id	sid	tid	token	lemma	pos
ejpam-6657	1	1	european	european	PROPN
ejpam-6657	1	2	journal	journal	PROPN
ejpam-6657	1	3	of	of	ADP
ejpam-6657	1	4	pure	pure	ADJ
ejpam-6657	1	5	and	and	CCONJ
ejpam-6657	1	6	applied	applied	ADJ
ejpam-6657	1	7	mathematics	mathematic	NOUN
ejpam-6657	1	8	2025	2025	NUM
ejpam-6657	1	9	,	,	PUNCT
ejpam-6657	1	10	vol	vol	NOUN
ejpam-6657	1	11	.	.	PROPN
ejpam-6657	1	12	18	18	NUM
ejpam-6657	1	13	,	,	PUNCT
ejpam-6657	1	14	issue	issue	NOUN
ejpam-6657	1	15	3	3	NUM
ejpam-6657	1	16	,	,	PUNCT
ejpam-6657	1	17	article	article	NOUN
ejpam-6657	1	18	number	number	NOUN
ejpam-6657	1	19	6657	6657	NUM
ejpam-6657	1	20	issn	issn	VERB
ejpam-6657	1	21	1307	1307	NUM
ejpam-6657	1	22	-	-	SYM
ejpam-6657	1	23	5543	5543	NUM
ejpam-6657	1	24	–	–	PUNCT
ejpam-6657	1	25	ejpam.com	ejpam.com	X
ejpam-6657	1	26	published	publish	VERB
ejpam-6657	1	27	by	by	ADP
ejpam-6657	1	28	new	new	PROPN
ejpam-6657	1	29	york	york	PROPN
ejpam-6657	1	30	business	business	PROPN
ejpam-6657	1	31	global	global	ADJ
ejpam-6657	1	32	certain	certain	ADJ
ejpam-6657	1	33	properties	property	NOUN
ejpam-6657	1	34	and	and	CCONJ
ejpam-6657	1	35	characterizations	characterization	NOUN
ejpam-6657	1	36	of	of	ADP
ejpam-6657	1	37	∆h	∆h	NOUN
ejpam-6657	1	38	-	-	PUNCT
ejpam-6657	1	39	truncated	truncate	VERB
ejpam-6657	1	40	exponential	exponential	NOUN
ejpam-6657	1	41	based	base	VERB
ejpam-6657	1	42	hermite	hermite	ADJ
ejpam-6657	1	43	polynomials	polynomial	VERB
ejpam-6657	1	44	haitham	haitham	PROPN
ejpam-6657	1	45	qawaqneh	qawaqneh	PROPN
ejpam-6657	1	46	1	1	NUM
ejpam-6657	1	47	,	,	PUNCT
ejpam-6657	1	48	waseem	waseem	PROPN
ejpam-6657	1	49	ahmad	ahmad	PROPN
ejpam-6657	1	50	khan	khan	PROPN
ejpam-6657	1	51	2	2	NUM
ejpam-6657	1	52	,	,	PUNCT
ejpam-6657	1	53	hassen	hassen	PROPN
ejpam-6657	1	54	aydi3,4,∗	aydi3,4,∗	PROPN
ejpam-6657	1	55	,	,	PUNCT
ejpam-6657	1	56	shahid	shahid	PROPN
ejpam-6657	1	57	ahmad	ahmad	PROPN
ejpam-6657	1	58	wani5	wani5	PROPN
ejpam-6657	1	59	,	,	PUNCT
ejpam-6657	1	60	prakash	prakash	PROPN
ejpam-6657	1	61	jadhav6	jadhav6	PROPN
ejpam-6657	1	62	1	1	NUM
ejpam-6657	1	63	department	department	NOUN
ejpam-6657	1	64	of	of	ADP
ejpam-6657	1	65	mathematics	mathematics	PROPN
ejpam-6657	1	66	,	,	PUNCT
ejpam-6657	1	67	al	al	PROPN
ejpam-6657	1	68	-	-	PROPN
ejpam-6657	1	69	zaytoonah	zaytoonah	PROPN
ejpam-6657	1	70	university	university	PROPN
ejpam-6657	1	71	of	of	ADP
ejpam-6657	1	72	jordan	jordan	PROPN
ejpam-6657	1	73	,	,	PUNCT
ejpam-6657	1	74	amman	amman	PROPN
ejpam-6657	1	75	11733	11733	NUM
ejpam-6657	1	76	,	,	PUNCT
ejpam-6657	1	77	jordan	jordan	PROPN
ejpam-6657	1	78	2	2	NUM
ejpam-6657	1	79	department	department	NOUN
ejpam-6657	1	80	of	of	ADP
ejpam-6657	1	81	electrical	electrical	ADJ
ejpam-6657	1	82	engineering	engineering	NOUN
ejpam-6657	1	83	,	,	PUNCT
ejpam-6657	1	84	prince	prince	PROPN
ejpam-6657	1	85	mohammad	mohammad	PROPN
ejpam-6657	1	86	bin	bin	PROPN
ejpam-6657	1	87	fahd	fahd	PROPN
ejpam-6657	1	88	university	university	PROPN
ejpam-6657	1	89	,	,	PUNCT
ejpam-6657	1	90	p.o	p.o	PROPN
ejpam-6657	1	91	box	box	PROPN
ejpam-6657	1	92	1664	1664	NUM
ejpam-6657	1	93	,	,	PUNCT
ejpam-6657	1	94	al	al	PROPN
ejpam-6657	1	95	khobar	khobar	PROPN
ejpam-6657	1	96	31952	31952	NUM
ejpam-6657	1	97	,	,	PUNCT
ejpam-6657	1	98	saudi	saudi	PROPN
ejpam-6657	1	99	arabia	arabia	PROPN
ejpam-6657	1	100	3	3	NUM
ejpam-6657	1	101	institut	institut	PROPN
ejpam-6657	1	102	supérieur	supérieur	PROPN
ejpam-6657	1	103	d’informatique	d’informatique	PROPN
ejpam-6657	1	104	et	et	NOUN
ejpam-6657	1	105	des	des	X
ejpam-6657	1	106	techniques	techniques	X
ejpam-6657	1	107	de	de	X
ejpam-6657	1	108	communication	communication	NOUN
ejpam-6657	1	109	,	,	PUNCT
ejpam-6657	1	110	université	université	ADJ
ejpam-6657	1	111	de	de	X
ejpam-6657	1	112	sousse	sousse	PROPN
ejpam-6657	1	113	,	,	PUNCT
ejpam-6657	1	114	h.	h.	PROPN
ejpam-6657	1	115	sousse	sousse	PROPN
ejpam-6657	1	116	4000	4000	NUM
ejpam-6657	1	117	,	,	PUNCT
ejpam-6657	1	118	tunisia	tunisia	PROPN
ejpam-6657	1	119	4	4	NUM
ejpam-6657	1	120	department	department	NOUN
ejpam-6657	1	121	of	of	ADP
ejpam-6657	1	122	mathematics	mathematic	NOUN
ejpam-6657	1	123	and	and	CCONJ
ejpam-6657	1	124	applied	apply	VERB
ejpam-6657	1	125	mathematics	mathematic	NOUN
ejpam-6657	1	126	,	,	PUNCT
ejpam-6657	1	127	sefako	sefako	VERB
ejpam-6657	1	128	makgatho	makgatho	PROPN
ejpam-6657	1	129	health	health	PROPN
ejpam-6657	1	130	sciences	sciences	PROPN
ejpam-6657	1	131	university	university	PROPN
ejpam-6657	1	132	,	,	PUNCT
ejpam-6657	1	133	ga	ga	PROPN
ejpam-6657	1	134	-	-	NOUN
ejpam-6657	1	135	rankuwa	rankuwa	PROPN
ejpam-6657	1	136	,	,	PUNCT
ejpam-6657	1	137	south	south	PROPN
ejpam-6657	1	138	africa	africa	PROPN
ejpam-6657	1	139	5	5	NUM
ejpam-6657	1	140	symbiosis	symbiosis	NOUN
ejpam-6657	1	141	institute	institute	NOUN
ejpam-6657	1	142	of	of	ADP
ejpam-6657	1	143	technology	technology	PROPN
ejpam-6657	1	144	,	,	PUNCT
ejpam-6657	1	145	pune	pune	NOUN
ejpam-6657	1	146	campus	campus	NOUN
ejpam-6657	1	147	,	,	PUNCT
ejpam-6657	1	148	symbiosis	symbiosis	NOUN
ejpam-6657	1	149	international	international	ADJ
ejpam-6657	1	150	(	(	PUNCT
ejpam-6657	1	151	deemed	deem	VERB
ejpam-6657	1	152	university	university	NOUN
ejpam-6657	1	153	)	)	PUNCT
ejpam-6657	1	154	(	(	PUNCT
ejpam-6657	1	155	siu	siu	NOUN
ejpam-6657	1	156	)	)	PUNCT
ejpam-6657	1	157	,	,	PUNCT
ejpam-6657	1	158	pune	pune	NOUN
ejpam-6657	1	159	,	,	PUNCT
ejpam-6657	1	160	india	india	PROPN
ejpam-6657	1	161	6	6	NUM
ejpam-6657	1	162	department	department	NOUN
ejpam-6657	1	163	of	of	ADP
ejpam-6657	1	164	mechanical	mechanical	ADJ
ejpam-6657	1	165	engineering	engineering	NOUN
ejpam-6657	1	166	,	,	PUNCT
ejpam-6657	1	167	srm	srm	PROPN
ejpam-6657	1	168	university	university	PROPN
ejpam-6657	1	169	ap	ap	PROPN
ejpam-6657	1	170	,	,	PUNCT
ejpam-6657	1	171	andhra	andhra	PROPN
ejpam-6657	1	172	pradesh	pradesh	PROPN
ejpam-6657	1	173	522240	522240	NUM
ejpam-6657	1	174	,	,	PUNCT
ejpam-6657	1	175	india	india	PROPN
ejpam-6657	1	176	abstract	abstract	NOUN
ejpam-6657	1	177	.	.	PUNCT
ejpam-6657	2	1	this	this	DET
ejpam-6657	2	2	article	article	NOUN
ejpam-6657	2	3	introduces	introduce	VERB
ejpam-6657	2	4	a	a	DET
ejpam-6657	2	5	novel	novel	ADJ
ejpam-6657	2	6	class	class	NOUN
ejpam-6657	2	7	of	of	ADP
ejpam-6657	2	8	∆h	∆h	NOUN
ejpam-6657	2	9	-	-	PUNCT
ejpam-6657	2	10	truncated	truncate	VERB
ejpam-6657	2	11	exponential	exponential	NOUN
ejpam-6657	2	12	-	-	PUNCT
ejpam-6657	2	13	based	base	VERB
ejpam-6657	2	14	hermite	hermite	ADJ
ejpam-6657	2	15	polynomials	polynomial	NOUN
ejpam-6657	2	16	and	and	CCONJ
ejpam-6657	2	17	examine	examine	VERB
ejpam-6657	2	18	their	their	PRON
ejpam-6657	2	19	fundamental	fundamental	ADJ
ejpam-6657	2	20	properties	property	NOUN
ejpam-6657	2	21	and	and	CCONJ
ejpam-6657	2	22	structural	structural	ADJ
ejpam-6657	2	23	identities	identity	NOUN
ejpam-6657	2	24	.	.	PUNCT
ejpam-6657	3	1	we	we	PRON
ejpam-6657	3	2	derive	derive	VERB
ejpam-6657	3	3	generating	generating	NOUN
ejpam-6657	3	4	functions	function	NOUN
ejpam-6657	3	5	,	,	PUNCT
ejpam-6657	3	6	recurrence	recurrence	NOUN
ejpam-6657	3	7	relations	relation	NOUN
ejpam-6657	3	8	,	,	PUNCT
ejpam-6657	3	9	and	and	CCONJ
ejpam-6657	3	10	explicit	explicit	ADJ
ejpam-6657	3	11	formulas	formula	NOUN
ejpam-6657	3	12	,	,	PUNCT
ejpam-6657	3	13	along	along	ADP
ejpam-6657	3	14	with	with	ADP
ejpam-6657	3	15	summation	summation	NOUN
ejpam-6657	3	16	identities	identity	NOUN
ejpam-6657	3	17	.	.	PUNCT
ejpam-6657	4	1	the	the	DET
ejpam-6657	4	2	study	study	NOUN
ejpam-6657	4	3	further	far	ADV
ejpam-6657	4	4	uncovers	uncover	NOUN
ejpam-6657	4	5	connections	connection	NOUN
ejpam-6657	4	6	with	with	ADP
ejpam-6657	4	7	the	the	DET
ejpam-6657	4	8	monomiality	monomiality	NOUN
ejpam-6657	4	9	principle	principle	NOUN
ejpam-6657	4	10	,	,	PUNCT
ejpam-6657	4	11	offering	offer	VERB
ejpam-6657	4	12	insights	insight	NOUN
ejpam-6657	4	13	into	into	ADP
ejpam-6657	4	14	their	their	PRON
ejpam-6657	4	15	underlying	underlying	ADJ
ejpam-6657	4	16	algebraic	algebraic	ADJ
ejpam-6657	4	17	framework	framework	NOUN
ejpam-6657	4	18	.	.	PUNCT
ejpam-6657	5	1	in	in	ADP
ejpam-6657	5	2	addition	addition	NOUN
ejpam-6657	5	3	,	,	PUNCT
ejpam-6657	5	4	an	an	DET
ejpam-6657	5	5	operational	operational	ADJ
ejpam-6657	5	6	formalism	formalism	NOUN
ejpam-6657	5	7	is	be	AUX
ejpam-6657	5	8	developed	develop	VERB
ejpam-6657	5	9	,	,	PUNCT
ejpam-6657	5	10	and	and	CCONJ
ejpam-6657	5	11	symmetric	symmetric	ADJ
ejpam-6657	5	12	identities	identity	NOUN
ejpam-6657	5	13	are	be	AUX
ejpam-6657	5	14	established	establish	VERB
ejpam-6657	5	15	to	to	PART
ejpam-6657	5	16	enhance	enhance	VERB
ejpam-6657	5	17	the	the	DET
ejpam-6657	5	18	theoretical	theoretical	ADJ
ejpam-6657	5	19	foundation	foundation	NOUN
ejpam-6657	5	20	of	of	ADP
ejpam-6657	5	21	these	these	DET
ejpam-6657	5	22	polynomials	polynomial	NOUN
ejpam-6657	5	23	.	.	PUNCT
ejpam-6657	6	1	2020	2020	NUM
ejpam-6657	6	2	mathematics	mathematic	NOUN
ejpam-6657	6	3	subject	subject	NOUN
ejpam-6657	6	4	classifications	classification	NOUN
ejpam-6657	6	5	:	:	PUNCT
ejpam-6657	6	6	33c45	33c45	NUM
ejpam-6657	6	7	,	,	PUNCT
ejpam-6657	6	8	33e20	33e20	NUM
ejpam-6657	6	9	,	,	PUNCT
ejpam-6657	6	10	33b10	33b10	NUM
ejpam-6657	6	11	,	,	PUNCT
ejpam-6657	6	12	33e30	33e30	NUM
ejpam-6657	6	13	,	,	PUNCT
ejpam-6657	6	14	11t23	11t23	NUM
ejpam-6657	6	15	.	.	PUNCT
ejpam-6657	7	1	key	key	ADJ
ejpam-6657	7	2	words	word	NOUN
ejpam-6657	7	3	and	and	CCONJ
ejpam-6657	7	4	phrases	phrase	NOUN
ejpam-6657	7	5	:	:	PUNCT
ejpam-6657	7	6	monomiality	monomiality	NOUN
ejpam-6657	7	7	principle	principle	NOUN
ejpam-6657	7	8	,	,	PUNCT
ejpam-6657	7	9	∆h	∆h	NOUN
ejpam-6657	7	10	-	-	PUNCT
ejpam-6657	7	11	truncated	truncate	VERB
ejpam-6657	7	12	exponential	exponential	ADJ
ejpam-6657	7	13	hermite	hermite	ADJ
ejpam-6657	7	14	appell	appell	PROPN
ejpam-6657	7	15	polynomials	polynomial	NOUN
ejpam-6657	7	16	,	,	PUNCT
ejpam-6657	7	17	explicit	explicit	ADJ
ejpam-6657	7	18	forms	form	NOUN
ejpam-6657	7	19	,	,	PUNCT
ejpam-6657	7	20	symmetry	symmetry	NOUN
ejpam-6657	7	21	identities	identity	NOUN
ejpam-6657	7	22	.	.	PUNCT
ejpam-6657	8	1	1	1	X
ejpam-6657	8	2	.	.	X
ejpam-6657	8	3	introduction	introduction	NOUN
ejpam-6657	8	4	and	and	CCONJ
ejpam-6657	8	5	preliminaries	preliminary	NOUN
ejpam-6657	8	6	polynomial	polynomial	ADJ
ejpam-6657	8	7	families	family	NOUN
ejpam-6657	8	8	form	form	VERB
ejpam-6657	8	9	a	a	DET
ejpam-6657	8	10	foundational	foundational	ADJ
ejpam-6657	8	11	pillar	pillar	NOUN
ejpam-6657	8	12	in	in	ADP
ejpam-6657	8	13	applied	applied	ADJ
ejpam-6657	8	14	mathematics	mathematic	NOUN
ejpam-6657	8	15	,	,	PUNCT
ejpam-6657	8	16	given	give	VERB
ejpam-6657	8	17	their	their	PRON
ejpam-6657	8	18	multifaceted	multifaceted	ADJ
ejpam-6657	8	19	characterizations	characterization	NOUN
ejpam-6657	8	20	—	—	PUNCT
ejpam-6657	8	21	ranging	range	VERB
ejpam-6657	8	22	from	from	ADP
ejpam-6657	8	23	orthogonality	orthogonality	NOUN
ejpam-6657	8	24	and	and	CCONJ
ejpam-6657	8	25	generating	generating	NOUN
ejpam-6657	8	26	functions	function	NOUN
ejpam-6657	8	27	to	to	PART
ejpam-6657	8	28	differential	differential	VERB
ejpam-6657	8	29	expressions	expression	NOUN
ejpam-6657	8	30	,	,	PUNCT
ejpam-6657	8	31	operational	operational	ADJ
ejpam-6657	8	32	techniques	technique	NOUN
ejpam-6657	8	33	,	,	PUNCT
ejpam-6657	8	34	integral	integral	ADJ
ejpam-6657	8	35	representations	representation	NOUN
ejpam-6657	8	36	,	,	PUNCT
ejpam-6657	8	37	and	and	CCONJ
ejpam-6657	8	38	recurrence	recurrence	NOUN
ejpam-6657	8	39	relations	relation	NOUN
ejpam-6657	8	40	.	.	PUNCT
ejpam-6657	9	1	due	due	ADP
ejpam-6657	9	2	to	to	ADP
ejpam-6657	9	3	their	their	PRON
ejpam-6657	9	4	versatile	versatile	ADJ
ejpam-6657	9	5	nature	nature	NOUN
ejpam-6657	9	6	and	and	CCONJ
ejpam-6657	9	7	diverse	diverse	ADJ
ejpam-6657	9	8	applications	application	NOUN
ejpam-6657	9	9	,	,	PUNCT
ejpam-6657	9	10	their	their	PRON
ejpam-6657	9	11	generalizations	generalization	NOUN
ejpam-6657	9	12	∗corresponding	∗corresponde	VERB
ejpam-6657	9	13	author	author	NOUN
ejpam-6657	9	14	.	.	PUNCT
ejpam-6657	10	1	doi	doi	NOUN
ejpam-6657	10	2	:	:	PUNCT
ejpam-6657	10	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6657	https://doi.org/10.29020/nybg.ejpam.v18i3.6657	NUM
ejpam-6657	10	4	email	email	NOUN
ejpam-6657	10	5	addresses	address	NOUN
ejpam-6657	10	6	:	:	PUNCT
ejpam-6657	10	7	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-6657	10	8	(	(	PUNCT
ejpam-6657	10	9	h.	h.	PROPN
ejpam-6657	10	10	qawaqneh	qawaqneh	PROPN
ejpam-6657	10	11	)	)	PUNCT
ejpam-6657	10	12	,	,	PUNCT
ejpam-6657	10	13	wkhan1@pmu.edu.sa	wkhan1@pmu.edu.sa	PROPN
ejpam-6657	10	14	(	(	PUNCT
ejpam-6657	10	15	w.	w.	PROPN
ejpam-6657	10	16	a.	a.	PROPN
ejpam-6657	10	17	khan	khan	PROPN
ejpam-6657	10	18	)	)	PUNCT
ejpam-6657	10	19	,	,	PUNCT
ejpam-6657	11	1	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	INTJ
ejpam-6657	11	2	(	(	PUNCT
ejpam-6657	11	3	h.	h.	PROPN
ejpam-6657	11	4	aydi	aydi	VERB
ejpam-6657	11	5	)	)	PUNCT
ejpam-6657	11	6	,	,	PUNCT
ejpam-6657	11	7	shahidwani177@gmail.com	shahidwani177@gmail.com	X
ejpam-6657	11	8	(	(	PUNCT
ejpam-6657	11	9	s.	s.	PROPN
ejpam-6657	11	10	a.	a.	PROPN
ejpam-6657	11	11	wani	wani	PROPN
ejpam-6657	11	12	)	)	PUNCT
ejpam-6657	11	13	,	,	PUNCT
ejpam-6657	11	14	prakash.j@srmap.edu.in	prakash.j@srmap.edu.in	PROPN
ejpam-6657	11	15	(	(	PUNCT
ejpam-6657	11	16	p.	p.	PROPN
ejpam-6657	11	17	jadhav	jadhav	PROPN
ejpam-6657	11	18	)	)	PUNCT
ejpam-6657	11	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6657	12	1	1	1	NUM
ejpam-6657	12	2	copyright	copyright	NOUN
ejpam-6657	12	3	:	:	PUNCT
ejpam-6657	12	4	©	©	PROPN
ejpam-6657	12	5	2025	2025	NUM
ejpam-6657	12	6	the	the	DET
ejpam-6657	12	7	author(s	author(s	NOUN
ejpam-6657	12	8	)	)	PUNCT
ejpam-6657	12	9	.	.	PUNCT
ejpam-6657	13	1	(	(	PUNCT
ejpam-6657	13	2	cc	cc	NOUN
ejpam-6657	13	3	by	by	ADP
ejpam-6657	13	4	-	-	PUNCT
ejpam-6657	13	5	nc	nc	PROPN
ejpam-6657	13	6	4.0	4.0	NUM
ejpam-6657	13	7	)	)	PUNCT
ejpam-6657	13	8	h.	h.	PROPN
ejpam-6657	13	9	qawaqneh	qawaqneh	PROPN
ejpam-6657	13	10	et	et	PROPN
ejpam-6657	13	11	al	al	PROPN
ejpam-6657	13	12	.	.	PUNCT
ejpam-6657	13	13	/	/	SYM
ejpam-6657	13	14	eur	eur	PROPN
ejpam-6657	13	15	.	.	PUNCT
ejpam-6657	14	1	j.	j.	PROPN
ejpam-6657	14	2	pure	pure	PROPN
ejpam-6657	14	3	appl	appl	PROPN
ejpam-6657	14	4	.	.	PROPN
ejpam-6657	14	5	math	math	PROPN
ejpam-6657	14	6	,	,	PUNCT
ejpam-6657	14	7	18	18	NUM
ejpam-6657	14	8	(	(	PUNCT
ejpam-6657	14	9	3	3	NUM
ejpam-6657	14	10	)	)	PUNCT
ejpam-6657	14	11	(	(	PUNCT
ejpam-6657	14	12	2025	2025	NUM
ejpam-6657	14	13	)	)	PUNCT
ejpam-6657	14	14	,	,	PUNCT
ejpam-6657	14	15	6657	6657	NUM
ejpam-6657	14	16	2	2	NUM
ejpam-6657	14	17	of	of	ADP
ejpam-6657	14	18	16	16	NUM
ejpam-6657	14	19	and	and	CCONJ
ejpam-6657	14	20	extensions	extension	NOUN
ejpam-6657	14	21	continue	continue	VERB
ejpam-6657	14	22	to	to	PART
ejpam-6657	14	23	garner	garner	VERB
ejpam-6657	14	24	significant	significant	ADJ
ejpam-6657	14	25	attention	attention	NOUN
ejpam-6657	14	26	across	across	ADP
ejpam-6657	14	27	mathematical	mathematical	ADJ
ejpam-6657	14	28	and	and	CCONJ
ejpam-6657	14	29	physical	physical	ADJ
ejpam-6657	14	30	sciences	science	NOUN
ejpam-6657	14	31	.	.	PUNCT
ejpam-6657	15	1	these	these	DET
ejpam-6657	15	2	formulations	formulation	NOUN
ejpam-6657	15	3	are	be	AUX
ejpam-6657	15	4	vital	vital	ADJ
ejpam-6657	15	5	not	not	PART
ejpam-6657	15	6	only	only	ADV
ejpam-6657	15	7	in	in	ADP
ejpam-6657	15	8	providing	provide	VERB
ejpam-6657	15	9	series	series	NOUN
ejpam-6657	15	10	expansions	expansion	NOUN
ejpam-6657	15	11	for	for	ADP
ejpam-6657	15	12	transcendental	transcendental	ADJ
ejpam-6657	15	13	functions	function	NOUN
ejpam-6657	15	14	in	in	ADP
ejpam-6657	15	15	mathematical	mathematical	ADJ
ejpam-6657	15	16	physics	physics	NOUN
ejpam-6657	15	17	but	but	CCONJ
ejpam-6657	15	18	also	also	ADV
ejpam-6657	15	19	in	in	ADP
ejpam-6657	15	20	shaping	shape	VERB
ejpam-6657	15	21	computational	computational	ADJ
ejpam-6657	15	22	and	and	CCONJ
ejpam-6657	15	23	analytical	analytical	ADJ
ejpam-6657	15	24	techniques	technique	NOUN
ejpam-6657	15	25	.	.	PUNCT
ejpam-6657	16	1	notable	notable	ADJ
ejpam-6657	16	2	studies	study	NOUN
ejpam-6657	16	3	in	in	ADP
ejpam-6657	16	4	this	this	DET
ejpam-6657	16	5	domain	domain	NOUN
ejpam-6657	16	6	include	include	VERB
ejpam-6657	16	7	extensive	extensive	ADJ
ejpam-6657	16	8	developments	development	NOUN
ejpam-6657	16	9	in	in	ADP
ejpam-6657	16	10	p	p	NOUN
ejpam-6657	16	11	-	-	PUNCT
ejpam-6657	16	12	adic	adic	ADJ
ejpam-6657	16	13	analysis	analysis	NOUN
ejpam-6657	16	14	,	,	PUNCT
ejpam-6657	16	15	q	q	NOUN
ejpam-6657	16	16	-	-	NOUN
ejpam-6657	16	17	analysis	analysis	NOUN
ejpam-6657	16	18	,	,	PUNCT
ejpam-6657	16	19	and	and	CCONJ
ejpam-6657	16	20	umbral	umbral	ADJ
ejpam-6657	16	21	calculus	calculus	NOUN
ejpam-6657	16	22	(	(	PUNCT
ejpam-6657	16	23	see	see	VERB
ejpam-6657	16	24	,	,	PUNCT
ejpam-6657	16	25	for	for	ADP
ejpam-6657	16	26	example	example	NOUN
ejpam-6657	16	27	,	,	PUNCT
ejpam-6657	16	28	[	[	X
ejpam-6657	16	29	1–5	1–5	X
ejpam-6657	16	30	]	]	X
ejpam-6657	16	31	)	)	PUNCT
ejpam-6657	16	32	.	.	PUNCT
ejpam-6657	17	1	among	among	ADP
ejpam-6657	17	2	these	these	DET
ejpam-6657	17	3	developments	development	NOUN
ejpam-6657	17	4	,	,	PUNCT
ejpam-6657	17	5	two	two	NUM
ejpam-6657	17	6	-	-	PUNCT
ejpam-6657	17	7	variable	variable	NOUN
ejpam-6657	17	8	special	special	ADJ
ejpam-6657	17	9	polynomials	polynomial	NOUN
ejpam-6657	17	10	have	have	AUX
ejpam-6657	17	11	emerged	emerge	VERB
ejpam-6657	17	12	as	as	ADP
ejpam-6657	17	13	highly	highly	ADV
ejpam-6657	17	14	potent	potent	ADJ
ejpam-6657	17	15	tools	tool	NOUN
ejpam-6657	17	16	,	,	PUNCT
ejpam-6657	17	17	facilitating	facilitate	VERB
ejpam-6657	17	18	the	the	DET
ejpam-6657	17	19	derivation	derivation	NOUN
ejpam-6657	17	20	of	of	ADP
ejpam-6657	17	21	efficient	efficient	ADJ
ejpam-6657	17	22	and	and	CCONJ
ejpam-6657	17	23	elegant	elegant	ADJ
ejpam-6657	17	24	identities	identity	NOUN
ejpam-6657	17	25	and	and	CCONJ
ejpam-6657	17	26	offering	offer	VERB
ejpam-6657	17	27	pathways	pathway	NOUN
ejpam-6657	17	28	to	to	ADP
ejpam-6657	17	29	novel	novel	ADJ
ejpam-6657	17	30	classes	class	NOUN
ejpam-6657	17	31	of	of	ADP
ejpam-6657	17	32	special	special	ADJ
ejpam-6657	17	33	polynomials	polynomial	NOUN
ejpam-6657	17	34	.	.	PUNCT
ejpam-6657	18	1	the	the	DET
ejpam-6657	18	2	inception	inception	NOUN
ejpam-6657	18	3	of	of	ADP
ejpam-6657	18	4	two	two	NUM
ejpam-6657	18	5	-	-	PUNCT
ejpam-6657	18	6	variable	variable	NOUN
ejpam-6657	18	7	appell	appell	NOUN
ejpam-6657	18	8	polynomials	polynomial	NOUN
ejpam-6657	18	9	by	by	ADP
ejpam-6657	18	10	bretti	bretti	PROPN
ejpam-6657	18	11	et	et	PROPN
ejpam-6657	18	12	al	al	PROPN
ejpam-6657	18	13	.	.	PUNCT
ejpam-6657	19	1	[	[	X
ejpam-6657	19	2	1	1	X
ejpam-6657	19	3	]	]	PUNCT
ejpam-6657	19	4	via	via	ADP
ejpam-6657	19	5	iterated	iterated	ADJ
ejpam-6657	19	6	isomorphism	isomorphism	PROPN
ejpam-6657	19	7	marked	mark	VERB
ejpam-6657	19	8	a	a	DET
ejpam-6657	19	9	pivotal	pivotal	ADJ
ejpam-6657	19	10	moment	moment	NOUN
ejpam-6657	19	11	,	,	PUNCT
ejpam-6657	19	12	followed	follow	VERB
ejpam-6657	19	13	by	by	ADP
ejpam-6657	19	14	the	the	DET
ejpam-6657	19	15	construction	construction	NOUN
ejpam-6657	19	16	and	and	CCONJ
ejpam-6657	19	17	study	study	NOUN
ejpam-6657	19	18	of	of	ADP
ejpam-6657	19	19	two	two	NUM
ejpam-6657	19	20	-	-	PUNCT
ejpam-6657	19	21	variable	variable	NOUN
ejpam-6657	19	22	truncated	truncate	VERB
ejpam-6657	19	23	exponential	exponential	NOUN
ejpam-6657	19	24	,	,	PUNCT
ejpam-6657	19	25	hermite	hermite	PROPN
ejpam-6657	19	26	,	,	PUNCT
ejpam-6657	19	27	legendre	legendre	PROPN
ejpam-6657	19	28	,	,	PUNCT
ejpam-6657	19	29	and	and	CCONJ
ejpam-6657	19	30	laguerre	laguerre	NOUN
ejpam-6657	19	31	polynomials	polynomial	NOUN
ejpam-6657	19	32	in	in	ADP
ejpam-6657	19	33	works	work	NOUN
ejpam-6657	19	34	such	such	ADJ
ejpam-6657	19	35	as	as	ADP
ejpam-6657	19	36	[	[	X
ejpam-6657	19	37	6–13	6–13	NOUN
ejpam-6657	19	38	]	]	PUNCT
ejpam-6657	19	39	.	.	PUNCT
ejpam-6657	20	1	despite	despite	SCONJ
ejpam-6657	20	2	their	their	PRON
ejpam-6657	20	3	relevance	relevance	NOUN
ejpam-6657	20	4	in	in	ADP
ejpam-6657	20	5	areas	area	NOUN
ejpam-6657	20	6	such	such	ADJ
ejpam-6657	20	7	as	as	ADP
ejpam-6657	20	8	quantum	quantum	ADJ
ejpam-6657	20	9	mechanics	mechanic	NOUN
ejpam-6657	20	10	and	and	CCONJ
ejpam-6657	20	11	optics	optic	NOUN
ejpam-6657	20	12	,	,	PUNCT
ejpam-6657	20	13	the	the	DET
ejpam-6657	20	14	tep	tep	PROPN
ejpam-6657	20	15	(	(	PUNCT
ejpam-6657	20	16	tep	tep	NOUN
ejpam-6657	20	17	)	)	PUNCT
ejpam-6657	20	18	remains	remain	VERB
ejpam-6657	20	19	relatively	relatively	ADV
ejpam-6657	20	20	underexplored	underexplored	ADJ
ejpam-6657	20	21	.	.	PUNCT
ejpam-6657	21	1	initially	initially	ADV
ejpam-6657	21	2	defined	define	VERB
ejpam-6657	21	3	by	by	ADP
ejpam-6657	21	4	andrews	andrews	PROPN
ejpam-6657	21	5	[	[	X
ejpam-6657	21	6	14	14	NUM
ejpam-6657	21	7	]	]	PUNCT
ejpam-6657	21	8	,	,	PUNCT
ejpam-6657	21	9	these	these	DET
ejpam-6657	21	10	polynomials	polynomial	NOUN
ejpam-6657	21	11	are	be	AUX
ejpam-6657	21	12	given	give	VERB
ejpam-6657	21	13	by	by	ADP
ejpam-6657	21	14	:	:	PUNCT
ejpam-6657	21	15	en(ξ1	en(ξ1	NUM
ejpam-6657	21	16	)	)	PUNCT
ejpam-6657	21	17	=	=	SYM
ejpam-6657	21	18	n∑	n∑	PROPN
ejpam-6657	21	19	k=0	k=0	PROPN
ejpam-6657	21	20	ξk1	ξk1	VERB
ejpam-6657	21	21	k	k	PROPN
ejpam-6657	21	22	!	!	PROPN
ejpam-6657	21	23	,	,	PUNCT
ejpam-6657	21	24	(	(	PUNCT
ejpam-6657	21	25	1	1	X
ejpam-6657	21	26	)	)	PUNCT
ejpam-6657	21	27	with	with	ADP
ejpam-6657	21	28	the	the	DET
ejpam-6657	21	29	limiting	limit	VERB
ejpam-6657	21	30	behavior	behavior	NOUN
ejpam-6657	21	31	lim	lim	PROPN
ejpam-6657	21	32	n→∞	n→∞	NUM
ejpam-6657	21	33	en(ξ1	en(ξ1	NOUN
ejpam-6657	21	34	)	)	PUNCT
ejpam-6657	21	35	=	=	SYM
ejpam-6657	21	36	eξ1	eξ1	NOUN
ejpam-6657	21	37	.	.	PUNCT
ejpam-6657	22	1	a	a	DET
ejpam-6657	22	2	detailed	detailed	ADJ
ejpam-6657	22	3	investigation	investigation	NOUN
ejpam-6657	22	4	of	of	ADP
ejpam-6657	22	5	their	their	PRON
ejpam-6657	22	6	properties	property	NOUN
ejpam-6657	22	7	was	be	AUX
ejpam-6657	22	8	later	later	ADV
ejpam-6657	22	9	initiated	initiate	VERB
ejpam-6657	22	10	by	by	ADP
ejpam-6657	22	11	dattoli	dattoli	NOUN
ejpam-6657	22	12	et	et	PROPN
ejpam-6657	22	13	al	al	PROPN
ejpam-6657	22	14	.	.	PUNCT
ejpam-6657	23	1	[	[	X
ejpam-6657	23	2	8	8	NUM
ejpam-6657	23	3	]	]	PUNCT
ejpam-6657	23	4	.	.	PUNCT
ejpam-6657	24	1	a	a	DET
ejpam-6657	24	2	key	key	ADJ
ejpam-6657	24	3	identity	identity	NOUN
ejpam-6657	24	4	for	for	ADP
ejpam-6657	24	5	the	the	DET
ejpam-6657	24	6	tep	tep	NOUN
ejpam-6657	24	7	follows	follow	VERB
ejpam-6657	24	8	from	from	ADP
ejpam-6657	24	9	their	their	PRON
ejpam-6657	24	10	integral	integral	ADJ
ejpam-6657	24	11	representation	representation	NOUN
ejpam-6657	24	12	:	:	PUNCT
ejpam-6657	24	13	en(ξ1	en(ξ1	X
ejpam-6657	24	14	)	)	PUNCT
ejpam-6657	24	15	=	=	SYM
ejpam-6657	24	16	1	1	NUM
ejpam-6657	24	17	n	n	NUM
ejpam-6657	24	18	!	!	PUNCT
ejpam-6657	24	19	∫	∫	PROPN
ejpam-6657	25	1	∞	∞	NOUN
ejpam-6657	25	2	0	0	X
ejpam-6657	26	1	e−ξ(ξ1	e−ξ(ξ1	ADJ
ejpam-6657	26	2	+	+	NUM
ejpam-6657	26	3	ξ)n	ξ)n	X
ejpam-6657	26	4	dξ	dξ	PROPN
ejpam-6657	26	5	,	,	PUNCT
ejpam-6657	26	6	(	(	PUNCT
ejpam-6657	26	7	2	2	X
ejpam-6657	26	8	)	)	PUNCT
ejpam-6657	26	9	derived	derive	VERB
ejpam-6657	26	10	using	use	VERB
ejpam-6657	26	11	the	the	DET
ejpam-6657	26	12	classical	classical	ADJ
ejpam-6657	26	13	gamma	gamma	NOUN
ejpam-6657	26	14	integral	integral	NOUN
ejpam-6657	26	15	:	:	PUNCT
ejpam-6657	26	16	n	n	CCONJ
ejpam-6657	26	17	!	!	PUNCT
ejpam-6657	26	18	=	=	SYM
ejpam-6657	27	1	∫	∫	PROPN
ejpam-6657	27	2	∞	∞	PROPN
ejpam-6657	27	3	0	0	NUM
ejpam-6657	28	1	e−ξ	e−ξ	PROPN
ejpam-6657	28	2	ξn	ξn	PROPN
ejpam-6657	28	3	dξ	dξ	PROPN
ejpam-6657	28	4	.	.	PUNCT
ejpam-6657	29	1	(	(	PUNCT
ejpam-6657	29	2	3	3	X
ejpam-6657	29	3	)	)	PUNCT
ejpam-6657	29	4	the	the	DET
ejpam-6657	29	5	ordinary	ordinary	ADJ
ejpam-6657	29	6	generating	generate	VERB
ejpam-6657	29	7	function	function	NOUN
ejpam-6657	29	8	of	of	ADP
ejpam-6657	29	9	en(µ1	en(µ1	NOUN
ejpam-6657	29	10	)	)	PUNCT
ejpam-6657	29	11	is	be	AUX
ejpam-6657	29	12	expressed	express	VERB
ejpam-6657	29	13	as	as	ADP
ejpam-6657	29	14	[	[	X
ejpam-6657	29	15	8	8	NUM
ejpam-6657	29	16	]	]	NOUN
ejpam-6657	29	17	:	:	PUNCT
ejpam-6657	29	18	∞∑	∞∑	NUM
ejpam-6657	29	19	n=0	n=0	NUM
ejpam-6657	29	20	en(ξ1)t	en(ξ1)t	NOUN
ejpam-6657	29	21	n	n	PROPN
ejpam-6657	29	22	=	=	SYM
ejpam-6657	29	23	eξ1	eξ1	PROPN
ejpam-6657	29	24	t	t	PROPN
ejpam-6657	29	25	1−	1−	NUM
ejpam-6657	29	26	t	t	PROPN
ejpam-6657	29	27	(	(	PUNCT
ejpam-6657	29	28	t	t	PROPN
ejpam-6657	29	29	∈	∈	PROPN
ejpam-6657	29	30	c	c	X
ejpam-6657	29	31	,	,	PUNCT
ejpam-6657	29	32	|t|	|t|	VERB
ejpam-6657	29	33	<	<	X
ejpam-6657	29	34	1	1	NUM
ejpam-6657	29	35	)	)	PUNCT
ejpam-6657	29	36	.	.	PUNCT
ejpam-6657	30	1	(	(	PUNCT
ejpam-6657	30	2	4	4	X
ejpam-6657	30	3	)	)	PUNCT
ejpam-6657	30	4	a	a	DET
ejpam-6657	30	5	significant	significant	ADJ
ejpam-6657	30	6	extension	extension	NOUN
ejpam-6657	30	7	of	of	ADP
ejpam-6657	30	8	the	the	DET
ejpam-6657	30	9	tep	tep	NOUN
ejpam-6657	30	10	to	to	ADP
ejpam-6657	30	11	two	two	NUM
ejpam-6657	30	12	variables	variable	NOUN
ejpam-6657	30	13	was	be	AUX
ejpam-6657	30	14	established	establish	VERB
ejpam-6657	30	15	by	by	ADP
ejpam-6657	30	16	dattoli	dattoli	NOUN
ejpam-6657	30	17	et	et	PROPN
ejpam-6657	30	18	al	al	PROPN
ejpam-6657	30	19	.	.	PUNCT
ejpam-6657	31	1	[	[	X
ejpam-6657	31	2	8	8	NUM
ejpam-6657	31	3	]	]	PUNCT
ejpam-6657	31	4	,	,	PUNCT
ejpam-6657	31	5	where	where	SCONJ
ejpam-6657	31	6	they	they	PRON
ejpam-6657	31	7	proved	prove	VERB
ejpam-6657	31	8	particularly	particularly	ADV
ejpam-6657	31	9	useful	useful	ADJ
ejpam-6657	31	10	in	in	ADP
ejpam-6657	31	11	problems	problem	NOUN
ejpam-6657	31	12	involving	involve	VERB
ejpam-6657	31	13	integrals	integral	NOUN
ejpam-6657	31	14	of	of	ADP
ejpam-6657	31	15	special	special	ADJ
ejpam-6657	31	16	functions	function	NOUN
ejpam-6657	31	17	and	and	CCONJ
ejpam-6657	31	18	physical	physical	ADJ
ejpam-6657	31	19	models	model	NOUN
ejpam-6657	31	20	.	.	PUNCT
ejpam-6657	32	1	the	the	DET
ejpam-6657	32	2	generating	generate	VERB
ejpam-6657	32	3	function	function	NOUN
ejpam-6657	32	4	for	for	ADP
ejpam-6657	32	5	the	the	DET
ejpam-6657	32	6	two	two	NUM
ejpam-6657	32	7	-	-	PUNCT
ejpam-6657	32	8	variable	variable	NOUN
ejpam-6657	32	9	version	version	NOUN
ejpam-6657	32	10	is	be	AUX
ejpam-6657	32	11	:	:	PUNCT
ejpam-6657	32	12	∞∑	∞∑	NUM
ejpam-6657	32	13	n=0	n=0	NUM
ejpam-6657	33	1	[	[	X
ejpam-6657	33	2	2]en(ξ1	2]en(ξ1	NUM
ejpam-6657	33	3	,	,	PUNCT
ejpam-6657	33	4	µ2)t	µ2)t	NOUN
ejpam-6657	33	5	n	n	PROPN
ejpam-6657	33	6	=	=	SYM
ejpam-6657	33	7	eξ1	eξ1	PROPN
ejpam-6657	33	8	t	t	NOUN
ejpam-6657	33	9	1−	1−	NUM
ejpam-6657	33	10	ξ2t2	ξ2t2	NUM
ejpam-6657	33	11	,	,	PUNCT
ejpam-6657	33	12	(	(	PUNCT
ejpam-6657	33	13	5	5	NUM
ejpam-6657	33	14	)	)	PUNCT
ejpam-6657	33	15	and	and	CCONJ
ejpam-6657	33	16	the	the	DET
ejpam-6657	33	17	corresponding	corresponding	ADJ
ejpam-6657	33	18	explicit	explicit	ADJ
ejpam-6657	33	19	representation	representation	NOUN
ejpam-6657	33	20	reads	read	VERB
ejpam-6657	33	21	:	:	PUNCT
ejpam-6657	33	22	[	[	X
ejpam-6657	33	23	2]en(ξ1	2]en(ξ1	NUM
ejpam-6657	33	24	,	,	PUNCT
ejpam-6657	33	25	ξ2	ξ2	NOUN
ejpam-6657	33	26	)	)	PUNCT
ejpam-6657	33	27	=	=	PUNCT
ejpam-6657	34	1	[	[	X
ejpam-6657	34	2	n2	n2	NOUN
ejpam-6657	34	3	]	]	X
ejpam-6657	34	4	∑	∑	PROPN
ejpam-6657	34	5	k=0	k=0	PROPN
ejpam-6657	34	6	ξk2	ξk2	X
ejpam-6657	34	7	ξn−2k	ξn−2k	NOUN
ejpam-6657	34	8	1	1	NUM
ejpam-6657	34	9	(	(	PUNCT
ejpam-6657	34	10	n−	n−	NOUN
ejpam-6657	34	11	2k	2k	NUM
ejpam-6657	34	12	)	)	PUNCT
ejpam-6657	34	13	!	!	PUNCT
ejpam-6657	34	14	.	.	PUNCT
ejpam-6657	35	1	(	(	PUNCT
ejpam-6657	35	2	6	6	X
ejpam-6657	35	3	)	)	PUNCT
ejpam-6657	35	4	h.	h.	NOUN
ejpam-6657	35	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	35	6	et	et	PROPN
ejpam-6657	35	7	al	al	PROPN
ejpam-6657	35	8	.	.	PUNCT
ejpam-6657	35	9	/	/	SYM
ejpam-6657	35	10	eur	eur	PROPN
ejpam-6657	35	11	.	.	PUNCT
ejpam-6657	36	1	j.	j.	PROPN
ejpam-6657	36	2	pure	pure	PROPN
ejpam-6657	36	3	appl	appl	PROPN
ejpam-6657	36	4	.	.	PROPN
ejpam-6657	36	5	math	math	PROPN
ejpam-6657	36	6	,	,	PUNCT
ejpam-6657	36	7	18	18	NUM
ejpam-6657	36	8	(	(	PUNCT
ejpam-6657	36	9	3	3	NUM
ejpam-6657	36	10	)	)	PUNCT
ejpam-6657	36	11	(	(	PUNCT
ejpam-6657	36	12	2025	2025	NUM
ejpam-6657	36	13	)	)	PUNCT
ejpam-6657	36	14	,	,	PUNCT
ejpam-6657	36	15	6657	6657	NUM
ejpam-6657	36	16	3	3	NUM
ejpam-6657	36	17	of	of	ADP
ejpam-6657	36	18	16	16	NUM
ejpam-6657	36	19	the	the	DET
ejpam-6657	36	20	generalized	generalized	ADJ
ejpam-6657	36	21	form	form	NOUN
ejpam-6657	36	22	involving	involve	VERB
ejpam-6657	36	23	higher	high	ADJ
ejpam-6657	36	24	-	-	PUNCT
ejpam-6657	36	25	order	order	NOUN
ejpam-6657	36	26	polynomials	polynomial	NOUN
ejpam-6657	36	27	is	be	AUX
