id	sid	tid	token	lemma	pos
ejpam-5656	1	1	european	european	PROPN
ejpam-5656	1	2	journal	journal	PROPN
ejpam-5656	1	3	of	of	ADP
ejpam-5656	1	4	pure	pure	ADJ
ejpam-5656	1	5	and	and	CCONJ
ejpam-5656	1	6	applied	applied	ADJ
ejpam-5656	1	7	mathematics	mathematic	NOUN
ejpam-5656	1	8	2025	2025	NUM
ejpam-5656	1	9	,	,	PUNCT
ejpam-5656	1	10	vol	vol	NOUN
ejpam-5656	1	11	.	.	PROPN
ejpam-5656	1	12	18	18	NUM
ejpam-5656	1	13	,	,	PUNCT
ejpam-5656	1	14	issue	issue	NOUN
ejpam-5656	1	15	1	1	NUM
ejpam-5656	1	16	,	,	PUNCT
ejpam-5656	1	17	article	article	NOUN
ejpam-5656	1	18	number	number	NOUN
ejpam-5656	1	19	5656	5656	NUM
ejpam-5656	1	20	issn	issn	PROPN
ejpam-5656	1	21	1307	1307	NUM
ejpam-5656	1	22	-	-	SYM
ejpam-5656	1	23	5543	5543	NUM
ejpam-5656	1	24	–	–	PUNCT
ejpam-5656	1	25	ejpam.com	ejpam.com	X
ejpam-5656	1	26	published	publish	VERB
ejpam-5656	1	27	by	by	ADP
ejpam-5656	1	28	new	new	PROPN
ejpam-5656	1	29	york	york	PROPN
ejpam-5656	1	30	business	business	PROPN
ejpam-5656	1	31	global	global	PROPN
ejpam-5656	1	32	the	the	DET
ejpam-5656	1	33	monomiality	monomiality	NOUN
ejpam-5656	1	34	principle	principle	NOUN
ejpam-5656	1	35	applied	apply	VERB
ejpam-5656	1	36	to	to	ADP
ejpam-5656	1	37	extensions	extension	NOUN
ejpam-5656	1	38	of	of	ADP
ejpam-5656	1	39	apostol	apostol	NOUN
ejpam-5656	1	40	-	-	PUNCT
ejpam-5656	1	41	type	type	NOUN
ejpam-5656	1	42	hermite	hermite	ADJ
ejpam-5656	1	43	polynomials	polynomial	NOUN
ejpam-5656	1	44	stiven	stiven	PROPN
ejpam-5656	1	45	dı́az1∗	dı́az1∗	PROPN
ejpam-5656	1	46	,	,	PUNCT
ejpam-5656	1	47	william	william	PROPN
ejpam-5656	1	48	ramı́rez1,2	ramı́rez1,2	PROPN
ejpam-5656	1	49	,	,	PUNCT
ejpam-5656	1	50	clemente	clemente	PROPN
ejpam-5656	1	51	cesarano2	cesarano2	PROPN
ejpam-5656	1	52	,	,	PUNCT
ejpam-5656	1	53	juan	juan	PROPN
ejpam-5656	1	54	hernández3	hernández3	PROPN
ejpam-5656	1	55	,	,	PUNCT
ejpam-5656	1	56	escarlin	escarlin	PROPN
ejpam-5656	1	57	claribel	claribel	PROPN
ejpam-5656	1	58	pérez	pérez	PROPN
ejpam-5656	1	59	rodŕıguez4	rodŕıguez4	PROPN
ejpam-5656	1	60	1	1	NUM
ejpam-5656	1	61	departamento	departamento	PROPN
ejpam-5656	1	62	de	de	PROPN
ejpam-5656	1	63	ciencias	ciencias	PROPN
ejpam-5656	1	64	naturales	naturales	PROPN
ejpam-5656	1	65	y	y	PROPN
ejpam-5656	1	66	exactas	exactas	PROPN
ejpam-5656	1	67	,	,	PUNCT
ejpam-5656	1	68	universidad	universidad	PROPN
ejpam-5656	1	69	de	de	PROPN
ejpam-5656	1	70	la	la	PROPN
ejpam-5656	1	71	costa	costa	PROPN
ejpam-5656	1	72	,	,	PUNCT
ejpam-5656	1	73	barranquilla	barranquilla	PROPN
ejpam-5656	1	74	,	,	PUNCT
ejpam-5656	1	75	colombia	colombia	PROPN
ejpam-5656	1	76	2	2	NUM
ejpam-5656	1	77	section	section	NOUN
ejpam-5656	1	78	of	of	ADP
ejpam-5656	1	79	mathematics	mathematics	PROPN
ejpam-5656	1	80	international	international	PROPN
ejpam-5656	1	81	telematic	telematic	ADJ
ejpam-5656	1	82	university	university	NOUN
ejpam-5656	1	83	uninettuno	uninettuno	NOUN
ejpam-5656	1	84	,	,	PUNCT
ejpam-5656	1	85	corso	corso	PROPN
ejpam-5656	1	86	vittorio	vittorio	PROPN
ejpam-5656	1	87	emanuele	emanuele	PROPN
ejpam-5656	1	88	ii	ii	PROPN
ejpam-5656	1	89	,	,	PUNCT
ejpam-5656	1	90	39	39	NUM
ejpam-5656	1	91	,	,	PUNCT
ejpam-5656	1	92	00186	00186	NUM
ejpam-5656	1	93	rome	rome	PROPN
ejpam-5656	1	94	,	,	PUNCT
ejpam-5656	1	95	italy	italy	PROPN
ejpam-5656	1	96	3	3	NUM
ejpam-5656	1	97	department	department	PROPN
ejpam-5656	1	98	of	of	ADP
ejpam-5656	1	99	mathematics	mathematic	NOUN
ejpam-5656	1	100	,	,	PUNCT
ejpam-5656	1	101	universidad	universidad	PROPN
ejpam-5656	1	102	autónoma	autónoma	PROPN
ejpam-5656	1	103	de	de	PROPN
ejpam-5656	1	104	santo	santo	PROPN
ejpam-5656	1	105	domingo	domingo	PROPN
ejpam-5656	1	106	,	,	PUNCT
ejpam-5656	1	107	dominican	dominican	PROPN
ejpam-5656	1	108	republic	republic	PROPN
ejpam-5656	1	109	4	4	NUM
ejpam-5656	1	110	ministerio	ministerio	PROPN
ejpam-5656	1	111	de	de	X
ejpam-5656	1	112	educación	educación	PROPN
ejpam-5656	1	113	de	de	X
ejpam-5656	1	114	la	la	PROPN
ejpam-5656	1	115	república	república	PROPN
ejpam-5656	1	116	dominicana	dominicana	PROPN
ejpam-5656	1	117	,	,	PUNCT
ejpam-5656	1	118	dominican	dominican	PROPN
ejpam-5656	1	119	republic	republic	PROPN
ejpam-5656	1	120	abstract	abstract	NOUN
ejpam-5656	1	121	.	.	PUNCT
ejpam-5656	2	1	in	in	ADP
ejpam-5656	2	2	this	this	DET
ejpam-5656	2	3	research	research	NOUN
ejpam-5656	2	4	paper	paper	NOUN
ejpam-5656	2	5	,	,	PUNCT
ejpam-5656	2	6	we	we	PRON
ejpam-5656	2	7	present	present	VERB
ejpam-5656	2	8	a	a	DET
ejpam-5656	2	9	class	class	NOUN
ejpam-5656	2	10	of	of	ADP
ejpam-5656	2	11	polynomials	polynomial	NOUN
ejpam-5656	2	12	referred	refer	VERB
ejpam-5656	2	13	to	to	ADP
ejpam-5656	2	14	as	as	ADP
ejpam-5656	2	15	apostol	apostol	NOUN
ejpam-5656	2	16	-	-	PUNCT
ejpam-5656	2	17	type	type	NOUN
ejpam-5656	2	18	hermite	hermite	PROPN
ejpam-5656	2	19	-	-	PUNCT
ejpam-5656	2	20	bernoulli	bernoulli	PROPN
ejpam-5656	2	21	/	/	SYM
ejpam-5656	2	22	euler	euler	NOUN
ejpam-5656	2	23	polynomials	polynomial	NOUN
ejpam-5656	2	24	uν(x	uν(x	PART
ejpam-5656	2	25	,	,	PUNCT
ejpam-5656	2	26	y	y	PROPN
ejpam-5656	2	27	;	;	PUNCT
ejpam-5656	2	28	ρ;µ	ρ;µ	NUM
ejpam-5656	2	29	)	)	PUNCT
ejpam-5656	2	30	,	,	PUNCT
ejpam-5656	2	31	which	which	PRON
ejpam-5656	2	32	can	can	AUX
ejpam-5656	2	33	be	be	AUX
ejpam-5656	2	34	given	give	VERB
ejpam-5656	2	35	by	by	ADP
ejpam-5656	2	36	the	the	DET
ejpam-5656	2	37	following	follow	VERB
ejpam-5656	2	38	generating	generate	VERB
ejpam-5656	2	39	function	function	NOUN
ejpam-5656	2	40	2−	2−	NUM
ejpam-5656	2	41	µ+	µ+	X
ejpam-5656	2	42	µ	µ	PROPN
ejpam-5656	2	43	2	2	NUM
ejpam-5656	2	44	ξ	ξ	NOUN
ejpam-5656	2	45	ρeξ	ρeξ	NOUN
ejpam-5656	2	46	+	+	CCONJ
ejpam-5656	2	47	(	(	PUNCT
ejpam-5656	2	48	1−	1−	NUM
ejpam-5656	2	49	µ	µ	NUM
ejpam-5656	2	50	)	)	PUNCT
ejpam-5656	2	51	exξ+yξ2	exξ+yξ2	NOUN
ejpam-5656	3	1	=	=	PUNCT
ejpam-5656	3	2	∞∑	∞∑	NUM
ejpam-5656	3	3	ν=0	ν=0	NOUN
ejpam-5656	3	4	uν(x	uν(x	NOUN
ejpam-5656	3	5	,	,	PUNCT
ejpam-5656	3	6	y	y	PROPN
ejpam-5656	3	7	;	;	PUNCT
ejpam-5656	3	8	ρ;µ	ρ;µ	NUM
ejpam-5656	3	9	)	)	PUNCT
ejpam-5656	3	10	ξν	ξν	ADP
ejpam-5656	3	11	ν	ν	PROPN
ejpam-5656	3	12	!	!	PROPN
ejpam-5656	3	13	,	,	PUNCT
ejpam-5656	3	14	for	for	ADP
ejpam-5656	3	15	some	some	DET
ejpam-5656	3	16	particular	particular	ADJ
ejpam-5656	3	17	values	value	NOUN
ejpam-5656	3	18	of	of	ADP
ejpam-5656	3	19	ρ	ρ	PROPN
ejpam-5656	3	20	and	and	CCONJ
ejpam-5656	3	21	µ.	µ.	PROPN
ejpam-5656	3	22	further	far	ADV
ejpam-5656	3	23	,	,	PUNCT
ejpam-5656	3	24	the	the	DET
ejpam-5656	3	25	summation	summation	NOUN
ejpam-5656	3	26	formulae	formulae	VERB
ejpam-5656	3	27	and	and	CCONJ
ejpam-5656	3	28	determinant	determinant	ADJ
ejpam-5656	3	29	forms	form	NOUN
ejpam-5656	3	30	of	of	ADP
ejpam-5656	3	31	these	these	DET
ejpam-5656	3	32	polynomials	polynomial	NOUN
ejpam-5656	3	33	are	be	AUX
ejpam-5656	3	34	derived	derive	VERB
ejpam-5656	3	35	.	.	PUNCT
ejpam-5656	4	1	this	this	DET
ejpam-5656	4	2	novel	novel	ADJ
ejpam-5656	4	3	family	family	NOUN
ejpam-5656	4	4	encompasses	encompass	VERB
ejpam-5656	4	5	both	both	CCONJ
ejpam-5656	4	6	the	the	DET
ejpam-5656	4	7	classical	classical	ADJ
ejpam-5656	4	8	appell	appell	ADJ
ejpam-5656	4	9	-	-	PUNCT
ejpam-5656	4	10	type	type	NOUN
ejpam-5656	4	11	polynomials	polynomial	NOUN
ejpam-5656	4	12	and	and	CCONJ
ejpam-5656	4	13	their	their	PRON
ejpam-5656	4	14	noteworthy	noteworthy	ADJ
ejpam-5656	4	15	extensions	extension	NOUN
ejpam-5656	4	16	.	.	PUNCT
ejpam-5656	5	1	our	our	PRON
ejpam-5656	5	2	investigations	investigation	NOUN
ejpam-5656	5	3	heavily	heavily	ADV
ejpam-5656	5	4	rely	rely	VERB
ejpam-5656	5	5	on	on	ADP
ejpam-5656	5	6	generating	generate	VERB
ejpam-5656	5	7	function	function	NOUN
ejpam-5656	5	8	techniques	technique	NOUN
ejpam-5656	5	9	,	,	PUNCT
ejpam-5656	5	10	supported	support	VERB
ejpam-5656	5	11	by	by	ADP
ejpam-5656	5	12	illustrative	illustrative	ADJ
ejpam-5656	5	13	examples	example	NOUN
ejpam-5656	5	14	to	to	PART
ejpam-5656	5	15	demonstrate	demonstrate	VERB
ejpam-5656	5	16	the	the	DET
ejpam-5656	5	17	validity	validity	NOUN
ejpam-5656	5	18	of	of	ADP
ejpam-5656	5	19	our	our	PRON
ejpam-5656	5	20	results	result	NOUN
ejpam-5656	5	21	.	.	PUNCT
ejpam-5656	6	1	furthermore	furthermore	ADV
ejpam-5656	6	2	,	,	PUNCT
ejpam-5656	6	3	we	we	PRON
ejpam-5656	6	4	introduce	introduce	VERB
ejpam-5656	6	5	derivative	derivative	ADJ
ejpam-5656	6	6	and	and	CCONJ
ejpam-5656	6	7	multiplicative	multiplicative	ADJ
ejpam-5656	6	8	operators	operator	NOUN
ejpam-5656	6	9	,	,	PUNCT
ejpam-5656	6	10	facilitating	facilitate	VERB
ejpam-5656	6	11	the	the	DET
ejpam-5656	6	12	definition	definition	NOUN
ejpam-5656	6	13	of	of	ADP
ejpam-5656	6	14	the	the	DET
ejpam-5656	6	15	apostol	apostol	NOUN
ejpam-5656	6	16	-	-	PUNCT
ejpam-5656	6	17	type	type	NOUN
ejpam-5656	6	18	hermite	hermite	PROPN
ejpam-5656	6	19	-	-	PUNCT
ejpam-5656	6	20	bernoulli	bernoulli	PROPN
ejpam-5656	6	21	/	/	SYM
ejpam-5656	6	22	euler	euler	NOUN
ejpam-5656	6	23	polynomials	polynomial	NOUN
ejpam-5656	6	24	as	as	ADP
ejpam-5656	6	25	a	a	DET
ejpam-5656	6	26	quasi	quasi	ADJ
ejpam-5656	6	27	-	-	ADJ
ejpam-5656	6	28	monomial	monomial	ADJ
ejpam-5656	6	29	set	set	NOUN
ejpam-5656	6	30	.	.	PUNCT
ejpam-5656	7	1	2020	2020	NUM
ejpam-5656	7	2	mathematics	mathematics	PROPN
ejpam-5656	7	3	subject	subject	NOUN
ejpam-5656	7	4	classifications	classification	NOUN
ejpam-5656	7	5	:	:	PUNCT
ejpam-5656	7	6	11b68	11b68	NUM
ejpam-5656	7	7	,	,	PUNCT
ejpam-5656	7	8	11b83	11b83	NUM
ejpam-5656	7	9	,	,	PUNCT
ejpam-5656	7	10	05a19	05a19	NUM
ejpam-5656	7	11	key	key	ADJ
ejpam-5656	7	12	words	word	NOUN
ejpam-5656	7	13	and	and	CCONJ
ejpam-5656	7	14	phrases	phrase	NOUN
ejpam-5656	7	15	:	:	PUNCT
ejpam-5656	7	16	appell	appell	ADJ
ejpam-5656	7	17	-	-	PUNCT
ejpam-5656	7	18	type	type	NOUN
ejpam-5656	7	19	polynomials	polynomial	NOUN
ejpam-5656	7	20	,	,	PUNCT
ejpam-5656	7	21	bernoulli	bernoulli	PROPN
ejpam-5656	7	22	and	and	CCONJ
ejpam-5656	7	23	euler	euler	NOUN
ejpam-5656	7	24	numbers	number	NOUN
ejpam-5656	7	25	and	and	CCONJ
ejpam-5656	7	26	polynomials	polynomial	NOUN
ejpam-5656	7	27	,	,	PUNCT
ejpam-5656	7	28	hermite	hermite	ADJ
ejpam-5656	7	29	polynomials	polynomial	NOUN
ejpam-5656	7	30	,	,	PUNCT
ejpam-5656	7	31	quasi	quasi	ADJ
ejpam-5656	7	32	-	-	ADJ
ejpam-5656	7	33	monomial	monomial	ADJ
ejpam-5656	7	34	1	1	NUM
ejpam-5656	7	35	.	.	PUNCT
ejpam-5656	8	1	introduction	introduction	NOUN
ejpam-5656	8	2	the	the	DET
ejpam-5656	8	3	appell	appell	NOUN
ejpam-5656	8	4	polynomials	polynomial	NOUN
ejpam-5656	8	5	{	{	PUNCT
ejpam-5656	8	6	an(x)}n=0,1,2	an(x)}n=0,1,2	ADJ
ejpam-5656	8	7	,	,	PUNCT
ejpam-5656	8	8	...	...	PUNCT
ejpam-5656	8	9	are	be	AUX
ejpam-5656	8	10	a	a	DET
ejpam-5656	8	11	family	family	NOUN
ejpam-5656	8	12	of	of	ADP
ejpam-5656	8	13	special	special	ADJ
ejpam-5656	8	14	functions	function	NOUN
ejpam-5656	8	15	introduced	introduce	VERB
ejpam-5656	8	16	by	by	ADP
ejpam-5656	8	17	the	the	DET
ejpam-5656	8	18	french	french	ADJ
ejpam-5656	8	19	mathematician	mathematician	NOUN
ejpam-5656	8	20	paul	paul	PROPN
ejpam-5656	8	21	appell	appell	PROPN
ejpam-5656	8	22	(	(	PUNCT
ejpam-5656	8	23	see	see	VERB
ejpam-5656	8	24	[	[	X
ejpam-5656	8	25	2	2	NUM
ejpam-5656	8	26	]	]	NUM
ejpam-5656	8	27	)	)	PUNCT
ejpam-5656	8	28	.	.	PUNCT
ejpam-5656	9	1	these	these	DET
ejpam-5656	9	2	polynomials	polynomial	NOUN
ejpam-5656	9	3	are	be	AUX
ejpam-5656	9	4	defined	define	VERB
ejpam-5656	9	5	by	by	ADP
ejpam-5656	9	6	a	a	DET
ejpam-5656	9	7	∗corresponding	∗corresponding	NOUN
ejpam-5656	9	8	author	author	NOUN
ejpam-5656	9	9	.	.	PUNCT
ejpam-5656	10	1	doi	doi	NOUN
ejpam-5656	10	2	:	:	PUNCT
ejpam-5656	10	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5656	https://doi.org/10.29020/nybg.ejpam.v18i1.5656	ADJ
ejpam-5656	10	4	email	email	NOUN
ejpam-5656	10	5	addresses	address	NOUN
ejpam-5656	10	6	:	:	PUNCT
ejpam-5656	10	7	sdiaz47@cuc.edu.co	sdiaz47@cuc.edu.co	X
ejpam-5656	10	8	(	(	PUNCT
ejpam-5656	10	9	s.	s.	PROPN
ejpam-5656	10	10	dı́az	dı́az	PROPN
ejpam-5656	10	11	)	)	PUNCT
ejpam-5656	10	12	,	,	PUNCT
ejpam-5656	10	13	wramirez4@cuc.edu.co	wramirez4@cuc.edu.co	X
ejpam-5656	10	14	w.	w.	PROPN
ejpam-5656	10	15	ramı́rez	ramı́rez	PROPN
ejpam-5656	10	16	,	,	PUNCT
ejpam-5656	10	17	clemente.cesarano@uninettunouniversity.net	clemente.cesarano@uninettunouniversity.net	PROPN
ejpam-5656	10	18	(	(	PUNCT
ejpam-5656	10	19	c.	c.	PROPN
ejpam-5656	10	20	cesarano	cesarano	PROPN
ejpam-5656	10	21	)	)	PUNCT
ejpam-5656	10	22	,	,	PUNCT
ejpam-5656	10	23	jhernandez14@uasd.edu.do	jhernandez14@uasd.edu.do	PROPN
ejpam-5656	10	24	(	(	PUNCT
ejpam-5656	10	25	j.	j.	PROPN
ejpam-5656	10	26	hernández	hernández	PROPN
ejpam-5656	10	27	)	)	PUNCT
ejpam-5656	10	28	,	,	PUNCT
ejpam-5656	10	29	escarlinperez05@gmail.com	escarlinperez05@gmail.com	PROPN
ejpam-5656	10	30	(	(	PUNCT
ejpam-5656	10	31	e.	e.	PROPN
ejpam-5656	10	32	c.	c.	PROPN
ejpam-5656	10	33	pérez	pérez	PROPN
ejpam-5656	10	34	rodŕıguez	rodŕıguez	PROPN
ejpam-5656	10	35	)	)	PUNCT
ejpam-5656	10	36	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5656	10	37	1	1	NUM
ejpam-5656	10	38	copyright	copyright	NOUN
ejpam-5656	10	39	:	:	PUNCT
ejpam-5656	11	1	©	©	PROPN
ejpam-5656	11	2	2025	2025	NUM
ejpam-5656	11	3	the	the	DET
ejpam-5656	11	4	author(s	author(s	NOUN
ejpam-5656	11	5	)	)	PUNCT
ejpam-5656	11	6	.	.	PUNCT
ejpam-5656	12	1	(	(	PUNCT
ejpam-5656	12	2	cc	cc	NOUN
ejpam-5656	12	3	by	by	ADP
ejpam-5656	12	4	-	-	PUNCT
ejpam-5656	12	5	nc	nc	PROPN
ejpam-5656	12	6	4.0	4.0	NUM
ejpam-5656	12	7	)	)	PUNCT
ejpam-5656	12	8	dı́az	dı́az	X
ejpam-5656	12	9	et	et	NOUN
ejpam-5656	12	10	al	al	PROPN
ejpam-5656	12	11	.	.	PUNCT
ejpam-5656	12	12	/	/	SYM
ejpam-5656	12	13	eur	eur	PROPN
ejpam-5656	12	14	.	.	PUNCT
ejpam-5656	13	1	j.	j.	PROPN
ejpam-5656	13	2	pure	pure	PROPN
ejpam-5656	13	3	appl	appl	PROPN
ejpam-5656	13	4	.	.	PROPN
ejpam-5656	13	5	math	math	PROPN
ejpam-5656	13	6	,	,	PUNCT
ejpam-5656	13	7	18	18	NUM
ejpam-5656	13	8	(	(	PUNCT
ejpam-5656	13	9	1	1	NUM
ejpam-5656	13	10	)	)	PUNCT
ejpam-5656	13	11	(	(	PUNCT
ejpam-5656	13	12	2025	2025	NUM
ejpam-5656	13	13	)	)	PUNCT
ejpam-5656	13	14	,	,	PUNCT
ejpam-5656	13	15	5656	5656	NUM
ejpam-5656	13	16	2	2	NUM
ejpam-5656	13	17	of	of	ADP
ejpam-5656	13	18	17	17	NUM
ejpam-5656	13	19	generating	generate	VERB
ejpam-5656	13	20	function	function	NOUN
ejpam-5656	13	21	a(ξ)exξ	a(ξ)exξ	ADV
ejpam-5656	13	22	=	=	PUNCT
ejpam-5656	14	1	∞∑	∞∑	NUM
ejpam-5656	14	2	ν=0	ν=0	NOUN
ejpam-5656	14	3	aν(x	aν(x	NOUN
ejpam-5656	14	4	)	)	PUNCT
ejpam-5656	14	5	ξν	ξν	ADP
ejpam-5656	15	1	ν	ν	X
ejpam-5656	15	2	!	!	PROPN
ejpam-5656	15	3	,	,	PUNCT
ejpam-5656	15	4	(	(	PUNCT
ejpam-5656	15	5	1	1	X
ejpam-5656	15	6	)	)	PUNCT
ejpam-5656	15	7	where	where	SCONJ
ejpam-5656	15	8	a(ξ	a(ξ	PROPN
ejpam-5656	15	9	)	)	PUNCT
ejpam-5656	15	10	is	be	AUX
ejpam-5656	15	11	given	give	VERB
ejpam-5656	15	12	by	by	ADP
ejpam-5656	15	13	a(ξ	a(ξ	PROPN
ejpam-5656	15	14	)	)	PUNCT
ejpam-5656	15	15	=	=	PUNCT
ejpam-5656	15	16	∞∑	∞∑	NUM
ejpam-5656	15	17	ν=0	ν=0	NOUN
ejpam-5656	15	18	αν	αν	NOUN
ejpam-5656	15	19	ξν	ξν	ADP
ejpam-5656	15	20	ν	ν	NOUN
ejpam-5656	15	21	!	!	PROPN
ejpam-5656	15	22	,	,	PUNCT
ejpam-5656	15	23	and	and	CCONJ
ejpam-5656	15	24	αν	αν	NOUN
ejpam-5656	15	25	are	be	AUX
ejpam-5656	15	26	real	real	ADJ
ejpam-5656	15	27	coefficients	coefficient	NOUN
ejpam-5656	15	28	.	.	PUNCT
ejpam-5656	16	1	further	far	ADV
ejpam-5656	16	2	,	,	PUNCT
ejpam-5656	16	3	an(x	an(x	PUNCT
ejpam-5656	16	4	)	)	PUNCT
ejpam-5656	16	5	satisfying	satisfy	VERB
ejpam-5656	16	6	the	the	DET
ejpam-5656	16	7	recursive	recursive	ADJ
ejpam-5656	16	8	relations	relation	NOUN
ejpam-5656	16	9	d	d	PROPN
ejpam-5656	16	10	dx	dx	PROPN
ejpam-5656	16	11	aν(x	aν(x	NUM
ejpam-5656	16	12	)	)	PUNCT
ejpam-5656	16	13	=	=	PUNCT
ejpam-5656	16	14	νaν−1(x	νaν−1(x	ADJ
ejpam-5656	16	15	)	)	PUNCT
ejpam-5656	16	16	.	.	PUNCT
ejpam-5656	17	1	(	(	PUNCT
ejpam-5656	17	2	2	2	X
ejpam-5656	17	3	)	)	PUNCT
ejpam-5656	17	4	the	the	DET
ejpam-5656	17	5	appell	appell	PROPN
ejpam-5656	17	6	polynomials	polynomial	NOUN
ejpam-5656	17	7	have	have	VERB
ejpam-5656	17	8	various	various	ADJ
ejpam-5656	17	9	properties	property	NOUN
ejpam-5656	17	10	that	that	PRON
ejpam-5656	17	11	make	make	VERB
ejpam-5656	17	12	them	they	PRON
ejpam-5656	17	13	useful	useful	ADJ
ejpam-5656	17	14	in	in	ADP
ejpam-5656	17	15	mathematical	mathematical	ADJ
ejpam-5656	17	16	analysis	analysis	NOUN
ejpam-5656	17	17	,	,	PUNCT
ejpam-5656	17	18	particularly	particularly	ADV
ejpam-5656	17	19	in	in	ADP
ejpam-5656	17	20	the	the	DET
ejpam-5656	17	21	study	study	NOUN
ejpam-5656	17	22	of	of	ADP
ejpam-5656	17	23	differential	differential	ADJ
ejpam-5656	17	24	equations	equation	NOUN
ejpam-5656	17	25	and	and	CCONJ
ejpam-5656	17	26	other	other	ADJ
ejpam-5656	17	27	fields	field	NOUN
ejpam-5656	17	28	[	[	X
ejpam-5656	17	29	15	15	NUM
ejpam-5656	17	30	,	,	PUNCT
ejpam-5656	17	31	18	18	NUM
ejpam-5656	17	32	]	]	PUNCT
ejpam-5656	17	33	.	.	PUNCT
ejpam-5656	18	1	famous	famous	ADJ
ejpam-5656	18	2	instances	instance	NOUN
ejpam-5656	18	3	of	of	ADP
ejpam-5656	18	4	polynomial	polynomial	ADJ
ejpam-5656	18	5	sequences	sequence	NOUN
ejpam-5656	18	6	that	that	PRON
ejpam-5656	18	7	satisfy	satisfy	VERB
ejpam-5656	18	8	(	(	PUNCT
ejpam-5656	18	9	1	1	NUM
ejpam-5656	18	10	)	)	PUNCT
ejpam-5656	18	11	,	,	PUNCT
ejpam-5656	18	12	or	or	CCONJ
ejpam-5656	18	13	equivalently	equivalently	ADV
ejpam-5656	18	14	the	the	DET
ejpam-5656	18	15	recursive	recursive	ADJ
ejpam-5656	18	16	relations	relation	NOUN
ejpam-5656	18	17	,	,	PUNCT
ejpam-5656	18	18	include	include	VERB
ejpam-5656	18	19	:	:	PUNCT
ejpam-5656	18	20	the	the	DET
ejpam-5656	18	21	polynomials	polynomial	NOUN
ejpam-5656	18	22	of	of	ADP
ejpam-5656	18	23	bernoulli	bernoulli	PROPN
ejpam-5656	18	24	and	and	CCONJ
ejpam-5656	18	25	euler	euler	PROPN
ejpam-5656	18	26	.	.	PUNCT
ejpam-5656	19	1	the	the	DET
ejpam-5656	19	2	exponential	exponential	ADJ
ejpam-5656	19	3	generating	generating	NOUN
ejpam-5656	19	4	function	function	NOUN
ejpam-5656	19	5	of	of	ADP
ejpam-5656	19	6	the	the	DET
ejpam-5656	19	7	geometric	geometric	ADJ
ejpam-5656	19	8	polynomials	polynomial	NOUN
ejpam-5656	19	9	of	of	ADP
ejpam-5656	19	10	bernoulli	bernoulli	PROPN
ejpam-5656	19	11	and	and	CCONJ
ejpam-5656	19	12	euler	euler	NOUN
ejpam-5656	19	13	are	be	AUX
ejpam-5656	19	14	given	give	VERB
ejpam-5656	19	15	by	by	ADP
ejpam-5656	19	16	(	(	PUNCT
ejpam-5656	19	17	see	see	VERB
ejpam-5656	19	18	[	[	X
ejpam-5656	19	19	1	1	NUM
ejpam-5656	19	20	,	,	PUNCT
ejpam-5656	19	21	23	23	NUM
ejpam-5656	19	22	]	]	PUNCT
ejpam-5656	19	23	):	):	PUNCT
ejpam-5656	19	24	ξexξ	ξexξ	PROPN
ejpam-5656	19	25	eξ	eξ	PROPN
ejpam-5656	20	1	−	−	NOUN
ejpam-5656	20	2	1	1	NUM
ejpam-5656	20	3	=	=	SYM
ejpam-5656	20	4	∞∑	∞∑	NUM
ejpam-5656	20	5	ν=0	ν=0	PRON
ejpam-5656	20	6	bν(x	bν(x	NOUN
ejpam-5656	20	7	)	)	PUNCT
ejpam-5656	20	8	ξν	ξν	ADP
ejpam-5656	20	9	ν	ν	X
ejpam-5656	20	10	!	!	PROPN
ejpam-5656	20	11	,	,	PUNCT
ejpam-5656	20	12	|ξ|	|ξ|	PROPN
ejpam-5656	20	13	<	<	X
ejpam-5656	20	14	2π	2π	NOUN
ejpam-5656	20	15	,	,	PUNCT
ejpam-5656	20	16	and	and	CCONJ
ejpam-5656	20	17	2exξ	2exξ	NUM
ejpam-5656	20	18	eξ	eξ	NOUN
ejpam-5656	20	19	+	+	NOUN
ejpam-5656	20	20	1	1	NUM
ejpam-5656	20	21	=	=	SYM
ejpam-5656	20	22	∞∑	∞∑	NUM
ejpam-5656	20	23	ν=0	ν=0	PRON
ejpam-5656	20	24	eν(x	eν(x	PROPN
ejpam-5656	20	25	)	)	PUNCT
ejpam-5656	20	26	ξν	ξν	ADV
ejpam-5656	21	1	ν	ν	X
ejpam-5656	21	2	!	!	PROPN
ejpam-5656	21	3	,	,	PUNCT
ejpam-5656	21	4	|ξ|	|ξ|	PROPN
ejpam-5656	21	5	<	<	X
ejpam-5656	21	6	π	π	PROPN
ejpam-5656	21	7	.	.	PUNCT
ejpam-5656	22	1	it	it	PRON
ejpam-5656	22	2	is	be	AUX
ejpam-5656	22	3	known	know	VERB
ejpam-5656	22	4	that	that	SCONJ
ejpam-5656	22	5	the	the	DET
ejpam-5656	22	6	bernoulli	bernoulli	NOUN
ejpam-5656	22	7	polynomials	polynomial	NOUN
ejpam-5656	22	8	can	can	AUX
ejpam-5656	22	9	be	be	AUX
ejpam-5656	22	10	expressed	express	VERB
ejpam-5656	22	11	in	in	ADP
ejpam-5656	22	12	terms	term	NOUN
ejpam-5656	22	13	of	of	ADP
ejpam-5656	22	14	the	the	DET
ejpam-5656	22	15	bernoulli	bernoulli	PROPN
ejpam-5656	22	16	numbers	number	NOUN
ejpam-5656	22	17	bs	bs	NOUN
ejpam-5656	22	18	.	.	PUNCT
ejpam-5656	23	1	in	in	ADP
ejpam-5656	23	2	fact	fact	NOUN
ejpam-5656	23	3	,	,	PUNCT
ejpam-5656	23	4	for	for	ADP
ejpam-5656	23	5	ν	ν	PRON
ejpam-5656	23	6	∈	∈	PROPN
ejpam-5656	23	7	n0	n0	NOUN
ejpam-5656	23	8	:	:	PUNCT
ejpam-5656	23	9	=	=	SYM
ejpam-5656	23	10	n∪{0	n∪{0	NOUN
ejpam-5656	23	11	}	}	PUNCT
ejpam-5656	23	12	,	,	PUNCT
ejpam-5656	23	13	using	use	VERB
ejpam-5656	23	14	the	the	DET
ejpam-5656	23	15	generating	generate	VERB
ejpam-5656	23	16	function	function	NOUN
ejpam-5656	23	17	of	of	ADP
ejpam-5656	23	18	the	the	DET
ejpam-5656	23	19	bernoulli	bernoulli	NOUN
ejpam-5656	23	20	polynomials	polynomial	NOUN
ejpam-5656	23	21	,	,	PUNCT
ejpam-5656	23	22	we	we	PRON
ejpam-5656	23	23	obtain	obtain	VERB
ejpam-5656	23	24	bν(x	bν(x	PUNCT
ejpam-5656	23	25	)	)	PUNCT
ejpam-5656	24	1	=	=	SYM
ejpam-5656	24	2	ν∑	ν∑	PROPN
ejpam-5656	25	1	s=0	s=0	PROPN
ejpam-5656	25	2	(	(	PUNCT
ejpam-5656	25	3	ν	ν	X
ejpam-5656	25	4	s	s	PART
ejpam-5656	25	5	)	)	PUNCT
ejpam-5656	25	6	bsx	bsx	PROPN
ejpam-5656	25	7	ν−s	ν−s	PROPN
ejpam-5656	25	8	.	.	PUNCT
ejpam-5656	26	1	analogously	analogously	ADV
ejpam-5656	26	2	,	,	PUNCT
ejpam-5656	26	3	the	the	DET
ejpam-5656	26	4	euler	euler	NOUN
ejpam-5656	26	5	polynomials	polynomial	NOUN
ejpam-5656	26	6	are	be	AUX
ejpam-5656	26	7	given	give	VERB
ejpam-5656	26	8	by	by	ADP
ejpam-5656	26	9	eν(x	eν(x	NOUN
ejpam-5656	26	10	)	)	PUNCT
ejpam-5656	27	1	=	=	SYM
ejpam-5656	27	2	ν∑	ν∑	PROPN
ejpam-5656	27	3	s=0	s=0	PROPN
ejpam-5656	27	4	(	(	PUNCT
ejpam-5656	27	5	ν	ν	X
ejpam-5656	27	6	s	s	PART
ejpam-5656	27	7	)	)	PUNCT
ejpam-5656	27	8	es	es	ADP
ejpam-5656	27	9	2s	2s	PROPN
ejpam-5656	27	10	(	(	PUNCT
ejpam-5656	27	11	x−	x−	PROPN
ejpam-5656	27	12	1	1	NUM
ejpam-5656	27	13	2	2	NUM
ejpam-5656	27	14	)	)	PUNCT
ejpam-5656	27	15	ν−s	ν−	NOUN
ejpam-5656	27	16	,	,	PUNCT
ejpam-5656	27	17	where	where	SCONJ
ejpam-5656	27	18	es	es	NOUN
ejpam-5656	27	19	are	be	AUX
ejpam-5656	27	20	the	the	DET
ejpam-5656	27	21	euler	euler	NOUN
ejpam-5656	27	22	numbers	number	NOUN
ejpam-5656	27	23	.	.	PUNCT
ejpam-5656	28	1	on	on	ADP
ejpam-5656	28	2	the	the	DET
ejpam-5656	28	3	other	other	ADJ
ejpam-5656	28	4	hand	hand	NOUN
ejpam-5656	28	5	,	,	PUNCT
ejpam-5656	28	6	f.	f.	PROPN
ejpam-5656	28	7	costabile	costabile	PROPN
ejpam-5656	28	8	et	et	PROPN
ejpam-5656	28	9	al	al	PROPN
ejpam-5656	28	10	.	.	PUNCT
ejpam-5656	29	1	[	[	X
ejpam-5656	29	2	9	9	NUM
ejpam-5656	29	3	]	]	PUNCT
ejpam-5656	29	4	have	have	AUX
ejpam-5656	29	5	presented	present	VERB
ejpam-5656	29	6	multiple	multiple	ADJ
ejpam-5656	29	7	approaches	approach	NOUN
ejpam-5656	29	8	to	to	ADP
ejpam-5656	29	9	appell	appell	ADJ
ejpam-5656	29	10	polynomials	polynomial	NOUN
ejpam-5656	29	11	using	use	VERB
ejpam-5656	29	12	a	a	DET
ejpam-5656	29	13	determinant	determinant	ADJ
ejpam-5656	29	14	-	-	PUNCT
ejpam-5656	29	15	based	base	VERB
ejpam-5656	29	16	definition	definition	NOUN
ejpam-5656	29	17	.	.	PUNCT
ejpam-5656	30	1	through	through	ADP
ejpam-5656	30	2	the	the	DET
ejpam-5656	30	3	application	application	NOUN
ejpam-5656	30	4	of	of	ADP
ejpam-5656	30	5	basic	basic	ADJ
ejpam-5656	30	6	linear	linear	PROPN
ejpam-5656	30	7	algebra	algebra	NOUN
ejpam-5656	30	8	techniques	technique	NOUN
ejpam-5656	30	9	,	,	PUNCT
ejpam-5656	30	10	these	these	DET
ejpam-5656	30	11	approaches	approach	NOUN
ejpam-5656	30	12	have	have	AUX
ejpam-5656	30	13	successfully	successfully	ADV
ejpam-5656	30	14	recovered	recover	VERB
ejpam-5656	30	15	the	the	DET
ejpam-5656	30	16	essential	essential	ADJ
ejpam-5656	30	17	properties	property	NOUN
ejpam-5656	30	18	of	of	ADP
ejpam-5656	30	19	the	the	DET
ejpam-5656	30	20	polynomials	polynomial	NOUN
ejpam-5656	30	21	.	.	PUNCT
ejpam-5656	31	1	furthermore	furthermore	ADV
ejpam-5656	31	2	,	,	PUNCT
ejpam-5656	31	3	a	a	DET
ejpam-5656	31	4	triangular	triangular	NOUN
ejpam-5656	31	5	theorem	theorem	VERB
ejpam-5656	31	6	establishes	establish	VERB
ejpam-5656	31	7	the	the	DET
ejpam-5656	31	8	equivalence	equivalence	NOUN
ejpam-5656	31	9	between	between	ADP
ejpam-5656	31	10	these	these	DET
ejpam-5656	31	11	different	different	ADJ
ejpam-5656	31	12	approaches	approach	NOUN
ejpam-5656	31	13	.	.	PUNCT
ejpam-5656	32	1	for	for	ADP
ejpam-5656	32	2	example	example	NOUN
ejpam-5656	32	3	,	,	PUNCT
ejpam-5656	32	4	the	the	DET
ejpam-5656	32	5	definition	definition	NOUN
ejpam-5656	32	6	for	for	ADP
ejpam-5656	32	7	bernoulli	bernoulli	NOUN
ejpam-5656	32	8	polynomials	polynomial	NOUN
ejpam-5656	32	9	using	use	VERB
ejpam-5656	32	10	a	a	DET
ejpam-5656	32	11	determinantal	determinantal	ADJ
ejpam-5656	32	12	approach	approach	NOUN
ejpam-5656	32	13	is	be	AUX
ejpam-5656	32	14	given	give	VERB
ejpam-5656	32	15	by	by	ADP
ejpam-5656	32	16	b0(x	b0(x	NOUN
ejpam-5656	32	17	)	)	PUNCT
ejpam-5656	32	18	=	=	SYM
ejpam-5656	32	19	1	1	NUM
ejpam-5656	32	20	,	,	PUNCT
ejpam-5656	32	21	dı́az	dı́az	X
ejpam-5656	32	22	et	et	NOUN
ejpam-5656	32	23	al	al	PROPN
ejpam-5656	32	24	.	.	PUNCT
ejpam-5656	32	25	/	/	SYM
ejpam-5656	32	26	eur	eur	PROPN
ejpam-5656	32	27	.	.	PUNCT
ejpam-5656	33	1	j.	j.	PROPN
ejpam-5656	33	2	pure	pure	PROPN
ejpam-5656	33	3	appl	appl	PROPN
ejpam-5656	33	4	.	.	PROPN
ejpam-5656	33	5	math	math	PROPN
ejpam-5656	33	6	,	,	PUNCT
ejpam-5656	33	7	18	18	NUM
ejpam-5656	33	8	(	(	PUNCT
ejpam-5656	33	9	1	1	NUM
ejpam-5656	33	10	)	)	PUNCT
ejpam-5656	33	11	(	(	PUNCT
ejpam-5656	33	12	2025	2025	NUM
ejpam-5656	33	13	)	)	PUNCT
ejpam-5656	33	14	,	,	PUNCT
ejpam-5656	33	15	5656	5656	NUM
ejpam-5656	33	16	3	3	NUM
ejpam-5656	33	17	of	of	ADP
ejpam-5656	33	18	17	17	NUM
ejpam-5656	33	19	bν(x	bν(x	NOUN
ejpam-5656	33	20	)	)	PUNCT
ejpam-5656	33	21	=	=	SYM
ejpam-5656	33	22	(	(	PUNCT
ejpam-5656	33	23	−1)ν	−1)ν	X
ejpam-5656	33	24	(	(	PUNCT
ejpam-5656	33	25	ν	ν	X
ejpam-5656	33	26	−	−	PROPN
ejpam-5656	33	27	1	1	NUM
ejpam-5656	33	28	)	)	PUNCT
ejpam-5656	33	29	!	!	PUNCT
ejpam-5656	34	1	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5656	34	2	1	1	NUM
ejpam-5656	34	3	x	x	SYM
ejpam-5656	34	4	x2	x2	PROPN
ejpam-5656	34	5	·	·	PUNCT
ejpam-5656	34	6	·	·	PUNCT
ejpam-5656	34	7	·	·	PUNCT
ejpam-5656	35	1	xν−1	xν−1	VERB
ejpam-5656	35	2	xν	xν	NOUN
