	-	-	PUNCT
ejpam-4825	163	8	lerch	lerch	PROPN
ejpam-4825	163	9	type	type	NOUN
ejpam-4825	163	10	poly	poly	ADJ
ejpam-4825	163	11	-	-	PUNCT
ejpam-4825	163	12	bernoulli	bernoulli	NOUN
ejpam-4825	163	13	polynomials	polynomial	NOUN
ejpam-4825	163	14	have	have	VERB
ejpam-4825	163	15	explicit	explicit	ADJ
ejpam-4825	163	16	explicit	explicit	ADJ
ejpam-4825	163	17	formula	formula	NOUN
ejpam-4825	163	18	involving	involve	VERB
ejpam-4825	163	19	stirling	stirling	NOUN
ejpam-4825	163	20	numbers	number	NOUN
ejpam-4825	163	21	.	.	PUNCT
ejpam-4825	164	1	n.	n.	PROPN
ejpam-4825	164	2	b.	b.	PROPN
ejpam-4825	164	3	lacpao	lacpao	PROPN
ejpam-4825	164	4	/	/	SYM
ejpam-4825	164	5	eur	eur	PROPN
ejpam-4825	164	6	.	.	PUNCT
ejpam-4825	165	1	j.	j.	PROPN
ejpam-4825	165	2	pure	pure	PROPN
ejpam-4825	165	3	appl	appl	PROPN
ejpam-4825	165	4	.	.	PROPN
ejpam-4825	165	5	math	math	PROPN
ejpam-4825	165	6	,	,	PUNCT
ejpam-4825	165	7	16	16	NUM
ejpam-4825	165	8	(	(	PUNCT
ejpam-4825	165	9	3	3	NUM
ejpam-4825	165	10	)	)	PUNCT
ejpam-4825	165	11	(	(	PUNCT
ejpam-4825	165	12	2023	2023	NUM
ejpam-4825	165	13	)	)	PUNCT
ejpam-4825	165	14	,	,	PUNCT
ejpam-4825	165	15	1747	1747	NUM
ejpam-4825	165	16	-	-	SYM
ejpam-4825	165	17	1761	1761	NUM
ejpam-4825	165	18	1754	1754	NUM
ejpam-4825	165	19	theorem	theorem	VERB
ejpam-4825	165	20	3	3	NUM
ejpam-4825	165	21	.	.	X
ejpam-4825	165	22	for	for	ADP
ejpam-4825	165	23	k	k	PROPN
ejpam-4825	165	24	∈	∈	PROPN
ejpam-4825	165	25	z	z	PROPN
ejpam-4825	165	26	,	,	PUNCT
ejpam-4825	165	27	n	n	PRON
ejpam-4825	165	28	≥	≥	NOUN
ejpam-4825	165	29	0	0	NUM
ejpam-4825	165	30	we	we	PRON
ejpam-4825	165	31	have	have	VERB
ejpam-4825	165	32	b(k	b(k	PROPN
ejpam-4825	165	33	)	)	PUNCT
ejpam-4825	165	34	n	n	CCONJ
ejpam-4825	165	35	,	,	PUNCT
ejpam-4825	165	36	a(x	a(x	PROPN
ejpam-4825	165	37	)	)	PUNCT
ejpam-4825	165	38	=	=	SYM
ejpam-4825	165	39	n∑	n∑	PROPN
ejpam-4825	165	40	s=0	s=0	PROPN
ejpam-4825	166	1	xn−s(−1)s−m	xn−s(−1)s−m	PROPN
ejpam-4825	167	1	(	(	PUNCT
ejpam-4825	167	2	n	n	X
ejpam-4825	167	3	s	s	PART
ejpam-4825	167	4	)	)	PUNCT
ejpam-4825	168	1	s∑	s∑	PROPN
ejpam-4825	168	2	m=0	m=0	PROPN
ejpam-4825	168	3	{	{	PUNCT
ejpam-4825	168	4	s	s	NOUN
ejpam-4825	168	5	m	m	VERB
ejpam-4825	168	6	}	}	PUNCT
ejpam-4825	168	7	m	m	VERB
ejpam-4825	168	8	!	!	PUNCT
ejpam-4825	169	1	(	(	PUNCT
ejpam-4825	169	2	m+	m+	NOUN
ejpam-4825	169	3	a)k	a)k	ADJ
ejpam-4825	169	4	.	.	PUNCT
ejpam-4825	170	1	proof	proof	NOUN
ejpam-4825	170	2	.	.	PUNCT
ejpam-4825	171	1	∞∑	∞∑	PRON
ejpam-4825	171	2	n=0	n=0	NUM
ejpam-4825	171	3	b(k	b(k	PROPN
ejpam-4825	171	4	)	)	PUNCT
ejpam-4825	171	5	n	n	CCONJ
ejpam-4825	171	6	,	,	PUNCT
ejpam-4825	171	7	a(x	a(x	PROPN
ejpam-4825	171	8	)	)	PUNCT
ejpam-4825	171	9	tn	tn	NOUN
ejpam-4825	171	10	n	n	NOUN
ejpam-4825	171	11	!	!	PUNCT
ejpam-4825	171	12	=	=	PUNCT
ejpam-4825	172	1	φ(1−	φ(1−	PROPN
ejpam-4825	172	2	e−t	e−t	PROPN
ejpam-4825	172	3	,	,	PUNCT
ejpam-4825	172	4	k	k	NOUN
ejpam-4825	172	5	,	,	PUNCT
ejpam-4825	172	6	a)ext	a)ext	PROPN
ejpam-4825	172	7	.	.	PUNCT
ejpam-4825	173	1	working	work	VERB
ejpam-4825	173	2	on	on	ADP
ejpam-4825	173	3	the	the	DET
ejpam-4825	173	4	right	right	ADJ
ejpam-4825	173	5	hand	hand	NOUN
ejpam-4825	173	6	side	side	NOUN
ejpam-4825	173	7	,	,	PUNCT
ejpam-4825	173	8	we	we	PRON
ejpam-4825	173	9	have	have	VERB
ejpam-4825	173	10	extφ(1−	extφ(1−	PROPN
ejpam-4825	173	11	e−t	e−t	NOUN
ejpam-4825	173	12	,	,	PUNCT
ejpam-4825	173	13	k	k	NOUN
ejpam-4825	173	14	,	,	PUNCT
ejpam-4825	173	15	a	a	PRON
ejpam-4825	173	16	)	)	PUNCT
ejpam-4825	173	17	=	=	SYM
ejpam-4825	173	18	(	(	PUNCT
ejpam-4825	173	19	∞∑	∞∑	NUM
ejpam-4825	173	20	s=0	s=0	X
ejpam-4825	173	21	(	(	PUNCT
ejpam-4825	173	22	xt)s	xt)s	PROPN
ejpam-4825	173	23	s	s	PROPN
ejpam-4825	173	24	!	!	PUNCT
ejpam-4825	173	25	)	)	PUNCT
ejpam-4825	174	1	(	(	PUNCT
ejpam-4825	174	2	∞∑	∞∑	NUM
ejpam-4825	174	3	m=0	m=0	PROPN
ejpam-4825	174	4	(	(	PUNCT
ejpam-4825	174	5	1−	1−	NUM
ejpam-4825	174	6	e−t)mr	e−t)mr	PROPN
ejpam-4825	174	7	(	(	PUNCT
ejpam-4825	174	8	m+	m+	NUM
ejpam-4825	174	9	a)k	a)k	ADJ
ejpam-4825	174	10	)	)	PUNCT
ejpam-4825	175	1	=	=	PUNCT
ejpam-4825	175	2	(	(	PUNCT
ejpam-4825	175	3	∞∑	∞∑	NUM
ejpam-4825	175	4	s=0	s=0	X
ejpam-4825	175	5	(	(	PUNCT
ejpam-4825	175	6	xt)s	xt)s	PROPN
ejpam-4825	175	7	s	s	PROPN
ejpam-4825	175	8	!	!	PUNCT
ejpam-4825	175	9	)	)	PUNCT
ejpam-4825	176	1	(	(	PUNCT
ejpam-4825	176	2	∞∑	∞∑	NUM
ejpam-4825	176	3	m=0	m=0	PROPN
ejpam-4825	176	4	(	(	PUNCT
ejpam-4825	176	5	e−t	e−t	X
ejpam-4825	176	6	−	−	PROPN
ejpam-4825	176	7	1))m(−1)m	1))m(−1)m	NUM
ejpam-4825	176	8	m	m	NOUN
ejpam-4825	176	9	!	!	PUNCT
ejpam-4825	177	1	m	m	VERB
ejpam-4825	177	2	!	!	PUNCT
ejpam-4825	178	1	(	(	PUNCT
ejpam-4825	178	2	m+	m+	NOUN
ejpam-4825	178	3	a)k	a)k	ADJ
ejpam-4825	178	4	)	)	PUNCT
ejpam-4825	179	1	=	=	PUNCT
ejpam-4825	179	2	(	(	PUNCT
ejpam-4825	179	3	∞∑	∞∑	NUM
ejpam-4825	179	4	s=0	s=0	X
ejpam-4825	179	5	(	(	PUNCT
ejpam-4825	179	6	xt)s	xt)s	PROPN
ejpam-4825	179	7	s	s	PROPN
ejpam-4825	179	8	!	!	PUNCT
ejpam-4825	179	9	)	)	PUNCT
ejpam-4825	179	10	(	(	PUNCT
ejpam-4825	179	11	∞∑	∞∑	NUM
ejpam-4825	179	12	m=0	m=0	PROPN
ejpam-4825	179	13	(	(	PUNCT
ejpam-4825	179	14	∞∑	∞∑	PROPN
ejpam-4825	179	15	n	n	NOUN
ejpam-4825	179	16	=	=	NOUN
ejpam-4825	179	17	m	m	PROPN
ejpam-4825	179	18	(	(	PUNCT
ejpam-4825	179	19	−1)n−m	−1)n−m	X
ejpam-4825	179	20	{	{	PUNCT
ejpam-4825	179	21	n	n	NOUN
ejpam-4825	179	22	m	m	VERB
ejpam-4825	179	23	}	}	PUNCT
ejpam-4825	179	24	m	m	PROPN
ejpam-4825	179	25	!	!	PUNCT
ejpam-4825	180	1	(	(	PUNCT
ejpam-4825	180	2	m+	m+	NOUN
ejpam-4825	180	3	a)k	a)k	ADJ
ejpam-4825	180	4	)	)	PUNCT
ejpam-4825	180	5	tn	tn	PROPN
ejpam-4825	180	6	n	n	PROPN
ejpam-4825	180	7	!	!	PUNCT
ejpam-4825	180	8	)	)	PUNCT
ejpam-4825	181	1	=	=	PUNCT
ejpam-4825	182	1	∞∑	∞∑	NUM
ejpam-4825	182	2	s=0	s=0	NOUN
ejpam-4825	182	3	s∑	s∑	PROPN
ejpam-4825	182	4	n=0	n=0	PRON
ejpam-4825	182	5	{	{	PUNCT
ejpam-4825	182	6	xs−n	xs−n	PROPN
ejpam-4825	182	7	(	(	PUNCT
ejpam-4825	182	8	s−	s−	PROPN
ejpam-4825	182	9	n	n	CCONJ
ejpam-4825	182	10	)	)	PUNCT
ejpam-4825	182	11	!	!	PUNCT
ejpam-4825	183	1	(	(	PUNCT
ejpam-4825	183	2	−1)n−mts−n	−1)n−mts−n	NOUN
ejpam-4825	183	3	(	(	PUNCT
ejpam-4825	183	4	n∑	n∑	PROPN
ejpam-4825	183	5	m=0	m=0	PROPN
ejpam-4825	183	6	(	(	PUNCT
ejpam-4825	183	7	{	{	PUNCT
ejpam-4825	183	8	n	n	X
ejpam-4825	183	9	m	m	VERB
ejpam-4825	183	10	}	}	PUNCT
ejpam-4825	183	11	m	m	PROPN
ejpam-4825	183	12	!	!	PUNCT
ejpam-4825	183	13	(	(	PUNCT
ejpam-4825	183	14	m+	m+	NOUN
ejpam-4825	183	15	a)k	a)k	ADJ
ejpam-4825	183	16	)	)	PUNCT
ejpam-4825	183	17	tn	tn	PROPN
ejpam-4825	183	18	n	n	PROPN
ejpam-4825	183	19	!	!	PUNCT
ejpam-4825	183	20	)	)	PUNCT
ejpam-4825	183	21	}	}	PUNCT
ejpam-4825	184	1	=	=	PUNCT
ejpam-4825	184	2	∞∑	∞∑	NUM
ejpam-4825	184	3	s=0	s=0	NOUN
ejpam-4825	184	4	s∑	s∑	PROPN
ejpam-4825	184	5	n=0	n=0	PRON
ejpam-4825	184	6	{	{	PUNCT
ejpam-4825	185	1	xs−n(−1)n−m	xs−n(−1)n−m	X
ejpam-4825	185	2	(	(	PUNCT
ejpam-4825	185	3	n∑	n∑	NOUN
ejpam-4825	185	4	m=0	m=0	PROPN
ejpam-4825	185	5	(	(	PUNCT
ejpam-4825	185	6	{	{	PUNCT
ejpam-4825	185	7	n	n	X
ejpam-4825	185	8	m	m	VERB
ejpam-4825	185	9	}	}	PUNCT
ejpam-4825	185	10	m	m	PROPN
ejpam-4825	185	11	!	!	PUNCT
ejpam-4825	186	1	(	(	PUNCT
ejpam-4825	186	2	m+	m+	NOUN
ejpam-4825	186	3	a)k	a)k	ADJ
ejpam-4825	186	4	)	)	PUNCT
ejpam-4825	187	1	s	s	X
ejpam-4825	187	2	!	!	PUNCT
ejpam-4825	188	1	(	(	PUNCT
ejpam-4825	188	2	s−	s−	PROPN
ejpam-4825	188	3	n)!n	n)!n	VERB
ejpam-4825	188	4	!	!	PUNCT
ejpam-4825	189	1	ts	ts	ADP
ejpam-4825	189	2	s	s	PROPN
ejpam-4825	189	3	!	!	PUNCT
ejpam-4825	189	4	)	)	PUNCT
ejpam-4825	189	5	}	}	PUNCT
ejpam-4825	190	1	=	=	SYM
ejpam-4825	190	2	∞∑	∞∑	NUM
ejpam-4825	190	3	s=0	s=0	X
ejpam-4825	190	4	{	{	PUNCT
ejpam-4825	190	5	s∑	s∑	PROPN
ejpam-4825	190	6	n=0	n=0	PUNCT
ejpam-4825	190	7	xs−n(−1)n−m	xs−n(−1)n−m	X
ejpam-4825	191	1	(	(	PUNCT
ejpam-4825	191	2	s	s	NOUN
ejpam-4825	191	3	n	n	NOUN
ejpam-4825	191	4	)	)	PUNCT
ejpam-4825	191	5	(	(	PUNCT
ejpam-4825	191	6	n∑	n∑	NOUN
ejpam-4825	191	7	m=0	m=0	PROPN
ejpam-4825	191	8	(	(	PUNCT
ejpam-4825	191	9	{	{	PUNCT
ejpam-4825	191	10	n	n	X
ejpam-4825	191	11	m	m	VERB
ejpam-4825	191	12	}	}	PUNCT
ejpam-4825	191	13	m	m	PROPN
ejpam-4825	191	14	!	!	PUNCT
ejpam-4825	192	1	(	(	PUNCT
ejpam-4825	192	2	m+	m+	NOUN
ejpam-4825	192	3	a)k	a)k	ADJ
ejpam-4825	192	4	)	)	PUNCT
ejpam-4825	192	5	)	)	PUNCT
ejpam-4825	192	6	}	}	PUNCT
ejpam-4825	193	1	ts	ts	ADP
ejpam-4825	193	2	s	s	PRON
ejpam-4825	193	3	!	!	PUNCT
ejpam-4825	193	4	=	=	NOUN
ejpam-4825	194	1	∞∑	∞∑	PRON
ejpam-4825	194	2	n=0	n=0	NUM
ejpam-4825	194	3	{	{	PUNCT
ejpam-4825	194	4	n∑	n∑	PROPN
ejpam-4825	194	5	s=0	s=0	PROPN
ejpam-4825	194	6	xn−s(−1)s−m	xn−s(−1)s−m	PROPN
ejpam-4825	195	1	(	(	PUNCT
ejpam-4825	195	2	n	n	NOUN
ejpam-4825	195	3	s	s	NOUN
ejpam-4825	195	4	)	)	PUNCT
ejpam-4825	195	5	(	(	PUNCT
ejpam-4825	195	6	s∑	s∑	PROPN
ejpam-4825	195	7	m=0	m=0	PROPN
ejpam-4825	195	8	(	(	PUNCT
ejpam-4825	195	9	{	{	PUNCT
ejpam-4825	195	10	s	s	VERB
ejpam-4825	195	11	m	m	VERB
ejpam-4825	195	12	}	}	PUNCT
ejpam-4825	195	13	m	m	VERB
ejpam-4825	195	14	!	!	PUNCT
ejpam-4825	196	1	(	(	PUNCT
ejpam-4825	196	2	m+	m+	NOUN
ejpam-4825	196	3	a)k	a)k	ADJ
ejpam-4825	196	4	)	)	PUNCT
ejpam-4825	196	5	)	)	PUNCT
ejpam-4825	196	6	}	}	PUNCT
ejpam-4825	196	7	tn	tn	PROPN
ejpam-4825	196	8	n	n	CCONJ
ejpam-4825	196	9	!	!	PUNCT
ejpam-4825	197	1	comparing	compare	VERB
ejpam-4825	197	2	the	the	DET
ejpam-4825	197	3	coefficients	coefficient	NOUN
ejpam-4825	197	4	gives	give	VERB
ejpam-4825	197	5	the	the	DET
ejpam-4825	197	6	result	result	NOUN
ejpam-4825	197	7	.	.	PUNCT
ejpam-4825	198	1	■	■	PUNCT
ejpam-4825	198	2	3	3	X
ejpam-4825	198	3	.	.	PUNCT
ejpam-4825	198	4	hurwitz	hurwitz	PROPN
ejpam-4825	198	5	-	-	PUNCT
ejpam-4825	198	6	lerch	lerch	PROPN
ejpam-4825	198	7	type	type	NOUN
ejpam-4825	198	8	multi	multi	ADJ
ejpam-4825	198	9	-	-	ADJ
ejpam-4825	198	10	poly	poly	ADJ
ejpam-4825	198	11	-	-	PUNCT
ejpam-4825	198	12	cauchy	cauchy	ADJ
ejpam-4825	198	13	and	and	CCONJ
ejpam-4825	198	14	multi	multi	ADJ
ejpam-4825	198	15	-	-	ADJ
ejpam-4825	198	16	poly	poly	ADJ
ejpam-4825	198	17	-	-	PUNCT
ejpam-4825	198	18	bernoulli	bernoulli	NOUN
ejpam-4825	198	19	polynomials	polynomial	NOUN
ejpam-4825	198	20	further	further	ADJ
ejpam-4825	198	21	generalization	generalization	NOUN
ejpam-4825	198	22	of	of	ADP
ejpam-4825	198	23	poly	poly	ADJ
ejpam-4825	198	24	-	-	PUNCT
ejpam-4825	198	25	cauchy	cauchy	ADJ
ejpam-4825	198	26	numbers	number	NOUN
ejpam-4825	198	27	of	of	ADP
ejpam-4825	198	28	the	the	DET
ejpam-4825	198	29	first	first	ADJ
ejpam-4825	198	30	and	and	CCONJ
ejpam-4825	198	31	second	second	ADJ
ejpam-4825	198	32	kind	kind	NOUN
ejpam-4825	198	33	was	be	AUX
ejpam-4825	198	34	defined	define	VERB
ejpam-4825	198	35	by	by	ADP
ejpam-4825	198	36	lacpao	lacpao	PROPN
ejpam-4825	198	37	et	et	PROPN
ejpam-4825	198	38	al	al	PROPN
ejpam-4825	198	39	.	.	PUNCT
ejpam-4825	199	1	[	[	X
ejpam-4825	199	2	14	14	NUM
ejpam-4825	199	3	]	]	PUNCT
ejpam-4825	199	4	in	in	ADP
ejpam-4825	199	5	polynomial	polynomial	ADJ
ejpam-4825	199	6	form	form	NOUN
ejpam-4825	199	7	by	by	ADP
ejpam-4825	199	8	means	mean	NOUN
ejpam-4825	199	9	of	of	ADP
ejpam-4825	199	10	multiple	multiple	ADJ
ejpam-4825	199	11	polylogarithm	polylogarithm	PROPN
ejpam-4825	199	12	function	function	PROPN
ejpam-4825	199	13	lik1,k2	lik1,k2	PROPN
ejpam-4825	199	14	,	,	PUNCT
ejpam-4825	199	15	·	·	PUNCT
ejpam-4825	199	16	·	·	PUNCT
ejpam-4825	199	17	·	·	PUNCT
ejpam-4825	199	18	,	,	PUNCT
ejpam-4825	199	19	kr(z	kr(z	NOUN
ejpam-4825	199	20	)	)	PUNCT
ejpam-4825	199	21	=	=	PUNCT
ejpam-4825	200	1	∑	∑	PUNCT
ejpam-4825	200	2	0	0	NUM
ejpam-4825	200	3	<	<	X
ejpam-4825	200	4	m1	m1	X
ejpam-4825	200	5	<	<	X
ejpam-4825	200	6	m2<···<mr	m2<···<mr	PROPN
ejpam-4825	200	7	zm1	zm1	PROPN
ejpam-4825	200	8	mk1	mk1	VERB
ejpam-4825	200	9	1	1	NUM
ejpam-4825	200	10	·	·	PUNCT
ejpam-4825	200	11	·	·	PUNCT
ejpam-4825	200	12	·	·	PUNCT
ejpam-4825	200	13	mkr	mkr	PROPN
ejpam-4825	200	14	r	r	NOUN
ejpam-4825	200	15	.	.	PUNCT
ejpam-4825	201	1	and	and	CCONJ
ejpam-4825	201	2	hurwitz	hurwitz	PROPN
ejpam-4825	201	3	-	-	PUNCT
ejpam-4825	201	4	lerch	lerch	PROPN
ejpam-4825	201	5	multi	multi	ADJ
ejpam-4825	201	6	-	-	ADJ
ejpam-4825	201	7	factorial	factorial	ADJ
ejpam-4825	201	8	zeta	zeta	NOUN
ejpam-4825	201	9	functions	function	NOUN
ejpam-4825	201	10	φf(z	φf(z	NUM
ejpam-4825	201	11	,	,	PUNCT
ejpam-4825	201	12	(	(	PUNCT
ejpam-4825	201	13	k1	k1	X
ejpam-4825	201	14	,	,	PUNCT
ejpam-4825	201	15	k2	k2	NOUN
ejpam-4825	201	16	,	,	PUNCT
ejpam-4825	201	17	·	·	PUNCT
ejpam-4825	201	18	·	·	PUNCT
ejpam-4825	201	19	·	·	PUNCT
ejpam-4825	201	20	,	,	PUNCT
ejpam-4825	201	21	kr	kr	PROPN
ejpam-4825	201	22	)	)	PUNCT
ejpam-4825	201	23	,	,	PUNCT
ejpam-4825	201	24	a	a	X
ejpam-4825	201	25	)	)	PUNCT
ejpam-4825	201	26	=	=	SYM
ejpam-4825	202	1	∑	∑	PUNCT
ejpam-4825	202	2	0≤m1	0≤m1	X
ejpam-4825	202	3	<	<	X
ejpam-4825	202	4	m2<···<mr	m2<···<mr	X
ejpam-4825	202	5	(	(	PUNCT