ejpam-6657	36	28	given	give	VERB
ejpam-6657	36	29	by	by	ADP
ejpam-6657	36	30	:	:	PUNCT
ejpam-6657	36	31	∞∑	∞∑	NUM
ejpam-6657	36	32	n=0	n=0	NUM
ejpam-6657	36	33	[	[	X
ejpam-6657	36	34	s]en(ξ1	s]en(ξ1	ADJ
ejpam-6657	36	35	,	,	PUNCT
ejpam-6657	36	36	ξ2)t	ξ2)t	ADJ
ejpam-6657	36	37	n	n	NOUN
ejpam-6657	36	38	=	=	SYM
ejpam-6657	36	39	eξ1	eξ1	PROPN
ejpam-6657	36	40	t	t	PROPN
ejpam-6657	36	41	1−	1−	NUM
ejpam-6657	36	42	ξ2ts	ξ2ts	NUM
ejpam-6657	36	43	,	,	PUNCT
ejpam-6657	36	44	(	(	PUNCT
ejpam-6657	36	45	7	7	NUM
ejpam-6657	36	46	)	)	PUNCT
ejpam-6657	36	47	with	with	ADP
ejpam-6657	36	48	explicit	explicit	ADJ
ejpam-6657	36	49	form	form	NOUN
ejpam-6657	36	50	:	:	PUNCT
ejpam-6657	36	51	[	[	X
ejpam-6657	36	52	s]en(ξ1	s]en(ξ1	ADJ
ejpam-6657	36	53	,	,	PUNCT
ejpam-6657	36	54	ξ2	ξ2	NOUN
ejpam-6657	36	55	)	)	PUNCT
ejpam-6657	36	56	=	=	PUNCT
ejpam-6657	37	1	[	[	X
ejpam-6657	37	2	ns	ns	X
ejpam-6657	37	3	]	]	X
ejpam-6657	37	4	∑	∑	PROPN
ejpam-6657	37	5	k=0	k=0	PROPN
ejpam-6657	37	6	ξk2	ξk2	PROPN
ejpam-6657	37	7	ξn−sk	ξn−sk	VERB
ejpam-6657	37	8	1	1	NUM
ejpam-6657	37	9	(	(	PUNCT
ejpam-6657	37	10	n−	n−	NOUN
ejpam-6657	37	11	sk	sk	NOUN
ejpam-6657	37	12	)	)	PUNCT
ejpam-6657	37	13	!	!	PUNCT
ejpam-6657	37	14	.	.	PUNCT
ejpam-6657	38	1	(	(	PUNCT
ejpam-6657	38	2	8)	8)	NUM
ejpam-6657	38	3	it	it	PRON
ejpam-6657	38	4	is	be	AUX
ejpam-6657	38	5	easy	easy	ADJ
ejpam-6657	38	6	to	to	PART
ejpam-6657	38	7	verify	verify	VERB
ejpam-6657	38	8	from	from	ADP
ejpam-6657	38	9	expressions	expression	NOUN
ejpam-6657	38	10	(	(	PUNCT
ejpam-6657	38	11	4	4	NUM
ejpam-6657	38	12	)	)	PUNCT
ejpam-6657	38	13	,	,	PUNCT
ejpam-6657	38	14	(	(	PUNCT
ejpam-6657	38	15	5	5	NUM
ejpam-6657	38	16	)	)	PUNCT
ejpam-6657	38	17	,	,	PUNCT
ejpam-6657	38	18	and	and	CCONJ
ejpam-6657	38	19	(	(	PUNCT
ejpam-6657	38	20	7	7	X
ejpam-6657	38	21	)	)	PUNCT
ejpam-6657	39	1	that	that	PRON
ejpam-6657	39	2	:	:	PUNCT
ejpam-6657	39	3	[	[	X
ejpam-6657	39	4	2]en(ξ1	2]en(ξ1	NUM
ejpam-6657	39	5	,	,	PUNCT
ejpam-6657	39	6	ξ2	ξ2	NOUN
ejpam-6657	39	7	)	)	PUNCT
ejpam-6657	40	1	=	=	SYM
ejpam-6657	40	2	e(2)n	e(2)n	NOUN
ejpam-6657	40	3	(	(	PUNCT
ejpam-6657	40	4	ξ1	ξ1	PROPN
ejpam-6657	40	5	,	,	PUNCT
ejpam-6657	40	6	ξ2	ξ2	NOUN
ejpam-6657	40	7	)	)	PUNCT
ejpam-6657	40	8	,	,	PUNCT
ejpam-6657	40	9	en(ξ1	en(ξ1	NOUN
ejpam-6657	40	10	)	)	PUNCT
ejpam-6657	40	11	=	=	SYM
ejpam-6657	40	12	e(1)n	e(1)n	PROPN
ejpam-6657	40	13	(	(	PUNCT
ejpam-6657	40	14	ξ1	ξ1	NOUN
ejpam-6657	40	15	,	,	PUNCT
ejpam-6657	40	16	1	1	NUM
ejpam-6657	40	17	)	)	PUNCT
ejpam-6657	40	18	.	.	PUNCT
ejpam-6657	41	1	a	a	DET
ejpam-6657	41	2	direct	direct	ADJ
ejpam-6657	41	3	consequence	consequence	NOUN
ejpam-6657	41	4	of	of	ADP
ejpam-6657	41	5	this	this	DET
ejpam-6657	41	6	formalism	formalism	NOUN
ejpam-6657	41	7	links	link	NOUN
ejpam-6657	41	8	the	the	DET
ejpam-6657	41	9	chebyshev	chebyshev	NOUN
ejpam-6657	41	10	polynomials	polynomial	NOUN
ejpam-6657	41	11	of	of	ADP
ejpam-6657	41	12	the	the	DET
ejpam-6657	41	13	second	second	ADJ
ejpam-6657	41	14	kind	kind	NOUN
ejpam-6657	41	15	un(µ2	un(µ2	ADP
ejpam-6657	41	16	)	)	PUNCT
ejpam-6657	41	17	to	to	ADP
ejpam-6657	41	18	the	the	DET
ejpam-6657	41	19	tep	tep	NOUN
ejpam-6657	41	20	:	:	PUNCT
ejpam-6657	41	21	un(ξ2	un(ξ2	NUM
ejpam-6657	41	22	)	)	PUNCT
ejpam-6657	41	23	=	=	PUNCT
ejpam-6657	42	1	[	[	X
ejpam-6657	42	2	2]en(0	2]en(0	NUM
ejpam-6657	42	3	,	,	PUNCT
ejpam-6657	42	4	ξ2	ξ2	NOUN
ejpam-6657	42	5	)	)	PUNCT
ejpam-6657	42	6	,	,	PUNCT
ejpam-6657	42	7	(	(	PUNCT
ejpam-6657	42	8	9	9	X
ejpam-6657	42	9	)	)	PUNCT
ejpam-6657	42	10	whose	whose	DET
ejpam-6657	42	11	generating	generating	NOUN
ejpam-6657	42	12	function	function	NOUN
ejpam-6657	42	13	is	be	AUX
ejpam-6657	42	14	well	well	ADV
ejpam-6657	42	15	-	-	PUNCT
ejpam-6657	42	16	known	know	VERB
ejpam-6657	42	17	[	[	X
ejpam-6657	42	18	14	14	NUM
ejpam-6657	42	19	]	]	X
ejpam-6657	42	20	:	:	PUNCT
ejpam-6657	42	21	∞∑	∞∑	NUM
ejpam-6657	42	22	n=0	n=0	NUM
ejpam-6657	42	23	un(ξ1)t	un(ξ1)t	ADP
ejpam-6657	42	24	n	n	NOUN
ejpam-6657	42	25	=	=	SYM
ejpam-6657	42	26	1	1	NUM
ejpam-6657	42	27	1−	1−	NUM
ejpam-6657	42	28	2ξ1t+	2ξ1t+	NUM
ejpam-6657	42	29	t2	t2	NOUN
ejpam-6657	42	30	,	,	PUNCT
ejpam-6657	42	31	(	(	PUNCT
ejpam-6657	42	32	|t|	|t|	ADP
ejpam-6657	42	33	<	<	X
ejpam-6657	42	34	1	1	NUM
ejpam-6657	42	35	,	,	PUNCT
ejpam-6657	42	36	ξ1	ξ1	NOUN
ejpam-6657	42	37	≤	≤	NOUN
ejpam-6657	42	38	1	1	NUM
ejpam-6657	42	39	)	)	PUNCT
ejpam-6657	42	40	.	.	PUNCT
ejpam-6657	43	1	(	(	PUNCT
ejpam-6657	43	2	10	10	NUM
ejpam-6657	43	3	)	)	PUNCT
ejpam-6657	43	4	in	in	ADP
ejpam-6657	43	5	the	the	DET
ejpam-6657	43	6	operational	operational	ADJ
ejpam-6657	43	7	calculus	calculus	NOUN
ejpam-6657	43	8	framework	framework	NOUN
ejpam-6657	43	9	,	,	PUNCT
ejpam-6657	43	10	the	the	DET
ejpam-6657	43	11	multiplicative	multiplicative	ADJ
ejpam-6657	43	12	and	and	CCONJ
ejpam-6657	43	13	derivative	derivative	ADJ
ejpam-6657	43	14	operators	operator	NOUN
ejpam-6657	43	15	for	for	ADP
ejpam-6657	43	16	the	the	DET
ejpam-6657	43	17	tep	tep	NOUN
ejpam-6657	43	18	are	be	AUX
ejpam-6657	43	19	identified	identify	VERB
ejpam-6657	43	20	as	as	ADP
ejpam-6657	43	21	:	:	PUNCT
ejpam-6657	43	22	m̂e(s	m̂e(s	NUM
ejpam-6657	43	23	)	)	PUNCT
ejpam-6657	43	24	=	=	SYM
ejpam-6657	44	1	ξ1	ξ1	NOUN
ejpam-6657	44	2	+	+	CCONJ
ejpam-6657	44	3	sξ2dξ2ξ2d	sξ2dξ2ξ2d	PROPN
ejpam-6657	44	4	s−1	s−1	PROPN
ejpam-6657	44	5	ξ1	ξ1	NOUN
ejpam-6657	44	6	,	,	PUNCT
ejpam-6657	44	7	(	(	PUNCT
ejpam-6657	44	8	11	11	NUM
ejpam-6657	44	9	)	)	PUNCT
ejpam-6657	44	10	p̂e(s	p̂e(s	NUM
ejpam-6657	44	11	)	)	PUNCT
ejpam-6657	45	1	=	=	NOUN
ejpam-6657	45	2	dξ2	dξ2	NOUN
ejpam-6657	45	3	,	,	PUNCT
ejpam-6657	45	4	(	(	PUNCT
ejpam-6657	45	5	12	12	NUM
ejpam-6657	45	6	)	)	PUNCT
ejpam-6657	45	7	signifying	signify	VERB
ejpam-6657	45	8	that	that	SCONJ
ejpam-6657	45	9	[	[	X
ejpam-6657	45	10	s]en(ξ1	s]en(ξ1	ADJ
ejpam-6657	45	11	,	,	PUNCT
ejpam-6657	45	12	ξ2	ξ2	ADJ
ejpam-6657	45	13	)	)	PUNCT
ejpam-6657	45	14	form	form	VERB
ejpam-6657	45	15	a	a	DET
ejpam-6657	45	16	quasi	quasi	ADJ
ejpam-6657	45	17	-	-	ADJ
ejpam-6657	45	18	monomial	monomial	ADJ
ejpam-6657	45	19	sequence	sequence	NOUN
ejpam-6657	45	20	[	[	X
ejpam-6657	45	21	2	2	NUM
ejpam-6657	45	22	]	]	PUNCT
ejpam-6657	45	23	.	.	PUNCT
ejpam-6657	46	1	this	this	DET
ejpam-6657	46	2	formalism	formalism	NOUN
ejpam-6657	46	3	has	have	AUX
ejpam-6657	46	4	been	be	AUX
ejpam-6657	46	5	further	far	ADV
ejpam-6657	46	6	expanded	expand	VERB
ejpam-6657	46	7	by	by	ADP
ejpam-6657	46	8	composing	compose	VERB
ejpam-6657	46	9	tep	tep	NOUN
ejpam-6657	46	10	with	with	ADP
ejpam-6657	46	11	appell	appell	ADJ
ejpam-6657	46	12	-	-	PUNCT
ejpam-6657	46	13	type	type	NOUN
ejpam-6657	46	14	structures	structure	NOUN
ejpam-6657	46	15	.	.	PUNCT
ejpam-6657	47	1	khan	khan	PROPN
ejpam-6657	48	1	[	[	X
ejpam-6657	48	2	15	15	NUM
ejpam-6657	48	3	]	]	PUNCT
ejpam-6657	48	4	introduced	introduce	VERB
ejpam-6657	48	5	the	the	DET
ejpam-6657	48	6	truncated	truncate	VERB
ejpam-6657	48	7	exponential	exponential	NOUN
ejpam-6657	48	8	-	-	PUNCT
ejpam-6657	48	9	based	base	VERB
ejpam-6657	48	10	appell	appell	NOUN
ejpam-6657	48	11	polynomials	polynomial	NOUN
ejpam-6657	48	12	through	through	ADP
ejpam-6657	48	13	:	:	PUNCT
ejpam-6657	48	14	∞∑	∞∑	NUM
ejpam-6657	48	15	n=0	n=0	NUM
ejpam-6657	48	16	[	[	X
ejpam-6657	48	17	s]en(ξ1	s]en(ξ1	ADJ
ejpam-6657	48	18	,	,	PUNCT
ejpam-6657	48	19	ξ2)t	ξ2)t	ADJ
ejpam-6657	48	20	n	n	NOUN
ejpam-6657	48	21	=	=	SYM
ejpam-6657	48	22	a(t	a(t	NOUN
ejpam-6657	48	23	)	)	PUNCT
ejpam-6657	48	24	eξ1	eξ1	PROPN
ejpam-6657	48	25	t	t	PROPN
ejpam-6657	48	26	1−	1−	NUM
ejpam-6657	48	27	ξ2ts	ξ2ts	NUM
ejpam-6657	48	28	,	,	PUNCT
ejpam-6657	48	29	(	(	PUNCT
ejpam-6657	48	30	13	13	NUM
ejpam-6657	48	31	)	)	PUNCT
ejpam-6657	48	32	where	where	SCONJ
ejpam-6657	48	33	a(t	a(t	NOUN
ejpam-6657	48	34	)	)	PUNCT
ejpam-6657	48	35	denotes	denote	VERB
ejpam-6657	48	36	the	the	DET
ejpam-6657	48	37	appell	appell	ADJ
ejpam-6657	48	38	-	-	PUNCT
ejpam-6657	48	39	type	type	NOUN
ejpam-6657	48	40	generating	generating	NOUN
ejpam-6657	48	41	function	function	NOUN
ejpam-6657	48	42	.	.	PUNCT
ejpam-6657	49	1	the	the	DET
ejpam-6657	49	2	origin	origin	NOUN
ejpam-6657	49	3	of	of	ADP
ejpam-6657	49	4	the	the	DET
ejpam-6657	49	5	monomiality	monomiality	NOUN
ejpam-6657	49	6	principle	principle	NOUN
ejpam-6657	49	7	dates	date	VERB
ejpam-6657	49	8	back	back	ADV
ejpam-6657	49	9	to	to	ADP
ejpam-6657	49	10	steffenson	steffenson	NOUN
ejpam-6657	49	11	’s	’s	PART
ejpam-6657	49	12	poweroid	poweroid	ADJ
ejpam-6657	49	13	method	method	NOUN
ejpam-6657	49	14	in	in	ADP
ejpam-6657	49	15	1941	1941	NUM
ejpam-6657	49	16	[	[	X
ejpam-6657	49	17	16	16	NUM
ejpam-6657	49	18	]	]	PUNCT
ejpam-6657	49	19	,	,	PUNCT
ejpam-6657	49	20	later	later	ADV
ejpam-6657	49	21	refined	refine	VERB
ejpam-6657	49	22	by	by	ADP
ejpam-6657	49	23	dattoli	dattoli	NOUN
ejpam-6657	49	24	[	[	X
ejpam-6657	49	25	7	7	NUM
ejpam-6657	49	26	]	]	PUNCT
ejpam-6657	49	27	.	.	PUNCT
ejpam-6657	50	1	a	a	DET
ejpam-6657	50	2	polynomial	polynomial	ADJ
ejpam-6657	50	3	sequence	sequence	NOUN
ejpam-6657	50	4	{	{	PUNCT
ejpam-6657	50	5	qn(ξ1	qn(ξ1	NOUN
ejpam-6657	50	6	)	)	PUNCT
ejpam-6657	50	7	}	}	PUNCT
ejpam-6657	50	8	is	be	AUX
ejpam-6657	50	9	quasi	quasi	ADJ
ejpam-6657	50	10	-	-	ADJ
ejpam-6657	50	11	monomial	monomial	ADJ
ejpam-6657	50	12	if	if	SCONJ
ejpam-6657	50	13	:	:	PUNCT
ejpam-6657	50	14	qn+1(ξ1	qn+1(ξ1	X
ejpam-6657	50	15	)	)	PUNCT
ejpam-6657	50	16	=	=	SYM
ejpam-6657	50	17	m̂{qn(ξ1	m̂{qn(ξ1	NOUN
ejpam-6657	50	18	)	)	PUNCT
ejpam-6657	50	19	}	}	PUNCT
ejpam-6657	50	20	,	,	PUNCT
ejpam-6657	50	21	(	(	PUNCT
ejpam-6657	50	22	14	14	NUM
ejpam-6657	50	23	)	)	PUNCT
ejpam-6657	50	24	n	n	PRON
ejpam-6657	50	25	qn−1(ξ1	qn−1(ξ1	NOUN
ejpam-6657	50	26	)	)	PUNCT
ejpam-6657	50	27	=	=	SYM
ejpam-6657	50	28	p̂{qn(ξ1	p̂{qn(ξ1	NOUN
ejpam-6657	50	29	)	)	PUNCT
ejpam-6657	50	30	}	}	PUNCT
ejpam-6657	50	31	,	,	PUNCT
ejpam-6657	50	32	(	(	PUNCT
ejpam-6657	50	33	15	15	NUM
ejpam-6657	50	34	)	)	PUNCT
ejpam-6657	50	35	and	and	CCONJ
ejpam-6657	50	36	the	the	DET
ejpam-6657	50	37	operators	operator	NOUN
ejpam-6657	50	38	satisfy	satisfy	VERB
ejpam-6657	50	39	the	the	DET
ejpam-6657	50	40	weyl	weyl	VERB
ejpam-6657	50	41	algebra	algebra	NOUN
ejpam-6657	50	42	:	:	PUNCT
ejpam-6657	50	43	[	[	X
ejpam-6657	50	44	p̂,m̂	p̂,m̂	X
ejpam-6657	50	45	]	]	X
ejpam-6657	50	46	=	=	SYM
ejpam-6657	51	1	1̂.	1̂.	NUM
ejpam-6657	51	2	(	(	PUNCT
ejpam-6657	51	3	16	16	NUM
ejpam-6657	51	4	)	)	PUNCT
ejpam-6657	51	5	h.	h.	PROPN
ejpam-6657	51	6	qawaqneh	qawaqneh	PROPN
ejpam-6657	52	1	et	et	PROPN
ejpam-6657	52	2	al	al	PROPN
ejpam-6657	52	3	.	.	PUNCT
ejpam-6657	52	4	/	/	SYM
ejpam-6657	52	5	eur	eur	PROPN
ejpam-6657	52	6	.	.	PUNCT
ejpam-6657	53	1	j.	j.	PROPN
ejpam-6657	53	2	pure	pure	PROPN
ejpam-6657	53	3	appl	appl	PROPN
ejpam-6657	53	4	.	.	PROPN
ejpam-6657	53	5	math	math	PROPN
ejpam-6657	53	6	,	,	PUNCT
ejpam-6657	53	7	18	18	NUM
ejpam-6657	53	8	(	(	PUNCT
ejpam-6657	53	9	3	3	NUM
ejpam-6657	53	10	)	)	PUNCT
ejpam-6657	53	11	(	(	PUNCT
ejpam-6657	53	12	2025	2025	NUM
ejpam-6657	53	13	)	)	PUNCT
ejpam-6657	53	14	,	,	PUNCT
ejpam-6657	53	15	6657	6657	NUM
ejpam-6657	53	16	4	4	NUM
ejpam-6657	53	17	of	of	ADP
ejpam-6657	53	18	16	16	NUM
ejpam-6657	53	19	the	the	DET
ejpam-6657	53	20	quasi	quasi	ADJ
ejpam-6657	53	21	-	-	ADJ
ejpam-6657	53	22	monomial	monomial	ADJ
ejpam-6657	53	23	property	property	NOUN
ejpam-6657	53	24	yields	yield	NOUN
ejpam-6657	53	25	key	key	ADJ
ejpam-6657	53	26	operational	operational	ADJ
ejpam-6657	53	27	identities	identity	NOUN
ejpam-6657	53	28	:	:	PUNCT
ejpam-6657	53	29	m̂p̂{qn(ξ1	m̂p̂{qn(ξ1	NUM
ejpam-6657	53	30	)	)	PUNCT
ejpam-6657	53	31	}	}	PUNCT
ejpam-6657	53	32	=	=	SYM
ejpam-6657	53	33	n	n	PRON
ejpam-6657	53	34	qn(ξ1	qn(ξ1	NOUN
ejpam-6657	53	35	)	)	PUNCT
ejpam-6657	53	36	,	,	PUNCT
ejpam-6657	53	37	(	(	PUNCT
ejpam-6657	53	38	17	17	NUM
ejpam-6657	53	39	)	)	PUNCT
ejpam-6657	53	40	qn(ξ1	qn(ξ1	NOUN
ejpam-6657	53	41	)	)	PUNCT
ejpam-6657	53	42	=	=	SYM
ejpam-6657	53	43	m̂n{1	m̂n{1	PROPN
ejpam-6657	53	44	}	}	PUNCT
ejpam-6657	53	45	,	,	PUNCT
ejpam-6657	53	46	(	(	PUNCT
ejpam-6657	53	47	18	18	NUM
ejpam-6657	53	48	)	)	PUNCT
ejpam-6657	53	49	etm̂{1	etm̂{1	NOUN
ejpam-6657	53	50	}	}	PUNCT
ejpam-6657	53	51	=	=	SYM
ejpam-6657	54	1	∞∑	∞∑	NUM
ejpam-6657	54	2	n=0	n=0	NUM
ejpam-6657	54	3	qn(ξ1	qn(ξ1	NOUN
ejpam-6657	54	4	)	)	PUNCT
ejpam-6657	54	5	tn	tn	NOUN
ejpam-6657	54	6	n	n	NUM
ejpam-6657	54	7	!	!	PROPN
ejpam-6657	54	8	,	,	PUNCT
ejpam-6657	54	9	(	(	PUNCT
ejpam-6657	54	10	19	19	NUM
ejpam-6657	54	11	)	)	PUNCT
ejpam-6657	54	12	as	as	SCONJ
ejpam-6657	54	13	outlined	outline	VERB
ejpam-6657	54	14	in	in	ADP
ejpam-6657	54	15	[	[	X
ejpam-6657	54	16	2	2	NUM
ejpam-6657	54	17	,	,	PUNCT
ejpam-6657	54	18	7	7	NUM
ejpam-6657	54	19	,	,	PUNCT
ejpam-6657	54	20	8	8	NUM
ejpam-6657	54	21	,	,	PUNCT
ejpam-6657	54	22	17–19	17–19	NUM
ejpam-6657	54	23	]	]	PUNCT
ejpam-6657	54	24	.	.	PUNCT
ejpam-6657	55	1	in	in	ADP
ejpam-6657	55	2	recent	recent	ADJ
ejpam-6657	55	3	years	year	NOUN
ejpam-6657	55	4	,	,	PUNCT
ejpam-6657	55	5	the	the	DET
ejpam-6657	55	6	introduction	introduction	NOUN
ejpam-6657	55	7	of	of	ADP
ejpam-6657	55	8	∆h	∆h	NOUN
ejpam-6657	55	9	-	-	PUNCT
ejpam-6657	55	10	type	type	NOUN
ejpam-6657	55	11	generalizations	generalization	NOUN
ejpam-6657	55	12	has	have	AUX
ejpam-6657	55	13	expanded	expand	VERB
ejpam-6657	55	14	the	the	DET
ejpam-6657	55	15	horizon	horizon	NOUN
ejpam-6657	55	16	of	of	ADP
ejpam-6657	55	17	special	special	ADJ
ejpam-6657	55	18	polynomial	polynomial	ADJ
ejpam-6657	55	19	theory	theory	NOUN
ejpam-6657	55	20	.	.	PUNCT
ejpam-6657	56	1	these	these	DET
ejpam-6657	56	2	constructions	construction	NOUN
ejpam-6657	56	3	utilize	utilize	VERB
ejpam-6657	56	4	the	the	DET
ejpam-6657	56	5	forward	forward	ADJ
ejpam-6657	56	6	difference	difference	NOUN
ejpam-6657	56	7	operator	operator	NOUN
ejpam-6657	56	8	:	:	PUNCT
ejpam-6657	56	9	∆h[g](ξ1	∆h[g](ξ1	X
ejpam-6657	56	10	)	)	PUNCT
ejpam-6657	56	11	=	=	SYM
ejpam-6657	56	12	g(ξ1	g(ξ1	NOUN
ejpam-6657	56	13	+	+	CCONJ
ejpam-6657	56	14	h)−	h)−	PROPN
ejpam-6657	56	15	g(ξ1	g(ξ1	NOUN
ejpam-6657	56	16	)	)	PUNCT
ejpam-6657	56	17	,	,	PUNCT
ejpam-6657	56	18	(	(	PUNCT
ejpam-6657	56	19	20	20	NUM
ejpam-6657	56	20	)	)	PUNCT
ejpam-6657	56	21	and	and	CCONJ
ejpam-6657	56	22	its	its	PRON
ejpam-6657	56	23	higher	high	ADJ
ejpam-6657	56	24	-	-	PUNCT
ejpam-6657	56	25	order	order	NOUN
ejpam-6657	56	26	form	form	NOUN
ejpam-6657	56	27	:	:	PUNCT
ejpam-6657	56	28	∆i	∆i	PROPN
ejpam-6657	56	29	h[g](ξ1	h[g](ξ1	PROPN
ejpam-6657	56	30	)	)	PUNCT
ejpam-6657	56	31	=	=	NOUN
ejpam-6657	57	1	i∑	i∑	PROPN
ejpam-6657	57	2	l=0	l=0	PROPN
ejpam-6657	57	3	(	(	PUNCT
ejpam-6657	57	4	−1)i−l	−1)i−l	PROPN
ejpam-6657	57	5	(	(	PUNCT
ejpam-6657	57	6	i	i	NOUN
ejpam-6657	57	7	l	l	NOUN
ejpam-6657	57	8	)	)	PUNCT
ejpam-6657	57	9	g(ξ1	g(ξ1	NOUN
ejpam-6657	57	10	+	+	CCONJ
ejpam-6657	57	11	lh	lh	PROPN
ejpam-6657	57	12	)	)	PUNCT
ejpam-6657	57	13	,	,	PUNCT
ejpam-6657	57	14	(	(	PUNCT
ejpam-6657	57	15	21	21	NUM
ejpam-6657	57	16	)	)	PUNCT
ejpam-6657	57	17	where	where	SCONJ
ejpam-6657	57	18	∆0	∆0	PRON
ejpam-6657	57	19	h	h	NOUN
ejpam-6657	58	1	=	=	PUNCT
ejpam-6657	58	2	i	i	PROPN
ejpam-6657	58	3	(	(	PUNCT
ejpam-6657	58	4	identity	identity	NOUN
ejpam-6657	58	5	)	)	PUNCT
ejpam-6657	58	6	,	,	PUNCT
ejpam-6657	58	7	∆1	∆1	NOUN
ejpam-6657	58	8	h	h	NOUN
ejpam-6657	58	9	=	=	SYM
ejpam-6657	58	10	∆h	∆h	PROPN
ejpam-6657	58	11	.	.	PUNCT
ejpam-6657	59	1	the	the	DET
ejpam-6657	59	2	∆h	∆h	NUM
ejpam-6657	59	3	-	-	PUNCT
ejpam-6657	59	4	appell	appell	NOUN
ejpam-6657	59	5	polynomials	polynomial	NOUN
ejpam-6657	59	6	a[h	a[h	X
ejpam-6657	59	7	]	]	PUNCT
ejpam-6657	59	8	n	n	CCONJ
ejpam-6657	59	9	(	(	PUNCT
ejpam-6657	59	10	ξ1	ξ1	PROPN
ejpam-6657	59	11	)	)	PUNCT
ejpam-6657	59	12	are	be	AUX
ejpam-6657	59	13	introduced	introduce	VERB
ejpam-6657	59	14	via	via	ADP
ejpam-6657	59	15	the	the	DET
ejpam-6657	59	16	generating	generate	VERB
ejpam-6657	59	17	function	function	NOUN
ejpam-6657	60	1	[	[	X
ejpam-6657	60	2	20	20	NUM
ejpam-6657	60	3	]	]	SYM
ejpam-6657	60	4	:	:	PUNCT
ejpam-6657	60	5	a(h	a(h	PROPN
ejpam-6657	60	6	;	;	PUNCT
ejpam-6657	60	7	t)(1	t)(1	X
ejpam-6657	60	8	+	+	CCONJ
ejpam-6657	60	9	ht	ht	X
ejpam-6657	60	10	)	)	PUNCT
ejpam-6657	60	11	ξ1	ξ1	NOUN
ejpam-6657	60	12	h	h	NOUN
ejpam-6657	60	13	=	=	PUNCT
ejpam-6657	60	14	∞∑	∞∑	DET
ejpam-6657	60	15	n=0	n=0	ADV
ejpam-6657	60	16	a[h	a[h	ADJ
ejpam-6657	60	17	]	]	PUNCT
ejpam-6657	60	18	n	n	CCONJ
ejpam-6657	60	19	(	(	PUNCT
ejpam-6657	60	20	ξ1	ξ1	PROPN
ejpam-6657	60	21	)	)	PUNCT
ejpam-6657	60	22	tn	tn	PROPN
ejpam-6657	60	23	n	n	PROPN
ejpam-6657	60	24	!	!	PROPN
ejpam-6657	60	25	,	,	PUNCT
ejpam-6657	60	26	(	(	PUNCT
ejpam-6657	60	27	22	22	NUM
ejpam-6657	60	28	)	)	PUNCT
ejpam-6657	60	29	with	with	ADP
ejpam-6657	60	30	the	the	DET
ejpam-6657	60	31	condition	condition	NOUN
ejpam-6657	60	32	:	:	PUNCT
ejpam-6657	61	1	a(h	a(h	PROPN
ejpam-6657	61	2	;	;	PUNCT
ejpam-6657	61	3	t	t	PROPN
ejpam-6657	61	4	)	)	PUNCT
ejpam-6657	61	5	=	=	PUNCT
ejpam-6657	62	1	∞∑	∞∑	ADJ
ejpam-6657	62	2	n=0	n=0	PROPN
ejpam-6657	62	3	an	an	X
ejpam-6657	62	4	,	,	PUNCT
ejpam-6657	62	5	h	h	PROPN
ejpam-6657	62	6	tn	tn	PROPN
ejpam-6657	62	7	n	n	PROPN
ejpam-6657	62	8	!	!	PROPN
ejpam-6657	62	9	,	,	PUNCT
ejpam-6657	62	10	a0,h	a0,h	PROPN
ejpam-6657	62	11	̸=	̸=	PROPN
ejpam-6657	62	12	0	0	NUM
ejpam-6657	62	13	.	.	PUNCT
ejpam-6657	63	1	(	(	PUNCT
ejpam-6657	63	2	23	23	NUM
ejpam-6657	63	3	)	)	PUNCT
ejpam-6657	63	4	the	the	DET
ejpam-6657	63	5	stirling	stirling	NOUN
ejpam-6657	63	6	numbers	number	NOUN
ejpam-6657	63	7	of	of	ADP
ejpam-6657	63	8	the	the	DET
ejpam-6657	63	9	first	first	ADJ
ejpam-6657	63	10	kind	kind	NOUN
ejpam-6657	63	11	,	,	PUNCT
ejpam-6657	63	12	s1(n	s1(n	PROPN
ejpam-6657	63	13	,	,	PUNCT
ejpam-6657	63	14	m	m	NOUN
ejpam-6657	63	15	)	)	PUNCT
ejpam-6657	63	16	,	,	PUNCT
ejpam-6657	63	17	are	be	AUX
ejpam-6657	63	18	crucial	crucial	ADJ
ejpam-6657	63	19	in	in	ADP
ejpam-6657	63	20	expressing	express	VERB
ejpam-6657	63	21	rising	rise	VERB
ejpam-6657	63	22	factorials	factorial	NOUN
ejpam-6657	63	23	,	,	PUNCT
ejpam-6657	63	24	as	as	SCONJ
ejpam-6657	63	25	given	give	VERB
ejpam-6657	63	26	by	by	ADP
ejpam-6657	63	27	the	the	DET
ejpam-6657	63	28	relation	relation	NOUN
ejpam-6657	63	29	:	:	PUNCT
ejpam-6657	63	30	(	(	PUNCT
ejpam-6657	63	31	ξ1)n	ξ1)n	NOUN
ejpam-6657	63	32	=	=	SYM
ejpam-6657	63	33	n∑	n∑	NOUN
ejpam-6657	63	34	m=0	m=0	PROPN
ejpam-6657	63	35	s1(n	s1(n	PROPN
ejpam-6657	63	36	,	,	PUNCT
ejpam-6657	63	37	m)µm	m)µm	PROPN
ejpam-6657	63	38	1	1	NUM
ejpam-6657	63	39	,	,	PUNCT
ejpam-6657	63	40	(	(	PUNCT
ejpam-6657	63	41	24	24	NUM
ejpam-6657	63	42	)	)	PUNCT
ejpam-6657	63	43	where	where	SCONJ
ejpam-6657	63	44	(	(	PUNCT
ejpam-6657	63	45	ξ1)0	ξ1)0	NOUN
ejpam-6657	63	46	=	=	SYM
ejpam-6657	63	47	1	1	NUM
ejpam-6657	63	48	and	and	CCONJ
ejpam-6657	63	49	(	(	PUNCT
ejpam-6657	63	50	ξ1)n	ξ1)n	NOUN
ejpam-6657	63	51	=	=	SYM
ejpam-6657	63	52	ξ(ξ1	ξ(ξ1	NOUN
ejpam-6657	63	53	−	−	NOUN
ejpam-6657	63	54	1	1	NUM
ejpam-6657	63	55	)	)	PUNCT
ejpam-6657	63	56	·	·	PUNCT
ejpam-6657	63	57	·	·	PUNCT
ejpam-6657	63	58	·	·	PUNCT
ejpam-6657	63	59	(	(	PUNCT
ejpam-6657	63	60	ξ1	ξ1	NOUN
ejpam-6657	63	61	−	−	PROPN
ejpam-6657	63	62	n+	n+	NOUN
ejpam-6657	63	63	1	1	NUM
ejpam-6657	63	64	)	)	PUNCT
ejpam-6657	63	65	.	.	PUNCT
ejpam-6657	64	1	the	the	DET
ejpam-6657	64	2	stirling	stirling	NOUN
ejpam-6657	64	3	numbers	number	NOUN
ejpam-6657	64	4	s1(n	s1(n	PROPN
ejpam-6657	64	5	,	,	PUNCT
ejpam-6657	64	6	m	m	NOUN
ejpam-6657	64	7	)	)	PUNCT
ejpam-6657	64	8	can	can	AUX
ejpam-6657	64	9	be	be	AUX
ejpam-6657	64	10	represented	represent	VERB
ejpam-6657	64	11	by	by	ADP
ejpam-6657	64	12	the	the	DET
ejpam-6657	64	13	following	follow	VERB
ejpam-6657	64	14	generating	generate	VERB
ejpam-6657	64	15	function	function	NOUN
ejpam-6657	65	1	[	[	X
ejpam-6657	65	2	21–23	21–23	NUM
ejpam-6657	65	3	]	]	X
ejpam-6657	65	4	:	:	PUNCT
ejpam-6657	65	5	1	1	NUM
ejpam-6657	65	6	m	m	NOUN
ejpam-6657	65	7	!	!	PUNCT
ejpam-6657	66	1	(	(	PUNCT
ejpam-6657	66	2	log(1	log(1	NOUN
ejpam-6657	66	3	+	+	CCONJ
ejpam-6657	66	4	t))m	t))m	NOUN
ejpam-6657	66	5	=	=	PUNCT
ejpam-6657	67	1	∞∑	∞∑	NUM
ejpam-6657	67	2	n	n	CCONJ
ejpam-6657	67	3	=	=	NOUN
ejpam-6657	67	4	m	m	NOUN
ejpam-6657	67	5	s1(n	s1(n	PROPN
ejpam-6657	67	6	,	,	PUNCT
ejpam-6657	67	7	m	m	NOUN
ejpam-6657	67	8	)	)	PUNCT
ejpam-6657	67	9	tn	tn	PROPN
ejpam-6657	67	10	n	n	PROPN
ejpam-6657	67	11	!	!	PROPN
ejpam-6657	67	12	,	,	PUNCT
ejpam-6657	67	13	(	(	PUNCT
ejpam-6657	67	14	m	m	NOUN
ejpam-6657	67	15	≥	≥	NOUN
ejpam-6657	67	16	0	0	NUM
ejpam-6657	67	17	)	)	PUNCT
ejpam-6657	67	18	.	.	PUNCT
ejpam-6657	68	1	(	(	PUNCT
ejpam-6657	68	2	25	25	NUM
ejpam-6657	68	3	)	)	PUNCT
ejpam-6657	68	4	for	for	ADP
ejpam-6657	68	5	n	n	PRON
ejpam-6657	68	6	≥	≥	NOUN
ejpam-6657	68	7	0	0	NUM
ejpam-6657	68	8	,	,	PUNCT
ejpam-6657	68	9	the	the	DET
ejpam-6657	68	10	∆h	∆h	PROPN
ejpam-6657	68	11	stirling	stirling	NOUN
ejpam-6657	68	12	numbers	number	NOUN
ejpam-6657	68	13	of	of	ADP
ejpam-6657	68	14	the	the	DET
ejpam-6657	68	15	first	first	ADJ
ejpam-6657	68	16	kind	kind	NOUN
ejpam-6657	68	17	are	be	AUX
ejpam-6657	68	18	defined	define	VERB
ejpam-6657	68	19	by	by	ADP
ejpam-6657	68	20	:	:	PUNCT
ejpam-6657	68	21	1	1	NUM
ejpam-6657	68	22	k	k	NOUN
ejpam-6657	68	23	!	!	PUNCT
ejpam-6657	69	1	(	(	PUNCT
ejpam-6657	69	2	logh(1	logh(1	NOUN
ejpam-6657	69	3	+	+	NUM
ejpam-6657	69	4	t))k	t))k	NOUN
ejpam-6657	69	5	=	=	SYM
ejpam-6657	69	6	∞∑	∞∑	NUM
ejpam-6657	69	7	n	n	CCONJ
ejpam-6657	69	8	=	=	PROPN
ejpam-6657	69	9	k	k	PROPN
ejpam-6657	69	10	s1,h(n	s1,h(n	PROPN
ejpam-6657	69	11	,	,	PUNCT
ejpam-6657	69	12	k	k	NOUN
ejpam-6657	69	13	)	)	PUNCT
ejpam-6657	69	14	tn	tn	PROPN
ejpam-6657	69	15	n	n	PROPN
ejpam-6657	69	16	!	!	PROPN
ejpam-6657	69	17	,	,	PUNCT
ejpam-6657	69	18	(	(	PUNCT
ejpam-6657	69	19	k	k	X
ejpam-6657	69	20	≥	≥	PROPN
ejpam-6657	69	21	0	0	NUM
ejpam-6657	69	22	)	)	PUNCT
ejpam-6657	69	23	.	.	PUNCT
ejpam-6657	70	1	(	(	PUNCT
ejpam-6657	70	2	26	26	NUM
ejpam-6657	70	3	)	)	PUNCT
ejpam-6657	70	4	h.	h.	PROPN
ejpam-6657	70	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	70	6	et	et	PROPN
ejpam-6657	70	7	al	al	PROPN
ejpam-6657	70	8	.	.	PUNCT
ejpam-6657	70	9	/	/	SYM
ejpam-6657	70	10	eur	eur	PROPN
ejpam-6657	70	11	.	.	PUNCT
ejpam-6657	71	1	j.	j.	PROPN
ejpam-6657	71	2	pure	pure	PROPN
ejpam-6657	71	3	appl	appl	PROPN
ejpam-6657	71	4	.	.	PROPN
ejpam-6657	71	5	math	math	PROPN
ejpam-6657	71	6	,	,	PUNCT
ejpam-6657	71	7	18	18	NUM
ejpam-6657	71	8	(	(	PUNCT
ejpam-6657	71	9	3	3	NUM
ejpam-6657	71	10	)	)	PUNCT
ejpam-6657	71	11	(	(	PUNCT
ejpam-6657	71	12	2025	2025	NUM
ejpam-6657	71	13	)	)	PUNCT
ejpam-6657	71	14	,	,	PUNCT
ejpam-6657	71	15	6657	6657	NUM
ejpam-6657	71	16	5	5	NUM
ejpam-6657	71	17	of	of	ADP
ejpam-6657	71	18	16	16	NUM
ejpam-6657	71	19	it	it	PRON
ejpam-6657	71	20	is	be	AUX
ejpam-6657	71	21	important	important	ADJ
ejpam-6657	71	22	to	to	PART
ejpam-6657	71	23	note	note	VERB
ejpam-6657	71	24	that	that	SCONJ
ejpam-6657	71	25	limh→0	limh→0	PROPN
ejpam-6657	71	26	s1,h(n	s1,h(n	NOUN
ejpam-6657	71	27	,	,	PUNCT
ejpam-6657	71	28	k	k	NOUN
ejpam-6657	71	29	)	)	PUNCT
ejpam-6657	71	30	=	=	SYM
ejpam-6657	71	31	s1(n	s1(n	PROPN
ejpam-6657	71	32	,	,	PUNCT
ejpam-6657	71	33	k	k	NOUN
ejpam-6657	71	34	)	)	PUNCT
ejpam-6657	71	35	.	.	PUNCT
ejpam-6657	72	1	the	the	DET
ejpam-6657	72	2	degenerate	degenerate	ADJ
ejpam-6657	72	3	hermite	hermite	ADJ
ejpam-6657	72	4	polynomials	polynomial	NOUN
ejpam-6657	72	5	are	be	AUX
ejpam-6657	72	6	defined	define	VERB
ejpam-6657	72	7	by	by	ADP
ejpam-6657	72	8	[	[	X
ejpam-6657	72	9	24	24	NUM
ejpam-6657	72	10	]	]	PUNCT
ejpam-6657	72	11	(	(	PUNCT
ejpam-6657	72	12	1	1	NUM
ejpam-6657	72	13	+	+	NUM
ejpam-6657	72	14	ht	ht	NOUN
ejpam-6657	72	15	)	)	PUNCT
ejpam-6657	72	16	ξ1	ξ1	PROPN
ejpam-6657	72	17	h	h	NOUN
ejpam-6657	72	18	(	(	PUNCT
ejpam-6657	72	19	1	1	NUM
ejpam-6657	72	20	+	+	NUM
ejpam-6657	72	21	ht2	ht2	NOUN
ejpam-6657	72	22	)	)	PUNCT
ejpam-6657	72	23	ξ2	ξ2	NOUN
ejpam-6657	72	24	h	h	NOUN
ejpam-6657	72	25	=	=	PUNCT
ejpam-6657	72	26	∞∑	∞∑	ADJ
ejpam-6657	72	27	n=0	n=0	NUM
ejpam-6657	72	28	h[h	h[h	NOUN
ejpam-6657	72	29	]	]	X
ejpam-6657	72	30	n	n	CCONJ
ejpam-6657	72	31	(	(	PUNCT
ejpam-6657	72	32	ξ1	ξ1	NOUN
ejpam-6657	72	33	,	,	PUNCT
ejpam-6657	72	34	ξ2	ξ2	NOUN
ejpam-6657	72	35	)	)	PUNCT
ejpam-6657	72	36	tn	tn	PROPN
ejpam-6657	72	37	n	n	PROPN
ejpam-6657	72	38	!	!	PUNCT
ejpam-6657	72	39	.	.	PUNCT
ejpam-6657	73	1	(	(	PUNCT
ejpam-6657	73	2	27	27	NUM
ejpam-6657	73	3	)	)	PUNCT
ejpam-6657	73	4	note	note	NOUN
ejpam-6657	73	5	that	that	SCONJ
ejpam-6657	73	6	lim	lim	PROPN
ejpam-6657	73	7	h→0	h→0	ADV
ejpam-6657	73	8	h[h	h[h	X
ejpam-6657	73	9	]	]	X
ejpam-6657	73	10	n	n	CCONJ
ejpam-6657	73	11	(	(	PUNCT
ejpam-6657	73	12	ξ1	ξ1	NOUN
ejpam-6657	73	13	,	,	PUNCT
ejpam-6657	73	14	ξ2	ξ2	NOUN
ejpam-6657	73	15	)	)	PUNCT
ejpam-6657	73	16	=	=	SYM
ejpam-6657	73	17	hn(ξ1	hn(ξ1	ADJ
ejpam-6657	73	18	,	,	PUNCT
ejpam-6657	73	19	ξ2	ξ2	NOUN
ejpam-6657	73	20	)	)	PUNCT
ejpam-6657	73	21	,	,	PUNCT
ejpam-6657	73	22	where	where	SCONJ
ejpam-6657	73	23	hn(ξ1	hn(ξ1	NOUN
ejpam-6657	73	24	,	,	PUNCT
ejpam-6657	73	25	ξ2	ξ2	NOUN
ejpam-6657	73	26	)	)	PUNCT
ejpam-6657	73	27	is	be	AUX
ejpam-6657	73	28	called	call	VERB
ejpam-6657	73	29	the	the	DET
ejpam-6657	73	30	2	2	NUM
ejpam-6657	73	31	-	-	PUNCT
ejpam-6657	73	32	variable	variable	ADJ
ejpam-6657	73	33	hermite	hermite	ADJ
ejpam-6657	73	34	polynomials	polynomial	NOUN
ejpam-6657	73	35	(	(	PUNCT
ejpam-6657	73	36	see	see	VERB
ejpam-6657	73	37	[	[	X
ejpam-6657	73	38	7	7	NUM
ejpam-6657	73	39	]	]	NUM
ejpam-6657	73	40	)	)	PUNCT
ejpam-6657	73	41	.	.	PUNCT
ejpam-6657	74	1	a	a	DET
ejpam-6657	74	2	generalized	generalized	ADJ
ejpam-6657	74	3	falling	fall	VERB
ejpam-6657	74	4	factorial	factorial	NOUN
ejpam-6657	74	5	sum	sum	NOUN
ejpam-6657	74	6	σk(n;h	σk(n;h	PROPN
ejpam-6657	74	7	)	)	PUNCT
ejpam-6657	74	8	can	can	AUX
ejpam-6657	74	9	be	be	AUX
ejpam-6657	74	10	defined	define	VERB
ejpam-6657	74	11	by	by	ADP
ejpam-6657	74	12	the	the	DET
ejpam-6657	74	13	generating	generate	VERB
ejpam-6657	74	14	function	function	NOUN
ejpam-6657	74	15	[	[	X
ejpam-6657	74	16	24–26	24–26	NUM
ejpam-6657	74	17	]	]	X
ejpam-6657	74	18	:	:	PUNCT
ejpam-6657	74	19	(	(	PUNCT
ejpam-6657	74	20	1	1	X
ejpam-6657	74	21	+	+	NUM
ejpam-6657	74	22	ht	ht	PROPN
ejpam-6657	74	23	)	)	PUNCT
ejpam-6657	74	24	(	(	PUNCT
ejpam-6657	74	25	n+1	n+1	NOUN
ejpam-6657	74	26	)	)	PUNCT
ejpam-6657	74	27	h	h	NOUN
ejpam-6657	74	28	−	−	NOUN
ejpam-6657	74	29	1	1	NUM
ejpam-6657	74	30	(	(	PUNCT
ejpam-6657	74	31	1	1	NUM
ejpam-6657	74	32	+	+	NUM
ejpam-6657	74	33	ht	ht	X
ejpam-6657	74	34	)	)	PUNCT
ejpam-6657	74	35	1	1	NUM
ejpam-6657	74	36	h	h	NOUN
ejpam-6657	74	37	−	−	NOUN
ejpam-6657	74	38	1	1	NUM
ejpam-6657	74	39	=	=	SYM
ejpam-6657	74	40	∞∑	∞∑	PRON
ejpam-6657	74	41	k=0	k=0	PROPN
ejpam-6657	74	42	σk(n;h	σk(n;h	PROPN
ejpam-6657	74	43	)	)	PUNCT
ejpam-6657	74	44	tk	tk	PROPN
ejpam-6657	75	1	k	k	PROPN
ejpam-6657	75	2	!	!	PUNCT
ejpam-6657	75	3	.	.	PUNCT
ejpam-6657	76	1	(	(	PUNCT
ejpam-6657	76	2	28	28	NUM
ejpam-6657	76	3	)	)	PUNCT
ejpam-6657	76	4	note	note	NOUN
ejpam-6657	76	5	that	that	SCONJ
ejpam-6657	76	6	limh→0	limh→0	PROPN
ejpam-6657	76	7	σk(n;h	σk(n;h	PROPN
ejpam-6657	76	8	)	)	PUNCT
ejpam-6657	76	9	=	=	SYM
ejpam-6657	76	10	sk(n	sk(n	X
ejpam-6657	76	11	)	)	PUNCT
ejpam-6657	76	12	.	.	PUNCT
ejpam-6657	77	1	this	this	DET
ejpam-6657	77	2	article	article	NOUN
ejpam-6657	77	3	is	be	AUX
ejpam-6657	77	4	organized	organize	VERB
ejpam-6657	77	5	as	as	SCONJ
ejpam-6657	77	6	follows	follow	VERB
ejpam-6657	77	7	.	.	PUNCT
ejpam-6657	78	1	in	in	ADP
ejpam-6657	78	2	section	section	NOUN
ejpam-6657	78	3	2	2	NUM
ejpam-6657	78	4	,	,	PUNCT
ejpam-6657	78	5	we	we	PRON
ejpam-6657	78	6	introduce	introduce	VERB
ejpam-6657	78	7	the	the	DET
ejpam-6657	78	8	novel	novel	ADJ
ejpam-6657	78	9	class	class	NOUN
ejpam-6657	78	10	of	of	ADP
ejpam-6657	78	11	∆htruncated	∆htruncate	VERB
ejpam-6657	78	12	exponential	exponential	NOUN
ejpam-6657	78	13	-	-	PUNCT
ejpam-6657	78	14	based	base	VERB
ejpam-6657	78	15	hermite	hermite	ADJ
ejpam-6657	78	16	polynomials	polynomial	NOUN
ejpam-6657	78	17	and	and	CCONJ
ejpam-6657	78	18	derive	derive	VERB
ejpam-6657	78	19	their	their	PRON
ejpam-6657	78	20	generating	generating	NOUN
ejpam-6657	78	21	functions	function	NOUN
ejpam-6657	78	22	,	,	PUNCT
ejpam-6657	78	23	recurrence	recurrence	NOUN
ejpam-6657	78	24	relations	relation	NOUN
ejpam-6657	78	25	,	,	PUNCT
ejpam-6657	78	26	and	and	CCONJ
ejpam-6657	78	27	explicit	explicit	ADJ
ejpam-6657	78	28	formulas	formula	NOUN
ejpam-6657	78	29	.	.	PUNCT
ejpam-6657	79	1	section	section	NOUN
ejpam-6657	79	2	3	3	NUM
ejpam-6657	79	3	is	be	AUX
ejpam-6657	79	4	devoted	devote	VERB
ejpam-6657	79	5	to	to	ADP
ejpam-6657	79	6	the	the	DET
ejpam-6657	79	7	derivation	derivation	NOUN
ejpam-6657	79	8	of	of	ADP
ejpam-6657	79	9	summation	summation	NOUN
ejpam-6657	79	10	identities	identity	NOUN
ejpam-6657	79	11	related	relate	VERB
ejpam-6657	79	12	to	to	ADP
