id	sid	tid	token	lemma	pos
ejpam-3583	1	1	european	european	PROPN
ejpam-3583	1	2	journal	journal	PROPN
ejpam-3583	1	3	of	of	ADP
ejpam-3583	1	4	pure	pure	ADJ
ejpam-3583	1	5	and	and	CCONJ
ejpam-3583	1	6	applied	apply	VERB
ejpam-3583	1	7	mathematics	mathematic	NOUN
ejpam-3583	1	8	vol	vol	NOUN
ejpam-3583	1	9	.	.	PROPN
ejpam-3583	2	1	12	12	NUM
ejpam-3583	2	2	,	,	PUNCT
ejpam-3583	2	3	no	no	INTJ
ejpam-3583	2	4	.	.	NOUN
ejpam-3583	2	5	4	4	NUM
ejpam-3583	2	6	,	,	PUNCT
ejpam-3583	2	7	2019	2019	NUM
ejpam-3583	2	8	,	,	PUNCT
ejpam-3583	2	9	1676	1676	NUM
ejpam-3583	2	10	-	-	SYM
ejpam-3583	2	11	1688	1688	NUM
ejpam-3583	2	12	issn	issn	PROPN
ejpam-3583	2	13	1307	1307	NUM
ejpam-3583	2	14	-	-	SYM
ejpam-3583	2	15	5543	5543	NUM
ejpam-3583	2	16	–	–	PUNCT
ejpam-3583	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3583	2	18	published	publish	VERB
ejpam-3583	2	19	by	by	ADP
ejpam-3583	2	20	new	new	PROPN
ejpam-3583	2	21	york	york	PROPN
ejpam-3583	2	22	business	business	PROPN
ejpam-3583	2	23	global	global	ADJ
ejpam-3583	2	24	hankel	hankel	NOUN
ejpam-3583	2	25	transform	transform	NOUN
ejpam-3583	2	26	of	of	ADP
ejpam-3583	2	27	the	the	DET
ejpam-3583	2	28	second	second	ADJ
ejpam-3583	2	29	form	form	NOUN
ejpam-3583	2	30	(	(	PUNCT
ejpam-3583	2	31	q	q	ADJ
ejpam-3583	2	32	,	,	PUNCT
ejpam-3583	2	33	r)-dowling	r)-dowle	VERB
ejpam-3583	2	34	numbers	number	NOUN
ejpam-3583	2	35	roberto	roberto	PROPN
ejpam-3583	2	36	b.	b.	PROPN
ejpam-3583	2	37	corcino1,∗	corcino1,∗	PROPN
ejpam-3583	2	38	,	,	PUNCT
ejpam-3583	2	39	jay	jay	PROPN
ejpam-3583	2	40	m.	m.	PROPN
ejpam-3583	2	41	ontolan1	ontolan1	PROPN
ejpam-3583	2	42	,	,	PUNCT
ejpam-3583	2	43	gladys	gladys	PROPN
ejpam-3583	2	44	jane	jane	PROPN
ejpam-3583	2	45	s.	s.	PROPN
ejpam-3583	2	46	rama1	rama1	PROPN
ejpam-3583	2	47	1	1	NUM
ejpam-3583	2	48	research	research	NOUN
ejpam-3583	2	49	institute	institute	NOUN
ejpam-3583	2	50	for	for	ADP
ejpam-3583	2	51	computational	computational	ADJ
ejpam-3583	2	52	mathematics	mathematic	NOUN
ejpam-3583	2	53	and	and	CCONJ
ejpam-3583	2	54	physics	physics	NOUN
ejpam-3583	2	55	,	,	PUNCT
ejpam-3583	2	56	cebu	cebu	NOUN
ejpam-3583	2	57	normal	normal	ADJ
ejpam-3583	2	58	university	university	NOUN
ejpam-3583	2	59	,	,	PUNCT
ejpam-3583	2	60	6000	6000	NUM
ejpam-3583	2	61	cebu	cebu	NOUN
ejpam-3583	2	62	city	city	NOUN
ejpam-3583	2	63	,	,	PUNCT
ejpam-3583	2	64	philippines	philippine	NOUN
ejpam-3583	2	65	abstract	abstract	ADJ
ejpam-3583	2	66	.	.	PUNCT
ejpam-3583	3	1	in	in	ADP
ejpam-3583	3	2	this	this	DET
ejpam-3583	3	3	paper	paper	NOUN
ejpam-3583	3	4	,	,	PUNCT
ejpam-3583	3	5	using	use	VERB
ejpam-3583	3	6	the	the	DET
ejpam-3583	3	7	rational	rational	ADJ
ejpam-3583	3	8	generating	generating	NOUN
ejpam-3583	3	9	for	for	ADP
ejpam-3583	3	10	the	the	DET
ejpam-3583	3	11	second	second	ADJ
ejpam-3583	3	12	form	form	NOUN
ejpam-3583	3	13	of	of	ADP
ejpam-3583	3	14	the	the	DET
ejpam-3583	3	15	q	q	NOUN
ejpam-3583	3	16	-	-	PUNCT
ejpam-3583	3	17	analogue	analogue	NOUN
ejpam-3583	3	18	of	of	ADP
ejpam-3583	3	19	r	r	NOUN
ejpam-3583	3	20	-	-	PUNCT
ejpam-3583	3	21	whitney	whitney	NOUN
ejpam-3583	3	22	numbers	number	NOUN
ejpam-3583	3	23	of	of	ADP
ejpam-3583	3	24	the	the	DET
ejpam-3583	3	25	second	second	ADJ
ejpam-3583	3	26	kind	kind	NOUN
ejpam-3583	3	27	,	,	PUNCT
ejpam-3583	3	28	certain	certain	ADJ
ejpam-3583	3	29	divisibility	divisibility	NOUN
ejpam-3583	3	30	property	property	NOUN
ejpam-3583	3	31	for	for	ADP
ejpam-3583	3	32	this	this	DET
ejpam-3583	3	33	form	form	NOUN
ejpam-3583	3	34	is	be	AUX
ejpam-3583	3	35	established	establish	VERB
ejpam-3583	3	36	.	.	PUNCT
ejpam-3583	4	1	moreover	moreover	ADV
ejpam-3583	4	2	,	,	PUNCT
ejpam-3583	4	3	the	the	DET
ejpam-3583	4	4	hankel	hankel	NOUN
ejpam-3583	4	5	transform	transform	VERB
ejpam-3583	4	6	for	for	ADP
ejpam-3583	4	7	the	the	DET
ejpam-3583	4	8	second	second	ADJ
ejpam-3583	4	9	form	form	NOUN
ejpam-3583	4	10	of	of	ADP
ejpam-3583	4	11	the	the	DET
ejpam-3583	4	12	q	q	NOUN
ejpam-3583	4	13	-	-	PUNCT
ejpam-3583	4	14	analogue	analogue	NOUN
ejpam-3583	4	15	of	of	ADP
ejpam-3583	4	16	r	r	NOUN
ejpam-3583	4	17	-	-	PUNCT
ejpam-3583	4	18	dowling	dowle	VERB
ejpam-3583	4	19	numbers	number	NOUN
ejpam-3583	4	20	is	be	AUX
ejpam-3583	4	21	derived	derive	VERB
ejpam-3583	4	22	.	.	PUNCT
ejpam-3583	5	1	2010	2010	NUM
ejpam-3583	5	2	mathematics	mathematic	NOUN
ejpam-3583	5	3	subject	subject	NOUN
ejpam-3583	5	4	classifications	classification	NOUN
ejpam-3583	5	5	:	:	PUNCT
ejpam-3583	5	6	05a15	05a15	NUM
ejpam-3583	5	7	,	,	PUNCT
ejpam-3583	5	8	11b65	11b65	NUM
ejpam-3583	5	9	,	,	PUNCT
ejpam-3583	5	10	11b73	11b73	NUM
ejpam-3583	5	11	key	key	ADJ
ejpam-3583	5	12	words	word	NOUN
ejpam-3583	5	13	and	and	CCONJ
ejpam-3583	5	14	phrases	phrase	NOUN
ejpam-3583	5	15	:	:	PUNCT
ejpam-3583	5	16	r	r	X
ejpam-3583	5	17	-	-	PUNCT
ejpam-3583	5	18	whitney	whitney	NOUN
ejpam-3583	5	19	numbers	number	NOUN
ejpam-3583	5	20	,	,	PUNCT
ejpam-3583	5	21	r	r	NOUN
ejpam-3583	5	22	-	-	PUNCT
ejpam-3583	5	23	dowling	dowle	VERB
ejpam-3583	5	24	numbers	number	NOUN
ejpam-3583	5	25	,	,	PUNCT
ejpam-3583	5	26	generating	generate	VERB
ejpam-3583	5	27	function	function	NOUN
ejpam-3583	5	28	,	,	PUNCT
ejpam-3583	5	29	qanalogue	qanalogue	NOUN
ejpam-3583	5	30	,	,	PUNCT
ejpam-3583	5	31	q	q	ADJ
ejpam-3583	5	32	-	-	PUNCT
ejpam-3583	5	33	exponential	exponential	ADJ
ejpam-3583	5	34	function	function	NOUN
ejpam-3583	5	35	,	,	PUNCT
ejpam-3583	5	36	a	a	DET
ejpam-3583	5	37	-	-	PUNCT
ejpam-3583	5	38	tableau	tableau	NOUN
ejpam-3583	5	39	,	,	PUNCT
ejpam-3583	5	40	convolution	convolution	NOUN
ejpam-3583	5	41	formula	formula	NOUN
ejpam-3583	5	42	,	,	PUNCT
ejpam-3583	5	43	hankel	hankel	NOUN
ejpam-3583	5	44	transform	transform	NOUN
ejpam-3583	5	45	,	,	PUNCT
ejpam-3583	5	46	hankel	hankel	NOUN
ejpam-3583	5	47	matrix	matrix	NOUN
ejpam-3583	5	48	,	,	PUNCT
ejpam-3583	5	49	k	k	ADJ
ejpam-3583	5	50	-	-	ADJ
ejpam-3583	5	51	binomial	binomial	ADJ
ejpam-3583	5	52	transform	transform	NOUN
ejpam-3583	5	53	1	1	NUM
ejpam-3583	5	54	.	.	PUNCT
ejpam-3583	5	55	introduction	introduction	NOUN
ejpam-3583	5	56	the	the	DET
ejpam-3583	5	57	matrix	matrix	NOUN
ejpam-3583	5	58	of	of	ADP
ejpam-3583	5	59	the	the	DET
ejpam-3583	5	60	form	form	NOUN
ejpam-3583	5	61			NOUN
ejpam-3583	5	62	a0	a0	NOUN
ejpam-3583	5	63	a1	a1	NOUN
ejpam-3583	5	64	a2	a2	PROPN
ejpam-3583	5	65	.	.	PUNCT
ejpam-3583	5	66	.	.	PUNCT
ejpam-3583	5	67	.	.	PUNCT
ejpam-3583	6	1	an	an	DET
ejpam-3583	6	2	a1	a1	NOUN
ejpam-3583	6	3	a2	a2	PROPN
ejpam-3583	6	4	a3	a3	NOUN
ejpam-3583	6	5	.	.	PUNCT
ejpam-3583	6	6	.	.	PUNCT
ejpam-3583	6	7	.	.	PUNCT
ejpam-3583	7	1	an+1	an+1	PROPN
ejpam-3583	7	2	a2	a2	PROPN
ejpam-3583	7	3	a3	a3	PROPN
ejpam-3583	7	4	a4	a4	PROPN
ejpam-3583	7	5	.	.	PUNCT
ejpam-3583	7	6	.	.	PUNCT
ejpam-3583	7	7	.	.	PUNCT
ejpam-3583	8	1	an+2	an+2	ADV
ejpam-3583	8	2	.	.	PUNCT
ejpam-3583	8	3	.	.	PUNCT
ejpam-3583	8	4	.	.	PUNCT
ejpam-3583	8	5	.	.	PUNCT
ejpam-3583	8	6	.	.	PUNCT
ejpam-3583	8	7	.	.	PUNCT
ejpam-3583	8	8	.	.	PUNCT
ejpam-3583	8	9	.	.	PUNCT
ejpam-3583	8	10	.	.	PUNCT
ejpam-3583	8	11	.	.	PUNCT
ejpam-3583	8	12	.	.	PUNCT
ejpam-3583	8	13	.	.	PUNCT
ejpam-3583	8	14	.	.	PUNCT
ejpam-3583	8	15	.	.	PUNCT
ejpam-3583	8	16	.	.	PUNCT
ejpam-3583	8	17	.	.	PUNCT
ejpam-3583	8	18	.	.	PUNCT
ejpam-3583	8	19	.	.	PUNCT
ejpam-3583	8	20	.	.	PUNCT
ejpam-3583	8	21	.	.	PUNCT
ejpam-3583	8	22	.	.	PUNCT
ejpam-3583	8	23	.	.	PUNCT
ejpam-3583	8	24	.	.	PUNCT
ejpam-3583	8	25	.	.	PUNCT
ejpam-3583	8	26	.	.	PUNCT
ejpam-3583	8	27	.	.	PUNCT
ejpam-3583	8	28	.	.	PUNCT
ejpam-3583	9	1	an	an	DET
ejpam-3583	9	2	an+1	an+1	NOUN
ejpam-3583	9	3	an+2	an+2	ADV
ejpam-3583	9	4	.	.	PUNCT
ejpam-3583	9	5	.	.	PUNCT
ejpam-3583	9	6	.	.	PUNCT
ejpam-3583	10	1	a2n	a2n	PROPN
ejpam-3583	10	2			PRON
ejpam-3583	10	3	(	(	PUNCT
ejpam-3583	10	4	1	1	X
ejpam-3583	10	5	)	)	PUNCT
ejpam-3583	10	6	whose	whose	DET
ejpam-3583	10	7	entries	entry	NOUN
ejpam-3583	10	8	are	be	AUX
ejpam-3583	10	9	the	the	DET
ejpam-3583	10	10	elements	element	NOUN
ejpam-3583	10	11	of	of	ADP
ejpam-3583	10	12	the	the	DET
ejpam-3583	10	13	sequence	sequence	NOUN
ejpam-3583	11	1	a	a	PRON
ejpam-3583	11	2	=	=	PUNCT
ejpam-3583	11	3	(	(	PUNCT
ejpam-3583	11	4	an)∞n=0	an)∞n=0	PROPN
ejpam-3583	11	5	was	be	AUX
ejpam-3583	11	6	defined	define	VERB
ejpam-3583	11	7	in	in	ADP
ejpam-3583	11	8	[	[	X
ejpam-3583	11	9	16	16	NUM
ejpam-3583	11	10	]	]	PUNCT
ejpam-3583	11	11	as	as	ADP
ejpam-3583	11	12	the	the	DET
ejpam-3583	11	13	hankel	hankel	NOUN
ejpam-3583	11	14	matrix	matrix	NOUN
ejpam-3583	11	15	of	of	ADP
ejpam-3583	11	16	order	order	NOUN
ejpam-3583	11	17	n	n	PROPN
ejpam-3583	11	18	of	of	ADP
ejpam-3583	11	19	a	a	DET
ejpam-3583	11	20	sequence	sequence	NOUN
ejpam-3583	11	21	a	a	NOUN
ejpam-3583	11	22	,	,	PUNCT
ejpam-3583	11	23	denoted	denote	VERB
ejpam-3583	11	24	by	by	ADP
ejpam-3583	11	25	hn	hn	PROPN
ejpam-3583	11	26	.	.	PUNCT
ejpam-3583	12	1	this	this	PRON
ejpam-3583	12	2	can	can	AUX
ejpam-3583	12	3	also	also	ADV
ejpam-3583	12	4	be	be	AUX
ejpam-3583	12	5	written	write	VERB
ejpam-3583	12	6	as	as	ADP
ejpam-3583	12	7	hn	hn	PROPN
ejpam-3583	12	8	=	=	PUNCT
ejpam-3583	12	9	(	(	PUNCT
ejpam-3583	12	10	ai+j)0≤i	ai+j)0≤i	NOUN
ejpam-3583	12	11	,	,	PUNCT
ejpam-3583	12	12	j≤n	j≤n	PROPN
ejpam-3583	12	13	.	.	PUNCT
ejpam-3583	13	1	in	in	ADP
ejpam-3583	13	2	the	the	DET
ejpam-3583	13	3	same	same	ADJ
ejpam-3583	13	4	paper	paper	NOUN
ejpam-3583	13	5	[	[	X
ejpam-3583	13	6	16	16	NUM
ejpam-3583	13	7	]	]	PUNCT
ejpam-3583	13	8	,	,	PUNCT
ejpam-3583	13	9	the	the	DET
ejpam-3583	13	10	hankel	hankel	NOUN
ejpam-3583	13	11	determinant	determinant	VERB
ejpam-3583	13	12	hn	hn	NOUN
ejpam-3583	13	13	of	of	ADP
ejpam-3583	13	14	order	order	NOUN
ejpam-3583	13	15	of	of	ADP
ejpam-3583	13	16	n	n	PROPN
ejpam-3583	13	17	of	of	ADP
ejpam-3583	13	18	a	a	PRON
ejpam-3583	13	19	was	be	AUX
ejpam-3583	13	20	defined	define	VERB
ejpam-3583	13	21	as	as	ADP
ejpam-3583	13	22	the	the	DET
ejpam-3583	13	23	determinant	determinant	NOUN
ejpam-3583	13	24	of	of	ADP
ejpam-3583	13	25	the	the	DET
ejpam-3583	13	26	corresponding	correspond	VERB
ejpam-3583	13	27	hankel	hankel	NOUN
ejpam-3583	13	28	matrix	matrix	NOUN
ejpam-3583	13	29	of	of	ADP
ejpam-3583	13	30	order	order	NOUN
ejpam-3583	13	31	n	n	CCONJ
ejpam-3583	13	32	,	,	PUNCT
ejpam-3583	13	33	(	(	PUNCT
ejpam-3583	13	34	i.e.	i.e.	X
ejpam-3583	13	35	hn	hn	X
ejpam-3583	13	36	=	=	NOUN
ejpam-3583	13	37	det(hn	det(hn	NOUN
ejpam-3583	13	38	)	)	PUNCT
ejpam-3583	13	39	)	)	PUNCT
ejpam-3583	13	40	and	and	CCONJ
ejpam-3583	13	41	the	the	DET
ejpam-3583	13	42	hankel	hankel	NOUN
ejpam-3583	13	43	transform	transform	NOUN
ejpam-3583	13	44	of	of	ADP
ejpam-3583	13	45	the	the	DET
ejpam-3583	13	46	sequence	sequence	NOUN
ejpam-3583	13	47	a	a	NOUN
ejpam-3583	13	48	,	,	PUNCT
ejpam-3583	13	49	denoted	denote	VERB
ejpam-3583	13	50	by	by	ADP
ejpam-3583	13	51	h(a	h(a	PROPN
ejpam-3583	13	52	)	)	PUNCT
ejpam-3583	13	53	,	,	PUNCT
ejpam-3583	13	54	was	be	AUX
ejpam-3583	13	55	defined	define	VERB
ejpam-3583	13	56	as	as	ADP
ejpam-3583	13	57	the	the	DET
ejpam-3583	13	58	sequence	sequence	NOUN
ejpam-3583	13	59	{	{	PUNCT
ejpam-3583	13	60	hn	hn	NOUN
ejpam-3583	13	61	}	}	PUNCT
ejpam-3583	13	62	of	of	ADP
ejpam-3583	13	63	hankel	hankel	NOUN
ejpam-3583	13	64	determinants	determinant	NOUN
ejpam-3583	13	65	of	of	ADP
ejpam-3583	13	66	a.	a.	NOUN
ejpam-3583	13	67	∗corresponding	∗corresponde	VERB
ejpam-3583	13	68	author	author	NOUN
ejpam-3583	13	69	.	.	PUNCT
ejpam-3583	14	1	doi	doi	NOUN
ejpam-3583	14	2	:	:	PUNCT
ejpam-3583	14	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3583	https://doi.org/10.29020/nybg.ejpam.v12i4.3583	PROPN
ejpam-3583	14	4	email	email	NOUN
ejpam-3583	14	5	addresses	address	NOUN
ejpam-3583	14	6	:	:	PUNCT
ejpam-3583	14	7	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-3583	14	8	(	(	PUNCT
ejpam-3583	14	9	r.	r.	PROPN
ejpam-3583	14	10	corcino	corcino	PROPN
ejpam-3583	14	11	)	)	PUNCT
ejpam-3583	14	12	,	,	PUNCT
ejpam-3583	14	13	ontolanjay@gmail.com	ontolanjay@gmail.com	X
ejpam-3583	14	14	(	(	PUNCT
ejpam-3583	14	15	j.	j.	PROPN
ejpam-3583	14	16	ontolan	ontolan	PROPN
ejpam-3583	14	17	)	)	PUNCT
ejpam-3583	14	18	,	,	PUNCT
ejpam-3583	14	19	gjsrama@yahoo.com	gjsrama@yahoo.com	X
ejpam-3583	14	20	(	(	PUNCT
ejpam-3583	14	21	g.	g.	PROPN
ejpam-3583	14	22	j.	j.	PROPN
ejpam-3583	14	23	rama	rama	PROPN
ejpam-3583	14	24	)	)	PUNCT
ejpam-3583	14	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3583	15	1	1676	1676	NUM
ejpam-3583	16	1	c	c	X
ejpam-3583	16	2	©	©	PROPN
ejpam-3583	16	3	2019	2019	NUM
ejpam-3583	16	4	ejpam	ejpam	NOUN
ejpam-3583	16	5	all	all	DET
ejpam-3583	16	6	rights	right	NOUN
ejpam-3583	16	7	reserved	reserve	VERB
ejpam-3583	16	8	.	.	PUNCT
ejpam-3583	17	1	r.	r.	PROPN
ejpam-3583	17	2	corcino	corcino	PROPN
ejpam-3583	17	3	,	,	PUNCT
ejpam-3583	17	4	j.	j.	PROPN
ejpam-3583	17	5	ontolan	ontolan	PROPN
ejpam-3583	17	6	,	,	PUNCT
ejpam-3583	17	7	g.	g.	PROPN
ejpam-3583	17	8	j.	j.	PROPN
ejpam-3583	17	9	rama	rama	PROPN
ejpam-3583	17	10	/	/	SYM
ejpam-3583	17	11	eur	eur	PROPN
ejpam-3583	17	12	.	.	PUNCT
ejpam-3583	18	1	j.	j.	PROPN
ejpam-3583	18	2	pure	pure	PROPN
ejpam-3583	18	3	appl	appl	PROPN
ejpam-3583	18	4	.	.	PROPN
ejpam-3583	18	5	math	math	PROPN
ejpam-3583	18	6	,	,	PUNCT
ejpam-3583	18	7	12	12	NUM
ejpam-3583	18	8	(	(	PUNCT
ejpam-3583	18	9	4	4	NUM
ejpam-3583	18	10	)	)	PUNCT
ejpam-3583	18	11	(	(	PUNCT
ejpam-3583	18	12	2019	2019	NUM
ejpam-3583	18	13	)	)	PUNCT
ejpam-3583	18	14	,	,	PUNCT
ejpam-3583	18	15	1676	1676	NUM
ejpam-3583	18	16	-	-	SYM
ejpam-3583	18	17	1688	1688	NUM
ejpam-3583	18	18	1677	1677	NUM
ejpam-3583	18	19	for	for	ADP
ejpam-3583	18	20	example	example	NOUN
ejpam-3583	18	21	,	,	PUNCT
ejpam-3583	18	22	the	the	DET
ejpam-3583	18	23	sequence	sequence	NOUN
ejpam-3583	18	24	of	of	ADP
ejpam-3583	18	25	(	(	PUNCT
ejpam-3583	18	26	r	r	NOUN
ejpam-3583	18	27	,	,	PUNCT
ejpam-3583	18	28	β)-bell	β)-bell	PUNCT
ejpam-3583	18	29	numbers	number	NOUN
ejpam-3583	18	30	in	in	ADP
ejpam-3583	18	31	[	[	X
ejpam-3583	18	32	12	12	NUM
ejpam-3583	18	33	,	,	PUNCT
ejpam-3583	18	34	15	15	NUM
ejpam-3583	18	35	]	]	PUNCT
ejpam-3583	18	36	,	,	PUNCT
ejpam-3583	18	37	denoted	denote	VERB
ejpam-3583	18	38	by	by	ADP
ejpam-3583	18	39	{	{	PUNCT
ejpam-3583	18	40	gn	gn	PROPN
ejpam-3583	18	41	,	,	PUNCT
ejpam-3583	18	42	r	r	NOUN
ejpam-3583	18	43	,	,	PUNCT
ejpam-3583	18	44	β	β	NOUN
ejpam-3583	18	45	}	}	PUNCT
ejpam-3583	18	46	,	,	PUNCT
ejpam-3583	18	47	has	have	AUX
ejpam-3583	18	48	possessed	possess	VERB
ejpam-3583	18	49	the	the	DET
ejpam-3583	18	50	following	follow	VERB
ejpam-3583	18	51	hankel	hankel	NOUN
ejpam-3583	18	52	transform	transform	NOUN
ejpam-3583	18	53	(	(	PUNCT
ejpam-3583	18	54	see	see	VERB
ejpam-3583	18	55	[	[	X
ejpam-3583	18	56	14	14	NUM
ejpam-3583	18	57	]	]	SYM
ejpam-3583	18	58	)	)	PUNCT
ejpam-3583	18	59	h(gn	h(gn	NOUN
ejpam-3583	18	60	,	,	PUNCT
ejpam-3583	18	61	r	r	NOUN
ejpam-3583	18	62	,	,	PUNCT
ejpam-3583	18	63	β	β	NOUN
ejpam-3583	18	64	)	)	PUNCT
ejpam-3583	18	65	=	=	SYM
ejpam-3583	18	66	n∏	n∏	PROPN
ejpam-3583	18	67	j=0	j=0	PROPN
ejpam-3583	18	68	βjj	βjj	PUNCT
ejpam-3583	18	69	!	!	PUNCT
ejpam-3583	18	70	.	.	PUNCT
ejpam-3583	19	1	as	as	SCONJ
ejpam-3583	19	2	mentioned	mention	VERB
ejpam-3583	19	3	in	in	ADP
ejpam-3583	19	4	[	[	X
ejpam-3583	19	5	16	16	NUM
ejpam-3583	19	6	]	]	PUNCT
ejpam-3583	19	7	,	,	PUNCT
ejpam-3583	19	8	one	one	PRON
ejpam-3583	19	9	can	can	AUX
ejpam-3583	19	10	easily	easily	ADV
ejpam-3583	19	11	verify	verify	VERB
ejpam-3583	19	12	that	that	SCONJ
ejpam-3583	19	13	the	the	DET
ejpam-3583	19	14	(	(	PUNCT
ejpam-3583	19	15	r	r	NOUN
ejpam-3583	19	16	,	,	PUNCT
ejpam-3583	19	17	β)-bell	β)-bell	PUNCT
ejpam-3583	19	18	numbers	number	NOUN
ejpam-3583	19	19	are	be	AUX
ejpam-3583	19	20	simply	simply	ADV
ejpam-3583	19	21	the	the	DET
ejpam-3583	19	22	r	r	NOUN
ejpam-3583	19	23	-	-	PUNCT
ejpam-3583	19	24	dowling	dowle	VERB
ejpam-3583	19	25	numbers	number	NOUN
ejpam-3583	19	26	dm	dm	NOUN
ejpam-3583	19	27	,	,	PUNCT
ejpam-3583	19	28	r(n	r(n	PROPN
ejpam-3583	19	29	)	)	PUNCT
ejpam-3583	19	30	,	,	PUNCT
ejpam-3583	19	31	which	which	PRON
ejpam-3583	19	32	are	be	AUX
ejpam-3583	19	33	defined	define	VERB
ejpam-3583	19	34	in	in	ADP
ejpam-3583	19	35	[	[	X
ejpam-3583	19	36	5	5	NUM
ejpam-3583	19	37	]	]	PUNCT
ejpam-3583	19	38	as	as	ADP
ejpam-3583	19	39	dm	dm	PROPN
ejpam-3583	19	40	,	,	PUNCT
ejpam-3583	19	41	r(n	r(n	PROPN
ejpam-3583	19	42	)	)	PUNCT
ejpam-3583	19	43	=	=	SYM
ejpam-3583	19	44	n∑	n∑	PROPN
ejpam-3583	19	45	k=0	k=0	PROPN
ejpam-3583	19	46	wm	wm	PROPN
ejpam-3583	19	47	,	,	PUNCT
ejpam-3583	19	48	r(n	r(n	PROPN
ejpam-3583	19	49	,	,	PUNCT
ejpam-3583	19	50	k	k	NOUN
ejpam-3583	19	51	)	)	PUNCT
ejpam-3583	19	52	where	where	SCONJ
ejpam-3583	19	53	wm	wm	PROPN
ejpam-3583	19	54	,	,	PUNCT
ejpam-3583	19	55	r(n	r(n	PROPN
ejpam-3583	19	56	,	,	PUNCT
ejpam-3583	19	57	k	k	NOUN
ejpam-3583	19	58	)	)	PUNCT
ejpam-3583	19	59	denotes	denote	VERB
ejpam-3583	19	60	the	the	DET
ejpam-3583	19	61	r	r	PROPN
ejpam-3583	19	62	-	-	PUNCT
ejpam-3583	19	63	whitney	whitney	NOUN
ejpam-3583	19	64	numbers	number	NOUN
ejpam-3583	19	65	of	of	ADP
ejpam-3583	19	66	the	the	DET
ejpam-3583	19	67	second	second	ADJ
ejpam-3583	19	68	kind	kind	NOUN
ejpam-3583	19	69	introduced	introduce	VERB
ejpam-3583	19	70	by	by	ADP
ejpam-3583	19	71	mezo	mezo	NOUN
ejpam-3583	19	72	in	in	ADP
ejpam-3583	19	73	[	[	X
ejpam-3583	19	74	29	29	NUM
ejpam-3583	19	75	]	]	PUNCT
ejpam-3583	19	76	.	.	PUNCT
ejpam-3583	20	1	in	in	ADP
ejpam-3583	20	2	[	[	X
ejpam-3583	20	3	14	14	NUM
ejpam-3583	20	4	]	]	PUNCT
ejpam-3583	20	5	,	,	PUNCT
ejpam-3583	20	6	the	the	DET
ejpam-3583	20	7	authors	author	NOUN
ejpam-3583	20	8	have	have	AUX
ejpam-3583	20	9	also	also	ADV
ejpam-3583	20	10	tried	try	VERB
ejpam-3583	20	11	to	to	PART
ejpam-3583	20	12	derive	derive	VERB
ejpam-3583	20	13	the	the	DET
ejpam-3583	20	14	hankel	hankel	NOUN
ejpam-3583	20	15	transform	transform	NOUN
ejpam-3583	20	16	of	of	ADP
ejpam-3583	20	17	the	the	DET
ejpam-3583	20	18	sequence	sequence	NOUN
ejpam-3583	20	19	of	of	ADP
ejpam-3583	20	20	q	q	NOUN
ejpam-3583	20	21	-	-	PUNCT
ejpam-3583	20	22	analogue	analogue	NOUN
ejpam-3583	20	23	of	of	ADP
ejpam-3583	20	24	(	(	PUNCT
ejpam-3583	20	25	r	r	NOUN
ejpam-3583	20	26	,	,	PUNCT
ejpam-3583	20	27	β)-bell	β)-bell	NOUN
ejpam-3583	20	28	numbers	number	NOUN
ejpam-3583	20	29	.	.	PUNCT
ejpam-3583	21	1	in	in	ADP
ejpam-3583	21	2	this	this	DET
ejpam-3583	21	3	attempt	attempt	NOUN
ejpam-3583	21	4	,	,	PUNCT
ejpam-3583	21	5	they	they	PRON
ejpam-3583	21	6	used	use	VERB
ejpam-3583	21	7	the	the	DET
ejpam-3583	21	8	q	q	ADJ
ejpam-3583	21	9	-	-	PUNCT
ejpam-3583	21	10	analogue	analogue	NOUN
ejpam-3583	21	11	defined	define	VERB
ejpam-3583	21	12	in	in	ADP
ejpam-3583	21	13	[	[	X
ejpam-3583	21	14	17	17	NUM
ejpam-3583	21	15	]	]	PUNCT
ejpam-3583	21	16	.	.	PUNCT
ejpam-3583	22	1	but	but	CCONJ
ejpam-3583	22	2	they	they	PRON
ejpam-3583	22	3	failed	fail	VERB
ejpam-3583	22	4	to	to	PART
ejpam-3583	22	5	derive	derive	VERB
ejpam-3583	22	6	it	it	PRON
ejpam-3583	22	7	.	.	PUNCT
ejpam-3583	23	1	just	just	ADV
ejpam-3583	23	2	recently	recently	ADV
ejpam-3583	23	3	,	,	PUNCT
ejpam-3583	23	4	another	another	DET
ejpam-3583	23	5	definition	definition	NOUN
ejpam-3583	23	6	of	of	ADP
ejpam-3583	23	7	q	q	NOUN
ejpam-3583	23	8	-	-	PUNCT
ejpam-3583	23	9	analogue	analogue	NOUN
ejpam-3583	23	10	of	of	ADP
ejpam-3583	23	11	r	r	NOUN
ejpam-3583	23	12	-	-	PUNCT
ejpam-3583	23	13	whitney	whitney	NOUN
ejpam-3583	23	14	numbers	number	NOUN
ejpam-3583	23	15	of	of	ADP
ejpam-3583	23	16	the	the	DET
ejpam-3583	23	17	second	second	ADJ
ejpam-3583	23	18	wm	wm	PROPN
ejpam-3583	23	19	,	,	PUNCT
ejpam-3583	23	20	r[n	r[n	NOUN
ejpam-3583	23	21	,	,	PUNCT
ejpam-3583	23	22	k]q	k]q	PROPN
ejpam-3583	23	23	was	be	AUX
ejpam-3583	23	24	introduced	introduce	VERB
ejpam-3583	23	25	in	in	ADP
ejpam-3583	23	26	[	[	X
ejpam-3583	23	27	13	13	NUM
ejpam-3583	23	28	,	,	PUNCT
ejpam-3583	23	29	16	16	NUM
ejpam-3583	23	30	]	]	PUNCT
ejpam-3583	23	31	by	by	ADP
ejpam-3583	23	32	means	mean	NOUN
ejpam-3583	23	33	of	of	ADP
ejpam-3583	23	34	the	the	DET
ejpam-3583	23	35	following	follow	VERB
ejpam-3583	23	36	triangular	triangular	NOUN
ejpam-3583	23	37	recurrence	recurrence	NOUN
ejpam-3583	23	38	relation	relation	PROPN
ejpam-3583	23	39	wm	wm	PROPN
ejpam-3583	23	40	,	,	PUNCT
ejpam-3583	23	41	r[n	r[n	NOUN
ejpam-3583	23	42	,	,	PUNCT
ejpam-3583	23	43	k]q	k]q	NOUN
ejpam-3583	23	44	=	=	SYM
ejpam-3583	23	45	qm(k−1)+rwm	qm(k−1)+rwm	PROPN
ejpam-3583	23	46	,	,	PUNCT
ejpam-3583	23	47	r[n−	r[n−	PROPN
ejpam-3583	23	48	1	1	NUM
ejpam-3583	23	49	,	,	PUNCT
ejpam-3583	23	50	k	k	PROPN
ejpam-3583	23	51	−	−	PROPN
ejpam-3583	24	1	1]q	1]q	PROPN
ejpam-3583	25	1	+	+	NUM
ejpam-3583	25	2	[	[	X
ejpam-3583	25	3	mk	mk	X
ejpam-3583	25	4	+	+	CCONJ
ejpam-3583	25	5	r]qwm	r]qwm	NOUN
ejpam-3583	25	6	,	,	PUNCT
ejpam-3583	25	7	r[n−	r[n−	PROPN
ejpam-3583	25	8	1	1	NUM
ejpam-3583	25	9	,	,	PUNCT
