id	sid	tid	token	lemma	pos
ejpam-6054	1	1	european	european	PROPN
ejpam-6054	1	2	journal	journal	PROPN
ejpam-6054	1	3	of	of	ADP
ejpam-6054	1	4	pure	pure	ADJ
ejpam-6054	1	5	and	and	CCONJ
ejpam-6054	1	6	applied	applied	ADJ
ejpam-6054	1	7	mathematics	mathematic	NOUN
ejpam-6054	1	8	2025	2025	NUM
ejpam-6054	1	9	,	,	PUNCT
ejpam-6054	1	10	vol	vol	NOUN
ejpam-6054	1	11	.	.	PROPN
ejpam-6054	1	12	18	18	NUM
ejpam-6054	1	13	,	,	PUNCT
ejpam-6054	1	14	issue	issue	NOUN
ejpam-6054	1	15	3	3	NUM
ejpam-6054	1	16	,	,	PUNCT
ejpam-6054	1	17	article	article	NOUN
ejpam-6054	1	18	number	number	NOUN
ejpam-6054	1	19	6054	6054	NUM
ejpam-6054	1	20	issn	issn	PROPN
ejpam-6054	1	21	1307	1307	NUM
ejpam-6054	1	22	-	-	SYM
ejpam-6054	1	23	5543	5543	NUM
ejpam-6054	1	24	–	–	PUNCT
ejpam-6054	1	25	ejpam.com	ejpam.com	X
ejpam-6054	1	26	published	publish	VERB
ejpam-6054	1	27	by	by	ADP
ejpam-6054	1	28	new	new	PROPN
ejpam-6054	1	29	york	york	PROPN
ejpam-6054	1	30	business	business	PROPN
ejpam-6054	1	31	global	global	PROPN
ejpam-6054	1	32	an	an	DET
ejpam-6054	1	33	analytical	analytical	ADJ
ejpam-6054	1	34	study	study	NOUN
ejpam-6054	1	35	of	of	ADP
ejpam-6054	1	36	two	two	NUM
ejpam-6054	1	37	-	-	PUNCT
ejpam-6054	1	38	dimensional	dimensional	ADJ
ejpam-6054	1	39	bell	bell	NOUN
ejpam-6054	1	40	polynomials	polynomial	NOUN
ejpam-6054	1	41	and	and	CCONJ
ejpam-6054	1	42	their	their	PRON
ejpam-6054	1	43	properties	property	NOUN
ejpam-6054	1	44	shahid	shahid	PROPN
ejpam-6054	1	45	ahmadwani1	ahmadwani1	PROPN
ejpam-6054	1	46	,	,	PUNCT
ejpam-6054	1	47	taghreed	taghreed	NOUN
ejpam-6054	1	48	alqurashi2	alqurashi2	NOUN
ejpam-6054	1	49	,	,	PUNCT
ejpam-6054	1	50	william	william	PROPN
ejpam-6054	1	51	ramı́rez3,4,∗	ramı́rez3,4,∗	PROPN
ejpam-6054	1	52	,	,	PUNCT
ejpam-6054	1	53	shilpa	shilpa	PROPN
ejpam-6054	1	54	malge1	malge1	PROPN
ejpam-6054	1	55	,	,	PUNCT
ejpam-6054	1	56	jesús	jesús	PROPN
ejpam-6054	1	57	david	david	PROPN
ejpam-6054	1	58	berŕıo	berŕıo	PROPN
ejpam-6054	1	59	valbuena5	valbuena5	PROPN
ejpam-6054	1	60	1symbiosis	1symbiosis	NUM
ejpam-6054	1	61	institute	institute	NOUN
ejpam-6054	1	62	of	of	ADP
ejpam-6054	1	63	technology	technology	PROPN
ejpam-6054	1	64	pune	pune	NOUN
ejpam-6054	1	65	,	,	PUNCT
ejpam-6054	1	66	symbiosis	symbiosis	NOUN
ejpam-6054	1	67	international	international	ADJ
ejpam-6054	1	68	(	(	PUNCT
ejpam-6054	1	69	deemed	deem	VERB
ejpam-6054	1	70	university	university	NOUN
ejpam-6054	1	71	)	)	PUNCT
ejpam-6054	1	72	,	,	PUNCT
ejpam-6054	1	73	pune	pune	NOUN
ejpam-6054	1	74	,	,	PUNCT
ejpam-6054	1	75	india	india	PROPN
ejpam-6054	1	76	2mathematics	2mathematics	NUM
ejpam-6054	1	77	department	department	NOUN
ejpam-6054	1	78	,	,	PUNCT
ejpam-6054	1	79	faculty	faculty	NOUN
ejpam-6054	1	80	of	of	ADP
ejpam-6054	1	81	science	science	NOUN
ejpam-6054	1	82	,	,	PUNCT
ejpam-6054	1	83	al	al	PROPN
ejpam-6054	1	84	-	-	PUNCT
ejpam-6054	1	85	baha	baha	PROPN
ejpam-6054	1	86	university	university	PROPN
ejpam-6054	1	87	,	,	PUNCT
ejpam-6054	1	88	65779	65779	NUM
ejpam-6054	1	89	-	-	SYM
ejpam-6054	1	90	7738	7738	NUM
ejpam-6054	1	91	albaha	albaha	NOUN
ejpam-6054	1	92	city	city	NOUN
ejpam-6054	1	93	,	,	PUNCT
ejpam-6054	1	94	kingdom	kingdom	NOUN
ejpam-6054	1	95	of	of	ADP
ejpam-6054	1	96	saudi	saudi	PROPN
ejpam-6054	1	97	,	,	PUNCT
ejpam-6054	1	98	arabia	arabia	PROPN
ejpam-6054	1	99	3	3	NUM
ejpam-6054	1	100	department	department	NOUN
ejpam-6054	1	101	of	of	ADP
ejpam-6054	1	102	natural	natural	ADJ
ejpam-6054	1	103	and	and	CCONJ
ejpam-6054	1	104	exact	exact	ADJ
ejpam-6054	1	105	sciences	science	NOUN
ejpam-6054	1	106	,	,	PUNCT
ejpam-6054	1	107	universidad	universidad	PROPN
ejpam-6054	1	108	de	de	PROPN
ejpam-6054	1	109	la	la	PROPN
ejpam-6054	1	110	costa	costa	PROPN
ejpam-6054	1	111	,	,	PUNCT
ejpam-6054	1	112	calle	calle	PROPN
ejpam-6054	1	113	58	58	NUM
ejpam-6054	1	114	n	n	NUM
ejpam-6054	1	115	55	55	NUM
ejpam-6054	1	116	-	-	SYM
ejpam-6054	1	117	66	66	NUM
ejpam-6054	1	118	,	,	PUNCT
ejpam-6054	1	119	080002	080002	NUM
ejpam-6054	1	120	barranquilla	barranquilla	NOUN
ejpam-6054	1	121	,	,	PUNCT
ejpam-6054	1	122	colombia	colombia	PROPN
ejpam-6054	1	123	4	4	NUM
ejpam-6054	1	124	section	section	NOUN
ejpam-6054	1	125	of	of	ADP
ejpam-6054	1	126	mathematics	mathematics	PROPN
ejpam-6054	1	127	international	international	PROPN
ejpam-6054	1	128	telematic	telematic	ADJ
ejpam-6054	1	129	university	university	NOUN
ejpam-6054	1	130	uninettuno	uninettuno	NOUN
ejpam-6054	1	131	,	,	PUNCT
ejpam-6054	1	132	corso	corso	PROPN
ejpam-6054	1	133	vittorio	vittorio	PROPN
ejpam-6054	1	134	emanuele	emanuele	PROPN
ejpam-6054	1	135	ii	ii	PROPN
ejpam-6054	1	136	,	,	PUNCT
ejpam-6054	1	137	39	39	NUM
ejpam-6054	1	138	,	,	PUNCT
ejpam-6054	1	139	00186	00186	NUM
ejpam-6054	1	140	rome	rome	PROPN
ejpam-6054	1	141	,	,	PUNCT
ejpam-6054	1	142	italy	italy	PROPN
ejpam-6054	1	143	5	5	NUM
ejpam-6054	1	144	universidad	universidad	PROPN
ejpam-6054	1	145	del	del	PROPN
ejpam-6054	1	146	atlántico	atlántico	PROPN
ejpam-6054	1	147	,	,	PUNCT
ejpam-6054	1	148	barranquilla	barranquilla	PROPN
ejpam-6054	1	149	,	,	PUNCT
ejpam-6054	1	150	colombia	colombia	PROPN
ejpam-6054	1	151	abstract	abstract	NOUN
ejpam-6054	1	152	.	.	PUNCT
ejpam-6054	2	1	this	this	DET
ejpam-6054	2	2	study	study	NOUN
ejpam-6054	2	3	investigates	investigate	VERB
ejpam-6054	2	4	two	two	NUM
ejpam-6054	2	5	-	-	PUNCT
ejpam-6054	2	6	dimensional	dimensional	ADJ
ejpam-6054	2	7	bell	bell	NOUN
ejpam-6054	2	8	polynomials	polynomial	NOUN
ejpam-6054	2	9	,	,	PUNCT
ejpam-6054	2	10	emphasizing	emphasize	VERB
ejpam-6054	2	11	their	their	PRON
ejpam-6054	2	12	fundamental	fundamental	ADJ
ejpam-6054	2	13	properties	property	NOUN
ejpam-6054	2	14	and	and	CCONJ
ejpam-6054	2	15	applications	application	NOUN
ejpam-6054	2	16	in	in	ADP
ejpam-6054	2	17	mathematical	mathematical	ADJ
ejpam-6054	2	18	analysis	analysis	NOUN
ejpam-6054	2	19	.	.	PUNCT
ejpam-6054	3	1	utilising	utilise	VERB
ejpam-6054	3	2	the	the	DET
ejpam-6054	3	3	framework	framework	NOUN
ejpam-6054	3	4	of	of	ADP
ejpam-6054	3	5	generating	generating	NOUN
ejpam-6054	3	6	functions	function	NOUN
ejpam-6054	3	7	,	,	PUNCT
ejpam-6054	3	8	we	we	PRON
ejpam-6054	3	9	derive	derive	VERB
ejpam-6054	3	10	explicit	explicit	ADJ
ejpam-6054	3	11	representations	representation	NOUN
ejpam-6054	3	12	,	,	PUNCT
ejpam-6054	3	13	summation	summation	NOUN
ejpam-6054	3	14	formulae	formulae	NOUN
ejpam-6054	3	15	,	,	PUNCT
ejpam-6054	3	16	recurrence	recurrence	NOUN
ejpam-6054	3	17	relations	relation	NOUN
ejpam-6054	3	18	,	,	PUNCT
ejpam-6054	3	19	and	and	CCONJ
ejpam-6054	3	20	addition	addition	NOUN
ejpam-6054	3	21	formulas	formula	NOUN
ejpam-6054	3	22	for	for	ADP
ejpam-6054	3	23	these	these	DET
ejpam-6054	3	24	polynomials	polynomial	NOUN
ejpam-6054	3	25	.	.	PUNCT
ejpam-6054	4	1	furthermore	furthermore	ADV
ejpam-6054	4	2	,	,	PUNCT
ejpam-6054	4	3	we	we	PRON
ejpam-6054	4	4	introduce	introduce	VERB
ejpam-6054	4	5	the	the	DET
ejpam-6054	4	6	2d	2d	NUM
ejpam-6054	4	7	bell	bell	NOUN
ejpam-6054	4	8	-	-	PUNCT
ejpam-6054	4	9	based	base	VERB
ejpam-6054	4	10	stirling	stirling	NOUN
ejpam-6054	4	11	polynomials	polynomial	NOUN
ejpam-6054	4	12	of	of	ADP
ejpam-6054	4	13	the	the	DET
ejpam-6054	4	14	second	second	ADJ
ejpam-6054	4	15	kind	kind	NOUN
ejpam-6054	4	16	and	and	CCONJ
ejpam-6054	4	17	explore	explore	VERB
ejpam-6054	4	18	their	their	PRON
ejpam-6054	4	19	associated	associated	ADJ
ejpam-6054	4	20	properties	property	NOUN
ejpam-6054	4	21	.	.	PUNCT
ejpam-6054	5	1	this	this	DET
ejpam-6054	5	2	research	research	NOUN
ejpam-6054	5	3	aims	aim	VERB
ejpam-6054	5	4	to	to	PART
ejpam-6054	5	5	enhance	enhance	VERB
ejpam-6054	5	6	the	the	DET
ejpam-6054	5	7	theoretical	theoretical	ADJ
ejpam-6054	5	8	understanding	understanding	NOUN
ejpam-6054	5	9	of	of	ADP
ejpam-6054	5	10	bell	bell	NOUN
ejpam-6054	5	11	polynomials	polynomial	NOUN
ejpam-6054	5	12	and	and	CCONJ
ejpam-6054	5	13	their	their	PRON
ejpam-6054	5	14	broader	broad	ADJ
ejpam-6054	5	15	applications	application	NOUN
ejpam-6054	5	16	in	in	ADP
ejpam-6054	5	17	mathematical	mathematical	ADJ
ejpam-6054	5	18	analysis	analysis	NOUN
ejpam-6054	5	19	.	.	PUNCT
ejpam-6054	6	1	2020	2020	NUM
ejpam-6054	6	2	mathematics	mathematic	NOUN
ejpam-6054	6	3	subject	subject	NOUN
ejpam-6054	6	4	classifications	classification	NOUN
ejpam-6054	6	5	:	:	PUNCT
ejpam-6054	6	6	33e20	33e20	NUM
ejpam-6054	6	7	,	,	PUNCT
ejpam-6054	6	8	33c45	33c45	NUM
ejpam-6054	6	9	,	,	PUNCT
ejpam-6054	6	10	33b10	33b10	NUM
ejpam-6054	6	11	,	,	PUNCT
ejpam-6054	6	12	33e30	33e30	NUM
ejpam-6054	6	13	,	,	PUNCT
ejpam-6054	6	14	11t23	11t23	DET
ejpam-6054	6	15	key	key	ADJ
ejpam-6054	6	16	words	word	NOUN
ejpam-6054	6	17	and	and	CCONJ
ejpam-6054	6	18	phrases	phrase	NOUN
ejpam-6054	6	19	:	:	PUNCT
ejpam-6054	6	20	2d	2d	NUM
ejpam-6054	6	21	special	special	ADJ
ejpam-6054	6	22	polynomials	polynomial	NOUN
ejpam-6054	6	23	,	,	PUNCT
ejpam-6054	6	24	generating	generate	VERB
ejpam-6054	6	25	function	function	NOUN
ejpam-6054	6	26	,	,	PUNCT
ejpam-6054	6	27	explicit	explicit	ADJ
ejpam-6054	6	28	form	form	NOUN
ejpam-6054	6	29	,	,	PUNCT
ejpam-6054	6	30	series	series	NOUN
ejpam-6054	6	31	representation	representation	NOUN
ejpam-6054	6	32	1	1	NUM
ejpam-6054	6	33	.	.	PUNCT
ejpam-6054	7	1	introduction	introduction	NOUN
ejpam-6054	7	2	and	and	CCONJ
ejpam-6054	7	3	preliminaries	preliminary	NOUN
ejpam-6054	7	4	a	a	DET
ejpam-6054	7	5	fascinating	fascinating	ADJ
ejpam-6054	7	6	class	class	NOUN
ejpam-6054	7	7	of	of	ADP
ejpam-6054	7	8	mathematical	mathematical	ADJ
ejpam-6054	7	9	functions	function	NOUN
ejpam-6054	7	10	,	,	PUNCT
ejpam-6054	7	11	namely	namely	ADV
ejpam-6054	7	12	special	special	ADJ
ejpam-6054	7	13	polynomials	polynomial	NOUN
ejpam-6054	7	14	,	,	PUNCT
ejpam-6054	7	15	are	be	AUX
ejpam-6054	7	16	characterized	characterize	VERB
ejpam-6054	7	17	by	by	ADP
ejpam-6054	7	18	unique	unique	ADJ
ejpam-6054	7	19	properties	property	NOUN
ejpam-6054	7	20	and	and	CCONJ
ejpam-6054	7	21	find	find	VERB
ejpam-6054	7	22	specific	specific	ADJ
ejpam-6054	7	23	significance	significance	NOUN
ejpam-6054	7	24	in	in	ADP
ejpam-6054	7	25	various	various	ADJ
ejpam-6054	7	26	mathematical	mathematical	ADJ
ejpam-6054	7	27	contexts	contexts	NOUN
ejpam-6054	7	28	,	,	PUNCT
ejpam-6054	7	29	for	for	ADP
ejpam-6054	7	30	example	example	NOUN
ejpam-6054	7	31	[	[	X
ejpam-6054	7	32	1–5	1–5	X
ejpam-6054	7	33	]	]	X
ejpam-6054	7	34	.	.	PUNCT
ejpam-6054	8	1	these	these	DET
ejpam-6054	8	2	polynomials	polynomial	NOUN
ejpam-6054	8	3	encompass	encompass	VERB
ejpam-6054	8	4	well	well	ADV
ejpam-6054	8	5	-	-	PUNCT
ejpam-6054	8	6	known	know	VERB
ejpam-6054	8	7	families	family	NOUN
ejpam-6054	8	8	such	such	ADJ
ejpam-6054	8	9	as	as	ADP
ejpam-6054	8	10	legendre	legendre	PROPN
ejpam-6054	8	11	polynomials	polynomial	NOUN
ejpam-6054	8	12	,	,	PUNCT
ejpam-6054	8	13	chebyshev	chebyshev	NOUN
ejpam-6054	8	14	polynomials	polynomial	NOUN
ejpam-6054	8	15	,	,	PUNCT
ejpam-6054	8	16	hermite	hermite	ADJ
ejpam-6054	8	17	polynomials	polynomial	NOUN
ejpam-6054	8	18	,	,	PUNCT
ejpam-6054	8	19	bell	bell	NOUN
ejpam-6054	8	20	polynomials	polynomial	NOUN
ejpam-6054	8	21	,	,	PUNCT
ejpam-6054	8	22	and	and	CCONJ
ejpam-6054	8	23	touchard	touchard	NOUN
ejpam-6054	8	24	polynomials	polynomial	NOUN
ejpam-6054	8	25	.	.	PUNCT
ejpam-6054	9	1	legendre	legendre	PROPN
ejpam-6054	9	2	polynomials	polynomial	NOUN
ejpam-6054	9	3	,	,	PUNCT
ejpam-6054	9	4	for	for	ADP
ejpam-6054	9	5	example	example	NOUN
ejpam-6054	9	6	,	,	PUNCT
ejpam-6054	9	7	arise	arise	VERB
ejpam-6054	9	8	in	in	ADP
ejpam-6054	9	9	problems	problem	NOUN
ejpam-6054	9	10	involving	involve	VERB
ejpam-6054	9	11	∗corresponding	∗corresponde	VERB
ejpam-6054	9	12	author	author	NOUN
ejpam-6054	9	13	.	.	PUNCT
ejpam-6054	10	1	doi	doi	NOUN
ejpam-6054	10	2	:	:	PUNCT
ejpam-6054	10	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6054	https://doi.org/10.29020/nybg.ejpam.v18i3.6054	PROPN
ejpam-6054	10	4	email	email	NOUN
ejpam-6054	10	5	addresses	address	NOUN
ejpam-6054	10	6	:	:	PUNCT
ejpam-6054	10	7	shahidwani177@gmail.com	shahidwani177@gmail.com	X
ejpam-6054	10	8	(	(	PUNCT
ejpam-6054	10	9	s.a	s.a	PROPN
ejpam-6054	10	10	.	.	PROPN
ejpam-6054	10	11	wani	wani	PROPN
ejpam-6054	10	12	)	)	PUNCT
ejpam-6054	10	13	,	,	PUNCT
ejpam-6054	10	14	talqorashi@bu.edu.sa	talqorashi@bu.edu.sa	PROPN
ejpam-6054	10	15	(	(	PUNCT
ejpam-6054	10	16	t.	t.	PROPN
ejpam-6054	10	17	alqurashi	alqurashi	PROPN
ejpam-6054	10	18	)	)	PUNCT
ejpam-6054	10	19	,	,	PUNCT
ejpam-6054	10	20	w.	w.	PROPN
ejpam-6054	10	21	ramı́rez	ramı́rez	PROPN
ejpam-6054	10	22	(	(	PUNCT
ejpam-6054	10	23	wramirez4@cuc.edu.co	wramirez4@cuc.edu.co	NOUN
ejpam-6054	10	24	)	)	PUNCT
ejpam-6054	10	25	,	,	PUNCT
ejpam-6054	10	26	shilpam@sitpune.edu.in	shilpam@sitpune.edu.in	PRON
ejpam-6054	10	27	(	(	PUNCT
ejpam-6054	10	28	s.	s.	PROPN
ejpam-6054	10	29	malge	malge	PROPN
ejpam-6054	10	30	)	)	PUNCT
ejpam-6054	10	31	,	,	PUNCT
ejpam-6054	10	32	jberriovalbuena@mail.uniatlantico.edu.co	jberriovalbuena@mail.uniatlantico.edu.co	X
ejpam-6054	10	33	(	(	PUNCT
ejpam-6054	10	34	j.	j.	PROPN
ejpam-6054	10	35	berŕıo	berŕıo	PROPN
ejpam-6054	10	36	)	)	PUNCT
ejpam-6054	10	37	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6054	10	38	1	1	NUM
ejpam-6054	10	39	copyright	copyright	NOUN
ejpam-6054	10	40	:	:	PUNCT
ejpam-6054	11	1	©	©	PROPN
ejpam-6054	11	2	2025	2025	NUM
ejpam-6054	11	3	the	the	DET
ejpam-6054	11	4	author(s	author(s	NOUN
ejpam-6054	11	5	)	)	PUNCT
ejpam-6054	11	6	.	.	PUNCT
ejpam-6054	12	1	(	(	PUNCT
ejpam-6054	12	2	cc	cc	NOUN
ejpam-6054	12	3	by	by	ADP
ejpam-6054	12	4	-	-	PUNCT
ejpam-6054	12	5	nc	nc	PROPN
ejpam-6054	12	6	4.0	4.0	NUM
ejpam-6054	12	7	)	)	PUNCT
ejpam-6054	12	8	s.	s.	PROPN
ejpam-6054	12	9	a.	a.	PROPN
ejpam-6054	12	10	wani	wani	PROPN
ejpam-6054	12	11	et	et	PROPN
ejpam-6054	12	12	al	al	PROPN
ejpam-6054	12	13	.	.	PUNCT
ejpam-6054	12	14	/	/	SYM
ejpam-6054	12	15	eur	eur	PROPN
ejpam-6054	12	16	.	.	PUNCT
ejpam-6054	13	1	j.	j.	PROPN
ejpam-6054	13	2	pure	pure	PROPN
ejpam-6054	13	3	appl	appl	PROPN
ejpam-6054	13	4	.	.	PROPN
ejpam-6054	13	5	math	math	PROPN
ejpam-6054	13	6	,	,	PUNCT
ejpam-6054	13	7	18	18	NUM
ejpam-6054	13	8	(	(	PUNCT
ejpam-6054	13	9	3	3	NUM
ejpam-6054	13	10	)	)	PUNCT
ejpam-6054	13	11	(	(	PUNCT
ejpam-6054	13	12	2025	2025	NUM
ejpam-6054	13	13	)	)	PUNCT
ejpam-6054	13	14	,	,	PUNCT
ejpam-6054	13	15	6054	6054	NUM
ejpam-6054	13	16	2	2	NUM
ejpam-6054	13	17	of	of	ADP
ejpam-6054	13	18	16	16	NUM
ejpam-6054	13	19	electrostatics	electrostatic	NOUN
ejpam-6054	13	20	and	and	CCONJ
ejpam-6054	13	21	fluid	fluid	ADJ
ejpam-6054	13	22	dynamics	dynamic	NOUN
ejpam-6054	13	23	,	,	PUNCT
ejpam-6054	13	24	while	while	SCONJ
ejpam-6054	13	25	chebyshev	chebyshev	NOUN
ejpam-6054	13	26	polynomials	polynomial	NOUN
ejpam-6054	13	27	have	have	VERB
ejpam-6054	13	28	applications	application	NOUN
ejpam-6054	13	29	in	in	ADP
ejpam-6054	13	30	numerical	numerical	ADJ
ejpam-6054	13	31	analysis	analysis	NOUN
ejpam-6054	13	32	and	and	CCONJ
ejpam-6054	13	33	signal	signal	NOUN
ejpam-6054	13	34	processing	processing	NOUN
ejpam-6054	13	35	.	.	PUNCT
ejpam-6054	14	1	on	on	ADP
ejpam-6054	14	2	the	the	DET
ejpam-6054	14	3	other	other	ADJ
ejpam-6054	14	4	hand	hand	NOUN
ejpam-6054	14	5	,	,	PUNCT
ejpam-6054	14	6	hermite	hermite	ADJ
ejpam-6054	14	7	polynomials	polynomial	NOUN
ejpam-6054	14	8	frequently	frequently	ADV
ejpam-6054	14	9	emerge	emerge	VERB
ejpam-6054	14	10	in	in	ADP
ejpam-6054	14	11	quantum	quantum	ADJ
ejpam-6054	14	12	mechanics	mechanic	NOUN
ejpam-6054	14	13	and	and	CCONJ
ejpam-6054	14	14	probability	probability	NOUN
ejpam-6054	14	15	theory	theory	NOUN
ejpam-6054	14	16	.	.	PUNCT
ejpam-6054	15	1	bell	bell	NOUN
ejpam-6054	15	2	and	and	CCONJ
ejpam-6054	15	3	touchard	touchard	NOUN
ejpam-6054	15	4	polynomials	polynomial	NOUN
ejpam-6054	15	5	also	also	ADV
ejpam-6054	15	6	play	play	VERB
ejpam-6054	15	7	important	important	ADJ
ejpam-6054	15	8	roles	role	NOUN
ejpam-6054	15	9	in	in	ADP
ejpam-6054	15	10	combinatorics	combinatoric	NOUN
ejpam-6054	15	11	and	and	CCONJ
ejpam-6054	15	12	number	number	NOUN
ejpam-6054	15	13	theory	theory	NOUN
ejpam-6054	15	14	.	.	PUNCT
ejpam-6054	16	1	studying	study	VERB
ejpam-6054	16	2	these	these	DET
ejpam-6054	16	3	special	special	ADJ
ejpam-6054	16	4	polynomials	polynomial	NOUN
ejpam-6054	16	5	and	and	CCONJ
ejpam-6054	16	6	their	their	PRON
ejpam-6054	16	7	applications	application	NOUN
ejpam-6054	16	8	is	be	AUX
ejpam-6054	16	9	essential	essential	ADJ
ejpam-6054	16	10	in	in	ADP
ejpam-6054	16	11	mathematical	mathematical	ADJ
ejpam-6054	16	12	physics	physics	NOUN
ejpam-6054	16	13	,	,	PUNCT
ejpam-6054	16	14	engineering	engineering	NOUN
ejpam-6054	16	15	,	,	PUNCT
ejpam-6054	16	16	computer	computer	NOUN
ejpam-6054	16	17	science	science	NOUN
ejpam-6054	16	18	,	,	PUNCT
ejpam-6054	16	19	and	and	CCONJ
ejpam-6054	16	20	other	other	ADJ
ejpam-6054	16	21	scientific	scientific	ADJ
ejpam-6054	16	22	disciplines	discipline	NOUN
ejpam-6054	16	23	.	.	PUNCT
ejpam-6054	17	1	on	on	ADP
ejpam-6054	17	2	the	the	DET
ejpam-6054	17	3	topic	topic	NOUN
ejpam-6054	17	4	of	of	ADP
ejpam-6054	17	5	polynomial	polynomial	ADJ
ejpam-6054	17	6	families	family	NOUN
ejpam-6054	17	7	and	and	CCONJ
ejpam-6054	17	8	their	their	PRON
ejpam-6054	17	9	various	various	ADJ
ejpam-6054	17	10	extensions	extension	NOUN
ejpam-6054	17	11	,	,	PUNCT
ejpam-6054	17	12	much	much	ADJ
ejpam-6054	17	13	research	research	NOUN
ejpam-6054	17	14	has	have	AUX
ejpam-6054	17	15	appeared	appear	VERB
ejpam-6054	17	16	in	in	ADP
ejpam-6054	17	17	the	the	DET
ejpam-6054	17	18	literature	literature	NOUN
ejpam-6054	17	19	(	(	PUNCT
ejpam-6054	17	20	see	see	VERB
ejpam-6054	17	21	,	,	PUNCT
ejpam-6054	17	22	for	for	ADP
ejpam-6054	17	23	example	example	NOUN
ejpam-6054	17	24	,	,	PUNCT
ejpam-6054	18	1	[	[	X
ejpam-6054	18	2	8–10	8–10	NOUN
ejpam-6054	18	3	,	,	PUNCT
ejpam-6054	18	4	13	13	NUM
ejpam-6054	18	5	]	]	NUM
ejpam-6054	18	6	)	)	PUNCT
ejpam-6054	18	7	.	.	PUNCT
ejpam-6054	19	1	the	the	DET
ejpam-6054	19	2	exploration	exploration	NOUN
ejpam-6054	19	3	of	of	ADP
ejpam-6054	19	4	special	special	ADJ
ejpam-6054	19	5	polynomials	polynomial	NOUN
ejpam-6054	19	6	in	in	ADP
ejpam-6054	19	7	general	general	ADJ
ejpam-6054	19	8	cases	case	NOUN
ejpam-6054	19	9	has	have	AUX
ejpam-6054	19	10	revealed	reveal	VERB
ejpam-6054	19	11	new	new	ADJ
ejpam-6054	19	12	properties	property	NOUN
ejpam-6054	19	13	and	and	CCONJ
ejpam-6054	19	14	applications	application	NOUN
ejpam-6054	19	15	,	,	PUNCT
ejpam-6054	19	16	greatly	greatly	ADV
ejpam-6054	19	17	expanding	expand	VERB
ejpam-6054	19	18	our	our	PRON
ejpam-6054	19	19	mathematical	mathematical	ADJ
ejpam-6054	19	20	understanding	understanding	NOUN
ejpam-6054	19	21	of	of	ADP
ejpam-6054	19	22	these	these	DET
ejpam-6054	19	23	polynomials	polynomial	NOUN
ejpam-6054	19	24	.	.	PUNCT
ejpam-6054	20	1	mathematicians	mathematician	NOUN
ejpam-6054	20	2	have	have	AUX
ejpam-6054	20	3	discovered	discover	VERB
ejpam-6054	20	4	unique	unique	ADJ
ejpam-6054	20	5	characteristics	characteristic	NOUN
ejpam-6054	20	6	,	,	PUNCT
ejpam-6054	20	7	relationships	relationship	NOUN
ejpam-6054	20	8	,	,	PUNCT
ejpam-6054	20	9	and	and	CCONJ
ejpam-6054	20	10	applications	application	NOUN
ejpam-6054	20	11	that	that	PRON
ejpam-6054	20	12	were	be	AUX
ejpam-6054	20	13	previously	previously	ADV
ejpam-6054	20	14	unknown	unknown	ADJ
ejpam-6054	20	15	,	,	PUNCT
ejpam-6054	20	16	enriching	enrich	VERB
ejpam-6054	20	17	the	the	DET
ejpam-6054	20	18	field	field	NOUN
ejpam-6054	20	19	of	of	ADP
ejpam-6054	20	20	mathematics	mathematic	NOUN
ejpam-6054	20	21	.	.	PUNCT
ejpam-6054	21	1	the	the	DET
ejpam-6054	21	2	study	study	NOUN
ejpam-6054	21	3	of	of	ADP
ejpam-6054	21	4	special	special	ADJ
ejpam-6054	21	5	polynomials	polynomial	NOUN
ejpam-6054	21	6	is	be	AUX
ejpam-6054	21	7	crucial	crucial	ADJ
ejpam-6054	21	8	due	due	ADP
ejpam-6054	21	9	to	to	ADP
ejpam-6054	21	10	their	their	PRON
ejpam-6054	21	11	frequent	frequent	ADJ
ejpam-6054	21	12	appearance	appearance	NOUN
ejpam-6054	21	13	in	in	ADP
ejpam-6054	21	14	solving	solve	VERB
ejpam-6054	21	15	“	"	PUNCT
ejpam-6054	21	16	differential	differential	ADJ
ejpam-6054	21	17	equations	equation	NOUN
ejpam-6054	21	18	,	,	PUNCT
ejpam-6054	21	19	orthogonal	orthogonal	ADJ
ejpam-6054	21	20	polynomial	polynomial	ADJ
ejpam-6054	21	21	theory	theory	NOUN
ejpam-6054	21	22	,	,	PUNCT
ejpam-6054	21	23	numerical	numerical	ADJ
ejpam-6054	21	24	analysis	analysis	NOUN
ejpam-6054	21	25	,	,	PUNCT
ejpam-6054	21	26	and	and	CCONJ
ejpam-6054	21	27	various	various	ADJ
ejpam-6054	21	28	other	other	ADJ
ejpam-6054	21	29	mathematical	mathematical	ADJ
ejpam-6054	21	30	and	and	CCONJ
ejpam-6054	21	31	computational	computational	ADJ
ejpam-6054	21	32	problems	problem	NOUN
ejpam-6054	21	33	”	"	PUNCT
ejpam-6054	21	34	.	.	PUNCT
ejpam-6054	22	1	these	these	DET
ejpam-6054	22	2	polynomials	polynomial	NOUN
ejpam-6054	22	3	exhibit	exhibit	VERB
ejpam-6054	22	4	specific	specific	ADJ
ejpam-6054	22	5	algebraic	algebraic	ADJ
ejpam-6054	22	6	structures	structure	NOUN
ejpam-6054	22	7	and	and	CCONJ
ejpam-6054	22	8	recurrence	recurrence	NOUN
ejpam-6054	22	9	relations	relation	NOUN
ejpam-6054	22	10	,	,	PUNCT
ejpam-6054	22	11	which	which	PRON
ejpam-6054	22	12	make	make	VERB
ejpam-6054	22	13	them	they	PRON
ejpam-6054	22	14	particularly	particularly	ADV
ejpam-6054	22	15	amenable	amenable	ADJ
ejpam-6054	22	16	to	to	ADP
ejpam-6054	22	17	analysis	analysis	NOUN
ejpam-6054	22	18	,	,	PUNCT
ejpam-6054	22	19	enhancing	enhance	VERB
ejpam-6054	22	20	the	the	DET
ejpam-6054	22	21	broader	broad	ADJ
ejpam-6054	22	22	study	study	NOUN
ejpam-6054	22	23	of	of	ADP
ejpam-6054	22	24	algebra	algebra	PROPN
ejpam-6054	22	25	and	and	CCONJ
ejpam-6054	22	26	mathematical	mathematical	ADJ
ejpam-6054	22	27	structures	structure	NOUN
ejpam-6054	22	28	.	.	PUNCT
ejpam-6054	23	1	additionally	additionally	ADV
ejpam-6054	23	2	,	,	PUNCT
ejpam-6054	23	3	special	special	ADJ
ejpam-6054	23	4	polynomials	polynomial	NOUN
ejpam-6054	23	5	have	have	VERB
ejpam-6054	23	6	profound	profound	ADJ
ejpam-6054	23	7	connections	connection	NOUN
ejpam-6054	23	8	to	to	ADP
ejpam-6054	23	9	other	other	ADJ
ejpam-6054	23	10	areas	area	NOUN
ejpam-6054	23	11	of	of	ADP
ejpam-6054	23	12	mathematics	mathematic	NOUN
ejpam-6054	23	13	,	,	PUNCT
ejpam-6054	23	14	such	such	ADJ
ejpam-6054	23	15	as	as	ADP
ejpam-6054	23	16	“	"	PUNCT