ejpam-6657	79	13	these	these	DET
ejpam-6657	79	14	polynomials	polynomial	NOUN
ejpam-6657	79	15	.	.	PUNCT
ejpam-6657	80	1	in	in	ADP
ejpam-6657	80	2	section	section	NOUN
ejpam-6657	80	3	4	4	NUM
ejpam-6657	80	4	,	,	PUNCT
ejpam-6657	80	5	we	we	PRON
ejpam-6657	80	6	explore	explore	VERB
ejpam-6657	80	7	their	their	PRON
ejpam-6657	80	8	connection	connection	NOUN
ejpam-6657	80	9	with	with	ADP
ejpam-6657	80	10	the	the	DET
ejpam-6657	80	11	monomiality	monomiality	NOUN
ejpam-6657	80	12	principle	principle	NOUN
ejpam-6657	80	13	and	and	CCONJ
ejpam-6657	80	14	develop	develop	VERB
ejpam-6657	80	15	an	an	DET
ejpam-6657	80	16	operational	operational	ADJ
ejpam-6657	80	17	formalism	formalism	NOUN
ejpam-6657	80	18	that	that	PRON
ejpam-6657	80	19	highlights	highlight	VERB
ejpam-6657	80	20	their	their	PRON
ejpam-6657	80	21	algebraic	algebraic	ADJ
ejpam-6657	80	22	structure	structure	NOUN
ejpam-6657	80	23	.	.	PUNCT
ejpam-6657	81	1	section	section	NOUN
ejpam-6657	81	2	5	5	NUM
ejpam-6657	81	3	presents	present	VERB
ejpam-6657	81	4	symmetric	symmetric	ADJ
ejpam-6657	81	5	identities	identity	NOUN
ejpam-6657	81	6	to	to	PART
ejpam-6657	81	7	further	far	ADV
ejpam-6657	81	8	enrich	enrich	VERB
ejpam-6657	81	9	the	the	DET
ejpam-6657	81	10	theoretical	theoretical	ADJ
ejpam-6657	81	11	framework	framework	NOUN
ejpam-6657	81	12	.	.	PUNCT
ejpam-6657	82	1	finally	finally	ADV
ejpam-6657	82	2	,	,	PUNCT
ejpam-6657	82	3	concluding	conclude	VERB
ejpam-6657	82	4	remarks	remark	NOUN
ejpam-6657	82	5	are	be	AUX
ejpam-6657	82	6	provided	provide	VERB
ejpam-6657	82	7	.	.	PUNCT
ejpam-6657	83	1	2	2	X
ejpam-6657	83	2	.	.	X
ejpam-6657	83	3	∆h	∆h	NUM
ejpam-6657	83	4	-	-	PUNCT
ejpam-6657	83	5	truncated	truncate	VERB
ejpam-6657	83	6	exponential	exponential	NOUN
ejpam-6657	83	7	-	-	PUNCT
ejpam-6657	83	8	based	base	VERB
ejpam-6657	83	9	hermite	hermite	ADJ
ejpam-6657	83	10	polynomials	polynomial	VERB
ejpam-6657	83	11	this	this	DET
ejpam-6657	83	12	section	section	NOUN
ejpam-6657	83	13	introduces	introduce	VERB
ejpam-6657	83	14	a	a	DET
ejpam-6657	83	15	new	new	ADJ
ejpam-6657	83	16	family	family	NOUN
ejpam-6657	83	17	of	of	ADP
ejpam-6657	83	18	three	three	NUM
ejpam-6657	83	19	-	-	PUNCT
ejpam-6657	83	20	variable	variable	NOUN
ejpam-6657	83	21	∆h	∆h	NOUN
ejpam-6657	83	22	-	-	PUNCT
ejpam-6657	83	23	truncated	truncate	VERB
ejpam-6657	83	24	exponential	exponential	NOUN
ejpam-6657	83	25	-	-	PUNCT
ejpam-6657	83	26	based	base	VERB
ejpam-6657	83	27	hermite	hermite	ADJ
ejpam-6657	83	28	polynomials	polynomial	NOUN
ejpam-6657	83	29	and	and	CCONJ
ejpam-6657	83	30	examines	examine	VERB
ejpam-6657	83	31	their	their	PRON
ejpam-6657	83	32	foundational	foundational	ADJ
ejpam-6657	83	33	properties	property	NOUN
ejpam-6657	83	34	.	.	PUNCT
ejpam-6657	84	1	it	it	PRON
ejpam-6657	84	2	significantly	significantly	ADV
ejpam-6657	84	3	enhances	enhance	VERB
ejpam-6657	84	4	the	the	DET
ejpam-6657	84	5	current	current	ADJ
ejpam-6657	84	6	understanding	understanding	NOUN
ejpam-6657	84	7	of	of	ADP
ejpam-6657	84	8	polynomial	polynomial	ADJ
ejpam-6657	84	9	theory	theory	NOUN
ejpam-6657	84	10	and	and	CCONJ
ejpam-6657	84	11	suggests	suggest	VERB
ejpam-6657	84	12	promising	promise	VERB
ejpam-6657	84	13	directions	direction	NOUN
ejpam-6657	84	14	for	for	ADP
ejpam-6657	84	15	further	further	ADJ
ejpam-6657	84	16	study	study	NOUN
ejpam-6657	84	17	.	.	PUNCT
ejpam-6657	85	1	the	the	DET
ejpam-6657	85	2	derivation	derivation	NOUN
ejpam-6657	85	3	of	of	ADP
ejpam-6657	85	4	the	the	DET
ejpam-6657	85	5	generating	generate	VERB
ejpam-6657	85	6	function	function	NOUN
ejpam-6657	85	7	for	for	ADP
ejpam-6657	85	8	e(r)h	e(r)h	PROPN
ejpam-6657	86	1	[	[	X
ejpam-6657	86	2	h	h	X
ejpam-6657	86	3	]	]	X
ejpam-6657	86	4	n	n	PROPN
ejpam-6657	86	5	(	(	PUNCT
ejpam-6657	86	6	ξ1	ξ1	PROPN
ejpam-6657	86	7	,	,	PUNCT
ejpam-6657	86	8	ξ2	ξ2	ADJ
ejpam-6657	86	9	,	,	PUNCT
ejpam-6657	86	10	ξ3	ξ3	PROPN
ejpam-6657	86	11	)	)	PUNCT
ejpam-6657	86	12	plays	play	VERB
ejpam-6657	86	13	a	a	DET
ejpam-6657	86	14	pivotal	pivotal	ADJ
ejpam-6657	86	15	role	role	NOUN
ejpam-6657	86	16	in	in	ADP
ejpam-6657	86	17	revealing	reveal	VERB
ejpam-6657	86	18	the	the	DET
ejpam-6657	86	19	structure	structure	NOUN
ejpam-6657	86	20	and	and	CCONJ
ejpam-6657	86	21	analytical	analytical	ADJ
ejpam-6657	86	22	behavior	behavior	NOUN
ejpam-6657	86	23	of	of	ADP
ejpam-6657	86	24	these	these	DET
ejpam-6657	86	25	polynomials	polynomial	NOUN
ejpam-6657	86	26	.	.	PUNCT
ejpam-6657	87	1	this	this	DET
ejpam-6657	87	2	construction	construction	NOUN
ejpam-6657	87	3	not	not	PART
ejpam-6657	87	4	only	only	ADV
ejpam-6657	87	5	aids	aid	NOUN
ejpam-6657	87	6	in	in	ADP
ejpam-6657	87	7	uncovering	uncover	VERB
ejpam-6657	87	8	key	key	ADJ
ejpam-6657	87	9	identities	identity	NOUN
ejpam-6657	87	10	and	and	CCONJ
ejpam-6657	87	11	recurrence	recurrence	NOUN
ejpam-6657	87	12	relations	relation	NOUN
ejpam-6657	87	13	but	but	CCONJ
ejpam-6657	87	14	also	also	ADV
ejpam-6657	87	15	enriches	enrich	VERB
ejpam-6657	87	16	their	their	PRON
ejpam-6657	87	17	connection	connection	NOUN
ejpam-6657	87	18	to	to	ADP
ejpam-6657	87	19	broader	broad	ADJ
ejpam-6657	87	20	mathematical	mathematical	ADJ
ejpam-6657	87	21	frameworks	framework	NOUN
ejpam-6657	87	22	.	.	PUNCT
ejpam-6657	88	1	to	to	PART
ejpam-6657	88	2	initiate	initiate	VERB
ejpam-6657	88	3	this	this	PRON
ejpam-6657	88	4	,	,	PUNCT
ejpam-6657	88	5	we	we	PRON
ejpam-6657	88	6	derive	derive	VERB
ejpam-6657	88	7	the	the	DET
ejpam-6657	88	8	generating	generate	VERB
ejpam-6657	88	9	function	function	NOUN
ejpam-6657	88	10	for	for	ADP
ejpam-6657	88	11	e(r)h	e(r)h	PROPN
ejpam-6657	89	1	[	[	X
ejpam-6657	89	2	h	h	X
ejpam-6657	89	3	]	]	X
ejpam-6657	89	4	n	n	PROPN
ejpam-6657	89	5	(	(	PUNCT
ejpam-6657	89	6	ξ1	ξ1	PROPN
ejpam-6657	89	7	,	,	PUNCT
ejpam-6657	89	8	ξ2	ξ2	ADJ
ejpam-6657	89	9	,	,	PUNCT
ejpam-6657	89	10	ξ3	ξ3	NOUN
ejpam-6657	89	11	)	)	PUNCT
ejpam-6657	89	12	by	by	ADP
ejpam-6657	89	13	establishing	establish	VERB
ejpam-6657	89	14	the	the	DET
ejpam-6657	89	15	following	following	ADJ
ejpam-6657	89	16	result	result	NOUN
ejpam-6657	89	17	:	:	PUNCT
ejpam-6657	89	18	theorem	theorem	NOUN
ejpam-6657	89	19	1	1	NUM
ejpam-6657	89	20	.	.	PUNCT
ejpam-6657	90	1	the	the	DET
ejpam-6657	90	2	generating	generate	VERB
ejpam-6657	90	3	function	function	NOUN
ejpam-6657	90	4	associated	associate	VERB
ejpam-6657	90	5	with	with	ADP
ejpam-6657	90	6	the	the	DET
ejpam-6657	90	7	three	three	NUM
ejpam-6657	90	8	-	-	PUNCT
ejpam-6657	90	9	variable	variable	NOUN
ejpam-6657	90	10	∆h	∆h	NOUN
ejpam-6657	90	11	-	-	PUNCT
ejpam-6657	90	12	truncated	truncate	VERB
ejpam-6657	90	13	exponential	exponential	NOUN
ejpam-6657	90	14	-	-	PUNCT
ejpam-6657	90	15	based	base	VERB
ejpam-6657	90	16	hermite	hermite	ADJ
ejpam-6657	90	17	polynomials	polynomial	VERB
ejpam-6657	90	18	e(r)h	e(r)h	PROPN
ejpam-6657	91	1	[	[	X
ejpam-6657	91	2	h	h	X
ejpam-6657	91	3	]	]	X
ejpam-6657	91	4	n	n	PROPN
ejpam-6657	91	5	(	(	PUNCT
ejpam-6657	91	6	ξ1	ξ1	PROPN
ejpam-6657	91	7	,	,	PUNCT
ejpam-6657	91	8	ξ2	ξ2	ADJ
ejpam-6657	91	9	,	,	PUNCT
ejpam-6657	91	10	ξ3	ξ3	NOUN
ejpam-6657	91	11	)	)	PUNCT
ejpam-6657	91	12	is	be	AUX
ejpam-6657	91	13	expressed	express	VERB
ejpam-6657	91	14	as	as	SCONJ
ejpam-6657	91	15	follows	follow	VERB
ejpam-6657	91	16	:	:	PUNCT
ejpam-6657	91	17	1	1	NUM
ejpam-6657	91	18	1−	1−	NUM
ejpam-6657	91	19	ξ3tr	ξ3tr	NUM
ejpam-6657	91	20	(	(	PUNCT
ejpam-6657	91	21	1	1	NUM
ejpam-6657	91	22	+	+	NUM
ejpam-6657	91	23	ht	ht	NOUN
ejpam-6657	91	24	)	)	PUNCT
ejpam-6657	91	25	ξ1	ξ1	PROPN
ejpam-6657	91	26	h	h	NOUN
ejpam-6657	91	27	(	(	PUNCT
ejpam-6657	91	28	1	1	NUM
ejpam-6657	91	29	+	+	NUM
ejpam-6657	91	30	ht2	ht2	NOUN
ejpam-6657	91	31	)	)	PUNCT
ejpam-6657	91	32	ξ2	ξ2	NOUN
ejpam-6657	91	33	h	h	NOUN
ejpam-6657	91	34	=	=	PUNCT
ejpam-6657	92	1	∞∑	∞∑	PRON
ejpam-6657	92	2	n=0	n=0	NUM
ejpam-6657	92	3	e(r)h	e(r)h	PROPN
ejpam-6657	93	1	[	[	X
ejpam-6657	93	2	h	h	X
ejpam-6657	93	3	]	]	X
ejpam-6657	93	4	n	n	PROPN
ejpam-6657	93	5	(	(	PUNCT
ejpam-6657	93	6	ξ1	ξ1	PROPN
ejpam-6657	93	7	,	,	PUNCT
ejpam-6657	93	8	ξ2	ξ2	ADJ
ejpam-6657	93	9	,	,	PUNCT
ejpam-6657	93	10	ξ3	ξ3	PROPN
ejpam-6657	93	11	)	)	PUNCT
ejpam-6657	93	12	tn	tn	PROPN
ejpam-6657	93	13	n	n	PROPN
ejpam-6657	93	14	!	!	PUNCT
ejpam-6657	93	15	.	.	PUNCT
ejpam-6657	94	1	(	(	PUNCT
ejpam-6657	94	2	29	29	NUM
ejpam-6657	94	3	)	)	PUNCT
ejpam-6657	94	4	h.	h.	PROPN
ejpam-6657	94	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	94	6	et	et	PROPN
ejpam-6657	94	7	al	al	PROPN
ejpam-6657	94	8	.	.	PUNCT
ejpam-6657	94	9	/	/	SYM
ejpam-6657	94	10	eur	eur	PROPN
ejpam-6657	94	11	.	.	PUNCT
ejpam-6657	95	1	j.	j.	PROPN
ejpam-6657	95	2	pure	pure	PROPN
ejpam-6657	95	3	appl	appl	PROPN
ejpam-6657	95	4	.	.	PROPN
ejpam-6657	95	5	math	math	PROPN
ejpam-6657	95	6	,	,	PUNCT
ejpam-6657	95	7	18	18	NUM
ejpam-6657	95	8	(	(	PUNCT
ejpam-6657	95	9	3	3	NUM
ejpam-6657	95	10	)	)	PUNCT
ejpam-6657	95	11	(	(	PUNCT
ejpam-6657	95	12	2025	2025	NUM
ejpam-6657	95	13	)	)	PUNCT
ejpam-6657	95	14	,	,	PUNCT
ejpam-6657	95	15	6657	6657	NUM
ejpam-6657	95	16	6	6	NUM
ejpam-6657	95	17	of	of	ADP
ejpam-6657	95	18	16	16	NUM
ejpam-6657	95	19	proof	proof	NOUN
ejpam-6657	95	20	.	.	PUNCT
ejpam-6657	96	1	consider	consider	VERB
ejpam-6657	96	2	the	the	DET
ejpam-6657	96	3	expansion	expansion	NOUN
ejpam-6657	96	4	of	of	ADP
ejpam-6657	96	5	1	1	NUM
ejpam-6657	96	6	1−ξ3tr	1−ξ3tr	NUM
ejpam-6657	96	7	(	(	PUNCT
ejpam-6657	96	8	1	1	NUM
ejpam-6657	96	9	+	+	NUM
ejpam-6657	96	10	ht	ht	NOUN
ejpam-6657	96	11	)	)	PUNCT
ejpam-6657	96	12	ξ1	ξ1	PROPN
ejpam-6657	96	13	h	h	NOUN
ejpam-6657	96	14	(	(	PUNCT
ejpam-6657	96	15	1	1	NUM
ejpam-6657	96	16	+	+	NUM
ejpam-6657	96	17	ht2	ht2	NOUN
ejpam-6657	96	18	)	)	PUNCT
ejpam-6657	96	19	ξ2	ξ2	NOUN
ejpam-6657	96	20	h	h	NOUN
ejpam-6657	96	21	around	around	ADP
ejpam-6657	96	22	ξ1	ξ1	PROPN
ejpam-6657	96	23	=	=	SYM
ejpam-6657	96	24	ξ2	ξ2	NOUN
ejpam-6657	96	25	=	=	SYM
ejpam-6657	96	26	ξ3	ξ3	NOUN
ejpam-6657	96	27	=	=	NOUN
ejpam-6657	96	28	0	0	PUNCT
ejpam-6657	96	29	using	use	VERB
ejpam-6657	96	30	a	a	DET
ejpam-6657	96	31	newton	newton	PROPN
ejpam-6657	96	32	series	series	NOUN
ejpam-6657	96	33	for	for	ADP
ejpam-6657	96	34	finite	finite	ADJ
ejpam-6657	96	35	differences	difference	NOUN
ejpam-6657	96	36	.	.	PUNCT
ejpam-6657	97	1	by	by	ADP
ejpam-6657	97	2	analyzing	analyze	VERB
ejpam-6657	97	3	the	the	DET
ejpam-6657	97	4	product	product	NOUN
ejpam-6657	97	5	expansion	expansion	NOUN
ejpam-6657	97	6	of	of	ADP
ejpam-6657	97	7	the	the	DET
ejpam-6657	97	8	functions	function	NOUN
ejpam-6657	97	9	(	(	PUNCT
ejpam-6657	97	10	1+ht	1+ht	X
ejpam-6657	97	11	)	)	PUNCT
ejpam-6657	97	12	ξ1	ξ1	NOUN
ejpam-6657	97	13	h	h	NOUN
ejpam-6657	97	14	and	and	CCONJ
ejpam-6657	97	15	(	(	PUNCT
ejpam-6657	97	16	1+ht2	1+ht2	ADJ
ejpam-6657	97	17	)	)	PUNCT
ejpam-6657	97	18	ξ2	ξ2	ADJ
ejpam-6657	97	19	h	h	NOUN
ejpam-6657	97	20	with	with	ADP
ejpam-6657	97	21	respect	respect	NOUN
ejpam-6657	97	22	to	to	ADP
ejpam-6657	97	23	powers	power	NOUN
ejpam-6657	97	24	of	of	ADP
ejpam-6657	97	25	t	t	PROPN
ejpam-6657	97	26	,	,	PUNCT
ejpam-6657	97	27	we	we	PRON
ejpam-6657	97	28	identify	identify	VERB
ejpam-6657	97	29	the	the	DET
ejpam-6657	97	30	coefficients	coefficient	NOUN
ejpam-6657	97	31	of	of	ADP
ejpam-6657	97	32	tn	tn	NOUN
ejpam-6657	97	33	n	n	CCONJ
ejpam-6657	97	34	!	!	PUNCT
ejpam-6657	98	1	as	as	ADP
ejpam-6657	98	2	the	the	DET
ejpam-6657	98	3	polynomials	polynomials	NOUN
ejpam-6657	99	1	e(r)h	e(r)h	PROPN
ejpam-6657	100	1	[	[	X
ejpam-6657	100	2	h	h	X
ejpam-6657	100	3	]	]	X
ejpam-6657	100	4	n	n	PROPN
ejpam-6657	100	5	(	(	PUNCT
ejpam-6657	100	6	ξ1	ξ1	PROPN
ejpam-6657	100	7	,	,	PUNCT
ejpam-6657	100	8	ξ2	ξ2	ADJ
ejpam-6657	100	9	,	,	PUNCT
ejpam-6657	100	10	ξ3	ξ3	PROPN
ejpam-6657	100	11	)	)	PUNCT
ejpam-6657	100	12	,	,	PUNCT
ejpam-6657	100	13	which	which	PRON
ejpam-6657	100	14	are	be	AUX
ejpam-6657	100	15	defined	define	VERB
ejpam-6657	100	16	in	in	ADP
ejpam-6657	100	17	equation	equation	NOUN
ejpam-6657	100	18	(	(	PUNCT
ejpam-6657	100	19	29	29	NUM
ejpam-6657	100	20	)	)	PUNCT
ejpam-6657	100	21	.	.	PUNCT
ejpam-6657	101	1	this	this	PRON
ejpam-6657	101	2	confirms	confirm	VERB
ejpam-6657	101	3	the	the	DET
ejpam-6657	101	4	generating	generate	VERB
ejpam-6657	101	5	function	function	NOUN
ejpam-6657	101	6	for	for	ADP
ejpam-6657	101	7	the	the	DET
ejpam-6657	101	8	three	three	NUM
ejpam-6657	101	9	-	-	PUNCT
ejpam-6657	101	10	variable	variable	NOUN
ejpam-6657	101	11	∆h	∆h	NOUN
ejpam-6657	101	12	-	-	PUNCT
ejpam-6657	101	13	truncated	truncate	VERB
ejpam-6657	101	14	exponential	exponential	NOUN
ejpam-6657	101	15	-	-	PUNCT
ejpam-6657	101	16	based	base	VERB
ejpam-6657	101	17	hermite	hermite	ADJ
ejpam-6657	101	18	polynomials	polynomial	VERB
ejpam-6657	101	19	e(r)h	e(r)h	PROPN
ejpam-6657	102	1	[	[	X
ejpam-6657	102	2	h	h	X
ejpam-6657	102	3	]	]	X
ejpam-6657	102	4	n	n	PROPN
ejpam-6657	102	5	(	(	PUNCT
ejpam-6657	102	6	ξ1	ξ1	PROPN
ejpam-6657	102	7	,	,	PUNCT
ejpam-6657	102	8	ξ2	ξ2	ADJ
ejpam-6657	102	9	,	,	PUNCT
ejpam-6657	102	10	ξ3	ξ3	PROPN
ejpam-6657	102	11	)	)	PUNCT
ejpam-6657	102	12	.	.	PUNCT
ejpam-6657	103	1	theorem	theorem	NOUN
ejpam-6657	103	2	2	2	NUM
ejpam-6657	103	3	.	.	X
ejpam-6657	103	4	for	for	SCONJ
ejpam-6657	103	5	the	the	DET
ejpam-6657	103	6	three	three	NUM
ejpam-6657	103	7	-	-	PUNCT
ejpam-6657	103	8	variable	variable	NOUN
ejpam-6657	103	9	∆h	∆h	NOUN
ejpam-6657	103	10	-	-	PUNCT
ejpam-6657	103	11	truncated	truncate	VERB
ejpam-6657	103	12	exponential	exponential	NOUN
ejpam-6657	103	13	-	-	PUNCT
ejpam-6657	103	14	based	base	VERB
ejpam-6657	103	15	hermite	hermite	ADJ
ejpam-6657	103	16	polynomials	polynomial	VERB
ejpam-6657	103	17	e(r)h	e(r)h	PROPN
ejpam-6657	104	1	[	[	X
ejpam-6657	104	2	h	h	X
ejpam-6657	104	3	]	]	X
ejpam-6657	104	4	n	n	PROPN
ejpam-6657	104	5	(	(	PUNCT
ejpam-6657	104	6	ξ1	ξ1	PROPN
ejpam-6657	104	7	,	,	PUNCT
ejpam-6657	104	8	ξ2	ξ2	ADJ
ejpam-6657	104	9	,	,	PUNCT
ejpam-6657	104	10	ξ3	ξ3	PROPN
ejpam-6657	104	11	)	)	PUNCT
ejpam-6657	104	12	,	,	PUNCT
ejpam-6657	104	13	the	the	DET
ejpam-6657	104	14	following	follow	VERB
ejpam-6657	104	15	relations	relation	NOUN
ejpam-6657	104	16	hold	hold	VERB
ejpam-6657	104	17	:	:	PUNCT
ejpam-6657	104	18	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	104	19	h	h	NOUN
ejpam-6657	104	20	e(r)h	e(r)h	PROPN
ejpam-6657	105	1	[	[	X
ejpam-6657	105	2	h	h	X
ejpam-6657	105	3	]	]	X
ejpam-6657	105	4	n	n	PROPN
ejpam-6657	105	5	(	(	PUNCT
ejpam-6657	105	6	ξ1	ξ1	PROPN
ejpam-6657	105	7	,	,	PUNCT
ejpam-6657	105	8	ξ2	ξ2	ADJ
ejpam-6657	105	9	,	,	PUNCT
ejpam-6657	105	10	ξ3	ξ3	NOUN
ejpam-6657	105	11	)	)	PUNCT
ejpam-6657	105	12	=	=	SYM
ejpam-6657	105	13	n	n	PRON
ejpam-6657	105	14	e(r)h	e(r)h	PROPN
ejpam-6657	106	1	[	[	X
ejpam-6657	106	2	h	h	X
ejpam-6657	106	3	]	]	X
ejpam-6657	106	4	n−1(ξ1	n−1(ξ1	ADP
ejpam-6657	106	5	,	,	PUNCT
ejpam-6657	106	6	ξ2	ξ2	ADJ
ejpam-6657	106	7	,	,	PUNCT
ejpam-6657	106	8	ξ3	ξ3	NOUN
ejpam-6657	106	9	)	)	PUNCT
ejpam-6657	107	1	ξ2∆h	ξ2∆h	ADJ
ejpam-6657	107	2	h	h	NOUN
ejpam-6657	107	3	e(r)h	e(r)h	PROPN
ejpam-6657	108	1	[	[	X
ejpam-6657	108	2	h	h	X
ejpam-6657	108	3	]	]	X
ejpam-6657	108	4	n	n	PROPN
ejpam-6657	108	5	(	(	PUNCT
ejpam-6657	108	6	ξ1	ξ1	PROPN
ejpam-6657	108	7	,	,	PUNCT
ejpam-6657	108	8	ξ2	ξ2	ADJ
ejpam-6657	108	9	,	,	PUNCT
ejpam-6657	108	10	ξ3	ξ3	NOUN
ejpam-6657	108	11	)	)	PUNCT
ejpam-6657	108	12	=	=	SYM
ejpam-6657	108	13	n(n−	n(n−	ADJ
ejpam-6657	108	14	1	1	NUM
ejpam-6657	108	15	)	)	PUNCT
ejpam-6657	108	16	e(r)h	e(r)h	PROPN
ejpam-6657	109	1	[	[	X
ejpam-6657	109	2	h	h	X
ejpam-6657	109	3	]	]	X
ejpam-6657	109	4	n−2(ξ1	n−2(ξ1	ADJ
ejpam-6657	109	5	,	,	PUNCT
ejpam-6657	109	6	ξ2	ξ2	ADJ
ejpam-6657	109	7	,	,	PUNCT
ejpam-6657	109	8	ξ3	ξ3	NOUN
ejpam-6657	109	9	)	)	PUNCT
ejpam-6657	109	10	.	.	PUNCT
ejpam-6657	110	1	(	(	PUNCT
ejpam-6657	110	2	30	30	X
ejpam-6657	110	3	)	)	PUNCT
ejpam-6657	110	4	proof	proof	NOUN
ejpam-6657	110	5	.	.	PUNCT
ejpam-6657	111	1	differentiating	differentiate	VERB
ejpam-6657	111	2	equation	equation	NOUN
ejpam-6657	111	3	(	(	PUNCT
ejpam-6657	111	4	29	29	NUM
ejpam-6657	111	5	)	)	PUNCT
ejpam-6657	111	6	with	with	ADP
ejpam-6657	111	7	respect	respect	NOUN
ejpam-6657	111	8	to	to	ADP
ejpam-6657	111	9	ξ1	ξ1	NOUN
ejpam-6657	111	10	and	and	CCONJ
ejpam-6657	111	11	applying	apply	VERB
ejpam-6657	111	12	expression	expression	NOUN
ejpam-6657	111	13	(	(	PUNCT
ejpam-6657	111	14	20	20	NUM
ejpam-6657	111	15	)	)	PUNCT
ejpam-6657	111	16	,	,	PUNCT
ejpam-6657	111	17	we	we	PRON
ejpam-6657	111	18	get	get	VERB
ejpam-6657	111	19	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	111	20	1	1	NUM
ejpam-6657	111	21	1−	1−	NUM
ejpam-6657	111	22	ξ3tr	ξ3tr	NUM
ejpam-6657	111	23	(	(	PUNCT
ejpam-6657	111	24	1+ht	1+ht	X
ejpam-6657	111	25	)	)	PUNCT
ejpam-6657	111	26	ξ1	ξ1	NOUN
ejpam-6657	111	27	h	h	NOUN
ejpam-6657	111	28	(	(	PUNCT
ejpam-6657	111	29	1+ht2	1+ht2	ADJ
ejpam-6657	111	30	)	)	PUNCT
ejpam-6657	111	31	ξ2	ξ2	NOUN
ejpam-6657	111	32	h	h	NOUN
ejpam-6657	112	1	=	=	NOUN
ejpam-6657	112	2	1	1	NUM
ejpam-6657	112	3	1−	1−	NUM
ejpam-6657	112	4	ξ3tr	ξ3tr	NUM
ejpam-6657	112	5	(	(	PUNCT
ejpam-6657	112	6	1+ht	1+ht	X
ejpam-6657	112	7	)	)	PUNCT
ejpam-6657	112	8	ξ1	ξ1	NOUN
ejpam-6657	112	9	+	+	PROPN
ejpam-6657	112	10	1	1	NUM
ejpam-6657	112	11	h	h	NOUN
ejpam-6657	112	12	(	(	PUNCT
ejpam-6657	112	13	1+ht2	1+ht2	ADJ
ejpam-6657	112	14	)	)	PUNCT
ejpam-6657	112	15	ξ2	ξ2	NOUN
ejpam-6657	112	16	h	h	NOUN
ejpam-6657	112	17	−	−	NOUN
ejpam-6657	112	18	1	1	NUM
ejpam-6657	112	19	1−	1−	NUM
ejpam-6657	112	20	ξ3tr	ξ3tr	NUM
ejpam-6657	112	21	(	(	PUNCT
ejpam-6657	112	22	1+ht	1+ht	X
ejpam-6657	112	23	)	)	PUNCT
ejpam-6657	112	24	ξ1	ξ1	NOUN
ejpam-6657	112	25	h	h	NOUN
ejpam-6657	112	26	(	(	PUNCT
ejpam-6657	112	27	1+ht2	1+ht2	ADJ
ejpam-6657	112	28	)	)	PUNCT
ejpam-6657	112	29	ξ2	ξ2	NOUN
ejpam-6657	112	30	h	h	NOUN
ejpam-6657	112	31	=	=	PUNCT
ejpam-6657	113	1	(	(	PUNCT
ejpam-6657	113	2	1	1	NUM
ejpam-6657	113	3	+	+	NUM
ejpam-6657	113	4	ht−	ht−	NOUN
ejpam-6657	113	5	1	1	NUM
ejpam-6657	113	6	)	)	PUNCT
ejpam-6657	113	7	1	1	NUM
ejpam-6657	113	8	1−	1−	NUM
ejpam-6657	113	9	ξ3tr	ξ3tr	NUM
ejpam-6657	113	10	(	(	PUNCT
ejpam-6657	113	11	1	1	NUM
ejpam-6657	113	12	+	+	NUM
ejpam-6657	113	13	ht	ht	NOUN
ejpam-6657	113	14	)	)	PUNCT
ejpam-6657	113	15	ξ1	ξ1	PROPN
ejpam-6657	113	16	h	h	NOUN
ejpam-6657	113	17	(	(	PUNCT
ejpam-6657	113	18	1	1	NUM
ejpam-6657	113	19	+	+	NUM
ejpam-6657	113	20	ht2	ht2	NOUN
ejpam-6657	113	21	)	)	PUNCT
ejpam-6657	113	22	ξ2	ξ2	NOUN
ejpam-6657	113	23	h	h	NOUN
ejpam-6657	114	1	=	=	SYM
ejpam-6657	114	2	ht	ht	PROPN
ejpam-6657	114	3	1	1	NUM
ejpam-6657	114	4	1−	1−	NUM
ejpam-6657	114	5	ξ3tr	ξ3tr	NUM
ejpam-6657	114	6	(	(	PUNCT
ejpam-6657	114	7	1	1	NUM
ejpam-6657	114	8	+	+	NUM
ejpam-6657	114	9	ht	ht	NOUN
ejpam-6657	114	10	)	)	PUNCT
ejpam-6657	114	11	ξ1	ξ1	PROPN
ejpam-6657	114	12	h	h	NOUN
ejpam-6657	114	13	(	(	PUNCT
ejpam-6657	114	14	1	1	NUM
ejpam-6657	114	15	+	+	NUM
ejpam-6657	114	16	ht2	ht2	NOUN
ejpam-6657	114	17	)	)	PUNCT
ejpam-6657	114	18	ξ2	ξ2	NOUN
ejpam-6657	114	19	h	h	NOUN
ejpam-6657	114	20	.	.	PUNCT
ejpam-6657	115	1	(	(	PUNCT
ejpam-6657	115	2	31	31	NUM
ejpam-6657	115	3	)	)	PUNCT
ejpam-6657	115	4	substituting	substitute	VERB
ejpam-6657	115	5	the	the	DET
ejpam-6657	115	6	right	right	ADJ
ejpam-6657	115	7	-	-	PUNCT
ejpam-6657	115	8	hand	hand	NOUN
ejpam-6657	115	9	side	side	NOUN
ejpam-6657	115	10	of	of	ADP
ejpam-6657	115	11	equation	equation	NOUN
ejpam-6657	115	12	(	(	PUNCT
ejpam-6657	115	13	29	29	NUM
ejpam-6657	115	14	)	)	PUNCT
ejpam-6657	115	15	into	into	ADP
ejpam-6657	115	16	(	(	PUNCT
ejpam-6657	115	17	31	31	NUM
ejpam-6657	115	18	)	)	PUNCT
ejpam-6657	115	19	,	,	PUNCT
ejpam-6657	115	20	we	we	PRON
ejpam-6657	115	21	obtain	obtain	VERB
ejpam-6657	115	22	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	115	23	∞∑	∞∑	PRON
ejpam-6657	115	24	n=0	n=0	NUM
ejpam-6657	115	25	e(r)h	e(r)h	PROPN
ejpam-6657	116	1	[	[	X
ejpam-6657	116	2	h	h	X
ejpam-6657	116	3	]	]	X
ejpam-6657	116	4	n	n	PROPN
ejpam-6657	116	5	(	(	PUNCT
ejpam-6657	116	6	ξ1	ξ1	PROPN
ejpam-6657	116	7	,	,	PUNCT
ejpam-6657	116	8	ξ2	ξ2	ADJ
ejpam-6657	116	9	,	,	PUNCT
ejpam-6657	116	10	ξ3	ξ3	PROPN
ejpam-6657	116	11	)	)	PUNCT
ejpam-6657	116	12	tn	tn	PROPN
ejpam-6657	116	13	n	n	ADV
ejpam-6657	116	14	!	!	PUNCT
ejpam-6657	117	1	=	=	NOUN
ejpam-6657	117	2	h	h	PROPN
ejpam-6657	118	1	∞∑	∞∑	PRON
ejpam-6657	118	2	n=0	n=0	NUM
ejpam-6657	118	3	e(r)h	e(r)h	PROPN
ejpam-6657	119	1	[	[	X
ejpam-6657	119	2	h	h	X
ejpam-6657	119	3	]	]	X
ejpam-6657	119	4	n	n	PROPN
ejpam-6657	119	5	(	(	PUNCT
ejpam-6657	119	6	ξ1	ξ1	PROPN
ejpam-6657	119	7	,	,	PUNCT
ejpam-6657	119	8	ξ2	ξ2	ADJ
ejpam-6657	119	9	,	,	PUNCT
ejpam-6657	119	10	ξ3	ξ3	NOUN
ejpam-6657	119	11	)	)	PUNCT
ejpam-6657	119	12	tn+1	tn+1	NOUN
ejpam-6657	119	13	n	n	X
ejpam-6657	119	14	!	!	PUNCT
ejpam-6657	119	15	.	.	PUNCT
ejpam-6657	120	1	(	(	PUNCT
ejpam-6657	120	2	32	32	NUM
ejpam-6657	120	3	)	)	PUNCT
ejpam-6657	120	4	now	now	ADV
ejpam-6657	120	5	,	,	PUNCT
ejpam-6657	120	6	replacing	replace	VERB
ejpam-6657	120	7	n	n	PRON
ejpam-6657	120	8	→	→	PUNCT
ejpam-6657	120	9	n−	n−	NOUN
ejpam-6657	120	10	1	1	NUM
ejpam-6657	120	11	on	on	ADP
ejpam-6657	120	12	the	the	DET
ejpam-6657	120	13	right	right	ADJ
ejpam-6657	120	14	-	-	PUNCT
ejpam-6657	120	15	hand	hand	NOUN
ejpam-6657	120	16	side	side	NOUN
ejpam-6657	120	17	of	of	ADP
ejpam-6657	120	18	the	the	DET
ejpam-6657	120	19	above	above	ADJ
ejpam-6657	120	20	expression	expression	NOUN
ejpam-6657	120	21	and	and	CCONJ
ejpam-6657	120	22	comparing	compare	VERB
ejpam-6657	120	23	the	the	DET
ejpam-6657	120	24	coefficients	coefficient	NOUN
ejpam-6657	120	25	of	of	ADP
ejpam-6657	120	26	like	like	ADP
ejpam-6657	120	27	powers	power	NOUN
ejpam-6657	120	28	of	of	ADP
ejpam-6657	120	29	t	t	PROPN
ejpam-6657	120	30	,	,	PUNCT
ejpam-6657	120	31	we	we	PRON
ejpam-6657	120	32	deduce	deduce	VERB
ejpam-6657	120	33	the	the	DET
ejpam-6657	120	34	identities	identity	NOUN
ejpam-6657	120	35	in	in	ADP
ejpam-6657	120	36	(	(	PUNCT
ejpam-6657	120	37	30	30	NUM
ejpam-6657	120	38	)	)	PUNCT
ejpam-6657	120	39	.	.	PUNCT
ejpam-6657	121	1	we	we	PRON
ejpam-6657	121	2	now	now	ADV
ejpam-6657	121	3	derive	derive	VERB
ejpam-6657	121	4	an	an	DET
ejpam-6657	121	5	explicit	explicit	ADJ
ejpam-6657	121	6	expression	expression	NOUN
ejpam-6657	121	7	satisfied	satisfy	VERB
ejpam-6657	121	8	by	by	ADP
ejpam-6657	121	9	the	the	DET
ejpam-6657	121	10	three	three	NUM
ejpam-6657	121	11	-	-	PUNCT
ejpam-6657	121	12	variable	variable	NOUN
ejpam-6657	121	13	∆h	∆h	NOUN
ejpam-6657	121	14	-	-	PUNCT
ejpam-6657	121	15	truncated	truncate	VERB
ejpam-6657	121	16	exponential	exponential	NOUN
ejpam-6657	121	17	-	-	PUNCT
ejpam-6657	121	18	based	base	VERB
ejpam-6657	121	19	hermite	hermite	ADJ
ejpam-6657	121	20	polynomials	polynomial	VERB
ejpam-6657	121	21	e(r)h	e(r)h	PROPN
ejpam-6657	122	1	[	[	X
ejpam-6657	122	2	h	h	X
ejpam-6657	122	3	]	]	X
ejpam-6657	122	4	n	n	PROPN
ejpam-6657	122	5	(	(	PUNCT
ejpam-6657	122	6	ξ1	ξ1	PROPN
ejpam-6657	122	7	,	,	PUNCT
ejpam-6657	122	8	ξ2	ξ2	ADJ
ejpam-6657	122	9	,	,	PUNCT
ejpam-6657	122	10	ξ3	ξ3	NOUN
ejpam-6657	122	11	)	)	PUNCT
ejpam-6657	122	12	as	as	SCONJ
ejpam-6657	122	13	follows	follow	VERB
ejpam-6657	122	14	:	:	PUNCT
ejpam-6657	122	15	theorem	theorem	NOUN
ejpam-6657	122	16	3	3	NUM
ejpam-6657	122	17	.	.	X
ejpam-6657	122	18	for	for	ADP
ejpam-6657	122	19	the	the	DET
ejpam-6657	122	20	three	three	NUM
ejpam-6657	122	21	-	-	PUNCT
ejpam-6657	122	22	variable	variable	NOUN
ejpam-6657	122	23	∆h	∆h	NOUN
ejpam-6657	122	24	-	-	PUNCT
ejpam-6657	122	25	truncated	truncate	VERB
ejpam-6657	122	26	exponential	exponential	NOUN
ejpam-6657	122	27	-	-	PUNCT
ejpam-6657	122	28	based	base	VERB
ejpam-6657	122	29	hermite	hermite	ADJ
ejpam-6657	122	30	polynomials	polynomial	VERB
ejpam-6657	122	31	e(r)h	e(r)h	PROPN
ejpam-6657	123	1	[	[	X
ejpam-6657	123	2	h	h	X
ejpam-6657	123	3	]	]	X
ejpam-6657	123	4	n	n	PROPN
ejpam-6657	123	5	(	(	PUNCT
ejpam-6657	123	6	ξ1	ξ1	PROPN
ejpam-6657	123	7	,	,	PUNCT
ejpam-6657	123	8	ξ2	ξ2	ADJ
ejpam-6657	123	9	,	,	PUNCT
ejpam-6657	123	10	ξ3	ξ3	PROPN
ejpam-6657	123	11	)	)	PUNCT
ejpam-6657	123	12	,	,	PUNCT
ejpam-6657	123	13	the	the	DET
ejpam-6657	123	14	following	follow	VERB
ejpam-6657	123	15	expression	expression	NOUN
ejpam-6657	123	16	holds	hold	VERB
ejpam-6657	123	17	:	:	PUNCT
ejpam-6657	124	1	h.	h.	PROPN
ejpam-6657	124	2	qawaqneh	qawaqneh	PROPN
ejpam-6657	124	3	et	et	PROPN
ejpam-6657	124	4	al	al	PROPN
ejpam-6657	124	5	.	.	PUNCT
ejpam-6657	124	6	/	/	SYM
ejpam-6657	124	7	eur	eur	PROPN
ejpam-6657	124	8	.	.	PUNCT
ejpam-6657	125	1	j.	j.	PROPN
ejpam-6657	125	2	pure	pure	PROPN
ejpam-6657	125	3	appl	appl	PROPN
ejpam-6657	125	4	.	.	PROPN
ejpam-6657	125	5	math	math	PROPN
ejpam-6657	125	6	,	,	PUNCT
ejpam-6657	125	7	18	18	NUM
ejpam-6657	125	8	(	(	PUNCT
ejpam-6657	125	9	3	3	NUM
ejpam-6657	125	10	)	)	PUNCT
ejpam-6657	125	11	(	(	PUNCT
ejpam-6657	125	12	2025	2025	NUM
ejpam-6657	125	13	)	)	PUNCT
ejpam-6657	125	14	,	,	PUNCT
ejpam-6657	125	15	6657	6657	NUM
ejpam-6657	125	16	7	7	NUM
ejpam-6657	125	17	of	of	ADP
ejpam-6657	125	18	16	16	NUM
ejpam-6657	125	19	e(r)h	e(r)h	PROPN
ejpam-6657	126	1	[	[	X
ejpam-6657	126	2	h	h	X
ejpam-6657	126	3	]	]	X
ejpam-6657	126	4	n	n	PROPN
ejpam-6657	126	5	(	(	PUNCT
ejpam-6657	126	6	ξ1	ξ1	PROPN
ejpam-6657	126	7	,	,	PUNCT
ejpam-6657	126	8	ξ2	ξ2	ADJ
ejpam-6657	126	9	,	,	PUNCT
ejpam-6657	126	10	ξ3	ξ3	NOUN
ejpam-6657	126	11	)	)	PUNCT
ejpam-6657	126	12	=	=	PUNCT
ejpam-6657	127	1	[	[	PUNCT
ejpam-6657	127	2	ξ1	ξ1	NOUN
ejpam-6657	127	3	h	h	NOUN
ejpam-6657	127	4	]	]	X
ejpam-6657	127	5	∑	∑	PUNCT
ejpam-6657	127	6	d=0	d=0	PROPN
ejpam-6657	127	7	(	(	PUNCT
ejpam-6657	127	8	n	n	NOUN
ejpam-6657	127	9	d	d	NOUN
ejpam-6657	127	10	)	)	PUNCT
ejpam-6657	127	11	(	(	PUNCT
ejpam-6657	127	12	ξ1	ξ1	NOUN
ejpam-6657	127	13	h	h	NOUN
ejpam-6657	127	14	d	d	NOUN
ejpam-6657	127	15	)	)	PUNCT
ejpam-6657	127	16	hd	hd	VERB
ejpam-6657	127	17	e(r)h	e(r)h	PROPN
ejpam-6657	128	1	[	[	X
ejpam-6657	128	2	h	h	X
ejpam-6657	128	3	]	]	X
ejpam-6657	128	4	n−d(0	n−d(0	NOUN
ejpam-6657	128	5	,	,	PUNCT
ejpam-6657	128	6	ξ2	ξ2	ADJ
ejpam-6657	128	7	,	,	PUNCT
ejpam-6657	128	8	ξ3	ξ3	NOUN
ejpam-6657	128	9	)	)	PUNCT
ejpam-6657	128	10	.	.	PUNCT
ejpam-6657	129	1	(	(	PUNCT
ejpam-6657	129	2	33	33	NUM
ejpam-6657	129	3	)	)	PUNCT
ejpam-6657	129	4	proof	proof	NOUN
ejpam-6657	129	5	.	.	PUNCT
ejpam-6657	130	1	consider	consider	VERB
ejpam-6657	130	2	the	the	DET
ejpam-6657	130	3	expansion	expansion	NOUN
ejpam-6657	130	4	of	of	ADP
ejpam-6657	130	5	the	the	DET
ejpam-6657	130	6	generating	generate	VERB
ejpam-6657	130	7	function	function	NOUN
ejpam-6657	130	8	(	(	PUNCT
ejpam-6657	130	9	29	29	NUM
ejpam-6657	130	10	):	):	PUNCT
ejpam-6657	130	11	1	1	NUM
ejpam-6657	130	12	1−	1−	NUM
ejpam-6657	130	13	ξ3tr	ξ3tr	NUM
ejpam-6657	130	14	(	(	PUNCT
ejpam-6657	130	15	1+ht	1+ht	X
ejpam-6657	130	16	)	)	PUNCT
ejpam-6657	130	17	ξ1	ξ1	NOUN
ejpam-6657	130	18	h	h	NOUN
ejpam-6657	130	19	(	(	PUNCT
ejpam-6657	130	20	1+ht2	1+ht2	ADJ
ejpam-6657	130	21	)	)	PUNCT
ejpam-6657	130	22	ξ2	ξ2	NOUN
ejpam-6657	130	23	h	h	NOUN
ejpam-6657	130	24	{	{	PUNCT
ejpam-6657	130	25	1	1	NUM
ejpam-6657	130	26	}	}	PUNCT
ejpam-6657	130	27	=	=	NOUN
ejpam-6657	130	28	[	[	PUNCT
ejpam-6657	130	29	ξ1	ξ1	NOUN
ejpam-6657	130	30	h	h	NOUN
ejpam-6657	130	31	]	]	X
ejpam-6657	130	32	∑	∑	PUNCT
ejpam-6657	130	33	d=0	d=0	PROPN
ejpam-6657	130	34	(	(	PUNCT
ejpam-6657	130	35	ξ1	ξ1	PROPN
ejpam-6657	130	36	h	h	NOUN
ejpam-6657	130	37	d	d	NOUN
ejpam-6657	130	38	)	)	PUNCT
ejpam-6657	130	39	(	(	PUNCT
ejpam-6657	130	40	ht)d	ht)d	PROPN
ejpam-6657	131	1	d	d	X
ejpam-6657	131	2	!	!	PUNCT
ejpam-6657	132	1	∞∑	∞∑	NUM
ejpam-6657	132	2	ϕ=0	ϕ=0	NOUN
ejpam-6657	133	1	e(r)h	e(r)h	PROPN
ejpam-6657	134	1	[	[	X
ejpam-6657	134	2	h	h	X
ejpam-6657	134	3	]	]	X
ejpam-6657	134	4	n	n	CCONJ
ejpam-6657	134	5	(	(	PUNCT
ejpam-6657	134	6	0	0	NUM
ejpam-6657	134	7	,	,	PUNCT
ejpam-6657	134	8	ξ2	ξ2	ADJ
ejpam-6657	134	9	,	,	PUNCT
ejpam-6657	134	10	ξ3	ξ3	NOUN
ejpam-6657	134	11	)	)	PUNCT
ejpam-6657	134	12	tn	tn	PROPN
ejpam-6657	135	1	n	n	PROPN
ejpam-6657	135	2	!	!	PUNCT
ejpam-6657	136	1	(	(	PUNCT
ejpam-6657	136	2	34	34	NUM
ejpam-6657	136	3	)	)	PUNCT
ejpam-6657	136	4	this	this	PRON
ejpam-6657	136	5	leads	lead	VERB
ejpam-6657	136	6	to	to	ADP
ejpam-6657	136	7	the	the	DET
ejpam-6657	136	8	equivalent	equivalent	ADJ
ejpam-6657	136	9	form	form	NOUN
ejpam-6657	136	10	:	:	PUNCT
ejpam-6657	137	1	∞∑	∞∑	NUM
ejpam-6657	137	2	ϕ=0	ϕ=0	NOUN
ejpam-6657	137	3	e(r)h	e(r)h	PROPN
ejpam-6657	137	4	[	[	X
ejpam-6657	137	5	h	h	X
ejpam-6657	137	6	]	]	X
ejpam-6657	137	7	n	n	PROPN
ejpam-6657	137	8	(	(	PUNCT
ejpam-6657	137	9	ξ1	ξ1	PROPN
ejpam-6657	137	10	,	,	PUNCT
ejpam-6657	137	11	ξ2	ξ2	ADJ
ejpam-6657	137	12	,	,	PUNCT
ejpam-6657	137	13	ξ3	ξ3	PROPN
ejpam-6657	137	14	)	)	PUNCT
ejpam-6657	137	15	tn	tn	PROPN
ejpam-6657	137	16	n	n	ADV
ejpam-6657	137	17	!	!	PUNCT
ejpam-6657	137	18	=	=	NOUN
ejpam-6657	138	1	∞∑	∞∑	NUM
ejpam-6657	138	2	n=0	n=0	PROPN
ejpam-6657	138	3	[	[	PUNCT
