id	sid	tid	token	lemma	pos
ejpam-4715	1	1	european	european	PROPN
ejpam-4715	1	2	journal	journal	PROPN
ejpam-4715	1	3	of	of	ADP
ejpam-4715	1	4	pure	pure	ADJ
ejpam-4715	1	5	and	and	CCONJ
ejpam-4715	1	6	applied	apply	VERB
ejpam-4715	1	7	mathematics	mathematic	NOUN
ejpam-4715	1	8	vol	vol	NOUN
ejpam-4715	1	9	.	.	PUNCT
ejpam-4715	2	1	16	16	NUM
ejpam-4715	2	2	,	,	PUNCT
ejpam-4715	2	3	no	no	INTJ
ejpam-4715	2	4	.	.	NOUN
ejpam-4715	2	5	2	2	NUM
ejpam-4715	2	6	,	,	PUNCT
ejpam-4715	2	7	2023	2023	NUM
ejpam-4715	2	8	,	,	PUNCT
ejpam-4715	2	9	934	934	NUM
ejpam-4715	2	10	-	-	SYM
ejpam-4715	2	11	943	943	NUM
ejpam-4715	2	12	issn	issn	PROPN
ejpam-4715	2	13	1307	1307	NUM
ejpam-4715	2	14	-	-	SYM
ejpam-4715	2	15	5543	5543	NUM
ejpam-4715	2	16	–	–	PUNCT
ejpam-4715	2	17	ejpam.com	ejpam.com	X
ejpam-4715	2	18	published	publish	VERB
ejpam-4715	2	19	by	by	ADP
ejpam-4715	2	20	new	new	PROPN
ejpam-4715	2	21	york	york	PROPN
ejpam-4715	2	22	business	business	PROPN
ejpam-4715	2	23	global	global	ADJ
ejpam-4715	2	24	on	on	ADP
ejpam-4715	2	25	divisibility	divisibility	NOUN
ejpam-4715	2	26	property	property	NOUN
ejpam-4715	2	27	of	of	ADP
ejpam-4715	2	28	type	type	NOUN
ejpam-4715	2	29	2	2	NUM
ejpam-4715	2	30	(	(	PUNCT
ejpam-4715	2	31	p	p	NOUN
ejpam-4715	2	32	,	,	PUNCT
ejpam-4715	3	1	q)-analogue	q)-analogue	NOUN
ejpam-4715	3	2	of	of	ADP
ejpam-4715	3	3	r	r	PROPN
ejpam-4715	3	4	-	-	PUNCT
ejpam-4715	3	5	whitney	whitney	NOUN
ejpam-4715	3	6	numbers	number	NOUN
ejpam-4715	3	7	of	of	ADP
ejpam-4715	3	8	the	the	DET
ejpam-4715	3	9	second	second	ADJ
ejpam-4715	3	10	kind	kind	NOUN
ejpam-4715	3	11	roberto	roberto	PROPN
ejpam-4715	3	12	b.	b.	PROPN
ejpam-4715	3	13	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-4715	3	14	,	,	PUNCT
ejpam-4715	3	15	cristina	cristina	PROPN
ejpam-4715	3	16	b.	b.	PROPN
ejpam-4715	4	1	corcino1,2	corcino1,2	PROPN
ejpam-4715	4	2	1	1	NUM
ejpam-4715	4	3	research	research	NOUN
ejpam-4715	4	4	institute	institute	NOUN
ejpam-4715	4	5	for	for	ADP
ejpam-4715	4	6	computational	computational	ADJ
ejpam-4715	4	7	mathematics	mathematic	NOUN
ejpam-4715	4	8	and	and	CCONJ
ejpam-4715	4	9	physics	physics	NOUN
ejpam-4715	4	10	,	,	PUNCT
ejpam-4715	4	11	cebu	cebu	NOUN
ejpam-4715	4	12	normal	normal	ADJ
ejpam-4715	4	13	university	university	NOUN
ejpam-4715	4	14	,	,	PUNCT
ejpam-4715	4	15	6000	6000	NUM
ejpam-4715	4	16	cebu	cebu	NOUN
ejpam-4715	4	17	city	city	NOUN
ejpam-4715	4	18	,	,	PUNCT
ejpam-4715	4	19	philippines	philippine	NOUN
ejpam-4715	4	20	2	2	NUM
ejpam-4715	4	21	mathematics	mathematics	NOUN
ejpam-4715	4	22	department	department	NOUN
ejpam-4715	4	23	,	,	PUNCT
ejpam-4715	4	24	cebu	cebu	NOUN
ejpam-4715	4	25	normal	normal	ADJ
ejpam-4715	4	26	university	university	NOUN
ejpam-4715	4	27	,	,	PUNCT
ejpam-4715	4	28	6000	6000	NUM
ejpam-4715	4	29	cebu	cebu	NOUN
ejpam-4715	4	30	city	city	NOUN
ejpam-4715	4	31	,	,	PUNCT
ejpam-4715	4	32	philippines	philippine	NOUN
ejpam-4715	4	33	abstract	abstract	ADJ
ejpam-4715	4	34	.	.	PUNCT
ejpam-4715	5	1	in	in	ADP
ejpam-4715	5	2	this	this	DET
ejpam-4715	5	3	paper	paper	NOUN
ejpam-4715	5	4	,	,	PUNCT
ejpam-4715	5	5	the	the	DET
ejpam-4715	5	6	divisibility	divisibility	NOUN
ejpam-4715	5	7	property	property	NOUN
ejpam-4715	5	8	of	of	ADP
ejpam-4715	5	9	the	the	DET
ejpam-4715	5	10	type	type	NOUN
ejpam-4715	5	11	2	2	NUM
ejpam-4715	5	12	(	(	PUNCT
ejpam-4715	5	13	p	p	NOUN
ejpam-4715	5	14	,	,	PUNCT
ejpam-4715	5	15	q)-analogue	q)-analogue	NOUN
ejpam-4715	5	16	of	of	ADP
ejpam-4715	5	17	the	the	DET
ejpam-4715	5	18	r	r	PROPN
ejpam-4715	5	19	-	-	PUNCT
ejpam-4715	5	20	whitney	whitney	NOUN
ejpam-4715	5	21	numbers	number	NOUN
ejpam-4715	5	22	of	of	ADP
ejpam-4715	5	23	the	the	DET
ejpam-4715	5	24	second	second	ADJ
ejpam-4715	5	25	kind	kind	NOUN
ejpam-4715	5	26	is	be	AUX
ejpam-4715	5	27	established	establish	VERB
ejpam-4715	5	28	.	.	PUNCT
ejpam-4715	6	1	more	more	ADV
ejpam-4715	6	2	precisely	precisely	ADV
ejpam-4715	6	3	,	,	PUNCT
ejpam-4715	6	4	a	a	DET
ejpam-4715	6	5	congruence	congruence	NOUN
ejpam-4715	6	6	relation	relation	NOUN
ejpam-4715	6	7	modulo	modulo	PROPN
ejpam-4715	6	8	pq	pq	PROPN
ejpam-4715	6	9	for	for	ADP
ejpam-4715	6	10	this	this	PRON
ejpam-4715	6	11	(	(	PUNCT
ejpam-4715	6	12	p	p	NOUN
ejpam-4715	6	13	,	,	PUNCT
ejpam-4715	6	14	q)-analogue	q)-analogue	NUM
ejpam-4715	6	15	is	be	AUX
ejpam-4715	6	16	derived	derive	VERB
ejpam-4715	6	17	.	.	PUNCT
ejpam-4715	7	1	2020	2020	NUM
ejpam-4715	7	2	mathematics	mathematic	NOUN
ejpam-4715	7	3	subject	subject	NOUN
ejpam-4715	7	4	classifications	classification	NOUN
ejpam-4715	7	5	:	:	PUNCT
ejpam-4715	7	6	05a19	05a19	NUM
ejpam-4715	7	7	,	,	PUNCT
ejpam-4715	7	8	05a30	05a30	NOUN
ejpam-4715	7	9	,	,	PUNCT
ejpam-4715	7	10	11b65	11b65	NUM
ejpam-4715	7	11	key	key	ADJ
ejpam-4715	7	12	words	word	NOUN
ejpam-4715	7	13	and	and	CCONJ
ejpam-4715	7	14	phrases	phrase	NOUN
ejpam-4715	7	15	:	:	PUNCT
ejpam-4715	7	16	r	r	X
ejpam-4715	7	17	-	-	PUNCT
ejpam-4715	7	18	whitney	whitney	NOUN
ejpam-4715	7	19	numbers	number	NOUN
ejpam-4715	7	20	,	,	PUNCT
ejpam-4715	7	21	r	r	NOUN
ejpam-4715	7	22	-	-	PUNCT
ejpam-4715	7	23	dowling	dowle	VERB
ejpam-4715	7	24	numbers	number	NOUN
ejpam-4715	7	25	,	,	PUNCT
ejpam-4715	7	26	stirling	stirling	NOUN
ejpam-4715	7	27	numbers	number	NOUN
ejpam-4715	7	28	,	,	PUNCT
ejpam-4715	7	29	bell	bell	NOUN
ejpam-4715	7	30	numbers	number	NOUN
ejpam-4715	7	31	,	,	PUNCT
ejpam-4715	7	32	congruence	congruence	PROPN
ejpam-4715	7	33	relation	relation	NOUN
ejpam-4715	7	34	,	,	PUNCT
ejpam-4715	7	35	divisibility	divisibility	NOUN
ejpam-4715	7	36	property	property	NOUN
ejpam-4715	7	37	,	,	PUNCT
ejpam-4715	7	38	binomial	binomial	ADJ
ejpam-4715	7	39	transform	transform	NOUN
ejpam-4715	7	40	,	,	PUNCT
ejpam-4715	7	41	hankel	hankel	NOUN
ejpam-4715	7	42	tranform	tranform	VERB
ejpam-4715	7	43	1	1	NUM
ejpam-4715	7	44	.	.	PUNCT
ejpam-4715	8	1	introduction	introduction	NOUN
ejpam-4715	8	2	the	the	DET
ejpam-4715	8	3	r	r	PROPN
ejpam-4715	8	4	-	-	PUNCT
ejpam-4715	8	5	whitney	whitney	NOUN
ejpam-4715	8	6	numbers	number	NOUN
ejpam-4715	8	7	of	of	ADP
ejpam-4715	8	8	the	the	DET
ejpam-4715	8	9	second	second	ADJ
ejpam-4715	8	10	kind	kind	NOUN
ejpam-4715	8	11	were	be	AUX
ejpam-4715	8	12	introduced	introduce	VERB
ejpam-4715	8	13	by	by	ADP
ejpam-4715	8	14	mezo	mezo	PROPN
ejpam-4715	9	1	[	[	X
ejpam-4715	9	2	18	18	NUM
ejpam-4715	9	3	]	]	PUNCT
ejpam-4715	9	4	as	as	ADP
ejpam-4715	9	5	coefficients	coefficient	NOUN
ejpam-4715	9	6	of	of	ADP
ejpam-4715	9	7	the	the	DET
ejpam-4715	9	8	following	follow	VERB
ejpam-4715	9	9	generating	generate	VERB
ejpam-4715	9	10	function	function	NOUN
ejpam-4715	9	11	:	:	PUNCT
ejpam-4715	9	12	(	(	PUNCT
ejpam-4715	9	13	mx+	mx+	NOUN
ejpam-4715	9	14	r)n	r)n	NOUN
ejpam-4715	9	15	=	=	SYM
ejpam-4715	9	16	n∑	n∑	DET
ejpam-4715	9	17	k=0	k=0	PROPN
ejpam-4715	9	18	mkwm	mkwm	PROPN
ejpam-4715	9	19	,	,	PUNCT
ejpam-4715	9	20	r(n	r(n	PROPN
ejpam-4715	9	21	,	,	PUNCT
ejpam-4715	9	22	k)x	k)x	X
ejpam-4715	9	23	k	k	NOUN
ejpam-4715	9	24	,	,	PUNCT
ejpam-4715	9	25	where	where	SCONJ
ejpam-4715	9	26	xk	xk	PROPN
ejpam-4715	9	27	=	=	SYM
ejpam-4715	9	28	x(x−	x(x−	PROPN
ejpam-4715	9	29	1	1	NUM
ejpam-4715	9	30	)	)	PUNCT
ejpam-4715	9	31	.	.	PUNCT
ejpam-4715	9	32	.	.	PUNCT
ejpam-4715	9	33	.	.	PUNCT
ejpam-4715	10	1	(	(	PUNCT
ejpam-4715	10	2	x−	x−	PROPN
ejpam-4715	10	3	k	k	PROPN
ejpam-4715	10	4	+	+	PROPN
ejpam-4715	10	5	1	1	NUM
ejpam-4715	10	6	)	)	PUNCT
ejpam-4715	10	7	.	.	PUNCT
ejpam-4715	11	1	these	these	DET
ejpam-4715	11	2	numbers	number	NOUN
ejpam-4715	11	3	satisfy	satisfy	VERB
ejpam-4715	11	4	the	the	DET
ejpam-4715	11	5	following	follow	VERB
ejpam-4715	11	6	properties	property	NOUN
ejpam-4715	11	7	:	:	PUNCT
ejpam-4715	12	1	1	1	X
ejpam-4715	12	2	.	.	X
ejpam-4715	12	3	the	the	DET
ejpam-4715	12	4	exponential	exponential	ADJ
ejpam-4715	12	5	generating	generating	NOUN
ejpam-4715	12	6	function	function	NOUN
ejpam-4715	12	7	∞∑	∞∑	PROPN
ejpam-4715	12	8	n=0	n=0	NUM
ejpam-4715	12	9	wm	wm	PROPN
ejpam-4715	12	10	,	,	PUNCT
ejpam-4715	12	11	r(n	r(n	PROPN
ejpam-4715	12	12	,	,	PUNCT
ejpam-4715	12	13	k	k	NOUN
ejpam-4715	12	14	)	)	PUNCT
ejpam-4715	12	15	zn	zn	PROPN
ejpam-4715	12	16	n	n	X
ejpam-4715	12	17	!	!	PUNCT
ejpam-4715	13	1	=	=	NOUN
ejpam-4715	13	2	erz	erz	PROPN
ejpam-4715	14	1	k	k	NOUN
ejpam-4715	14	2	!	!	PUNCT
ejpam-4715	15	1	(	(	PUNCT
ejpam-4715	15	2	emz	emz	PROPN
ejpam-4715	15	3	−	−	PROPN
ejpam-4715	15	4	1	1	NUM
ejpam-4715	15	5	m	m	NOUN
ejpam-4715	15	6	)	)	PUNCT
ejpam-4715	16	1	k	k	NOUN
ejpam-4715	16	2	,	,	PUNCT
ejpam-4715	16	3	2	2	X
ejpam-4715	16	4	.	.	PUNCT
ejpam-4715	17	1	the	the	DET
ejpam-4715	17	2	explicit	explicit	ADJ
ejpam-4715	17	3	formula	formula	NOUN
ejpam-4715	17	4	wm	wm	PROPN
ejpam-4715	17	5	,	,	PUNCT
ejpam-4715	17	6	r(n	r(n	PROPN
ejpam-4715	17	7	,	,	PUNCT
ejpam-4715	17	8	k	k	NOUN
ejpam-4715	17	9	)	)	PUNCT
ejpam-4715	17	10	=	=	SYM
ejpam-4715	17	11	1	1	NUM
ejpam-4715	17	12	mkk	mkk	PROPN
ejpam-4715	17	13	!	!	PUNCT
ejpam-4715	17	14	k∑	k∑	PROPN
ejpam-4715	18	1	i=0	i=0	PROPN
ejpam-4715	18	2	(	(	PUNCT
ejpam-4715	18	3	k	k	NOUN
ejpam-4715	18	4	i	i	PROPN
ejpam-4715	18	5	)	)	PUNCT
ejpam-4715	18	6	(	(	PUNCT
ejpam-4715	18	7	−1)k−i(mi+	−1)k−i(mi+	NOUN
ejpam-4715	18	8	r)n	r)n	NOUN
ejpam-4715	18	9	,	,	PUNCT
ejpam-4715	18	10	∗corresponding	∗corresponde	VERB
ejpam-4715	18	11	author	author	NOUN
ejpam-4715	18	12	.	.	PUNCT
ejpam-4715	19	1	doi	doi	NOUN
ejpam-4715	19	2	:	:	PUNCT
ejpam-4715	19	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4715	https://doi.org/10.29020/nybg.ejpam.v16i2.4715	NOUN
ejpam-4715	19	4	email	email	NOUN
ejpam-4715	19	5	addresses	address	VERB
ejpam-4715	19	6	:	:	PUNCT
ejpam-4715	19	7	rcorcino@yahoo.com	rcorcino@yahoo.com	PROPN
ejpam-4715	19	8	(	(	PUNCT
ejpam-4715	19	9	r.	r.	PROPN
ejpam-4715	19	10	b.	b.	PROPN
ejpam-4715	19	11	corcino	corcino	PROPN
ejpam-4715	19	12	)	)	PUNCT
ejpam-4715	19	13	,	,	PUNCT
ejpam-4715	19	14	corcinoc@cnu.edu.ph	corcinoc@cnu.edu.ph	PROPN
ejpam-4715	19	15	(	(	PUNCT
ejpam-4715	19	16	c.	c.	PROPN
ejpam-4715	19	17	c.	c.	PROPN
ejpam-4715	19	18	corcino	corcino	PROPN
ejpam-4715	19	19	)	)	PUNCT
ejpam-4715	19	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4715	19	21	934	934	NUM
ejpam-4715	19	22	©	©	PROPN
ejpam-4715	19	23	2023	2023	NUM
ejpam-4715	19	24	ejpam	ejpam	NOUN
ejpam-4715	19	25	all	all	DET
ejpam-4715	19	26	rights	right	NOUN
ejpam-4715	19	27	reserved	reserve	VERB
ejpam-4715	19	28	.	.	PUNCT
ejpam-4715	20	1	r.	r.	PROPN
ejpam-4715	20	2	b.	b.	PROPN
ejpam-4715	20	3	corcino	corcino	PROPN
ejpam-4715	20	4	,	,	PUNCT
ejpam-4715	20	5	c.	c.	PROPN
ejpam-4715	20	6	b.	b.	PROPN
ejpam-4715	20	7	corcino	corcino	PROPN
ejpam-4715	20	8	/	/	SYM
ejpam-4715	20	9	eur	eur	PROPN
ejpam-4715	20	10	.	.	PUNCT
ejpam-4715	21	1	j.	j.	PROPN
ejpam-4715	21	2	pure	pure	PROPN
ejpam-4715	21	3	appl	appl	PROPN
ejpam-4715	21	4	.	.	PROPN
ejpam-4715	21	5	math	math	PROPN
ejpam-4715	21	6	,	,	PUNCT
ejpam-4715	21	7	16	16	NUM
ejpam-4715	21	8	(	(	PUNCT
ejpam-4715	21	9	2	2	NUM
ejpam-4715	21	10	)	)	PUNCT
ejpam-4715	21	11	(	(	PUNCT
ejpam-4715	21	12	2023	2023	NUM
ejpam-4715	21	13	)	)	PUNCT
ejpam-4715	21	14	,	,	PUNCT
ejpam-4715	21	15	934	934	NUM
ejpam-4715	21	16	-	-	SYM
ejpam-4715	21	17	943	943	NUM
ejpam-4715	21	18	935	935	NUM
ejpam-4715	21	19	3	3	NUM
ejpam-4715	21	20	.	.	PUNCT
ejpam-4715	22	1	the	the	DET
ejpam-4715	22	2	triangular	triangular	NOUN
ejpam-4715	22	3	recurrence	recurrence	NOUN
ejpam-4715	22	4	relation	relation	PROPN
ejpam-4715	22	5	wm	wm	PROPN
ejpam-4715	22	6	,	,	PUNCT
ejpam-4715	22	7	r(n	r(n	PROPN
ejpam-4715	22	8	,	,	PUNCT
ejpam-4715	22	9	k	k	NOUN
ejpam-4715	22	10	)	)	PUNCT
ejpam-4715	22	11	=	=	SYM
ejpam-4715	22	12	wm	wm	PROPN
ejpam-4715	22	13	,	,	PUNCT
ejpam-4715	22	14	r(n−	r(n−	NOUN
ejpam-4715	22	15	1	1	NUM
ejpam-4715	22	16	,	,	PUNCT
ejpam-4715	22	17	k	k	PROPN
ejpam-4715	22	18	−	−	PROPN
ejpam-4715	22	19	1	1	NUM
ejpam-4715	22	20	)	)	PUNCT
ejpam-4715	22	21	+	+	CCONJ
ejpam-4715	22	22	(	(	PUNCT
ejpam-4715	22	23	km+	km+	PROPN
ejpam-4715	22	24	r)wm	r)wm	PROPN
ejpam-4715	22	25	,	,	PUNCT
ejpam-4715	22	26	r(n−	r(n−	NOUN
ejpam-4715	22	27	1	1	NUM
ejpam-4715	22	28	,	,	PUNCT
ejpam-4715	22	29	k	k	NOUN
ejpam-4715	22	30	)	)	PUNCT
ejpam-4715	22	31	.	.	PUNCT
ejpam-4715	23	1	these	these	DET
ejpam-4715	23	2	properties	property	NOUN
ejpam-4715	23	3	are	be	AUX
ejpam-4715	23	4	exactly	exactly	ADV
ejpam-4715	23	5	the	the	DET
ejpam-4715	23	6	same	same	ADJ
ejpam-4715	23	7	properties	property	NOUN
ejpam-4715	23	8	that	that	PRON
ejpam-4715	23	9	the	the	DET
ejpam-4715	23	10	(	(	PUNCT
ejpam-4715	23	11	r	r	NOUN
ejpam-4715	23	12	,	,	PUNCT
ejpam-4715	23	13	β)-stirling	β)-stirle	VERB
ejpam-4715	23	14	numbers	number	NOUN
ejpam-4715	23	15	in	in	ADP
ejpam-4715	23	16	[	[	X
ejpam-4715	23	17	7	7	NUM
ejpam-4715	23	18	]	]	PUNCT
ejpam-4715	23	19	have	have	AUX
ejpam-4715	23	20	possessed	possess	VERB
ejpam-4715	23	21	.	.	PUNCT
ejpam-4715	24	1	this	this	PRON
ejpam-4715	24	2	implies	imply	VERB
ejpam-4715	24	3	that	that	SCONJ
ejpam-4715	24	4	the	the	DET
ejpam-4715	24	5	r	r	PROPN
ejpam-4715	24	6	-	-	PUNCT
ejpam-4715	24	7	whitney	whitney	NOUN
ejpam-4715	24	8	numbers	number	NOUN
ejpam-4715	24	9	of	of	ADP
ejpam-4715	24	10	the	the	DET
ejpam-4715	24	11	second	second	ADJ
ejpam-4715	24	12	kind	kind	NOUN
ejpam-4715	24	13	and	and	CCONJ
ejpam-4715	24	14	the	the	DET
ejpam-4715	24	15	(	(	PUNCT
ejpam-4715	24	16	r	r	NOUN
ejpam-4715	24	17	,	,	PUNCT
ejpam-4715	24	18	β)-stirling	β)-stirling	VERB
ejpam-4715	24	19	numbers	number	NOUN
ejpam-4715	24	20	are	be	AUX
ejpam-4715	24	21	equivalent	equivalent	ADJ
ejpam-4715	24	22	.	.	PUNCT
ejpam-4715	25	1	more	more	ADJ
ejpam-4715	25	2	properties	property	NOUN
ejpam-4715	25	3	of	of	ADP
ejpam-4715	25	4	these	these	DET
ejpam-4715	25	5	numbers	number	NOUN
ejpam-4715	25	6	can	can	AUX
ejpam-4715	25	7	be	be	AUX
ejpam-4715	25	8	found	find	VERB
ejpam-4715	25	9	in	in	ADP
ejpam-4715	25	10	[	[	X
ejpam-4715	25	11	2	2	NUM
ejpam-4715	25	12	,	,	PUNCT
ejpam-4715	25	13	4	4	NUM
ejpam-4715	25	14	,	,	PUNCT
ejpam-4715	25	15	5	5	NUM
ejpam-4715	25	16	,	,	PUNCT
ejpam-4715	25	17	7	7	NUM
ejpam-4715	25	18	,	,	PUNCT
ejpam-4715	25	19	18	18	NUM
ejpam-4715	25	20	]	]	PUNCT
ejpam-4715	25	21	.	.	PUNCT
ejpam-4715	26	1	one	one	NUM
ejpam-4715	26	2	of	of	ADP
ejpam-4715	26	3	the	the	DET
ejpam-4715	26	4	early	early	ADJ
ejpam-4715	26	5	studies	study	NOUN
ejpam-4715	26	6	on	on	ADP
ejpam-4715	26	7	q	q	NOUN
ejpam-4715	26	8	-	-	PUNCT
ejpam-4715	26	9	analogue	analogue	NOUN
ejpam-4715	26	10	of	of	ADP
ejpam-4715	26	11	stirling	stirling	NOUN
ejpam-4715	26	12	numbers	number	NOUN
ejpam-4715	26	13	of	of	ADP
ejpam-4715	26	14	the	the	DET
ejpam-4715	26	15	second	second	ADJ
ejpam-4715	26	16	kind	kind	NOUN
ejpam-4715	26	17	was	be	AUX
ejpam-4715	26	18	introduced	introduce	VERB
ejpam-4715	26	19	by	by	ADP
ejpam-4715	26	20	carlitz	carlitz	NOUN
ejpam-4715	26	21	in	in	ADP
ejpam-4715	26	22	[	[	X
ejpam-4715	26	23	1	1	NUM
ejpam-4715	26	24	]	]	PUNCT
ejpam-4715	26	25	in	in	ADP
ejpam-4715	26	26	connection	connection	NOUN
ejpam-4715	26	27	with	with	ADP
ejpam-4715	26	28	a	a	DET
ejpam-4715	26	29	problem	problem	NOUN
ejpam-4715	26	30	in	in	ADP
ejpam-4715	26	31	abelian	abelian	ADJ
ejpam-4715	26	32	groups	group	NOUN
ejpam-4715	26	33	.	.	PUNCT
ejpam-4715	27	1	this	this	PRON
ejpam-4715	27	2	is	be	AUX
ejpam-4715	27	3	known	know	VERB
ejpam-4715	27	4	as	as	ADP
ejpam-4715	27	5	q	q	ADJ
ejpam-4715	27	6	-	-	PUNCT
ejpam-4715	27	7	stirling	stirling	ADJ
ejpam-4715	27	8	numbers	number	NOUN
ejpam-4715	27	9	of	of	ADP
ejpam-4715	27	10	the	the	DET
ejpam-4715	27	11	second	second	ADJ
ejpam-4715	27	12	kind	kind	NOUN
ejpam-4715	27	13	and	and	CCONJ
ejpam-4715	27	14	is	be	AUX
ejpam-4715	27	15	defined	define	VERB
ejpam-4715	27	16	in	in	ADP
ejpam-4715	27	17	terms	term	NOUN
ejpam-4715	27	18	of	of	ADP
ejpam-4715	27	19	the	the	DET
ejpam-4715	27	20	following	follow	VERB
ejpam-4715	27	21	recurrence	recurrence	PROPN
ejpam-4715	27	22	relation	relation	PROPN
ejpam-4715	27	23	sq[n	sq[n	PROPN
ejpam-4715	27	24	,	,	PUNCT
ejpam-4715	27	25	k	k	X
ejpam-4715	28	1	]	]	X
ejpam-4715	28	2	=	=	PUNCT
ejpam-4715	28	3	sq[n−	sq[n−	NOUN
ejpam-4715	28	4	1	1	NUM
ejpam-4715	28	5	,	,	PUNCT
ejpam-4715	28	6	k	k	PROPN
ejpam-4715	28	7	−	−	PROPN
ejpam-4715	28	8	1	1	NUM
ejpam-4715	28	9	]	]	PUNCT
ejpam-4715	28	10	+	+	CCONJ
ejpam-4715	28	11	[	[	X
ejpam-4715	28	12	k]qsq[n−	k]qsq[n−	NOUN
ejpam-4715	28	13	1	1	NUM
ejpam-4715	28	14	,	,	PUNCT
ejpam-4715	28	15	k	k	NOUN
ejpam-4715	28	16	]	]	X
ejpam-4715	28	17	,	,	PUNCT