ejpam-6054	23	17	combinatorics	combinatoric	NOUN
ejpam-6054	23	18	,	,	PUNCT
ejpam-6054	23	19	number	number	NOUN
ejpam-6054	23	20	theory	theory	NOUN
ejpam-6054	23	21	,	,	PUNCT
ejpam-6054	23	22	and	and	CCONJ
ejpam-6054	23	23	analysis	analysis	NOUN
ejpam-6054	23	24	”	"	PUNCT
ejpam-6054	23	25	.	.	PUNCT
ejpam-6054	24	1	these	these	DET
ejpam-6054	24	2	interconnections	interconnection	NOUN
ejpam-6054	24	3	promote	promote	VERB
ejpam-6054	24	4	interdisciplinary	interdisciplinary	ADJ
ejpam-6054	24	5	research	research	NOUN
ejpam-6054	24	6	and	and	CCONJ
ejpam-6054	24	7	the	the	DET
ejpam-6054	24	8	advancement	advancement	NOUN
ejpam-6054	24	9	of	of	ADP
ejpam-6054	24	10	mathematical	mathematical	ADJ
ejpam-6054	24	11	theories	theory	NOUN
ejpam-6054	24	12	,	,	PUNCT
ejpam-6054	24	13	leading	lead	VERB
ejpam-6054	24	14	to	to	ADP
ejpam-6054	24	15	broader	broad	ADJ
ejpam-6054	24	16	implications	implication	NOUN
ejpam-6054	24	17	across	across	ADP
ejpam-6054	24	18	scientific	scientific	ADJ
ejpam-6054	24	19	and	and	CCONJ
ejpam-6054	24	20	applied	apply	VERB
ejpam-6054	24	21	fields	field	NOUN
ejpam-6054	24	22	.	.	PUNCT
ejpam-6054	25	1	consequently	consequently	ADV
ejpam-6054	25	2	,	,	PUNCT
ejpam-6054	25	3	the	the	DET
ejpam-6054	25	4	ongoing	ongoing	ADJ
ejpam-6054	25	5	research	research	NOUN
ejpam-6054	25	6	and	and	CCONJ
ejpam-6054	25	7	discoveries	discovery	NOUN
ejpam-6054	25	8	in	in	ADP
ejpam-6054	25	9	the	the	DET
ejpam-6054	25	10	properties	property	NOUN
ejpam-6054	25	11	of	of	ADP
ejpam-6054	25	12	special	special	ADJ
ejpam-6054	25	13	polynomials	polynomial	NOUN
ejpam-6054	25	14	continue	continue	VERB
ejpam-6054	25	15	to	to	PART
ejpam-6054	25	16	play	play	VERB
ejpam-6054	25	17	a	a	DET
ejpam-6054	25	18	vital	vital	ADJ
ejpam-6054	25	19	role	role	NOUN
ejpam-6054	25	20	in	in	ADP
ejpam-6054	25	21	advancing	advance	VERB
ejpam-6054	25	22	both	both	CCONJ
ejpam-6054	25	23	pure	pure	ADJ
ejpam-6054	25	24	and	and	CCONJ
ejpam-6054	25	25	applied	applied	ADJ
ejpam-6054	25	26	mathematics	mathematic	NOUN
ejpam-6054	25	27	.	.	PUNCT
ejpam-6054	26	1	one	one	NUM
ejpam-6054	26	2	of	of	ADP
ejpam-6054	26	3	the	the	DET
ejpam-6054	26	4	most	most	ADV
ejpam-6054	26	5	intriguing	intriguing	ADJ
ejpam-6054	26	6	and	and	CCONJ
ejpam-6054	26	7	significant	significant	ADJ
ejpam-6054	26	8	classes	class	NOUN
ejpam-6054	26	9	of	of	ADP
ejpam-6054	26	10	polynomial	polynomial	ADJ
ejpam-6054	26	11	sequences	sequence	NOUN
ejpam-6054	26	12	and	and	CCONJ
ejpam-6054	26	13	numbers	number	NOUN
ejpam-6054	26	14	is	be	AUX
ejpam-6054	26	15	the	the	DET
ejpam-6054	26	16	stirling	stirling	NOUN
ejpam-6054	26	17	numbers	number	NOUN
ejpam-6054	26	18	.	.	PUNCT
ejpam-6054	27	1	these	these	DET
ejpam-6054	27	2	numbers	number	NOUN
ejpam-6054	27	3	form	form	VERB
ejpam-6054	27	4	a	a	DET
ejpam-6054	27	5	family	family	NOUN
ejpam-6054	27	6	that	that	PRON
ejpam-6054	27	7	is	be	AUX
ejpam-6054	27	8	essential	essential	ADJ
ejpam-6054	27	9	in	in	ADP
ejpam-6054	27	10	combinatorics	combinatoric	NOUN
ejpam-6054	27	11	,	,	PUNCT
ejpam-6054	27	12	particularly	particularly	ADV
ejpam-6054	27	13	in	in	ADP
ejpam-6054	27	14	problems	problem	NOUN
ejpam-6054	27	15	related	relate	VERB
ejpam-6054	27	16	to	to	ADP
ejpam-6054	27	17	permutations	permutation	NOUN
ejpam-6054	27	18	,	,	PUNCT
ejpam-6054	27	19	combinations	combination	NOUN
ejpam-6054	27	20	,	,	PUNCT
ejpam-6054	27	21	and	and	CCONJ
ejpam-6054	27	22	partitions	partition	NOUN
ejpam-6054	27	23	,	,	PUNCT
ejpam-6054	27	24	for	for	ADP
ejpam-6054	27	25	example	example	NOUN
ejpam-6054	27	26	,	,	PUNCT
ejpam-6054	27	27	[	[	X
ejpam-6054	27	28	6	6	NUM
ejpam-6054	27	29	,	,	PUNCT
ejpam-6054	27	30	7	7	NUM
ejpam-6054	27	31	,	,	PUNCT
ejpam-6054	27	32	14–19	14–19	NUM
ejpam-6054	27	33	]	]	PUNCT
ejpam-6054	27	34	.	.	PUNCT
ejpam-6054	28	1	there	there	PRON
ejpam-6054	28	2	are	be	VERB
ejpam-6054	28	3	two	two	NUM
ejpam-6054	28	4	primary	primary	ADJ
ejpam-6054	28	5	types	type	NOUN
ejpam-6054	28	6	of	of	ADP
ejpam-6054	28	7	stirling	stirling	NOUN
ejpam-6054	28	8	numbers	number	NOUN
ejpam-6054	28	9	,	,	PUNCT
ejpam-6054	28	10	each	each	PRON
ejpam-6054	28	11	serving	serve	VERB
ejpam-6054	28	12	a	a	DET
ejpam-6054	28	13	distinct	distinct	ADJ
ejpam-6054	28	14	purpose	purpose	NOUN
ejpam-6054	28	15	in	in	ADP
ejpam-6054	28	16	combinatorial	combinatorial	ADJ
ejpam-6054	28	17	mathematics	mathematic	NOUN
ejpam-6054	28	18	:	:	PUNCT
ejpam-6054	28	19	the	the	DET
ejpam-6054	28	20	stirling	stirling	NOUN
ejpam-6054	28	21	numbers	number	NOUN
ejpam-6054	28	22	of	of	ADP
ejpam-6054	28	23	the	the	DET
ejpam-6054	28	24	first	first	ADJ
ejpam-6054	28	25	kind	kind	NOUN
ejpam-6054	28	26	,	,	PUNCT
ejpam-6054	28	27	denoted	denote	VERB
ejpam-6054	28	28	as	as	ADP
ejpam-6054	28	29	s1(n	s1(n	PROPN
ejpam-6054	28	30	,	,	PUNCT
ejpam-6054	28	31	ϵ	ϵ	NOUN
ejpam-6054	28	32	)	)	PUNCT
ejpam-6054	28	33	,	,	PUNCT
ejpam-6054	28	34	and	and	CCONJ
ejpam-6054	28	35	the	the	DET
ejpam-6054	28	36	stirling	stirling	NOUN
ejpam-6054	28	37	numbers	number	NOUN
ejpam-6054	28	38	of	of	ADP
ejpam-6054	28	39	the	the	DET
ejpam-6054	28	40	second	second	ADJ
ejpam-6054	28	41	kind	kind	NOUN
ejpam-6054	28	42	,	,	PUNCT
ejpam-6054	28	43	denoted	denote	VERB
ejpam-6054	28	44	as	as	ADP
ejpam-6054	28	45	s2(n	s2(n	NOUN
ejpam-6054	28	46	,	,	PUNCT
ejpam-6054	28	47	ϵ	ϵ	NOUN
ejpam-6054	28	48	)	)	PUNCT
ejpam-6054	28	49	.	.	PUNCT
ejpam-6054	29	1	the	the	DET
ejpam-6054	29	2	stirling	stirling	NOUN
ejpam-6054	29	3	numbers	number	NOUN
ejpam-6054	29	4	of	of	ADP
ejpam-6054	29	5	the	the	DET
ejpam-6054	29	6	first	first	ADJ
ejpam-6054	29	7	kind	kind	NOUN
ejpam-6054	29	8	,	,	PUNCT
ejpam-6054	29	9	s1(n	s1(n	PROPN
ejpam-6054	29	10	,	,	PUNCT
ejpam-6054	29	11	ϵ	ϵ	NOUN
ejpam-6054	29	12	)	)	PUNCT
ejpam-6054	29	13	,	,	PUNCT
ejpam-6054	29	14	represent	represent	VERB
ejpam-6054	29	15	the	the	DET
ejpam-6054	29	16	number	number	NOUN
ejpam-6054	29	17	of	of	ADP
ejpam-6054	29	18	permutations	permutation	NOUN
ejpam-6054	29	19	of	of	ADP
ejpam-6054	29	20	n	n	PRON
ejpam-6054	29	21	elements	element	NOUN
ejpam-6054	29	22	that	that	PRON
ejpam-6054	29	23	contain	contain	VERB
ejpam-6054	29	24	exactly	exactly	ADV
ejpam-6054	29	25	ϵ	ϵ	ADP
ejpam-6054	29	26	cycles	cycle	NOUN
ejpam-6054	29	27	.	.	PUNCT
ejpam-6054	30	1	this	this	PRON
ejpam-6054	30	2	means	mean	VERB
ejpam-6054	30	3	they	they	PRON
ejpam-6054	30	4	count	count	VERB
ejpam-6054	30	5	the	the	DET
ejpam-6054	30	6	number	number	NOUN
ejpam-6054	30	7	of	of	ADP
ejpam-6054	30	8	ways	way	NOUN
ejpam-6054	30	9	to	to	PART
ejpam-6054	30	10	arrange	arrange	VERB
ejpam-6054	30	11	n	n	DET
ejpam-6054	30	12	distinct	distinct	ADJ
ejpam-6054	30	13	elements	element	NOUN
ejpam-6054	30	14	into	into	ADP
ejpam-6054	30	15	ϵ	ϵ	PRON
ejpam-6054	30	16	cyclic	cyclic	ADJ
ejpam-6054	30	17	groups	group	NOUN
ejpam-6054	30	18	.	.	PUNCT
ejpam-6054	31	1	on	on	ADP
ejpam-6054	31	2	the	the	DET
ejpam-6054	31	3	other	other	ADJ
ejpam-6054	31	4	hand	hand	NOUN
ejpam-6054	31	5	,	,	PUNCT
ejpam-6054	31	6	the	the	DET
ejpam-6054	31	7	stirling	stirling	NOUN
ejpam-6054	31	8	numbers	number	NOUN
ejpam-6054	31	9	of	of	ADP
ejpam-6054	31	10	the	the	DET
ejpam-6054	31	11	second	second	ADJ
ejpam-6054	31	12	kind	kind	NOUN
ejpam-6054	31	13	,	,	PUNCT
ejpam-6054	31	14	s2(n	s2(n	PROPN
ejpam-6054	31	15	,	,	PUNCT
ejpam-6054	31	16	ϵ	ϵ	NOUN
ejpam-6054	31	17	)	)	PUNCT
ejpam-6054	31	18	,	,	PUNCT
ejpam-6054	31	19	quantify	quantify	VERB
ejpam-6054	31	20	the	the	DET
ejpam-6054	31	21	number	number	NOUN
ejpam-6054	31	22	of	of	ADP
ejpam-6054	31	23	ways	way	NOUN
ejpam-6054	31	24	to	to	PART
ejpam-6054	31	25	partition	partition	VERB
ejpam-6054	31	26	a	a	DET
ejpam-6054	31	27	set	set	NOUN
ejpam-6054	31	28	of	of	ADP
ejpam-6054	31	29	n	n	DET
ejpam-6054	31	30	distinct	distinct	ADJ
ejpam-6054	31	31	elements	element	NOUN
ejpam-6054	31	32	into	into	ADP
ejpam-6054	31	33	ϵ	ϵ	PRON
ejpam-6054	31	34	non	non	ADJ
ejpam-6054	31	35	-	-	ADJ
ejpam-6054	31	36	empty	empty	ADJ
ejpam-6054	31	37	,	,	PUNCT
ejpam-6054	31	38	indistinguishable	indistinguishable	ADJ
ejpam-6054	31	39	subsets	subset	NOUN
ejpam-6054	31	40	,	,	PUNCT
ejpam-6054	31	41	where	where	SCONJ
ejpam-6054	31	42	the	the	DET
ejpam-6054	31	43	order	order	NOUN
ejpam-6054	31	44	of	of	ADP
ejpam-6054	31	45	these	these	DET
ejpam-6054	31	46	subsets	subset	NOUN
ejpam-6054	31	47	does	do	AUX
ejpam-6054	31	48	not	not	PART
ejpam-6054	31	49	matter	matter	VERB
ejpam-6054	31	50	.	.	PUNCT
ejpam-6054	32	1	these	these	DET
ejpam-6054	32	2	numbers	number	NOUN
ejpam-6054	32	3	are	be	AUX
ejpam-6054	32	4	significant	significant	ADJ
ejpam-6054	32	5	in	in	ADP
ejpam-6054	32	6	various	various	ADJ
ejpam-6054	32	7	mathematical	mathematical	ADJ
ejpam-6054	32	8	and	and	CCONJ
ejpam-6054	32	9	applied	apply	VERB
ejpam-6054	32	10	fields	field	NOUN
ejpam-6054	32	11	,	,	PUNCT
ejpam-6054	32	12	including	include	VERB
ejpam-6054	32	13	combinatorics	combinatoric	NOUN
ejpam-6054	32	14	,	,	PUNCT
ejpam-6054	32	15	where	where	SCONJ
ejpam-6054	32	16	they	they	PRON
ejpam-6054	32	17	facilitate	facilitate	VERB
ejpam-6054	32	18	the	the	DET
ejpam-6054	32	19	understanding	understanding	NOUN
ejpam-6054	32	20	and	and	CCONJ
ejpam-6054	32	21	solving	solve	VERB
ejpam-6054	32	22	problems	problem	NOUN
ejpam-6054	32	23	related	relate	VERB
ejpam-6054	32	24	to	to	ADP
ejpam-6054	32	25	permutations	permutation	NOUN
ejpam-6054	32	26	and	and	CCONJ
ejpam-6054	32	27	partitions	partition	NOUN
ejpam-6054	32	28	.	.	PUNCT
ejpam-6054	33	1	their	their	PRON
ejpam-6054	33	2	utility	utility	NOUN
ejpam-6054	33	3	extends	extend	VERB
ejpam-6054	33	4	to	to	ADP
ejpam-6054	33	5	areas	area	NOUN
ejpam-6054	33	6	such	such	ADJ
ejpam-6054	33	7	as	as	ADP
ejpam-6054	33	8	algebra	algebra	NOUN
ejpam-6054	33	9	,	,	PUNCT
ejpam-6054	33	10	probability	probability	NOUN
ejpam-6054	33	11	,	,	PUNCT
ejpam-6054	33	12	and	and	CCONJ
ejpam-6054	33	13	the	the	DET
ejpam-6054	33	14	analysis	analysis	NOUN
ejpam-6054	33	15	of	of	ADP
ejpam-6054	33	16	algorithms	algorithm	NOUN
ejpam-6054	33	17	,	,	PUNCT
ejpam-6054	33	18	underscoring	underscore	VERB
ejpam-6054	33	19	their	their	PRON
ejpam-6054	33	20	importance	importance	NOUN
ejpam-6054	33	21	in	in	ADP
ejpam-6054	33	22	both	both	CCONJ
ejpam-6054	33	23	theoretical	theoretical	ADJ
ejpam-6054	33	24	and	and	CCONJ
ejpam-6054	33	25	practical	practical	ADJ
ejpam-6054	33	26	applications	application	NOUN
ejpam-6054	33	27	of	of	ADP
ejpam-6054	33	28	mathematics	mathematic	NOUN
ejpam-6054	33	29	.	.	PUNCT
ejpam-6054	34	1	stirling	stirling	NOUN
ejpam-6054	34	2	numbers	number	NOUN
ejpam-6054	34	3	are	be	AUX
ejpam-6054	34	4	widely	widely	ADV
ejpam-6054	34	5	used	use	VERB
ejpam-6054	34	6	in	in	ADP
ejpam-6054	34	7	combinatorics	combinatoric	NOUN
ejpam-6054	34	8	for	for	ADP
ejpam-6054	34	9	counting	count	VERB
ejpam-6054	34	10	permutations	permutation	NOUN
ejpam-6054	34	11	,	,	PUNCT
ejpam-6054	34	12	combinations	combination	NOUN
ejpam-6054	34	13	,	,	PUNCT
ejpam-6054	34	14	and	and	CCONJ
ejpam-6054	34	15	partitions	partition	NOUN
ejpam-6054	34	16	.	.	PUNCT
ejpam-6054	35	1	“	"	PUNCT
ejpam-6054	35	2	stirling	stirling	NOUN
ejpam-6054	35	3	polynomials	polynomial	NOUN
ejpam-6054	35	4	of	of	ADP
ejpam-6054	35	5	the	the	DET
ejpam-6054	35	6	second	second	ADJ
ejpam-6054	35	7	kind	kind	NOUN
ejpam-6054	35	8	”	"	PUNCT
ejpam-6054	35	9	,	,	PUNCT
ejpam-6054	35	10	denoted	denote	VERB
ejpam-6054	35	11	as	as	ADP
ejpam-6054	35	12	s2(n	s2(n	NOUN
ejpam-6054	35	13	,	,	PUNCT
ejpam-6054	35	14	ϵ	ϵ	X
ejpam-6054	35	15	;	;	PUNCT
ejpam-6054	35	16	q1	q1	NOUN
ejpam-6054	35	17	)	)	PUNCT
ejpam-6054	35	18	,	,	PUNCT
ejpam-6054	35	19	are	be	AUX
ejpam-6054	35	20	associated	associate	VERB
ejpam-6054	35	21	with	with	ADP
ejpam-6054	35	22	exponential	exponential	ADJ
ejpam-6054	35	23	generating	generating	NOUN
ejpam-6054	35	24	functions	function	NOUN
ejpam-6054	35	25	.	.	PUNCT
ejpam-6054	36	1	the	the	DET
ejpam-6054	36	2	exponential	exponential	ADJ
ejpam-6054	36	3	generating	generating	NOUN
ejpam-6054	36	4	function	function	NOUN
ejpam-6054	36	5	for	for	ADP
ejpam-6054	36	6	stirling	stirling	NOUN
ejpam-6054	36	7	polys	poly	NOUN
ejpam-6054	36	8	.	.	PUNCT
ejpam-6054	37	1	a.	a.	PROPN
ejpam-6054	37	2	wani	wani	PROPN
ejpam-6054	37	3	et	et	PROPN
ejpam-6054	37	4	al	al	PROPN
ejpam-6054	37	5	.	.	PUNCT
ejpam-6054	37	6	/	/	SYM
ejpam-6054	37	7	eur	eur	PROPN
ejpam-6054	37	8	.	.	PUNCT
ejpam-6054	38	1	j.	j.	PROPN
ejpam-6054	38	2	pure	pure	PROPN
ejpam-6054	38	3	appl	appl	PROPN
ejpam-6054	38	4	.	.	PROPN
ejpam-6054	38	5	math	math	PROPN
ejpam-6054	38	6	,	,	PUNCT
ejpam-6054	38	7	18	18	NUM
ejpam-6054	38	8	(	(	PUNCT
ejpam-6054	38	9	3	3	NUM
ejpam-6054	38	10	)	)	PUNCT
ejpam-6054	38	11	(	(	PUNCT
ejpam-6054	38	12	2025	2025	NUM
ejpam-6054	38	13	)	)	PUNCT
ejpam-6054	38	14	,	,	PUNCT
ejpam-6054	38	15	6054	6054	NUM
ejpam-6054	38	16	3	3	NUM
ejpam-6054	38	17	of	of	ADP
ejpam-6054	38	18	16	16	NUM
ejpam-6054	38	19	nomials	nomial	NOUN
ejpam-6054	38	20	of	of	ADP
ejpam-6054	38	21	the	the	DET
ejpam-6054	38	22	second	second	ADJ
ejpam-6054	38	23	kind	kind	NOUN
ejpam-6054	38	24	is	be	AUX
ejpam-6054	38	25	given	give	VERB
ejpam-6054	38	26	by	by	ADP
ejpam-6054	38	27	:	:	PUNCT
ejpam-6054	38	28	∞∑	∞∑	PROPN
ejpam-6054	38	29	n=0	n=0	PROPN
ejpam-6054	38	30	s2(n	s2(n	PROPN
ejpam-6054	38	31	,	,	PUNCT
ejpam-6054	38	32	ϵ	ϵ	X
ejpam-6054	38	33	;	;	PUNCT
ejpam-6054	38	34	q1	q1	PROPN
ejpam-6054	38	35	)	)	PUNCT
ejpam-6054	38	36	ξ	ξ	PROPN
ejpam-6054	38	37	n	n	NUM
ejpam-6054	38	38	n	n	NOUN
ejpam-6054	38	39	!	!	PUNCT
ejpam-6054	39	1	=	=	PUNCT
ejpam-6054	39	2	(	(	PUNCT
ejpam-6054	39	3	eξq1	eξq1	PROPN
ejpam-6054	39	4	−	−	PROPN
ejpam-6054	39	5	1)ϵ	1)ϵ	NUM
ejpam-6054	39	6	ϵ	ϵ	X
ejpam-6054	39	7	!	!	PUNCT
ejpam-6054	39	8	.	.	PUNCT
ejpam-6054	40	1	(	(	PUNCT
ejpam-6054	40	2	1	1	X
ejpam-6054	40	3	)	)	PUNCT
ejpam-6054	40	4	certainly	certainly	ADV
ejpam-6054	40	5	,	,	PUNCT
ejpam-6054	40	6	the	the	DET
ejpam-6054	40	7	exponential	exponential	ADJ
ejpam-6054	40	8	generating	generating	NOUN
ejpam-6054	40	9	function	function	NOUN
ejpam-6054	40	10	for	for	ADP
ejpam-6054	40	11	stirling	stirling	NOUN
ejpam-6054	40	12	numbers	number	NOUN
ejpam-6054	40	13	of	of	ADP
ejpam-6054	40	14	the	the	DET
ejpam-6054	40	15	second	second	ADJ
ejpam-6054	40	16	kind	kind	ADJ
ejpam-6054	40	17	simplifies	simplifie	NOUN
ejpam-6054	40	18	to	to	ADP
ejpam-6054	40	19	the	the	DET
ejpam-6054	40	20	following	follow	VERB
ejpam-6054	40	21	expression	expression	NOUN
ejpam-6054	40	22	when	when	SCONJ
ejpam-6054	40	23	q1	q1	PROPN
ejpam-6054	40	24	=	=	NOUN
ejpam-6054	40	25	1	1	NUM
ejpam-6054	40	26	:	:	PUNCT
ejpam-6054	40	27	∞∑	∞∑	NUM
ejpam-6054	40	28	n=0	n=0	PROPN
ejpam-6054	40	29	s2(n	s2(n	PROPN
ejpam-6054	40	30	,	,	PUNCT
ejpam-6054	40	31	ϵ	ϵ	NOUN
ejpam-6054	40	32	)	)	PUNCT
ejpam-6054	40	33	ξ	ξ	PROPN
ejpam-6054	40	34	n	n	NUM
ejpam-6054	40	35	n	n	NOUN
ejpam-6054	40	36	!	!	PUNCT
ejpam-6054	41	1	=	=	PUNCT
ejpam-6054	41	2	(	(	PUNCT
ejpam-6054	41	3	eξ	eξ	PROPN
ejpam-6054	41	4	−	−	PROPN
ejpam-6054	41	5	1)ϵ	1)ϵ	NUM
ejpam-6054	41	6	ϵ	ϵ	X
ejpam-6054	41	7	!	!	PUNCT
ejpam-6054	41	8	.	.	PUNCT
ejpam-6054	42	1	(	(	PUNCT
ejpam-6054	42	2	2	2	X
ejpam-6054	42	3	)	)	PUNCT
ejpam-6054	42	4	further	far	ADV
ejpam-6054	42	5	,	,	PUNCT
ejpam-6054	42	6	the	the	DET
ejpam-6054	42	7	recurrence	recurrence	NOUN
ejpam-6054	42	8	relation	relation	NOUN
ejpam-6054	42	9	for	for	ADP
ejpam-6054	42	10	stirling	stirling	NOUN
ejpam-6054	42	11	numbers	number	NOUN
ejpam-6054	42	12	of	of	ADP
ejpam-6054	42	13	the	the	DET
ejpam-6054	42	14	second	second	ADJ
ejpam-6054	42	15	kind	kind	NOUN
ejpam-6054	42	16	s2(n	s2(n	VERB
ejpam-6054	42	17	,	,	PUNCT
ejpam-6054	42	18	ϵ	ϵ	NUM
ejpam-6054	42	19	)	)	PUNCT
ejpam-6054	42	20	can	can	AUX
ejpam-6054	42	21	be	be	AUX
ejpam-6054	42	22	computed	compute	VERB
ejpam-6054	42	23	using	use	VERB
ejpam-6054	42	24	the	the	DET
ejpam-6054	42	25	recurrence	recurrence	NOUN
ejpam-6054	42	26	relation	relation	NOUN
ejpam-6054	42	27	:	:	PUNCT
ejpam-6054	42	28	qn1	qn1	ADP
ejpam-6054	42	29	=	=	SYM
ejpam-6054	42	30	∞∑	∞∑	PROPN
ejpam-6054	42	31	n=0	n=0	NUM
ejpam-6054	42	32	s2(n	s2(n	PROPN
ejpam-6054	42	33	,	,	PUNCT
ejpam-6054	42	34	ϵ	ϵ	NOUN
ejpam-6054	42	35	)	)	PUNCT
ejpam-6054	42	36	(	(	PUNCT
ejpam-6054	42	37	q1)ϵ	q1)ϵ	ADJ
ejpam-6054	42	38	(	(	PUNCT
ejpam-6054	42	39	3	3	NUM
ejpam-6054	42	40	)	)	PUNCT
ejpam-6054	42	41	or	or	CCONJ
ejpam-6054	42	42	(	(	PUNCT
ejpam-6054	42	43	q1)n	q1)n	NOUN
ejpam-6054	42	44	=	=	SYM
ejpam-6054	42	45	n∑	n∑	PROPN
ejpam-6054	42	46	ϵ=0	ϵ=0	PROPN
ejpam-6054	42	47	s2(n	s2(n	PROPN
ejpam-6054	42	48	,	,	PUNCT
ejpam-6054	42	49	ϵ	ϵ	NOUN
ejpam-6054	42	50	)	)	PUNCT
ejpam-6054	42	51	q	q	PROPN
ejpam-6054	42	52	ϵ	ϵ	PROPN
ejpam-6054	42	53	1	1	NUM
ejpam-6054	42	54	,	,	PUNCT
ejpam-6054	42	55	(	(	PUNCT
ejpam-6054	42	56	4	4	NUM
ejpam-6054	42	57	)	)	PUNCT
ejpam-6054	42	58	where	where	SCONJ
ejpam-6054	42	59	,	,	PUNCT
ejpam-6054	42	60	the	the	DET
ejpam-6054	42	61	falling	fall	VERB
ejpam-6054	42	62	factorial	factorial	NOUN
ejpam-6054	42	63	is	be	AUX
ejpam-6054	42	64	given	give	VERB
ejpam-6054	42	65	by	by	ADP
ejpam-6054	42	66	(	(	PUNCT
ejpam-6054	42	67	q1)ϵ	q1)ϵ	NOUN
ejpam-6054	42	68	=	=	PUNCT
ejpam-6054	42	69	q1(q1	q1(q1	NUM
ejpam-6054	42	70	−	−	PROPN
ejpam-6054	42	71	1)(q2	1)(q2	NUM
ejpam-6054	42	72	−	−	NOUN
ejpam-6054	42	73	2	2	NUM
ejpam-6054	42	74	)	)	PUNCT
ejpam-6054	42	75	·	·	PUNCT
ejpam-6054	42	76	·	·	PUNCT
ejpam-6054	42	77	·	·	PUNCT
ejpam-6054	42	78	(	(	PUNCT
ejpam-6054	42	79	q1	q1	INTJ
ejpam-6054	42	80	−	−	PROPN
ejpam-6054	42	81	(	(	PUNCT
ejpam-6054	42	82	ϵ−	ϵ−	NOUN
ejpam-6054	42	83	1	1	NUM
ejpam-6054	42	84	)	)	PUNCT
ejpam-6054	42	85	)	)	PUNCT
ejpam-6054	42	86	.	.	PUNCT
ejpam-6054	43	1	additionally	additionally	ADV
ejpam-6054	43	2	,	,	PUNCT
ejpam-6054	43	3	for	for	ADP
ejpam-6054	43	4	every	every	DET
ejpam-6054	43	5	non	non	ADJ
ejpam-6054	43	6	-	-	ADJ
ejpam-6054	43	7	negative	negative	ADJ
ejpam-6054	43	8	integer	integer	NOUN
ejpam-6054	43	9	ϵ	ϵ	X
ejpam-6054	43	10	in	in	ADP
ejpam-6054	43	11	the	the	DET
ejpam-6054	43	12	set	set	NOUN
ejpam-6054	43	13	of	of	ADP
ejpam-6054	43	14	natural	natural	ADJ
ejpam-6054	43	15	numbers	number	NOUN
ejpam-6054	43	16	,	,	PUNCT
ejpam-6054	43	17	the	the	DET
ejpam-6054	43	18	following	follow	VERB
ejpam-6054	43	19	expression	expression	NOUN
ejpam-6054	43	20	holds	hold	VERB
ejpam-6054	43	21	true	true	ADJ
ejpam-6054	43	22	:	:	PUNCT
ejpam-6054	43	23	sϵ(n	sϵ(n	NUM
ejpam-6054	43	24	)	)	PUNCT
ejpam-6054	44	1	=	=	SYM
ejpam-6054	44	2	n∑	n∑	PROPN
ejpam-6054	44	3	l=0	l=0	PROPN
ejpam-6054	44	4	lϵ.	lϵ.	VERB
ejpam-6054	44	5	the	the	DET
ejpam-6054	44	6	sum	sum	NOUN
ejpam-6054	44	7	of	of	ADP
ejpam-6054	44	8	integer	integer	NOUN
ejpam-6054	44	9	powers	power	NOUN
ejpam-6054	44	10	is	be	AUX
ejpam-6054	44	11	referred	refer	VERB
ejpam-6054	44	12	to	to	ADP
ejpam-6054	44	13	as	as	ADP
ejpam-6054	44	14	the	the	DET
ejpam-6054	44	15	“	"	PUNCT
ejpam-6054	44	16	sum	sum	NOUN
ejpam-6054	44	17	of	of	ADP
ejpam-6054	44	18	integer	integer	NOUN
ejpam-6054	44	19	powers	power	NOUN
ejpam-6054	44	20	”	"	PUNCT
ejpam-6054	44	21	,	,	PUNCT
ejpam-6054	44	22	and	and	CCONJ
ejpam-6054	44	23	the	the	DET
ejpam-6054	44	24	exponential	exponential	ADJ
ejpam-6054	44	25	generating	generating	NOUN
ejpam-6054	44	26	function	function	NOUN
ejpam-6054	44	27	for	for	ADP
ejpam-6054	44	28	sϵ(n	sϵ(n	NUM
ejpam-6054	44	29	)	)	PUNCT
ejpam-6054	44	30	is	be	AUX
ejpam-6054	44	31	as	as	SCONJ
ejpam-6054	44	32	follows	follow	VERB
ejpam-6054	44	33	:	:	PUNCT
ejpam-6054	44	34	∞∑	∞∑	NUM
ejpam-6054	44	35	ϵ=0	ϵ=0	NOUN
ejpam-6054	44	36	sϵ(n	sϵ(n	NUM
ejpam-6054	44	37	)	)	PUNCT
ejpam-6054	44	38	ξϵ	ξϵ	NOUN
ejpam-6054	44	39	ϵ	ϵ	X
ejpam-6054	44	40	!	!	PUNCT
ejpam-6054	45	1	=	=	SYM
ejpam-6054	45	2	e(n+1)ξ−1	e(n+1)ξ−1	PROPN
ejpam-6054	45	3	eξ	eξ	NOUN
ejpam-6054	45	4	−	−	NOUN
ejpam-6054	45	5	1	1	NUM
ejpam-6054	45	6	.	.	PUNCT
ejpam-6054	46	1	(	(	PUNCT
ejpam-6054	46	2	5	5	X
ejpam-6054	46	3	)	)	PUNCT
ejpam-6054	46	4	the	the	DET
ejpam-6054	46	5	concepts	concept	NOUN
ejpam-6054	46	6	mentioned	mention	VERB
ejpam-6054	46	7	are	be	AUX
ejpam-6054	46	8	crucial	crucial	ADJ
ejpam-6054	46	9	in	in	ADP
ejpam-6054	46	10	combinatorics	combinatoric	NOUN
ejpam-6054	46	11	and	and	CCONJ
ejpam-6054	46	12	are	be	AUX
ejpam-6054	46	13	widely	widely	ADV
ejpam-6054	46	14	used	use	VERB
ejpam-6054	46	15	to	to	PART
ejpam-6054	46	16	solve	solve	VERB
ejpam-6054	46	17	counting	counting	NOUN
ejpam-6054	46	18	problems	problem	NOUN
ejpam-6054	46	19	involving	involve	VERB
ejpam-6054	46	20	the	the	DET
ejpam-6054	46	21	organisation	organisation	NOUN
ejpam-6054	46	22	of	of	ADP
ejpam-6054	46	23	distinguishable	distinguishable	ADJ
ejpam-6054	46	24	objects	object	NOUN
ejpam-6054	46	25	into	into	ADP
ejpam-6054	46	26	partitions	partition	NOUN
ejpam-6054	46	27	and	and	CCONJ
ejpam-6054	46	28	subsets	subset	NOUN
ejpam-6054	46	29	.	.	PUNCT
ejpam-6054	47	1	the	the	DET
ejpam-6054	47	2	incredible	incredible	ADJ
ejpam-6054	47	3	power	power	NOUN
ejpam-6054	47	4	of	of	ADP
ejpam-6054	47	5	exponential	exponential	ADJ
ejpam-6054	47	6	operators	operator	NOUN
ejpam-6054	47	7	shines	shine	VERB
ejpam-6054	47	8	through	through	ADV
ejpam-6054	47	9	,	,	PUNCT
ejpam-6054	47	10	especially	especially	ADV
ejpam-6054	47	11	when	when	SCONJ
ejpam-6054	47	12	solving	solve	VERB
ejpam-6054	47	13	differential	differential	ADJ
ejpam-6054	47	14	equations	equation	NOUN
ejpam-6054	47	15	.	.	PUNCT
ejpam-6054	48	1	these	these	DET
ejpam-6054	48	2	operators	operator	NOUN
ejpam-6054	48	3	simplify	simplify	VERB
ejpam-6054	48	4	the	the	DET
ejpam-6054	48	5	analysis	analysis	NOUN
ejpam-6054	48	6	and	and	CCONJ
ejpam-6054	48	7	offer	offer	VERB
ejpam-6054	48	8	a	a	DET
ejpam-6054	48	9	convenient	convenient	ADJ
ejpam-6054	48	10	way	way	NOUN
ejpam-6054	48	11	to	to	PART
ejpam-6054	48	12	express	express	VERB
ejpam-6054	48	13	solutions	solution	NOUN
ejpam-6054	48	14	.	.	PUNCT
ejpam-6054	49	1	bell	bell	PROPN
ejpam-6054	49	2	’s	’s	PART
ejpam-6054	49	3	groundbreaking	groundbreake	VERB
ejpam-6054	49	4	work	work	NOUN
ejpam-6054	49	5	(	(	PUNCT
ejpam-6054	49	6	bell	bell	NOUN
ejpam-6054	49	7	,	,	PUNCT
ejpam-6054	49	8	2010	2010	NUM
ejpam-6054	49	9	)	)	PUNCT
ejpam-6054	49	10	presents	present	VERB
ejpam-6054	49	11	a	a	DET
ejpam-6054	49	12	comprehensive	comprehensive	ADJ
ejpam-6054	49	13	exploration	exploration	NOUN
ejpam-6054	49	14	of	of	ADP
ejpam-6054	49	15	the	the	DET
ejpam-6054	49	16	foundational	foundational	ADJ