ejpam-5656	35	3	1	1	NUM
ejpam-5656	35	4	1	1	NUM
ejpam-5656	35	5	2	2	NUM
ejpam-5656	35	6	1	1	NUM
ejpam-5656	35	7	3	3	NUM
ejpam-5656	35	8	·	·	PUNCT
ejpam-5656	35	9	·	·	PUNCT
ejpam-5656	35	10	·	·	PUNCT
ejpam-5656	36	1	1	1	NUM
ejpam-5656	36	2	ν−1	ν−1	ADV
ejpam-5656	36	3	1	1	NUM
ejpam-5656	36	4	ν	ν	NOUN
ejpam-5656	36	5	0	0	NUM
ejpam-5656	36	6	1	1	NUM
ejpam-5656	36	7	1	1	NUM
ejpam-5656	36	8	·	·	PUNCT
ejpam-5656	36	9	·	·	PUNCT
ejpam-5656	36	10	·	·	PUNCT
ejpam-5656	37	1	1	1	NUM
ejpam-5656	37	2	1	1	NUM
ejpam-5656	37	3	0	0	NUM
ejpam-5656	37	4	0	0	NUM
ejpam-5656	37	5	2	2	NUM
ejpam-5656	37	6	·	·	PUNCT
ejpam-5656	37	7	·	·	PUNCT
ejpam-5656	37	8	·	·	PUNCT
ejpam-5656	38	1	ν	ν	X
ejpam-5656	38	2	−	−	NUM
ejpam-5656	38	3	1	1	NUM
ejpam-5656	38	4	ν	ν	NOUN
ejpam-5656	38	5	...	...	PUNCT
ejpam-5656	38	6	...	...	PUNCT
ejpam-5656	38	7	.	.	PUNCT
ejpam-5656	38	8	.	.	PUNCT
ejpam-5656	38	9	.	.	PUNCT
ejpam-5656	39	1	...	...	PUNCT
ejpam-5656	39	2	...	...	PUNCT
ejpam-5656	40	1	...	...	PUNCT
ejpam-5656	40	2	...	...	PUNCT
ejpam-5656	41	1	0	0	NUM
ejpam-5656	41	2	0	0	NUM
ejpam-5656	41	3	·	·	PUNCT
ejpam-5656	41	4	·	·	PUNCT
ejpam-5656	41	5	·	·	PUNCT
ejpam-5656	41	6	·	·	PUNCT
ejpam-5656	41	7	·	·	PUNCT
ejpam-5656	41	8	·	·	PUNCT
ejpam-5656	41	9	(	(	PUNCT
ejpam-5656	41	10	ν−1	ν−1	INTJ
ejpam-5656	41	11	ν−2	ν−2	NOUN
ejpam-5656	41	12	)	)	PUNCT
ejpam-5656	41	13	(	(	PUNCT
ejpam-5656	41	14	ν	ν	X
ejpam-5656	41	15	ν−2	ν−2	PROPN
ejpam-5656	41	16	)	)	PUNCT
ejpam-5656	41	17	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5656	41	18	,	,	PUNCT
ejpam-5656	41	19	ν	ν	X
ejpam-5656	41	20	=	=	SYM
ejpam-5656	41	21	1	1	NUM
ejpam-5656	41	22	,	,	PUNCT
ejpam-5656	41	23	2	2	NUM
ejpam-5656	41	24	,	,	PUNCT
ejpam-5656	41	25	3	3	NUM
ejpam-5656	41	26	,	,	PUNCT
ejpam-5656	41	27	·	·	PUNCT
ejpam-5656	41	28	·	·	PUNCT
ejpam-5656	41	29	·	·	PUNCT
ejpam-5656	41	30	(	(	PUNCT
ejpam-5656	41	31	3	3	X
ejpam-5656	41	32	)	)	PUNCT
ejpam-5656	41	33	over	over	ADP
ejpam-5656	41	34	the	the	DET
ejpam-5656	41	35	years	year	NOUN
ejpam-5656	41	36	,	,	PUNCT
ejpam-5656	41	37	there	there	PRON
ejpam-5656	41	38	have	have	AUX
ejpam-5656	41	39	been	be	AUX
ejpam-5656	41	40	further	further	ADJ
ejpam-5656	41	41	explorations	exploration	NOUN
ejpam-5656	41	42	and	and	CCONJ
ejpam-5656	41	43	expansion	expansion	NOUN
ejpam-5656	41	44	of	of	ADP
ejpam-5656	41	45	the	the	DET
ejpam-5656	41	46	aforementioned	aforementioned	ADJ
ejpam-5656	41	47	polynomials	polynomial	NOUN
ejpam-5656	41	48	,	,	PUNCT
ejpam-5656	41	49	leading	lead	VERB
ejpam-5656	41	50	to	to	ADP
ejpam-5656	41	51	the	the	DET
ejpam-5656	41	52	inclusion	inclusion	NOUN
ejpam-5656	41	53	of	of	ADP
ejpam-5656	41	54	new	new	ADJ
ejpam-5656	41	55	families	family	NOUN
ejpam-5656	41	56	and	and	CCONJ
ejpam-5656	41	57	generalizations	generalization	NOUN
ejpam-5656	41	58	[	[	X
ejpam-5656	41	59	16	16	NUM
ejpam-5656	41	60	]	]	PUNCT
ejpam-5656	41	61	.	.	PUNCT
ejpam-5656	42	1	recently	recently	ADV
ejpam-5656	42	2	,	,	PUNCT
ejpam-5656	42	3	h.	h.	PROPN
ejpam-5656	42	4	belbachir	belbachir	PROPN
ejpam-5656	42	5	et	et	PROPN
ejpam-5656	42	6	al	al	PROPN
ejpam-5656	42	7	.	.	PUNCT
ejpam-5656	43	1	[	[	X
ejpam-5656	43	2	3	3	NUM
ejpam-5656	43	3	]	]	PUNCT
ejpam-5656	43	4	introduced	introduce	VERB
ejpam-5656	43	5	and	and	CCONJ
ejpam-5656	43	6	studied	study	VERB
ejpam-5656	43	7	properties	property	NOUN
ejpam-5656	43	8	of	of	ADP
ejpam-5656	43	9	a	a	DET
ejpam-5656	43	10	class	class	NOUN
ejpam-5656	43	11	of	of	ADP
ejpam-5656	43	12	polynomials	polynomial	NOUN
ejpam-5656	43	13	,	,	PUNCT
ejpam-5656	43	14	uν(x	uν(x	NUM
ejpam-5656	43	15	;	;	PUNCT
ejpam-5656	43	16	ρ;µ	ρ;µ	NUM
ejpam-5656	43	17	)	)	PUNCT
ejpam-5656	43	18	,	,	PUNCT
ejpam-5656	43	19	called	call	VERB
ejpam-5656	43	20	unified	unified	ADJ
ejpam-5656	43	21	bernoulli	bernoulli	PROPN
ejpam-5656	43	22	-	-	PUNCT
ejpam-5656	43	23	euler	euler	NOUN
ejpam-5656	43	24	polynomials	polynomial	NOUN
ejpam-5656	43	25	of	of	ADP
ejpam-5656	43	26	apostol	apostol	NOUN
ejpam-5656	43	27	type	type	NOUN
ejpam-5656	43	28	and	and	CCONJ
ejpam-5656	43	29	defined	define	VERB
ejpam-5656	43	30	by	by	ADP
ejpam-5656	43	31	the	the	DET
ejpam-5656	43	32	following	follow	VERB
ejpam-5656	43	33	power	power	NOUN
ejpam-5656	43	34	series	series	NOUN
ejpam-5656	43	35	:	:	PUNCT
ejpam-5656	43	36	2−	2−	NUM
ejpam-5656	43	37	µ+	µ+	X
ejpam-5656	43	38	µ	µ	PROPN
ejpam-5656	43	39	2	2	NUM
ejpam-5656	43	40	ξ	ξ	NOUN
ejpam-5656	43	41	ρeξ	ρeξ	NOUN
ejpam-5656	43	42	+	+	CCONJ
ejpam-5656	43	43	(	(	PUNCT
ejpam-5656	43	44	1−	1−	NUM
ejpam-5656	43	45	µ	µ	NOUN
ejpam-5656	43	46	)	)	PUNCT
ejpam-5656	43	47	exξ	exξ	NOUN
ejpam-5656	43	48	=	=	PUNCT
ejpam-5656	44	1	∞∑	∞∑	NUM
ejpam-5656	44	2	ν=0	ν=0	NOUN
ejpam-5656	44	3	uν(x	uν(x	NOUN
ejpam-5656	44	4	;	;	PUNCT
ejpam-5656	44	5	ρ;µ	ρ;µ	NUM
ejpam-5656	44	6	)	)	PUNCT
ejpam-5656	44	7	ξν	ξν	ADP
ejpam-5656	44	8	ν	ν	PROPN
ejpam-5656	44	9	!	!	PROPN
ejpam-5656	44	10	,	,	PUNCT
ejpam-5656	44	11	(	(	PUNCT
ejpam-5656	44	12	4	4	X
ejpam-5656	44	13	)	)	PUNCT
ejpam-5656	44	14	where	where	SCONJ
ejpam-5656	44	15	∣∣∣∣ln	∣∣∣∣ln	NOUN
ejpam-5656	44	16	(	(	PUNCT
ejpam-5656	44	17	ρ	ρ	PROPN
ejpam-5656	44	18	1−	1−	NUM
ejpam-5656	44	19	µ	µ	X
ejpam-5656	44	20	)	)	PUNCT
ejpam-5656	45	1	+	+	NUM
ejpam-5656	45	2	ξ	ξ	X
ejpam-5656	45	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5656	45	4	<	<	X
ejpam-5656	45	5	π	π	PROPN
ejpam-5656	45	6	,	,	PUNCT
ejpam-5656	45	7	0	0	NUM
ejpam-5656	45	8	≤	≤	NOUN
ejpam-5656	45	9	µ	µ	X
ejpam-5656	45	10	<	<	X
ejpam-5656	45	11	1	1	NUM
ejpam-5656	45	12	,	,	PUNCT
ejpam-5656	45	13	and	and	CCONJ
ejpam-5656	45	14	∣∣∣∣ln	∣∣∣∣ln	AUX
ejpam-5656	45	15	(	(	PUNCT
ejpam-5656	45	16	ρ	ρ	NUM
ejpam-5656	45	17	µ−	µ−	PROPN
ejpam-5656	45	18	1	1	NUM
ejpam-5656	45	19	)	)	PUNCT
ejpam-5656	45	20	+	+	CCONJ
ejpam-5656	45	21	ξ	ξ	X
ejpam-5656	45	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5656	45	23	<	<	X
ejpam-5656	45	24	2π	2π	NOUN
ejpam-5656	45	25	,	,	PUNCT
ejpam-5656	45	26	otherwise	otherwise	ADV
ejpam-5656	45	27	.	.	PUNCT
ejpam-5656	45	28	note	note	VERB
ejpam-5656	45	29	that	that	SCONJ
ejpam-5656	45	30	for	for	ADP
ejpam-5656	45	31	particular	particular	ADJ
ejpam-5656	45	32	values	value	NOUN
ejpam-5656	45	33	in	in	ADP
ejpam-5656	45	34	the	the	DET
ejpam-5656	45	35	parameters	parameter	NOUN
ejpam-5656	45	36	µ	µ	X
ejpam-5656	45	37	and	and	CCONJ
ejpam-5656	45	38	ρ	ρ	PROPN
ejpam-5656	45	39	,	,	PUNCT
ejpam-5656	45	40	we	we	PRON
ejpam-5656	45	41	can	can	AUX
ejpam-5656	45	42	obtain	obtain	VERB
ejpam-5656	45	43	in	in	ADP
ejpam-5656	45	44	(	(	PUNCT
ejpam-5656	45	45	4	4	NUM
ejpam-5656	45	46	)	)	PUNCT
ejpam-5656	45	47	,	,	PUNCT
ejpam-5656	45	48	the	the	DET
ejpam-5656	45	49	polynomials	polynomial	NOUN
ejpam-5656	45	50	of	of	ADP
ejpam-5656	45	51	bernoulli	bernoulli	PROPN
ejpam-5656	45	52	and	and	CCONJ
ejpam-5656	45	53	euler	euler	PROPN
ejpam-5656	45	54	(	(	PUNCT
ejpam-5656	45	55	as	as	ADV
ejpam-5656	45	56	well	well	ADV
ejpam-5656	45	57	as	as	ADP
ejpam-5656	45	58	apostol	apostol	NOUN
ejpam-5656	45	59	-	-	PUNCT
ejpam-5656	45	60	bernoulli	bernoulli	NOUN
ejpam-5656	45	61	and	and	CCONJ
ejpam-5656	45	62	apostol	apostol	NOUN
ejpam-5656	45	63	-	-	PUNCT
ejpam-5656	45	64	euler	euler	NOUN
ejpam-5656	45	65	,	,	PUNCT
ejpam-5656	45	66	see	see	VERB
ejpam-5656	45	67	[	[	X
ejpam-5656	45	68	1	1	NUM
ejpam-5656	45	69	]	]	NUM
ejpam-5656	45	70	)	)	PUNCT
ejpam-5656	45	71	.	.	PUNCT
ejpam-5656	46	1	however	however	ADV
ejpam-5656	46	2	,	,	PUNCT
ejpam-5656	46	3	this	this	DET
ejpam-5656	46	4	particular	particular	ADJ
ejpam-5656	46	5	family	family	NOUN
ejpam-5656	46	6	does	do	AUX
ejpam-5656	46	7	not	not	PART
ejpam-5656	46	8	take	take	VERB
ejpam-5656	46	9	into	into	ADP
ejpam-5656	46	10	account	account	NOUN
ejpam-5656	46	11	degenerate	degenerate	ADJ
ejpam-5656	46	12	polynomials	polynomial	NOUN
ejpam-5656	46	13	,	,	PUNCT
ejpam-5656	46	14	and	and	CCONJ
ejpam-5656	46	15	apostol	apostol	NOUN
ejpam-5656	46	16	-	-	PUNCT
ejpam-5656	46	17	type	type	NOUN
ejpam-5656	46	18	hermite	hermite	ADJ
ejpam-5656	46	19	polynomials	polynomial	NOUN
ejpam-5656	46	20	(	(	PUNCT
ejpam-5656	46	21	called	call	VERB
ejpam-5656	46	22	hybrid	hybrid	ADJ
ejpam-5656	46	23	polynomials	polynomial	NOUN
ejpam-5656	46	24	by	by	ADP
ejpam-5656	46	25	some	some	DET
ejpam-5656	46	26	authors	author	NOUN
ejpam-5656	46	27	)	)	PUNCT
ejpam-5656	46	28	that	that	PRON
ejpam-5656	46	29	have	have	AUX
ejpam-5656	46	30	garnered	garner	VERB
ejpam-5656	46	31	the	the	DET
ejpam-5656	46	32	attention	attention	NOUN
ejpam-5656	46	33	of	of	ADP
ejpam-5656	46	34	various	various	ADJ
ejpam-5656	46	35	researchers	researcher	NOUN
ejpam-5656	46	36	and	and	CCONJ
ejpam-5656	46	37	play	play	VERB
ejpam-5656	46	38	an	an	DET
ejpam-5656	46	39	important	important	ADJ
ejpam-5656	46	40	role	role	NOUN
ejpam-5656	46	41	in	in	ADP
ejpam-5656	46	42	many	many	ADJ
ejpam-5656	46	43	problems	problem	NOUN
ejpam-5656	46	44	.	.	PUNCT
ejpam-5656	47	1	in	in	ADP
ejpam-5656	47	2	the	the	DET
ejpam-5656	47	3	paper	paper	NOUN
ejpam-5656	47	4	[	[	X
ejpam-5656	47	5	10	10	NUM
ejpam-5656	47	6	]	]	PUNCT
ejpam-5656	47	7	,	,	PUNCT
ejpam-5656	47	8	an	an	DET
ejpam-5656	47	9	extension	extension	NOUN
ejpam-5656	47	10	of	of	ADP
ejpam-5656	47	11	(	(	PUNCT
ejpam-5656	47	12	4	4	NUM
ejpam-5656	47	13	)	)	PUNCT
ejpam-5656	47	14	to	to	PART
ejpam-5656	47	15	degenerate	degenerate	ADJ
ejpam-5656	47	16	polynomials	polynomial	NOUN
ejpam-5656	47	17	was	be	AUX
ejpam-5656	47	18	already	already	ADV
ejpam-5656	47	19	carried	carry	VERB
ejpam-5656	47	20	out	out	ADP
ejpam-5656	47	21	but	but	CCONJ
ejpam-5656	47	22	to	to	ADP
ejpam-5656	47	23	the	the	DET
ejpam-5656	47	24	best	good	ADJ
ejpam-5656	47	25	of	of	ADP
ejpam-5656	47	26	our	our	PRON
ejpam-5656	47	27	knowledge	knowledge	NOUN
ejpam-5656	47	28	,	,	PUNCT
ejpam-5656	47	29	an	an	DET
ejpam-5656	47	30	extension	extension	NOUN
ejpam-5656	47	31	with	with	ADP
ejpam-5656	47	32	the	the	DET
ejpam-5656	47	33	apostol	apostol	NOUN
ejpam-5656	47	34	-	-	PUNCT
ejpam-5656	47	35	type	type	NOUN
ejpam-5656	47	36	hermite	hermite	ADJ
ejpam-5656	47	37	polynomials	polynomial	NOUN
ejpam-5656	47	38	has	have	AUX
ejpam-5656	47	39	not	not	PART
ejpam-5656	47	40	been	be	AUX
ejpam-5656	47	41	developed	develop	VERB
ejpam-5656	47	42	and	and	CCONJ
ejpam-5656	47	43	remains	remain	VERB
ejpam-5656	47	44	an	an	DET
ejpam-5656	47	45	open	open	ADJ
ejpam-5656	47	46	problem	problem	NOUN
ejpam-5656	47	47	.	.	PUNCT
ejpam-5656	48	1	it	it	PRON
ejpam-5656	48	2	is	be	AUX
ejpam-5656	48	3	important	important	ADJ
ejpam-5656	48	4	to	to	PART
ejpam-5656	48	5	highlight	highlight	VERB
ejpam-5656	48	6	that	that	SCONJ
ejpam-5656	48	7	the	the	DET
ejpam-5656	48	8	polynomial	polynomial	ADJ
ejpam-5656	48	9	family	family	NOUN
ejpam-5656	48	10	introduced	introduce	VERB
ejpam-5656	48	11	by	by	ADP
ejpam-5656	48	12	h.	h.	PROPN
ejpam-5656	48	13	belbachir	belbachir	PROPN
ejpam-5656	48	14	et	et	PROPN
ejpam-5656	48	15	al	al	PROPN
ejpam-5656	48	16	.	.	PROPN
ejpam-5656	48	17	does	do	AUX
ejpam-5656	48	18	not	not	PART
ejpam-5656	48	19	constitute	constitute	VERB
ejpam-5656	48	20	a	a	DET
ejpam-5656	48	21	unification	unification	NOUN
ejpam-5656	48	22	of	of	ADP
ejpam-5656	48	23	the	the	DET
ejpam-5656	48	24	aforementioned	aforementioned	ADJ
ejpam-5656	48	25	polynomial	polynomial	ADJ
ejpam-5656	48	26	families	family	NOUN
ejpam-5656	48	27	.	.	PUNCT
ejpam-5656	49	1	by	by	ADP
ejpam-5656	49	2	applying	apply	VERB
ejpam-5656	49	3	the	the	DET
ejpam-5656	49	4	reduction	reduction	NOUN
ejpam-5656	49	5	method	method	NOUN
ejpam-5656	49	6	outlined	outline	VERB
ejpam-5656	49	7	in	in	ADP
ejpam-5656	49	8	theorem	theorem	NOUN
ejpam-5656	49	9	4	4	NUM
ejpam-5656	49	10	by	by	ADP
ejpam-5656	49	11	l.	l.	PROPN
ejpam-5656	49	12	navas	navas	PROPN
ejpam-5656	49	13	et	et	PROPN
ejpam-5656	49	14	al	al	PROPN
ejpam-5656	49	15	.	.	PROPN
ejpam-5656	49	16	,	,	PUNCT
ejpam-5656	49	17	we	we	PRON
ejpam-5656	49	18	can	can	AUX
ejpam-5656	49	19	effectively	effectively	ADV
ejpam-5656	49	20	reduce	reduce	VERB
ejpam-5656	49	21	this	this	DET
ejpam-5656	49	22	polynomial	polynomial	ADJ
ejpam-5656	49	23	family	family	NOUN
ejpam-5656	49	24	to	to	ADP
ejpam-5656	49	25	a	a	DET
ejpam-5656	49	26	linear	linear	ADJ
ejpam-5656	49	27	combination	combination	NOUN
ejpam-5656	49	28	of	of	ADP
ejpam-5656	49	29	apostol	apostol	NOUN
ejpam-5656	49	30	-	-	PUNCT
ejpam-5656	49	31	euler	euler	NOUN
ejpam-5656	49	32	and	and	CCONJ
ejpam-5656	49	33	apostol	apostol	NOUN
ejpam-5656	49	34	-	-	PUNCT
ejpam-5656	49	35	bernoulli	bernoulli	NOUN
ejpam-5656	49	36	polynomials	polynomial	NOUN
ejpam-5656	49	37	(	(	PUNCT
ejpam-5656	49	38	see	see	VERB
ejpam-5656	49	39	[	[	X
ejpam-5656	49	40	3	3	NUM
ejpam-5656	49	41	,	,	PUNCT
ejpam-5656	49	42	17	17	NUM
ejpam-5656	49	43	]	]	PUNCT
ejpam-5656	49	44	)	)	PUNCT
ejpam-5656	49	45	.	.	PUNCT
ejpam-5656	50	1	uν(x	uν(x	PROPN
ejpam-5656	50	2	;	;	PUNCT
ejpam-5656	50	3	ρ;µ	ρ;µ	NUM
ejpam-5656	50	4	)	)	PUNCT
ejpam-5656	51	1	=	=	SYM
ejpam-5656	52	1	1	1	NUM
ejpam-5656	52	2	1−	1−	NUM
ejpam-5656	52	3	µ	µ	X
ejpam-5656	52	4	[	[	X
ejpam-5656	52	5	(	(	PUNCT
ejpam-5656	52	6	1−	1−	NUM
ejpam-5656	52	7	µ	µ	NUM
ejpam-5656	52	8	2	2	NUM
ejpam-5656	52	9	)	)	PUNCT
ejpam-5656	52	10	eν	eν	PROPN
ejpam-5656	52	11	(	(	PUNCT
ejpam-5656	52	12	x	x	X
ejpam-5656	52	13	;	;	PUNCT
ejpam-5656	52	14	ρ	ρ	PROPN
ejpam-5656	52	15	1−	1−	NUM
ejpam-5656	52	16	µ	µ	X
ejpam-5656	52	17	)	)	PUNCT
ejpam-5656	52	18	−	−	PROPN
ejpam-5656	52	19	µ	µ	PROPN
ejpam-5656	52	20	2	2	NUM
ejpam-5656	52	21	bν	bν	NOUN
ejpam-5656	52	22	(	(	PUNCT
ejpam-5656	52	23	x	x	X
ejpam-5656	52	24	;	;	PUNCT
ejpam-5656	52	25	ρ	ρ	NUM
ejpam-5656	52	26	µ−	µ−	PROPN
ejpam-5656	52	27	1	1	NUM
ejpam-5656	52	28	)	)	PUNCT
ejpam-5656	52	29	]	]	PUNCT
ejpam-5656	52	30	,	,	PUNCT
ejpam-5656	52	31	where	where	SCONJ
ejpam-5656	52	32	ξexξ	ξexξ	PROPN
ejpam-5656	52	33	ρeξ	ρeξ	NOUN
ejpam-5656	52	34	−	−	NOUN
ejpam-5656	52	35	1	1	NUM
ejpam-5656	52	36	=	=	SYM
ejpam-5656	52	37	∞∑	∞∑	NUM
ejpam-5656	52	38	ν=0	ν=0	NOUN
ejpam-5656	52	39	bν(x	bν(x	NOUN
ejpam-5656	52	40	;	;	PUNCT
ejpam-5656	52	41	ρ	ρ	X
ejpam-5656	52	42	)	)	PUNCT
ejpam-5656	52	43	ξν	ξν	ADP
ejpam-5656	52	44	ν	ν	PROPN
ejpam-5656	52	45	!	!	PROPN
ejpam-5656	52	46	,	,	PUNCT
ejpam-5656	52	47	dı́az	dı́az	X
ejpam-5656	52	48	et	et	PROPN
ejpam-5656	52	49	al	al	PROPN
ejpam-5656	52	50	.	.	PUNCT
ejpam-5656	52	51	/	/	SYM
ejpam-5656	52	52	eur	eur	PROPN
ejpam-5656	52	53	.	.	PUNCT
ejpam-5656	53	1	j.	j.	PROPN
ejpam-5656	53	2	pure	pure	PROPN
ejpam-5656	53	3	appl	appl	PROPN
ejpam-5656	53	4	.	.	PROPN
ejpam-5656	53	5	math	math	PROPN
ejpam-5656	53	6	,	,	PUNCT
ejpam-5656	53	7	18	18	NUM
ejpam-5656	53	8	(	(	PUNCT
ejpam-5656	53	9	1	1	NUM
ejpam-5656	53	10	)	)	PUNCT
ejpam-5656	53	11	(	(	PUNCT
ejpam-5656	53	12	2025	2025	NUM
ejpam-5656	53	13	)	)	PUNCT
ejpam-5656	53	14	,	,	PUNCT
ejpam-5656	53	15	5656	5656	NUM
ejpam-5656	53	16	4	4	NUM
ejpam-5656	53	17	of	of	ADP
ejpam-5656	53	18	17	17	NUM
ejpam-5656	53	19	and	and	CCONJ
ejpam-5656	53	20	2exξ	2exξ	NUM
ejpam-5656	53	21	ρeξ	ρeξ	NOUN
ejpam-5656	54	1	+	+	CCONJ
ejpam-5656	54	2	1	1	X
ejpam-5656	54	3	=	=	SYM
ejpam-5656	54	4	∞∑	∞∑	NUM
ejpam-5656	54	5	ν=0	ν=0	NOUN
ejpam-5656	54	6	eν(x	eν(x	NOUN
ejpam-5656	54	7	;	;	PUNCT
ejpam-5656	54	8	ρ	ρ	NUM
ejpam-5656	54	9	)	)	PUNCT
ejpam-5656	54	10	ξν	ξν	ADV
ejpam-5656	54	11	ν	ν	PROPN
ejpam-5656	54	12	!	!	PUNCT
ejpam-5656	54	13	.	.	PUNCT
ejpam-5656	55	1	the	the	DET
ejpam-5656	55	2	primary	primary	ADJ
ejpam-5656	55	3	objective	objective	NOUN
ejpam-5656	55	4	of	of	ADP
ejpam-5656	55	5	this	this	DET
ejpam-5656	55	6	paper	paper	NOUN
ejpam-5656	55	7	is	be	AUX
ejpam-5656	55	8	to	to	PART
ejpam-5656	55	9	define	define	VERB
ejpam-5656	55	10	and	and	CCONJ
ejpam-5656	55	11	explore	explore	VERB
ejpam-5656	55	12	an	an	DET
ejpam-5656	55	13	extension	extension	NOUN
ejpam-5656	55	14	of	of	ADP
ejpam-5656	55	15	apostoltype	apostoltype	ADJ
ejpam-5656	55	16	hermite	hermite	ADJ
ejpam-5656	55	17	polynomials	polynomial	NOUN
ejpam-5656	55	18	utilizing	utilize	VERB
ejpam-5656	55	19	the	the	DET
ejpam-5656	55	20	polynomials	polynomial	NOUN
ejpam-5656	55	21	presented	present	VERB
ejpam-5656	55	22	in	in	ADP
ejpam-5656	55	23	equation	equation	NOUN
ejpam-5656	55	24	(	(	PUNCT
ejpam-5656	55	25	4	4	NUM
ejpam-5656	55	26	)	)	PUNCT
ejpam-5656	55	27	.	.	PUNCT
ejpam-5656	56	1	the	the	DET
ejpam-5656	56	2	properties	property	NOUN
ejpam-5656	56	3	of	of	ADP
ejpam-5656	56	4	this	this	DET
ejpam-5656	56	5	polynomial	polynomial	ADJ
ejpam-5656	56	6	family	family	NOUN
ejpam-5656	56	7	,	,	PUNCT
ejpam-5656	56	8	which	which	PRON
ejpam-5656	56	9	we	we	PRON
ejpam-5656	56	10	shall	shall	AUX
ejpam-5656	56	11	refer	refer	VERB
ejpam-5656	56	12	to	to	ADP
ejpam-5656	56	13	as	as	ADP
ejpam-5656	56	14	apostol	apostol	NOUN
ejpam-5656	56	15	-	-	PUNCT
ejpam-5656	56	16	type	type	NOUN
ejpam-5656	56	17	hermite	hermite	PROPN
ejpam-5656	56	18	-	-	PUNCT
ejpam-5656	56	19	bernoulli	bernoulli	PROPN
ejpam-5656	56	20	/	/	SYM
ejpam-5656	56	21	euler	euler	NOUN
ejpam-5656	56	22	polynomials	polynomial	NOUN
ejpam-5656	56	23	,	,	PUNCT
ejpam-5656	56	24	are	be	AUX
ejpam-5656	56	25	characterized	characterize	VERB
ejpam-5656	56	26	by	by	ADP
ejpam-5656	56	27	their	their	PRON
ejpam-5656	56	28	generating	generating	NOUN
ejpam-5656	56	29	functions	function	NOUN
ejpam-5656	56	30	,	,	PUNCT
ejpam-5656	56	31	summation	summation	NOUN
ejpam-5656	56	32	formulae	formulae	NOUN
ejpam-5656	56	33	,	,	PUNCT
ejpam-5656	56	34	and	and	CCONJ
ejpam-5656	56	35	determinant	determinant	ADJ
ejpam-5656	56	36	forms	form	NOUN
ejpam-5656	56	37	.	.	PUNCT
ejpam-5656	57	1	these	these	DET
ejpam-5656	57	2	polynomials	polynomial	NOUN
ejpam-5656	57	3	encompass	encompass	VERB
ejpam-5656	57	4	classical	classical	ADJ
ejpam-5656	57	5	appell	appell	ADJ
ejpam-5656	57	6	-	-	PUNCT
ejpam-5656	57	7	type	type	NOUN
ejpam-5656	57	8	polynomials	polynomial	NOUN
ejpam-5656	57	9	and	and	CCONJ
ejpam-5656	57	10	their	their	PRON
ejpam-5656	57	11	notable	notable	ADJ
ejpam-5656	57	12	extensions	extension	NOUN
ejpam-5656	57	13	,	,	PUNCT
ejpam-5656	57	14	as	as	SCONJ
ejpam-5656	57	15	they	they	PRON
ejpam-5656	57	16	satisfy	satisfy	VERB
ejpam-5656	57	17	the	the	DET
ejpam-5656	57	18	differential	differential	ADJ
ejpam-5656	57	19	equations	equation	NOUN
ejpam-5656	57	20	(	(	PUNCT
ejpam-5656	57	21	2	2	NUM
ejpam-5656	57	22	)	)	PUNCT
ejpam-5656	57	23	.	.	PUNCT
ejpam-5656	58	1	however	however	ADV
ejpam-5656	58	2	,	,	PUNCT
ejpam-5656	58	3	it	it	PRON
ejpam-5656	58	4	is	be	AUX
ejpam-5656	58	5	crucial	crucial	ADJ
ejpam-5656	58	6	to	to	PART
ejpam-5656	58	7	clarify	clarify	VERB
ejpam-5656	58	8	that	that	SCONJ
ejpam-5656	58	9	,	,	PUNCT
ejpam-5656	58	10	within	within	ADP
ejpam-5656	58	11	the	the	DET
ejpam-5656	58	12	scope	scope	NOUN
ejpam-5656	58	13	of	of	ADP
ejpam-5656	58	14	our	our	PRON
ejpam-5656	58	15	study	study	NOUN
ejpam-5656	58	16	,	,	PUNCT
ejpam-5656	58	17	we	we	PRON
ejpam-5656	58	18	will	will	AUX
ejpam-5656	58	19	utilize	utilize	VERB
ejpam-5656	58	20	the	the	DET
ejpam-5656	58	21	polynomials	polynomial	NOUN
ejpam-5656	58	22	presented	present	VERB
ejpam-5656	58	23	in	in	ADP
ejpam-5656	58	24	equation	equation	NOUN
ejpam-5656	58	25	(	(	PUNCT
ejpam-5656	58	26	4	4	NUM
ejpam-5656	58	27	)	)	PUNCT
ejpam-5656	58	28	without	without	ADP
ejpam-5656	58	29	asserting	assert	VERB
ejpam-5656	58	30	them	they	PRON
ejpam-5656	58	31	as	as	ADP
ejpam-5656	58	32	a	a	DET
ejpam-5656	58	33	unification	unification	NOUN
ejpam-5656	58	34	of	of	ADP
ejpam-5656	58	35	pre	pre	ADJ
ejpam-5656	58	36	-	-	ADJ
ejpam-5656	58	37	existing	exist	VERB
ejpam-5656	58	38	polynomial	polynomial	ADJ
ejpam-5656	58	39	families	family	NOUN
ejpam-5656	58	40	.	.	PUNCT
ejpam-5656	59	1	on	on	ADP
ejpam-5656	59	2	the	the	DET
ejpam-5656	59	3	other	other	ADJ
ejpam-5656	59	4	hand	hand	NOUN
ejpam-5656	59	5	,	,	PUNCT
ejpam-5656	59	6	the	the	DET
ejpam-5656	59	7	monomiality	monomiality	NOUN
ejpam-5656	59	8	principle	principle	NOUN
ejpam-5656	59	9	,	,	PUNCT
ejpam-5656	59	10	in	in	ADP
ejpam-5656	59	11	conjunction	conjunction	NOUN
ejpam-5656	59	12	with	with	ADP
ejpam-5656	59	13	the	the	DET
ejpam-5656	59	14	associated	associated	ADJ
ejpam-5656	59	15	operational	operational	ADJ
ejpam-5656	59	16	formalism	formalism	NOUN
ejpam-5656	59	17	,	,	PUNCT
ejpam-5656	59	18	has	have	AUX
ejpam-5656	59	19	proven	prove	VERB
ejpam-5656	59	20	to	to	PART
ejpam-5656	59	21	be	be	AUX
ejpam-5656	59	22	a	a	DET
ejpam-5656	59	23	robust	robust	ADJ
ejpam-5656	59	24	tool	tool	NOUN
ejpam-5656	59	25	for	for	ADP
ejpam-5656	59	26	probing	probe	VERB
ejpam-5656	59	27	the	the	DET
ejpam-5656	59	28	properties	property	NOUN
ejpam-5656	59	29	of	of	ADP
ejpam-5656	59	30	a	a	DET
ejpam-5656	59	31	wide	wide	ADJ
ejpam-5656	59	32	range	range	NOUN
ejpam-5656	59	33	of	of	ADP
ejpam-5656	59	34	polynomials	polynomial	NOUN
ejpam-5656	59	35	.	.	PUNCT
ejpam-5656	60	1	this	this	DET
ejpam-5656	60	2	principle	principle	NOUN
ejpam-5656	60	3	has	have	AUX
ejpam-5656	60	4	been	be	AUX
ejpam-5656	60	5	refined	refine	VERB
ejpam-5656	60	6	and	and	CCONJ
ejpam-5656	60	7	elaborated	elaborate	VERB
ejpam-5656	60	8	upon	upon	SCONJ
ejpam-5656	60	9	by	by	ADP
ejpam-5656	60	10	various	various	ADJ
ejpam-5656	60	11	researchers	researcher	NOUN
ejpam-5656	60	12	,	,	PUNCT
ejpam-5656	60	13	further	far	ADV
ejpam-5656	60	14	contributing	contribute	VERB
ejpam-5656	60	15	to	to	ADP
ejpam-5656	60	16	the	the	DET
ejpam-5656	60	17	understanding	understanding	NOUN
ejpam-5656	60	18	of	of	ADP
ejpam-5656	60	19	the	the	DET
ejpam-5656	60	20	properties	property	NOUN
ejpam-5656	60	21	and	and	CCONJ
ejpam-5656	60	22	behaviors	behavior	NOUN
ejpam-5656	60	23	of	of	ADP
ejpam-5656	60	24	polynomials	polynomial	NOUN
ejpam-5656	60	25	.	.	PUNCT
ejpam-5656	61	1	in	in	ADP
ejpam-5656	61	2	this	this	DET
ejpam-5656	61	3	paper	paper	NOUN
ejpam-5656	61	4	,	,	PUNCT
ejpam-5656	61	5	the	the	DET
ejpam-5656	61	6	derivative	derivative	ADJ
ejpam-5656	61	7	and	and	CCONJ
ejpam-5656	61	8	multiplicative	multiplicative	ADJ
ejpam-5656	61	9	operators	operator	NOUN
ejpam-5656	61	10	are	be	AUX
ejpam-5656	61	11	established	establish	VERB
ejpam-5656	61	12	that	that	PRON
ejpam-5656	61	13	allow	allow	VERB
ejpam-5656	61	14	the	the	DET
ejpam-5656	61	15	set	set	NOUN
ejpam-5656	61	16	of	of	ADP
ejpam-5656	61	17	the	the	DET
ejpam-5656	61	18	apostol	apostol	NOUN
ejpam-5656	61	19	-	-	PUNCT
ejpam-5656	61	20	type	type	NOUN
ejpam-5656	61	21	hermite	hermite	PROPN
ejpam-5656	61	22	-	-	PUNCT
ejpam-5656	61	23	bernoulli	bernoulli	PROPN
ejpam-5656	61	24	/	/	SYM
ejpam-5656	61	25	euler	euler	NOUN
ejpam-5656	61	26	polynomials	polynomial	NOUN
ejpam-5656	61	27	to	to	PART
ejpam-5656	61	28	be	be	AUX
ejpam-5656	61	29	defined	define	VERB
ejpam-5656	61	30	as	as	ADP
ejpam-5656	61	31	quasi	quasi	ADJ
ejpam-5656	61	32	-	-	ADJ
ejpam-5656	61	33	monomial	monomial	ADJ
ejpam-5656	61	34	set	set	NOUN
ejpam-5656	61	35	.	.	PUNCT
ejpam-5656	62	1	in	in	ADP
ejpam-5656	62	2	summary	summary	NOUN
ejpam-5656	62	3	,	,	PUNCT
ejpam-5656	62	4	this	this	DET
ejpam-5656	62	5	document	document	NOUN
ejpam-5656	62	6	provides	provide	VERB
ejpam-5656	62	7	an	an	DET
ejpam-5656	62	8	overview	overview	NOUN
ejpam-5656	62	9	of	of	ADP
ejpam-5656	62	10	the	the	DET
ejpam-5656	62	11	unified	unify	VERB
ejpam-5656	62	12	apostol	apostol	NOUN
ejpam-5656	62	13	-	-	PUNCT
ejpam-5656	62	14	type	type	NOUN
ejpam-5656	62	15	hermite	hermite	ADJ
ejpam-5656	62	16	bernoulli	bernoulli	PROPN
ejpam-5656	62	17	/	/	SYM
ejpam-5656	62	18	euler	euler	NOUN
ejpam-5656	62	19	polynomials	polynomial	NOUN
ejpam-5656	62	20	,	,	PUNCT
ejpam-5656	62	21	their	their	PRON
ejpam-5656	62	22	properties	property	NOUN
ejpam-5656	62	23	,	,	PUNCT
ejpam-5656	62	24	and	and	CCONJ
ejpam-5656	62	25	their	their	PRON
ejpam-5656	62	26	applications	application	NOUN
ejpam-5656	62	27	.	.	PUNCT
ejpam-5656	63	1	it	it	PRON
ejpam-5656	63	2	also	also	ADV
ejpam-5656	63	3	highlights	highlight	VERB
ejpam-5656	63	4	the	the	DET
ejpam-5656	63	5	influence	influence	NOUN
ejpam-5656	63	6	of	of	ADP
ejpam-5656	63	7	previous	previous	ADJ
ejpam-5656	63	8	research	research	NOUN
ejpam-5656	63	9	in	in	ADP
ejpam-5656	63	10	the	the	DET
ejpam-5656	63	11	field	field	NOUN
ejpam-5656	63	12	and	and	CCONJ
ejpam-5656	63	13	presents	present	VERB
ejpam-5656	63	14	new	new	ADJ
ejpam-5656	63	15	findings	finding	NOUN
ejpam-5656	63	16	related	relate	VERB
ejpam-5656	63	17	to	to	ADP
ejpam-5656	63	18	the	the	DET
ejpam-5656	63	19	algebraic	algebraic	ADJ
ejpam-5656	63	20	and	and	CCONJ
ejpam-5656	63	21	differential	differential	ADJ
ejpam-5656	63	22	properties	property	NOUN
ejpam-5656	63	23	of	of	ADP
ejpam-5656	63	24	these	these	DET
ejpam-5656	63	25	polynomials	polynomial	NOUN
ejpam-5656	63	26	.	.	PUNCT
ejpam-5656	64	1	the	the	DET
ejpam-5656	64	2	study	study	NOUN
ejpam-5656	64	3	of	of	ADP
ejpam-5656	64	4	these	these	DET
ejpam-5656	64	5	polynomials	polynomial	NOUN
ejpam-5656	64	6	has	have	AUX
ejpam-5656	64	7	been	be	AUX
ejpam-5656	64	8	enriched	enrich	VERB
ejpam-5656	64	9	by	by	ADP
ejpam-5656	64	10	the	the	DET
ejpam-5656	64	11	exploration	exploration	NOUN
ejpam-5656	64	12	of	of	ADP
ejpam-5656	64	13	the	the	DET
ejpam-5656	64	14	monomiality	monomiality	NOUN
ejpam-5656	64	15	principle	principle	NOUN
ejpam-5656	64	16	and	and	CCONJ
ejpam-5656	64	17	its	its	PRON
ejpam-5656	64	18	associated	associated	ADJ
ejpam-5656	64	19	operational	operational	ADJ
ejpam-5656	64	20	techniques	technique	NOUN
ejpam-5656	64	21	,	,	PUNCT
ejpam-5656	64	22	further	far	ADV
ejpam-5656	64	23	contributing	contribute	VERB
ejpam-5656	64	24	to	to	ADP
ejpam-5656	64	25	the	the	DET
ejpam-5656	64	26	understanding	understanding	NOUN
ejpam-5656	64	27	of	of	ADP
ejpam-5656	64	28	their	their	PRON
ejpam-5656	64	29	properties	property	NOUN
ejpam-5656	64	30	and	and	CCONJ
ejpam-5656	64	31	behaviors	behavior	NOUN
ejpam-5656	64	32	.	.	PUNCT
ejpam-5656	65	1	2	2	X
ejpam-5656	65	2	.	.	X
ejpam-5656	65	3	apostol	apostol	NOUN
ejpam-5656	65	4	-	-	PUNCT
ejpam-5656	65	5	type	type	NOUN
ejpam-5656	65	6	hermite	hermite	PROPN
ejpam-5656	65	7	-	-	PUNCT
ejpam-5656	65	8	bernoulli	bernoulli	PROPN
ejpam-5656	65	9	/	/	SYM
ejpam-5656	65	10	euler	euler	NOUN
ejpam-5656	65	11	polynomials	polynomial	NOUN
ejpam-5656	65	12	in	in	ADP