ejpam-3583	25	10	k]q	k]q	PROPN
ejpam-3583	25	11	.	.	PUNCT
ejpam-3583	26	1	(	(	PUNCT
ejpam-3583	26	2	2	2	NUM
ejpam-3583	26	3	)	)	PUNCT
ejpam-3583	26	4	from	from	ADP
ejpam-3583	26	5	this	this	DET
ejpam-3583	26	6	definition	definition	NOUN
ejpam-3583	26	7	,	,	PUNCT
ejpam-3583	26	8	two	two	NUM
ejpam-3583	26	9	more	more	ADJ
ejpam-3583	26	10	forms	form	NOUN
ejpam-3583	26	11	of	of	ADP
ejpam-3583	26	12	the	the	DET
ejpam-3583	26	13	q	q	NOUN
ejpam-3583	26	14	-	-	PUNCT
ejpam-3583	26	15	analogue	analogue	NOUN
ejpam-3583	26	16	were	be	AUX
ejpam-3583	26	17	defined	define	VERB
ejpam-3583	26	18	in	in	ADP
ejpam-3583	26	19	[	[	X
ejpam-3583	26	20	13	13	NUM
ejpam-3583	26	21	,	,	PUNCT
ejpam-3583	26	22	16	16	NUM
ejpam-3583	26	23	]	]	PUNCT
ejpam-3583	26	24	as	as	ADP
ejpam-3583	26	25	w	w	PROPN
ejpam-3583	26	26	∗m	∗m	NOUN
ejpam-3583	26	27	,	,	PUNCT
ejpam-3583	26	28	r[n	r[n	NOUN
ejpam-3583	26	29	,	,	PUNCT
ejpam-3583	26	30	k]q	k]q	ADV
ejpam-3583	26	31	:	:	PUNCT
ejpam-3583	26	32	=	=	SYM
ejpam-3583	26	33	q−kr−m(k2)wm	q−kr−m(k2)wm	NOUN
ejpam-3583	26	34	,	,	PUNCT
ejpam-3583	26	35	r[n	r[n	NOUN
ejpam-3583	26	36	,	,	PUNCT
ejpam-3583	26	37	k]q	k]q	X
ejpam-3583	26	38	(	(	PUNCT
ejpam-3583	26	39	3	3	NUM
ejpam-3583	26	40	)	)	PUNCT
ejpam-3583	26	41	w̃m	w̃m	PROPN
ejpam-3583	26	42	,	,	PUNCT
ejpam-3583	26	43	r[n	r[n	NOUN
ejpam-3583	26	44	,	,	PUNCT
ejpam-3583	26	45	k]q	k]q	ADV
ejpam-3583	26	46	:	:	PUNCT
ejpam-3583	26	47	=	=	NUM
ejpam-3583	26	48	qkrw	qkrw	ADJ
ejpam-3583	26	49	∗m	∗m	NOUN
ejpam-3583	26	50	,	,	PUNCT
ejpam-3583	26	51	r[n	r[n	NOUN
ejpam-3583	26	52	,	,	PUNCT
ejpam-3583	26	53	k]q	k]q	NOUN
ejpam-3583	26	54	=	=	SYM
ejpam-3583	26	55	q−m(k2)wm	q−m(k2)wm	NOUN
ejpam-3583	26	56	,	,	PUNCT
ejpam-3583	26	57	r[n	r[n	NOUN
ejpam-3583	26	58	,	,	PUNCT
ejpam-3583	26	59	k]q	k]q	PROPN
ejpam-3583	26	60	,	,	PUNCT
ejpam-3583	26	61	(	(	PUNCT
ejpam-3583	26	62	4	4	X
ejpam-3583	26	63	)	)	PUNCT
ejpam-3583	26	64	where	where	SCONJ
ejpam-3583	26	65	w	w	ADP
ejpam-3583	26	66	∗m	∗m	NOUN
ejpam-3583	26	67	,	,	PUNCT
ejpam-3583	26	68	r[n	r[n	NOUN
ejpam-3583	26	69	,	,	PUNCT
ejpam-3583	26	70	k]q	k]q	NOUN
ejpam-3583	26	71	and	and	CCONJ
ejpam-3583	26	72	w̃m	w̃m	PROPN
ejpam-3583	26	73	,	,	PUNCT
ejpam-3583	26	74	r[n	r[n	NOUN
ejpam-3583	26	75	,	,	PUNCT
ejpam-3583	26	76	k]q	k]q	NOUN
ejpam-3583	26	77	denote	denote	VERB
ejpam-3583	26	78	the	the	DET
ejpam-3583	26	79	second	second	ADJ
ejpam-3583	26	80	and	and	CCONJ
ejpam-3583	26	81	third	third	ADJ
ejpam-3583	26	82	forms	form	NOUN
ejpam-3583	26	83	of	of	ADP
ejpam-3583	26	84	the	the	DET
ejpam-3583	26	85	q	q	NOUN
ejpam-3583	26	86	-	-	PUNCT
ejpam-3583	26	87	analogue	analogue	NOUN
ejpam-3583	26	88	,	,	PUNCT
ejpam-3583	26	89	respectively	respectively	ADV
ejpam-3583	26	90	.	.	PUNCT
ejpam-3583	27	1	corresponding	correspond	VERB
ejpam-3583	27	2	to	to	ADP
ejpam-3583	27	3	these	these	PRON
ejpam-3583	27	4	,	,	PUNCT
ejpam-3583	27	5	three	three	NUM
ejpam-3583	27	6	forms	form	NOUN
ejpam-3583	27	7	of	of	ADP
ejpam-3583	27	8	q	q	NOUN
ejpam-3583	27	9	-	-	PUNCT
ejpam-3583	27	10	analogues	analogue	NOUN
ejpam-3583	27	11	for	for	ADP
ejpam-3583	27	12	r	r	NOUN
ejpam-3583	27	13	-	-	PUNCT
ejpam-3583	27	14	dowling	dowle	VERB
ejpam-3583	27	15	numbers	number	NOUN
ejpam-3583	27	16	may	may	AUX
ejpam-3583	27	17	be	be	AUX
ejpam-3583	27	18	defined	define	VERB
ejpam-3583	27	19	as	as	SCONJ
ejpam-3583	27	20	follows	follow	VERB
ejpam-3583	27	21	:	:	PUNCT
ejpam-3583	28	1	dm	dm	NUM
ejpam-3583	28	2	,	,	PUNCT
ejpam-3583	28	3	r[n]q	r[n]q	NOUN
ejpam-3583	28	4	:	:	PUNCT
ejpam-3583	29	1	=	=	SYM
ejpam-3583	29	2	n∑	n∑	PROPN
ejpam-3583	29	3	k=0	k=0	PROPN
ejpam-3583	29	4	wm	wm	PROPN
ejpam-3583	29	5	,	,	PUNCT
ejpam-3583	29	6	r[n	r[n	NOUN
ejpam-3583	29	7	,	,	PUNCT
ejpam-3583	29	8	k]q	k]q	X
ejpam-3583	29	9	(	(	PUNCT
ejpam-3583	29	10	5	5	NUM
ejpam-3583	29	11	)	)	PUNCT
ejpam-3583	29	12	d∗m	d∗m	NOUN
ejpam-3583	29	13	,	,	PUNCT
ejpam-3583	29	14	r[n]q	r[n]q	NOUN
ejpam-3583	29	15	:	:	PUNCT
ejpam-3583	29	16	=	=	SYM
ejpam-3583	29	17	n∑	n∑	PROPN
ejpam-3583	29	18	k=0	k=0	PROPN
ejpam-3583	29	19	w	w	ADP
ejpam-3583	29	20	∗m	∗m	PROPN
ejpam-3583	29	21	,	,	PUNCT
ejpam-3583	29	22	r[n	r[n	NOUN
ejpam-3583	29	23	,	,	PUNCT
ejpam-3583	29	24	k]q	k]q	X
ejpam-3583	29	25	(	(	PUNCT
ejpam-3583	29	26	6	6	NUM
ejpam-3583	29	27	)	)	PUNCT
ejpam-3583	29	28	d̃m	d̃m	PROPN
ejpam-3583	29	29	,	,	PUNCT
ejpam-3583	29	30	r[n]q	r[n]q	VERB
ejpam-3583	29	31	:	:	PUNCT
ejpam-3583	29	32	=	=	SYM
ejpam-3583	29	33	n∑	n∑	PROPN
ejpam-3583	29	34	k=0	k=0	PROPN
ejpam-3583	29	35	w̃m	w̃m	PROPN
ejpam-3583	29	36	,	,	PUNCT
ejpam-3583	29	37	r[n	r[n	NOUN
ejpam-3583	29	38	,	,	PUNCT
ejpam-3583	29	39	k]q	k]q	PROPN
ejpam-3583	29	40	.	.	PUNCT
ejpam-3583	30	1	(	(	PUNCT
ejpam-3583	30	2	7	7	X
ejpam-3583	30	3	)	)	PUNCT
ejpam-3583	30	4	however	however	ADV
ejpam-3583	30	5	,	,	PUNCT
ejpam-3583	30	6	among	among	ADP
ejpam-3583	30	7	these	these	DET
ejpam-3583	30	8	three	three	NUM
ejpam-3583	30	9	forms	form	NOUN
ejpam-3583	30	10	,	,	PUNCT
ejpam-3583	30	11	only	only	ADV
ejpam-3583	30	12	the	the	DET
ejpam-3583	30	13	third	third	ADJ
ejpam-3583	30	14	form	form	NOUN
ejpam-3583	30	15	was	be	AUX
ejpam-3583	30	16	considered	consider	VERB
ejpam-3583	30	17	in	in	ADP
ejpam-3583	30	18	[	[	X
ejpam-3583	30	19	16	16	NUM
ejpam-3583	30	20	]	]	PUNCT
ejpam-3583	30	21	and	and	CCONJ
ejpam-3583	30	22	was	be	AUX
ejpam-3583	30	23	given	give	VERB
ejpam-3583	30	24	the	the	DET
ejpam-3583	30	25	hankel	hankel	NOUN
ejpam-3583	30	26	transform	transform	NOUN
ejpam-3583	30	27	as	as	SCONJ
ejpam-3583	30	28	follows	follow	VERB
ejpam-3583	30	29	h(d̃m	h(d̃m	PROPN
ejpam-3583	30	30	,	,	PUNCT
ejpam-3583	30	31	r[n]q	r[n]q	NOUN
ejpam-3583	30	32	)	)	PUNCT
ejpam-3583	30	33	=	=	PUNCT
ejpam-3583	31	1	qm(n+1	qm(n+1	PROPN
ejpam-3583	31	2	3	3	NUM
ejpam-3583	31	3	)	)	PUNCT
ejpam-3583	31	4	−rn(n+1)[0]qm	−rn(n+1)[0]qm	NOUN
ejpam-3583	31	5	!	!	PUNCT
ejpam-3583	32	1	[	[	X
ejpam-3583	32	2	1]qm	1]qm	NUM
ejpam-3583	32	3	!	!	PUNCT
ejpam-3583	32	4	.	.	PUNCT
ejpam-3583	32	5	.	.	PUNCT
ejpam-3583	32	6	.	.	PUNCT
ejpam-3583	33	1	[	[	X
ejpam-3583	33	2	n]qm	n]qm	NOUN
ejpam-3583	33	3	!	!	PUNCT
ejpam-3583	34	1	[	[	X
ejpam-3583	34	2	m	m	X
ejpam-3583	34	3	]	]	X
ejpam-3583	34	4	(	(	PUNCT
ejpam-3583	34	5	n+1	n+1	PROPN
ejpam-3583	34	6	2	2	X
ejpam-3583	34	7	)	)	PUNCT
ejpam-3583	34	8	q	q	NOUN
ejpam-3583	34	9	.	.	PUNCT
ejpam-3583	35	1	(	(	PUNCT
ejpam-3583	35	2	8)	8)	PROPN
ejpam-3583	35	3	r.	r.	PROPN
ejpam-3583	35	4	corcino	corcino	PROPN
ejpam-3583	35	5	,	,	PUNCT
ejpam-3583	35	6	j.	j.	PROPN
ejpam-3583	35	7	ontolan	ontolan	PROPN
ejpam-3583	35	8	,	,	PUNCT
ejpam-3583	35	9	g.	g.	PROPN
ejpam-3583	35	10	j.	j.	PROPN
ejpam-3583	35	11	rama	rama	PROPN
ejpam-3583	35	12	/	/	SYM
ejpam-3583	35	13	eur	eur	PROPN
ejpam-3583	35	14	.	.	PUNCT
ejpam-3583	36	1	j.	j.	PROPN
ejpam-3583	36	2	pure	pure	PROPN
ejpam-3583	36	3	appl	appl	PROPN
ejpam-3583	36	4	.	.	PROPN
ejpam-3583	36	5	math	math	PROPN
ejpam-3583	36	6	,	,	PUNCT
ejpam-3583	36	7	12	12	NUM
ejpam-3583	36	8	(	(	PUNCT
ejpam-3583	36	9	4	4	NUM
ejpam-3583	36	10	)	)	PUNCT
ejpam-3583	36	11	(	(	PUNCT
ejpam-3583	36	12	2019	2019	NUM
ejpam-3583	36	13	)	)	PUNCT
ejpam-3583	36	14	,	,	PUNCT
ejpam-3583	36	15	1676	1676	NUM
ejpam-3583	36	16	-	-	SYM
ejpam-3583	36	17	1688	1688	NUM
ejpam-3583	36	18	1678	1678	NUM
ejpam-3583	36	19	this	this	DET
ejpam-3583	36	20	hankel	hankel	NOUN
ejpam-3583	36	21	transform	transform	NOUN
ejpam-3583	36	22	was	be	AUX
ejpam-3583	36	23	derived	derive	VERB
ejpam-3583	36	24	using	use	VERB
ejpam-3583	36	25	the	the	DET
ejpam-3583	36	26	hankel	hankel	NOUN
ejpam-3583	36	27	transform	transform	NOUN
ejpam-3583	36	28	of	of	ADP
ejpam-3583	36	29	q	q	ADJ
ejpam-3583	36	30	-	-	ADJ
ejpam-3583	36	31	exponential	exponential	ADJ
ejpam-3583	36	32	polynomials	polynomial	NOUN
ejpam-3583	36	33	in	in	ADP
ejpam-3583	36	34	[	[	X
ejpam-3583	36	35	20	20	NUM
ejpam-3583	36	36	]	]	PUNCT
ejpam-3583	36	37	,	,	PUNCT
ejpam-3583	36	38	the	the	DET
ejpam-3583	36	39	layman	layman	NOUN
ejpam-3583	36	40	’s	’s	PART
ejpam-3583	36	41	theorem	theorem	NOUN
ejpam-3583	36	42	in	in	ADP
ejpam-3583	36	43	[	[	X
ejpam-3583	36	44	26	26	NUM
ejpam-3583	36	45	]	]	PUNCT
ejpam-3583	36	46	and	and	CCONJ
ejpam-3583	36	47	the	the	DET
ejpam-3583	36	48	spivey	spivey	PROPN
ejpam-3583	36	49	-	-	PUNCT
ejpam-3583	36	50	steil	steil	PROPN
ejpam-3583	36	51	theorem	theorem	VERB
ejpam-3583	36	52	in	in	ADP
ejpam-3583	36	53	[	[	X
ejpam-3583	36	54	34	34	NUM
ejpam-3583	36	55	]	]	PUNCT
ejpam-3583	36	56	.	.	PUNCT
ejpam-3583	37	1	this	this	DET
ejpam-3583	37	2	method	method	NOUN
ejpam-3583	37	3	can	can	AUX
ejpam-3583	37	4	not	not	PART
ejpam-3583	37	5	be	be	AUX
ejpam-3583	37	6	used	use	VERB
ejpam-3583	37	7	to	to	PART
ejpam-3583	37	8	derive	derive	VERB
ejpam-3583	37	9	the	the	DET
ejpam-3583	37	10	hankel	hankel	NOUN
ejpam-3583	37	11	transform	transform	NOUN
ejpam-3583	37	12	of	of	ADP
ejpam-3583	37	13	the	the	DET
ejpam-3583	37	14	first	first	ADJ
ejpam-3583	37	15	and	and	CCONJ
ejpam-3583	37	16	second	second	ADJ
ejpam-3583	37	17	forms	form	NOUN
ejpam-3583	37	18	of	of	ADP
ejpam-3583	37	19	q	q	NOUN
ejpam-3583	37	20	-	-	PUNCT
ejpam-3583	37	21	analogues	analogue	NOUN
ejpam-3583	37	22	for	for	ADP
ejpam-3583	37	23	r	r	NOUN
ejpam-3583	37	24	-	-	PUNCT
ejpam-3583	37	25	dowling	dowle	VERB
ejpam-3583	37	26	numbers	number	NOUN
ejpam-3583	37	27	.	.	PUNCT
ejpam-3583	38	1	but	but	CCONJ
ejpam-3583	38	2	the	the	DET
ejpam-3583	38	3	method	method	NOUN
ejpam-3583	38	4	used	use	VERB
ejpam-3583	38	5	by	by	ADP
ejpam-3583	38	6	cigler	cigler	NOUN
ejpam-3583	38	7	in	in	ADP
ejpam-3583	38	8	[	[	X
ejpam-3583	38	9	8	8	NUM
ejpam-3583	38	10	]	]	PUNCT
ejpam-3583	38	11	is	be	AUX
ejpam-3583	38	12	found	find	VERB
ejpam-3583	38	13	to	to	PART
ejpam-3583	38	14	be	be	AUX
ejpam-3583	38	15	useful	useful	ADJ
ejpam-3583	38	16	to	to	PART
ejpam-3583	38	17	derive	derive	VERB
ejpam-3583	38	18	the	the	DET
ejpam-3583	38	19	hankel	hankel	NOUN
ejpam-3583	38	20	transforms	transform	VERB
ejpam-3583	38	21	for	for	ADP
ejpam-3583	38	22	the	the	DET
ejpam-3583	38	23	second	second	ADJ
ejpam-3583	38	24	form	form	NOUN
ejpam-3583	38	25	of	of	ADP
ejpam-3583	38	26	the	the	DET
ejpam-3583	38	27	q	q	NOUN
ejpam-3583	38	28	-	-	PUNCT
ejpam-3583	38	29	analogue	analogue	NOUN
ejpam-3583	38	30	of	of	ADP
ejpam-3583	38	31	r	r	NOUN
ejpam-3583	38	32	-	-	PUNCT
ejpam-3583	38	33	dowling	dowle	VERB
ejpam-3583	38	34	numbers	number	NOUN
ejpam-3583	38	35	.	.	PUNCT
ejpam-3583	39	1	in	in	ADP
ejpam-3583	39	2	this	this	DET
ejpam-3583	39	3	paper	paper	NOUN
ejpam-3583	39	4	,	,	PUNCT
ejpam-3583	39	5	the	the	DET
ejpam-3583	39	6	hankel	hankel	NOUN
ejpam-3583	39	7	transform	transform	VERB
ejpam-3583	39	8	for	for	ADP
ejpam-3583	39	9	the	the	DET
ejpam-3583	39	10	sequence	sequence	NOUN
ejpam-3583	39	11	(	(	PUNCT
ejpam-3583	39	12	d∗m	d∗m	ADV
ejpam-3583	39	13	,	,	PUNCT
ejpam-3583	39	14	r[n]q	r[n]q	NOUN
ejpam-3583	39	15	)	)	PUNCT
ejpam-3583	39	16	∞	∞	PROPN
ejpam-3583	39	17	n=0	n=0	PROPN
ejpam-3583	39	18	will	will	AUX
ejpam-3583	39	19	be	be	AUX
ejpam-3583	39	20	established	establish	VERB
ejpam-3583	39	21	using	use	VERB
ejpam-3583	39	22	cigler	cigler	NOUN
ejpam-3583	39	23	’s	’s	PART
ejpam-3583	39	24	method	method	NOUN
ejpam-3583	39	25	[	[	X
ejpam-3583	39	26	8	8	NUM
ejpam-3583	39	27	]	]	PUNCT
ejpam-3583	39	28	.	.	PUNCT
ejpam-3583	40	1	however	however	ADV
ejpam-3583	40	2	,	,	PUNCT
ejpam-3583	40	3	a	a	DET
ejpam-3583	40	4	more	more	ADV
ejpam-3583	40	5	general	general	ADJ
ejpam-3583	40	6	form	form	NOUN
ejpam-3583	40	7	of	of	ADP
ejpam-3583	40	8	d∗m	d∗m	NOUN
ejpam-3583	40	9	,	,	PUNCT
ejpam-3583	40	10	r[n]q	r[n]q	NOUN
ejpam-3583	40	11	,	,	PUNCT
ejpam-3583	40	12	denoted	denote	VERB
ejpam-3583	40	13	by	by	ADP
ejpam-3583	40	14	ϕn[x	ϕn[x	PROPN
ejpam-3583	40	15	,	,	PUNCT
ejpam-3583	40	16	r	r	NOUN
ejpam-3583	40	17	,	,	PUNCT
ejpam-3583	40	18	m]q	m]q	PROPN
ejpam-3583	40	19	,	,	PUNCT
ejpam-3583	40	20	is	be	AUX
ejpam-3583	40	21	considered	consider	VERB
ejpam-3583	40	22	,	,	PUNCT
ejpam-3583	40	23	which	which	PRON
ejpam-3583	40	24	is	be	AUX
ejpam-3583	40	25	defined	define	VERB
ejpam-3583	40	26	in	in	ADP
ejpam-3583	40	27	polynomial	polynomial	ADJ
ejpam-3583	40	28	form	form	NOUN
ejpam-3583	40	29	as	as	SCONJ
ejpam-3583	40	30	follows	follow	VERB
ejpam-3583	40	31	:	:	PUNCT
ejpam-3583	40	32	ϕn[x	ϕn[x	PROPN
ejpam-3583	40	33	,	,	PUNCT
ejpam-3583	40	34	r	r	NOUN
ejpam-3583	40	35	,	,	PUNCT
ejpam-3583	40	36	m]q	m]q	NOUN
ejpam-3583	40	37	=	=	SYM
ejpam-3583	40	38	n∑	n∑	PROPN
ejpam-3583	40	39	k=0	k=0	PROPN
ejpam-3583	41	1	w	w	ADP
ejpam-3583	41	2	∗m	∗m	PROPN
ejpam-3583	41	3	,	,	PUNCT
ejpam-3583	41	4	r[n	r[n	NOUN
ejpam-3583	41	5	,	,	PUNCT
ejpam-3583	41	6	k][x]nq	k][x]nq	X
ejpam-3583	41	7	,	,	PUNCT
ejpam-3583	41	8	(	(	PUNCT
ejpam-3583	41	9	9	9	X
ejpam-3583	41	10	)	)	PUNCT
ejpam-3583	41	11	such	such	ADJ
ejpam-3583	41	12	that	that	SCONJ
ejpam-3583	41	13	,	,	PUNCT
ejpam-3583	41	14	when	when	SCONJ
ejpam-3583	41	15	x	x	X
ejpam-3583	41	16	=	=	SYM
ejpam-3583	41	17	1	1	NUM
ejpam-3583	41	18	,	,	PUNCT
ejpam-3583	41	19	ϕn[1	ϕn[1	PROPN
ejpam-3583	41	20	,	,	PUNCT
ejpam-3583	41	21	r	r	NOUN
ejpam-3583	41	22	,	,	PUNCT
ejpam-3583	41	23	m]q	m]q	NOUN
ejpam-3583	41	24	=	=	SYM
ejpam-3583	41	25	d∗m	d∗m	NOUN
ejpam-3583	41	26	,	,	PUNCT
ejpam-3583	41	27	r[n]q	r[n]q	NOUN
ejpam-3583	41	28	.	.	PUNCT
ejpam-3583	42	1	2	2	NUM
ejpam-3583	42	2	.	.	X
ejpam-3583	42	3	a	a	DET
ejpam-3583	42	4	q	q	NOUN
ejpam-3583	42	5	-	-	PUNCT
ejpam-3583	42	6	analogue	analogue	NOUN
ejpam-3583	42	7	of	of	ADP
ejpam-3583	42	8	wm	wm	PROPN
ejpam-3583	42	9	,	,	PUNCT
ejpam-3583	42	10	r(n	r(n	PROPN
ejpam-3583	42	11	,	,	PUNCT
ejpam-3583	42	12	k	k	NOUN
ejpam-3583	42	13	):	):	PUNCT
ejpam-3583	42	14	second	second	ADJ
ejpam-3583	42	15	form	form	NOUN
ejpam-3583	42	16	the	the	DET
ejpam-3583	42	17	second	second	ADJ
ejpam-3583	42	18	form	form	NOUN
ejpam-3583	42	19	of	of	ADP
ejpam-3583	42	20	q	q	NOUN
ejpam-3583	42	21	-	-	PUNCT
ejpam-3583	42	22	analogue	analogue	NOUN
ejpam-3583	42	23	of	of	ADP
ejpam-3583	42	24	wm	wm	PROPN
ejpam-3583	42	25	,	,	PUNCT
ejpam-3583	42	26	r(n	r(n	PROPN
ejpam-3583	42	27	,	,	PUNCT
ejpam-3583	42	28	k	k	NOUN
ejpam-3583	42	29	)	)	PUNCT
ejpam-3583	42	30	is	be	AUX
ejpam-3583	42	31	a	a	DET
ejpam-3583	42	32	kind	kind	NOUN
ejpam-3583	42	33	of	of	ADP
ejpam-3583	42	34	generalization	generalization	NOUN
ejpam-3583	42	35	of	of	ADP
ejpam-3583	42	36	the	the	DET
ejpam-3583	42	37	qanalogue	qanalogue	NOUN
ejpam-3583	42	38	considered	consider	VERB
ejpam-3583	42	39	by	by	ADP
ejpam-3583	42	40	cigler	cigler	NOUN
ejpam-3583	42	41	[	[	X
ejpam-3583	42	42	8	8	NUM
ejpam-3583	42	43	]	]	PUNCT
ejpam-3583	42	44	.	.	PUNCT
ejpam-3583	43	1	this	this	DET
ejpam-3583	43	2	q	q	ADJ
ejpam-3583	43	3	-	-	PUNCT
ejpam-3583	43	4	analogue	analogue	NOUN
ejpam-3583	43	5	possessed	possess	VERB
ejpam-3583	43	6	several	several	ADJ
ejpam-3583	43	7	properties	property	NOUN
ejpam-3583	43	8	(	(	PUNCT
ejpam-3583	43	9	see	see	VERB
ejpam-3583	43	10	[	[	X
ejpam-3583	43	11	13	13	NUM
ejpam-3583	43	12	]	]	PUNCT
ejpam-3583	43	13	)	)	PUNCT
ejpam-3583	43	14	including	include	VERB
ejpam-3583	43	15	certain	certain	ADJ
ejpam-3583	43	16	combinatorial	combinatorial	ADJ
ejpam-3583	43	17	interpretation	interpretation	NOUN
ejpam-3583	43	18	in	in	ADP
ejpam-3583	43	19	terms	term	NOUN
ejpam-3583	43	20	of	of	ADP
ejpam-3583	43	21	a	a	DET
ejpam-3583	43	22	-	-	PUNCT
ejpam-3583	43	23	tableau	tableau	NOUN
ejpam-3583	43	24	,	,	PUNCT
ejpam-3583	43	25	which	which	PRON
ejpam-3583	43	26	is	be	AUX
ejpam-3583	43	27	defined	define	VERB
ejpam-3583	43	28	in	in	ADP
ejpam-3583	43	29	[	[	X
ejpam-3583	43	30	27	27	NUM
ejpam-3583	43	31	]	]	PUNCT
ejpam-3583	43	32	to	to	PART
ejpam-3583	43	33	be	be	AUX
ejpam-3583	43	34	a	a	DET
ejpam-3583	43	35	list	list	NOUN
ejpam-3583	43	36	φ	φ	NOUN
ejpam-3583	43	37	of	of	ADP
ejpam-3583	43	38	column	column	PROPN
ejpam-3583	43	39	c	c	PROPN
ejpam-3583	43	40	of	of	ADP
ejpam-3583	43	41	a	a	DET
ejpam-3583	43	42	ferrer	ferrer	PROPN
ejpam-3583	43	43	’s	’s	PART
ejpam-3583	43	44	diagram	diagram	NOUN
ejpam-3583	43	45	of	of	ADP
ejpam-3583	43	46	a	a	DET
ejpam-3583	43	47	partition	partition	NOUN
ejpam-3583	43	48	λ(by	λ(by	NOUN
ejpam-3583	43	49	decreasing	decrease	VERB
ejpam-3583	43	50	order	order	NOUN
ejpam-3583	43	51	of	of	ADP
ejpam-3583	43	52	length	length	NOUN
ejpam-3583	43	53	)	)	PUNCT
ejpam-3583	43	54	such	such	ADJ
ejpam-3583	43	55	that	that	SCONJ
ejpam-3583	43	56	the	the	DET
ejpam-3583	43	57	lengths	length	NOUN
ejpam-3583	43	58	|c|	|c|	PROPN
ejpam-3583	43	59	are	be	AUX
ejpam-3583	43	60	part	part	NOUN
ejpam-3583	43	61	of	of	ADP
ejpam-3583	43	62	the	the	DET
ejpam-3583	43	63	sequence	sequence	NOUN
ejpam-3583	43	64	a	a	PRON
ejpam-3583	43	65	=	=	SYM
ejpam-3583	43	66	(	(	PUNCT
ejpam-3583	43	67	ri)i≥0	ri)i≥0	PROPN
ejpam-3583	43	68	,	,	PUNCT
ejpam-3583	43	69	a	a	DET
ejpam-3583	43	70	strictly	strictly	ADV
ejpam-3583	43	71	increasing	increase	VERB
ejpam-3583	43	72	sequence	sequence	NOUN
ejpam-3583	43	73	of	of	ADP
ejpam-3583	43	74	nonnegative	nonnegative	ADJ
ejpam-3583	43	75	integers	integer	NOUN
ejpam-3583	43	76	.	.	PUNCT
ejpam-3583	44	1	by	by	ADP
ejpam-3583	44	2	making	make	VERB
ejpam-3583	44	3	use	use	NOUN
ejpam-3583	44	4	of	of	ADP
ejpam-3583	44	5	the	the	DET
ejpam-3583	44	6	following	follow	VERB
ejpam-3583	44	7	explicit	explicit	ADJ
ejpam-3583	44	8	formula	formula	NOUN
ejpam-3583	44	9	in	in	ADP
ejpam-3583	44	10	symmetric	symmetric	ADJ
ejpam-3583	44	11	function	function	NOUN
ejpam-3583	44	12	form	form	NOUN
ejpam-3583	44	13	[	[	X
ejpam-3583	44	14	13	13	NUM
ejpam-3583	44	15	]	]	SYM
ejpam-3583	44	16	wm	wm	PROPN
ejpam-3583	44	17	,	,	PUNCT
ejpam-3583	44	18	r[n	r[n	NOUN
ejpam-3583	44	19	,	,	PUNCT
ejpam-3583	44	20	k]q	k]q	NOUN
ejpam-3583	44	21	=	=	SYM
ejpam-3583	44	22	qm(k2)+kr	qm(k2)+kr	PROPN
ejpam-3583	44	23	∑	∑	ADV
ejpam-3583	44	24	s1+s2+···sk	s1+s2+···sk	NOUN
ejpam-3583	44	25	=	=	NOUN
ejpam-3583	44	26	n−k	n−k	NOUN
ejpam-3583	44	27	k∏	k∏	NOUN
ejpam-3583	44	28	j=1	j=1	NOUN
ejpam-3583	45	1	[	[	X
ejpam-3583	45	2	mj	mj	X
ejpam-3583	45	3	+	+	X
ejpam-3583	46	1	r	r	X
ejpam-3583	46	2	]	]	X
ejpam-3583	46	3	sj	sj	NOUN
ejpam-3583	46	4	q	q	NOUN
ejpam-3583	46	5	=	=	PUNCT
ejpam-3583	46	6	∑	∑	PROPN
ejpam-3583	46	7	0≤j1≤j2≤···jn−k≤k	0≤j1≤j2≤···jn−k≤k	NUM
ejpam-3583	46	8	qm(k2)+kr	qm(k2)+kr	PROPN
ejpam-3583	46	9	n−k∏	n−k∏	PROPN
ejpam-3583	46	10	i=1	i=1	PUNCT
ejpam-3583	47	1	[	[	X
ejpam-3583	47	2	mji	mji	ADJ
ejpam-3583	47	3	+	+	X
ejpam-3583	47	4	r]q	r]q	NOUN
ejpam-3583	47	5	,	,	PUNCT
ejpam-3583	47	6	(	(	PUNCT
ejpam-3583	47	7	10	10	NUM
ejpam-3583	47	8	)	)	PUNCT
ejpam-3583	47	9	we	we	PRON
ejpam-3583	47	10	have	have	VERB
ejpam-3583	47	11	w	w	ADP
ejpam-3583	47	12	∗m	∗m	NOUN
ejpam-3583	47	13	,	,	PUNCT
ejpam-3583	47	14	r[n	r[n	NOUN
ejpam-3583	47	15	,	,	PUNCT
ejpam-3583	47	16	k]q	k]q	NOUN
ejpam-3583	47	17	=	=	SYM
ejpam-3583	47	18	∑	∑	PUNCT
ejpam-3583	47	19	0≤j1≤j2≤···≤jn−k≤k	0≤j1≤j2≤···≤jn−k≤k	NUM
ejpam-3583	47	20	n−k∏	n−k∏	PROPN
ejpam-3583	47	21	i=1	i=1	PUNCT
ejpam-3583	48	1	[	[	X
ejpam-3583	48	2	mji	mji	ADJ
ejpam-3583	48	3	+	+	X
ejpam-3583	48	4	r]q	r]q	NOUN
ejpam-3583	48	5	.	.	PUNCT
ejpam-3583	49	1	(	(	PUNCT
ejpam-3583	49	2	11	11	NUM
ejpam-3583	49	3	)	)	PUNCT
ejpam-3583	49	4	in	in	ADP
ejpam-3583	49	5	[	[	X
ejpam-3583	49	6	16	16	NUM
ejpam-3583	49	7	]	]	PUNCT
ejpam-3583	49	8	,	,	PUNCT
ejpam-3583	49	9	w	w	PROPN
ejpam-3583	49	10	∗m	∗m	NOUN
ejpam-3583	49	11	,	,	PUNCT
ejpam-3583	49	12	r[n	r[n	NOUN
ejpam-3583	49	13	,	,	PUNCT
ejpam-3583	49	14	k	k	NOUN
ejpam-3583	49	15	]	]	PUNCT
ejpam-3583	49	16	was	be	AUX
ejpam-3583	49	17	expressed	express	VERB
ejpam-3583	49	18	as	as	ADP
ejpam-3583	49	19	w	w	PROPN
ejpam-3583	49	20	∗m	∗m	NOUN
ejpam-3583	49	21	,	,	PUNCT
ejpam-3583	49	22	r[n	r[n	NOUN
ejpam-3583	49	23	,	,	PUNCT
ejpam-3583	49	24	k	k	X
ejpam-3583	49	25	]	]	X
ejpam-3583	49	26	=	=	PUNCT
ejpam-3583	49	27	∑	∑	PUNCT
ejpam-3583	49	28	φ∈ta	φ∈ta	PROPN
ejpam-3583	49	29	r	r	NOUN
ejpam-3583	49	30	(	(	PUNCT
ejpam-3583	49	31	k	k	NOUN
ejpam-3583	49	32	,	,	PUNCT
ejpam-3583	49	33	n−k	n−k	NOUN
ejpam-3583	49	34	)	)	PUNCT
ejpam-3583	49	35	∏	∏	PROPN
ejpam-3583	49	36	c∈φ	c∈φ	PROPN
ejpam-3583	49	37	ω(|c|	ω(|c|	PROPN
ejpam-3583	49	38	)	)	PUNCT
ejpam-3583	49	39	where	where	SCONJ
ejpam-3583	49	40	tar	tar	NOUN
ejpam-3583	49	41	(	(	PUNCT
ejpam-3583	49	42	h	h	NOUN
ejpam-3583	49	43	,	,	PUNCT
ejpam-3583	49	44	l	l	NOUN
ejpam-3583	49	45	)	)	PUNCT
ejpam-3583	49	46	denotes	denote	VERB
ejpam-3583	49	47	the	the	DET
ejpam-3583	49	48	set	set	NOUN
ejpam-3583	49	49	of	of	ADP
ejpam-3583	49	50	a	a	DET
ejpam-3583	49	51	-	-	PUNCT
ejpam-3583	49	52	tableau	tableau	NOUN
ejpam-3583	49	53	with	with	ADP
ejpam-3583	49	54	l	l	NOUN
ejpam-3583	49	55	columns	column	NOUN
ejpam-3583	49	56	of	of	ADP
ejpam-3583	49	57	lengths	length	NOUN
ejpam-3583	49	58	|c|	|c|	PROPN
ejpam-3583	49	59	≤	≤	NUM
ejpam-3583	49	60	h	h	NOUN
ejpam-3583	49	61	and	and	CCONJ
ejpam-3583	49	62	ω(|c|	ω(|c|	NUM