ejpam-6054	49	17	formalism	formalism	NOUN
ejpam-6054	49	18	.	.	PUNCT
ejpam-6054	50	1	it	it	PRON
ejpam-6054	50	2	brilliantly	brilliantly	ADV
ejpam-6054	50	3	demonstrates	demonstrate	VERB
ejpam-6054	50	4	that	that	SCONJ
ejpam-6054	50	5	by	by	ADP
ejpam-6054	50	6	making	make	VERB
ejpam-6054	50	7	a	a	DET
ejpam-6054	50	8	suitable	suitable	ADJ
ejpam-6054	50	9	change	change	NOUN
ejpam-6054	50	10	of	of	ADP
ejpam-6054	50	11	variable	variable	NOUN
ejpam-6054	50	12	,	,	PUNCT
ejpam-6054	50	13	the	the	DET
ejpam-6054	50	14	effect	effect	NOUN
ejpam-6054	50	15	of	of	ADP
ejpam-6054	50	16	the	the	DET
ejpam-6054	50	17	operator	operator	NOUN
ejpam-6054	50	18	on	on	ADP
ejpam-6054	50	19	a	a	DET
ejpam-6054	50	20	given	give	VERB
ejpam-6054	50	21	function	function	NOUN
ejpam-6054	50	22	of	of	ADP
ejpam-6054	50	23	q1	q1	PROPN
ejpam-6054	50	24	can	can	AUX
ejpam-6054	50	25	be	be	AUX
ejpam-6054	50	26	viewed	view	VERB
ejpam-6054	50	27	as	as	ADP
ejpam-6054	50	28	that	that	PRON
ejpam-6054	50	29	of	of	ADP
ejpam-6054	50	30	a	a	DET
ejpam-6054	50	31	traditional	traditional	ADJ
ejpam-6054	50	32	shift	shift	NOUN
ejpam-6054	50	33	operator	operator	NOUN
ejpam-6054	50	34	.	.	PUNCT
ejpam-6054	51	1	in	in	ADP
ejpam-6054	51	2	other	other	ADJ
ejpam-6054	51	3	words	word	NOUN
ejpam-6054	51	4	,	,	PUNCT
ejpam-6054	51	5	for	for	ADP
ejpam-6054	51	6	any	any	DET
ejpam-6054	51	7	parameter	parameter	NOUN
ejpam-6054	51	8	µ	µ	NOUN
ejpam-6054	51	9	,	,	PUNCT
ejpam-6054	51	10	applying	apply	VERB
ejpam-6054	51	11	the	the	DET
ejpam-6054	51	12	shift	shift	NOUN
ejpam-6054	51	13	operator	operator	NOUN
ejpam-6054	51	14	exp(µ∂q1	exp(µ∂q1	NOUN
ejpam-6054	51	15	)	)	PUNCT
ejpam-6054	51	16	to	to	ADP
ejpam-6054	51	17	any	any	DET
ejpam-6054	51	18	function	function	NOUN
ejpam-6054	51	19	of	of	ADP
ejpam-6054	51	20	q1	q1	PROPN
ejpam-6054	51	21	yields	yield	VERB
ejpam-6054	51	22	the	the	DET
ejpam-6054	51	23	following	follow	VERB
ejpam-6054	51	24	remarkable	remarkable	ADJ
ejpam-6054	51	25	result	result	NOUN
ejpam-6054	51	26	:	:	PUNCT
ejpam-6054	51	27	exp(µ∂q1){f(q1	exp(µ∂q1){f(q1	NOUN
ejpam-6054	51	28	)	)	PUNCT
ejpam-6054	51	29	}	}	PUNCT
ejpam-6054	52	1	=	=	PUNCT
ejpam-6054	52	2	∞∑	∞∑	NUM
ejpam-6054	52	3	n=0	n=0	PROPN
ejpam-6054	52	4	∂n	∂n	PROPN
ejpam-6054	52	5	q1f(q1	q1f(q1	PROPN
ejpam-6054	52	6	)	)	PUNCT
ejpam-6054	52	7	µn	µn	PROPN
ejpam-6054	52	8	n	n	X
ejpam-6054	52	9	!	!	PUNCT
ejpam-6054	52	10	=	=	PUNCT
ejpam-6054	53	1	∞∑	∞∑	DET
ejpam-6054	53	2	n=0	n=0	NUM
ejpam-6054	53	3	fn(q1	fn(q1	NOUN
ejpam-6054	53	4	)	)	PUNCT
ejpam-6054	53	5	µn	µn	PROPN
ejpam-6054	53	6	n	n	X
ejpam-6054	53	7	!	!	PUNCT
ejpam-6054	53	8	=	=	VERB
ejpam-6054	53	9	f(q1	f(q1	NOUN
ejpam-6054	53	10	+	+	CCONJ
ejpam-6054	53	11	µ	µ	NOUN
ejpam-6054	53	12	)	)	PUNCT
ejpam-6054	53	13	,	,	PUNCT
ejpam-6054	53	14	(	(	PUNCT
ejpam-6054	53	15	6	6	X
ejpam-6054	53	16	)	)	PUNCT
ejpam-6054	53	17	s.	s.	PROPN
ejpam-6054	53	18	a.	a.	PROPN
ejpam-6054	53	19	wani	wani	PROPN
ejpam-6054	53	20	et	et	PROPN
ejpam-6054	53	21	al	al	PROPN
ejpam-6054	53	22	.	.	PUNCT
ejpam-6054	53	23	/	/	SYM
ejpam-6054	53	24	eur	eur	PROPN
ejpam-6054	53	25	.	.	PUNCT
ejpam-6054	54	1	j.	j.	PROPN
ejpam-6054	54	2	pure	pure	PROPN
ejpam-6054	54	3	appl	appl	PROPN
ejpam-6054	54	4	.	.	PROPN
ejpam-6054	54	5	math	math	PROPN
ejpam-6054	54	6	,	,	PUNCT
ejpam-6054	54	7	18	18	NUM
ejpam-6054	54	8	(	(	PUNCT
ejpam-6054	54	9	3	3	NUM
ejpam-6054	54	10	)	)	PUNCT
ejpam-6054	54	11	(	(	PUNCT
ejpam-6054	54	12	2025	2025	NUM
ejpam-6054	54	13	)	)	PUNCT
ejpam-6054	54	14	,	,	PUNCT
ejpam-6054	54	15	6054	6054	NUM
ejpam-6054	54	16	4	4	NUM
ejpam-6054	54	17	of	of	ADP
ejpam-6054	54	18	16	16	NUM
ejpam-6054	54	19	where	where	SCONJ
ejpam-6054	54	20	∂n	∂n	PROPN
ejpam-6054	54	21	q1	q1	PROPN
ejpam-6054	54	22	=	=	PROPN
ejpam-6054	54	23	∂n	∂n	PROPN
ejpam-6054	54	24	∂qn1	∂qn1	NOUN
ejpam-6054	54	25	.	.	PUNCT
ejpam-6054	55	1	this	this	DET
ejpam-6054	55	2	result	result	NOUN
ejpam-6054	55	3	illustrates	illustrate	VERB
ejpam-6054	55	4	that	that	SCONJ
ejpam-6054	55	5	the	the	DET
ejpam-6054	55	6	operator	operator	NOUN
ejpam-6054	55	7	exp(µ∂q1	exp(µ∂q1	NOUN
ejpam-6054	55	8	)	)	PUNCT
ejpam-6054	55	9	effectively	effectively	ADV
ejpam-6054	55	10	shifts	shift	VERB
ejpam-6054	55	11	the	the	DET
ejpam-6054	55	12	argument	argument	NOUN
ejpam-6054	55	13	of	of	ADP
ejpam-6054	55	14	the	the	DET
ejpam-6054	55	15	function	function	NOUN
ejpam-6054	55	16	f	f	PROPN
ejpam-6054	55	17	by	by	ADP
ejpam-6054	55	18	µ	µ	NUM
ejpam-6054	55	19	,	,	PUNCT
ejpam-6054	55	20	simplifying	simplify	VERB
ejpam-6054	55	21	the	the	DET
ejpam-6054	55	22	manipulation	manipulation	NOUN
ejpam-6054	55	23	and	and	CCONJ
ejpam-6054	55	24	solution	solution	NOUN
ejpam-6054	55	25	of	of	ADP
ejpam-6054	55	26	differential	differential	ADJ
ejpam-6054	55	27	equations	equation	NOUN
ejpam-6054	55	28	by	by	ADP
ejpam-6054	55	29	transforming	transform	VERB
ejpam-6054	55	30	them	they	PRON
ejpam-6054	55	31	into	into	ADP
ejpam-6054	55	32	algebraic	algebraic	ADJ
ejpam-6054	55	33	problems	problem	NOUN
ejpam-6054	55	34	.	.	PUNCT
ejpam-6054	56	1	the	the	DET
ejpam-6054	56	2	following	follow	VERB
ejpam-6054	56	3	identities	identity	NOUN
ejpam-6054	56	4	are	be	AUX
ejpam-6054	56	5	exploited	exploit	VERB
ejpam-6054	56	6	from	from	ADP
ejpam-6054	56	7	(	(	PUNCT
ejpam-6054	56	8	6	6	NUM
ejpam-6054	56	9	):	):	PUNCT
ejpam-6054	56	10	exp(µ	exp(µ	PROPN
ejpam-6054	56	11	q21∂q1){f(q1	q21∂q1){f(q1	NOUN
ejpam-6054	56	12	)	)	PUNCT
ejpam-6054	56	13	}	}	PUNCT
ejpam-6054	57	1	=	=	SYM
ejpam-6054	57	2	f	f	PROPN
ejpam-6054	57	3	(	(	PUNCT
ejpam-6054	57	4	q1	q1	PROPN
ejpam-6054	57	5	1−	1−	NUM
ejpam-6054	57	6	µq1	µq1	NOUN
ejpam-6054	57	7	)	)	PUNCT
ejpam-6054	57	8	,	,	PUNCT
ejpam-6054	57	9	(	(	PUNCT
ejpam-6054	57	10	7	7	X
ejpam-6054	57	11	)	)	PUNCT
ejpam-6054	57	12	exp(µ∂q1){qn1	exp(µ∂q1){qn1	NOUN
ejpam-6054	57	13	}	}	PUNCT
ejpam-6054	57	14	=	=	SYM
ejpam-6054	57	15	(	(	PUNCT
ejpam-6054	57	16	q1	q1	PROPN
ejpam-6054	57	17	+	+	CCONJ
ejpam-6054	57	18	µ	µ	X
ejpam-6054	57	19	)	)	PUNCT
ejpam-6054	57	20	n	n	NOUN
ejpam-6054	57	21	,	,	PUNCT
ejpam-6054	57	22	exp(µ∂n	exp(µ∂n	PROPN
ejpam-6054	57	23	q1){e	q1){e	PROPN
ejpam-6054	57	24	q1	q1	NOUN
ejpam-6054	57	25	}	}	PUNCT
ejpam-6054	57	26	=	=	SYM
ejpam-6054	57	27	eq1+µ	eq1+µ	NOUN
ejpam-6054	57	28	,	,	PUNCT
ejpam-6054	57	29	exp(µq1	exp(µq1	NOUN
ejpam-6054	57	30	∂q1)f{q1	∂q1)f{q1	PRON
ejpam-6054	57	31	}	}	PUNCT
ejpam-6054	57	32	=	=	SYM
ejpam-6054	57	33	f(eq1µ	f(eq1µ	NOUN
ejpam-6054	57	34	)	)	PUNCT
ejpam-6054	57	35	.	.	PUNCT
ejpam-6054	58	1	one	one	NUM
ejpam-6054	58	2	important	important	ADJ
ejpam-6054	58	3	class	class	NOUN
ejpam-6054	58	4	of	of	ADP
ejpam-6054	58	5	special	special	ADJ
ejpam-6054	58	6	polynomials	polynomial	NOUN
ejpam-6054	58	7	is	be	AUX
ejpam-6054	58	8	the	the	DET
ejpam-6054	58	9	bell	bell	PROPN
ejpam-6054	58	10	polynomials	polynomial	NOUN
ejpam-6054	58	11	[	[	X
ejpam-6054	58	12	1	1	NUM
ejpam-6054	58	13	]	]	PUNCT
ejpam-6054	58	14	,	,	PUNCT
ejpam-6054	58	15	named	name	VERB
ejpam-6054	58	16	after	after	ADP
ejpam-6054	58	17	mathematician	mathematician	PROPN
ejpam-6054	58	18	eric	eric	PROPN
ejpam-6054	58	19	temple	temple	PROPN
ejpam-6054	58	20	bell	bell	PROPN
ejpam-6054	58	21	.	.	PUNCT
ejpam-6054	59	1	bell	bell	NOUN
ejpam-6054	59	2	polynomials	polynomial	NOUN
ejpam-6054	59	3	play	play	VERB
ejpam-6054	59	4	a	a	DET
ejpam-6054	59	5	crucial	crucial	ADJ
ejpam-6054	59	6	role	role	NOUN
ejpam-6054	59	7	in	in	ADP
ejpam-6054	59	8	representing	represent	VERB
ejpam-6054	59	9	the	the	DET
ejpam-6054	59	10	partial	partial	ADJ
ejpam-6054	59	11	bell	bell	NOUN
ejpam-6054	59	12	polynomials	polynomial	NOUN
ejpam-6054	59	13	,	,	PUNCT
ejpam-6054	59	14	which	which	PRON
ejpam-6054	59	15	correspond	correspond	VERB
ejpam-6054	59	16	to	to	ADP
ejpam-6054	59	17	the	the	DET
ejpam-6054	59	18	partial	partial	ADJ
ejpam-6054	59	19	derivatives	derivative	NOUN
ejpam-6054	59	20	of	of	ADP
ejpam-6054	59	21	the	the	DET
ejpam-6054	59	22	exponential	exponential	ADJ
ejpam-6054	59	23	generating	generating	NOUN
ejpam-6054	59	24	function	function	NOUN
ejpam-6054	59	25	.	.	PUNCT
ejpam-6054	60	1	these	these	DET
ejpam-6054	60	2	polynomials	polynomial	NOUN
ejpam-6054	60	3	have	have	VERB
ejpam-6054	60	4	wide	wide	ADV
ejpam-6054	60	5	-	-	PUNCT
ejpam-6054	60	6	ranging	range	VERB
ejpam-6054	60	7	applications	application	NOUN
ejpam-6054	60	8	in	in	ADP
ejpam-6054	60	9	fields	field	NOUN
ejpam-6054	60	10	such	such	ADJ
ejpam-6054	60	11	as	as	ADP
ejpam-6054	60	12	combinatorics	combinatoric	NOUN
ejpam-6054	60	13	,	,	PUNCT
ejpam-6054	60	14	probability	probability	NOUN
ejpam-6054	60	15	theory	theory	NOUN
ejpam-6054	60	16	,	,	PUNCT
ejpam-6054	60	17	and	and	CCONJ
ejpam-6054	60	18	the	the	DET
ejpam-6054	60	19	analysis	analysis	NOUN
ejpam-6054	60	20	of	of	ADP
ejpam-6054	60	21	algorithms	algorithm	NOUN
ejpam-6054	60	22	.	.	PUNCT
ejpam-6054	61	1	bell	bell	NOUN
ejpam-6054	61	2	polynomials	polynomial	NOUN
ejpam-6054	61	3	are	be	AUX
ejpam-6054	61	4	particularly	particularly	ADV
ejpam-6054	61	5	valuable	valuable	ADJ
ejpam-6054	61	6	for	for	ADP
ejpam-6054	61	7	counting	count	VERB
ejpam-6054	61	8	and	and	CCONJ
ejpam-6054	61	9	enumerating	enumerate	VERB
ejpam-6054	61	10	various	various	ADJ
ejpam-6054	61	11	combinatorial	combinatorial	ADJ
ejpam-6054	61	12	structures	structure	NOUN
ejpam-6054	61	13	in	in	ADP
ejpam-6054	61	14	combinatorics	combinatoric	NOUN
ejpam-6054	61	15	.	.	PUNCT
ejpam-6054	62	1	they	they	PRON
ejpam-6054	62	2	describe	describe	VERB
ejpam-6054	62	3	partitions	partition	NOUN
ejpam-6054	62	4	of	of	ADP
ejpam-6054	62	5	sets	set	NOUN
ejpam-6054	62	6	,	,	PUNCT
ejpam-6054	62	7	which	which	PRON
ejpam-6054	62	8	involve	involve	VERB
ejpam-6054	62	9	dividing	divide	VERB
ejpam-6054	62	10	a	a	DET
ejpam-6054	62	11	set	set	NOUN
ejpam-6054	62	12	into	into	ADP
ejpam-6054	62	13	nonoverlapping	nonoverlapping	ADJ
ejpam-6054	62	14	subsets	subset	NOUN
ejpam-6054	62	15	,	,	PUNCT
ejpam-6054	62	16	and	and	CCONJ
ejpam-6054	62	17	compositions	composition	NOUN
ejpam-6054	62	18	of	of	ADP
ejpam-6054	62	19	integers	integer	NOUN
ejpam-6054	62	20	,	,	PUNCT
ejpam-6054	62	21	where	where	SCONJ
ejpam-6054	62	22	an	an	DET
ejpam-6054	62	23	integer	integer	NOUN
ejpam-6054	62	24	is	be	AUX
ejpam-6054	62	25	expressed	express	VERB
ejpam-6054	62	26	as	as	ADP
ejpam-6054	62	27	the	the	DET
ejpam-6054	62	28	sum	sum	NOUN
ejpam-6054	62	29	of	of	ADP
ejpam-6054	62	30	ordered	order	VERB
ejpam-6054	62	31	integers	integer	NOUN
ejpam-6054	62	32	.	.	PUNCT
ejpam-6054	63	1	the	the	DET
ejpam-6054	63	2	utility	utility	NOUN
ejpam-6054	63	3	of	of	ADP
ejpam-6054	63	4	bell	bell	NOUN
ejpam-6054	63	5	polynomials	polynomial	NOUN
ejpam-6054	63	6	extends	extend	VERB
ejpam-6054	63	7	to	to	ADP
ejpam-6054	63	8	the	the	DET
ejpam-6054	63	9	analysis	analysis	NOUN
ejpam-6054	63	10	of	of	ADP
ejpam-6054	63	11	algorithms	algorithm	NOUN
ejpam-6054	63	12	,	,	PUNCT
ejpam-6054	63	13	where	where	SCONJ
ejpam-6054	63	14	they	they	PRON
ejpam-6054	63	15	help	help	VERB
ejpam-6054	63	16	in	in	ADP
ejpam-6054	63	17	understanding	understand	VERB
ejpam-6054	63	18	the	the	DET
ejpam-6054	63	19	performance	performance	NOUN
ejpam-6054	63	20	and	and	CCONJ
ejpam-6054	63	21	behaviour	behaviour	NOUN
ejpam-6054	63	22	of	of	ADP
ejpam-6054	63	23	combinatorial	combinatorial	ADJ
ejpam-6054	63	24	algorithms	algorithm	NOUN
ejpam-6054	63	25	.	.	PUNCT
ejpam-6054	64	1	notable	notable	ADJ
ejpam-6054	64	2	works	work	NOUN
ejpam-6054	64	3	that	that	PRON
ejpam-6054	64	4	explore	explore	VERB
ejpam-6054	64	5	these	these	DET
ejpam-6054	64	6	applications	application	NOUN
ejpam-6054	64	7	include	include	VERB
ejpam-6054	64	8	references	reference	NOUN
ejpam-6054	64	9	[	[	X
ejpam-6054	64	10	11	11	NUM
ejpam-6054	64	11	,	,	PUNCT
ejpam-6054	64	12	12	12	NUM
ejpam-6054	64	13	,	,	PUNCT
ejpam-6054	64	14	14–19	14–19	NUM
ejpam-6054	64	15	]	]	PUNCT
ejpam-6054	64	16	,	,	PUNCT
ejpam-6054	64	17	which	which	PRON
ejpam-6054	64	18	delve	delve	VERB
ejpam-6054	64	19	into	into	ADP
ejpam-6054	64	20	the	the	DET
ejpam-6054	64	21	diverse	diverse	ADJ
ejpam-6054	64	22	and	and	CCONJ
ejpam-6054	64	23	significant	significant	ADJ
ejpam-6054	64	24	uses	use	NOUN
ejpam-6054	64	25	of	of	ADP
ejpam-6054	64	26	bell	bell	NOUN
ejpam-6054	64	27	polynomials	polynomial	NOUN
ejpam-6054	64	28	in	in	ADP
ejpam-6054	64	29	these	these	DET
ejpam-6054	64	30	mathematical	mathematical	ADJ
ejpam-6054	64	31	domains	domain	NOUN
ejpam-6054	64	32	.	.	PUNCT
ejpam-6054	65	1	through	through	ADP
ejpam-6054	65	2	these	these	DET
ejpam-6054	65	3	applications	application	NOUN
ejpam-6054	65	4	,	,	PUNCT
ejpam-6054	65	5	bell	bell	NOUN
ejpam-6054	65	6	polynomials	polynomial	NOUN
ejpam-6054	65	7	demonstrate	demonstrate	VERB
ejpam-6054	65	8	their	their	PRON
ejpam-6054	65	9	versatility	versatility	NOUN
ejpam-6054	65	10	and	and	CCONJ
ejpam-6054	65	11	importance	importance	NOUN
ejpam-6054	65	12	in	in	ADP
ejpam-6054	65	13	solving	solve	VERB
ejpam-6054	65	14	complex	complex	ADJ
ejpam-6054	65	15	problems	problem	NOUN
ejpam-6054	65	16	and	and	CCONJ
ejpam-6054	65	17	providing	provide	VERB
ejpam-6054	65	18	insights	insight	NOUN
ejpam-6054	65	19	across	across	ADP
ejpam-6054	65	20	various	various	ADJ
ejpam-6054	65	21	areas	area	NOUN
ejpam-6054	65	22	of	of	ADP
ejpam-6054	65	23	mathematical	mathematical	ADJ
ejpam-6054	65	24	research	research	NOUN
ejpam-6054	65	25	.	.	PUNCT
ejpam-6054	66	1	these	these	DET
ejpam-6054	66	2	polynomials	polynomial	NOUN
ejpam-6054	66	3	are	be	AUX
ejpam-6054	66	4	a	a	DET
ejpam-6054	66	5	sequence	sequence	NOUN
ejpam-6054	66	6	that	that	PRON
ejpam-6054	66	7	arises	arise	VERB
ejpam-6054	66	8	in	in	ADP
ejpam-6054	66	9	combinatorics	combinatoric	NOUN
ejpam-6054	66	10	and	and	CCONJ
ejpam-6054	66	11	is	be	AUX
ejpam-6054	66	12	denoted	denote	VERB
ejpam-6054	66	13	as	as	ADP
ejpam-6054	66	14	b	b	PROPN
ejpam-6054	66	15	[	[	X
ejpam-6054	66	16	j	j	X
ejpam-6054	66	17	]	]	X
ejpam-6054	66	18	n	n	PROPN
ejpam-6054	66	19	(	(	PUNCT
ejpam-6054	66	20	q1	q1	PROPN
ejpam-6054	66	21	)	)	PUNCT
ejpam-6054	66	22	.	.	PUNCT
ejpam-6054	67	1	the	the	DET
ejpam-6054	67	2	following	follow	VERB
ejpam-6054	67	3	exponential	exponential	ADJ
ejpam-6054	67	4	generating	generating	NOUN
ejpam-6054	67	5	function	function	NOUN
ejpam-6054	67	6	defines	define	VERB
ejpam-6054	67	7	them	they	PRON
ejpam-6054	67	8	:	:	PUNCT
ejpam-6054	67	9	∞∑	∞∑	NUM
ejpam-6054	67	10	n=0	n=0	PUNCT
ejpam-6054	67	11	b[j	b[j	NOUN
ejpam-6054	67	12	]	]	PUNCT
ejpam-6054	67	13	n	n	CCONJ
ejpam-6054	67	14	(	(	PUNCT
ejpam-6054	67	15	q1	q1	PROPN
ejpam-6054	67	16	)	)	PUNCT
ejpam-6054	67	17	ξn	ξn	NOUN
ejpam-6054	67	18	n	n	NOUN
ejpam-6054	67	19	!	!	PUNCT
ejpam-6054	68	1	=	=	PUNCT
ejpam-6054	69	1	eq1(e	eq1(e	PROPN
ejpam-6054	69	2	ξ−1	ξ−1	PROPN
ejpam-6054	69	3	)	)	PUNCT
ejpam-6054	69	4	.	.	PUNCT
ejpam-6054	70	1	(	(	PUNCT
ejpam-6054	70	2	8)	8)	NUM
ejpam-6054	70	3	for	for	ADP
ejpam-6054	70	4	the	the	DET
ejpam-6054	70	5	case	case	NOUN
ejpam-6054	70	6	where	where	SCONJ
ejpam-6054	70	7	q1	q1	NOUN
ejpam-6054	70	8	=	=	SYM
ejpam-6054	70	9	1	1	NUM
ejpam-6054	70	10	,	,	PUNCT
ejpam-6054	70	11	the	the	DET
ejpam-6054	70	12	bell	bell	NOUN
ejpam-6054	70	13	polynomials	polynomial	VERB
ejpam-6054	70	14	simplify	simplify	VERB
ejpam-6054	70	15	to	to	ADP
ejpam-6054	70	16	the	the	DET
ejpam-6054	70	17	bell	bell	PROPN
ejpam-6054	70	18	numbers	number	NOUN
ejpam-6054	70	19	according	accord	VERB
ejpam-6054	70	20	to	to	ADP
ejpam-6054	70	21	the	the	DET
ejpam-6054	70	22	following	follow	VERB
ejpam-6054	70	23	relation	relation	NOUN
ejpam-6054	70	24	:	:	PUNCT
ejpam-6054	70	25	∞∑	∞∑	NUM
ejpam-6054	70	26	n=0	n=0	NUM
ejpam-6054	70	27	b[j	b[j	NOUN
ejpam-6054	70	28	]	]	PUNCT
ejpam-6054	70	29	n	n	PRON
ejpam-6054	70	30	ξn	ξn	NOUN
ejpam-6054	70	31	n	n	X
ejpam-6054	70	32	!	!	PUNCT
ejpam-6054	71	1	=	=	PRON
ejpam-6054	71	2	ee	ee	PROPN
ejpam-6054	71	3	ξ−1	ξ−1	PROPN
ejpam-6054	71	4	.	.	PUNCT
ejpam-6054	72	1	bell	bell	PROPN
ejpam-6054	72	2	polynomials	polynomial	NOUN
ejpam-6054	72	3	are	be	AUX
ejpam-6054	72	4	an	an	DET
ejpam-6054	72	5	incredibly	incredibly	ADV
ejpam-6054	72	6	versatile	versatile	ADJ
ejpam-6054	72	7	and	and	CCONJ
ejpam-6054	72	8	powerful	powerful	ADJ
ejpam-6054	72	9	framework	framework	NOUN
ejpam-6054	72	10	that	that	PRON
ejpam-6054	72	11	offers	offer	VERB
ejpam-6054	72	12	deep	deep	ADJ
ejpam-6054	72	13	insights	insight	NOUN
ejpam-6054	72	14	into	into	ADP
ejpam-6054	72	15	combinatorial	combinatorial	ADJ
ejpam-6054	72	16	structures	structure	NOUN
ejpam-6054	72	17	,	,	PUNCT
ejpam-6054	72	18	particularly	particularly	ADV
ejpam-6054	72	19	in	in	ADP
ejpam-6054	72	20	partitioning	partitioning	NOUN
ejpam-6054	72	21	,	,	PUNCT
ejpam-6054	72	22	generating	generating	NOUN
ejpam-6054	72	23	functions	function	NOUN
ejpam-6054	72	24	,	,	PUNCT
ejpam-6054	72	25	and	and	CCONJ
ejpam-6054	72	26	algebraic	algebraic	ADJ
ejpam-6054	72	27	combinatorics	combinatoric	NOUN
ejpam-6054	72	28	.	.	PUNCT
ejpam-6054	73	1	their	their	PRON
ejpam-6054	73	2	significance	significance	NOUN
ejpam-6054	73	3	in	in	ADP
ejpam-6054	73	4	mathematics	mathematic	NOUN
ejpam-6054	73	5	can	can	AUX
ejpam-6054	73	6	not	not	PART
ejpam-6054	73	7	be	be	AUX
ejpam-6054	73	8	overstated	overstate	VERB
ejpam-6054	73	9	,	,	PUNCT
ejpam-6054	73	10	as	as	SCONJ
ejpam-6054	73	11	they	they	PRON
ejpam-6054	73	12	provide	provide	VERB
ejpam-6054	73	13	an	an	DET
ejpam-6054	73	14	effective	effective	ADJ
ejpam-6054	73	15	tool	tool	NOUN
ejpam-6054	73	16	for	for	ADP
ejpam-6054	73	17	counting	count	VERB
ejpam-6054	73	18	problems	problem	NOUN
ejpam-6054	73	19	and	and	CCONJ
ejpam-6054	73	20	analyzing	analyze	VERB
ejpam-6054	73	21	discrete	discrete	ADJ
ejpam-6054	73	22	structures	structure	NOUN
ejpam-6054	73	23	.	.	PUNCT
ejpam-6054	74	1	s.	s.	PROPN
ejpam-6054	74	2	a.	a.	PROPN
ejpam-6054	74	3	wani	wani	PROPN
ejpam-6054	74	4	et	et	PROPN
ejpam-6054	74	5	al	al	PROPN
ejpam-6054	74	6	.	.	PUNCT
ejpam-6054	74	7	/	/	SYM
ejpam-6054	74	8	eur	eur	PROPN
ejpam-6054	74	9	.	.	PUNCT
ejpam-6054	75	1	j.	j.	PROPN
ejpam-6054	75	2	pure	pure	PROPN
ejpam-6054	75	3	appl	appl	PROPN
ejpam-6054	75	4	.	.	PROPN
ejpam-6054	75	5	math	math	PROPN
ejpam-6054	75	6	,	,	PUNCT
ejpam-6054	75	7	18	18	NUM
ejpam-6054	75	8	(	(	PUNCT
ejpam-6054	75	9	3	3	NUM
ejpam-6054	75	10	)	)	PUNCT
ejpam-6054	75	11	(	(	PUNCT
ejpam-6054	75	12	2025	2025	NUM
ejpam-6054	75	13	)	)	PUNCT
ejpam-6054	75	14	,	,	PUNCT
ejpam-6054	75	15	6054	6054	NUM
ejpam-6054	75	16	5	5	NUM
ejpam-6054	75	17	of	of	ADP
ejpam-6054	75	18	16	16	NUM
ejpam-6054	75	19	here	here	ADV
ejpam-6054	76	1	,	,	PUNCT
ejpam-6054	76	2	we	we	PRON
ejpam-6054	76	3	have	have	AUX
ejpam-6054	76	4	made	make	VERB
ejpam-6054	76	5	a	a	DET
ejpam-6054	76	6	significant	significant	ADJ
ejpam-6054	76	7	advancement	advancement	NOUN
ejpam-6054	76	8	in	in	ADP
ejpam-6054	76	9	the	the	DET
ejpam-6054	76	10	field	field	NOUN
ejpam-6054	76	11	by	by	ADP
ejpam-6054	76	12	developing	develop	VERB
ejpam-6054	76	13	a	a	DET
ejpam-6054	76	14	new	new	ADJ
ejpam-6054	76	15	formulation	formulation	NOUN
ejpam-6054	76	16	for	for	ADP
ejpam-6054	76	17	the	the	DET
ejpam-6054	76	18	generating	generating	NOUN
ejpam-6054	76	19	relation	relation	NOUN
ejpam-6054	76	20	of	of	ADP
ejpam-6054	76	21	2d	2d	NUM
ejpam-6054	76	22	bell	bell	NOUN
ejpam-6054	76	23	polynomials	polynomial	NOUN
ejpam-6054	76	24	given	give	VERB
ejpam-6054	76	25	by	by	ADP
ejpam-6054	76	26	the	the	DET
ejpam-6054	76	27	generating	generate	VERB
ejpam-6054	76	28	expression	expression	NOUN
ejpam-6054	76	29	:	:	PUNCT
ejpam-6054	76	30	∞∑	∞∑	NUM
ejpam-6054	76	31	n=0	n=0	NUM
ejpam-6054	76	32	b[j	b[j	NOUN
ejpam-6054	76	33	]	]	PUNCT
ejpam-6054	76	34	n	n	PROPN
ejpam-6054	76	35	(	(	PUNCT
ejpam-6054	76	36	q1	q1	PROPN
ejpam-6054	76	37	,	,	PUNCT
ejpam-6054	76	38	q2	q2	NOUN
ejpam-6054	76	39	)	)	PUNCT
ejpam-6054	76	40	ξn	ξn	NOUN
ejpam-6054	76	41	n	n	NOUN
ejpam-6054	76	42	!	!	PUNCT
ejpam-6054	77	1	=	=	NOUN
ejpam-6054	78	1	eq1(e	eq1(e	NUM
ejpam-6054	78	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	78	3	.	.	PUNCT
ejpam-6054	79	1	(	(	PUNCT
ejpam-6054	79	2	9	9	NUM
ejpam-6054	79	3	)	)	PUNCT
ejpam-6054	79	4	for	for	ADP
ejpam-6054	79	5	,	,	PUNCT
ejpam-6054	79	6	q2	q2	NOUN
ejpam-6054	79	7	=	=	SYM
ejpam-6054	79	8	0	0	NUM
ejpam-6054	80	1	in	in	ADP
ejpam-6054	80	2	(	(	PUNCT
ejpam-6054	80	3	9	9	NUM
ejpam-6054	80	4	)	)	PUNCT
ejpam-6054	80	5	,	,	PUNCT
ejpam-6054	80	6	the	the	DET
ejpam-6054	80	7	2d	2d	NUM
ejpam-6054	80	8	bell	bell	PROPN
ejpam-6054	80	9	polynomials	polynomial	NOUN
ejpam-6054	80	10	b	b	PROPN
ejpam-6054	81	1	[	[	X
ejpam-6054	81	2	j	j	X
ejpam-6054	81	3	]	]	X
ejpam-6054	81	4	n	n	PROPN
ejpam-6054	81	5	(	(	PUNCT
ejpam-6054	81	6	q1	q1	PROPN
ejpam-6054	81	7	,	,	PUNCT
ejpam-6054	81	8	q2	q2	NOUN
ejpam-6054	81	9	)	)	PUNCT
ejpam-6054	81	10	reduce	reduce	VERB
ejpam-6054	81	11	to	to	ADP
ejpam-6054	81	12	the	the	DET
ejpam-6054	81	13	bell	bell	NOUN
ejpam-6054	81	14	polynomials	polynomial	NOUN
ejpam-6054	81	15	given	give	VERB
ejpam-6054	81	16	by	by	ADP
ejpam-6054	81	17	(	(	PUNCT
ejpam-6054	81	18	8)	8)	NUM
ejpam-6054	81	19	.	.	PUNCT
ejpam-6054	82	1	in	in	ADP
ejpam-6054	82	2	the	the	DET
ejpam-6054	82	3	upcoming	upcoming	ADJ
ejpam-6054	82	4	sections	section	NOUN
ejpam-6054	82	5	,	,	PUNCT
ejpam-6054	82	6	we	we	PRON
ejpam-6054	82	7	will	will	AUX
ejpam-6054	82	8	explore	explore	VERB
ejpam-6054	82	9	these	these	DET
ejpam-6054	82	10	mathematical	mathematical	ADJ
ejpam-6054	82	11	marvels	marvel	NOUN
ejpam-6054	82	12	,	,	PUNCT
ejpam-6054	82	13	uncovering	uncover	VERB
ejpam-6054	82	14	their	their	PRON
ejpam-6054	82	15	intricate	intricate	ADJ
ejpam-6054	82	16	properties	property	NOUN
ejpam-6054	82	17	and	and	CCONJ
ejpam-6054	82	18	unveiling	unveil	VERB
ejpam-6054	82	19	their	their	PRON
ejpam-6054	82	20	remarkable	remarkable	ADJ
ejpam-6054	82	21	applications	application	NOUN
ejpam-6054	82	22	.	.	PUNCT
ejpam-6054	83	1	in	in	ADP
ejpam-6054	83	2	section	section	NOUN
ejpam-6054	83	3	2	2	NUM
ejpam-6054	83	4	,	,	PUNCT
ejpam-6054	83	5	we	we	PRON
ejpam-6054	83	6	dive	dive	VERB
ejpam-6054	83	7	headfirst	headfirst	VERB
ejpam-6054	83	8	into	into	ADP
ejpam-6054	83	9	the	the	DET
ejpam-6054	83	10	realm	realm	NOUN
ejpam-6054	83	11	of	of	ADP
ejpam-6054	83	12	generating	generating	NOUN
ejpam-6054	83	13	functions	function	NOUN
ejpam-6054	83	14	,	,	PUNCT
ejpam-6054	83	15	where	where	SCONJ
ejpam-6054	83	16	we	we	PRON
