id	sid	tid	token	lemma	pos
ejpam-5559	1	1	european	european	PROPN
ejpam-5559	1	2	journal	journal	PROPN
ejpam-5559	1	3	of	of	ADP
ejpam-5559	1	4	pure	pure	ADJ
ejpam-5559	1	5	and	and	CCONJ
ejpam-5559	1	6	applied	applied	ADJ
ejpam-5559	1	7	mathematics	mathematic	NOUN
ejpam-5559	1	8	2025	2025	NUM
ejpam-5559	1	9	,	,	PUNCT
ejpam-5559	1	10	vol	vol	NOUN
ejpam-5559	1	11	.	.	PROPN
ejpam-5559	1	12	18	18	NUM
ejpam-5559	1	13	,	,	PUNCT
ejpam-5559	1	14	issue	issue	NOUN
ejpam-5559	1	15	1	1	NUM
ejpam-5559	1	16	,	,	PUNCT
ejpam-5559	1	17	article	article	NOUN
ejpam-5559	1	18	number	number	NOUN
ejpam-5559	1	19	5559	5559	NUM
ejpam-5559	1	20	issn	issn	PROPN
ejpam-5559	1	21	1307	1307	NUM
ejpam-5559	1	22	-	-	SYM
ejpam-5559	1	23	5543	5543	NUM
ejpam-5559	1	24	–	–	PUNCT
ejpam-5559	1	25	ejpam.com	ejpam.com	X
ejpam-5559	1	26	published	publish	VERB
ejpam-5559	1	27	by	by	ADP
ejpam-5559	1	28	new	new	PROPN
ejpam-5559	1	29	york	york	PROPN
ejpam-5559	1	30	business	business	PROPN
ejpam-5559	1	31	global	global	VERB
ejpam-5559	1	32	some	some	DET
ejpam-5559	1	33	properties	property	NOUN
ejpam-5559	1	34	of	of	ADP
ejpam-5559	1	35	the	the	DET
ejpam-5559	1	36	bell	bell	NOUN
ejpam-5559	1	37	-	-	PUNCT
ejpam-5559	1	38	based	base	VERB
ejpam-5559	1	39	apostol	apostol	NOUN
ejpam-5559	1	40	-	-	PUNCT
ejpam-5559	1	41	frobeniustype	frobeniustype	NOUN
ejpam-5559	1	42	tangent	tangent	NOUN
ejpam-5559	1	43	polynomials	polynomial	NOUN
ejpam-5559	1	44	jay	jay	PROPN
ejpam-5559	1	45	ontolan1,∗	ontolan1,∗	PROPN
ejpam-5559	1	46	,	,	PUNCT
ejpam-5559	1	47	jeneveb	jeneveb	PROPN
ejpam-5559	1	48	malusay1	malusay1	PROPN
ejpam-5559	1	49	,	,	PUNCT
ejpam-5559	1	50	edward	edward	PROPN
ejpam-5559	1	51	kiunisala1	kiunisala1	PROPN
ejpam-5559	1	52	,	,	PUNCT
ejpam-5559	1	53	joris	joris	PROPN
ejpam-5559	1	54	buloron1	buloron1	PROPN
ejpam-5559	1	55	1	1	NUM
ejpam-5559	1	56	mathematics	mathematics	PROPN
ejpam-5559	1	57	department	department	NOUN
ejpam-5559	1	58	,	,	PUNCT
ejpam-5559	1	59	cebu	cebu	NOUN
ejpam-5559	1	60	normal	normal	ADJ
ejpam-5559	1	61	university	university	NOUN
ejpam-5559	1	62	,	,	PUNCT
ejpam-5559	1	63	cebu	cebu	NOUN
ejpam-5559	1	64	city	city	NOUN
ejpam-5559	1	65	,	,	PUNCT
ejpam-5559	1	66	6000	6000	NUM
ejpam-5559	1	67	,	,	PUNCT
ejpam-5559	1	68	philippines	philippine	NOUN
ejpam-5559	1	69	abstract	abstract	ADJ
ejpam-5559	1	70	.	.	PUNCT
ejpam-5559	2	1	in	in	ADP
ejpam-5559	2	2	this	this	DET
ejpam-5559	2	3	paper	paper	NOUN
ejpam-5559	2	4	,	,	PUNCT
ejpam-5559	2	5	we	we	PRON
ejpam-5559	2	6	introduce	introduce	VERB
ejpam-5559	2	7	a	a	DET
ejpam-5559	2	8	new	new	ADJ
ejpam-5559	2	9	class	class	NOUN
ejpam-5559	2	10	of	of	ADP
ejpam-5559	2	11	frobenius	frobenius	ADJ
ejpam-5559	2	12	-	-	PUNCT
ejpam-5559	2	13	tangent	tangent	NOUN
ejpam-5559	2	14	polynomials	polynomial	NOUN
ejpam-5559	2	15	,	,	PUNCT
ejpam-5559	2	16	derived	derive	VERB
ejpam-5559	2	17	from	from	ADP
ejpam-5559	2	18	the	the	DET
ejpam-5559	2	19	bell	bell	NOUN
ejpam-5559	2	20	numbers	number	NOUN
ejpam-5559	2	21	and	and	CCONJ
ejpam-5559	2	22	apostol	apostol	NOUN
ejpam-5559	2	23	-	-	PUNCT
ejpam-5559	2	24	type	type	NOUN
ejpam-5559	2	25	functions	function	NOUN
ejpam-5559	2	26	.	.	PUNCT
ejpam-5559	3	1	we	we	PRON
ejpam-5559	3	2	conduct	conduct	VERB
ejpam-5559	3	3	a	a	DET
ejpam-5559	3	4	detailed	detailed	ADJ
ejpam-5559	3	5	investigation	investigation	NOUN
ejpam-5559	3	6	into	into	ADP
ejpam-5559	3	7	the	the	DET
ejpam-5559	3	8	properties	property	NOUN
ejpam-5559	3	9	of	of	ADP
ejpam-5559	3	10	these	these	DET
ejpam-5559	3	11	polynomials	polynomial	NOUN
ejpam-5559	3	12	,	,	PUNCT
ejpam-5559	3	13	utilizing	utilize	VERB
ejpam-5559	3	14	various	various	ADJ
ejpam-5559	3	15	analytical	analytical	ADJ
ejpam-5559	3	16	techniques	technique	NOUN
ejpam-5559	3	17	.	.	PUNCT
ejpam-5559	4	1	by	by	ADP
ejpam-5559	4	2	employing	employ	VERB
ejpam-5559	4	3	generating	generating	NOUN
ejpam-5559	4	4	functions	function	NOUN
ejpam-5559	4	5	for	for	ADP
ejpam-5559	4	6	bell	bell	NOUN
ejpam-5559	4	7	-	-	PUNCT
ejpam-5559	4	8	based	base	VERB
ejpam-5559	4	9	apostol	apostol	NOUN
ejpam-5559	4	10	-	-	PUNCT
ejpam-5559	4	11	frobenius	frobenius	NOUN
ejpam-5559	4	12	-	-	PUNCT
ejpam-5559	4	13	type	type	NOUN
ejpam-5559	4	14	tangent	tangent	NOUN
ejpam-5559	4	15	polynomials	polynomial	NOUN
ejpam-5559	4	16	of	of	ADP
ejpam-5559	4	17	higher	high	ADJ
ejpam-5559	4	18	order	order	NOUN
ejpam-5559	4	19	,	,	PUNCT
ejpam-5559	4	20	we	we	PRON
ejpam-5559	4	21	obtain	obtain	VERB
ejpam-5559	4	22	both	both	CCONJ
ejpam-5559	4	23	explicit	explicit	ADJ
ejpam-5559	4	24	and	and	CCONJ
ejpam-5559	4	25	implicit	implicit	ADJ
ejpam-5559	4	26	summation	summation	NOUN
ejpam-5559	4	27	formulas	formula	NOUN
ejpam-5559	4	28	and	and	CCONJ
ejpam-5559	4	29	its	its	PRON
ejpam-5559	4	30	relation	relation	NOUN
ejpam-5559	4	31	to	to	ADP
ejpam-5559	4	32	appell	appell	NOUN
ejpam-5559	4	33	polynomials	polynomial	NOUN
ejpam-5559	4	34	.	.	PUNCT
ejpam-5559	5	1	2020	2020	NUM
ejpam-5559	5	2	mathematics	mathematic	NOUN
ejpam-5559	5	3	subject	subject	NOUN
ejpam-5559	5	4	classifications	classification	NOUN
ejpam-5559	5	5	:	:	PUNCT
ejpam-5559	5	6	05a15	05a15	NUM
ejpam-5559	5	7	,	,	PUNCT
ejpam-5559	5	8	11b68	11b68	NUM
ejpam-5559	5	9	,	,	PUNCT
ejpam-5559	5	10	11b73	11b73	NUM
ejpam-5559	5	11	,	,	PUNCT
ejpam-5559	5	12	26c05	26c05	NUM
ejpam-5559	5	13	,	,	PUNCT
ejpam-5559	5	14	33b10	33b10	NUM
ejpam-5559	5	15	key	key	ADJ
ejpam-5559	5	16	words	word	NOUN
ejpam-5559	5	17	and	and	CCONJ
ejpam-5559	5	18	phrases	phrase	NOUN
ejpam-5559	5	19	:	:	PUNCT
ejpam-5559	5	20	tangent	tangent	NOUN
ejpam-5559	5	21	polynomials	polynomial	NOUN
ejpam-5559	5	22	,	,	PUNCT
ejpam-5559	5	23	bell	bell	NOUN
ejpam-5559	5	24	polynomials	polynomial	NOUN
ejpam-5559	5	25	,	,	PUNCT
ejpam-5559	5	26	apostol	apostol	NOUN
ejpam-5559	5	27	-	-	PUNCT
ejpam-5559	5	28	frobeniustype	frobeniustype	NOUN
ejpam-5559	5	29	poly	poly	ADJ
ejpam-5559	5	30	-	-	PUNCT
ejpam-5559	5	31	tangent	tangent	NOUN
ejpam-5559	5	32	polynomials	polynomial	NOUN
ejpam-5559	5	33	,	,	PUNCT
ejpam-5559	5	34	bell	bell	NOUN
ejpam-5559	5	35	-	-	PUNCT
ejpam-5559	5	36	based	base	VERB
ejpam-5559	5	37	apostol	apostol	NOUN
ejpam-5559	5	38	-	-	PUNCT
ejpam-5559	5	39	frobenius	frobenius	NOUN
ejpam-5559	5	40	-	-	PUNCT
ejpam-5559	5	41	type	type	NOUN
ejpam-5559	5	42	poly	poly	ADJ
ejpam-5559	5	43	-	-	PUNCT
ejpam-5559	5	44	tangent	tangent	NOUN
ejpam-5559	5	45	polynomials	polynomial	NOUN
ejpam-5559	5	46	,	,	PUNCT
ejpam-5559	5	47	stirling	stirling	NOUN
ejpam-5559	5	48	numbers	number	NOUN
ejpam-5559	5	49	,	,	PUNCT
ejpam-5559	5	50	appell	appell	ADJ
ejpam-5559	5	51	polynomials	polynomial	NOUN
ejpam-5559	5	52	1	1	NUM
ejpam-5559	5	53	.	.	PUNCT
ejpam-5559	5	54	introduction	introduction	NOUN
ejpam-5559	5	55	in	in	ADP
ejpam-5559	5	56	mathematical	mathematical	ADJ
ejpam-5559	5	57	analysis	analysis	NOUN
ejpam-5559	5	58	,	,	PUNCT
ejpam-5559	5	59	special	special	ADJ
ejpam-5559	5	60	polynomials	polynomial	NOUN
ejpam-5559	5	61	play	play	VERB
ejpam-5559	5	62	a	a	DET
ejpam-5559	5	63	pivotal	pivotal	ADJ
ejpam-5559	5	64	role	role	NOUN
ejpam-5559	5	65	due	due	ADP
ejpam-5559	5	66	to	to	ADP
ejpam-5559	5	67	their	their	PRON
ejpam-5559	5	68	extensive	extensive	ADJ
ejpam-5559	5	69	applications	application	NOUN
ejpam-5559	5	70	across	across	ADP
ejpam-5559	5	71	various	various	ADJ
ejpam-5559	5	72	domains	domain	NOUN
ejpam-5559	5	73	.	.	PUNCT
ejpam-5559	6	1	among	among	ADP
ejpam-5559	6	2	these	these	PRON
ejpam-5559	6	3	,	,	PUNCT
ejpam-5559	6	4	the	the	DET
ejpam-5559	6	5	frobenius	frobenius	NOUN
ejpam-5559	6	6	-	-	PUNCT
ejpam-5559	6	7	tangent	tangent	NOUN
ejpam-5559	6	8	polynomials	polynomial	NOUN
ejpam-5559	6	9	have	have	AUX
ejpam-5559	6	10	garnered	garner	VERB
ejpam-5559	6	11	significant	significant	ADJ
ejpam-5559	6	12	attention	attention	NOUN
ejpam-5559	6	13	.	.	PUNCT
ejpam-5559	7	1	these	these	DET
ejpam-5559	7	2	polynomials	polynomial	NOUN
ejpam-5559	7	3	,	,	PUNCT
ejpam-5559	7	4	denoted	denote	VERB
ejpam-5559	7	5	as	as	ADP
ejpam-5559	7	6	tn(x	tn(x	PUNCT
ejpam-5559	7	7	)	)	PUNCT
ejpam-5559	7	8	,	,	PUNCT
ejpam-5559	7	9	are	be	AUX
ejpam-5559	7	10	defined	define	VERB
ejpam-5559	7	11	by	by	ADP
ejpam-5559	7	12	the	the	DET
ejpam-5559	7	13	generating	generate	VERB
ejpam-5559	7	14	function	function	NOUN
ejpam-5559	7	15	(	(	PUNCT
ejpam-5559	7	16	[	[	X
ejpam-5559	7	17	11]),[12	11]),[12	NOUN
ejpam-5559	7	18	]	]	PUNCT
ejpam-5559	7	19	)	)	PUNCT
ejpam-5559	7	20	∞∑	∞∑	PRON
ejpam-5559	7	21	n=0	n=0	NUM
ejpam-5559	7	22	tn(x	tn(x	ADP
ejpam-5559	7	23	)	)	PUNCT
ejpam-5559	7	24	zn	zn	NOUN
ejpam-5559	7	25	n	n	X
ejpam-5559	7	26	!	!	PUNCT
ejpam-5559	8	1	=	=	PUNCT
ejpam-5559	8	2	(	(	PUNCT
ejpam-5559	8	3	2	2	X
ejpam-5559	8	4	e2z	e2z	NOUN
ejpam-5559	8	5	+	+	NOUN
ejpam-5559	8	6	1	1	NUM
ejpam-5559	8	7	exz	exz	VERB
ejpam-5559	8	8	)	)	PUNCT
ejpam-5559	8	9	,	,	PUNCT
ejpam-5559	8	10	(	(	PUNCT
ejpam-5559	8	11	1	1	X
ejpam-5559	8	12	)	)	PUNCT
ejpam-5559	8	13	where	where	SCONJ
ejpam-5559	8	14	tn(0	tn(0	ADP
ejpam-5559	8	15	)	)	PUNCT
ejpam-5559	8	16	=	=	SYM
ejpam-5559	8	17	tn	tn	PROPN
ejpam-5559	8	18	,	,	PUNCT
ejpam-5559	8	19	the	the	DET
ejpam-5559	8	20	tangent	tangent	NOUN
ejpam-5559	8	21	numbers	number	NOUN
ejpam-5559	8	22	defined	define	VERB
ejpam-5559	8	23	coefficient	coefficient	NOUN
ejpam-5559	8	24	of	of	ADP
ejpam-5559	8	25	the	the	DET
ejpam-5559	8	26	following	follow	VERB
ejpam-5559	8	27	series	series	NOUN
ejpam-5559	8	28	expansion	expansion	NOUN
ejpam-5559	8	29	of	of	ADP
ejpam-5559	8	30	the	the	DET
ejpam-5559	8	31	tangent	tangent	NOUN
ejpam-5559	8	32	function	function	NOUN
ejpam-5559	8	33	(	(	PUNCT
ejpam-5559	8	34	[	[	X
ejpam-5559	8	35	13	13	NUM
ejpam-5559	8	36	]	]	SYM
ejpam-5559	8	37	)	)	PUNCT
ejpam-5559	8	38	tan	tan	NOUN
ejpam-5559	8	39	z	z	NOUN
ejpam-5559	8	40	=	=	PUNCT
ejpam-5559	9	1	∞∑	∞∑	NUM
ejpam-5559	9	2	n=0	n=0	NUM
ejpam-5559	9	3	(	(	PUNCT
ejpam-5559	9	4	−1)n+1t2n+1	−1)n+1t2n+1	X
ejpam-5559	9	5	z2n+1	z2n+1	NUM
ejpam-5559	9	6	(	(	PUNCT
ejpam-5559	9	7	2n+	2n+	NUM
ejpam-5559	9	8	1	1	NUM
ejpam-5559	9	9	)	)	PUNCT
ejpam-5559	9	10	!	!	PUNCT
ejpam-5559	10	1	,	,	PUNCT
ejpam-5559	10	2	(	(	PUNCT
ejpam-5559	10	3	2	2	X
ejpam-5559	10	4	)	)	PUNCT
ejpam-5559	10	5	∗corresponding	∗corresponde	VERB
ejpam-5559	10	6	author	author	NOUN
ejpam-5559	10	7	.	.	PUNCT
ejpam-5559	11	1	doi	doi	NOUN
ejpam-5559	11	2	:	:	PUNCT
ejpam-5559	11	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5559	https://doi.org/10.29020/nybg.ejpam.v18i1.5559	PRON
ejpam-5559	11	4	email	email	NOUN
ejpam-5559	11	5	addresses	address	NOUN
ejpam-5559	11	6	:	:	PUNCT
ejpam-5559	11	7	ontolanj@cnu.edu.ph	ontolanj@cnu.edu.ph	PROPN
ejpam-5559	11	8	(	(	PUNCT
ejpam-5559	11	9	j.	j.	PROPN
ejpam-5559	11	10	ontolan	ontolan	PROPN
ejpam-5559	11	11	)	)	PUNCT
ejpam-5559	11	12	,	,	PUNCT
ejpam-5559	11	13	malusayj@cnu.edu.ph	malusayj@cnu.edu.ph	PROPN
ejpam-5559	11	14	(	(	PUNCT
ejpam-5559	11	15	j.	j.	PROPN
ejpam-5559	11	16	malusay	malusay	PROPN
ejpam-5559	11	17	)	)	PUNCT
ejpam-5559	11	18	,	,	PUNCT
ejpam-5559	11	19	kiunisalae@cnu.edu.ph	kiunisalae@cnu.edu.ph	PROPN
ejpam-5559	11	20	(	(	PUNCT
ejpam-5559	11	21	e.	e.	PROPN
ejpam-5559	11	22	kiunisala	kiunisala	PROPN
ejpam-5559	11	23	)	)	PUNCT
ejpam-5559	11	24	,	,	PUNCT
ejpam-5559	11	25	buloronj@cnu.edu.ph	buloronj@cnu.edu.ph	PROPN
ejpam-5559	11	26	(	(	PUNCT
ejpam-5559	11	27	j.	j.	PROPN
ejpam-5559	11	28	buloron	buloron	PROPN
ejpam-5559	11	29	)	)	PUNCT
ejpam-5559	11	30	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5559	12	1	1	1	NUM
ejpam-5559	12	2	copyright	copyright	NOUN
ejpam-5559	12	3	:	:	PUNCT
ejpam-5559	12	4	©	©	PROPN
ejpam-5559	12	5	2025	2025	NUM
ejpam-5559	12	6	the	the	DET
ejpam-5559	12	7	author(s	author(s	NOUN
ejpam-5559	12	8	)	)	PUNCT
ejpam-5559	12	9	.	.	PUNCT
ejpam-5559	13	1	(	(	PUNCT
ejpam-5559	13	2	cc	cc	NOUN
ejpam-5559	13	3	by	by	ADP
ejpam-5559	13	4	-	-	PUNCT
ejpam-5559	13	5	nc	nc	PROPN
ejpam-5559	13	6	4.0	4.0	NUM
ejpam-5559	13	7	)	)	PUNCT
ejpam-5559	13	8	j.	j.	PROPN
ejpam-5559	13	9	ontolan	ontolan	PROPN
ejpam-5559	13	10	et	et	PROPN
ejpam-5559	13	11	al	al	PROPN
ejpam-5559	13	12	.	.	PUNCT
ejpam-5559	13	13	/	/	SYM
ejpam-5559	13	14	eur	eur	PROPN
ejpam-5559	13	15	.	.	PUNCT
ejpam-5559	14	1	j.	j.	PROPN
ejpam-5559	14	2	pure	pure	PROPN
ejpam-5559	14	3	appl	appl	PROPN
ejpam-5559	14	4	.	.	PROPN
ejpam-5559	14	5	math	math	PROPN
ejpam-5559	14	6	,	,	PUNCT
ejpam-5559	14	7	18	18	NUM
ejpam-5559	14	8	(	(	PUNCT
ejpam-5559	14	9	1	1	NUM
ejpam-5559	14	10	)	)	PUNCT
ejpam-5559	14	11	(	(	PUNCT
ejpam-5559	14	12	2025	2025	NUM
ejpam-5559	14	13	)	)	PUNCT
ejpam-5559	14	14	,	,	PUNCT
ejpam-5559	14	15	5559	5559	NUM
ejpam-5559	14	16	2	2	NUM
ejpam-5559	14	17	of	of	ADP
ejpam-5559	14	18	16	16	NUM
ejpam-5559	14	19	with	with	ADP
ejpam-5559	14	20	t0	t0	PROPN
ejpam-5559	14	21	=	=	SYM
ejpam-5559	14	22	1	1	NUM
ejpam-5559	14	23	and	and	CCONJ
ejpam-5559	14	24	t2n	t2n	PROPN
ejpam-5559	14	25	=	=	SYM
ejpam-5559	14	26	0	0	NUM
ejpam-5559	14	27	,	,	PUNCT
ejpam-5559	14	28	n	n	PRON
ejpam-5559	14	29	∈	∈	PROPN
ejpam-5559	14	30	n.	n.	NOUN
ejpam-5559	14	31	they	they	PRON
ejpam-5559	14	32	emerge	emerge	VERB
ejpam-5559	14	33	naturally	naturally	ADV
ejpam-5559	14	34	in	in	ADP
ejpam-5559	14	35	the	the	DET
ejpam-5559	14	36	study	study	NOUN
ejpam-5559	14	37	of	of	ADP
ejpam-5559	14	38	differential	differential	ADJ
ejpam-5559	14	39	equations	equation	NOUN
ejpam-5559	14	40	and	and	CCONJ
ejpam-5559	14	41	have	have	VERB
ejpam-5559	14	42	applications	application	NOUN
ejpam-5559	14	43	in	in	ADP
ejpam-5559	14	44	numerical	numerical	ADJ
ejpam-5559	14	45	analysis	analysis	NOUN
ejpam-5559	14	46	and	and	CCONJ
ejpam-5559	14	47	approximation	approximation	NOUN
ejpam-5559	14	48	theory	theory	NOUN
ejpam-5559	14	49	.	.	PUNCT
ejpam-5559	15	1	parallel	parallel	ADJ
ejpam-5559	15	2	to	to	ADP
ejpam-5559	15	3	this	this	PRON
ejpam-5559	15	4	,	,	PUNCT
ejpam-5559	15	5	the	the	DET
ejpam-5559	15	6	apostol	apostol	NOUN
ejpam-5559	15	7	polynomials	polynomial	NOUN
ejpam-5559	15	8	,	,	PUNCT
ejpam-5559	15	9	particularly	particularly	ADV
ejpam-5559	15	10	the	the	DET
ejpam-5559	15	11	apostol	apostol	NOUN
ejpam-5559	15	12	-	-	PUNCT
ejpam-5559	15	13	bernoulli	bernoulli	NOUN
ejpam-5559	15	14	and	and	CCONJ
ejpam-5559	15	15	apostoleuler	apostoleuler	NOUN
ejpam-5559	15	16	polynomials	polynomial	NOUN
ejpam-5559	15	17	,	,	PUNCT
ejpam-5559	15	18	have	have	AUX
ejpam-5559	15	19	been	be	AUX
ejpam-5559	15	20	extensively	extensively	ADV
ejpam-5559	15	21	studied	study	VERB
ejpam-5559	15	22	.	.	PUNCT
ejpam-5559	16	1	the	the	DET
ejpam-5559	16	2	apostol	apostol	NOUN
ejpam-5559	16	3	-	-	PUNCT
ejpam-5559	16	4	bernoulli	bernoulli	NOUN
ejpam-5559	16	5	polynomials	polynomials	PROPN
ejpam-5559	16	6	b	b	PROPN
ejpam-5559	16	7	(	(	PUNCT
ejpam-5559	16	8	a	a	NOUN
ejpam-5559	16	9	)	)	PUNCT
ejpam-5559	16	10	n	n	NOUN
ejpam-5559	16	11	(	(	PUNCT
ejpam-5559	16	12	x	x	X
ejpam-5559	16	13	)	)	PUNCT
ejpam-5559	16	14	are	be	AUX
ejpam-5559	16	15	defined	define	VERB
ejpam-5559	16	16	via	via	ADP
ejpam-5559	16	17	the	the	DET
ejpam-5559	16	18	generating	generate	VERB
ejpam-5559	16	19	function	function	NOUN
ejpam-5559	16	20	:	:	PUNCT
ejpam-5559	16	21	∞∑	∞∑	NUM
ejpam-5559	16	22	n=0	n=0	NUM
ejpam-5559	16	23	b(a	b(a	X
ejpam-5559	16	24	)	)	PUNCT
ejpam-5559	16	25	n	n	CCONJ
ejpam-5559	16	26	(	(	PUNCT
ejpam-5559	16	27	x	x	X
ejpam-5559	16	28	)	)	PUNCT
ejpam-5559	16	29	tn	tn	PROPN
ejpam-5559	16	30	n	n	NOUN
ejpam-5559	16	31	!	!	PUNCT
ejpam-5559	17	1	=	=	NOUN
ejpam-5559	17	2	text	text	NOUN
ejpam-5559	17	3	aet	aet	NOUN
ejpam-5559	18	1	−	−	PROPN
ejpam-5559	18	2	1	1	NUM
ejpam-5559	18	3	,	,	PUNCT
ejpam-5559	18	4	(	(	PUNCT
ejpam-5559	18	5	3	3	X
ejpam-5559	18	6	)	)	PUNCT
ejpam-5559	18	7	where	where	SCONJ
ejpam-5559	18	8	a	a	PRON
ejpam-5559	18	9	is	be	AUX
ejpam-5559	18	10	a	a	DET
ejpam-5559	18	11	non	non	ADJ
ejpam-5559	18	12	-	-	ADJ
ejpam-5559	18	13	zero	zero	NUM
ejpam-5559	18	14	parameter	parameter	NOUN
ejpam-5559	18	15	.	.	PUNCT
ejpam-5559	19	1	these	these	DET
ejpam-5559	19	2	polynomials	polynomial	NOUN
ejpam-5559	19	3	generalize	generalize	VERB
ejpam-5559	19	4	the	the	DET
ejpam-5559	19	5	classical	classical	ADJ
ejpam-5559	19	6	bernoulli	bernoulli	NOUN
ejpam-5559	19	7	polynomials	polynomial	NOUN
ejpam-5559	19	8	and	and	CCONJ
ejpam-5559	19	9	have	have	VERB
ejpam-5559	19	10	applications	application	NOUN
ejpam-5559	19	11	in	in	ADP
ejpam-5559	19	12	number	number	NOUN
ejpam-5559	19	13	theory	theory	NOUN
ejpam-5559	19	14	and	and	CCONJ
ejpam-5559	19	15	combinatorics	combinatoric	NOUN
ejpam-5559	19	16	.	.	PUNCT
ejpam-5559	20	1	bell	bell	PROPN
ejpam-5559	20	2	polynomials	polynomial	NOUN
ejpam-5559	20	3	,	,	PUNCT
ejpam-5559	20	4	denoted	denote	VERB
ejpam-5559	20	5	as	as	ADP
ejpam-5559	20	6	bn(x	bn(x	NOUN
ejpam-5559	20	7	)	)	PUNCT
ejpam-5559	20	8	,	,	PUNCT
ejpam-5559	20	9	are	be	AUX
ejpam-5559	20	10	another	another	DET
ejpam-5559	20	11	important	important	ADJ
ejpam-5559	20	12	class	class	NOUN
ejpam-5559	20	13	,	,	PUNCT
ejpam-5559	20	14	defined	define	VERB
ejpam-5559	20	15	by	by	ADP
ejpam-5559	20	16	the	the	DET
ejpam-5559	20	17	generating	generate	VERB
ejpam-5559	20	18	function	function	NOUN
ejpam-5559	20	19	:	:	PUNCT
ejpam-5559	20	20	∞∑	∞∑	NUM
ejpam-5559	20	21	n=0	n=0	NUM
ejpam-5559	20	22	bn(x	bn(x	NUM
ejpam-5559	20	23	)	)	PUNCT
ejpam-5559	20	24	tn	tn	PROPN
ejpam-5559	20	25	n	n	PROPN
ejpam-5559	20	26	!	!	PUNCT
ejpam-5559	21	1	=	=	SYM
ejpam-5559	21	2	ex(e	ex(e	NOUN
ejpam-5559	21	3	t−1	t−1	NOUN
ejpam-5559	21	4	)	)	PUNCT
ejpam-5559	21	5	.	.	PUNCT
ejpam-5559	22	1	(	(	PUNCT
ejpam-5559	22	2	4	4	X
ejpam-5559	22	3	)	)	PUNCT
ejpam-5559	22	4	they	they	PRON
ejpam-5559	22	5	are	be	AUX
ejpam-5559	22	6	instrumental	instrumental	ADJ
ejpam-5559	22	7	in	in	ADP
ejpam-5559	22	8	the	the	DET
ejpam-5559	22	9	study	study	NOUN
ejpam-5559	22	10	of	of	ADP
ejpam-5559	22	11	combinatorial	combinatorial	ADJ
ejpam-5559	22	12	structures	structure	NOUN
ejpam-5559	22	13	and	and	CCONJ
ejpam-5559	22	14	have	have	VERB
ejpam-5559	22	15	applications	application	NOUN
ejpam-5559	22	16	in	in	ADP
ejpam-5559	22	17	the	the	DET
ejpam-5559	22	18	theory	theory	NOUN
ejpam-5559	22	19	of	of	ADP
ejpam-5559	22	20	partitions	partition	NOUN
ejpam-5559	22	21	and	and	CCONJ
ejpam-5559	22	22	moments	moment	NOUN
ejpam-5559	22	23	of	of	ADP
ejpam-5559	22	24	probability	probability	NOUN
ejpam-5559	22	25	distributions	distribution	NOUN
ejpam-5559	22	26	.	.	PUNCT
ejpam-5559	23	1	in	in	ADP
ejpam-5559	23	2	the	the	DET
ejpam-5559	23	3	framework	framework	NOUN
ejpam-5559	23	4	of	of	ADP
ejpam-5559	23	5	orthogonal	orthogonal	ADJ
ejpam-5559	23	6	polynomials	polynomial	NOUN
ejpam-5559	23	7	,	,	PUNCT
ejpam-5559	23	8	it	it	PRON
ejpam-5559	23	9	is	be	AUX
ejpam-5559	23	10	noteworthy	noteworthy	ADJ
ejpam-5559	23	11	that	that	SCONJ
ejpam-5559	23	12	certain	certain	ADJ
ejpam-5559	23	13	classes	class	NOUN
ejpam-5559	23	14	of	of	ADP
ejpam-5559	23	15	apostol	apostol	NOUN
ejpam-5559	23	16	and	and	CCONJ
ejpam-5559	23	17	bell	bell	NOUN
ejpam-5559	23	18	polynomials	polynomial	NOUN
ejpam-5559	23	19	exhibit	exhibit	VERB
ejpam-5559	23	20	orthogonality	orthogonality	NOUN
ejpam-5559	23	21	properties	property	NOUN
ejpam-5559	23	22	under	under	ADP
ejpam-5559	23	23	specific	specific	ADJ
ejpam-5559	23	24	weight	weight	NOUN
ejpam-5559	23	25	functions	function	NOUN
ejpam-5559	23	26	.	.	PUNCT
ejpam-5559	24	1	for	for	ADP
ejpam-5559	24	2	instance	instance	NOUN
ejpam-5559	24	3	,	,	PUNCT
ejpam-5559	24	4	the	the	DET
ejpam-5559	24	5	study	study	NOUN
ejpam-5559	24	6	by	by	ADP
ejpam-5559	24	7	luo	luo	PROPN
ejpam-5559	24	8	and	and	CCONJ
ejpam-5559	24	9	srivastava	srivastava	PROPN
ejpam-5559	24	10	[	[	X
ejpam-5559	24	11	8	8	NUM
ejpam-5559	24	12	]	]	X
ejpam-5559	24	13	looks	look	VERB
ejpam-5559	24	14	into	into	ADP
ejpam-5559	24	15	some	some	DET
ejpam-5559	24	16	generalizations	generalization	NOUN
ejpam-5559	24	17	of	of	ADP
ejpam-5559	24	18	apostol	apostol	NOUN
ejpam-5559	24	19	-	-	PUNCT
ejpam-5559	24	20	bernoulli	bernoulli	NOUN
ejpam-5559	24	21	and	and	CCONJ
ejpam-5559	24	22	apostol	apostol	NOUN
ejpam-5559	24	23	-	-	PUNCT
ejpam-5559	24	24	euler	euler	NOUN
ejpam-5559	24	25	polynomials	polynomial	NOUN
ejpam-5559	24	26	,	,	PUNCT
ejpam-5559	24	27	exploring	explore	VERB
ejpam-5559	24	28	their	their	PRON
ejpam-5559	24	29	orthogonality	orthogonality	NOUN
ejpam-5559	24	30	and	and	CCONJ
ejpam-5559	24	31	other	other	ADJ
ejpam-5559	24	32	properties	property	NOUN
ejpam-5559	24	33	.	.	PUNCT
ejpam-5559	25	1	similarly	similarly	ADV
ejpam-5559	25	2	,	,	PUNCT
ejpam-5559	25	3	the	the	DET
ejpam-5559	25	4	work	work	NOUN
ejpam-5559	25	5	by	by	ADP
ejpam-5559	25	6	kurt	kurt	PROPN
ejpam-5559	25	7	[	[	X
ejpam-5559	25	8	7	7	NUM
ejpam-5559	25	9	]	]	PUNCT
ejpam-5559	25	10	introduces	introduce	VERB
ejpam-5559	25	11	new	new	ADJ
ejpam-5559	25	12	families	family	NOUN
ejpam-5559	25	13	of	of	ADP
ejpam-5559	25	14	polynomials	polynomial	NOUN
ejpam-5559	25	15	associated	associate	VERB
ejpam-5559	25	16	with	with	ADP
ejpam-5559	25	17	the	the	DET
ejpam-5559	25	18	bell	bell	PROPN
ejpam-5559	25	19	numbers	number	NOUN
ejpam-5559	25	20	and	and	CCONJ
ejpam-5559	25	21	polynomials	polynomial	NOUN
ejpam-5559	25	22	,	,	PUNCT
ejpam-5559	25	23	discussing	discuss	VERB
ejpam-5559	25	24	their	their	PRON
ejpam-5559	25	25	potential	potential	ADJ
ejpam-5559	25	26	orthogonality	orthogonality	NOUN
ejpam-5559	25	27	under	under	ADP
ejpam-5559	25	28	certain	certain	ADJ
ejpam-5559	25	29	conditions	condition	NOUN
ejpam-5559	25	30	.	.	PUNCT
ejpam-5559	26	1	additionally	additionally	ADV
ejpam-5559	26	2	,	,	PUNCT
ejpam-5559	26	3	recent	recent	ADJ
ejpam-5559	26	4	research	research	NOUN
ejpam-5559	26	5	by	by	ADP
ejpam-5559	26	6	khan	khan	PROPN
ejpam-5559	26	7	and	and	CCONJ
ejpam-5559	26	8	riaz	riaz	PROPN
ejpam-5559	27	1	[	[	X
ejpam-5559	27	2	6	6	NUM
ejpam-5559	27	3	]	]	PUNCT
ejpam-5559	27	4	investigates	investigate	VERB
ejpam-5559	27	5	certain	certain	ADJ
ejpam-5559	27	6	subclasses	subclass	NOUN
ejpam-5559	27	7	of	of	ADP
ejpam-5559	27	8	apostol	apostol	NOUN
ejpam-5559	27	9	-	-	PUNCT
ejpam-5559	27	10	type	type	NOUN
ejpam-5559	27	11	polynomials	polynomial	NOUN
ejpam-5559	27	12	,	,	PUNCT
ejpam-5559	27	13	providing	provide	VERB
ejpam-5559	27	14	insights	insight	NOUN
ejpam-5559	27	15	into	into	ADP
ejpam-5559	27	16	their	their	PRON
ejpam-5559	27	17	structural	structural	ADJ
ejpam-5559	27	18	properties	property	NOUN
ejpam-5559	27	19	within	within	ADP
ejpam-5559	27	20	the	the	DET
ejpam-5559	27	21	orthogonal	orthogonal	ADJ
ejpam-5559	27	22	polynomial	polynomial	ADJ
ejpam-5559	27	23	framework	framework	NOUN
ejpam-5559	27	24	.	.	PUNCT
ejpam-5559	28	1	further	further	ADJ
ejpam-5559	28	2	studies	study	NOUN
ejpam-5559	28	3	have	have	AUX
ejpam-5559	28	4	expanded	expand	VERB
ejpam-5559	28	5	the	the	DET
ejpam-5559	28	6	landscape	landscape	NOUN
ejpam-5559	28	7	of	of	ADP
ejpam-5559	28	8	these	these	DET
ejpam-5559	28	9	polynomials	polynomial	NOUN
ejpam-5559	28	10	.	.	PUNCT
ejpam-5559	29	1	dattoli	dattoli	NOUN
ejpam-5559	29	2	et	et	PROPN
ejpam-5559	29	3	al	al	PROPN
ejpam-5559	29	4	.	.	PUNCT
ejpam-5559	30	1	[	[	X
ejpam-5559	30	2	5	5	NUM
ejpam-5559	30	3	]	]	PUNCT
ejpam-5559	30	4	introduced	introduce	VERB
ejpam-5559	30	5	a	a	DET
ejpam-5559	30	6	family	family	NOUN
ejpam-5559	30	7	of	of	ADP
ejpam-5559	30	8	hybrid	hybrid	ADJ
ejpam-5559	30	9	polynomials	polynomial	NOUN
ejpam-5559	30	10	that	that	PRON
ejpam-5559	30	11	exhibit	exhibit	VERB
ejpam-5559	30	12	characteristics	characteristic	NOUN
ejpam-5559	30	13	of	of	ADP
ejpam-5559	30	14	both	both	CCONJ
ejpam-5559	30	15	hermite	hermite	ADJ
ejpam-5559	30	16	and	and	CCONJ
ejpam-5559	30	17	laguerre	laguerre	NOUN
ejpam-5559	30	18	polynomials	polynomial	NOUN
ejpam-5559	30	19	,	,	PUNCT
ejpam-5559	30	20	enriching	enrich	VERB
ejpam-5559	30	21	the	the	DET
ejpam-5559	30	22	theory	theory	NOUN
ejpam-5559	30	23	of	of	ADP
ejpam-5559	30	24	special	special	ADJ
ejpam-5559	30	25	functions	function	NOUN
ejpam-5559	30	26	.	.	PUNCT
ejpam-5559	31	1	ramı́rez	ramı́rez	NOUN
ejpam-5559	31	2	and	and	CCONJ
ejpam-5559	31	3	cesarano	cesarano	PROPN
ejpam-5559	32	1	[	[	X
ejpam-5559	32	2	9	9	NUM
ejpam-5559	32	3	]	]	PUNCT
ejpam-5559	32	4	explored	explore	VERB
ejpam-5559	32	5	new	new	ADJ
ejpam-5559	32	6	classes	class	NOUN
ejpam-5559	32	7	of	of	ADP
ejpam-5559	32	8	degenerated	degenerated	ADJ
ejpam-5559	32	9	generalized	generalized	ADJ
ejpam-5559	32	10	apostol	apostol	NOUN
ejpam-5559	32	11	-	-	PUNCT
ejpam-5559	32	12	bernoulli	bernoulli	NOUN
ejpam-5559	32	13	,	,	PUNCT
ejpam-5559	32	14	apostol	apostol	NOUN
ejpam-5559	32	15	-	-	PUNCT
ejpam-5559	32	16	euler	euler	NOUN
ejpam-5559	32	17	,	,	PUNCT
ejpam-5559	32	18	and	and	CCONJ
ejpam-5559	32	19	apostol	apostol	NOUN
ejpam-5559	32	20	-	-	PUNCT
ejpam-5559	32	21	genocchi	genocchi	PROPN
ejpam-5559	32	22	polynomials	polynomial	NOUN
ejpam-5559	32	23	,	,	PUNCT
ejpam-5559	32	24	deriving	derive	VERB
ejpam-5559	32	25	explicit	explicit	ADJ
ejpam-5559	32	26	expressions	expression	NOUN
ejpam-5559	32	27	and	and	CCONJ
ejpam-5559	32	28	recurrence	recurrence	NOUN
ejpam-5559	32	29	relations	relation	NOUN
ejpam-5559	32	30	.	.	PUNCT
ejpam-5559	33	1	in	in	ADP
ejpam-5559	33	2	a	a	DET
ejpam-5559	33	3	subsequent	subsequent	ADJ
ejpam-5559	33	4	work	work	NOUN
ejpam-5559	33	5	,	,	PUNCT
ejpam-5559	33	6	ramı́rez	ramı́rez	PROPN
ejpam-5559	33	7	et	et	PROPN
ejpam-5559	33	8	al	al	PROPN
ejpam-5559	33	9	.	.	PUNCT
ejpam-5559	34	1	[	[	X
ejpam-5559	34	2	10	10	NUM
ejpam-5559	34	3	]	]	PUNCT
ejpam-5559	34	4	presented	present	VERB
ejpam-5559	34	5	new	new	ADJ
ejpam-5559	34	6	results	result	NOUN
ejpam-5559	34	7	for	for	ADP
ejpam-5559	34	8	these	these	DET
ejpam-5559	34	9	degenerated	degenerated	ADJ
ejpam-5559	34	10	polynomials	polynomial	NOUN
ejpam-5559	34	11	,	,	PUNCT
ejpam-5559	34	12	establishing	establish	VERB
ejpam-5559	34	13	algebraic	algebraic	ADJ
ejpam-5559	34	14	relationships	relationship	NOUN