ejpam-4825	202	6	zmr	zmr	PROPN
ejpam-4825	202	7	r∏	r∏	PROPN
ejpam-4825	202	8	i=1	i=1	PROPN
ejpam-4825	202	9	1	1	NUM
ejpam-4825	202	10	mi!(mi	mi!(mi	NOUN
ejpam-4825	202	11	+	+	CCONJ
ejpam-4825	202	12	a−	a−	NOUN
ejpam-4825	202	13	r	r	NOUN
ejpam-4825	202	14	+	+	CCONJ
ejpam-4825	202	15	i)ki	i)ki	PROPN
ejpam-4825	202	16	)	)	PUNCT
ejpam-4825	202	17	,	,	PUNCT
ejpam-4825	202	18	(	(	PUNCT
ejpam-4825	202	19	4	4	X
ejpam-4825	202	20	)	)	PUNCT
ejpam-4825	202	21	n.	n.	NOUN
ejpam-4825	202	22	b.	b.	PROPN
ejpam-4825	202	23	lacpao	lacpao	PROPN
ejpam-4825	202	24	/	/	SYM
ejpam-4825	202	25	eur	eur	PROPN
ejpam-4825	202	26	.	.	PUNCT
ejpam-4825	203	1	j.	j.	PROPN
ejpam-4825	203	2	pure	pure	PROPN
ejpam-4825	203	3	appl	appl	PROPN
ejpam-4825	203	4	.	.	PROPN
ejpam-4825	203	5	math	math	PROPN
ejpam-4825	203	6	,	,	PUNCT
ejpam-4825	203	7	16	16	NUM
ejpam-4825	203	8	(	(	PUNCT
ejpam-4825	203	9	3	3	NUM
ejpam-4825	203	10	)	)	PUNCT
ejpam-4825	203	11	(	(	PUNCT
ejpam-4825	203	12	2023	2023	NUM
ejpam-4825	203	13	)	)	PUNCT
ejpam-4825	203	14	,	,	PUNCT
ejpam-4825	203	15	1747	1747	NUM
ejpam-4825	203	16	-	-	SYM
ejpam-4825	203	17	1761	1761	NUM
ejpam-4825	203	18	1755	1755	NUM
ejpam-4825	203	19	respectively	respectively	ADV
ejpam-4825	203	20	.	.	PUNCT
ejpam-4825	204	1	when	when	SCONJ
ejpam-4825	204	2	r	r	NOUN
ejpam-4825	204	3	=	=	SYM
ejpam-4825	204	4	1	1	NUM
ejpam-4825	204	5	,	,	PUNCT
ejpam-4825	204	6	(	(	PUNCT
ejpam-4825	204	7	4	4	X
ejpam-4825	204	8	)	)	PUNCT
ejpam-4825	204	9	gives	give	VERB
ejpam-4825	204	10	φf(z	φf(z	NUM
ejpam-4825	204	11	,	,	PUNCT
ejpam-4825	204	12	k1	k1	NOUN
ejpam-4825	204	13	,	,	PUNCT
ejpam-4825	204	14	a	a	PRON
ejpam-4825	204	15	)	)	PUNCT
ejpam-4825	205	1	=	=	PUNCT
ejpam-4825	205	2	∑	∑	PUNCT
ejpam-4825	205	3	0≤m1	0≤m1	NUM
ejpam-4825	205	4	zm1	zm1	PROPN
ejpam-4825	205	5	m1!(m1	m1!(m1	NOUN
ejpam-4825	206	1	+	+	CCONJ
ejpam-4825	206	2	a)k1	a)k1	PROPN
ejpam-4825	206	3	,	,	PUNCT
ejpam-4825	206	4	the	the	DET
ejpam-4825	206	5	hurwitz	hurwitz	PROPN
ejpam-4825	206	6	-	-	PUNCT
ejpam-4825	206	7	lerch	lerch	PROPN
ejpam-4825	206	8	factorial	factorial	PROPN
ejpam-4825	206	9	zeta	zeta	PROPN
ejpam-4825	206	10	function	function	NOUN
ejpam-4825	206	11	.	.	PUNCT
ejpam-4825	207	1	these	these	DET
ejpam-4825	207	2	polynomials	polynomial	NOUN
ejpam-4825	207	3	,	,	PUNCT
ejpam-4825	207	4	denoted	denote	VERB
ejpam-4825	207	5	by	by	ADP
ejpam-4825	207	6	c	c	PROPN
ejpam-4825	207	7	(	(	PUNCT
ejpam-4825	207	8	k1,k2	k1,k2	PROPN
ejpam-4825	207	9	,	,	PUNCT
ejpam-4825	207	10	·	·	PUNCT
ejpam-4825	207	11	·	·	PUNCT
ejpam-4825	207	12	·	·	PUNCT
ejpam-4825	207	13	,	,	PUNCT
ejpam-4825	207	14	kr	kr	PROPN
ejpam-4825	207	15	)	)	PUNCT
ejpam-4825	207	16	n	n	PROPN
ejpam-4825	207	17	(	(	PUNCT
ejpam-4825	207	18	x	x	X
ejpam-4825	207	19	)	)	PUNCT
ejpam-4825	207	20	and	and	CCONJ
ejpam-4825	207	21	ĉ	ĉ	PRON
ejpam-4825	207	22	(	(	PUNCT
ejpam-4825	207	23	k1,k2	k1,k2	PROPN
ejpam-4825	207	24	,	,	PUNCT
ejpam-4825	207	25	·	·	PUNCT
ejpam-4825	207	26	·	·	PUNCT
ejpam-4825	207	27	·	·	PUNCT
ejpam-4825	207	28	,	,	PUNCT
ejpam-4825	207	29	kr	kr	PROPN
ejpam-4825	207	30	)	)	PUNCT
ejpam-4825	207	31	n	n	PROPN
ejpam-4825	207	32	(	(	PUNCT
ejpam-4825	207	33	x	x	X
ejpam-4825	207	34	)	)	PUNCT
ejpam-4825	207	35	,	,	PUNCT
ejpam-4825	207	36	are	be	AUX
ejpam-4825	207	37	respectively	respectively	ADV
ejpam-4825	207	38	defined	define	VERB
ejpam-4825	207	39	by	by	ADP
ejpam-4825	207	40	(	(	PUNCT
ejpam-4825	207	41	1	1	NUM
ejpam-4825	207	42	+	+	CCONJ
ejpam-4825	207	43	t)xlifk1,k2	t)xlifk1,k2	ADV
ejpam-4825	207	44	,	,	PUNCT
ejpam-4825	207	45	·	·	PUNCT
ejpam-4825	207	46	·	·	PUNCT
ejpam-4825	207	47	·	·	PUNCT
ejpam-4825	207	48	,	,	PUNCT
ejpam-4825	207	49	kr(ln(1	kr(ln(1	PROPN
ejpam-4825	207	50	+	+	CCONJ
ejpam-4825	207	51	t	t	PROPN
ejpam-4825	207	52	)	)	PUNCT
ejpam-4825	207	53	)	)	PUNCT
ejpam-4825	208	1	=	=	PUNCT
ejpam-4825	209	1	∞∑	∞∑	ADJ
ejpam-4825	209	2	n=0	n=0	NUM
ejpam-4825	209	3	c(k1,k2	c(k1,k2	NOUN
ejpam-4825	209	4	,	,	PUNCT
ejpam-4825	209	5	·	·	PUNCT
ejpam-4825	209	6	·	·	PUNCT
ejpam-4825	209	7	·	·	PUNCT
ejpam-4825	209	8	,	,	PUNCT
ejpam-4825	209	9	kr)n	kr)n	PROPN
ejpam-4825	209	10	(	(	PUNCT
ejpam-4825	209	11	x	x	NOUN
ejpam-4825	209	12	)	)	PUNCT
ejpam-4825	209	13	tn	tn	PROPN
ejpam-4825	209	14	n	n	CCONJ
ejpam-4825	209	15	!	!	PROPN
ejpam-4825	209	16	,	,	PUNCT
ejpam-4825	209	17	lifk1,k2	lifk1,k2	PROPN
ejpam-4825	209	18	,	,	PUNCT
ejpam-4825	209	19	·	·	PUNCT
ejpam-4825	209	20	·	·	PUNCT
ejpam-4825	209	21	·	·	PUNCT
ejpam-4825	209	22	,	,	PUNCT
ejpam-4825	209	23	kr(−	kr(−	PROPN
ejpam-4825	210	1	ln(1	ln(1	PROPN
ejpam-4825	210	2	+	+	PROPN
ejpam-4825	210	3	t	t	PROPN
ejpam-4825	210	4	)	)	PUNCT
ejpam-4825	210	5	)	)	PUNCT
ejpam-4825	210	6	(	(	PUNCT
ejpam-4825	210	7	1	1	NUM
ejpam-4825	210	8	+	+	CCONJ
ejpam-4825	210	9	t)x	t)x	PUNCT
ejpam-4825	210	10	=	=	PUNCT
ejpam-4825	210	11	∞∑	∞∑	NUM
ejpam-4825	210	12	n=0	n=0	ADJ
ejpam-4825	210	13	ĉ(k1,k2	ĉ(k1,k2	NOUN
ejpam-4825	210	14	,	,	PUNCT
ejpam-4825	210	15	·	·	PUNCT
ejpam-4825	210	16	·	·	PUNCT
ejpam-4825	210	17	·	·	PUNCT
ejpam-4825	210	18	,	,	PUNCT
ejpam-4825	210	19	kr)n	kr)n	PROPN
ejpam-4825	210	20	(	(	PUNCT
ejpam-4825	210	21	x	x	NOUN
ejpam-4825	210	22	)	)	PUNCT
ejpam-4825	210	23	tn	tn	PROPN
ejpam-4825	210	24	n	n	NUM
ejpam-4825	210	25	!	!	PUNCT
ejpam-4825	210	26	.	.	PUNCT
ejpam-4825	211	1	we	we	PRON
ejpam-4825	211	2	define	define	VERB
ejpam-4825	211	3	the	the	DET
ejpam-4825	211	4	hurwitz	hurwitz	PROPN
ejpam-4825	211	5	-	-	PUNCT
ejpam-4825	211	6	lerch	lerch	PROPN
ejpam-4825	211	7	type	type	NOUN
ejpam-4825	211	8	multi	multi	ADJ
ejpam-4825	211	9	-	-	ADJ
ejpam-4825	211	10	poly	poly	ADJ
ejpam-4825	211	11	-	-	PUNCT
ejpam-4825	211	12	cauchy	cauchy	NOUN
ejpam-4825	211	13	polynomials	polynomial	NOUN
ejpam-4825	211	14	of	of	ADP
ejpam-4825	211	15	the	the	DET
ejpam-4825	211	16	first	first	ADJ
ejpam-4825	211	17	and	and	CCONJ
ejpam-4825	211	18	second	second	ADJ
ejpam-4825	211	19	kind	kind	NOUN
ejpam-4825	211	20	analogous	analogous	ADJ
ejpam-4825	211	21	to	to	ADP
ejpam-4825	211	22	the	the	DET
ejpam-4825	211	23	definitions	definition	NOUN
ejpam-4825	211	24	of	of	ADP
ejpam-4825	211	25	hurwitz	hurwitz	PROPN
ejpam-4825	211	26	-	-	PUNCT
ejpam-4825	211	27	lerch	lerch	PROPN
ejpam-4825	211	28	type	type	NOUN
ejpam-4825	211	29	poly	poly	ADJ
ejpam-4825	211	30	-	-	PUNCT
ejpam-4825	211	31	cauchy	cauchy	NOUN
ejpam-4825	211	32	polynomials	polynomial	NOUN
ejpam-4825	211	33	as	as	SCONJ
ejpam-4825	211	34	follows	follow	VERB
ejpam-4825	211	35	:	:	PUNCT
ejpam-4825	211	36	definition	definition	NOUN
ejpam-4825	211	37	4	4	NUM
ejpam-4825	211	38	.	.	PUNCT
ejpam-4825	212	1	the	the	DET
ejpam-4825	212	2	hurwitz	hurwitz	PROPN
ejpam-4825	212	3	-	-	PUNCT
ejpam-4825	212	4	lerch	lerch	PROPN
ejpam-4825	212	5	type	type	NOUN
ejpam-4825	212	6	multi	multi	ADJ
ejpam-4825	212	7	-	-	ADJ
ejpam-4825	212	8	poly	poly	ADJ
ejpam-4825	212	9	-	-	PUNCT
ejpam-4825	212	10	cauchy	cauchy	NOUN
ejpam-4825	212	11	polynomials	polynomial	NOUN
ejpam-4825	212	12	of	of	ADP
ejpam-4825	212	13	the	the	DET
ejpam-4825	212	14	first	first	ADJ
ejpam-4825	212	15	kind	kind	NOUN
ejpam-4825	212	16	are	be	AUX
ejpam-4825	212	17	defined	define	VERB
ejpam-4825	212	18	by	by	ADP
ejpam-4825	212	19	(	(	PUNCT
ejpam-4825	212	20	1	1	NUM
ejpam-4825	212	21	+	+	NUM
ejpam-4825	212	22	t)xφf(ln(1	t)xφf(ln(1	NOUN
ejpam-4825	212	23	+	+	X
ejpam-4825	212	24	t	t	NOUN
ejpam-4825	212	25	)	)	PUNCT
ejpam-4825	212	26	,	,	PUNCT
ejpam-4825	212	27	(	(	PUNCT
ejpam-4825	212	28	k1	k1	NOUN
ejpam-4825	212	29	,	,	PUNCT
ejpam-4825	212	30	k2	k2	NOUN
ejpam-4825	212	31	,	,	PUNCT
ejpam-4825	212	32	·	·	PUNCT
ejpam-4825	212	33	·	·	PUNCT
ejpam-4825	212	34	·	·	PUNCT
ejpam-4825	212	35	,	,	PUNCT
ejpam-4825	212	36	kr	kr	PROPN
ejpam-4825	212	37	)	)	PUNCT
ejpam-4825	212	38	,	,	PUNCT
ejpam-4825	212	39	a	a	X
ejpam-4825	212	40	)	)	PUNCT
ejpam-4825	212	41	=	=	PUNCT
ejpam-4825	213	1	∞∑	∞∑	PRON
ejpam-4825	213	2	n=0	n=0	NUM
ejpam-4825	213	3	c(k1,k2	c(k1,k2	NOUN
ejpam-4825	213	4	,	,	PUNCT
ejpam-4825	213	5	·	·	PUNCT
ejpam-4825	213	6	·	·	PUNCT
ejpam-4825	213	7	·	·	PUNCT
ejpam-4825	213	8	,	,	PUNCT
ejpam-4825	213	9	kr)n	kr)n	PROPN
ejpam-4825	213	10	(	(	PUNCT
ejpam-4825	213	11	x	x	X
ejpam-4825	213	12	,	,	PUNCT
ejpam-4825	213	13	a	a	PRON
ejpam-4825	213	14	)	)	PUNCT
ejpam-4825	213	15	tn	tn	NOUN
ejpam-4825	213	16	n	n	CCONJ
ejpam-4825	213	17	!	!	PUNCT
ejpam-4825	213	18	.	.	PUNCT
ejpam-4825	214	1	definition	definition	NOUN
ejpam-4825	214	2	5	5	NUM
ejpam-4825	214	3	.	.	PUNCT
ejpam-4825	215	1	the	the	DET
ejpam-4825	215	2	hurwitz	hurwitz	PROPN
ejpam-4825	215	3	-	-	PUNCT
ejpam-4825	215	4	lerch	lerch	PROPN
ejpam-4825	215	5	type	type	NOUN
ejpam-4825	215	6	multi	multi	ADJ
ejpam-4825	215	7	-	-	ADJ
ejpam-4825	215	8	poly	poly	ADJ
ejpam-4825	215	9	-	-	PUNCT
ejpam-4825	215	10	cauchy	cauchy	NOUN
ejpam-4825	215	11	polynomials	polynomial	NOUN
ejpam-4825	215	12	of	of	ADP
ejpam-4825	215	13	the	the	DET
ejpam-4825	215	14	second	second	ADJ
ejpam-4825	215	15	kind	kind	NOUN
ejpam-4825	215	16	are	be	AUX
ejpam-4825	215	17	defined	define	VERB
ejpam-4825	215	18	by	by	ADP
ejpam-4825	215	19	φf(−	φf(−	NOUN
ejpam-4825	215	20	ln(1	ln(1	PROPN
ejpam-4825	215	21	+	+	PROPN
ejpam-4825	215	22	t	t	NOUN
ejpam-4825	215	23	)	)	PUNCT
ejpam-4825	215	24	,	,	PUNCT
ejpam-4825	215	25	(	(	PUNCT
ejpam-4825	215	26	k1	k1	NOUN
ejpam-4825	215	27	,	,	PUNCT
ejpam-4825	215	28	k2	k2	NOUN
ejpam-4825	215	29	,	,	PUNCT
ejpam-4825	215	30	·	·	PUNCT
ejpam-4825	215	31	·	·	PUNCT
ejpam-4825	215	32	·	·	PUNCT
ejpam-4825	215	33	,	,	PUNCT
ejpam-4825	215	34	kr	kr	PROPN
ejpam-4825	215	35	)	)	PUNCT
ejpam-4825	215	36	,	,	PUNCT
ejpam-4825	215	37	a	a	X
ejpam-4825	215	38	)	)	PUNCT
ejpam-4825	215	39	(	(	PUNCT
ejpam-4825	215	40	1	1	NUM
ejpam-4825	215	41	+	+	CCONJ
ejpam-4825	215	42	t)x	t)x	PUNCT
ejpam-4825	215	43	=	=	PUNCT
ejpam-4825	215	44	∞∑	∞∑	NUM
ejpam-4825	215	45	n=0	n=0	ADJ
ejpam-4825	215	46	ĉ(k1,k2	ĉ(k1,k2	NOUN
ejpam-4825	215	47	,	,	PUNCT
ejpam-4825	215	48	·	·	PUNCT
ejpam-4825	215	49	·	·	PUNCT
ejpam-4825	215	50	·	·	PUNCT
ejpam-4825	215	51	,	,	PUNCT
ejpam-4825	215	52	kr)n	kr)n	PROPN
ejpam-4825	215	53	(	(	PUNCT
ejpam-4825	215	54	x	x	X
ejpam-4825	215	55	,	,	PUNCT
ejpam-4825	215	56	a	a	PRON
ejpam-4825	215	57	)	)	PUNCT
ejpam-4825	215	58	tn	tn	NOUN
ejpam-4825	215	59	n	n	CCONJ
ejpam-4825	215	60	!	!	PROPN
ejpam-4825	215	61	.	.	PUNCT
ejpam-4825	216	1	similarly	similarly	ADV
ejpam-4825	216	2	,	,	PUNCT
ejpam-4825	216	3	these	these	DET
ejpam-4825	216	4	polynomials	polynomial	NOUN
ejpam-4825	216	5	have	have	VERB
ejpam-4825	216	6	explicit	explicit	ADJ
ejpam-4825	216	7	formula	formula	NOUN
ejpam-4825	216	8	involving	involve	VERB
ejpam-4825	216	9	stirling	stirling	NOUN
ejpam-4825	216	10	numbers	number	NOUN
ejpam-4825	216	11	.	.	PUNCT
ejpam-4825	217	1	theorem	theorem	VERB
ejpam-4825	217	2	4	4	NUM
ejpam-4825	217	3	.	.	NOUN
ejpam-4825	217	4	for	for	ADP
ejpam-4825	217	5	k1	k1	NOUN
ejpam-4825	217	6	,	,	PUNCT
ejpam-4825	217	7	k2	k2	NOUN
ejpam-4825	217	8	,	,	PUNCT
ejpam-4825	217	9	·	·	PUNCT
ejpam-4825	217	10	·	·	PUNCT
ejpam-4825	217	11	·	·	PUNCT
ejpam-4825	217	12	,	,	PUNCT
ejpam-4825	217	13	kr	kr	PROPN
ejpam-4825	217	14	∈	∈	PROPN
ejpam-4825	217	15	z	z	PROPN
ejpam-4825	217	16	,	,	PUNCT
ejpam-4825	217	17	n	n	X
ejpam-4825	217	18	≥	≥	NOUN
ejpam-4825	217	19	0	0	NUM
ejpam-4825	217	20	,	,	PUNCT
ejpam-4825	217	21	we	we	PRON
ejpam-4825	217	22	have	have	VERB
ejpam-4825	217	23	cn(k1	cn(k1	NOUN
ejpam-4825	217	24	,	,	PUNCT
ejpam-4825	217	25	k2	k2	NOUN
ejpam-4825	217	26	,	,	PUNCT
ejpam-4825	217	27	·	·	PUNCT
ejpam-4825	217	28	·	·	PUNCT
ejpam-4825	217	29	·	·	PUNCT
ejpam-4825	217	30	,	,	PUNCT
ejpam-4825	217	31	kr)(x	kr)(x	PROPN
ejpam-4825	217	32	,	,	PUNCT
ejpam-4825	217	33	a	a	PRON
ejpam-4825	217	34	)	)	PUNCT
ejpam-4825	217	35	(	(	PUNCT
ejpam-4825	217	36	5	5	NUM
ejpam-4825	217	37	)	)	PUNCT
ejpam-4825	217	38	=	=	SYM
ejpam-4825	217	39	n∑	n∑	NOUN
ejpam-4825	217	40	k=0	k=0	PROPN
ejpam-4825	218	1	x	x	X
ejpam-4825	218	2	!	!	PUNCT
ejpam-4825	218	3	(	(	PUNCT
ejpam-4825	218	4	x−	x−	PROPN
ejpam-4825	218	5	k	k	PROPN
ejpam-4825	218	6	)	)	PUNCT
ejpam-4825	218	7	!	!	PUNCT
ejpam-4825	219	1	(	(	PUNCT
ejpam-4825	219	2	−1)n−k	−1)n−k	X
ejpam-4825	219	3	(	(	PUNCT
ejpam-4825	219	4	n	n	X
ejpam-4825	219	5	k	k	PROPN
ejpam-4825	219	6	)	)	PUNCT
ejpam-4825	219	7	n−k∑	n−k∑	NOUN
ejpam-4825	219	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	220	1	(	(	PUNCT
ejpam-4825	220	2	(	(	PUNCT
ejpam-4825	220	3	−1)mr	−1)mr	NOUN
ejpam-4825	220	4	[	[	PUNCT
ejpam-4825	220	5	n−k	n−k	NOUN
ejpam-4825	220	6	mr	mr	PROPN
ejpam-4825	220	7	]	]	X
ejpam-4825	220	8	(	(	PUNCT
ejpam-4825	220	9	mr	mr	PROPN
ejpam-4825	220	10	+	+	PROPN
ejpam-4825	220	11	a)kr	a)kr	PROPN
ejpam-4825	221	1	r−1∏	r−1∏	PROPN
ejpam-4825	221	2	i=1	i=1	PRON
ejpam-4825	221	3	1	1	NUM
ejpam-4825	221	4	(	(	PUNCT
ejpam-4825	221	5	mi)!(mi	mi)!(mi	X
ejpam-4825	221	6	+	+	CCONJ
ejpam-4825	221	7	a−	a−	PROPN
ejpam-4825	221	8	r	r	NOUN