ejpam-6054	83	17	introduce	introduce	VERB
ejpam-6054	83	18	2d	2d	NUM
ejpam-6054	83	19	bell	bell	NOUN
ejpam-6054	83	20	polynomials	polynomial	NOUN
ejpam-6054	83	21	.	.	PUNCT
ejpam-6054	84	1	further	far	ADV
ejpam-6054	84	2	,	,	PUNCT
ejpam-6054	84	3	we	we	PRON
ejpam-6054	84	4	derive	derive	VERB
ejpam-6054	84	5	explicit	explicit	ADJ
ejpam-6054	84	6	representations	representation	NOUN
ejpam-6054	84	7	and	and	CCONJ
ejpam-6054	84	8	unveil	unveil	ADJ
ejpam-6054	84	9	summation	summation	NOUN
ejpam-6054	84	10	formulae	formulae	NOUN
ejpam-6054	84	11	,	,	PUNCT
ejpam-6054	84	12	recurrence	recurrence	NOUN
ejpam-6054	84	13	relations	relation	NOUN
ejpam-6054	84	14	,	,	PUNCT
ejpam-6054	84	15	and	and	CCONJ
ejpam-6054	84	16	addition	addition	NOUN
ejpam-6054	84	17	formulas	formula	NOUN
ejpam-6054	84	18	,	,	PUNCT
ejpam-6054	84	19	all	all	PRON
ejpam-6054	84	20	while	while	SCONJ
ejpam-6054	84	21	shedding	shed	VERB
ejpam-6054	84	22	light	light	NOUN
ejpam-6054	84	23	on	on	ADP
ejpam-6054	84	24	their	their	PRON
ejpam-6054	84	25	profound	profound	ADJ
ejpam-6054	84	26	connection	connection	NOUN
ejpam-6054	84	27	to	to	ADP
ejpam-6054	84	28	stirling	stirling	NOUN
ejpam-6054	84	29	polynomials	polynomial	NOUN
ejpam-6054	84	30	of	of	ADP
ejpam-6054	84	31	the	the	DET
ejpam-6054	84	32	second	second	ADJ
ejpam-6054	84	33	kind	kind	NOUN
ejpam-6054	84	34	.	.	PUNCT
ejpam-6054	85	1	in	in	ADP
ejpam-6054	85	2	section	section	NOUN
ejpam-6054	85	3	3	3	NUM
ejpam-6054	85	4	,	,	PUNCT
ejpam-6054	85	5	we	we	PRON
ejpam-6054	85	6	delve	delve	VERB
ejpam-6054	85	7	deeper	deeply	ADV
ejpam-6054	85	8	into	into	ADP
ejpam-6054	85	9	these	these	DET
ejpam-6054	85	10	polynomials	polynomial	NOUN
ejpam-6054	85	11	’	'	PUNCT
ejpam-6054	85	12	matrix	matrix	NOUN
ejpam-6054	85	13	form	form	NOUN
ejpam-6054	85	14	and	and	CCONJ
ejpam-6054	85	15	product	product	NOUN
ejpam-6054	85	16	formula	formula	NOUN
ejpam-6054	85	17	,	,	PUNCT
ejpam-6054	85	18	unveiling	unveil	VERB
ejpam-6054	85	19	their	their	PRON
ejpam-6054	85	20	structural	structural	ADJ
ejpam-6054	85	21	insights	insight	NOUN
ejpam-6054	85	22	into	into	ADP
ejpam-6054	85	23	their	their	PRON
ejpam-6054	85	24	inner	inner	ADJ
ejpam-6054	85	25	workings	working	NOUN
ejpam-6054	85	26	.	.	PUNCT
ejpam-6054	86	1	in	in	ADP
ejpam-6054	86	2	section	section	NOUN
ejpam-6054	86	3	4	4	NUM
ejpam-6054	86	4	,	,	PUNCT
ejpam-6054	86	5	where	where	SCONJ
ejpam-6054	86	6	we	we	PRON
ejpam-6054	86	7	introduce	introduce	VERB
ejpam-6054	86	8	the	the	DET
ejpam-6054	86	9	2d	2d	NUM
ejpam-6054	86	10	bell	bell	NOUN
ejpam-6054	86	11	-	-	PUNCT
ejpam-6054	86	12	based	base	VERB
ejpam-6054	86	13	stirling	stirling	NOUN
ejpam-6054	86	14	polynomials	polynomial	NOUN
ejpam-6054	86	15	of	of	ADP
ejpam-6054	86	16	the	the	DET
ejpam-6054	86	17	second	second	ADJ
ejpam-6054	86	18	kind	kind	NOUN
ejpam-6054	86	19	,	,	PUNCT
ejpam-6054	86	20	expanding	expand	VERB
ejpam-6054	86	21	the	the	DET
ejpam-6054	86	22	horizons	horizon	NOUN
ejpam-6054	86	23	of	of	ADP
ejpam-6054	86	24	our	our	PRON
ejpam-6054	86	25	understanding	understanding	NOUN
ejpam-6054	86	26	even	even	ADV
ejpam-6054	86	27	further	far	ADV
ejpam-6054	86	28	.	.	PUNCT
ejpam-6054	87	1	the	the	DET
ejpam-6054	87	2	conclusion	conclusion	NOUN
ejpam-6054	87	3	is	be	AUX
ejpam-6054	87	4	provided	provide	VERB
ejpam-6054	87	5	last	last	ADV
ejpam-6054	87	6	.	.	PUNCT
ejpam-6054	88	1	for	for	ADP
ejpam-6054	88	2	j	j	PROPN
ejpam-6054	88	3	=	=	SYM
ejpam-6054	88	4	3	3	PROPN
ejpam-6054	88	5	,	,	PUNCT
ejpam-6054	88	6	the	the	DET
ejpam-6054	88	7	first	first	ADJ
ejpam-6054	88	8	five	five	NUM
ejpam-6054	88	9	2d	2d	NUM
ejpam-6054	88	10	bell	bell	NOUN
ejpam-6054	88	11	polynomials	polynomial	NOUN
ejpam-6054	88	12	are	be	AUX
ejpam-6054	88	13	as	as	SCONJ
ejpam-6054	88	14	follows	follow	VERB
ejpam-6054	88	15	:	:	PUNCT
ejpam-6054	88	16	b	b	X
ejpam-6054	89	1	[	[	X
ejpam-6054	89	2	3	3	NUM
ejpam-6054	89	3	]	]	SYM
ejpam-6054	89	4	0	0	NUM
ejpam-6054	89	5	(	(	PUNCT
ejpam-6054	89	6	q1	q1	PROPN
ejpam-6054	89	7	,	,	PUNCT
ejpam-6054	89	8	q2	q2	NOUN
ejpam-6054	89	9	)	)	PUNCT
ejpam-6054	90	1	=	=	SYM
ejpam-6054	90	2	1	1	NUM
ejpam-6054	90	3	,	,	PUNCT
ejpam-6054	90	4	b	b	X
ejpam-6054	91	1	[	[	X
ejpam-6054	91	2	3	3	NUM
ejpam-6054	91	3	]	]	SYM
ejpam-6054	91	4	1	1	NUM
ejpam-6054	91	5	(	(	PUNCT
ejpam-6054	91	6	q1	q1	PROPN
ejpam-6054	91	7	,	,	PUNCT
ejpam-6054	91	8	q2	q2	NOUN
ejpam-6054	91	9	)	)	PUNCT
ejpam-6054	91	10	=	=	SYM
ejpam-6054	91	11	q1	q1	PROPN
ejpam-6054	91	12	,	,	PUNCT
ejpam-6054	91	13	b	b	X
ejpam-6054	92	1	[	[	X
ejpam-6054	92	2	3	3	NUM
ejpam-6054	92	3	]	]	SYM
ejpam-6054	92	4	2	2	NUM
ejpam-6054	92	5	(	(	PUNCT
ejpam-6054	92	6	q1	q1	PROPN
ejpam-6054	92	7	,	,	PUNCT
ejpam-6054	92	8	q2	q2	NOUN
ejpam-6054	92	9	)	)	PUNCT
ejpam-6054	92	10	=	=	SYM
ejpam-6054	92	11	q21	q21	PROPN
ejpam-6054	92	12	+	+	SYM
ejpam-6054	92	13	q1	q1	PROPN
ejpam-6054	92	14	,	,	PUNCT
ejpam-6054	92	15	b	b	X
ejpam-6054	93	1	[	[	X
ejpam-6054	93	2	3	3	NUM
ejpam-6054	93	3	]	]	SYM
ejpam-6054	93	4	3	3	NUM
ejpam-6054	93	5	(	(	PUNCT
ejpam-6054	93	6	q1	q1	PROPN
ejpam-6054	93	7	,	,	PUNCT
ejpam-6054	93	8	q2	q2	NOUN
ejpam-6054	93	9	)	)	PUNCT
ejpam-6054	93	10	=	=	PUNCT
ejpam-6054	94	1	q31	q31	ADJ
ejpam-6054	94	2	+	+	NUM
ejpam-6054	94	3	3q21	3q21	NOUN
ejpam-6054	94	4	+	+	NUM
ejpam-6054	94	5	q1	q1	PROPN
ejpam-6054	94	6	+	+	CCONJ
ejpam-6054	94	7	6q2	6q2	NUM
ejpam-6054	94	8	,	,	PUNCT
ejpam-6054	94	9	b	b	X
ejpam-6054	95	1	[	[	X
ejpam-6054	95	2	j	j	X
ejpam-6054	95	3	]	]	X
ejpam-6054	95	4	4	4	NUM
ejpam-6054	95	5	(	(	PUNCT
ejpam-6054	95	6	q1	q1	PROPN
ejpam-6054	95	7	,	,	PUNCT
ejpam-6054	95	8	q2	q2	NOUN
ejpam-6054	95	9	)	)	PUNCT
ejpam-6054	95	10	=	=	PRON
ejpam-6054	95	11	q41	q41	ADV
ejpam-6054	96	1	+	+	CCONJ
ejpam-6054	96	2	6q31	6q31	ADJ
ejpam-6054	97	1	+	+	CCONJ
ejpam-6054	97	2	7q21	7q21	NOUN
ejpam-6054	98	1	+	+	NUM
ejpam-6054	98	2	q1	q1	NOUN
ejpam-6054	98	3	+	+	CCONJ
ejpam-6054	99	1	36q2	36q2	NUM
ejpam-6054	99	2	+	+	NUM
ejpam-6054	99	3	24q1q2	24q1q2	NOUN
ejpam-6054	99	4	.	.	PUNCT
ejpam-6054	100	1	figure	figure	VERB
ejpam-6054	100	2	1	1	NUM
ejpam-6054	100	3	:	:	PUNCT
ejpam-6054	100	4	b[3	b[3	PROPN
ejpam-6054	100	5	]	]	X
ejpam-6054	100	6	3	3	NUM
ejpam-6054	100	7	(	(	PUNCT
ejpam-6054	100	8	q1	q1	PROPN
ejpam-6054	100	9	,	,	PUNCT
ejpam-6054	100	10	q2	q2	NOUN
ejpam-6054	100	11	)	)	PUNCT
ejpam-6054	101	1	=	=	PUNCT
ejpam-6054	102	1	q31	q31	ADJ
ejpam-6054	102	2	+	+	NUM
ejpam-6054	102	3	3q21	3q21	NOUN
ejpam-6054	102	4	+	+	NUM
ejpam-6054	102	5	q1	q1	NOUN
ejpam-6054	102	6	+	+	CCONJ
ejpam-6054	102	7	6q2	6q2	NUM
ejpam-6054	102	8	figure	figure	NOUN
ejpam-6054	102	9	2	2	NUM
ejpam-6054	102	10	:	:	PUNCT
ejpam-6054	102	11	b[4	b[4	NOUN
ejpam-6054	102	12	]	]	X
ejpam-6054	102	13	3	3	NUM
ejpam-6054	102	14	(	(	PUNCT
ejpam-6054	102	15	q1	q1	PROPN
ejpam-6054	102	16	,	,	PUNCT
ejpam-6054	102	17	q2	q2	NOUN
ejpam-6054	102	18	)	)	PUNCT
ejpam-6054	103	1	=	=	PRON
ejpam-6054	103	2	q41	q41	ADV
ejpam-6054	104	1	+	+	CCONJ
ejpam-6054	104	2	6q31	6q31	ADJ
ejpam-6054	105	1	+	+	CCONJ
ejpam-6054	105	2	7q21	7q21	NOUN
ejpam-6054	106	1	+	+	NUM
ejpam-6054	106	2	q1	q1	NOUN
ejpam-6054	106	3	+	+	CCONJ
ejpam-6054	107	1	36q2	36q2	NUM
ejpam-6054	107	2	+	+	NUM
ejpam-6054	107	3	24q1q2	24q1q2	ADJ
ejpam-6054	107	4	s.	s.	PROPN
ejpam-6054	107	5	a.	a.	PROPN
ejpam-6054	107	6	wani	wani	PROPN
ejpam-6054	107	7	et	et	PROPN
ejpam-6054	107	8	al	al	PROPN
ejpam-6054	107	9	.	.	PUNCT
ejpam-6054	107	10	/	/	SYM
ejpam-6054	107	11	eur	eur	PROPN
ejpam-6054	107	12	.	.	PUNCT
ejpam-6054	108	1	j.	j.	PROPN
ejpam-6054	108	2	pure	pure	PROPN
ejpam-6054	108	3	appl	appl	PROPN
ejpam-6054	108	4	.	.	PROPN
ejpam-6054	108	5	math	math	PROPN
ejpam-6054	108	6	,	,	PUNCT
ejpam-6054	108	7	18	18	NUM
ejpam-6054	108	8	(	(	PUNCT
ejpam-6054	108	9	3	3	NUM
ejpam-6054	108	10	)	)	PUNCT
ejpam-6054	108	11	(	(	PUNCT
ejpam-6054	108	12	2025	2025	NUM
ejpam-6054	108	13	)	)	PUNCT
ejpam-6054	108	14	,	,	PUNCT
ejpam-6054	108	15	6054	6054	NUM
ejpam-6054	108	16	6	6	NUM
ejpam-6054	108	17	of	of	ADP
ejpam-6054	108	18	16	16	NUM
ejpam-6054	108	19	2	2	NUM
ejpam-6054	108	20	.	.	X
ejpam-6054	108	21	2d	2d	PROPN
ejpam-6054	108	22	bell	bell	PROPN
ejpam-6054	108	23	polynomials	polynomial	VERB
ejpam-6054	108	24	the	the	DET
ejpam-6054	108	25	2d	2d	NUM
ejpam-6054	108	26	special	special	ADJ
ejpam-6054	108	27	bell	bell	NOUN
ejpam-6054	108	28	polynomials	polynomial	NOUN
ejpam-6054	108	29	play	play	VERB
ejpam-6054	108	30	a	a	DET
ejpam-6054	108	31	crucial	crucial	ADJ
ejpam-6054	108	32	role	role	NOUN
ejpam-6054	108	33	in	in	ADP
ejpam-6054	108	34	combinatorial	combinatorial	ADJ
ejpam-6054	108	35	analysis	analysis	NOUN
ejpam-6054	108	36	,	,	PUNCT
ejpam-6054	108	37	number	number	NOUN
ejpam-6054	108	38	theory	theory	NOUN
ejpam-6054	108	39	,	,	PUNCT
ejpam-6054	108	40	and	and	CCONJ
ejpam-6054	108	41	statistical	statistical	ADJ
ejpam-6054	108	42	mechanics	mechanic	NOUN
ejpam-6054	108	43	.	.	PUNCT
ejpam-6054	109	1	they	they	PRON
ejpam-6054	109	2	express	express	VERB
ejpam-6054	109	3	multivariate	multivariate	NOUN
ejpam-6054	109	4	exponential	exponential	NOUN
ejpam-6054	109	5	generating	generating	NOUN
ejpam-6054	109	6	functions	function	NOUN
ejpam-6054	109	7	and	and	CCONJ
ejpam-6054	109	8	find	find	VERB
ejpam-6054	109	9	applications	application	NOUN
ejpam-6054	109	10	in	in	ADP
ejpam-6054	109	11	studying	study	VERB
ejpam-6054	109	12	combinatorial	combinatorial	ADJ
ejpam-6054	109	13	structures	structure	NOUN
ejpam-6054	109	14	and	and	CCONJ
ejpam-6054	109	15	problems	problem	NOUN
ejpam-6054	109	16	in	in	ADP
ejpam-6054	109	17	discrete	discrete	ADJ
ejpam-6054	109	18	mathematics	mathematic	NOUN
ejpam-6054	109	19	.	.	PUNCT
ejpam-6054	110	1	additionally	additionally	ADV
ejpam-6054	110	2	,	,	PUNCT
ejpam-6054	110	3	they	they	PRON
ejpam-6054	110	4	are	be	AUX
ejpam-6054	110	5	used	use	VERB
ejpam-6054	110	6	in	in	ADP
ejpam-6054	110	7	number	number	NOUN
ejpam-6054	110	8	theory	theory	NOUN
ejpam-6054	110	9	to	to	PART
ejpam-6054	110	10	investigate	investigate	VERB
ejpam-6054	110	11	properties	property	NOUN
ejpam-6054	110	12	of	of	ADP
ejpam-6054	110	13	partitions	partition	NOUN
ejpam-6054	110	14	,	,	PUNCT
ejpam-6054	110	15	compositions	composition	NOUN
ejpam-6054	110	16	,	,	PUNCT
ejpam-6054	110	17	and	and	CCONJ
ejpam-6054	110	18	other	other	ADJ
ejpam-6054	110	19	combinatorial	combinatorial	ADJ
ejpam-6054	110	20	objects	object	NOUN
ejpam-6054	110	21	.	.	PUNCT
ejpam-6054	111	1	in	in	ADP
ejpam-6054	111	2	statistical	statistical	ADJ
ejpam-6054	111	3	mechanics	mechanic	NOUN
ejpam-6054	111	4	,	,	PUNCT
ejpam-6054	111	5	these	these	DET
ejpam-6054	111	6	polynomials	polynomial	NOUN
ejpam-6054	111	7	are	be	AUX
ejpam-6054	111	8	employed	employ	VERB
ejpam-6054	111	9	to	to	PART
ejpam-6054	111	10	analyze	analyze	VERB
ejpam-6054	111	11	the	the	DET
ejpam-6054	111	12	behavior	behavior	NOUN
ejpam-6054	111	13	of	of	ADP
ejpam-6054	111	14	systems	system	NOUN
ejpam-6054	111	15	with	with	ADP
ejpam-6054	111	16	two	two	NUM
ejpam-6054	111	17	-	-	PUNCT
ejpam-6054	111	18	dimensional	dimensional	ADJ
ejpam-6054	111	19	degrees	degree	NOUN
ejpam-6054	111	20	of	of	ADP
ejpam-6054	111	21	freedom	freedom	NOUN
ejpam-6054	111	22	,	,	PUNCT
ejpam-6054	111	23	providing	provide	VERB
ejpam-6054	111	24	insights	insight	NOUN
ejpam-6054	111	25	into	into	ADP
ejpam-6054	111	26	the	the	DET
ejpam-6054	111	27	thermodynamic	thermodynamic	ADJ
ejpam-6054	111	28	properties	property	NOUN
ejpam-6054	111	29	and	and	CCONJ
ejpam-6054	111	30	phase	phase	NOUN
ejpam-6054	111	31	transitions	transition	NOUN
ejpam-6054	111	32	of	of	ADP
ejpam-6054	111	33	physical	physical	ADJ
ejpam-6054	111	34	systems	system	NOUN
ejpam-6054	111	35	.	.	PUNCT
ejpam-6054	112	1	furthermore	furthermore	ADV
ejpam-6054	112	2	,	,	PUNCT
ejpam-6054	112	3	in	in	ADP
ejpam-6054	112	4	applied	applied	ADJ
ejpam-6054	112	5	mathematics	mathematic	NOUN
ejpam-6054	112	6	and	and	CCONJ
ejpam-6054	112	7	engineering	engineering	NOUN
ejpam-6054	112	8	,	,	PUNCT
ejpam-6054	112	9	2d	2d	NUM
ejpam-6054	112	10	special	special	ADJ
ejpam-6054	112	11	bell	bell	NOUN
ejpam-6054	112	12	polynomials	polynomial	NOUN
ejpam-6054	112	13	are	be	AUX
ejpam-6054	112	14	utilized	utilize	VERB
ejpam-6054	112	15	in	in	ADP
ejpam-6054	112	16	problems	problem	NOUN
ejpam-6054	112	17	involving	involve	VERB
ejpam-6054	112	18	complex	complex	ADJ
ejpam-6054	112	19	systems	system	NOUN
ejpam-6054	112	20	with	with	ADP
ejpam-6054	112	21	multiple	multiple	ADJ
ejpam-6054	112	22	variables	variable	NOUN
ejpam-6054	112	23	,	,	PUNCT
ejpam-6054	112	24	offering	offer	VERB
ejpam-6054	112	25	a	a	DET
ejpam-6054	112	26	systematic	systematic	ADJ
ejpam-6054	112	27	framework	framework	NOUN
ejpam-6054	112	28	for	for	ADP
ejpam-6054	112	29	modelling	modelling	NOUN
ejpam-6054	112	30	and	and	CCONJ
ejpam-6054	112	31	analysis	analysis	NOUN
ejpam-6054	112	32	.	.	PUNCT
ejpam-6054	113	1	overall	overall	ADV
ejpam-6054	113	2	,	,	PUNCT
ejpam-6054	113	3	the	the	DET
ejpam-6054	113	4	significance	significance	NOUN
ejpam-6054	113	5	of	of	ADP
ejpam-6054	113	6	2d	2d	NUM
ejpam-6054	113	7	special	special	ADJ
ejpam-6054	113	8	bell	bell	NOUN
ejpam-6054	113	9	polynomials	polynomial	NOUN
ejpam-6054	113	10	lies	lie	VERB
ejpam-6054	113	11	in	in	ADP
ejpam-6054	113	12	their	their	PRON
ejpam-6054	113	13	ability	ability	NOUN
ejpam-6054	113	14	to	to	PART
ejpam-6054	113	15	bridge	bridge	VERB
ejpam-6054	113	16	theoretical	theoretical	ADJ
ejpam-6054	113	17	concepts	concept	NOUN
ejpam-6054	113	18	with	with	ADP
ejpam-6054	113	19	practical	practical	ADJ
ejpam-6054	113	20	applications	application	NOUN
ejpam-6054	113	21	across	across	ADP
ejpam-6054	113	22	diverse	diverse	ADJ
ejpam-6054	113	23	disciplines	discipline	NOUN
ejpam-6054	113	24	,	,	PUNCT
ejpam-6054	113	25	making	make	VERB
ejpam-6054	113	26	them	they	PRON
ejpam-6054	113	27	invaluable	invaluable	ADJ
ejpam-6054	113	28	tools	tool	NOUN
ejpam-6054	113	29	for	for	ADP
ejpam-6054	113	30	mathematical	mathematical	ADJ
ejpam-6054	113	31	research	research	NOUN
ejpam-6054	113	32	and	and	CCONJ
ejpam-6054	113	33	problem	problem	NOUN
ejpam-6054	113	34	-	-	PUNCT
ejpam-6054	113	35	solving	solving	NOUN
ejpam-6054	113	36	in	in	ADP
ejpam-6054	113	37	various	various	ADJ
ejpam-6054	113	38	fields	field	NOUN
ejpam-6054	113	39	.	.	PUNCT
ejpam-6054	114	1	here	here	ADV
ejpam-6054	114	2	,	,	PUNCT
ejpam-6054	114	3	in	in	ADP
ejpam-6054	114	4	this	this	DET
ejpam-6054	114	5	section	section	NOUN
ejpam-6054	114	6	,	,	PUNCT
ejpam-6054	114	7	we	we	PRON
ejpam-6054	114	8	derive	derive	VERB
ejpam-6054	114	9	the	the	DET
ejpam-6054	114	10	explicit	explicit	ADJ
ejpam-6054	114	11	forms	form	NOUN
ejpam-6054	114	12	and	and	CCONJ
ejpam-6054	114	13	certain	certain	ADJ
ejpam-6054	114	14	other	other	ADJ
ejpam-6054	114	15	properties	property	NOUN
ejpam-6054	114	16	of	of	ADP
ejpam-6054	114	17	2d	2d	NUM
ejpam-6054	114	18	bell	bell	NOUN
ejpam-6054	114	19	polynomials	polynomial	NOUN
ejpam-6054	114	20	denoted	denote	VERB
ejpam-6054	114	21	by	by	ADP
ejpam-6054	114	22	b	b	PROPN
ejpam-6054	114	23	[	[	X
ejpam-6054	114	24	j	j	X
ejpam-6054	114	25	]	]	X
ejpam-6054	114	26	n	n	PROPN
ejpam-6054	114	27	(	(	PUNCT
ejpam-6054	114	28	q1	q1	PROPN
ejpam-6054	114	29	,	,	PUNCT
ejpam-6054	114	30	q2	q2	NOUN
ejpam-6054	114	31	)	)	PUNCT
ejpam-6054	114	32	as	as	SCONJ
ejpam-6054	114	33	follows	follow	VERB
ejpam-6054	114	34	:	:	PUNCT
ejpam-6054	114	35	theorem	theorem	NOUN
ejpam-6054	114	36	1	1	NUM
ejpam-6054	114	37	.	.	PUNCT
ejpam-6054	115	1	the	the	DET
ejpam-6054	115	2	2d	2d	NUM
ejpam-6054	115	3	bell	bell	NOUN
ejpam-6054	115	4	polynomials	polynomial	NOUN
ejpam-6054	115	5	denoted	denote	VERB
ejpam-6054	115	6	by	by	ADP
ejpam-6054	115	7	b	b	PROPN
ejpam-6054	115	8	[	[	X
ejpam-6054	115	9	j	j	X
ejpam-6054	115	10	]	]	X
ejpam-6054	115	11	n	n	PROPN
ejpam-6054	115	12	(	(	PUNCT
ejpam-6054	115	13	q1	q1	PROPN
ejpam-6054	115	14	,	,	PUNCT
ejpam-6054	115	15	q2	q2	NOUN
ejpam-6054	115	16	)	)	PUNCT
ejpam-6054	115	17	satisfy	satisfy	VERB
ejpam-6054	115	18	the	the	DET
ejpam-6054	115	19	listed	list	VERB
ejpam-6054	115	20	explicit	explicit	ADJ
ejpam-6054	115	21	form	form	NOUN
ejpam-6054	115	22	:	:	PUNCT
ejpam-6054	115	23	b[j	b[j	NOUN
ejpam-6054	115	24	]	]	PUNCT
ejpam-6054	115	25	n	n	PROPN
ejpam-6054	115	26	(	(	PUNCT
ejpam-6054	115	27	q1	q1	PROPN
ejpam-6054	115	28	,	,	PUNCT
ejpam-6054	115	29	q2	q2	NOUN
ejpam-6054	115	30	)	)	PUNCT
ejpam-6054	115	31	=	=	NOUN
ejpam-6054	116	1	[	[	PUNCT
ejpam-6054	116	2	n]∑	n]∑	X
ejpam-6054	116	3	s=0	s=0	X
ejpam-6054	116	4	(	(	PUNCT
ejpam-6054	116	5	n	n	X
ejpam-6054	116	6	s	s	PART
ejpam-6054	116	7	)	)	PUNCT
ejpam-6054	116	8	b	b	PROPN
ejpam-6054	117	1	[	[	X
ejpam-6054	117	2	j	j	X
ejpam-6054	117	3	]	]	X
ejpam-6054	117	4	n−s(q1	n−s(q1	PROPN
ejpam-6054	117	5	)	)	PUNCT
ejpam-6054	117	6	s2(s	s2(s	PROPN
ejpam-6054	117	7	,	,	PUNCT
ejpam-6054	117	8	k	k	NOUN
ejpam-6054	117	9	)	)	PUNCT
ejpam-6054	117	10	(	(	PUNCT
ejpam-6054	117	11	e	e	X
ejpam-6054	117	12	ξ	ξ	X
ejpam-6054	117	13	−	−	PROPN
ejpam-6054	117	14	1)jk−k	1)jk−k	PROPN
ejpam-6054	117	15	1−	1−	NUM
ejpam-6054	117	16	q2	q2	NOUN
ejpam-6054	117	17	.	.	PUNCT
ejpam-6054	118	1	(	(	PUNCT
ejpam-6054	118	2	10	10	NUM
ejpam-6054	118	3	)	)	PUNCT
ejpam-6054	118	4	proof	proof	NOUN
ejpam-6054	118	5	.	.	PUNCT
ejpam-6054	119	1	the	the	DET
ejpam-6054	119	2	expression	expression	NOUN
ejpam-6054	119	3	denoted	denote	VERB
ejpam-6054	119	4	by	by	ADP
ejpam-6054	119	5	(	(	PUNCT
ejpam-6054	119	6	9	9	NUM
ejpam-6054	119	7	)	)	PUNCT
ejpam-6054	119	8	can	can	AUX
ejpam-6054	119	9	be	be	AUX
ejpam-6054	119	10	expressed	express	VERB
ejpam-6054	119	11	in	in	ADP
ejpam-6054	119	12	view	view	NOUN
ejpam-6054	119	13	of	of	ADP
ejpam-6054	119	14	the	the	DET
ejpam-6054	119	15	identity	identity	NOUN
ejpam-6054	119	16	ea+b	ea+b	NUM
ejpam-6054	119	17	=	=	SYM
ejpam-6054	119	18	eaeb	eaeb	PROPN
ejpam-6054	119	19	,	,	PUNCT
ejpam-6054	119	20	as	as	ADP
ejpam-6054	119	21	eq1(e	eq1(e	PROPN
ejpam-6054	119	22	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	119	23	=	=	PUNCT
ejpam-6054	120	1	eq1(e	eq1(e	NUM
ejpam-6054	120	2	ξ−1)eq2(e	ξ−1)eq2(e	NOUN
ejpam-6054	120	3	ξ−1)j	ξ−1)j	NOUN
ejpam-6054	120	4	=	=	PUNCT
ejpam-6054	121	1	(	(	PUNCT
ejpam-6054	121	2	∞∑	∞∑	NUM
ejpam-6054	121	3	n=0	n=0	NUM
ejpam-6054	121	4	b[j	b[j	NOUN
ejpam-6054	121	5	]	]	PUNCT
ejpam-6054	121	6	n	n	CCONJ
ejpam-6054	121	7	(	(	PUNCT
ejpam-6054	121	8	q1	q1	PROPN
ejpam-6054	121	9	)	)	PUNCT
ejpam-6054	121	10	ξn	ξn	NOUN
ejpam-6054	121	11	n	n	X
ejpam-6054	121	12	!	!	PUNCT
ejpam-6054	121	13	)	)	PUNCT
ejpam-6054	122	1	(	(	PUNCT
ejpam-6054	122	2	∞∑	∞∑	NUM
ejpam-6054	122	3	r=0	r=0	PROPN
ejpam-6054	122	4	qr2	qr2	NOUN
ejpam-6054	122	5	r	r	NOUN
ejpam-6054	122	6	!	!	PUNCT
ejpam-6054	122	7	(	(	PUNCT
ejpam-6054	122	8	eξ	eξ	PROPN
ejpam-6054	122	9	−	−	PROPN
ejpam-6054	122	10	1)jr	1)jr	PROPN
ejpam-6054	122	11	)	)	PUNCT
ejpam-6054	123	1	=	=	PUNCT
ejpam-6054	123	2	∞∑	∞∑	PRON
ejpam-6054	123	3	n=0	n=0	NUM
ejpam-6054	123	4	b[j	b[j	NOUN
ejpam-6054	123	5	]	]	PUNCT
ejpam-6054	123	6	n	n	PROPN
ejpam-6054	123	7	(	(	PUNCT
ejpam-6054	123	8	q1	q1	PROPN
ejpam-6054	123	9	,	,	PUNCT
ejpam-6054	123	10	q2	q2	NOUN
ejpam-6054	123	11	)	)	PUNCT
ejpam-6054	123	12	ξn	ξn	PROPN
ejpam-6054	123	13	n	n	X
ejpam-6054	123	14	!	!	PUNCT
ejpam-6054	123	15	.	.	PUNCT
ejpam-6054	124	1	expand	expand	VERB
ejpam-6054	124	2	the	the	DET
ejpam-6054	124	3	second	second	ADJ
ejpam-6054	124	4	exponential	exponential	NOUN
ejpam-6054	124	5	using	use	VERB
ejpam-6054	124	6	stirling	stirling	NOUN
ejpam-6054	124	7	numbers	number	NOUN
ejpam-6054	124	8	given	give	VERB
ejpam-6054	124	9	by	by	ADP
ejpam-6054	124	10	expression	expression	NOUN
ejpam-6054	124	11	(	(	PUNCT
ejpam-6054	124	12	2	2	NUM
ejpam-6054	124	13	)	)	PUNCT
ejpam-6054	124	14	,	,	PUNCT
ejpam-6054	124	15	and	and	CCONJ
ejpam-6054	124	16	(	(	PUNCT
ejpam-6054	124	17	eξ	eξ	PROPN
ejpam-6054	124	18	−	−	PROPN
ejpam-6054	125	1	1)jr	1)jr	PROPN
ejpam-6054	125	2	can	can	AUX
ejpam-6054	125	3	be	be	AUX
ejpam-6054	125	4	written	write	VERB
ejpam-6054	125	5	using	use	VERB
ejpam-6054	125	6	a	a	DET
ejpam-6054	125	7	convolution	convolution	NOUN
ejpam-6054	125	8	involving	involve	VERB
ejpam-6054	125	9	stirling	stirling	NOUN
ejpam-6054	125	10	numbers	number	NOUN
ejpam-6054	125	11	:	:	PUNCT
ejpam-6054	125	12	(	(	PUNCT
ejpam-6054	125	13	eξ−1)jr	eξ−1)jr	NOUN
ejpam-6054	125	14	=	=	PUNCT
ejpam-6054	125	15	∑∞	∑∞	X
ejpam-6054	125	16	s=0	s=0	X
ejpam-6054	125	17	s2(s	s2(s	PROPN
ejpam-6054	125	18	,	,	PUNCT
ejpam-6054	125	19	k	k	NOUN
ejpam-6054	125	20	)	)	PUNCT
ejpam-6054	125	21	(	(	PUNCT
ejpam-6054	125	22	e	e	X
ejpam-6054	125	23	ξ−	ξ−	PROPN
ejpam-6054	125	24	1)jk−k	1)jk−k	PROPN
ejpam-6054	125	25	ξs	ξs	VERB
ejpam-6054	125	26	s	s	NOUN
ejpam-6054	125	27	!	!	PUNCT
ejpam-6054	125	28	,	,	PUNCT
ejpam-6054	125	29	,	,	PUNCT
ejpam-6054	125	30	it	it	PRON
ejpam-6054	125	31	follows	follow	VERB
ejpam-6054	125	32	that	that	SCONJ
ejpam-6054	125	33	eq1(e	eq1(e	PROPN
ejpam-6054	125	34	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	125	35	=	=	PUNCT
ejpam-6054	126	1	∞∑	∞∑	ADJ
ejpam-6054	126	2	n=0	n=0	NUM
ejpam-6054	126	3	b[j	b[j	NOUN
ejpam-6054	126	4	]	]	PUNCT
ejpam-6054	126	5	n	n	PROPN
ejpam-6054	126	6	(	(	PUNCT
ejpam-6054	126	7	q1	q1	PROPN
ejpam-6054	126	8	,	,	PUNCT
ejpam-6054	126	9	q2	q2	NOUN
ejpam-6054	126	10	)	)	PUNCT
ejpam-6054	126	11	ξn	ξn	NOUN
ejpam-6054	126	12	n	n	NOUN
ejpam-6054	126	13	!	!	PUNCT
ejpam-6054	126	14	=	=	PUNCT
ejpam-6054	127	1	(	(	PUNCT
ejpam-6054	127	2	∞∑	∞∑	NUM
ejpam-6054	127	3	n=0	n=0	NUM
ejpam-6054	127	4	b[j	b[j	NOUN
ejpam-6054	127	5	]	]	PUNCT
ejpam-6054	127	6	n	n	CCONJ
ejpam-6054	127	7	(	(	PUNCT
ejpam-6054	127	8	q1	q1	PROPN
ejpam-6054	127	9	)	)	PUNCT
ejpam-6054	127	10	ξn	ξn	NOUN
ejpam-6054	127	11	n	n	X
ejpam-6054	127	12	!	!	PUNCT
ejpam-6054	127	13	)	)	PUNCT
ejpam-6054	128	1	(	(	PUNCT
ejpam-6054	128	2	∞∑	∞∑	NUM
ejpam-6054	128	3	s=0	s=0	X
ejpam-6054	128	4	s2(s	s2(s	PROPN
ejpam-6054	128	5	,	,	PUNCT
ejpam-6054	128	6	k	k	NOUN
ejpam-6054	128	7	)	)	PUNCT
ejpam-6054	128	8	(	(	PUNCT
ejpam-6054	128	9	e	e	X
ejpam-6054	128	10	ξ	ξ	X
ejpam-6054	128	11	−	−	PROPN
ejpam-6054	128	12	1)jk−k	1)jk−k	PROPN
ejpam-6054	128	13	1−	1−	NUM
ejpam-6054	128	14	q2	q2	NOUN
ejpam-6054	128	15	ξs	ξs	VERB
ejpam-6054	128	16	s	s	PROPN
ejpam-6054	128	17	!	!	PUNCT
ejpam-6054	128	18	)	)	PUNCT
ejpam-6054	128	19	.	.	PUNCT
ejpam-6054	129	1	applying	apply	VERB
ejpam-6054	129	2	the	the	DET