ejpam-4715	28	18	[	[	X
ejpam-4715	28	19	k]q	k]q	X
ejpam-4715	28	20	=	=	SYM
ejpam-4715	28	21	1−	1−	NUM
ejpam-4715	28	22	qk	qk	NOUN
ejpam-4715	28	23	1−	1−	NUM
ejpam-4715	28	24	q	q	NOUN
ejpam-4715	28	25	such	such	ADJ
ejpam-4715	28	26	that	that	SCONJ
ejpam-4715	28	27	,	,	PUNCT
ejpam-4715	28	28	when	when	SCONJ
ejpam-4715	28	29	q	q	X
ejpam-4715	28	30	→	→	SYM
ejpam-4715	28	31	1	1	NUM
ejpam-4715	28	32	,	,	PUNCT
ejpam-4715	28	33	this	this	PRON
ejpam-4715	28	34	gives	give	VERB
ejpam-4715	28	35	the	the	DET
ejpam-4715	28	36	triangular	triangular	NOUN
ejpam-4715	28	37	recurrence	recurrence	NOUN
ejpam-4715	28	38	relation	relation	NOUN
ejpam-4715	28	39	for	for	ADP
ejpam-4715	28	40	the	the	DET
ejpam-4715	28	41	classical	classical	ADJ
ejpam-4715	28	42	stirling	stirling	NOUN
ejpam-4715	28	43	numbers	number	NOUN
ejpam-4715	28	44	of	of	ADP
ejpam-4715	28	45	the	the	DET
ejpam-4715	28	46	second	second	ADJ
ejpam-4715	28	47	kind	kind	NOUN
ejpam-4715	28	48	s(n	s(n	PROPN
ejpam-4715	28	49	,	,	PUNCT
ejpam-4715	28	50	k	k	NOUN
ejpam-4715	28	51	)	)	PUNCT
ejpam-4715	28	52	s(n	s(n	PROPN
ejpam-4715	28	53	,	,	PUNCT
ejpam-4715	28	54	k	k	NOUN
ejpam-4715	28	55	)	)	PUNCT
ejpam-4715	28	56	=	=	SYM
ejpam-4715	28	57	s(n−	s(n−	PROPN
ejpam-4715	28	58	1	1	NUM
ejpam-4715	28	59	,	,	PUNCT
ejpam-4715	28	60	k	k	PROPN
ejpam-4715	28	61	−	−	PROPN
ejpam-4715	28	62	1	1	NUM
ejpam-4715	28	63	)	)	PUNCT
ejpam-4715	29	1	+	+	CCONJ
ejpam-4715	29	2	ks(n−	ks(n−	PROPN
ejpam-4715	29	3	1	1	NUM
ejpam-4715	29	4	,	,	PUNCT
ejpam-4715	29	5	k	k	NOUN
ejpam-4715	29	6	)	)	PUNCT
ejpam-4715	29	7	.	.	PUNCT
ejpam-4715	30	1	another	another	DET
ejpam-4715	30	2	version	version	NOUN
ejpam-4715	30	3	of	of	ADP
ejpam-4715	30	4	definition	definition	NOUN
ejpam-4715	30	5	of	of	ADP
ejpam-4715	30	6	this	this	DET
ejpam-4715	30	7	q	q	NOUN
ejpam-4715	30	8	-	-	PUNCT
ejpam-4715	30	9	analogue	analogue	NOUN
ejpam-4715	30	10	was	be	AUX
ejpam-4715	30	11	adapted	adapt	VERB
ejpam-4715	30	12	in	in	ADP
ejpam-4715	30	13	[	[	X
ejpam-4715	30	14	17	17	NUM
ejpam-4715	30	15	]	]	PUNCT
ejpam-4715	30	16	as	as	SCONJ
ejpam-4715	30	17	follows	follow	VERB
ejpam-4715	30	18	sq[n	sq[n	PROPN
ejpam-4715	30	19	,	,	PUNCT
ejpam-4715	30	20	k	k	X
ejpam-4715	30	21	]	]	X
ejpam-4715	30	22	=	=	SYM
ejpam-4715	30	23	qk−1sq[n−	qk−1sq[n−	NOUN
ejpam-4715	30	24	1	1	NUM
ejpam-4715	30	25	,	,	PUNCT
ejpam-4715	30	26	k	k	PROPN
ejpam-4715	30	27	−	−	PROPN
ejpam-4715	31	1	1	1	NUM
ejpam-4715	31	2	]	]	PUNCT
ejpam-4715	31	3	+	+	CCONJ
ejpam-4715	32	1	[	[	X
ejpam-4715	32	2	k]qsq[n−	k]qsq[n−	NOUN
ejpam-4715	32	3	1	1	NUM
ejpam-4715	32	4	,	,	PUNCT
ejpam-4715	32	5	k	k	NOUN
ejpam-4715	32	6	]	]	X
ejpam-4715	32	7	.	.	PUNCT
ejpam-4715	33	1	(	(	PUNCT
ejpam-4715	33	2	1	1	X
ejpam-4715	33	3	)	)	PUNCT
ejpam-4715	33	4	through	through	ADP
ejpam-4715	33	5	this	this	DET
ejpam-4715	33	6	definition	definition	NOUN
ejpam-4715	33	7	,	,	PUNCT
ejpam-4715	33	8	the	the	DET
ejpam-4715	33	9	hankel	hankel	NOUN
ejpam-4715	33	10	transform	transform	NOUN
ejpam-4715	33	11	of	of	ADP
ejpam-4715	33	12	q	q	ADJ
ejpam-4715	33	13	-	-	ADJ
ejpam-4715	33	14	exponential	exponential	ADJ
ejpam-4715	33	15	polynomials	polynomial	NOUN
ejpam-4715	33	16	and	and	CCONJ
ejpam-4715	33	17	numbers	number	NOUN
ejpam-4715	33	18	was	be	AUX
ejpam-4715	33	19	successfully	successfully	ADV
ejpam-4715	33	20	established	establish	VERB
ejpam-4715	33	21	,	,	PUNCT
ejpam-4715	33	22	which	which	PRON
ejpam-4715	33	23	may	may	AUX
ejpam-4715	33	24	be	be	AUX
ejpam-4715	33	25	considered	consider	VERB
ejpam-4715	33	26	as	as	ADP
ejpam-4715	33	27	the	the	DET
ejpam-4715	33	28	hankel	hankel	NOUN
ejpam-4715	33	29	transform	transform	NOUN
ejpam-4715	33	30	of	of	ADP
ejpam-4715	33	31	a	a	DET
ejpam-4715	33	32	certain	certain	ADJ
ejpam-4715	33	33	q	q	NOUN
ejpam-4715	33	34	-	-	PUNCT
ejpam-4715	33	35	analogue	analogue	NOUN
ejpam-4715	33	36	of	of	ADP
ejpam-4715	33	37	bell	bell	NOUN
ejpam-4715	33	38	polynomials	polynomial	NOUN
ejpam-4715	33	39	and	and	CCONJ
ejpam-4715	33	40	numbers	number	NOUN
ejpam-4715	33	41	.	.	PUNCT
ejpam-4715	34	1	there	there	PRON
ejpam-4715	34	2	are	be	VERB
ejpam-4715	34	3	many	many	ADJ
ejpam-4715	34	4	ways	way	NOUN
ejpam-4715	34	5	to	to	PART
ejpam-4715	34	6	define	define	VERB
ejpam-4715	34	7	q	q	ADJ
ejpam-4715	34	8	-	-	PUNCT
ejpam-4715	34	9	analogue	analogue	NOUN
ejpam-4715	34	10	of	of	ADP
ejpam-4715	34	11	stirling	stirling	NOUN
ejpam-4715	34	12	-	-	PUNCT
ejpam-4715	34	13	type	type	NOUN
ejpam-4715	34	14	and	and	CCONJ
ejpam-4715	34	15	bell	bell	NOUN
ejpam-4715	34	16	-	-	PUNCT
ejpam-4715	34	17	type	type	NOUN
ejpam-4715	34	18	numbers	number	NOUN
ejpam-4715	34	19	(	(	PUNCT
ejpam-4715	34	20	see	see	VERB
ejpam-4715	34	21	[	[	X
ejpam-4715	34	22	6	6	NUM
ejpam-4715	34	23	,	,	PUNCT
ejpam-4715	34	24	8–10	8–10	NOUN
ejpam-4715	34	25	,	,	PUNCT
ejpam-4715	34	26	12	12	NUM
ejpam-4715	34	27	,	,	PUNCT
ejpam-4715	34	28	14	14	NUM
ejpam-4715	34	29	]	]	PUNCT
ejpam-4715	34	30	)	)	PUNCT
ejpam-4715	34	31	.	.	PUNCT
ejpam-4715	35	1	however	however	ADV
ejpam-4715	35	2	,	,	PUNCT
ejpam-4715	35	3	in	in	ADP
ejpam-4715	35	4	the	the	DET
ejpam-4715	35	5	desire	desire	NOUN
ejpam-4715	35	6	to	to	PART
ejpam-4715	35	7	establish	establish	VERB
ejpam-4715	35	8	the	the	DET
ejpam-4715	35	9	hankel	hankel	NOUN
ejpam-4715	35	10	transform	transform	NOUN
ejpam-4715	35	11	of	of	ADP
ejpam-4715	35	12	q	q	NOUN
ejpam-4715	35	13	-	-	PUNCT
ejpam-4715	35	14	analogue	analogue	NOUN
ejpam-4715	35	15	of	of	ADP
ejpam-4715	35	16	generalized	generalized	ADJ
ejpam-4715	35	17	bell	bell	NOUN
ejpam-4715	35	18	numbers	number	NOUN
ejpam-4715	35	19	,	,	PUNCT
ejpam-4715	35	20	corcino	corcino	PROPN
ejpam-4715	35	21	et	et	NOUN
ejpam-4715	35	22	al	al	PROPN
ejpam-4715	35	23	.	.	PUNCT
ejpam-4715	36	1	[	[	X
ejpam-4715	36	2	11	11	NUM
ejpam-4715	36	3	]	]	PUNCT
ejpam-4715	36	4	were	be	AUX
ejpam-4715	36	5	motivated	motivate	VERB
ejpam-4715	36	6	to	to	PART
ejpam-4715	36	7	define	define	VERB
ejpam-4715	36	8	a	a	DET
ejpam-4715	36	9	q	q	NOUN
ejpam-4715	36	10	-	-	PUNCT
ejpam-4715	36	11	analogue	analogue	NOUN
ejpam-4715	36	12	of	of	ADP
ejpam-4715	36	13	r	r	NOUN
ejpam-4715	36	14	-	-	PUNCT
ejpam-4715	36	15	whitney	whitney	NOUN
ejpam-4715	36	16	numbers	number	NOUN
ejpam-4715	36	17	of	of	ADP
ejpam-4715	36	18	the	the	DET
ejpam-4715	36	19	second	second	ADJ
ejpam-4715	36	20	kind	kind	NOUN
ejpam-4715	36	21	parallel	parallel	ADJ
ejpam-4715	36	22	to	to	ADP
ejpam-4715	36	23	that	that	PRON
ejpam-4715	36	24	in	in	ADP
ejpam-4715	36	25	(	(	PUNCT
ejpam-4715	36	26	1	1	NUM
ejpam-4715	36	27	)	)	PUNCT
ejpam-4715	36	28	as	as	SCONJ
ejpam-4715	36	29	follows	follow	VERB
ejpam-4715	36	30	:	:	PUNCT
ejpam-4715	36	31	wm	wm	X
ejpam-4715	36	32	,	,	PUNCT
ejpam-4715	36	33	r[n	r[n	NOUN
ejpam-4715	36	34	,	,	PUNCT
ejpam-4715	36	35	k]q	k]q	NOUN
ejpam-4715	36	36	=	=	SYM
ejpam-4715	36	37	qm(k−1)−rwm	qm(k−1)−rwm	PROPN
ejpam-4715	36	38	,	,	PUNCT
ejpam-4715	36	39	r[n−	r[n−	PROPN
ejpam-4715	36	40	1	1	NUM
ejpam-4715	36	41	,	,	PUNCT
ejpam-4715	36	42	k	k	PROPN
ejpam-4715	37	1	−	−	PROPN
ejpam-4715	37	2	1]q	1]q	PROPN
ejpam-4715	38	1	+	+	NUM
ejpam-4715	38	2	[	[	X
ejpam-4715	38	3	mk	mk	X
ejpam-4715	38	4	−	−	PROPN
ejpam-4715	38	5	r]qwm	r]qwm	NOUN
ejpam-4715	38	6	,	,	PUNCT
ejpam-4715	38	7	r[n−	r[n−	PROPN
ejpam-4715	38	8	1	1	NUM
ejpam-4715	38	9	,	,	PUNCT
ejpam-4715	38	10	k]q	k]q	PROPN
ejpam-4715	38	11	.	.	PUNCT
ejpam-4715	39	1	(	(	PUNCT
ejpam-4715	39	2	2	2	X
ejpam-4715	39	3	)	)	PUNCT
ejpam-4715	39	4	two	two	NUM
ejpam-4715	39	5	more	more	ADJ
ejpam-4715	39	6	forms	form	NOUN
ejpam-4715	39	7	of	of	ADP
ejpam-4715	39	8	this	this	DET
ejpam-4715	39	9	q	q	NOUN
ejpam-4715	39	10	-	-	PUNCT
ejpam-4715	39	11	analogue	analogue	NOUN
ejpam-4715	39	12	,	,	PUNCT
ejpam-4715	39	13	denoted	denote	VERB
ejpam-4715	39	14	by	by	ADP
ejpam-4715	39	15	w	w	PROPN
ejpam-4715	39	16	∗	∗	PROPN
ejpam-4715	39	17	m	m	PROPN
ejpam-4715	39	18	,	,	PUNCT
ejpam-4715	39	19	r[n	r[n	NOUN
ejpam-4715	39	20	,	,	PUNCT
ejpam-4715	39	21	k]q	k]q	NOUN
ejpam-4715	39	22	and	and	CCONJ
ejpam-4715	39	23	w̃m	w̃m	PROPN
ejpam-4715	39	24	,	,	PUNCT
ejpam-4715	39	25	r[n	r[n	NOUN
ejpam-4715	39	26	,	,	PUNCT
ejpam-4715	39	27	k]q	k]q	PROPN
ejpam-4715	39	28	,	,	PUNCT
ejpam-4715	39	29	were	be	AUX
ejpam-4715	39	30	respectively	respectively	ADV
ejpam-4715	39	31	defined	define	VERB
ejpam-4715	39	32	by	by	ADP
ejpam-4715	39	33	w	w	PROPN
ejpam-4715	39	34	∗	∗	PROPN
ejpam-4715	39	35	m	m	PROPN
ejpam-4715	39	36	,	,	PUNCT
ejpam-4715	39	37	r[n	r[n	NOUN
ejpam-4715	39	38	,	,	PUNCT
ejpam-4715	39	39	k]q	k]q	ADV
ejpam-4715	39	40	:	:	PUNCT
ejpam-4715	39	41	=	=	SYM
ejpam-4715	39	42	q−kr+m(k2)wm	q−kr+m(k2)wm	NOUN
ejpam-4715	39	43	,	,	PUNCT
ejpam-4715	39	44	r[n	r[n	NOUN
ejpam-4715	39	45	,	,	PUNCT
ejpam-4715	39	46	k]q	k]q	PROPN
ejpam-4715	39	47	,	,	PUNCT
ejpam-4715	39	48	w̃m	w̃m	PROPN
ejpam-4715	39	49	,	,	PUNCT
ejpam-4715	39	50	r[n	r[n	NOUN
ejpam-4715	39	51	,	,	PUNCT
ejpam-4715	39	52	k]q	k]q	ADV
ejpam-4715	39	53	:	:	PUNCT
ejpam-4715	40	1	=	=	SYM
ejpam-4715	40	2	q−krw	q−krw	PROPN
ejpam-4715	40	3	∗	∗	PROPN
ejpam-4715	40	4	m	m	PROPN
ejpam-4715	40	5	,	,	PUNCT
ejpam-4715	40	6	r[n	r[n	NOUN
ejpam-4715	40	7	,	,	PUNCT
ejpam-4715	40	8	k]q	k]q	NOUN
ejpam-4715	40	9	=	=	SYM
ejpam-4715	40	10	q−m(k2)wm	q−m(k2)wm	NOUN
ejpam-4715	40	11	,	,	PUNCT
ejpam-4715	40	12	r[n	r[n	NOUN
ejpam-4715	40	13	,	,	PUNCT
ejpam-4715	40	14	k	k	X
ejpam-4715	40	15	]	]	X
ejpam-4715	40	16	.	.	PUNCT
ejpam-4715	41	1	the	the	DET
ejpam-4715	41	2	corresponding	corresponding	ADJ
ejpam-4715	41	3	q	q	NOUN
ejpam-4715	41	4	-	-	PUNCT
ejpam-4715	41	5	analogues	analogue	NOUN
ejpam-4715	41	6	of	of	ADP
ejpam-4715	41	7	generalized	generalized	ADJ
ejpam-4715	41	8	bell	bell	NOUN
ejpam-4715	41	9	numbers	number	NOUN
ejpam-4715	41	10	,	,	PUNCT
ejpam-4715	41	11	also	also	ADV
ejpam-4715	41	12	known	know	VERB
ejpam-4715	41	13	as	as	ADP
ejpam-4715	41	14	q	q	NOUN
ejpam-4715	41	15	-	-	PUNCT
ejpam-4715	41	16	analogues	analogue	NOUN
ejpam-4715	41	17	of	of	ADP
ejpam-4715	41	18	r	r	NOUN
ejpam-4715	41	19	-	-	PUNCT
ejpam-4715	41	20	dowling	dowle	VERB
ejpam-4715	41	21	numbers	number	NOUN
ejpam-4715	41	22	,	,	PUNCT
ejpam-4715	41	23	were	be	AUX
ejpam-4715	41	24	also	also	ADV
ejpam-4715	41	25	defined	define	VERB
ejpam-4715	41	26	in	in	ADP
ejpam-4715	41	27	three	three	NUM
ejpam-4715	41	28	forms	form	NOUN
ejpam-4715	41	29	as	as	ADP
ejpam-4715	41	30	(	(	PUNCT
ejpam-4715	41	31	see	see	VERB
ejpam-4715	41	32	[	[	X
ejpam-4715	41	33	3	3	NUM
ejpam-4715	41	34	,	,	PUNCT
ejpam-4715	41	35	11	11	NUM
ejpam-4715	41	36	,	,	PUNCT
ejpam-4715	41	37	13	13	NUM
ejpam-4715	41	38	,	,	PUNCT
ejpam-4715	41	39	15	15	NUM
ejpam-4715	41	40	]	]	PUNCT
ejpam-4715	41	41	)	)	PUNCT
ejpam-4715	41	42	dm	dm	PROPN
ejpam-4715	41	43	,	,	PUNCT
ejpam-4715	41	44	r[n]q	r[n]q	NOUN
ejpam-4715	41	45	:	:	PUNCT
ejpam-4715	41	46	=	=	SYM
ejpam-4715	41	47	n∑	n∑	PROPN
ejpam-4715	41	48	k=0	k=0	PROPN
ejpam-4715	41	49	wm	wm	PROPN
ejpam-4715	41	50	,	,	PUNCT
ejpam-4715	41	51	r[n	r[n	NOUN
ejpam-4715	41	52	,	,	PUNCT
ejpam-4715	41	53	k]q	k]q	PROPN
ejpam-4715	41	54	,	,	PUNCT
ejpam-4715	41	55	r.	r.	PROPN
ejpam-4715	41	56	b.	b.	PROPN
ejpam-4715	41	57	corcino	corcino	PROPN
ejpam-4715	41	58	,	,	PUNCT
ejpam-4715	41	59	c.	c.	PROPN
ejpam-4715	41	60	b.	b.	PROPN
ejpam-4715	41	61	corcino	corcino	PROPN
ejpam-4715	41	62	/	/	SYM
ejpam-4715	41	63	eur	eur	PROPN
ejpam-4715	41	64	.	.	PUNCT
ejpam-4715	42	1	j.	j.	PROPN
ejpam-4715	42	2	pure	pure	PROPN
ejpam-4715	42	3	appl	appl	PROPN
ejpam-4715	42	4	.	.	PROPN
ejpam-4715	42	5	math	math	PROPN
ejpam-4715	42	6	,	,	PUNCT
ejpam-4715	42	7	16	16	NUM
ejpam-4715	42	8	(	(	PUNCT
ejpam-4715	42	9	2	2	NUM
ejpam-4715	42	10	)	)	PUNCT
ejpam-4715	42	11	(	(	PUNCT
ejpam-4715	42	12	2023	2023	NUM
ejpam-4715	42	13	)	)	PUNCT
ejpam-4715	42	14	,	,	PUNCT
ejpam-4715	42	15	934	934	NUM
ejpam-4715	42	16	-	-	SYM
ejpam-4715	42	17	943	943	NUM
ejpam-4715	42	18	936	936	NUM
ejpam-4715	42	19	d∗	d∗	PROPN
ejpam-4715	42	20	m	m	PROPN
ejpam-4715	42	21	,	,	PUNCT
ejpam-4715	42	22	r[n]q	r[n]q	INTJ
ejpam-4715	42	23	:	:	PUNCT
ejpam-4715	42	24	=	=	SYM
ejpam-4715	42	25	n∑	n∑	PROPN
ejpam-4715	42	26	k=0	k=0	PROPN
ejpam-4715	42	27	w	w	PROPN
ejpam-4715	42	28	∗	∗	PROPN
ejpam-4715	42	29	m	m	PROPN
ejpam-4715	42	30	,	,	PUNCT
ejpam-4715	42	31	r[n	r[n	NOUN
ejpam-4715	42	32	,	,	PUNCT
ejpam-4715	42	33	k]q	k]q	PROPN
ejpam-4715	42	34	,	,	PUNCT
ejpam-4715	42	35	and	and	CCONJ
ejpam-4715	42	36	d̃m	d̃m	PROPN
ejpam-4715	42	37	,	,	PUNCT
ejpam-4715	42	38	r[n]q	r[n]q	VERB
ejpam-4715	42	39	:	:	PUNCT
ejpam-4715	42	40	=	=	SYM
ejpam-4715	42	41	n∑	n∑	PROPN
ejpam-4715	42	42	k=0	k=0	PROPN
ejpam-4715	42	43	w̃m	w̃m	PROPN
ejpam-4715	42	44	,	,	PUNCT
ejpam-4715	42	45	r[n	r[n	NOUN
ejpam-4715	42	46	,	,	PUNCT
ejpam-4715	42	47	k]q	k]q	PROPN
ejpam-4715	42	48	.	.	PUNCT
ejpam-4715	43	1	where	where	SCONJ
ejpam-4715	43	2	dm	dm	NOUN
ejpam-4715	43	3	,	,	PUNCT
ejpam-4715	43	4	r[n]q	r[n]q	NOUN
ejpam-4715	43	5	,	,	PUNCT
ejpam-4715	43	6	d	d	PROPN
ejpam-4715	43	7	∗	∗	PROPN
ejpam-4715	43	8	m	m	PROPN
ejpam-4715	43	9	,	,	PUNCT
ejpam-4715	43	10	r[n]q	r[n]q	NOUN
ejpam-4715	43	11	and	and	CCONJ
ejpam-4715	43	12	d̃m	d̃m	PROPN
ejpam-4715	43	13	,	,	PUNCT
ejpam-4715	43	14	r[n]q	r[n]q	PROPN
ejpam-4715	43	15	denote	denote	VERB
ejpam-4715	43	16	the	the	DET
ejpam-4715	43	17	first	first	ADJ
ejpam-4715	43	18	,	,	PUNCT
ejpam-4715	43	19	second	second	ADJ
ejpam-4715	43	20	and	and	CCONJ
ejpam-4715	43	21	third	third	ADJ
ejpam-4715	43	22	form	form	NOUN
ejpam-4715	43	23	of	of	ADP
ejpam-4715	43	24	the	the	DET
ejpam-4715	43	25	qanalogues	qanalogue	NOUN
ejpam-4715	43	26	of	of	ADP
ejpam-4715	43	27	r	r	NOUN
ejpam-4715	43	28	-	-	PUNCT
ejpam-4715	43	29	dowling	dowle	VERB
ejpam-4715	43	30	numbers	number	NOUN
ejpam-4715	43	31	,	,	PUNCT
ejpam-4715	43	32	respectively	respectively	ADV
ejpam-4715	43	33	.	.	PUNCT
ejpam-4715	44	1	the	the	DET
ejpam-4715	44	2	hankel	hankel	NOUN
ejpam-4715	44	3	transforms	transform	VERB
ejpam-4715	44	4	ofdm	ofdm	NOUN
ejpam-4715	44	5	,	,	PUNCT
ejpam-4715	44	6	r[n]q	r[n]q	NOUN
ejpam-4715	44	7	,	,	PUNCT
ejpam-4715	44	8	d	d	PROPN
ejpam-4715	44	9	∗	∗	PROPN
ejpam-4715	44	10	m	m	PROPN
ejpam-4715	44	11	,	,	PUNCT
ejpam-4715	44	12	r[n]q	r[n]q	NOUN
ejpam-4715	44	13	and	and	CCONJ
ejpam-4715	44	14	d̃m	d̃m	PROPN
ejpam-4715	44	15	,	,	PUNCT
ejpam-4715	44	16	r[n]q	r[n]q	PROPN
ejpam-4715	44	17	were	be	AUX
ejpam-4715	44	18	successfully	successfully	ADV
ejpam-4715	44	19	established	establish	VERB
ejpam-4715	44	20	in	in	ADP
ejpam-4715	44	21	[	[	X
ejpam-4715	44	22	3	3	NUM
ejpam-4715	44	23	,	,	PUNCT
ejpam-4715	44	24	11	11	NUM
ejpam-4715	44	25	,	,	PUNCT
ejpam-4715	44	26	15	15	NUM
ejpam-4715	44	27	]	]	PUNCT
ejpam-4715	44	28	.	.	PUNCT
ejpam-4715	45	1	to	to	PART
ejpam-4715	45	2	extend	extend	VERB
ejpam-4715	45	3	these	these	DET
ejpam-4715	45	4	research	research	NOUN
ejpam-4715	45	5	studies	study	NOUN
ejpam-4715	45	6	,	,	PUNCT
ejpam-4715	45	7	a	a	DET
ejpam-4715	45	8	certain	certain	ADJ
ejpam-4715	45	9	(	(	PUNCT
ejpam-4715	45	10	p	p	NOUN
ejpam-4715	45	11	,	,	PUNCT
ejpam-4715	45	12	q)-analogue	q)-analogue	NOUN
ejpam-4715	45	13	of	of	ADP
ejpam-4715	45	14	r	r	PROPN
ejpam-4715	45	15	-	-	PUNCT
ejpam-4715	45	16	whitney	whitney	NOUN
ejpam-4715	45	17	numbers	number	NOUN
ejpam-4715	45	18	of	of	ADP
ejpam-4715	45	19	the	the	DET
ejpam-4715	45	20	second	second	ADJ
ejpam-4715	45	21	kind	kind	NOUN
ejpam-4715	45	22	,	,	PUNCT
ejpam-4715	45	23	denoted	denote	VERB
ejpam-4715	45	24	by	by	ADP
ejpam-4715	45	25	wm	wm	PROPN
ejpam-4715	45	26	,	,	PUNCT
ejpam-4715	45	27	r[n	r[n	NOUN
ejpam-4715	45	28	,	,	PUNCT
ejpam-4715	45	29	k]p	k]p	NOUN
ejpam-4715	45	30	,	,	PUNCT
ejpam-4715	45	31	q	q	X
ejpam-4715	45	32	,	,	PUNCT
ejpam-4715	45	33	was	be	AUX
ejpam-4715	45	34	defined	define	VERB
ejpam-4715	45	35	in	in	ADP
ejpam-4715	45	36	[	[	X
ejpam-4715	45	37	16	16	NUM
ejpam-4715	45	38	]	]	PUNCT
ejpam-4715	45	39	as	as	ADP
ejpam-4715	45	40	coefficients	coefficient	NOUN
ejpam-4715	45	41	of	of	ADP
ejpam-4715	45	42	the	the	DET
ejpam-4715	45	43	following	follow	VERB
ejpam-4715	45	44	generating	generate	VERB
ejpam-4715	45	45	function	function	NOUN
ejpam-4715	45	46	:	:	PUNCT
ejpam-4715	46	1	[	[	X
ejpam-4715	46	2	mt+	mt+	NOUN
ejpam-4715	46	3	r]np	r]np	PROPN
ejpam-4715	46	4	,	,	PUNCT
ejpam-4715	46	5	q	q	NOUN
ejpam-4715	46	6	=	=	SYM
ejpam-4715	46	7	n∑	n∑	PROPN
ejpam-4715	46	8	k=0	k=0	PROPN
ejpam-4715	46	9	wm	wm	PROPN
ejpam-4715	46	10	,	,	PUNCT
ejpam-4715	46	11	r[n	r[n	NOUN
ejpam-4715	46	12	,	,	PUNCT
ejpam-4715	46	13	k]p	k]p	NOUN
ejpam-4715	46	14	,	,	PUNCT