ejpam-4825	221	9	+	+	PUNCT
ejpam-4825	221	10	i)ki	i)ki	PROPN
ejpam-4825	221	11	)	)	PUNCT
ejpam-4825	221	12	.	.	PUNCT
ejpam-4825	222	1	proof	proof	NOUN
ejpam-4825	222	2	.	.	PUNCT
ejpam-4825	223	1	∞∑	∞∑	PRON
ejpam-4825	223	2	n=0	n=0	NUM
ejpam-4825	223	3	cn(k1	cn(k1	NOUN
ejpam-4825	223	4	,	,	PUNCT
ejpam-4825	223	5	k2	k2	NOUN
ejpam-4825	223	6	,	,	PUNCT
ejpam-4825	223	7	·	·	PUNCT
ejpam-4825	223	8	·	·	PUNCT
ejpam-4825	223	9	·	·	PUNCT
ejpam-4825	223	10	,	,	PUNCT
ejpam-4825	223	11	kr)(x	kr)(x	PROPN
ejpam-4825	223	12	,	,	PUNCT
ejpam-4825	223	13	a	a	PRON
ejpam-4825	223	14	)	)	PUNCT
ejpam-4825	223	15	tn	tn	NOUN
ejpam-4825	223	16	n	n	NOUN
ejpam-4825	223	17	!	!	PUNCT
ejpam-4825	223	18	=	=	PUNCT
ejpam-4825	224	1	(	(	PUNCT
ejpam-4825	224	2	1	1	NUM
ejpam-4825	224	3	+	+	NUM
ejpam-4825	224	4	t)xφf(ln(1	t)xφf(ln(1	X
ejpam-4825	224	5	+	+	X
ejpam-4825	224	6	t	t	NOUN
ejpam-4825	224	7	)	)	PUNCT
ejpam-4825	224	8	,	,	PUNCT
ejpam-4825	224	9	(	(	PUNCT
ejpam-4825	224	10	k1	k1	NOUN
ejpam-4825	224	11	,	,	PUNCT
ejpam-4825	224	12	k2	k2	NOUN
ejpam-4825	224	13	,	,	PUNCT
ejpam-4825	224	14	·	·	PUNCT
ejpam-4825	224	15	·	·	PUNCT
ejpam-4825	224	16	·	·	PUNCT
ejpam-4825	224	17	,	,	PUNCT
ejpam-4825	224	18	kr	kr	PROPN
ejpam-4825	224	19	)	)	PUNCT
ejpam-4825	224	20	,	,	PUNCT
ejpam-4825	224	21	a	a	PRON
ejpam-4825	224	22	)	)	PUNCT
ejpam-4825	225	1	n.	n.	PROPN
ejpam-4825	225	2	b.	b.	PROPN
ejpam-4825	225	3	lacpao	lacpao	PROPN
ejpam-4825	225	4	/	/	SYM
ejpam-4825	225	5	eur	eur	PROPN
ejpam-4825	225	6	.	.	PUNCT
ejpam-4825	226	1	j.	j.	PROPN
ejpam-4825	226	2	pure	pure	PROPN
ejpam-4825	226	3	appl	appl	PROPN
ejpam-4825	226	4	.	.	PROPN
ejpam-4825	226	5	math	math	PROPN
ejpam-4825	226	6	,	,	PUNCT
ejpam-4825	226	7	16	16	NUM
ejpam-4825	226	8	(	(	PUNCT
ejpam-4825	226	9	3	3	NUM
ejpam-4825	226	10	)	)	PUNCT
ejpam-4825	226	11	(	(	PUNCT
ejpam-4825	226	12	2023	2023	NUM
ejpam-4825	226	13	)	)	PUNCT
ejpam-4825	226	14	,	,	PUNCT
ejpam-4825	226	15	1747	1747	NUM
ejpam-4825	226	16	-	-	SYM
ejpam-4825	226	17	1761	1761	NUM
ejpam-4825	226	18	1756	1756	NUM
ejpam-4825	226	19	working	work	VERB
ejpam-4825	226	20	on	on	ADP
ejpam-4825	226	21	the	the	DET
ejpam-4825	226	22	right	right	ADJ
ejpam-4825	226	23	hand	hand	NOUN
ejpam-4825	226	24	side	side	NOUN
ejpam-4825	226	25	,	,	PUNCT
ejpam-4825	226	26	we	we	PRON
ejpam-4825	226	27	have	have	AUX
ejpam-4825	226	28	(	(	PUNCT
ejpam-4825	226	29	1	1	NUM
ejpam-4825	226	30	+	+	NUM
ejpam-4825	226	31	t)xφf(ln(1	t)xφf(ln(1	NOUN
ejpam-4825	226	32	+	+	X
ejpam-4825	226	33	t	t	NOUN
ejpam-4825	226	34	)	)	PUNCT
ejpam-4825	226	35	,	,	PUNCT
ejpam-4825	226	36	(	(	PUNCT
ejpam-4825	226	37	k1	k1	NOUN
ejpam-4825	226	38	,	,	PUNCT
ejpam-4825	226	39	k2	k2	NOUN
ejpam-4825	226	40	,	,	PUNCT
ejpam-4825	226	41	·	·	PUNCT
ejpam-4825	226	42	·	·	PUNCT
ejpam-4825	226	43	·	·	PUNCT
ejpam-4825	226	44	,	,	PUNCT
ejpam-4825	226	45	kr	kr	PROPN
ejpam-4825	226	46	)	)	PUNCT
ejpam-4825	226	47	,	,	PUNCT
ejpam-4825	226	48	a	a	X
ejpam-4825	226	49	)	)	PUNCT
ejpam-4825	226	50	=	=	PUNCT
ejpam-4825	227	1	∞∑	∞∑	NUM
ejpam-4825	227	2	k=0	k=0	PUNCT
ejpam-4825	227	3	(	(	PUNCT
ejpam-4825	227	4	x	x	SYM
ejpam-4825	227	5	k	k	X
ejpam-4825	227	6	)	)	PUNCT
ejpam-4825	227	7	tk	tk	PROPN
ejpam-4825	227	8	∑	∑	PROPN
ejpam-4825	227	9	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	PUNCT
ejpam-4825	227	10	(	(	PUNCT
ejpam-4825	227	11	ln(1	ln(1	NOUN
ejpam-4825	227	12	+	+	NUM
ejpam-4825	227	13	t))mr	t))mr	NOUN
ejpam-4825	227	14	m1!(m1	m1!(m1	NOUN
ejpam-4825	227	15	+	+	CCONJ
ejpam-4825	227	16	a−	a−	PROPN
ejpam-4825	227	17	r	r	NOUN
ejpam-4825	227	18	+	+	CCONJ
ejpam-4825	227	19	1)k1m2!(m2	1)k1m2!(m2	NUM
ejpam-4825	227	20	+	+	CCONJ
ejpam-4825	227	21	a−	a−	PROPN
ejpam-4825	227	22	r	r	NOUN
ejpam-4825	227	23	+	+	CCONJ
ejpam-4825	227	24	2)k2	2)k2	NUM
ejpam-4825	227	25	·	·	PUNCT
ejpam-4825	227	26	·	·	PUNCT
ejpam-4825	227	27	·	·	PUNCT
ejpam-4825	227	28	mr!(mr	mr!(mr	NOUN
ejpam-4825	228	1	+	+	X
ejpam-4825	229	1	a)kr	a)kr	PROPN
ejpam-4825	229	2	=	=	PUNCT
ejpam-4825	229	3	∞∑	∞∑	NUM
ejpam-4825	229	4	k=0	k=0	PROPN
ejpam-4825	229	5	(	(	PUNCT
ejpam-4825	229	6	x	x	SYM
ejpam-4825	229	7	k	k	X
ejpam-4825	229	8	)	)	PUNCT
ejpam-4825	229	9	tk	tk	PROPN
ejpam-4825	229	10	∑	∑	PROPN
ejpam-4825	229	11	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	229	12	(	(	PUNCT
ejpam-4825	229	13	(	(	PUNCT
ejpam-4825	229	14	ln(1	ln(1	NOUN
ejpam-4825	229	15	+	+	NUM
ejpam-4825	229	16	t))mr	t))mr	NOUN
ejpam-4825	229	17	mr	mr	PROPN
ejpam-4825	229	18	!	!	PROPN
ejpam-4825	229	19	1	1	NUM
ejpam-4825	229	20	(	(	PUNCT
ejpam-4825	230	1	mr	mr	PROPN
ejpam-4825	230	2	+	+	PROPN
ejpam-4825	230	3	a)kr	a)kr	PROPN
ejpam-4825	230	4	r−1∏	r−1∏	PROPN
ejpam-4825	230	5	i=1	i=1	PRON
ejpam-4825	230	6	1	1	NUM
ejpam-4825	230	7	(	(	PUNCT
ejpam-4825	230	8	mi)!(mi	mi)!(mi	X
ejpam-4825	230	9	+	+	CCONJ
ejpam-4825	230	10	a−	a−	PROPN
ejpam-4825	230	11	r	r	NOUN
ejpam-4825	230	12	+	+	PUNCT
ejpam-4825	230	13	i)ki	i)ki	PROPN
ejpam-4825	230	14	)	)	PUNCT
ejpam-4825	231	1	=	=	PUNCT
ejpam-4825	232	1	∞∑	∞∑	NUM
ejpam-4825	232	2	k=0	k=0	PUNCT
ejpam-4825	232	3	(	(	PUNCT
ejpam-4825	232	4	x	x	SYM
ejpam-4825	232	5	k	k	X
ejpam-4825	232	6	)	)	PUNCT
ejpam-4825	232	7	tk	tk	PROPN
ejpam-4825	232	8	∑	∑	PROPN
ejpam-4825	232	9	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	PROPN
ejpam-4825	232	10	(	(	PUNCT
ejpam-4825	232	11	∞∑	∞∑	PROPN
ejpam-4825	232	12	n	n	NOUN
ejpam-4825	232	13	=	=	PRON
ejpam-4825	232	14	mr	mr	PROPN
ejpam-4825	232	15	(	(	PUNCT
ejpam-4825	232	16	−1)n−mr	−1)n−mr	PROPN
ejpam-4825	232	17	[	[	PUNCT
ejpam-4825	232	18	n	n	CCONJ
ejpam-4825	232	19	mr	mr	PROPN
ejpam-4825	232	20	]	]	PUNCT
ejpam-4825	232	21	tn	tn	PROPN
ejpam-4825	232	22	n	n	PROPN
ejpam-4825	232	23	!	!	PROPN
ejpam-4825	232	24	1	1	NUM
ejpam-4825	232	25	(	(	PUNCT
ejpam-4825	232	26	mr	mr	PROPN
ejpam-4825	232	27	+	+	PROPN
ejpam-4825	232	28	a)kr	a)kr	PROPN
ejpam-4825	232	29	r−1∏	r−1∏	ADP
ejpam-4825	232	30	i=1	i=1	PROPN
ejpam-4825	232	31	1	1	NUM
ejpam-4825	232	32	mi!(mi	mi!(mi	NOUN
ejpam-4825	232	33	+	+	CCONJ
ejpam-4825	232	34	a−	a−	NOUN
ejpam-4825	232	35	r	r	NOUN
ejpam-4825	232	36	+	+	PUNCT
ejpam-4825	232	37	i)ki	i)ki	PROPN
ejpam-4825	232	38	)	)	PUNCT
ejpam-4825	232	39	=	=	PUNCT
ejpam-4825	233	1	∞∑	∞∑	NUM
ejpam-4825	233	2	k=0	k=0	PUNCT
ejpam-4825	233	3	(	(	PUNCT
ejpam-4825	233	4	x	x	SYM
ejpam-4825	233	5	k	k	X
ejpam-4825	233	6	)	)	PUNCT
ejpam-4825	233	7	tk	tk	PROPN
ejpam-4825	233	8	∞∑	∞∑	PROPN
ejpam-4825	233	9	n=0	n=0	PROPN
ejpam-4825	233	10	n∑	n∑	NOUN
ejpam-4825	233	11	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	234	1	(	(	PUNCT
ejpam-4825	234	2	(	(	PUNCT
ejpam-4825	234	3	−1)n−mr	−1)n−mr	PROPN
ejpam-4825	234	4	[	[	PUNCT
ejpam-4825	234	5	n	n	CCONJ
ejpam-4825	234	6	mr	mr	PROPN
ejpam-4825	234	7	]	]	X
ejpam-4825	234	8	(	(	PUNCT
ejpam-4825	234	9	mr	mr	PROPN
ejpam-4825	234	10	+	+	PROPN
ejpam-4825	234	11	a)kr	a)kr	PROPN
ejpam-4825	234	12	r−1∏	r−1∏	PROPN
ejpam-4825	234	13	i=1	i=1	PRON
ejpam-4825	234	14	1	1	NUM
ejpam-4825	234	15	(	(	PUNCT
ejpam-4825	234	16	mi)!(mi	mi)!(mi	X
ejpam-4825	234	17	+	+	CCONJ
ejpam-4825	234	18	a−	a−	ADJ
ejpam-4825	234	19	r	r	NOUN
ejpam-4825	234	20	+	+	PUNCT
ejpam-4825	234	21	i)ki	i)ki	PROPN
ejpam-4825	234	22	tn	tn	PROPN
ejpam-4825	234	23	n	n	NOUN
ejpam-4825	234	24	!	!	PUNCT
ejpam-4825	234	25	)	)	PUNCT
ejpam-4825	235	1	=	=	PUNCT
ejpam-4825	236	1	∞∑	∞∑	NUM
ejpam-4825	236	2	k=0	k=0	PUNCT
ejpam-4825	236	3	(	(	PUNCT
ejpam-4825	236	4	x	x	SYM
ejpam-4825	236	5	k	k	X
ejpam-4825	236	6	)	)	PUNCT
ejpam-4825	236	7	tk	tk	PROPN
ejpam-4825	236	8	∞∑	∞∑	PROPN
ejpam-4825	236	9	n=0	n=0	NUM
ejpam-4825	236	10	(	(	PUNCT
ejpam-4825	236	11	−1)n	−1)n	PROPN
ejpam-4825	236	12	n∑	n∑	PROPN
ejpam-4825	236	13	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	237	1	(	(	PUNCT
ejpam-4825	237	2	(	(	PUNCT
ejpam-4825	237	3	−1)mr	−1)mr	X
ejpam-4825	237	4	[	[	PUNCT
ejpam-4825	237	5	n	n	CCONJ
ejpam-4825	237	6	mr	mr	PROPN
ejpam-4825	237	7	]	]	X
ejpam-4825	237	8	(	(	PUNCT
ejpam-4825	237	9	mr	mr	PROPN
ejpam-4825	237	10	+	+	PROPN
ejpam-4825	237	11	a)kr	a)kr	PROPN
ejpam-4825	237	12	r−1∏	r−1∏	PROPN
ejpam-4825	237	13	i=1	i=1	PRON
ejpam-4825	237	14	1	1	NUM
ejpam-4825	237	15	(	(	PUNCT
ejpam-4825	237	16	mi)!(mi	mi)!(mi	X
ejpam-4825	237	17	+	+	CCONJ
ejpam-4825	237	18	a−	a−	PROPN
ejpam-4825	237	19	r	r	NOUN
ejpam-4825	237	20	+	+	CCONJ
ejpam-4825	237	21	i)ki	i)ki	PROPN
ejpam-4825	237	22	)	)	PUNCT
ejpam-4825	237	23	tn	tn	PROPN
ejpam-4825	237	24	n	n	ADV
ejpam-4825	237	25	!	!	PUNCT
ejpam-4825	237	26	=	=	NOUN
ejpam-4825	238	1	∞∑	∞∑	PRON
ejpam-4825	238	2	k=0	k=0	PUNCT
ejpam-4825	238	3	∞∑	∞∑	ADJ
ejpam-4825	238	4	n=0	n=0	NUM
ejpam-4825	238	5	x	x	X
ejpam-4825	238	6	!	!	PUNCT
ejpam-4825	239	1	(	(	PUNCT
ejpam-4825	240	1	x−	x−	PROPN
ejpam-4825	240	2	k	k	PROPN
ejpam-4825	240	3	)	)	PUNCT
ejpam-4825	240	4	!	!	PUNCT
ejpam-4825	241	1	(	(	PUNCT
ejpam-4825	241	2	−1)n	−1)n	PROPN
ejpam-4825	241	3	n∑	n∑	NOUN
ejpam-4825	241	4	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	241	5	(	(	PUNCT
ejpam-4825	241	6	(	(	PUNCT
ejpam-4825	241	7	−1)mr	−1)mr	X
ejpam-4825	241	8	[	[	PUNCT
ejpam-4825	241	9	n	n	CCONJ
ejpam-4825	241	10	mr	mr	PROPN
ejpam-4825	241	11	]	]	X
ejpam-4825	241	12	(	(	PUNCT
ejpam-4825	241	13	mr	mr	PROPN
ejpam-4825	241	14	+	+	PROPN
ejpam-4825	241	15	a)kr	a)kr	PROPN
ejpam-4825	241	16	r−1∏	r−1∏	PROPN
ejpam-4825	241	17	i=1	i=1	PRON
ejpam-4825	241	18	1	1	NUM
ejpam-4825	241	19	(	(	PUNCT
ejpam-4825	241	20	mi)!(mi	mi)!(mi	X
ejpam-4825	241	21	+	+	CCONJ
ejpam-4825	241	22	a−	a−	PROPN
ejpam-4825	241	23	r	r	NOUN
ejpam-4825	241	24	+	+	PUNCT
ejpam-4825	241	25	i)ki	i)ki	PROPN
ejpam-4825	241	26	)	)	PUNCT
ejpam-4825	241	27	tn+k(n+	tn+k(n+	PROPN
ejpam-4825	242	1	k	k	X
ejpam-4825	242	2	)	)	PUNCT
ejpam-4825	242	3	!	!	PUNCT
ejpam-4825	243	1	k!n!(n+	k!n!(n+	PROPN
ejpam-4825	244	1	k	k	X
ejpam-4825	244	2	)	)	PUNCT
ejpam-4825	244	3	!	!	PUNCT
ejpam-4825	245	1	=	=	PUNCT
ejpam-4825	246	1	∞∑	∞∑	DET
ejpam-4825	246	2	k=0	k=0	PUNCT
ejpam-4825	246	3	∞∑	∞∑	NUM
ejpam-4825	246	4	n	n	X
ejpam-4825	246	5	=	=	X
ejpam-4825	246	6	k	k	NOUN
ejpam-4825	246	7	x	x	X
ejpam-4825	246	8	!	!	PUNCT
ejpam-4825	246	9	(	(	PUNCT
ejpam-4825	246	10	x−	x−	PROPN
ejpam-4825	246	11	k	k	PROPN
ejpam-4825	246	12	)	)	PUNCT
ejpam-4825	246	13	!	!	PUNCT
ejpam-4825	247	1	(	(	PUNCT
ejpam-4825	247	2	−1)n−k	−1)n−k	VERB
ejpam-4825	247	3	n−k∑	n−k∑	NOUN
ejpam-4825	247	4	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	248	1	(	(	PUNCT
ejpam-4825	248	2	(	(	PUNCT
ejpam-4825	248	3	−1)mr	−1)mr	NOUN
ejpam-4825	248	4	[	[	PUNCT
ejpam-4825	248	5	n−k	n−k	NOUN
ejpam-4825	248	6	mr	mr	PROPN
ejpam-4825	248	7	]	]	X
ejpam-4825	248	8	(	(	PUNCT
ejpam-4825	248	9	mr	mr	PROPN
ejpam-4825	248	10	+	+	PROPN
ejpam-4825	248	11	a)kr	a)kr	PROPN
ejpam-4825	248	12	r−1∏	r−1∏	PROPN
ejpam-4825	248	13	i=1	i=1	PRON
ejpam-4825	248	14	1	1	NUM
ejpam-4825	248	15	(	(	PUNCT
ejpam-4825	248	16	mi)!(mi	mi)!(mi	X
ejpam-4825	248	17	+	+	CCONJ
ejpam-4825	248	18	a−	a−	PROPN
ejpam-4825	248	19	r	r	NOUN
ejpam-4825	248	20	+	+	CCONJ
ejpam-4825	248	21	i)ki	i)ki	PROPN
ejpam-4825	248	22	)	)	PUNCT
ejpam-4825	248	23	tnn	tnn	PROPN
ejpam-4825	248	24	!	!	PUNCT
ejpam-4825	248	25	k!(n−	k!(n−	PROPN
ejpam-4825	248	26	k)!n	k)!n	VERB
ejpam-4825	248	27	!	!	PUNCT
ejpam-4825	249	1	=	=	NOUN
ejpam-4825	250	1	∞∑	∞∑	PRON
ejpam-4825	250	2	n=0	n=0	NUM
ejpam-4825	250	3	{	{	PUNCT
ejpam-4825	250	4	n∑	n∑	NOUN
ejpam-4825	250	5	k=0	k=0	PROPN
ejpam-4825	250	6	x	x	X
ejpam-4825	250	7	!	!	PUNCT
ejpam-4825	250	8	(	(	PUNCT
ejpam-4825	250	9	x−	x−	PROPN
ejpam-4825	250	10	k	k	PROPN
ejpam-4825	250	11	)	)	PUNCT
ejpam-4825	250	12	!	!	PUNCT
ejpam-4825	251	1	(	(	PUNCT
ejpam-4825	251	2	−1)n−k	−1)n−k	X
ejpam-4825	251	3	(	(	PUNCT
ejpam-4825	251	4	n	n	X
ejpam-4825	251	5	k	k	PROPN
ejpam-4825	251	6	)	)	PUNCT
ejpam-4825	251	7	n−k∑	n−k∑	NOUN
ejpam-4825	251	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	252	1	(	(	PUNCT
ejpam-4825	252	2	(	(	PUNCT
ejpam-4825	252	3	−1)mr	−1)mr	NOUN
ejpam-4825	252	4	[	[	PUNCT
ejpam-4825	252	5	n−k	n−k	NOUN
ejpam-4825	252	6	mr	mr	PROPN
ejpam-4825	252	7	]	]	X
ejpam-4825	252	8	(	(	PUNCT
ejpam-4825	252	9	mr	mr	PROPN
ejpam-4825	252	10	+	+	PROPN
ejpam-4825	252	11	a)kr	a)kr	PROPN
ejpam-4825	252	12	r−1∏	r−1∏	PROPN
ejpam-4825	252	13	i=1	i=1	PRON
ejpam-4825	252	14	1	1	NUM
ejpam-4825	252	15	(	(	PUNCT
ejpam-4825	252	16	mi)!(mi	mi)!(mi	X
ejpam-4825	252	17	+	+	CCONJ
ejpam-4825	252	18	a−	a−	PROPN
ejpam-4825	252	19	r	r	NOUN
ejpam-4825	252	20	+	+	CCONJ
ejpam-4825	252	21	i)ki	i)ki	PROPN
ejpam-4825	252	22	)	)	PUNCT
ejpam-4825	252	23	}	}	PUNCT
ejpam-4825	252	24	tn	tn	PROPN
ejpam-4825	252	25	n	n	X
ejpam-4825	252	26	!	!	PUNCT
ejpam-4825	252	27	.	.	PUNCT
ejpam-4825	253	1	it	it	PRON
ejpam-4825	253	2	follows	follow	VERB
ejpam-4825	253	3	that	that	SCONJ
ejpam-4825	253	4	∞∑	∞∑	NUM
ejpam-4825	253	5	n=0	n=0	NUM
ejpam-4825	253	6	cn(k1	cn(k1	NOUN
ejpam-4825	253	7	,	,	PUNCT
ejpam-4825	253	8	k2	k2	NOUN
ejpam-4825	253	9	,	,	PUNCT