ejpam-6054	129	3	cauchy	cauchy	ADJ
ejpam-6054	129	4	product	product	NOUN
ejpam-6054	129	5	for	for	ADP
ejpam-6054	129	6	power	power	NOUN
ejpam-6054	129	7	series	series	NOUN
ejpam-6054	129	8	:(	:(	PUNCT
ejpam-6054	130	1	∞∑	∞∑	NOUN
ejpam-6054	130	2	n=0	n=0	PUNCT
ejpam-6054	130	3	an	an	DET
ejpam-6054	130	4	ξn	ξn	NOUN
ejpam-6054	130	5	n	n	X
ejpam-6054	130	6	!	!	PUNCT
ejpam-6054	130	7	)	)	PUNCT
ejpam-6054	131	1	(	(	PUNCT
ejpam-6054	131	2	∞∑	∞∑	NUM
ejpam-6054	131	3	s=0	s=0	NOUN
ejpam-6054	131	4	bs	bs	X
ejpam-6054	131	5	ξs	ξs	NOUN
ejpam-6054	131	6	s	s	PROPN
ejpam-6054	131	7	!	!	PUNCT
ejpam-6054	131	8	)	)	PUNCT
ejpam-6054	132	1	=	=	PUNCT
ejpam-6054	133	1	∞∑	∞∑	NUM
ejpam-6054	133	2	n=0	n=0	NUM
ejpam-6054	133	3	(	(	PUNCT
ejpam-6054	133	4	n∑	n∑	PROPN
ejpam-6054	133	5	s=0	s=0	PROPN
ejpam-6054	133	6	(	(	PUNCT
ejpam-6054	133	7	n	n	X
ejpam-6054	133	8	s	s	PART
ejpam-6054	133	9	)	)	PUNCT
ejpam-6054	133	10	an−sbs	an−sbs	NOUN
ejpam-6054	133	11	)	)	PUNCT
ejpam-6054	133	12	ξn	ξn	PROPN
ejpam-6054	133	13	n	n	X
ejpam-6054	133	14	!	!	PUNCT
ejpam-6054	133	15	.	.	PUNCT
ejpam-6054	134	1	in	in	ADP
ejpam-6054	134	2	preceding	precede	VERB
ejpam-6054	134	3	expression	expression	NOUN
ejpam-6054	134	4	,	,	PUNCT
ejpam-6054	134	5	it	it	PRON
ejpam-6054	134	6	follows	follow	VERB
ejpam-6054	134	7	that	that	SCONJ
ejpam-6054	134	8	∞∑	∞∑	NUM
ejpam-6054	134	9	n=0	n=0	NUM
ejpam-6054	134	10	b[j	b[j	NOUN
ejpam-6054	134	11	]	]	PUNCT
ejpam-6054	134	12	n	n	PROPN
ejpam-6054	134	13	(	(	PUNCT
ejpam-6054	134	14	q1	q1	PROPN
ejpam-6054	134	15	,	,	PUNCT
ejpam-6054	134	16	q2	q2	NOUN
ejpam-6054	134	17	)	)	PUNCT
ejpam-6054	134	18	ξn	ξn	NOUN
ejpam-6054	134	19	n	n	NOUN
ejpam-6054	134	20	!	!	PUNCT
ejpam-6054	134	21	=	=	NOUN
ejpam-6054	135	1	∞∑	∞∑	PRON
ejpam-6054	135	2	n=0	n=0	NUM
ejpam-6054	135	3	(	(	PUNCT
ejpam-6054	135	4	n∑	n∑	PROPN
ejpam-6054	135	5	s=0	s=0	PROPN
ejpam-6054	135	6	(	(	PUNCT
ejpam-6054	135	7	n	n	X
ejpam-6054	135	8	s	s	PART
ejpam-6054	135	9	)	)	PUNCT
ejpam-6054	135	10	b	b	PROPN
ejpam-6054	136	1	[	[	X
ejpam-6054	136	2	j	j	X
ejpam-6054	136	3	]	]	X
ejpam-6054	136	4	n−s(q1	n−s(q1	PROPN
ejpam-6054	136	5	)	)	PUNCT
ejpam-6054	136	6	s2(s	s2(s	PROPN
ejpam-6054	136	7	,	,	PUNCT
ejpam-6054	136	8	k	k	NOUN
ejpam-6054	136	9	)	)	PUNCT
ejpam-6054	136	10	(	(	PUNCT
ejpam-6054	136	11	e	e	X
ejpam-6054	136	12	ξ	ξ	X
ejpam-6054	136	13	−	−	PROPN
ejpam-6054	136	14	1)jk−k	1)jk−k	PROPN
ejpam-6054	136	15	1−	1−	NUM
ejpam-6054	136	16	q2	q2	NOUN
ejpam-6054	136	17	)	)	PUNCT
ejpam-6054	136	18	ξn	ξn	PROPN
ejpam-6054	136	19	n	n	X
ejpam-6054	136	20	!	!	PUNCT
ejpam-6054	136	21	.	.	PUNCT
ejpam-6054	137	1	s.	s.	PROPN
ejpam-6054	137	2	a.	a.	PROPN
ejpam-6054	137	3	wani	wani	PROPN
ejpam-6054	137	4	et	et	PROPN
ejpam-6054	137	5	al	al	PROPN
ejpam-6054	137	6	.	.	PUNCT
ejpam-6054	137	7	/	/	SYM
ejpam-6054	137	8	eur	eur	PROPN
ejpam-6054	137	9	.	.	PUNCT
ejpam-6054	138	1	j.	j.	PROPN
ejpam-6054	138	2	pure	pure	PROPN
ejpam-6054	138	3	appl	appl	PROPN
ejpam-6054	138	4	.	.	PROPN
ejpam-6054	138	5	math	math	PROPN
ejpam-6054	138	6	,	,	PUNCT
ejpam-6054	138	7	18	18	NUM
ejpam-6054	138	8	(	(	PUNCT
ejpam-6054	138	9	3	3	NUM
ejpam-6054	138	10	)	)	PUNCT
ejpam-6054	138	11	(	(	PUNCT
ejpam-6054	138	12	2025	2025	NUM
ejpam-6054	138	13	)	)	PUNCT
ejpam-6054	138	14	,	,	PUNCT
ejpam-6054	138	15	6054	6054	NUM
ejpam-6054	138	16	7	7	NUM
ejpam-6054	138	17	of	of	ADP
ejpam-6054	138	18	16	16	NUM
ejpam-6054	138	19	by	by	ADP
ejpam-6054	138	20	comparing	compare	VERB
ejpam-6054	138	21	the	the	DET
ejpam-6054	138	22	coefficients	coefficient	NOUN
ejpam-6054	138	23	of	of	ADP
ejpam-6054	138	24	ξn	ξn	PROPN
ejpam-6054	138	25	n	n	X
ejpam-6054	138	26	!	!	PUNCT
ejpam-6054	139	1	on	on	ADP
ejpam-6054	139	2	both	both	DET
ejpam-6054	139	3	sides	side	NOUN
ejpam-6054	139	4	of	of	ADP
ejpam-6054	139	5	the	the	DET
ejpam-6054	139	6	original	original	ADJ
ejpam-6054	139	7	generating	generating	NOUN
ejpam-6054	139	8	function	function	NOUN
ejpam-6054	139	9	,	,	PUNCT
ejpam-6054	139	10	we	we	PRON
ejpam-6054	139	11	conclude	conclude	VERB
ejpam-6054	139	12	:	:	PUNCT
ejpam-6054	139	13	b[j	b[j	NOUN
ejpam-6054	139	14	]	]	PUNCT
ejpam-6054	139	15	n	n	PROPN
ejpam-6054	139	16	(	(	PUNCT
ejpam-6054	139	17	q1	q1	PROPN
ejpam-6054	139	18	,	,	PUNCT
ejpam-6054	139	19	q2	q2	NOUN
ejpam-6054	139	20	)	)	PUNCT
ejpam-6054	140	1	=	=	SYM
ejpam-6054	140	2	n∑	n∑	PROPN
ejpam-6054	140	3	s=0	s=0	PROPN
ejpam-6054	140	4	(	(	PUNCT
ejpam-6054	140	5	n	n	X
ejpam-6054	140	6	s	s	PART
ejpam-6054	140	7	)	)	PUNCT
ejpam-6054	140	8	b	b	PROPN
ejpam-6054	141	1	[	[	X
ejpam-6054	141	2	j	j	X
ejpam-6054	141	3	]	]	X
ejpam-6054	141	4	n−s(q1	n−s(q1	PROPN
ejpam-6054	141	5	)	)	PUNCT
ejpam-6054	141	6	s2(s	s2(s	PROPN
ejpam-6054	141	7	,	,	PUNCT
ejpam-6054	141	8	k	k	NOUN
ejpam-6054	141	9	)	)	PUNCT
ejpam-6054	141	10	(	(	PUNCT
ejpam-6054	141	11	e	e	X
ejpam-6054	141	12	ξ	ξ	X
ejpam-6054	141	13	−	−	PROPN
ejpam-6054	141	14	1)jk−k	1)jk−k	PROPN
ejpam-6054	141	15	1−	1−	NUM
ejpam-6054	141	16	q2	q2	NOUN
ejpam-6054	141	17	.	.	PUNCT
ejpam-6054	142	1	this	this	PRON
ejpam-6054	142	2	completes	complete	VERB
ejpam-6054	142	3	the	the	DET
ejpam-6054	142	4	proof	proof	NOUN
ejpam-6054	142	5	.	.	PUNCT
ejpam-6054	143	1	theorem	theorem	NOUN
ejpam-6054	143	2	2	2	NUM
ejpam-6054	143	3	.	.	PUNCT
ejpam-6054	144	1	the	the	DET
ejpam-6054	144	2	bell	bell	PROPN
ejpam-6054	144	3	polynomials	polynomial	VERB
ejpam-6054	144	4	b	b	PROPN
ejpam-6054	145	1	[	[	X
ejpam-6054	145	2	j	j	X
ejpam-6054	145	3	]	]	X
ejpam-6054	145	4	n	n	PROPN
ejpam-6054	145	5	(	(	PUNCT
ejpam-6054	145	6	q1	q1	PROPN
ejpam-6054	145	7	,	,	PUNCT
ejpam-6054	145	8	q2	q2	NOUN
ejpam-6054	145	9	)	)	PUNCT
ejpam-6054	145	10	,	,	PUNCT
ejpam-6054	145	11	have	have	VERB
ejpam-6054	145	12	a	a	DET
ejpam-6054	145	13	series	series	NOUN
ejpam-6054	145	14	representation	representation	NOUN
ejpam-6054	145	15	as	as	SCONJ
ejpam-6054	145	16	listed	list	VERB
ejpam-6054	145	17	below	below	ADV
ejpam-6054	145	18	:	:	PUNCT
ejpam-6054	146	1	b[j	b[j	NOUN
ejpam-6054	146	2	]	]	PUNCT
ejpam-6054	146	3	n	n	PROPN
ejpam-6054	146	4	(	(	PUNCT
ejpam-6054	146	5	q1	q1	PROPN
ejpam-6054	146	6	,	,	PUNCT
ejpam-6054	146	7	q2	q2	NOUN
ejpam-6054	146	8	)	)	PUNCT
ejpam-6054	146	9	=	=	NOUN
ejpam-6054	147	1	[	[	PUNCT
ejpam-6054	147	2	n]∑	n]∑	X
ejpam-6054	147	3	s=0	s=0	X
ejpam-6054	147	4	(	(	PUNCT
ejpam-6054	147	5	n	n	X
ejpam-6054	147	6	s	s	PART
ejpam-6054	147	7	)	)	PUNCT
ejpam-6054	147	8	s2(n−	s2(n−	NOUN
ejpam-6054	147	9	s	s	PROPN
ejpam-6054	147	10	,	,	PUNCT
ejpam-6054	147	11	l	l	NOUN
ejpam-6054	147	12	)	)	PUNCT
ejpam-6054	147	13	1−	1−	NUM
ejpam-6054	147	14	q1	q1	PROPN
ejpam-6054	147	15	s2(s	s2(s	PROPN
ejpam-6054	147	16	,	,	PUNCT
ejpam-6054	147	17	k	k	NOUN
ejpam-6054	147	18	)	)	PUNCT
ejpam-6054	147	19	(	(	PUNCT
ejpam-6054	147	20	e	e	X
ejpam-6054	147	21	ξ	ξ	X
ejpam-6054	147	22	−	−	PROPN
ejpam-6054	147	23	1)jk−k	1)jk−k	PROPN
ejpam-6054	147	24	1−	1−	NUM
ejpam-6054	147	25	q2	q2	NOUN
ejpam-6054	147	26	.	.	PUNCT
ejpam-6054	148	1	(	(	PUNCT
ejpam-6054	148	2	11	11	NUM
ejpam-6054	148	3	)	)	PUNCT
ejpam-6054	148	4	proof	proof	NOUN
ejpam-6054	148	5	.	.	PUNCT
ejpam-6054	149	1	the	the	DET
ejpam-6054	149	2	expression	expression	NOUN
ejpam-6054	149	3	denoted	denote	VERB
ejpam-6054	149	4	by	by	ADP
ejpam-6054	149	5	(	(	PUNCT
ejpam-6054	149	6	9	9	NUM
ejpam-6054	149	7	)	)	PUNCT
ejpam-6054	149	8	can	can	AUX
ejpam-6054	149	9	be	be	AUX
ejpam-6054	149	10	expressed	express	VERB
ejpam-6054	149	11	in	in	ADP
ejpam-6054	149	12	the	the	DET
ejpam-6054	149	13	form	form	NOUN
ejpam-6054	149	14	eq1(e	eq1(e	PROPN
ejpam-6054	149	15	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	149	16	=	=	PUNCT
ejpam-6054	150	1	eq1(e	eq1(e	NUM
ejpam-6054	150	2	ξ−1)eq2(e	ξ−1)eq2(e	NOUN
ejpam-6054	150	3	ξ−1)j	ξ−1)j	NOUN
ejpam-6054	150	4	.	.	PUNCT
ejpam-6054	151	1	using	use	VERB
ejpam-6054	151	2	the	the	DET
ejpam-6054	151	3	expression	expression	NOUN
ejpam-6054	151	4	(	(	PUNCT
ejpam-6054	151	5	1)–(4	1)–(4	NUM
ejpam-6054	151	6	)	)	PUNCT
ejpam-6054	151	7	into	into	ADP
ejpam-6054	151	8	the	the	DET
ejpam-6054	151	9	right	right	ADJ
ejpam-6054	151	10	-	-	PUNCT
ejpam-6054	151	11	hand	hand	NOUN
ejpam-6054	151	12	side	side	NOUN
ejpam-6054	151	13	of	of	ADP
ejpam-6054	151	14	the	the	DET
ejpam-6054	151	15	previous	previous	ADJ
ejpam-6054	151	16	expression	expression	NOUN
ejpam-6054	151	17	,	,	PUNCT
ejpam-6054	151	18	we	we	PRON
ejpam-6054	151	19	determine	determine	VERB
ejpam-6054	151	20	eq1(e	eq1(e	PROPN
ejpam-6054	151	21	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	151	22	=	=	PUNCT
ejpam-6054	152	1	∞∑	∞∑	NUM
ejpam-6054	152	2	l=0	l=0	PROPN
ejpam-6054	152	3	∞∑	∞∑	PRON
ejpam-6054	152	4	n=0	n=0	NUM
ejpam-6054	152	5	q1	q1	NOUN
ejpam-6054	152	6	ls2(n	ls2(n	PROPN
ejpam-6054	152	7	,	,	PUNCT
ejpam-6054	152	8	l	l	NOUN
ejpam-6054	152	9	)	)	PUNCT
ejpam-6054	152	10	ξn	ξn	NOUN
ejpam-6054	152	11	n	n	X
ejpam-6054	152	12	!	!	PUNCT
ejpam-6054	152	13	(	(	PUNCT
ejpam-6054	152	14	eξ	eξ	PROPN
ejpam-6054	152	15	−	−	PROPN
ejpam-6054	152	16	1)jk−kn	1)jk−kn	NUM
ejpam-6054	152	17	!	!	PUNCT
ejpam-6054	153	1	∞∑	∞∑	NUM
ejpam-6054	153	2	r=0	r=0	PROPN
ejpam-6054	153	3	∞∑	∞∑	NUM
ejpam-6054	153	4	s=0	s=0	PROPN
ejpam-6054	153	5	q2	q2	PROPN
ejpam-6054	153	6	rs2(s	rs2(s	PROPN
ejpam-6054	153	7	,	,	PUNCT
ejpam-6054	153	8	k	k	NOUN
ejpam-6054	153	9	)	)	PUNCT
ejpam-6054	153	10	ξs	ξs	VERB
ejpam-6054	153	11	s	s	PROPN
ejpam-6054	153	12	!	!	PUNCT
ejpam-6054	153	13	(	(	PUNCT
ejpam-6054	153	14	eξ	eξ	X
ejpam-6054	153	15	−	−	PROPN
ejpam-6054	153	16	1)jk−k	1)jk−k	NOUN
ejpam-6054	153	17	.	.	PUNCT
ejpam-6054	154	1	placing	place	VERB
ejpam-6054	154	2	the	the	DET
ejpam-6054	154	3	right	right	ADJ
ejpam-6054	154	4	-	-	PUNCT
ejpam-6054	154	5	hand	hand	NOUN
ejpam-6054	154	6	side	side	NOUN
ejpam-6054	154	7	of	of	ADP
ejpam-6054	154	8	the	the	DET
ejpam-6054	154	9	equation	equation	NOUN
ejpam-6054	154	10	(	(	PUNCT
ejpam-6054	154	11	9	9	NUM
ejpam-6054	154	12	)	)	PUNCT
ejpam-6054	154	13	into	into	ADP
ejpam-6054	154	14	the	the	DET
ejpam-6054	154	15	left	left	ADJ
ejpam-6054	154	16	-	-	PUNCT
ejpam-6054	154	17	hand	hand	NOUN
ejpam-6054	154	18	side	side	NOUN
ejpam-6054	154	19	of	of	ADP
ejpam-6054	154	20	the	the	DET
ejpam-6054	154	21	preceding	precede	VERB
ejpam-6054	154	22	expression	expression	NOUN
ejpam-6054	154	23	and	and	CCONJ
ejpam-6054	154	24	then	then	ADV
ejpam-6054	154	25	simplifying	simplify	VERB
ejpam-6054	154	26	the	the	DET
ejpam-6054	154	27	right	right	ADJ
ejpam-6054	154	28	-	-	PUNCT
ejpam-6054	154	29	hand	hand	NOUN
ejpam-6054	154	30	side	side	NOUN
ejpam-6054	154	31	,	,	PUNCT
ejpam-6054	154	32	we	we	PRON
ejpam-6054	154	33	can	can	AUX
ejpam-6054	154	34	conclude	conclude	VERB
ejpam-6054	154	35	that	that	SCONJ
ejpam-6054	154	36	∞∑	∞∑	NUM
ejpam-6054	154	37	n=0	n=0	NUM
ejpam-6054	154	38	b[j	b[j	NOUN
ejpam-6054	154	39	]	]	PUNCT
ejpam-6054	154	40	n	n	PROPN
ejpam-6054	154	41	(	(	PUNCT
ejpam-6054	154	42	q1	q1	PROPN
ejpam-6054	154	43	,	,	PUNCT
ejpam-6054	154	44	q2	q2	NOUN
ejpam-6054	154	45	)	)	PUNCT
ejpam-6054	154	46	ξn	ξn	NOUN
ejpam-6054	154	47	n	n	NOUN
ejpam-6054	154	48	!	!	PUNCT
ejpam-6054	154	49	=	=	NOUN
ejpam-6054	155	1	∞∑	∞∑	PRON
ejpam-6054	155	2	n=0	n=0	NUM
ejpam-6054	155	3	∞∑	∞∑	PROPN
ejpam-6054	155	4	s=0	s=0	PROPN
ejpam-6054	155	5	s2(n	s2(n	PROPN
ejpam-6054	155	6	,	,	PUNCT
ejpam-6054	155	7	l	l	NOUN
ejpam-6054	155	8	)	)	PUNCT
ejpam-6054	155	9	1−	1−	NUM
ejpam-6054	155	10	q1	q1	PROPN
ejpam-6054	155	11	s2(s	s2(s	PROPN
ejpam-6054	155	12	,	,	PUNCT
ejpam-6054	155	13	k	k	NOUN
ejpam-6054	155	14	)	)	PUNCT
ejpam-6054	155	15	(	(	PUNCT
ejpam-6054	155	16	e	e	X
ejpam-6054	155	17	ξ	ξ	X
ejpam-6054	155	18	−	−	PROPN
ejpam-6054	155	19	1)jk−k	1)jk−k	PROPN
ejpam-6054	155	20	1−	1−	NUM
ejpam-6054	155	21	q2	q2	NOUN
ejpam-6054	155	22	ξn+s	ξn+s	NUM
ejpam-6054	155	23	n	n	CCONJ
ejpam-6054	155	24	!	!	PUNCT
ejpam-6054	155	25	s	s	X
ejpam-6054	155	26	!	!	PUNCT
ejpam-6054	155	27	.	.	PUNCT
ejpam-6054	156	1	rearranging	rearrange	VERB
ejpam-6054	156	2	the	the	DET
ejpam-6054	156	3	series	series	NOUN
ejpam-6054	156	4	,	,	PUNCT
ejpam-6054	156	5	we	we	PRON
ejpam-6054	156	6	can	can	AUX
ejpam-6054	156	7	substitute	substitute	VERB
ejpam-6054	156	8	n	n	CCONJ
ejpam-6054	156	9	−	−	PROPN
ejpam-6054	156	10	s	s	PROPN
ejpam-6054	156	11	for	for	ADP
ejpam-6054	156	12	n	n	NOUN
ejpam-6054	156	13	into	into	ADP
ejpam-6054	156	14	the	the	DET
ejpam-6054	156	15	right	right	ADJ
ejpam-6054	156	16	-	-	PUNCT
ejpam-6054	156	17	hand	hand	NOUN
ejpam-6054	156	18	side	side	NOUN
ejpam-6054	156	19	of	of	ADP
ejpam-6054	156	20	the	the	DET
ejpam-6054	156	21	preceding	precede	VERB
ejpam-6054	156	22	expression	expression	NOUN
ejpam-6054	156	23	and	and	CCONJ
ejpam-6054	156	24	then	then	ADV
ejpam-6054	156	25	simplifying	simplify	VERB
ejpam-6054	156	26	the	the	DET
ejpam-6054	156	27	right	right	ADJ
ejpam-6054	156	28	-	-	PUNCT
ejpam-6054	156	29	hand	hand	NOUN
ejpam-6054	156	30	side	side	NOUN
ejpam-6054	156	31	,	,	PUNCT
ejpam-6054	156	32	we	we	PRON
ejpam-6054	156	33	can	can	AUX
ejpam-6054	156	34	conclude	conclude	VERB
ejpam-6054	156	35	that	that	SCONJ
ejpam-6054	156	36	∞∑	∞∑	NUM
ejpam-6054	156	37	n=0	n=0	NUM
ejpam-6054	156	38	b[j	b[j	NOUN
ejpam-6054	156	39	]	]	PUNCT
ejpam-6054	156	40	n	n	PROPN
ejpam-6054	156	41	(	(	PUNCT
ejpam-6054	156	42	q1	q1	PROPN
ejpam-6054	156	43	,	,	PUNCT
ejpam-6054	156	44	q2	q2	NOUN
ejpam-6054	156	45	)	)	PUNCT
ejpam-6054	156	46	ξn	ξn	NOUN
ejpam-6054	156	47	n	n	NOUN
ejpam-6054	156	48	!	!	PUNCT
ejpam-6054	156	49	=	=	NOUN
ejpam-6054	157	1	∞∑	∞∑	NUM
ejpam-6054	157	2	n=0	n=0	NUM
ejpam-6054	158	1	[	[	X
ejpam-6054	158	2	n∑	n∑	NOUN
ejpam-6054	158	3	s=0	s=0	PROPN
ejpam-6054	158	4	(	(	PUNCT
ejpam-6054	158	5	n	n	X
ejpam-6054	158	6	s	s	PART
ejpam-6054	158	7	)	)	PUNCT
ejpam-6054	158	8	s2(n−	s2(n−	NOUN
ejpam-6054	158	9	s	s	PROPN
ejpam-6054	158	10	,	,	PUNCT
ejpam-6054	158	11	l	l	NOUN
ejpam-6054	158	12	)	)	PUNCT
ejpam-6054	158	13	1−	1−	NUM
ejpam-6054	158	14	q1	q1	PROPN
ejpam-6054	158	15	s2(s	s2(s	PROPN
ejpam-6054	158	16	,	,	PUNCT
ejpam-6054	158	17	k)(e	k)(e	PRON
ejpam-6054	158	18	ξ	ξ	X
ejpam-6054	158	19	−	−	PROPN
ejpam-6054	158	20	1)jk−k	1)jk−k	NUM
ejpam-6054	158	21	1−	1−	NUM
ejpam-6054	158	22	q2	q2	NOUN
ejpam-6054	158	23	ξn	ξn	PROPN
ejpam-6054	158	24	n	n	X
ejpam-6054	158	25	!	!	PUNCT
ejpam-6054	158	26	.	.	PUNCT
ejpam-6054	159	1	while	while	SCONJ
ejpam-6054	159	2	comparing	compare	VERB
ejpam-6054	159	3	the	the	DET
ejpam-6054	159	4	similar	similar	ADJ
ejpam-6054	159	5	abilities	ability	NOUN
ejpam-6054	159	6	of	of	ADP
ejpam-6054	159	7	ξn	ξn	PROPN
ejpam-6054	159	8	n	n	X
ejpam-6054	159	9	!	!	PUNCT
ejpam-6054	160	1	in	in	ADP
ejpam-6054	160	2	the	the	DET
ejpam-6054	160	3	preceding	precede	VERB
ejpam-6054	160	4	statement	statement	NOUN
ejpam-6054	160	5	,	,	PUNCT
ejpam-6054	160	6	we	we	PRON
ejpam-6054	160	7	arrive	arrive	VERB
ejpam-6054	160	8	at	at	ADP
ejpam-6054	160	9	statement	statement	NOUN
ejpam-6054	160	10	(	(	PUNCT
ejpam-6054	160	11	11	11	NUM
ejpam-6054	160	12	)	)	PUNCT
ejpam-6054	160	13	.	.	PUNCT
ejpam-6054	161	1	theorem	theorem	NOUN
ejpam-6054	161	2	3	3	NUM
ejpam-6054	161	3	.	.	PUNCT
ejpam-6054	162	1	the	the	DET
ejpam-6054	162	2	2d	2d	NUM
ejpam-6054	162	3	bell	bell	NOUN
ejpam-6054	162	4	polynomials	polynomial	NOUN
ejpam-6054	162	5	denoted	denote	VERB
ejpam-6054	162	6	by	by	ADP
ejpam-6054	162	7	b	b	PROPN
ejpam-6054	162	8	[	[	X
ejpam-6054	162	9	j	j	X
ejpam-6054	162	10	]	]	X
ejpam-6054	162	11	n	n	PROPN
ejpam-6054	162	12	(	(	PUNCT
ejpam-6054	162	13	q1	q1	PROPN
ejpam-6054	162	14	,	,	PUNCT
ejpam-6054	162	15	q2	q2	NOUN
ejpam-6054	162	16	)	)	PUNCT
ejpam-6054	162	17	.	.	PUNCT
ejpam-6054	163	1	then	then	ADV
ejpam-6054	163	2	the	the	DET
ejpam-6054	163	3	following	follow	VERB
ejpam-6054	163	4	summation	summation	NOUN
ejpam-6054	163	5	formulas	formula	NOUN
ejpam-6054	163	6	hold	hold	VERB
ejpam-6054	163	7	.	.	PUNCT
ejpam-6054	164	1	b[j	b[j	NOUN
ejpam-6054	164	2	]	]	PUNCT
ejpam-6054	164	3	n	n	PROPN
ejpam-6054	164	4	(	(	PUNCT
ejpam-6054	164	5	q1	q1	PROPN
ejpam-6054	164	6	+	+	CCONJ
ejpam-6054	164	7	q3	q3	PROPN
ejpam-6054	164	8	,	,	PUNCT
ejpam-6054	164	9	q2	q2	NOUN
ejpam-6054	164	10	)	)	PUNCT
ejpam-6054	165	1	=	=	SYM
ejpam-6054	166	1	n∑	n∑	NOUN
ejpam-6054	166	2	k=0	k=0	PROPN
ejpam-6054	166	3	(	(	PUNCT
ejpam-6054	166	4	n	n	X
ejpam-6054	166	5	k	k	NOUN
ejpam-6054	166	6	)	)	PUNCT
ejpam-6054	166	7	b	b	PROPN
ejpam-6054	167	1	[	[	X
ejpam-6054	167	2	j	j	X
ejpam-6054	167	3	]	]	X
ejpam-6054	167	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	167	5	,	,	PUNCT
ejpam-6054	167	6	q3)b	q3)b	PROPN
ejpam-6054	168	1	[	[	X
ejpam-6054	168	2	j	j	X
ejpam-6054	168	3	]	]	X
ejpam-6054	168	4	k	k	PROPN
ejpam-6054	168	5	(	(	PUNCT
ejpam-6054	168	6	q2	q2	NOUN
ejpam-6054	168	7	)	)	PUNCT
ejpam-6054	168	8	.	.	PUNCT
ejpam-6054	169	1	s.	s.	PROPN
ejpam-6054	169	2	a.	a.	PROPN
ejpam-6054	169	3	wani	wani	PROPN
ejpam-6054	169	4	et	et	PROPN
ejpam-6054	169	5	al	al	PROPN
ejpam-6054	169	6	.	.	PUNCT
ejpam-6054	169	7	/	/	SYM
ejpam-6054	169	8	eur	eur	PROPN
ejpam-6054	169	9	.	.	PUNCT
ejpam-6054	170	1	j.	j.	PROPN
ejpam-6054	170	2	pure	pure	PROPN
ejpam-6054	170	3	appl	appl	PROPN
ejpam-6054	170	4	.	.	PROPN
ejpam-6054	170	5	math	math	PROPN
ejpam-6054	170	6	,	,	PUNCT
ejpam-6054	170	7	18	18	NUM
ejpam-6054	170	8	(	(	PUNCT
ejpam-6054	170	9	3	3	NUM
ejpam-6054	170	10	)	)	PUNCT
ejpam-6054	170	11	(	(	PUNCT
ejpam-6054	170	12	2025	2025	NUM
ejpam-6054	170	13	)	)	PUNCT
ejpam-6054	170	14	,	,	PUNCT
ejpam-6054	170	15	6054	6054	NUM
ejpam-6054	170	16	8	8	NUM
ejpam-6054	170	17	of	of	ADP
ejpam-6054	170	18	16	16	NUM
ejpam-6054	170	19	proof	proof	NOUN
ejpam-6054	170	20	.	.	PUNCT
ejpam-6054	171	1	by	by	ADP
ejpam-6054	171	2	(	(	PUNCT
ejpam-6054	171	3	9	9	NUM
ejpam-6054	171	4	)	)	PUNCT
ejpam-6054	171	5	and	and	CCONJ
ejpam-6054	171	6	(	(	PUNCT
ejpam-6054	171	7	8)	8)	NUM
ejpam-6054	171	8	,	,	PUNCT
ejpam-6054	171	9	we	we	PRON
ejpam-6054	171	10	have	have	VERB
ejpam-6054	171	11	∞∑	∞∑	NUM
ejpam-6054	171	12	n=0	n=0	NUM
ejpam-6054	171	13	b[j	b[j	NOUN
ejpam-6054	171	14	]	]	PUNCT
ejpam-6054	171	15	n	n	PROPN
ejpam-6054	171	16	(	(	PUNCT
ejpam-6054	171	17	q1	q1	PROPN
ejpam-6054	171	18	+	+	CCONJ
ejpam-6054	171	19	q3	q3	PROPN
ejpam-6054	171	20	,	,	PUNCT
ejpam-6054	171	21	q2	q2	NOUN
ejpam-6054	171	22	)	)	PUNCT
ejpam-6054	171	23	ξn	ξn	PROPN
ejpam-6054	171	24	n	n	NOUN
ejpam-6054	171	25	!	!	PUNCT
ejpam-6054	172	1	=	=	SYM
ejpam-6054	172	2	e(q1+q2)(eξ−1)+q3(eξ−1)j	e(q1+q2)(eξ−1)+q3(eξ−1)j	NOUN
ejpam-6054	173	1	=	=	PUNCT
ejpam-6054	173	2	∞∑	∞∑	ADJ
ejpam-6054	173	3	n=0	n=0	NUM
ejpam-6054	173	4	b[j	b[j	NOUN
ejpam-6054	173	5	]	]	PUNCT
ejpam-6054	173	6	n	n	PROPN
ejpam-6054	173	7	(	(	PUNCT
ejpam-6054	173	8	q1	q1	PROPN
ejpam-6054	173	9	,	,	PUNCT
ejpam-6054	173	10	q3	q3	PROPN
ejpam-6054	173	11	)	)	PUNCT
ejpam-6054	173	12	ξn	ξn	NOUN
ejpam-6054	173	13	n	n	NOUN
ejpam-6054	173	14	!	!	PUNCT
ejpam-6054	174	1	∞∑	∞∑	NUM
ejpam-6054	174	2	k=0	k=0	PROPN
ejpam-6054	174	3	b	b	PROPN
ejpam-6054	175	1	[	[	X
ejpam-6054	175	2	j	j	X
ejpam-6054	175	3	]	]	X
ejpam-6054	175	4	k	k	PROPN
ejpam-6054	175	5	(	(	PUNCT
ejpam-6054	175	6	q2	q2	NOUN
ejpam-6054	175	7	)	)	PUNCT
ejpam-6054	175	8	ξk	ξk	ADP
ejpam-6054	175	9	k	k	PROPN
ejpam-6054	175	10	!	!	PUNCT
ejpam-6054	176	1	=	=	PUNCT
ejpam-6054	177	1	∞∑	∞∑	NUM
ejpam-6054	177	2	n=0	n=0	PUNCT
ejpam-6054	177	3	[	[	PUNCT
ejpam-6054	177	4	n∑	n∑	NOUN
ejpam-6054	177	5	k=0	k=0	PROPN
ejpam-6054	177	6	(	(	PUNCT
ejpam-6054	177	7	n	n	X
ejpam-6054	177	8	k	k	NOUN
ejpam-6054	177	9	)	)	PUNCT
ejpam-6054	177	10	b	b	PROPN
ejpam-6054	178	1	[	[	X
ejpam-6054	178	2	j	j	X
ejpam-6054	178	3	]	]	X
ejpam-6054	178	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	178	5	,	,	PUNCT
ejpam-6054	178	6	q3)b	q3)b	PROPN
ejpam-6054	179	1	[	[	X
ejpam-6054	179	2	j	j	X
ejpam-6054	179	3	]	]	X
ejpam-6054	179	4	k	k	PROPN
ejpam-6054	179	5	(	(	PUNCT
ejpam-6054	179	6	q2	q2	NOUN
ejpam-6054	179	7	)	)	PUNCT
ejpam-6054	179	8	]	]	PUNCT
ejpam-6054	180	1	ξn	ξn	PROPN
ejpam-6054	180	2	n	n	X
ejpam-6054	180	3	!	!	PUNCT
ejpam-6054	180	4	.	.	PUNCT
ejpam-6054	181	1	finally	finally	ADV
ejpam-6054	181	2	equating	equate	VERB
ejpam-6054	181	3	the	the	DET
ejpam-6054	181	4	coefficients	coefficient	NOUN
ejpam-6054	181	5	of	of	ADP
ejpam-6054	181	6	ξn	ξn	PROPN
ejpam-6054	181	7	n	n	X
ejpam-6054	181	8	!	!	PUNCT
ejpam-6054	181	9	of	of	ADP
ejpam-6054	181	10	both	both	DET
ejpam-6054	181	11	sides	side	NOUN
ejpam-6054	181	12	,	,	PUNCT
ejpam-6054	181	13	we	we	PRON
ejpam-6054	181	14	get	get	VERB
ejpam-6054	181	15	the	the	DET
ejpam-6054	181	16	asserted	assert	VERB
ejpam-6054	181	17	theorem	theorem	ADJ
ejpam-6054	181	18	8	8	NUM
ejpam-6054	181	19	.	.	PUNCT
ejpam-6054	181	20	theorem	theorem	VERB
ejpam-6054	181	21	4	4	NUM
ejpam-6054	181	22	.	.	X
ejpam-6054	182	1	for	for	ADP
ejpam-6054	182	2	any	any	DET
ejpam-6054	182	3	arbitrary	arbitrary	ADJ
ejpam-6054	182	4	n	n	CCONJ
ejpam-6054	182	5	∈	∈	PROPN
ejpam-6054	182	6	n	n	CCONJ
ejpam-6054	182	7	,	,	PUNCT
ejpam-6054	182	8	the	the	DET
ejpam-6054	182	9	following	follow	VERB
ejpam-6054	182	10	relation	relation	NOUN
ejpam-6054	182	11	hold	hold	VERB
ejpam-6054	182	12	true	true	ADJ
ejpam-6054	182	13	:	:	PUNCT
ejpam-6054	182	14	b[j	b[j	NOUN
ejpam-6054	182	15	]	]	PUNCT
ejpam-6054	182	16	n	n	PROPN
ejpam-6054	182	17	(	(	PUNCT
ejpam-6054	182	18	q1	q1	PROPN
ejpam-6054	182	19	+	+	CCONJ
ejpam-6054	182	20	1	1	NUM
ejpam-6054	182	21	,	,	PUNCT
ejpam-6054	182	22	q2)−	q2)−	ADJ
ejpam-6054	182	23	b[j	b[j	NOUN
ejpam-6054	182	24	]	]	X
ejpam-6054	182	25	n	n	PROPN
ejpam-6054	182	26	(	(	PUNCT
ejpam-6054	182	27	q1	q1	PROPN
ejpam-6054	182	28	,	,	PUNCT
ejpam-6054	182	29	q2	q2	NOUN
ejpam-6054	182	30	)	)	PUNCT
ejpam-6054	183	1	=	=	SYM
ejpam-6054	184	1	n∑	n∑	NOUN
ejpam-6054	184	2	k=0	k=0	PROPN
ejpam-6054	184	3	(	(	PUNCT
ejpam-6054	184	4	n	n	X
ejpam-6054	184	5	k	k	NOUN
ejpam-6054	184	6	)	)	PUNCT
ejpam-6054	184	7	b	b	PROPN
ejpam-6054	185	1	[	[	X
ejpam-6054	185	2	j	j	X
ejpam-6054	185	3	]	]	X
ejpam-6054	185	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	185	5	,	,	PUNCT
ejpam-6054	185	6	q2)b	q2)b	NOUN
ejpam-6054	185	7	[	[	X
ejpam-6054	185	8	j	j	X
ejpam-6054	185	9	]	]	X
ejpam-6054	185	10	k	k	PROPN
ejpam-6054	185	11	−	−	PROPN
ejpam-6054	185	12	b[j	b[j	NOUN
ejpam-6054	185	13	]	]	X
ejpam-6054	185	14	n	n	PROPN
ejpam-6054	185	15	(	(	PUNCT
ejpam-6054	185	16	q1	q1	PROPN
ejpam-6054	185	17	,	,	PUNCT
ejpam-6054	185	18	q2	q2	NOUN
ejpam-6054	185	19	)	)	PUNCT
ejpam-6054	185	20	.	.	PUNCT
