id	sid	tid	token	lemma	pos
ejpam-6658	1	1	european	european	PROPN
ejpam-6658	1	2	journal	journal	PROPN
ejpam-6658	1	3	of	of	ADP
ejpam-6658	1	4	pure	pure	ADJ
ejpam-6658	1	5	and	and	CCONJ
ejpam-6658	1	6	applied	applied	ADJ
ejpam-6658	1	7	mathematics	mathematic	NOUN
ejpam-6658	1	8	2025	2025	NUM
ejpam-6658	1	9	,	,	PUNCT
ejpam-6658	1	10	vol	vol	NOUN
ejpam-6658	1	11	.	.	PROPN
ejpam-6658	1	12	18	18	NUM
ejpam-6658	1	13	,	,	PUNCT
ejpam-6658	1	14	issue	issue	NOUN
ejpam-6658	1	15	3	3	NUM
ejpam-6658	1	16	,	,	PUNCT
ejpam-6658	1	17	article	article	NOUN
ejpam-6658	1	18	number	number	NOUN
ejpam-6658	1	19	6658	6658	NUM
ejpam-6658	1	20	issn	issn	PROPN
ejpam-6658	1	21	1307	1307	NUM
ejpam-6658	1	22	-	-	SYM
ejpam-6658	1	23	5543	5543	NUM
ejpam-6658	1	24	–	–	PUNCT
ejpam-6658	1	25	ejpam.com	ejpam.com	X
ejpam-6658	1	26	published	publish	VERB
ejpam-6658	1	27	by	by	ADP
ejpam-6658	1	28	new	new	PROPN
ejpam-6658	1	29	york	york	PROPN
ejpam-6658	1	30	business	business	PROPN
ejpam-6658	1	31	global	global	ADJ
ejpam-6658	1	32	bivariate	bivariate	ADJ
ejpam-6658	1	33	kind	kind	NOUN
ejpam-6658	1	34	of	of	ADP
ejpam-6658	1	35	generalized	generalized	ADJ
ejpam-6658	1	36	laguerre	laguerre	NOUN
ejpam-6658	1	37	-	-	PUNCT
ejpam-6658	1	38	based	base	VERB
ejpam-6658	1	39	appell	appell	NOUN
ejpam-6658	1	40	polynomials	polynomial	NOUN
ejpam-6658	1	41	with	with	ADP
ejpam-6658	1	42	applications	application	NOUN
ejpam-6658	1	43	to	to	ADP
ejpam-6658	1	44	special	special	ADJ
ejpam-6658	1	45	polynomials	polynomial	NOUN
ejpam-6658	1	46	waseem	waseem	PROPN
ejpam-6658	1	47	ahmad	ahmad	PROPN
ejpam-6658	1	48	khan1	khan1	PROPN
ejpam-6658	1	49	,	,	PUNCT
ejpam-6658	1	50	haitham	haitham	PROPN
ejpam-6658	1	51	qawaqneh2	qawaqneh2	PROPN
ejpam-6658	1	52	,	,	PUNCT
ejpam-6658	1	53	hassen	hassen	PROPN
ejpam-6658	1	54	aydi3,4,∗	aydi3,4,∗	ADJ
ejpam-6658	1	55	1	1	NUM
ejpam-6658	1	56	department	department	NOUN
ejpam-6658	1	57	of	of	ADP
ejpam-6658	1	58	electrical	electrical	ADJ
ejpam-6658	1	59	engineering	engineering	NOUN
ejpam-6658	1	60	,	,	PUNCT
ejpam-6658	1	61	prince	prince	PROPN
ejpam-6658	1	62	mohammad	mohammad	PROPN
ejpam-6658	1	63	bin	bin	PROPN
ejpam-6658	1	64	fahd	fahd	PROPN
ejpam-6658	1	65	university	university	PROPN
ejpam-6658	1	66	,	,	PUNCT
ejpam-6658	1	67	p.o	p.o	PROPN
ejpam-6658	1	68	box	box	PROPN
ejpam-6658	1	69	1664	1664	NUM
ejpam-6658	1	70	,	,	PUNCT
ejpam-6658	1	71	al	al	PROPN
ejpam-6658	1	72	khobar	khobar	PROPN
ejpam-6658	1	73	31952	31952	NUM
ejpam-6658	1	74	,	,	PUNCT
ejpam-6658	1	75	saudi	saudi	PROPN
ejpam-6658	1	76	arabia	arabia	PROPN
ejpam-6658	1	77	2	2	NUM
ejpam-6658	1	78	department	department	NOUN
ejpam-6658	1	79	of	of	ADP
ejpam-6658	1	80	mathematics	mathematics	PROPN
ejpam-6658	1	81	,	,	PUNCT
ejpam-6658	1	82	al	al	PROPN
ejpam-6658	1	83	-	-	PROPN
ejpam-6658	1	84	zaytoonah	zaytoonah	PROPN
ejpam-6658	1	85	university	university	PROPN
ejpam-6658	1	86	of	of	ADP
ejpam-6658	1	87	jordan	jordan	PROPN
ejpam-6658	1	88	,	,	PUNCT
ejpam-6658	1	89	amman	amman	PROPN
ejpam-6658	1	90	11733	11733	NUM
ejpam-6658	1	91	,	,	PUNCT
ejpam-6658	1	92	jordan	jordan	PROPN
ejpam-6658	1	93	.	.	PUNCT
ejpam-6658	2	1	3	3	NUM
ejpam-6658	2	2	institut	institut	PROPN
ejpam-6658	2	3	supérieur	supérieur	PROPN
ejpam-6658	2	4	d’informatique	d’informatique	PROPN
ejpam-6658	2	5	et	et	NOUN
ejpam-6658	2	6	des	des	X
ejpam-6658	2	7	techniques	techniques	X
ejpam-6658	2	8	de	de	X
ejpam-6658	2	9	communication	communication	NOUN
ejpam-6658	2	10	,	,	PUNCT
ejpam-6658	2	11	université	université	ADJ
ejpam-6658	2	12	de	de	X
ejpam-6658	2	13	sousse	sousse	PROPN
ejpam-6658	2	14	,	,	PUNCT
ejpam-6658	2	15	h.	h.	PROPN
ejpam-6658	2	16	sousse	sousse	PROPN
ejpam-6658	2	17	4000	4000	NUM
ejpam-6658	2	18	,	,	PUNCT
ejpam-6658	2	19	tunisia	tunisia	PROPN
ejpam-6658	2	20	4	4	NUM
ejpam-6658	2	21	department	department	NOUN
ejpam-6658	2	22	of	of	ADP
ejpam-6658	2	23	mathematics	mathematic	NOUN
ejpam-6658	2	24	and	and	CCONJ
ejpam-6658	2	25	applied	apply	VERB
ejpam-6658	2	26	mathematics	mathematic	NOUN
ejpam-6658	2	27	,	,	PUNCT
ejpam-6658	2	28	sefako	sefako	VERB
ejpam-6658	2	29	makgatho	makgatho	PROPN
ejpam-6658	2	30	health	health	PROPN
ejpam-6658	2	31	sciences	sciences	PROPN
ejpam-6658	2	32	university	university	PROPN
ejpam-6658	2	33	,	,	PUNCT
ejpam-6658	2	34	ga	ga	PROPN
ejpam-6658	2	35	-	-	NOUN
ejpam-6658	2	36	rankuwa	rankuwa	PROPN
ejpam-6658	2	37	,	,	PUNCT
ejpam-6658	2	38	south	south	PROPN
ejpam-6658	2	39	africa	africa	PROPN
ejpam-6658	2	40	abstract	abstract	PROPN
ejpam-6658	2	41	.	.	PUNCT
ejpam-6658	3	1	in	in	ADP
ejpam-6658	3	2	this	this	DET
ejpam-6658	3	3	paper	paper	NOUN
ejpam-6658	3	4	,	,	PUNCT
ejpam-6658	3	5	we	we	PRON
ejpam-6658	3	6	introduce	introduce	VERB
ejpam-6658	3	7	a	a	DET
ejpam-6658	3	8	new	new	ADJ
ejpam-6658	3	9	generalization	generalization	NOUN
ejpam-6658	3	10	of	of	ADP
ejpam-6658	3	11	laguerre	laguerre	NOUN
ejpam-6658	3	12	and	and	CCONJ
ejpam-6658	3	13	laguerre	laguerre	NOUN
ejpam-6658	3	14	-	-	PUNCT
ejpam-6658	3	15	based	base	VERB
ejpam-6658	3	16	appell	appell	ADJ
ejpam-6658	3	17	polynomials	polynomial	NOUN
ejpam-6658	3	18	and	and	CCONJ
ejpam-6658	3	19	investigate	investigate	VERB
ejpam-6658	3	20	their	their	PRON
ejpam-6658	3	21	fundamental	fundamental	ADJ
ejpam-6658	3	22	properties	property	NOUN
ejpam-6658	3	23	.	.	PUNCT
ejpam-6658	4	1	we	we	PRON
ejpam-6658	4	2	derive	derive	VERB
ejpam-6658	4	3	a	a	DET
ejpam-6658	4	4	recurrence	recurrence	NOUN
ejpam-6658	4	5	relation	relation	NOUN
ejpam-6658	4	6	,	,	PUNCT
ejpam-6658	4	7	multiplicative	multiplicative	ADJ
ejpam-6658	4	8	and	and	CCONJ
ejpam-6658	4	9	derivative	derivative	ADJ
ejpam-6658	4	10	operators	operator	NOUN
ejpam-6658	4	11	,	,	PUNCT
ejpam-6658	4	12	and	and	CCONJ
ejpam-6658	4	13	differential	differential	ADJ
ejpam-6658	4	14	equation	equation	NOUN
ejpam-6658	4	15	by	by	ADP
ejpam-6658	4	16	verifying	verify	VERB
ejpam-6658	4	17	quasi	quasi	NOUN
ejpam-6658	4	18	-	-	NOUN
ejpam-6658	4	19	monomiality	monomiality	NOUN
ejpam-6658	4	20	.	.	PUNCT
ejpam-6658	5	1	also	also	ADV
ejpam-6658	5	2	,	,	PUNCT
ejpam-6658	5	3	the	the	DET
ejpam-6658	5	4	series	series	NOUN
ejpam-6658	5	5	representation	representation	NOUN
ejpam-6658	5	6	and	and	CCONJ
ejpam-6658	5	7	determinant	determinant	ADJ
ejpam-6658	5	8	representation	representation	NOUN
ejpam-6658	5	9	for	for	ADP
ejpam-6658	5	10	this	this	DET
ejpam-6658	5	11	novel	novel	ADJ
ejpam-6658	5	12	polynomial	polynomial	ADJ
ejpam-6658	5	13	family	family	NOUN
ejpam-6658	5	14	are	be	AUX
ejpam-6658	5	15	established	establish	VERB
ejpam-6658	5	16	.	.	PUNCT
ejpam-6658	6	1	furthermore	furthermore	ADV
ejpam-6658	6	2	,	,	PUNCT
ejpam-6658	6	3	we	we	PRON
ejpam-6658	6	4	define	define	VERB
ejpam-6658	6	5	subpolynomials	subpolynomial	NOUN
ejpam-6658	6	6	within	within	ADP
ejpam-6658	6	7	this	this	DET
ejpam-6658	6	8	framework	framework	NOUN
ejpam-6658	6	9	,	,	PUNCT
ejpam-6658	6	10	namely	namely	ADV
ejpam-6658	6	11	generalized	generalized	ADJ
ejpam-6658	6	12	laguerre	laguerre	NOUN
ejpam-6658	6	13	-	-	PUNCT
ejpam-6658	6	14	hermite	hermite	ADJ
ejpam-6658	6	15	appell	appell	ADJ
ejpam-6658	6	16	polynomials	polynomial	NOUN
ejpam-6658	6	17	and	and	CCONJ
ejpam-6658	6	18	establish	establish	VERB
ejpam-6658	6	19	their	their	PRON
ejpam-6658	6	20	corresponding	corresponding	ADJ
ejpam-6658	6	21	results	result	NOUN
ejpam-6658	6	22	.	.	PUNCT
ejpam-6658	7	1	additionally	additionally	ADV
ejpam-6658	7	2	,	,	PUNCT
ejpam-6658	7	3	laguerre	laguerre	NOUN
ejpam-6658	7	4	-	-	PUNCT
ejpam-6658	7	5	hermite	hermite	NOUN
ejpam-6658	7	6	-	-	PUNCT
ejpam-6658	7	7	bernoulli	bernoulli	PROPN
ejpam-6658	7	8	,	,	PUNCT
ejpam-6658	7	9	euler	euler	NOUN
ejpam-6658	7	10	and	and	CCONJ
ejpam-6658	7	11	genocchi	genocchi	PROPN
ejpam-6658	7	12	polynomials	polynomial	NOUN
ejpam-6658	7	13	are	be	AUX
ejpam-6658	7	14	obtained	obtain	VERB
ejpam-6658	7	15	,	,	PUNCT
ejpam-6658	7	16	and	and	CCONJ
ejpam-6658	7	17	explore	explore	VERB
ejpam-6658	7	18	their	their	PRON
ejpam-6658	7	19	structural	structural	ADJ
ejpam-6658	7	20	and	and	CCONJ
ejpam-6658	7	21	operational	operational	ADJ
ejpam-6658	7	22	characteristics	characteristic	NOUN
ejpam-6658	7	23	.	.	PUNCT
ejpam-6658	8	1	the	the	DET
ejpam-6658	8	2	results	result	NOUN
ejpam-6658	8	3	obtained	obtain	VERB
ejpam-6658	8	4	contribute	contribute	NOUN
ejpam-6658	8	5	to	to	ADP
ejpam-6658	8	6	the	the	DET
ejpam-6658	8	7	broader	broad	ADJ
ejpam-6658	8	8	study	study	NOUN
ejpam-6658	8	9	of	of	ADP
ejpam-6658	8	10	special	special	ADJ
ejpam-6658	8	11	polynomials	polynomial	NOUN
ejpam-6658	8	12	and	and	CCONJ
ejpam-6658	8	13	their	their	PRON
ejpam-6658	8	14	applications	application	NOUN
ejpam-6658	8	15	in	in	ADP
ejpam-6658	8	16	mathematical	mathematical	ADJ
ejpam-6658	8	17	physics	physics	NOUN
ejpam-6658	8	18	and	and	CCONJ
ejpam-6658	8	19	differential	differential	ADJ
ejpam-6658	8	20	equations	equation	NOUN
ejpam-6658	8	21	.	.	PUNCT
ejpam-6658	9	1	2020	2020	NUM
ejpam-6658	9	2	mathematics	mathematic	NOUN
ejpam-6658	9	3	subject	subject	NOUN
ejpam-6658	9	4	classifications	classification	NOUN
ejpam-6658	9	5	:	:	PUNCT
ejpam-6658	9	6	33e20	33e20	NUM
ejpam-6658	9	7	,	,	PUNCT
ejpam-6658	9	8	33c45	33c45	NUM
ejpam-6658	9	9	,	,	PUNCT
ejpam-6658	9	10	33b10	33b10	NUM
ejpam-6658	9	11	,	,	PUNCT
ejpam-6658	9	12	33e30	33e30	NUM
ejpam-6658	9	13	,	,	PUNCT
ejpam-6658	9	14	11t23	11t23	NUM
ejpam-6658	9	15	,	,	PUNCT
ejpam-6658	9	16	11b83	11b83	NUM
ejpam-6658	9	17	,	,	PUNCT
ejpam-6658	9	18	11b68	11b68	NUM
ejpam-6658	9	19	key	key	ADJ
ejpam-6658	9	20	words	word	NOUN
ejpam-6658	9	21	and	and	CCONJ
ejpam-6658	9	22	phrases	phrase	NOUN
ejpam-6658	9	23	:	:	PUNCT
ejpam-6658	9	24	laguerre	laguerre	NOUN
ejpam-6658	9	25	polynomials	polynomial	NOUN
ejpam-6658	9	26	,	,	PUNCT
ejpam-6658	9	27	laguerre	laguerre	NOUN
ejpam-6658	9	28	-	-	PUNCT
ejpam-6658	9	29	based	base	VERB
ejpam-6658	9	30	appell	appell	NOUN
ejpam-6658	9	31	polynomials	polynomial	NOUN
ejpam-6658	9	32	,	,	PUNCT
ejpam-6658	9	33	monomiality	monomiality	NOUN
ejpam-6658	9	34	principle	principle	NOUN
ejpam-6658	9	35	,	,	PUNCT
ejpam-6658	9	36	explicit	explicit	ADJ
ejpam-6658	9	37	form	form	NOUN
ejpam-6658	9	38	,	,	PUNCT
ejpam-6658	9	39	operational	operational	ADJ
ejpam-6658	9	40	connection	connection	NOUN
ejpam-6658	9	41	,	,	PUNCT
ejpam-6658	9	42	determinant	determinant	ADJ
ejpam-6658	9	43	form	form	NOUN
ejpam-6658	9	44	1	1	NUM
ejpam-6658	9	45	.	.	PUNCT
ejpam-6658	10	1	introduction	introduction	NOUN
ejpam-6658	10	2	and	and	CCONJ
ejpam-6658	10	3	preliminary	preliminary	ADJ
ejpam-6658	10	4	results	result	NOUN
ejpam-6658	10	5	it	it	PRON
ejpam-6658	10	6	is	be	AUX
ejpam-6658	10	7	well	well	ADV
ejpam-6658	10	8	established	establish	VERB
ejpam-6658	10	9	that	that	SCONJ
ejpam-6658	10	10	special	special	ADJ
ejpam-6658	10	11	polynomials	polynomial	NOUN
ejpam-6658	10	12	in	in	ADP
ejpam-6658	10	13	two	two	NUM
ejpam-6658	10	14	variables	variable	NOUN
ejpam-6658	10	15	provide	provide	VERB
ejpam-6658	10	16	new	new	ADJ
ejpam-6658	10	17	analytical	analytical	ADJ
ejpam-6658	10	18	tools	tool	NOUN
ejpam-6658	10	19	for	for	ADP
ejpam-6658	10	20	solving	solve	VERB
ejpam-6658	10	21	a	a	DET
ejpam-6658	10	22	broad	broad	ADJ
ejpam-6658	10	23	range	range	NOUN
ejpam-6658	10	24	of	of	ADP
ejpam-6658	10	25	partial	partial	ADJ
ejpam-6658	10	26	differential	differential	ADJ
ejpam-6658	10	27	equations	equation	NOUN
ejpam-6658	10	28	frequently	frequently	ADV
ejpam-6658	10	29	encountered	encounter	VERB
ejpam-6658	10	30	in	in	ADP
ejpam-6658	10	31	physical	physical	ADJ
ejpam-6658	10	32	problems	problem	NOUN
ejpam-6658	10	33	.	.	PUNCT
ejpam-6658	11	1	the	the	DET
ejpam-6658	11	2	introduction	introduction	NOUN
ejpam-6658	11	3	of	of	ADP
ejpam-6658	11	4	the	the	DET
ejpam-6658	11	5	two	two	NUM
ejpam-6658	11	6	-	-	PUNCT
ejpam-6658	11	7	variable	variable	NOUN
ejpam-6658	11	8	laguerre	laguerre	NOUN
ejpam-6658	11	9	polynomials	polynomial	NOUN
ejpam-6658	11	10	,	,	PUNCT
ejpam-6658	11	11	denoted	denote	VERB
ejpam-6658	11	12	as	as	ADP
ejpam-6658	11	13	ln(r1	ln(r1	NOUN
ejpam-6658	11	14	,	,	PUNCT
ejpam-6658	11	15	r2	r2	PROPN
ejpam-6658	11	16	)	)	PUNCT
ejpam-6658	12	1	[	[	X
ejpam-6658	12	2	1–10	1–10	NOUN
ejpam-6658	12	3	]	]	PUNCT
ejpam-6658	12	4	,	,	PUNCT
ejpam-6658	12	5	is	be	AUX
ejpam-6658	12	6	of	of	ADP
ejpam-6658	12	7	significant	significant	ADJ
ejpam-6658	12	8	interest	interest	NOUN
ejpam-6658	12	9	due	due	ADP
ejpam-6658	12	10	to	to	ADP
ejpam-6658	12	11	their	their	PRON
ejpam-6658	12	12	intrinsic	intrinsic	ADJ
ejpam-6658	12	13	mathematical	mathematical	ADJ
ejpam-6658	12	14	properties	property	NOUN
ejpam-6658	12	15	and	and	CCONJ
ejpam-6658	12	16	extensive	extensive	ADJ
ejpam-6658	12	17	applications	application	NOUN
ejpam-6658	12	18	in	in	ADP
ejpam-6658	12	19	physics	physics	NOUN
ejpam-6658	12	20	.	.	PUNCT
ejpam-6658	13	1	∗corresponding	∗corresponde	VERB
ejpam-6658	13	2	author	author	NOUN
ejpam-6658	13	3	.	.	PUNCT
ejpam-6658	14	1	doi	doi	NOUN
ejpam-6658	14	2	:	:	PUNCT
ejpam-6658	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6658	https://doi.org/10.29020/nybg.ejpam.v18i3.6658	PROPN
ejpam-6658	14	4	email	email	NOUN
ejpam-6658	14	5	addresses	address	NOUN
ejpam-6658	14	6	:	:	PUNCT
ejpam-6658	14	7	wkhan1@pmu.edu.sa	wkhan1@pmu.edu.sa	PROPN
ejpam-6658	14	8	(	(	PUNCT
ejpam-6658	14	9	w.	w.	PROPN
ejpam-6658	14	10	a.	a.	PROPN
ejpam-6658	14	11	khan	khan	PROPN
ejpam-6658	14	12	)	)	PUNCT
ejpam-6658	14	13	,	,	PUNCT
ejpam-6658	14	14	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-6658	14	15	(	(	PUNCT
ejpam-6658	14	16	h.	h.	PROPN
ejpam-6658	14	17	qawaqneh	qawaqneh	PROPN
ejpam-6658	14	18	)	)	PUNCT
ejpam-6658	14	19	,	,	PUNCT
ejpam-6658	14	20	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	PROPN
ejpam-6658	14	21	(	(	PUNCT
ejpam-6658	14	22	h.	h.	PROPN
ejpam-6658	14	23	aydi	aydi	ADJ
ejpam-6658	14	24	)	)	PUNCT
ejpam-6658	14	25	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6658	14	26	1	1	NUM
ejpam-6658	14	27	copyright	copyright	NOUN
ejpam-6658	14	28	:	:	PUNCT
ejpam-6658	15	1	©	©	PROPN
ejpam-6658	15	2	2025	2025	NUM
ejpam-6658	15	3	the	the	DET
ejpam-6658	15	4	author(s	author(s	NOUN
ejpam-6658	15	5	)	)	PUNCT
ejpam-6658	15	6	.	.	PUNCT
ejpam-6658	16	1	(	(	PUNCT
ejpam-6658	16	2	cc	cc	NOUN
ejpam-6658	16	3	by	by	ADP
ejpam-6658	16	4	-	-	PUNCT
ejpam-6658	16	5	nc	nc	PROPN
ejpam-6658	16	6	4.0	4.0	NUM
ejpam-6658	16	7	)	)	PUNCT
ejpam-6658	16	8	w.	w.	PROPN
ejpam-6658	16	9	a.	a.	PROPN
ejpam-6658	16	10	khan	khan	PROPN
ejpam-6658	16	11	,	,	PUNCT
ejpam-6658	16	12	h.	h.	PROPN
ejpam-6658	16	13	qawaqneh	qawaqneh	PROPN
ejpam-6658	16	14	,	,	PUNCT
ejpam-6658	16	15	h.	h.	PROPN
ejpam-6658	16	16	aydi	aydi	VERB
ejpam-6658	16	17	/	/	SYM
ejpam-6658	16	18	eur	eur	NOUN
ejpam-6658	16	19	.	.	PUNCT
ejpam-6658	17	1	j.	j.	PROPN
ejpam-6658	17	2	pure	pure	PROPN
ejpam-6658	17	3	appl	appl	PROPN
ejpam-6658	17	4	.	.	PROPN
ejpam-6658	17	5	math	math	PROPN
ejpam-6658	17	6	,	,	PUNCT
ejpam-6658	17	7	18	18	NUM
ejpam-6658	17	8	(	(	PUNCT
ejpam-6658	17	9	3	3	NUM
ejpam-6658	17	10	)	)	PUNCT
ejpam-6658	17	11	(	(	PUNCT
ejpam-6658	17	12	2025	2025	NUM
ejpam-6658	17	13	)	)	PUNCT
ejpam-6658	17	14	,	,	PUNCT
ejpam-6658	17	15	6658	6658	NUM
ejpam-6658	17	16	2	2	NUM
ejpam-6658	17	17	of	of	ADP
ejpam-6658	17	18	22	22	NUM
ejpam-6658	17	19	the	the	DET
ejpam-6658	17	20	two	two	NUM
ejpam-6658	17	21	-	-	PUNCT
ejpam-6658	17	22	variable	variable	NOUN
ejpam-6658	17	23	laguerre	laguerre	NOUN
ejpam-6658	17	24	polynomials	polynomial	NOUN
ejpam-6658	17	25	(	(	PUNCT
ejpam-6658	17	26	2vlp	2vlp	NUM
ejpam-6658	17	27	)	)	PUNCT
ejpam-6658	17	28	ln(r1	ln(r1	NOUN
ejpam-6658	17	29	,	,	PUNCT
ejpam-6658	17	30	r2	r2	PROPN
ejpam-6658	17	31	)	)	PUNCT
ejpam-6658	17	32	are	be	AUX
ejpam-6658	17	33	characterized	characterize	VERB
ejpam-6658	17	34	by	by	ADP
ejpam-6658	17	35	the	the	DET
ejpam-6658	17	36	following	follow	VERB
ejpam-6658	17	37	generating	generate	VERB
ejpam-6658	17	38	function	function	NOUN
ejpam-6658	17	39	[	[	X
ejpam-6658	17	40	11	11	NUM
ejpam-6658	17	41	]	]	PUNCT
ejpam-6658	17	42	:	:	PUNCT
ejpam-6658	17	43	er2tj0(2	er2tj0(2	PUNCT
ejpam-6658	17	44	√	√	ADP
ejpam-6658	17	45	r1	r1	PROPN
ejpam-6658	17	46	t	t	PROPN
ejpam-6658	17	47	)	)	PUNCT
ejpam-6658	17	48	=	=	PUNCT
ejpam-6658	18	1	∞∑	∞∑	PRON
ejpam-6658	18	2	n=0	n=0	NUM
ejpam-6658	18	3	ln(r1	ln(r1	NOUN
ejpam-6658	18	4	,	,	PUNCT
ejpam-6658	18	5	r2	r2	PROPN
ejpam-6658	18	6	)	)	PUNCT
ejpam-6658	18	7	tn	tn	PROPN
ejpam-6658	18	8	n	n	PROPN
ejpam-6658	18	9	!	!	PUNCT
ejpam-6658	18	10	.	.	PUNCT
ejpam-6658	19	1	(	(	PUNCT
ejpam-6658	19	2	1	1	X
ejpam-6658	19	3	)	)	PUNCT
ejpam-6658	19	4	where	where	SCONJ
ejpam-6658	19	5	j0(r1	j0(r1	NOUN
ejpam-6658	19	6	t	t	PROPN
ejpam-6658	19	7	)	)	PUNCT
ejpam-6658	19	8	represents	represent	VERB
ejpam-6658	19	9	the	the	DET
ejpam-6658	19	10	ordinary	ordinary	ADJ
ejpam-6658	19	11	bessel	bessel	ADJ
ejpam-6658	19	12	function	function	NOUN
ejpam-6658	19	13	of	of	ADP
ejpam-6658	19	14	the	the	DET
ejpam-6658	19	15	first	first	ADJ
ejpam-6658	19	16	kind	kind	NOUN
ejpam-6658	19	17	of	of	ADP
ejpam-6658	19	18	order	order	NOUN
ejpam-6658	19	19	zero	zero	NUM
ejpam-6658	20	1	[	[	X
ejpam-6658	20	2	12	12	NUM
ejpam-6658	20	3	]	]	PUNCT
ejpam-6658	20	4	,	,	PUNCT
ejpam-6658	20	5	defined	define	VERB
ejpam-6658	20	6	as	as	ADP
ejpam-6658	20	7	:	:	PUNCT
ejpam-6658	20	8	r	r	NOUN
ejpam-6658	20	9	n	n	NUM
ejpam-6658	20	10	2	2	NUM
ejpam-6658	20	11	1	1	NUM
ejpam-6658	20	12	jn(2	jn(2	PROPN
ejpam-6658	20	13	√	√	NOUN
ejpam-6658	20	14	r1	r1	PROPN
ejpam-6658	20	15	)	)	PUNCT
ejpam-6658	20	16	=	=	PUNCT
ejpam-6658	21	1	∞∑	∞∑	NUM
ejpam-6658	21	2	k=0	k=0	PROPN
ejpam-6658	21	3	(	(	PUNCT
ejpam-6658	21	4	−1)k	−1)k	PROPN
ejpam-6658	21	5	(	(	PUNCT
ejpam-6658	21	6	√	√	PROPN
ejpam-6658	21	7	r1	r1	PROPN
ejpam-6658	21	8	)	)	PUNCT
ejpam-6658	21	9	k	k	PROPN
ejpam-6658	21	10	k!(n+	k!(n+	PROPN
ejpam-6658	21	11	k	k	PROPN
ejpam-6658	21	12	)	)	PUNCT
ejpam-6658	21	13	!	!	PUNCT
ejpam-6658	21	14	.	.	PUNCT
ejpam-6658	22	1	(	(	PUNCT
ejpam-6658	22	2	2	2	X
ejpam-6658	22	3	)	)	PUNCT
ejpam-6658	22	4	additionally	additionally	ADV
ejpam-6658	22	5	,	,	PUNCT
ejpam-6658	22	6	we	we	PRON
ejpam-6658	22	7	note	note	VERB
ejpam-6658	22	8	that	that	SCONJ
ejpam-6658	22	9	:	:	PUNCT
ejpam-6658	22	10	exp(−αd−1	exp(−αd−1	X
ejpam-6658	22	11	r1	r1	PROPN
ejpam-6658	22	12	)	)	PUNCT
ejpam-6658	22	13	=	=	PUNCT
ejpam-6658	23	1	j0(2	j0(2	PROPN
ejpam-6658	23	2	√	√	PROPN
ejpam-6658	23	3	αr1	αr1	NOUN
ejpam-6658	23	4	)	)	PUNCT
ejpam-6658	23	5	,	,	PUNCT
ejpam-6658	23	6	d−n	d−n	NOUN
ejpam-6658	23	7	r1	r1	NOUN
ejpam-6658	23	8	{	{	PUNCT
ejpam-6658	23	9	1	1	NUM
ejpam-6658	23	10	}	}	PUNCT
ejpam-6658	23	11	:	:	PUNCT
ejpam-6658	23	12	=	=	SYM
ejpam-6658	23	13	rn1	rn1	PROPN
ejpam-6658	23	14	/n	/n	PUNCT
ejpam-6658	23	15	!	!	PUNCT
ejpam-6658	24	1	(	(	PUNCT
ejpam-6658	24	2	3	3	X
ejpam-6658	24	3	)	)	PUNCT
ejpam-6658	24	4	is	be	AUX
ejpam-6658	24	5	the	the	DET
ejpam-6658	24	6	inverse	inverse	ADJ
ejpam-6658	24	7	differential	differential	NOUN
ejpam-6658	24	8	operator	operator	NOUN
ejpam-6658	24	9	.	.	PUNCT
ejpam-6658	25	1	the	the	DET
ejpam-6658	25	2	class	class	NOUN
ejpam-6658	25	3	of	of	ADP
ejpam-6658	25	4	appell	appell	ADJ
ejpam-6658	25	5	polynomial	polynomial	ADJ
ejpam-6658	25	6	sequences	sequence	NOUN
ejpam-6658	26	1	[	[	X
ejpam-6658	26	2	13	13	NUM
ejpam-6658	26	3	]	]	PUNCT
ejpam-6658	26	4	appears	appear	VERB
ejpam-6658	26	5	in	in	ADP
ejpam-6658	26	6	numerous	numerous	ADJ
ejpam-6658	26	7	applied	apply	VERB
ejpam-6658	26	8	mathematics	mathematic	NOUN
ejpam-6658	26	9	problems	problem	NOUN
ejpam-6658	26	10	,	,	PUNCT
ejpam-6658	26	11	theoretical	theoretical	ADJ
ejpam-6658	26	12	physics	physics	NOUN
ejpam-6658	26	13	,	,	PUNCT
ejpam-6658	26	14	approximation	approximation	NOUN
ejpam-6658	26	15	theory	theory	NOUN
ejpam-6658	26	16	,	,	PUNCT
ejpam-6658	26	17	and	and	CCONJ
ejpam-6658	26	18	other	other	ADJ
ejpam-6658	26	19	mathematical	mathematical	ADJ
ejpam-6658	26	20	disciplines	discipline	NOUN
ejpam-6658	26	21	.	.	PUNCT
ejpam-6658	27	1	these	these	DET
ejpam-6658	27	2	sequences	sequence	NOUN
ejpam-6658	27	3	are	be	AUX
ejpam-6658	27	4	defined	define	VERB
ejpam-6658	27	5	through	through	ADP
ejpam-6658	27	6	the	the	DET
ejpam-6658	27	7	generating	generate	VERB
ejpam-6658	27	8	function	function	NOUN
ejpam-6658	27	9	:	:	PUNCT
ejpam-6658	27	10	r(r1	r(r1	PROPN
ejpam-6658	27	11	,	,	PUNCT
ejpam-6658	27	12	t	t	PROPN
ejpam-6658	27	13	)	)	PUNCT
ejpam-6658	27	14	:	:	PUNCT
ejpam-6658	28	1	=	=	PUNCT
ejpam-6658	28	2	r(t)er1	r(t)er1	NOUN
ejpam-6658	28	3	t	t	NOUN
ejpam-6658	28	4	=	=	SYM
ejpam-6658	28	5	∞∑	∞∑	NUM
ejpam-6658	28	6	n=0	n=0	NUM
ejpam-6658	28	7	rn(r1	rn(r1	NOUN
ejpam-6658	28	8	)	)	PUNCT
ejpam-6658	28	9	tn	tn	PROPN
ejpam-6658	28	10	n	n	PROPN
ejpam-6658	28	11	!	!	PROPN
ejpam-6658	28	12	,	,	PUNCT
ejpam-6658	28	13	rn	rn	PROPN
ejpam-6658	28	14	:	:	PUNCT
ejpam-6658	28	15	=	=	SYM
ejpam-6658	28	16	rn(0	rn(0	PROPN
ejpam-6658	28	17	)	)	PUNCT
ejpam-6658	28	18	,	,	PUNCT
ejpam-6658	28	19	(	(	PUNCT
ejpam-6658	28	20	4	4	X
ejpam-6658	28	21	)	)	PUNCT
ejpam-6658	28	22	where	where	SCONJ
ejpam-6658	28	23	r(t	r(t	NOUN
ejpam-6658	28	24	)	)	PUNCT
ejpam-6658	28	25	is	be	AUX
ejpam-6658	28	26	an	an	DET
ejpam-6658	28	27	analytic	analytic	ADJ
ejpam-6658	28	28	function	function	NOUN
ejpam-6658	28	29	at	at	ADP
ejpam-6658	28	30	t	t	PROPN
ejpam-6658	28	31	=	=	SYM
ejpam-6658	28	32	0	0	NUM
ejpam-6658	28	33	,	,	PUNCT
ejpam-6658	28	34	expressed	express	VERB
ejpam-6658	28	35	as	as	ADP
ejpam-6658	28	36	:	:	PUNCT
ejpam-6658	28	37	r(t	r(t	NOUN
ejpam-6658	28	38	)	)	PUNCT
ejpam-6658	28	39	=	=	PUNCT
ejpam-6658	29	1	∞∑	∞∑	PROPN
ejpam-6658	29	2	n=0	n=0	NUM
ejpam-6658	29	3	rn	rn	PROPN
ejpam-6658	29	4	tn	tn	PROPN
ejpam-6658	29	5	n	n	CCONJ
ejpam-6658	29	6	!	!	PUNCT
ejpam-6658	29	7	,	,	PUNCT
ejpam-6658	29	8	r0	r0	NOUN
ejpam-6658	29	9	̸=	̸=	PROPN
ejpam-6658	29	10	0	0	NUM
ejpam-6658	29	11	,	,	PUNCT
ejpam-6658	29	12	ri	ri	PROPN
ejpam-6658	30	1	(	(	PUNCT
ejpam-6658	30	2	i	i	NOUN
ejpam-6658	30	3	=	=	NOUN
ejpam-6658	30	4	0	0	NUM
ejpam-6658	30	5	,	,	PUNCT
ejpam-6658	30	6	1	1	NUM
ejpam-6658	30	7	,	,	PUNCT
ejpam-6658	30	8	2	2	NUM
ejpam-6658	30	9	,	,	PUNCT
ejpam-6658	30	10	·	·	PUNCT
ejpam-6658	30	11	·	·	PUNCT
ejpam-6658	30	12	·	·	PUNCT
ejpam-6658	30	13	)	)	PUNCT
ejpam-6658	31	1	being	be	AUX
ejpam-6658	31	2	real	real	ADJ
ejpam-6658	31	3	coefficients	coefficient	NOUN
ejpam-6658	31	4	.	.	PUNCT
ejpam-6658	32	1	(	(	PUNCT
ejpam-6658	32	2	5	5	X
ejpam-6658	32	3	)	)	PUNCT
ejpam-6658	32	4	the	the	DET
ejpam-6658	32	5	appell	appell	PROPN
ejpam-6658	32	6	polynomials	polynomial	NOUN
ejpam-6658	32	7	rn(r1	rn(r1	NOUN
ejpam-6658	32	8	)	)	PUNCT
ejpam-6658	32	9	are	be	AUX
ejpam-6658	32	10	explicitly	explicitly	ADV
ejpam-6658	32	11	given	give	VERB
ejpam-6658	32	12	by	by	ADP
ejpam-6658	32	13	the	the	DET
ejpam-6658	32	14	series	series	NOUN
ejpam-6658	32	15	expansion	expansion	NOUN
ejpam-6658	32	16	:	:	PUNCT
ejpam-6658	32	17	rn(r1	rn(r1	NOUN
ejpam-6658	32	18	)	)	PUNCT
ejpam-6658	33	1	=	=	SYM
ejpam-6658	33	2	n∑	n∑	NOUN
ejpam-6658	33	3	k=0	k=0	PROPN
ejpam-6658	33	4	(	(	PUNCT
ejpam-6658	33	5	n	n	CCONJ
ejpam-6658	33	6	k	k	X
ejpam-6658	33	7	)	)	PUNCT
ejpam-6658	33	8	rn−k	rn−k	PROPN
ejpam-6658	33	9	r	r	NOUN
ejpam-6658	33	10	k	k	PROPN
ejpam-6658	33	11	1	1	NUM
ejpam-6658	33	12	,	,	PUNCT
ejpam-6658	33	13	r′	r′	NOUN
ejpam-6658	33	14	n(r1	n(r1	NOUN
ejpam-6658	33	15	)	)	PUNCT
ejpam-6658	33	16	=	=	SYM
ejpam-6658	33	17	n	n	PRON
ejpam-6658	33	18	rn−1(r1	rn−1(r1	PROPN
ejpam-6658	33	19	)	)	PUNCT
ejpam-6658	33	20	.	.	PUNCT
ejpam-6658	34	1	(	(	PUNCT
ejpam-6658	34	2	6	6	NUM
ejpam-6658	34	3	)	)	PUNCT
ejpam-6658	34	4	by	by	ADP
ejpam-6658	34	5	appropriately	appropriately	ADV
ejpam-6658	34	6	selecting	select	VERB
ejpam-6658	34	7	r(t	r(t	NOUN
ejpam-6658	34	8	)	)	PUNCT
ejpam-6658	34	9	,	,	PUNCT
ejpam-6658	34	10	various	various	ADJ
ejpam-6658	34	11	members	member	NOUN
ejpam-6658	34	12	of	of	ADP
ejpam-6658	34	13	the	the	DET
ejpam-6658	34	14	appell	appell	ADJ
ejpam-6658	34	15	polynomial	polynomial	ADJ
ejpam-6658	34	16	family	family	NOUN
ejpam-6658	34	17	can	can	AUX
ejpam-6658	34	18	be	be	AUX
ejpam-6658	34	19	derived	derive	VERB
ejpam-6658	34	20	.	.	PUNCT
ejpam-6658	35	1	these	these	PRON
ejpam-6658	35	2	are	be	AUX
ejpam-6658	35	3	listed	list	VERB
ejpam-6658	35	4	in	in	ADP
ejpam-6658	35	5	table	table	NOUN
ejpam-6658	35	6	1	1	NUM
ejpam-6658	35	7	below	below	ADV
ejpam-6658	35	8	:	:	PUNCT
ejpam-6658	35	9	table	table	NOUN
ejpam-6658	35	10	1	1	NUM
ejpam-6658	35	11	.	.	PUNCT
ejpam-6658	36	1	certain	certain	ADJ
ejpam-6658	36	2	members	member	NOUN
ejpam-6658	36	3	belonging	belong	VERB
ejpam-6658	36	4	to	to	ADP
ejpam-6658	36	5	the	the	DET
ejpam-6658	36	6	appell	appell	PROPN
ejpam-6658	36	7	family	family	NOUN
ejpam-6658	36	8	w.	w.	PROPN
ejpam-6658	36	9	a.	a.	PROPN
ejpam-6658	36	10	khan	khan	PROPN
ejpam-6658	36	11	,	,	PUNCT
ejpam-6658	36	12	h.	h.	PROPN
ejpam-6658	36	13	qawaqneh	qawaqneh	PROPN
ejpam-6658	36	14	,	,	PUNCT
ejpam-6658	36	15	h.	h.	PROPN
ejpam-6658	36	16	aydi	aydi	VERB
ejpam-6658	36	17	/	/	SYM
ejpam-6658	36	18	eur	eur	NOUN
ejpam-6658	36	19	.	.	PUNCT
ejpam-6658	37	1	j.	j.	PROPN
ejpam-6658	37	2	pure	pure	PROPN
ejpam-6658	37	3	appl	appl	PROPN
ejpam-6658	37	4	.	.	PROPN
ejpam-6658	37	5	math	math	PROPN
ejpam-6658	37	6	,	,	PUNCT
ejpam-6658	37	7	18	18	NUM
ejpam-6658	37	8	(	(	PUNCT
ejpam-6658	37	9	3	3	NUM
ejpam-6658	37	10	)	)	PUNCT
ejpam-6658	37	11	(	(	PUNCT
ejpam-6658	37	12	2025	2025	NUM
ejpam-6658	37	13	)	)	PUNCT
ejpam-6658	37	14	,	,	PUNCT
ejpam-6658	37	15	6658	6658	NUM
ejpam-6658	37	16	3	3	NUM
ejpam-6658	37	17	of	of	ADP
ejpam-6658	37	18	22	22	NUM
ejpam-6658	37	19	s.no	s.no	NOUN
ejpam-6658	37	20	.	.	NOUN
ejpam-6658	37	21	name	name	NOUN
ejpam-6658	37	22	of	of	ADP
ejpam-6658	37	23	polynomials	polynomial	NOUN
ejpam-6658	37	24	r(t	r(t	NOUN
ejpam-6658	37	25	)	)	PUNCT
ejpam-6658	37	26	generating	generate	VERB
ejpam-6658	37	27	function	function	NOUN
ejpam-6658	37	28	series	series	PROPN
ejpam-6658	37	29	definition	definition	PROPN
ejpam-6658	37	30	i.	i.	PROPN
ejpam-6658	37	31	bernoulli	bernoulli	PROPN
ejpam-6658	37	32	t	t	PROPN
ejpam-6658	37	33	et−1	et−1	PROPN
ejpam-6658	37	34	(	(	PUNCT
ejpam-6658	37	35	t	t	PROPN
ejpam-6658	37	36	et−1	et−1	PROPN
ejpam-6658	37	37	)	)	PUNCT
ejpam-6658	37	38	er1	er1	PROPN
ejpam-6658	37	39	t	t	PROPN
ejpam-6658	37	40	=	=	SYM
ejpam-6658	38	1	∞∑	∞∑	DET
ejpam-6658	38	2	n=0	n=0	NUM
ejpam-6658	38	3	bn(r1	bn(r1	PROPN
ejpam-6658	38	4	)	)	PUNCT
ejpam-6658	38	5	tn	tn	PROPN
ejpam-6658	38	6	n	n	NOUN
ejpam-6658	38	7	!	!	PUNCT
ejpam-6658	38	8	bn(r1	bn(r1	PROPN
ejpam-6658	38	9	)	)	PUNCT
ejpam-6658	39	1	=	=	SYM
ejpam-6658	39	2	n∑	n∑	NOUN
ejpam-6658	39	3	k=0	k=0	PROPN
ejpam-6658	39	4	(	(	PUNCT
ejpam-6658	39	5	n	n	X
ejpam-6658	39	6	k	k	PROPN
ejpam-6658	39	7	)	)	PUNCT
ejpam-6658	39	8	bkr	bkr	PROPN
ejpam-6658	39	9	n−k	n−k	NOUN
ejpam-6658	39	10	1	1	NUM
ejpam-6658	39	11	polynomials	polynomial	NOUN
ejpam-6658	39	12	(	(	PUNCT
ejpam-6658	39	13	t	t	NOUN
ejpam-6658	39	14	et−1	et−1	PROPN
ejpam-6658	39	15	)	)	PUNCT
ejpam-6658	40	1	=	=	PUNCT
ejpam-6658	41	1	∞∑	∞∑	PRON
ejpam-6658	41	2	n=0	n=0	NUM
ejpam-6658	41	3	bn	bn	NUM
ejpam-6658	41	4	tn	tn	NOUN
ejpam-6658	41	5	n	n	PROPN
ejpam-6658	41	6	!	!	PUNCT
ejpam-6658	42	1	and	and	CCONJ
ejpam-6658	42	2	numbers	number	NOUN
ejpam-6658	42	3	[	[	X
ejpam-6658	42	4	14	14	NUM
ejpam-6658	42	5	]	]	PUNCT
ejpam-6658	42	6	bn(:=	bn(:=	PROPN
ejpam-6658	42	7	bn(0	bn(0	PROPN
ejpam-6658	42	8	)	)	PUNCT
ejpam-6658	42	9	=	=	SYM
ejpam-6658	42	10	bn(1	bn(1	NOUN
ejpam-6658	42	11	)	)	PUNCT
ejpam-6658	42	12	)	)	PUNCT
ejpam-6658	42	13	ii	ii	PROPN
ejpam-6658	42	14	.	.	PUNCT
ejpam-6658	42	15	euler	euler	PROPN
ejpam-6658	42	16	2	2	NUM
ejpam-6658	42	17	et+1	et+1	PROPN
ejpam-6658	42	18	(	(	PUNCT
ejpam-6658	42	19	2	2	NUM
ejpam-6658	42	20	et+1	et+1	NOUN
ejpam-6658	42	21	)	)	PUNCT
ejpam-6658	42	22	er1	er1	PROPN
ejpam-6658	42	23	t	t	PROPN
ejpam-6658	42	24	=	=	SYM
ejpam-6658	43	1	∞∑	∞∑	PROPN
ejpam-6658	43	2	n=0	n=0	NUM
ejpam-6658	43	3	en(r1	en(r1	NOUN
ejpam-6658	43	4	)	)	PUNCT
ejpam-6658	43	5	tn	tn	PROPN
ejpam-6658	43	6	n	n	NOUN
ejpam-6658	43	7	!	!	PUNCT
ejpam-6658	44	1	en(r1	en(r1	NOUN
ejpam-6658	44	2	)	)	PUNCT
ejpam-6658	45	1	=	=	SYM
ejpam-6658	45	2	n∑	n∑	NOUN
ejpam-6658	45	3	k=0	k=0	PROPN
ejpam-6658	45	4	(	(	PUNCT
ejpam-6658	45	5	n	n	X
ejpam-6658	45	6	k	k	X
ejpam-6658	45	7	)	)	PUNCT
ejpam-6658	45	8	ek	ek	PROPN
ejpam-6658	45	9	2k	2k	PROPN
ejpam-6658	45	10	(	(	PUNCT
ejpam-6658	45	11	r1	r1	PROPN
ejpam-6658	45	12	−	−	PROPN
ejpam-6658	45	13	1	1	NUM
ejpam-6658	45	14	2	2	NUM
ejpam-6658	45	15	)	)	PUNCT
ejpam-6658	45	16	n−k	n−k	NOUN
ejpam-6658	45	17	polynomials	polynomial	VERB
ejpam-6658	45	18	2et	2et	NOUN
ejpam-6658	45	19	e2t+1	e2t+1	PUNCT
ejpam-6658	46	1	=	=	SYM
ejpam-6658	46	2	∞∑	∞∑	PROPN
ejpam-6658	46	3	n=0	n=0	NUM
ejpam-6658	46	4	en	en	ADP
ejpam-6658	46	5	tn	tn	NOUN
ejpam-6658	46	6	n	n	X
ejpam-6658	46	7	!	!	PUNCT
ejpam-6658	47	1	and	and	CCONJ
ejpam-6658	47	2	numbers	number	NOUN
ejpam-6658	47	3	[	[	X
ejpam-6658	47	4	14	14	NUM
ejpam-6658	47	5	]	]	PUNCT
ejpam-6658	47	6	en	en	X
ejpam-6658	47	7	:	:	PUNCT
ejpam-6658	47	8	=	=	SYM
ejpam-6658	47	9	2nen	2nen	NUM
ejpam-6658	47	10	(	(	PUNCT
ejpam-6658	47	11	1	1	NUM
ejpam-6658	47	12	2	2	NUM
ejpam-6658	47	13	)	)	PUNCT
ejpam-6658	47	14	iii	iii	PROPN
ejpam-6658	47	15	.	.	PUNCT
ejpam-6658	48	1	genocchi	genocchi	PROPN
ejpam-6658	48	2	2	2	NUM
ejpam-6658	48	3	t	t	NOUN
ejpam-6658	48	4	et+1	et+1	PROPN
ejpam-6658	48	5	(	(	PUNCT
ejpam-6658	48	6	2	2	NUM
ejpam-6658	48	7	t	t	NOUN
ejpam-6658	48	8	et+1	et+1	PROPN
ejpam-6658	48	9	)	)	PUNCT
ejpam-6658	48	10	er1	er1	PROPN
ejpam-6658	48	11	t	t	PROPN
ejpam-6658	48	12	=	=	SYM
ejpam-6658	48	13	∞∑	∞∑	PROPN
ejpam-6658	48	14	n=0	n=0	PROPN
ejpam-6658	48	15	gn(r1	gn(r1	PROPN
ejpam-6658	48	16	)	)	PUNCT
ejpam-6658	48	17	tn	tn	PROPN
ejpam-6658	48	18	n	n	PROPN
ejpam-6658	48	19	!	!	PUNCT
ejpam-6658	48	20	gn(r1	gn(r1	PROPN
ejpam-6658	48	21	)	)	PUNCT
ejpam-6658	49	1	=	=	SYM
ejpam-6658	49	2	n∑	n∑	NOUN
ejpam-6658	49	3	k=0	k=0	PROPN
ejpam-6658	49	4	(	(	PUNCT
ejpam-6658	49	5	n	n	CCONJ
ejpam-6658	49	6	k	k	X
ejpam-6658	49	7	)	)	PUNCT
ejpam-6658	49	8	gkr	gkr	PROPN
ejpam-6658	49	9	n−k	n−k	NOUN
ejpam-6658	49	10	1	1	NUM
ejpam-6658	49	11	polynomials	polynomial	NOUN
ejpam-6658	49	12	2	2	NUM
ejpam-6658	49	13	t	t	NOUN
ejpam-6658	49	14	et+1	et+1	NOUN
ejpam-6658	50	1	=	=	SYM
ejpam-6658	50	2	∞∑	∞∑	NUM
ejpam-6658	50	3	n=1	n=1	PROPN
ejpam-6658	50	4	gn	gn	PROPN
ejpam-6658	50	5	tn	tn	PROPN
ejpam-6658	50	6	n	n	PROPN
ejpam-6658	50	7	!	!	PUNCT
ejpam-6658	51	1	and	and	CCONJ
ejpam-6658	51	2	numbers	number	NOUN
ejpam-6658	51	3	[	[	X
ejpam-6658	51	4	?	?	PUNCT
ejpam-6658	51	5	]	]	PUNCT
ejpam-6658	52	1	gn	gn	INTJ
ejpam-6658	52	2	:	:	PUNCT
ejpam-6658	52	3	=	=	PUNCT
ejpam-6658	52	4	gn(0	gn(0	NOUN
ejpam-6658	52	5	)	)	PUNCT
ejpam-6658	52	6	to	to	PART
ejpam-6658	52	7	facilitate	facilitate	VERB
ejpam-6658	52	8	further	further	ADJ
ejpam-6658	52	9	computations	computation	NOUN
ejpam-6658	52	10	,	,	PUNCT
ejpam-6658	52	11	we	we	PRON
ejpam-6658	52	12	present	present	VERB
ejpam-6658	52	13	the	the	DET
ejpam-6658	52	14	initial	initial	ADJ
ejpam-6658	52	15	values	value	NOUN
ejpam-6658	52	16	of	of	ADP
ejpam-6658	52	17	bernoulli	bernoulli	PROPN
ejpam-6658	52	18	numbers	number	NOUN
ejpam-6658	52	19	bn	bn	ADV
ejpam-6658	52	20	,	,	PUNCT
ejpam-6658	52	21	euler	euler	NOUN
ejpam-6658	52	22	numbers	number	NOUN
ejpam-6658	52	23	en	en	ADV
ejpam-6658	52	24	,	,	PUNCT
ejpam-6658	52	25	and	and	CCONJ
ejpam-6658	52	26	genocchi	genocchi	PROPN
ejpam-6658	52	27	numbers	number	NOUN
ejpam-6658	52	28	gn	gn	PROPN
ejpam-6658	52	29	in	in	ADP
ejpam-6658	52	30	table	table	NOUN
ejpam-6658	52	31	2	2	NUM
ejpam-6658	52	32	below	below	ADV
ejpam-6658	52	33	:	:	PUNCT
ejpam-6658	52	34	table	table	NOUN
ejpam-6658	52	35	2	2	NUM
ejpam-6658	52	36	.	.	PUNCT
ejpam-6658	52	37	values	value	NOUN
ejpam-6658	52	38	of	of	ADP
ejpam-6658	52	39	five	five	NUM
ejpam-6658	52	40	four	four	NUM
ejpam-6658	52	41	bn	bn	NOUN
ejpam-6658	52	42	,	,	PUNCT
ejpam-6658	52	43	en	en	X
ejpam-6658	52	44	and	and	CCONJ
ejpam-6658	52	45	gn	gn	PROPN
ejpam-6658	52	46	n	n	ADV
ejpam-6658	52	47	0	0	NUM
ejpam-6658	52	48	1	1	NUM
ejpam-6658	52	49	2	2	NUM
ejpam-6658	52	50	3	3	NUM
ejpam-6658	52	51	4	4	NUM
ejpam-6658	52	52	bn	bn	NUM
ejpam-6658	52	53	1	1	NUM
ejpam-6658	52	54	±	±	NUM
ejpam-6658	52	55	1	1	NUM
ejpam-6658	52	56	2	2	NUM
ejpam-6658	52	57	1	1	NUM
ejpam-6658	52	58	6	6	NUM
ejpam-6658	52	59	0	0	NUM
ejpam-6658	52	60	−	−	NOUN
ejpam-6658	52	61	1	1	NUM
ejpam-6658	52	62	30	30	NUM
ejpam-6658	52	63	en	en	PROPN
ejpam-6658	52	64	1	1	NUM
ejpam-6658	52	65	0	0	NUM
ejpam-6658	52	66	-1	-1	SYM
ejpam-6658	52	67	0	0	NUM
ejpam-6658	52	68	5	5	NUM
ejpam-6658	52	69	gn	gn	NOUN
ejpam-6658	52	70	0	0	NUM
ejpam-6658	52	71	1	1	NUM
ejpam-6658	52	72	-1	-1	SYM
ejpam-6658	52	73	0	0	NUM
ejpam-6658	52	74	1	1	NUM
ejpam-6658	52	75	in	in	ADP
ejpam-6658	52	76	2012	2012	NUM
ejpam-6658	52	77	,	,	PUNCT
ejpam-6658	52	78	khan	khan	PROPN
ejpam-6658	52	79	and	and	CCONJ
ejpam-6658	52	80	raza	raza	PROPN
ejpam-6658	53	1	[	[	X
ejpam-6658	53	2	15	15	NUM
ejpam-6658	53	3	]	]	PUNCT
ejpam-6658	53	4	introduced	introduce	VERB
ejpam-6658	53	5	and	and	CCONJ
ejpam-6658	53	6	analyzed	analyze	VERB
ejpam-6658	53	7	a	a	DET
ejpam-6658	53	8	hybrid	hybrid	ADJ
ejpam-6658	53	9	class	class	NOUN
ejpam-6658	53	10	of	of	ADP
ejpam-6658	53	11	laguerre	laguerre	NOUN
ejpam-6658	53	12	-	-	PUNCT
ejpam-6658	53	13	sheffer	sheffer	NOUN
ejpam-6658	53	14	polynomials	polynomial	NOUN
ejpam-6658	53	15	,	,	PUNCT
ejpam-6658	53	16	denoted	denote	VERB
ejpam-6658	53	17	as	as	ADP
ejpam-6658	53	18	lsn(r1	lsn(r1	NOUN
ejpam-6658	53	19	,	,	PUNCT
ejpam-6658	53	20	r2	r2	PROPN
ejpam-6658	53	21	)	)	PUNCT
ejpam-6658	53	22	,	,	PUNCT
ejpam-6658	53	23	which	which	PRON
ejpam-6658	53	24	are	be	AUX
ejpam-6658	53	25	defined	define	VERB
ejpam-6658	53	26	via	via	ADP
ejpam-6658	53	27	the	the	DET
ejpam-6658	53	28	generating	generate	VERB
ejpam-6658	53	29	function	function	NOUN
ejpam-6658	53	30	:	:	PUNCT
ejpam-6658	53	31	r(t	r(t	NOUN
ejpam-6658	53	32	)	)	PUNCT
ejpam-6658	53	33	er2h(t	er2h(t	NUM
ejpam-6658	53	34	)	)	PUNCT
ejpam-6658	54	1	j0(2	j0(2	PROPN
ejpam-6658	54	2	√	√	ADV
ejpam-6658	54	3	r1h(t	r1h(t	NOUN
ejpam-6658	54	4	)	)	PUNCT
ejpam-6658	54	5	)	)	PUNCT
ejpam-6658	55	1	=	=	PUNCT
ejpam-6658	56	1	∞∑	∞∑	NUM
ejpam-6658	56	2	n=0	n=0	NUM
ejpam-6658	56	3	lsn(r1	lsn(r1	NOUN
ejpam-6658	56	4	,	,	PUNCT
ejpam-6658	56	5	r2	r2	PROPN
ejpam-6658	56	6	)	)	PUNCT
ejpam-6658	56	7	tn	tn	PROPN
ejpam-6658	56	8	n	n	PROPN
ejpam-6658	56	9	!	!	PUNCT
ejpam-6658	56	10	.	.	PUNCT
ejpam-6658	57	1	(	(	PUNCT
ejpam-6658	57	2	7	7	X
ejpam-6658	57	3	)	)	PUNCT
ejpam-6658	57	4	since	since	SCONJ
ejpam-6658	57	5	sheffer	sheffer	NOUN
ejpam-6658	57	6	polynomials	polynomial	NOUN
ejpam-6658	57	7	sn(r1	sn(r1	NOUN
ejpam-6658	57	8	)	)	PUNCT
ejpam-6658	58	1	[	[	X
ejpam-6658	58	2	16	16	NUM
ejpam-6658	58	3	]	]	PUNCT
ejpam-6658	58	4	reduce	reduce	VERB
ejpam-6658	58	5	to	to	ADP
ejpam-6658	58	6	appell	appell	ADJ
ejpam-6658	58	7	polynomialsrn(r1	polynomialsrn(r1	NOUN
ejpam-6658	58	8	)	)	PUNCT
ejpam-6658	58	9	whenh(t	whenh(t	NOUN
ejpam-6658	58	10	)	)	PUNCT
ejpam-6658	58	11	=	=	SYM
ejpam-6658	58	12	t	t	PROPN
ejpam-6658	58	13	,	,	PUNCT
ejpam-6658	58	14	choosing	choose	VERB
ejpam-6658	58	15	h(t	h(t	PRON
ejpam-6658	58	16	)	)	PUNCT
ejpam-6658	59	1	=	=	SYM
ejpam-6658	59	2	t	t	NOUN
ejpam-6658	59	3	in	in	ADP
ejpam-6658	59	4	equation	equation	NOUN
ejpam-6658	59	5	(	(	PUNCT
ejpam-6658	59	6	7	7	X
ejpam-6658	59	7	)	)	PUNCT
ejpam-6658	59	8	leads	lead	VERB
ejpam-6658	59	9	to	to	ADP
ejpam-6658	59	10	the	the	DET
ejpam-6658	59	11	hybrid	hybrid	PROPN
ejpam-6658	59	12	legendre	legendre	PROPN
ejpam-6658	59	13	-	-	PUNCT
ejpam-6658	59	14	appell	appell	NOUN
ejpam-6658	59	15	polynomials	polynomial	NOUN
ejpam-6658	59	16	(	(	PUNCT
ejpam-6658	59	17	leap	leap	PROPN
ejpam-6658	59	18	)	)	PUNCT
ejpam-6658	59	19	,	,	PUNCT
ejpam-6658	59	20	defined	define	VERB
ejpam-6658	59	21	by	by	ADP
ejpam-6658	59	22	:	:	PUNCT
ejpam-6658	59	23	r(t	r(t	NOUN
ejpam-6658	59	24	)	)	PUNCT
ejpam-6658	59	25	er2	er2	ADP
ejpam-6658	59	26	t	t	PROPN
ejpam-6658	59	27	j0(2	j0(2	PROPN
ejpam-6658	59	28	√	√	PROPN
ejpam-6658	59	29	r1	r1	PROPN
ejpam-6658	59	30	t	t	PROPN
ejpam-6658	59	31	)	)	PUNCT
ejpam-6658	59	32	=	=	PUNCT
ejpam-6658	60	1	∞∑	∞∑	PRON
ejpam-6658	60	2	n=0	n=0	NUM
ejpam-6658	60	3	lrn(r1	lrn(r1	NOUN
ejpam-6658	60	4	,	,	PUNCT
ejpam-6658	60	5	r2	r2	PROPN
ejpam-6658	60	6	)	)	PUNCT
ejpam-6658	60	7	tn	tn	PROPN
ejpam-6658	60	8	n	n	CCONJ
ejpam-6658	60	9	!	!	PROPN
ejpam-6658	60	10	,	,	PUNCT
ejpam-6658	60	11	(	(	PUNCT
ejpam-6658	60	12	8)	8)	NUM
ejpam-6658	60	13	or	or	CCONJ
ejpam-6658	60	14	equivalently	equivalently	ADV
ejpam-6658	60	15	,	,	PUNCT
ejpam-6658	60	16	r(t	r(t	NOUN
ejpam-6658	60	17	)	)	PUNCT
ejpam-6658	60	18	er2	er2	ADP
ejpam-6658	60	19	t	t	PROPN
ejpam-6658	60	20	c0(r1	c0(r1	PROPN
ejpam-6658	60	21	t	t	PROPN
ejpam-6658	60	22	)	)	PUNCT
ejpam-6658	60	23	=	=	PUNCT
ejpam-6658	61	1	∞∑	∞∑	PRON
ejpam-6658	61	2	n=0	n=0	NUM
ejpam-6658	61	3	lrn(r1	lrn(r1	NOUN
ejpam-6658	61	4	,	,	PUNCT
ejpam-6658	61	5	r2	r2	PROPN
ejpam-6658	61	6	)	)	PUNCT
ejpam-6658	61	7	tn	tn	PROPN
ejpam-6658	61	8	n	n	CCONJ
ejpam-6658	61	9	!	!	PROPN
ejpam-6658	61	10	,	,	PUNCT
ejpam-6658	62	1	(	(	PUNCT
ejpam-6658	62	2	9	9	X
ejpam-6658	62	3	)	)	PUNCT
ejpam-6658	62	4	where	where	SCONJ
ejpam-6658	62	5	c0(r1	c0(r1	NOUN
ejpam-6658	62	6	)	)	PUNCT
ejpam-6658	62	7	denotes	denote	VERB
ejpam-6658	62	8	the	the	DET
ejpam-6658	62	9	0th	0th	ADJ
ejpam-6658	62	10	order	order	NOUN
ejpam-6658	62	11	bessel	bessel	NOUN
ejpam-6658	62	12	tricomi	tricomi	NOUN
ejpam-6658	62	13	function	function	VERB
ejpam-6658	62	14	[	[	X
ejpam-6658	62	15	14	14	NUM
ejpam-6658	62	16	]	]	PUNCT
ejpam-6658	62	17	.	.	PUNCT
ejpam-6658	63	1	the	the	DET
ejpam-6658	63	2	nth	nth	NOUN
ejpam-6658	63	3	-	-	PUNCT
ejpam-6658	63	4	order	order	NOUN
ejpam-6658	63	5	tricomi	tricomi	NOUN
ejpam-6658	63	6	functions	function	NOUN
ejpam-6658	63	7	cn(r1	cn(r1	NOUN
ejpam-6658	63	8	)	)	PUNCT
ejpam-6658	63	9	are	be	AUX
ejpam-6658	63	10	defined	define	VERB
ejpam-6658	63	11	as	as	ADP
ejpam-6658	63	12	cn(r1	cn(r1	NOUN
ejpam-6658	63	13	)	)	PUNCT
ejpam-6658	63	14	=	=	PUNCT
ejpam-6658	64	1	∞∑	∞∑	NUM
ejpam-6658	64	2	k=0	k=0	PROPN
ejpam-6658	64	3	(	(	PUNCT
ejpam-6658	64	4	−1)krk1	−1)krk1	NUM
ejpam-6658	64	5	k!(n+	k!(n+	PROPN
ejpam-6658	64	6	k	k	NOUN
ejpam-6658	64	7	)	)	PUNCT
ejpam-6658	64	8	!	!	PUNCT
ejpam-6658	64	9	.	.	PUNCT
ejpam-6658	65	1	(	(	PUNCT
ejpam-6658	65	2	10	10	NUM
ejpam-6658	65	3	)	)	PUNCT
ejpam-6658	65	4	w.	w.	PROPN
ejpam-6658	65	5	a.	a.	PROPN
ejpam-6658	65	6	khan	khan	PROPN
ejpam-6658	65	7	,	,	PUNCT
ejpam-6658	65	8	h.	h.	PROPN
ejpam-6658	65	9	qawaqneh	qawaqneh	PROPN
ejpam-6658	65	10	,	,	PUNCT
ejpam-6658	65	11	h.	h.	PROPN
ejpam-6658	65	12	aydi	aydi	VERB
ejpam-6658	65	13	/	/	SYM
ejpam-6658	65	14	eur	eur	NOUN
ejpam-6658	65	15	.	.	PUNCT
ejpam-6658	66	1	j.	j.	PROPN
ejpam-6658	66	2	pure	pure	PROPN
ejpam-6658	66	3	appl	appl	PROPN
ejpam-6658	66	4	.	.	PROPN
ejpam-6658	66	5	math	math	PROPN
ejpam-6658	66	6	,	,	PUNCT
ejpam-6658	66	7	18	18	NUM
ejpam-6658	66	8	(	(	PUNCT
ejpam-6658	66	9	3	3	NUM
ejpam-6658	66	10	)	)	PUNCT
ejpam-6658	66	11	(	(	PUNCT
ejpam-6658	66	12	2025	2025	NUM
ejpam-6658	66	13	)	)	PUNCT
ejpam-6658	66	14	,	,	PUNCT
ejpam-6658	66	15	6658	6658	NUM
ejpam-6658	66	16	4	4	NUM
ejpam-6658	66	17	of	of	ADP
ejpam-6658	66	18	22	22	NUM
ejpam-6658	66	19	we	we	PRON
ejpam-6658	66	20	also	also	ADV
ejpam-6658	66	21	note	note	VERB
ejpam-6658	66	22	that	that	SCONJ
ejpam-6658	66	23	exp(−αd̂−1	exp(−αd̂−1	PROPN