ejpam-4715	46	15	q[mt|m]kp	q[mt|m]kp	NOUN
ejpam-4715	46	16	,	,	PUNCT
ejpam-4715	46	17	q	q	X
ejpam-4715	46	18	(	(	PUNCT
ejpam-4715	46	19	3	3	NUM
ejpam-4715	46	20	)	)	PUNCT
ejpam-4715	46	21	where	where	SCONJ
ejpam-4715	46	22	[	[	X
ejpam-4715	46	23	t|m]np	t|m]np	ADP
ejpam-4715	46	24	,	,	PUNCT
ejpam-4715	46	25	q	q	PROPN
ejpam-4715	46	26	=	=	SYM
ejpam-4715	46	27	n−1∏	n−1∏	PROPN
ejpam-4715	46	28	j=0	j=0	PROPN
ejpam-4715	46	29	[	[	PUNCT
ejpam-4715	46	30	t−	t−	ADP
ejpam-4715	46	31	jm]p	jm]p	PROPN
ejpam-4715	46	32	,	,	PUNCT
ejpam-4715	46	33	q.	q.	PROPN
ejpam-4715	46	34	(	(	PUNCT
ejpam-4715	46	35	4	4	NUM
ejpam-4715	46	36	)	)	PUNCT
ejpam-4715	46	37	the	the	DET
ejpam-4715	46	38	orthogonality	orthogonality	NOUN
ejpam-4715	46	39	and	and	CCONJ
ejpam-4715	46	40	inverse	inverse	NOUN
ejpam-4715	46	41	relations	relation	NOUN
ejpam-4715	46	42	,	,	PUNCT
ejpam-4715	46	43	an	an	DET
ejpam-4715	46	44	explicit	explicit	ADJ
ejpam-4715	46	45	formula	formula	NOUN
ejpam-4715	46	46	,	,	PUNCT
ejpam-4715	46	47	and	and	CCONJ
ejpam-4715	46	48	a	a	DET
ejpam-4715	46	49	kind	kind	NOUN
ejpam-4715	46	50	of	of	ADP
ejpam-4715	46	51	exponential	exponential	ADJ
ejpam-4715	46	52	generating	generating	NOUN
ejpam-4715	46	53	function	function	NOUN
ejpam-4715	46	54	of	of	ADP
ejpam-4715	46	55	wm	wm	PROPN
ejpam-4715	46	56	,	,	PUNCT
ejpam-4715	46	57	r[n	r[n	NOUN
ejpam-4715	46	58	,	,	PUNCT
ejpam-4715	46	59	k]p	k]p	NOUN
ejpam-4715	46	60	,	,	PUNCT
ejpam-4715	46	61	q	q	PUNCT
ejpam-4715	46	62	were	be	AUX
ejpam-4715	46	63	already	already	ADV
ejpam-4715	46	64	obtained	obtain	VERB
ejpam-4715	46	65	.	.	PUNCT
ejpam-4715	47	1	unfortunately	unfortunately	ADV
ejpam-4715	47	2	,	,	PUNCT
ejpam-4715	47	3	its	its	PRON
ejpam-4715	47	4	hankel	hankel	NOUN
ejpam-4715	47	5	transform	transform	NOUN
ejpam-4715	47	6	was	be	AUX
ejpam-4715	47	7	not	not	PART
ejpam-4715	47	8	successfully	successfully	ADV
ejpam-4715	47	9	established	establish	VERB
ejpam-4715	47	10	using	use	VERB
ejpam-4715	47	11	the	the	DET
ejpam-4715	47	12	method	method	NOUN
ejpam-4715	47	13	applied	apply	VERB
ejpam-4715	47	14	in	in	ADP
ejpam-4715	47	15	[	[	X
ejpam-4715	47	16	3	3	NUM
ejpam-4715	47	17	,	,	PUNCT
ejpam-4715	47	18	11	11	NUM
ejpam-4715	47	19	,	,	PUNCT
ejpam-4715	47	20	15	15	NUM
ejpam-4715	47	21	]	]	PUNCT
ejpam-4715	47	22	.	.	PUNCT
ejpam-4715	48	1	this	this	DET
ejpam-4715	48	2	motivated	motivated	ADJ
ejpam-4715	48	3	corcino	corcino	NOUN
ejpam-4715	48	4	et	et	PROPN
ejpam-4715	48	5	al	al	PROPN
ejpam-4715	48	6	.	.	PUNCT
ejpam-4715	49	1	[	[	X
ejpam-4715	49	2	19	19	NUM
ejpam-4715	49	3	]	]	PUNCT
ejpam-4715	49	4	to	to	PART
ejpam-4715	49	5	define	define	VERB
ejpam-4715	49	6	the	the	DET
ejpam-4715	49	7	type	type	NOUN
ejpam-4715	49	8	2	2	NUM
ejpam-4715	49	9	(	(	PUNCT
ejpam-4715	49	10	p	p	NOUN
ejpam-4715	49	11	,	,	PUNCT
ejpam-4715	49	12	q)-analogue	q)-analogue	NOUN
ejpam-4715	49	13	of	of	ADP
ejpam-4715	49	14	r	r	PROPN
ejpam-4715	49	15	-	-	PUNCT
ejpam-4715	49	16	whitney	whitney	NOUN
ejpam-4715	49	17	numbers	number	NOUN
ejpam-4715	49	18	of	of	ADP
ejpam-4715	49	19	the	the	DET
ejpam-4715	49	20	second	second	ADJ
ejpam-4715	49	21	kind	kind	NOUN
ejpam-4715	49	22	,	,	PUNCT
ejpam-4715	49	23	denoted	denote	VERB
ejpam-4715	49	24	by	by	ADP
ejpam-4715	49	25	wm	wm	PROPN
ejpam-4715	49	26	,	,	PUNCT
ejpam-4715	49	27	r[n	r[n	PROPN
ejpam-4715	49	28	,	,	PUNCT
ejpam-4715	49	29	k	k	NOUN
ejpam-4715	49	30	;	;	PUNCT
ejpam-4715	49	31	t]p	t]p	X
ejpam-4715	49	32	,	,	PUNCT
ejpam-4715	49	33	q	q	X
ejpam-4715	49	34	,	,	PUNCT
ejpam-4715	49	35	as	as	SCONJ
ejpam-4715	49	36	follows	follow	VERB
ejpam-4715	49	37	:	:	PUNCT
ejpam-4715	49	38	wm	wm	PROPN
ejpam-4715	49	39	,	,	PUNCT
ejpam-4715	49	40	r[n+1	r[n+1	PROPN
ejpam-4715	49	41	,	,	PUNCT
ejpam-4715	49	42	k	k	NOUN
ejpam-4715	49	43	;	;	PUNCT
ejpam-4715	49	44	t]p	t]p	X
ejpam-4715	49	45	,	,	PUNCT
ejpam-4715	49	46	q	q	PROPN
ejpam-4715	49	47	=	=	PROPN
ejpam-4715	49	48	qm(k−1)+rwm	qm(k−1)+rwm	PROPN
ejpam-4715	49	49	,	,	PUNCT
ejpam-4715	49	50	r[n	r[n	NOUN
ejpam-4715	49	51	,	,	PUNCT
ejpam-4715	49	52	k−	k−	NOUN
ejpam-4715	49	53	1	1	NUM
ejpam-4715	49	54	;	;	PUNCT
ejpam-4715	49	55	t]p	t]p	X
ejpam-4715	49	56	,	,	PUNCT
ejpam-4715	49	57	q	q	X
ejpam-4715	50	1	+	+	CCONJ
ejpam-4715	50	2	[	[	X
ejpam-4715	50	3	mk+	mk+	ADJ
ejpam-4715	50	4	r]p	r]p	NOUN
ejpam-4715	50	5	,	,	PUNCT
ejpam-4715	50	6	qp	qp	ADP
ejpam-4715	50	7	mt−kmwm	mt−kmwm	NOUN
ejpam-4715	50	8	,	,	PUNCT
ejpam-4715	50	9	r[n	r[n	NOUN
ejpam-4715	50	10	,	,	PUNCT
ejpam-4715	50	11	k	k	NOUN
ejpam-4715	50	12	;	;	PUNCT
ejpam-4715	50	13	t]p	t]p	NOUN
ejpam-4715	50	14	,	,	PUNCT
ejpam-4715	50	15	q.	q.	PROPN
ejpam-4715	50	16	(	(	PUNCT
ejpam-4715	50	17	5	5	NUM
ejpam-4715	50	18	)	)	PUNCT
ejpam-4715	50	19	the	the	DET
ejpam-4715	50	20	second	second	ADJ
ejpam-4715	50	21	form	form	NOUN
ejpam-4715	50	22	was	be	AUX
ejpam-4715	50	23	then	then	ADV
ejpam-4715	50	24	defined	define	VERB
ejpam-4715	50	25	as	as	SCONJ
ejpam-4715	50	26	follows	follow	VERB
ejpam-4715	50	27	:	:	PUNCT
ejpam-4715	50	28	w	w	NOUN
ejpam-4715	50	29	∗	∗	NOUN
ejpam-4715	50	30	m	m	PROPN
ejpam-4715	50	31	,	,	PUNCT
ejpam-4715	50	32	r[n	r[n	NOUN
ejpam-4715	50	33	,	,	PUNCT
ejpam-4715	50	34	k	k	NOUN
ejpam-4715	50	35	;	;	PUNCT
ejpam-4715	50	36	t]p	t]p	X
ejpam-4715	50	37	,	,	PUNCT
ejpam-4715	50	38	q	q	NOUN
ejpam-4715	50	39	:	:	PUNCT
ejpam-4715	50	40	=	=	SYM
ejpam-4715	50	41	q−kr−m(k2)wm	q−kr−m(k2)wm	NOUN
ejpam-4715	50	42	,	,	PUNCT
ejpam-4715	50	43	r[n	r[n	NOUN
ejpam-4715	50	44	,	,	PUNCT
ejpam-4715	50	45	k	k	NOUN
ejpam-4715	50	46	;	;	PUNCT
ejpam-4715	50	47	t]p	t]p	NOUN
ejpam-4715	50	48	,	,	PUNCT
ejpam-4715	50	49	q.	q.	PROPN
ejpam-4715	50	50	(	(	PUNCT
ejpam-4715	50	51	6	6	NUM
ejpam-4715	50	52	)	)	PUNCT
ejpam-4715	50	53	several	several	ADJ
ejpam-4715	50	54	properties	property	NOUN
ejpam-4715	50	55	of	of	ADP
ejpam-4715	50	56	these	these	PRON
ejpam-4715	50	57	(	(	PUNCT
ejpam-4715	50	58	p	p	NOUN
ejpam-4715	50	59	,	,	PUNCT
ejpam-4715	50	60	q)-analogues	q)-analogue	NOUN
ejpam-4715	50	61	were	be	AUX
ejpam-4715	50	62	established	establish	VERB
ejpam-4715	50	63	in	in	ADP
ejpam-4715	50	64	[	[	X
ejpam-4715	50	65	19	19	NUM
ejpam-4715	50	66	]	]	PUNCT
ejpam-4715	50	67	including	include	VERB
ejpam-4715	50	68	their	their	PRON
ejpam-4715	50	69	hankel	hankel	NOUN
ejpam-4715	50	70	transforms	transform	VERB
ejpam-4715	50	71	,	,	PUNCT
ejpam-4715	50	72	which	which	PRON
ejpam-4715	50	73	are	be	AUX
ejpam-4715	50	74	given	give	VERB
ejpam-4715	50	75	by	by	ADP
ejpam-4715	50	76	det	det	PROPN
ejpam-4715	50	77	(	(	PUNCT
ejpam-4715	50	78	wm	wm	PROPN
ejpam-4715	50	79	,	,	PUNCT
ejpam-4715	50	80	r[s+	r[s+	PROPN
ejpam-4715	50	81	i+	i+	NUM
ejpam-4715	51	1	j	j	PROPN
ejpam-4715	51	2	,	,	PUNCT
ejpam-4715	51	3	s+	s+	PUNCT
ejpam-4715	51	4	j	j	PROPN
ejpam-4715	51	5	;	;	PUNCT
ejpam-4715	51	6	t]p	t]p	PROPN
ejpam-4715	51	7	,	,	PUNCT
ejpam-4715	51	8	q)0≤i	q)0≤i	NOUN
ejpam-4715	51	9	,	,	PUNCT
ejpam-4715	51	10	j≤n	j≤n	X
ejpam-4715	51	11	=	=	SYM
ejpam-4715	51	12	n∏	n∏	PROPN
ejpam-4715	51	13	k=0	k=0	PROPN
ejpam-4715	51	14	qm	qm	PROPN
ejpam-4715	51	15	(	(	PUNCT
ejpam-4715	51	16	s+k	s+k	X
ejpam-4715	51	17	2	2	NUM
ejpam-4715	51	18	)	)	PUNCT
ejpam-4715	52	1	+	+	ADJ
ejpam-4715	52	2	(	(	PUNCT
ejpam-4715	52	3	s+k)rpnmt[m(s+	s+k)rpnmt[m(s+	VERB
ejpam-4715	52	4	k	k	NOUN
ejpam-4715	52	5	)	)	PUNCT
ejpam-4715	53	1	+	+	CCONJ
ejpam-4715	53	2	r]kp	r]kp	PROPN
ejpam-4715	53	3	,	,	PUNCT
ejpam-4715	53	4	q	q	PUNCT
ejpam-4715	53	5	det(w	det(w	VERB
ejpam-4715	53	6	∗	∗	NOUN
ejpam-4715	53	7	m	m	NOUN
ejpam-4715	53	8	,	,	PUNCT
ejpam-4715	53	9	r[s+	r[s+	VERB
ejpam-4715	53	10	i+	i+	NUM
ejpam-4715	54	1	j	j	PROPN
ejpam-4715	54	2	,	,	PUNCT
ejpam-4715	54	3	s+	s+	PUNCT
ejpam-4715	54	4	j	j	PROPN
ejpam-4715	54	5	;	;	PUNCT
ejpam-4715	54	6	t]p	t]p	PROPN
ejpam-4715	54	7	,	,	PUNCT
ejpam-4715	54	8	q)0≤i	q)0≤i	NOUN
ejpam-4715	54	9	,	,	PUNCT
ejpam-4715	54	10	j≤n	j≤n	X
ejpam-4715	54	11	=	=	SYM
ejpam-4715	54	12	n∏	n∏	PROPN
ejpam-4715	54	13	k=0	k=0	PROPN
ejpam-4715	54	14	pnmt[m(s+	pnmt[m(s+	NOUN
ejpam-4715	54	15	k	k	NOUN
ejpam-4715	54	16	)	)	PUNCT
ejpam-4715	55	1	+	+	CCONJ
ejpam-4715	55	2	r]kp	r]kp	PROPN
ejpam-4715	55	3	,	,	PUNCT
ejpam-4715	55	4	q.	q.	NOUN
ejpam-4715	55	5	on	on	ADP
ejpam-4715	55	6	the	the	DET
ejpam-4715	55	7	other	other	ADJ
ejpam-4715	55	8	hand	hand	NOUN
ejpam-4715	55	9	,	,	PUNCT
ejpam-4715	55	10	the	the	DET
ejpam-4715	55	11	first	first	ADJ
ejpam-4715	55	12	,	,	PUNCT
ejpam-4715	55	13	second	second	ADJ
ejpam-4715	55	14	and	and	CCONJ
ejpam-4715	55	15	third	third	ADJ
ejpam-4715	55	16	forms	form	NOUN
ejpam-4715	55	17	of	of	ADP
ejpam-4715	55	18	type	type	NOUN
ejpam-4715	55	19	2	2	NUM
ejpam-4715	55	20	(	(	PUNCT
ejpam-4715	55	21	p	p	NOUN
ejpam-4715	55	22	,	,	PUNCT
ejpam-4715	55	23	q)-analogue	q)-analogue	NOUN
ejpam-4715	55	24	of	of	ADP
ejpam-4715	55	25	the	the	DET
ejpam-4715	55	26	r	r	NOUN
ejpam-4715	55	27	-	-	PUNCT
ejpam-4715	55	28	dowling	dowle	VERB
ejpam-4715	55	29	numbers	number	NOUN
ejpam-4715	55	30	,	,	PUNCT
ejpam-4715	55	31	denoted	denote	VERB
ejpam-4715	55	32	by	by	ADP
ejpam-4715	55	33	dm	dm	PROPN
ejpam-4715	55	34	,	,	PUNCT
ejpam-4715	55	35	r[n]p	r[n]p	ADJ
ejpam-4715	55	36	,	,	PUNCT
ejpam-4715	55	37	q	q	NOUN
ejpam-4715	55	38	,	,	PUNCT
ejpam-4715	55	39	d	d	PROPN
ejpam-4715	55	40	∗	∗	X
ejpam-4715	55	41	m	m	PROPN
ejpam-4715	55	42	,	,	PUNCT
ejpam-4715	55	43	r[n]p	r[n]p	ADJ
ejpam-4715	55	44	,	,	PUNCT
ejpam-4715	55	45	q	q	NOUN
ejpam-4715	55	46	and	and	CCONJ
ejpam-4715	55	47	d̃m	d̃m	PROPN
ejpam-4715	55	48	,	,	PUNCT
ejpam-4715	55	49	r[n]p	r[n]p	VERB
ejpam-4715	55	50	,	,	PUNCT
ejpam-4715	55	51	q	q	PUNCT
ejpam-4715	55	52	were	be	AUX
ejpam-4715	55	53	defined	define	VERB
ejpam-4715	55	54	respectively	respectively	ADV
ejpam-4715	55	55	in	in	ADP
ejpam-4715	55	56	[	[	X
ejpam-4715	55	57	19	19	NUM
ejpam-4715	55	58	]	]	PUNCT
ejpam-4715	55	59	as	as	SCONJ
ejpam-4715	55	60	follows	follow	VERB
ejpam-4715	55	61	:	:	PUNCT
ejpam-4715	55	62	dm	dm	NUM
ejpam-4715	55	63	,	,	PUNCT
ejpam-4715	55	64	r[n]p	r[n]p	ADJ
ejpam-4715	55	65	,	,	PUNCT
ejpam-4715	55	66	q	q	NOUN
ejpam-4715	55	67	:	:	PUNCT
ejpam-4715	55	68	=	=	SYM
ejpam-4715	55	69	n∑	n∑	PROPN
ejpam-4715	55	70	k=0	k=0	PROPN
ejpam-4715	55	71	wm	wm	PROPN
ejpam-4715	55	72	,	,	PUNCT
ejpam-4715	55	73	r[n	r[n	PROPN
ejpam-4715	55	74	,	,	PUNCT
ejpam-4715	55	75	k	k	NOUN
ejpam-4715	55	76	;	;	PUNCT
ejpam-4715	55	77	t]p	t]p	X
ejpam-4715	55	78	,	,	PUNCT
ejpam-4715	55	79	q	q	X
ejpam-4715	55	80	,	,	PUNCT
ejpam-4715	55	81	r.	r.	PROPN
ejpam-4715	55	82	b.	b.	PROPN
ejpam-4715	55	83	corcino	corcino	PROPN
ejpam-4715	55	84	,	,	PUNCT
ejpam-4715	55	85	c.	c.	PROPN
ejpam-4715	55	86	b.	b.	PROPN
ejpam-4715	55	87	corcino	corcino	PROPN
ejpam-4715	55	88	/	/	SYM
ejpam-4715	55	89	eur	eur	PROPN
ejpam-4715	55	90	.	.	PUNCT
ejpam-4715	56	1	j.	j.	PROPN
ejpam-4715	56	2	pure	pure	PROPN
ejpam-4715	56	3	appl	appl	PROPN
ejpam-4715	56	4	.	.	PROPN
ejpam-4715	56	5	math	math	PROPN
ejpam-4715	56	6	,	,	PUNCT
ejpam-4715	56	7	16	16	NUM
ejpam-4715	56	8	(	(	PUNCT
ejpam-4715	56	9	2	2	NUM
ejpam-4715	56	10	)	)	PUNCT
ejpam-4715	56	11	(	(	PUNCT
ejpam-4715	56	12	2023	2023	NUM
ejpam-4715	56	13	)	)	PUNCT
ejpam-4715	56	14	,	,	PUNCT
ejpam-4715	56	15	934	934	NUM
ejpam-4715	56	16	-	-	SYM
ejpam-4715	56	17	943	943	NUM
ejpam-4715	56	18	937	937	NUM
ejpam-4715	56	19	d∗	d∗	PROPN
ejpam-4715	56	20	m	m	PROPN
ejpam-4715	56	21	,	,	PUNCT
ejpam-4715	56	22	r[n]p	r[n]p	VERB
ejpam-4715	56	23	,	,	PUNCT
ejpam-4715	56	24	q	q	NOUN
ejpam-4715	56	25	:	:	PUNCT
ejpam-4715	56	26	=	=	SYM
ejpam-4715	56	27	n∑	n∑	PROPN
ejpam-4715	56	28	k=0	k=0	PROPN
ejpam-4715	56	29	w	w	PROPN
ejpam-4715	56	30	∗	∗	PROPN
ejpam-4715	56	31	m	m	PROPN
ejpam-4715	56	32	,	,	PUNCT
ejpam-4715	56	33	r[n	r[n	NOUN
ejpam-4715	56	34	,	,	PUNCT
ejpam-4715	56	35	k	k	NOUN
ejpam-4715	56	36	;	;	PUNCT
ejpam-4715	56	37	t]p	t]p	X
ejpam-4715	56	38	,	,	PUNCT
ejpam-4715	56	39	q	q	NOUN
ejpam-4715	56	40	,	,	PUNCT
ejpam-4715	56	41	d̃m	d̃m	PROPN
ejpam-4715	56	42	,	,	PUNCT
ejpam-4715	56	43	r[n]p	r[n]p	VERB
ejpam-4715	56	44	,	,	PUNCT
ejpam-4715	56	45	q	q	NOUN
ejpam-4715	56	46	:	:	PUNCT
ejpam-4715	56	47	=	=	SYM
ejpam-4715	56	48	n∑	n∑	PROPN
ejpam-4715	56	49	k=0	k=0	PROPN
ejpam-4715	56	50	w̃m	w̃m	PROPN
ejpam-4715	56	51	,	,	PUNCT
ejpam-4715	56	52	r[n	r[n	NOUN
ejpam-4715	56	53	,	,	PUNCT
ejpam-4715	56	54	k	k	NOUN
ejpam-4715	56	55	;	;	PUNCT
ejpam-4715	56	56	t]p	t]p	X
ejpam-4715	56	57	,	,	PUNCT
ejpam-4715	56	58	q	q	NOUN
ejpam-4715	56	59	,	,	PUNCT
ejpam-4715	56	60	where	where	SCONJ
ejpam-4715	56	61	w̃m	w̃m	PROPN
ejpam-4715	56	62	,	,	PUNCT
ejpam-4715	56	63	r[n	r[n	NOUN
ejpam-4715	56	64	,	,	PUNCT
ejpam-4715	56	65	k	k	NOUN
ejpam-4715	56	66	;	;	PUNCT
ejpam-4715	56	67	t]p	t]p	X
ejpam-4715	56	68	,	,	PUNCT
ejpam-4715	56	69	q	q	NOUN
ejpam-4715	56	70	=	=	PUNCT
ejpam-4715	56	71	qkrw	qkrw	NOUN
ejpam-4715	56	72	∗	∗	NOUN
ejpam-4715	56	73	m	m	PROPN
ejpam-4715	56	74	,	,	PUNCT
ejpam-4715	56	75	r[n	r[n	VERB
ejpam-4715	56	76	,	,	PUNCT
ejpam-4715	56	77	k	k	NOUN
ejpam-4715	56	78	;	;	PUNCT
ejpam-4715	56	79	t]p	t]p	X
ejpam-4715	56	80	,	,	PUNCT
ejpam-4715	56	81	q	q	X
ejpam-4715	56	82	(	(	PUNCT
ejpam-4715	56	83	7	7	NUM
ejpam-4715	56	84	)	)	PUNCT
ejpam-4715	56	85	denotes	denote	VERB
ejpam-4715	56	86	the	the	DET
ejpam-4715	56	87	third	third	ADJ
ejpam-4715	56	88	form	form	NOUN
ejpam-4715	56	89	of	of	ADP
ejpam-4715	56	90	the	the	DET
ejpam-4715	56	91	(	(	PUNCT
ejpam-4715	56	92	p	p	NOUN
ejpam-4715	56	93	,	,	PUNCT
ejpam-4715	56	94	q)-analogue	q)-analogue	NOUN
ejpam-4715	56	95	of	of	ADP
ejpam-4715	56	96	the	the	DET
ejpam-4715	56	97	r	r	PROPN
ejpam-4715	56	98	-	-	PUNCT
ejpam-4715	56	99	whitney	whitney	NOUN
ejpam-4715	56	100	numbers	number	NOUN
ejpam-4715	56	101	of	of	ADP
ejpam-4715	56	102	the	the	DET
ejpam-4715	56	103	second	second	ADJ
ejpam-4715	56	104	kind	kind	NOUN
ejpam-4715	56	105	.	.	PUNCT
ejpam-4715	57	1	among	among	ADP
ejpam-4715	57	2	these	these	DET
ejpam-4715	57	3	three	three	NUM
ejpam-4715	57	4	forms	form	NOUN
ejpam-4715	57	5	,	,	PUNCT
ejpam-4715	57	6	only	only	ADV
ejpam-4715	57	7	the	the	DET
ejpam-4715	57	8	second	second	ADJ
ejpam-4715	57	9	form	form	NOUN
ejpam-4715	57	10	was	be	AUX
ejpam-4715	57	11	provided	provide	VERB
ejpam-4715	57	12	a	a	DET
ejpam-4715	57	13	hankel	hankel	NOUN
ejpam-4715	57	14	transform	transform	NOUN
ejpam-4715	57	15	,	,	PUNCT
ejpam-4715	57	16	which	which	PRON
ejpam-4715	57	17	is	be	AUX
ejpam-4715	57	18	given	give	VERB
ejpam-4715	57	19	by	by	ADP
ejpam-4715	57	20	h(d∗	h(d∗	X
ejpam-4715	57	21	m	m	PROPN
ejpam-4715	57	22	,	,	PUNCT
ejpam-4715	57	23	r[n]p	r[n]p	ADJ
ejpam-4715	57	24	,	,	PUNCT
ejpam-4715	57	25	q	q	NOUN
ejpam-4715	57	26	)	)	PUNCT
ejpam-4715	57	27	=	=	SYM
ejpam-4715	57	28	(	(	PUNCT
ejpam-4715	57	29	q	q	X
ejpam-4715	57	30	p	p	NOUN
ejpam-4715	57	31	)	)	PUNCT
ejpam-4715	57	32	n(n2	n(n2	NOUN
ejpam-4715	57	33	+	+	ADJ
ejpam-4715	57	34	3n+8	3n+8	NUM
ejpam-4715	57	35	)	)	PUNCT
ejpam-4715	57	36	6	6	NUM
ejpam-4715	57	37	+	+	NOUN
ejpam-4715	57	38	r−1(n2	r−1(n2	X
ejpam-4715	57	39	)	)	PUNCT
ejpam-4715	57	40	(	(	PUNCT
ejpam-4715	57	41	[	[	X
ejpam-4715	57	42	m	m	X
ejpam-4715	57	43	]	]	X
ejpam-4715	57	44	q	q	X
ejpam-4715	57	45	p	p	NOUN
ejpam-4715	57	46	)	)	PUNCT
ejpam-4715	57	47	(	(	PUNCT
ejpam-4715	57	48	n	n	PROPN
ejpam-4715	57	49	2	2	NUM
ejpam-4715	57	50	)	)	PUNCT
ejpam-4715	58	1	n−1∏	n−1∏	PROPN
ejpam-4715	58	2	k=0	k=0	PROPN
ejpam-4715	59	1	[	[	X
ejpam-4715	59	2	k	k	X
ejpam-4715	59	3	]	]	X
ejpam-4715	59	4	(	(	PUNCT
ejpam-4715	59	5	q	q	PROPN
ejpam-4715	59	6	p	p	NOUN
ejpam-4715	59	7	)	)	PUNCT
ejpam-4715	59	8	m	m	PROPN
ejpam-4715	59	9	!	!	PUNCT
ejpam-4715	59	10	.	.	PUNCT
ejpam-4715	60	1	the	the	DET
ejpam-4715	60	2	main	main	ADJ
ejpam-4715	60	3	objective	objective	NOUN
ejpam-4715	60	4	of	of	ADP
ejpam-4715	60	5	this	this	DET
ejpam-4715	60	6	study	study	NOUN
ejpam-4715	60	7	is	be	AUX
ejpam-4715	60	8	to	to	PART
ejpam-4715	60	9	establish	establish	VERB
ejpam-4715	60	10	additional	additional	ADJ
ejpam-4715	60	11	property	property	NOUN
ejpam-4715	60	12	of	of	ADP
ejpam-4715	60	13	the	the	DET
ejpam-4715	60	14	type	type	NOUN
ejpam-4715	60	15	2	2	NUM
ejpam-4715	60	16	(	(	PUNCT
ejpam-4715	60	17	p	p	NOUN
ejpam-4715	60	18	,	,	PUNCT
ejpam-4715	60	19	q)analogues	q)analogue	NOUN
ejpam-4715	60	20	of	of	ADP
ejpam-4715	60	21	the	the	DET
ejpam-4715	60	22	r	r	NOUN
ejpam-4715	60	23	-	-	PUNCT
ejpam-4715	60	24	whitney	whitney	NOUN
ejpam-4715	60	25	numbers	number	NOUN
ejpam-4715	60	26	of	of	ADP
ejpam-4715	60	27	the	the	DET
ejpam-4715	60	28	second	second	ADJ