ejpam-5656	65	13	this	this	DET
ejpam-5656	65	14	section	section	NOUN
ejpam-5656	65	15	,	,	PUNCT
ejpam-5656	65	16	we	we	PRON
ejpam-5656	65	17	define	define	VERB
ejpam-5656	65	18	a	a	DET
ejpam-5656	65	19	new	new	ADJ
ejpam-5656	65	20	family	family	NOUN
ejpam-5656	65	21	of	of	ADP
ejpam-5656	65	22	polynomials	polynomial	NOUN
ejpam-5656	65	23	termed	term	VERB
ejpam-5656	65	24	the	the	DET
ejpam-5656	65	25	apostol	apostol	NOUN
ejpam-5656	65	26	-	-	PUNCT
ejpam-5656	65	27	type	type	NOUN
ejpam-5656	65	28	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	65	29	/	/	SYM
ejpam-5656	65	30	euler	euler	NOUN
ejpam-5656	65	31	polynomials	polynomial	NOUN
ejpam-5656	65	32	and	and	CCONJ
ejpam-5656	65	33	delve	delve	VERB
ejpam-5656	65	34	into	into	ADP
ejpam-5656	65	35	their	their	PRON
ejpam-5656	65	36	algebraic	algebraic	ADJ
ejpam-5656	65	37	and	and	CCONJ
ejpam-5656	65	38	differential	differential	ADJ
ejpam-5656	65	39	properties	property	NOUN
ejpam-5656	65	40	.	.	PUNCT
ejpam-5656	66	1	definition	definition	NOUN
ejpam-5656	66	2	1	1	NUM
ejpam-5656	66	3	.	.	PUNCT
ejpam-5656	67	1	let	let	VERB
ejpam-5656	67	2	ρ	ρ	PROPN
ejpam-5656	67	3	>	>	X
ejpam-5656	67	4	0	0	PROPN
ejpam-5656	67	5	,	,	PUNCT
ejpam-5656	67	6	µ	µ	PRON
ejpam-5656	67	7	≥	≥	NOUN
ejpam-5656	67	8	0	0	NUM
ejpam-5656	67	9	such	such	ADJ
ejpam-5656	67	10	that	that	SCONJ
ejpam-5656	67	11	µ	µ	ADJ
ejpam-5656	67	12	̸=	̸=	PROPN
ejpam-5656	67	13	1	1	NUM
ejpam-5656	67	14	.	.	PUNCT
ejpam-5656	68	1	we	we	PRON
ejpam-5656	68	2	introduce	introduce	VERB
ejpam-5656	68	3	the	the	DET
ejpam-5656	68	4	apostol	apostol	NOUN
ejpam-5656	68	5	-	-	PUNCT
ejpam-5656	68	6	type	type	NOUN
ejpam-5656	68	7	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	68	8	/	/	SYM
ejpam-5656	68	9	euler	euler	NOUN
ejpam-5656	68	10	polynomials	polynomial	NOUN
ejpam-5656	68	11	as	as	SCONJ
ejpam-5656	68	12	follows	follow	VERB
ejpam-5656	68	13	:	:	PUNCT
ejpam-5656	68	14	φ(ρ	φ(ρ	NUM
ejpam-5656	68	15	,	,	PUNCT
ejpam-5656	68	16	µ	µ	NUM
ejpam-5656	68	17	,	,	PUNCT
ejpam-5656	68	18	ξ)exξ+yξ2	ξ)exξ+yξ2	X
ejpam-5656	68	19	=	=	PUNCT
ejpam-5656	68	20	∞∑	∞∑	NUM
ejpam-5656	68	21	ν=0	ν=0	NOUN
ejpam-5656	68	22	uν(x	uν(x	NOUN
ejpam-5656	68	23	,	,	PUNCT
ejpam-5656	68	24	y	y	PROPN
ejpam-5656	68	25	;	;	PUNCT
ejpam-5656	68	26	ρ;µ	ρ;µ	NUM
ejpam-5656	68	27	)	)	PUNCT
ejpam-5656	68	28	ξν	ξν	ADP
ejpam-5656	68	29	ν	ν	PROPN
ejpam-5656	68	30	!	!	PROPN
ejpam-5656	68	31	,	,	PUNCT
ejpam-5656	68	32	(	(	PUNCT
ejpam-5656	68	33	5	5	X
ejpam-5656	68	34	)	)	PUNCT
ejpam-5656	68	35	where	where	SCONJ
ejpam-5656	68	36	φ(ρ	φ(ρ	NUM
ejpam-5656	68	37	,	,	PUNCT
ejpam-5656	68	38	µ	µ	NOUN
ejpam-5656	68	39	,	,	PUNCT
ejpam-5656	68	40	ξ	ξ	NOUN
ejpam-5656	68	41	)	)	PUNCT
ejpam-5656	68	42	:	:	PUNCT
ejpam-5656	68	43	=	=	SYM
ejpam-5656	68	44	2−	2−	NUM
ejpam-5656	68	45	µ+	µ+	X
ejpam-5656	68	46	µ	µ	PROPN
ejpam-5656	68	47	2	2	NUM
ejpam-5656	68	48	ξ	ξ	NOUN
ejpam-5656	68	49	ρeξ	ρeξ	NOUN
ejpam-5656	68	50	+	+	CCONJ
ejpam-5656	68	51	(	(	PUNCT
ejpam-5656	68	52	1−	1−	NUM
ejpam-5656	68	53	µ	µ	NUM
ejpam-5656	68	54	)	)	PUNCT
ejpam-5656	68	55	,	,	PUNCT
ejpam-5656	68	56	as	as	ADV
ejpam-5656	68	57	long	long	ADV
ejpam-5656	68	58	as	as	ADP
ejpam-5656	68	59	∣∣∣∣ln	∣∣∣∣ln	NOUN
ejpam-5656	68	60	(	(	PUNCT
ejpam-5656	68	61	ρ	ρ	PROPN
ejpam-5656	68	62	1−	1−	NUM
ejpam-5656	68	63	µ	µ	X
ejpam-5656	68	64	)	)	PUNCT
ejpam-5656	68	65	+	+	NUM
ejpam-5656	68	66	ξ	ξ	X
ejpam-5656	68	67	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5656	68	68	<	<	X
ejpam-5656	68	69	π	π	PROPN
ejpam-5656	68	70	,	,	PUNCT
ejpam-5656	68	71	0	0	NUM
ejpam-5656	68	72	≤	≤	NOUN
ejpam-5656	68	73	µ	µ	X
ejpam-5656	68	74	<	<	X
ejpam-5656	68	75	1	1	NUM
ejpam-5656	68	76	,	,	PUNCT
ejpam-5656	68	77	dı́az	dı́az	X
ejpam-5656	68	78	et	et	NOUN
ejpam-5656	68	79	al	al	PROPN
ejpam-5656	68	80	.	.	PUNCT
ejpam-5656	68	81	/	/	SYM
ejpam-5656	68	82	eur	eur	PROPN
ejpam-5656	68	83	.	.	PUNCT
ejpam-5656	69	1	j.	j.	PROPN
ejpam-5656	69	2	pure	pure	PROPN
ejpam-5656	69	3	appl	appl	PROPN
ejpam-5656	69	4	.	.	PROPN
ejpam-5656	69	5	math	math	PROPN
ejpam-5656	69	6	,	,	PUNCT
ejpam-5656	69	7	18	18	NUM
ejpam-5656	69	8	(	(	PUNCT
ejpam-5656	69	9	1	1	NUM
ejpam-5656	69	10	)	)	PUNCT
ejpam-5656	69	11	(	(	PUNCT
ejpam-5656	69	12	2025	2025	NUM
ejpam-5656	69	13	)	)	PUNCT
ejpam-5656	69	14	,	,	PUNCT
ejpam-5656	69	15	5656	5656	NUM
ejpam-5656	69	16	5	5	NUM
ejpam-5656	69	17	of	of	ADP
ejpam-5656	69	18	17	17	NUM
ejpam-5656	69	19	and	and	CCONJ
ejpam-5656	69	20	∣∣∣∣ln	∣∣∣∣ln	PROPN
ejpam-5656	69	21	(	(	PUNCT
ejpam-5656	69	22	ρ	ρ	NUM
ejpam-5656	69	23	µ−	µ−	PROPN
ejpam-5656	69	24	1	1	NUM
ejpam-5656	69	25	)	)	PUNCT
ejpam-5656	69	26	+	+	CCONJ
ejpam-5656	69	27	ξ	ξ	X
ejpam-5656	69	28	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5656	69	29	<	<	X
ejpam-5656	69	30	2π	2π	NOUN
ejpam-5656	69	31	,	,	PUNCT
ejpam-5656	69	32	otherwise	otherwise	ADV
ejpam-5656	69	33	.	.	PUNCT
ejpam-5656	70	1	furthermore	furthermore	ADV
ejpam-5656	70	2	,	,	PUNCT
ejpam-5656	70	3	the	the	DET
ejpam-5656	70	4	apostol	apostol	NOUN
ejpam-5656	70	5	-	-	PUNCT
ejpam-5656	70	6	type	type	NOUN
ejpam-5656	70	7	hermite	hermite	PROPN
ejpam-5656	70	8	-	-	PUNCT
ejpam-5656	70	9	bernoulli	bernoulli	PROPN
ejpam-5656	70	10	/	/	SYM
ejpam-5656	70	11	euler	euler	NOUN
ejpam-5656	70	12	numbers	number	NOUN
ejpam-5656	70	13	are	be	AUX
ejpam-5656	70	14	given	give	VERB
ejpam-5656	70	15	by	by	ADP
ejpam-5656	70	16	uν(ρ;µ	uν(ρ;µ	PROPN
ejpam-5656	70	17	)	)	PUNCT
ejpam-5656	70	18	:	:	PUNCT
ejpam-5656	71	1	=	=	PUNCT
ejpam-5656	71	2	uν(0	uν(0	PROPN
ejpam-5656	71	3	,	,	PUNCT
ejpam-5656	71	4	0	0	NUM
ejpam-5656	71	5	;	;	PUNCT
ejpam-5656	71	6	ρ;µ	ρ;µ	NUM
ejpam-5656	71	7	)	)	PUNCT
ejpam-5656	71	8	.	.	PUNCT
ejpam-5656	72	1	(	(	PUNCT
ejpam-5656	72	2	6	6	NUM
ejpam-5656	72	3	)	)	PUNCT
ejpam-5656	72	4	in	in	ADP
ejpam-5656	72	5	the	the	DET
ejpam-5656	72	6	following	following	NOUN
ejpam-5656	72	7	,	,	PUNCT
ejpam-5656	72	8	we	we	PRON
ejpam-5656	72	9	provide	provide	VERB
ejpam-5656	72	10	some	some	DET
ejpam-5656	72	11	illustrative	illustrative	ADJ
ejpam-5656	72	12	examples	example	NOUN
ejpam-5656	72	13	showing	show	VERB
ejpam-5656	72	14	the	the	DET
ejpam-5656	72	15	existence	existence	NOUN
ejpam-5656	72	16	of	of	ADP
ejpam-5656	72	17	polynomials	polynomial	NOUN
ejpam-5656	72	18	un(x	un(x	NOUN
ejpam-5656	72	19	,	,	PUNCT
ejpam-5656	72	20	y	y	PROPN
ejpam-5656	72	21	;	;	PUNCT
ejpam-5656	72	22	ρ;µ	ρ;µ	NUM
ejpam-5656	72	23	)	)	PUNCT
ejpam-5656	72	24	.	.	PUNCT
ejpam-5656	73	1	example	example	NOUN
ejpam-5656	74	1	1	1	NUM
ejpam-5656	74	2	.	.	X
ejpam-5656	75	1	for	for	ADP
ejpam-5656	75	2	ρ	ρ	PROPN
ejpam-5656	75	3	=	=	SYM
ejpam-5656	75	4	1	1	NUM
ejpam-5656	75	5	,	,	PUNCT
ejpam-5656	75	6	µ	µ	X
ejpam-5656	75	7	=	=	SYM
ejpam-5656	75	8	2	2	NUM
ejpam-5656	75	9	,	,	PUNCT
ejpam-5656	75	10	we	we	PRON
ejpam-5656	75	11	have	have	VERB
ejpam-5656	75	12	ν	ν	NOUN
ejpam-5656	75	13	uν(x	uν(x	PROPN
ejpam-5656	75	14	,	,	PUNCT
ejpam-5656	75	15	y	y	PROPN
ejpam-5656	75	16	;	;	PUNCT
ejpam-5656	75	17	1	1	NUM
ejpam-5656	75	18	;	;	PUNCT
ejpam-5656	75	19	2	2	NUM
ejpam-5656	75	20	)	)	PUNCT
ejpam-5656	75	21	0	0	NUM
ejpam-5656	75	22	1	1	NUM
ejpam-5656	75	23	1	1	NUM
ejpam-5656	75	24	x−	x−	PROPN
ejpam-5656	75	25	1	1	NUM
ejpam-5656	75	26	2	2	NUM
ejpam-5656	75	27	2	2	NUM
ejpam-5656	75	28	x2	x2	NOUN
ejpam-5656	75	29	−	−	PROPN
ejpam-5656	75	30	x+	x+	PUNCT
ejpam-5656	75	31	2y	2y	PROPN
ejpam-5656	76	1	+	+	CCONJ
ejpam-5656	76	2	1	1	NUM
ejpam-5656	76	3	6	6	NUM
ejpam-5656	76	4	3	3	NUM
ejpam-5656	76	5	x3	x3	NOUN
ejpam-5656	76	6	−	−	PROPN
ejpam-5656	76	7	3	3	NUM
ejpam-5656	76	8	2	2	NUM
ejpam-5656	76	9	x2	x2	NOUN
ejpam-5656	77	1	+	+	CCONJ
ejpam-5656	77	2	(	(	PUNCT
ejpam-5656	77	3	6y	6y	NOUN
ejpam-5656	77	4	+	+	CCONJ
ejpam-5656	77	5	1	1	NUM
ejpam-5656	77	6	2	2	NUM
ejpam-5656	77	7	)	)	PUNCT
ejpam-5656	77	8	x+	x+	X
ejpam-5656	77	9	3y	3y	NUM
ejpam-5656	77	10	4	4	NUM
ejpam-5656	77	11	x4	x4	NOUN
ejpam-5656	77	12	−	−	PROPN
ejpam-5656	77	13	2x3	2x3	NUM
ejpam-5656	77	14	+	+	CCONJ
ejpam-5656	77	15	(	(	PUNCT
ejpam-5656	77	16	12y	12y	NOUN
ejpam-5656	77	17	+	+	CCONJ
ejpam-5656	77	18	1)x2	1)x2	NUM
ejpam-5656	77	19	−	−	PROPN
ejpam-5656	77	20	12y2	12y2	NUM
ejpam-5656	78	1	+	+	NUM
ejpam-5656	78	2	2y	2y	PROPN
ejpam-5656	78	3	−	−	NOUN
ejpam-5656	78	4	1	1	NUM
ejpam-5656	78	5	60	60	NUM
ejpam-5656	78	6	example	example	NOUN
ejpam-5656	78	7	2	2	NUM
ejpam-5656	78	8	.	.	X
ejpam-5656	78	9	for	for	ADP
ejpam-5656	78	10	ρ	ρ	PROPN
ejpam-5656	78	11	=	=	SYM
ejpam-5656	78	12	2	2	NUM
ejpam-5656	78	13	,	,	PUNCT
ejpam-5656	78	14	µ	µ	X
ejpam-5656	78	15	=	=	SYM
ejpam-5656	78	16	1	1	NUM
ejpam-5656	78	17	,	,	PUNCT
ejpam-5656	78	18	we	we	PRON
ejpam-5656	78	19	have	have	VERB
ejpam-5656	78	20	ν	ν	NOUN
ejpam-5656	78	21	uν(x	uν(x	PROPN
ejpam-5656	78	22	,	,	PUNCT
ejpam-5656	78	23	y	y	PROPN
ejpam-5656	78	24	;	;	PUNCT
ejpam-5656	78	25	2	2	NUM
ejpam-5656	78	26	;	;	PUNCT
ejpam-5656	78	27	1	1	NUM
ejpam-5656	78	28	)	)	PUNCT
ejpam-5656	78	29	0	0	NUM
ejpam-5656	78	30	1	1	NUM
ejpam-5656	78	31	2	2	NUM
ejpam-5656	78	32	1	1	NUM
ejpam-5656	78	33	1	1	NUM
ejpam-5656	78	34	2	2	NUM
ejpam-5656	78	35	x−	x−	PROPN
ejpam-5656	78	36	1	1	NUM
ejpam-5656	78	37	4	4	NUM
ejpam-5656	78	38	2	2	NUM
ejpam-5656	78	39	1	1	NUM
ejpam-5656	78	40	2	2	NUM
ejpam-5656	78	41	x2	x2	NOUN
ejpam-5656	78	42	−	−	NOUN
ejpam-5656	78	43	1	1	NUM
ejpam-5656	78	44	2	2	NUM
ejpam-5656	78	45	x+	x+	VERB
ejpam-5656	78	46	y	y	NOUN
ejpam-5656	78	47	3	3	NUM
ejpam-5656	78	48	1	1	NUM
ejpam-5656	78	49	2	2	NUM
ejpam-5656	78	50	x3	x3	NOUN
ejpam-5656	78	51	−	−	NOUN
ejpam-5656	78	52	3	3	NUM
ejpam-5656	78	53	4	4	NUM
ejpam-5656	78	54	x2	x2	NOUN
ejpam-5656	79	1	+	+	CCONJ
ejpam-5656	79	2	3xy	3xy	ADJ
ejpam-5656	79	3	−	−	NOUN
ejpam-5656	79	4	3	3	NUM
ejpam-5656	79	5	2	2	NUM
ejpam-5656	79	6	y	y	NOUN
ejpam-5656	79	7	+	+	NOUN
ejpam-5656	79	8	1	1	NUM
ejpam-5656	79	9	4	4	NUM
ejpam-5656	79	10	4	4	NUM
ejpam-5656	79	11	1	1	NUM
ejpam-5656	79	12	2	2	NUM
ejpam-5656	79	13	x4	x4	NOUN
ejpam-5656	79	14	−	−	NOUN
ejpam-5656	79	15	x3	x3	PROPN
ejpam-5656	80	1	+	+	CCONJ
ejpam-5656	80	2	6yx2	6yx2	NUM
ejpam-5656	80	3	−	−	PROPN
ejpam-5656	80	4	6yx+	6yx+	NOUN
ejpam-5656	80	5	x+	x+	PUNCT
ejpam-5656	80	6	6y2	6y2	NUM
ejpam-5656	80	7	−	−	NOUN
ejpam-5656	80	8	1	1	NUM
ejpam-5656	80	9	2	2	NUM
ejpam-5656	80	10	the	the	DET
ejpam-5656	80	11	characteristics	characteristic	NOUN
ejpam-5656	80	12	of	of	ADP
ejpam-5656	80	13	hermite	hermite	ADJ
ejpam-5656	80	14	polynomials	polynomial	NOUN
ejpam-5656	80	15	in	in	ADP
ejpam-5656	80	16	two	two	NUM
ejpam-5656	80	17	variables	variable	NOUN
ejpam-5656	80	18	have	have	VERB
ejpam-5656	80	19	a	a	DET
ejpam-5656	80	20	crucial	crucial	ADJ
ejpam-5656	80	21	role	role	NOUN
ejpam-5656	80	22	in	in	ADP
ejpam-5656	80	23	investigating	investigate	VERB
ejpam-5656	80	24	the	the	DET
ejpam-5656	80	25	apostol	apostol	NOUN
ejpam-5656	80	26	-	-	PUNCT
ejpam-5656	80	27	type	type	NOUN
ejpam-5656	80	28	hermite	hermite	PROPN
ejpam-5656	80	29	-	-	PUNCT
ejpam-5656	80	30	bernoulli	bernoulli	PROPN
ejpam-5656	80	31	/	/	SYM
ejpam-5656	80	32	euler	euler	NOUN
ejpam-5656	80	33	polynomials	polynomial	NOUN
ejpam-5656	80	34	,	,	PUNCT
ejpam-5656	80	35	offering	offer	VERB
ejpam-5656	80	36	valuable	valuable	ADJ
ejpam-5656	80	37	insights	insight	NOUN
ejpam-5656	80	38	into	into	ADP
ejpam-5656	80	39	their	their	PRON
ejpam-5656	80	40	properties	property	NOUN
ejpam-5656	80	41	and	and	CCONJ
ejpam-5656	80	42	behaviors	behavior	NOUN
ejpam-5656	80	43	.	.	PUNCT
ejpam-5656	81	1	we	we	PRON
ejpam-5656	81	2	recall	recall	VERB
ejpam-5656	81	3	that	that	SCONJ
ejpam-5656	81	4	the	the	DET
ejpam-5656	81	5	hermite	hermite	ADJ
ejpam-5656	81	6	polynomials	polynomial	NOUN
ejpam-5656	81	7	in	in	ADP
ejpam-5656	81	8	two	two	NUM
ejpam-5656	81	9	variables	variable	NOUN
ejpam-5656	81	10	,	,	PUNCT
ejpam-5656	81	11	hν(x	hν(x	X
ejpam-5656	81	12	,	,	PUNCT
ejpam-5656	81	13	y	y	PROPN
ejpam-5656	81	14	)	)	PUNCT
ejpam-5656	81	15	,	,	PUNCT
ejpam-5656	81	16	satisfies	satisfy	VERB
ejpam-5656	81	17	the	the	DET
ejpam-5656	81	18	generating	generate	VERB
ejpam-5656	81	19	equation	equation	NOUN
ejpam-5656	81	20	(	(	PUNCT
ejpam-5656	81	21	see	see	VERB
ejpam-5656	81	22	[	[	X
ejpam-5656	81	23	6	6	NUM
ejpam-5656	81	24	]	]	PUNCT
ejpam-5656	81	25	and	and	CCONJ
ejpam-5656	81	26	[	[	X
ejpam-5656	81	27	7	7	NUM
ejpam-5656	81	28	,	,	PUNCT
ejpam-5656	81	29	eq	eq	NOUN
ejpam-5656	81	30	.	.	PROPN
ejpam-5656	81	31	2	2	NUM
ejpam-5656	81	32	]	]	PUNCT
ejpam-5656	81	33	):	):	PUNCT
ejpam-5656	81	34	exξ+yξ2	exξ+yξ2	X
ejpam-5656	81	35	=	=	PUNCT
ejpam-5656	82	1	∞∑	∞∑	NUM
ejpam-5656	82	2	ν=0	ν=0	NOUN
ejpam-5656	82	3	hν(x	hν(x	ADV
ejpam-5656	82	4	,	,	PUNCT
ejpam-5656	82	5	y	y	PROPN
ejpam-5656	82	6	)	)	PUNCT
ejpam-5656	82	7	ξν	ξν	ADP
ejpam-5656	82	8	ν	ν	X
ejpam-5656	82	9	!	!	PUNCT
ejpam-5656	82	10	.	.	PUNCT
ejpam-5656	83	1	(	(	PUNCT
ejpam-5656	83	2	7	7	X
ejpam-5656	83	3	)	)	PUNCT
ejpam-5656	83	4	additionally	additionally	ADV
ejpam-5656	83	5	,	,	PUNCT
ejpam-5656	83	6	h0(x	h0(x	PROPN
ejpam-5656	83	7	,	,	PUNCT
ejpam-5656	83	8	y	y	NOUN
ejpam-5656	83	9	)	)	PUNCT
ejpam-5656	83	10	=	=	SYM
ejpam-5656	84	1	1	1	NUM
ejpam-5656	84	2	dı́az	dı́az	X
ejpam-5656	84	3	et	et	NOUN
ejpam-5656	84	4	al	al	PROPN
ejpam-5656	84	5	.	.	PUNCT
ejpam-5656	84	6	/	/	SYM
ejpam-5656	84	7	eur	eur	PROPN
ejpam-5656	84	8	.	.	PUNCT
ejpam-5656	85	1	j.	j.	PROPN
ejpam-5656	85	2	pure	pure	PROPN
ejpam-5656	85	3	appl	appl	PROPN
ejpam-5656	85	4	.	.	PROPN
ejpam-5656	85	5	math	math	PROPN
ejpam-5656	85	6	,	,	PUNCT
ejpam-5656	85	7	18	18	NUM
ejpam-5656	85	8	(	(	PUNCT
ejpam-5656	85	9	1	1	NUM
ejpam-5656	85	10	)	)	PUNCT
ejpam-5656	85	11	(	(	PUNCT
ejpam-5656	85	12	2025	2025	NUM
ejpam-5656	85	13	)	)	PUNCT
ejpam-5656	85	14	,	,	PUNCT
ejpam-5656	85	15	5656	5656	NUM
ejpam-5656	85	16	6	6	NUM
ejpam-5656	85	17	of	of	ADP
ejpam-5656	85	18	17	17	NUM
ejpam-5656	85	19	and	and	CCONJ
ejpam-5656	85	20	the	the	DET
ejpam-5656	85	21	following	follow	VERB
ejpam-5656	85	22	identity	identity	NOUN
ejpam-5656	85	23	is	be	AUX
ejpam-5656	85	24	hold	hold	NOUN
ejpam-5656	85	25	(	(	PUNCT
ejpam-5656	85	26	see	see	VERB
ejpam-5656	85	27	[	[	X
ejpam-5656	85	28	5	5	NUM
ejpam-5656	85	29	,	,	PUNCT
ejpam-5656	85	30	eq	eq	NOUN
ejpam-5656	85	31	.	.	PROPN
ejpam-5656	85	32	18	18	NUM
ejpam-5656	85	33	]	]	PUNCT
ejpam-5656	85	34	):	):	PUNCT
ejpam-5656	85	35	∂	∂	X
ejpam-5656	85	36	∂y	∂y	PROPN
ejpam-5656	85	37	hν(x	hν(x	PROPN
ejpam-5656	85	38	,	,	PUNCT
ejpam-5656	85	39	y	y	NOUN
ejpam-5656	85	40	)	)	PUNCT
ejpam-5656	85	41	=	=	PUNCT
ejpam-5656	85	42	ν(ν	ν(ν	NOUN
ejpam-5656	85	43	−	−	ADP
ejpam-5656	85	44	1)hν−2(x	1)hν−2(x	NUM
ejpam-5656	85	45	,	,	PUNCT
ejpam-5656	85	46	y	y	NOUN
ejpam-5656	85	47	)	)	PUNCT
ejpam-5656	85	48	=	=	SYM
ejpam-5656	86	1	∂2	∂2	PROPN
ejpam-5656	86	2	∂x2	∂x2	NOUN
ejpam-5656	86	3	hν(x	hν(x	PROPN
ejpam-5656	86	4	,	,	PUNCT
ejpam-5656	86	5	y	y	NOUN
ejpam-5656	86	6	)	)	PUNCT
ejpam-5656	86	7	.	.	PUNCT
ejpam-5656	87	1	(	(	PUNCT
ejpam-5656	87	2	8)	8)	NUM
ejpam-5656	87	3	below	below	ADV
ejpam-5656	87	4	,	,	PUNCT
ejpam-5656	87	5	we	we	PRON
ejpam-5656	87	6	elucidate	elucidate	VERB
ejpam-5656	87	7	several	several	ADJ
ejpam-5656	87	8	properties	property	NOUN
ejpam-5656	87	9	of	of	ADP
ejpam-5656	87	10	the	the	DET
ejpam-5656	87	11	apostol	apostol	NOUN
ejpam-5656	87	12	-	-	PUNCT
ejpam-5656	87	13	type	type	NOUN
ejpam-5656	87	14	hermite	hermite	PROPN
ejpam-5656	87	15	-	-	PUNCT
ejpam-5656	87	16	bernoulli	bernoulli	PROPN
ejpam-5656	87	17	/	/	SYM
ejpam-5656	87	18	euler	euler	NOUN
ejpam-5656	87	19	polynomials	polynomial	NOUN
ejpam-5656	87	20	using	use	VERB
ejpam-5656	87	21	the	the	DET
ejpam-5656	87	22	generating	generate	VERB
ejpam-5656	87	23	function	function	NOUN
ejpam-5656	87	24	approach	approach	NOUN
ejpam-5656	87	25	.	.	PUNCT
ejpam-5656	88	1	proposition	proposition	NOUN
ejpam-5656	88	2	1	1	NUM
ejpam-5656	88	3	.	.	PUNCT
ejpam-5656	89	1	let	let	VERB
ejpam-5656	89	2	ρ	ρ	PROPN
ejpam-5656	89	3	>	>	X
ejpam-5656	89	4	0	0	PROPN
ejpam-5656	89	5	,	,	PUNCT
ejpam-5656	89	6	µ	µ	PRON
ejpam-5656	89	7	≥	≥	NOUN
ejpam-5656	89	8	0	0	NUM
ejpam-5656	89	9	such	such	ADJ
ejpam-5656	89	10	that	that	SCONJ
ejpam-5656	89	11	µ	µ	ADJ
ejpam-5656	89	12	̸=	̸=	PROPN
ejpam-5656	89	13	1	1	NUM
ejpam-5656	89	14	.	.	PUNCT
ejpam-5656	90	1	the	the	DET
ejpam-5656	90	2	following	follow	VERB
ejpam-5656	90	3	relationship	relationship	NOUN
ejpam-5656	90	4	holds	hold	VERB
ejpam-5656	90	5	:	:	PUNCT
ejpam-5656	90	6	uν(x+	uν(x+	PROPN
ejpam-5656	90	7	z	z	X
ejpam-5656	90	8	,	,	PUNCT
ejpam-5656	90	9	y	y	PROPN
ejpam-5656	91	1	+	+	CCONJ
ejpam-5656	91	2	w	w	PROPN
ejpam-5656	91	3	;	;	PUNCT
ejpam-5656	91	4	ρ;µ	ρ;µ	NUM
ejpam-5656	91	5	)	)	PUNCT
ejpam-5656	91	6	=	=	SYM
ejpam-5656	91	7	ν∑	ν∑	PROPN
ejpam-5656	92	1	k=0	k=0	PROPN
ejpam-5656	92	2	(	(	PUNCT
ejpam-5656	92	3	ν	ν	X
ejpam-5656	92	4	k	k	PROPN
ejpam-5656	92	5	)	)	PUNCT
ejpam-5656	92	6	hν−k(z	hν−k(z	PROPN
ejpam-5656	92	7	,	,	PUNCT
ejpam-5656	92	8	w)uk(x	w)uk(x	PROPN
ejpam-5656	92	9	,	,	PUNCT
ejpam-5656	92	10	y	y	PROPN
ejpam-5656	92	11	;	;	PUNCT
ejpam-5656	92	12	ρ;µ	ρ;µ	NUM
ejpam-5656	92	13	)	)	PUNCT
ejpam-5656	92	14	,	,	PUNCT
ejpam-5656	92	15	(	(	PUNCT
ejpam-5656	92	16	9	9	X
ejpam-5656	92	17	)	)	PUNCT
ejpam-5656	92	18	where	where	SCONJ
ejpam-5656	92	19	hk	hk	PROPN
ejpam-5656	92	20	are	be	AUX
ejpam-5656	92	21	the	the	DET
ejpam-5656	92	22	hermite	hermite	ADJ
ejpam-5656	92	23	polynomials	polynomial	NOUN
ejpam-5656	92	24	.	.	PUNCT
ejpam-5656	93	1	proof	proof	NOUN
ejpam-5656	93	2	.	.	PUNCT
ejpam-5656	94	1	by	by	ADP
ejpam-5656	94	2	the	the	DET
ejpam-5656	94	3	following	follow	VERB
ejpam-5656	94	4	identity	identity	NOUN
ejpam-5656	94	5	(	(	PUNCT
ejpam-5656	94	6	see	see	VERB
ejpam-5656	94	7	[	[	X
ejpam-5656	94	8	14	14	NUM
ejpam-5656	94	9	,	,	PUNCT
ejpam-5656	94	10	p.	p.	NOUN
ejpam-5656	94	11	18	18	NUM
ejpam-5656	94	12	,	,	PUNCT
ejpam-5656	94	13	eq	eq	NOUN
ejpam-5656	94	14	.	.	PROPN
ejpam-5656	94	15	0.36	0.36	NUM
ejpam-5656	94	16	]	]	PUNCT
ejpam-5656	94	17	and	and	CCONJ
ejpam-5656	94	18	[	[	X
ejpam-5656	94	19	4	4	NUM
ejpam-5656	94	20	,	,	PUNCT
ejpam-5656	94	21	p.	p.	NOUN
ejpam-5656	94	22	463	463	NUM
ejpam-5656	94	23	,	,	PUNCT
ejpam-5656	94	24	def	def	ADJ
ejpam-5656	94	25	.	.	PUNCT
ejpam-5656	95	1	9.4.6	9.4.6	NUM
ejpam-5656	95	2	]	]	PUNCT
ejpam-5656	95	3	):	):	PUNCT
ejpam-5656	95	4	(	(	PUNCT
ejpam-5656	95	5	∞∑	∞∑	NUM
ejpam-5656	95	6	n=0	n=0	PROPN
ejpam-5656	95	7	an	an	PRON
ejpam-5656	95	8	)	)	PUNCT
ejpam-5656	95	9	(	(	PUNCT
ejpam-5656	95	10	∞∑	∞∑	NUM
ejpam-5656	95	11	n=0	n=0	NUM
ejpam-5656	95	12	bn	bn	NOUN
ejpam-5656	95	13	)	)	PUNCT
ejpam-5656	95	14	=	=	PUNCT
ejpam-5656	96	1	∞∑	∞∑	NUM
ejpam-5656	96	2	n=0	n=0	NUM
ejpam-5656	96	3	n∑	n∑	PROPN
ejpam-5656	96	4	k=0	k=0	PROPN
ejpam-5656	97	1	an−kbk	an−kbk	PROPN
ejpam-5656	97	2	,	,	PUNCT
ejpam-5656	97	3	(	(	PUNCT
ejpam-5656	97	4	10	10	NUM
ejpam-5656	97	5	)	)	PUNCT
ejpam-5656	97	6	and	and	CCONJ
ejpam-5656	97	7	the	the	DET
ejpam-5656	97	8	generating	generating	NOUN
ejpam-5656	97	9	functions	function	NOUN
ejpam-5656	97	10	(	(	PUNCT
ejpam-5656	97	11	5	5	NUM
ejpam-5656	97	12	)	)	PUNCT
ejpam-5656	97	13	and	and	CCONJ
ejpam-5656	97	14	(	(	PUNCT
ejpam-5656	97	15	7	7	NUM
ejpam-5656	97	16	)	)	PUNCT
ejpam-5656	97	17	,	,	PUNCT
ejpam-5656	97	18	we	we	PRON
ejpam-5656	97	19	have	have	VERB
ejpam-5656	97	20	∞∑	∞∑	NUM
ejpam-5656	97	21	ν=0	ν=0	PRON
ejpam-5656	97	22	uν(x+	uν(x+	PROPN
ejpam-5656	97	23	z	z	PROPN
ejpam-5656	97	24	,	,	PUNCT
ejpam-5656	97	25	y	y	PROPN
ejpam-5656	97	26	+	+	CCONJ
ejpam-5656	97	27	w	w	PROPN
ejpam-5656	97	28	;	;	PUNCT
ejpam-5656	97	29	ρ;µ	ρ;µ	NUM
ejpam-5656	97	30	)	)	PUNCT
ejpam-5656	97	31	ξν	ξν	ADP
ejpam-5656	97	32	ν	ν	X
ejpam-5656	97	33	!	!	PUNCT
ejpam-5656	98	1	=	=	SYM
ejpam-5656	98	2	φ(ρ	φ(ρ	PROPN
ejpam-5656	98	3	,	,	PUNCT
ejpam-5656	98	4	µ	µ	NUM
ejpam-5656	98	5	,	,	PUNCT
ejpam-5656	98	6	ξ)eξx+ξ2yeξz+ξ2w	ξ)eξx+ξ2yeξz+ξ2w	X
ejpam-5656	98	7	=	=	PUNCT
ejpam-5656	98	8	(	(	PUNCT
ejpam-5656	98	9	∞∑	∞∑	NUM
ejpam-5656	98	10	ν=0	ν=0	PROPN
ejpam-5656	98	11	uν(x	uν(x	NOUN
ejpam-5656	98	12	,	,	PUNCT
ejpam-5656	98	13	y	y	PROPN
ejpam-5656	98	14	;	;	PUNCT
ejpam-5656	98	15	ρ;µ	ρ;µ	NUM
ejpam-5656	98	16	)	)	PUNCT
ejpam-5656	98	17	ξν	ξν	ADP
ejpam-5656	98	18	ν	ν	PROPN
ejpam-5656	98	19	!	!	PUNCT
ejpam-5656	98	20	)	)	PUNCT
ejpam-5656	99	1	(	(	PUNCT
ejpam-5656	99	2	∞∑	∞∑	NUM
ejpam-5656	99	3	ν=0	ν=0	NOUN
ejpam-5656	99	4	hν(z	hν(z	NOUN
ejpam-5656	99	5	,	,	PUNCT
ejpam-5656	99	6	w	w	NOUN
ejpam-5656	99	7	)	)	PUNCT
ejpam-5656	99	8	ξν	ξν	ADV
ejpam-5656	99	9	ν	ν	PROPN
ejpam-5656	99	10	!	!	PUNCT
ejpam-5656	99	11	)	)	PUNCT
ejpam-5656	100	1	=	=	PUNCT
ejpam-5656	101	1	∞∑	∞∑	NUM
ejpam-5656	101	2	ν=0	ν=0	NOUN
ejpam-5656	101	3	(	(	PUNCT
ejpam-5656	101	4	ν∑	ν∑	X
ejpam-5656	101	5	k=0	k=0	PROPN
ejpam-5656	101	6	(	(	PUNCT
ejpam-5656	101	7	ν	ν	X
ejpam-5656	101	8	k	k	PROPN
ejpam-5656	101	9	)	)	PUNCT
ejpam-5656	101	10	hν−k(z	hν−k(z	PROPN
ejpam-5656	101	11	,	,	PUNCT
ejpam-5656	101	12	w)uk(x	w)uk(x	PROPN
ejpam-5656	101	13	,	,	PUNCT
ejpam-5656	101	14	y	y	PROPN
ejpam-5656	101	15	;	;	PUNCT
ejpam-5656	101	16	ρ;µ	ρ;µ	NUM
ejpam-5656	101	17	)	)	PUNCT
ejpam-5656	101	18	)	)	PUNCT
ejpam-5656	101	19	ξν	ξν	ADP
ejpam-5656	101	20	ν	ν	X
ejpam-5656	101	21	!	!	PUNCT
ejpam-5656	101	22	.	.	PUNCT
ejpam-5656	102	1	by	by	ADP
ejpam-5656	102	2	utilizing	utilize	VERB
ejpam-5656	102	3	the	the	DET
ejpam-5656	102	4	product	product	NOUN
ejpam-5656	102	5	series	series	NOUN
ejpam-5656	102	6	and	and	CCONJ
ejpam-5656	102	7	subsequently	subsequently	ADV
ejpam-5656	102	8	equating	equate	VERB
ejpam-5656	102	9	the	the	DET
ejpam-5656	102	10	coefficients	coefficient	NOUN
ejpam-5656	102	11	of	of	ADP
ejpam-5656	102	12	ξν	ξν	NOUN
ejpam-5656	102	13	/	/	SYM
ejpam-5656	102	14	ν	ν	NOUN
ejpam-5656	102	15	!	!	PUNCT
ejpam-5656	102	16	on	on	ADP
ejpam-5656	102	17	both	both	DET
ejpam-5656	102	18	sides	side	NOUN
ejpam-5656	102	19	,	,	PUNCT
ejpam-5656	102	20	we	we	PRON
ejpam-5656	102	21	derive	derive	VERB
ejpam-5656	102	22	the	the	DET
ejpam-5656	102	23	identity	identity	NOUN
ejpam-5656	102	24	.	.	PUNCT
ejpam-5656	103	1	remark	remark	NOUN
ejpam-5656	103	2	1	1	NUM
ejpam-5656	103	3	.	.	PUNCT
ejpam-5656	104	1	if	if	SCONJ
ejpam-5656	104	2	x	x	PRON
ejpam-5656	104	3	:	:	PUNCT
ejpam-5656	104	4	=	=	SYM
ejpam-5656	104	5	0	0	NUM
ejpam-5656	104	6	,	,	PUNCT
ejpam-5656	104	7	z	z	NOUN
ejpam-5656	104	8	:	:	PUNCT
ejpam-5656	104	9	=	=	SYM
ejpam-5656	104	10	x	x	X
ejpam-5656	104	11	,	,	PUNCT
ejpam-5656	104	12	y	y	PROPN
ejpam-5656	104	13	:	:	PUNCT
ejpam-5656	104	14	=	=	SYM
ejpam-5656	104	15	0	0	PUNCT
ejpam-5656	104	16	and	and	CCONJ
ejpam-5656	104	17	w	w	ADP
ejpam-5656	104	18	:	:	PUNCT
ejpam-5656	104	19	=	=	SYM
ejpam-5656	104	20	y	y	PROPN
ejpam-5656	104	21	in	in	ADP
ejpam-5656	104	22	(	(	PUNCT
ejpam-5656	104	23	9	9	NUM
ejpam-5656	104	24	)	)	PUNCT
ejpam-5656	104	25	,	,	PUNCT
ejpam-5656	104	26	then	then	ADV
ejpam-5656	104	27	the	the	DET
ejpam-5656	104	28	identity	identity	NOUN
ejpam-5656	104	29	becomes	become	VERB
ejpam-5656	104	30	uν(x	uν(x	PRON
ejpam-5656	104	31	,	,	PUNCT
ejpam-5656	104	32	y	y	PROPN
ejpam-5656	104	33	;	;	PUNCT
ejpam-5656	104	34	ρ;µ	ρ;µ	NUM
ejpam-5656	104	35	)	)	PUNCT
ejpam-5656	105	1	=	=	SYM
ejpam-5656	105	2	ν∑	ν∑	PROPN
ejpam-5656	106	1	k=0	k=0	PROPN
ejpam-5656	106	2	(	(	PUNCT
ejpam-5656	106	3	ν	ν	X
ejpam-5656	106	4	k	k	X
ejpam-5656	106	5	)	)	PUNCT
ejpam-5656	106	6	hν−k(x	hν−k(x	PROPN
ejpam-5656	106	7	,	,	PUNCT
ejpam-5656	106	8	y)uk(ρ;µ	y)uk(ρ;µ	NOUN
ejpam-5656	106	9	)	)	PUNCT
ejpam-5656	106	10	.	.	PUNCT
ejpam-5656	107	1	(	(	PUNCT
ejpam-5656	107	2	11	11	NUM
ejpam-5656	107	3	)	)	PUNCT
ejpam-5656	107	4	remark	remark	NOUN
ejpam-5656	107	5	2	2	NUM
ejpam-5656	107	6	.	.	PUNCT
ejpam-5656	108	1	if	if	SCONJ
ejpam-5656	108	2	we	we	PRON
ejpam-5656	108	3	substitute	substitute	VERB
ejpam-5656	108	4	z	z	NOUN
ejpam-5656	108	5	:	:	PUNCT
ejpam-5656	108	6	=	=	NOUN
ejpam-5656	108	7	−x	−x	NOUN
ejpam-5656	108	8	and	and	CCONJ
ejpam-5656	108	9	w	w	NOUN
ejpam-5656	108	10	:	:	PUNCT
ejpam-5656	108	11	=	=	VERB
ejpam-5656	108	12	−y	−y	VERB
ejpam-5656	108	13	into	into	ADP
ejpam-5656	108	14	equation	equation	NOUN
ejpam-5656	108	15	(	(	PUNCT
ejpam-5656	108	16	9	9	NUM
ejpam-5656	108	17	)	)	PUNCT
ejpam-5656	108	18	,	,	PUNCT
ejpam-5656	108	19	we	we	PRON
ejpam-5656	108	20	can	can	AUX
ejpam-5656	108	21	represent	represent	VERB
ejpam-5656	108	22	the	the	DET
ejpam-5656	108	23	apostol	apostol	NOUN
ejpam-5656	108	24	-	-	PUNCT
ejpam-5656	108	25	type	type	NOUN
ejpam-5656	108	26	hermite	hermite	PROPN
ejpam-5656	108	27	-	-	PUNCT
ejpam-5656	108	28	bernoulli	bernoulli	PROPN
ejpam-5656	108	29	/	/	SYM
ejpam-5656	108	30	euler	euler	NOUN
ejpam-5656	108	31	numbers	number	NOUN
ejpam-5656	108	32	as	as	ADP
ejpam-5656	108	33	a	a	DET
ejpam-5656	108	34	function	function	NOUN
ejpam-5656	108	35	of	of	ADP
ejpam-5656	108	36	the	the	DET
ejpam-5656	108	37	corresponding	correspond	VERB
ejpam-5656	108	38	apostoltype	apostoltype	ADJ
ejpam-5656	108	39	hermite	hermite	PROPN
ejpam-5656	108	40	-	-	PUNCT
ejpam-5656	108	41	bernoulli	bernoulli	PROPN
ejpam-5656	108	42	/	/	SYM
ejpam-5656	108	43	euler	euler	NOUN
ejpam-5656	108	44	polynomials	polynomial	NOUN
ejpam-5656	108	45	:	:	PUNCT
ejpam-5656	108	46	uν(ρ;µ	uν(ρ;µ	PROPN
ejpam-5656	108	47	)	)	PUNCT
ejpam-5656	108	48	=	=	SYM
ejpam-5656	108	49	ν∑	ν∑	PROPN
ejpam-5656	109	1	k=0	k=0	PROPN
ejpam-5656	109	2	(	(	PUNCT
ejpam-5656	109	3	ν	ν	X
ejpam-5656	109	4	k	k	PROPN
ejpam-5656	109	5	)	)	PUNCT
ejpam-5656	109	6	hν−k(−x,−y)uk(x	hν−k(−x,−y)uk(x	PROPN
ejpam-5656	109	7	,	,	PUNCT
ejpam-5656	109	8	y	y	PROPN
ejpam-5656	109	9	;	;	PUNCT
ejpam-5656	109	10	ρ;µ	ρ;µ	NUM
ejpam-5656	109	11	)	)	PUNCT
ejpam-5656	109	12	.	.	PUNCT
ejpam-5656	110	1	dı́az	dı́az	X
ejpam-5656	110	2	et	et	PROPN
ejpam-5656	110	3	al	al	PROPN
ejpam-5656	110	4	.	.	PUNCT
ejpam-5656	110	5	/	/	SYM
ejpam-5656	110	6	eur	eur	PROPN
ejpam-5656	110	7	.	.	PUNCT
ejpam-5656	111	1	j.	j.	PROPN
ejpam-5656	111	2	pure	pure	PROPN
ejpam-5656	111	3	appl	appl	PROPN
ejpam-5656	111	4	.	.	PROPN
ejpam-5656	111	5	math	math	PROPN
ejpam-5656	111	6	,	,	PUNCT
ejpam-5656	111	7	18	18	NUM
ejpam-5656	111	8	(	(	PUNCT
ejpam-5656	111	9	1	1	NUM
ejpam-5656	111	10	)	)	PUNCT
ejpam-5656	111	11	(	(	PUNCT
ejpam-5656	111	12	2025	2025	NUM