ejpam-6054	186	1	(	(	PUNCT
ejpam-6054	186	2	12	12	NUM
ejpam-6054	186	3	)	)	PUNCT
ejpam-6054	186	4	proof	proof	NOUN
ejpam-6054	186	5	.	.	PUNCT
ejpam-6054	187	1	utilizing	utilize	VERB
ejpam-6054	187	2	the	the	DET
ejpam-6054	187	3	expression	expression	NOUN
ejpam-6054	187	4	(	(	PUNCT
ejpam-6054	187	5	9	9	NUM
ejpam-6054	187	6	)	)	PUNCT
ejpam-6054	187	7	,	,	PUNCT
ejpam-6054	187	8	we	we	PRON
ejpam-6054	187	9	find	find	VERB
ejpam-6054	187	10	∞∑	∞∑	NUM
ejpam-6054	187	11	n=0	n=0	PROPN
ejpam-6054	187	12	[	[	PUNCT
ejpam-6054	187	13	b[j	b[j	NOUN
ejpam-6054	187	14	]	]	PUNCT
ejpam-6054	187	15	n	n	PROPN
ejpam-6054	187	16	(	(	PUNCT
ejpam-6054	187	17	q1	q1	PROPN
ejpam-6054	187	18	+	+	CCONJ
ejpam-6054	187	19	1	1	NUM
ejpam-6054	187	20	,	,	PUNCT
ejpam-6054	187	21	q2)−	q2)−	ADJ
ejpam-6054	187	22	b[j	b[j	NOUN
ejpam-6054	187	23	]	]	X
ejpam-6054	187	24	n	n	PROPN
ejpam-6054	187	25	(	(	PUNCT
ejpam-6054	187	26	q1	q1	PROPN
ejpam-6054	187	27	,	,	PUNCT
ejpam-6054	187	28	q2	q2	NOUN
ejpam-6054	187	29	)	)	PUNCT
ejpam-6054	187	30	]	]	PUNCT
ejpam-6054	188	1	ξn	ξn	PROPN
ejpam-6054	188	2	n	n	X
ejpam-6054	188	3	!	!	PUNCT
ejpam-6054	188	4	=	=	PUNCT
ejpam-6054	189	1	e(q1	e(q1	NOUN
ejpam-6054	190	1	+	+	PROPN
ejpam-6054	190	2	1)(eξ−1)+q2(eξ−1)j	1)(eξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	190	3	−	−	NOUN
ejpam-6054	190	4	eq1(e	eq1(e	PROPN
ejpam-6054	190	5	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	190	6	=	=	PUNCT
ejpam-6054	191	1	eq1(e	eq1(e	NUM
ejpam-6054	191	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	191	3	[	[	PUNCT
ejpam-6054	191	4	ee	ee	ADP
ejpam-6054	191	5	ξ−1	ξ−1	PROPN
ejpam-6054	191	6	−	−	NOUN
ejpam-6054	191	7	1	1	NUM
ejpam-6054	191	8	]	]	PUNCT
ejpam-6054	191	9	=	=	PUNCT
ejpam-6054	191	10	∞∑	∞∑	NUM
ejpam-6054	191	11	n=0	n=0	PUNCT
ejpam-6054	191	12	[	[	PUNCT
ejpam-6054	191	13	n∑	n∑	NOUN
ejpam-6054	191	14	k=0	k=0	PROPN
ejpam-6054	191	15	(	(	PUNCT
ejpam-6054	191	16	n	n	X
ejpam-6054	191	17	k	k	NOUN
ejpam-6054	191	18	)	)	PUNCT
ejpam-6054	191	19	b	b	PROPN
ejpam-6054	192	1	[	[	X
ejpam-6054	192	2	j	j	X
ejpam-6054	192	3	]	]	X
ejpam-6054	192	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	192	5	,	,	PUNCT
ejpam-6054	192	6	q2)bn(q1	q2)bn(q1	PROPN
ejpam-6054	192	7	,	,	PUNCT
ejpam-6054	192	8	q2)bk	q2)bk	PROPN
ejpam-6054	192	9	]	]	PUNCT
ejpam-6054	192	10	ξn	ξn	PROPN
ejpam-6054	192	11	n	n	X
ejpam-6054	192	12	!	!	PUNCT
ejpam-6054	192	13	.	.	PUNCT
ejpam-6054	193	1	by	by	ADP
ejpam-6054	193	2	equating	equate	VERB
ejpam-6054	193	3	both	both	DET
ejpam-6054	193	4	sides	side	NOUN
ejpam-6054	193	5	,	,	PUNCT
ejpam-6054	193	6	we	we	PRON
ejpam-6054	193	7	obtained	obtain	VERB
ejpam-6054	193	8	the	the	DET
ejpam-6054	193	9	result	result	NOUN
ejpam-6054	193	10	(	(	PUNCT
ejpam-6054	193	11	12	12	NUM
ejpam-6054	193	12	)	)	PUNCT
ejpam-6054	193	13	.	.	PUNCT
ejpam-6054	194	1	theorem	theorem	ADJ
ejpam-6054	194	2	5	5	NUM
ejpam-6054	194	3	.	.	PUNCT
ejpam-6054	194	4	for	for	ADP
ejpam-6054	194	5	n	n	PRON
ejpam-6054	194	6	≥	≥	NUM
ejpam-6054	194	7	1	1	NUM
ejpam-6054	194	8	,	,	PUNCT
ejpam-6054	194	9	let	let	VERB
ejpam-6054	194	10	b	b	X
ejpam-6054	194	11	[	[	X
ejpam-6054	194	12	j	j	X
ejpam-6054	194	13	]	]	X
ejpam-6054	194	14	n	n	PROPN
ejpam-6054	194	15	(	(	PUNCT
ejpam-6054	194	16	q1	q1	PROPN
ejpam-6054	194	17	,	,	PUNCT
ejpam-6054	194	18	q2	q2	NOUN
ejpam-6054	194	19	)	)	PUNCT
ejpam-6054	194	20	be	be	VERB
ejpam-6054	194	21	the	the	DET
ejpam-6054	194	22	2d	2d	NUM
ejpam-6054	194	23	bell	bell	NOUN
ejpam-6054	194	24	polynomials	polynomial	NOUN
ejpam-6054	194	25	.	.	PUNCT
ejpam-6054	195	1	then	then	ADV
ejpam-6054	195	2	we	we	PRON
ejpam-6054	195	3	have	have	VERB
ejpam-6054	195	4	∂	∂	ADJ
ejpam-6054	195	5	∂q1	∂q1	NOUN
ejpam-6054	195	6	b[j	b[j	NOUN
ejpam-6054	195	7	]	]	PUNCT
ejpam-6054	195	8	n	n	PROPN
ejpam-6054	195	9	(	(	PUNCT
ejpam-6054	195	10	q1	q1	PROPN
ejpam-6054	195	11	,	,	PUNCT
ejpam-6054	195	12	q2	q2	NOUN
ejpam-6054	195	13	)	)	PUNCT
ejpam-6054	195	14	=	=	SYM
ejpam-6054	196	1	1	1	NUM
ejpam-6054	196	2	(	(	PUNCT
ejpam-6054	196	3	n2	n2	NOUN
ejpam-6054	196	4	+	+	CCONJ
ejpam-6054	196	5	n	n	CCONJ
ejpam-6054	196	6	)	)	PUNCT
ejpam-6054	196	7	n∑	n∑	PUNCT
ejpam-6054	196	8	k=0	k=0	PROPN
ejpam-6054	196	9	(	(	PUNCT
ejpam-6054	196	10	n+	n+	ADP
ejpam-6054	196	11	1	1	NUM
ejpam-6054	196	12	k	k	X
ejpam-6054	196	13	)	)	PUNCT
ejpam-6054	196	14	b	b	X
ejpam-6054	197	1	[	[	X
ejpam-6054	197	2	j	j	X
ejpam-6054	197	3	]	]	X
ejpam-6054	197	4	k	k	PROPN
ejpam-6054	197	5	(	(	PUNCT
ejpam-6054	197	6	q1	q1	PROPN
ejpam-6054	197	7	,	,	PUNCT
ejpam-6054	197	8	q2	q2	NOUN
ejpam-6054	197	9	)	)	PUNCT
ejpam-6054	197	10	(	(	PUNCT
ejpam-6054	197	11	13	13	NUM
ejpam-6054	197	12	)	)	PUNCT
ejpam-6054	197	13	and	and	CCONJ
ejpam-6054	197	14	∂	∂	NUM
ejpam-6054	197	15	∂q2	∂q2	NOUN
ejpam-6054	197	16	b[j	b[j	NOUN
ejpam-6054	197	17	]	]	X
ejpam-6054	197	18	n	n	PROPN
ejpam-6054	197	19	(	(	PUNCT
ejpam-6054	197	20	q1	q1	PROPN
ejpam-6054	197	21	,	,	PUNCT
ejpam-6054	197	22	q2	q2	NOUN
ejpam-6054	197	23	)	)	PUNCT
ejpam-6054	197	24	=	=	SYM
ejpam-6054	198	1	n∑	n∑	NOUN
ejpam-6054	198	2	k=0	k=0	PROPN
ejpam-6054	198	3	(	(	PUNCT
ejpam-6054	198	4	n	n	X
ejpam-6054	198	5	k	k	NOUN
ejpam-6054	198	6	)	)	PUNCT
ejpam-6054	198	7	b	b	PROPN
ejpam-6054	199	1	[	[	X
ejpam-6054	199	2	j	j	X
ejpam-6054	199	3	]	]	X
ejpam-6054	199	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	199	5	,	,	PUNCT
ejpam-6054	199	6	q2)j!s2(k	q2)j!s2(k	PROPN
ejpam-6054	199	7	,	,	PUNCT
ejpam-6054	199	8	j	j	PROPN
ejpam-6054	199	9	)	)	PUNCT
ejpam-6054	199	10	.	.	PUNCT
ejpam-6054	200	1	(	(	PUNCT
ejpam-6054	200	2	14	14	NUM
ejpam-6054	200	3	)	)	PUNCT
ejpam-6054	200	4	proof	proof	NOUN
ejpam-6054	200	5	.	.	PUNCT
ejpam-6054	201	1	(	(	PUNCT
ejpam-6054	201	2	see	see	VERB
ejpam-6054	201	3	(	(	PUNCT
ejpam-6054	201	4	13	13	NUM
ejpam-6054	201	5	)	)	PUNCT
ejpam-6054	201	6	)	)	PUNCT
ejpam-6054	201	7	.	.	PUNCT
ejpam-6054	202	1	differentiating	differentiate	VERB
ejpam-6054	202	2	partially	partially	ADV
ejpam-6054	202	3	with	with	ADP
ejpam-6054	202	4	respect	respect	NOUN
ejpam-6054	202	5	to	to	ADP
ejpam-6054	202	6	the	the	DET
ejpam-6054	202	7	variable	variable	ADJ
ejpam-6054	202	8	q1	q1	PROPN
ejpam-6054	202	9	on	on	ADP
ejpam-6054	202	10	both	both	DET
ejpam-6054	202	11	sides	side	NOUN
ejpam-6054	202	12	of	of	ADP
ejpam-6054	202	13	the	the	DET
ejpam-6054	202	14	generating	generate	VERB
ejpam-6054	202	15	function	function	NOUN
ejpam-6054	202	16	:	:	PUNCT
ejpam-6054	202	17	∞∑	∞∑	NUM
ejpam-6054	202	18	n=0	n=0	NUM
ejpam-6054	202	19	b[j	b[j	NOUN
ejpam-6054	202	20	]	]	PUNCT
ejpam-6054	202	21	n	n	PROPN
ejpam-6054	202	22	(	(	PUNCT
ejpam-6054	202	23	q1	q1	PROPN
ejpam-6054	202	24	,	,	PUNCT
ejpam-6054	202	25	q2	q2	NOUN
ejpam-6054	202	26	)	)	PUNCT
ejpam-6054	202	27	ξn	ξn	NOUN
ejpam-6054	202	28	n	n	NOUN
ejpam-6054	202	29	!	!	PUNCT
ejpam-6054	203	1	=	=	NOUN
ejpam-6054	204	1	eq1(e	eq1(e	NUM
ejpam-6054	204	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	204	3	,	,	PUNCT
ejpam-6054	204	4	s.	s.	PROPN
ejpam-6054	204	5	a.	a.	PROPN
ejpam-6054	204	6	wani	wani	PROPN
ejpam-6054	204	7	et	et	PROPN
ejpam-6054	204	8	al	al	PROPN
ejpam-6054	204	9	.	.	PUNCT
ejpam-6054	204	10	/	/	SYM
ejpam-6054	204	11	eur	eur	PROPN
ejpam-6054	204	12	.	.	PUNCT
ejpam-6054	205	1	j.	j.	PROPN
ejpam-6054	205	2	pure	pure	PROPN
ejpam-6054	205	3	appl	appl	PROPN
ejpam-6054	205	4	.	.	PROPN
ejpam-6054	205	5	math	math	PROPN
ejpam-6054	205	6	,	,	PUNCT
ejpam-6054	205	7	18	18	NUM
ejpam-6054	205	8	(	(	PUNCT
ejpam-6054	205	9	3	3	NUM
ejpam-6054	205	10	)	)	PUNCT
ejpam-6054	205	11	(	(	PUNCT
ejpam-6054	205	12	2025	2025	NUM
ejpam-6054	205	13	)	)	PUNCT
ejpam-6054	205	14	,	,	PUNCT
ejpam-6054	205	15	6054	6054	NUM
ejpam-6054	205	16	9	9	NUM
ejpam-6054	205	17	of	of	ADP
ejpam-6054	205	18	16	16	NUM
ejpam-6054	205	19	we	we	PRON
ejpam-6054	205	20	get	get	VERB
ejpam-6054	205	21	∂	∂	NOUN
ejpam-6054	205	22	∂q1	∂q1	NOUN
ejpam-6054	205	23	[	[	PUNCT
ejpam-6054	205	24	∞∑	∞∑	NUM
ejpam-6054	205	25	n=0	n=0	NUM
ejpam-6054	205	26	b[j	b[j	NOUN
ejpam-6054	205	27	]	]	PUNCT
ejpam-6054	205	28	n	n	PROPN
ejpam-6054	205	29	(	(	PUNCT
ejpam-6054	205	30	q1	q1	PROPN
ejpam-6054	205	31	,	,	PUNCT
ejpam-6054	205	32	q2	q2	NOUN
ejpam-6054	205	33	)	)	PUNCT
ejpam-6054	205	34	ξn	ξn	NOUN
ejpam-6054	205	35	n	n	NOUN
ejpam-6054	205	36	!	!	PUNCT
ejpam-6054	205	37	]	]	PUNCT
ejpam-6054	206	1	=	=	SYM
ejpam-6054	206	2	∂	∂	NUM
ejpam-6054	206	3	∂q1	∂q1	NOUN
ejpam-6054	206	4	[	[	PUNCT
ejpam-6054	206	5	eq1(e	eq1(e	X
ejpam-6054	206	6	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	206	7	]	]	PUNCT
ejpam-6054	206	8	=	=	PUNCT
ejpam-6054	207	1	eq1(e	eq1(e	NUM
ejpam-6054	207	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	207	3	(	(	PUNCT
ejpam-6054	207	4	eξ	eξ	NOUN
ejpam-6054	207	5	−	−	PROPN
ejpam-6054	207	6	1	1	NUM
ejpam-6054	207	7	)	)	PUNCT
ejpam-6054	207	8	.	.	PUNCT
ejpam-6054	208	1	using	use	VERB
ejpam-6054	208	2	the	the	DET
ejpam-6054	208	3	generating	generate	VERB
ejpam-6054	208	4	function	function	NOUN
ejpam-6054	208	5	of	of	ADP
ejpam-6054	208	6	b	b	PROPN
ejpam-6054	208	7	[	[	X
ejpam-6054	208	8	j	j	X
ejpam-6054	208	9	]	]	X
ejpam-6054	208	10	n	n	PROPN
ejpam-6054	208	11	(	(	PUNCT
ejpam-6054	208	12	q1	q1	PROPN
ejpam-6054	208	13	,	,	PUNCT
ejpam-6054	208	14	q2	q2	NOUN
ejpam-6054	208	15	)	)	PUNCT
ejpam-6054	208	16	,	,	PUNCT
ejpam-6054	208	17	we	we	PRON
ejpam-6054	208	18	substitute	substitute	VERB
ejpam-6054	208	19	:	:	PUNCT
ejpam-6054	208	20	eq1(e	eq1(e	PROPN
ejpam-6054	208	21	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	208	22	(	(	PUNCT
ejpam-6054	208	23	eξ	eξ	NOUN
ejpam-6054	208	24	−	−	PROPN
ejpam-6054	208	25	1	1	NUM
ejpam-6054	208	26	)	)	PUNCT
ejpam-6054	208	27	=	=	NOUN
ejpam-6054	209	1	[	[	PUNCT
ejpam-6054	209	2	∞∑	∞∑	NUM
ejpam-6054	209	3	n=0	n=0	NUM
ejpam-6054	209	4	b[j	b[j	NOUN
ejpam-6054	209	5	]	]	PUNCT
ejpam-6054	209	6	n	n	PROPN
ejpam-6054	209	7	(	(	PUNCT
ejpam-6054	209	8	q1	q1	PROPN
ejpam-6054	209	9	,	,	PUNCT
ejpam-6054	209	10	q2	q2	NOUN
ejpam-6054	209	11	)	)	PUNCT
ejpam-6054	209	12	ξn	ξn	NOUN
ejpam-6054	209	13	n	n	NOUN
ejpam-6054	209	14	!	!	PUNCT
ejpam-6054	210	1	]	]	X
ejpam-6054	210	2	[	[	PUNCT
ejpam-6054	210	3	∞∑	∞∑	NUM
ejpam-6054	210	4	r=1	r=1	NOUN
ejpam-6054	210	5	ξr	ξr	ADP
ejpam-6054	210	6	r	r	NOUN
ejpam-6054	210	7	!	!	PUNCT
ejpam-6054	210	8	]	]	PUNCT
ejpam-6054	211	1	=	=	PUNCT
ejpam-6054	212	1	∞∑	∞∑	NUM
ejpam-6054	212	2	n=0	n=0	NUM
ejpam-6054	212	3	n∑	n∑	NOUN
ejpam-6054	212	4	k=0	k=0	PROPN
ejpam-6054	212	5	(	(	PUNCT
ejpam-6054	212	6	n+	n+	ADP
ejpam-6054	212	7	1	1	NUM
ejpam-6054	212	8	k	k	X
ejpam-6054	212	9	)	)	PUNCT
ejpam-6054	212	10	b	b	X
ejpam-6054	213	1	[	[	X
ejpam-6054	213	2	j	j	X
ejpam-6054	213	3	]	]	X
ejpam-6054	213	4	k	k	PROPN
ejpam-6054	213	5	(	(	PUNCT
ejpam-6054	213	6	q1	q1	PROPN
ejpam-6054	213	7	,	,	PUNCT
ejpam-6054	213	8	q2	q2	NOUN
ejpam-6054	213	9	)	)	PUNCT
ejpam-6054	213	10	ξn+1	ξn+1	NOUN
ejpam-6054	213	11	(	(	PUNCT
ejpam-6054	213	12	n+	n+	NOUN
ejpam-6054	213	13	1	1	NUM
ejpam-6054	213	14	)	)	PUNCT
ejpam-6054	213	15	!	!	PUNCT
ejpam-6054	213	16	.	.	PUNCT
ejpam-6054	214	1	equating	equate	VERB
ejpam-6054	214	2	the	the	DET
ejpam-6054	214	3	coefficients	coefficient	NOUN
ejpam-6054	214	4	of	of	ADP
ejpam-6054	214	5	ξn	ξn	PROPN
ejpam-6054	214	6	n	n	X
ejpam-6054	214	7	!	!	PUNCT
ejpam-6054	215	1	on	on	ADP
ejpam-6054	215	2	both	both	DET
ejpam-6054	215	3	sides	side	NOUN
ejpam-6054	215	4	gives	give	VERB
ejpam-6054	215	5	:	:	PUNCT
ejpam-6054	215	6	∂	∂	NUM
ejpam-6054	215	7	∂q1	∂q1	NOUN
ejpam-6054	215	8	b[j	b[j	NOUN
ejpam-6054	215	9	]	]	PUNCT
ejpam-6054	215	10	n	n	PROPN
ejpam-6054	215	11	(	(	PUNCT
ejpam-6054	215	12	q1	q1	PROPN
ejpam-6054	215	13	,	,	PUNCT
ejpam-6054	215	14	q2	q2	NOUN
ejpam-6054	215	15	)	)	PUNCT
ejpam-6054	215	16	=	=	SYM
ejpam-6054	216	1	1	1	NUM
ejpam-6054	216	2	(	(	PUNCT
ejpam-6054	216	3	n2	n2	NOUN
ejpam-6054	216	4	+	+	CCONJ
ejpam-6054	216	5	n	n	CCONJ
ejpam-6054	216	6	)	)	PUNCT
ejpam-6054	216	7	n∑	n∑	PUNCT
ejpam-6054	216	8	k=0	k=0	PROPN
ejpam-6054	216	9	(	(	PUNCT
ejpam-6054	216	10	n+	n+	ADP
ejpam-6054	216	11	1	1	NUM
ejpam-6054	216	12	k	k	X
ejpam-6054	216	13	)	)	PUNCT
ejpam-6054	216	14	b	b	X
ejpam-6054	217	1	[	[	X
ejpam-6054	217	2	j	j	X
ejpam-6054	217	3	]	]	X
ejpam-6054	217	4	k	k	PROPN
ejpam-6054	217	5	(	(	PUNCT
ejpam-6054	217	6	q1	q1	PROPN
ejpam-6054	217	7	,	,	PUNCT
ejpam-6054	217	8	q2	q2	NOUN
ejpam-6054	217	9	)	)	PUNCT
ejpam-6054	217	10	.	.	PUNCT
ejpam-6054	218	1	proof	proof	NOUN
ejpam-6054	218	2	.	.	PUNCT
ejpam-6054	219	1	(	(	PUNCT
ejpam-6054	219	2	see	see	VERB
ejpam-6054	219	3	(	(	PUNCT
ejpam-6054	219	4	14	14	NUM
ejpam-6054	219	5	)	)	PUNCT
ejpam-6054	219	6	)	)	PUNCT
ejpam-6054	219	7	.	.	PUNCT
ejpam-6054	220	1	differentiating	differentiate	VERB
ejpam-6054	220	2	partially	partially	ADV
ejpam-6054	220	3	with	with	ADP
ejpam-6054	220	4	respect	respect	NOUN
ejpam-6054	220	5	to	to	ADP
ejpam-6054	220	6	the	the	DET
ejpam-6054	220	7	variable	variable	ADJ
ejpam-6054	220	8	q2	q2	NOUN
ejpam-6054	220	9	on	on	ADP
ejpam-6054	220	10	both	both	DET
ejpam-6054	220	11	sides	side	NOUN
ejpam-6054	220	12	of	of	ADP
ejpam-6054	220	13	the	the	DET
ejpam-6054	220	14	generating	generate	VERB
ejpam-6054	220	15	function	function	NOUN
ejpam-6054	220	16	:	:	PUNCT
ejpam-6054	220	17	∞∑	∞∑	NUM
ejpam-6054	220	18	n=0	n=0	NUM
ejpam-6054	220	19	b[j	b[j	NOUN
ejpam-6054	220	20	]	]	PUNCT
ejpam-6054	220	21	n	n	PROPN
ejpam-6054	220	22	(	(	PUNCT
ejpam-6054	220	23	q1	q1	PROPN
ejpam-6054	220	24	,	,	PUNCT
ejpam-6054	220	25	q2	q2	NOUN
ejpam-6054	220	26	)	)	PUNCT
ejpam-6054	220	27	ξn	ξn	NOUN
ejpam-6054	220	28	n	n	NOUN
ejpam-6054	220	29	!	!	PUNCT
ejpam-6054	221	1	=	=	NOUN
ejpam-6054	222	1	eq1(e	eq1(e	NUM
ejpam-6054	222	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	222	3	,	,	PUNCT
ejpam-6054	222	4	we	we	PRON
ejpam-6054	222	5	get	get	VERB
ejpam-6054	222	6	∂	∂	NOUN
ejpam-6054	222	7	∂q2	∂q2	NOUN
ejpam-6054	222	8	[	[	PUNCT
ejpam-6054	222	9	∞∑	∞∑	NUM
ejpam-6054	222	10	n=0	n=0	PUNCT
ejpam-6054	222	11	b[j	b[j	NOUN
ejpam-6054	222	12	]	]	PUNCT
ejpam-6054	222	13	n	n	PROPN
ejpam-6054	222	14	(	(	PUNCT
ejpam-6054	222	15	q1	q1	PROPN
ejpam-6054	222	16	,	,	PUNCT
ejpam-6054	222	17	q2	q2	NOUN
ejpam-6054	222	18	)	)	PUNCT
ejpam-6054	222	19	ξn	ξn	NOUN
ejpam-6054	222	20	n	n	NOUN
ejpam-6054	222	21	!	!	PUNCT
ejpam-6054	222	22	]	]	PUNCT
ejpam-6054	223	1	=	=	SYM
ejpam-6054	223	2	∂	∂	NUM
ejpam-6054	223	3	∂q2	∂q2	NOUN
ejpam-6054	223	4	[	[	PUNCT
ejpam-6054	223	5	eq1(e	eq1(e	PROPN
ejpam-6054	223	6	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	223	7	]	]	PUNCT
ejpam-6054	223	8	=	=	PUNCT
ejpam-6054	224	1	eq1(e	eq1(e	NUM
ejpam-6054	224	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	224	3	(	(	PUNCT
ejpam-6054	224	4	eξ	eξ	PROPN
ejpam-6054	224	5	−	−	PROPN
ejpam-6054	224	6	1)j	1)j	PROPN
ejpam-6054	224	7	.	.	PUNCT
ejpam-6054	225	1	recall	recall	VERB
ejpam-6054	225	2	that	that	SCONJ
ejpam-6054	225	3	the	the	DET
ejpam-6054	225	4	exponential	exponential	ADJ
ejpam-6054	225	5	generating	generating	NOUN
ejpam-6054	225	6	function	function	NOUN
ejpam-6054	225	7	of	of	ADP
ejpam-6054	225	8	j!s2(n	j!s2(n	PROPN
ejpam-6054	225	9	,	,	PUNCT
ejpam-6054	225	10	j	j	NOUN
ejpam-6054	225	11	)	)	PUNCT
ejpam-6054	225	12	is	be	AUX
ejpam-6054	225	13	:	:	PUNCT
ejpam-6054	225	14	(	(	PUNCT
ejpam-6054	225	15	eξ	eξ	INTJ
ejpam-6054	225	16	−	−	PROPN
ejpam-6054	225	17	1)j	1)j	NUM
ejpam-6054	225	18	=	=	PUNCT
ejpam-6054	226	1	∞∑	∞∑	PRON
ejpam-6054	226	2	n=0	n=0	NUM
ejpam-6054	226	3	j!s2(n	j!s2(n	NOUN
ejpam-6054	226	4	,	,	PUNCT
ejpam-6054	226	5	j	j	NOUN
ejpam-6054	226	6	)	)	PUNCT
ejpam-6054	226	7	ξn	ξn	PROPN
ejpam-6054	226	8	n	n	X
ejpam-6054	226	9	!	!	PUNCT
ejpam-6054	226	10	.	.	PUNCT
ejpam-6054	227	1	so	so	ADV
ejpam-6054	227	2	,	,	PUNCT
ejpam-6054	227	3	we	we	PRON
ejpam-6054	227	4	compute	compute	VERB
ejpam-6054	227	5	:	:	PUNCT
ejpam-6054	227	6	eq1(e	eq1(e	PROPN
ejpam-6054	227	7	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	227	8	(	(	PUNCT
ejpam-6054	227	9	eξ	eξ	NOUN
ejpam-6054	227	10	−	−	PROPN
ejpam-6054	227	11	1)j	1)j	NUM
ejpam-6054	227	12	=	=	PUNCT
ejpam-6054	228	1	[	[	PUNCT
ejpam-6054	228	2	∞∑	∞∑	NUM
ejpam-6054	228	3	n=0	n=0	NUM
ejpam-6054	228	4	b[j	b[j	NOUN
ejpam-6054	228	5	]	]	PUNCT
ejpam-6054	228	6	n	n	PROPN
ejpam-6054	228	7	(	(	PUNCT
ejpam-6054	228	8	q1	q1	PROPN
ejpam-6054	228	9	,	,	PUNCT
ejpam-6054	228	10	q2	q2	NOUN
ejpam-6054	228	11	)	)	PUNCT
ejpam-6054	228	12	ξn	ξn	NOUN
ejpam-6054	228	13	n	n	NOUN
ejpam-6054	228	14	!	!	PUNCT
ejpam-6054	229	1	]	]	X
ejpam-6054	229	2	[	[	PUNCT
ejpam-6054	229	3	∞∑	∞∑	PROPN
ejpam-6054	229	4	m=0	m=0	PROPN
ejpam-6054	229	5	j!s2(m	j!s2(m	PROPN
ejpam-6054	229	6	,	,	PUNCT
ejpam-6054	229	7	j	j	PROPN
ejpam-6054	229	8	)	)	PUNCT
ejpam-6054	229	9	ξm	ξm	PROPN
ejpam-6054	229	10	m	m	NOUN
ejpam-6054	229	11	!	!	PUNCT
ejpam-6054	229	12	]	]	PUNCT
ejpam-6054	230	1	=	=	PUNCT
ejpam-6054	231	1	∞∑	∞∑	NUM
ejpam-6054	231	2	n=0	n=0	NUM
ejpam-6054	231	3	n∑	n∑	NOUN
ejpam-6054	231	4	k=0	k=0	PROPN
ejpam-6054	231	5	(	(	PUNCT
ejpam-6054	231	6	n	n	X
ejpam-6054	231	7	k	k	NOUN
ejpam-6054	231	8	)	)	PUNCT
ejpam-6054	231	9	b	b	PROPN
ejpam-6054	232	1	[	[	X
ejpam-6054	232	2	j	j	X
ejpam-6054	232	3	]	]	X
ejpam-6054	232	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	232	5	,	,	PUNCT
ejpam-6054	232	6	q2)j!s2(k	q2)j!s2(k	PROPN
ejpam-6054	232	7	,	,	PUNCT
ejpam-6054	232	8	j	j	PROPN
ejpam-6054	232	9	)	)	PUNCT
ejpam-6054	232	10	ξn	ξn	PROPN
ejpam-6054	232	11	n	n	X
ejpam-6054	232	12	!	!	PUNCT
ejpam-6054	232	13	.	.	PUNCT
ejpam-6054	233	1	s.	s.	PROPN
ejpam-6054	233	2	a.	a.	PROPN
ejpam-6054	233	3	wani	wani	PROPN
ejpam-6054	233	4	et	et	PROPN
ejpam-6054	233	5	al	al	PROPN
ejpam-6054	233	6	.	.	PUNCT
ejpam-6054	233	7	/	/	SYM
ejpam-6054	233	8	eur	eur	PROPN
ejpam-6054	233	9	.	.	PUNCT
ejpam-6054	234	1	j.	j.	PROPN
ejpam-6054	234	2	pure	pure	PROPN
ejpam-6054	234	3	appl	appl	PROPN
ejpam-6054	234	4	.	.	PROPN
ejpam-6054	234	5	math	math	PROPN
ejpam-6054	234	6	,	,	PUNCT
ejpam-6054	234	7	18	18	NUM
ejpam-6054	234	8	(	(	PUNCT
ejpam-6054	234	9	3	3	NUM
ejpam-6054	234	10	)	)	PUNCT
ejpam-6054	234	11	(	(	PUNCT
ejpam-6054	234	12	2025	2025	NUM
ejpam-6054	234	13	)	)	PUNCT
ejpam-6054	234	14	,	,	PUNCT
ejpam-6054	234	15	6054	6054	NUM
ejpam-6054	234	16	10	10	NUM
ejpam-6054	234	17	of	of	ADP
ejpam-6054	234	18	16	16	NUM
ejpam-6054	234	19	equating	equate	VERB
ejpam-6054	234	20	coefficients	coefficient	NOUN
ejpam-6054	234	21	of	of	ADP
ejpam-6054	234	22	ξn	ξn	PROPN
ejpam-6054	234	23	n	n	X
ejpam-6054	234	24	!	!	PUNCT
ejpam-6054	234	25	yields	yield	NOUN
ejpam-6054	234	26	:	:	PUNCT
ejpam-6054	234	27	∂	∂	NUM
ejpam-6054	234	28	∂q2	∂q2	NOUN
ejpam-6054	234	29	b[j	b[j	NOUN
ejpam-6054	234	30	]	]	X
ejpam-6054	234	31	n	n	PROPN
ejpam-6054	234	32	(	(	PUNCT
ejpam-6054	234	33	q1	q1	PROPN
ejpam-6054	234	34	,	,	PUNCT
ejpam-6054	234	35	q2	q2	NOUN
ejpam-6054	234	36	)	)	PUNCT
ejpam-6054	235	1	=	=	SYM
ejpam-6054	236	1	n∑	n∑	NOUN
ejpam-6054	236	2	k=0	k=0	PROPN
ejpam-6054	236	3	(	(	PUNCT
ejpam-6054	236	4	n	n	X
ejpam-6054	236	5	k	k	NOUN
ejpam-6054	236	6	)	)	PUNCT
ejpam-6054	236	7	b	b	PROPN
ejpam-6054	237	1	[	[	X
ejpam-6054	237	2	j	j	X
ejpam-6054	237	3	]	]	X
ejpam-6054	237	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	237	5	,	,	PUNCT
ejpam-6054	237	6	q2)j!s2(k	q2)j!s2(k	PROPN
ejpam-6054	237	7	,	,	PUNCT
ejpam-6054	237	8	j	j	PROPN
ejpam-6054	237	9	)	)	PUNCT
ejpam-6054	237	10	.	.	PUNCT
ejpam-6054	238	1	theorem	theorem	VERB
ejpam-6054	238	2	6	6	NUM
ejpam-6054	238	3	.	.	PUNCT
ejpam-6054	238	4	for	for	ADP
ejpam-6054	238	5	n	n	PRON
ejpam-6054	238	6	≥	≥	NOUN
ejpam-6054	238	7	0	0	NUM
ejpam-6054	238	8	,	,	PUNCT
ejpam-6054	238	9	let	let	VERB
ejpam-6054	238	10	{	{	PUNCT
ejpam-6054	238	11	b	b	X
ejpam-6054	238	12	[	[	X
ejpam-6054	238	13	j	j	X
ejpam-6054	238	14	]	]	X
ejpam-6054	238	15	n	n	PROPN
ejpam-6054	238	16	(	(	PUNCT
ejpam-6054	238	17	q1	q1	PROPN
ejpam-6054	238	18	,	,	PUNCT
ejpam-6054	238	19	q2	q2	NOUN
ejpam-6054	238	20	)	)	PUNCT
ejpam-6054	238	21	}	}	PUNCT
ejpam-6054	238	22	n≥0	n≥0	NOUN
ejpam-6054	238	23	be	be	VERB
ejpam-6054	238	24	the	the	DET
ejpam-6054	238	25	sequences	sequence	NOUN
ejpam-6054	238	26	of	of	ADP
ejpam-6054	238	27	2d	2d	NUM
ejpam-6054	238	28	bell	bell	NOUN
ejpam-6054	238	29	polynomials	polynomial	NOUN
ejpam-6054	238	30	in	in	ADP
ejpam-6054	238	31	the	the	DET
ejpam-6054	238	32	variable	variable	ADJ
ejpam-6054	238	33	q1	q1	PROPN
ejpam-6054	238	34	,	,	PUNCT
ejpam-6054	238	35	q2	q2	NOUN
ejpam-6054	238	36	and	and	CCONJ
ejpam-6054	238	37	q3	q3	PROPN
ejpam-6054	238	38	,	,	PUNCT
ejpam-6054	238	39	they	they	PRON
ejpam-6054	238	40	satisfy	satisfy	VERB
ejpam-6054	238	41	the	the	DET
ejpam-6054	238	42	following	follow	VERB
ejpam-6054	238	43	relation	relation	NOUN
ejpam-6054	238	44	n∑	n∑	PROPN
ejpam-6054	239	1	k=0	k=0	PROPN
ejpam-6054	240	1	(	(	PUNCT
ejpam-6054	240	2	n	n	X
ejpam-6054	240	3	k	k	NOUN
ejpam-6054	240	4	)	)	PUNCT
ejpam-6054	241	1	[	[	PUNCT
ejpam-6054	241	2	b	b	X
ejpam-6054	241	3	[	[	X
ejpam-6054	241	4	j	j	X
ejpam-6054	241	5	]	]	X
ejpam-6054	241	6	k	k	PROPN
ejpam-6054	241	7	(	(	PUNCT
ejpam-6054	241	8	q1	q1	PROPN
ejpam-6054	241	9	+	+	CCONJ
ejpam-6054	241	10	q3	q3	PROPN
ejpam-6054	241	11	,	,	PUNCT
ejpam-6054	241	12	q2)b	q2)b	NOUN
ejpam-6054	241	13	[	[	X
ejpam-6054	241	14	j	j	X
ejpam-6054	241	15	]	]	X
ejpam-6054	241	16	n−k(2q2)−	n−k(2q2)−	PROPN
ejpam-6054	241	17	b	b	X
ejpam-6054	242	1	[	[	X
ejpam-6054	242	2	j	j	X
ejpam-6054	242	3	]	]	X
ejpam-6054	242	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	242	5	,	,	PUNCT
ejpam-6054	242	6	q2)b	q2)b	NOUN
ejpam-6054	242	7	[	[	X
ejpam-6054	242	8	j	j	X
ejpam-6054	242	9	]	]	X
ejpam-6054	242	10	n	n	PROPN
ejpam-6054	242	11	(	(	PUNCT
ejpam-6054	242	12	q3	q3	PROPN
ejpam-6054	242	13	,	,	PUNCT
ejpam-6054	242	14	q2	q2	NOUN
ejpam-6054	242	15	)	)	PUNCT
ejpam-6054	242	16	]	]	PUNCT
ejpam-6054	243	1	=	=	PUNCT
ejpam-6054	243	2	0	0	X
ejpam-6054	243	3	.	.	PUNCT
ejpam-6054	244	1	proof	proof	NOUN
ejpam-6054	244	2	.	.	PUNCT
ejpam-6054	245	1	let	let	VERB
ejpam-6054	245	2	’s	’s	NOUN
ejpam-6054	245	3	consider	consider	VERB
ejpam-6054	245	4	the	the	DET
ejpam-6054	245	5	following	follow	VERB
ejpam-6054	245	6	expressions	expression	NOUN
ejpam-6054	245	7	eq1(e	eq1(e	PROPN
ejpam-6054	245	8	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	245	9	=	=	PUNCT
ejpam-6054	246	1	∞∑	∞∑	ADJ
ejpam-6054	246	2	n=0	n=0	NUM
ejpam-6054	246	3	b[j	b[j	NOUN