ejpam-3583	49	63	)	)	PUNCT
ejpam-3583	50	1	=	=	NOUN
ejpam-3583	51	1	[	[	X
ejpam-3583	51	2	m|c|+r]q	m|c|+r]q	ADJ
ejpam-3583	51	3	.	.	PUNCT
ejpam-3583	52	1	using	use	VERB
ejpam-3583	52	2	the	the	DET
ejpam-3583	52	3	combinatorics	combinatoric	NOUN
ejpam-3583	52	4	of	of	ADP
ejpam-3583	52	5	a	a	DET
ejpam-3583	52	6	-	-	PUNCT
ejpam-3583	52	7	tableau	tableau	NOUN
ejpam-3583	52	8	,	,	PUNCT
ejpam-3583	52	9	the	the	DET
ejpam-3583	52	10	following	follow	VERB
ejpam-3583	52	11	identities	identity	NOUN
ejpam-3583	52	12	were	be	AUX
ejpam-3583	52	13	established	establish	VERB
ejpam-3583	52	14	r.	r.	PROPN
ejpam-3583	52	15	corcino	corcino	PROPN
ejpam-3583	52	16	,	,	PUNCT
ejpam-3583	52	17	j.	j.	PROPN
ejpam-3583	52	18	ontolan	ontolan	PROPN
ejpam-3583	52	19	,	,	PUNCT
ejpam-3583	52	20	g.	g.	PROPN
ejpam-3583	52	21	j.	j.	PROPN
ejpam-3583	52	22	rama	rama	PROPN
ejpam-3583	52	23	/	/	SYM
ejpam-3583	52	24	eur	eur	PROPN
ejpam-3583	52	25	.	.	PUNCT
ejpam-3583	53	1	j.	j.	PROPN
ejpam-3583	53	2	pure	pure	PROPN
ejpam-3583	53	3	appl	appl	PROPN
ejpam-3583	53	4	.	.	PROPN
ejpam-3583	53	5	math	math	PROPN
ejpam-3583	53	6	,	,	PUNCT
ejpam-3583	53	7	12	12	NUM
ejpam-3583	53	8	(	(	PUNCT
ejpam-3583	53	9	4	4	NUM
ejpam-3583	53	10	)	)	PUNCT
ejpam-3583	53	11	(	(	PUNCT
ejpam-3583	53	12	2019	2019	NUM
ejpam-3583	53	13	)	)	PUNCT
ejpam-3583	53	14	,	,	PUNCT
ejpam-3583	53	15	1676	1676	NUM
ejpam-3583	53	16	-	-	SYM
ejpam-3583	53	17	1688	1688	NUM
ejpam-3583	53	18	1679	1679	NUM
ejpam-3583	53	19	in	in	ADP
ejpam-3583	53	20	[	[	X
ejpam-3583	53	21	16	16	NUM
ejpam-3583	53	22	]	]	X
ejpam-3583	53	23	:	:	PUNCT
ejpam-3583	53	24	w	w	NOUN
ejpam-3583	53	25	∗m	∗m	NOUN
ejpam-3583	53	26	,	,	PUNCT
ejpam-3583	53	27	r[n	r[n	NOUN
ejpam-3583	53	28	,	,	PUNCT
ejpam-3583	53	29	k]q	k]q	NOUN
ejpam-3583	53	30	=	=	SYM
ejpam-3583	53	31	n∑	n∑	PROPN
ejpam-3583	53	32	j	j	PROPN
ejpam-3583	54	1	=	=	PROPN
ejpam-3583	54	2	k	k	PROPN
ejpam-3583	54	3	(	(	PUNCT
ejpam-3583	54	4	−1)n−j	−1)n−j	X
ejpam-3583	54	5	(	(	PUNCT
ejpam-3583	54	6	n	n	X
ejpam-3583	54	7	j	j	NOUN
ejpam-3583	54	8	)	)	PUNCT
ejpam-3583	54	9	q−nr2	q−nr2	INTJ
ejpam-3583	55	1	[	[	X
ejpam-3583	55	2	r2	r2	X
ejpam-3583	55	3	]	]	PUNCT
ejpam-3583	55	4	n−j	n−j	X
ejpam-3583	55	5	q	q	X
ejpam-3583	55	6	w	w	PROPN
ejpam-3583	55	7	∗m	∗m	NOUN
ejpam-3583	55	8	,	,	PUNCT
ejpam-3583	55	9	r1	r1	PROPN
ejpam-3583	55	10	[	[	X
ejpam-3583	55	11	j	j	PROPN
ejpam-3583	55	12	,	,	PUNCT
ejpam-3583	55	13	k]q	k]q	PROPN
ejpam-3583	55	14	(	(	PUNCT
ejpam-3583	55	15	12	12	NUM
ejpam-3583	55	16	)	)	PUNCT
ejpam-3583	55	17	w	w	NOUN
ejpam-3583	55	18	∗m	∗m	NOUN
ejpam-3583	55	19	,	,	PUNCT
ejpam-3583	55	20	r[n+	r[n+	NOUN
ejpam-3583	55	21	1,m+	1,m+	NUM
ejpam-3583	55	22	j	j	PROPN
ejpam-3583	56	1	+	+	CCONJ
ejpam-3583	56	2	1]q	1]q	NUM
ejpam-3583	56	3	=	=	SYM
ejpam-3583	56	4	n∑	n∑	PROPN
ejpam-3583	56	5	k=0	k=0	PROPN
ejpam-3583	57	1	w	w	PROPN
ejpam-3583	57	2	∗m	∗m	PROPN
ejpam-3583	57	3	,	,	PUNCT
ejpam-3583	57	4	r[k	r[k	PROPN
ejpam-3583	57	5	,	,	PUNCT
ejpam-3583	57	6	m]qw	m]qw	PROPN
ejpam-3583	57	7	∗	∗	NOUN
ejpam-3583	57	8	m	m	PROPN
ejpam-3583	57	9	,	,	PUNCT
ejpam-3583	57	10	r−m−1[n−	r−m−1[n−	PROPN
ejpam-3583	57	11	k	k	PROPN
ejpam-3583	57	12	,	,	PUNCT
ejpam-3583	57	13	j]q	j]q	PROPN
ejpam-3583	57	14	(	(	PUNCT
ejpam-3583	57	15	13	13	NUM
ejpam-3583	57	16	)	)	PUNCT
ejpam-3583	57	17	w	w	NOUN
ejpam-3583	57	18	∗m	∗m	NOUN
ejpam-3583	57	19	,	,	PUNCT
ejpam-3583	57	20	r[s+	r[s+	VERB
ejpam-3583	57	21	p	p	NOUN
ejpam-3583	57	22	,	,	PUNCT
ejpam-3583	57	23	t]q	t]q	NOUN
ejpam-3583	57	24	=	=	SYM
ejpam-3583	57	25	min{t	min{t	PROPN
ejpam-3583	57	26	,	,	PUNCT
ejpam-3583	57	27	s}∑	s}∑	NOUN
ejpam-3583	57	28	k	k	PROPN
ejpam-3583	58	1	=	=	NOUN
ejpam-3583	58	2	max{0,t−p	max{0,t−p	ADJ
ejpam-3583	58	3	}	}	PUNCT
ejpam-3583	58	4	w	w	PROPN
ejpam-3583	58	5	∗m	∗m	NOUN
ejpam-3583	58	6	,	,	PUNCT
ejpam-3583	58	7	r[s	r[s	PROPN
ejpam-3583	58	8	,	,	PUNCT
ejpam-3583	58	9	k]qw	k]qw	PROPN
ejpam-3583	58	10	∗	∗	NOUN
ejpam-3583	58	11	m	m	PROPN
ejpam-3583	58	12	,	,	PUNCT
ejpam-3583	58	13	r+mk[p	r+mk[p	PROPN
ejpam-3583	58	14	,	,	PUNCT
ejpam-3583	58	15	t−	t−	PROPN
ejpam-3583	58	16	k]q	k]q	PROPN
ejpam-3583	58	17	.	.	PUNCT
ejpam-3583	59	1	(	(	PUNCT
ejpam-3583	59	2	14	14	NUM
ejpam-3583	59	3	)	)	PUNCT
ejpam-3583	59	4	moreover	moreover	ADV
ejpam-3583	59	5	,	,	PUNCT
ejpam-3583	59	6	the	the	DET
ejpam-3583	59	7	convolution	convolution	NOUN
ejpam-3583	59	8	-	-	PUNCT
ejpam-3583	59	9	type	type	NOUN
ejpam-3583	59	10	identity	identity	NOUN
ejpam-3583	59	11	(	(	PUNCT
ejpam-3583	59	12	14	14	NUM
ejpam-3583	59	13	)	)	PUNCT
ejpam-3583	59	14	has	have	AUX
ejpam-3583	59	15	been	be	AUX
ejpam-3583	59	16	used	use	VERB
ejpam-3583	59	17	in	in	ADP
ejpam-3583	59	18	[	[	X
ejpam-3583	59	19	13	13	NUM
ejpam-3583	59	20	]	]	PUNCT
ejpam-3583	59	21	to	to	PART
ejpam-3583	59	22	derive	derive	VERB
ejpam-3583	59	23	the	the	DET
ejpam-3583	59	24	following	follow	VERB
ejpam-3583	59	25	hankel	hankel	NOUN
ejpam-3583	59	26	determinant	determinant	PROPN
ejpam-3583	59	27	det	det	PROPN
ejpam-3583	59	28	(	(	PUNCT
ejpam-3583	59	29	w	w	PROPN
ejpam-3583	59	30	∗m	∗m	PROPN
ejpam-3583	59	31	,	,	PUNCT
ejpam-3583	59	32	r[s+	r[s+	VERB
ejpam-3583	59	33	i+	i+	NUM
ejpam-3583	60	1	j	j	PROPN
ejpam-3583	60	2	,	,	PUNCT
ejpam-3583	60	3	s+	s+	ADV
ejpam-3583	60	4	j]q	j]q	PROPN
ejpam-3583	60	5	)	)	PUNCT
ejpam-3583	60	6	0≤i	0≤i	PROPN
ejpam-3583	60	7	,	,	PUNCT
ejpam-3583	60	8	j≤n	j≤n	X
ejpam-3583	60	9	=	=	SYM
ejpam-3583	60	10	n∏	n∏	PROPN
ejpam-3583	60	11	k=0	k=0	PROPN
ejpam-3583	61	1	[	[	X
ejpam-3583	61	2	m(s+	m(s+	X
ejpam-3583	61	3	k	k	NOUN
ejpam-3583	61	4	)	)	PUNCT
ejpam-3583	62	1	+	+	CCONJ
ejpam-3583	62	2	r]kq	r]kq	VERB
ejpam-3583	62	3	.	.	PUNCT
ejpam-3583	63	1	another	another	DET
ejpam-3583	63	2	interesting	interesting	ADJ
ejpam-3583	63	3	property	property	NOUN
ejpam-3583	63	4	of	of	ADP
ejpam-3583	63	5	w	w	PROPN
ejpam-3583	63	6	∗m	∗m	NOUN
ejpam-3583	63	7	,	,	PUNCT
ejpam-3583	63	8	r[n	r[n	NOUN
ejpam-3583	63	9	,	,	PUNCT
ejpam-3583	63	10	k]q	k]q	ADJ
ejpam-3583	63	11	is	be	AUX
ejpam-3583	63	12	the	the	DET
ejpam-3583	63	13	divisibility	divisibility	NOUN
ejpam-3583	63	14	property	property	NOUN
ejpam-3583	63	15	.	.	PUNCT
ejpam-3583	64	1	one	one	PRON
ejpam-3583	64	2	can	can	AUX
ejpam-3583	64	3	easily	easily	ADV
ejpam-3583	64	4	observe	observe	VERB
ejpam-3583	64	5	that	that	SCONJ
ejpam-3583	64	6	,	,	PUNCT
ejpam-3583	64	7	using	use	VERB
ejpam-3583	64	8	the	the	DET
ejpam-3583	64	9	triangular	triangular	NOUN
ejpam-3583	64	10	recurrence	recurrence	NOUN
ejpam-3583	64	11	relation	relation	NOUN
ejpam-3583	64	12	of	of	ADP
ejpam-3583	64	13	wm	wm	PROPN
ejpam-3583	64	14	,	,	PUNCT
ejpam-3583	64	15	r[n	r[n	NOUN
ejpam-3583	64	16	,	,	PUNCT
ejpam-3583	64	17	k]q	k]q	NOUN
ejpam-3583	64	18	in	in	ADV
ejpam-3583	64	19	(	(	PUNCT
ejpam-3583	64	20	2	2	NUM
ejpam-3583	64	21	)	)	PUNCT
ejpam-3583	64	22	,	,	PUNCT
ejpam-3583	64	23	we	we	PRON
ejpam-3583	64	24	can	can	AUX
ejpam-3583	64	25	generate	generate	VERB
ejpam-3583	64	26	the	the	DET
ejpam-3583	64	27	following	follow	VERB
ejpam-3583	64	28	table	table	NOUN
ejpam-3583	64	29	of	of	ADP
ejpam-3583	64	30	values	value	NOUN
ejpam-3583	64	31	n	n	CCONJ
ejpam-3583	64	32	/	/	SYM
ejpam-3583	64	33	k	k	NOUN
ejpam-3583	64	34	0	0	NUM
ejpam-3583	64	35	1	1	NUM
ejpam-3583	64	36	2	2	NUM
ejpam-3583	64	37	3	3	NUM
ejpam-3583	64	38	0	0	NUM
ejpam-3583	64	39	1	1	NUM
ejpam-3583	64	40	1	1	NUM
ejpam-3583	65	1	[	[	NOUN
ejpam-3583	65	2	r]q	r]q	NOUN
ejpam-3583	65	3	qr	qr	NOUN
ejpam-3583	65	4	2	2	NUM
ejpam-3583	65	5	[	[	X
ejpam-3583	65	6	r]2q	r]2q	NOUN
ejpam-3583	65	7	qr	qr	NOUN
ejpam-3583	65	8	(	(	PUNCT
ejpam-3583	65	9	[	[	X
ejpam-3583	65	10	r]q	r]q	NOUN
ejpam-3583	65	11	+	+	X
ejpam-3583	65	12	[	[	X
ejpam-3583	65	13	m+	m+	NUM
ejpam-3583	65	14	r]q	r]q	NOUN
ejpam-3583	65	15	)	)	PUNCT
ejpam-3583	65	16	qm+2r	qm+2r	NOUN
ejpam-3583	65	17	2	2	NUM
ejpam-3583	65	18	[	[	NOUN
ejpam-3583	65	19	r]2q	r]2q	NOUN
ejpam-3583	65	20	qr	qr	NOUN
ejpam-3583	65	21	(	(	PUNCT
ejpam-3583	65	22	[	[	X
ejpam-3583	65	23	r]q	r]q	NOUN
ejpam-3583	65	24	+	+	X
ejpam-3583	65	25	[	[	X
ejpam-3583	65	26	m+	m+	NUM
ejpam-3583	65	27	r]q	r]q	NOUN
ejpam-3583	65	28	)	)	PUNCT
ejpam-3583	65	29	qm+2r	qm+2r	NOUN
ejpam-3583	65	30	3	3	NUM
ejpam-3583	65	31	[	[	X
ejpam-3583	65	32	r]3q	r]3q	X
ejpam-3583	65	33	qr[r]2q	qr[r]2q	PROPN
ejpam-3583	65	34	+	+	CCONJ
ejpam-3583	65	35	qr[r]q[m+	qr[r]q[m+	PROPN
ejpam-3583	65	36	r]q	r]q	NOUN
ejpam-3583	65	37	qm+2r	qm+2r	NOUN
ejpam-3583	65	38	(	(	PUNCT
ejpam-3583	65	39	[	[	X
ejpam-3583	65	40	r]q	r]q	NOUN
ejpam-3583	65	41	+	+	X
ejpam-3583	66	1	[	[	X
ejpam-3583	66	2	m+	m+	NUM
ejpam-3583	66	3	r]q	r]q	NOUN
ejpam-3583	66	4	)	)	PUNCT
ejpam-3583	66	5	q3m+3r	q3m+3r	NOUN
ejpam-3583	67	1	+	+	NOUN
ejpam-3583	67	2	qr[m+	qr[m+	NOUN
ejpam-3583	67	3	r]2q	r]2q	NOUN
ejpam-3583	67	4	qm+2r	qm+2r	NOUN
ejpam-3583	67	5	(	(	PUNCT
ejpam-3583	67	6	+	+	ADP
ejpam-3583	67	7	[	[	X
ejpam-3583	67	8	2m+	2m+	NUM
ejpam-3583	67	9	r]q	r]q	NOUN
ejpam-3583	67	10	)	)	PUNCT
ejpam-3583	67	11	then	then	ADV
ejpam-3583	67	12	,	,	PUNCT
ejpam-3583	67	13	we	we	PRON
ejpam-3583	67	14	can	can	AUX
ejpam-3583	67	15	generate	generate	VERB
ejpam-3583	67	16	the	the	DET
ejpam-3583	67	17	first	first	ADJ
ejpam-3583	67	18	values	value	NOUN
ejpam-3583	67	19	of	of	ADP
ejpam-3583	67	20	w	w	PROPN
ejpam-3583	67	21	∗m	∗m	NOUN
ejpam-3583	67	22	,	,	PUNCT
ejpam-3583	67	23	r[n	r[n	NOUN
ejpam-3583	67	24	,	,	PUNCT
ejpam-3583	67	25	k]q	k]q	PROPN
ejpam-3583	67	26	as	as	SCONJ
ejpam-3583	67	27	follows	follow	VERB
ejpam-3583	67	28	n	n	CCONJ
ejpam-3583	67	29	/	/	SYM
ejpam-3583	67	30	k	k	NOUN
ejpam-3583	67	31	0	0	NUM
ejpam-3583	67	32	1	1	NUM
ejpam-3583	67	33	2	2	NUM
ejpam-3583	67	34	3	3	NUM
ejpam-3583	67	35	0	0	NUM
ejpam-3583	67	36	1	1	NUM
ejpam-3583	67	37	1	1	NUM
ejpam-3583	68	1	[	[	NOUN
ejpam-3583	68	2	r]q	r]q	NOUN
ejpam-3583	68	3	1	1	NUM
ejpam-3583	68	4	2	2	NUM
ejpam-3583	69	1	[	[	X
ejpam-3583	69	2	r]2q	r]2q	NOUN
ejpam-3583	69	3	[	[	X
ejpam-3583	69	4	r]q	r]q	NOUN
ejpam-3583	69	5	+	+	X
ejpam-3583	70	1	[	[	X
ejpam-3583	70	2	m+	m+	NUM
ejpam-3583	70	3	r]q	r]q	VERB
ejpam-3583	70	4	1	1	NUM
ejpam-3583	70	5	3	3	NUM
ejpam-3583	70	6	[	[	X
ejpam-3583	70	7	r]3q	r]3q	X
ejpam-3583	71	1	[	[	X
ejpam-3583	71	2	r]2q	r]2q	NOUN
ejpam-3583	71	3	+	+	X
ejpam-3583	71	4	[	[	X
ejpam-3583	71	5	r]q[m+	r]q[m+	NOUN
ejpam-3583	71	6	r]q	r]q	VERB
ejpam-3583	71	7	+	+	CCONJ
ejpam-3583	72	1	[	[	X
ejpam-3583	72	2	m+	m+	X
ejpam-3583	72	3	r]2q	r]2q	NOUN
ejpam-3583	73	1	[	[	NOUN
ejpam-3583	73	2	r]q	r]q	NOUN
ejpam-3583	73	3	+	+	X
ejpam-3583	73	4	[	[	X
ejpam-3583	73	5	m+	m+	NUM
ejpam-3583	73	6	r]q	r]q	NOUN
ejpam-3583	73	7	+	+	X
ejpam-3583	74	1	[	[	X
ejpam-3583	74	2	2m+	2m+	NUM
ejpam-3583	74	3	r]q	r]q	NOUN
ejpam-3583	74	4	1	1	NUM
ejpam-3583	74	5	note	note	NOUN
ejpam-3583	74	6	that	that	SCONJ
ejpam-3583	74	7	[	[	X
ejpam-3583	74	8	n]q	n]q	NOUN
ejpam-3583	74	9	=	=	SYM
ejpam-3583	74	10	1	1	NUM
ejpam-3583	74	11	+	+	CCONJ
ejpam-3583	74	12	q+	q+	ADV
ejpam-3583	74	13	q2	q2	NOUN
ejpam-3583	74	14	+	+	X
ejpam-3583	74	15	.	.	PUNCT
ejpam-3583	74	16	.	.	PUNCT
ejpam-3583	75	1	.+	.+	NOUN
ejpam-3583	76	1	qn−1	qn−1	PROPN
ejpam-3583	76	2	.	.	PROPN
ejpam-3583	76	3	based	base	VERB
ejpam-3583	76	4	on	on	ADP
ejpam-3583	76	5	the	the	DET
ejpam-3583	76	6	preceding	precede	VERB
ejpam-3583	76	7	table	table	NOUN
ejpam-3583	76	8	,	,	PUNCT
ejpam-3583	76	9	the	the	DET
ejpam-3583	76	10	constant	constant	ADJ
ejpam-3583	76	11	values	value	NOUN
ejpam-3583	76	12	of	of	ADP
ejpam-3583	76	13	w	w	PROPN
ejpam-3583	76	14	∗m	∗m	NOUN
ejpam-3583	76	15	,	,	PUNCT
ejpam-3583	76	16	r[n	r[n	NOUN
ejpam-3583	76	17	,	,	PUNCT
ejpam-3583	76	18	k]q	k]q	NOUN
ejpam-3583	76	19	from	from	ADP
ejpam-3583	76	20	row	row	NOUN
ejpam-3583	76	21	0	0	NUM
ejpam-3583	76	22	to	to	PART
ejpam-3583	76	23	row	row	VERB
ejpam-3583	76	24	3	3	NUM
ejpam-3583	76	25	form	form	NOUN
ejpam-3583	76	26	the	the	DET
ejpam-3583	76	27	following	follow	VERB
ejpam-3583	76	28	triangle	triangle	NOUN
ejpam-3583	76	29	of	of	ADP
ejpam-3583	76	30	numbers	number	NOUN
ejpam-3583	76	31	1	1	NUM
ejpam-3583	76	32	1	1	NUM
ejpam-3583	76	33	1	1	NUM
ejpam-3583	76	34	1	1	NUM
ejpam-3583	76	35	2	2	NUM
ejpam-3583	76	36	1	1	NUM
ejpam-3583	76	37	1	1	NUM
ejpam-3583	76	38	3	3	NUM
ejpam-3583	76	39	3	3	NUM
ejpam-3583	76	40	1	1	NUM
ejpam-3583	76	41	.	.	PUNCT
ejpam-3583	76	42	r.	r.	PROPN
ejpam-3583	76	43	corcino	corcino	PROPN
ejpam-3583	76	44	,	,	PUNCT
ejpam-3583	76	45	j.	j.	PROPN
ejpam-3583	76	46	ontolan	ontolan	PROPN
ejpam-3583	76	47	,	,	PUNCT
ejpam-3583	76	48	g.	g.	PROPN
ejpam-3583	76	49	j.	j.	PROPN
ejpam-3583	76	50	rama	rama	PROPN
ejpam-3583	76	51	/	/	SYM
ejpam-3583	76	52	eur	eur	PROPN
ejpam-3583	76	53	.	.	PUNCT
ejpam-3583	77	1	j.	j.	PROPN
ejpam-3583	77	2	pure	pure	PROPN
ejpam-3583	77	3	appl	appl	PROPN
ejpam-3583	77	4	.	.	PROPN
ejpam-3583	77	5	math	math	PROPN
ejpam-3583	77	6	,	,	PUNCT
ejpam-3583	77	7	12	12	NUM
ejpam-3583	77	8	(	(	PUNCT
ejpam-3583	77	9	4	4	NUM
ejpam-3583	77	10	)	)	PUNCT
ejpam-3583	77	11	(	(	PUNCT
ejpam-3583	77	12	2019	2019	NUM
ejpam-3583	77	13	)	)	PUNCT
ejpam-3583	77	14	,	,	PUNCT
ejpam-3583	77	15	1676	1676	NUM
ejpam-3583	77	16	-	-	SYM
ejpam-3583	77	17	1688	1688	NUM
ejpam-3583	77	18	1680	1680	NUM
ejpam-3583	77	19	this	this	PRON
ejpam-3583	77	20	can	can	AUX
ejpam-3583	77	21	be	be	AUX
ejpam-3583	77	22	written	write	VERB
ejpam-3583	77	23	as	as	ADP
ejpam-3583	77	24	(	(	PUNCT
ejpam-3583	77	25	0	0	NUM
ejpam-3583	77	26	0	0	NUM
ejpam-3583	77	27	)	)	PUNCT
ejpam-3583	77	28	(	(	PUNCT
ejpam-3583	77	29	1	1	NUM
ejpam-3583	77	30	0	0	NUM
ejpam-3583	77	31	)	)	PUNCT
ejpam-3583	77	32	(	(	PUNCT
ejpam-3583	77	33	1	1	NUM
ejpam-3583	77	34	1	1	NUM
ejpam-3583	77	35	)	)	PUNCT
ejpam-3583	77	36	(	(	PUNCT
ejpam-3583	77	37	2	2	NUM
ejpam-3583	77	38	0	0	NUM
ejpam-3583	77	39	)	)	PUNCT
ejpam-3583	77	40	(	(	PUNCT
ejpam-3583	77	41	2	2	NUM
ejpam-3583	77	42	1	1	NUM
ejpam-3583	77	43	)	)	PUNCT
ejpam-3583	77	44	(	(	PUNCT
ejpam-3583	77	45	2	2	NUM
ejpam-3583	77	46	2	2	NUM
ejpam-3583	77	47	)	)	PUNCT
ejpam-3583	77	48	(	(	PUNCT
ejpam-3583	77	49	3	3	NUM
ejpam-3583	77	50	0	0	NUM
ejpam-3583	77	51	)	)	PUNCT
ejpam-3583	77	52	(	(	PUNCT
ejpam-3583	77	53	3	3	NUM
ejpam-3583	77	54	1	1	NUM
ejpam-3583	77	55	)	)	PUNCT
ejpam-3583	77	56	(	(	PUNCT
ejpam-3583	77	57	3	3	NUM
ejpam-3583	77	58	2	2	NUM
ejpam-3583	77	59	)	)	PUNCT
ejpam-3583	77	60	(	(	PUNCT
ejpam-3583	77	61	3	3	NUM
ejpam-3583	77	62	3	3	NUM
ejpam-3583	77	63	)	)	PUNCT
ejpam-3583	77	64	,	,	PUNCT
ejpam-3583	77	65	which	which	PRON
ejpam-3583	77	66	is	be	AUX
ejpam-3583	77	67	a	a	DET
ejpam-3583	77	68	portion	portion	NOUN
ejpam-3583	77	69	of	of	ADP
ejpam-3583	77	70	pascal	pascal	PROPN
ejpam-3583	77	71	’s	’s	PART
ejpam-3583	77	72	triangle	triangle	NOUN
ejpam-3583	77	73	.	.	PUNCT
ejpam-3583	78	1	the	the	DET
ejpam-3583	78	2	following	follow	VERB
ejpam-3583	78	3	theorem	theorem	NOUN
ejpam-3583	78	4	generalizes	generalize	VERB
ejpam-3583	78	5	the	the	DET
ejpam-3583	78	6	above	above	ADJ
ejpam-3583	78	7	observation	observation	NOUN
ejpam-3583	78	8	.	.	PUNCT
ejpam-3583	79	1	theorem	theorem	VERB
ejpam-3583	79	2	2.1	2.1	NUM
ejpam-3583	79	3	.	.	PUNCT
ejpam-3583	80	1	the	the	DET
ejpam-3583	80	2	q	q	NOUN
ejpam-3583	80	3	-	-	PUNCT
ejpam-3583	80	4	analogue	analogue	NOUN
ejpam-3583	80	5	w	w	PROPN
ejpam-3583	80	6	∗m	∗m	NOUN
ejpam-3583	80	7	,	,	PUNCT
ejpam-3583	80	8	r[n	r[n	NOUN
ejpam-3583	80	9	,	,	PUNCT
ejpam-3583	80	10	k]q	k]q	VERB
ejpam-3583	80	11	satisfies	satisfy	VERB
ejpam-3583	80	12	the	the	DET
ejpam-3583	80	13	following	follow	VERB
ejpam-3583	80	14	congruence	congruence	PROPN
ejpam-3583	80	15	relations	relation	NOUN
ejpam-3583	80	16	w	w	ADP
ejpam-3583	80	17	∗m	∗m	NOUN
ejpam-3583	80	18	,	,	PUNCT
ejpam-3583	80	19	r[n	r[n	NOUN
ejpam-3583	80	20	,	,	PUNCT
ejpam-3583	80	21	k]q	k]q	NOUN
ejpam-3583	80	22	≡	≡	PROPN
ejpam-3583	80	23	(	(	PUNCT
ejpam-3583	80	24	n	n	NOUN
ejpam-3583	80	25	k	k	PROPN
ejpam-3583	80	26	)	)	PUNCT
ejpam-3583	80	27	(	(	PUNCT
ejpam-3583	80	28	mod	mod	PROPN
ejpam-3583	80	29	q	q	NOUN
ejpam-3583	80	30	)	)	PUNCT
ejpam-3583	80	31	.	.	PUNCT
ejpam-3583	81	1	(	(	PUNCT
ejpam-3583	81	2	15	15	X
ejpam-3583	81	3	)	)	PUNCT
ejpam-3583	81	4	proof	proof	NOUN
ejpam-3583	81	5	.	.	PUNCT
ejpam-3583	82	1	we	we	PRON
ejpam-3583	82	2	recall	recall	VERB
ejpam-3583	82	3	the	the	DET
ejpam-3583	82	4	rational	rational	ADJ
ejpam-3583	82	5	generating	generating	NOUN
ejpam-3583	82	6	function	function	NOUN
ejpam-3583	82	7	[	[	X
ejpam-3583	82	8	13	13	NUM
ejpam-3583	82	9	]	]	PUNCT
ejpam-3583	82	10	for	for	ADP
ejpam-3583	82	11	w	w	PROPN
ejpam-3583	82	12	∗m	∗m	NOUN
ejpam-3583	82	13	,	,	PUNCT
ejpam-3583	82	14	r[n	r[n	NOUN
ejpam-3583	82	15	,	,	PUNCT
ejpam-3583	82	16	k]q	k]q	NOUN
ejpam-3583	82	17	is	be	AUX
ejpam-3583	82	18	given	give	VERB
ejpam-3583	82	19	by	by	ADP
ejpam-3583	82	20	ψ∗k(t	ψ∗k(t	PUNCT
ejpam-3583	82	21	)	)	PUNCT
ejpam-3583	82	22	=	=	PUNCT
ejpam-3583	83	1	∑	∑	PUNCT
ejpam-3583	83	2	n≥0	n≥0	PROPN
ejpam-3583	83	3	w	w	PROPN
ejpam-3583	83	4	∗m	∗m	NOUN
ejpam-3583	83	5	,	,	PUNCT
ejpam-3583	83	6	r[n	r[n	NOUN
ejpam-3583	83	7	,	,	PUNCT
ejpam-3583	83	8	k]q[t	k]q[t	X
ejpam-3583	83	9	]	]	X
ejpam-3583	83	10	n	n	PRON
ejpam-3583	83	11	q	q	NOUN
ejpam-3583	84	1	=	=	PUNCT
ejpam-3583	85	1	[	[	X
ejpam-3583	85	2	t]kq∏k	t]kq∏k	PROPN
ejpam-3583	85	3	j=0(1−	j=0(1−	PROPN
ejpam-3583	85	4	[	[	X
ejpam-3583	85	5	mj	mj	X
ejpam-3583	85	6	+	+	NUM
ejpam-3583	85	7	r]q[t]q	r]q[t]q	NUM
ejpam-3583	85	8	)	)	PUNCT
ejpam-3583	85	9	.	.	PUNCT
ejpam-3583	86	1	since	since	SCONJ
ejpam-3583	86	2	1	1	NUM
ejpam-3583	86	3	1−	1−	NUM
ejpam-3583	86	4	[	[	X
ejpam-3583	86	5	mj	mj	NOUN
ejpam-3583	86	6	+	+	NUM
ejpam-3583	86	7	r]q[t]q	r]q[t]q	NOUN
ejpam-3583	86	8	=	=	NOUN
ejpam-3583	86	9	∑	∑	PUNCT
ejpam-3583	86	10	n≥0	n≥0	PROPN
ejpam-3583	86	11	[	[	X
ejpam-3583	86	12	mj	mj	NOUN
ejpam-3583	86	13	+	+	NOUN
ejpam-3583	86	14	r]nq	r]nq	X
ejpam-3583	86	15	[	[	X
ejpam-3583	86	16	t]nq	t]nq	NOUN
ejpam-3583	86	17	=	=	SYM
ejpam-3583	86	18	∑	∑	PUNCT
ejpam-3583	86	19	n≥0	n≥0	PROPN
ejpam-3583	86	20	(	(	PUNCT
ejpam-3583	86	21	1	1	NUM
ejpam-3583	86	22	+	+	NOUN
ejpam-3583	86	23	q	q	NOUN
ejpam-3583	86	24	+	+	NUM
ejpam-3583	86	25	q2	q2	NOUN
ejpam-3583	86	26	+	+	CCONJ
ejpam-3583	86	27	...	...	PUNCT
ejpam-3583	86	28	+	+	NUM
ejpam-3583	86	29	qmj+r−1)n[t]nq	qmj+r−1)n[t]nq	NOUN
ejpam-3583	86	30	=	=	SYM
ejpam-3583	86	31	∑	∑	PUNCT
ejpam-3583	86	32	n≥0	n≥0	PROPN
ejpam-3583	86	33	(	(	PUNCT
ejpam-3583	86	34	1	1	NUM
ejpam-3583	86	35	+	+	CCONJ
ejpam-3583	86	36	qy)n[t]nq	qy)n[t]nq	NOUN
ejpam-3583	86	37	,	,	PUNCT
ejpam-3583	86	38	where	where	SCONJ
ejpam-3583	86	39	y	y	PROPN
ejpam-3583	86	40	in	in	ADP
ejpam-3583	86	41	q.	q.	PROPN
ejpam-3583	86	42	then	then	ADV
ejpam-3583	86	43	1	1	NUM
ejpam-3583	86	44	1−	1−	NUM
ejpam-3583	86	45	[	[	X
ejpam-3583	86	46	mj	mj	X
ejpam-3583	86	47	+	+	NUM
ejpam-3583	86	48	r]q[t]q	r]q[t]q	NOUN
ejpam-3583	86	49	=	=	NOUN
ejpam-3583	86	50	∑	∑	PROPN
ejpam-3583	86	51	n≥0	n≥0	PROPN
ejpam-3583	86	52	(	(	PUNCT
ejpam-3583	86	53	1	1	NUM
ejpam-3583	86	54	+	+	NOUN
ejpam-3583	86	55	qzn)[t]nq	qzn)[t]nq	NOUN
ejpam-3583	86	56	for	for	ADP
ejpam-3583	86	57	some	some	DET
ejpam-3583	86	58	polynomial	polynomial	ADJ
ejpam-3583	86	59	zn	zn	PROPN
ejpam-3583	86	60	in	in	ADP
ejpam-3583	86	61	q.	q.	PROPN
ejpam-3583	86	62	hence	hence	ADV
ejpam-3583	86	63	,	,	PUNCT
ejpam-3583	86	64	1	1	NUM
ejpam-3583	86	65	1−	1−	NUM
ejpam-3583	86	66	[	[	X
ejpam-3583	86	67	mj	mj	X
ejpam-3583	86	68	+	+	NUM
ejpam-3583	86	69	r]q[t]q	r]q[t]q	NOUN
ejpam-3583	86	70	=	=	NOUN
ejpam-3583	86	71	∑	∑	PUNCT
ejpam-3583	86	72	n≥0	n≥0	PROPN
ejpam-3583	86	73	[	[	X
ejpam-3583	86	74	t]nq	t]nq	NOUN
ejpam-3583	86	75	+	+	CCONJ
ejpam-3583	86	76	q	q	NOUN
ejpam-3583	86	77	∑	∑	PUNCT
ejpam-3583	86	78	n≥0	n≥0	PROPN
ejpam-3583	86	79	zn[t]nq	zn[t]nq	PROPN
ejpam-3583	86	80	≡	≡	PROPN
ejpam-3583	86	81	∑	∑	PROPN
ejpam-3583	86	82	n≥0	n≥0	PROPN
ejpam-3583	86	83	[	[	X
ejpam-3583	86	84	t]nq	t]nq	X
ejpam-3583	86	85	(	(	PUNCT
ejpam-3583	86	86	mod	mod	PROPN
ejpam-3583	86	87	q	q	ADJ
ejpam-3583	86	88	)	)	PUNCT
ejpam-3583	86	89	≡	≡	PROPN
ejpam-3583	86	90	(	(	PUNCT
ejpam-3583	86	91	1	1	NUM
ejpam-3583	86	92	1−	1−	NUM
ejpam-3583	86	93	[	[	X
ejpam-3583	86	94	t]q	t]q	X
ejpam-3583	86	95	)	)	PUNCT
ejpam-3583	86	96	(	(	PUNCT
ejpam-3583	86	97	mod	mod	PROPN
ejpam-3583	86	98	q	q	NOUN
ejpam-3583	86	99	)	)	PUNCT
ejpam-3583	86	100	then	then	ADV
ejpam-3583	86	101	ψ∗k(t	ψ∗k(t	PUNCT
ejpam-3583	86	102	)	)	PUNCT
ejpam-3583	86	103	=	=	PUNCT
ejpam-3583	86	104	∑	∑	PUNCT
ejpam-3583	86	105	n≥0	n≥0	PROPN
ejpam-3583	86	106	w	w	PROPN
ejpam-3583	86	107	∗m	∗m	NOUN
ejpam-3583	86	108	,	,	PUNCT
ejpam-3583	86	109	r[n	r[n	NOUN
ejpam-3583	86	110	,	,	PUNCT
ejpam-3583	86	111	k]q[t	k]q[t	X
ejpam-3583	86	112	]	]	X
ejpam-3583	86	113	n	n	PRON
ejpam-3583	86	114	q	q	NOUN
ejpam-3583	87	1	=	=	PUNCT
ejpam-3583	88	1	[	[	X
ejpam-3583	88	2	t]kq∏k	t]kq∏k	PROPN
ejpam-3583	88	3	j=0(1−	j=0(1−	PROPN
ejpam-3583	88	4	[	[	X