ejpam-5656	111	13	)	)	PUNCT
ejpam-5656	111	14	,	,	PUNCT
ejpam-5656	111	15	5656	5656	NUM
ejpam-5656	111	16	7	7	NUM
ejpam-5656	111	17	of	of	ADP
ejpam-5656	111	18	17	17	NUM
ejpam-5656	111	19	here	here	ADV
ejpam-5656	112	1	,	,	PUNCT
ejpam-5656	112	2	we	we	PRON
ejpam-5656	112	3	present	present	VERB
ejpam-5656	112	4	the	the	DET
ejpam-5656	112	5	result	result	NOUN
ejpam-5656	112	6	of	of	ADP
ejpam-5656	112	7	the	the	DET
ejpam-5656	112	8	convolution	convolution	NOUN
ejpam-5656	112	9	involving	involve	VERB
ejpam-5656	112	10	the	the	DET
ejpam-5656	112	11	apostol	apostol	NOUN
ejpam-5656	112	12	-	-	PUNCT
ejpam-5656	112	13	type	type	NOUN
ejpam-5656	112	14	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	112	15	/	/	SYM
ejpam-5656	112	16	euler	euler	NOUN
ejpam-5656	112	17	polynomials	polynomial	NOUN
ejpam-5656	112	18	.	.	PUNCT
ejpam-5656	113	1	proposition	proposition	NOUN
ejpam-5656	113	2	2	2	NUM
ejpam-5656	113	3	.	.	PUNCT
ejpam-5656	114	1	the	the	DET
ejpam-5656	114	2	following	follow	VERB
ejpam-5656	114	3	identity	identity	NOUN
ejpam-5656	114	4	holds	hold	VERB
ejpam-5656	114	5	:	:	PUNCT
ejpam-5656	114	6	ν∑	ν∑	PROPN
ejpam-5656	114	7	ω=0	ω=0	X
ejpam-5656	114	8	(	(	PUNCT
ejpam-5656	114	9	ν	ν	PROPN
ejpam-5656	114	10	ω	ω	PROPN
ejpam-5656	114	11	)	)	PUNCT
ejpam-5656	115	1	uν−ω(x	uν−ω(x	PROPN
ejpam-5656	115	2	,	,	PUNCT
ejpam-5656	115	3	y	y	PROPN
ejpam-5656	115	4	;	;	PUNCT
ejpam-5656	115	5	ρ;µ)uω(x	ρ;µ)uω(x	VERB
ejpam-5656	115	6	,	,	PUNCT
ejpam-5656	115	7	y	y	PROPN
ejpam-5656	115	8	;	;	PUNCT
ejpam-5656	115	9	ρ;µ	ρ;µ	NUM
ejpam-5656	115	10	)	)	PUNCT
ejpam-5656	115	11	=	=	SYM
ejpam-5656	115	12	ν∑	ν∑	PROPN
ejpam-5656	116	1	ω=0	ω=0	X
ejpam-5656	116	2	(	(	PUNCT
ejpam-5656	116	3	ν	ν	PROPN
ejpam-5656	116	4	ω	ω	PROPN
ejpam-5656	116	5	)	)	PUNCT
ejpam-5656	116	6	uν−ω(ρ	uν−ω(ρ	PROPN
ejpam-5656	116	7	,	,	PUNCT
ejpam-5656	116	8	µ)uω(2x	µ)uω(2x	VERB
ejpam-5656	116	9	,	,	PUNCT
ejpam-5656	116	10	2y	2y	NUM
ejpam-5656	116	11	;	;	PUNCT
ejpam-5656	116	12	ρ;µ	ρ;µ	NUM
ejpam-5656	116	13	)	)	PUNCT
ejpam-5656	116	14	.	.	PUNCT
ejpam-5656	117	1	proof	proof	NOUN
ejpam-5656	117	2	.	.	PUNCT
ejpam-5656	118	1	by	by	ADP
ejpam-5656	118	2	(	(	PUNCT
ejpam-5656	118	3	10	10	NUM
ejpam-5656	118	4	)	)	PUNCT
ejpam-5656	118	5	and	and	CCONJ
ejpam-5656	118	6	(	(	PUNCT
ejpam-5656	118	7	6	6	NUM
ejpam-5656	118	8	)	)	PUNCT
ejpam-5656	118	9	,	,	PUNCT
ejpam-5656	118	10	we	we	PRON
ejpam-5656	118	11	have	have	VERB
ejpam-5656	118	12	∞∑	∞∑	NUM
ejpam-5656	118	13	ν=0	ν=0	PRON
ejpam-5656	118	14	ν∑	ν∑	NOUN
ejpam-5656	119	1	ω=0	ω=0	X
ejpam-5656	120	1	(	(	PUNCT
ejpam-5656	120	2	ν	ν	PROPN
ejpam-5656	120	3	ω	ω	PROPN
ejpam-5656	120	4	)	)	PUNCT
ejpam-5656	120	5	uν−ω(x	uν−ω(x	PROPN
ejpam-5656	120	6	,	,	PUNCT
ejpam-5656	120	7	y	y	PROPN
ejpam-5656	120	8	;	;	PUNCT
ejpam-5656	120	9	ρ;µ)uω(x	ρ;µ)uω(x	VERB
ejpam-5656	120	10	,	,	PUNCT
ejpam-5656	120	11	y	y	PROPN
ejpam-5656	120	12	;	;	PUNCT
ejpam-5656	120	13	ρ;µ	ρ;µ	NUM
ejpam-5656	120	14	)	)	PUNCT
ejpam-5656	120	15	ξν	ξν	ADP
ejpam-5656	121	1	ν	ν	X
ejpam-5656	121	2	!	!	PUNCT
ejpam-5656	121	3	=	=	PUNCT
ejpam-5656	122	1	∞∑	∞∑	NUM
ejpam-5656	122	2	ν=0	ν=0	NOUN
ejpam-5656	122	3	uν(x	uν(x	NOUN
ejpam-5656	122	4	,	,	PUNCT
ejpam-5656	122	5	y	y	PROPN
ejpam-5656	122	6	;	;	PUNCT
ejpam-5656	122	7	ρ;µ	ρ;µ	NUM
ejpam-5656	122	8	)	)	PUNCT
ejpam-5656	122	9	ξν	ξν	ADP
ejpam-5656	122	10	ν	ν	X
ejpam-5656	122	11	!	!	PUNCT
ejpam-5656	123	1	∞∑	∞∑	NUM
ejpam-5656	123	2	ν=0	ν=0	PROPN
ejpam-5656	123	3	uν(x	uν(x	NOUN
ejpam-5656	123	4	,	,	PUNCT
ejpam-5656	123	5	y	y	PROPN
ejpam-5656	123	6	;	;	PUNCT
ejpam-5656	123	7	ρ;µ	ρ;µ	NUM
ejpam-5656	123	8	)	)	PUNCT
ejpam-5656	123	9	ξν	ξν	ADP
ejpam-5656	123	10	ν	ν	X
ejpam-5656	123	11	!	!	PUNCT
ejpam-5656	124	1	=	=	SYM
ejpam-5656	124	2	φ2(ρ	φ2(ρ	PROPN
ejpam-5656	124	3	,	,	PUNCT
ejpam-5656	124	4	µ	µ	NOUN
ejpam-5656	124	5	,	,	PUNCT
ejpam-5656	124	6	ξ)e2xξ+2yξ2	ξ)e2xξ+2yξ2	NOUN
ejpam-5656	124	7	=	=	PUNCT
ejpam-5656	124	8	∞∑	∞∑	NUM
ejpam-5656	124	9	ν=0	ν=0	PROPN
ejpam-5656	124	10	uν(ρ	uν(ρ	SYM
ejpam-5656	124	11	,	,	PUNCT
ejpam-5656	124	12	µ	µ	NOUN
ejpam-5656	124	13	)	)	PUNCT
ejpam-5656	124	14	ξν	ξν	ADV
ejpam-5656	124	15	ν	ν	X
ejpam-5656	124	16	!	!	PUNCT
ejpam-5656	125	1	∞∑	∞∑	NUM
ejpam-5656	125	2	ν=0	ν=0	NOUN
ejpam-5656	125	3	uν(2x	uν(2x	ADJ
ejpam-5656	125	4	,	,	PUNCT
ejpam-5656	125	5	2y	2y	NUM
ejpam-5656	125	6	;	;	PUNCT
ejpam-5656	125	7	ρ;µ	ρ;µ	NUM
ejpam-5656	125	8	)	)	PUNCT
ejpam-5656	125	9	ξν	ξν	ADP
ejpam-5656	125	10	ν	ν	X
ejpam-5656	125	11	!	!	PUNCT
ejpam-5656	126	1	=	=	NOUN
ejpam-5656	127	1	∞∑	∞∑	NUM
ejpam-5656	127	2	ν=0	ν=0	PRON
ejpam-5656	127	3	ν∑	ν∑	X
ejpam-5656	127	4	ω=0	ω=0	X
ejpam-5656	127	5	(	(	PUNCT
ejpam-5656	127	6	ν	ν	PROPN
ejpam-5656	127	7	ω	ω	PROPN
ejpam-5656	127	8	)	)	PUNCT
ejpam-5656	128	1	uν−ω(ρ	uν−ω(ρ	PROPN
ejpam-5656	128	2	,	,	PUNCT
ejpam-5656	128	3	µ)uω(2x	µ)uω(2x	VERB
ejpam-5656	128	4	,	,	PUNCT
ejpam-5656	128	5	2y	2y	NUM
ejpam-5656	128	6	;	;	PUNCT
ejpam-5656	128	7	ρ;µ	ρ;µ	NUM
ejpam-5656	128	8	)	)	PUNCT
ejpam-5656	128	9	ξν	ξν	ADP
ejpam-5656	128	10	ν	ν	X
ejpam-5656	128	11	!	!	PUNCT
ejpam-5656	128	12	.	.	PUNCT
ejpam-5656	129	1	by	by	ADP
ejpam-5656	129	2	comparing	compare	VERB
ejpam-5656	129	3	the	the	DET
ejpam-5656	129	4	coefficients	coefficient	NOUN
ejpam-5656	129	5	of	of	ADP
ejpam-5656	129	6	ξν	ξν	NOUN
ejpam-5656	129	7	ν	ν	NOUN
ejpam-5656	129	8	!	!	PUNCT
ejpam-5656	130	1	on	on	ADP
ejpam-5656	130	2	both	both	DET
ejpam-5656	130	3	sides	side	NOUN
ejpam-5656	130	4	of	of	ADP
ejpam-5656	130	5	the	the	DET
ejpam-5656	130	6	equation	equation	NOUN
ejpam-5656	130	7	above	above	ADV
ejpam-5656	130	8	,	,	PUNCT
ejpam-5656	130	9	we	we	PRON
ejpam-5656	130	10	derive	derive	VERB
ejpam-5656	130	11	the	the	DET
ejpam-5656	130	12	identity	identity	NOUN
ejpam-5656	130	13	.	.	PUNCT
ejpam-5656	131	1	for	for	ADP
ejpam-5656	131	2	the	the	DET
ejpam-5656	131	3	subsequent	subsequent	ADJ
ejpam-5656	131	4	property	property	NOUN
ejpam-5656	131	5	,	,	PUNCT
ejpam-5656	131	6	we	we	PRON
ejpam-5656	131	7	employ	employ	VERB
ejpam-5656	131	8	the	the	DET
ejpam-5656	131	9	following	follow	VERB
ejpam-5656	131	10	identity	identity	NOUN
ejpam-5656	131	11	[	[	X
ejpam-5656	131	12	24	24	NUM
ejpam-5656	131	13	,	,	PUNCT
ejpam-5656	131	14	p.	p.	NOUN
ejpam-5656	131	15	52	52	NUM
ejpam-5656	131	16	]	]	SYM
ejpam-5656	131	17	:	:	PUNCT
ejpam-5656	131	18	∞∑	∞∑	NUM
ejpam-5656	131	19	ν=0	ν=0	PROPN
ejpam-5656	131	20	f(ν	f(ν	NOUN
ejpam-5656	131	21	)	)	PUNCT
ejpam-5656	131	22	(	(	PUNCT
ejpam-5656	131	23	x+	x+	X
ejpam-5656	131	24	y)ν	y)ν	X
ejpam-5656	131	25	ν	ν	X
ejpam-5656	131	26	!	!	PUNCT
ejpam-5656	131	27	=	=	PUNCT
ejpam-5656	132	1	∞∑	∞∑	NUM
ejpam-5656	132	2	l	l	NOUN
ejpam-5656	132	3	,	,	PUNCT
ejpam-5656	132	4	m=0	m=0	PROPN
ejpam-5656	132	5	f(l	f(l	VERB
ejpam-5656	132	6	+	+	PROPN
ejpam-5656	132	7	m	m	NOUN
ejpam-5656	132	8	)	)	PUNCT
ejpam-5656	132	9	xlym	xlym	PROPN
ejpam-5656	132	10	l!m	l!m	PROPN
ejpam-5656	132	11	!	!	PUNCT
ejpam-5656	132	12	.	.	PUNCT
ejpam-5656	133	1	(	(	PUNCT
ejpam-5656	133	2	12	12	NUM
ejpam-5656	133	3	)	)	PUNCT
ejpam-5656	133	4	proposition	proposition	NOUN
ejpam-5656	133	5	3	3	NUM
ejpam-5656	133	6	.	.	PUNCT
ejpam-5656	134	1	the	the	DET
ejpam-5656	134	2	following	follow	VERB
ejpam-5656	134	3	implicit	implicit	ADJ
ejpam-5656	134	4	summation	summation	NOUN
ejpam-5656	134	5	formula	formula	NOUN
ejpam-5656	134	6	for	for	ADP
ejpam-5656	134	7	apostol	apostol	NOUN
ejpam-5656	134	8	-	-	PUNCT
ejpam-5656	134	9	type	type	NOUN
ejpam-5656	134	10	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	134	11	/	/	SYM
ejpam-5656	134	12	euler	euler	NOUN
ejpam-5656	134	13	polynomials	polynomial	NOUN
ejpam-5656	134	14	uν(x	uν(x	PART
ejpam-5656	134	15	,	,	PUNCT
ejpam-5656	134	16	y	y	PROPN
ejpam-5656	134	17	;	;	PUNCT
ejpam-5656	134	18	ρ;µ	ρ;µ	NUM
ejpam-5656	134	19	)	)	PUNCT
ejpam-5656	134	20	holds	hold	VERB
ejpam-5656	134	21	:	:	PUNCT
ejpam-5656	134	22	ul+m(z	ul+m(z	PROPN
ejpam-5656	134	23	,	,	PUNCT
ejpam-5656	134	24	y	y	PROPN
ejpam-5656	134	25	;	;	PUNCT
ejpam-5656	134	26	ρ;µ	ρ;µ	NUM
ejpam-5656	134	27	)	)	PUNCT
ejpam-5656	134	28	=	=	SYM
ejpam-5656	135	1	l	l	NOUN
ejpam-5656	135	2	,	,	PUNCT
ejpam-5656	135	3	m∑	m∑	ADP
ejpam-5656	135	4	p	p	X
ejpam-5656	135	5	,	,	PUNCT
ejpam-5656	135	6	q=0	q=0	PROPN
ejpam-5656	135	7	(	(	PUNCT
ejpam-5656	135	8	l	l	NOUN
ejpam-5656	135	9	p	p	NOUN
ejpam-5656	135	10	)	)	PUNCT
ejpam-5656	135	11	(	(	PUNCT
ejpam-5656	135	12	m	m	NOUN
ejpam-5656	135	13	q	q	NOUN
ejpam-5656	135	14	)	)	PUNCT
ejpam-5656	135	15	(	(	PUNCT
ejpam-5656	135	16	z	z	NOUN
ejpam-5656	135	17	−	−	PROPN
ejpam-5656	135	18	x)p+qul+m−(p+q)(x	x)p+qul+m−(p+q)(x	PROPN
ejpam-5656	135	19	,	,	PUNCT
ejpam-5656	135	20	y	y	PROPN
ejpam-5656	135	21	;	;	PUNCT
ejpam-5656	135	22	ρ;µ	ρ;µ	NUM
ejpam-5656	135	23	)	)	PUNCT
ejpam-5656	135	24	.	.	PUNCT
ejpam-5656	136	1	proof	proof	NOUN
ejpam-5656	136	2	.	.	PUNCT
ejpam-5656	137	1	by	by	ADP
ejpam-5656	137	2	(	(	PUNCT
ejpam-5656	137	3	12	12	NUM
ejpam-5656	137	4	)	)	PUNCT
ejpam-5656	137	5	,	,	PUNCT
ejpam-5656	137	6	we	we	PRON
ejpam-5656	137	7	have	have	VERB
ejpam-5656	137	8	φ(ρ	φ(ρ	NUM
ejpam-5656	137	9	,	,	PUNCT
ejpam-5656	137	10	µ	µ	NOUN
ejpam-5656	137	11	,	,	PUNCT
ejpam-5656	137	12	ξ	ξ	X
ejpam-5656	137	13	+	+	NUM
ejpam-5656	137	14	t)ex(ξ+t)+y(ξ+t)2	t)ex(ξ+t)+y(ξ+t)2	NOUN
ejpam-5656	137	15	=	=	SYM
ejpam-5656	137	16	∞∑	∞∑	NUM
ejpam-5656	137	17	ν=0	ν=0	PROPN
ejpam-5656	137	18	uν(x	uν(x	NOUN
ejpam-5656	137	19	,	,	PUNCT
ejpam-5656	137	20	y	y	PROPN
ejpam-5656	137	21	;	;	PUNCT
ejpam-5656	137	22	ρ;µ	ρ;µ	NUM
ejpam-5656	137	23	)	)	PUNCT
ejpam-5656	137	24	(	(	PUNCT
ejpam-5656	137	25	ξ	ξ	X
ejpam-5656	137	26	+	+	X
ejpam-5656	137	27	t)ν	t)ν	NOUN
ejpam-5656	137	28	ν	ν	NOUN
ejpam-5656	137	29	!	!	PUNCT
ejpam-5656	137	30	=	=	PUNCT
ejpam-5656	138	1	∞∑	∞∑	NUM
ejpam-5656	138	2	l	l	NOUN
ejpam-5656	138	3	,	,	PUNCT
ejpam-5656	138	4	m=0	m=0	PROPN
ejpam-5656	138	5	ul+m(x	ul+m(x	PROPN
ejpam-5656	138	6	,	,	PUNCT
ejpam-5656	138	7	y	y	PROPN
ejpam-5656	138	8	;	;	PUNCT
ejpam-5656	138	9	ρ;µ	ρ;µ	NUM
ejpam-5656	138	10	)	)	PUNCT
ejpam-5656	138	11	ξltm	ξltm	PROPN
ejpam-5656	138	12	l!m	l!m	PROPN
ejpam-5656	138	13	!	!	PROPN
ejpam-5656	138	14	,	,	PUNCT
ejpam-5656	138	15	dı́az	dı́az	X
ejpam-5656	138	16	et	et	PROPN
ejpam-5656	138	17	al	al	PROPN
ejpam-5656	138	18	.	.	PUNCT
ejpam-5656	138	19	/	/	SYM
ejpam-5656	138	20	eur	eur	PROPN
ejpam-5656	138	21	.	.	PUNCT
ejpam-5656	139	1	j.	j.	PROPN
ejpam-5656	139	2	pure	pure	PROPN
ejpam-5656	139	3	appl	appl	PROPN
ejpam-5656	139	4	.	.	PROPN
ejpam-5656	139	5	math	math	PROPN
ejpam-5656	139	6	,	,	PUNCT
ejpam-5656	139	7	18	18	NUM
ejpam-5656	139	8	(	(	PUNCT
ejpam-5656	139	9	1	1	NUM
ejpam-5656	139	10	)	)	PUNCT
ejpam-5656	139	11	(	(	PUNCT
ejpam-5656	139	12	2025	2025	NUM
ejpam-5656	139	13	)	)	PUNCT
ejpam-5656	139	14	,	,	PUNCT
ejpam-5656	139	15	5656	5656	NUM
ejpam-5656	139	16	8	8	NUM
ejpam-5656	139	17	of	of	ADP
ejpam-5656	139	18	17	17	NUM
ejpam-5656	139	19	or	or	CCONJ
ejpam-5656	139	20	equivalently	equivalently	ADV
ejpam-5656	139	21	φ(ρ	φ(ρ	NUM
ejpam-5656	139	22	,	,	PUNCT
ejpam-5656	139	23	µ	µ	NOUN
ejpam-5656	139	24	,	,	PUNCT
ejpam-5656	139	25	ξ	ξ	PROPN
ejpam-5656	139	26	+	+	CCONJ
ejpam-5656	139	27	t)ey(ξ+t)2	t)ey(ξ+t)2	PROPN
ejpam-5656	139	28	=	=	SYM
ejpam-5656	139	29	e−x(ξ+t	e−x(ξ+t	PROPN
ejpam-5656	139	30	)	)	PUNCT
ejpam-5656	139	31	∞∑	∞∑	NUM
ejpam-5656	139	32	l	l	NOUN
ejpam-5656	139	33	,	,	PUNCT
ejpam-5656	139	34	m=0	m=0	PROPN
ejpam-5656	139	35	ul+m(x	ul+m(x	PROPN
ejpam-5656	139	36	,	,	PUNCT
ejpam-5656	139	37	y	y	PROPN
ejpam-5656	139	38	;	;	PUNCT
ejpam-5656	139	39	ρ;µ	ρ;µ	NUM
ejpam-5656	139	40	)	)	PUNCT
ejpam-5656	139	41	ξltm	ξltm	PROPN
ejpam-5656	139	42	l!m	l!m	PROPN
ejpam-5656	139	43	!	!	PUNCT
ejpam-5656	139	44	.	.	PUNCT
ejpam-5656	140	1	(	(	PUNCT
ejpam-5656	140	2	13	13	NUM
ejpam-5656	140	3	)	)	PUNCT
ejpam-5656	140	4	by	by	ADP
ejpam-5656	140	5	performing	perform	VERB
ejpam-5656	140	6	the	the	DET
ejpam-5656	140	7	previous	previous	ADJ
ejpam-5656	140	8	procedure	procedure	NOUN
ejpam-5656	140	9	,	,	PUNCT
ejpam-5656	140	10	but	but	CCONJ
ejpam-5656	140	11	replacing	replace	VERB
ejpam-5656	140	12	x	x	PUNCT
ejpam-5656	140	13	with	with	ADP
ejpam-5656	140	14	z	z	PROPN
ejpam-5656	140	15	,	,	PUNCT
ejpam-5656	140	16	we	we	PRON
ejpam-5656	140	17	now	now	ADV
ejpam-5656	140	18	obtain	obtain	VERB
ejpam-5656	140	19	φ(ρ	φ(ρ	NUM
ejpam-5656	140	20	,	,	PUNCT
ejpam-5656	140	21	µ	µ	NOUN
ejpam-5656	140	22	,	,	PUNCT
ejpam-5656	140	23	ξ	ξ	PROPN
ejpam-5656	140	24	+	+	CCONJ
ejpam-5656	140	25	t)ey(ξ+t)2	t)ey(ξ+t)2	PROPN
ejpam-5656	140	26	=	=	SYM
ejpam-5656	140	27	e−z(ξ+t	e−z(ξ+t	NUM
ejpam-5656	140	28	)	)	PUNCT
ejpam-5656	140	29	∞∑	∞∑	NUM
ejpam-5656	140	30	l	l	NOUN
ejpam-5656	140	31	,	,	PUNCT
ejpam-5656	140	32	m=0	m=0	PROPN
ejpam-5656	140	33	ul+m(z	ul+m(z	PROPN
ejpam-5656	140	34	,	,	PUNCT
ejpam-5656	140	35	y	y	PROPN
ejpam-5656	140	36	;	;	PUNCT
ejpam-5656	140	37	ρ;µ	ρ;µ	NUM
ejpam-5656	140	38	)	)	PUNCT
ejpam-5656	140	39	ξltm	ξltm	PROPN
ejpam-5656	140	40	l!m	l!m	PROPN
ejpam-5656	140	41	!	!	PUNCT
ejpam-5656	140	42	.	.	PUNCT
ejpam-5656	141	1	(	(	PUNCT
ejpam-5656	141	2	14	14	NUM
ejpam-5656	141	3	)	)	PUNCT
ejpam-5656	141	4	then	then	ADV
ejpam-5656	141	5	,	,	PUNCT
ejpam-5656	141	6	by	by	ADP
ejpam-5656	141	7	equating	equate	VERB
ejpam-5656	141	8	equations	equation	NOUN
ejpam-5656	141	9	(	(	PUNCT
ejpam-5656	141	10	13	13	NUM
ejpam-5656	141	11	)	)	PUNCT
ejpam-5656	141	12	and	and	CCONJ
ejpam-5656	141	13	(	(	PUNCT
ejpam-5656	141	14	14	14	NUM
ejpam-5656	141	15	)	)	PUNCT
ejpam-5656	141	16	,	,	PUNCT
ejpam-5656	141	17	we	we	PRON
ejpam-5656	141	18	get	get	VERB
ejpam-5656	141	19	∞∑	∞∑	NUM
ejpam-5656	141	20	l	l	NOUN
ejpam-5656	141	21	,	,	PUNCT
ejpam-5656	141	22	m=0	m=0	PROPN
ejpam-5656	141	23	ul+m(z	ul+m(z	PROPN
ejpam-5656	141	24	,	,	PUNCT
ejpam-5656	141	25	y	y	PROPN
ejpam-5656	141	26	;	;	PUNCT
ejpam-5656	141	27	ρ;µ	ρ;µ	NUM
ejpam-5656	141	28	)	)	PUNCT
ejpam-5656	141	29	ξltm	ξltm	PROPN
ejpam-5656	141	30	l!m	l!m	PROPN
ejpam-5656	141	31	!	!	PUNCT
ejpam-5656	141	32	=	=	PUNCT
ejpam-5656	142	1	e(z−x)(ξ+t	e(z−x)(ξ+t	INTJ
ejpam-5656	142	2	)	)	PUNCT
ejpam-5656	142	3	∞∑	∞∑	NUM
ejpam-5656	142	4	l	l	NOUN
ejpam-5656	142	5	,	,	PUNCT
ejpam-5656	142	6	m=0	m=0	PROPN
ejpam-5656	142	7	ul+m(x	ul+m(x	PROPN
ejpam-5656	142	8	,	,	PUNCT
ejpam-5656	142	9	y	y	PROPN
ejpam-5656	142	10	;	;	PUNCT
ejpam-5656	142	11	ρ;µ	ρ;µ	NUM
ejpam-5656	142	12	)	)	PUNCT
ejpam-5656	142	13	ξltm	ξltm	PROPN
ejpam-5656	142	14	l!m	l!m	PROPN
ejpam-5656	142	15	!	!	PUNCT
ejpam-5656	142	16	.	.	PUNCT
ejpam-5656	143	1	now	now	ADV
ejpam-5656	143	2	,	,	PUNCT
ejpam-5656	143	3	by	by	ADP
ejpam-5656	143	4	the	the	DET
ejpam-5656	143	5	exponential	exponential	ADJ
ejpam-5656	143	6	series	series	NOUN
ejpam-5656	143	7	,	,	PUNCT
ejpam-5656	143	8	(	(	PUNCT
ejpam-5656	143	9	12	12	NUM
ejpam-5656	143	10	)	)	PUNCT
ejpam-5656	143	11	and	and	CCONJ
ejpam-5656	143	12	(	(	PUNCT
ejpam-5656	143	13	10	10	NUM
ejpam-5656	143	14	)	)	PUNCT
ejpam-5656	143	15	,	,	PUNCT
ejpam-5656	143	16	we	we	PRON
ejpam-5656	143	17	obtain	obtain	VERB
ejpam-5656	143	18	∞∑	∞∑	NUM
ejpam-5656	143	19	l	l	NOUN
ejpam-5656	143	20	,	,	PUNCT
ejpam-5656	143	21	m=0	m=0	PROPN
ejpam-5656	143	22	ul+m(z	ul+m(z	PROPN
ejpam-5656	143	23	,	,	PUNCT
ejpam-5656	143	24	y	y	PROPN
ejpam-5656	143	25	;	;	PUNCT
ejpam-5656	143	26	ρ;µ	ρ;µ	NUM
ejpam-5656	143	27	)	)	PUNCT
ejpam-5656	143	28	ξltm	ξltm	PROPN
ejpam-5656	143	29	l!m	l!m	PROPN
ejpam-5656	143	30	!	!	PUNCT
ejpam-5656	143	31	=	=	PUNCT
ejpam-5656	144	1	∞∑	∞∑	NUM
ejpam-5656	144	2	ν=0	ν=0	NOUN
ejpam-5656	144	3	(	(	PUNCT
ejpam-5656	144	4	z	z	NOUN
ejpam-5656	144	5	−	−	NOUN
ejpam-5656	144	6	x)ν	x)ν	NOUN
ejpam-5656	144	7	(	(	PUNCT
ejpam-5656	144	8	ξ	ξ	X
ejpam-5656	144	9	+	+	X
ejpam-5656	144	10	t)ν	t)ν	NOUN
ejpam-5656	144	11	ν	ν	NOUN
ejpam-5656	144	12	!	!	PUNCT
ejpam-5656	145	1	∞∑	∞∑	NUM
ejpam-5656	145	2	l	l	NOUN
ejpam-5656	145	3	,	,	PUNCT
ejpam-5656	145	4	m=0	m=0	PROPN
ejpam-5656	145	5	ul+m(x	ul+m(x	PROPN
ejpam-5656	145	6	,	,	PUNCT
ejpam-5656	145	7	y	y	PROPN
ejpam-5656	145	8	;	;	PUNCT
ejpam-5656	145	9	ρ;µ	ρ;µ	NUM
ejpam-5656	145	10	)	)	PUNCT
ejpam-5656	145	11	ξltm	ξltm	PROPN
ejpam-5656	145	12	l!m	l!m	PROPN
ejpam-5656	145	13	!	!	PUNCT
ejpam-5656	145	14	=	=	NOUN
ejpam-5656	146	1	∞∑	∞∑	NUM
ejpam-5656	146	2	p	p	X
ejpam-5656	146	3	,	,	PUNCT
ejpam-5656	146	4	q=0	q=0	X
ejpam-5656	146	5	(	(	PUNCT
ejpam-5656	146	6	z	z	NOUN
ejpam-5656	146	7	−	−	PROPN
ejpam-5656	146	8	x)p+q	x)p+q	PROPN
ejpam-5656	146	9	ξ	ξ	PROPN
ejpam-5656	146	10	ptq	ptq	PROPN
ejpam-5656	146	11	p!q	p!q	PROPN
ejpam-5656	146	12	!	!	PUNCT
ejpam-5656	147	1	∞∑	∞∑	NUM
ejpam-5656	147	2	l	l	NOUN
ejpam-5656	147	3	,	,	PUNCT
ejpam-5656	147	4	m=0	m=0	PROPN
ejpam-5656	147	5	ul+m(x	ul+m(x	PROPN
ejpam-5656	147	6	,	,	PUNCT
ejpam-5656	147	7	y	y	PROPN
ejpam-5656	147	8	;	;	PUNCT
ejpam-5656	147	9	ρ;µ	ρ;µ	NUM
ejpam-5656	147	10	)	)	PUNCT
ejpam-5656	147	11	ξltm	ξltm	PROPN
ejpam-5656	147	12	l!m	l!m	PROPN
ejpam-5656	147	13	!	!	PUNCT
ejpam-5656	147	14	=	=	PUNCT
ejpam-5656	148	1	∞∑	∞∑	NUM
ejpam-5656	148	2	l	l	NOUN
ejpam-5656	148	3	,	,	PUNCT
ejpam-5656	148	4	m=0	m=0	PROPN
ejpam-5656	148	5	l	l	NOUN
ejpam-5656	148	6	,	,	PUNCT
ejpam-5656	148	7	m∑	m∑	ADP
ejpam-5656	148	8	p	p	X
ejpam-5656	148	9	,	,	PUNCT
ejpam-5656	148	10	q=0	q=0	PROPN
ejpam-5656	148	11	(	(	PUNCT
ejpam-5656	148	12	l	l	NOUN
ejpam-5656	148	13	p	p	NOUN
ejpam-5656	148	14	)	)	PUNCT
ejpam-5656	148	15	(	(	PUNCT
ejpam-5656	148	16	m	m	NOUN
ejpam-5656	148	17	q	q	NOUN
ejpam-5656	148	18	)	)	PUNCT
ejpam-5656	148	19	(	(	PUNCT
ejpam-5656	148	20	z	z	NOUN
ejpam-5656	148	21	−	−	PROPN
ejpam-5656	148	22	x)p+qul+m−(p+q)(x	x)p+qul+m−(p+q)(x	PROPN
ejpam-5656	148	23	,	,	PUNCT
ejpam-5656	148	24	y	y	PROPN
ejpam-5656	148	25	;	;	PUNCT
ejpam-5656	148	26	ρ;µ	ρ;µ	NUM
ejpam-5656	148	27	)	)	PUNCT
ejpam-5656	148	28	ξltm	ξltm	PROPN
ejpam-5656	148	29	l!m	l!m	PROPN
ejpam-5656	148	30	!	!	PUNCT
ejpam-5656	148	31	.	.	PUNCT
ejpam-5656	149	1	by	by	ADP
ejpam-5656	149	2	comparing	compare	VERB
ejpam-5656	149	3	the	the	DET
ejpam-5656	149	4	coefficients	coefficient	NOUN
ejpam-5656	149	5	of	of	ADP
ejpam-5656	149	6	ξltm	ξltm	PROPN
ejpam-5656	149	7	l!m	l!m	PROPN
ejpam-5656	149	8	!	!	PUNCT
ejpam-5656	150	1	on	on	ADP
ejpam-5656	150	2	both	both	DET
ejpam-5656	150	3	sides	side	NOUN
ejpam-5656	150	4	of	of	ADP
ejpam-5656	150	5	the	the	DET
ejpam-5656	150	6	equation	equation	NOUN
ejpam-5656	150	7	above	above	ADV
ejpam-5656	150	8	,	,	PUNCT
ejpam-5656	150	9	we	we	PRON
ejpam-5656	150	10	derive	derive	VERB
ejpam-5656	150	11	the	the	DET
ejpam-5656	150	12	identity	identity	NOUN
ejpam-5656	150	13	.	.	PUNCT
ejpam-5656	151	1	below	below	ADV
ejpam-5656	151	2	,	,	PUNCT
ejpam-5656	151	3	we	we	PRON
ejpam-5656	151	4	introduce	introduce	VERB
ejpam-5656	151	5	both	both	CCONJ
ejpam-5656	151	6	the	the	DET
ejpam-5656	151	7	differentiation	differentiation	NOUN
ejpam-5656	151	8	and	and	CCONJ
ejpam-5656	151	9	integration	integration	NOUN
ejpam-5656	151	10	of	of	ADP
ejpam-5656	151	11	the	the	DET
ejpam-5656	151	12	apostol	apostol	NOUN
ejpam-5656	151	13	-	-	PUNCT
ejpam-5656	151	14	type	type	NOUN
ejpam-5656	151	15	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	151	16	/	/	SYM
ejpam-5656	151	17	euler	euler	NOUN
ejpam-5656	151	18	polynomials	polynomial	NOUN
ejpam-5656	151	19	.	.	PUNCT
ejpam-5656	152	1	proposition	proposition	NOUN
ejpam-5656	152	2	4	4	NUM
ejpam-5656	152	3	.	.	PUNCT
ejpam-5656	153	1	let	let	VERB
ejpam-5656	153	2	ρ	ρ	PROPN
ejpam-5656	153	3	>	>	X
ejpam-5656	153	4	0	0	PROPN
ejpam-5656	153	5	,	,	PUNCT
ejpam-5656	153	6	µ	µ	PRON
ejpam-5656	153	7	≥	≥	NOUN
ejpam-5656	153	8	0	0	NUM
ejpam-5656	153	9	such	such	ADJ
ejpam-5656	153	10	that	that	SCONJ
ejpam-5656	153	11	µ	µ	ADJ
ejpam-5656	153	12	̸=	̸=	PROPN
ejpam-5656	153	13	1	1	NUM
ejpam-5656	153	14	.	.	PUNCT
ejpam-5656	154	1	the	the	DET
ejpam-5656	154	2	following	follow	VERB
ejpam-5656	154	3	properties	property	NOUN
ejpam-5656	154	4	are	be	AUX
ejpam-5656	154	5	maintained	maintain	VERB
ejpam-5656	154	6	:	:	PUNCT
ejpam-5656	154	7	∂	∂	NUM
ejpam-5656	154	8	∂x	∂x	PROPN
ejpam-5656	154	9	uν(x	uν(x	SYM
ejpam-5656	154	10	,	,	PUNCT
ejpam-5656	154	11	y	y	PROPN
ejpam-5656	154	12	;	;	PUNCT
ejpam-5656	154	13	ρ;µ	ρ;µ	NUM
ejpam-5656	154	14	)	)	PUNCT
ejpam-5656	154	15	=	=	SYM
ejpam-5656	154	16	νuν−1(x	νuν−1(x	PROPN
ejpam-5656	154	17	,	,	PUNCT
ejpam-5656	154	18	y	y	PROPN
ejpam-5656	154	19	;	;	PUNCT
ejpam-5656	154	20	ρ;µ	ρ;µ	NUM
ejpam-5656	154	21	)	)	PUNCT
ejpam-5656	154	22	,	,	PUNCT
ejpam-5656	154	23	(	(	PUNCT
ejpam-5656	154	24	15	15	NUM
ejpam-5656	154	25	)	)	PUNCT
ejpam-5656	154	26	∂	∂	NOUN
ejpam-5656	154	27	∂y	∂y	PROPN
ejpam-5656	154	28	uν(x	uν(x	PROPN
ejpam-5656	154	29	,	,	PUNCT
ejpam-5656	154	30	y	y	PROPN
ejpam-5656	154	31	;	;	PUNCT
ejpam-5656	154	32	ρ;µ	ρ;µ	NUM
ejpam-5656	154	33	)	)	PUNCT
ejpam-5656	154	34	=	=	PUNCT
ejpam-5656	154	35	ν(ν	ν(ν	NOUN
ejpam-5656	154	36	−	−	PROPN
ejpam-5656	154	37	1)uν−2(x	1)uν−2(x	NUM
ejpam-5656	154	38	,	,	PUNCT
ejpam-5656	154	39	y	y	PROPN
ejpam-5656	154	40	;	;	PUNCT
ejpam-5656	154	41	ρ;µ	ρ;µ	NUM
ejpam-5656	154	42	)	)	PUNCT
ejpam-5656	154	43	.	.	PUNCT
ejpam-5656	155	1	proof	proof	NOUN
ejpam-5656	155	2	.	.	PUNCT
ejpam-5656	156	1	initially	initially	ADV
ejpam-5656	156	2	,	,	PUNCT
ejpam-5656	156	3	notice	notice	VERB
ejpam-5656	156	4	that	that	SCONJ
ejpam-5656	156	5	∂	∂	ADJ
ejpam-5656	156	6	∂x	∂x	PROPN
ejpam-5656	156	7	∞∑	∞∑	NUM
ejpam-5656	156	8	ν=0	ν=0	PROPN
ejpam-5656	156	9	uν(x	uν(x	NOUN
ejpam-5656	156	10	,	,	PUNCT
ejpam-5656	156	11	y	y	PROPN
ejpam-5656	156	12	;	;	PUNCT
ejpam-5656	156	13	ρ	ρ	PROPN
ejpam-5656	156	14	,	,	PUNCT
ejpam-5656	156	15	µ	µ	NOUN
ejpam-5656	156	16	)	)	PUNCT
ejpam-5656	156	17	ξν	ξν	ADV
ejpam-5656	156	18	ν	ν	X
ejpam-5656	156	19	!	!	PUNCT
ejpam-5656	157	1	=	=	SYM
ejpam-5656	157	2	∂	∂	NUM
ejpam-5656	157	3	∂x	∂x	PROPN
ejpam-5656	157	4	∞∑	∞∑	NUM
ejpam-5656	157	5	ν=1	ν=1	NUM
ejpam-5656	157	6	uν(x	uν(x	PROPN
ejpam-5656	157	7	,	,	PUNCT
ejpam-5656	157	8	y	y	PROPN
ejpam-5656	157	9	;	;	PUNCT
ejpam-5656	157	10	ρ;µ	ρ;µ	NUM
ejpam-5656	157	11	)	)	PUNCT
ejpam-5656	157	12	ξν	ξν	ADP
ejpam-5656	158	1	ν	ν	PROPN
ejpam-5656	158	2	!	!	PUNCT
ejpam-5656	158	3	.	.	PUNCT
ejpam-5656	159	1	(	(	PUNCT
ejpam-5656	159	2	16	16	NUM
ejpam-5656	159	3	)	)	PUNCT
ejpam-5656	159	4	dı́az	dı́az	X
ejpam-5656	159	5	et	et	NOUN
ejpam-5656	159	6	al	al	PROPN
ejpam-5656	159	7	.	.	PUNCT
ejpam-5656	159	8	/	/	SYM
ejpam-5656	159	9	eur	eur	PROPN
ejpam-5656	159	10	.	.	PUNCT
ejpam-5656	160	1	j.	j.	PROPN
ejpam-5656	160	2	pure	pure	PROPN
ejpam-5656	160	3	appl	appl	PROPN
ejpam-5656	160	4	.	.	PROPN
ejpam-5656	160	5	math	math	PROPN
ejpam-5656	160	6	,	,	PUNCT
ejpam-5656	160	7	18	18	NUM
ejpam-5656	160	8	(	(	PUNCT
ejpam-5656	160	9	1	1	NUM
ejpam-5656	160	10	)	)	PUNCT
ejpam-5656	160	11	(	(	PUNCT
ejpam-5656	160	12	2025	2025	NUM
ejpam-5656	160	13	)	)	PUNCT
ejpam-5656	160	14	,	,	PUNCT
ejpam-5656	160	15	5656	5656	NUM
ejpam-5656	160	16	9	9	NUM
ejpam-5656	160	17	of	of	ADP
ejpam-5656	160	18	17	17	NUM
ejpam-5656	160	19	on	on	ADP
ejpam-5656	160	20	the	the	DET
ejpam-5656	160	21	other	other	ADJ
ejpam-5656	160	22	hand	hand	NOUN
ejpam-5656	160	23	,	,	PUNCT
ejpam-5656	160	24	∂	∂	NUM
ejpam-5656	160	25	∂x	∂x	PROPN
ejpam-5656	160	26	φ(ρ	φ(ρ	PROPN
ejpam-5656	160	27	,	,	PUNCT
ejpam-5656	160	28	µ	µ	NUM
ejpam-5656	160	29	,	,	PUNCT
ejpam-5656	160	30	ξ)exξ+yξ2	ξ)exξ+yξ2	X
ejpam-5656	160	31	=	=	PUNCT
ejpam-5656	161	1	∞∑	∞∑	NUM
ejpam-5656	161	2	ν=0	ν=0	NOUN
ejpam-5656	161	3	uν(x	uν(x	NOUN
ejpam-5656	161	4	,	,	PUNCT
ejpam-5656	161	5	y	y	PROPN
ejpam-5656	161	6	;	;	PUNCT
ejpam-5656	161	7	ρ;µ	ρ;µ	NUM
ejpam-5656	161	8	)	)	PUNCT
ejpam-5656	161	9	ξν+1	ξν+1	NUM
ejpam-5656	161	10	ν	ν	NOUN
ejpam-5656	161	11	!	!	PUNCT
ejpam-5656	161	12	=	=	NOUN
ejpam-5656	162	1	∞∑	∞∑	NUM
ejpam-5656	162	2	ν=1	ν=1	NUM
ejpam-5656	162	3	νuν−1(x	νuν−1(x	NOUN
ejpam-5656	162	4	,	,	PUNCT
ejpam-5656	162	5	y	y	PROPN
ejpam-5656	162	6	;	;	PUNCT
ejpam-5656	162	7	ρ;µ	ρ;µ	NUM
ejpam-5656	162	8	)	)	PUNCT
ejpam-5656	162	9	ξν	ξν	ADP
ejpam-5656	162	10	ν	ν	PROPN
ejpam-5656	162	11	!	!	PUNCT
ejpam-5656	162	12	.	.	PUNCT
ejpam-5656	163	1	(	(	PUNCT
ejpam-5656	163	2	17	17	NUM
ejpam-5656	163	3	)	)	PUNCT
ejpam-5656	163	4	by	by	ADP
ejpam-5656	163	5	comparing	compare	VERB
ejpam-5656	163	6	(	(	PUNCT
ejpam-5656	163	7	16	16	NUM
ejpam-5656	163	8	)	)	PUNCT
ejpam-5656	163	9	and	and	CCONJ
ejpam-5656	163	10	(	(	PUNCT
ejpam-5656	163	11	17	17	NUM
ejpam-5656	163	12	)	)	PUNCT
ejpam-5656	163	13	,	,	PUNCT
ejpam-5656	163	14	we	we	PRON
ejpam-5656	163	15	obtain	obtain	VERB
ejpam-5656	163	16	(	(	PUNCT
ejpam-5656	163	17	15	15	NUM
ejpam-5656	163	18	)	)	PUNCT
ejpam-5656	163	19	.	.	PUNCT
ejpam-5656	164	1	now	now	ADV
ejpam-5656	164	2	,	,	PUNCT
ejpam-5656	164	3	∂	∂	X
ejpam-5656	164	4	∂y	∂y	SYM
ejpam-5656	164	5	φ(ρ	φ(ρ	PROPN
ejpam-5656	164	6	,	,	PUNCT
ejpam-5656	164	7	µ	µ	NUM
ejpam-5656	164	8	,	,	PUNCT
ejpam-5656	164	9	ξ)exξ+yξ2	ξ)exξ+yξ2	X
ejpam-5656	164	10	=	=	PUNCT
ejpam-5656	164	11	∞∑	∞∑	NUM
ejpam-5656	164	12	ν=0	ν=0	NOUN
ejpam-5656	164	13	uν(x	uν(x	NOUN
ejpam-5656	164	14	,	,	PUNCT
ejpam-5656	164	15	y	y	PROPN
ejpam-5656	164	16	;	;	PUNCT
ejpam-5656	164	17	ρ;µ	ρ;µ	NUM
ejpam-5656	164	18	)	)	PUNCT
ejpam-5656	164	19	ξν+2	ξν+2	NUM
ejpam-5656	164	20	ν	ν	NOUN
ejpam-5656	164	21	!	!	PUNCT
ejpam-5656	164	22	=	=	PUNCT
ejpam-5656	165	1	∞∑	∞∑	NUM
ejpam-5656	165	2	ν=2	ν=2	NUM
ejpam-5656	165	3	uν−2(x	uν−2(x	PROPN
ejpam-5656	165	4	,	,	PUNCT
ejpam-5656	165	5	y	y	PROPN
ejpam-5656	165	6	;	;	PUNCT
ejpam-5656	165	7	ρ;µ	ρ;µ	NUM
ejpam-5656	165	8	)	)	PUNCT
ejpam-5656	165	9	ξν	ξν	ADV
ejpam-5656	165	10	(	(	PUNCT
ejpam-5656	165	11	ν	ν	X
ejpam-5656	165	12	−	−	PROPN
ejpam-5656	165	13	2	2	NUM
ejpam-5656	165	14	)	)	PUNCT
ejpam-5656	165	15	!	!	PUNCT
ejpam-5656	166	1	=	=	PUNCT
ejpam-5656	167	1	∞∑	∞∑	NUM
ejpam-5656	167	2	ν=0	ν=0	PRON
ejpam-5656	167	3	ν(ν	ν(ν	NOUN
ejpam-5656	167	4	−	−	PROPN
ejpam-5656	167	5	1)uν−2(x	1)uν−2(x	NUM
ejpam-5656	167	6	,	,	PUNCT
ejpam-5656	167	7	y	y	PROPN
ejpam-5656	167	8	;	;	PUNCT
ejpam-5656	167	9	ρ;µ	ρ;µ	NUM
ejpam-5656	167	10	)	)	PUNCT
ejpam-5656	167	11	ξν	ξν	ADP
ejpam-5656	167	12	ν	ν	PROPN
ejpam-5656	167	13	!	!	PUNCT
ejpam-5656	167	14	.	.	PUNCT
ejpam-5656	168	1	remark	remark	PROPN
ejpam-5656	168	2	3	3	NUM