ejpam-4825	253	10	·	·	PUNCT
ejpam-4825	253	11	·	·	PUNCT
ejpam-4825	253	12	·	·	PUNCT
ejpam-4825	253	13	,	,	PUNCT
ejpam-4825	253	14	kr)(x	kr)(x	PROPN
ejpam-4825	253	15	,	,	PUNCT
ejpam-4825	253	16	a	a	PRON
ejpam-4825	253	17	)	)	PUNCT
ejpam-4825	253	18	tn	tn	PROPN
ejpam-4825	253	19	n	n	PROPN
ejpam-4825	253	20	!	!	PUNCT
ejpam-4825	254	1	n.	n.	PROPN
ejpam-4825	254	2	b.	b.	PROPN
ejpam-4825	255	1	lacpao	lacpao	PROPN
ejpam-4825	255	2	/	/	SYM
ejpam-4825	255	3	eur	eur	PROPN
ejpam-4825	255	4	.	.	PUNCT
ejpam-4825	256	1	j.	j.	PROPN
ejpam-4825	256	2	pure	pure	PROPN
ejpam-4825	256	3	appl	appl	PROPN
ejpam-4825	256	4	.	.	PROPN
ejpam-4825	256	5	math	math	PROPN
ejpam-4825	256	6	,	,	PUNCT
ejpam-4825	256	7	16	16	NUM
ejpam-4825	256	8	(	(	PUNCT
ejpam-4825	256	9	3	3	NUM
ejpam-4825	256	10	)	)	PUNCT
ejpam-4825	256	11	(	(	PUNCT
ejpam-4825	256	12	2023	2023	NUM
ejpam-4825	256	13	)	)	PUNCT
ejpam-4825	256	14	,	,	PUNCT
ejpam-4825	256	15	1747	1747	NUM
ejpam-4825	256	16	-	-	SYM
ejpam-4825	256	17	1761	1761	NUM
ejpam-4825	256	18	1757	1757	NUM
ejpam-4825	256	19	=	=	PUNCT
ejpam-4825	257	1	∞∑	∞∑	NUM
ejpam-4825	257	2	n=0	n=0	NUM
ejpam-4825	257	3	{	{	PUNCT
ejpam-4825	257	4	n∑	n∑	NOUN
ejpam-4825	257	5	k=0	k=0	PROPN
ejpam-4825	257	6	x	x	X
ejpam-4825	257	7	!	!	PUNCT
ejpam-4825	257	8	(	(	PUNCT
ejpam-4825	257	9	x−	x−	PROPN
ejpam-4825	257	10	k	k	PROPN
ejpam-4825	257	11	)	)	PUNCT
ejpam-4825	257	12	!	!	PUNCT
ejpam-4825	258	1	(	(	PUNCT
ejpam-4825	258	2	−1)n−k	−1)n−k	X
ejpam-4825	258	3	(	(	PUNCT
ejpam-4825	258	4	n	n	X
ejpam-4825	258	5	k	k	PROPN
ejpam-4825	258	6	)	)	PUNCT
ejpam-4825	258	7	n−k∑	n−k∑	NOUN
ejpam-4825	258	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	259	1	(	(	PUNCT
ejpam-4825	259	2	(	(	PUNCT
ejpam-4825	259	3	−1)mr	−1)mr	NOUN
ejpam-4825	259	4	[	[	PUNCT
ejpam-4825	259	5	n−k	n−k	NOUN
ejpam-4825	259	6	mr	mr	PROPN
ejpam-4825	259	7	]	]	X
ejpam-4825	259	8	(	(	PUNCT
ejpam-4825	259	9	mr	mr	PROPN
ejpam-4825	259	10	+	+	PROPN
ejpam-4825	259	11	a)kr	a)kr	PROPN
ejpam-4825	259	12	r−1∏	r−1∏	PROPN
ejpam-4825	259	13	i=1	i=1	PRON
ejpam-4825	259	14	1	1	NUM
ejpam-4825	259	15	(	(	PUNCT
ejpam-4825	259	16	mi)!(mi	mi)!(mi	X
ejpam-4825	259	17	+	+	CCONJ
ejpam-4825	259	18	a−	a−	PROPN
ejpam-4825	259	19	r	r	NOUN
ejpam-4825	259	20	+	+	CCONJ
ejpam-4825	259	21	i)ki	i)ki	PROPN
ejpam-4825	259	22	)	)	PUNCT
ejpam-4825	259	23	}	}	PUNCT
ejpam-4825	259	24	tn	tn	PROPN
ejpam-4825	259	25	n	n	X
ejpam-4825	259	26	!	!	PUNCT
ejpam-4825	259	27	.	.	PUNCT
ejpam-4825	260	1	equating	equate	VERB
ejpam-4825	260	2	the	the	DET
ejpam-4825	260	3	coefficients	coefficient	NOUN
ejpam-4825	260	4	gives	give	VERB
ejpam-4825	260	5	the	the	DET
ejpam-4825	260	6	result	result	NOUN
ejpam-4825	260	7	.	.	PUNCT
ejpam-4825	261	1	■	■	PUNCT
ejpam-4825	261	2	theorem	theorem	ADJ
ejpam-4825	261	3	5	5	NUM
ejpam-4825	261	4	.	.	NOUN
ejpam-4825	261	5	for	for	ADP
ejpam-4825	261	6	k1	k1	NOUN
ejpam-4825	261	7	,	,	PUNCT
ejpam-4825	261	8	k2	k2	NOUN
ejpam-4825	261	9	,	,	PUNCT
ejpam-4825	261	10	·	·	PUNCT
ejpam-4825	261	11	·	·	PUNCT
ejpam-4825	261	12	·	·	PUNCT
ejpam-4825	261	13	,	,	PUNCT
ejpam-4825	261	14	kr	kr	PROPN
ejpam-4825	261	15	∈	∈	PROPN
ejpam-4825	261	16	z	z	PROPN
ejpam-4825	261	17	,	,	PUNCT
ejpam-4825	261	18	n	n	X
ejpam-4825	261	19	≥	≥	NOUN
ejpam-4825	261	20	0	0	NUM
ejpam-4825	261	21	,	,	PUNCT
ejpam-4825	261	22	we	we	PRON
ejpam-4825	261	23	have	have	VERB
ejpam-4825	261	24	ĉn(k1	ĉn(k1	PROPN
ejpam-4825	261	25	,	,	PUNCT
ejpam-4825	261	26	k2	k2	NOUN
ejpam-4825	261	27	,	,	PUNCT
ejpam-4825	261	28	·	·	PUNCT
ejpam-4825	261	29	·	·	PUNCT
ejpam-4825	261	30	·	·	PUNCT
ejpam-4825	261	31	,	,	PUNCT
ejpam-4825	261	32	kr)(x	kr)(x	PROPN
ejpam-4825	261	33	,	,	PUNCT
ejpam-4825	261	34	a	a	PRON
ejpam-4825	261	35	)	)	PUNCT
ejpam-4825	261	36	=	=	SYM
ejpam-4825	261	37	n∑	n∑	NOUN
ejpam-4825	261	38	k=0	k=0	PROPN
ejpam-4825	261	39	(	(	PUNCT
ejpam-4825	261	40	x+	x+	X
ejpam-4825	261	41	k	k	NOUN
ejpam-4825	261	42	−	−	NOUN
ejpam-4825	261	43	1	1	NUM
ejpam-4825	261	44	)	)	PUNCT
ejpam-4825	261	45	!	!	PUNCT
ejpam-4825	262	1	(	(	PUNCT
ejpam-4825	262	2	x−	x−	PROPN
ejpam-4825	262	3	k	k	PROPN
ejpam-4825	262	4	)	)	PUNCT
ejpam-4825	262	5	!	!	PUNCT
ejpam-4825	263	1	(	(	PUNCT
ejpam-4825	263	2	−1)n	−1)n	X
ejpam-4825	263	3	(	(	PUNCT
ejpam-4825	263	4	n	n	X
ejpam-4825	263	5	k	k	PROPN
ejpam-4825	263	6	)	)	PUNCT
ejpam-4825	263	7	n−k∑	n−k∑	NOUN
ejpam-4825	263	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	264	1	(	(	PUNCT
ejpam-4825	264	2	[	[	PUNCT
ejpam-4825	264	3	n−k	n−k	NOUN
ejpam-4825	264	4	mr	mr	PROPN
ejpam-4825	264	5	]	]	X
ejpam-4825	264	6	(	(	PUNCT
ejpam-4825	264	7	mr	mr	PROPN
ejpam-4825	264	8	+	+	PROPN
ejpam-4825	264	9	a)kr	a)kr	PROPN
ejpam-4825	264	10	r−1∏	r−1∏	ADP
ejpam-4825	264	11	i=1	i=1	PROPN
ejpam-4825	264	12	1	1	NUM
ejpam-4825	264	13	mi!(mi	mi!(mi	NOUN
ejpam-4825	264	14	+	+	CCONJ
ejpam-4825	264	15	a−	a−	NOUN
ejpam-4825	264	16	r	r	NOUN
ejpam-4825	264	17	+	+	PUNCT
ejpam-4825	264	18	i)ki	i)ki	PROPN
ejpam-4825	264	19	)	)	PUNCT
ejpam-4825	264	20	.	.	PUNCT
ejpam-4825	265	1	proof	proof	NOUN
ejpam-4825	265	2	.	.	PUNCT
ejpam-4825	266	1	∞∑	∞∑	PRON
ejpam-4825	266	2	n=0	n=0	NUM
ejpam-4825	266	3	cn(k1	cn(k1	NOUN
ejpam-4825	266	4	,	,	PUNCT
ejpam-4825	266	5	k2	k2	NOUN
ejpam-4825	266	6	,	,	PUNCT
ejpam-4825	266	7	·	·	PUNCT
ejpam-4825	266	8	·	·	PUNCT
ejpam-4825	266	9	·	·	PUNCT
ejpam-4825	266	10	,	,	PUNCT
ejpam-4825	266	11	kr)(x	kr)(x	PROPN
ejpam-4825	266	12	,	,	PUNCT
ejpam-4825	266	13	a	a	PRON
ejpam-4825	266	14	)	)	PUNCT
ejpam-4825	266	15	tn	tn	NOUN
ejpam-4825	266	16	n	n	NOUN
ejpam-4825	266	17	!	!	PUNCT
ejpam-4825	267	1	=	=	SYM
ejpam-4825	267	2	1	1	NUM
ejpam-4825	267	3	(	(	PUNCT
ejpam-4825	267	4	1	1	NUM
ejpam-4825	267	5	+	+	CCONJ
ejpam-4825	267	6	t)x	t)x	PUNCT
ejpam-4825	267	7	φf(−	φf(−	ADV
ejpam-4825	268	1	ln(1	ln(1	PROPN
ejpam-4825	268	2	+	+	NUM
ejpam-4825	268	3	t	t	NOUN
ejpam-4825	268	4	)	)	PUNCT
ejpam-4825	268	5	,	,	PUNCT
ejpam-4825	268	6	(	(	PUNCT
ejpam-4825	268	7	k1	k1	NOUN
ejpam-4825	268	8	,	,	PUNCT
ejpam-4825	268	9	k2	k2	NOUN
ejpam-4825	268	10	,	,	PUNCT
ejpam-4825	268	11	·	·	PUNCT
ejpam-4825	268	12	·	·	PUNCT
ejpam-4825	268	13	·	·	PUNCT
ejpam-4825	268	14	,	,	PUNCT
ejpam-4825	268	15	kr	kr	PROPN
ejpam-4825	268	16	)	)	PUNCT
ejpam-4825	268	17	,	,	PUNCT
ejpam-4825	268	18	a	a	X
ejpam-4825	268	19	)	)	PUNCT
ejpam-4825	268	20	working	work	VERB
ejpam-4825	268	21	on	on	ADP
ejpam-4825	268	22	the	the	DET
ejpam-4825	268	23	right	right	ADJ
ejpam-4825	268	24	hand	hand	NOUN
ejpam-4825	268	25	side	side	NOUN
ejpam-4825	268	26	,	,	PUNCT
ejpam-4825	268	27	we	we	PRON
ejpam-4825	268	28	have	have	VERB
ejpam-4825	268	29	1	1	NUM
ejpam-4825	268	30	(	(	PUNCT
ejpam-4825	268	31	1	1	NUM
ejpam-4825	268	32	+	+	CCONJ
ejpam-4825	268	33	t)x	t)x	PUNCT
ejpam-4825	268	34	φf(−	φf(−	ADV
ejpam-4825	269	1	ln(1	ln(1	PROPN
ejpam-4825	269	2	+	+	NUM
ejpam-4825	269	3	t	t	NOUN
ejpam-4825	269	4	)	)	PUNCT
ejpam-4825	269	5	,	,	PUNCT
ejpam-4825	269	6	(	(	PUNCT
ejpam-4825	269	7	k1	k1	NOUN
ejpam-4825	269	8	,	,	PUNCT
ejpam-4825	269	9	k2	k2	NOUN
ejpam-4825	269	10	,	,	PUNCT
ejpam-4825	269	11	·	·	PUNCT
ejpam-4825	269	12	·	·	PUNCT
ejpam-4825	269	13	·	·	PUNCT
ejpam-4825	269	14	,	,	PUNCT
ejpam-4825	269	15	kr	kr	PROPN
ejpam-4825	269	16	)	)	PUNCT
ejpam-4825	269	17	,	,	PUNCT
ejpam-4825	269	18	a	a	X
ejpam-4825	269	19	)	)	PUNCT
ejpam-4825	270	1	=	=	PUNCT
ejpam-4825	271	1	∞∑	∞∑	NUM
ejpam-4825	271	2	k=0	k=0	PROPN
ejpam-4825	271	3	(	(	PUNCT
ejpam-4825	271	4	x+	x+	X
ejpam-4825	271	5	k	k	NOUN
ejpam-4825	271	6	−	−	PROPN
ejpam-4825	271	7	1	1	NUM
ejpam-4825	271	8	k	k	NOUN
ejpam-4825	271	9	)	)	PUNCT
ejpam-4825	271	10	(	(	PUNCT
ejpam-4825	271	11	−1)ktk	−1)ktk	PROPN
ejpam-4825	271	12	∑	∑	PUNCT
ejpam-4825	271	13	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	271	14	(	(	PUNCT
ejpam-4825	271	15	−	−	PROPN
ejpam-4825	271	16	ln(1	ln(1	NOUN
ejpam-4825	271	17	+	+	NUM
ejpam-4825	271	18	t))mr	t))mr	NOUN
ejpam-4825	271	19	m1!(m1	m1!(m1	NOUN
ejpam-4825	271	20	+	+	CCONJ
ejpam-4825	271	21	a−	a−	PROPN
ejpam-4825	271	22	r	r	NOUN
ejpam-4825	271	23	+	+	CCONJ
ejpam-4825	271	24	1)k1m2!(m2	1)k1m2!(m2	NUM
ejpam-4825	271	25	+	+	CCONJ
ejpam-4825	271	26	a−	a−	PROPN
ejpam-4825	271	27	r	r	NOUN
ejpam-4825	271	28	+	+	CCONJ
ejpam-4825	271	29	2)k2	2)k2	NUM
ejpam-4825	271	30	·	·	PUNCT
ejpam-4825	271	31	·	·	PUNCT
ejpam-4825	271	32	·	·	PUNCT
ejpam-4825	271	33	mr!(mr	mr!(mr	NOUN
ejpam-4825	271	34	+	+	X
ejpam-4825	272	1	a)kr	a)kr	PROPN
ejpam-4825	272	2	=	=	PUNCT
ejpam-4825	272	3	∞∑	∞∑	NUM
ejpam-4825	272	4	k=0	k=0	PROPN
ejpam-4825	272	5	(	(	PUNCT
ejpam-4825	272	6	x+	x+	X
ejpam-4825	272	7	k	k	NOUN
ejpam-4825	272	8	−	−	PROPN
ejpam-4825	272	9	1	1	NUM
ejpam-4825	272	10	k	k	NOUN
ejpam-4825	272	11	)	)	PUNCT
ejpam-4825	272	12	(	(	PUNCT
ejpam-4825	272	13	−1)ktk	−1)ktk	PROPN
ejpam-4825	272	14	∑	∑	PUNCT
ejpam-4825	272	15	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	273	1	(	(	PUNCT
ejpam-4825	273	2	(	(	PUNCT
ejpam-4825	273	3	ln(1	ln(1	NOUN
ejpam-4825	273	4	+	+	NUM
ejpam-4825	273	5	t))mr(−1)mr	t))mr(−1)mr	NOUN
ejpam-4825	273	6	mr	mr	PROPN
ejpam-4825	273	7	!	!	PROPN
ejpam-4825	273	8	1	1	NUM
ejpam-4825	273	9	(	(	PUNCT
ejpam-4825	273	10	mr	mr	PROPN
ejpam-4825	273	11	+	+	PROPN
ejpam-4825	273	12	a)kr	a)kr	PROPN
ejpam-4825	273	13	r−1∏	r−1∏	ADP
ejpam-4825	273	14	i=1	i=1	PROPN
ejpam-4825	273	15	1	1	NUM
ejpam-4825	273	16	mi!(mi	mi!(mi	NOUN
ejpam-4825	273	17	+	+	CCONJ
ejpam-4825	273	18	a−	a−	NOUN
ejpam-4825	273	19	r	r	NOUN
ejpam-4825	273	20	+	+	PUNCT
ejpam-4825	273	21	i)ki	i)ki	PROPN
ejpam-4825	273	22	)	)	PUNCT
ejpam-4825	273	23	=	=	PUNCT
ejpam-4825	274	1	∞∑	∞∑	NUM
ejpam-4825	274	2	k=0	k=0	PROPN
ejpam-4825	274	3	(	(	PUNCT
ejpam-4825	274	4	x+	x+	X
ejpam-4825	274	5	k	k	NOUN
ejpam-4825	274	6	−	−	PROPN
ejpam-4825	274	7	1	1	NUM
ejpam-4825	274	8	k	k	NOUN
ejpam-4825	274	9	)	)	PUNCT
ejpam-4825	274	10	(	(	PUNCT
ejpam-4825	274	11	−1)ktk	−1)ktk	PROPN
ejpam-4825	274	12	∑	∑	PUNCT
ejpam-4825	274	13	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	274	14	(	(	PUNCT
ejpam-4825	274	15	∞∑	∞∑	NUM
ejpam-4825	274	16	n	n	NOUN
ejpam-4825	274	17	=	=	PRON
ejpam-4825	274	18	mr	mr	PROPN
ejpam-4825	274	19	(	(	PUNCT
ejpam-4825	274	20	−1)n−mr	−1)n−mr	PROPN
ejpam-4825	274	21	[	[	PUNCT
ejpam-4825	274	22	n	n	CCONJ
ejpam-4825	274	23	mr	mr	PROPN
ejpam-4825	274	24	]	]	PUNCT
ejpam-4825	274	25	(	(	PUNCT
ejpam-4825	274	26	−1)mr	−1)mr	PROPN
ejpam-4825	274	27	tn	tn	NOUN
ejpam-4825	274	28	n	n	CCONJ
ejpam-4825	274	29	!	!	PROPN
ejpam-4825	274	30	1	1	NUM
ejpam-4825	274	31	(	(	PUNCT
ejpam-4825	274	32	mr	mr	PROPN
ejpam-4825	274	33	+	+	PROPN
ejpam-4825	274	34	a)kr	a)kr	PROPN
ejpam-4825	274	35	r−1∏	r−1∏	ADP
ejpam-4825	274	36	i=1	i=1	PROPN
ejpam-4825	274	37	1	1	NUM
ejpam-4825	274	38	mi!(mi	mi!(mi	NOUN
ejpam-4825	274	39	+	+	CCONJ
ejpam-4825	274	40	a−	a−	NOUN
ejpam-4825	274	41	r	r	NOUN
ejpam-4825	274	42	+	+	PUNCT
ejpam-4825	274	43	i)ki	i)ki	PROPN
ejpam-4825	274	44	)	)	PUNCT
ejpam-4825	274	45	=	=	PUNCT
ejpam-4825	275	1	∞∑	∞∑	NUM
ejpam-4825	275	2	k=0	k=0	PROPN
ejpam-4825	275	3	(	(	PUNCT
ejpam-4825	275	4	x+	x+	X
ejpam-4825	275	5	k	k	NOUN
ejpam-4825	275	6	−	−	PROPN
ejpam-4825	275	7	1	1	NUM
ejpam-4825	275	8	k	k	NOUN
ejpam-4825	275	9	)	)	PUNCT
ejpam-4825	275	10	(	(	PUNCT
ejpam-4825	275	11	−1)ktk	−1)ktk	PROPN
ejpam-4825	275	12	n.	n.	PROPN
ejpam-4825	275	13	b.	b.	PROPN
ejpam-4825	275	14	lacpao	lacpao	PROPN
ejpam-4825	275	15	/	/	SYM
ejpam-4825	275	16	eur	eur	PROPN
ejpam-4825	275	17	.	.	PUNCT
ejpam-4825	276	1	j.	j.	PROPN
ejpam-4825	276	2	pure	pure	PROPN
ejpam-4825	276	3	appl	appl	PROPN
ejpam-4825	276	4	.	.	PROPN
ejpam-4825	276	5	math	math	PROPN
ejpam-4825	276	6	,	,	PUNCT
ejpam-4825	276	7	16	16	NUM
ejpam-4825	276	8	(	(	PUNCT
ejpam-4825	276	9	3	3	NUM
ejpam-4825	276	10	)	)	PUNCT
ejpam-4825	276	11	(	(	PUNCT
ejpam-4825	276	12	2023	2023	NUM
ejpam-4825	276	13	)	)	PUNCT
ejpam-4825	276	14	,	,	PUNCT
ejpam-4825	276	15	1747	1747	NUM
ejpam-4825	276	16	-	-	SYM
ejpam-4825	276	17	1761	1761	NUM
ejpam-4825	276	18	1758	1758	NUM
ejpam-4825	276	19	∞∑	∞∑	PROPN
ejpam-4825	276	20	n=0	n=0	PROPN
ejpam-4825	276	21	n∑	n∑	NOUN
ejpam-4825	276	22	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	276	23	(	(	PUNCT
ejpam-4825	276	24	(	(	PUNCT
ejpam-4825	276	25	−1)n	−1)n	X
ejpam-4825	276	26	[	[	PUNCT
ejpam-4825	276	27	n	n	CCONJ
ejpam-4825	276	28	mr	mr	PROPN
ejpam-4825	276	29	]	]	X
ejpam-4825	276	30	(	(	PUNCT
ejpam-4825	277	1	mr	mr	PROPN
ejpam-4825	277	2	+	+	PROPN
ejpam-4825	277	3	a)kr	a)kr	PROPN
ejpam-4825	277	4	r−1∏	r−1∏	ADP
ejpam-4825	277	5	i=1	i=1	PROPN
ejpam-4825	277	6	1	1	NUM
ejpam-4825	277	7	mi!(mi	mi!(mi	NOUN
ejpam-4825	277	8	+	+	CCONJ
ejpam-4825	277	9	a−	a−	NOUN
ejpam-4825	277	10	r	r	NOUN
ejpam-4825	277	11	+	+	PUNCT
ejpam-4825	277	12	i)ki	i)ki	PROPN
ejpam-4825	277	13	tn	tn	PROPN
ejpam-4825	277	14	n	n	NOUN
ejpam-4825	277	15	!	!	PUNCT
ejpam-4825	277	16	)	)	PUNCT
ejpam-4825	278	1	=	=	PUNCT
ejpam-4825	279	1	∞∑	∞∑	NUM
ejpam-4825	279	2	k=0	k=0	PROPN