ejpam-6658	66	24	r1	r1	PROPN
ejpam-6658	66	25	)	)	PUNCT
ejpam-6658	67	1	=	=	PUNCT
ejpam-6658	67	2	c0(αx	c0(αx	NOUN
ejpam-6658	67	3	)	)	PUNCT
ejpam-6658	67	4	,	,	PUNCT
ejpam-6658	68	1	d̂−n	d̂−n	VERB
ejpam-6658	68	2	r1	r1	NOUN
ejpam-6658	68	3	{	{	PUNCT
ejpam-6658	68	4	1	1	NUM
ejpam-6658	68	5	}	}	PUNCT
ejpam-6658	68	6	:	:	PUNCT
ejpam-6658	68	7	=	=	SYM
ejpam-6658	68	8	rn1	rn1	PROPN
ejpam-6658	68	9	n	n	X
ejpam-6658	68	10	!	!	PUNCT
ejpam-6658	68	11	.	.	PUNCT
ejpam-6658	69	1	(	(	PUNCT
ejpam-6658	69	2	11	11	NUM
ejpam-6658	69	3	)	)	PUNCT
ejpam-6658	69	4	further	far	ADV
ejpam-6658	69	5	,	,	PUNCT
ejpam-6658	69	6	it	it	PRON
ejpam-6658	69	7	can	can	AUX
ejpam-6658	69	8	be	be	AUX
ejpam-6658	69	9	expressed	express	VERB
ejpam-6658	69	10	as	as	ADP
ejpam-6658	69	11	r(t	r(t	NOUN
ejpam-6658	69	12	)	)	PUNCT
ejpam-6658	69	13	eyt	eyt	PROPN
ejpam-6658	69	14	e−d−1	e−d−1	PROPN
ejpam-6658	69	15	r1	r1	PROPN
ejpam-6658	69	16	t	t	NOUN
ejpam-6658	69	17	=	=	PUNCT
ejpam-6658	70	1	∞∑	∞∑	ADJ
ejpam-6658	70	2	n=0	n=0	NUM
ejpam-6658	70	3	lrn(r1	lrn(r1	NOUN
ejpam-6658	70	4	,	,	PUNCT
ejpam-6658	70	5	r2	r2	PROPN
ejpam-6658	70	6	)	)	PUNCT
ejpam-6658	70	7	tn	tn	PROPN
ejpam-6658	70	8	n	n	PROPN
ejpam-6658	70	9	!	!	PUNCT
ejpam-6658	70	10	.	.	PUNCT
ejpam-6658	71	1	(	(	PUNCT
ejpam-6658	71	2	12	12	NUM
ejpam-6658	71	3	)	)	PUNCT
ejpam-6658	71	4	the	the	DET
ejpam-6658	71	5	hybrid	hybrid	ADJ
ejpam-6658	71	6	lap	lap	NOUN
ejpam-6658	71	7	lrn(r1	lrn(r1	NOUN
ejpam-6658	71	8	,	,	PUNCT
ejpam-6658	71	9	r2	r2	PROPN
ejpam-6658	71	10	)	)	PUNCT
ejpam-6658	71	11	satisfies	satisfy	VERB
ejpam-6658	71	12	the	the	DET
ejpam-6658	71	13	series	series	NOUN
ejpam-6658	71	14	expansion	expansion	NOUN
ejpam-6658	71	15	:	:	PUNCT
ejpam-6658	71	16	lrn(r1	lrn(r1	ADJ
ejpam-6658	71	17	,	,	PUNCT
ejpam-6658	71	18	r2	r2	PROPN
ejpam-6658	71	19	)	)	PUNCT
ejpam-6658	71	20	=	=	SYM
ejpam-6658	72	1	n	n	X
ejpam-6658	72	2	!	!	PUNCT
ejpam-6658	72	3	n∑	n∑	PUNCT
ejpam-6658	73	1	k=0	k=0	PROPN
ejpam-6658	73	2	ln−k(r2)r	ln−k(r2)r	VERB
ejpam-6658	73	3	k	k	NOUN
ejpam-6658	73	4	1	1	NUM
ejpam-6658	73	5	(	(	PUNCT
ejpam-6658	73	6	n−	n−	NOUN
ejpam-6658	73	7	k)!(k!)2	k)!(k!)2	PROPN
ejpam-6658	73	8	.	.	PUNCT
ejpam-6658	74	1	(	(	PUNCT
ejpam-6658	74	2	13	13	NUM
ejpam-6658	74	3	)	)	PUNCT
ejpam-6658	74	4	by	by	ADP
ejpam-6658	74	5	appropriately	appropriately	ADV
ejpam-6658	74	6	choosing	choose	VERB
ejpam-6658	74	7	r(t	r(t	NOUN
ejpam-6658	74	8	)	)	PUNCT
ejpam-6658	74	9	,	,	PUNCT
ejpam-6658	74	10	various	various	ADJ
ejpam-6658	74	11	members	member	NOUN
ejpam-6658	74	12	of	of	ADP
ejpam-6658	74	13	the	the	DET
ejpam-6658	74	14	hybrid	hybrid	ADJ
ejpam-6658	74	15	lap	lap	NOUN
ejpam-6658	74	16	family	family	NOUN
ejpam-6658	74	17	can	can	AUX
ejpam-6658	74	18	be	be	AUX
ejpam-6658	74	19	derived	derive	VERB
ejpam-6658	74	20	.	.	PUNCT
ejpam-6658	75	1	these	these	PRON
ejpam-6658	75	2	are	be	AUX
ejpam-6658	75	3	summarized	summarize	VERB
ejpam-6658	75	4	in	in	ADP
ejpam-6658	75	5	table	table	NOUN
ejpam-6658	75	6	3	3	NUM
ejpam-6658	75	7	:	:	PUNCT
ejpam-6658	75	8	table	table	NOUN
ejpam-6658	75	9	3	3	NUM
ejpam-6658	75	10	.	.	PUNCT
ejpam-6658	76	1	certain	certain	ADJ
ejpam-6658	76	2	members	member	NOUN
ejpam-6658	76	3	belonging	belong	VERB
ejpam-6658	76	4	to	to	ADP
ejpam-6658	76	5	the	the	DET
ejpam-6658	76	6	lap	lap	NOUN
ejpam-6658	76	7	family	family	NOUN
ejpam-6658	76	8	s.	s.	PROPN
ejpam-6658	76	9	name	name	PROPN
ejpam-6658	76	10	of	of	ADP
ejpam-6658	76	11	hybrid	hybrid	NOUN
ejpam-6658	76	12	r(t	r(t	NOUN
ejpam-6658	76	13	)	)	PUNCT
ejpam-6658	76	14	generating	generate	VERB
ejpam-6658	76	15	function	function	NOUN
ejpam-6658	76	16	series	series	NOUN
ejpam-6658	76	17	definition	definition	NOUN
ejpam-6658	76	18	no	no	INTJ
ejpam-6658	76	19	.	.	PUNCT
ejpam-6658	77	1	polynomials	polynomials	PROPN
ejpam-6658	77	2	i.	i.	PROPN
ejpam-6658	77	3	hybrid	hybrid	PROPN
ejpam-6658	77	4	laguerre	laguerre	PROPN
ejpam-6658	77	5	-	-	PUNCT
ejpam-6658	77	6	bernoulli	bernoulli	PROPN
ejpam-6658	77	7	t	t	PROPN
ejpam-6658	77	8	et−1	et−1	PROPN
ejpam-6658	77	9	(	(	PUNCT
ejpam-6658	77	10	t	t	PROPN
ejpam-6658	77	11	et−1	et−1	PROPN
ejpam-6658	77	12	)	)	PUNCT
ejpam-6658	77	13	er2	er2	ADP
ejpam-6658	77	14	t	t	PROPN
ejpam-6658	77	15	j0(2	j0(2	PROPN
ejpam-6658	77	16	√	√	PROPN
ejpam-6658	77	17	r1	r1	PROPN
ejpam-6658	77	18	t	t	NOUN
ejpam-6658	77	19	=	=	SYM
ejpam-6658	77	20	∞∑	∞∑	PROPN
ejpam-6658	77	21	n=0	n=0	NUM
ejpam-6658	77	22	lbn(r1	lbn(r1	PROPN
ejpam-6658	77	23	,	,	PUNCT
ejpam-6658	77	24	r2	r2	PROPN
ejpam-6658	77	25	)	)	PUNCT
ejpam-6658	77	26	tn	tn	PROPN
ejpam-6658	77	27	n	n	PROPN
ejpam-6658	77	28	!	!	PUNCT
ejpam-6658	78	1	lbn(r1	lbn(r1	PROPN
ejpam-6658	78	2	,	,	PUNCT
ejpam-6658	78	3	r2	r2	PROPN
ejpam-6658	78	4	)	)	PUNCT
ejpam-6658	78	5	=	=	SYM
ejpam-6658	79	1	n	n	X
ejpam-6658	79	2	!	!	PUNCT
ejpam-6658	80	1	n∑	n∑	PUNCT
ejpam-6658	80	2	k=0	k=0	PROPN
ejpam-6658	80	3	(	(	PUNCT
ejpam-6658	80	4	−1)kbn−k(r2)rk1	−1)kbn−k(r2)rk1	NOUN
ejpam-6658	80	5	(	(	PUNCT
ejpam-6658	80	6	n−k)!(k!)2	n−k)!(k!)2	PROPN
ejpam-6658	80	7	polynomials	polynomials	PROPN
ejpam-6658	80	8	ii	ii	PROPN
ejpam-6658	80	9	.	.	PUNCT
ejpam-6658	80	10	hybrid	hybrid	PROPN
ejpam-6658	80	11	laguerre	laguerre	NOUN
ejpam-6658	80	12	-	-	PUNCT
ejpam-6658	80	13	euler	euler	NOUN
ejpam-6658	80	14	2	2	NUM
ejpam-6658	80	15	et+1	et+1	PROPN
ejpam-6658	80	16	(	(	PUNCT
ejpam-6658	80	17	2	2	NUM
ejpam-6658	80	18	et+1	et+1	NOUN
ejpam-6658	80	19	)	)	PUNCT
ejpam-6658	80	20	er2	er2	ADP
ejpam-6658	80	21	t	t	PROPN
ejpam-6658	80	22	j0(2	j0(2	PROPN
ejpam-6658	80	23	√	√	PROPN
ejpam-6658	80	24	r1	r1	PROPN
ejpam-6658	80	25	t	t	NOUN
ejpam-6658	80	26	=	=	SYM
ejpam-6658	81	1	∞∑	∞∑	NUM
ejpam-6658	81	2	n=0	n=0	NUM
ejpam-6658	81	3	len(r1	len(r1	NOUN
ejpam-6658	81	4	,	,	PUNCT
ejpam-6658	81	5	r2	r2	PROPN
ejpam-6658	81	6	)	)	PUNCT
ejpam-6658	81	7	tn	tn	PROPN
ejpam-6658	81	8	n	n	CCONJ
ejpam-6658	81	9	!	!	PUNCT
ejpam-6658	81	10	len(r1	len(r1	PROPN
ejpam-6658	81	11	,	,	PUNCT
ejpam-6658	81	12	r2	r2	PROPN
ejpam-6658	81	13	)	)	PUNCT
ejpam-6658	81	14	=	=	SYM
ejpam-6658	81	15	n	n	X
ejpam-6658	81	16	!	!	PUNCT
ejpam-6658	82	1	n∑	n∑	PUNCT
ejpam-6658	82	2	k=0	k=0	PROPN
ejpam-6658	82	3	(	(	PUNCT
ejpam-6658	82	4	−1)ken−k(r2)rk1	−1)ken−k(r2)rk1	PROPN
ejpam-6658	82	5	(	(	PUNCT
ejpam-6658	82	6	n−k)!(k!)2	n−k)!(k!)2	PROPN
ejpam-6658	82	7	polynomials	polynomials	PROPN
ejpam-6658	82	8	iii	iii	PROPN
ejpam-6658	82	9	.	.	PUNCT
ejpam-6658	82	10	hybrid	hybrid	ADJ
ejpam-6658	82	11	laguerre	laguerre	NOUN
ejpam-6658	82	12	-	-	PUNCT
ejpam-6658	82	13	genocchi	genocchi	PROPN
ejpam-6658	82	14	2	2	NUM
ejpam-6658	82	15	t	t	NOUN
ejpam-6658	82	16	et+1	et+1	PROPN
ejpam-6658	82	17	(	(	PUNCT
ejpam-6658	82	18	2	2	NUM
ejpam-6658	82	19	t	t	NOUN
ejpam-6658	82	20	et+1	et+1	NOUN
ejpam-6658	82	21	)	)	PUNCT
ejpam-6658	82	22	er2	er2	ADP
ejpam-6658	82	23	t	t	PROPN
ejpam-6658	82	24	j0(2	j0(2	PROPN
ejpam-6658	82	25	√	√	PROPN
ejpam-6658	82	26	r1	r1	PROPN
ejpam-6658	82	27	t	t	NOUN
ejpam-6658	82	28	=	=	SYM
ejpam-6658	83	1	∞∑	∞∑	NUM
ejpam-6658	83	2	n=0	n=0	NUM
ejpam-6658	83	3	lgn(r1	lgn(r1	PROPN
ejpam-6658	83	4	,	,	PUNCT
ejpam-6658	83	5	r2	r2	PROPN
ejpam-6658	83	6	)	)	PUNCT
ejpam-6658	83	7	tn	tn	PROPN
ejpam-6658	83	8	n	n	NOUN
ejpam-6658	83	9	!	!	PUNCT
ejpam-6658	84	1	lgn(r1	lgn(r1	PROPN
ejpam-6658	84	2	,	,	PUNCT
ejpam-6658	84	3	r2	r2	PROPN
ejpam-6658	84	4	)	)	PUNCT
ejpam-6658	84	5	=	=	SYM
ejpam-6658	84	6	n	n	X
ejpam-6658	84	7	!	!	PUNCT
ejpam-6658	85	1	n∑	n∑	PUNCT
ejpam-6658	85	2	k=0	k=0	PROPN
ejpam-6658	85	3	(	(	PUNCT
ejpam-6658	85	4	−1)kgn−k(r2)rk1	−1)kgn−k(r2)rk1	NOUN
ejpam-6658	85	5	(	(	PUNCT
ejpam-6658	85	6	n−k)!(k!)2	n−k)!(k!)2	X
ejpam-6658	85	7	polynomials	polynomial	VERB
ejpam-6658	85	8	the	the	DET
ejpam-6658	85	9	2	2	NUM
ejpam-6658	85	10	-	-	PUNCT
ejpam-6658	85	11	variable	variable	ADJ
ejpam-6658	85	12	general	general	ADJ
ejpam-6658	85	13	polynomials	polynomial	NOUN
ejpam-6658	85	14	(	(	PUNCT
ejpam-6658	85	15	2vgp	2vgp	NOUN
ejpam-6658	85	16	)	)	PUNCT
ejpam-6658	85	17	denoted	denote	VERB
ejpam-6658	85	18	by	by	ADP
ejpam-6658	85	19	pn(r1	pn(r1	NOUN
ejpam-6658	85	20	,	,	PUNCT
ejpam-6658	85	21	r2	r2	PROPN
ejpam-6658	85	22	)	)	PUNCT
ejpam-6658	85	23	are	be	AUX
ejpam-6658	85	24	specified	specify	VERB
ejpam-6658	85	25	by	by	ADP
ejpam-6658	85	26	generating	generate	VERB
ejpam-6658	85	27	relation	relation	NOUN
ejpam-6658	86	1	[	[	X
ejpam-6658	86	2	17	17	NUM
ejpam-6658	86	3	]	]	SYM
ejpam-6658	86	4	:	:	PUNCT
ejpam-6658	86	5	exp(r1t)ψ(r2	exp(r1t)ψ(r2	PROPN
ejpam-6658	86	6	,	,	PUNCT
ejpam-6658	86	7	t	t	PROPN
ejpam-6658	86	8	)	)	PUNCT
ejpam-6658	86	9	=	=	PUNCT
ejpam-6658	87	1	∞∑	∞∑	PRON
ejpam-6658	87	2	n=0	n=0	NUM
ejpam-6658	87	3	pn(r1	pn(r1	NOUN
ejpam-6658	87	4	,	,	PUNCT
ejpam-6658	87	5	r2	r2	PROPN
ejpam-6658	87	6	)	)	PUNCT
ejpam-6658	87	7	tn	tn	PROPN
ejpam-6658	87	8	n	n	PROPN
ejpam-6658	87	9	!	!	PROPN
ejpam-6658	87	10	,	,	PUNCT
ejpam-6658	87	11	(	(	PUNCT
ejpam-6658	87	12	p0(r1	p0(r1	NOUN
ejpam-6658	87	13	,	,	PUNCT
ejpam-6658	87	14	r2	r2	PROPN
ejpam-6658	87	15	)	)	PUNCT
ejpam-6658	87	16	=	=	SYM
ejpam-6658	87	17	1	1	NUM
ejpam-6658	87	18	)	)	PUNCT
ejpam-6658	87	19	,	,	PUNCT
ejpam-6658	87	20	(	(	PUNCT
ejpam-6658	87	21	14	14	NUM
ejpam-6658	87	22	)	)	PUNCT
ejpam-6658	87	23	where	where	SCONJ
ejpam-6658	87	24	ψ(r2	ψ(r2	NOUN
ejpam-6658	87	25	,	,	PUNCT
ejpam-6658	87	26	t	t	PROPN
ejpam-6658	87	27	)	)	PUNCT
ejpam-6658	87	28	has	have	AUX
ejpam-6658	87	29	(	(	PUNCT
ejpam-6658	87	30	at	at	ADP
ejpam-6658	87	31	least	least	ADJ
ejpam-6658	87	32	the	the	DET
ejpam-6658	87	33	formal	formal	ADJ
ejpam-6658	87	34	)	)	PUNCT
ejpam-6658	87	35	series	series	NOUN
ejpam-6658	87	36	expansion	expansion	NOUN
ejpam-6658	87	37	ψ(r2	ψ(r2	NOUN
ejpam-6658	87	38	,	,	PUNCT
ejpam-6658	87	39	t	t	PROPN
ejpam-6658	87	40	)	)	PUNCT
ejpam-6658	87	41	=	=	PUNCT
ejpam-6658	88	1	∞∑	∞∑	NUM
ejpam-6658	88	2	k=0	k=0	PROPN
ejpam-6658	88	3	ψk(r2	ψk(r2	ADV
ejpam-6658	88	4	)	)	PUNCT
ejpam-6658	88	5	tk	tk	PROPN
ejpam-6658	89	1	k	k	PROPN
ejpam-6658	89	2	!	!	PROPN
ejpam-6658	89	3	,	,	PUNCT
ejpam-6658	89	4	(	(	PUNCT
ejpam-6658	89	5	ψ0(r2	ψ0(r2	NOUN
ejpam-6658	89	6	)	)	PUNCT
ejpam-6658	89	7	̸=	̸=	PROPN
ejpam-6658	89	8	0	0	NUM
ejpam-6658	89	9	)	)	PUNCT
ejpam-6658	89	10	.	.	PUNCT
ejpam-6658	90	1	(	(	PUNCT
ejpam-6658	90	2	15	15	NUM
ejpam-6658	90	3	)	)	PUNCT
ejpam-6658	90	4	the	the	DET
ejpam-6658	90	5	foundational	foundational	ADJ
ejpam-6658	90	6	idea	idea	NOUN
ejpam-6658	90	7	of	of	ADP
ejpam-6658	90	8	the	the	DET
ejpam-6658	90	9	monomiality	monomiality	NOUN
ejpam-6658	90	10	principle	principle	NOUN
ejpam-6658	90	11	dates	date	VERB
ejpam-6658	90	12	back	back	ADV
ejpam-6658	90	13	to	to	ADP
ejpam-6658	90	14	1941	1941	NUM
ejpam-6658	90	15	when	when	SCONJ
ejpam-6658	90	16	steffenson	steffenson	NOUN
ejpam-6658	90	17	[	[	X
ejpam-6658	90	18	18	18	NUM
ejpam-6658	90	19	]	]	PUNCT
ejpam-6658	90	20	first	first	ADV
ejpam-6658	90	21	introduced	introduce	VERB
ejpam-6658	90	22	the	the	DET
ejpam-6658	90	23	concept	concept	NOUN
ejpam-6658	90	24	through	through	ADP
ejpam-6658	90	25	the	the	DET
ejpam-6658	90	26	notion	notion	NOUN
ejpam-6658	90	27	of	of	ADP
ejpam-6658	90	28	poweroid	poweroid	ADJ
ejpam-6658	90	29	.	.	PUNCT
ejpam-6658	91	1	this	this	DET
ejpam-6658	91	2	approach	approach	NOUN
ejpam-6658	91	3	was	be	AUX
ejpam-6658	91	4	later	later	ADV
ejpam-6658	91	5	refined	refine	VERB
ejpam-6658	91	6	and	and	CCONJ
ejpam-6658	91	7	extended	extend	VERB
ejpam-6658	91	8	by	by	ADP
ejpam-6658	91	9	dattoli	dattoli	NOUN
ejpam-6658	92	1	[	[	X
ejpam-6658	92	2	19	19	NUM
ejpam-6658	92	3	]	]	PUNCT
ejpam-6658	92	4	,	,	PUNCT
ejpam-6658	92	5	paving	pave	VERB
ejpam-6658	92	6	the	the	DET
ejpam-6658	92	7	way	way	NOUN
ejpam-6658	92	8	for	for	ADP
ejpam-6658	92	9	further	further	ADJ
ejpam-6658	92	10	advancements	advancement	NOUN
ejpam-6658	92	11	in	in	ADP
ejpam-6658	92	12	the	the	DET
ejpam-6658	92	13	field	field	NOUN
ejpam-6658	92	14	.	.	PUNCT
ejpam-6658	93	1	the	the	DET
ejpam-6658	93	2	monomiality	monomiality	NOUN
ejpam-6658	93	3	principle	principle	NOUN
ejpam-6658	93	4	asserts	assert	VERB
ejpam-6658	93	5	that	that	SCONJ
ejpam-6658	93	6	the	the	DET
ejpam-6658	93	7	operators	operator	NOUN
ejpam-6658	93	8	m̂	m̂	PROPN
ejpam-6658	93	9	and	and	CCONJ
ejpam-6658	93	10	p̂	p̂	NOUN
ejpam-6658	93	11	act	act	PROPN
ejpam-6658	93	12	,	,	PUNCT
ejpam-6658	93	13	respectively	respectively	ADV
ejpam-6658	93	14	,	,	PUNCT
ejpam-6658	93	15	as	as	ADP
ejpam-6658	93	16	multiplicative	multiplicative	ADJ
ejpam-6658	93	17	and	and	CCONJ
ejpam-6658	93	18	differential	differential	ADJ
ejpam-6658	93	19	operators	operator	NOUN
ejpam-6658	93	20	for	for	ADP
ejpam-6658	93	21	a	a	DET
ejpam-6658	93	22	given	give	VERB
ejpam-6658	93	23	polynomial	polynomial	ADJ
ejpam-6658	93	24	sequence	sequence	NOUN
ejpam-6658	93	25	{	{	PUNCT
ejpam-6658	93	26	qn(r1)}n∈n	qn(r1)}n∈n	NOUN
ejpam-6658	93	27	.	.	PUNCT
ejpam-6658	94	1	more	more	ADV
ejpam-6658	94	2	specifically	specifically	ADV
ejpam-6658	94	3	,	,	PUNCT
ejpam-6658	94	4	these	these	DET
ejpam-6658	94	5	operators	operator	NOUN
ejpam-6658	94	6	satisfy	satisfy	VERB
ejpam-6658	94	7	the	the	DET
ejpam-6658	94	8	fundamental	fundamental	ADJ
ejpam-6658	94	9	recurrence	recurrence	NOUN
ejpam-6658	94	10	relations	relation	NOUN
ejpam-6658	94	11	:	:	PUNCT
ejpam-6658	94	12	w.	w.	PROPN
ejpam-6658	94	13	a.	a.	PROPN
ejpam-6658	94	14	khan	khan	PROPN
ejpam-6658	94	15	,	,	PUNCT
ejpam-6658	94	16	h.	h.	PROPN
ejpam-6658	94	17	qawaqneh	qawaqneh	PROPN
ejpam-6658	94	18	,	,	PUNCT
ejpam-6658	94	19	h.	h.	PROPN
ejpam-6658	94	20	aydi	aydi	VERB
ejpam-6658	94	21	/	/	SYM
ejpam-6658	94	22	eur	eur	NOUN
ejpam-6658	94	23	.	.	PUNCT
ejpam-6658	95	1	j.	j.	PROPN
ejpam-6658	95	2	pure	pure	PROPN
ejpam-6658	95	3	appl	appl	PROPN
ejpam-6658	95	4	.	.	PROPN
ejpam-6658	95	5	math	math	PROPN
ejpam-6658	95	6	,	,	PUNCT
ejpam-6658	95	7	18	18	NUM
ejpam-6658	95	8	(	(	PUNCT
ejpam-6658	95	9	3	3	NUM
ejpam-6658	95	10	)	)	PUNCT
ejpam-6658	95	11	(	(	PUNCT
ejpam-6658	95	12	2025	2025	NUM
ejpam-6658	95	13	)	)	PUNCT
ejpam-6658	95	14	,	,	PUNCT
ejpam-6658	95	15	6658	6658	NUM
ejpam-6658	95	16	5	5	NUM
ejpam-6658	95	17	of	of	ADP
ejpam-6658	95	18	22	22	NUM
ejpam-6658	95	19	qn+1(r1	qn+1(r1	NOUN
ejpam-6658	95	20	)	)	PUNCT
ejpam-6658	95	21	=	=	SYM
ejpam-6658	95	22	m̂{qn(r1	m̂{qn(r1	NOUN
ejpam-6658	95	23	)	)	PUNCT
ejpam-6658	95	24	}	}	PUNCT
ejpam-6658	95	25	,	,	PUNCT
ejpam-6658	95	26	(	(	PUNCT
ejpam-6658	95	27	16	16	NUM
ejpam-6658	95	28	)	)	PUNCT
ejpam-6658	95	29	and	and	CCONJ
ejpam-6658	95	30	n	n	PRON
ejpam-6658	95	31	qn−1(r1	qn−1(r1	PROPN
ejpam-6658	95	32	)	)	PUNCT
ejpam-6658	95	33	=	=	SYM
ejpam-6658	95	34	p̂{qn(r1	p̂{qn(r1	NOUN
ejpam-6658	95	35	)	)	PUNCT
ejpam-6658	95	36	}	}	PUNCT
ejpam-6658	95	37	.	.	PUNCT
ejpam-6658	96	1	(	(	PUNCT
ejpam-6658	96	2	17	17	NUM
ejpam-6658	96	3	)	)	PUNCT
ejpam-6658	96	4	a	a	DET
ejpam-6658	96	5	polynomial	polynomial	ADJ
ejpam-6658	96	6	sequence	sequence	NOUN
ejpam-6658	96	7	{	{	PUNCT
ejpam-6658	96	8	qn(r1)}n∈n	qn(r1)}n∈n	ADV
ejpam-6658	96	9	that	that	PRON
ejpam-6658	96	10	adheres	adhere	VERB
ejpam-6658	96	11	to	to	ADP
ejpam-6658	96	12	these	these	DET
ejpam-6658	96	13	operator	operator	NOUN
ejpam-6658	96	14	relations	relation	NOUN
ejpam-6658	96	15	is	be	AUX
ejpam-6658	96	16	referred	refer	VERB
ejpam-6658	96	17	to	to	ADP
ejpam-6658	96	18	as	as	ADP
ejpam-6658	96	19	a	a	DET
ejpam-6658	96	20	quasi	quasi	ADJ
ejpam-6658	96	21	-	-	ADJ
ejpam-6658	96	22	monomial	monomial	ADJ
ejpam-6658	96	23	set	set	NOUN
ejpam-6658	96	24	.	.	PUNCT
ejpam-6658	97	1	such	such	DET
ejpam-6658	97	2	a	a	DET
ejpam-6658	97	3	set	set	NOUN
ejpam-6658	97	4	must	must	AUX
ejpam-6658	97	5	also	also	ADV
ejpam-6658	97	6	satisfy	satisfy	VERB
ejpam-6658	97	7	the	the	DET
ejpam-6658	97	8	fundamental	fundamental	ADJ
ejpam-6658	97	9	commutation	commutation	NOUN
ejpam-6658	97	10	relation	relation	NOUN
ejpam-6658	97	11	:	:	PUNCT
ejpam-6658	98	1	[	[	X
ejpam-6658	98	2	p̂,m̂	p̂,m̂	X
ejpam-6658	98	3	]	]	X
ejpam-6658	98	4	=	=	PUNCT
ejpam-6658	98	5	p̂m̂	p̂m̂	AUX
ejpam-6658	98	6	−	−	PROPN
ejpam-6658	98	7	m̂p̂	m̂p̂	NOUN
ejpam-6658	98	8	=	=	SYM
ejpam-6658	98	9	1̂	1̂	PROPN
ejpam-6658	98	10	,	,	PUNCT
ejpam-6658	98	11	(	(	PUNCT
ejpam-6658	98	12	18	18	NUM
ejpam-6658	98	13	)	)	PUNCT
ejpam-6658	98	14	which	which	PRON
ejpam-6658	98	15	aligns	align	VERB
ejpam-6658	98	16	naturally	naturally	ADV
ejpam-6658	98	17	with	with	ADP
ejpam-6658	98	18	the	the	DET
ejpam-6658	98	19	algebraic	algebraic	ADJ
ejpam-6658	98	20	framework	framework	NOUN
ejpam-6658	98	21	of	of	ADP
ejpam-6658	98	22	the	the	DET
ejpam-6658	98	23	weyl	weyl	VERB
ejpam-6658	98	24	algebra	algebra	NOUN
ejpam-6658	98	25	.	.	PUNCT
ejpam-6658	99	1	if	if	SCONJ
ejpam-6658	99	2	a	a	DET
ejpam-6658	99	3	polynomial	polynomial	ADJ
ejpam-6658	99	4	sequence	sequence	NOUN
ejpam-6658	99	5	{	{	PUNCT
ejpam-6658	99	6	qn(r1)}n∈n	qn(r1)}n∈n	PROPN
ejpam-6658	99	7	is	be	AUX
ejpam-6658	99	8	quasi	quasi	ADJ
ejpam-6658	99	9	-	-	ADJ
ejpam-6658	99	10	monomial	monomial	ADJ
ejpam-6658	99	11	,	,	PUNCT
ejpam-6658	99	12	its	its	PRON
ejpam-6658	99	13	defining	define	VERB
ejpam-6658	99	14	properties	property	NOUN
ejpam-6658	99	15	can	can	AUX
ejpam-6658	99	16	be	be	AUX
ejpam-6658	99	17	derived	derive	VERB
ejpam-6658	99	18	directly	directly	ADV
ejpam-6658	99	19	from	from	ADP
ejpam-6658	99	20	the	the	DET
ejpam-6658	99	21	characteristics	characteristic	NOUN
ejpam-6658	99	22	of	of	ADP
ejpam-6658	99	23	the	the	DET
ejpam-6658	99	24	operators	operator	NOUN
ejpam-6658	99	25	m̂	m̂	PROPN
ejpam-6658	99	26	and	and	CCONJ
ejpam-6658	99	27	p̂.	p̂.	PROPN
ejpam-6658	99	28	specifically	specifically	ADV
ejpam-6658	99	29	,	,	PUNCT
ejpam-6658	99	30	the	the	DET
ejpam-6658	99	31	following	follow	VERB
ejpam-6658	99	32	key	key	ADJ
ejpam-6658	99	33	properties	property	NOUN
ejpam-6658	99	34	hold	hold	VERB
ejpam-6658	99	35	:	:	PUNCT
ejpam-6658	99	36	(	(	PUNCT
ejpam-6658	99	37	i	i	NOUN
ejpam-6658	99	38	)	)	PUNCT
ejpam-6658	99	39	the	the	DET
ejpam-6658	99	40	polynomials	polynomial	NOUN
ejpam-6658	99	41	qn(r1	qn(r1	PART
ejpam-6658	99	42	)	)	PUNCT
ejpam-6658	99	43	satisfy	satisfy	VERB
ejpam-6658	99	44	a	a	DET
ejpam-6658	99	45	differential	differential	ADJ
ejpam-6658	99	46	equation	equation	NOUN
ejpam-6658	99	47	of	of	ADP
ejpam-6658	99	48	the	the	DET
ejpam-6658	99	49	form	form	NOUN
ejpam-6658	99	50	:	:	PUNCT
ejpam-6658	99	51	m̂p̂{qn(r1	m̂p̂{qn(r1	PROPN
ejpam-6658	99	52	)	)	PUNCT
ejpam-6658	99	53	}	}	PUNCT
ejpam-6658	100	1	=	=	SYM
ejpam-6658	100	2	n	n	NUM
ejpam-6658	100	3	qn(r1	qn(r1	NOUN
ejpam-6658	100	4	)	)	PUNCT
ejpam-6658	100	5	,	,	PUNCT
ejpam-6658	100	6	(	(	PUNCT
ejpam-6658	100	7	19	19	NUM
ejpam-6658	100	8	)	)	PUNCT
ejpam-6658	100	9	provided	provide	VERB
ejpam-6658	100	10	that	that	PRON
ejpam-6658	100	11	m̂	m̂	NOUN
ejpam-6658	100	12	and	and	CCONJ
ejpam-6658	100	13	p̂	p̂	NOUN
ejpam-6658	100	14	admit	admit	VERB
ejpam-6658	100	15	suitable	suitable	ADJ
ejpam-6658	100	16	differential	differential	ADJ
ejpam-6658	100	17	representations	representation	NOUN
ejpam-6658	100	18	.	.	PUNCT
ejpam-6658	101	1	(	(	PUNCT
ejpam-6658	101	2	ii	ii	NOUN
ejpam-6658	101	3	)	)	PUNCT
ejpam-6658	101	4	an	an	DET
ejpam-6658	101	5	explicit	explicit	ADJ
ejpam-6658	101	6	formula	formula	NOUN
ejpam-6658	101	7	for	for	ADP
ejpam-6658	101	8	qn(r1	qn(r1	NOUN
ejpam-6658	101	9	)	)	PUNCT
ejpam-6658	101	10	can	can	AUX
ejpam-6658	101	11	be	be	AUX
ejpam-6658	101	12	expressed	express	VERB
ejpam-6658	101	13	as	as	ADP
ejpam-6658	101	14	:	:	PUNCT
ejpam-6658	101	15	qn(r1	qn(r1	X
ejpam-6658	101	16	)	)	PUNCT
ejpam-6658	101	17	=	=	NOUN
ejpam-6658	101	18	m̂n	m̂n	X
ejpam-6658	101	19	{	{	PUNCT
ejpam-6658	101	20	1	1	NUM
ejpam-6658	101	21	}	}	PUNCT
ejpam-6658	101	22	,	,	PUNCT
ejpam-6658	101	23	(	(	PUNCT
ejpam-6658	101	24	20	20	NUM
ejpam-6658	101	25	)	)	PUNCT
ejpam-6658	101	26	with	with	ADP
ejpam-6658	101	27	the	the	DET
ejpam-6658	101	28	initial	initial	ADJ
ejpam-6658	101	29	condition	condition	NOUN
ejpam-6658	101	30	q0(r1	q0(r1	NOUN
ejpam-6658	101	31	)	)	PUNCT
ejpam-6658	101	32	=	=	SYM
ejpam-6658	101	33	1	1	X
ejpam-6658	101	34	.	.	PUNCT
ejpam-6658	101	35	(	(	PUNCT
ejpam-6658	101	36	iii	iii	X
ejpam-6658	101	37	)	)	PUNCT
ejpam-6658	101	38	the	the	DET
ejpam-6658	101	39	exponential	exponential	ADJ
ejpam-6658	101	40	generating	generating	NOUN
ejpam-6658	101	41	function	function	NOUN
ejpam-6658	101	42	of	of	ADP
ejpam-6658	101	43	qn(r1	qn(r1	NOUN
ejpam-6658	101	44	)	)	PUNCT
ejpam-6658	101	45	is	be	AUX
ejpam-6658	101	46	given	give	VERB
ejpam-6658	101	47	by	by	ADP
ejpam-6658	101	48	:	:	PUNCT
ejpam-6658	101	49	etm̂{1	etm̂{1	ADJ
ejpam-6658	101	50	}	}	PUNCT
ejpam-6658	101	51	=	=	PUNCT
ejpam-6658	102	1	∞∑	∞∑	NUM
ejpam-6658	102	2	n=0	n=0	NUM
ejpam-6658	102	3	qn(r1	qn(r1	NUM
ejpam-6658	102	4	)	)	PUNCT
ejpam-6658	102	5	tn	tn	PROPN
ejpam-6658	102	6	n	n	CCONJ
ejpam-6658	102	7	!	!	PUNCT
ejpam-6658	102	8	(	(	PUNCT
ejpam-6658	102	9	|t|	|t|	PROPN
ejpam-6658	102	10	<	<	X
ejpam-6658	102	11	∞	∞	NOUN
ejpam-6658	102	12	)	)	PUNCT
ejpam-6658	102	13	,	,	PUNCT
ejpam-6658	102	14	(	(	PUNCT
ejpam-6658	102	15	21	21	NUM
ejpam-6658	102	16	)	)	PUNCT
ejpam-6658	102	17	which	which	PRON
ejpam-6658	102	18	follows	follow	VERB
ejpam-6658	102	19	directly	directly	ADV
ejpam-6658	102	20	from	from	ADP
ejpam-6658	102	21	equation	equation	NOUN
ejpam-6658	102	22	(	(	PUNCT
ejpam-6658	102	23	20	20	NUM
ejpam-6658	102	24	)	)	PUNCT
ejpam-6658	102	25	.	.	PUNCT
ejpam-6658	103	1	for	for	ADP
ejpam-6658	103	2	more	more	ADJ
ejpam-6658	103	3	details	detail	NOUN
ejpam-6658	103	4	,	,	PUNCT
ejpam-6658	103	5	see	see	VERB
ejpam-6658	103	6	[	[	X
ejpam-6658	103	7	17	17	NUM
ejpam-6658	103	8	,	,	PUNCT
ejpam-6658	103	9	20–27	20–27	NUM
ejpam-6658	103	10	]	]	PUNCT
ejpam-6658	103	11	.	.	PUNCT
ejpam-6658	104	1	the	the	DET
ejpam-6658	104	2	operational	operational	ADJ
ejpam-6658	104	3	framework	framework	NOUN
ejpam-6658	104	4	outlined	outline	VERB
ejpam-6658	104	5	above	above	ADV
ejpam-6658	104	6	has	have	AUX
ejpam-6658	104	7	found	find	VERB
ejpam-6658	104	8	extensive	extensive	ADJ
ejpam-6658	104	9	applications	application	NOUN
ejpam-6658	104	10	across	across	ADP
ejpam-6658	104	11	various	various	ADJ
ejpam-6658	104	12	fields	field	NOUN
ejpam-6658	104	13	,	,	PUNCT
ejpam-6658	104	14	including	include	VERB
ejpam-6658	104	15	classical	classical	ADJ
ejpam-6658	104	16	optics	optic	NOUN
ejpam-6658	104	17	,	,	PUNCT
ejpam-6658	104	18	quantum	quantum	NOUN
ejpam-6658	104	19	mechanics	mechanic	NOUN
ejpam-6658	104	20	,	,	PUNCT
ejpam-6658	104	21	and	and	CCONJ
ejpam-6658	104	22	different	different	ADJ
ejpam-6658	104	23	branches	branch	NOUN
ejpam-6658	104	24	of	of	ADP
ejpam-6658	104	25	mathematical	mathematical	ADJ
ejpam-6658	104	26	physics	physics	NOUN
ejpam-6658	104	27	.	.	PUNCT
ejpam-6658	105	1	these	these	DET
ejpam-6658	105	2	techniques	technique	NOUN
ejpam-6658	105	3	offer	offer	VERB
ejpam-6658	105	4	robust	robust	ADJ
ejpam-6658	105	5	analytical	analytical	ADJ
ejpam-6658	105	6	tools	tool	NOUN
ejpam-6658	105	7	for	for	ADP
ejpam-6658	105	8	studying	study	VERB
ejpam-6658	105	9	diverse	diverse	ADJ
ejpam-6658	105	10	polynomial	polynomial	ADJ
ejpam-6658	105	11	families	family	NOUN
ejpam-6658	105	12	.	.	PUNCT
ejpam-6658	106	1	motivated	motivate	VERB
ejpam-6658	106	2	by	by	ADP
ejpam-6658	106	3	these	these	DET
ejpam-6658	106	4	developments	development	NOUN
ejpam-6658	106	5	,	,	PUNCT
ejpam-6658	106	6	we	we	PRON
ejpam-6658	106	7	introduce	introduce	VERB
ejpam-6658	106	8	a	a	DET
ejpam-6658	106	9	new	new	ADJ
ejpam-6658	106	10	generalize	generalize	VERB
ejpam-6658	106	11	laguerre	laguerre	NOUN
ejpam-6658	106	12	-	-	PUNCT
ejpam-6658	106	13	based	base	VERB
ejpam-6658	106	14	appell	appell	NOUN
ejpam-6658	106	15	polynomials	polynomial	NOUN
ejpam-6658	106	16	plrn(r1	plrn(r1	NOUN
ejpam-6658	106	17	,	,	PUNCT
ejpam-6658	106	18	r2	r2	PROPN
ejpam-6658	106	19	,	,	PUNCT
ejpam-6658	106	20	r3	r3	PROPN
ejpam-6658	106	21	)	)	PUNCT
ejpam-6658	106	22	.	.	PUNCT
ejpam-6658	107	1	the	the	DET
ejpam-6658	107	2	structure	structure	NOUN
ejpam-6658	107	3	of	of	ADP
ejpam-6658	107	4	this	this	DET
ejpam-6658	107	5	paper	paper	NOUN
ejpam-6658	107	6	is	be	AUX
ejpam-6658	107	7	as	as	SCONJ
ejpam-6658	107	8	follows	follow	VERB
ejpam-6658	107	9	:	:	PUNCT
ejpam-6658	107	10	in	in	ADP
ejpam-6658	107	11	section	section	NOUN
ejpam-6658	107	12	2	2	NUM
ejpam-6658	107	13	,	,	PUNCT
ejpam-6658	107	14	we	we	PRON
ejpam-6658	107	15	define	define	VERB
ejpam-6658	107	16	the	the	DET
ejpam-6658	107	17	new	new	ADJ
ejpam-6658	107	18	generalization	generalization	NOUN
ejpam-6658	107	19	of	of	ADP
ejpam-6658	107	20	laguerre	laguerre	NOUN
ejpam-6658	107	21	and	and	CCONJ
ejpam-6658	107	22	laguerre	laguerre	NOUN
ejpam-6658	107	23	-	-	PUNCT
ejpam-6658	107	24	based	base	VERB
ejpam-6658	107	25	appell	appell	ADJ
ejpam-6658	107	26	polynomials	polynomial	NOUN
ejpam-6658	107	27	and	and	CCONJ
ejpam-6658	107	28	explore	explore	VERB
ejpam-6658	107	29	their	their	PRON
ejpam-6658	107	30	key	key	ADJ
ejpam-6658	107	31	properties	property	NOUN
ejpam-6658	107	32	,	,	PUNCT
ejpam-6658	107	33	including	include	VERB
ejpam-6658	107	34	recurrence	recurrence	NOUN
ejpam-6658	107	35	relations	relation	NOUN
ejpam-6658	107	36	,	,	PUNCT
ejpam-6658	107	37	associated	associated	ADJ
ejpam-6658	107	38	operators	operator	NOUN
ejpam-6658	107	39	,	,	PUNCT
ejpam-6658	107	40	and	and	CCONJ
ejpam-6658	107	41	differential	differential	ADJ
ejpam-6658	107	42	equations	equation	NOUN
ejpam-6658	107	43	.	.	PUNCT
ejpam-6658	108	1	section	section	NOUN
ejpam-6658	108	2	3	3	NUM
ejpam-6658	108	3	focuses	focus	VERB
ejpam-6658	108	4	on	on	ADP
ejpam-6658	108	5	the	the	DET
ejpam-6658	108	6	series	series	NOUN
ejpam-6658	108	7	expansions	expansion	NOUN
ejpam-6658	108	8	and	and	CCONJ
ejpam-6658	108	9	determinant	determinant	ADJ
ejpam-6658	108	10	representations	representation	NOUN
ejpam-6658	108	11	of	of	ADP
ejpam-6658	108	12	these	these	DET
ejpam-6658	108	13	generalized	generalized	ADJ
ejpam-6658	108	14	polynomials	polynomial	NOUN
ejpam-6658	108	15	.	.	PUNCT
ejpam-6658	109	1	in	in	ADP
ejpam-6658	109	2	section	section	NOUN
ejpam-6658	109	3	4	4	NUM
ejpam-6658	109	4	,	,	PUNCT
ejpam-6658	109	5	we	we	PRON
ejpam-6658	109	6	examine	examine	VERB
ejpam-6658	109	7	specific	specific	ADJ
ejpam-6658	109	8	subfamilies	subfamily	NOUN
ejpam-6658	109	9	and	and	CCONJ
ejpam-6658	109	10	establish	establish	VERB
ejpam-6658	109	11	their	their	PRON
ejpam-6658	109	12	distinctive	distinctive	ADJ
ejpam-6658	109	13	properties	property	NOUN
ejpam-6658	109	14	.	.	PUNCT
ejpam-6658	110	1	finally	finally	ADV
ejpam-6658	110	2	,	,	PUNCT
ejpam-6658	110	3	the	the	DET
ejpam-6658	110	4	paper	paper	NOUN
ejpam-6658	110	5	concludes	conclude	VERB
ejpam-6658	110	6	with	with	ADP
ejpam-6658	110	7	some	some	DET
ejpam-6658	110	8	remarks	remark	NOUN
ejpam-6658	110	9	summarizing	summarize	VERB
ejpam-6658	110	10	our	our	PRON
ejpam-6658	110	11	findings	finding	NOUN
ejpam-6658	110	12	and	and	CCONJ
ejpam-6658	110	13	future	future	ADJ
ejpam-6658	110	14	research	research	NOUN
ejpam-6658	110	15	directions	direction	NOUN
ejpam-6658	110	16	.	.	PUNCT
ejpam-6658	111	1	w.	w.	PROPN
ejpam-6658	111	2	a.	a.	PROPN
ejpam-6658	111	3	khan	khan	PROPN
ejpam-6658	111	4	,	,	PUNCT
ejpam-6658	111	5	h.	h.	PROPN
ejpam-6658	111	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	111	7	,	,	PUNCT
ejpam-6658	111	8	h.	h.	PROPN
ejpam-6658	111	9	aydi	aydi	VERB
ejpam-6658	111	10	/	/	SYM
ejpam-6658	111	11	eur	eur	NOUN
ejpam-6658	111	12	.	.	PUNCT
ejpam-6658	112	1	j.	j.	PROPN
ejpam-6658	112	2	pure	pure	PROPN
ejpam-6658	112	3	appl	appl	PROPN
ejpam-6658	112	4	.	.	PROPN
ejpam-6658	112	5	math	math	PROPN
ejpam-6658	112	6	,	,	PUNCT
ejpam-6658	112	7	18	18	NUM
ejpam-6658	112	8	(	(	PUNCT
ejpam-6658	112	9	3	3	NUM
ejpam-6658	112	10	)	)	PUNCT
ejpam-6658	112	11	(	(	PUNCT
ejpam-6658	112	12	2025	2025	NUM
ejpam-6658	112	13	)	)	PUNCT
ejpam-6658	112	14	,	,	PUNCT
ejpam-6658	112	15	6658	6658	NUM
ejpam-6658	112	16	6	6	NUM
ejpam-6658	112	17	of	of	ADP
ejpam-6658	112	18	22	22	NUM
ejpam-6658	112	19	2	2	NUM
ejpam-6658	112	20	.	.	PUNCT
ejpam-6658	113	1	the	the	DET
ejpam-6658	113	2	new	new	ADJ
ejpam-6658	113	3	generalization	generalization	NOUN
ejpam-6658	113	4	of	of	ADP
ejpam-6658	113	5	laguerre	laguerre	NOUN
ejpam-6658	113	6	and	and	CCONJ
ejpam-6658	113	7	laguerre	laguerre	NOUN
ejpam-6658	113	8	-	-	PUNCT
ejpam-6658	113	9	based	base	VERB
ejpam-6658	113	10	appell	appell	NOUN
ejpam-6658	113	11	polynomials	polynomial	NOUN
ejpam-6658	113	12	this	this	DET
ejpam-6658	113	13	section	section	NOUN
ejpam-6658	113	14	of	of	ADP
ejpam-6658	113	15	our	our	PRON
ejpam-6658	113	16	research	research	NOUN
ejpam-6658	113	17	paper	paper	NOUN
ejpam-6658	113	18	introduces	introduce	VERB
ejpam-6658	113	19	the	the	DET
ejpam-6658	113	20	new	new	ADJ
ejpam-6658	113	21	generalization	generalization	NOUN
ejpam-6658	113	22	of	of	ADP
ejpam-6658	113	23	three	three	NUM
ejpam-6658	113	24	-	-	PUNCT
ejpam-6658	113	25	variable	variable	NOUN
ejpam-6658	113	26	laguerre	laguerre	NOUN
ejpam-6658	113	27	-	-	PUNCT
ejpam-6658	113	28	based	base	VERB
ejpam-6658	113	29	appell	appell	NOUN
ejpam-6658	113	30	polynomials	polynomial	NOUN
ejpam-6658	113	31	,	,	PUNCT
ejpam-6658	113	32	denoted	denote	VERB
ejpam-6658	113	33	as	as	ADP
ejpam-6658	113	34	plrn(r1	plrn(r1	NOUN
ejpam-6658	113	35	,	,	PUNCT
ejpam-6658	113	36	r2	r2	PROPN
ejpam-6658	113	37	,	,	PUNCT
ejpam-6658	113	38	r3	r3	PROPN
ejpam-6658	113	39	)	)	PUNCT
ejpam-6658	113	40	.	.	PUNCT
ejpam-6658	114	1	we	we	PRON
ejpam-6658	114	2	present	present	VERB
ejpam-6658	114	3	their	their	PRON
ejpam-6658	114	4	series	series	NOUN
ejpam-6658	114	5	expansion	expansion	NOUN
ejpam-6658	114	6	,	,	PUNCT
ejpam-6658	114	7	quasi	quasi	ADJ
ejpam-6658	114	8	-	-	ADJ
ejpam-6658	114	9	monomial	monomial	ADJ
ejpam-6658	114	10	property	property	NOUN
ejpam-6658	114	11	,	,	PUNCT
ejpam-6658	114	12	operational	operational	ADJ
ejpam-6658	114	13	formulas	formula	NOUN
ejpam-6658	114	14	,	,	PUNCT
ejpam-6658	114	15	and	and	CCONJ
ejpam-6658	114	16	corresponding	corresponding	ADJ
ejpam-6658	114	17	differential	differential	ADJ
ejpam-6658	114	18	equations	equation	NOUN
ejpam-6658	114	19	.	.	PUNCT
ejpam-6658	115	1	our	our	PRON
ejpam-6658	115	2	study	study	NOUN
ejpam-6658	115	3	initiates	initiate	VERB
ejpam-6658	115	4	with	with	ADP
ejpam-6658	115	5	the	the	DET
ejpam-6658	115	6	construction	construction	NOUN
ejpam-6658	115	7	of	of	ADP
ejpam-6658	115	8	a	a	DET
ejpam-6658	115	9	novel	novel	ADJ
ejpam-6658	115	10	generalization	generalization	NOUN
ejpam-6658	115	11	of	of	ADP
ejpam-6658	115	12	threevariable	threevariable	ADJ
ejpam-6658	115	13	laguerre	laguerre	NOUN
ejpam-6658	115	14	polynomials	polynomial	NOUN
ejpam-6658	115	15	,	,	PUNCT
ejpam-6658	115	16	denoted	denote	VERB
ejpam-6658	115	17	as	as	ADP
ejpam-6658	115	18	3vlp	3vlp	NUM
ejpam-6658	115	19	pln(r1	pln(r1	NOUN
ejpam-6658	115	20	,	,	PUNCT
ejpam-6658	115	21	r2	r2	PROPN
ejpam-6658	115	22	,	,	PUNCT
ejpam-6658	115	23	r3	r3	PROPN
ejpam-6658	115	24	)	)	PUNCT
ejpam-6658	115	25	.	.	PUNCT
ejpam-6658	116	1	utilizing	utilize	VERB
ejpam-6658	116	2	the	the	DET
ejpam-6658	116	3	relations	relation	NOUN
ejpam-6658	116	4	(	(	PUNCT
ejpam-6658	116	5	1	1	NUM
ejpam-6658	116	6	)	)	PUNCT
ejpam-6658	116	7	and	and	CCONJ
ejpam-6658	116	8	(	(	PUNCT
ejpam-6658	116	9	14	14	NUM
ejpam-6658	116	10	)	)	PUNCT
ejpam-6658	116	11	,	,	PUNCT
ejpam-6658	116	12	we	we	PRON
ejpam-6658	116	13	introduce	introduce	VERB
ejpam-6658	116	14	the	the	DET
ejpam-6658	116	15	new	new	ADJ
ejpam-6658	116	16	generalization	generalization	NOUN
ejpam-6658	116	17	of	of	ADP
ejpam-6658	116	18	three	three	NUM
ejpam-6658	116	19	variable	variable	ADJ
ejpam-6658	116	20	laguerre	laguerre	NOUN
ejpam-6658	116	21	polynomials	polynomial	VERB
ejpam-6658	116	22	plυ(r1	plυ(r1	NOUN
ejpam-6658	116	23	,	,	PUNCT
ejpam-6658	116	24	r2	r2	PROPN
ejpam-6658	116	25	,	,	PUNCT
ejpam-6658	116	26	r3	r3	PROPN
ejpam-6658	116	27	)	)	PUNCT
ejpam-6658	116	28	in	in	ADP
ejpam-6658	116	29	the	the	DET
ejpam-6658	116	30	following	follow	VERB
ejpam-6658	116	31	form	form	NOUN
ejpam-6658	116	32	:	:	PUNCT
ejpam-6658	116	33	er1tψ(r2	er1tψ(r2	PROPN
ejpam-6658	116	34	,	,	PUNCT
ejpam-6658	116	35	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	116	36	t	t	PROPN
ejpam-6658	116	37	)	)	PUNCT
ejpam-6658	116	38	=	=	PUNCT
ejpam-6658	117	1	∞∑	∞∑	PRON
ejpam-6658	117	2	n=0	n=0	NUM
ejpam-6658	117	3	pln(r1	pln(r1	PROPN
ejpam-6658	117	4	,	,	PUNCT
ejpam-6658	117	5	r2	r2	PROPN
ejpam-6658	117	6	,	,	PUNCT
ejpam-6658	117	7	r3	r3	PROPN
ejpam-6658	117	8	)	)	PUNCT
ejpam-6658	117	9	tn	tn	PROPN
ejpam-6658	117	10	n	n	PROPN
ejpam-6658	117	11	!	!	PROPN
ejpam-6658	117	12	,	,	PUNCT
ejpam-6658	117	13	(	(	PUNCT
ejpam-6658	117	14	p0(r1	p0(r1	NOUN
ejpam-6658	117	15	,	,	PUNCT
ejpam-6658	117	16	r2	r2	PROPN
ejpam-6658	117	17	)	)	PUNCT
ejpam-6658	117	18	=	=	SYM
ejpam-6658	118	1	1	1	NUM
ejpam-6658	118	2	)	)	PUNCT
ejpam-6658	118	3	.	.	PUNCT
ejpam-6658	119	1	(	(	PUNCT
ejpam-6658	119	2	22	22	NUM
ejpam-6658	119	3	)	)	PUNCT
ejpam-6658	119	4	by	by	ADP
ejpam-6658	119	5	simplifying	simplify	VERB
ejpam-6658	119	6	the	the	DET
ejpam-6658	119	7	left	left	ADJ
ejpam-6658	119	8	-	-	PUNCT
ejpam-6658	119	9	hand	hand	NOUN
ejpam-6658	119	10	side	side	NOUN
ejpam-6658	119	11	of	of	ADP
ejpam-6658	119	12	equation	equation	NOUN
ejpam-6658	119	13	(	(	PUNCT
ejpam-6658	119	14	22	22	NUM
ejpam-6658	119	15	)	)	PUNCT
ejpam-6658	119	16	using	use	VERB
ejpam-6658	119	17	equations	equation	NOUN
ejpam-6658	119	18	(	(	PUNCT
ejpam-6658	119	19	2	2	NUM
ejpam-6658	119	20	)	)	PUNCT
ejpam-6658	119	21	and	and	CCONJ
ejpam-6658	119	22	(	(	PUNCT
ejpam-6658	119	23	15	15	NUM
ejpam-6658	119	24	)	)	PUNCT
ejpam-6658	119	25	,	,	PUNCT
ejpam-6658	119	26	we	we	PRON
ejpam-6658	119	27	derive	derive	VERB
ejpam-6658	119	28	the	the	DET
ejpam-6658	119	29	subsequent	subsequent	ADJ
ejpam-6658	119	30	series	series	NOUN
ejpam-6658	119	31	representations	representation	NOUN
ejpam-6658	119	32	for	for	ADP
ejpam-6658	119	33	the	the	DET
ejpam-6658	119	34	generalized	generalized	ADJ
ejpam-6658	119	35	three	three	NUM
ejpam-6658	119	36	-	-	PUNCT
ejpam-6658	119	37	variable	variable	ADJ
ejpam-6658	119	38	laguerre	laguerre	NOUN
ejpam-6658	119	39	polynomials	polynomial	VERB
ejpam-6658	119	40	3v	3v	NUM
ejpam-6658	119	41	lp	lp	ADP
ejpam-6658	119	42	pln(r1	pln(r1	PROPN
ejpam-6658	119	43	,	,	PUNCT
ejpam-6658	119	44	r2	r2	PROPN
ejpam-6658	119	45	,	,	PUNCT
ejpam-6658	119	46	r3	r3	PROPN
ejpam-6658	119	47	)	)	PUNCT
ejpam-6658	119	48	holds	hold	VERB
ejpam-6658	119	49	:	:	PUNCT
ejpam-6658	120	1	pln(r1	pln(r1	NOUN
ejpam-6658	120	2	,	,	PUNCT
ejpam-6658	120	3	r2	r2	PROPN
ejpam-6658	120	4	,	,	PUNCT
ejpam-6658	120	5	r3	r3	PROPN
ejpam-6658	120	6	)	)	PUNCT
ejpam-6658	120	7	=	=	SYM
ejpam-6658	121	1	n∑	n∑	PROPN
ejpam-6658	121	2	m=0	m=0	PROPN
ejpam-6658	121	3	(	(	PUNCT
ejpam-6658	121	4	n	n	NOUN
ejpam-6658	121	5	m	m	PROPN
ejpam-6658	121	6	)	)	PUNCT
ejpam-6658	121	7	ψm(r2)ln−m(r1	ψm(r2)ln−m(r1	PROPN
ejpam-6658	121	8	,	,	PUNCT
ejpam-6658	121	9	r3	r3	PROPN
ejpam-6658	121	10	)	)	PUNCT
ejpam-6658	121	11	.	.	PUNCT
ejpam-6658	122	1	(	(	PUNCT
ejpam-6658	122	2	23	23	NUM
ejpam-6658	122	3	)	)	PUNCT
ejpam-6658	122	4	we	we	PRON
ejpam-6658	122	5	present	present	VERB
ejpam-6658	122	6	the	the	DET
ejpam-6658	122	7	derived	derive	VERB
ejpam-6658	122	8	quasi	quasi	ADJ
ejpam-6658	122	9	-	-	ADJ
ejpam-6658	122	10	monomial	monomial	ADJ
ejpam-6658	122	11	identities	identity	NOUN
ejpam-6658	122	12	for	for	ADP
ejpam-6658	122	13	the	the	DET
ejpam-6658	122	14	three	three	NUM
ejpam-6658	122	15	-	-	PUNCT
ejpam-6658	122	16	variable	variable	NOUN
ejpam-6658	122	17	laguerre	laguerre	NOUN
ejpam-6658	122	18	polynomials	polynomial	VERB
ejpam-6658	122	19	3v	3v	NUM
ejpam-6658	122	20	lep	lep	PROPN
ejpam-6658	122	21	,	,	PUNCT
ejpam-6658	122	22	denoted	denote	VERB
ejpam-6658	122	23	as	as	ADP
ejpam-6658	122	24	pln(r1	pln(r1	NOUN
ejpam-6658	122	25	,	,	PUNCT
ejpam-6658	122	26	r2	r2	PROPN
ejpam-6658	122	27	,	,	PUNCT
ejpam-6658	122	28	r3	r3	PROPN
ejpam-6658	122	29	)	)	PUNCT
ejpam-6658	122	30	.	.	PUNCT
ejpam-6658	123	1	theorem	theorem	NOUN
ejpam-6658	123	2	1	1	NUM
ejpam-6658	123	3	.	.	PUNCT
ejpam-6658	124	1	the	the	DET
ejpam-6658	124	2	new	new	ADJ
ejpam-6658	124	3	generalization	generalization	NOUN
ejpam-6658	124	4	of	of	ADP
ejpam-6658	124	5	three	three	NUM
ejpam-6658	124	6	variable	variable	ADJ
ejpam-6658	124	7	laguerre	laguerre	NOUN
ejpam-6658	124	8	polynomials	polynomial	VERB
ejpam-6658	124	9	3vlp	3vlp	NUM
ejpam-6658	124	10	pln(r1	pln(r1	NOUN
ejpam-6658	124	11	,	,	PUNCT
ejpam-6658	124	12	r2	r2	PROPN
ejpam-6658	124	13	,	,	PUNCT
ejpam-6658	124	14	r3	r3	PROPN
ejpam-6658	124	15	)	)	PUNCT
ejpam-6658	124	16	demonstrate	demonstrate	VERB
ejpam-6658	124	17	quasi	quasi	NOUN
ejpam-6658	124	18	monomials	monomial	VERB
ejpam-6658	124	19	properties	property	NOUN
ejpam-6658	124	20	under	under	ADP
ejpam-6658	124	21	the	the	DET
ejpam-6658	124	22	following	follow	VERB
ejpam-6658	124	23	multiplicative	multiplicative	ADJ
ejpam-6658	124	24	and	and	CCONJ
ejpam-6658	124	25	derivative	derivative	ADJ
ejpam-6658	124	26	operators	operator	NOUN
ejpam-6658	124	27	:	:	PUNCT
ejpam-6658	124	28	m̂3v	m̂3v	ADJ
ejpam-6658	124	29	glep	glep	VERB
ejpam-6658	124	30	=	=	SYM
ejpam-6658	124	31	r1	r1	PROPN
ejpam-6658	124	32	+	+	CCONJ
ejpam-6658	124	33	ψ	ψ	X
ejpam-6658	124	34	′	′	NUM
ejpam-6658	124	35	(	(	PUNCT
ejpam-6658	124	36	r2	r2	PROPN
ejpam-6658	124	37	,	,	PUNCT
ejpam-6658	124	38	d̂r1	d̂r1	PROPN
ejpam-6658	124	39	)	)	PUNCT
ejpam-6658	124	40	ψ(r2	ψ(r2	NOUN
ejpam-6658	124	41	,	,	PUNCT
ejpam-6658	124	42	d̂r1	d̂r1	PROPN
ejpam-6658	124	43	)	)	PUNCT
ejpam-6658	125	1	−	−	PROPN
ejpam-6658	126	1	nd̂−1	nd̂−1	PROPN
ejpam-6658	126	2	r3	r3	PROPN
ejpam-6658	126	3	,	,	PUNCT
ejpam-6658	126	4	(	(	PUNCT
ejpam-6658	126	5	24	24	NUM
ejpam-6658	126	6	)	)	PUNCT
ejpam-6658	126	7	and	and	CCONJ
ejpam-6658	126	8	p̂3v	p̂3v	ADJ
ejpam-6658	126	9	glep	glep	NOUN
ejpam-6658	126	10	=	=	SYM
ejpam-6658	126	11	d̂r1	d̂r1	PROPN
ejpam-6658	126	12	,	,	PUNCT
ejpam-6658	126	13	(	(	PUNCT
ejpam-6658	126	14	25	25	NUM
ejpam-6658	126	15	)	)	PUNCT
ejpam-6658	126	16	respectively	respectively	ADV
ejpam-6658	126	17	.	.	PUNCT
ejpam-6658	127	1	proof	proof	NOUN
ejpam-6658	127	2	.	.	PUNCT
ejpam-6658	128	1	by	by	ADP
ejpam-6658	128	2	differentiating	differentiate	VERB
ejpam-6658	128	3	equation	equation	NOUN
ejpam-6658	128	4	(	(	PUNCT
ejpam-6658	128	5	22	22	NUM
ejpam-6658	128	6	)	)	PUNCT
ejpam-6658	128	7	w.r.t	w.r.t	NOUN
ejpam-6658	128	8	.	.	PUNCT
ejpam-6658	129	1	t	t	PROPN
ejpam-6658	129	2	on	on	ADP
ejpam-6658	129	3	both	both	DET
ejpam-6658	129	4	sides	side	NOUN
ejpam-6658	129	5	,	,	PUNCT
ejpam-6658	129	6	it	it	PRON
ejpam-6658	129	7	follows	follow	VERB
ejpam-6658	129	8	that	that	SCONJ
ejpam-6658	129	9	∞∑	∞∑	NUM
ejpam-6658	129	10	n=0	n=0	ADJ
ejpam-6658	129	11	pln+1(r1	pln+1(r1	NOUN
ejpam-6658	129	12	,	,	PUNCT
ejpam-6658	129	13	r2	r2	NOUN
ejpam-6658	129	14	,	,	PUNCT
ejpam-6658	129	15	r3	r3	PROPN
ejpam-6658	129	16	)	)	PUNCT
ejpam-6658	129	17	tn	tn	PROPN
ejpam-6658	129	18	n	n	PROPN
ejpam-6658	129	19	!	!	PUNCT
ejpam-6658	130	1	=	=	PUNCT
ejpam-6658	131	1	xer1tψ(r2	xer1tψ(r2	PROPN
ejpam-6658	131	2	,	,	PUNCT
ejpam-6658	131	3	t)c0(r3t)+	t)c0(r3t)+	NOUN
ejpam-6658	131	4	ψ	ψ	ADJ
ejpam-6658	131	5	′	′	NUM
ejpam-6658	131	6	(	(	PUNCT
ejpam-6658	131	7	r2	r2	PROPN
ejpam-6658	131	8	,	,	PUNCT
ejpam-6658	131	9	t	t	PROPN
ejpam-6658	131	10	)	)	PUNCT
ejpam-6658	131	11	ψ(r2	ψ(r2	NOUN
ejpam-6658	131	12	,	,	PUNCT
ejpam-6658	131	13	t	t	PROPN
ejpam-6658	131	14	)	)	PUNCT
ejpam-6658	131	15	er1tψ(r2	er1tψ(r2	NOUN
ejpam-6658	131	16	,	,	PUNCT
ejpam-6658	131	17	t)c0(r3t)+	t)c0(r3t)+	NOUN