ejpam-5656	168	3	.	.	PUNCT
ejpam-5656	169	1	an	an	DET
ejpam-5656	169	2	alternative	alternative	ADJ
ejpam-5656	169	3	method	method	NOUN
ejpam-5656	169	4	to	to	PART
ejpam-5656	169	5	compute	compute	VERB
ejpam-5656	169	6	the	the	DET
ejpam-5656	169	7	derivative	derivative	NOUN
ejpam-5656	169	8	with	with	ADP
ejpam-5656	169	9	respect	respect	NOUN
ejpam-5656	169	10	to	to	ADP
ejpam-5656	169	11	y	y	PROPN
ejpam-5656	169	12	is	be	AUX
ejpam-5656	169	13	by	by	ADP
ejpam-5656	169	14	utilizing	utilize	VERB
ejpam-5656	169	15	the	the	DET
ejpam-5656	169	16	representation	representation	NOUN
ejpam-5656	169	17	(	(	PUNCT
ejpam-5656	169	18	11	11	NUM
ejpam-5656	169	19	)	)	PUNCT
ejpam-5656	169	20	and	and	CCONJ
ejpam-5656	169	21	employing	employ	VERB
ejpam-5656	169	22	the	the	DET
ejpam-5656	169	23	identity	identity	NOUN
ejpam-5656	169	24	(	(	PUNCT
ejpam-5656	169	25	8)	8)	NUM
ejpam-5656	169	26	.	.	PUNCT
ejpam-5656	169	27	note	note	VERB
ejpam-5656	169	28	that	that	SCONJ
ejpam-5656	169	29	,	,	PUNCT
ejpam-5656	169	30	∂	∂	NUM
ejpam-5656	169	31	∂y	∂y	PROPN
ejpam-5656	169	32	uν(x	uν(x	PROPN
ejpam-5656	169	33	,	,	PUNCT
ejpam-5656	169	34	y	y	PROPN
ejpam-5656	169	35	;	;	PUNCT
ejpam-5656	169	36	ρ;µ	ρ;µ	NUM
ejpam-5656	169	37	)	)	PUNCT
ejpam-5656	169	38	=	=	SYM
ejpam-5656	170	1	ν∑	ν∑	PROPN
ejpam-5656	171	1	k=0	k=0	PROPN
ejpam-5656	171	2	(	(	PUNCT
ejpam-5656	171	3	ν	ν	X
ejpam-5656	171	4	k	k	X
ejpam-5656	171	5	)	)	PUNCT
ejpam-5656	171	6	uν(ρ;µ	uν(ρ;µ	PROPN
ejpam-5656	171	7	)	)	PUNCT
ejpam-5656	171	8	∂2	∂2	PROPN
ejpam-5656	171	9	∂x2	∂x2	NOUN
ejpam-5656	171	10	hk(x	hk(x	NOUN
ejpam-5656	171	11	,	,	PUNCT
ejpam-5656	171	12	y	y	NOUN
ejpam-5656	171	13	)	)	PUNCT
ejpam-5656	171	14	=	=	SYM
ejpam-5656	172	1	ν∑	ν∑	PROPN
ejpam-5656	173	1	k=2	k=2	PROPN
ejpam-5656	174	1	(	(	PUNCT
ejpam-5656	174	2	ν	ν	X
ejpam-5656	174	3	k	k	X
ejpam-5656	174	4	)	)	PUNCT
ejpam-5656	175	1	k(k	k(k	ADV
ejpam-5656	175	2	−	−	PROPN
ejpam-5656	175	3	1)uν(ρ;µ)hk−2(x	1)uν(ρ;µ)hk−2(x	NUM
ejpam-5656	175	4	,	,	PUNCT
ejpam-5656	175	5	y	y	PROPN
ejpam-5656	175	6	)	)	PUNCT
ejpam-5656	175	7	.	.	PUNCT
ejpam-5656	176	1	remark	remark	PROPN
ejpam-5656	176	2	4	4	NUM
ejpam-5656	176	3	.	.	PUNCT
ejpam-5656	176	4	note	note	VERB
ejpam-5656	176	5	that	that	SCONJ
ejpam-5656	176	6	by	by	ADP
ejpam-5656	176	7	repeatedly	repeatedly	ADV
ejpam-5656	176	8	differentiating	differentiate	VERB
ejpam-5656	176	9	with	with	ADP
ejpam-5656	176	10	respect	respect	NOUN
ejpam-5656	176	11	to	to	ADP
ejpam-5656	176	12	x	x	PUNCT
ejpam-5656	176	13	and	and	CCONJ
ejpam-5656	176	14	applying	apply	VERB
ejpam-5656	176	15	the	the	DET
ejpam-5656	176	16	induction	induction	NOUN
ejpam-5656	176	17	principle	principle	NOUN
ejpam-5656	176	18	on	on	ADP
ejpam-5656	176	19	m	m	PROPN
ejpam-5656	176	20	,	,	PUNCT
ejpam-5656	176	21	we	we	PRON
ejpam-5656	176	22	can	can	AUX
ejpam-5656	176	23	obtain	obtain	VERB
ejpam-5656	176	24	the	the	DET
ejpam-5656	176	25	m	m	NOUN
ejpam-5656	176	26	-	-	PUNCT
ejpam-5656	176	27	th	th	VERB
ejpam-5656	176	28	order	order	NOUN
ejpam-5656	176	29	derivative	derivative	NOUN
ejpam-5656	176	30	of	of	ADP
ejpam-5656	176	31	the	the	DET
ejpam-5656	176	32	polynomial	polynomial	ADJ
ejpam-5656	176	33	:	:	PUNCT
ejpam-5656	176	34	∂l	∂l	PROPN
ejpam-5656	176	35	∂xl	∂xl	PROPN
ejpam-5656	176	36	uν(x	uν(x	SYM
ejpam-5656	176	37	,	,	PUNCT
ejpam-5656	176	38	y	y	PROPN
ejpam-5656	176	39	;	;	PUNCT
ejpam-5656	176	40	ρ;µ	ρ;µ	NUM
ejpam-5656	176	41	)	)	PUNCT
ejpam-5656	177	1	=	=	NOUN
ejpam-5656	177	2	(	(	PUNCT
ejpam-5656	177	3	ν)luν−l(x	ν)luν−l(x	PROPN
ejpam-5656	177	4	,	,	PUNCT
ejpam-5656	177	5	y	y	PROPN
ejpam-5656	177	6	;	;	PUNCT
ejpam-5656	177	7	ρ;µ	ρ;µ	NUM
ejpam-5656	177	8	)	)	PUNCT
ejpam-5656	177	9	,	,	PUNCT
ejpam-5656	177	10	where	where	SCONJ
ejpam-5656	177	11	(	(	PUNCT
ejpam-5656	177	12	ν)l	ν)l	NOUN
ejpam-5656	177	13	:	:	PUNCT
ejpam-5656	177	14	=	=	PUNCT
ejpam-5656	177	15	ν(ν	ν(ν	NOUN
ejpam-5656	177	16	−	−	ADP
ejpam-5656	177	17	1	1	NUM
ejpam-5656	177	18	)	)	PUNCT
ejpam-5656	177	19	·	·	PUNCT
ejpam-5656	177	20	·	·	PUNCT
ejpam-5656	177	21	·	·	PUNCT
ejpam-5656	177	22	(	(	PUNCT
ejpam-5656	177	23	ν	ν	X
ejpam-5656	177	24	−	−	PROPN
ejpam-5656	177	25	l	l	NOUN
ejpam-5656	177	26	+	+	NOUN
ejpam-5656	177	27	1	1	NUM
ejpam-5656	177	28	)	)	PUNCT
ejpam-5656	177	29	and	and	CCONJ
ejpam-5656	177	30	0	0	NUM
ejpam-5656	177	31	≤	≤	NOUN
ejpam-5656	177	32	l.	l.	NOUN
ejpam-5656	177	33	proposition	proposition	NOUN
ejpam-5656	177	34	5	5	NUM
ejpam-5656	177	35	.	.	PUNCT
ejpam-5656	178	1	let	let	VERB
ejpam-5656	178	2	ρ	ρ	PROPN
ejpam-5656	178	3	>	>	X
ejpam-5656	178	4	0	0	PROPN
ejpam-5656	178	5	,	,	PUNCT
ejpam-5656	178	6	µ	µ	PRON
ejpam-5656	178	7	≥	≥	NOUN
ejpam-5656	178	8	0	0	NUM
ejpam-5656	178	9	such	such	ADJ
ejpam-5656	178	10	that	that	SCONJ
ejpam-5656	178	11	µ	µ	ADJ
ejpam-5656	178	12	̸=	̸=	PROPN
ejpam-5656	178	13	1	1	NUM
ejpam-5656	178	14	.	.	PUNCT
ejpam-5656	179	1	then∫	then∫	NOUN
ejpam-5656	179	2	x1	x1	NOUN
ejpam-5656	179	3	x0	x0	PROPN
ejpam-5656	179	4	uν(x	uν(x	SYM
ejpam-5656	179	5	,	,	PUNCT
ejpam-5656	179	6	y	y	PROPN
ejpam-5656	179	7	;	;	PUNCT
ejpam-5656	179	8	ρ;µ	ρ;µ	NUM
ejpam-5656	179	9	)	)	PUNCT
ejpam-5656	179	10	dx	dx	PROPN
ejpam-5656	180	1	=	=	PUNCT
ejpam-5656	180	2	1	1	NUM
ejpam-5656	180	3	ν	ν	NOUN
ejpam-5656	180	4	+	+	NOUN
ejpam-5656	180	5	1	1	NUM
ejpam-5656	180	6	[	[	X
ejpam-5656	180	7	uν+1(x1	uν+1(x1	ADJ
ejpam-5656	180	8	,	,	PUNCT
ejpam-5656	180	9	y	y	NOUN
ejpam-5656	180	10	;	;	PUNCT
ejpam-5656	180	11	ρ;µ)−	ρ;µ)−	NOUN
ejpam-5656	180	12	uν+1(x0	uν+1(x0	NOUN
ejpam-5656	180	13	,	,	PUNCT
ejpam-5656	180	14	y	y	PROPN
ejpam-5656	180	15	;	;	PUNCT
ejpam-5656	180	16	ρ;µ	ρ;µ	NUM
ejpam-5656	180	17	)	)	PUNCT
ejpam-5656	180	18	]	]	PUNCT
ejpam-5656	180	19	.	.	PUNCT
ejpam-5656	181	1	proof	proof	NOUN
ejpam-5656	181	2	.	.	PUNCT
ejpam-5656	182	1	the	the	DET
ejpam-5656	182	2	result	result	NOUN
ejpam-5656	182	3	can	can	AUX
ejpam-5656	182	4	be	be	AUX
ejpam-5656	182	5	readily	readily	ADV
ejpam-5656	182	6	inferred	infer	VERB
ejpam-5656	182	7	from	from	ADP
ejpam-5656	182	8	proposition	proposition	NOUN
ejpam-5656	182	9	4	4	NUM
ejpam-5656	182	10	.	.	PUNCT
ejpam-5656	183	1	in	in	ADP
ejpam-5656	183	2	[	[	X
ejpam-5656	183	3	9	9	NUM
ejpam-5656	183	4	]	]	PUNCT
ejpam-5656	183	5	,	,	PUNCT
ejpam-5656	183	6	the	the	DET
ejpam-5656	183	7	authors	author	NOUN
ejpam-5656	183	8	presented	present	VERB
ejpam-5656	183	9	a	a	DET
ejpam-5656	183	10	general	general	ADJ
ejpam-5656	183	11	approach	approach	NOUN
ejpam-5656	183	12	for	for	ADP
ejpam-5656	183	13	determining	determine	VERB
ejpam-5656	183	14	the	the	DET
ejpam-5656	183	15	appell	appell	ADJ
ejpam-5656	183	16	polynomials	polynomial	NOUN
ejpam-5656	183	17	that	that	PRON
ejpam-5656	183	18	fulfill	fulfill	VERB
ejpam-5656	183	19	the	the	DET
ejpam-5656	183	20	recursive	recursive	ADJ
ejpam-5656	183	21	relations	relation	NOUN
ejpam-5656	183	22	.	.	PUNCT
ejpam-5656	184	1	essentially	essentially	ADV
ejpam-5656	184	2	,	,	PUNCT
ejpam-5656	184	3	provided	provide	VERB
ejpam-5656	184	4	a	a	DET
ejpam-5656	184	5	method	method	NOUN
ejpam-5656	184	6	for	for	ADP
ejpam-5656	184	7	finding	find	VERB
ejpam-5656	184	8	these	these	DET
ejpam-5656	184	9	polynomials	polynomial	NOUN
ejpam-5656	184	10	by	by	ADP
ejpam-5656	184	11	using	use	VERB
ejpam-5656	184	12	a	a	DET
ejpam-5656	184	13	power	power	NOUN
ejpam-5656	184	14	series	series	NOUN
ejpam-5656	184	15	expression	expression	NOUN
ejpam-5656	184	16	.	.	PUNCT
ejpam-5656	185	1	following	follow	VERB
ejpam-5656	185	2	that	that	DET
ejpam-5656	185	3	approach	approach	NOUN
ejpam-5656	185	4	,	,	PUNCT
ejpam-5656	185	5	we	we	PRON
ejpam-5656	185	6	have	have	VERB
ejpam-5656	185	7	dı́az	dı́az	X
ejpam-5656	185	8	et	et	PROPN
ejpam-5656	185	9	al	al	PROPN
ejpam-5656	185	10	.	.	PUNCT
ejpam-5656	185	11	/	/	SYM
ejpam-5656	185	12	eur	eur	PROPN
ejpam-5656	185	13	.	.	PUNCT
ejpam-5656	186	1	j.	j.	PROPN
ejpam-5656	186	2	pure	pure	PROPN
ejpam-5656	186	3	appl	appl	PROPN
ejpam-5656	186	4	.	.	PROPN
ejpam-5656	186	5	math	math	PROPN
ejpam-5656	186	6	,	,	PUNCT
ejpam-5656	186	7	18	18	NUM
ejpam-5656	186	8	(	(	PUNCT
ejpam-5656	186	9	1	1	NUM
ejpam-5656	186	10	)	)	PUNCT
ejpam-5656	186	11	(	(	PUNCT
ejpam-5656	186	12	2025	2025	NUM
ejpam-5656	186	13	)	)	PUNCT
ejpam-5656	186	14	,	,	PUNCT
ejpam-5656	186	15	5656	5656	NUM
ejpam-5656	186	16	10	10	NUM
ejpam-5656	186	17	of	of	ADP
ejpam-5656	186	18	17	17	NUM
ejpam-5656	186	19	φ(ρ	φ(ρ	NUM
ejpam-5656	186	20	,	,	PUNCT
ejpam-5656	186	21	µ	µ	NOUN
ejpam-5656	186	22	,	,	PUNCT
ejpam-5656	186	23	ξ	ξ	NOUN
ejpam-5656	186	24	)	)	PUNCT
ejpam-5656	186	25	=	=	SYM
ejpam-5656	187	1	∞∑	∞∑	PRON
ejpam-5656	187	2	n=0	n=0	SYM
ejpam-5656	187	3	un(ρ;µ	un(ρ;µ	ADJ
ejpam-5656	187	4	)	)	PUNCT
ejpam-5656	187	5	ξn	ξn	NOUN
ejpam-5656	187	6	n	n	X
ejpam-5656	187	7	!	!	PUNCT
ejpam-5656	187	8	.	.	PUNCT
ejpam-5656	188	1	now	now	ADV
ejpam-5656	188	2	,	,	PUNCT
ejpam-5656	188	3	let	let	VERB
ejpam-5656	188	4	ζ	ζ	NOUN
ejpam-5656	188	5	a	a	DET
ejpam-5656	188	6	function	function	NOUN
ejpam-5656	188	7	give	give	VERB
ejpam-5656	188	8	by	by	ADP
ejpam-5656	188	9	taylor	taylor	PROPN
ejpam-5656	188	10	series	series	PROPN
ejpam-5656	188	11	expansion	expansion	NOUN
ejpam-5656	188	12	(	(	PUNCT
ejpam-5656	188	13	in	in	ADP
ejpam-5656	188	14	ξ	ξ	NOUN
ejpam-5656	188	15	)	)	PUNCT
ejpam-5656	188	16	at	at	ADP
ejpam-5656	188	17	the	the	DET
ejpam-5656	188	18	origin	origin	NOUN
ejpam-5656	188	19	,	,	PUNCT
ejpam-5656	188	20	that	that	PRON
ejpam-5656	188	21	is	be	AUX
ejpam-5656	188	22	ζ(ξ	ζ(ξ	PROPN
ejpam-5656	188	23	)	)	PUNCT
ejpam-5656	188	24	:	:	PUNCT
ejpam-5656	189	1	=	=	NOUN
ejpam-5656	189	2	∞∑	∞∑	ADJ
ejpam-5656	189	3	n=0	n=0	NUM
ejpam-5656	189	4	δn	δn	NOUN
ejpam-5656	189	5	ξn	ξn	PROPN
ejpam-5656	189	6	n	n	CCONJ
ejpam-5656	189	7	!	!	PUNCT
ejpam-5656	189	8	,	,	PUNCT
ejpam-5656	189	9	(	(	PUNCT
ejpam-5656	189	10	18	18	NUM
ejpam-5656	189	11	)	)	PUNCT
ejpam-5656	189	12	such	such	ADJ
ejpam-5656	189	13	that	that	SCONJ
ejpam-5656	189	14	φ(ρ	φ(ρ	PROPN
ejpam-5656	189	15	,	,	PUNCT
ejpam-5656	189	16	µ	µ	NOUN
ejpam-5656	189	17	,	,	PUNCT
ejpam-5656	189	18	ξ)ζ(ξ	ξ)ζ(ξ	NOUN
ejpam-5656	189	19	)	)	PUNCT
ejpam-5656	189	20	=	=	SYM
ejpam-5656	189	21	1	1	NUM
ejpam-5656	189	22	,	,	PUNCT
ejpam-5656	189	23	where	where	SCONJ
ejpam-5656	189	24	δn	δn	NOUN
ejpam-5656	189	25	is	be	AUX
ejpam-5656	189	26	a	a	DET
ejpam-5656	189	27	sequence	sequence	NOUN
ejpam-5656	189	28	.	.	PUNCT
ejpam-5656	190	1	then	then	ADV
ejpam-5656	190	2	,	,	PUNCT
ejpam-5656	190	3	applying	apply	VERB
ejpam-5656	190	4	the	the	DET
ejpam-5656	190	5	rules	rule	NOUN
ejpam-5656	190	6	of	of	ADP
ejpam-5656	190	7	cauchy	cauchy	ADJ
ejpam-5656	190	8	product	product	NOUN
ejpam-5656	190	9	(	(	PUNCT
ejpam-5656	190	10	10	10	NUM
ejpam-5656	190	11	)	)	PUNCT
ejpam-5656	190	12	,	,	PUNCT
ejpam-5656	190	13	we	we	PRON
ejpam-5656	190	14	obtain	obtain	VERB
ejpam-5656	190	15	φ(ρ	φ(ρ	NUM
ejpam-5656	190	16	,	,	PUNCT
ejpam-5656	190	17	µ	µ	NOUN
ejpam-5656	190	18	,	,	PUNCT
ejpam-5656	190	19	ξ)ζ(ξ	ξ)ζ(ξ	NOUN
ejpam-5656	190	20	)	)	PUNCT
ejpam-5656	190	21	=	=	PUNCT
ejpam-5656	191	1	∞∑	∞∑	NUM
ejpam-5656	191	2	n=0	n=0	NUM
ejpam-5656	191	3	n∑	n∑	NOUN
ejpam-5656	191	4	k=0	k=0	PROPN
ejpam-5656	191	5	(	(	PUNCT
ejpam-5656	191	6	n	n	X
ejpam-5656	191	7	k	k	X
ejpam-5656	191	8	)	)	PUNCT
ejpam-5656	191	9	uk(ρ;µ)δn−k	uk(ρ;µ)δn−k	PROPN
ejpam-5656	191	10	ξk	ξk	ADP
ejpam-5656	191	11	k	k	PROPN
ejpam-5656	191	12	!	!	PUNCT
ejpam-5656	191	13	.	.	PUNCT
ejpam-5656	192	1	thus	thus	ADV
ejpam-5656	192	2	,	,	PUNCT
ejpam-5656	192	3	n∑	n∑	PRON
ejpam-5656	192	4	k=0	k=0	PROPN
ejpam-5656	192	5	(	(	PUNCT
ejpam-5656	192	6	n	n	X
ejpam-5656	192	7	k	k	X
ejpam-5656	192	8	)	)	PUNCT
ejpam-5656	192	9	uk(ρ;µ)δn−k	uk(ρ;µ)δn−k	PROPN
ejpam-5656	192	10	=	=	PRON
ejpam-5656	192	11			PROPN
ejpam-5656	192	12	1	1	NUM
ejpam-5656	192	13	,	,	PUNCT
ejpam-5656	192	14	for	for	ADP
ejpam-5656	192	15	n	n	NOUN
ejpam-5656	192	16	=	=	SYM
ejpam-5656	192	17	0	0	NUM
ejpam-5656	192	18	,	,	PUNCT
ejpam-5656	192	19	0	0	NUM
ejpam-5656	192	20	,	,	PUNCT
ejpam-5656	192	21	for	for	ADP
ejpam-5656	192	22	n	n	X
ejpam-5656	192	23	>	>	X
ejpam-5656	192	24	0	0	NUM
ejpam-5656	192	25	.	.	PUNCT
ejpam-5656	193	1	hence	hence	ADV
ejpam-5656	193	2	,	,	PUNCT
ejpam-5656	193	3			NUM
ejpam-5656	193	4	δ0	δ0	NOUN
ejpam-5656	193	5	=	=	SYM
ejpam-5656	193	6	1	1	NUM
ejpam-5656	193	7	u0	u0	ADJ
ejpam-5656	193	8	,	,	PUNCT
ejpam-5656	193	9	δn	δn	ADJ
ejpam-5656	193	10	=	=	SYM
ejpam-5656	193	11	−	−	PROPN
ejpam-5656	193	12	1	1	NUM
ejpam-5656	193	13	u0	u0	NOUN
ejpam-5656	193	14	(	(	PUNCT
ejpam-5656	193	15	n∑	n∑	INTJ
ejpam-5656	193	16	k=1	k=1	PROPN
ejpam-5656	193	17	(	(	PUNCT
ejpam-5656	193	18	n	n	X
ejpam-5656	193	19	k	k	NOUN
ejpam-5656	193	20	)	)	PUNCT
ejpam-5656	193	21	uk(ρ;µ)δn−k	uk(ρ;µ)δn−k	PROPN
ejpam-5656	193	22	)	)	PUNCT
ejpam-5656	193	23	,	,	PUNCT
ejpam-5656	193	24	where	where	SCONJ
ejpam-5656	193	25	u0	u0	ADJ
ejpam-5656	193	26	:	:	PUNCT
ejpam-5656	193	27	=	=	SYM
ejpam-5656	193	28	u0(ρ	u0(ρ	PROPN
ejpam-5656	193	29	,	,	PUNCT
ejpam-5656	193	30	µ	µ	NOUN
ejpam-5656	193	31	)	)	PUNCT
ejpam-5656	193	32	.	.	PUNCT
ejpam-5656	194	1	proposition	proposition	NOUN
ejpam-5656	194	2	6	6	NUM
ejpam-5656	194	3	.	.	PUNCT
ejpam-5656	195	1	the	the	DET
ejpam-5656	195	2	following	follow	VERB
ejpam-5656	195	3	identity	identity	NOUN
ejpam-5656	195	4	hold	hold	NOUN
ejpam-5656	195	5	:	:	PUNCT
ejpam-5656	195	6	u0(x	u0(x	NUM
ejpam-5656	195	7	,	,	PUNCT
ejpam-5656	195	8	y	y	PROPN
ejpam-5656	195	9	;	;	PUNCT
ejpam-5656	195	10	ρ;µ	ρ;µ	NUM
ejpam-5656	195	11	)	)	PUNCT
ejpam-5656	195	12	=	=	SYM
ejpam-5656	195	13	1	1	NUM
ejpam-5656	195	14	δ0	δ0	NOUN
ejpam-5656	195	15	.	.	PUNCT
ejpam-5656	196	1	un(x	un(x	PROPN
ejpam-5656	196	2	,	,	PUNCT
ejpam-5656	196	3	y	y	PROPN
ejpam-5656	196	4	;	;	PUNCT
ejpam-5656	196	5	ρ;µ	ρ;µ	NUM
ejpam-5656	196	6	)	)	PUNCT
ejpam-5656	196	7	=	=	PRON
ejpam-5656	196	8	(	(	PUNCT
ejpam-5656	196	9	−1)n	−1)n	PROPN
ejpam-5656	196	10	δn+1	δn+1	PROPN
ejpam-5656	196	11	0	0	NUM
ejpam-5656	196	12	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5656	196	13	h0(x	h0(x	PROPN
ejpam-5656	196	14	,	,	PUNCT
ejpam-5656	196	15	y	y	NOUN
ejpam-5656	196	16	)	)	PUNCT
ejpam-5656	196	17	h1(x	h1(x	PROPN
ejpam-5656	196	18	,	,	PUNCT
ejpam-5656	196	19	y	y	NOUN
ejpam-5656	196	20	)	)	PUNCT
ejpam-5656	196	21	·	·	PUNCT
ejpam-5656	196	22	·	·	PUNCT
ejpam-5656	196	23	·	·	PUNCT
ejpam-5656	196	24	·	·	PUNCT
ejpam-5656	196	25	·	·	PUNCT
ejpam-5656	196	26	·	·	PUNCT
ejpam-5656	197	1	hn−1(x	hn−1(x	VERB
ejpam-5656	197	2	,	,	PUNCT
ejpam-5656	197	3	y	y	NOUN
ejpam-5656	197	4	)	)	PUNCT
ejpam-5656	197	5	hn(x	hn(x	ADP
ejpam-5656	197	6	,	,	PUNCT
ejpam-5656	197	7	y	y	NOUN
ejpam-5656	197	8	)	)	PUNCT
ejpam-5656	197	9	δ0	δ0	NOUN
ejpam-5656	197	10	δ1	δ1	NOUN
ejpam-5656	197	11	·	·	PUNCT
ejpam-5656	197	12	·	·	PUNCT
ejpam-5656	197	13	·	·	PUNCT
ejpam-5656	197	14	·	·	PUNCT
ejpam-5656	197	15	·	·	PUNCT
ejpam-5656	197	16	·	·	PUNCT
ejpam-5656	198	1	δn−1	δn−1	NUM
ejpam-5656	198	2	δn	δn	NOUN
ejpam-5656	198	3	0	0	NUM
ejpam-5656	198	4	δ0	δ0	NOUN
ejpam-5656	198	5	·	·	PUNCT
ejpam-5656	198	6	·	·	PUNCT
ejpam-5656	198	7	·	·	PUNCT
ejpam-5656	198	8	·	·	PUNCT
ejpam-5656	198	9	·	·	PUNCT
ejpam-5656	198	10	·	·	PUNCT
ejpam-5656	198	11	(	(	PUNCT
ejpam-5656	198	12	n−1	n−1	PROPN
ejpam-5656	198	13	1	1	NUM
ejpam-5656	198	14	)	)	PUNCT
ejpam-5656	198	15	δn−2	δn−2	PROPN
ejpam-5656	198	16	(	(	PUNCT
ejpam-5656	198	17	n	n	NOUN
ejpam-5656	198	18	1	1	NUM
ejpam-5656	198	19	)	)	PUNCT
ejpam-5656	198	20	δn−1	δn−1	PROPN
ejpam-5656	198	21	0	0	NUM
ejpam-5656	198	22	0	0	NUM
ejpam-5656	198	23	.	.	PUNCT
ejpam-5656	198	24	.	.	PUNCT
ejpam-5656	198	25	.	.	PUNCT
ejpam-5656	199	1	(	(	PUNCT
ejpam-5656	199	2	n−1	n−1	PROPN
ejpam-5656	199	3	2	2	NUM
ejpam-5656	199	4	)	)	PUNCT
ejpam-5656	199	5	δn−3	δn−3	PROPN
ejpam-5656	199	6	(	(	PUNCT
ejpam-5656	199	7	n	n	NOUN
ejpam-5656	199	8	2	2	X
ejpam-5656	199	9	)	)	PUNCT
ejpam-5656	199	10	δn−2	δn−2	PROPN
ejpam-5656	199	11	...	...	PUNCT
ejpam-5656	199	12	...	...	PUNCT
ejpam-5656	199	13	.	.	PUNCT
ejpam-5656	199	14	.	.	PUNCT
ejpam-5656	199	15	.	.	PUNCT
ejpam-5656	200	1	...	...	PUNCT
ejpam-5656	200	2	...	...	PUNCT
ejpam-5656	201	1	...	...	PUNCT
ejpam-5656	201	2	...	...	PUNCT
ejpam-5656	202	1	0	0	NUM
ejpam-5656	202	2	·	·	PUNCT
ejpam-5656	202	3	·	·	PUNCT
ejpam-5656	202	4	·	·	PUNCT
ejpam-5656	202	5	·	·	PUNCT
ejpam-5656	202	6	·	·	PUNCT
ejpam-5656	202	7	·	·	PUNCT
ejpam-5656	202	8	·	·	PUNCT
ejpam-5656	202	9	·	·	PUNCT
ejpam-5656	202	10	·	·	PUNCT
ejpam-5656	203	1	δ0	δ0	NOUN
ejpam-5656	203	2	(	(	PUNCT
ejpam-5656	203	3	n	n	CCONJ
ejpam-5656	203	4	n−1	n−1	PROPN
ejpam-5656	203	5	)	)	PUNCT
ejpam-5656	203	6	δ1	δ1	NOUN
ejpam-5656	203	7	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5656	203	8	.	.	PUNCT
ejpam-5656	204	1	(	(	PUNCT
ejpam-5656	204	2	19	19	NUM
ejpam-5656	204	3	)	)	PUNCT
ejpam-5656	204	4	dı́az	dı́az	X
ejpam-5656	204	5	et	et	NOUN
ejpam-5656	204	6	al	al	PROPN
ejpam-5656	204	7	.	.	PUNCT
ejpam-5656	204	8	/	/	SYM
ejpam-5656	204	9	eur	eur	PROPN
ejpam-5656	204	10	.	.	PUNCT
ejpam-5656	205	1	j.	j.	PROPN
ejpam-5656	205	2	pure	pure	PROPN
ejpam-5656	205	3	appl	appl	PROPN
ejpam-5656	205	4	.	.	PROPN
ejpam-5656	205	5	math	math	PROPN
ejpam-5656	205	6	,	,	PUNCT
ejpam-5656	205	7	18	18	NUM
ejpam-5656	205	8	(	(	PUNCT
ejpam-5656	205	9	1	1	NUM
ejpam-5656	205	10	)	)	PUNCT
ejpam-5656	205	11	(	(	PUNCT
ejpam-5656	205	12	2025	2025	NUM
ejpam-5656	205	13	)	)	PUNCT
ejpam-5656	205	14	,	,	PUNCT
ejpam-5656	205	15	5656	5656	NUM
ejpam-5656	205	16	11	11	NUM
ejpam-5656	205	17	of	of	ADP
ejpam-5656	205	18	17	17	NUM
ejpam-5656	205	19	proof	proof	NOUN
ejpam-5656	205	20	.	.	PUNCT
ejpam-5656	206	1	observe	observe	VERB
ejpam-5656	206	2	that	that	SCONJ
ejpam-5656	206	3	(	(	PUNCT
ejpam-5656	206	4	∞∑	∞∑	PRON
ejpam-5656	206	5	n=0	n=0	SYM
ejpam-5656	206	6	un(ρ;µ	un(ρ;µ	ADJ
ejpam-5656	206	7	)	)	PUNCT
ejpam-5656	206	8	ξn	ξn	PROPN
ejpam-5656	206	9	n	n	X
ejpam-5656	206	10	!	!	PUNCT
ejpam-5656	206	11	)	)	PUNCT
ejpam-5656	207	1	(	(	PUNCT
ejpam-5656	207	2	∞∑	∞∑	NUM
ejpam-5656	207	3	n=0	n=0	NUM
ejpam-5656	207	4	hn(x	hn(x	X
ejpam-5656	207	5	,	,	PUNCT
ejpam-5656	207	6	y	y	NOUN
ejpam-5656	207	7	)	)	PUNCT
ejpam-5656	207	8	ξn	ξn	NOUN
ejpam-5656	207	9	n	n	NOUN
ejpam-5656	207	10	!	!	PUNCT
ejpam-5656	207	11	)	)	PUNCT
ejpam-5656	208	1	=	=	PUNCT
ejpam-5656	209	1	∞∑	∞∑	PRON
ejpam-5656	209	2	n=0	n=0	NUM
ejpam-5656	209	3	un(x	un(x	NUM
ejpam-5656	209	4	,	,	PUNCT
ejpam-5656	209	5	y	y	PROPN
ejpam-5656	209	6	;	;	PUNCT
ejpam-5656	209	7	ρ;µ	ρ;µ	NUM
ejpam-5656	209	8	)	)	PUNCT
ejpam-5656	209	9	ξn	ξn	NOUN
ejpam-5656	209	10	n	n	X
ejpam-5656	209	11	!	!	PUNCT
ejpam-5656	209	12	.	.	PUNCT
ejpam-5656	210	1	(	(	PUNCT
ejpam-5656	210	2	20	20	X
ejpam-5656	210	3	)	)	PUNCT
ejpam-5656	210	4	multiplying	multiply	VERB
ejpam-5656	210	5	both	both	DET
ejpam-5656	210	6	sides	side	NOUN
ejpam-5656	210	7	of	of	ADP
ejpam-5656	210	8	equation	equation	NOUN
ejpam-5656	210	9	(	(	PUNCT
ejpam-5656	210	10	20	20	NUM
ejpam-5656	210	11	)	)	PUNCT
ejpam-5656	210	12	by	by	ADP
ejpam-5656	210	13	(	(	PUNCT
ejpam-5656	210	14	18	18	NUM
ejpam-5656	210	15	)	)	PUNCT
ejpam-5656	210	16	,	,	PUNCT
ejpam-5656	210	17	we	we	PRON
ejpam-5656	210	18	obtain	obtain	VERB
ejpam-5656	210	19	∞∑	∞∑	NUM
ejpam-5656	210	20	n=0	n=0	NUM
ejpam-5656	210	21	hn(x	hn(x	X
ejpam-5656	210	22	,	,	PUNCT
ejpam-5656	210	23	y	y	NOUN
ejpam-5656	210	24	)	)	PUNCT
ejpam-5656	210	25	ξn	ξn	NOUN
ejpam-5656	210	26	n	n	NOUN
ejpam-5656	210	27	!	!	PUNCT
ejpam-5656	210	28	=	=	NOUN
ejpam-5656	211	1	∞∑	∞∑	PRON
ejpam-5656	211	2	n=0	n=0	NUM
ejpam-5656	211	3	n∑	n∑	NOUN
ejpam-5656	211	4	k=0	k=0	PROPN
ejpam-5656	211	5	(	(	PUNCT
ejpam-5656	211	6	n	n	X
ejpam-5656	211	7	k	k	NOUN
ejpam-5656	211	8	)	)	PUNCT
ejpam-5656	211	9	uk(x	uk(x	ADP
ejpam-5656	211	10	,	,	PUNCT
ejpam-5656	211	11	y	y	PROPN
ejpam-5656	211	12	;	;	PUNCT
ejpam-5656	211	13	ρ;µ)δn−k	ρ;µ)δn−k	X
ejpam-5656	211	14	ξk	ξk	ADP
ejpam-5656	211	15	k	k	X
ejpam-5656	211	16	!	!	PUNCT
ejpam-5656	211	17	.	.	PUNCT
ejpam-5656	212	1	by	by	ADP
ejpam-5656	212	2	multiplying	multiply	VERB
ejpam-5656	212	3	the	the	DET
ejpam-5656	212	4	aforementioned	aforementioned	ADJ
ejpam-5656	212	5	equation	equation	NOUN
ejpam-5656	212	6	,	,	PUNCT
ejpam-5656	212	7	we	we	PRON
ejpam-5656	212	8	arrive	arrive	VERB
ejpam-5656	212	9	at	at	ADP
ejpam-5656	212	10	the	the	DET
ejpam-5656	212	11	subsequent	subsequent	ADJ
ejpam-5656	212	12	infinite	infinite	ADJ
ejpam-5656	212	13	system	system	NOUN
ejpam-5656	212	14	of	of	ADP
ejpam-5656	212	15	equations	equation	NOUN
ejpam-5656	212	16	in	in	ADP
ejpam-5656	212	17	the	the	DET
ejpam-5656	212	18	unknown	unknown	ADJ
ejpam-5656	212	19	variables	variable	NOUN
ejpam-5656	212	20	:	:	PUNCT
ejpam-5656	212	21	h0(x	h0(x	NUM
ejpam-5656	212	22	,	,	PUNCT
ejpam-5656	212	23	y	y	NOUN
ejpam-5656	212	24	)	)	PUNCT
ejpam-5656	212	25	=	=	SYM
ejpam-5656	213	1	u0(x	u0(x	PROPN
ejpam-5656	213	2	,	,	PUNCT
ejpam-5656	213	3	y	y	NOUN
ejpam-5656	213	4	;	;	PUNCT
ejpam-5656	213	5	ρ;µ)δ0	ρ;µ)δ0	PROPN
ejpam-5656	213	6	,	,	PUNCT
ejpam-5656	213	7	h1(x	h1(x	NOUN
ejpam-5656	213	8	,	,	PUNCT
ejpam-5656	213	9	y	y	NOUN
ejpam-5656	213	10	)	)	PUNCT
ejpam-5656	213	11	=	=	SYM
ejpam-5656	214	1	u0(x	u0(x	PROPN
ejpam-5656	214	2	,	,	PUNCT
ejpam-5656	214	3	y	y	PROPN
ejpam-5656	214	4	;	;	PUNCT
ejpam-5656	214	5	ρ;µ)δ1	ρ;µ)δ1	PROPN
ejpam-5656	214	6	+	+	CCONJ
ejpam-5656	214	7	u1(x	u1(x	PROPN
ejpam-5656	214	8	,	,	PUNCT
ejpam-5656	214	9	y	y	NOUN
ejpam-5656	214	10	;	;	PUNCT
ejpam-5656	214	11	ρ;µ)δ0	ρ;µ)δ0	PROPN
ejpam-5656	214	12	,	,	PUNCT
ejpam-5656	214	13	...	...	PUNCT
ejpam-5656	214	14	...	...	PUNCT
ejpam-5656	214	15	...	...	PUNCT
ejpam-5656	215	1	hn(x	hn(x	X
ejpam-5656	215	2	,	,	PUNCT
ejpam-5656	215	3	y	y	NOUN
ejpam-5656	215	4	)	)	PUNCT
ejpam-5656	215	5	=	=	SYM
ejpam-5656	215	6	u0(x	u0(x	PROPN
ejpam-5656	215	7	,	,	PUNCT
ejpam-5656	215	8	y	y	PROPN
ejpam-5656	215	9	;	;	PUNCT
ejpam-5656	215	10	ρ;µ)δn	ρ;µ)δn	PROPN
ejpam-5656	215	11	+	+	CCONJ
ejpam-5656	215	12	(	(	PUNCT
ejpam-5656	215	13	n	n	ADV
ejpam-5656	215	14	1	1	NUM
ejpam-5656	215	15	)	)	PUNCT
ejpam-5656	215	16	u1(x	u1(x	PROPN
ejpam-5656	215	17	,	,	PUNCT
ejpam-5656	215	18	y	y	PRON
ejpam-5656	215	19	;	;	PUNCT
ejpam-5656	215	20	ρ;µ)δ0	ρ;µ)δ0	ADP
ejpam-5656	215	21	+	+	X
ejpam-5656	215	22	·	·	PUNCT
ejpam-5656	215	23	·	·	PUNCT
ejpam-5656	215	24	·	·	PUNCT
ejpam-5656	215	25	+	+	CCONJ
ejpam-5656	215	26	un(x	un(x	NUM
ejpam-5656	215	27	,	,	PUNCT
ejpam-5656	215	28	y	y	NOUN
ejpam-5656	215	29	;	;	PUNCT
ejpam-5656	215	30	ρ;µ)δ0	ρ;µ)δ0	ADP
ejpam-5656	215	31	.	.	PROPN
ejpam-5656	215	32	due	due	ADP
ejpam-5656	215	33	to	to	ADP
ejpam-5656	215	34	the	the	DET
ejpam-5656	215	35	specific	specific	ADJ
ejpam-5656	215	36	structure	structure	NOUN
ejpam-5656	215	37	of	of	ADP
ejpam-5656	215	38	the	the	DET
ejpam-5656	215	39	aforementioned	aforementioned	ADJ
ejpam-5656	215	40	system	system	NOUN
ejpam-5656	215	41	(	(	PUNCT
ejpam-5656	215	42	lower	low	ADJ
ejpam-5656	215	43	triangular	triangular	NOUN
ejpam-5656	215	44	)	)	PUNCT
ejpam-5656	215	45	,	,	PUNCT
ejpam-5656	215	46	we	we	PRON
ejpam-5656	215	47	can	can	AUX
ejpam-5656	215	48	determine	determine	VERB
ejpam-5656	215	49	the	the	DET
ejpam-5656	215	50	unknown	unknown	ADJ
ejpam-5656	215	51	variables	variable	NOUN
ejpam-5656	215	52	un(x	un(x	SYM
ejpam-5656	215	53	,	,	PUNCT
ejpam-5656	215	54	y	y	PROPN
ejpam-5656	215	55	;	;	PUNCT
ejpam-5656	215	56	ρ	ρ	PROPN
ejpam-5656	215	57	,	,	PUNCT
ejpam-5656	215	58	µ	µ	NOUN
ejpam-5656	215	59	)	)	PUNCT
ejpam-5656	215	60	by	by	ADP
ejpam-5656	215	61	exclusively	exclusively	ADV
ejpam-5656	215	62	utilizing	utilize	VERB
ejpam-5656	215	63	the	the	DET
ejpam-5656	215	64	first	first	ADJ
ejpam-5656	215	65	n+1	n+1	PROPN
ejpam-5656	215	66	equations	equation	NOUN
ejpam-5656	215	67	.	.	PUNCT
ejpam-5656	216	1	this	this	PRON
ejpam-5656	216	2	can	can	AUX
ejpam-5656	216	3	be	be	AUX
ejpam-5656	216	4	achieved	achieve	VERB
ejpam-5656	216	5	by	by	ADP
ejpam-5656	216	6	employing	employ	VERB
ejpam-5656	216	7	cramer	cramer	PROPN
ejpam-5656	216	8	’s	’s	PART
ejpam-5656	216	9	rule	rule	NOUN
ejpam-5656	216	10	,	,	PUNCT
ejpam-5656	216	11	which	which	PRON
ejpam-5656	216	12	facilitates	facilitate	VERB
ejpam-5656	216	13	the	the	DET
ejpam-5656	216	14	computation	computation	NOUN
ejpam-5656	216	15	of	of	ADP
ejpam-5656	216	16	the	the	DET
ejpam-5656	216	17	solution	solution	NOUN
ejpam-5656	216	18	.	.	PUNCT
ejpam-5656	217	1	un(x	un(x	PROPN
ejpam-5656	217	2	,	,	PUNCT
ejpam-5656	217	3	y	y	PROPN
ejpam-5656	217	4	;	;	PUNCT
ejpam-5656	217	5	ρ	ρ	PROPN
ejpam-5656	217	6	,	,	PUNCT
ejpam-5656	217	7	µ	µ	NOUN
ejpam-5656	217	8	)	)	PUNCT
ejpam-5656	217	9	=	=	SYM
ejpam-5656	217	10	1	1	NUM
ejpam-5656	217	11	δn+1	δn+1	NOUN
ejpam-5656	217	12	0	0	NUM
ejpam-5656	217	13	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5656	217	14	δ0	δ0	NOUN
ejpam-5656	217	15	0	0	NUM
ejpam-5656	217	16	0	0	NUM
ejpam-5656	217	17	0	0	NUM
ejpam-5656	217	18	·	·	PUNCT
ejpam-5656	217	19	·	·	PUNCT
ejpam-5656	217	20	·	·	PUNCT
ejpam-5656	218	1	h0(x	h0(x	NUM
ejpam-5656	218	2	,	,	PUNCT
ejpam-5656	218	3	y	y	NOUN
ejpam-5656	218	4	)	)	PUNCT
ejpam-5656	218	5	δ1	δ1	NOUN
ejpam-5656	218	6	δ0	δ0	NOUN
ejpam-5656	218	7	0	0	NUM
ejpam-5656	218	8	0	0	NUM
ejpam-5656	218	9	·	·	PUNCT
ejpam-5656	218	10	·	·	PUNCT
ejpam-5656	218	11	·	·	PUNCT
ejpam-5656	219	1	h1(x	h1(x	X
ejpam-5656	219	2	,	,	PUNCT
ejpam-5656	219	3	y	y	NOUN
ejpam-5656	219	4	)	)	PUNCT
ejpam-5656	219	5	δ2	δ2	VERB
ejpam-5656	219	6	(	(	PUNCT
ejpam-5656	219	7	2	2	NUM
ejpam-5656	219	8	1	1	NUM
ejpam-5656	219	9	)	)	PUNCT
ejpam-5656	219	10	δ1	δ1	NOUN
ejpam-5656	219	11	δ0	δ0	NOUN
ejpam-5656	219	12	0	0	NUM
ejpam-5656	219	13	·	·	PUNCT
ejpam-5656	219	14	·	·	PUNCT
ejpam-5656	219	15	·	·	PUNCT
ejpam-5656	220	1	h2(x	h2(x	NUM
ejpam-5656	220	2	,	,	PUNCT
ejpam-5656	220	3	y	y	PROPN
ejpam-5656	220	4	)	)	PUNCT
ejpam-5656	220	5	...	...	PUNCT
ejpam-5656	220	6	...	...	PUNCT
ejpam-5656	220	7	.	.	PUNCT
ejpam-5656	220	8	.	.	PUNCT
ejpam-5656	220	9	.	.	PUNCT
ejpam-5656	221	1	...	...	PUNCT
ejpam-5656	222	1	δn−1	δn−1	NUM
ejpam-5656	222	2	(	(	PUNCT
ejpam-5656	222	3	n−1	n−1	PROPN
ejpam-5656	222	4	1	1	NUM
ejpam-5656	222	5	)	)	PUNCT
ejpam-5656	222	6	δn−2	δn−2	PROPN
ejpam-5656	222	7	(	(	PUNCT
ejpam-5656	222	8	n−2	n−2	PROPN