ejpam-4825	279	3	(	(	PUNCT
ejpam-4825	279	4	x+	x+	X
ejpam-4825	279	5	k	k	NOUN
ejpam-4825	279	6	−	−	PROPN
ejpam-4825	279	7	1	1	NUM
ejpam-4825	279	8	k	k	NOUN
ejpam-4825	279	9	)	)	PUNCT
ejpam-4825	279	10	(	(	PUNCT
ejpam-4825	279	11	−1)ktk	−1)ktk	PROPN
ejpam-4825	279	12	∞∑	∞∑	PROPN
ejpam-4825	279	13	n=0	n=0	NUM
ejpam-4825	279	14	(	(	PUNCT
ejpam-4825	279	15	−1)n	−1)n	PROPN
ejpam-4825	279	16	n∑	n∑	NOUN
ejpam-4825	279	17	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	279	18	(	(	PUNCT
ejpam-4825	279	19	[	[	PUNCT
ejpam-4825	279	20	n	n	CCONJ
ejpam-4825	279	21	mr	mr	PROPN
ejpam-4825	279	22	]	]	X
ejpam-4825	279	23	(	(	PUNCT
ejpam-4825	279	24	mr	mr	PROPN
ejpam-4825	279	25	+	+	PROPN
ejpam-4825	279	26	a)kr	a)kr	PROPN
ejpam-4825	279	27	r−1∏	r−1∏	ADP
ejpam-4825	279	28	i=1	i=1	PROPN
ejpam-4825	279	29	1	1	NUM
ejpam-4825	279	30	mi!(mi	mi!(mi	NOUN
ejpam-4825	279	31	+	+	CCONJ
ejpam-4825	279	32	a−	a−	NOUN
ejpam-4825	279	33	r	r	NOUN
ejpam-4825	279	34	+	+	CCONJ
ejpam-4825	279	35	i)ki	i)ki	PROPN
ejpam-4825	279	36	)	)	PUNCT
ejpam-4825	279	37	tn	tn	PROPN
ejpam-4825	279	38	n	n	ADV
ejpam-4825	279	39	!	!	PUNCT
ejpam-4825	279	40	=	=	NOUN
ejpam-4825	280	1	∞∑	∞∑	PRON
ejpam-4825	280	2	k=0	k=0	PUNCT
ejpam-4825	280	3	∞∑	∞∑	NUM
ejpam-4825	280	4	n=0	n=0	NUM
ejpam-4825	280	5	(	(	PUNCT
ejpam-4825	280	6	x+	x+	X
ejpam-4825	280	7	k	k	NOUN
ejpam-4825	280	8	−	−	NOUN
ejpam-4825	280	9	1	1	NUM
ejpam-4825	280	10	)	)	PUNCT
ejpam-4825	280	11	!	!	PUNCT
ejpam-4825	281	1	(	(	PUNCT
ejpam-4825	281	2	x−	x−	PROPN
ejpam-4825	281	3	1	1	NUM
ejpam-4825	281	4	)	)	PUNCT
ejpam-4825	281	5	!	!	PUNCT
ejpam-4825	282	1	(	(	PUNCT
ejpam-4825	282	2	−1)n+k	−1)n+k	NUM
ejpam-4825	282	3	n∑	n∑	PRON
ejpam-4825	282	4	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	283	1	(	(	PUNCT
ejpam-4825	283	2	[	[	PUNCT
ejpam-4825	283	3	n	n	CCONJ
ejpam-4825	283	4	mr	mr	PROPN
ejpam-4825	283	5	]	]	X
ejpam-4825	283	6	(	(	PUNCT
ejpam-4825	283	7	mr	mr	PROPN
ejpam-4825	283	8	+	+	PROPN
ejpam-4825	283	9	a)kr	a)kr	PROPN
ejpam-4825	283	10	r−1∏	r−1∏	ADP
ejpam-4825	283	11	i=1	i=1	PROPN
ejpam-4825	283	12	1	1	NUM
ejpam-4825	283	13	mi!(mi	mi!(mi	NOUN
ejpam-4825	283	14	+	+	CCONJ
ejpam-4825	283	15	a−	a−	NOUN
ejpam-4825	283	16	r	r	NOUN
ejpam-4825	283	17	+	+	CCONJ
ejpam-4825	283	18	i)ki	i)ki	PROPN
ejpam-4825	283	19	)	)	PUNCT
ejpam-4825	283	20	tn+k(n+	tn+k(n+	PROPN
ejpam-4825	284	1	k	k	X
ejpam-4825	284	2	)	)	PUNCT
ejpam-4825	284	3	!	!	PUNCT
ejpam-4825	285	1	k!n!(n+	k!n!(n+	PROPN
ejpam-4825	286	1	k	k	X
ejpam-4825	286	2	)	)	PUNCT
ejpam-4825	286	3	!	!	PUNCT
ejpam-4825	287	1	=	=	PUNCT
ejpam-4825	288	1	∞∑	∞∑	DET
ejpam-4825	288	2	k=0	k=0	PUNCT
ejpam-4825	288	3	∞∑	∞∑	NUM
ejpam-4825	288	4	n	n	X
ejpam-4825	288	5	=	=	SYM
ejpam-4825	288	6	k	k	X
ejpam-4825	288	7	(	(	PUNCT
ejpam-4825	288	8	x+	x+	PROPN
ejpam-4825	288	9	k	k	NOUN
ejpam-4825	288	10	−	−	NOUN
ejpam-4825	288	11	1	1	NUM
ejpam-4825	288	12	)	)	PUNCT
ejpam-4825	288	13	!	!	PUNCT
ejpam-4825	289	1	(	(	PUNCT
ejpam-4825	289	2	x−	x−	PROPN
ejpam-4825	289	3	1	1	NUM
ejpam-4825	289	4	)	)	PUNCT
ejpam-4825	289	5	!	!	PUNCT
ejpam-4825	290	1	(	(	PUNCT
ejpam-4825	290	2	−1)n	−1)n	PROPN
ejpam-4825	290	3	n−k∑	n−k∑	NOUN
ejpam-4825	290	4	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	290	5	(	(	PUNCT
ejpam-4825	290	6	[	[	PUNCT
ejpam-4825	290	7	n−k	n−k	NOUN
ejpam-4825	290	8	mr	mr	PROPN
ejpam-4825	290	9	]	]	X
ejpam-4825	290	10	(	(	PUNCT
ejpam-4825	290	11	mr	mr	PROPN
ejpam-4825	290	12	+	+	PROPN
ejpam-4825	290	13	a)kr	a)kr	PROPN
ejpam-4825	290	14	r−1∏	r−1∏	ADP
ejpam-4825	290	15	i=1	i=1	PROPN
ejpam-4825	290	16	1	1	NUM
ejpam-4825	290	17	mi!(mi	mi!(mi	NOUN
ejpam-4825	290	18	+	+	CCONJ
ejpam-4825	290	19	a−	a−	NOUN
ejpam-4825	290	20	r	r	NOUN
ejpam-4825	290	21	+	+	CCONJ
ejpam-4825	290	22	i)ki	i)ki	PROPN
ejpam-4825	290	23	)	)	PUNCT
ejpam-4825	290	24	tnn	tnn	PROPN
ejpam-4825	290	25	!	!	PUNCT
ejpam-4825	290	26	k!(n−	k!(n−	PROPN
ejpam-4825	290	27	k)!n	k)!n	VERB
ejpam-4825	290	28	!	!	PUNCT
ejpam-4825	291	1	=	=	NOUN
ejpam-4825	292	1	∞∑	∞∑	PRON
ejpam-4825	292	2	n=0	n=0	NUM
ejpam-4825	292	3	{	{	PUNCT
ejpam-4825	292	4	n∑	n∑	NOUN
ejpam-4825	292	5	k=0	k=0	PROPN
ejpam-4825	292	6	(	(	PUNCT
ejpam-4825	292	7	x+	x+	X
ejpam-4825	292	8	k	k	NOUN
ejpam-4825	292	9	−	−	NOUN
ejpam-4825	292	10	1	1	NUM
ejpam-4825	292	11	)	)	PUNCT
ejpam-4825	292	12	!	!	PUNCT
ejpam-4825	293	1	(	(	PUNCT
ejpam-4825	293	2	x−	x−	PROPN
ejpam-4825	293	3	1	1	NUM
ejpam-4825	293	4	)	)	PUNCT
ejpam-4825	293	5	!	!	PUNCT
ejpam-4825	294	1	(	(	PUNCT
ejpam-4825	294	2	−1)n	−1)n	X
ejpam-4825	294	3	(	(	PUNCT
ejpam-4825	294	4	n	n	X
ejpam-4825	294	5	k	k	PROPN
ejpam-4825	294	6	)	)	PUNCT
ejpam-4825	294	7	n−k∑	n−k∑	NOUN
ejpam-4825	294	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	295	1	(	(	PUNCT
ejpam-4825	295	2	[	[	PUNCT
ejpam-4825	295	3	n−k	n−k	NOUN
ejpam-4825	295	4	mr	mr	PROPN
ejpam-4825	295	5	]	]	X
ejpam-4825	295	6	(	(	PUNCT
ejpam-4825	295	7	mr	mr	PROPN
ejpam-4825	295	8	+	+	PROPN
ejpam-4825	295	9	a)kr	a)kr	PROPN
ejpam-4825	295	10	r−1∏	r−1∏	ADP
ejpam-4825	295	11	i=1	i=1	PROPN
ejpam-4825	295	12	1	1	NUM
ejpam-4825	295	13	mi!(mi	mi!(mi	NOUN
ejpam-4825	295	14	+	+	CCONJ
ejpam-4825	295	15	a−	a−	NOUN
ejpam-4825	295	16	r	r	NOUN
ejpam-4825	295	17	+	+	CCONJ
ejpam-4825	295	18	i)ki	i)ki	PROPN
ejpam-4825	295	19	)	)	PUNCT
ejpam-4825	295	20	}	}	PUNCT
ejpam-4825	295	21	tn	tn	PROPN
ejpam-4825	295	22	n	n	X
ejpam-4825	295	23	!	!	PUNCT
ejpam-4825	295	24	.	.	PUNCT
ejpam-4825	296	1	it	it	PRON
ejpam-4825	296	2	follows	follow	VERB
ejpam-4825	296	3	that	that	SCONJ
ejpam-4825	296	4	∞∑	∞∑	NUM
ejpam-4825	296	5	n=0	n=0	NUM
ejpam-4825	296	6	ĉn(k1	ĉn(k1	PROPN
ejpam-4825	296	7	,	,	PUNCT
ejpam-4825	296	8	k2	k2	NOUN
ejpam-4825	296	9	,	,	PUNCT
ejpam-4825	296	10	·	·	PUNCT
ejpam-4825	296	11	·	·	PUNCT
ejpam-4825	296	12	·	·	PUNCT
ejpam-4825	296	13	,	,	PUNCT
ejpam-4825	296	14	kr)(x	kr)(x	PROPN
ejpam-4825	296	15	,	,	PUNCT
ejpam-4825	296	16	a	a	PRON
ejpam-4825	296	17	)	)	PUNCT
ejpam-4825	296	18	tn	tn	NOUN
ejpam-4825	296	19	n	n	NOUN
ejpam-4825	296	20	!	!	PUNCT
ejpam-4825	296	21	=	=	NOUN
ejpam-4825	297	1	∞∑	∞∑	PRON
ejpam-4825	297	2	n=0	n=0	NUM
ejpam-4825	297	3	{	{	PUNCT
ejpam-4825	297	4	n∑	n∑	NOUN
ejpam-4825	297	5	k=0	k=0	PROPN
ejpam-4825	297	6	(	(	PUNCT
ejpam-4825	297	7	x+	x+	X
ejpam-4825	297	8	k	k	NOUN
ejpam-4825	297	9	−	−	NOUN
ejpam-4825	297	10	1	1	NUM
ejpam-4825	297	11	)	)	PUNCT
ejpam-4825	297	12	!	!	PUNCT
ejpam-4825	298	1	(	(	PUNCT
ejpam-4825	298	2	x−	x−	PROPN
ejpam-4825	298	3	1	1	NUM
ejpam-4825	298	4	)	)	PUNCT
ejpam-4825	298	5	!	!	PUNCT
ejpam-4825	299	1	(	(	PUNCT
ejpam-4825	299	2	−1)n	−1)n	X
ejpam-4825	299	3	(	(	PUNCT
ejpam-4825	299	4	n	n	X
ejpam-4825	299	5	k	k	PROPN
ejpam-4825	299	6	)	)	PUNCT
ejpam-4825	299	7	n−k∑	n−k∑	NOUN
ejpam-4825	299	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	300	1	(	(	PUNCT
ejpam-4825	300	2	[	[	PUNCT
ejpam-4825	300	3	n−k	n−k	NOUN
ejpam-4825	300	4	mr	mr	PROPN
ejpam-4825	300	5	]	]	X
ejpam-4825	300	6	(	(	PUNCT
ejpam-4825	300	7	mr	mr	PROPN
ejpam-4825	300	8	+	+	PROPN
ejpam-4825	300	9	a)kr	a)kr	PROPN
ejpam-4825	300	10	r−1∏	r−1∏	ADP
ejpam-4825	300	11	i=1	i=1	PROPN
ejpam-4825	300	12	1	1	NUM
ejpam-4825	300	13	mi!(mi	mi!(mi	NOUN
ejpam-4825	300	14	+	+	CCONJ
ejpam-4825	300	15	a−	a−	NOUN
ejpam-4825	300	16	r	r	NOUN
ejpam-4825	300	17	+	+	CCONJ
ejpam-4825	300	18	i)ki	i)ki	PROPN
ejpam-4825	300	19	)	)	PUNCT
ejpam-4825	300	20	}	}	PUNCT
ejpam-4825	300	21	tn	tn	PROPN
ejpam-4825	300	22	n	n	X
ejpam-4825	300	23	!	!	PUNCT
ejpam-4825	300	24	.	.	PUNCT
ejpam-4825	301	1	the	the	DET
ejpam-4825	301	2	result	result	NOUN
ejpam-4825	301	3	follows	follow	VERB
ejpam-4825	301	4	by	by	ADP
ejpam-4825	301	5	comparing	compare	VERB
ejpam-4825	301	6	the	the	DET
ejpam-4825	301	7	coefficients	coefficient	NOUN
ejpam-4825	301	8	.	.	PUNCT
ejpam-4825	302	1	■	■	PUNCT
ejpam-4825	302	2	corcino	corcino	NOUN
ejpam-4825	302	3	et	et	PROPN
ejpam-4825	302	4	.	.	PUNCT
ejpam-4825	303	1	al	al	PROPN
ejpam-4825	303	2	.	.	PROPN
ejpam-4825	303	3	defined	define	VERB
ejpam-4825	303	4	the	the	DET
ejpam-4825	303	5	hurwitz	hurwitz	PROPN
ejpam-4825	303	6	-	-	PUNCT
ejpam-4825	303	7	lerch	lerch	PROPN
ejpam-4825	303	8	multi	multi	ADJ
ejpam-4825	303	9	-	-	ADJ
ejpam-4825	303	10	poly	poly	ADJ
ejpam-4825	303	11	bernoulli	bernoulli	NOUN
ejpam-4825	303	12	polynomials	polynomial	NOUN
ejpam-4825	303	13	as	as	SCONJ
ejpam-4825	303	14	follows	follow	VERB
ejpam-4825	303	15	:	:	PUNCT
ejpam-4825	303	16	the	the	DET
ejpam-4825	303	17	hurwitz	hurwitz	PROPN
ejpam-4825	303	18	-	-	PUNCT
ejpam-4825	303	19	lerch	lerch	PROPN
ejpam-4825	303	20	type	type	NOUN
ejpam-4825	303	21	multi	multi	ADJ
ejpam-4825	303	22	-	-	ADJ
ejpam-4825	303	23	poly	poly	ADJ
ejpam-4825	303	24	-	-	PUNCT
ejpam-4825	303	25	bernoulli	bernoulli	NOUN
ejpam-4825	303	26	numbers	number	NOUN
ejpam-4825	303	27	b	b	PROPN
ejpam-4825	303	28	(	(	PUNCT
ejpam-4825	303	29	k1,k2	k1,k2	PROPN
ejpam-4825	303	30	,	,	PUNCT
ejpam-4825	303	31	·	·	PUNCT
ejpam-4825	303	32	·	·	PUNCT
ejpam-4825	303	33	·	·	PUNCT
ejpam-4825	303	34	,	,	PUNCT
ejpam-4825	303	35	kr	kr	PROPN
ejpam-4825	303	36	)	)	PUNCT
ejpam-4825	303	37	n	n	CCONJ
ejpam-4825	303	38	(	(	PUNCT
ejpam-4825	303	39	a	a	X
ejpam-4825	303	40	)	)	PUNCT
ejpam-4825	303	41	are	be	AUX
ejpam-4825	303	42	defined	define	VERB
ejpam-4825	303	43	by	by	ADP
ejpam-4825	303	44	the	the	DET
ejpam-4825	303	45	generating	generate	VERB
ejpam-4825	303	46	function	function	NOUN
ejpam-4825	303	47	φ((1−	φ((1−	NUM
ejpam-4825	303	48	e−t	e−t	NOUN
ejpam-4825	303	49	)	)	PUNCT
ejpam-4825	303	50	,	,	PUNCT
ejpam-4825	303	51	(	(	PUNCT
ejpam-4825	303	52	k1	k1	NOUN
ejpam-4825	303	53	,	,	PUNCT
ejpam-4825	303	54	k2	k2	NOUN
ejpam-4825	303	55	,	,	PUNCT
ejpam-4825	303	56	·	·	PUNCT
ejpam-4825	303	57	·	·	PUNCT
ejpam-4825	303	58	·	·	PUNCT
ejpam-4825	303	59	,	,	PUNCT
ejpam-4825	303	60	kr	kr	PROPN
ejpam-4825	303	61	)	)	PUNCT
ejpam-4825	303	62	,	,	PUNCT
ejpam-4825	303	63	a	a	X
ejpam-4825	303	64	)	)	PUNCT
ejpam-4825	304	1	=	=	PUNCT
ejpam-4825	305	1	∞∑	∞∑	PRON
ejpam-4825	305	2	n=0	n=0	NUM
ejpam-4825	305	3	b(k1,k2	b(k1,k2	NOUN
ejpam-4825	305	4	,	,	PUNCT
ejpam-4825	305	5	·	·	PUNCT
ejpam-4825	305	6	·	·	PUNCT
ejpam-4825	305	7	·	·	PUNCT
ejpam-4825	305	8	,	,	PUNCT
ejpam-4825	305	9	kr	kr	PROPN
ejpam-4825	305	10	)	)	PUNCT
ejpam-4825	305	11	n	n	CCONJ
ejpam-4825	305	12	(	(	PUNCT
ejpam-4825	305	13	a	a	X
ejpam-4825	305	14	)	)	PUNCT
ejpam-4825	305	15	tn	tn	NOUN
ejpam-4825	305	16	n	n	NUM
ejpam-4825	305	17	!	!	PUNCT
ejpam-4825	305	18	.	.	PUNCT
ejpam-4825	306	1	(	(	PUNCT
ejpam-4825	306	2	6	6	X
ejpam-4825	306	3	)	)	PUNCT
ejpam-4825	306	4	n.	n.	PROPN
ejpam-4825	306	5	b.	b.	PROPN
ejpam-4825	306	6	lacpao	lacpao	PROPN
ejpam-4825	306	7	/	/	SYM
ejpam-4825	306	8	eur	eur	PROPN
ejpam-4825	306	9	.	.	PUNCT
ejpam-4825	307	1	j.	j.	PROPN
ejpam-4825	307	2	pure	pure	PROPN
ejpam-4825	307	3	appl	appl	PROPN
ejpam-4825	307	4	.	.	PROPN
ejpam-4825	307	5	math	math	PROPN
ejpam-4825	307	6	,	,	PUNCT
ejpam-4825	307	7	16	16	NUM
ejpam-4825	307	8	(	(	PUNCT
ejpam-4825	307	9	3	3	NUM
ejpam-4825	307	10	)	)	PUNCT
ejpam-4825	307	11	(	(	PUNCT
ejpam-4825	307	12	2023	2023	NUM
ejpam-4825	307	13	)	)	PUNCT
ejpam-4825	307	14	,	,	PUNCT
ejpam-4825	307	15	1747	1747	NUM
ejpam-4825	307	16	-	-	SYM
ejpam-4825	307	17	1761	1761	NUM
ejpam-4825	307	18	1759	1759	NUM
ejpam-4825	307	19	they	they	PRON
ejpam-4825	307	20	established	establish	VERB
ejpam-4825	307	21	an	an	DET
ejpam-4825	307	22	explicit	explicit	ADJ
ejpam-4825	307	23	formula	formula	NOUN
ejpam-4825	307	24	of	of	ADP
ejpam-4825	307	25	hurwitz	hurwitz	PROPN
ejpam-4825	307	26	-	-	PUNCT
ejpam-4825	307	27	lerch	lerch	PROPN
ejpam-4825	307	28	multi	multi	ADJ
ejpam-4825	307	29	-	-	ADJ
ejpam-4825	307	30	poly	poly	ADJ
ejpam-4825	307	31	-	-	PUNCT
ejpam-4825	307	32	bernoulli	bernoulli	NOUN
ejpam-4825	307	33	polynomials	polynomial	NOUN
ejpam-4825	307	34	in	in	ADP
ejpam-4825	307	35	[	[	X
ejpam-4825	307	36	9	9	NUM
ejpam-4825	307	37	,	,	PUNCT
ejpam-4825	307	38	theorem	theorem	VERB
ejpam-4825	307	39	3.1	3.1	NUM
ejpam-4825	307	40	]	]	PUNCT
ejpam-4825	307	41	.	.	PUNCT
ejpam-4825	308	1	parallel	parallel	ADJ
ejpam-4825	308	2	to	to	ADP
ejpam-4825	308	3	this	this	PRON
ejpam-4825	308	4	,	,	PUNCT
ejpam-4825	308	5	we	we	PRON
ejpam-4825	308	6	obtained	obtain	VERB
ejpam-4825	308	7	an	an	DET
ejpam-4825	308	8	explicit	explicit	ADJ
ejpam-4825	308	9	formula	formula	NOUN
ejpam-4825	308	10	of	of	ADP
ejpam-4825	308	11	hurwitz	hurwitz	PROPN
ejpam-4825	308	12	-	-	PUNCT
ejpam-4825	308	13	lerch	lerch	PROPN
ejpam-4825	308	14	multipoly	multipoly	PROPN
ejpam-4825	308	15	-	-	PUNCT
ejpam-4825	308	16	bernoulli	bernoulli	NOUN
ejpam-4825	308	17	-	-	PUNCT
ejpam-4825	308	18	polynomials	polynomial	NOUN
ejpam-4825	308	19	in	in	ADP
ejpam-4825	308	20	terms	term	NOUN
ejpam-4825	308	21	of	of	ADP
ejpam-4825	308	22	stirling	stirling	NOUN
ejpam-4825	308	23	numbers	number	NOUN
ejpam-4825	308	24	of	of	ADP
ejpam-4825	308	25	the	the	DET
ejpam-4825	308	26	second	second	ADJ