ejpam-6658	131	18	(	(	PUNCT
ejpam-6658	131	19	∞∑	∞∑	NUM
ejpam-6658	131	20	n=0	n=0	NUM
ejpam-6658	131	21	(	(	PUNCT
ejpam-6658	131	22	−1)nrn3nt	−1)nrn3nt	PROPN
ejpam-6658	131	23	n−1	n−1	PROPN
ejpam-6658	131	24	(	(	PUNCT
ejpam-6658	131	25	[	[	X
ejpam-6658	131	26	n]!)2	n]!)2	NOUN
ejpam-6658	131	27	)	)	PUNCT
ejpam-6658	131	28	er1tψ(r2	er1tψ(r2	PROPN
ejpam-6658	131	29	,	,	PUNCT
ejpam-6658	131	30	t	t	PROPN
ejpam-6658	131	31	)	)	PUNCT
ejpam-6658	131	32	∞∑	∞∑	ADJ
ejpam-6658	131	33	n=0	n=0	PUNCT
ejpam-6658	131	34	psn+1(r1	psn+1(r1	PROPN
ejpam-6658	131	35	,	,	PUNCT
ejpam-6658	131	36	r2	r2	PROPN
ejpam-6658	131	37	,	,	PUNCT
ejpam-6658	131	38	r3	r3	PROPN
ejpam-6658	131	39	)	)	PUNCT
ejpam-6658	131	40	tn	tn	PROPN
ejpam-6658	131	41	n	n	PROPN
ejpam-6658	131	42	!	!	PUNCT
ejpam-6658	131	43	=	=	PUNCT
ejpam-6658	132	1	(	(	PUNCT
ejpam-6658	132	2	r1	r1	PROPN
ejpam-6658	132	3	+	+	CCONJ
ejpam-6658	132	4	ψ	ψ	X
ejpam-6658	132	5	′	′	NUM
ejpam-6658	133	1	(	(	PUNCT
ejpam-6658	134	1	r2	r2	PROPN
ejpam-6658	134	2	,	,	PUNCT
ejpam-6658	134	3	t	t	PROPN
ejpam-6658	134	4	)	)	PUNCT
ejpam-6658	134	5	ψ(r2	ψ(r2	NOUN
ejpam-6658	134	6	,	,	PUNCT
ejpam-6658	134	7	t	t	PROPN
ejpam-6658	134	8	)	)	PUNCT
ejpam-6658	134	9	)	)	PUNCT
ejpam-6658	134	10	er1tψ(r2	er1tψ(r2	NOUN
ejpam-6658	134	11	,	,	PUNCT
ejpam-6658	134	12	t)c0(−r3t2)+	t)c0(−r3t2)+	PROPN
ejpam-6658	134	13	(	(	PUNCT
ejpam-6658	134	14	∞∑	∞∑	NUM
ejpam-6658	134	15	n=0	n=0	NUM
ejpam-6658	134	16	(	(	PUNCT
ejpam-6658	134	17	−1)n+1rn+1	−1)n+1rn+1	ADJ
ejpam-6658	134	18	3	3	NUM
ejpam-6658	134	19	tn	tn	NOUN
ejpam-6658	134	20	(	(	PUNCT
ejpam-6658	134	21	[	[	X
ejpam-6658	134	22	n+	n+	NOUN
ejpam-6658	134	23	1]!)2	1]!)2	NUM
ejpam-6658	134	24	)	)	PUNCT
ejpam-6658	134	25	er1tψ(r2	er1tψ(r2	PROPN
ejpam-6658	134	26	,	,	PUNCT
ejpam-6658	134	27	t	t	PROPN
ejpam-6658	134	28	)	)	PUNCT
ejpam-6658	134	29	.	.	PUNCT
ejpam-6658	135	1	utilizing	utilize	VERB
ejpam-6658	135	2	equation	equation	NOUN
ejpam-6658	135	3	(	(	PUNCT
ejpam-6658	135	4	22	22	NUM
ejpam-6658	135	5	)	)	PUNCT
ejpam-6658	135	6	,	,	PUNCT
ejpam-6658	135	7	we	we	PRON
ejpam-6658	135	8	have	have	VERB
ejpam-6658	135	9	w.	w.	PROPN
ejpam-6658	135	10	a.	a.	PROPN
ejpam-6658	135	11	khan	khan	PROPN
ejpam-6658	135	12	,	,	PUNCT
ejpam-6658	135	13	h.	h.	PROPN
ejpam-6658	135	14	qawaqneh	qawaqneh	PROPN
ejpam-6658	135	15	,	,	PUNCT
ejpam-6658	135	16	h.	h.	PROPN
ejpam-6658	135	17	aydi	aydi	VERB
ejpam-6658	135	18	/	/	SYM
ejpam-6658	135	19	eur	eur	NOUN
ejpam-6658	135	20	.	.	PUNCT
ejpam-6658	136	1	j.	j.	PROPN
ejpam-6658	136	2	pure	pure	PROPN
ejpam-6658	136	3	appl	appl	PROPN
ejpam-6658	136	4	.	.	PROPN
ejpam-6658	136	5	math	math	PROPN
ejpam-6658	136	6	,	,	PUNCT
ejpam-6658	136	7	18	18	NUM
ejpam-6658	136	8	(	(	PUNCT
ejpam-6658	136	9	3	3	NUM
ejpam-6658	136	10	)	)	PUNCT
ejpam-6658	136	11	(	(	PUNCT
ejpam-6658	136	12	2025	2025	NUM
ejpam-6658	136	13	)	)	PUNCT
ejpam-6658	136	14	,	,	PUNCT
ejpam-6658	136	15	6658	6658	NUM
ejpam-6658	136	16	7	7	NUM
ejpam-6658	136	17	of	of	ADP
ejpam-6658	136	18	22	22	NUM
ejpam-6658	136	19	∞∑	∞∑	NUM
ejpam-6658	136	20	n=0	n=0	PUNCT
ejpam-6658	136	21	pln+1(r1	pln+1(r1	NOUN
ejpam-6658	136	22	,	,	PUNCT
ejpam-6658	136	23	r2	r2	NOUN
ejpam-6658	136	24	,	,	PUNCT
ejpam-6658	136	25	r3	r3	PROPN
ejpam-6658	136	26	)	)	PUNCT
ejpam-6658	136	27	tn	tn	PROPN
ejpam-6658	136	28	n	n	PROPN
ejpam-6658	136	29	!	!	PUNCT
ejpam-6658	137	1	=	=	PUNCT
ejpam-6658	137	2	(	(	PUNCT
ejpam-6658	137	3	r1	r1	PROPN
ejpam-6658	137	4	+	+	CCONJ
ejpam-6658	137	5	ψ	ψ	X
ejpam-6658	137	6	′	′	NUM
ejpam-6658	137	7	(	(	PUNCT
ejpam-6658	137	8	r2	r2	PROPN
ejpam-6658	137	9	,	,	PUNCT
ejpam-6658	137	10	t	t	PROPN
ejpam-6658	137	11	)	)	PUNCT
ejpam-6658	137	12	ψ(r2	ψ(r2	NOUN
ejpam-6658	137	13	,	,	PUNCT
ejpam-6658	137	14	t	t	PROPN
ejpam-6658	137	15	)	)	PUNCT
ejpam-6658	137	16	)	)	PUNCT
ejpam-6658	138	1	∞∑	∞∑	PRON
ejpam-6658	138	2	n=0	n=0	NUM
ejpam-6658	138	3	pln(r1	pln(r1	PROPN
ejpam-6658	138	4	,	,	PUNCT
ejpam-6658	138	5	r2	r2	PROPN
ejpam-6658	138	6	,	,	PUNCT
ejpam-6658	138	7	r3	r3	PROPN
ejpam-6658	138	8	)	)	PUNCT
ejpam-6658	138	9	tn	tn	PROPN
ejpam-6658	138	10	n	n	CCONJ
ejpam-6658	138	11	!	!	PUNCT
ejpam-6658	139	1	+	+	CCONJ
ejpam-6658	139	2	(	(	PUNCT
ejpam-6658	139	3	∞∑	∞∑	NUM
ejpam-6658	139	4	n=0	n=0	NUM
ejpam-6658	139	5	(	(	PUNCT
ejpam-6658	139	6	−1)n+1rn+1	−1)n+1rn+1	ADJ
ejpam-6658	139	7	3	3	NUM
ejpam-6658	139	8	(	(	PUNCT
ejpam-6658	139	9	n+	n+	NUM
ejpam-6658	139	10	1)tn	1)tn	NUM
ejpam-6658	139	11	(	(	PUNCT
ejpam-6658	139	12	[	[	X
ejpam-6658	139	13	n+	n+	NUM
ejpam-6658	139	14	1]!)2	1]!)2	NUM
ejpam-6658	139	15	)	)	PUNCT
ejpam-6658	139	16	er1tψ(r2	er1tψ(r2	PROPN
ejpam-6658	139	17	,	,	PUNCT
ejpam-6658	139	18	t	t	PROPN
ejpam-6658	139	19	)	)	PUNCT
ejpam-6658	139	20	.	.	PUNCT
ejpam-6658	140	1	(	(	PUNCT
ejpam-6658	140	2	26	26	NUM
ejpam-6658	140	3	)	)	PUNCT
ejpam-6658	140	4	differentiating	differentiate	VERB
ejpam-6658	140	5	the	the	DET
ejpam-6658	140	6	above	above	ADJ
ejpam-6658	140	7	equation	equation	NOUN
ejpam-6658	140	8	w.r.t	w.r.t	NOUN
ejpam-6658	140	9	.	.	PUNCT
ejpam-6658	141	1	r3	r3	PROPN
ejpam-6658	141	2	,	,	PUNCT
ejpam-6658	141	3	we	we	PRON
ejpam-6658	141	4	have	have	VERB
ejpam-6658	141	5	∞∑	∞∑	NUM
ejpam-6658	141	6	n=0	n=0	PROPN
ejpam-6658	141	7	dr3	dr3	PROPN
ejpam-6658	141	8	pln+1(r1	pln+1(r1	NOUN
ejpam-6658	141	9	,	,	PUNCT
ejpam-6658	141	10	r2	r2	PROPN
ejpam-6658	141	11	,	,	PUNCT
ejpam-6658	141	12	r3	r3	PROPN
ejpam-6658	141	13	)	)	PUNCT
ejpam-6658	141	14	tn	tn	PROPN
ejpam-6658	141	15	n	n	PROPN
ejpam-6658	141	16	!	!	PUNCT
ejpam-6658	142	1	=	=	PUNCT
ejpam-6658	142	2	(	(	PUNCT
ejpam-6658	142	3	r1	r1	PROPN
ejpam-6658	142	4	+	+	CCONJ
ejpam-6658	142	5	ψ	ψ	X
ejpam-6658	142	6	′	′	NUM
ejpam-6658	142	7	(	(	PUNCT
ejpam-6658	142	8	r2	r2	PROPN
ejpam-6658	142	9	,	,	PUNCT
ejpam-6658	142	10	t	t	PROPN
ejpam-6658	142	11	)	)	PUNCT
ejpam-6658	142	12	ψ(r2	ψ(r2	NOUN
ejpam-6658	142	13	,	,	PUNCT
ejpam-6658	142	14	t	t	PROPN
ejpam-6658	142	15	)	)	PUNCT
ejpam-6658	142	16	)	)	PUNCT
ejpam-6658	143	1	∞∑	∞∑	PRON
ejpam-6658	143	2	n=0	n=0	PROPN
ejpam-6658	143	3	dr3	dr3	PROPN
ejpam-6658	143	4	pln(r1	pln(r1	PROPN
ejpam-6658	143	5	,	,	PUNCT
ejpam-6658	143	6	r2	r2	PROPN
ejpam-6658	143	7	,	,	PUNCT
ejpam-6658	143	8	r3	r3	PROPN
ejpam-6658	143	9	)	)	PUNCT
ejpam-6658	143	10	tn	tn	PROPN
ejpam-6658	143	11	n	n	PROPN
ejpam-6658	143	12	!	!	PUNCT
ejpam-6658	143	13	−	−	PROPN
ejpam-6658	144	1	n	n	PRON
ejpam-6658	144	2	∞∑	∞∑	PROPN
ejpam-6658	144	3	n=0	n=0	NUM
ejpam-6658	144	4	pln(r1	pln(r1	PROPN
ejpam-6658	144	5	,	,	PUNCT
ejpam-6658	144	6	r2	r2	PROPN
ejpam-6658	144	7	,	,	PUNCT
ejpam-6658	144	8	r3	r3	PROPN
ejpam-6658	144	9	)	)	PUNCT
ejpam-6658	144	10	tn	tn	PROPN
ejpam-6658	144	11	n	n	PROPN
ejpam-6658	144	12	!	!	PUNCT
ejpam-6658	144	13	.	.	PUNCT
ejpam-6658	145	1	(	(	PUNCT
ejpam-6658	145	2	27	27	NUM
ejpam-6658	145	3	)	)	PUNCT
ejpam-6658	145	4	consequently	consequently	ADV
ejpam-6658	145	5	,	,	PUNCT
ejpam-6658	145	6	dr1	dr1	PROPN
ejpam-6658	145	7	{	{	PUNCT
ejpam-6658	145	8	er1tψ(r2	er1tψ(r2	PROPN
ejpam-6658	145	9	,	,	PUNCT
ejpam-6658	145	10	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	145	11	t	t	PROPN
ejpam-6658	145	12	)	)	PUNCT
ejpam-6658	145	13	}	}	PUNCT
ejpam-6658	145	14	=	=	SYM
ejpam-6658	145	15	ter1tψ(r2	ter1tψ(r2	PROPN
ejpam-6658	145	16	,	,	PUNCT
ejpam-6658	145	17	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	145	18	t	t	PROPN
ejpam-6658	145	19	)	)	PUNCT
ejpam-6658	145	20	,	,	PUNCT
ejpam-6658	145	21	(	(	PUNCT
ejpam-6658	145	22	28	28	NUM
ejpam-6658	145	23	)	)	PUNCT
ejpam-6658	145	24	and	and	CCONJ
ejpam-6658	145	25	ψ	ψ	X
ejpam-6658	145	26	′	′	NUM
ejpam-6658	145	27	(	(	PUNCT
ejpam-6658	145	28	r2,t	r2,t	NOUN
ejpam-6658	145	29	)	)	PUNCT
ejpam-6658	145	30	ψ(r2,t	ψ(r2,t	PROPN
ejpam-6658	145	31	)	)	PUNCT
ejpam-6658	145	32	possesses	possess	VERB
ejpam-6658	145	33	power	power	NOUN
ejpam-6658	145	34	series	series	PROPN
ejpam-6658	145	35	expansion	expansion	NOUN
ejpam-6658	145	36	in	in	ADP
ejpam-6658	145	37	t	t	PROPN
ejpam-6658	145	38	with	with	ADP
ejpam-6658	145	39	ψ(r2	ψ(r2	NOUN
ejpam-6658	145	40	,	,	PUNCT
ejpam-6658	145	41	t	t	PROPN
ejpam-6658	145	42	)	)	PUNCT
ejpam-6658	145	43	being	be	AUX
ejpam-6658	145	44	the	the	DET
ejpam-6658	145	45	invertible	invertible	ADJ
ejpam-6658	145	46	series	series	NOUN
ejpam-6658	145	47	of	of	ADP
ejpam-6658	145	48	t.	t.	PROPN
ejpam-6658	145	49	operating	operate	VERB
ejpam-6658	145	50	d−1	d−1	PROPN
ejpam-6658	145	51	r3	r3	PROPN
ejpam-6658	145	52	to	to	ADP
ejpam-6658	145	53	equation	equation	NOUN
ejpam-6658	145	54	(	(	PUNCT
ejpam-6658	145	55	27	27	NUM
ejpam-6658	145	56	)	)	PUNCT
ejpam-6658	145	57	on	on	ADP
ejpam-6658	145	58	both	both	DET
ejpam-6658	145	59	sides	side	NOUN
ejpam-6658	145	60	,	,	PUNCT
ejpam-6658	145	61	we	we	PRON
ejpam-6658	145	62	have	have	VERB
ejpam-6658	145	63	∞∑	∞∑	NUM
ejpam-6658	145	64	n=0	n=0	NOUN
ejpam-6658	145	65	pln+1(r1	pln+1(r1	NOUN
ejpam-6658	145	66	,	,	PUNCT
ejpam-6658	145	67	r2	r2	NOUN
ejpam-6658	145	68	,	,	PUNCT
ejpam-6658	145	69	r3	r3	PROPN
ejpam-6658	145	70	)	)	PUNCT
ejpam-6658	145	71	tn	tn	PROPN
ejpam-6658	145	72	n	n	PROPN
ejpam-6658	145	73	!	!	PUNCT
ejpam-6658	146	1	=	=	NOUN
ejpam-6658	147	1	∞∑	∞∑	PRON
ejpam-6658	147	2	n=0	n=0	NUM
ejpam-6658	147	3	(	(	PUNCT
ejpam-6658	147	4	r1	r1	PROPN
ejpam-6658	147	5	+	+	CCONJ
ejpam-6658	147	6	ψ	ψ	X
ejpam-6658	147	7	′	′	NUM
ejpam-6658	147	8	(	(	PUNCT
ejpam-6658	147	9	r2	r2	PROPN
ejpam-6658	147	10	,	,	PUNCT
ejpam-6658	147	11	t	t	PROPN
ejpam-6658	147	12	)	)	PUNCT
ejpam-6658	147	13	ψ(r2	ψ(r2	NOUN
ejpam-6658	147	14	,	,	PUNCT
ejpam-6658	147	15	t	t	PROPN
ejpam-6658	147	16	)	)	PUNCT
ejpam-6658	147	17	−	−	PROPN
ejpam-6658	147	18	nd−1	nd−1	PROPN
ejpam-6658	147	19	r3	r3	PROPN
ejpam-6658	147	20	)	)	PUNCT
ejpam-6658	147	21	pln(r1	pln(r1	PROPN
ejpam-6658	147	22	,	,	PUNCT
ejpam-6658	147	23	r2	r2	PROPN
ejpam-6658	147	24	,	,	PUNCT
ejpam-6658	147	25	r3	r3	PROPN
ejpam-6658	147	26	)	)	PUNCT
ejpam-6658	147	27	tn	tn	PROPN
ejpam-6658	147	28	n	n	PROPN
ejpam-6658	147	29	!	!	PUNCT
ejpam-6658	147	30	.	.	PUNCT
ejpam-6658	148	1	(	(	PUNCT
ejpam-6658	148	2	29	29	NUM
ejpam-6658	148	3	)	)	PUNCT
ejpam-6658	148	4	in	in	ADP
ejpam-6658	148	5	light	light	NOUN
ejpam-6658	148	6	of	of	ADP
ejpam-6658	148	7	(	(	PUNCT
ejpam-6658	148	8	16	16	NUM
ejpam-6658	148	9	)	)	PUNCT
ejpam-6658	148	10	and	and	CCONJ
ejpam-6658	148	11	(	(	PUNCT
ejpam-6658	148	12	29	29	NUM
ejpam-6658	148	13	)	)	PUNCT
ejpam-6658	148	14	,	,	PUNCT
ejpam-6658	148	15	we	we	PRON
ejpam-6658	148	16	obtain	obtain	VERB
ejpam-6658	148	17	the	the	DET
ejpam-6658	148	18	assertion	assertion	NOUN
ejpam-6658	148	19	(	(	PUNCT
ejpam-6658	148	20	24	24	NUM
ejpam-6658	148	21	)	)	PUNCT
ejpam-6658	148	22	.	.	PUNCT
ejpam-6658	149	1	similarly	similarly	ADV
ejpam-6658	149	2	,	,	PUNCT
ejpam-6658	149	3	by	by	ADP
ejpam-6658	149	4	applying	apply	VERB
ejpam-6658	149	5	identity	identity	NOUN
ejpam-6658	149	6	(	(	PUNCT
ejpam-6658	149	7	28	28	NUM
ejpam-6658	149	8	)	)	PUNCT
ejpam-6658	149	9	to	to	ADP
ejpam-6658	149	10	(	(	PUNCT
ejpam-6658	149	11	22	22	NUM
ejpam-6658	149	12	)	)	PUNCT
ejpam-6658	149	13	,	,	PUNCT
ejpam-6658	149	14	we	we	PRON
ejpam-6658	149	15	get	get	VERB
ejpam-6658	149	16	dr1	dr1	PROPN
ejpam-6658	149	17	{	{	PUNCT
ejpam-6658	149	18	∞∑	∞∑	PROPN
ejpam-6658	149	19	n=0	n=0	NUM
ejpam-6658	149	20	pln(r1	pln(r1	PROPN
ejpam-6658	149	21	,	,	PUNCT
ejpam-6658	149	22	r2	r2	PROPN
ejpam-6658	149	23	,	,	PUNCT
ejpam-6658	149	24	r3	r3	PROPN
ejpam-6658	149	25	)	)	PUNCT
ejpam-6658	149	26	tn	tn	PROPN
ejpam-6658	149	27	n	n	PROPN
ejpam-6658	149	28	!	!	PUNCT
ejpam-6658	149	29	}	}	PUNCT
ejpam-6658	150	1	=	=	PUNCT
ejpam-6658	150	2	∞∑	∞∑	NUM
ejpam-6658	150	3	n=1	n=1	PROPN
ejpam-6658	150	4	pln−1(r1	pln−1(r1	NOUN
ejpam-6658	150	5	,	,	PUNCT
ejpam-6658	150	6	r2	r2	PROPN
ejpam-6658	150	7	,	,	PUNCT
ejpam-6658	150	8	r3	r3	PROPN
ejpam-6658	150	9	)	)	PUNCT
ejpam-6658	150	10	tn	tn	PROPN
ejpam-6658	151	1	(	(	PUNCT
ejpam-6658	151	2	n−	n−	NOUN
ejpam-6658	151	3	1	1	NUM
ejpam-6658	151	4	)	)	PUNCT
ejpam-6658	151	5	!	!	PUNCT
ejpam-6658	152	1	(	(	PUNCT
ejpam-6658	152	2	30	30	NUM
ejpam-6658	152	3	)	)	PUNCT
ejpam-6658	152	4	by	by	ADP
ejpam-6658	152	5	matching	match	VERB
ejpam-6658	152	6	the	the	DET
ejpam-6658	152	7	coefficients	coefficient	NOUN
ejpam-6658	152	8	of	of	ADP
ejpam-6658	152	9	same	same	ADJ
ejpam-6658	152	10	exponents	exponent	NOUN
ejpam-6658	152	11	of	of	ADP
ejpam-6658	152	12	t	t	PROPN
ejpam-6658	152	13	on	on	ADP
ejpam-6658	152	14	both	both	DET
ejpam-6658	152	15	sides	side	NOUN
ejpam-6658	152	16	of	of	ADP
ejpam-6658	152	17	(	(	PUNCT
ejpam-6658	152	18	30	30	NUM
ejpam-6658	152	19	)	)	PUNCT
ejpam-6658	152	20	,	,	PUNCT
ejpam-6658	152	21	it	it	PRON
ejpam-6658	152	22	follows	follow	VERB
ejpam-6658	152	23	that	that	SCONJ
ejpam-6658	152	24	dr1	dr1	PROPN
ejpam-6658	152	25	{	{	PUNCT
ejpam-6658	152	26	pln(r1	pln(r1	PROPN
ejpam-6658	152	27	,	,	PUNCT
ejpam-6658	152	28	r2	r2	PROPN
ejpam-6658	152	29	,	,	PUNCT
ejpam-6658	152	30	r3	r3	PROPN
ejpam-6658	152	31	)	)	PUNCT
ejpam-6658	152	32	}	}	PUNCT
ejpam-6658	152	33	=	=	SYM
ejpam-6658	152	34	npln−1(r1	npln−1(r1	NOUN
ejpam-6658	152	35	,	,	PUNCT
ejpam-6658	152	36	r2	r2	PROPN
ejpam-6658	152	37	,	,	PUNCT
ejpam-6658	152	38	r3	r3	PROPN
ejpam-6658	152	39	)	)	PUNCT
ejpam-6658	152	40	,	,	PUNCT
ejpam-6658	152	41	n	n	PRON
ejpam-6658	152	42	⪰	⪰	VERB
ejpam-6658	152	43	1	1	NUM
ejpam-6658	152	44	.	.	PUNCT
ejpam-6658	153	1	(	(	PUNCT
ejpam-6658	153	2	31	31	NUM
ejpam-6658	153	3	)	)	PUNCT
ejpam-6658	153	4	thus	thus	ADV
ejpam-6658	153	5	in	in	ADP
ejpam-6658	153	6	view	view	NOUN
ejpam-6658	153	7	of	of	ADP
ejpam-6658	153	8	(	(	PUNCT
ejpam-6658	153	9	17	17	NUM
ejpam-6658	153	10	)	)	PUNCT
ejpam-6658	153	11	and	and	CCONJ
ejpam-6658	153	12	(	(	PUNCT
ejpam-6658	153	13	31	31	NUM
ejpam-6658	153	14	)	)	PUNCT
ejpam-6658	153	15	,	,	PUNCT
ejpam-6658	153	16	we	we	PRON
ejpam-6658	153	17	get	get	VERB
ejpam-6658	153	18	the	the	DET
ejpam-6658	153	19	assertion	assertion	NOUN
ejpam-6658	153	20	(	(	PUNCT
ejpam-6658	153	21	25	25	NUM
ejpam-6658	153	22	)	)	PUNCT
ejpam-6658	153	23	.	.	PUNCT
ejpam-6658	154	1	theorem	theorem	NOUN
ejpam-6658	154	2	2	2	NUM
ejpam-6658	154	3	.	.	PUNCT
ejpam-6658	155	1	the	the	DET
ejpam-6658	155	2	following	follow	VERB
ejpam-6658	155	3	differential	differential	ADJ
ejpam-6658	155	4	equations	equation	NOUN
ejpam-6658	155	5	for	for	ADP
ejpam-6658	155	6	3	3	NUM
ejpam-6658	155	7	-	-	PUNCT
ejpam-6658	155	8	variable	variable	ADJ
ejpam-6658	155	9	generalized	generalize	VERB
ejpam-6658	155	10	laguerre	laguerre	NOUN
ejpam-6658	155	11	polynomials	polynomial	VERB
ejpam-6658	155	12	3v	3v	NUM
ejpam-6658	155	13	glp	glp	PROPN
ejpam-6658	155	14	pln(r1	pln(r1	PROPN
ejpam-6658	155	15	,	,	PUNCT
ejpam-6658	155	16	r2	r2	PROPN
ejpam-6658	155	17	,	,	PUNCT
ejpam-6658	155	18	r3	r3	PROPN
ejpam-6658	155	19	)	)	PUNCT
ejpam-6658	155	20	as	as	ADP
ejpam-6658	155	21	:(	:(	PUNCT
ejpam-6658	155	22	r1d̂r1	r1d̂r1	NOUN
ejpam-6658	155	23	+	+	CCONJ
ejpam-6658	155	24	ψ	ψ	X
ejpam-6658	155	25	′	′	NUM
ejpam-6658	155	26	(	(	PUNCT
ejpam-6658	155	27	r2	r2	PROPN
ejpam-6658	155	28	,	,	PUNCT
ejpam-6658	155	29	d̂r1	d̂r1	PROPN
ejpam-6658	155	30	)	)	PUNCT
ejpam-6658	155	31	ψ(r2	ψ(r2	NOUN
ejpam-6658	155	32	,	,	PUNCT
ejpam-6658	155	33	d̂r1	d̂r1	PROPN
ejpam-6658	155	34	)	)	PUNCT
ejpam-6658	155	35	d̂r1	d̂r1	PROPN
ejpam-6658	156	1	−	−	PROPN
ejpam-6658	157	1	nd̂−1	nd̂−1	CCONJ
ejpam-6658	157	2	r3	r3	PROPN
ejpam-6658	157	3	d̂r1	d̂r1	PROPN
ejpam-6658	157	4	−	−	PROPN
ejpam-6658	157	5	n	n	CCONJ
ejpam-6658	157	6	)	)	PUNCT
ejpam-6658	157	7	pln(r1	pln(r1	PROPN
ejpam-6658	157	8	,	,	PUNCT
ejpam-6658	157	9	r2	r2	PROPN
ejpam-6658	157	10	,	,	PUNCT
ejpam-6658	157	11	r3	r3	PROPN
ejpam-6658	157	12	)	)	PUNCT
ejpam-6658	157	13	=	=	SYM
ejpam-6658	157	14	0	0	NUM
ejpam-6658	157	15	,	,	PUNCT
ejpam-6658	157	16	(	(	PUNCT
ejpam-6658	157	17	32	32	NUM
ejpam-6658	157	18	)	)	PUNCT
ejpam-6658	157	19	w.	w.	PROPN
ejpam-6658	157	20	a.	a.	PROPN
ejpam-6658	157	21	khan	khan	PROPN
ejpam-6658	157	22	,	,	PUNCT
ejpam-6658	157	23	h.	h.	PROPN
ejpam-6658	157	24	qawaqneh	qawaqneh	PROPN
ejpam-6658	157	25	,	,	PUNCT
ejpam-6658	157	26	h.	h.	PROPN
ejpam-6658	157	27	aydi	aydi	VERB
ejpam-6658	157	28	/	/	SYM
ejpam-6658	157	29	eur	eur	NOUN
ejpam-6658	157	30	.	.	PUNCT
ejpam-6658	158	1	j.	j.	PROPN
ejpam-6658	158	2	pure	pure	PROPN
ejpam-6658	158	3	appl	appl	PROPN
ejpam-6658	158	4	.	.	PROPN
ejpam-6658	158	5	math	math	PROPN
ejpam-6658	158	6	,	,	PUNCT
ejpam-6658	158	7	18	18	NUM
ejpam-6658	158	8	(	(	PUNCT
ejpam-6658	158	9	3	3	NUM
ejpam-6658	158	10	)	)	PUNCT
ejpam-6658	158	11	(	(	PUNCT
ejpam-6658	158	12	2025	2025	NUM
ejpam-6658	158	13	)	)	PUNCT
ejpam-6658	158	14	,	,	PUNCT
ejpam-6658	158	15	6658	6658	NUM
ejpam-6658	158	16	8	8	NUM
ejpam-6658	158	17	of	of	ADP
ejpam-6658	158	18	22	22	NUM
ejpam-6658	158	19	proof	proof	NOUN
ejpam-6658	158	20	.	.	PUNCT
ejpam-6658	159	1	in	in	ADP
ejpam-6658	159	2	view	view	NOUN
ejpam-6658	159	3	of	of	ADP
ejpam-6658	159	4	equations	equation	NOUN
ejpam-6658	159	5	(	(	PUNCT
ejpam-6658	159	6	24	24	NUM
ejpam-6658	159	7	)	)	PUNCT
ejpam-6658	159	8	and	and	CCONJ
ejpam-6658	159	9	(	(	PUNCT
ejpam-6658	159	10	25	25	NUM
ejpam-6658	159	11	)	)	PUNCT
ejpam-6658	159	12	in	in	ADP
ejpam-6658	159	13	(	(	PUNCT
ejpam-6658	159	14	19	19	NUM
ejpam-6658	159	15	)	)	PUNCT
ejpam-6658	159	16	,	,	PUNCT
ejpam-6658	159	17	we	we	PRON
ejpam-6658	159	18	get	get	VERB
ejpam-6658	159	19	(	(	PUNCT
ejpam-6658	159	20	r1dr1	r1dr1	NOUN
ejpam-6658	159	21	+	+	NOUN
ejpam-6658	159	22	ψ	ψ	NOUN
ejpam-6658	159	23	′	′	NUM
ejpam-6658	159	24	(	(	PUNCT
ejpam-6658	159	25	r2	r2	PROPN
ejpam-6658	159	26	,	,	PUNCT
ejpam-6658	159	27	d̂r1	d̂r1	PROPN
ejpam-6658	159	28	)	)	PUNCT
ejpam-6658	159	29	ψ(r2	ψ(r2	NOUN
ejpam-6658	159	30	,	,	PUNCT
ejpam-6658	159	31	d̂r1	d̂r1	PROPN
ejpam-6658	159	32	)	)	PUNCT
ejpam-6658	160	1	dr1	dr1	PROPN
ejpam-6658	160	2	−	−	PROPN
ejpam-6658	161	1	nd̂−1	nd̂−1	PROPN
ejpam-6658	161	2	r3	r3	PROPN
ejpam-6658	161	3	dr1	dr1	PROPN
ejpam-6658	161	4	)	)	PUNCT
ejpam-6658	162	1	pln(r1	pln(r1	PROPN
ejpam-6658	162	2	,	,	PUNCT
ejpam-6658	162	3	r2	r2	PROPN
ejpam-6658	162	4	,	,	PUNCT
ejpam-6658	162	5	r3	r3	PROPN
ejpam-6658	162	6	)	)	PUNCT
ejpam-6658	162	7	=	=	SYM
ejpam-6658	162	8	n	n	PRON
ejpam-6658	162	9	pln(r1	pln(r1	PROPN
ejpam-6658	162	10	,	,	PUNCT
ejpam-6658	162	11	r2	r2	PROPN
ejpam-6658	162	12	,	,	PUNCT
ejpam-6658	162	13	r3	r3	PROPN
ejpam-6658	162	14	)	)	PUNCT
ejpam-6658	162	15	.	.	PUNCT
ejpam-6658	163	1	upon	upon	SCONJ
ejpam-6658	163	2	solving	solve	VERB
ejpam-6658	163	3	the	the	DET
ejpam-6658	163	4	above	above	ADJ
ejpam-6658	163	5	equation	equation	NOUN
ejpam-6658	163	6	,	,	PUNCT
ejpam-6658	163	7	we	we	PRON
ejpam-6658	163	8	get	get	VERB
ejpam-6658	163	9	the	the	DET
ejpam-6658	163	10	assertion	assertion	NOUN
ejpam-6658	163	11	(	(	PUNCT
ejpam-6658	163	12	32	32	NUM
ejpam-6658	163	13	)	)	PUNCT
ejpam-6658	163	14	of	of	ADP
ejpam-6658	163	15	theorem	theorem	ADJ
ejpam-6658	163	16	2.2	2.2	NUM
ejpam-6658	163	17	.	.	PUNCT
ejpam-6658	164	1	remark	remark	PROPN
ejpam-6658	164	2	1	1	NUM
ejpam-6658	164	3	.	.	PUNCT
ejpam-6658	165	1	since	since	SCONJ
ejpam-6658	165	2	p0(r1	p0(r1	NOUN
ejpam-6658	165	3	,	,	PUNCT
ejpam-6658	165	4	r2	r2	PROPN
ejpam-6658	165	5	)	)	PUNCT
ejpam-6658	165	6	=	=	SYM
ejpam-6658	165	7	1	1	NUM
ejpam-6658	165	8	,	,	PUNCT
ejpam-6658	165	9	therefore	therefore	ADV
ejpam-6658	165	10	in	in	ADP
ejpam-6658	165	11	view	view	NOUN
ejpam-6658	165	12	of	of	ADP
ejpam-6658	165	13	monomiality	monomiality	NOUN
ejpam-6658	165	14	principle	principle	NOUN
ejpam-6658	165	15	equation	equation	NOUN
ejpam-6658	165	16	(	(	PUNCT
ejpam-6658	165	17	15	15	NUM
ejpam-6658	165	18	)	)	PUNCT
ejpam-6658	165	19	,	,	PUNCT
ejpam-6658	165	20	we	we	PRON
ejpam-6658	165	21	have	have	VERB
ejpam-6658	165	22	pln(r1	pln(r1	NOUN
ejpam-6658	165	23	,	,	PUNCT
ejpam-6658	165	24	r2	r2	PROPN
ejpam-6658	165	25	,	,	PUNCT
ejpam-6658	165	26	r3	r3	PROPN
ejpam-6658	165	27	)	)	PUNCT
ejpam-6658	165	28	=	=	PUNCT
ejpam-6658	166	1	(	(	PUNCT
ejpam-6658	166	2	r1	r1	PROPN
ejpam-6658	166	3	+	+	CCONJ
ejpam-6658	166	4	ψ	ψ	X
ejpam-6658	166	5	′	′	NUM
ejpam-6658	166	6	(	(	PUNCT
ejpam-6658	166	7	r2	r2	PROPN
ejpam-6658	166	8	,	,	PUNCT
ejpam-6658	166	9	d̂r1	d̂r1	PROPN
ejpam-6658	166	10	)	)	PUNCT
ejpam-6658	166	11	ψ(r2	ψ(r2	NOUN
ejpam-6658	166	12	,	,	PUNCT
ejpam-6658	166	13	d̂r1	d̂r1	PROPN
ejpam-6658	166	14	)	)	PUNCT
ejpam-6658	167	1	−	−	PROPN
ejpam-6658	168	1	nd̂−1	nd̂−1	PROPN
ejpam-6658	168	2	r3	r3	PROPN
ejpam-6658	168	3	)	)	PUNCT
ejpam-6658	168	4	n	n	CCONJ
ejpam-6658	168	5	{	{	PUNCT
ejpam-6658	168	6	1	1	NUM
ejpam-6658	168	7	}	}	PUNCT
ejpam-6658	168	8	,	,	PUNCT
ejpam-6658	168	9	(	(	PUNCT
ejpam-6658	168	10	p0(r1	p0(r1	NOUN
ejpam-6658	168	11	,	,	PUNCT
ejpam-6658	168	12	r2	r2	PROPN
ejpam-6658	168	13	)	)	PUNCT
ejpam-6658	168	14	=	=	SYM
ejpam-6658	168	15	1	1	NUM
ejpam-6658	168	16	)	)	PUNCT
ejpam-6658	168	17	.	.	PUNCT
ejpam-6658	169	1	also	also	ADV
ejpam-6658	169	2	,	,	PUNCT
ejpam-6658	169	3	in	in	ADP
ejpam-6658	169	4	view	view	NOUN
ejpam-6658	169	5	of	of	ADP
ejpam-6658	169	6	equations	equation	NOUN
ejpam-6658	169	7	(	(	PUNCT
ejpam-6658	169	8	15	15	NUM
ejpam-6658	169	9	)	)	PUNCT
ejpam-6658	169	10	,	,	PUNCT
ejpam-6658	169	11	(	(	PUNCT
ejpam-6658	169	12	22	22	NUM
ejpam-6658	169	13	)	)	PUNCT
ejpam-6658	169	14	and	and	CCONJ
ejpam-6658	169	15	(	(	PUNCT
ejpam-6658	169	16	24	24	NUM
ejpam-6658	169	17	)	)	PUNCT
ejpam-6658	169	18	,	,	PUNCT
ejpam-6658	169	19	we	we	PRON
ejpam-6658	169	20	have	have	VERB
ejpam-6658	169	21	exp	exp	NOUN
ejpam-6658	169	22	(	(	PUNCT
ejpam-6658	169	23	m̂3v	m̂3v	ADV
ejpam-6658	169	24	gp	gp	NOUN
ejpam-6658	169	25	)	)	PUNCT
ejpam-6658	169	26	{	{	PUNCT
ejpam-6658	169	27	1	1	NUM
ejpam-6658	169	28	}	}	PUNCT
ejpam-6658	169	29	=	=	NOUN
ejpam-6658	169	30	er1tψ(r2	er1tψ(r2	PROPN
ejpam-6658	169	31	,	,	PUNCT
ejpam-6658	169	32	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	169	33	t	t	PROPN
ejpam-6658	169	34	)	)	PUNCT
ejpam-6658	169	35	=	=	PUNCT
ejpam-6658	170	1	∞∑	∞∑	NUM
ejpam-6658	170	2	υ=0	υ=0	PUNCT
ejpam-6658	170	3	pln(r1	pln(r1	NOUN
ejpam-6658	170	4	,	,	PUNCT
ejpam-6658	170	5	r2	r2	PROPN
ejpam-6658	170	6	,	,	PUNCT
ejpam-6658	170	7	r3	r3	PROPN
ejpam-6658	170	8	)	)	PUNCT
ejpam-6658	170	9	tn	tn	PROPN
ejpam-6658	170	10	n	n	PROPN
ejpam-6658	170	11	!	!	PUNCT
ejpam-6658	170	12	.	.	PUNCT
ejpam-6658	171	1	(	(	PUNCT
ejpam-6658	171	2	33	33	NUM
ejpam-6658	171	3	)	)	PUNCT
ejpam-6658	171	4	now	now	ADV
ejpam-6658	171	5	,	,	PUNCT
ejpam-6658	171	6	we	we	PRON
ejpam-6658	171	7	proceed	proceed	VERB
ejpam-6658	171	8	to	to	PART
ejpam-6658	171	9	introduce	introduce	VERB
ejpam-6658	171	10	the	the	DET
ejpam-6658	171	11	new	new	ADJ
ejpam-6658	171	12	generalization	generalization	NOUN
ejpam-6658	171	13	of	of	ADP
ejpam-6658	171	14	3	3	NUM
ejpam-6658	171	15	-	-	PUNCT
ejpam-6658	171	16	variable	variable	NOUN
ejpam-6658	171	17	laguerre	laguerre	NOUN
ejpam-6658	171	18	-	-	PUNCT
ejpam-6658	171	19	based	base	VERB
ejpam-6658	171	20	appell	appell	NOUN
ejpam-6658	171	21	polynomials	polynomial	NOUN
ejpam-6658	171	22	(	(	PUNCT
ejpam-6658	171	23	3vlbap	3vlbap	NUM
ejpam-6658	171	24	)	)	PUNCT
ejpam-6658	171	25	.	.	PUNCT
ejpam-6658	172	1	to	to	PART
ejpam-6658	172	2	obtain	obtain	VERB
ejpam-6658	172	3	the	the	DET
ejpam-6658	172	4	generating	generating	NOUN
ejpam-6658	172	5	functions	function	NOUN
ejpam-6658	172	6	for	for	ADP
ejpam-6658	172	7	the	the	DET
ejpam-6658	172	8	newly	newly	ADV
ejpam-6658	172	9	generalized	generalize	VERB
ejpam-6658	172	10	three	three	NUM
ejpam-6658	172	11	-	-	PUNCT
ejpam-6658	172	12	variable	variable	NOUN
ejpam-6658	172	13	laguerre	laguerre	NOUN
ejpam-6658	172	14	-	-	PUNCT
ejpam-6658	172	15	based	base	VERB
ejpam-6658	172	16	appell	appell	NOUN
ejpam-6658	172	17	polynomials	polynomial	NOUN
ejpam-6658	172	18	,	,	PUNCT
ejpam-6658	172	19	we	we	PRON
ejpam-6658	172	20	utilize	utilize	VERB
ejpam-6658	172	21	the	the	DET
ejpam-6658	172	22	exponential	exponential	ADJ
ejpam-6658	172	23	generating	generating	NOUN
ejpam-6658	172	24	function	function	NOUN
ejpam-6658	172	25	associated	associate	VERB
ejpam-6658	172	26	with	with	ADP
ejpam-6658	172	27	appell	appell	ADJ
ejpam-6658	172	28	polynomials	polynomial	NOUN
ejpam-6658	172	29	.	.	PUNCT
ejpam-6658	173	1	thus	thus	ADV
ejpam-6658	173	2	,	,	PUNCT
ejpam-6658	173	3	replacing	replace	VERB
ejpam-6658	173	4	r1	r1	NOUN
ejpam-6658	173	5	in	in	ADP
ejpam-6658	173	6	the	the	DET
ejpam-6658	173	7	left	left	ADJ
ejpam-6658	173	8	hand	hand	NOUN
ejpam-6658	173	9	side	side	NOUN
ejpam-6658	173	10	of	of	ADP
ejpam-6658	173	11	(	(	PUNCT
ejpam-6658	173	12	5	5	NUM
ejpam-6658	173	13	)	)	PUNCT
ejpam-6658	173	14	by	by	ADP
ejpam-6658	173	15	the	the	DET
ejpam-6658	173	16	multiplicative	multiplicative	ADJ
ejpam-6658	173	17	operator	operator	NOUN
ejpam-6658	173	18	pln(r1	pln(r1	PROPN
ejpam-6658	173	19	,	,	PUNCT
ejpam-6658	173	20	r2	r2	PROPN
ejpam-6658	173	21	,	,	PUNCT
ejpam-6658	173	22	r3	r3	PROPN
ejpam-6658	173	23	)	)	PUNCT
ejpam-6658	173	24	given	give	VERB
ejpam-6658	173	25	by	by	ADP
ejpam-6658	173	26	(	(	PUNCT
ejpam-6658	173	27	24	24	NUM
ejpam-6658	173	28	)	)	PUNCT
ejpam-6658	173	29	denoting	denote	VERB
ejpam-6658	173	30	the	the	DET
ejpam-6658	173	31	new	new	ADJ
ejpam-6658	173	32	generalization	generalization	NOUN
ejpam-6658	173	33	of	of	ADP
ejpam-6658	173	34	3	3	NUM
ejpam-6658	173	35	-	-	PUNCT
ejpam-6658	173	36	variable	variable	NOUN
ejpam-6658	173	37	laguerre	laguerre	NOUN
ejpam-6658	173	38	-	-	PUNCT
ejpam-6658	173	39	based	base	VERB
ejpam-6658	173	40	appell	appell	NOUN
ejpam-6658	173	41	polynomials	polynomial	NOUN
ejpam-6658	173	42	plrn(r1	plrn(r1	NOUN
ejpam-6658	173	43	,	,	PUNCT
ejpam-6658	173	44	r2	r2	PROPN
ejpam-6658	173	45	,	,	PUNCT
ejpam-6658	173	46	r3	r3	PROPN
ejpam-6658	173	47	)	)	PUNCT
ejpam-6658	173	48	,	,	PUNCT
ejpam-6658	173	49	we	we	PRON
ejpam-6658	173	50	get	get	VERB
ejpam-6658	173	51	r(t	r(t	NOUN
ejpam-6658	173	52	)	)	PUNCT
ejpam-6658	173	53	exp	exp	NOUN
ejpam-6658	173	54	(	(	PUNCT
ejpam-6658	173	55	m̂3v	m̂3v	ADV
ejpam-6658	173	56	gp	gp	NOUN
ejpam-6658	173	57	)	)	PUNCT
ejpam-6658	173	58	{	{	PUNCT
ejpam-6658	173	59	1	1	NUM
ejpam-6658	173	60	}	}	PUNCT
ejpam-6658	173	61	=	=	PUNCT
ejpam-6658	173	62	∞∑	∞∑	PRON
ejpam-6658	173	63	n=0	n=0	NUM
ejpam-6658	173	64	plrn(r1	plrn(r1	NOUN
ejpam-6658	173	65	,	,	PUNCT
ejpam-6658	173	66	r2	r2	PROPN
ejpam-6658	173	67	,	,	PUNCT
ejpam-6658	173	68	r3	r3	PROPN
ejpam-6658	173	69	)	)	PUNCT
ejpam-6658	173	70	tn	tn	PROPN
ejpam-6658	173	71	n	n	PROPN
ejpam-6658	173	72	!	!	PROPN
ejpam-6658	173	73	,	,	PUNCT
ejpam-6658	173	74	(	(	PUNCT
ejpam-6658	173	75	34	34	NUM
ejpam-6658	173	76	)	)	PUNCT
ejpam-6658	173	77	which	which	PRON
ejpam-6658	173	78	on	on	ADP
ejpam-6658	173	79	using	use	VERB
ejpam-6658	173	80	equation	equation	NOUN
ejpam-6658	173	81	(	(	PUNCT
ejpam-6658	173	82	24	24	NUM
ejpam-6658	173	83	)	)	PUNCT
ejpam-6658	173	84	,	,	PUNCT
ejpam-6658	173	85	we	we	PRON
ejpam-6658	173	86	get	get	VERB
ejpam-6658	173	87	the	the	DET
ejpam-6658	173	88	following	follow	VERB
ejpam-6658	173	89	two	two	NUM
ejpam-6658	173	90	equivalent	equivalent	ADJ
ejpam-6658	173	91	forms	form	NOUN
ejpam-6658	173	92	of	of	ADP
ejpam-6658	173	93	plrn(r1	plrn(r1	NOUN
ejpam-6658	173	94	,	,	PUNCT
ejpam-6658	173	95	r2	r2	PROPN
ejpam-6658	173	96	,	,	PUNCT
ejpam-6658	173	97	r3	r3	PROPN
ejpam-6658	173	98	):	):	PUNCT
ejpam-6658	173	99	r(t	r(t	NOUN
ejpam-6658	173	100	)	)	PUNCT
ejpam-6658	173	101	exp	exp	NOUN
ejpam-6658	173	102	(	(	PUNCT
ejpam-6658	173	103	r1	r1	PROPN
ejpam-6658	173	104	+	+	CCONJ
ejpam-6658	173	105	ψ	ψ	X
ejpam-6658	173	106	′	′	NUM
ejpam-6658	173	107	(	(	PUNCT
ejpam-6658	173	108	r2	r2	PROPN
ejpam-6658	173	109	,	,	PUNCT
ejpam-6658	173	110	d̂r1	d̂r1	PROPN
ejpam-6658	173	111	ψ(r2	ψ(r2	NOUN
ejpam-6658	173	112	,	,	PUNCT
ejpam-6658	173	113	d̂r1	d̂r1	PROPN
ejpam-6658	173	114	−	−	PROPN
ejpam-6658	174	1	nd̂−1	nd̂−1	PROPN
ejpam-6658	174	2	r3	r3	PROPN
ejpam-6658	174	3	)	)	PUNCT
ejpam-6658	174	4	{	{	PUNCT
ejpam-6658	174	5	1	1	NUM
ejpam-6658	174	6	}	}	PUNCT
ejpam-6658	174	7	=	=	PUNCT
ejpam-6658	174	8	∞∑	∞∑	PRON
ejpam-6658	174	9	n=0	n=0	NUM
ejpam-6658	174	10	plrn(r1	plrn(r1	NOUN
ejpam-6658	174	11	,	,	PUNCT
ejpam-6658	174	12	r2	r2	PROPN
ejpam-6658	174	13	,	,	PUNCT
ejpam-6658	174	14	r3	r3	PROPN
ejpam-6658	174	15	)	)	PUNCT
ejpam-6658	174	16	tn	tn	PROPN
ejpam-6658	174	17	n	n	PROPN
ejpam-6658	174	18	!	!	PUNCT
ejpam-6658	174	19	.	.	PUNCT
ejpam-6658	175	1	(	(	PUNCT
ejpam-6658	175	2	35	35	NUM
ejpam-6658	175	3	)	)	PUNCT
ejpam-6658	175	4	using	use	VERB
ejpam-6658	175	5	the	the	DET
ejpam-6658	175	6	relation	relation	NOUN
ejpam-6658	175	7	(	(	PUNCT
ejpam-6658	175	8	33	33	NUM
ejpam-6658	175	9	)	)	PUNCT
ejpam-6658	175	10	in	in	ADP
ejpam-6658	175	11	the	the	DET
ejpam-6658	175	12	left	left	ADJ
ejpam-6658	175	13	hand	hand	NOUN
ejpam-6658	175	14	side	side	NOUN
ejpam-6658	175	15	of	of	ADP
ejpam-6658	175	16	equation	equation	NOUN
ejpam-6658	175	17	(	(	PUNCT
ejpam-6658	175	18	34	34	NUM
ejpam-6658	175	19	)	)	PUNCT
ejpam-6658	175	20	,	,	PUNCT
ejpam-6658	175	21	the	the	DET
ejpam-6658	175	22	generating	generate	VERB
ejpam-6658	175	23	function	function	NOUN
ejpam-6658	175	24	for	for	ADP
ejpam-6658	175	25	the	the	DET
ejpam-6658	175	26	new	new	ADJ
ejpam-6658	175	27	generalization	generalization	NOUN
ejpam-6658	175	28	of	of	ADP
ejpam-6658	175	29	3	3	NUM
ejpam-6658	175	30	-	-	PUNCT
ejpam-6658	175	31	variable	variable	NOUN
ejpam-6658	175	32	laguerre	laguerre	NOUN
ejpam-6658	175	33	-	-	PUNCT
ejpam-6658	175	34	based	base	VERB
ejpam-6658	175	35	appell	appell	NOUN
ejpam-6658	175	36	polynomials	polynomial	NOUN
ejpam-6658	175	37	plrn(r1	plrn(r1	NOUN
ejpam-6658	175	38	,	,	PUNCT
ejpam-6658	175	39	r2	r2	PROPN
ejpam-6658	175	40	,	,	PUNCT
ejpam-6658	175	41	r3	r3	PROPN
ejpam-6658	175	42	)	)	PUNCT
ejpam-6658	175	43	in	in	ADP
ejpam-6658	175	44	the	the	DET
ejpam-6658	175	45	following	follow	VERB
ejpam-6658	175	46	form	form	NOUN
ejpam-6658	175	47	:	:	PUNCT
ejpam-6658	175	48	r(t)er1tψ(r2	r(t)er1tψ(r2	NOUN
ejpam-6658	175	49	,	,	PUNCT
ejpam-6658	175	50	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	175	51	t	t	PROPN
ejpam-6658	175	52	)	)	PUNCT
ejpam-6658	175	53	=	=	PUNCT
ejpam-6658	176	1	∞∑	∞∑	PRON
ejpam-6658	176	2	n=0	n=0	NUM
ejpam-6658	176	3	plrn(r1	plrn(r1	NOUN
ejpam-6658	176	4	,	,	PUNCT
ejpam-6658	176	5	r2	r2	PROPN
ejpam-6658	176	6	,	,	PUNCT
ejpam-6658	176	7	r3	r3	PROPN
ejpam-6658	176	8	)	)	PUNCT
ejpam-6658	176	9	tn	tn	PROPN
ejpam-6658	176	10	n	n	PROPN
ejpam-6658	176	11	!	!	PUNCT
ejpam-6658	176	12	.	.	PUNCT
ejpam-6658	177	1	(	(	PUNCT
ejpam-6658	177	2	36	36	NUM
ejpam-6658	177	3	)	)	PUNCT
ejpam-6658	177	4	where	where	SCONJ
ejpam-6658	177	5	r(t	r(t	NOUN
ejpam-6658	177	6	)	)	PUNCT
ejpam-6658	177	7	=	=	PUNCT
ejpam-6658	178	1	∞∑	∞∑	NUM
ejpam-6658	178	2	k=0	k=0	PUNCT
ejpam-6658	178	3	αk	αk	ADP
ejpam-6658	178	4	tk	tk	PROPN
ejpam-6658	178	5	k	k	PROPN
ejpam-6658	178	6	!	!	PROPN
ejpam-6658	178	7	,	,	PUNCT
ejpam-6658	178	8	α0	α0	ADJ
ejpam-6658	178	9	̸=	̸=	PROPN
ejpam-6658	178	10	0	0	NUM
ejpam-6658	178	11	ψ(r2	ψ(r2	NOUN
ejpam-6658	178	12	,	,	PUNCT
ejpam-6658	178	13	t	t	PROPN
ejpam-6658	178	14	)	)	PUNCT
ejpam-6658	178	15	=	=	PUNCT
ejpam-6658	179	1	∞∑	∞∑	NUM
ejpam-6658	179	2	k=0	k=0	PROPN
ejpam-6658	179	3	ψk(r2	ψk(r2	ADV
ejpam-6658	179	4	)	)	PUNCT
ejpam-6658	179	5	tk	tk	PROPN
ejpam-6658	180	1	k	k	PROPN
ejpam-6658	180	2	!	!	PROPN
ejpam-6658	180	3	,	,	PUNCT
ejpam-6658	180	4	ψ0	ψ0	ADV
ejpam-6658	180	5	̸=	̸=	PROPN
ejpam-6658	180	6	0	0	NUM
ejpam-6658	180	7	.	.	PUNCT
ejpam-6658	181	1	(	(	PUNCT
ejpam-6658	181	2	37	37	NUM
ejpam-6658	181	3	)	)	PUNCT
ejpam-6658	181	4	w.	w.	PROPN
ejpam-6658	181	5	a.	a.	PROPN
ejpam-6658	181	6	khan	khan	PROPN
ejpam-6658	181	7	,	,	PUNCT
ejpam-6658	181	8	h.	h.	PROPN
ejpam-6658	181	9	qawaqneh	qawaqneh	PROPN
ejpam-6658	181	10	,	,	PUNCT
ejpam-6658	181	11	h.	h.	PROPN
ejpam-6658	181	12	aydi	aydi	VERB
ejpam-6658	181	13	/	/	SYM
ejpam-6658	181	14	eur	eur	NOUN
ejpam-6658	181	15	.	.	PUNCT
ejpam-6658	182	1	j.	j.	PROPN
ejpam-6658	182	2	pure	pure	PROPN
ejpam-6658	182	3	appl	appl	PROPN
ejpam-6658	182	4	.	.	PROPN
ejpam-6658	182	5	math	math	PROPN
ejpam-6658	182	6	,	,	PUNCT
ejpam-6658	182	7	18	18	NUM
ejpam-6658	182	8	(	(	PUNCT
ejpam-6658	182	9	3	3	NUM
ejpam-6658	182	10	)	)	PUNCT
ejpam-6658	182	11	(	(	PUNCT
ejpam-6658	182	12	2025	2025	NUM
ejpam-6658	182	13	)	)	PUNCT
ejpam-6658	182	14	,	,	PUNCT
ejpam-6658	182	15	6658	6658	NUM
ejpam-6658	182	16	9	9	NUM
ejpam-6658	182	17	of	of	ADP
ejpam-6658	182	18	22	22	NUM
ejpam-6658	182	19	theorem	theorem	NOUN
ejpam-6658	182	20	3	3	NUM
ejpam-6658	182	21	.	.	PUNCT
ejpam-6658	183	1	the	the	DET
ejpam-6658	183	2	generalized	generalize	VERB
ejpam-6658	183	3	laguerre	laguerre	NOUN
ejpam-6658	183	4	-	-	PUNCT
ejpam-6658	183	5	based	base	VERB
ejpam-6658	183	6	appell	appell	NOUN
ejpam-6658	183	7	polynomials	polynomial	NOUN
ejpam-6658	183	8	plrn(r1	plrn(r1	NOUN
ejpam-6658	183	9	,	,	PUNCT
ejpam-6658	183	10	r2	r2	PROPN
ejpam-6658	183	11	,	,	PUNCT
ejpam-6658	183	12	r3	r3	PROPN
ejpam-6658	183	13	)	)	PUNCT
ejpam-6658	183	14	satisfy	satisfy	VERB
ejpam-6658	183	15	the	the	DET
ejpam-6658	183	16	following	follow	VERB
ejpam-6658	183	17	recurrence	recurrence	NOUN
ejpam-6658	183	18	relation	relation	PROPN
ejpam-6658	183	19	:	:	PUNCT
ejpam-6658	183	20	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	183	21	,	,	PUNCT
ejpam-6658	183	22	r2	r2	PROPN
ejpam-6658	183	23	,	,	PUNCT
ejpam-6658	183	24	r3	r3	PROPN
ejpam-6658	183	25	)	)	PUNCT
ejpam-6658	183	26	=	=	SYM
ejpam-6658	184	1	n∑	n∑	NOUN
ejpam-6658	184	2	k=0	k=0	PROPN
ejpam-6658	184	3	(	(	PUNCT
ejpam-6658	184	4	n	n	X
ejpam-6658	184	5	k	k	PROPN
ejpam-6658	184	6	)	)	PUNCT
ejpam-6658	184	7	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	184	8	,	,	PUNCT
ejpam-6658	184	9	r2	r2	PROPN
ejpam-6658	184	10	,	,	PUNCT
ejpam-6658	184	11	r3)γk+r1plrn(r1	r3)γk+r1plrn(r1	PROPN
ejpam-6658	184	12	,	,	PUNCT
ejpam-6658	184	13	r2	r2	PROPN
ejpam-6658	184	14	,	,	PUNCT
ejpam-6658	184	15	r3)+	r3)+	PROPN
ejpam-6658	184	16	n∑	n∑	NOUN
ejpam-6658	184	17	k=0	k=0	PROPN
ejpam-6658	184	18	(	(	PUNCT
ejpam-6658	184	19	n	n	X
ejpam-6658	184	20	k	k	PROPN
ejpam-6658	184	21	)	)	PUNCT
ejpam-6658	184	22	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	184	23	,	,	PUNCT
ejpam-6658	184	24	r2	r2	NOUN
ejpam-6658	184	25	,	,	PUNCT
ejpam-6658	184	26	r3)ρk(r2	r3)ρk(r2	PROPN
ejpam-6658	184	27	)	)	PUNCT
ejpam-6658	184	28	−nd−1	−nd−1	NUM
ejpam-6658	184	29	r3	r3	PROPN
ejpam-6658	184	30	plrn−1(r1	plrn−1(r1	NOUN
ejpam-6658	184	31	,	,	PUNCT
ejpam-6658	184	32	r2	r2	PROPN
ejpam-6658	184	33	,	,	PUNCT
ejpam-6658	184	34	r3	r3	PROPN
ejpam-6658	184	35	)	)	PUNCT
ejpam-6658	184	36	.	.	PUNCT
ejpam-6658	185	1	(	(	PUNCT
ejpam-6658	185	2	38	38	NUM
ejpam-6658	185	3	)	)	PUNCT
ejpam-6658	185	4	where	where	SCONJ
ejpam-6658	185	5	r′(t	r′(t	NOUN
ejpam-6658	185	6	)	)	PUNCT
ejpam-6658	185	7	r(t	r(t	NOUN
ejpam-6658	185	8	)	)	PUNCT
ejpam-6658	185	9	=	=	PUNCT
ejpam-6658	186	1	∞∑	∞∑	NUM
ejpam-6658	186	2	k=0	k=0	PROPN
ejpam-6658	186	3	γk	γk	PROPN
ejpam-6658	186	4	tk	tk	PROPN
ejpam-6658	186	5	k	k	PROPN
ejpam-6658	186	6	!	!	PROPN
ejpam-6658	186	7	,	,	PUNCT
ejpam-6658	186	8	ψt(r2	ψt(r2	PROPN
ejpam-6658	186	9	,	,	PUNCT
ejpam-6658	186	10	t	t	NOUN
ejpam-6658	186	11	)	)	PUNCT
ejpam-6658	186	12	ψ(r2	ψ(r2	NOUN
ejpam-6658	186	13	,	,	PUNCT
ejpam-6658	186	14	t	t	PROPN
ejpam-6658	186	15	)	)	PUNCT
ejpam-6658	186	16	=	=	PUNCT
ejpam-6658	187	1	∞∑	∞∑	NUM
ejpam-6658	187	2	k=0	k=0	PROPN
ejpam-6658	187	3	ρk(r2	ρk(r2	NUM
ejpam-6658	187	4	)	)	PUNCT
ejpam-6658	187	5	tk	tk	PROPN
ejpam-6658	187	6	k	k	PROPN
ejpam-6658	187	7	!	!	PROPN
ejpam-6658	187	8	,	,	PUNCT
ejpam-6658	187	9	ψt(r2	ψt(r2	PROPN
ejpam-6658	187	10	,	,	PUNCT
ejpam-6658	187	11	t	t	PROPN
ejpam-6658	187	12	)	)	PUNCT
ejpam-6658	187	13	=	=	SYM
ejpam-6658	187	14	∂	∂	NUM
ejpam-6658	188	1	∂t	∂t	PROPN
ejpam-6658	188	2	ψ(r2	ψ(r2	NOUN
ejpam-6658	188	3	,	,	PUNCT
ejpam-6658	188	4	t	t	PROPN
ejpam-6658	188	5	)	)	PUNCT
ejpam-6658	188	6	(	(	PUNCT
ejpam-6658	188	7	39	39	NUM
ejpam-6658	188	8	)	)	PUNCT
ejpam-6658	188	9	and	and	CCONJ
ejpam-6658	188	10	d−1	d−1	PROPN
ejpam-6658	188	11	r3	r3	PROPN
ejpam-6658	188	12	is	be	AUX
ejpam-6658	188	13	the	the	DET
ejpam-6658	188	14	inverse	inverse	NOUN
ejpam-6658	188	15	of	of	ADP
ejpam-6658	188	16	dr3	dr3	PROPN
ejpam-6658	188	17	.	.	PUNCT
ejpam-6658	189	1	proof	proof	NOUN
ejpam-6658	189	2	.	.	PUNCT
ejpam-6658	190	1	by	by	ADP
ejpam-6658	190	2	differentiating	differentiate	VERB
ejpam-6658	190	3	both	both	DET
ejpam-6658	190	4	sides	side	NOUN
ejpam-6658	190	5	of	of	ADP
ejpam-6658	190	6	equation	equation	NOUN
ejpam-6658	190	7	(	(	PUNCT
ejpam-6658	190	8	36	36	NUM
ejpam-6658	190	9	)	)	PUNCT
ejpam-6658	190	10	with	with	ADP
ejpam-6658	190	11	respect	respect	NOUN
ejpam-6658	190	12	to	to	ADP
ejpam-6658	190	13	t	t	PROPN
ejpam-6658	190	14	,	,	PUNCT
ejpam-6658	190	15	we	we	PRON
ejpam-6658	190	16	obtain	obtain	VERB
ejpam-6658	190	17	the	the	DET
ejpam-6658	190	18	following	following	NOUN
ejpam-6658	190	19	:	:	PUNCT
ejpam-6658	190	20	∞∑	∞∑	NUM
ejpam-6658	190	21	n=0	n=0	NUM
ejpam-6658	190	22	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	190	23	,	,	PUNCT
ejpam-6658	190	24	r2	r2	PROPN
ejpam-6658	190	25	,	,	PUNCT
ejpam-6658	190	26	r3	r3	PROPN
ejpam-6658	190	27	)	)	PUNCT
ejpam-6658	190	28	tn	tn	PROPN
ejpam-6658	190	29	n	n	PROPN
ejpam-6658	190	30	!	!	PUNCT
ejpam-6658	191	1	=	=	PUNCT
ejpam-6658	192	1	r′(t	r′(t	ADJ
ejpam-6658	192	2	)	)	PUNCT
ejpam-6658	192	3	r(t	r(t	NOUN
ejpam-6658	192	4	)	)	PUNCT
ejpam-6658	192	5	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	192	6	,	,	PUNCT
ejpam-6658	192	7	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	192	8	t	t	PROPN
ejpam-6658	192	9	)	)	PUNCT
ejpam-6658	193	1	+	+	NUM
ejpam-6658	193	2	r1r(t)er1tψ(r2	r1r(t)er1tψ(r2	NOUN
ejpam-6658	193	3	,	,	PUNCT
ejpam-6658	193	4	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	193	5	t	t	PROPN
ejpam-6658	193	6	)	)	PUNCT
ejpam-6658	194	1	+	+	CCONJ
ejpam-6658	194	2	ψt(r2	ψt(r2	PROPN
ejpam-6658	194	3	,	,	PUNCT
ejpam-6658	194	4	t	t	NOUN
ejpam-6658	194	5	)	)	PUNCT
ejpam-6658	194	6	ψ(r2	ψ(r2	NOUN
ejpam-6658	194	7	,	,	PUNCT
ejpam-6658	194	8	t	t	NOUN
ejpam-6658	194	9	)	)	PUNCT
ejpam-6658	194	10	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	194	11	,	,	PUNCT
ejpam-6658	194	12	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	194	13	t	t	PROPN
ejpam-6658	194	14	)	)	PUNCT
ejpam-6658	195	1	+	+	CCONJ
ejpam-6658	195	2	(	(	PUNCT
ejpam-6658	195	3	∞∑	∞∑	NUM
ejpam-6658	195	4	n=0	n=0	NUM
ejpam-6658	195	5	rn3nt	rn3nt	NOUN
ejpam-6658	195	6	n−1	n−1	PROPN
ejpam-6658	195	7	(	(	PUNCT
ejpam-6658	195	8	[	[	X
ejpam-6658	195	9	n]!)2	n]!)2	NOUN
ejpam-6658	195	10	)	)	PUNCT
ejpam-6658	195	11	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	195	12	,	,	PUNCT
ejpam-6658	195	13	t	t	PROPN
ejpam-6658	195	14	)	)	PUNCT
ejpam-6658	195	15	(	(	PUNCT
ejpam-6658	195	16	40	40	NUM
ejpam-6658	195	17	)	)	PUNCT
ejpam-6658	195	18	using	use	VERB
ejpam-6658	195	19	(	(	PUNCT
ejpam-6658	195	20	39	39	NUM
ejpam-6658	195	21	)	)	PUNCT
ejpam-6658	195	22	,	,	PUNCT
ejpam-6658	195	23	we	we	PRON
ejpam-6658	195	24	have	have	VERB
ejpam-6658	195	25	∞∑	∞∑	NUM
ejpam-6658	195	26	n=0	n=0	NUM
ejpam-6658	195	27	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	195	28	,	,	PUNCT
ejpam-6658	195	29	r2	r2	PROPN
ejpam-6658	195	30	,	,	PUNCT
ejpam-6658	195	31	r3	r3	PROPN
ejpam-6658	195	32	)	)	PUNCT
ejpam-6658	195	33	tn	tn	PROPN
ejpam-6658	195	34	n	n	PROPN
ejpam-6658	195	35	!	!	PUNCT
ejpam-6658	196	1	=	=	PUNCT
ejpam-6658	196	2	(	(	PUNCT
ejpam-6658	196	3	∞∑	∞∑	NUM
ejpam-6658	196	4	k=0	k=0	PROPN
ejpam-6658	196	5	γk	γk	PROPN