ejpam-5656	222	9	2	2	NUM
ejpam-5656	222	10	)	)	PUNCT
ejpam-5656	222	11	δn−3	δn−3	PROPN
ejpam-5656	222	12	·	·	PUNCT
ejpam-5656	222	13	·	·	PUNCT
ejpam-5656	222	14	·	·	PUNCT
ejpam-5656	222	15	·	·	PUNCT
ejpam-5656	222	16	·	·	PUNCT
ejpam-5656	222	17	·	·	PUNCT
ejpam-5656	222	18	hn−1(x	hn−1(x	VERB
ejpam-5656	222	19	,	,	PUNCT
ejpam-5656	222	20	y	y	NOUN
ejpam-5656	222	21	)	)	PUNCT
ejpam-5656	222	22	δn	δn	NOUN
ejpam-5656	222	23	(	(	PUNCT
ejpam-5656	222	24	n	n	NOUN
ejpam-5656	222	25	1	1	NUM
ejpam-5656	222	26	)	)	PUNCT
ejpam-5656	222	27	δn−1	δn−1	PROPN
ejpam-5656	222	28	(	(	PUNCT
ejpam-5656	222	29	n	n	NOUN
ejpam-5656	222	30	2	2	X
ejpam-5656	222	31	)	)	PUNCT
ejpam-5656	222	32	δn−2	δn−2	PROPN
ejpam-5656	222	33	(	(	PUNCT
ejpam-5656	222	34	n	n	NOUN
ejpam-5656	222	35	3	3	NUM
ejpam-5656	222	36	)	)	PUNCT
ejpam-5656	222	37	δn−3	δn−3	PROPN
ejpam-5656	222	38	·	·	PUNCT
ejpam-5656	222	39	·	·	PUNCT
ejpam-5656	222	40	·	·	PUNCT
ejpam-5656	222	41	hn(x	hn(x	NUM
ejpam-5656	222	42	,	,	PUNCT
ejpam-5656	222	43	y	y	PROPN
ejpam-5656	222	44	)	)	PUNCT
ejpam-5656	222	45	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5656	222	46	.	.	PUNCT
ejpam-5656	223	1	by	by	ADP
ejpam-5656	223	2	transposition	transposition	NOUN
ejpam-5656	223	3	of	of	ADP
ejpam-5656	223	4	the	the	DET
ejpam-5656	223	5	previous	previous	ADJ
ejpam-5656	223	6	,	,	PUNCT
ejpam-5656	223	7	we	we	PRON
ejpam-5656	223	8	obtain	obtain	VERB
ejpam-5656	223	9	un(x	un(x	NOUN
ejpam-5656	223	10	,	,	PUNCT
ejpam-5656	223	11	y	y	PROPN
ejpam-5656	223	12	;	;	PUNCT
ejpam-5656	223	13	ρ	ρ	PROPN
ejpam-5656	223	14	,	,	PUNCT
ejpam-5656	223	15	µ	µ	NOUN
ejpam-5656	223	16	)	)	PUNCT
ejpam-5656	223	17	=	=	SYM
ejpam-5656	223	18	1	1	NUM
ejpam-5656	223	19	δn+1	δn+1	NOUN
ejpam-5656	223	20	0	0	NUM
ejpam-5656	223	21	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-5656	223	22	δ0	δ0	NOUN
ejpam-5656	223	23	δ1	δ1	NOUN
ejpam-5656	223	24	δ2	δ2	VERB
ejpam-5656	223	25	·	·	PUNCT
ejpam-5656	223	26	·	·	PUNCT
ejpam-5656	223	27	·	·	PUNCT
ejpam-5656	224	1	δn−1	δn−1	NUM
ejpam-5656	224	2	δn	δn	NOUN
ejpam-5656	224	3	0	0	NUM
ejpam-5656	224	4	δ0	δ0	NOUN
ejpam-5656	224	5	(	(	PUNCT
ejpam-5656	224	6	2	2	NUM
ejpam-5656	224	7	1	1	NUM
ejpam-5656	224	8	)	)	PUNCT
ejpam-5656	224	9	δ1	δ1	NOUN
ejpam-5656	224	10	·	·	PUNCT
ejpam-5656	224	11	·	·	PUNCT
ejpam-5656	224	12	·	·	PUNCT
ejpam-5656	224	13	(	(	PUNCT
ejpam-5656	224	14	n−1	n−1	PROPN
ejpam-5656	224	15	1	1	NUM
ejpam-5656	224	16	)	)	PUNCT
ejpam-5656	224	17	δn−2	δn−2	PROPN
ejpam-5656	224	18	(	(	PUNCT
ejpam-5656	224	19	n	n	NOUN
ejpam-5656	224	20	1	1	NUM
ejpam-5656	224	21	)	)	PUNCT
ejpam-5656	224	22	γn−1	γn−1	NOUN
ejpam-5656	224	23	0	0	NUM
ejpam-5656	224	24	0	0	NUM
ejpam-5656	224	25	δ0	δ0	NOUN
ejpam-5656	224	26	·	·	PUNCT
ejpam-5656	224	27	·	·	PUNCT
ejpam-5656	224	28	·	·	PUNCT
ejpam-5656	224	29	(	(	PUNCT
ejpam-5656	224	30	n−1	n−1	PROPN
ejpam-5656	224	31	2	2	NUM
ejpam-5656	224	32	)	)	PUNCT
ejpam-5656	224	33	δn−3	δn−3	PROPN
ejpam-5656	224	34	(	(	PUNCT
ejpam-5656	224	35	n	n	NOUN
ejpam-5656	224	36	2	2	X
ejpam-5656	224	37	)	)	PUNCT
ejpam-5656	224	38	δn−2	δn−2	PROPN
ejpam-5656	224	39	·	·	PUNCT
ejpam-5656	224	40	·	·	PUNCT
ejpam-5656	224	41	·	·	PUNCT
ejpam-5656	224	42	.	.	PUNCT
ejpam-5656	224	43	.	.	PUNCT
ejpam-5656	224	44	·	·	PUNCT
ejpam-5656	224	45	·	·	PUNCT
ejpam-5656	224	46	·	·	PUNCT
ejpam-5656	224	47	·	·	PUNCT
ejpam-5656	224	48	·	·	PUNCT
ejpam-5656	224	49	·	·	PUNCT
ejpam-5656	224	50	·	·	PUNCT
ejpam-5656	224	51	·	·	PUNCT
ejpam-5656	224	52	·	·	PUNCT
ejpam-5656	224	53	·	·	PUNCT
ejpam-5656	224	54	·	·	PUNCT
ejpam-5656	224	55	·	·	PUNCT
ejpam-5656	224	56	·	·	PUNCT
ejpam-5656	224	57	0	0	NUM
ejpam-5656	224	58	0	0	NUM
ejpam-5656	224	59	0	0	NUM
ejpam-5656	224	60	·	·	PUNCT
ejpam-5656	224	61	·	·	PUNCT
ejpam-5656	224	62	·	·	PUNCT
ejpam-5656	225	1	δ0	δ0	NOUN
ejpam-5656	225	2	(	(	PUNCT
ejpam-5656	225	3	n	n	CCONJ
ejpam-5656	225	4	n−1	n−1	PROPN
ejpam-5656	225	5	)	)	PUNCT
ejpam-5656	225	6	δ1	δ1	NOUN
ejpam-5656	225	7	h0(x	h0(x	PROPN
ejpam-5656	225	8	)	)	PUNCT
ejpam-5656	225	9	h1(x	h1(x	NOUN
ejpam-5656	225	10	)	)	PUNCT
ejpam-5656	225	11	h2(x	h2(x	PROPN
ejpam-5656	225	12	)	)	PUNCT
ejpam-5656	225	13	·	·	PUNCT
ejpam-5656	225	14	·	·	PUNCT
ejpam-5656	225	15	·	·	PUNCT
ejpam-5656	225	16	hn−1(x	hn−1(x	NOUN
ejpam-5656	225	17	)	)	PUNCT
ejpam-5656	225	18	hn(x	hn(x	ADP
ejpam-5656	225	19	)	)	PUNCT
ejpam-5656	225	20	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5656	225	21	.	.	PUNCT
ejpam-5656	226	1	now	now	ADV
ejpam-5656	226	2	,	,	PUNCT
ejpam-5656	226	3	by	by	ADP
ejpam-5656	226	4	moving	move	VERB
ejpam-5656	226	5	the	the	DET
ejpam-5656	226	6	ith	ith	PROPN
ejpam-5656	226	7	row	row	NOUN
ejpam-5656	226	8	to	to	ADP
ejpam-5656	226	9	the	the	DET
ejpam-5656	226	10	(	(	PUNCT
ejpam-5656	226	11	i+1)th	i+1)th	NOUN
ejpam-5656	226	12	position	position	NOUN
ejpam-5656	226	13	,	,	PUNCT
ejpam-5656	226	14	where	where	SCONJ
ejpam-5656	226	15	i	i	PRON
ejpam-5656	226	16	=	=	NOUN
ejpam-5656	226	17	1	1	NUM
ejpam-5656	226	18	,	,	PUNCT
ejpam-5656	226	19	2	2	NUM
ejpam-5656	226	20	,	,	PUNCT
ejpam-5656	226	21	·	·	PUNCT
ejpam-5656	226	22	·	·	PUNCT
ejpam-5656	226	23	·	·	PUNCT
ejpam-5656	226	24	,	,	PUNCT
ejpam-5656	226	25	n	n	CCONJ
ejpam-5656	226	26	,	,	PUNCT
ejpam-5656	226	27	we	we	PRON
ejpam-5656	226	28	get	get	VERB
ejpam-5656	226	29	the	the	DET
ejpam-5656	226	30	desired	desire	VERB
ejpam-5656	226	31	result	result	NOUN
ejpam-5656	226	32	asserted	assert	VERB
ejpam-5656	226	33	.	.	PUNCT
ejpam-5656	227	1	now	now	ADV
ejpam-5656	227	2	,	,	PUNCT
ejpam-5656	227	3	we	we	PRON
ejpam-5656	227	4	will	will	AUX
ejpam-5656	227	5	proceed	proceed	VERB
ejpam-5656	227	6	with	with	ADP
ejpam-5656	227	7	the	the	DET
ejpam-5656	227	8	determinant	determinant	ADJ
ejpam-5656	227	9	representation	representation	NOUN
ejpam-5656	227	10	for	for	ADP
ejpam-5656	227	11	the	the	DET
ejpam-5656	227	12	one	one	NUM
ejpam-5656	227	13	specific	specific	ADJ
ejpam-5656	227	14	case	case	NOUN
ejpam-5656	227	15	of	of	ADP
ejpam-5656	227	16	the	the	DET
ejpam-5656	227	17	polynomials	polynomial	NOUN
ejpam-5656	227	18	illustrated	illustrate	VERB
ejpam-5656	227	19	in	in	ADP
ejpam-5656	227	20	examples	example	NOUN
ejpam-5656	227	21	1	1	NUM
ejpam-5656	227	22	.	.	PUNCT
ejpam-5656	227	23	dı́az	dı́az	VERB
ejpam-5656	227	24	et	et	PROPN
ejpam-5656	227	25	al	al	PROPN
ejpam-5656	227	26	.	.	PUNCT
ejpam-5656	227	27	/	/	SYM
ejpam-5656	227	28	eur	eur	PROPN
ejpam-5656	227	29	.	.	PUNCT
ejpam-5656	228	1	j.	j.	PROPN
ejpam-5656	228	2	pure	pure	PROPN
ejpam-5656	228	3	appl	appl	PROPN
ejpam-5656	228	4	.	.	PROPN
ejpam-5656	228	5	math	math	PROPN
ejpam-5656	228	6	,	,	PUNCT
ejpam-5656	228	7	18	18	NUM
ejpam-5656	228	8	(	(	PUNCT
ejpam-5656	228	9	1	1	NUM
ejpam-5656	228	10	)	)	PUNCT
ejpam-5656	228	11	(	(	PUNCT
ejpam-5656	228	12	2025	2025	NUM
ejpam-5656	228	13	)	)	PUNCT
ejpam-5656	228	14	,	,	PUNCT
ejpam-5656	228	15	5656	5656	NUM
ejpam-5656	228	16	12	12	NUM
ejpam-5656	228	17	of	of	ADP
ejpam-5656	228	18	17	17	NUM
ejpam-5656	228	19	example	example	NOUN
ejpam-5656	228	20	3	3	NUM
ejpam-5656	228	21	.	.	X
ejpam-5656	229	1	for	for	ADP
ejpam-5656	229	2	ρ	ρ	PROPN
ejpam-5656	229	3	=	=	SYM
ejpam-5656	229	4	1	1	NUM
ejpam-5656	229	5	and	and	CCONJ
ejpam-5656	229	6	µ	µ	X
ejpam-5656	229	7	=	=	SYM
ejpam-5656	229	8	2	2	NUM
ejpam-5656	229	9	,	,	PUNCT
ejpam-5656	229	10	we	we	PRON
ejpam-5656	229	11	have	have	VERB
ejpam-5656	229	12	u0(x	u0(x	NUM
ejpam-5656	229	13	,	,	PUNCT
ejpam-5656	229	14	y	y	PROPN
ejpam-5656	229	15	;	;	PUNCT
ejpam-5656	229	16	1	1	NUM
ejpam-5656	229	17	;	;	PUNCT
ejpam-5656	229	18	2	2	X
ejpam-5656	229	19	)	)	PUNCT
ejpam-5656	229	20	=	=	SYM
ejpam-5656	229	21	1	1	NUM
ejpam-5656	229	22	,	,	PUNCT
ejpam-5656	229	23	u1(x	u1(x	PROPN
ejpam-5656	229	24	,	,	PUNCT
ejpam-5656	229	25	y	y	PROPN
ejpam-5656	229	26	;	;	PUNCT
ejpam-5656	229	27	1	1	NUM
ejpam-5656	229	28	;	;	PUNCT
ejpam-5656	229	29	2	2	X
ejpam-5656	229	30	)	)	PUNCT
ejpam-5656	229	31	=	=	SYM
ejpam-5656	229	32	−	−	PROPN
ejpam-5656	229	33	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5656	229	34	1	1	NUM
ejpam-5656	229	35	x	x	SYM
ejpam-5656	229	36	1	1	NUM
ejpam-5656	229	37	1	1	NUM
ejpam-5656	229	38	2	2	NUM
ejpam-5656	229	39	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5656	229	40	,	,	PUNCT
ejpam-5656	229	41	u2(x	u2(x	PROPN
ejpam-5656	229	42	,	,	PUNCT
ejpam-5656	229	43	y	y	PROPN
ejpam-5656	229	44	;	;	PUNCT
ejpam-5656	229	45	1	1	NUM
ejpam-5656	229	46	;	;	PUNCT
ejpam-5656	229	47	2	2	X
ejpam-5656	229	48	)	)	PUNCT
ejpam-5656	229	49	=	=	PUNCT
ejpam-5656	230	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5656	230	2	1	1	NUM
ejpam-5656	230	3	x	x	SYM
ejpam-5656	230	4	x2	x2	NOUN
ejpam-5656	231	1	+	+	CCONJ
ejpam-5656	231	2	2y	2y	NUM
ejpam-5656	231	3	1	1	NUM
ejpam-5656	231	4	1	1	NUM
ejpam-5656	231	5	2	2	NUM
ejpam-5656	231	6	1	1	NUM
ejpam-5656	231	7	3	3	NUM
ejpam-5656	231	8	0	0	NUM
ejpam-5656	231	9	1	1	NUM
ejpam-5656	231	10	1	1	NUM
ejpam-5656	231	11	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5656	231	12	,	,	PUNCT
ejpam-5656	231	13	u3(x	u3(x	PROPN
ejpam-5656	231	14	,	,	PUNCT
ejpam-5656	231	15	y	y	PROPN
ejpam-5656	231	16	;	;	PUNCT
ejpam-5656	231	17	1	1	NUM
ejpam-5656	231	18	;	;	PUNCT
ejpam-5656	231	19	2	2	X
ejpam-5656	231	20	)	)	PUNCT
ejpam-5656	231	21	=	=	SYM
ejpam-5656	231	22	−	−	PROPN
ejpam-5656	231	23	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5656	231	24	1	1	NUM
ejpam-5656	231	25	x	x	SYM
ejpam-5656	231	26	x2	x2	NOUN
ejpam-5656	232	1	+	+	CCONJ
ejpam-5656	232	2	2y	2y	ADJ
ejpam-5656	232	3	x3	x3	VERB
ejpam-5656	233	1	+	+	CCONJ
ejpam-5656	233	2	6xy	6xy	ADJ
ejpam-5656	233	3	1	1	NUM
ejpam-5656	233	4	1	1	NUM
ejpam-5656	233	5	2	2	NUM
ejpam-5656	233	6	1	1	NUM
ejpam-5656	233	7	3	3	NUM
ejpam-5656	233	8	1	1	NUM
ejpam-5656	233	9	4	4	NUM
ejpam-5656	233	10	0	0	NUM
ejpam-5656	233	11	1	1	NUM
ejpam-5656	233	12	1	1	NUM
ejpam-5656	233	13	1	1	NUM
ejpam-5656	233	14	0	0	NUM
ejpam-5656	233	15	0	0	NUM
ejpam-5656	233	16	1	1	NUM
ejpam-5656	233	17	3	3	NUM
ejpam-5656	233	18	2	2	NUM
ejpam-5656	233	19	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	NOUN
ejpam-5656	233	20	.	.	PUNCT
ejpam-5656	234	1	example	example	NOUN
ejpam-5656	235	1	4	4	NUM
ejpam-5656	235	2	.	.	PUNCT
ejpam-5656	235	3	when	when	SCONJ
ejpam-5656	235	4	y	y	PROPN
ejpam-5656	235	5	=	=	SYM
ejpam-5656	235	6	0	0	PROPN
ejpam-5656	235	7	,	,	PUNCT
ejpam-5656	235	8	with	with	ADP
ejpam-5656	235	9	ρ	ρ	PROPN
ejpam-5656	235	10	=	=	SYM
ejpam-5656	235	11	1	1	NUM
ejpam-5656	235	12	and	and	CCONJ
ejpam-5656	235	13	µ	µ	X
ejpam-5656	235	14	=	=	SYM
ejpam-5656	235	15	2	2	NUM
ejpam-5656	235	16	,	,	PUNCT
ejpam-5656	235	17	the	the	DET
ejpam-5656	235	18	bernoulli	bernoulli	NOUN
ejpam-5656	235	19	polynomials	polynomial	NOUN
ejpam-5656	235	20	are	be	AUX
ejpam-5656	235	21	expressed	express	VERB
ejpam-5656	235	22	in	in	ADP
ejpam-5656	235	23	determinant	determinant	ADJ
ejpam-5656	235	24	form	form	NOUN
ejpam-5656	235	25	as	as	SCONJ
ejpam-5656	235	26	shown	show	VERB
ejpam-5656	235	27	in	in	ADP
ejpam-5656	235	28	(	(	PUNCT
ejpam-5656	235	29	3	3	NUM
ejpam-5656	235	30	)	)	PUNCT
ejpam-5656	235	31	.	.	PUNCT
ejpam-5656	236	1	to	to	PART
ejpam-5656	236	2	better	well	ADV
ejpam-5656	236	3	understand	understand	VERB
ejpam-5656	236	4	the	the	DET
ejpam-5656	236	5	following	follow	VERB
ejpam-5656	236	6	result	result	NOUN
ejpam-5656	236	7	,	,	PUNCT
ejpam-5656	236	8	it	it	PRON
ejpam-5656	236	9	is	be	AUX
ejpam-5656	236	10	important	important	ADJ
ejpam-5656	236	11	to	to	PART
ejpam-5656	236	12	recall	recall	VERB
ejpam-5656	236	13	that	that	SCONJ
ejpam-5656	236	14	the	the	DET
ejpam-5656	236	15	apostoltype	apostoltype	ADJ
ejpam-5656	236	16	hermite	hermite	ADJ
ejpam-5656	236	17	-	-	PUNCT
ejpam-5656	236	18	bernoulli	bernoulli	NOUN
ejpam-5656	236	19	polynomials	polynomial	NOUN
ejpam-5656	236	20	are	be	AUX
ejpam-5656	236	21	given	give	VERB
ejpam-5656	236	22	by	by	ADP
ejpam-5656	236	23	(	(	PUNCT
ejpam-5656	236	24	refer	refer	VERB
ejpam-5656	236	25	to	to	ADP
ejpam-5656	236	26	[	[	X
ejpam-5656	236	27	12	12	NUM
ejpam-5656	236	28	]	]	PUNCT
ejpam-5656	236	29	):	):	PUNCT
ejpam-5656	236	30	ξexξ+yξ2	ξexξ+yξ2	PUNCT
ejpam-5656	237	1	λeξ	λeξ	NOUN
ejpam-5656	237	2	−	−	NOUN
ejpam-5656	237	3	1	1	NUM
ejpam-5656	237	4	=	=	SYM
ejpam-5656	237	5	∞∑	∞∑	NUM
ejpam-5656	237	6	ν=0	ν=0	DET
ejpam-5656	237	7	bν(x	bν(x	NOUN
ejpam-5656	237	8	,	,	PUNCT
ejpam-5656	237	9	y;λ	y;λ	PROPN
ejpam-5656	237	10	)	)	PUNCT
ejpam-5656	237	11	ξν	ξν	ADP
ejpam-5656	237	12	ν	ν	PROPN
ejpam-5656	237	13	!	!	PROPN
ejpam-5656	237	14	,	,	PUNCT
ejpam-5656	237	15	|ξ	|ξ	X
ejpam-5656	237	16	+	+	CCONJ
ejpam-5656	237	17	ln(λ)|	ln(λ)|	X
ejpam-5656	237	18	<	<	X
ejpam-5656	237	19	2π	2π	NOUN
ejpam-5656	237	20	,	,	PUNCT
ejpam-5656	237	21	and	and	CCONJ
ejpam-5656	237	22	the	the	DET
ejpam-5656	237	23	apostol	apostol	NOUN
ejpam-5656	237	24	-	-	PUNCT
ejpam-5656	237	25	type	type	NOUN
ejpam-5656	237	26	hermite	hermite	ADJ
ejpam-5656	237	27	-	-	PUNCT
ejpam-5656	237	28	euler	euler	NOUN
ejpam-5656	237	29	polynomials	polynomial	NOUN
ejpam-5656	237	30	are	be	AUX
ejpam-5656	237	31	given	give	VERB
ejpam-5656	237	32	by	by	ADP
ejpam-5656	237	33	(	(	PUNCT
ejpam-5656	237	34	see	see	VERB
ejpam-5656	237	35	[	[	X
ejpam-5656	237	36	19	19	NUM
ejpam-5656	237	37	]	]	PUNCT
ejpam-5656	237	38	):	):	PUNCT
ejpam-5656	237	39	2exξ+yξ2	2exξ+yξ2	NUM
ejpam-5656	237	40	λeξ	λeξ	NOUN
ejpam-5656	237	41	+	+	CCONJ
ejpam-5656	237	42	1	1	NUM
ejpam-5656	237	43	=	=	SYM
ejpam-5656	237	44	∞∑	∞∑	NUM
ejpam-5656	237	45	ν=0	ν=0	NOUN
ejpam-5656	237	46	eν(x	eν(x	NOUN
ejpam-5656	237	47	,	,	PUNCT
ejpam-5656	237	48	y;λ	y;λ	PROPN
ejpam-5656	237	49	)	)	PUNCT
ejpam-5656	237	50	ξν	ξν	ADP
ejpam-5656	237	51	ν	ν	PROPN
ejpam-5656	237	52	!	!	PROPN
ejpam-5656	237	53	,	,	PUNCT
ejpam-5656	237	54	|ξ	|ξ	X
ejpam-5656	237	55	+	+	CCONJ
ejpam-5656	237	56	ln(λ)|	ln(λ)|	X
ejpam-5656	237	57	<	<	X
ejpam-5656	237	58	π	π	PROPN
ejpam-5656	237	59	.	.	PUNCT
ejpam-5656	237	60	proposition	proposition	NOUN
ejpam-5656	237	61	7	7	NUM
ejpam-5656	237	62	.	.	PUNCT
ejpam-5656	238	1	let	let	VERB
ejpam-5656	238	2	µ	µ	X
ejpam-5656	238	3	>	>	ADP
ejpam-5656	238	4	1	1	NUM
ejpam-5656	238	5	.	.	PUNCT
ejpam-5656	239	1	then	then	ADV
ejpam-5656	239	2	,	,	PUNCT
ejpam-5656	239	3	uν(x	uν(x	ADV
ejpam-5656	239	4	,	,	PUNCT
ejpam-5656	239	5	y	y	PROPN
ejpam-5656	239	6	;	;	PUNCT
ejpam-5656	239	7	ρ;µ	ρ;µ	NUM
ejpam-5656	239	8	)	)	PUNCT
ejpam-5656	239	9	=	=	SYM
ejpam-5656	239	10	1	1	NUM
ejpam-5656	239	11	1−	1−	NUM
ejpam-5656	239	12	µ	µ	X
ejpam-5656	239	13	[	[	PUNCT
ejpam-5656	239	14	(	(	PUNCT
ejpam-5656	239	15	2−	2−	NUM
ejpam-5656	239	16	µ)eν(x	µ)eν(x	NOUN
ejpam-5656	239	17	,	,	PUNCT
ejpam-5656	239	18	y;λ)−	y;λ)−	PROPN
ejpam-5656	239	19	µ	µ	PROPN
ejpam-5656	239	20	2	2	NUM
ejpam-5656	239	21	bν(x	bν(x	NOUN
ejpam-5656	239	22	,	,	PUNCT
ejpam-5656	239	23	y;−λ	y;−λ	PROPN
ejpam-5656	239	24	)	)	PUNCT
ejpam-5656	239	25	]	]	PUNCT
ejpam-5656	239	26	,	,	PUNCT
ejpam-5656	239	27	where	where	SCONJ
ejpam-5656	239	28	λ	λ	X
ejpam-5656	239	29	:	:	PUNCT
ejpam-5656	239	30	=	=	SYM
ejpam-5656	239	31	ρ	ρ	PROPN
ejpam-5656	239	32	1−	1−	NUM
ejpam-5656	239	33	µ	µ	NOUN
ejpam-5656	239	34	.	.	PUNCT
ejpam-5656	240	1	proof	proof	NOUN
ejpam-5656	240	2	.	.	PUNCT
ejpam-5656	241	1	note	note	VERB
ejpam-5656	241	2	that	that	SCONJ
ejpam-5656	241	3	,	,	PUNCT
ejpam-5656	241	4	2−	2−	NUM
ejpam-5656	241	5	µ+	µ+	X
ejpam-5656	241	6	µ	µ	PROPN
ejpam-5656	241	7	2	2	NUM
ejpam-5656	241	8	ξ	ξ	NOUN
ejpam-5656	241	9	ρeξ	ρeξ	NOUN
ejpam-5656	241	10	+	+	CCONJ
ejpam-5656	241	11	(	(	PUNCT
ejpam-5656	241	12	1−	1−	NUM
ejpam-5656	241	13	µ	µ	NUM
ejpam-5656	241	14	)	)	PUNCT
ejpam-5656	241	15	=	=	PUNCT
ejpam-5656	241	16	(	(	PUNCT
ejpam-5656	241	17	1−	1−	NUM
ejpam-5656	241	18	µ	µ	NUM
ejpam-5656	241	19	)	)	PUNCT
ejpam-5656	242	1	+	+	CCONJ
ejpam-5656	242	2	1	1	NUM
ejpam-5656	242	3	+	+	SYM
ejpam-5656	242	4	µ	µ	DET
ejpam-5656	242	5	2	2	NUM
ejpam-5656	242	6	ξ	ξ	PROPN
ejpam-5656	242	7	(	(	PUNCT
ejpam-5656	242	8	1−	1−	NUM
ejpam-5656	242	9	µ	µ	NUM
ejpam-5656	242	10	)	)	PUNCT
ejpam-5656	242	11	(	(	PUNCT
ejpam-5656	242	12	ρ	ρ	PROPN
ejpam-5656	242	13	1−	1−	NUM
ejpam-5656	242	14	µ	µ	PRON
ejpam-5656	242	15	eξ	eξ	NOUN
ejpam-5656	242	16	+	+	NOUN
ejpam-5656	242	17	1	1	NUM
ejpam-5656	242	18	)	)	PUNCT
ejpam-5656	242	19	=	=	SYM
ejpam-5656	243	1	1	1	NUM
ejpam-5656	243	2	+	+	NUM
ejpam-5656	243	3	1	1	NUM
ejpam-5656	243	4	+	+	SYM
ejpam-5656	243	5	µ	µ	PRON
ejpam-5656	243	6	2	2	NUM
ejpam-5656	243	7	ξ	ξ	PROPN
ejpam-5656	243	8	1−	1−	NUM
ejpam-5656	243	9	µ	µ	PROPN
ejpam-5656	243	10	ρ	ρ	PROPN
ejpam-5656	243	11	1−	1−	NUM
ejpam-5656	243	12	µ	µ	PRON
ejpam-5656	243	13	eξ	eξ	NOUN
ejpam-5656	243	14	+	+	NOUN
ejpam-5656	243	15	1	1	NUM
ejpam-5656	243	16	=	=	SYM
ejpam-5656	243	17	1	1	NUM
ejpam-5656	243	18	+	+	NUM
ejpam-5656	243	19	2	2	NUM
ejpam-5656	243	20	+	+	CCONJ
ejpam-5656	243	21	µξ	µξ	ADP
ejpam-5656	243	22	2(1−	2(1−	NUM
ejpam-5656	243	23	µ	µ	NUM
ejpam-5656	243	24	)	)	PUNCT
ejpam-5656	243	25	ρ	ρ	PROPN
ejpam-5656	243	26	1−	1−	NUM
ejpam-5656	243	27	µ	µ	PRON
ejpam-5656	243	28	eξ	eξ	NOUN
ejpam-5656	243	29	+	+	NOUN
ejpam-5656	243	30	1	1	NUM
ejpam-5656	243	31	.	.	PUNCT
ejpam-5656	243	32	dı́az	dı́az	VERB
ejpam-5656	243	33	et	et	PROPN
ejpam-5656	243	34	al	al	PROPN
ejpam-5656	243	35	.	.	PUNCT
ejpam-5656	243	36	/	/	SYM
ejpam-5656	243	37	eur	eur	PROPN
ejpam-5656	243	38	.	.	PUNCT
ejpam-5656	244	1	j.	j.	PROPN
ejpam-5656	244	2	pure	pure	PROPN
ejpam-5656	244	3	appl	appl	PROPN
ejpam-5656	244	4	.	.	PROPN
ejpam-5656	244	5	math	math	PROPN
ejpam-5656	244	6	,	,	PUNCT
ejpam-5656	244	7	18	18	NUM
ejpam-5656	244	8	(	(	PUNCT
ejpam-5656	244	9	1	1	NUM
ejpam-5656	244	10	)	)	PUNCT
ejpam-5656	244	11	(	(	PUNCT
ejpam-5656	244	12	2025	2025	NUM
ejpam-5656	244	13	)	)	PUNCT
ejpam-5656	244	14	,	,	PUNCT
ejpam-5656	244	15	5656	5656	NUM
ejpam-5656	244	16	13	13	NUM
ejpam-5656	244	17	of	of	ADP
ejpam-5656	244	18	17	17	NUM
ejpam-5656	244	19	let	let	VERB
ejpam-5656	244	20	λ	λ	X
ejpam-5656	244	21	:	:	PUNCT
ejpam-5656	244	22	=	=	SYM
ejpam-5656	244	23	ρ	ρ	PROPN
ejpam-5656	244	24	1−	1−	NUM
ejpam-5656	244	25	µ	µ	NOUN
ejpam-5656	244	26	.	.	PUNCT
ejpam-5656	245	1	then	then	ADV
ejpam-5656	245	2	,	,	PUNCT
ejpam-5656	245	3	2−	2−	NUM
ejpam-5656	245	4	µ+	µ+	X
ejpam-5656	245	5	µ	µ	PROPN
ejpam-5656	245	6	2	2	NUM
ejpam-5656	245	7	ξ	ξ	NOUN
ejpam-5656	245	8	ρeξ	ρeξ	NOUN
ejpam-5656	245	9	+	+	CCONJ
ejpam-5656	245	10	(	(	PUNCT
ejpam-5656	245	11	1−	1−	NUM
ejpam-5656	245	12	µ	µ	NUM
ejpam-5656	245	13	)	)	PUNCT
ejpam-5656	245	14	=	=	SYM
ejpam-5656	246	1	1	1	NUM
ejpam-5656	246	2	λeξ	λeξ	NOUN
ejpam-5656	246	3	+	+	NOUN
ejpam-5656	246	4	1	1	NUM
ejpam-5656	246	5	+	+	NUM
ejpam-5656	246	6	1	1	NUM
ejpam-5656	246	7	(	(	PUNCT
ejpam-5656	246	8	1−	1−	NUM
ejpam-5656	246	9	µ)(λeξ	µ)(λeξ	NOUN
ejpam-5656	246	10	+	+	SYM
ejpam-5656	246	11	1	1	NUM
ejpam-5656	246	12	)	)	PUNCT
ejpam-5656	246	13	+	+	CCONJ
ejpam-5656	246	14	µξ	µξ	ADP
ejpam-5656	246	15	2(1−	2(1−	NUM
ejpam-5656	246	16	µ)(λeξ	µ)(λeξ	NOUN
ejpam-5656	246	17	+	+	SYM
ejpam-5656	246	18	1	1	X
ejpam-5656	246	19	)	)	PUNCT
ejpam-5656	246	20	=	=	SYM
ejpam-5656	246	21	2−	2−	NUM
ejpam-5656	246	22	µ	µ	NOUN
ejpam-5656	246	23	1−	1−	NUM
ejpam-5656	246	24	µ	µ	PRON
ejpam-5656	246	25	1	1	NUM
ejpam-5656	246	26	λeξ	λeξ	NOUN
ejpam-5656	246	27	+	+	NOUN
ejpam-5656	246	28	1	1	NUM
ejpam-5656	246	29	−	−	NOUN
ejpam-5656	246	30	µ	µ	X
ejpam-5656	246	31	2(1−	2(1−	NUM
ejpam-5656	246	32	µ	µ	NUM
ejpam-5656	246	33	)	)	PUNCT
ejpam-5656	246	34	ξ	ξ	PROPN
ejpam-5656	246	35	(	(	PUNCT
ejpam-5656	246	36	−λ)eξ	−λ)eξ	NOUN
ejpam-5656	246	37	+	+	NOUN
ejpam-5656	246	38	1	1	NUM
ejpam-5656	246	39	.	.	PUNCT
ejpam-5656	247	1	it	it	PRON
ejpam-5656	247	2	follows	follow	VERB
ejpam-5656	247	3	from	from	ADP
ejpam-5656	247	4	(	(	PUNCT
ejpam-5656	247	5	5	5	NUM
ejpam-5656	247	6	)	)	PUNCT
ejpam-5656	247	7	that	that	SCONJ
ejpam-5656	247	8	∞∑	∞∑	NUM
ejpam-5656	247	9	ν=0	ν=0	NOUN
ejpam-5656	247	10	uν(x	uν(x	NOUN
ejpam-5656	247	11	,	,	PUNCT
ejpam-5656	247	12	y	y	PROPN
ejpam-5656	247	13	;	;	PUNCT
ejpam-5656	247	14	ρ;µ	ρ;µ	NUM
ejpam-5656	247	15	)	)	PUNCT
ejpam-5656	247	16	ξν	ξν	ADP
ejpam-5656	247	17	ν	ν	X
ejpam-5656	247	18	!	!	PUNCT
ejpam-5656	248	1	=	=	PRON
ejpam-5656	248	2	2−	2−	NUM
ejpam-5656	248	3	µ	µ	NOUN
ejpam-5656	248	4	1−	1−	NUM
ejpam-5656	248	5	µ	µ	PRON
ejpam-5656	248	6	1	1	NUM
ejpam-5656	248	7	λeξ	λeξ	NOUN
ejpam-5656	248	8	+	+	NOUN
ejpam-5656	248	9	1	1	NUM
ejpam-5656	248	10	exξ+yξ2	exξ+yξ2	NOUN
ejpam-5656	248	11	−	−	PROPN
ejpam-5656	248	12	µ	µ	SYM
ejpam-5656	248	13	2(1−	2(1−	NUM
ejpam-5656	248	14	µ	µ	NUM
ejpam-5656	248	15	)	)	PUNCT
ejpam-5656	248	16	ξ	ξ	PROPN
ejpam-5656	248	17	(	(	PUNCT
ejpam-5656	248	18	−λ)eξ	−λ)eξ	NUM
ejpam-5656	248	19	+	+	NUM
ejpam-5656	248	20	1	1	NUM
ejpam-5656	248	21	exξ+yξ2	exξ+yξ2	X
ejpam-5656	248	22	=	=	PUNCT
ejpam-5656	248	23	2−	2−	NUM
ejpam-5656	248	24	µ	µ	NOUN
ejpam-5656	248	25	1−	1−	NUM
ejpam-5656	248	26	µ	µ	PRON
ejpam-5656	248	27	∞∑	∞∑	NUM
ejpam-5656	248	28	ν=0	ν=0	PRON
ejpam-5656	248	29	eν(x	eν(x	PROPN
ejpam-5656	248	30	,	,	PUNCT
ejpam-5656	248	31	y;λ	y;λ	PROPN
ejpam-5656	248	32	)	)	PUNCT
ejpam-5656	248	33	ξν	ξν	ADP
ejpam-5656	249	1	ν	ν	X
ejpam-5656	249	2	!	!	PUNCT
ejpam-5656	249	3	−	−	PROPN
ejpam-5656	249	4	µ	µ	X
ejpam-5656	249	5	2(1−	2(1−	NUM
ejpam-5656	249	6	µ	µ	NUM
ejpam-5656	249	7	)	)	PUNCT
ejpam-5656	249	8	∞∑	∞∑	NUM
ejpam-5656	249	9	ν=0	ν=0	PRON
ejpam-5656	249	10	bν(x	bν(x	NOUN
ejpam-5656	249	11	,	,	PUNCT
ejpam-5656	249	12	y;−λ	y;−λ	PROPN
ejpam-5656	249	13	)	)	PUNCT
ejpam-5656	249	14	ξν	ξν	ADP
ejpam-5656	249	15	ν	ν	PROPN
ejpam-5656	249	16	!	!	PUNCT
ejpam-5656	249	17	.	.	PUNCT
ejpam-5656	250	1	remark	remark	PROPN
ejpam-5656	250	2	5	5	NUM
ejpam-5656	250	3	.	.	PUNCT
ejpam-5656	250	4	based	base	VERB
ejpam-5656	250	5	on	on	ADP
ejpam-5656	250	6	the	the	DET
ejpam-5656	250	7	earlier	early	ADJ
ejpam-5656	250	8	findings	finding	NOUN
ejpam-5656	250	9	,	,	PUNCT
ejpam-5656	250	10	it	it	PRON
ejpam-5656	250	11	can	can	AUX
ejpam-5656	250	12	be	be	AUX
ejpam-5656	250	13	asserted	assert	VERB
ejpam-5656	250	14	that	that	SCONJ
ejpam-5656	250	15	the	the	DET
ejpam-5656	250	16	apostol	apostol	NOUN
ejpam-5656	250	17	-	-	PUNCT
ejpam-5656	250	18	type	type	NOUN
ejpam-5656	250	19	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	250	20	/	/	SYM
ejpam-5656	250	21	euler	euler	NOUN
ejpam-5656	250	22	polynomials	polynomial	NOUN
ejpam-5656	250	23	can	can	AUX
ejpam-5656	250	24	be	be	AUX
ejpam-5656	250	25	expressed	express	VERB
ejpam-5656	250	26	as	as	ADP
ejpam-5656	250	27	a	a	DET
ejpam-5656	250	28	linear	linear	ADJ
ejpam-5656	250	29	combination	combination	NOUN
ejpam-5656	250	30	of	of	ADP
ejpam-5656	250	31	the	the	DET
ejpam-5656	250	32	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	250	33	and	and	CCONJ
ejpam-5656	250	34	hermite	hermite	PROPN
ejpam-5656	250	35	-	-	PUNCT
ejpam-5656	250	36	euler	euler	NOUN
ejpam-5656	250	37	polynomials	polynomial	NOUN
ejpam-5656	250	38	for	for	ADP
ejpam-5656	250	39	µ	µ	NOUN
ejpam-5656	250	40	>	>	X
ejpam-5656	250	41	1	1	NUM
ejpam-5656	250	42	.	.	PUNCT
ejpam-5656	251	1	some	some	DET
ejpam-5656	251	2	sources	source	NOUN
ejpam-5656	251	3	refer	refer	VERB
ejpam-5656	251	4	to	to	ADP
ejpam-5656	251	5	this	this	DET
ejpam-5656	251	6	phenomenon	phenomenon	NOUN
ejpam-5656	251	7	as	as	ADP
ejpam-5656	251	8	unification	unification	NOUN
ejpam-5656	251	9	,	,	PUNCT
ejpam-5656	251	10	which	which	PRON
ejpam-5656	251	11	is	be	AUX
ejpam-5656	251	12	the	the	DET
ejpam-5656	251	13	rationale	rationale	NOUN
ejpam-5656	251	14	behind	behind	ADP
ejpam-5656	251	15	our	our	PRON
ejpam-5656	251	16	chosen	choose	VERB
ejpam-5656	251	17	nomenclature	nomenclature	NOUN
ejpam-5656	251	18	.	.	PUNCT
ejpam-5656	252	1	3	3	X
ejpam-5656	252	2	.	.	X
ejpam-5656	252	3	monomiality	monomiality	NOUN
ejpam-5656	252	4	principle	principle	VERB
ejpam-5656	252	5	the	the	DET
ejpam-5656	252	6	concepts	concept	NOUN
ejpam-5656	252	7	of	of	ADP
ejpam-5656	252	8	quasi	quasi	NOUN
ejpam-5656	252	9	-	-	ADJ
ejpam-5656	252	10	monomial	monomial	ADJ
ejpam-5656	252	11	and	and	CCONJ
ejpam-5656	252	12	the	the	DET
ejpam-5656	252	13	monomiality	monomiality	NOUN
ejpam-5656	252	14	principle	principle	NOUN
ejpam-5656	252	15	are	be	AUX
ejpam-5656	252	16	indeed	indeed	ADV
ejpam-5656	252	17	technical	technical	ADJ
ejpam-5656	252	18	and	and	CCONJ
ejpam-5656	252	19	may	may	AUX
ejpam-5656	252	20	require	require	VERB
ejpam-5656	252	21	further	further	ADJ
ejpam-5656	252	22	elaboration	elaboration	NOUN
ejpam-5656	252	23	for	for	ADP
ejpam-5656	252	24	readers	reader	NOUN
ejpam-5656	252	25	unfamiliar	unfamiliar	ADJ
ejpam-5656	252	26	with	with	ADP
ejpam-5656	252	27	them	they	PRON
ejpam-5656	252	28	.	.	PUNCT
ejpam-5656	253	1	in	in	ADP
ejpam-5656	253	2	our	our	PRON
ejpam-5656	253	3	work	work	NOUN
ejpam-5656	253	4	,	,	PUNCT
ejpam-5656	253	5	we	we	PRON
ejpam-5656	253	6	have	have	AUX
ejpam-5656	253	7	outlined	outline	VERB
ejpam-5656	253	8	the	the	DET
ejpam-5656	253	9	monomiality	monomiality	NOUN
ejpam-5656	253	10	principle	principle	NOUN
ejpam-5656	253	11	as	as	ADP
ejpam-5656	253	12	a	a	DET
ejpam-5656	253	13	framework	framework	NOUN
ejpam-5656	253	14	that	that	PRON
ejpam-5656	253	15	generalizes	generalize	VERB
ejpam-5656	253	16	the	the	DET
ejpam-5656	253	17	behavior	behavior	NOUN
ejpam-5656	253	18	of	of	ADP
ejpam-5656	253	19	special	special	ADJ
ejpam-5656	253	20	polynomials	polynomial	NOUN
ejpam-5656	253	21	through	through	ADP
ejpam-5656	253	22	abstract	abstract	ADJ
ejpam-5656	253	23	definitions	definition	NOUN
ejpam-5656	253	24	of	of	ADP
ejpam-5656	253	25	derivative	derivative	ADJ
ejpam-5656	253	26	and	and	CCONJ
ejpam-5656	253	27	multiplicative	multiplicative	ADJ
ejpam-5656	253	28	operators	operator	NOUN
ejpam-5656	253	29	,	,	PUNCT
ejpam-5656	253	30	treating	treat	VERB
ejpam-5656	253	31	these	these	DET
ejpam-5656	253	32	polynomials	polynomial	NOUN
ejpam-5656	253	33	analogously	analogously	ADV
ejpam-5656	253	34	to	to	ADP
ejpam-5656	253	35	ordinary	ordinary	ADJ
ejpam-5656	253	36	monomials	monomial	NOUN
ejpam-5656	253	37	.	.	PUNCT
ejpam-5656	254	1	this	this	DET
ejpam-5656	254	2	principle	principle	NOUN
ejpam-5656	254	3	extends	extend	VERB
ejpam-5656	254	4	the	the	DET