ejpam-5559	34	15	and	and	CCONJ
ejpam-5559	34	16	recurrence	recurrence	NOUN
ejpam-5559	34	17	formulas	formula	NOUN
ejpam-5559	34	18	.	.	PUNCT
ejpam-5559	35	1	the	the	DET
ejpam-5559	35	2	study	study	NOUN
ejpam-5559	35	3	of	of	ADP
ejpam-5559	35	4	special	special	ADJ
ejpam-5559	35	5	numbers	number	NOUN
ejpam-5559	35	6	such	such	ADJ
ejpam-5559	35	7	as	as	ADP
ejpam-5559	35	8	the	the	DET
ejpam-5559	35	9	tangent	tangent	NOUN
ejpam-5559	35	10	numbers	number	NOUN
ejpam-5559	35	11	,	,	PUNCT
ejpam-5559	35	12	bernoulli	bernoulli	NOUN
ejpam-5559	35	13	numbers	number	NOUN
ejpam-5559	35	14	,	,	PUNCT
ejpam-5559	35	15	euler	euler	NOUN
ejpam-5559	35	16	numbers	number	NOUN
ejpam-5559	35	17	,	,	PUNCT
ejpam-5559	35	18	and	and	CCONJ
ejpam-5559	35	19	genocchi	genocchi	PROPN
ejpam-5559	35	20	numbers	number	NOUN
ejpam-5559	35	21	has	have	AUX
ejpam-5559	35	22	become	become	VERB
ejpam-5559	35	23	an	an	DET
ejpam-5559	35	24	interesting	interesting	ADJ
ejpam-5559	35	25	area	area	NOUN
ejpam-5559	35	26	for	for	ADP
ejpam-5559	35	27	many	many	ADJ
ejpam-5559	35	28	mathematicians	mathematician	NOUN
ejpam-5559	35	29	(	(	PUNCT
ejpam-5559	35	30	[	[	X
ejpam-5559	35	31	2],[4],[14	2],[4],[14	NUM
ejpam-5559	35	32	]	]	X
ejpam-5559	35	33	)	)	PUNCT
ejpam-5559	35	34	.	.	PUNCT
ejpam-5559	36	1	tangent	tangent	ADJ
ejpam-5559	36	2	numbers	number	NOUN
ejpam-5559	36	3	and	and	CCONJ
ejpam-5559	36	4	polynomials	polynomial	NOUN
ejpam-5559	36	5	possess	possess	VERB
ejpam-5559	36	6	many	many	ADJ
ejpam-5559	36	7	significant	significant	ADJ
ejpam-5559	36	8	properties	property	NOUN
ejpam-5559	36	9	that	that	PRON
ejpam-5559	36	10	can	can	AUX
ejpam-5559	36	11	be	be	AUX
ejpam-5559	36	12	found	find	VERB
ejpam-5559	36	13	in	in	ADP
ejpam-5559	36	14	mathematics	mathematic	NOUN
ejpam-5559	36	15	and	and	CCONJ
ejpam-5559	36	16	physics	physic	NOUN
ejpam-5559	36	17	.	.	PUNCT
ejpam-5559	37	1	analogues	analogue	NOUN
ejpam-5559	37	2	and	and	CCONJ
ejpam-5559	37	3	symmetric	symmetric	ADJ
ejpam-5559	37	4	properties	property	NOUN
ejpam-5559	37	5	for	for	ADP
ejpam-5559	37	6	tangent	tangent	NOUN
ejpam-5559	37	7	polynomials	polynomial	NOUN
ejpam-5559	37	8	are	be	AUX
ejpam-5559	37	9	derived	derive	VERB
ejpam-5559	37	10	in	in	ADP
ejpam-5559	37	11	[	[	X
ejpam-5559	37	12	12	12	NUM
ejpam-5559	37	13	]	]	PUNCT
ejpam-5559	37	14	and	and	CCONJ
ejpam-5559	37	15	[	[	X
ejpam-5559	37	16	11	11	NUM
ejpam-5559	37	17	]	]	PUNCT
ejpam-5559	37	18	.	.	PUNCT
ejpam-5559	38	1	building	build	VERB
ejpam-5559	38	2	upon	upon	SCONJ
ejpam-5559	38	3	these	these	DET
ejpam-5559	38	4	foundational	foundational	ADJ
ejpam-5559	38	5	studies	study	NOUN
ejpam-5559	38	6	,	,	PUNCT
ejpam-5559	38	7	this	this	DET
ejpam-5559	38	8	paper	paper	NOUN
ejpam-5559	38	9	aims	aim	VERB
ejpam-5559	38	10	to	to	PART
ejpam-5559	38	11	explore	explore	VERB
ejpam-5559	38	12	higher	high	ADJ
ejpam-5559	38	13	-	-	PUNCT
ejpam-5559	38	14	order	order	NOUN
ejpam-5559	38	15	bivariate	bivariate	ADJ
ejpam-5559	38	16	bell	bell	NOUN
ejpam-5559	38	17	-	-	PUNCT
ejpam-5559	38	18	based	base	VERB
ejpam-5559	38	19	apostol	apostol	NOUN
ejpam-5559	38	20	-	-	PUNCT
ejpam-5559	38	21	frobenius	frobenius	NOUN
ejpam-5559	38	22	-	-	PUNCT
ejpam-5559	38	23	type	type	NOUN
ejpam-5559	38	24	poly	poly	ADJ
ejpam-5559	38	25	-	-	PUNCT
ejpam-5559	38	26	tangent	tangent	NOUN
ejpam-5559	38	27	polynomials	polynomial	NOUN
ejpam-5559	38	28	.	.	PUNCT
ejpam-5559	39	1	we	we	PRON
ejpam-5559	39	2	will	will	AUX
ejpam-5559	39	3	derive	derive	VERB
ejpam-5559	39	4	explicit	explicit	ADJ
ejpam-5559	39	5	representations	representation	NOUN
ejpam-5559	39	6	and	and	CCONJ
ejpam-5559	39	7	investigate	investigate	VERB
ejpam-5559	39	8	their	their	PRON
ejpam-5559	39	9	structural	structural	ADJ
ejpam-5559	39	10	properties	property	NOUN
ejpam-5559	39	11	.	.	PUNCT
ejpam-5559	40	1	j.	j.	PROPN
ejpam-5559	40	2	ontolan	ontolan	PROPN
ejpam-5559	40	3	et	et	PROPN
ejpam-5559	40	4	al	al	PROPN
ejpam-5559	40	5	.	.	PUNCT
ejpam-5559	40	6	/	/	SYM
ejpam-5559	40	7	eur	eur	PROPN
ejpam-5559	40	8	.	.	PUNCT
ejpam-5559	41	1	j.	j.	PROPN
ejpam-5559	41	2	pure	pure	PROPN
ejpam-5559	41	3	appl	appl	PROPN
ejpam-5559	41	4	.	.	PROPN
ejpam-5559	41	5	math	math	PROPN
ejpam-5559	41	6	,	,	PUNCT
ejpam-5559	41	7	18	18	NUM
ejpam-5559	41	8	(	(	PUNCT
ejpam-5559	41	9	1	1	NUM
ejpam-5559	41	10	)	)	PUNCT
ejpam-5559	41	11	(	(	PUNCT
ejpam-5559	41	12	2025	2025	NUM
ejpam-5559	41	13	)	)	PUNCT
ejpam-5559	41	14	,	,	PUNCT
ejpam-5559	41	15	5559	5559	NUM
ejpam-5559	41	16	3	3	NUM
ejpam-5559	41	17	of	of	ADP
ejpam-5559	41	18	16	16	NUM
ejpam-5559	41	19	the	the	DET
ejpam-5559	41	20	bell	bell	NOUN
ejpam-5559	41	21	-	-	PUNCT
ejpam-5559	41	22	based	base	VERB
ejpam-5559	41	23	apostol	apostol	NOUN
ejpam-5559	41	24	-	-	PUNCT
ejpam-5559	41	25	frobenius	frobenius	NOUN
ejpam-5559	41	26	-	-	PUNCT
ejpam-5559	41	27	type	type	NOUN
ejpam-5559	41	28	tangent	tangent	NOUN
ejpam-5559	41	29	polynomials	polynomial	VERB
ejpam-5559	41	30	btn(x	btn(x	PROPN
ejpam-5559	41	31	,	,	PUNCT
ejpam-5559	41	32	y	y	PROPN
ejpam-5559	41	33	,	,	PUNCT
ejpam-5559	41	34	u	u	NOUN
ejpam-5559	41	35	,	,	PUNCT
ejpam-5559	41	36	λ	λ	X
ejpam-5559	41	37	)	)	PUNCT
ejpam-5559	41	38	is	be	AUX
ejpam-5559	41	39	defined	define	VERB
ejpam-5559	41	40	by	by	ADP
ejpam-5559	41	41	the	the	DET
ejpam-5559	41	42	generating	generate	VERB
ejpam-5559	41	43	function	function	NOUN
ejpam-5559	41	44	∞∑	∞∑	PRON
ejpam-5559	41	45	n=0	n=0	SYM
ejpam-5559	41	46	btn(x	btn(x	PROPN
ejpam-5559	41	47	,	,	PUNCT
ejpam-5559	41	48	y	y	PROPN
ejpam-5559	41	49	,	,	PUNCT
ejpam-5559	41	50	u	u	NOUN
ejpam-5559	41	51	,	,	PUNCT
ejpam-5559	41	52	λ	λ	PROPN
ejpam-5559	41	53	)	)	PUNCT
ejpam-5559	41	54	tn	tn	PROPN
ejpam-5559	41	55	n	n	PROPN
ejpam-5559	41	56	!	!	PUNCT
ejpam-5559	42	1	=	=	PUNCT
ejpam-5559	42	2	(	(	PUNCT
ejpam-5559	42	3	1−	1−	NUM
ejpam-5559	42	4	u	u	NOUN
ejpam-5559	42	5	λe2	λe2	PROPN
ejpam-5559	42	6	t	t	PROPN
ejpam-5559	42	7	−	−	PROPN
ejpam-5559	42	8	u	u	PROPN
ejpam-5559	42	9	)	)	PUNCT
ejpam-5559	42	10	ext+y(et−1	ext+y(et−1	PROPN
ejpam-5559	42	11	)	)	PUNCT
ejpam-5559	42	12	.	.	PUNCT
ejpam-5559	43	1	this	this	PRON
ejpam-5559	43	2	paves	pave	VERB
ejpam-5559	43	3	way	way	NOUN
ejpam-5559	43	4	to	to	ADP
ejpam-5559	43	5	our	our	PRON
ejpam-5559	43	6	working	work	VERB
ejpam-5559	43	7	definition	definition	NOUN
ejpam-5559	43	8	of	of	ADP
ejpam-5559	43	9	the	the	DET
ejpam-5559	43	10	bell	bell	NOUN
ejpam-5559	43	11	-	-	PUNCT
ejpam-5559	43	12	based	base	VERB
ejpam-5559	43	13	apostol	apostol	NOUN
ejpam-5559	43	14	-	-	PUNCT
ejpam-5559	43	15	frobenius	frobenius	NOUN
ejpam-5559	43	16	-	-	PUNCT
ejpam-5559	43	17	type	type	NOUN
ejpam-5559	43	18	tangent	tangent	NOUN
ejpam-5559	43	19	polynomials	polynomial	NOUN
ejpam-5559	43	20	of	of	ADP
ejpam-5559	43	21	higher	high	ADJ
ejpam-5559	43	22	order	order	NOUN
ejpam-5559	43	23	bt	bt	NOUN
ejpam-5559	43	24	r	r	NOUN
ejpam-5559	43	25	n(x	n(x	PROPN
ejpam-5559	43	26	,	,	PUNCT
ejpam-5559	43	27	y	y	PROPN
ejpam-5559	43	28	,	,	PUNCT
ejpam-5559	43	29	u	u	NOUN
ejpam-5559	43	30	,	,	PUNCT
ejpam-5559	43	31	λ	λ	NOUN
ejpam-5559	43	32	)	)	PUNCT
ejpam-5559	43	33	defined	define	VERB
ejpam-5559	43	34	by	by	ADP
ejpam-5559	43	35	the	the	DET
ejpam-5559	43	36	generating	generate	VERB
ejpam-5559	43	37	function	function	NOUN
ejpam-5559	43	38	∞∑	∞∑	PRON
ejpam-5559	43	39	n=0	n=0	NUM
ejpam-5559	43	40	bt	bt	NOUN
ejpam-5559	43	41	(	(	PUNCT
ejpam-5559	43	42	r	r	NOUN
ejpam-5559	43	43	)	)	PUNCT
ejpam-5559	43	44	n	n	NOUN
ejpam-5559	43	45	(	(	PUNCT
ejpam-5559	43	46	x	x	X
ejpam-5559	43	47	,	,	PUNCT
ejpam-5559	43	48	y;u	y;u	PROPN
ejpam-5559	43	49	,	,	PUNCT
ejpam-5559	43	50	λ	λ	PROPN
ejpam-5559	43	51	)	)	PUNCT
ejpam-5559	43	52	tn	tn	PROPN
ejpam-5559	43	53	n	n	PROPN
ejpam-5559	43	54	!	!	PUNCT
ejpam-5559	44	1	=	=	PUNCT
ejpam-5559	44	2	(	(	PUNCT
ejpam-5559	44	3	1−	1−	NUM
ejpam-5559	44	4	u	u	NOUN
ejpam-5559	44	5	λe2	λe2	PROPN
ejpam-5559	44	6	t	t	PROPN
ejpam-5559	44	7	−	−	PROPN
ejpam-5559	44	8	u	u	PROPN
ejpam-5559	44	9	)	)	PUNCT
ejpam-5559	44	10	r	r	NOUN
ejpam-5559	44	11	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	44	12	)	)	PUNCT
ejpam-5559	44	13	.	.	PUNCT
ejpam-5559	45	1	(	(	PUNCT
ejpam-5559	45	2	5	5	X
ejpam-5559	45	3	)	)	PUNCT
ejpam-5559	45	4	the	the	DET
ejpam-5559	45	5	next	next	ADJ
ejpam-5559	45	6	three	three	NUM
ejpam-5559	45	7	functions	function	NOUN
ejpam-5559	45	8	are	be	AUX
ejpam-5559	45	9	special	special	ADJ
ejpam-5559	45	10	cases	case	NOUN
ejpam-5559	45	11	of	of	ADP
ejpam-5559	45	12	(	(	PUNCT
ejpam-5559	45	13	5	5	NUM
ejpam-5559	45	14	)	)	PUNCT
ejpam-5559	45	15	;	;	PUNCT
ejpam-5559	45	16	when	when	SCONJ
ejpam-5559	45	17	x	x	SYM
ejpam-5559	45	18	=	=	SYM
ejpam-5559	45	19	0	0	NUM
ejpam-5559	45	20	and	and	CCONJ
ejpam-5559	45	21	y	y	PROPN
ejpam-5559	45	22	̸=	̸=	PROPN
ejpam-5559	45	23	0	0	NUM
ejpam-5559	45	24	,	,	PUNCT
ejpam-5559	45	25	we	we	PRON
ejpam-5559	45	26	obtain	obtain	VERB
ejpam-5559	45	27	bt	bt	NOUN
ejpam-5559	45	28	(	(	PUNCT
ejpam-5559	45	29	r	r	NOUN
ejpam-5559	45	30	)	)	PUNCT
ejpam-5559	45	31	n	n	CCONJ
ejpam-5559	45	32	(	(	PUNCT
ejpam-5559	45	33	y	y	PROPN
ejpam-5559	45	34	,	,	PUNCT
ejpam-5559	45	35	u	u	NOUN
ejpam-5559	45	36	,	,	PUNCT
ejpam-5559	45	37	λ	λ	NOUN
ejpam-5559	45	38	)	)	PUNCT
ejpam-5559	45	39	defined	define	VERB
ejpam-5559	45	40	by	by	ADP
ejpam-5559	45	41	∞∑	∞∑	DET
ejpam-5559	45	42	n=0	n=0	NUM
ejpam-5559	45	43	bt	bt	NOUN
ejpam-5559	45	44	(	(	PUNCT
ejpam-5559	45	45	r	r	NOUN
ejpam-5559	45	46	)	)	PUNCT
ejpam-5559	45	47	n	n	CCONJ
ejpam-5559	45	48	(	(	PUNCT
ejpam-5559	45	49	y	y	PROPN
ejpam-5559	45	50	,	,	PUNCT
ejpam-5559	45	51	u	u	NOUN
ejpam-5559	45	52	,	,	PUNCT
ejpam-5559	45	53	λ	λ	PROPN
ejpam-5559	45	54	)	)	PUNCT
ejpam-5559	45	55	tn	tn	PROPN
ejpam-5559	45	56	n	n	PROPN
ejpam-5559	45	57	!	!	PUNCT
ejpam-5559	46	1	=	=	PUNCT
ejpam-5559	46	2	(	(	PUNCT
ejpam-5559	46	3	1−	1−	NUM
ejpam-5559	46	4	u	u	NOUN
ejpam-5559	46	5	λe2	λe2	PROPN
ejpam-5559	46	6	t	t	PROPN
ejpam-5559	46	7	−	−	PROPN
ejpam-5559	46	8	u	u	NOUN
ejpam-5559	46	9	)	)	PUNCT
ejpam-5559	46	10	r	r	NOUN
ejpam-5559	46	11	ey(e	ey(e	X
ejpam-5559	46	12	t−1	t−1	PROPN
ejpam-5559	46	13	)	)	PUNCT
ejpam-5559	46	14	,	,	PUNCT
ejpam-5559	46	15	(	(	PUNCT
ejpam-5559	46	16	6	6	X
ejpam-5559	46	17	)	)	PUNCT
ejpam-5559	46	18	known	know	VERB
ejpam-5559	46	19	as	as	ADP
ejpam-5559	46	20	bell	bell	NOUN
ejpam-5559	46	21	-	-	PUNCT
ejpam-5559	46	22	based	base	VERB
ejpam-5559	46	23	apostol	apostol	NOUN
ejpam-5559	46	24	-	-	PUNCT
ejpam-5559	46	25	frobenius	frobenius	NOUN
ejpam-5559	46	26	-	-	PUNCT
ejpam-5559	46	27	type	type	NOUN
ejpam-5559	46	28	tangent	tangent	NOUN
ejpam-5559	46	29	numbers	number	NOUN
ejpam-5559	46	30	of	of	ADP
ejpam-5559	46	31	higher	high	ADJ
ejpam-5559	46	32	order	order	NOUN
ejpam-5559	46	33	.	.	PUNCT
ejpam-5559	47	1	when	when	SCONJ
ejpam-5559	47	2	y	y	PROPN
ejpam-5559	47	3	=	=	PROPN
ejpam-5559	47	4	0	0	PUNCT
ejpam-5559	47	5	and	and	CCONJ
ejpam-5559	47	6	x	x	SYM
ejpam-5559	47	7	̸=	̸=	PROPN
ejpam-5559	47	8	0	0	NUM
ejpam-5559	47	9	we	we	PRON
ejpam-5559	47	10	have	have	VERB
ejpam-5559	47	11	the	the	DET
ejpam-5559	47	12	polynomial	polynomial	ADJ
ejpam-5559	47	13	t	t	NOUN
ejpam-5559	47	14	r	r	NOUN
ejpam-5559	47	15	n(x	n(x	PROPN
ejpam-5559	47	16	,	,	PUNCT
ejpam-5559	47	17	u	u	NOUN
ejpam-5559	47	18	,	,	PUNCT
ejpam-5559	47	19	λ	λ	NOUN
ejpam-5559	47	20	)	)	PUNCT
ejpam-5559	47	21	defined	define	VERB
ejpam-5559	47	22	by	by	ADP
ejpam-5559	47	23	∞∑	∞∑	NUM
ejpam-5559	47	24	n=0	n=0	NUM
ejpam-5559	47	25	t	t	NOUN
ejpam-5559	47	26	r	r	NOUN
ejpam-5559	47	27	n(x	n(x	PROPN
ejpam-5559	47	28	,	,	PUNCT
ejpam-5559	47	29	u	u	NOUN
ejpam-5559	47	30	,	,	PUNCT
ejpam-5559	47	31	λ	λ	PROPN
ejpam-5559	47	32	)	)	PUNCT
ejpam-5559	47	33	tn	tn	PROPN
ejpam-5559	47	34	n	n	PROPN
ejpam-5559	47	35	!	!	PUNCT
ejpam-5559	48	1	=	=	PUNCT
ejpam-5559	48	2	(	(	PUNCT
ejpam-5559	48	3	1−	1−	NUM
ejpam-5559	48	4	u	u	NOUN
ejpam-5559	48	5	λe2	λe2	PROPN
ejpam-5559	48	6	t	t	PROPN
ejpam-5559	48	7	−	−	PROPN
ejpam-5559	48	8	u	u	NOUN
ejpam-5559	48	9	)	)	PUNCT
ejpam-5559	48	10	r	r	NOUN
ejpam-5559	48	11	ext	ext	NOUN
ejpam-5559	48	12	,	,	PUNCT
ejpam-5559	48	13	(	(	PUNCT
ejpam-5559	48	14	7	7	X
ejpam-5559	48	15	)	)	PUNCT
ejpam-5559	48	16	known	know	VERB
ejpam-5559	48	17	as	as	ADP
ejpam-5559	48	18	apostol	apostol	NOUN
ejpam-5559	48	19	-	-	PUNCT
ejpam-5559	48	20	frobenius	frobenius	NOUN
ejpam-5559	48	21	-	-	PUNCT
ejpam-5559	48	22	type	type	NOUN
ejpam-5559	48	23	tangent	tangent	NOUN
ejpam-5559	48	24	polynomials	polynomial	NOUN
ejpam-5559	48	25	of	of	ADP
ejpam-5559	48	26	higher	high	ADJ
ejpam-5559	48	27	order	order	NOUN
ejpam-5559	48	28	.	.	PUNCT
ejpam-5559	49	1	lastly	lastly	ADV
ejpam-5559	49	2	,	,	PUNCT
ejpam-5559	49	3	when	when	SCONJ
ejpam-5559	49	4	both	both	DET
ejpam-5559	49	5	x	x	SYM
ejpam-5559	49	6	=	=	PUNCT
ejpam-5559	49	7	y	y	NOUN
ejpam-5559	49	8	=	=	SYM
ejpam-5559	49	9	0	0	NUM
ejpam-5559	49	10	we	we	PRON
ejpam-5559	49	11	have	have	VERB
ejpam-5559	49	12	the	the	DET
ejpam-5559	49	13	polynomial	polynomial	ADJ
ejpam-5559	49	14	t	t	NOUN
ejpam-5559	49	15	(	(	PUNCT
ejpam-5559	49	16	r	r	NOUN
ejpam-5559	49	17	)	)	PUNCT
ejpam-5559	49	18	n	n	CCONJ
ejpam-5559	49	19	(	(	PUNCT
ejpam-5559	49	20	u	u	NOUN
ejpam-5559	49	21	,	,	PUNCT
ejpam-5559	49	22	λ	λ	NOUN
ejpam-5559	49	23	)	)	PUNCT
ejpam-5559	49	24	defined	define	VERB
ejpam-5559	49	25	by	by	ADP
ejpam-5559	49	26	∞∑	∞∑	NUM
ejpam-5559	49	27	n=0	n=0	PROPN
ejpam-5559	49	28	t	t	NOUN
ejpam-5559	49	29	(	(	PUNCT
ejpam-5559	49	30	r	r	NOUN
ejpam-5559	49	31	)	)	PUNCT
ejpam-5559	49	32	n	n	CCONJ
ejpam-5559	49	33	(	(	PUNCT
ejpam-5559	49	34	u	u	NOUN
ejpam-5559	49	35	,	,	PUNCT
ejpam-5559	49	36	λ	λ	PROPN
ejpam-5559	49	37	)	)	PUNCT
ejpam-5559	49	38	tn	tn	PROPN
ejpam-5559	49	39	n	n	PROPN
ejpam-5559	49	40	!	!	PUNCT
ejpam-5559	50	1	=	=	PUNCT
ejpam-5559	50	2	(	(	PUNCT
ejpam-5559	50	3	1−	1−	NUM
ejpam-5559	50	4	u	u	NOUN
ejpam-5559	50	5	λe2	λe2	PROPN
ejpam-5559	50	6	t	t	PROPN
ejpam-5559	50	7	−	−	PROPN
ejpam-5559	50	8	u	u	PROPN
ejpam-5559	50	9	)	)	PUNCT
ejpam-5559	50	10	r	r	NOUN
ejpam-5559	50	11	,	,	PUNCT
ejpam-5559	50	12	(	(	PUNCT
ejpam-5559	50	13	8)	8)	NUM
ejpam-5559	50	14	known	know	VERB
ejpam-5559	50	15	as	as	ADP
ejpam-5559	50	16	apostol	apostol	NOUN
ejpam-5559	50	17	-	-	PUNCT
ejpam-5559	50	18	frobenius	frobenius	NOUN
ejpam-5559	50	19	-	-	PUNCT
ejpam-5559	50	20	type	type	NOUN
ejpam-5559	50	21	tangent	tangent	NOUN
ejpam-5559	50	22	numbers	number	NOUN
ejpam-5559	50	23	of	of	ADP
ejpam-5559	50	24	higher	high	ADJ
ejpam-5559	50	25	order	order	NOUN
ejpam-5559	50	26	.	.	PUNCT
ejpam-5559	51	1	meanwhile	meanwhile	ADV
ejpam-5559	51	2	,	,	PUNCT
ejpam-5559	51	3	in	in	ADP
ejpam-5559	51	4	[	[	X
ejpam-5559	51	5	1	1	X
ejpam-5559	51	6	]	]	PUNCT
ejpam-5559	51	7	we	we	PRON
ejpam-5559	51	8	define	define	VERB
ejpam-5559	51	9	a	a	DET
ejpam-5559	51	10	sequence	sequence	NOUN
ejpam-5559	51	11	of	of	ADP
ejpam-5559	51	12	polynomials	polynomial	NOUN
ejpam-5559	51	13	{	{	PUNCT
ejpam-5559	51	14	pn(x)}∞0	pn(x)}∞0	NOUN
ejpam-5559	51	15	satisfying	satisfy	VERB
ejpam-5559	51	16	p	p	X
ejpam-5559	51	17	′	′	NUM
ejpam-5559	51	18	n(x	n(x	PROPN
ejpam-5559	51	19	)	)	PUNCT
ejpam-5559	51	20	=	=	SYM
ejpam-5559	51	21	npn−1(x	npn−1(x	NOUN
ejpam-5559	51	22	)	)	PUNCT
ejpam-5559	51	23	,	,	PUNCT
ejpam-5559	51	24	n	n	X
ejpam-5559	51	25	≥	≥	NOUN
ejpam-5559	51	26	1	1	NUM
ejpam-5559	51	27	,	,	PUNCT
ejpam-5559	51	28	(	(	PUNCT
ejpam-5559	51	29	9	9	NUM
ejpam-5559	51	30	)	)	PUNCT
ejpam-5559	51	31	as	as	ADP
ejpam-5559	51	32	appell	appell	NOUN
ejpam-5559	51	33	polynomials	polynomial	NOUN
ejpam-5559	51	34	.	.	PUNCT
ejpam-5559	52	1	moreover	moreover	ADV
ejpam-5559	52	2	,	,	PUNCT
ejpam-5559	52	3	[	[	X
ejpam-5559	52	4	3	3	NUM
ejpam-5559	52	5	]	]	PUNCT
ejpam-5559	52	6	,	,	PUNCT
ejpam-5559	52	7	[	[	X
ejpam-5559	52	8	15	15	NUM
ejpam-5559	52	9	]	]	PUNCT
ejpam-5559	52	10	,	,	PUNCT
ejpam-5559	52	11	and	and	CCONJ
ejpam-5559	52	12	[	[	X
ejpam-5559	52	13	16	16	NUM
ejpam-5559	52	14	]	]	PUNCT
ejpam-5559	52	15	established	establish	VERB
ejpam-5559	52	16	an	an	DET
ejpam-5559	52	17	important	important	ADJ
ejpam-5559	52	18	characterization	characterization	NOUN
ejpam-5559	52	19	of	of	ADP
ejpam-5559	52	20	appell	appell	ADJ
ejpam-5559	52	21	polynomials	polynomial	NOUN
ejpam-5559	52	22	in	in	ADP
ejpam-5559	52	23	the	the	DET
ejpam-5559	52	24	following	follow	VERB
ejpam-5559	52	25	equivalent	equivalent	ADJ
ejpam-5559	52	26	conditions	condition	NOUN
ejpam-5559	52	27	:	:	PUNCT
ejpam-5559	52	28	(	(	PUNCT
ejpam-5559	52	29	a	a	X
ejpam-5559	52	30	)	)	PUNCT
ejpam-5559	52	31	{	{	PUNCT
ejpam-5559	52	32	pn(x)}∞0	pn(x)}∞0	PROPN
ejpam-5559	52	33	is	be	AUX
ejpam-5559	52	34	a	a	DET
ejpam-5559	52	35	sequence	sequence	NOUN
ejpam-5559	52	36	of	of	ADP
ejpam-5559	52	37	appell	appell	ADJ
ejpam-5559	52	38	polynomials	polynomial	NOUN
ejpam-5559	52	39	.	.	PUNCT
ejpam-5559	53	1	j.	j.	PROPN
ejpam-5559	53	2	ontolan	ontolan	PROPN
ejpam-5559	53	3	et	et	PROPN
ejpam-5559	53	4	al	al	PROPN
ejpam-5559	53	5	.	.	PUNCT
ejpam-5559	53	6	/	/	SYM
ejpam-5559	53	7	eur	eur	PROPN
ejpam-5559	53	8	.	.	PUNCT
ejpam-5559	54	1	j.	j.	PROPN
ejpam-5559	54	2	pure	pure	PROPN
ejpam-5559	54	3	appl	appl	PROPN
ejpam-5559	54	4	.	.	PROPN
ejpam-5559	54	5	math	math	PROPN
ejpam-5559	54	6	,	,	PUNCT
ejpam-5559	54	7	18	18	NUM
ejpam-5559	54	8	(	(	PUNCT
ejpam-5559	54	9	1	1	NUM
ejpam-5559	54	10	)	)	PUNCT
ejpam-5559	54	11	(	(	PUNCT
ejpam-5559	54	12	2025	2025	NUM
ejpam-5559	54	13	)	)	PUNCT
ejpam-5559	54	14	,	,	PUNCT
ejpam-5559	54	15	5559	5559	NUM
ejpam-5559	54	16	4	4	NUM
ejpam-5559	54	17	of	of	ADP
ejpam-5559	54	18	16	16	NUM
ejpam-5559	54	19	(	(	PUNCT
ejpam-5559	54	20	b	b	NOUN
ejpam-5559	54	21	)	)	PUNCT
ejpam-5559	54	22	{	{	PUNCT
ejpam-5559	54	23	pn(x)}∞0	pn(x)}∞0	PROPN
ejpam-5559	54	24	has	have	VERB
ejpam-5559	54	25	a	a	DET
ejpam-5559	54	26	generating	generate	VERB
ejpam-5559	54	27	function	function	NOUN
ejpam-5559	54	28	of	of	ADP
ejpam-5559	54	29	the	the	DET
ejpam-5559	54	30	form	form	NOUN
ejpam-5559	54	31	a(t)ext	a(t)ext	NOUN
ejpam-5559	54	32	=	=	PUNCT
ejpam-5559	54	33	∞∑	∞∑	PRON
ejpam-5559	54	34	n=0	n=0	NUM
ejpam-5559	54	35	pn(x	pn(x	X
ejpam-5559	54	36	)	)	PUNCT
ejpam-5559	54	37	tn	tn	NOUN
ejpam-5559	54	38	n	n	X
ejpam-5559	54	39	!	!	PROPN
ejpam-5559	54	40	,	,	PUNCT
ejpam-5559	54	41	(	(	PUNCT
ejpam-5559	54	42	10	10	NUM
ejpam-5559	54	43	)	)	PUNCT
ejpam-5559	54	44	where	where	SCONJ
ejpam-5559	54	45	a(t	a(t	NOUN
ejpam-5559	54	46	)	)	PUNCT
ejpam-5559	54	47	is	be	AUX
ejpam-5559	54	48	a	a	DET
ejpam-5559	54	49	formal	formal	ADJ
ejpam-5559	54	50	power	power	NOUN
ejpam-5559	54	51	series	series	NOUN
ejpam-5559	54	52	independent	independent	ADJ
ejpam-5559	54	53	of	of	ADP
ejpam-5559	54	54	x	x	PUNCT
ejpam-5559	54	55	with	with	ADP
ejpam-5559	54	56	a(0	a(0	PROPN
ejpam-5559	54	57	)	)	PUNCT
ejpam-5559	54	58	̸=	̸=	PROPN
ejpam-5559	54	59	0	0	NUM
ejpam-5559	54	60	.	.	PUNCT
ejpam-5559	55	1	(	(	PUNCT
ejpam-5559	55	2	c	c	X
ejpam-5559	55	3	)	)	PUNCT
ejpam-5559	55	4	there	there	PRON
ejpam-5559	55	5	exists	exist	VERB
ejpam-5559	55	6	a	a	DET
ejpam-5559	55	7	sequence	sequence	NOUN
ejpam-5559	55	8	{	{	PUNCT
ejpam-5559	55	9	an}∞n=0	an}∞n=0	VERB
ejpam-5559	55	10	with	with	ADP
ejpam-5559	55	11	a0	a0	PROPN
ejpam-5559	55	12	̸=	̸=	PROPN
ejpam-5559	55	13	0	0	NUM
ejpam-5559	55	14	such	such	ADJ
ejpam-5559	55	15	that	that	PRON
ejpam-5559	55	16	pn(x	pn(x	PUNCT
ejpam-5559	55	17	)	)	PUNCT
ejpam-5559	55	18	=	=	SYM
ejpam-5559	56	1	n∑	n∑	NOUN
ejpam-5559	56	2	k=0	k=0	PROPN
ejpam-5559	56	3	(	(	PUNCT
ejpam-5559	56	4	n	n	X
ejpam-5559	56	5	k	k	NOUN
ejpam-5559	56	6	)	)	PUNCT
ejpam-5559	56	7	an−kx	an−kx	PROPN
ejpam-5559	56	8	k.	k.	NOUN
ejpam-5559	57	1	(	(	PUNCT
ejpam-5559	57	2	11	11	NUM
ejpam-5559	57	3	)	)	PUNCT
ejpam-5559	57	4	(	(	PUNCT
ejpam-5559	57	5	d	d	X
ejpam-5559	57	6	)	)	PUNCT
ejpam-5559	57	7	there	there	PRON
ejpam-5559	57	8	exists	exist	VERB
ejpam-5559	57	9	a	a	DET
ejpam-5559	57	10	sequence	sequence	NOUN
ejpam-5559	57	11	{	{	PUNCT
ejpam-5559	57	12	an}∞n=0	an}∞n=0	VERB
ejpam-5559	57	13	with	with	ADP
ejpam-5559	57	14	a0	a0	PROPN
ejpam-5559	57	15	̸=	̸=	PROPN
ejpam-5559	57	16	0	0	NUM
ejpam-5559	57	17	such	such	ADJ
ejpam-5559	57	18	that	that	PRON
ejpam-5559	57	19	pn(x	pn(x	PUNCT
ejpam-5559	57	20	)	)	PUNCT
ejpam-5559	57	21	=	=	SYM
ejpam-5559	57	22	(	(	PUNCT
ejpam-5559	57	23	∞∑	∞∑	PROPN
ejpam-5559	57	24	k=0	k=0	PROPN
ejpam-5559	57	25	ak	ak	PROPN
ejpam-5559	57	26	k	k	PROPN
ejpam-5559	57	27	!	!	PUNCT
ejpam-5559	58	1	dk	dk	PROPN
ejpam-5559	58	2	)	)	PUNCT
ejpam-5559	59	1	xn	xn	PROPN
ejpam-5559	59	2	,	,	PUNCT
ejpam-5559	59	3	(	(	PUNCT
ejpam-5559	59	4	12	12	NUM
ejpam-5559	59	5	)	)	PUNCT
ejpam-5559	59	6	where	where	SCONJ
ejpam-5559	59	7	d	d	NOUN
ejpam-5559	59	8	=	=	SYM
ejpam-5559	59	9	d	d	X
ejpam-5559	59	10	dx	dx	PROPN
ejpam-5559	59	11	.	.	PUNCT
ejpam-5559	60	1	the	the	DET
ejpam-5559	60	2	next	next	ADJ
ejpam-5559	60	3	lemma	lemma	PROPN
ejpam-5559	60	4	will	will	AUX
ejpam-5559	60	5	be	be	AUX
ejpam-5559	60	6	useful	useful	ADJ
ejpam-5559	60	7	in	in	ADP
ejpam-5559	60	8	some	some	PRON
ejpam-5559	60	9	of	of	ADP
ejpam-5559	60	10	our	our	PRON
ejpam-5559	60	11	results	result	NOUN
ejpam-5559	60	12	.	.	PUNCT
ejpam-5559	61	1	lemma	lemma	PROPN
ejpam-5559	61	2	1	1	X
ejpam-5559	61	3	.	.	PUNCT
ejpam-5559	62	1	let	let	VERB
ejpam-5559	62	2	f	f	PRON
ejpam-5559	62	3	be	be	AUX
ejpam-5559	62	4	a	a	DET
ejpam-5559	62	5	function	function	NOUN
ejpam-5559	62	6	and	and	CCONJ
ejpam-5559	62	7	{	{	PUNCT
ejpam-5559	62	8	f(n)}∞0	f(n)}∞0	NOUN
ejpam-5559	62	9	a	a	DET
ejpam-5559	62	10	sequence	sequence	NOUN
ejpam-5559	62	11	and	and	CCONJ
ejpam-5559	62	12	coefficients	coefficient	NOUN
ejpam-5559	62	13	of	of	ADP
ejpam-5559	62	14	the	the	DET
ejpam-5559	62	15	power	power	NOUN
ejpam-5559	62	16	series	series	NOUN
ejpam-5559	62	17	∞∑	∞∑	PROPN
ejpam-5559	62	18	n=0	n=0	NUM
ejpam-5559	62	19	f(n	f(n	PROPN
ejpam-5559	62	20	)	)	PUNCT
ejpam-5559	62	21	(	(	PUNCT
ejpam-5559	62	22	x+	x+	X
ejpam-5559	62	23	y)n	y)n	NUM
ejpam-5559	62	24	n	n	ADV
ejpam-5559	62	25	!	!	PUNCT
ejpam-5559	62	26	.	.	PUNCT
ejpam-5559	63	1	there	there	PRON
ejpam-5559	63	2	exists	exist	VERB
ejpam-5559	63	3	a	a	DET
ejpam-5559	63	4	pair	pair	NOUN
ejpam-5559	63	5	of	of	ADP
ejpam-5559	63	6	integers	integer	NOUN
ejpam-5559	63	7	n	n	ADJ
ejpam-5559	63	8	and	and	CCONJ
ejpam-5559	63	9	m	m	VERB
ejpam-5559	63	10	such	such	ADJ
ejpam-5559	63	11	that	that	SCONJ
ejpam-5559	63	12	∞∑	∞∑	NUM
ejpam-5559	63	13	n=0	n=0	NUM
ejpam-5559	63	14	f(n	f(n	PROPN
ejpam-5559	63	15	)	)	PUNCT
ejpam-5559	63	16	(	(	PUNCT
ejpam-5559	63	17	x+	x+	X
ejpam-5559	63	18	y)n	y)n	NUM
ejpam-5559	63	19	n	n	X
ejpam-5559	63	20	!	!	PUNCT
ejpam-5559	64	1	=	=	NOUN
ejpam-5559	65	1	∞∑	∞∑	NUM
ejpam-5559	65	2	m=0	m=0	PROPN
ejpam-5559	65	3	∞∑	∞∑	ADJ
ejpam-5559	65	4	n=0	n=0	PROPN
ejpam-5559	65	5	f(m+	f(m+	NOUN
ejpam-5559	65	6	n	n	CCONJ
ejpam-5559	65	7	)	)	PUNCT
ejpam-5559	65	8	xmyn	xmyn	PROPN
ejpam-5559	66	1	m!n	m!n	PROPN
ejpam-5559	66	2	!	!	PROPN
ejpam-5559	66	3	,	,	PUNCT
ejpam-5559	66	4	(	(	PUNCT
ejpam-5559	66	5	13	13	NUM
ejpam-5559	66	6	)	)	PUNCT
ejpam-5559	66	7	where	where	SCONJ
ejpam-5559	66	8	n	n	X
ejpam-5559	66	9	=	=	SYM
ejpam-5559	66	10	n+m	n+m	PROPN
ejpam-5559	66	11	.	.	PUNCT
ejpam-5559	67	1	proof	proof	NOUN
ejpam-5559	67	2	.	.	PUNCT
ejpam-5559	68	1	for	for	ADP
ejpam-5559	68	2	each	each	DET
ejpam-5559	68	3	n	n	PRON
ejpam-5559	68	4	∈	∈	PROPN
ejpam-5559	68	5	n	n	CCONJ
ejpam-5559	68	6	,	,	PUNCT
ejpam-5559	68	7	we	we	PRON
ejpam-5559	68	8	write	write	VERB
ejpam-5559	68	9	f(n	f(n	PROPN
ejpam-5559	68	10	)	)	PUNCT
ejpam-5559	68	11	(	(	PUNCT
ejpam-5559	68	12	x+	x+	X
ejpam-5559	68	13	y)n	y)n	NUM
ejpam-5559	68	14	n	n	X
ejpam-5559	68	15	!	!	PUNCT
ejpam-5559	69	1	=	=	SYM
ejpam-5559	69	2	f(n	f(n	PROPN
ejpam-5559	69	3	)	)	PUNCT
ejpam-5559	70	1	n∑	n∑	PROPN
ejpam-5559	70	2	i=0	i=0	PROPN
ejpam-5559	70	3	(	(	PUNCT
ejpam-5559	70	4	n	n	X
ejpam-5559	70	5	i	i	PRON
ejpam-5559	70	6	)	)	PUNCT
ejpam-5559	70	7	xiyn−i	xiyn−i	PROPN
ejpam-5559	70	8	n	n	NOUN
ejpam-5559	70	9	!	!	PUNCT
ejpam-5559	71	1	=	=	PUNCT
ejpam-5559	72	1	n∑	n∑	PROPN
ejpam-5559	72	2	i=0	i=0	PROPN
ejpam-5559	72	3	f(n	f(n	PROPN
ejpam-5559	72	4	)	)	PUNCT
ejpam-5559	72	5	(	(	PUNCT
ejpam-5559	72	6	n	n	X
ejpam-5559	72	7	i	i	PRON
ejpam-5559	72	8	)	)	PUNCT
ejpam-5559	72	9	xiyn−i	xiyn−i	PROPN
ejpam-5559	73	1	n	n	NOUN
ejpam-5559	73	2	!	!	PUNCT
ejpam-5559	74	1	=	=	PUNCT
ejpam-5559	75	1	n∑	n∑	PROPN
ejpam-5559	75	2	i=0	i=0	PROPN
ejpam-5559	75	3	f(n	f(n	PROPN
ejpam-5559	75	4	)	)	PUNCT
ejpam-5559	75	5	n	n	CCONJ
ejpam-5559	75	6	!	!	PUNCT
ejpam-5559	76	1	(	(	PUNCT
ejpam-5559	76	2	n−i)!i!x	n−i)!i!x	PROPN
ejpam-5559	76	3	iyn−i	iyn−i	NOUN
ejpam-5559	76	4	n	n	NOUN
ejpam-5559	76	5	!	!	PUNCT
ejpam-5559	77	1	j.	j.	PROPN
ejpam-5559	77	2	ontolan	ontolan	PROPN
ejpam-5559	77	3	et	et	PROPN
ejpam-5559	77	4	al	al	PROPN
ejpam-5559	77	5	.	.	PUNCT
ejpam-5559	77	6	/	/	SYM
ejpam-5559	77	7	eur	eur	PROPN
ejpam-5559	77	8	.	.	PUNCT
ejpam-5559	78	1	j.	j.	PROPN
ejpam-5559	78	2	pure	pure	PROPN
ejpam-5559	78	3	appl	appl	PROPN
ejpam-5559	78	4	.	.	PROPN
ejpam-5559	78	5	math	math	PROPN
ejpam-5559	78	6	,	,	PUNCT
ejpam-5559	78	7	18	18	NUM
ejpam-5559	78	8	(	(	PUNCT
ejpam-5559	78	9	1	1	NUM
ejpam-5559	78	10	)	)	PUNCT
ejpam-5559	78	11	(	(	PUNCT
ejpam-5559	78	12	2025	2025	NUM
ejpam-5559	78	13	)	)	PUNCT
ejpam-5559	78	14	,	,	PUNCT
ejpam-5559	78	15	5559	5559	NUM
ejpam-5559	78	16	5	5	NUM
ejpam-5559	78	17	of	of	ADP
ejpam-5559	78	18	16	16	NUM
ejpam-5559	78	19	=	=	SYM
ejpam-5559	78	20	n∑	n∑	PROPN
ejpam-5559	78	21	i=0	i=0	PROPN
ejpam-5559	78	22	f(n	f(n	PROPN
ejpam-5559	78	23	)	)	PUNCT
ejpam-5559	78	24	xiyn−i	xiyn−i	PROPN
ejpam-5559	78	25	(	(	PUNCT
ejpam-5559	78	26	n	n	CCONJ
ejpam-5559	78	27	−	−	PROPN
ejpam-5559	78	28	i)!i	i)!i	ADJ
ejpam-5559	78	29	!	!	PUNCT
ejpam-5559	79	1	=	=	SYM
ejpam-5559	80	1	n∑	n∑	PROPN
ejpam-5559	80	2	i=0	i=0	PROPN
ejpam-5559	80	3	f((n	f((n	NOUN
ejpam-5559	80	4	−	−	PROPN
ejpam-5559	81	1	i	i	NOUN
ejpam-5559	81	2	)	)	PUNCT
ejpam-5559	82	1	+	+	CCONJ
ejpam-5559	82	2	i	i	X