ejpam-6658	196	6	tk	tk	PROPN
ejpam-6658	196	7	k	k	PROPN
ejpam-6658	196	8	!	!	PUNCT
ejpam-6658	196	9	)	)	PUNCT
ejpam-6658	197	1	(	(	PUNCT
ejpam-6658	197	2	∞∑	∞∑	NUM
ejpam-6658	197	3	n=0	n=0	NUM
ejpam-6658	197	4	plrn(r1	plrn(r1	NOUN
ejpam-6658	197	5	,	,	PUNCT
ejpam-6658	197	6	r2	r2	PROPN
ejpam-6658	197	7	,	,	PUNCT
ejpam-6658	197	8	r3	r3	PROPN
ejpam-6658	197	9	)	)	PUNCT
ejpam-6658	197	10	tn	tn	PROPN
ejpam-6658	197	11	n	n	PROPN
ejpam-6658	197	12	!	!	PUNCT
ejpam-6658	197	13	)	)	PUNCT
ejpam-6658	198	1	+	+	CCONJ
ejpam-6658	198	2	(	(	PUNCT
ejpam-6658	198	3	∞∑	∞∑	DET
ejpam-6658	198	4	k=0	k=0	PROPN
ejpam-6658	198	5	ρk(r2	ρk(r2	NUM
ejpam-6658	198	6	)	)	PUNCT
ejpam-6658	198	7	tk	tk	PROPN
ejpam-6658	198	8	k	k	PROPN
ejpam-6658	198	9	!	!	PUNCT
ejpam-6658	198	10	)	)	PUNCT
ejpam-6658	199	1	(	(	PUNCT
ejpam-6658	199	2	∞∑	∞∑	NUM
ejpam-6658	199	3	n=0	n=0	NUM
ejpam-6658	199	4	plrn(r1	plrn(r1	NOUN
ejpam-6658	199	5	,	,	PUNCT
ejpam-6658	199	6	r2	r2	PROPN
ejpam-6658	199	7	,	,	PUNCT
ejpam-6658	199	8	r3	r3	PROPN
ejpam-6658	199	9	)	)	PUNCT
ejpam-6658	199	10	tn	tn	PROPN
ejpam-6658	199	11	n	n	PROPN
ejpam-6658	199	12	!	!	PUNCT
ejpam-6658	199	13	)	)	PUNCT
ejpam-6658	200	1	+	+	ADV
ejpam-6658	200	2	r1	r1	VERB
ejpam-6658	200	3	∞∑	∞∑	PRON
ejpam-6658	200	4	n=0	n=0	NUM
ejpam-6658	200	5	plrn(r1	plrn(r1	NOUN
ejpam-6658	200	6	,	,	PUNCT
ejpam-6658	200	7	r2	r2	PROPN
ejpam-6658	200	8	,	,	PUNCT
ejpam-6658	200	9	r3	r3	PROPN
ejpam-6658	200	10	)	)	PUNCT
ejpam-6658	200	11	tn	tn	PROPN
ejpam-6658	200	12	n	n	CCONJ
ejpam-6658	200	13	!	!	PUNCT
ejpam-6658	201	1	+	+	CCONJ
ejpam-6658	201	2	(	(	PUNCT
ejpam-6658	201	3	∞∑	∞∑	NUM
ejpam-6658	201	4	n=0	n=0	NUM
ejpam-6658	201	5	rn3nt	rn3nt	NOUN
ejpam-6658	201	6	n−1	n−1	PROPN
ejpam-6658	201	7	(	(	PUNCT
ejpam-6658	201	8	[	[	X
ejpam-6658	201	9	n]!)2	n]!)2	NOUN
ejpam-6658	201	10	)	)	PUNCT
ejpam-6658	201	11	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	201	12	,	,	PUNCT
ejpam-6658	201	13	t	t	PROPN
ejpam-6658	201	14	)	)	PUNCT
ejpam-6658	201	15	.	.	PUNCT
ejpam-6658	202	1	(	(	PUNCT
ejpam-6658	202	2	41	41	NUM
ejpam-6658	202	3	)	)	PUNCT
ejpam-6658	202	4	hence	hence	ADV
ejpam-6658	202	5	,	,	PUNCT
ejpam-6658	202	6	when	when	SCONJ
ejpam-6658	202	7	use	use	VERB
ejpam-6658	202	8	the	the	DET
ejpam-6658	202	9	cauchy	cauchy	NOUN
ejpam-6658	202	10	product	product	NOUN
ejpam-6658	202	11	,	,	PUNCT
ejpam-6658	202	12	we	we	PRON
ejpam-6658	202	13	obtain	obtain	VERB
ejpam-6658	202	14	∞∑	∞∑	PRON
ejpam-6658	202	15	n=0	n=0	NUM
ejpam-6658	202	16	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	202	17	,	,	PUNCT
ejpam-6658	202	18	r2	r2	PROPN
ejpam-6658	202	19	,	,	PUNCT
ejpam-6658	202	20	r3	r3	PROPN
ejpam-6658	202	21	)	)	PUNCT
ejpam-6658	202	22	tn	tn	PROPN
ejpam-6658	202	23	n	n	PROPN
ejpam-6658	202	24	!	!	PUNCT
ejpam-6658	203	1	=	=	NOUN
ejpam-6658	204	1	∞∑	∞∑	PRON
ejpam-6658	204	2	n=0	n=0	NUM
ejpam-6658	204	3	n∑	n∑	NOUN
ejpam-6658	204	4	k=0	k=0	PROPN
ejpam-6658	204	5	(	(	PUNCT
ejpam-6658	204	6	n	n	X
ejpam-6658	204	7	k	k	PROPN
ejpam-6658	204	8	)	)	PUNCT
ejpam-6658	204	9	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	204	10	,	,	PUNCT
ejpam-6658	204	11	r2	r2	PROPN
ejpam-6658	204	12	,	,	PUNCT
ejpam-6658	204	13	r3)γk	r3)γk	PROPN
ejpam-6658	204	14	tn	tn	PROPN
ejpam-6658	204	15	n	n	CCONJ
ejpam-6658	204	16	!	!	PUNCT
ejpam-6658	205	1	+	+	CCONJ
ejpam-6658	205	2	∞∑	∞∑	NUM
ejpam-6658	205	3	n=0	n=0	NUM
ejpam-6658	205	4	n∑	n∑	NOUN
ejpam-6658	205	5	k=0	k=0	PROPN
ejpam-6658	205	6	(	(	PUNCT
ejpam-6658	205	7	n	n	X
ejpam-6658	205	8	k	k	PROPN
ejpam-6658	205	9	)	)	PUNCT
ejpam-6658	206	1	ρk(r2)plrn−k(r1	ρk(r2)plrn−k(r1	PROPN
ejpam-6658	206	2	,	,	PUNCT
ejpam-6658	206	3	r2	r2	PROPN
ejpam-6658	206	4	,	,	PUNCT
ejpam-6658	206	5	r3	r3	PROPN
ejpam-6658	206	6	)	)	PUNCT
ejpam-6658	206	7	tn	tn	PROPN
ejpam-6658	206	8	n	n	CCONJ
ejpam-6658	206	9	!	!	PUNCT
ejpam-6658	207	1	+	+	CCONJ
ejpam-6658	207	2	r1	r1	PROPN
ejpam-6658	207	3	∞∑	∞∑	PROPN
ejpam-6658	207	4	n=0	n=0	NUM
ejpam-6658	207	5	psrn(r1	psrn(r1	NOUN
ejpam-6658	207	6	,	,	PUNCT
ejpam-6658	207	7	r2	r2	PROPN
ejpam-6658	207	8	,	,	PUNCT
ejpam-6658	207	9	r3	r3	PROPN
ejpam-6658	207	10	)	)	PUNCT
ejpam-6658	207	11	tn	tn	PROPN
ejpam-6658	207	12	n	n	CCONJ
ejpam-6658	207	13	!	!	PUNCT
ejpam-6658	208	1	+	+	CCONJ
ejpam-6658	208	2	(	(	PUNCT
ejpam-6658	208	3	∞∑	∞∑	DET
ejpam-6658	208	4	n=0	n=0	NUM
ejpam-6658	208	5	rn+1	rn+1	NUM
ejpam-6658	208	6	3	3	NUM
ejpam-6658	208	7	(	(	PUNCT
ejpam-6658	208	8	n+	n+	NUM
ejpam-6658	208	9	1)tn	1)tn	NUM
ejpam-6658	208	10	(	(	PUNCT
ejpam-6658	208	11	[	[	X
ejpam-6658	208	12	n+	n+	ADJ
ejpam-6658	208	13	1]!)2	1]!)2	NUM
ejpam-6658	208	14	)	)	PUNCT
ejpam-6658	208	15	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	208	16	,	,	PUNCT
ejpam-6658	208	17	t	t	PROPN
ejpam-6658	208	18	)	)	PUNCT
ejpam-6658	208	19	.	.	PUNCT
ejpam-6658	209	1	(	(	PUNCT
ejpam-6658	209	2	42	42	X
ejpam-6658	209	3	)	)	PUNCT
ejpam-6658	209	4	taking	take	VERB
ejpam-6658	209	5	the	the	DET
ejpam-6658	209	6	derivative	derivative	NOUN
ejpam-6658	209	7	of	of	ADP
ejpam-6658	209	8	both	both	DET
ejpam-6658	209	9	sides	side	NOUN
ejpam-6658	209	10	of	of	ADP
ejpam-6658	209	11	the	the	DET
ejpam-6658	209	12	last	last	ADJ
ejpam-6658	209	13	equation	equation	NOUN
ejpam-6658	209	14	with	with	ADP
ejpam-6658	209	15	respect	respect	NOUN
ejpam-6658	209	16	to	to	ADP
ejpam-6658	209	17	r3	r3	PROPN
ejpam-6658	209	18	,	,	PUNCT
ejpam-6658	209	19	we	we	PRON
ejpam-6658	209	20	get	get	VERB
ejpam-6658	209	21	∞∑	∞∑	NUM
ejpam-6658	209	22	n=0	n=0	PROPN
ejpam-6658	209	23	dr3	dr3	PROPN
ejpam-6658	209	24	{	{	PUNCT
ejpam-6658	209	25	plrn+1(r1	plrn+1(r1	PROPN
ejpam-6658	209	26	,	,	PUNCT
ejpam-6658	209	27	r2	r2	PROPN
ejpam-6658	209	28	,	,	PUNCT
ejpam-6658	209	29	r3	r3	PROPN
ejpam-6658	209	30	)	)	PUNCT
ejpam-6658	209	31	]	]	PUNCT
ejpam-6658	209	32	tn	tn	PROPN
ejpam-6658	209	33	n	n	PROPN
ejpam-6658	209	34	!	!	PUNCT
ejpam-6658	210	1	=	=	NOUN
ejpam-6658	211	1	∞∑	∞∑	PRON
ejpam-6658	211	2	n=0	n=0	NUM
ejpam-6658	211	3	n∑	n∑	NOUN
ejpam-6658	211	4	k=0	k=0	PROPN
ejpam-6658	211	5	(	(	PUNCT
ejpam-6658	211	6	n	n	X
ejpam-6658	211	7	k	k	PROPN
ejpam-6658	211	8	)	)	PUNCT
ejpam-6658	211	9	dr3	dr3	PROPN
ejpam-6658	211	10	{	{	PUNCT
ejpam-6658	211	11	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	211	12	,	,	PUNCT
ejpam-6658	211	13	r2	r2	PROPN
ejpam-6658	211	14	,	,	PUNCT
ejpam-6658	211	15	r3	r3	PROPN
ejpam-6658	211	16	)	)	PUNCT
ejpam-6658	211	17	}	}	PUNCT
ejpam-6658	211	18	γk	γk	PROPN
ejpam-6658	211	19	tn	tn	PROPN
ejpam-6658	211	20	n	n	PROPN
ejpam-6658	211	21	!	!	PUNCT
ejpam-6658	211	22	w.	w.	PROPN
ejpam-6658	211	23	a.	a.	PROPN
ejpam-6658	211	24	khan	khan	PROPN
ejpam-6658	211	25	,	,	PUNCT
ejpam-6658	211	26	h.	h.	PROPN
ejpam-6658	211	27	qawaqneh	qawaqneh	PROPN
ejpam-6658	211	28	,	,	PUNCT
ejpam-6658	211	29	h.	h.	PROPN
ejpam-6658	211	30	aydi	aydi	VERB
ejpam-6658	211	31	/	/	SYM
ejpam-6658	211	32	eur	eur	NOUN
ejpam-6658	211	33	.	.	PUNCT
ejpam-6658	212	1	j.	j.	PROPN
ejpam-6658	212	2	pure	pure	PROPN
ejpam-6658	212	3	appl	appl	PROPN
ejpam-6658	212	4	.	.	PROPN
ejpam-6658	212	5	math	math	PROPN
ejpam-6658	212	6	,	,	PUNCT
ejpam-6658	212	7	18	18	NUM
ejpam-6658	212	8	(	(	PUNCT
ejpam-6658	212	9	3	3	NUM
ejpam-6658	212	10	)	)	PUNCT
ejpam-6658	212	11	(	(	PUNCT
ejpam-6658	212	12	2025	2025	NUM
ejpam-6658	212	13	)	)	PUNCT
ejpam-6658	212	14	,	,	PUNCT
ejpam-6658	212	15	6658	6658	NUM
ejpam-6658	212	16	10	10	NUM
ejpam-6658	212	17	of	of	ADP
ejpam-6658	212	18	22	22	NUM
ejpam-6658	212	19	+	+	CCONJ
ejpam-6658	213	1	∞∑	∞∑	NUM
ejpam-6658	213	2	n=0	n=0	NUM
ejpam-6658	213	3	n∑	n∑	NOUN
ejpam-6658	213	4	k=0	k=0	PROPN
ejpam-6658	213	5	(	(	PUNCT
ejpam-6658	213	6	n	n	X
ejpam-6658	213	7	k	k	NOUN
ejpam-6658	213	8	)	)	PUNCT
ejpam-6658	213	9	ρk(r2)dr3	ρk(r2)dr3	PROPN
ejpam-6658	213	10	{	{	PUNCT
ejpam-6658	213	11	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	213	12	,	,	PUNCT
ejpam-6658	213	13	r2	r2	PROPN
ejpam-6658	213	14	,	,	PUNCT
ejpam-6658	213	15	r3	r3	PROPN
ejpam-6658	213	16	)	)	PUNCT
ejpam-6658	213	17	}	}	PUNCT
ejpam-6658	213	18	tn	tn	PROPN
ejpam-6658	213	19	n	n	NOUN
ejpam-6658	213	20	!	!	PUNCT
ejpam-6658	214	1	+	+	CCONJ
ejpam-6658	214	2	r1	r1	PROPN
ejpam-6658	214	3	∞∑	∞∑	PROPN
ejpam-6658	214	4	n=0	n=0	PROPN
ejpam-6658	214	5	dr3	dr3	PROPN
ejpam-6658	214	6	{	{	PUNCT
ejpam-6658	214	7	plrn(r1	plrn(r1	NOUN
ejpam-6658	214	8	,	,	PUNCT
ejpam-6658	214	9	r2	r2	PROPN
ejpam-6658	214	10	,	,	PUNCT
ejpam-6658	214	11	r3	r3	PROPN
ejpam-6658	214	12	)	)	PUNCT
ejpam-6658	214	13	}	}	PUNCT
ejpam-6658	214	14	tn	tn	PROPN
ejpam-6658	214	15	n	n	NOUN
ejpam-6658	214	16	!	!	PUNCT
ejpam-6658	215	1	−n	−n	PROPN
ejpam-6658	215	2	∞∑	∞∑	ADJ
ejpam-6658	215	3	n=0	n=0	PUNCT
ejpam-6658	215	4	plrn−1(r1	plrn−1(r1	NOUN
ejpam-6658	215	5	,	,	PUNCT
ejpam-6658	215	6	r2	r2	PROPN
ejpam-6658	215	7	,	,	PUNCT
ejpam-6658	215	8	r3	r3	PROPN
ejpam-6658	215	9	)	)	PUNCT
ejpam-6658	215	10	tn	tn	PROPN
ejpam-6658	215	11	n	n	PROPN
ejpam-6658	215	12	!	!	PUNCT
ejpam-6658	215	13	.	.	PUNCT
ejpam-6658	216	1	(	(	PUNCT
ejpam-6658	216	2	43	43	X
ejpam-6658	216	3	)	)	PUNCT
ejpam-6658	216	4	applying	apply	VERB
ejpam-6658	216	5	d−1	d−1	PROPN
ejpam-6658	216	6	r3	r3	PROPN
ejpam-6658	216	7	to	to	ADP
ejpam-6658	216	8	both	both	DET
ejpam-6658	216	9	sides	side	NOUN
ejpam-6658	216	10	of	of	ADP
ejpam-6658	216	11	the	the	DET
ejpam-6658	216	12	above	above	ADJ
ejpam-6658	216	13	equation	equation	NOUN
ejpam-6658	216	14	,	,	PUNCT
ejpam-6658	216	15	we	we	PRON
ejpam-6658	216	16	get	get	VERB
ejpam-6658	216	17	∞∑	∞∑	NUM
ejpam-6658	216	18	n=0	n=0	NUM
ejpam-6658	216	19	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	216	20	,	,	PUNCT
ejpam-6658	216	21	r2	r2	PROPN
ejpam-6658	216	22	,	,	PUNCT
ejpam-6658	216	23	r3	r3	PROPN
ejpam-6658	216	24	)	)	PUNCT
ejpam-6658	216	25	tn	tn	PROPN
ejpam-6658	216	26	n	n	PROPN
ejpam-6658	216	27	!	!	PUNCT
ejpam-6658	217	1	=	=	NOUN
ejpam-6658	218	1	∞∑	∞∑	PRON
ejpam-6658	218	2	n=0	n=0	NUM
ejpam-6658	218	3	n∑	n∑	NOUN
ejpam-6658	218	4	k=0	k=0	PROPN
ejpam-6658	218	5	(	(	PUNCT
ejpam-6658	218	6	n	n	X
ejpam-6658	218	7	k	k	PROPN
ejpam-6658	218	8	)	)	PUNCT
ejpam-6658	218	9	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	218	10	,	,	PUNCT
ejpam-6658	218	11	r2	r2	PROPN
ejpam-6658	218	12	,	,	PUNCT
ejpam-6658	218	13	r3)γk	r3)γk	PROPN
ejpam-6658	218	14	tn	tn	PROPN
ejpam-6658	218	15	n	n	CCONJ
ejpam-6658	218	16	!	!	PUNCT
ejpam-6658	219	1	+	+	CCONJ
ejpam-6658	219	2	∞∑	∞∑	NUM
ejpam-6658	219	3	n=0	n=0	NUM
ejpam-6658	219	4	n∑	n∑	NOUN
ejpam-6658	219	5	k=0	k=0	PROPN
ejpam-6658	219	6	(	(	PUNCT
ejpam-6658	219	7	n	n	X
ejpam-6658	219	8	k	k	PROPN
ejpam-6658	219	9	)	)	PUNCT
ejpam-6658	220	1	ρk(r2)plrn−k(r1	ρk(r2)plrn−k(r1	PROPN
ejpam-6658	220	2	,	,	PUNCT
ejpam-6658	220	3	r2	r2	PROPN
ejpam-6658	220	4	,	,	PUNCT
ejpam-6658	220	5	r3	r3	PROPN
ejpam-6658	220	6	)	)	PUNCT
ejpam-6658	220	7	tn	tn	PROPN
ejpam-6658	220	8	n	n	CCONJ
ejpam-6658	220	9	!	!	PUNCT
ejpam-6658	221	1	+	+	CCONJ
ejpam-6658	221	2	r1	r1	PROPN
ejpam-6658	221	3	∞∑	∞∑	PRON
ejpam-6658	221	4	n=0	n=0	NUM
ejpam-6658	221	5	plrn(r1	plrn(r1	NOUN
ejpam-6658	221	6	,	,	PUNCT
ejpam-6658	221	7	r2	r2	PROPN
ejpam-6658	221	8	,	,	PUNCT
ejpam-6658	221	9	r3	r3	PROPN
ejpam-6658	221	10	)	)	PUNCT
ejpam-6658	221	11	tn	tn	PROPN
ejpam-6658	221	12	n	n	PROPN
ejpam-6658	221	13	!	!	PUNCT
ejpam-6658	222	1	−	−	PROPN
ejpam-6658	223	1	n	n	PRON
ejpam-6658	223	2	∞∑	∞∑	PROPN
ejpam-6658	223	3	n=0	n=0	PROPN
ejpam-6658	223	4	d−1	d−1	PROPN
ejpam-6658	223	5	r3	r3	PROPN
ejpam-6658	223	6	plrn−1(r1	plrn−1(r1	NOUN
ejpam-6658	223	7	,	,	PUNCT
ejpam-6658	223	8	r2	r2	PROPN
ejpam-6658	223	9	,	,	PUNCT
ejpam-6658	223	10	r3	r3	PROPN
ejpam-6658	223	11	)	)	PUNCT
ejpam-6658	223	12	tn	tn	PROPN
ejpam-6658	223	13	n	n	PROPN
ejpam-6658	223	14	!	!	PUNCT
ejpam-6658	223	15	.	.	PUNCT
ejpam-6658	224	1	(	(	PUNCT
ejpam-6658	224	2	44	44	NUM
ejpam-6658	224	3	)	)	PUNCT
ejpam-6658	224	4	thus	thus	ADV
ejpam-6658	224	5	,	,	PUNCT
ejpam-6658	224	6	equating	equate	VERB
ejpam-6658	224	7	the	the	DET
ejpam-6658	224	8	coefficients	coefficient	NOUN
ejpam-6658	224	9	of	of	ADP
ejpam-6658	224	10	tn	tn	NOUN
ejpam-6658	224	11	n	n	X
ejpam-6658	224	12	!	!	PUNCT
ejpam-6658	225	1	on	on	ADP
ejpam-6658	225	2	both	both	DET
ejpam-6658	225	3	sides	side	NOUN
ejpam-6658	225	4	of	of	ADP
ejpam-6658	225	5	the	the	DET
ejpam-6658	225	6	above	above	ADJ
ejpam-6658	225	7	equation	equation	NOUN
ejpam-6658	225	8	(	(	PUNCT
ejpam-6658	225	9	44	44	NUM
ejpam-6658	225	10	)	)	PUNCT
ejpam-6658	225	11	,	,	PUNCT
ejpam-6658	225	12	we	we	PRON
ejpam-6658	225	13	get	get	VERB
ejpam-6658	225	14	assertion	assertion	NOUN
ejpam-6658	225	15	(	(	PUNCT
ejpam-6658	225	16	38	38	NUM
ejpam-6658	225	17	)	)	PUNCT
ejpam-6658	225	18	.	.	PUNCT
ejpam-6658	226	1	theorem	theorem	ADJ
ejpam-6658	226	2	4	4	NUM
ejpam-6658	226	3	.	.	PUNCT
ejpam-6658	227	1	the	the	DET
ejpam-6658	227	2	generalized	generalize	VERB
ejpam-6658	227	3	laguerre	laguerre	NOUN
ejpam-6658	227	4	-	-	PUNCT
ejpam-6658	227	5	based	base	VERB
ejpam-6658	227	6	appell	appell	NOUN
ejpam-6658	227	7	polynomials	polynomial	NOUN
ejpam-6658	227	8	plrn(r1	plrn(r1	NOUN
ejpam-6658	227	9	,	,	PUNCT
ejpam-6658	227	10	r2	r2	PROPN
ejpam-6658	227	11	,	,	PUNCT
ejpam-6658	227	12	r3	r3	PROPN
ejpam-6658	227	13	)	)	PUNCT
ejpam-6658	227	14	satisfy	satisfy	VERB
ejpam-6658	227	15	the	the	DET
ejpam-6658	227	16	multiplicative	multiplicative	ADJ
ejpam-6658	227	17	and	and	CCONJ
ejpam-6658	227	18	derivative	derivative	ADJ
ejpam-6658	227	19	operators	operator	NOUN
ejpam-6658	227	20	as	as	SCONJ
ejpam-6658	227	21	follows	follow	VERB
ejpam-6658	227	22	:	:	PUNCT
ejpam-6658	227	23	m̂	m̂	PROPN
ejpam-6658	227	24	=	=	SYM
ejpam-6658	227	25	r1	r1	PROPN
ejpam-6658	227	26	+	+	CCONJ
ejpam-6658	227	27	r′(d̂r1	r′(d̂r1	PROPN
ejpam-6658	227	28	)	)	PUNCT
ejpam-6658	227	29	r(d̂r1	r(d̂r1	PROPN
ejpam-6658	227	30	)	)	PUNCT
ejpam-6658	228	1	+	+	NUM
ejpam-6658	228	2	ψ	ψ	X
ejpam-6658	228	3	′	′	NUM
ejpam-6658	228	4	(	(	PUNCT
ejpam-6658	228	5	r2	r2	PROPN
ejpam-6658	228	6	,	,	PUNCT
ejpam-6658	228	7	d̂r1	d̂r1	PROPN
ejpam-6658	228	8	)	)	PUNCT
ejpam-6658	228	9	ψ(r2	ψ(r2	NOUN
ejpam-6658	228	10	,	,	PUNCT
ejpam-6658	228	11	d̂r1	d̂r1	PROPN
ejpam-6658	228	12	)	)	PUNCT
ejpam-6658	229	1	−	−	PROPN
ejpam-6658	229	2	nd−1	nd−1	PROPN
ejpam-6658	229	3	r3	r3	PROPN
ejpam-6658	229	4	,	,	PUNCT
ejpam-6658	229	5	(	(	PUNCT
ejpam-6658	229	6	45	45	NUM
ejpam-6658	229	7	)	)	PUNCT
ejpam-6658	229	8	and	and	CCONJ
ejpam-6658	229	9	p̂	p̂	X
ejpam-6658	230	1	=	=	SYM
ejpam-6658	230	2	dr1	dr1	PROPN
ejpam-6658	230	3	,	,	PUNCT
ejpam-6658	230	4	(	(	PUNCT
ejpam-6658	230	5	46	46	NUM
ejpam-6658	230	6	)	)	PUNCT
ejpam-6658	230	7	respectively	respectively	ADV
ejpam-6658	230	8	.	.	PUNCT
ejpam-6658	231	1	proof	proof	NOUN
ejpam-6658	231	2	.	.	PUNCT
ejpam-6658	232	1	taking	take	VERB
ejpam-6658	232	2	the	the	DET
ejpam-6658	232	3	derivative	derivative	NOUN
ejpam-6658	232	4	with	with	ADP
ejpam-6658	232	5	respect	respect	NOUN
ejpam-6658	232	6	to	to	ADP
ejpam-6658	232	7	t	t	PROPN
ejpam-6658	232	8	on	on	ADP
ejpam-6658	232	9	both	both	DET
ejpam-6658	232	10	sides	side	NOUN
ejpam-6658	232	11	of	of	ADP
ejpam-6658	232	12	(	(	PUNCT
ejpam-6658	232	13	36	36	NUM
ejpam-6658	232	14	)	)	PUNCT
ejpam-6658	232	15	,	,	PUNCT
ejpam-6658	232	16	we	we	PRON
ejpam-6658	232	17	have	have	VERB
ejpam-6658	232	18	∞∑	∞∑	NUM
ejpam-6658	232	19	n=0	n=0	NUM
ejpam-6658	232	20	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	232	21	,	,	PUNCT
ejpam-6658	232	22	r2	r2	PROPN
ejpam-6658	232	23	,	,	PUNCT
ejpam-6658	232	24	r3	r3	PROPN
ejpam-6658	232	25	)	)	PUNCT
ejpam-6658	232	26	tn	tn	PROPN
ejpam-6658	232	27	n	n	PROPN
ejpam-6658	232	28	!	!	PUNCT
ejpam-6658	233	1	=	=	PUNCT
ejpam-6658	234	1	r′(t	r′(t	ADJ
ejpam-6658	234	2	)	)	PUNCT
ejpam-6658	234	3	r(t	r(t	NOUN
ejpam-6658	234	4	)	)	PUNCT
ejpam-6658	234	5	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	234	6	,	,	PUNCT
ejpam-6658	234	7	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	234	8	t	t	PROPN
ejpam-6658	234	9	)	)	PUNCT
ejpam-6658	235	1	+	+	NUM
ejpam-6658	235	2	r1r(t)er1tψ(r2	r1r(t)er1tψ(r2	NOUN
ejpam-6658	235	3	,	,	PUNCT
ejpam-6658	235	4	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	235	5	t	t	PROPN
ejpam-6658	235	6	)	)	PUNCT
ejpam-6658	236	1	+	+	NUM
ejpam-6658	236	2	ψ	ψ	X
ejpam-6658	236	3	′	′	NUM
ejpam-6658	236	4	(	(	PUNCT
ejpam-6658	236	5	r2	r2	PROPN
ejpam-6658	236	6	,	,	PUNCT
ejpam-6658	236	7	t	t	PROPN
ejpam-6658	236	8	)	)	PUNCT
ejpam-6658	236	9	ψ(r2	ψ(r2	NOUN
ejpam-6658	236	10	,	,	PUNCT
ejpam-6658	236	11	t	t	NOUN
ejpam-6658	236	12	)	)	PUNCT
ejpam-6658	236	13	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	236	14	,	,	PUNCT
ejpam-6658	236	15	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	236	16	t	t	PROPN
ejpam-6658	236	17	)	)	PUNCT
ejpam-6658	237	1	+	+	CCONJ
ejpam-6658	237	2	(	(	PUNCT
ejpam-6658	237	3	∞∑	∞∑	NUM
ejpam-6658	237	4	n=0	n=0	NUM
ejpam-6658	237	5	(	(	PUNCT
ejpam-6658	237	6	−1)nrn3nt	−1)nrn3nt	PROPN
ejpam-6658	237	7	n−1	n−1	PROPN
ejpam-6658	237	8	(	(	PUNCT
ejpam-6658	237	9	[	[	X
ejpam-6658	237	10	n]!)2	n]!)2	NOUN
ejpam-6658	237	11	)	)	PUNCT
ejpam-6658	237	12	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	237	13	,	,	PUNCT
ejpam-6658	237	14	t	t	PROPN
ejpam-6658	237	15	)	)	PUNCT
ejpam-6658	237	16	(	(	PUNCT
ejpam-6658	237	17	47	47	NUM
ejpam-6658	237	18	)	)	PUNCT
ejpam-6658	237	19	∞∑	∞∑	PRON
ejpam-6658	237	20	n=0	n=0	NUM
ejpam-6658	237	21	psrn+1(r1	psrn+1(r1	NOUN
ejpam-6658	237	22	,	,	PUNCT
ejpam-6658	237	23	r2	r2	PROPN
ejpam-6658	237	24	,	,	PUNCT
ejpam-6658	237	25	r3	r3	PROPN
ejpam-6658	237	26	)	)	PUNCT
ejpam-6658	237	27	tn	tn	PROPN
ejpam-6658	237	28	n	n	PROPN
ejpam-6658	237	29	!	!	PUNCT
ejpam-6658	237	30	=	=	PUNCT
ejpam-6658	238	1	(	(	PUNCT
ejpam-6658	238	2	r1	r1	NOUN
ejpam-6658	238	3	+	+	CCONJ
ejpam-6658	238	4	r′(t	r′(t	ADJ
ejpam-6658	238	5	)	)	PUNCT
ejpam-6658	238	6	r(t	r(t	NOUN
ejpam-6658	238	7	)	)	PUNCT
ejpam-6658	239	1	+	+	PUNCT
ejpam-6658	239	2	ψ	ψ	X
ejpam-6658	239	3	′	′	NUM
ejpam-6658	239	4	(	(	PUNCT
ejpam-6658	239	5	r2	r2	PROPN
ejpam-6658	239	6	,	,	PUNCT
ejpam-6658	239	7	t	t	PROPN
ejpam-6658	239	8	)	)	PUNCT
ejpam-6658	239	9	ψ(r2	ψ(r2	NOUN
ejpam-6658	239	10	,	,	PUNCT
ejpam-6658	239	11	t	t	PROPN
ejpam-6658	239	12	)	)	PUNCT
ejpam-6658	239	13	)	)	PUNCT
ejpam-6658	240	1	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	240	2	,	,	PUNCT
ejpam-6658	240	3	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	240	4	t	t	PROPN
ejpam-6658	240	5	)	)	PUNCT
ejpam-6658	241	1	+	+	CCONJ
ejpam-6658	241	2	(	(	PUNCT
ejpam-6658	241	3	∞∑	∞∑	NUM
ejpam-6658	241	4	n=0	n=0	NUM
ejpam-6658	241	5	(	(	PUNCT
ejpam-6658	241	6	−1)n+1rn+1	−1)n+1rn+1	ADJ
ejpam-6658	241	7	3	3	NUM
ejpam-6658	241	8	(	(	PUNCT
ejpam-6658	241	9	n+	n+	NUM
ejpam-6658	241	10	1)tn	1)tn	NUM
ejpam-6658	241	11	(	(	PUNCT
ejpam-6658	241	12	[	[	X
ejpam-6658	241	13	n+	n+	ADJ
ejpam-6658	241	14	1]!)2	1]!)2	NUM
ejpam-6658	241	15	)	)	PUNCT
ejpam-6658	241	16	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	241	17	,	,	PUNCT
ejpam-6658	241	18	t	t	PROPN
ejpam-6658	241	19	)	)	PUNCT
ejpam-6658	241	20	.	.	PUNCT
ejpam-6658	242	1	(	(	PUNCT
ejpam-6658	242	2	48	48	NUM
ejpam-6658	242	3	)	)	PUNCT
ejpam-6658	242	4	w.	w.	PROPN
ejpam-6658	242	5	a.	a.	PROPN
ejpam-6658	242	6	khan	khan	PROPN
ejpam-6658	242	7	,	,	PUNCT
ejpam-6658	242	8	h.	h.	PROPN
ejpam-6658	242	9	qawaqneh	qawaqneh	PROPN
ejpam-6658	242	10	,	,	PUNCT
ejpam-6658	242	11	h.	h.	PROPN
ejpam-6658	242	12	aydi	aydi	VERB
ejpam-6658	242	13	/	/	SYM
ejpam-6658	242	14	eur	eur	NOUN
ejpam-6658	242	15	.	.	PUNCT
ejpam-6658	243	1	j.	j.	PROPN
ejpam-6658	243	2	pure	pure	PROPN
ejpam-6658	243	3	appl	appl	PROPN
ejpam-6658	243	4	.	.	PROPN
ejpam-6658	243	5	math	math	PROPN
ejpam-6658	243	6	,	,	PUNCT
ejpam-6658	243	7	18	18	NUM
ejpam-6658	243	8	(	(	PUNCT
ejpam-6658	243	9	3	3	NUM
ejpam-6658	243	10	)	)	PUNCT
ejpam-6658	243	11	(	(	PUNCT
ejpam-6658	243	12	2025	2025	NUM
ejpam-6658	243	13	)	)	PUNCT
ejpam-6658	243	14	,	,	PUNCT
ejpam-6658	243	15	6658	6658	NUM
ejpam-6658	243	16	11	11	NUM
ejpam-6658	243	17	of	of	ADP
ejpam-6658	243	18	22	22	NUM
ejpam-6658	243	19	by	by	ADP
ejpam-6658	243	20	using	use	VERB
ejpam-6658	243	21	equation	equation	NOUN
ejpam-6658	243	22	(	(	PUNCT
ejpam-6658	243	23	36	36	NUM
ejpam-6658	243	24	)	)	PUNCT
ejpam-6658	244	1	,	,	PUNCT
ejpam-6658	244	2	we	we	PRON
ejpam-6658	244	3	get	get	VERB
ejpam-6658	244	4	∞∑	∞∑	NUM
ejpam-6658	244	5	n=0	n=0	NUM
ejpam-6658	244	6	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	244	7	,	,	PUNCT
ejpam-6658	244	8	r2	r2	PROPN
ejpam-6658	244	9	,	,	PUNCT
ejpam-6658	244	10	r3	r3	PROPN
ejpam-6658	244	11	)	)	PUNCT
ejpam-6658	244	12	tn	tn	PROPN
ejpam-6658	244	13	n	n	PROPN
ejpam-6658	244	14	!	!	PUNCT
ejpam-6658	245	1	=	=	PUNCT
ejpam-6658	245	2	(	(	PUNCT
ejpam-6658	245	3	r1	r1	NOUN
ejpam-6658	245	4	+	+	CCONJ
ejpam-6658	245	5	r′(t	r′(t	ADJ
ejpam-6658	245	6	)	)	PUNCT
ejpam-6658	245	7	r(t	r(t	NOUN
ejpam-6658	245	8	)	)	PUNCT
ejpam-6658	246	1	+	+	PUNCT
ejpam-6658	246	2	ψ	ψ	X
ejpam-6658	246	3	′	′	NUM
ejpam-6658	246	4	(	(	PUNCT
ejpam-6658	246	5	r2	r2	PROPN
ejpam-6658	246	6	,	,	PUNCT
ejpam-6658	246	7	t	t	PROPN
ejpam-6658	246	8	)	)	PUNCT
ejpam-6658	246	9	ψ(r2	ψ(r2	NOUN
ejpam-6658	246	10	,	,	PUNCT
ejpam-6658	246	11	t	t	PROPN
ejpam-6658	246	12	)	)	PUNCT
ejpam-6658	246	13	)	)	PUNCT
ejpam-6658	247	1	∞∑	∞∑	PRON
ejpam-6658	247	2	n=0	n=0	NUM
ejpam-6658	247	3	plrn(r1	plrn(r1	NOUN
ejpam-6658	247	4	,	,	PUNCT
ejpam-6658	247	5	r2	r2	PROPN
ejpam-6658	247	6	,	,	PUNCT
ejpam-6658	247	7	r3	r3	PROPN
ejpam-6658	247	8	)	)	PUNCT
ejpam-6658	247	9	tn	tn	PROPN
ejpam-6658	247	10	n	n	CCONJ
ejpam-6658	247	11	!	!	PUNCT
ejpam-6658	248	1	+	+	CCONJ
ejpam-6658	248	2	(	(	PUNCT
ejpam-6658	248	3	∞∑	∞∑	NUM
ejpam-6658	248	4	n=0	n=0	NUM
ejpam-6658	248	5	(	(	PUNCT
ejpam-6658	248	6	−1)n+1rn+1	−1)n+1rn+1	ADJ
ejpam-6658	248	7	3	3	NUM
ejpam-6658	248	8	(	(	PUNCT
ejpam-6658	248	9	n+	n+	NUM
ejpam-6658	248	10	1)tn	1)tn	NUM
ejpam-6658	248	11	(	(	PUNCT
ejpam-6658	248	12	[	[	X
ejpam-6658	248	13	n+	n+	ADJ
ejpam-6658	248	14	1]!)2	1]!)2	NUM
ejpam-6658	248	15	)	)	PUNCT
ejpam-6658	248	16	r(t)er1tψ(r2	r(t)er1tψ(r2	PROPN
ejpam-6658	248	17	,	,	PUNCT
ejpam-6658	248	18	t	t	PROPN
ejpam-6658	248	19	)	)	PUNCT
ejpam-6658	248	20	.	.	PUNCT
ejpam-6658	249	1	(	(	PUNCT
ejpam-6658	249	2	49	49	X
ejpam-6658	249	3	)	)	PUNCT
ejpam-6658	249	4	taking	take	VERB
ejpam-6658	249	5	the	the	DET
ejpam-6658	249	6	derivative	derivative	NOUN
ejpam-6658	249	7	of	of	ADP
ejpam-6658	249	8	both	both	DET
ejpam-6658	249	9	sides	side	NOUN
ejpam-6658	249	10	of	of	ADP
ejpam-6658	249	11	the	the	DET
ejpam-6658	249	12	last	last	ADJ
ejpam-6658	249	13	equation	equation	NOUN
ejpam-6658	249	14	with	with	ADP
ejpam-6658	249	15	respect	respect	NOUN
ejpam-6658	249	16	to	to	ADP
ejpam-6658	249	17	r3	r3	PROPN
ejpam-6658	249	18	,	,	PUNCT
ejpam-6658	249	19	we	we	PRON
ejpam-6658	249	20	get	get	VERB
ejpam-6658	249	21	∞∑	∞∑	PRON
ejpam-6658	249	22	n=0	n=0	ADJ
ejpam-6658	249	23	dr3plrn+1(r1	dr3plrn+1(r1	NOUN
ejpam-6658	249	24	,	,	PUNCT
ejpam-6658	249	25	r2	r2	PROPN
ejpam-6658	249	26	,	,	PUNCT
ejpam-6658	249	27	r3	r3	PROPN
ejpam-6658	249	28	)	)	PUNCT
ejpam-6658	249	29	tn	tn	PROPN
ejpam-6658	249	30	n	n	PROPN
ejpam-6658	249	31	!	!	PUNCT
ejpam-6658	250	1	=	=	PUNCT
ejpam-6658	250	2	(	(	PUNCT
ejpam-6658	250	3	r1	r1	NOUN
ejpam-6658	250	4	+	+	CCONJ
ejpam-6658	250	5	r′(t	r′(t	ADJ
ejpam-6658	250	6	)	)	PUNCT
ejpam-6658	250	7	r(t	r(t	NOUN
ejpam-6658	250	8	)	)	PUNCT
ejpam-6658	251	1	+	+	PUNCT
ejpam-6658	251	2	ψ	ψ	X
ejpam-6658	251	3	′	′	NUM
ejpam-6658	251	4	(	(	PUNCT
ejpam-6658	251	5	r2	r2	PROPN
ejpam-6658	251	6	,	,	PUNCT
ejpam-6658	251	7	t	t	PROPN
ejpam-6658	251	8	)	)	PUNCT
ejpam-6658	251	9	ψ(r2	ψ(r2	NOUN
ejpam-6658	251	10	,	,	PUNCT
ejpam-6658	251	11	t	t	PROPN
ejpam-6658	251	12	)	)	PUNCT
ejpam-6658	251	13	)	)	PUNCT
ejpam-6658	252	1	∞∑	∞∑	PRON
ejpam-6658	252	2	n=0	n=0	NUM
ejpam-6658	252	3	dr3plrn(r1	dr3plrn(r1	NOUN
ejpam-6658	252	4	,	,	PUNCT
ejpam-6658	252	5	r2	r2	PROPN
ejpam-6658	252	6	,	,	PUNCT
ejpam-6658	252	7	r3	r3	PROPN
ejpam-6658	252	8	)	)	PUNCT
ejpam-6658	252	9	tn	tn	PROPN
ejpam-6658	252	10	n	n	PROPN
ejpam-6658	252	11	!	!	PUNCT
ejpam-6658	253	1	−n	−n	PROPN
ejpam-6658	253	2	∞∑	∞∑	PRON
ejpam-6658	253	3	n=0	n=0	NUM
ejpam-6658	253	4	plrn(r1	plrn(r1	NOUN
ejpam-6658	253	5	,	,	PUNCT
ejpam-6658	253	6	r2	r2	PROPN
ejpam-6658	253	7	,	,	PUNCT
ejpam-6658	253	8	r3	r3	PROPN
ejpam-6658	253	9	)	)	PUNCT
ejpam-6658	253	10	tn	tn	PROPN
ejpam-6658	253	11	n	n	PROPN
ejpam-6658	253	12	!	!	PUNCT
ejpam-6658	253	13	.	.	PUNCT
ejpam-6658	254	1	(	(	PUNCT
ejpam-6658	254	2	50	50	X
ejpam-6658	254	3	)	)	PUNCT
ejpam-6658	254	4	applying	apply	VERB
ejpam-6658	254	5	d−1	d−1	PROPN
ejpam-6658	254	6	r3	r3	PROPN
ejpam-6658	254	7	to	to	ADP
ejpam-6658	254	8	both	both	DET
ejpam-6658	254	9	sides	side	NOUN
ejpam-6658	254	10	of	of	ADP
ejpam-6658	254	11	the	the	DET
ejpam-6658	254	12	above	above	ADJ
ejpam-6658	254	13	equation	equation	NOUN
ejpam-6658	254	14	,	,	PUNCT
ejpam-6658	254	15	we	we	PRON
ejpam-6658	254	16	get	get	VERB
ejpam-6658	254	17	∞∑	∞∑	NUM
ejpam-6658	254	18	n=0	n=0	NUM
ejpam-6658	254	19	plrn+1(r1	plrn+1(r1	NOUN
ejpam-6658	254	20	,	,	PUNCT
ejpam-6658	254	21	r2	r2	PROPN
ejpam-6658	254	22	,	,	PUNCT
ejpam-6658	254	23	r3	r3	PROPN
ejpam-6658	254	24	)	)	PUNCT
ejpam-6658	254	25	tn	tn	PROPN
ejpam-6658	254	26	n	n	PROPN
ejpam-6658	254	27	!	!	PUNCT
ejpam-6658	255	1	=	=	NOUN
ejpam-6658	256	1	∞∑	∞∑	PRON
ejpam-6658	256	2	n=0	n=0	NUM
ejpam-6658	256	3	(	(	PUNCT
ejpam-6658	256	4	r1	r1	NOUN
ejpam-6658	256	5	+	+	CCONJ
ejpam-6658	256	6	r′(t	r′(t	ADJ
ejpam-6658	256	7	)	)	PUNCT
ejpam-6658	256	8	r(t	r(t	NOUN
ejpam-6658	256	9	)	)	PUNCT
ejpam-6658	257	1	+	+	PUNCT
ejpam-6658	257	2	ψ	ψ	X
ejpam-6658	257	3	′	′	NUM
ejpam-6658	257	4	(	(	PUNCT
ejpam-6658	257	5	r2	r2	PROPN
ejpam-6658	257	6	,	,	PUNCT
ejpam-6658	257	7	t	t	PROPN
ejpam-6658	257	8	)	)	PUNCT
ejpam-6658	257	9	ψ(r2	ψ(r2	NOUN
ejpam-6658	257	10	,	,	PUNCT
ejpam-6658	257	11	t	t	PROPN
ejpam-6658	257	12	)	)	PUNCT
ejpam-6658	257	13	−	−	PROPN
ejpam-6658	257	14	nd−1	nd−1	PROPN
ejpam-6658	257	15	r3	r3	PROPN
ejpam-6658	257	16	)	)	PUNCT
ejpam-6658	257	17	plrn(r1	plrn(r1	NOUN
ejpam-6658	257	18	,	,	PUNCT
ejpam-6658	257	19	r2	r2	PROPN
ejpam-6658	257	20	,	,	PUNCT
ejpam-6658	257	21	r3	r3	PROPN
ejpam-6658	257	22	)	)	PUNCT
ejpam-6658	257	23	tn	tn	PROPN
ejpam-6658	257	24	n	n	PROPN
ejpam-6658	257	25	!	!	PUNCT
ejpam-6658	257	26	.	.	PUNCT
ejpam-6658	258	1	(	(	PUNCT
ejpam-6658	258	2	51	51	NUM
ejpam-6658	258	3	)	)	PUNCT
ejpam-6658	258	4	in	in	ADP
ejpam-6658	258	5	view	view	NOUN
ejpam-6658	258	6	of	of	ADP
ejpam-6658	258	7	(	(	PUNCT
ejpam-6658	258	8	16	16	NUM
ejpam-6658	258	9	)	)	PUNCT
ejpam-6658	258	10	and	and	CCONJ
ejpam-6658	258	11	(	(	PUNCT
ejpam-6658	258	12	51	51	NUM
ejpam-6658	258	13	)	)	PUNCT
ejpam-6658	258	14	,	,	PUNCT
ejpam-6658	258	15	we	we	PRON
ejpam-6658	258	16	get	get	VERB
ejpam-6658	258	17	the	the	DET
ejpam-6658	258	18	assertion	assertion	NOUN
ejpam-6658	258	19	(	(	PUNCT
ejpam-6658	258	20	45	45	NUM
ejpam-6658	258	21	)	)	PUNCT
ejpam-6658	258	22	.	.	PUNCT
ejpam-6658	259	1	again	again	ADV
ejpam-6658	259	2	in	in	ADP
ejpam-6658	259	3	view	view	NOUN
ejpam-6658	259	4	of	of	ADP
ejpam-6658	259	5	(	(	PUNCT
ejpam-6658	259	6	17	17	NUM
ejpam-6658	259	7	)	)	PUNCT
ejpam-6658	259	8	and	and	CCONJ
ejpam-6658	259	9	(	(	PUNCT
ejpam-6658	259	10	36	36	NUM
ejpam-6658	259	11	)	)	PUNCT
ejpam-6658	259	12	,	,	PUNCT
ejpam-6658	259	13	we	we	PRON
ejpam-6658	259	14	get	get	VERB
ejpam-6658	259	15	the	the	DET
ejpam-6658	259	16	assertion	assertion	NOUN
ejpam-6658	259	17	(	(	PUNCT
ejpam-6658	259	18	46	46	NUM
ejpam-6658	259	19	)	)	PUNCT
ejpam-6658	259	20	.	.	PUNCT
ejpam-6658	260	1	theorem	theorem	NOUN
ejpam-6658	260	2	5	5	NUM
ejpam-6658	260	3	.	.	PUNCT
ejpam-6658	261	1	the	the	DET
ejpam-6658	261	2	generalized	generalize	VERB
ejpam-6658	261	3	laguerre	laguerre	NOUN
ejpam-6658	261	4	-	-	PUNCT
ejpam-6658	261	5	based	base	VERB
ejpam-6658	261	6	appell	appell	NOUN
ejpam-6658	261	7	polynomials	polynomial	NOUN
ejpam-6658	261	8	plrn(r1	plrn(r1	NOUN
ejpam-6658	261	9	,	,	PUNCT
ejpam-6658	261	10	r2	r2	PROPN
ejpam-6658	261	11	,	,	PUNCT
ejpam-6658	261	12	r3	r3	PROPN
ejpam-6658	261	13	)	)	PUNCT
ejpam-6658	261	14	satisfies	satisfy	VERB
ejpam-6658	261	15	the	the	DET
ejpam-6658	261	16	differential	differential	ADJ
ejpam-6658	261	17	equation	equation	NOUN
ejpam-6658	261	18	as	as	SCONJ
ejpam-6658	261	19	follows	follow	VERB
ejpam-6658	261	20	:(	:(	PUNCT
ejpam-6658	261	21	r1dr1	r1dr1	NOUN
ejpam-6658	261	22	+	+	CCONJ
ejpam-6658	261	23	r′(d̂r1	r′(d̂r1	PROPN
ejpam-6658	261	24	)	)	PUNCT
ejpam-6658	261	25	r(d̂r1	r(d̂r1	PROPN
ejpam-6658	261	26	)	)	PUNCT
ejpam-6658	262	1	dr1	dr1	PROPN
ejpam-6658	262	2	+	+	NUM
ejpam-6658	262	3	ψ	ψ	X
ejpam-6658	262	4	′	′	NUM
ejpam-6658	262	5	(	(	PUNCT
ejpam-6658	262	6	r2	r2	PROPN
ejpam-6658	262	7	,	,	PUNCT
ejpam-6658	262	8	d̂r1	d̂r1	PROPN
ejpam-6658	262	9	)	)	PUNCT
ejpam-6658	262	10	ψ(r2	ψ(r2	NOUN
ejpam-6658	262	11	,	,	PUNCT
ejpam-6658	262	12	d̂r1	d̂r1	PROPN
ejpam-6658	262	13	)	)	PUNCT
ejpam-6658	263	1	dr1	dr1	PROPN
ejpam-6658	263	2	−	−	PROPN
ejpam-6658	263	3	ndr1d	ndr1d	PROPN
ejpam-6658	263	4	−1	−1	PROPN
ejpam-6658	263	5	r3	r3	PROPN
ejpam-6658	263	6	−	−	PROPN
ejpam-6658	263	7	n	n	CCONJ
ejpam-6658	263	8	)	)	PUNCT
ejpam-6658	263	9	plrn(r1	plrn(r1	NOUN
ejpam-6658	263	10	,	,	PUNCT
ejpam-6658	263	11	r2	r2	PROPN
ejpam-6658	263	12	,	,	PUNCT
ejpam-6658	263	13	r3	r3	PROPN
ejpam-6658	263	14	)	)	PUNCT
ejpam-6658	263	15	=	=	SYM
ejpam-6658	264	1	0	0	X
ejpam-6658	264	2	.	.	PUNCT
ejpam-6658	265	1	(	(	PUNCT
ejpam-6658	265	2	52	52	NUM
ejpam-6658	265	3	)	)	PUNCT
ejpam-6658	265	4	proof	proof	NOUN
ejpam-6658	265	5	.	.	PUNCT
ejpam-6658	266	1	in	in	ADP
ejpam-6658	266	2	view	view	NOUN
ejpam-6658	266	3	of	of	ADP
ejpam-6658	266	4	equations	equation	NOUN
ejpam-6658	266	5	(	(	PUNCT
ejpam-6658	266	6	45	45	NUM
ejpam-6658	266	7	)	)	PUNCT
ejpam-6658	266	8	,	,	PUNCT
ejpam-6658	266	9	(	(	PUNCT
ejpam-6658	266	10	46	46	NUM
ejpam-6658	266	11	)	)	PUNCT
ejpam-6658	266	12	in	in	ADP
ejpam-6658	266	13	(	(	PUNCT
ejpam-6658	266	14	19	19	NUM
ejpam-6658	266	15	)	)	PUNCT
ejpam-6658	266	16	,	,	PUNCT
ejpam-6658	266	17	we	we	PRON
ejpam-6658	266	18	get	get	VERB
ejpam-6658	266	19	the	the	DET
ejpam-6658	266	20	assertion	assertion	NOUN
ejpam-6658	266	21	(	(	PUNCT
ejpam-6658	266	22	52	52	NUM
ejpam-6658	266	23	)	)	PUNCT
ejpam-6658	266	24	.	.	PUNCT
ejpam-6658	267	1	so	so	ADV
ejpam-6658	267	2	,	,	PUNCT
ejpam-6658	267	3	we	we	PRON
ejpam-6658	267	4	omit	omit	VERB
ejpam-6658	267	5	the	the	DET
ejpam-6658	267	6	proof	proof	NOUN
ejpam-6658	267	7	.	.	PUNCT
ejpam-6658	268	1	3	3	X
ejpam-6658	268	2	.	.	X
ejpam-6658	268	3	series	series	NOUN
ejpam-6658	268	4	representation	representation	NOUN
ejpam-6658	268	5	and	and	CCONJ
ejpam-6658	268	6	determinant	determinant	ADJ
ejpam-6658	268	7	form	form	NOUN
ejpam-6658	268	8	hybrid	hybrid	ADJ
ejpam-6658	268	9	special	special	ADJ
ejpam-6658	268	10	polynomials	polynomial	NOUN
ejpam-6658	268	11	play	play	VERB
ejpam-6658	268	12	a	a	DET
ejpam-6658	268	13	crucial	crucial	ADJ
ejpam-6658	268	14	role	role	NOUN
ejpam-6658	268	15	in	in	ADP
ejpam-6658	268	16	mathematical	mathematical	ADJ
ejpam-6658	268	17	analysis	analysis	NOUN
ejpam-6658	268	18	due	due	ADP
ejpam-6658	268	19	to	to	ADP
ejpam-6658	268	20	their	their	PRON
ejpam-6658	268	21	rich	rich	ADJ
ejpam-6658	268	22	structural	structural	ADJ
ejpam-6658	268	23	properties	property	NOUN
ejpam-6658	268	24	.	.	PUNCT
ejpam-6658	269	1	their	their	PRON
ejpam-6658	269	2	series	series	NOUN
ejpam-6658	269	3	representation	representation	NOUN
ejpam-6658	269	4	provides	provide	VERB
ejpam-6658	269	5	explicit	explicit	ADJ
ejpam-6658	269	6	forms	form	NOUN
ejpam-6658	269	7	and	and	CCONJ
ejpam-6658	269	8	recurrence	recurrence	NOUN
ejpam-6658	269	9	relations	relation	NOUN
ejpam-6658	269	10	,	,	PUNCT
ejpam-6658	269	11	aiding	aid	VERB
ejpam-6658	269	12	in	in	ADP
ejpam-6658	269	13	solving	solve	VERB
ejpam-6658	269	14	differential	differential	NOUN
ejpam-6658	269	15	and	and	CCONJ
ejpam-6658	269	16	functional	functional	ADJ
ejpam-6658	269	17	equations	equation	NOUN
ejpam-6658	269	18	.	.	PUNCT
ejpam-6658	270	1	the	the	DET
ejpam-6658	270	2	determinant	determinant	ADJ
ejpam-6658	270	3	form	form	NOUN
ejpam-6658	270	4	of	of	ADP
ejpam-6658	270	5	these	these	DET
ejpam-6658	270	6	polynomials	polynomial	NOUN
ejpam-6658	270	7	offers	offer	VERB
ejpam-6658	270	8	a	a	DET
ejpam-6658	270	9	compact	compact	ADJ
ejpam-6658	270	10	and	and	CCONJ
ejpam-6658	270	11	elegant	elegant	ADJ
ejpam-6658	270	12	way	way	NOUN
ejpam-6658	270	13	to	to	PART
ejpam-6658	270	14	analyze	analyze	VERB
ejpam-6658	270	15	their	their	PRON
ejpam-6658	270	16	algebraic	algebraic	ADJ
ejpam-6658	270	17	and	and	CCONJ
ejpam-6658	270	18	combinatorial	combinatorial	ADJ
ejpam-6658	270	19	properties	property	NOUN
ejpam-6658	270	20	.	.	PUNCT
ejpam-6658	271	1	it	it	PRON
ejpam-6658	271	2	facilitates	facilitate	VERB
ejpam-6658	271	3	the	the	DET
ejpam-6658	271	4	study	study	NOUN
ejpam-6658	271	5	of	of	ADP
ejpam-6658	271	6	orthogonality	orthogonality	NOUN
ejpam-6658	271	7	,	,	PUNCT
ejpam-6658	271	8	symmetry	symmetry	NOUN
ejpam-6658	271	9	,	,	PUNCT
ejpam-6658	271	10	and	and	CCONJ
ejpam-6658	271	11	transformation	transformation	NOUN
ejpam-6658	271	12	identities	identity	NOUN
ejpam-6658	271	13	.	.	PUNCT
ejpam-6658	272	1	hybrid	hybrid	ADJ
ejpam-6658	272	2	polynomials	polynomial	NOUN
ejpam-6658	272	3	also	also	ADV
ejpam-6658	272	4	bridge	bridge	VERB
ejpam-6658	272	5	classical	classical	ADJ
ejpam-6658	272	6	and	and	CCONJ
ejpam-6658	272	7	modern	modern	ADJ
ejpam-6658	272	8	polynomial	polynomial	ADJ
ejpam-6658	272	9	families	family	NOUN
ejpam-6658	272	10	,	,	PUNCT
ejpam-6658	272	11	extending	extend	VERB
ejpam-6658	272	12	their	their	PRON
ejpam-6658	272	13	applicability	applicability	NOUN
ejpam-6658	272	14	in	in	ADP
ejpam-6658	272	15	mathematical	mathematical	ADJ
ejpam-6658	272	16	physics	physics	NOUN
ejpam-6658	272	17	and	and	CCONJ
ejpam-6658	272	18	engineering	engineering	NOUN
ejpam-6658	272	19	.	.	PUNCT
ejpam-6658	273	1	their	their	PRON
ejpam-6658	273	2	determinant	determinant	ADJ
ejpam-6658	273	3	representation	representation	NOUN
ejpam-6658	273	4	helps	help	VERB
ejpam-6658	273	5	in	in	ADP
ejpam-6658	273	6	computing	compute	VERB
ejpam-6658	273	7	higher	high	ADJ
ejpam-6658	273	8	-	-	PUNCT
ejpam-6658	273	9	order	order	NOUN
ejpam-6658	273	10	coefficients	coefficient	NOUN
ejpam-6658	273	11	efficiently	efficiently	ADV
ejpam-6658	273	12	.	.	PUNCT
ejpam-6658	274	1	these	these	DET
ejpam-6658	274	2	polynomials	polynomial	NOUN
ejpam-6658	274	3	are	be	AUX
ejpam-6658	274	4	widely	widely	ADV
ejpam-6658	274	5	used	use	VERB
ejpam-6658	274	6	in	in	ADP
ejpam-6658	274	7	approximation	approximation	NOUN
ejpam-6658	274	8	theory	theory	NOUN
ejpam-6658	274	9	and	and	CCONJ
ejpam-6658	274	10	numerical	numerical	ADJ
ejpam-6658	274	11	analysis	analysis	NOUN
ejpam-6658	274	12	.	.	PUNCT
ejpam-6658	275	1	overall	overall	ADV
ejpam-6658	275	2	,	,	PUNCT
ejpam-6658	275	3	they	they	PRON
ejpam-6658	275	4	contribute	contribute	VERB
ejpam-6658	275	5	significantly	significantly	ADV
ejpam-6658	275	6	to	to	ADP
ejpam-6658	275	7	both	both	CCONJ
ejpam-6658	275	8	theoretical	theoretical	ADJ
ejpam-6658	275	9	and	and	CCONJ
ejpam-6658	275	10	applied	apply	VERB
ejpam-6658	275	11	mathematical	mathematical	ADJ
ejpam-6658	275	12	research	research	NOUN
ejpam-6658	275	13	.	.	PUNCT
ejpam-6658	276	1	w.	w.	PROPN
ejpam-6658	276	2	a.	a.	PROPN
ejpam-6658	276	3	khan	khan	PROPN
ejpam-6658	276	4	,	,	PUNCT
ejpam-6658	276	5	h.	h.	PROPN
ejpam-6658	276	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	276	7	,	,	PUNCT
ejpam-6658	276	8	h.	h.	PROPN
ejpam-6658	276	9	aydi	aydi	VERB
ejpam-6658	276	10	/	/	SYM
ejpam-6658	276	11	eur	eur	NOUN
ejpam-6658	276	12	.	.	PUNCT
ejpam-6658	277	1	j.	j.	PROPN
ejpam-6658	277	2	pure	pure	PROPN
ejpam-6658	277	3	appl	appl	PROPN
ejpam-6658	277	4	.	.	PROPN
ejpam-6658	277	5	math	math	PROPN
ejpam-6658	277	6	,	,	PUNCT
ejpam-6658	277	7	18	18	NUM
ejpam-6658	277	8	(	(	PUNCT
ejpam-6658	277	9	3	3	NUM
ejpam-6658	277	10	)	)	PUNCT
ejpam-6658	277	11	(	(	PUNCT
ejpam-6658	277	12	2025	2025	NUM
ejpam-6658	277	13	)	)	PUNCT
ejpam-6658	277	14	,	,	PUNCT
ejpam-6658	277	15	6658	6658	NUM
ejpam-6658	277	16	12	12	NUM
ejpam-6658	277	17	of	of	ADP
ejpam-6658	277	18	22	22	NUM
ejpam-6658	277	19	theorem	theorem	NOUN
ejpam-6658	277	20	6	6	NUM
ejpam-6658	277	21	.	.	PUNCT
ejpam-6658	278	1	the	the	DET
ejpam-6658	278	2	3	3	NUM
ejpam-6658	278	3	-	-	PUNCT
ejpam-6658	278	4	variable	variable	ADJ
ejpam-6658	278	5	generalized	generalize	VERB
ejpam-6658	278	6	laguerre	laguerre	NOUN
ejpam-6658	278	7	-	-	PUNCT
ejpam-6658	278	8	based	base	VERB
ejpam-6658	278	9	appell	appell	NOUN
ejpam-6658	278	10	polynomials	polynomial	NOUN
ejpam-6658	278	11	plrn(r1	plrn(r1	NOUN
ejpam-6658	278	12	,	,	PUNCT
ejpam-6658	278	13	r2	r2	PROPN
ejpam-6658	278	14	,	,	PUNCT
ejpam-6658	278	15	r3	r3	PROPN
ejpam-6658	278	16	)	)	PUNCT
ejpam-6658	278	17	are	be	AUX
ejpam-6658	278	18	defined	define	VERB
ejpam-6658	278	19	by	by	ADP
ejpam-6658	278	20	the	the	DET
ejpam-6658	278	21	series	series	NOUN
ejpam-6658	278	22	:	:	PUNCT
ejpam-6658	278	23	plrn(r1	plrn(r1	NOUN
ejpam-6658	278	24	,	,	PUNCT
ejpam-6658	278	25	r2	r2	PROPN
ejpam-6658	278	26	,	,	PUNCT
ejpam-6658	278	27	r3	r3	PROPN
ejpam-6658	278	28	)	)	PUNCT
ejpam-6658	279	1	=	=	SYM
ejpam-6658	279	2	n∑	n∑	NOUN
ejpam-6658	279	3	k=0	k=0	PROPN
ejpam-6658	279	4	(	(	PUNCT
ejpam-6658	279	5	n	n	X
ejpam-6658	279	6	k	k	X
ejpam-6658	279	7	)	)	PUNCT
ejpam-6658	279	8	rk	rk	PROPN
ejpam-6658	279	9	pln−k(r1	pln−k(r1	NOUN
ejpam-6658	279	10	,	,	PUNCT
ejpam-6658	279	11	r2	r2	PROPN
ejpam-6658	279	12	,	,	PUNCT
ejpam-6658	279	13	r3	r3	PROPN
ejpam-6658	279	14	)	)	PUNCT
ejpam-6658	279	15	,	,	PUNCT
ejpam-6658	279	16	(	(	PUNCT
ejpam-6658	279	17	53	53	NUM
ejpam-6658	279	18	)	)	PUNCT
ejpam-6658	279	19	with	with	ADP
ejpam-6658	279	20	rk	rk	NOUN
ejpam-6658	279	21	is	be	AUX
ejpam-6658	279	22	given	give	VERB
ejpam-6658	279	23	by	by	ADP
ejpam-6658	279	24	equation	equation	NOUN
ejpam-6658	279	25	(	(	PUNCT
ejpam-6658	279	26	5	5	NUM
ejpam-6658	279	27	)	)	PUNCT
ejpam-6658	279	28	.	.	PUNCT
ejpam-6658	280	1	proof	proof	NOUN
ejpam-6658	280	2	.	.	PUNCT
ejpam-6658	281	1	in	in	ADP
ejpam-6658	281	2	view	view	NOUN
ejpam-6658	281	3	of	of	ADP
ejpam-6658	281	4	equation	equation	NOUN
ejpam-6658	281	5	(	(	PUNCT
ejpam-6658	281	6	36	36	NUM
ejpam-6658	281	7	)	)	PUNCT
ejpam-6658	281	8	,	,	PUNCT
ejpam-6658	281	9	we	we	PRON
ejpam-6658	281	10	can	can	AUX
ejpam-6658	281	11	write	write	VERB
ejpam-6658	281	12	∞∑	∞∑	PRON
ejpam-6658	281	13	υ=0	υ=0	PUNCT
ejpam-6658	281	14	plrn(r1	plrn(r1	NOUN
ejpam-6658	281	15	,	,	PUNCT
ejpam-6658	281	16	r2	r2	PROPN
ejpam-6658	281	17	,	,	PUNCT
ejpam-6658	281	18	r3	r3	PROPN
ejpam-6658	281	19	)	)	PUNCT
ejpam-6658	281	20	tn	tn	PROPN
ejpam-6658	281	21	n	n	PROPN
ejpam-6658	281	22	!	!	PUNCT
ejpam-6658	282	1	=	=	NOUN
ejpam-6658	282	2	r(t	r(t	NOUN
ejpam-6658	282	3	)	)	PUNCT
ejpam-6658	282	4	∞∑	∞∑	PROPN
ejpam-6658	282	5	n=0	n=0	NUM
ejpam-6658	282	6	pln(r1	pln(r1	PROPN
ejpam-6658	282	7	,	,	PUNCT
ejpam-6658	282	8	r2	r2	PROPN
ejpam-6658	282	9	,	,	PUNCT
ejpam-6658	282	10	r3	r3	PROPN
ejpam-6658	282	11	)	)	PUNCT
ejpam-6658	282	12	tn	tn	PROPN
ejpam-6658	282	13	n	n	PROPN
ejpam-6658	282	14	!	!	PUNCT
ejpam-6658	282	15	.	.	PUNCT
ejpam-6658	283	1	(	(	PUNCT
ejpam-6658	283	2	54	54	NUM
ejpam-6658	283	3	)	)	PUNCT
ejpam-6658	283	4	using	use	VERB
ejpam-6658	283	5	the	the	DET
ejpam-6658	283	6	expansion	expansion	NOUN
ejpam-6658	283	7	(	(	PUNCT
ejpam-6658	283	8	5	5	NUM
ejpam-6658	283	9	)	)	PUNCT
ejpam-6658	283	10	of	of	ADP