ejpam-6657	138	4	ξ1	ξ1	NOUN
ejpam-6657	138	5	h	h	NOUN
ejpam-6657	138	6	]	]	X
ejpam-6657	138	7	∑	∑	PUNCT
ejpam-6657	138	8	d=0	d=0	PROPN
ejpam-6657	138	9	(	(	PUNCT
ejpam-6657	138	10	ξ1	ξ1	PROPN
ejpam-6657	138	11	h	h	NOUN
ejpam-6657	138	12	d	d	NOUN
ejpam-6657	138	13	)	)	PUNCT
ejpam-6657	138	14	hd	hd	VERB
ejpam-6657	138	15	e(r)h	e(r)h	PROPN
ejpam-6657	139	1	[	[	X
ejpam-6657	139	2	h	h	X
ejpam-6657	139	3	]	]	X
ejpam-6657	139	4	n	n	CCONJ
ejpam-6657	139	5	(	(	PUNCT
ejpam-6657	139	6	0	0	NUM
ejpam-6657	139	7	,	,	PUNCT
ejpam-6657	139	8	ξ2	ξ2	ADJ
ejpam-6657	139	9	,	,	PUNCT
ejpam-6657	139	10	ξ3	ξ3	NOUN
ejpam-6657	139	11	)	)	PUNCT
ejpam-6657	139	12	tn+d	tn+d	NUM
ejpam-6657	139	13	n	n	CCONJ
ejpam-6657	139	14	!	!	PUNCT
ejpam-6657	140	1	d	d	X
ejpam-6657	140	2	!	!	PUNCT
ejpam-6657	140	3	.	.	PUNCT
ejpam-6657	141	1	(	(	PUNCT
ejpam-6657	141	2	35	35	NUM
ejpam-6657	141	3	)	)	PUNCT
ejpam-6657	141	4	now	now	ADV
ejpam-6657	141	5	,	,	PUNCT
ejpam-6657	141	6	replacing	replace	VERB
ejpam-6657	141	7	n	n	PRON
ejpam-6657	141	8	→	→	PUNCT
ejpam-6657	141	9	n−	n−	NOUN
ejpam-6657	141	10	d	d	PROPN
ejpam-6657	141	11	on	on	ADP
ejpam-6657	141	12	the	the	DET
ejpam-6657	141	13	right	right	ADJ
ejpam-6657	141	14	-	-	PUNCT
ejpam-6657	141	15	hand	hand	NOUN
ejpam-6657	141	16	side	side	NOUN
ejpam-6657	141	17	of	of	ADP
ejpam-6657	141	18	the	the	DET
ejpam-6657	141	19	above	above	ADJ
ejpam-6657	141	20	expression	expression	NOUN
ejpam-6657	141	21	,	,	PUNCT
ejpam-6657	141	22	we	we	PRON
ejpam-6657	141	23	get	get	VERB
ejpam-6657	141	24	:	:	PUNCT
ejpam-6657	141	25	∞∑	∞∑	PRON
ejpam-6657	141	26	n=0	n=0	NUM
ejpam-6657	141	27	e(r)h	e(r)h	PROPN
ejpam-6657	142	1	[	[	X
ejpam-6657	142	2	h	h	X
ejpam-6657	142	3	]	]	X
ejpam-6657	142	4	n	n	PROPN
ejpam-6657	142	5	(	(	PUNCT
ejpam-6657	142	6	ξ1	ξ1	PROPN
ejpam-6657	142	7	,	,	PUNCT
ejpam-6657	142	8	ξ2	ξ2	ADJ
ejpam-6657	142	9	,	,	PUNCT
ejpam-6657	142	10	ξ3	ξ3	PROPN
ejpam-6657	142	11	)	)	PUNCT
ejpam-6657	142	12	tn	tn	PROPN
ejpam-6657	142	13	n	n	ADV
ejpam-6657	142	14	!	!	PUNCT
ejpam-6657	142	15	=	=	NOUN
ejpam-6657	143	1	∞∑	∞∑	NUM
ejpam-6657	143	2	n=0	n=0	PROPN
ejpam-6657	143	3	[	[	PUNCT
ejpam-6657	143	4	ξ1	ξ1	NOUN
ejpam-6657	143	5	h	h	NOUN
ejpam-6657	143	6	]	]	X
ejpam-6657	143	7	∑	∑	PUNCT
ejpam-6657	143	8	d=0	d=0	PROPN
ejpam-6657	143	9	(	(	PUNCT
ejpam-6657	143	10	ξ1	ξ1	PROPN
ejpam-6657	143	11	h	h	NOUN
ejpam-6657	143	12	d	d	NOUN
ejpam-6657	143	13	)	)	PUNCT
ejpam-6657	143	14	hd	hd	VERB
ejpam-6657	143	15	e(r)h	e(r)h	PROPN
ejpam-6657	144	1	[	[	X
ejpam-6657	144	2	h	h	X
ejpam-6657	144	3	]	]	X
ejpam-6657	144	4	n−d(0	n−d(0	NOUN
ejpam-6657	144	5	,	,	PUNCT
ejpam-6657	144	6	ξ2	ξ2	ADJ
ejpam-6657	144	7	,	,	PUNCT
ejpam-6657	144	8	ξ3	ξ3	PROPN
ejpam-6657	144	9	)	)	PUNCT
ejpam-6657	144	10	tn	tn	PROPN
ejpam-6657	144	11	(	(	PUNCT
ejpam-6657	144	12	n−	n−	NOUN
ejpam-6657	144	13	d	d	NOUN
ejpam-6657	144	14	)	)	PUNCT
ejpam-6657	144	15	!	!	PUNCT
ejpam-6657	145	1	d	d	X
ejpam-6657	145	2	!	!	PUNCT
ejpam-6657	145	3	.	.	PUNCT
ejpam-6657	146	1	(	(	PUNCT
ejpam-6657	146	2	36	36	NUM
ejpam-6657	146	3	)	)	PUNCT
ejpam-6657	146	4	multiplying	multiplying	NOUN
ejpam-6657	146	5	and	and	CCONJ
ejpam-6657	146	6	dividing	divide	VERB
ejpam-6657	146	7	the	the	DET
ejpam-6657	146	8	right	right	ADJ
ejpam-6657	146	9	-	-	PUNCT
ejpam-6657	146	10	hand	hand	NOUN
ejpam-6657	146	11	side	side	NOUN
ejpam-6657	146	12	of	of	ADP
ejpam-6657	146	13	equation	equation	NOUN
ejpam-6657	146	14	(	(	PUNCT
ejpam-6657	146	15	36	36	NUM
ejpam-6657	146	16	)	)	PUNCT
ejpam-6657	146	17	by	by	ADP
ejpam-6657	146	18	n	n	X
ejpam-6657	146	19	!	!	PUNCT
ejpam-6657	147	1	and	and	CCONJ
ejpam-6657	147	2	then	then	ADV
ejpam-6657	147	3	comparing	compare	VERB
ejpam-6657	147	4	coefficients	coefficient	NOUN
ejpam-6657	147	5	of	of	ADP
ejpam-6657	147	6	like	like	ADP
ejpam-6657	147	7	powers	power	NOUN
ejpam-6657	147	8	of	of	ADP
ejpam-6657	147	9	t	t	PROPN
ejpam-6657	147	10	on	on	ADP
ejpam-6657	147	11	both	both	DET
ejpam-6657	147	12	sides	side	NOUN
ejpam-6657	147	13	yields	yield	VERB
ejpam-6657	147	14	the	the	DET
ejpam-6657	147	15	required	require	VERB
ejpam-6657	147	16	identity	identity	NOUN
ejpam-6657	147	17	in	in	ADP
ejpam-6657	147	18	(	(	PUNCT
ejpam-6657	147	19	33	33	NUM
ejpam-6657	147	20	)	)	PUNCT
ejpam-6657	147	21	.	.	PUNCT
ejpam-6657	148	1	theorem	theorem	ADJ
ejpam-6657	148	2	4	4	NUM
ejpam-6657	148	3	.	.	X
ejpam-6657	149	1	for	for	ADP
ejpam-6657	149	2	the	the	DET
ejpam-6657	149	3	three	three	NUM
ejpam-6657	149	4	-	-	PUNCT
ejpam-6657	149	5	variable	variable	NOUN
ejpam-6657	149	6	∆h	∆h	NOUN
ejpam-6657	149	7	-	-	PUNCT
ejpam-6657	149	8	truncated	truncate	VERB
ejpam-6657	149	9	exponential	exponential	NOUN
ejpam-6657	149	10	-	-	PUNCT
ejpam-6657	149	11	based	base	VERB
ejpam-6657	149	12	hermite	hermite	ADJ
ejpam-6657	149	13	polynomials	polynomial	VERB
ejpam-6657	149	14	e(r)h	e(r)h	PROPN
ejpam-6657	150	1	[	[	X
ejpam-6657	150	2	h	h	X
ejpam-6657	150	3	]	]	X
ejpam-6657	150	4	n	n	PROPN
ejpam-6657	150	5	(	(	PUNCT
ejpam-6657	150	6	ξ1	ξ1	PROPN
ejpam-6657	150	7	,	,	PUNCT
ejpam-6657	150	8	ξ2	ξ2	ADJ
ejpam-6657	150	9	,	,	PUNCT
ejpam-6657	150	10	ξ3	ξ3	PROPN
ejpam-6657	150	11	)	)	PUNCT
ejpam-6657	150	12	,	,	PUNCT
ejpam-6657	150	13	the	the	DET
ejpam-6657	150	14	following	follow	VERB
ejpam-6657	150	15	series	series	NOUN
ejpam-6657	150	16	representations	representation	NOUN
ejpam-6657	150	17	hold	hold	VERB
ejpam-6657	150	18	:	:	PUNCT
ejpam-6657	150	19	e(r)h	e(r)h	PROPN
ejpam-6657	151	1	[	[	X
ejpam-6657	151	2	h	h	X
ejpam-6657	151	3	]	]	X
ejpam-6657	151	4	n	n	PROPN
ejpam-6657	151	5	(	(	PUNCT
ejpam-6657	151	6	ξ1	ξ1	PROPN
ejpam-6657	151	7	,	,	PUNCT
ejpam-6657	151	8	ξ2	ξ2	ADJ
ejpam-6657	151	9	,	,	PUNCT
ejpam-6657	151	10	ξ3	ξ3	NOUN
ejpam-6657	151	11	)	)	PUNCT
ejpam-6657	151	12	=	=	PUNCT
ejpam-6657	151	13	n	n	X
ejpam-6657	151	14	!	!	PUNCT
ejpam-6657	152	1	[	[	X
ejpam-6657	152	2	n	n	X
ejpam-6657	152	3	2	2	NUM
ejpam-6657	152	4	]	]	PUNCT
ejpam-6657	152	5	∑	∑	PUNCT
ejpam-6657	152	6	k=0	k=0	X
ejpam-6657	152	7	(	(	PUNCT
ejpam-6657	152	8	−	−	PROPN
ejpam-6657	152	9	ξ2	ξ2	PROPN
ejpam-6657	152	10	h	h	NOUN
ejpam-6657	152	11	)	)	PUNCT
ejpam-6657	152	12	k(−h)ke	k(−h)ke	X
ejpam-6657	152	13	(	(	PUNCT
ejpam-6657	152	14	r	r	NOUN
ejpam-6657	152	15	)	)	PUNCT
ejpam-6657	152	16	n−2k(ξ1	n−2k(ξ1	ADJ
ejpam-6657	152	17	,	,	PUNCT
ejpam-6657	152	18	ξ3;h	ξ3;h	NOUN
ejpam-6657	152	19	)	)	PUNCT
ejpam-6657	152	20	k!(n−	k!(n−	NOUN
ejpam-6657	152	21	2k	2k	NUM
ejpam-6657	152	22	)	)	PUNCT
ejpam-6657	152	23	!	!	PUNCT
ejpam-6657	153	1	,	,	PUNCT
ejpam-6657	153	2	(	(	PUNCT
ejpam-6657	153	3	37	37	NUM
ejpam-6657	153	4	)	)	PUNCT
ejpam-6657	153	5	and	and	CCONJ
ejpam-6657	153	6	e(r)h	e(r)h	PROPN
ejpam-6657	154	1	[	[	X
ejpam-6657	154	2	h	h	X
ejpam-6657	154	3	]	]	X
ejpam-6657	154	4	n	n	PROPN
ejpam-6657	154	5	(	(	PUNCT
ejpam-6657	154	6	ξ1	ξ1	PROPN
ejpam-6657	154	7	,	,	PUNCT
ejpam-6657	154	8	ξ2	ξ2	ADJ
ejpam-6657	154	9	,	,	PUNCT
ejpam-6657	154	10	ξ3	ξ3	NOUN
ejpam-6657	154	11	)	)	PUNCT
ejpam-6657	154	12	=	=	PUNCT
ejpam-6657	154	13	n	n	X
ejpam-6657	154	14	!	!	PUNCT
ejpam-6657	155	1	[	[	X
ejpam-6657	155	2	n	n	X
ejpam-6657	155	3	r	r	NOUN
ejpam-6657	155	4	]	]	PUNCT
ejpam-6657	155	5	∑	∑	PUNCT
ejpam-6657	155	6	k=0	k=0	X
ejpam-6657	155	7	ξk3h	ξk3h	PROPN
ejpam-6657	156	1	[	[	X
ejpam-6657	156	2	h	h	X
ejpam-6657	156	3	]	]	X
ejpam-6657	156	4	n−rk(ξ1	n−rk(ξ1	ADJ
ejpam-6657	156	5	,	,	PUNCT
ejpam-6657	156	6	ξ2	ξ2	NOUN
ejpam-6657	156	7	)	)	PUNCT
ejpam-6657	157	1	(	(	PUNCT
ejpam-6657	157	2	n−	n−	NOUN
ejpam-6657	157	3	rk	rk	NOUN
ejpam-6657	157	4	)	)	PUNCT
ejpam-6657	157	5	!	!	PUNCT
ejpam-6657	157	6	.	.	PUNCT
ejpam-6657	158	1	(	(	PUNCT
ejpam-6657	158	2	38	38	NUM
ejpam-6657	158	3	)	)	PUNCT
ejpam-6657	158	4	proof	proof	NOUN
ejpam-6657	158	5	.	.	PUNCT
ejpam-6657	159	1	by	by	ADP
ejpam-6657	159	2	utilizing	utilize	VERB
ejpam-6657	159	3	equations	equation	NOUN
ejpam-6657	159	4	(	(	PUNCT
ejpam-6657	159	5	7	7	NUM
ejpam-6657	159	6	)	)	PUNCT
ejpam-6657	159	7	,	,	PUNCT
ejpam-6657	159	8	(	(	PUNCT
ejpam-6657	159	9	27	27	NUM
ejpam-6657	159	10	)	)	PUNCT
ejpam-6657	159	11	,	,	PUNCT
ejpam-6657	159	12	and	and	CCONJ
ejpam-6657	159	13	(	(	PUNCT
ejpam-6657	159	14	29	29	NUM
ejpam-6657	159	15	)	)	PUNCT
ejpam-6657	159	16	,	,	PUNCT
ejpam-6657	159	17	the	the	DET
ejpam-6657	159	18	results	result	NOUN
ejpam-6657	159	19	in	in	ADP
ejpam-6657	159	20	(	(	PUNCT
ejpam-6657	159	21	37	37	NUM
ejpam-6657	159	22	)	)	PUNCT
ejpam-6657	159	23	and	and	CCONJ
ejpam-6657	159	24	(	(	PUNCT
ejpam-6657	159	25	38	38	NUM
ejpam-6657	159	26	)	)	PUNCT
ejpam-6657	159	27	follow	follow	VERB
ejpam-6657	159	28	directly	directly	ADV
ejpam-6657	159	29	.	.	PUNCT
ejpam-6657	160	1	h.	h.	PROPN
ejpam-6657	160	2	qawaqneh	qawaqneh	PROPN
ejpam-6657	160	3	et	et	PROPN
ejpam-6657	160	4	al	al	PROPN
ejpam-6657	160	5	.	.	PUNCT
ejpam-6657	160	6	/	/	SYM
ejpam-6657	160	7	eur	eur	PROPN
ejpam-6657	160	8	.	.	PUNCT
ejpam-6657	161	1	j.	j.	PROPN
ejpam-6657	161	2	pure	pure	PROPN
ejpam-6657	161	3	appl	appl	PROPN
ejpam-6657	161	4	.	.	PROPN
ejpam-6657	161	5	math	math	PROPN
ejpam-6657	161	6	,	,	PUNCT
ejpam-6657	161	7	18	18	NUM
ejpam-6657	161	8	(	(	PUNCT
ejpam-6657	161	9	3	3	NUM
ejpam-6657	161	10	)	)	PUNCT
ejpam-6657	161	11	(	(	PUNCT
ejpam-6657	161	12	2025	2025	NUM
ejpam-6657	161	13	)	)	PUNCT
ejpam-6657	161	14	,	,	PUNCT
ejpam-6657	161	15	6657	6657	NUM
ejpam-6657	161	16	8	8	NUM
ejpam-6657	161	17	of	of	ADP
ejpam-6657	161	18	16	16	NUM
ejpam-6657	161	19	3	3	NUM
ejpam-6657	161	20	.	.	PUNCT
ejpam-6657	161	21	summation	summation	NOUN
ejpam-6657	161	22	formulae	formulae	NOUN
ejpam-6657	161	23	in	in	ADP
ejpam-6657	161	24	this	this	DET
ejpam-6657	161	25	section	section	NOUN
ejpam-6657	162	1	,	,	PUNCT
ejpam-6657	162	2	we	we	PRON
ejpam-6657	162	3	present	present	VERB
ejpam-6657	162	4	concise	concise	ADJ
ejpam-6657	162	5	summation	summation	NOUN
ejpam-6657	162	6	formulae	formulae	NOUN
ejpam-6657	162	7	for	for	ADP
ejpam-6657	162	8	special	special	ADJ
ejpam-6657	162	9	two	two	NUM
ejpam-6657	162	10	-	-	PUNCT
ejpam-6657	162	11	variable	variable	NOUN
ejpam-6657	162	12	polynomials	polynomial	NOUN
ejpam-6657	162	13	.	.	PUNCT
ejpam-6657	163	1	these	these	DET
ejpam-6657	163	2	expressions	expression	NOUN
ejpam-6657	163	3	offer	offer	VERB
ejpam-6657	163	4	efficient	efficient	ADJ
ejpam-6657	163	5	methods	method	NOUN
ejpam-6657	163	6	to	to	PART
ejpam-6657	163	7	compute	compute	VERB
ejpam-6657	163	8	sums	sum	NOUN
ejpam-6657	163	9	and	and	CCONJ
ejpam-6657	163	10	explore	explore	VERB
ejpam-6657	163	11	structural	structural	ADJ
ejpam-6657	163	12	properties	property	NOUN
ejpam-6657	163	13	,	,	PUNCT
ejpam-6657	163	14	aiding	aid	VERB
ejpam-6657	163	15	in	in	ADP
ejpam-6657	163	16	analysis	analysis	NOUN
ejpam-6657	163	17	across	across	ADP
ejpam-6657	163	18	combinatorics	combinatoric	NOUN
ejpam-6657	163	19	,	,	PUNCT
ejpam-6657	163	20	probability	probability	NOUN
ejpam-6657	163	21	,	,	PUNCT
ejpam-6657	163	22	and	and	CCONJ
ejpam-6657	163	23	mathematical	mathematical	ADJ
ejpam-6657	163	24	physics	physics	NOUN
ejpam-6657	163	25	.	.	PUNCT
ejpam-6657	164	1	we	we	PRON
ejpam-6657	164	2	now	now	ADV
ejpam-6657	164	3	establish	establish	VERB
ejpam-6657	164	4	the	the	DET
ejpam-6657	164	5	following	follow	VERB
ejpam-6657	164	6	results	result	NOUN
ejpam-6657	164	7	.	.	PUNCT
ejpam-6657	165	1	theorem	theorem	NOUN
ejpam-6657	165	2	5	5	NUM
ejpam-6657	165	3	.	.	PUNCT
ejpam-6657	166	1	let	let	VERB
ejpam-6657	166	2	e(r)h	e(r)h	PROPN
ejpam-6657	167	1	[	[	X
ejpam-6657	167	2	h	h	X
ejpam-6657	167	3	]	]	X
ejpam-6657	167	4	n	n	PROPN
ejpam-6657	167	5	(	(	PUNCT
ejpam-6657	167	6	ξ1	ξ1	PROPN
ejpam-6657	167	7	,	,	PUNCT
ejpam-6657	167	8	ξ2	ξ2	ADJ
ejpam-6657	167	9	,	,	PUNCT
ejpam-6657	167	10	ξ3	ξ3	NOUN
ejpam-6657	167	11	)	)	PUNCT
ejpam-6657	167	12	denote	denote	VERB
ejpam-6657	167	13	the	the	DET
ejpam-6657	167	14	∆h	∆h	NOUN
ejpam-6657	167	15	-	-	PUNCT
ejpam-6657	167	16	truncated	truncate	VERB
ejpam-6657	167	17	exponential	exponential	NOUN
ejpam-6657	167	18	-	-	PUNCT
ejpam-6657	167	19	based	base	VERB
ejpam-6657	167	20	hermite	hermite	ADJ
ejpam-6657	167	21	polynomials	polynomial	NOUN
ejpam-6657	167	22	of	of	ADP
ejpam-6657	167	23	order	order	NOUN
ejpam-6657	167	24	r.	r.	PROPN
ejpam-6657	167	25	then	then	ADV
ejpam-6657	167	26	,	,	PUNCT
ejpam-6657	167	27	the	the	DET
ejpam-6657	167	28	following	follow	VERB
ejpam-6657	167	29	identity	identity	NOUN
ejpam-6657	167	30	holds	hold	VERB
ejpam-6657	167	31	:	:	PUNCT
ejpam-6657	168	1	e(r)h	e(r)h	PROPN
ejpam-6657	169	1	[	[	X
ejpam-6657	169	2	h	h	X
ejpam-6657	169	3	]	]	X
ejpam-6657	169	4	n	n	PROPN
ejpam-6657	169	5	(	(	PUNCT
ejpam-6657	169	6	ξ1	ξ1	NOUN
ejpam-6657	169	7	+	+	CCONJ
ejpam-6657	169	8	1	1	NUM
ejpam-6657	169	9	,	,	PUNCT
ejpam-6657	169	10	ξ2	ξ2	ADJ
ejpam-6657	169	11	,	,	PUNCT
ejpam-6657	169	12	ξ3	ξ3	NOUN
ejpam-6657	169	13	)	)	PUNCT
ejpam-6657	169	14	=	=	SYM
ejpam-6657	170	1	n∑	n∑	NOUN
ejpam-6657	170	2	k=0	k=0	PROPN
ejpam-6657	170	3	(	(	PUNCT
ejpam-6657	170	4	n	n	X
ejpam-6657	170	5	k	k	X
ejpam-6657	170	6	)	)	PUNCT
ejpam-6657	170	7	e(r)h	e(r)h	PROPN
ejpam-6657	171	1	[	[	X
ejpam-6657	171	2	h	h	X
ejpam-6657	171	3	]	]	X
ejpam-6657	171	4	n−k(ξ1	n−k(ξ1	ADJ
ejpam-6657	171	5	,	,	PUNCT
ejpam-6657	171	6	ξ2	ξ2	NOUN
ejpam-6657	171	7	,	,	PUNCT
ejpam-6657	171	8	ξ3)(−	ξ3)(−	PROPN
ejpam-6657	171	9	1	1	NUM
ejpam-6657	171	10	h	h	NOUN
ejpam-6657	171	11	)	)	PUNCT
ejpam-6657	171	12	k(−h)k	k(−h)k	PROPN
ejpam-6657	171	13	.	.	PUNCT
ejpam-6657	172	1	(	(	PUNCT
ejpam-6657	172	2	39	39	NUM
ejpam-6657	172	3	)	)	PUNCT
ejpam-6657	172	4	proof	proof	NOUN
ejpam-6657	172	5	.	.	PUNCT
ejpam-6657	173	1	utilizing	utilize	VERB
ejpam-6657	173	2	the	the	DET
ejpam-6657	173	3	generating	generate	VERB
ejpam-6657	173	4	function	function	NOUN
ejpam-6657	173	5	(	(	PUNCT
ejpam-6657	173	6	29	29	NUM
ejpam-6657	173	7	)	)	PUNCT
ejpam-6657	173	8	,	,	PUNCT
ejpam-6657	173	9	we	we	PRON
ejpam-6657	173	10	proceed	proceed	VERB
ejpam-6657	173	11	as	as	SCONJ
ejpam-6657	173	12	follows	follow	VERB
ejpam-6657	173	13	:	:	PUNCT
ejpam-6657	173	14	∞∑	∞∑	PRON
ejpam-6657	173	15	n=0	n=0	NUM
ejpam-6657	173	16	e(r)h	e(r)h	PROPN
ejpam-6657	174	1	[	[	X
ejpam-6657	174	2	h	h	X
ejpam-6657	174	3	]	]	X
ejpam-6657	174	4	n	n	PROPN
ejpam-6657	174	5	(	(	PUNCT
ejpam-6657	174	6	ξ1	ξ1	PROPN
ejpam-6657	174	7	+	+	PROPN
ejpam-6657	174	8	1	1	NUM
ejpam-6657	174	9	,	,	PUNCT
ejpam-6657	174	10	ξ2	ξ2	ADJ
ejpam-6657	174	11	,	,	PUNCT
ejpam-6657	174	12	ξ3	ξ3	NOUN
ejpam-6657	174	13	)	)	PUNCT
ejpam-6657	174	14	tn	tn	PROPN
ejpam-6657	174	15	n	n	PROPN
ejpam-6657	174	16	!	!	PUNCT
ejpam-6657	175	1	−	−	PROPN
ejpam-6657	176	1	∞∑	∞∑	PRON
ejpam-6657	176	2	n=0	n=0	NUM
ejpam-6657	176	3	e(r)h	e(r)h	PROPN
ejpam-6657	177	1	[	[	X
ejpam-6657	177	2	h	h	X
ejpam-6657	177	3	]	]	X
ejpam-6657	177	4	n	n	PROPN
ejpam-6657	177	5	(	(	PUNCT
ejpam-6657	177	6	ξ1	ξ1	PROPN
ejpam-6657	177	7	,	,	PUNCT
ejpam-6657	177	8	ξ2	ξ2	ADJ
ejpam-6657	177	9	,	,	PUNCT
ejpam-6657	177	10	ξ3	ξ3	PROPN
ejpam-6657	177	11	)	)	PUNCT
ejpam-6657	177	12	tn	tn	PROPN
ejpam-6657	177	13	n	n	ADV
ejpam-6657	177	14	!	!	PUNCT
ejpam-6657	178	1	=	=	SYM
ejpam-6657	178	2	1	1	NUM
ejpam-6657	178	3	1−	1−	NUM
ejpam-6657	178	4	ξ3tr	ξ3tr	NUM
ejpam-6657	178	5	(	(	PUNCT
ejpam-6657	178	6	1+ht	1+ht	X
ejpam-6657	178	7	)	)	PUNCT
ejpam-6657	178	8	ξ1	ξ1	NOUN
ejpam-6657	178	9	h	h	NOUN
ejpam-6657	178	10	(	(	PUNCT
ejpam-6657	178	11	1+ht2	1+ht2	ADJ
ejpam-6657	178	12	)	)	PUNCT
ejpam-6657	178	13	ξ2	ξ2	NOUN
ejpam-6657	178	14	h	h	NOUN
ejpam-6657	178	15	(	(	PUNCT
ejpam-6657	178	16	(	(	PUNCT
ejpam-6657	178	17	1	1	NUM
ejpam-6657	178	18	+	+	NUM
ejpam-6657	178	19	ht	ht	X
ejpam-6657	178	20	)	)	PUNCT
ejpam-6657	178	21	1	1	NUM
ejpam-6657	178	22	h	h	NOUN
ejpam-6657	178	23	−	−	NOUN
ejpam-6657	178	24	1	1	NUM
ejpam-6657	178	25	)	)	PUNCT
ejpam-6657	178	26	=	=	NOUN
ejpam-6657	179	1	∞∑	∞∑	PRON
ejpam-6657	179	2	n=0	n=0	NUM
ejpam-6657	179	3	e(r)h	e(r)h	PROPN
ejpam-6657	180	1	[	[	X
ejpam-6657	180	2	h	h	X
ejpam-6657	180	3	]	]	X
ejpam-6657	180	4	n	n	PROPN
ejpam-6657	180	5	(	(	PUNCT
ejpam-6657	180	6	ξ1	ξ1	PROPN
ejpam-6657	180	7	,	,	PUNCT
ejpam-6657	180	8	ξ2	ξ2	ADJ
ejpam-6657	180	9	,	,	PUNCT
ejpam-6657	180	10	ξ3	ξ3	PROPN
ejpam-6657	180	11	)	)	PUNCT
ejpam-6657	180	12	tn	tn	PROPN
ejpam-6657	180	13	n	n	PROPN
ejpam-6657	180	14	!	!	PUNCT
ejpam-6657	181	1	(	(	PUNCT
ejpam-6657	181	2	∞∑	∞∑	X
ejpam-6657	181	3	k=0	k=0	PROPN
ejpam-6657	181	4	(	(	PUNCT
ejpam-6657	181	5	−1	−1	NOUN
ejpam-6657	181	6	h	h	NOUN
ejpam-6657	181	7	)	)	PUNCT
ejpam-6657	181	8	k(−h)k	k(−h)k	PROPN
ejpam-6657	181	9	tk	tk	PROPN
ejpam-6657	182	1	k	k	PROPN
ejpam-6657	182	2	!	!	PUNCT
ejpam-6657	183	1	−	−	PROPN
ejpam-6657	183	2	1	1	NUM
ejpam-6657	183	3	)	)	PUNCT
ejpam-6657	184	1	=	=	NOUN
ejpam-6657	185	1	∞∑	∞∑	NUM
ejpam-6657	185	2	n=0	n=0	NUM
ejpam-6657	185	3	n∑	n∑	NOUN
ejpam-6657	185	4	k=0	k=0	PROPN
ejpam-6657	185	5	(	(	PUNCT
ejpam-6657	185	6	n	n	X
ejpam-6657	185	7	k	k	X
ejpam-6657	185	8	)	)	PUNCT
ejpam-6657	185	9	e(r)h	e(r)h	PROPN
ejpam-6657	186	1	[	[	X
ejpam-6657	186	2	h	h	X
ejpam-6657	186	3	]	]	X
ejpam-6657	186	4	n−k(ξ1	n−k(ξ1	ADJ
ejpam-6657	186	5	,	,	PUNCT
ejpam-6657	186	6	ξ2	ξ2	NOUN
ejpam-6657	186	7	,	,	PUNCT
ejpam-6657	186	8	ξ3)(−	ξ3)(−	PROPN
ejpam-6657	186	9	1	1	NUM
ejpam-6657	186	10	h	h	NOUN
ejpam-6657	186	11	)	)	PUNCT
ejpam-6657	186	12	k(−h)k	k(−h)k	PROPN
ejpam-6657	186	13	tn	tn	PROPN
ejpam-6657	186	14	n	n	PROPN
ejpam-6657	186	15	!	!	PUNCT
ejpam-6657	187	1	−	−	PROPN
ejpam-6657	188	1	∞∑	∞∑	PRON
ejpam-6657	188	2	n=0	n=0	NUM
ejpam-6657	188	3	e(r)h	e(r)h	PROPN
ejpam-6657	189	1	[	[	X
ejpam-6657	189	2	h	h	X
ejpam-6657	189	3	]	]	X
ejpam-6657	189	4	n	n	PROPN
ejpam-6657	189	5	(	(	PUNCT
ejpam-6657	189	6	ξ1	ξ1	PROPN
ejpam-6657	189	7	,	,	PUNCT
ejpam-6657	189	8	ξ2	ξ2	ADJ
ejpam-6657	189	9	,	,	PUNCT
ejpam-6657	189	10	ξ3	ξ3	PROPN
ejpam-6657	189	11	)	)	PUNCT
ejpam-6657	189	12	tn	tn	PROPN
ejpam-6657	189	13	n	n	PROPN
ejpam-6657	189	14	!	!	PUNCT
ejpam-6657	190	1	(	(	PUNCT
ejpam-6657	190	2	40	40	NUM
ejpam-6657	190	3	)	)	PUNCT
ejpam-6657	190	4	by	by	ADP
ejpam-6657	190	5	equating	equate	VERB
ejpam-6657	190	6	the	the	DET
ejpam-6657	190	7	coefficients	coefficient	NOUN
ejpam-6657	190	8	of	of	ADP
ejpam-6657	190	9	powers	power	NOUN
ejpam-6657	190	10	of	of	ADP
ejpam-6657	190	11	t	t	PROPN
ejpam-6657	190	12	on	on	ADP
ejpam-6657	190	13	both	both	DET
ejpam-6657	190	14	sides	side	NOUN
ejpam-6657	190	15	,	,	PUNCT
ejpam-6657	190	16	the	the	DET
ejpam-6657	190	17	identity	identity	NOUN
ejpam-6657	190	18	(	(	PUNCT
ejpam-6657	190	19	39	39	NUM
ejpam-6657	190	20	)	)	PUNCT
ejpam-6657	190	21	is	be	AUX
ejpam-6657	190	22	established	establish	VERB
ejpam-6657	190	23	.	.	PUNCT
ejpam-6657	191	1	next	next	ADV
ejpam-6657	191	2	,	,	PUNCT
ejpam-6657	191	3	we	we	PRON
ejpam-6657	191	4	derive	derive	VERB
ejpam-6657	191	5	the	the	DET
ejpam-6657	191	6	explicit	explicit	ADJ
ejpam-6657	191	7	expressions	expression	NOUN
ejpam-6657	191	8	satisfied	satisfy	VERB
ejpam-6657	191	9	by	by	ADP
ejpam-6657	191	10	the	the	DET
ejpam-6657	191	11	bivariate	bivariate	ADJ
ejpam-6657	191	12	∆h	∆h	PROPN
ejpam-6657	191	13	-	-	PUNCT
ejpam-6657	191	14	truncated	truncate	VERB
ejpam-6657	191	15	exponentialbased	exponentialbase	VERB
ejpam-6657	191	16	hermite	hermite	ADJ
ejpam-6657	191	17	polynomials	polynomial	VERB
ejpam-6657	191	18	e(r)h	e(r)h	PROPN
ejpam-6657	192	1	[	[	X
ejpam-6657	192	2	h	h	X
ejpam-6657	192	3	]	]	X
ejpam-6657	192	4	n	n	PROPN
ejpam-6657	192	5	(	(	PUNCT
ejpam-6657	192	6	ξ1	ξ1	PROPN
ejpam-6657	192	7	,	,	PUNCT
ejpam-6657	192	8	ξ2	ξ2	ADJ
ejpam-6657	192	9	,	,	PUNCT
ejpam-6657	192	10	ξ3	ξ3	NOUN
ejpam-6657	192	11	)	)	PUNCT
ejpam-6657	192	12	of	of	ADP
ejpam-6657	192	13	order	order	NOUN
ejpam-6657	192	14	r	r	NOUN
ejpam-6657	192	15	,	,	PUNCT
ejpam-6657	192	16	through	through	ADP
ejpam-6657	192	17	the	the	DET
ejpam-6657	192	18	following	follow	VERB
ejpam-6657	192	19	result	result	NOUN
ejpam-6657	192	20	:	:	PUNCT
ejpam-6657	192	21	theorem	theorem	VERB
ejpam-6657	192	22	6	6	NUM
ejpam-6657	192	23	.	.	PUNCT
ejpam-6657	192	24	for	for	SCONJ
ejpam-6657	192	25	the	the	DET
ejpam-6657	192	26	three	three	NUM
ejpam-6657	192	27	-	-	PUNCT
ejpam-6657	192	28	variable	variable	NOUN
ejpam-6657	192	29	∆h	∆h	NOUN
ejpam-6657	192	30	-	-	PUNCT
ejpam-6657	192	31	truncated	truncate	VERB
ejpam-6657	192	32	exponential	exponential	NOUN
ejpam-6657	192	33	-	-	PUNCT
ejpam-6657	192	34	based	base	VERB
ejpam-6657	192	35	hermite	hermite	ADJ
ejpam-6657	192	36	polynomials	polynomial	VERB
ejpam-6657	192	37	e(r)h	e(r)h	PROPN
ejpam-6657	193	1	[	[	X
ejpam-6657	193	2	h	h	X
ejpam-6657	193	3	]	]	X
ejpam-6657	193	4	n	n	PROPN
ejpam-6657	193	5	(	(	PUNCT
ejpam-6657	193	6	ξ1	ξ1	PROPN
ejpam-6657	193	7	,	,	PUNCT
ejpam-6657	193	8	ξ2	ξ2	ADJ
ejpam-6657	193	9	,	,	PUNCT
ejpam-6657	193	10	ξ3	ξ3	NOUN
ejpam-6657	193	11	)	)	PUNCT
ejpam-6657	193	12	of	of	ADP
ejpam-6657	193	13	order	order	NOUN
ejpam-6657	193	14	r	r	NOUN
ejpam-6657	193	15	,	,	PUNCT
ejpam-6657	193	16	the	the	DET
ejpam-6657	193	17	following	follow	VERB
ejpam-6657	193	18	structural	structural	ADJ
ejpam-6657	193	19	identities	identity	NOUN
ejpam-6657	193	20	are	be	AUX
ejpam-6657	193	21	valid	valid	ADJ
ejpam-6657	193	22	:	:	PUNCT
ejpam-6657	193	23	e(r)h	e(r)h	PROPN
ejpam-6657	194	1	[	[	X
ejpam-6657	194	2	h	h	X
ejpam-6657	194	3	]	]	X
ejpam-6657	194	4	n	n	PROPN
ejpam-6657	194	5	(	(	PUNCT
ejpam-6657	194	6	ξ1	ξ1	PROPN
ejpam-6657	194	7	,	,	PUNCT
ejpam-6657	194	8	ξ2	ξ2	ADJ
ejpam-6657	194	9	,	,	PUNCT
ejpam-6657	194	10	ξ3	ξ3	NOUN
ejpam-6657	194	11	)	)	PUNCT
ejpam-6657	194	12	=	=	SYM
ejpam-6657	195	1	n∑	n∑	NOUN
ejpam-6657	195	2	k=0	k=0	PROPN
ejpam-6657	195	3	(	(	PUNCT
ejpam-6657	195	4	n	n	X
ejpam-6657	195	5	k	k	X
ejpam-6657	195	6	)	)	PUNCT
ejpam-6657	195	7	e(r)h	e(r)h	PROPN
ejpam-6657	196	1	[	[	X
ejpam-6657	196	2	h	h	X
ejpam-6657	196	3	]	]	X
ejpam-6657	196	4	n−k(0	n−k(0	ADJ
ejpam-6657	196	5	,	,	PUNCT
ejpam-6657	196	6	ξ2	ξ2	ADJ
ejpam-6657	196	7	,	,	PUNCT
ejpam-6657	196	8	ξ3	ξ3	NOUN
ejpam-6657	196	9	)	)	PUNCT
ejpam-6657	196	10	(	(	PUNCT
ejpam-6657	196	11	−ξ1	−ξ1	PROPN
ejpam-6657	196	12	h	h	PROPN
ejpam-6657	196	13	)	)	PUNCT
ejpam-6657	197	1	k	k	NOUN
ejpam-6657	197	2	(	(	PUNCT
ejpam-6657	197	3	−h)k	−h)k	PROPN
ejpam-6657	197	4	,	,	PUNCT
ejpam-6657	197	5	(	(	PUNCT
ejpam-6657	197	6	41	41	NUM
ejpam-6657	197	7	)	)	PUNCT
ejpam-6657	197	8	e(r)h	e(r)h	PROPN
ejpam-6657	198	1	[	[	X
ejpam-6657	198	2	h	h	X
ejpam-6657	198	3	]	]	X
ejpam-6657	198	4	n	n	PROPN
ejpam-6657	198	5	(	(	PUNCT
ejpam-6657	198	6	ξ1	ξ1	PROPN
ejpam-6657	198	7	,	,	PUNCT
ejpam-6657	198	8	ξ2	ξ2	ADJ
ejpam-6657	198	9	,	,	PUNCT
ejpam-6657	198	10	ξ3	ξ3	NOUN
ejpam-6657	198	11	)	)	PUNCT
ejpam-6657	198	12	=	=	SYM
ejpam-6657	199	1	n∑	n∑	NOUN
ejpam-6657	199	2	k=0	k=0	PROPN
ejpam-6657	199	3	(	(	PUNCT
ejpam-6657	199	4	n	n	X
ejpam-6657	199	5	k	k	X
ejpam-6657	199	6	)	)	PUNCT
ejpam-6657	199	7	e(r)h	e(r)h	PROPN
ejpam-6657	200	1	[	[	X
ejpam-6657	200	2	h	h	X
ejpam-6657	200	3	]	]	X
ejpam-6657	200	4	n−k(ξ1	n−k(ξ1	PROPN
ejpam-6657	200	5	−	−	PROPN
ejpam-6657	200	6	p	p	PROPN
ejpam-6657	200	7	,	,	PUNCT
ejpam-6657	200	8	ξ2	ξ2	ADJ
ejpam-6657	200	9	,	,	PUNCT
ejpam-6657	200	10	ξ3	ξ3	NOUN
ejpam-6657	200	11	)	)	PUNCT
ejpam-6657	200	12	(	(	PUNCT
ejpam-6657	200	13	−p	−p	NOUN
ejpam-6657	200	14	h	h	NOUN
ejpam-6657	200	15	)	)	PUNCT
ejpam-6657	201	1	k	k	NOUN
ejpam-6657	201	2	(	(	PUNCT
ejpam-6657	201	3	−h)k	−h)k	PROPN
ejpam-6657	201	4	,	,	PUNCT
ejpam-6657	201	5	(	(	PUNCT
ejpam-6657	201	6	42	42	NUM
ejpam-6657	201	7	)	)	PUNCT
ejpam-6657	201	8	e(r)h	e(r)h	PROPN
ejpam-6657	202	1	[	[	X
ejpam-6657	202	2	h	h	X
ejpam-6657	202	3	]	]	X
ejpam-6657	202	4	n	n	PROPN
ejpam-6657	202	5	(	(	PUNCT
ejpam-6657	202	6	ξ1	ξ1	PROPN
ejpam-6657	202	7	+	+	CCONJ
ejpam-6657	202	8	s	s	PROPN
ejpam-6657	202	9	,	,	PUNCT
ejpam-6657	202	10	ξ2	ξ2	ADJ
ejpam-6657	202	11	,	,	PUNCT
ejpam-6657	202	12	ξ3	ξ3	NOUN
ejpam-6657	202	13	)	)	PUNCT
ejpam-6657	202	14	=	=	SYM
ejpam-6657	203	1	n∑	n∑	NOUN
ejpam-6657	203	2	k=0	k=0	PROPN
ejpam-6657	203	3	(	(	PUNCT
ejpam-6657	203	4	n	n	X
ejpam-6657	203	5	k	k	X
ejpam-6657	203	6	)	)	PUNCT
ejpam-6657	203	7	e(r)h	e(r)h	PROPN
ejpam-6657	204	1	[	[	X
ejpam-6657	204	2	h	h	X
ejpam-6657	204	3	]	]	X
ejpam-6657	204	4	n−k(ξ1	n−k(ξ1	PROPN
ejpam-6657	204	5	,	,	PUNCT
ejpam-6657	204	6	ξ2	ξ2	ADJ
ejpam-6657	204	7	,	,	PUNCT
ejpam-6657	204	8	ξ3	ξ3	NOUN
ejpam-6657	204	9	)	)	PUNCT
ejpam-6657	204	10	(	(	PUNCT
ejpam-6657	204	11	−	−	PROPN
ejpam-6657	204	12	s	s	NOUN
ejpam-6657	204	13	h	h	NOUN
ejpam-6657	204	14	)	)	PUNCT
ejpam-6657	205	1	k	k	NOUN
ejpam-6657	205	2	(	(	PUNCT
ejpam-6657	205	3	−h)k	−h)k	PROPN
ejpam-6657	205	4	,	,	PUNCT
ejpam-6657	205	5	(	(	PUNCT
ejpam-6657	205	6	43	43	NUM
ejpam-6657	205	7	)	)	PUNCT
ejpam-6657	205	8	e(r)h	e(r)h	PROPN
ejpam-6657	206	1	[	[	X
ejpam-6657	206	2	h	h	X
ejpam-6657	206	3	]	]	X
ejpam-6657	206	4	n	n	PROPN
ejpam-6657	206	5	(	(	PUNCT
ejpam-6657	206	6	ξ1	ξ1	PROPN
ejpam-6657	206	7	,	,	PUNCT
ejpam-6657	206	8	ξ2	ξ2	ADJ
ejpam-6657	206	9	,	,	PUNCT
ejpam-6657	206	10	ξ3	ξ3	NOUN
ejpam-6657	206	11	)	)	PUNCT
ejpam-6657	206	12	=	=	SYM
ejpam-6657	207	1	n∑	n∑	NOUN
ejpam-6657	207	2	l=0	l=0	PROPN
ejpam-6657	207	3	l∑	l∑	PUNCT
ejpam-6657	208	1	k=0	k=0	PROPN
ejpam-6657	208	2	(	(	PUNCT
ejpam-6657	208	3	n	n	X
ejpam-6657	208	4	l	l	NOUN
ejpam-6657	208	5	)	)	PUNCT
ejpam-6657	209	1	e(r)h	e(r)h	PROPN
ejpam-6657	210	1	[	[	X
ejpam-6657	210	2	h	h	X
ejpam-6657	210	3	]	]	X
ejpam-6657	210	4	n−l(0	n−l(0	NOUN
ejpam-6657	210	5	,	,	PUNCT
ejpam-6657	210	6	ξ2	ξ2	ADJ
ejpam-6657	210	7	,	,	PUNCT
ejpam-6657	210	8	ξ3	ξ3	NOUN
ejpam-6657	210	9	)	)	PUNCT
ejpam-6657	210	10	(	(	PUNCT
ejpam-6657	210	11	ξ1	ξ1	NOUN
ejpam-6657	210	12	h	h	NOUN
ejpam-6657	210	13	)	)	PUNCT
ejpam-6657	210	14	k	k	PROPN
ejpam-6657	210	15	hls1(l	hls1(l	X
ejpam-6657	210	16	,	,	PUNCT
ejpam-6657	210	17	k	k	NOUN
ejpam-6657	210	18	)	)	PUNCT
ejpam-6657	210	19	,	,	PUNCT
ejpam-6657	210	20	(	(	PUNCT
ejpam-6657	210	21	44	44	NUM
ejpam-6657	210	22	)	)	PUNCT
ejpam-6657	210	23	e(r)h	e(r)h	PROPN
ejpam-6657	211	1	[	[	X
ejpam-6657	211	2	h	h	X
ejpam-6657	211	3	]	]	X
ejpam-6657	211	4	n	n	PROPN
ejpam-6657	211	5	(	(	PUNCT
ejpam-6657	211	6	ξ1	ξ1	PROPN
ejpam-6657	211	7	,	,	PUNCT
ejpam-6657	211	8	ξ2	ξ2	ADJ
ejpam-6657	211	9	,	,	PUNCT
ejpam-6657	211	10	ξ3	ξ3	NOUN
ejpam-6657	211	11	)	)	PUNCT
ejpam-6657	211	12	=	=	SYM
ejpam-6657	212	1	n∑	n∑	NOUN
ejpam-6657	212	2	l=0	l=0	PROPN
ejpam-6657	212	3	l∑	l∑	PUNCT
ejpam-6657	213	1	k=0	k=0	PROPN
ejpam-6657	213	2	(	(	PUNCT
ejpam-6657	213	3	n	n	X
ejpam-6657	213	4	l	l	NOUN
ejpam-6657	213	5	)	)	PUNCT
ejpam-6657	214	1	e(r)h	e(r)h	PROPN
ejpam-6657	215	1	[	[	X
ejpam-6657	215	2	h	h	X
ejpam-6657	215	3	]	]	X
ejpam-6657	215	4	n−l(0	n−l(0	NOUN
ejpam-6657	215	5	,	,	PUNCT
ejpam-6657	215	6	ξ2	ξ2	ADJ
ejpam-6657	215	7	,	,	PUNCT
ejpam-6657	215	8	ξ3	ξ3	NOUN
ejpam-6657	215	9	)	)	PUNCT
ejpam-6657	215	10	(	(	PUNCT
ejpam-6657	215	11	ξ1	ξ1	NOUN
ejpam-6657	215	12	h	h	NOUN
ejpam-6657	215	13	)	)	PUNCT
ejpam-6657	216	1	k	k	X
ejpam-6657	216	2	,	,	PUNCT
ejpam-6657	216	3	h	h	PROPN
ejpam-6657	216	4	hls1,h(l	hls1,h(l	PROPN
ejpam-6657	216	5	,	,	PUNCT
ejpam-6657	216	6	k	k	NOUN
ejpam-6657	216	7	)	)	PUNCT
ejpam-6657	216	8	.	.	PUNCT
ejpam-6657	217	1	(	(	PUNCT
ejpam-6657	217	2	45	45	NUM
ejpam-6657	217	3	)	)	PUNCT
ejpam-6657	217	4	h.	h.	PROPN
ejpam-6657	217	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	217	6	et	et	PROPN
ejpam-6657	217	7	al	al	PROPN
ejpam-6657	217	8	.	.	PUNCT
ejpam-6657	217	9	/	/	SYM
ejpam-6657	217	10	eur	eur	PROPN
ejpam-6657	217	11	.	.	PUNCT
ejpam-6657	218	1	j.	j.	PROPN
ejpam-6657	218	2	pure	pure	PROPN
ejpam-6657	218	3	appl	appl	PROPN
ejpam-6657	218	4	.	.	PROPN
ejpam-6657	218	5	math	math	PROPN
ejpam-6657	218	6	,	,	PUNCT
ejpam-6657	218	7	18	18	NUM
ejpam-6657	218	8	(	(	PUNCT
ejpam-6657	218	9	3	3	NUM
ejpam-6657	218	10	)	)	PUNCT
ejpam-6657	218	11	(	(	PUNCT
ejpam-6657	218	12	2025	2025	NUM
ejpam-6657	218	13	)	)	PUNCT
ejpam-6657	218	14	,	,	PUNCT
ejpam-6657	218	15	6657	6657	NUM
ejpam-6657	218	16	9	9	NUM
ejpam-6657	218	17	of	of	ADP
ejpam-6657	218	18	16	16	NUM
ejpam-6657	218	19	proof	proof	NOUN
ejpam-6657	218	20	.	.	PUNCT
ejpam-6657	219	1	we	we	PRON
ejpam-6657	219	2	expand	expand	VERB
ejpam-6657	219	3	the	the	DET
ejpam-6657	219	4	generating	generate	VERB
ejpam-6657	219	5	function	function	NOUN
ejpam-6657	219	6	(	(	PUNCT
ejpam-6657	219	7	29	29	NUM
ejpam-6657	219	8	)	)	PUNCT
ejpam-6657	219	9	in	in	ADP
ejpam-6657	219	10	the	the	DET
ejpam-6657	219	11	following	following	ADJ
ejpam-6657	219	12	way	way	NOUN
ejpam-6657	219	13	:(	:(	PUNCT
ejpam-6657	220	1	∞∑	∞∑	NUM
ejpam-6657	220	2	n=0	n=0	NUM
ejpam-6657	220	3	e(r)h	e(r)h	PROPN
ejpam-6657	221	1	[	[	X
ejpam-6657	221	2	h	h	X
ejpam-6657	221	3	]	]	X
ejpam-6657	221	4	n	n	CCONJ
ejpam-6657	221	5	(	(	PUNCT
ejpam-6657	221	6	0	0	NUM
ejpam-6657	221	7	,	,	PUNCT
ejpam-6657	221	8	ξ2	ξ2	ADJ
ejpam-6657	221	9	,	,	PUNCT
ejpam-6657	221	10	ξ3	ξ3	NOUN
ejpam-6657	221	11	)	)	PUNCT
ejpam-6657	221	12	tn	tn	PROPN
ejpam-6657	221	13	n	n	PROPN
ejpam-6657	221	14	!	!	PUNCT
ejpam-6657	221	15	)	)	PUNCT
ejpam-6657	222	1	(	(	PUNCT