ejpam-5656	254	5	heisenberg	heisenberg	PROPN
ejpam-5656	254	6	–	–	PUNCT
ejpam-5656	254	7	weyl	weyl	VERB
ejpam-5656	254	8	group	group	NOUN
ejpam-5656	254	9	,	,	PUNCT
ejpam-5656	254	10	allowing	allow	VERB
ejpam-5656	254	11	for	for	ADP
ejpam-5656	254	12	a	a	DET
ejpam-5656	254	13	unified	unified	ADJ
ejpam-5656	254	14	examination	examination	NOUN
ejpam-5656	254	15	of	of	ADP
ejpam-5656	254	16	diverse	diverse	ADJ
ejpam-5656	254	17	polynomial	polynomial	ADJ
ejpam-5656	254	18	families	family	NOUN
ejpam-5656	254	19	and	and	CCONJ
ejpam-5656	254	20	their	their	PRON
ejpam-5656	254	21	properties	property	NOUN
ejpam-5656	254	22	.	.	PUNCT
ejpam-5656	255	1	additionally	additionally	ADV
ejpam-5656	255	2	,	,	PUNCT
ejpam-5656	255	3	we	we	PRON
ejpam-5656	255	4	reference	reference	VERB
ejpam-5656	255	5	foundational	foundational	ADJ
ejpam-5656	255	6	works	work	NOUN
ejpam-5656	255	7	[	[	X
ejpam-5656	255	8	8	8	NUM
ejpam-5656	255	9	,	,	PUNCT
ejpam-5656	255	10	11	11	NUM
ejpam-5656	255	11	,	,	PUNCT
ejpam-5656	255	12	13	13	NUM
ejpam-5656	255	13	,	,	PUNCT
ejpam-5656	255	14	20–22	20–22	NUM
ejpam-5656	255	15	]	]	PUNCT
ejpam-5656	255	16	that	that	PRON
ejpam-5656	255	17	provide	provide	VERB
ejpam-5656	255	18	a	a	DET
ejpam-5656	255	19	deeper	deep	ADJ
ejpam-5656	255	20	exploration	exploration	NOUN
ejpam-5656	255	21	of	of	ADP
ejpam-5656	255	22	this	this	DET
ejpam-5656	255	23	principle	principle	NOUN
ejpam-5656	255	24	and	and	CCONJ
ejpam-5656	255	25	its	its	PRON
ejpam-5656	255	26	applications	application	NOUN
ejpam-5656	255	27	.	.	PUNCT
ejpam-5656	256	1	the	the	DET
ejpam-5656	256	2	operators	operator	NOUN
ejpam-5656	256	3	m̂	m̂	PROPN
ejpam-5656	256	4	and	and	CCONJ
ejpam-5656	256	5	d̂	d̂	PROPN
ejpam-5656	256	6	function	function	VERB
ejpam-5656	256	7	dually	dually	ADV
ejpam-5656	256	8	as	as	ADP
ejpam-5656	256	9	both	both	CCONJ
ejpam-5656	256	10	multiplicative	multiplicative	ADJ
ejpam-5656	256	11	and	and	CCONJ
ejpam-5656	256	12	derivative	derivative	ADJ
ejpam-5656	256	13	operators	operator	NOUN
ejpam-5656	256	14	within	within	ADP
ejpam-5656	256	15	the	the	DET
ejpam-5656	256	16	context	context	NOUN
ejpam-5656	256	17	of	of	ADP
ejpam-5656	256	18	a	a	DET
ejpam-5656	256	19	polynomial	polynomial	ADJ
ejpam-5656	256	20	set	set	NOUN
ejpam-5656	256	21	{	{	PUNCT
ejpam-5656	256	22	bm(u)}m∈n	bm(u)}m∈n	ADJ
ejpam-5656	256	23	,	,	PUNCT
ejpam-5656	256	24	adhering	adhere	VERB
ejpam-5656	256	25	to	to	ADP
ejpam-5656	256	26	the	the	DET
ejpam-5656	256	27	following	follow	VERB
ejpam-5656	256	28	expressions	expression	NOUN
ejpam-5656	256	29	:	:	PUNCT
ejpam-5656	256	30	bm+1(u	bm+1(u	NOUN
ejpam-5656	256	31	)	)	PUNCT
ejpam-5656	256	32	=	=	SYM
ejpam-5656	256	33	m̂{bm(u	m̂{bm(u	PROPN
ejpam-5656	256	34	)	)	PUNCT
ejpam-5656	256	35	}	}	PUNCT
ejpam-5656	256	36	(	(	PUNCT
ejpam-5656	256	37	21	21	NUM
ejpam-5656	256	38	)	)	PUNCT
ejpam-5656	256	39	and	and	CCONJ
ejpam-5656	256	40	m	m	PROPN
ejpam-5656	256	41	bm−1(u	bm−1(u	NOUN
ejpam-5656	256	42	)	)	PUNCT
ejpam-5656	256	43	=	=	SYM
ejpam-5656	256	44	d̂{bm(u	d̂{bm(u	NOUN
ejpam-5656	256	45	)	)	PUNCT
ejpam-5656	256	46	}	}	PUNCT
ejpam-5656	256	47	.	.	PUNCT
ejpam-5656	257	1	the	the	DET
ejpam-5656	257	2	set	set	PROPN
ejpam-5656	257	3	{	{	PUNCT
ejpam-5656	257	4	bm(u)}m∈n	bm(u)}m∈n	NUM
ejpam-5656	257	5	manipulated	manipulate	VERB
ejpam-5656	257	6	by	by	ADP
ejpam-5656	257	7	these	these	DET
ejpam-5656	257	8	operators	operator	NOUN
ejpam-5656	257	9	is	be	AUX
ejpam-5656	257	10	termed	term	VERB
ejpam-5656	257	11	a	a	DET
ejpam-5656	257	12	quasi	quasi	NOUN
ejpam-5656	257	13	-	-	ADJ
ejpam-5656	257	14	monomial	monomial	ADJ
ejpam-5656	257	15	and	and	CCONJ
ejpam-5656	257	16	must	must	AUX
ejpam-5656	257	17	adhere	adhere	VERB
ejpam-5656	257	18	to	to	ADP
ejpam-5656	257	19	the	the	DET
ejpam-5656	257	20	formula	formula	NOUN
ejpam-5656	257	21	:	:	PUNCT
ejpam-5656	257	22	[	[	X
ejpam-5656	257	23	d̂,m̂	d̂,m̂	X
ejpam-5656	257	24	]	]	PUNCT
ejpam-5656	257	25	=	=	SYM
ejpam-5656	257	26	d̂m̂	d̂m̂	X
ejpam-5656	257	27	−	−	NOUN
ejpam-5656	257	28	m̂d̂	m̂d̂	NOUN
ejpam-5656	257	29	=	=	SYM
ejpam-5656	257	30	1̂	1̂	NOUN
ejpam-5656	257	31	,	,	PUNCT
ejpam-5656	257	32	dı́az	dı́az	X
ejpam-5656	257	33	et	et	PROPN
ejpam-5656	257	34	al	al	PROPN
ejpam-5656	257	35	.	.	PUNCT
ejpam-5656	257	36	/	/	SYM
ejpam-5656	257	37	eur	eur	PROPN
ejpam-5656	257	38	.	.	PUNCT
ejpam-5656	258	1	j.	j.	PROPN
ejpam-5656	258	2	pure	pure	PROPN
ejpam-5656	258	3	appl	appl	PROPN
ejpam-5656	258	4	.	.	PROPN
ejpam-5656	258	5	math	math	PROPN
ejpam-5656	258	6	,	,	PUNCT
ejpam-5656	258	7	18	18	NUM
ejpam-5656	258	8	(	(	PUNCT
ejpam-5656	258	9	1	1	NUM
ejpam-5656	258	10	)	)	PUNCT
ejpam-5656	258	11	(	(	PUNCT
ejpam-5656	258	12	2025	2025	NUM
ejpam-5656	258	13	)	)	PUNCT
ejpam-5656	258	14	,	,	PUNCT
ejpam-5656	258	15	5656	5656	NUM
ejpam-5656	258	16	14	14	NUM
ejpam-5656	258	17	of	of	ADP
ejpam-5656	258	18	17	17	NUM
ejpam-5656	258	19	displaying	display	VERB
ejpam-5656	258	20	a	a	DET
ejpam-5656	258	21	weyl	weyl	VERB
ejpam-5656	258	22	group	group	NOUN
ejpam-5656	258	23	structure	structure	NOUN
ejpam-5656	258	24	.	.	PUNCT
ejpam-5656	259	1	the	the	DET
ejpam-5656	259	2	properties	property	NOUN
ejpam-5656	259	3	of	of	ADP
ejpam-5656	259	4	m̂	m̂	PROPN
ejpam-5656	259	5	and	and	CCONJ
ejpam-5656	259	6	d̂	d̂	PUNCT
ejpam-5656	259	7	determine	determine	VERB
ejpam-5656	259	8	the	the	DET
ejpam-5656	259	9	characteristics	characteristic	NOUN
ejpam-5656	259	10	of	of	ADP
ejpam-5656	259	11	the	the	DET
ejpam-5656	259	12	quasi	quasi	ADJ
ejpam-5656	259	13	-	-	ADJ
ejpam-5656	259	14	monomial	monomial	ADJ
ejpam-5656	259	15	set	set	NOUN
ejpam-5656	259	16	{	{	PUNCT
ejpam-5656	259	17	bm(u)}m∈n	bm(u)}m∈n	NUM
ejpam-5656	259	18	:	:	PUNCT
ejpam-5656	259	19	for	for	ADP
ejpam-5656	259	20	example	example	NOUN
ejpam-5656	259	21	,	,	PUNCT
ejpam-5656	259	22	bm(u	bm(u	NOUN
ejpam-5656	259	23	)	)	PUNCT
ejpam-5656	259	24	satisfies	satisfy	VERB
ejpam-5656	259	25	the	the	DET
ejpam-5656	259	26	differential	differential	ADJ
ejpam-5656	259	27	equation	equation	NOUN
ejpam-5656	259	28	m̂d̂{bm(u	m̂d̂{bm(u	NOUN
ejpam-5656	259	29	)	)	PUNCT
ejpam-5656	259	30	}	}	PUNCT
ejpam-5656	259	31	=	=	SYM
ejpam-5656	259	32	mbm(u	mbm(u	PROPN
ejpam-5656	259	33	)	)	PUNCT
ejpam-5656	259	34	,	,	PUNCT
ejpam-5656	259	35	if	if	SCONJ
ejpam-5656	259	36	m̂	m̂	PROPN
ejpam-5656	259	37	and	and	CCONJ
ejpam-5656	259	38	d̂	d̂	PROPN
ejpam-5656	259	39	have	have	VERB
ejpam-5656	259	40	differential	differential	ADJ
ejpam-5656	259	41	realizations	realization	NOUN
ejpam-5656	259	42	.	.	PUNCT
ejpam-5656	260	1	theorem	theorem	NOUN
ejpam-5656	260	2	1	1	NUM
ejpam-5656	260	3	.	.	PUNCT
ejpam-5656	261	1	the	the	DET
ejpam-5656	261	2	operators	operator	NOUN
ejpam-5656	261	3	m̂	m̂	PROPN
ejpam-5656	261	4	and	and	CCONJ
ejpam-5656	261	5	d̂	d̂	PROPN
ejpam-5656	261	6	associated	associate	VERB
ejpam-5656	261	7	with	with	ADP
ejpam-5656	261	8	the	the	DET
ejpam-5656	261	9	apostol	apostol	NOUN
ejpam-5656	261	10	-	-	PUNCT
ejpam-5656	261	11	type	type	NOUN
ejpam-5656	261	12	hermite	hermite	PROPN
ejpam-5656	261	13	-	-	PUNCT
ejpam-5656	261	14	bernoulli	bernoulli	PROPN
ejpam-5656	261	15	/	/	SYM
ejpam-5656	261	16	euler	euler	NOUN
ejpam-5656	261	17	polynomials	polynomial	NOUN
ejpam-5656	261	18	uν(x	uν(x	PART
ejpam-5656	261	19	,	,	PUNCT
ejpam-5656	261	20	y	y	PROPN
ejpam-5656	261	21	;	;	PUNCT
ejpam-5656	261	22	ρ;µ	ρ;µ	NUM
ejpam-5656	261	23	)	)	PUNCT
ejpam-5656	261	24	are	be	AUX
ejpam-5656	261	25	given	give	VERB
ejpam-5656	261	26	by	by	ADP
ejpam-5656	261	27	m̂	m̂	PROPN
ejpam-5656	261	28	:	:	PUNCT
ejpam-5656	261	29	=	=	SYM
ejpam-5656	261	30	ψ(ρ	ψ(ρ	PROPN
ejpam-5656	261	31	,	,	PUNCT
ejpam-5656	261	32	µ	µ	NOUN
ejpam-5656	261	33	,	,	PUNCT
ejpam-5656	261	34	ξ	ξ	NOUN
ejpam-5656	261	35	)	)	PUNCT
ejpam-5656	261	36	+	+	CCONJ
ejpam-5656	261	37	x+	x+	ADJ
ejpam-5656	261	38	2y	2y	PROPN
ejpam-5656	261	39	∂	∂	NOUN
ejpam-5656	261	40	∂x	∂x	NOUN
ejpam-5656	261	41	and	and	CCONJ
ejpam-5656	261	42	d̂	d̂	NUM
ejpam-5656	261	43	:	:	PUNCT
ejpam-5656	261	44	=	=	SYM
ejpam-5656	261	45	∂	∂	NUM
ejpam-5656	261	46	∂x	∂x	PROPN
ejpam-5656	261	47	.	.	PUNCT
ejpam-5656	262	1	where	where	SCONJ
ejpam-5656	262	2	ψ(ρ	ψ(ρ	PROPN
ejpam-5656	262	3	,	,	PUNCT
ejpam-5656	262	4	µ	µ	NOUN
ejpam-5656	262	5	,	,	PUNCT
ejpam-5656	262	6	ξ	ξ	NOUN
ejpam-5656	262	7	)	)	PUNCT
ejpam-5656	262	8	:	:	PUNCT
ejpam-5656	262	9	=	=	SYM
ejpam-5656	262	10	µ/2	µ/2	X
ejpam-5656	262	11	2−	2−	NUM
ejpam-5656	262	12	µ+	µ+	X
ejpam-5656	262	13	µ	µ	PROPN
ejpam-5656	262	14	2	2	NUM
ejpam-5656	262	15	ξ	ξ	PRON
ejpam-5656	262	16	−	−	NOUN
ejpam-5656	262	17	ρeξ	ρeξ	NOUN
ejpam-5656	262	18	ρeξ	ρeξ	NOUN
ejpam-5656	262	19	+	+	CCONJ
ejpam-5656	262	20	1−	1−	NUM
ejpam-5656	262	21	µ	µ	NOUN
ejpam-5656	262	22	.	.	PUNCT
ejpam-5656	263	1	proof	proof	NOUN
ejpam-5656	263	2	.	.	PUNCT
ejpam-5656	264	1	differentiating	differentiate	VERB
ejpam-5656	264	2	the	the	DET
ejpam-5656	264	3	generating	generating	NOUN
ejpam-5656	264	4	relation	relation	NOUN
ejpam-5656	264	5	(	(	PUNCT
ejpam-5656	264	6	5	5	NUM
ejpam-5656	264	7	)	)	PUNCT
ejpam-5656	264	8	with	with	ADP
ejpam-5656	264	9	respect	respect	NOUN
ejpam-5656	264	10	to	to	ADP
ejpam-5656	264	11	the	the	DET
ejpam-5656	264	12	variable	variable	ADJ
ejpam-5656	264	13	ξ	ξ	PROPN
ejpam-5656	264	14	,	,	PUNCT
ejpam-5656	264	15	it	it	PRON
ejpam-5656	264	16	follows	follow	VERB
ejpam-5656	264	17	that	that	PRON
ejpam-5656	264	18	∂	∂	NUM
ejpam-5656	264	19	∂ξ	∂ξ	NOUN
ejpam-5656	264	20	(	(	PUNCT
ejpam-5656	264	21	φ(ρ	φ(ρ	PROPN
ejpam-5656	264	22	,	,	PUNCT
ejpam-5656	264	23	µ	µ	NUM
ejpam-5656	264	24	,	,	PUNCT
ejpam-5656	264	25	ξ)exξ+yξ2	ξ)exξ+yξ2	X
ejpam-5656	264	26	)	)	PUNCT
ejpam-5656	265	1	=	=	PUNCT
ejpam-5656	265	2	∞∑	∞∑	NUM
ejpam-5656	265	3	ν=0	ν=0	PROPN
ejpam-5656	265	4	uν+1(x	uν+1(x	NOUN
ejpam-5656	265	5	,	,	PUNCT
ejpam-5656	265	6	y	y	PROPN
ejpam-5656	265	7	;	;	PUNCT
ejpam-5656	265	8	ρ;µ	ρ;µ	NUM
ejpam-5656	265	9	)	)	PUNCT
ejpam-5656	265	10	ξν	ξν	ADP
ejpam-5656	265	11	ν	ν	X
ejpam-5656	265	12	!	!	PUNCT
ejpam-5656	265	13	.	.	PUNCT
ejpam-5656	266	1	now	now	ADV
ejpam-5656	266	2	,	,	PUNCT
ejpam-5656	266	3	since	since	SCONJ
ejpam-5656	266	4	∂	∂	NOUN
ejpam-5656	266	5	∂ξ	∂ξ	PROPN
ejpam-5656	266	6	(	(	PUNCT
ejpam-5656	266	7	φ(ρ	φ(ρ	PROPN
ejpam-5656	266	8	,	,	PUNCT
ejpam-5656	266	9	µ	µ	NUM
ejpam-5656	266	10	,	,	PUNCT
ejpam-5656	266	11	ξ)exξ+yξ2	ξ)exξ+yξ2	PROPN
ejpam-5656	266	12	)	)	PUNCT
ejpam-5656	267	1	=	=	SYM
ejpam-5656	267	2			PROPN
ejpam-5656	267	3	µ/2	µ/2	NUM
ejpam-5656	267	4	2−	2−	NUM
ejpam-5656	267	5	µ+	µ+	X
ejpam-5656	267	6	µ	µ	PROPN
ejpam-5656	267	7	2	2	NUM
ejpam-5656	267	8	ξ	ξ	PRON
ejpam-5656	267	9	−	−	NOUN
ejpam-5656	267	10	ρeξ	ρeξ	NOUN
ejpam-5656	267	11	ρeξ	ρeξ	NOUN
ejpam-5656	267	12	+	+	CCONJ
ejpam-5656	267	13	1−	1−	NUM
ejpam-5656	267	14	µ	µ	NUM
ejpam-5656	267	15	+	+	CCONJ
ejpam-5656	267	16	x+	x+	ADJ
ejpam-5656	267	17	2yξ	2yξ	PROPN
ejpam-5656	267	18	(φ(ρ	(φ(ρ	PROPN
ejpam-5656	267	19	,	,	PUNCT
ejpam-5656	267	20	µ	µ	NUM
ejpam-5656	267	21	,	,	PUNCT
ejpam-5656	267	22	ξ)exξ+yξ2	ξ)exξ+yξ2	PROPN
ejpam-5656	267	23	)	)	PUNCT
ejpam-5656	267	24	,	,	PUNCT
ejpam-5656	267	25	then	then	ADV
ejpam-5656	267	26	∞∑	∞∑	NUM
ejpam-5656	267	27	ν=0	ν=0	PROPN
ejpam-5656	267	28			PROPN
ejpam-5656	267	29	µ/2	µ/2	ADV
ejpam-5656	267	30	2−	2−	NUM
ejpam-5656	267	31	µ+	µ+	X
ejpam-5656	267	32	µ	µ	PROPN
ejpam-5656	267	33	2	2	NUM
ejpam-5656	267	34	ξ	ξ	PRON
ejpam-5656	267	35	−	−	NOUN
ejpam-5656	267	36	ρeξ	ρeξ	NOUN
ejpam-5656	267	37	ρeξ	ρeξ	NOUN
ejpam-5656	267	38	+	+	CCONJ
ejpam-5656	267	39	1−	1−	NUM
ejpam-5656	267	40	µ	µ	X
ejpam-5656	267	41	+	+	CCONJ
ejpam-5656	267	42	x+	x+	ADJ
ejpam-5656	267	43	2y	2y	PROPN
ejpam-5656	267	44	d	d	NOUN
ejpam-5656	267	45	dx	dx	PROPN
ejpam-5656	267	46	uν(x	uν(x	NUM
ejpam-5656	267	47	,	,	PUNCT
ejpam-5656	267	48	y	y	PROPN
ejpam-5656	267	49	;	;	PUNCT
ejpam-5656	267	50	ρ;µ	ρ;µ	NUM
ejpam-5656	267	51	)	)	PUNCT
ejpam-5656	267	52	ξν	ξν	ADP
ejpam-5656	267	53	ν	ν	X
ejpam-5656	267	54	!	!	PUNCT
ejpam-5656	267	55	=	=	PUNCT
ejpam-5656	268	1	∞∑	∞∑	NUM
ejpam-5656	268	2	ν=0	ν=0	PRON
ejpam-5656	268	3	uν+1(x	uν+1(x	NOUN
ejpam-5656	268	4	,	,	PUNCT
ejpam-5656	268	5	y	y	PROPN
ejpam-5656	268	6	;	;	PUNCT
ejpam-5656	268	7	ρ;µ	ρ;µ	NUM
ejpam-5656	268	8	)	)	PUNCT
ejpam-5656	268	9	ξν	ξν	ADP
ejpam-5656	268	10	ν	ν	PROPN
ejpam-5656	268	11	!	!	PUNCT
ejpam-5656	268	12	.	.	PUNCT
ejpam-5656	269	1	(	(	PUNCT
ejpam-5656	269	2	22	22	NUM
ejpam-5656	269	3	)	)	PUNCT
ejpam-5656	269	4	by	by	ADP
ejpam-5656	269	5	equating	equate	VERB
ejpam-5656	269	6	the	the	DET
ejpam-5656	269	7	coefficients	coefficient	NOUN
ejpam-5656	269	8	of	of	ADP
ejpam-5656	269	9	corresponding	correspond	VERB
ejpam-5656	269	10	powers	power	NOUN
ejpam-5656	269	11	of	of	ADP
ejpam-5656	269	12	ξ	ξ	PROPN
ejpam-5656	269	13	on	on	ADP
ejpam-5656	269	14	both	both	DET
ejpam-5656	269	15	sides	side	NOUN
ejpam-5656	269	16	of	of	ADP
ejpam-5656	269	17	equation	equation	NOUN
ejpam-5656	269	18	(	(	PUNCT
ejpam-5656	269	19	22	22	NUM
ejpam-5656	269	20	)	)	PUNCT
ejpam-5656	269	21	and	and	CCONJ
ejpam-5656	269	22	applying	apply	VERB
ejpam-5656	269	23	the	the	DET
ejpam-5656	269	24	monomiality	monomiality	NOUN
ejpam-5656	269	25	principle	principle	NOUN
ejpam-5656	269	26	equation	equation	NOUN
ejpam-5656	269	27	(	(	PUNCT
ejpam-5656	269	28	21	21	NUM
ejpam-5656	269	29	)	)	PUNCT
ejpam-5656	269	30	,	,	PUNCT
ejpam-5656	269	31	we	we	PRON
ejpam-5656	269	32	deduce	deduce	VERB
ejpam-5656	269	33	the	the	DET
ejpam-5656	269	34	operator	operator	NOUN
ejpam-5656	269	35	m̂.	m̂.	VERB
ejpam-5656	269	36	additionally	additionally	ADV
ejpam-5656	269	37	,	,	PUNCT
ejpam-5656	269	38	proposition	proposition	NOUN
ejpam-5656	269	39	4	4	NUM
ejpam-5656	269	40	establishes	establish	VERB
ejpam-5656	269	41	that	that	SCONJ
ejpam-5656	269	42	d̂	d̂	PRON
ejpam-5656	269	43	=	=	SYM
ejpam-5656	269	44	∂	∂	NUM
ejpam-5656	269	45	∂x	∂x	PROPN
ejpam-5656	269	46	.	.	PUNCT
ejpam-5656	270	1	proposition	proposition	NOUN
ejpam-5656	270	2	8	8	NUM
ejpam-5656	270	3	.	.	PUNCT
ejpam-5656	271	1	the	the	DET
ejpam-5656	271	2	apostol	apostol	NOUN
ejpam-5656	271	3	-	-	PUNCT
ejpam-5656	271	4	type	type	NOUN
ejpam-5656	271	5	hermite	hermite	PROPN
ejpam-5656	271	6	-	-	PUNCT
ejpam-5656	271	7	bernoulli	bernoulli	PROPN
ejpam-5656	271	8	/	/	SYM
ejpam-5656	271	9	euler	euler	NOUN
ejpam-5656	271	10	polynomials	polynomial	NOUN
ejpam-5656	271	11	satisfy	satisfy	VERB
ejpam-5656	271	12	the	the	DET
ejpam-5656	271	13	succeeding	succeed	VERB
ejpam-5656	271	14	differential	differential	ADJ
ejpam-5656	271	15	equation	equation	NOUN
ejpam-5656	271	16	:	:	PUNCT
ejpam-5656	271	17	[	[	PUNCT
ejpam-5656	271	18	(	(	PUNCT
ejpam-5656	271	19	ψ(ρ	ψ(ρ	PROPN
ejpam-5656	271	20	,	,	PUNCT
ejpam-5656	271	21	µ	µ	NOUN
ejpam-5656	271	22	,	,	PUNCT
ejpam-5656	271	23	ξ	ξ	NOUN
ejpam-5656	271	24	)	)	PUNCT
ejpam-5656	271	25	+	+	NUM
ejpam-5656	271	26	x	x	X
ejpam-5656	271	27	)	)	PUNCT
ejpam-5656	271	28	∂	∂	NUM
ejpam-5656	271	29	∂x	∂x	PROPN
ejpam-5656	271	30	+	+	CCONJ
ejpam-5656	271	31	2y	2y	PROPN
ejpam-5656	271	32	∂2	∂2	ADJ
ejpam-5656	271	33	∂x2	∂x2	NOUN
ejpam-5656	271	34	]	]	PUNCT
ejpam-5656	271	35	uν(x	uν(x	X
ejpam-5656	271	36	,	,	PUNCT
ejpam-5656	271	37	y	y	PROPN
ejpam-5656	271	38	;	;	PUNCT
ejpam-5656	271	39	ρ;µ	ρ;µ	NUM
ejpam-5656	271	40	)	)	PUNCT
ejpam-5656	271	41	=	=	SYM
ejpam-5656	271	42	νuν(x	νuν(x	PROPN
ejpam-5656	271	43	,	,	PUNCT
ejpam-5656	271	44	y	y	PROPN
ejpam-5656	271	45	;	;	PUNCT
ejpam-5656	271	46	ρ;µ	ρ;µ	NUM
ejpam-5656	271	47	)	)	PUNCT
ejpam-5656	271	48	.	.	PUNCT
ejpam-5656	272	1	dı́az	dı́az	X
ejpam-5656	272	2	et	et	PROPN
ejpam-5656	272	3	al	al	PROPN
ejpam-5656	272	4	.	.	PUNCT
ejpam-5656	272	5	/	/	SYM
ejpam-5656	272	6	eur	eur	PROPN
ejpam-5656	272	7	.	.	PUNCT
ejpam-5656	273	1	j.	j.	PROPN
ejpam-5656	273	2	pure	pure	PROPN
ejpam-5656	273	3	appl	appl	PROPN
ejpam-5656	273	4	.	.	PROPN
ejpam-5656	273	5	math	math	PROPN
ejpam-5656	273	6	,	,	PUNCT
ejpam-5656	273	7	18	18	NUM
ejpam-5656	273	8	(	(	PUNCT
ejpam-5656	273	9	1	1	NUM
ejpam-5656	273	10	)	)	PUNCT
ejpam-5656	273	11	(	(	PUNCT
ejpam-5656	273	12	2025	2025	NUM
ejpam-5656	273	13	)	)	PUNCT
ejpam-5656	273	14	,	,	PUNCT
ejpam-5656	273	15	5656	5656	NUM
ejpam-5656	273	16	15	15	NUM
ejpam-5656	273	17	of	of	ADP
ejpam-5656	273	18	17	17	NUM
ejpam-5656	273	19	proof	proof	NOUN
ejpam-5656	273	20	.	.	PUNCT
ejpam-5656	274	1	the	the	DET
ejpam-5656	274	2	outcome	outcome	NOUN
ejpam-5656	274	3	is	be	AUX
ejpam-5656	274	4	instantaneous	instantaneous	ADJ
ejpam-5656	274	5	given	give	VERB
ejpam-5656	274	6	that	that	DET
ejpam-5656	274	7	d̂uν(x	d̂uν(x	PROPN
ejpam-5656	274	8	,	,	PUNCT
ejpam-5656	274	9	y	y	PROPN
ejpam-5656	274	10	;	;	PUNCT
ejpam-5656	274	11	ρ;µ	ρ;µ	NUM
ejpam-5656	274	12	)	)	PUNCT
ejpam-5656	274	13	=	=	SYM
ejpam-5656	274	14	νuν−1(x	νuν−1(x	PROPN
ejpam-5656	274	15	,	,	PUNCT
ejpam-5656	274	16	y	y	PROPN
ejpam-5656	274	17	;	;	PUNCT
ejpam-5656	274	18	ρ;µ	ρ;µ	NUM
ejpam-5656	274	19	)	)	PUNCT
ejpam-5656	274	20	and	and	CCONJ
ejpam-5656	274	21	m̂uν−1(x	m̂uν−1(x	PROPN
ejpam-5656	274	22	,	,	PUNCT
ejpam-5656	274	23	y	y	PROPN
ejpam-5656	274	24	;	;	PUNCT
ejpam-5656	274	25	ρ;µ	ρ;µ	NUM
ejpam-5656	274	26	)	)	PUNCT
ejpam-5656	274	27	=	=	SYM
ejpam-5656	274	28	νuν(x	νuν(x	PROPN
ejpam-5656	274	29	,	,	PUNCT
ejpam-5656	274	30	y	y	PROPN
ejpam-5656	274	31	;	;	PUNCT
ejpam-5656	274	32	ρ;µ	ρ;µ	NUM
ejpam-5656	274	33	)	)	PUNCT
ejpam-5656	274	34	.	.	PUNCT
ejpam-5656	275	1	4	4	X
ejpam-5656	275	2	.	.	X
ejpam-5656	275	3	conclusions	conclusion	NOUN
ejpam-5656	275	4	in	in	ADP
ejpam-5656	275	5	this	this	DET
ejpam-5656	275	6	work	work	NOUN
ejpam-5656	275	7	,	,	PUNCT
ejpam-5656	275	8	we	we	PRON
ejpam-5656	275	9	introduced	introduce	VERB
ejpam-5656	275	10	a	a	DET
ejpam-5656	275	11	novel	novel	ADJ
ejpam-5656	275	12	class	class	NOUN
ejpam-5656	275	13	of	of	ADP
ejpam-5656	275	14	polynomials	polynomial	NOUN
ejpam-5656	275	15	,	,	PUNCT
ejpam-5656	275	16	the	the	DET
ejpam-5656	275	17	apostol	apostol	NOUN
ejpam-5656	275	18	-	-	PUNCT
ejpam-5656	275	19	type	type	NOUN
ejpam-5656	275	20	hermitebernoulli	hermitebernoulli	PROPN
ejpam-5656	275	21	/	/	SYM
ejpam-5656	275	22	euler	euler	NOUN
ejpam-5656	275	23	polynomials	polynomial	NOUN
ejpam-5656	275	24	,	,	PUNCT
ejpam-5656	275	25	denoted	denote	VERB
ejpam-5656	275	26	as	as	ADP
ejpam-5656	275	27	uν(x	uν(x	NOUN
ejpam-5656	275	28	,	,	PUNCT
ejpam-5656	275	29	y	y	PROPN
ejpam-5656	275	30	;	;	PUNCT
ejpam-5656	275	31	ρ;µ	ρ;µ	NUM
ejpam-5656	275	32	)	)	PUNCT
ejpam-5656	275	33	,	,	PUNCT
ejpam-5656	275	34	and	and	CCONJ
ejpam-5656	275	35	explored	explore	VERB
ejpam-5656	275	36	their	their	PRON
ejpam-5656	275	37	fundamental	fundamental	ADJ
ejpam-5656	275	38	properties	property	NOUN
ejpam-5656	275	39	.	.	PUNCT
ejpam-5656	276	1	these	these	DET
ejpam-5656	276	2	polynomials	polynomial	NOUN
ejpam-5656	276	3	were	be	AUX
ejpam-5656	276	4	defined	define	VERB
ejpam-5656	276	5	via	via	ADP
ejpam-5656	276	6	a	a	DET
ejpam-5656	276	7	generating	generate	VERB
ejpam-5656	276	8	function	function	NOUN
ejpam-5656	276	9	,	,	PUNCT
ejpam-5656	276	10	enabling	enable	VERB
ejpam-5656	276	11	us	we	PRON
ejpam-5656	276	12	to	to	PART
ejpam-5656	276	13	derive	derive	VERB
ejpam-5656	276	14	their	their	PRON
ejpam-5656	276	15	summation	summation	NOUN
ejpam-5656	276	16	formulae	formulae	ADJ
ejpam-5656	276	17	and	and	CCONJ
ejpam-5656	276	18	determinant	determinant	ADJ
ejpam-5656	276	19	forms	form	NOUN
ejpam-5656	276	20	.	.	PUNCT
ejpam-5656	277	1	this	this	DET
ejpam-5656	277	2	new	new	ADJ
ejpam-5656	277	3	family	family	NOUN
ejpam-5656	277	4	not	not	PART
ejpam-5656	277	5	only	only	ADV
ejpam-5656	277	6	generalizes	generalize	VERB
ejpam-5656	277	7	the	the	DET
ejpam-5656	277	8	classical	classical	ADJ
ejpam-5656	277	9	appell	appell	ADJ
ejpam-5656	277	10	-	-	PUNCT
ejpam-5656	277	11	type	type	NOUN
ejpam-5656	277	12	polynomials	polynomial	NOUN
ejpam-5656	277	13	but	but	CCONJ
ejpam-5656	277	14	also	also	ADV
ejpam-5656	277	15	extends	extend	VERB
ejpam-5656	277	16	their	their	PRON
ejpam-5656	277	17	applicability	applicability	NOUN
ejpam-5656	277	18	in	in	ADP
ejpam-5656	277	19	mathematical	mathematical	ADJ
ejpam-5656	277	20	analysis	analysis	NOUN
ejpam-5656	277	21	.	.	PUNCT
ejpam-5656	278	1	the	the	DET
ejpam-5656	278	2	generating	generate	VERB
ejpam-5656	278	3	function	function	NOUN
ejpam-5656	278	4	techniques	technique	NOUN
ejpam-5656	278	5	employed	employ	VERB
ejpam-5656	278	6	in	in	ADP
ejpam-5656	278	7	this	this	DET
ejpam-5656	278	8	study	study	NOUN
ejpam-5656	278	9	proved	prove	VERB
ejpam-5656	278	10	instrumental	instrumental	ADJ
ejpam-5656	278	11	in	in	ADP
ejpam-5656	278	12	establishing	establish	VERB
ejpam-5656	278	13	the	the	DET
ejpam-5656	278	14	key	key	ADJ
ejpam-5656	278	15	properties	property	NOUN
ejpam-5656	278	16	of	of	ADP
ejpam-5656	278	17	these	these	DET
ejpam-5656	278	18	polynomials	polynomial	NOUN
ejpam-5656	278	19	.	.	PUNCT
ejpam-5656	279	1	additionally	additionally	ADV
ejpam-5656	279	2	,	,	PUNCT
ejpam-5656	279	3	the	the	DET
ejpam-5656	279	4	introduction	introduction	NOUN
ejpam-5656	279	5	of	of	ADP
ejpam-5656	279	6	derivative	derivative	ADJ
ejpam-5656	279	7	and	and	CCONJ
ejpam-5656	279	8	multiplicative	multiplicative	ADJ
ejpam-5656	279	9	operators	operator	NOUN
ejpam-5656	279	10	facilitated	facilitate	VERB
ejpam-5656	279	11	their	their	PRON
ejpam-5656	279	12	representation	representation	NOUN
ejpam-5656	279	13	as	as	ADP
ejpam-5656	279	14	a	a	DET
ejpam-5656	279	15	quasi	quasi	ADJ
ejpam-5656	279	16	-	-	ADJ
ejpam-5656	279	17	monomial	monomial	ADJ
ejpam-5656	279	18	set	set	NOUN
ejpam-5656	279	19	,	,	PUNCT
ejpam-5656	279	20	thereby	thereby	ADV
ejpam-5656	279	21	expanding	expand	VERB
ejpam-5656	279	22	their	their	PRON
ejpam-5656	279	23	potential	potential	ADJ
ejpam-5656	279	24	applications	application	NOUN
ejpam-5656	279	25	in	in	ADP
ejpam-5656	279	26	various	various	ADJ
ejpam-5656	279	27	branches	branch	NOUN
ejpam-5656	279	28	of	of	ADP
ejpam-5656	279	29	mathematics	mathematic	NOUN
ejpam-5656	279	30	and	and	CCONJ
ejpam-5656	279	31	related	related	ADJ
ejpam-5656	279	32	fields	field	NOUN
ejpam-5656	279	33	.	.	PUNCT
ejpam-5656	280	1	the	the	DET
ejpam-5656	280	2	illustrative	illustrative	ADJ
ejpam-5656	280	3	examples	example	NOUN
ejpam-5656	280	4	provided	provide	VERB
ejpam-5656	280	5	throughout	throughout	ADP
ejpam-5656	280	6	the	the	DET
ejpam-5656	280	7	paper	paper	NOUN
ejpam-5656	280	8	demonstrate	demonstrate	VERB
ejpam-5656	280	9	the	the	DET
ejpam-5656	280	10	validity	validity	NOUN
ejpam-5656	280	11	and	and	CCONJ
ejpam-5656	280	12	versatility	versatility	NOUN
ejpam-5656	280	13	of	of	ADP
ejpam-5656	280	14	the	the	DET
ejpam-5656	280	15	results	result	NOUN
ejpam-5656	280	16	,	,	PUNCT
ejpam-5656	280	17	paving	pave	VERB
ejpam-5656	280	18	the	the	DET
ejpam-5656	280	19	way	way	NOUN
ejpam-5656	280	20	for	for	ADP
ejpam-5656	280	21	further	further	ADJ
ejpam-5656	280	22	investigations	investigation	NOUN
ejpam-5656	280	23	into	into	ADP
ejpam-5656	280	24	the	the	DET
ejpam-5656	280	25	applications	application	NOUN
ejpam-5656	280	26	and	and	CCONJ
ejpam-5656	280	27	extensions	extension	NOUN
ejpam-5656	280	28	of	of	ADP
ejpam-5656	280	29	these	these	DET
ejpam-5656	280	30	polynomials	polynomial	NOUN
ejpam-5656	280	31	.	.	PUNCT
ejpam-5656	281	1	funding	fund	VERB
ejpam-5656	281	2	the	the	DET
ejpam-5656	281	3	research	research	NOUN
ejpam-5656	281	4	of	of	ADP
ejpam-5656	281	5	juan	juan	PROPN
ejpam-5656	281	6	hernández	hernández	PROPN
ejpam-5656	281	7	has	have	AUX
ejpam-5656	281	8	been	be	AUX
ejpam-5656	281	9	partially	partially	ADV
ejpam-5656	281	10	supported	support	VERB
ejpam-5656	281	11	by	by	ADP
ejpam-5656	281	12	the	the	DET
ejpam-5656	281	13	fondo	fondo	PROPN
ejpam-5656	281	14	nacional	nacional	PROPN
ejpam-5656	281	15	de	de	PROPN
ejpam-5656	281	16	innovación	innovación	PROPN
ejpam-5656	281	17	y	y	PROPN
ejpam-5656	281	18	desarrollo	desarrollo	NOUN
ejpam-5656	282	1	cient́ıfico	cient́ıfico	VERB
ejpam-5656	282	2	y	y	NOUN
ejpam-5656	282	3	tecnológico	tecnológico	NOUN
ejpam-5656	282	4	(	(	PUNCT
ejpam-5656	282	5	fondocyt	fondocyt	NOUN
ejpam-5656	282	6	)	)	PUNCT
ejpam-5656	282	7	,	,	PUNCT
ejpam-5656	282	8	dominican	dominican	PROPN
ejpam-5656	282	9	republic	republic	NOUN
ejpam-5656	282	10	,	,	PUNCT
ejpam-5656	282	11	under	under	ADP
ejpam-5656	282	12	grant	grant	NOUN
ejpam-5656	282	13	2023	2023	NUM
ejpam-5656	282	14	-	-	SYM
ejpam-5656	282	15	1	1	NUM
ejpam-5656	282	16	-	-	PUNCT
ejpam-5656	282	17	1d1	1d1	NOUN
ejpam-5656	282	18	-	-	PUNCT
ejpam-5656	282	19	0490	0490	NUM
ejpam-5656	282	20	.	.	PUNCT
ejpam-5656	283	1	references	reference	NOUN
ejpam-5656	283	2	[	[	X
ejpam-5656	283	3	1	1	NUM
ejpam-5656	283	4	]	]	PUNCT
ejpam-5656	283	5	t	t	PROPN
ejpam-5656	283	6	m	m	PROPN
ejpam-5656	283	7	apostol	apostol	NOUN
ejpam-5656	283	8	.	.	PUNCT
ejpam-5656	284	1	introduction	introduction	NOUN
ejpam-5656	284	2	to	to	ADP
ejpam-5656	284	3	analytic	analytic	ADJ
ejpam-5656	284	4	number	number	NOUN
ejpam-5656	284	5	theory	theory	NOUN
ejpam-5656	284	6	.	.	PUNCT
ejpam-5656	285	1	springer	springer	NOUN
ejpam-5656	285	2	science	science	PROPN
ejpam-5656	285	3	&	&	CCONJ
ejpam-5656	285	4	business	business	NOUN
ejpam-5656	285	5	media	medium	NOUN
ejpam-5656	285	6	,	,	PUNCT
ejpam-5656	285	7	1998	1998	NUM
ejpam-5656	285	8	.	.	PUNCT
ejpam-5656	286	1	[	[	X
ejpam-5656	286	2	2	2	X
ejpam-5656	286	3	]	]	X
ejpam-5656	286	4	p	p	X
ejpam-5656	286	5	appell	appell	ADV
ejpam-5656	286	6	.	.	PUNCT
ejpam-5656	287	1	sur	sur	PROPN
ejpam-5656	287	2	une	une	PROPN
ejpam-5656	287	3	classe	classe	PROPN
ejpam-5656	287	4	de	de	PROPN
ejpam-5656	287	5	polynomes	polynomes	PROPN
ejpam-5656	287	6	.	.	PUNCT
ejpam-5656	288	1	ann	ann	PROPN
ejpam-5656	288	2	.	.	PUNCT
ejpam-5656	288	3	sci	sci	PROPN
ejpam-5656	288	4	.	.	PROPN
ejpam-5656	288	5	ecole	ecole	PROPN
ejpam-5656	288	6	norm	norm	PROPN
ejpam-5656	288	7	.	.	PUNCT
ejpam-5656	289	1	sup	sup	NOUN
ejpam-5656	289	2	.	.	PROPN
ejpam-5656	289	3	,	,	PUNCT
ejpam-5656	289	4	9:119–144	9:119–144	NUM
ejpam-5656	289	5	,	,	PUNCT
ejpam-5656	289	6	1880	1880	NUM
ejpam-5656	289	7	.	.	PUNCT
ejpam-5656	290	1	[	[	X
ejpam-5656	290	2	3	3	NUM
ejpam-5656	290	3	]	]	PUNCT
ejpam-5656	290	4	h	h	NOUN
ejpam-5656	290	5	belbachir	belbachir	NOUN