ejpam-4715	60	29	kind	kind	NOUN
ejpam-4715	60	30	.	.	PUNCT
ejpam-4715	61	1	more	more	ADV
ejpam-4715	61	2	precisely	precisely	ADV
ejpam-4715	61	3	,	,	PUNCT
ejpam-4715	61	4	the	the	DET
ejpam-4715	61	5	divisibility	divisibility	NOUN
ejpam-4715	61	6	property	property	NOUN
ejpam-4715	61	7	of	of	ADP
ejpam-4715	61	8	these	these	DET
ejpam-4715	61	9	type	type	NOUN
ejpam-4715	61	10	2	2	NUM
ejpam-4715	61	11	(	(	PUNCT
ejpam-4715	61	12	p	p	NOUN
ejpam-4715	61	13	,	,	PUNCT
ejpam-4715	61	14	q)-analogues	q)-analogue	NOUN
ejpam-4715	61	15	will	will	AUX
ejpam-4715	61	16	be	be	AUX
ejpam-4715	61	17	discussed	discuss	VERB
ejpam-4715	61	18	thoroughly	thoroughly	ADV
ejpam-4715	61	19	.	.	PUNCT
ejpam-4715	62	1	2	2	X
ejpam-4715	62	2	.	.	X
ejpam-4715	62	3	preliminary	preliminary	ADJ
ejpam-4715	62	4	results	result	NOUN
ejpam-4715	62	5	this	this	DET
ejpam-4715	62	6	section	section	NOUN
ejpam-4715	62	7	provides	provide	VERB
ejpam-4715	62	8	a	a	DET
ejpam-4715	62	9	brief	brief	ADJ
ejpam-4715	62	10	discussion	discussion	NOUN
ejpam-4715	62	11	on	on	ADP
ejpam-4715	62	12	some	some	DET
ejpam-4715	62	13	relations	relation	NOUN
ejpam-4715	62	14	that	that	PRON
ejpam-4715	62	15	are	be	AUX
ejpam-4715	62	16	necessary	necessary	ADJ
ejpam-4715	62	17	in	in	ADP
ejpam-4715	62	18	deriving	derive	VERB
ejpam-4715	62	19	the	the	DET
ejpam-4715	62	20	divisibility	divisibility	NOUN
ejpam-4715	62	21	property	property	NOUN
ejpam-4715	62	22	of	of	ADP
ejpam-4715	62	23	the	the	DET
ejpam-4715	62	24	type	type	NOUN
ejpam-4715	62	25	2	2	NUM
ejpam-4715	62	26	(	(	PUNCT
ejpam-4715	62	27	p	p	NOUN
ejpam-4715	62	28	,	,	PUNCT
ejpam-4715	62	29	q)-analogue	q)-analogue	NOUN
ejpam-4715	62	30	of	of	ADP
ejpam-4715	62	31	the	the	DET
ejpam-4715	62	32	r	r	PROPN
ejpam-4715	62	33	-	-	PUNCT
ejpam-4715	62	34	whitney	whitney	NOUN
ejpam-4715	62	35	numbers	number	NOUN
ejpam-4715	62	36	of	of	ADP
ejpam-4715	62	37	the	the	DET
ejpam-4715	62	38	second	second	ADJ
ejpam-4715	62	39	kind	kind	NOUN
ejpam-4715	62	40	w	w	PROPN
ejpam-4715	62	41	∗	∗	PROPN
ejpam-4715	62	42	m	m	PROPN
ejpam-4715	62	43	,	,	PUNCT
ejpam-4715	62	44	r[n	r[n	NOUN
ejpam-4715	62	45	,	,	PUNCT
ejpam-4715	62	46	k	k	NOUN
ejpam-4715	62	47	;	;	PUNCT
ejpam-4715	62	48	t]p	t]p	NOUN
ejpam-4715	62	49	,	,	PUNCT
ejpam-4715	62	50	q.	q.	PROPN
ejpam-4715	62	51	multiplying	multiply	VERB
ejpam-4715	62	52	both	both	DET
ejpam-4715	62	53	sides	side	NOUN
ejpam-4715	62	54	of	of	ADP
ejpam-4715	62	55	the	the	DET
ejpam-4715	62	56	recurrence	recurrence	NOUN
ejpam-4715	62	57	relation	relation	NOUN
ejpam-4715	62	58	in	in	ADP
ejpam-4715	62	59	(	(	PUNCT
ejpam-4715	62	60	5	5	NUM
ejpam-4715	62	61	)	)	PUNCT
ejpam-4715	62	62	by	by	ADP
ejpam-4715	62	63	q−kr−m(k2	q−kr−m(k2	NOUN
ejpam-4715	62	64	)	)	PUNCT
ejpam-4715	62	65	yields	yield	NOUN
ejpam-4715	62	66	q−kr−m(k2)wm	q−kr−m(k2)wm	NOUN
ejpam-4715	62	67	,	,	PUNCT
ejpam-4715	62	68	r[n+	r[n+	NOUN
ejpam-4715	62	69	1	1	NUM
ejpam-4715	62	70	,	,	PUNCT
ejpam-4715	62	71	k	k	NOUN
ejpam-4715	62	72	;	;	PUNCT
ejpam-4715	62	73	t]p	t]p	X
ejpam-4715	62	74	,	,	PUNCT
ejpam-4715	62	75	q	q	X
ejpam-4715	62	76	=	=	SYM
ejpam-4715	62	77	q−kr−m(k2)qm(k−1)+rwm	q−kr−m(k2)qm(k−1)+rwm	PROPN
ejpam-4715	62	78	,	,	PUNCT
ejpam-4715	62	79	r[n	r[n	NOUN
ejpam-4715	62	80	,	,	PUNCT
ejpam-4715	62	81	k	k	PROPN
ejpam-4715	62	82	−	−	PROPN
ejpam-4715	62	83	1	1	NUM
ejpam-4715	62	84	;	;	PUNCT
ejpam-4715	63	1	t]p	t]p	X
ejpam-4715	63	2	,	,	PUNCT
ejpam-4715	63	3	q	q	X
ejpam-4715	63	4	+	+	CCONJ
ejpam-4715	63	5	q−kr−m(k2)[mk	q−kr−m(k2)[mk	ADV
ejpam-4715	63	6	+	+	CCONJ
ejpam-4715	63	7	r]p	r]p	NOUN
ejpam-4715	63	8	,	,	PUNCT
ejpam-4715	63	9	qp	qp	ADP
ejpam-4715	63	10	mt−kmwm	mt−kmwm	NOUN
ejpam-4715	63	11	,	,	PUNCT
ejpam-4715	63	12	r[n	r[n	NOUN
ejpam-4715	63	13	,	,	PUNCT
ejpam-4715	63	14	k	k	NOUN
ejpam-4715	63	15	;	;	PUNCT
ejpam-4715	63	16	t]p	t]p	X
ejpam-4715	63	17	,	,	PUNCT
ejpam-4715	63	18	q	q	PROPN
ejpam-4715	63	19	q−kr−m(k2)wm	q−kr−m(k2)wm	NOUN
ejpam-4715	63	20	,	,	PUNCT
ejpam-4715	63	21	r[n+	r[n+	NOUN
ejpam-4715	63	22	1	1	NUM
ejpam-4715	63	23	,	,	PUNCT
ejpam-4715	63	24	k	k	NOUN
ejpam-4715	63	25	;	;	PUNCT
ejpam-4715	63	26	t]p	t]p	X
ejpam-4715	63	27	,	,	PUNCT
ejpam-4715	63	28	q	q	NOUN
ejpam-4715	63	29	=	=	PRON
ejpam-4715	63	30	q−(k−1)r−m(k−1	q−(k−1)r−m(k−1	PROPN
ejpam-4715	63	31	2	2	NUM
ejpam-4715	63	32	)	)	PUNCT
ejpam-4715	63	33	wm	wm	PROPN
ejpam-4715	63	34	,	,	PUNCT
ejpam-4715	63	35	r[n	r[n	PROPN
ejpam-4715	63	36	,	,	PUNCT
ejpam-4715	63	37	k	k	PROPN
ejpam-4715	63	38	−	−	PROPN
ejpam-4715	63	39	1	1	NUM
ejpam-4715	63	40	;	;	PUNCT
ejpam-4715	63	41	t]p	t]p	X
ejpam-4715	63	42	,	,	PUNCT
ejpam-4715	63	43	q	q	X
ejpam-4715	64	1	+	+	PUNCT
ejpam-4715	64	2	[	[	X
ejpam-4715	64	3	mk	mk	X
ejpam-4715	64	4	+	+	CCONJ
ejpam-4715	64	5	r]p	r]p	PROPN
ejpam-4715	64	6	,	,	PUNCT
ejpam-4715	64	7	qp	qp	ADP
ejpam-4715	64	8	mt−kmq−kr−m(k2)wm	mt−kmq−kr−m(k2)wm	NOUN
ejpam-4715	64	9	,	,	PUNCT
ejpam-4715	64	10	r[n	r[n	NOUN
ejpam-4715	64	11	,	,	PUNCT
ejpam-4715	64	12	k	k	NOUN
ejpam-4715	64	13	;	;	PUNCT
ejpam-4715	64	14	t]p	t]p	NOUN
ejpam-4715	64	15	,	,	PUNCT
ejpam-4715	64	16	q.	q.	PROPN
ejpam-4715	64	17	applying	apply	VERB
ejpam-4715	64	18	(	(	PUNCT
ejpam-4715	64	19	6	6	NUM
ejpam-4715	64	20	)	)	PUNCT
ejpam-4715	64	21	consequently	consequently	ADV
ejpam-4715	64	22	gives	give	VERB
ejpam-4715	64	23	w	w	PROPN
ejpam-4715	64	24	∗	∗	NOUN
ejpam-4715	64	25	m	m	PROPN
ejpam-4715	64	26	,	,	PUNCT
ejpam-4715	64	27	r[n+	r[n+	NOUN
ejpam-4715	64	28	1	1	NUM
ejpam-4715	64	29	,	,	PUNCT
ejpam-4715	64	30	k	k	NOUN
ejpam-4715	64	31	;	;	PUNCT
ejpam-4715	64	32	t]p	t]p	X
ejpam-4715	64	33	,	,	PUNCT
ejpam-4715	64	34	q	q	NOUN
ejpam-4715	64	35	=	=	PUNCT
ejpam-4715	64	36	w	w	PROPN
ejpam-4715	64	37	∗	∗	PROPN
ejpam-4715	64	38	m	m	PROPN
ejpam-4715	64	39	,	,	PUNCT
ejpam-4715	64	40	r[n	r[n	VERB
ejpam-4715	64	41	,	,	PUNCT
ejpam-4715	64	42	k	k	PROPN
ejpam-4715	65	1	−	−	PROPN
ejpam-4715	66	1	1	1	NUM
ejpam-4715	66	2	;	;	PUNCT
ejpam-4715	66	3	t]p	t]p	X
ejpam-4715	66	4	,	,	PUNCT
ejpam-4715	66	5	q	q	X
ejpam-4715	67	1	+	+	PUNCT
ejpam-4715	67	2	[	[	X
ejpam-4715	67	3	mk	mk	X
ejpam-4715	67	4	+	+	CCONJ
ejpam-4715	67	5	r]p	r]p	PROPN
ejpam-4715	67	6	,	,	PUNCT
ejpam-4715	67	7	qp	qp	ADP
ejpam-4715	67	8	mt−kmw	mt−kmw	NOUN
ejpam-4715	67	9	∗	∗	PROPN
ejpam-4715	67	10	m	m	PROPN
ejpam-4715	67	11	,	,	PUNCT
ejpam-4715	67	12	r[n	r[n	VERB
ejpam-4715	67	13	,	,	PUNCT
ejpam-4715	67	14	k	k	NOUN
ejpam-4715	67	15	;	;	PUNCT
ejpam-4715	67	16	t]p	t]p	NOUN
ejpam-4715	67	17	,	,	PUNCT
ejpam-4715	67	18	q.	q.	PROPN
ejpam-4715	67	19	(	(	PUNCT
ejpam-4715	67	20	8)	8)	NUM
ejpam-4715	67	21	this	this	DET
ejpam-4715	67	22	relation	relation	NOUN
ejpam-4715	67	23	can	can	AUX
ejpam-4715	67	24	be	be	AUX
ejpam-4715	67	25	used	use	VERB
ejpam-4715	67	26	to	to	PART
ejpam-4715	67	27	generate	generate	VERB
ejpam-4715	67	28	the	the	DET
ejpam-4715	67	29	following	follow	VERB
ejpam-4715	67	30	first	first	ADJ
ejpam-4715	67	31	few	few	ADJ
ejpam-4715	67	32	values	value	NOUN
ejpam-4715	67	33	of	of	ADP
ejpam-4715	67	34	w	w	PROPN
ejpam-4715	67	35	∗	∗	NOUN
ejpam-4715	67	36	m	m	PROPN
ejpam-4715	67	37	,	,	PUNCT
ejpam-4715	67	38	r[n	r[n	NOUN
ejpam-4715	67	39	,	,	PUNCT
ejpam-4715	67	40	k	k	NOUN
ejpam-4715	67	41	;	;	PUNCT
ejpam-4715	67	42	t]p	t]p	X
ejpam-4715	67	43	,	,	PUNCT
ejpam-4715	67	44	q	q	NOUN
ejpam-4715	67	45	:	:	PUNCT
ejpam-4715	67	46	by	by	ADP
ejpam-4715	67	47	repeated	repeat	VERB
ejpam-4715	67	48	application	application	NOUN
ejpam-4715	67	49	of	of	ADP
ejpam-4715	67	50	(	(	PUNCT
ejpam-4715	67	51	8)	8)	NUM
ejpam-4715	67	52	,	,	PUNCT
ejpam-4715	67	53	we	we	PRON
ejpam-4715	67	54	can	can	AUX
ejpam-4715	67	55	easily	easily	ADV
ejpam-4715	67	56	derive	derive	VERB
ejpam-4715	67	57	the	the	DET
ejpam-4715	67	58	following	follow	VERB
ejpam-4715	67	59	vertical	vertical	ADJ
ejpam-4715	67	60	recurrence	recurrence	PROPN
ejpam-4715	67	61	relation	relation	PROPN
ejpam-4715	67	62	.	.	PUNCT
ejpam-4715	68	1	theorem	theorem	VERB
ejpam-4715	68	2	2.1	2.1	NUM
ejpam-4715	68	3	.	.	PUNCT
ejpam-4715	69	1	for	for	ADP
ejpam-4715	69	2	nonnegative	nonnegative	ADJ
ejpam-4715	69	3	integers	integer	NOUN
ejpam-4715	69	4	n	n	PRON
ejpam-4715	69	5	and	and	CCONJ
ejpam-4715	69	6	k	k	NOUN
ejpam-4715	69	7	,	,	PUNCT
ejpam-4715	69	8	and	and	CCONJ
ejpam-4715	69	9	real	real	ADJ
ejpam-4715	69	10	number	number	NOUN
ejpam-4715	69	11	r	r	NOUN
ejpam-4715	69	12	,	,	PUNCT
ejpam-4715	69	13	the	the	DET
ejpam-4715	69	14	(	(	PUNCT
ejpam-4715	69	15	p	p	NOUN
ejpam-4715	69	16	,	,	PUNCT
ejpam-4715	69	17	q)-analogue	q)-analogue	NOUN
ejpam-4715	69	18	of	of	ADP
ejpam-4715	69	19	r	r	PROPN
ejpam-4715	69	20	-	-	PUNCT
ejpam-4715	69	21	whitney	whitney	NOUN
ejpam-4715	69	22	numbers	number	NOUN
ejpam-4715	69	23	of	of	ADP
ejpam-4715	69	24	the	the	DET
ejpam-4715	69	25	second	second	ADJ
ejpam-4715	69	26	kind	kind	NOUN
ejpam-4715	69	27	satisfies	satisfy	VERB
ejpam-4715	69	28	the	the	DET
ejpam-4715	69	29	following	follow	VERB
ejpam-4715	69	30	vertical	vertical	ADJ
ejpam-4715	69	31	recurrence	recurrence	NOUN
ejpam-4715	69	32	relation	relation	PROPN
ejpam-4715	69	33	w	w	PROPN
ejpam-4715	69	34	∗	∗	PROPN
ejpam-4715	69	35	m	m	PROPN
ejpam-4715	69	36	,	,	PUNCT
ejpam-4715	69	37	r[n+	r[n+	NOUN
ejpam-4715	69	38	1	1	NUM
ejpam-4715	69	39	,	,	PUNCT
ejpam-4715	69	40	k	k	PROPN
ejpam-4715	70	1	+	+	PROPN
ejpam-4715	70	2	1	1	NUM
ejpam-4715	70	3	;	;	PUNCT
ejpam-4715	70	4	t]p	t]p	X
ejpam-4715	70	5	,	,	PUNCT
ejpam-4715	70	6	q	q	PROPN
ejpam-4715	70	7	=	=	PUNCT
ejpam-4715	70	8	n∑	n∑	PROPN
ejpam-4715	70	9	j	j	PROPN
ejpam-4715	71	1	=	=	PROPN
ejpam-4715	71	2	k	k	PROPN
ejpam-4715	72	1	[	[	X
ejpam-4715	72	2	m(k	m(k	PROPN
ejpam-4715	72	3	+	+	CCONJ
ejpam-4715	72	4	1	1	NUM
ejpam-4715	72	5	)	)	PUNCT
ejpam-4715	72	6	+	+	NUM
ejpam-4715	72	7	r]n−j	r]n−j	NOUN
ejpam-4715	72	8	p	p	X
ejpam-4715	72	9	,	,	PUNCT
ejpam-4715	72	10	q	q	PROPN
ejpam-4715	72	11	p(n−j)[mt−(k+1)m]w	p(n−j)[mt−(k+1)m]w	PROPN
ejpam-4715	72	12	∗	∗	NOUN
ejpam-4715	72	13	m	m	PROPN
ejpam-4715	72	14	,	,	PUNCT
ejpam-4715	72	15	r[j	r[j	NOUN
ejpam-4715	72	16	,	,	PUNCT
ejpam-4715	72	17	k	k	NOUN
ejpam-4715	72	18	;	;	PUNCT
ejpam-4715	72	19	t]p	t]p	NOUN
ejpam-4715	72	20	,	,	PUNCT
ejpam-4715	72	21	q.	q.	PROPN
ejpam-4715	72	22	(	(	PUNCT
ejpam-4715	72	23	9	9	NUM
ejpam-4715	72	24	)	)	PUNCT
ejpam-4715	72	25	r.	r.	PROPN
ejpam-4715	72	26	b.	b.	PROPN
ejpam-4715	72	27	corcino	corcino	PROPN
ejpam-4715	72	28	,	,	PUNCT
ejpam-4715	72	29	c.	c.	PROPN
ejpam-4715	72	30	b.	b.	PROPN
ejpam-4715	72	31	corcino	corcino	PROPN
ejpam-4715	72	32	/	/	SYM
ejpam-4715	72	33	eur	eur	PROPN
ejpam-4715	72	34	.	.	PUNCT
ejpam-4715	73	1	j.	j.	PROPN
ejpam-4715	73	2	pure	pure	PROPN
ejpam-4715	73	3	appl	appl	PROPN
ejpam-4715	73	4	.	.	PROPN
ejpam-4715	73	5	math	math	PROPN
ejpam-4715	73	6	,	,	PUNCT
ejpam-4715	73	7	16	16	NUM
ejpam-4715	73	8	(	(	PUNCT
ejpam-4715	73	9	2	2	NUM
ejpam-4715	73	10	)	)	PUNCT
ejpam-4715	73	11	(	(	PUNCT
ejpam-4715	73	12	2023	2023	NUM
ejpam-4715	73	13	)	)	PUNCT
ejpam-4715	73	14	,	,	PUNCT
ejpam-4715	73	15	934	934	NUM
ejpam-4715	73	16	-	-	SYM
ejpam-4715	73	17	943	943	NUM
ejpam-4715	73	18	938	938	NUM
ejpam-4715	73	19	n	n	NOUN
ejpam-4715	73	20	/	/	SYM
ejpam-4715	73	21	k	k	NOUN
ejpam-4715	73	22	0	0	NUM
ejpam-4715	73	23	1	1	NUM
ejpam-4715	73	24	2	2	NUM
ejpam-4715	73	25	3	3	NUM
ejpam-4715	73	26	0	0	NUM
ejpam-4715	73	27	1	1	NUM
ejpam-4715	73	28	1	1	NUM
ejpam-4715	73	29	[	[	X
ejpam-4715	73	30	r]p	r]p	NOUN
ejpam-4715	73	31	,	,	PUNCT
ejpam-4715	73	32	qp	qp	ADP
ejpam-4715	73	33	mt	mt	PROPN
ejpam-4715	73	34	1	1	NUM
ejpam-4715	73	35	2	2	NUM
ejpam-4715	73	36	[	[	X
ejpam-4715	73	37	r]2p	r]2p	NOUN
ejpam-4715	73	38	,	,	PUNCT
ejpam-4715	73	39	qp	qp	ADP
ejpam-4715	73	40	2mt	2mt	NOUN
ejpam-4715	74	1	[	[	X
ejpam-4715	74	2	r]p	r]p	NOUN
ejpam-4715	74	3	,	,	PUNCT
ejpam-4715	74	4	qp	qp	ADP
ejpam-4715	74	5	mt	mt	PROPN
ejpam-4715	74	6	+	+	PROPN
ejpam-4715	75	1	[	[	X
ejpam-4715	75	2	m+	m+	NUM
ejpam-4715	75	3	r]p	r]p	NOUN
ejpam-4715	75	4	,	,	PUNCT
ejpam-4715	75	5	qp	qp	ADP
ejpam-4715	75	6	m(t−1	m(t−1	PROPN
ejpam-4715	75	7	)	)	PUNCT
ejpam-4715	75	8	1	1	NUM
ejpam-4715	75	9	3	3	NUM
ejpam-4715	76	1	[	[	X
ejpam-4715	76	2	r]3p	r]3p	NOUN
ejpam-4715	76	3	,	,	PUNCT
ejpam-4715	76	4	qp	qp	ADP
ejpam-4715	76	5	3mt	3mt	NOUN
ejpam-4715	77	1	[	[	X
ejpam-4715	77	2	r]2p	r]2p	NOUN
ejpam-4715	77	3	,	,	PUNCT
ejpam-4715	77	4	qp	qp	ADP
ejpam-4715	77	5	2mt	2mt	NOUN
ejpam-4715	78	1	+	+	CCONJ
ejpam-4715	79	1	[	[	X
ejpam-4715	79	2	r]p	r]p	NOUN
ejpam-4715	79	3	,	,	PUNCT
ejpam-4715	79	4	q[m+	q[m+	ADJ
ejpam-4715	79	5	r]p	r]p	NOUN
ejpam-4715	79	6	,	,	PUNCT
ejpam-4715	79	7	qp	qp	ADP
ejpam-4715	79	8	m(2t−1	m(2t−1	PROPN
ejpam-4715	79	9	)	)	PUNCT
ejpam-4715	80	1	[	[	X
ejpam-4715	80	2	r]p	r]p	NOUN
ejpam-4715	80	3	,	,	PUNCT
ejpam-4715	80	4	qp	qp	ADP
ejpam-4715	80	5	mt	mt	PROPN
ejpam-4715	80	6	+	+	CCONJ
ejpam-4715	80	7	2[m+	2[m+	NUM
ejpam-4715	80	8	r]p	r]p	NOUN
ejpam-4715	80	9	,	,	PUNCT
ejpam-4715	80	10	qp	qp	ADP
ejpam-4715	80	11	m(t−1	m(t−1	PROPN
ejpam-4715	80	12	)	)	PUNCT
ejpam-4715	80	13	1	1	NUM
ejpam-4715	81	1	+	+	ADJ
ejpam-4715	81	2	[	[	X
ejpam-4715	81	3	m+	m+	NUM
ejpam-4715	81	4	r]2p	r]2p	PROPN
ejpam-4715	81	5	,	,	PUNCT
ejpam-4715	81	6	qp	qp	ADP
ejpam-4715	81	7	2m(t−1	2m(t−1	NUM
ejpam-4715	81	8	)	)	PUNCT
ejpam-4715	81	9	table	table	NOUN
ejpam-4715	81	10	1	1	NUM
ejpam-4715	81	11	:	:	PUNCT
ejpam-4715	81	12	the	the	DET
ejpam-4715	81	13	first	first	ADJ
ejpam-4715	81	14	values	value	NOUN
ejpam-4715	81	15	of	of	ADP
ejpam-4715	81	16	w	w	PROPN
ejpam-4715	81	17	∗	∗	NOUN
ejpam-4715	81	18	m	m	PROPN
ejpam-4715	81	19	,	,	PUNCT
ejpam-4715	81	20	r[n	r[n	NOUN
ejpam-4715	81	21	,	,	PUNCT
ejpam-4715	81	22	k	k	NOUN
ejpam-4715	81	23	;	;	PUNCT
ejpam-4715	81	24	t]p	t]p	X
ejpam-4715	81	25	,	,	PUNCT
ejpam-4715	81	26	q	q	PRON
ejpam-4715	81	27	one	one	PRON
ejpam-4715	81	28	can	can	AUX
ejpam-4715	81	29	easily	easily	ADV
ejpam-4715	81	30	verify	verify	VERB
ejpam-4715	81	31	relation	relation	NOUN
ejpam-4715	81	32	(	(	PUNCT
ejpam-4715	81	33	9	9	X
ejpam-4715	81	34	)	)	PUNCT
ejpam-4715	81	35	using	use	VERB
ejpam-4715	81	36	the	the	DET
ejpam-4715	81	37	values	value	NOUN
ejpam-4715	81	38	of	of	ADP
ejpam-4715	81	39	w	w	PROPN
ejpam-4715	81	40	∗	∗	NOUN
ejpam-4715	81	41	m	m	PROPN
ejpam-4715	81	42	,	,	PUNCT
ejpam-4715	81	43	r[n	r[n	NOUN
ejpam-4715	81	44	,	,	PUNCT
ejpam-4715	81	45	k	k	NOUN
ejpam-4715	81	46	;	;	PUNCT
ejpam-4715	81	47	t]p	t]p	X
ejpam-4715	81	48	,	,	PUNCT
ejpam-4715	81	49	q	q	NOUN
ejpam-4715	81	50	in	in	ADP
ejpam-4715	81	51	table	table	NOUN
ejpam-4715	81	52	1	1	NUM
ejpam-4715	81	53	.	.	PUNCT
ejpam-4715	82	1	now	now	ADV
ejpam-4715	82	2	,	,	PUNCT
ejpam-4715	82	3	let	let	VERB
ejpam-4715	82	4	us	we	PRON
ejpam-4715	82	5	derive	derive	VERB
ejpam-4715	82	6	the	the	DET
ejpam-4715	82	7	rational	rational	ADJ
ejpam-4715	82	8	generating	generating	NOUN
ejpam-4715	82	9	function	function	NOUN
ejpam-4715	82	10	for	for	ADP
ejpam-4715	82	11	w	w	PROPN
ejpam-4715	82	12	∗	∗	NOUN
ejpam-4715	82	13	m	m	PROPN
ejpam-4715	82	14	,	,	PUNCT
ejpam-4715	82	15	r[n	r[n	NOUN
ejpam-4715	82	16	,	,	PUNCT
ejpam-4715	82	17	k	k	NOUN
ejpam-4715	82	18	;	;	PUNCT
ejpam-4715	82	19	t]p	t]p	PROPN
ejpam-4715	82	20	,	,	PUNCT
ejpam-4715	82	21	q.	q.	PROPN
ejpam-4715	82	22	suppose	suppose	VERB
ejpam-4715	82	23	that	that	SCONJ
ejpam-4715	82	24	ψ∗	ψ∗	PROPN
ejpam-4715	82	25	k(x	k(x	PROPN
ejpam-4715	82	26	)	)	PUNCT
ejpam-4715	82	27	=	=	PUNCT
ejpam-4715	83	1	∞∑	∞∑	NUM
ejpam-4715	83	2	n	n	CCONJ
ejpam-4715	83	3	=	=	SYM
ejpam-4715	83	4	k	k	PROPN
ejpam-4715	83	5	w	w	PROPN
ejpam-4715	83	6	∗	∗	PROPN
ejpam-4715	83	7	m	m	PROPN
ejpam-4715	83	8	,	,	PUNCT
ejpam-4715	83	9	r[n	r[n	NOUN
ejpam-4715	83	10	,	,	PUNCT
ejpam-4715	83	11	k	k	X
ejpam-4715	83	12	;	;	PUNCT
ejpam-4715	83	13	t]p	t]p	X
ejpam-4715	83	14	,	,	PUNCT
ejpam-4715	83	15	qx	qx	PROPN
ejpam-4715	83	16	n−k	n−k	NOUN
ejpam-4715	83	17	.	.	PUNCT
ejpam-4715	84	1	when	when	SCONJ
ejpam-4715	84	2	k	k	PROPN
ejpam-4715	84	3	=	=	SYM
ejpam-4715	84	4	0	0	PROPN
ejpam-4715	84	5	,	,	PUNCT
ejpam-4715	84	6	(	(	PUNCT
ejpam-4715	84	7	8)	8)	NUM
ejpam-4715	84	8	reduces	reduce	VERB
ejpam-4715	84	9	to	to	ADP
ejpam-4715	84	10	w	w	PROPN
ejpam-4715	84	11	∗	∗	PROPN
ejpam-4715	84	12	m	m	PROPN
ejpam-4715	84	13	,	,	PUNCT
ejpam-4715	84	14	r[n+	r[n+	NOUN
ejpam-4715	84	15	1	1	NUM
ejpam-4715	84	16	,	,	PUNCT
ejpam-4715	84	17	0	0	NUM
ejpam-4715	84	18	;	;	PUNCT
ejpam-4715	84	19	t]p	t]p	X
ejpam-4715	84	20	,	,	PUNCT
ejpam-4715	84	21	q	q	NOUN
ejpam-4715	84	22	=	=	PUNCT
ejpam-4715	85	1	[	[	X
ejpam-4715	85	2	r]p	r]p	NOUN