ejpam-5559	82	3	)	)	PUNCT
ejpam-5559	82	4	xiyn−i	xiyn−i	PROPN
ejpam-5559	82	5	(	(	PUNCT
ejpam-5559	82	6	n	n	CCONJ
ejpam-5559	82	7	−	−	PROPN
ejpam-5559	82	8	i)!i	i)!i	ADJ
ejpam-5559	82	9	!	!	PUNCT
ejpam-5559	83	1	=	=	NOUN
ejpam-5559	84	1	∞∑	∞∑	NUM
ejpam-5559	84	2	n=0	n=0	NUM
ejpam-5559	84	3	n∑	n∑	NOUN
ejpam-5559	84	4	i=0	i=0	ADJ
ejpam-5559	84	5	f((n	f((n	NOUN
ejpam-5559	84	6	−	−	PROPN
ejpam-5559	84	7	i	i	NOUN
ejpam-5559	84	8	)	)	PUNCT
ejpam-5559	85	1	+	+	CCONJ
ejpam-5559	85	2	i	i	X
ejpam-5559	85	3	)	)	PUNCT
ejpam-5559	85	4	xiyn−i	xiyn−i	PROPN
ejpam-5559	85	5	(	(	PUNCT
ejpam-5559	85	6	n	n	CCONJ
ejpam-5559	85	7	−	−	PROPN
ejpam-5559	85	8	i)!i	i)!i	ADJ
ejpam-5559	85	9	!	!	PUNCT
ejpam-5559	86	1	∞∑	∞∑	PRON
ejpam-5559	86	2	n=0	n=0	NUM
ejpam-5559	86	3	f(n	f(n	PROPN
ejpam-5559	86	4	)	)	PUNCT
ejpam-5559	86	5	(	(	PUNCT
ejpam-5559	86	6	x+	x+	X
ejpam-5559	86	7	y)n	y)n	NUM
ejpam-5559	86	8	n	n	X
ejpam-5559	86	9	!	!	PUNCT
ejpam-5559	87	1	=	=	NOUN
ejpam-5559	88	1	∞∑	∞∑	NUM
ejpam-5559	88	2	m=0	m=0	PROPN
ejpam-5559	88	3	∞∑	∞∑	ADJ
ejpam-5559	88	4	n=0	n=0	PROPN
ejpam-5559	88	5	f(m+	f(m+	NOUN
ejpam-5559	88	6	n	n	CCONJ
ejpam-5559	88	7	)	)	PUNCT
ejpam-5559	88	8	xmyn	xmyn	PROPN
ejpam-5559	89	1	m!n	m!n	PROPN
ejpam-5559	89	2	!	!	PROPN
ejpam-5559	89	3	.	.	PUNCT
ejpam-5559	90	1	in	in	ADP
ejpam-5559	90	2	this	this	DET
ejpam-5559	90	3	study	study	NOUN
ejpam-5559	90	4	,	,	PUNCT
ejpam-5559	90	5	the	the	DET
ejpam-5559	90	6	authors	author	NOUN
ejpam-5559	90	7	are	be	AUX
ejpam-5559	90	8	interested	interested	ADJ
ejpam-5559	90	9	to	to	PART
ejpam-5559	90	10	explore	explore	VERB
ejpam-5559	90	11	some	some	DET
ejpam-5559	90	12	properties	property	NOUN
ejpam-5559	90	13	of	of	ADP
ejpam-5559	90	14	bell	bell	NOUN
ejpam-5559	90	15	-	-	PUNCT
ejpam-5559	90	16	based	base	VERB
ejpam-5559	90	17	apostol	apostol	NOUN
ejpam-5559	90	18	-	-	PUNCT
ejpam-5559	90	19	frobenius	frobenius	NOUN
ejpam-5559	90	20	-	-	PUNCT
ejpam-5559	90	21	type	type	NOUN
ejpam-5559	90	22	tangent	tangent	NOUN
ejpam-5559	90	23	polynomials	polynomial	NOUN
ejpam-5559	90	24	of	of	ADP
ejpam-5559	90	25	higher	high	ADJ
ejpam-5559	90	26	order	order	NOUN
ejpam-5559	90	27	bt	bt	NOUN
ejpam-5559	90	28	(	(	PUNCT
ejpam-5559	90	29	r	r	NOUN
ejpam-5559	90	30	)	)	PUNCT
ejpam-5559	90	31	n	n	NOUN
ejpam-5559	90	32	(	(	PUNCT
ejpam-5559	90	33	x	x	X
ejpam-5559	90	34	,	,	PUNCT
ejpam-5559	90	35	y;u	y;u	PROPN
ejpam-5559	90	36	,	,	PUNCT
ejpam-5559	90	37	λ	λ	NOUN
ejpam-5559	90	38	)	)	PUNCT
ejpam-5559	90	39	in	in	ADP
ejpam-5559	90	40	terms	term	NOUN
ejpam-5559	90	41	of	of	ADP
ejpam-5559	90	42	the	the	DET
ejpam-5559	90	43	three	three	NUM
ejpam-5559	90	44	aforementioned	aforementioned	ADJ
ejpam-5559	90	45	cases	case	NOUN
ejpam-5559	90	46	(	(	PUNCT
ejpam-5559	90	47	6	6	NUM
ejpam-5559	90	48	)	)	PUNCT
ejpam-5559	90	49	,	,	PUNCT
ejpam-5559	90	50	(	(	PUNCT
ejpam-5559	90	51	7	7	NUM
ejpam-5559	90	52	)	)	PUNCT
ejpam-5559	90	53	,	,	PUNCT
ejpam-5559	90	54	and	and	CCONJ
ejpam-5559	90	55	(	(	PUNCT
ejpam-5559	90	56	8)	8)	NUM
ejpam-5559	90	57	.	.	NOUN
ejpam-5559	91	1	2	2	NUM
ejpam-5559	91	2	.	.	NOUN
ejpam-5559	91	3	higher	high	ADJ
ejpam-5559	91	4	order	order	NOUN
ejpam-5559	91	5	bivariate	bivariate	ADJ
ejpam-5559	91	6	bell	bell	NOUN
ejpam-5559	91	7	-	-	PUNCT
ejpam-5559	91	8	based	base	VERB
ejpam-5559	91	9	apostol	apostol	NOUN
ejpam-5559	91	10	-	-	PUNCT
ejpam-5559	91	11	frobenius	frobenius	NOUN
ejpam-5559	91	12	-	-	PUNCT
ejpam-5559	91	13	type	type	NOUN
ejpam-5559	91	14	tangent	tangent	NOUN
ejpam-5559	91	15	polynomials	polynomial	VERB
ejpam-5559	91	16	the	the	DET
ejpam-5559	91	17	following	follow	VERB
ejpam-5559	91	18	theorems	theorem	NOUN
ejpam-5559	91	19	contain	contain	VERB
ejpam-5559	91	20	identities	identity	NOUN
ejpam-5559	91	21	for	for	ADP
ejpam-5559	91	22	the	the	DET
ejpam-5559	91	23	bivariate	bivariate	ADJ
ejpam-5559	91	24	bell	bell	NOUN
ejpam-5559	91	25	-	-	PUNCT
ejpam-5559	91	26	based	base	VERB
ejpam-5559	91	27	apostolfrobeniustype	apostolfrobeniustype	NOUN
ejpam-5559	91	28	tangent	tangent	NOUN
ejpam-5559	91	29	polynomials	polynomial	NOUN
ejpam-5559	91	30	of	of	ADP
ejpam-5559	91	31	higher	high	ADJ
ejpam-5559	91	32	order	order	NOUN
ejpam-5559	91	33	expressed	express	VERB
ejpam-5559	91	34	in	in	ADP
ejpam-5559	91	35	terms	term	NOUN
ejpam-5559	91	36	of	of	ADP
ejpam-5559	91	37	(	(	PUNCT
ejpam-5559	91	38	6	6	NUM
ejpam-5559	91	39	)	)	PUNCT
ejpam-5559	91	40	,	,	PUNCT
ejpam-5559	91	41	(	(	PUNCT
ejpam-5559	91	42	7	7	NUM
ejpam-5559	91	43	)	)	PUNCT
ejpam-5559	91	44	,	,	PUNCT
ejpam-5559	91	45	and	and	CCONJ
ejpam-5559	91	46	(	(	PUNCT
ejpam-5559	91	47	8)	8)	NUM
ejpam-5559	91	48	and	and	CCONJ
ejpam-5559	91	49	the	the	DET
ejpam-5559	91	50	bell	bell	NOUN
ejpam-5559	91	51	polyomials	polyomial	NOUN
ejpam-5559	91	52	.	.	PUNCT
ejpam-5559	92	1	theorem	theorem	NOUN
ejpam-5559	92	2	1	1	NUM
ejpam-5559	92	3	.	.	PUNCT
ejpam-5559	93	1	the	the	DET
ejpam-5559	93	2	bell	bell	NOUN
ejpam-5559	93	3	-	-	PUNCT
ejpam-5559	93	4	based	base	VERB
ejpam-5559	93	5	apostol	apostol	NOUN
ejpam-5559	93	6	-	-	PUNCT
ejpam-5559	93	7	frobenius	frobenius	NOUN
ejpam-5559	93	8	-	-	PUNCT
ejpam-5559	93	9	type	type	NOUN
ejpam-5559	93	10	tangent	tangent	NOUN
ejpam-5559	93	11	polynomials	polynomial	NOUN
ejpam-5559	93	12	of	of	ADP
ejpam-5559	93	13	higher	high	ADJ
ejpam-5559	93	14	order	order	NOUN
ejpam-5559	93	15	bt	bt	NOUN
ejpam-5559	93	16	(	(	PUNCT
ejpam-5559	93	17	r	r	NOUN
ejpam-5559	93	18	)	)	PUNCT
ejpam-5559	93	19	n	n	NOUN
ejpam-5559	93	20	(	(	PUNCT
ejpam-5559	93	21	x	x	X
ejpam-5559	93	22	,	,	PUNCT
ejpam-5559	93	23	y;u	y;u	PROPN
ejpam-5559	93	24	,	,	PUNCT
ejpam-5559	93	25	λ	λ	NOUN
ejpam-5559	93	26	)	)	PUNCT
ejpam-5559	93	27	satisfies	satisfy	VERB
ejpam-5559	93	28	the	the	DET
ejpam-5559	93	29	equation	equation	NOUN
ejpam-5559	93	30	bt	bt	INTJ
ejpam-5559	93	31	(	(	PUNCT
ejpam-5559	93	32	r	r	NOUN
ejpam-5559	93	33	)	)	PUNCT
ejpam-5559	93	34	n	n	NOUN
ejpam-5559	93	35	(	(	PUNCT
ejpam-5559	93	36	x	x	X
ejpam-5559	93	37	,	,	PUNCT
ejpam-5559	93	38	y;u	y;u	PROPN
ejpam-5559	93	39	,	,	PUNCT
ejpam-5559	93	40	λ	λ	NOUN
ejpam-5559	93	41	)	)	PUNCT
ejpam-5559	93	42	=	=	SYM
ejpam-5559	94	1	n∑	n∑	NOUN
ejpam-5559	94	2	k=0	k=0	PROPN
ejpam-5559	94	3	(	(	PUNCT
ejpam-5559	94	4	n	n	X
ejpam-5559	94	5	k	k	PROPN
ejpam-5559	94	6	)	)	PUNCT
ejpam-5559	94	7	t	t	PROPN
ejpam-5559	94	8	(	(	PUNCT
ejpam-5559	94	9	r	r	NOUN
ejpam-5559	94	10	)	)	PUNCT
ejpam-5559	94	11	n	n	CCONJ
ejpam-5559	94	12	(	(	PUNCT
ejpam-5559	94	13	x;u	x;u	PROPN
ejpam-5559	94	14	,	,	PUNCT
ejpam-5559	94	15	λ)bn−k(y	λ)bn−k(y	NOUN
ejpam-5559	94	16	)	)	PUNCT
ejpam-5559	94	17	(	(	PUNCT
ejpam-5559	94	18	14	14	NUM
ejpam-5559	94	19	)	)	PUNCT
ejpam-5559	94	20	where	where	SCONJ
ejpam-5559	94	21	bn(y	bn(y	NUM
ejpam-5559	94	22	)	)	PUNCT
ejpam-5559	94	23	is	be	AUX
ejpam-5559	94	24	the	the	DET
ejpam-5559	94	25	bell	bell	PROPN
ejpam-5559	94	26	polynomial	polynomial	NOUN
ejpam-5559	94	27	defined	define	VERB
ejpam-5559	94	28	by	by	ADP
ejpam-5559	94	29	the	the	DET
ejpam-5559	94	30	generating	generate	VERB
ejpam-5559	94	31	function	function	NOUN
ejpam-5559	94	32	∞∑	∞∑	PROPN
ejpam-5559	94	33	n=0	n=0	NUM
ejpam-5559	94	34	bn(y	bn(y	NUM
ejpam-5559	94	35	)	)	PUNCT
ejpam-5559	94	36	tn	tn	PROPN
ejpam-5559	94	37	n	n	PROPN
ejpam-5559	94	38	!	!	PUNCT
ejpam-5559	95	1	=	=	PRON
ejpam-5559	95	2	ey(e	ey(e	PUNCT
ejpam-5559	95	3	t−1	t−1	PROPN
ejpam-5559	95	4	)	)	PUNCT
ejpam-5559	95	5	.	.	PUNCT
ejpam-5559	96	1	proof	proof	NOUN
ejpam-5559	96	2	.	.	PUNCT
ejpam-5559	97	1	we	we	PRON
ejpam-5559	97	2	write	write	VERB
ejpam-5559	97	3	∞∑	∞∑	PRON
ejpam-5559	97	4	n=0	n=0	NUM
ejpam-5559	97	5	bt	bt	NOUN
ejpam-5559	97	6	(	(	PUNCT
ejpam-5559	97	7	r	r	NOUN
ejpam-5559	97	8	)	)	PUNCT
ejpam-5559	97	9	n	n	NOUN
ejpam-5559	97	10	(	(	PUNCT
ejpam-5559	97	11	x	x	X
ejpam-5559	97	12	,	,	PUNCT
ejpam-5559	97	13	y;u	y;u	PROPN
ejpam-5559	97	14	,	,	PUNCT
ejpam-5559	97	15	λ	λ	PROPN
ejpam-5559	97	16	)	)	PUNCT
ejpam-5559	97	17	tn	tn	PROPN
ejpam-5559	97	18	n	n	PROPN
ejpam-5559	97	19	!	!	PUNCT
ejpam-5559	98	1	=	=	PUNCT
ejpam-5559	98	2	(	(	PUNCT
ejpam-5559	98	3	(	(	PUNCT
ejpam-5559	98	4	1−	1−	NUM
ejpam-5559	98	5	u	u	NOUN
ejpam-5559	98	6	)	)	PUNCT
ejpam-5559	98	7	λe2	λe2	PROPN
ejpam-5559	98	8	t	t	NOUN
ejpam-5559	98	9	−	−	PROPN
ejpam-5559	98	10	u	u	PROPN
ejpam-5559	98	11	)	)	PUNCT
ejpam-5559	98	12	r	r	NOUN
ejpam-5559	98	13	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	98	14	)	)	PUNCT
ejpam-5559	98	15	=	=	PRON
ejpam-5559	98	16	{	{	PUNCT
ejpam-5559	98	17	(	(	PUNCT
ejpam-5559	98	18	(	(	PUNCT
ejpam-5559	98	19	1−	1−	NUM
ejpam-5559	98	20	u	u	NOUN
ejpam-5559	98	21	)	)	PUNCT
ejpam-5559	98	22	λe2	λe2	PROPN
ejpam-5559	98	23	t	t	NOUN
ejpam-5559	98	24	−	−	PROPN
ejpam-5559	98	25	u	u	NOUN
ejpam-5559	98	26	)	)	PUNCT
ejpam-5559	98	27	r	r	NOUN
ejpam-5559	98	28	ext	ext	NOUN
ejpam-5559	98	29	}	}	PUNCT
ejpam-5559	98	30	ey(e	ey(e	X
ejpam-5559	98	31	t−1	t−1	PROPN
ejpam-5559	98	32	)	)	PUNCT
ejpam-5559	98	33	=	=	NOUN
ejpam-5559	99	1	(	(	PUNCT
ejpam-5559	99	2	∞∑	∞∑	NUM
ejpam-5559	99	3	n=0	n=0	PROPN
ejpam-5559	99	4	t	t	NOUN
ejpam-5559	99	5	(	(	PUNCT
ejpam-5559	99	6	r	r	NOUN
ejpam-5559	99	7	)	)	PUNCT
ejpam-5559	99	8	n	n	CCONJ
ejpam-5559	99	9	(	(	PUNCT
ejpam-5559	99	10	x;u	x;u	PROPN
ejpam-5559	99	11	,	,	PUNCT
ejpam-5559	99	12	λ	λ	NOUN
ejpam-5559	99	13	)	)	PUNCT
ejpam-5559	99	14	tn	tn	PROPN
ejpam-5559	99	15	n	n	PROPN
ejpam-5559	99	16	!	!	PUNCT
ejpam-5559	99	17	)	)	PUNCT
ejpam-5559	100	1	(	(	PUNCT
ejpam-5559	100	2	∞∑	∞∑	NUM
ejpam-5559	100	3	n=0	n=0	NUM
ejpam-5559	100	4	bn(y	bn(y	NUM
ejpam-5559	100	5	)	)	PUNCT
ejpam-5559	100	6	tn	tn	PROPN
ejpam-5559	100	7	n	n	PROPN
ejpam-5559	100	8	!	!	PUNCT
ejpam-5559	100	9	)	)	PUNCT
ejpam-5559	101	1	j.	j.	PROPN
ejpam-5559	101	2	ontolan	ontolan	PROPN
ejpam-5559	101	3	et	et	PROPN
ejpam-5559	101	4	al	al	PROPN
ejpam-5559	101	5	.	.	PUNCT
ejpam-5559	101	6	/	/	SYM
ejpam-5559	101	7	eur	eur	PROPN
ejpam-5559	101	8	.	.	PUNCT
ejpam-5559	102	1	j.	j.	PROPN
ejpam-5559	102	2	pure	pure	PROPN
ejpam-5559	102	3	appl	appl	PROPN
ejpam-5559	102	4	.	.	PROPN
ejpam-5559	102	5	math	math	PROPN
ejpam-5559	102	6	,	,	PUNCT
ejpam-5559	102	7	18	18	NUM
ejpam-5559	102	8	(	(	PUNCT
ejpam-5559	102	9	1	1	NUM
ejpam-5559	102	10	)	)	PUNCT
ejpam-5559	102	11	(	(	PUNCT
ejpam-5559	102	12	2025	2025	NUM
ejpam-5559	102	13	)	)	PUNCT
ejpam-5559	102	14	,	,	PUNCT
ejpam-5559	102	15	5559	5559	NUM
ejpam-5559	102	16	6	6	NUM
ejpam-5559	102	17	of	of	ADP
ejpam-5559	102	18	16	16	NUM
ejpam-5559	102	19	=	=	SYM
ejpam-5559	102	20	∞∑	∞∑	NUM
ejpam-5559	102	21	n=0	n=0	PROPN
ejpam-5559	102	22	{	{	PUNCT
ejpam-5559	102	23	n∑	n∑	NOUN
ejpam-5559	102	24	k=0	k=0	PROPN
ejpam-5559	102	25	(	(	PUNCT
ejpam-5559	102	26	n	n	X
ejpam-5559	102	27	k	k	PROPN
ejpam-5559	102	28	)	)	PUNCT
ejpam-5559	102	29	t	t	PROPN
ejpam-5559	102	30	(	(	PUNCT
ejpam-5559	102	31	r	r	NOUN
ejpam-5559	102	32	)	)	PUNCT
ejpam-5559	102	33	k	k	NOUN
ejpam-5559	102	34	(	(	PUNCT
ejpam-5559	102	35	x;u	x;u	PROPN
ejpam-5559	102	36	,	,	PUNCT
ejpam-5559	102	37	λ)bn−k(y	λ)bn−k(y	NOUN
ejpam-5559	102	38	)	)	PUNCT
ejpam-5559	102	39	}	}	PUNCT
ejpam-5559	102	40	tn	tn	PROPN
ejpam-5559	102	41	n	n	X
ejpam-5559	102	42	!	!	PUNCT
ejpam-5559	102	43	.	.	PUNCT
ejpam-5559	103	1	comparing	compare	VERB
ejpam-5559	103	2	coefficients	coefficient	NOUN
ejpam-5559	103	3	,	,	PUNCT
ejpam-5559	103	4	we	we	PRON
ejpam-5559	103	5	obtain	obtain	VERB
ejpam-5559	103	6	the	the	DET
ejpam-5559	103	7	desired	desire	VERB
ejpam-5559	103	8	result	result	NOUN
ejpam-5559	103	9	bt	bt	PROPN
ejpam-5559	103	10	(	(	PUNCT
ejpam-5559	103	11	r	r	NOUN
ejpam-5559	103	12	)	)	PUNCT
ejpam-5559	103	13	n	n	NOUN
ejpam-5559	103	14	(	(	PUNCT
ejpam-5559	103	15	x	x	X
ejpam-5559	103	16	,	,	PUNCT
ejpam-5559	103	17	y;u	y;u	PROPN
ejpam-5559	103	18	,	,	PUNCT
ejpam-5559	103	19	λ	λ	NOUN
ejpam-5559	103	20	)	)	PUNCT
ejpam-5559	103	21	=	=	SYM
ejpam-5559	104	1	n∑	n∑	NOUN
ejpam-5559	104	2	k=0	k=0	PROPN
ejpam-5559	104	3	(	(	PUNCT
ejpam-5559	104	4	n	n	X
ejpam-5559	104	5	k	k	PROPN
ejpam-5559	104	6	)	)	PUNCT
ejpam-5559	104	7	t	t	PROPN
ejpam-5559	104	8	(	(	PUNCT
ejpam-5559	104	9	r	r	NOUN
ejpam-5559	104	10	)	)	PUNCT
ejpam-5559	104	11	k	k	NOUN
ejpam-5559	104	12	(	(	PUNCT
ejpam-5559	104	13	x;u	x;u	PROPN
ejpam-5559	104	14	,	,	PUNCT
ejpam-5559	104	15	λ)bn−k(y	λ)bn−k(y	NOUN
ejpam-5559	104	16	)	)	PUNCT
ejpam-5559	104	17	.	.	PUNCT
ejpam-5559	105	1	theorem	theorem	NOUN
ejpam-5559	105	2	2	2	NUM
ejpam-5559	105	3	.	.	PUNCT
ejpam-5559	106	1	the	the	DET
ejpam-5559	106	2	function	function	NOUN
ejpam-5559	106	3	bt	bt	PROPN
ejpam-5559	106	4	(	(	PUNCT
ejpam-5559	106	5	r	r	NOUN
ejpam-5559	106	6	)	)	PUNCT
ejpam-5559	106	7	n	n	NOUN
ejpam-5559	106	8	(	(	PUNCT
ejpam-5559	106	9	x	x	X
ejpam-5559	106	10	,	,	PUNCT
ejpam-5559	106	11	y;u	y;u	PROPN
ejpam-5559	106	12	,	,	PUNCT
ejpam-5559	106	13	λ	λ	NOUN
ejpam-5559	106	14	)	)	PUNCT
ejpam-5559	106	15	satisfies	satisfy	VERB
ejpam-5559	106	16	the	the	DET
ejpam-5559	106	17	equation	equation	NOUN
ejpam-5559	106	18	bt	bt	INTJ
ejpam-5559	106	19	(	(	PUNCT
ejpam-5559	106	20	r	r	NOUN
ejpam-5559	106	21	)	)	PUNCT
ejpam-5559	106	22	n	n	NOUN
ejpam-5559	106	23	(	(	PUNCT
ejpam-5559	106	24	x	x	X
ejpam-5559	106	25	,	,	PUNCT
ejpam-5559	106	26	y;u	y;u	PROPN
ejpam-5559	106	27	,	,	PUNCT
ejpam-5559	106	28	λ	λ	NOUN
ejpam-5559	106	29	)	)	PUNCT
ejpam-5559	107	1	=	=	SYM
ejpam-5559	107	2	n∑	n∑	NOUN
ejpam-5559	107	3	k=0	k=0	PROPN
ejpam-5559	107	4	(	(	PUNCT
ejpam-5559	107	5	n	n	X
ejpam-5559	107	6	k	k	PROPN
ejpam-5559	107	7	)	)	PUNCT
ejpam-5559	107	8	t	t	PROPN
ejpam-5559	107	9	(	(	PUNCT
ejpam-5559	107	10	r	r	NOUN
ejpam-5559	107	11	)	)	PUNCT
ejpam-5559	107	12	n	n	CCONJ
ejpam-5559	107	13	(	(	PUNCT
ejpam-5559	107	14	u	u	NOUN
ejpam-5559	107	15	,	,	PUNCT
ejpam-5559	107	16	λ)bn−k(x	λ)bn−k(x	PROPN
ejpam-5559	107	17	,	,	PUNCT
ejpam-5559	107	18	y	y	NOUN
ejpam-5559	107	19	)	)	PUNCT
ejpam-5559	107	20	(	(	PUNCT
ejpam-5559	107	21	15	15	NUM
ejpam-5559	107	22	)	)	PUNCT
ejpam-5559	107	23	where	where	SCONJ
ejpam-5559	107	24	bn(x	bn(x	X
ejpam-5559	107	25	,	,	PUNCT
ejpam-5559	107	26	y	y	NOUN
ejpam-5559	107	27	)	)	PUNCT
ejpam-5559	107	28	is	be	AUX
ejpam-5559	107	29	the	the	DET
ejpam-5559	107	30	bivariate	bivariate	ADJ
ejpam-5559	107	31	bell	bell	NOUN
ejpam-5559	107	32	polynomial	polynomial	NOUN
ejpam-5559	107	33	defined	define	VERB
ejpam-5559	107	34	by	by	ADP
ejpam-5559	107	35	the	the	DET
ejpam-5559	107	36	generating	generate	VERB
ejpam-5559	107	37	function	function	NOUN
ejpam-5559	108	1	∞∑	∞∑	PRON
ejpam-5559	108	2	n=0	n=0	NUM
ejpam-5559	108	3	bn(x	bn(x	NUM
ejpam-5559	108	4	,	,	PUNCT
ejpam-5559	108	5	y	y	NOUN
ejpam-5559	108	6	)	)	PUNCT
ejpam-5559	108	7	tn	tn	PROPN
ejpam-5559	108	8	n	n	PROPN
ejpam-5559	108	9	!	!	PUNCT
ejpam-5559	109	1	=	=	PUNCT
ejpam-5559	109	2	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	109	3	)	)	PUNCT
ejpam-5559	109	4	.	.	PUNCT
ejpam-5559	110	1	proof	proof	NOUN
ejpam-5559	110	2	.	.	PUNCT
ejpam-5559	111	1	we	we	PRON
ejpam-5559	111	2	start	start	VERB
ejpam-5559	111	3	with	with	ADP
ejpam-5559	111	4	∞∑	∞∑	NUM
ejpam-5559	111	5	n=0	n=0	NUM
ejpam-5559	111	6	bt	bt	NOUN
ejpam-5559	111	7	(	(	PUNCT
ejpam-5559	111	8	r	r	NOUN
ejpam-5559	111	9	)	)	PUNCT
ejpam-5559	111	10	n	n	NOUN
ejpam-5559	111	11	(	(	PUNCT
ejpam-5559	111	12	x	x	X
ejpam-5559	111	13	,	,	PUNCT
ejpam-5559	111	14	y;u	y;u	PROPN
ejpam-5559	111	15	,	,	PUNCT
ejpam-5559	111	16	λ	λ	PROPN
ejpam-5559	111	17	)	)	PUNCT
ejpam-5559	111	18	tn	tn	PROPN
ejpam-5559	111	19	n	n	PROPN
ejpam-5559	111	20	!	!	PUNCT
ejpam-5559	112	1	=	=	PUNCT
ejpam-5559	112	2	(	(	PUNCT
ejpam-5559	112	3	(	(	PUNCT
ejpam-5559	112	4	1−	1−	NUM
ejpam-5559	112	5	u	u	NOUN
ejpam-5559	112	6	)	)	PUNCT
ejpam-5559	112	7	λe2	λe2	PROPN
ejpam-5559	112	8	t	t	NOUN
ejpam-5559	112	9	−	−	PROPN
ejpam-5559	112	10	u	u	PROPN
ejpam-5559	112	11	)	)	PUNCT
ejpam-5559	112	12	r	r	NOUN
ejpam-5559	112	13	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	112	14	)	)	PUNCT
ejpam-5559	112	15	=	=	NOUN
ejpam-5559	113	1	(	(	PUNCT
ejpam-5559	113	2	∞∑	∞∑	NUM
ejpam-5559	113	3	n=0	n=0	PROPN
ejpam-5559	113	4	t	t	NOUN
ejpam-5559	113	5	(	(	PUNCT
ejpam-5559	113	6	r	r	NOUN
ejpam-5559	113	7	)	)	PUNCT
ejpam-5559	113	8	n	n	CCONJ
ejpam-5559	113	9	(	(	PUNCT
ejpam-5559	113	10	u	u	NOUN
ejpam-5559	113	11	,	,	PUNCT
ejpam-5559	113	12	λ	λ	PROPN
ejpam-5559	113	13	)	)	PUNCT
ejpam-5559	113	14	tn	tn	PROPN
ejpam-5559	113	15	n	n	PROPN
ejpam-5559	113	16	!	!	PUNCT
ejpam-5559	113	17	)	)	PUNCT
ejpam-5559	114	1	(	(	PUNCT
ejpam-5559	114	2	∞∑	∞∑	NUM
ejpam-5559	114	3	n=0	n=0	PROPN
ejpam-5559	114	4	bn(x	bn(x	NUM
ejpam-5559	114	5	,	,	PUNCT
ejpam-5559	114	6	y	y	NOUN
ejpam-5559	114	7	)	)	PUNCT
ejpam-5559	114	8	tn	tn	PROPN
ejpam-5559	114	9	n	n	PROPN
ejpam-5559	114	10	!	!	PUNCT
ejpam-5559	114	11	)	)	PUNCT
ejpam-5559	115	1	=	=	PUNCT
ejpam-5559	116	1	∞∑	∞∑	NUM
ejpam-5559	116	2	n=0	n=0	NUM
ejpam-5559	116	3	{	{	PUNCT
ejpam-5559	116	4	n∑	n∑	NOUN
ejpam-5559	116	5	k=0	k=0	PROPN
ejpam-5559	116	6	(	(	PUNCT
ejpam-5559	116	7	n	n	X
ejpam-5559	116	8	k	k	PROPN
ejpam-5559	116	9	)	)	PUNCT
ejpam-5559	116	10	t	t	PROPN
ejpam-5559	116	11	(	(	PUNCT
ejpam-5559	116	12	r	r	NOUN
ejpam-5559	116	13	)	)	PUNCT
ejpam-5559	116	14	k	k	NOUN
ejpam-5559	116	15	(	(	PUNCT
ejpam-5559	116	16	u	u	NOUN
ejpam-5559	116	17	,	,	PUNCT
ejpam-5559	116	18	λ)bn−k(x	λ)bn−k(x	PROPN
ejpam-5559	116	19	,	,	PUNCT
ejpam-5559	116	20	y	y	NOUN
ejpam-5559	116	21	)	)	PUNCT
ejpam-5559	116	22	}	}	PUNCT
ejpam-5559	116	23	tn	tn	PROPN
ejpam-5559	116	24	n	n	X
ejpam-5559	116	25	!	!	PUNCT
ejpam-5559	116	26	.	.	PUNCT
ejpam-5559	117	1	comparing	compare	VERB
ejpam-5559	117	2	coefficients	coefficient	NOUN
ejpam-5559	117	3	,	,	PUNCT
ejpam-5559	117	4	bt	bt	X
ejpam-5559	117	5	(	(	PUNCT
ejpam-5559	117	6	r	r	NOUN
ejpam-5559	117	7	)	)	PUNCT
ejpam-5559	117	8	n	n	NOUN
ejpam-5559	117	9	(	(	PUNCT
ejpam-5559	117	10	x	x	X
ejpam-5559	117	11	,	,	PUNCT
ejpam-5559	117	12	y;u	y;u	PROPN
ejpam-5559	117	13	,	,	PUNCT
ejpam-5559	117	14	λ	λ	NOUN
ejpam-5559	117	15	)	)	PUNCT
ejpam-5559	117	16	=	=	SYM
ejpam-5559	117	17	n∑	n∑	NOUN
ejpam-5559	117	18	k=0	k=0	PROPN
ejpam-5559	117	19	(	(	PUNCT
ejpam-5559	117	20	n	n	X
ejpam-5559	117	21	k	k	PROPN
ejpam-5559	117	22	)	)	PUNCT
ejpam-5559	117	23	t	t	PROPN
ejpam-5559	117	24	(	(	PUNCT
ejpam-5559	117	25	r	r	NOUN
ejpam-5559	117	26	)	)	PUNCT
ejpam-5559	117	27	k	k	NOUN
ejpam-5559	117	28	(	(	PUNCT
ejpam-5559	117	29	u	u	NOUN
ejpam-5559	117	30	,	,	PUNCT
ejpam-5559	117	31	λ)bn−k(x	λ)bn−k(x	PROPN
ejpam-5559	117	32	,	,	PUNCT
ejpam-5559	117	33	y	y	NOUN
ejpam-5559	117	34	)	)	PUNCT
ejpam-5559	117	35	.	.	PUNCT
ejpam-5559	118	1	as	as	SCONJ
ejpam-5559	118	2	desired	desire	VERB
ejpam-5559	118	3	.	.	PUNCT
ejpam-5559	119	1	in	in	ADP
ejpam-5559	119	2	view	view	NOUN
ejpam-5559	119	3	of	of	ADP
ejpam-5559	119	4	(	(	PUNCT
ejpam-5559	119	5	5	5	NUM
ejpam-5559	119	6	)	)	PUNCT
ejpam-5559	119	7	,	,	PUNCT
ejpam-5559	119	8	we	we	PRON
ejpam-5559	119	9	can	can	AUX
ejpam-5559	119	10	express	express	VERB
ejpam-5559	119	11	the	the	DET
ejpam-5559	119	12	bivariate	bivariate	ADJ
ejpam-5559	119	13	bell	bell	NOUN
ejpam-5559	119	14	polynomial	polynomial	PROPN
ejpam-5559	119	15	bn(x	bn(x	X
ejpam-5559	119	16	,	,	PUNCT
ejpam-5559	119	17	y	y	NOUN
ejpam-5559	119	18	)	)	PUNCT
ejpam-5559	119	19	as	as	ADP
ejpam-5559	119	20	bn(x	bn(x	X
ejpam-5559	119	21	,	,	PUNCT
ejpam-5559	119	22	y	y	NOUN
ejpam-5559	119	23	)	)	PUNCT
ejpam-5559	119	24	=	=	SYM
ejpam-5559	119	25	bt	bt	PROPN
ejpam-5559	119	26	(	(	PUNCT
ejpam-5559	119	27	0	0	NUM
ejpam-5559	119	28	)	)	PUNCT
ejpam-5559	119	29	n	n	NOUN
ejpam-5559	119	30	(	(	PUNCT
ejpam-5559	119	31	x	x	X
ejpam-5559	119	32	,	,	PUNCT
ejpam-5559	119	33	y;u	y;u	PROPN
ejpam-5559	119	34	,	,	PUNCT
ejpam-5559	119	35	λ	λ	PROPN
ejpam-5559	119	36	)	)	PUNCT
ejpam-5559	119	37	,	,	PUNCT
ejpam-5559	119	38	(	(	PUNCT
ejpam-5559	119	39	16	16	NUM
ejpam-5559	119	40	)	)	PUNCT
ejpam-5559	119	41	which	which	PRON
ejpam-5559	119	42	allows	allow	VERB
ejpam-5559	119	43	as	as	SCONJ
ejpam-5559	119	44	to	to	PART
ejpam-5559	119	45	write	write	VERB
ejpam-5559	119	46	the	the	DET
ejpam-5559	119	47	result	result	NOUN
ejpam-5559	119	48	from	from	ADP
ejpam-5559	119	49	theorem	theorem	ADJ
ejpam-5559	119	50	1.2	1.2	NUM
ejpam-5559	119	51	into	into	ADP
ejpam-5559	119	52	bt	bt	PROPN
ejpam-5559	119	53	(	(	PUNCT
ejpam-5559	119	54	r	r	NOUN
ejpam-5559	119	55	)	)	PUNCT
ejpam-5559	119	56	n	n	NOUN
ejpam-5559	119	57	(	(	PUNCT
ejpam-5559	119	58	x	x	X
ejpam-5559	119	59	,	,	PUNCT
ejpam-5559	119	60	y;u	y;u	PROPN
ejpam-5559	119	61	,	,	PUNCT
ejpam-5559	119	62	λ	λ	NOUN
ejpam-5559	119	63	)	)	PUNCT
ejpam-5559	119	64	=	=	SYM
ejpam-5559	119	65	n∑	n∑	NOUN
ejpam-5559	119	66	k=0	k=0	PROPN
ejpam-5559	119	67	(	(	PUNCT
ejpam-5559	119	68	n	n	X
ejpam-5559	119	69	k	k	PROPN
ejpam-5559	119	70	)	)	PUNCT
ejpam-5559	119	71	t	t	PROPN
ejpam-5559	119	72	(	(	PUNCT
ejpam-5559	119	73	r	r	NOUN
ejpam-5559	119	74	)	)	PUNCT
ejpam-5559	119	75	k	k	NOUN
ejpam-5559	119	76	(	(	PUNCT
ejpam-5559	119	77	u	u	NOUN
ejpam-5559	119	78	,	,	PUNCT
ejpam-5559	119	79	λ)bt	λ)bt	PROPN
ejpam-5559	119	80	(	(	PUNCT
ejpam-5559	119	81	0	0	NUM
ejpam-5559	119	82	)	)	PUNCT
ejpam-5559	119	83	n−k(x	n−k(x	NOUN
ejpam-5559	119	84	,	,	PUNCT
ejpam-5559	119	85	y;u	y;u	PROPN
ejpam-5559	119	86	,	,	PUNCT
ejpam-5559	119	87	λ	λ	PROPN
ejpam-5559	119	88	)	)	PUNCT
ejpam-5559	119	89	.	.	PUNCT
ejpam-5559	120	1	j.	j.	PROPN
ejpam-5559	120	2	ontolan	ontolan	PROPN
ejpam-5559	120	3	et	et	PROPN
ejpam-5559	120	4	al	al	PROPN
ejpam-5559	120	5	.	.	PUNCT
ejpam-5559	120	6	/	/	SYM
ejpam-5559	120	7	eur	eur	PROPN
ejpam-5559	120	8	.	.	PUNCT
ejpam-5559	121	1	j.	j.	PROPN
ejpam-5559	121	2	pure	pure	PROPN
ejpam-5559	121	3	appl	appl	PROPN
ejpam-5559	121	4	.	.	PROPN
ejpam-5559	121	5	math	math	PROPN
ejpam-5559	121	6	,	,	PUNCT
ejpam-5559	121	7	18	18	NUM
ejpam-5559	121	8	(	(	PUNCT
ejpam-5559	121	9	1	1	NUM
ejpam-5559	121	10	)	)	PUNCT
ejpam-5559	121	11	(	(	PUNCT
ejpam-5559	121	12	2025	2025	NUM
ejpam-5559	121	13	)	)	PUNCT
ejpam-5559	121	14	,	,	PUNCT
ejpam-5559	121	15	5559	5559	NUM
ejpam-5559	121	16	7	7	NUM
ejpam-5559	121	17	of	of	ADP
ejpam-5559	121	18	16	16	NUM
ejpam-5559	121	19	theorem	theorem	NOUN
ejpam-5559	121	20	3	3	NUM
ejpam-5559	121	21	.	.	PUNCT
ejpam-5559	122	1	the	the	DET
ejpam-5559	122	2	function	function	NOUN
ejpam-5559	122	3	bt	bt	PROPN
ejpam-5559	122	4	(	(	PUNCT
ejpam-5559	122	5	r	r	NOUN
ejpam-5559	122	6	)	)	PUNCT
ejpam-5559	122	7	n	n	NOUN
ejpam-5559	122	8	(	(	PUNCT
ejpam-5559	122	9	x	x	X
ejpam-5559	122	10	,	,	PUNCT
ejpam-5559	122	11	y;u	y;u	PROPN
ejpam-5559	122	12	,	,	PUNCT
ejpam-5559	122	13	λ	λ	NOUN
ejpam-5559	122	14	)	)	PUNCT
ejpam-5559	122	15	satisfies	satisfy	VERB
ejpam-5559	122	16	the	the	DET
ejpam-5559	122	17	equation	equation	NOUN
ejpam-5559	122	18	bt	bt	INTJ
ejpam-5559	122	19	(	(	PUNCT
ejpam-5559	122	20	r	r	NOUN
ejpam-5559	122	21	)	)	PUNCT
ejpam-5559	122	22	n	n	NOUN
ejpam-5559	122	23	(	(	PUNCT
ejpam-5559	122	24	x	x	X
ejpam-5559	122	25	,	,	PUNCT
ejpam-5559	122	26	y;u	y;u	PROPN
ejpam-5559	122	27	,	,	PUNCT
ejpam-5559	122	28	λ	λ	NOUN
ejpam-5559	122	29	)	)	PUNCT
ejpam-5559	123	1	=	=	SYM
ejpam-5559	123	2	n∑	n∑	NOUN
ejpam-5559	123	3	k=0	k=0	PROPN
ejpam-5559	123	4	(	(	PUNCT
ejpam-5559	123	5	n	n	X
ejpam-5559	123	6	k	k	NOUN
ejpam-5559	123	7	)	)	PUNCT
ejpam-5559	123	8	bt	bt	PROPN
ejpam-5559	123	9	(	(	PUNCT
ejpam-5559	123	10	r	r	NOUN
ejpam-5559	123	11	)	)	PUNCT
ejpam-5559	123	12	n−k(y	n−k(y	PROPN
ejpam-5559	123	13	,	,	PUNCT
ejpam-5559	123	14	u	u	NOUN
ejpam-5559	123	15	,	,	PUNCT
ejpam-5559	123	16	λ)x	λ)x	ADJ
ejpam-5559	123	17	k.	k.	PROPN
ejpam-5559	123	18	(	(	PUNCT
ejpam-5559	123	19	17	17	NUM
ejpam-5559	123	20	)	)	PUNCT
ejpam-5559	123	21	proof	proof	NOUN
ejpam-5559	123	22	.	.	PUNCT
ejpam-5559	124	1	writing	write	VERB
ejpam-5559	124	2	∞∑	∞∑	PRON
ejpam-5559	124	3	n=0	n=0	NUM
ejpam-5559	124	4	bt	bt	NOUN
ejpam-5559	124	5	(	(	PUNCT
ejpam-5559	124	6	r	r	NOUN
ejpam-5559	124	7	)	)	PUNCT
ejpam-5559	124	8	n	n	NOUN
ejpam-5559	124	9	(	(	PUNCT
ejpam-5559	124	10	x	x	X
ejpam-5559	124	11	,	,	PUNCT
ejpam-5559	124	12	y;u	y;u	PROPN
ejpam-5559	124	13	,	,	PUNCT
ejpam-5559	124	14	λ	λ	PROPN
ejpam-5559	124	15	)	)	PUNCT
ejpam-5559	124	16	tn	tn	PROPN
ejpam-5559	124	17	n	n	PROPN
ejpam-5559	124	18	!	!	PUNCT
ejpam-5559	125	1	=	=	PUNCT
ejpam-5559	125	2	(	(	PUNCT
ejpam-5559	125	3	(	(	PUNCT
ejpam-5559	125	4	1−	1−	NUM
ejpam-5559	125	5	u	u	NOUN
ejpam-5559	125	6	)	)	PUNCT
ejpam-5559	125	7	λe2	λe2	PROPN
ejpam-5559	125	8	t	t	NOUN
ejpam-5559	125	9	−	−	PROPN
ejpam-5559	125	10	u	u	NOUN
ejpam-5559	125	11	)	)	PUNCT
ejpam-5559	125	12	r	r	NOUN
ejpam-5559	125	13	ey(e	ey(e	X
ejpam-5559	125	14	t−1)ext	t−1)ext	NOUN
ejpam-5559	126	1	=	=	PUNCT
ejpam-5559	126	2	(	(	PUNCT
ejpam-5559	126	3	∞∑	∞∑	PROPN
ejpam-5559	126	4	n=0	n=0	NUM
ejpam-5559	126	5	bt	bt	NOUN
ejpam-5559	126	6	(	(	PUNCT
ejpam-5559	126	7	r	r	NOUN
ejpam-5559	126	8	)	)	PUNCT
ejpam-5559	126	9	n	n	CCONJ
ejpam-5559	126	10	(	(	PUNCT
ejpam-5559	126	11	y;u	y;u	PROPN
ejpam-5559	126	12	,	,	PUNCT
ejpam-5559	126	13	λ	λ	PROPN
ejpam-5559	126	14	)	)	PUNCT
ejpam-5559	126	15	tn	tn	PROPN
ejpam-5559	126	16	n	n	PROPN
ejpam-5559	126	17	!	!	PUNCT
ejpam-5559	126	18	)	)	PUNCT
ejpam-5559	127	1	(	(	PUNCT
ejpam-5559	127	2	∞∑	∞∑	NUM
ejpam-5559	127	3	n=0	n=0	NUM
ejpam-5559	127	4	(	(	PUNCT
ejpam-5559	127	5	xt)n	xt)n	PROPN
ejpam-5559	127	6	n	n	CCONJ
ejpam-5559	127	7	!	!	PUNCT
ejpam-5559	127	8	)	)	PUNCT
ejpam-5559	128	1	=	=	PUNCT
ejpam-5559	129	1	∞∑	∞∑	NUM
ejpam-5559	129	2	n=0	n=0	NUM
ejpam-5559	129	3	{	{	PUNCT
ejpam-5559	129	4	n∑	n∑	NOUN
ejpam-5559	129	5	k=0	k=0	PROPN
ejpam-5559	129	6	(	(	PUNCT
ejpam-5559	129	7	n	n	X
ejpam-5559	129	8	k	k	NOUN
ejpam-5559	129	9	)	)	PUNCT
ejpam-5559	129	10	bt	bt	PROPN
ejpam-5559	129	11	(	(	PUNCT
ejpam-5559	129	12	r	r	NOUN
ejpam-5559	129	13	)	)	PUNCT
ejpam-5559	129	14	k	k	NOUN
ejpam-5559	129	15	(	(	PUNCT
ejpam-5559	129	16	y;u	y;u	PROPN
ejpam-5559	129	17	,	,	PUNCT
ejpam-5559	129	18	λ)xn−k	λ)xn−k	PROPN
ejpam-5559	129	19	}	}	PUNCT
ejpam-5559	129	20	tn	tn	PROPN