ejpam-6658	283	11	r(t	r(t	NOUN
ejpam-6658	283	12	)	)	PUNCT
ejpam-6658	283	13	from	from	ADP
ejpam-6658	283	14	the	the	DET
ejpam-6658	283	15	left	left	ADJ
ejpam-6658	283	16	-	-	PUNCT
ejpam-6658	283	17	hand	hand	NOUN
ejpam-6658	283	18	side	side	NOUN
ejpam-6658	283	19	of	of	ADP
ejpam-6658	283	20	equation	equation	NOUN
ejpam-6658	283	21	(	(	PUNCT
ejpam-6658	283	22	54	54	NUM
ejpam-6658	283	23	)	)	PUNCT
ejpam-6658	283	24	,	,	PUNCT
ejpam-6658	283	25	we	we	PRON
ejpam-6658	283	26	simplify	simplify	VERB
ejpam-6658	283	27	and	and	CCONJ
ejpam-6658	283	28	then	then	ADV
ejpam-6658	283	29	equate	equate	VERB
ejpam-6658	283	30	the	the	DET
ejpam-6658	283	31	coefficients	coefficient	NOUN
ejpam-6658	283	32	of	of	ADP
ejpam-6658	283	33	like	like	ADP
ejpam-6658	283	34	powers	power	NOUN
ejpam-6658	283	35	of	of	ADP
ejpam-6658	283	36	δ	δ	PROPN
ejpam-6658	283	37	on	on	ADP
ejpam-6658	283	38	both	both	DET
ejpam-6658	283	39	sides	side	NOUN
ejpam-6658	283	40	of	of	ADP
ejpam-6658	283	41	the	the	DET
ejpam-6658	283	42	resulting	result	VERB
ejpam-6658	283	43	equation	equation	NOUN
ejpam-6658	283	44	,	,	PUNCT
ejpam-6658	283	45	leading	lead	VERB
ejpam-6658	283	46	us	we	PRON
ejpam-6658	283	47	to	to	ADP
ejpam-6658	283	48	assertion	assertion	NOUN
ejpam-6658	283	49	(	(	PUNCT
ejpam-6658	283	50	53	53	NUM
ejpam-6658	283	51	)	)	PUNCT
ejpam-6658	283	52	.	.	PUNCT
ejpam-6658	284	1	theorem	theorem	VERB
ejpam-6658	284	2	7	7	NUM
ejpam-6658	284	3	.	.	PUNCT
ejpam-6658	285	1	the	the	DET
ejpam-6658	285	2	generalized	generalize	VERB
ejpam-6658	285	3	laguerre	laguerre	NOUN
ejpam-6658	285	4	-	-	PUNCT
ejpam-6658	285	5	based	base	VERB
ejpam-6658	285	6	appell	appell	NOUN
ejpam-6658	285	7	polynomials	polynomial	NOUN
ejpam-6658	285	8	plrn(r1	plrn(r1	NOUN
ejpam-6658	285	9	,	,	PUNCT
ejpam-6658	285	10	r2	r2	PROPN
ejpam-6658	285	11	,	,	PUNCT
ejpam-6658	285	12	r3	r3	PROPN
ejpam-6658	285	13	)	)	PUNCT
ejpam-6658	285	14	has	have	VERB
ejpam-6658	285	15	the	the	DET
ejpam-6658	285	16	following	follow	VERB
ejpam-6658	285	17	determinant	determinant	ADJ
ejpam-6658	285	18	representation	representation	NOUN
ejpam-6658	285	19	plrn	plrn	NOUN
ejpam-6658	285	20	,	,	PUNCT
ejpam-6658	285	21	q(r1	q(r1	PROPN
ejpam-6658	285	22	,	,	PUNCT
ejpam-6658	285	23	r2	r2	PROPN
ejpam-6658	285	24	,	,	PUNCT
ejpam-6658	285	25	r3	r3	PROPN
ejpam-6658	285	26	)	)	PUNCT
ejpam-6658	285	27	=	=	PRON
ejpam-6658	285	28	(	(	PUNCT
ejpam-6658	285	29	−1)n	−1)n	X
ejpam-6658	285	30	(	(	PUNCT
ejpam-6658	285	31	β0)n+1	β0)n+1	PROPN
ejpam-6658	285	32	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	ADJ
ejpam-6658	285	33	1	1	NUM
ejpam-6658	285	34	pl1(r1	pl1(r1	NOUN
ejpam-6658	285	35	,	,	PUNCT
ejpam-6658	285	36	r2	r2	PROPN
ejpam-6658	285	37	,	,	PUNCT
ejpam-6658	285	38	r3	r3	PROPN
ejpam-6658	285	39	)	)	PUNCT
ejpam-6658	285	40	pl2(r1	pl2(r1	NOUN
ejpam-6658	285	41	,	,	PUNCT
ejpam-6658	285	42	r2	r2	PROPN
ejpam-6658	285	43	,	,	PUNCT
ejpam-6658	285	44	r3	r3	PROPN
ejpam-6658	285	45	)	)	PUNCT
ejpam-6658	285	46	...	...	PUNCT
ejpam-6658	286	1	pln−1(r1	pln−1(r1	NOUN
ejpam-6658	286	2	,	,	PUNCT
ejpam-6658	286	3	r2	r2	PROPN
ejpam-6658	286	4	,	,	PUNCT
ejpam-6658	286	5	r3	r3	PROPN
ejpam-6658	286	6	)	)	PUNCT
ejpam-6658	286	7	pl(m	pl(m	PROPN
ejpam-6658	286	8	)	)	PUNCT
ejpam-6658	287	1	n	n	CCONJ
ejpam-6658	287	2	(	(	PUNCT
ejpam-6658	287	3	r1	r1	PROPN
ejpam-6658	287	4	,	,	PUNCT
ejpam-6658	287	5	r2	r2	PROPN
ejpam-6658	287	6	,	,	PUNCT
ejpam-6658	287	7	r3	r3	PROPN
ejpam-6658	287	8	)	)	PUNCT
ejpam-6658	287	9	β0	β0	PROPN
ejpam-6658	287	10	β1	β1	PROPN
ejpam-6658	287	11	β2	β2	PROPN
ejpam-6658	287	12	...	...	PUNCT
ejpam-6658	288	1	βn−1	βn−1	ADJ
ejpam-6658	288	2	βn	βn	NOUN
ejpam-6658	288	3	0	0	NUM
ejpam-6658	288	4	β0	β0	NOUN
ejpam-6658	288	5	(	(	PUNCT
ejpam-6658	288	6	2	2	NUM
ejpam-6658	288	7	1	1	NUM
ejpam-6658	288	8	)	)	PUNCT
ejpam-6658	288	9	β1	β1	NOUN
ejpam-6658	288	10	...	...	PUNCT
ejpam-6658	289	1	(	(	PUNCT
ejpam-6658	289	2	n−1	n−1	PROPN
ejpam-6658	289	3	1	1	NUM
ejpam-6658	289	4	)	)	PUNCT
ejpam-6658	289	5	βn−2	βn−2	ADV
ejpam-6658	289	6	(	(	PUNCT
ejpam-6658	289	7	n	n	NOUN
ejpam-6658	289	8	1	1	NUM
ejpam-6658	289	9	)	)	PUNCT
ejpam-6658	289	10	βn−1	βn−1	ADV
ejpam-6658	289	11	0	0	NUM
ejpam-6658	289	12	0	0	NUM
ejpam-6658	289	13	β0	β0	NOUN
ejpam-6658	289	14	...	...	PUNCT
ejpam-6658	290	1	(	(	PUNCT
ejpam-6658	290	2	n−1	n−1	PROPN
ejpam-6658	290	3	1	1	NUM
ejpam-6658	290	4	)	)	PUNCT
ejpam-6658	290	5	βn−3	βn−3	PROPN
ejpam-6658	290	6	(	(	PUNCT
ejpam-6658	290	7	n	n	NOUN
ejpam-6658	290	8	2	2	NUM
ejpam-6658	290	9	)	)	PUNCT
ejpam-6658	290	10	βn−2	βn−2	ADV
ejpam-6658	290	11	...	...	PUNCT
ejpam-6658	290	12	...	...	PUNCT
ejpam-6658	290	13	...	...	PUNCT
ejpam-6658	290	14	...	...	PUNCT
ejpam-6658	290	15	...	...	PUNCT
ejpam-6658	291	1	0	0	NUM
ejpam-6658	291	2	0	0	NUM
ejpam-6658	291	3	0	0	NUM
ejpam-6658	291	4	...	...	PUNCT
ejpam-6658	292	1	β0	β0	NOUN
ejpam-6658	292	2	(	(	PUNCT
ejpam-6658	292	3	n	n	CCONJ
ejpam-6658	292	4	n−1	n−1	PROPN
ejpam-6658	292	5	)	)	PUNCT
ejpam-6658	292	6	β1	β1	PROPN
ejpam-6658	292	7	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	292	8	,	,	PUNCT
ejpam-6658	292	9	(	(	PUNCT
ejpam-6658	292	10	55	55	NUM
ejpam-6658	292	11	)	)	PUNCT
ejpam-6658	292	12	where	where	SCONJ
ejpam-6658	292	13	∑∞	∑∞	NOUN
ejpam-6658	292	14	n=0	n=0	PUNCT
ejpam-6658	292	15	pln(r1	pln(r1	PROPN
ejpam-6658	292	16	,	,	PUNCT
ejpam-6658	292	17	r2	r2	PROPN
ejpam-6658	292	18	,	,	PUNCT
ejpam-6658	292	19	r3	r3	PROPN
ejpam-6658	292	20	)	)	PUNCT
ejpam-6658	292	21	tn	tn	PROPN
ejpam-6658	292	22	n	n	PROPN
ejpam-6658	292	23	!	!	PUNCT
ejpam-6658	293	1	=	=	SYM
ejpam-6658	293	2	er1tψ(r2	er1tψ(r2	PROPN
ejpam-6658	293	3	,	,	PUNCT
ejpam-6658	293	4	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	293	5	t	t	PROPN
ejpam-6658	293	6	)	)	PUNCT
ejpam-6658	293	7	,	,	PUNCT
ejpam-6658	293	8	1	1	NUM
ejpam-6658	293	9	r(t	r(t	NOUN
ejpam-6658	293	10	)	)	PUNCT
ejpam-6658	293	11	=	=	SYM
ejpam-6658	294	1	∑∞	∑∞	NOUN
ejpam-6658	294	2	k=0	k=0	PROPN
ejpam-6658	294	3	βk	βk	ADP
ejpam-6658	294	4	tk	tk	PROPN
ejpam-6658	294	5	k	k	PROPN
ejpam-6658	294	6	!	!	PUNCT
ejpam-6658	294	7	.	.	PUNCT
ejpam-6658	295	1	proof	proof	NOUN
ejpam-6658	295	2	.	.	PUNCT
ejpam-6658	296	1	using	use	VERB
ejpam-6658	296	2	the	the	DET
ejpam-6658	296	3	series	series	NOUN
ejpam-6658	296	4	representation	representation	NOUN
ejpam-6658	296	5	of	of	ADP
ejpam-6658	296	6	1	1	NUM
ejpam-6658	296	7	r(t	r(t	NOUN
ejpam-6658	296	8	)	)	PUNCT
ejpam-6658	296	9	as	as	SCONJ
ejpam-6658	296	10	follows	follow	VERB
ejpam-6658	296	11	:	:	PUNCT
ejpam-6658	296	12	[	[	X
ejpam-6658	296	13	r(t)]−1	r(t)]−1	X
ejpam-6658	296	14	=	=	VERB
ejpam-6658	296	15	∞∑	∞∑	NUM
ejpam-6658	296	16	k=0	k=0	PROPN
ejpam-6658	296	17	βk	βk	ADP
ejpam-6658	296	18	tk	tk	PROPN
ejpam-6658	296	19	k	k	PROPN
ejpam-6658	296	20	!	!	PROPN
ejpam-6658	296	21	,	,	PUNCT
ejpam-6658	296	22	using	use	VERB
ejpam-6658	296	23	the	the	DET
ejpam-6658	296	24	generation	generation	NOUN
ejpam-6658	296	25	function	function	NOUN
ejpam-6658	296	26	(	(	PUNCT
ejpam-6658	296	27	22	22	NUM
ejpam-6658	296	28	)	)	PUNCT
ejpam-6658	296	29	,	,	PUNCT
ejpam-6658	296	30	we	we	PRON
ejpam-6658	296	31	get	get	VERB
ejpam-6658	296	32	er1tψ(r2	er1tψ(r2	NOUN
ejpam-6658	296	33	,	,	PUNCT
ejpam-6658	296	34	t)c0(r3	t)c0(r3	PROPN
ejpam-6658	296	35	t	t	PROPN
ejpam-6658	296	36	)	)	PUNCT
ejpam-6658	296	37	=	=	PUNCT
ejpam-6658	297	1	(	(	PUNCT
ejpam-6658	297	2	∞∑	∞∑	PROPN
ejpam-6658	297	3	k=0	k=0	PROPN
ejpam-6658	297	4	βk	βk	ADP
ejpam-6658	297	5	tk	tk	PROPN
ejpam-6658	297	6	k	k	PROPN
ejpam-6658	297	7	!	!	PUNCT
ejpam-6658	297	8	)	)	PUNCT
ejpam-6658	298	1	(	(	PUNCT
ejpam-6658	298	2	∞∑	∞∑	NUM
ejpam-6658	298	3	n=0	n=0	NUM
ejpam-6658	298	4	plrn(r1	plrn(r1	NOUN
ejpam-6658	298	5	,	,	PUNCT
ejpam-6658	298	6	r2	r2	PROPN
ejpam-6658	298	7	,	,	PUNCT
ejpam-6658	298	8	r3	r3	PROPN
ejpam-6658	298	9	)	)	PUNCT
ejpam-6658	298	10	tn	tn	PROPN
ejpam-6658	298	11	n	n	PROPN
ejpam-6658	298	12	!	!	PUNCT
ejpam-6658	298	13	)	)	PUNCT
ejpam-6658	298	14	.	.	PUNCT
ejpam-6658	299	1	hence	hence	ADV
ejpam-6658	299	2	∞∑	∞∑	NUM
ejpam-6658	299	3	n=0	n=0	NUM
ejpam-6658	299	4	plrn(r1	plrn(r1	NOUN
ejpam-6658	299	5	,	,	PUNCT
ejpam-6658	299	6	r2	r2	PROPN
ejpam-6658	299	7	,	,	PUNCT
ejpam-6658	299	8	r3	r3	PROPN
ejpam-6658	299	9	)	)	PUNCT
ejpam-6658	299	10	tn	tn	PROPN
ejpam-6658	299	11	n	n	PROPN
ejpam-6658	299	12	!	!	PUNCT
ejpam-6658	300	1	=	=	PUNCT
ejpam-6658	301	1	(	(	PUNCT
ejpam-6658	301	2	∞∑	∞∑	PROPN
ejpam-6658	301	3	k=0	k=0	PROPN
ejpam-6658	301	4	βk	βk	ADP
ejpam-6658	301	5	tk	tk	PROPN
ejpam-6658	301	6	k	k	PROPN
ejpam-6658	301	7	!	!	PUNCT
ejpam-6658	301	8	)	)	PUNCT
ejpam-6658	302	1	(	(	PUNCT
ejpam-6658	302	2	∞∑	∞∑	NUM
ejpam-6658	302	3	n=0	n=0	NUM
ejpam-6658	302	4	plrn(r1	plrn(r1	NOUN
ejpam-6658	302	5	,	,	PUNCT
ejpam-6658	302	6	r2	r2	PROPN
ejpam-6658	302	7	,	,	PUNCT
ejpam-6658	302	8	r3	r3	PROPN
ejpam-6658	302	9	)	)	PUNCT
ejpam-6658	302	10	tn	tn	PROPN
ejpam-6658	302	11	n	n	PROPN
ejpam-6658	302	12	!	!	PUNCT
ejpam-6658	302	13	)	)	PUNCT
ejpam-6658	302	14	.	.	PUNCT
ejpam-6658	303	1	w.	w.	PROPN
ejpam-6658	303	2	a.	a.	PROPN
ejpam-6658	303	3	khan	khan	PROPN
ejpam-6658	303	4	,	,	PUNCT
ejpam-6658	303	5	h.	h.	PROPN
ejpam-6658	303	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	303	7	,	,	PUNCT
ejpam-6658	303	8	h.	h.	PROPN
ejpam-6658	303	9	aydi	aydi	VERB
ejpam-6658	303	10	/	/	SYM
ejpam-6658	303	11	eur	eur	NOUN
ejpam-6658	303	12	.	.	PUNCT
ejpam-6658	304	1	j.	j.	PROPN
ejpam-6658	304	2	pure	pure	PROPN
ejpam-6658	304	3	appl	appl	PROPN
ejpam-6658	304	4	.	.	PROPN
ejpam-6658	304	5	math	math	PROPN
ejpam-6658	304	6	,	,	PUNCT
ejpam-6658	304	7	18	18	NUM
ejpam-6658	304	8	(	(	PUNCT
ejpam-6658	304	9	3	3	NUM
ejpam-6658	304	10	)	)	PUNCT
ejpam-6658	304	11	(	(	PUNCT
ejpam-6658	304	12	2025	2025	NUM
ejpam-6658	304	13	)	)	PUNCT
ejpam-6658	304	14	,	,	PUNCT
ejpam-6658	304	15	6658	6658	NUM
ejpam-6658	304	16	13	13	NUM
ejpam-6658	304	17	of	of	ADP
ejpam-6658	304	18	22	22	NUM
ejpam-6658	304	19	applying	apply	VERB
ejpam-6658	304	20	the	the	DET
ejpam-6658	304	21	cauchy	cauchy	NOUN
ejpam-6658	304	22	product	product	NOUN
ejpam-6658	304	23	,	,	PUNCT
ejpam-6658	304	24	we	we	PRON
ejpam-6658	304	25	have	have	VERB
ejpam-6658	304	26	∞∑	∞∑	NUM
ejpam-6658	304	27	n=0	n=0	NUM
ejpam-6658	304	28	plrn(r1	plrn(r1	NOUN
ejpam-6658	304	29	,	,	PUNCT
ejpam-6658	304	30	r2	r2	PROPN
ejpam-6658	304	31	,	,	PUNCT
ejpam-6658	304	32	r3	r3	PROPN
ejpam-6658	304	33	)	)	PUNCT
ejpam-6658	304	34	tn	tn	PROPN
ejpam-6658	304	35	n	n	PROPN
ejpam-6658	304	36	!	!	PUNCT
ejpam-6658	305	1	=	=	NOUN
ejpam-6658	306	1	∞∑	∞∑	PRON
ejpam-6658	306	2	n=0	n=0	NUM
ejpam-6658	306	3	n∑	n∑	NOUN
ejpam-6658	306	4	k=0	k=0	PROPN
ejpam-6658	306	5	(	(	PUNCT
ejpam-6658	306	6	n	n	X
ejpam-6658	306	7	k	k	NOUN
ejpam-6658	306	8	)	)	PUNCT
ejpam-6658	306	9	βk	βk	ADP
ejpam-6658	306	10	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	306	11	,	,	PUNCT
ejpam-6658	306	12	r2	r2	PROPN
ejpam-6658	306	13	,	,	PUNCT
ejpam-6658	306	14	r3	r3	PROPN
ejpam-6658	306	15	)	)	PUNCT
ejpam-6658	306	16	tn	tn	PROPN
ejpam-6658	306	17	n	n	PROPN
ejpam-6658	306	18	!	!	PUNCT
ejpam-6658	306	19	.	.	PUNCT
ejpam-6658	307	1	by	by	ADP
ejpam-6658	307	2	comparing	compare	VERB
ejpam-6658	307	3	the	the	DET
ejpam-6658	307	4	coefficients	coefficient	NOUN
ejpam-6658	307	5	of	of	ADP
ejpam-6658	307	6	tn	tn	NOUN
ejpam-6658	307	7	n	n	ADP
ejpam-6658	307	8	!	!	PUNCT
ejpam-6658	308	1	from	from	ADP
ejpam-6658	308	2	the	the	DET
ejpam-6658	308	3	polynomial	polynomial	ADJ
ejpam-6658	308	4	equation	equation	NOUN
ejpam-6658	308	5	,	,	PUNCT
ejpam-6658	308	6	we	we	PRON
ejpam-6658	308	7	get	get	VERB
ejpam-6658	308	8	plrn(r1	plrn(r1	NOUN
ejpam-6658	308	9	,	,	PUNCT
ejpam-6658	308	10	r2	r2	PROPN
ejpam-6658	308	11	,	,	PUNCT
ejpam-6658	308	12	r3	r3	PROPN
ejpam-6658	308	13	)	)	PUNCT
ejpam-6658	309	1	=	=	SYM
ejpam-6658	310	1	n∑	n∑	NOUN
ejpam-6658	310	2	k=0	k=0	PROPN
ejpam-6658	310	3	(	(	PUNCT
ejpam-6658	310	4	n	n	X
ejpam-6658	310	5	k	k	NOUN
ejpam-6658	310	6	)	)	PUNCT
ejpam-6658	310	7	βk	βk	ADP
ejpam-6658	310	8	plrn−k(r1	plrn−k(r1	PROPN
ejpam-6658	310	9	,	,	PUNCT
ejpam-6658	310	10	r2	r2	PROPN
ejpam-6658	310	11	,	,	PUNCT
ejpam-6658	310	12	r3	r3	PROPN
ejpam-6658	310	13	)	)	PUNCT
ejpam-6658	310	14	,	,	PUNCT
ejpam-6658	310	15	n	n	PROPN
ejpam-6658	310	16	∈	∈	PROPN
ejpam-6658	310	17	n0	n0	PROPN
ejpam-6658	310	18	.	.	PUNCT
ejpam-6658	311	1	so	so	ADV
ejpam-6658	311	2	,	,	PUNCT
ejpam-6658	311	3	we	we	PRON
ejpam-6658	311	4	obtain	obtain	VERB
ejpam-6658	311	5	the	the	DET
ejpam-6658	311	6	system	system	NOUN
ejpam-6658	311	7	of	of	ADP
ejpam-6658	311	8	equations	equation	NOUN
ejpam-6658	311	9	as	as	SCONJ
ejpam-6658	311	10	follows	follow	VERB
ejpam-6658	311	11	:	:	PUNCT
ejpam-6658	311	12	pl0(r1	pl0(r1	NOUN
ejpam-6658	311	13	,	,	PUNCT
ejpam-6658	311	14	r2	r2	PROPN
ejpam-6658	311	15	,	,	PUNCT
ejpam-6658	311	16	r3	r3	PROPN
ejpam-6658	311	17	)	)	PUNCT
ejpam-6658	311	18	=	=	SYM
ejpam-6658	311	19	β0	β0	PROPN
ejpam-6658	311	20	plr0(r1	plr0(r1	PROPN
ejpam-6658	311	21	,	,	PUNCT
ejpam-6658	311	22	r2	r2	PROPN
ejpam-6658	311	23	,	,	PUNCT
ejpam-6658	311	24	r3	r3	PROPN
ejpam-6658	311	25	)	)	PUNCT
ejpam-6658	311	26	,	,	PUNCT
ejpam-6658	311	27	pl1(r1	pl1(r1	NOUN
ejpam-6658	311	28	,	,	PUNCT
ejpam-6658	311	29	r2	r2	PROPN
ejpam-6658	311	30	,	,	PUNCT
ejpam-6658	311	31	r3	r3	PROPN
ejpam-6658	311	32	)	)	PUNCT
ejpam-6658	311	33	=	=	SYM
ejpam-6658	311	34	β0	β0	NOUN
ejpam-6658	311	35	plr1(r1	plr1(r1	NOUN
ejpam-6658	311	36	,	,	PUNCT
ejpam-6658	311	37	r2	r2	PROPN
ejpam-6658	311	38	,	,	PUNCT
ejpam-6658	311	39	r3	r3	PROPN
ejpam-6658	311	40	)	)	PUNCT
ejpam-6658	312	1	+	+	CCONJ
ejpam-6658	312	2	β1	β1	PROPN
ejpam-6658	312	3	plr0(r1	plr0(r1	PROPN
ejpam-6658	312	4	,	,	PUNCT
ejpam-6658	312	5	r2	r2	PROPN
ejpam-6658	312	6	,	,	PUNCT
ejpam-6658	312	7	r3	r3	PROPN
ejpam-6658	312	8	)	)	PUNCT
ejpam-6658	312	9	,	,	PUNCT
ejpam-6658	312	10	pl2(r1	pl2(r1	PROPN
ejpam-6658	312	11	,	,	PUNCT
ejpam-6658	312	12	r2	r2	PROPN
ejpam-6658	312	13	,	,	PUNCT
ejpam-6658	312	14	r3	r3	PROPN
ejpam-6658	312	15	)	)	PUNCT
ejpam-6658	312	16	=	=	PUNCT
ejpam-6658	312	17	β0	β0	PROPN
ejpam-6658	312	18	plr2(r1	plr2(r1	PROPN
ejpam-6658	312	19	,	,	PUNCT
ejpam-6658	312	20	r2	r2	PROPN
ejpam-6658	312	21	,	,	PUNCT
ejpam-6658	312	22	r3	r3	PROPN
ejpam-6658	312	23	)	)	PUNCT
ejpam-6658	312	24	+	+	CCONJ
ejpam-6658	312	25	(	(	PUNCT
ejpam-6658	312	26	2	2	NUM
ejpam-6658	312	27	1	1	NUM
ejpam-6658	312	28	)	)	PUNCT
ejpam-6658	312	29	β1	β1	PROPN
ejpam-6658	312	30	plr1(r1	plr1(r1	NOUN
ejpam-6658	312	31	,	,	PUNCT
ejpam-6658	312	32	r2	r2	PROPN
ejpam-6658	312	33	,	,	PUNCT
ejpam-6658	312	34	r3	r3	PROPN
ejpam-6658	312	35	)	)	PUNCT
ejpam-6658	312	36	+	+	NUM
ejpam-6658	312	37	β2	β2	PROPN
ejpam-6658	312	38	plr0(r1	plr0(r1	PROPN
ejpam-6658	312	39	,	,	PUNCT
ejpam-6658	312	40	r2	r2	PROPN
ejpam-6658	312	41	,	,	PUNCT
ejpam-6658	312	42	r3	r3	PROPN
ejpam-6658	312	43	)	)	PUNCT
ejpam-6658	312	44	,	,	PUNCT
ejpam-6658	312	45	...	...	PUNCT
ejpam-6658	313	1	pln−1(r1	pln−1(r1	NOUN
ejpam-6658	313	2	,	,	PUNCT
ejpam-6658	313	3	r2	r2	PROPN
ejpam-6658	313	4	,	,	PUNCT
ejpam-6658	313	5	r3	r3	PROPN
ejpam-6658	313	6	)	)	PUNCT
ejpam-6658	313	7	=	=	SYM
ejpam-6658	313	8	β0	β0	ADJ
ejpam-6658	313	9	plrn−1(r1	plrn−1(r1	NOUN
ejpam-6658	313	10	,	,	PUNCT
ejpam-6658	313	11	r2	r2	PROPN
ejpam-6658	313	12	,	,	PUNCT
ejpam-6658	313	13	r3)+	r3)+	NOUN
ejpam-6658	313	14	(	(	PUNCT
ejpam-6658	313	15	n−	n−	NOUN
ejpam-6658	313	16	1	1	NUM
ejpam-6658	313	17	1	1	X
ejpam-6658	313	18	)	)	PUNCT
ejpam-6658	313	19	β1	β1	PROPN
ejpam-6658	313	20	plrn−2(r1	plrn−2(r1	NOUN
ejpam-6658	313	21	,	,	PUNCT
ejpam-6658	313	22	r2	r2	PROPN
ejpam-6658	313	23	,	,	PUNCT
ejpam-6658	313	24	r3)+	r3)+	PROPN
ejpam-6658	313	25	·	·	PUNCT
ejpam-6658	313	26	·	·	PUNCT
ejpam-6658	313	27	·	·	PUNCT
ejpam-6658	313	28	+	+	ADJ
ejpam-6658	313	29	βn−1	βn−1	PROPN
ejpam-6658	313	30	plr0(r1	plr0(r1	PROPN
ejpam-6658	313	31	,	,	PUNCT
ejpam-6658	313	32	r2	r2	PROPN
ejpam-6658	313	33	,	,	PUNCT
ejpam-6658	313	34	r3	r3	PROPN
ejpam-6658	313	35	)	)	PUNCT
ejpam-6658	313	36	,	,	PUNCT
ejpam-6658	313	37	plrn(r1	plrn(r1	NOUN
ejpam-6658	313	38	,	,	PUNCT
ejpam-6658	313	39	r2	r2	PROPN
ejpam-6658	313	40	,	,	PUNCT
ejpam-6658	313	41	r3	r3	PROPN
ejpam-6658	313	42	)	)	PUNCT
ejpam-6658	313	43	=	=	SYM
ejpam-6658	314	1	β0	β0	NOUN
ejpam-6658	314	2	plrn(r1	plrn(r1	NOUN
ejpam-6658	314	3	,	,	PUNCT
ejpam-6658	314	4	r2	r2	PROPN
ejpam-6658	314	5	,	,	PUNCT
ejpam-6658	314	6	r3)+	r3)+	NOUN
ejpam-6658	314	7	(	(	PUNCT
ejpam-6658	314	8	n	n	CCONJ
ejpam-6658	314	9	1	1	X
ejpam-6658	314	10	)	)	PUNCT
ejpam-6658	314	11	β1	β1	PROPN
ejpam-6658	314	12	plrn−1(r1	plrn−1(r1	NOUN
ejpam-6658	314	13	,	,	PUNCT
ejpam-6658	314	14	r2	r2	PROPN
ejpam-6658	314	15	,	,	PUNCT
ejpam-6658	314	16	r3)+	r3)+	PROPN
ejpam-6658	314	17	·	·	PUNCT
ejpam-6658	314	18	·	·	PUNCT
ejpam-6658	314	19	·	·	PUNCT
ejpam-6658	314	20	+	+	ADJ
ejpam-6658	314	21	βn	βn	ADJ
ejpam-6658	314	22	plr0(r1	plr0(r1	PROPN
ejpam-6658	314	23	,	,	PUNCT
ejpam-6658	314	24	r2	r2	PROPN
ejpam-6658	314	25	,	,	PUNCT
ejpam-6658	314	26	r3	r3	PROPN
ejpam-6658	314	27	)	)	PUNCT
ejpam-6658	314	28	.	.	PUNCT
ejpam-6658	315	1	applying	apply	VERB
ejpam-6658	315	2	cramers	cramer	NOUN
ejpam-6658	315	3	’	'	PUNCT
ejpam-6658	315	4	rule	rule	NOUN
ejpam-6658	315	5	,	,	PUNCT
ejpam-6658	315	6	we	we	PRON
ejpam-6658	315	7	get	get	VERB
ejpam-6658	315	8	plrn(r1	plrn(r1	NOUN
ejpam-6658	315	9	,	,	PUNCT
ejpam-6658	315	10	r2	r2	PROPN
ejpam-6658	315	11	,	,	PUNCT
ejpam-6658	315	12	r3	r3	PROPN
ejpam-6658	315	13	)	)	PUNCT
ejpam-6658	315	14	=	=	PUNCT
ejpam-6658	316	1	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	316	2	β0	β0	PROPN
ejpam-6658	316	3	0	0	NUM
ejpam-6658	316	4	...	...	SYM
ejpam-6658	316	5	0	0	NUM
ejpam-6658	317	1	pl0(r1	pl0(r1	NOUN
ejpam-6658	317	2	,	,	PUNCT
ejpam-6658	317	3	r2	r2	PROPN
ejpam-6658	317	4	,	,	PUNCT
ejpam-6658	317	5	r3	r3	PROPN
ejpam-6658	317	6	)	)	PUNCT
ejpam-6658	317	7	β1	β1	PROPN
ejpam-6658	317	8	β0	β0	PROPN
ejpam-6658	317	9	...	...	PROPN
ejpam-6658	317	10	0	0	NUM
ejpam-6658	318	1	pl1(r1	pl1(r1	NOUN
ejpam-6658	318	2	,	,	PUNCT
ejpam-6658	318	3	r2	r2	PROPN
ejpam-6658	318	4	,	,	PUNCT
ejpam-6658	318	5	r3	r3	PROPN
ejpam-6658	318	6	)	)	PUNCT
ejpam-6658	318	7	β2	β2	NOUN
ejpam-6658	318	8	(	(	PUNCT
ejpam-6658	318	9	2	2	NUM
ejpam-6658	318	10	1	1	NUM
ejpam-6658	318	11	)	)	PUNCT
ejpam-6658	318	12	β1	β1	NOUN
ejpam-6658	318	13	...	...	PUNCT
ejpam-6658	318	14	0	0	NUM
ejpam-6658	318	15	pl2(r1	pl2(r1	NOUN
ejpam-6658	318	16	,	,	PUNCT
ejpam-6658	318	17	r2	r2	PROPN
ejpam-6658	318	18	,	,	PUNCT
ejpam-6658	318	19	r3	r3	PROPN
ejpam-6658	318	20	)	)	PUNCT
ejpam-6658	318	21	β3	β3	PROPN
ejpam-6658	318	22	(	(	PUNCT
ejpam-6658	318	23	3	3	NUM
ejpam-6658	318	24	2	2	NUM
ejpam-6658	318	25	)	)	PUNCT
ejpam-6658	318	26	β2	β2	NOUN
ejpam-6658	318	27	...	...	PUNCT
ejpam-6658	318	28	0	0	NUM
ejpam-6658	319	1	pl3(r1	pl3(r1	NOUN
ejpam-6658	319	2	,	,	PUNCT
ejpam-6658	319	3	r2	r2	PROPN
ejpam-6658	319	4	,	,	PUNCT
ejpam-6658	319	5	r3	r3	PROPN
ejpam-6658	319	6	)	)	PUNCT
ejpam-6658	319	7	...	...	PUNCT
ejpam-6658	319	8	...	...	PUNCT
ejpam-6658	319	9	...	...	PUNCT
ejpam-6658	319	10	...	...	PUNCT
ejpam-6658	320	1	...	...	PUNCT
ejpam-6658	321	1	βn−1	βn−1	INTJ
ejpam-6658	321	2	(	(	PUNCT
ejpam-6658	321	3	n−1	n−1	PROPN
ejpam-6658	321	4	1	1	NUM
ejpam-6658	321	5	)	)	PUNCT
ejpam-6658	321	6	βn−2	βn−2	ADV
ejpam-6658	321	7	...	...	PUNCT
ejpam-6658	321	8	β0	β0	ADJ
ejpam-6658	321	9	pln−1(r1	pln−1(r1	NOUN
ejpam-6658	321	10	,	,	PUNCT
ejpam-6658	321	11	r2	r2	PROPN
ejpam-6658	321	12	,	,	PUNCT
ejpam-6658	321	13	r3	r3	PROPN
ejpam-6658	321	14	)	)	PUNCT
ejpam-6658	321	15	βn	βn	NOUN
ejpam-6658	321	16	(	(	PUNCT
ejpam-6658	321	17	n	n	NOUN
ejpam-6658	321	18	1	1	NUM
ejpam-6658	321	19	)	)	PUNCT
ejpam-6658	321	20	βn−1	βn−1	PROPN
ejpam-6658	321	21	...	...	PUNCT
ejpam-6658	321	22	(	(	PUNCT
ejpam-6658	321	23	n	n	X
ejpam-6658	321	24	n−1	n−1	PROPN
ejpam-6658	321	25	)	)	PUNCT
ejpam-6658	321	26	β1	β1	PROPN
ejpam-6658	321	27	plm(r1	plm(r1	PROPN
ejpam-6658	321	28	,	,	PUNCT
ejpam-6658	321	29	r2	r2	PROPN
ejpam-6658	321	30	,	,	PUNCT
ejpam-6658	321	31	r3	r3	PROPN
ejpam-6658	321	32	)	)	PUNCT
ejpam-6658	321	33	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	321	34	β0	β0	PROPN
ejpam-6658	321	35	0	0	NUM
ejpam-6658	321	36	...	...	PUNCT
ejpam-6658	321	37	0	0	NUM
ejpam-6658	321	38	0	0	NUM
ejpam-6658	322	1	β1	β1	PROPN
ejpam-6658	322	2	β0	β0	PROPN
ejpam-6658	322	3	...	...	PROPN
ejpam-6658	323	1	0	0	NUM
ejpam-6658	323	2	0	0	NUM
ejpam-6658	323	3	β2	β2	NOUN
ejpam-6658	323	4	(	(	PUNCT
ejpam-6658	323	5	2	2	NUM
ejpam-6658	323	6	1	1	NUM
ejpam-6658	323	7	)	)	PUNCT
ejpam-6658	323	8	β1	β1	NOUN
ejpam-6658	323	9	...	...	PUNCT
ejpam-6658	323	10	0	0	NUM
ejpam-6658	323	11	0	0	NUM
ejpam-6658	323	12	β3	β3	PROPN
ejpam-6658	323	13	(	(	PUNCT
ejpam-6658	323	14	3	3	NUM
ejpam-6658	323	15	2	2	NUM
ejpam-6658	323	16	)	)	PUNCT
ejpam-6658	323	17	β2	β2	NOUN
ejpam-6658	323	18	...	...	PUNCT
ejpam-6658	323	19	0	0	NUM
ejpam-6658	323	20	0	0	NUM
ejpam-6658	323	21	...	...	PUNCT
ejpam-6658	323	22	...	...	PUNCT
ejpam-6658	323	23	...	...	PUNCT
ejpam-6658	323	24	...	...	PUNCT
ejpam-6658	323	25	...	...	PUNCT
ejpam-6658	324	1	βn−1	βn−1	INTJ
ejpam-6658	324	2	(	(	PUNCT
ejpam-6658	324	3	n−1	n−1	PROPN
ejpam-6658	324	4	1	1	NUM
ejpam-6658	324	5	)	)	PUNCT
ejpam-6658	324	6	βn−2	βn−2	ADV
ejpam-6658	324	7	...	...	PUNCT
ejpam-6658	325	1	β0	β0	NOUN
ejpam-6658	325	2	0	0	NUM
ejpam-6658	325	3	βn	βn	PROPN
ejpam-6658	325	4	(	(	PUNCT
ejpam-6658	325	5	n	n	NOUN
ejpam-6658	325	6	1	1	NUM
ejpam-6658	325	7	)	)	PUNCT
ejpam-6658	325	8	βn−1	βn−1	PROPN
ejpam-6658	325	9	...	...	PUNCT
ejpam-6658	325	10	(	(	PUNCT
ejpam-6658	325	11	n	n	X
ejpam-6658	325	12	n−1	n−1	PROPN
ejpam-6658	325	13	)	)	PUNCT
ejpam-6658	325	14	β1	β1	PROPN
ejpam-6658	325	15	β0	β0	PROPN
ejpam-6658	325	16	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	325	17	.	.	PUNCT
ejpam-6658	326	1	w.	w.	PROPN
ejpam-6658	326	2	a.	a.	PROPN
ejpam-6658	326	3	khan	khan	PROPN
ejpam-6658	326	4	,	,	PUNCT
ejpam-6658	326	5	h.	h.	PROPN
ejpam-6658	326	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	326	7	,	,	PUNCT
ejpam-6658	326	8	h.	h.	PROPN
ejpam-6658	326	9	aydi	aydi	VERB
ejpam-6658	326	10	/	/	SYM
ejpam-6658	326	11	eur	eur	NOUN
ejpam-6658	326	12	.	.	PUNCT
ejpam-6658	327	1	j.	j.	PROPN
ejpam-6658	327	2	pure	pure	PROPN
ejpam-6658	327	3	appl	appl	PROPN
ejpam-6658	327	4	.	.	PROPN
ejpam-6658	327	5	math	math	PROPN
ejpam-6658	327	6	,	,	PUNCT
ejpam-6658	327	7	18	18	NUM
ejpam-6658	327	8	(	(	PUNCT
ejpam-6658	327	9	3	3	NUM
ejpam-6658	327	10	)	)	PUNCT
ejpam-6658	327	11	(	(	PUNCT
ejpam-6658	327	12	2025	2025	NUM
ejpam-6658	327	13	)	)	PUNCT
ejpam-6658	327	14	,	,	PUNCT
ejpam-6658	327	15	6658	6658	NUM
ejpam-6658	327	16	14	14	NUM
ejpam-6658	327	17	of	of	ADP
ejpam-6658	327	18	22	22	NUM
ejpam-6658	327	19	by	by	ADP
ejpam-6658	327	20	taking	take	VERB
ejpam-6658	327	21	the	the	DET
ejpam-6658	327	22	transpose	transpose	NOUN
ejpam-6658	327	23	in	in	ADP
ejpam-6658	327	24	the	the	DET
ejpam-6658	327	25	last	last	ADJ
ejpam-6658	327	26	equation	equation	NOUN
ejpam-6658	327	27	,	,	PUNCT
ejpam-6658	327	28	we	we	PRON
ejpam-6658	327	29	have	have	AUX
ejpam-6658	327	30	plrn(r1	plrn(r1	NOUN
ejpam-6658	327	31	,	,	PUNCT
ejpam-6658	327	32	r2	r2	PROPN
ejpam-6658	327	33	,	,	PUNCT
ejpam-6658	327	34	r3	r3	PROPN
ejpam-6658	327	35	)	)	PUNCT
ejpam-6658	327	36	=	=	SYM
ejpam-6658	328	1	1	1	NUM
ejpam-6658	328	2	(	(	PUNCT
ejpam-6658	328	3	β0)n+1	β0)n+1	PROPN
ejpam-6658	328	4	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	328	5	β0	β0	PROPN
ejpam-6658	328	6	β1	β1	PROPN
ejpam-6658	328	7	...	...	PUNCT
ejpam-6658	329	1	βn−1	βn−1	ADJ
ejpam-6658	329	2	βn	βn	NOUN
ejpam-6658	329	3	0	0	NUM
ejpam-6658	329	4	β0	β0	NOUN
ejpam-6658	329	5	...	...	PUNCT
ejpam-6658	330	1	(	(	PUNCT
ejpam-6658	330	2	n−1	n−1	PROPN
ejpam-6658	330	3	1	1	NUM
ejpam-6658	330	4	)	)	PUNCT
ejpam-6658	330	5	βn−2	βn−2	ADV
ejpam-6658	330	6	(	(	PUNCT
ejpam-6658	330	7	n	n	NOUN
ejpam-6658	330	8	1	1	NUM
ejpam-6658	330	9	)	)	PUNCT
ejpam-6658	330	10	βn−1	βn−1	ADV
ejpam-6658	330	11	0	0	NUM
ejpam-6658	330	12	0	0	NUM
ejpam-6658	330	13	...	...	PUNCT
ejpam-6658	331	1	(	(	PUNCT
ejpam-6658	331	2	n−1	n−1	PROPN
ejpam-6658	331	3	1	1	NUM
ejpam-6658	331	4	)	)	PUNCT
ejpam-6658	331	5	βn−3	βn−3	PROPN
ejpam-6658	331	6	(	(	PUNCT
ejpam-6658	331	7	n	n	NOUN
ejpam-6658	331	8	2	2	NUM
ejpam-6658	331	9	)	)	PUNCT
ejpam-6658	331	10	βn−2	βn−2	ADV
ejpam-6658	331	11	...	...	PUNCT
ejpam-6658	331	12	...	...	PUNCT
ejpam-6658	331	13	...	...	PUNCT
ejpam-6658	331	14	...	...	PUNCT
ejpam-6658	331	15	...	...	PUNCT
ejpam-6658	332	1	0	0	NUM
ejpam-6658	332	2	0	0	NUM
ejpam-6658	332	3	...	...	PUNCT
ejpam-6658	333	1	β0	β0	NOUN
ejpam-6658	333	2	(	(	PUNCT
ejpam-6658	333	3	n	n	CCONJ
ejpam-6658	333	4	n−1	n−1	PROPN
ejpam-6658	333	5	)	)	PUNCT
ejpam-6658	333	6	β1	β1	PROPN
ejpam-6658	333	7	pl0(r1	pl0(r1	PRON
ejpam-6658	333	8	,	,	PUNCT
ejpam-6658	333	9	r2	r2	PROPN
ejpam-6658	333	10	,	,	PUNCT
ejpam-6658	333	11	r3	r3	PROPN
ejpam-6658	333	12	)	)	PUNCT
ejpam-6658	333	13	pl1(r1	pl1(r1	NOUN
ejpam-6658	333	14	,	,	PUNCT
ejpam-6658	333	15	r2	r2	PROPN
ejpam-6658	333	16	,	,	PUNCT
ejpam-6658	333	17	r3	r3	PROPN
ejpam-6658	333	18	)	)	PUNCT
ejpam-6658	333	19	...	...	PUNCT
ejpam-6658	334	1	pln−1(r1	pln−1(r1	NOUN
ejpam-6658	334	2	,	,	PUNCT
ejpam-6658	334	3	r2	r2	PROPN
ejpam-6658	334	4	,	,	PUNCT
ejpam-6658	334	5	r3	r3	PROPN
ejpam-6658	334	6	)	)	PUNCT
ejpam-6658	334	7	pl(m	pl(m	PROPN
ejpam-6658	334	8	)	)	PUNCT
ejpam-6658	335	1	n	n	CCONJ
ejpam-6658	335	2	(	(	PUNCT
ejpam-6658	335	3	r1	r1	PROPN
ejpam-6658	335	4	,	,	PUNCT
ejpam-6658	335	5	r2	r2	PROPN
ejpam-6658	335	6	,	,	PUNCT
ejpam-6658	335	7	r3	r3	PROPN
ejpam-6658	335	8	)	)	PUNCT
ejpam-6658	335	9	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-6658	335	10	.	.	PUNCT
ejpam-6658	336	1	thus	thus	ADV
ejpam-6658	336	2	,	,	PUNCT
ejpam-6658	336	3	simple	simple	ADJ
ejpam-6658	336	4	row	row	NOUN
ejpam-6658	336	5	operations	operation	NOUN
ejpam-6658	336	6	are	be	AUX
ejpam-6658	336	7	used	use	VERB
ejpam-6658	336	8	to	to	PART
ejpam-6658	336	9	finish	finish	VERB
ejpam-6658	336	10	the	the	DET
ejpam-6658	336	11	proof	proof	NOUN
ejpam-6658	336	12	.	.	PUNCT
ejpam-6658	337	1	4	4	X
ejpam-6658	337	2	.	.	X
ejpam-6658	337	3	applications	application	NOUN
ejpam-6658	337	4	this	this	DET
ejpam-6658	337	5	study	study	NOUN
ejpam-6658	337	6	extends	extend	VERB
ejpam-6658	337	7	the	the	DET
ejpam-6658	337	8	exploration	exploration	NOUN
ejpam-6658	337	9	of	of	ADP
ejpam-6658	337	10	recently	recently	ADV
ejpam-6658	337	11	introduced	introduce	VERB
ejpam-6658	337	12	polynomials	polynomial	NOUN
ejpam-6658	337	13	,	,	PUNCT
ejpam-6658	337	14	focusing	focus	VERB
ejpam-6658	337	15	on	on	ADP
ejpam-6658	337	16	the	the	DET
ejpam-6658	337	17	examination	examination	NOUN
ejpam-6658	337	18	of	of	ADP
ejpam-6658	337	19	the	the	DET
ejpam-6658	337	20	generalization	generalization	NOUN
ejpam-6658	337	21	of	of	ADP
ejpam-6658	337	22	three	three	NUM
ejpam-6658	337	23	-	-	PUNCT
ejpam-6658	337	24	variable	variable	NOUN
ejpam-6658	337	25	laguerre	laguerre	NOUN
ejpam-6658	337	26	-	-	PUNCT
ejpam-6658	337	27	based	base	VERB
ejpam-6658	337	28	appell	appell	NOUN
ejpam-6658	337	29	polynomials	polynomial	NOUN
ejpam-6658	337	30	.	.	PUNCT
ejpam-6658	338	1	specifically	specifically	ADV
ejpam-6658	338	2	,	,	PUNCT
ejpam-6658	338	3	when	when	SCONJ
ejpam-6658	338	4	considering	consider	VERB
ejpam-6658	338	5	the	the	DET
ejpam-6658	338	6	case	case	NOUN
ejpam-6658	338	7	where	where	SCONJ
ejpam-6658	338	8	ψ(r2	ψ(r2	NOUN
ejpam-6658	338	9	,	,	PUNCT
ejpam-6658	338	10	t	t	PROPN
ejpam-6658	338	11	)	)	PUNCT
ejpam-6658	338	12	=	=	PUNCT
ejpam-6658	338	13	er2	er2	ADP
ejpam-6658	338	14	t	t	PROPN
ejpam-6658	338	15	2	2	NUM
ejpam-6658	338	16	in	in	ADP
ejpam-6658	338	17	the	the	DET
ejpam-6658	338	18	generating	generate	VERB
ejpam-6658	338	19	function	function	NOUN
ejpam-6658	338	20	(	(	PUNCT
ejpam-6658	338	21	36	36	NUM
ejpam-6658	338	22	)	)	PUNCT
ejpam-6658	338	23	,	,	PUNCT
ejpam-6658	338	24	which	which	PRON
ejpam-6658	338	25	results	result	VERB
ejpam-6658	338	26	in	in	ADP
ejpam-6658	338	27	the	the	DET
ejpam-6658	338	28	reduction	reduction	NOUN
ejpam-6658	338	29	of	of	ADP
ejpam-6658	338	30	3v	3v	NUM
ejpam-6658	338	31	lap	lap	NOUN
ejpam-6658	338	32	plrn(r1	plrn(r1	NOUN
ejpam-6658	338	33	,	,	PUNCT
ejpam-6658	338	34	r2	r2	PROPN
ejpam-6658	338	35	,	,	PUNCT
ejpam-6658	338	36	r3	r3	PROPN
ejpam-6658	338	37	)	)	PUNCT
ejpam-6658	338	38	to	to	ADP
ejpam-6658	338	39	the	the	DET
ejpam-6658	338	40	laguerre	laguerre	NOUN
ejpam-6658	338	41	-	-	PUNCT
ejpam-6658	338	42	hermiteappell	hermiteappell	NOUN
ejpam-6658	338	43	polynomials	polynomial	NOUN
ejpam-6658	338	44	(	(	PUNCT
ejpam-6658	338	45	lhap	lhap	PROPN
ejpam-6658	338	46	)	)	PUNCT
ejpam-6658	338	47	phrn(r1	phrn(r1	NOUN
ejpam-6658	338	48	,	,	PUNCT
ejpam-6658	338	49	r2	r2	PROPN
ejpam-6658	338	50	,	,	PUNCT
ejpam-6658	338	51	r3	r3	PROPN
ejpam-6658	338	52	)	)	PUNCT
ejpam-6658	338	53	can	can	AUX
ejpam-6658	338	54	be	be	AUX
ejpam-6658	338	55	characterized	characterize	VERB
ejpam-6658	338	56	by	by	ADP
ejpam-6658	338	57	a	a	DET
ejpam-6658	338	58	specific	specific	ADJ
ejpam-6658	338	59	generating	generating	NOUN
ejpam-6658	338	60	function	function	NOUN
ejpam-6658	338	61	.	.	PUNCT
ejpam-6658	339	1	r(t)er1t+r2t2c0(r3	r(t)er1t+r2t2c0(r3	NOUN
ejpam-6658	339	2	t	t	PROPN
ejpam-6658	339	3	)	)	PUNCT
ejpam-6658	340	1	=	=	PUNCT
ejpam-6658	341	1	∞∑	∞∑	PRON
ejpam-6658	341	2	n=0	n=0	NUM
ejpam-6658	341	3	phrn(r1	phrn(r1	NOUN
ejpam-6658	341	4	,	,	PUNCT
ejpam-6658	341	5	r2	r2	PROPN
ejpam-6658	341	6	,	,	PUNCT
ejpam-6658	341	7	r3	r3	PROPN
ejpam-6658	341	8	)	)	PUNCT
ejpam-6658	341	9	tn	tn	PROPN
ejpam-6658	341	10	n	n	PROPN
ejpam-6658	341	11	!	!	PUNCT
ejpam-6658	341	12	.	.	PUNCT
ejpam-6658	342	1	(	(	PUNCT
ejpam-6658	342	2	56	56	NUM
ejpam-6658	342	3	)	)	PUNCT
ejpam-6658	342	4	in	in	ADP
ejpam-6658	342	5	other	other	ADJ
ejpam-6658	342	6	words	word	NOUN
ejpam-6658	342	7	,	,	PUNCT
ejpam-6658	342	8	we	we	PRON
ejpam-6658	342	9	note	note	VERB
ejpam-6658	342	10	that	that	SCONJ
ejpam-6658	342	11	phrn(r1	phrn(r1	NOUN
ejpam-6658	342	12	,	,	PUNCT
ejpam-6658	342	13	r2	r2	PROPN
ejpam-6658	342	14	,	,	PUNCT
ejpam-6658	342	15	r3	r3	PROPN
ejpam-6658	342	16	)	)	PUNCT
ejpam-6658	342	17	=	=	SYM
ejpam-6658	342	18	exp	exp	NOUN
ejpam-6658	342	19	(	(	PUNCT
ejpam-6658	342	20	−d̂−1	−d̂−1	PROPN
ejpam-6658	342	21	r3	r3	PROPN
ejpam-6658	342	22	∂	∂	NOUN
ejpam-6658	342	23	∂r1	∂r1	PROPN
ejpam-6658	342	24	)	)	PUNCT
ejpam-6658	342	25	{	{	PUNCT
ejpam-6658	342	26	hrn(r1	hrn(r1	X
ejpam-6658	342	27	,	,	PUNCT
ejpam-6658	342	28	r2	r2	PROPN
ejpam-6658	342	29	)	)	PUNCT
ejpam-6658	342	30	}	}	PUNCT
ejpam-6658	342	31	=	=	SYM
ejpam-6658	342	32	exp	exp	NOUN
ejpam-6658	342	33	(	(	PUNCT
ejpam-6658	342	34	r2	r2	PROPN
ejpam-6658	342	35	∂2	∂2	PROPN
ejpam-6658	342	36	∂r21	∂r21	NOUN
ejpam-6658	342	37	)	)	PUNCT
ejpam-6658	342	38	{	{	PUNCT
ejpam-6658	342	39	lrn(r1	lrn(r1	PROPN
ejpam-6658	342	40	,	,	PUNCT
ejpam-6658	342	41	r3	r3	PROPN
ejpam-6658	342	42	)	)	PUNCT
ejpam-6658	342	43	}	}	PUNCT
ejpam-6658	342	44	.	.	PUNCT
ejpam-6658	343	1	(	(	PUNCT
ejpam-6658	343	2	57	57	NUM
ejpam-6658	343	3	)	)	PUNCT
ejpam-6658	343	4	theorem	theorem	NOUN
ejpam-6658	343	5	8	8	NUM
ejpam-6658	343	6	.	.	PUNCT
ejpam-6658	344	1	the	the	DET
ejpam-6658	344	2	three	three	NUM
ejpam-6658	344	3	variable	variable	ADJ
ejpam-6658	344	4	laguerre	laguerre	NOUN
ejpam-6658	344	5	-	-	PUNCT
ejpam-6658	344	6	hermite	hermite	NOUN
ejpam-6658	344	7	-	-	PUNCT
ejpam-6658	344	8	based	base	VERB
ejpam-6658	344	9	appell	appell	ADJ
ejpam-6658	344	10	polynomials	polynomial	NOUN
ejpam-6658	344	11	are	be	AUX
ejpam-6658	344	12	defined	define	VERB
ejpam-6658	344	13	by	by	ADP
ejpam-6658	344	14	the	the	DET
ejpam-6658	344	15	series	series	NOUN
ejpam-6658	344	16	:	:	PUNCT
ejpam-6658	344	17	phrn(r1	phrn(r1	NOUN
ejpam-6658	344	18	,	,	PUNCT
ejpam-6658	344	19	r2	r2	PROPN
ejpam-6658	344	20	,	,	PUNCT
ejpam-6658	344	21	r3	r3	PROPN
ejpam-6658	344	22	)	)	PUNCT
ejpam-6658	344	23	=	=	SYM
ejpam-6658	344	24	n∑	n∑	NOUN
ejpam-6658	344	25	k=0	k=0	PROPN
ejpam-6658	344	26	(	(	PUNCT
ejpam-6658	344	27	n	n	X
ejpam-6658	344	28	k	k	X
ejpam-6658	344	29	)	)	PUNCT
ejpam-6658	344	30	rk	rk	PROPN
ejpam-6658	344	31	phn−k(r1	phn−k(r1	NOUN
ejpam-6658	344	32	,	,	PUNCT
ejpam-6658	344	33	r2	r2	PROPN
ejpam-6658	344	34	,	,	PUNCT
ejpam-6658	344	35	r3	r3	PROPN
ejpam-6658	344	36	)	)	PUNCT
ejpam-6658	344	37	.	.	PUNCT
ejpam-6658	345	1	(	(	PUNCT
ejpam-6658	345	2	58	58	X
ejpam-6658	345	3	)	)	PUNCT
ejpam-6658	345	4	proof	proof	NOUN
ejpam-6658	345	5	.	.	PUNCT
ejpam-6658	346	1	in	in	ADP
ejpam-6658	346	2	view	view	NOUN
ejpam-6658	346	3	of	of	ADP
ejpam-6658	346	4	(	(	PUNCT
ejpam-6658	346	5	56	56	NUM
ejpam-6658	346	6	)	)	PUNCT
ejpam-6658	346	7	,	,	PUNCT
ejpam-6658	346	8	we	we	PRON
ejpam-6658	346	9	have	have	VERB
ejpam-6658	346	10	∞∑	∞∑	NUM
ejpam-6658	346	11	n=0	n=0	NUM
ejpam-6658	346	12	phrn(r1	phrn(r1	NOUN
ejpam-6658	346	13	,	,	PUNCT
ejpam-6658	346	14	r2	r2	PROPN
ejpam-6658	346	15	,	,	PUNCT
ejpam-6658	346	16	r3	r3	PROPN
ejpam-6658	346	17	)	)	PUNCT
ejpam-6658	346	18	tn	tn	PROPN
ejpam-6658	346	19	n	n	PROPN
ejpam-6658	346	20	!	!	PUNCT
ejpam-6658	347	1	=	=	NOUN
ejpam-6658	347	2	r(t	r(t	NOUN
ejpam-6658	347	3	)	)	PUNCT
ejpam-6658	347	4	∞∑	∞∑	PROPN
ejpam-6658	347	5	n=0	n=0	PUNCT
ejpam-6658	347	6	phn(r1	phn(r1	NOUN
ejpam-6658	347	7	,	,	PUNCT
ejpam-6658	347	8	r2	r2	PROPN
ejpam-6658	347	9	,	,	PUNCT
ejpam-6658	347	10	r3	r3	PROPN
ejpam-6658	347	11	)	)	PUNCT
ejpam-6658	347	12	tn	tn	PROPN
ejpam-6658	347	13	n	n	PROPN
ejpam-6658	347	14	!	!	PUNCT
ejpam-6658	347	15	.	.	PUNCT
ejpam-6658	348	1	(	(	PUNCT
ejpam-6658	348	2	59	59	NUM
ejpam-6658	348	3	)	)	PUNCT
ejpam-6658	348	4	now	now	ADV
ejpam-6658	348	5	,	,	PUNCT
ejpam-6658	348	6	by	by	ADP
ejpam-6658	348	7	using	use	VERB
ejpam-6658	348	8	the	the	DET
ejpam-6658	348	9	expansion	expansion	NOUN
ejpam-6658	348	10	of	of	ADP
ejpam-6658	348	11	r(t	r(t	NOUN
ejpam-6658	348	12	)	)	PUNCT
ejpam-6658	348	13	from	from	ADP
ejpam-6658	348	14	the	the	DET
ejpam-6658	348	15	left	left	ADJ
ejpam-6658	348	16	-	-	PUNCT
ejpam-6658	348	17	hand	hand	NOUN
ejpam-6658	348	18	side	side	NOUN
ejpam-6658	348	19	of	of	ADP
ejpam-6658	348	20	equation	equation	NOUN
ejpam-6658	348	21	(	(	PUNCT
ejpam-6658	348	22	59	59	NUM
ejpam-6658	348	23	)	)	PUNCT
ejpam-6658	348	24	,	,	PUNCT
ejpam-6658	348	25	we	we	PRON
ejpam-6658	348	26	can	can	AUX
ejpam-6658	348	27	simplify	simplify	VERB
ejpam-6658	348	28	and	and	CCONJ
ejpam-6658	348	29	equate	equate	VERB
ejpam-6658	348	30	the	the	DET
ejpam-6658	348	31	coefficients	coefficient	NOUN
ejpam-6658	348	32	of	of	ADP
ejpam-6658	348	33	like	like	ADP
ejpam-6658	348	34	powers	power	NOUN
ejpam-6658	348	35	of	of	ADP
ejpam-6658	348	36	t	t	PROPN
ejpam-6658	348	37	on	on	ADP
ejpam-6658	348	38	both	both	DET
ejpam-6658	348	39	sides	side	NOUN
ejpam-6658	348	40	of	of	ADP
ejpam-6658	348	41	the	the	DET
ejpam-6658	348	42	resulting	result	VERB
ejpam-6658	348	43	equation	equation	NOUN
ejpam-6658	348	44	to	to	PART
ejpam-6658	348	45	obtain	obtain	VERB
ejpam-6658	348	46	assertion	assertion	NOUN
ejpam-6658	348	47	(	(	PUNCT
ejpam-6658	348	48	58	58	NUM
ejpam-6658	348	49	)	)	PUNCT
ejpam-6658	348	50	.	.	PUNCT
ejpam-6658	349	1	next	next	ADV
ejpam-6658	349	2	,	,	PUNCT
ejpam-6658	349	3	we	we	PRON
ejpam-6658	349	4	will	will	AUX
ejpam-6658	349	5	demonstrate	demonstrate	VERB
ejpam-6658	349	6	the	the	DET
ejpam-6658	349	7	determinant	determinant	ADJ
ejpam-6658	349	8	form	form	NOUN
ejpam-6658	349	9	for	for	ADP
ejpam-6658	349	10	phrn(r1	phrn(r1	NOUN
ejpam-6658	349	11	,	,	PUNCT
ejpam-6658	349	12	r2	r2	PROPN
ejpam-6658	349	13	,	,	PUNCT
ejpam-6658	349	14	r3	r3	PROPN
ejpam-6658	349	15	)	)	PUNCT
ejpam-6658	349	16	using	use	VERB
ejpam-6658	349	17	an	an	DET
ejpam-6658	349	18	approach	approach	NOUN
ejpam-6658	349	19	similar	similar	ADJ
ejpam-6658	349	20	to	to	ADP
ejpam-6658	349	21	that	that	PRON
ejpam-6658	349	22	presented	present	VERB
ejpam-6658	349	23	in	in	ADP
ejpam-6658	349	24	[	[	X
ejpam-6658	349	25	28	28	NUM
ejpam-6658	349	26	,	,	PUNCT
ejpam-6658	349	27	29	29	NUM
ejpam-6658	349	28	]	]	PUNCT
ejpam-6658	349	29	,	,	PUNCT
ejpam-6658	349	30	taking	take	VERB
ejpam-6658	349	31	into	into	ADP
ejpam-6658	349	32	account	account	NOUN
ejpam-6658	349	33	equation	equation	NOUN
ejpam-6658	349	34	(	(	PUNCT
ejpam-6658	349	35	56	56	NUM
ejpam-6658	349	36	)	)	PUNCT
ejpam-6658	349	37	.	.	PUNCT
ejpam-6658	350	1	w.	w.	PROPN
ejpam-6658	350	2	a.	a.	PROPN
ejpam-6658	350	3	khan	khan	PROPN
ejpam-6658	350	4	,	,	PUNCT
ejpam-6658	350	5	h.	h.	PROPN
ejpam-6658	350	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	350	7	,	,	PUNCT
ejpam-6658	350	8	h.	h.	PROPN
ejpam-6658	350	9	aydi	aydi	VERB
ejpam-6658	350	10	/	/	SYM
ejpam-6658	350	11	eur	eur	NOUN
ejpam-6658	350	12	.	.	PUNCT
ejpam-6658	351	1	j.	j.	PROPN
ejpam-6658	351	2	pure	pure	PROPN
ejpam-6658	351	3	appl	appl	PROPN
ejpam-6658	351	4	.	.	PROPN
ejpam-6658	351	5	math	math	PROPN
ejpam-6658	351	6	,	,	PUNCT
ejpam-6658	351	7	18	18	NUM
ejpam-6658	351	8	(	(	PUNCT
ejpam-6658	351	9	3	3	NUM
ejpam-6658	351	10	)	)	PUNCT
ejpam-6658	351	11	(	(	PUNCT
ejpam-6658	351	12	2025	2025	NUM
ejpam-6658	351	13	)	)	PUNCT
ejpam-6658	351	14	,	,	PUNCT
ejpam-6658	351	15	6658	6658	NUM
ejpam-6658	351	16	15	15	NUM
ejpam-6658	351	17	of	of	ADP
ejpam-6658	351	18	22	22	NUM
ejpam-6658	351	19	theorem	theorem	NOUN
ejpam-6658	351	20	9	9	NUM
ejpam-6658	351	21	.	.	PUNCT
ejpam-6658	352	1	the	the	DET
ejpam-6658	352	2	determinant	determinant	ADJ
ejpam-6658	352	3	representation	representation	NOUN
ejpam-6658	352	4	of	of	ADP
ejpam-6658	352	5	3	3	NUM
ejpam-6658	352	6	-	-	PUNCT
ejpam-6658	352	7	variable	variable	NOUN
ejpam-6658	352	8	laguerre	laguerre	NOUN
ejpam-6658	352	9	-	-	PUNCT
ejpam-6658	352	10	hermite	hermite	ADJ
ejpam-6658	352	11	-	-	PUNCT
ejpam-6658	352	12	appell	appell	NOUN
ejpam-6658	352	13	polynomials	polynomial	NOUN
ejpam-6658	352	14	phrn(r1	phrn(r1	NOUN
ejpam-6658	352	15	,	,	PUNCT
ejpam-6658	352	16	r2	r2	PROPN
ejpam-6658	352	17	,	,	PUNCT
ejpam-6658	352	18	r3	r3	PROPN
ejpam-6658	352	19	)	)	PUNCT
ejpam-6658	352	20	of	of	ADP
ejpam-6658	352	21	degree	degree	NOUN
ejpam-6658	352	22	n	n	NOUN
ejpam-6658	352	23	is	be	AUX
ejpam-6658	352	24	phr0(r1	phr0(r1	PROPN
ejpam-6658	352	25	,	,	PUNCT
ejpam-6658	352	26	r2	r2	PROPN
ejpam-6658	352	27	,	,	PUNCT
ejpam-6658	352	28	r3	r3	PROPN
ejpam-6658	352	29	)	)	PUNCT
ejpam-6658	352	30	=	=	SYM
ejpam-6658	353	1	1	1	NUM
ejpam-6658	353	2	β0	β0	NOUN
ejpam-6658	353	3	,	,	PUNCT
ejpam-6658	353	4	phrn(r1	phrn(r1	NOUN
ejpam-6658	353	5	,	,	PUNCT
ejpam-6658	353	6	r2	r2	PROPN
ejpam-6658	353	7	,	,	PUNCT
ejpam-6658	353	8	r3	r3	PROPN
ejpam-6658	353	9	)	)	PUNCT
ejpam-6658	353	10	=	=	PRON
ejpam-6658	353	11	(	(	PUNCT
ejpam-6658	353	12	−1)n	−1)n	X
ejpam-6658	353	13	(	(	PUNCT
ejpam-6658	353	14	β0)n+1	β0)n+1	PROPN
ejpam-6658	353	15	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	ADJ
ejpam-6658	353	16	1	1	NUM
ejpam-6658	353	17	ph1(r1	ph1(r1	NOUN
ejpam-6658	353	18	,	,	PUNCT
ejpam-6658	353	19	r2	r2	PROPN
ejpam-6658	353	20	,	,	PUNCT
ejpam-6658	353	21	r3	r3	PROPN
ejpam-6658	353	22	)	)	PUNCT
ejpam-6658	353	23	ph2(r1	ph2(r1	NOUN
ejpam-6658	353	24	,	,	PUNCT
ejpam-6658	353	25	r2	r2	PROPN
ejpam-6658	353	26	,	,	PUNCT
ejpam-6658	353	27	r3	r3	PROPN
ejpam-6658	353	28	)	)	PUNCT
ejpam-6658	353	29	...	...	PUNCT
ejpam-6658	354	1	phn−1(r1	phn−1(r1	NOUN
ejpam-6658	354	2	,	,	PUNCT
ejpam-6658	354	3	r2	r2	PROPN
ejpam-6658	354	4	,	,	PUNCT
ejpam-6658	354	5	r3	r3	PROPN
ejpam-6658	354	6	)	)	PUNCT
ejpam-6658	354	7	phn(r1	phn(r1	PROPN