ejpam-4715	85	3	,	,	PUNCT
ejpam-4715	85	4	qp	qp	ADP
ejpam-4715	85	5	mtw	mtw	PROPN
ejpam-4715	85	6	∗	∗	NOUN
ejpam-4715	85	7	m	m	PROPN
ejpam-4715	85	8	,	,	PUNCT
ejpam-4715	85	9	r[n	r[n	NOUN
ejpam-4715	85	10	,	,	PUNCT
ejpam-4715	85	11	0	0	NUM
ejpam-4715	85	12	;	;	PUNCT
ejpam-4715	85	13	t]p	t]p	NOUN
ejpam-4715	85	14	,	,	PUNCT
ejpam-4715	85	15	q.	q.	NOUN
ejpam-4715	85	16	by	by	ADP
ejpam-4715	85	17	repeated	repeat	VERB
ejpam-4715	85	18	application	application	NOUN
ejpam-4715	85	19	of	of	ADP
ejpam-4715	85	20	(	(	PUNCT
ejpam-4715	85	21	8)	8)	NUM
ejpam-4715	85	22	,	,	PUNCT
ejpam-4715	85	23	this	this	PRON
ejpam-4715	85	24	inductively	inductively	ADV
ejpam-4715	85	25	gives	give	VERB
ejpam-4715	85	26	w	w	PROPN
ejpam-4715	85	27	∗	∗	NOUN
ejpam-4715	85	28	m	m	PROPN
ejpam-4715	85	29	,	,	PUNCT
ejpam-4715	85	30	r[n+	r[n+	NOUN
ejpam-4715	85	31	1	1	NUM
ejpam-4715	85	32	,	,	PUNCT
ejpam-4715	85	33	0	0	NUM
ejpam-4715	85	34	;	;	PUNCT
ejpam-4715	85	35	t]p	t]p	X
ejpam-4715	85	36	,	,	PUNCT
ejpam-4715	85	37	q	q	NOUN
ejpam-4715	86	1	=	=	PUNCT
ejpam-4715	87	1	[	[	X
ejpam-4715	87	2	r]p	r]p	NOUN
ejpam-4715	87	3	,	,	PUNCT
ejpam-4715	87	4	qp	qp	ADP
ejpam-4715	87	5	mtw	mtw	PROPN
ejpam-4715	87	6	∗	∗	NOUN
ejpam-4715	87	7	m	m	PROPN
ejpam-4715	87	8	,	,	PUNCT
ejpam-4715	87	9	r[n	r[n	NOUN
ejpam-4715	87	10	,	,	PUNCT
ejpam-4715	87	11	0	0	NUM
ejpam-4715	87	12	;	;	PUNCT
ejpam-4715	87	13	t]p	t]p	X
ejpam-4715	87	14	,	,	PUNCT
ejpam-4715	87	15	q	q	NOUN
ejpam-4715	87	16	=	=	SYM
ejpam-4715	87	17	(	(	PUNCT
ejpam-4715	87	18	[	[	X
ejpam-4715	87	19	r]p	r]p	NOUN
ejpam-4715	87	20	,	,	PUNCT
ejpam-4715	87	21	qp	qp	ADP
ejpam-4715	87	22	mt	mt	PROPN
ejpam-4715	87	23	)	)	PUNCT
ejpam-4715	87	24	2	2	PROPN
ejpam-4715	87	25	w	w	PROPN
ejpam-4715	87	26	∗	∗	NOUN
ejpam-4715	87	27	m	m	PROPN
ejpam-4715	87	28	,	,	PUNCT
ejpam-4715	87	29	r[n−	r[n−	ADJ
ejpam-4715	87	30	1	1	NUM
ejpam-4715	87	31	,	,	PUNCT
ejpam-4715	87	32	0	0	NUM
ejpam-4715	87	33	;	;	PUNCT
ejpam-4715	87	34	t]p	t]p	X
ejpam-4715	87	35	,	,	PUNCT
ejpam-4715	87	36	q	q	NOUN
ejpam-4715	87	37	...	...	PUNCT
ejpam-4715	87	38	=	=	PUNCT
ejpam-4715	87	39	(	(	PUNCT
ejpam-4715	87	40	[	[	X
ejpam-4715	87	41	r]p	r]p	NOUN
ejpam-4715	87	42	,	,	PUNCT
ejpam-4715	87	43	qp	qp	ADP
ejpam-4715	87	44	mt	mt	PROPN
ejpam-4715	87	45	)	)	PUNCT
ejpam-4715	87	46	n+1	n+1	PROPN
ejpam-4715	87	47	w	w	PROPN
ejpam-4715	87	48	∗	∗	X
ejpam-4715	87	49	m	m	PROPN
ejpam-4715	87	50	,	,	PUNCT
ejpam-4715	87	51	r[0	r[0	PROPN
ejpam-4715	87	52	,	,	PUNCT
ejpam-4715	87	53	0	0	NUM
ejpam-4715	87	54	;	;	PUNCT
ejpam-4715	87	55	t]p	t]p	X
ejpam-4715	87	56	,	,	PUNCT
ejpam-4715	87	57	q	q	NOUN
ejpam-4715	87	58	=	=	SYM
ejpam-4715	87	59	(	(	PUNCT
ejpam-4715	87	60	[	[	X
ejpam-4715	87	61	r]p	r]p	NOUN
ejpam-4715	87	62	,	,	PUNCT
ejpam-4715	87	63	qp	qp	ADP
ejpam-4715	87	64	mt	mt	PROPN
ejpam-4715	87	65	)	)	PUNCT
ejpam-4715	87	66	n+1	n+1	PROPN
ejpam-4715	87	67	.	.	PUNCT
ejpam-4715	88	1	hence	hence	ADV
ejpam-4715	88	2	,	,	PUNCT
ejpam-4715	88	3	ψ∗	ψ∗	NOUN
ejpam-4715	88	4	0(x	0(x	NOUN
ejpam-4715	88	5	)	)	PUNCT
ejpam-4715	89	1	=	=	PUNCT
ejpam-4715	90	1	∞∑	∞∑	PRON
ejpam-4715	90	2	n=0	n=0	NUM
ejpam-4715	90	3	w	w	NOUN
ejpam-4715	90	4	∗	∗	NOUN
ejpam-4715	90	5	m	m	PROPN
ejpam-4715	90	6	,	,	PUNCT
ejpam-4715	90	7	r[n	r[n	NOUN
ejpam-4715	90	8	,	,	PUNCT
ejpam-4715	90	9	0	0	NUM
ejpam-4715	90	10	;	;	PUNCT
ejpam-4715	90	11	t]p	t]p	X
ejpam-4715	90	12	,	,	PUNCT
ejpam-4715	90	13	qx	qx	PROPN
ejpam-4715	90	14	n	n	NOUN
ejpam-4715	90	15	=	=	SYM
ejpam-4715	90	16	1	1	NUM
ejpam-4715	90	17	(	(	PUNCT
ejpam-4715	90	18	1−	1−	NUM
ejpam-4715	90	19	xpmt[r]p	xpmt[r]p	NUM
ejpam-4715	90	20	,	,	PUNCT
ejpam-4715	90	21	q	q	NOUN
ejpam-4715	90	22	)	)	PUNCT
ejpam-4715	90	23	.	.	PUNCT
ejpam-4715	91	1	when	when	SCONJ
ejpam-4715	91	2	k	k	PROPN
ejpam-4715	91	3	>	>	X
ejpam-4715	91	4	0	0	PUNCT
ejpam-4715	91	5	and	and	CCONJ
ejpam-4715	91	6	applying	apply	VERB
ejpam-4715	91	7	the	the	DET
ejpam-4715	91	8	triangular	triangular	NOUN
ejpam-4715	91	9	recurrence	recurrence	NOUN
ejpam-4715	91	10	relation	relation	NOUN
ejpam-4715	91	11	in	in	ADP
ejpam-4715	91	12	(	(	PUNCT
ejpam-4715	91	13	5	5	NUM
ejpam-4715	91	14	)	)	PUNCT
ejpam-4715	91	15	,	,	PUNCT
ejpam-4715	91	16	we	we	PRON
ejpam-4715	91	17	have	have	VERB
ejpam-4715	91	18	ψ∗	ψ∗	NOUN
ejpam-4715	91	19	k(x	k(x	PROPN
ejpam-4715	91	20	)	)	PUNCT
ejpam-4715	92	1	=	=	PUNCT
ejpam-4715	93	1	∞∑	∞∑	NUM
ejpam-4715	93	2	n	n	CCONJ
ejpam-4715	93	3	=	=	SYM
ejpam-4715	93	4	k	k	PROPN
ejpam-4715	93	5	w	w	PROPN
ejpam-4715	93	6	∗	∗	PROPN
ejpam-4715	93	7	m	m	PROPN
ejpam-4715	93	8	,	,	PUNCT
ejpam-4715	93	9	r[n	r[n	NOUN
ejpam-4715	93	10	,	,	PUNCT
ejpam-4715	93	11	k	k	X
ejpam-4715	93	12	;	;	PUNCT
ejpam-4715	93	13	t]p	t]p	X
ejpam-4715	93	14	,	,	PUNCT
ejpam-4715	93	15	qx	qx	PROPN
ejpam-4715	93	16	n−k	n−k	NOUN
ejpam-4715	93	17	=	=	NUM
ejpam-4715	93	18	∞∑	∞∑	NUM
ejpam-4715	93	19	n−1	n−1	PROPN
ejpam-4715	93	20	=	=	PROPN
ejpam-4715	93	21	k−1	k−1	PROPN
ejpam-4715	93	22	w	w	PROPN
ejpam-4715	93	23	∗	∗	PROPN
ejpam-4715	93	24	m	m	PROPN
ejpam-4715	93	25	,	,	PUNCT
ejpam-4715	93	26	r[n−	r[n−	PROPN
ejpam-4715	93	27	1	1	NUM
ejpam-4715	93	28	,	,	PUNCT
ejpam-4715	93	29	k	k	PROPN
ejpam-4715	93	30	−	−	PROPN
ejpam-4715	93	31	1	1	NUM
ejpam-4715	93	32	;	;	PUNCT
ejpam-4715	93	33	t]p	t]p	ADP
ejpam-4715	93	34	,	,	PUNCT
ejpam-4715	93	35	qx	qx	PROPN
ejpam-4715	93	36	(	(	PUNCT
ejpam-4715	93	37	n−1)(k−1	n−1)(k−1	PROPN
ejpam-4715	93	38	)	)	PUNCT
ejpam-4715	93	39	+	+	CCONJ
ejpam-4715	93	40	xpmt−km[mk	xpmt−km[mk	PROPN
ejpam-4715	93	41	+	+	CCONJ
ejpam-4715	93	42	r]p	r]p	PROPN
ejpam-4715	93	43	,	,	PUNCT
ejpam-4715	93	44	q	q	PROPN
ejpam-4715	93	45	∞∑	∞∑	PROPN
ejpam-4715	93	46	n−1	n−1	PROPN
ejpam-4715	93	47	=	=	PROPN
ejpam-4715	93	48	k	k	PROPN
ejpam-4715	93	49	w	w	PROPN
ejpam-4715	93	50	∗	∗	PROPN
ejpam-4715	93	51	m	m	PROPN
ejpam-4715	93	52	,	,	PUNCT
ejpam-4715	93	53	r[n−	r[n−	PROPN
ejpam-4715	93	54	1	1	NUM
ejpam-4715	93	55	,	,	PUNCT
ejpam-4715	93	56	k	k	NOUN
ejpam-4715	93	57	;	;	PUNCT
ejpam-4715	93	58	t]p	t]p	X
ejpam-4715	93	59	,	,	PUNCT
ejpam-4715	93	60	qx	qx	PROPN
ejpam-4715	93	61	n−1−k	n−1−k	NOUN
ejpam-4715	93	62	=	=	NOUN
ejpam-4715	93	63	ψ∗	ψ∗	NOUN
ejpam-4715	93	64	k−1(x	k−1(x	PROPN
ejpam-4715	93	65	)	)	PUNCT
ejpam-4715	93	66	+	+	CCONJ
ejpam-4715	93	67	xpm(t−k)[mk	xpm(t−k)[mk	NUM
ejpam-4715	93	68	+	+	NUM
ejpam-4715	93	69	r]p	r]p	PROPN
ejpam-4715	93	70	,	,	PUNCT
ejpam-4715	93	71	qψ	qψ	ADP
ejpam-4715	93	72	∗	∗	NOUN
ejpam-4715	93	73	k(x	k(x	PROPN
ejpam-4715	93	74	)	)	PUNCT
ejpam-4715	94	1	solving	solve	VERB
ejpam-4715	94	2	for	for	ADP
ejpam-4715	94	3	ψ∗	ψ∗	PROPN
ejpam-4715	94	4	k(t	k(t	PROPN
ejpam-4715	94	5	)	)	PUNCT
ejpam-4715	94	6	yields	yield	VERB
ejpam-4715	94	7	ψ∗	ψ∗	PROPN
ejpam-4715	94	8	k(x	k(x	PROPN
ejpam-4715	94	9	)	)	PUNCT
ejpam-4715	94	10	=	=	PUNCT
ejpam-4715	95	1	1	1	NUM
ejpam-4715	95	2	1−	1−	NUM
ejpam-4715	95	3	xpm(t−k)[mk	xpm(t−k)[mk	NUM
ejpam-4715	95	4	+	+	CCONJ
ejpam-4715	95	5	r]p	r]p	PROPN
ejpam-4715	95	6	,	,	PUNCT
ejpam-4715	95	7	q	q	NOUN
ejpam-4715	95	8	ψ∗	ψ∗	NOUN
ejpam-4715	95	9	k−1(x	k−1(x	PROPN
ejpam-4715	95	10	)	)	PUNCT
ejpam-4715	95	11	.	.	PUNCT
ejpam-4715	96	1	applying	apply	VERB
ejpam-4715	96	2	backward	backward	ADJ
ejpam-4715	96	3	substitution	substitution	NOUN
ejpam-4715	96	4	gives	give	VERB
ejpam-4715	96	5	the	the	DET
ejpam-4715	96	6	following	follow	VERB
ejpam-4715	96	7	rational	rational	ADJ
ejpam-4715	96	8	generating	generating	NOUN
ejpam-4715	96	9	function	function	NOUN
ejpam-4715	96	10	forwm	forwm	NOUN
ejpam-4715	96	11	,	,	PUNCT
ejpam-4715	96	12	r[n	r[n	NOUN
ejpam-4715	96	13	,	,	PUNCT
ejpam-4715	96	14	k	k	NOUN
ejpam-4715	96	15	;	;	PUNCT
ejpam-4715	96	16	t]p	t]p	PROPN
ejpam-4715	96	17	,	,	PUNCT
ejpam-4715	96	18	q.	q.	PROPN
ejpam-4715	96	19	r.	r.	PROPN
ejpam-4715	96	20	b.	b.	PROPN
ejpam-4715	96	21	corcino	corcino	PROPN
ejpam-4715	96	22	,	,	PUNCT
ejpam-4715	96	23	c.	c.	PROPN
ejpam-4715	96	24	b.	b.	PROPN
ejpam-4715	96	25	corcino	corcino	PROPN
ejpam-4715	96	26	/	/	SYM
ejpam-4715	96	27	eur	eur	PROPN
ejpam-4715	96	28	.	.	PUNCT
ejpam-4715	97	1	j.	j.	PROPN
ejpam-4715	97	2	pure	pure	PROPN
ejpam-4715	97	3	appl	appl	PROPN
ejpam-4715	97	4	.	.	PROPN
ejpam-4715	97	5	math	math	PROPN
ejpam-4715	97	6	,	,	PUNCT
ejpam-4715	97	7	16	16	NUM
ejpam-4715	97	8	(	(	PUNCT
ejpam-4715	97	9	2	2	NUM
ejpam-4715	97	10	)	)	PUNCT
ejpam-4715	97	11	(	(	PUNCT
ejpam-4715	97	12	2023	2023	NUM
ejpam-4715	97	13	)	)	PUNCT
ejpam-4715	97	14	,	,	PUNCT
ejpam-4715	97	15	934	934	NUM
ejpam-4715	97	16	-	-	SYM
ejpam-4715	97	17	943	943	NUM
ejpam-4715	97	18	939	939	NUM
ejpam-4715	97	19	theorem	theorem	NOUN
ejpam-4715	97	20	2.2	2.2	NUM
ejpam-4715	97	21	.	.	PUNCT
ejpam-4715	98	1	for	for	ADP
ejpam-4715	98	2	nonnegative	nonnegative	ADJ
ejpam-4715	98	3	integers	integer	NOUN
ejpam-4715	98	4	n	n	PRON
ejpam-4715	98	5	and	and	CCONJ
ejpam-4715	98	6	k	k	NOUN
ejpam-4715	98	7	,	,	PUNCT
ejpam-4715	98	8	and	and	CCONJ
ejpam-4715	98	9	real	real	ADJ
ejpam-4715	98	10	number	number	NOUN
ejpam-4715	98	11	r	r	NOUN
ejpam-4715	98	12	,	,	PUNCT
ejpam-4715	98	13	the	the	DET
ejpam-4715	98	14	(	(	PUNCT
ejpam-4715	98	15	p	p	NOUN
ejpam-4715	98	16	,	,	PUNCT
ejpam-4715	98	17	q)-analogue	q)-analogue	NOUN
ejpam-4715	98	18	wm	wm	PROPN
ejpam-4715	98	19	,	,	PUNCT
ejpam-4715	98	20	r[n	r[n	PROPN
ejpam-4715	98	21	,	,	PUNCT
ejpam-4715	98	22	k	k	NOUN
ejpam-4715	98	23	;	;	PUNCT
ejpam-4715	98	24	t]p	t]p	X
ejpam-4715	98	25	,	,	PUNCT
ejpam-4715	98	26	q	q	PUNCT
ejpam-4715	98	27	satisfies	satisfy	VERB
ejpam-4715	98	28	the	the	DET
ejpam-4715	98	29	following	follow	VERB
ejpam-4715	98	30	rational	rational	ADJ
ejpam-4715	98	31	generating	generating	NOUN
ejpam-4715	98	32	function	function	NOUN
ejpam-4715	98	33	ψ∗	ψ∗	PROPN
ejpam-4715	98	34	k(x	k(x	PROPN
ejpam-4715	98	35	)	)	PUNCT
ejpam-4715	98	36	=	=	PUNCT
ejpam-4715	99	1	∞∑	∞∑	NUM
ejpam-4715	99	2	n	n	CCONJ
ejpam-4715	99	3	=	=	SYM
ejpam-4715	99	4	k	k	PROPN
ejpam-4715	99	5	w	w	PROPN
ejpam-4715	99	6	∗	∗	PROPN
ejpam-4715	99	7	m	m	PROPN
ejpam-4715	99	8	,	,	PUNCT
ejpam-4715	99	9	r[n	r[n	NOUN
ejpam-4715	99	10	,	,	PUNCT
ejpam-4715	99	11	k	k	X
ejpam-4715	99	12	;	;	PUNCT
ejpam-4715	99	13	t]p	t]p	X
ejpam-4715	99	14	,	,	PUNCT
ejpam-4715	99	15	qx	qx	PROPN
ejpam-4715	99	16	n−k	n−k	NOUN
ejpam-4715	99	17	=	=	SYM
ejpam-4715	99	18	1∏k	1∏k	NUM
ejpam-4715	99	19	j=0(1−	j=0(1−	PROPN
ejpam-4715	99	20	xpm(t−j)[mj	xpm(t−j)[mj	PUNCT
ejpam-4715	99	21	+	+	CCONJ
ejpam-4715	99	22	r]p	r]p	PROPN
ejpam-4715	99	23	,	,	PUNCT
ejpam-4715	99	24	q	q	NOUN
ejpam-4715	99	25	)	)	PUNCT
ejpam-4715	99	26	.	.	PUNCT
ejpam-4715	100	1	(	(	PUNCT
ejpam-4715	100	2	10	10	NUM
ejpam-4715	100	3	)	)	PUNCT
ejpam-4715	100	4	remark	remark	NOUN
ejpam-4715	100	5	2.3	2.3	NUM
ejpam-4715	100	6	.	.	PUNCT
ejpam-4715	101	1	this	this	DET
ejpam-4715	101	2	rational	rational	ADJ
ejpam-4715	101	3	generating	generating	NOUN
ejpam-4715	101	4	function	function	NOUN
ejpam-4715	101	5	plays	play	VERB
ejpam-4715	101	6	an	an	DET
ejpam-4715	101	7	important	important	ADJ
ejpam-4715	101	8	role	role	NOUN
ejpam-4715	101	9	in	in	ADP
ejpam-4715	101	10	proving	prove	VERB
ejpam-4715	101	11	the	the	DET
ejpam-4715	101	12	main	main	ADJ
ejpam-4715	101	13	result	result	NOUN
ejpam-4715	101	14	of	of	ADP
ejpam-4715	101	15	the	the	DET
ejpam-4715	101	16	paper	paper	NOUN
ejpam-4715	101	17	.	.	PUNCT
ejpam-4715	102	1	3	3	X
ejpam-4715	102	2	.	.	X
ejpam-4715	102	3	divisibility	divisibility	NOUN
ejpam-4715	102	4	property	property	NOUN
ejpam-4715	102	5	in	in	ADP
ejpam-4715	102	6	this	this	DET
ejpam-4715	102	7	section	section	NOUN
ejpam-4715	102	8	,	,	PUNCT
ejpam-4715	102	9	the	the	DET
ejpam-4715	102	10	congruence	congruence	PROPN
ejpam-4715	102	11	relation	relation	NOUN
ejpam-4715	102	12	modulo	modulo	PROPN
ejpam-4715	102	13	pq	pq	PROPN
ejpam-4715	102	14	for	for	ADP
ejpam-4715	102	15	the	the	DET
ejpam-4715	102	16	type	type	NOUN
ejpam-4715	102	17	2	2	NUM
ejpam-4715	102	18	(	(	PUNCT
ejpam-4715	102	19	p	p	NOUN
ejpam-4715	102	20	,	,	PUNCT
ejpam-4715	102	21	q)-analogue	q)-analogue	NOUN
ejpam-4715	102	22	of	of	ADP
ejpam-4715	102	23	the	the	DET
ejpam-4715	102	24	r	r	PROPN
ejpam-4715	102	25	-	-	PUNCT
ejpam-4715	102	26	whitney	whitney	NOUN
ejpam-4715	102	27	numbers	number	NOUN
ejpam-4715	102	28	of	of	ADP
ejpam-4715	102	29	the	the	DET
ejpam-4715	102	30	second	second	ADJ
ejpam-4715	102	31	kind	kind	NOUN
ejpam-4715	102	32	w	w	PROPN
ejpam-4715	102	33	∗	∗	PROPN
ejpam-4715	102	34	m	m	PROPN
ejpam-4715	102	35	,	,	PUNCT
ejpam-4715	102	36	r[n	r[n	NOUN
ejpam-4715	102	37	,	,	PUNCT
ejpam-4715	102	38	k	k	NOUN
ejpam-4715	102	39	;	;	PUNCT
ejpam-4715	102	40	t]p	t]p	NOUN
ejpam-4715	102	41	,	,	PUNCT
ejpam-4715	102	42	q	q	PUNCT
ejpam-4715	102	43	will	will	AUX
ejpam-4715	102	44	be	be	AUX
ejpam-4715	102	45	established	establish	VERB
ejpam-4715	102	46	using	use	VERB
ejpam-4715	102	47	the	the	DET
ejpam-4715	102	48	rational	rational	ADJ
ejpam-4715	102	49	generating	generating	NOUN
ejpam-4715	102	50	function	function	NOUN
ejpam-4715	102	51	in	in	ADP
ejpam-4715	102	52	(	(	PUNCT
ejpam-4715	102	53	10	10	NUM
ejpam-4715	102	54	)	)	PUNCT
ejpam-4715	102	55	.	.	PUNCT
ejpam-4715	103	1	using	use	VERB
ejpam-4715	103	2	the	the	DET
ejpam-4715	103	3	values	value	NOUN
ejpam-4715	103	4	of	of	ADP
ejpam-4715	103	5	w	w	PROPN
ejpam-4715	103	6	∗	∗	NOUN
ejpam-4715	103	7	m	m	PROPN
ejpam-4715	103	8	,	,	PUNCT
ejpam-4715	103	9	r[n	r[n	NOUN
ejpam-4715	103	10	,	,	PUNCT
ejpam-4715	103	11	k	k	NOUN
ejpam-4715	103	12	;	;	PUNCT
ejpam-4715	103	13	t]p	t]p	X
ejpam-4715	103	14	,	,	PUNCT
ejpam-4715	103	15	q	q	NOUN
ejpam-4715	103	16	in	in	ADP
ejpam-4715	103	17	table	table	NOUN
ejpam-4715	103	18	1	1	NUM
ejpam-4715	103	19	,	,	PUNCT
ejpam-4715	103	20	we	we	PRON
ejpam-4715	103	21	observe	observe	VERB
ejpam-4715	103	22	that	that	SCONJ
ejpam-4715	103	23	,	,	PUNCT
ejpam-4715	103	24	with	with	ADP
ejpam-4715	103	25	[	[	X
ejpam-4715	103	26	t]p	t]p	X
ejpam-4715	103	27	,	,	PUNCT
ejpam-4715	103	28	q	q	NOUN
ejpam-4715	103	29	=	=	SYM
ejpam-4715	103	30	pt−1	pt−1	PROPN
ejpam-4715	103	31	+	+	CCONJ
ejpam-4715	103	32	pt−2q	pt−2q	PROPN
ejpam-4715	104	1	+	+	CCONJ
ejpam-4715	104	2	pt−3q2	pt−3q2	VERB
ejpam-4715	104	3	+	+	X
ejpam-4715	104	4	.	.	PUNCT
ejpam-4715	104	5	.	.	PUNCT
ejpam-4715	105	1	.+	.+	NOUN
ejpam-4715	105	2	pqt−2	pqt−2	PROPN
ejpam-4715	105	3	+	+	CCONJ
ejpam-4715	105	4	qt−1	qt−1	PROPN
ejpam-4715	105	5	,	,	PUNCT
ejpam-4715	105	6	the	the	DET
ejpam-4715	105	7	polynomial	polynomial	ADJ
ejpam-4715	105	8	expressions	expression	NOUN
ejpam-4715	105	9	of	of	ADP
ejpam-4715	105	10	w	w	PROPN
ejpam-4715	105	11	∗	∗	NOUN
ejpam-4715	105	12	m	m	PROPN
ejpam-4715	105	13	,	,	PUNCT
ejpam-4715	105	14	r[n	r[n	NOUN
ejpam-4715	105	15	,	,	PUNCT
ejpam-4715	105	16	k]q	k]q	NOUN
ejpam-4715	105	17	from	from	ADP
ejpam-4715	105	18	row	row	NOUN
ejpam-4715	105	19	0	0	NUM
ejpam-4715	105	20	to	to	PART
ejpam-4715	105	21	row	row	VERB
ejpam-4715	105	22	3	3	NUM
ejpam-4715	105	23	,	,	PUNCT
ejpam-4715	105	24	if	if	SCONJ
ejpam-4715	105	25	they	they	PRON
ejpam-4715	105	26	are	be	AUX
ejpam-4715	105	27	divided	divide	VERB
ejpam-4715	105	28	by	by	ADP
ejpam-4715	105	29	pq	pq	PROPN
ejpam-4715	105	30	,	,	PUNCT
ejpam-4715	105	31	the	the	DET
ejpam-4715	105	32	remainders	remainder	NOUN
ejpam-4715	105	33	form	form	VERB
ejpam-4715	105	34	the	the	DET
ejpam-4715	105	35	following	follow	VERB
ejpam-4715	105	36	triangle	triangle	NOUN
ejpam-4715	105	37	of	of	ADP
ejpam-4715	105	38	expressions	expression	NOUN
ejpam-4715	105	39	in	in	ADP
ejpam-4715	105	40	p	p	X
ejpam-4715	105	41	:	:	SYM
ejpam-4715	105	42	1	1	NUM
ejpam-4715	105	43	pmt+r−1	pmt+r−1	NUM
ejpam-4715	105	44	1	1	NUM
ejpam-4715	105	45	p2(mt+r−1	p2(mt+r−1	NOUN
ejpam-4715	105	46	)	)	PUNCT
ejpam-4715	106	1	2pmt+r−1	2pmt+r−1	NUM
ejpam-4715	106	2	1	1	NUM
ejpam-4715	106	3	p3(mt+r−1	p3(mt+r−1	NOUN
ejpam-4715	106	4	)	)	PUNCT
ejpam-4715	106	5	3p2(mt+r−1	3p2(mt+r−1	NUM
ejpam-4715	106	6	)	)	PUNCT
ejpam-4715	106	7	3pmt+r−1	3pmt+r−1	NUM
ejpam-4715	107	1	1	1	NUM
ejpam-4715	107	2	.	.	PUNCT
ejpam-4715	108	1	this	this	PRON
ejpam-4715	108	2	can	can	AUX
ejpam-4715	108	3	further	far	ADV
ejpam-4715	108	4	be	be	AUX
ejpam-4715	108	5	written	write	VERB
ejpam-4715	108	6	as	as	ADP
ejpam-4715	108	7	(	(	PUNCT
ejpam-4715	108	8	0	0	NUM
ejpam-4715	108	9	0	0	NUM
ejpam-4715	108	10	)	)	PUNCT
ejpam-4715	108	11	(	(	PUNCT
ejpam-4715	108	12	1	1	NUM
ejpam-4715	108	13	0	0	NUM
ejpam-4715	108	14	)	)	PUNCT
ejpam-4715	108	15	pmt+r−1	pmt+r−1	NOUN
ejpam-4715	108	16	(	(	PUNCT
ejpam-4715	108	17	1	1	NUM
ejpam-4715	108	18	1	1	NUM