ejpam-5559	129	21	n	n	X
ejpam-5559	129	22	!	!	PUNCT
ejpam-5559	129	23	.	.	PUNCT
ejpam-5559	130	1	comparing	compare	VERB
ejpam-5559	130	2	coefficients	coefficient	NOUN
ejpam-5559	130	3	,	,	PUNCT
ejpam-5559	130	4	bt	bt	X
ejpam-5559	130	5	(	(	PUNCT
ejpam-5559	130	6	r	r	NOUN
ejpam-5559	130	7	)	)	PUNCT
ejpam-5559	130	8	n	n	NOUN
ejpam-5559	130	9	(	(	PUNCT
ejpam-5559	130	10	x	x	X
ejpam-5559	130	11	,	,	PUNCT
ejpam-5559	130	12	y;u	y;u	PROPN
ejpam-5559	130	13	,	,	PUNCT
ejpam-5559	130	14	λ	λ	NOUN
ejpam-5559	130	15	)	)	PUNCT
ejpam-5559	130	16	=	=	SYM
ejpam-5559	131	1	n∑	n∑	NOUN
ejpam-5559	131	2	k=0	k=0	PROPN
ejpam-5559	131	3	(	(	PUNCT
ejpam-5559	131	4	n	n	X
ejpam-5559	131	5	k	k	NOUN
ejpam-5559	131	6	)	)	PUNCT
ejpam-5559	131	7	bt	bt	PROPN
ejpam-5559	131	8	(	(	PUNCT
ejpam-5559	131	9	r	r	NOUN
ejpam-5559	131	10	)	)	PUNCT
ejpam-5559	131	11	k	k	NOUN
ejpam-5559	131	12	(	(	PUNCT
ejpam-5559	131	13	y;u	y;u	PROPN
ejpam-5559	131	14	,	,	PUNCT
ejpam-5559	131	15	λ)xn−k	λ)xn−k	NOUN
ejpam-5559	132	1	=	=	SYM
ejpam-5559	132	2	n∑	n∑	NOUN
ejpam-5559	132	3	k=0	k=0	PROPN
ejpam-5559	132	4	(	(	PUNCT
ejpam-5559	132	5	n	n	X
ejpam-5559	132	6	k	k	NOUN
ejpam-5559	132	7	)	)	PUNCT
ejpam-5559	132	8	bt	bt	PROPN
ejpam-5559	132	9	(	(	PUNCT
ejpam-5559	132	10	r	r	NOUN
ejpam-5559	132	11	)	)	PUNCT
ejpam-5559	132	12	n−k(y;u	n−k(y;u	ADJ
ejpam-5559	132	13	,	,	PUNCT
ejpam-5559	132	14	λ)x	λ)x	NOUN
ejpam-5559	132	15	k	k	X
ejpam-5559	132	16	as	as	SCONJ
ejpam-5559	132	17	desired	desire	VERB
ejpam-5559	132	18	.	.	PUNCT
ejpam-5559	133	1	the	the	DET
ejpam-5559	133	2	next	next	ADJ
ejpam-5559	133	3	theorem	theorem	NOUN
ejpam-5559	133	4	contains	contain	VERB
ejpam-5559	133	5	the	the	DET
ejpam-5559	133	6	addition	addition	NOUN
ejpam-5559	133	7	formula	formula	NOUN
ejpam-5559	133	8	for	for	ADP
ejpam-5559	133	9	bivariate	bivariate	ADJ
ejpam-5559	133	10	bell	bell	NOUN
ejpam-5559	133	11	-	-	PUNCT
ejpam-5559	133	12	based	base	VERB
ejpam-5559	133	13	apostolfrobenius	apostolfrobenius	NOUN
ejpam-5559	133	14	-	-	PUNCT
ejpam-5559	133	15	type	type	NOUN
ejpam-5559	133	16	tangent	tangent	NOUN
ejpam-5559	133	17	polynomials	polynomial	NOUN
ejpam-5559	133	18	of	of	ADP
ejpam-5559	133	19	higher	high	ADJ
ejpam-5559	133	20	order	order	NOUN
ejpam-5559	133	21	.	.	PUNCT
ejpam-5559	134	1	theorem	theorem	ADJ
ejpam-5559	134	2	4	4	NUM
ejpam-5559	134	3	.	.	PUNCT
ejpam-5559	135	1	the	the	DET
ejpam-5559	135	2	bell	bell	NOUN
ejpam-5559	135	3	-	-	PUNCT
ejpam-5559	135	4	based	base	VERB
ejpam-5559	135	5	apostol	apostol	NOUN
ejpam-5559	135	6	-	-	PUNCT
ejpam-5559	135	7	frobenius	frobenius	NOUN
ejpam-5559	135	8	-	-	PUNCT
ejpam-5559	135	9	type	type	NOUN
ejpam-5559	135	10	tangent	tangent	NOUN
ejpam-5559	135	11	polynomials	polynomial	NOUN
ejpam-5559	135	12	of	of	ADP
ejpam-5559	135	13	higher	high	ADJ
ejpam-5559	135	14	order	order	NOUN
ejpam-5559	135	15	bt	bt	NOUN
ejpam-5559	135	16	(	(	PUNCT
ejpam-5559	135	17	r	r	NOUN
ejpam-5559	135	18	)	)	PUNCT
ejpam-5559	135	19	n	n	NOUN
ejpam-5559	135	20	(	(	PUNCT
ejpam-5559	135	21	x	x	X
ejpam-5559	135	22	,	,	PUNCT
ejpam-5559	135	23	y;u	y;u	PROPN
ejpam-5559	135	24	,	,	PUNCT
ejpam-5559	135	25	λ	λ	NOUN
ejpam-5559	135	26	)	)	PUNCT
ejpam-5559	135	27	satisfies	satisfy	VERB
ejpam-5559	135	28	the	the	DET
ejpam-5559	135	29	equation	equation	NOUN
ejpam-5559	135	30	bt	bt	INTJ
ejpam-5559	135	31	(	(	PUNCT
ejpam-5559	135	32	r	r	NOUN
ejpam-5559	135	33	)	)	PUNCT
ejpam-5559	135	34	n	n	CCONJ
ejpam-5559	135	35	(	(	PUNCT
ejpam-5559	135	36	x+	x+	PROPN
ejpam-5559	135	37	y	y	PROPN
ejpam-5559	135	38	,	,	PUNCT
ejpam-5559	135	39	z;u	z;u	PROPN
ejpam-5559	135	40	,	,	PUNCT
ejpam-5559	135	41	λ	λ	NOUN
ejpam-5559	135	42	)	)	PUNCT
ejpam-5559	135	43	=	=	SYM
ejpam-5559	136	1	n∑	n∑	NOUN
ejpam-5559	136	2	k=0	k=0	PROPN
ejpam-5559	136	3	(	(	PUNCT
ejpam-5559	136	4	n	n	X
ejpam-5559	136	5	k	k	PROPN
ejpam-5559	136	6	)	)	PUNCT
ejpam-5559	136	7	t	t	PROPN
ejpam-5559	136	8	(	(	PUNCT
ejpam-5559	136	9	r	r	NOUN
ejpam-5559	136	10	)	)	PUNCT
ejpam-5559	136	11	k	k	NOUN
ejpam-5559	136	12	(	(	PUNCT
ejpam-5559	136	13	x;u	x;u	PROPN
ejpam-5559	136	14	,	,	PUNCT
ejpam-5559	136	15	λ)bn−k(y	λ)bn−k(y	PROPN
ejpam-5559	136	16	,	,	PUNCT
ejpam-5559	136	17	z	z	NOUN
ejpam-5559	136	18	)	)	PUNCT
ejpam-5559	136	19	(	(	PUNCT
ejpam-5559	136	20	18	18	NUM
ejpam-5559	136	21	)	)	PUNCT
ejpam-5559	136	22	proof	proof	NOUN
ejpam-5559	136	23	.	.	PUNCT
ejpam-5559	137	1	we	we	PRON
ejpam-5559	137	2	start	start	VERB
ejpam-5559	137	3	by	by	ADP
ejpam-5559	137	4	writing	write	VERB
ejpam-5559	137	5	∞∑	∞∑	PRON
ejpam-5559	137	6	n=0	n=0	NUM
ejpam-5559	137	7	bt	bt	NOUN
ejpam-5559	137	8	(	(	PUNCT
ejpam-5559	137	9	r	r	NOUN
ejpam-5559	137	10	)	)	PUNCT
ejpam-5559	137	11	n	n	CCONJ
ejpam-5559	137	12	(	(	PUNCT
ejpam-5559	137	13	x+	x+	PROPN
ejpam-5559	137	14	y	y	PROPN
ejpam-5559	137	15	,	,	PUNCT
ejpam-5559	137	16	z;u	z;u	PROPN
ejpam-5559	137	17	,	,	PUNCT
ejpam-5559	137	18	λ	λ	NOUN
ejpam-5559	137	19	)	)	PUNCT
ejpam-5559	137	20	tn	tn	PROPN
ejpam-5559	137	21	n	n	PROPN
ejpam-5559	137	22	!	!	PUNCT
ejpam-5559	138	1	=	=	PUNCT
ejpam-5559	138	2	(	(	PUNCT
ejpam-5559	138	3	(	(	PUNCT
ejpam-5559	138	4	1−	1−	NUM
ejpam-5559	138	5	u	u	NOUN
ejpam-5559	138	6	)	)	PUNCT
ejpam-5559	138	7	λe2	λe2	PROPN
ejpam-5559	138	8	t	t	NOUN
ejpam-5559	138	9	−	−	PROPN
ejpam-5559	138	10	u	u	NOUN
ejpam-5559	138	11	)	)	PUNCT
ejpam-5559	138	12	r	r	NOUN
ejpam-5559	138	13	e(x+y)t+z(et−1	e(x+y)t+z(et−1	NOUN
ejpam-5559	138	14	)	)	PUNCT
ejpam-5559	139	1	=	=	PRON
ejpam-5559	139	2	{	{	PUNCT
ejpam-5559	139	3	(	(	PUNCT
ejpam-5559	139	4	(	(	PUNCT
ejpam-5559	139	5	1−	1−	NUM
ejpam-5559	139	6	u	u	NOUN
ejpam-5559	139	7	)	)	PUNCT
ejpam-5559	139	8	λe2	λe2	PROPN
ejpam-5559	139	9	t	t	NOUN
ejpam-5559	139	10	−	−	PROPN
ejpam-5559	139	11	u	u	NOUN
ejpam-5559	139	12	)	)	PUNCT
ejpam-5559	139	13	r	r	NOUN
ejpam-5559	139	14	ext	ext	NOUN
ejpam-5559	139	15	}	}	PUNCT
ejpam-5559	139	16	eyt+z(et−1	eyt+z(et−1	PROPN
ejpam-5559	139	17	)	)	PUNCT
ejpam-5559	139	18	=	=	NOUN
ejpam-5559	139	19	(	(	PUNCT
ejpam-5559	139	20	∞∑	∞∑	NUM
ejpam-5559	139	21	n=0	n=0	PROPN
ejpam-5559	139	22	t	t	NOUN
ejpam-5559	139	23	(	(	PUNCT
ejpam-5559	139	24	r	r	NOUN
ejpam-5559	139	25	)	)	PUNCT
ejpam-5559	139	26	n	n	CCONJ
ejpam-5559	139	27	(	(	PUNCT
ejpam-5559	139	28	x;u	x;u	PROPN
ejpam-5559	139	29	,	,	PUNCT
ejpam-5559	139	30	λ	λ	NOUN
ejpam-5559	139	31	)	)	PUNCT
ejpam-5559	139	32	tn	tn	PROPN
ejpam-5559	139	33	n	n	PROPN
ejpam-5559	139	34	!	!	PUNCT
ejpam-5559	139	35	)	)	PUNCT
ejpam-5559	140	1	(	(	PUNCT
ejpam-5559	140	2	∞∑	∞∑	NUM
ejpam-5559	140	3	n=0	n=0	PROPN
ejpam-5559	140	4	bn(y	bn(y	NUM
ejpam-5559	140	5	,	,	PUNCT
ejpam-5559	140	6	z	z	NOUN
ejpam-5559	140	7	)	)	PUNCT
ejpam-5559	140	8	tn	tn	PROPN
ejpam-5559	140	9	n	n	CCONJ
ejpam-5559	140	10	!	!	PUNCT
ejpam-5559	140	11	)	)	PUNCT
ejpam-5559	141	1	=	=	PUNCT
ejpam-5559	142	1	∞∑	∞∑	NUM
ejpam-5559	142	2	n=0	n=0	NUM
ejpam-5559	142	3	{	{	PUNCT
ejpam-5559	142	4	n∑	n∑	NOUN
ejpam-5559	142	5	k=0	k=0	PROPN
ejpam-5559	142	6	(	(	PUNCT
ejpam-5559	142	7	n	n	X
ejpam-5559	142	8	k	k	PROPN
ejpam-5559	142	9	)	)	PUNCT
ejpam-5559	142	10	t	t	PROPN
ejpam-5559	142	11	(	(	PUNCT
ejpam-5559	142	12	r	r	NOUN
ejpam-5559	142	13	)	)	PUNCT
ejpam-5559	142	14	k	k	NOUN
ejpam-5559	142	15	(	(	PUNCT
ejpam-5559	142	16	x;u	x;u	PROPN
ejpam-5559	142	17	,	,	PUNCT
ejpam-5559	142	18	λ)bn−k(y	λ)bn−k(y	PROPN
ejpam-5559	142	19	,	,	PUNCT
ejpam-5559	142	20	z	z	NOUN
ejpam-5559	142	21	)	)	PUNCT
ejpam-5559	142	22	}	}	PUNCT
ejpam-5559	142	23	tn	tn	PROPN
ejpam-5559	142	24	n	n	NOUN
ejpam-5559	142	25	!	!	PUNCT
ejpam-5559	142	26	.	.	PUNCT
ejpam-5559	143	1	j.	j.	PROPN
ejpam-5559	143	2	ontolan	ontolan	PROPN
ejpam-5559	143	3	et	et	PROPN
ejpam-5559	143	4	al	al	PROPN
ejpam-5559	143	5	.	.	PUNCT
ejpam-5559	143	6	/	/	SYM
ejpam-5559	143	7	eur	eur	PROPN
ejpam-5559	143	8	.	.	PUNCT
ejpam-5559	144	1	j.	j.	PROPN
ejpam-5559	144	2	pure	pure	PROPN
ejpam-5559	144	3	appl	appl	PROPN
ejpam-5559	144	4	.	.	PROPN
ejpam-5559	144	5	math	math	PROPN
ejpam-5559	144	6	,	,	PUNCT
ejpam-5559	144	7	18	18	NUM
ejpam-5559	144	8	(	(	PUNCT
ejpam-5559	144	9	1	1	NUM
ejpam-5559	144	10	)	)	PUNCT
ejpam-5559	144	11	(	(	PUNCT
ejpam-5559	144	12	2025	2025	NUM
ejpam-5559	144	13	)	)	PUNCT
ejpam-5559	144	14	,	,	PUNCT
ejpam-5559	144	15	5559	5559	NUM
ejpam-5559	144	16	8	8	NUM
ejpam-5559	144	17	of	of	ADP
ejpam-5559	144	18	16	16	NUM
ejpam-5559	144	19	comparing	compare	VERB
ejpam-5559	144	20	coefficients	coefficient	NOUN
ejpam-5559	144	21	,	,	PUNCT
ejpam-5559	144	22	we	we	PRON
ejpam-5559	144	23	obtain	obtain	VERB
ejpam-5559	144	24	the	the	DET
ejpam-5559	144	25	desired	desire	VERB
ejpam-5559	144	26	result	result	NOUN
ejpam-5559	144	27	bt	bt	PROPN
ejpam-5559	144	28	(	(	PUNCT
ejpam-5559	144	29	r	r	NOUN
ejpam-5559	144	30	)	)	PUNCT
ejpam-5559	144	31	n	n	CCONJ
ejpam-5559	144	32	(	(	PUNCT
ejpam-5559	144	33	x+	x+	PROPN
ejpam-5559	144	34	y	y	PROPN
ejpam-5559	144	35	,	,	PUNCT
ejpam-5559	144	36	z;u	z;u	PROPN
ejpam-5559	144	37	,	,	PUNCT
ejpam-5559	144	38	λ	λ	NOUN
ejpam-5559	144	39	)	)	PUNCT
ejpam-5559	144	40	=	=	SYM
ejpam-5559	144	41	n∑	n∑	NOUN
ejpam-5559	144	42	k=0	k=0	PROPN
ejpam-5559	144	43	(	(	PUNCT
ejpam-5559	144	44	n	n	X
ejpam-5559	144	45	k	k	PROPN
ejpam-5559	144	46	)	)	PUNCT
ejpam-5559	144	47	t	t	PROPN
ejpam-5559	144	48	(	(	PUNCT
ejpam-5559	144	49	r	r	NOUN
ejpam-5559	144	50	)	)	PUNCT
ejpam-5559	144	51	k	k	NOUN
ejpam-5559	144	52	(	(	PUNCT
ejpam-5559	144	53	x;u	x;u	PROPN
ejpam-5559	144	54	,	,	PUNCT
ejpam-5559	144	55	λ)bn−k(y	λ)bn−k(y	PROPN
ejpam-5559	144	56	,	,	PUNCT
ejpam-5559	144	57	z	z	NOUN
ejpam-5559	144	58	)	)	PUNCT
ejpam-5559	144	59	.	.	PUNCT
ejpam-5559	145	1	implicit	implicit	ADJ
ejpam-5559	145	2	summation	summation	NOUN
ejpam-5559	145	3	formula	formula	NOUN
ejpam-5559	145	4	within	within	ADP
ejpam-5559	145	5	this	this	DET
ejpam-5559	145	6	section	section	NOUN
ejpam-5559	145	7	,	,	PUNCT
ejpam-5559	145	8	we	we	PRON
ejpam-5559	145	9	will	will	AUX
ejpam-5559	145	10	derive	derive	VERB
ejpam-5559	145	11	different	different	ADJ
ejpam-5559	145	12	summation	summation	NOUN
ejpam-5559	145	13	formulas	formula	NOUN
ejpam-5559	145	14	for	for	ADP
ejpam-5559	145	15	bt	bt	PROPN
ejpam-5559	145	16	(	(	PUNCT
ejpam-5559	145	17	r	r	NOUN
ejpam-5559	145	18	)	)	PUNCT
ejpam-5559	145	19	n	n	CCONJ
ejpam-5559	145	20	(	(	PUNCT
ejpam-5559	145	21	x+y	x+y	NUM
ejpam-5559	145	22	,	,	PUNCT
ejpam-5559	145	23	z;u	z;u	PROPN
ejpam-5559	145	24	,	,	PUNCT
ejpam-5559	145	25	λ	λ	PROPN
ejpam-5559	145	26	)	)	PUNCT
ejpam-5559	145	27	,	,	PUNCT
ejpam-5559	145	28	establishing	establish	VERB
ejpam-5559	145	29	implicit	implicit	ADJ
ejpam-5559	145	30	connections	connection	NOUN
ejpam-5559	145	31	among	among	ADP
ejpam-5559	145	32	the	the	DET
ejpam-5559	145	33	variables	variable	NOUN
ejpam-5559	145	34	by	by	ADP
ejpam-5559	145	35	considering	consider	VERB
ejpam-5559	145	36	them	they	PRON
ejpam-5559	145	37	as	as	ADP
ejpam-5559	145	38	arguments	argument	NOUN
ejpam-5559	145	39	.	.	PUNCT
ejpam-5559	146	1	the	the	DET
ejpam-5559	146	2	subsequent	subsequent	ADJ
ejpam-5559	146	3	theorem	theorem	NOUN
ejpam-5559	146	4	shows	show	VERB
ejpam-5559	146	5	a	a	DET
ejpam-5559	146	6	particular	particular	ADJ
ejpam-5559	146	7	expression	expression	NOUN
ejpam-5559	146	8	of	of	ADP
ejpam-5559	146	9	these	these	DET
ejpam-5559	146	10	summation	summation	NOUN
ejpam-5559	146	11	formulas	formula	NOUN
ejpam-5559	146	12	.	.	PUNCT
ejpam-5559	147	1	theorem	theorem	NOUN
ejpam-5559	147	2	5	5	NUM
ejpam-5559	147	3	.	.	PUNCT
ejpam-5559	148	1	the	the	DET
ejpam-5559	148	2	bivariate	bivariate	ADJ
ejpam-5559	148	3	bell	bell	NOUN
ejpam-5559	148	4	-	-	PUNCT
ejpam-5559	148	5	based	base	VERB
ejpam-5559	148	6	apostol	apostol	NOUN
ejpam-5559	148	7	-	-	PUNCT
ejpam-5559	148	8	frobenius	frobenius	NOUN
ejpam-5559	148	9	-	-	PUNCT
ejpam-5559	148	10	type	type	NOUN
ejpam-5559	148	11	tangent	tangent	NOUN
ejpam-5559	148	12	polynomials	polynomial	NOUN
ejpam-5559	148	13	of	of	ADP
ejpam-5559	148	14	higher	high	ADJ
ejpam-5559	148	15	order	order	NOUN
ejpam-5559	148	16	bt	bt	NOUN
ejpam-5559	148	17	(	(	PUNCT
ejpam-5559	148	18	r	r	NOUN
ejpam-5559	148	19	)	)	PUNCT
ejpam-5559	148	20	n	n	NOUN
ejpam-5559	148	21	(	(	PUNCT
ejpam-5559	148	22	x	x	X
ejpam-5559	148	23	,	,	PUNCT
ejpam-5559	148	24	y;u	y;u	PROPN
ejpam-5559	148	25	,	,	PUNCT
ejpam-5559	148	26	λ	λ	NOUN
ejpam-5559	148	27	)	)	PUNCT
ejpam-5559	148	28	satisfy	satisfy	VERB
ejpam-5559	148	29	the	the	DET
ejpam-5559	148	30	summation	summation	NOUN
ejpam-5559	148	31	formula	formula	NOUN
ejpam-5559	148	32	:	:	PUNCT
ejpam-5559	148	33	bt	bt	PROPN
ejpam-5559	148	34	(	(	PUNCT
ejpam-5559	148	35	r1+r2	r1+r2	PROPN
ejpam-5559	148	36	)	)	PUNCT
ejpam-5559	148	37	n	n	CCONJ
ejpam-5559	149	1	(	(	PUNCT
ejpam-5559	149	2	x1	x1	PROPN
ejpam-5559	149	3	+	+	NUM
ejpam-5559	149	4	x2	x2	PROPN
ejpam-5559	149	5	,	,	PUNCT
ejpam-5559	149	6	y2	y2	PROPN
ejpam-5559	149	7	+	+	CCONJ
ejpam-5559	149	8	y2;u	y2;u	PROPN
ejpam-5559	149	9	,	,	PUNCT
ejpam-5559	149	10	λ	λ	NOUN
ejpam-5559	149	11	)	)	PUNCT
ejpam-5559	149	12	=	=	SYM
ejpam-5559	149	13	n∑	n∑	NOUN
ejpam-5559	149	14	k=0	k=0	PROPN
ejpam-5559	149	15	(	(	PUNCT
ejpam-5559	149	16	n	n	X
ejpam-5559	149	17	k	k	NOUN
ejpam-5559	149	18	)	)	PUNCT
ejpam-5559	149	19	bt	bt	PROPN
ejpam-5559	149	20	(	(	PUNCT
ejpam-5559	149	21	r1	r1	PROPN
ejpam-5559	149	22	)	)	PUNCT
ejpam-5559	150	1	k	k	PROPN
ejpam-5559	150	2	(	(	PUNCT
ejpam-5559	150	3	x1	x1	PROPN
ejpam-5559	150	4	,	,	PUNCT
ejpam-5559	150	5	y1;u	y1;u	PROPN
ejpam-5559	150	6	,	,	PUNCT
ejpam-5559	150	7	λ)bg	λ)bg	PROPN
ejpam-5559	150	8	(	(	PUNCT
ejpam-5559	150	9	r2	r2	PROPN
ejpam-5559	150	10	)	)	PUNCT
ejpam-5559	150	11	n−k(x2	n−k(x2	PROPN
ejpam-5559	150	12	,	,	PUNCT
ejpam-5559	150	13	y2;u	y2;u	PROPN
ejpam-5559	150	14	,	,	PUNCT
ejpam-5559	150	15	λ	λ	NOUN
ejpam-5559	150	16	)	)	PUNCT
ejpam-5559	150	17	(	(	PUNCT
ejpam-5559	150	18	19	19	NUM
ejpam-5559	150	19	)	)	PUNCT
ejpam-5559	150	20	proof	proof	NOUN
ejpam-5559	150	21	.	.	PUNCT
ejpam-5559	151	1	we	we	PRON
ejpam-5559	151	2	can	can	AUX
ejpam-5559	151	3	express	express	VERB
ejpam-5559	151	4	the	the	DET
ejpam-5559	151	5	right	right	ADJ
ejpam-5559	151	6	hand	hand	NOUN
ejpam-5559	151	7	side	side	NOUN
ejpam-5559	151	8	of	of	ADP
ejpam-5559	151	9	(	(	PUNCT
ejpam-5559	151	10	5	5	NUM
ejpam-5559	151	11	)	)	PUNCT
ejpam-5559	151	12	as	as	SCONJ
ejpam-5559	151	13	follows	follow	VERB
ejpam-5559	151	14	:	:	PUNCT
ejpam-5559	151	15	(	(	PUNCT
ejpam-5559	151	16	(	(	PUNCT
ejpam-5559	151	17	1−	1−	NUM
ejpam-5559	151	18	u	u	NOUN
ejpam-5559	151	19	)	)	PUNCT
ejpam-5559	151	20	λe2	λe2	PROPN
ejpam-5559	151	21	t	t	NOUN
ejpam-5559	152	1	−	−	PROPN
ejpam-5559	152	2	u	u	NOUN
ejpam-5559	152	3	)	)	PUNCT
ejpam-5559	152	4	r1+r2	r1+r2	PROPN
ejpam-5559	152	5	e(x1+x2)t+(y1+y2)(et−1	e(x1+x2)t+(y1+y2)(et−1	PROPN
ejpam-5559	152	6	)	)	PUNCT
ejpam-5559	153	1	=	=	PRON
ejpam-5559	153	2	{	{	PUNCT
ejpam-5559	153	3	(	(	PUNCT
ejpam-5559	153	4	(	(	PUNCT
ejpam-5559	153	5	1−	1−	NUM
ejpam-5559	153	6	u	u	NOUN
ejpam-5559	153	7	)	)	PUNCT
ejpam-5559	153	8	λe2	λe2	PROPN
ejpam-5559	153	9	t	t	NOUN
ejpam-5559	153	10	−	−	PROPN
ejpam-5559	153	11	u	u	PROPN
ejpam-5559	153	12	)	)	PUNCT
ejpam-5559	153	13	r1	r1	PROPN
ejpam-5559	153	14	ex1t+y1(et−1	ex1t+y1(et−1	NOUN
ejpam-5559	153	15	)	)	PUNCT
ejpam-5559	153	16	}	}	PUNCT
ejpam-5559	153	17	{	{	PUNCT
ejpam-5559	153	18	(	(	PUNCT
ejpam-5559	153	19	(	(	PUNCT
ejpam-5559	153	20	1−	1−	NUM
ejpam-5559	153	21	u	u	NOUN
ejpam-5559	153	22	)	)	PUNCT
ejpam-5559	153	23	λe2	λe2	PROPN
ejpam-5559	153	24	t	t	NOUN
ejpam-5559	153	25	−	−	PROPN
ejpam-5559	153	26	u	u	PROPN
ejpam-5559	153	27	)	)	PUNCT
ejpam-5559	153	28	r2	r2	PROPN
ejpam-5559	153	29	ex2t+y2(et−1	ex2t+y2(et−1	NOUN
ejpam-5559	153	30	)	)	PUNCT
ejpam-5559	153	31	}	}	PUNCT
ejpam-5559	153	32	∞∑	∞∑	PROPN
ejpam-5559	153	33	n=0	n=0	NUM
ejpam-5559	153	34	bt	bt	NOUN
ejpam-5559	153	35	(	(	PUNCT
ejpam-5559	153	36	r1+r2	r1+r2	PROPN
ejpam-5559	153	37	)	)	PUNCT
ejpam-5559	153	38	n	n	CCONJ
ejpam-5559	153	39	(	(	PUNCT
ejpam-5559	153	40	x1	x1	PROPN
ejpam-5559	153	41	+	+	NUM
ejpam-5559	153	42	x2	x2	PROPN
ejpam-5559	153	43	,	,	PUNCT
ejpam-5559	153	44	y2	y2	PROPN
ejpam-5559	153	45	+	+	CCONJ
ejpam-5559	153	46	y2;u	y2;u	PROPN
ejpam-5559	153	47	,	,	PUNCT
ejpam-5559	153	48	λ	λ	NOUN
ejpam-5559	153	49	)	)	PUNCT
ejpam-5559	153	50	tn	tn	PROPN
ejpam-5559	153	51	n	n	PROPN
ejpam-5559	153	52	!	!	PUNCT
ejpam-5559	154	1	=	=	PUNCT
ejpam-5559	155	1	(	(	PUNCT
ejpam-5559	155	2	∞∑	∞∑	DET
ejpam-5559	155	3	n=0	n=0	NUM
ejpam-5559	155	4	bt	bt	NOUN
ejpam-5559	155	5	(	(	PUNCT
ejpam-5559	155	6	r1	r1	PROPN
ejpam-5559	155	7	)	)	PUNCT
ejpam-5559	155	8	n	n	CCONJ
ejpam-5559	155	9	(	(	PUNCT
ejpam-5559	155	10	x1	x1	PROPN
ejpam-5559	155	11	,	,	PUNCT
ejpam-5559	155	12	y1;u	y1;u	PROPN
ejpam-5559	155	13	,	,	PUNCT
ejpam-5559	155	14	λ	λ	PROPN
ejpam-5559	155	15	)	)	PUNCT
ejpam-5559	155	16	tn	tn	PROPN
ejpam-5559	155	17	n	n	PROPN
ejpam-5559	155	18	!	!	PUNCT
ejpam-5559	155	19	)	)	PUNCT
ejpam-5559	156	1	(	(	PUNCT
ejpam-5559	156	2	∞∑	∞∑	PRON
ejpam-5559	156	3	n=0	n=0	NUM
ejpam-5559	156	4	bt	bt	NOUN
ejpam-5559	156	5	(	(	PUNCT
ejpam-5559	156	6	r2	r2	PROPN
ejpam-5559	156	7	)	)	PUNCT
ejpam-5559	156	8	n	n	CCONJ
ejpam-5559	156	9	(	(	PUNCT
ejpam-5559	156	10	x2	x2	PROPN
ejpam-5559	156	11	,	,	PUNCT
ejpam-5559	156	12	y2;u	y2;u	PROPN
ejpam-5559	156	13	,	,	PUNCT
ejpam-5559	156	14	λ	λ	NOUN
ejpam-5559	156	15	)	)	PUNCT
ejpam-5559	156	16	tn	tn	PROPN
ejpam-5559	156	17	n	n	PROPN
ejpam-5559	156	18	!	!	PUNCT
ejpam-5559	156	19	)	)	PUNCT
ejpam-5559	157	1	=	=	PUNCT
ejpam-5559	158	1	∞∑	∞∑	NUM
ejpam-5559	158	2	n=0	n=0	NUM
ejpam-5559	158	3	n∑	n∑	PROPN
ejpam-5559	158	4	k=0	k=0	PROPN
ejpam-5559	158	5	bt	bt	PROPN
ejpam-5559	158	6	(	(	PUNCT
ejpam-5559	158	7	r1	r1	PROPN
ejpam-5559	158	8	)	)	PUNCT
ejpam-5559	158	9	n	n	CCONJ
ejpam-5559	158	10	(	(	PUNCT
ejpam-5559	158	11	x1	x1	PROPN
ejpam-5559	158	12	,	,	PUNCT
ejpam-5559	158	13	y1;u	y1;u	PROPN
ejpam-5559	158	14	,	,	PUNCT
ejpam-5559	158	15	λ)bt	λ)bt	PROPN
ejpam-5559	158	16	(	(	PUNCT
ejpam-5559	158	17	r2	r2	PROPN
ejpam-5559	158	18	)	)	PUNCT
ejpam-5559	158	19	n−k(x2	n−k(x2	PROPN
ejpam-5559	158	20	,	,	PUNCT
ejpam-5559	158	21	y2;u	y2;u	PROPN
ejpam-5559	158	22	,	,	PUNCT
ejpam-5559	158	23	λ	λ	NOUN
ejpam-5559	158	24	)	)	PUNCT
ejpam-5559	158	25	(	(	PUNCT
ejpam-5559	158	26	n	n	X
ejpam-5559	158	27	k	k	NOUN
ejpam-5559	158	28	)	)	PUNCT
ejpam-5559	158	29	.	.	PUNCT
ejpam-5559	159	1	comparing	compare	VERB
ejpam-5559	159	2	coefficients	coefficient	NOUN
ejpam-5559	159	3	,	,	PUNCT
ejpam-5559	159	4	we	we	PRON
ejpam-5559	159	5	obtain	obtain	VERB
ejpam-5559	159	6	the	the	DET
ejpam-5559	159	7	desired	desire	VERB
ejpam-5559	159	8	result	result	NOUN
ejpam-5559	159	9	bt	bt	PROPN
ejpam-5559	159	10	(	(	PUNCT
ejpam-5559	159	11	r1+r2	r1+r2	PROPN
ejpam-5559	159	12	)	)	PUNCT
ejpam-5559	159	13	n	n	CCONJ
ejpam-5559	159	14	(	(	PUNCT
ejpam-5559	159	15	x1	x1	PROPN
ejpam-5559	160	1	+	+	NUM
ejpam-5559	160	2	x2	x2	PROPN
ejpam-5559	160	3	,	,	PUNCT
ejpam-5559	160	4	y2	y2	PROPN
ejpam-5559	160	5	+	+	CCONJ
ejpam-5559	160	6	y2;u	y2;u	PROPN
ejpam-5559	160	7	,	,	PUNCT
ejpam-5559	160	8	λ	λ	NOUN
ejpam-5559	160	9	)	)	PUNCT
ejpam-5559	160	10	=	=	SYM
ejpam-5559	161	1	n∑	n∑	NOUN
ejpam-5559	161	2	k=0	k=0	PROPN
ejpam-5559	161	3	(	(	PUNCT
ejpam-5559	161	4	n	n	X
ejpam-5559	161	5	k	k	NOUN
ejpam-5559	161	6	)	)	PUNCT
ejpam-5559	161	7	bt	bt	PROPN
ejpam-5559	161	8	(	(	PUNCT
ejpam-5559	161	9	r1	r1	PROPN
ejpam-5559	161	10	)	)	PUNCT
ejpam-5559	161	11	k	k	PROPN
ejpam-5559	161	12	(	(	PUNCT
ejpam-5559	161	13	x1	x1	PROPN
ejpam-5559	161	14	,	,	PUNCT
ejpam-5559	161	15	y1;u	y1;u	PROPN
ejpam-5559	161	16	,	,	PUNCT
ejpam-5559	161	17	λ)bt	λ)bt	PROPN
ejpam-5559	161	18	(	(	PUNCT
ejpam-5559	161	19	r2	r2	PROPN
ejpam-5559	161	20	)	)	PUNCT
ejpam-5559	161	21	n−k(x2	n−k(x2	PROPN
ejpam-5559	161	22	,	,	PUNCT
ejpam-5559	161	23	y2;u	y2;u	PROPN
ejpam-5559	161	24	,	,	PUNCT
ejpam-5559	161	25	λ	λ	NOUN
ejpam-5559	161	26	)	)	PUNCT
ejpam-5559	161	27	.	.	PUNCT
ejpam-5559	162	1	remark	remark	PROPN
ejpam-5559	162	2	1	1	NUM
ejpam-5559	162	3	.	.	PUNCT
ejpam-5559	163	1	when	when	SCONJ
ejpam-5559	163	2	r1	r1	PROPN
ejpam-5559	163	3	=	=	SYM
ejpam-5559	163	4	r	r	PROPN
ejpam-5559	163	5	,	,	PUNCT
ejpam-5559	163	6	r2	r2	PROPN
ejpam-5559	163	7	=	=	SYM
ejpam-5559	163	8	0	0	PROPN
ejpam-5559	163	9	,	,	PUNCT
ejpam-5559	163	10	x1	x1	NOUN
ejpam-5559	163	11	=	=	SYM
ejpam-5559	163	12	x	x	X
ejpam-5559	163	13	,	,	PUNCT
ejpam-5559	163	14	x2	x2	PROPN
ejpam-5559	163	15	=	=	SYM
ejpam-5559	163	16	1,y1	1,y1	NUM
ejpam-5559	163	17	=	=	SYM
ejpam-5559	163	18	y	y	PROPN
ejpam-5559	163	19	,	,	PUNCT
ejpam-5559	163	20	y2	y2	PROPN
ejpam-5559	163	21	=	=	SYM
ejpam-5559	163	22	0	0	PROPN
ejpam-5559	163	23	,	,	PUNCT
ejpam-5559	163	24	the	the	DET
ejpam-5559	163	25	summation	summation	NOUN
ejpam-5559	163	26	formula	formula	NOUN
ejpam-5559	163	27	in	in	ADP
ejpam-5559	163	28	(	(	PUNCT
ejpam-5559	163	29	19	19	NUM
ejpam-5559	163	30	)	)	PUNCT
ejpam-5559	163	31	reduces	reduce	VERB
ejpam-5559	163	32	to	to	ADP
ejpam-5559	163	33	bt	bt	PROPN
ejpam-5559	163	34	(	(	PUNCT
ejpam-5559	163	35	r	r	NOUN
ejpam-5559	163	36	)	)	PUNCT
ejpam-5559	163	37	n	n	CCONJ
ejpam-5559	163	38	(	(	PUNCT
ejpam-5559	163	39	x+	x+	PROPN
ejpam-5559	163	40	1	1	NUM
ejpam-5559	163	41	,	,	PUNCT
ejpam-5559	163	42	y;u	y;u	PROPN
ejpam-5559	163	43	,	,	PUNCT
ejpam-5559	163	44	λ	λ	NOUN
ejpam-5559	163	45	)	)	PUNCT
ejpam-5559	163	46	=	=	SYM
ejpam-5559	164	1	n∑	n∑	NOUN
ejpam-5559	164	2	k=0	k=0	PROPN
ejpam-5559	164	3	(	(	PUNCT
ejpam-5559	164	4	n	n	X
ejpam-5559	164	5	k	k	NOUN
ejpam-5559	164	6	)	)	PUNCT
ejpam-5559	164	7	bt	bt	PROPN
ejpam-5559	164	8	(	(	PUNCT
ejpam-5559	164	9	r	r	NOUN
ejpam-5559	164	10	)	)	PUNCT
ejpam-5559	164	11	k	k	NOUN
ejpam-5559	164	12	(	(	PUNCT
ejpam-5559	164	13	x	x	X
ejpam-5559	164	14	,	,	PUNCT
ejpam-5559	164	15	y;u	y;u	PROPN
ejpam-5559	164	16	,	,	PUNCT
ejpam-5559	164	17	λ)bn−k(1	λ)bn−k(1	NOUN
ejpam-5559	164	18	,	,	PUNCT
ejpam-5559	164	19	0	0	NUM
ejpam-5559	164	20	)	)	PUNCT
ejpam-5559	164	21	=	=	SYM
ejpam-5559	165	1	n∑	n∑	NOUN
ejpam-5559	165	2	k=0	k=0	PROPN
ejpam-5559	165	3	(	(	PUNCT
ejpam-5559	165	4	n	n	X
ejpam-5559	165	5	k	k	NOUN
ejpam-5559	165	6	)	)	PUNCT
ejpam-5559	165	7	bt	bt	PROPN
ejpam-5559	165	8	(	(	PUNCT
ejpam-5559	165	9	r	r	NOUN
ejpam-5559	165	10	)	)	PUNCT
ejpam-5559	165	11	k	k	NOUN
ejpam-5559	165	12	(	(	PUNCT
ejpam-5559	165	13	x	x	NOUN
ejpam-5559	165	14	,	,	PUNCT
ejpam-5559	165	15	y;u	y;u	PROPN
ejpam-5559	165	16	,	,	PUNCT
ejpam-5559	165	17	λ	λ	PROPN
ejpam-5559	165	18	)	)	PUNCT
ejpam-5559	165	19	.	.	PUNCT
ejpam-5559	166	1	(	(	PUNCT
ejpam-5559	166	2	20	20	NUM
ejpam-5559	166	3	)	)	PUNCT
ejpam-5559	166	4	j.	j.	PROPN
ejpam-5559	166	5	ontolan	ontolan	PROPN
ejpam-5559	166	6	et	et	PROPN
ejpam-5559	166	7	al	al	PROPN
ejpam-5559	166	8	.	.	PUNCT
ejpam-5559	166	9	/	/	SYM
ejpam-5559	166	10	eur	eur	PROPN
ejpam-5559	166	11	.	.	PUNCT
ejpam-5559	167	1	j.	j.	PROPN
ejpam-5559	167	2	pure	pure	PROPN
ejpam-5559	167	3	appl	appl	PROPN
ejpam-5559	167	4	.	.	PROPN
ejpam-5559	167	5	math	math	PROPN
ejpam-5559	167	6	,	,	PUNCT
ejpam-5559	167	7	18	18	NUM
ejpam-5559	167	8	(	(	PUNCT
ejpam-5559	167	9	1	1	NUM
ejpam-5559	167	10	)	)	PUNCT
ejpam-5559	167	11	(	(	PUNCT
ejpam-5559	167	12	2025	2025	NUM
ejpam-5559	167	13	)	)	PUNCT
ejpam-5559	167	14	,	,	PUNCT
ejpam-5559	167	15	5559	5559	NUM
ejpam-5559	167	16	9	9	NUM
ejpam-5559	167	17	of	of	ADP
ejpam-5559	167	18	16	16	NUM
ejpam-5559	167	19	on	on	ADP
ejpam-5559	167	20	the	the	DET
ejpam-5559	167	21	other	other	ADJ
ejpam-5559	167	22	hand	hand	NOUN
ejpam-5559	167	23	,	,	PUNCT
ejpam-5559	167	24	when	when	SCONJ
ejpam-5559	167	25	y	y	PROPN
ejpam-5559	167	26	=	=	SYM
ejpam-5559	167	27	1	1	NUM
ejpam-5559	167	28	,	,	PUNCT
ejpam-5559	167	29	(	(	PUNCT
ejpam-5559	167	30	18	18	NUM
ejpam-5559	167	31	)	)	PUNCT
ejpam-5559	167	32	gives	give	VERB
ejpam-5559	167	33	bt	bt	PROPN
ejpam-5559	167	34	(	(	PUNCT
ejpam-5559	167	35	r	r	NOUN
ejpam-5559	167	36	)	)	PUNCT
ejpam-5559	167	37	n	n	CCONJ
ejpam-5559	167	38	(	(	PUNCT
ejpam-5559	167	39	x+	x+	PROPN
ejpam-5559	167	40	1	1	NUM
ejpam-5559	167	41	,	,	PUNCT
ejpam-5559	167	42	z;u	z;u	PROPN
ejpam-5559	167	43	,	,	PUNCT
ejpam-5559	167	44	λ	λ	NOUN
ejpam-5559	167	45	)	)	PUNCT
ejpam-5559	167	46	=	=	SYM
ejpam-5559	167	47	n∑	n∑	NOUN
ejpam-5559	167	48	k=0	k=0	PROPN
ejpam-5559	167	49	(	(	PUNCT
ejpam-5559	167	50	n	n	X
ejpam-5559	167	51	k	k	PROPN
ejpam-5559	167	52	)	)	PUNCT
ejpam-5559	167	53	t	t	PROPN
ejpam-5559	167	54	(	(	PUNCT
ejpam-5559	167	55	r	r	NOUN
ejpam-5559	167	56	)	)	PUNCT
ejpam-5559	167	57	k	k	NOUN
ejpam-5559	167	58	(	(	PUNCT
ejpam-5559	167	59	x;u	x;u	PROPN
ejpam-5559	167	60	,	,	PUNCT
ejpam-5559	167	61	λ)bn−k(1	λ)bn−k(1	NOUN
ejpam-5559	167	62	,	,	PUNCT
ejpam-5559	167	63	z	z	NOUN
ejpam-5559	167	64	)	)	PUNCT
ejpam-5559	167	65	.	.	PUNCT
ejpam-5559	168	1	(	(	PUNCT
ejpam-5559	168	2	21	21	NUM
ejpam-5559	168	3	)	)	PUNCT
ejpam-5559	168	4	replacing	replace	VERB
ejpam-5559	168	5	z	z	NOUN
ejpam-5559	168	6	with	with	ADP
ejpam-5559	168	7	y	y	PROPN
ejpam-5559	168	8	in	in	ADP
ejpam-5559	168	9	(	(	PUNCT
ejpam-5559	168	10	21	21	NUM
ejpam-5559	168	11	)	)	PUNCT
ejpam-5559	168	12	and	and	CCONJ
ejpam-5559	168	13	compare	compare	VERB
ejpam-5559	168	14	it	it	PRON
ejpam-5559	168	15	to	to	ADP
ejpam-5559	168	16	(	(	PUNCT
ejpam-5559	168	17	20	20	NUM
ejpam-5559	168	18	)	)	PUNCT
ejpam-5559	168	19	yields	yield	NOUN
ejpam-5559	168	20	n∑	n∑	PROPN
ejpam-5559	168	21	k=0	k=0	PROPN
ejpam-5559	168	22	(	(	PUNCT
ejpam-5559	168	23	n	n	X
ejpam-5559	168	24	k	k	PROPN
ejpam-5559	168	25	)	)	PUNCT
ejpam-5559	168	26	t	t	PROPN
ejpam-5559	168	27	(	(	PUNCT
ejpam-5559	168	28	r	r	NOUN
ejpam-5559	168	29	)	)	PUNCT
ejpam-5559	168	30	k	k	NOUN
ejpam-5559	168	31	(	(	PUNCT
ejpam-5559	168	32	x;u	x;u	PROPN
ejpam-5559	168	33	,	,	PUNCT
ejpam-5559	168	34	λ)bn−k(1	λ)bn−k(1	NOUN
ejpam-5559	168	35	,	,	PUNCT
ejpam-5559	168	36	y	y	NOUN
ejpam-5559	168	37	)	)	PUNCT
ejpam-5559	169	1	=	=	SYM
ejpam-5559	169	2	n∑	n∑	NOUN