ejpam-4825	308	27	kind	kind	NOUN
ejpam-4825	308	28	as	as	SCONJ
ejpam-4825	308	29	follows	follow	VERB
ejpam-4825	308	30	:	:	PUNCT
ejpam-4825	308	31	theorem	theorem	NOUN
ejpam-4825	308	32	6	6	NUM
ejpam-4825	308	33	.	.	PUNCT
ejpam-4825	308	34	for	for	ADP
ejpam-4825	308	35	k1	k1	NOUN
ejpam-4825	308	36	,	,	PUNCT
ejpam-4825	308	37	k2	k2	NOUN
ejpam-4825	308	38	,	,	PUNCT
ejpam-4825	308	39	·	·	PUNCT
ejpam-4825	308	40	·	·	PUNCT
ejpam-4825	308	41	·	·	PUNCT
ejpam-4825	308	42	,	,	PUNCT
ejpam-4825	308	43	kr	kr	PROPN
ejpam-4825	308	44	∈	∈	PROPN
ejpam-4825	308	45	z	z	PROPN
ejpam-4825	308	46	,	,	PUNCT
ejpam-4825	308	47	n	n	X
ejpam-4825	308	48	≥	≥	NOUN
ejpam-4825	308	49	0	0	NUM
ejpam-4825	308	50	,	,	PUNCT
ejpam-4825	308	51	we	we	PRON
ejpam-4825	308	52	have	have	VERB
ejpam-4825	308	53	b(k1,k2	b(k1,k2	NOUN
ejpam-4825	308	54	,	,	PUNCT
ejpam-4825	308	55	·	·	PUNCT
ejpam-4825	308	56	·	·	PUNCT
ejpam-4825	308	57	·	·	PUNCT
ejpam-4825	308	58	,	,	PUNCT
ejpam-4825	308	59	kr	kr	PROPN
ejpam-4825	308	60	)	)	PUNCT
ejpam-4825	308	61	n	n	PROPN
ejpam-4825	308	62	(	(	PUNCT
ejpam-4825	308	63	x	x	X
ejpam-4825	308	64	,	,	PUNCT
ejpam-4825	308	65	a	a	NOUN
ejpam-4825	308	66	)	)	PUNCT
ejpam-4825	308	67	=	=	SYM
ejpam-4825	309	1	n∑	n∑	NOUN
ejpam-4825	309	2	k=0	k=0	PROPN
ejpam-4825	309	3	(	(	PUNCT
ejpam-4825	309	4	rx)k(−1)n−k	rx)k(−1)n−k	PROPN
ejpam-4825	309	5	(	(	PUNCT
ejpam-4825	309	6	n	n	X
ejpam-4825	309	7	k	k	PROPN
ejpam-4825	309	8	)	)	PUNCT
ejpam-4825	309	9	n−k∑	n−k∑	NOUN
ejpam-4825	309	10	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	310	1	(	(	PUNCT
ejpam-4825	310	2	(	(	PUNCT
ejpam-4825	310	3	−1)mrmr	−1)mrmr	X
ejpam-4825	310	4	!	!	PUNCT
ejpam-4825	310	5	{	{	PUNCT
ejpam-4825	310	6	n−k	n−k	NOUN
ejpam-4825	310	7	mr	mr	PROPN
ejpam-4825	310	8	}	}	PUNCT
ejpam-4825	310	9	(	(	PUNCT
ejpam-4825	311	1	mr	mr	PROPN
ejpam-4825	311	2	+	+	PROPN
ejpam-4825	311	3	a)kr	a)kr	PROPN
ejpam-4825	311	4	r−1∏	r−1∏	PROPN
ejpam-4825	311	5	i=1	i=1	PRON
ejpam-4825	311	6	1	1	NUM
ejpam-4825	311	7	(	(	PUNCT
ejpam-4825	311	8	mi	mi	NOUN
ejpam-4825	311	9	+	+	CCONJ
ejpam-4825	311	10	a−	a−	PROPN
ejpam-4825	311	11	r	r	NOUN
ejpam-4825	311	12	+	+	CCONJ
ejpam-4825	311	13	i)ki	i)ki	PROPN
ejpam-4825	311	14	)	)	PUNCT
ejpam-4825	311	15	proof	proof	NOUN
ejpam-4825	311	16	.	.	PUNCT
ejpam-4825	312	1	∞∑	∞∑	PRON
ejpam-4825	312	2	n=0	n=0	PROPN
ejpam-4825	312	3	b(k1,k2	b(k1,k2	NOUN
ejpam-4825	312	4	,	,	PUNCT
ejpam-4825	312	5	·	·	PUNCT
ejpam-4825	312	6	·	·	PUNCT
ejpam-4825	312	7	·	·	PUNCT
ejpam-4825	312	8	,	,	PUNCT
ejpam-4825	312	9	kr	kr	PROPN
ejpam-4825	312	10	)	)	PUNCT
ejpam-4825	312	11	n	n	PROPN
ejpam-4825	312	12	(	(	PUNCT
ejpam-4825	312	13	x	x	X
ejpam-4825	312	14	,	,	PUNCT
ejpam-4825	312	15	a	a	PRON
ejpam-4825	312	16	)	)	PUNCT
ejpam-4825	312	17	tn	tn	NOUN
ejpam-4825	312	18	n	n	NOUN
ejpam-4825	312	19	!	!	PUNCT
ejpam-4825	312	20	=	=	SYM
ejpam-4825	313	1	erxtφ(1−	erxtφ(1−	NOUN
ejpam-4825	313	2	e−t	e−t	NOUN
ejpam-4825	313	3	,	,	PUNCT
ejpam-4825	313	4	(	(	PUNCT
ejpam-4825	313	5	k1	k1	NOUN
ejpam-4825	313	6	,	,	PUNCT
ejpam-4825	313	7	k2	k2	NOUN
ejpam-4825	313	8	,	,	PUNCT
ejpam-4825	313	9	·	·	PUNCT
ejpam-4825	313	10	·	·	PUNCT
ejpam-4825	313	11	·	·	PUNCT
ejpam-4825	313	12	,	,	PUNCT
ejpam-4825	313	13	kr	kr	PROPN
ejpam-4825	313	14	)	)	PUNCT
ejpam-4825	313	15	,	,	PUNCT
ejpam-4825	313	16	a	a	X
ejpam-4825	313	17	)	)	PUNCT
ejpam-4825	313	18	working	work	VERB
ejpam-4825	313	19	on	on	ADP
ejpam-4825	313	20	the	the	DET
ejpam-4825	313	21	right	right	ADJ
ejpam-4825	313	22	hand	hand	NOUN
ejpam-4825	313	23	side	side	NOUN
ejpam-4825	313	24	,	,	PUNCT
ejpam-4825	313	25	we	we	PRON
ejpam-4825	313	26	get	get	VERB
ejpam-4825	313	27	erxtφ(1−	erxtφ(1−	NOUN
ejpam-4825	313	28	e−t	e−t	NOUN
ejpam-4825	313	29	,	,	PUNCT
ejpam-4825	313	30	(	(	PUNCT
ejpam-4825	313	31	k1	k1	NOUN
ejpam-4825	313	32	,	,	PUNCT
ejpam-4825	313	33	k2	k2	NOUN
ejpam-4825	313	34	,	,	PUNCT
ejpam-4825	313	35	·	·	PUNCT
ejpam-4825	313	36	·	·	PUNCT
ejpam-4825	313	37	·	·	PUNCT
ejpam-4825	313	38	,	,	PUNCT
ejpam-4825	313	39	kr	kr	PROPN
ejpam-4825	313	40	)	)	PUNCT
ejpam-4825	313	41	,	,	PUNCT
ejpam-4825	313	42	a	a	X
ejpam-4825	313	43	)	)	PUNCT
ejpam-4825	313	44	=	=	PUNCT
ejpam-4825	314	1	∞∑	∞∑	NUM
ejpam-4825	314	2	k=0	k=0	PROPN
ejpam-4825	314	3	(	(	PUNCT
ejpam-4825	314	4	rxt)k	rxt)k	PROPN
ejpam-4825	314	5	k	k	X
ejpam-4825	314	6	!	!	PUNCT
ejpam-4825	314	7	∑	∑	PUNCT
ejpam-4825	314	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	314	9	(	(	PUNCT
ejpam-4825	314	10	1−	1−	NUM
ejpam-4825	314	11	e−t)mr	e−t)mr	PROPN
ejpam-4825	314	12	(	(	PUNCT
ejpam-4825	314	13	m1	m1	PROPN
ejpam-4825	314	14	+	+	CCONJ
ejpam-4825	314	15	a−	a−	PROPN
ejpam-4825	314	16	r	r	NOUN
ejpam-4825	314	17	+	+	CCONJ
ejpam-4825	314	18	1)k1(m2	1)k1(m2	NUM
ejpam-4825	314	19	+	+	CCONJ
ejpam-4825	314	20	a−	a−	PROPN
ejpam-4825	314	21	r	r	NOUN
ejpam-4825	314	22	+	+	CCONJ
ejpam-4825	314	23	2)k2	2)k2	NUM
ejpam-4825	314	24	·	·	PUNCT
ejpam-4825	314	25	·	·	PUNCT
ejpam-4825	314	26	·	·	PUNCT
ejpam-4825	314	27	(	(	PUNCT
ejpam-4825	314	28	mr	mr	PROPN
ejpam-4825	314	29	+	+	PROPN
ejpam-4825	314	30	a)kr	a)kr	PROPN
ejpam-4825	314	31	=	=	PUNCT
ejpam-4825	315	1	∞∑	∞∑	NUM
ejpam-4825	315	2	k=0	k=0	PROPN
ejpam-4825	315	3	(	(	PUNCT
ejpam-4825	315	4	rxt)k	rxt)k	ADJ
ejpam-4825	315	5	k!∑	k!∑	NOUN
ejpam-4825	315	6	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	PUNCT
ejpam-4825	315	7	(	(	PUNCT
ejpam-4825	315	8	−1)mrmr	−1)mrmr	PROPN
ejpam-4825	315	9	!	!	PUNCT
ejpam-4825	316	1	(	(	PUNCT
ejpam-4825	316	2	m1	m1	PROPN
ejpam-4825	316	3	+	+	CCONJ
ejpam-4825	316	4	a−	a−	PROPN
ejpam-4825	316	5	r	r	NOUN
ejpam-4825	316	6	+	+	CCONJ
ejpam-4825	316	7	1)k1(m2	1)k1(m2	NUM
ejpam-4825	316	8	+	+	CCONJ
ejpam-4825	316	9	a−	a−	PROPN
ejpam-4825	316	10	r	r	NOUN
ejpam-4825	316	11	+	+	CCONJ
ejpam-4825	316	12	2)k2	2)k2	NUM
ejpam-4825	316	13	·	·	PUNCT
ejpam-4825	316	14	·	·	PUNCT
ejpam-4825	316	15	·	·	PUNCT
ejpam-4825	317	1	(	(	PUNCT
ejpam-4825	317	2	mr	mr	PROPN
ejpam-4825	317	3	+	+	PROPN
ejpam-4825	317	4	a)kr	a)kr	PROPN
ejpam-4825	317	5	(	(	PUNCT
ejpam-4825	317	6	e−t	e−t	NOUN
ejpam-4825	317	7	−	−	PROPN
ejpam-4825	317	8	1)mr	1)mr	NUM
ejpam-4825	317	9	mr	mr	PROPN
ejpam-4825	317	10	!	!	PUNCT
ejpam-4825	317	11	=	=	PUNCT
ejpam-4825	318	1	∞∑	∞∑	NUM
ejpam-4825	318	2	k=0	k=0	PROPN
ejpam-4825	318	3	(	(	PUNCT
ejpam-4825	318	4	rxt)k	rxt)k	PROPN
ejpam-4825	318	5	k	k	X
ejpam-4825	318	6	!	!	PUNCT
ejpam-4825	318	7	∑	∑	PUNCT
ejpam-4825	318	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	318	9	(	(	PUNCT
ejpam-4825	318	10	∞∑	∞∑	NUM
ejpam-4825	318	11	n	n	NOUN
ejpam-4825	318	12	=	=	ADJ
ejpam-4825	318	13	mr	mr	PROPN
ejpam-4825	318	14	(	(	PUNCT
ejpam-4825	318	15	−1)mrmr	−1)mrmr	PROPN
ejpam-4825	318	16	!	!	PUNCT
ejpam-4825	318	17	{	{	PUNCT
ejpam-4825	319	1	n	n	DET
ejpam-4825	319	2	mr	mr	PROPN
ejpam-4825	319	3	}	}	PUNCT
ejpam-4825	319	4	(	(	PUNCT
ejpam-4825	319	5	−t)n	−t)n	PROPN
ejpam-4825	319	6	n	n	X
ejpam-4825	319	7	!	!	PROPN
ejpam-4825	319	8	1	1	NUM
ejpam-4825	319	9	(	(	PUNCT
ejpam-4825	319	10	mr	mr	PROPN
ejpam-4825	319	11	+	+	PROPN
ejpam-4825	319	12	a)kr	a)kr	PROPN
ejpam-4825	319	13	r−1∏	r−1∏	PROPN
ejpam-4825	319	14	i=1	i=1	PRON
ejpam-4825	319	15	1	1	NUM
ejpam-4825	319	16	(	(	PUNCT
ejpam-4825	319	17	mi	mi	NOUN
ejpam-4825	319	18	+	+	CCONJ
ejpam-4825	319	19	a−	a−	PROPN
ejpam-4825	319	20	r	r	NOUN
ejpam-4825	319	21	+	+	PUNCT
ejpam-4825	319	22	i)ki	i)ki	PROPN
ejpam-4825	319	23	)	)	PUNCT
ejpam-4825	319	24	=	=	PUNCT
ejpam-4825	320	1	∞∑	∞∑	NUM
ejpam-4825	320	2	k=0	k=0	PROPN
ejpam-4825	320	3	(	(	PUNCT
ejpam-4825	320	4	rxt)k	rxt)k	PROPN
ejpam-4825	320	5	k	k	X
ejpam-4825	320	6	!	!	PUNCT
ejpam-4825	320	7	∑	∑	PUNCT
ejpam-4825	320	8	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	320	9	(	(	PUNCT
ejpam-4825	320	10	∞∑	∞∑	NUM
ejpam-4825	320	11	n	n	NOUN
ejpam-4825	320	12	=	=	ADJ
ejpam-4825	320	13	mr	mr	PROPN
ejpam-4825	320	14	(	(	PUNCT
ejpam-4825	320	15	−1)n+mrmr	−1)n+mrmr	PROPN
ejpam-4825	320	16	!	!	PUNCT
ejpam-4825	320	17	{	{	PUNCT
ejpam-4825	321	1	n	n	PRON
ejpam-4825	321	2	mr	mr	PROPN
ejpam-4825	321	3	}	}	PUNCT
ejpam-4825	321	4	tn	tn	PROPN
ejpam-4825	321	5	n	n	CCONJ
ejpam-4825	321	6	!	!	PROPN
ejpam-4825	321	7	1	1	NUM
ejpam-4825	321	8	(	(	PUNCT
ejpam-4825	321	9	mr	mr	PROPN
ejpam-4825	321	10	+	+	PROPN
ejpam-4825	321	11	a)kr	a)kr	PROPN
ejpam-4825	322	1	r−1∏	r−1∏	PROPN
ejpam-4825	322	2	i=1	i=1	PRON
ejpam-4825	322	3	1	1	NUM
ejpam-4825	322	4	(	(	PUNCT
ejpam-4825	322	5	mi	mi	NOUN
ejpam-4825	322	6	+	+	CCONJ
ejpam-4825	322	7	a−	a−	PROPN
ejpam-4825	322	8	r	r	NOUN
ejpam-4825	322	9	+	+	PUNCT
ejpam-4825	322	10	i)ki	i)ki	PROPN
ejpam-4825	322	11	)	)	PUNCT
ejpam-4825	322	12	=	=	PUNCT
ejpam-4825	323	1	∞∑	∞∑	NUM
ejpam-4825	323	2	k=0	k=0	PROPN
ejpam-4825	323	3	(	(	PUNCT
ejpam-4825	323	4	rxt)k	rxt)k	PROPN
ejpam-4825	323	5	k	k	NOUN
ejpam-4825	323	6	!	!	PUNCT
ejpam-4825	324	1	∞∑	∞∑	ADJ
ejpam-4825	324	2	n=0	n=0	PROPN
ejpam-4825	324	3	n∑	n∑	NOUN
ejpam-4825	324	4	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	324	5	(	(	PUNCT
ejpam-4825	324	6	(	(	PUNCT
ejpam-4825	324	7	−1)n+mrmr	−1)n+mrmr	PROPN
ejpam-4825	324	8	!	!	PUNCT
ejpam-4825	324	9	{	{	PUNCT
ejpam-4825	325	1	n	n	DET
ejpam-4825	325	2	mr	mr	PROPN
ejpam-4825	325	3	}	}	PUNCT
ejpam-4825	325	4	(	(	PUNCT
ejpam-4825	325	5	mr	mr	PROPN
ejpam-4825	325	6	+	+	PROPN
ejpam-4825	325	7	a)kr	a)kr	PROPN
ejpam-4825	325	8	r−1∏	r−1∏	PROPN
ejpam-4825	325	9	i=1	i=1	PRON
ejpam-4825	325	10	1	1	NUM
ejpam-4825	325	11	(	(	PUNCT
ejpam-4825	325	12	mi	mi	NOUN
ejpam-4825	325	13	+	+	CCONJ
ejpam-4825	325	14	a−	a−	PROPN
ejpam-4825	325	15	r	r	NOUN
ejpam-4825	325	16	+	+	CCONJ
ejpam-4825	325	17	i)ki	i)ki	PROPN
ejpam-4825	325	18	)	)	PUNCT
ejpam-4825	325	19	tn	tn	PROPN
ejpam-4825	325	20	n	n	ADV
ejpam-4825	325	21	!	!	PUNCT
ejpam-4825	325	22	=	=	NOUN
ejpam-4825	326	1	∞∑	∞∑	PRON
ejpam-4825	326	2	k=0	k=0	PUNCT
ejpam-4825	326	3	∞∑	∞∑	ADJ
ejpam-4825	326	4	n=0	n=0	NUM
ejpam-4825	326	5	(	(	PUNCT
ejpam-4825	326	6	rx)k(−1)n	rx)k(−1)n	PROPN
ejpam-4825	326	7	n.	n.	PROPN
ejpam-4825	326	8	b.	b.	PROPN
ejpam-4825	327	1	lacpao	lacpao	PROPN
ejpam-4825	327	2	/	/	SYM
ejpam-4825	327	3	eur	eur	PROPN
ejpam-4825	327	4	.	.	PUNCT
ejpam-4825	328	1	j.	j.	PROPN
ejpam-4825	328	2	pure	pure	PROPN
ejpam-4825	328	3	appl	appl	PROPN
ejpam-4825	328	4	.	.	PROPN
ejpam-4825	328	5	math	math	PROPN
ejpam-4825	328	6	,	,	PUNCT
ejpam-4825	328	7	16	16	NUM
ejpam-4825	328	8	(	(	PUNCT
ejpam-4825	328	9	3	3	NUM
ejpam-4825	328	10	)	)	PUNCT
ejpam-4825	328	11	(	(	PUNCT
ejpam-4825	328	12	2023	2023	NUM
ejpam-4825	328	13	)	)	PUNCT
ejpam-4825	328	14	,	,	PUNCT
ejpam-4825	328	15	1747	1747	NUM
ejpam-4825	328	16	-	-	SYM
ejpam-4825	328	17	1761	1761	NUM
ejpam-4825	328	18	1760	1760	NUM
ejpam-4825	328	19	n∑	n∑	NOUN
ejpam-4825	328	20	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	329	1	(	(	PUNCT
ejpam-4825	329	2	(	(	PUNCT
ejpam-4825	329	3	−1)mrmr	−1)mrmr	X
ejpam-4825	329	4	!	!	PUNCT
ejpam-4825	329	5	{	{	PUNCT
ejpam-4825	330	1	n	n	DET
ejpam-4825	330	2	mr	mr	PROPN
ejpam-4825	330	3	}	}	PUNCT
ejpam-4825	330	4	(	(	PUNCT
ejpam-4825	330	5	mr	mr	PROPN
ejpam-4825	330	6	+	+	PROPN
ejpam-4825	330	7	a)kr	a)kr	PROPN
ejpam-4825	330	8	r−1∏	r−1∏	PROPN
ejpam-4825	330	9	i=1	i=1	PRON
ejpam-4825	330	10	1	1	NUM
ejpam-4825	330	11	(	(	PUNCT
ejpam-4825	330	12	mi	mi	NOUN
ejpam-4825	330	13	+	+	CCONJ
ejpam-4825	330	14	a−	a−	PROPN
ejpam-4825	330	15	r	r	NOUN
ejpam-4825	330	16	+	+	CCONJ
ejpam-4825	330	17	i)ki	i)ki	PROPN
ejpam-4825	330	18	)	)	PUNCT
ejpam-4825	330	19	tn+k(n+	tn+k(n+	PROPN
ejpam-4825	331	1	k	k	X
ejpam-4825	331	2	)	)	PUNCT
ejpam-4825	331	3	!	!	PUNCT
ejpam-4825	332	1	k!n!(n+	k!n!(n+	PROPN
ejpam-4825	333	1	k	k	X
ejpam-4825	333	2	)	)	PUNCT
ejpam-4825	333	3	!	!	PUNCT
ejpam-4825	334	1	=	=	PUNCT
ejpam-4825	335	1	∞∑	∞∑	DET
ejpam-4825	335	2	k=0	k=0	PUNCT
ejpam-4825	335	3	∞∑	∞∑	NUM
ejpam-4825	335	4	n	n	CCONJ
ejpam-4825	335	5	=	=	SYM
ejpam-4825	335	6	k	k	X
ejpam-4825	335	7	(	(	PUNCT
ejpam-4825	335	8	rx)k(−1)n−k	rx)k(−1)n−k	PROPN
ejpam-4825	335	9	n−k∑	n−k∑	NOUN
ejpam-4825	335	10	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	335	11	(	(	PUNCT
ejpam-4825	335	12	(	(	PUNCT
ejpam-4825	335	13	−1)mrmr	−1)mrmr	X
ejpam-4825	335	14	!	!	PUNCT
ejpam-4825	335	15	{	{	PUNCT
ejpam-4825	335	16	n−k	n−k	NOUN
ejpam-4825	335	17	mr	mr	PROPN
ejpam-4825	335	18	}	}	PUNCT
ejpam-4825	335	19	(	(	PUNCT
ejpam-4825	335	20	mr	mr	PROPN
ejpam-4825	335	21	+	+	PROPN
ejpam-4825	335	22	a)kr	a)kr	PROPN
ejpam-4825	335	23	r−1∏	r−1∏	PROPN
ejpam-4825	335	24	i=1	i=1	PRON
ejpam-4825	335	25	1	1	NUM
ejpam-4825	335	26	(	(	PUNCT
ejpam-4825	335	27	mi	mi	NOUN
ejpam-4825	335	28	+	+	CCONJ
ejpam-4825	335	29	a−	a−	PROPN
ejpam-4825	335	30	r	r	NOUN
ejpam-4825	335	31	+	+	CCONJ
ejpam-4825	335	32	i)ki	i)ki	PROPN
ejpam-4825	335	33	)	)	PUNCT
ejpam-4825	335	34	tnn	tnn	PROPN
ejpam-4825	335	35	!	!	PUNCT
ejpam-4825	335	36	k!(n−	k!(n−	PROPN
ejpam-4825	335	37	k)!n	k)!n	VERB
ejpam-4825	335	38	!	!	PUNCT