ejpam-3583	88	5	mj	mj	X
ejpam-3583	88	6	+	+	NUM
ejpam-3583	88	7	r]q[t]q	r]q[t]q	NUM
ejpam-3583	88	8	)	)	PUNCT
ejpam-3583	88	9	r.	r.	PROPN
ejpam-3583	88	10	corcino	corcino	PROPN
ejpam-3583	88	11	,	,	PUNCT
ejpam-3583	88	12	j.	j.	PROPN
ejpam-3583	88	13	ontolan	ontolan	PROPN
ejpam-3583	88	14	,	,	PUNCT
ejpam-3583	88	15	g.	g.	PROPN
ejpam-3583	88	16	j.	j.	PROPN
ejpam-3583	88	17	rama	rama	PROPN
ejpam-3583	88	18	/	/	SYM
ejpam-3583	88	19	eur	eur	PROPN
ejpam-3583	88	20	.	.	PUNCT
ejpam-3583	89	1	j.	j.	PROPN
ejpam-3583	89	2	pure	pure	PROPN
ejpam-3583	89	3	appl	appl	PROPN
ejpam-3583	89	4	.	.	PROPN
ejpam-3583	89	5	math	math	PROPN
ejpam-3583	89	6	,	,	PUNCT
ejpam-3583	89	7	12	12	NUM
ejpam-3583	89	8	(	(	PUNCT
ejpam-3583	89	9	4	4	NUM
ejpam-3583	89	10	)	)	PUNCT
ejpam-3583	89	11	(	(	PUNCT
ejpam-3583	89	12	2019	2019	NUM
ejpam-3583	89	13	)	)	PUNCT
ejpam-3583	89	14	,	,	PUNCT
ejpam-3583	89	15	1676	1676	NUM
ejpam-3583	89	16	-	-	SYM
ejpam-3583	89	17	1688	1688	NUM
ejpam-3583	89	18	1681	1681	NUM
ejpam-3583	89	19	≡	≡	PROPN
ejpam-3583	90	1	[	[	X
ejpam-3583	90	2	t]kq	t]kq	PROPN
ejpam-3583	90	3	(	(	PUNCT
ejpam-3583	90	4	1	1	NUM
ejpam-3583	90	5	(	(	PUNCT
ejpam-3583	90	6	1−	1−	NUM
ejpam-3583	91	1	[	[	X
ejpam-3583	91	2	t]q)k+1	t]q)k+1	PROPN
ejpam-3583	91	3	)	)	PUNCT
ejpam-3583	91	4	(	(	PUNCT
ejpam-3583	91	5	mod	mod	PROPN
ejpam-3583	91	6	q	q	NOUN
ejpam-3583	91	7	)	)	PUNCT
ejpam-3583	91	8	.	.	PUNCT
ejpam-3583	92	1	using	use	VERB
ejpam-3583	92	2	the	the	DET
ejpam-3583	92	3	newton	newton	PROPN
ejpam-3583	92	4	’s	’s	PART
ejpam-3583	92	5	binomial	binomial	PROPN
ejpam-3583	92	6	theorem	theorem	NOUN
ejpam-3583	92	7	,	,	PUNCT
ejpam-3583	92	8	we	we	PRON
ejpam-3583	92	9	have∑	have∑	VERB
ejpam-3583	92	10	n≥0	n≥0	PROPN
ejpam-3583	92	11	w	w	PROPN
ejpam-3583	92	12	∗m	∗m	NOUN
ejpam-3583	92	13	,	,	PUNCT
ejpam-3583	92	14	r[n	r[n	NOUN
ejpam-3583	92	15	,	,	PUNCT
ejpam-3583	92	16	k]q[t	k]q[t	X
ejpam-3583	92	17	]	]	X
ejpam-3583	92	18	n	n	PRON
ejpam-3583	92	19	q	q	PROPN
ejpam-3583	92	20	≡	≡	PROPN
ejpam-3583	93	1	[	[	X
ejpam-3583	93	2	t]kq	t]kq	X
ejpam-3583	93	3	∑	∑	PUNCT
ejpam-3583	93	4	n≥0	n≥0	PROPN
ejpam-3583	93	5	(	(	PUNCT
ejpam-3583	93	6	n+	n+	X
ejpam-3583	93	7	(	(	PUNCT
ejpam-3583	93	8	k	k	PROPN
ejpam-3583	93	9	+	+	PROPN
ejpam-3583	93	10	1)−	1)−	PROPN
ejpam-3583	93	11	1	1	NUM
ejpam-3583	93	12	n	n	NOUN
ejpam-3583	93	13	)	)	PUNCT
ejpam-3583	94	1	[	[	X
ejpam-3583	94	2	t]nq	t]nq	X
ejpam-3583	94	3	(	(	PUNCT
ejpam-3583	94	4	mod	mod	PROPN
ejpam-3583	94	5	q	q	ADJ
ejpam-3583	94	6	)	)	PUNCT
ejpam-3583	94	7	≡	≡	PROPN
ejpam-3583	94	8	∑	∑	PUNCT
ejpam-3583	94	9	n≥0	n≥0	PROPN
ejpam-3583	94	10	(	(	PUNCT
ejpam-3583	94	11	n+	n+	NUM
ejpam-3583	94	12	k	k	NOUN
ejpam-3583	94	13	n	n	CCONJ
ejpam-3583	94	14	)	)	PUNCT
ejpam-3583	95	1	[	[	X
ejpam-3583	95	2	t]n+kq	t]n+kq	X
ejpam-3583	95	3	(	(	PUNCT
ejpam-3583	95	4	mod	mod	PROPN
ejpam-3583	95	5	q	q	ADJ
ejpam-3583	95	6	)	)	PUNCT
ejpam-3583	95	7	≡	≡	PROPN
ejpam-3583	95	8	∑	∑	PROPN
ejpam-3583	95	9	n≥k	n≥k	PROPN
ejpam-3583	95	10	(	(	PUNCT
ejpam-3583	95	11	n−	n−	NOUN
ejpam-3583	95	12	k	k	NOUN
ejpam-3583	95	13	+	+	CCONJ
ejpam-3583	95	14	k	k	PROPN
ejpam-3583	95	15	n−	n−	NOUN
ejpam-3583	95	16	k	k	PROPN
ejpam-3583	95	17	)	)	PUNCT
ejpam-3583	96	1	[	[	X
ejpam-3583	96	2	t]n+k−kq	t]n+k−kq	X
ejpam-3583	96	3	(	(	PUNCT
ejpam-3583	96	4	mod	mod	PROPN
ejpam-3583	96	5	q	q	ADJ
ejpam-3583	96	6	)	)	PUNCT
ejpam-3583	96	7	≡	≡	PROPN
ejpam-3583	96	8	∑	∑	PROPN
ejpam-3583	96	9	n≥k	n≥k	PROPN
ejpam-3583	96	10	(	(	PUNCT
ejpam-3583	96	11	n	n	NOUN
ejpam-3583	96	12	k	k	NOUN
ejpam-3583	96	13	)	)	PUNCT
ejpam-3583	97	1	[	[	X
ejpam-3583	97	2	t]nq	t]nq	X
ejpam-3583	97	3	(	(	PUNCT
ejpam-3583	97	4	mod	mod	PROPN
ejpam-3583	97	5	q	q	NOUN
ejpam-3583	97	6	)	)	PUNCT
ejpam-3583	97	7	.	.	PUNCT
ejpam-3583	98	1	comparing	compare	VERB
ejpam-3583	98	2	the	the	DET
ejpam-3583	98	3	coefficients	coefficient	NOUN
ejpam-3583	98	4	of	of	ADP
ejpam-3583	98	5	[	[	X
ejpam-3583	98	6	t]nq	t]nq	NOUN
ejpam-3583	98	7	completes	complete	VERB
ejpam-3583	98	8	the	the	DET
ejpam-3583	98	9	proof	proof	NOUN
ejpam-3583	98	10	of	of	ADP
ejpam-3583	98	11	the	the	DET
ejpam-3583	98	12	theorem	theorem	NOUN
ejpam-3583	98	13	.	.	PROPN
ejpam-3583	98	14	3	3	X
ejpam-3583	98	15	.	.	X
ejpam-3583	98	16	hankel	hankel	NOUN
ejpam-3583	98	17	transform	transform	NOUN
ejpam-3583	98	18	of	of	ADP
ejpam-3583	98	19	d∗m	d∗m	NOUN
ejpam-3583	98	20	,	,	PUNCT
ejpam-3583	98	21	r[n]q	r[n]q	NOUN
ejpam-3583	98	22	we	we	PRON
ejpam-3583	98	23	recall	recall	VERB
ejpam-3583	98	24	that	that	SCONJ
ejpam-3583	98	25	the	the	DET
ejpam-3583	98	26	horizontal	horizontal	ADJ
ejpam-3583	98	27	generating	generating	NOUN
ejpam-3583	98	28	function	function	NOUN
ejpam-3583	98	29	for	for	ADP
ejpam-3583	98	30	wm	wm	PROPN
ejpam-3583	98	31	,	,	PUNCT
ejpam-3583	98	32	r[n	r[n	NOUN
ejpam-3583	98	33	,	,	PUNCT
ejpam-3583	98	34	k]q	k]q	NOUN
ejpam-3583	98	35	is	be	AUX
ejpam-3583	98	36	given	give	VERB
ejpam-3583	98	37	by	by	ADP
ejpam-3583	98	38	n∑	n∑	PROPN
ejpam-3583	98	39	k=0	k=0	PROPN
ejpam-3583	98	40	wm	wm	PROPN
ejpam-3583	98	41	,	,	PUNCT
ejpam-3583	98	42	r[n	r[n	PROPN
ejpam-3583	98	43	,	,	PUNCT
ejpam-3583	98	44	k]q[x−	k]q[x−	PROPN
ejpam-3583	98	45	r|m]k	r|m]k	NUM
ejpam-3583	98	46	,	,	PUNCT
ejpam-3583	98	47	q	q	X
ejpam-3583	98	48	=	=	PUNCT
ejpam-3583	99	1	[	[	X
ejpam-3583	99	2	x]nq	x]nq	X
ejpam-3583	99	3	.	.	PUNCT
ejpam-3583	100	1	(	(	PUNCT
ejpam-3583	100	2	16	16	NUM
ejpam-3583	100	3	)	)	PUNCT
ejpam-3583	100	4	using	use	VERB
ejpam-3583	100	5	the	the	DET
ejpam-3583	100	6	fact	fact	NOUN
ejpam-3583	100	7	that	that	SCONJ
ejpam-3583	100	8	[	[	X
ejpam-3583	100	9	x−	x−	PROPN
ejpam-3583	100	10	r|m]k	r|m]k	PROPN
ejpam-3583	100	11	,	,	PUNCT
ejpam-3583	100	12	q	q	X
ejpam-3583	100	13	=	=	SYM
ejpam-3583	100	14	q−kr−m(k2)〈x〉r	q−kr−m(k2)〈x〉r	X
ejpam-3583	100	15	,	,	PUNCT
ejpam-3583	100	16	m	m	PROPN
ejpam-3583	100	17	,	,	PUNCT
ejpam-3583	100	18	k	k	NOUN
ejpam-3583	100	19	,	,	PUNCT
ejpam-3583	100	20	where	where	SCONJ
ejpam-3583	100	21	〈	〈	PROPN
ejpam-3583	100	22	x〉r	x〉r	PROPN
ejpam-3583	100	23	,	,	PUNCT
ejpam-3583	100	24	m	m	PROPN
ejpam-3583	100	25	,	,	PUNCT
ejpam-3583	100	26	k	k	PROPN
ejpam-3583	100	27	=	=	SYM
ejpam-3583	100	28	∏n−1	∏n−1	PROPN
ejpam-3583	100	29	j=0	j=0	PROPN
ejpam-3583	100	30	(	(	PUNCT
ejpam-3583	100	31	[	[	X
ejpam-3583	100	32	x]q	x]q	ADJ
ejpam-3583	100	33	−	−	PROPN
ejpam-3583	101	1	[	[	X
ejpam-3583	101	2	r	r	X
ejpam-3583	101	3	+	+	X
ejpam-3583	101	4	jm]q	jm]q	PROPN
ejpam-3583	101	5	)	)	PUNCT
ejpam-3583	101	6	,	,	PUNCT
ejpam-3583	101	7	we	we	PRON
ejpam-3583	101	8	can	can	AUX
ejpam-3583	101	9	write	write	VERB
ejpam-3583	101	10	(	(	PUNCT
ejpam-3583	101	11	16	16	NUM
ejpam-3583	101	12	)	)	PUNCT
ejpam-3583	101	13	as	as	SCONJ
ejpam-3583	101	14	follows	follow	VERB
ejpam-3583	101	15	n∑	n∑	PROPN
ejpam-3583	101	16	k=0	k=0	PROPN
ejpam-3583	101	17	q−kr−m(k2)wm	q−kr−m(k2)wm	PROPN
ejpam-3583	101	18	,	,	PUNCT
ejpam-3583	101	19	r[n	r[n	NOUN
ejpam-3583	101	20	,	,	PUNCT
ejpam-3583	101	21	k]q〈x〉r	k]q〈x〉r	PROPN
ejpam-3583	101	22	,	,	PUNCT
ejpam-3583	101	23	m	m	PROPN
ejpam-3583	101	24	,	,	PUNCT
ejpam-3583	101	25	k	k	X
ejpam-3583	102	1	=	=	PUNCT
ejpam-3583	103	1	[	[	X
ejpam-3583	103	2	x]nq	x]nq	X
ejpam-3583	103	3	n∑	n∑	PROPN
ejpam-3583	103	4	k=0	k=0	PROPN
ejpam-3583	104	1	w	w	PROPN
ejpam-3583	104	2	∗m	∗m	PROPN
ejpam-3583	104	3	,	,	PUNCT
ejpam-3583	104	4	r[n	r[n	NOUN
ejpam-3583	104	5	,	,	PUNCT
ejpam-3583	104	6	k]q〈x〉r	k]q〈x〉r	PROPN
ejpam-3583	104	7	,	,	PUNCT
ejpam-3583	104	8	m	m	PROPN
ejpam-3583	104	9	,	,	PUNCT
ejpam-3583	104	10	k	k	X
ejpam-3583	104	11	=	=	PUNCT
ejpam-3583	105	1	[	[	X
ejpam-3583	105	2	x]nq	x]nq	X
ejpam-3583	105	3	.	.	PUNCT
ejpam-3583	106	1	using	use	VERB
ejpam-3583	106	2	the	the	DET
ejpam-3583	106	3	method	method	NOUN
ejpam-3583	106	4	of	of	ADP
ejpam-3583	106	5	cigler	cigler	NOUN
ejpam-3583	106	6	[	[	X
ejpam-3583	106	7	8	8	NUM
ejpam-3583	106	8	]	]	PUNCT
ejpam-3583	106	9	,	,	PUNCT
ejpam-3583	106	10	let	let	VERB
ejpam-3583	106	11	d[n	d[n	NOUN
ejpam-3583	106	12	,	,	PUNCT
ejpam-3583	106	13	k	k	X
ejpam-3583	106	14	]	]	X
ejpam-3583	106	15	=	=	SYM
ejpam-3583	106	16	det	det	X
ejpam-3583	106	17	(	(	PUNCT
ejpam-3583	106	18	ai+j+k	ai+j+k	ADJ
ejpam-3583	106	19	)	)	PUNCT
ejpam-3583	106	20	n−1	n−1	PROPN
ejpam-3583	106	21	i	i	PROPN
ejpam-3583	106	22	,	,	PUNCT
ejpam-3583	106	23	j=0	j=0	PROPN
ejpam-3583	106	24	denote	denote	VERB
ejpam-3583	106	25	the	the	DET
ejpam-3583	106	26	kth	kth	PROPN
ejpam-3583	106	27	hankel	hankel	NOUN
ejpam-3583	106	28	determinant	determinant	ADJ
ejpam-3583	106	29	.	.	PUNCT
ejpam-3583	107	1	that	that	PRON
ejpam-3583	107	2	is	is	ADV
ejpam-3583	107	3	,	,	PUNCT
ejpam-3583	107	4	the	the	DET
ejpam-3583	107	5	0th	0th	ADJ
ejpam-3583	107	6	hankel	hankel	NOUN
ejpam-3583	107	7	determinant	determinant	ADJ
ejpam-3583	107	8	is	be	AUX
ejpam-3583	107	9	given	give	VERB
ejpam-3583	107	10	by	by	ADP
ejpam-3583	107	11	d[n	d[n	NOUN
ejpam-3583	107	12	,	,	PUNCT
ejpam-3583	107	13	0	0	NUM
ejpam-3583	107	14	]	]	PUNCT
ejpam-3583	107	15	=	=	SYM
ejpam-3583	107	16	det	det	PROPN
ejpam-3583	107	17			PROPN
ejpam-3583	107	18	a0	a0	PROPN
ejpam-3583	107	19	a1	a1	PROPN
ejpam-3583	107	20	a2	a2	PROPN
ejpam-3583	107	21	.	.	PUNCT
ejpam-3583	107	22	.	.	PUNCT
ejpam-3583	107	23	.	.	PUNCT
ejpam-3583	108	1	an−1	an−1	ADJ
ejpam-3583	108	2	a1	a1	NOUN
ejpam-3583	108	3	a2	a2	PROPN
ejpam-3583	108	4	a3	a3	NOUN
ejpam-3583	108	5	.	.	PUNCT
ejpam-3583	108	6	.	.	PUNCT
ejpam-3583	108	7	.	.	PUNCT
ejpam-3583	109	1	an	an	PRON
ejpam-3583	109	2	.	.	PUNCT
ejpam-3583	109	3	.	.	PUNCT
ejpam-3583	109	4	.	.	PUNCT
ejpam-3583	109	5	.	.	PUNCT
ejpam-3583	109	6	.	.	PUNCT
ejpam-3583	109	7	.	.	PUNCT
ejpam-3583	109	8	.	.	PUNCT
ejpam-3583	109	9	.	.	PUNCT
ejpam-3583	109	10	.	.	PUNCT
ejpam-3583	109	11	.	.	PUNCT
ejpam-3583	109	12	.	.	PUNCT
ejpam-3583	109	13	.	.	PUNCT
ejpam-3583	109	14	.	.	PUNCT
ejpam-3583	109	15	.	.	PUNCT
ejpam-3583	109	16	.	.	PUNCT
ejpam-3583	109	17	.	.	PUNCT
ejpam-3583	109	18	.	.	PUNCT
ejpam-3583	109	19	.	.	PUNCT
ejpam-3583	109	20	.	.	PUNCT
ejpam-3583	109	21	.	.	PUNCT
ejpam-3583	109	22	.	.	PUNCT
ejpam-3583	109	23	.	.	PUNCT
ejpam-3583	109	24	.	.	PUNCT
ejpam-3583	109	25	.	.	PUNCT
ejpam-3583	109	26	.	.	PUNCT
ejpam-3583	109	27	.	.	PUNCT
ejpam-3583	109	28	.	.	PUNCT
ejpam-3583	109	29	.	.	PUNCT
ejpam-3583	110	1	an−1	an−1	ADV
ejpam-3583	110	2	an	an	DET
ejpam-3583	110	3	an+1	an+1	NOUN
ejpam-3583	110	4	.	.	PUNCT
ejpam-3583	110	5	.	.	PUNCT
ejpam-3583	110	6	.	.	PUNCT
ejpam-3583	111	1	a2n−2	a2n−2	ADP
ejpam-3583	111	2			PROPN
ejpam-3583	111	3	r.	r.	PROPN
ejpam-3583	111	4	corcino	corcino	PROPN
ejpam-3583	111	5	,	,	PUNCT
ejpam-3583	111	6	j.	j.	PROPN
ejpam-3583	111	7	ontolan	ontolan	PROPN
ejpam-3583	111	8	,	,	PUNCT
ejpam-3583	111	9	g.	g.	PROPN
ejpam-3583	111	10	j.	j.	PROPN
ejpam-3583	111	11	rama	rama	PROPN
ejpam-3583	111	12	/	/	SYM
ejpam-3583	111	13	eur	eur	PROPN
ejpam-3583	111	14	.	.	PUNCT
ejpam-3583	112	1	j.	j.	PROPN
ejpam-3583	112	2	pure	pure	PROPN
ejpam-3583	112	3	appl	appl	PROPN
ejpam-3583	112	4	.	.	PROPN
ejpam-3583	112	5	math	math	PROPN
ejpam-3583	112	6	,	,	PUNCT
ejpam-3583	112	7	12	12	NUM
ejpam-3583	112	8	(	(	PUNCT
ejpam-3583	112	9	4	4	NUM
ejpam-3583	112	10	)	)	PUNCT
ejpam-3583	112	11	(	(	PUNCT
ejpam-3583	112	12	2019	2019	NUM
ejpam-3583	112	13	)	)	PUNCT
ejpam-3583	112	14	,	,	PUNCT
ejpam-3583	112	15	1676	1676	NUM
ejpam-3583	112	16	-	-	SYM
ejpam-3583	112	17	1688	1688	NUM
ejpam-3583	112	18	1682	1682	NUM
ejpam-3583	112	19	and	and	CCONJ
ejpam-3583	112	20	the	the	DET
ejpam-3583	112	21	1st	1st	ADJ
ejpam-3583	112	22	hankel	hankel	NOUN
ejpam-3583	112	23	determinant	determinant	ADJ
ejpam-3583	112	24	is	be	AUX
ejpam-3583	112	25	given	give	VERB
ejpam-3583	112	26	by	by	ADP
ejpam-3583	112	27	d[n	d[n	NOUN
ejpam-3583	112	28	,	,	PUNCT
ejpam-3583	112	29	1	1	NUM
ejpam-3583	112	30	]	]	PUNCT
ejpam-3583	112	31	=	=	SYM
ejpam-3583	112	32	det	det	PROPN
ejpam-3583	112	33			NOUN
ejpam-3583	112	34	a1	a1	PROPN
ejpam-3583	112	35	a2	a2	PROPN
ejpam-3583	112	36	a3	a3	NOUN
ejpam-3583	112	37	.	.	PUNCT
ejpam-3583	112	38	.	.	PUNCT
ejpam-3583	112	39	.	.	PUNCT
ejpam-3583	113	1	an	an	DET
ejpam-3583	113	2	a2	a2	PROPN
ejpam-3583	113	3	a3	a3	NOUN
ejpam-3583	113	4	a4	a4	PROPN
ejpam-3583	113	5	.	.	PUNCT
ejpam-3583	113	6	.	.	PUNCT
ejpam-3583	113	7	.	.	PUNCT
ejpam-3583	114	1	an+1	an+1	INTJ
ejpam-3583	114	2	.	.	PUNCT
ejpam-3583	114	3	.	.	PUNCT
ejpam-3583	114	4	.	.	PUNCT
ejpam-3583	114	5	.	.	PUNCT
ejpam-3583	114	6	.	.	PUNCT
ejpam-3583	114	7	.	.	PUNCT
ejpam-3583	114	8	.	.	PUNCT
ejpam-3583	114	9	.	.	PUNCT
ejpam-3583	114	10	.	.	PUNCT
ejpam-3583	114	11	.	.	PUNCT
ejpam-3583	114	12	.	.	PUNCT
ejpam-3583	114	13	.	.	PUNCT
ejpam-3583	114	14	.	.	PUNCT
ejpam-3583	114	15	.	.	PUNCT
ejpam-3583	114	16	.	.	PUNCT
ejpam-3583	114	17	.	.	PUNCT
ejpam-3583	114	18	.	.	PUNCT
ejpam-3583	114	19	.	.	PUNCT
ejpam-3583	114	20	.	.	PUNCT
ejpam-3583	114	21	.	.	PUNCT
ejpam-3583	114	22	.	.	PUNCT
ejpam-3583	114	23	.	.	PUNCT
ejpam-3583	114	24	.	.	PUNCT
ejpam-3583	114	25	.	.	PUNCT
ejpam-3583	114	26	.	.	PUNCT
ejpam-3583	114	27	.	.	PUNCT
ejpam-3583	114	28	.	.	PUNCT
ejpam-3583	114	29	.	.	PUNCT
ejpam-3583	115	1	an	an	DET
ejpam-3583	115	2	an+1	an+1	NOUN
ejpam-3583	115	3	an+2	an+2	ADV
ejpam-3583	115	4	.	.	PUNCT
ejpam-3583	115	5	.	.	PUNCT
ejpam-3583	115	6	.	.	PUNCT
ejpam-3583	116	1	a2n−1	a2n−1	PROPN
ejpam-3583	116	2			PROPN
ejpam-3583	116	3	.	.	PUNCT
ejpam-3583	117	1	now	now	ADV
ejpam-3583	117	2	,	,	PUNCT
ejpam-3583	117	3	define	define	VERB
ejpam-3583	117	4	a	a	DET
ejpam-3583	117	5	linear	linear	ADJ
ejpam-3583	117	6	functional	functional	ADJ
ejpam-3583	117	7	f	f	NOUN
ejpam-3583	117	8	on	on	ADP
ejpam-3583	117	9	the	the	DET
ejpam-3583	117	10	polynomial	polynomial	NOUN
ejpam-3583	117	11	by	by	ADP
ejpam-3583	117	12	f	f	PROPN
ejpam-3583	117	13	(	(	PUNCT
ejpam-3583	117	14	xn	xn	PROPN
ejpam-3583	117	15	)	)	PUNCT
ejpam-3583	117	16	=	=	PUNCT
ejpam-3583	118	1	an	an	PRON
ejpam-3583	118	2	by	by	ADP
ejpam-3583	118	3	gram	gram	NOUN
ejpam-3583	118	4	-	-	PUNCT
ejpam-3583	118	5	schmidt	schmidt	NOUN
ejpam-3583	118	6	orthogonalization	orthogonalization	NOUN
ejpam-3583	118	7	process	process	NOUN
ejpam-3583	118	8	,	,	PUNCT
ejpam-3583	118	9	there	there	PRON
ejpam-3583	118	10	exists	exist	VERB
ejpam-3583	118	11	a	a	DET
ejpam-3583	118	12	sequence	sequence	NOUN
ejpam-3583	118	13	of	of	ADP
ejpam-3583	118	14	orthogonal	orthogonal	ADJ
ejpam-3583	118	15	polynomials	polynomial	NOUN
ejpam-3583	118	16	pn(x	pn(x	X
ejpam-3583	118	17	)	)	PUNCT
ejpam-3583	118	18	=	=	SYM
ejpam-3583	119	1	c0,n	c0,n	ADJ
ejpam-3583	119	2	+	+	X
ejpam-3583	119	3	c1,nx+	c1,nx+	PROPN
ejpam-3583	119	4	.	.	PUNCT
ejpam-3583	119	5	.	.	PUNCT
ejpam-3583	120	1	.+	.+	NOUN
ejpam-3583	120	2	cn−1,nx	cn−1,nx	VERB
ejpam-3583	121	1	n−1	n−1	PROPN
ejpam-3583	122	1	+	+	NUM
ejpam-3583	122	2	xn	xn	PROPN
ejpam-3583	122	3	(	(	PUNCT
ejpam-3583	122	4	cn	cn	PROPN
ejpam-3583	122	5	,	,	PUNCT
ejpam-3583	122	6	n	n	NOUN
ejpam-3583	122	7	=	=	SYM
ejpam-3583	122	8	1	1	NUM
ejpam-3583	122	9	)	)	PUNCT
ejpam-3583	122	10	with	with	ADP
ejpam-3583	122	11	respect	respect	NOUN
ejpam-3583	122	12	to	to	ADP
ejpam-3583	122	13	f	f	PROPN
ejpam-3583	122	14	such	such	ADJ
ejpam-3583	122	15	that	that	PRON
ejpam-3583	122	16	pn(x	pn(x	PUNCT
ejpam-3583	122	17	)	)	PUNCT
ejpam-3583	122	18	=	=	SYM
ejpam-3583	122	19	1	1	NUM
ejpam-3583	122	20	d[n	d[n	NOUN
ejpam-3583	122	21	,	,	PUNCT
ejpam-3583	122	22	0	0	NUM
ejpam-3583	122	23	]	]	X
ejpam-3583	122	24	det	det	PROPN
ejpam-3583	122	25			NOUN
ejpam-3583	122	26	a0	a0	PROPN
ejpam-3583	122	27	a1	a1	NOUN
ejpam-3583	122	28	a2	a2	PROPN
ejpam-3583	122	29	.	.	PUNCT
ejpam-3583	122	30	.	.	PUNCT
ejpam-3583	122	31	.	.	PUNCT
ejpam-3583	123	1	an−1	an−1	ADJ
ejpam-3583	123	2	1	1	NUM
ejpam-3583	123	3	a1	a1	NOUN
ejpam-3583	123	4	a2	a2	PROPN
ejpam-3583	123	5	a3	a3	NOUN
ejpam-3583	123	6	.	.	PUNCT
ejpam-3583	123	7	.	.	PUNCT
ejpam-3583	123	8	.	.	PUNCT
ejpam-3583	124	1	an	an	DET
ejpam-3583	124	2	x	x	PROPN
ejpam-3583	124	3	a2	a2	PROPN
ejpam-3583	124	4	a3	a3	NOUN
ejpam-3583	124	5	a4	a4	PROPN
ejpam-3583	124	6	.	.	PUNCT
ejpam-3583	124	7	.	.	PUNCT
ejpam-3583	124	8	.	.	PUNCT
ejpam-3583	125	1	an+1	an+1	AUX
ejpam-3583	126	1	x2	x2	INTJ
ejpam-3583	126	2	.	.	PUNCT
ejpam-3583	126	3	.	.	PUNCT
ejpam-3583	126	4	.	.	PUNCT
ejpam-3583	126	5	.	.	PUNCT
ejpam-3583	126	6	.	.	PUNCT
ejpam-3583	126	7	.	.	PUNCT
ejpam-3583	126	8	.	.	PUNCT
ejpam-3583	126	9	.	.	PUNCT
ejpam-3583	126	10	.	.	PUNCT
ejpam-3583	126	11	.	.	PUNCT
ejpam-3583	126	12	.	.	PUNCT
ejpam-3583	126	13	.	.	PUNCT
ejpam-3583	126	14	.	.	PUNCT
ejpam-3583	126	15	.	.	PUNCT
ejpam-3583	126	16	.	.	PUNCT
ejpam-3583	126	17	.	.	PUNCT
ejpam-3583	126	18	.	.	PUNCT
ejpam-3583	126	19	.	.	PUNCT
ejpam-3583	126	20	.	.	PUNCT
ejpam-3583	126	21	.	.	PUNCT
ejpam-3583	126	22	.	.	PUNCT
ejpam-3583	126	23	.	.	PUNCT
ejpam-3583	126	24	.	.	PUNCT
ejpam-3583	126	25	.	.	PUNCT
ejpam-3583	126	26	.	.	PUNCT
ejpam-3583	126	27	.	.	PUNCT
ejpam-3583	126	28	.	.	PUNCT
ejpam-3583	127	1	an	an	DET
ejpam-3583	127	2	an+1	an+1	NOUN
ejpam-3583	127	3	an+2	an+2	ADV
ejpam-3583	127	4	.	.	PUNCT
ejpam-3583	127	5	.	.	PUNCT
ejpam-3583	127	6	.	.	PUNCT
ejpam-3583	128	1	a2n	a2n	PROPN
ejpam-3583	128	2	.	.	PUNCT
ejpam-3583	129	1	xn	xn	PROPN
ejpam-3583	129	2			PROPN
ejpam-3583	129	3	(	(	PUNCT
ejpam-3583	129	4	17	17	NUM
ejpam-3583	129	5	)	)	PUNCT
ejpam-3583	129	6	where	where	SCONJ
ejpam-3583	129	7	pn(x	pn(x	ADP
ejpam-3583	129	8	)	)	PUNCT
ejpam-3583	129	9	:	:	PUNCT
ejpam-3583	130	1	=	=	SYM
ejpam-3583	130	2	1	1	X
ejpam-3583	130	3	.	.	PUNCT
ejpam-3583	131	1	this	this	PRON
ejpam-3583	131	2	means	mean	VERB
ejpam-3583	131	3	that	that	SCONJ
ejpam-3583	132	1	f	f	PROPN
ejpam-3583	132	2	(	(	PUNCT
ejpam-3583	132	3	pnpk	pnpk	PROPN
ejpam-3583	132	4	)	)	PUNCT
ejpam-3583	132	5	=	=	SYM
ejpam-3583	132	6	dn[n	dn[n	NOUN
ejpam-3583	132	7	=	=	SYM
ejpam-3583	132	8	k	k	X
ejpam-3583	132	9	]	]	X
ejpam-3583	132	10	with	with	ADP
ejpam-3583	132	11	dn	dn	PROPN
ejpam-3583	132	12	6=	6=	PROPN
ejpam-3583	132	13	0	0	NUM
ejpam-3583	132	14	.	.	PUNCT
ejpam-3583	133	1	then	then	ADV
ejpam-3583	133	2	d[n	d[n	VERB
ejpam-3583	133	3	,	,	PUNCT
ejpam-3583	133	4	0	0	NUM
ejpam-3583	133	5	]	]	PUNCT
ejpam-3583	133	6	=	=	PUNCT
ejpam-3583	133	7	n−1∏	n−1∏	PROPN
ejpam-3583	133	8	i=0	i=0	PROPN
ejpam-3583	133	9	di	di	PROPN
ejpam-3583	133	10	.	.	PUNCT
ejpam-3583	134	1	clearly	clearly	ADV
ejpam-3583	134	2	,	,	PUNCT
ejpam-3583	134	3	from	from	ADP
ejpam-3583	134	4	(	(	PUNCT
ejpam-3583	134	5	17	17	NUM
ejpam-3583	134	6	)	)	PUNCT
ejpam-3583	134	7	,	,	PUNCT
ejpam-3583	134	8	we	we	PRON
ejpam-3583	134	9	have	have	VERB
ejpam-3583	134	10	pn(0	pn(0	NOUN
ejpam-3583	134	11	)	)	PUNCT
ejpam-3583	134	12	=	=	VERB
ejpam-3583	135	1	c0,n	c0,n	ADJ
ejpam-3583	135	2	=	=	SYM
ejpam-3583	135	3	1	1	NUM
ejpam-3583	135	4	d[n	d[n	NOUN
ejpam-3583	135	5	,	,	PUNCT
ejpam-3583	135	6	0	0	NUM
ejpam-3583	135	7	]	]	PUNCT
ejpam-3583	135	8	(	(	PUNCT
ejpam-3583	135	9	−1)nd[n	−1)nd[n	NOUN
ejpam-3583	135	10	,	,	PUNCT
ejpam-3583	135	11	1	1	NUM
ejpam-3583	135	12	]	]	PUNCT
ejpam-3583	135	13	.	.	PUNCT
ejpam-3583	136	1	hence	hence	ADV
ejpam-3583	136	2	,	,	PUNCT
ejpam-3583	136	3	we	we	PRON
ejpam-3583	136	4	have	have	VERB
ejpam-3583	136	5	d[n	d[n	NOUN
ejpam-3583	136	6	,	,	PUNCT
ejpam-3583	136	7	1	1	NUM
ejpam-3583	136	8	]	]	PUNCT
ejpam-3583	136	9	=	=	SYM
ejpam-3583	136	10	d[n	d[n	PROPN
ejpam-3583	136	11	,	,	PUNCT
ejpam-3583	136	12	0](−1)npn(0	0](−1)npn(0	NUM
ejpam-3583	136	13	)	)	PUNCT
ejpam-3583	136	14	.	.	PUNCT
ejpam-3583	137	1	(	(	PUNCT
ejpam-3583	137	2	18	18	NUM
ejpam-3583	137	3	)	)	PUNCT
ejpam-3583	137	4	first	first	ADV
ejpam-3583	137	5	,	,	PUNCT
ejpam-3583	137	6	let	let	VERB
ejpam-3583	137	7	us	we	PRON
ejpam-3583	137	8	consider	consider	VERB
ejpam-3583	137	9	the	the	DET
ejpam-3583	137	10	hankel	hankel	NOUN
ejpam-3583	137	11	transform	transform	NOUN
ejpam-3583	137	12	of	of	ADP
ejpam-3583	137	13	ϕn[x	ϕn[x	PROPN
ejpam-3583	137	14	,	,	PUNCT
ejpam-3583	137	15	r	r	PROPN
ejpam-3583	137	16	,	,	PUNCT
ejpam-3583	137	17	m]q	m]q	X
ejpam-3583	137	18	corresponding	correspond	VERB
ejpam-3583	137	19	to	to	ADP
ejpam-3583	137	20	the	the	DET
ejpam-3583	137	21	0th	0th	ADJ
ejpam-3583	137	22	hankel	hankel	NOUN
ejpam-3583	137	23	determinant	determinant	ADJ
ejpam-3583	137	24	.	.	PUNCT
ejpam-3583	138	1	theorem	theorem	VERB
ejpam-3583	138	2	3.1	3.1	NUM
ejpam-3583	138	3	.	.	PUNCT
ejpam-3583	139	1	the	the	DET
ejpam-3583	139	2	hankel	hankel	NOUN
ejpam-3583	139	3	transform	transform	NOUN
ejpam-3583	139	4	of	of	ADP
ejpam-3583	139	5	ϕn[x	ϕn[x	PROPN
ejpam-3583	139	6	,	,	PUNCT
ejpam-3583	139	7	r	r	PROPN
ejpam-3583	139	8	,	,	PUNCT
ejpam-3583	139	9	m]q	m]q	X
ejpam-3583	139	10	corresponding	correspond	VERB
ejpam-3583	139	11	to	to	ADP
ejpam-3583	139	12	the	the	DET
ejpam-3583	139	13	0th	0th	ADJ
ejpam-3583	139	14	hankel	hankel	NOUN
ejpam-3583	139	15	determinant	determinant	ADJ
ejpam-3583	139	16	is	be	AUX
ejpam-3583	139	17	given	give	VERB