ejpam-4715	108	19	)	)	PUNCT
ejpam-4715	108	20	(	(	PUNCT
ejpam-4715	108	21	2	2	NUM
ejpam-4715	108	22	0	0	NUM
ejpam-4715	108	23	)	)	PUNCT
ejpam-4715	108	24	p2(mt+r−1	p2(mt+r−1	NUM
ejpam-4715	108	25	)	)	PUNCT
ejpam-4715	108	26	(	(	PUNCT
ejpam-4715	108	27	2	2	NUM
ejpam-4715	108	28	1	1	NUM
ejpam-4715	108	29	)	)	PUNCT
ejpam-4715	108	30	pmt+r−1	pmt+r−1	NOUN
ejpam-4715	108	31	(	(	PUNCT
ejpam-4715	108	32	2	2	NUM
ejpam-4715	108	33	2	2	NUM
ejpam-4715	108	34	)	)	PUNCT
ejpam-4715	108	35	(	(	PUNCT
ejpam-4715	108	36	3	3	NUM
ejpam-4715	108	37	0	0	NUM
ejpam-4715	108	38	)	)	PUNCT
ejpam-4715	109	1	p3(mt+r−1	p3(mt+r−1	NOUN
ejpam-4715	109	2	)	)	PUNCT
ejpam-4715	109	3	(	(	PUNCT
ejpam-4715	109	4	3	3	NUM
ejpam-4715	109	5	1	1	NUM
ejpam-4715	109	6	)	)	PUNCT
ejpam-4715	109	7	p2(mt+r−1	p2(mt+r−1	PROPN
ejpam-4715	109	8	)	)	PUNCT
ejpam-4715	109	9	(	(	PUNCT
ejpam-4715	109	10	3	3	NUM
ejpam-4715	109	11	2	2	NUM
ejpam-4715	109	12	)	)	PUNCT
ejpam-4715	109	13	pmt+r−1	pmt+r−1	NOUN
ejpam-4715	109	14	(	(	PUNCT
ejpam-4715	109	15	3	3	NUM
ejpam-4715	109	16	3	3	NUM
ejpam-4715	109	17	)	)	PUNCT
ejpam-4715	109	18	,	,	PUNCT
ejpam-4715	109	19	to	to	PART
ejpam-4715	109	20	generalize	generalize	VERB
ejpam-4715	109	21	this	this	DET
ejpam-4715	109	22	observation	observation	NOUN
ejpam-4715	109	23	,	,	PUNCT
ejpam-4715	109	24	the	the	DET
ejpam-4715	109	25	next	next	ADJ
ejpam-4715	109	26	theorem	theorem	NOUN
ejpam-4715	109	27	contains	contain	VERB
ejpam-4715	109	28	the	the	DET
ejpam-4715	109	29	divisibility	divisibility	NOUN
ejpam-4715	109	30	property	property	NOUN
ejpam-4715	109	31	of	of	ADP
ejpam-4715	109	32	w	w	PROPN
ejpam-4715	109	33	∗	∗	PROPN
ejpam-4715	109	34	m	m	PROPN
ejpam-4715	109	35	,	,	PUNCT
ejpam-4715	109	36	r[n	r[n	NOUN
ejpam-4715	109	37	,	,	PUNCT
ejpam-4715	109	38	k	k	NOUN
ejpam-4715	109	39	;	;	PUNCT
ejpam-4715	109	40	t]p	t]p	PROPN
ejpam-4715	109	41	,	,	PUNCT
ejpam-4715	109	42	q.	q.	PROPN
ejpam-4715	109	43	theorem	theorem	VERB
ejpam-4715	109	44	3.1	3.1	NUM
ejpam-4715	109	45	.	.	PUNCT
ejpam-4715	110	1	for	for	ADP
ejpam-4715	110	2	nonnegative	nonnegative	ADJ
ejpam-4715	110	3	integers	integer	NOUN
ejpam-4715	110	4	n	n	PRON
ejpam-4715	110	5	and	and	CCONJ
ejpam-4715	110	6	k	k	NOUN
ejpam-4715	110	7	,	,	PUNCT
ejpam-4715	110	8	the	the	DET
ejpam-4715	110	9	type	type	NOUN
ejpam-4715	110	10	2	2	NUM
ejpam-4715	110	11	(	(	PUNCT
ejpam-4715	110	12	p	p	NOUN
ejpam-4715	110	13	,	,	PUNCT
ejpam-4715	110	14	q)-analogue	q)-analogue	NOUN
ejpam-4715	110	15	of	of	ADP
ejpam-4715	110	16	the	the	DET
ejpam-4715	110	17	rwhitney	rwhitney	NOUN
ejpam-4715	110	18	numbers	number	NOUN
ejpam-4715	110	19	of	of	ADP
ejpam-4715	110	20	the	the	DET
ejpam-4715	110	21	second	second	ADJ
ejpam-4715	110	22	kind	kind	NOUN
ejpam-4715	110	23	wm	wm	PROPN
ejpam-4715	110	24	,	,	PUNCT
ejpam-4715	110	25	r[n	r[n	NOUN
ejpam-4715	110	26	,	,	PUNCT
ejpam-4715	110	27	k	k	NOUN
ejpam-4715	110	28	;	;	PUNCT
ejpam-4715	110	29	t]p	t]p	X
ejpam-4715	110	30	,	,	PUNCT
ejpam-4715	110	31	q	q	PUNCT
ejpam-4715	110	32	satisfies	satisfy	VERB
ejpam-4715	110	33	the	the	DET
ejpam-4715	110	34	following	follow	VERB
ejpam-4715	110	35	congruence	congruence	PROPN
ejpam-4715	110	36	relation	relation	PROPN
ejpam-4715	110	37	w	w	PROPN
ejpam-4715	110	38	∗	∗	PROPN
ejpam-4715	110	39	m	m	PROPN
ejpam-4715	110	40	,	,	PUNCT
ejpam-4715	110	41	r[n	r[n	NOUN
ejpam-4715	110	42	,	,	PUNCT
ejpam-4715	110	43	k	k	NOUN
ejpam-4715	110	44	;	;	PUNCT
ejpam-4715	110	45	t]p	t]p	NOUN
ejpam-4715	110	46	,	,	PUNCT
ejpam-4715	110	47	q	q	PROPN
ejpam-4715	110	48	≡	≡	PROPN
ejpam-4715	110	49	(	(	PUNCT
ejpam-4715	110	50	n	n	X
ejpam-4715	110	51	k	k	NOUN
ejpam-4715	110	52	)	)	PUNCT
ejpam-4715	111	1	p(n−k)(mt+r−1	p(n−k)(mt+r−1	X
ejpam-4715	111	2	)	)	PUNCT
ejpam-4715	111	3	mod	mod	PROPN
ejpam-4715	111	4	pq	pq	PROPN
ejpam-4715	111	5	.	.	PUNCT
ejpam-4715	112	1	(	(	PUNCT
ejpam-4715	112	2	11	11	NUM
ejpam-4715	112	3	)	)	PUNCT
ejpam-4715	112	4	proof	proof	NOUN
ejpam-4715	112	5	.	.	PUNCT
ejpam-4715	113	1	the	the	DET
ejpam-4715	113	2	polynomial	polynomial	ADJ
ejpam-4715	113	3	[	[	X
ejpam-4715	113	4	t]p	t]p	X
ejpam-4715	113	5	,	,	PUNCT
ejpam-4715	113	6	q	q	NOUN
ejpam-4715	113	7	can	can	AUX
ejpam-4715	113	8	be	be	AUX
ejpam-4715	113	9	written	write	VERB
ejpam-4715	113	10	as	as	ADP
ejpam-4715	113	11	[	[	X
ejpam-4715	113	12	t]p	t]p	X
ejpam-4715	113	13	,	,	PUNCT
ejpam-4715	113	14	q	q	NOUN
ejpam-4715	113	15	=	=	SYM
ejpam-4715	113	16	pt−1	pt−1	PROPN
ejpam-4715	113	17	+	+	CCONJ
ejpam-4715	113	18	qt−1	qt−1	PROPN
ejpam-4715	113	19	+	+	X
ejpam-4715	113	20	pqy	pqy	PROPN
ejpam-4715	113	21	,	,	PUNCT
ejpam-4715	113	22	r.	r.	PROPN
ejpam-4715	113	23	b.	b.	PROPN
ejpam-4715	113	24	corcino	corcino	PROPN
ejpam-4715	113	25	,	,	PUNCT
ejpam-4715	113	26	c.	c.	PROPN
ejpam-4715	113	27	b.	b.	PROPN
ejpam-4715	113	28	corcino	corcino	PROPN
ejpam-4715	113	29	/	/	SYM
ejpam-4715	113	30	eur	eur	PROPN
ejpam-4715	113	31	.	.	PUNCT
ejpam-4715	114	1	j.	j.	PROPN
ejpam-4715	114	2	pure	pure	PROPN
ejpam-4715	114	3	appl	appl	PROPN
ejpam-4715	114	4	.	.	PROPN
ejpam-4715	114	5	math	math	PROPN
ejpam-4715	114	6	,	,	PUNCT
ejpam-4715	114	7	16	16	NUM
ejpam-4715	114	8	(	(	PUNCT
ejpam-4715	114	9	2	2	NUM
ejpam-4715	114	10	)	)	PUNCT
ejpam-4715	114	11	(	(	PUNCT
ejpam-4715	114	12	2023	2023	NUM
ejpam-4715	114	13	)	)	PUNCT
ejpam-4715	114	14	,	,	PUNCT
ejpam-4715	114	15	934	934	NUM
ejpam-4715	114	16	-	-	SYM
ejpam-4715	114	17	943	943	NUM
ejpam-4715	114	18	940	940	NUM
ejpam-4715	114	19	where	where	SCONJ
ejpam-4715	114	20	y	y	PROPN
ejpam-4715	114	21	is	be	AUX
ejpam-4715	114	22	a	a	DET
ejpam-4715	114	23	polynomial	polynomial	NOUN
ejpam-4715	114	24	in	in	ADP
ejpam-4715	114	25	p	p	PROPN
ejpam-4715	114	26	and	and	CCONJ
ejpam-4715	114	27	q.	q.	PROPN
ejpam-4715	114	28	then	then	ADV
ejpam-4715	115	1	,	,	PUNCT
ejpam-4715	115	2	we	we	PRON
ejpam-4715	115	3	have	have	VERB
ejpam-4715	115	4	1∏k	1∏k	NUM
ejpam-4715	115	5	j=0(1−	j=0(1−	PROPN
ejpam-4715	115	6	xpm(t−j)[mj	xpm(t−j)[mj	PUNCT
ejpam-4715	116	1	+	+	CCONJ
ejpam-4715	116	2	r]p	r]p	PROPN
ejpam-4715	116	3	,	,	PUNCT
ejpam-4715	116	4	q	q	NOUN
ejpam-4715	116	5	)	)	PUNCT
ejpam-4715	116	6	=	=	SYM
ejpam-4715	117	1	∞∑	∞∑	NUM
ejpam-4715	117	2	n=0	n=0	PUNCT
ejpam-4715	117	3	(	(	PUNCT
ejpam-4715	117	4	xpm(t−j)[mj	xpm(t−j)[mj	PROPN
ejpam-4715	117	5	+	+	NUM
ejpam-4715	117	6	r]p	r]p	PROPN
ejpam-4715	117	7	,	,	PUNCT
ejpam-4715	117	8	q	q	NOUN
ejpam-4715	117	9	)	)	PUNCT
ejpam-4715	117	10	n	n	NOUN
ejpam-4715	117	11	=	=	SYM
ejpam-4715	117	12	∞∑	∞∑	ADJ
ejpam-4715	117	13	n=0	n=0	NUM
ejpam-4715	117	14	pnm(t−j)(pmj+r−1	pnm(t−j)(pmj+r−1	NOUN
ejpam-4715	117	15	+	+	CCONJ
ejpam-4715	117	16	qmj+r−1	qmj+r−1	ADJ
ejpam-4715	117	17	+	+	CCONJ
ejpam-4715	117	18	pqy)nxn	pqy)nxn	ADJ
ejpam-4715	117	19	=	=	SYM
ejpam-4715	117	20	∞∑	∞∑	NUM
ejpam-4715	117	21	n=0	n=0	NUM
ejpam-4715	117	22	pn(mt+r−j)xn	pn(mt+r−j)xn	NOUN
ejpam-4715	117	23	+	+	CCONJ
ejpam-4715	117	24	pq	pq	NOUN
ejpam-4715	117	25	∞∑	∞∑	NUM
ejpam-4715	117	26	n=0	n=0	NUM
ejpam-4715	117	27	ẑnx	ẑnx	NOUN
ejpam-4715	117	28	n	n	CCONJ
ejpam-4715	117	29	,	,	PUNCT
ejpam-4715	117	30	where	where	SCONJ
ejpam-4715	117	31	ẑn	ẑn	NOUN
ejpam-4715	117	32	is	be	AUX
ejpam-4715	117	33	a	a	DET
ejpam-4715	117	34	polynomial	polynomial	NOUN
ejpam-4715	117	35	in	in	ADP
ejpam-4715	117	36	p	p	PROPN
ejpam-4715	117	37	and	and	CCONJ
ejpam-4715	117	38	q.	q.	NOUN
ejpam-4715	117	39	it	it	PRON
ejpam-4715	117	40	follows	follow	VERB
ejpam-4715	117	41	that	that	SCONJ
ejpam-4715	117	42	1∏k	1∏k	NUM
ejpam-4715	117	43	j=0(1−	j=0(1−	PROPN
ejpam-4715	117	44	xpm(t−j)[mj	xpm(t−j)[mj	PUNCT
ejpam-4715	118	1	+	+	CCONJ
ejpam-4715	118	2	r]p	r]p	PROPN
ejpam-4715	118	3	,	,	PUNCT
ejpam-4715	118	4	q	q	NOUN
ejpam-4715	118	5	)	)	PUNCT
ejpam-4715	118	6	=	=	SYM
ejpam-4715	119	1	∞∑	∞∑	PRON
ejpam-4715	119	2	n=0	n=0	PUNCT
ejpam-4715	119	3	pn(mt+r−j)xn	pn(mt+r−j)xn	DET
ejpam-4715	119	4	mod	mod	PROPN
ejpam-4715	119	5	pq	pq	PROPN
ejpam-4715	119	6	=	=	NOUN
ejpam-4715	119	7	1	1	NUM
ejpam-4715	119	8	1−	1−	NUM
ejpam-4715	119	9	pmt+r−1x	pmt+r−1x	NUM
ejpam-4715	119	10	mod	mod	PROPN
ejpam-4715	119	11	pq	pq	PROPN
ejpam-4715	119	12	.	.	PUNCT
ejpam-4715	120	1	thus	thus	ADV
ejpam-4715	120	2	,	,	PUNCT
ejpam-4715	120	3	using	use	VERB
ejpam-4715	120	4	(	(	PUNCT
ejpam-4715	120	5	10	10	NUM
ejpam-4715	120	6	)	)	PUNCT
ejpam-4715	120	7	,	,	PUNCT
ejpam-4715	120	8	we	we	PRON
ejpam-4715	120	9	have	have	VERB
ejpam-4715	120	10	∞∑	∞∑	NUM
ejpam-4715	120	11	n	n	CCONJ
ejpam-4715	120	12	=	=	SYM
ejpam-4715	120	13	k	k	PROPN
ejpam-4715	120	14	w	w	PROPN
ejpam-4715	120	15	∗	∗	PROPN
ejpam-4715	120	16	m	m	PROPN
ejpam-4715	120	17	,	,	PUNCT
ejpam-4715	120	18	r[n	r[n	NOUN
ejpam-4715	120	19	,	,	PUNCT
ejpam-4715	120	20	k	k	X
ejpam-4715	120	21	;	;	PUNCT
ejpam-4715	120	22	t]p	t]p	X
ejpam-4715	120	23	,	,	PUNCT
ejpam-4715	120	24	qx	qx	PROPN
ejpam-4715	120	25	n−k	n−k	NOUN
ejpam-4715	120	26	≡	≡	PROPN
ejpam-4715	120	27	1	1	NUM
ejpam-4715	120	28	(	(	PUNCT
ejpam-4715	120	29	1−	1−	NUM
ejpam-4715	120	30	pmt+r−1x)k+1	pmt+r−1x)k+1	ADJ
ejpam-4715	120	31	mod	mod	PROPN
ejpam-4715	120	32	pq	pq	PROPN
ejpam-4715	120	33	≡	≡	PROPN
ejpam-4715	121	1	∞∑	∞∑	ADJ
ejpam-4715	121	2	n=0	n=0	NUM
ejpam-4715	121	3	(	(	PUNCT
ejpam-4715	121	4	n+	n+	X
ejpam-4715	121	5	(	(	PUNCT
ejpam-4715	121	6	k	k	PROPN
ejpam-4715	121	7	+	+	PROPN
ejpam-4715	121	8	1)−	1)−	PROPN
ejpam-4715	121	9	1	1	NUM
ejpam-4715	121	10	n	n	NOUN
ejpam-4715	121	11	)	)	PUNCT
ejpam-4715	121	12	pn(mt+r−1)xn	pn(mt+r−1)xn	PROPN
ejpam-4715	121	13	mod	mod	PROPN
ejpam-4715	121	14	pq	pq	PROPN
ejpam-4715	121	15	≡	≡	PROPN
ejpam-4715	122	1	∞∑	∞∑	PROPN
ejpam-4715	122	2	n	n	PROPN
ejpam-4715	122	3	=	=	SYM
ejpam-4715	122	4	k	k	X
ejpam-4715	122	5	(	(	PUNCT
ejpam-4715	122	6	n	n	X
ejpam-4715	122	7	k	k	PROPN
ejpam-4715	122	8	)	)	PUNCT
ejpam-4715	122	9	p(n−k)(mt+r−1)xn−k	p(n−k)(mt+r−1)xn−k	PROPN
ejpam-4715	122	10	mod	mod	PROPN
ejpam-4715	122	11	pq	pq	PROPN
ejpam-4715	122	12	.	.	PROPN
ejpam-4715	122	13	comparing	compare	VERB
ejpam-4715	122	14	the	the	DET
ejpam-4715	122	15	coefficients	coefficient	NOUN
ejpam-4715	122	16	of	of	ADP
ejpam-4715	122	17	xn−k	xn−k	PROPN
ejpam-4715	122	18	completes	complete	VERB
ejpam-4715	122	19	the	the	DET
ejpam-4715	122	20	proof	proof	NOUN
ejpam-4715	122	21	of	of	ADP
ejpam-4715	122	22	the	the	DET
ejpam-4715	122	23	theorem	theorem	PROPN
ejpam-4715	122	24	.	.	PROPN
ejpam-4715	122	25	remark	remark	PROPN
ejpam-4715	122	26	3.2	3.2	NUM
ejpam-4715	122	27	.	.	PUNCT
ejpam-4715	123	1	using	use	VERB
ejpam-4715	123	2	(	(	PUNCT
ejpam-4715	123	3	6	6	NUM
ejpam-4715	123	4	)	)	PUNCT
ejpam-4715	123	5	and	and	CCONJ
ejpam-4715	123	6	theorem	theorem	VERB
ejpam-4715	123	7	3.1	3.1	NUM
ejpam-4715	123	8	,	,	PUNCT
ejpam-4715	123	9	the	the	DET
ejpam-4715	123	10	first	first	ADJ
ejpam-4715	123	11	form	form	NOUN
ejpam-4715	123	12	of	of	ADP
ejpam-4715	123	13	the	the	DET
ejpam-4715	123	14	type	type	NOUN
ejpam-4715	123	15	2	2	NUM
ejpam-4715	123	16	(	(	PUNCT
ejpam-4715	123	17	p	p	NOUN
ejpam-4715	123	18	,	,	PUNCT
ejpam-4715	123	19	q)-analogues	q)-analogue	NOUN
ejpam-4715	123	20	of	of	ADP
ejpam-4715	123	21	the	the	DET
ejpam-4715	123	22	r	r	NOUN
ejpam-4715	123	23	-	-	PUNCT
ejpam-4715	123	24	whitney	whitney	NOUN
ejpam-4715	123	25	numbers	number	NOUN
ejpam-4715	123	26	of	of	ADP
ejpam-4715	123	27	the	the	DET
ejpam-4715	123	28	second	second	ADJ
ejpam-4715	123	29	kind	kind	NOUN
ejpam-4715	123	30	satisfies	satisfy	VERB
ejpam-4715	123	31	the	the	DET
ejpam-4715	123	32	following	follow	VERB
ejpam-4715	123	33	congruence	congruence	PROPN
ejpam-4715	123	34	relation	relation	NOUN
ejpam-4715	123	35	modulo	modulo	PROPN
ejpam-4715	123	36	pq	pq	PROPN
ejpam-4715	123	37	:	:	PUNCT
ejpam-4715	123	38	wm	wm	PROPN
ejpam-4715	123	39	,	,	PUNCT
ejpam-4715	123	40	r[n	r[n	PROPN
ejpam-4715	123	41	,	,	PUNCT
ejpam-4715	123	42	k	k	NOUN
ejpam-4715	123	43	;	;	PUNCT
ejpam-4715	123	44	t]p	t]p	NOUN
ejpam-4715	123	45	,	,	PUNCT
ejpam-4715	123	46	q	q	PROPN
ejpam-4715	123	47	≡	≡	PROPN
ejpam-4715	123	48	(	(	PUNCT
ejpam-4715	123	49	n	n	X
ejpam-4715	123	50	k	k	PROPN
ejpam-4715	123	51	)	)	PUNCT
ejpam-4715	123	52	p(n−k)(mt+r−1)qkr+m(k2	p(n−k)(mt+r−1)qkr+m(k2	PROPN
ejpam-4715	123	53	)	)	PUNCT
ejpam-4715	124	1	mod	mod	PROPN
ejpam-4715	124	2	pq	pq	PROPN
ejpam-4715	124	3	(	(	PUNCT
ejpam-4715	124	4	12	12	NUM
ejpam-4715	124	5	)	)	PUNCT
ejpam-4715	124	6	≡	≡	PROPN
ejpam-4715	124	7	{	{	PUNCT
ejpam-4715	124	8	qnr+m(n2	qnr+m(n2	ADV
ejpam-4715	124	9	)	)	PUNCT
ejpam-4715	124	10	mod	mod	PROPN
ejpam-4715	124	11	pq	pq	PROPN
ejpam-4715	124	12	,	,	PUNCT
ejpam-4715	124	13	for	for	ADP
ejpam-4715	124	14	n	n	NOUN
ejpam-4715	124	15	=	=	SYM
ejpam-4715	124	16	k	k	PROPN
ejpam-4715	124	17	0	0	NUM
ejpam-4715	124	18	mod	mod	PROPN
ejpam-4715	124	19	pq	pq	PROPN
ejpam-4715	124	20	,	,	PUNCT
ejpam-4715	124	21	otherwise	otherwise	ADV
ejpam-4715	124	22	.	.	PUNCT
ejpam-4715	125	1	moreover	moreover	ADV
ejpam-4715	125	2	,	,	PUNCT
ejpam-4715	125	3	using	use	VERB
ejpam-4715	125	4	(	(	PUNCT
ejpam-4715	125	5	7	7	NUM
ejpam-4715	125	6	)	)	PUNCT
ejpam-4715	125	7	and	and	CCONJ
ejpam-4715	125	8	theorem	theorem	VERB
ejpam-4715	125	9	3.1	3.1	NUM
ejpam-4715	125	10	,	,	PUNCT
ejpam-4715	125	11	the	the	DET
ejpam-4715	125	12	third	third	ADJ
ejpam-4715	125	13	form	form	NOUN
ejpam-4715	125	14	of	of	ADP
ejpam-4715	125	15	the	the	DET
ejpam-4715	125	16	type	type	NOUN
ejpam-4715	125	17	2	2	NUM
ejpam-4715	125	18	(	(	PUNCT
ejpam-4715	125	19	p	p	NOUN
ejpam-4715	125	20	,	,	PUNCT
ejpam-4715	125	21	q)-analogues	q)-analogue	NOUN
ejpam-4715	125	22	of	of	ADP
ejpam-4715	125	23	the	the	DET
ejpam-4715	125	24	r	r	NOUN
ejpam-4715	125	25	-	-	PUNCT
ejpam-4715	125	26	whitney	whitney	NOUN
ejpam-4715	125	27	numbers	number	NOUN
ejpam-4715	125	28	of	of	ADP
ejpam-4715	125	29	the	the	DET
ejpam-4715	125	30	second	second	ADJ
ejpam-4715	125	31	kind	kind	NOUN
ejpam-4715	125	32	satisfies	satisfy	VERB
ejpam-4715	125	33	the	the	DET
ejpam-4715	125	34	following	follow	VERB
ejpam-4715	125	35	congruence	congruence	PROPN
ejpam-4715	125	36	relation	relation	NOUN
ejpam-4715	125	37	modulo	modulo	PROPN
ejpam-4715	125	38	pq	pq	PROPN
ejpam-4715	125	39	:	:	PUNCT
ejpam-4715	125	40	w̃m	w̃m	PROPN
ejpam-4715	125	41	,	,	PUNCT
ejpam-4715	125	42	r[n	r[n	NOUN
ejpam-4715	125	43	,	,	PUNCT
ejpam-4715	125	44	k	k	NOUN
ejpam-4715	125	45	;	;	PUNCT
ejpam-4715	125	46	t]p	t]p	NOUN
ejpam-4715	125	47	,	,	PUNCT
ejpam-4715	125	48	q	q	PROPN
ejpam-4715	125	49	≡	≡	PROPN
ejpam-4715	125	50	(	(	PUNCT
ejpam-4715	125	51	n	n	NOUN
ejpam-4715	125	52	k	k	NOUN
ejpam-4715	125	53	)	)	PUNCT
ejpam-4715	125	54	p(n−k)(mt+r−1)qkr	p(n−k)(mt+r−1)qkr	NOUN
ejpam-4715	125	55	mod	mod	PROPN
ejpam-4715	125	56	pq	pq	PROPN
ejpam-4715	125	57	(	(	PUNCT
ejpam-4715	125	58	13	13	NUM
ejpam-4715	125	59	)	)	PUNCT
ejpam-4715	125	60	r.	r.	PROPN
ejpam-4715	125	61	b.	b.	PROPN
ejpam-4715	125	62	corcino	corcino	PROPN
ejpam-4715	125	63	,	,	PUNCT
ejpam-4715	125	64	c.	c.	PROPN
ejpam-4715	125	65	b.	b.	PROPN
ejpam-4715	125	66	corcino	corcino	PROPN
ejpam-4715	125	67	/	/	SYM
ejpam-4715	125	68	eur	eur	PROPN
ejpam-4715	125	69	.	.	PUNCT
ejpam-4715	126	1	j.	j.	PROPN
ejpam-4715	126	2	pure	pure	PROPN
ejpam-4715	126	3	appl	appl	PROPN
ejpam-4715	126	4	.	.	PROPN
ejpam-4715	126	5	math	math	PROPN
ejpam-4715	126	6	,	,	PUNCT
ejpam-4715	126	7	16	16	NUM
ejpam-4715	126	8	(	(	PUNCT
ejpam-4715	126	9	2	2	NUM
ejpam-4715	126	10	)	)	PUNCT
ejpam-4715	126	11	(	(	PUNCT
ejpam-4715	126	12	2023	2023	NUM
ejpam-4715	126	13	)	)	PUNCT
ejpam-4715	126	14	,	,	PUNCT
ejpam-4715	126	15	934	934	NUM
ejpam-4715	126	16	-	-	SYM
ejpam-4715	126	17	943	943	NUM
ejpam-4715	126	18	941	941	NUM
ejpam-4715	126	19	≡	≡	PROPN
ejpam-4715	126	20	{	{	PUNCT
ejpam-4715	126	21	qnr	qnr	PROPN
ejpam-4715	126	22	mod	mod	PROPN
ejpam-4715	126	23	pq	pq	PROPN
ejpam-4715	126	24	,	,	PUNCT
ejpam-4715	126	25	for	for	ADP
ejpam-4715	126	26	n	n	NOUN
ejpam-4715	126	27	=	=	SYM
ejpam-4715	126	28	k	k	PROPN
ejpam-4715	126	29	0	0	NUM
ejpam-4715	126	30	mod	mod	PROPN
ejpam-4715	126	31	pq	pq	PROPN
ejpam-4715	126	32	,	,	PUNCT
ejpam-4715	126	33	otherwise	otherwise	ADV
ejpam-4715	126	34	.	.	PUNCT
ejpam-4715	127	1	remark	remark	VERB
ejpam-4715	127	2	3.3	3.3	NUM
ejpam-4715	127	3	.	.	PUNCT
ejpam-4715	128	1	when	when	SCONJ
ejpam-4715	128	2	p	p	NOUN
ejpam-4715	128	3	=	=	NOUN
ejpam-4715	128	4	1	1	NUM
ejpam-4715	128	5	,	,	PUNCT
ejpam-4715	128	6	the	the	DET
ejpam-4715	128	7	congruence	congruence	PROPN
ejpam-4715	128	8	relation	relation	NOUN
ejpam-4715	128	9	in	in	ADP
ejpam-4715	128	10	(	(	PUNCT