ejpam-5559	169	3	k=0	k=0	PROPN
ejpam-5559	169	4	(	(	PUNCT
ejpam-5559	169	5	n	n	X
ejpam-5559	169	6	k	k	NOUN
ejpam-5559	169	7	)	)	PUNCT
ejpam-5559	169	8	bt	bt	PROPN
ejpam-5559	169	9	(	(	PUNCT
ejpam-5559	169	10	r	r	NOUN
ejpam-5559	169	11	)	)	PUNCT
ejpam-5559	169	12	k	k	NOUN
ejpam-5559	169	13	(	(	PUNCT
ejpam-5559	169	14	x	x	NOUN
ejpam-5559	169	15	,	,	PUNCT
ejpam-5559	169	16	y;u	y;u	PROPN
ejpam-5559	169	17	,	,	PUNCT
ejpam-5559	169	18	λ	λ	PROPN
ejpam-5559	169	19	)	)	PUNCT
ejpam-5559	169	20	.	.	PUNCT
ejpam-5559	170	1	in	in	ADP
ejpam-5559	170	2	view	view	NOUN
ejpam-5559	170	3	of	of	ADP
ejpam-5559	170	4	(	(	PUNCT
ejpam-5559	170	5	5	5	NUM
ejpam-5559	170	6	)	)	PUNCT
ejpam-5559	170	7	,	,	PUNCT
ejpam-5559	170	8	notice	notice	VERB
ejpam-5559	170	9	that	that	SCONJ
ejpam-5559	170	10	we	we	PRON
ejpam-5559	170	11	can	can	AUX
ejpam-5559	170	12	write	write	VERB
ejpam-5559	170	13	∞∑	∞∑	PRON
ejpam-5559	170	14	n=0	n=0	NUM
ejpam-5559	170	15	bt	bt	NOUN
ejpam-5559	170	16	(	(	PUNCT
ejpam-5559	170	17	r	r	NOUN
ejpam-5559	170	18	)	)	PUNCT
ejpam-5559	170	19	n	n	NOUN
ejpam-5559	170	20	(	(	PUNCT
ejpam-5559	170	21	x	x	X
ejpam-5559	170	22	,	,	PUNCT
ejpam-5559	170	23	y;u	y;u	PROPN
ejpam-5559	170	24	,	,	PUNCT
ejpam-5559	170	25	λ	λ	PROPN
ejpam-5559	170	26	)	)	PUNCT
ejpam-5559	170	27	(	(	PUNCT
ejpam-5559	170	28	t+	t+	NOUN
ejpam-5559	170	29	v)n	v)n	NOUN
ejpam-5559	170	30	n	n	CCONJ
ejpam-5559	170	31	!	!	PUNCT
ejpam-5559	171	1	=	=	PUNCT
ejpam-5559	172	1	(	(	PUNCT
ejpam-5559	172	2	1−	1−	NUM
ejpam-5559	172	3	u	u	NOUN
ejpam-5559	172	4	λe2(t+v	λe2(t+v	NOUN
ejpam-5559	172	5	)	)	PUNCT
ejpam-5559	172	6	−	−	PROPN
ejpam-5559	172	7	u	u	NOUN
ejpam-5559	172	8	)	)	PUNCT
ejpam-5559	172	9	r	r	NOUN
ejpam-5559	172	10	ex(t+v)+y(et+v−1	ex(t+v)+y(et+v−1	NOUN
ejpam-5559	172	11	)	)	PUNCT
ejpam-5559	172	12	which	which	PRON
ejpam-5559	172	13	allows	allow	VERB
ejpam-5559	172	14	us	we	PRON
ejpam-5559	172	15	to	to	PART
ejpam-5559	172	16	express	express	VERB
ejpam-5559	172	17	(	(	PUNCT
ejpam-5559	172	18	1−	1−	NUM
ejpam-5559	172	19	u	u	NOUN
ejpam-5559	172	20	λe2(t+v	λe2(t+v	NOUN
ejpam-5559	172	21	)	)	PUNCT
ejpam-5559	172	22	−	−	PROPN
ejpam-5559	172	23	u	u	NOUN
ejpam-5559	172	24	)	)	PUNCT
ejpam-5559	172	25	r	r	NOUN
ejpam-5559	172	26	ex(t+v)ey(e	ex(t+v)ey(e	X
ejpam-5559	172	27	t+v−1	t+v−1	X
ejpam-5559	172	28	)	)	PUNCT
ejpam-5559	172	29	=	=	PUNCT
ejpam-5559	173	1	∞∑	∞∑	ADJ
ejpam-5559	173	2	n=0	n=0	NUM
ejpam-5559	173	3	bt	bt	NOUN
ejpam-5559	173	4	(	(	PUNCT
ejpam-5559	173	5	r	r	NOUN
ejpam-5559	173	6	)	)	PUNCT
ejpam-5559	173	7	n	n	NOUN
ejpam-5559	173	8	(	(	PUNCT
ejpam-5559	173	9	x	x	X
ejpam-5559	173	10	,	,	PUNCT
ejpam-5559	173	11	y;u	y;u	PROPN
ejpam-5559	173	12	,	,	PUNCT
ejpam-5559	173	13	λ	λ	PROPN
ejpam-5559	173	14	)	)	PUNCT
ejpam-5559	173	15	(	(	PUNCT
ejpam-5559	173	16	t+	t+	NOUN
ejpam-5559	173	17	v)n	v)n	NOUN
ejpam-5559	173	18	n	n	CCONJ
ejpam-5559	173	19	!	!	PUNCT
ejpam-5559	173	20	,	,	PUNCT
ejpam-5559	173	21	consequently	consequently	ADV
ejpam-5559	173	22	(	(	PUNCT
ejpam-5559	173	23	1−	1−	NUM
ejpam-5559	173	24	u	u	NOUN
ejpam-5559	173	25	λe2(t+v	λe2(t+v	NOUN
ejpam-5559	173	26	)	)	PUNCT
ejpam-5559	173	27	−	−	PROPN
ejpam-5559	173	28	u	u	NOUN
ejpam-5559	173	29	)	)	PUNCT
ejpam-5559	173	30	r	r	NOUN
ejpam-5559	173	31	ey(e	ey(e	X
ejpam-5559	173	32	t+v−1	t+v−1	PROPN
ejpam-5559	173	33	)	)	PUNCT
ejpam-5559	173	34	=	=	SYM
ejpam-5559	173	35	e−x(t+v	e−x(t+v	PROPN
ejpam-5559	173	36	)	)	PUNCT
ejpam-5559	173	37	∞∑	∞∑	PRON
ejpam-5559	173	38	n=0	n=0	NUM
ejpam-5559	173	39	bt	bt	NOUN
ejpam-5559	173	40	(	(	PUNCT
ejpam-5559	173	41	r	r	NOUN
ejpam-5559	173	42	)	)	PUNCT
ejpam-5559	173	43	n	n	NOUN
ejpam-5559	173	44	(	(	PUNCT
ejpam-5559	173	45	x	x	X
ejpam-5559	173	46	,	,	PUNCT
ejpam-5559	173	47	y;u	y;u	PROPN
ejpam-5559	173	48	,	,	PUNCT
ejpam-5559	173	49	λ	λ	PROPN
ejpam-5559	173	50	)	)	PUNCT
ejpam-5559	173	51	(	(	PUNCT
ejpam-5559	173	52	t+	t+	NOUN
ejpam-5559	173	53	v)n	v)n	NOUN
ejpam-5559	173	54	n	n	X
ejpam-5559	173	55	!	!	PUNCT
ejpam-5559	173	56	.	.	PUNCT
ejpam-5559	174	1	(	(	PUNCT
ejpam-5559	174	2	22	22	X
ejpam-5559	174	3	)	)	PUNCT
ejpam-5559	174	4	applying	apply	VERB
ejpam-5559	174	5	(	(	PUNCT
ejpam-5559	174	6	13	13	NUM
ejpam-5559	174	7	)	)	PUNCT
ejpam-5559	174	8	,	,	PUNCT
ejpam-5559	174	9	we	we	PRON
ejpam-5559	174	10	obtain	obtain	VERB
ejpam-5559	174	11	(	(	PUNCT
ejpam-5559	174	12	1−	1−	NUM
ejpam-5559	174	13	u	u	NOUN
ejpam-5559	174	14	λe2(t+v	λe2(t+v	NOUN
ejpam-5559	174	15	)	)	PUNCT
ejpam-5559	174	16	−	−	PROPN
ejpam-5559	174	17	u	u	NOUN
ejpam-5559	174	18	)	)	PUNCT
ejpam-5559	174	19	r	r	NOUN
ejpam-5559	174	20	ey(e	ey(e	X
ejpam-5559	174	21	t+v−1	t+v−1	PROPN
ejpam-5559	174	22	)	)	PUNCT
ejpam-5559	174	23	=	=	SYM
ejpam-5559	174	24	e−x(t+v	e−x(t+v	PROPN
ejpam-5559	174	25	)	)	PUNCT
ejpam-5559	175	1	∞∑	∞∑	DET
ejpam-5559	175	2	k=0	k=0	PUNCT
ejpam-5559	175	3	∞∑	∞∑	NUM
ejpam-5559	175	4	l=0	l=0	PROPN
ejpam-5559	175	5	bt	bt	NOUN
ejpam-5559	175	6	(	(	PUNCT
ejpam-5559	175	7	r	r	NOUN
ejpam-5559	175	8	)	)	PUNCT
ejpam-5559	175	9	k+l(x	k+l(x	PROPN
ejpam-5559	175	10	,	,	PUNCT
ejpam-5559	175	11	y;u	y;u	PROPN
ejpam-5559	175	12	,	,	PUNCT
ejpam-5559	175	13	λ	λ	PROPN
ejpam-5559	175	14	)	)	PUNCT
ejpam-5559	175	15	tk	tk	PROPN
ejpam-5559	175	16	k	k	PROPN
ejpam-5559	175	17	!	!	PUNCT
ejpam-5559	175	18	vl	vl	PROPN
ejpam-5559	175	19	l	l	PROPN
ejpam-5559	175	20	!	!	PUNCT
ejpam-5559	175	21	.	.	PUNCT
ejpam-5559	176	1	(	(	PUNCT
ejpam-5559	176	2	23	23	X
ejpam-5559	176	3	)	)	PUNCT
ejpam-5559	176	4	replacing	replace	VERB
ejpam-5559	176	5	x	x	PUNCT
ejpam-5559	176	6	with	with	ADP
ejpam-5559	176	7	z	z	PROPN
ejpam-5559	176	8	,	,	PUNCT
ejpam-5559	176	9	equation	equation	NOUN
ejpam-5559	176	10	(	(	PUNCT
ejpam-5559	176	11	23	23	NUM
ejpam-5559	176	12	)	)	PUNCT
ejpam-5559	176	13	becomes	become	VERB
ejpam-5559	176	14	(	(	PUNCT
ejpam-5559	176	15	(	(	PUNCT
ejpam-5559	176	16	1−	1−	NUM
ejpam-5559	176	17	u	u	NOUN
ejpam-5559	176	18	)	)	PUNCT
ejpam-5559	176	19	λe2(t+v	λe2(t+v	NOUN
ejpam-5559	176	20	)	)	PUNCT
ejpam-5559	176	21	−	−	PROPN
ejpam-5559	176	22	u	u	NOUN
ejpam-5559	176	23	)	)	PUNCT
ejpam-5559	176	24	r	r	NOUN
ejpam-5559	176	25	ey(e	ey(e	X
ejpam-5559	176	26	t+v−1	t+v−1	PROPN
ejpam-5559	176	27	)	)	PUNCT
ejpam-5559	176	28	=	=	SYM
ejpam-5559	176	29	e−z(t+v	e−z(t+v	NOUN
ejpam-5559	176	30	)	)	PUNCT
ejpam-5559	176	31	∞∑	∞∑	PRON
ejpam-5559	176	32	k=0	k=0	PUNCT
ejpam-5559	176	33	∞∑	∞∑	NUM
ejpam-5559	176	34	l=0	l=0	PROPN
ejpam-5559	176	35	bt	bt	NOUN
ejpam-5559	176	36	(	(	PUNCT
ejpam-5559	176	37	r	r	NOUN
ejpam-5559	176	38	)	)	PUNCT
ejpam-5559	176	39	k+l(z	k+l(z	NOUN
ejpam-5559	176	40	,	,	PUNCT
ejpam-5559	176	41	y;u	y;u	PROPN
ejpam-5559	176	42	,	,	PUNCT
ejpam-5559	176	43	λ	λ	PROPN
ejpam-5559	176	44	)	)	PUNCT
ejpam-5559	176	45	tk	tk	PROPN
ejpam-5559	176	46	k	k	PROPN
ejpam-5559	176	47	!	!	PUNCT
ejpam-5559	177	1	vl	vl	PROPN
ejpam-5559	177	2	l	l	NOUN
ejpam-5559	177	3	!	!	PUNCT
ejpam-5559	177	4	(	(	PUNCT
ejpam-5559	177	5	(	(	PUNCT
ejpam-5559	177	6	1−	1−	NUM
ejpam-5559	177	7	u	u	NOUN
ejpam-5559	177	8	)	)	PUNCT
ejpam-5559	177	9	λe2(t+v	λe2(t+v	NOUN
ejpam-5559	177	10	)	)	PUNCT
ejpam-5559	178	1	−	−	PROPN
ejpam-5559	178	2	u	u	NOUN
ejpam-5559	178	3	)	)	PUNCT
ejpam-5559	178	4	r	r	NOUN
ejpam-5559	178	5	ey(e	ey(e	X
ejpam-5559	178	6	t+v−1)ex(t+v	t+v−1)ex(t+v	PROPN
ejpam-5559	178	7	)	)	PUNCT
ejpam-5559	178	8	=	=	SYM
ejpam-5559	178	9	ex(t+v)e−z(t+v	ex(t+v)e−z(t+v	NOUN
ejpam-5559	178	10	)	)	PUNCT
ejpam-5559	178	11	∞∑	∞∑	PRON
ejpam-5559	178	12	k=0	k=0	PUNCT
ejpam-5559	178	13	∞∑	∞∑	NUM
ejpam-5559	178	14	l=0	l=0	PROPN
ejpam-5559	178	15	bt	bt	NOUN
ejpam-5559	178	16	(	(	PUNCT
ejpam-5559	178	17	r	r	NOUN
ejpam-5559	178	18	)	)	PUNCT
ejpam-5559	178	19	k+l(z	k+l(z	NOUN
ejpam-5559	178	20	,	,	PUNCT
ejpam-5559	178	21	y;u	y;u	PROPN
ejpam-5559	178	22	,	,	PUNCT
ejpam-5559	178	23	λ	λ	PROPN
ejpam-5559	178	24	)	)	PUNCT
ejpam-5559	178	25	tk	tk	PROPN
ejpam-5559	178	26	k	k	PROPN
ejpam-5559	178	27	!	!	PUNCT
ejpam-5559	178	28	vl	vl	PROPN
ejpam-5559	178	29	l	l	NOUN
ejpam-5559	178	30	!	!	PUNCT
ejpam-5559	178	31	(	(	PUNCT
ejpam-5559	178	32	(	(	PUNCT
ejpam-5559	178	33	1−	1−	NUM
ejpam-5559	178	34	u	u	NOUN
ejpam-5559	178	35	)	)	PUNCT
ejpam-5559	178	36	λe2(t+v	λe2(t+v	NOUN
ejpam-5559	178	37	)	)	PUNCT
ejpam-5559	178	38	−	−	PROPN
ejpam-5559	178	39	u	u	NOUN
ejpam-5559	178	40	)	)	PUNCT
ejpam-5559	178	41	r	r	NOUN
ejpam-5559	178	42	ex(t+v)+y(et+v−1	ex(t+v)+y(et+v−1	NOUN
ejpam-5559	178	43	)	)	PUNCT
ejpam-5559	178	44	=	=	SYM
ejpam-5559	178	45	e(x−z)(t+v	e(x−z)(t+v	NOUN
ejpam-5559	178	46	)	)	PUNCT
ejpam-5559	178	47	∞∑	∞∑	PROPN
ejpam-5559	178	48	k=0	k=0	PUNCT
ejpam-5559	178	49	∞∑	∞∑	NUM
ejpam-5559	178	50	l=0	l=0	PROPN
ejpam-5559	178	51	bt	bt	NOUN
ejpam-5559	178	52	(	(	PUNCT
ejpam-5559	178	53	r	r	NOUN
ejpam-5559	178	54	)	)	PUNCT
ejpam-5559	178	55	k+l(z	k+l(z	NOUN
ejpam-5559	178	56	,	,	PUNCT
ejpam-5559	178	57	y;u	y;u	PROPN
ejpam-5559	178	58	,	,	PUNCT
ejpam-5559	178	59	λ	λ	PROPN
ejpam-5559	178	60	)	)	PUNCT
ejpam-5559	178	61	tk	tk	PROPN
ejpam-5559	179	1	k	k	PROPN
ejpam-5559	179	2	!	!	PUNCT
ejpam-5559	179	3	vl	vl	PROPN
ejpam-5559	179	4	l	l	PROPN
ejpam-5559	179	5	!	!	PUNCT
ejpam-5559	180	1	thus	thus	ADV
ejpam-5559	180	2	,	,	PUNCT
ejpam-5559	180	3	using	use	VERB
ejpam-5559	180	4	(	(	PUNCT
ejpam-5559	180	5	13	13	NUM
ejpam-5559	180	6	)	)	PUNCT
ejpam-5559	180	7	again	again	ADV
ejpam-5559	180	8	,	,	PUNCT
ejpam-5559	180	9	we	we	PRON
ejpam-5559	180	10	have	have	VERB
ejpam-5559	180	11	j.	j.	PROPN
ejpam-5559	180	12	ontolan	ontolan	PROPN
ejpam-5559	180	13	et	et	PROPN
ejpam-5559	180	14	al	al	PROPN
ejpam-5559	180	15	.	.	PUNCT
ejpam-5559	180	16	/	/	SYM
ejpam-5559	180	17	eur	eur	PROPN
ejpam-5559	180	18	.	.	PUNCT
ejpam-5559	181	1	j.	j.	PROPN
ejpam-5559	181	2	pure	pure	PROPN
ejpam-5559	181	3	appl	appl	PROPN
ejpam-5559	181	4	.	.	PROPN
ejpam-5559	181	5	math	math	PROPN
ejpam-5559	181	6	,	,	PUNCT
ejpam-5559	181	7	18	18	NUM
ejpam-5559	181	8	(	(	PUNCT
ejpam-5559	181	9	1	1	NUM
ejpam-5559	181	10	)	)	PUNCT
ejpam-5559	181	11	(	(	PUNCT
ejpam-5559	181	12	2025	2025	NUM
ejpam-5559	181	13	)	)	PUNCT
ejpam-5559	181	14	,	,	PUNCT
ejpam-5559	181	15	5559	5559	NUM
ejpam-5559	181	16	10	10	NUM
ejpam-5559	181	17	of	of	ADP
ejpam-5559	181	18	16	16	NUM
ejpam-5559	181	19	∑	∑	SYM
ejpam-5559	181	20	k	k	PROPN
ejpam-5559	181	21	,	,	PUNCT
ejpam-5559	181	22	l≥0	l≥0	NOUN
ejpam-5559	181	23	bt	bt	NOUN
ejpam-5559	181	24	(	(	PUNCT
ejpam-5559	181	25	r	r	NOUN
ejpam-5559	181	26	)	)	PUNCT
ejpam-5559	181	27	k+l(x	k+l(x	PROPN
ejpam-5559	181	28	,	,	PUNCT
ejpam-5559	181	29	y;u	y;u	PROPN
ejpam-5559	181	30	,	,	PUNCT
ejpam-5559	181	31	λ	λ	PROPN
ejpam-5559	181	32	)	)	PUNCT
ejpam-5559	181	33	tk	tk	PROPN
ejpam-5559	182	1	k	k	PROPN
ejpam-5559	182	2	!	!	PUNCT
ejpam-5559	182	3	vl	vl	PROPN
ejpam-5559	182	4	l	l	NOUN
ejpam-5559	182	5	!	!	PUNCT
ejpam-5559	183	1	=	=	SYM
ejpam-5559	183	2	e(x−z)(t+v	e(x−z)(t+v	PROPN
ejpam-5559	183	3	)	)	PUNCT
ejpam-5559	183	4	∑	∑	PROPN
ejpam-5559	183	5	k	k	X
ejpam-5559	183	6	,	,	PUNCT
ejpam-5559	183	7	l≥0	l≥0	NOUN
ejpam-5559	183	8	bt	bt	NOUN
ejpam-5559	183	9	(	(	PUNCT
ejpam-5559	183	10	r	r	NOUN
ejpam-5559	183	11	)	)	PUNCT
ejpam-5559	183	12	k+l(z	k+l(z	NOUN
ejpam-5559	183	13	,	,	PUNCT
ejpam-5559	183	14	y;u	y;u	PROPN
ejpam-5559	183	15	,	,	PUNCT
ejpam-5559	183	16	λ	λ	PROPN
ejpam-5559	183	17	)	)	PUNCT
ejpam-5559	183	18	tk	tk	PROPN
ejpam-5559	184	1	k	k	PROPN
ejpam-5559	184	2	!	!	PUNCT
ejpam-5559	184	3	vl	vl	PROPN
ejpam-5559	184	4	l	l	NOUN
ejpam-5559	184	5	!	!	PUNCT
ejpam-5559	185	1	=	=	PUNCT
ejpam-5559	185	2	(	(	PUNCT
ejpam-5559	185	3	∞∑	∞∑	NUM
ejpam-5559	185	4	n=0	n=0	NUM
ejpam-5559	185	5	(	(	PUNCT
ejpam-5559	185	6	x−	x−	PROPN
ejpam-5559	185	7	z)n	z)n	X
ejpam-5559	185	8	(	(	PUNCT
ejpam-5559	185	9	t+	t+	X
ejpam-5559	185	10	v)n	v)n	NOUN
ejpam-5559	185	11	n	n	X
ejpam-5559	185	12	!	!	PUNCT
ejpam-5559	185	13	)	)	PUNCT
ejpam-5559	186	1	∑	∑	X
ejpam-5559	187	1	k	k	X
ejpam-5559	187	2	,	,	PUNCT
ejpam-5559	187	3	l≥0	l≥0	NOUN
ejpam-5559	187	4	bt	bt	NOUN
ejpam-5559	187	5	(	(	PUNCT
ejpam-5559	187	6	r	r	NOUN
ejpam-5559	187	7	)	)	PUNCT
ejpam-5559	187	8	k+l(z	k+l(z	NOUN
ejpam-5559	187	9	,	,	PUNCT
ejpam-5559	187	10	y;u	y;u	PROPN
ejpam-5559	187	11	,	,	PUNCT
ejpam-5559	187	12	λ	λ	PROPN
ejpam-5559	187	13	)	)	PUNCT
ejpam-5559	187	14	tk	tk	PROPN
ejpam-5559	187	15	k	k	PROPN
ejpam-5559	187	16	!	!	PUNCT
ejpam-5559	187	17	vl	vl	PROPN
ejpam-5559	188	1	l	l	NOUN
ejpam-5559	188	2	!	!	PUNCT
ejpam-5559	189	1			PROPN
ejpam-5559	189	2	=	=	SYM
ejpam-5559	189	3			PROPN
ejpam-5559	189	4	∑	∑	PUNCT
ejpam-5559	189	5	n	n	CCONJ
ejpam-5559	189	6	,	,	PUNCT
ejpam-5559	189	7	m≥0	m≥0	PROPN
ejpam-5559	189	8	(	(	PUNCT
ejpam-5559	189	9	x−	x−	PROPN
ejpam-5559	189	10	z)n+m	z)n+m	PROPN
ejpam-5559	189	11	tn	tn	PROPN
ejpam-5559	189	12	n	n	PROPN
ejpam-5559	189	13	!	!	PUNCT
ejpam-5559	189	14	vm	vm	PROPN
ejpam-5559	189	15	m	m	PROPN
ejpam-5559	189	16	!	!	PUNCT
ejpam-5559	189	17	∑	∑	PROPN
ejpam-5559	190	1	k	k	NOUN
ejpam-5559	190	2	,	,	PUNCT
ejpam-5559	190	3	l≥0	l≥0	PROPN
ejpam-5559	190	4	bt	bt	NOUN
ejpam-5559	190	5	(	(	PUNCT
ejpam-5559	190	6	r	r	NOUN
ejpam-5559	190	7	)	)	PUNCT
ejpam-5559	190	8	k+l(z	k+l(z	NOUN
ejpam-5559	190	9	,	,	PUNCT
ejpam-5559	190	10	y;u	y;u	PROPN
ejpam-5559	190	11	,	,	PUNCT
ejpam-5559	190	12	λ	λ	PROPN
ejpam-5559	190	13	)	)	PUNCT
ejpam-5559	190	14	tk	tk	PROPN
ejpam-5559	191	1	k	k	PROPN
ejpam-5559	191	2	!	!	PUNCT
ejpam-5559	191	3	vl	vl	PROPN
ejpam-5559	191	4	l	l	NOUN
ejpam-5559	191	5	!	!	PUNCT
ejpam-5559	192	1			PROPN
ejpam-5559	192	2	=	=	SYM
ejpam-5559	192	3	∑	∑	PUNCT
ejpam-5559	192	4	k	k	X
ejpam-5559	192	5	,	,	PUNCT
ejpam-5559	192	6	l≥0	l≥0	NOUN
ejpam-5559	192	7			PUNCT
ejpam-5559	192	8	k	k	NOUN
ejpam-5559	192	9	,	,	PUNCT
ejpam-5559	192	10	l∑	l∑	PROPN
ejpam-5559	193	1	k	k	X
ejpam-5559	193	2	,	,	PUNCT
ejpam-5559	193	3	m=0	m=0	PROPN
ejpam-5559	193	4	(	(	PUNCT
ejpam-5559	193	5	k	k	NOUN
ejpam-5559	193	6	n	n	PROPN
ejpam-5559	193	7	)	)	PUNCT
ejpam-5559	193	8	(	(	PUNCT
ejpam-5559	193	9	l	l	NOUN
ejpam-5559	193	10	m	m	VERB
ejpam-5559	193	11	)	)	PUNCT
ejpam-5559	193	12	(	(	PUNCT
ejpam-5559	193	13	x−	x−	PROPN
ejpam-5559	193	14	z)n+m	z)n+m	PROPN
ejpam-5559	193	15	bt	bt	PROPN
ejpam-5559	193	16	(	(	PUNCT
ejpam-5559	193	17	r	r	NOUN
ejpam-5559	193	18	)	)	PUNCT
ejpam-5559	193	19	k+l(z	k+l(z	NOUN
ejpam-5559	193	20	,	,	PUNCT
ejpam-5559	193	21	y;u	y;u	PROPN
ejpam-5559	193	22	,	,	PUNCT
ejpam-5559	193	23	λ	λ	NOUN
ejpam-5559	193	24	)	)	PUNCT
ejpam-5559	193	25			PROPN
ejpam-5559	193	26	tk	tk	PROPN
ejpam-5559	193	27	k	k	PROPN
ejpam-5559	193	28	!	!	PUNCT
ejpam-5559	193	29	vl	vl	PROPN
ejpam-5559	193	30	l	l	PROPN
ejpam-5559	193	31	!	!	PUNCT
ejpam-5559	193	32	.	.	PUNCT
ejpam-5559	194	1	comparing	compare	VERB
ejpam-5559	194	2	coefficients	coefficient	NOUN
ejpam-5559	194	3	,	,	PUNCT
ejpam-5559	194	4	we	we	PRON
ejpam-5559	194	5	then	then	ADV
ejpam-5559	194	6	have	have	VERB
ejpam-5559	194	7	∑	∑	PROPN
ejpam-5559	194	8	k	k	X
ejpam-5559	194	9	,	,	PUNCT
ejpam-5559	194	10	l≥0	l≥0	NOUN
ejpam-5559	194	11	bt	bt	NOUN
ejpam-5559	194	12	(	(	PUNCT
ejpam-5559	194	13	r	r	NOUN
ejpam-5559	194	14	)	)	PUNCT
ejpam-5559	194	15	k+l(x	k+l(x	PROPN
ejpam-5559	194	16	,	,	PUNCT
ejpam-5559	194	17	y;u	y;u	PROPN
ejpam-5559	194	18	,	,	PUNCT
ejpam-5559	194	19	λ	λ	PROPN
ejpam-5559	194	20	)	)	PUNCT
ejpam-5559	194	21	=	=	SYM
ejpam-5559	195	1	k	k	NOUN
ejpam-5559	195	2	,	,	PUNCT
ejpam-5559	195	3	l∑	l∑	PROPN
ejpam-5559	195	4	n	n	CCONJ
ejpam-5559	195	5	,	,	PUNCT
ejpam-5559	195	6	m=0	m=0	PROPN
ejpam-5559	195	7	(	(	PUNCT
ejpam-5559	195	8	k	k	NOUN
ejpam-5559	195	9	n	n	PROPN
ejpam-5559	195	10	)	)	PUNCT
ejpam-5559	195	11	(	(	PUNCT
ejpam-5559	195	12	l	l	NOUN
ejpam-5559	195	13	m	m	VERB
ejpam-5559	195	14	)	)	PUNCT
ejpam-5559	195	15	(	(	PUNCT
ejpam-5559	195	16	x−	x−	PROPN
ejpam-5559	195	17	z)n+m	z)n+m	PROPN
ejpam-5559	195	18	btk+l−n−m(z	btk+l−n−m(z	PROPN
ejpam-5559	195	19	,	,	PUNCT
ejpam-5559	195	20	y;u	y;u	PROPN
ejpam-5559	195	21	,	,	PUNCT
ejpam-5559	195	22	λ	λ	PROPN
ejpam-5559	195	23	)	)	PUNCT
ejpam-5559	195	24	,	,	PUNCT
ejpam-5559	195	25	which	which	PRON
ejpam-5559	195	26	proves	prove	VERB
ejpam-5559	195	27	our	our	PRON
ejpam-5559	195	28	next	next	ADJ
ejpam-5559	195	29	theorem	theorem	NOUN
ejpam-5559	195	30	.	.	PUNCT
ejpam-5559	195	31	theorem	theorem	VERB
ejpam-5559	195	32	6	6	NUM
ejpam-5559	195	33	.	.	PUNCT
ejpam-5559	196	1	the	the	DET
ejpam-5559	196	2	bivariate	bivariate	ADJ
ejpam-5559	196	3	bell	bell	NOUN
ejpam-5559	196	4	-	-	PUNCT
ejpam-5559	196	5	based	base	VERB
ejpam-5559	196	6	apostol	apostol	NOUN
ejpam-5559	196	7	-	-	PUNCT
ejpam-5559	196	8	frobenius	frobenius	NOUN
ejpam-5559	196	9	-	-	PUNCT
ejpam-5559	196	10	type	type	NOUN
ejpam-5559	196	11	tangent	tangent	NOUN
ejpam-5559	196	12	polynomials	polynomial	NOUN
ejpam-5559	196	13	of	of	ADP
ejpam-5559	196	14	higher	high	ADJ
ejpam-5559	196	15	order	order	NOUN
ejpam-5559	196	16	bt	bt	NOUN
ejpam-5559	196	17	(	(	PUNCT
ejpam-5559	196	18	r	r	NOUN
ejpam-5559	196	19	)	)	PUNCT
ejpam-5559	196	20	n	n	NOUN
ejpam-5559	196	21	(	(	PUNCT
ejpam-5559	196	22	x	x	X
ejpam-5559	196	23	,	,	PUNCT
ejpam-5559	196	24	y;u	y;u	PROPN
ejpam-5559	196	25	,	,	PUNCT
ejpam-5559	196	26	λ	λ	NOUN
ejpam-5559	196	27	)	)	PUNCT
ejpam-5559	196	28	satisfy	satisfy	VERB
ejpam-5559	196	29	the	the	DET
ejpam-5559	196	30	summation	summation	NOUN
ejpam-5559	196	31	formula	formula	NOUN
ejpam-5559	196	32	∑	∑	PROPN
ejpam-5559	196	33	k	k	NOUN
ejpam-5559	196	34	,	,	PUNCT
ejpam-5559	196	35	l≥0	l≥0	NOUN
ejpam-5559	196	36	bt	bt	NOUN
ejpam-5559	196	37	(	(	PUNCT
ejpam-5559	196	38	r	r	NOUN
ejpam-5559	196	39	)	)	PUNCT
ejpam-5559	196	40	k+l(x	k+l(x	PROPN
ejpam-5559	196	41	,	,	PUNCT
ejpam-5559	196	42	y;u	y;u	PROPN
ejpam-5559	196	43	,	,	PUNCT
ejpam-5559	196	44	λ	λ	PROPN
ejpam-5559	196	45	)	)	PUNCT
ejpam-5559	196	46	=	=	SYM
ejpam-5559	197	1	k	k	NOUN
ejpam-5559	197	2	,	,	PUNCT
ejpam-5559	197	3	l∑	l∑	PROPN
ejpam-5559	197	4	n	n	CCONJ
ejpam-5559	197	5	,	,	PUNCT
ejpam-5559	197	6	m=0	m=0	PROPN
ejpam-5559	197	7	(	(	PUNCT
ejpam-5559	197	8	k	k	NOUN
ejpam-5559	197	9	n	n	PROPN
ejpam-5559	197	10	)	)	PUNCT
ejpam-5559	197	11	(	(	PUNCT
ejpam-5559	197	12	l	l	NOUN
ejpam-5559	197	13	m	m	VERB
ejpam-5559	197	14	)	)	PUNCT
ejpam-5559	197	15	(	(	PUNCT
ejpam-5559	197	16	x−	x−	PROPN
ejpam-5559	197	17	z)n+m	z)n+m	PROPN
ejpam-5559	197	18	btk+l−n−m(z	btk+l−n−m(z	PROPN
ejpam-5559	197	19	,	,	PUNCT
ejpam-5559	197	20	y;u	y;u	PROPN
ejpam-5559	197	21	,	,	PUNCT
ejpam-5559	197	22	λ	λ	PROPN
ejpam-5559	197	23	)	)	PUNCT
ejpam-5559	197	24	.	.	PUNCT
ejpam-5559	198	1	(	(	PUNCT
ejpam-5559	198	2	24	24	NUM
ejpam-5559	198	3	)	)	PUNCT
ejpam-5559	198	4	the	the	DET
ejpam-5559	198	5	next	next	ADJ
ejpam-5559	198	6	result	result	NOUN
ejpam-5559	198	7	provides	provide	VERB
ejpam-5559	198	8	the	the	DET
ejpam-5559	198	9	difference	difference	NOUN
ejpam-5559	198	10	when	when	SCONJ
ejpam-5559	198	11	x	x	X
ejpam-5559	198	12	in	in	ADP
ejpam-5559	198	13	bt	bt	PROPN
ejpam-5559	198	14	(	(	PUNCT
ejpam-5559	198	15	r	r	NOUN
ejpam-5559	198	16	)	)	PUNCT
ejpam-5559	198	17	n	n	NOUN
ejpam-5559	198	18	(	(	PUNCT
ejpam-5559	198	19	x	x	X
ejpam-5559	198	20	,	,	PUNCT
ejpam-5559	198	21	y;u	y;u	PROPN
ejpam-5559	198	22	,	,	PUNCT
ejpam-5559	198	23	λ	λ	PROPN
ejpam-5559	198	24	)	)	PUNCT
ejpam-5559	198	25	is	be	AUX
ejpam-5559	198	26	shifted	shift	VERB
ejpam-5559	198	27	by	by	ADP
ejpam-5559	198	28	1	1	NUM
ejpam-5559	198	29	.	.	PUNCT
ejpam-5559	198	30	theorem	theorem	VERB
ejpam-5559	198	31	7	7	NUM
ejpam-5559	198	32	.	.	NOUN
ejpam-5559	198	33	for	for	ADP
ejpam-5559	198	34	n	n	PRON
ejpam-5559	198	35	≥	≥	NUM
ejpam-5559	198	36	1	1	NUM
ejpam-5559	198	37	,	,	PUNCT
ejpam-5559	198	38	the	the	DET
ejpam-5559	198	39	difference	difference	NOUN
ejpam-5559	198	40	bt	bt	NOUN
ejpam-5559	198	41	(	(	PUNCT
ejpam-5559	198	42	r	r	NOUN
ejpam-5559	198	43	)	)	PUNCT
ejpam-5559	198	44	n	n	CCONJ
ejpam-5559	198	45	(	(	PUNCT
ejpam-5559	198	46	x+	x+	PROPN
ejpam-5559	198	47	1	1	NUM
ejpam-5559	198	48	,	,	PUNCT
ejpam-5559	198	49	y;u	y;u	PROPN
ejpam-5559	198	50	,	,	PUNCT
ejpam-5559	198	51	λ)−b	λ)−b	PROPN
ejpam-5559	198	52	t	t	NOUN
ejpam-5559	198	53	(	(	PUNCT
ejpam-5559	198	54	r	r	NOUN
ejpam-5559	198	55	)	)	PUNCT
ejpam-5559	198	56	n	n	NOUN
ejpam-5559	198	57	(	(	PUNCT
ejpam-5559	198	58	x	x	X
ejpam-5559	198	59	,	,	PUNCT
ejpam-5559	198	60	y;u	y;u	PROPN
ejpam-5559	198	61	,	,	PUNCT
ejpam-5559	198	62	λ	λ	PROPN
ejpam-5559	198	63	)	)	PUNCT
ejpam-5559	198	64	is	be	AUX
ejpam-5559	198	65	given	give	VERB
ejpam-5559	198	66	by	by	ADP
ejpam-5559	198	67	the	the	DET
ejpam-5559	198	68	difference	difference	NOUN
ejpam-5559	198	69	formula	formula	NOUN
ejpam-5559	199	1	bt	bt	INTJ
ejpam-5559	199	2	(	(	PUNCT
ejpam-5559	199	3	r	r	NOUN
ejpam-5559	199	4	)	)	PUNCT
ejpam-5559	199	5	n	n	CCONJ
ejpam-5559	199	6	(	(	PUNCT
ejpam-5559	199	7	x+	x+	PROPN
ejpam-5559	199	8	1	1	NUM
ejpam-5559	199	9	,	,	PUNCT
ejpam-5559	199	10	y;u	y;u	PROPN
ejpam-5559	199	11	,	,	PUNCT
ejpam-5559	199	12	λ)−	λ)−	PROPN
ejpam-5559	199	13	bt	bt	PROPN
ejpam-5559	199	14	(	(	PUNCT
ejpam-5559	199	15	r	r	NOUN
ejpam-5559	199	16	)	)	PUNCT
ejpam-5559	199	17	n	n	NOUN
ejpam-5559	199	18	(	(	PUNCT
ejpam-5559	199	19	x	x	X
ejpam-5559	199	20	,	,	PUNCT
ejpam-5559	199	21	y;u	y;u	PROPN
ejpam-5559	199	22	,	,	PUNCT
ejpam-5559	199	23	λ	λ	NOUN
ejpam-5559	199	24	)	)	PUNCT
ejpam-5559	199	25	=	=	SYM
ejpam-5559	199	26	n−1∑	n−1∑	PROPN
ejpam-5559	199	27	k=0	k=0	PROPN
ejpam-5559	199	28	(	(	PUNCT
ejpam-5559	199	29	n	n	X
ejpam-5559	199	30	k	k	NOUN
ejpam-5559	199	31	)	)	PUNCT
ejpam-5559	199	32	bt	bt	PROPN
ejpam-5559	199	33	(	(	PUNCT
ejpam-5559	199	34	r	r	NOUN
ejpam-5559	199	35	)	)	PUNCT
ejpam-5559	199	36	k	k	NOUN
ejpam-5559	199	37	(	(	PUNCT
ejpam-5559	199	38	x	x	NOUN
ejpam-5559	199	39	,	,	PUNCT
ejpam-5559	199	40	y;u	y;u	PROPN
ejpam-5559	199	41	,	,	PUNCT
ejpam-5559	199	42	λ	λ	PROPN
ejpam-5559	199	43	)	)	PUNCT
ejpam-5559	199	44	.	.	PUNCT
ejpam-5559	200	1	(	(	PUNCT
ejpam-5559	200	2	25	25	NUM
ejpam-5559	200	3	)	)	PUNCT
ejpam-5559	200	4	proof	proof	NOUN
ejpam-5559	200	5	.	.	PUNCT
ejpam-5559	201	1	∞∑	∞∑	PRON
ejpam-5559	201	2	n=0	n=0	NUM
ejpam-5559	201	3	bt	bt	NOUN
ejpam-5559	201	4	(	(	PUNCT
ejpam-5559	201	5	r	r	NOUN
ejpam-5559	201	6	)	)	PUNCT
ejpam-5559	201	7	n	n	CCONJ
ejpam-5559	201	8	(	(	PUNCT
ejpam-5559	201	9	x+	x+	PROPN
ejpam-5559	201	10	1	1	NUM
ejpam-5559	201	11	,	,	PUNCT
ejpam-5559	201	12	y;u	y;u	PROPN
ejpam-5559	201	13	,	,	PUNCT
ejpam-5559	201	14	λ	λ	PROPN
ejpam-5559	201	15	)	)	PUNCT
ejpam-5559	201	16	tn	tn	PROPN
ejpam-5559	201	17	n	n	PROPN
ejpam-5559	201	18	!	!	PUNCT
ejpam-5559	202	1	−	−	PROPN
ejpam-5559	203	1	∞∑	∞∑	PRON
ejpam-5559	203	2	n=0	n=0	NUM
ejpam-5559	203	3	bt	bt	NOUN
ejpam-5559	203	4	(	(	PUNCT
ejpam-5559	203	5	r	r	NOUN
ejpam-5559	203	6	)	)	PUNCT
ejpam-5559	203	7	n	n	NOUN
ejpam-5559	203	8	(	(	PUNCT
ejpam-5559	203	9	x	x	X
ejpam-5559	203	10	,	,	PUNCT
ejpam-5559	203	11	y;u	y;u	PROPN
ejpam-5559	203	12	,	,	PUNCT
ejpam-5559	203	13	λ	λ	PROPN
ejpam-5559	203	14	)	)	PUNCT
ejpam-5559	203	15	tn	tn	PROPN
ejpam-5559	203	16	n	n	PROPN
ejpam-5559	203	17	!	!	PUNCT
ejpam-5559	203	18	=	=	PUNCT
ejpam-5559	204	1	(	(	PUNCT
ejpam-5559	204	2	(	(	PUNCT
ejpam-5559	204	3	1−	1−	NUM
ejpam-5559	204	4	u	u	NOUN
ejpam-5559	204	5	)	)	PUNCT
ejpam-5559	204	6	λe2	λe2	PROPN
ejpam-5559	204	7	t	t	NOUN
ejpam-5559	204	8	−	−	PROPN
ejpam-5559	204	9	u	u	NOUN
ejpam-5559	204	10	)	)	PUNCT
ejpam-5559	204	11	r	r	NOUN
ejpam-5559	204	12	e(x+1)t+y(et−1	e(x+1)t+y(et−1	NOUN
ejpam-5559	204	13	)	)	PUNCT
ejpam-5559	204	14	−	−	PROPN
ejpam-5559	204	15	(	(	PUNCT
ejpam-5559	204	16	(	(	PUNCT
ejpam-5559	204	17	1−	1−	NUM
ejpam-5559	204	18	u	u	NOUN
ejpam-5559	204	19	)	)	PUNCT
ejpam-5559	204	20	λe2	λe2	PROPN
ejpam-5559	204	21	t	t	NOUN
ejpam-5559	204	22	−	−	PROPN
ejpam-5559	204	23	u	u	PROPN
ejpam-5559	204	24	)	)	PUNCT
ejpam-5559	204	25	r	r	NOUN
ejpam-5559	204	26	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	204	27	)	)	PUNCT
ejpam-5559	204	28	j.	j.	PROPN
ejpam-5559	204	29	ontolan	ontolan	PROPN
ejpam-5559	204	30	et	et	PROPN
ejpam-5559	204	31	al	al	PROPN
ejpam-5559	204	32	.	.	PUNCT
ejpam-5559	204	33	/	/	SYM
ejpam-5559	204	34	eur	eur	PROPN
ejpam-5559	204	35	.	.	PUNCT
ejpam-5559	205	1	j.	j.	PROPN
ejpam-5559	205	2	pure	pure	PROPN
ejpam-5559	205	3	appl	appl	PROPN
ejpam-5559	205	4	.	.	PROPN
ejpam-5559	205	5	math	math	PROPN
ejpam-5559	205	6	,	,	PUNCT
ejpam-5559	205	7	18	18	NUM
ejpam-5559	205	8	(	(	PUNCT
ejpam-5559	205	9	1	1	NUM
ejpam-5559	205	10	)	)	PUNCT
ejpam-5559	205	11	(	(	PUNCT
ejpam-5559	205	12	2025	2025	NUM
ejpam-5559	205	13	)	)	PUNCT
ejpam-5559	205	14	,	,	PUNCT
ejpam-5559	205	15	5559	5559	NUM
ejpam-5559	205	16	11	11	NUM
ejpam-5559	205	17	of	of	ADP
ejpam-5559	205	18	16	16	NUM
ejpam-5559	205	19	=	=	SYM
ejpam-5559	205	20	(	(	PUNCT
ejpam-5559	205	21	(	(	PUNCT
ejpam-5559	205	22	1−	1−	NUM
ejpam-5559	205	23	u	u	NOUN
ejpam-5559	205	24	)	)	PUNCT
ejpam-5559	205	25	λe2	λe2	PROPN
ejpam-5559	205	26	t	t	NOUN
ejpam-5559	205	27	−	−	PROPN
ejpam-5559	205	28	u	u	NOUN
ejpam-5559	205	29	)	)	PUNCT
ejpam-5559	205	30	r	r	NOUN
ejpam-5559	205	31	ext+y(et−1)(et	ext+y(et−1)(et	NOUN
ejpam-5559	205	32	−	−	ADP
ejpam-5559	205	33	1	1	NUM
ejpam-5559	205	34	)	)	PUNCT
ejpam-5559	205	35	=	=	NOUN
ejpam-5559	205	36	(	(	PUNCT
ejpam-5559	205	37	∞∑	∞∑	PRON
ejpam-5559	205	38	n=0	n=0	NUM
ejpam-5559	205	39	bt	bt	NOUN
ejpam-5559	205	40	(	(	PUNCT
ejpam-5559	205	41	r	r	NOUN
ejpam-5559	205	42	)	)	PUNCT
ejpam-5559	205	43	n	n	NOUN
ejpam-5559	205	44	(	(	PUNCT
ejpam-5559	205	45	x	x	X
ejpam-5559	205	46	,	,	PUNCT
ejpam-5559	205	47	y;u	y;u	PROPN
ejpam-5559	205	48	,	,	PUNCT
ejpam-5559	205	49	λ	λ	PROPN
ejpam-5559	205	50	)	)	PUNCT
ejpam-5559	205	51	tn	tn	PROPN
ejpam-5559	205	52	n	n	PROPN
ejpam-5559	205	53	!	!	PUNCT
ejpam-5559	205	54	)	)	PUNCT
ejpam-5559	206	1	∑	∑	NOUN
ejpam-5559	206	2	n≥0	n≥0	PROPN
ejpam-5559	206	3	tn+1	tn+1	NOUN
ejpam-5559	206	4	(	(	PUNCT
ejpam-5559	206	5	n+	n+	NOUN
ejpam-5559	206	6	1	1	NUM
ejpam-5559	206	7	)	)	PUNCT
ejpam-5559	206	8	!	!	PUNCT
ejpam-5559	207	1			PROPN