ejpam-3583	139	18	by	by	ADP
ejpam-3583	139	19	h(ϕn[x	h(ϕn[x	ADJ
ejpam-3583	139	20	,	,	PUNCT
ejpam-3583	139	21	r	r	NOUN
ejpam-3583	139	22	,	,	PUNCT
ejpam-3583	139	23	m]q	m]q	NOUN
ejpam-3583	139	24	)	)	PUNCT
ejpam-3583	139	25	=	=	SYM
ejpam-3583	140	1	(	(	PUNCT
ejpam-3583	140	2	[	[	X
ejpam-3583	140	3	m]q[x]q	m]q[x]q	NOUN
ejpam-3583	140	4	)	)	PUNCT
ejpam-3583	140	5	(	(	PUNCT
ejpam-3583	140	6	n2	n2	NOUN
ejpam-3583	140	7	)	)	PUNCT
ejpam-3583	140	8	qr	qr	NOUN
ejpam-3583	140	9	(	(	PUNCT
ejpam-3583	140	10	n	n	PROPN
ejpam-3583	140	11	2)+(n3	2)+(n3	NUM
ejpam-3583	140	12	)	)	PUNCT
ejpam-3583	141	1	n−1∏	n−1∏	PROPN
ejpam-3583	141	2	k=0	k=0	PROPN
ejpam-3583	142	1	[	[	X
ejpam-3583	142	2	k]qm	k]qm	PROPN
ejpam-3583	142	3	!	!	PUNCT
ejpam-3583	142	4	r.	r.	PROPN
ejpam-3583	142	5	corcino	corcino	PROPN
ejpam-3583	142	6	,	,	PUNCT
ejpam-3583	142	7	j.	j.	PROPN
ejpam-3583	142	8	ontolan	ontolan	PROPN
ejpam-3583	142	9	,	,	PUNCT
ejpam-3583	142	10	g.	g.	PROPN
ejpam-3583	142	11	j.	j.	PROPN
ejpam-3583	142	12	rama	rama	PROPN
ejpam-3583	142	13	/	/	SYM
ejpam-3583	142	14	eur	eur	PROPN
ejpam-3583	142	15	.	.	PUNCT
ejpam-3583	143	1	j.	j.	PROPN
ejpam-3583	143	2	pure	pure	PROPN
ejpam-3583	143	3	appl	appl	PROPN
ejpam-3583	143	4	.	.	PROPN
ejpam-3583	143	5	math	math	PROPN
ejpam-3583	143	6	,	,	PUNCT
ejpam-3583	143	7	12	12	NUM
ejpam-3583	143	8	(	(	PUNCT
ejpam-3583	143	9	4	4	NUM
ejpam-3583	143	10	)	)	PUNCT
ejpam-3583	143	11	(	(	PUNCT
ejpam-3583	143	12	2019	2019	NUM
ejpam-3583	143	13	)	)	PUNCT
ejpam-3583	143	14	,	,	PUNCT
ejpam-3583	143	15	1676	1676	NUM
ejpam-3583	143	16	-	-	SYM
ejpam-3583	143	17	1688	1688	NUM
ejpam-3583	143	18	1683	1683	NUM
ejpam-3583	143	19	proof	proof	NOUN
ejpam-3583	143	20	.	.	PUNCT
ejpam-3583	144	1	we	we	PRON
ejpam-3583	144	2	prove	prove	VERB
ejpam-3583	144	3	this	this	DET
ejpam-3583	144	4	theorem	theorem	NOUN
ejpam-3583	144	5	using	use	VERB
ejpam-3583	144	6	the	the	DET
ejpam-3583	144	7	method	method	NOUN
ejpam-3583	144	8	of	of	ADP
ejpam-3583	144	9	cigler	cigler	NOUN
ejpam-3583	144	10	[	[	X
ejpam-3583	144	11	8	8	NUM
ejpam-3583	144	12	]	]	PUNCT
ejpam-3583	144	13	.	.	PUNCT
ejpam-3583	145	1	first	first	ADV
ejpam-3583	145	2	,	,	PUNCT
ejpam-3583	145	3	consider	consider	VERB
ejpam-3583	145	4	a	a	DET
ejpam-3583	145	5	linear	linear	ADJ
ejpam-3583	145	6	operator	operator	NOUN
ejpam-3583	145	7	ur	ur	INTJ
ejpam-3583	145	8	,	,	PUNCT
ejpam-3583	145	9	q	q	NOUN
ejpam-3583	145	10	on	on	ADP
ejpam-3583	145	11	the	the	DET
ejpam-3583	145	12	polynomials	polynomial	NOUN
ejpam-3583	145	13	defined	define	VERB
ejpam-3583	145	14	by	by	ADP
ejpam-3583	145	15	ur	ur	INTJ
ejpam-3583	145	16	,	,	PUNCT
ejpam-3583	145	17	q〈x〉r	q〈x〉r	PROPN
ejpam-3583	145	18	,	,	PUNCT
ejpam-3583	145	19	m	m	PROPN
ejpam-3583	145	20	,	,	PUNCT
ejpam-3583	145	21	n	n	NOUN
ejpam-3583	145	22	=	=	PUNCT
ejpam-3583	146	1	[	[	X
ejpam-3583	146	2	x]nq	x]nq	X
ejpam-3583	146	3	where	where	SCONJ
ejpam-3583	146	4	ur	ur	INTJ
ejpam-3583	146	5	,	,	PUNCT
ejpam-3583	146	6	q[x]qu	q[x]qu	NOUN
ejpam-3583	146	7	−1	−1	NOUN
ejpam-3583	146	8	r	r	NOUN
ejpam-3583	146	9	,	,	PUNCT
ejpam-3583	146	10	q	q	NOUN
ejpam-3583	146	11	=	=	PUNCT
ejpam-3583	147	1	[	[	X
ejpam-3583	147	2	x]q(1	x]q(1	NOUN
ejpam-3583	148	1	+	+	X
ejpam-3583	149	1	[	[	X
ejpam-3583	149	2	x]−rq	x]−rq	X
ejpam-3583	149	3	d[x]rq	d[x]rq	PROPN
ejpam-3583	149	4	)	)	PUNCT
ejpam-3583	149	5	then	then	ADV
ejpam-3583	149	6	,	,	PUNCT
ejpam-3583	149	7	we	we	PRON
ejpam-3583	149	8	have	have	VERB
ejpam-3583	149	9	ur	ur	INTJ
ejpam-3583	149	10	,	,	PUNCT
ejpam-3583	149	11	q[x]qu	q[x]qu	NOUN
ejpam-3583	149	12	−1	−1	NOUN
ejpam-3583	149	13	r	r	NOUN
ejpam-3583	149	14	,	,	PUNCT
ejpam-3583	149	15	q	q	X
ejpam-3583	150	1	[	[	X
ejpam-3583	150	2	x]nq	x]nq	X
ejpam-3583	150	3	=	=	SYM
ejpam-3583	150	4	ur[x]q〈x〉r	ur[x]q〈x〉r	X
ejpam-3583	150	5	,	,	PUNCT
ejpam-3583	150	6	m	m	PROPN
ejpam-3583	150	7	,	,	PUNCT
ejpam-3583	150	8	n	n	NOUN
ejpam-3583	150	9	=	=	SYM
ejpam-3583	150	10	ur	ur	INTJ
ejpam-3583	150	11	,	,	PUNCT
ejpam-3583	150	12	q(〈x〉r	q(〈x〉r	PROPN
ejpam-3583	150	13	,	,	PUNCT
ejpam-3583	150	14	m	m	PROPN
ejpam-3583	150	15	,	,	PUNCT
ejpam-3583	150	16	n+1	n+1	PROPN
ejpam-3583	151	1	+	+	PUNCT
ejpam-3583	151	2	[	[	X
ejpam-3583	151	3	r	r	X
ejpam-3583	151	4	+	+	X
ejpam-3583	151	5	n]q〈x〉r	n]q〈x〉r	ADJ
ejpam-3583	151	6	,	,	PUNCT
ejpam-3583	151	7	m	m	NOUN
ejpam-3583	151	8	,	,	PUNCT
ejpam-3583	151	9	n	n	CCONJ
ejpam-3583	151	10	)	)	PUNCT
ejpam-3583	152	1	=	=	VERB
ejpam-3583	153	1	[	[	X
ejpam-3583	153	2	x]n+1	x]n+1	X
ejpam-3583	153	3	q	q	X
ejpam-3583	154	1	+	+	PUNCT
ejpam-3583	154	2	[	[	X
ejpam-3583	154	3	r	r	NOUN
ejpam-3583	154	4	+	+	CCONJ
ejpam-3583	154	5	n]q[x]nq	n]q[x]nq	NOUN
ejpam-3583	154	6	=	=	PUNCT
ejpam-3583	155	1	[	[	X
ejpam-3583	155	2	x]q(1	x]q(1	NOUN
ejpam-3583	156	1	+	+	X
ejpam-3583	157	1	[	[	X
ejpam-3583	157	2	x]−rq	x]−rq	X
ejpam-3583	157	3	d[x]rq)[x]nq	d[x]rq)[x]nq	NOUN
ejpam-3583	157	4	.	.	PUNCT
ejpam-3583	158	1	let	let	VERB
ejpam-3583	158	2	fr	fr	NOUN
ejpam-3583	158	3	,	,	PUNCT
ejpam-3583	158	4	q	q	PUNCT
ejpam-3583	158	5	be	be	AUX
ejpam-3583	158	6	the	the	DET
ejpam-3583	158	7	linear	linear	ADJ
ejpam-3583	158	8	function	function	NOUN
ejpam-3583	158	9	defined	define	VERB
ejpam-3583	158	10	by	by	ADP
ejpam-3583	158	11	fr	fr	PROPN
ejpam-3583	158	12	,	,	PUNCT
ejpam-3583	158	13	q(〈x〉r	q(〈x〉r	NUM
ejpam-3583	158	14	,	,	PUNCT
ejpam-3583	158	15	m	m	NOUN
ejpam-3583	158	16	,	,	PUNCT
ejpam-3583	158	17	n	n	CCONJ
ejpam-3583	158	18	)	)	PUNCT
ejpam-3583	158	19	=	=	PUNCT
ejpam-3583	159	1	[	[	X
ejpam-3583	159	2	a]nq	a]nq	NUM
ejpam-3583	159	3	.	.	PUNCT
ejpam-3583	160	1	the	the	DET
ejpam-3583	160	2	orthogonal	orthogonal	ADJ
ejpam-3583	160	3	polynomial	polynomial	NOUN
ejpam-3583	160	4	with	with	ADP
ejpam-3583	160	5	respect	respect	NOUN
ejpam-3583	160	6	to	to	ADP
ejpam-3583	160	7	fr	fr	PROPN
ejpam-3583	160	8	,	,	PUNCT
ejpam-3583	160	9	q	q	PUNCT
ejpam-3583	160	10	is	be	AUX
ejpam-3583	160	11	given	give	VERB
ejpam-3583	160	12	by	by	ADP
ejpam-3583	160	13	hn	hn	PROPN
ejpam-3583	160	14	,	,	PUNCT
ejpam-3583	160	15	q(x	q(x	PROPN
ejpam-3583	160	16	,	,	PUNCT
ejpam-3583	160	17	a	a	DET
ejpam-3583	160	18	,	,	PUNCT
ejpam-3583	160	19	r	r	NOUN
ejpam-3583	160	20	,	,	PUNCT
ejpam-3583	160	21	m	m	NOUN
ejpam-3583	160	22	)	)	PUNCT
ejpam-3583	161	1	=	=	SYM
ejpam-3583	161	2	n∑	n∑	NOUN
ejpam-3583	161	3	k=0	k=0	PROPN
ejpam-3583	161	4	(	(	PUNCT
ejpam-3583	161	5	−[a]q	−[a]q	X
ejpam-3583	161	6	)	)	PUNCT
ejpam-3583	161	7	kq	kq	PROPN
ejpam-3583	161	8	(	(	PUNCT
ejpam-3583	161	9	k	k	PROPN
ejpam-3583	161	10	2	2	NUM
ejpam-3583	161	11	)	)	PUNCT
ejpam-3583	161	12	[	[	PUNCT
ejpam-3583	161	13	n	n	X
ejpam-3583	161	14	k	k	NOUN
ejpam-3583	161	15	]	]	X
ejpam-3583	161	16	q	q	PUNCT
ejpam-3583	161	17	〈	〈	PROPN
ejpam-3583	161	18	x〉r	x〉r	PROPN
ejpam-3583	161	19	,	,	PUNCT
ejpam-3583	161	20	m	m	PROPN
ejpam-3583	161	21	,	,	PUNCT
ejpam-3583	161	22	n−k	n−k	NOUN
ejpam-3583	161	23	,	,	PUNCT
ejpam-3583	161	24	which	which	PRON
ejpam-3583	161	25	is	be	AUX
ejpam-3583	161	26	a	a	DET
ejpam-3583	161	27	kind	kind	NOUN
ejpam-3583	161	28	of	of	ADP
ejpam-3583	161	29	q	q	NOUN
ejpam-3583	161	30	-	-	PUNCT
ejpam-3583	161	31	poisson	poisson	ADJ
ejpam-3583	161	32	-	-	PUNCT
ejpam-3583	161	33	charlier	charlier	NOUN
ejpam-3583	161	34	polynomials	polynomial	NOUN
ejpam-3583	161	35	satisfying	satisfy	VERB
ejpam-3583	161	36	the	the	DET
ejpam-3583	161	37	following	follow	VERB
ejpam-3583	161	38	recurrence	recurrence	NOUN
ejpam-3583	161	39	relation	relation	NOUN
ejpam-3583	161	40	hn+1,q(x	hn+1,q(x	PROPN
ejpam-3583	161	41	,	,	PUNCT
ejpam-3583	161	42	a	a	DET
ejpam-3583	161	43	,	,	PUNCT
ejpam-3583	161	44	r	r	NOUN
ejpam-3583	161	45	,	,	PUNCT
ejpam-3583	161	46	m	m	NOUN
ejpam-3583	161	47	)	)	PUNCT
ejpam-3583	161	48	=	=	SYM
ejpam-3583	161	49	(	(	PUNCT
ejpam-3583	162	1	[	[	X
ejpam-3583	162	2	x]q	x]q	ADJ
ejpam-3583	162	3	−	−	PROPN
ejpam-3583	163	1	[	[	X
ejpam-3583	163	2	mn+	mn+	NOUN
ejpam-3583	163	3	r]q	r]q	VERB
ejpam-3583	163	4	−	−	PROPN
ejpam-3583	163	5	qn[a]q)hn	qn[a]q)hn	NOUN
ejpam-3583	163	6	,	,	PUNCT
ejpam-3583	163	7	q(x	q(x	NOUN
ejpam-3583	163	8	,	,	PUNCT
ejpam-3583	163	9	a	a	DET
ejpam-3583	163	10	,	,	PUNCT
ejpam-3583	163	11	r	r	NOUN
ejpam-3583	163	12	,	,	PUNCT
ejpam-3583	163	13	m	m	NOUN
ejpam-3583	163	14	)	)	PUNCT
ejpam-3583	163	15	−	−	PROPN
ejpam-3583	164	1	qr+mn−1[a]q[n]qhn−1,q(x	qr+mn−1[a]q[n]qhn−1,q(x	PROPN
ejpam-3583	164	2	,	,	PUNCT
ejpam-3583	164	3	a	a	PRON
ejpam-3583	164	4	,	,	PUNCT
ejpam-3583	164	5	r	r	NOUN
ejpam-3583	164	6	,	,	PUNCT
ejpam-3583	164	7	m	m	NOUN
ejpam-3583	164	8	)	)	PUNCT
ejpam-3583	164	9	.	.	PUNCT
ejpam-3583	165	1	now	now	ADV
ejpam-3583	165	2	,	,	PUNCT
ejpam-3583	165	3	consider	consider	VERB
ejpam-3583	165	4	the	the	DET
ejpam-3583	165	5	following	follow	VERB
ejpam-3583	165	6	polynomial	polynomial	NOUN
ejpam-3583	165	7	in	in	ADP
ejpam-3583	165	8	[	[	X
ejpam-3583	165	9	x]q	x]q	ADJ
ejpam-3583	165	10	pn	pn	PROPN
ejpam-3583	165	11	,	,	PUNCT
ejpam-3583	165	12	q(x	q(x	PROPN
ejpam-3583	165	13	,	,	PUNCT
ejpam-3583	165	14	a	a	PRON
ejpam-3583	165	15	)	)	PUNCT
ejpam-3583	166	1	=	=	SYM
ejpam-3583	166	2	n−1∏	n−1∏	PROPN
ejpam-3583	166	3	k=0	k=0	PROPN
ejpam-3583	166	4	(	(	PUNCT
ejpam-3583	166	5	[	[	X
ejpam-3583	166	6	x]q	x]q	ADJ
ejpam-3583	166	7	−	−	PROPN
ejpam-3583	166	8	qk[a]q	qk[a]q	PROPN
ejpam-3583	166	9	)	)	PUNCT
ejpam-3583	166	10	=	=	PUNCT
ejpam-3583	166	11	n∑	n∑	NOUN
ejpam-3583	166	12	k=0	k=0	PROPN
ejpam-3583	166	13	(	(	PUNCT
ejpam-3583	166	14	−[a]q	−[a]q	X
ejpam-3583	166	15	)	)	PUNCT
ejpam-3583	166	16	kq	kq	PROPN
ejpam-3583	166	17	(	(	PUNCT
ejpam-3583	166	18	k	k	PROPN
ejpam-3583	166	19	2	2	NUM
ejpam-3583	166	20	)	)	PUNCT
ejpam-3583	166	21	[	[	PUNCT
ejpam-3583	166	22	n	n	X
ejpam-3583	166	23	k	k	X
ejpam-3583	166	24	]	]	PUNCT
ejpam-3583	166	25	q	q	X
ejpam-3583	167	1	[	[	X
ejpam-3583	167	2	x]n−kq	x]n−kq	X
ejpam-3583	167	3	.	.	PUNCT
ejpam-3583	168	1	by	by	ADP
ejpam-3583	168	2	applying	apply	VERB
ejpam-3583	168	3	the	the	DET
ejpam-3583	168	4	linear	linear	ADJ
ejpam-3583	168	5	operator	operator	NOUN
ejpam-3583	168	6	ur	ur	INTJ
ejpam-3583	168	7	,	,	PUNCT
ejpam-3583	168	8	q	q	NOUN
ejpam-3583	168	9	:	:	PUNCT
ejpam-3583	168	10	〈	〈	PROPN
ejpam-3583	168	11	x〉r	x〉r	PROPN
ejpam-3583	168	12	,	,	PUNCT
ejpam-3583	168	13	m	m	PROPN
ejpam-3583	168	14	,	,	PUNCT
ejpam-3583	168	15	k	k	PROPN
ejpam-3583	168	16	7→	7→	PROPN
ejpam-3583	169	1	[	[	X
ejpam-3583	169	2	x]kq	x]kq	PROPN
ejpam-3583	169	3	to	to	ADP
ejpam-3583	169	4	hn	hn	PRON
ejpam-3583	169	5	,	,	PUNCT
ejpam-3583	169	6	q(x	q(x	PROPN
ejpam-3583	169	7	,	,	PUNCT
ejpam-3583	169	8	a	a	PRON
ejpam-3583	169	9	,	,	PUNCT
ejpam-3583	169	10	r	r	NOUN
ejpam-3583	169	11	,	,	PUNCT
ejpam-3583	169	12	m	m	NOUN
ejpam-3583	169	13	)	)	PUNCT
ejpam-3583	169	14	,	,	PUNCT
ejpam-3583	169	15	urhn	urhn	X
ejpam-3583	169	16	,	,	PUNCT
ejpam-3583	169	17	q(x	q(x	NOUN
ejpam-3583	169	18	,	,	PUNCT
ejpam-3583	169	19	a	a	DET
ejpam-3583	169	20	,	,	PUNCT
ejpam-3583	169	21	r	r	NOUN
ejpam-3583	169	22	,	,	PUNCT
ejpam-3583	169	23	m	m	NOUN
ejpam-3583	169	24	)	)	PUNCT
ejpam-3583	169	25	=	=	SYM
ejpam-3583	169	26	n∑	n∑	NOUN
ejpam-3583	169	27	k=0	k=0	PROPN
ejpam-3583	169	28	(	(	PUNCT
ejpam-3583	169	29	−[a]q	−[a]q	X
ejpam-3583	169	30	)	)	PUNCT
ejpam-3583	169	31	kq	kq	PROPN
ejpam-3583	169	32	(	(	PUNCT
ejpam-3583	169	33	k	k	PROPN
ejpam-3583	169	34	2	2	NUM
ejpam-3583	169	35	)	)	PUNCT
ejpam-3583	169	36	[	[	PUNCT
ejpam-3583	169	37	n	n	X
ejpam-3583	169	38	k	k	X
ejpam-3583	169	39	]	]	PUNCT
ejpam-3583	169	40	q	q	X
ejpam-3583	170	1	[	[	X
ejpam-3583	170	2	x]n−kq	x]n−kq	X
ejpam-3583	170	3	=	=	SYM
ejpam-3583	170	4	pn	pn	PROPN
ejpam-3583	170	5	,	,	PUNCT
ejpam-3583	170	6	q(x	q(x	PROPN
ejpam-3583	170	7	,	,	PUNCT
ejpam-3583	170	8	a	a	PRON
ejpam-3583	170	9	)	)	PUNCT
ejpam-3583	170	10	.	.	PUNCT
ejpam-3583	171	1	this	this	PRON
ejpam-3583	171	2	implies	imply	VERB
ejpam-3583	171	3	that	that	SCONJ
ejpam-3583	171	4	u−1r	u−1r	PROPN
ejpam-3583	171	5	,	,	PUNCT
ejpam-3583	171	6	q	q	X
ejpam-3583	171	7	(	(	PUNCT
ejpam-3583	171	8	pn	pn	NOUN
ejpam-3583	171	9	,	,	PUNCT
ejpam-3583	171	10	q(x	q(x	PROPN
ejpam-3583	171	11	,	,	PUNCT
ejpam-3583	171	12	a	a	PRON
ejpam-3583	171	13	)	)	PUNCT
ejpam-3583	171	14	)	)	PUNCT
ejpam-3583	172	1	=	=	SYM
ejpam-3583	172	2	hn	hn	PROPN
ejpam-3583	172	3	,	,	PUNCT
ejpam-3583	172	4	q(x	q(x	PROPN
ejpam-3583	172	5	,	,	PUNCT
ejpam-3583	172	6	a	a	PRON
ejpam-3583	172	7	,	,	PUNCT
ejpam-3583	172	8	r	r	NOUN
ejpam-3583	172	9	,	,	PUNCT
ejpam-3583	172	10	m	m	NOUN
ejpam-3583	172	11	)	)	PUNCT
ejpam-3583	172	12	.	.	PUNCT
ejpam-3583	173	1	then	then	ADV
ejpam-3583	173	2	ur[x]qhn	ur[x]qhn	NOUN
ejpam-3583	173	3	,	,	PUNCT
ejpam-3583	173	4	q(x	q(x	PROPN
ejpam-3583	173	5	,	,	PUNCT
ejpam-3583	173	6	a	a	DET
ejpam-3583	173	7	,	,	PUNCT
ejpam-3583	173	8	r	r	NOUN
ejpam-3583	173	9	,	,	PUNCT
ejpam-3583	173	10	m	m	NOUN
ejpam-3583	173	11	)	)	PUNCT
ejpam-3583	173	12	=	=	PRON
ejpam-3583	174	1	ur[x]qu	ur[x]qu	NOUN
ejpam-3583	174	2	−1	−1	NOUN
ejpam-3583	174	3	r	r	NOUN
ejpam-3583	174	4	,	,	PUNCT
ejpam-3583	174	5	q	q	X
ejpam-3583	174	6	(	(	PUNCT
ejpam-3583	174	7	pn	pn	NOUN
ejpam-3583	174	8	,	,	PUNCT
ejpam-3583	174	9	q(x	q(x	PROPN
ejpam-3583	174	10	,	,	PUNCT
ejpam-3583	174	11	a	a	PRON
ejpam-3583	174	12	)	)	PUNCT
ejpam-3583	174	13	)	)	PUNCT
ejpam-3583	174	14	=	=	PUNCT
ejpam-3583	175	1	[	[	X
ejpam-3583	175	2	x]q(1	x]q(1	NOUN
ejpam-3583	175	3	+	+	X
ejpam-3583	176	1	[	[	X
ejpam-3583	176	2	x]−rq	x]−rq	X
ejpam-3583	176	3	d[x]rq)pn	d[x]rq)pn	NOUN
ejpam-3583	176	4	,	,	PUNCT
ejpam-3583	176	5	q(x	q(x	PROPN
ejpam-3583	176	6	,	,	PUNCT
ejpam-3583	176	7	a	a	PRON
ejpam-3583	176	8	)	)	PUNCT
ejpam-3583	176	9	r.	r.	PROPN
ejpam-3583	176	10	corcino	corcino	PROPN
ejpam-3583	176	11	,	,	PUNCT
ejpam-3583	176	12	j.	j.	PROPN
ejpam-3583	176	13	ontolan	ontolan	PROPN
ejpam-3583	176	14	,	,	PUNCT
ejpam-3583	176	15	g.	g.	PROPN
ejpam-3583	176	16	j.	j.	PROPN
ejpam-3583	176	17	rama	rama	PROPN
ejpam-3583	176	18	/	/	SYM
ejpam-3583	176	19	eur	eur	PROPN
ejpam-3583	176	20	.	.	PUNCT
ejpam-3583	177	1	j.	j.	PROPN
ejpam-3583	177	2	pure	pure	PROPN
ejpam-3583	177	3	appl	appl	PROPN
ejpam-3583	177	4	.	.	PROPN
ejpam-3583	177	5	math	math	PROPN
ejpam-3583	177	6	,	,	PUNCT
ejpam-3583	177	7	12	12	NUM
ejpam-3583	177	8	(	(	PUNCT
ejpam-3583	177	9	4	4	NUM
ejpam-3583	177	10	)	)	PUNCT
ejpam-3583	177	11	(	(	PUNCT
ejpam-3583	177	12	2019	2019	NUM
ejpam-3583	177	13	)	)	PUNCT
ejpam-3583	177	14	,	,	PUNCT
ejpam-3583	177	15	1676	1676	NUM
ejpam-3583	177	16	-	-	SYM
ejpam-3583	177	17	1688	1688	NUM
ejpam-3583	177	18	1684	1684	NUM
ejpam-3583	177	19	=	=	SYM
ejpam-3583	178	1	[	[	X
ejpam-3583	178	2	x]qpn	x]qpn	X
ejpam-3583	178	3	,	,	PUNCT
ejpam-3583	178	4	q(x	q(x	PROPN
ejpam-3583	178	5	,	,	PUNCT
ejpam-3583	178	6	a	a	PRON
ejpam-3583	178	7	)	)	PUNCT
ejpam-3583	178	8	+	+	PUNCT
ejpam-3583	179	1	[	[	X
ejpam-3583	179	2	r	r	X
ejpam-3583	179	3	+	+	ADJ
ejpam-3583	179	4	mn]qpn	mn]qpn	PROPN
ejpam-3583	179	5	,	,	PUNCT
ejpam-3583	179	6	q(x	q(x	PROPN
ejpam-3583	179	7	,	,	PUNCT
ejpam-3583	179	8	a	a	PRON
ejpam-3583	179	9	)	)	PUNCT
ejpam-3583	179	10	note	note	NOUN
ejpam-3583	179	11	that	that	SCONJ
ejpam-3583	179	12	pn+1,q(x	pn+1,q(x	NOUN
ejpam-3583	179	13	,	,	PUNCT
ejpam-3583	179	14	q	q	NOUN
ejpam-3583	179	15	)	)	PUNCT
ejpam-3583	179	16	=	=	SYM
ejpam-3583	179	17	n∏	n∏	PROPN
ejpam-3583	179	18	k=0	k=0	PROPN
ejpam-3583	179	19	(	(	PUNCT
ejpam-3583	179	20	[	[	X
ejpam-3583	179	21	x]q	x]q	ADJ
ejpam-3583	179	22	−	−	PROPN
ejpam-3583	179	23	qk[a]q	qk[a]q	PROPN
ejpam-3583	179	24	)	)	PUNCT
ejpam-3583	179	25	=	=	PUNCT
ejpam-3583	180	1	(	(	PUNCT
ejpam-3583	180	2	[	[	X
ejpam-3583	180	3	x]q	x]q	NOUN
ejpam-3583	180	4	−	−	PROPN
ejpam-3583	180	5	qn[a]q	qn[a]q	PROPN
ejpam-3583	180	6	)	)	PUNCT
ejpam-3583	180	7	pn	pn	PROPN
ejpam-3583	180	8	,	,	PUNCT
ejpam-3583	180	9	q(x	q(x	PROPN
ejpam-3583	180	10	,	,	PUNCT
ejpam-3583	180	11	q	q	NOUN
ejpam-3583	180	12	)	)	PUNCT
ejpam-3583	180	13	.	.	PUNCT
ejpam-3583	181	1	hence	hence	ADV
ejpam-3583	181	2	,	,	PUNCT
ejpam-3583	181	3	[	[	X
ejpam-3583	181	4	x]qpn	x]qpn	X
ejpam-3583	181	5	,	,	PUNCT
ejpam-3583	181	6	q(x	q(x	PROPN
ejpam-3583	181	7	,	,	PUNCT
ejpam-3583	181	8	a	a	PRON
ejpam-3583	181	9	)	)	PUNCT
ejpam-3583	181	10	=	=	SYM
ejpam-3583	181	11	pn+1,q(x	pn+1,q(x	PROPN
ejpam-3583	181	12	,	,	PUNCT
ejpam-3583	181	13	a	a	PRON
ejpam-3583	181	14	)	)	PUNCT
ejpam-3583	181	15	+	+	PUNCT
ejpam-3583	182	1	[	[	X
ejpam-3583	182	2	a]qq	a]qq	ADJ
ejpam-3583	182	3	npn	npn	NOUN
ejpam-3583	182	4	,	,	PUNCT
ejpam-3583	182	5	q(x	q(x	PROPN
ejpam-3583	182	6	,	,	PUNCT
ejpam-3583	182	7	a	a	PRON
ejpam-3583	182	8	)	)	PUNCT
ejpam-3583	182	9	.	.	PUNCT
ejpam-3583	183	1	using	use	VERB
ejpam-3583	183	2	the	the	DET
ejpam-3583	183	3	fact	fact	NOUN
ejpam-3583	183	4	that	that	SCONJ
ejpam-3583	184	1	[	[	X
ejpam-3583	184	2	r	r	X
ejpam-3583	184	3	+	+	NOUN
ejpam-3583	184	4	mn]q	mn]q	NOUN
ejpam-3583	184	5	=	=	PUNCT
ejpam-3583	185	1	[	[	X
ejpam-3583	185	2	r]q	r]q	NOUN
ejpam-3583	185	3	+	+	X
ejpam-3583	185	4	qr[mn]q	qr[mn]q	X
ejpam-3583	185	5	,	,	PUNCT
ejpam-3583	185	6	we	we	PRON
ejpam-3583	185	7	have	have	AUX
ejpam-3583	185	8	ur[x]hn	ur[x]hn	VERB
ejpam-3583	185	9	,	,	PUNCT
ejpam-3583	185	10	q(x	q(x	PROPN
ejpam-3583	185	11	,	,	PUNCT
ejpam-3583	185	12	a	a	DET
ejpam-3583	185	13	,	,	PUNCT
ejpam-3583	185	14	r	r	NOUN
ejpam-3583	185	15	,	,	PUNCT
ejpam-3583	185	16	m	m	NOUN
ejpam-3583	185	17	)	)	PUNCT
ejpam-3583	185	18	=	=	SYM
ejpam-3583	185	19	pn+1,q(x	pn+1,q(x	PROPN
ejpam-3583	185	20	,	,	PUNCT
ejpam-3583	185	21	a	a	PRON
ejpam-3583	185	22	)	)	PUNCT
ejpam-3583	185	23	+	+	PUNCT
ejpam-3583	186	1	[	[	X
ejpam-3583	186	2	a]qq	a]qq	ADJ
ejpam-3583	186	3	npn	npn	NOUN
ejpam-3583	186	4	,	,	PUNCT
ejpam-3583	186	5	q(x	q(x	NOUN
ejpam-3583	186	6	,	,	PUNCT
ejpam-3583	186	7	a	a	PRON
ejpam-3583	186	8	)	)	PUNCT
ejpam-3583	186	9	+	+	CCONJ
ejpam-3583	186	10	(	(	PUNCT
ejpam-3583	186	11	[	[	X
ejpam-3583	186	12	r]q	r]q	NOUN
ejpam-3583	186	13	+	+	X
ejpam-3583	186	14	qr[mn]q)pn	qr[mn]q)pn	ADJ
ejpam-3583	186	15	,	,	PUNCT
ejpam-3583	186	16	q(x	q(x	PROPN
ejpam-3583	186	17	,	,	PUNCT
ejpam-3583	186	18	a	a	PRON
ejpam-3583	186	19	)	)	PUNCT
ejpam-3583	186	20	=	=	SYM
ejpam-3583	186	21	pn+1,q(x	pn+1,q(x	PROPN
ejpam-3583	186	22	,	,	PUNCT
ejpam-3583	186	23	a	a	PRON
ejpam-3583	186	24	)	)	PUNCT
ejpam-3583	186	25	+	+	PUNCT
ejpam-3583	187	1	[	[	X
ejpam-3583	187	2	a]qq	a]qq	ADJ
ejpam-3583	187	3	npn	npn	NOUN
ejpam-3583	187	4	,	,	PUNCT
ejpam-3583	187	5	q(x	q(x	NOUN
ejpam-3583	187	6	,	,	PUNCT
ejpam-3583	187	7	a	a	PRON
ejpam-3583	187	8	)	)	PUNCT
ejpam-3583	187	9	+	+	CCONJ
ejpam-3583	188	1	[	[	X
ejpam-3583	188	2	r]qpn	r]qpn	ADJ
ejpam-3583	188	3	,	,	PUNCT
ejpam-3583	188	4	q(x	q(x	PROPN
ejpam-3583	188	5	,	,	PUNCT
ejpam-3583	188	6	a	a	PRON
ejpam-3583	188	7	)	)	PUNCT
ejpam-3583	188	8	+	+	CCONJ
ejpam-3583	188	9	qr[mn]qpn	qr[mn]qpn	NOUN
ejpam-3583	188	10	,	,	PUNCT
ejpam-3583	188	11	q(x	q(x	PROPN
ejpam-3583	188	12	,	,	PUNCT
ejpam-3583	188	13	a	a	PRON
ejpam-3583	188	14	)	)	PUNCT
ejpam-3583	188	15	=	=	SYM
ejpam-3583	188	16	pn+1,q(x	pn+1,q(x	PROPN
ejpam-3583	188	17	,	,	PUNCT
ejpam-3583	188	18	a	a	PRON
ejpam-3583	188	19	)	)	PUNCT
ejpam-3583	188	20	+	+	PUNCT
ejpam-3583	188	21	[	[	X
ejpam-3583	188	22	a]qq	a]qq	ADJ
ejpam-3583	188	23	npn	npn	NOUN
ejpam-3583	188	24	,	,	PUNCT
ejpam-3583	188	25	q(x	q(x	NOUN
ejpam-3583	188	26	,	,	PUNCT
ejpam-3583	188	27	a	a	PRON
ejpam-3583	188	28	)	)	PUNCT
ejpam-3583	188	29	+	+	CCONJ
ejpam-3583	189	1	[	[	X
ejpam-3583	189	2	r]qpn	r]qpn	ADJ
ejpam-3583	189	3	,	,	PUNCT
ejpam-3583	189	4	q(x	q(x	PROPN
ejpam-3583	189	5	,	,	PUNCT
ejpam-3583	189	6	a	a	PRON
ejpam-3583	189	7	)	)	PUNCT
ejpam-3583	189	8	+	+	NUM
ejpam-3583	189	9	qr[mn]q[x]qpn−1,q(x	qr[mn]q[x]qpn−1,q(x	PROPN
ejpam-3583	189	10	,	,	PUNCT
ejpam-3583	189	11	a	a	PRON
ejpam-3583	189	12	)	)	PUNCT
ejpam-3583	189	13	.	.	PUNCT
ejpam-3583	189	14	also	also	ADV
ejpam-3583	189	15	,	,	PUNCT
ejpam-3583	189	16	[	[	X
ejpam-3583	189	17	x]qpn−1,q(x	x]qpn−1,q(x	X
ejpam-3583	189	18	,	,	PUNCT
ejpam-3583	189	19	a	a	PRON
ejpam-3583	189	20	)	)	PUNCT
ejpam-3583	189	21	=	=	SYM
ejpam-3583	189	22	pn	pn	PROPN
ejpam-3583	189	23	,	,	PUNCT
ejpam-3583	189	24	q(x	q(x	PROPN
ejpam-3583	189	25	,	,	PUNCT
ejpam-3583	189	26	a	a	PRON
ejpam-3583	189	27	)	)	PUNCT
ejpam-3583	189	28	+	+	PUNCT
ejpam-3583	190	1	[	[	X
ejpam-3583	190	2	a]qq	a]qq	ADJ
ejpam-3583	190	3	n−1pn−1,q(x	n−1pn−1,q(x	PROPN
ejpam-3583	190	4	,	,	PUNCT
ejpam-3583	190	5	a	a	PRON
ejpam-3583	190	6	)	)	PUNCT
ejpam-3583	190	7	.	.	PUNCT
ejpam-3583	191	1	then	then	ADV
ejpam-3583	191	2	ur[x]hn	ur[x]hn	NOUN
ejpam-3583	191	3	,	,	PUNCT
ejpam-3583	191	4	q(x	q(x	PROPN
ejpam-3583	191	5	,	,	PUNCT
ejpam-3583	191	6	a	a	DET
ejpam-3583	191	7	,	,	PUNCT
ejpam-3583	191	8	r	r	NOUN
ejpam-3583	191	9	,	,	PUNCT
ejpam-3583	191	10	m	m	NOUN
ejpam-3583	191	11	)	)	PUNCT
ejpam-3583	191	12	=	=	SYM
ejpam-3583	191	13	pn+1,q(x	pn+1,q(x	PROPN
ejpam-3583	191	14	,	,	PUNCT