ejpam-5656	290	6	,	,	PUNCT
ejpam-5656	290	7	y.	y.	PROPN
ejpam-5656	290	8	djemmada	djemmada	PROPN
ejpam-5656	290	9	,	,	PUNCT
ejpam-5656	290	10	and	and	CCONJ
ejpam-5656	290	11	s.	s.	PROPN
ejpam-5656	290	12	hadj	hadj	PROPN
ejpam-5656	290	13	-	-	PUNCT
ejpam-5656	290	14	brahim	brahim	PROPN
ejpam-5656	290	15	.	.	PUNCT
ejpam-5656	291	1	unified	unify	VERB
ejpam-5656	291	2	bernoulli	bernoulli	PROPN
ejpam-5656	291	3	-	-	PUNCT
ejpam-5656	291	4	euler	euler	NOUN
ejpam-5656	291	5	polynomials	polynomial	NOUN
ejpam-5656	291	6	of	of	ADP
ejpam-5656	291	7	apostol	apostol	PROPN
ejpam-5656	291	8	type	type	NOUN
ejpam-5656	291	9	.	.	PUNCT
ejpam-5656	292	1	indian	indian	PROPN
ejpam-5656	292	2	j	j	PROPN
ejpam-5656	292	3	pure	pure	ADJ
ejpam-5656	292	4	appl	appl	PROPN
ejpam-5656	292	5	math	math	NOUN
ejpam-5656	292	6	,	,	PUNCT
ejpam-5656	292	7	54(1):76–83	54(1):76–83	NUM
ejpam-5656	292	8	,	,	PUNCT
ejpam-5656	292	9	2023	2023	NUM
ejpam-5656	292	10	.	.	PUNCT
ejpam-5656	293	1	[	[	X
ejpam-5656	293	2	4	4	NUM
ejpam-5656	293	3	]	]	X
ejpam-5656	293	4	e	e	PROPN
ejpam-5656	293	5	d	d	PROPN
ejpam-5656	293	6	bloch	bloch	PROPN
ejpam-5656	293	7	.	.	PUNCT
ejpam-5656	294	1	the	the	DET
ejpam-5656	294	2	real	real	ADJ
ejpam-5656	294	3	numbers	number	NOUN
ejpam-5656	294	4	and	and	CCONJ
ejpam-5656	294	5	real	real	ADJ
ejpam-5656	294	6	analysis	analysis	NOUN
ejpam-5656	294	7	.	.	PUNCT
ejpam-5656	295	1	springer	springer	NOUN
ejpam-5656	295	2	new	new	PROPN
ejpam-5656	295	3	york	york	PROPN
ejpam-5656	295	4	,	,	PUNCT
ejpam-5656	295	5	2011	2011	NUM
ejpam-5656	295	6	.	.	PUNCT
ejpam-5656	296	1	[	[	X
ejpam-5656	296	2	5	5	NUM
ejpam-5656	296	3	]	]	PUNCT
ejpam-5656	296	4	c	c	NOUN
ejpam-5656	296	5	cesarano	cesarano	PROPN
ejpam-5656	296	6	.	.	PUNCT
ejpam-5656	297	1	monomiality	monomiality	NOUN
ejpam-5656	297	2	principle	principle	NOUN
ejpam-5656	297	3	and	and	CCONJ
ejpam-5656	297	4	related	relate	VERB
ejpam-5656	297	5	operational	operational	ADJ
ejpam-5656	297	6	techniques	technique	NOUN
ejpam-5656	297	7	for	for	ADP
ejpam-5656	297	8	orthogonal	orthogonal	ADJ
ejpam-5656	297	9	polynomials	polynomial	NOUN
ejpam-5656	297	10	and	and	CCONJ
ejpam-5656	297	11	special	special	ADJ
ejpam-5656	297	12	functions	function	NOUN
ejpam-5656	297	13	.	.	PUNCT
ejpam-5656	298	1	int	int	NOUN
ejpam-5656	298	2	.	.	PUNCT
ejpam-5656	299	1	journal	journal	PROPN
ejpam-5656	299	2	of	of	ADP
ejpam-5656	299	3	pure	pure	ADJ
ejpam-5656	299	4	mathematics	mathematic	NOUN
ejpam-5656	299	5	,	,	PUNCT
ejpam-5656	299	6	1(1):1–7	1(1):1–7	NUM
ejpam-5656	299	7	,	,	PUNCT
ejpam-5656	299	8	2014	2014	NUM
ejpam-5656	299	9	.	.	PUNCT
ejpam-5656	300	1	[	[	X
ejpam-5656	300	2	6	6	NUM
ejpam-5656	300	3	]	]	PUNCT
ejpam-5656	300	4	c	c	NOUN
ejpam-5656	300	5	cesarano	cesarano	PROPN
ejpam-5656	300	6	.	.	PUNCT
ejpam-5656	301	1	operational	operational	ADJ
ejpam-5656	301	2	methods	method	NOUN
ejpam-5656	301	3	for	for	ADP
ejpam-5656	301	4	hermite	hermite	ADJ
ejpam-5656	301	5	polynomials	polynomial	NOUN
ejpam-5656	301	6	.	.	PUNCT
ejpam-5656	302	1	int	int	NOUN
ejpam-5656	302	2	.	.	PUNCT
ejpam-5656	303	1	j.	j.	PROPN
ejpam-5656	303	2	math	math	PROPN
ejpam-5656	303	3	models	model	NOUN
ejpam-5656	303	4	methods	method	NOUN
ejpam-5656	303	5	appl	appl	PROPN
ejpam-5656	303	6	.	.	PUNCT
ejpam-5656	304	1	sc	sc	PROPN
ejpam-5656	304	2	.	.	PROPN
ejpam-5656	304	3	,	,	PUNCT
ejpam-5656	304	4	16:48–52	16:48–52	NUM
ejpam-5656	304	5	,	,	PUNCT
ejpam-5656	304	6	2022	2022	NUM
ejpam-5656	304	7	.	.	PUNCT
ejpam-5656	305	1	dı́az	dı́az	X
ejpam-5656	305	2	et	et	PROPN
ejpam-5656	305	3	al	al	PROPN
ejpam-5656	305	4	.	.	PUNCT
ejpam-5656	305	5	/	/	SYM
ejpam-5656	305	6	eur	eur	PROPN
ejpam-5656	305	7	.	.	PUNCT
ejpam-5656	306	1	j.	j.	PROPN
ejpam-5656	306	2	pure	pure	PROPN
ejpam-5656	306	3	appl	appl	PROPN
ejpam-5656	306	4	.	.	PROPN
ejpam-5656	306	5	math	math	PROPN
ejpam-5656	306	6	,	,	PUNCT
ejpam-5656	306	7	18	18	NUM
ejpam-5656	306	8	(	(	PUNCT
ejpam-5656	306	9	1	1	NUM
ejpam-5656	306	10	)	)	PUNCT
ejpam-5656	306	11	(	(	PUNCT
ejpam-5656	306	12	2025	2025	NUM
ejpam-5656	306	13	)	)	PUNCT
ejpam-5656	306	14	,	,	PUNCT
ejpam-5656	306	15	5656	5656	NUM
ejpam-5656	306	16	16	16	NUM
ejpam-5656	306	17	of	of	ADP
ejpam-5656	306	18	17	17	NUM
ejpam-5656	307	1	[	[	X
ejpam-5656	307	2	7	7	NUM
ejpam-5656	307	3	]	]	X
ejpam-5656	307	4	c	c	NOUN
ejpam-5656	307	5	cesarano	cesarano	PROPN
ejpam-5656	307	6	,	,	PUNCT
ejpam-5656	307	7	w	w	PROPN
ejpam-5656	307	8	ramı́rez	ramı́rez	PROPN
ejpam-5656	307	9	,	,	PUNCT
ejpam-5656	307	10	and	and	CCONJ
ejpam-5656	307	11	s	s	PROPN
ejpam-5656	307	12	khan	khan	PROPN
ejpam-5656	307	13	.	.	PUNCT
ejpam-5656	308	1	a	a	DET
ejpam-5656	308	2	new	new	ADJ
ejpam-5656	308	3	class	class	NOUN
ejpam-5656	308	4	of	of	ADP
ejpam-5656	308	5	degenerate	degenerate	ADJ
ejpam-5656	308	6	apostol	apostol	NOUN
ejpam-5656	308	7	-	-	PUNCT
ejpam-5656	308	8	type	type	NOUN
ejpam-5656	308	9	hermite	hermite	ADJ
ejpam-5656	308	10	polynomials	polynomial	NOUN
ejpam-5656	308	11	and	and	CCONJ
ejpam-5656	308	12	applications	application	NOUN
ejpam-5656	308	13	.	.	PUNCT
ejpam-5656	309	1	dolomites	dolomite	NOUN
ejpam-5656	309	2	res	re	NOUN
ejpam-5656	309	3	.	.	PUNCT
ejpam-5656	310	1	notes	notes	PROPN
ejpam-5656	310	2	approx	approx	PROPN
ejpam-5656	310	3	.	.	PROPN
ejpam-5656	310	4	,	,	PUNCT
ejpam-5656	310	5	15(1	15(1	NUM
ejpam-5656	310	6	)	)	PUNCT
ejpam-5656	310	7	,	,	PUNCT
ejpam-5656	310	8	2022	2022	NUM
ejpam-5656	310	9	.	.	PUNCT
ejpam-5656	311	1	[	[	X
ejpam-5656	311	2	8	8	NUM
ejpam-5656	311	3	]	]	X
ejpam-5656	311	4	c	c	AUX
ejpam-5656	311	5	cesarano	cesarano	PROPN
ejpam-5656	311	6	and	and	CCONJ
ejpam-5656	311	7	w	w	AUX
ejpam-5656	311	8	ramŕez	ramŕez	PROPN
ejpam-5656	311	9	.	.	PUNCT
ejpam-5656	312	1	applying	apply	VERB
ejpam-5656	312	2	the	the	DET
ejpam-5656	312	3	monomiality	monomiality	NOUN
ejpam-5656	312	4	principle	principle	NOUN
ejpam-5656	312	5	to	to	ADP
ejpam-5656	312	6	the	the	DET
ejpam-5656	312	7	new	new	ADJ
ejpam-5656	312	8	family	family	NOUN
ejpam-5656	312	9	of	of	ADP
ejpam-5656	312	10	apostol	apostol	PROPN
ejpam-5656	312	11	hermite	hermite	PROPN
ejpam-5656	312	12	bernoulli	bernoulli	NOUN
ejpam-5656	312	13	-	-	PUNCT
ejpam-5656	312	14	type	type	NOUN
ejpam-5656	312	15	polynomials	polynomial	NOUN
ejpam-5656	312	16	.	.	PUNCT
ejpam-5656	313	1	commun	commun	PROPN
ejpam-5656	313	2	.	.	PUNCT
ejpam-5656	314	1	appl	appl	PROPN
ejpam-5656	314	2	.	.	PUNCT
ejpam-5656	315	1	ind	ind	PROPN
ejpam-5656	315	2	.	.	PUNCT
ejpam-5656	316	1	math	math	PROPN
ejpam-5656	316	2	.	.	PUNCT
ejpam-5656	316	3	,	,	PUNCT
ejpam-5656	316	4	15(2):28–35	15(2):28–35	NUM
ejpam-5656	316	5	,	,	PUNCT
ejpam-5656	316	6	2024	2024	NUM
ejpam-5656	316	7	.	.	PUNCT
ejpam-5656	317	1	[	[	X
ejpam-5656	317	2	9	9	NUM
ejpam-5656	317	3	]	]	X
ejpam-5656	317	4	f	f	X
ejpam-5656	317	5	a	a	DET
ejpam-5656	317	6	costabile	costabile	NOUN
ejpam-5656	317	7	and	and	CCONJ
ejpam-5656	317	8	e	e	PROPN
ejpam-5656	317	9	longo	longo	PROPN
ejpam-5656	317	10	.	.	PUNCT
ejpam-5656	318	1	a	a	DET
ejpam-5656	318	2	determinantal	determinantal	ADJ
ejpam-5656	318	3	approach	approach	NOUN
ejpam-5656	318	4	to	to	ADP
ejpam-5656	318	5	appell	appell	ADJ
ejpam-5656	318	6	polynomials	polynomial	NOUN
ejpam-5656	318	7	.	.	PUNCT
ejpam-5656	319	1	j.	j.	PROPN
ejpam-5656	319	2	comput	comput	PROPN
ejpam-5656	319	3	.	.	PUNCT
ejpam-5656	320	1	appl	appl	PROPN
ejpam-5656	320	2	.	.	PROPN
ejpam-5656	320	3	math	math	PROPN
ejpam-5656	320	4	.	.	PUNCT
ejpam-5656	320	5	,	,	PUNCT
ejpam-5656	321	1	234(5):1528–1542	234(5):1528–1542	NUM
ejpam-5656	321	2	,	,	PUNCT
ejpam-5656	321	3	2010	2010	NUM
ejpam-5656	321	4	.	.	PUNCT
ejpam-5656	322	1	[	[	X
ejpam-5656	322	2	10	10	NUM
ejpam-5656	322	3	]	]	X
ejpam-5656	322	4	d	d	X
ejpam-5656	322	5	bedoya	bedoya	PROPN
ejpam-5656	322	6	and	and	CCONJ
ejpam-5656	322	7	c	c	AUX
ejpam-5656	322	8	cesarano	cesarano	PROPN
ejpam-5656	322	9	and	and	CCONJ
ejpam-5656	322	10	s	s	X
ejpam-5656	322	11	dı́az	dı́az	NOUN
ejpam-5656	322	12	and	and	CCONJ
ejpam-5656	322	13	w	w	PROPN
ejpam-5656	322	14	ramı́rez	ramı́rez	PROPN
ejpam-5656	322	15	.	.	PUNCT
ejpam-5656	323	1	new	new	ADJ
ejpam-5656	323	2	classes	class	NOUN
ejpam-5656	323	3	of	of	ADP
ejpam-5656	323	4	degenerate	degenerate	ADJ
ejpam-5656	323	5	unified	unified	ADJ
ejpam-5656	323	6	polynomials	polynomial	NOUN
ejpam-5656	323	7	.	.	PUNCT
ejpam-5656	324	1	axioms	axiom	NOUN
ejpam-5656	324	2	,	,	PUNCT
ejpam-5656	324	3	12(1	12(1	NUM
ejpam-5656	324	4	)	)	PUNCT
ejpam-5656	324	5	,	,	PUNCT
ejpam-5656	324	6	2023	2023	NUM
ejpam-5656	324	7	.	.	PUNCT
ejpam-5656	325	1	[	[	X
ejpam-5656	325	2	11	11	NUM
ejpam-5656	325	3	]	]	SYM
ejpam-5656	325	4	g	g	NOUN
ejpam-5656	325	5	dattoli	dattoli	NOUN
ejpam-5656	325	6	.	.	PUNCT
ejpam-5656	326	1	hermite	hermite	ADJ
ejpam-5656	326	2	-	-	PUNCT
ejpam-5656	326	3	bessel	bessel	NOUN
ejpam-5656	326	4	and	and	CCONJ
ejpam-5656	326	5	laguerre	laguerre	NOUN
ejpam-5656	326	6	-	-	PUNCT
ejpam-5656	326	7	bessel	bessel	NOUN
ejpam-5656	326	8	functions	function	NOUN
ejpam-5656	326	9	:	:	PUNCT
ejpam-5656	326	10	a	a	DET
ejpam-5656	326	11	by	by	ADP
ejpam-5656	326	12	-	-	PUNCT
ejpam-5656	326	13	product	product	NOUN
ejpam-5656	326	14	of	of	ADP
ejpam-5656	326	15	the	the	DET
ejpam-5656	326	16	monomiality	monomiality	NOUN
ejpam-5656	326	17	principle	principle	NOUN
ejpam-5656	326	18	.	.	PUNCT
ejpam-5656	327	1	proc	proc	NOUN
ejpam-5656	327	2	.	.	PUNCT
ejpam-5656	328	1	melfi	melfi	PROPN
ejpam-5656	328	2	sch	sch	PROPN
ejpam-5656	328	3	.	.	PUNCT
ejpam-5656	329	1	adv	adv	PROPN
ejpam-5656	329	2	.	.	PUNCT
ejpam-5656	329	3	top	top	PROPN
ejpam-5656	329	4	.	.	PUNCT
ejpam-5656	330	1	math	math	NOUN
ejpam-5656	330	2	.	.	PUNCT
ejpam-5656	331	1	phys	phy	NOUN
ejpam-5656	331	2	.	.	PUNCT
ejpam-5656	331	3	,	,	PUNCT
ejpam-5656	331	4	1:147–164	1:147–164	NOUN
ejpam-5656	331	5	,	,	PUNCT
ejpam-5656	331	6	2000	2000	NUM
ejpam-5656	331	7	.	.	PUNCT
ejpam-5656	332	1	[	[	X
ejpam-5656	332	2	12	12	NUM
ejpam-5656	332	3	]	]	X
ejpam-5656	332	4	g	g	NOUN
ejpam-5656	332	5	dattoli	dattoli	NOUN
ejpam-5656	332	6	,	,	PUNCT
ejpam-5656	332	7	s	s	VERB
ejpam-5656	332	8	lorenzutta	lorenzutta	ADJ
ejpam-5656	332	9	,	,	PUNCT
ejpam-5656	332	10	and	and	CCONJ
ejpam-5656	332	11	c	c	ADP
ejpam-5656	332	12	cesarano	cesarano	PROPN
ejpam-5656	332	13	.	.	PUNCT
ejpam-5656	333	1	finite	finite	PROPN
ejpam-5656	333	2	sums	sum	NOUN
ejpam-5656	333	3	and	and	CCONJ
ejpam-5656	333	4	generalized	generalized	ADJ
ejpam-5656	333	5	forms	form	NOUN
ejpam-5656	333	6	of	of	ADP
ejpam-5656	333	7	bernoulli	bernoulli	NOUN
ejpam-5656	333	8	polynomials	polynomial	NOUN
ejpam-5656	333	9	.	.	PUNCT
ejpam-5656	334	1	rendiconti	rendiconti	PROPN
ejpam-5656	334	2	di	di	PROPN
ejpam-5656	334	3	matematica	matematica	PROPN
ejpam-5656	334	4	e	e	PROPN
ejpam-5656	334	5	delle	delle	PROPN
ejpam-5656	334	6	sue	sue	PROPN
ejpam-5656	334	7	applicazioni	applicazioni	PROPN
ejpam-5656	334	8	.	.	PUNCT
ejpam-5656	335	1	serie	serie	PROPN
ejpam-5656	335	2	vii	vii	PROPN
ejpam-5656	335	3	,	,	PUNCT
ejpam-5656	335	4	19	19	NUM
ejpam-5656	335	5	,	,	PUNCT
ejpam-5656	335	6	01	01	NUM
ejpam-5656	335	7	1999	1999	NUM
ejpam-5656	335	8	.	.	PUNCT
ejpam-5656	336	1	[	[	X
ejpam-5656	336	2	13	13	NUM
ejpam-5656	336	3	]	]	SYM
ejpam-5656	336	4	g	g	NOUN
ejpam-5656	336	5	dattoli	dattoli	NOUN
ejpam-5656	336	6	,	,	PUNCT
ejpam-5656	336	7	m	m	VERB
ejpam-5656	336	8	migliorati	migliorati	ADJ
ejpam-5656	336	9	,	,	PUNCT
ejpam-5656	336	10	and	and	CCONJ
ejpam-5656	336	11	h	h	PROPN
ejpam-5656	336	12	m	m	PROPN
ejpam-5656	336	13	srivastava	srivastava	PROPN
ejpam-5656	336	14	.	.	PUNCT
ejpam-5656	337	1	sheffer	sheffer	PROPN
ejpam-5656	337	2	polynomials	polynomial	NOUN
ejpam-5656	337	3	,	,	PUNCT
ejpam-5656	337	4	monomiality	monomiality	NOUN
ejpam-5656	337	5	principle	principle	NOUN
ejpam-5656	337	6	,	,	PUNCT
ejpam-5656	337	7	algebraic	algebraic	ADJ
ejpam-5656	337	8	methods	method	NOUN
ejpam-5656	337	9	and	and	CCONJ
ejpam-5656	337	10	the	the	DET
ejpam-5656	337	11	theory	theory	NOUN
ejpam-5656	337	12	of	of	ADP
ejpam-5656	337	13	classical	classical	ADJ
ejpam-5656	337	14	polynomials	polynomial	NOUN
ejpam-5656	337	15	.	.	PUNCT
ejpam-5656	338	1	mathematical	mathematical	ADJ
ejpam-5656	338	2	and	and	CCONJ
ejpam-5656	338	3	computer	computer	NOUN
ejpam-5656	338	4	modelling	modelling	NOUN
ejpam-5656	338	5	,	,	PUNCT
ejpam-5656	338	6	45(9):1033–1041	45(9):1033–1041	PROPN
ejpam-5656	338	7	,	,	PUNCT
ejpam-5656	338	8	2007	2007	NUM
ejpam-5656	338	9	.	.	PUNCT
ejpam-5656	339	1	[	[	X
ejpam-5656	339	2	14	14	NUM
ejpam-5656	339	3	]	]	X
ejpam-5656	339	4	i	i	PRON
ejpam-5656	339	5	s	s	VERB
ejpam-5656	339	6	gradshteyn	gradshteyn	ADJ
ejpam-5656	340	1	and	and	CCONJ
ejpam-5656	340	2	i	i	PRON
ejpam-5656	340	3	m	m	VERB
ejpam-5656	340	4	ryzhik	ryzhik	ADJ
ejpam-5656	340	5	.	.	PUNCT
ejpam-5656	341	1	table	table	NOUN
ejpam-5656	341	2	of	of	ADP
ejpam-5656	341	3	integrals	integral	NOUN
ejpam-5656	341	4	,	,	PUNCT
ejpam-5656	341	5	series	series	NOUN
ejpam-5656	341	6	,	,	PUNCT
ejpam-5656	341	7	and	and	CCONJ
ejpam-5656	341	8	products	product	NOUN
ejpam-5656	341	9	.	.	PUNCT
ejpam-5656	342	1	elsevier	elsevier	NOUN
ejpam-5656	342	2	/	/	SYM
ejpam-5656	342	3	academic	academic	ADJ
ejpam-5656	342	4	press	press	NOUN
ejpam-5656	342	5	,	,	PUNCT
ejpam-5656	342	6	amsterdam	amsterdam	PROPN
ejpam-5656	342	7	,	,	PUNCT
ejpam-5656	342	8	seventh	seventh	ADJ
ejpam-5656	342	9	edition	edition	NOUN
ejpam-5656	342	10	,	,	PUNCT
ejpam-5656	342	11	2007	2007	NUM
ejpam-5656	342	12	.	.	PUNCT
ejpam-5656	343	1	[	[	X
ejpam-5656	343	2	15	15	NUM
ejpam-5656	343	3	]	]	X
ejpam-5656	343	4	n.	n.	PROPN
ejpam-5656	343	5	a.	a.	PROPN
ejpam-5656	343	6	khan	khan	PROPN
ejpam-5656	343	7	,	,	PUNCT
ejpam-5656	343	8	o.	o.	PROPN
ejpam-5656	343	9	i.	i.	PROPN
ejpam-5656	343	10	khalaf	khalaf	PROPN
ejpam-5656	343	11	,	,	PUNCT
ejpam-5656	343	12	c	c	PROPN
ejpam-5656	343	13	a	a	DET
ejpam-5656	343	14	romero	romero	PROPN
ejpam-5656	343	15	,	,	PUNCT
ejpam-5656	343	16	m	m	PROPN
ejpam-5656	343	17	sulaiman	sulaiman	NOUN
ejpam-5656	343	18	,	,	PUNCT
ejpam-5656	343	19	and	and	CCONJ
ejpam-5656	343	20	m	m	VERB
ejpam-5656	343	21	a	a	DET
ejpam-5656	343	22	bakar	bakar	NOUN
ejpam-5656	343	23	.	.	PUNCT
ejpam-5656	344	1	application	application	NOUN
ejpam-5656	344	2	of	of	ADP
ejpam-5656	344	3	euler	euler	PROPN
ejpam-5656	344	4	neural	neural	ADJ
ejpam-5656	344	5	networks	network	NOUN
ejpam-5656	344	6	with	with	ADP
ejpam-5656	344	7	soft	soft	ADJ
ejpam-5656	344	8	computing	computing	NOUN
ejpam-5656	344	9	paradigm	paradigm	NOUN
ejpam-5656	344	10	to	to	PART
ejpam-5656	344	11	solve	solve	VERB
ejpam-5656	344	12	nonlinear	nonlinear	ADJ
ejpam-5656	344	13	problems	problem	NOUN
ejpam-5656	344	14	arising	arise	VERB
ejpam-5656	344	15	in	in	ADP
ejpam-5656	344	16	heat	heat	NOUN
ejpam-5656	344	17	transfer	transfer	NOUN
ejpam-5656	344	18	.	.	PUNCT
ejpam-5656	345	1	entropy	entropy	PROPN
ejpam-5656	345	2	,	,	PUNCT
ejpam-5656	345	3	23(8	23(8	NOUN
ejpam-5656	345	4	)	)	PUNCT
ejpam-5656	345	5	,	,	PUNCT
ejpam-5656	345	6	2021	2021	NUM
ejpam-5656	345	7	.	.	PUNCT
ejpam-5656	346	1	[	[	X
ejpam-5656	346	2	16	16	NUM
ejpam-5656	346	3	]	]	X
ejpam-5656	346	4	qiu	qiu	PROPN
ejpam-5656	346	5	-	-	PUNCT
ejpam-5656	346	6	ming	ming	PROPN
ejpam-5656	346	7	luo	luo	PROPN
ejpam-5656	346	8	and	and	CCONJ
ejpam-5656	346	9	h.m	h.m	PROPN
ejpam-5656	346	10	.	.	PROPN
ejpam-5656	346	11	srivastava	srivastava	PROPN
ejpam-5656	346	12	.	.	PUNCT
ejpam-5656	347	1	some	some	DET
ejpam-5656	347	2	generalizations	generalization	NOUN
ejpam-5656	347	3	of	of	ADP
ejpam-5656	347	4	the	the	DET
ejpam-5656	347	5	apostol	apostol	NOUN
ejpam-5656	347	6	–	–	PUNCT
ejpam-5656	347	7	bernoulli	bernoulli	NOUN
ejpam-5656	347	8	and	and	CCONJ
ejpam-5656	347	9	apostol	apostol	NOUN
ejpam-5656	347	10	–	–	PUNCT
ejpam-5656	347	11	euler	euler	NOUN
ejpam-5656	347	12	polynomials	polynomial	NOUN
ejpam-5656	347	13	.	.	PUNCT
ejpam-5656	348	1	journal	journal	PROPN
ejpam-5656	348	2	of	of	ADP
ejpam-5656	348	3	mathematical	mathematical	ADJ
ejpam-5656	348	4	analysis	analysis	NOUN
ejpam-5656	348	5	and	and	CCONJ
ejpam-5656	348	6	applications	application	NOUN
ejpam-5656	348	7	,	,	PUNCT
ejpam-5656	348	8	308(1):290–302	308(1):290–302	NUM
ejpam-5656	348	9	,	,	PUNCT
ejpam-5656	348	10	2005	2005	NUM
ejpam-5656	348	11	.	.	PUNCT
ejpam-5656	349	1	[	[	X
ejpam-5656	349	2	17	17	NUM
ejpam-5656	349	3	]	]	X
ejpam-5656	349	4	l	l	PROPN
ejpam-5656	349	5	navas	navas	PROPN
ejpam-5656	349	6	,	,	PUNCT
ejpam-5656	349	7	f	f	PROPN
ejpam-5656	349	8	ruiz	ruiz	NOUN
ejpam-5656	349	9	,	,	PUNCT
ejpam-5656	349	10	and	and	CCONJ
ejpam-5656	349	11	j	j	PROPN
ejpam-5656	349	12	l	l	PROPN
ejpam-5656	349	13	varona	varona	PROPN
ejpam-5656	349	14	.	.	PUNCT
ejpam-5656	350	1	existence	existence	NOUN
ejpam-5656	350	2	and	and	CCONJ
ejpam-5656	350	3	reduction	reduction	NOUN
ejpam-5656	350	4	of	of	ADP
ejpam-5656	350	5	generalized	generalized	ADJ
ejpam-5656	350	6	apostolbernoulli	apostolbernoulli	NOUN
ejpam-5656	350	7	,	,	PUNCT
ejpam-5656	350	8	apostol	apostol	NOUN
ejpam-5656	350	9	-	-	PUNCT
ejpam-5656	350	10	euler	euler	NOUN
ejpam-5656	350	11	and	and	CCONJ
ejpam-5656	350	12	apostol	apostol	NOUN
ejpam-5656	350	13	-	-	PUNCT
ejpam-5656	350	14	genocchi	genocchi	PROPN
ejpam-5656	350	15	polynomials	polynomial	NOUN
ejpam-5656	350	16	.	.	PUNCT
ejpam-5656	351	1	archivum	archivum	PROPN
ejpam-5656	351	2	mathematicum	mathematicum	PROPN
ejpam-5656	351	3	,	,	PUNCT
ejpam-5656	351	4	55(3):157–165	55(3):157–165	PROPN
ejpam-5656	351	5	,	,	PUNCT
ejpam-5656	351	6	01	01	NUM
ejpam-5656	351	7	2019	2019	NUM
ejpam-5656	351	8	.	.	PUNCT
ejpam-5656	352	1	[	[	X
ejpam-5656	352	2	18	18	NUM
ejpam-5656	352	3	]	]	X
ejpam-5656	352	4	s	s	PART
ejpam-5656	352	5	nemati	nemati	NOUN
ejpam-5656	352	6	and	and	CCONJ
ejpam-5656	352	7	d	d	NOUN
ejpam-5656	352	8	fm	fm	PROPN
ejpam-5656	352	9	torres	torre	NOUN
ejpam-5656	352	10	.	.	PUNCT
ejpam-5656	353	1	application	application	NOUN
ejpam-5656	353	2	of	of	ADP
ejpam-5656	353	3	bernoulli	bernoulli	NOUN
ejpam-5656	353	4	polynomials	polynomial	NOUN
ejpam-5656	353	5	for	for	ADP
ejpam-5656	353	6	solving	solve	VERB
ejpam-5656	353	7	variableorder	variableorder	NOUN
ejpam-5656	353	8	fractional	fractional	ADJ
ejpam-5656	353	9	optimal	optimal	ADJ
ejpam-5656	353	10	control	control	NOUN
ejpam-5656	353	11	-	-	PUNCT
ejpam-5656	353	12	affine	affine	NOUN
ejpam-5656	353	13	problems	problem	NOUN
ejpam-5656	353	14	.	.	PUNCT
ejpam-5656	354	1	axioms	axiom	NOUN
ejpam-5656	354	2	,	,	PUNCT
ejpam-5656	354	3	9(4	9(4	NUM
ejpam-5656	354	4	)	)	PUNCT
ejpam-5656	354	5	,	,	PUNCT
ejpam-5656	354	6	2020	2020	NUM
ejpam-5656	354	7	.	.	PUNCT
ejpam-5656	355	1	[	[	X
ejpam-5656	355	2	19	19	NUM
ejpam-5656	355	3	]	]	X
ejpam-5656	355	4	m	m	VERB
ejpam-5656	355	5	a	a	DET
ejpam-5656	355	6	pathan	pathan	NOUN
ejpam-5656	355	7	and	and	CCONJ
ejpam-5656	355	8	w	w	ADP
ejpam-5656	355	9	a	a	DET
ejpam-5656	355	10	khan	khan	PROPN
ejpam-5656	355	11	.	.	PUNCT
ejpam-5656	356	1	some	some	DET
ejpam-5656	356	2	implicit	implicit	ADJ
ejpam-5656	356	3	summation	summation	NOUN
ejpam-5656	356	4	formulas	formula	NOUN
ejpam-5656	356	5	and	and	CCONJ
ejpam-5656	356	6	symmetric	symmetric	ADJ
ejpam-5656	356	7	identities	identity	NOUN
ejpam-5656	356	8	for	for	ADP
ejpam-5656	356	9	the	the	DET
ejpam-5656	356	10	generalized	generalize	VERB
ejpam-5656	356	11	hermite	hermite	ADJ
ejpam-5656	356	12	–	–	PUNCT
ejpam-5656	356	13	euler	euler	NOUN
ejpam-5656	356	14	polynomials	polynomial	NOUN
ejpam-5656	356	15	.	.	PUNCT
ejpam-5656	357	1	east	east	PROPN
ejpam-5656	357	2	-	-	PUNCT
ejpam-5656	357	3	west	west	PROPN
ejpam-5656	357	4	j.	j.	PROPN
ejpam-5656	357	5	maths	maths	PROPN
ejpam-5656	357	6	.	.	PUNCT
ejpam-5656	357	7	,	,	PUNCT
ejpam-5656	358	1	16(1):92	16(1):92	NUM
ejpam-5656	358	2	–	–	PUNCT
ejpam-5656	358	3	109	109	NUM
ejpam-5656	358	4	,	,	PUNCT
ejpam-5656	358	5	2014	2014	NUM
ejpam-5656	358	6	.	.	PUNCT
ejpam-5656	359	1	[	[	X
ejpam-5656	359	2	20	20	NUM
ejpam-5656	359	3	]	]	X
ejpam-5656	359	4	y.	y.	PROPN
ejpam-5656	359	5	quintana	quintana	PROPN
ejpam-5656	359	6	,	,	PUNCT
ejpam-5656	359	7	c.	c.	PROPN
ejpam-5656	359	8	cesarano	cesarano	PROPN
ejpam-5656	359	9	,	,	PUNCT
ejpam-5656	359	10	and	and	CCONJ
ejpam-5656	359	11	w.	w.	PROPN
ejpam-5656	359	12	ramı́rez	ramı́rez	PROPN
ejpam-5656	359	13	.	.	PROPN
ejpam-5656	359	14	degenerate	degenerate	ADJ
ejpam-5656	359	15	versions	version	NOUN
ejpam-5656	359	16	of	of	ADP
ejpam-5656	359	17	hypergeometric	hypergeometric	ADJ
ejpam-5656	359	18	bernoulli	bernoulli	NOUN
ejpam-5656	359	19	-	-	PUNCT
ejpam-5656	359	20	euler	euler	NOUN
ejpam-5656	359	21	polynomials	polynomial	NOUN
ejpam-5656	359	22	.	.	PUNCT
ejpam-5656	360	1	lobachevskii	lobachevskii	PROPN
ejpam-5656	360	2	j.	j.	PROPN
ejpam-5656	360	3	math	math	PROPN
ejpam-5656	360	4	.	.	PUNCT
ejpam-5656	360	5	,	,	PUNCT
ejpam-5656	360	6	45(8):3509–3521	45(8):3509–3521	NUM
ejpam-5656	360	7	,	,	PUNCT
ejpam-5656	360	8	2024	2024	NUM
ejpam-5656	360	9	.	.	PUNCT
ejpam-5656	361	1	[	[	X
ejpam-5656	361	2	21	21	NUM
ejpam-5656	361	3	]	]	X
ejpam-5656	361	4	y.	y.	PROPN
ejpam-5656	361	5	quintana	quintana	PROPN
ejpam-5656	361	6	,	,	PUNCT
ejpam-5656	361	7	c.	c.	PROPN
ejpam-5656	361	8	cesarano	cesarano	PROPN
ejpam-5656	361	9	,	,	PUNCT
ejpam-5656	361	10	and	and	CCONJ
ejpam-5656	361	11	w.	w.	PROPN
ejpam-5656	361	12	ramı́rez	ramı́rez	PROPN
ejpam-5656	361	13	.	.	PUNCT
ejpam-5656	362	1	a	a	DET
ejpam-5656	362	2	survey	survey	NOUN
ejpam-5656	362	3	on	on	ADP
ejpam-5656	362	4	orthogonal	orthogonal	ADJ
ejpam-5656	362	5	polynomials	polynomial	NOUN
ejpam-5656	362	6	from	from	ADP
ejpam-5656	362	7	a	a	DET
ejpam-5656	362	8	monomiality	monomiality	NOUN
ejpam-5656	362	9	principle	principle	ADJ
ejpam-5656	362	10	point	point	NOUN
ejpam-5656	362	11	of	of	ADP
ejpam-5656	362	12	view	view	NOUN
ejpam-5656	362	13	.	.	PUNCT
ejpam-5656	363	1	encyclopedia	encyclopedia	NOUN
ejpam-5656	363	2	.	.	PUNCT
ejpam-5656	363	3	,	,	PUNCT
ejpam-5656	363	4	4:1355–1366	4:1355–1366	NUM
ejpam-5656	363	5	,	,	PUNCT
ejpam-5656	363	6	2024	2024	NUM
ejpam-5656	363	7	.	.	PUNCT
ejpam-5656	364	1	[	[	X
ejpam-5656	364	2	22	22	NUM
ejpam-5656	364	3	]	]	X
ejpam-5656	364	4	y	y	PROPN
ejpam-5656	364	5	quintana	quintana	PROPN
ejpam-5656	364	6	and	and	CCONJ
ejpam-5656	364	7	w	w	PROPN
ejpam-5656	364	8	ramı́rez	ramı́rez	PROPN
ejpam-5656	364	9	.	.	PUNCT
ejpam-5656	365	1	a	a	DET
ejpam-5656	365	2	degenerate	degenerate	ADJ
ejpam-5656	365	3	version	version	NOUN
ejpam-5656	365	4	of	of	ADP
ejpam-5656	365	5	hypergeometric	hypergeometric	ADJ
ejpam-5656	365	6	bernoulli	bernoulli	NOUN
ejpam-5656	365	7	polynomials	polynomial	NOUN
ejpam-5656	365	8	:	:	PUNCT
ejpam-5656	365	9	announcement	announcement	NOUN
ejpam-5656	365	10	of	of	ADP
ejpam-5656	365	11	results	result	NOUN
ejpam-5656	365	12	.	.	PUNCT
ejpam-5656	366	1	commun	commun	PROPN
ejpam-5656	366	2	.	.	PUNCT
ejpam-5656	367	1	appl	appl	PROPN
ejpam-5656	367	2	.	.	PUNCT
ejpam-5656	368	1	ind	ind	PROPN
ejpam-5656	368	2	.	.	PUNCT
ejpam-5656	369	1	math	math	NOUN
ejpam-5656	369	2	.	.	PUNCT
ejpam-5656	369	3	,	,	PUNCT
ejpam-5656	370	1	15(2):36–43	15(2):36–43	NUM
ejpam-5656	370	2	,	,	PUNCT
ejpam-5656	370	3	2024	2024	NUM
ejpam-5656	370	4	.	.	PUNCT
ejpam-5656	371	1	[	[	X
ejpam-5656	371	2	23	23	NUM
ejpam-5656	371	3	]	]	X
ejpam-5656	371	4	w	w	PROPN
ejpam-5656	371	5	ramı́rez	ramı́rez	PROPN
ejpam-5656	371	6	,	,	PUNCT
ejpam-5656	371	7	c	c	NOUN
ejpam-5656	371	8	cesarano	cesarano	PROPN
ejpam-5656	371	9	,	,	PUNCT
ejpam-5656	371	10	d	d	PROPN
ejpam-5656	371	11	bedoya	bedoya	PROPN
ejpam-5656	371	12	,	,	PUNCT
ejpam-5656	371	13	c	c	NOUN
ejpam-5656	371	14	kızılates	kızılate	NOUN
ejpam-5656	371	15	,	,	PUNCT
ejpam-5656	371	16	and	and	CCONJ
ejpam-5656	371	17	c	c	NOUN
ejpam-5656	371	18	s	s	NOUN
ejpam-5656	371	19	ryoo	ryoo	NOUN
ejpam-5656	371	20	.	.	PUNCT
ejpam-5656	372	1	on	on	ADP
ejpam-5656	372	2	certain	certain	ADJ
ejpam-5656	372	3	properties	property	NOUN
ejpam-5656	372	4	of	of	ADP
ejpam-5656	372	5	three	three	NUM
ejpam-5656	372	6	parametric	parametric	ADJ
ejpam-5656	372	7	kinds	kind	NOUN
ejpam-5656	372	8	of	of	ADP
ejpam-5656	372	9	apostol	apostol	NOUN
ejpam-5656	372	10	-	-	PUNCT
ejpam-5656	372	11	type	type	NOUN
ejpam-5656	372	12	unified	unified	ADJ
ejpam-5656	372	13	bernoulli	bernoulli	NOUN
ejpam-5656	372	14	-	-	PUNCT
ejpam-5656	372	15	euler	euler	NOUN
ejpam-5656	372	16	polynomials	polynomial	NOUN
ejpam-5656	372	17	.	.	PUNCT
ejpam-5656	373	1	aims	aim	VERB
ejpam-5656	373	2	mathematics	mathematic	NOUN
ejpam-5656	373	3	.	.	PUNCT
ejpam-5656	373	4	,	,	PUNCT
ejpam-5656	374	1	10(1):137–158	10(1):137–158	NUM
ejpam-5656	374	2	,	,	PUNCT
ejpam-5656	374	3	2025	2025	NUM
ejpam-5656	374	4	.	.	PUNCT
ejpam-5656	375	1	[	[	X
ejpam-5656	375	2	24	24	NUM
ejpam-5656	375	3	]	]	X
ejpam-5656	375	4	h	h	PROPN
ejpam-5656	375	5	m	m	PROPN
ejpam-5656	375	6	srivastava	srivastava	PROPN
ejpam-5656	375	7	and	and	CCONJ
ejpam-5656	375	8	h	h	PROPN
ejpam-5656	375	9	l	l	PROPN
ejpam-5656	375	10	manocha	manocha	NOUN
ejpam-5656	375	11	.	.	PUNCT
ejpam-5656	376	1	a	a	DET
ejpam-5656	376	2	treatise	treatise	NOUN
ejpam-5656	376	3	on	on	ADP
ejpam-5656	376	4	generating	generating	NOUN
ejpam-5656	376	5	functions	function	NOUN
ejpam-5656	376	6	.	.	PUNCT
ejpam-5656	377	1	new	new	PROPN
ejpam-5656	377	2	york	york	PROPN
ejpam-5656	377	3	:	:	PUNCT
ejpam-5656	377	4	dı́az	dı́az	X
ejpam-5656	377	5	et	et	PROPN
ejpam-5656	377	6	al	al	PROPN
ejpam-5656	377	7	.	.	PUNCT
ejpam-5656	377	8	/	/	SYM
ejpam-5656	377	9	eur	eur	PROPN
ejpam-5656	377	10	.	.	PUNCT
ejpam-5656	378	1	j.	j.	PROPN
ejpam-5656	378	2	pure	pure	PROPN
ejpam-5656	378	3	appl	appl	PROPN
ejpam-5656	378	4	.	.	PROPN
ejpam-5656	378	5	math	math	PROPN
ejpam-5656	378	6	,	,	PUNCT
ejpam-5656	378	7	18	18	NUM
ejpam-5656	378	8	(	(	PUNCT
ejpam-5656	378	9	1	1	NUM
ejpam-5656	378	10	)	)	PUNCT
ejpam-5656	378	11	(	(	PUNCT
ejpam-5656	378	12	2025	2025	NUM
ejpam-5656	378	13	)	)	PUNCT
ejpam-5656	378	14	,	,	PUNCT
ejpam-5656	378	15	5656	5656	NUM
ejpam-5656	378	16	17	17	NUM
ejpam-5656	378	17	of	of	ADP
ejpam-5656	378	18	17	17	NUM
ejpam-5656	378	19	halsted	halsted	ADJ
ejpam-5656	378	20	press	press	NOUN
ejpam-5656	378	21	,	,	PUNCT
ejpam-5656	378	22	1984	1984	NUM
ejpam-5656	378	23	.	.	PUNCT