ejpam-6054	246	4	]	]	PUNCT
ejpam-6054	246	5	n	n	PROPN
ejpam-6054	246	6	(	(	PUNCT
ejpam-6054	246	7	q1	q1	PROPN
ejpam-6054	246	8	,	,	PUNCT
ejpam-6054	246	9	q2	q2	NOUN
ejpam-6054	246	10	)	)	PUNCT
ejpam-6054	246	11	ξn	ξn	PROPN
ejpam-6054	246	12	n	n	X
ejpam-6054	246	13	!	!	PUNCT
ejpam-6054	246	14	(	(	PUNCT
ejpam-6054	246	15	15	15	NUM
ejpam-6054	246	16	)	)	PUNCT
ejpam-6054	246	17	and	and	CCONJ
ejpam-6054	246	18	eq3(e	eq3(e	VERB
ejpam-6054	246	19	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	246	20	=	=	PUNCT
ejpam-6054	246	21	∞∑	∞∑	PRON
ejpam-6054	246	22	n=0	n=0	NUM
ejpam-6054	246	23	b[j	b[j	NOUN
ejpam-6054	246	24	]	]	PUNCT
ejpam-6054	246	25	n	n	PROPN
ejpam-6054	246	26	(	(	PUNCT
ejpam-6054	246	27	q3	q3	PROPN
ejpam-6054	246	28	,	,	PUNCT
ejpam-6054	246	29	q2	q2	NOUN
ejpam-6054	246	30	)	)	PUNCT
ejpam-6054	246	31	ξn	ξn	PROPN
ejpam-6054	246	32	n	n	X
ejpam-6054	246	33	!	!	PUNCT
ejpam-6054	246	34	.	.	PUNCT
ejpam-6054	247	1	(	(	PUNCT
ejpam-6054	247	2	16	16	NUM
ejpam-6054	247	3	)	)	PUNCT
ejpam-6054	247	4	from	from	ADP
ejpam-6054	247	5	(	(	PUNCT
ejpam-6054	247	6	15	15	NUM
ejpam-6054	247	7	)	)	PUNCT
ejpam-6054	247	8	and	and	CCONJ
ejpam-6054	247	9	(	(	PUNCT
ejpam-6054	247	10	16	16	NUM
ejpam-6054	247	11	)	)	PUNCT
ejpam-6054	247	12	,	,	PUNCT
ejpam-6054	247	13	we	we	PRON
ejpam-6054	247	14	have	have	VERB
ejpam-6054	247	15	e(q1+q3)(eξ−1)+q2(eξ−1)je2q2(e	e(q1+q3)(eξ−1)+q2(eξ−1)je2q2(e	NOUN
ejpam-6054	247	16	ξ−1)j	ξ−1)j	NOUN
ejpam-6054	247	17	=	=	PUNCT
ejpam-6054	247	18	(	(	PUNCT
ejpam-6054	247	19	∞∑	∞∑	NUM
ejpam-6054	247	20	n=0	n=0	NUM
ejpam-6054	247	21	b[j	b[j	NOUN
ejpam-6054	247	22	]	]	PUNCT
ejpam-6054	247	23	n	n	PROPN
ejpam-6054	247	24	(	(	PUNCT
ejpam-6054	247	25	q1	q1	PROPN
ejpam-6054	247	26	,	,	PUNCT
ejpam-6054	247	27	q2	q2	NOUN
ejpam-6054	247	28	)	)	PUNCT
ejpam-6054	247	29	ξn	ξn	PROPN
ejpam-6054	247	30	n	n	X
ejpam-6054	247	31	!	!	PUNCT
ejpam-6054	247	32	)	)	PUNCT
ejpam-6054	248	1	(	(	PUNCT
ejpam-6054	248	2	∞∑	∞∑	NUM
ejpam-6054	248	3	n=0	n=0	NUM
ejpam-6054	248	4	b[j	b[j	NOUN
ejpam-6054	248	5	]	]	PUNCT
ejpam-6054	248	6	n	n	PROPN
ejpam-6054	248	7	(	(	PUNCT
ejpam-6054	248	8	q3	q3	PROPN
ejpam-6054	248	9	,	,	PUNCT
ejpam-6054	248	10	q2	q2	NOUN
ejpam-6054	248	11	)	)	PUNCT
ejpam-6054	248	12	ξn	ξn	PROPN
ejpam-6054	248	13	n	n	X
ejpam-6054	248	14	!	!	PUNCT
ejpam-6054	248	15	)	)	PUNCT
ejpam-6054	249	1	(	(	PUNCT
ejpam-6054	249	2	∞∑	∞∑	NUM
ejpam-6054	249	3	n=0	n=0	NUM
ejpam-6054	249	4	b[j	b[j	NOUN
ejpam-6054	249	5	]	]	PUNCT
ejpam-6054	249	6	n	n	PROPN
ejpam-6054	249	7	(	(	PUNCT
ejpam-6054	249	8	q1	q1	PROPN
ejpam-6054	249	9	+	+	CCONJ
ejpam-6054	249	10	q3	q3	PROPN
ejpam-6054	249	11	,	,	PUNCT
ejpam-6054	249	12	q2	q2	NOUN
ejpam-6054	249	13	)	)	PUNCT
ejpam-6054	249	14	ξn	ξn	PROPN
ejpam-6054	249	15	n	n	X
ejpam-6054	249	16	!	!	PUNCT
ejpam-6054	249	17	)	)	PUNCT
ejpam-6054	250	1	(	(	PUNCT
ejpam-6054	250	2	∞∑	∞∑	NUM
ejpam-6054	250	3	n=0	n=0	NUM
ejpam-6054	250	4	b[j	b[j	NOUN
ejpam-6054	250	5	]	]	PUNCT
ejpam-6054	250	6	n	n	CCONJ
ejpam-6054	250	7	(	(	PUNCT
ejpam-6054	250	8	0	0	NUM
ejpam-6054	250	9	,	,	PUNCT
ejpam-6054	250	10	2q2	2q2	NUM
ejpam-6054	250	11	)	)	PUNCT
ejpam-6054	250	12	ξn	ξn	PROPN
ejpam-6054	250	13	n	n	X
ejpam-6054	250	14	!	!	PUNCT
ejpam-6054	250	15	)	)	PUNCT
ejpam-6054	251	1	=	=	PUNCT
ejpam-6054	251	2	(	(	PUNCT
ejpam-6054	251	3	∞∑	∞∑	NUM
ejpam-6054	251	4	n=0	n=0	NUM
ejpam-6054	251	5	b[j	b[j	NOUN
ejpam-6054	251	6	]	]	PUNCT
ejpam-6054	251	7	n	n	PROPN
ejpam-6054	251	8	(	(	PUNCT
ejpam-6054	251	9	q1	q1	PROPN
ejpam-6054	251	10	,	,	PUNCT
ejpam-6054	251	11	q2	q2	NOUN
ejpam-6054	251	12	)	)	PUNCT
ejpam-6054	251	13	ξn	ξn	PROPN
ejpam-6054	251	14	n	n	X
ejpam-6054	251	15	!	!	PUNCT
ejpam-6054	251	16	)	)	PUNCT
ejpam-6054	252	1	(	(	PUNCT
ejpam-6054	252	2	∞∑	∞∑	NUM
ejpam-6054	252	3	n=0	n=0	NUM
ejpam-6054	252	4	b[j	b[j	NOUN
ejpam-6054	252	5	]	]	PUNCT
ejpam-6054	252	6	n	n	PROPN
ejpam-6054	252	7	(	(	PUNCT
ejpam-6054	252	8	q3	q3	PROPN
ejpam-6054	252	9	,	,	PUNCT
ejpam-6054	252	10	q2	q2	NOUN
ejpam-6054	252	11	)	)	PUNCT
ejpam-6054	252	12	ξn	ξn	PROPN
ejpam-6054	252	13	n	n	X
ejpam-6054	252	14	!	!	PUNCT
ejpam-6054	252	15	)	)	PUNCT
ejpam-6054	253	1	∞∑	∞∑	DET
ejpam-6054	253	2	n=0	n=0	NUM
ejpam-6054	253	3	n∑	n∑	NOUN
ejpam-6054	253	4	k=0	k=0	PROPN
ejpam-6054	253	5	(	(	PUNCT
ejpam-6054	253	6	n	n	X
ejpam-6054	253	7	k	k	NOUN
ejpam-6054	253	8	)	)	PUNCT
ejpam-6054	253	9	b	b	PROPN
ejpam-6054	254	1	[	[	X
ejpam-6054	254	2	j	j	X
ejpam-6054	254	3	]	]	X
ejpam-6054	254	4	k	k	PROPN
ejpam-6054	254	5	(	(	PUNCT
ejpam-6054	254	6	q1	q1	PROPN
ejpam-6054	254	7	+	+	CCONJ
ejpam-6054	254	8	q3	q3	PROPN
ejpam-6054	254	9	,	,	PUNCT
ejpam-6054	254	10	q2)b	q2)b	NOUN
ejpam-6054	254	11	[	[	X
ejpam-6054	254	12	j	j	X
ejpam-6054	254	13	]	]	X
ejpam-6054	254	14	n−k(2q2	n−k(2q2	NOUN
ejpam-6054	254	15	)	)	PUNCT
ejpam-6054	254	16	ξn	ξn	NOUN
ejpam-6054	254	17	n	n	NOUN
ejpam-6054	254	18	!	!	PUNCT
ejpam-6054	254	19	=	=	NOUN
ejpam-6054	255	1	∞∑	∞∑	DET
ejpam-6054	255	2	n=0	n=0	NUM
ejpam-6054	255	3	n∑	n∑	NOUN
ejpam-6054	255	4	k=0	k=0	PROPN
ejpam-6054	255	5	(	(	PUNCT
ejpam-6054	255	6	n	n	X
ejpam-6054	255	7	k	k	NOUN
ejpam-6054	255	8	)	)	PUNCT
ejpam-6054	255	9	b	b	PROPN
ejpam-6054	256	1	[	[	X
ejpam-6054	256	2	j	j	X
ejpam-6054	256	3	]	]	X
ejpam-6054	256	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	256	5	,	,	PUNCT
ejpam-6054	256	6	q2)b	q2)b	NOUN
ejpam-6054	256	7	[	[	X
ejpam-6054	256	8	j	j	X
ejpam-6054	256	9	]	]	X
ejpam-6054	256	10	n	n	PROPN
ejpam-6054	256	11	(	(	PUNCT
ejpam-6054	256	12	q3	q3	PROPN
ejpam-6054	256	13	,	,	PUNCT
ejpam-6054	256	14	q2	q2	NOUN
ejpam-6054	256	15	)	)	PUNCT
ejpam-6054	256	16	ξn	ξn	PROPN
ejpam-6054	256	17	n	n	NOUN
ejpam-6054	256	18	!	!	PUNCT
ejpam-6054	257	1	n∑	n∑	PUNCT
ejpam-6054	257	2	k=0	k=0	PROPN
ejpam-6054	257	3	(	(	PUNCT
ejpam-6054	257	4	n	n	X
ejpam-6054	257	5	k	k	NOUN
ejpam-6054	257	6	)	)	PUNCT
ejpam-6054	257	7	b	b	PROPN
ejpam-6054	258	1	[	[	X
ejpam-6054	258	2	j	j	X
ejpam-6054	258	3	]	]	X
ejpam-6054	258	4	k	k	PROPN
ejpam-6054	258	5	(	(	PUNCT
ejpam-6054	258	6	q1	q1	PROPN
ejpam-6054	258	7	+	+	CCONJ
ejpam-6054	258	8	q3	q3	PROPN
ejpam-6054	258	9	,	,	PUNCT
ejpam-6054	258	10	q2)b	q2)b	NOUN
ejpam-6054	258	11	[	[	X
ejpam-6054	258	12	j	j	X
ejpam-6054	258	13	]	]	X
ejpam-6054	258	14	n−k(2q2	n−k(2q2	PUNCT
ejpam-6054	258	15	)	)	PUNCT
ejpam-6054	258	16	=	=	SYM
ejpam-6054	259	1	n∑	n∑	NOUN
ejpam-6054	259	2	k=0	k=0	PROPN
ejpam-6054	259	3	(	(	PUNCT
ejpam-6054	259	4	n	n	X
ejpam-6054	259	5	k	k	NOUN
ejpam-6054	259	6	)	)	PUNCT
ejpam-6054	259	7	b	b	PROPN
ejpam-6054	260	1	[	[	X
ejpam-6054	260	2	j	j	X
ejpam-6054	260	3	]	]	X
ejpam-6054	260	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	260	5	,	,	PUNCT
ejpam-6054	260	6	q2)b	q2)b	NOUN
ejpam-6054	260	7	[	[	X
ejpam-6054	260	8	j	j	X
ejpam-6054	260	9	]	]	X
ejpam-6054	260	10	n	n	PROPN
ejpam-6054	260	11	(	(	PUNCT
ejpam-6054	260	12	q3	q3	PROPN
ejpam-6054	260	13	,	,	PUNCT
ejpam-6054	260	14	q2	q2	NOUN
ejpam-6054	260	15	)	)	PUNCT
ejpam-6054	260	16	.	.	PUNCT
ejpam-6054	261	1	therefore	therefore	ADV
ejpam-6054	261	2	,	,	PUNCT
ejpam-6054	261	3	n∑	n∑	PROPN
ejpam-6054	261	4	k=0	k=0	PROPN
ejpam-6054	261	5	(	(	PUNCT
ejpam-6054	261	6	n	n	X
ejpam-6054	261	7	k	k	NOUN
ejpam-6054	261	8	)	)	PUNCT
ejpam-6054	261	9	[	[	PUNCT
ejpam-6054	261	10	b	b	X
ejpam-6054	261	11	[	[	X
ejpam-6054	261	12	j	j	X
ejpam-6054	261	13	]	]	X
ejpam-6054	261	14	k	k	PROPN
ejpam-6054	261	15	(	(	PUNCT
ejpam-6054	261	16	q1	q1	PROPN
ejpam-6054	261	17	+	+	CCONJ
ejpam-6054	261	18	q3	q3	PROPN
ejpam-6054	261	19	,	,	PUNCT
ejpam-6054	261	20	q2)b	q2)b	NOUN
ejpam-6054	261	21	[	[	X
ejpam-6054	261	22	j	j	X
ejpam-6054	261	23	]	]	X
ejpam-6054	261	24	n−k(2q2)−	n−k(2q2)−	PROPN
ejpam-6054	261	25	b	b	X
ejpam-6054	262	1	[	[	X
ejpam-6054	262	2	j	j	X
ejpam-6054	262	3	]	]	X
ejpam-6054	262	4	n−k(q1	n−k(q1	PROPN
ejpam-6054	262	5	,	,	PUNCT
ejpam-6054	262	6	q2)b	q2)b	NOUN
ejpam-6054	262	7	[	[	X
ejpam-6054	262	8	j	j	X
ejpam-6054	262	9	]	]	X
ejpam-6054	262	10	n	n	PROPN
ejpam-6054	262	11	(	(	PUNCT
ejpam-6054	262	12	q3	q3	PROPN
ejpam-6054	262	13	,	,	PUNCT
ejpam-6054	262	14	q2	q2	NOUN
ejpam-6054	262	15	)	)	PUNCT
ejpam-6054	262	16	]	]	PUNCT
ejpam-6054	263	1	=	=	PUNCT
ejpam-6054	263	2	0	0	X
ejpam-6054	263	3	.	.	PUNCT
ejpam-6054	264	1	s.	s.	PROPN
ejpam-6054	264	2	a.	a.	PROPN
ejpam-6054	264	3	wani	wani	PROPN
ejpam-6054	264	4	et	et	PROPN
ejpam-6054	264	5	al	al	PROPN
ejpam-6054	264	6	.	.	PUNCT
ejpam-6054	264	7	/	/	SYM
ejpam-6054	264	8	eur	eur	PROPN
ejpam-6054	264	9	.	.	PUNCT
ejpam-6054	265	1	j.	j.	PROPN
ejpam-6054	265	2	pure	pure	PROPN
ejpam-6054	265	3	appl	appl	PROPN
ejpam-6054	265	4	.	.	PROPN
ejpam-6054	265	5	math	math	PROPN
ejpam-6054	265	6	,	,	PUNCT
ejpam-6054	265	7	18	18	NUM
ejpam-6054	265	8	(	(	PUNCT
ejpam-6054	265	9	3	3	NUM
ejpam-6054	265	10	)	)	PUNCT
ejpam-6054	265	11	(	(	PUNCT
ejpam-6054	265	12	2025	2025	NUM
ejpam-6054	265	13	)	)	PUNCT
ejpam-6054	265	14	,	,	PUNCT
ejpam-6054	265	15	6054	6054	NUM
ejpam-6054	265	16	11	11	NUM
ejpam-6054	265	17	of	of	ADP
ejpam-6054	265	18	16	16	NUM
ejpam-6054	265	19	3	3	NUM
ejpam-6054	265	20	.	.	PUNCT
ejpam-6054	266	1	the	the	DET
ejpam-6054	266	2	2d	2d	NUM
ejpam-6054	266	3	bell	bell	NOUN
ejpam-6054	266	4	-	-	PUNCT
ejpam-6054	266	5	based	base	VERB
ejpam-6054	266	6	stirling	stirling	NOUN
ejpam-6054	266	7	polynomials	polynomial	NOUN
ejpam-6054	266	8	of	of	ADP
ejpam-6054	266	9	the	the	DET
ejpam-6054	266	10	second	second	ADJ
ejpam-6054	266	11	kind	kind	NOUN
ejpam-6054	266	12	definition	definition	NOUN
ejpam-6054	266	13	1	1	NUM
ejpam-6054	266	14	.	.	PUNCT
ejpam-6054	267	1	∞∑	∞∑	NUM
ejpam-6054	267	2	n=0	n=0	ADJ
ejpam-6054	267	3	bs	bs	NOUN
ejpam-6054	267	4	[	[	X
ejpam-6054	267	5	j	j	X
ejpam-6054	267	6	]	]	X
ejpam-6054	267	7	2	2	NUM
ejpam-6054	267	8	(	(	PUNCT
ejpam-6054	267	9	n	n	CCONJ
ejpam-6054	267	10	,	,	PUNCT
ejpam-6054	267	11	ϵ	ϵ	X
ejpam-6054	267	12	;	;	PUNCT
ejpam-6054	267	13	q1	q1	PROPN
ejpam-6054	267	14	,	,	PUNCT
ejpam-6054	267	15	q2	q2	NOUN
ejpam-6054	267	16	)	)	PUNCT
ejpam-6054	267	17	ξn	ξn	PROPN
ejpam-6054	267	18	n	n	NOUN
ejpam-6054	267	19	!	!	PUNCT
ejpam-6054	267	20	=	=	PUNCT
ejpam-6054	268	1	(	(	PUNCT
ejpam-6054	268	2	eξ	eξ	PROPN
ejpam-6054	268	3	−	−	PROPN
ejpam-6054	268	4	1)ϵ	1)ϵ	NUM
ejpam-6054	268	5	ϵ	ϵ	X
ejpam-6054	268	6	!	!	PUNCT
ejpam-6054	269	1	eq1(e	eq1(e	PROPN
ejpam-6054	269	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	269	3	.	.	PUNCT
ejpam-6054	270	1	(	(	PUNCT
ejpam-6054	270	2	17	17	NUM
ejpam-6054	270	3	)	)	PUNCT
ejpam-6054	270	4	this	this	DET
ejpam-6054	270	5	description	description	NOUN
ejpam-6054	270	6	serves	serve	VERB
ejpam-6054	270	7	as	as	ADP
ejpam-6054	270	8	a	a	DET
ejpam-6054	270	9	foundational	foundational	ADJ
ejpam-6054	270	10	concept	concept	NOUN
ejpam-6054	270	11	,	,	PUNCT
ejpam-6054	270	12	establishing	establish	VERB
ejpam-6054	270	13	the	the	DET
ejpam-6054	270	14	basis	basis	NOUN
ejpam-6054	270	15	for	for	ADP
ejpam-6054	270	16	additional	additional	ADJ
ejpam-6054	270	17	exploration	exploration	NOUN
ejpam-6054	270	18	and	and	CCONJ
ejpam-6054	270	19	comprehension	comprehension	NOUN
ejpam-6054	270	20	of	of	ADP
ejpam-6054	270	21	these	these	DET
ejpam-6054	270	22	polynomials	polynomial	NOUN
ejpam-6054	270	23	’	'	PUNCT
ejpam-6054	270	24	important	important	ADJ
ejpam-6054	270	25	implications	implication	NOUN
ejpam-6054	270	26	and	and	CCONJ
ejpam-6054	270	27	possible	possible	ADJ
ejpam-6054	270	28	applications	application	NOUN
ejpam-6054	270	29	in	in	ADP
ejpam-6054	270	30	the	the	DET
ejpam-6054	270	31	broader	broad	ADJ
ejpam-6054	270	32	realm	realm	NOUN
ejpam-6054	270	33	of	of	ADP
ejpam-6054	270	34	mathematics	mathematic	NOUN
ejpam-6054	270	35	.	.	PUNCT
ejpam-6054	271	1	for	for	ADP
ejpam-6054	271	2	ϵ	ϵ	PROPN
ejpam-6054	271	3	,	,	PUNCT
ejpam-6054	271	4	j	j	PROPN
ejpam-6054	271	5	=	=	SYM
ejpam-6054	271	6	2	2	NUM
ejpam-6054	271	7	,	,	PUNCT
ejpam-6054	271	8	the	the	DET
ejpam-6054	271	9	first	first	ADJ
ejpam-6054	271	10	four	four	NUM
ejpam-6054	271	11	two	two	NUM
ejpam-6054	271	12	-	-	PUNCT
ejpam-6054	271	13	variable	variable	NOUN
ejpam-6054	271	14	bell	bell	NOUN
ejpam-6054	271	15	-	-	PUNCT
ejpam-6054	271	16	based	base	VERB
ejpam-6054	271	17	stirling	stirling	NOUN
ejpam-6054	271	18	polynomials	polynomial	NOUN
ejpam-6054	271	19	are	be	AUX
ejpam-6054	271	20	as	as	SCONJ
ejpam-6054	271	21	follows	follow	VERB
ejpam-6054	271	22	:	:	PUNCT
ejpam-6054	271	23	bs	bs	PROPN
ejpam-6054	272	1	[	[	X
ejpam-6054	272	2	2	2	NUM
ejpam-6054	272	3	]	]	SYM
ejpam-6054	272	4	2	2	NUM
ejpam-6054	272	5	(	(	PUNCT
ejpam-6054	272	6	0	0	NUM
ejpam-6054	272	7	,	,	PUNCT
ejpam-6054	272	8	2	2	NUM
ejpam-6054	272	9	;	;	PUNCT
ejpam-6054	272	10	q1	q1	PROPN
ejpam-6054	272	11	,	,	PUNCT
ejpam-6054	272	12	q2	q2	NOUN
ejpam-6054	272	13	)	)	PUNCT
ejpam-6054	272	14	=	=	SYM
ejpam-6054	272	15	1	1	NUM
ejpam-6054	272	16	2	2	NUM
ejpam-6054	272	17	,	,	PUNCT
ejpam-6054	272	18	bs	bs	X
ejpam-6054	273	1	[	[	X
ejpam-6054	273	2	2	2	NUM
ejpam-6054	273	3	]	]	SYM
ejpam-6054	273	4	2	2	NUM
ejpam-6054	273	5	(	(	PUNCT
ejpam-6054	273	6	1	1	NUM
ejpam-6054	273	7	,	,	PUNCT
ejpam-6054	273	8	2	2	NUM
ejpam-6054	273	9	;	;	PUNCT
ejpam-6054	273	10	q1	q1	PROPN
ejpam-6054	273	11	,	,	PUNCT
ejpam-6054	273	12	q2	q2	NOUN
ejpam-6054	273	13	)	)	PUNCT
ejpam-6054	273	14	=	=	SYM
ejpam-6054	273	15	1	1	NUM
ejpam-6054	273	16	2	2	NUM
ejpam-6054	273	17	q1	q1	NOUN
ejpam-6054	273	18	+	+	CCONJ
ejpam-6054	273	19	1	1	NUM
ejpam-6054	273	20	2	2	NUM
ejpam-6054	273	21	,	,	PUNCT
ejpam-6054	273	22	bs	bs	X
ejpam-6054	274	1	[	[	X
ejpam-6054	274	2	2	2	NUM
ejpam-6054	274	3	]	]	SYM
ejpam-6054	274	4	2	2	NUM
ejpam-6054	274	5	(	(	PUNCT
ejpam-6054	274	6	2	2	NUM
ejpam-6054	274	7	,	,	PUNCT
ejpam-6054	274	8	2	2	NUM
ejpam-6054	274	9	;	;	PUNCT
ejpam-6054	274	10	q1	q1	PROPN
ejpam-6054	274	11	,	,	PUNCT
ejpam-6054	274	12	q2	q2	NOUN
ejpam-6054	274	13	)	)	PUNCT
ejpam-6054	274	14	=	=	SYM
ejpam-6054	274	15	1	1	NUM
ejpam-6054	274	16	2	2	NUM
ejpam-6054	274	17	q21	q21	NOUN
ejpam-6054	274	18	+	+	CCONJ
ejpam-6054	274	19	3	3	NUM
ejpam-6054	274	20	2	2	NUM
ejpam-6054	274	21	q1	q1	NOUN
ejpam-6054	274	22	+	+	CCONJ
ejpam-6054	274	23	q2	q2	NOUN
ejpam-6054	274	24	+	+	CCONJ
ejpam-6054	274	25	7	7	NUM
ejpam-6054	274	26	12	12	NUM
ejpam-6054	274	27	,	,	PUNCT
ejpam-6054	274	28	bs	bs	PROPN
ejpam-6054	275	1	[	[	X
ejpam-6054	275	2	2	2	NUM
ejpam-6054	275	3	]	]	SYM
ejpam-6054	275	4	2	2	NUM
ejpam-6054	275	5	(	(	PUNCT
ejpam-6054	275	6	3	3	NUM
ejpam-6054	275	7	,	,	PUNCT
ejpam-6054	275	8	2	2	NUM
ejpam-6054	275	9	;	;	PUNCT
ejpam-6054	275	10	q1	q1	PROPN
ejpam-6054	275	11	,	,	PUNCT
ejpam-6054	275	12	q2	q2	NOUN
ejpam-6054	275	13	)	)	PUNCT
ejpam-6054	275	14	=	=	SYM
ejpam-6054	275	15	1	1	NUM
ejpam-6054	275	16	2	2	NUM
ejpam-6054	275	17	q31	q31	NOUN
ejpam-6054	275	18	+	+	NUM
ejpam-6054	275	19	3q21	3q21	NUM
ejpam-6054	276	1	+	+	CCONJ
ejpam-6054	276	2	3q1q2	3q1q2	ADJ
ejpam-6054	276	3	+	+	CCONJ
ejpam-6054	276	4	6q2	6q2	NUM
ejpam-6054	276	5	+	+	CCONJ
ejpam-6054	276	6	3	3	NUM
ejpam-6054	276	7	4	4	NUM
ejpam-6054	276	8	.	.	PUNCT
ejpam-6054	277	1	figure	figure	VERB
ejpam-6054	277	2	3	3	NUM
ejpam-6054	277	3	:	:	SYM
ejpam-6054	277	4	1	1	NUM
ejpam-6054	277	5	2	2	NUM
ejpam-6054	277	6	q21	q21	NOUN
ejpam-6054	277	7	+	+	CCONJ
ejpam-6054	277	8	3	3	NUM
ejpam-6054	277	9	2	2	NUM
ejpam-6054	277	10	q1	q1	NOUN
ejpam-6054	277	11	+	+	CCONJ
ejpam-6054	277	12	q2	q2	NOUN
ejpam-6054	277	13	+	+	CCONJ
ejpam-6054	277	14	7	7	NUM
ejpam-6054	277	15	12	12	NUM
ejpam-6054	277	16	figure	figure	NOUN
ejpam-6054	277	17	4	4	NUM
ejpam-6054	277	18	:	:	SYM
ejpam-6054	277	19	1	1	NUM
ejpam-6054	277	20	2	2	NUM
ejpam-6054	277	21	q31	q31	NOUN
ejpam-6054	277	22	+	+	NUM
ejpam-6054	277	23	3q21	3q21	NUM
ejpam-6054	278	1	+	+	CCONJ
ejpam-6054	278	2	3q1q2	3q1q2	ADJ
ejpam-6054	278	3	+	+	CCONJ
ejpam-6054	278	4	6q2	6q2	NUM
ejpam-6054	278	5	+	+	CCONJ
ejpam-6054	278	6	3	3	NUM
ejpam-6054	278	7	4	4	NUM
ejpam-6054	278	8	remark	remark	NOUN
ejpam-6054	278	9	1	1	NUM
ejpam-6054	278	10	.	.	PUNCT
ejpam-6054	279	1	the	the	DET
ejpam-6054	279	2	expression	expression	NOUN
ejpam-6054	279	3	given	give	VERB
ejpam-6054	279	4	by	by	ADP
ejpam-6054	279	5	(	(	PUNCT
ejpam-6054	279	6	17	17	NUM
ejpam-6054	279	7	)	)	PUNCT
ejpam-6054	279	8	yields	yield	VERB
ejpam-6054	279	9	a	a	DET
ejpam-6054	279	10	set	set	NOUN
ejpam-6054	279	11	of	of	ADP
ejpam-6054	279	12	polynomials	polynomial	NOUN
ejpam-6054	279	13	called	call	VERB
ejpam-6054	279	14	the	the	DET
ejpam-6054	279	15	bellstirling	bellstirle	VERB
ejpam-6054	279	16	polynomials	polynomial	NOUN
ejpam-6054	279	17	of	of	ADP
ejpam-6054	279	18	the	the	DET
ejpam-6054	279	19	second	second	ADJ
ejpam-6054	279	20	kind	kind	NOUN
ejpam-6054	279	21	when	when	SCONJ
ejpam-6054	279	22	we	we	PRON
ejpam-6054	279	23	substitute	substitute	VERB
ejpam-6054	279	24	q2	q2	NOUN
ejpam-6054	279	25	=	=	SYM
ejpam-6054	279	26	0	0	PROPN
ejpam-6054	279	27	.	.	PUNCT
ejpam-6054	280	1	this	this	DET
ejpam-6054	280	2	set	set	NOUN
ejpam-6054	280	3	of	of	ADP
ejpam-6054	280	4	polynomials	polynomial	NOUN
ejpam-6054	280	5	is	be	AUX
ejpam-6054	280	6	expressed	express	VERB
ejpam-6054	280	7	as	as	ADP
ejpam-6054	280	8	:	:	PUNCT
ejpam-6054	280	9	∞∑	∞∑	NUM
ejpam-6054	280	10	n=0	n=0	PROPN
ejpam-6054	280	11	bs2(n	bs2(n	PROPN
ejpam-6054	280	12	,	,	PUNCT
ejpam-6054	280	13	ϵ	ϵ	X
ejpam-6054	280	14	;	;	PUNCT
ejpam-6054	280	15	q1	q1	PROPN
ejpam-6054	280	16	)	)	PUNCT
ejpam-6054	280	17	ξn	ξn	PROPN
ejpam-6054	280	18	n	n	NOUN
ejpam-6054	280	19	!	!	PUNCT
ejpam-6054	281	1	=	=	PUNCT
ejpam-6054	281	2	(	(	PUNCT
ejpam-6054	281	3	eξ	eξ	PROPN
ejpam-6054	281	4	−	−	PROPN
ejpam-6054	281	5	1)ϵ	1)ϵ	NUM
ejpam-6054	281	6	ϵ	ϵ	X
ejpam-6054	281	7	!	!	PUNCT
ejpam-6054	282	1	eq1(e	eq1(e	PROPN
ejpam-6054	282	2	ξ−1	ξ−1	PROPN
ejpam-6054	282	3	)	)	PUNCT
ejpam-6054	282	4	.	.	PUNCT
ejpam-6054	283	1	remark	remark	PROPN
ejpam-6054	283	2	2	2	NUM
ejpam-6054	283	3	.	.	PUNCT
ejpam-6054	284	1	after	after	ADP
ejpam-6054	284	2	substituting	substitute	VERB
ejpam-6054	284	3	q1	q1	PROPN
ejpam-6054	284	4	=	=	SYM
ejpam-6054	284	5	q2	q2	PROPN
ejpam-6054	284	6	=	=	SYM
ejpam-6054	284	7	0	0	PUNCT
ejpam-6054	284	8	into	into	ADP
ejpam-6054	284	9	the	the	DET
ejpam-6054	284	10	expression	expression	NOUN
ejpam-6054	284	11	from	from	ADP
ejpam-6054	284	12	(	(	PUNCT
ejpam-6054	284	13	17	17	NUM
ejpam-6054	284	14	)	)	PUNCT
ejpam-6054	284	15	,	,	PUNCT
ejpam-6054	284	16	a	a	DET
ejpam-6054	284	17	group	group	NOUN
ejpam-6054	284	18	of	of	ADP
ejpam-6054	284	19	polynomials	polynomial	NOUN
ejpam-6054	284	20	called	call	VERB
ejpam-6054	284	21	the	the	DET
ejpam-6054	284	22	stirling	stirling	NOUN
ejpam-6054	284	23	numbers	number	NOUN
ejpam-6054	284	24	of	of	ADP
ejpam-6054	284	25	the	the	DET
ejpam-6054	284	26	second	second	ADJ
ejpam-6054	284	27	kind	kind	NOUN
ejpam-6054	284	28	,	,	PUNCT
ejpam-6054	284	29	as	as	SCONJ
ejpam-6054	284	30	shown	show	VERB
ejpam-6054	284	31	in	in	ADP
ejpam-6054	284	32	(	(	PUNCT
ejpam-6054	284	33	2	2	NUM
ejpam-6054	284	34	)	)	PUNCT
ejpam-6054	285	1	,	,	PUNCT
ejpam-6054	285	2	is	be	AUX
ejpam-6054	285	3	derived	derive	VERB
ejpam-6054	285	4	.	.	PUNCT
ejpam-6054	286	1	s.	s.	PROPN
ejpam-6054	286	2	a.	a.	PROPN
ejpam-6054	286	3	wani	wani	PROPN
ejpam-6054	286	4	et	et	PROPN
ejpam-6054	286	5	al	al	PROPN
ejpam-6054	286	6	.	.	PUNCT
ejpam-6054	286	7	/	/	SYM
ejpam-6054	286	8	eur	eur	PROPN
ejpam-6054	286	9	.	.	PUNCT
ejpam-6054	287	1	j.	j.	PROPN
ejpam-6054	287	2	pure	pure	PROPN
ejpam-6054	287	3	appl	appl	PROPN
ejpam-6054	287	4	.	.	PROPN
ejpam-6054	287	5	math	math	PROPN
ejpam-6054	287	6	,	,	PUNCT
ejpam-6054	287	7	18	18	NUM
ejpam-6054	287	8	(	(	PUNCT
ejpam-6054	287	9	3	3	NUM
ejpam-6054	287	10	)	)	PUNCT
ejpam-6054	287	11	(	(	PUNCT
ejpam-6054	287	12	2025	2025	NUM
ejpam-6054	287	13	)	)	PUNCT
ejpam-6054	287	14	,	,	PUNCT
ejpam-6054	287	15	6054	6054	NUM
ejpam-6054	287	16	12	12	NUM
ejpam-6054	287	17	of	of	ADP
ejpam-6054	287	18	16	16	NUM
ejpam-6054	287	19	theorem	theorem	NOUN
ejpam-6054	287	20	7	7	NUM
ejpam-6054	287	21	.	.	X
ejpam-6054	287	22	for	for	ADP
ejpam-6054	287	23	any	any	DET
ejpam-6054	287	24	non	non	ADJ
ejpam-6054	287	25	-	-	ADJ
ejpam-6054	287	26	negative	negative	ADJ
ejpam-6054	287	27	integer	integer	NOUN
ejpam-6054	287	28	n	n	CCONJ
ejpam-6054	287	29	,	,	PUNCT
ejpam-6054	287	30	the	the	DET
ejpam-6054	287	31	stirling	stirling	NOUN
ejpam-6054	287	32	polynomials	polynomial	NOUN
ejpam-6054	287	33	of	of	ADP
ejpam-6054	287	34	the	the	DET
ejpam-6054	287	35	second	second	ADJ
ejpam-6054	287	36	kind	kind	NOUN
ejpam-6054	287	37	based	base	VERB
ejpam-6054	287	38	on	on	ADP
ejpam-6054	287	39	2d	2d	NUM
ejpam-6054	287	40	bell	bell	NOUN
ejpam-6054	287	41	numbers	number	NOUN
ejpam-6054	287	42	exhibit	exhibit	VERB
ejpam-6054	287	43	the	the	DET
ejpam-6054	287	44	following	follow	VERB
ejpam-6054	287	45	correlation	correlation	NOUN
ejpam-6054	287	46	:	:	PUNCT
ejpam-6054	288	1	n∑	n∑	PROPN
ejpam-6054	288	2	l=0	l=0	PROPN
ejpam-6054	288	3	(	(	PUNCT
ejpam-6054	288	4	n	n	X
ejpam-6054	288	5	l	l	NOUN
ejpam-6054	288	6	)	)	PUNCT
ejpam-6054	289	1	s2(l	s2(l	PROPN
ejpam-6054	289	2	,	,	PUNCT
ejpam-6054	289	3	ϵ)bn−l(q1	ϵ)bn−l(q1	PROPN
ejpam-6054	289	4	,	,	PUNCT
ejpam-6054	289	5	q2	q2	NOUN
ejpam-6054	289	6	)	)	PUNCT
ejpam-6054	289	7	=	=	SYM
ejpam-6054	290	1	bs2(n	bs2(n	PROPN
ejpam-6054	290	2	,	,	PUNCT
ejpam-6054	290	3	ϵ	ϵ	X
ejpam-6054	290	4	;	;	PUNCT
ejpam-6054	290	5	q1	q1	PROPN
ejpam-6054	290	6	,	,	PUNCT
ejpam-6054	290	7	q2	q2	NOUN
ejpam-6054	290	8	)	)	PUNCT
ejpam-6054	290	9	.	.	PUNCT
ejpam-6054	291	1	proof	proof	NOUN
ejpam-6054	291	2	.	.	PUNCT
ejpam-6054	292	1	the	the	DET
ejpam-6054	292	2	expression	expression	NOUN
ejpam-6054	292	3	labelled	label	VERB
ejpam-6054	292	4	as	as	ADP
ejpam-6054	292	5	(	(	PUNCT
ejpam-6054	292	6	17	17	NUM
ejpam-6054	292	7	)	)	PUNCT
ejpam-6054	292	8	can	can	AUX
ejpam-6054	292	9	be	be	AUX
ejpam-6054	292	10	expressed	express	VERB
ejpam-6054	292	11	as	as	ADP
ejpam-6054	292	12	:	:	PUNCT
ejpam-6054	292	13	∞∑	∞∑	NUM
ejpam-6054	292	14	n=0	n=0	PROPN
ejpam-6054	292	15	bs2(n	bs2(n	PROPN
ejpam-6054	292	16	,	,	PUNCT
ejpam-6054	292	17	ϵ	ϵ	X
ejpam-6054	292	18	;	;	PUNCT
ejpam-6054	292	19	q1	q1	PROPN
ejpam-6054	292	20	,	,	PUNCT
ejpam-6054	292	21	q2	q2	NOUN
ejpam-6054	292	22	)	)	PUNCT
ejpam-6054	292	23	ξn	ξn	PROPN
ejpam-6054	292	24	n	n	NOUN
ejpam-6054	292	25	!	!	PUNCT
ejpam-6054	293	1	=	=	PUNCT
ejpam-6054	293	2	(	(	PUNCT
ejpam-6054	293	3	eξ	eξ	PROPN
ejpam-6054	293	4	−	−	PROPN
ejpam-6054	293	5	1)ϵ	1)ϵ	NUM