ejpam-6657	222	2	∞∑	∞∑	X
ejpam-6657	222	3	k=0	k=0	PROPN
ejpam-6657	222	4	(	(	PUNCT
ejpam-6657	222	5	−ξ1	−ξ1	PROPN
ejpam-6657	222	6	h	h	PROPN
ejpam-6657	222	7	)	)	PUNCT
ejpam-6657	222	8	k	k	PROPN
ejpam-6657	222	9	(	(	PUNCT
ejpam-6657	222	10	−h)k	−h)k	NOUN
ejpam-6657	222	11	tk	tk	PROPN
ejpam-6657	222	12	k	k	PROPN
ejpam-6657	222	13	!	!	PUNCT
ejpam-6657	222	14	)	)	PUNCT
ejpam-6657	223	1	=	=	X
ejpam-6657	224	1	∞∑	∞∑	PRON
ejpam-6657	224	2	n=0	n=0	NUM
ejpam-6657	224	3	e(r)h	e(r)h	PROPN
ejpam-6657	225	1	[	[	X
ejpam-6657	225	2	h	h	X
ejpam-6657	225	3	]	]	X
ejpam-6657	225	4	n	n	PROPN
ejpam-6657	225	5	(	(	PUNCT
ejpam-6657	225	6	ξ1	ξ1	PROPN
ejpam-6657	225	7	,	,	PUNCT
ejpam-6657	225	8	ξ2	ξ2	ADJ
ejpam-6657	225	9	,	,	PUNCT
ejpam-6657	225	10	ξ3	ξ3	PROPN
ejpam-6657	225	11	)	)	PUNCT
ejpam-6657	225	12	tn	tn	PROPN
ejpam-6657	225	13	n	n	CCONJ
ejpam-6657	225	14	!	!	PROPN
ejpam-6657	225	15	,	,	PUNCT
ejpam-6657	225	16	applying	apply	VERB
ejpam-6657	225	17	the	the	DET
ejpam-6657	225	18	cauchy	cauchy	ADJ
ejpam-6657	225	19	product	product	NOUN
ejpam-6657	225	20	on	on	ADP
ejpam-6657	225	21	the	the	DET
ejpam-6657	225	22	left	left	ADJ
ejpam-6657	225	23	-	-	PUNCT
ejpam-6657	225	24	hand	hand	NOUN
ejpam-6657	225	25	side	side	NOUN
ejpam-6657	225	26	and	and	CCONJ
ejpam-6657	225	27	comparing	compare	VERB
ejpam-6657	225	28	like	like	ADP
ejpam-6657	225	29	powers	power	NOUN
ejpam-6657	225	30	of	of	ADP
ejpam-6657	225	31	t	t	PROPN
ejpam-6657	225	32	,	,	PUNCT
ejpam-6657	225	33	equation	equation	NOUN
ejpam-6657	225	34	(	(	PUNCT
ejpam-6657	225	35	39	39	NUM
ejpam-6657	225	36	)	)	PUNCT
ejpam-6657	225	37	is	be	AUX
ejpam-6657	225	38	validated	validate	VERB
ejpam-6657	225	39	.	.	PUNCT
ejpam-6657	226	1	in	in	ADP
ejpam-6657	226	2	a	a	DET
ejpam-6657	226	3	similar	similar	ADJ
ejpam-6657	226	4	fashion	fashion	NOUN
ejpam-6657	226	5	,	,	PUNCT
ejpam-6657	226	6	identities	identity	NOUN
ejpam-6657	226	7	(	(	PUNCT
ejpam-6657	226	8	40	40	NUM
ejpam-6657	226	9	)	)	PUNCT
ejpam-6657	226	10	and	and	CCONJ
ejpam-6657	226	11	(	(	PUNCT
ejpam-6657	226	12	41	41	NUM
ejpam-6657	226	13	)	)	PUNCT
ejpam-6657	226	14	follow	follow	VERB
ejpam-6657	226	15	directly	directly	ADV
ejpam-6657	226	16	.	.	PUNCT
ejpam-6657	227	1	furthermore	furthermore	ADV
ejpam-6657	227	2	,	,	PUNCT
ejpam-6657	227	3	from	from	ADP
ejpam-6657	227	4	equation	equation	NOUN
ejpam-6657	227	5	(	(	PUNCT
ejpam-6657	227	6	29	29	NUM
ejpam-6657	227	7	)	)	PUNCT
ejpam-6657	227	8	,	,	PUNCT
ejpam-6657	227	9	we	we	PRON
ejpam-6657	227	10	have	have	VERB
ejpam-6657	227	11	:	:	PUNCT
ejpam-6657	227	12	∞∑	∞∑	PRON
ejpam-6657	227	13	n=0	n=0	NUM
ejpam-6657	227	14	e(r)h	e(r)h	PROPN
ejpam-6657	228	1	[	[	X
ejpam-6657	228	2	h	h	X
ejpam-6657	228	3	]	]	X
ejpam-6657	228	4	n	n	PROPN
ejpam-6657	228	5	(	(	PUNCT
ejpam-6657	228	6	ξ1	ξ1	PROPN
ejpam-6657	228	7	,	,	PUNCT
ejpam-6657	228	8	ξ2	ξ2	ADJ
ejpam-6657	228	9	,	,	PUNCT
ejpam-6657	228	10	ξ3	ξ3	PROPN
ejpam-6657	228	11	)	)	PUNCT
ejpam-6657	228	12	tn	tn	PROPN
ejpam-6657	228	13	n	n	ADV
ejpam-6657	228	14	!	!	PUNCT
ejpam-6657	229	1	=	=	SYM
ejpam-6657	229	2	1	1	NUM
ejpam-6657	229	3	1−	1−	NUM
ejpam-6657	229	4	ξ3tr	ξ3tr	NUM
ejpam-6657	229	5	elog((1+ht	elog((1+ht	NOUN
ejpam-6657	229	6	)	)	PUNCT
ejpam-6657	229	7	ξ1	ξ1	NOUN
ejpam-6657	229	8	h	h	NOUN
ejpam-6657	229	9	)	)	PUNCT
ejpam-6657	229	10	(	(	PUNCT
ejpam-6657	229	11	1	1	X
ejpam-6657	229	12	+	+	NUM
ejpam-6657	229	13	ht2	ht2	NOUN
ejpam-6657	229	14	)	)	PUNCT
ejpam-6657	229	15	ξ2	ξ2	NOUN
ejpam-6657	229	16	h	h	NOUN
ejpam-6657	229	17	.	.	PUNCT
ejpam-6657	230	1	(	(	PUNCT
ejpam-6657	230	2	46	46	X
ejpam-6657	230	3	)	)	PUNCT
ejpam-6657	230	4	employing	employ	VERB
ejpam-6657	230	5	equation	equation	NOUN
ejpam-6657	230	6	(	(	PUNCT
ejpam-6657	230	7	1	1	NUM
ejpam-6657	230	8	)	)	PUNCT
ejpam-6657	230	9	,	,	PUNCT
ejpam-6657	230	10	the	the	DET
ejpam-6657	230	11	expression	expression	NOUN
ejpam-6657	230	12	becomes	become	VERB
ejpam-6657	230	13	:	:	PUNCT
ejpam-6657	230	14	∞∑	∞∑	NUM
ejpam-6657	230	15	n=0	n=0	NUM
ejpam-6657	230	16	e(r)h	e(r)h	PROPN
ejpam-6657	231	1	[	[	X
ejpam-6657	231	2	h	h	X
ejpam-6657	231	3	]	]	X
ejpam-6657	231	4	n	n	PROPN
ejpam-6657	231	5	(	(	PUNCT
ejpam-6657	231	6	ξ1	ξ1	PROPN
ejpam-6657	231	7	,	,	PUNCT
ejpam-6657	231	8	ξ2	ξ2	ADJ
ejpam-6657	231	9	,	,	PUNCT
ejpam-6657	231	10	ξ3	ξ3	PROPN
ejpam-6657	231	11	)	)	PUNCT
ejpam-6657	231	12	tn	tn	PROPN
ejpam-6657	231	13	n	n	PROPN
ejpam-6657	231	14	!	!	PUNCT
ejpam-6657	232	1	=	=	PUNCT
ejpam-6657	233	1	(	(	PUNCT
ejpam-6657	233	2	∞∑	∞∑	NUM
ejpam-6657	233	3	n=0	n=0	NUM
ejpam-6657	233	4	e(r)h	e(r)h	PROPN
ejpam-6657	234	1	[	[	X
ejpam-6657	234	2	h	h	X
ejpam-6657	234	3	]	]	X
ejpam-6657	234	4	n	n	CCONJ
ejpam-6657	234	5	(	(	PUNCT
ejpam-6657	234	6	0	0	NUM
ejpam-6657	234	7	,	,	PUNCT
ejpam-6657	234	8	ξ2	ξ2	ADJ
ejpam-6657	234	9	,	,	PUNCT
ejpam-6657	234	10	ξ3	ξ3	NOUN
ejpam-6657	234	11	)	)	PUNCT
ejpam-6657	234	12	tn	tn	PROPN
ejpam-6657	234	13	n	n	PROPN
ejpam-6657	234	14	!	!	PUNCT
ejpam-6657	234	15	)	)	PUNCT
ejpam-6657	235	1	(	(	PUNCT
ejpam-6657	235	2	∞∑	∞∑	X
ejpam-6657	235	3	k=0	k=0	PROPN
ejpam-6657	235	4	(	(	PUNCT
ejpam-6657	235	5	ξ1	ξ1	NOUN
ejpam-6657	235	6	h	h	NOUN
ejpam-6657	235	7	)	)	PUNCT
ejpam-6657	235	8	k	k	X
ejpam-6657	235	9	log(1	log(1	NOUN
ejpam-6657	235	10	+	+	CCONJ
ejpam-6657	236	1	ht)k	ht)k	PROPN
ejpam-6657	236	2	k	k	PROPN
ejpam-6657	236	3	!	!	PUNCT
ejpam-6657	236	4	)	)	PUNCT
ejpam-6657	237	1	,	,	PUNCT
ejpam-6657	237	2	(	(	PUNCT
ejpam-6657	237	3	47	47	NUM
ejpam-6657	237	4	)	)	PUNCT
ejpam-6657	237	5	substituting	substitute	VERB
ejpam-6657	237	6	equation	equation	NOUN
ejpam-6657	237	7	(	(	PUNCT
ejpam-6657	237	8	25	25	NUM
ejpam-6657	237	9	)	)	PUNCT
ejpam-6657	237	10	leads	lead	VERB
ejpam-6657	237	11	to	to	ADP
ejpam-6657	237	12	:	:	PUNCT
ejpam-6657	238	1	∞∑	∞∑	NUM
ejpam-6657	238	2	n=0	n=0	NUM
ejpam-6657	238	3	e(r)h	e(r)h	PROPN
ejpam-6657	239	1	[	[	X
ejpam-6657	239	2	h	h	X
ejpam-6657	239	3	]	]	X
ejpam-6657	239	4	n	n	PROPN
ejpam-6657	239	5	(	(	PUNCT
ejpam-6657	239	6	ξ1	ξ1	PROPN
ejpam-6657	239	7	,	,	PUNCT
ejpam-6657	239	8	ξ2	ξ2	ADJ
ejpam-6657	239	9	,	,	PUNCT
ejpam-6657	239	10	ξ3	ξ3	PROPN
ejpam-6657	239	11	)	)	PUNCT
ejpam-6657	239	12	tn	tn	PROPN
ejpam-6657	239	13	n	n	PROPN
ejpam-6657	239	14	!	!	PUNCT
ejpam-6657	240	1	=	=	PUNCT
ejpam-6657	241	1	(	(	PUNCT
ejpam-6657	241	2	∞∑	∞∑	NUM
ejpam-6657	241	3	n=0	n=0	NUM
ejpam-6657	241	4	e(r)h	e(r)h	PROPN
ejpam-6657	242	1	[	[	X
ejpam-6657	242	2	h	h	X
ejpam-6657	242	3	]	]	X
ejpam-6657	242	4	n	n	CCONJ
ejpam-6657	242	5	(	(	PUNCT
ejpam-6657	242	6	0	0	NUM
ejpam-6657	242	7	,	,	PUNCT
ejpam-6657	242	8	ξ2	ξ2	ADJ
ejpam-6657	242	9	,	,	PUNCT
ejpam-6657	242	10	ξ3	ξ3	NOUN
ejpam-6657	242	11	)	)	PUNCT
ejpam-6657	242	12	tn	tn	PROPN
ejpam-6657	242	13	n	n	PROPN
ejpam-6657	242	14	!	!	PUNCT
ejpam-6657	242	15	)	)	PUNCT
ejpam-6657	243	1	(	(	PUNCT
ejpam-6657	243	2	∞∑	∞∑	X
ejpam-6657	243	3	k=0	k=0	PROPN
ejpam-6657	243	4	(	(	PUNCT
ejpam-6657	243	5	ξ1	ξ1	NOUN
ejpam-6657	243	6	h	h	NOUN
ejpam-6657	243	7	)	)	PUNCT
ejpam-6657	243	8	k	k	PROPN
ejpam-6657	244	1	∞∑	∞∑	NUM
ejpam-6657	244	2	l	l	NOUN
ejpam-6657	244	3	=	=	PROPN
ejpam-6657	244	4	k	k	X
ejpam-6657	244	5	s1(l	s1(l	PROPN
ejpam-6657	244	6	,	,	PUNCT
ejpam-6657	244	7	k)h	k)h	VERB
ejpam-6657	244	8	l	l	NOUN
ejpam-6657	244	9	t	t	NOUN
ejpam-6657	244	10	l	l	NOUN
ejpam-6657	244	11	l	l	NOUN
ejpam-6657	244	12	!	!	PUNCT
ejpam-6657	244	13	)	)	PUNCT
ejpam-6657	245	1	∞∑	∞∑	PRON
ejpam-6657	245	2	n=0	n=0	NUM
ejpam-6657	245	3	e(r)h	e(r)h	PROPN
ejpam-6657	246	1	[	[	X
ejpam-6657	246	2	h	h	X
ejpam-6657	246	3	]	]	X
ejpam-6657	246	4	n	n	PROPN
ejpam-6657	246	5	(	(	PUNCT
ejpam-6657	246	6	ξ1	ξ1	PROPN
ejpam-6657	246	7	,	,	PUNCT
ejpam-6657	246	8	ξ2	ξ2	ADJ
ejpam-6657	246	9	,	,	PUNCT
ejpam-6657	246	10	ξ3	ξ3	PROPN
ejpam-6657	246	11	)	)	PUNCT
ejpam-6657	246	12	tn	tn	PROPN
ejpam-6657	246	13	n	n	PROPN
ejpam-6657	246	14	!	!	PUNCT
ejpam-6657	247	1	=	=	PUNCT
ejpam-6657	248	1	(	(	PUNCT
ejpam-6657	248	2	∞∑	∞∑	NUM
ejpam-6657	248	3	n=0	n=0	NUM
ejpam-6657	248	4	e(r)h	e(r)h	PROPN
ejpam-6657	249	1	[	[	X
ejpam-6657	249	2	h	h	X
ejpam-6657	249	3	]	]	X
ejpam-6657	249	4	n	n	CCONJ
ejpam-6657	249	5	(	(	PUNCT
ejpam-6657	249	6	0	0	NUM
ejpam-6657	249	7	,	,	PUNCT
ejpam-6657	249	8	ξ2	ξ2	ADJ
ejpam-6657	249	9	,	,	PUNCT
ejpam-6657	249	10	ξ3	ξ3	NOUN
ejpam-6657	249	11	)	)	PUNCT
ejpam-6657	249	12	tn	tn	PROPN
ejpam-6657	249	13	n	n	PROPN
ejpam-6657	249	14	!	!	PUNCT
ejpam-6657	249	15	)	)	PUNCT
ejpam-6657	250	1	(	(	PUNCT
ejpam-6657	250	2	∞∑	∞∑	NUM
ejpam-6657	250	3	l=0	l=0	PROPN
ejpam-6657	250	4	l∑	l∑	PUNCT
ejpam-6657	251	1	k=0	k=0	PROPN
ejpam-6657	251	2	(	(	PUNCT
ejpam-6657	251	3	ξ1	ξ1	NOUN
ejpam-6657	251	4	h	h	NOUN
ejpam-6657	251	5	)	)	PUNCT
ejpam-6657	251	6	k	k	PROPN
ejpam-6657	251	7	s1(l	s1(l	PROPN
ejpam-6657	251	8	,	,	PUNCT
ejpam-6657	251	9	k)h	k)h	VERB
ejpam-6657	251	10	l	l	NOUN
ejpam-6657	251	11	t	t	NOUN
ejpam-6657	251	12	l	l	NOUN
ejpam-6657	251	13	l	l	NOUN
ejpam-6657	251	14	!	!	PUNCT
ejpam-6657	251	15	)	)	PUNCT
ejpam-6657	251	16	.	.	PUNCT
ejpam-6657	252	1	(	(	PUNCT
ejpam-6657	252	2	48	48	NUM
ejpam-6657	252	3	)	)	PUNCT
ejpam-6657	252	4	by	by	ADP
ejpam-6657	252	5	replacing	replace	VERB
ejpam-6657	252	6	n	n	PRON
ejpam-6657	252	7	with	with	ADP
ejpam-6657	252	8	n−	n−	PROPN
ejpam-6657	252	9	l	l	NOUN
ejpam-6657	252	10	on	on	ADP
ejpam-6657	252	11	the	the	DET
ejpam-6657	252	12	right	right	ADJ
ejpam-6657	252	13	-	-	PUNCT
ejpam-6657	252	14	hand	hand	NOUN
ejpam-6657	252	15	side	side	NOUN
ejpam-6657	252	16	and	and	CCONJ
ejpam-6657	252	17	comparing	compare	VERB
ejpam-6657	252	18	coefficients	coefficient	NOUN
ejpam-6657	252	19	of	of	ADP
ejpam-6657	252	20	tn	tn	NOUN
ejpam-6657	252	21	,	,	PUNCT
ejpam-6657	252	22	identity	identity	NOUN
ejpam-6657	252	23	(	(	PUNCT
ejpam-6657	252	24	44	44	NUM
ejpam-6657	252	25	)	)	PUNCT
ejpam-6657	252	26	is	be	AUX
ejpam-6657	252	27	obtained	obtain	VERB
ejpam-6657	252	28	.	.	PUNCT
ejpam-6657	253	1	now	now	ADV
ejpam-6657	253	2	,	,	PUNCT
ejpam-6657	253	3	using	use	VERB
ejpam-6657	253	4	(	(	PUNCT
ejpam-6657	253	5	26	26	NUM
ejpam-6657	253	6	)	)	PUNCT
ejpam-6657	253	7	along	along	ADP
ejpam-6657	253	8	with	with	ADP
ejpam-6657	253	9	(	(	PUNCT
ejpam-6657	253	10	29	29	NUM
ejpam-6657	253	11	)	)	PUNCT
ejpam-6657	253	12	,	,	PUNCT
ejpam-6657	253	13	we	we	PRON
ejpam-6657	253	14	have	have	VERB
ejpam-6657	253	15	:	:	PUNCT
ejpam-6657	254	1	∞∑	∞∑	PRON
ejpam-6657	254	2	n=0	n=0	NUM
ejpam-6657	254	3	e(r)h	e(r)h	PROPN
ejpam-6657	255	1	[	[	X
ejpam-6657	255	2	h	h	X
ejpam-6657	255	3	]	]	X
ejpam-6657	255	4	n	n	PROPN
ejpam-6657	255	5	(	(	PUNCT
ejpam-6657	255	6	ξ1	ξ1	PROPN
ejpam-6657	255	7	,	,	PUNCT
ejpam-6657	255	8	ξ2	ξ2	ADJ
ejpam-6657	255	9	,	,	PUNCT
ejpam-6657	255	10	ξ3	ξ3	PROPN
ejpam-6657	255	11	)	)	PUNCT
ejpam-6657	255	12	tn	tn	PROPN
ejpam-6657	255	13	n	n	ADV
ejpam-6657	255	14	!	!	PUNCT
ejpam-6657	256	1	=	=	SYM
ejpam-6657	256	2	1	1	NUM
ejpam-6657	256	3	1−	1−	NUM
ejpam-6657	256	4	ξ3tr	ξ3tr	NUM
ejpam-6657	256	5	(	(	PUNCT
ejpam-6657	256	6	1	1	NUM
ejpam-6657	256	7	+	+	NUM
ejpam-6657	256	8	ht2	ht2	NOUN
ejpam-6657	256	9	)	)	PUNCT
ejpam-6657	256	10	ξ2	ξ2	NOUN
ejpam-6657	256	11	h	h	NOUN
ejpam-6657	256	12	e	e	X
ejpam-6657	256	13	logh((1+ht	logh((1+ht	PROPN
ejpam-6657	256	14	)	)	PUNCT
ejpam-6657	256	15	ξ1	ξ1	NOUN
ejpam-6657	256	16	h	h	NOUN
ejpam-6657	256	17	)	)	PUNCT
ejpam-6657	256	18	h	h	NOUN
ejpam-6657	256	19	.	.	PUNCT
ejpam-6657	257	1	(	(	PUNCT
ejpam-6657	257	2	49	49	NUM
ejpam-6657	257	3	)	)	PUNCT
ejpam-6657	258	1	∞∑	∞∑	PRON
ejpam-6657	258	2	n=0	n=0	NUM
ejpam-6657	258	3	e(r)h	e(r)h	PROPN
ejpam-6657	259	1	[	[	X
ejpam-6657	259	2	h	h	X
ejpam-6657	259	3	]	]	X
ejpam-6657	259	4	n	n	PROPN
ejpam-6657	259	5	(	(	PUNCT
ejpam-6657	259	6	ξ1	ξ1	PROPN
ejpam-6657	259	7	,	,	PUNCT
ejpam-6657	259	8	ξ2	ξ2	ADJ
ejpam-6657	259	9	,	,	PUNCT
ejpam-6657	259	10	ξ3	ξ3	PROPN
ejpam-6657	259	11	)	)	PUNCT
ejpam-6657	259	12	tn	tn	PROPN
ejpam-6657	259	13	n	n	PROPN
ejpam-6657	259	14	!	!	PUNCT
ejpam-6657	260	1	=	=	PUNCT
ejpam-6657	260	2	(	(	PUNCT
ejpam-6657	260	3	∞∑	∞∑	NUM
ejpam-6657	260	4	n=0	n=0	NUM
ejpam-6657	260	5	erh[h	erh[h	NOUN
ejpam-6657	260	6	]	]	PUNCT
ejpam-6657	260	7	n	n	CCONJ
ejpam-6657	260	8	(	(	PUNCT
ejpam-6657	260	9	0	0	NUM
ejpam-6657	260	10	,	,	PUNCT
ejpam-6657	260	11	ξ2	ξ2	ADJ
ejpam-6657	260	12	,	,	PUNCT
ejpam-6657	260	13	ξ3	ξ3	NOUN
ejpam-6657	260	14	)	)	PUNCT
ejpam-6657	260	15	tn	tn	PROPN
ejpam-6657	260	16	n	n	PROPN
ejpam-6657	260	17	!	!	PUNCT
ejpam-6657	260	18	)	)	PUNCT
ejpam-6657	261	1	(	(	PUNCT
ejpam-6657	261	2	∞∑	∞∑	X
ejpam-6657	261	3	k=0	k=0	PROPN
ejpam-6657	261	4	(	(	PUNCT
ejpam-6657	261	5	ξ1	ξ1	NOUN
ejpam-6657	261	6	h	h	NOUN
ejpam-6657	261	7	)	)	PUNCT
ejpam-6657	261	8	k	k	X
ejpam-6657	261	9	,	,	PUNCT
ejpam-6657	261	10	h	h	NOUN
ejpam-6657	262	1	logh(1	logh(1	PROPN
ejpam-6657	262	2	+	+	PROPN
ejpam-6657	262	3	ht)k	ht)k	PROPN
ejpam-6657	262	4	k	k	PROPN
ejpam-6657	262	5	!	!	PUNCT
ejpam-6657	262	6	)	)	PUNCT
ejpam-6657	262	7	,	,	PUNCT
ejpam-6657	262	8	(	(	PUNCT
ejpam-6657	262	9	50	50	X
ejpam-6657	262	10	)	)	PUNCT
ejpam-6657	263	1	∞∑	∞∑	PRON
ejpam-6657	263	2	n=0	n=0	NUM
ejpam-6657	263	3	e(r)h	e(r)h	PROPN
ejpam-6657	264	1	[	[	X
ejpam-6657	264	2	h	h	X
ejpam-6657	264	3	]	]	X
ejpam-6657	264	4	n	n	PROPN
ejpam-6657	264	5	(	(	PUNCT
ejpam-6657	264	6	ξ1	ξ1	PROPN
ejpam-6657	264	7	,	,	PUNCT
ejpam-6657	264	8	ξ2	ξ2	ADJ
ejpam-6657	264	9	,	,	PUNCT
ejpam-6657	264	10	ξ3	ξ3	PROPN
ejpam-6657	264	11	)	)	PUNCT
ejpam-6657	264	12	tn	tn	PROPN
ejpam-6657	264	13	n	n	PROPN
ejpam-6657	264	14	!	!	PUNCT
ejpam-6657	265	1	=	=	PUNCT
ejpam-6657	266	1	(	(	PUNCT
ejpam-6657	266	2	∞∑	∞∑	NUM
ejpam-6657	266	3	n=0	n=0	NUM
ejpam-6657	266	4	e(r)h	e(r)h	PROPN
ejpam-6657	267	1	[	[	X
ejpam-6657	267	2	h	h	X
ejpam-6657	267	3	]	]	X
ejpam-6657	267	4	n	n	CCONJ
ejpam-6657	267	5	(	(	PUNCT
ejpam-6657	267	6	0	0	NUM
ejpam-6657	267	7	,	,	PUNCT
ejpam-6657	267	8	ξ2	ξ2	ADJ
ejpam-6657	267	9	,	,	PUNCT
ejpam-6657	267	10	ξ3	ξ3	NOUN
ejpam-6657	267	11	)	)	PUNCT
ejpam-6657	267	12	tn	tn	PROPN
ejpam-6657	267	13	n	n	PROPN
ejpam-6657	267	14	!	!	PUNCT
ejpam-6657	267	15	)	)	PUNCT
ejpam-6657	268	1	(	(	PUNCT
ejpam-6657	268	2	∞∑	∞∑	NUM
ejpam-6657	268	3	l=0	l=0	PROPN
ejpam-6657	268	4	l∑	l∑	PUNCT
ejpam-6657	269	1	k=0	k=0	PROPN
ejpam-6657	269	2	(	(	PUNCT
ejpam-6657	269	3	ξ1	ξ1	NOUN
ejpam-6657	269	4	h	h	NOUN
ejpam-6657	269	5	)	)	PUNCT
ejpam-6657	270	1	k	k	X
ejpam-6657	270	2	,	,	PUNCT
ejpam-6657	270	3	h	h	PROPN
ejpam-6657	270	4	s1,h(l	s1,h(l	ADJ
ejpam-6657	270	5	,	,	PUNCT
ejpam-6657	270	6	k)h	k)h	VERB
ejpam-6657	270	7	l	l	NOUN
ejpam-6657	270	8	t	t	NOUN
ejpam-6657	270	9	l	l	NOUN
ejpam-6657	270	10	l	l	NOUN
ejpam-6657	270	11	!	!	PUNCT
ejpam-6657	270	12	)	)	PUNCT
ejpam-6657	270	13	.	.	PUNCT
ejpam-6657	271	1	(	(	PUNCT
ejpam-6657	271	2	51	51	NUM
ejpam-6657	271	3	)	)	PUNCT
ejpam-6657	271	4	substituting	substitute	VERB
ejpam-6657	271	5	n	n	NOUN
ejpam-6657	271	6	by	by	ADP
ejpam-6657	271	7	n−	n−	PROPN
ejpam-6657	271	8	l	l	NOUN
ejpam-6657	271	9	and	and	CCONJ
ejpam-6657	271	10	comparing	compare	VERB
ejpam-6657	271	11	corresponding	corresponding	ADJ
ejpam-6657	271	12	coefficients	coefficient	NOUN
ejpam-6657	271	13	of	of	ADP
ejpam-6657	271	14	t	t	PROPN
ejpam-6657	271	15	,	,	PUNCT
ejpam-6657	271	16	we	we	PRON
ejpam-6657	271	17	confirm	confirm	VERB
ejpam-6657	271	18	identity	identity	NOUN
ejpam-6657	271	19	(	(	PUNCT
ejpam-6657	271	20	45	45	NUM
ejpam-6657	271	21	)	)	PUNCT
ejpam-6657	271	22	.	.	PUNCT
ejpam-6657	272	1	h.	h.	PROPN
ejpam-6657	272	2	qawaqneh	qawaqneh	PROPN
ejpam-6657	272	3	et	et	PROPN
ejpam-6657	272	4	al	al	PROPN
ejpam-6657	272	5	.	.	PUNCT
ejpam-6657	272	6	/	/	SYM
ejpam-6657	272	7	eur	eur	PROPN
ejpam-6657	272	8	.	.	PUNCT
ejpam-6657	273	1	j.	j.	PROPN
ejpam-6657	273	2	pure	pure	PROPN
ejpam-6657	273	3	appl	appl	PROPN
ejpam-6657	273	4	.	.	PROPN
ejpam-6657	273	5	math	math	PROPN
ejpam-6657	273	6	,	,	PUNCT
ejpam-6657	273	7	18	18	NUM
ejpam-6657	273	8	(	(	PUNCT
ejpam-6657	273	9	3	3	NUM
ejpam-6657	273	10	)	)	PUNCT
ejpam-6657	273	11	(	(	PUNCT
ejpam-6657	273	12	2025	2025	NUM
ejpam-6657	273	13	)	)	PUNCT
ejpam-6657	273	14	,	,	PUNCT
ejpam-6657	273	15	6657	6657	NUM
ejpam-6657	273	16	10	10	NUM
ejpam-6657	273	17	of	of	ADP
ejpam-6657	273	18	16	16	NUM
ejpam-6657	273	19	4	4	NUM
ejpam-6657	273	20	.	.	PUNCT
ejpam-6657	273	21	monomiality	monomiality	NOUN
ejpam-6657	273	22	principle	principle	NOUN
ejpam-6657	273	23	the	the	DET
ejpam-6657	273	24	monomiality	monomiality	NOUN
ejpam-6657	273	25	principle	principle	NOUN
ejpam-6657	273	26	is	be	AUX
ejpam-6657	273	27	a	a	DET
ejpam-6657	273	28	core	core	NOUN
ejpam-6657	273	29	concept	concept	NOUN
ejpam-6657	273	30	in	in	ADP
ejpam-6657	273	31	polynomial	polynomial	ADJ
ejpam-6657	273	32	theory	theory	NOUN
ejpam-6657	273	33	.	.	PUNCT
ejpam-6657	274	1	it	it	PRON
ejpam-6657	274	2	states	state	VERB
ejpam-6657	274	3	that	that	SCONJ
ejpam-6657	274	4	any	any	DET
ejpam-6657	274	5	polynomial	polynomial	NOUN
ejpam-6657	274	6	can	can	AUX
ejpam-6657	274	7	be	be	AUX
ejpam-6657	274	8	written	write	VERB
ejpam-6657	274	9	uniquely	uniquely	ADV
ejpam-6657	274	10	as	as	ADP
ejpam-6657	274	11	a	a	DET
ejpam-6657	274	12	linear	linear	ADJ
ejpam-6657	274	13	combination	combination	NOUN
ejpam-6657	274	14	of	of	ADP
ejpam-6657	274	15	monomials	monomial	NOUN
ejpam-6657	274	16	(	(	PUNCT
ejpam-6657	274	17	powers	power	NOUN
ejpam-6657	274	18	of	of	ADP
ejpam-6657	274	19	a	a	DET
ejpam-6657	274	20	variable	variable	NOUN
ejpam-6657	274	21	)	)	PUNCT
ejpam-6657	274	22	.	.	PUNCT
ejpam-6657	275	1	this	this	DET
ejpam-6657	275	2	form	form	NOUN
ejpam-6657	275	3	simplifies	simplify	VERB
ejpam-6657	275	4	analysis	analysis	NOUN
ejpam-6657	275	5	and	and	CCONJ
ejpam-6657	275	6	helps	helps	AUX
ejpam-6657	275	7	extract	extract	VERB
ejpam-6657	275	8	key	key	ADJ
ejpam-6657	275	9	properties	property	NOUN
ejpam-6657	275	10	like	like	ADP
ejpam-6657	275	11	degree	degree	NOUN
ejpam-6657	275	12	and	and	CCONJ
ejpam-6657	275	13	roots	root	NOUN
ejpam-6657	275	14	.	.	PUNCT
ejpam-6657	276	1	monomiality	monomiality	NOUN
ejpam-6657	276	2	representations	representation	NOUN
ejpam-6657	276	3	are	be	AUX
ejpam-6657	276	4	widely	widely	ADV
ejpam-6657	276	5	used	use	VERB
ejpam-6657	276	6	in	in	ADP
ejpam-6657	276	7	computations	computation	NOUN
ejpam-6657	276	8	such	such	ADJ
ejpam-6657	276	9	as	as	ADP
ejpam-6657	276	10	interpolation	interpolation	NOUN
ejpam-6657	276	11	,	,	PUNCT
ejpam-6657	276	12	approximation	approximation	NOUN
ejpam-6657	276	13	,	,	PUNCT
ejpam-6657	276	14	and	and	CCONJ
ejpam-6657	276	15	integration	integration	NOUN
ejpam-6657	276	16	.	.	PUNCT
ejpam-6657	277	1	they	they	PRON
ejpam-6657	277	2	also	also	ADV
ejpam-6657	277	3	appear	appear	VERB
ejpam-6657	277	4	in	in	ADP
ejpam-6657	277	5	physics	physics	NOUN
ejpam-6657	277	6	,	,	PUNCT
ejpam-6657	277	7	control	control	NOUN
ejpam-6657	277	8	theory	theory	NOUN
ejpam-6657	277	9	,	,	PUNCT
ejpam-6657	277	10	and	and	CCONJ
ejpam-6657	277	11	signal	signal	NOUN
ejpam-6657	277	12	processing	processing	NOUN
ejpam-6657	277	13	,	,	PUNCT
ejpam-6657	277	14	where	where	SCONJ
ejpam-6657	277	15	polynomials	polynomial	NOUN
ejpam-6657	277	16	model	model	VERB
ejpam-6657	277	17	complex	complex	ADJ
ejpam-6657	277	18	systems	system	NOUN
ejpam-6657	277	19	.	.	PUNCT
ejpam-6657	278	1	the	the	DET
ejpam-6657	278	2	principle	principle	NOUN
ejpam-6657	278	3	was	be	AUX
ejpam-6657	278	4	introduced	introduce	VERB
ejpam-6657	278	5	via	via	ADP
ejpam-6657	278	6	poweroids	poweroid	NOUN
ejpam-6657	278	7	by	by	ADP
ejpam-6657	278	8	steffensen	steffensen	NOUN
ejpam-6657	278	9	in	in	ADP
ejpam-6657	278	10	1941	1941	NUM
ejpam-6657	278	11	[	[	X
ejpam-6657	278	12	16	16	NUM
ejpam-6657	278	13	]	]	PUNCT
ejpam-6657	278	14	,	,	PUNCT
ejpam-6657	278	15	and	and	CCONJ
ejpam-6657	278	16	later	later	ADV
ejpam-6657	278	17	extended	extend	VERB
ejpam-6657	278	18	by	by	ADP
ejpam-6657	278	19	dattoli	dattoli	NOUN
ejpam-6657	278	20	[	[	X
ejpam-6657	278	21	27	27	NUM
ejpam-6657	278	22	,	,	PUNCT
ejpam-6657	278	23	28	28	NUM
ejpam-6657	278	24	]	]	PUNCT
ejpam-6657	278	25	.	.	PUNCT
ejpam-6657	279	1	these	these	DET
ejpam-6657	279	2	methods	method	NOUN
ejpam-6657	279	3	,	,	PUNCT
ejpam-6657	279	4	grounded	ground	VERB
ejpam-6657	279	5	in	in	ADP
ejpam-6657	279	6	mathematical	mathematical	ADJ
ejpam-6657	279	7	physics	physics	NOUN
ejpam-6657	279	8	,	,	PUNCT
ejpam-6657	279	9	quantum	quantum	NOUN
ejpam-6657	279	10	mechanics	mechanic	NOUN
ejpam-6657	279	11	,	,	PUNCT
ejpam-6657	279	12	and	and	CCONJ
ejpam-6657	279	13	optics	optic	NOUN
ejpam-6657	279	14	,	,	PUNCT
ejpam-6657	279	15	remain	remain	VERB
ejpam-6657	279	16	vital	vital	ADJ
ejpam-6657	279	17	tools	tool	NOUN
ejpam-6657	279	18	in	in	ADP
ejpam-6657	279	19	modern	modern	ADJ
ejpam-6657	279	20	research	research	NOUN
ejpam-6657	279	21	.	.	PUNCT
ejpam-6657	280	1	in	in	ADP
ejpam-6657	280	2	this	this	DET
ejpam-6657	280	3	section	section	NOUN
ejpam-6657	280	4	,	,	PUNCT
ejpam-6657	280	5	we	we	PRON
ejpam-6657	280	6	validate	validate	VERB
ejpam-6657	280	7	the	the	DET
ejpam-6657	280	8	monomiality	monomiality	NOUN
ejpam-6657	280	9	principle	principle	NOUN
ejpam-6657	280	10	for	for	ADP
ejpam-6657	280	11	the	the	DET
ejpam-6657	280	12	three	three	NUM
ejpam-6657	280	13	-	-	PUNCT
ejpam-6657	280	14	variable	variable	NOUN
ejpam-6657	280	15	∆h	∆h	NOUN
ejpam-6657	280	16	-	-	PUNCT
ejpam-6657	280	17	truncated	truncate	VERB
ejpam-6657	280	18	exponential	exponential	NOUN
ejpam-6657	280	19	-	-	PUNCT
ejpam-6657	280	20	based	base	VERB
ejpam-6657	280	21	hermite	hermite	ADJ
ejpam-6657	280	22	polynomials	polynomial	NOUN
ejpam-6657	280	23	,	,	PUNCT
ejpam-6657	280	24	denoted	denote	VERB
ejpam-6657	280	25	e(r)h	e(r)h	PROPN
ejpam-6657	281	1	[	[	X
ejpam-6657	281	2	h	h	X
ejpam-6657	281	3	]	]	X
ejpam-6657	281	4	n	n	PROPN
ejpam-6657	281	5	(	(	PUNCT
ejpam-6657	281	6	ξ1	ξ1	PROPN
ejpam-6657	281	7	,	,	PUNCT
ejpam-6657	281	8	ξ2	ξ2	ADJ
ejpam-6657	281	9	,	,	PUNCT
ejpam-6657	281	10	ξ3	ξ3	PROPN
ejpam-6657	281	11	)	)	PUNCT
ejpam-6657	281	12	.	.	PUNCT
ejpam-6657	282	1	we	we	PRON
ejpam-6657	282	2	confirm	confirm	VERB
ejpam-6657	282	3	this	this	PRON
ejpam-6657	282	4	by	by	ADP
ejpam-6657	282	5	establishing	establish	VERB
ejpam-6657	282	6	the	the	DET
ejpam-6657	282	7	following	following	ADJ
ejpam-6657	282	8	results	result	NOUN
ejpam-6657	282	9	.	.	PUNCT
ejpam-6657	283	1	theorem	theorem	VERB
ejpam-6657	283	2	7	7	NUM
ejpam-6657	283	3	.	.	PUNCT
ejpam-6657	284	1	the	the	DET
ejpam-6657	284	2	∆h	∆h	PROPN
ejpam-6657	284	3	-	-	PUNCT
ejpam-6657	284	4	truncated	truncate	VERB
ejpam-6657	284	5	exponential	exponential	NOUN
ejpam-6657	284	6	-	-	PUNCT
ejpam-6657	284	7	based	base	VERB
ejpam-6657	284	8	hermite	hermite	ADJ
ejpam-6657	284	9	polynomials	polynomial	VERB
ejpam-6657	284	10	e(r)h	e(r)h	PROPN
ejpam-6657	285	1	[	[	X
ejpam-6657	285	2	h	h	X
ejpam-6657	285	3	]	]	X
ejpam-6657	285	4	n	n	PROPN
ejpam-6657	285	5	(	(	PUNCT
ejpam-6657	285	6	ξ1	ξ1	PROPN
ejpam-6657	285	7	,	,	PUNCT
ejpam-6657	285	8	ξ2	ξ2	ADJ
ejpam-6657	285	9	,	,	PUNCT
ejpam-6657	285	10	ξ3	ξ3	NOUN
ejpam-6657	285	11	)	)	PUNCT
ejpam-6657	285	12	satisfy	satisfy	VERB
ejpam-6657	285	13	the	the	DET
ejpam-6657	285	14	following	follow	VERB
ejpam-6657	285	15	multiplicative	multiplicative	ADJ
ejpam-6657	285	16	and	and	CCONJ
ejpam-6657	285	17	derivative	derivative	ADJ
ejpam-6657	285	18	operators	operator	NOUN
ejpam-6657	285	19	:	:	PUNCT
ejpam-6657	285	20	m̂	m̂	X
ejpam-6657	285	21	e(r	e(r	NUM
ejpam-6657	285	22	)	)	PUNCT
ejpam-6657	285	23	h[h	h[h	NOUN
ejpam-6657	285	24	]	]	PUNCT
ejpam-6657	285	25	n	n	CCONJ
ejpam-6657	285	26	(	(	PUNCT
ejpam-6657	285	27	ξ1,ξ2,ξ3	ξ1,ξ2,ξ3	ADJ
ejpam-6657	285	28	)	)	PUNCT
ejpam-6657	285	29	=	=	PUNCT
ejpam-6657	286	1	(	(	PUNCT
ejpam-6657	286	2	ξ1	ξ1	NOUN
ejpam-6657	286	3	1	1	NUM
ejpam-6657	286	4	+	+	NUM
ejpam-6657	286	5	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	286	6	+	+	CCONJ
ejpam-6657	286	7	rξ3dξ3ξ3	rξ3dξ3ξ3	PUNCT
ejpam-6657	286	8	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	286	9	r−1	r−1	PROPN
ejpam-6657	286	10	h	h	NOUN
ejpam-6657	286	11	+	+	CCONJ
ejpam-6657	286	12	2nξ2h	2nξ2h	NUM
ejpam-6657	286	13	h+	h+	PUNCT
ejpam-6657	286	14	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	286	15	2	2	NUM
ejpam-6657	286	16	)	)	PUNCT
ejpam-6657	286	17	,	,	PUNCT
ejpam-6657	286	18	(	(	PUNCT
ejpam-6657	286	19	52	52	NUM
ejpam-6657	286	20	)	)	PUNCT
ejpam-6657	286	21	and	and	CCONJ
ejpam-6657	286	22	p̂	p̂	NOUN
ejpam-6657	286	23	e(r	e(r	NUM
ejpam-6657	286	24	)	)	PUNCT
ejpam-6657	286	25	h[h	h[h	NOUN
ejpam-6657	286	26	]	]	PUNCT
ejpam-6657	286	27	n	n	CCONJ
ejpam-6657	286	28	(	(	PUNCT
ejpam-6657	286	29	ξ1,ξ2,ξ3	ξ1,ξ2,ξ3	ADJ
ejpam-6657	286	30	)	)	PUNCT
ejpam-6657	286	31	=	=	PUNCT
ejpam-6657	286	32	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	286	33	h	h	NOUN
ejpam-6657	286	34	.	.	PUNCT
ejpam-6657	287	1	(	(	PUNCT
ejpam-6657	287	2	53	53	NUM
ejpam-6657	287	3	)	)	PUNCT
ejpam-6657	287	4	proof	proof	NOUN
ejpam-6657	287	5	.	.	PUNCT
ejpam-6657	288	1	by	by	ADP
ejpam-6657	288	2	differentiating	differentiate	VERB
ejpam-6657	288	3	equation	equation	NOUN
ejpam-6657	288	4	(	(	PUNCT
ejpam-6657	288	5	29	29	NUM
ejpam-6657	288	6	)	)	PUNCT
ejpam-6657	288	7	with	with	ADP
ejpam-6657	288	8	respect	respect	NOUN
ejpam-6657	288	9	to	to	ADP
ejpam-6657	288	10	ξ1	ξ1	NOUN
ejpam-6657	288	11	and	and	CCONJ
ejpam-6657	288	12	using	use	VERB
ejpam-6657	288	13	the	the	DET
ejpam-6657	288	14	identity	identity	NOUN
ejpam-6657	288	15	(	(	PUNCT
ejpam-6657	288	16	12	12	NUM
ejpam-6657	288	17	)	)	PUNCT
ejpam-6657	288	18	,	,	PUNCT
ejpam-6657	288	19	we	we	PRON
ejpam-6657	288	20	get	get	VERB
ejpam-6657	288	21	:	:	PUNCT
ejpam-6657	288	22	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	288	23	{	{	PUNCT
ejpam-6657	288	24	1	1	NUM
ejpam-6657	288	25	1−	1−	NUM
ejpam-6657	288	26	ξ3tr	ξ3tr	NUM
ejpam-6657	288	27	(	(	PUNCT
ejpam-6657	288	28	1	1	NUM
ejpam-6657	288	29	+	+	NUM
ejpam-6657	288	30	ht	ht	NOUN
ejpam-6657	288	31	)	)	PUNCT
ejpam-6657	288	32	ξ1	ξ1	PROPN
ejpam-6657	288	33	h	h	NOUN
ejpam-6657	288	34	(	(	PUNCT
ejpam-6657	288	35	1	1	NUM
ejpam-6657	288	36	+	+	NUM
ejpam-6657	288	37	ht2	ht2	NOUN
ejpam-6657	288	38	)	)	PUNCT
ejpam-6657	288	39	ξ2	ξ2	NOUN
ejpam-6657	288	40	h	h	NOUN
ejpam-6657	288	41	}	}	PUNCT
ejpam-6657	288	42	=	=	SYM
ejpam-6657	289	1	1	1	NUM
ejpam-6657	289	2	1−	1−	NUM
ejpam-6657	289	3	ξ3tr	ξ3tr	NUM
ejpam-6657	289	4	(	(	PUNCT
ejpam-6657	289	5	1	1	X
ejpam-6657	289	6	+	+	NUM
ejpam-6657	289	7	ht	ht	X
ejpam-6657	289	8	)	)	PUNCT
ejpam-6657	289	9	ξ1+h	ξ1+h	PROPN
ejpam-6657	289	10	h	h	NOUN
ejpam-6657	289	11	(	(	PUNCT
ejpam-6657	289	12	1	1	NUM
ejpam-6657	289	13	+	+	NUM
ejpam-6657	289	14	ht2	ht2	NOUN
ejpam-6657	289	15	)	)	PUNCT
ejpam-6657	289	16	ξ2	ξ2	NOUN
ejpam-6657	289	17	h	h	NOUN
ejpam-6657	289	18	−	−	NOUN
ejpam-6657	289	19	1	1	NUM
ejpam-6657	289	20	1−	1−	NUM
ejpam-6657	289	21	ξ3tr	ξ3tr	NUM
ejpam-6657	289	22	(	(	PUNCT
ejpam-6657	289	23	1	1	NUM
ejpam-6657	289	24	+	+	NUM
ejpam-6657	289	25	ht	ht	NOUN
ejpam-6657	289	26	)	)	PUNCT
ejpam-6657	289	27	ξ1	ξ1	PROPN
ejpam-6657	289	28	h	h	NOUN
ejpam-6657	289	29	(	(	PUNCT
ejpam-6657	289	30	1	1	NUM
ejpam-6657	289	31	+	+	NUM
ejpam-6657	289	32	ht2	ht2	NOUN
ejpam-6657	289	33	)	)	PUNCT
ejpam-6657	289	34	ξ2	ξ2	NOUN
ejpam-6657	289	35	h	h	NOUN
ejpam-6657	289	36	=	=	PUNCT
ejpam-6657	290	1	(	(	PUNCT
ejpam-6657	290	2	1	1	NUM
ejpam-6657	290	3	+	+	NUM
ejpam-6657	290	4	ht−	ht−	NOUN
ejpam-6657	290	5	1	1	NUM
ejpam-6657	290	6	)	)	PUNCT
ejpam-6657	290	7	1	1	NUM
ejpam-6657	290	8	1−	1−	NUM
ejpam-6657	290	9	ξ3tr	ξ3tr	NUM
ejpam-6657	290	10	(	(	PUNCT
ejpam-6657	290	11	1	1	NUM
ejpam-6657	290	12	+	+	NUM
ejpam-6657	290	13	ht	ht	NOUN
ejpam-6657	290	14	)	)	PUNCT
ejpam-6657	290	15	ξ1	ξ1	PROPN
ejpam-6657	290	16	h	h	NOUN
ejpam-6657	290	17	(	(	PUNCT
ejpam-6657	290	18	1	1	NUM
ejpam-6657	290	19	+	+	NUM
ejpam-6657	290	20	ht2	ht2	NOUN
ejpam-6657	290	21	)	)	PUNCT
ejpam-6657	290	22	ξ2	ξ2	NOUN
ejpam-6657	290	23	h	h	NOUN
ejpam-6657	291	1	=	=	SYM
ejpam-6657	291	2	ht	ht	PROPN
ejpam-6657	291	3	1	1	NUM
ejpam-6657	291	4	1−	1−	NUM
ejpam-6657	291	5	ξ3tr	ξ3tr	NUM
ejpam-6657	291	6	(	(	PUNCT
ejpam-6657	291	7	1	1	NUM
ejpam-6657	291	8	+	+	NUM
ejpam-6657	291	9	ht	ht	NOUN
ejpam-6657	291	10	)	)	PUNCT
ejpam-6657	291	11	ξ1	ξ1	PROPN
ejpam-6657	291	12	h	h	NOUN
ejpam-6657	291	13	(	(	PUNCT
ejpam-6657	291	14	1	1	NUM
ejpam-6657	291	15	+	+	NUM
ejpam-6657	291	16	ht2	ht2	NOUN
ejpam-6657	291	17	)	)	PUNCT
ejpam-6657	291	18	ξ2	ξ2	NOUN
ejpam-6657	291	19	h	h	NOUN
ejpam-6657	291	20	,	,	PUNCT
ejpam-6657	291	21	(	(	PUNCT
ejpam-6657	291	22	54	54	NUM
ejpam-6657	291	23	)	)	PUNCT
ejpam-6657	291	24	which	which	PRON
ejpam-6657	291	25	leads	lead	VERB
ejpam-6657	291	26	to	to	ADP
ejpam-6657	291	27	the	the	DET
ejpam-6657	291	28	identity	identity	NOUN
ejpam-6657	291	29	:	:	PUNCT
ejpam-6657	291	30	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	291	31	h	h	NOUN
ejpam-6657	291	32	[	[	PUNCT
ejpam-6657	292	1	∞∑	∞∑	PROPN
ejpam-6657	292	2	n=0	n=0	NUM
ejpam-6657	292	3	e(r)h	e(r)h	PROPN
ejpam-6657	293	1	[	[	X
ejpam-6657	293	2	h	h	X
ejpam-6657	293	3	]	]	X