ejpam-3583	191	15	a	a	PRON
ejpam-3583	191	16	)	)	PUNCT
ejpam-3583	191	17	+	+	PUNCT
ejpam-3583	192	1	[	[	X
ejpam-3583	192	2	a]qq	a]qq	ADJ
ejpam-3583	192	3	npn	npn	NOUN
ejpam-3583	192	4	,	,	PUNCT
ejpam-3583	192	5	q(x	q(x	NOUN
ejpam-3583	192	6	,	,	PUNCT
ejpam-3583	192	7	a	a	PRON
ejpam-3583	192	8	)	)	PUNCT
ejpam-3583	192	9	+	+	CCONJ
ejpam-3583	193	1	[	[	X
ejpam-3583	193	2	r]qpn	r]qpn	ADJ
ejpam-3583	193	3	,	,	PUNCT
ejpam-3583	193	4	q(x	q(x	PROPN
ejpam-3583	193	5	,	,	PUNCT
ejpam-3583	193	6	a	a	PRON
ejpam-3583	193	7	)	)	PUNCT
ejpam-3583	193	8	+	+	NUM
ejpam-3583	193	9	qr[mn]q(pn	qr[mn]q(pn	NOUN
ejpam-3583	193	10	,	,	PUNCT
ejpam-3583	193	11	q(x	q(x	PROPN
ejpam-3583	193	12	,	,	PUNCT
ejpam-3583	193	13	a	a	PRON
ejpam-3583	193	14	)	)	PUNCT
ejpam-3583	193	15	+	+	PUNCT
ejpam-3583	194	1	[	[	X
ejpam-3583	194	2	a]qq	a]qq	ADJ
ejpam-3583	194	3	n−1pn−1,q(x	n−1pn−1,q(x	PROPN
ejpam-3583	194	4	,	,	PUNCT
ejpam-3583	194	5	a	a	PRON
ejpam-3583	194	6	)	)	PUNCT
ejpam-3583	194	7	)	)	PUNCT
ejpam-3583	195	1	=	=	SYM
ejpam-3583	195	2	pn+1,q(x	pn+1,q(x	PROPN
ejpam-3583	195	3	,	,	PUNCT
ejpam-3583	195	4	a	a	PRON
ejpam-3583	195	5	)	)	PUNCT
ejpam-3583	195	6	+	+	PUNCT
ejpam-3583	196	1	[	[	X
ejpam-3583	196	2	a]qq	a]qq	ADJ
ejpam-3583	196	3	npn	npn	NOUN
ejpam-3583	196	4	,	,	PUNCT
ejpam-3583	196	5	q(x	q(x	NOUN
ejpam-3583	196	6	,	,	PUNCT
ejpam-3583	196	7	a	a	PRON
ejpam-3583	196	8	)	)	PUNCT
ejpam-3583	196	9	+	+	CCONJ
ejpam-3583	197	1	[	[	X
ejpam-3583	197	2	r]qpn	r]qpn	ADJ
ejpam-3583	197	3	,	,	PUNCT
ejpam-3583	197	4	q(x	q(x	PROPN
ejpam-3583	197	5	,	,	PUNCT
ejpam-3583	197	6	a	a	PRON
ejpam-3583	197	7	)	)	PUNCT
ejpam-3583	197	8	+	+	CCONJ
ejpam-3583	197	9	qr[mn]qpn(x	qr[mn]qpn(x	ADJ
ejpam-3583	197	10	,	,	PUNCT
ejpam-3583	197	11	a	a	NOUN
ejpam-3583	197	12	)	)	PUNCT
ejpam-3583	197	13	+	+	PUNCT
ejpam-3583	197	14	[	[	X
ejpam-3583	197	15	a]q[mn]qq	a]q[mn]qq	ADJ
ejpam-3583	197	16	r+n−1pn−1,q(x	r+n−1pn−1,q(x	PROPN
ejpam-3583	197	17	,	,	PUNCT
ejpam-3583	197	18	a	a	PRON
ejpam-3583	197	19	)	)	PUNCT
ejpam-3583	197	20	applying	apply	VERB
ejpam-3583	197	21	u−1r	u−1r	PROPN
ejpam-3583	197	22	,	,	PUNCT
ejpam-3583	197	23	q	q	ADJ
ejpam-3583	197	24	yields	yield	NOUN
ejpam-3583	197	25	[	[	X
ejpam-3583	197	26	x]qhn	x]qhn	NOUN
ejpam-3583	197	27	,	,	PUNCT
ejpam-3583	197	28	q(x	q(x	NOUN
ejpam-3583	197	29	,	,	PUNCT
ejpam-3583	197	30	a	a	DET
ejpam-3583	197	31	,	,	PUNCT
ejpam-3583	197	32	r	r	NOUN
ejpam-3583	197	33	,	,	PUNCT
ejpam-3583	197	34	m	m	NOUN
ejpam-3583	197	35	)	)	PUNCT
ejpam-3583	197	36	=	=	SYM
ejpam-3583	197	37	hn+1,q(x	hn+1,q(x	PROPN
ejpam-3583	197	38	,	,	PUNCT
ejpam-3583	197	39	a	a	PRON
ejpam-3583	197	40	,	,	PUNCT
ejpam-3583	197	41	r	r	NOUN
ejpam-3583	197	42	,	,	PUNCT
ejpam-3583	197	43	m	m	NOUN
ejpam-3583	197	44	)	)	PUNCT
ejpam-3583	198	1	+	+	CCONJ
ejpam-3583	198	2	(	(	PUNCT
ejpam-3583	198	3	[	[	X
ejpam-3583	198	4	a]qq	a]qq	ADJ
ejpam-3583	198	5	n	n	NOUN
ejpam-3583	198	6	+	+	X
ejpam-3583	199	1	[	[	PUNCT
ejpam-3583	199	2	r]q	r]q	NOUN
ejpam-3583	199	3	+	+	X
ejpam-3583	199	4	qr[mn]q)hn	qr[mn]q)hn	ADV
ejpam-3583	199	5	,	,	PUNCT
ejpam-3583	199	6	q(x	q(x	PROPN
ejpam-3583	199	7	,	,	PUNCT
ejpam-3583	199	8	a	a	PRON
ejpam-3583	199	9	,	,	PUNCT
ejpam-3583	199	10	r	r	NOUN
ejpam-3583	199	11	,	,	PUNCT
ejpam-3583	199	12	m	m	NOUN
ejpam-3583	199	13	)	)	PUNCT
ejpam-3583	199	14	+	+	CCONJ
ejpam-3583	200	1	[	[	X
ejpam-3583	200	2	a]q[mn]qq	a]q[mn]qq	PROPN
ejpam-3583	200	3	r+n−1hn−1,q(x	r+n−1hn−1,q(x	PROPN
ejpam-3583	200	4	,	,	PUNCT
ejpam-3583	200	5	a	a	PRON
ejpam-3583	200	6	,	,	PUNCT
ejpam-3583	200	7	r	r	NOUN
ejpam-3583	200	8	,	,	PUNCT
ejpam-3583	200	9	m	m	NOUN
ejpam-3583	200	10	)	)	PUNCT
ejpam-3583	200	11	.	.	PUNCT
ejpam-3583	201	1	clearly	clearly	ADV
ejpam-3583	201	2	,	,	PUNCT
ejpam-3583	201	3	fr	fr	INTJ
ejpam-3583	201	4	,	,	PUNCT
ejpam-3583	201	5	q(hn	q(hn	PROPN
ejpam-3583	201	6	,	,	PUNCT
ejpam-3583	201	7	q(x	q(x	PROPN
ejpam-3583	201	8	,	,	PUNCT
ejpam-3583	201	9	a	a	PRON
ejpam-3583	201	10	,	,	PUNCT
ejpam-3583	201	11	r	r	NOUN
ejpam-3583	201	12	,	,	PUNCT
ejpam-3583	201	13	m	m	NOUN
ejpam-3583	201	14	)	)	PUNCT
ejpam-3583	201	15	)	)	PUNCT
ejpam-3583	202	1	=	=	SYM
ejpam-3583	202	2	n∑	n∑	NOUN
ejpam-3583	202	3	k=0	k=0	PROPN
ejpam-3583	202	4	(	(	PUNCT
ejpam-3583	202	5	−[a]q	−[a]q	X
ejpam-3583	202	6	)	)	PUNCT
ejpam-3583	202	7	k	k	NOUN
ejpam-3583	203	1	q	q	X
ejpam-3583	203	2	(	(	PUNCT
ejpam-3583	203	3	k	k	NOUN
ejpam-3583	203	4	2	2	X
ejpam-3583	203	5	)	)	PUNCT
ejpam-3583	203	6	[	[	PUNCT
ejpam-3583	203	7	n	n	X
ejpam-3583	203	8	k	k	X
ejpam-3583	203	9	]	]	X
ejpam-3583	203	10	q	q	X
ejpam-3583	204	1	[	[	X
ejpam-3583	204	2	a]nq	a]nq	X
ejpam-3583	204	3	=	=	SYM
ejpam-3583	204	4	pn	pn	PROPN
ejpam-3583	204	5	,	,	PUNCT
ejpam-3583	204	6	q(a	q(a	PROPN
ejpam-3583	204	7	,	,	PUNCT
ejpam-3583	204	8	a	a	PRON
ejpam-3583	204	9	)	)	PUNCT
ejpam-3583	204	10	=	=	SYM
ejpam-3583	204	11	0	0	NUM
ejpam-3583	204	12	,	,	PUNCT
ejpam-3583	204	13	which	which	PRON
ejpam-3583	204	14	implies	imply	VERB
ejpam-3583	204	15	dn	dn	PROPN
ejpam-3583	204	16	,	,	PUNCT
ejpam-3583	204	17	q	q	X
ejpam-3583	204	18	=	=	SYM
ejpam-3583	204	19	fr	fr	PROPN
ejpam-3583	204	20	,	,	PUNCT
ejpam-3583	204	21	q([x]nq	q([x]nq	PROPN
ejpam-3583	204	22	hn	hn	PROPN
ejpam-3583	204	23	,	,	PUNCT
ejpam-3583	204	24	q(x	q(x	PROPN
ejpam-3583	204	25	,	,	PUNCT
ejpam-3583	204	26	a	a	PRON
ejpam-3583	204	27	,	,	PUNCT
ejpam-3583	204	28	r	r	NOUN
ejpam-3583	204	29	,	,	PUNCT
ejpam-3583	204	30	m	m	NOUN
ejpam-3583	204	31	)	)	PUNCT
ejpam-3583	204	32	)	)	PUNCT
ejpam-3583	205	1	=	=	PUNCT
ejpam-3583	206	1	qr+n−1[mn]q[a]q	qr+n−1[mn]q[a]q	INTJ
ejpam-3583	206	2	fr	fr	PROPN
ejpam-3583	206	3	,	,	PUNCT
ejpam-3583	206	4	q([x]n−1q	q([x]n−1q	PROPN
ejpam-3583	206	5	hn−1,q(x	hn−1,q(x	X
ejpam-3583	206	6	,	,	PUNCT
ejpam-3583	206	7	a	a	PRON
ejpam-3583	206	8	,	,	PUNCT
ejpam-3583	206	9	r	r	NOUN
ejpam-3583	206	10	,	,	PUNCT
ejpam-3583	206	11	m	m	NOUN
ejpam-3583	206	12	)	)	PUNCT
ejpam-3583	206	13	)	)	PUNCT
ejpam-3583	207	1	=	=	PUNCT
ejpam-3583	207	2	n∏	n∏	NOUN
ejpam-3583	207	3	k=1	k=1	PUNCT
ejpam-3583	207	4	qr+k−1[mk]q[a]q	qr+k−1[mk]q[a]q	NOUN
ejpam-3583	207	5	=	=	PUNCT
ejpam-3583	207	6	n∏	n∏	NOUN
ejpam-3583	207	7	k=1	k=1	X
ejpam-3583	207	8	qr+k−1[k]qm	qr+k−1[k]qm	ADP
ejpam-3583	208	1	[	[	PUNCT
ejpam-3583	208	2	m]q[a]q	m]q[a]q	NOUN
ejpam-3583	208	3	=	=	SYM
ejpam-3583	208	4	(	(	PUNCT
ejpam-3583	208	5	qr[a]q[m]q	qr[a]q[m]q	PROPN
ejpam-3583	208	6	)	)	PUNCT
ejpam-3583	208	7	n	n	PRON
ejpam-3583	208	8	q	q	NOUN
ejpam-3583	208	9	(	(	PUNCT
ejpam-3583	208	10	n	n	NOUN
ejpam-3583	208	11	2)[n]qm	2)[n]qm	NUM
ejpam-3583	208	12	!	!	PUNCT
ejpam-3583	209	1	hence	hence	ADV
ejpam-3583	209	2	,	,	PUNCT
ejpam-3583	209	3	we	we	PRON
ejpam-3583	209	4	have	have	VERB
ejpam-3583	209	5	d[n	d[n	NOUN
ejpam-3583	209	6	,	,	PUNCT
ejpam-3583	209	7	0]q	0]q	X
ejpam-3583	210	1	=	=	PUNCT
ejpam-3583	210	2	n−1∏	n−1∏	PROPN
ejpam-3583	210	3	k=0	k=0	PROPN
ejpam-3583	210	4	dk	dk	PROPN
ejpam-3583	210	5	,	,	PUNCT
ejpam-3583	210	6	q	q	PROPN
ejpam-3583	210	7	r.	r.	PROPN
ejpam-3583	210	8	corcino	corcino	PROPN
ejpam-3583	210	9	,	,	PUNCT
ejpam-3583	210	10	j.	j.	PROPN
ejpam-3583	210	11	ontolan	ontolan	PROPN
ejpam-3583	210	12	,	,	PUNCT
ejpam-3583	210	13	g.	g.	PROPN
ejpam-3583	210	14	j.	j.	PROPN
ejpam-3583	210	15	rama	rama	PROPN
ejpam-3583	210	16	/	/	SYM
ejpam-3583	210	17	eur	eur	PROPN
ejpam-3583	210	18	.	.	PUNCT
ejpam-3583	211	1	j.	j.	PROPN
ejpam-3583	211	2	pure	pure	PROPN
ejpam-3583	211	3	appl	appl	PROPN
ejpam-3583	211	4	.	.	PROPN
ejpam-3583	211	5	math	math	PROPN
ejpam-3583	211	6	,	,	PUNCT
ejpam-3583	211	7	12	12	NUM
ejpam-3583	211	8	(	(	PUNCT
ejpam-3583	211	9	4	4	NUM
ejpam-3583	211	10	)	)	PUNCT
ejpam-3583	211	11	(	(	PUNCT
ejpam-3583	211	12	2019	2019	NUM
ejpam-3583	211	13	)	)	PUNCT
ejpam-3583	211	14	,	,	PUNCT
ejpam-3583	211	15	1676	1676	NUM
ejpam-3583	211	16	-	-	SYM
ejpam-3583	211	17	1688	1688	NUM
ejpam-3583	211	18	1685	1685	NUM
ejpam-3583	211	19	=	=	SYM
ejpam-3583	211	20	n−1∏	n−1∏	PROPN
ejpam-3583	211	21	k=0	k=0	PROPN
ejpam-3583	211	22	(	(	PUNCT
ejpam-3583	211	23	qr[m]q[x]q	qr[m]q[x]q	X
ejpam-3583	211	24	)	)	PUNCT
ejpam-3583	212	1	k	k	X
ejpam-3583	213	1	q	q	X
ejpam-3583	213	2	(	(	PUNCT
ejpam-3583	213	3	k	k	PROPN
ejpam-3583	213	4	2)[k]qm	2)[k]qm	PROPN
ejpam-3583	213	5	!	!	PUNCT
ejpam-3583	214	1	=	=	PUNCT
ejpam-3583	214	2	(	(	PUNCT
ejpam-3583	214	3	qr[m]q[x]q	qr[m]q[x]q	NUM
ejpam-3583	214	4	)	)	PUNCT
ejpam-3583	214	5	0	0	PUNCT
ejpam-3583	215	1	+	+	NOUN
ejpam-3583	215	2	1	1	NUM
ejpam-3583	215	3	+	+	NOUN
ejpam-3583	215	4	2+	2+	NUM
ejpam-3583	215	5	...	...	PUNCT
ejpam-3583	215	6	+n−1	+n−1	PROPN
ejpam-3583	215	7	q	q	X
ejpam-3583	215	8	(	(	PUNCT
ejpam-3583	215	9	0	0	NUM
ejpam-3583	215	10	2)+(12)+(22)+	2)+(12)+(22)+	NUM
ejpam-3583	215	11	...	...	PUNCT
ejpam-3583	215	12	+(n−1	+(n−1	PROPN
ejpam-3583	215	13	2	2	X
ejpam-3583	215	14	)	)	PUNCT
ejpam-3583	215	15	n−1∏	n−1∏	PROPN
ejpam-3583	215	16	k=0	k=0	PROPN
ejpam-3583	216	1	[	[	X
ejpam-3583	216	2	k]qm	k]qm	X
ejpam-3583	216	3	!	!	PUNCT
ejpam-3583	216	4	=	=	PUNCT
ejpam-3583	216	5	(	(	PUNCT
ejpam-3583	216	6	qr[m]q[x]q	qr[m]q[x]q	NUM
ejpam-3583	216	7	)	)	PUNCT
ejpam-3583	216	8	(	(	PUNCT
ejpam-3583	216	9	n2	n2	NOUN
ejpam-3583	216	10	)	)	PUNCT
ejpam-3583	216	11	q	q	NOUN
ejpam-3583	216	12	(	(	PUNCT
ejpam-3583	216	13	n	n	NOUN
ejpam-3583	216	14	3	3	NUM
ejpam-3583	216	15	)	)	PUNCT
ejpam-3583	216	16	n−1∏	n−1∏	PROPN
ejpam-3583	216	17	k=0	k=0	PROPN
ejpam-3583	217	1	[	[	X
ejpam-3583	217	2	k]qm	k]qm	X
ejpam-3583	217	3	!	!	PUNCT
ejpam-3583	217	4	.	.	PUNCT
ejpam-3583	218	1	this	this	PRON
ejpam-3583	218	2	is	be	AUX
ejpam-3583	218	3	exactly	exactly	ADV
ejpam-3583	218	4	the	the	DET
ejpam-3583	218	5	desired	desire	VERB
ejpam-3583	218	6	hankel	hankel	NOUN
ejpam-3583	218	7	transform	transform	VERB
ejpam-3583	218	8	.	.	PUNCT
ejpam-3583	219	1	as	as	ADP
ejpam-3583	219	2	an	an	DET
ejpam-3583	219	3	immediate	immediate	ADJ
ejpam-3583	219	4	consequence	consequence	NOUN
ejpam-3583	219	5	of	of	ADP
ejpam-3583	219	6	theorem	theorem	NOUN
ejpam-3583	219	7	3.1	3.1	NUM
ejpam-3583	219	8	,	,	PUNCT
ejpam-3583	219	9	we	we	PRON
ejpam-3583	219	10	have	have	VERB
ejpam-3583	219	11	the	the	DET
ejpam-3583	219	12	following	follow	VERB
ejpam-3583	219	13	corollary	corollary	NOUN
ejpam-3583	219	14	.	.	PUNCT
ejpam-3583	220	1	corollary	corollary	ADJ
ejpam-3583	220	2	3.2	3.2	NUM
ejpam-3583	220	3	.	.	PUNCT
ejpam-3583	221	1	the	the	DET
ejpam-3583	221	2	hankel	hankel	NOUN
ejpam-3583	221	3	transform	transform	NOUN
ejpam-3583	221	4	of	of	ADP
ejpam-3583	221	5	d∗m	d∗m	NOUN
ejpam-3583	221	6	,	,	PUNCT
ejpam-3583	221	7	r[n]q	r[n]q	NOUN
ejpam-3583	221	8	is	be	AUX
ejpam-3583	221	9	given	give	VERB
ejpam-3583	221	10	by	by	ADP
ejpam-3583	221	11	h(d∗m	h(d∗m	PROPN
ejpam-3583	221	12	,	,	PUNCT
ejpam-3583	221	13	r[n]q	r[n]q	NOUN
ejpam-3583	221	14	)	)	PUNCT
ejpam-3583	221	15	=	=	PUNCT
ejpam-3583	222	1	[	[	X
ejpam-3583	222	2	m	m	X
ejpam-3583	222	3	]	]	X
ejpam-3583	222	4	(	(	PUNCT
ejpam-3583	222	5	n2	n2	NOUN
ejpam-3583	222	6	)	)	PUNCT
ejpam-3583	222	7	q	q	NOUN
ejpam-3583	223	1	q	q	NOUN
ejpam-3583	223	2	(	(	PUNCT
ejpam-3583	223	3	n	n	NOUN
ejpam-3583	223	4	3)+r	3)+r	NUM
ejpam-3583	223	5	(	(	PUNCT
ejpam-3583	223	6	n	n	NOUN
ejpam-3583	223	7	2	2	NUM
ejpam-3583	223	8	)	)	PUNCT
ejpam-3583	223	9	n−1∏	n−1∏	PROPN
ejpam-3583	223	10	k=0	k=0	PROPN
ejpam-3583	224	1	[	[	X
ejpam-3583	224	2	k]qm	k]qm	X
ejpam-3583	224	3	!	!	PUNCT
ejpam-3583	225	1	proof	proof	NOUN
ejpam-3583	225	2	.	.	PUNCT
ejpam-3583	226	1	this	this	PRON
ejpam-3583	226	2	can	can	AUX
ejpam-3583	226	3	easily	easily	ADV
ejpam-3583	226	4	be	be	AUX
ejpam-3583	226	5	derived	derive	VERB
ejpam-3583	226	6	from	from	ADP
ejpam-3583	226	7	theorem	theorem	ADJ
ejpam-3583	226	8	3.1	3.1	NUM
ejpam-3583	226	9	by	by	ADP
ejpam-3583	226	10	letting	let	VERB
ejpam-3583	226	11	x	x	SYM
ejpam-3583	226	12	=	=	SYM
ejpam-3583	226	13	1	1	X
ejpam-3583	226	14	.	.	PUNCT
ejpam-3583	226	15	remark	remark	VERB
ejpam-3583	226	16	3.3	3.3	NUM
ejpam-3583	226	17	.	.	PUNCT
ejpam-3583	227	1	when	when	SCONJ
ejpam-3583	227	2	m	m	VERB
ejpam-3583	227	3	=	=	SYM
ejpam-3583	227	4	1	1	NUM
ejpam-3583	227	5	,	,	PUNCT
ejpam-3583	227	6	the	the	DET
ejpam-3583	227	7	hankel	hankel	NOUN
ejpam-3583	227	8	tranform	tranform	VERB
ejpam-3583	227	9	in	in	ADP
ejpam-3583	227	10	corollary	corollary	ADJ
ejpam-3583	227	11	3.2	3.2	NUM
ejpam-3583	227	12	yields	yield	NOUN
ejpam-3583	227	13	h(d∗1,r[n]q	h(d∗1,r[n]q	PRON
ejpam-3583	227	14	)	)	PUNCT
ejpam-3583	228	1	=	=	SYM
ejpam-3583	229	1	q	q	ADJ
ejpam-3583	229	2	(	(	PUNCT
ejpam-3583	229	3	n	n	NUM
ejpam-3583	229	4	3)+r	3)+r	NUM
ejpam-3583	229	5	(	(	PUNCT
ejpam-3583	229	6	n	n	NOUN
ejpam-3583	229	7	2	2	NUM
ejpam-3583	229	8	)	)	PUNCT
ejpam-3583	229	9	n−1∏	n−1∏	PROPN
ejpam-3583	229	10	k=0	k=0	PROPN
ejpam-3583	230	1	[	[	X
ejpam-3583	230	2	k]q	k]q	NOUN
ejpam-3583	230	3	!	!	PUNCT
ejpam-3583	230	4	,	,	PUNCT
ejpam-3583	230	5	which	which	PRON
ejpam-3583	230	6	is	be	AUX
ejpam-3583	230	7	exactly	exactly	ADV
ejpam-3583	230	8	the	the	DET
ejpam-3583	230	9	hankel	hankel	NOUN
ejpam-3583	230	10	transform	transform	NOUN
ejpam-3583	230	11	of	of	ADP
ejpam-3583	230	12	the	the	DET
ejpam-3583	230	13	second	second	ADJ
ejpam-3583	230	14	form	form	NOUN
ejpam-3583	230	15	of	of	ADP
ejpam-3583	230	16	q	q	ADJ
ejpam-3583	230	17	-	-	ADJ
ejpam-3583	230	18	noncentral	noncentral	ADJ
ejpam-3583	230	19	bell	bell	NOUN
ejpam-3583	230	20	numbers	number	NOUN
ejpam-3583	230	21	b̂q	b̂q	PROPN
ejpam-3583	230	22	n	n	CCONJ
ejpam-3583	230	23	,	,	PUNCT
ejpam-3583	230	24	a	a	PRON
ejpam-3583	230	25	when	when	SCONJ
ejpam-3583	230	26	r	r	NOUN
ejpam-3583	230	27	=	=	SYM
ejpam-3583	230	28	−a	−a	NOUN
ejpam-3583	230	29	in	in	ADP
ejpam-3583	230	30	[	[	X
ejpam-3583	230	31	11	11	NUM
ejpam-3583	230	32	]	]	PUNCT
ejpam-3583	230	33	defined	define	VERB
ejpam-3583	230	34	by	by	ADP
ejpam-3583	230	35	b̂q	b̂q	PROPN
ejpam-3583	230	36	n	n	CCONJ
ejpam-3583	230	37	,	,	PUNCT
ejpam-3583	230	38	a	a	DET
ejpam-3583	230	39	=	=	SYM
ejpam-3583	230	40	n∑	n∑	PROPN
ejpam-3583	230	41	k=0	k=0	PROPN
ejpam-3583	230	42	s∗a[n	s∗a[n	NUM
ejpam-3583	230	43	,	,	PUNCT
ejpam-3583	230	44	k	k	X
ejpam-3583	230	45	]	]	PUNCT
ejpam-3583	230	46	.	.	PUNCT
ejpam-3583	231	1	remark	remark	PROPN
ejpam-3583	231	2	3.4	3.4	NUM
ejpam-3583	231	3	.	.	PUNCT
ejpam-3583	232	1	when	when	SCONJ
ejpam-3583	232	2	q	q	ADJ
ejpam-3583	232	3	→	→	SYM
ejpam-3583	232	4	1	1	NUM
ejpam-3583	232	5	,	,	PUNCT
ejpam-3583	232	6	corollary	corollary	ADJ
ejpam-3583	232	7	3.2	3.2	NUM
ejpam-3583	232	8	gives	give	VERB
ejpam-3583	232	9	h(d∗m	h(d∗m	NOUN
ejpam-3583	232	10	,	,	PUNCT
ejpam-3583	232	11	r(n	r(n	PROPN
ejpam-3583	232	12	)	)	PUNCT
ejpam-3583	232	13	)	)	PUNCT
ejpam-3583	233	1	=	=	SYM
ejpam-3583	233	2	m(n2	m(n2	NOUN
ejpam-3583	233	3	)	)	PUNCT
ejpam-3583	233	4	n−1∏	n−1∏	PROPN
ejpam-3583	233	5	k=0	k=0	PROPN
ejpam-3583	233	6	k	k	PROPN
ejpam-3583	233	7	!	!	PROPN
ejpam-3583	233	8	,	,	PUNCT
ejpam-3583	233	9	which	which	PRON
ejpam-3583	233	10	is	be	AUX
ejpam-3583	233	11	exactly	exactly	ADV
ejpam-3583	233	12	the	the	DET
ejpam-3583	233	13	hankel	hankel	NOUN
ejpam-3583	233	14	transform	transform	NOUN
ejpam-3583	233	15	of	of	ADP
ejpam-3583	233	16	(	(	PUNCT
ejpam-3583	233	17	r	r	NOUN
ejpam-3583	233	18	,	,	PUNCT
ejpam-3583	233	19	β)-bell	β)-bell	PUNCT
ejpam-3583	233	20	numbers	number	NOUN
ejpam-3583	233	21	gn	gn	PROPN
ejpam-3583	233	22	,	,	PUNCT
ejpam-3583	233	23	β	β	X
ejpam-3583	233	24	,	,	PUNCT
ejpam-3583	233	25	r	r	NOUN
ejpam-3583	233	26	with	with	ADP
ejpam-3583	233	27	β	β	X
ejpam-3583	233	28	=	=	PUNCT
ejpam-3583	233	29	m	m	VERB
ejpam-3583	233	30	in	in	ADP
ejpam-3583	233	31	[	[	X
ejpam-3583	233	32	14	14	NUM
ejpam-3583	233	33	]	]	PUNCT
ejpam-3583	233	34	.	.	PUNCT
ejpam-3583	234	1	theorem	theorem	VERB
ejpam-3583	234	2	3.5	3.5	NUM
ejpam-3583	234	3	.	.	PUNCT
ejpam-3583	235	1	the	the	DET
ejpam-3583	235	2	hankel	hankel	NOUN
ejpam-3583	235	3	transform	transform	NOUN
ejpam-3583	235	4	of	of	ADP
ejpam-3583	235	5	ϕn[x	ϕn[x	PROPN
ejpam-3583	235	6	,	,	PUNCT
ejpam-3583	235	7	r	r	PROPN
ejpam-3583	235	8	,	,	PUNCT
ejpam-3583	235	9	m]q	m]q	X
ejpam-3583	235	10	corresponding	correspond	VERB
ejpam-3583	235	11	to	to	ADP
ejpam-3583	235	12	the	the	DET
ejpam-3583	235	13	1st	1st	ADJ
ejpam-3583	235	14	hankel	hankel	NOUN
ejpam-3583	235	15	determinant	determinant	ADJ
ejpam-3583	235	16	d[n	d[n	NOUN
ejpam-3583	235	17	,	,	PUNCT
ejpam-3583	235	18	1]q	1]q	NUM
ejpam-3583	235	19	is	be	AUX
ejpam-3583	235	20	given	give	VERB
ejpam-3583	235	21	by	by	ADP
ejpam-3583	235	22	h	h	PROPN
ejpam-3583	235	23	(	(	PUNCT
ejpam-3583	235	24	ϕn[x	ϕn[x	PROPN
ejpam-3583	235	25	,	,	PUNCT
ejpam-3583	235	26	r	r	NOUN
ejpam-3583	235	27	,	,	PUNCT
ejpam-3583	235	28	m]q	m]q	NOUN
ejpam-3583	235	29	)	)	PUNCT
ejpam-3583	235	30	=	=	SYM
ejpam-3583	235	31	d[n	d[n	PROPN
ejpam-3583	235	32	,	,	PUNCT
ejpam-3583	235	33	1]q	1]q	PROPN
ejpam-3583	235	34	=	=	SYM
ejpam-3583	235	35	(	(	PUNCT
ejpam-3583	235	36	[	[	X
ejpam-3583	235	37	m]q[x]q	m]q[x]q	NOUN
ejpam-3583	235	38	)	)	PUNCT
ejpam-3583	235	39	(	(	PUNCT
ejpam-3583	235	40	n2	n2	NOUN
ejpam-3583	235	41	)	)	PUNCT
ejpam-3583	235	42	qr	qr	NOUN
ejpam-3583	235	43	(	(	PUNCT
ejpam-3583	235	44	n	n	PROPN
ejpam-3583	235	45	2)+(n3	2)+(n3	NUM
ejpam-3583	235	46	)	)	PUNCT
ejpam-3583	236	1	n−1∏	n−1∏	PROPN
ejpam-3583	236	2	k=0	k=0	PROPN
ejpam-3583	237	1	[	[	X
ejpam-3583	237	2	k]qm	k]qm	X
ejpam-3583	237	3	!	!	PUNCT
ejpam-3583	238	1	n∑	n∑	X
ejpam-3583	238	2	k=0	k=0	PROPN
ejpam-3583	238	3	(	(	PUNCT
ejpam-3583	238	4	−1)n[x]kqq	−1)n[x]kqq	PROPN
ejpam-3583	238	5	(	(	PUNCT
ejpam-3583	238	6	k2	k2	NOUN
ejpam-3583	238	7	)	)	PUNCT
ejpam-3583	238	8	[	[	PUNCT
ejpam-3583	239	1	n	n	X
ejpam-3583	239	2	k	k	NOUN
ejpam-3583	239	3	]	]	PUNCT
ejpam-3583	239	4	q	q	PUNCT
ejpam-3583	240	1	k−1∏	k−1∏	NOUN
ejpam-3583	240	2	j=0	j=0	PROPN
ejpam-3583	241	1	[	[	X
ejpam-3583	241	2	r	r	X
ejpam-3583	241	3	+	+	PROPN
ejpam-3583	241	4	jm]q	jm]q	PROPN
ejpam-3583	241	5	.	.	PUNCT
ejpam-3583	242	1	references	reference	NOUN
ejpam-3583	242	2	1686	1686	NUM
ejpam-3583	242	3	proof	proof	NOUN
ejpam-3583	242	4	.	.	PUNCT
ejpam-3583	243	1	taking	take	VERB
ejpam-3583	243	2	[	[	PRON
ejpam-3583	243	3	pn(x)]q	pn(x)]q	NOUN
ejpam-3583	243	4	=	=	SYM
ejpam-3583	243	5	hn	hn	PROPN
ejpam-3583	243	6	,	,	PUNCT
ejpam-3583	243	7	q(x	q(x	PROPN
ejpam-3583	243	8	,	,	PUNCT
ejpam-3583	243	9	a	a	PRON
ejpam-3583	243	10	,	,	PUNCT
ejpam-3583	243	11	r	r	NOUN
ejpam-3583	243	12	,	,	PUNCT
ejpam-3583	243	13	m	m	NOUN
ejpam-3583	243	14	)	)	PUNCT
ejpam-3583	243	15	,	,	PUNCT
ejpam-3583	243	16	we	we	PRON
ejpam-3583	243	17	can	can	AUX
ejpam-3583	243	18	compute	compute	VERB
ejpam-3583	243	19	the	the	DET
ejpam-3583	243	20	desired	desire	VERB
ejpam-3583	243	21	hankel	hankel	NOUN
ejpam-3583	243	22	transform	transform	VERB
ejpam-3583	243	23	using	use	VERB
ejpam-3583	243	24	(	(	PUNCT
ejpam-3583	243	25	18	18	NUM
ejpam-3583	243	26	)	)	PUNCT
ejpam-3583	243	27	with	with	ADP
ejpam-3583	243	28	[	[	X
ejpam-3583	243	29	pn(0)]q	pn(0)]q	X
ejpam-3583	243	30	=	=	SYM
ejpam-3583	243	31	hn	hn	PROPN
ejpam-3583	243	32	,	,	PUNCT
ejpam-3583	243	33	q(0	q(0	PROPN
ejpam-3583	243	34	,	,	PUNCT
ejpam-3583	243	35	a	a	PRON
ejpam-3583	243	36	,	,	PUNCT
ejpam-3583	243	37	r	r	NOUN
ejpam-3583	243	38	,	,	PUNCT
ejpam-3583	243	39	m	m	NOUN
ejpam-3583	243	40	)	)	PUNCT
ejpam-3583	244	1	=	=	SYM
ejpam-3583	244	2	n∑	n∑	NOUN
ejpam-3583	244	3	k=0	k=0	PROPN
ejpam-3583	244	4	(	(	PUNCT
ejpam-3583	244	5	−[a]q	−[a]q	X
ejpam-3583	244	6	)	)	PUNCT
ejpam-3583	244	7	k	k	NOUN
ejpam-3583	245	1	q	q	X
ejpam-3583	245	2	(	(	PUNCT
ejpam-3583	245	3	k	k	NOUN
ejpam-3583	245	4	2	2	X
ejpam-3583	245	5	)	)	PUNCT
ejpam-3583	245	6	[	[	PUNCT
ejpam-3583	245	7	n	n	X
ejpam-3583	245	8	k	k	X
ejpam-3583	245	9	]	]	PUNCT
ejpam-3583	245	10	q	q	X
ejpam-3583	246	1	[	[	X
ejpam-3583	246	2	0−	0−	NUM
ejpam-3583	246	3	r|m]k	r|m]k	NUM
ejpam-3583	246	4	,	,	PUNCT
ejpam-3583	246	5	q	q	NOUN
ejpam-3583	246	6	=	=	SYM
ejpam-3583	246	7	n∑	n∑	NOUN
ejpam-3583	246	8	k=0	k=0	PROPN
ejpam-3583	246	9	(	(	PUNCT
ejpam-3583	246	10	−1)k[a]kqq	−1)k[a]kqq	NUM
ejpam-3583	246	11	(	(	PUNCT
ejpam-3583	246	12	k2	k2	NOUN
ejpam-3583	246	13	)	)	PUNCT
ejpam-3583	246	14	[	[	PUNCT
ejpam-3583	246	15	n	n	X
ejpam-3583	246	16	k	k	X
ejpam-3583	246	17	]	]	X
ejpam-3583	246	18	q	q	X
ejpam-3583	246	19	(	(	PUNCT
ejpam-3583	246	20	−1)k	−1)k	PROPN
ejpam-3583	246	21	k−1∏	k−1∏	PROPN
ejpam-3583	246	22	j=0	j=0	PUNCT
ejpam-3583	247	1	[	[	X
ejpam-3583	247	2	r	r	X
ejpam-3583	247	3	+	+	NUM
ejpam-3583	247	4	jm]q	jm]q	NOUN
ejpam-3583	247	5	=	=	SYM
ejpam-3583	247	6	n∑	n∑	NOUN
ejpam-3583	247	7	k=0	k=0	PROPN
ejpam-3583	248	1	[	[	X
ejpam-3583	248	2	a]kqq	a]kqq	X
ejpam-3583	248	3	(	(	PUNCT
ejpam-3583	248	4	k2	k2	NOUN
ejpam-3583	248	5	)	)	PUNCT
ejpam-3583	248	6	[	[	PUNCT
ejpam-3583	248	7	n	n	X
ejpam-3583	248	8	k	k	NOUN
ejpam-3583	248	9	]	]	PUNCT
ejpam-3583	248	10	q	q	PUNCT
ejpam-3583	249	1	k−1∏	k−1∏	NOUN
ejpam-3583	249	2	j=0	j=0	PROPN