ejpam-5559	208	1	=	=	PUNCT
ejpam-5559	209	1	∞∑	∞∑	NUM
ejpam-5559	209	2	n=0	n=0	PRON
ejpam-5559	209	3	{	{	PUNCT
ejpam-5559	209	4	n∑	n∑	NOUN
ejpam-5559	209	5	k=0	k=0	PROPN
ejpam-5559	209	6	(	(	PUNCT
ejpam-5559	209	7	n+	n+	ADP
ejpam-5559	209	8	1	1	NUM
ejpam-5559	209	9	k	k	X
ejpam-5559	209	10	)	)	PUNCT
ejpam-5559	209	11	bt	bt	NOUN
ejpam-5559	209	12	(	(	PUNCT
ejpam-5559	209	13	r	r	NOUN
ejpam-5559	209	14	)	)	PUNCT
ejpam-5559	209	15	k	k	NOUN
ejpam-5559	209	16	(	(	PUNCT
ejpam-5559	209	17	x	x	NOUN
ejpam-5559	209	18	,	,	PUNCT
ejpam-5559	209	19	y;u	y;u	PROPN
ejpam-5559	209	20	,	,	PUNCT
ejpam-5559	209	21	λ	λ	NOUN
ejpam-5559	209	22	)	)	PUNCT
ejpam-5559	209	23	}	}	PUNCT
ejpam-5559	209	24	tn+1	tn+1	PROPN
ejpam-5559	209	25	(	(	PUNCT
ejpam-5559	209	26	n+	n+	NOUN
ejpam-5559	209	27	1	1	NUM
ejpam-5559	209	28	)	)	PUNCT
ejpam-5559	209	29	!	!	PUNCT
ejpam-5559	210	1	=	=	PUNCT
ejpam-5559	211	1	∞∑	∞∑	NUM
ejpam-5559	211	2	n=1	n=1	PROPN
ejpam-5559	211	3	{	{	PUNCT
ejpam-5559	211	4	n−1∑	n−1∑	PROPN
ejpam-5559	211	5	k=0	k=0	PROPN
ejpam-5559	211	6	(	(	PUNCT
ejpam-5559	211	7	n	n	X
ejpam-5559	211	8	k	k	NOUN
ejpam-5559	211	9	)	)	PUNCT
ejpam-5559	211	10	bt	bt	PROPN
ejpam-5559	211	11	(	(	PUNCT
ejpam-5559	211	12	r	r	NOUN
ejpam-5559	211	13	)	)	PUNCT
ejpam-5559	211	14	k	k	NOUN
ejpam-5559	211	15	(	(	PUNCT
ejpam-5559	211	16	x	x	NOUN
ejpam-5559	211	17	,	,	PUNCT
ejpam-5559	211	18	y;u	y;u	PROPN
ejpam-5559	211	19	,	,	PUNCT
ejpam-5559	211	20	λ	λ	NOUN
ejpam-5559	211	21	)	)	PUNCT
ejpam-5559	211	22	}	}	PUNCT
ejpam-5559	211	23	tn	tn	PROPN
ejpam-5559	211	24	n	n	X
ejpam-5559	211	25	!	!	PUNCT
ejpam-5559	211	26	.	.	PUNCT
ejpam-5559	212	1	comparing	compare	VERB
ejpam-5559	212	2	coefficients	coefficient	NOUN
ejpam-5559	212	3	,	,	PUNCT
ejpam-5559	212	4	bt	bt	X
ejpam-5559	212	5	(	(	PUNCT
ejpam-5559	212	6	r	r	NOUN
ejpam-5559	212	7	)	)	PUNCT
ejpam-5559	212	8	n	n	CCONJ
ejpam-5559	212	9	(	(	PUNCT
ejpam-5559	212	10	x+	x+	PROPN
ejpam-5559	212	11	1	1	NUM
ejpam-5559	212	12	,	,	PUNCT
ejpam-5559	212	13	y;u	y;u	PROPN
ejpam-5559	212	14	,	,	PUNCT
ejpam-5559	212	15	λ)−	λ)−	PROPN
ejpam-5559	212	16	bt	bt	PROPN
ejpam-5559	212	17	(	(	PUNCT
ejpam-5559	212	18	r	r	NOUN
ejpam-5559	212	19	)	)	PUNCT
ejpam-5559	212	20	k	k	NOUN
ejpam-5559	212	21	(	(	PUNCT
ejpam-5559	212	22	x	x	NOUN
ejpam-5559	212	23	,	,	PUNCT
ejpam-5559	212	24	y;u	y;u	PROPN
ejpam-5559	212	25	,	,	PUNCT
ejpam-5559	212	26	λ	λ	NOUN
ejpam-5559	212	27	)	)	PUNCT
ejpam-5559	212	28	=	=	SYM
ejpam-5559	212	29	n−1∑	n−1∑	PROPN
ejpam-5559	212	30	k=0	k=0	PROPN
ejpam-5559	212	31	(	(	PUNCT
ejpam-5559	212	32	n	n	X
ejpam-5559	212	33	k	k	NOUN
ejpam-5559	212	34	)	)	PUNCT
ejpam-5559	212	35	bt	bt	PROPN
ejpam-5559	212	36	(	(	PUNCT
ejpam-5559	212	37	r	r	NOUN
ejpam-5559	212	38	)	)	PUNCT
ejpam-5559	212	39	k	k	NOUN
ejpam-5559	212	40	(	(	PUNCT
ejpam-5559	212	41	x	x	NOUN
ejpam-5559	212	42	,	,	PUNCT
ejpam-5559	212	43	y;u	y;u	PROPN
ejpam-5559	212	44	,	,	PUNCT
ejpam-5559	212	45	λ	λ	NOUN
ejpam-5559	212	46	)	)	PUNCT
ejpam-5559	212	47	as	as	SCONJ
ejpam-5559	212	48	desired	desire	VERB
ejpam-5559	212	49	.	.	PUNCT
ejpam-5559	213	1	stirling	stirling	NOUN
ejpam-5559	213	2	number	number	NOUN
ejpam-5559	213	3	of	of	ADP
ejpam-5559	213	4	second	second	ADJ
ejpam-5559	213	5	kind	kind	NOUN
ejpam-5559	213	6	and	and	CCONJ
ejpam-5559	213	7	bivariate	bivariate	ADJ
ejpam-5559	213	8	bell	bell	NOUN
ejpam-5559	213	9	polynomials	polynomial	NOUN
ejpam-5559	213	10	in	in	ADP
ejpam-5559	213	11	this	this	DET
ejpam-5559	213	12	subsection	subsection	NOUN
ejpam-5559	213	13	,	,	PUNCT
ejpam-5559	213	14	we	we	PRON
ejpam-5559	213	15	derive	derive	VERB
ejpam-5559	213	16	some	some	DET
ejpam-5559	213	17	formulas	formula	NOUN
ejpam-5559	213	18	displaying	display	VERB
ejpam-5559	213	19	relationship	relationship	NOUN
ejpam-5559	213	20	of	of	ADP
ejpam-5559	213	21	bt	bt	PROPN
ejpam-5559	213	22	(	(	PUNCT
ejpam-5559	213	23	r	r	NOUN
ejpam-5559	213	24	)	)	PUNCT
ejpam-5559	213	25	n	n	NOUN
ejpam-5559	213	26	(	(	PUNCT
ejpam-5559	213	27	x	x	X
ejpam-5559	213	28	,	,	PUNCT
ejpam-5559	213	29	y;u	y;u	PROPN
ejpam-5559	213	30	,	,	PUNCT
ejpam-5559	213	31	λ	λ	PROPN
ejpam-5559	213	32	)	)	PUNCT
ejpam-5559	213	33	with	with	ADP
ejpam-5559	213	34	the	the	DET
ejpam-5559	213	35	stirling	stirling	NOUN
ejpam-5559	213	36	numbers	number	NOUN
ejpam-5559	213	37	of	of	ADP
ejpam-5559	213	38	second	second	ADJ
ejpam-5559	213	39	kind	kind	NOUN
ejpam-5559	213	40	and	and	CCONJ
ejpam-5559	213	41	bivariate	bivariate	ADJ
ejpam-5559	213	42	bell	bell	NOUN
ejpam-5559	213	43	polynomials	polynomial	NOUN
ejpam-5559	213	44	.	.	PUNCT
ejpam-5559	214	1	theorem	theorem	VERB
ejpam-5559	214	2	8	8	NUM
ejpam-5559	214	3	.	.	PUNCT
ejpam-5559	215	1	the	the	DET
ejpam-5559	215	2	bivariate	bivariate	ADJ
ejpam-5559	215	3	bell	bell	NOUN
ejpam-5559	215	4	-	-	PUNCT
ejpam-5559	215	5	based	base	VERB
ejpam-5559	215	6	apostol	apostol	NOUN
ejpam-5559	215	7	-	-	PUNCT
ejpam-5559	215	8	frobenius	frobenius	NOUN
ejpam-5559	215	9	-	-	PUNCT
ejpam-5559	215	10	type	type	NOUN
ejpam-5559	215	11	tangent	tangent	NOUN
ejpam-5559	215	12	polynomials	polynomial	NOUN
ejpam-5559	215	13	of	of	ADP
ejpam-5559	215	14	higher	high	ADJ
ejpam-5559	215	15	order	order	NOUN
ejpam-5559	215	16	bt	bt	NOUN
ejpam-5559	215	17	(	(	PUNCT
ejpam-5559	215	18	r	r	NOUN
ejpam-5559	215	19	)	)	PUNCT
ejpam-5559	215	20	n	n	NOUN
ejpam-5559	215	21	(	(	PUNCT
ejpam-5559	215	22	x	x	X
ejpam-5559	215	23	,	,	PUNCT
ejpam-5559	215	24	y;u	y;u	PROPN
ejpam-5559	215	25	,	,	PUNCT
ejpam-5559	215	26	λ	λ	NOUN
ejpam-5559	215	27	)	)	PUNCT
ejpam-5559	215	28	satisfy	satisfy	VERB
ejpam-5559	215	29	the	the	DET
ejpam-5559	215	30	summation	summation	NOUN
ejpam-5559	215	31	formula	formula	NOUN
ejpam-5559	215	32	bt	bt	INTJ
ejpam-5559	215	33	(	(	PUNCT
ejpam-5559	215	34	r	r	NOUN
ejpam-5559	215	35	)	)	PUNCT
ejpam-5559	215	36	n	n	NOUN
ejpam-5559	215	37	(	(	PUNCT
ejpam-5559	215	38	x	x	X
ejpam-5559	215	39	,	,	PUNCT
ejpam-5559	215	40	y;u	y;u	PROPN
ejpam-5559	215	41	,	,	PUNCT
ejpam-5559	215	42	λ	λ	NOUN
ejpam-5559	215	43	)	)	PUNCT
ejpam-5559	215	44	=	=	SYM
ejpam-5559	216	1	n∑	n∑	PROPN
ejpam-5559	216	2	k=0	k=0	PROPN
ejpam-5559	216	3	k∑	k∑	PROPN
ejpam-5559	216	4	j=0	j=0	PROPN
ejpam-5559	216	5	(	(	PUNCT
ejpam-5559	216	6	n	n	X
ejpam-5559	216	7	k	k	NOUN
ejpam-5559	216	8	)	)	PUNCT
ejpam-5559	216	9	(	(	PUNCT
ejpam-5559	216	10	x)js(k	x)js(k	X
ejpam-5559	216	11	,	,	PUNCT
ejpam-5559	216	12	j)bt	j)bt	PROPN
ejpam-5559	216	13	(	(	PUNCT
ejpam-5559	216	14	r	r	NOUN
ejpam-5559	216	15	)	)	PUNCT
ejpam-5559	216	16	n−k(y;u	n−k(y;u	ADJ
ejpam-5559	216	17	,	,	PUNCT
ejpam-5559	216	18	λ	λ	X
ejpam-5559	216	19	)	)	PUNCT
ejpam-5559	216	20	.	.	PUNCT
ejpam-5559	217	1	(	(	PUNCT
ejpam-5559	217	2	26	26	NUM
ejpam-5559	217	3	)	)	PUNCT
ejpam-5559	217	4	proof	proof	NOUN
ejpam-5559	217	5	.	.	PUNCT
ejpam-5559	218	1	using	use	VERB
ejpam-5559	218	2	(	(	PUNCT
ejpam-5559	218	3	5	5	NUM
ejpam-5559	218	4	)	)	PUNCT
ejpam-5559	218	5	,	,	PUNCT
ejpam-5559	218	6	we	we	PRON
ejpam-5559	218	7	write	write	VERB
ejpam-5559	218	8	∞∑	∞∑	PRON
ejpam-5559	218	9	n=0	n=0	NUM
ejpam-5559	218	10	bt	bt	NOUN
ejpam-5559	218	11	(	(	PUNCT
ejpam-5559	218	12	r	r	NOUN
ejpam-5559	218	13	)	)	PUNCT
ejpam-5559	218	14	n	n	NOUN
ejpam-5559	218	15	(	(	PUNCT
ejpam-5559	218	16	x	x	X
ejpam-5559	218	17	,	,	PUNCT
ejpam-5559	218	18	y;u	y;u	PROPN
ejpam-5559	218	19	,	,	PUNCT
ejpam-5559	218	20	λ	λ	PROPN
ejpam-5559	218	21	)	)	PUNCT
ejpam-5559	218	22	tn	tn	PROPN
ejpam-5559	218	23	n	n	PROPN
ejpam-5559	218	24	!	!	PUNCT
ejpam-5559	219	1	=	=	PUNCT
ejpam-5559	219	2	(	(	PUNCT
ejpam-5559	219	3	(	(	PUNCT
ejpam-5559	219	4	1−	1−	NUM
ejpam-5559	219	5	u	u	NOUN
ejpam-5559	219	6	)	)	PUNCT
ejpam-5559	219	7	λe2	λe2	PROPN
ejpam-5559	219	8	t	t	NOUN
ejpam-5559	219	9	−	−	PROPN
ejpam-5559	219	10	u	u	PROPN
ejpam-5559	219	11	)	)	PUNCT
ejpam-5559	219	12	r	r	NOUN
ejpam-5559	219	13	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	219	14	)	)	PUNCT
ejpam-5559	219	15	=	=	PRON
ejpam-5559	220	1	(	(	PUNCT
ejpam-5559	220	2	(	(	PUNCT
ejpam-5559	220	3	1−	1−	NUM
ejpam-5559	220	4	u	u	NOUN
ejpam-5559	220	5	)	)	PUNCT
ejpam-5559	220	6	λe2	λe2	PROPN
ejpam-5559	220	7	t	t	NOUN
ejpam-5559	220	8	−	−	PROPN
ejpam-5559	220	9	u	u	NOUN
ejpam-5559	220	10	)	)	PUNCT
ejpam-5559	220	11	r	r	NOUN
ejpam-5559	220	12	ey(e	ey(e	X
ejpam-5559	220	13	t−1)ext	t−1)ext	NOUN
ejpam-5559	220	14	=	=	PUNCT
ejpam-5559	220	15	(	(	PUNCT
ejpam-5559	220	16	(	(	PUNCT
ejpam-5559	220	17	1−	1−	NUM
ejpam-5559	220	18	u	u	NOUN
ejpam-5559	220	19	)	)	PUNCT
ejpam-5559	220	20	λe2	λe2	PROPN
ejpam-5559	220	21	t	t	NOUN
ejpam-5559	220	22	−	−	PROPN
ejpam-5559	220	23	u	u	NOUN
ejpam-5559	220	24	)	)	PUNCT
ejpam-5559	220	25	r	r	NOUN
ejpam-5559	220	26	ey(e	ey(e	PUNCT
ejpam-5559	220	27	t−1)(1	t−1)(1	PROPN
ejpam-5559	220	28	+	+	CCONJ
ejpam-5559	220	29	et	et	NOUN
ejpam-5559	220	30	−	−	NOUN
ejpam-5559	220	31	1)x	1)x	NUM
ejpam-5559	220	32	=	=	SYM
ejpam-5559	220	33	(	(	PUNCT
ejpam-5559	220	34	∞∑	∞∑	PROPN
ejpam-5559	220	35	n=0	n=0	NUM
ejpam-5559	220	36	bt	bt	NOUN
ejpam-5559	220	37	(	(	PUNCT
ejpam-5559	220	38	r	r	NOUN
ejpam-5559	220	39	)	)	PUNCT
ejpam-5559	220	40	n	n	CCONJ
ejpam-5559	220	41	(	(	PUNCT
ejpam-5559	220	42	y;u	y;u	PROPN
ejpam-5559	220	43	,	,	PUNCT
ejpam-5559	220	44	λ	λ	PROPN
ejpam-5559	220	45	)	)	PUNCT
ejpam-5559	220	46	tn	tn	PROPN
ejpam-5559	220	47	n	n	PROPN
ejpam-5559	220	48	!	!	PUNCT
ejpam-5559	220	49	)	)	PUNCT
ejpam-5559	221	1			PROPN
ejpam-5559	221	2	∞∑	∞∑	NUM
ejpam-5559	221	3	j=0	j=0	PROPN
ejpam-5559	221	4	(	(	PUNCT
ejpam-5559	221	5	x	x	SYM
ejpam-5559	221	6	j	j	PROPN
ejpam-5559	221	7	)	)	PUNCT
ejpam-5559	221	8	(	(	PUNCT
ejpam-5559	221	9	et	et	NOUN
ejpam-5559	221	10	−	−	PROPN
ejpam-5559	221	11	1)j	1)j	NUM
ejpam-5559	222	1			PROPN
ejpam-5559	223	1	j.	j.	PROPN
ejpam-5559	223	2	ontolan	ontolan	PROPN
ejpam-5559	223	3	et	et	PROPN
ejpam-5559	223	4	al	al	PROPN
ejpam-5559	223	5	.	.	PUNCT
ejpam-5559	223	6	/	/	SYM
ejpam-5559	223	7	eur	eur	PROPN
ejpam-5559	223	8	.	.	PUNCT
ejpam-5559	224	1	j.	j.	PROPN
ejpam-5559	224	2	pure	pure	PROPN
ejpam-5559	224	3	appl	appl	PROPN
ejpam-5559	224	4	.	.	PROPN
ejpam-5559	224	5	math	math	PROPN
ejpam-5559	224	6	,	,	PUNCT
ejpam-5559	224	7	18	18	NUM
ejpam-5559	224	8	(	(	PUNCT
ejpam-5559	224	9	1	1	NUM
ejpam-5559	224	10	)	)	PUNCT
ejpam-5559	224	11	(	(	PUNCT
ejpam-5559	224	12	2025	2025	NUM
ejpam-5559	224	13	)	)	PUNCT
ejpam-5559	224	14	,	,	PUNCT
ejpam-5559	224	15	5559	5559	NUM
ejpam-5559	224	16	12	12	NUM
ejpam-5559	224	17	of	of	ADP
ejpam-5559	224	18	16	16	NUM
ejpam-5559	224	19	=	=	SYM
ejpam-5559	224	20	(	(	PUNCT
ejpam-5559	224	21	∞∑	∞∑	PROPN
ejpam-5559	224	22	n=0	n=0	NUM
ejpam-5559	224	23	bt	bt	NOUN
ejpam-5559	224	24	(	(	PUNCT
ejpam-5559	224	25	r	r	NOUN
ejpam-5559	224	26	)	)	PUNCT
ejpam-5559	224	27	n	n	CCONJ
ejpam-5559	224	28	(	(	PUNCT
ejpam-5559	224	29	y;u	y;u	PROPN
ejpam-5559	224	30	,	,	PUNCT
ejpam-5559	224	31	λ	λ	PROPN
ejpam-5559	224	32	)	)	PUNCT
ejpam-5559	224	33	tn	tn	PROPN
ejpam-5559	224	34	n	n	PROPN
ejpam-5559	224	35	!	!	PUNCT
ejpam-5559	224	36	)	)	PUNCT
ejpam-5559	225	1			PROPN
ejpam-5559	225	2	∞∑	∞∑	NUM
ejpam-5559	225	3	j=0	j=0	PROPN
ejpam-5559	225	4	x	x	X
ejpam-5559	225	5	!	!	PUNCT
ejpam-5559	226	1	(	(	PUNCT
ejpam-5559	227	1	x−	x−	PROPN
ejpam-5559	227	2	j	j	PROPN
ejpam-5559	227	3	)	)	PUNCT
ejpam-5559	227	4	!	!	PUNCT
ejpam-5559	228	1	(	(	PUNCT
ejpam-5559	228	2	et	et	X
ejpam-5559	228	3	−	−	PROPN
ejpam-5559	228	4	1)j	1)j	NUM
ejpam-5559	228	5	j	j	PROPN
ejpam-5559	228	6	!	!	PUNCT
ejpam-5559	229	1			PROPN
ejpam-5559	230	1	=	=	PUNCT
ejpam-5559	231	1	(	(	PUNCT
ejpam-5559	231	2	∞∑	∞∑	PROPN
ejpam-5559	231	3	n=0	n=0	NUM
ejpam-5559	231	4	bt	bt	NOUN
ejpam-5559	231	5	(	(	PUNCT
ejpam-5559	231	6	r	r	NOUN
ejpam-5559	231	7	)	)	PUNCT
ejpam-5559	231	8	n	n	CCONJ
ejpam-5559	231	9	(	(	PUNCT
ejpam-5559	231	10	y;u	y;u	PROPN
ejpam-5559	231	11	,	,	PUNCT
ejpam-5559	231	12	λ	λ	PROPN
ejpam-5559	231	13	)	)	PUNCT
ejpam-5559	231	14	tn	tn	PROPN
ejpam-5559	231	15	n	n	PROPN
ejpam-5559	231	16	!	!	PUNCT
ejpam-5559	231	17	)	)	PUNCT
ejpam-5559	232	1			PROPN
ejpam-5559	232	2	∞∑	∞∑	NUM
ejpam-5559	232	3	j=0	j=0	PROPN
ejpam-5559	232	4	(	(	PUNCT
ejpam-5559	232	5	x)j	x)j	X
ejpam-5559	232	6	(	(	PUNCT
ejpam-5559	232	7	et	et	NOUN
ejpam-5559	232	8	−	−	PROPN
ejpam-5559	232	9	1)j	1)j	NUM
ejpam-5559	232	10	j	j	PROPN
ejpam-5559	232	11	!	!	PUNCT
ejpam-5559	233	1			PROPN
ejpam-5559	234	1	=	=	PUNCT
ejpam-5559	235	1	(	(	PUNCT
ejpam-5559	235	2	∞∑	∞∑	PROPN
ejpam-5559	235	3	n=0	n=0	NUM
ejpam-5559	235	4	bt	bt	NOUN
ejpam-5559	235	5	(	(	PUNCT
ejpam-5559	235	6	r	r	NOUN
ejpam-5559	235	7	)	)	PUNCT
ejpam-5559	235	8	n	n	CCONJ
ejpam-5559	235	9	(	(	PUNCT
ejpam-5559	235	10	y;u	y;u	PROPN
ejpam-5559	235	11	,	,	PUNCT
ejpam-5559	235	12	λ	λ	PROPN
ejpam-5559	235	13	)	)	PUNCT
ejpam-5559	235	14	tn	tn	PROPN
ejpam-5559	235	15	n	n	PROPN
ejpam-5559	235	16	!	!	PUNCT
ejpam-5559	235	17	)	)	PUNCT
ejpam-5559	236	1			PROPN
ejpam-5559	236	2	∞∑	∞∑	NUM
ejpam-5559	236	3	j=0	j=0	PROPN
ejpam-5559	236	4	(	(	PUNCT
ejpam-5559	236	5	x)j	x)j	X
ejpam-5559	236	6	∞∑	∞∑	NUM
ejpam-5559	236	7	n=0	n=0	PUNCT
ejpam-5559	236	8	s(n	s(n	PROPN
ejpam-5559	236	9	,	,	PUNCT
ejpam-5559	236	10	j	j	NOUN
ejpam-5559	236	11	)	)	PUNCT
ejpam-5559	236	12	tn	tn	PROPN
ejpam-5559	236	13	n	n	NOUN
ejpam-5559	236	14	!	!	PUNCT
ejpam-5559	237	1			PROPN
ejpam-5559	237	2	=	=	PUNCT
ejpam-5559	238	1	(	(	PUNCT
ejpam-5559	238	2	∞∑	∞∑	PROPN
ejpam-5559	238	3	n=0	n=0	NUM
ejpam-5559	238	4	bt	bt	NOUN
ejpam-5559	238	5	(	(	PUNCT
ejpam-5559	238	6	r	r	NOUN
ejpam-5559	238	7	)	)	PUNCT
ejpam-5559	238	8	n	n	CCONJ
ejpam-5559	238	9	(	(	PUNCT
ejpam-5559	238	10	y;u	y;u	PROPN
ejpam-5559	238	11	,	,	PUNCT
ejpam-5559	238	12	λ	λ	PROPN
ejpam-5559	238	13	)	)	PUNCT
ejpam-5559	238	14	tn	tn	PROPN
ejpam-5559	238	15	n	n	PROPN
ejpam-5559	238	16	!	!	PUNCT
ejpam-5559	238	17	)	)	PUNCT
ejpam-5559	239	1			PROPN
ejpam-5559	239	2	∞∑	∞∑	PROPN
ejpam-5559	239	3	n=0	n=0	NUM
ejpam-5559	239	4			PUNCT
ejpam-5559	239	5	∞∑	∞∑	NUM
ejpam-5559	239	6	j=0	j=0	PROPN
ejpam-5559	239	7	(	(	PUNCT
ejpam-5559	239	8	x)js(n	x)js(n	PROPN
ejpam-5559	239	9	,	,	PUNCT
ejpam-5559	239	10	j	j	NOUN
ejpam-5559	239	11	)	)	PUNCT
ejpam-5559	239	12			PROPN
ejpam-5559	239	13	tn	tn	NOUN
ejpam-5559	239	14	n	n	ADV
ejpam-5559	239	15	!	!	PUNCT
ejpam-5559	240	1			PROPN
ejpam-5559	240	2	=	=	PUNCT
ejpam-5559	241	1	∞∑	∞∑	NUM
ejpam-5559	241	2	n=0	n=0	NUM
ejpam-5559	241	3	n∑	n∑	NOUN
ejpam-5559	241	4	k=0	k=0	PROPN
ejpam-5559	241	5	(	(	PUNCT
ejpam-5559	241	6	n	n	X
ejpam-5559	241	7	k	k	NOUN
ejpam-5559	241	8	)	)	PUNCT
ejpam-5559	241	9			PUNCT
ejpam-5559	241	10	∞∑	∞∑	NUM
ejpam-5559	241	11	j=0	j=0	PROPN
ejpam-5559	241	12	(	(	PUNCT
ejpam-5559	241	13	x)js(k	x)js(k	PROPN
ejpam-5559	241	14	,	,	PUNCT
ejpam-5559	241	15	j)bt	j)bt	PROPN
ejpam-5559	241	16	(	(	PUNCT
ejpam-5559	241	17	r	r	NOUN
ejpam-5559	241	18	)	)	PUNCT
ejpam-5559	241	19	n−k(y;u	n−k(y;u	ADJ
ejpam-5559	241	20	,	,	PUNCT
ejpam-5559	241	21	λ	λ	NOUN
ejpam-5559	241	22	)	)	PUNCT
ejpam-5559	241	23			PROPN
ejpam-5559	241	24	tn	tn	NOUN
ejpam-5559	241	25	n	n	CCONJ
ejpam-5559	241	26	!	!	PUNCT
ejpam-5559	241	27	=	=	PUNCT
ejpam-5559	242	1	∞∑	∞∑	PRON
ejpam-5559	242	2	n=0	n=0	NUM
ejpam-5559	242	3			PUNCT
ejpam-5559	242	4	n∑	n∑	NOUN
ejpam-5559	242	5	k=0	k=0	PROPN
ejpam-5559	242	6	(	(	PUNCT
ejpam-5559	242	7	n	n	X
ejpam-5559	242	8	k	k	NOUN
ejpam-5559	242	9	)	)	PUNCT
ejpam-5559	243	1	∞∑	∞∑	NUM
ejpam-5559	243	2	j=0	j=0	PROPN
ejpam-5559	243	3	(	(	PUNCT
ejpam-5559	243	4	x)js(k	x)js(k	PROPN
ejpam-5559	243	5	,	,	PUNCT
ejpam-5559	243	6	j)bt	j)bt	PROPN
ejpam-5559	243	7	(	(	PUNCT
ejpam-5559	243	8	r	r	NOUN
ejpam-5559	243	9	)	)	PUNCT
ejpam-5559	243	10	n−k(y;u	n−k(y;u	ADJ
ejpam-5559	243	11	,	,	PUNCT
ejpam-5559	243	12	λ	λ	NOUN
ejpam-5559	243	13	)	)	PUNCT
ejpam-5559	243	14			PROPN
ejpam-5559	243	15	tn	tn	PROPN
ejpam-5559	243	16	n	n	CCONJ
ejpam-5559	243	17	!	!	PUNCT
ejpam-5559	243	18	.	.	PUNCT
ejpam-5559	244	1	comparing	compare	VERB
ejpam-5559	244	2	coefficients	coefficient	NOUN
ejpam-5559	244	3	of	of	ADP
ejpam-5559	244	4	tn	tn	NOUN
ejpam-5559	244	5	n	n	CCONJ
ejpam-5559	244	6	!	!	PUNCT
ejpam-5559	245	1	we	we	PRON
ejpam-5559	245	2	obtain	obtain	VERB
ejpam-5559	245	3	,	,	PUNCT
ejpam-5559	245	4	bt	bt	NOUN
ejpam-5559	245	5	(	(	PUNCT
ejpam-5559	245	6	r	r	NOUN
ejpam-5559	245	7	)	)	PUNCT
ejpam-5559	245	8	n	n	NOUN
ejpam-5559	245	9	(	(	PUNCT
ejpam-5559	245	10	x	x	X
ejpam-5559	245	11	,	,	PUNCT
ejpam-5559	245	12	y;u	y;u	PROPN
ejpam-5559	245	13	,	,	PUNCT
ejpam-5559	245	14	λ	λ	NOUN
ejpam-5559	245	15	)	)	PUNCT
ejpam-5559	245	16	=	=	SYM
ejpam-5559	246	1	n∑	n∑	PROPN
ejpam-5559	246	2	k=0	k=0	PROPN
ejpam-5559	246	3	∞∑	∞∑	NUM
ejpam-5559	246	4	j=0	j=0	PROPN
ejpam-5559	246	5	(	(	PUNCT
ejpam-5559	246	6	n	n	NOUN
ejpam-5559	246	7	k	k	NOUN
ejpam-5559	246	8	)	)	PUNCT
ejpam-5559	246	9	(	(	PUNCT
ejpam-5559	246	10	x)js(k	x)js(k	X
ejpam-5559	246	11	,	,	PUNCT
ejpam-5559	246	12	j)bt	j)bt	PROPN
ejpam-5559	246	13	(	(	PUNCT
ejpam-5559	246	14	r	r	NOUN
ejpam-5559	246	15	)	)	PUNCT
ejpam-5559	246	16	n−k(y;u	n−k(y;u	ADJ
ejpam-5559	246	17	,	,	PUNCT
ejpam-5559	246	18	λ	λ	X
ejpam-5559	246	19	)	)	PUNCT
ejpam-5559	246	20	=	=	SYM
ejpam-5559	247	1	n∑	n∑	PROPN
ejpam-5559	247	2	k=0	k=0	PROPN
ejpam-5559	247	3	k∑	k∑	PROPN
ejpam-5559	247	4	j=0	j=0	PROPN
ejpam-5559	247	5	(	(	PUNCT
ejpam-5559	247	6	n	n	X
ejpam-5559	247	7	k	k	NOUN
ejpam-5559	247	8	)	)	PUNCT
ejpam-5559	247	9	(	(	PUNCT
ejpam-5559	247	10	x)js(k	x)js(k	X
ejpam-5559	247	11	,	,	PUNCT
ejpam-5559	247	12	j)bt	j)bt	PROPN
ejpam-5559	247	13	(	(	PUNCT
ejpam-5559	247	14	r	r	NOUN
ejpam-5559	247	15	)	)	PUNCT
ejpam-5559	247	16	n−k(y;u	n−k(y;u	PROPN
ejpam-5559	247	17	,	,	PUNCT
ejpam-5559	247	18	λ	λ	X
ejpam-5559	247	19	)	)	PUNCT
ejpam-5559	247	20	,	,	PUNCT
ejpam-5559	247	21	which	which	PRON
ejpam-5559	247	22	proves	prove	VERB
ejpam-5559	247	23	the	the	DET
ejpam-5559	247	24	theorem	theorem	NOUN
ejpam-5559	247	25	.	.	PUNCT
ejpam-5559	248	1	the	the	DET
ejpam-5559	248	2	next	next	ADJ
ejpam-5559	248	3	result	result	NOUN
ejpam-5559	248	4	expresses	express	VERB
ejpam-5559	248	5	the	the	DET
ejpam-5559	248	6	bivariate	bivariate	ADJ
ejpam-5559	248	7	bell	bell	NOUN
ejpam-5559	248	8	polynomials	polynomial	NOUN
ejpam-5559	248	9	in	in	ADP
ejpam-5559	248	10	terms	term	NOUN
ejpam-5559	248	11	of	of	ADP
ejpam-5559	248	12	bivariate	bivariate	ADJ
ejpam-5559	248	13	bell	bell	NOUN
ejpam-5559	248	14	-	-	PUNCT
ejpam-5559	248	15	based	base	VERB
ejpam-5559	248	16	apostol	apostol	NOUN
ejpam-5559	248	17	-	-	PUNCT
ejpam-5559	248	18	frobenius	frobenius	NOUN
ejpam-5559	248	19	-	-	PUNCT
ejpam-5559	248	20	type	type	NOUN
ejpam-5559	248	21	tangent	tangent	NOUN
ejpam-5559	248	22	polynomials	polynomial	NOUN
ejpam-5559	248	23	.	.	PUNCT
ejpam-5559	249	1	theorem	theorem	VERB
ejpam-5559	249	2	9	9	NUM
ejpam-5559	249	3	.	.	PUNCT
ejpam-5559	250	1	the	the	DET
ejpam-5559	250	2	bivariate	bivariate	ADJ
ejpam-5559	250	3	bell	bell	NOUN
ejpam-5559	250	4	polynomials	polynomial	NOUN
ejpam-5559	250	5	follows	follow	VERB
ejpam-5559	250	6	the	the	DET
ejpam-5559	250	7	relation	relation	NOUN
ejpam-5559	250	8	bn(x	bn(x	NOUN
ejpam-5559	250	9	,	,	PUNCT
ejpam-5559	250	10	y	y	NOUN
ejpam-5559	250	11	)	)	PUNCT
ejpam-5559	250	12	=	=	PUNCT
ejpam-5559	250	13	λbtn(x+	λbtn(x+	X
ejpam-5559	250	14	2	2	NUM
ejpam-5559	250	15	,	,	PUNCT
ejpam-5559	250	16	y;u	y;u	PROPN
ejpam-5559	250	17	,	,	PUNCT
ejpam-5559	250	18	λ)−	λ)−	PROPN
ejpam-5559	250	19	ubtn(x	ubtn(x	PROPN
ejpam-5559	250	20	,	,	PUNCT
ejpam-5559	250	21	y;u	y;u	PROPN
ejpam-5559	250	22	,	,	PUNCT
ejpam-5559	250	23	λ	λ	PROPN
ejpam-5559	250	24	)	)	PUNCT
ejpam-5559	250	25	(	(	PUNCT
ejpam-5559	250	26	1−	1−	NUM
ejpam-5559	250	27	u	u	NOUN
ejpam-5559	250	28	)	)	PUNCT
ejpam-5559	250	29	.	.	PUNCT
ejpam-5559	251	1	(	(	PUNCT
ejpam-5559	251	2	27	27	NUM
ejpam-5559	251	3	)	)	PUNCT
ejpam-5559	251	4	proof	proof	NOUN
ejpam-5559	251	5	.	.	PUNCT
ejpam-5559	252	1	from	from	ADP
ejpam-5559	252	2	(	(	PUNCT
ejpam-5559	252	3	16	16	NUM
ejpam-5559	252	4	)	)	PUNCT
ejpam-5559	252	5	,	,	PUNCT
ejpam-5559	252	6	we	we	PRON
ejpam-5559	252	7	can	can	AUX
ejpam-5559	252	8	write	write	VERB
ejpam-5559	252	9	∞∑	∞∑	PRON
ejpam-5559	252	10	n=0	n=0	NUM
ejpam-5559	252	11	bn(x	bn(x	NUM
ejpam-5559	252	12	,	,	PUNCT
ejpam-5559	252	13	y	y	NOUN
ejpam-5559	252	14	)	)	PUNCT
ejpam-5559	252	15	tn	tn	PROPN
ejpam-5559	252	16	n	n	PROPN
ejpam-5559	252	17	!	!	PUNCT
ejpam-5559	253	1	=	=	SYM
ejpam-5559	253	2	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	253	3	)	)	PUNCT
ejpam-5559	254	1	=	=	NOUN
ejpam-5559	254	2	(	(	PUNCT
ejpam-5559	254	3	λe2	λe2	PROPN
ejpam-5559	254	4	t	t	PROPN
ejpam-5559	254	5	−	−	PROPN
ejpam-5559	254	6	u	u	PROPN
ejpam-5559	254	7	(	(	PUNCT
ejpam-5559	254	8	1−	1−	NUM
ejpam-5559	254	9	u	u	NOUN
ejpam-5559	254	10	)	)	PUNCT
ejpam-5559	254	11	)	)	PUNCT
ejpam-5559	254	12	(	(	PUNCT
ejpam-5559	254	13	(	(	PUNCT
ejpam-5559	254	14	1−	1−	NUM
ejpam-5559	254	15	u	u	NOUN
ejpam-5559	254	16	)	)	PUNCT
ejpam-5559	254	17	λe2	λe2	PROPN
ejpam-5559	254	18	t	t	PROPN
ejpam-5559	254	19	−	−	NOUN
ejpam-5559	254	20	u	u	PROPN
ejpam-5559	254	21	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	254	22	)	)	PUNCT
ejpam-5559	254	23	)	)	PUNCT
ejpam-5559	255	1	j.	j.	PROPN
ejpam-5559	255	2	ontolan	ontolan	PROPN
ejpam-5559	255	3	et	et	PROPN
ejpam-5559	255	4	al	al	PROPN
ejpam-5559	255	5	.	.	PUNCT
ejpam-5559	255	6	/	/	SYM
ejpam-5559	255	7	eur	eur	PROPN
ejpam-5559	255	8	.	.	PUNCT
ejpam-5559	256	1	j.	j.	PROPN
ejpam-5559	256	2	pure	pure	PROPN
ejpam-5559	256	3	appl	appl	PROPN
ejpam-5559	256	4	.	.	PROPN
ejpam-5559	256	5	math	math	PROPN
ejpam-5559	256	6	,	,	PUNCT
ejpam-5559	256	7	18	18	NUM
ejpam-5559	256	8	(	(	PUNCT
ejpam-5559	256	9	1	1	NUM
ejpam-5559	256	10	)	)	PUNCT
ejpam-5559	256	11	(	(	PUNCT
ejpam-5559	256	12	2025	2025	NUM
ejpam-5559	256	13	)	)	PUNCT
ejpam-5559	256	14	,	,	PUNCT
ejpam-5559	256	15	5559	5559	NUM
ejpam-5559	256	16	13	13	NUM
ejpam-5559	256	17	of	of	ADP
ejpam-5559	256	18	16	16	NUM
ejpam-5559	256	19	=	=	SYM
ejpam-5559	256	20	1	1	NUM
ejpam-5559	256	21	(	(	PUNCT
ejpam-5559	256	22	1−	1−	NUM
ejpam-5559	256	23	u	u	NOUN
ejpam-5559	256	24	)	)	PUNCT
ejpam-5559	256	25	(	(	PUNCT
ejpam-5559	256	26	λ	λ	X
ejpam-5559	256	27	(	(	PUNCT
ejpam-5559	256	28	(	(	PUNCT
ejpam-5559	256	29	1−	1−	NUM
ejpam-5559	256	30	u	u	NOUN
ejpam-5559	256	31	)	)	PUNCT
ejpam-5559	256	32	λe2	λe2	PROPN
ejpam-5559	256	33	t	t	NOUN
ejpam-5559	256	34	−	−	NOUN
ejpam-5559	256	35	u	u	PROPN
ejpam-5559	256	36	e(x+2)t+y(et−1	e(x+2)t+y(et−1	PROPN
ejpam-5559	256	37	)	)	PUNCT
ejpam-5559	256	38	)	)	PUNCT
ejpam-5559	257	1	−	−	PROPN
ejpam-5559	257	2	u	u	NOUN
ejpam-5559	257	3	(	(	PUNCT
ejpam-5559	257	4	(	(	PUNCT
ejpam-5559	257	5	1−	1−	NUM
ejpam-5559	257	6	u	u	NOUN
ejpam-5559	257	7	)	)	PUNCT
ejpam-5559	257	8	λe2	λe2	PROPN
ejpam-5559	257	9	t	t	PROPN
ejpam-5559	257	10	−	−	NOUN
ejpam-5559	257	11	u	u	PROPN
ejpam-5559	257	12	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	257	13	)	)	PUNCT
ejpam-5559	257	14	)	)	PUNCT
ejpam-5559	257	15	)	)	PUNCT
ejpam-5559	258	1	=	=	SYM
ejpam-5559	258	2	1	1	NUM
ejpam-5559	258	3	(	(	PUNCT
ejpam-5559	258	4	1−	1−	NUM
ejpam-5559	258	5	u	u	NOUN
ejpam-5559	258	6	)	)	PUNCT
ejpam-5559	258	7	(	(	PUNCT
ejpam-5559	258	8	λ	λ	X
ejpam-5559	258	9	∞∑	∞∑	PROPN
ejpam-5559	258	10	n=0	n=0	NUM
ejpam-5559	258	11	btn(x+	btn(x+	ADV
ejpam-5559	258	12	2	2	NUM
ejpam-5559	258	13	,	,	PUNCT
ejpam-5559	258	14	y;u	y;u	PROPN
ejpam-5559	258	15	,	,	PUNCT
ejpam-5559	258	16	λ	λ	PROPN
ejpam-5559	258	17	)	)	PUNCT
ejpam-5559	258	18	tn	tn	PROPN
ejpam-5559	258	19	n	n	PROPN
ejpam-5559	258	20	!	!	PUNCT
ejpam-5559	258	21	−	−	PROPN
ejpam-5559	259	1	u	u	PRON
ejpam-5559	259	2	∞∑	∞∑	ADJ
ejpam-5559	259	3	n=0	n=0	PROPN
ejpam-5559	259	4	btn(x	btn(x	PROPN
ejpam-5559	259	5	,	,	PUNCT
ejpam-5559	259	6	y;u	y;u	PROPN
ejpam-5559	259	7	,	,	PUNCT
ejpam-5559	259	8	λ	λ	PROPN
ejpam-5559	259	9	)	)	PUNCT
ejpam-5559	259	10	tn	tn	PROPN
ejpam-5559	259	11	n	n	PROPN
ejpam-5559	259	12	!	!	PUNCT
ejpam-5559	259	13	)	)	PUNCT
ejpam-5559	260	1	=	=	PUNCT
ejpam-5559	260	2	λ	λ	X
ejpam-5559	260	3	1−	1−	NUM
ejpam-5559	260	4	u	u	NOUN
ejpam-5559	260	5	∞∑	∞∑	NOUN
ejpam-5559	260	6	n=−1	n=−1	ADV
ejpam-5559	260	7	btn(x+	btn(x+	ADV
ejpam-5559	260	8	2	2	NUM
ejpam-5559	260	9	,	,	PUNCT
ejpam-5559	260	10	y;u	y;u	PROPN
ejpam-5559	260	11	,	,	PUNCT
ejpam-5559	260	12	λ	λ	PROPN
ejpam-5559	260	13	)	)	PUNCT
ejpam-5559	260	14	tn	tn	PROPN
ejpam-5559	260	15	n	n	PROPN
ejpam-5559	260	16	!	!	PUNCT
ejpam-5559	261	1	−	−	PROPN
ejpam-5559	261	2	u	u	NOUN
ejpam-5559	261	3	1−	1−	NUM
ejpam-5559	261	4	u	u	NOUN
ejpam-5559	261	5	∞∑	∞∑	VERB
ejpam-5559	261	6	n=−1	n=−1	ADV
ejpam-5559	261	7	btn(x	btn(x	PROPN
ejpam-5559	261	8	,	,	PUNCT
ejpam-5559	261	9	y;u	y;u	PROPN
ejpam-5559	261	10	,	,	PUNCT
ejpam-5559	261	11	λ	λ	PROPN
ejpam-5559	261	12	)	)	PUNCT
ejpam-5559	261	13	tn	tn	PROPN
ejpam-5559	261	14	n	n	NUM
ejpam-5559	261	15	!	!	PUNCT
ejpam-5559	261	16	.	.	PUNCT
ejpam-5559	262	1	comparing	compare	VERB
ejpam-5559	262	2	coefficients	coefficient	NOUN
ejpam-5559	262	3	,	,	PUNCT
ejpam-5559	262	4	bn(x	bn(x	NUM
ejpam-5559	262	5	,	,	PUNCT
ejpam-5559	262	6	y	y	NOUN
ejpam-5559	262	7	)	)	PUNCT
ejpam-5559	262	8	=	=	PUNCT
ejpam-5559	262	9	λbtn(x+	λbtn(x+	X
ejpam-5559	262	10	2	2	NUM
ejpam-5559	262	11	,	,	PUNCT
ejpam-5559	262	12	y;u	y;u	PROPN
ejpam-5559	262	13	,	,	PUNCT
ejpam-5559	262	14	λ)−	λ)−	PROPN
ejpam-5559	262	15	ubtn(x	ubtn(x	PROPN
ejpam-5559	262	16	,	,	PUNCT
ejpam-5559	262	17	y;u	y;u	PROPN
ejpam-5559	262	18	,	,	PUNCT
ejpam-5559	262	19	λ	λ	PROPN
ejpam-5559	262	20	)	)	PUNCT
ejpam-5559	262	21	(	(	PUNCT
ejpam-5559	262	22	1−	1−	NUM
ejpam-5559	262	23	u	u	NOUN
ejpam-5559	262	24	)	)	PUNCT
ejpam-5559	262	25	.	.	PUNCT
ejpam-5559	263	1	derivative	derivative	ADJ
ejpam-5559	263	2	formulas	formula	NOUN
ejpam-5559	263	3	derivative	derivative	ADJ
ejpam-5559	263	4	formulas	formula	NOUN
ejpam-5559	263	5	for	for	ADP
ejpam-5559	263	6	special	special	ADJ
ejpam-5559	263	7	polynomials	polynomial	NOUN
ejpam-5559	263	8	are	be	AUX