ejpam-6657	293	4	n	n	PROPN
ejpam-6657	293	5	(	(	PUNCT
ejpam-6657	293	6	ξ1	ξ1	PROPN
ejpam-6657	293	7	,	,	PUNCT
ejpam-6657	293	8	ξ2	ξ2	ADJ
ejpam-6657	293	9	,	,	PUNCT
ejpam-6657	293	10	ξ3	ξ3	PROPN
ejpam-6657	293	11	)	)	PUNCT
ejpam-6657	293	12	tn	tn	PROPN
ejpam-6657	293	13	n	n	NUM
ejpam-6657	293	14	!	!	PUNCT
ejpam-6657	293	15	]	]	PUNCT
ejpam-6657	294	1	=	=	PUNCT
ejpam-6657	294	2	t	t	X
ejpam-6657	294	3	[	[	PUNCT
ejpam-6657	294	4	∞∑	∞∑	PROPN
ejpam-6657	294	5	n=0	n=0	NUM
ejpam-6657	294	6	e(r)h	e(r)h	PROPN
ejpam-6657	295	1	[	[	X
ejpam-6657	295	2	h	h	X
ejpam-6657	295	3	]	]	X
ejpam-6657	295	4	n	n	PROPN
ejpam-6657	295	5	(	(	PUNCT
ejpam-6657	295	6	ξ1	ξ1	PROPN
ejpam-6657	295	7	,	,	PUNCT
ejpam-6657	295	8	ξ2	ξ2	ADJ
ejpam-6657	295	9	,	,	PUNCT
ejpam-6657	295	10	ξ3	ξ3	PROPN
ejpam-6657	295	11	)	)	PUNCT
ejpam-6657	295	12	tn	tn	PROPN
ejpam-6657	295	13	n	n	NUM
ejpam-6657	295	14	!	!	PUNCT
ejpam-6657	295	15	]	]	PUNCT
ejpam-6657	295	16	.	.	PUNCT
ejpam-6657	296	1	(	(	PUNCT
ejpam-6657	296	2	55	55	NUM
ejpam-6657	296	3	)	)	PUNCT
ejpam-6657	296	4	next	next	ADV
ejpam-6657	296	5	,	,	PUNCT
ejpam-6657	296	6	differentiating	differentiate	VERB
ejpam-6657	296	7	equation	equation	NOUN
ejpam-6657	296	8	(	(	PUNCT
ejpam-6657	296	9	29	29	NUM
ejpam-6657	296	10	)	)	PUNCT
ejpam-6657	296	11	with	with	ADP
ejpam-6657	296	12	respect	respect	NOUN
ejpam-6657	296	13	to	to	ADP
ejpam-6657	296	14	t	t	PROPN
ejpam-6657	296	15	,	,	PUNCT
ejpam-6657	296	16	we	we	PRON
ejpam-6657	296	17	obtain	obtain	VERB
ejpam-6657	296	18	:	:	PUNCT
ejpam-6657	296	19	∂	∂	NUM
ejpam-6657	296	20	∂t	∂t	PROPN
ejpam-6657	296	21	{	{	PUNCT
ejpam-6657	296	22	1	1	NUM
ejpam-6657	296	23	1−	1−	NUM
ejpam-6657	296	24	ξ3tr	ξ3tr	NUM
ejpam-6657	296	25	(	(	PUNCT
ejpam-6657	296	26	1	1	NUM
ejpam-6657	296	27	+	+	NUM
ejpam-6657	296	28	ht	ht	NOUN
ejpam-6657	296	29	)	)	PUNCT
ejpam-6657	296	30	ξ1	ξ1	PROPN
ejpam-6657	296	31	h	h	NOUN
ejpam-6657	296	32	(	(	PUNCT
ejpam-6657	296	33	1	1	NUM
ejpam-6657	296	34	+	+	NUM
ejpam-6657	296	35	ht2	ht2	NOUN
ejpam-6657	296	36	)	)	PUNCT
ejpam-6657	296	37	ξ2	ξ2	NOUN
ejpam-6657	297	1	h	h	NOUN
ejpam-6657	297	2	}	}	PUNCT
ejpam-6657	297	3	=	=	SYM
ejpam-6657	297	4	∂	∂	NUM
ejpam-6657	297	5	∂t	∂t	PROPN
ejpam-6657	297	6	{	{	PUNCT
ejpam-6657	297	7	∞∑	∞∑	PROPN
ejpam-6657	297	8	n=0	n=0	NUM
ejpam-6657	297	9	e(r)h	e(r)h	PROPN
ejpam-6657	298	1	[	[	X
ejpam-6657	298	2	h	h	X
ejpam-6657	298	3	]	]	X
ejpam-6657	298	4	n	n	PROPN
ejpam-6657	298	5	(	(	PUNCT
ejpam-6657	298	6	ξ1	ξ1	PROPN
ejpam-6657	298	7	,	,	PUNCT
ejpam-6657	298	8	ξ2	ξ2	ADJ
ejpam-6657	298	9	,	,	PUNCT
ejpam-6657	298	10	ξ3	ξ3	PROPN
ejpam-6657	298	11	)	)	PUNCT
ejpam-6657	298	12	tn	tn	PROPN
ejpam-6657	298	13	n	n	PROPN
ejpam-6657	298	14	!	!	PUNCT
ejpam-6657	298	15	}	}	PUNCT
ejpam-6657	299	1	(	(	PUNCT
ejpam-6657	299	2	56	56	X
ejpam-6657	299	3	)	)	PUNCT
ejpam-6657	299	4	h.	h.	PROPN
ejpam-6657	299	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	299	6	et	et	PROPN
ejpam-6657	299	7	al	al	PROPN
ejpam-6657	299	8	.	.	PUNCT
ejpam-6657	299	9	/	/	SYM
ejpam-6657	299	10	eur	eur	PROPN
ejpam-6657	299	11	.	.	PUNCT
ejpam-6657	300	1	j.	j.	PROPN
ejpam-6657	300	2	pure	pure	PROPN
ejpam-6657	300	3	appl	appl	PROPN
ejpam-6657	300	4	.	.	PROPN
ejpam-6657	300	5	math	math	PROPN
ejpam-6657	300	6	,	,	PUNCT
ejpam-6657	300	7	18	18	NUM
ejpam-6657	300	8	(	(	PUNCT
ejpam-6657	300	9	3	3	NUM
ejpam-6657	300	10	)	)	PUNCT
ejpam-6657	300	11	(	(	PUNCT
ejpam-6657	300	12	2025	2025	NUM
ejpam-6657	300	13	)	)	PUNCT
ejpam-6657	300	14	,	,	PUNCT
ejpam-6657	300	15	6657	6657	NUM
ejpam-6657	300	16	11	11	NUM
ejpam-6657	300	17	of	of	ADP
ejpam-6657	300	18	16	16	NUM
ejpam-6657	300	19	(	(	PUNCT
ejpam-6657	300	20	ξ1	ξ1	NOUN
ejpam-6657	300	21	1	1	NUM
ejpam-6657	300	22	+	+	CCONJ
ejpam-6657	300	23	ht	ht	PROPN
ejpam-6657	301	1	+	+	PROPN
ejpam-6657	301	2	rξ3dξ3ξ3	rξ3dξ3ξ3	PROPN
ejpam-6657	301	3	t	t	PROPN
ejpam-6657	301	4	r−1	r−1	PROPN
ejpam-6657	301	5	+	+	CCONJ
ejpam-6657	301	6	2nξ2	2nξ2	NUM
ejpam-6657	301	7	1	1	NUM
ejpam-6657	301	8	+	+	CCONJ
ejpam-6657	301	9	ht2	ht2	NOUN
ejpam-6657	301	10	)	)	PUNCT
ejpam-6657	301	11	{	{	PUNCT
ejpam-6657	302	1	∞∑	∞∑	PRON
ejpam-6657	302	2	n=0	n=0	NUM
ejpam-6657	302	3	e(r)h	e(r)h	PROPN
ejpam-6657	303	1	[	[	X
ejpam-6657	303	2	h	h	X
ejpam-6657	303	3	]	]	X
ejpam-6657	303	4	n	n	PROPN
ejpam-6657	303	5	(	(	PUNCT
ejpam-6657	303	6	ξ1	ξ1	PROPN
ejpam-6657	303	7	,	,	PUNCT
ejpam-6657	303	8	ξ2	ξ2	ADJ
ejpam-6657	303	9	,	,	PUNCT
ejpam-6657	303	10	ξ3	ξ3	PROPN
ejpam-6657	303	11	)	)	PUNCT
ejpam-6657	303	12	tn	tn	PROPN
ejpam-6657	303	13	n	n	PROPN
ejpam-6657	303	14	!	!	PUNCT
ejpam-6657	303	15	}	}	PUNCT
ejpam-6657	304	1	=	=	SYM
ejpam-6657	304	2	n	n	PRON
ejpam-6657	305	1	∞∑	∞∑	PRON
ejpam-6657	305	2	n=0	n=0	PUNCT
ejpam-6657	305	3	e(r)h	e(r)h	PROPN
ejpam-6657	306	1	[	[	X
ejpam-6657	306	2	h	h	X
ejpam-6657	306	3	]	]	X
ejpam-6657	306	4	n	n	PROPN
ejpam-6657	306	5	(	(	PUNCT
ejpam-6657	306	6	ξ1	ξ1	PROPN
ejpam-6657	306	7	,	,	PUNCT
ejpam-6657	306	8	ξ2	ξ2	ADJ
ejpam-6657	306	9	,	,	PUNCT
ejpam-6657	306	10	ξ3	ξ3	NOUN
ejpam-6657	306	11	)	)	PUNCT
ejpam-6657	306	12	tn−1	tn−1	PROPN
ejpam-6657	306	13	n	n	PRON
ejpam-6657	306	14	!	!	PUNCT
ejpam-6657	306	15	.	.	PUNCT
ejpam-6657	307	1	(	(	PUNCT
ejpam-6657	307	2	57	57	X
ejpam-6657	307	3	)	)	PUNCT
ejpam-6657	307	4	applying	apply	VERB
ejpam-6657	307	5	identity	identity	NOUN
ejpam-6657	307	6	(	(	PUNCT
ejpam-6657	307	7	29	29	NUM
ejpam-6657	307	8	)	)	PUNCT
ejpam-6657	307	9	and	and	CCONJ
ejpam-6657	307	10	shifting	shift	VERB
ejpam-6657	307	11	n	n	X
ejpam-6657	307	12	→	→	SYM
ejpam-6657	307	13	n	n	CCONJ
ejpam-6657	307	14	+	+	CCONJ
ejpam-6657	307	15	1	1	NUM
ejpam-6657	307	16	on	on	ADP
ejpam-6657	307	17	the	the	DET
ejpam-6657	307	18	right	right	ADJ
ejpam-6657	307	19	-	-	PUNCT
ejpam-6657	307	20	hand	hand	NOUN
ejpam-6657	307	21	side	side	NOUN
ejpam-6657	307	22	of	of	ADP
ejpam-6657	307	23	(	(	PUNCT
ejpam-6657	307	24	57	57	NUM
ejpam-6657	307	25	)	)	PUNCT
ejpam-6657	307	26	,	,	PUNCT
ejpam-6657	307	27	we	we	PRON
ejpam-6657	307	28	derive	derive	VERB
ejpam-6657	307	29	the	the	DET
ejpam-6657	307	30	operator	operator	NOUN
ejpam-6657	307	31	formula	formula	NOUN
ejpam-6657	307	32	(	(	PUNCT
ejpam-6657	307	33	52	52	NUM
ejpam-6657	307	34	)	)	PUNCT
ejpam-6657	307	35	.	.	PUNCT
ejpam-6657	308	1	moreover	moreover	ADV
ejpam-6657	308	2	,	,	PUNCT
ejpam-6657	308	3	from	from	ADP
ejpam-6657	308	4	identities	identity	NOUN
ejpam-6657	308	5	(	(	PUNCT
ejpam-6657	308	6	15	15	NUM
ejpam-6657	308	7	)	)	PUNCT
ejpam-6657	308	8	and	and	CCONJ
ejpam-6657	308	9	(	(	PUNCT
ejpam-6657	308	10	55	55	NUM
ejpam-6657	308	11	)	)	PUNCT
ejpam-6657	308	12	,	,	PUNCT
ejpam-6657	308	13	it	it	PRON
ejpam-6657	308	14	follows	follow	VERB
ejpam-6657	308	15	:	:	PUNCT
ejpam-6657	308	16	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	308	17	h	h	NOUN
ejpam-6657	308	18	[	[	PUNCT
ejpam-6657	308	19	∞∑	∞∑	PROPN
ejpam-6657	308	20	n=0	n=0	NUM
ejpam-6657	308	21	e(r)h	e(r)h	PROPN
ejpam-6657	309	1	[	[	X
ejpam-6657	309	2	h	h	X
ejpam-6657	309	3	]	]	X
ejpam-6657	309	4	n	n	PROPN
ejpam-6657	309	5	(	(	PUNCT
ejpam-6657	309	6	ξ1	ξ1	PROPN
ejpam-6657	309	7	,	,	PUNCT
ejpam-6657	309	8	ξ2	ξ2	ADJ
ejpam-6657	309	9	,	,	PUNCT
ejpam-6657	309	10	ξ3	ξ3	PROPN
ejpam-6657	309	11	)	)	PUNCT
ejpam-6657	309	12	tn	tn	PROPN
ejpam-6657	309	13	n	n	NUM
ejpam-6657	309	14	!	!	PUNCT
ejpam-6657	309	15	]	]	PUNCT
ejpam-6657	310	1	=	=	PUNCT
ejpam-6657	311	1	n	n	X
ejpam-6657	311	2	[	[	PUNCT
ejpam-6657	311	3	∞∑	∞∑	PROPN
ejpam-6657	311	4	n=0	n=0	NUM
ejpam-6657	311	5	e(r)h	e(r)h	PROPN
ejpam-6657	312	1	[	[	X
ejpam-6657	312	2	h	h	X
ejpam-6657	312	3	]	]	X
ejpam-6657	312	4	n−1(ξ1	n−1(ξ1	ADP
ejpam-6657	312	5	,	,	PUNCT
ejpam-6657	312	6	ξ2	ξ2	ADJ
ejpam-6657	312	7	,	,	PUNCT
ejpam-6657	312	8	ξ3	ξ3	NOUN
ejpam-6657	312	9	)	)	PUNCT
ejpam-6657	312	10	tn	tn	PROPN
ejpam-6657	312	11	n	n	PROPN
ejpam-6657	312	12	!	!	PUNCT
ejpam-6657	312	13	]	]	PUNCT
ejpam-6657	312	14	,	,	PUNCT
ejpam-6657	312	15	(	(	PUNCT
ejpam-6657	312	16	58	58	X
ejpam-6657	312	17	)	)	PUNCT
ejpam-6657	312	18	yielding	yield	VERB
ejpam-6657	312	19	the	the	DET
ejpam-6657	312	20	derivative	derivative	ADJ
ejpam-6657	312	21	operator	operator	NOUN
ejpam-6657	312	22	form	form	NOUN
ejpam-6657	312	23	in	in	ADP
ejpam-6657	312	24	(	(	PUNCT
ejpam-6657	312	25	53	53	NUM
ejpam-6657	312	26	)	)	PUNCT
ejpam-6657	312	27	.	.	PUNCT
ejpam-6657	313	1	now	now	ADV
ejpam-6657	313	2	,	,	PUNCT
ejpam-6657	313	3	we	we	PRON
ejpam-6657	313	4	derive	derive	VERB
ejpam-6657	313	5	the	the	DET
ejpam-6657	313	6	differential	differential	ADJ
ejpam-6657	313	7	equation	equation	NOUN
ejpam-6657	313	8	satisfied	satisfy	VERB
ejpam-6657	313	9	by	by	ADP
ejpam-6657	313	10	the	the	DET
ejpam-6657	313	11	∆h	∆h	PROPN
ejpam-6657	313	12	-	-	PUNCT
ejpam-6657	313	13	truncated	truncate	VERB
ejpam-6657	313	14	exponentialbased	exponentialbase	VERB
ejpam-6657	313	15	hermite	hermite	ADJ
ejpam-6657	313	16	polynomials	polynomial	VERB
ejpam-6657	313	17	erh	erh	PROPN
ejpam-6657	314	1	[	[	X
ejpam-6657	314	2	h	h	X
ejpam-6657	314	3	]	]	X
ejpam-6657	314	4	n	n	PROPN
ejpam-6657	314	5	(	(	PUNCT
ejpam-6657	314	6	ξ1	ξ1	PROPN
ejpam-6657	314	7	,	,	PUNCT
ejpam-6657	314	8	ξ2	ξ2	ADJ
ejpam-6657	314	9	,	,	PUNCT
ejpam-6657	314	10	ξ3	ξ3	PROPN
ejpam-6657	314	11	)	)	PUNCT
ejpam-6657	314	12	through	through	ADP
ejpam-6657	314	13	the	the	DET
ejpam-6657	314	14	following	follow	VERB
ejpam-6657	314	15	result	result	NOUN
ejpam-6657	314	16	:	:	PUNCT
ejpam-6657	314	17	theorem	theorem	VERB
ejpam-6657	314	18	8	8	NUM
ejpam-6657	314	19	.	.	PUNCT
ejpam-6657	315	1	the	the	DET
ejpam-6657	315	2	∆h	∆h	PROPN
ejpam-6657	315	3	-	-	PUNCT
ejpam-6657	315	4	truncated	truncate	VERB
ejpam-6657	315	5	exponential	exponential	NOUN
ejpam-6657	315	6	-	-	PUNCT
ejpam-6657	315	7	based	base	VERB
ejpam-6657	315	8	hermite	hermite	ADJ
ejpam-6657	315	9	polynomials	polynomial	VERB
ejpam-6657	315	10	e(r)h	e(r)h	PROPN
ejpam-6657	316	1	[	[	X
ejpam-6657	316	2	h	h	X
ejpam-6657	316	3	]	]	X
ejpam-6657	316	4	n	n	PROPN
ejpam-6657	316	5	(	(	PUNCT
ejpam-6657	316	6	ξ1	ξ1	PROPN
ejpam-6657	316	7	,	,	PUNCT
ejpam-6657	316	8	ξ2	ξ2	ADJ
ejpam-6657	316	9	,	,	PUNCT
ejpam-6657	316	10	ξ3	ξ3	NOUN
ejpam-6657	316	11	)	)	PUNCT
ejpam-6657	316	12	obey	obey	VERB
ejpam-6657	316	13	the	the	DET
ejpam-6657	316	14	differential	differential	ADJ
ejpam-6657	316	15	equation	equation	NOUN
ejpam-6657	316	16	:(	:(	PUNCT
ejpam-6657	317	1	ξ1	ξ1	NOUN
ejpam-6657	317	2	1	1	NUM
ejpam-6657	318	1	+	+	NUM
ejpam-6657	318	2	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	318	3	+	+	CCONJ
ejpam-6657	318	4	rξ3dξ3ξ3	rξ3dξ3ξ3	PUNCT
ejpam-6657	318	5	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	318	6	r−1	r−1	PROPN
ejpam-6657	318	7	h	h	NOUN
ejpam-6657	318	8	+	+	CCONJ
ejpam-6657	318	9	2nξ2h	2nξ2h	NUM
ejpam-6657	318	10	h+	h+	PUNCT
ejpam-6657	318	11	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	318	12	2	2	NUM
ejpam-6657	318	13	−	−	PROPN
ejpam-6657	318	14	nh	nh	PROPN
ejpam-6657	318	15	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	318	16	)	)	PUNCT
ejpam-6657	318	17	e(r)h	e(r)h	PROPN
ejpam-6657	319	1	[	[	X
ejpam-6657	319	2	h	h	X
ejpam-6657	319	3	]	]	X
ejpam-6657	319	4	n	n	PROPN
ejpam-6657	319	5	(	(	PUNCT
ejpam-6657	319	6	ξ1	ξ1	PROPN
ejpam-6657	319	7	,	,	PUNCT
ejpam-6657	319	8	ξ2	ξ2	ADJ
ejpam-6657	319	9	,	,	PUNCT
ejpam-6657	319	10	ξ3	ξ3	NOUN
ejpam-6657	319	11	)	)	PUNCT
ejpam-6657	319	12	=	=	SYM
ejpam-6657	319	13	0	0	X
ejpam-6657	319	14	.	.	PUNCT
ejpam-6657	320	1	(	(	PUNCT
ejpam-6657	320	2	59	59	NUM
ejpam-6657	320	3	)	)	PUNCT
ejpam-6657	320	4	proof	proof	NOUN
ejpam-6657	320	5	.	.	PUNCT
ejpam-6657	321	1	substituting	substitute	VERB
ejpam-6657	321	2	the	the	DET
ejpam-6657	321	3	operator	operator	NOUN
ejpam-6657	321	4	forms	form	NOUN
ejpam-6657	321	5	(	(	PUNCT
ejpam-6657	321	6	52	52	NUM
ejpam-6657	321	7	)	)	PUNCT
ejpam-6657	321	8	and	and	CCONJ
ejpam-6657	321	9	(	(	PUNCT
ejpam-6657	321	10	53	53	NUM
ejpam-6657	321	11	)	)	PUNCT
ejpam-6657	321	12	into	into	ADP
ejpam-6657	321	13	the	the	DET
ejpam-6657	321	14	identity	identity	NOUN
ejpam-6657	321	15	(	(	PUNCT
ejpam-6657	321	16	17	17	NUM
ejpam-6657	321	17	)	)	PUNCT
ejpam-6657	321	18	,	,	PUNCT
ejpam-6657	321	19	we	we	PRON
ejpam-6657	321	20	get	get	VERB
ejpam-6657	321	21	:(	:(	PUNCT
ejpam-6657	321	22	ξ1	ξ1	NOUN
ejpam-6657	321	23	1	1	NUM
ejpam-6657	321	24	+	+	PUNCT
ejpam-6657	321	25	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	321	26	+	+	CCONJ
ejpam-6657	321	27	rξ3dξ3ξ3	rξ3dξ3ξ3	PUNCT
ejpam-6657	321	28	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	321	29	r−1	r−1	PROPN
ejpam-6657	321	30	h	h	NOUN
ejpam-6657	321	31	+	+	CCONJ
ejpam-6657	321	32	2nξ2h	2nξ2h	NUM
ejpam-6657	321	33	h+	h+	PUNCT
ejpam-6657	321	34	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	321	35	2	2	NUM
ejpam-6657	321	36	)	)	PUNCT
ejpam-6657	322	1	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	322	2	h	h	NOUN
ejpam-6657	322	3	e(r)h	e(r)h	PROPN
ejpam-6657	323	1	[	[	X
ejpam-6657	323	2	h	h	X
ejpam-6657	323	3	]	]	X
ejpam-6657	323	4	n	n	PROPN
ejpam-6657	323	5	(	(	PUNCT
ejpam-6657	323	6	ξ1	ξ1	PROPN
ejpam-6657	323	7	,	,	PUNCT
ejpam-6657	323	8	ξ2	ξ2	ADJ
ejpam-6657	323	9	,	,	PUNCT
ejpam-6657	323	10	ξ3	ξ3	NOUN
ejpam-6657	323	11	)	)	PUNCT
ejpam-6657	323	12	=	=	PUNCT
ejpam-6657	324	1	ne(r)h	ne(r)h	NUM
ejpam-6657	325	1	[	[	X
ejpam-6657	325	2	h	h	X
ejpam-6657	325	3	]	]	X
ejpam-6657	325	4	n	n	PROPN
ejpam-6657	325	5	(	(	PUNCT
ejpam-6657	325	6	ξ1	ξ1	PROPN
ejpam-6657	325	7	,	,	PUNCT
ejpam-6657	325	8	ξ2	ξ2	ADJ
ejpam-6657	325	9	,	,	PUNCT
ejpam-6657	325	10	ξ3	ξ3	NOUN
ejpam-6657	325	11	)	)	PUNCT
ejpam-6657	325	12	.	.	PUNCT
ejpam-6657	326	1	(	(	PUNCT
ejpam-6657	326	2	60	60	X
ejpam-6657	326	3	)	)	PUNCT
ejpam-6657	326	4	simplifying	simplify	VERB
ejpam-6657	326	5	the	the	DET
ejpam-6657	326	6	above	above	ADJ
ejpam-6657	326	7	yields	yield	NOUN
ejpam-6657	326	8	the	the	DET
ejpam-6657	326	9	claimed	claim	VERB
ejpam-6657	326	10	result	result	NOUN
ejpam-6657	326	11	(	(	PUNCT
ejpam-6657	326	12	59	59	NUM
ejpam-6657	326	13	)	)	PUNCT
ejpam-6657	326	14	.	.	PUNCT
ejpam-6657	327	1	we	we	PRON
ejpam-6657	327	2	now	now	ADV
ejpam-6657	327	3	establish	establish	VERB
ejpam-6657	327	4	the	the	DET
ejpam-6657	327	5	following	follow	VERB
ejpam-6657	327	6	operational	operational	ADJ
ejpam-6657	327	7	formula	formula	NOUN
ejpam-6657	327	8	involving	involve	VERB
ejpam-6657	327	9	e(r)h	e(r)h	PROPN
ejpam-6657	328	1	[	[	X
ejpam-6657	328	2	h	h	X
ejpam-6657	328	3	]	]	X
ejpam-6657	328	4	n	n	PROPN
ejpam-6657	328	5	(	(	PUNCT
ejpam-6657	328	6	ξ1	ξ1	PROPN
ejpam-6657	328	7	,	,	PUNCT
ejpam-6657	328	8	ξ2	ξ2	ADJ
ejpam-6657	328	9	,	,	PUNCT
ejpam-6657	328	10	ξ3	ξ3	NOUN
ejpam-6657	328	11	):	):	PUNCT
ejpam-6657	328	12	theorem	theorem	NOUN
ejpam-6657	328	13	9	9	NUM
ejpam-6657	328	14	.	.	PUNCT
ejpam-6657	329	1	the	the	DET
ejpam-6657	329	2	following	follow	VERB
ejpam-6657	329	3	operational	operational	ADJ
ejpam-6657	329	4	relation	relation	NOUN
ejpam-6657	329	5	holds	hold	VERB
ejpam-6657	329	6	between	between	ADP
ejpam-6657	329	7	the	the	DET
ejpam-6657	329	8	∆h	∆h	PROPN
ejpam-6657	329	9	-	-	PUNCT
ejpam-6657	329	10	truncated	truncate	VERB
ejpam-6657	329	11	exponentialbased	exponentialbase	VERB
ejpam-6657	329	12	hermite	hermite	ADJ
ejpam-6657	329	13	polynomials	polynomial	VERB
ejpam-6657	329	14	e(r)h	e(r)h	PROPN
ejpam-6657	330	1	[	[	X
ejpam-6657	330	2	h	h	X
ejpam-6657	330	3	]	]	X
ejpam-6657	330	4	n	n	PROPN
ejpam-6657	330	5	(	(	PUNCT
ejpam-6657	330	6	ξ1	ξ1	PROPN
ejpam-6657	330	7	,	,	PUNCT
ejpam-6657	330	8	ξ2	ξ2	ADJ
ejpam-6657	330	9	,	,	PUNCT
ejpam-6657	330	10	ξ3	ξ3	NOUN
ejpam-6657	330	11	)	)	PUNCT
ejpam-6657	330	12	and	and	CCONJ
ejpam-6657	330	13	the	the	DET
ejpam-6657	330	14	∆h	∆h	PROPN
ejpam-6657	330	15	-	-	PUNCT
ejpam-6657	330	16	hermite	hermite	ADJ
ejpam-6657	330	17	polynomials	polynomial	NOUN
ejpam-6657	330	18	h[h	h[h	NOUN
ejpam-6657	330	19	]	]	PUNCT
ejpam-6657	330	20	n	n	PROPN
ejpam-6657	330	21	(	(	PUNCT
ejpam-6657	330	22	ξ1	ξ1	NOUN
ejpam-6657	330	23	,	,	PUNCT
ejpam-6657	330	24	ξ2	ξ2	ADJ
ejpam-6657	330	25	):	):	PUNCT
ejpam-6657	330	26	e(r)h	e(r)h	PROPN
ejpam-6657	331	1	[	[	X
ejpam-6657	331	2	h	h	X
ejpam-6657	331	3	]	]	X
ejpam-6657	331	4	n	n	PROPN
ejpam-6657	331	5	(	(	PUNCT
ejpam-6657	331	6	ξ1	ξ1	PROPN
ejpam-6657	331	7	,	,	PUNCT
ejpam-6657	331	8	ξ2	ξ2	ADJ
ejpam-6657	331	9	,	,	PUNCT
ejpam-6657	331	10	ξ3	ξ3	NOUN
ejpam-6657	331	11	)	)	PUNCT
ejpam-6657	331	12	=	=	PUNCT
ejpam-6657	331	13	exp(rξ3dξ3ξ3	exp(rξ3dξ3ξ3	PUNCT
ejpam-6657	331	14	ξ1∆h	ξ1∆h	NOUN
ejpam-6657	331	15	r	r	NOUN
ejpam-6657	331	16	h	h	NOUN
ejpam-6657	331	17	)	)	PUNCT
ejpam-6657	331	18	{	{	PUNCT
ejpam-6657	331	19	h[h	h[h	NOUN
ejpam-6657	331	20	]	]	PUNCT
ejpam-6657	331	21	n	n	CCONJ
ejpam-6657	331	22	(	(	PUNCT
ejpam-6657	331	23	ξ1	ξ1	NOUN
ejpam-6657	331	24	,	,	PUNCT
ejpam-6657	331	25	ξ2	ξ2	NOUN
ejpam-6657	331	26	)	)	PUNCT
ejpam-6657	331	27	}	}	PUNCT
ejpam-6657	331	28	.	.	PUNCT
ejpam-6657	332	1	(	(	PUNCT
ejpam-6657	332	2	61	61	NUM
ejpam-6657	332	3	)	)	PUNCT
ejpam-6657	332	4	proof	proof	NOUN
ejpam-6657	332	5	.	.	PUNCT
ejpam-6657	333	1	using	use	VERB
ejpam-6657	333	2	equations	equation	NOUN
ejpam-6657	333	3	(	(	PUNCT
ejpam-6657	333	4	27	27	NUM
ejpam-6657	333	5	)	)	PUNCT
ejpam-6657	333	6	and	and	CCONJ
ejpam-6657	333	7	(	(	PUNCT
ejpam-6657	333	8	58	58	NUM
ejpam-6657	333	9	)	)	PUNCT
ejpam-6657	333	10	,	,	PUNCT
ejpam-6657	333	11	and	and	CCONJ
ejpam-6657	333	12	applying	apply	VERB
ejpam-6657	333	13	identity	identity	NOUN
ejpam-6657	333	14	(	(	PUNCT
ejpam-6657	333	15	29	29	NUM
ejpam-6657	333	16	)	)	PUNCT
ejpam-6657	333	17	,	,	PUNCT
ejpam-6657	333	18	the	the	DET
ejpam-6657	333	19	result	result	NOUN
ejpam-6657	333	20	follows	follow	VERB
ejpam-6657	333	21	immediately	immediately	ADV
ejpam-6657	333	22	.	.	PUNCT
ejpam-6657	334	1	5	5	X
ejpam-6657	334	2	.	.	X
ejpam-6657	334	3	symmetric	symmetric	ADJ
ejpam-6657	334	4	identities	identity	NOUN
ejpam-6657	334	5	in	in	ADP
ejpam-6657	334	6	this	this	DET
ejpam-6657	334	7	section	section	NOUN
ejpam-6657	334	8	,	,	PUNCT
ejpam-6657	334	9	we	we	PRON
ejpam-6657	334	10	investigate	investigate	VERB
ejpam-6657	334	11	symmetric	symmetric	ADJ
ejpam-6657	334	12	identities	identity	NOUN
ejpam-6657	334	13	inherent	inherent	ADJ
ejpam-6657	334	14	to	to	ADP
ejpam-6657	334	15	the	the	DET
ejpam-6657	334	16	three	three	NUM
ejpam-6657	334	17	-	-	PUNCT
ejpam-6657	334	18	variable	variable	ADJ
ejpam-6657	334	19	∆h	∆h	PROPN
ejpam-6657	334	20	special	special	ADJ
ejpam-6657	334	21	polynomials	polynomial	NOUN
ejpam-6657	334	22	.	.	PUNCT
ejpam-6657	335	1	these	these	DET
ejpam-6657	335	2	identities	identity	NOUN
ejpam-6657	335	3	unveil	unveil	VERB
ejpam-6657	335	4	intriguing	intriguing	ADJ
ejpam-6657	335	5	relationships	relationship	NOUN
ejpam-6657	335	6	between	between	ADP
ejpam-6657	335	7	the	the	DET
ejpam-6657	335	8	variables	variable	NOUN
ejpam-6657	335	9	and	and	CCONJ
ejpam-6657	335	10	coefficients	coefficient	NOUN
ejpam-6657	335	11	within	within	ADP
ejpam-6657	335	12	the	the	DET
ejpam-6657	335	13	polynomials	polynomial	NOUN
ejpam-6657	335	14	,	,	PUNCT
ejpam-6657	335	15	shedding	shed	VERB
ejpam-6657	335	16	light	light	NOUN
ejpam-6657	335	17	on	on	ADP
ejpam-6657	335	18	their	their	PRON
ejpam-6657	335	19	underlying	underlying	ADJ
ejpam-6657	335	20	symmetrical	symmetrical	ADJ
ejpam-6657	335	21	properties	property	NOUN
ejpam-6657	335	22	.	.	PUNCT
ejpam-6657	336	1	by	by	ADP
ejpam-6657	336	2	exploring	explore	VERB
ejpam-6657	336	3	how	how	SCONJ
ejpam-6657	336	4	the	the	DET
ejpam-6657	336	5	polynomials	polynomial	NOUN
ejpam-6657	336	6	behave	behave	VERB
ejpam-6657	336	7	under	under	ADP
ejpam-6657	336	8	transformations	transformation	NOUN
ejpam-6657	336	9	that	that	PRON
ejpam-6657	336	10	interchange	interchange	VERB
ejpam-6657	336	11	the	the	DET
ejpam-6657	336	12	variables	variable	NOUN
ejpam-6657	336	13	or	or	CCONJ
ejpam-6657	336	14	coefficients	coefficient	NOUN
ejpam-6657	336	15	,	,	PUNCT
ejpam-6657	336	16	we	we	PRON
ejpam-6657	336	17	uncover	uncover	VERB
ejpam-6657	336	18	profound	profound	ADJ
ejpam-6657	336	19	connections	connection	NOUN
ejpam-6657	336	20	that	that	PRON
ejpam-6657	336	21	extend	extend	VERB
ejpam-6657	336	22	beyond	beyond	ADP
ejpam-6657	336	23	h.	h.	PROPN
ejpam-6657	336	24	qawaqneh	qawaqneh	PROPN
ejpam-6657	337	1	et	et	PROPN
ejpam-6657	337	2	al	al	PROPN
ejpam-6657	337	3	.	.	PUNCT
ejpam-6657	337	4	/	/	SYM
ejpam-6657	337	5	eur	eur	PROPN
ejpam-6657	337	6	.	.	PUNCT
ejpam-6657	338	1	j.	j.	PROPN
ejpam-6657	338	2	pure	pure	PROPN
ejpam-6657	338	3	appl	appl	PROPN
ejpam-6657	338	4	.	.	PROPN
ejpam-6657	338	5	math	math	PROPN
ejpam-6657	338	6	,	,	PUNCT
ejpam-6657	338	7	18	18	NUM
ejpam-6657	338	8	(	(	PUNCT
ejpam-6657	338	9	3	3	NUM
ejpam-6657	338	10	)	)	PUNCT
ejpam-6657	338	11	(	(	PUNCT
ejpam-6657	338	12	2025	2025	NUM
ejpam-6657	338	13	)	)	PUNCT
ejpam-6657	338	14	,	,	PUNCT
ejpam-6657	338	15	6657	6657	NUM
ejpam-6657	338	16	12	12	NUM
ejpam-6657	338	17	of	of	ADP
ejpam-6657	338	18	16	16	NUM
ejpam-6657	338	19	their	their	PRON
ejpam-6657	338	20	initial	initial	ADJ
ejpam-6657	338	21	definitions	definition	NOUN
ejpam-6657	338	22	.	.	PUNCT
ejpam-6657	339	1	these	these	DET
ejpam-6657	339	2	symmetric	symmetric	ADJ
ejpam-6657	339	3	identities	identity	NOUN
ejpam-6657	339	4	not	not	PART
ejpam-6657	339	5	only	only	ADV
ejpam-6657	339	6	deepen	deepen	VERB
ejpam-6657	339	7	our	our	PRON
ejpam-6657	339	8	understanding	understanding	NOUN
ejpam-6657	339	9	of	of	ADP
ejpam-6657	339	10	the	the	DET
ejpam-6657	339	11	polynomials	polynomial	NOUN
ejpam-6657	339	12	themselves	themselves	PRON
ejpam-6657	339	13	but	but	CCONJ
ejpam-6657	339	14	also	also	ADV
ejpam-6657	339	15	offer	offer	VERB
ejpam-6657	339	16	valuable	valuable	ADJ
ejpam-6657	339	17	insights	insight	NOUN
ejpam-6657	339	18	into	into	ADP
ejpam-6657	339	19	broader	broad	ADJ
ejpam-6657	339	20	mathematical	mathematical	ADJ
ejpam-6657	339	21	structures	structure	NOUN
ejpam-6657	339	22	and	and	CCONJ
ejpam-6657	339	23	phenomena	phenomenon	NOUN
ejpam-6657	339	24	.	.	PUNCT
ejpam-6657	340	1	through	through	ADP
ejpam-6657	340	2	systematic	systematic	ADJ
ejpam-6657	340	3	examination	examination	NOUN
ejpam-6657	340	4	and	and	CCONJ
ejpam-6657	340	5	rigorous	rigorous	ADJ
ejpam-6657	340	6	derivation	derivation	NOUN
ejpam-6657	340	7	,	,	PUNCT
ejpam-6657	340	8	we	we	PRON
ejpam-6657	340	9	establish	establish	VERB
ejpam-6657	340	10	a	a	DET
ejpam-6657	340	11	comprehensive	comprehensive	ADJ
ejpam-6657	340	12	framework	framework	NOUN
ejpam-6657	340	13	for	for	ADP
ejpam-6657	340	14	understanding	understanding	NOUN
ejpam-6657	340	15	and	and	CCONJ
ejpam-6657	340	16	exploiting	exploit	VERB
ejpam-6657	340	17	the	the	DET
ejpam-6657	340	18	symmetrical	symmetrical	ADJ
ejpam-6657	340	19	properties	property	NOUN
ejpam-6657	340	20	of	of	ADP
ejpam-6657	340	21	these	these	DET
ejpam-6657	340	22	two	two	NUM
ejpam-6657	340	23	-	-	PUNCT
ejpam-6657	340	24	variable	variable	ADJ
ejpam-6657	340	25	special	special	ADJ
ejpam-6657	340	26	polynomials	polynomial	NOUN
ejpam-6657	340	27	,	,	PUNCT
ejpam-6657	340	28	paving	pave	VERB
ejpam-6657	340	29	the	the	DET
ejpam-6657	340	30	way	way	NOUN
ejpam-6657	340	31	for	for	ADP
ejpam-6657	340	32	further	further	ADJ
ejpam-6657	340	33	advancements	advancement	NOUN
ejpam-6657	340	34	in	in	ADP
ejpam-6657	340	35	both	both	CCONJ
ejpam-6657	340	36	theoretical	theoretical	ADJ
ejpam-6657	340	37	analyses	analysis	NOUN
ejpam-6657	340	38	and	and	CCONJ
ejpam-6657	340	39	practical	practical	ADJ
ejpam-6657	340	40	applications	application	NOUN
ejpam-6657	340	41	.	.	PUNCT
ejpam-6657	341	1	theorem	theorem	VERB
ejpam-6657	341	2	10	10	NUM
ejpam-6657	341	3	.	.	PUNCT
ejpam-6657	342	1	for	for	ADP
ejpam-6657	342	2	a	a	DET
ejpam-6657	342	3	̸=	̸=	PROPN
ejpam-6657	342	4	b	b	PROPN
ejpam-6657	342	5	,	,	PUNCT
ejpam-6657	342	6	a	a	PRON
ejpam-6657	342	7	,	,	PUNCT
ejpam-6657	342	8	b	b	X
ejpam-6657	342	9	>	>	X
ejpam-6657	342	10	0	0	PROPN
ejpam-6657	342	11	and	and	CCONJ
ejpam-6657	342	12	xi1	xi1	PROPN
ejpam-6657	342	13	,	,	PUNCT
ejpam-6657	342	14	ξ2	ξ2	PROPN
ejpam-6657	342	15	,	,	PUNCT
ejpam-6657	342	16	ν1	ν1	NOUN
ejpam-6657	342	17	,	,	PUNCT
ejpam-6657	342	18	ν2	ν2	NOUN
ejpam-6657	342	19	,	,	PUNCT
ejpam-6657	342	20	ϕ1	ϕ1	NOUN
ejpam-6657	342	21	,	,	PUNCT
ejpam-6657	342	22	ϕ2	ϕ2	ADV
ejpam-6657	342	23	∈	∈	PROPN
ejpam-6657	342	24	c	c	NOUN
ejpam-6657	342	25	,	,	PUNCT
ejpam-6657	342	26	we	we	PRON
ejpam-6657	342	27	have	have	VERB
ejpam-6657	342	28	n∑	n∑	NOUN
ejpam-6657	342	29	γ=0	γ=0	PROPN
ejpam-6657	342	30	(	(	PUNCT
ejpam-6657	342	31	n	n	CCONJ
ejpam-6657	342	32	γ	γ	X
ejpam-6657	342	33	)	)	PUNCT
ejpam-6657	342	34	an−γbγe(r)h	an−γbγe(r)h	PROPN
ejpam-6657	343	1	[	[	X
ejpam-6657	343	2	h	h	X
ejpam-6657	343	3	]	]	X
ejpam-6657	343	4	n−γ(aξ1	n−γ(aξ1	PROPN
ejpam-6657	343	5	,	,	PUNCT
ejpam-6657	343	6	aν1	aν1	NOUN
ejpam-6657	343	7	,	,	PUNCT
ejpam-6657	343	8	aϕ1)e(r)h	aϕ1)e(r)h	PROPN
ejpam-6657	344	1	[	[	X
ejpam-6657	344	2	h	h	X
ejpam-6657	344	3	]	]	X
ejpam-6657	344	4	γ	γ	X
ejpam-6657	344	5	(	(	PUNCT
ejpam-6657	344	6	bξ2	bξ2	PROPN
ejpam-6657	344	7	,	,	PUNCT
ejpam-6657	344	8	bν2	bν2	NOUN
ejpam-6657	344	9	,	,	PUNCT
ejpam-6657	344	10	bϕ2	bϕ2	NOUN
ejpam-6657	344	11	)	)	PUNCT
ejpam-6657	344	12	=	=	SYM
ejpam-6657	345	1	n∑	n∑	NOUN
ejpam-6657	345	2	γ=0	γ=0	PROPN
ejpam-6657	345	3	(	(	PUNCT
ejpam-6657	345	4	n	n	CCONJ
ejpam-6657	345	5	γ	γ	X
ejpam-6657	345	6	)	)	PUNCT
ejpam-6657	345	7	aγbn−γ	aγbn−γ	PROPN
ejpam-6657	345	8	e(r)h	e(r)h	PROPN
ejpam-6657	346	1	[	[	X
ejpam-6657	346	2	h	h	X
ejpam-6657	346	3	]	]	X
ejpam-6657	346	4	n−γ(aξ2	n−γ(aξ2	PROPN
ejpam-6657	346	5	,	,	PUNCT
ejpam-6657	346	6	aν2	aν2	PROPN
ejpam-6657	346	7	,	,	PUNCT
ejpam-6657	346	8	aϕ2)e(r)h	aϕ2)e(r)h	PROPN
ejpam-6657	347	1	[	[	X
ejpam-6657	347	2	h	h	X
ejpam-6657	347	3	]	]	X
ejpam-6657	347	4	γ	γ	X
ejpam-6657	347	5	(	(	PUNCT
ejpam-6657	347	6	bξ1	bξ1	PROPN
ejpam-6657	347	7	,	,	PUNCT
ejpam-6657	347	8	bν1	bν1	NOUN
ejpam-6657	347	9	,	,	PUNCT
ejpam-6657	347	10	bϕ1	bϕ1	PROPN
ejpam-6657	347	11	)	)	PUNCT
ejpam-6657	347	12	.	.	PUNCT
ejpam-6657	348	1	(	(	PUNCT
ejpam-6657	348	2	62	62	NUM
ejpam-6657	348	3	)	)	PUNCT
ejpam-6657	348	4	proof	proof	NOUN
ejpam-6657	348	5	.	.	PUNCT
ejpam-6657	349	1	let	let	VERB
ejpam-6657	349	2	a(t	a(t	VERB
ejpam-6657	349	3	)	)	PUNCT
ejpam-6657	349	4	=	=	SYM
ejpam-6657	350	1	1	1	NUM
ejpam-6657	350	2	1−	1−	NUM
ejpam-6657	350	3	ϕ1(abt)2	ϕ1(abt)2	PROPN
ejpam-6657	350	4	1	1	NUM
ejpam-6657	350	5	1−	1−	NUM
ejpam-6657	350	6	ϕ2(abt)2	ϕ2(abt)2	PROPN
ejpam-6657	350	7	(	(	PUNCT
ejpam-6657	350	8	1	1	NUM
ejpam-6657	350	9	+	+	NUM
ejpam-6657	350	10	ht	ht	PROPN
ejpam-6657	350	11	)	)	PUNCT
ejpam-6657	350	12	ab(ξ1+ξ2	ab(ξ1+ξ2	NOUN
ejpam-6657	350	13	)	)	PUNCT
ejpam-6657	350	14	h	h	NOUN
ejpam-6657	350	15	(	(	PUNCT
ejpam-6657	350	16	1	1	NUM
ejpam-6657	350	17	+	+	NUM
ejpam-6657	350	18	ht2	ht2	NOUN
ejpam-6657	350	19	)	)	PUNCT
ejpam-6657	350	20	ab(ν1+ν2	ab(ν1+ν2	NOUN
ejpam-6657	350	21	)	)	PUNCT
ejpam-6657	350	22	h	h	NOUN
ejpam-6657	350	23	(	(	PUNCT
ejpam-6657	350	24	63	63	NUM
ejpam-6657	350	25	)	)	PUNCT
ejpam-6657	350	26	=	=	NOUN
ejpam-6657	351	1	∞∑	∞∑	PRON
ejpam-6657	351	2	n=0	n=0	NUM
ejpam-6657	351	3	e(r)h	e(r)h	PROPN
ejpam-6657	352	1	[	[	X
ejpam-6657	352	2	h	h	X
ejpam-6657	352	3	]	]	X
ejpam-6657	352	4	γ	γ	X
ejpam-6657	352	5	(	(	PUNCT
ejpam-6657	352	6	bξ1	bξ1	PROPN
ejpam-6657	352	7	,	,	PUNCT
ejpam-6657	352	8	bν1	bν1	NOUN
ejpam-6657	352	9	,	,	PUNCT
ejpam-6657	352	10	bϕ1	bϕ1	PROPN
ejpam-6657	352	11	)	)	PUNCT
ejpam-6657	352	12	(	(	PUNCT
ejpam-6657	352	13	bt)γ	bt)γ	PROPN
ejpam-6657	352	14	γ	γ	X
ejpam-6657	352	15	!	!	PUNCT
ejpam-6657	353	1	∞∑	∞∑	PRON
ejpam-6657	353	2	n=0	n=0	NUM
ejpam-6657	353	3	e(r)h	e(r)h	PROPN
ejpam-6657	354	1	[	[	X
ejpam-6657	354	2	h	h	X
ejpam-6657	354	3	]	]	X
ejpam-6657	354	4	n	n	CCONJ
ejpam-6657	354	5	(	(	PUNCT
ejpam-6657	354	6	aξ2	aξ2	PROPN
ejpam-6657	354	7	,	,	PUNCT
ejpam-6657	354	8	aν2	aν2	NOUN
ejpam-6657	354	9	,	,	PUNCT
ejpam-6657	354	10	aϕ2	aϕ2	NOUN
ejpam-6657	354	11	)	)	PUNCT
ejpam-6657	354	12	(	(	PUNCT
ejpam-6657	354	13	at)n	at)n	PROPN
ejpam-6657	354	14	n	n	X
ejpam-6657	354	15	!	!	PUNCT
ejpam-6657	354	16	=	=	NOUN
ejpam-6657	355	1	∞∑	∞∑	PRON
ejpam-6657	355	2	n=0	n=0	PUNCT
ejpam-6657	355	3			PROPN
ejpam-6657	355	4	n∑	n∑	NOUN
ejpam-6657	355	5	γ=0	γ=0	PROPN
ejpam-6657	355	6	(	(	PUNCT
ejpam-6657	355	7	n	n	CCONJ
ejpam-6657	355	8	γ	γ	X
ejpam-6657	355	9	)	)	PUNCT
ejpam-6657	355	10	an−γbγe(r)h	an−γbγe(r)h	PROPN
ejpam-6657	356	1	[	[	X
ejpam-6657	356	2	h	h	X
ejpam-6657	356	3	]	]	X
ejpam-6657	356	4	n−γ(aξ1	n−γ(aξ1	PROPN
ejpam-6657	356	5	,	,	PUNCT
ejpam-6657	356	6	aν1	aν1	NOUN
ejpam-6657	356	7	,	,	PUNCT
ejpam-6657	356	8	aϕ1)e(r)h	aϕ1)e(r)h	PROPN
ejpam-6657	357	1	[	[	X
ejpam-6657	357	2	h	h	X
ejpam-6657	357	3	]	]	X
ejpam-6657	357	4	γ	γ	X
ejpam-6657	357	5	(	(	PUNCT
ejpam-6657	357	6	bξ2	bξ2	PROPN
ejpam-6657	357	7	,	,	PUNCT
ejpam-6657	357	8	bν2	bν2	NOUN
ejpam-6657	357	9	,	,	PUNCT
ejpam-6657	357	10	bϕ2	bϕ2	NOUN
ejpam-6657	357	11	)	)	PUNCT