ejpam-3583	250	1	[	[	X
ejpam-3583	250	2	r	r	X
ejpam-3583	250	3	+	+	X
ejpam-3583	250	4	jm]q	jm]q	PROPN
ejpam-3583	250	5	.	.	PUNCT
ejpam-3583	251	1	hence	hence	ADV
ejpam-3583	251	2	,	,	PUNCT
ejpam-3583	251	3	we	we	PRON
ejpam-3583	251	4	have	have	VERB
ejpam-3583	251	5	h	h	NOUN
ejpam-3583	251	6	(	(	PUNCT
ejpam-3583	251	7	ϕn[x	ϕn[x	PROPN
ejpam-3583	251	8	,	,	PUNCT
ejpam-3583	251	9	r	r	NOUN
ejpam-3583	251	10	,	,	PUNCT
ejpam-3583	251	11	m]q	m]q	NOUN
ejpam-3583	251	12	)	)	PUNCT
ejpam-3583	251	13	=	=	SYM
ejpam-3583	251	14	d[n	d[n	PROPN
ejpam-3583	251	15	,	,	PUNCT
ejpam-3583	251	16	1]q	1]q	PROPN
ejpam-3583	251	17	=	=	PUNCT
ejpam-3583	251	18	d[n	d[n	PROPN
ejpam-3583	251	19	,	,	PUNCT
ejpam-3583	251	20	0]q(−1)n[pn(0)]q	0]q(−1)n[pn(0)]q	PROPN
ejpam-3583	252	1	=	=	SYM
ejpam-3583	253	1	(	(	PUNCT
ejpam-3583	253	2	[	[	X
ejpam-3583	253	3	m]q[x]q	m]q[x]q	NOUN
ejpam-3583	253	4	)	)	PUNCT
ejpam-3583	253	5	(	(	PUNCT
ejpam-3583	253	6	n2	n2	NOUN
ejpam-3583	253	7	)	)	PUNCT
ejpam-3583	253	8	qr	qr	NOUN
ejpam-3583	253	9	(	(	PUNCT
ejpam-3583	253	10	n	n	PROPN
ejpam-3583	253	11	2)+(n3	2)+(n3	NUM
ejpam-3583	253	12	)	)	PUNCT
ejpam-3583	253	13	n−1∏	n−1∏	PROPN
ejpam-3583	253	14	k=0	k=0	PROPN
ejpam-3583	254	1	[	[	X
ejpam-3583	254	2	k]qm	k]qm	X
ejpam-3583	254	3	!	!	PUNCT
ejpam-3583	255	1	n∑	n∑	X
ejpam-3583	255	2	k=0	k=0	PROPN
ejpam-3583	255	3	(	(	PUNCT
ejpam-3583	255	4	−1)n[x]kqq	−1)n[x]kqq	PROPN
ejpam-3583	255	5	(	(	PUNCT
ejpam-3583	255	6	k2	k2	NOUN
ejpam-3583	255	7	)	)	PUNCT
ejpam-3583	255	8	[	[	PUNCT
ejpam-3583	256	1	n	n	X
ejpam-3583	256	2	k	k	NOUN
ejpam-3583	256	3	]	]	PUNCT
ejpam-3583	256	4	q	q	PUNCT
ejpam-3583	257	1	k−1∏	k−1∏	NOUN
ejpam-3583	257	2	j=0	j=0	PROPN
ejpam-3583	258	1	[	[	X
ejpam-3583	258	2	r	r	X
ejpam-3583	258	3	+	+	X
ejpam-3583	258	4	jm]q	jm]q	PROPN
ejpam-3583	258	5	.	.	PUNCT
ejpam-3583	259	1	4	4	X
ejpam-3583	259	2	.	.	X
ejpam-3583	259	3	recommendation	recommendation	NOUN
ejpam-3583	259	4	we	we	PRON
ejpam-3583	259	5	observe	observe	VERB
ejpam-3583	259	6	that	that	SCONJ
ejpam-3583	259	7	the	the	DET
ejpam-3583	259	8	hankel	hankel	NOUN
ejpam-3583	259	9	transform	transform	NOUN
ejpam-3583	259	10	of	of	ADP
ejpam-3583	259	11	the	the	DET
ejpam-3583	259	12	second	second	ADJ
ejpam-3583	259	13	and	and	CCONJ
ejpam-3583	259	14	third	third	ADJ
ejpam-3583	259	15	forms	form	NOUN
ejpam-3583	259	16	of	of	ADP
ejpam-3583	259	17	the	the	DET
ejpam-3583	259	18	q	q	NOUN
ejpam-3583	259	19	-	-	PUNCT
ejpam-3583	259	20	analogue	analogue	NOUN
ejpam-3583	259	21	of	of	ADP
ejpam-3583	259	22	r	r	NOUN
ejpam-3583	259	23	-	-	PUNCT
ejpam-3583	259	24	dowling	dowle	VERB
ejpam-3583	259	25	numbers	number	NOUN
ejpam-3583	259	26	are	be	AUX
ejpam-3583	259	27	obtained	obtain	VERB
ejpam-3583	259	28	using	use	VERB
ejpam-3583	259	29	different	different	ADJ
ejpam-3583	259	30	methods	method	NOUN
ejpam-3583	259	31	.	.	PUNCT
ejpam-3583	260	1	it	it	PRON
ejpam-3583	260	2	would	would	AUX
ejpam-3583	260	3	be	be	AUX
ejpam-3583	260	4	interesting	interesting	ADJ
ejpam-3583	260	5	to	to	PART
ejpam-3583	260	6	find	find	VERB
ejpam-3583	260	7	a	a	DET
ejpam-3583	260	8	method	method	NOUN
ejpam-3583	260	9	that	that	PRON
ejpam-3583	260	10	can	can	AUX
ejpam-3583	260	11	be	be	AUX
ejpam-3583	260	12	used	use	VERB
ejpam-3583	260	13	to	to	PART
ejpam-3583	260	14	establish	establish	VERB
ejpam-3583	260	15	the	the	DET
ejpam-3583	260	16	hankel	hankel	NOUN
ejpam-3583	260	17	transform	transform	NOUN
ejpam-3583	260	18	of	of	ADP
ejpam-3583	260	19	the	the	DET
ejpam-3583	260	20	first	first	ADJ
ejpam-3583	260	21	form	form	NOUN
ejpam-3583	260	22	of	of	ADP
ejpam-3583	260	23	the	the	DET
ejpam-3583	260	24	q	q	NOUN
ejpam-3583	260	25	-	-	PUNCT
ejpam-3583	260	26	analogue	analogue	NOUN
ejpam-3583	260	27	of	of	ADP
ejpam-3583	260	28	r	r	NOUN
ejpam-3583	260	29	-	-	PUNCT
ejpam-3583	260	30	dowling	dowle	VERB
ejpam-3583	260	31	numbers	number	NOUN
ejpam-3583	260	32	.	.	PUNCT
ejpam-3583	261	1	it	it	PRON
ejpam-3583	261	2	may	may	AUX
ejpam-3583	261	3	be	be	AUX
ejpam-3583	261	4	possible	possible	ADJ
ejpam-3583	261	5	that	that	SCONJ
ejpam-3583	261	6	this	this	DET
ejpam-3583	261	7	method	method	NOUN
ejpam-3583	261	8	is	be	AUX
ejpam-3583	261	9	closely	closely	ADV
ejpam-3583	261	10	related	relate	VERB
ejpam-3583	261	11	to	to	ADP
ejpam-3583	261	12	the	the	DET
ejpam-3583	261	13	one	one	NOUN
ejpam-3583	261	14	being	be	AUX
ejpam-3583	261	15	applied	apply	VERB
ejpam-3583	261	16	in	in	ADP
ejpam-3583	261	17	this	this	DET
ejpam-3583	261	18	paper	paper	NOUN
ejpam-3583	261	19	.	.	PUNCT
ejpam-3583	262	1	data	datum	NOUN
ejpam-3583	262	2	availability	availability	NOUN
ejpam-3583	262	3	.	.	PUNCT
ejpam-3583	263	1	no	no	DET
ejpam-3583	263	2	data	datum	NOUN
ejpam-3583	263	3	were	be	AUX
ejpam-3583	263	4	used	use	VERB
ejpam-3583	263	5	to	to	PART
ejpam-3583	263	6	support	support	VERB
ejpam-3583	263	7	this	this	DET
ejpam-3583	263	8	study	study	NOUN
ejpam-3583	263	9	.	.	PUNCT
ejpam-3583	264	1	acknowledgements	acknowledgement	NOUN
ejpam-3583	264	2	this	this	DET
ejpam-3583	264	3	research	research	NOUN
ejpam-3583	264	4	has	have	AUX
ejpam-3583	264	5	been	be	AUX
ejpam-3583	264	6	funded	fund	VERB
ejpam-3583	264	7	by	by	ADP
ejpam-3583	264	8	cebu	cebu	PROPN
ejpam-3583	264	9	normal	normal	ADJ
ejpam-3583	264	10	university	university	PROPN
ejpam-3583	264	11	(	(	PUNCT
ejpam-3583	264	12	cnu	cnu	PROPN
ejpam-3583	264	13	)	)	PUNCT
ejpam-3583	264	14	and	and	CCONJ
ejpam-3583	264	15	the	the	DET
ejpam-3583	264	16	commission	commission	NOUN
ejpam-3583	264	17	on	on	ADP
ejpam-3583	264	18	higher	high	ADJ
ejpam-3583	264	19	education	education	NOUN
ejpam-3583	264	20	grants	grant	NOUN
ejpam-3583	264	21	-	-	PUNCT
ejpam-3583	264	22	in	in	ADP
ejpam-3583	264	23	-	-	PUNCT
ejpam-3583	264	24	aid	aid	NOUN
ejpam-3583	264	25	for	for	ADP
ejpam-3583	264	26	research	research	NOUN
ejpam-3583	264	27	(	(	PUNCT
ejpam-3583	264	28	ched	che	VERB
ejpam-3583	264	29	-	-	PUNCT
ejpam-3583	264	30	gia	gia	NOUN
ejpam-3583	264	31	)	)	PUNCT
ejpam-3583	264	32	.	.	PUNCT
ejpam-3583	265	1	references	reference	NOUN
ejpam-3583	265	2	[	[	X
ejpam-3583	265	3	1	1	NUM
ejpam-3583	265	4	]	]	PUNCT
ejpam-3583	265	5	m.	m.	NOUN
ejpam-3583	265	6	aigner	aigner	NOUN
ejpam-3583	265	7	,	,	PUNCT
ejpam-3583	265	8	a	a	DET
ejpam-3583	265	9	characterization	characterization	NOUN
ejpam-3583	265	10	of	of	ADP
ejpam-3583	265	11	the	the	DET
ejpam-3583	265	12	bell	bell	NOUN
ejpam-3583	265	13	numbers	number	NOUN
ejpam-3583	265	14	,	,	PUNCT
ejpam-3583	265	15	discrete	discrete	ADJ
ejpam-3583	265	16	math	math	NOUN
ejpam-3583	265	17	.	.	PUNCT
ejpam-3583	266	1	205	205	NUM
ejpam-3583	266	2	(	(	PUNCT
ejpam-3583	266	3	1999	1999	NUM
ejpam-3583	266	4	)	)	PUNCT
ejpam-3583	266	5	,	,	PUNCT
ejpam-3583	266	6	207	207	NUM
ejpam-3583	266	7	-	-	SYM
ejpam-3583	266	8	210	210	NUM
ejpam-3583	266	9	.	.	PUNCT
ejpam-3583	267	1	[	[	X
ejpam-3583	267	2	2	2	NUM
ejpam-3583	267	3	]	]	X
ejpam-3583	267	4	a.z	a.z	PROPN
ejpam-3583	267	5	.	.	PROPN
ejpam-3583	267	6	broder	broder	PROPN
ejpam-3583	267	7	,	,	PUNCT
ejpam-3583	267	8	the	the	DET
ejpam-3583	267	9	r	r	NOUN
ejpam-3583	267	10	-	-	PUNCT
ejpam-3583	267	11	stirling	stirling	NOUN
ejpam-3583	267	12	numbers	number	NOUN
ejpam-3583	267	13	,	,	PUNCT
ejpam-3583	267	14	discrete	discrete	ADJ
ejpam-3583	267	15	math	math	NOUN
ejpam-3583	267	16	.	.	PUNCT
ejpam-3583	268	1	49(1984	49(1984	X
ejpam-3583	268	2	)	)	PUNCT
ejpam-3583	268	3	,	,	PUNCT
ejpam-3583	268	4	241	241	PROPN
ejpam-3583	268	5	-	-	SYM
ejpam-3583	268	6	259	259	NUM
ejpam-3583	268	7	.	.	PUNCT
ejpam-3583	269	1	[	[	X
ejpam-3583	269	2	3	3	NUM
ejpam-3583	269	3	]	]	X
ejpam-3583	269	4	carlitz	carlitz	PROPN
ejpam-3583	269	5	,	,	PUNCT
ejpam-3583	269	6	l.	l.	PROPN
ejpam-3583	269	7	,	,	PUNCT
ejpam-3583	269	8	q	q	ADJ
ejpam-3583	269	9	-	-	PUNCT
ejpam-3583	269	10	bernoulli	bernoulli	NOUN
ejpam-3583	269	11	numbers	number	NOUN
ejpam-3583	269	12	and	and	CCONJ
ejpam-3583	269	13	polynomials	polynomial	NOUN
ejpam-3583	269	14	.	.	PUNCT
ejpam-3583	270	1	duke	duke	PROPN
ejpam-3583	270	2	math	math	PROPN
ejpam-3583	270	3	.	.	PUNCT
ejpam-3583	271	1	j.	j.	PROPN
ejpam-3583	271	2	15	15	NUM
ejpam-3583	271	3	(	(	PUNCT
ejpam-3583	271	4	1948	1948	NUM
ejpam-3583	271	5	)	)	PUNCT
ejpam-3583	271	6	987	987	NUM
ejpam-3583	271	7	-	-	SYM
ejpam-3583	271	8	1000	1000	NUM
ejpam-3583	271	9	.	.	PUNCT
ejpam-3583	272	1	references	reference	NOUN
ejpam-3583	272	2	1687	1687	NUM
ejpam-3583	272	3	[	[	X
ejpam-3583	272	4	4	4	NUM
ejpam-3583	272	5	]	]	SYM
ejpam-3583	272	6	ch.a	ch.a	NOUN
ejpam-3583	272	7	.	.	PUNCT
ejpam-3583	273	1	charalambides	charalambide	NOUN
ejpam-3583	274	1	and	and	CCONJ
ejpam-3583	275	1	j.	j.	PROPN
ejpam-3583	275	2	singh	singh	PROPN
ejpam-3583	275	3	,	,	PUNCT
ejpam-3583	275	4	a	a	DET
ejpam-3583	275	5	review	review	NOUN
ejpam-3583	275	6	of	of	ADP
ejpam-3583	275	7	the	the	DET
ejpam-3583	275	8	stirling	stirling	NOUN
ejpam-3583	275	9	numbers	number	NOUN
ejpam-3583	275	10	,	,	PUNCT
ejpam-3583	275	11	their	their	PRON
ejpam-3583	275	12	generalization	generalization	NOUN
ejpam-3583	275	13	and	and	CCONJ
ejpam-3583	275	14	statistical	statistical	ADJ
ejpam-3583	275	15	applications	application	NOUN
ejpam-3583	275	16	,	,	PUNCT
ejpam-3583	275	17	commun	commun	PROPN
ejpam-3583	275	18	.	.	PUNCT
ejpam-3583	275	19	statist.-theory	statist.-theory	ADJ
ejpam-3583	275	20	meth	meth	NOUN
ejpam-3583	275	21	.	.	PUNCT
ejpam-3583	276	1	20(8	20(8	NUM
ejpam-3583	276	2	)	)	PUNCT
ejpam-3583	276	3	(	(	PUNCT
ejpam-3583	276	4	1988	1988	NUM
ejpam-3583	276	5	)	)	PUNCT
ejpam-3583	276	6	,	,	PUNCT
ejpam-3583	276	7	2533	2533	NUM
ejpam-3583	276	8	-	-	SYM
ejpam-3583	276	9	2595	2595	NUM
ejpam-3583	276	10	.	.	PUNCT
ejpam-3583	277	1	[	[	X
ejpam-3583	277	2	5	5	NUM
ejpam-3583	277	3	]	]	X
ejpam-3583	277	4	g.s	g.s	PROPN
ejpam-3583	277	5	.	.	PROPN
ejpam-3583	277	6	cheon	cheon	PROPN
ejpam-3583	277	7	and	and	CCONJ
ejpam-3583	277	8	j.h	j.h	PROPN
ejpam-3583	277	9	.	.	PROPN
ejpam-3583	277	10	jung	jung	PROPN
ejpam-3583	277	11	,	,	PUNCT
ejpam-3583	277	12	r	r	PROPN
ejpam-3583	277	13	-	-	PUNCT
ejpam-3583	277	14	whitney	whitney	NOUN
ejpam-3583	277	15	number	number	NOUN
ejpam-3583	277	16	of	of	ADP
ejpam-3583	277	17	dowling	dowling	NOUN
ejpam-3583	277	18	lattices	lattice	NOUN
ejpam-3583	277	19	,	,	PUNCT
ejpam-3583	277	20	discrete	discrete	ADJ
ejpam-3583	277	21	math	math	NOUN
ejpam-3583	277	22	.	.	PUNCT
ejpam-3583	278	1	312(2012	312(2012	NUM
ejpam-3583	278	2	)	)	PUNCT
ejpam-3583	278	3	,	,	PUNCT
ejpam-3583	278	4	2337–2348	2337–2348	NUM
ejpam-3583	278	5	.	.	PUNCT
ejpam-3583	279	1	[	[	X
ejpam-3583	279	2	6	6	NUM
ejpam-3583	279	3	]	]	PUNCT
ejpam-3583	279	4	j.	j.	PROPN
ejpam-3583	279	5	cigler	cigler	PROPN
ejpam-3583	279	6	,	,	PUNCT
ejpam-3583	279	7	a	a	DET
ejpam-3583	279	8	new	new	ADJ
ejpam-3583	279	9	q	q	NOUN
ejpam-3583	279	10	-	-	PUNCT
ejpam-3583	279	11	analog	analog	NOUN
ejpam-3583	279	12	of	of	ADP
ejpam-3583	279	13	stirling	stirling	NOUN
ejpam-3583	279	14	numbers	number	NOUN
ejpam-3583	279	15	.	.	PUNCT
ejpam-3583	280	1	sitzunber	sitzunber	PROPN
ejpam-3583	280	2	.	.	PUNCT
ejpam-3583	281	1	abt	abt	PROPN
ejpam-3583	281	2	.	.	PUNCT
ejpam-3583	282	1	ii	ii	PROPN
ejpam-3583	282	2	.	.	PUNCT
ejpam-3583	283	1	201.(1992	201.(1992	NUM
ejpam-3583	283	2	)	)	PUNCT
ejpam-3583	283	3	97	97	NUM
ejpam-3583	283	4	-	-	SYM
ejpam-3583	283	5	109	109	NUM
ejpam-3583	283	6	.	.	PUNCT
ejpam-3583	284	1	[	[	X
ejpam-3583	284	2	7	7	X
ejpam-3583	284	3	]	]	X
ejpam-3583	284	4	j.	j.	PROPN
ejpam-3583	284	5	cigler	cigler	PROPN
ejpam-3583	284	6	,	,	PUNCT
ejpam-3583	284	7	eine	eine	PROPN
ejpam-3583	284	8	charakterisierung	charakterisierung	PROPN
ejpam-3583	284	9	der	der	PROPN
ejpam-3583	284	10	q	q	NOUN
ejpam-3583	284	11	-	-	PUNCT
ejpam-3583	284	12	exponentialpolynome	exponentialpolynome	ADJ
ejpam-3583	284	13	,	,	PUNCT
ejpam-3583	284	14	sterreich	sterreich	ADJ
ejpam-3583	284	15	.	.	PUNCT
ejpam-3583	284	16	akad	akad	PROPN
ejpam-3583	284	17	.	.	PUNCT
ejpam-3583	285	1	wiss	wiss	PROPN
ejpam-3583	285	2	.	.	PUNCT
ejpam-3583	286	1	math.-natur	math.-natur	PROPN
ejpam-3583	286	2	.	.	PUNCT
ejpam-3583	287	1	kl	kl	PROPN
ejpam-3583	287	2	.	.	PUNCT
ejpam-3583	287	3	sitzungsber	sitzungsber	PROPN
ejpam-3583	287	4	.	.	PUNCT
ejpam-3583	288	1	ii	ii	PROPN
ejpam-3583	288	2	,	,	PUNCT
ejpam-3583	288	3	208	208	NUM
ejpam-3583	288	4	(	(	PUNCT
ejpam-3583	288	5	1999	1999	NUM
ejpam-3583	288	6	)	)	PUNCT
ejpam-3583	288	7	143157	143157	NUM
ejpam-3583	288	8	.	.	PUNCT
ejpam-3583	289	1	[	[	X
ejpam-3583	289	2	8	8	X
ejpam-3583	289	3	]	]	X
ejpam-3583	289	4	j.	j.	PROPN
ejpam-3583	289	5	cigler	cigler	PROPN
ejpam-3583	289	6	,	,	PUNCT
ejpam-3583	289	7	hankel	hankel	NOUN
ejpam-3583	289	8	determinants	determinant	NOUN
ejpam-3583	289	9	of	of	ADP
ejpam-3583	289	10	generalized	generalized	ADJ
ejpam-3583	289	11	q	q	ADJ
ejpam-3583	289	12	-	-	ADJ
ejpam-3583	289	13	exponential	exponential	ADJ
ejpam-3583	289	14	polynomials	polynomial	NOUN
ejpam-3583	289	15	,	,	PUNCT
ejpam-3583	289	16	arxiv:0909.5581v1	arxiv:0909.5581v1	NOUN
ejpam-3583	289	17	[	[	X
ejpam-3583	289	18	math.co	math.co	X
ejpam-3583	289	19	]	]	X
ejpam-3583	289	20	.	.	PUNCT
ejpam-3583	290	1	available	available	ADJ
ejpam-3583	290	2	at	at	ADP
ejpam-3583	290	3	https://arxiv.org/abs/0909.5581	https://arxiv.org/abs/0909.5581	NOUN
ejpam-3583	290	4	.	.	PUNCT
ejpam-3583	291	1	[	[	X
ejpam-3583	291	2	9	9	NUM
ejpam-3583	291	3	]	]	PUNCT
ejpam-3583	291	4	l.	l.	PROPN
ejpam-3583	291	5	comtet	comtet	PROPN
ejpam-3583	291	6	,	,	PUNCT
ejpam-3583	291	7	advanced	advanced	ADJ
ejpam-3583	291	8	combinatorics	combinatoric	NOUN
ejpam-3583	291	9	,	,	PUNCT
ejpam-3583	291	10	reidel	reidel	PROPN
ejpam-3583	291	11	,	,	PUNCT
ejpam-3583	291	12	dordrecht	dordrecht	PROPN
ejpam-3583	291	13	,	,	PUNCT
ejpam-3583	291	14	the	the	DET
ejpam-3583	291	15	netherlands	netherlands	PROPN
ejpam-3583	291	16	,	,	PUNCT
ejpam-3583	291	17	1974	1974	NUM
ejpam-3583	291	18	.	.	PUNCT
ejpam-3583	292	1	[	[	X
ejpam-3583	292	2	10	10	NUM
ejpam-3583	292	3	]	]	X
ejpam-3583	292	4	k.	k.	PROPN
ejpam-3583	292	5	conrad	conrad	PROPN
ejpam-3583	292	6	,	,	PUNCT
ejpam-3583	292	7	a	a	DET
ejpam-3583	292	8	q	q	NOUN
ejpam-3583	292	9	-	-	PUNCT
ejpam-3583	292	10	analogue	analogue	NOUN
ejpam-3583	292	11	of	of	ADP
ejpam-3583	292	12	mahler	mahler	PROPN
ejpam-3583	292	13	expansions	expansion	NOUN
ejpam-3583	292	14	i	i	PRON
ejpam-3583	292	15	,	,	PUNCT
ejpam-3583	292	16	adv	adv	PROPN
ejpam-3583	292	17	.	.	PUNCT
ejpam-3583	292	18	in	in	ADP
ejpam-3583	292	19	math	math	NOUN
ejpam-3583	292	20	.	.	PUNCT
ejpam-3583	293	1	153	153	NUM
ejpam-3583	293	2	(	(	PUNCT
ejpam-3583	293	3	2000	2000	NUM
ejpam-3583	293	4	)	)	PUNCT
ejpam-3583	293	5	,	,	PUNCT
ejpam-3583	293	6	185–230	185–230	NUM
ejpam-3583	293	7	.	.	PUNCT
ejpam-3583	294	1	[	[	X
ejpam-3583	294	2	11	11	NUM
ejpam-3583	294	3	]	]	X
ejpam-3583	294	4	c.b	c.b	PROPN
ejpam-3583	294	5	.	.	PROPN
ejpam-3583	294	6	corcino	corcino	PROPN
ejpam-3583	294	7	,	,	PUNCT
ejpam-3583	294	8	r.b	r.b	PROPN
ejpam-3583	294	9	.	.	PROPN
ejpam-3583	294	10	corcino	corcino	PROPN
ejpam-3583	294	11	,	,	PUNCT
ejpam-3583	294	12	j.m	j.m	PROPN
ejpam-3583	294	13	.	.	PROPN
ejpam-3583	294	14	ontolan	ontolan	PROPN
ejpam-3583	294	15	,	,	PUNCT
ejpam-3583	294	16	c.m	c.m	PROPN
ejpam-3583	294	17	.	.	PROPN
ejpam-3583	294	18	perez	perez	PROPN
ejpam-3583	294	19	-	-	PUNCT
ejpam-3583	294	20	fernandez	fernandez	PROPN
ejpam-3583	294	21	,	,	PUNCT
ejpam-3583	294	22	and	and	CCONJ
ejpam-3583	294	23	e.r	e.r	PROPN
ejpam-3583	294	24	.	.	PROPN
ejpam-3583	294	25	cantallopez	cantallopez	PROPN
ejpam-3583	294	26	,	,	PUNCT
ejpam-3583	294	27	the	the	DET
ejpam-3583	294	28	hankel	hankel	NOUN
ejpam-3583	294	29	transform	transform	NOUN
ejpam-3583	294	30	of	of	ADP
ejpam-3583	294	31	q	q	ADJ
ejpam-3583	294	32	-	-	ADJ
ejpam-3583	294	33	noncentral	noncentral	ADJ
ejpam-3583	294	34	bell	bell	NOUN
ejpam-3583	294	35	numbers	number	NOUN
ejpam-3583	294	36	,	,	PUNCT
ejpam-3583	294	37	int	int	NOUN
ejpam-3583	294	38	.	.	PUNCT
ejpam-3583	295	1	j.	j.	PROPN
ejpam-3583	295	2	math	math	PROPN
ejpam-3583	295	3	.	.	PUNCT
ejpam-3583	296	1	math	math	NOUN
ejpam-3583	296	2	.	.	PUNCT
ejpam-3583	297	1	sci	sci	PROPN
ejpam-3583	297	2	.	.	PROPN
ejpam-3583	297	3	,	,	PUNCT
ejpam-3583	297	4	volume	volume	NOUN
ejpam-3583	297	5	2015	2015	NUM
ejpam-3583	297	6	,	,	PUNCT
ejpam-3583	297	7	article	article	NOUN
ejpam-3583	297	8	i	i	PROPN
ejpam-3583	297	9	d	d	PROPN
ejpam-3583	297	10	417327	417327	NUM
ejpam-3583	297	11	,	,	PUNCT
ejpam-3583	297	12	10	10	NUM
ejpam-3583	297	13	pages	page	NOUN
ejpam-3583	297	14	.	.	PUNCT
ejpam-3583	298	1	[	[	X
ejpam-3583	298	2	12	12	NUM
ejpam-3583	298	3	]	]	X
ejpam-3583	298	4	r.b	r.b	PROPN
ejpam-3583	298	5	.	.	PROPN
ejpam-3583	298	6	corcino	corcino	PROPN
ejpam-3583	298	7	,	,	PUNCT
ejpam-3583	298	8	the	the	DET
ejpam-3583	298	9	(	(	PUNCT
ejpam-3583	298	10	r	r	NOUN
ejpam-3583	298	11	,	,	PUNCT
ejpam-3583	298	12	β)-stirling	β)-stirle	VERB
ejpam-3583	298	13	numbers	number	NOUN
ejpam-3583	298	14	.	.	PUNCT
ejpam-3583	299	1	mindanao	mindanao	PROPN
ejpam-3583	299	2	forum	forum	PROPN
ejpam-3583	299	3	.	.	PUNCT
ejpam-3583	300	1	14(2	14(2	NUM
ejpam-3583	300	2	)	)	PUNCT
ejpam-3583	300	3	(	(	PUNCT
ejpam-3583	300	4	1999	1999	NUM
ejpam-3583	300	5	)	)	PUNCT
ejpam-3583	301	1	[	[	X
ejpam-3583	301	2	13	13	NUM
ejpam-3583	301	3	]	]	X
ejpam-3583	301	4	r.b	r.b	PROPN
ejpam-3583	301	5	.	.	PROPN
ejpam-3583	301	6	corcino	corcino	PROPN
ejpam-3583	301	7	,	,	PUNCT
ejpam-3583	301	8	j.t	j.t	PROPN
ejpam-3583	301	9	.	.	PROPN
ejpam-3583	301	10	cañete	cañete	PROPN
ejpam-3583	301	11	,	,	PUNCT
ejpam-3583	301	12	jay	jay	PROPN
ejpam-3583	301	13	m.	m.	NOUN
ejpam-3583	301	14	ontolan	ontolan	PROPN
ejpam-3583	301	15	,	,	PUNCT
ejpam-3583	301	16	and	and	CCONJ
ejpam-3583	301	17	m.r	m.r	PROPN
ejpam-3583	301	18	.	.	PROPN
ejpam-3583	301	19	latayada	latayada	PROPN
ejpam-3583	301	20	,	,	PUNCT
ejpam-3583	301	21	a	a	DET
ejpam-3583	301	22	q	q	NOUN
ejpam-3583	301	23	-	-	PUNCT
ejpam-3583	301	24	analogue	analogue	NOUN
ejpam-3583	301	25	of	of	ADP
ejpam-3583	301	26	r	r	NOUN
ejpam-3583	301	27	-	-	PUNCT
ejpam-3583	301	28	whitney	whitney	NOUN
ejpam-3583	301	29	numbers	number	NOUN
ejpam-3583	301	30	of	of	ADP
ejpam-3583	301	31	the	the	DET
ejpam-3583	301	32	second	second	ADJ
ejpam-3583	301	33	kind	kind	NOUN
ejpam-3583	301	34	,	,	PUNCT
ejpam-3583	301	35	arxiv:1907.03094v2	arxiv:1907.03094v2	PRON
ejpam-3583	302	1	[	[	X
ejpam-3583	302	2	math.co	math.co	X
ejpam-3583	302	3	]	]	X
ejpam-3583	302	4	.	.	PUNCT
ejpam-3583	303	1	available	available	ADJ
ejpam-3583	303	2	at	at	ADP
ejpam-3583	303	3	http://arxiv.org/abs/1907.03094v2	http://arxiv.org/abs/1907.03094v2	PROPN
ejpam-3583	303	4	.	.	PUNCT
ejpam-3583	304	1	[	[	X
ejpam-3583	304	2	14	14	NUM
ejpam-3583	304	3	]	]	X
ejpam-3583	304	4	r.b	r.b	PROPN
ejpam-3583	304	5	.	.	PROPN
ejpam-3583	304	6	corcino	corcino	PROPN
ejpam-3583	304	7	and	and	CCONJ
ejpam-3583	304	8	c.b	c.b	PROPN
ejpam-3583	304	9	.	.	PROPN
ejpam-3583	304	10	corcino	corcino	PROPN
ejpam-3583	304	11	,	,	PUNCT
ejpam-3583	304	12	the	the	DET
ejpam-3583	304	13	hankel	hankel	NOUN
ejpam-3583	304	14	transform	transform	NOUN
ejpam-3583	304	15	of	of	ADP
ejpam-3583	304	16	generalized	generalized	ADJ
ejpam-3583	304	17	bell	bell	NOUN
ejpam-3583	304	18	numbers	number	NOUN
ejpam-3583	304	19	and	and	CCONJ
ejpam-3583	304	20	its	its	PRON
ejpam-3583	304	21	q	q	NOUN
ejpam-3583	304	22	-	-	PUNCT
ejpam-3583	304	23	analogue	analogue	NOUN
ejpam-3583	304	24	,	,	PUNCT
ejpam-3583	304	25	util	util	NOUN
ejpam-3583	304	26	.	.	PUNCT
ejpam-3583	304	27	math	math	NOUN
ejpam-3583	304	28	.	.	PUNCT
ejpam-3583	304	29	,	,	PUNCT
ejpam-3583	304	30	89	89	NUM
ejpam-3583	304	31	(	(	PUNCT
ejpam-3583	304	32	2012	2012	NUM
ejpam-3583	304	33	)	)	PUNCT
ejpam-3583	304	34	,	,	PUNCT
ejpam-3583	304	35	297	297	NUM
ejpam-3583	304	36	-	-	SYM
ejpam-3583	304	37	309	309	NUM
ejpam-3583	304	38	.	.	PUNCT
ejpam-3583	305	1	[	[	X
ejpam-3583	305	2	15	15	NUM
ejpam-3583	305	3	]	]	X
ejpam-3583	305	4	r.b	r.b	PROPN
ejpam-3583	305	5	.	.	PROPN
ejpam-3583	305	6	corcino	corcino	PROPN
ejpam-3583	305	7	,	,	PUNCT
ejpam-3583	305	8	c.b	c.b	PROPN
ejpam-3583	305	9	.	.	PROPN
ejpam-3583	305	10	corcino	corcino	PROPN
ejpam-3583	305	11	,	,	PUNCT
ejpam-3583	305	12	and	and	CCONJ
ejpam-3583	305	13	r.	r.	PROPN
ejpam-3583	305	14	aldema	aldema	PROPN
ejpam-3583	305	15	,	,	PUNCT
ejpam-3583	305	16	asymptotic	asymptotic	ADJ
ejpam-3583	305	17	normality	normality	NOUN
ejpam-3583	305	18	of	of	ADP
ejpam-3583	305	19	the	the	DET
ejpam-3583	305	20	(	(	PUNCT
ejpam-3583	305	21	r	r	NOUN
ejpam-3583	305	22	,	,	PUNCT
ejpam-3583	305	23	β)stirling	β)stirle	VERB
ejpam-3583	305	24	numbers	number	NOUN
ejpam-3583	305	25	,	,	PUNCT
ejpam-3583	305	26	ars	ar	VERB
ejpam-3583	305	27	combin	combin	NOUN
ejpam-3583	305	28	.	.	PUNCT
ejpam-3583	305	29	,	,	PUNCT
ejpam-3583	305	30	81	81	NUM
ejpam-3583	305	31	(	(	PUNCT
ejpam-3583	305	32	2006	2006	NUM
ejpam-3583	305	33	)	)	PUNCT