ejpam-6658	354	8	,	,	PUNCT
ejpam-6658	354	9	r2	r2	PROPN
ejpam-6658	354	10	,	,	PUNCT
ejpam-6658	354	11	r3	r3	PROPN
ejpam-6658	354	12	)	)	PUNCT
ejpam-6658	354	13	β0	β0	PROPN
ejpam-6658	354	14	β1	β1	PROPN
ejpam-6658	354	15	β2	β2	PROPN
ejpam-6658	354	16	...	...	PUNCT
ejpam-6658	355	1	βn−1	βn−1	ADJ
ejpam-6658	355	2	βn	βn	NOUN
ejpam-6658	355	3	0	0	NUM
ejpam-6658	355	4	β0	β0	NOUN
ejpam-6658	355	5	(	(	PUNCT
ejpam-6658	355	6	2	2	NUM
ejpam-6658	355	7	1	1	NUM
ejpam-6658	355	8	)	)	PUNCT
ejpam-6658	355	9	β1	β1	NOUN
ejpam-6658	355	10	...	...	PUNCT
ejpam-6658	356	1	(	(	PUNCT
ejpam-6658	356	2	n−1	n−1	PROPN
ejpam-6658	356	3	1	1	NUM
ejpam-6658	356	4	)	)	PUNCT
ejpam-6658	356	5	βn−2	βn−2	ADV
ejpam-6658	356	6	(	(	PUNCT
ejpam-6658	356	7	n	n	NOUN
ejpam-6658	356	8	1	1	NUM
ejpam-6658	356	9	)	)	PUNCT
ejpam-6658	356	10	βn−1	βn−1	ADV
ejpam-6658	356	11	0	0	NUM
ejpam-6658	356	12	0	0	NUM
ejpam-6658	356	13	β0	β0	NOUN
ejpam-6658	356	14	...	...	PUNCT
ejpam-6658	357	1	(	(	PUNCT
ejpam-6658	357	2	n−1	n−1	PROPN
ejpam-6658	357	3	1	1	NUM
ejpam-6658	357	4	)	)	PUNCT
ejpam-6658	357	5	βn−3	βn−3	PROPN
ejpam-6658	357	6	(	(	PUNCT
ejpam-6658	357	7	n	n	NOUN
ejpam-6658	357	8	2	2	NUM
ejpam-6658	357	9	)	)	PUNCT
ejpam-6658	357	10	βn−2	βn−2	ADV
ejpam-6658	357	11	...	...	PUNCT
ejpam-6658	357	12	...	...	PUNCT
ejpam-6658	357	13	...	...	PUNCT
ejpam-6658	357	14	...	...	PUNCT
ejpam-6658	357	15	...	...	PUNCT
ejpam-6658	358	1	0	0	NUM
ejpam-6658	358	2	0	0	NUM
ejpam-6658	358	3	0	0	NUM
ejpam-6658	358	4	...	...	PUNCT
ejpam-6658	359	1	β0,q	β0,q	PROPN
ejpam-6658	359	2	(	(	PUNCT
ejpam-6658	359	3	n	n	CCONJ
ejpam-6658	359	4	n−1	n−1	PROPN
ejpam-6658	359	5	)	)	PUNCT
ejpam-6658	359	6	β1	β1	PROPN
ejpam-6658	359	7	∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	359	8	,	,	PUNCT
ejpam-6658	359	9	(	(	PUNCT
ejpam-6658	359	10	60	60	NUM
ejpam-6658	359	11	)	)	PUNCT
ejpam-6658	359	12	βn	βn	NOUN
ejpam-6658	360	1	=	=	SYM
ejpam-6658	360	2	−	−	PROPN
ejpam-6658	360	3	1	1	NUM
ejpam-6658	360	4	r0	r0	NOUN
ejpam-6658	360	5	(	(	PUNCT
ejpam-6658	360	6	n∑	n∑	INTJ
ejpam-6658	360	7	k=1	k=1	PROPN
ejpam-6658	360	8	(	(	PUNCT
ejpam-6658	360	9	n	n	X
ejpam-6658	360	10	k	k	PROPN
ejpam-6658	360	11	)	)	PUNCT
ejpam-6658	360	12	rkβn−k	rkβn−k	PROPN
ejpam-6658	360	13	)	)	PUNCT
ejpam-6658	360	14	,	,	PUNCT
ejpam-6658	360	15	n	n	NOUN
ejpam-6658	360	16	=	=	SYM
ejpam-6658	360	17	0	0	NUM
ejpam-6658	360	18	,	,	PUNCT
ejpam-6658	360	19	1	1	NUM
ejpam-6658	360	20	,	,	PUNCT
ejpam-6658	360	21	2	2	NUM
ejpam-6658	360	22	,	,	PUNCT
ejpam-6658	360	23	.	.	PUNCT
ejpam-6658	360	24	.	.	PUNCT
ejpam-6658	360	25	.	.	PUNCT
ejpam-6658	361	1	,	,	PUNCT
ejpam-6658	361	2	where	where	SCONJ
ejpam-6658	361	3	β0	β0	PROPN
ejpam-6658	361	4	̸=	̸=	PROPN
ejpam-6658	361	5	0	0	NUM
ejpam-6658	361	6	,	,	PUNCT
ejpam-6658	361	7	β0	β0	NOUN
ejpam-6658	361	8	=	=	SYM
ejpam-6658	361	9	1	1	NUM
ejpam-6658	361	10	r0,q	r0,q	PROPN
ejpam-6658	361	11	and	and	CCONJ
ejpam-6658	361	12	phn(r1	phn(r1	PROPN
ejpam-6658	361	13	,	,	PUNCT
ejpam-6658	361	14	r2	r2	PROPN
ejpam-6658	361	15	,	,	PUNCT
ejpam-6658	361	16	r3	r3	PROPN
ejpam-6658	361	17	)	)	PUNCT
ejpam-6658	361	18	,	,	PUNCT
ejpam-6658	361	19	n	n	NOUN
ejpam-6658	361	20	=	=	SYM
ejpam-6658	361	21	0	0	NUM
ejpam-6658	361	22	,	,	PUNCT
ejpam-6658	361	23	1	1	NUM
ejpam-6658	361	24	,	,	PUNCT
ejpam-6658	361	25	2	2	NUM
ejpam-6658	361	26	,	,	PUNCT
ejpam-6658	361	27	.	.	PUNCT
ejpam-6658	361	28	.	.	PUNCT
ejpam-6658	361	29	.	.	PUNCT
ejpam-6658	362	1	,	,	PUNCT
ejpam-6658	362	2	are	be	AUX
ejpam-6658	362	3	the	the	DET
ejpam-6658	362	4	three	three	NUM
ejpam-6658	362	5	variable	variable	ADJ
ejpam-6658	362	6	qlegendre	qlegendre	NOUN
ejpam-6658	362	7	-	-	PUNCT
ejpam-6658	362	8	hermite	hermite	ADJ
ejpam-6658	362	9	polynomials	polynomial	NOUN
ejpam-6658	362	10	.	.	PUNCT
ejpam-6658	363	1	proof	proof	NOUN
ejpam-6658	363	2	.	.	PUNCT
ejpam-6658	364	1	by	by	ADP
ejpam-6658	364	2	inserting	insert	VERB
ejpam-6658	364	3	the	the	DET
ejpam-6658	364	4	series	series	NOUN
ejpam-6658	364	5	forms	form	NOUN
ejpam-6658	364	6	of	of	ADP
ejpam-6658	364	7	the	the	DET
ejpam-6658	364	8	new	new	ADJ
ejpam-6658	364	9	generalization	generalization	NOUN
ejpam-6658	364	10	of	of	ADP
ejpam-6658	364	11	the	the	DET
ejpam-6658	364	12	three	three	NUM
ejpam-6658	364	13	-	-	PUNCT
ejpam-6658	364	14	variable	variable	NOUN
ejpam-6658	364	15	laguerre	laguerre	NOUN
ejpam-6658	364	16	-	-	PUNCT
ejpam-6658	364	17	hermite	hermite	ADJ
ejpam-6658	364	18	polynomials	polynomial	NOUN
ejpam-6658	364	19	into	into	ADP
ejpam-6658	364	20	the	the	DET
ejpam-6658	364	21	generating	generate	VERB
ejpam-6658	364	22	function	function	NOUN
ejpam-6658	364	23	of	of	ADP
ejpam-6658	364	24	the	the	DET
ejpam-6658	364	25	three	three	NUM
ejpam-6658	364	26	-	-	PUNCT
ejpam-6658	364	27	variable	variable	NOUN
ejpam-6658	364	28	laguerrehermite	laguerrehermite	NOUN
ejpam-6658	364	29	-	-	PUNCT
ejpam-6658	364	30	appell	appell	NOUN
ejpam-6658	364	31	polynomials	polynomial	NOUN
ejpam-6658	364	32	,	,	PUNCT
ejpam-6658	364	33	we	we	PRON
ejpam-6658	364	34	obtain	obtain	VERB
ejpam-6658	364	35	:	:	PUNCT
ejpam-6658	364	36	r(t	r(t	NOUN
ejpam-6658	364	37	)	)	PUNCT
ejpam-6658	364	38	∞∑	∞∑	PROPN
ejpam-6658	364	39	n=0	n=0	PUNCT
ejpam-6658	364	40	phn(r1	phn(r1	NOUN
ejpam-6658	364	41	,	,	PUNCT
ejpam-6658	364	42	r2	r2	PROPN
ejpam-6658	364	43	,	,	PUNCT
ejpam-6658	364	44	r3	r3	PROPN
ejpam-6658	364	45	)	)	PUNCT
ejpam-6658	364	46	tn	tn	PROPN
ejpam-6658	364	47	n	n	PROPN
ejpam-6658	364	48	!	!	PUNCT
ejpam-6658	364	49	=	=	NOUN
ejpam-6658	365	1	∞∑	∞∑	PRON
ejpam-6658	365	2	n=0	n=0	NUM
ejpam-6658	365	3	phrn(r1	phrn(r1	NOUN
ejpam-6658	365	4	,	,	PUNCT
ejpam-6658	365	5	r2	r2	PROPN
ejpam-6658	365	6	,	,	PUNCT
ejpam-6658	365	7	r3	r3	PROPN
ejpam-6658	365	8	)	)	PUNCT
ejpam-6658	365	9	tn	tn	PROPN
ejpam-6658	365	10	n	n	PROPN
ejpam-6658	365	11	!	!	PUNCT
ejpam-6658	365	12	.	.	PUNCT
ejpam-6658	366	1	(	(	PUNCT
ejpam-6658	366	2	61	61	NUM
ejpam-6658	366	3	)	)	PUNCT
ejpam-6658	366	4	by	by	ADP
ejpam-6658	366	5	multiplying	multiply	VERB
ejpam-6658	366	6	1	1	NUM
ejpam-6658	366	7	r(t	r(t	NOUN
ejpam-6658	366	8	)	)	PUNCT
ejpam-6658	366	9	=	=	PUNCT
ejpam-6658	367	1	∞∑	∞∑	NUM
ejpam-6658	367	2	k=0	k=0	PROPN
ejpam-6658	367	3	βk	βk	ADP
ejpam-6658	367	4	tk	tk	PROPN
ejpam-6658	367	5	k	k	PROPN
ejpam-6658	367	6	!	!	PROPN
ejpam-6658	367	7	,	,	PUNCT
ejpam-6658	367	8	(	(	PUNCT
ejpam-6658	367	9	62	62	NUM
ejpam-6658	367	10	)	)	PUNCT
ejpam-6658	367	11	on	on	ADP
ejpam-6658	367	12	both	both	DET
ejpam-6658	367	13	sides	side	NOUN
ejpam-6658	367	14	,	,	PUNCT
ejpam-6658	367	15	it	it	PRON
ejpam-6658	367	16	follows	follow	VERB
ejpam-6658	367	17	that	that	SCONJ
ejpam-6658	367	18	∞∑	∞∑	NUM
ejpam-6658	367	19	n=0	n=0	PUNCT
ejpam-6658	367	20	phn(r1	phn(r1	NOUN
ejpam-6658	367	21	,	,	PUNCT
ejpam-6658	367	22	r2	r2	PROPN
ejpam-6658	367	23	,	,	PUNCT
ejpam-6658	367	24	r3	r3	PROPN
ejpam-6658	367	25	)	)	PUNCT
ejpam-6658	367	26	tn	tn	PROPN
ejpam-6658	367	27	n	n	PROPN
ejpam-6658	367	28	!	!	PUNCT
ejpam-6658	367	29	=	=	NOUN
ejpam-6658	368	1	∞∑	∞∑	PRON
ejpam-6658	368	2	k=0	k=0	PROPN
ejpam-6658	368	3	βk	βk	ADP
ejpam-6658	368	4	tk	tk	PROPN
ejpam-6658	368	5	k	k	PROPN
ejpam-6658	368	6	!	!	PUNCT
ejpam-6658	369	1	∞∑	∞∑	PRON
ejpam-6658	369	2	n=0	n=0	NUM
ejpam-6658	369	3	phrn(r1	phrn(r1	NOUN
ejpam-6658	369	4	,	,	PUNCT
ejpam-6658	369	5	r2	r2	PROPN
ejpam-6658	369	6	,	,	PUNCT
ejpam-6658	369	7	r3	r3	PROPN
ejpam-6658	369	8	)	)	PUNCT
ejpam-6658	369	9	tn	tn	PROPN
ejpam-6658	369	10	n	n	PROPN
ejpam-6658	369	11	!	!	PUNCT
ejpam-6658	369	12	.	.	PUNCT
ejpam-6658	370	1	(	(	PUNCT
ejpam-6658	370	2	63	63	NUM
ejpam-6658	370	3	)	)	PUNCT
ejpam-6658	370	4	applying	apply	VERB
ejpam-6658	370	5	cauchy	cauchy	ADJ
ejpam-6658	370	6	product	product	NOUN
ejpam-6658	370	7	in	in	ADP
ejpam-6658	370	8	(	(	PUNCT
ejpam-6658	370	9	63	63	NUM
ejpam-6658	370	10	)	)	PUNCT
ejpam-6658	370	11	gives	give	VERB
ejpam-6658	370	12	phn(r1	phn(r1	NOUN
ejpam-6658	370	13	,	,	PUNCT
ejpam-6658	370	14	r2	r2	PROPN
ejpam-6658	370	15	,	,	PUNCT
ejpam-6658	370	16	r3	r3	PROPN
ejpam-6658	370	17	)	)	PUNCT
ejpam-6658	371	1	=	=	SYM
ejpam-6658	372	1	n∑	n∑	NOUN
ejpam-6658	372	2	k=0	k=0	PROPN
ejpam-6658	372	3	(	(	PUNCT
ejpam-6658	372	4	n	n	X
ejpam-6658	372	5	k	k	NOUN
ejpam-6658	372	6	)	)	PUNCT
ejpam-6658	372	7	βk	βk	ADP
ejpam-6658	372	8	phrn−k(r1	phrn−k(r1	PROPN
ejpam-6658	372	9	,	,	PUNCT
ejpam-6658	372	10	r2	r2	PROPN
ejpam-6658	372	11	,	,	PUNCT
ejpam-6658	372	12	r3	r3	PROPN
ejpam-6658	372	13	)	)	PUNCT
ejpam-6658	372	14	.	.	PUNCT
ejpam-6658	373	1	(	(	PUNCT
ejpam-6658	373	2	64	64	NUM
ejpam-6658	373	3	)	)	PUNCT
ejpam-6658	373	4	this	this	DET
ejpam-6658	373	5	equality	equality	NOUN
ejpam-6658	373	6	leads	lead	VERB
ejpam-6658	373	7	to	to	ADP
ejpam-6658	373	8	a	a	DET
ejpam-6658	373	9	system	system	NOUN
ejpam-6658	373	10	of	of	ADP
ejpam-6658	373	11	n	n	PRON
ejpam-6658	373	12	equations	equation	NOUN
ejpam-6658	373	13	with	with	ADP
ejpam-6658	373	14	the	the	DET
ejpam-6658	373	15	unknowns	unknown	NOUN
ejpam-6658	373	16	rn(r1	rn(r1	NOUN
ejpam-6658	373	17	,	,	PUNCT
ejpam-6658	373	18	r2	r2	PROPN
ejpam-6658	373	19	,	,	PUNCT
ejpam-6658	373	20	r3	r3	PROPN
ejpam-6658	373	21	)	)	PUNCT
ejpam-6658	373	22	,	,	PUNCT
ejpam-6658	373	23	where	where	SCONJ
ejpam-6658	373	24	n	n	X
ejpam-6658	373	25	=	=	SYM
ejpam-6658	373	26	0	0	NUM
ejpam-6658	373	27	,	,	PUNCT
ejpam-6658	373	28	1	1	NUM
ejpam-6658	373	29	,	,	PUNCT
ejpam-6658	373	30	2	2	NUM
ejpam-6658	373	31	,	,	PUNCT
ejpam-6658	373	32	.	.	PUNCT
ejpam-6658	373	33	.	.	PUNCT
ejpam-6658	373	34	.	.	PUNCT
ejpam-6658	374	1	to	to	PART
ejpam-6658	374	2	solve	solve	VERB
ejpam-6658	374	3	this	this	DET
ejpam-6658	374	4	system	system	NOUN
ejpam-6658	374	5	using	use	VERB
ejpam-6658	374	6	cramer	cramer	PROPN
ejpam-6658	374	7	’s	’s	PART
ejpam-6658	374	8	rule	rule	NOUN
ejpam-6658	374	9	,	,	PUNCT
ejpam-6658	374	10	we	we	PRON
ejpam-6658	374	11	note	note	VERB
ejpam-6658	374	12	that	that	SCONJ
ejpam-6658	374	13	the	the	DET
ejpam-6658	374	14	denominator	denominator	NOUN
ejpam-6658	374	15	is	be	AUX
ejpam-6658	374	16	the	the	DET
ejpam-6658	374	17	determinant	determinant	NOUN
ejpam-6658	374	18	of	of	ADP
ejpam-6658	374	19	a	a	DET
ejpam-6658	374	20	lower	low	ADJ
ejpam-6658	374	21	triangular	triangular	NOUN
ejpam-6658	374	22	matrix	matrix	NOUN
ejpam-6658	374	23	,	,	PUNCT
ejpam-6658	374	24	which	which	PRON
ejpam-6658	374	25	has	have	VERB
ejpam-6658	374	26	a	a	DET
ejpam-6658	374	27	determinant	determinant	NOUN
ejpam-6658	374	28	of	of	ADP
ejpam-6658	374	29	(	(	PUNCT
ejpam-6658	374	30	β0	β0	PROPN
ejpam-6658	374	31	)	)	PUNCT
ejpam-6658	374	32	n+1	n+1	PROPN
ejpam-6658	374	33	.	.	PUNCT
ejpam-6658	374	34	by	by	ADP
ejpam-6658	374	35	taking	take	VERB
ejpam-6658	374	36	w.	w.	PROPN
ejpam-6658	374	37	a.	a.	PROPN
ejpam-6658	374	38	khan	khan	PROPN
ejpam-6658	374	39	,	,	PUNCT
ejpam-6658	374	40	h.	h.	PROPN
ejpam-6658	374	41	qawaqneh	qawaqneh	PROPN
ejpam-6658	374	42	,	,	PUNCT
ejpam-6658	374	43	h.	h.	PROPN
ejpam-6658	374	44	aydi	aydi	VERB
ejpam-6658	374	45	/	/	SYM
ejpam-6658	374	46	eur	eur	NOUN
ejpam-6658	374	47	.	.	PUNCT
ejpam-6658	375	1	j.	j.	PROPN
ejpam-6658	375	2	pure	pure	PROPN
ejpam-6658	375	3	appl	appl	PROPN
ejpam-6658	375	4	.	.	PROPN
ejpam-6658	375	5	math	math	PROPN
ejpam-6658	375	6	,	,	PUNCT
ejpam-6658	375	7	18	18	NUM
ejpam-6658	375	8	(	(	PUNCT
ejpam-6658	375	9	3	3	NUM
ejpam-6658	375	10	)	)	PUNCT
ejpam-6658	375	11	(	(	PUNCT
ejpam-6658	375	12	2025	2025	NUM
ejpam-6658	375	13	)	)	PUNCT
ejpam-6658	375	14	,	,	PUNCT
ejpam-6658	375	15	6658	6658	NUM
ejpam-6658	375	16	16	16	NUM
ejpam-6658	375	17	of	of	ADP
ejpam-6658	375	18	22	22	NUM
ejpam-6658	375	19	the	the	DET
ejpam-6658	375	20	transpose	transpose	NOUN
ejpam-6658	375	21	of	of	ADP
ejpam-6658	375	22	the	the	DET
ejpam-6658	375	23	numerator	numerator	NOUN
ejpam-6658	375	24	and	and	CCONJ
ejpam-6658	375	25	replacing	replace	VERB
ejpam-6658	375	26	the	the	DET
ejpam-6658	375	27	ith	ith	PROPN
ejpam-6658	375	28	row	row	NOUN
ejpam-6658	375	29	with	with	ADP
ejpam-6658	375	30	the	the	DET
ejpam-6658	375	31	(	(	PUNCT
ejpam-6658	375	32	i	i	NOUN
ejpam-6658	375	33	+	+	NOUN
ejpam-6658	375	34	1)th	1)th	NUM
ejpam-6658	375	35	position	position	NOUN
ejpam-6658	375	36	for	for	ADP
ejpam-6658	375	37	i	i	PRON
ejpam-6658	375	38	=	=	NOUN
ejpam-6658	375	39	1	1	NUM
ejpam-6658	375	40	,	,	PUNCT
ejpam-6658	375	41	2	2	NUM
ejpam-6658	375	42	,	,	PUNCT
ejpam-6658	375	43	.	.	PUNCT
ejpam-6658	375	44	.	.	PUNCT
ejpam-6658	376	1	.	.	PUNCT
ejpam-6658	377	1	,	,	PUNCT
ejpam-6658	377	2	n−	n−	NOUN
ejpam-6658	377	3	1	1	NUM
ejpam-6658	377	4	,	,	PUNCT
ejpam-6658	377	5	we	we	PRON
ejpam-6658	377	6	obtain	obtain	VERB
ejpam-6658	377	7	the	the	DET
ejpam-6658	377	8	desired	desire	VERB
ejpam-6658	377	9	result	result	NOUN
ejpam-6658	377	10	.	.	PUNCT
ejpam-6658	378	1	we	we	PRON
ejpam-6658	378	2	will	will	AUX
ejpam-6658	378	3	now	now	ADV
ejpam-6658	378	4	demonstrate	demonstrate	VERB
ejpam-6658	378	5	the	the	DET
ejpam-6658	378	6	multiplicative	multiplicative	ADJ
ejpam-6658	378	7	and	and	CCONJ
ejpam-6658	378	8	derivative	derivative	ADJ
ejpam-6658	378	9	operators	operator	NOUN
ejpam-6658	378	10	of	of	ADP
ejpam-6658	378	11	phrn(r1	phrn(r1	NOUN
ejpam-6658	378	12	,	,	PUNCT
ejpam-6658	378	13	r2	r2	PROPN
ejpam-6658	378	14	,	,	PUNCT
ejpam-6658	378	15	r3	r3	PROPN
ejpam-6658	378	16	)	)	PUNCT
ejpam-6658	378	17	.	.	PUNCT
ejpam-6658	379	1	the	the	DET
ejpam-6658	379	2	following	follow	VERB
ejpam-6658	379	3	theorem	theorem	NOUN
ejpam-6658	379	4	is	be	AUX
ejpam-6658	379	5	presented	present	VERB
ejpam-6658	379	6	:	:	PUNCT
ejpam-6658	379	7	theorem	theorem	VERB
ejpam-6658	379	8	10	10	NUM
ejpam-6658	379	9	.	.	PUNCT
ejpam-6658	380	1	the	the	DET
ejpam-6658	380	2	generalization	generalization	NOUN
ejpam-6658	380	3	of	of	ADP
ejpam-6658	380	4	laguerre	laguerre	NOUN
ejpam-6658	380	5	-	-	PUNCT
ejpam-6658	380	6	hermite	hermite	NOUN
ejpam-6658	380	7	-	-	PUNCT
ejpam-6658	380	8	based	base	VERB
ejpam-6658	380	9	appell	appell	NOUN
ejpam-6658	380	10	polynomials	polynomial	NOUN
ejpam-6658	380	11	satisfies	satisfy	VERB
ejpam-6658	380	12	the	the	DET
ejpam-6658	380	13	multiplicative	multiplicative	ADJ
ejpam-6658	380	14	and	and	CCONJ
ejpam-6658	380	15	derivative	derivative	ADJ
ejpam-6658	380	16	operators	operator	NOUN
ejpam-6658	380	17	as	as	SCONJ
ejpam-6658	380	18	follows	follow	VERB
ejpam-6658	380	19	:	:	PUNCT
ejpam-6658	380	20	m̂	m̂	PROPN
ejpam-6658	380	21	=	=	SYM
ejpam-6658	380	22	r1	r1	PROPN
ejpam-6658	380	23	+	+	CCONJ
ejpam-6658	380	24	r′(d̂r1	r′(d̂r1	PROPN
ejpam-6658	380	25	)	)	PUNCT
ejpam-6658	380	26	r(d̂r1	r(d̂r1	PROPN
ejpam-6658	380	27	)	)	PUNCT
ejpam-6658	381	1	−	−	PROPN
ejpam-6658	382	1	n	n	CCONJ
ejpam-6658	382	2	(	(	PUNCT
ejpam-6658	382	3	r2	r2	PROPN
ejpam-6658	382	4	+	+	PROPN
ejpam-6658	382	5	d−1	d−1	PROPN
ejpam-6658	382	6	r3	r3	PROPN
ejpam-6658	382	7	)	)	PUNCT
ejpam-6658	382	8	,	,	PUNCT
ejpam-6658	382	9	(	(	PUNCT
ejpam-6658	382	10	65	65	NUM
ejpam-6658	382	11	)	)	PUNCT
ejpam-6658	382	12	and	and	CCONJ
ejpam-6658	382	13	p̂	p̂	X
ejpam-6658	382	14	=	=	SYM
ejpam-6658	382	15	dr1	dr1	PROPN
ejpam-6658	382	16	,	,	PUNCT
ejpam-6658	382	17	(	(	PUNCT
ejpam-6658	382	18	66	66	NUM
ejpam-6658	382	19	)	)	PUNCT
ejpam-6658	382	20	respectively	respectively	ADV
ejpam-6658	382	21	.	.	PUNCT
ejpam-6658	383	1	proof	proof	NOUN
ejpam-6658	383	2	.	.	PUNCT
ejpam-6658	384	1	utilizing	utilize	VERB
ejpam-6658	384	2	the	the	DET
ejpam-6658	384	3	derivative	derivative	NOUN
ejpam-6658	384	4	with	with	ADP
ejpam-6658	384	5	respect	respect	NOUN
ejpam-6658	384	6	to	to	ADP
ejpam-6658	384	7	t	t	PROPN
ejpam-6658	384	8	on	on	ADP
ejpam-6658	384	9	both	both	DET
ejpam-6658	384	10	sides	side	NOUN
ejpam-6658	384	11	of	of	ADP
ejpam-6658	384	12	equation	equation	NOUN
ejpam-6658	384	13	(	(	PUNCT
ejpam-6658	384	14	56	56	NUM
ejpam-6658	384	15	)	)	PUNCT
ejpam-6658	384	16	,	,	PUNCT
ejpam-6658	384	17	we	we	PRON
ejpam-6658	384	18	find	find	VERB
ejpam-6658	384	19	∞∑	∞∑	NUM
ejpam-6658	384	20	n=0	n=0	NUM
ejpam-6658	384	21	phrn+1(r1	phrn+1(r1	NOUN
ejpam-6658	384	22	,	,	PUNCT
ejpam-6658	384	23	r2	r2	PROPN
ejpam-6658	384	24	,	,	PUNCT
ejpam-6658	384	25	r3	r3	PROPN
ejpam-6658	384	26	)	)	PUNCT
ejpam-6658	384	27	tn	tn	PROPN
ejpam-6658	384	28	n	n	PROPN
ejpam-6658	384	29	!	!	PUNCT
ejpam-6658	385	1	=	=	PUNCT
ejpam-6658	386	1	r′(t	r′(t	ADJ
ejpam-6658	386	2	)	)	PUNCT
ejpam-6658	386	3	r(t	r(t	NOUN
ejpam-6658	386	4	)	)	PUNCT
ejpam-6658	386	5	r(t)er1t+r2t2c0(r3t)+r1r(t)er1t+r2t2c0(r3t)+2r2tr(t)er1t+r2t2c0(r3	r(t)er1t+r2t2c0(r3t)+r1r(t)er1t+r2t2c0(r3t)+2r2tr(t)er1t+r2t2c0(r3	PROPN
ejpam-6658	386	6	t	t	PROPN
ejpam-6658	386	7	)	)	PUNCT
ejpam-6658	387	1	+	+	CCONJ
ejpam-6658	387	2	(	(	PUNCT
ejpam-6658	387	3	∞∑	∞∑	NUM
ejpam-6658	387	4	n=0	n=0	NUM
ejpam-6658	387	5	(	(	PUNCT
ejpam-6658	387	6	−1)nrn3nt	−1)nrn3nt	PROPN
ejpam-6658	387	7	n−1	n−1	PROPN
ejpam-6658	387	8	(	(	PUNCT
ejpam-6658	387	9	[	[	X
ejpam-6658	387	10	n]!)2	n]!)2	PROPN
ejpam-6658	387	11	)	)	PUNCT
ejpam-6658	387	12	r(t)er1t+r2t2	r(t)er1t+r2t2	PROPN
ejpam-6658	387	13	(	(	PUNCT
ejpam-6658	387	14	67	67	NUM
ejpam-6658	387	15	)	)	PUNCT
ejpam-6658	387	16	∞∑	∞∑	PRON
ejpam-6658	387	17	n=0	n=0	NUM
ejpam-6658	387	18	phrn+1(r1	phrn+1(r1	NOUN
ejpam-6658	387	19	,	,	PUNCT
ejpam-6658	387	20	r2	r2	PROPN
ejpam-6658	387	21	,	,	PUNCT
ejpam-6658	387	22	r3	r3	PROPN
ejpam-6658	387	23	)	)	PUNCT
ejpam-6658	387	24	tn	tn	PROPN
ejpam-6658	387	25	n	n	PROPN
ejpam-6658	387	26	!	!	PUNCT
ejpam-6658	387	27	=	=	PUNCT
ejpam-6658	388	1	(	(	PUNCT
ejpam-6658	388	2	r1	r1	NOUN
ejpam-6658	388	3	+	+	CCONJ
ejpam-6658	388	4	r′(t	r′(t	ADJ
ejpam-6658	388	5	)	)	PUNCT
ejpam-6658	388	6	r(t	r(t	NOUN
ejpam-6658	388	7	)	)	PUNCT
ejpam-6658	388	8	−	−	PROPN
ejpam-6658	388	9	nr2	nr2	PROPN
ejpam-6658	388	10	)	)	PUNCT
ejpam-6658	388	11	r(t)er1t+r2t2c0(r3	r(t)er1t+r2t2c0(r3	PROPN
ejpam-6658	388	12	t	t	PROPN
ejpam-6658	388	13	)	)	PUNCT
ejpam-6658	388	14	+	+	CCONJ
ejpam-6658	388	15	(	(	PUNCT
ejpam-6658	388	16	∞∑	∞∑	NUM
ejpam-6658	388	17	n=0	n=0	NUM
ejpam-6658	388	18	(	(	PUNCT
ejpam-6658	388	19	−1)n+1rn+1	−1)n+1rn+1	ADJ
ejpam-6658	388	20	3	3	NUM
ejpam-6658	388	21	(	(	PUNCT
ejpam-6658	388	22	n+	n+	NUM
ejpam-6658	388	23	1)tn	1)tn	NUM
ejpam-6658	388	24	(	(	PUNCT
ejpam-6658	388	25	[	[	X
ejpam-6658	388	26	n+	n+	NUM
ejpam-6658	388	27	1]!)2	1]!)2	NUM
ejpam-6658	388	28	)	)	PUNCT
ejpam-6658	388	29	r(t)er1t+r2t2	r(t)er1t+r2t2	PROPN
ejpam-6658	388	30	.	.	PUNCT
ejpam-6658	389	1	(	(	PUNCT
ejpam-6658	389	2	68	68	NUM
ejpam-6658	389	3	)	)	PUNCT
ejpam-6658	389	4	by	by	ADP
ejpam-6658	389	5	using	use	VERB
ejpam-6658	389	6	equation	equation	NOUN
ejpam-6658	389	7	(	(	PUNCT
ejpam-6658	389	8	56	56	NUM
ejpam-6658	389	9	)	)	PUNCT
ejpam-6658	389	10	,	,	PUNCT
ejpam-6658	389	11	we	we	PRON
ejpam-6658	389	12	get	get	VERB
ejpam-6658	389	13	∞∑	∞∑	NUM
ejpam-6658	389	14	n=0	n=0	NUM
ejpam-6658	389	15	phrn+1(r1	phrn+1(r1	NOUN
ejpam-6658	389	16	,	,	PUNCT
ejpam-6658	389	17	r2	r2	PROPN
ejpam-6658	389	18	,	,	PUNCT
ejpam-6658	389	19	r3	r3	PROPN
ejpam-6658	389	20	)	)	PUNCT
ejpam-6658	389	21	tn	tn	PROPN
ejpam-6658	389	22	n	n	PROPN
ejpam-6658	389	23	!	!	PUNCT
ejpam-6658	390	1	=	=	PUNCT
ejpam-6658	390	2	(	(	PUNCT
ejpam-6658	390	3	r1	r1	NOUN
ejpam-6658	390	4	+	+	CCONJ
ejpam-6658	390	5	r′(t	r′(t	ADJ
ejpam-6658	390	6	)	)	PUNCT
ejpam-6658	390	7	r(t	r(t	NOUN
ejpam-6658	390	8	)	)	PUNCT
ejpam-6658	390	9	−	−	PROPN
ejpam-6658	390	10	nr2	nr2	PROPN
ejpam-6658	390	11	)	)	PUNCT
ejpam-6658	390	12	∞∑	∞∑	PRON
ejpam-6658	390	13	n=0	n=0	NUM
ejpam-6658	390	14	phrn(r1	phrn(r1	NOUN
ejpam-6658	390	15	,	,	PUNCT
ejpam-6658	390	16	r2	r2	PROPN
ejpam-6658	390	17	,	,	PUNCT
ejpam-6658	390	18	r3	r3	PROPN
ejpam-6658	390	19	)	)	PUNCT
ejpam-6658	390	20	tn	tn	PROPN
ejpam-6658	390	21	n	n	CCONJ
ejpam-6658	390	22	!	!	PUNCT
ejpam-6658	391	1	+	+	CCONJ
ejpam-6658	391	2	(	(	PUNCT
ejpam-6658	391	3	∞∑	∞∑	NUM
ejpam-6658	391	4	n=0	n=0	NUM
ejpam-6658	391	5	(	(	PUNCT
ejpam-6658	391	6	−1)n+1rn+1	−1)n+1rn+1	ADJ
ejpam-6658	391	7	3	3	NUM
ejpam-6658	391	8	(	(	PUNCT
ejpam-6658	391	9	n+	n+	NUM
ejpam-6658	391	10	1)tn	1)tn	NUM
ejpam-6658	391	11	(	(	PUNCT
ejpam-6658	391	12	[	[	X
ejpam-6658	391	13	n+	n+	NUM
ejpam-6658	391	14	1]!)2	1]!)2	NUM
ejpam-6658	391	15	)	)	PUNCT
ejpam-6658	391	16	r(t)er1t+r2t2	r(t)er1t+r2t2	PROPN
ejpam-6658	391	17	.	.	PUNCT
ejpam-6658	392	1	(	(	PUNCT
ejpam-6658	392	2	69	69	NUM
ejpam-6658	392	3	)	)	PUNCT
ejpam-6658	392	4	on	on	ADP
ejpam-6658	392	5	differentiating	differentiate	VERB
ejpam-6658	392	6	both	both	DET
ejpam-6658	392	7	sides	side	NOUN
ejpam-6658	392	8	of	of	ADP
ejpam-6658	392	9	the	the	DET
ejpam-6658	392	10	last	last	ADJ
ejpam-6658	392	11	equation	equation	NOUN
ejpam-6658	392	12	with	with	ADP
ejpam-6658	392	13	respect	respect	NOUN
ejpam-6658	392	14	to	to	ADP
ejpam-6658	392	15	r3	r3	PROPN
ejpam-6658	392	16	,	,	PUNCT
ejpam-6658	392	17	we	we	PRON
ejpam-6658	392	18	obtain	obtain	VERB
ejpam-6658	392	19	:	:	PUNCT
ejpam-6658	392	20	∞∑	∞∑	NUM
ejpam-6658	392	21	n=0	n=0	NUM
ejpam-6658	392	22	dr3phrn+1(r1	dr3phrn+1(r1	NOUN
ejpam-6658	392	23	,	,	PUNCT
ejpam-6658	392	24	r2	r2	PROPN
ejpam-6658	392	25	,	,	PUNCT
ejpam-6658	392	26	r3	r3	PROPN
ejpam-6658	392	27	)	)	PUNCT
ejpam-6658	392	28	tn	tn	PROPN
ejpam-6658	392	29	n	n	PROPN
ejpam-6658	392	30	!	!	PUNCT
ejpam-6658	393	1	=	=	PUNCT
ejpam-6658	393	2	(	(	PUNCT
ejpam-6658	393	3	r1	r1	NOUN
ejpam-6658	393	4	+	+	CCONJ
ejpam-6658	393	5	r′(t	r′(t	ADJ
ejpam-6658	393	6	)	)	PUNCT
ejpam-6658	393	7	r(t	r(t	NOUN
ejpam-6658	393	8	)	)	PUNCT
ejpam-6658	393	9	−	−	PROPN
ejpam-6658	393	10	nr2	nr2	PROPN
ejpam-6658	393	11	)	)	PUNCT
ejpam-6658	393	12	∞∑	∞∑	PRON
ejpam-6658	393	13	n=0	n=0	NUM
ejpam-6658	393	14	dr3phrn(r1	dr3phrn(r1	NOUN
ejpam-6658	393	15	,	,	PUNCT
ejpam-6658	393	16	r2	r2	PROPN
ejpam-6658	393	17	,	,	PUNCT
ejpam-6658	393	18	r3	r3	PROPN
ejpam-6658	393	19	)	)	PUNCT
ejpam-6658	393	20	tn	tn	PROPN
ejpam-6658	393	21	n	n	PROPN
ejpam-6658	393	22	!	!	PUNCT
ejpam-6658	394	1	−n	−n	PROPN
ejpam-6658	394	2	∞∑	∞∑	ADJ
ejpam-6658	394	3	n=0	n=0	NUM
ejpam-6658	394	4	phrn(r1	phrn(r1	NOUN
ejpam-6658	394	5	,	,	PUNCT
ejpam-6658	394	6	r2	r2	PROPN
ejpam-6658	394	7	,	,	PUNCT
ejpam-6658	394	8	r3	r3	PROPN
ejpam-6658	394	9	)	)	PUNCT
ejpam-6658	394	10	tn	tn	PROPN
ejpam-6658	394	11	n	n	PROPN
ejpam-6658	394	12	!	!	PUNCT
ejpam-6658	394	13	.	.	PUNCT
ejpam-6658	395	1	(	(	PUNCT
ejpam-6658	395	2	70	70	X
ejpam-6658	395	3	)	)	PUNCT
ejpam-6658	395	4	w.	w.	PROPN
ejpam-6658	395	5	a.	a.	PROPN
ejpam-6658	395	6	khan	khan	PROPN
ejpam-6658	395	7	,	,	PUNCT
ejpam-6658	395	8	h.	h.	PROPN
ejpam-6658	395	9	qawaqneh	qawaqneh	PROPN
ejpam-6658	395	10	,	,	PUNCT
ejpam-6658	395	11	h.	h.	PROPN
ejpam-6658	395	12	aydi	aydi	VERB
ejpam-6658	395	13	/	/	SYM
ejpam-6658	395	14	eur	eur	NOUN
ejpam-6658	395	15	.	.	PUNCT
ejpam-6658	396	1	j.	j.	PROPN
ejpam-6658	396	2	pure	pure	PROPN
ejpam-6658	396	3	appl	appl	PROPN
ejpam-6658	396	4	.	.	PROPN
ejpam-6658	396	5	math	math	PROPN
ejpam-6658	396	6	,	,	PUNCT
ejpam-6658	396	7	18	18	NUM
ejpam-6658	396	8	(	(	PUNCT
ejpam-6658	396	9	3	3	NUM
ejpam-6658	396	10	)	)	PUNCT
ejpam-6658	396	11	(	(	PUNCT
ejpam-6658	396	12	2025	2025	NUM
ejpam-6658	396	13	)	)	PUNCT
ejpam-6658	396	14	,	,	PUNCT
ejpam-6658	396	15	6658	6658	NUM
ejpam-6658	396	16	17	17	NUM
ejpam-6658	396	17	of	of	ADP
ejpam-6658	396	18	22	22	NUM
ejpam-6658	396	19	applying	apply	VERB
ejpam-6658	396	20	d−1	d−1	PROPN
ejpam-6658	396	21	r3	r3	PROPN
ejpam-6658	396	22	to	to	ADP
ejpam-6658	396	23	both	both	DET
ejpam-6658	396	24	sides	side	NOUN
ejpam-6658	396	25	of	of	ADP
ejpam-6658	396	26	the	the	DET
ejpam-6658	396	27	above	above	ADJ
ejpam-6658	396	28	equation	equation	NOUN
ejpam-6658	396	29	,	,	PUNCT
ejpam-6658	396	30	we	we	PRON
ejpam-6658	396	31	get	get	VERB
ejpam-6658	396	32	∞∑	∞∑	NUM
ejpam-6658	396	33	n=0	n=0	NUM
ejpam-6658	396	34	phrn+1(r1	phrn+1(r1	NOUN
ejpam-6658	396	35	,	,	PUNCT
ejpam-6658	396	36	r2	r2	PROPN
ejpam-6658	396	37	,	,	PUNCT
ejpam-6658	396	38	r3	r3	PROPN
ejpam-6658	396	39	)	)	PUNCT
ejpam-6658	396	40	tn	tn	PROPN
ejpam-6658	396	41	n	n	PROPN
ejpam-6658	396	42	!	!	PUNCT
ejpam-6658	397	1	=	=	NOUN
ejpam-6658	398	1	∞∑	∞∑	PRON
ejpam-6658	398	2	n=0	n=0	NUM
ejpam-6658	398	3	(	(	PUNCT
ejpam-6658	398	4	r1	r1	NOUN
ejpam-6658	398	5	+	+	CCONJ
ejpam-6658	398	6	r′(t	r′(t	ADJ
ejpam-6658	398	7	)	)	PUNCT
ejpam-6658	398	8	r(t	r(t	NOUN
ejpam-6658	398	9	)	)	PUNCT
ejpam-6658	398	10	−	−	PROPN
ejpam-6658	399	1	n	n	CCONJ
ejpam-6658	399	2	(	(	PUNCT
ejpam-6658	399	3	r2	r2	PROPN
ejpam-6658	399	4	+	+	PROPN
ejpam-6658	399	5	d−1	d−1	PROPN
ejpam-6658	399	6	r3	r3	PROPN
ejpam-6658	399	7	)	)	PUNCT
ejpam-6658	399	8	)	)	PUNCT
ejpam-6658	399	9	phrn(r1	phrn(r1	NOUN
ejpam-6658	399	10	,	,	PUNCT
ejpam-6658	399	11	r2	r2	PROPN
ejpam-6658	399	12	,	,	PUNCT
ejpam-6658	399	13	r3	r3	PROPN
ejpam-6658	399	14	)	)	PUNCT
ejpam-6658	399	15	tn	tn	PROPN
ejpam-6658	399	16	n	n	PROPN
ejpam-6658	399	17	!	!	PUNCT
ejpam-6658	399	18	.	.	PUNCT
ejpam-6658	400	1	(	(	PUNCT
ejpam-6658	400	2	71	71	NUM
ejpam-6658	400	3	)	)	PUNCT
ejpam-6658	400	4	in	in	ADP
ejpam-6658	400	5	view	view	NOUN
ejpam-6658	400	6	of	of	ADP
ejpam-6658	400	7	(	(	PUNCT
ejpam-6658	400	8	16	16	NUM
ejpam-6658	400	9	)	)	PUNCT
ejpam-6658	400	10	and	and	CCONJ
ejpam-6658	400	11	(	(	PUNCT
ejpam-6658	400	12	71	71	NUM
ejpam-6658	400	13	)	)	PUNCT
ejpam-6658	400	14	,	,	PUNCT
ejpam-6658	400	15	we	we	PRON
ejpam-6658	400	16	get	get	VERB
ejpam-6658	400	17	the	the	DET
ejpam-6658	400	18	assertion	assertion	NOUN
ejpam-6658	400	19	(	(	PUNCT
ejpam-6658	400	20	65	65	NUM
ejpam-6658	400	21	)	)	PUNCT
ejpam-6658	400	22	.	.	PUNCT
ejpam-6658	401	1	again	again	ADV
ejpam-6658	401	2	in	in	ADP
ejpam-6658	401	3	view	view	NOUN
ejpam-6658	401	4	of	of	ADP
ejpam-6658	401	5	(	(	PUNCT
ejpam-6658	401	6	17	17	NUM
ejpam-6658	401	7	)	)	PUNCT
ejpam-6658	401	8	and	and	CCONJ
ejpam-6658	401	9	(	(	PUNCT
ejpam-6658	401	10	56	56	NUM
ejpam-6658	401	11	)	)	PUNCT
ejpam-6658	401	12	,	,	PUNCT
ejpam-6658	401	13	we	we	PRON
ejpam-6658	401	14	get	get	VERB
ejpam-6658	401	15	the	the	DET
ejpam-6658	401	16	assertion	assertion	NOUN
ejpam-6658	401	17	(	(	PUNCT
ejpam-6658	401	18	66	66	NUM
ejpam-6658	401	19	)	)	PUNCT
ejpam-6658	401	20	.	.	PUNCT
ejpam-6658	402	1	theorem	theorem	VERB
ejpam-6658	402	2	11	11	NUM
ejpam-6658	402	3	.	.	PUNCT
ejpam-6658	403	1	the	the	DET
ejpam-6658	403	2	following	follow	VERB
ejpam-6658	403	3	differential	differential	ADJ
ejpam-6658	403	4	equation	equation	NOUN
ejpam-6658	403	5	for	for	ADP
ejpam-6658	403	6	phrn(r1	phrn(r1	NOUN
ejpam-6658	403	7	,	,	PUNCT
ejpam-6658	403	8	r2	r2	PROPN
ejpam-6658	403	9	,	,	PUNCT
ejpam-6658	403	10	r3	r3	PROPN
ejpam-6658	403	11	)	)	PUNCT
ejpam-6658	403	12	holds	hold	VERB
ejpam-6658	403	13	true	true	ADJ
ejpam-6658	403	14	:(	:(	PUNCT
ejpam-6658	403	15	r1dr1	r1dr1	NOUN
ejpam-6658	403	16	+	+	CCONJ
ejpam-6658	403	17	r′(dr1	r′(dr1	PROPN
ejpam-6658	403	18	)	)	PUNCT
ejpam-6658	403	19	r(dr1	r(dr1	NOUN
ejpam-6658	403	20	)	)	PUNCT
ejpam-6658	404	1	−	−	PROPN
ejpam-6658	405	1	n	n	CCONJ
ejpam-6658	405	2	(	(	PUNCT
ejpam-6658	405	3	r2	r2	PROPN
ejpam-6658	405	4	+	+	PROPN
ejpam-6658	405	5	d−1	d−1	PROPN
ejpam-6658	405	6	r3	r3	PROPN
ejpam-6658	405	7	)	)	PUNCT
ejpam-6658	405	8	dr1	dr1	PROPN
ejpam-6658	405	9	−	−	PROPN
ejpam-6658	405	10	n	n	CCONJ
ejpam-6658	405	11	)	)	PUNCT
ejpam-6658	405	12	phrn(r1	phrn(r1	NOUN
ejpam-6658	405	13	,	,	PUNCT
ejpam-6658	405	14	r2	r2	PROPN
ejpam-6658	405	15	,	,	PUNCT
ejpam-6658	405	16	r3	r3	PROPN
ejpam-6658	405	17	)	)	PUNCT
ejpam-6658	405	18	=	=	SYM
ejpam-6658	406	1	0	0	X
ejpam-6658	406	2	.	.	PUNCT
ejpam-6658	407	1	(	(	PUNCT
ejpam-6658	407	2	72	72	X
ejpam-6658	407	3	)	)	PUNCT
ejpam-6658	407	4	proof	proof	NOUN
ejpam-6658	407	5	.	.	PUNCT
ejpam-6658	408	1	using	use	VERB
ejpam-6658	408	2	(	(	PUNCT
ejpam-6658	408	3	65	65	NUM
ejpam-6658	408	4	)	)	PUNCT
ejpam-6658	408	5	and	and	CCONJ
ejpam-6658	408	6	(	(	PUNCT
ejpam-6658	408	7	66	66	NUM
ejpam-6658	408	8	)	)	PUNCT
ejpam-6658	408	9	in	in	ADP
ejpam-6658	408	10	(	(	PUNCT
ejpam-6658	408	11	19	19	NUM
ejpam-6658	408	12	)	)	PUNCT
ejpam-6658	408	13	,	,	PUNCT
ejpam-6658	408	14	we	we	PRON
ejpam-6658	408	15	get	get	VERB
ejpam-6658	408	16	(	(	PUNCT
ejpam-6658	408	17	r1dr1	r1dr1	NOUN
ejpam-6658	408	18	+	+	CCONJ
ejpam-6658	408	19	r′(d̂r1	r′(d̂r1	PROPN
ejpam-6658	408	20	)	)	PUNCT
ejpam-6658	408	21	r(d̂r1	r(d̂r1	PROPN
ejpam-6658	408	22	)	)	PUNCT
ejpam-6658	409	1	dr1	dr1	PROPN
ejpam-6658	409	2	−	−	PROPN
ejpam-6658	409	3	n	n	CCONJ
ejpam-6658	409	4	(	(	PUNCT
ejpam-6658	409	5	r2	r2	PROPN
ejpam-6658	409	6	+	+	PROPN
ejpam-6658	409	7	d−1	d−1	PROPN
ejpam-6658	409	8	r3	r3	PROPN
ejpam-6658	409	9	)	)	PUNCT
ejpam-6658	409	10	dr1	dr1	PROPN
ejpam-6658	409	11	)	)	PUNCT
ejpam-6658	409	12	phrn(r1	phrn(r1	NOUN
ejpam-6658	409	13	,	,	PUNCT
ejpam-6658	409	14	r2	r2	PROPN
ejpam-6658	409	15	,	,	PUNCT
ejpam-6658	409	16	r3	r3	PROPN
ejpam-6658	409	17	)	)	PUNCT
ejpam-6658	409	18	=	=	SYM
ejpam-6658	410	1	n	n	PRON
ejpam-6658	410	2	phrn(r1	phrn(r1	NOUN
ejpam-6658	410	3	,	,	PUNCT
ejpam-6658	410	4	r2	r2	PROPN
ejpam-6658	410	5	,	,	PUNCT
ejpam-6658	410	6	r3	r3	PROPN
ejpam-6658	410	7	)	)	PUNCT
ejpam-6658	410	8	.	.	PUNCT
ejpam-6658	411	1	(	(	PUNCT
ejpam-6658	411	2	73	73	NUM
ejpam-6658	411	3	)	)	PUNCT
ejpam-6658	411	4	upon	upon	SCONJ
ejpam-6658	411	5	the	the	DET
ejpam-6658	411	6	simplification	simplification	NOUN
ejpam-6658	411	7	,	,	PUNCT
ejpam-6658	411	8	we	we	PRON
ejpam-6658	411	9	get	get	VERB
ejpam-6658	411	10	the	the	DET
ejpam-6658	411	11	assertion	assertion	NOUN
ejpam-6658	411	12	(	(	PUNCT
ejpam-6658	411	13	72	72	NUM
ejpam-6658	411	14	)	)	PUNCT
ejpam-6658	411	15	.	.	PUNCT
ejpam-6658	412	1	5	5	X
ejpam-6658	412	2	.	.	X
ejpam-6658	412	3	examples	example	NOUN
ejpam-6658	412	4	the	the	DET
ejpam-6658	412	5	appell	appell	ADJ
ejpam-6658	412	6	polynomial	polynomial	ADJ
ejpam-6658	412	7	family	family	NOUN
ejpam-6658	412	8	,	,	PUNCT
ejpam-6658	412	9	defined	define	VERB
ejpam-6658	412	10	by	by	ADP
ejpam-6658	412	11	the	the	DET
ejpam-6658	412	12	parameter	parameter	NOUN
ejpam-6658	412	13	function	function	NOUN
ejpam-6658	412	14	r(t	r(t	NOUN
ejpam-6658	412	15	)	)	PUNCT
ejpam-6658	412	16	,	,	PUNCT
ejpam-6658	412	17	provides	provide	VERB
ejpam-6658	412	18	solutions	solution	NOUN
ejpam-6658	412	19	to	to	ADP
ejpam-6658	412	20	specific	specific	ADJ
ejpam-6658	412	21	differential	differential	ADJ
ejpam-6658	412	22	equations	equation	NOUN
ejpam-6658	412	23	.	.	PUNCT
ejpam-6658	413	1	different	different	ADJ
ejpam-6658	413	2	choices	choice	NOUN
ejpam-6658	413	3	of	of	ADP
ejpam-6658	413	4	r(t	r(t	NOUN
ejpam-6658	413	5	)	)	PUNCT
ejpam-6658	413	6	generate	generate	VERB
ejpam-6658	413	7	various	various	ADJ
ejpam-6658	413	8	polynomials	polynomial	NOUN
ejpam-6658	413	9	,	,	PUNCT
ejpam-6658	413	10	allowing	allow	VERB
ejpam-6658	413	11	adaptability	adaptability	NOUN
ejpam-6658	413	12	in	in	ADP
ejpam-6658	413	13	mathematical	mathematical	ADJ
ejpam-6658	413	14	modeling	modeling	NOUN
ejpam-6658	413	15	.	.	PUNCT
ejpam-6658	414	1	this	this	DET
ejpam-6658	414	2	flexibility	flexibility	NOUN
ejpam-6658	414	3	makes	make	VERB
ejpam-6658	414	4	them	they	PRON
ejpam-6658	414	5	valuable	valuable	ADJ
ejpam-6658	414	6	in	in	ADP
ejpam-6658	414	7	physics	physics	NOUN
ejpam-6658	414	8	,	,	PUNCT
ejpam-6658	414	9	engineering	engineering	NOUN
ejpam-6658	414	10	,	,	PUNCT
ejpam-6658	414	11	and	and	CCONJ
ejpam-6658	414	12	other	other	ADJ
ejpam-6658	414	13	scientific	scientific	ADJ
ejpam-6658	414	14	fields	field	NOUN
ejpam-6658	414	15	.	.	PUNCT
ejpam-6658	415	1	table	table	NOUN
ejpam-6658	415	2	1	1	NUM
ejpam-6658	415	3	systematically	systematically	ADV
ejpam-6658	415	4	presents	present	VERB
ejpam-6658	415	5	their	their	PRON
ejpam-6658	415	6	generating	generating	NOUN
ejpam-6658	415	7	functions	function	NOUN
ejpam-6658	415	8	,	,	PUNCT
ejpam-6658	415	9	series	series	NOUN
ejpam-6658	415	10	definitions	definition	NOUN
ejpam-6658	415	11	,	,	PUNCT
ejpam-6658	415	12	and	and	CCONJ
ejpam-6658	415	13	numerical	numerical	ADJ
ejpam-6658	415	14	values	value	NOUN
ejpam-6658	415	15	.	.	PUNCT
ejpam-6658	416	1	generating	generating	NOUN
ejpam-6658	416	2	functions	function	NOUN
ejpam-6658	416	3	offer	offer	VERB
ejpam-6658	416	4	concise	concise	ADJ
ejpam-6658	416	5	power	power	NOUN
ejpam-6658	416	6	series	series	NOUN
ejpam-6658	416	7	representations	representation	NOUN
ejpam-6658	416	8	,	,	PUNCT
ejpam-6658	416	9	aiding	aid	VERB
ejpam-6658	416	10	analytical	analytical	ADJ
ejpam-6658	416	11	manipulation	manipulation	NOUN
ejpam-6658	416	12	.	.	PUNCT
ejpam-6658	417	1	series	series	NOUN
ejpam-6658	417	2	definitions	definition	NOUN
ejpam-6658	417	3	provide	provide	VERB
ejpam-6658	417	4	formal	formal	ADJ
ejpam-6658	417	5	expressions	expression	NOUN
ejpam-6658	417	6	crucial	crucial	ADJ
ejpam-6658	417	7	for	for	ADP
ejpam-6658	417	8	problem	problem	NOUN
ejpam-6658	417	9	-	-	PUNCT
ejpam-6658	417	10	solving	solving	NOUN
ejpam-6658	417	11	and	and	CCONJ
ejpam-6658	417	12	computation	computation	NOUN
ejpam-6658	417	13	.	.	PUNCT
ejpam-6658	418	1	numerical	numerical	ADJ
ejpam-6658	418	2	values	value	NOUN
ejpam-6658	418	3	enhance	enhance	VERB
ejpam-6658	418	4	practical	practical	ADJ
ejpam-6658	418	5	understanding	understanding	NOUN
ejpam-6658	418	6	and	and	CCONJ
ejpam-6658	418	7	facilitate	facilitate	VERB
ejpam-6658	418	8	real	real	ADJ
ejpam-6658	418	9	-	-	PUNCT
ejpam-6658	418	10	world	world	NOUN
ejpam-6658	418	11	applications	application	NOUN
ejpam-6658	418	12	.	.	PUNCT
ejpam-6658	419	1	these	these	DET
ejpam-6658	419	2	polynomials	polynomial	NOUN
ejpam-6658	419	3	are	be	AUX
ejpam-6658	419	4	widely	widely	ADV
ejpam-6658	419	5	used	use	VERB
ejpam-6658	419	6	in	in	ADP
ejpam-6658	419	7	probability	probability	NOUN
ejpam-6658	419	8	theory	theory	NOUN
ejpam-6658	419	9	,	,	PUNCT
ejpam-6658	419	10	quantum	quantum	NOUN
ejpam-6658	419	11	mechanics	mechanic	NOUN
ejpam-6658	419	12	,	,	PUNCT
ejpam-6658	419	13	and	and	CCONJ
ejpam-6658	419	14	signal	signal	ADJ
ejpam-6658	419	15	processing	processing	NOUN
ejpam-6658	419	16	.	.	PUNCT
ejpam-6658	420	1	their	their	PRON
ejpam-6658	420	2	versatility	versatility	NOUN
ejpam-6658	420	3	allows	allow	VERB
ejpam-6658	420	4	specialized	specialized	ADJ
ejpam-6658	420	5	solutions	solution	NOUN
ejpam-6658	420	6	for	for	ADP
ejpam-6658	420	7	complex	complex	ADJ
ejpam-6658	420	8	mathematical	mathematical	ADJ
ejpam-6658	420	9	problems	problem	NOUN
ejpam-6658	420	10	.	.	PUNCT
ejpam-6658	421	1	overall	overall	ADV
ejpam-6658	421	2	,	,	PUNCT
ejpam-6658	421	3	the	the	DET
ejpam-6658	421	4	appell	appell	ADJ
ejpam-6658	421	5	polynomial	polynomial	ADJ
ejpam-6658	421	6	family	family	NOUN
ejpam-6658	421	7	serves	serve	VERB
ejpam-6658	421	8	as	as	ADP
ejpam-6658	421	9	a	a	DET
ejpam-6658	421	10	powerful	powerful	ADJ
ejpam-6658	421	11	tool	tool	NOUN
ejpam-6658	421	12	in	in	ADP
ejpam-6658	421	13	scientific	scientific	ADJ
ejpam-6658	421	14	research	research	NOUN
ejpam-6658	421	15	.	.	PUNCT
ejpam-6658	422	1	the	the	DET
ejpam-6658	422	2	bernoulli	bernoulli	PROPN
ejpam-6658	422	3	,	,	PUNCT
ejpam-6658	422	4	euler	euler	NOUN
ejpam-6658	422	5	,	,	PUNCT
ejpam-6658	422	6	and	and	CCONJ
ejpam-6658	422	7	genocchi	genocchi	PROPN
ejpam-6658	422	8	numbers	number	NOUN
ejpam-6658	422	9	are	be	AUX
ejpam-6658	422	10	foundational	foundational	ADJ
ejpam-6658	422	11	in	in	ADP
ejpam-6658	422	12	mathematics	mathematic	NOUN
ejpam-6658	422	13	,	,	PUNCT
ejpam-6658	422	14	with	with	ADP
ejpam-6658	422	15	applications	application	NOUN
ejpam-6658	422	16	in	in	ADP
ejpam-6658	422	17	number	number	NOUN
ejpam-6658	422	18	theory	theory	NOUN
ejpam-6658	422	19	,	,	PUNCT
ejpam-6658	422	20	combinatorics	combinatoric	NOUN
ejpam-6658	422	21	,	,	PUNCT
ejpam-6658	422	22	algebraic	algebraic	ADJ
ejpam-6658	422	23	geometry	geometry	NOUN
ejpam-6658	422	24	,	,	PUNCT
ejpam-6658	422	25	and	and	CCONJ
ejpam-6658	422	26	more	more	ADJ
ejpam-6658	422	27	.	.	PUNCT
ejpam-6658	423	1	bernoulli	bernoulli	NOUN
ejpam-6658	423	2	numbers	number	NOUN
ejpam-6658	423	3	appear	appear	VERB
ejpam-6658	423	4	in	in	ADP
ejpam-6658	423	5	polynomials	polynomial	NOUN
ejpam-6658	423	6	and	and	CCONJ
ejpam-6658	423	7	the	the	DET
ejpam-6658	423	8	euler	euler	NOUN
ejpam-6658	423	9	-	-	PUNCT
ejpam-6658	423	10	maclaurin	maclaurin	NOUN
ejpam-6658	423	11	formula	formula	NOUN
ejpam-6658	423	12	,	,	PUNCT
ejpam-6658	423	13	while	while	SCONJ
ejpam-6658	423	14	euler	euler	NOUN
ejpam-6658	423	15	numbers	number	NOUN
ejpam-6658	423	16	contribute	contribute	VERB
ejpam-6658	423	17	to	to	ADP
ejpam-6658	423	18	modular	modular	ADJ
ejpam-6658	423	19	forms	form	NOUN
ejpam-6658	423	20	and	and	CCONJ
ejpam-6658	423	21	elliptic	elliptic	ADJ
ejpam-6658	423	22	curve	curve	NOUN
ejpam-6658	423	23	theory	theory	NOUN
ejpam-6658	423	24	.	.	PUNCT
ejpam-6658	424	1	genocchi	genocchi	PROPN
ejpam-6658	424	2	numbers	number	NOUN
ejpam-6658	424	3	play	play	VERB
ejpam-6658	424	4	a	a	DET
ejpam-6658	424	5	key	key	ADJ
ejpam-6658	424	6	role	role	NOUN
ejpam-6658	424	7	in	in	ADP
ejpam-6658	424	8	combinatorial	combinatorial	ADJ
ejpam-6658	424	9	problems	problem	NOUN
ejpam-6658	424	10	,	,	PUNCT
ejpam-6658	424	11	graph	graph	NOUN
ejpam-6658	424	12	theory	theory	NOUN
ejpam-6658	424	13	,	,	PUNCT
ejpam-6658	424	14	and	and	CCONJ
ejpam-6658	424	15	automata	automata	NOUN
ejpam-6658	424	16	theory	theory	NOUN
ejpam-6658	424	17	.	.	PUNCT
ejpam-6658	425	1	these	these	DET
ejpam-6658	425	2	numbers	number	NOUN
ejpam-6658	425	3	connect	connect	VERB
ejpam-6658	425	4	to	to	ADP
ejpam-6658	425	5	hyperbolic	hyperbolic	ADJ
ejpam-6658	425	6	secant	secant	ADJ
ejpam-6658	425	7	functions	function	NOUN
ejpam-6658	425	8	and	and	CCONJ
ejpam-6658	425	9	have	have	VERB
ejpam-6658	425	10	implications	implication	NOUN
ejpam-6658	425	11	in	in	ADP
ejpam-6658	425	12	quantum	quantum	ADJ
ejpam-6658	425	13	field	field	NOUN
ejpam-6658	425	14	theory	theory	NOUN
ejpam-6658	425	15	and	and	CCONJ
ejpam-6658	425	16	signal	signal	NOUN
ejpam-6658	425	17	processing	processing	NOUN
ejpam-6658	425	18	.	.	PUNCT
ejpam-6658	426	1	by	by	ADP
ejpam-6658	426	2	treating	treat	VERB
ejpam-6658	426	3	them	they	PRON
ejpam-6658	426	4	as	as	ADP
ejpam-6658	426	5	members	member	NOUN
ejpam-6658	426	6	of	of	ADP
ejpam-6658	426	7	the	the	DET
ejpam-6658	426	8	appell	appell	PROPN
ejpam-6658	426	9	family	family	NOUN
ejpam-6658	426	10	,	,	PUNCT
ejpam-6658	426	11	new	new	ADJ
ejpam-6658	426	12	polynomials	polynomial	NOUN
ejpam-6658	426	13	like	like	ADP
ejpam-6658	426	14	the	the	DET
ejpam-6658	426	15	two	two	NUM
ejpam-6658	426	16	-	-	PUNCT
ejpam-6658	426	17	iterated	iterate	VERB
ejpam-6658	426	18	degenerate	degenerate	ADJ
ejpam-6658	426	19	hermite	hermite	ADJ
ejpam-6658	426	20	-	-	PUNCT
ejpam-6658	426	21	appell	appell	ADJ
ejpam-6658	426	22	polynomials	polynomial	NOUN
ejpam-6658	426	23	are	be	AUX
ejpam-6658	426	24	derived	derive	VERB
ejpam-6658	426	25	,	,	PUNCT
ejpam-6658	426	26	offering	offer	VERB
ejpam-6658	426	27	rich	rich	ADJ
ejpam-6658	426	28	research	research	NOUN
ejpam-6658	426	29	opportunities	opportunity	NOUN
ejpam-6658	426	30	in	in	ADP
ejpam-6658	426	31	their	their	PRON
ejpam-6658	426	32	generating	generating	NOUN
ejpam-6658	426	33	expressions	expression	NOUN
ejpam-6658	426	34	and	and	CCONJ
ejpam-6658	426	35	characteristics	characteristic	NOUN
ejpam-6658	426	36	.	.	PUNCT
ejpam-6658	427	1	as	as	ADP
ejpam-6658	427	2	a	a	DET
ejpam-6658	427	3	result	result	NOUN
ejpam-6658	427	4	,	,	PUNCT
ejpam-6658	427	5	different	different	ADJ
ejpam-6658	427	6	members	member	NOUN
ejpam-6658	427	7	of	of	ADP
ejpam-6658	427	8	phrn(r1	phrn(r1	NOUN
ejpam-6658	427	9	,	,	PUNCT
ejpam-6658	427	10	r2	r2	PROPN
ejpam-6658	427	11	,	,	PUNCT
ejpam-6658	427	12	r3	r3	PROPN
ejpam-6658	427	13	)	)	PUNCT
ejpam-6658	427	14	appear	appear	VERB