ejpam-5559	263	9	fundamental	fundamental	ADJ
ejpam-5559	263	10	tools	tool	NOUN
ejpam-5559	263	11	in	in	ADP
ejpam-5559	263	12	mathematics	mathematic	NOUN
ejpam-5559	263	13	and	and	CCONJ
ejpam-5559	263	14	its	its	PRON
ejpam-5559	263	15	applications	application	NOUN
ejpam-5559	263	16	to	to	ADP
ejpam-5559	263	17	physics	physics	NOUN
ejpam-5559	263	18	,	,	PUNCT
ejpam-5559	263	19	engineering	engineering	NOUN
ejpam-5559	263	20	,	,	PUNCT
ejpam-5559	263	21	and	and	CCONJ
ejpam-5559	263	22	other	other	ADJ
ejpam-5559	263	23	scientific	scientific	ADJ
ejpam-5559	263	24	fields	field	NOUN
ejpam-5559	263	25	.	.	PUNCT
ejpam-5559	264	1	these	these	DET
ejpam-5559	264	2	formulas	formula	NOUN
ejpam-5559	264	3	facilitate	facilitate	VERB
ejpam-5559	264	4	the	the	DET
ejpam-5559	264	5	analysis	analysis	NOUN
ejpam-5559	264	6	of	of	ADP
ejpam-5559	264	7	the	the	DET
ejpam-5559	264	8	behavior	behavior	NOUN
ejpam-5559	264	9	and	and	CCONJ
ejpam-5559	264	10	properties	property	NOUN
ejpam-5559	264	11	of	of	ADP
ejpam-5559	264	12	special	special	ADJ
ejpam-5559	264	13	polynomials	polynomial	NOUN
ejpam-5559	264	14	by	by	ADP
ejpam-5559	264	15	quantifying	quantify	VERB
ejpam-5559	264	16	their	their	PRON
ejpam-5559	264	17	rates	rate	NOUN
ejpam-5559	264	18	of	of	ADP
ejpam-5559	264	19	change	change	NOUN
ejpam-5559	264	20	,	,	PUNCT
ejpam-5559	264	21	a	a	DET
ejpam-5559	264	22	central	central	ADJ
ejpam-5559	264	23	aspect	aspect	NOUN
ejpam-5559	264	24	in	in	ADP
ejpam-5559	264	25	calculus	calculus	NOUN
ejpam-5559	264	26	and	and	CCONJ
ejpam-5559	264	27	mathematical	mathematical	ADJ
ejpam-5559	264	28	analysis	analysis	NOUN
ejpam-5559	264	29	for	for	ADP
ejpam-5559	264	30	understanding	understand	VERB
ejpam-5559	264	31	function	function	NOUN
ejpam-5559	264	32	dynamics	dynamic	NOUN
ejpam-5559	264	33	.	.	PUNCT
ejpam-5559	265	1	moreover	moreover	ADV
ejpam-5559	265	2	,	,	PUNCT
ejpam-5559	265	3	they	they	PRON
ejpam-5559	265	4	are	be	AUX
ejpam-5559	265	5	instrumental	instrumental	ADJ
ejpam-5559	265	6	in	in	ADP
ejpam-5559	265	7	the	the	DET
ejpam-5559	265	8	manipulation	manipulation	NOUN
ejpam-5559	265	9	of	of	ADP
ejpam-5559	265	10	generating	generating	NOUN
ejpam-5559	265	11	functions	function	NOUN
ejpam-5559	265	12	,	,	PUNCT
ejpam-5559	265	13	which	which	PRON
ejpam-5559	265	14	encode	encode	VERB
ejpam-5559	265	15	sequences	sequence	NOUN
ejpam-5559	265	16	of	of	ADP
ejpam-5559	265	17	polynomial	polynomial	ADJ
ejpam-5559	265	18	coefficients	coefficient	NOUN
ejpam-5559	265	19	.	.	PUNCT
ejpam-5559	266	1	generating	generate	VERB
ejpam-5559	266	2	functions	function	NOUN
ejpam-5559	266	3	,	,	PUNCT
ejpam-5559	266	4	in	in	ADP
ejpam-5559	266	5	turn	turn	NOUN
ejpam-5559	266	6	,	,	PUNCT
ejpam-5559	266	7	play	play	VERB
ejpam-5559	266	8	a	a	DET
ejpam-5559	266	9	crucial	crucial	ADJ
ejpam-5559	266	10	role	role	NOUN
ejpam-5559	266	11	in	in	ADP
ejpam-5559	266	12	combinatorics	combinatoric	NOUN
ejpam-5559	266	13	,	,	PUNCT
ejpam-5559	266	14	number	number	NOUN
ejpam-5559	266	15	theory	theory	NOUN
ejpam-5559	266	16	,	,	PUNCT
ejpam-5559	266	17	and	and	CCONJ
ejpam-5559	266	18	discrete	discrete	ADJ
ejpam-5559	266	19	mathematics	mathematic	NOUN
ejpam-5559	266	20	,	,	PUNCT
ejpam-5559	266	21	particularly	particularly	ADV
ejpam-5559	266	22	for	for	ADP
ejpam-5559	266	23	problems	problem	NOUN
ejpam-5559	266	24	involving	involve	VERB
ejpam-5559	266	25	counting	counting	NOUN
ejpam-5559	266	26	and	and	CCONJ
ejpam-5559	266	27	enumeration	enumeration	NOUN
ejpam-5559	266	28	.	.	PUNCT
ejpam-5559	267	1	the	the	DET
ejpam-5559	267	2	next	next	ADJ
ejpam-5559	267	3	theorem	theorem	NOUN
ejpam-5559	267	4	contains	contain	VERB
ejpam-5559	267	5	the	the	DET
ejpam-5559	267	6	derivative	derivative	ADJ
ejpam-5559	267	7	formula	formula	NOUN
ejpam-5559	267	8	for	for	ADP
ejpam-5559	267	9	bt	bt	PROPN
ejpam-5559	267	10	(	(	PUNCT
ejpam-5559	267	11	r	r	NOUN
ejpam-5559	267	12	)	)	PUNCT
ejpam-5559	267	13	n	n	NOUN
ejpam-5559	267	14	(	(	PUNCT
ejpam-5559	267	15	x	x	X
ejpam-5559	267	16	,	,	PUNCT
ejpam-5559	267	17	y;u	y;u	PROPN
ejpam-5559	267	18	,	,	PUNCT
ejpam-5559	267	19	λ	λ	PROPN
ejpam-5559	267	20	)	)	PUNCT
ejpam-5559	267	21	with	with	ADP
ejpam-5559	267	22	respect	respect	NOUN
ejpam-5559	267	23	to	to	ADP
ejpam-5559	267	24	the	the	DET
ejpam-5559	267	25	variable	variable	ADJ
ejpam-5559	267	26	x.	x.	NOUN
ejpam-5559	267	27	theorem	theorem	VERB
ejpam-5559	267	28	10	10	NUM
ejpam-5559	267	29	.	.	PUNCT
ejpam-5559	268	1	the	the	DET
ejpam-5559	268	2	following	follow	VERB
ejpam-5559	268	3	derivative	derivative	ADJ
ejpam-5559	268	4	formula	formula	NOUN
ejpam-5559	268	5	holds	hold	VERB
ejpam-5559	268	6	∂	∂	ADJ
ejpam-5559	268	7	∂x	∂x	PROPN
ejpam-5559	268	8	bt	bt	NOUN
ejpam-5559	268	9	(	(	PUNCT
ejpam-5559	268	10	r	r	NOUN
ejpam-5559	268	11	)	)	PUNCT
ejpam-5559	268	12	n	n	NOUN
ejpam-5559	268	13	(	(	PUNCT
ejpam-5559	268	14	x	x	X
ejpam-5559	268	15	,	,	PUNCT
ejpam-5559	268	16	y;u	y;u	PROPN
ejpam-5559	268	17	,	,	PUNCT
ejpam-5559	268	18	λ	λ	NOUN
ejpam-5559	268	19	)	)	PUNCT
ejpam-5559	268	20	=	=	PUNCT
ejpam-5559	268	21	nbt	nbt	VERB
ejpam-5559	268	22	(	(	PUNCT
ejpam-5559	268	23	r	r	NOUN
ejpam-5559	268	24	)	)	PUNCT
ejpam-5559	268	25	n−1(x	n−1(x	PROPN
ejpam-5559	268	26	,	,	PUNCT
ejpam-5559	268	27	y;u	y;u	PROPN
ejpam-5559	268	28	,	,	PUNCT
ejpam-5559	268	29	λ	λ	PROPN
ejpam-5559	268	30	)	)	PUNCT
ejpam-5559	268	31	.	.	PUNCT
ejpam-5559	269	1	(	(	PUNCT
ejpam-5559	269	2	28	28	NUM
ejpam-5559	269	3	)	)	PUNCT
ejpam-5559	269	4	proof	proof	NOUN
ejpam-5559	269	5	.	.	PUNCT
ejpam-5559	270	1	applying	apply	VERB
ejpam-5559	270	2	∂	∂	NOUN
ejpam-5559	270	3	∂y	∂y	PRON
ejpam-5559	270	4	to	to	PART
ejpam-5559	270	5	(	(	PUNCT
ejpam-5559	270	6	5	5	NUM
ejpam-5559	270	7	)	)	PUNCT
ejpam-5559	270	8	,	,	PUNCT
ejpam-5559	270	9	∂	∂	NUM
ejpam-5559	270	10	∂x	∂x	PROPN
ejpam-5559	270	11	∞∑	∞∑	PROPN
ejpam-5559	270	12	n=0	n=0	NUM
ejpam-5559	270	13	bt	bt	NOUN
ejpam-5559	270	14	(	(	PUNCT
ejpam-5559	270	15	r	r	NOUN
ejpam-5559	270	16	)	)	PUNCT
ejpam-5559	270	17	n	n	NOUN
ejpam-5559	270	18	(	(	PUNCT
ejpam-5559	270	19	x	x	X
ejpam-5559	270	20	,	,	PUNCT
ejpam-5559	270	21	y;u	y;u	PROPN
ejpam-5559	270	22	,	,	PUNCT
ejpam-5559	270	23	λ	λ	PROPN
ejpam-5559	270	24	)	)	PUNCT
ejpam-5559	270	25	tn	tn	PROPN
ejpam-5559	270	26	n	n	NOUN
ejpam-5559	270	27	!	!	PUNCT
ejpam-5559	271	1	=	=	SYM
ejpam-5559	271	2	∂	∂	NUM
ejpam-5559	271	3	∂x	∂x	PROPN
ejpam-5559	271	4	(	(	PUNCT
ejpam-5559	271	5	(	(	PUNCT
ejpam-5559	271	6	1−	1−	NUM
ejpam-5559	271	7	u	u	NOUN
ejpam-5559	271	8	)	)	PUNCT
ejpam-5559	271	9	λe2	λe2	PROPN
ejpam-5559	271	10	t	t	NOUN
ejpam-5559	271	11	−	−	PROPN
ejpam-5559	271	12	u	u	PROPN
ejpam-5559	271	13	)	)	PUNCT
ejpam-5559	271	14	r	r	NOUN
ejpam-5559	271	15	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	271	16	)	)	PUNCT
ejpam-5559	271	17	∞∑	∞∑	PRON
ejpam-5559	271	18	n=0	n=0	NUM
ejpam-5559	271	19	∂	∂	NUM
ejpam-5559	271	20	∂x	∂x	PROPN
ejpam-5559	271	21	bt	bt	NOUN
ejpam-5559	271	22	(	(	PUNCT
ejpam-5559	271	23	r	r	NOUN
ejpam-5559	271	24	)	)	PUNCT
ejpam-5559	271	25	n	n	NOUN
ejpam-5559	271	26	(	(	PUNCT
ejpam-5559	271	27	x	x	X
ejpam-5559	271	28	,	,	PUNCT
ejpam-5559	271	29	y;u	y;u	PROPN
ejpam-5559	271	30	,	,	PUNCT
ejpam-5559	271	31	λ	λ	PROPN
ejpam-5559	271	32	)	)	PUNCT
ejpam-5559	271	33	tn	tn	PROPN
ejpam-5559	271	34	n	n	PROPN
ejpam-5559	271	35	!	!	PUNCT
ejpam-5559	271	36	=	=	PUNCT
ejpam-5559	272	1	(	(	PUNCT
ejpam-5559	272	2	(	(	PUNCT
ejpam-5559	272	3	1−	1−	NUM
ejpam-5559	272	4	u	u	NOUN
ejpam-5559	272	5	)	)	PUNCT
ejpam-5559	272	6	λe2	λe2	PROPN
ejpam-5559	272	7	t	t	NOUN
ejpam-5559	272	8	−	−	PROPN
ejpam-5559	272	9	u	u	PROPN
ejpam-5559	272	10	)	)	PUNCT
ejpam-5559	272	11	r	r	NOUN
ejpam-5559	272	12	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	272	13	)	)	PUNCT
ejpam-5559	272	14	t	t	PROPN
ejpam-5559	272	15	=	=	SYM
ejpam-5559	272	16	t	t	PROPN
ejpam-5559	272	17	∞∑	∞∑	PROPN
ejpam-5559	272	18	n=0	n=0	NUM
ejpam-5559	272	19	bt	bt	NOUN
ejpam-5559	272	20	(	(	PUNCT
ejpam-5559	272	21	r	r	NOUN
ejpam-5559	272	22	)	)	PUNCT
ejpam-5559	272	23	n	n	NOUN
ejpam-5559	272	24	(	(	PUNCT
ejpam-5559	272	25	x	x	X
ejpam-5559	272	26	,	,	PUNCT
ejpam-5559	272	27	y;u	y;u	PROPN
ejpam-5559	272	28	,	,	PUNCT
ejpam-5559	272	29	λ	λ	PROPN
ejpam-5559	272	30	)	)	PUNCT
ejpam-5559	272	31	tn	tn	PROPN
ejpam-5559	272	32	n	n	NOUN
ejpam-5559	272	33	!	!	PUNCT
ejpam-5559	273	1	=	=	PUNCT
ejpam-5559	274	1	∞∑	∞∑	PRON
ejpam-5559	274	2	n=0	n=0	NUM
ejpam-5559	274	3	bt	bt	NOUN
ejpam-5559	274	4	(	(	PUNCT
ejpam-5559	274	5	r	r	NOUN
ejpam-5559	274	6	)	)	PUNCT
ejpam-5559	274	7	n	n	NOUN
ejpam-5559	274	8	(	(	PUNCT
ejpam-5559	274	9	x	x	X
ejpam-5559	274	10	,	,	PUNCT
ejpam-5559	274	11	y;u	y;u	PROPN
ejpam-5559	274	12	,	,	PUNCT
ejpam-5559	274	13	λ	λ	NOUN
ejpam-5559	274	14	)	)	PUNCT
ejpam-5559	274	15	tn+1	tn+1	NOUN
ejpam-5559	274	16	n	n	X
ejpam-5559	274	17	!	!	PUNCT
ejpam-5559	275	1	j.	j.	PROPN
ejpam-5559	275	2	ontolan	ontolan	PROPN
ejpam-5559	275	3	et	et	PROPN
ejpam-5559	275	4	al	al	PROPN
ejpam-5559	275	5	.	.	PUNCT
ejpam-5559	275	6	/	/	SYM
ejpam-5559	275	7	eur	eur	PROPN
ejpam-5559	275	8	.	.	PUNCT
ejpam-5559	276	1	j.	j.	PROPN
ejpam-5559	276	2	pure	pure	PROPN
ejpam-5559	276	3	appl	appl	PROPN
ejpam-5559	276	4	.	.	PROPN
ejpam-5559	276	5	math	math	PROPN
ejpam-5559	276	6	,	,	PUNCT
ejpam-5559	276	7	18	18	NUM
ejpam-5559	276	8	(	(	PUNCT
ejpam-5559	276	9	1	1	NUM
ejpam-5559	276	10	)	)	PUNCT
ejpam-5559	276	11	(	(	PUNCT
ejpam-5559	276	12	2025	2025	NUM
ejpam-5559	276	13	)	)	PUNCT
ejpam-5559	276	14	,	,	PUNCT
ejpam-5559	276	15	5559	5559	NUM
ejpam-5559	276	16	14	14	NUM
ejpam-5559	276	17	of	of	ADP
ejpam-5559	276	18	16	16	NUM
ejpam-5559	276	19	=	=	SYM
ejpam-5559	276	20	∞∑	∞∑	NOUN
ejpam-5559	276	21	n=1	n=1	PROPN
ejpam-5559	276	22	nbt	nbt	VERB
ejpam-5559	276	23	(	(	PUNCT
ejpam-5559	276	24	r	r	NOUN
ejpam-5559	276	25	)	)	PUNCT
ejpam-5559	276	26	n−1(x	n−1(x	PROPN
ejpam-5559	276	27	,	,	PUNCT
ejpam-5559	276	28	y;u	y;u	PROPN
ejpam-5559	276	29	,	,	PUNCT
ejpam-5559	276	30	λ	λ	PROPN
ejpam-5559	276	31	)	)	PUNCT
ejpam-5559	276	32	tn	tn	PROPN
ejpam-5559	276	33	n	n	PROPN
ejpam-5559	276	34	!	!	PUNCT
ejpam-5559	276	35	.	.	PUNCT
ejpam-5559	277	1	consequently	consequently	ADV
ejpam-5559	277	2	,	,	PUNCT
ejpam-5559	277	3	∂	∂	NUM
ejpam-5559	277	4	∂x	∂x	PROPN
ejpam-5559	277	5	bt	bt	NOUN
ejpam-5559	277	6	(	(	PUNCT
ejpam-5559	277	7	r	r	NOUN
ejpam-5559	277	8	)	)	PUNCT
ejpam-5559	277	9	n	n	NOUN
ejpam-5559	277	10	(	(	PUNCT
ejpam-5559	277	11	x	x	X
ejpam-5559	277	12	,	,	PUNCT
ejpam-5559	277	13	y;u	y;u	PROPN
ejpam-5559	277	14	,	,	PUNCT
ejpam-5559	277	15	λ	λ	NOUN
ejpam-5559	277	16	)	)	PUNCT
ejpam-5559	277	17	=	=	PUNCT
ejpam-5559	277	18	nbt	nbt	VERB
ejpam-5559	277	19	(	(	PUNCT
ejpam-5559	277	20	r	r	NOUN
ejpam-5559	277	21	)	)	PUNCT
ejpam-5559	277	22	n−1(x	n−1(x	PROPN
ejpam-5559	277	23	,	,	PUNCT
ejpam-5559	277	24	y;u	y;u	PROPN
ejpam-5559	277	25	,	,	PUNCT
ejpam-5559	277	26	λ	λ	PROPN
ejpam-5559	277	27	)	)	PUNCT
ejpam-5559	277	28	.	.	PUNCT
ejpam-5559	278	1	remark	remark	PROPN
ejpam-5559	278	2	2	2	NUM
ejpam-5559	278	3	.	.	PUNCT
ejpam-5559	279	1	the	the	DET
ejpam-5559	279	2	relation	relation	NOUN
ejpam-5559	279	3	in	in	ADP
ejpam-5559	279	4	(	(	PUNCT
ejpam-5559	279	5	28	28	NUM
ejpam-5559	279	6	)	)	PUNCT
ejpam-5559	279	7	shows	show	VERB
ejpam-5559	279	8	that	that	SCONJ
ejpam-5559	279	9	the	the	DET
ejpam-5559	279	10	sequence	sequence	NOUN
ejpam-5559	279	11	of	of	ADP
ejpam-5559	279	12	polynomials	polynomial	NOUN
ejpam-5559	279	13	bt	bt	INTJ
ejpam-5559	279	14	(	(	PUNCT
ejpam-5559	279	15	r	r	NOUN
ejpam-5559	279	16	)	)	PUNCT
ejpam-5559	279	17	n	n	NOUN
ejpam-5559	279	18	(	(	PUNCT
ejpam-5559	279	19	x	x	X
ejpam-5559	279	20	,	,	PUNCT
ejpam-5559	279	21	y;u	y;u	PROPN
ejpam-5559	279	22	,	,	PUNCT
ejpam-5559	279	23	λ	λ	NOUN
ejpam-5559	279	24	)	)	PUNCT
ejpam-5559	279	25	satisfy	satisfy	NOUN
ejpam-5559	279	26	(	(	PUNCT
ejpam-5559	279	27	9	9	NUM
ejpam-5559	279	28	)	)	PUNCT
ejpam-5559	279	29	,	,	PUNCT
ejpam-5559	279	30	thus	thus	ADV
ejpam-5559	279	31	bt	bt	X
ejpam-5559	279	32	(	(	PUNCT
ejpam-5559	279	33	r	r	NOUN
ejpam-5559	279	34	)	)	PUNCT
ejpam-5559	279	35	n	n	NOUN
ejpam-5559	279	36	(	(	PUNCT
ejpam-5559	279	37	x	x	X
ejpam-5559	279	38	,	,	PUNCT
ejpam-5559	279	39	y;u	y;u	PROPN
ejpam-5559	279	40	,	,	PUNCT
ejpam-5559	279	41	λ	λ	X
ejpam-5559	279	42	)	)	PUNCT
ejpam-5559	279	43	is	be	AUX
ejpam-5559	279	44	a	a	DET
ejpam-5559	279	45	sequence	sequence	NOUN
ejpam-5559	279	46	of	of	ADP
ejpam-5559	279	47	appell	appell	ADJ
ejpam-5559	279	48	polynomials	polynomial	NOUN
ejpam-5559	279	49	.	.	PUNCT
ejpam-5559	280	1	the	the	DET
ejpam-5559	280	2	polynomials	polynomial	NOUN
ejpam-5559	280	3	bt	bt	INTJ
ejpam-5559	280	4	(	(	PUNCT
ejpam-5559	280	5	r	r	NOUN
ejpam-5559	280	6	)	)	PUNCT
ejpam-5559	280	7	n	n	NOUN
ejpam-5559	280	8	(	(	PUNCT
ejpam-5559	280	9	x	x	X
ejpam-5559	280	10	,	,	PUNCT
ejpam-5559	280	11	y;u	y;u	PROPN
ejpam-5559	280	12	,	,	PUNCT
ejpam-5559	280	13	λ	λ	X
ejpam-5559	280	14	)	)	PUNCT
ejpam-5559	280	15	are	be	AUX
ejpam-5559	280	16	anticipated	anticipate	VERB
ejpam-5559	280	17	to	to	PART
ejpam-5559	280	18	exhibit	exhibit	VERB
ejpam-5559	280	19	the	the	DET
ejpam-5559	280	20	following	following	ADJ
ejpam-5559	280	21	characteristics	characteristic	NOUN
ejpam-5559	280	22	:	:	PUNCT
ejpam-5559	280	23	(	(	PUNCT
ejpam-5559	280	24	1	1	X
ejpam-5559	280	25	)	)	PUNCT
ejpam-5559	280	26	equation	equation	NOUN
ejpam-5559	280	27	(	(	PUNCT
ejpam-5559	280	28	5	5	NUM
ejpam-5559	280	29	)	)	PUNCT
ejpam-5559	280	30	reflects	reflect	VERB
ejpam-5559	280	31	(	(	PUNCT
ejpam-5559	280	32	10	10	NUM
ejpam-5559	280	33	)	)	PUNCT
ejpam-5559	280	34	,	,	PUNCT
ejpam-5559	280	35	that	that	ADV
ejpam-5559	280	36	is	is	ADV
ejpam-5559	280	37	,	,	PUNCT
ejpam-5559	280	38	(	(	PUNCT
ejpam-5559	280	39	1−	1−	NUM
ejpam-5559	280	40	u	u	NOUN
ejpam-5559	280	41	λe2	λe2	PROPN
ejpam-5559	280	42	t	t	PROPN
ejpam-5559	280	43	−	−	PROPN
ejpam-5559	280	44	u	u	NOUN
ejpam-5559	280	45	)	)	PUNCT
ejpam-5559	280	46	r	r	NOUN
ejpam-5559	280	47	ey(e	ey(e	X
ejpam-5559	280	48	t−1)ext	t−1)ext	NOUN
ejpam-5559	280	49	=	=	PUNCT
ejpam-5559	281	1	∞∑	∞∑	ADJ
ejpam-5559	281	2	n=0	n=0	NUM
ejpam-5559	281	3	bt	bt	NOUN
ejpam-5559	281	4	(	(	PUNCT
ejpam-5559	281	5	r	r	NOUN
ejpam-5559	281	6	)	)	PUNCT
ejpam-5559	281	7	n	n	NOUN
ejpam-5559	281	8	(	(	PUNCT
ejpam-5559	281	9	x	x	X
ejpam-5559	281	10	,	,	PUNCT
ejpam-5559	281	11	y;u	y;u	PROPN
ejpam-5559	281	12	,	,	PUNCT
ejpam-5559	281	13	λ	λ	PROPN
ejpam-5559	281	14	)	)	PUNCT
ejpam-5559	281	15	tn	tn	PROPN
ejpam-5559	281	16	n	n	NUM
ejpam-5559	281	17	!	!	PUNCT
ejpam-5559	281	18	where	where	SCONJ
ejpam-5559	281	19	a(t	a(t	NOUN
ejpam-5559	281	20	)	)	PUNCT
ejpam-5559	281	21	=	=	SYM
ejpam-5559	281	22	(	(	PUNCT
ejpam-5559	281	23	1−u	1−u	NUM
ejpam-5559	281	24	λe2t−u	λe2t−u	NOUN
ejpam-5559	281	25	)	)	PUNCT
ejpam-5559	282	1	r	r	NOUN
ejpam-5559	282	2	ey(e	ey(e	X
ejpam-5559	282	3	t−1	t−1	PROPN
ejpam-5559	282	4	)	)	PUNCT
ejpam-5559	282	5	is	be	AUX
ejpam-5559	282	6	independent	independent	ADJ
ejpam-5559	282	7	of	of	ADP
ejpam-5559	282	8	x	x	PUNCT
ejpam-5559	282	9	with	with	ADP
ejpam-5559	282	10	a(0	a(0	PROPN
ejpam-5559	282	11	)	)	PUNCT
ejpam-5559	282	12	̸=	̸=	PROPN
ejpam-5559	282	13	0	0	NUM
ejpam-5559	282	14	.	.	PUNCT
ejpam-5559	283	1	(	(	PUNCT
ejpam-5559	283	2	2	2	X
ejpam-5559	283	3	)	)	PUNCT
ejpam-5559	283	4	result	result	NOUN
ejpam-5559	283	5	in	in	ADP
ejpam-5559	283	6	(	(	PUNCT
ejpam-5559	283	7	17	17	NUM
ejpam-5559	283	8	)	)	PUNCT
ejpam-5559	283	9	demonstrates	demonstrate	VERB
ejpam-5559	283	10	(	(	PUNCT
ejpam-5559	283	11	11	11	NUM
ejpam-5559	283	12	)	)	PUNCT
ejpam-5559	283	13	and	and	CCONJ
ejpam-5559	283	14	(	(	PUNCT
ejpam-5559	283	15	12	12	NUM
ejpam-5559	283	16	)	)	PUNCT
ejpam-5559	283	17	,	,	PUNCT
ejpam-5559	283	18	bt	bt	X
ejpam-5559	283	19	(	(	PUNCT
ejpam-5559	283	20	r	r	NOUN
ejpam-5559	283	21	)	)	PUNCT
ejpam-5559	283	22	n	n	NOUN
ejpam-5559	283	23	(	(	PUNCT
ejpam-5559	283	24	x	x	X
ejpam-5559	283	25	,	,	PUNCT
ejpam-5559	283	26	y;u	y;u	PROPN
ejpam-5559	283	27	,	,	PUNCT
ejpam-5559	283	28	λ	λ	PROPN
ejpam-5559	283	29	)	)	PUNCT
ejpam-5559	284	1	=	=	SYM
ejpam-5559	284	2	n∑	n∑	X
ejpam-5559	284	3	j=0	j=0	PROPN
ejpam-5559	284	4	(	(	PUNCT
ejpam-5559	284	5	n	n	CCONJ
ejpam-5559	284	6	j	j	NOUN
ejpam-5559	284	7	)	)	PUNCT
ejpam-5559	284	8	cjx	cjx	ADJ
ejpam-5559	284	9	n−j	n−j	ADV
ejpam-5559	284	10	bt	bt	NOUN
ejpam-5559	284	11	(	(	PUNCT
ejpam-5559	284	12	r	r	NOUN
ejpam-5559	284	13	)	)	PUNCT
ejpam-5559	284	14	n	n	NOUN
ejpam-5559	284	15	(	(	PUNCT
ejpam-5559	284	16	x	x	X
ejpam-5559	284	17	,	,	PUNCT
ejpam-5559	284	18	y;u	y;u	PROPN
ejpam-5559	284	19	,	,	PUNCT
ejpam-5559	284	20	λ	λ	NOUN
ejpam-5559	284	21	)	)	PUNCT
ejpam-5559	284	22	=	=	SYM
ejpam-5559	285	1			PROPN
ejpam-5559	285	2	n∑	n∑	PROPN
ejpam-5559	285	3	j=0	j=0	PROPN
ejpam-5559	285	4	cj	cj	PROPN
ejpam-5559	285	5	j	j	PROPN
ejpam-5559	285	6	!	!	PUNCT
ejpam-5559	285	7	dj	dj	PROPN
ejpam-5559	285	8	xn	xn	PUNCT
ejpam-5559	285	9	where	where	SCONJ
ejpam-5559	285	10	cj	cj	NOUN
ejpam-5559	285	11	=	=	NOUN
ejpam-5559	285	12	bt	bt	PROPN
ejpam-5559	285	13	(	(	PUNCT
ejpam-5559	285	14	r	r	NOUN
ejpam-5559	285	15	)	)	PUNCT
ejpam-5559	285	16	j	j	NOUN
ejpam-5559	285	17	(	(	PUNCT
ejpam-5559	285	18	y;u	y;u	PROPN
ejpam-5559	285	19	,	,	PUNCT
ejpam-5559	285	20	λ	λ	NOUN
ejpam-5559	285	21	)	)	PUNCT
ejpam-5559	285	22	and	and	CCONJ
ejpam-5559	285	23	d	d	NOUN
ejpam-5559	285	24	=	=	SYM
ejpam-5559	286	1	d	d	X
ejpam-5559	286	2	dx	dx	PROPN
ejpam-5559	286	3	.	.	PUNCT
ejpam-5559	287	1	the	the	DET
ejpam-5559	287	2	last	last	ADJ
ejpam-5559	287	3	result	result	NOUN
ejpam-5559	287	4	shows	show	VERB
ejpam-5559	287	5	the	the	DET
ejpam-5559	287	6	derivative	derivative	NOUN
ejpam-5559	287	7	of	of	ADP
ejpam-5559	287	8	bt	bt	PROPN
ejpam-5559	287	9	(	(	PUNCT
ejpam-5559	287	10	r	r	NOUN
ejpam-5559	287	11	)	)	PUNCT
ejpam-5559	287	12	n	n	NOUN
ejpam-5559	287	13	(	(	PUNCT
ejpam-5559	287	14	x	x	X
ejpam-5559	287	15	,	,	PUNCT
ejpam-5559	287	16	y;u	y;u	PROPN
ejpam-5559	287	17	,	,	PUNCT
ejpam-5559	287	18	λ	λ	PROPN
ejpam-5559	287	19	)	)	PUNCT
ejpam-5559	287	20	with	with	ADP
ejpam-5559	287	21	respect	respect	NOUN
ejpam-5559	287	22	to	to	ADP
ejpam-5559	287	23	y.	y.	PROPN
ejpam-5559	287	24	theorem	theorem	PROPN
ejpam-5559	287	25	11	11	NUM
ejpam-5559	287	26	.	.	PUNCT
ejpam-5559	288	1	the	the	DET
ejpam-5559	288	2	derivative	derivative	ADJ
ejpam-5559	288	3	formula	formula	NOUN
ejpam-5559	288	4	given	give	VERB
ejpam-5559	288	5	by	by	ADP
ejpam-5559	288	6	∂	∂	NUM
ejpam-5559	288	7	∂y	∂y	PROPN
ejpam-5559	288	8	bt	bt	PROPN
ejpam-5559	288	9	(	(	PUNCT
ejpam-5559	288	10	r	r	NOUN
ejpam-5559	288	11	)	)	PUNCT
ejpam-5559	288	12	n	n	NOUN
ejpam-5559	288	13	(	(	PUNCT
ejpam-5559	288	14	x	x	X
ejpam-5559	288	15	,	,	PUNCT
ejpam-5559	288	16	y;u	y;u	PROPN
ejpam-5559	288	17	,	,	PUNCT
ejpam-5559	288	18	λ	λ	NOUN
ejpam-5559	288	19	)	)	PUNCT
ejpam-5559	288	20	=	=	SYM
ejpam-5559	288	21	bt	bt	NOUN
ejpam-5559	288	22	(	(	PUNCT
ejpam-5559	288	23	r	r	NOUN
ejpam-5559	288	24	)	)	PUNCT
ejpam-5559	288	25	n	n	CCONJ
ejpam-5559	288	26	(	(	PUNCT
ejpam-5559	288	27	x+	x+	PROPN
ejpam-5559	288	28	1	1	NUM
ejpam-5559	288	29	,	,	PUNCT
ejpam-5559	288	30	y;u	y;u	PROPN
ejpam-5559	288	31	,	,	PUNCT
ejpam-5559	288	32	λ)−	λ)−	PROPN
ejpam-5559	288	33	bt	bt	PROPN
ejpam-5559	288	34	(	(	PUNCT
ejpam-5559	288	35	r	r	NOUN
ejpam-5559	288	36	)	)	PUNCT
ejpam-5559	288	37	n	n	NOUN
ejpam-5559	288	38	(	(	PUNCT
ejpam-5559	288	39	x	x	X
ejpam-5559	288	40	,	,	PUNCT
ejpam-5559	288	41	y;u	y;u	PROPN
ejpam-5559	288	42	,	,	PUNCT
ejpam-5559	288	43	λ	λ	PROPN
ejpam-5559	288	44	)	)	PUNCT
ejpam-5559	288	45	(	(	PUNCT
ejpam-5559	288	46	29	29	NUM
ejpam-5559	288	47	)	)	PUNCT
ejpam-5559	288	48	holds	hold	VERB
ejpam-5559	288	49	for	for	ADP
ejpam-5559	288	50	bt	bt	PROPN
ejpam-5559	288	51	(	(	PUNCT
ejpam-5559	288	52	r	r	NOUN
ejpam-5559	288	53	)	)	PUNCT
ejpam-5559	288	54	n	n	NOUN
ejpam-5559	288	55	(	(	PUNCT
ejpam-5559	288	56	x	x	X
ejpam-5559	288	57	,	,	PUNCT
ejpam-5559	288	58	y;u	y;u	PROPN
ejpam-5559	288	59	,	,	PUNCT
ejpam-5559	288	60	λ	λ	NOUN
ejpam-5559	288	61	)	)	PUNCT
ejpam-5559	288	62	.	.	PUNCT
ejpam-5559	289	1	proof	proof	NOUN
ejpam-5559	289	2	.	.	PUNCT
ejpam-5559	290	1	applying	apply	VERB
ejpam-5559	290	2	∂	∂	NOUN
ejpam-5559	290	3	∂x	∂x	PROPN
ejpam-5559	290	4	to	to	ADP
ejpam-5559	290	5	both	both	DET
ejpam-5559	290	6	sides	side	NOUN
ejpam-5559	290	7	of	of	ADP
ejpam-5559	290	8	(	(	PUNCT
ejpam-5559	290	9	5	5	X
ejpam-5559	290	10	)	)	PUNCT
ejpam-5559	290	11	∞∑	∞∑	NUM
ejpam-5559	290	12	n=0	n=0	NUM
ejpam-5559	290	13	∂	∂	NOUN
ejpam-5559	290	14	∂y	∂y	X
ejpam-5559	290	15	bt	bt	NOUN
ejpam-5559	290	16	(	(	PUNCT
ejpam-5559	290	17	r	r	NOUN
ejpam-5559	290	18	)	)	PUNCT
ejpam-5559	290	19	n	n	NOUN
ejpam-5559	290	20	(	(	PUNCT
ejpam-5559	290	21	x	x	X
ejpam-5559	290	22	,	,	PUNCT
ejpam-5559	290	23	y;u	y;u	PROPN
ejpam-5559	290	24	,	,	PUNCT
ejpam-5559	290	25	λ	λ	PROPN
ejpam-5559	290	26	)	)	PUNCT
ejpam-5559	290	27	tn	tn	PROPN
ejpam-5559	290	28	n	n	PROPN
ejpam-5559	290	29	!	!	PUNCT
ejpam-5559	291	1	=	=	PUNCT
ejpam-5559	291	2	(	(	PUNCT
ejpam-5559	291	3	(	(	PUNCT
ejpam-5559	291	4	1−	1−	NUM
ejpam-5559	291	5	u	u	NOUN
ejpam-5559	291	6	)	)	PUNCT
ejpam-5559	291	7	λe2	λe2	PROPN
ejpam-5559	291	8	t	t	NOUN
ejpam-5559	291	9	−	−	PROPN
ejpam-5559	291	10	u	u	NOUN
ejpam-5559	291	11	)	)	PUNCT
ejpam-5559	291	12	r	r	NOUN
ejpam-5559	291	13	ext+y(et−1)(et	ext+y(et−1)(et	NOUN
ejpam-5559	291	14	−	−	ADP
ejpam-5559	291	15	1	1	X
ejpam-5559	291	16	)	)	PUNCT
ejpam-5559	291	17	j.	j.	PROPN
ejpam-5559	291	18	ontolan	ontolan	PROPN
ejpam-5559	291	19	et	et	PROPN
ejpam-5559	291	20	al	al	PROPN
ejpam-5559	291	21	.	.	PUNCT
ejpam-5559	291	22	/	/	SYM
ejpam-5559	291	23	eur	eur	PROPN
ejpam-5559	291	24	.	.	PUNCT
ejpam-5559	292	1	j.	j.	PROPN
ejpam-5559	292	2	pure	pure	PROPN
ejpam-5559	292	3	appl	appl	PROPN
ejpam-5559	292	4	.	.	PROPN
ejpam-5559	292	5	math	math	PROPN
ejpam-5559	292	6	,	,	PUNCT
ejpam-5559	292	7	18	18	NUM
ejpam-5559	292	8	(	(	PUNCT
ejpam-5559	292	9	1	1	NUM
ejpam-5559	292	10	)	)	PUNCT
ejpam-5559	292	11	(	(	PUNCT
ejpam-5559	292	12	2025	2025	NUM
ejpam-5559	292	13	)	)	PUNCT
ejpam-5559	292	14	,	,	PUNCT
ejpam-5559	292	15	5559	5559	NUM
ejpam-5559	292	16	15	15	NUM
ejpam-5559	292	17	of	of	ADP
ejpam-5559	292	18	16	16	NUM
ejpam-5559	292	19	=	=	SYM
ejpam-5559	292	20	(	(	PUNCT
ejpam-5559	292	21	(	(	PUNCT
ejpam-5559	292	22	1−	1−	NUM
ejpam-5559	292	23	u	u	NOUN
ejpam-5559	292	24	)	)	PUNCT
ejpam-5559	292	25	λe2	λe2	PROPN
ejpam-5559	292	26	t	t	NOUN
ejpam-5559	292	27	−	−	PROPN
ejpam-5559	292	28	u	u	NOUN
ejpam-5559	292	29	)	)	PUNCT
ejpam-5559	292	30	r	r	NOUN
ejpam-5559	292	31	e(x+1)t+y(et−1	e(x+1)t+y(et−1	NOUN
ejpam-5559	292	32	)	)	PUNCT
ejpam-5559	292	33	−	−	PROPN
ejpam-5559	293	1	(	(	PUNCT
ejpam-5559	293	2	(	(	PUNCT
ejpam-5559	293	3	1−	1−	NUM
ejpam-5559	293	4	u	u	NOUN
ejpam-5559	293	5	)	)	PUNCT
ejpam-5559	293	6	λe2	λe2	PROPN
ejpam-5559	293	7	t	t	NOUN
ejpam-5559	293	8	−	−	PROPN
ejpam-5559	293	9	u	u	PROPN
ejpam-5559	293	10	)	)	PUNCT
ejpam-5559	293	11	r	r	NOUN
ejpam-5559	293	12	ext+y(et−1	ext+y(et−1	NOUN
ejpam-5559	293	13	)	)	PUNCT
ejpam-5559	294	1	=	=	PUNCT
ejpam-5559	295	1	∞∑	∞∑	ADJ
ejpam-5559	295	2	n=0	n=0	NUM
ejpam-5559	295	3	bt	bt	NOUN
ejpam-5559	295	4	(	(	PUNCT
ejpam-5559	295	5	r	r	NOUN
ejpam-5559	295	6	)	)	PUNCT
ejpam-5559	295	7	n	n	CCONJ
ejpam-5559	295	8	(	(	PUNCT
ejpam-5559	295	9	x+	x+	PROPN
ejpam-5559	295	10	1	1	NUM
ejpam-5559	295	11	,	,	PUNCT
ejpam-5559	295	12	y;u	y;u	PROPN
ejpam-5559	295	13	,	,	PUNCT
ejpam-5559	295	14	λ	λ	PROPN
ejpam-5559	295	15	)	)	PUNCT
ejpam-5559	295	16	tn	tn	PROPN
ejpam-5559	295	17	n	n	PROPN
ejpam-5559	295	18	!	!	PUNCT
ejpam-5559	296	1	−	−	PROPN
ejpam-5559	297	1	∞∑	∞∑	PRON
ejpam-5559	297	2	n=0	n=0	NUM
ejpam-5559	297	3	bt	bt	NOUN
ejpam-5559	297	4	(	(	PUNCT
ejpam-5559	297	5	r	r	NOUN
ejpam-5559	297	6	)	)	PUNCT
ejpam-5559	297	7	n	n	NOUN
ejpam-5559	297	8	(	(	PUNCT
ejpam-5559	297	9	x	x	X
ejpam-5559	297	10	,	,	PUNCT
ejpam-5559	297	11	y;u	y;u	PROPN
ejpam-5559	297	12	,	,	PUNCT
ejpam-5559	297	13	λ	λ	PROPN
ejpam-5559	297	14	)	)	PUNCT
ejpam-5559	297	15	tn	tn	PROPN
ejpam-5559	297	16	n	n	NOUN
ejpam-5559	297	17	!	!	PUNCT
ejpam-5559	297	18	=	=	NOUN
ejpam-5559	298	1	∞∑	∞∑	PRON
ejpam-5559	298	2	n=0	n=0	NUM
ejpam-5559	298	3	{	{	PUNCT
ejpam-5559	298	4	bt	bt	X
ejpam-5559	298	5	(	(	PUNCT
ejpam-5559	298	6	r	r	NOUN
ejpam-5559	298	7	)	)	PUNCT
ejpam-5559	298	8	n	n	CCONJ
ejpam-5559	298	9	(	(	PUNCT
ejpam-5559	298	10	x+	x+	PROPN
ejpam-5559	298	11	1	1	NUM
ejpam-5559	298	12	,	,	PUNCT
ejpam-5559	298	13	y;u	y;u	PROPN
ejpam-5559	298	14	,	,	PUNCT
ejpam-5559	298	15	λ)−	λ)−	PROPN
ejpam-5559	298	16	bt	bt	PROPN
ejpam-5559	298	17	(	(	PUNCT
ejpam-5559	298	18	r	r	NOUN
ejpam-5559	298	19	)	)	PUNCT
ejpam-5559	298	20	n	n	NOUN
ejpam-5559	298	21	(	(	PUNCT
ejpam-5559	298	22	x	x	X
ejpam-5559	298	23	,	,	PUNCT
ejpam-5559	298	24	y;u	y;u	PROPN
ejpam-5559	298	25	,	,	PUNCT
ejpam-5559	298	26	λ	λ	NOUN
ejpam-5559	298	27	)	)	PUNCT
ejpam-5559	298	28	}	}	PUNCT
ejpam-5559	298	29	tn	tn	PROPN
ejpam-5559	298	30	n	n	PROPN
ejpam-5559	298	31	!	!	PUNCT
ejpam-5559	298	32	∂	∂	PUNCT
ejpam-5559	298	33	∂y	∂y	NUM
ejpam-5559	298	34	bt	bt	PROPN
ejpam-5559	298	35	(	(	PUNCT
ejpam-5559	298	36	r	r	NOUN
ejpam-5559	298	37	)	)	PUNCT
ejpam-5559	298	38	n	n	NOUN
ejpam-5559	298	39	(	(	PUNCT
ejpam-5559	298	40	x	x	X
ejpam-5559	298	41	,	,	PUNCT
ejpam-5559	298	42	y;u	y;u	PROPN
ejpam-5559	298	43	,	,	PUNCT
ejpam-5559	298	44	λ	λ	NOUN
ejpam-5559	298	45	)	)	PUNCT
ejpam-5559	298	46	=	=	SYM
ejpam-5559	298	47	bt	bt	NOUN
ejpam-5559	298	48	(	(	PUNCT
ejpam-5559	298	49	r	r	NOUN
ejpam-5559	298	50	)	)	PUNCT
ejpam-5559	298	51	n	n	CCONJ
ejpam-5559	298	52	(	(	PUNCT
ejpam-5559	298	53	x+	x+	PROPN
ejpam-5559	298	54	1	1	NUM
ejpam-5559	298	55	,	,	PUNCT
ejpam-5559	298	56	y;u	y;u	PROPN
ejpam-5559	298	57	,	,	PUNCT
ejpam-5559	298	58	λ)−	λ)−	PROPN
ejpam-5559	298	59	bt	bt	PROPN
ejpam-5559	298	60	(	(	PUNCT
ejpam-5559	298	61	r	r	NOUN
ejpam-5559	298	62	)	)	PUNCT