ejpam-4825	336	1	=	=	NOUN
ejpam-4825	337	1	∞∑	∞∑	PRON
ejpam-4825	337	2	n=0	n=0	NUM
ejpam-4825	337	3	{	{	PUNCT
ejpam-4825	337	4	n∑	n∑	NOUN
ejpam-4825	337	5	k=0	k=0	PROPN
ejpam-4825	337	6	(	(	PUNCT
ejpam-4825	337	7	rx)k(−1)n−k	rx)k(−1)n−k	PROPN
ejpam-4825	337	8	(	(	PUNCT
ejpam-4825	337	9	n	n	X
ejpam-4825	337	10	k	k	PROPN
ejpam-4825	337	11	)	)	PUNCT
ejpam-4825	337	12	n−k∑	n−k∑	NOUN
ejpam-4825	337	13	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	338	1	(	(	PUNCT
ejpam-4825	338	2	(	(	PUNCT
ejpam-4825	338	3	−1)mrmr	−1)mrmr	X
ejpam-4825	338	4	!	!	PUNCT
ejpam-4825	338	5	{	{	PUNCT
ejpam-4825	338	6	n−k	n−k	NOUN
ejpam-4825	338	7	mr	mr	PROPN
ejpam-4825	338	8	}	}	PUNCT
ejpam-4825	338	9	(	(	PUNCT
ejpam-4825	338	10	mr	mr	PROPN
ejpam-4825	338	11	+	+	PROPN
ejpam-4825	338	12	a)kr	a)kr	PROPN
ejpam-4825	338	13	r−1∏	r−1∏	PROPN
ejpam-4825	338	14	i=1	i=1	PRON
ejpam-4825	338	15	1	1	NUM
ejpam-4825	338	16	(	(	PUNCT
ejpam-4825	338	17	mi	mi	NOUN
ejpam-4825	338	18	+	+	CCONJ
ejpam-4825	338	19	a−	a−	PROPN
ejpam-4825	338	20	r	r	NOUN
ejpam-4825	338	21	+	+	CCONJ
ejpam-4825	338	22	i)ki	i)ki	PROPN
ejpam-4825	338	23	)	)	PUNCT
ejpam-4825	338	24	}	}	PUNCT
ejpam-4825	338	25	tn	tn	PROPN
ejpam-4825	338	26	n	n	X
ejpam-4825	338	27	!	!	PUNCT
ejpam-4825	338	28	.	.	PUNCT
ejpam-4825	339	1	it	it	PRON
ejpam-4825	339	2	follows	follow	VERB
ejpam-4825	339	3	that	that	SCONJ
ejpam-4825	339	4	∞∑	∞∑	NUM
ejpam-4825	339	5	n=0	n=0	PROPN
ejpam-4825	339	6	b(k1,k2	b(k1,k2	NOUN
ejpam-4825	339	7	,	,	PUNCT
ejpam-4825	339	8	·	·	PUNCT
ejpam-4825	339	9	·	·	PUNCT
ejpam-4825	339	10	·	·	PUNCT
ejpam-4825	339	11	,	,	PUNCT
ejpam-4825	339	12	kr	kr	PROPN
ejpam-4825	339	13	)	)	PUNCT
ejpam-4825	339	14	n	n	PROPN
ejpam-4825	339	15	(	(	PUNCT
ejpam-4825	339	16	x	x	X
ejpam-4825	339	17	,	,	PUNCT
ejpam-4825	339	18	a	a	PRON
ejpam-4825	339	19	)	)	PUNCT
ejpam-4825	339	20	tn	tn	NOUN
ejpam-4825	339	21	n	n	NOUN
ejpam-4825	339	22	!	!	PUNCT
ejpam-4825	339	23	=	=	NOUN
ejpam-4825	340	1	∞∑	∞∑	PRON
ejpam-4825	340	2	n=0	n=0	NUM
ejpam-4825	340	3	{	{	PUNCT
ejpam-4825	340	4	n∑	n∑	NOUN
ejpam-4825	340	5	k=0	k=0	PROPN
ejpam-4825	340	6	(	(	PUNCT
ejpam-4825	340	7	rx)k(−1)n−k	rx)k(−1)n−k	PROPN
ejpam-4825	340	8	(	(	PUNCT
ejpam-4825	340	9	n	n	X
ejpam-4825	340	10	k	k	PROPN
ejpam-4825	340	11	)	)	PUNCT
ejpam-4825	340	12	n−k∑	n−k∑	NOUN
ejpam-4825	340	13	0≤m1≤m2≤···≤mr	0≤m1≤m2≤···≤mr	NUM
ejpam-4825	341	1	(	(	PUNCT
ejpam-4825	341	2	(	(	PUNCT
ejpam-4825	341	3	−1)mrmr	−1)mrmr	X
ejpam-4825	341	4	!	!	PUNCT
ejpam-4825	341	5	{	{	PUNCT
ejpam-4825	341	6	n−k	n−k	NOUN
ejpam-4825	341	7	mr	mr	PROPN
ejpam-4825	341	8	}	}	PUNCT
ejpam-4825	341	9	(	(	PUNCT
ejpam-4825	341	10	mr	mr	PROPN
ejpam-4825	341	11	+	+	PROPN
ejpam-4825	341	12	a)kr	a)kr	PROPN
ejpam-4825	341	13	r−1∏	r−1∏	PROPN
ejpam-4825	341	14	i=1	i=1	PRON
ejpam-4825	341	15	1	1	NUM
ejpam-4825	341	16	(	(	PUNCT
ejpam-4825	341	17	mi	mi	NOUN
ejpam-4825	341	18	+	+	CCONJ
ejpam-4825	341	19	a−	a−	PROPN
ejpam-4825	341	20	r	r	NOUN
ejpam-4825	341	21	+	+	CCONJ
ejpam-4825	341	22	i)ki	i)ki	PROPN
ejpam-4825	341	23	)	)	PUNCT
ejpam-4825	341	24	}	}	PUNCT
ejpam-4825	341	25	tn	tn	PROPN
ejpam-4825	341	26	n	n	X
ejpam-4825	341	27	!	!	PUNCT
ejpam-4825	341	28	.	.	PUNCT
ejpam-4825	342	1	comparing	compare	VERB
ejpam-4825	342	2	the	the	DET
ejpam-4825	342	3	coefficients	coefficient	NOUN
ejpam-4825	342	4	proves	prove	VERB
ejpam-4825	342	5	the	the	DET
ejpam-4825	342	6	theorem	theorem	NOUN
ejpam-4825	342	7	.	.	PUNCT
ejpam-4825	343	1	■	■	PUNCT
ejpam-4825	343	2	4	4	X
ejpam-4825	343	3	.	.	PUNCT
ejpam-4825	343	4	conclusions	conclusion	NOUN
ejpam-4825	343	5	this	this	DET
ejpam-4825	343	6	paper	paper	NOUN
ejpam-4825	343	7	defined	define	VERB
ejpam-4825	343	8	variations	variation	NOUN
ejpam-4825	343	9	of	of	ADP
ejpam-4825	343	10	poly	poly	ADJ
ejpam-4825	343	11	-	-	PUNCT
ejpam-4825	343	12	cauchy	cauchy	ADJ
ejpam-4825	343	13	and	and	CCONJ
ejpam-4825	343	14	poly	poly	ADJ
ejpam-4825	343	15	-	-	PUNCT
ejpam-4825	343	16	bernoulli	bernoulli	NOUN
ejpam-4825	343	17	polynomials	polynomial	NOUN
ejpam-4825	343	18	called	call	VERB
ejpam-4825	343	19	the	the	DET
ejpam-4825	343	20	hurwitz	hurwitz	PROPN
ejpam-4825	343	21	-	-	PUNCT
ejpam-4825	343	22	lerch	lerch	PROPN
ejpam-4825	343	23	poly	poly	ADJ
ejpam-4825	343	24	-	-	PUNCT
ejpam-4825	343	25	cauchy	cauchy	ADJ
ejpam-4825	343	26	and	and	CCONJ
ejpam-4825	343	27	poly	poly	ADJ
ejpam-4825	343	28	-	-	PUNCT
ejpam-4825	343	29	bernoulli	bernoulli	NOUN
ejpam-4825	343	30	polynomials	polynomial	NOUN
ejpam-4825	343	31	and	and	CCONJ
ejpam-4825	343	32	hurwitz	hurwitz	PROPN
ejpam-4825	343	33	-	-	PUNCT
ejpam-4825	343	34	lerch	lerch	PROPN
ejpam-4825	343	35	multi	multi	PROPN
ejpam-4825	343	36	poly	poly	ADJ
ejpam-4825	343	37	-	-	PUNCT
ejpam-4825	343	38	cauchy	cauchy	NOUN
ejpam-4825	343	39	polynomials	polynomial	NOUN
ejpam-4825	343	40	using	use	VERB
ejpam-4825	343	41	polylogarithm	polylogarithm	PROPN
ejpam-4825	343	42	factorial	factorial	NOUN
ejpam-4825	343	43	and	and	CCONJ
ejpam-4825	343	44	multiple	multiple	ADJ
ejpam-4825	343	45	polylogarithm	polylogarithm	PROPN
ejpam-4825	343	46	factorial	factorial	NOUN
ejpam-4825	343	47	functions	function	NOUN
ejpam-4825	343	48	,	,	PUNCT
ejpam-4825	343	49	respectively	respectively	ADV
ejpam-4825	343	50	.	.	PUNCT
ejpam-4825	344	1	moreover	moreover	ADV
ejpam-4825	344	2	,	,	PUNCT
ejpam-4825	344	3	explicit	explicit	ADJ
ejpam-4825	344	4	formulas	formula	NOUN
ejpam-4825	344	5	parallel	parallel	ADJ
ejpam-4825	344	6	to	to	ADP
ejpam-4825	344	7	those	those	PRON
ejpam-4825	344	8	of	of	ADP
ejpam-4825	344	9	poly	poly	ADJ
ejpam-4825	344	10	-	-	PUNCT
ejpam-4825	344	11	cauchy	cauchy	ADJ
ejpam-4825	344	12	and	and	CCONJ
ejpam-4825	344	13	poly	poly	ADJ
ejpam-4825	344	14	-	-	PUNCT
ejpam-4825	344	15	bernoulli	bernoulli	NOUN
ejpam-4825	344	16	polynomials	polynomial	NOUN
ejpam-4825	344	17	were	be	AUX
ejpam-4825	344	18	explored	explore	VERB
ejpam-4825	344	19	and	and	CCONJ
ejpam-4825	344	20	obtained	obtain	VERB
ejpam-4825	344	21	.	.	PUNCT
ejpam-4825	345	1	these	these	DET
ejpam-4825	345	2	types	type	NOUN
ejpam-4825	345	3	of	of	ADP
ejpam-4825	345	4	polynomials	polynomial	NOUN
ejpam-4825	345	5	could	could	AUX
ejpam-4825	345	6	have	have	VERB
ejpam-4825	345	7	significant	significant	ADJ
ejpam-4825	345	8	applications	application	NOUN
ejpam-4825	345	9	in	in	ADP
ejpam-4825	345	10	the	the	DET
ejpam-4825	345	11	field	field	NOUN
ejpam-4825	345	12	of	of	ADP
ejpam-4825	345	13	numerical	numerical	ADJ
ejpam-4825	345	14	analysis	analysis	NOUN
ejpam-4825	345	15	,	,	PUNCT
ejpam-4825	345	16	analytic	analytic	ADJ
ejpam-4825	345	17	number	number	NOUN
ejpam-4825	345	18	theory	theory	NOUN
ejpam-4825	345	19	and	and	CCONJ
ejpam-4825	345	20	difference	difference	NOUN
ejpam-4825	345	21	-	-	PUNCT
ejpam-4825	345	22	differential	differential	NOUN
ejpam-4825	345	23	equations	equation	NOUN
ejpam-4825	345	24	.	.	PUNCT
ejpam-4825	346	1	the	the	DET
ejpam-4825	346	2	generalizations	generalization	NOUN
ejpam-4825	346	3	of	of	ADP
ejpam-4825	346	4	these	these	DET
ejpam-4825	346	5	polynomials	polynomial	NOUN
ejpam-4825	346	6	yield	yield	VERB
ejpam-4825	346	7	symmetries	symmetry	NOUN
ejpam-4825	346	8	for	for	ADP
ejpam-4825	346	9	stirling	stirling	NOUN
ejpam-4825	346	10	number	number	NOUN
ejpam-4825	346	11	series	series	NOUN
ejpam-4825	346	12	and	and	CCONJ
ejpam-4825	346	13	lead	lead	VERB
ejpam-4825	346	14	to	to	ADP
ejpam-4825	346	15	a	a	DET
ejpam-4825	346	16	unified	unified	ADJ
ejpam-4825	346	17	investigation	investigation	NOUN
ejpam-4825	346	18	of	of	ADP
ejpam-4825	346	19	algebraic	algebraic	ADJ
ejpam-4825	346	20	properties	property	NOUN
ejpam-4825	346	21	for	for	ADP
ejpam-4825	346	22	these	these	DET
ejpam-4825	346	23	polynomials	polynomial	NOUN
ejpam-4825	346	24	.	.	PUNCT
ejpam-4825	347	1	furthermore	furthermore	ADV
ejpam-4825	347	2	,	,	PUNCT
ejpam-4825	347	3	future	future	ADJ
ejpam-4825	347	4	researches	research	NOUN
ejpam-4825	347	5	may	may	AUX
ejpam-4825	347	6	include	include	VERB
ejpam-4825	347	7	properties	property	NOUN
ejpam-4825	347	8	of	of	ADP
ejpam-4825	347	9	these	these	DET
ejpam-4825	347	10	polynomials	polynomial	NOUN
ejpam-4825	347	11	with	with	ADP
ejpam-4825	347	12	multiple	multiple	ADJ
ejpam-4825	347	13	parameters	parameter	NOUN
ejpam-4825	347	14	and	and	CCONJ
ejpam-4825	347	15	relations	relation	NOUN
ejpam-4825	347	16	to	to	ADP
ejpam-4825	347	17	other	other	ADJ
ejpam-4825	347	18	family	family	NOUN
ejpam-4825	347	19	of	of	ADP
ejpam-4825	347	20	polynomials	polynomial	NOUN
ejpam-4825	347	21	.	.	PUNCT
ejpam-4825	348	1	acknowledgements	acknowledgement	NOUN
ejpam-4825	348	2	this	this	DET
ejpam-4825	348	3	research	research	NOUN
ejpam-4825	348	4	is	be	AUX
ejpam-4825	348	5	funded	fund	VERB
ejpam-4825	348	6	by	by	ADP
ejpam-4825	348	7	bukidnon	bukidnon	NOUN
ejpam-4825	348	8	state	state	PROPN
ejpam-4825	348	9	university	university	PROPN
ejpam-4825	348	10	center	center	NOUN
ejpam-4825	348	11	for	for	ADP
ejpam-4825	348	12	mathematics	mathematic	NOUN
ejpam-4825	348	13	innovations	innovation	NOUN
ejpam-4825	348	14	.	.	PUNCT
ejpam-4825	349	1	the	the	DET
ejpam-4825	349	2	author	author	NOUN
ejpam-4825	349	3	would	would	AUX
ejpam-4825	349	4	also	also	ADV
ejpam-4825	349	5	like	like	VERB
ejpam-4825	349	6	to	to	PART
ejpam-4825	349	7	express	express	VERB
ejpam-4825	349	8	his	his	PRON
ejpam-4825	349	9	sincere	sincere	ADJ
ejpam-4825	349	10	gratitude	gratitude	NOUN
ejpam-4825	349	11	to	to	ADP
ejpam-4825	349	12	the	the	DET
ejpam-4825	349	13	editor	editor	NOUN
ejpam-4825	349	14	and	and	CCONJ
ejpam-4825	349	15	referees	referee	NOUN
ejpam-4825	349	16	for	for	ADP
ejpam-4825	349	17	the	the	DET
ejpam-4825	349	18	improvement	improvement	NOUN
ejpam-4825	349	19	of	of	ADP
ejpam-4825	349	20	this	this	DET
ejpam-4825	349	21	paper	paper	NOUN
ejpam-4825	349	22	and	and	CCONJ
ejpam-4825	349	23	for	for	ADP
ejpam-4825	349	24	making	make	VERB
ejpam-4825	349	25	this	this	DET
ejpam-4825	349	26	journal	journal	NOUN
ejpam-4825	349	27	successful	successful	ADJ
ejpam-4825	349	28	.	.	PUNCT
ejpam-4825	350	1	references	reference	NOUN
ejpam-4825	350	2	1761	1761	NUM
ejpam-4825	350	3	references	reference	NOUN
ejpam-4825	350	4	[	[	X
ejpam-4825	350	5	1	1	X
ejpam-4825	350	6	]	]	PUNCT
ejpam-4825	350	7	t.	t.	PROPN
ejpam-4825	350	8	arakawa	arakawa	PROPN
ejpam-4825	350	9	and	and	CCONJ
ejpam-4825	350	10	m.	m.	NOUN
ejpam-4825	350	11	kaneko	kaneko	PROPN
ejpam-4825	350	12	.	.	PUNCT
ejpam-4825	351	1	on	on	ADP
ejpam-4825	351	2	poly	poly	ADJ
ejpam-4825	351	3	-	-	PUNCT
ejpam-4825	351	4	bernoulli	bernoulli	NOUN
ejpam-4825	351	5	numbers	number	NOUN
ejpam-4825	351	6	.	.	PUNCT
ejpam-4825	352	1	comment	comment	NOUN
ejpam-4825	352	2	math	math	PROPN
ejpam-4825	352	3	.	.	PUNCT
ejpam-4825	353	1	univ	univ	PROPN
ejpam-4825	353	2	.	.	PUNCT
ejpam-4825	354	1	st	st	PROPN
ejpam-4825	354	2	.	.	PROPN
ejpam-4825	354	3	paul	paul	PROPN
ejpam-4825	354	4	,	,	PUNCT
ejpam-4825	354	5	48(2):159–167	48(2):159–167	PROPN
ejpam-4825	354	6	,	,	PUNCT
ejpam-4825	354	7	1999	1999	NUM
ejpam-4825	354	8	.	.	PUNCT
ejpam-4825	355	1	[	[	X
ejpam-4825	355	2	2	2	NUM
ejpam-4825	355	3	]	]	PUNCT
ejpam-4825	355	4	a.	a.	NOUN
ejpam-4825	355	5	bayad	bayad	NOUN
ejpam-4825	355	6	and	and	CCONJ
ejpam-4825	355	7	y.	y.	PROPN
ejpam-4825	355	8	hamahata	hamahata	PROPN
ejpam-4825	355	9	.	.	PUNCT
ejpam-4825	356	1	polylogarithms	polylogarithm	NOUN
ejpam-4825	356	2	and	and	CCONJ
ejpam-4825	356	3	poly	poly	ADJ
ejpam-4825	356	4	-	-	PUNCT
ejpam-4825	356	5	bernoulli	bernoulli	NOUN
ejpam-4825	356	6	polynomials	polynomial	NOUN
ejpam-4825	356	7	.	.	PUNCT
ejpam-4825	357	1	kyushu	kyushu	PROPN
ejpam-4825	357	2	j.	j.	PROPN
ejpam-4825	357	3	math	math	PROPN
ejpam-4825	357	4	.	.	PUNCT
ejpam-4825	357	5	,	,	PUNCT
ejpam-4825	357	6	65:15–24	65:15–24	PROPN
ejpam-4825	357	7	,	,	PUNCT
ejpam-4825	357	8	2011	2011	NUM
ejpam-4825	357	9	.	.	PUNCT
ejpam-4825	358	1	[	[	X
ejpam-4825	358	2	3	3	X
ejpam-4825	358	3	]	]	X
ejpam-4825	358	4	d.	d.	PROPN
ejpam-4825	358	5	bedoya	bedoya	PROPN
ejpam-4825	358	6	,	,	PUNCT
ejpam-4825	358	7	c.	c.	PROPN
ejpam-4825	358	8	cesarano	cesarano	PROPN
ejpam-4825	358	9	,	,	PUNCT
ejpam-4825	358	10	s.	s.	PROPN
ejpam-4825	358	11	dı́az	dı́az	PROPN
ejpam-4825	358	12	,	,	PUNCT
ejpam-4825	358	13	and	and	CCONJ
ejpam-4825	358	14	w.	w.	PROPN
ejpam-4825	358	15	ramı́rez	ramı́rez	PROPN
ejpam-4825	358	16	.	.	PUNCT
ejpam-4825	359	1	new	new	ADJ
ejpam-4825	359	2	classes	class	NOUN
ejpam-4825	359	3	of	of	ADP
ejpam-4825	359	4	degenerate	degenerate	ADJ
ejpam-4825	359	5	unified	unified	ADJ
ejpam-4825	359	6	polynomials	polynomial	NOUN
ejpam-4825	359	7	.	.	PUNCT
ejpam-4825	360	1	axioms	axiom	NOUN
ejpam-4825	360	2	,	,	PUNCT
ejpam-4825	360	3	12(1	12(1	NUM
ejpam-4825	360	4	)	)	PUNCT
ejpam-4825	360	5	,	,	PUNCT
ejpam-4825	360	6	2023	2023	NUM
ejpam-4825	360	7	.	.	PUNCT
ejpam-4825	361	1	[	[	X
ejpam-4825	361	2	4	4	X
ejpam-4825	361	3	]	]	PUNCT
ejpam-4825	361	4	m.	m.	NOUN