ejpam-6657	357	12			PROPN
ejpam-6657	357	13	tn	tn	PROPN
ejpam-6657	357	14	n	n	NOUN
ejpam-6657	357	15	!	!	PUNCT
ejpam-6657	357	16	.	.	PUNCT
ejpam-6657	358	1	(	(	PUNCT
ejpam-6657	358	2	64	64	NUM
ejpam-6657	358	3	)	)	PUNCT
ejpam-6657	358	4	similarly	similarly	ADV
ejpam-6657	358	5	,	,	PUNCT
ejpam-6657	358	6	we	we	PRON
ejpam-6657	358	7	have	have	AUX
ejpam-6657	358	8	a(t	a(t	VERB
ejpam-6657	358	9	)	)	PUNCT
ejpam-6657	359	1	=	=	NOUN
ejpam-6657	360	1	∞∑	∞∑	NUM
ejpam-6657	360	2	ϕ=0	ϕ=0	NOUN
ejpam-6657	361	1			PROPN
ejpam-6657	361	2	n∑	n∑	NOUN
ejpam-6657	361	3	γ=0	γ=0	PROPN
ejpam-6657	361	4	(	(	PUNCT
ejpam-6657	361	5	n	n	CCONJ
ejpam-6657	361	6	γ	γ	X
ejpam-6657	361	7	)	)	PUNCT
ejpam-6657	361	8	aγbn−γ	aγbn−γ	PROPN
ejpam-6657	361	9	e(r)h	e(r)h	PROPN
ejpam-6657	362	1	[	[	X
ejpam-6657	362	2	h	h	X
ejpam-6657	362	3	]	]	X
ejpam-6657	362	4	n−γ(aξ2	n−γ(aξ2	PROPN
ejpam-6657	362	5	,	,	PUNCT
ejpam-6657	362	6	aν2	aν2	PROPN
ejpam-6657	362	7	,	,	PUNCT
ejpam-6657	362	8	aϕ2)e(r)h	aϕ2)e(r)h	PROPN
ejpam-6657	363	1	[	[	X
ejpam-6657	363	2	h	h	X
ejpam-6657	363	3	]	]	X
ejpam-6657	363	4	γ	γ	X
ejpam-6657	363	5	(	(	PUNCT
ejpam-6657	363	6	bξ1	bξ1	PROPN
ejpam-6657	363	7	,	,	PUNCT
ejpam-6657	363	8	bν1	bν1	NOUN
ejpam-6657	363	9	,	,	PUNCT
ejpam-6657	363	10	bϕ1	bϕ1	PROPN
ejpam-6657	363	11	)	)	PUNCT
ejpam-6657	363	12			PROPN
ejpam-6657	363	13	tn	tn	PROPN
ejpam-6657	363	14	n	n	NOUN
ejpam-6657	363	15	!	!	PUNCT
ejpam-6657	363	16	.	.	PUNCT
ejpam-6657	364	1	(	(	PUNCT
ejpam-6657	364	2	65	65	NUM
ejpam-6657	364	3	)	)	PUNCT
ejpam-6657	364	4	comparing	compare	VERB
ejpam-6657	364	5	the	the	DET
ejpam-6657	364	6	coefficients	coefficient	NOUN
ejpam-6657	364	7	of	of	ADP
ejpam-6657	364	8	t	t	PROPN
ejpam-6657	364	9	on	on	ADP
ejpam-6657	364	10	both	both	DET
ejpam-6657	364	11	sides	side	NOUN
ejpam-6657	364	12	of	of	ADP
ejpam-6657	364	13	last	last	ADJ
ejpam-6657	364	14	equations	equation	NOUN
ejpam-6657	364	15	,	,	PUNCT
ejpam-6657	364	16	we	we	PRON
ejpam-6657	364	17	get	get	VERB
ejpam-6657	364	18	(	(	PUNCT
ejpam-6657	364	19	62	62	NUM
ejpam-6657	364	20	)	)	PUNCT
ejpam-6657	364	21	.	.	PUNCT
ejpam-6657	365	1	theorem	theorem	VERB
ejpam-6657	365	2	11	11	NUM
ejpam-6657	365	3	.	.	PUNCT
ejpam-6657	366	1	for	for	ADP
ejpam-6657	366	2	a	a	DET
ejpam-6657	366	3	̸=	̸=	PROPN
ejpam-6657	366	4	b	b	PROPN
ejpam-6657	366	5	,	,	PUNCT
ejpam-6657	366	6	a	a	PRON
ejpam-6657	366	7	,	,	PUNCT
ejpam-6657	366	8	b	b	X
ejpam-6657	366	9	>	>	X
ejpam-6657	366	10	0	0	NUM
ejpam-6657	366	11	and	and	CCONJ
ejpam-6657	366	12	ξ	ξ	PROPN
ejpam-6657	366	13	,	,	PUNCT
ejpam-6657	366	14	ν	ν	PROPN
ejpam-6657	366	15	,	,	PUNCT
ejpam-6657	366	16	ϕ	ϕ	PROPN
ejpam-6657	366	17	∈	∈	PROPN
ejpam-6657	366	18	c	c	X
ejpam-6657	366	19	,	,	PUNCT
ejpam-6657	366	20	we	we	PRON
ejpam-6657	366	21	have	have	VERB
ejpam-6657	366	22	n∑	n∑	PROPN
ejpam-6657	366	23	k=0	k=0	PROPN
ejpam-6657	366	24	k∑	k∑	PROPN
ejpam-6657	367	1	γ=0	γ=0	PROPN
ejpam-6657	367	2	(	(	PUNCT
ejpam-6657	367	3	n	n	X
ejpam-6657	367	4	k	k	NOUN
ejpam-6657	367	5	)	)	PUNCT
ejpam-6657	367	6	(	(	PUNCT
ejpam-6657	367	7	k	k	PROPN
ejpam-6657	367	8	γ	γ	X
ejpam-6657	367	9	)	)	PUNCT
ejpam-6657	367	10	an−γbγ+1βn−k(h)e(r)h	an−γbγ+1βn−k(h)e(r)h	PROPN
ejpam-6657	368	1	[	[	X
ejpam-6657	368	2	h	h	X
ejpam-6657	368	3	]	]	X
ejpam-6657	368	4	k−γ(bξ	k−γ(bξ	PROPN
ejpam-6657	368	5	,	,	PUNCT
ejpam-6657	368	6	bν	bν	PROPN
ejpam-6657	368	7	,	,	PUNCT
ejpam-6657	368	8	bϕ)σγ(a−	bϕ)σγ(a−	PROPN
ejpam-6657	368	9	1;h	1;h	NUM
ejpam-6657	368	10	)	)	PUNCT
ejpam-6657	368	11	=	=	SYM
ejpam-6657	369	1	n∑	n∑	PROPN
ejpam-6657	369	2	k=0	k=0	PROPN
ejpam-6657	369	3	k∑	k∑	PROPN
ejpam-6657	369	4	γ=0	γ=0	PROPN
ejpam-6657	370	1	(	(	PUNCT
ejpam-6657	370	2	n	n	X
ejpam-6657	370	3	k	k	NOUN
ejpam-6657	370	4	)	)	PUNCT
ejpam-6657	370	5	(	(	PUNCT
ejpam-6657	370	6	k	k	NOUN
ejpam-6657	370	7	γ	γ	X
ejpam-6657	370	8	)	)	PUNCT
ejpam-6657	370	9	bn−γaγ+1βn−k(h)e(r)h	bn−γaγ+1βn−k(h)e(r)h	PROPN
ejpam-6657	371	1	[	[	X
ejpam-6657	371	2	h	h	X
ejpam-6657	371	3	]	]	X
ejpam-6657	371	4	k−γ(aξ	k−γ(aξ	PROPN
ejpam-6657	371	5	,	,	PUNCT
ejpam-6657	371	6	aν	aν	NOUN
ejpam-6657	371	7	,	,	PUNCT
ejpam-6657	371	8	aϕ)σγ(b−	aϕ)σγ(b−	NOUN
ejpam-6657	371	9	1;h	1;h	NUM
ejpam-6657	371	10	)	)	PUNCT
ejpam-6657	371	11	.	.	PUNCT
ejpam-6657	372	1	(	(	PUNCT
ejpam-6657	372	2	66	66	NUM
ejpam-6657	372	3	)	)	PUNCT
ejpam-6657	372	4	h.	h.	PROPN
ejpam-6657	372	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	372	6	et	et	PROPN
ejpam-6657	372	7	al	al	PROPN
ejpam-6657	372	8	.	.	PUNCT
ejpam-6657	372	9	/	/	SYM
ejpam-6657	372	10	eur	eur	PROPN
ejpam-6657	372	11	.	.	PUNCT
ejpam-6657	373	1	j.	j.	PROPN
ejpam-6657	373	2	pure	pure	PROPN
ejpam-6657	373	3	appl	appl	PROPN
ejpam-6657	373	4	.	.	PROPN
ejpam-6657	373	5	math	math	PROPN
ejpam-6657	373	6	,	,	PUNCT
ejpam-6657	373	7	18	18	NUM
ejpam-6657	373	8	(	(	PUNCT
ejpam-6657	373	9	3	3	NUM
ejpam-6657	373	10	)	)	PUNCT
ejpam-6657	373	11	(	(	PUNCT
ejpam-6657	373	12	2025	2025	NUM
ejpam-6657	373	13	)	)	PUNCT
ejpam-6657	373	14	,	,	PUNCT
ejpam-6657	373	15	6657	6657	NUM
ejpam-6657	373	16	13	13	NUM
ejpam-6657	373	17	of	of	ADP
ejpam-6657	373	18	16	16	NUM
ejpam-6657	373	19	proof	proof	NOUN
ejpam-6657	373	20	.	.	PUNCT
ejpam-6657	374	1	consider	consider	VERB
ejpam-6657	374	2	b(t	b(t	NOUN
ejpam-6657	374	3	)	)	PUNCT
ejpam-6657	374	4	=	=	SYM
ejpam-6657	374	5	1	1	NUM
ejpam-6657	374	6	1−	1−	NUM
ejpam-6657	374	7	ϕ(abt)2	ϕ(abt)2	NOUN
ejpam-6657	375	1	(	(	PUNCT
ejpam-6657	375	2	1	1	NUM
ejpam-6657	375	3	+	+	NUM
ejpam-6657	375	4	ht	ht	NOUN
ejpam-6657	375	5	)	)	PUNCT
ejpam-6657	375	6	abξ	abξ	NOUN
ejpam-6657	375	7	h	h	NOUN
ejpam-6657	375	8	(	(	PUNCT
ejpam-6657	375	9	1	1	NUM
ejpam-6657	375	10	+	+	NUM
ejpam-6657	375	11	ht2	ht2	NOUN
ejpam-6657	375	12	)	)	PUNCT
ejpam-6657	375	13	abν	abν	NOUN
ejpam-6657	375	14	h	h	NOUN
ejpam-6657	375	15	(	(	PUNCT
ejpam-6657	375	16	(	(	PUNCT
ejpam-6657	375	17	1	1	NUM
ejpam-6657	375	18	+	+	NUM
ejpam-6657	375	19	ht	ht	PROPN
ejpam-6657	375	20	)	)	PUNCT
ejpam-6657	375	21	ab	ab	PROPN
ejpam-6657	375	22	h	h	NOUN
ejpam-6657	375	23	−	−	PROPN
ejpam-6657	375	24	1	1	NUM
ejpam-6657	375	25	)	)	PUNCT
ejpam-6657	375	26	(	(	PUNCT
ejpam-6657	375	27	(	(	PUNCT
ejpam-6657	375	28	1	1	NUM
ejpam-6657	375	29	+	+	NUM
ejpam-6657	375	30	ht	ht	PROPN
ejpam-6657	375	31	)	)	PUNCT
ejpam-6657	375	32	a	a	DET
ejpam-6657	375	33	h	h	NOUN
ejpam-6657	376	1	−	−	PROPN
ejpam-6657	377	1	1)((1	1)((1	PROPN
ejpam-6657	378	1	+	+	CCONJ
ejpam-6657	378	2	ht	ht	PROPN
ejpam-6657	378	3	)	)	PUNCT
ejpam-6657	378	4	b	b	PROPN
ejpam-6657	378	5	h	h	NOUN
ejpam-6657	378	6	−	−	PROPN
ejpam-6657	379	1	1)2	1)2	NUM
ejpam-6657	379	2	=	=	SYM
ejpam-6657	379	3	abt	abt	INTJ
ejpam-6657	379	4	(	(	PUNCT
ejpam-6657	379	5	(	(	PUNCT
ejpam-6657	379	6	1	1	NUM
ejpam-6657	379	7	+	+	NUM
ejpam-6657	379	8	ht	ht	PROPN
ejpam-6657	379	9	)	)	PUNCT
ejpam-6657	379	10	a	a	DET
ejpam-6657	379	11	h	h	NOUN
ejpam-6657	379	12	−	−	NOUN
ejpam-6657	379	13	1	1	NUM
ejpam-6657	379	14	)	)	PUNCT
ejpam-6657	379	15	1	1	NUM
ejpam-6657	379	16	1−	1−	NUM
ejpam-6657	379	17	ϕ(abt)2	ϕ(abt)2	NOUN
ejpam-6657	379	18	(	(	PUNCT
ejpam-6657	379	19	1	1	NUM
ejpam-6657	379	20	+	+	NUM
ejpam-6657	379	21	ht	ht	NOUN
ejpam-6657	379	22	)	)	PUNCT
ejpam-6657	379	23	abξ	abξ	NOUN
ejpam-6657	379	24	h	h	NOUN
ejpam-6657	379	25	(	(	PUNCT
ejpam-6657	379	26	1	1	NUM
ejpam-6657	379	27	+	+	NUM
ejpam-6657	379	28	ht2	ht2	NOUN
ejpam-6657	379	29	)	)	PUNCT
ejpam-6657	379	30	abν	abν	NOUN
ejpam-6657	379	31	h	h	NOUN
ejpam-6657	379	32	(	(	PUNCT
ejpam-6657	379	33	(	(	PUNCT
ejpam-6657	379	34	1	1	NUM
ejpam-6657	379	35	+	+	NUM
ejpam-6657	379	36	ht	ht	PROPN
ejpam-6657	379	37	)	)	PUNCT
ejpam-6657	379	38	ab	ab	PROPN
ejpam-6657	379	39	h	h	NOUN
ejpam-6657	379	40	−	−	PROPN
ejpam-6657	380	1	1	1	NUM
ejpam-6657	380	2	)	)	PUNCT
ejpam-6657	380	3	(	(	PUNCT
ejpam-6657	380	4	(	(	PUNCT
ejpam-6657	380	5	1	1	NUM
ejpam-6657	380	6	+	+	NUM
ejpam-6657	380	7	ht	ht	PROPN
ejpam-6657	380	8	)	)	PUNCT
ejpam-6657	380	9	b	b	PROPN
ejpam-6657	380	10	h	h	NOUN
ejpam-6657	381	1	−	−	NOUN
ejpam-6657	381	2	1	1	NUM
ejpam-6657	381	3	)	)	PUNCT
ejpam-6657	381	4	=	=	SYM
ejpam-6657	382	1	b	b	PROPN
ejpam-6657	382	2	∞∑	∞∑	PROPN
ejpam-6657	382	3	n=0	n=0	NUM
ejpam-6657	382	4	βn(h	βn(h	NUM
ejpam-6657	382	5	)	)	PUNCT
ejpam-6657	382	6	(	(	PUNCT
ejpam-6657	382	7	at)n	at)n	PROPN
ejpam-6657	382	8	n	n	CCONJ
ejpam-6657	382	9	!	!	PUNCT
ejpam-6657	383	1	∞∑	∞∑	NUM
ejpam-6657	383	2	k=0	k=0	PUNCT
ejpam-6657	383	3	e(r)h	e(r)h	PROPN
ejpam-6657	384	1	[	[	X
ejpam-6657	384	2	h	h	X
ejpam-6657	384	3	]	]	X
ejpam-6657	384	4	k	k	X
ejpam-6657	384	5	(	(	PUNCT
ejpam-6657	384	6	bξ	bξ	PROPN
ejpam-6657	384	7	,	,	PUNCT
ejpam-6657	384	8	bν	bν	ADJ
ejpam-6657	384	9	,	,	PUNCT
ejpam-6657	384	10	bϕ	bϕ	ADP
ejpam-6657	384	11	)	)	PUNCT
ejpam-6657	384	12	(	(	PUNCT
ejpam-6657	384	13	at)k	at)k	PROPN
ejpam-6657	384	14	k	k	X
ejpam-6657	384	15	!	!	PUNCT
ejpam-6657	385	1	∞∑	∞∑	ADJ
ejpam-6657	385	2	γ=0	γ=0	NUM
ejpam-6657	385	3	σγ(a−	σγ(a−	ADP
ejpam-6657	385	4	1;h	1;h	NUM
ejpam-6657	385	5	)	)	PUNCT
ejpam-6657	385	6	(	(	PUNCT
ejpam-6657	385	7	bt)γ	bt)γ	PROPN
ejpam-6657	385	8	γ	γ	X
ejpam-6657	385	9	!	!	PUNCT
ejpam-6657	385	10	=	=	PUNCT
ejpam-6657	385	11	b	b	PROPN
ejpam-6657	386	1	∞∑	∞∑	PRON
ejpam-6657	386	2	n=0	n=0	NUM
ejpam-6657	386	3	βn(h	βn(h	NUM
ejpam-6657	386	4	)	)	PUNCT
ejpam-6657	386	5	(	(	PUNCT
ejpam-6657	386	6	at)n	at)n	PROPN
ejpam-6657	386	7	n	n	CCONJ
ejpam-6657	386	8	!	!	PUNCT
ejpam-6657	387	1	∞∑	∞∑	NUM
ejpam-6657	387	2	k=0	k=0	PROPN
ejpam-6657	387	3	k∑	k∑	PROPN
ejpam-6657	387	4	γ=0	γ=0	PROPN
ejpam-6657	388	1	(	(	PUNCT
ejpam-6657	388	2	k	k	X
ejpam-6657	388	3	γ	γ	X
ejpam-6657	388	4	)	)	PUNCT
ejpam-6657	389	1	ak−γbγe(r)h	ak−γbγe(r)h	PROPN
ejpam-6657	390	1	[	[	X
ejpam-6657	390	2	h	h	X
ejpam-6657	390	3	]	]	X
ejpam-6657	390	4	k−γ(bξ	k−γ(bξ	PROPN
ejpam-6657	390	5	,	,	PUNCT
ejpam-6657	390	6	bν	bν	PROPN
ejpam-6657	390	7	,	,	PUNCT
ejpam-6657	390	8	bϕ)σγ(a−	bϕ)σγ(a−	PROPN
ejpam-6657	390	9	1;h	1;h	NUM
ejpam-6657	390	10	)	)	PUNCT
ejpam-6657	390	11	tk	tk	PROPN
ejpam-6657	390	12	k	k	NOUN
ejpam-6657	390	13	!	!	PUNCT
ejpam-6657	390	14	=	=	PUNCT
ejpam-6657	391	1	∞∑	∞∑	PRON
ejpam-6657	391	2	n=0	n=0	PUNCT
ejpam-6657	391	3			PROPN
ejpam-6657	391	4	n∑	n∑	PROPN
ejpam-6657	391	5	k=0	k=0	PROPN
ejpam-6657	391	6	k∑	k∑	PROPN
ejpam-6657	391	7	γ=0	γ=0	PROPN
ejpam-6657	392	1	(	(	PUNCT
ejpam-6657	392	2	n	n	X
ejpam-6657	392	3	k	k	NOUN
ejpam-6657	392	4	)	)	PUNCT
ejpam-6657	392	5	(	(	PUNCT
ejpam-6657	392	6	k	k	PROPN
ejpam-6657	392	7	γ	γ	X
ejpam-6657	392	8	)	)	PUNCT
ejpam-6657	392	9	an−γbγ+1βn−k(h)e(r)h	an−γbγ+1βn−k(h)e(r)h	PROPN
ejpam-6657	393	1	[	[	X
ejpam-6657	393	2	h	h	X
ejpam-6657	393	3	]	]	X
ejpam-6657	393	4	k−γ(bξ	k−γ(bξ	PROPN
ejpam-6657	393	5	,	,	PUNCT
ejpam-6657	393	6	bν	bν	PROPN
ejpam-6657	393	7	,	,	PUNCT
ejpam-6657	393	8	bϕ)σγ(a−	bϕ)σγ(a−	PROPN
ejpam-6657	393	9	1;h	1;h	NUM
ejpam-6657	393	10	)	)	PUNCT
ejpam-6657	393	11			PROPN
ejpam-6657	393	12	tn	tn	PROPN
ejpam-6657	393	13	n	n	NOUN
ejpam-6657	393	14	!	!	PUNCT
ejpam-6657	393	15	.	.	PUNCT
ejpam-6657	394	1	(	(	PUNCT
ejpam-6657	394	2	67	67	NUM
ejpam-6657	394	3	)	)	PUNCT
ejpam-6657	394	4	similarly	similarly	ADV
ejpam-6657	394	5	,	,	PUNCT
ejpam-6657	394	6	we	we	PRON
ejpam-6657	394	7	have	have	VERB
ejpam-6657	394	8	b(t	b(t	VERB
ejpam-6657	394	9	)	)	PUNCT
ejpam-6657	394	10	=	=	PUNCT
ejpam-6657	395	1	∞∑	∞∑	ADJ
ejpam-6657	395	2	n=0	n=0	PUNCT
ejpam-6657	395	3			PROPN
ejpam-6657	395	4	n∑	n∑	PROPN
ejpam-6657	395	5	k=0	k=0	PROPN
ejpam-6657	395	6	k∑	k∑	PROPN
ejpam-6657	395	7	γ=0	γ=0	PROPN
ejpam-6657	396	1	(	(	PUNCT
ejpam-6657	396	2	n	n	X
ejpam-6657	396	3	k	k	NOUN
ejpam-6657	396	4	)	)	PUNCT
ejpam-6657	396	5	(	(	PUNCT
ejpam-6657	396	6	k	k	NOUN
ejpam-6657	396	7	γ	γ	X
ejpam-6657	396	8	)	)	PUNCT
ejpam-6657	396	9	bn−γaγ+1βn−k(h)e(r)h	bn−γaγ+1βn−k(h)e(r)h	PROPN
ejpam-6657	397	1	[	[	X
ejpam-6657	397	2	h	h	X
ejpam-6657	397	3	]	]	X
ejpam-6657	397	4	k−γ(aξ	k−γ(aξ	PROPN
ejpam-6657	397	5	,	,	PUNCT
ejpam-6657	397	6	aν	aν	NOUN
ejpam-6657	397	7	,	,	PUNCT
ejpam-6657	397	8	aϕ)σγ(b−	aϕ)σγ(b−	NOUN
ejpam-6657	397	9	1;h	1;h	NUM
ejpam-6657	397	10	)	)	PUNCT
ejpam-6657	397	11			PROPN
ejpam-6657	397	12	tn	tn	PROPN
ejpam-6657	397	13	n	n	NOUN
ejpam-6657	397	14	!	!	PUNCT
ejpam-6657	397	15	.	.	PUNCT
ejpam-6657	398	1	(	(	PUNCT
ejpam-6657	398	2	68	68	NUM
ejpam-6657	398	3	)	)	PUNCT
ejpam-6657	398	4	comparing	compare	VERB
ejpam-6657	398	5	the	the	DET
ejpam-6657	398	6	coefficients	coefficient	NOUN
ejpam-6657	398	7	of	of	ADP
ejpam-6657	398	8	t	t	PROPN
ejpam-6657	398	9	on	on	ADP
ejpam-6657	398	10	both	both	DET
ejpam-6657	398	11	sides	side	NOUN
ejpam-6657	398	12	of	of	ADP
ejpam-6657	398	13	last	last	ADJ
ejpam-6657	398	14	equations	equation	NOUN
ejpam-6657	398	15	,	,	PUNCT
ejpam-6657	398	16	we	we	PRON
ejpam-6657	398	17	get	get	VERB
ejpam-6657	398	18	(	(	PUNCT
ejpam-6657	398	19	66	66	NUM
ejpam-6657	398	20	)	)	PUNCT
ejpam-6657	398	21	.	.	PUNCT
ejpam-6657	399	1	6	6	X
ejpam-6657	399	2	.	.	X
ejpam-6657	399	3	conclusion	conclusion	NOUN
ejpam-6657	399	4	in	in	ADP
ejpam-6657	399	5	this	this	DET
ejpam-6657	399	6	study	study	NOUN
ejpam-6657	399	7	,	,	PUNCT
ejpam-6657	399	8	we	we	PRON
ejpam-6657	399	9	have	have	AUX
ejpam-6657	399	10	introduced	introduce	VERB
ejpam-6657	399	11	a	a	DET
ejpam-6657	399	12	novel	novel	ADJ
ejpam-6657	399	13	class	class	NOUN
ejpam-6657	399	14	of	of	ADP
ejpam-6657	399	15	∆h	∆h	NOUN
ejpam-6657	399	16	-	-	PUNCT
ejpam-6657	399	17	truncated	truncate	VERB
ejpam-6657	399	18	exponential	exponential	NOUN
ejpam-6657	399	19	-	-	PUNCT
ejpam-6657	399	20	based	base	VERB
ejpam-6657	399	21	hermite	hermite	ADJ
ejpam-6657	399	22	polynomials	polynomial	NOUN
ejpam-6657	399	23	and	and	CCONJ
ejpam-6657	399	24	established	establish	VERB
ejpam-6657	399	25	their	their	PRON
ejpam-6657	399	26	fundamental	fundamental	ADJ
ejpam-6657	399	27	properties	property	NOUN
ejpam-6657	399	28	,	,	PUNCT
ejpam-6657	399	29	including	include	VERB
ejpam-6657	399	30	generating	generating	NOUN
ejpam-6657	399	31	functions	function	NOUN
ejpam-6657	399	32	,	,	PUNCT
ejpam-6657	399	33	recurrence	recurrence	NOUN
ejpam-6657	399	34	relations	relation	NOUN
ejpam-6657	399	35	,	,	PUNCT
ejpam-6657	399	36	explicit	explicit	ADJ
ejpam-6657	399	37	formulas	formula	NOUN
ejpam-6657	399	38	,	,	PUNCT
ejpam-6657	399	39	and	and	CCONJ
ejpam-6657	399	40	summation	summation	NOUN
ejpam-6657	399	41	identities	identity	NOUN
ejpam-6657	399	42	.	.	PUNCT
ejpam-6657	400	1	the	the	DET
ejpam-6657	400	2	connection	connection	NOUN
ejpam-6657	400	3	with	with	ADP
ejpam-6657	400	4	the	the	DET
ejpam-6657	400	5	monomiality	monomiality	NOUN
ejpam-6657	400	6	principle	principle	NOUN
ejpam-6657	400	7	has	have	AUX
ejpam-6657	400	8	been	be	AUX
ejpam-6657	400	9	explored	explore	VERB
ejpam-6657	400	10	to	to	PART
ejpam-6657	400	11	reveal	reveal	VERB
ejpam-6657	400	12	their	their	PRON
ejpam-6657	400	13	underlying	underlie	VERB
ejpam-6657	400	14	algebraic	algebraic	ADJ
ejpam-6657	400	15	structure	structure	NOUN
ejpam-6657	400	16	,	,	PUNCT
ejpam-6657	400	17	and	and	CCONJ
ejpam-6657	400	18	an	an	DET
ejpam-6657	400	19	operational	operational	ADJ
ejpam-6657	400	20	formalism	formalism	NOUN
ejpam-6657	400	21	has	have	AUX
ejpam-6657	400	22	been	be	AUX
ejpam-6657	400	23	developed	develop	VERB
ejpam-6657	400	24	.	.	PUNCT
ejpam-6657	401	1	additionally	additionally	ADV
ejpam-6657	401	2	,	,	PUNCT
ejpam-6657	401	3	symmetric	symmetric	ADJ
ejpam-6657	401	4	identities	identity	NOUN
ejpam-6657	401	5	have	have	AUX
ejpam-6657	401	6	been	be	AUX
ejpam-6657	401	7	presented	present	VERB
ejpam-6657	401	8	to	to	PART
ejpam-6657	401	9	further	far	ADV
ejpam-6657	401	10	deepen	deepen	VERB
ejpam-6657	401	11	the	the	DET
ejpam-6657	401	12	theoretical	theoretical	ADJ
ejpam-6657	401	13	understanding	understanding	NOUN
ejpam-6657	401	14	of	of	ADP
ejpam-6657	401	15	these	these	DET
ejpam-6657	401	16	polynomials	polynomial	NOUN
ejpam-6657	401	17	.	.	PUNCT
ejpam-6657	402	1	these	these	DET
ejpam-6657	402	2	results	result	NOUN
ejpam-6657	402	3	lay	lay	VERB
ejpam-6657	402	4	a	a	DET
ejpam-6657	402	5	solid	solid	ADJ
ejpam-6657	402	6	foundation	foundation	NOUN
ejpam-6657	402	7	for	for	ADP
ejpam-6657	402	8	future	future	ADJ
ejpam-6657	402	9	investigations	investigation	NOUN
ejpam-6657	402	10	and	and	CCONJ
ejpam-6657	402	11	potential	potential	ADJ
ejpam-6657	402	12	applications	application	NOUN
ejpam-6657	402	13	in	in	ADP
ejpam-6657	402	14	both	both	CCONJ
ejpam-6657	402	15	pure	pure	ADJ
ejpam-6657	402	16	and	and	CCONJ
ejpam-6657	402	17	applied	applied	ADJ
ejpam-6657	402	18	mathematics	mathematic	NOUN
ejpam-6657	402	19	.	.	PUNCT
ejpam-6657	403	1	future	future	ADJ
ejpam-6657	403	2	research	research	NOUN
ejpam-6657	403	3	can	can	AUX
ejpam-6657	403	4	explore	explore	VERB
ejpam-6657	403	5	several	several	ADJ
ejpam-6657	403	6	directions	direction	NOUN
ejpam-6657	403	7	,	,	PUNCT
ejpam-6657	403	8	including	include	VERB
ejpam-6657	403	9	the	the	DET
ejpam-6657	403	10	development	development	NOUN
ejpam-6657	403	11	of	of	ADP
ejpam-6657	403	12	q	q	NOUN
ejpam-6657	403	13	-	-	PUNCT
ejpam-6657	403	14	analogues	analogue	NOUN
ejpam-6657	403	15	and	and	CCONJ
ejpam-6657	403	16	degenerate	degenerate	ADJ
ejpam-6657	403	17	forms	form	NOUN
ejpam-6657	403	18	of	of	ADP
ejpam-6657	403	19	the	the	DET
ejpam-6657	403	20	proposed	propose	VERB
ejpam-6657	403	21	polynomials	polynomial	NOUN
ejpam-6657	403	22	to	to	PART
ejpam-6657	403	23	study	study	VERB
ejpam-6657	403	24	associated	associate	VERB
ejpam-6657	403	25	q	q	ADJ
ejpam-6657	403	26	-	-	PUNCT
ejpam-6657	403	27	difference	difference	NOUN
ejpam-6657	403	28	equations	equation	NOUN
ejpam-6657	403	29	and	and	CCONJ
ejpam-6657	403	30	limiting	limit	VERB
ejpam-6657	403	31	behaviors	behavior	NOUN
ejpam-6657	403	32	.	.	PUNCT
ejpam-6657	404	1	investigating	investigate	VERB
ejpam-6657	404	2	orthogonality	orthogonality	NOUN
ejpam-6657	404	3	conditions	condition	NOUN
ejpam-6657	404	4	and	and	CCONJ
ejpam-6657	404	5	suitable	suitable	ADJ
ejpam-6657	404	6	weight	weight	NOUN
ejpam-6657	404	7	functions	function	NOUN
ejpam-6657	404	8	will	will	AUX
ejpam-6657	404	9	help	help	AUX
ejpam-6657	404	10	identify	identify	VERB
ejpam-6657	404	11	inner	inner	ADJ
ejpam-6657	404	12	product	product	NOUN
ejpam-6657	404	13	spaces	space	NOUN
ejpam-6657	404	14	where	where	SCONJ
ejpam-6657	404	15	these	these	DET
ejpam-6657	404	16	polynomials	polynomial	NOUN
ejpam-6657	404	17	are	be	AUX
ejpam-6657	404	18	orthogonal	orthogonal	ADJ
ejpam-6657	404	19	.	.	PUNCT
ejpam-6657	405	1	their	their	PRON
ejpam-6657	405	2	application	application	NOUN
ejpam-6657	405	3	in	in	ADP
ejpam-6657	405	4	interpolation	interpolation	NOUN
ejpam-6657	405	5	,	,	PUNCT
ejpam-6657	405	6	approximation	approximation	NOUN
ejpam-6657	405	7	theory	theory	NOUN
ejpam-6657	405	8	,	,	PUNCT
ejpam-6657	405	9	and	and	CCONJ
ejpam-6657	405	10	spectral	spectral	ADJ
ejpam-6657	405	11	methods	method	NOUN
ejpam-6657	405	12	also	also	ADV
ejpam-6657	405	13	warrants	warrant	VERB
ejpam-6657	405	14	attention	attention	NOUN
ejpam-6657	405	15	,	,	PUNCT
ejpam-6657	405	16	particularly	particularly	ADV
ejpam-6657	405	17	in	in	ADP
ejpam-6657	405	18	solving	solve	VERB
ejpam-6657	405	19	differential	differential	NOUN
ejpam-6657	405	20	or	or	CCONJ
ejpam-6657	405	21	integral	integral	ADJ
ejpam-6657	405	22	equations	equation	NOUN
ejpam-6657	405	23	.	.	PUNCT
ejpam-6657	406	1	potential	potential	ADJ
ejpam-6657	406	2	uses	use	NOUN
ejpam-6657	406	3	in	in	ADP
ejpam-6657	406	4	mathematical	mathematical	ADJ
ejpam-6657	406	5	physics	physics	NOUN
ejpam-6657	406	6	and	and	CCONJ
ejpam-6657	406	7	engineering	engineering	NOUN
ejpam-6657	406	8	—	—	PUNCT
ejpam-6657	406	9	such	such	ADJ
ejpam-6657	406	10	as	as	ADP
ejpam-6657	406	11	quantum	quantum	NOUN
ejpam-6657	406	12	systems	system	NOUN
ejpam-6657	406	13	and	and	CCONJ
ejpam-6657	406	14	signal	signal	ADJ
ejpam-6657	406	15	analysis	analysis	NOUN
ejpam-6657	406	16	—	—	PUNCT
ejpam-6657	406	17	highlight	highlight	VERB
ejpam-6657	406	18	their	their	PRON
ejpam-6657	406	19	applied	apply	VERB
ejpam-6657	406	20	significance	significance	NOUN
ejpam-6657	406	21	.	.	PUNCT
ejpam-6657	407	1	additionally	additionally	ADV
ejpam-6657	407	2	,	,	PUNCT
ejpam-6657	407	3	a	a	DET
ejpam-6657	407	4	detailed	detailed	ADJ
ejpam-6657	407	5	study	study	NOUN
ejpam-6657	407	6	of	of	ADP
ejpam-6657	407	7	asymptotic	asymptotic	ADJ
ejpam-6657	407	8	properties	property	NOUN
ejpam-6657	407	9	and	and	CCONJ
ejpam-6657	407	10	zero	zero	NUM
ejpam-6657	407	11	distributions	distribution	NOUN
ejpam-6657	407	12	using	use	VERB
ejpam-6657	407	13	analytic	analytic	ADJ
ejpam-6657	407	14	and	and	CCONJ
ejpam-6657	407	15	numerical	numerical	ADJ
ejpam-6657	407	16	tools	tool	NOUN
ejpam-6657	407	17	could	could	AUX
ejpam-6657	407	18	offer	offer	VERB
ejpam-6657	407	19	deeper	deep	ADJ
ejpam-6657	407	20	insights	insight	NOUN
ejpam-6657	407	21	into	into	ADP
ejpam-6657	407	22	their	their	PRON
ejpam-6657	407	23	structural	structural	ADJ
ejpam-6657	407	24	behavior	behavior	NOUN
ejpam-6657	407	25	.	.	PUNCT
ejpam-6657	408	1	h.	h.	PROPN
ejpam-6657	408	2	qawaqneh	qawaqneh	PROPN
ejpam-6657	408	3	et	et	PROPN
ejpam-6657	408	4	al	al	PROPN
ejpam-6657	408	5	.	.	PUNCT
ejpam-6657	408	6	/	/	SYM
ejpam-6657	408	7	eur	eur	PROPN
ejpam-6657	408	8	.	.	PUNCT
ejpam-6657	409	1	j.	j.	PROPN
ejpam-6657	409	2	pure	pure	PROPN
ejpam-6657	409	3	appl	appl	PROPN
ejpam-6657	409	4	.	.	PROPN
ejpam-6657	409	5	math	math	PROPN
ejpam-6657	409	6	,	,	PUNCT
ejpam-6657	409	7	18	18	NUM
ejpam-6657	409	8	(	(	PUNCT
ejpam-6657	409	9	3	3	NUM
ejpam-6657	409	10	)	)	PUNCT
ejpam-6657	409	11	(	(	PUNCT
ejpam-6657	409	12	2025	2025	NUM
ejpam-6657	409	13	)	)	PUNCT
ejpam-6657	409	14	,	,	PUNCT
ejpam-6657	409	15	6657	6657	NUM
ejpam-6657	409	16	14	14	NUM
ejpam-6657	409	17	of	of	ADP
ejpam-6657	409	18	16	16	NUM
ejpam-6657	409	19	availability	availability	NOUN
ejpam-6657	409	20	of	of	ADP
ejpam-6657	409	21	data	datum	NOUN
ejpam-6657	409	22	and	and	CCONJ
ejpam-6657	409	23	materials	material	NOUN
ejpam-6657	409	24	not	not	PART
ejpam-6657	409	25	applicable	applicable	ADJ
ejpam-6657	409	26	.	.	PUNCT
ejpam-6657	410	1	competing	compete	VERB
ejpam-6657	410	2	interests	interest	NOUN
ejpam-6657	410	3	the	the	DET
ejpam-6657	410	4	authors	author	NOUN
ejpam-6657	410	5	declare	declare	VERB
ejpam-6657	410	6	no	no	DET
ejpam-6657	410	7	competing	compete	VERB
ejpam-6657	410	8	interests	interest	NOUN
ejpam-6657	410	9	.	.	PUNCT
ejpam-6657	411	1	acknowledgments	acknowledgment	NOUN
ejpam-6657	411	2	the	the	DET
ejpam-6657	411	3	authors	author	NOUN
ejpam-6657	411	4	acknowledge	acknowledge	VERB
ejpam-6657	411	5	the	the	DET
ejpam-6657	411	6	financial	financial	ADJ
ejpam-6657	411	7	support	support	NOUN
ejpam-6657	411	8	from	from	ADP
ejpam-6657	411	9	al	al	PROPN
ejpam-6657	411	10	-	-	PROPN
ejpam-6657	411	11	zaytoonah	zaytoonah	PROPN
ejpam-6657	411	12	university	university	PROPN
ejpam-6657	411	13	of	of	ADP
ejpam-6657	411	14	jordan	jordan	PROPN
ejpam-6657	411	15	,	,	PUNCT
ejpam-6657	411	16	amman	amman	PROPN
ejpam-6657	411	17	11733	11733	NUM
ejpam-6657	411	18	,	,	PUNCT
ejpam-6657	411	19	jordan	jordan	PROPN
ejpam-6657	411	20	.	.	PUNCT
ejpam-6657	412	1	references	reference	NOUN
ejpam-6657	412	2	[	[	X
ejpam-6657	412	3	1	1	NUM
ejpam-6657	412	4	]	]	PUNCT
ejpam-6657	412	5	gabriella	gabriella	PROPN
ejpam-6657	412	6	bretti	bretti	PROPN
ejpam-6657	412	7	,	,	PUNCT
ejpam-6657	412	8	c.	c.	PROPN
ejpam-6657	412	9	cesarano	cesarano	PROPN
ejpam-6657	412	10	,	,	PUNCT
ejpam-6657	412	11	and	and	CCONJ
ejpam-6657	412	12	paolo	paolo	PROPN
ejpam-6657	412	13	emilio	emilio	PROPN
ejpam-6657	412	14	ricci	ricci	PROPN
ejpam-6657	412	15	.	.	PUNCT
ejpam-6657	413	1	laguerre	laguerre	NOUN
ejpam-6657	413	2	-	-	PUNCT
ejpam-6657	413	3	type	type	NOUN
ejpam-6657	413	4	exponentials	exponential	NOUN
ejpam-6657	413	5	and	and	CCONJ
ejpam-6657	413	6	generalized	generalize	VERB
ejpam-6657	413	7	appell	appell	ADJ
ejpam-6657	413	8	polynomials	polynomial	NOUN
ejpam-6657	413	9	.	.	PUNCT
ejpam-6657	414	1	computers	computer	NOUN
ejpam-6657	414	2	&	&	CCONJ
ejpam-6657	414	3	mathematics	mathematics	PROPN
ejpam-6657	414	4	with	with	ADP
ejpam-6657	414	5	applications	application	NOUN
ejpam-6657	414	6	,	,	PUNCT
ejpam-6657	414	7	48(5	48(5	NOUN
ejpam-6657	414	8	-	-	PUNCT
ejpam-6657	414	9	6):833–839	6):833–839	NOUN
ejpam-6657	414	10	,	,	PUNCT
ejpam-6657	414	11	2004	2004	NUM
ejpam-6657	414	12	.	.	PUNCT
ejpam-6657	415	1	[	[	X
ejpam-6657	415	2	2	2	X
ejpam-6657	415	3	]	]	PUNCT
ejpam-6657	415	4	h.	h.	PROPN
ejpam-6657	415	5	m.	m.	PROPN
ejpam-6657	415	6	srivastava	srivastava	PROPN
ejpam-6657	415	7	,	,	PUNCT
ejpam-6657	415	8	serkan	serkan	ADJ
ejpam-6657	415	9	araci	araci	PROPN
ejpam-6657	415	10	,	,	PUNCT
ejpam-6657	415	11	waseem	waseem	PROPN
ejpam-6657	415	12	a.	a.	PROPN
ejpam-6657	415	13	khan	khan	PROPN
ejpam-6657	415	14	,	,	PUNCT
ejpam-6657	415	15	and	and	CCONJ
ejpam-6657	415	16	mehmet	mehmet	PROPN
ejpam-6657	415	17	acikgoz	acikgoz	PROPN
ejpam-6657	415	18	.	.	PUNCT
ejpam-6657	416	1	a	a	DET
ejpam-6657	416	2	note	note	NOUN
ejpam-6657	416	3	on	on	ADP
ejpam-6657	416	4	the	the	DET
ejpam-6657	416	5	truncated	truncate	VERB
ejpam-6657	416	6	-	-	PUNCT
ejpam-6657	416	7	exponential	exponential	NOUN
ejpam-6657	416	8	based	base	VERB
ejpam-6657	416	9	apostol	apostol	NOUN
ejpam-6657	416	10	-	-	PUNCT
ejpam-6657	416	11	type	type	NOUN
ejpam-6657	416	12	polynomials	polynomial	NOUN
ejpam-6657	416	13	.	.	PUNCT
ejpam-6657	417	1	symmetry	symmetry	NOUN
ejpam-6657	417	2	,	,	PUNCT
ejpam-6657	417	3	11(4):538	11(4):538	NUM
ejpam-6657	417	4	,	,	PUNCT
ejpam-6657	417	5	2019	2019	NUM
ejpam-6657	417	6	.	.	PUNCT
ejpam-6657	418	1	[	[	X
ejpam-6657	418	2	3	3	X
ejpam-6657	418	3	]	]	X
ejpam-6657	418	4	noor	noor	PROPN
ejpam-6657	418	5	alam	alam	PROPN
ejpam-6657	418	6	,	,	PUNCT
ejpam-6657	418	7	shahid	shahid	PROPN
ejpam-6657	418	8	ahmad	ahmad	PROPN
ejpam-6657	418	9	wani	wani	PROPN
ejpam-6657	418	10	,	,	PUNCT
ejpam-6657	418	11	waseem	waseem	PROPN
ejpam-6657	418	12	ahmad	ahmad	PROPN
ejpam-6657	418	13	khan	khan	PROPN
ejpam-6657	418	14	,	,	PUNCT
ejpam-6657	418	15	and	and	CCONJ
ejpam-6657	418	16	hasan	hasan	PROPN
ejpam-6657	418	17	nihal	nihal	PROPN
ejpam-6657	418	18	zaidi	zaidi	PROPN
ejpam-6657	418	19	.	.	PUNCT
ejpam-6657	419	1	investigating	investigate	VERB
ejpam-6657	419	2	the	the	DET
ejpam-6657	419	3	properties	property	NOUN
ejpam-6657	419	4	and	and	CCONJ
ejpam-6657	419	5	dynamic	dynamic	ADJ
ejpam-6657	419	6	applications	application	NOUN
ejpam-6657	419	7	of	of	ADP
ejpam-6657	419	8	δh	δh	ADP
ejpam-6657	419	9	legendre	legendre	PROPN
ejpam-6657	419	10	–	–	PUNCT
ejpam-6657	419	11	appell	appell	NOUN
ejpam-6657	419	12	polynomials	polynomial	NOUN
ejpam-6657	419	13	.	.	PUNCT
ejpam-6657	420	1	mathematics	mathematic	NOUN
ejpam-6657	420	2	,	,	PUNCT
ejpam-6657	420	3	12(13):1973	12(13):1973	NUM
ejpam-6657	420	4	,	,	PUNCT
ejpam-6657	420	5	2024	2024	NUM
ejpam-6657	420	6	.	.	PUNCT
ejpam-6657	421	1	[	[	X
ejpam-6657	421	2	4	4	NUM
ejpam-6657	421	3	]	]	X
ejpam-6657	421	4	noor	noor	PROPN
ejpam-6657	421	5	alam	alam	PROPN
ejpam-6657	421	6	,	,	PUNCT
ejpam-6657	421	7	shahid	shahid	PROPN
ejpam-6657	421	8	ahmad	ahmad	PROPN
ejpam-6657	421	9	wani	wani	PROPN
ejpam-6657	421	10	,	,	PUNCT
ejpam-6657	421	11	waseem	waseem	PROPN
ejpam-6657	421	12	ahmad	ahmad	PROPN
ejpam-6657	421	13	khan	khan	PROPN
ejpam-6657	421	14	,	,	PUNCT
ejpam-6657	421	15	fakhredine	fakhredine	PROPN
ejpam-6657	421	16	gassem	gassem	NOUN
ejpam-6657	421	17	,	,	PUNCT
ejpam-6657	421	18	and	and	CCONJ
ejpam-6657	421	19	anas	anas	PROPN
ejpam-6657	421	20	altaleb	altaleb	PROPN
ejpam-6657	421	21	.	.	PUNCT
ejpam-6657	422	1	exploring	explore	VERB
ejpam-6657	422	2	properties	property	NOUN
ejpam-6657	422	3	and	and	CCONJ
ejpam-6657	422	4	applications	application	NOUN
ejpam-6657	422	5	of	of	ADP
ejpam-6657	422	6	laguerre	laguerre	NOUN
ejpam-6657	422	7	special	special	ADJ
ejpam-6657	422	8	polynomials	polynomial	NOUN
ejpam-6657	422	9	involving	involve	VERB
ejpam-6657	422	10	the	the	DET
ejpam-6657	422	11	δh	δh	ADJ
ejpam-6657	422	12	form	form	NOUN
ejpam-6657	422	13	.	.	PUNCT
ejpam-6657	423	1	symmetry	symmetry	NOUN
ejpam-6657	423	2	,	,	PUNCT
ejpam-6657	423	3	16(9):1154	16(9):1154	NUM
ejpam-6657	423	4	,	,	PUNCT
ejpam-6657	423	5	2024	2024	NUM
ejpam-6657	423	6	.	.	PUNCT
ejpam-6657	424	1	[	[	X
ejpam-6657	424	2	5	5	NUM
ejpam-6657	424	3	]	]	PUNCT
ejpam-6657	424	4	waseem	waseem	PROPN
ejpam-6657	424	5	ahmad	ahmad	PROPN
ejpam-6657	424	6	khan	khan	PROPN
ejpam-6657	424	7	and	and	CCONJ
ejpam-6657	424	8	maryam	maryam	PROPN
ejpam-6657	424	9	salem	salem	PROPN
ejpam-6657	424	10	alatawi	alatawi	VERB
ejpam-6657	424	11	.	.	PUNCT
ejpam-6657	425	1	a	a	DET
ejpam-6657	425	2	note	note	NOUN
ejpam-6657	425	3	on	on	ADP
ejpam-6657	425	4	modified	modified	ADJ
ejpam-6657	425	5	degenerate	degenerate	ADJ
ejpam-6657	425	6	changhee	changhee	NOUN
ejpam-6657	425	7	–	–	PUNCT
ejpam-6657	425	8	genocchi	genocchi	PROPN
ejpam-6657	425	9	polynomials	polynomial	NOUN