ejpam-4715	128	11	11	11	NUM
ejpam-4715	128	12	)	)	PUNCT
ejpam-4715	128	13	reduces	reduce	VERB
ejpam-4715	128	14	to	to	ADP
ejpam-4715	128	15	w	w	PROPN
ejpam-4715	128	16	∗	∗	NOUN
ejpam-4715	128	17	m	m	PROPN
ejpam-4715	128	18	,	,	PUNCT
ejpam-4715	128	19	r[n	r[n	NOUN
ejpam-4715	128	20	,	,	PUNCT
ejpam-4715	128	21	k]q	k]q	NOUN
ejpam-4715	128	22	=	=	SYM
ejpam-4715	128	23	w	w	NOUN
ejpam-4715	128	24	∗	∗	NOUN
ejpam-4715	128	25	m	m	PROPN
ejpam-4715	128	26	,	,	PUNCT
ejpam-4715	128	27	r[n	r[n	NOUN
ejpam-4715	128	28	,	,	PUNCT
ejpam-4715	128	29	k	k	NOUN
ejpam-4715	128	30	;	;	PUNCT
ejpam-4715	129	1	t]1,q	t]1,q	ADJ
ejpam-4715	129	2	≡	≡	PROPN
ejpam-4715	129	3	(	(	PUNCT
ejpam-4715	129	4	n	n	X
ejpam-4715	129	5	k	k	NOUN
ejpam-4715	129	6	)	)	PUNCT
ejpam-4715	129	7	mod	mod	PROPN
ejpam-4715	129	8	q	q	X
ejpam-4715	129	9	,	,	PUNCT
ejpam-4715	129	10	which	which	PRON
ejpam-4715	129	11	is	be	AUX
ejpam-4715	129	12	exactly	exactly	ADV
ejpam-4715	129	13	the	the	DET
ejpam-4715	129	14	congruence	congruence	NOUN
ejpam-4715	129	15	relation	relation	NOUN
ejpam-4715	129	16	in	in	ADP
ejpam-4715	129	17	[	[	X
ejpam-4715	129	18	15	15	NUM
ejpam-4715	129	19	,	,	PUNCT
ejpam-4715	129	20	theorem	theorem	VERB
ejpam-4715	129	21	2.1	2.1	NUM
ejpam-4715	129	22	]	]	PUNCT
ejpam-4715	129	23	for	for	ADP
ejpam-4715	129	24	the	the	DET
ejpam-4715	129	25	second	second	ADJ
ejpam-4715	129	26	form	form	NOUN
ejpam-4715	129	27	of	of	ADP
ejpam-4715	129	28	(	(	PUNCT
ejpam-4715	129	29	q	q	INTJ
ejpam-4715	129	30	,	,	PUNCT
ejpam-4715	129	31	r)whitney	r)whitney	NOUN
ejpam-4715	129	32	numbers	number	NOUN
ejpam-4715	129	33	of	of	ADP
ejpam-4715	129	34	the	the	DET
ejpam-4715	129	35	second	second	ADJ
ejpam-4715	129	36	kind	kind	NOUN
ejpam-4715	129	37	.	.	PUNCT
ejpam-4715	130	1	moreover	moreover	ADV
ejpam-4715	130	2	,	,	PUNCT
ejpam-4715	130	3	the	the	DET
ejpam-4715	130	4	congruence	congruence	PROPN
ejpam-4715	130	5	relations	relation	NOUN
ejpam-4715	130	6	in	in	ADP
ejpam-4715	130	7	(	(	PUNCT
ejpam-4715	130	8	12	12	NUM
ejpam-4715	130	9	)	)	PUNCT
ejpam-4715	130	10	and	and	CCONJ
ejpam-4715	130	11	(	(	PUNCT
ejpam-4715	130	12	13	13	NUM
ejpam-4715	130	13	)	)	PUNCT
ejpam-4715	130	14	reduce	reduce	VERB
ejpam-4715	130	15	to	to	ADP
ejpam-4715	130	16	wm	wm	PROPN
ejpam-4715	130	17	,	,	PUNCT
ejpam-4715	130	18	r[n	r[n	NOUN
ejpam-4715	130	19	,	,	PUNCT
ejpam-4715	130	20	k]q	k]q	NOUN
ejpam-4715	130	21	=	=	SYM
ejpam-4715	130	22	wm	wm	PROPN
ejpam-4715	130	23	,	,	PUNCT
ejpam-4715	130	24	r[n	r[n	NOUN
ejpam-4715	130	25	,	,	PUNCT
ejpam-4715	130	26	k	k	NOUN
ejpam-4715	130	27	;	;	PUNCT
ejpam-4715	130	28	t]1,q	t]1,q	ADJ
ejpam-4715	130	29	≡	≡	PROPN
ejpam-4715	130	30	(	(	PUNCT
ejpam-4715	130	31	n	n	NOUN
ejpam-4715	130	32	k	k	NOUN
ejpam-4715	130	33	)	)	PUNCT
ejpam-4715	130	34	qkr+m(k2	qkr+m(k2	PROPN
ejpam-4715	130	35	)	)	PUNCT
ejpam-4715	130	36	≡	≡	PROPN
ejpam-4715	130	37	0	0	NUM
ejpam-4715	131	1	mod	mod	PROPN
ejpam-4715	132	1	q	q	X
ejpam-4715	133	1	w̃m	w̃m	PROPN
ejpam-4715	133	2	,	,	PUNCT
ejpam-4715	133	3	r[n	r[n	NOUN
ejpam-4715	133	4	,	,	PUNCT
ejpam-4715	133	5	k]q	k]q	NOUN
ejpam-4715	133	6	=	=	SYM
ejpam-4715	133	7	w̃m	w̃m	X
ejpam-4715	133	8	,	,	PUNCT
ejpam-4715	133	9	r[n	r[n	NOUN
ejpam-4715	133	10	,	,	PUNCT
ejpam-4715	133	11	k	k	NOUN
ejpam-4715	133	12	;	;	PUNCT
ejpam-4715	133	13	t]1,q	t]1,q	ADJ
ejpam-4715	133	14	≡	≡	PROPN
ejpam-4715	133	15	(	(	PUNCT
ejpam-4715	133	16	n	n	X
ejpam-4715	133	17	k	k	NOUN
ejpam-4715	133	18	)	)	PUNCT
ejpam-4715	133	19	qkr	qkr	NOUN
ejpam-4715	133	20	≡	≡	PROPN
ejpam-4715	133	21	0	0	NUM
ejpam-4715	134	1	mod	mod	PROPN
ejpam-4715	134	2	q	q	NOUN
ejpam-4715	134	3	,	,	PUNCT
ejpam-4715	134	4	which	which	PRON
ejpam-4715	134	5	are	be	AUX
ejpam-4715	134	6	the	the	DET
ejpam-4715	134	7	congruence	congruence	PROPN
ejpam-4715	134	8	relations	relation	NOUN
ejpam-4715	134	9	for	for	ADP
ejpam-4715	134	10	the	the	DET
ejpam-4715	134	11	first	first	ADJ
ejpam-4715	134	12	and	and	CCONJ
ejpam-4715	134	13	third	third	ADJ
ejpam-4715	134	14	forms	form	NOUN
ejpam-4715	134	15	of	of	ADP
ejpam-4715	134	16	(	(	PUNCT
ejpam-4715	134	17	q	q	ADJ
ejpam-4715	134	18	,	,	PUNCT
ejpam-4715	134	19	r)-whitney	r)-whitney	NOUN
ejpam-4715	134	20	numbers	number	NOUN
ejpam-4715	134	21	of	of	ADP
ejpam-4715	134	22	the	the	DET
ejpam-4715	134	23	second	second	ADJ
ejpam-4715	134	24	kind	kind	NOUN
ejpam-4715	134	25	.	.	PUNCT
ejpam-4715	135	1	we	we	PRON
ejpam-4715	135	2	recall	recall	VERB
ejpam-4715	135	3	that	that	SCONJ
ejpam-4715	135	4	,	,	PUNCT
ejpam-4715	135	5	for	for	ADP
ejpam-4715	135	6	a	a	DET
ejpam-4715	135	7	prime	prime	ADJ
ejpam-4715	135	8	p	p	NOUN
ejpam-4715	135	9	,	,	PUNCT
ejpam-4715	135	10	the	the	DET
ejpam-4715	135	11	p	p	ADJ
ejpam-4715	135	12	-	-	PUNCT
ejpam-4715	135	13	adic	adic	NOUN
ejpam-4715	135	14	valuation	valuation	NOUN
ejpam-4715	135	15	νp(n	νp(n	PROPN
ejpam-4715	135	16	)	)	PUNCT
ejpam-4715	135	17	of	of	ADP
ejpam-4715	135	18	n	n	PROPN
ejpam-4715	135	19	is	be	AUX
ejpam-4715	135	20	defined	define	VERB
ejpam-4715	135	21	to	to	PART
ejpam-4715	135	22	be	be	AUX
ejpam-4715	135	23	the	the	DET
ejpam-4715	135	24	largest	large	ADJ
ejpam-4715	135	25	exponent	exponent	NOUN
ejpam-4715	135	26	k	k	PROPN
ejpam-4715	135	27	such	such	ADJ
ejpam-4715	135	28	that	that	PRON
ejpam-4715	135	29	pk|n	pk|n	VERB
ejpam-4715	135	30	.	.	PUNCT
ejpam-4715	136	1	moreover	moreover	ADV
ejpam-4715	136	2	,	,	PUNCT
ejpam-4715	136	3	the	the	DET
ejpam-4715	136	4	p	p	NOUN
ejpam-4715	136	5	-	-	PUNCT
ejpam-4715	136	6	adic	adic	ADJ
ejpam-4715	136	7	valuation	valuation	NOUN
ejpam-4715	136	8	of	of	ADP
ejpam-4715	136	9	the	the	DET
ejpam-4715	136	10	rational	rational	ADJ
ejpam-4715	136	11	number	number	NOUN
ejpam-4715	136	12	n	n	PRON
ejpam-4715	136	13	m	m	VERB
ejpam-4715	136	14	is	be	AUX
ejpam-4715	136	15	defined	define	VERB
ejpam-4715	136	16	by	by	ADP
ejpam-4715	136	17	νp	νp	X
ejpam-4715	136	18	(	(	PUNCT
ejpam-4715	136	19	n	n	NOUN
ejpam-4715	136	20	m	m	NOUN
ejpam-4715	136	21	)	)	PUNCT
ejpam-4715	137	1	=	=	PUNCT
ejpam-4715	137	2	νp(n)−	νp(n)−	NOUN
ejpam-4715	137	3	νp(m	νp(m	NOUN
ejpam-4715	137	4	)	)	PUNCT
ejpam-4715	137	5	.	.	PUNCT
ejpam-4715	138	1	furthermore	furthermore	ADV
ejpam-4715	138	2	,	,	PUNCT
ejpam-4715	138	3	the	the	DET
ejpam-4715	138	4	p	p	NOUN
ejpam-4715	138	5	-	-	PUNCT
ejpam-4715	138	6	adic	adic	ADJ
ejpam-4715	138	7	absolute	absolute	ADJ
ejpam-4715	138	8	value	value	NOUN
ejpam-4715	138	9	|n|p	|n|p	NOUN
ejpam-4715	138	10	of	of	ADP
ejpam-4715	138	11	n	n	NUM
ejpam-4715	138	12	is	be	AUX
ejpam-4715	138	13	defined	define	VERB
ejpam-4715	138	14	by	by	ADP
ejpam-4715	138	15	|n|p	|n|p	NOUN
ejpam-4715	138	16	=	=	SYM
ejpam-4715	138	17	1	1	NUM
ejpam-4715	138	18	pνp(n	pνp(n	PROPN
ejpam-4715	138	19	)	)	PUNCT
ejpam-4715	138	20	.	.	PUNCT
ejpam-4715	139	1	clearly	clearly	ADV
ejpam-4715	139	2	,	,	PUNCT
ejpam-4715	139	3	when	when	SCONJ
ejpam-4715	139	4	q	q	NOUN
ejpam-4715	139	5	is	be	AUX
ejpam-4715	139	6	prime	prime	ADJ
ejpam-4715	139	7	,	,	PUNCT
ejpam-4715	139	8	νq	νq	PROPN
ejpam-4715	139	9	(	(	PUNCT
ejpam-4715	139	10	wm	wm	PROPN
ejpam-4715	139	11	,	,	PUNCT
ejpam-4715	139	12	r[n	r[n	NOUN
ejpam-4715	139	13	,	,	PUNCT
ejpam-4715	139	14	k]q	k]q	NOUN
ejpam-4715	139	15	)	)	PUNCT
ejpam-4715	139	16	=	=	PUNCT
ejpam-4715	140	1	kr	kr	PROPN
ejpam-4715	140	2	+	+	PROPN
ejpam-4715	140	3	m	m	PROPN
ejpam-4715	140	4	(	(	PUNCT
ejpam-4715	140	5	k	k	NOUN
ejpam-4715	140	6	2	2	X
ejpam-4715	140	7	)	)	PUNCT
ejpam-4715	140	8	νq	νq	PROPN
ejpam-4715	140	9	(	(	PUNCT
ejpam-4715	140	10	w̃m	w̃m	PROPN
ejpam-4715	140	11	,	,	PUNCT
ejpam-4715	140	12	r[n	r[n	NOUN
ejpam-4715	140	13	,	,	PUNCT
ejpam-4715	140	14	k]q	k]q	NOUN
ejpam-4715	140	15	)	)	PUNCT
ejpam-4715	140	16	=	=	SYM
ejpam-4715	141	1	kr	kr	PROPN
ejpam-4715	141	2	.	.	PUNCT
ejpam-4715	142	1	consequently	consequently	ADV
ejpam-4715	142	2	,	,	PUNCT
ejpam-4715	142	3	νq	νq	PROPN
ejpam-4715	142	4	(	(	PUNCT
ejpam-4715	142	5	wm	wm	PROPN
ejpam-4715	142	6	,	,	PUNCT
ejpam-4715	142	7	r[n	r[n	NOUN
ejpam-4715	142	8	,	,	PUNCT
ejpam-4715	142	9	k]q	k]q	NOUN
ejpam-4715	142	10	w̃m	w̃m	PROPN
ejpam-4715	142	11	,	,	PUNCT
ejpam-4715	142	12	r[n	r[n	NOUN
ejpam-4715	142	13	,	,	PUNCT
ejpam-4715	142	14	k]q	k]q	NOUN
ejpam-4715	142	15	)	)	PUNCT
ejpam-4715	142	16	=	=	SYM
ejpam-4715	142	17	νq	νq	PROPN
ejpam-4715	142	18	(	(	PUNCT
ejpam-4715	142	19	wm	wm	PROPN
ejpam-4715	142	20	,	,	PUNCT
ejpam-4715	142	21	r[n	r[n	PROPN
ejpam-4715	142	22	,	,	PUNCT
ejpam-4715	142	23	k]q)−	k]q)−	NOUN
ejpam-4715	142	24	νq	νq	PROPN
ejpam-4715	142	25	(	(	PUNCT
ejpam-4715	142	26	w̃m	w̃m	PROPN
ejpam-4715	142	27	,	,	PUNCT
ejpam-4715	142	28	r[n	r[n	NOUN
ejpam-4715	142	29	,	,	PUNCT
ejpam-4715	142	30	k]q	k]q	NOUN
ejpam-4715	142	31	)	)	PUNCT
ejpam-4715	143	1	=	=	PUNCT
ejpam-4715	143	2	m	m	PROPN
ejpam-4715	143	3	(	(	PUNCT
ejpam-4715	143	4	k	k	NOUN
ejpam-4715	143	5	2	2	NUM
ejpam-4715	143	6	)	)	PUNCT
ejpam-4715	143	7	.	.	PUNCT
ejpam-4715	144	1	also	also	ADV
ejpam-4715	144	2	,	,	PUNCT
ejpam-4715	144	3	one	one	PRON
ejpam-4715	144	4	can	can	AUX
ejpam-4715	144	5	easily	easily	ADV
ejpam-4715	144	6	see	see	VERB
ejpam-4715	144	7	that	that	SCONJ
ejpam-4715	144	8	νq	νq	PROPN
ejpam-4715	144	9	(	(	PUNCT
ejpam-4715	144	10	w	w	PROPN
ejpam-4715	144	11	∗	∗	PROPN
ejpam-4715	144	12	m	m	PROPN
ejpam-4715	144	13	,	,	PUNCT
ejpam-4715	144	14	r[n	r[n	NOUN
ejpam-4715	144	15	,	,	PUNCT
ejpam-4715	144	16	k]q	k]q	NOUN
ejpam-4715	144	17	−	−	PROPN
ejpam-4715	144	18	(	(	PUNCT
ejpam-4715	144	19	n	n	NOUN
ejpam-4715	144	20	k	k	NOUN
ejpam-4715	144	21	)	)	PUNCT
ejpam-4715	144	22	)	)	PUNCT
ejpam-4715	145	1	=	=	SYM
ejpam-4715	145	2	qνp(w	qνp(w	PROPN
ejpam-4715	145	3	∗	∗	NOUN
ejpam-4715	145	4	m	m	PROPN
ejpam-4715	145	5	,	,	PUNCT
ejpam-4715	145	6	r[n	r[n	NOUN
ejpam-4715	145	7	,	,	PUNCT
ejpam-4715	145	8	k]q−	k]q−	PROPN
ejpam-4715	145	9	(	(	PUNCT
ejpam-4715	145	10	n	n	X
ejpam-4715	145	11	k	k	NOUN
ejpam-4715	145	12	)	)	PUNCT
ejpam-4715	145	13	)	)	PUNCT
ejpam-4715	146	1	∣∣∣∣w	∣∣∣∣w	PROPN
ejpam-4715	146	2	∗	∗	NUM
ejpam-4715	146	3	m	m	PROPN
ejpam-4715	146	4	,	,	PUNCT
ejpam-4715	146	5	r[n	r[n	VERB
ejpam-4715	146	6	,	,	PUNCT
ejpam-4715	146	7	k]q	k]q	NOUN
ejpam-4715	146	8	−	−	PROPN
ejpam-4715	147	1	(	(	PUNCT
ejpam-4715	147	2	n	n	X
ejpam-4715	147	3	k	k	PROPN
ejpam-4715	147	4	)	)	PUNCT
ejpam-4715	147	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4715	147	6	q	q	NOUN
ejpam-4715	147	7	=	=	NOUN
ejpam-4715	147	8	1	1	X
ejpam-4715	147	9	.	.	PUNCT
ejpam-4715	147	10	references	reference	NOUN
ejpam-4715	147	11	942	942	NUM
ejpam-4715	147	12	acknowledgements	acknowledgement	NOUN
ejpam-4715	147	13	the	the	DET
ejpam-4715	147	14	authors	author	NOUN
ejpam-4715	147	15	are	be	AUX
ejpam-4715	147	16	grateful	grateful	ADJ
ejpam-4715	147	17	to	to	PART
ejpam-4715	147	18	cebu	cebu	VERB
ejpam-4715	147	19	normal	normal	ADJ
ejpam-4715	147	20	university	university	NOUN
ejpam-4715	147	21	(	(	PUNCT
ejpam-4715	147	22	cnu	cnu	PROPN
ejpam-4715	147	23	)	)	PUNCT
ejpam-4715	147	24	for	for	ADP
ejpam-4715	147	25	partially	partially	ADV
ejpam-4715	147	26	funding	fund	VERB
ejpam-4715	147	27	this	this	DET
ejpam-4715	147	28	research	research	NOUN
ejpam-4715	147	29	project	project	NOUN
ejpam-4715	147	30	through	through	ADP
ejpam-4715	147	31	its	its	PRON
ejpam-4715	147	32	research	research	NOUN
ejpam-4715	147	33	institute	institute	NOUN
ejpam-4715	147	34	for	for	ADP
ejpam-4715	147	35	computational	computational	ADJ
ejpam-4715	147	36	mathematics	mathematic	NOUN
ejpam-4715	147	37	and	and	CCONJ
ejpam-4715	147	38	physics	physics	PROPN
ejpam-4715	147	39	(	(	PUNCT
ejpam-4715	147	40	ricmp	ricmp	PROPN
ejpam-4715	147	41	)	)	PUNCT
ejpam-4715	147	42	.	.	PUNCT
ejpam-4715	148	1	they	they	PRON
ejpam-4715	148	2	are	be	AUX
ejpam-4715	148	3	also	also	ADV
ejpam-4715	148	4	grateful	grateful	ADJ
ejpam-4715	148	5	to	to	ADP
ejpam-4715	148	6	the	the	DET
ejpam-4715	148	7	two	two	NUM
ejpam-4715	148	8	referees	referee	NOUN
ejpam-4715	148	9	for	for	ADP
ejpam-4715	148	10	their	their	PRON
ejpam-4715	148	11	valuable	valuable	ADJ
ejpam-4715	148	12	time	time	NOUN
ejpam-4715	148	13	in	in	ADP
ejpam-4715	148	14	reviewing	review	VERB
ejpam-4715	148	15	the	the	DET
ejpam-4715	148	16	paper	paper	NOUN
ejpam-4715	148	17	.	.	PUNCT
ejpam-4715	149	1	references	reference	NOUN
ejpam-4715	149	2	[	[	X
ejpam-4715	149	3	1	1	NUM
ejpam-4715	149	4	]	]	PUNCT
ejpam-4715	149	5	l.	l.	PROPN
ejpam-4715	149	6	carlitz	carlitz	PROPN
ejpam-4715	149	7	.	.	PUNCT
ejpam-4715	150	1	q	q	ADJ
ejpam-4715	150	2	-	-	PUNCT
ejpam-4715	150	3	bernoulli	bernoulli	NOUN
ejpam-4715	150	4	numbers	number	NOUN
ejpam-4715	150	5	and	and	CCONJ
ejpam-4715	150	6	polynomials	polynomial	NOUN
ejpam-4715	150	7	.	.	PUNCT
ejpam-4715	151	1	duke	duke	PROPN
ejpam-4715	151	2	math	math	PROPN
ejpam-4715	151	3	.	.	PUNCT
ejpam-4715	152	1	j.	j.	PROPN
ejpam-4715	152	2	,	,	PUNCT
ejpam-4715	152	3	15:987–1000	15:987–1000	PROPN
ejpam-4715	152	4	.	.	PROPN
ejpam-4715	152	5	,	,	PUNCT
ejpam-4715	152	6	1948	1948	NUM
ejpam-4715	152	7	.	.	PUNCT
ejpam-4715	153	1	[	[	X
ejpam-4715	153	2	2	2	NUM
ejpam-4715	153	3	]	]	X
ejpam-4715	153	4	g.s	g.s	PROPN
ejpam-4715	153	5	.	.	PROPN
ejpam-4715	153	6	cheon	cheon	PROPN
ejpam-4715	153	7	and	and	CCONJ
ejpam-4715	153	8	j.h	j.h	PROPN
ejpam-4715	153	9	.	.	PROPN
ejpam-4715	153	10	jung	jung	PROPN
ejpam-4715	153	11	.	.	PUNCT
ejpam-4715	154	1	r	r	X
ejpam-4715	154	2	-	-	PUNCT
ejpam-4715	154	3	whitney	whitney	NOUN
ejpam-4715	154	4	number	number	NOUN
ejpam-4715	154	5	of	of	ADP
ejpam-4715	154	6	dowling	dowle	VERB
ejpam-4715	154	7	lattices	lattice	NOUN
ejpam-4715	154	8	.	.	PUNCT
ejpam-4715	155	1	discrete	discrete	ADJ
ejpam-4715	155	2	math	math	NOUN
ejpam-4715	155	3	.	.	PUNCT
ejpam-4715	155	4	,	,	PUNCT
ejpam-4715	155	5	312:2337–2348	312:2337–2348	NUM
ejpam-4715	155	6	,	,	PUNCT
ejpam-4715	155	7	2012	2012	NUM
ejpam-4715	155	8	.	.	PUNCT
ejpam-4715	156	1	[	[	X
ejpam-4715	156	2	3	3	X
ejpam-4715	156	3	]	]	X
ejpam-4715	156	4	r.	r.	PROPN
ejpam-4715	156	5	b.	b.	PROPN
ejpam-4715	156	6	corcino	corcino	PROPN
ejpam-4715	156	7	.	.	PUNCT
ejpam-4715	157	1	hankel	hankel	PROPN
ejpam-4715	157	2	transform	transform	NOUN
ejpam-4715	157	3	of	of	ADP
ejpam-4715	157	4	the	the	DET
ejpam-4715	157	5	first	first	ADJ
ejpam-4715	157	6	form	form	NOUN
ejpam-4715	157	7	(	(	PUNCT
ejpam-4715	157	8	q	q	ADJ
ejpam-4715	157	9	,	,	PUNCT
ejpam-4715	157	10	r)-dowling	r)-dowle	VERB
ejpam-4715	157	11	numbers	number	NOUN
ejpam-4715	157	12	.	.	PUNCT
ejpam-4715	158	1	eur	eur	PROPN
ejpam-4715	158	2	.	.	PUNCT
ejpam-4715	159	1	j.	j.	PROPN
ejpam-4715	159	2	pure	pure	PROPN
ejpam-4715	159	3	appl	appl	PROPN
ejpam-4715	159	4	.	.	PUNCT
ejpam-4715	159	5	math	math	PROPN
ejpam-4715	159	6	.	.	PUNCT
ejpam-4715	159	7	,	,	PUNCT
ejpam-4715	160	1	14(3):746–759	14(3):746–759	PROPN
ejpam-4715	160	2	.	.	PROPN
ejpam-4715	160	3	,	,	PUNCT
ejpam-4715	160	4	2021	2021	NUM
ejpam-4715	160	5	.	.	PUNCT
ejpam-4715	161	1	[	[	X
ejpam-4715	161	2	4	4	NUM
ejpam-4715	161	3	]	]	PUNCT
ejpam-4715	161	4	r.	r.	PROPN
ejpam-4715	161	5	b.	b.	PROPN
ejpam-4715	161	6	corcino	corcino	PROPN
ejpam-4715	161	7	and	and	CCONJ
ejpam-4715	161	8	c.	c.	PROPN
ejpam-4715	161	9	b.	b.	PROPN
ejpam-4715	161	10	corcino	corcino	PROPN
ejpam-4715	161	11	.	.	PUNCT
ejpam-4715	162	1	on	on	ADP
ejpam-4715	162	2	the	the	DET
ejpam-4715	162	3	maximum	maximum	NOUN
ejpam-4715	162	4	of	of	ADP
ejpam-4715	162	5	the	the	DET
ejpam-4715	162	6	generalized	generalized	ADJ
ejpam-4715	162	7	stirling	stirling	NOUN
ejpam-4715	162	8	numbers	number	NOUN
ejpam-4715	162	9	.	.	PUNCT
ejpam-4715	163	1	util	util	PROPN
ejpam-4715	163	2	.	.	PUNCT
ejpam-4715	164	1	math	math	NOUN
ejpam-4715	164	2	.	.	PUNCT
ejpam-4715	164	3	,	,	PUNCT
ejpam-4715	165	1	86:241–256	86:241–256	PROPN
ejpam-4715	165	2	,	,	PUNCT
ejpam-4715	165	3	2011	2011	NUM
ejpam-4715	165	4	.	.	PUNCT
ejpam-4715	166	1	[	[	X
ejpam-4715	166	2	5	5	NUM
ejpam-4715	166	3	]	]	PUNCT
ejpam-4715	166	4	r.	r.	PROPN
ejpam-4715	166	5	b.	b.	PROPN
ejpam-4715	166	6	corcino	corcino	PROPN
ejpam-4715	166	7	,	,	PUNCT
ejpam-4715	166	8	c.	c.	PROPN
ejpam-4715	166	9	b.	b.	PROPN
ejpam-4715	166	10	corcino	corcino	PROPN
ejpam-4715	166	11	,	,	PUNCT
ejpam-4715	166	12	and	and	CCONJ
ejpam-4715	166	13	r.	r.	PROPN
ejpam-4715	166	14	aldema	aldema	PROPN
ejpam-4715	166	15	.	.	PUNCT
ejpam-4715	167	1	asymptotic	asymptotic	ADJ
ejpam-4715	167	2	normality	normality	NOUN
ejpam-4715	167	3	of	of	ADP
ejpam-4715	167	4	the	the	DET
ejpam-4715	167	5	(	(	PUNCT
ejpam-4715	167	6	r	r	NOUN
ejpam-4715	167	7	,	,	PUNCT
ejpam-4715	167	8	β)stirling	β)stirle	VERB