ejpam-6658	427	15	as	as	ADP
ejpam-6658	427	16	laguerre	laguerre	NOUN
ejpam-6658	427	17	-	-	PUNCT
ejpam-6658	427	18	hermite	hermite	NOUN
ejpam-6658	427	19	-	-	PUNCT
ejpam-6658	427	20	based	base	VERB
ejpam-6658	427	21	bernoulli	bernoulli	PROPN
ejpam-6658	427	22	w.	w.	PROPN
ejpam-6658	427	23	a.	a.	PROPN
ejpam-6658	427	24	khan	khan	PROPN
ejpam-6658	427	25	,	,	PUNCT
ejpam-6658	427	26	h.	h.	PROPN
ejpam-6658	427	27	qawaqneh	qawaqneh	PROPN
ejpam-6658	427	28	,	,	PUNCT
ejpam-6658	427	29	h.	h.	PROPN
ejpam-6658	427	30	aydi	aydi	VERB
ejpam-6658	427	31	/	/	SYM
ejpam-6658	427	32	eur	eur	NOUN
ejpam-6658	427	33	.	.	PUNCT
ejpam-6658	428	1	j.	j.	PROPN
ejpam-6658	428	2	pure	pure	PROPN
ejpam-6658	428	3	appl	appl	PROPN
ejpam-6658	428	4	.	.	PROPN
ejpam-6658	428	5	math	math	PROPN
ejpam-6658	428	6	,	,	PUNCT
ejpam-6658	428	7	18	18	NUM
ejpam-6658	428	8	(	(	PUNCT
ejpam-6658	428	9	3	3	NUM
ejpam-6658	428	10	)	)	PUNCT
ejpam-6658	428	11	(	(	PUNCT
ejpam-6658	428	12	2025	2025	NUM
ejpam-6658	428	13	)	)	PUNCT
ejpam-6658	428	14	,	,	PUNCT
ejpam-6658	428	15	6658	6658	NUM
ejpam-6658	428	16	18	18	NUM
ejpam-6658	428	17	of	of	ADP
ejpam-6658	428	18	22	22	NUM
ejpam-6658	428	19	polynomials	polynomial	NOUN
ejpam-6658	428	20	phbn(r1	phbn(r1	NOUN
ejpam-6658	428	21	,	,	PUNCT
ejpam-6658	428	22	r2	r2	PROPN
ejpam-6658	428	23	,	,	PUNCT
ejpam-6658	428	24	r3	r3	PROPN
ejpam-6658	428	25	)	)	PUNCT
ejpam-6658	428	26	,	,	PUNCT
ejpam-6658	428	27	laguerre	laguerre	NOUN
ejpam-6658	428	28	-	-	PUNCT
ejpam-6658	428	29	hermite	hermite	ADJ
ejpam-6658	428	30	-	-	PUNCT
ejpam-6658	428	31	euler	euler	NOUN
ejpam-6658	428	32	polynomials	polynomial	NOUN
ejpam-6658	428	33	phen(r1	phen(r1	NOUN
ejpam-6658	428	34	,	,	PUNCT
ejpam-6658	428	35	r2	r2	PROPN
ejpam-6658	428	36	,	,	PUNCT
ejpam-6658	428	37	r3	r3	PROPN
ejpam-6658	428	38	)	)	PUNCT
ejpam-6658	428	39	,	,	PUNCT
ejpam-6658	428	40	and	and	CCONJ
ejpam-6658	428	41	laguerre	laguerre	NOUN
ejpam-6658	428	42	-	-	PUNCT
ejpam-6658	428	43	hermite	hermite	ADJ
ejpam-6658	428	44	-	-	PUNCT
ejpam-6658	428	45	genocchi	genocchi	PROPN
ejpam-6658	428	46	polynomials	polynomial	VERB
ejpam-6658	428	47	phgn(r1	phgn(r1	NOUN
ejpam-6658	428	48	,	,	PUNCT
ejpam-6658	428	49	r2	r2	PROPN
ejpam-6658	428	50	,	,	PUNCT
ejpam-6658	428	51	r3	r3	PROPN
ejpam-6658	428	52	)	)	PUNCT
ejpam-6658	428	53	.	.	PUNCT
ejpam-6658	429	1	the	the	DET
ejpam-6658	429	2	following	follow	VERB
ejpam-6658	429	3	expressions	expression	NOUN
ejpam-6658	429	4	can	can	AUX
ejpam-6658	429	5	be	be	AUX
ejpam-6658	429	6	used	use	VERB
ejpam-6658	429	7	to	to	PART
ejpam-6658	429	8	cast	cast	VERB
ejpam-6658	429	9	these	these	DET
ejpam-6658	429	10	polynomials	polynomial	NOUN
ejpam-6658	429	11	:	:	PUNCT
ejpam-6658	429	12	t	t	X
ejpam-6658	429	13	et	et	NOUN
ejpam-6658	429	14	−	−	PROPN
ejpam-6658	429	15	1	1	NUM
ejpam-6658	429	16	er1t+r2t2c0(r3	er1t+r2t2c0(r3	PROPN
ejpam-6658	429	17	t	t	NOUN
ejpam-6658	429	18	)	)	PUNCT
ejpam-6658	429	19	=	=	PUNCT
ejpam-6658	430	1	∞∑	∞∑	PRON
ejpam-6658	430	2	n=0	n=0	PUNCT
ejpam-6658	430	3	phbn(r1	phbn(r1	NOUN
ejpam-6658	430	4	,	,	PUNCT
ejpam-6658	430	5	r2	r2	PROPN
ejpam-6658	430	6	,	,	PUNCT
ejpam-6658	430	7	r3	r3	PROPN
ejpam-6658	430	8	)	)	PUNCT
ejpam-6658	430	9	tn	tn	PROPN
ejpam-6658	430	10	n	n	PROPN
ejpam-6658	430	11	!	!	PROPN
ejpam-6658	430	12	,	,	PUNCT
ejpam-6658	430	13	(	(	PUNCT
ejpam-6658	430	14	74	74	X
ejpam-6658	430	15	)	)	PUNCT
ejpam-6658	430	16	2	2	NUM
ejpam-6658	430	17	et	et	NOUN
ejpam-6658	430	18	+	+	NOUN
ejpam-6658	430	19	1	1	NUM
ejpam-6658	430	20	er1t+r2t2c0(r3	er1t+r2t2c0(r3	NOUN
ejpam-6658	430	21	t	t	NOUN
ejpam-6658	430	22	)	)	PUNCT
ejpam-6658	430	23	=	=	PUNCT
ejpam-6658	431	1	∞∑	∞∑	PRON
ejpam-6658	431	2	n=0	n=0	NUM
ejpam-6658	431	3	phen(r1	phen(r1	NOUN
ejpam-6658	431	4	,	,	PUNCT
ejpam-6658	431	5	r2	r2	PROPN
ejpam-6658	431	6	,	,	PUNCT
ejpam-6658	431	7	r3	r3	PROPN
ejpam-6658	431	8	)	)	PUNCT
ejpam-6658	431	9	tn	tn	PROPN
ejpam-6658	431	10	n	n	PROPN
ejpam-6658	431	11	!	!	PROPN
ejpam-6658	431	12	,	,	PUNCT
ejpam-6658	431	13	(	(	PUNCT
ejpam-6658	431	14	75	75	NUM
ejpam-6658	431	15	)	)	PUNCT
ejpam-6658	431	16	and	and	CCONJ
ejpam-6658	431	17	2	2	NUM
ejpam-6658	431	18	t	t	NOUN
ejpam-6658	431	19	et	et	NOUN
ejpam-6658	431	20	+	+	CCONJ
ejpam-6658	431	21	1	1	NUM
ejpam-6658	431	22	er1t+r2t2c0(r3	er1t+r2t2c0(r3	NOUN
ejpam-6658	431	23	t	t	NOUN
ejpam-6658	431	24	)	)	PUNCT
ejpam-6658	431	25	=	=	PUNCT
ejpam-6658	432	1	∞∑	∞∑	NUM
ejpam-6658	432	2	n=0	n=0	NUM
ejpam-6658	432	3	phgn(r1	phgn(r1	NOUN
ejpam-6658	432	4	,	,	PUNCT
ejpam-6658	432	5	r2	r2	PROPN
ejpam-6658	432	6	,	,	PUNCT
ejpam-6658	432	7	r3	r3	PROPN
ejpam-6658	432	8	)	)	PUNCT
ejpam-6658	432	9	tn	tn	PROPN
ejpam-6658	432	10	n	n	PROPN
ejpam-6658	432	11	!	!	PUNCT
ejpam-6658	432	12	.	.	PUNCT
ejpam-6658	433	1	(	(	PUNCT
ejpam-6658	433	2	76	76	NUM
ejpam-6658	433	3	)	)	PUNCT
ejpam-6658	433	4	for	for	ADP
ejpam-6658	433	5	instance	instance	NOUN
ejpam-6658	433	6	the	the	DET
ejpam-6658	433	7	laguerre	laguerre	NOUN
ejpam-6658	433	8	-	-	PUNCT
ejpam-6658	433	9	hermite	hermite	NOUN
ejpam-6658	433	10	-	-	PUNCT
ejpam-6658	433	11	based	base	VERB
ejpam-6658	433	12	bernoulli	bernoulli	NOUN
ejpam-6658	433	13	polynomials	polynomial	VERB
ejpam-6658	433	14	phbn(r1	phbn(r1	NOUN
ejpam-6658	433	15	,	,	PUNCT
ejpam-6658	433	16	r2	r2	PROPN
ejpam-6658	433	17	,	,	PUNCT
ejpam-6658	433	18	r3	r3	PROPN
ejpam-6658	433	19	)	)	PUNCT
ejpam-6658	433	20	,	,	PUNCT
ejpam-6658	433	21	laguerrehermite	laguerrehermite	PROPN
ejpam-6658	433	22	-	-	PUNCT
ejpam-6658	433	23	euler	euler	NOUN
ejpam-6658	433	24	polynomials	polynomial	NOUN
ejpam-6658	433	25	phen(r1	phen(r1	NOUN
ejpam-6658	433	26	,	,	PUNCT
ejpam-6658	433	27	r2	r2	PROPN
ejpam-6658	433	28	,	,	PUNCT
ejpam-6658	433	29	r3	r3	PROPN
ejpam-6658	433	30	)	)	PUNCT
ejpam-6658	433	31	,	,	PUNCT
ejpam-6658	433	32	and	and	CCONJ
ejpam-6658	433	33	laguerre	laguerre	NOUN
ejpam-6658	433	34	-	-	PUNCT
ejpam-6658	433	35	hermite	hermite	ADJ
ejpam-6658	433	36	-	-	PUNCT
ejpam-6658	433	37	genocchi	genocchi	PROPN
ejpam-6658	433	38	polynomials	polynomial	VERB
ejpam-6658	433	39	phgn(r1	phgn(r1	NOUN
ejpam-6658	433	40	,	,	PUNCT
ejpam-6658	433	41	r2	r2	PROPN
ejpam-6658	433	42	,	,	PUNCT
ejpam-6658	433	43	r3	r3	PROPN
ejpam-6658	433	44	)	)	PUNCT
ejpam-6658	433	45	are	be	AUX
ejpam-6658	433	46	defined	define	VERB
ejpam-6658	433	47	by	by	ADP
ejpam-6658	433	48	the	the	DET
ejpam-6658	433	49	following	follow	VERB
ejpam-6658	433	50	operational	operational	ADJ
ejpam-6658	433	51	identities	identity	NOUN
ejpam-6658	433	52	:	:	PUNCT
ejpam-6658	433	53	phbn(r1	phbn(r1	NOUN
ejpam-6658	433	54	,	,	PUNCT
ejpam-6658	433	55	r2	r2	PROPN
ejpam-6658	433	56	,	,	PUNCT
ejpam-6658	433	57	r3	r3	PROPN
ejpam-6658	433	58	)	)	PUNCT
ejpam-6658	433	59	=	=	SYM
ejpam-6658	433	60	exp	exp	NOUN
ejpam-6658	433	61	(	(	PUNCT
ejpam-6658	433	62	−d̂−1	−d̂−1	PROPN
ejpam-6658	433	63	r3	r3	PROPN
ejpam-6658	433	64	∂	∂	NOUN
ejpam-6658	433	65	∂r1	∂r1	PROPN
ejpam-6658	433	66	)	)	PUNCT
ejpam-6658	433	67	{	{	PUNCT
ejpam-6658	433	68	hbn(r1	hbn(r1	ADV
ejpam-6658	433	69	,	,	PUNCT
ejpam-6658	433	70	r2	r2	PROPN
ejpam-6658	433	71	)	)	PUNCT
ejpam-6658	433	72	}	}	PUNCT
ejpam-6658	433	73	=	=	SYM
ejpam-6658	433	74	exp	exp	NOUN
ejpam-6658	433	75	(	(	PUNCT
ejpam-6658	433	76	r2	r2	PROPN
ejpam-6658	433	77	∂2	∂2	PROPN
ejpam-6658	433	78	∂r21	∂r21	NOUN
ejpam-6658	433	79	)	)	PUNCT
ejpam-6658	433	80	{	{	PUNCT
ejpam-6658	433	81	lbn(r1	lbn(r1	PROPN
ejpam-6658	433	82	,	,	PUNCT
ejpam-6658	433	83	r3	r3	PROPN
ejpam-6658	433	84	)	)	PUNCT
ejpam-6658	433	85	}	}	PUNCT
ejpam-6658	433	86	,	,	PUNCT
ejpam-6658	433	87	(	(	PUNCT
ejpam-6658	433	88	77	77	X
ejpam-6658	433	89	)	)	PUNCT
ejpam-6658	433	90	phen(r1	phen(r1	NOUN
ejpam-6658	433	91	,	,	PUNCT
ejpam-6658	433	92	r2	r2	PROPN
ejpam-6658	433	93	,	,	PUNCT
ejpam-6658	433	94	r3	r3	PROPN
ejpam-6658	433	95	)	)	PUNCT
ejpam-6658	433	96	=	=	SYM
ejpam-6658	433	97	exp	exp	NOUN
ejpam-6658	433	98	(	(	PUNCT
ejpam-6658	433	99	−d̂−1	−d̂−1	PROPN
ejpam-6658	433	100	r3	r3	PROPN
ejpam-6658	433	101	∂	∂	NOUN
ejpam-6658	433	102	∂r1	∂r1	PROPN
ejpam-6658	433	103	)	)	PUNCT
ejpam-6658	433	104	{	{	PUNCT
ejpam-6658	433	105	hen(r1	hen(r1	ADV
ejpam-6658	433	106	,	,	PUNCT
ejpam-6658	433	107	r2	r2	PROPN
ejpam-6658	433	108	)	)	PUNCT
ejpam-6658	433	109	}	}	PUNCT
ejpam-6658	433	110	=	=	SYM
ejpam-6658	433	111	exp	exp	NOUN
ejpam-6658	433	112	(	(	PUNCT
ejpam-6658	433	113	r2	r2	PROPN
ejpam-6658	433	114	∂2	∂2	PROPN
ejpam-6658	433	115	∂r21	∂r21	NOUN
ejpam-6658	433	116	)	)	PUNCT
ejpam-6658	433	117	{	{	PUNCT
ejpam-6658	433	118	len(r1	len(r1	PROPN
ejpam-6658	433	119	,	,	PUNCT
ejpam-6658	433	120	r3	r3	PROPN
ejpam-6658	433	121	)	)	PUNCT
ejpam-6658	433	122	}	}	PUNCT
ejpam-6658	433	123	,	,	PUNCT
ejpam-6658	433	124	(	(	PUNCT
ejpam-6658	433	125	78	78	NUM
ejpam-6658	433	126	)	)	PUNCT
ejpam-6658	433	127	and	and	CCONJ
ejpam-6658	433	128	phgn(r1	phgn(r1	NOUN
ejpam-6658	433	129	,	,	PUNCT
ejpam-6658	433	130	r2	r2	PROPN
ejpam-6658	433	131	,	,	PUNCT
ejpam-6658	433	132	r3	r3	PROPN
ejpam-6658	433	133	)	)	PUNCT
ejpam-6658	433	134	=	=	SYM
ejpam-6658	433	135	exp	exp	NOUN
ejpam-6658	433	136	(	(	PUNCT
ejpam-6658	433	137	−d̂−1	−d̂−1	PROPN
ejpam-6658	433	138	r3	r3	PROPN
ejpam-6658	433	139	∂	∂	NOUN
ejpam-6658	433	140	∂r1	∂r1	PROPN
ejpam-6658	433	141	)	)	PUNCT
ejpam-6658	433	142	{	{	PUNCT
ejpam-6658	433	143	hgn(r1	hgn(r1	NOUN
ejpam-6658	433	144	,	,	PUNCT
ejpam-6658	433	145	r2	r2	PROPN
ejpam-6658	433	146	)	)	PUNCT
ejpam-6658	433	147	}	}	PUNCT
ejpam-6658	433	148	=	=	SYM
ejpam-6658	433	149	exp	exp	NOUN
ejpam-6658	433	150	(	(	PUNCT
ejpam-6658	433	151	r2	r2	PROPN
ejpam-6658	433	152	∂2	∂2	PROPN
ejpam-6658	433	153	∂r21	∂r21	NOUN
ejpam-6658	433	154	)	)	PUNCT
ejpam-6658	433	155	{	{	PUNCT
ejpam-6658	433	156	lgn(r1	lgn(r1	PROPN
ejpam-6658	433	157	,	,	PUNCT
ejpam-6658	433	158	r3	r3	PROPN
ejpam-6658	433	159	)	)	PUNCT
ejpam-6658	433	160	}	}	PUNCT
ejpam-6658	433	161	.	.	PUNCT
ejpam-6658	434	1	(	(	PUNCT
ejpam-6658	434	2	79	79	NUM
ejpam-6658	434	3	)	)	PUNCT
ejpam-6658	434	4	similarly	similarly	ADV
ejpam-6658	434	5	,	,	PUNCT
ejpam-6658	434	6	a	a	DET
ejpam-6658	434	7	similar	similar	ADJ
ejpam-6658	434	8	method	method	NOUN
ejpam-6658	434	9	can	can	AUX
ejpam-6658	434	10	be	be	AUX
ejpam-6658	434	11	used	use	VERB
ejpam-6658	434	12	to	to	PART
ejpam-6658	434	13	draw	draw	VERB
ejpam-6658	434	14	corresponding	corresponding	ADJ
ejpam-6658	434	15	results	result	NOUN
ejpam-6658	434	16	for	for	ADP
ejpam-6658	434	17	these	these	DET
ejpam-6658	434	18	polynomials	polynomial	NOUN
ejpam-6658	434	19	.	.	PUNCT
ejpam-6658	435	1	the	the	DET
ejpam-6658	435	2	monomiality	monomiality	NOUN
ejpam-6658	435	3	principle	principle	NOUN
ejpam-6658	435	4	,	,	PUNCT
ejpam-6658	435	5	which	which	PRON
ejpam-6658	435	6	looks	look	VERB
ejpam-6658	435	7	at	at	ADP
ejpam-6658	435	8	how	how	SCONJ
ejpam-6658	435	9	polynomials	polynomial	NOUN
ejpam-6658	435	10	behave	behave	VERB
ejpam-6658	435	11	in	in	ADP
ejpam-6658	435	12	respect	respect	NOUN
ejpam-6658	435	13	to	to	ADP
ejpam-6658	435	14	their	their	PRON
ejpam-6658	435	15	monomial	monomial	ADJ
ejpam-6658	435	16	coefficients	coefficient	NOUN
ejpam-6658	435	17	,	,	PUNCT
ejpam-6658	435	18	is	be	AUX
ejpam-6658	435	19	one	one	NUM
ejpam-6658	435	20	such	such	ADJ
ejpam-6658	435	21	result	result	NOUN
ejpam-6658	435	22	.	.	PUNCT
ejpam-6658	436	1	extensive	extensive	ADJ
ejpam-6658	436	2	study	study	NOUN
ejpam-6658	436	3	of	of	ADP
ejpam-6658	436	4	the	the	DET
ejpam-6658	436	5	monomiality	monomiality	NOUN
ejpam-6658	436	6	principle	principle	NOUN
ejpam-6658	436	7	provides	provide	VERB
ejpam-6658	436	8	important	important	ADJ
ejpam-6658	436	9	information	information	NOUN
ejpam-6658	436	10	about	about	ADP
ejpam-6658	436	11	the	the	DET
ejpam-6658	436	12	structure	structure	NOUN
ejpam-6658	436	13	and	and	CCONJ
ejpam-6658	436	14	characteristics	characteristic	NOUN
ejpam-6658	436	15	of	of	ADP
ejpam-6658	436	16	these	these	DET
ejpam-6658	436	17	polynomials	polynomial	NOUN
ejpam-6658	436	18	.	.	PUNCT
ejpam-6658	437	1	moreover	moreover	ADV
ejpam-6658	437	2	,	,	PUNCT
ejpam-6658	437	3	the	the	DET
ejpam-6658	437	4	polynomials	polynomial	NOUN
ejpam-6658	437	5	’	'	PUNCT
ejpam-6658	437	6	explicit	explicit	ADJ
ejpam-6658	437	7	expressions	expression	NOUN
ejpam-6658	437	8	can	can	AUX
ejpam-6658	437	9	be	be	AUX
ejpam-6658	437	10	found	find	VERB
ejpam-6658	437	11	,	,	PUNCT
ejpam-6658	437	12	offering	offer	VERB
ejpam-6658	437	13	a	a	DET
ejpam-6658	437	14	distinct	distinct	ADJ
ejpam-6658	437	15	depiction	depiction	NOUN
ejpam-6658	437	16	of	of	ADP
ejpam-6658	437	17	their	their	PRON
ejpam-6658	437	18	coefficients	coefficient	NOUN
ejpam-6658	437	19	and	and	CCONJ
ejpam-6658	437	20	terms	term	NOUN
ejpam-6658	437	21	.	.	PUNCT
ejpam-6658	438	1	this	this	PRON
ejpam-6658	438	2	makes	make	VERB
ejpam-6658	438	3	it	it	PRON
ejpam-6658	438	4	easier	easy	ADJ
ejpam-6658	438	5	to	to	PART
ejpam-6658	438	6	comprehend	comprehend	VERB
ejpam-6658	438	7	and	and	CCONJ
ejpam-6658	438	8	analyze	analyze	VERB
ejpam-6658	438	9	the	the	DET
ejpam-6658	438	10	polynomials	polynomial	NOUN
ejpam-6658	438	11	.	.	PUNCT
ejpam-6658	439	1	examining	examine	VERB
ejpam-6658	439	2	the	the	DET
ejpam-6658	439	3	differential	differential	ADJ
ejpam-6658	439	4	equations	equation	NOUN
ejpam-6658	439	5	that	that	SCONJ
ejpam-6658	439	6	these	these	DET
ejpam-6658	439	7	polynomials	polynomial	NOUN
ejpam-6658	439	8	satisfy	satisfy	VERB
ejpam-6658	439	9	is	be	AUX
ejpam-6658	439	10	another	another	DET
ejpam-6658	439	11	line	line	NOUN
ejpam-6658	439	12	of	of	ADP
ejpam-6658	439	13	inquiry	inquiry	NOUN
ejpam-6658	439	14	.	.	PUNCT
ejpam-6658	440	1	there	there	PRON
ejpam-6658	440	2	are	be	VERB
ejpam-6658	440	3	relationships	relationship	NOUN
ejpam-6658	440	4	between	between	ADP
ejpam-6658	440	5	these	these	DET
ejpam-6658	440	6	polynomials	polynomial	NOUN
ejpam-6658	440	7	and	and	CCONJ
ejpam-6658	440	8	other	other	ADJ
ejpam-6658	440	9	mathematical	mathematical	ADJ
ejpam-6658	440	10	ideas	idea	NOUN
ejpam-6658	440	11	that	that	PRON
ejpam-6658	440	12	can	can	AUX
ejpam-6658	440	13	be	be	AUX
ejpam-6658	440	14	found	find	VERB
ejpam-6658	440	15	by	by	ADP
ejpam-6658	440	16	investigating	investigate	VERB
ejpam-6658	440	17	the	the	DET
ejpam-6658	440	18	related	relate	VERB
ejpam-6658	440	19	differential	differential	ADJ
ejpam-6658	440	20	equations	equation	NOUN
ejpam-6658	440	21	.	.	PUNCT
ejpam-6658	441	1	it	it	PRON
ejpam-6658	441	2	also	also	ADV
ejpam-6658	441	3	enables	enable	VERB
ejpam-6658	441	4	in	in	ADP
ejpam-6658	441	5	-	-	PUNCT
ejpam-6658	441	6	depth	depth	NOUN
ejpam-6658	441	7	comprehension	comprehension	NOUN
ejpam-6658	441	8	by	by	ADP
ejpam-6658	441	9	enabling	enable	VERB
ejpam-6658	441	10	researchers	researcher	NOUN
ejpam-6658	441	11	to	to	PART
ejpam-6658	441	12	examine	examine	VERB
ejpam-6658	441	13	their	their	PRON
ejpam-6658	441	14	behavior	behavior	NOUN
ejpam-6658	441	15	in	in	ADP
ejpam-6658	441	16	a	a	DET
ejpam-6658	441	17	variety	variety	NOUN
ejpam-6658	441	18	of	of	ADP
ejpam-6658	441	19	scenarios	scenario	NOUN
ejpam-6658	441	20	.	.	PUNCT
ejpam-6658	442	1	furthermore	furthermore	ADV
ejpam-6658	442	2	,	,	PUNCT
ejpam-6658	442	3	determinant	determinant	ADJ
ejpam-6658	442	4	forms	form	NOUN
ejpam-6658	442	5	investigation	investigation	NOUN
ejpam-6658	442	6	for	for	ADP
ejpam-6658	442	7	these	these	DET
ejpam-6658	442	8	polynomials	polynomial	NOUN
ejpam-6658	442	9	offers	offer	VERB
ejpam-6658	442	10	an	an	DET
ejpam-6658	442	11	important	important	ADJ
ejpam-6658	442	12	and	and	CCONJ
ejpam-6658	442	13	interesting	interesting	ADJ
ejpam-6658	442	14	research	research	NOUN
ejpam-6658	442	15	avenue	avenue	PROPN
ejpam-6658	442	16	.	.	PUNCT
ejpam-6658	443	1	you	you	PRON
ejpam-6658	443	2	can	can	AUX
ejpam-6658	443	3	use	use	VERB
ejpam-6658	443	4	determinants	determinant	NOUN
ejpam-6658	443	5	,	,	PUNCT
ejpam-6658	443	6	which	which	PRON
ejpam-6658	443	7	are	be	AUX
ejpam-6658	443	8	mathematical	mathematical	ADJ
ejpam-6658	443	9	entities	entity	NOUN
ejpam-6658	443	10	that	that	PRON
ejpam-6658	443	11	describe	describe	VERB
ejpam-6658	443	12	particular	particular	ADJ
ejpam-6658	443	13	aspects	aspect	NOUN
ejpam-6658	443	14	of	of	ADP
ejpam-6658	443	15	matrices	matrix	NOUN
ejpam-6658	443	16	,	,	PUNCT
ejpam-6658	443	17	to	to	PART
ejpam-6658	443	18	make	make	VERB
ejpam-6658	443	19	links	link	NOUN
ejpam-6658	443	20	between	between	ADP
ejpam-6658	443	21	these	these	DET
ejpam-6658	443	22	polynomials	polynomial	NOUN
ejpam-6658	443	23	and	and	CCONJ
ejpam-6658	443	24	linear	linear	PROPN
ejpam-6658	443	25	algebra	algebra	NOUN
ejpam-6658	443	26	.	.	PUNCT
ejpam-6658	444	1	this	this	DET
ejpam-6658	444	2	endeavor	endeavor	NOUN
ejpam-6658	444	3	creates	create	VERB
ejpam-6658	444	4	new	new	ADJ
ejpam-6658	444	5	opportunities	opportunity	NOUN
ejpam-6658	444	6	for	for	ADP
ejpam-6658	444	7	further	further	ADJ
ejpam-6658	444	8	understanding	understanding	NOUN
ejpam-6658	444	9	and	and	CCONJ
ejpam-6658	444	10	applications	application	NOUN
ejpam-6658	444	11	in	in	ADP
ejpam-6658	444	12	a	a	DET
ejpam-6658	444	13	larger	large	ADJ
ejpam-6658	444	14	mathematical	mathematical	ADJ
ejpam-6658	444	15	environment	environment	NOUN
ejpam-6658	444	16	.	.	PUNCT
ejpam-6658	445	1	w.	w.	PROPN
ejpam-6658	445	2	a.	a.	PROPN
ejpam-6658	445	3	khan	khan	PROPN
ejpam-6658	445	4	,	,	PUNCT
ejpam-6658	445	5	h.	h.	PROPN
ejpam-6658	445	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	445	7	,	,	PUNCT
ejpam-6658	445	8	h.	h.	PROPN
ejpam-6658	445	9	aydi	aydi	VERB
ejpam-6658	445	10	/	/	SYM
ejpam-6658	445	11	eur	eur	NOUN
ejpam-6658	445	12	.	.	PUNCT
ejpam-6658	446	1	j.	j.	PROPN
ejpam-6658	446	2	pure	pure	PROPN
ejpam-6658	446	3	appl	appl	PROPN
ejpam-6658	446	4	.	.	PROPN
ejpam-6658	446	5	math	math	PROPN
ejpam-6658	446	6	,	,	PUNCT
ejpam-6658	446	7	18	18	NUM
ejpam-6658	446	8	(	(	PUNCT
ejpam-6658	446	9	3	3	NUM
ejpam-6658	446	10	)	)	PUNCT
ejpam-6658	446	11	(	(	PUNCT
ejpam-6658	446	12	2025	2025	NUM
ejpam-6658	446	13	)	)	PUNCT
ejpam-6658	446	14	,	,	PUNCT
ejpam-6658	446	15	6658	6658	NUM
ejpam-6658	446	16	19	19	NUM
ejpam-6658	446	17	of	of	ADP
ejpam-6658	446	18	22	22	NUM
ejpam-6658	446	19	furthermore	furthermore	ADV
ejpam-6658	446	20	,	,	PUNCT
ejpam-6658	446	21	in	in	ADP
ejpam-6658	446	22	view	view	NOUN
ejpam-6658	446	23	of	of	ADP
ejpam-6658	446	24	expressions	expression	NOUN
ejpam-6658	446	25	(	(	PUNCT
ejpam-6658	446	26	60	60	NUM
ejpam-6658	446	27	)	)	PUNCT
ejpam-6658	446	28	,	,	PUNCT
ejpam-6658	446	29	the	the	DET
ejpam-6658	446	30	polynomials	polynomial	NOUN
ejpam-6658	446	31	phbn(r1	phbn(r1	NOUN
ejpam-6658	446	32	,	,	PUNCT
ejpam-6658	446	33	r2	r2	PROPN
ejpam-6658	446	34	,	,	PUNCT
ejpam-6658	446	35	r3	r3	PROPN
ejpam-6658	446	36	)	)	PUNCT
ejpam-6658	446	37	,	,	PUNCT
ejpam-6658	446	38	phen(r1	phen(r1	NOUN
ejpam-6658	446	39	,	,	PUNCT
ejpam-6658	446	40	r2	r2	PROPN
ejpam-6658	446	41	,	,	PUNCT
ejpam-6658	446	42	r3	r3	PROPN
ejpam-6658	446	43	)	)	PUNCT
ejpam-6658	446	44	and	and	CCONJ
ejpam-6658	446	45	phgn(r1	phgn(r1	NOUN
ejpam-6658	446	46	,	,	PUNCT
ejpam-6658	446	47	r2	r2	PROPN
ejpam-6658	446	48	,	,	PUNCT
ejpam-6658	446	49	r3	r3	PROPN
ejpam-6658	446	50	)	)	PUNCT
ejpam-6658	446	51	satisfy	satisfy	VERB
ejpam-6658	446	52	the	the	DET
ejpam-6658	446	53	following	follow	VERB
ejpam-6658	446	54	determinant	determinant	ADJ
ejpam-6658	446	55	representations	representation	NOUN
ejpam-6658	446	56	:	:	PUNCT
ejpam-6658	446	57	phbn(r1	phbn(r1	NOUN
ejpam-6658	446	58	,	,	PUNCT
ejpam-6658	446	59	r2	r2	PROPN
ejpam-6658	446	60	,	,	PUNCT
ejpam-6658	446	61	r3	r3	PROPN
ejpam-6658	446	62	)	)	PUNCT
ejpam-6658	446	63	=	=	PRON
ejpam-6658	447	1	(	(	PUNCT
ejpam-6658	447	2	−1)n	−1)n	X
ejpam-6658	447	3	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	447	4	1	1	NUM
ejpam-6658	447	5	ph1(r1	ph1(r1	NOUN
ejpam-6658	447	6	,	,	PUNCT
ejpam-6658	447	7	r2	r2	PROPN
ejpam-6658	447	8	,	,	PUNCT
ejpam-6658	447	9	r3	r3	PROPN
ejpam-6658	447	10	)	)	PUNCT
ejpam-6658	447	11	ph2(r1	ph2(r1	NOUN
ejpam-6658	447	12	,	,	PUNCT
ejpam-6658	447	13	r2	r2	PROPN
ejpam-6658	447	14	,	,	PUNCT
ejpam-6658	447	15	r3	r3	PROPN
ejpam-6658	447	16	)	)	PUNCT
ejpam-6658	447	17	·	·	PUNCT
ejpam-6658	447	18	·	·	PUNCT
ejpam-6658	447	19	·	·	PUNCT
ejpam-6658	447	20	phn−1(r1	phn−1(r1	PROPN
ejpam-6658	447	21	,	,	PUNCT
ejpam-6658	447	22	r2	r2	PROPN
ejpam-6658	447	23	,	,	PUNCT
ejpam-6658	447	24	r3	r3	PROPN
ejpam-6658	447	25	)	)	PUNCT
ejpam-6658	447	26	phn(r1	phn(r1	PROPN
ejpam-6658	447	27	,	,	PUNCT
ejpam-6658	447	28	r2	r2	PROPN
ejpam-6658	447	29	,	,	PUNCT
ejpam-6658	447	30	r3	r3	PROPN
ejpam-6658	447	31	)	)	PUNCT
ejpam-6658	447	32	1	1	NUM
ejpam-6658	447	33	1	1	NUM
ejpam-6658	447	34	2	2	NUM
ejpam-6658	447	35	1	1	NUM
ejpam-6658	447	36	3	3	NUM
ejpam-6658	447	37	·	·	PUNCT
ejpam-6658	447	38	·	·	PUNCT
ejpam-6658	447	39	·	·	PUNCT
ejpam-6658	448	1	1	1	NUM
ejpam-6658	448	2	n	n	NUM
ejpam-6658	448	3	1	1	NUM
ejpam-6658	448	4	n+1	n+1	NUM
ejpam-6658	448	5	0	0	NUM
ejpam-6658	448	6	1	1	NUM
ejpam-6658	448	7	(	(	PUNCT
ejpam-6658	448	8	2	2	NUM
ejpam-6658	448	9	1	1	NUM
ejpam-6658	448	10	)	)	PUNCT
ejpam-6658	448	11	1	1	NUM
ejpam-6658	448	12	2	2	NUM
ejpam-6658	448	13	·	·	PUNCT
ejpam-6658	448	14	·	·	PUNCT
ejpam-6658	448	15	·	·	PUNCT
ejpam-6658	448	16	(	(	PUNCT
ejpam-6658	448	17	n−1	n−1	PROPN
ejpam-6658	448	18	1	1	NUM
ejpam-6658	448	19	)	)	PUNCT
ejpam-6658	448	20	1	1	NUM
ejpam-6658	448	21	n−1	n−1	PROPN
ejpam-6658	448	22	(	(	PUNCT
ejpam-6658	448	23	n	n	NOUN
ejpam-6658	448	24	1	1	NUM
ejpam-6658	448	25	)	)	PUNCT
ejpam-6658	448	26	1	1	NUM
ejpam-6658	448	27	n	n	SYM
ejpam-6658	448	28	0	0	NUM
ejpam-6658	448	29	0	0	NUM
ejpam-6658	448	30	1	1	NUM
ejpam-6658	448	31	·	·	PUNCT
ejpam-6658	448	32	·	·	PUNCT
ejpam-6658	448	33	·	·	PUNCT
ejpam-6658	448	34	(	(	PUNCT
ejpam-6658	448	35	n−1	n−1	PROPN
ejpam-6658	448	36	2	2	NUM
ejpam-6658	448	37	)	)	PUNCT
ejpam-6658	448	38	1	1	NUM
ejpam-6658	448	39	n−2	n−2	PROPN
ejpam-6658	448	40	(	(	PUNCT
ejpam-6658	448	41	n	n	NOUN
ejpam-6658	448	42	2	2	NUM
ejpam-6658	448	43	)	)	PUNCT
ejpam-6658	448	44	1	1	NUM
ejpam-6658	448	45	n−1	n−1	PROPN
ejpam-6658	448	46	.	.	PUNCT
ejpam-6658	448	47	.	.	PUNCT
ejpam-6658	448	48	.	.	PUNCT
ejpam-6658	448	49	·	·	PUNCT
ejpam-6658	448	50	·	·	PUNCT
ejpam-6658	448	51	·	·	PUNCT
ejpam-6658	448	52	.	.	PUNCT
ejpam-6658	448	53	.	.	PUNCT
ejpam-6658	448	54	.	.	PUNCT
ejpam-6658	448	55	.	.	PUNCT
ejpam-6658	448	56	.	.	PUNCT
ejpam-6658	448	57	·	·	PUNCT
ejpam-6658	448	58	·	·	PUNCT
ejpam-6658	448	59	·	·	PUNCT
ejpam-6658	448	60	.	.	PUNCT
ejpam-6658	448	61	.	.	PUNCT
ejpam-6658	449	1	0	0	NUM
ejpam-6658	450	1	0	0	NUM
ejpam-6658	450	2	0	0	NUM
ejpam-6658	450	3	·	·	PUNCT
ejpam-6658	450	4	·	·	PUNCT
ejpam-6658	450	5	·	·	PUNCT
ejpam-6658	450	6	1	1	NUM
ejpam-6658	450	7	(	(	PUNCT
ejpam-6658	450	8	n	n	NUM
ejpam-6658	450	9	n−1	n−1	PROPN
ejpam-6658	450	10	)	)	PUNCT
ejpam-6658	450	11	1	1	NUM
ejpam-6658	450	12	2	2	NUM
ejpam-6658	450	13	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-6658	450	14	,	,	PUNCT
ejpam-6658	450	15	(	(	PUNCT
ejpam-6658	450	16	80	80	NUM
ejpam-6658	450	17	)	)	PUNCT
ejpam-6658	450	18	phen(r1	phen(r1	NOUN
ejpam-6658	450	19	,	,	PUNCT
ejpam-6658	450	20	r2	r2	PROPN
ejpam-6658	450	21	,	,	PUNCT
ejpam-6658	450	22	r3	r3	PROPN
ejpam-6658	450	23	)	)	PUNCT
ejpam-6658	450	24	=	=	PRON
ejpam-6658	450	25	(	(	PUNCT
ejpam-6658	450	26	−1)n	−1)n	X
ejpam-6658	450	27	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	450	28	1	1	NUM
ejpam-6658	450	29	ph1(r1	ph1(r1	NOUN
ejpam-6658	450	30	,	,	PUNCT
ejpam-6658	450	31	r2	r2	PROPN
ejpam-6658	450	32	,	,	PUNCT
ejpam-6658	450	33	r3	r3	PROPN
ejpam-6658	450	34	)	)	PUNCT
ejpam-6658	450	35	ph2(r1	ph2(r1	NOUN
ejpam-6658	450	36	,	,	PUNCT
ejpam-6658	450	37	r2	r2	PROPN
ejpam-6658	450	38	,	,	PUNCT
ejpam-6658	450	39	r3	r3	PROPN
ejpam-6658	450	40	)	)	PUNCT
ejpam-6658	450	41	·	·	PUNCT
ejpam-6658	450	42	·	·	PUNCT
ejpam-6658	450	43	·	·	PUNCT
ejpam-6658	450	44	phn−1(r1	phn−1(r1	PROPN
ejpam-6658	450	45	,	,	PUNCT
ejpam-6658	450	46	r2	r2	PROPN
ejpam-6658	450	47	,	,	PUNCT
ejpam-6658	450	48	r3	r3	PROPN
ejpam-6658	450	49	)	)	PUNCT
ejpam-6658	450	50	phn(r1	phn(r1	PROPN
ejpam-6658	450	51	,	,	PUNCT
ejpam-6658	450	52	r2	r2	PROPN
ejpam-6658	450	53	,	,	PUNCT
ejpam-6658	450	54	r3	r3	PROPN
ejpam-6658	450	55	)	)	PUNCT
ejpam-6658	450	56	1	1	NUM
ejpam-6658	450	57	1	1	NUM
ejpam-6658	450	58	2	2	NUM
ejpam-6658	450	59	1	1	NUM
ejpam-6658	450	60	2(1)2	2(1)2	NUM
ejpam-6658	450	61	·	·	PUNCT
ejpam-6658	450	62	·	·	PUNCT
ejpam-6658	450	63	·	·	PUNCT
ejpam-6658	450	64	1	1	NUM
ejpam-6658	450	65	2(1)n−1	2(1)n−1	NUM
ejpam-6658	450	66	1	1	NUM
ejpam-6658	450	67	2(1)n	2(1)n	NUM
ejpam-6658	450	68	0	0	NUM
ejpam-6658	450	69	1	1	NUM
ejpam-6658	450	70	(	(	PUNCT
ejpam-6658	450	71	2	2	NUM
ejpam-6658	450	72	1	1	NUM
ejpam-6658	450	73	)	)	PUNCT
ejpam-6658	450	74	1	1	NUM
ejpam-6658	450	75	2	2	NUM
ejpam-6658	450	76	·	·	PUNCT
ejpam-6658	450	77	·	·	PUNCT
ejpam-6658	450	78	·	·	PUNCT
ejpam-6658	450	79	(	(	PUNCT
ejpam-6658	450	80	n−1	n−1	PROPN
ejpam-6658	450	81	1	1	NUM
ejpam-6658	450	82	)	)	PUNCT
ejpam-6658	450	83	1	1	NUM
ejpam-6658	450	84	2(1)n−2	2(1)n−2	NUM
ejpam-6658	450	85	(	(	PUNCT
ejpam-6658	450	86	n	n	NOUN
ejpam-6658	450	87	1	1	NUM
ejpam-6658	450	88	)	)	PUNCT
ejpam-6658	450	89	1	1	NUM
ejpam-6658	450	90	2(1)n−1	2(1)n−1	NUM
ejpam-6658	450	91	0	0	NUM
ejpam-6658	450	92	0	0	NUM
ejpam-6658	450	93	1	1	NUM
ejpam-6658	450	94	·	·	PUNCT
ejpam-6658	450	95	·	·	PUNCT
ejpam-6658	450	96	·	·	PUNCT
ejpam-6658	450	97	(	(	PUNCT
ejpam-6658	450	98	n−1	n−1	PROPN
ejpam-6658	450	99	2	2	NUM
ejpam-6658	450	100	)	)	PUNCT
ejpam-6658	450	101	1	1	NUM
ejpam-6658	450	102	2(1)n−3	2(1)n−3	NUM
ejpam-6658	450	103	(	(	PUNCT
ejpam-6658	450	104	n	n	NOUN
ejpam-6658	450	105	2	2	NUM
ejpam-6658	450	106	)	)	PUNCT
ejpam-6658	450	107	1	1	NUM
ejpam-6658	450	108	2(1)n−2	2(1)n−2	NUM
ejpam-6658	450	109	.	.	PUNCT
ejpam-6658	450	110	.	.	PUNCT
ejpam-6658	450	111	.	.	PUNCT
ejpam-6658	450	112	·	·	PUNCT
ejpam-6658	450	113	·	·	PUNCT
ejpam-6658	450	114	·	·	PUNCT
ejpam-6658	450	115	.	.	PUNCT
ejpam-6658	450	116	.	.	PUNCT
ejpam-6658	450	117	.	.	PUNCT
ejpam-6658	450	118	.	.	PUNCT
ejpam-6658	450	119	.	.	PUNCT
ejpam-6658	450	120	·	·	PUNCT
ejpam-6658	450	121	·	·	PUNCT
ejpam-6658	450	122	·	·	PUNCT
ejpam-6658	450	123	.	.	PUNCT
ejpam-6658	450	124	.	.	PUNCT
ejpam-6658	451	1	0	0	NUM
ejpam-6658	452	1	0	0	NUM
ejpam-6658	452	2	0	0	NUM
ejpam-6658	452	3	·	·	PUNCT
ejpam-6658	452	4	·	·	PUNCT
ejpam-6658	452	5	·	·	PUNCT
ejpam-6658	452	6	1	1	NUM
ejpam-6658	452	7	(	(	PUNCT
ejpam-6658	452	8	n	n	NUM
ejpam-6658	452	9	n−1	n−1	PROPN
ejpam-6658	452	10	)	)	PUNCT
ejpam-6658	452	11	1	1	NUM
ejpam-6658	452	12	2	2	NUM
ejpam-6658	452	13	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-6658	452	14	,	,	PUNCT
ejpam-6658	452	15	(	(	PUNCT
ejpam-6658	452	16	81	81	NUM
ejpam-6658	452	17	)	)	PUNCT
ejpam-6658	452	18	and	and	CCONJ
ejpam-6658	452	19	phgn(r1	phgn(r1	NOUN
ejpam-6658	452	20	,	,	PUNCT
ejpam-6658	452	21	r2	r2	PROPN
ejpam-6658	452	22	,	,	PUNCT
ejpam-6658	452	23	r3	r3	PROPN
ejpam-6658	452	24	)	)	PUNCT
ejpam-6658	452	25	=	=	PRON
ejpam-6658	452	26	(	(	PUNCT
ejpam-6658	452	27	−1)n	−1)n	X
ejpam-6658	452	28	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	452	29	1	1	NUM
ejpam-6658	452	30	ph1(r1	ph1(r1	NOUN
ejpam-6658	452	31	,	,	PUNCT
ejpam-6658	452	32	r2	r2	PROPN
ejpam-6658	452	33	,	,	PUNCT
ejpam-6658	452	34	r3	r3	PROPN
ejpam-6658	452	35	)	)	PUNCT
ejpam-6658	452	36	ph2(r1	ph2(r1	NOUN
ejpam-6658	452	37	,	,	PUNCT
ejpam-6658	452	38	r2	r2	PROPN
ejpam-6658	452	39	,	,	PUNCT
ejpam-6658	452	40	r3	r3	PROPN
ejpam-6658	452	41	)	)	PUNCT
ejpam-6658	452	42	·	·	PUNCT
ejpam-6658	452	43	·	·	PUNCT
ejpam-6658	452	44	·	·	PUNCT
ejpam-6658	452	45	phn−1(r1	phn−1(r1	PROPN
ejpam-6658	452	46	,	,	PUNCT
ejpam-6658	452	47	r2	r2	PROPN
ejpam-6658	452	48	,	,	PUNCT
ejpam-6658	452	49	r3	r3	PROPN
ejpam-6658	452	50	)	)	PUNCT
ejpam-6658	452	51	phn(r1	phn(r1	PROPN
ejpam-6658	452	52	,	,	PUNCT
ejpam-6658	452	53	r2	r2	PROPN
ejpam-6658	452	54	,	,	PUNCT
ejpam-6658	452	55	r3	r3	PROPN
ejpam-6658	452	56	)	)	PUNCT
ejpam-6658	452	57	0	0	NUM
ejpam-6658	452	58	1	1	NUM
ejpam-6658	452	59	2	2	NUM
ejpam-6658	452	60	(	(	PUNCT
ejpam-6658	452	61	2	2	NUM
ejpam-6658	452	62	1	1	NUM
ejpam-6658	452	63	)	)	PUNCT
ejpam-6658	452	64	(	(	PUNCT
ejpam-6658	452	65	1)2	1)2	NUM
ejpam-6658	452	66	4	4	NUM
ejpam-6658	452	67	·	·	PUNCT
ejpam-6658	452	68	·	·	PUNCT
ejpam-6658	452	69	·	·	PUNCT
ejpam-6658	452	70	(	(	PUNCT
ejpam-6658	452	71	n−1	n−1	PROPN
ejpam-6658	452	72	1	1	NUM
ejpam-6658	452	73	)	)	PUNCT
ejpam-6658	452	74	(	(	PUNCT
ejpam-6658	452	75	1)n−1	1)n−1	NUM
ejpam-6658	452	76	2(n−1	2(n−1	NUM
ejpam-6658	452	77	)	)	PUNCT
ejpam-6658	452	78	(	(	PUNCT
ejpam-6658	452	79	n	n	NOUN
ejpam-6658	452	80	1	1	NUM
ejpam-6658	452	81	)	)	PUNCT
ejpam-6658	452	82	(	(	PUNCT
ejpam-6658	452	83	1)n	1)n	X
ejpam-6658	452	84	2n	2n	NUM
ejpam-6658	452	85	0	0	SYM
ejpam-6658	452	86	0	0	NUM
ejpam-6658	452	87	1	1	NUM
ejpam-6658	452	88	2	2	NUM
ejpam-6658	452	89	·	·	PUNCT
ejpam-6658	452	90	·	·	PUNCT
ejpam-6658	452	91	·	·	PUNCT
ejpam-6658	452	92	(	(	PUNCT
ejpam-6658	452	93	n−1	n−1	PROPN
ejpam-6658	452	94	2	2	NUM
ejpam-6658	452	95	)	)	PUNCT
ejpam-6658	452	96	(	(	PUNCT
ejpam-6658	452	97	1)n−2	1)n−2	NUM
ejpam-6658	452	98	2(n−2	2(n−2	NOUN
ejpam-6658	452	99	)	)	PUNCT
ejpam-6658	452	100	(	(	PUNCT
ejpam-6658	452	101	n	n	NOUN
ejpam-6658	452	102	2	2	NUM
ejpam-6658	452	103	)	)	PUNCT
ejpam-6658	452	104	(	(	PUNCT
ejpam-6658	452	105	1)n−1	1)n−1	NUM
ejpam-6658	452	106	2(n−1	2(n−1	NUM
ejpam-6658	452	107	)	)	PUNCT
ejpam-6658	452	108	...	...	PUNCT
ejpam-6658	452	109	...	...	PUNCT
ejpam-6658	452	110	...	...	PUNCT
ejpam-6658	452	111	.	.	PUNCT
ejpam-6658	452	112	.	.	PUNCT
ejpam-6658	452	113	.	.	PUNCT
ejpam-6658	452	114	...	...	PUNCT
ejpam-6658	453	1	...	...	PUNCT
ejpam-6658	454	1	0	0	NUM
ejpam-6658	454	2	0	0	NUM
ejpam-6658	454	3	0	0	NUM
ejpam-6658	454	4	·	·	PUNCT
ejpam-6658	454	5	·	·	PUNCT
ejpam-6658	454	6	·	·	PUNCT
ejpam-6658	454	7	1	1	NUM
ejpam-6658	454	8	2	2	NUM
ejpam-6658	454	9	(	(	PUNCT
ejpam-6658	454	10	n	n	NUM
ejpam-6658	454	11	n−1	n−1	PROPN
ejpam-6658	454	12	)	)	PUNCT
ejpam-6658	454	13	(	(	PUNCT
ejpam-6658	454	14	1)2	1)2	NUM
ejpam-6658	454	15	4	4	NUM
ejpam-6658	454	16	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6658	454	17	.	.	PUNCT
ejpam-6658	455	1	(	(	PUNCT
ejpam-6658	455	2	82	82	X
ejpam-6658	455	3	)	)	PUNCT
ejpam-6658	455	4	w.	w.	PROPN
ejpam-6658	455	5	a.	a.	PROPN
ejpam-6658	455	6	khan	khan	PROPN
ejpam-6658	455	7	,	,	PUNCT
ejpam-6658	455	8	h.	h.	PROPN
ejpam-6658	455	9	qawaqneh	qawaqneh	PROPN
ejpam-6658	455	10	,	,	PUNCT
ejpam-6658	455	11	h.	h.	PROPN
ejpam-6658	455	12	aydi	aydi	VERB
ejpam-6658	455	13	/	/	SYM
ejpam-6658	455	14	eur	eur	NOUN
ejpam-6658	455	15	.	.	PUNCT
ejpam-6658	456	1	j.	j.	PROPN
ejpam-6658	456	2	pure	pure	PROPN
ejpam-6658	456	3	appl	appl	PROPN
ejpam-6658	456	4	.	.	PROPN
ejpam-6658	456	5	math	math	PROPN
ejpam-6658	456	6	,	,	PUNCT
ejpam-6658	456	7	18	18	NUM
ejpam-6658	456	8	(	(	PUNCT
ejpam-6658	456	9	3	3	NUM
ejpam-6658	456	10	)	)	PUNCT
ejpam-6658	456	11	(	(	PUNCT
ejpam-6658	456	12	2025	2025	NUM
ejpam-6658	456	13	)	)	PUNCT
ejpam-6658	456	14	,	,	PUNCT
ejpam-6658	456	15	6658	6658	NUM
ejpam-6658	456	16	20	20	NUM
ejpam-6658	456	17	of	of	ADP
ejpam-6658	456	18	22	22	NUM
ejpam-6658	456	19	6	6	NUM
ejpam-6658	456	20	.	.	PUNCT
ejpam-6658	457	1	concluding	conclude	VERB
ejpam-6658	457	2	remarks	remark	NOUN
ejpam-6658	457	3	in	in	ADP
ejpam-6658	457	4	this	this	DET
ejpam-6658	457	5	study	study	NOUN
ejpam-6658	457	6	,	,	PUNCT
ejpam-6658	457	7	we	we	PRON
ejpam-6658	457	8	introduced	introduce	VERB
ejpam-6658	457	9	and	and	CCONJ
ejpam-6658	457	10	systematically	systematically	ADV
ejpam-6658	457	11	analyzed	analyze	VERB
ejpam-6658	457	12	a	a	DET
ejpam-6658	457	13	new	new	ADJ
ejpam-6658	457	14	generalization	generalization	NOUN
ejpam-6658	457	15	of	of	ADP
ejpam-6658	457	16	laguerre	laguerre	NOUN
ejpam-6658	457	17	and	and	CCONJ
ejpam-6658	457	18	laguerre	laguerre	NOUN
ejpam-6658	457	19	-	-	PUNCT
ejpam-6658	457	20	based	base	VERB
ejpam-6658	457	21	appell	appell	NOUN
ejpam-6658	457	22	polynomials	polynomial	NOUN
ejpam-6658	457	23	.	.	PUNCT
ejpam-6658	458	1	through	through	ADP
ejpam-6658	458	2	a	a	DET
ejpam-6658	458	3	detailed	detailed	ADJ
ejpam-6658	458	4	exploration	exploration	NOUN
ejpam-6658	458	5	of	of	ADP
ejpam-6658	458	6	their	their	PRON
ejpam-6658	458	7	fundamental	fundamental	ADJ
ejpam-6658	458	8	properties	property	NOUN
ejpam-6658	458	9	,	,	PUNCT
ejpam-6658	458	10	we	we	PRON
ejpam-6658	458	11	established	establish	VERB
ejpam-6658	458	12	recurrence	recurrence	NOUN
ejpam-6658	458	13	relations	relation	NOUN
ejpam-6658	458	14	,	,	PUNCT
ejpam-6658	458	15	multiplicative	multiplicative	ADJ
ejpam-6658	458	16	and	and	CCONJ
ejpam-6658	458	17	derivative	derivative	ADJ
ejpam-6658	458	18	operators	operator	NOUN
ejpam-6658	458	19	,	,	PUNCT
ejpam-6658	458	20	and	and	CCONJ
ejpam-6658	458	21	a	a	DET
ejpam-6658	458	22	governing	govern	VERB
ejpam-6658	458	23	differential	differential	ADJ
ejpam-6658	458	24	equation	equation	NOUN
ejpam-6658	458	25	via	via	ADP
ejpam-6658	458	26	quasi	quasi	NOUN
ejpam-6658	458	27	-	-	NOUN
ejpam-6658	458	28	monomiality	monomiality	NOUN
ejpam-6658	458	29	.	.	PUNCT
ejpam-6658	459	1	the	the	DET
ejpam-6658	459	2	derivation	derivation	NOUN
ejpam-6658	459	3	of	of	ADP
ejpam-6658	459	4	both	both	DET
ejpam-6658	459	5	series	series	NOUN
ejpam-6658	459	6	and	and	CCONJ
ejpam-6658	459	7	determinant	determinant	ADJ
ejpam-6658	459	8	representations	representation	NOUN
ejpam-6658	459	9	further	further	ADJ
ejpam-6658	459	10	highlights	highlight	NOUN
ejpam-6658	459	11	the	the	DET
ejpam-6658	459	12	structural	structural	ADJ
ejpam-6658	459	13	depth	depth	NOUN
ejpam-6658	459	14	of	of	ADP
ejpam-6658	459	15	this	this	DET
ejpam-6658	459	16	novel	novel	ADJ
ejpam-6658	459	17	polynomial	polynomial	ADJ
ejpam-6658	459	18	family	family	NOUN
ejpam-6658	459	19	.	.	PUNCT
ejpam-6658	460	1	additionally	additionally	ADV
ejpam-6658	460	2	,	,	PUNCT
ejpam-6658	460	3	the	the	DET
ejpam-6658	460	4	introduction	introduction	NOUN
ejpam-6658	460	5	of	of	ADP
ejpam-6658	460	6	generalized	generalized	ADJ
ejpam-6658	460	7	laguerre	laguerre	NOUN
ejpam-6658	460	8	-	-	PUNCT
ejpam-6658	460	9	hermite	hermite	ADJ
ejpam-6658	460	10	appell	appell	NOUN
ejpam-6658	460	11	polynomials	polynomial	NOUN
ejpam-6658	460	12	,	,	PUNCT
ejpam-6658	460	13	along	along	ADP
ejpam-6658	460	14	with	with	ADP
ejpam-6658	460	15	their	their	PRON
ejpam-6658	460	16	specific	specific	ADJ
ejpam-6658	460	17	cases	case	NOUN
ejpam-6658	460	18	involving	involve	VERB
ejpam-6658	460	19	bernoulli	bernoulli	PROPN
ejpam-6658	460	20	,	,	PUNCT
ejpam-6658	460	21	euler	euler	NOUN
ejpam-6658	460	22	,	,	PUNCT
ejpam-6658	460	23	and	and	CCONJ
ejpam-6658	460	24	genocchi	genocchi	PROPN
ejpam-6658	460	25	polynomials	polynomial	NOUN
ejpam-6658	460	26	,	,	PUNCT
ejpam-6658	460	27	enriches	enrich	VERB
ejpam-6658	460	28	the	the	DET
ejpam-6658	460	29	framework	framework	NOUN
ejpam-6658	460	30	of	of	ADP
ejpam-6658	460	31	special	special	ADJ
ejpam-6658	460	32	functions	function	NOUN
ejpam-6658	460	33	.	.	PUNCT
ejpam-6658	461	1	these	these	DET
ejpam-6658	461	2	findings	finding	NOUN
ejpam-6658	461	3	contribute	contribute	VERB
ejpam-6658	461	4	to	to	ADP
ejpam-6658	461	5	the	the	DET
ejpam-6658	461	6	broader	broad	ADJ
ejpam-6658	461	7	understanding	understanding	NOUN
ejpam-6658	461	8	of	of	ADP
ejpam-6658	461	9	polynomial	polynomial	ADJ
ejpam-6658	461	10	sequences	sequence	NOUN
ejpam-6658	461	11	and	and	CCONJ
ejpam-6658	461	12	their	their	PRON
ejpam-6658	461	13	applications	application	NOUN
ejpam-6658	461	14	in	in	ADP
ejpam-6658	461	15	mathematical	mathematical	ADJ
ejpam-6658	461	16	physics	physics	NOUN
ejpam-6658	461	17	and	and	CCONJ
ejpam-6658	461	18	differential	differential	ADJ
ejpam-6658	461	19	equations	equation	NOUN
ejpam-6658	461	20	.	.	PUNCT
ejpam-6658	462	1	for	for	ADP
ejpam-6658	462	2	future	future	ADJ
ejpam-6658	462	3	research	research	NOUN
ejpam-6658	462	4	,	,	PUNCT
ejpam-6658	462	5	the	the	DET
ejpam-6658	462	6	investigation	investigation	NOUN
ejpam-6658	462	7	of	of	ADP
ejpam-6658	462	8	these	these	DET
ejpam-6658	462	9	polynomials	polynomial	NOUN
ejpam-6658	462	10	in	in	ADP
ejpam-6658	462	11	the	the	DET
ejpam-6658	462	12	context	context	NOUN
ejpam-6658	462	13	of	of	ADP
ejpam-6658	462	14	orthogonality	orthogonality	NOUN
ejpam-6658	462	15	and	and	CCONJ
ejpam-6658	462	16	integral	integral	ADJ
ejpam-6658	462	17	transforms	transform	NOUN
ejpam-6658	462	18	could	could	AUX
ejpam-6658	462	19	provide	provide	VERB
ejpam-6658	462	20	further	further	ADJ
ejpam-6658	462	21	insights	insight	NOUN
ejpam-6658	462	22	into	into	ADP
ejpam-6658	462	23	their	their	PRON
ejpam-6658	462	24	analytical	analytical	ADJ
ejpam-6658	462	25	properties	property	NOUN
ejpam-6658	462	26	.	.	PUNCT
ejpam-6658	463	1	exploring	explore	VERB
ejpam-6658	463	2	their	their	PRON
ejpam-6658	463	3	connections	connection	NOUN
ejpam-6658	463	4	with	with	ADP
ejpam-6658	463	5	fractional	fractional	ADJ
ejpam-6658	463	6	calculus	calculus	NOUN
ejpam-6658	463	7	and	and	CCONJ
ejpam-6658	463	8	special	special	ADJ
ejpam-6658	463	9	function	function	NOUN
ejpam-6658	463	10	theory	theory	NOUN
ejpam-6658	463	11	may	may	AUX
ejpam-6658	463	12	yield	yield	VERB
ejpam-6658	463	13	new	new	ADJ
ejpam-6658	463	14	results	result	NOUN
ejpam-6658	463	15	with	with	ADP
ejpam-6658	463	16	applications	application	NOUN
ejpam-6658	463	17	in	in	ADP
ejpam-6658	463	18	approximation	approximation	NOUN
ejpam-6658	463	19	theory	theory	NOUN
ejpam-6658	463	20	and	and	CCONJ
ejpam-6658	463	21	signal	signal	ADJ
ejpam-6658	463	22	processing	processing	NOUN
ejpam-6658	463	23	.	.	PUNCT
ejpam-6658	464	1	furthermore	furthermore	ADV
ejpam-6658	464	2	,	,	PUNCT
ejpam-6658	464	3	the	the	DET
ejpam-6658	464	4	study	study	NOUN
ejpam-6658	464	5	of	of	ADP
ejpam-6658	464	6	their	their	PRON
ejpam-6658	464	7	extensions	extension	NOUN
ejpam-6658	464	8	in	in	ADP
ejpam-6658	464	9	the	the	DET
ejpam-6658	464	10	framework	framework	NOUN
ejpam-6658	464	11	of	of	ADP
ejpam-6658	464	12	q	q	NOUN
ejpam-6658	464	13	-	-	PUNCT
ejpam-6658	464	14	calculus	calculus	NOUN
ejpam-6658	464	15	and	and	CCONJ
ejpam-6658	464	16	number	number	NOUN
ejpam-6658	464	17	theory	theory	NOUN
ejpam-6658	464	18	could	could	AUX
ejpam-6658	464	19	reveal	reveal	VERB
ejpam-6658	464	20	deeper	deep	ADJ
ejpam-6658	464	21	algebraic	algebraic	ADJ
ejpam-6658	464	22	and	and	CCONJ
ejpam-6658	464	23	combinatorial	combinatorial	ADJ
ejpam-6658	464	24	properties	property	NOUN
ejpam-6658	464	25	.	.	PUNCT
ejpam-6658	465	1	finally	finally	ADV
ejpam-6658	465	2	,	,	PUNCT
ejpam-6658	465	3	the	the	DET
ejpam-6658	465	4	numerical	numerical	ADJ
ejpam-6658	465	5	aspects	aspect	NOUN
ejpam-6658	465	6	and	and	CCONJ
ejpam-6658	465	7	computational	computational	ADJ
ejpam-6658	465	8	implementations	implementation	NOUN
ejpam-6658	465	9	of	of	ADP
ejpam-6658	465	10	these	these	DET
ejpam-6658	465	11	polynomials	polynomial	NOUN
ejpam-6658	465	12	can	can	AUX
ejpam-6658	465	13	be	be	AUX
ejpam-6658	465	14	explored	explore	VERB
ejpam-6658	465	15	for	for	ADP
ejpam-6658	465	16	potential	potential	ADJ
ejpam-6658	465	17	applications	application	NOUN
ejpam-6658	465	18	in	in	ADP
ejpam-6658	465	19	scientific	scientific	ADJ
ejpam-6658	465	20	computing	computing	NOUN
ejpam-6658	465	21	and	and	CCONJ
ejpam-6658	465	22	engineering	engineering	NOUN
ejpam-6658	465	23	.	.	PUNCT
ejpam-6658	466	1	availability	availability	NOUN
ejpam-6658	466	2	of	of	ADP
ejpam-6658	466	3	data	datum	NOUN