ejpam-6657	425	10	of	of	ADP
ejpam-6657	425	11	the	the	DET
ejpam-6657	425	12	second	second	ADJ
ejpam-6657	425	13	kind	kind	NOUN
ejpam-6657	425	14	.	.	PUNCT
ejpam-6657	426	1	symmetry	symmetry	NOUN
ejpam-6657	426	2	,	,	PUNCT
ejpam-6657	426	3	15(1):136	15(1):136	NOUN
ejpam-6657	426	4	,	,	PUNCT
ejpam-6657	426	5	2023	2023	NUM
ejpam-6657	426	6	.	.	PUNCT
ejpam-6657	427	1	[	[	X
ejpam-6657	427	2	6	6	NUM
ejpam-6657	427	3	]	]	X
ejpam-6657	427	4	paul	paul	PROPN
ejpam-6657	427	5	appell	appell	PROPN
ejpam-6657	427	6	and	and	CCONJ
ejpam-6657	427	7	joseph	joseph	PROPN
ejpam-6657	427	8	kampé	kampé	PROPN
ejpam-6657	427	9	de	de	PROPN
ejpam-6657	427	10	fériet	fériet	PROPN
ejpam-6657	427	11	.	.	PUNCT
ejpam-6657	427	12	fonctions	fonction	NOUN
ejpam-6657	427	13	hypergéométriques	hypergéométrique	VERB
ejpam-6657	427	14	et	et	NOUN
ejpam-6657	427	15	hypersphériques	hypersphérique	NOUN
ejpam-6657	427	16	:	:	PUNCT
ejpam-6657	427	17	polynômes	polynôme	NOUN
ejpam-6657	427	18	d’hermite	d’hermite	NOUN
ejpam-6657	427	19	.	.	PUNCT
ejpam-6657	428	1	gauthier	gauthier	NOUN
ejpam-6657	428	2	-	-	PUNCT
ejpam-6657	428	3	villars	villars	PROPN
ejpam-6657	428	4	,	,	PUNCT
ejpam-6657	428	5	1926	1926	NUM
ejpam-6657	428	6	.	.	PUNCT
ejpam-6657	429	1	[	[	X
ejpam-6657	429	2	7	7	X
ejpam-6657	429	3	]	]	X
ejpam-6657	429	4	g.	g.	NOUN
ejpam-6657	429	5	dattoli	dattoli	PROPN
ejpam-6657	429	6	.	.	PUNCT
ejpam-6657	430	1	hermite	hermite	ADJ
ejpam-6657	430	2	-	-	PUNCT
ejpam-6657	430	3	bessel	bessel	NOUN
ejpam-6657	430	4	and	and	CCONJ
ejpam-6657	430	5	laguerre	laguerre	NOUN
ejpam-6657	430	6	-	-	PUNCT
ejpam-6657	430	7	bessel	bessel	NOUN
ejpam-6657	430	8	functions	function	NOUN
ejpam-6657	430	9	:	:	PUNCT
ejpam-6657	430	10	a	a	DET
ejpam-6657	430	11	by	by	ADP
ejpam-6657	430	12	-	-	PUNCT
ejpam-6657	430	13	product	product	NOUN
ejpam-6657	430	14	of	of	ADP
ejpam-6657	430	15	the	the	DET
ejpam-6657	430	16	monomiality	monomiality	NOUN
ejpam-6657	430	17	principle	principle	NOUN
ejpam-6657	430	18	.	.	PUNCT
ejpam-6657	431	1	proceedings	proceeding	NOUN
ejpam-6657	431	2	of	of	ADP
ejpam-6657	431	3	the	the	DET
ejpam-6657	431	4	melfi	melfi	PROPN
ejpam-6657	431	5	school	school	NOUN
ejpam-6657	431	6	on	on	ADP
ejpam-6657	431	7	advanced	advanced	ADJ
ejpam-6657	431	8	topics	topic	NOUN
ejpam-6657	431	9	in	in	ADP
ejpam-6657	431	10	mathematics	mathematic	NOUN
ejpam-6657	431	11	and	and	CCONJ
ejpam-6657	431	12	physics	physics	NOUN
ejpam-6657	431	13	,	,	PUNCT
ejpam-6657	431	14	pages	page	NOUN
ejpam-6657	431	15	147–164	147–164	NUM
ejpam-6657	431	16	.	.	PUNCT
ejpam-6657	432	1	[	[	X
ejpam-6657	432	2	8	8	X
ejpam-6657	432	3	]	]	X
ejpam-6657	432	4	giuseppe	giuseppe	PROPN
ejpam-6657	432	5	dattoli	dattoli	PROPN
ejpam-6657	432	6	,	,	PUNCT
ejpam-6657	432	7	clemente	clemente	PROPN
ejpam-6657	432	8	cesarano	cesarano	PROPN
ejpam-6657	432	9	,	,	PUNCT
ejpam-6657	432	10	and	and	CCONJ
ejpam-6657	432	11	dario	dario	PROPN
ejpam-6657	432	12	sacchetti	sacchetti	VERB
ejpam-6657	432	13	.	.	PUNCT
ejpam-6657	433	1	a	a	DET
ejpam-6657	433	2	note	note	NOUN
ejpam-6657	433	3	on	on	ADP
ejpam-6657	433	4	truncated	truncated	ADJ
ejpam-6657	433	5	polynomials	polynomial	NOUN
ejpam-6657	433	6	.	.	PUNCT
ejpam-6657	434	1	applied	apply	VERB
ejpam-6657	434	2	mathematics	mathematic	NOUN
ejpam-6657	434	3	and	and	CCONJ
ejpam-6657	434	4	computation	computation	NOUN
ejpam-6657	434	5	,	,	PUNCT
ejpam-6657	434	6	134(2	134(2	NUM
ejpam-6657	434	7	-	-	SYM
ejpam-6657	434	8	3):595–605	3):595–605	NUM
ejpam-6657	434	9	,	,	PUNCT
ejpam-6657	434	10	2003	2003	NUM
ejpam-6657	434	11	.	.	PUNCT
ejpam-6657	435	1	[	[	X
ejpam-6657	435	2	9	9	NUM
ejpam-6657	435	3	]	]	X
ejpam-6657	435	4	g.	g.	NOUN
ejpam-6657	435	5	dattoli	dattoli	PROPN
ejpam-6657	435	6	,	,	PUNCT
ejpam-6657	435	7	s.	s.	PROPN
ejpam-6657	435	8	lorenzutta	lorenzutta	PROPN
ejpam-6657	435	9	,	,	PUNCT
ejpam-6657	435	10	a.	a.	NOUN
ejpam-6657	435	11	m.	m.	NOUN
ejpam-6657	435	12	mancho	mancho	PROPN
ejpam-6657	435	13	,	,	PUNCT
ejpam-6657	435	14	and	and	CCONJ
ejpam-6657	435	15	a.	a.	PROPN
ejpam-6657	435	16	torre	torre	PROPN
ejpam-6657	435	17	.	.	PUNCT
ejpam-6657	436	1	generalized	generalize	VERB
ejpam-6657	436	2	polynomials	polynomial	NOUN
ejpam-6657	436	3	and	and	CCONJ
ejpam-6657	436	4	associated	associate	VERB
ejpam-6657	436	5	operational	operational	ADJ
ejpam-6657	436	6	identities	identity	NOUN
ejpam-6657	436	7	.	.	PUNCT
ejpam-6657	437	1	journal	journal	NOUN
ejpam-6657	437	2	of	of	ADP
ejpam-6657	437	3	computational	computational	ADJ
ejpam-6657	437	4	and	and	CCONJ
ejpam-6657	437	5	applied	applied	ADJ
ejpam-6657	437	6	mathematics	mathematic	NOUN
ejpam-6657	437	7	,	,	PUNCT
ejpam-6657	437	8	108(1	108(1	NUM
ejpam-6657	437	9	-	-	SYM
ejpam-6657	437	10	2):209–218	2):209–218	NUM
ejpam-6657	437	11	,	,	PUNCT
ejpam-6657	437	12	1999	1999	NUM
ejpam-6657	437	13	.	.	PUNCT
ejpam-6657	438	1	[	[	X
ejpam-6657	438	2	10	10	NUM
ejpam-6657	438	3	]	]	PUNCT
ejpam-6657	438	4	t.	t.	PROPN
ejpam-6657	438	5	kanan	kanan	PROPN
ejpam-6657	438	6	,	,	PUNCT
ejpam-6657	438	7	m.	m.	NOUN
ejpam-6657	438	8	elbes	elbes	PROPN
ejpam-6657	438	9	,	,	PUNCT
ejpam-6657	438	10	k.	k.	PROPN
ejpam-6657	438	11	abu	abu	PROPN
ejpam-6657	438	12	maria	maria	PROPN
ejpam-6657	438	13	,	,	PUNCT
ejpam-6657	438	14	and	and	CCONJ
ejpam-6657	438	15	m.	m.	NOUN
ejpam-6657	438	16	alia	alia	PROPN
ejpam-6657	438	17	.	.	PUNCT
ejpam-6657	439	1	exploring	explore	VERB
ejpam-6657	439	2	the	the	DET
ejpam-6657	439	3	potential	potential	NOUN
ejpam-6657	439	4	of	of	ADP
ejpam-6657	439	5	iotbased	iotbase	VERB
ejpam-6657	439	6	learning	learn	VERB
ejpam-6657	439	7	environments	environment	NOUN
ejpam-6657	439	8	in	in	ADP
ejpam-6657	439	9	education	education	NOUN
ejpam-6657	439	10	.	.	PUNCT
ejpam-6657	440	1	international	international	ADJ
ejpam-6657	440	2	journal	journal	NOUN
ejpam-6657	440	3	of	of	ADP
ejpam-6657	440	4	advances	advance	NOUN
ejpam-6657	440	5	in	in	ADP
ejpam-6657	440	6	soft	soft	ADJ
ejpam-6657	440	7	computing	computing	NOUN
ejpam-6657	440	8	and	and	CCONJ
ejpam-6657	440	9	its	its	PRON
ejpam-6657	440	10	applications	application	NOUN
ejpam-6657	440	11	,	,	PUNCT
ejpam-6657	440	12	15(2	15(2	NUM
ejpam-6657	440	13	)	)	PUNCT
ejpam-6657	440	14	,	,	PUNCT
ejpam-6657	440	15	2023	2023	NUM
ejpam-6657	440	16	.	.	PUNCT
ejpam-6657	441	1	h.	h.	PROPN
ejpam-6657	441	2	qawaqneh	qawaqneh	PROPN
ejpam-6657	441	3	et	et	PROPN
ejpam-6657	441	4	al	al	PROPN
ejpam-6657	441	5	.	.	PUNCT
ejpam-6657	441	6	/	/	SYM
ejpam-6657	441	7	eur	eur	PROPN
ejpam-6657	441	8	.	.	PUNCT
ejpam-6657	442	1	j.	j.	PROPN
ejpam-6657	442	2	pure	pure	PROPN
ejpam-6657	442	3	appl	appl	PROPN
ejpam-6657	442	4	.	.	PROPN
ejpam-6657	442	5	math	math	PROPN
ejpam-6657	442	6	,	,	PUNCT
ejpam-6657	442	7	18	18	NUM
ejpam-6657	442	8	(	(	PUNCT
ejpam-6657	442	9	3	3	NUM
ejpam-6657	442	10	)	)	PUNCT
ejpam-6657	442	11	(	(	PUNCT
ejpam-6657	442	12	2025	2025	NUM
ejpam-6657	442	13	)	)	PUNCT
ejpam-6657	442	14	,	,	PUNCT
ejpam-6657	442	15	6657	6657	NUM
ejpam-6657	442	16	15	15	NUM
ejpam-6657	442	17	of	of	ADP
ejpam-6657	442	18	16	16	NUM
ejpam-6657	443	1	[	[	X
ejpam-6657	443	2	11	11	NUM
ejpam-6657	443	3	]	]	X
ejpam-6657	443	4	duha	duha	NOUN
ejpam-6657	443	5	abu	abu	PROPN
ejpam-6657	443	6	judeh	judeh	PROPN
ejpam-6657	443	7	and	and	CCONJ
ejpam-6657	443	8	m.	m.	PROPN
ejpam-6657	443	9	abu	abu	PROPN
ejpam-6657	443	10	hammad	hammad	PROPN
ejpam-6657	443	11	.	.	PUNCT
ejpam-6657	444	1	applications	application	NOUN
ejpam-6657	444	2	of	of	ADP
ejpam-6657	444	3	conformable	conformable	ADJ
ejpam-6657	444	4	fractional	fractional	ADJ
ejpam-6657	444	5	pareto	pareto	ADJ
ejpam-6657	444	6	probability	probability	NOUN
ejpam-6657	444	7	distribution	distribution	NOUN
ejpam-6657	444	8	.	.	PUNCT
ejpam-6657	445	1	international	international	ADJ
ejpam-6657	445	2	journal	journal	NOUN
ejpam-6657	445	3	of	of	ADP
ejpam-6657	445	4	advances	advance	NOUN
ejpam-6657	445	5	in	in	ADP
ejpam-6657	445	6	soft	soft	ADJ
ejpam-6657	445	7	computing	computing	NOUN
ejpam-6657	445	8	and	and	CCONJ
ejpam-6657	445	9	applications	application	NOUN
ejpam-6657	445	10	,	,	PUNCT
ejpam-6657	445	11	14(2):115–124	14(2):115–124	NUM
ejpam-6657	445	12	,	,	PUNCT
ejpam-6657	445	13	2022	2022	NUM
ejpam-6657	445	14	.	.	PUNCT
ejpam-6657	446	1	[	[	X
ejpam-6657	446	2	12	12	NUM
ejpam-6657	446	3	]	]	PUNCT
ejpam-6657	446	4	haitham	haitham	PROPN
ejpam-6657	446	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	446	6	,	,	PUNCT
ejpam-6657	446	7	mohd	mohd	PROPN
ejpam-6657	446	8	salmi	salmi	PROPN
ejpam-6657	446	9	md	md	PROPN
ejpam-6657	446	10	noorani	noorani	PROPN
ejpam-6657	446	11	,	,	PUNCT
ejpam-6657	446	12	hassen	hassen	PROPN
ejpam-6657	446	13	aydi	aydi	VERB
ejpam-6657	446	14	,	,	PUNCT
ejpam-6657	446	15	amjed	amjed	PROPN
ejpam-6657	446	16	zraiqat	zraiqat	PROPN
ejpam-6657	446	17	,	,	PUNCT
ejpam-6657	446	18	and	and	CCONJ
ejpam-6657	446	19	arslan	arslan	PROPN
ejpam-6657	446	20	hojat	hojat	PROPN
ejpam-6657	446	21	ansari	ansari	PROPN
ejpam-6657	446	22	.	.	PUNCT
ejpam-6657	447	1	on	on	ADP
ejpam-6657	447	2	fixed	fix	VERB
ejpam-6657	447	3	point	point	NOUN
ejpam-6657	447	4	results	result	NOUN
ejpam-6657	447	5	in	in	ADP
ejpam-6657	447	6	partial	partial	ADJ
ejpam-6657	447	7	b	b	NOUN
ejpam-6657	447	8	-	-	PUNCT
ejpam-6657	447	9	metric	metric	ADJ
ejpam-6657	447	10	spaces	space	NOUN
ejpam-6657	447	11	.	.	PUNCT
ejpam-6657	448	1	journal	journal	NOUN
ejpam-6657	448	2	of	of	ADP
ejpam-6657	448	3	function	function	NOUN
ejpam-6657	448	4	spaces	space	NOUN
ejpam-6657	448	5	,	,	PUNCT
ejpam-6657	448	6	2021(1):8769190	2021(1):8769190	NUM
ejpam-6657	448	7	,	,	PUNCT
ejpam-6657	448	8	2021	2021	NUM
ejpam-6657	448	9	.	.	PUNCT
ejpam-6657	449	1	[	[	X
ejpam-6657	449	2	13	13	NUM
ejpam-6657	449	3	]	]	PUNCT
ejpam-6657	449	4	haitham	haitham	PROPN
ejpam-6657	449	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	449	6	,	,	PUNCT
ejpam-6657	449	7	mohd	mohd	PROPN
ejpam-6657	449	8	salmi	salmi	PROPN
ejpam-6657	449	9	md	md	PROPN
ejpam-6657	449	10	noorani	noorani	PROPN
ejpam-6657	449	11	,	,	PUNCT
ejpam-6657	449	12	and	and	CCONJ
ejpam-6657	449	13	hassen	hassen	PROPN
ejpam-6657	449	14	aydi	aydi	VERB
ejpam-6657	449	15	.	.	PUNCT
ejpam-6657	450	1	some	some	DET
ejpam-6657	450	2	new	new	ADJ
ejpam-6657	450	3	characterizations	characterization	NOUN
ejpam-6657	450	4	and	and	CCONJ
ejpam-6657	450	5	results	result	NOUN
ejpam-6657	450	6	for	for	ADP
ejpam-6657	450	7	fuzzy	fuzzy	ADJ
ejpam-6657	450	8	contractions	contraction	NOUN
ejpam-6657	450	9	in	in	ADP
ejpam-6657	450	10	fuzzy	fuzzy	ADJ
ejpam-6657	450	11	b	b	X
ejpam-6657	450	12	-	-	PUNCT
ejpam-6657	450	13	metric	metric	ADJ
ejpam-6657	450	14	spaces	space	NOUN
ejpam-6657	450	15	and	and	CCONJ
ejpam-6657	450	16	applications	application	NOUN
ejpam-6657	450	17	.	.	PUNCT
ejpam-6657	451	1	aims	aim	VERB
ejpam-6657	451	2	mathematics	mathematics	PROPN
ejpam-6657	451	3	,	,	PUNCT
ejpam-6657	451	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-6657	451	5	,	,	PUNCT
ejpam-6657	451	6	2023	2023	NUM
ejpam-6657	451	7	.	.	PUNCT
ejpam-6657	452	1	[	[	X
ejpam-6657	452	2	14	14	NUM
ejpam-6657	452	3	]	]	X
ejpam-6657	452	4	larry	larry	PROPN
ejpam-6657	452	5	c.	c.	PROPN
ejpam-6657	452	6	andrews	andrews	PROPN
ejpam-6657	452	7	.	.	PUNCT
ejpam-6657	452	8	special	special	ADJ
ejpam-6657	452	9	functions	function	NOUN
ejpam-6657	452	10	of	of	ADP
ejpam-6657	452	11	mathematics	mathematic	NOUN
ejpam-6657	452	12	for	for	ADP
ejpam-6657	452	13	engineers	engineer	NOUN
ejpam-6657	452	14	,	,	PUNCT
ejpam-6657	452	15	volume	volume	NOUN
ejpam-6657	452	16	49	49	NUM
ejpam-6657	452	17	.	.	PUNCT
ejpam-6657	453	1	spie	spie	ADJ
ejpam-6657	453	2	press	press	NOUN
ejpam-6657	453	3	,	,	PUNCT
ejpam-6657	453	4	1998	1998	NUM
ejpam-6657	453	5	.	.	PUNCT
ejpam-6657	454	1	[	[	X
ejpam-6657	454	2	15	15	NUM
ejpam-6657	454	3	]	]	PUNCT
ejpam-6657	454	4	subuhi	subuhi	PROPN
ejpam-6657	454	5	khan	khan	PROPN
ejpam-6657	454	6	,	,	PUNCT
ejpam-6657	454	7	ghazala	ghazala	PROPN
ejpam-6657	454	8	yasmin	yasmin	PROPN
ejpam-6657	454	9	,	,	PUNCT
ejpam-6657	454	10	and	and	CCONJ
ejpam-6657	454	11	naeem	naeem	PROPN
ejpam-6657	454	12	ahmad	ahmad	PROPN
ejpam-6657	454	13	.	.	PUNCT
ejpam-6657	455	1	a	a	DET
ejpam-6657	455	2	note	note	NOUN
ejpam-6657	455	3	on	on	ADP
ejpam-6657	455	4	truncated	truncate	VERB
ejpam-6657	455	5	exponentialbased	exponentialbase	VERB
ejpam-6657	455	6	appell	appell	NOUN
ejpam-6657	455	7	polynomials	polynomial	NOUN
ejpam-6657	455	8	.	.	PUNCT
ejpam-6657	456	1	bulletin	bulletin	NOUN
ejpam-6657	456	2	of	of	ADP
ejpam-6657	456	3	the	the	DET
ejpam-6657	456	4	malaysian	malaysian	PROPN
ejpam-6657	456	5	mathematical	mathematical	PROPN
ejpam-6657	456	6	sciences	sciences	PROPN
ejpam-6657	456	7	society	society	NOUN
ejpam-6657	456	8	,	,	PUNCT
ejpam-6657	456	9	40:373–388	40:373–388	PROPN
ejpam-6657	456	10	,	,	PUNCT
ejpam-6657	456	11	2017	2017	NUM
ejpam-6657	456	12	.	.	PUNCT
ejpam-6657	457	1	[	[	X
ejpam-6657	457	2	16	16	NUM
ejpam-6657	457	3	]	]	X
ejpam-6657	457	4	j.	j.	PROPN
ejpam-6657	457	5	steffensen	steffensen	PROPN
ejpam-6657	457	6	.	.	PUNCT
ejpam-6657	458	1	the	the	DET
ejpam-6657	458	2	poweroid	poweroid	ADJ
ejpam-6657	458	3	,	,	PUNCT
ejpam-6657	458	4	an	an	DET
ejpam-6657	458	5	extension	extension	NOUN
ejpam-6657	458	6	of	of	ADP
ejpam-6657	458	7	the	the	DET
ejpam-6657	458	8	mathematical	mathematical	ADJ
ejpam-6657	458	9	notion	notion	NOUN
ejpam-6657	458	10	of	of	ADP
ejpam-6657	458	11	power	power	NOUN
ejpam-6657	458	12	.	.	PUNCT
ejpam-6657	459	1	1941	1941	NUM
ejpam-6657	459	2	.	.	PUNCT
ejpam-6657	460	1	[	[	X
ejpam-6657	460	2	17	17	NUM
ejpam-6657	460	3	]	]	PUNCT
ejpam-6657	460	4	ibtehal	ibtehal	PROPN
ejpam-6657	460	5	alazman	alazman	NOUN
ejpam-6657	460	6	,	,	PUNCT
ejpam-6657	460	7	badr	badr	PROPN
ejpam-6657	460	8	saad	saad	PROPN
ejpam-6657	460	9	t.	t.	PROPN
ejpam-6657	460	10	alkahtani	alkahtani	PROPN
ejpam-6657	460	11	,	,	PUNCT
ejpam-6657	460	12	and	and	CCONJ
ejpam-6657	460	13	shahid	shahid	PROPN
ejpam-6657	460	14	ahmad	ahmad	PROPN
ejpam-6657	460	15	wani	wani	PROPN
ejpam-6657	460	16	.	.	PUNCT
ejpam-6657	461	1	certain	certain	ADJ
ejpam-6657	461	2	properties	property	NOUN
ejpam-6657	461	3	of	of	ADP
ejpam-6657	461	4	δh	δh	ADP
ejpam-6657	461	5	multi	multi	ADJ
ejpam-6657	461	6	-	-	ADJ
ejpam-6657	461	7	variate	variate	ADJ
ejpam-6657	461	8	hermite	hermite	ADJ
ejpam-6657	461	9	polynomials	polynomial	NOUN
ejpam-6657	461	10	.	.	PUNCT
ejpam-6657	462	1	symmetry	symmetry	NOUN
ejpam-6657	462	2	,	,	PUNCT
ejpam-6657	462	3	15(4):839	15(4):839	NOUN
ejpam-6657	462	4	,	,	PUNCT
ejpam-6657	462	5	2023	2023	NUM
ejpam-6657	462	6	.	.	PUNCT
ejpam-6657	463	1	[	[	X
ejpam-6657	463	2	18	18	NUM
ejpam-6657	463	3	]	]	PUNCT
ejpam-6657	463	4	shahid	shahid	PROPN
ejpam-6657	463	5	ahmad	ahmad	PROPN
ejpam-6657	463	6	wani	wani	PROPN
ejpam-6657	463	7	,	,	PUNCT
ejpam-6657	463	8	waseem	waseem	PROPN
ejpam-6657	463	9	ahmad	ahmad	PROPN
ejpam-6657	463	10	khan	khan	PROPN
ejpam-6657	463	11	,	,	PUNCT
ejpam-6657	463	12	taghreed	taghreed	NOUN
ejpam-6657	463	13	alqurashi	alqurashi	PROPN
ejpam-6657	463	14	,	,	PUNCT
ejpam-6657	463	15	javid	javid	PROPN
ejpam-6657	463	16	gani	gani	PROPN
ejpam-6657	463	17	dar	dar	PROPN
ejpam-6657	463	18	,	,	PUNCT
ejpam-6657	463	19	and	and	CCONJ
ejpam-6657	463	20	dxion	dxion	NOUN
ejpam-6657	463	21	salcedo	salcedo	PROPN
ejpam-6657	463	22	.	.	PUNCT
ejpam-6657	464	1	certain	certain	ADJ
ejpam-6657	464	2	properties	property	NOUN
ejpam-6657	464	3	of	of	ADP
ejpam-6657	464	4	δh	δh	ADP
ejpam-6657	464	5	legendre	legendre	PROPN
ejpam-6657	464	6	polynomials	polynomial	NOUN
ejpam-6657	464	7	and	and	CCONJ
ejpam-6657	464	8	applications	application	NOUN
ejpam-6657	464	9	in	in	ADP
ejpam-6657	464	10	computer	computer	NOUN
ejpam-6657	464	11	modelling	modelling	NOUN
ejpam-6657	464	12	.	.	PUNCT
ejpam-6657	465	1	european	european	ADJ
ejpam-6657	465	2	journal	journal	PROPN
ejpam-6657	465	3	of	of	ADP
ejpam-6657	465	4	pure	pure	ADJ
ejpam-6657	465	5	and	and	CCONJ
ejpam-6657	465	6	applied	applied	ADJ
ejpam-6657	465	7	mathematics	mathematic	NOUN
ejpam-6657	465	8	,	,	PUNCT
ejpam-6657	465	9	18(2):5886	18(2):5886	NUM
ejpam-6657	465	10	,	,	PUNCT
ejpam-6657	465	11	2025	2025	NUM
ejpam-6657	465	12	.	.	PUNCT
ejpam-6657	466	1	[	[	X
ejpam-6657	466	2	19	19	NUM
ejpam-6657	466	3	]	]	X
ejpam-6657	466	4	r.	r.	PROPN
ejpam-6657	466	5	alyusof	alyusof	PROPN
ejpam-6657	466	6	and	and	CCONJ
ejpam-6657	466	7	s.	s.	PROPN
ejpam-6657	466	8	a.	a.	PROPN
ejpam-6657	466	9	wani	wani	PROPN
ejpam-6657	466	10	.	.	PUNCT
ejpam-6657	467	1	certain	certain	ADJ
ejpam-6657	467	2	properties	property	NOUN
ejpam-6657	467	3	and	and	CCONJ
ejpam-6657	467	4	applications	application	NOUN
ejpam-6657	467	5	of	of	ADP
ejpam-6657	467	6	δh	δh	ADP
ejpam-6657	467	7	hybrid	hybrid	ADJ
ejpam-6657	467	8	special	special	ADJ
ejpam-6657	467	9	polynomials	polynomial	NOUN
ejpam-6657	467	10	associated	associate	VERB
ejpam-6657	467	11	with	with	ADP
ejpam-6657	467	12	appell	appell	PROPN
ejpam-6657	467	13	sequences	sequence	NOUN
ejpam-6657	467	14	,	,	PUNCT
ejpam-6657	467	15	2023	2023	NUM
ejpam-6657	467	16	.	.	PUNCT
ejpam-6657	468	1	[	[	X
ejpam-6657	468	2	20	20	NUM
ejpam-6657	468	3	]	]	X
ejpam-6657	468	4	francesco	francesco	PROPN
ejpam-6657	468	5	a.	a.	PROPN
ejpam-6657	468	6	costabile	costabile	PROPN
ejpam-6657	468	7	and	and	CCONJ
ejpam-6657	468	8	elisabetta	elisabetta	PROPN
ejpam-6657	468	9	longo	longo	PROPN
ejpam-6657	468	10	.	.	PUNCT
ejpam-6657	469	1	δh	δh	NOUN
ejpam-6657	469	2	-	-	ADJ
ejpam-6657	469	3	appell	appell	ADJ
ejpam-6657	469	4	sequences	sequence	NOUN
ejpam-6657	469	5	and	and	CCONJ
ejpam-6657	469	6	related	relate	VERB
ejpam-6657	469	7	interpolation	interpolation	NOUN
ejpam-6657	469	8	problem	problem	NOUN
ejpam-6657	469	9	.	.	PUNCT
ejpam-6657	470	1	numerical	numerical	ADJ
ejpam-6657	470	2	algorithms	algorithms	PROPN
ejpam-6657	470	3	,	,	PUNCT
ejpam-6657	470	4	63:165–186	63:165–186	PROPN
ejpam-6657	470	5	,	,	PUNCT
ejpam-6657	470	6	2013	2013	NUM
ejpam-6657	470	7	.	.	PUNCT
ejpam-6657	471	1	[	[	X
ejpam-6657	471	2	21	21	NUM
ejpam-6657	471	3	]	]	X
ejpam-6657	471	4	h.	h.	PROPN
ejpam-6657	471	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	471	6	,	,	PUNCT
ejpam-6657	471	7	h.	h.	PROPN
ejpam-6657	471	8	a.	a.	PROPN
ejpam-6657	471	9	hammad	hammad	PROPN
ejpam-6657	471	10	,	,	PUNCT
ejpam-6657	471	11	and	and	CCONJ
ejpam-6657	471	12	h.	h.	PROPN
ejpam-6657	471	13	aydi	aydi	VERB
ejpam-6657	471	14	.	.	PUNCT
ejpam-6657	472	1	exploring	explore	VERB
ejpam-6657	472	2	new	new	ADJ
ejpam-6657	472	3	geometric	geometric	ADJ
ejpam-6657	472	4	contraction	contraction	NOUN
ejpam-6657	472	5	mappings	mapping	NOUN
ejpam-6657	472	6	and	and	CCONJ
ejpam-6657	472	7	their	their	PRON
ejpam-6657	472	8	applications	application	NOUN
ejpam-6657	472	9	in	in	ADP
ejpam-6657	472	10	fractional	fractional	ADJ
ejpam-6657	472	11	metric	metric	ADJ
ejpam-6657	472	12	spaces	space	NOUN
ejpam-6657	472	13	,	,	PUNCT
ejpam-6657	472	14	2024	2024	NUM
ejpam-6657	472	15	.	.	PUNCT
ejpam-6657	473	1	[	[	X
ejpam-6657	473	2	22	22	NUM
ejpam-6657	473	3	]	]	PUNCT
ejpam-6657	473	4	muhammad	muhammad	PROPN
ejpam-6657	473	5	nazam	nazam	PROPN
ejpam-6657	473	6	,	,	PUNCT
ejpam-6657	473	7	hassen	hassen	PROPN
ejpam-6657	473	8	aydi	aydi	ADV
ejpam-6657	473	9	,	,	PUNCT
ejpam-6657	473	10	mohd	mohd	PROPN
ejpam-6657	473	11	salmi	salmi	PROPN
ejpam-6657	473	12	noorani	noorani	PROPN
ejpam-6657	473	13	,	,	PUNCT
ejpam-6657	473	14	and	and	CCONJ
ejpam-6657	473	15	haitham	haitham	PROPN
ejpam-6657	473	16	qawaqneh	qawaqneh	PROPN
ejpam-6657	473	17	.	.	PUNCT
ejpam-6657	474	1	existence	existence	NOUN
ejpam-6657	474	2	of	of	ADP
ejpam-6657	474	3	fixed	fix	VERB
ejpam-6657	474	4	points	point	NOUN
ejpam-6657	474	5	of	of	ADP
ejpam-6657	474	6	four	four	NUM
ejpam-6657	474	7	maps	map	NOUN
ejpam-6657	474	8	for	for	ADP
ejpam-6657	474	9	a	a	DET
ejpam-6657	474	10	new	new	ADJ
ejpam-6657	474	11	generalized	generalized	ADJ
ejpam-6657	474	12	f	f	NOUN
ejpam-6657	474	13	-	-	PUNCT
ejpam-6657	474	14	contraction	contraction	NOUN
ejpam-6657	474	15	and	and	CCONJ
ejpam-6657	474	16	an	an	DET
ejpam-6657	474	17	application	application	NOUN
ejpam-6657	474	18	.	.	PUNCT
ejpam-6657	475	1	journal	journal	NOUN
ejpam-6657	475	2	of	of	ADP
ejpam-6657	475	3	function	function	NOUN
ejpam-6657	475	4	spaces	space	NOUN
ejpam-6657	475	5	,	,	PUNCT
ejpam-6657	475	6	2019(1):5980312	2019(1):5980312	NUM
ejpam-6657	475	7	,	,	PUNCT
ejpam-6657	475	8	2019	2019	NUM
ejpam-6657	475	9	.	.	PUNCT
ejpam-6657	476	1	[	[	X
ejpam-6657	476	2	23	23	NUM
ejpam-6657	476	3	]	]	PUNCT
ejpam-6657	476	4	haitham	haitham	PROPN
ejpam-6657	476	5	qawaqneh	qawaqneh	PROPN
ejpam-6657	476	6	,	,	PUNCT
ejpam-6657	476	7	mohd	mohd	PROPN
ejpam-6657	476	8	salmi	salmi	PROPN
ejpam-6657	476	9	noorani	noorani	PROPN
ejpam-6657	476	10	,	,	PUNCT
ejpam-6657	476	11	hassen	hassen	PROPN
ejpam-6657	476	12	aydi	aydi	ADV
ejpam-6657	476	13	,	,	PUNCT
ejpam-6657	476	14	and	and	CCONJ
ejpam-6657	476	15	wasfi	wasfi	ADV
ejpam-6657	476	16	shatanawi	shatanawi	ADJ
ejpam-6657	476	17	.	.	PUNCT
ejpam-6657	477	1	on	on	ADP
ejpam-6657	477	2	common	common	ADJ
ejpam-6657	477	3	fixed	fix	VERB
ejpam-6657	477	4	point	point	NOUN
ejpam-6657	477	5	results	result	NOUN
ejpam-6657	477	6	for	for	ADP
ejpam-6657	477	7	new	new	ADJ
ejpam-6657	477	8	contractions	contraction	NOUN
ejpam-6657	477	9	with	with	ADP
ejpam-6657	477	10	applications	application	NOUN
ejpam-6657	477	11	to	to	PART
ejpam-6657	477	12	graph	graph	VERB
ejpam-6657	477	13	and	and	CCONJ
ejpam-6657	477	14	integral	integral	ADJ
ejpam-6657	477	15	equations	equation	NOUN
ejpam-6657	477	16	.	.	PUNCT
ejpam-6657	478	1	mathematics	mathematic	NOUN
ejpam-6657	478	2	,	,	PUNCT
ejpam-6657	478	3	7(11):1082	7(11):1082	NOUN
ejpam-6657	478	4	,	,	PUNCT
ejpam-6657	478	5	2019	2019	NUM
ejpam-6657	478	6	.	.	PUNCT
ejpam-6657	479	1	[	[	X
ejpam-6657	479	2	24	24	NUM
ejpam-6657	479	3	]	]	PUNCT
ejpam-6657	479	4	waseem	waseem	PROPN
ejpam-6657	479	5	a.	a.	PROPN
ejpam-6657	479	6	khan	khan	PROPN
ejpam-6657	479	7	.	.	PUNCT
ejpam-6657	480	1	a	a	DET
ejpam-6657	480	2	note	note	NOUN
ejpam-6657	480	3	on	on	ADP
ejpam-6657	480	4	degenerate	degenerate	ADJ
ejpam-6657	480	5	hermite	hermite	ADJ
ejpam-6657	480	6	poly	poly	ADJ
ejpam-6657	480	7	-	-	PUNCT
ejpam-6657	480	8	bernoulli	bernoulli	NOUN
ejpam-6657	480	9	numbers	number	NOUN
ejpam-6657	480	10	and	and	CCONJ
ejpam-6657	480	11	polynomials	polynomial	NOUN
ejpam-6657	480	12	.	.	PUNCT
ejpam-6657	481	1	journal	journal	NOUN
ejpam-6657	481	2	of	of	ADP
ejpam-6657	481	3	classical	classical	ADJ
ejpam-6657	481	4	analysis	analysis	NOUN
ejpam-6657	481	5	,	,	PUNCT
ejpam-6657	481	6	8(1):65–76	8(1):65–76	NUM
ejpam-6657	481	7	,	,	PUNCT
ejpam-6657	481	8	2016	2016	NUM
ejpam-6657	481	9	.	.	PUNCT
ejpam-6657	482	1	[	[	X
ejpam-6657	482	2	25	25	NUM
ejpam-6657	482	3	]	]	PUNCT
ejpam-6657	482	4	waseem	waseem	PROPN
ejpam-6657	482	5	ahmad	ahmad	PROPN
ejpam-6657	482	6	khan	khan	PROPN
ejpam-6657	482	7	,	,	PUNCT
ejpam-6657	482	8	ugur	ugur	PROPN
ejpam-6657	482	9	duran	duran	PROPN
ejpam-6657	482	10	,	,	PUNCT
ejpam-6657	482	11	jihad	jihad	NOUN
ejpam-6657	482	12	younis	younis	PROPN
ejpam-6657	482	13	,	,	PUNCT
ejpam-6657	482	14	and	and	CCONJ
ejpam-6657	482	15	cheon	cheon	PROPN
ejpam-6657	482	16	seoung	seoung	PROPN
ejpam-6657	482	17	ryoo	ryoo	NOUN
ejpam-6657	482	18	.	.	PUNCT
ejpam-6657	483	1	on	on	ADP
ejpam-6657	483	2	some	some	DET
ejpam-6657	483	3	extensions	extension	NOUN
ejpam-6657	483	4	for	for	ADP
ejpam-6657	483	5	degenerate	degenerate	ADJ
ejpam-6657	483	6	frobenius	frobenius	NOUN
ejpam-6657	483	7	-	-	PUNCT
ejpam-6657	483	8	euler	euler	NOUN
ejpam-6657	483	9	-	-	PUNCT
ejpam-6657	483	10	genocchi	genocchi	PROPN
ejpam-6657	483	11	polynomials	polynomial	VERB
ejpam-6657	483	12	with	with	ADP
ejpam-6657	483	13	applications	application	NOUN
ejpam-6657	483	14	in	in	ADP
ejpam-6657	483	15	computer	computer	NOUN
ejpam-6657	483	16	modeling	modeling	NOUN
ejpam-6657	483	17	.	.	PUNCT
ejpam-6657	484	1	applied	apply	VERB
ejpam-6657	484	2	mathematics	mathematic	NOUN
ejpam-6657	484	3	in	in	ADP
ejpam-6657	484	4	science	science	NOUN
ejpam-6657	484	5	and	and	CCONJ
ejpam-6657	484	6	engineering	engineering	NOUN
ejpam-6657	484	7	,	,	PUNCT
ejpam-6657	484	8	32(1):2297072	32(1):2297072	NUM
ejpam-6657	484	9	,	,	PUNCT
ejpam-6657	484	10	2024	2024	NUM
ejpam-6657	484	11	.	.	PUNCT
ejpam-6657	485	1	[	[	X
ejpam-6657	485	2	26	26	NUM
ejpam-6657	485	3	]	]	PUNCT
ejpam-6657	485	4	waseem	waseem	PROPN
ejpam-6657	485	5	a.	a.	PROPN
ejpam-6657	485	6	khan	khan	PROPN
ejpam-6657	485	7	,	,	PUNCT
ejpam-6657	485	8	abdulghani	abdulghani	ADJ
ejpam-6657	485	9	muhyi	muhyi	PROPN
ejpam-6657	485	10	,	,	PUNCT
ejpam-6657	485	11	rifaqat	rifaqat	PROPN
ejpam-6657	485	12	ali	ali	PROPN
ejpam-6657	485	13	,	,	PUNCT
ejpam-6657	485	14	khaled	khaled	PROPN
ejpam-6657	485	15	ahmad	ahmad	PROPN
ejpam-6657	485	16	hassan	hassan	PROPN
ejpam-6657	485	17	alzobydi	alzobydi	PROPN
ejpam-6657	485	18	,	,	PUNCT
ejpam-6657	485	19	manoj	manoj	PROPN
ejpam-6657	485	20	singh	singh	PROPN
ejpam-6657	485	21	,	,	PUNCT
ejpam-6657	485	22	and	and	CCONJ
ejpam-6657	485	23	praveen	praveen	PROPN
ejpam-6657	485	24	agarwal	agarwal	PROPN
ejpam-6657	485	25	.	.	PUNCT
ejpam-6657	486	1	a	a	DET
ejpam-6657	486	2	new	new	ADJ
ejpam-6657	486	3	family	family	NOUN
ejpam-6657	486	4	of	of	ADP
ejpam-6657	486	5	degenerate	degenerate	ADJ
ejpam-6657	486	6	poly	poly	ADJ
ejpam-6657	486	7	-	-	PUNCT
ejpam-6657	486	8	bernoulli	bernoulli	NOUN
ejpam-6657	486	9	polynomials	polynomial	NOUN
ejpam-6657	486	10	of	of	ADP
ejpam-6657	486	11	the	the	DET
ejpam-6657	486	12	second	second	ADJ
ejpam-6657	486	13	kind	kind	NOUN
ejpam-6657	486	14	with	with	ADP
ejpam-6657	486	15	its	its	PRON
ejpam-6657	486	16	certain	certain	ADJ
ejpam-6657	486	17	related	related	ADJ
ejpam-6657	486	18	properties	property	NOUN
ejpam-6657	486	19	.	.	PUNCT
ejpam-6657	487	1	aims	aim	VERB
ejpam-6657	487	2	mathematics	mathematic	NOUN
ejpam-6657	487	3	,	,	PUNCT
ejpam-6657	487	4	6(11):12680–12697	6(11):12680–12697	NUM
ejpam-6657	487	5	,	,	PUNCT
ejpam-6657	487	6	2021	2021	NUM
ejpam-6657	487	7	.	.	PUNCT
ejpam-6657	488	1	h.	h.	PROPN
ejpam-6657	488	2	qawaqneh	qawaqneh	PROPN
ejpam-6657	488	3	et	et	PROPN
ejpam-6657	488	4	al	al	PROPN
ejpam-6657	488	5	.	.	PUNCT
ejpam-6657	488	6	/	/	SYM
ejpam-6657	488	7	eur	eur	PROPN
ejpam-6657	488	8	.	.	PUNCT
ejpam-6657	489	1	j.	j.	PROPN
ejpam-6657	489	2	pure	pure	PROPN
ejpam-6657	489	3	appl	appl	PROPN
ejpam-6657	489	4	.	.	PROPN
ejpam-6657	489	5	math	math	PROPN
ejpam-6657	489	6	,	,	PUNCT
ejpam-6657	489	7	18	18	NUM
ejpam-6657	489	8	(	(	PUNCT
ejpam-6657	489	9	3	3	NUM
ejpam-6657	489	10	)	)	PUNCT
ejpam-6657	489	11	(	(	PUNCT
ejpam-6657	489	12	2025	2025	NUM
ejpam-6657	489	13	)	)	PUNCT
ejpam-6657	489	14	,	,	PUNCT
ejpam-6657	489	15	6657	6657	NUM
ejpam-6657	489	16	16	16	NUM
ejpam-6657	489	17	of	of	ADP
ejpam-6657	489	18	16	16	NUM
ejpam-6657	490	1	[	[	X
ejpam-6657	490	2	27	27	NUM
ejpam-6657	490	3	]	]	X
ejpam-6657	490	4	g.	g.	NOUN
ejpam-6657	490	5	dattoli	dattoli	PROPN
ejpam-6657	490	6	.	.	PUNCT
ejpam-6657	491	1	generalized	generalized	ADJ
ejpam-6657	491	2	polynomials	polynomial	NOUN
ejpam-6657	491	3	,	,	PUNCT
ejpam-6657	491	4	operational	operational	ADJ
ejpam-6657	491	5	identities	identity	NOUN
ejpam-6657	491	6	and	and	CCONJ
ejpam-6657	491	7	their	their	PRON
ejpam-6657	491	8	applications	application	NOUN
ejpam-6657	491	9	.	.	PUNCT
ejpam-6657	492	1	journal	journal	NOUN
ejpam-6657	492	2	of	of	ADP
ejpam-6657	492	3	computational	computational	ADJ
ejpam-6657	492	4	and	and	CCONJ
ejpam-6657	492	5	applied	applied	ADJ
ejpam-6657	492	6	mathematics	mathematic	NOUN
ejpam-6657	492	7	,	,	PUNCT
ejpam-6657	492	8	118(1	118(1	NUM
ejpam-6657	492	9	-	-	SYM
ejpam-6657	492	10	2):111–123	2):111–123	NUM
ejpam-6657	492	11	,	,	PUNCT
ejpam-6657	492	12	2000	2000	NUM
ejpam-6657	492	13	.	.	PUNCT
ejpam-6657	493	1	[	[	X
ejpam-6657	493	2	28	28	NUM
ejpam-6657	493	3	]	]	X
ejpam-6657	493	4	g.	g.	NOUN
ejpam-6657	493	5	dattoli	dattoli	PROPN
ejpam-6657	493	6	,	,	PUNCT
ejpam-6657	493	7	p.	p.	PROPN
ejpam-6657	493	8	e.	e.	PROPN
ejpam-6657	493	9	ricci	ricci	PROPN
ejpam-6657	493	10	,	,	PUNCT
ejpam-6657	493	11	c.	c.	PROPN
ejpam-6657	493	12	cesarano	cesarano	PROPN
ejpam-6657	493	13	,	,	PUNCT
ejpam-6657	493	14	and	and	CCONJ
ejpam-6657	493	15	l.	l.	PROPN
ejpam-6657	493	16	vázquez	vázquez	PROPN
ejpam-6657	493	17	.	.	PROPN
ejpam-6657	493	18	special	special	ADJ
ejpam-6657	493	19	polynomials	polynomial	NOUN
ejpam-6657	493	20	and	and	CCONJ
ejpam-6657	493	21	fractional	fractional	ADJ
ejpam-6657	493	22	calculus	calculus	NOUN
ejpam-6657	493	23	.	.	PUNCT
ejpam-6657	494	1	mathematical	mathematical	ADJ
ejpam-6657	494	2	and	and	CCONJ
ejpam-6657	494	3	computer	computer	NOUN
ejpam-6657	494	4	modelling	modelling	NOUN
ejpam-6657	494	5	,	,	PUNCT
ejpam-6657	494	6	37(7	37(7	PROPN
ejpam-6657	494	7	-	-	PUNCT
ejpam-6657	494	8	8):729–733	8):729–733	NUM
ejpam-6657	494	9	,	,	PUNCT
ejpam-6657	494	10	2003	2003	NUM
ejpam-6657	494	11	.	.	PUNCT