ejpam-5559	298	63	n	n	NOUN
ejpam-5559	298	64	(	(	PUNCT
ejpam-5559	298	65	x	x	X
ejpam-5559	298	66	,	,	PUNCT
ejpam-5559	298	67	y;u	y;u	PROPN
ejpam-5559	298	68	,	,	PUNCT
ejpam-5559	298	69	λ	λ	PROPN
ejpam-5559	298	70	)	)	PUNCT
ejpam-5559	298	71	.	.	PUNCT
ejpam-5559	299	1	remark	remark	PROPN
ejpam-5559	299	2	3	3	NUM
ejpam-5559	299	3	.	.	PUNCT
ejpam-5559	300	1	combining	combine	VERB
ejpam-5559	300	2	the	the	DET
ejpam-5559	300	3	results	result	NOUN
ejpam-5559	300	4	from	from	ADP
ejpam-5559	300	5	(	(	PUNCT
ejpam-5559	300	6	25	25	NUM
ejpam-5559	300	7	)	)	PUNCT
ejpam-5559	300	8	and	and	CCONJ
ejpam-5559	300	9	(	(	PUNCT
ejpam-5559	300	10	29	29	NUM
ejpam-5559	300	11	)	)	PUNCT
ejpam-5559	300	12	,	,	PUNCT
ejpam-5559	300	13	we	we	PRON
ejpam-5559	300	14	obtain	obtain	VERB
ejpam-5559	300	15	the	the	DET
ejpam-5559	300	16	equation	equation	NOUN
ejpam-5559	300	17	∂	∂	NOUN
ejpam-5559	300	18	∂y	∂y	PROPN
ejpam-5559	300	19	bt	bt	PROPN
ejpam-5559	300	20	(	(	PUNCT
ejpam-5559	300	21	r	r	NOUN
ejpam-5559	300	22	)	)	PUNCT
ejpam-5559	300	23	n	n	NOUN
ejpam-5559	300	24	(	(	PUNCT
ejpam-5559	300	25	x	x	X
ejpam-5559	300	26	,	,	PUNCT
ejpam-5559	300	27	y;u	y;u	PROPN
ejpam-5559	300	28	,	,	PUNCT
ejpam-5559	300	29	λ	λ	NOUN
ejpam-5559	300	30	)	)	PUNCT
ejpam-5559	300	31	=	=	SYM
ejpam-5559	301	1	n−1∑	n−1∑	PROPN
ejpam-5559	301	2	k=0	k=0	PROPN
ejpam-5559	301	3	(	(	PUNCT
ejpam-5559	301	4	n	n	X
ejpam-5559	301	5	k	k	NOUN
ejpam-5559	301	6	)	)	PUNCT
ejpam-5559	301	7	bt	bt	PROPN
ejpam-5559	301	8	(	(	PUNCT
ejpam-5559	301	9	r	r	NOUN
ejpam-5559	301	10	)	)	PUNCT
ejpam-5559	301	11	k	k	NOUN
ejpam-5559	301	12	(	(	PUNCT
ejpam-5559	301	13	x	x	NOUN
ejpam-5559	301	14	,	,	PUNCT
ejpam-5559	301	15	y;u	y;u	PROPN
ejpam-5559	301	16	,	,	PUNCT
ejpam-5559	301	17	λ	λ	PROPN
ejpam-5559	301	18	)	)	PUNCT
ejpam-5559	301	19	.	.	PUNCT
ejpam-5559	302	1	(	(	PUNCT
ejpam-5559	302	2	30	30	NUM
ejpam-5559	302	3	)	)	PUNCT
ejpam-5559	302	4	to	to	PART
ejpam-5559	302	5	see	see	VERB
ejpam-5559	302	6	this	this	PRON
ejpam-5559	302	7	,	,	PUNCT
ejpam-5559	302	8	consider	consider	VERB
ejpam-5559	302	9	the	the	DET
ejpam-5559	302	10	example	example	NOUN
ejpam-5559	302	11	below	below	ADV
ejpam-5559	302	12	.	.	PUNCT
ejpam-5559	303	1	we	we	PRON
ejpam-5559	303	2	use	use	VERB
ejpam-5559	303	3	(	(	PUNCT
ejpam-5559	303	4	5	5	NUM
ejpam-5559	303	5	)	)	PUNCT
ejpam-5559	303	6	to	to	PART
ejpam-5559	303	7	get	get	VERB
ejpam-5559	303	8	the	the	DET
ejpam-5559	303	9	following	follow	VERB
ejpam-5559	303	10	polynomials	polynomial	NOUN
ejpam-5559	303	11	bt	bt	INTJ
ejpam-5559	303	12	(	(	PUNCT
ejpam-5559	303	13	r	r	NOUN
ejpam-5559	303	14	)	)	PUNCT
ejpam-5559	303	15	0	0	NUM
ejpam-5559	304	1	(	(	PUNCT
ejpam-5559	304	2	x	x	NOUN
ejpam-5559	304	3	,	,	PUNCT
ejpam-5559	304	4	y;u	y;u	PROPN
ejpam-5559	304	5	,	,	PUNCT
ejpam-5559	304	6	λ	λ	NOUN
ejpam-5559	304	7	)	)	PUNCT
ejpam-5559	304	8	=	=	SYM
ejpam-5559	304	9	(	(	PUNCT
ejpam-5559	304	10	u−	u−	PROPN
ejpam-5559	304	11	1	1	NUM
ejpam-5559	304	12	u−	u−	PROPN
ejpam-5559	304	13	λ	λ	NOUN
ejpam-5559	304	14	)	)	PUNCT
ejpam-5559	304	15	r	r	NOUN
ejpam-5559	304	16	,	,	PUNCT
ejpam-5559	304	17	bt	bt	X
ejpam-5559	304	18	(	(	PUNCT
ejpam-5559	304	19	r	r	NOUN
ejpam-5559	304	20	)	)	PUNCT
ejpam-5559	304	21	1	1	NUM
ejpam-5559	304	22	(	(	PUNCT
ejpam-5559	304	23	x	x	NOUN
ejpam-5559	304	24	,	,	PUNCT
ejpam-5559	304	25	y;u	y;u	PROPN
ejpam-5559	304	26	,	,	PUNCT
ejpam-5559	304	27	λ	λ	NOUN
ejpam-5559	304	28	)	)	PUNCT
ejpam-5559	304	29	=	=	SYM
ejpam-5559	305	1	(	(	PUNCT
ejpam-5559	305	2	u−1	u−1	PROPN
ejpam-5559	305	3	u−λ	u−λ	ADV
ejpam-5559	305	4	)	)	PUNCT
ejpam-5559	305	5	r	r	NOUN
ejpam-5559	305	6	(	(	PUNCT
ejpam-5559	305	7	λ(2r	λ(2r	X
ejpam-5559	305	8	−	−	PROPN
ejpam-5559	305	9	x−	x−	PROPN
ejpam-5559	305	10	y	y	PROPN
ejpam-5559	305	11	)	)	PUNCT
ejpam-5559	306	1	+	+	CCONJ
ejpam-5559	306	2	u(x+	u(x+	PROPN
ejpam-5559	306	3	y	y	X
ejpam-5559	306	4	)	)	PUNCT
ejpam-5559	306	5	)	)	PUNCT
ejpam-5559	307	1	u−	u−	PROPN
ejpam-5559	307	2	λ	λ	PROPN
ejpam-5559	307	3	,	,	PUNCT
ejpam-5559	307	4	bt	bt	PROPN
ejpam-5559	307	5	(	(	PUNCT
ejpam-5559	307	6	r	r	NOUN
ejpam-5559	307	7	)	)	PUNCT
ejpam-5559	307	8	2	2	NUM
ejpam-5559	307	9	(	(	PUNCT
ejpam-5559	307	10	x	x	NOUN
ejpam-5559	307	11	,	,	PUNCT
ejpam-5559	307	12	y;u	y;u	PROPN
ejpam-5559	307	13	,	,	PUNCT
ejpam-5559	307	14	λ	λ	NOUN
ejpam-5559	307	15	)	)	PUNCT
ejpam-5559	307	16	=	=	SYM
ejpam-5559	307	17	(	(	PUNCT
ejpam-5559	307	18	x+	x+	X
ejpam-5559	307	19	y)2	y)2	NOUN
ejpam-5559	307	20	(	(	PUNCT
ejpam-5559	307	21	1−	1−	NUM
ejpam-5559	307	22	u	u	NOUN
ejpam-5559	307	23	λ−	λ−	PROPN
ejpam-5559	307	24	u	u	NOUN
ejpam-5559	307	25	)	)	PUNCT
ejpam-5559	308	1	r	r	NOUN
ejpam-5559	308	2	+	+	NOUN
ejpam-5559	308	3	y	y	PROPN
ejpam-5559	308	4	(	(	PUNCT
ejpam-5559	308	5	1−	1−	NUM
ejpam-5559	308	6	u	u	NOUN
ejpam-5559	308	7	λ−	λ−	PROPN
ejpam-5559	308	8	u	u	NOUN
ejpam-5559	308	9	)	)	PUNCT
ejpam-5559	309	1	r	r	NOUN
ejpam-5559	309	2	+	+	NUM
ejpam-5559	309	3	8λ2r(1−	8λ2r(1−	NUM
ejpam-5559	309	4	u	u	NOUN
ejpam-5559	309	5	)	)	PUNCT
ejpam-5559	309	6	(	(	PUNCT
ejpam-5559	309	7	1−u	1−u	NUM
ejpam-5559	309	8	λ−u	λ−u	NOUN
ejpam-5559	309	9	)	)	PUNCT
ejpam-5559	310	1	r−1	r−1	PROPN
ejpam-5559	310	2	(	(	PUNCT
ejpam-5559	310	3	λ−	λ−	PROPN
ejpam-5559	310	4	u)3	u)3	PROPN
ejpam-5559	310	5	+	+	CCONJ
ejpam-5559	310	6	4λ2(r	4λ2(r	ADJ
ejpam-5559	310	7	−	−	ADP
ejpam-5559	310	8	1)r(1−	1)r(1−	NUM
ejpam-5559	310	9	u)2	u)2	NOUN
ejpam-5559	310	10	(	(	PUNCT
ejpam-5559	310	11	1−u	1−u	NUM
ejpam-5559	310	12	λ−u	λ−u	NOUN
ejpam-5559	310	13	)	)	PUNCT
ejpam-5559	310	14	r−2	r−2	PROPN
ejpam-5559	310	15	(	(	PUNCT
ejpam-5559	310	16	λ−	λ−	PROPN
ejpam-5559	310	17	u)4	u)4	NOUN
ejpam-5559	310	18	−	−	PROPN
ejpam-5559	310	19	2λr(1−	2λr(1−	NUM
ejpam-5559	310	20	u)(x+	u)(x+	PROPN
ejpam-5559	310	21	y	y	NOUN
ejpam-5559	310	22	)	)	PUNCT
ejpam-5559	310	23	(	(	PUNCT
ejpam-5559	310	24	1−u	1−u	NUM
ejpam-5559	310	25	λ−u	λ−u	NOUN
ejpam-5559	310	26	)	)	PUNCT
ejpam-5559	310	27	r−1	r−1	PROPN
ejpam-5559	310	28	(	(	PUNCT
ejpam-5559	310	29	λ−	λ−	PROPN
ejpam-5559	310	30	u)2	u)2	ADV
ejpam-5559	310	31	−	−	PROPN
ejpam-5559	310	32	2λr(1−	2λr(1−	NUM
ejpam-5559	310	33	u)(x+	u)(x+	ADJ
ejpam-5559	310	34	y	y	NOUN
ejpam-5559	310	35	+	+	NOUN
ejpam-5559	310	36	2	2	NUM
ejpam-5559	310	37	)	)	PUNCT
ejpam-5559	310	38	(	(	PUNCT
ejpam-5559	310	39	1−u	1−u	NUM
ejpam-5559	310	40	λ−u	λ−u	NOUN
ejpam-5559	310	41	)	)	PUNCT
ejpam-5559	310	42	r−1	r−1	PROPN
ejpam-5559	310	43	(	(	PUNCT
ejpam-5559	310	44	λ−	λ−	PROPN
ejpam-5559	310	45	u)2	u)2	PROPN
ejpam-5559	310	46	.	.	PUNCT
ejpam-5559	311	1	one	one	PRON
ejpam-5559	311	2	can	can	AUX
ejpam-5559	311	3	verify	verify	VERB
ejpam-5559	311	4	using	use	VERB
ejpam-5559	311	5	the	the	DET
ejpam-5559	311	6	above	above	ADJ
ejpam-5559	311	7	polynomials	polynomial	NOUN
ejpam-5559	311	8	that	that	PRON
ejpam-5559	311	9	∂	∂	ADJ
ejpam-5559	311	10	∂y	∂y	X
ejpam-5559	311	11	bt	bt	NOUN
ejpam-5559	311	12	(	(	PUNCT
ejpam-5559	311	13	r	r	NOUN
ejpam-5559	311	14	)	)	PUNCT
ejpam-5559	311	15	2	2	NUM
ejpam-5559	311	16	(	(	PUNCT
ejpam-5559	311	17	x	x	NOUN
ejpam-5559	311	18	,	,	PUNCT
ejpam-5559	311	19	y;u	y;u	PROPN
ejpam-5559	311	20	,	,	PUNCT
ejpam-5559	311	21	λ	λ	PROPN
ejpam-5559	311	22	)	)	PUNCT
ejpam-5559	311	23	=	=	SYM
ejpam-5559	312	1	(	(	PUNCT
ejpam-5559	312	2	2	2	NUM
ejpam-5559	312	3	0	0	NUM
ejpam-5559	312	4	)	)	PUNCT
ejpam-5559	312	5	bt	bt	NOUN
ejpam-5559	312	6	(	(	PUNCT
ejpam-5559	312	7	r	r	NOUN
ejpam-5559	312	8	)	)	PUNCT
ejpam-5559	312	9	0	0	NUM
ejpam-5559	313	1	(	(	PUNCT
ejpam-5559	313	2	x	x	NOUN
ejpam-5559	313	3	,	,	PUNCT
ejpam-5559	313	4	y;u	y;u	PROPN
ejpam-5559	313	5	,	,	PUNCT
ejpam-5559	313	6	λ	λ	NOUN
ejpam-5559	313	7	)	)	PUNCT
ejpam-5559	314	1	+	+	CCONJ
ejpam-5559	314	2	(	(	PUNCT
ejpam-5559	314	3	2	2	NUM
ejpam-5559	314	4	1	1	NUM
ejpam-5559	314	5	)	)	PUNCT
ejpam-5559	314	6	bt	bt	NOUN
ejpam-5559	314	7	(	(	PUNCT
ejpam-5559	314	8	r	r	NOUN
ejpam-5559	314	9	)	)	PUNCT
ejpam-5559	314	10	1	1	NUM
ejpam-5559	314	11	(	(	PUNCT
ejpam-5559	314	12	x	x	NOUN
ejpam-5559	314	13	,	,	PUNCT
ejpam-5559	314	14	y;u	y;u	PROPN
ejpam-5559	314	15	,	,	PUNCT
ejpam-5559	314	16	λ	λ	NOUN
ejpam-5559	314	17	)	)	PUNCT
ejpam-5559	314	18	.	.	PUNCT
ejpam-5559	315	1	acknowledgements	acknowledgement	NOUN
ejpam-5559	315	2	this	this	DET
ejpam-5559	315	3	research	research	NOUN
ejpam-5559	315	4	has	have	AUX
ejpam-5559	315	5	been	be	AUX
ejpam-5559	315	6	funded	fund	VERB
ejpam-5559	315	7	by	by	ADP
ejpam-5559	315	8	cebu	cebu	PROPN
ejpam-5559	315	9	normal	normal	ADJ
ejpam-5559	315	10	university	university	PROPN
ejpam-5559	315	11	(	(	PUNCT
ejpam-5559	315	12	cnu	cnu	PROPN
ejpam-5559	315	13	)	)	PUNCT
ejpam-5559	315	14	through	through	ADP
ejpam-5559	315	15	its	its	PRON
ejpam-5559	315	16	center	center	NOUN
ejpam-5559	315	17	for	for	ADP
ejpam-5559	315	18	research	research	NOUN
ejpam-5559	315	19	and	and	CCONJ
ejpam-5559	315	20	development	development	NOUN
ejpam-5559	315	21	(	(	PUNCT
ejpam-5559	315	22	crd	crd	PROPN
ejpam-5559	315	23	)	)	PUNCT
ejpam-5559	315	24	.	.	PUNCT
ejpam-5559	316	1	j.	j.	PROPN
ejpam-5559	316	2	ontolan	ontolan	PROPN
ejpam-5559	316	3	et	et	PROPN
ejpam-5559	316	4	al	al	PROPN
ejpam-5559	316	5	.	.	PUNCT
ejpam-5559	316	6	/	/	SYM
ejpam-5559	316	7	eur	eur	PROPN
ejpam-5559	316	8	.	.	PUNCT
ejpam-5559	317	1	j.	j.	PROPN
ejpam-5559	317	2	pure	pure	PROPN
ejpam-5559	317	3	appl	appl	PROPN
ejpam-5559	317	4	.	.	PROPN
ejpam-5559	317	5	math	math	PROPN
ejpam-5559	317	6	,	,	PUNCT
ejpam-5559	317	7	18	18	NUM
ejpam-5559	317	8	(	(	PUNCT
ejpam-5559	317	9	1	1	NUM
ejpam-5559	317	10	)	)	PUNCT
ejpam-5559	317	11	(	(	PUNCT
ejpam-5559	317	12	2025	2025	NUM
ejpam-5559	317	13	)	)	PUNCT
ejpam-5559	317	14	,	,	PUNCT
ejpam-5559	317	15	5559	5559	NUM
ejpam-5559	317	16	16	16	NUM
ejpam-5559	317	17	of	of	ADP
ejpam-5559	317	18	16	16	NUM
ejpam-5559	317	19	references	reference	NOUN
ejpam-5559	317	20	[	[	X
ejpam-5559	317	21	1	1	NUM
ejpam-5559	317	22	]	]	X
ejpam-5559	317	23	paul	paul	PROPN
ejpam-5559	317	24	appell	appell	PROPN
ejpam-5559	317	25	.	.	PUNCT
ejpam-5559	318	1	sur	sur	PROPN
ejpam-5559	318	2	une	une	PROPN
ejpam-5559	318	3	classe	classe	PROPN
ejpam-5559	318	4	de	de	PROPN
ejpam-5559	318	5	polynômes	polynômes	PROPN
ejpam-5559	318	6	.	.	PUNCT
ejpam-5559	319	1	in	in	ADP
ejpam-5559	319	2	annales	annale	NOUN
ejpam-5559	319	3	scientifiques	scientifique	NOUN
ejpam-5559	319	4	de	de	ADP
ejpam-5559	319	5	l’école	l’école	ADJ
ejpam-5559	319	6	normale	normale	PROPN
ejpam-5559	319	7	supérieure	supérieure	PROPN
ejpam-5559	319	8	,	,	PUNCT
ejpam-5559	319	9	volume	volume	NOUN
ejpam-5559	319	10	9	9	NUM
ejpam-5559	319	11	,	,	PUNCT
ejpam-5559	319	12	pages	page	NOUN
ejpam-5559	319	13	119–144	119–144	NUM
ejpam-5559	319	14	,	,	PUNCT
ejpam-5559	319	15	1880	1880	NUM
ejpam-5559	319	16	.	.	PUNCT
ejpam-5559	320	1	[	[	X
ejpam-5559	320	2	2	2	NUM
ejpam-5559	320	3	]	]	X
ejpam-5559	320	4	serkan	serkan	ADJ
ejpam-5559	320	5	araci	araci	PROPN
ejpam-5559	320	6	,	,	PUNCT
ejpam-5559	320	7	mehmet	mehmet	PROPN
ejpam-5559	320	8	acikgoz	acikgoz	PROPN
ejpam-5559	320	9	,	,	PUNCT
ejpam-5559	320	10	and	and	CCONJ
ejpam-5559	320	11	e	e	X
ejpam-5559	320	12	sen	sen	PROPN
ejpam-5559	320	13	.	.	PROPN
ejpam-5559	321	1	a	a	DET
ejpam-5559	321	2	note	note	NOUN
ejpam-5559	321	3	on	on	ADP
ejpam-5559	321	4	the	the	DET
ejpam-5559	321	5	p	p	NOUN
ejpam-5559	321	6	-	-	PUNCT
ejpam-5559	321	7	adic	adic	ADJ
ejpam-5559	321	8	interpolation	interpolation	NOUN
ejpam-5559	321	9	function	function	NOUN
ejpam-5559	321	10	for	for	ADP
ejpam-5559	321	11	multiple	multiple	ADJ
ejpam-5559	321	12	generalized	generalize	VERB
ejpam-5559	321	13	genocchi	genocchi	NOUN
ejpam-5559	321	14	numbers	number	NOUN
ejpam-5559	321	15	.	.	PUNCT
ejpam-5559	322	1	turkish	turkish	ADJ
ejpam-5559	322	2	journal	journal	NOUN
ejpam-5559	322	3	of	of	ADP
ejpam-5559	322	4	analysis	analysis	NOUN
ejpam-5559	322	5	and	and	CCONJ
ejpam-5559	322	6	number	number	NOUN
ejpam-5559	322	7	theory	theory	NOUN
ejpam-5559	322	8	,	,	PUNCT
ejpam-5559	322	9	1(1):17–22	1(1):17–22	NUM
ejpam-5559	322	10	,	,	PUNCT
ejpam-5559	322	11	2013	2013	NUM
ejpam-5559	322	12	.	.	PUNCT
ejpam-5559	323	1	[	[	X
ejpam-5559	323	2	3	3	X
ejpam-5559	323	3	]	]	X
ejpam-5559	323	4	theodore	theodore	PROPN
ejpam-5559	323	5	s	s	PART
ejpam-5559	323	6	chihara	chihara	NOUN
ejpam-5559	323	7	.	.	PUNCT
ejpam-5559	324	1	an	an	DET
ejpam-5559	324	2	introduction	introduction	NOUN
ejpam-5559	324	3	to	to	ADP
ejpam-5559	324	4	orthogonal	orthogonal	ADJ
ejpam-5559	324	5	polynomials	polynomial	NOUN
ejpam-5559	324	6	.	.	PUNCT
ejpam-5559	325	1	courier	courier	NOUN
ejpam-5559	325	2	corporation	corporation	NOUN
ejpam-5559	325	3	,	,	PUNCT
ejpam-5559	325	4	2011	2011	NUM
ejpam-5559	325	5	.	.	PUNCT
ejpam-5559	326	1	[	[	X
ejpam-5559	326	2	4	4	NUM
ejpam-5559	326	3	]	]	X
ejpam-5559	326	4	cb	cb	PROPN
ejpam-5559	326	5	corcino	corcino	PROPN
ejpam-5559	326	6	,	,	PUNCT
ejpam-5559	326	7	b	b	NOUN
ejpam-5559	326	8	damgo	damgo	ADJ
ejpam-5559	326	9	,	,	PUNCT
ejpam-5559	326	10	and	and	CCONJ
ejpam-5559	326	11	rb	rb	PROPN
ejpam-5559	326	12	corcino	corcino	NOUN
ejpam-5559	326	13	.	.	PUNCT
ejpam-5559	327	1	fourier	fouri	ADJ
ejpam-5559	327	2	expansions	expansion	NOUN
ejpam-5559	327	3	for	for	ADP
ejpam-5559	327	4	genocchi	genocchi	NOUN
ejpam-5559	327	5	polynomials	polynomial	NOUN
ejpam-5559	327	6	of	of	ADP
ejpam-5559	327	7	higher	high	ADJ
ejpam-5559	327	8	order	order	NOUN
ejpam-5559	327	9	.	.	PUNCT
ejpam-5559	328	1	j.	j.	PROPN
ejpam-5559	328	2	math	math	PROPN
ejpam-5559	328	3	.	.	PUNCT
ejpam-5559	329	1	comput	comput	NOUN
ejpam-5559	329	2	.	.	PUNCT
ejpam-5559	330	1	sci	sci	PROPN
ejpam-5559	330	2	,	,	PUNCT
ejpam-5559	330	3	22:59–72	22:59–72	NUM
ejpam-5559	330	4	,	,	PUNCT
ejpam-5559	330	5	2020	2020	NUM
ejpam-5559	330	6	.	.	PUNCT
ejpam-5559	331	1	[	[	X
ejpam-5559	331	2	5	5	X
ejpam-5559	331	3	]	]	PUNCT
ejpam-5559	331	4	g.	g.	NOUN
ejpam-5559	331	5	dattoli	dattoli	PROPN
ejpam-5559	331	6	,	,	PUNCT
ejpam-5559	331	7	s.	s.	PROPN
ejpam-5559	331	8	lorenzutta	lorenzutta	PROPN
ejpam-5559	331	9	,	,	PUNCT
ejpam-5559	331	10	p.e	p.e	PROPN
ejpam-5559	331	11	.	.	PROPN
ejpam-5559	331	12	ricci	ricci	PROPN
ejpam-5559	331	13	,	,	PUNCT
ejpam-5559	331	14	and	and	CCONJ
ejpam-5559	331	15	c.	c.	PROPN
ejpam-5559	331	16	cesarano	cesarano	PROPN
ejpam-5559	331	17	.	.	PUNCT
ejpam-5559	332	1	on	on	ADP
ejpam-5559	332	2	a	a	DET
ejpam-5559	332	3	family	family	NOUN
ejpam-5559	332	4	of	of	ADP
ejpam-5559	332	5	hybrid	hybrid	ADJ
ejpam-5559	332	6	polynomials	polynomial	NOUN
ejpam-5559	332	7	.	.	PUNCT
ejpam-5559	333	1	integral	integral	ADJ
ejpam-5559	333	2	transforms	transform	NOUN
ejpam-5559	333	3	and	and	CCONJ
ejpam-5559	333	4	special	special	ADJ
ejpam-5559	333	5	functions	function	NOUN
ejpam-5559	333	6	,	,	PUNCT
ejpam-5559	333	7	15(6):485–490	15(6):485–490	NUM
ejpam-5559	333	8	,	,	PUNCT
ejpam-5559	333	9	2004	2004	NUM
ejpam-5559	333	10	.	.	PUNCT
ejpam-5559	334	1	[	[	X
ejpam-5559	334	2	6	6	NUM
ejpam-5559	334	3	]	]	X
ejpam-5559	334	4	w.a	w.a	PROPN
ejpam-5559	334	5	.	.	PROPN
ejpam-5559	334	6	khan	khan	PROPN
ejpam-5559	334	7	and	and	CCONJ
ejpam-5559	334	8	m.	m.	PROPN
ejpam-5559	334	9	riaz	riaz	PROPN
ejpam-5559	334	10	.	.	PUNCT
ejpam-5559	335	1	some	some	DET
ejpam-5559	335	2	subclasses	subclass	NOUN
ejpam-5559	335	3	of	of	ADP
ejpam-5559	335	4	apostol	apostol	NOUN
ejpam-5559	335	5	-	-	PUNCT
ejpam-5559	335	6	type	type	NOUN
ejpam-5559	335	7	polynomials	polynomial	NOUN
ejpam-5559	335	8	and	and	CCONJ
ejpam-5559	335	9	their	their	PRON
ejpam-5559	335	10	properties	property	NOUN
ejpam-5559	335	11	.	.	PUNCT
ejpam-5559	336	1	international	international	ADJ
ejpam-5559	336	2	journal	journal	PROPN
ejpam-5559	336	3	of	of	ADP
ejpam-5559	336	4	mathematical	mathematical	ADJ
ejpam-5559	336	5	analysis	analysis	NOUN
ejpam-5559	336	6	,	,	PUNCT
ejpam-5559	336	7	21(69):3457–3470	21(69):3457–3470	NUM
ejpam-5559	336	8	,	,	PUNCT
ejpam-5559	336	9	2022	2022	NUM
ejpam-5559	336	10	.	.	PUNCT
ejpam-5559	337	1	[	[	X
ejpam-5559	337	2	7	7	X
ejpam-5559	337	3	]	]	X
ejpam-5559	337	4	v.	v.	ADP
ejpam-5559	337	5	kurt	kurt	PROPN
ejpam-5559	337	6	.	.	PUNCT
ejpam-5559	338	1	new	new	ADJ
ejpam-5559	338	2	families	family	NOUN
ejpam-5559	338	3	of	of	ADP
ejpam-5559	338	4	polynomials	polynomial	NOUN
ejpam-5559	338	5	associated	associate	VERB
ejpam-5559	338	6	with	with	ADP
ejpam-5559	338	7	the	the	DET
ejpam-5559	338	8	bell	bell	PROPN
ejpam-5559	338	9	numbers	number	NOUN
ejpam-5559	338	10	and	and	CCONJ
ejpam-5559	338	11	polynomials	polynomial	NOUN
ejpam-5559	338	12	.	.	PUNCT
ejpam-5559	339	1	carpathian	carpathian	ADJ
ejpam-5559	339	2	mathematical	mathematical	ADJ
ejpam-5559	339	3	publications	publication	NOUN
ejpam-5559	339	4	,	,	PUNCT
ejpam-5559	339	5	14(2):354–363	14(2):354–363	PROPN
ejpam-5559	339	6	,	,	PUNCT
ejpam-5559	339	7	2007	2007	NUM
ejpam-5559	339	8	.	.	PUNCT
ejpam-5559	340	1	[	[	X
ejpam-5559	340	2	8	8	NUM
ejpam-5559	340	3	]	]	X
ejpam-5559	340	4	q.m	q.m	PROPN
ejpam-5559	340	5	.	.	PROPN
ejpam-5559	340	6	luo	luo	PROPN
ejpam-5559	340	7	and	and	CCONJ
ejpam-5559	340	8	h.m	h.m	PROPN
ejpam-5559	340	9	.	.	PROPN
ejpam-5559	340	10	srivastava	srivastava	PROPN
ejpam-5559	340	11	.	.	PUNCT
ejpam-5559	341	1	some	some	DET
ejpam-5559	341	2	generalizations	generalization	NOUN
ejpam-5559	341	3	of	of	ADP
ejpam-5559	341	4	apostol	apostol	NOUN
ejpam-5559	341	5	-	-	PUNCT
ejpam-5559	341	6	bernoulli	bernoulli	NOUN
ejpam-5559	341	7	and	and	CCONJ
ejpam-5559	341	8	apostoleuler	apostoleuler	NOUN
ejpam-5559	341	9	polynomials	polynomial	NOUN
ejpam-5559	341	10	.	.	PUNCT
ejpam-5559	342	1	journal	journal	PROPN
ejpam-5559	342	2	of	of	ADP
ejpam-5559	342	3	mathematical	mathematical	ADJ
ejpam-5559	342	4	analysis	analysis	NOUN
ejpam-5559	342	5	and	and	CCONJ
ejpam-5559	342	6	applications	application	NOUN
ejpam-5559	342	7	,	,	PUNCT
ejpam-5559	342	8	308(1):290	308(1):290	NUM
ejpam-5559	342	9	–	–	PUNCT
ejpam-5559	342	10	302	302	NUM
ejpam-5559	342	11	,	,	PUNCT
ejpam-5559	342	12	2005	2005	NUM
ejpam-5559	342	13	.	.	PUNCT
ejpam-5559	343	1	[	[	X
ejpam-5559	343	2	9	9	NUM
ejpam-5559	343	3	]	]	X
ejpam-5559	343	4	w.	w.	PROPN
ejpam-5559	343	5	ramı́rez	ramı́rez	PROPN
ejpam-5559	343	6	and	and	CCONJ
ejpam-5559	343	7	c.	c.	PROPN
ejpam-5559	343	8	cesarano	cesarano	PROPN
ejpam-5559	343	9	.	.	PUNCT
ejpam-5559	344	1	some	some	DET
ejpam-5559	344	2	new	new	ADJ
ejpam-5559	344	3	classes	class	NOUN
ejpam-5559	344	4	of	of	ADP
ejpam-5559	344	5	degenerated	degenerated	ADJ
ejpam-5559	344	6	generalized	generalized	ADJ
ejpam-5559	344	7	apostolbernoulli	apostolbernoulli	NOUN
ejpam-5559	344	8	,	,	PUNCT
ejpam-5559	344	9	apostol	apostol	NOUN
ejpam-5559	344	10	-	-	PUNCT
ejpam-5559	344	11	euler	euler	NOUN
ejpam-5559	344	12	and	and	CCONJ
ejpam-5559	344	13	apostol	apostol	NOUN
ejpam-5559	344	14	-	-	PUNCT
ejpam-5559	344	15	genocchi	genocchi	PROPN
ejpam-5559	344	16	polynomials	polynomial	NOUN
ejpam-5559	344	17	.	.	PUNCT
ejpam-5559	345	1	carpathian	carpathian	ADJ
ejpam-5559	345	2	mathematical	mathematical	ADJ
ejpam-5559	345	3	publications	publication	NOUN
ejpam-5559	345	4	,	,	PUNCT
ejpam-5559	345	5	14(2):354–363	14(2):354–363	NUM
ejpam-5559	345	6	,	,	PUNCT
ejpam-5559	345	7	2022	2022	NUM
ejpam-5559	345	8	.	.	PUNCT
ejpam-5559	346	1	[	[	X
ejpam-5559	346	2	10	10	NUM
ejpam-5559	346	3	]	]	X
ejpam-5559	346	4	w.	w.	PROPN
ejpam-5559	346	5	ramı́rez	ramı́rez	PROPN
ejpam-5559	346	6	,	,	PUNCT
ejpam-5559	346	7	c.	c.	PROPN
ejpam-5559	346	8	cesarano	cesarano	PROPN
ejpam-5559	346	9	,	,	PUNCT
ejpam-5559	346	10	and	and	CCONJ
ejpam-5559	346	11	s.	s.	PROPN
ejpam-5559	346	12	dı́az	dı́az	PROPN
ejpam-5559	346	13	.	.	PUNCT
ejpam-5559	347	1	new	new	ADJ
ejpam-5559	347	2	results	result	NOUN
ejpam-5559	347	3	for	for	ADP
ejpam-5559	347	4	degenerated	degenerated	ADJ
ejpam-5559	347	5	generalized	generalized	ADJ
ejpam-5559	347	6	apostol	apostol	NOUN
ejpam-5559	347	7	–	–	PUNCT
ejpam-5559	347	8	bernoulli	bernoulli	NOUN
ejpam-5559	347	9	,	,	PUNCT
ejpam-5559	347	10	apostol	apostol	NOUN
ejpam-5559	347	11	–	–	PUNCT
ejpam-5559	347	12	euler	euler	NOUN
ejpam-5559	347	13	and	and	CCONJ
ejpam-5559	347	14	apostol	apostol	PROPN
ejpam-5559	347	15	–	–	PUNCT
ejpam-5559	347	16	genocchi	genocchi	PROPN
ejpam-5559	347	17	polynomials	polynomial	NOUN
ejpam-5559	347	18	.	.	PUNCT
ejpam-5559	348	1	wseas	wseas	VERB
ejpam-5559	348	2	transactions	transaction	NOUN
ejpam-5559	348	3	on	on	ADP
ejpam-5559	348	4	mathematics	mathematic	NOUN
ejpam-5559	348	5	,	,	PUNCT
ejpam-5559	348	6	21:604–608	21:604–608	NUM
ejpam-5559	348	7	,	,	PUNCT
ejpam-5559	348	8	2022	2022	NUM
ejpam-5559	348	9	.	.	PUNCT
ejpam-5559	349	1	[	[	X
ejpam-5559	349	2	11	11	NUM
ejpam-5559	349	3	]	]	X
ejpam-5559	349	4	cs	cs	ADJ
ejpam-5559	349	5	ryoo	ryoo	NOUN
ejpam-5559	349	6	.	.	PUNCT
ejpam-5559	350	1	a	a	DET
ejpam-5559	350	2	note	note	NOUN
ejpam-5559	350	3	on	on	ADP
ejpam-5559	350	4	the	the	DET
ejpam-5559	350	5	tangent	tangent	ADJ
ejpam-5559	350	6	numbers	number	NOUN
ejpam-5559	350	7	and	and	CCONJ
ejpam-5559	350	8	polynomials	polynomial	NOUN
ejpam-5559	350	9	.	.	PUNCT
ejpam-5559	351	1	adv	adv	PROPN
ejpam-5559	351	2	.	.	PUNCT
ejpam-5559	352	1	studies	study	NOUN
ejpam-5559	352	2	theor	theor	PROPN
ejpam-5559	352	3	.	.	PUNCT
ejpam-5559	353	1	phys	phy	NOUN
ejpam-5559	353	2	,	,	PUNCT
ejpam-5559	353	3	7(9):447–454	7(9):447–454	NUM
ejpam-5559	353	4	,	,	PUNCT
ejpam-5559	353	5	2013	2013	NUM
ejpam-5559	353	6	.	.	PUNCT
ejpam-5559	354	1	[	[	X
ejpam-5559	354	2	12	12	NUM
ejpam-5559	354	3	]	]	X
ejpam-5559	354	4	cs	cs	ADJ
ejpam-5559	354	5	ryoo	ryoo	NOUN
ejpam-5559	354	6	.	.	PUNCT
ejpam-5559	355	1	on	on	ADP
ejpam-5559	355	2	the	the	DET
ejpam-5559	355	3	analogues	analogue	NOUN
ejpam-5559	355	4	of	of	ADP
ejpam-5559	355	5	tangent	tangent	ADJ
ejpam-5559	355	6	numbers	number	NOUN
ejpam-5559	355	7	and	and	CCONJ
ejpam-5559	355	8	polynomials	polynomial	NOUN
ejpam-5559	355	9	associated	associate	VERB
ejpam-5559	355	10	with	with	ADP
ejpam-5559	355	11	p	p	NOUN
ejpam-5559	355	12	-	-	PUNCT
ejpam-5559	355	13	adic	adic	NOUN
ejpam-5559	355	14	integral	integral	NOUN
ejpam-5559	355	15	on	on	ADP
ejpam-5559	355	16	zp	zp	PROPN
ejpam-5559	355	17	.	.	PROPN
ejpam-5559	355	18	applied	apply	VERB
ejpam-5559	355	19	mathematical	mathematical	ADJ
ejpam-5559	355	20	sciences	science	NOUN
ejpam-5559	355	21	,	,	PUNCT
ejpam-5559	355	22	7(64):3177–3183	7(64):3177–3183	NUM
ejpam-5559	355	23	,	,	PUNCT
ejpam-5559	355	24	2013	2013	NUM
ejpam-5559	355	25	.	.	PUNCT
ejpam-5559	356	1	[	[	X
ejpam-5559	356	2	13	13	NUM
ejpam-5559	356	3	]	]	X
ejpam-5559	356	4	cs	cs	ADJ
ejpam-5559	356	5	ryoo	ryoo	NOUN
ejpam-5559	356	6	.	.	PUNCT
ejpam-5559	357	1	a	a	DET
ejpam-5559	357	2	numerical	numerical	ADJ
ejpam-5559	357	3	investigation	investigation	NOUN
ejpam-5559	357	4	on	on	ADP
ejpam-5559	357	5	the	the	DET
ejpam-5559	357	6	zeros	zero	NOUN
ejpam-5559	357	7	of	of	ADP
ejpam-5559	357	8	the	the	DET
ejpam-5559	357	9	tangent	tangent	NOUN
ejpam-5559	357	10	polynomials	polynomial	NOUN
ejpam-5559	357	11	.	.	PUNCT
ejpam-5559	358	1	journal	journal	NOUN
ejpam-5559	358	2	of	of	ADP
ejpam-5559	358	3	applied	apply	VERB
ejpam-5559	358	4	mathematics	mathematics	PROPN
ejpam-5559	358	5	&	&	CCONJ
ejpam-5559	358	6	informatics	informatics	PROPN
ejpam-5559	358	7	,	,	PUNCT
ejpam-5559	358	8	32(3	32(3	NUM
ejpam-5559	358	9	4):315–322	4):315–322	NUM
ejpam-5559	358	10	,	,	PUNCT
ejpam-5559	358	11	2014	2014	NUM
ejpam-5559	358	12	.	.	PUNCT
ejpam-5559	359	1	[	[	X
ejpam-5559	359	2	14	14	NUM
ejpam-5559	359	3	]	]	X
ejpam-5559	359	4	cs	cs	ADJ
ejpam-5559	359	5	ryoo	ryoo	NOUN
ejpam-5559	359	6	.	.	PUNCT
ejpam-5559	360	1	differential	differential	ADJ
ejpam-5559	360	2	equations	equation	NOUN
ejpam-5559	360	3	associated	associate	VERB
ejpam-5559	360	4	with	with	ADP
ejpam-5559	360	5	tangent	tangent	NOUN
ejpam-5559	360	6	numbers	number	NOUN
ejpam-5559	360	7	.	.	PUNCT
ejpam-5559	361	1	journal	journal	NOUN
ejpam-5559	361	2	of	of	ADP
ejpam-5559	361	3	applied	apply	VERB
ejpam-5559	361	4	mathematics	mathematics	PROPN
ejpam-5559	361	5	&	&	CCONJ
ejpam-5559	361	6	informatics	informatics	PROPN
ejpam-5559	361	7	,	,	PUNCT
ejpam-5559	361	8	34(5	34(5	NUM
ejpam-5559	361	9	6):487–494	6):487–494	NUM
ejpam-5559	361	10	,	,	PUNCT
ejpam-5559	361	11	2016	2016	NUM
ejpam-5559	361	12	.	.	PUNCT
ejpam-5559	362	1	[	[	X
ejpam-5559	362	2	15	15	NUM
ejpam-5559	362	3	]	]	X
ejpam-5559	362	4	james	james	PROPN
ejpam-5559	362	5	shohat	shohat	PROPN
ejpam-5559	362	6	.	.	PUNCT
ejpam-5559	363	1	the	the	DET
ejpam-5559	363	2	relation	relation	NOUN
ejpam-5559	363	3	of	of	ADP
ejpam-5559	363	4	the	the	DET
ejpam-5559	363	5	classical	classical	ADJ
ejpam-5559	363	6	orthogonal	orthogonal	ADJ
ejpam-5559	363	7	polynomials	polynomial	NOUN
ejpam-5559	363	8	to	to	ADP
ejpam-5559	363	9	the	the	DET
ejpam-5559	363	10	polynomials	polynomial	NOUN
ejpam-5559	363	11	of	of	ADP
ejpam-5559	363	12	appell	appell	PROPN
ejpam-5559	363	13	.	.	PUNCT
ejpam-5559	364	1	american	american	ADJ
ejpam-5559	364	2	journal	journal	PROPN
ejpam-5559	364	3	of	of	ADP
ejpam-5559	364	4	mathematics	mathematic	NOUN
ejpam-5559	364	5	,	,	PUNCT
ejpam-5559	364	6	58(3):453–464	58(3):453–464	PROPN
ejpam-5559	364	7	,	,	PUNCT
ejpam-5559	364	8	1936	1936	NUM
ejpam-5559	364	9	.	.	PUNCT
ejpam-5559	365	1	[	[	X
ejpam-5559	365	2	16	16	NUM
ejpam-5559	365	3	]	]	X
ejpam-5559	365	4	g.	g.	PROPN
ejpam-5559	365	5	szegő.	szegő.	NOUN
ejpam-5559	365	6	orthogonal	orthogonal	ADJ
ejpam-5559	365	7	polynomials	polynomial	NOUN
ejpam-5559	365	8	.	.	PUNCT
ejpam-5559	366	1	american	american	ADJ
ejpam-5559	366	2	math	math	PROPN
ejpam-5559	366	3	.	.	PUNCT
ejpam-5559	367	1	soc	soc	NOUN
ejpam-5559	367	2	:	:	PUNCT
ejpam-5559	367	3	colloquium	colloquium	NOUN
ejpam-5559	367	4	publ	publ	NOUN
ejpam-5559	367	5	.	.	PUNCT
ejpam-5559	368	1	american	american	PROPN
ejpam-5559	368	2	mathematical	mathematical	PROPN
ejpam-5559	368	3	society	society	NOUN
ejpam-5559	368	4	,	,	PUNCT
ejpam-5559	368	5	1975	1975	NUM
ejpam-5559	368	6	.	.	PUNCT