ejpam-6658	466	4	and	and	CCONJ
ejpam-6658	466	5	materials	material	NOUN
ejpam-6658	466	6	not	not	PART
ejpam-6658	466	7	applicable	applicable	ADJ
ejpam-6658	466	8	.	.	PUNCT
ejpam-6658	467	1	competing	compete	VERB
ejpam-6658	467	2	interests	interest	NOUN
ejpam-6658	467	3	the	the	DET
ejpam-6658	467	4	authors	author	NOUN
ejpam-6658	467	5	declare	declare	VERB
ejpam-6658	467	6	no	no	DET
ejpam-6658	467	7	competing	compete	VERB
ejpam-6658	467	8	interests	interest	NOUN
ejpam-6658	467	9	.	.	PUNCT
ejpam-6658	468	1	authors	author	NOUN
ejpam-6658	468	2	’	'	PUNCT
ejpam-6658	468	3	contributions	contribution	NOUN
ejpam-6658	468	4	all	all	DET
ejpam-6658	468	5	authors	author	NOUN
ejpam-6658	468	6	contributed	contribute	VERB
ejpam-6658	468	7	equally	equally	ADV
ejpam-6658	468	8	to	to	ADP
ejpam-6658	468	9	the	the	DET
ejpam-6658	468	10	article	article	NOUN
ejpam-6658	468	11	.	.	PUNCT
ejpam-6658	469	1	acknowledgements	acknowledgement	NOUN
ejpam-6658	469	2	the	the	DET
ejpam-6658	469	3	authors	author	NOUN
ejpam-6658	469	4	acknowledge	acknowledge	VERB
ejpam-6658	469	5	the	the	DET
ejpam-6658	469	6	financial	financial	ADJ
ejpam-6658	469	7	support	support	NOUN
ejpam-6658	469	8	from	from	ADP
ejpam-6658	469	9	al	al	PROPN
ejpam-6658	469	10	-	-	PROPN
ejpam-6658	469	11	zaytoonah	zaytoonah	PROPN
ejpam-6658	469	12	university	university	PROPN
ejpam-6658	469	13	of	of	ADP
ejpam-6658	469	14	jordan	jordan	PROPN
ejpam-6658	469	15	,	,	PUNCT
ejpam-6658	469	16	amman	amman	PROPN
ejpam-6658	469	17	11733	11733	NUM
ejpam-6658	469	18	,	,	PUNCT
ejpam-6658	469	19	jordan	jordan	PROPN
ejpam-6658	469	20	.	.	PUNCT
ejpam-6658	470	1	references	reference	NOUN
ejpam-6658	470	2	[	[	X
ejpam-6658	470	3	1	1	NUM
ejpam-6658	470	4	]	]	PUNCT
ejpam-6658	470	5	g	g	NOUN
ejpam-6658	470	6	dattoli	dattoli	NOUN
ejpam-6658	470	7	and	and	CCONJ
ejpam-6658	470	8	a	a	DET
ejpam-6658	470	9	torre	torre	PROPN
ejpam-6658	470	10	.	.	PUNCT
ejpam-6658	471	1	operational	operational	ADJ
ejpam-6658	471	2	methods	method	NOUN
ejpam-6658	471	3	and	and	CCONJ
ejpam-6658	471	4	two	two	NUM
ejpam-6658	471	5	variable	variable	ADJ
ejpam-6658	471	6	laguerre	laguerre	NOUN
ejpam-6658	471	7	polynomials	polynomial	NOUN
ejpam-6658	471	8	.	.	PUNCT
ejpam-6658	472	1	atti	atti	PROPN
ejpam-6658	472	2	accad	accad	PROPN
ejpam-6658	472	3	.	.	PUNCT
ejpam-6658	473	1	sci	sci	PROPN
ejpam-6658	473	2	.	.	PUNCT
ejpam-6658	473	3	torino	torino	PROPN
ejpam-6658	473	4	cl	cl	NOUN
ejpam-6658	473	5	.	.	PUNCT
ejpam-6658	474	1	sci	sci	PROPN
ejpam-6658	474	2	.	.	PROPN
ejpam-6658	474	3	fis	fis	PROPN
ejpam-6658	474	4	.	.	PUNCT
ejpam-6658	474	5	mat	mat	PROPN
ejpam-6658	474	6	.	.	PUNCT
ejpam-6658	474	7	natur	natur	PROPN
ejpam-6658	474	8	,	,	PUNCT
ejpam-6658	474	9	132:3–9	132:3–9	NUM
ejpam-6658	474	10	,	,	PUNCT
ejpam-6658	474	11	1998	1998	NUM
ejpam-6658	474	12	.	.	PUNCT
ejpam-6658	475	1	w.	w.	PROPN
ejpam-6658	475	2	a.	a.	PROPN
ejpam-6658	475	3	khan	khan	PROPN
ejpam-6658	475	4	,	,	PUNCT
ejpam-6658	475	5	h.	h.	PROPN
ejpam-6658	475	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	475	7	,	,	PUNCT
ejpam-6658	475	8	h.	h.	PROPN
ejpam-6658	475	9	aydi	aydi	VERB
ejpam-6658	475	10	/	/	SYM
ejpam-6658	475	11	eur	eur	NOUN
ejpam-6658	475	12	.	.	PUNCT
ejpam-6658	476	1	j.	j.	PROPN
ejpam-6658	476	2	pure	pure	PROPN
ejpam-6658	476	3	appl	appl	PROPN
ejpam-6658	476	4	.	.	PROPN
ejpam-6658	476	5	math	math	PROPN
ejpam-6658	476	6	,	,	PUNCT
ejpam-6658	476	7	18	18	NUM
ejpam-6658	476	8	(	(	PUNCT
ejpam-6658	476	9	3	3	NUM
ejpam-6658	476	10	)	)	PUNCT
ejpam-6658	476	11	(	(	PUNCT
ejpam-6658	476	12	2025	2025	NUM
ejpam-6658	476	13	)	)	PUNCT
ejpam-6658	476	14	,	,	PUNCT
ejpam-6658	476	15	6658	6658	NUM
ejpam-6658	476	16	21	21	NUM
ejpam-6658	476	17	of	of	ADP
ejpam-6658	476	18	22	22	NUM
ejpam-6658	476	19	[	[	X
ejpam-6658	476	20	2	2	NUM
ejpam-6658	476	21	]	]	X
ejpam-6658	476	22	noor	noor	PROPN
ejpam-6658	476	23	alam	alam	PROPN
ejpam-6658	476	24	,	,	PUNCT
ejpam-6658	476	25	waseem	waseem	PROPN
ejpam-6658	476	26	ahmad	ahmad	PROPN
ejpam-6658	476	27	khan	khan	PROPN
ejpam-6658	476	28	,	,	PUNCT
ejpam-6658	476	29	can	can	AUX
ejpam-6658	476	30	kızılateş	kızılateş	PROPN
ejpam-6658	476	31	,	,	PUNCT
ejpam-6658	476	32	and	and	CCONJ
ejpam-6658	476	33	cheon	cheon	PROPN
ejpam-6658	476	34	seoung	seoung	PROPN
ejpam-6658	476	35	ryoo	ryoo	NOUN
ejpam-6658	476	36	.	.	PUNCT
ejpam-6658	477	1	twovariable	twovariable	ADJ
ejpam-6658	477	2	q	q	ADJ
ejpam-6658	477	3	-	-	ADJ
ejpam-6658	477	4	general	general	ADJ
ejpam-6658	477	5	-	-	PUNCT
ejpam-6658	477	6	appell	appell	NOUN
ejpam-6658	477	7	polynomials	polynomial	NOUN
ejpam-6658	477	8	within	within	ADP
ejpam-6658	477	9	the	the	DET
ejpam-6658	477	10	context	context	NOUN
ejpam-6658	477	11	of	of	ADP
ejpam-6658	477	12	the	the	DET
ejpam-6658	477	13	monomiality	monomiality	NOUN
ejpam-6658	477	14	principle	principle	NOUN
ejpam-6658	477	15	.	.	PUNCT
ejpam-6658	478	1	mathematics	mathematic	NOUN
ejpam-6658	478	2	,	,	PUNCT
ejpam-6658	478	3	13(5):765	13(5):765	NUM
ejpam-6658	478	4	,	,	PUNCT
ejpam-6658	478	5	2025	2025	NUM
ejpam-6658	478	6	.	.	PUNCT
ejpam-6658	479	1	[	[	X
ejpam-6658	479	2	3	3	X
ejpam-6658	479	3	]	]	X
ejpam-6658	479	4	naeem	naeem	PROPN
ejpam-6658	479	5	ahmad	ahmad	PROPN
ejpam-6658	479	6	and	and	CCONJ
ejpam-6658	479	7	waseem	waseem	PROPN
ejpam-6658	479	8	ahmad	ahmad	PROPN
ejpam-6658	479	9	khan	khan	PROPN
ejpam-6658	479	10	.	.	PUNCT
ejpam-6658	480	1	insights	insight	NOUN
ejpam-6658	480	2	into	into	ADP
ejpam-6658	480	3	new	new	ADJ
ejpam-6658	480	4	generalization	generalization	NOUN
ejpam-6658	480	5	of	of	ADP
ejpam-6658	480	6	qlegendre	qlegendre	NOUN
ejpam-6658	480	7	-	-	PUNCT
ejpam-6658	480	8	based	base	VERB
ejpam-6658	480	9	appell	appell	NOUN
ejpam-6658	480	10	polynomials	polynomial	NOUN
ejpam-6658	480	11	:	:	PUNCT
ejpam-6658	480	12	properties	property	NOUN
ejpam-6658	480	13	and	and	CCONJ
ejpam-6658	480	14	quasi	quasi	NOUN
ejpam-6658	480	15	monomiality	monomiality	NOUN
ejpam-6658	480	16	.	.	PUNCT
ejpam-6658	481	1	mathematics	mathematic	NOUN
ejpam-6658	481	2	,	,	PUNCT
ejpam-6658	481	3	13(6):955	13(6):955	NUM
ejpam-6658	481	4	,	,	PUNCT
ejpam-6658	481	5	2025	2025	NUM
ejpam-6658	481	6	.	.	PUNCT
ejpam-6658	482	1	[	[	X
ejpam-6658	482	2	4	4	X
ejpam-6658	482	3	]	]	PUNCT
ejpam-6658	482	4	naeem	naeem	PROPN
ejpam-6658	482	5	ahmad	ahmad	PROPN
ejpam-6658	482	6	and	and	CCONJ
ejpam-6658	482	7	waseem	waseem	PROPN
ejpam-6658	482	8	ahmad	ahmad	PROPN
ejpam-6658	482	9	khan	khan	PROPN
ejpam-6658	482	10	.	.	PUNCT
ejpam-6658	483	1	a	a	DET
ejpam-6658	483	2	new	new	ADJ
ejpam-6658	483	3	generalization	generalization	NOUN
ejpam-6658	483	4	of	of	ADP
ejpam-6658	483	5	q	q	NOUN
ejpam-6658	483	6	-	-	PUNCT
ejpam-6658	483	7	laguerre	laguerre	NOUN
ejpam-6658	483	8	-	-	PUNCT
ejpam-6658	483	9	based	base	VERB
ejpam-6658	483	10	appell	appell	ADJ
ejpam-6658	483	11	polynomials	polynomial	NOUN
ejpam-6658	483	12	and	and	CCONJ
ejpam-6658	483	13	quasi	quasi	NOUN
ejpam-6658	483	14	-	-	NOUN
ejpam-6658	483	15	monomiality	monomiality	NOUN
ejpam-6658	483	16	.	.	PUNCT
ejpam-6658	484	1	symmetry	symmetry	NOUN
ejpam-6658	484	2	,	,	PUNCT
ejpam-6658	484	3	17(3):439	17(3):439	NUM
ejpam-6658	484	4	,	,	PUNCT
ejpam-6658	484	5	2025	2025	NUM
ejpam-6658	484	6	.	.	PUNCT
ejpam-6658	485	1	[	[	X
ejpam-6658	485	2	5	5	NUM
ejpam-6658	485	3	]	]	PUNCT
ejpam-6658	485	4	waseem	waseem	PROPN
ejpam-6658	485	5	ahmad	ahmad	PROPN
ejpam-6658	485	6	khan	khan	PROPN
ejpam-6658	485	7	,	,	PUNCT
ejpam-6658	485	8	divesh	divesh	PROPN
ejpam-6658	485	9	srivastava	srivastava	PROPN
ejpam-6658	485	10	,	,	PUNCT
ejpam-6658	485	11	and	and	CCONJ
ejpam-6658	485	12	kottakkaran	kottakkaran	VERB
ejpam-6658	485	13	soppy	soppy	PROPN
ejpam-6658	485	14	nisar	nisar	PROPN
ejpam-6658	485	15	.	.	PUNCT
ejpam-6658	486	1	a	a	DET
ejpam-6658	486	2	new	new	ADJ
ejpam-6658	486	3	class	class	NOUN
ejpam-6658	486	4	of	of	ADP
ejpam-6658	486	5	generalized	generalized	ADJ
ejpam-6658	486	6	polynomials	polynomial	NOUN
ejpam-6658	486	7	associated	associate	VERB
ejpam-6658	486	8	with	with	ADP
ejpam-6658	486	9	milne	milne	PROPN
ejpam-6658	486	10	-	-	PUNCT
ejpam-6658	486	11	thomsons	thomson	NOUN
ejpam-6658	486	12	-	-	PUNCT
ejpam-6658	486	13	based	base	VERB
ejpam-6658	486	14	poly	poly	ADJ
ejpam-6658	486	15	-	-	PUNCT
ejpam-6658	486	16	bernoulli	bernoulli	NOUN
ejpam-6658	486	17	polynomials	polynomial	NOUN
ejpam-6658	486	18	.	.	PUNCT
ejpam-6658	487	1	miskolc	miskolc	ADJ
ejpam-6658	487	2	mathematical	mathematical	ADJ
ejpam-6658	487	3	journal	journal	NOUN
ejpam-6658	487	4	,	,	PUNCT
ejpam-6658	487	5	25(2):793–803	25(2):793–803	PROPN
ejpam-6658	487	6	,	,	PUNCT
ejpam-6658	487	7	2024	2024	NUM
ejpam-6658	487	8	.	.	PUNCT
ejpam-6658	488	1	[	[	X
ejpam-6658	488	2	6	6	NUM
ejpam-6658	488	3	]	]	PUNCT
ejpam-6658	488	4	waseem	waseem	PROPN
ejpam-6658	488	5	a	a	DET
ejpam-6658	488	6	khan	khan	PROPN
ejpam-6658	488	7	,	,	PUNCT
ejpam-6658	488	8	jihad	jihad	PROPN
ejpam-6658	488	9	younis	younis	PROPN
ejpam-6658	488	10	,	,	PUNCT
ejpam-6658	488	11	and	and	CCONJ
ejpam-6658	488	12	mohd	mohd	PROPN
ejpam-6658	488	13	nadeem	nadeem	PROPN
ejpam-6658	488	14	.	.	PUNCT
ejpam-6658	489	1	construction	construction	NOUN
ejpam-6658	489	2	of	of	ADP
ejpam-6658	489	3	partially	partially	ADV
ejpam-6658	489	4	degenerate	degenerate	ADJ
ejpam-6658	489	5	laguerre	laguerre	NOUN
ejpam-6658	489	6	–	–	PUNCT
ejpam-6658	489	7	bernoulli	bernoulli	NOUN
ejpam-6658	489	8	polynomials	polynomial	NOUN
ejpam-6658	489	9	of	of	ADP
ejpam-6658	489	10	the	the	DET
ejpam-6658	489	11	first	first	ADJ
ejpam-6658	489	12	kind	kind	NOUN
ejpam-6658	489	13	.	.	PUNCT
ejpam-6658	490	1	applied	apply	VERB
ejpam-6658	490	2	mathematics	mathematic	NOUN
ejpam-6658	490	3	in	in	ADP
ejpam-6658	490	4	science	science	NOUN
ejpam-6658	490	5	and	and	CCONJ
ejpam-6658	490	6	engineering	engineering	NOUN
ejpam-6658	490	7	,	,	PUNCT
ejpam-6658	490	8	30(1):362–375	30(1):362–375	PROPN
ejpam-6658	490	9	,	,	PUNCT
ejpam-6658	490	10	2022	2022	NUM
ejpam-6658	490	11	.	.	PUNCT
ejpam-6658	491	1	[	[	X
ejpam-6658	491	2	7	7	X
ejpam-6658	491	3	]	]	PUNCT
ejpam-6658	491	4	t.	t.	PROPN
ejpam-6658	491	5	kanan	kanan	PROPN
ejpam-6658	491	6	,	,	PUNCT
ejpam-6658	491	7	m.	m.	NOUN
ejpam-6658	491	8	elbes	elbes	PROPN
ejpam-6658	491	9	,	,	PUNCT
ejpam-6658	491	10	k.	k.	PROPN
ejpam-6658	491	11	abu	abu	PROPN
ejpam-6658	491	12	maria	maria	PROPN
ejpam-6658	491	13	,	,	PUNCT
ejpam-6658	491	14	and	and	CCONJ
ejpam-6658	491	15	m.	m.	NOUN
ejpam-6658	491	16	alia	alia	PROPN
ejpam-6658	491	17	.	.	PUNCT
ejpam-6658	492	1	exploring	explore	VERB
ejpam-6658	492	2	the	the	DET
ejpam-6658	492	3	potential	potential	NOUN
ejpam-6658	492	4	of	of	ADP
ejpam-6658	492	5	iotbased	iotbase	VERB
ejpam-6658	492	6	learning	learn	VERB
ejpam-6658	492	7	environments	environment	NOUN
ejpam-6658	492	8	in	in	ADP
ejpam-6658	492	9	education	education	NOUN
ejpam-6658	492	10	.	.	PUNCT
ejpam-6658	493	1	international	international	ADJ
ejpam-6658	493	2	journal	journal	NOUN
ejpam-6658	493	3	of	of	ADP
ejpam-6658	493	4	advances	advance	NOUN
ejpam-6658	493	5	in	in	ADP
ejpam-6658	493	6	soft	soft	ADJ
ejpam-6658	493	7	computing	computing	NOUN
ejpam-6658	493	8	and	and	CCONJ
ejpam-6658	493	9	its	its	PRON
ejpam-6658	493	10	applications	application	NOUN
ejpam-6658	493	11	,	,	PUNCT
ejpam-6658	493	12	15	15	NUM
ejpam-6658	493	13	,	,	PUNCT
ejpam-6658	493	14	2023	2023	NUM
ejpam-6658	493	15	.	.	PUNCT
ejpam-6658	494	1	[	[	X
ejpam-6658	494	2	8	8	NUM
ejpam-6658	494	3	]	]	X
ejpam-6658	494	4	duha	duha	NOUN
ejpam-6658	494	5	abu	abu	PROPN
ejpam-6658	494	6	judeh	judeh	PROPN
ejpam-6658	494	7	and	and	CCONJ
ejpam-6658	494	8	m	m	PROPN
ejpam-6658	494	9	abu	abu	PROPN
ejpam-6658	494	10	hammad	hammad	PROPN
ejpam-6658	494	11	.	.	PUNCT
ejpam-6658	495	1	applications	application	NOUN
ejpam-6658	495	2	of	of	ADP
ejpam-6658	495	3	conformable	conformable	ADJ
ejpam-6658	495	4	fractional	fractional	ADJ
ejpam-6658	495	5	pareto	pareto	ADJ
ejpam-6658	495	6	probability	probability	NOUN
ejpam-6658	495	7	distribution	distribution	NOUN
ejpam-6658	495	8	.	.	PUNCT
ejpam-6658	496	1	int	int	NOUN
ejpam-6658	496	2	.	.	PUNCT
ejpam-6658	497	1	j.	j.	PROPN
ejpam-6658	497	2	advance	advance	VERB
ejpam-6658	497	3	soft	soft	ADJ
ejpam-6658	497	4	compu	compu	PROPN
ejpam-6658	497	5	.	.	PUNCT
ejpam-6658	498	1	appl	appl	PROPN
ejpam-6658	498	2	,	,	PUNCT
ejpam-6658	498	3	14(2):115–124	14(2):115–124	NUM
ejpam-6658	498	4	,	,	PUNCT
ejpam-6658	498	5	2022	2022	NUM
ejpam-6658	498	6	.	.	PUNCT
ejpam-6658	499	1	[	[	X
ejpam-6658	499	2	9	9	X
ejpam-6658	499	3	]	]	X
ejpam-6658	499	4	muhammad	muhammad	PROPN
ejpam-6658	499	5	nazam	nazam	PROPN
ejpam-6658	499	6	,	,	PUNCT
ejpam-6658	499	7	hassen	hassen	PROPN
ejpam-6658	499	8	aydi	aydi	ADV
ejpam-6658	499	9	,	,	PUNCT
ejpam-6658	499	10	mohd	mohd	PROPN
ejpam-6658	499	11	salmi	salmi	PROPN
ejpam-6658	499	12	noorani	noorani	PROPN
ejpam-6658	499	13	,	,	PUNCT
ejpam-6658	499	14	and	and	CCONJ
ejpam-6658	499	15	haitham	haitham	PROPN
ejpam-6658	499	16	qawaqneh	qawaqneh	PROPN
ejpam-6658	499	17	.	.	PUNCT
ejpam-6658	500	1	existence	existence	NOUN
ejpam-6658	500	2	of	of	ADP
ejpam-6658	500	3	fixed	fix	VERB
ejpam-6658	500	4	points	point	NOUN
ejpam-6658	500	5	of	of	ADP
ejpam-6658	500	6	four	four	NUM
ejpam-6658	500	7	maps	map	NOUN
ejpam-6658	500	8	for	for	ADP
ejpam-6658	500	9	a	a	DET
ejpam-6658	500	10	new	new	ADJ
ejpam-6658	500	11	generalized	generalized	ADJ
ejpam-6658	500	12	f	f	NOUN
ejpam-6658	500	13	-	-	PUNCT
ejpam-6658	500	14	contraction	contraction	NOUN
ejpam-6658	500	15	and	and	CCONJ
ejpam-6658	500	16	an	an	DET
ejpam-6658	500	17	application	application	NOUN
ejpam-6658	500	18	.	.	PUNCT
ejpam-6658	501	1	journal	journal	NOUN
ejpam-6658	501	2	of	of	ADP
ejpam-6658	501	3	function	function	NOUN
ejpam-6658	501	4	spaces	space	NOUN
ejpam-6658	501	5	,	,	PUNCT
ejpam-6658	501	6	2019(1):5980312	2019(1):5980312	NUM
ejpam-6658	501	7	,	,	PUNCT
ejpam-6658	501	8	2019	2019	NUM
ejpam-6658	501	9	.	.	PUNCT
ejpam-6658	502	1	[	[	X
ejpam-6658	502	2	10	10	NUM
ejpam-6658	502	3	]	]	X
ejpam-6658	502	4	haitham	haitham	PROPN
ejpam-6658	502	5	qawaqneh	qawaqneh	PROPN
ejpam-6658	502	6	,	,	PUNCT
ejpam-6658	502	7	mohd	mohd	PROPN
ejpam-6658	502	8	salmi	salmi	PROPN
ejpam-6658	502	9	noorani	noorani	PROPN
ejpam-6658	502	10	,	,	PUNCT
ejpam-6658	502	11	hassen	hassen	PROPN
ejpam-6658	502	12	aydi	aydi	ADV
ejpam-6658	502	13	,	,	PUNCT
ejpam-6658	502	14	and	and	CCONJ
ejpam-6658	502	15	wasfi	wasfi	ADV
ejpam-6658	502	16	shatanawi	shatanawi	ADJ
ejpam-6658	502	17	.	.	PUNCT
ejpam-6658	503	1	on	on	ADP
ejpam-6658	503	2	common	common	ADJ
ejpam-6658	503	3	fixed	fix	VERB
ejpam-6658	503	4	point	point	NOUN
ejpam-6658	503	5	results	result	NOUN
ejpam-6658	503	6	for	for	ADP
ejpam-6658	503	7	new	new	ADJ
ejpam-6658	503	8	contractions	contraction	NOUN
ejpam-6658	503	9	with	with	ADP
ejpam-6658	503	10	applications	application	NOUN
ejpam-6658	503	11	to	to	PART
ejpam-6658	503	12	graph	graph	VERB
ejpam-6658	503	13	and	and	CCONJ
ejpam-6658	503	14	integral	integral	ADJ
ejpam-6658	503	15	equations	equation	NOUN
ejpam-6658	503	16	.	.	PUNCT
ejpam-6658	504	1	mathematics	mathematic	NOUN
ejpam-6658	504	2	,	,	PUNCT
ejpam-6658	504	3	7(11):1082	7(11):1082	NOUN
ejpam-6658	504	4	,	,	PUNCT
ejpam-6658	504	5	2019	2019	NUM
ejpam-6658	504	6	.	.	PUNCT
ejpam-6658	505	1	[	[	X
ejpam-6658	505	2	11	11	NUM
ejpam-6658	505	3	]	]	PUNCT
ejpam-6658	505	4	mohra	mohra	NOUN
ejpam-6658	505	5	zayed	zaye	VERB
ejpam-6658	505	6	,	,	PUNCT
ejpam-6658	505	7	waseem	waseem	PROPN
ejpam-6658	505	8	ahmad	ahmad	PROPN
ejpam-6658	505	9	khan	khan	PROPN
ejpam-6658	505	10	,	,	PUNCT
ejpam-6658	505	11	cheon	cheon	PROPN
ejpam-6658	505	12	seoung	seoung	PROPN
ejpam-6658	505	13	ryoo	ryoo	NOUN
ejpam-6658	505	14	,	,	PUNCT
ejpam-6658	505	15	and	and	CCONJ
ejpam-6658	505	16	ugur	ugur	PROPN
ejpam-6658	505	17	duran	duran	PROPN
ejpam-6658	505	18	.	.	PUNCT
ejpam-6658	506	1	an	an	DET
ejpam-6658	506	2	exploratory	exploratory	ADJ
ejpam-6658	506	3	study	study	NOUN
ejpam-6658	506	4	on	on	ADP
ejpam-6658	506	5	bivariate	bivariate	ADJ
ejpam-6658	506	6	extended	extended	ADJ
ejpam-6658	506	7	q	q	ADJ
ejpam-6658	506	8	-	-	PUNCT
ejpam-6658	506	9	laguerre	laguerre	NOUN
ejpam-6658	506	10	-	-	PUNCT
ejpam-6658	506	11	based	base	VERB
ejpam-6658	506	12	appell	appell	NOUN
ejpam-6658	506	13	polynomials	polynomial	NOUN
ejpam-6658	506	14	with	with	ADP
ejpam-6658	506	15	some	some	DET
ejpam-6658	506	16	applications	application	NOUN
ejpam-6658	506	17	.	.	PUNCT
ejpam-6658	507	1	aims	aim	VERB
ejpam-6658	507	2	mathematics	mathematic	NOUN
ejpam-6658	507	3	,	,	PUNCT
ejpam-6658	507	4	10(6):12841–12867	10(6):12841–12867	NUM
ejpam-6658	507	5	,	,	PUNCT
ejpam-6658	507	6	2025	2025	NUM
ejpam-6658	507	7	.	.	PUNCT
ejpam-6658	508	1	[	[	X
ejpam-6658	508	2	12	12	NUM
ejpam-6658	508	3	]	]	X
ejpam-6658	508	4	larry	larry	PROPN
ejpam-6658	508	5	c	c	PROPN
ejpam-6658	508	6	andrews	andrews	PROPN
ejpam-6658	508	7	.	.	PUNCT
ejpam-6658	508	8	special	special	ADJ
ejpam-6658	508	9	functions	function	NOUN
ejpam-6658	508	10	of	of	ADP
ejpam-6658	508	11	mathematics	mathematic	NOUN
ejpam-6658	508	12	for	for	ADP
ejpam-6658	508	13	engineers	engineer	NOUN
ejpam-6658	508	14	,	,	PUNCT
ejpam-6658	508	15	volume	volume	NOUN
ejpam-6658	508	16	49	49	NUM
ejpam-6658	508	17	.	.	PUNCT
ejpam-6658	509	1	spie	spie	ADJ
ejpam-6658	509	2	press	press	NOUN
ejpam-6658	509	3	,	,	PUNCT
ejpam-6658	509	4	1998	1998	NUM
ejpam-6658	509	5	.	.	PUNCT
ejpam-6658	510	1	[	[	X
ejpam-6658	510	2	13	13	NUM
ejpam-6658	510	3	]	]	X
ejpam-6658	510	4	paul	paul	PROPN
ejpam-6658	510	5	appell	appell	PROPN
ejpam-6658	510	6	.	.	PUNCT
ejpam-6658	511	1	sur	sur	PROPN
ejpam-6658	511	2	une	une	PROPN
ejpam-6658	511	3	classe	classe	PROPN
ejpam-6658	511	4	de	de	PROPN
ejpam-6658	511	5	polynômes	polynômes	PROPN
ejpam-6658	511	6	.	.	PUNCT
ejpam-6658	512	1	in	in	ADP
ejpam-6658	512	2	annales	annale	NOUN
ejpam-6658	512	3	scientifiques	scientifique	NOUN
ejpam-6658	512	4	de	de	ADP
ejpam-6658	512	5	l’école	l’école	ADJ
ejpam-6658	512	6	normale	normale	PROPN
ejpam-6658	512	7	supérieure	supérieure	PROPN
ejpam-6658	512	8	,	,	PUNCT
ejpam-6658	512	9	volume	volume	NOUN
ejpam-6658	512	10	9	9	NUM
ejpam-6658	512	11	,	,	PUNCT
ejpam-6658	512	12	pages	page	NOUN
ejpam-6658	512	13	119–144	119–144	NUM
ejpam-6658	512	14	,	,	PUNCT
ejpam-6658	512	15	1880	1880	NUM
ejpam-6658	512	16	.	.	PUNCT
ejpam-6658	513	1	[	[	X
ejpam-6658	513	2	14	14	NUM
ejpam-6658	513	3	]	]	X
ejpam-6658	513	4	rp	rp	X
ejpam-6658	513	5	boas	boas	PROPN
ejpam-6658	513	6	jr	jr	PROPN
ejpam-6658	513	7	.	.	PROPN
ejpam-6658	513	8	higher	high	ADJ
ejpam-6658	513	9	transcendental	transcendental	ADJ
ejpam-6658	513	10	functions	function	NOUN
ejpam-6658	513	11	.	.	PUNCT
ejpam-6658	514	1	vol	vol	NOUN
ejpam-6658	514	2	.	.	PUNCT
ejpam-6658	515	1	iii	iii	PROPN
ejpam-6658	515	2	.	.	PROPN
ejpam-6658	515	3	based	base	VERB
ejpam-6658	515	4	in	in	ADP
ejpam-6658	515	5	part	part	NOUN
ejpam-6658	515	6	on	on	ADP
ejpam-6658	515	7	notes	note	NOUN
ejpam-6658	515	8	left	leave	VERB
ejpam-6658	515	9	by	by	ADP
ejpam-6658	515	10	harry	harry	PROPN
ejpam-6658	515	11	bateman	bateman	PROPN
ejpam-6658	515	12	.	.	PROPN
ejpam-6658	515	13	bateman	bateman	PROPN
ejpam-6658	515	14	project	project	PROPN
ejpam-6658	515	15	staff	staff	NOUN
ejpam-6658	515	16	,	,	PUNCT
ejpam-6658	515	17	a.	a.	NOUN
ejpam-6658	515	18	erdélyi	erdélyi	PROPN
ejpam-6658	515	19	,	,	PUNCT
ejpam-6658	515	20	ed	ed	NOUN
ejpam-6658	515	21	.	.	PUNCT
ejpam-6658	515	22	mcgraw	mcgraw	PROPN
ejpam-6658	515	23	-	-	PUNCT
ejpam-6658	515	24	hill	hill	PROPN
ejpam-6658	515	25	,	,	PUNCT
ejpam-6658	515	26	new	new	PROPN
ejpam-6658	515	27	york	york	PROPN
ejpam-6658	515	28	-	-	PUNCT
ejpam-6658	515	29	london	london	PROPN
ejpam-6658	515	30	,	,	PUNCT
ejpam-6658	515	31	1955	1955	NUM
ejpam-6658	515	32	.	.	PUNCT
ejpam-6658	516	1	xviii+	xviii+	PUNCT
ejpam-6658	517	1	292	292	NUM
ejpam-6658	517	2	pp	pp	NOUN
ejpam-6658	517	3	.	.	PUNCT
ejpam-6658	518	1	6.50.science	6.50.science	NUM
ejpam-6658	518	2	,	,	PUNCT
ejpam-6658	518	3	122(3163	122(3163	NUM
ejpam-6658	518	4	)	)	PUNCT
ejpam-6658	518	5	:	:	PUNCT
ejpam-6658	519	1	290−−290	290−−290	NUM
ejpam-6658	519	2	,	,	PUNCT
ejpam-6658	519	3	1955	1955	NUM
ejpam-6658	519	4	.	.	PUNCT
ejpam-6658	520	1	[	[	X
ejpam-6658	520	2	15	15	NUM
ejpam-6658	520	3	]	]	X
ejpam-6658	520	4	subuhi	subuhi	PROPN
ejpam-6658	520	5	khan	khan	PROPN
ejpam-6658	520	6	and	and	CCONJ
ejpam-6658	520	7	nusrat	nusrat	PROPN
ejpam-6658	520	8	raza	raza	PROPN
ejpam-6658	520	9	.	.	PUNCT
ejpam-6658	521	1	monomiality	monomiality	NOUN
ejpam-6658	521	2	principle	principle	NOUN
ejpam-6658	521	3	,	,	PUNCT
ejpam-6658	521	4	operational	operational	ADJ
ejpam-6658	521	5	methods	method	NOUN
ejpam-6658	521	6	and	and	CCONJ
ejpam-6658	521	7	family	family	NOUN
ejpam-6658	521	8	of	of	ADP
ejpam-6658	521	9	laguerre	laguerre	NOUN
ejpam-6658	521	10	–	–	PUNCT
ejpam-6658	521	11	sheffer	sheffer	NOUN
ejpam-6658	521	12	polynomials	polynomial	NOUN
ejpam-6658	521	13	.	.	PUNCT
ejpam-6658	522	1	journal	journal	PROPN
ejpam-6658	522	2	of	of	ADP
ejpam-6658	522	3	mathematical	mathematical	ADJ
ejpam-6658	522	4	analysis	analysis	NOUN
ejpam-6658	522	5	and	and	CCONJ
ejpam-6658	522	6	applications	application	NOUN
ejpam-6658	522	7	,	,	PUNCT
ejpam-6658	522	8	387(1):90–102	387(1):90–102	NUM
ejpam-6658	522	9	,	,	PUNCT
ejpam-6658	522	10	2012	2012	NUM
ejpam-6658	522	11	.	.	PUNCT
ejpam-6658	523	1	[	[	X
ejpam-6658	523	2	16	16	NUM
ejpam-6658	523	3	]	]	X
ejpam-6658	523	4	i.	i.	PROPN
ejpam-6658	523	5	sheffer	sheffer	PROPN
ejpam-6658	523	6	.	.	PUNCT
ejpam-6658	524	1	some	some	DET
ejpam-6658	524	2	properties	property	NOUN
ejpam-6658	524	3	of	of	ADP
ejpam-6658	524	4	polynomial	polynomial	ADJ
ejpam-6658	524	5	sets	set	NOUN
ejpam-6658	524	6	of	of	ADP
ejpam-6658	524	7	type	type	NOUN
ejpam-6658	524	8	zero	zero	NUM
ejpam-6658	524	9	.	.	PUNCT
ejpam-6658	524	10	1939	1939	NUM
ejpam-6658	524	11	.	.	PUNCT
ejpam-6658	525	1	[	[	X
ejpam-6658	525	2	17	17	NUM
ejpam-6658	525	3	]	]	X
ejpam-6658	525	4	waseem	waseem	PROPN
ejpam-6658	525	5	ahmad	ahmad	PROPN
ejpam-6658	525	6	khan	khan	PROPN
ejpam-6658	525	7	,	,	PUNCT
ejpam-6658	525	8	khidir	khidir	PROPN
ejpam-6658	525	9	shaib	shaib	PROPN
ejpam-6658	525	10	mohamed	mohamed	PROPN
ejpam-6658	525	11	,	,	PUNCT
ejpam-6658	525	12	francesco	francesco	PROPN
ejpam-6658	525	13	aldo	aldo	PROPN
ejpam-6658	525	14	costabile	costabile	PROPN
ejpam-6658	525	15	,	,	PUNCT
ejpam-6658	525	16	can	can	AUX
ejpam-6658	525	17	kızılates	kızılate	NOUN
ejpam-6658	525	18	,	,	PUNCT
ejpam-6658	525	19	and	and	CCONJ
ejpam-6658	525	20	cheon	cheon	PROPN
ejpam-6658	525	21	seoung	seoung	PROPN
ejpam-6658	525	22	ryoo	ryoo	NOUN
ejpam-6658	525	23	.	.	PUNCT
ejpam-6658	526	1	finding	find	VERB
ejpam-6658	526	2	the	the	DET
ejpam-6658	526	3	q	q	ADJ
ejpam-6658	526	4	-	-	PUNCT
ejpam-6658	526	5	appell	appell	ADJ
ejpam-6658	526	6	convolution	convolution	NOUN
ejpam-6658	526	7	of	of	ADP
ejpam-6658	526	8	certain	certain	ADJ
ejpam-6658	526	9	polynomials	polynomial	NOUN
ejpam-6658	526	10	within	within	ADP
ejpam-6658	526	11	the	the	DET
ejpam-6658	526	12	context	context	NOUN
ejpam-6658	526	13	of	of	ADP
ejpam-6658	526	14	quantum	quantum	NOUN
ejpam-6658	526	15	calculus	calculus	NOUN
ejpam-6658	526	16	.	.	PUNCT
ejpam-6658	527	1	relation	relation	NOUN
ejpam-6658	527	2	,	,	PUNCT
ejpam-6658	527	3	6:8	6:8	NUM
ejpam-6658	527	4	,	,	PUNCT
ejpam-6658	527	5	2025	2025	NUM
ejpam-6658	527	6	.	.	PUNCT
ejpam-6658	528	1	[	[	X
ejpam-6658	528	2	18	18	NUM
ejpam-6658	528	3	]	]	X
ejpam-6658	528	4	j.	j.	PROPN
ejpam-6658	528	5	steffensen	steffensen	PROPN
ejpam-6658	528	6	.	.	PUNCT
ejpam-6658	529	1	the	the	DET
ejpam-6658	529	2	poweroid	poweroid	ADJ
ejpam-6658	529	3	,	,	PUNCT
ejpam-6658	529	4	an	an	DET
ejpam-6658	529	5	extension	extension	NOUN
ejpam-6658	529	6	of	of	ADP
ejpam-6658	529	7	the	the	DET
ejpam-6658	529	8	mathematical	mathematical	ADJ
ejpam-6658	529	9	notion	notion	NOUN
ejpam-6658	529	10	of	of	ADP
ejpam-6658	529	11	power	power	NOUN
ejpam-6658	529	12	.	.	PUNCT
ejpam-6658	530	1	1941	1941	NUM
ejpam-6658	530	2	.	.	PUNCT
ejpam-6658	531	1	w.	w.	PROPN
ejpam-6658	531	2	a.	a.	PROPN
ejpam-6658	531	3	khan	khan	PROPN
ejpam-6658	531	4	,	,	PUNCT
ejpam-6658	531	5	h.	h.	PROPN
ejpam-6658	531	6	qawaqneh	qawaqneh	PROPN
ejpam-6658	531	7	,	,	PUNCT
ejpam-6658	531	8	h.	h.	PROPN
ejpam-6658	531	9	aydi	aydi	VERB
ejpam-6658	531	10	/	/	SYM
ejpam-6658	531	11	eur	eur	NOUN
ejpam-6658	531	12	.	.	PUNCT
ejpam-6658	532	1	j.	j.	PROPN
ejpam-6658	532	2	pure	pure	PROPN
ejpam-6658	532	3	appl	appl	PROPN
ejpam-6658	532	4	.	.	PROPN
ejpam-6658	532	5	math	math	PROPN
ejpam-6658	532	6	,	,	PUNCT
ejpam-6658	532	7	18	18	NUM
ejpam-6658	532	8	(	(	PUNCT
ejpam-6658	532	9	3	3	NUM
ejpam-6658	532	10	)	)	PUNCT
ejpam-6658	532	11	(	(	PUNCT
ejpam-6658	532	12	2025	2025	NUM
ejpam-6658	532	13	)	)	PUNCT
ejpam-6658	532	14	,	,	PUNCT
ejpam-6658	532	15	6658	6658	NUM
ejpam-6658	532	16	22	22	NUM
ejpam-6658	532	17	of	of	ADP
ejpam-6658	532	18	22	22	NUM
ejpam-6658	533	1	[	[	X
ejpam-6658	533	2	19	19	NUM
ejpam-6658	533	3	]	]	SYM
ejpam-6658	533	4	g	g	NOUN
ejpam-6658	533	5	dattoli	dattoli	NOUN
ejpam-6658	533	6	.	.	PUNCT
ejpam-6658	534	1	hermite	hermite	ADJ
ejpam-6658	534	2	-	-	PUNCT
ejpam-6658	534	3	bessel	bessel	NOUN
ejpam-6658	534	4	and	and	CCONJ
ejpam-6658	534	5	laguerre	laguerre	NOUN
ejpam-6658	534	6	-	-	PUNCT
ejpam-6658	534	7	bessel	bessel	NOUN
ejpam-6658	534	8	functions	function	NOUN
ejpam-6658	534	9	:	:	PUNCT
ejpam-6658	534	10	a	a	DET
ejpam-6658	534	11	by	by	ADP
ejpam-6658	534	12	-	-	PUNCT
ejpam-6658	534	13	product	product	NOUN
ejpam-6658	534	14	ot	ot	NOUN
ejpam-6658	534	15	the	the	DET
ejpam-6658	534	16	monomiality	monomiality	NOUN
ejpam-6658	534	17	principle	principle	NOUN
ejpam-6658	534	18	,	,	PUNCT
ejpam-6658	534	19	advanced	advanced	ADJ
ejpam-6658	534	20	special	special	ADJ
ejpam-6658	534	21	functions	function	NOUN
ejpam-6658	534	22	and	and	CCONJ
ejpam-6658	534	23	applications	application	NOUN
ejpam-6658	534	24	.	.	PUNCT
ejpam-6658	535	1	proceedings	proceeding	NOUN
ejpam-6658	535	2	of	of	ADP
ejpam-6658	535	3	the	the	DET
ejpam-6658	535	4	melfi	melfi	PROPN
ejpam-6658	535	5	school	school	NOUN
ejpam-6658	535	6	on	on	ADP
ejpam-6658	535	7	advanced	advanced	ADJ
ejpam-6658	535	8	topics	topic	NOUN
ejpam-6658	535	9	in	in	ADP
ejpam-6658	535	10	mathematics	mathematic	NOUN
ejpam-6658	535	11	and	and	CCONJ
ejpam-6658	535	12	physics	physics	NOUN
ejpam-6658	535	13	,	,	PUNCT
ejpam-6658	535	14	pages	page	NOUN
ejpam-6658	535	15	147–164	147–164	NUM
ejpam-6658	535	16	.	.	PUNCT
ejpam-6658	536	1	[	[	X
ejpam-6658	536	2	20	20	NUM
ejpam-6658	536	3	]	]	PUNCT
ejpam-6658	536	4	subuhi	subuhi	PROPN
ejpam-6658	536	5	khan	khan	PROPN
ejpam-6658	536	6	,	,	PUNCT
ejpam-6658	536	7	mumtaz	mumtaz	PROPN
ejpam-6658	536	8	riyasat	riyasat	PROPN
ejpam-6658	536	9	,	,	PUNCT
ejpam-6658	536	10	and	and	CCONJ
ejpam-6658	536	11	shahid	shahid	PROPN
ejpam-6658	536	12	ahmad	ahmad	PROPN
ejpam-6658	536	13	wani	wani	PROPN
ejpam-6658	536	14	.	.	PUNCT
ejpam-6658	537	1	on	on	ADP
ejpam-6658	537	2	some	some	DET
ejpam-6658	537	3	classes	class	NOUN
ejpam-6658	537	4	of	of	ADP
ejpam-6658	537	5	differential	differential	ADJ
ejpam-6658	537	6	equations	equation	NOUN
ejpam-6658	537	7	and	and	CCONJ
ejpam-6658	537	8	associated	associate	VERB
ejpam-6658	537	9	integral	integral	ADJ
ejpam-6658	537	10	equations	equation	NOUN
ejpam-6658	537	11	for	for	ADP
ejpam-6658	537	12	the	the	DET
ejpam-6658	537	13	laguerre	laguerre	NOUN
ejpam-6658	537	14	–	–	PUNCT
ejpam-6658	537	15	appell	appell	NOUN
ejpam-6658	537	16	polynomials	polynomial	NOUN
ejpam-6658	537	17	.	.	PUNCT
ejpam-6658	538	1	advances	advance	NOUN
ejpam-6658	538	2	in	in	ADP
ejpam-6658	538	3	pure	pure	ADJ
ejpam-6658	538	4	and	and	CCONJ
ejpam-6658	538	5	applied	applied	ADJ
ejpam-6658	538	6	mathematics	mathematic	NOUN
ejpam-6658	538	7	,	,	PUNCT
ejpam-6658	538	8	9(3):185–194	9(3):185–194	NOUN
ejpam-6658	538	9	,	,	PUNCT
ejpam-6658	538	10	2018	2018	NUM
ejpam-6658	538	11	.	.	PUNCT
ejpam-6658	539	1	[	[	X
ejpam-6658	539	2	21	21	NUM
ejpam-6658	539	3	]	]	PUNCT
ejpam-6658	539	4	waseem	waseem	PROPN
ejpam-6658	539	5	ahmad	ahmad	PROPN
ejpam-6658	539	6	khan	khan	PROPN
ejpam-6658	539	7	,	,	PUNCT
ejpam-6658	539	8	khidir	khidir	PROPN
ejpam-6658	539	9	shaib	shaib	PROPN
ejpam-6658	539	10	mohamed	mohamed	PROPN
ejpam-6658	539	11	,	,	PUNCT
ejpam-6658	539	12	francesco	francesco	PROPN
ejpam-6658	539	13	aldo	aldo	PROPN
ejpam-6658	539	14	costabile	costabile	PROPN
ejpam-6658	539	15	,	,	PUNCT
ejpam-6658	539	16	shahid	shahid	PROPN
ejpam-6658	539	17	ahmad	ahmad	PROPN
ejpam-6658	539	18	wani	wani	PROPN
ejpam-6658	539	19	,	,	PUNCT
ejpam-6658	539	20	and	and	CCONJ
ejpam-6658	539	21	alawia	alawia	PROPN
ejpam-6658	539	22	adam	adam	PROPN
ejpam-6658	539	23	.	.	PUNCT
ejpam-6658	540	1	a	a	DET
ejpam-6658	540	2	new	new	ADJ
ejpam-6658	540	3	generalization	generalization	NOUN
ejpam-6658	540	4	of	of	ADP
ejpam-6658	540	5	m	m	PROPN
ejpam-6658	540	6	th	th	NOUN
ejpam-6658	540	7	-	-	PUNCT
ejpam-6658	540	8	order	order	NOUN
ejpam-6658	540	9	laguerre	laguerre	NOUN
ejpam-6658	540	10	-	-	PUNCT
ejpam-6658	540	11	based	base	VERB
ejpam-6658	540	12	appell	appell	NOUN
ejpam-6658	540	13	polynomials	polynomial	NOUN
ejpam-6658	540	14	associated	associate	VERB
ejpam-6658	540	15	with	with	ADP
ejpam-6658	540	16	two	two	NUM
ejpam-6658	540	17	-	-	PUNCT
ejpam-6658	540	18	variable	variable	ADJ
ejpam-6658	540	19	general	general	ADJ
ejpam-6658	540	20	polynomials	polynomial	NOUN
ejpam-6658	540	21	.	.	PUNCT
ejpam-6658	541	1	mathematics	mathematic	NOUN
ejpam-6658	541	2	,	,	PUNCT
ejpam-6658	541	3	13(13):2179	13(13):2179	NUM
ejpam-6658	541	4	,	,	PUNCT
ejpam-6658	541	5	2025	2025	NUM
ejpam-6658	541	6	.	.	PUNCT
ejpam-6658	542	1	[	[	X
ejpam-6658	542	2	22	22	NUM
ejpam-6658	542	3	]	]	PUNCT
ejpam-6658	542	4	waseem	waseem	PROPN
ejpam-6658	542	5	ahmad	ahmad	PROPN
ejpam-6658	542	6	khan	khan	PROPN
ejpam-6658	542	7	,	,	PUNCT
ejpam-6658	542	8	mofareh	mofareh	PROPN
ejpam-6658	542	9	alhazmi	alhazmi	NOUN
ejpam-6658	542	10	,	,	PUNCT
ejpam-6658	542	11	and	and	CCONJ
ejpam-6658	542	12	tabinda	tabinda	NOUN
ejpam-6658	542	13	nahid	nahid	PROPN
ejpam-6658	542	14	.	.	PUNCT
ejpam-6658	543	1	a	a	DET
ejpam-6658	543	2	novel	novel	ADJ
ejpam-6658	543	3	family	family	NOUN
ejpam-6658	543	4	of	of	ADP
ejpam-6658	543	5	q	q	NOUN
ejpam-6658	543	6	-	-	PUNCT
ejpam-6658	543	7	mittagleffler	mittagleffler	NOUN
ejpam-6658	543	8	-	-	PUNCT
ejpam-6658	543	9	based	base	VERB
ejpam-6658	543	10	bessel	bessel	NOUN
ejpam-6658	543	11	and	and	CCONJ
ejpam-6658	543	12	tricomi	tricomi	NOUN
ejpam-6658	543	13	functions	function	NOUN
ejpam-6658	543	14	via	via	ADP
ejpam-6658	543	15	umbral	umbral	ADJ
ejpam-6658	543	16	approach	approach	NOUN
ejpam-6658	543	17	.	.	PUNCT
ejpam-6658	544	1	symmetry	symmetry	NOUN
ejpam-6658	544	2	,	,	PUNCT
ejpam-6658	544	3	16(12):1580	16(12):1580	NUM
ejpam-6658	544	4	,	,	PUNCT
ejpam-6658	544	5	2024	2024	NUM
ejpam-6658	544	6	.	.	PUNCT
ejpam-6658	545	1	[	[	X
ejpam-6658	545	2	23	23	NUM
ejpam-6658	545	3	]	]	PUNCT
ejpam-6658	545	4	waseem	waseem	PROPN
ejpam-6658	545	5	ahmad	ahmad	PROPN
ejpam-6658	545	6	khan	khan	PROPN
ejpam-6658	545	7	,	,	PUNCT
ejpam-6658	545	8	ugur	ugur	PROPN
ejpam-6658	545	9	duran	duran	PROPN
ejpam-6658	545	10	,	,	PUNCT
ejpam-6658	545	11	jihad	jihad	NOUN
ejpam-6658	545	12	younis	younis	PROPN
ejpam-6658	545	13	,	,	PUNCT
ejpam-6658	545	14	and	and	CCONJ
ejpam-6658	545	15	cheon	cheon	PROPN
ejpam-6658	545	16	seoung	seoung	PROPN
ejpam-6658	545	17	ryoo	ryoo	NOUN
ejpam-6658	545	18	.	.	PUNCT
ejpam-6658	546	1	on	on	ADP
ejpam-6658	546	2	some	some	DET
ejpam-6658	546	3	extensions	extension	NOUN
ejpam-6658	546	4	for	for	ADP
ejpam-6658	546	5	degenerate	degenerate	ADJ
ejpam-6658	546	6	frobenius	frobenius	NOUN
ejpam-6658	546	7	-	-	PUNCT
ejpam-6658	546	8	euler	euler	NOUN
ejpam-6658	546	9	-	-	PUNCT
ejpam-6658	546	10	genocchi	genocchi	PROPN
ejpam-6658	546	11	polynomials	polynomial	VERB
ejpam-6658	546	12	with	with	ADP
ejpam-6658	546	13	applications	application	NOUN
ejpam-6658	546	14	in	in	ADP
ejpam-6658	546	15	computer	computer	NOUN
ejpam-6658	546	16	modeling	modeling	NOUN
ejpam-6658	546	17	.	.	PUNCT
ejpam-6658	547	1	applied	apply	VERB
ejpam-6658	547	2	mathematics	mathematic	NOUN
ejpam-6658	547	3	in	in	ADP
ejpam-6658	547	4	science	science	NOUN
ejpam-6658	547	5	and	and	CCONJ
ejpam-6658	547	6	engineering	engineering	NOUN
ejpam-6658	547	7	,	,	PUNCT
ejpam-6658	547	8	32(1):2297072	32(1):2297072	NUM
ejpam-6658	547	9	,	,	PUNCT
ejpam-6658	547	10	2024	2024	NUM
ejpam-6658	547	11	.	.	PUNCT
ejpam-6658	548	1	[	[	X
ejpam-6658	548	2	24	24	NUM
ejpam-6658	548	3	]	]	SYM
ejpam-6658	548	4	waseem	waseem	PROPN
ejpam-6658	548	5	ahmad	ahmad	PROPN
ejpam-6658	548	6	khan	khan	PROPN
ejpam-6658	548	7	and	and	CCONJ
ejpam-6658	548	8	maryam	maryam	PROPN
ejpam-6658	548	9	salem	salem	PROPN
ejpam-6658	548	10	alatawi	alatawi	VERB
ejpam-6658	548	11	.	.	PUNCT
ejpam-6658	549	1	a	a	DET
ejpam-6658	549	2	note	note	NOUN
ejpam-6658	549	3	on	on	ADP
ejpam-6658	549	4	modified	modified	ADJ
ejpam-6658	549	5	degenerate	degenerate	ADJ
ejpam-6658	549	6	changhee	changhee	NOUN
ejpam-6658	549	7	–	–	PUNCT
ejpam-6658	549	8	genocchi	genocchi	PROPN
ejpam-6658	549	9	polynomials	polynomial	NOUN
ejpam-6658	549	10	of	of	ADP
ejpam-6658	549	11	the	the	DET
ejpam-6658	549	12	second	second	ADJ
ejpam-6658	549	13	kind	kind	NOUN
ejpam-6658	549	14	.	.	PUNCT
ejpam-6658	550	1	symmetry	symmetry	NOUN
ejpam-6658	550	2	,	,	PUNCT
ejpam-6658	550	3	15(1):136	15(1):136	NOUN
ejpam-6658	550	4	,	,	PUNCT
ejpam-6658	550	5	2023	2023	NUM
ejpam-6658	550	6	.	.	PUNCT
ejpam-6658	551	1	[	[	X
ejpam-6658	551	2	25	25	NUM
ejpam-6658	551	3	]	]	X
ejpam-6658	551	4	haitham	haitham	PROPN
ejpam-6658	551	5	qawaqneh	qawaqneh	PROPN
ejpam-6658	551	6	,	,	PUNCT
ejpam-6658	551	7	mohd	mohd	PROPN
ejpam-6658	551	8	salmi	salmi	PROPN
ejpam-6658	551	9	md	md	PROPN
ejpam-6658	551	10	noorani	noorani	PROPN
ejpam-6658	551	11	,	,	PUNCT
ejpam-6658	551	12	hassen	hassen	PROPN
ejpam-6658	551	13	aydi	aydi	VERB
ejpam-6658	551	14	,	,	PUNCT
ejpam-6658	551	15	amjed	amjed	PROPN
ejpam-6658	551	16	zraiqat	zraiqat	PROPN
ejpam-6658	551	17	,	,	PUNCT
ejpam-6658	551	18	and	and	CCONJ
ejpam-6658	551	19	arslan	arslan	PROPN
ejpam-6658	551	20	hojat	hojat	PROPN
ejpam-6658	551	21	ansari	ansari	PROPN
ejpam-6658	551	22	.	.	PUNCT
ejpam-6658	552	1	on	on	ADP
ejpam-6658	552	2	fixed	fix	VERB
ejpam-6658	552	3	point	point	NOUN
ejpam-6658	552	4	results	result	NOUN
ejpam-6658	552	5	in	in	ADP
ejpam-6658	552	6	partial	partial	ADJ
ejpam-6658	552	7	b	b	NOUN
ejpam-6658	552	8	-	-	PUNCT
ejpam-6658	552	9	metric	metric	ADJ
ejpam-6658	552	10	spaces	space	NOUN
ejpam-6658	552	11	.	.	PUNCT
ejpam-6658	553	1	journal	journal	NOUN
ejpam-6658	553	2	of	of	ADP
ejpam-6658	553	3	function	function	NOUN
ejpam-6658	553	4	spaces	space	NOUN
ejpam-6658	553	5	,	,	PUNCT
ejpam-6658	553	6	2021(1):8769190	2021(1):8769190	NUM
ejpam-6658	553	7	,	,	PUNCT
ejpam-6658	553	8	2021	2021	NUM
ejpam-6658	553	9	.	.	PUNCT
ejpam-6658	554	1	[	[	X
ejpam-6658	554	2	26	26	NUM
ejpam-6658	554	3	]	]	X
ejpam-6658	554	4	haitham	haitham	PROPN
ejpam-6658	554	5	qawaqneh	qawaqneh	PROPN
ejpam-6658	554	6	,	,	PUNCT
ejpam-6658	554	7	mohd	mohd	PROPN
ejpam-6658	554	8	salmi	salmi	PROPN
ejpam-6658	554	9	md	md	PROPN
ejpam-6658	554	10	noorani	noorani	PROPN
ejpam-6658	554	11	,	,	PUNCT
ejpam-6658	554	12	and	and	CCONJ
ejpam-6658	554	13	hassen	hassen	PROPN
ejpam-6658	554	14	aydi	aydi	VERB
ejpam-6658	554	15	.	.	PUNCT
ejpam-6658	555	1	some	some	DET
ejpam-6658	555	2	new	new	ADJ
ejpam-6658	555	3	characterizations	characterization	NOUN
ejpam-6658	555	4	and	and	CCONJ
ejpam-6658	555	5	results	result	NOUN
ejpam-6658	555	6	for	for	ADP
ejpam-6658	555	7	fuzzy	fuzzy	ADJ
ejpam-6658	555	8	contractions	contraction	NOUN
ejpam-6658	555	9	in	in	ADP
ejpam-6658	555	10	fuzzy	fuzzy	ADJ
ejpam-6658	555	11	b	b	X
ejpam-6658	555	12	-	-	PUNCT
ejpam-6658	555	13	metric	metric	ADJ
ejpam-6658	555	14	spaces	space	NOUN
ejpam-6658	555	15	and	and	CCONJ
ejpam-6658	555	16	applications	application	NOUN
ejpam-6658	555	17	.	.	PUNCT
ejpam-6658	556	1	aims	aim	VERB
ejpam-6658	556	2	mathematics	mathematics	PROPN
ejpam-6658	556	3	,	,	PUNCT
ejpam-6658	556	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-6658	556	5	,	,	PUNCT
ejpam-6658	556	6	2023	2023	NUM
ejpam-6658	556	7	.	.	PUNCT
ejpam-6658	557	1	[	[	X
ejpam-6658	557	2	27	27	NUM
ejpam-6658	557	3	]	]	X
ejpam-6658	557	4	h	h	NOUN
ejpam-6658	557	5	qawaqneh	qawaqneh	PROPN
ejpam-6658	557	6	,	,	PUNCT
ejpam-6658	557	7	ha	ha	INTJ
ejpam-6658	557	8	hammad	hammad	PROPN
ejpam-6658	557	9	,	,	PUNCT
ejpam-6658	557	10	and	and	CCONJ
ejpam-6658	557	11	h	h	NOUN
ejpam-6658	557	12	aydi	aydi	VERB
ejpam-6658	557	13	.	.	PUNCT
ejpam-6658	558	1	exploring	explore	VERB
ejpam-6658	558	2	new	new	ADJ
ejpam-6658	558	3	geometric	geometric	ADJ
ejpam-6658	558	4	contraction	contraction	NOUN
ejpam-6658	558	5	mappings	mapping	NOUN
ejpam-6658	558	6	and	and	CCONJ
ejpam-6658	558	7	their	their	PRON
ejpam-6658	558	8	applications	application	NOUN
ejpam-6658	558	9	in	in	ADP
ejpam-6658	558	10	fractional	fractional	ADJ
ejpam-6658	558	11	metric	metric	ADJ
ejpam-6658	558	12	spaces	space	NOUN
ejpam-6658	558	13	,	,	PUNCT
ejpam-6658	558	14	aims	aim	VERB
ejpam-6658	558	15	math	math	NOUN
ejpam-6658	558	16	.	.	PUNCT
ejpam-6658	559	1	9	9	NUM
ejpam-6658	559	2	(	(	PUNCT
ejpam-6658	559	3	2024	2024	NUM
ejpam-6658	559	4	)	)	PUNCT
ejpam-6658	559	5	,	,	PUNCT
ejpam-6658	559	6	521–541	521–541	NUM
ejpam-6658	559	7	.	.	PUNCT
ejpam-6658	560	1	[	[	X
ejpam-6658	560	2	28	28	NUM
ejpam-6658	560	3	]	]	X
ejpam-6658	560	4	francesco	francesco	PROPN
ejpam-6658	560	5	aldo	aldo	PROPN
ejpam-6658	560	6	costabile	costabile	PROPN
ejpam-6658	560	7	,	,	PUNCT
ejpam-6658	560	8	maria	maria	PROPN
ejpam-6658	560	9	italia	italia	PROPN
ejpam-6658	560	10	gualtieri	gualtieri	PROPN
ejpam-6658	560	11	,	,	PUNCT
ejpam-6658	560	12	and	and	CCONJ
ejpam-6658	560	13	anna	anna	PROPN
ejpam-6658	560	14	napoli	napoli	PROPN
ejpam-6658	560	15	.	.	PUNCT
ejpam-6658	561	1	general	general	ADJ
ejpam-6658	561	2	bivariate	bivariate	ADJ
ejpam-6658	561	3	appell	appell	ADJ
ejpam-6658	561	4	polynomials	polynomial	NOUN
ejpam-6658	561	5	via	via	ADP
ejpam-6658	561	6	matrix	matrix	NOUN
ejpam-6658	561	7	calculus	calculus	NOUN
ejpam-6658	561	8	and	and	CCONJ
ejpam-6658	561	9	related	relate	VERB
ejpam-6658	561	10	interpolation	interpolation	NOUN
ejpam-6658	561	11	hints	hint	NOUN
ejpam-6658	561	12	.	.	PUNCT
ejpam-6658	562	1	mathematics	mathematic	NOUN
ejpam-6658	562	2	,	,	PUNCT
ejpam-6658	562	3	9(9):964	9(9):964	NUM
ejpam-6658	562	4	,	,	PUNCT
ejpam-6658	562	5	2021	2021	NUM
ejpam-6658	562	6	.	.	PUNCT
ejpam-6658	563	1	[	[	X
ejpam-6658	563	2	29	29	NUM
ejpam-6658	563	3	]	]	X
ejpam-6658	563	4	francesco	francesco	NOUN
ejpam-6658	563	5	a	a	DET
ejpam-6658	563	6	costabile	costabile	NOUN
ejpam-6658	563	7	,	,	PUNCT
ejpam-6658	563	8	maria	maria	PROPN
ejpam-6658	563	9	italia	italia	PROPN
ejpam-6658	563	10	gualtieri	gualtieri	PROPN
ejpam-6658	563	11	,	,	PUNCT
ejpam-6658	563	12	and	and	CCONJ
ejpam-6658	563	13	anna	anna	PROPN
ejpam-6658	563	14	napoli	napoli	PROPN
ejpam-6658	563	15	.	.	PUNCT
ejpam-6658	564	1	bivariate	bivariate	ADJ
ejpam-6658	564	2	general	general	ADJ
ejpam-6658	564	3	appell	appell	ADJ
ejpam-6658	564	4	interpolation	interpolation	NOUN
ejpam-6658	564	5	problem	problem	NOUN
ejpam-6658	564	6	.	.	PUNCT
ejpam-6658	565	1	numerical	numerical	ADJ
ejpam-6658	565	2	algorithms	algorithms	PROPN
ejpam-6658	565	3	,	,	PUNCT
ejpam-6658	565	4	91(2):531–556	91(2):531–556	NOUN
ejpam-6658	565	5	,	,	PUNCT
ejpam-6658	565	6	2022	2022	NUM
ejpam-6658	565	7	.	.	PUNCT