ejpam-4715	167	9	numbers	number	NOUN
ejpam-4715	167	10	.	.	PUNCT
ejpam-4715	168	1	ars	ars	PROPN
ejpam-4715	168	2	combin	combin	PROPN
ejpam-4715	168	3	.	.	PUNCT
ejpam-4715	168	4	,	,	PUNCT
ejpam-4715	168	5	81:81–96	81:81–96	PROPN
ejpam-4715	168	6	,	,	PUNCT
ejpam-4715	168	7	2006	2006	NUM
ejpam-4715	168	8	.	.	PUNCT
ejpam-4715	169	1	[	[	X
ejpam-4715	169	2	6	6	NUM
ejpam-4715	169	3	]	]	PUNCT
ejpam-4715	169	4	r.	r.	PROPN
ejpam-4715	169	5	b.	b.	PROPN
ejpam-4715	169	6	corcino	corcino	PROPN
ejpam-4715	169	7	,	,	PUNCT
ejpam-4715	169	8	c.b	c.b	PROPN
ejpam-4715	169	9	.	.	PROPN
ejpam-4715	169	10	corcino	corcino	PROPN
ejpam-4715	169	11	,	,	PUNCT
ejpam-4715	169	12	j.m	j.m	PROPN
ejpam-4715	169	13	.	.	PROPN
ejpam-4715	169	14	ontolan	ontolan	PROPN
ejpam-4715	169	15	,	,	PUNCT
ejpam-4715	169	16	c.m	c.m	PROPN
ejpam-4715	169	17	.	.	PROPN
ejpam-4715	169	18	perez	perez	PROPN
ejpam-4715	169	19	,	,	PUNCT
ejpam-4715	169	20	and	and	CCONJ
ejpam-4715	169	21	e.r	e.r	PROPN
ejpam-4715	169	22	.	.	PROPN
ejpam-4715	169	23	cantallopez	cantallopez	PROPN
ejpam-4715	169	24	.	.	PUNCT
ejpam-4715	170	1	the	the	DET
ejpam-4715	170	2	hankel	hankel	NOUN
ejpam-4715	170	3	transform	transform	NOUN
ejpam-4715	170	4	of	of	ADP
ejpam-4715	170	5	q	q	ADJ
ejpam-4715	170	6	-	-	ADJ
ejpam-4715	170	7	noncentral	noncentral	ADJ
ejpam-4715	170	8	bell	bell	NOUN
ejpam-4715	170	9	numbers	number	NOUN
ejpam-4715	170	10	.	.	PUNCT
ejpam-4715	171	1	international	international	ADJ
ejpam-4715	171	2	journal	journal	NOUN
ejpam-4715	171	3	of	of	ADP
ejpam-4715	171	4	mathematics	mathematics	PROPN
ejpam-4715	171	5	and	and	CCONJ
ejpam-4715	171	6	mathematical	mathematical	ADJ
ejpam-4715	171	7	sciences	science	NOUN
ejpam-4715	171	8	,	,	PUNCT
ejpam-4715	171	9	2015	2015	NUM
ejpam-4715	171	10	,	,	PUNCT
ejpam-4715	171	11	2015	2015	NUM
ejpam-4715	171	12	.	.	PUNCT
ejpam-4715	172	1	[	[	X
ejpam-4715	172	2	7	7	X
ejpam-4715	172	3	]	]	X
ejpam-4715	172	4	r.b	r.b	PROPN
ejpam-4715	172	5	.	.	PROPN
ejpam-4715	172	6	corcino	corcino	PROPN
ejpam-4715	172	7	.	.	PUNCT
ejpam-4715	173	1	the	the	DET
ejpam-4715	173	2	(	(	PUNCT
ejpam-4715	173	3	r	r	NOUN
ejpam-4715	173	4	,	,	PUNCT
ejpam-4715	173	5	β)-stirling	β)-stirle	VERB
ejpam-4715	173	6	numbers	number	NOUN
ejpam-4715	173	7	.	.	PUNCT
ejpam-4715	174	1	mindanao	mindanao	PROPN
ejpam-4715	174	2	forum	forum	PROPN
ejpam-4715	174	3	,	,	PUNCT
ejpam-4715	174	4	14(2):91–100	14(2):91–100	NUM
ejpam-4715	174	5	,	,	PUNCT
ejpam-4715	174	6	1999	1999	NUM
ejpam-4715	174	7	.	.	PUNCT
ejpam-4715	175	1	[	[	X
ejpam-4715	175	2	8	8	NUM
ejpam-4715	175	3	]	]	X
ejpam-4715	175	4	r.b	r.b	PROPN
ejpam-4715	175	5	.	.	PROPN
ejpam-4715	175	6	corcino	corcino	PROPN
ejpam-4715	175	7	and	and	CCONJ
ejpam-4715	175	8	c.	c.	PROPN
ejpam-4715	175	9	barrientos	barrientos	PROPN
ejpam-4715	175	10	.	.	PUNCT
ejpam-4715	176	1	some	some	DET
ejpam-4715	176	2	theorems	theorem	NOUN
ejpam-4715	176	3	on	on	ADP
ejpam-4715	176	4	the	the	DET
ejpam-4715	176	5	q	q	NOUN
ejpam-4715	176	6	-	-	PUNCT
ejpam-4715	176	7	analogue	analogue	NOUN
ejpam-4715	176	8	of	of	ADP
ejpam-4715	176	9	the	the	DET
ejpam-4715	176	10	generalized	generalized	ADJ
ejpam-4715	176	11	stirling	stirling	NOUN
ejpam-4715	176	12	numbers	number	NOUN
ejpam-4715	176	13	.	.	PUNCT
ejpam-4715	177	1	bulletin	bulletin	NOUN
ejpam-4715	177	2	of	of	ADP
ejpam-4715	177	3	the	the	DET
ejpam-4715	177	4	malaysian	malaysian	PROPN
ejpam-4715	177	5	mathematical	mathematical	PROPN
ejpam-4715	177	6	sciences	sciences	PROPN
ejpam-4715	177	7	society	society	NOUN
ejpam-4715	177	8	,	,	PUNCT
ejpam-4715	177	9	34(3):487	34(3):487	NUM
ejpam-4715	177	10	–	–	PUNCT
ejpam-4715	177	11	501	501	NUM
ejpam-4715	177	12	.	.	NUM
ejpam-4715	177	13	,	,	PUNCT
ejpam-4715	177	14	2011	2011	NUM
ejpam-4715	177	15	.	.	PUNCT
ejpam-4715	178	1	[	[	X
ejpam-4715	178	2	9	9	NUM
ejpam-4715	178	3	]	]	X
ejpam-4715	178	4	r.b	r.b	PROPN
ejpam-4715	178	5	.	.	PROPN
ejpam-4715	178	6	corcino	corcino	PROPN
ejpam-4715	178	7	and	and	CCONJ
ejpam-4715	178	8	c.b	c.b	PROPN
ejpam-4715	178	9	.	.	PROPN
ejpam-4715	178	10	corcino	corcino	PROPN
ejpam-4715	178	11	.	.	PUNCT
ejpam-4715	179	1	the	the	DET
ejpam-4715	179	2	hankel	hankel	NOUN
ejpam-4715	179	3	transform	transform	NOUN
ejpam-4715	179	4	of	of	ADP
ejpam-4715	179	5	generalized	generalized	ADJ
ejpam-4715	179	6	bell	bell	NOUN
ejpam-4715	179	7	numbers	number	NOUN
ejpam-4715	179	8	and	and	CCONJ
ejpam-4715	179	9	its	its	PRON
ejpam-4715	179	10	q	q	NOUN
ejpam-4715	179	11	-	-	PUNCT
ejpam-4715	179	12	analogue	analogue	NOUN
ejpam-4715	179	13	.	.	PUNCT
ejpam-4715	180	1	util	util	PROPN
ejpam-4715	180	2	.	.	PUNCT
ejpam-4715	181	1	math	math	NOUN
ejpam-4715	181	2	.	.	PUNCT
ejpam-4715	181	3	,	,	PUNCT
ejpam-4715	182	1	89:297–309	89:297–309	NUM
ejpam-4715	182	2	,	,	PUNCT
ejpam-4715	182	3	2012	2012	NUM
ejpam-4715	182	4	.	.	PUNCT
ejpam-4715	183	1	[	[	X
ejpam-4715	183	2	10	10	NUM
ejpam-4715	183	3	]	]	X
ejpam-4715	183	4	r.b	r.b	PROPN
ejpam-4715	183	5	.	.	PROPN
ejpam-4715	183	6	corcino	corcino	PROPN
ejpam-4715	183	7	,	,	PUNCT
ejpam-4715	183	8	l.c	l.c	PROPN
ejpam-4715	183	9	.	.	PROPN
ejpam-4715	183	10	hsu	hsu	PROPN
ejpam-4715	183	11	,	,	PUNCT
ejpam-4715	183	12	,	,	PUNCT
ejpam-4715	183	13	and	and	CCONJ
ejpam-4715	183	14	e.l	e.l	PROPN
ejpam-4715	183	15	.	.	PROPN
ejpam-4715	183	16	tan	tan	PROPN
ejpam-4715	183	17	.	.	PUNCT
ejpam-4715	184	1	a	a	DET
ejpam-4715	184	2	q	q	NOUN
ejpam-4715	184	3	-	-	PUNCT
ejpam-4715	184	4	analogue	analogue	NOUN
ejpam-4715	184	5	of	of	ADP
ejpam-4715	184	6	generalized	generalized	ADJ
ejpam-4715	184	7	stirling	stirling	NOUN
ejpam-4715	184	8	numbers	number	NOUN
ejpam-4715	184	9	.	.	PUNCT
ejpam-4715	185	1	fibonacci	fibonacci	NOUN
ejpam-4715	185	2	quart	quart	PROPN
ejpam-4715	185	3	.	.	PUNCT
ejpam-4715	185	4	,	,	PUNCT
ejpam-4715	185	5	44:154–165	44:154–165	PROPN
ejpam-4715	185	6	,	,	PUNCT
ejpam-4715	185	7	2006	2006	NUM
ejpam-4715	185	8	.	.	PUNCT
ejpam-4715	186	1	[	[	X
ejpam-4715	186	2	11	11	NUM
ejpam-4715	186	3	]	]	X
ejpam-4715	186	4	r.b	r.b	PROPN
ejpam-4715	186	5	.	.	PROPN
ejpam-4715	186	6	corcino	corcino	PROPN
ejpam-4715	186	7	,	,	PUNCT
ejpam-4715	186	8	m.r	m.r	PROPN
ejpam-4715	186	9	.	.	PROPN
ejpam-4715	186	10	latayada	latayada	PROPN
ejpam-4715	186	11	,	,	PUNCT
ejpam-4715	186	12	and	and	CCONJ
ejpam-4715	186	13	m.p	m.p	PROPN
ejpam-4715	186	14	.	.	PROPN
ejpam-4715	186	15	vega	vega	PROPN
ejpam-4715	186	16	.	.	PUNCT
ejpam-4715	187	1	hankel	hankel	PROPN
ejpam-4715	187	2	transform	transform	NOUN
ejpam-4715	187	3	of	of	ADP
ejpam-4715	187	4	(	(	PUNCT
ejpam-4715	187	5	q	q	ADJ
ejpam-4715	187	6	,	,	PUNCT
ejpam-4715	187	7	r)-dowling	r)-dowling	ADJ
ejpam-4715	187	8	numbers	number	NOUN
ejpam-4715	187	9	.	.	PUNCT
ejpam-4715	188	1	eur	eur	PROPN
ejpam-4715	188	2	.	.	PUNCT
ejpam-4715	189	1	j.	j.	PROPN
ejpam-4715	189	2	pure	pure	PROPN
ejpam-4715	189	3	appl	appl	PROPN
ejpam-4715	189	4	.	.	PUNCT
ejpam-4715	189	5	math	math	PROPN
ejpam-4715	189	6	.	.	PUNCT
ejpam-4715	189	7	,	,	PUNCT
ejpam-4715	190	1	12(2):279–293	12(2):279–293	PROPN
ejpam-4715	190	2	,	,	PUNCT
ejpam-4715	190	3	2019	2019	NUM
ejpam-4715	190	4	.	.	PUNCT
ejpam-4715	191	1	[	[	X
ejpam-4715	191	2	12	12	NUM
ejpam-4715	191	3	]	]	X
ejpam-4715	191	4	r.b	r.b	PROPN
ejpam-4715	191	5	.	.	PROPN
ejpam-4715	191	6	corcino	corcino	PROPN
ejpam-4715	191	7	and	and	CCONJ
ejpam-4715	191	8	c.b	c.b	PROPN
ejpam-4715	191	9	.	.	PROPN
ejpam-4715	191	10	montero	montero	PROPN
ejpam-4715	191	11	.	.	PUNCT
ejpam-4715	192	1	a	a	DET
ejpam-4715	192	2	q	q	NOUN
ejpam-4715	192	3	-	-	PUNCT
ejpam-4715	192	4	analogue	analogue	NOUN
ejpam-4715	192	5	of	of	ADP
ejpam-4715	192	6	rucinski	rucinski	ADJ
ejpam-4715	192	7	-	-	PUNCT
ejpam-4715	192	8	voigt	voigt	NOUN
ejpam-4715	192	9	numbers	number	NOUN
ejpam-4715	192	10	.	.	PUNCT
ejpam-4715	193	1	isrn	isrn	NOUN
ejpam-4715	193	2	discrete	discrete	VERB
ejpam-4715	193	3	mathematics	mathematic	NOUN
ejpam-4715	193	4	,	,	PUNCT
ejpam-4715	193	5	2012:592818	2012:592818	NUM
ejpam-4715	193	6	,	,	PUNCT
ejpam-4715	193	7	2012	2012	NUM
ejpam-4715	193	8	.	.	PUNCT
ejpam-4715	194	1	[	[	X
ejpam-4715	194	2	13	13	NUM
ejpam-4715	194	3	]	]	X
ejpam-4715	194	4	r.b	r.b	PROPN
ejpam-4715	194	5	.	.	PROPN
ejpam-4715	194	6	corcino	corcino	PROPN
ejpam-4715	194	7	,	,	PUNCT
ejpam-4715	194	8	j.m	j.m	PROPN
ejpam-4715	194	9	.	.	PROPN
ejpam-4715	194	10	ontolan	ontolan	PROPN
ejpam-4715	194	11	,	,	PUNCT
ejpam-4715	194	12	and	and	CCONJ
ejpam-4715	194	13	m.r	m.r	PROPN
ejpam-4715	194	14	.	.	PROPN
ejpam-4715	194	15	lobrigas	lobrigas	PROPN
ejpam-4715	194	16	.	.	PUNCT
ejpam-4715	195	1	explicit	explicit	ADJ
ejpam-4715	195	2	formulas	formula	NOUN
ejpam-4715	195	3	for	for	ADP
ejpam-4715	195	4	the	the	DET
ejpam-4715	195	5	first	first	ADJ
ejpam-4715	195	6	form	form	NOUN
ejpam-4715	195	7	(	(	PUNCT
ejpam-4715	195	8	q	q	ADJ
ejpam-4715	195	9	,	,	PUNCT
ejpam-4715	195	10	r)-dowling	r)-dowle	VERB
ejpam-4715	195	11	numbers	number	NOUN
ejpam-4715	195	12	and	and	CCONJ
ejpam-4715	195	13	(	(	PUNCT
ejpam-4715	195	14	q	q	ADJ
ejpam-4715	195	15	,	,	PUNCT
ejpam-4715	195	16	r)-whitney	r)-whitney	ADJ
ejpam-4715	195	17	-	-	PUNCT
ejpam-4715	195	18	lah	lah	NOUN
ejpam-4715	195	19	numbers	number	NOUN
ejpam-4715	195	20	.	.	PUNCT
ejpam-4715	196	1	eur	eur	PROPN
ejpam-4715	196	2	.	.	PUNCT
ejpam-4715	197	1	j.	j.	PROPN
ejpam-4715	197	2	pure	pure	PROPN
ejpam-4715	197	3	appl	appl	PROPN
ejpam-4715	197	4	.	.	PUNCT
ejpam-4715	197	5	math	math	PROPN
ejpam-4715	197	6	.	.	PUNCT
ejpam-4715	197	7	,	,	PUNCT
ejpam-4715	197	8	14(1):65–81	14(1):65–81	NUM
ejpam-4715	197	9	,	,	PUNCT
ejpam-4715	197	10	2021	2021	NUM
ejpam-4715	197	11	.	.	PUNCT
ejpam-4715	198	1	references	reference	NOUN
ejpam-4715	198	2	943	943	NUM
ejpam-4715	199	1	[	[	X
ejpam-4715	199	2	14	14	NUM
ejpam-4715	199	3	]	]	X
ejpam-4715	199	4	r.b	r.b	PROPN
ejpam-4715	199	5	.	.	PROPN
ejpam-4715	199	6	corcino	corcino	PROPN
ejpam-4715	199	7	,	,	PUNCT
ejpam-4715	199	8	j.m	j.m	PROPN
ejpam-4715	199	9	.	.	PROPN
ejpam-4715	199	10	ontolan	ontolan	PROPN
ejpam-4715	199	11	,	,	PUNCT
ejpam-4715	199	12	j.	j.	PROPN
ejpam-4715	199	13	ca	can	AUX
ejpam-4715	199	14	nete	nete	PROPN
ejpam-4715	199	15	,	,	PUNCT
ejpam-4715	199	16	and	and	CCONJ
ejpam-4715	199	17	m.r	m.r	PROPN
ejpam-4715	199	18	.	.	PROPN
ejpam-4715	199	19	latayada	latayada	PROPN
ejpam-4715	199	20	.	.	PUNCT
ejpam-4715	200	1	a	a	DET
ejpam-4715	200	2	q	q	NOUN
ejpam-4715	200	3	-	-	PUNCT
ejpam-4715	200	4	analogue	analogue	NOUN
ejpam-4715	200	5	of	of	ADP
ejpam-4715	200	6	rwhitney	rwhitney	NOUN
ejpam-4715	200	7	numbers	number	NOUN
ejpam-4715	200	8	of	of	ADP
ejpam-4715	200	9	the	the	DET
ejpam-4715	200	10	second	second	ADJ
ejpam-4715	200	11	kind	kind	NOUN
ejpam-4715	200	12	and	and	CCONJ
ejpam-4715	200	13	its	its	PRON
ejpam-4715	200	14	hankel	hankel	NOUN
ejpam-4715	200	15	transform	transform	NOUN
ejpam-4715	200	16	.	.	PUNCT
ejpam-4715	201	1	j.	j.	PROPN
ejpam-4715	201	2	math	math	PROPN
ejpam-4715	201	3	.	.	PUNCT
ejpam-4715	202	1	computer	computer	NOUN
ejpam-4715	202	2	sci	sci	PROPN
ejpam-4715	202	3	.	.	PROPN
ejpam-4715	202	4	,	,	PUNCT
ejpam-4715	202	5	21:258–272	21:258–272	PROPN
ejpam-4715	202	6	,	,	PUNCT
ejpam-4715	202	7	2020	2020	NUM
ejpam-4715	202	8	.	.	PUNCT
ejpam-4715	203	1	[	[	X
ejpam-4715	203	2	15	15	NUM
ejpam-4715	203	3	]	]	X
ejpam-4715	203	4	r.b	r.b	PROPN
ejpam-4715	203	5	.	.	PROPN
ejpam-4715	203	6	corcino	corcino	PROPN
ejpam-4715	203	7	,	,	PUNCT
ejpam-4715	203	8	j.m	j.m	PROPN
ejpam-4715	203	9	.	.	PROPN
ejpam-4715	203	10	ontolan	ontolan	PROPN
ejpam-4715	203	11	,	,	PUNCT
ejpam-4715	203	12	and	and	CCONJ
ejpam-4715	203	13	g.s	g.s	PROPN
ejpam-4715	203	14	.	.	PROPN
ejpam-4715	203	15	rama	rama	PROPN
ejpam-4715	203	16	.	.	PUNCT
ejpam-4715	204	1	hankel	hankel	PROPN
ejpam-4715	204	2	transform	transform	NOUN
ejpam-4715	204	3	of	of	ADP
ejpam-4715	204	4	the	the	DET
ejpam-4715	204	5	second	second	ADJ
ejpam-4715	204	6	form	form	NOUN
ejpam-4715	204	7	(	(	PUNCT
ejpam-4715	204	8	q	q	NOUN
ejpam-4715	204	9	,	,	PUNCT
ejpam-4715	204	10	r)-dowling	r)-dowling	ADJ
ejpam-4715	204	11	numbers	number	NOUN
ejpam-4715	204	12	.	.	PUNCT
ejpam-4715	205	1	eur	eur	PROPN
ejpam-4715	205	2	.	.	PUNCT
ejpam-4715	206	1	j.	j.	PROPN
ejpam-4715	206	2	pure	pure	PROPN
ejpam-4715	206	3	appl	appl	PROPN
ejpam-4715	206	4	.	.	PUNCT
ejpam-4715	206	5	math	math	PROPN
ejpam-4715	206	6	.	.	PUNCT
ejpam-4715	206	7	,	,	PUNCT
ejpam-4715	207	1	12(4):1676–1688	12(4):1676–1688	NUM
ejpam-4715	207	2	,	,	PUNCT
ejpam-4715	207	3	2019	2019	NUM
ejpam-4715	207	4	.	.	PUNCT
ejpam-4715	208	1	[	[	X
ejpam-4715	208	2	16	16	NUM
ejpam-4715	208	3	]	]	X
ejpam-4715	208	4	r.b	r.b	PROPN
ejpam-4715	208	5	.	.	PROPN
ejpam-4715	208	6	corcino	corcino	PROPN
ejpam-4715	208	7	,	,	PUNCT
ejpam-4715	208	8	m.p	m.p	PROPN
ejpam-4715	208	9	.	.	PROPN
ejpam-4715	208	10	vega	vega	PROPN
ejpam-4715	208	11	,	,	PUNCT
ejpam-4715	208	12	and	and	CCONJ
ejpam-4715	208	13	a.m.	a.m.	PROPN
ejpam-4715	208	14	dibagulun	dibagulun	PROPN
ejpam-4715	208	15	.	.	PUNCT
ejpam-4715	209	1	a	a	DET
ejpam-4715	209	2	(	(	PUNCT
ejpam-4715	209	3	p	p	NOUN
ejpam-4715	209	4	,	,	PUNCT
ejpam-4715	209	5	q)-analogue	q)-analogue	NOUN
ejpam-4715	209	6	of	of	ADP
ejpam-4715	209	7	qi	qi	NOUN
ejpam-4715	209	8	-	-	PUNCT
ejpam-4715	209	9	type	type	NOUN
ejpam-4715	209	10	formula	formula	NOUN
ejpam-4715	209	11	for	for	ADP
ejpam-4715	209	12	r	r	NOUN
ejpam-4715	209	13	-	-	PUNCT
ejpam-4715	209	14	dowling	dowle	VERB
ejpam-4715	209	15	numbers	number	NOUN
ejpam-4715	209	16	.	.	PUNCT
ejpam-4715	210	1	j.	j.	PROPN
ejpam-4715	210	2	math	math	PROPN
ejpam-4715	210	3	.	.	PUNCT
ejpam-4715	211	1	computer	computer	NOUN
ejpam-4715	211	2	sci	sci	PROPN
ejpam-4715	211	3	.	.	PROPN
ejpam-4715	211	4	,	,	PUNCT
ejpam-4715	211	5	24:273–286	24:273–286	PROPN
ejpam-4715	211	6	.	.	PROPN
ejpam-4715	211	7	,	,	PUNCT
ejpam-4715	211	8	2021	2021	NUM
ejpam-4715	211	9	.	.	PUNCT
ejpam-4715	212	1	[	[	X
ejpam-4715	212	2	17	17	NUM
ejpam-4715	212	3	]	]	X
ejpam-4715	212	4	r.	r.	PROPN
ejpam-4715	212	5	ehrenborg	ehrenborg	PROPN
ejpam-4715	212	6	.	.	PUNCT
ejpam-4715	213	1	determinants	determinant	NOUN
ejpam-4715	213	2	of	of	ADP
ejpam-4715	213	3	involving	involve	VERB
ejpam-4715	213	4	q	q	ADJ
ejpam-4715	213	5	-	-	PUNCT
ejpam-4715	213	6	stirling	stirling	NOUN
ejpam-4715	213	7	numbers	number	NOUN
ejpam-4715	213	8	.	.	PUNCT
ejpam-4715	214	1	advances	advance	NOUN
ejpam-4715	214	2	in	in	ADP
ejpam-4715	214	3	applied	applied	ADJ
ejpam-4715	214	4	mathematics	mathematic	NOUN
ejpam-4715	214	5	,	,	PUNCT
ejpam-4715	214	6	31:630–642	31:630–642	PROPN
ejpam-4715	214	7	,	,	PUNCT
ejpam-4715	214	8	2003	2003	NUM
ejpam-4715	214	9	.	.	PUNCT
ejpam-4715	215	1	[	[	X
ejpam-4715	215	2	18	18	NUM
ejpam-4715	215	3	]	]	PUNCT
ejpam-4715	215	4	i.	i.	NOUN
ejpam-4715	215	5	mező.	mező.	X
ejpam-4715	215	6	a	a	DET
ejpam-4715	215	7	new	new	ADJ
ejpam-4715	215	8	formula	formula	NOUN
ejpam-4715	215	9	for	for	ADP
ejpam-4715	215	10	the	the	DET
ejpam-4715	215	11	bernoulli	bernoulli	NOUN
ejpam-4715	215	12	polynomials	polynomial	NOUN
ejpam-4715	215	13	.	.	PUNCT
ejpam-4715	216	1	result	result	VERB
ejpam-4715	216	2	.	.	PUNCT
ejpam-4715	217	1	math	math	NOUN
ejpam-4715	217	2	.	.	PUNCT
ejpam-4715	217	3	,	,	PUNCT
ejpam-4715	218	1	58(3):329–335	58(3):329–335	PROPN
ejpam-4715	218	2	,	,	PUNCT
ejpam-4715	218	3	2010	2010	NUM
ejpam-4715	218	4	.	.	PUNCT
ejpam-4715	219	1	[	[	X
ejpam-4715	219	2	19	19	NUM
ejpam-4715	219	3	]	]	X
ejpam-4715	219	4	m.p	m.p	PROPN
ejpam-4715	219	5	.	.	PROPN
ejpam-4715	219	6	vega	vega	PROPN
ejpam-4715	219	7	r.b	r.b	PROPN
ejpam-4715	219	8	.	.	PROPN
ejpam-4715	219	9	corcino	corcino	PROPN
ejpam-4715	219	10	and	and	CCONJ
ejpam-4715	219	11	a.m.	a.m.	PROPN
ejpam-4715	219	12	dibagulun	dibagulun	PROPN
ejpam-4715	219	13	.	.	PUNCT
ejpam-4715	220	1	a	a	DET
ejpam-4715	220	2	(	(	PUNCT
ejpam-4715	220	3	p	p	NOUN
ejpam-4715	220	4	,	,	PUNCT
ejpam-4715	220	5	q)-analogue	q)-analogue	NOUN
ejpam-4715	220	6	of	of	ADP
ejpam-4715	220	7	qi	qi	NOUN
ejpam-4715	220	8	-	-	PUNCT
ejpam-4715	220	9	type	type	NOUN
ejpam-4715	220	10	formula	formula	NOUN
ejpam-4715	220	11	for	for	ADP
ejpam-4715	220	12	r	r	NOUN
ejpam-4715	220	13	-	-	PUNCT
ejpam-4715	220	14	dowling	dowle	VERB
ejpam-4715	220	15	numbers	number	NOUN
ejpam-4715	220	16	.	.	PUNCT
ejpam-4715	221	1	axioms	axiom	NOUN
ejpam-4715	221	2	,	,	PUNCT
ejpam-4715	221	3	10	10	NUM
ejpam-4715	221	4	:	:	PUNCT
ejpam-4715	221	5	article	article	NOUN
ejpam-4715	221	6	343	343	NUM
ejpam-4715	221	7	,	,	PUNCT
ejpam-4715	221	8	2021	2021	NUM
ejpam-4715	221	9	.	.	PUNCT