ejpam-3583	305	34	,	,	PUNCT
ejpam-3583	305	35	81	81	NUM
ejpam-3583	305	36	-	-	SYM
ejpam-3583	305	37	96	96	NUM
ejpam-3583	305	38	.	.	PUNCT
ejpam-3583	306	1	[	[	X
ejpam-3583	306	2	16	16	NUM
ejpam-3583	306	3	]	]	X
ejpam-3583	306	4	r.b	r.b	PROPN
ejpam-3583	306	5	.	.	PROPN
ejpam-3583	306	6	corcino	corcino	PROPN
ejpam-3583	306	7	,	,	PUNCT
ejpam-3583	306	8	m.r	m.r	PROPN
ejpam-3583	306	9	.	.	PROPN
ejpam-3583	306	10	latayada	latayada	PROPN
ejpam-3583	306	11	and	and	CCONJ
ejpam-3583	306	12	m.p	m.p	PROPN
ejpam-3583	306	13	.	.	PROPN
ejpam-3583	306	14	vega	vega	PROPN
ejpam-3583	306	15	,	,	PUNCT
ejpam-3583	306	16	hankel	hankel	NOUN
ejpam-3583	306	17	transform	transform	NOUN
ejpam-3583	306	18	of	of	ADP
ejpam-3583	306	19	(	(	PUNCT
ejpam-3583	306	20	q	q	ADJ
ejpam-3583	306	21	,	,	PUNCT
ejpam-3583	306	22	r)-dowling	r)-dowling	ADJ
ejpam-3583	306	23	numbers	number	NOUN
ejpam-3583	306	24	,	,	PUNCT
ejpam-3583	306	25	eur	eur	PROPN
ejpam-3583	306	26	.	.	PUNCT
ejpam-3583	307	1	j.	j.	PROPN
ejpam-3583	307	2	pure	pure	PROPN
ejpam-3583	307	3	appl	appl	PROPN
ejpam-3583	307	4	.	.	PUNCT
ejpam-3583	307	5	math	math	PROPN
ejpam-3583	307	6	.	.	PUNCT
ejpam-3583	307	7	,	,	PUNCT
ejpam-3583	307	8	12(2	12(2	NUM
ejpam-3583	307	9	)	)	PUNCT
ejpam-3583	307	10	(	(	PUNCT
ejpam-3583	307	11	2019	2019	NUM
ejpam-3583	307	12	)	)	PUNCT
ejpam-3583	307	13	,	,	PUNCT
ejpam-3583	307	14	279–293	279–293	NUM
ejpam-3583	307	15	.	.	PUNCT
ejpam-3583	308	1	[	[	X
ejpam-3583	308	2	17	17	NUM
ejpam-3583	308	3	]	]	X
ejpam-3583	308	4	r.b	r.b	PROPN
ejpam-3583	308	5	.	.	PROPN
ejpam-3583	308	6	corcino	corcino	PROPN
ejpam-3583	308	7	and	and	CCONJ
ejpam-3583	308	8	c.b	c.b	PROPN
ejpam-3583	308	9	.	.	PROPN
ejpam-3583	308	10	montero	montero	PROPN
ejpam-3583	308	11	,	,	PUNCT
ejpam-3583	308	12	a	a	DET
ejpam-3583	308	13	q	q	NOUN
ejpam-3583	308	14	-	-	PUNCT
ejpam-3583	308	15	analogue	analogue	NOUN
ejpam-3583	308	16	of	of	ADP
ejpam-3583	308	17	rucinski	rucinski	ADJ
ejpam-3583	308	18	-	-	PUNCT
ejpam-3583	308	19	voigt	voigt	NOUN
ejpam-3583	308	20	numbers	number	NOUN
ejpam-3583	308	21	,	,	PUNCT
ejpam-3583	308	22	isrn	isrn	NOUN
ejpam-3583	308	23	discrete	discrete	VERB
ejpam-3583	308	24	mathematics	mathematic	NOUN
ejpam-3583	308	25	,	,	PUNCT
ejpam-3583	308	26	volume	volume	NOUN
ejpam-3583	308	27	2012	2012	NUM
ejpam-3583	308	28	,	,	PUNCT
ejpam-3583	308	29	article	article	NOUN
ejpam-3583	308	30	i	i	PROPN
ejpam-3583	308	31	d	d	PROPN
ejpam-3583	308	32	592818	592818	NUM
ejpam-3583	308	33	,	,	PUNCT
ejpam-3583	308	34	18	18	NUM
ejpam-3583	308	35	pages	page	NOUN
ejpam-3583	308	36	,	,	PUNCT
ejpam-3583	308	37	doi:10.5402/2012/592818	doi:10.5402/2012/592818	VERB
ejpam-3583	308	38	[	[	X
ejpam-3583	308	39	18	18	NUM
ejpam-3583	308	40	]	]	PUNCT
ejpam-3583	308	41	a.	a.	NOUN
ejpam-3583	308	42	cvetković	cvetković	PROPN
ejpam-3583	308	43	,	,	PUNCT
ejpam-3583	308	44	p.	p.	NOUN
ejpam-3583	308	45	rajković	rajković	NOUN
ejpam-3583	308	46	,	,	PUNCT
ejpam-3583	308	47	and	and	CCONJ
ejpam-3583	308	48	m.	m.	NOUN
ejpam-3583	308	49	ivković	ivković	ADJ
ejpam-3583	308	50	,	,	PUNCT
ejpam-3583	308	51	catalan	catalan	NOUN
ejpam-3583	308	52	numbers	number	NOUN
ejpam-3583	308	53	,	,	PUNCT
ejpam-3583	308	54	the	the	DET
ejpam-3583	308	55	hankel	hankel	NOUN
ejpam-3583	308	56	transform	transform	VERB
ejpam-3583	308	57	and	and	CCONJ
ejpam-3583	308	58	fibonnaci	fibonnaci	PROPN
ejpam-3583	308	59	numbers	number	NOUN
ejpam-3583	308	60	,	,	PUNCT
ejpam-3583	308	61	j.	j.	PROPN
ejpam-3583	308	62	integer	integer	PROPN
ejpam-3583	308	63	seq	seq	PROPN
ejpam-3583	308	64	.	.	PROPN
ejpam-3583	308	65	,	,	PUNCT
ejpam-3583	308	66	5(2002	5(2002	NUM
ejpam-3583	308	67	)	)	PUNCT
ejpam-3583	308	68	,	,	PUNCT
ejpam-3583	308	69	article	article	NOUN
ejpam-3583	308	70	02.1.3	02.1.3	PUNCT
ejpam-3583	309	1	[	[	X
ejpam-3583	309	2	19	19	NUM
ejpam-3583	309	3	]	]	PUNCT
ejpam-3583	309	4	m.	m.	NOUN
ejpam-3583	309	5	desainte	desainte	PROPN
ejpam-3583	309	6	-	-	PUNCT
ejpam-3583	309	7	catherine	catherine	PROPN
ejpam-3583	309	8	and	and	CCONJ
ejpam-3583	309	9	x.	x.	PROPN
ejpam-3583	309	10	g.	g.	PROPN
ejpam-3583	309	11	viennot	viennot	PROPN
ejpam-3583	309	12	,	,	PUNCT
ejpam-3583	309	13	enumeration	enumeration	NOUN
ejpam-3583	309	14	of	of	ADP
ejpam-3583	309	15	certain	certain	ADJ
ejpam-3583	309	16	young	young	ADJ
ejpam-3583	309	17	tableaux	tableau	NOUN
ejpam-3583	309	18	with	with	ADP
ejpam-3583	309	19	bound	bind	VERB
ejpam-3583	309	20	height	height	NOUN
ejpam-3583	309	21	,	,	PUNCT
ejpam-3583	309	22	combinatorie	combinatorie	NOUN
ejpam-3583	309	23	énumérative	énumérative	NOUN
ejpam-3583	309	24	(	(	PUNCT
ejpam-3583	309	25	montreal	montreal	PROPN
ejpam-3583	309	26	1985	1985	NUM
ejpam-3583	309	27	)	)	PUNCT
ejpam-3583	309	28	,	,	PUNCT
ejpam-3583	309	29	lect	lect	PROPN
ejpam-3583	309	30	.	.	PUNCT
ejpam-3583	309	31	notes	note	NOUN
ejpam-3583	309	32	in	in	ADP
ejpam-3583	309	33	math	math	NOUN
ejpam-3583	309	34	.	.	PUNCT
ejpam-3583	310	1	1234	1234	NUM
ejpam-3583	310	2	(	(	PUNCT
ejpam-3583	310	3	1986	1986	NUM
ejpam-3583	310	4	)	)	PUNCT
ejpam-3583	310	5	,	,	PUNCT
ejpam-3583	310	6	58	58	NUM
ejpam-3583	310	7	-	-	SYM
ejpam-3583	310	8	67	67	NUM
ejpam-3583	310	9	.	.	PUNCT
ejpam-3583	311	1	references	reference	NOUN
ejpam-3583	311	2	1688	1688	NUM
ejpam-3583	311	3	[	[	X
ejpam-3583	311	4	20	20	NUM
ejpam-3583	311	5	]	]	X
ejpam-3583	311	6	r.	r.	PROPN
ejpam-3583	311	7	ehrenborg	ehrenborg	PROPN
ejpam-3583	311	8	,	,	PUNCT
ejpam-3583	311	9	determinants	determinant	NOUN
ejpam-3583	311	10	of	of	ADP
ejpam-3583	311	11	involving	involve	VERB
ejpam-3583	311	12	q	q	ADJ
ejpam-3583	311	13	-	-	PUNCT
ejpam-3583	311	14	stirling	stirling	NOUN
ejpam-3583	311	15	numbers	number	NOUN
ejpam-3583	311	16	,	,	PUNCT
ejpam-3583	311	17	advances	advance	NOUN
ejpam-3583	311	18	in	in	ADP
ejpam-3583	311	19	applied	apply	VERB
ejpam-3583	311	20	mathematics	mathematic	NOUN
ejpam-3583	311	21	,	,	PUNCT
ejpam-3583	311	22	31(2003	31(2003	NUM
ejpam-3583	311	23	)	)	PUNCT
ejpam-3583	311	24	,	,	PUNCT
ejpam-3583	311	25	630	630	NUM
ejpam-3583	311	26	-	-	SYM
ejpam-3583	311	27	642	642	NUM
ejpam-3583	311	28	.	.	PUNCT
ejpam-3583	312	1	[	[	X
ejpam-3583	312	2	21	21	NUM
ejpam-3583	312	3	]	]	X
ejpam-3583	312	4	r.	r.	PROPN
ejpam-3583	312	5	ehrenborg	ehrenborg	PROPN
ejpam-3583	312	6	,	,	PUNCT
ejpam-3583	312	7	the	the	DET
ejpam-3583	312	8	hankel	hankel	NOUN
ejpam-3583	312	9	determinant	determinant	ADJ
ejpam-3583	312	10	of	of	ADP
ejpam-3583	312	11	exponential	exponential	ADJ
ejpam-3583	312	12	polynomials	polynomial	NOUN
ejpam-3583	312	13	,	,	PUNCT
ejpam-3583	312	14	amer	amer	PROPN
ejpam-3583	312	15	.	.	PROPN
ejpam-3583	312	16	math	math	PROPN
ejpam-3583	312	17	.	.	PUNCT
ejpam-3583	313	1	monthly	monthly	ADJ
ejpam-3583	313	2	,	,	PUNCT
ejpam-3583	313	3	107(2000	107(2000	NUM
ejpam-3583	313	4	)	)	PUNCT
ejpam-3583	313	5	,	,	PUNCT
ejpam-3583	313	6	557	557	NUM
ejpam-3583	313	7	-	-	SYM
ejpam-3583	313	8	560	560	NUM
ejpam-3583	313	9	[	[	X
ejpam-3583	313	10	22	22	NUM
ejpam-3583	313	11	]	]	PUNCT
ejpam-3583	313	12	m.	m.	NOUN
ejpam-3583	313	13	garcia	garcia	PROPN
ejpam-3583	313	14	-	-	PUNCT
ejpam-3583	313	15	armas	armas	PROPN
ejpam-3583	313	16	and	and	CCONJ
ejpam-3583	313	17	b.	b.	PROPN
ejpam-3583	313	18	a.	a.	PROPN
ejpam-3583	313	19	seturaman	seturaman	PROPN
ejpam-3583	313	20	,	,	PUNCT
ejpam-3583	313	21	a	a	DET
ejpam-3583	313	22	note	note	NOUN
ejpam-3583	313	23	on	on	ADP
ejpam-3583	313	24	the	the	DET
ejpam-3583	313	25	hankel	hankel	NOUN
ejpam-3583	313	26	transform	transform	NOUN
ejpam-3583	313	27	of	of	ADP
ejpam-3583	313	28	the	the	DET
ejpam-3583	313	29	central	central	ADJ
ejpam-3583	313	30	binomial	binomial	ADJ
ejpam-3583	313	31	coefficients	coefficient	NOUN
ejpam-3583	313	32	,	,	PUNCT
ejpam-3583	313	33	j.	j.	PROPN
ejpam-3583	313	34	integer	integer	PROPN
ejpam-3583	313	35	seq	seq	PROPN
ejpam-3583	313	36	.	.	PUNCT
ejpam-3583	313	37	11(2008	11(2008	PROPN
ejpam-3583	313	38	)	)	PUNCT
ejpam-3583	313	39	,	,	PUNCT
ejpam-3583	313	40	article	article	NOUN
ejpam-3583	313	41	08.5.8	08.5.8	NOUN
ejpam-3583	313	42	.	.	PUNCT
ejpam-3583	314	1	[	[	X
ejpam-3583	314	2	23	23	NUM
ejpam-3583	314	3	]	]	X
ejpam-3583	314	4	h.w	h.w	PROPN
ejpam-3583	314	5	.	.	PROPN
ejpam-3583	314	6	gould	gould	PROPN
ejpam-3583	314	7	,	,	PUNCT
ejpam-3583	314	8	the	the	DET
ejpam-3583	314	9	q	q	ADJ
ejpam-3583	314	10	-	-	PUNCT
ejpam-3583	314	11	stirling	stirling	ADJ
ejpam-3583	314	12	number	number	NOUN
ejpam-3583	314	13	of	of	ADP
ejpam-3583	314	14	the	the	DET
ejpam-3583	314	15	first	first	ADJ
ejpam-3583	314	16	and	and	CCONJ
ejpam-3583	314	17	second	second	ADJ
ejpam-3583	314	18	kinds	kind	NOUN
ejpam-3583	314	19	.	.	PUNCT
ejpam-3583	315	1	duke	duke	PROPN
ejpam-3583	315	2	math	math	PROPN
ejpam-3583	315	3	.	.	PUNCT
ejpam-3583	316	1	j.	j.	PROPN
ejpam-3583	316	2	28(1968	28(1968	PROPN
ejpam-3583	316	3	)	)	PUNCT
ejpam-3583	316	4	281	281	NUM
ejpam-3583	316	5	-	-	SYM
ejpam-3583	316	6	289	289	NUM
ejpam-3583	316	7	.	.	PUNCT
ejpam-3583	317	1	[	[	X
ejpam-3583	317	2	24	24	NUM
ejpam-3583	317	3	]	]	PUNCT
ejpam-3583	317	4	m.	m.	NOUN
ejpam-3583	317	5	s.	s.	PROPN
ejpam-3583	317	6	kim	kim	PROPN
ejpam-3583	317	7	and	and	CCONJ
ejpam-3583	317	8	j.	j.	PROPN
ejpam-3583	317	9	w.	w.	PROPN
ejpam-3583	317	10	son	son	PROPN
ejpam-3583	317	11	,	,	PUNCT
ejpam-3583	317	12	a	a	DET
ejpam-3583	317	13	note	note	NOUN
ejpam-3583	317	14	on	on	ADP
ejpam-3583	317	15	q	q	ADJ
ejpam-3583	317	16	-	-	PUNCT
ejpam-3583	317	17	difference	difference	NOUN
ejpam-3583	317	18	operators	operator	NOUN
ejpam-3583	317	19	,	,	PUNCT
ejpam-3583	317	20	commun	commun	PROPN
ejpam-3583	317	21	.	.	PUNCT
ejpam-3583	318	1	korean	korean	ADJ
ejpam-3583	318	2	math	math	PROPN
ejpam-3583	318	3	.	.	PUNCT
ejpam-3583	319	1	soc	soc	PROPN
ejpam-3583	319	2	.	.	PUNCT
ejpam-3583	320	1	17	17	NUM
ejpam-3583	320	2	(	(	PUNCT
ejpam-3583	320	3	2002	2002	NUM
ejpam-3583	320	4	)	)	PUNCT
ejpam-3583	320	5	,	,	PUNCT
ejpam-3583	320	6	no	no	INTJ
ejpam-3583	320	7	.	.	NOUN
ejpam-3583	320	8	3	3	NUM
ejpam-3583	320	9	,	,	PUNCT
ejpam-3583	320	10	pp	pp	ADJ
ejpam-3583	320	11	.	.	PUNCT
ejpam-3583	320	12	423	423	NUM
ejpam-3583	320	13	-	-	SYM
ejpam-3583	320	14	430	430	NUM
ejpam-3583	320	15	[	[	X
ejpam-3583	320	16	25	25	NUM
ejpam-3583	320	17	]	]	PUNCT
ejpam-3583	320	18	m.	m.	NOUN
ejpam-3583	320	19	koutras	koutra	NOUN
ejpam-3583	320	20	.	.	PUNCT
ejpam-3583	321	1	non	non	ADJ
ejpam-3583	321	2	-	-	ADJ
ejpam-3583	321	3	central	central	ADJ
ejpam-3583	321	4	stirling	stirling	NOUN
ejpam-3583	321	5	numbers	number	NOUN
ejpam-3583	321	6	and	and	CCONJ
ejpam-3583	321	7	some	some	DET
ejpam-3583	321	8	applications	application	NOUN
ejpam-3583	321	9	.	.	PUNCT
ejpam-3583	322	1	discrete	discrete	ADJ
ejpam-3583	322	2	math.42	math.42	NOUN
ejpam-3583	322	3	(	(	PUNCT
ejpam-3583	322	4	1982):73	1982):73	NUM
ejpam-3583	322	5	-	-	SYM
ejpam-3583	322	6	89	89	NUM
ejpam-3583	322	7	.	.	PUNCT
ejpam-3583	323	1	[	[	X
ejpam-3583	323	2	26	26	NUM
ejpam-3583	323	3	]	]	X
ejpam-3583	323	4	j.w	j.w	PROPN
ejpam-3583	323	5	.	.	PROPN
ejpam-3583	323	6	layman	layman	PROPN
ejpam-3583	323	7	,	,	PUNCT
ejpam-3583	323	8	the	the	DET
ejpam-3583	323	9	hankel	hankel	NOUN
ejpam-3583	323	10	transform	transform	NOUN
ejpam-3583	323	11	and	and	CCONJ
ejpam-3583	323	12	some	some	PRON
ejpam-3583	323	13	of	of	ADP
ejpam-3583	323	14	its	its	PRON
ejpam-3583	323	15	properties	property	NOUN
ejpam-3583	323	16	,	,	PUNCT
ejpam-3583	323	17	j.	j.	PROPN
ejpam-3583	323	18	integer	integer	PROPN
ejpam-3583	323	19	seq	seq	PROPN
ejpam-3583	323	20	.	.	PROPN
ejpam-3583	323	21	4	4	NUM
ejpam-3583	323	22	(	(	PUNCT
ejpam-3583	323	23	2001	2001	NUM
ejpam-3583	323	24	)	)	PUNCT
ejpam-3583	323	25	,	,	PUNCT
ejpam-3583	323	26	article	article	NOUN
ejpam-3583	323	27	01.1.5	01.1.5	PUNCT
ejpam-3583	323	28	.	.	PUNCT
ejpam-3583	324	1	[	[	X
ejpam-3583	324	2	27	27	NUM
ejpam-3583	324	3	]	]	X
ejpam-3583	324	4	a.	a.	PROPN
ejpam-3583	324	5	de	de	PROPN
ejpam-3583	324	6	medicis	medicis	PROPN
ejpam-3583	324	7	and	and	CCONJ
ejpam-3583	324	8	p.	p.	PROPN
ejpam-3583	324	9	leroux	leroux	PROPN
ejpam-3583	324	10	,	,	PUNCT
ejpam-3583	324	11	generalized	generalize	VERB
ejpam-3583	324	12	stirling	stirling	NOUN
ejpam-3583	324	13	numbers	number	NOUN
ejpam-3583	324	14	,	,	PUNCT
ejpam-3583	324	15	convolution	convolution	NOUN
ejpam-3583	324	16	formulae	formulae	NOUN
ejpam-3583	324	17	and	and	CCONJ
ejpam-3583	324	18	p	p	X
ejpam-3583	324	19	,	,	PUNCT
ejpam-3583	324	20	q	q	NOUN
ejpam-3583	324	21	-	-	PUNCT
ejpam-3583	324	22	analogues	analogue	NOUN
ejpam-3583	324	23	,	,	PUNCT
ejpam-3583	324	24	can	can	AUX
ejpam-3583	324	25	.	.	PUNCT
ejpam-3583	325	1	j.	j.	PROPN
ejpam-3583	325	2	math	math	PROPN
ejpam-3583	325	3	47(3	47(3	PROPN
ejpam-3583	325	4	)	)	PUNCT
ejpam-3583	325	5	(	(	PUNCT
ejpam-3583	325	6	1995	1995	NUM
ejpam-3583	325	7	)	)	PUNCT
ejpam-3583	325	8	,	,	PUNCT
ejpam-3583	325	9	474	474	NUM
ejpam-3583	325	10	-	-	SYM
ejpam-3583	325	11	499	499	NUM
ejpam-3583	325	12	.	.	PUNCT
ejpam-3583	326	1	[	[	X
ejpam-3583	326	2	28	28	NUM
ejpam-3583	326	3	]	]	X
ejpam-3583	326	4	i.	i.	PROPN
ejpam-3583	326	5	mező	mező	PROPN
ejpam-3583	326	6	,	,	PUNCT
ejpam-3583	326	7	on	on	ADP
ejpam-3583	326	8	the	the	DET
ejpam-3583	326	9	maximum	maximum	NOUN
ejpam-3583	326	10	of	of	ADP
ejpam-3583	326	11	r	r	NOUN
ejpam-3583	326	12	-	-	PUNCT
ejpam-3583	326	13	stirling	stirling	NOUN
ejpam-3583	326	14	numbers	number	NOUN
ejpam-3583	326	15	,	,	PUNCT
ejpam-3583	326	16	adv	adv	PROPN
ejpam-3583	326	17	.	.	PUNCT
ejpam-3583	327	1	in	in	ADP
ejpam-3583	327	2	appl	appl	PROPN
ejpam-3583	327	3	.	.	PUNCT
ejpam-3583	327	4	math	math	NOUN
ejpam-3583	327	5	.	.	PUNCT
ejpam-3583	327	6	41(3	41(3	X
ejpam-3583	327	7	)	)	PUNCT
ejpam-3583	327	8	(	(	PUNCT
ejpam-3583	327	9	2008	2008	NUM
ejpam-3583	327	10	)	)	PUNCT
ejpam-3583	327	11	,	,	PUNCT
ejpam-3583	327	12	293	293	NUM
ejpam-3583	327	13	-	-	SYM
ejpam-3583	327	14	306	306	NUM
ejpam-3583	327	15	.	.	PUNCT
ejpam-3583	328	1	[	[	X
ejpam-3583	328	2	29	29	NUM
ejpam-3583	328	3	]	]	X
ejpam-3583	328	4	i.	i.	PROPN
ejpam-3583	328	5	mező	mező	PROPN
ejpam-3583	328	6	,	,	PUNCT
ejpam-3583	328	7	a	a	DET
ejpam-3583	328	8	new	new	ADJ
ejpam-3583	328	9	formula	formula	NOUN
ejpam-3583	328	10	for	for	ADP
ejpam-3583	328	11	the	the	DET
ejpam-3583	328	12	bernoulli	bernoulli	NOUN
ejpam-3583	328	13	polynomials	polynomial	NOUN
ejpam-3583	328	14	,	,	PUNCT
ejpam-3583	328	15	result	result	NOUN
ejpam-3583	328	16	.	.	PUNCT
ejpam-3583	329	1	math	math	NOUN
ejpam-3583	329	2	.	.	PUNCT
ejpam-3583	330	1	58(3	58(3	NUM
ejpam-3583	330	2	)	)	PUNCT
ejpam-3583	330	3	(	(	PUNCT
ejpam-3583	330	4	2010	2010	NUM
ejpam-3583	330	5	)	)	PUNCT
ejpam-3583	330	6	,	,	PUNCT
ejpam-3583	330	7	329	329	NUM
ejpam-3583	330	8	-	-	SYM
ejpam-3583	330	9	335	335	NUM
ejpam-3583	330	10	.	.	PUNCT
ejpam-3583	331	1	[	[	X
ejpam-3583	331	2	30	30	NUM
ejpam-3583	331	3	]	]	X
ejpam-3583	331	4	i.	i.	PROPN
ejpam-3583	331	5	mező	mező	PROPN
ejpam-3583	331	6	,	,	PUNCT
ejpam-3583	331	7	the	the	DET
ejpam-3583	331	8	r	r	NOUN
ejpam-3583	331	9	-	-	PUNCT
ejpam-3583	331	10	bell	bell	NOUN
ejpam-3583	331	11	numbers	number	NOUN
ejpam-3583	331	12	,	,	PUNCT
ejpam-3583	331	13	j.	j.	PROPN
ejpam-3583	331	14	integer	integer	PROPN
ejpam-3583	331	15	seq	seq	PROPN
ejpam-3583	331	16	.	.	PROPN
ejpam-3583	331	17	14	14	NUM
ejpam-3583	331	18	(	(	PUNCT
ejpam-3583	331	19	2011	2011	NUM
ejpam-3583	331	20	)	)	PUNCT
ejpam-3583	331	21	,	,	PUNCT
ejpam-3583	331	22	article	article	NOUN
ejpam-3583	331	23	11.1.1	11.1.1	NUM
ejpam-3583	331	24	.	.	PUNCT
ejpam-3583	332	1	[	[	X
ejpam-3583	332	2	31	31	NUM
ejpam-3583	332	3	]	]	PUNCT
ejpam-3583	332	4	c.	c.	NOUN
ejpam-3583	332	5	radoux	radoux	NOUN
ejpam-3583	332	6	,	,	PUNCT
ejpam-3583	332	7	déterminat	déterminat	PROPN
ejpam-3583	332	8	de	de	X
ejpam-3583	332	9	hankel	hankel	PROPN
ejpam-3583	332	10	construit	construit	PROPN
ejpam-3583	332	11	sur	sur	PROPN
ejpam-3583	332	12	des	des	PROPN
ejpam-3583	332	13	polynomes	polynomes	PROPN
ejpam-3583	332	14	liés	liés	PROPN
ejpam-3583	332	15	aux	aux	PROPN
ejpam-3583	332	16	nombres	nombres	PROPN
ejpam-3583	332	17	de	de	X
ejpam-3583	332	18	dérangements	dérangements	PROPN
ejpam-3583	332	19	,	,	PUNCT
ejpam-3583	332	20	european	european	PROPN
ejpam-3583	332	21	journal	journal	PROPN
ejpam-3583	332	22	of	of	ADP
ejpam-3583	332	23	combinatorics	combinatoric	NOUN
ejpam-3583	332	24	12(1991	12(1991	NUM
ejpam-3583	332	25	)	)	PUNCT
ejpam-3583	332	26	327	327	NUM
ejpam-3583	332	27	-	-	SYM
ejpam-3583	332	28	329	329	NUM
ejpam-3583	333	1	[	[	X
ejpam-3583	333	2	32	32	NUM
ejpam-3583	333	3	]	]	PUNCT
ejpam-3583	333	4	j.	j.	PROPN
ejpam-3583	333	5	riordan	riordan	PROPN
ejpam-3583	333	6	,	,	PUNCT
ejpam-3583	333	7	combinatorial	combinatorial	ADJ
ejpam-3583	333	8	identities	identity	NOUN
ejpam-3583	333	9	,	,	PUNCT
ejpam-3583	333	10	wiley	wiley	PROPN
ejpam-3583	333	11	,	,	PUNCT
ejpam-3583	333	12	new	new	PROPN
ejpam-3583	333	13	york	york	PROPN
ejpam-3583	333	14	,	,	PUNCT
ejpam-3583	333	15	1968	1968	NUM
ejpam-3583	333	16	[	[	X
ejpam-3583	333	17	33	33	NUM
ejpam-3583	333	18	]	]	X
ejpam-3583	333	19	n.	n.	PROPN
ejpam-3583	333	20	j.	j.	PROPN
ejpam-3583	333	21	sloane	sloane	PROPN
ejpam-3583	333	22	,	,	PUNCT
ejpam-3583	333	23	the	the	DET
ejpam-3583	333	24	on	on	ADP
ejpam-3583	333	25	-	-	PUNCT
ejpam-3583	333	26	line	line	NOUN
ejpam-3583	333	27	encyclopedia	encyclopedia	NOUN
ejpam-3583	333	28	of	of	ADP
ejpam-3583	333	29	integer	integer	NOUN
ejpam-3583	333	30	sequences	sequence	NOUN
ejpam-3583	333	31	,	,	PUNCT
ejpam-3583	333	32	http://www.research.att.com/	http://www.research.att.com/	NOUN
ejpam-3583	333	33	njas	njas	ADJ
ejpam-3583	333	34	/	/	SYM
ejpam-3583	333	35	sequences	sequence	NOUN
ejpam-3583	333	36	.	.	PUNCT
ejpam-3583	334	1	[	[	X
ejpam-3583	334	2	34	34	NUM
ejpam-3583	334	3	]	]	X
ejpam-3583	334	4	m.z	m.z	PROPN
ejpam-3583	334	5	.	.	PROPN
ejpam-3583	334	6	spivey	spivey	PROPN
ejpam-3583	334	7	and	and	CCONJ
ejpam-3583	334	8	l.	l.	PROPN
ejpam-3583	334	9	l.	l.	PROPN
ejpam-3583	334	10	steil	steil	PROPN
ejpam-3583	334	11	,	,	PUNCT
ejpam-3583	334	12	the	the	DET
ejpam-3583	334	13	k	k	ADJ
ejpam-3583	334	14	-	-	ADJ
ejpam-3583	334	15	binomial	binomial	ADJ
ejpam-3583	334	16	transform	transform	NOUN
ejpam-3583	334	17	and	and	CCONJ
ejpam-3583	334	18	the	the	DET
ejpam-3583	334	19	hankel	hankel	NOUN
ejpam-3583	334	20	transform	transform	NOUN
ejpam-3583	334	21	,	,	PUNCT
ejpam-3583	334	22	j.	j.	PROPN
ejpam-3583	334	23	integer	integer	PROPN
ejpam-3583	334	24	sq	sq	PROPN
ejpam-3583	334	25	.	.	PROPN
ejpam-3583	334	26	9(2006	9(2006	NUM
ejpam-3583	334	27	)	)	PUNCT
ejpam-3583	334	28	,	,	PUNCT
ejpam-3583	334	29	article	article	NOUN
ejpam-3583	334	30	06.1.1	06.1.1	NOUN
ejpam-3583	335	1	[	[	X
ejpam-3583	335	2	35	35	NUM
ejpam-3583	335	3	]	]	X
ejpam-3583	335	4	u.	u.	PROPN
ejpam-3583	335	5	tamm	tamm	PROPN
ejpam-3583	335	6	,	,	PUNCT
ejpam-3583	335	7	some	some	DET
ejpam-3583	335	8	aspects	aspect	NOUN
ejpam-3583	335	9	of	of	ADP
ejpam-3583	335	10	hankel	hankel	NOUN
ejpam-3583	335	11	matrices	matrix	NOUN
ejpam-3583	335	12	in	in	ADP
ejpam-3583	335	13	coding	code	VERB
ejpam-3583	335	14	theory	theory	NOUN
ejpam-3583	335	15	and	and	CCONJ
ejpam-3583	335	16	combinatorics	combinatoric	NOUN
ejpam-3583	335	17	,	,	PUNCT
ejpam-3583	335	18	electron	electron	PROPN
ejpam-3583	335	19	.	.	PUNCT
ejpam-3583	336	1	j.	j.	PROPN
ejpam-3583	336	2	combin	combin	PROPN
ejpam-3583	336	3	.	.	PUNCT
ejpam-3583	337	1	8(1	8(1	NOUN
ejpam-3583	337	2	)	)	PUNCT
ejpam-3583	337	3	a1(2001	a1(2001	NOUN
ejpam-3583	337	4	)	)	PUNCT
ejpam-3583	338	1	[	[	X
ejpam-3583	338	2	36	36	NUM
ejpam-3583	338	3	]	]	X
ejpam-3583	338	4	r.	r.	PROPN
ejpam-3583	338	5	vein	vein	PROPN
ejpam-3583	338	6	and	and	CCONJ
ejpam-3583	338	7	a.	a.	NOUN
ejpam-3583	338	8	dale	dale	PROPN
ejpam-3583	338	9	,	,	PUNCT
ejpam-3583	338	10	determinants	determinant	NOUN
ejpam-3583	338	11	and	and	CCONJ
ejpam-3583	338	12	their	their	PRON
ejpam-3583	338	13	applications	application	NOUN
ejpam-3583	338	14	in	in	ADP
ejpam-3583	338	15	mathematical	mathematical	ADJ
ejpam-3583	338	16	physics	physics	NOUN
ejpam-3583	338	17	,	,	PUNCT
ejpam-3583	338	18	springer	springer	NOUN
ejpam-3583	338	19	,	,	PUNCT
ejpam-3583	338	20	1991	1991	NUM
ejpam-3583	338	21	[	[	X
ejpam-3583	338	22	37	37	NUM
ejpam-3583	338	23	]	]	X
ejpam-3583	338	24	daniel	daniel	PROPN
ejpam-3583	338	25	zelinsky	zelinsky	PROPN
ejpam-3583	338	26	,	,	PUNCT
ejpam-3583	338	27	a	a	DET
ejpam-3583	338	28	first	first	ADJ
ejpam-3583	338	29	course	course	NOUN
ejpam-3583	338	30	in	in	ADP
ejpam-3583	338	31	linear	linear	PROPN
ejpam-3583	338	32	algebra	algebra	PROPN
ejpam-3583	338	33	,	,	PUNCT
ejpam-3583	338	34	2ed	2ed	NOUN
ejpam-3583	338	35	,	,	PUNCT
ejpam-3583	338	36	academic	academic	ADJ
ejpam-3583	338	37	press	press	NOUN
ejpam-3583	338	38	,	,	PUNCT
ejpam-3583	338	39	inc	inc	PROPN
ejpam-3583	338	40	.	.	PROPN
ejpam-3583	338	41	,1973	,1973	PUNCT