ejpam-4825	361	5	cenkci	cenkci	NOUN
ejpam-4825	361	6	and	and	CCONJ
ejpam-4825	361	7	p.	p.	PROPN
ejpam-4825	361	8	young	young	ADJ
ejpam-4825	361	9	.	.	PUNCT
ejpam-4825	362	1	generalizations	generalization	NOUN
ejpam-4825	362	2	of	of	ADP
ejpam-4825	362	3	poly	poly	ADJ
ejpam-4825	362	4	-	-	PUNCT
ejpam-4825	362	5	bernoulli	bernoulli	NOUN
ejpam-4825	362	6	and	and	CCONJ
ejpam-4825	362	7	poly	poly	ADJ
ejpam-4825	362	8	-	-	PUNCT
ejpam-4825	362	9	cauchy	cauchy	NOUN
ejpam-4825	362	10	numbers	number	NOUN
ejpam-4825	362	11	.	.	PUNCT
ejpam-4825	363	1	eur	eur	PROPN
ejpam-4825	363	2	.	.	PUNCT
ejpam-4825	364	1	j.	j.	PROPN
ejpam-4825	364	2	math	math	PROPN
ejpam-4825	364	3	.	.	PUNCT
ejpam-4825	364	4	,	,	PUNCT
ejpam-4825	364	5	1(5):799–828	1(5):799–828	PROPN
ejpam-4825	364	6	,	,	PUNCT
ejpam-4825	364	7	2015	2015	NUM
ejpam-4825	364	8	.	.	PUNCT
ejpam-4825	365	1	[	[	X
ejpam-4825	365	2	5	5	X
ejpam-4825	365	3	]	]	PUNCT
ejpam-4825	365	4	c.	c.	PROPN
ejpam-4825	365	5	cesarano	cesarano	PROPN
ejpam-4825	365	6	,	,	PUNCT
ejpam-4825	365	7	w.	w.	PROPN
ejpam-4825	365	8	ramı́rez	ramı́rez	PROPN
ejpam-4825	365	9	,	,	PUNCT
ejpam-4825	365	10	s.	s.	PROPN
ejpam-4825	365	11	dı́as	dı́as	PROPN
ejpam-4825	365	12	,	,	PUNCT
ejpam-4825	365	13	a.	a.	NOUN
ejpam-4825	365	14	shamaoon	shamaoon	NOUN
ejpam-4825	365	15	,	,	PUNCT
ejpam-4825	365	16	and	and	CCONJ
ejpam-4825	365	17	w.	w.	PROPN
ejpam-4825	365	18	khan	khan	PROPN
ejpam-4825	365	19	.	.	PUNCT
ejpam-4825	366	1	on	on	ADP
ejpam-4825	366	2	apostol	apostol	NOUN
ejpam-4825	366	3	-	-	PUNCT
ejpam-4825	366	4	type	type	NOUN
ejpam-4825	366	5	hermite	hermite	ADJ
ejpam-4825	366	6	degenerated	degenerated	ADJ
ejpam-4825	366	7	polynomials	polynomial	NOUN
ejpam-4825	366	8	.	.	PUNCT
ejpam-4825	367	1	mathematics	mathematic	NOUN
ejpam-4825	367	2	,	,	PUNCT
ejpam-4825	367	3	11(8	11(8	NUM
ejpam-4825	367	4	)	)	PUNCT
ejpam-4825	367	5	,	,	PUNCT
ejpam-4825	367	6	2023	2023	NUM
ejpam-4825	367	7	.	.	PUNCT
ejpam-4825	368	1	[	[	X
ejpam-4825	368	2	6	6	NUM
ejpam-4825	368	3	]	]	PUNCT
ejpam-4825	368	4	l.	l.	PROPN
ejpam-4825	368	5	comtet	comtet	PROPN
ejpam-4825	368	6	.	.	PUNCT
ejpam-4825	369	1	advanced	advanced	ADJ
ejpam-4825	369	2	combinatorics	combinatoric	NOUN
ejpam-4825	369	3	.	.	PUNCT
ejpam-4825	370	1	the	the	DET
ejpam-4825	370	2	art	art	NOUN
ejpam-4825	370	3	of	of	ADP
ejpam-4825	370	4	finite	finite	NOUN
ejpam-4825	370	5	and	and	CCONJ
ejpam-4825	370	6	infinite	infinite	ADJ
ejpam-4825	370	7	expansions	expansion	NOUN
ejpam-4825	370	8	.	.	PUNCT
ejpam-4825	371	1	d.	d.	PROPN
ejpam-4825	371	2	reidel	reidel	PROPN
ejpam-4825	371	3	publishing	publishing	PROPN
ejpam-4825	371	4	company	company	NOUN
ejpam-4825	371	5	,	,	PUNCT
ejpam-4825	371	6	dordrecht	dordrecht	PROPN
ejpam-4825	371	7	,	,	PUNCT
ejpam-4825	371	8	holland	holland	PROPN
ejpam-4825	371	9	,	,	PUNCT
ejpam-4825	371	10	1974	1974	NUM
ejpam-4825	371	11	.	.	PUNCT
ejpam-4825	372	1	[	[	X
ejpam-4825	372	2	7	7	X
ejpam-4825	372	3	]	]	X
ejpam-4825	372	4	c.	c.	PROPN
ejpam-4825	372	5	corcino	corcino	PROPN
ejpam-4825	372	6	,	,	PUNCT
ejpam-4825	372	7	r.	r.	PROPN
ejpam-4825	372	8	corcino	corcino	PROPN
ejpam-4825	372	9	,	,	PUNCT
ejpam-4825	372	10	t.	t.	PROPN
ejpam-4825	372	11	komatsu	komatsu	PROPN
ejpam-4825	372	12	,	,	PUNCT
ejpam-4825	372	13	and	and	CCONJ
ejpam-4825	372	14	h.	h.	PROPN
ejpam-4825	372	15	jolany	jolany	PROPN
ejpam-4825	372	16	.	.	PUNCT
ejpam-4825	373	1	on	on	ADP
ejpam-4825	373	2	multi	multi	ADJ
ejpam-4825	373	3	poly	poly	ADJ
ejpam-4825	373	4	-	-	PUNCT
ejpam-4825	373	5	bernoulli	bernoulli	NOUN
ejpam-4825	373	6	polynomials	polynomial	NOUN
ejpam-4825	373	7	.	.	PUNCT
ejpam-4825	374	1	journal	journal	PROPN
ejpam-4825	374	2	of	of	ADP
ejpam-4825	374	3	inequalities	inequality	NOUN
ejpam-4825	374	4	and	and	CCONJ
ejpam-4825	374	5	special	special	ADJ
ejpam-4825	374	6	functions	function	NOUN
ejpam-4825	374	7	,	,	PUNCT
ejpam-4825	374	8	10(2):21–34	10(2):21–34	NUM
ejpam-4825	374	9	,	,	PUNCT
ejpam-4825	374	10	2019	2019	NUM
ejpam-4825	374	11	.	.	PUNCT
ejpam-4825	375	1	[	[	X
ejpam-4825	375	2	8	8	NUM
ejpam-4825	375	3	]	]	X
ejpam-4825	375	4	r.	r.	PROPN
ejpam-4825	375	5	corcino	corcino	PROPN
ejpam-4825	375	6	.	.	PUNCT
ejpam-4825	376	1	multi	multi	ADJ
ejpam-4825	376	2	poly	poly	ADJ
ejpam-4825	376	3	-	-	PUNCT
ejpam-4825	376	4	bernoulli	bernoulli	NOUN
ejpam-4825	376	5	and	and	CCONJ
ejpam-4825	376	6	multi	multi	ADJ
ejpam-4825	376	7	poly	poly	ADJ
ejpam-4825	376	8	-	-	PUNCT
ejpam-4825	376	9	euler	euler	NOUN
ejpam-4825	376	10	polynomials	polynomial	NOUN
ejpam-4825	376	11	.	.	PUNCT
ejpam-4825	377	1	in	in	ADP
ejpam-4825	377	2	h.	h.	PROPN
ejpam-4825	377	3	dutta	dutta	PROPN
ejpam-4825	377	4	and	and	CCONJ
ejpam-4825	377	5	j.	j.	PROPN
ejpam-4825	377	6	peters	peters	PROPN
ejpam-4825	377	7	,	,	PUNCT
ejpam-4825	377	8	editors	editor	NOUN
ejpam-4825	377	9	,	,	PUNCT
ejpam-4825	377	10	applied	apply	VERB
ejpam-4825	377	11	mathematical	mathematical	ADJ
ejpam-4825	377	12	analysis	analysis	NOUN
ejpam-4825	377	13	:	:	PUNCT
ejpam-4825	377	14	theory	theory	NOUN
ejpam-4825	377	15	,	,	PUNCT
ejpam-4825	377	16	methods	method	NOUN
ejpam-4825	377	17	,	,	PUNCT
ejpam-4825	377	18	and	and	CCONJ
ejpam-4825	377	19	applications	application	NOUN
ejpam-4825	377	20	.	.	PUNCT
ejpam-4825	377	21	,	,	PUNCT
ejpam-4825	377	22	pages	page	VERB
ejpam-4825	377	23	679–721	679–721	NUM
ejpam-4825	377	24	.	.	PUNCT
ejpam-4825	378	1	springer	springer	NOUN
ejpam-4825	378	2	international	international	ADJ
ejpam-4825	378	3	publishing	publishing	NOUN
ejpam-4825	378	4	,	,	PUNCT
ejpam-4825	378	5	cham	cham	NOUN
ejpam-4825	378	6	,	,	PUNCT
ejpam-4825	378	7	2020	2020	NUM
ejpam-4825	378	8	.	.	PUNCT
ejpam-4825	379	1	[	[	X
ejpam-4825	379	2	9	9	NUM
ejpam-4825	379	3	]	]	X
ejpam-4825	379	4	r.	r.	PROPN
ejpam-4825	379	5	corcino	corcino	PROPN
ejpam-4825	379	6	and	and	CCONJ
ejpam-4825	379	7	h.	h.	PROPN
ejpam-4825	379	8	jolany	jolany	PROPN
ejpam-4825	379	9	.	.	PUNCT
ejpam-4825	380	1	explicit	explicit	ADJ
ejpam-4825	380	2	formula	formula	NOUN
ejpam-4825	380	3	for	for	ADP
ejpam-4825	380	4	generalization	generalization	NOUN
ejpam-4825	380	5	of	of	ADP
ejpam-4825	380	6	poly	poly	ADJ
ejpam-4825	380	7	-	-	PUNCT
ejpam-4825	380	8	bernoulli	bernoulli	NOUN
ejpam-4825	380	9	numbers	number	NOUN
ejpam-4825	380	10	and	and	CCONJ
ejpam-4825	380	11	polynomials	polynomial	NOUN
ejpam-4825	380	12	with	with	ADP
ejpam-4825	380	13	a	a	DET
ejpam-4825	380	14	,	,	PUNCT
ejpam-4825	380	15	b	b	NOUN
ejpam-4825	380	16	,	,	PUNCT
ejpam-4825	380	17	c	c	PROPN
ejpam-4825	380	18	parameters	parameter	NOUN
ejpam-4825	380	19	.	.	PUNCT
ejpam-4825	381	1	jour	jour	PROPN
ejpam-4825	381	2	.	.	PUNCT
ejpam-4825	381	3	clas	clas	PROPN
ejpam-4825	381	4	.	.	PUNCT
ejpam-4825	382	1	anal	anal	PROPN
ejpam-4825	382	2	.	.	PROPN
ejpam-4825	382	3	,	,	PUNCT
ejpam-4825	382	4	6(2):119–135	6(2):119–135	NOUN
ejpam-4825	382	5	,	,	PUNCT
ejpam-4825	382	6	2015	2015	NUM
ejpam-4825	382	7	.	.	PUNCT
ejpam-4825	383	1	[	[	X
ejpam-4825	383	2	10	10	NUM
ejpam-4825	383	3	]	]	X
ejpam-4825	383	4	h.	h.	PROPN
ejpam-4825	383	5	jolany	jolany	PROPN
ejpam-4825	383	6	,	,	PUNCT
ejpam-4825	383	7	r.	r.	PROPN
ejpam-4825	383	8	corcino	corcino	PROPN
ejpam-4825	383	9	,	,	PUNCT
ejpam-4825	383	10	and	and	CCONJ
ejpam-4825	383	11	t.	t.	PROPN
ejpam-4825	383	12	komatsu	komatsu	NOUN
ejpam-4825	383	13	.	.	PUNCT
ejpam-4825	384	1	more	more	ADJ
ejpam-4825	384	2	properties	property	NOUN
ejpam-4825	384	3	on	on	ADP
ejpam-4825	384	4	multi	multi	ADJ
ejpam-4825	384	5	-	-	ADJ
ejpam-4825	384	6	poly	poly	ADJ
ejpam-4825	384	7	-	-	PUNCT
ejpam-4825	384	8	euler	euler	NOUN
ejpam-4825	384	9	polynomials	polynomial	NOUN
ejpam-4825	384	10	.	.	PUNCT
ejpam-4825	385	1	bol	bol	NOUN
ejpam-4825	385	2	.	.	PUNCT
ejpam-4825	386	1	soc	soc	PROPN
ejpam-4825	386	2	.	.	PUNCT
ejpam-4825	387	1	mat	mat	PROPN
ejpam-4825	387	2	.	.	PUNCT
ejpam-4825	387	3	mex	mex	PROPN
ejpam-4825	387	4	.	.	PROPN
ejpam-4825	387	5	,	,	PUNCT
ejpam-4825	387	6	21:149–162	21:149–162	PROPN
ejpam-4825	387	7	,	,	PUNCT
ejpam-4825	387	8	2015	2015	NUM
ejpam-4825	387	9	.	.	PUNCT
ejpam-4825	388	1	[	[	X
ejpam-4825	388	2	11	11	NUM
ejpam-4825	388	3	]	]	PUNCT
ejpam-4825	388	4	m.	m.	NOUN
ejpam-4825	388	5	kaneko	kaneko	PROPN
ejpam-4825	388	6	.	.	PUNCT
ejpam-4825	388	7	poly	poly	ADJ
ejpam-4825	388	8	-	-	PUNCT
ejpam-4825	388	9	bernoulli	bernoulli	NOUN
ejpam-4825	388	10	numbers	number	NOUN
ejpam-4825	388	11	.	.	PUNCT
ejpam-4825	389	1	j.	j.	PROPN
ejpam-4825	389	2	théor	théor	PROPN
ejpam-4825	389	3	.	.	PUNCT
ejpam-4825	389	4	nombres	nombre	NOUN
ejpam-4825	389	5	bordeaux	bordeaux	PROPN
ejpam-4825	389	6	,	,	PUNCT
ejpam-4825	389	7	9(1):221–228	9(1):221–228	NUM
ejpam-4825	389	8	,	,	PUNCT
ejpam-4825	389	9	1997	1997	NUM
ejpam-4825	389	10	.	.	PUNCT
ejpam-4825	390	1	[	[	X
ejpam-4825	390	2	12	12	NUM
ejpam-4825	390	3	]	]	PUNCT
ejpam-4825	390	4	t.	t.	PROPN
ejpam-4825	390	5	komatsu	komatsu	PROPN
ejpam-4825	390	6	.	.	PUNCT
ejpam-4825	391	1	poly	poly	ADJ
ejpam-4825	391	2	-	-	PUNCT
ejpam-4825	391	3	cauchy	cauchy	NOUN
ejpam-4825	391	4	numbers	number	NOUN
ejpam-4825	391	5	.	.	PUNCT
ejpam-4825	392	1	kyushu	kyushu	PROPN
ejpam-4825	392	2	j.	j.	PROPN
ejpam-4825	392	3	math	math	PROPN
ejpam-4825	392	4	.	.	PUNCT
ejpam-4825	392	5	,	,	PUNCT
ejpam-4825	393	1	67(1):143–153	67(1):143–153	PROPN
ejpam-4825	393	2	,	,	PUNCT
ejpam-4825	393	3	2013	2013	NUM
ejpam-4825	393	4	.	.	PUNCT
ejpam-4825	394	1	[	[	X
ejpam-4825	394	2	13	13	NUM
ejpam-4825	394	3	]	]	PUNCT
ejpam-4825	394	4	t.	t.	PROPN
ejpam-4825	394	5	komatsu	komatsu	PROPN
ejpam-4825	394	6	and	and	CCONJ
ejpam-4825	394	7	k.	k.	PROPN
ejpam-4825	394	8	kamano	kamano	PROPN
ejpam-4825	394	9	.	.	PUNCT
ejpam-4825	395	1	poly	poly	ADJ
ejpam-4825	395	2	-	-	PUNCT
ejpam-4825	395	3	cauchy	cauchy	NOUN
ejpam-4825	395	4	polynomials	polynomial	NOUN
ejpam-4825	395	5	.	.	PUNCT
ejpam-4825	396	1	msk	msk	PROPN
ejpam-4825	396	2	.	.	PUNCT
ejpam-4825	396	3	jour	jour	PROPN
ejpam-4825	396	4	.	.	PUNCT
ejpam-4825	396	5	comb	comb	PROPN
ejpam-4825	396	6	.	.	PUNCT
ejpam-4825	397	1	num	num	ADJ
ejpam-4825	397	2	.	.	PUNCT
ejpam-4825	398	1	theo	theo	PROPN
ejpam-4825	398	2	.	.	PROPN
ejpam-4825	398	3	,	,	PUNCT
ejpam-4825	398	4	3(2):61–87	3(2):61–87	NUM
ejpam-4825	398	5	,	,	PUNCT
ejpam-4825	398	6	2013	2013	NUM
ejpam-4825	398	7	.	.	PUNCT
ejpam-4825	399	1	[	[	X
ejpam-4825	399	2	14	14	NUM
ejpam-4825	399	3	]	]	X
ejpam-4825	399	4	n.	n.	PROPN
ejpam-4825	399	5	lacpao	lacpao	PROPN
ejpam-4825	399	6	,	,	PUNCT
ejpam-4825	399	7	r.	r.	PROPN
ejpam-4825	399	8	corcino	corcino	PROPN
ejpam-4825	399	9	,	,	PUNCT
ejpam-4825	399	10	and	and	CCONJ
ejpam-4825	399	11	m.	m.	PROPN
ejpam-4825	399	12	vega	vega	PROPN
ejpam-4825	399	13	.	.	PUNCT
ejpam-4825	399	14	hurwitz	hurwitz	PROPN
ejpam-4825	399	15	-	-	PUNCT
ejpam-4825	399	16	lerch	lerch	PROPN
ejpam-4825	399	17	type	type	NOUN
ejpam-4825	399	18	multi	multi	ADJ
ejpam-4825	399	19	poly	poly	ADJ
ejpam-4825	399	20	-	-	PUNCT
ejpam-4825	399	21	cauchy	cauchy	NOUN
ejpam-4825	399	22	numbers	number	NOUN
ejpam-4825	399	23	.	.	PUNCT
ejpam-4825	400	1	mathematics	mathematic	NOUN
ejpam-4825	400	2	,	,	PUNCT
ejpam-4825	400	3	7(4):355	7(4):355	NUM
ejpam-4825	400	4	,	,	PUNCT
ejpam-4825	400	5	2019	2019	NUM
ejpam-4825	400	6	.	.	PUNCT
ejpam-4825	401	1	[	[	X
ejpam-4825	401	2	15	15	NUM
ejpam-4825	401	3	]	]	X
ejpam-4825	401	4	d.	d.	PROPN
ejpam-4825	401	5	merlini	merlini	PROPN
ejpam-4825	401	6	,	,	PUNCT
ejpam-4825	401	7	r.	r.	PROPN
ejpam-4825	401	8	sprugnoli	sprugnoli	PROPN
ejpam-4825	401	9	,	,	PUNCT
ejpam-4825	401	10	and	and	CCONJ
ejpam-4825	401	11	c.	c.	PROPN
ejpam-4825	401	12	verri	verri	PROPN
ejpam-4825	401	13	.	.	PUNCT
ejpam-4825	402	1	the	the	DET
ejpam-4825	402	2	cauchy	cauchy	PROPN
ejpam-4825	402	3	numbers	number	NOUN
ejpam-4825	402	4	.	.	PUNCT
ejpam-4825	403	1	disc	disc	PROPN
ejpam-4825	403	2	.	.	PUNCT
ejpam-4825	403	3	math	math	NOUN
ejpam-4825	403	4	.	.	PUNCT
ejpam-4825	403	5	,	,	PUNCT
ejpam-4825	403	6	306(16):1906–1920	306(16):1906–1920	NUM
ejpam-4825	403	7	,	,	PUNCT
ejpam-4825	403	8	2006	2006	NUM
ejpam-4825	403	9	.	.	PUNCT
ejpam-4825	404	1	[	[	X
ejpam-4825	404	2	16	16	NUM
ejpam-4825	404	3	]	]	X
ejpam-4825	404	4	l.	l.	PROPN
ejpam-4825	404	5	yingying	yingying	PROPN
ejpam-4825	404	6	.	.	PUNCT
ejpam-4825	405	1	on	on	ADP
ejpam-4825	405	2	euler	euler	PROPN
ejpam-4825	405	3	’s	’s	PART
ejpam-4825	405	4	constant	constant	ADJ
ejpam-4825	405	5	calculating	calculating	NOUN
ejpam-4825	405	6	sums	sum	NOUN
ejpam-4825	405	7	by	by	ADP
ejpam-4825	405	8	integrals	integral	NOUN
ejpam-4825	405	9	.	.	PUNCT
ejpam-4825	406	1	amer	amer	PROPN
ejpam-4825	406	2	.	.	PUNCT
ejpam-4825	406	3	math	math	PROPN
ejpam-4825	406	4	.	.	PUNCT
ejpam-4825	407	1	ass	ass	PROPN
ejpam-4825	407	2	.	.	PUNCT
ejpam-4825	407	3	amer	amer	PROPN
ejpam-4825	407	4	.	.	PROPN
ejpam-4825	407	5	,	,	PUNCT
ejpam-4825	407	6	109(9):845–850	109(9):845–850	NUM
ejpam-4825	407	7	,	,	PUNCT
ejpam-4825	407	8	2002	2002	NUM
ejpam-4825	407	9	.	.	PUNCT