ejpam-6054	293	6	ϵ	ϵ	X
ejpam-6054	293	7	!	!	PUNCT
ejpam-6054	294	1	eq1(e	eq1(e	PROPN
ejpam-6054	294	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	294	3	=	=	PUNCT
ejpam-6054	295	1	∞∑	∞∑	PROPN
ejpam-6054	295	2	n=ϵ	n=ϵ	PROPN
ejpam-6054	295	3	s2(n	s2(n	PROPN
ejpam-6054	295	4	,	,	PUNCT
ejpam-6054	295	5	ϵ	ϵ	NOUN
ejpam-6054	295	6	)	)	PUNCT
ejpam-6054	295	7	ξn	ξn	NOUN
ejpam-6054	295	8	n	n	NOUN
ejpam-6054	295	9	!	!	PUNCT
ejpam-6054	296	1	∞∑	∞∑	ADJ
ejpam-6054	296	2	n=0	n=0	NUM
ejpam-6054	296	3	b[j	b[j	NOUN
ejpam-6054	296	4	]	]	PUNCT
ejpam-6054	296	5	n	n	PROPN
ejpam-6054	296	6	(	(	PUNCT
ejpam-6054	296	7	q1	q1	PROPN
ejpam-6054	296	8	,	,	PUNCT
ejpam-6054	296	9	q2	q2	NOUN
ejpam-6054	296	10	)	)	PUNCT
ejpam-6054	296	11	ξn	ξn	PROPN
ejpam-6054	296	12	n	n	CCONJ
ejpam-6054	296	13	!	!	PROPN
ejpam-6054	296	14	,	,	PUNCT
ejpam-6054	296	15	the	the	DET
ejpam-6054	296	16	above	above	ADJ
ejpam-6054	296	17	expression	expression	NOUN
ejpam-6054	296	18	can	can	AUX
ejpam-6054	296	19	be	be	AUX
ejpam-6054	296	20	expressed	express	VERB
ejpam-6054	296	21	in	in	ADP
ejpam-6054	296	22	another	another	DET
ejpam-6054	296	23	form	form	NOUN
ejpam-6054	296	24	as	as	ADP
ejpam-6054	296	25	∞∑	∞∑	NUM
ejpam-6054	296	26	n=0	n=0	NUM
ejpam-6054	296	27	bs2(n	bs2(n	PROPN
ejpam-6054	296	28	,	,	PUNCT
ejpam-6054	296	29	ϵ	ϵ	X
ejpam-6054	296	30	;	;	PUNCT
ejpam-6054	296	31	q1	q1	PROPN
ejpam-6054	296	32	,	,	PUNCT
ejpam-6054	296	33	q2	q2	NOUN
ejpam-6054	296	34	)	)	PUNCT
ejpam-6054	296	35	ξn	ξn	NOUN
ejpam-6054	296	36	n	n	NOUN
ejpam-6054	296	37	!	!	PUNCT
ejpam-6054	296	38	=	=	NOUN
ejpam-6054	297	1	∞∑	∞∑	PRON
ejpam-6054	297	2	n=0	n=0	NUM
ejpam-6054	297	3	n∑	n∑	X
ejpam-6054	297	4	l=0	l=0	PROPN
ejpam-6054	297	5	(	(	PUNCT
ejpam-6054	297	6	n	n	X
ejpam-6054	297	7	l	l	NOUN
ejpam-6054	297	8	)	)	PUNCT
ejpam-6054	297	9	s2(l	s2(l	PROPN
ejpam-6054	297	10	,	,	PUNCT
ejpam-6054	297	11	ϵ	ϵ	NOUN
ejpam-6054	297	12	)	)	PUNCT
ejpam-6054	297	13	b	b	NOUN
ejpam-6054	298	1	[	[	X
ejpam-6054	298	2	j	j	X
ejpam-6054	298	3	]	]	X
ejpam-6054	298	4	n−l(q1	n−l(q1	PROPN
ejpam-6054	298	5	,	,	PUNCT
ejpam-6054	298	6	q2	q2	NOUN
ejpam-6054	298	7	)	)	PUNCT
ejpam-6054	298	8	ξn	ξn	PROPN
ejpam-6054	298	9	n	n	X
ejpam-6054	298	10	!	!	PUNCT
ejpam-6054	298	11	.	.	PUNCT
ejpam-6054	299	1	(	(	PUNCT
ejpam-6054	299	2	18	18	NUM
ejpam-6054	299	3	)	)	PUNCT
ejpam-6054	299	4	we	we	PRON
ejpam-6054	299	5	achieve	achieve	VERB
ejpam-6054	299	6	the	the	DET
ejpam-6054	299	7	expected	expect	VERB
ejpam-6054	299	8	outcome	outcome	NOUN
ejpam-6054	299	9	by	by	ADP
ejpam-6054	299	10	contrasting	contrast	VERB
ejpam-6054	299	11	the	the	DET
ejpam-6054	299	12	exponents	exponent	NOUN
ejpam-6054	299	13	of	of	ADP
ejpam-6054	299	14	identical	identical	ADJ
ejpam-6054	299	15	powers	power	NOUN
ejpam-6054	299	16	of	of	ADP
ejpam-6054	299	17	ξ	ξ	PROPN
ejpam-6054	299	18	.	.	PUNCT
ejpam-6054	300	1	remark	remark	PROPN
ejpam-6054	300	2	3	3	NUM
ejpam-6054	300	3	.	.	PUNCT
ejpam-6054	301	1	the	the	DET
ejpam-6054	301	2	correlation	correlation	NOUN
ejpam-6054	301	3	satisfied	satisfy	VERB
ejpam-6054	301	4	by	by	ADP
ejpam-6054	301	5	the	the	DET
ejpam-6054	301	6	bell	bell	NOUN
ejpam-6054	301	7	-	-	PUNCT
ejpam-6054	301	8	based	base	VERB
ejpam-6054	301	9	stirling	stirling	NOUN
ejpam-6054	301	10	polynomials	polynomial	NOUN
ejpam-6054	301	11	of	of	ADP
ejpam-6054	301	12	the	the	DET
ejpam-6054	301	13	second	second	ADJ
ejpam-6054	301	14	kind	kind	NOUN
ejpam-6054	301	15	is	be	AUX
ejpam-6054	301	16	obtained	obtain	VERB
ejpam-6054	301	17	by	by	ADP
ejpam-6054	301	18	substituting	substitute	VERB
ejpam-6054	301	19	q2	q2	NOUN
ejpam-6054	301	20	=	=	SYM
ejpam-6054	301	21	0	0	PUNCT
ejpam-6054	301	22	into	into	ADP
ejpam-6054	301	23	the	the	DET
ejpam-6054	301	24	expression	expression	NOUN
ejpam-6054	301	25	given	give	VERB
ejpam-6054	301	26	by	by	ADP
ejpam-6054	301	27	(	(	PUNCT
ejpam-6054	301	28	17	17	NUM
ejpam-6054	301	29	)	)	PUNCT
ejpam-6054	301	30	as	as	ADP
ejpam-6054	301	31	:	:	PUNCT
ejpam-6054	301	32	n∑	n∑	ADJ
ejpam-6054	301	33	l=0	l=0	PROPN
ejpam-6054	301	34	(	(	PUNCT
ejpam-6054	301	35	n	n	X
ejpam-6054	301	36	l	l	NOUN
ejpam-6054	301	37	)	)	PUNCT
ejpam-6054	302	1	s2(l	s2(l	PROPN
ejpam-6054	302	2	,	,	PUNCT
ejpam-6054	302	3	ϵ)bn−l(q1	ϵ)bn−l(q1	PROPN
ejpam-6054	302	4	)	)	PUNCT
ejpam-6054	302	5	=	=	SYM
ejpam-6054	303	1	bs2(n	bs2(n	PROPN
ejpam-6054	303	2	,	,	PUNCT
ejpam-6054	303	3	ϵ	ϵ	X
ejpam-6054	303	4	;	;	PUNCT
ejpam-6054	303	5	q1	q1	NOUN
ejpam-6054	303	6	)	)	PUNCT
ejpam-6054	303	7	,	,	PUNCT
ejpam-6054	303	8	for	for	SCONJ
ejpam-6054	303	9	a	a	DET
ejpam-6054	303	10	non	non	ADJ
ejpam-6054	303	11	-	-	ADJ
ejpam-6054	303	12	negative	negative	ADJ
ejpam-6054	303	13	integer	integer	NOUN
ejpam-6054	303	14	n.	n.	NOUN
ejpam-6054	303	15	theorem	theorem	VERB
ejpam-6054	303	16	8	8	NUM
ejpam-6054	303	17	.	.	PUNCT
ejpam-6054	304	1	the	the	DET
ejpam-6054	304	2	2d	2d	NUM
ejpam-6054	304	3	bell	bell	NOUN
ejpam-6054	304	4	-	-	PUNCT
ejpam-6054	304	5	based	base	VERB
ejpam-6054	304	6	stirling	stirling	NOUN
ejpam-6054	304	7	polynomials	polynomial	NOUN
ejpam-6054	304	8	of	of	ADP
ejpam-6054	304	9	the	the	DET
ejpam-6054	304	10	second	second	ADJ
ejpam-6054	304	11	kind	kind	NOUN
ejpam-6054	304	12	can	can	AUX
ejpam-6054	304	13	be	be	AUX
ejpam-6054	304	14	obtained	obtain	VERB
ejpam-6054	304	15	for	for	ADP
ejpam-6054	304	16	a	a	DET
ejpam-6054	304	17	non	non	ADJ
ejpam-6054	304	18	-	-	ADJ
ejpam-6054	304	19	negative	negative	ADJ
ejpam-6054	304	20	integer	integer	NOUN
ejpam-6054	304	21	n.	n.	NOUN
ejpam-6054	304	22	there	there	PRON
ejpam-6054	304	23	are	be	VERB
ejpam-6054	304	24	applicable	applicable	ADJ
ejpam-6054	304	25	summation	summation	NOUN
ejpam-6054	304	26	formulas	formula	NOUN
ejpam-6054	304	27	for	for	ADP
ejpam-6054	304	28	these	these	DET
ejpam-6054	304	29	polynomials	polynomial	NOUN
ejpam-6054	304	30	:	:	PUNCT
ejpam-6054	305	1	bs	bs	ADP
ejpam-6054	305	2	[	[	X
ejpam-6054	305	3	j	j	X
ejpam-6054	305	4	]	]	X
ejpam-6054	305	5	2	2	NUM
ejpam-6054	305	6	(	(	PUNCT
ejpam-6054	305	7	n	n	CCONJ
ejpam-6054	305	8	,	,	PUNCT
ejpam-6054	305	9	ϵ	ϵ	X
ejpam-6054	305	10	;	;	PUNCT
ejpam-6054	305	11	q1	q1	PROPN
ejpam-6054	305	12	+	+	CCONJ
ejpam-6054	305	13	q3	q3	PROPN
ejpam-6054	305	14	,	,	PUNCT
ejpam-6054	305	15	q2	q2	NOUN
ejpam-6054	305	16	+	+	CCONJ
ejpam-6054	305	17	q4	q4	PROPN
ejpam-6054	305	18	)	)	PUNCT
ejpam-6054	305	19	=	=	SYM
ejpam-6054	306	1	n∑	n∑	NOUN
ejpam-6054	306	2	k=0	k=0	PROPN
ejpam-6054	306	3	(	(	PUNCT
ejpam-6054	306	4	n	n	X
ejpam-6054	306	5	k	k	NOUN
ejpam-6054	306	6	)	)	PUNCT
ejpam-6054	306	7	bs	bs	PROPN
ejpam-6054	306	8	[	[	X
ejpam-6054	306	9	j	j	X
ejpam-6054	306	10	]	]	X
ejpam-6054	306	11	2	2	NUM
ejpam-6054	306	12	(	(	PUNCT
ejpam-6054	306	13	n−	n−	NOUN
ejpam-6054	306	14	k	k	PROPN
ejpam-6054	306	15	,	,	PUNCT
ejpam-6054	306	16	ϵ	ϵ	X
ejpam-6054	306	17	;	;	PUNCT
ejpam-6054	306	18	q1	q1	NOUN
ejpam-6054	306	19	,	,	PUNCT
ejpam-6054	306	20	q2)b	q2)b	NOUN
ejpam-6054	306	21	[	[	X
ejpam-6054	306	22	j	j	X
ejpam-6054	306	23	]	]	X
ejpam-6054	306	24	k	k	PROPN
ejpam-6054	306	25	(	(	PUNCT
ejpam-6054	306	26	q3	q3	PROPN
ejpam-6054	306	27	,	,	PUNCT
ejpam-6054	306	28	q4	q4	PROPN
ejpam-6054	306	29	)	)	PUNCT
ejpam-6054	306	30	.	.	PUNCT
ejpam-6054	307	1	proof	proof	NOUN
ejpam-6054	307	2	.	.	PUNCT
ejpam-6054	308	1	let	let	VERB
ejpam-6054	308	2	’s	’s	PRON
ejpam-6054	308	3	examine	examine	VERB
ejpam-6054	308	4	the	the	DET
ejpam-6054	308	5	generating	generate	VERB
ejpam-6054	308	6	functions	function	NOUN
ejpam-6054	308	7	provided	provide	VERB
ejpam-6054	308	8	in	in	ADP
ejpam-6054	308	9	equations	equation	NOUN
ejpam-6054	308	10	(	(	PUNCT
ejpam-6054	308	11	17	17	NUM
ejpam-6054	308	12	)	)	PUNCT
ejpam-6054	308	13	and	and	CCONJ
ejpam-6054	308	14	(	(	PUNCT
ejpam-6054	308	15	9	9	NUM
ejpam-6054	308	16	)	)	PUNCT
ejpam-6054	308	17	.	.	PUNCT
ejpam-6054	309	1	as	as	ADP
ejpam-6054	309	2	a	a	DET
ejpam-6054	309	3	result	result	NOUN
ejpam-6054	309	4	,	,	PUNCT
ejpam-6054	309	5	we	we	PRON
ejpam-6054	309	6	obtain	obtain	VERB
ejpam-6054	309	7	∞∑	∞∑	NUM
ejpam-6054	309	8	n=0	n=0	SYM
ejpam-6054	309	9	bs	bs	NOUN
ejpam-6054	309	10	[	[	X
ejpam-6054	309	11	j	j	X
ejpam-6054	309	12	]	]	X
ejpam-6054	309	13	2	2	NUM
ejpam-6054	309	14	(	(	PUNCT
ejpam-6054	309	15	n	n	CCONJ
ejpam-6054	309	16	,	,	PUNCT
ejpam-6054	309	17	ϵ	ϵ	X
ejpam-6054	309	18	;	;	PUNCT
ejpam-6054	309	19	q1	q1	PROPN
ejpam-6054	309	20	+	+	CCONJ
ejpam-6054	309	21	q3	q3	PROPN
ejpam-6054	309	22	,	,	PUNCT
ejpam-6054	309	23	q2	q2	NOUN
ejpam-6054	309	24	+	+	CCONJ
ejpam-6054	309	25	q4	q4	PROPN
ejpam-6054	309	26	)	)	PUNCT
ejpam-6054	309	27	ξn	ξn	PROPN
ejpam-6054	309	28	n	n	NOUN
ejpam-6054	309	29	!	!	PUNCT
ejpam-6054	310	1	=	=	PUNCT
ejpam-6054	310	2	(	(	PUNCT
ejpam-6054	310	3	eξ	eξ	PROPN
ejpam-6054	310	4	−	−	PROPN
ejpam-6054	310	5	1)ϵ	1)ϵ	NUM
ejpam-6054	310	6	ϵ	ϵ	X
ejpam-6054	310	7	!	!	PUNCT
ejpam-6054	310	8	e(q1+q3)(eξ−1)+(q2+q4)(eξ−1)j	e(q1+q3)(eξ−1)+(q2+q4)(eξ−1)j	NOUN
ejpam-6054	311	1	=	=	PUNCT
ejpam-6054	311	2	(	(	PUNCT
ejpam-6054	311	3	eξ	eξ	PROPN
ejpam-6054	311	4	−	−	PROPN
ejpam-6054	311	5	1)ϵ	1)ϵ	NUM
ejpam-6054	311	6	ϵ	ϵ	X
ejpam-6054	311	7	!	!	PUNCT
ejpam-6054	312	1	eq1(e	eq1(e	PROPN
ejpam-6054	312	2	ξ−1)+q2(eξ−1)jeq3(e	ξ−1)+q2(eξ−1)jeq3(e	ADP
ejpam-6054	313	1	ξ−1)+q4(eξ−1)j	ξ−1)+q4(eξ−1)j	PROPN
ejpam-6054	313	2	s.	s.	PROPN
ejpam-6054	313	3	a.	a.	PROPN
ejpam-6054	313	4	wani	wani	PROPN
ejpam-6054	313	5	et	et	PROPN
ejpam-6054	313	6	al	al	PROPN
ejpam-6054	313	7	.	.	PUNCT
ejpam-6054	313	8	/	/	SYM
ejpam-6054	313	9	eur	eur	PROPN
ejpam-6054	313	10	.	.	PUNCT
ejpam-6054	314	1	j.	j.	PROPN
ejpam-6054	314	2	pure	pure	PROPN
ejpam-6054	314	3	appl	appl	PROPN
ejpam-6054	314	4	.	.	PROPN
ejpam-6054	314	5	math	math	PROPN
ejpam-6054	314	6	,	,	PUNCT
ejpam-6054	314	7	18	18	NUM
ejpam-6054	314	8	(	(	PUNCT
ejpam-6054	314	9	3	3	NUM
ejpam-6054	314	10	)	)	PUNCT
ejpam-6054	314	11	(	(	PUNCT
ejpam-6054	314	12	2025	2025	NUM
ejpam-6054	314	13	)	)	PUNCT
ejpam-6054	314	14	,	,	PUNCT
ejpam-6054	314	15	6054	6054	NUM
ejpam-6054	314	16	13	13	NUM
ejpam-6054	314	17	of	of	ADP
ejpam-6054	314	18	16	16	NUM
ejpam-6054	314	19	=	=	SYM
ejpam-6054	314	20	∞∑	∞∑	NUM
ejpam-6054	314	21	n=0	n=0	ADJ
ejpam-6054	314	22	bs	bs	NOUN
ejpam-6054	315	1	[	[	X
ejpam-6054	315	2	j	j	X
ejpam-6054	315	3	]	]	X
ejpam-6054	315	4	2	2	NUM
ejpam-6054	315	5	(	(	PUNCT
ejpam-6054	315	6	n	n	CCONJ
ejpam-6054	315	7	,	,	PUNCT
ejpam-6054	315	8	ϵ	ϵ	X
ejpam-6054	315	9	;	;	PUNCT
ejpam-6054	315	10	q1	q1	PROPN
ejpam-6054	315	11	,	,	PUNCT
ejpam-6054	315	12	q2	q2	NOUN
ejpam-6054	315	13	)	)	PUNCT
ejpam-6054	315	14	ξn	ξn	NOUN
ejpam-6054	315	15	n	n	NOUN
ejpam-6054	315	16	!	!	PUNCT
ejpam-6054	316	1	∞∑	∞∑	ADJ
ejpam-6054	316	2	n=0	n=0	NUM
ejpam-6054	316	3	b[j	b[j	NOUN
ejpam-6054	316	4	]	]	PUNCT
ejpam-6054	316	5	n	n	CCONJ
ejpam-6054	316	6	(	(	PUNCT
ejpam-6054	316	7	q3	q3	PROPN
ejpam-6054	316	8	,	,	PUNCT
ejpam-6054	316	9	q4	q4	PROPN
ejpam-6054	316	10	)	)	PUNCT
ejpam-6054	316	11	ξn	ξn	PROPN
ejpam-6054	316	12	n	n	NOUN
ejpam-6054	316	13	!	!	PUNCT
ejpam-6054	316	14	=	=	NOUN
ejpam-6054	317	1	∞∑	∞∑	PRON
ejpam-6054	317	2	n=0	n=0	NUM
ejpam-6054	317	3	n∑	n∑	NOUN
ejpam-6054	317	4	k=0	k=0	PROPN
ejpam-6054	317	5	(	(	PUNCT
ejpam-6054	317	6	n	n	X
ejpam-6054	317	7	k	k	NOUN
ejpam-6054	317	8	)	)	PUNCT
ejpam-6054	317	9	bs	bs	PROPN
ejpam-6054	317	10	[	[	X
ejpam-6054	317	11	j	j	X
ejpam-6054	317	12	]	]	X
ejpam-6054	317	13	2	2	NUM
ejpam-6054	317	14	(	(	PUNCT
ejpam-6054	317	15	n−	n−	NOUN
ejpam-6054	317	16	k	k	PROPN
ejpam-6054	317	17	,	,	PUNCT
ejpam-6054	317	18	ϵ	ϵ	X
ejpam-6054	317	19	;	;	PUNCT
ejpam-6054	317	20	q1	q1	NOUN
ejpam-6054	317	21	,	,	PUNCT
ejpam-6054	317	22	q2)b	q2)b	NOUN
ejpam-6054	317	23	[	[	X
ejpam-6054	317	24	j	j	X
ejpam-6054	317	25	]	]	X
ejpam-6054	317	26	k	k	PROPN
ejpam-6054	317	27	(	(	PUNCT
ejpam-6054	317	28	q3	q3	PROPN
ejpam-6054	317	29	,	,	PUNCT
ejpam-6054	317	30	q4	q4	PROPN
ejpam-6054	317	31	)	)	PUNCT
ejpam-6054	317	32	ξn	ξn	PROPN
ejpam-6054	317	33	n	n	X
ejpam-6054	317	34	!	!	PUNCT
ejpam-6054	317	35	.	.	PUNCT
ejpam-6054	318	1	at	at	ADP
ejpam-6054	318	2	last	last	ADV
ejpam-6054	318	3	,	,	PUNCT
ejpam-6054	318	4	by	by	ADP
ejpam-6054	318	5	setting	set	VERB
ejpam-6054	318	6	the	the	DET
ejpam-6054	318	7	coefficients	coefficient	NOUN
ejpam-6054	318	8	of	of	ADP
ejpam-6054	318	9	ξn	ξn	PROPN
ejpam-6054	318	10	n	n	X
ejpam-6054	318	11	!	!	X
ejpam-6054	318	12	equal	equal	ADJ
ejpam-6054	318	13	on	on	ADP
ejpam-6054	318	14	both	both	DET
ejpam-6054	318	15	sides	side	NOUN
ejpam-6054	318	16	,	,	PUNCT
ejpam-6054	318	17	we	we	PRON
ejpam-6054	318	18	prove	prove	VERB
ejpam-6054	318	19	theorem	theorem	ADJ
ejpam-6054	318	20	8	8	NUM
ejpam-6054	318	21	as	as	SCONJ
ejpam-6054	318	22	claimed	claim	VERB
ejpam-6054	318	23	.	.	PUNCT
ejpam-6054	319	1	theorem	theorem	ADJ
ejpam-6054	319	2	9	9	NUM
ejpam-6054	319	3	.	.	PUNCT
ejpam-6054	320	1	the	the	DET
ejpam-6054	320	2	2d	2d	NUM
ejpam-6054	320	3	bell	bell	NOUN
ejpam-6054	320	4	-	-	PUNCT
ejpam-6054	320	5	based	base	VERB
ejpam-6054	320	6	stirling	stirling	NOUN
ejpam-6054	320	7	polynomials	polynomial	NOUN
ejpam-6054	320	8	of	of	ADP
ejpam-6054	320	9	the	the	DET
ejpam-6054	320	10	second	second	ADJ
ejpam-6054	320	11	kind	kind	NOUN
ejpam-6054	320	12	should	should	AUX
ejpam-6054	320	13	be	be	AUX
ejpam-6054	320	14	considered	consider	VERB
ejpam-6054	320	15	for	for	ADP
ejpam-6054	320	16	a	a	DET
ejpam-6054	320	17	non	non	ADJ
ejpam-6054	320	18	-	-	ADJ
ejpam-6054	320	19	negative	negative	ADJ
ejpam-6054	320	20	integer	integer	NOUN
ejpam-6054	320	21	n.	n.	NOUN
ejpam-6054	320	22	the	the	DET
ejpam-6054	320	23	following	follow	VERB
ejpam-6054	320	24	relation	relation	NOUN
ejpam-6054	320	25	is	be	AUX
ejpam-6054	320	26	valid	valid	ADJ
ejpam-6054	320	27	:	:	PUNCT
ejpam-6054	320	28	bs	bs	X
ejpam-6054	321	1	[	[	X
ejpam-6054	321	2	j+β	j+β	X
ejpam-6054	321	3	]	]	X
ejpam-6054	321	4	2	2	NUM
ejpam-6054	321	5	(	(	PUNCT
ejpam-6054	321	6	n	n	CCONJ
ejpam-6054	321	7	,	,	PUNCT
ejpam-6054	321	8	ϵ	ϵ	X
ejpam-6054	321	9	;	;	PUNCT
ejpam-6054	321	10	q1	q1	PROPN
ejpam-6054	321	11	,	,	PUNCT
ejpam-6054	321	12	q2	q2	NOUN
ejpam-6054	321	13	)	)	PUNCT
ejpam-6054	322	1	=	=	SYM
ejpam-6054	323	1	n∑	n∑	NOUN
ejpam-6054	323	2	k=0	k=0	PROPN
ejpam-6054	323	3	(	(	PUNCT
ejpam-6054	323	4	n	n	X
ejpam-6054	323	5	k	k	NOUN
ejpam-6054	323	6	)	)	PUNCT
ejpam-6054	323	7	bs	bs	PROPN
ejpam-6054	323	8	[	[	X
ejpam-6054	323	9	j	j	X
ejpam-6054	323	10	]	]	X
ejpam-6054	323	11	2	2	NUM
ejpam-6054	323	12	(	(	PUNCT
ejpam-6054	323	13	n−	n−	NOUN
ejpam-6054	323	14	k	k	PROPN
ejpam-6054	323	15	,	,	PUNCT
ejpam-6054	323	16	ϵ	ϵ	X
ejpam-6054	323	17	;	;	PUNCT
ejpam-6054	323	18	q1	q1	NOUN
ejpam-6054	323	19	,	,	PUNCT
ejpam-6054	323	20	q2)b	q2)b	NOUN
ejpam-6054	323	21	[	[	X
ejpam-6054	323	22	β	β	X
ejpam-6054	323	23	]	]	X
ejpam-6054	323	24	k	k	X
ejpam-6054	323	25	.	.	PUNCT
ejpam-6054	324	1	proof	proof	NOUN
ejpam-6054	324	2	.	.	PUNCT
ejpam-6054	325	1	by	by	ADP
ejpam-6054	325	2	(	(	PUNCT
ejpam-6054	325	3	17	17	NUM
ejpam-6054	325	4	)	)	PUNCT
ejpam-6054	325	5	,	,	PUNCT
ejpam-6054	325	6	we	we	PRON
ejpam-6054	325	7	have	have	VERB
ejpam-6054	325	8	∞∑	∞∑	NUM
ejpam-6054	325	9	n=0	n=0	ADJ
ejpam-6054	325	10	bs	bs	NOUN
ejpam-6054	326	1	[	[	X
ejpam-6054	326	2	j+β	j+β	X
ejpam-6054	326	3	]	]	X
ejpam-6054	326	4	2	2	NUM
ejpam-6054	326	5	(	(	PUNCT
ejpam-6054	326	6	n	n	CCONJ
ejpam-6054	326	7	,	,	PUNCT
ejpam-6054	326	8	ϵ	ϵ	X
ejpam-6054	326	9	;	;	PUNCT
ejpam-6054	326	10	q1	q1	PROPN
ejpam-6054	326	11	,	,	PUNCT
ejpam-6054	326	12	q2	q2	NOUN
ejpam-6054	326	13	)	)	PUNCT
ejpam-6054	326	14	ξn	ξn	PROPN
ejpam-6054	326	15	n	n	NOUN
ejpam-6054	326	16	!	!	PUNCT
ejpam-6054	326	17	=	=	PUNCT
ejpam-6054	326	18	(	(	PUNCT
ejpam-6054	326	19	eξ	eξ	PROPN
ejpam-6054	326	20	−	−	PROPN
ejpam-6054	326	21	1)ϵ	1)ϵ	NUM
ejpam-6054	326	22	ϵ	ϵ	X
ejpam-6054	326	23	!	!	PUNCT
ejpam-6054	327	1	eq1(e	eq1(e	PROPN
ejpam-6054	327	2	ξ−1)+q2(eξ−1)j+β	ξ−1)+q2(eξ−1)j+β	PROPN
ejpam-6054	327	3	=	=	SYM
ejpam-6054	327	4	(	(	PUNCT
ejpam-6054	327	5	eξ	eξ	PROPN
ejpam-6054	327	6	−	−	PROPN
ejpam-6054	327	7	1)ϵ	1)ϵ	NUM
ejpam-6054	327	8	ϵ	ϵ	X
ejpam-6054	327	9	!	!	PUNCT
ejpam-6054	328	1	eq1(e	eq1(e	PROPN
ejpam-6054	328	2	ξ−1)+q2(eξ−1)je(e	ξ−1)+q2(eξ−1)je(e	NOUN
ejpam-6054	328	3	ξ−1)β	ξ−1)β	NOUN
ejpam-6054	328	4	=	=	SYM
ejpam-6054	328	5	∞∑	∞∑	NUM
ejpam-6054	328	6	n=0	n=0	ADJ
ejpam-6054	328	7	bs	bs	NOUN
ejpam-6054	328	8	[	[	X
ejpam-6054	328	9	j	j	X
ejpam-6054	328	10	]	]	X
ejpam-6054	328	11	2	2	NUM
ejpam-6054	328	12	(	(	PUNCT
ejpam-6054	328	13	n	n	CCONJ
ejpam-6054	328	14	,	,	PUNCT
ejpam-6054	328	15	ϵ	ϵ	X
ejpam-6054	328	16	;	;	PUNCT
ejpam-6054	328	17	q1	q1	PROPN
ejpam-6054	328	18	,	,	PUNCT
ejpam-6054	328	19	q2	q2	NOUN
ejpam-6054	328	20	)	)	PUNCT
ejpam-6054	328	21	ξn	ξn	NOUN
ejpam-6054	328	22	n	n	NOUN
ejpam-6054	328	23	!	!	PUNCT
ejpam-6054	329	1	∞∑	∞∑	ADJ
ejpam-6054	329	2	n=0	n=0	NUM
ejpam-6054	329	3	b[β	b[β	NOUN
ejpam-6054	329	4	]	]	X
ejpam-6054	329	5	n	n	PRON
ejpam-6054	329	6	ξn	ξn	NOUN
ejpam-6054	329	7	n	n	X
ejpam-6054	329	8	!	!	PUNCT
ejpam-6054	329	9	=	=	NOUN
ejpam-6054	330	1	∞∑	∞∑	PRON
ejpam-6054	330	2	n=0	n=0	NUM
ejpam-6054	330	3	n∑	n∑	NOUN
ejpam-6054	330	4	k=0	k=0	PROPN
ejpam-6054	330	5	(	(	PUNCT
ejpam-6054	330	6	n	n	X
ejpam-6054	330	7	k	k	NOUN
ejpam-6054	330	8	)	)	PUNCT
ejpam-6054	330	9	bs	bs	PROPN
ejpam-6054	330	10	[	[	X
ejpam-6054	330	11	j	j	X
ejpam-6054	330	12	]	]	X
ejpam-6054	330	13	2	2	NUM
ejpam-6054	330	14	(	(	PUNCT
ejpam-6054	330	15	n−	n−	NOUN
ejpam-6054	330	16	k	k	PROPN
ejpam-6054	330	17	,	,	PUNCT
ejpam-6054	330	18	ϵ	ϵ	X
ejpam-6054	330	19	;	;	PUNCT
ejpam-6054	330	20	q1	q1	NOUN
ejpam-6054	330	21	,	,	PUNCT
ejpam-6054	330	22	q2)b	q2)b	NOUN
ejpam-6054	330	23	[	[	X
ejpam-6054	330	24	β	β	X
ejpam-6054	330	25	]	]	X
ejpam-6054	330	26	k	k	PROPN
ejpam-6054	330	27	ξn	ξn	PROPN
ejpam-6054	330	28	n	n	X
ejpam-6054	330	29	!	!	PUNCT
ejpam-6054	330	30	.	.	PUNCT
ejpam-6054	331	1	finally	finally	ADV
ejpam-6054	331	2	,	,	PUNCT
ejpam-6054	331	3	by	by	ADP
ejpam-6054	331	4	setting	set	VERB
ejpam-6054	331	5	the	the	DET
ejpam-6054	331	6	coefficients	coefficient	NOUN
ejpam-6054	331	7	of	of	ADP
ejpam-6054	331	8	fracξnn	fracξnn	PROPN
ejpam-6054	331	9	!	!	PUNCT
ejpam-6054	332	1	equal	equal	ADJ
ejpam-6054	332	2	on	on	ADP
ejpam-6054	332	3	both	both	DET
ejpam-6054	332	4	sides	side	NOUN
ejpam-6054	332	5	,	,	PUNCT
ejpam-6054	332	6	we	we	PRON
ejpam-6054	332	7	prove	prove	VERB
ejpam-6054	332	8	theorem	theorem	ADJ
ejpam-6054	332	9	9	9	NUM
ejpam-6054	332	10	as	as	SCONJ
ejpam-6054	332	11	claimed	claim	VERB
ejpam-6054	332	12	.	.	PUNCT
ejpam-6054	333	1	theorem	theorem	ADJ
ejpam-6054	333	2	10	10	NUM
ejpam-6054	333	3	.	.	PUNCT
ejpam-6054	334	1	for	for	ADP
ejpam-6054	334	2	every	every	DET
ejpam-6054	334	3	n	n	PRON
ejpam-6054	334	4	≥	≥	NOUN
ejpam-6054	334	5	1	1	NUM
ejpam-6054	334	6	,	,	PUNCT
ejpam-6054	334	7	if	if	SCONJ
ejpam-6054	334	8	we	we	PRON
ejpam-6054	334	9	let	let	VERB
ejpam-6054	334	10	s	s	PRON
ejpam-6054	334	11	[	[	X
ejpam-6054	334	12	j	j	X
ejpam-6054	334	13	]	]	X
ejpam-6054	334	14	2	2	NUM
ejpam-6054	334	15	(	(	PUNCT
ejpam-6054	334	16	n	n	CCONJ
ejpam-6054	334	17	,	,	PUNCT
ejpam-6054	334	18	ϵ	ϵ	X
ejpam-6054	334	19	;	;	PUNCT
ejpam-6054	334	20	q1	q1	PROPN
ejpam-6054	334	21	,	,	PUNCT
ejpam-6054	334	22	q2	q2	NOUN
ejpam-6054	334	23	)	)	PUNCT
ejpam-6054	334	24	represent	represent	VERB
ejpam-6054	334	25	the	the	DET
ejpam-6054	334	26	2d	2d	NUM
ejpam-6054	334	27	stirling	stirling	NOUN
ejpam-6054	334	28	polynomials	polynomial	NOUN
ejpam-6054	334	29	of	of	ADP
ejpam-6054	334	30	the	the	DET
ejpam-6054	334	31	second	second	ADJ
ejpam-6054	334	32	kind	kind	NOUN
ejpam-6054	334	33	based	base	VERB
ejpam-6054	334	34	on	on	ADP
ejpam-6054	334	35	the	the	DET
ejpam-6054	334	36	bell	bell	NOUN
ejpam-6054	334	37	numbers	number	NOUN
ejpam-6054	334	38	,	,	PUNCT
ejpam-6054	334	39	then	then	ADV
ejpam-6054	334	40	the	the	DET
ejpam-6054	334	41	following	follow	VERB
ejpam-6054	334	42	holds	hold	VERB
ejpam-6054	334	43	:	:	PUNCT
ejpam-6054	334	44	∂	∂	NUM
ejpam-6054	334	45	∂q1	∂q1	NOUN
ejpam-6054	334	46	s	s	PART
ejpam-6054	334	47	[	[	X
ejpam-6054	334	48	j	j	X
ejpam-6054	334	49	]	]	X
ejpam-6054	334	50	2	2	NUM
ejpam-6054	334	51	(	(	PUNCT
ejpam-6054	334	52	n	n	CCONJ
ejpam-6054	334	53	,	,	PUNCT
ejpam-6054	334	54	ϵ	ϵ	X
ejpam-6054	334	55	;	;	PUNCT
ejpam-6054	334	56	q1	q1	PROPN
ejpam-6054	334	57	,	,	PUNCT
ejpam-6054	334	58	q2	q2	NOUN
ejpam-6054	334	59	)	)	PUNCT
ejpam-6054	335	1	=	=	SYM
ejpam-6054	336	1	n∑	n∑	NOUN
ejpam-6054	336	2	k=0	k=0	PROPN
ejpam-6054	336	3	(	(	PUNCT
ejpam-6054	336	4	n	n	X
ejpam-6054	336	5	k	k	NOUN
ejpam-6054	336	6	)	)	PUNCT
ejpam-6054	336	7	s	s	PART
ejpam-6054	337	1	[	[	X
ejpam-6054	337	2	j	j	X
ejpam-6054	337	3	]	]	X
ejpam-6054	337	4	2	2	NUM
ejpam-6054	337	5	(	(	PUNCT
ejpam-6054	337	6	n−	n−	NOUN
ejpam-6054	337	7	k	k	PROPN
ejpam-6054	337	8	,	,	PUNCT
ejpam-6054	337	9	ϵ	ϵ	X
ejpam-6054	337	10	;	;	PUNCT
ejpam-6054	337	11	q1	q1	NOUN
ejpam-6054	337	12	,	,	PUNCT
ejpam-6054	337	13	q2)−	q2)−	PROPN
ejpam-6054	337	14	s	s	PROPN
ejpam-6054	338	1	[	[	X
ejpam-6054	338	2	j	j	X
ejpam-6054	338	3	]	]	X
ejpam-6054	338	4	2	2	NUM
ejpam-6054	338	5	(	(	PUNCT
ejpam-6054	338	6	n	n	CCONJ
ejpam-6054	338	7	,	,	PUNCT
ejpam-6054	338	8	ϵ	ϵ	X
ejpam-6054	338	9	;	;	PUNCT
ejpam-6054	338	10	q1	q1	PROPN
ejpam-6054	338	11	,	,	PUNCT
ejpam-6054	338	12	q2	q2	NOUN
ejpam-6054	338	13	)	)	PUNCT
ejpam-6054	338	14	(	(	PUNCT
ejpam-6054	338	15	19	19	NUM
ejpam-6054	338	16	)	)	PUNCT
ejpam-6054	338	17	and	and	CCONJ
ejpam-6054	338	18	∂	∂	NUM
ejpam-6054	338	19	∂q2	∂q2	NOUN
ejpam-6054	338	20	s	s	PART
ejpam-6054	338	21	[	[	X
ejpam-6054	338	22	j	j	X
ejpam-6054	338	23	]	]	X
ejpam-6054	338	24	2	2	NUM
ejpam-6054	338	25	(	(	PUNCT
ejpam-6054	338	26	n	n	CCONJ
ejpam-6054	338	27	,	,	PUNCT
ejpam-6054	338	28	ϵ	ϵ	X
ejpam-6054	338	29	;	;	PUNCT
ejpam-6054	338	30	q1	q1	PROPN
ejpam-6054	338	31	,	,	PUNCT
ejpam-6054	338	32	q2	q2	NOUN
ejpam-6054	338	33	)	)	PUNCT
ejpam-6054	339	1	=	=	SYM
ejpam-6054	340	1	n∑	n∑	NOUN
ejpam-6054	340	2	k=0	k=0	PROPN
ejpam-6054	340	3	(	(	PUNCT
ejpam-6054	340	4	n	n	X
ejpam-6054	340	5	k	k	NOUN
ejpam-6054	340	6	)	)	PUNCT
ejpam-6054	340	7	s	s	PART
ejpam-6054	341	1	[	[	X
ejpam-6054	341	2	j	j	X
ejpam-6054	341	3	]	]	X
ejpam-6054	341	4	2	2	NUM
ejpam-6054	341	5	(	(	PUNCT
ejpam-6054	341	6	n−	n−	NOUN
ejpam-6054	341	7	k	k	PROPN
ejpam-6054	341	8	,	,	PUNCT
ejpam-6054	341	9	ϵ	ϵ	X
ejpam-6054	341	10	;	;	PUNCT
ejpam-6054	341	11	q1	q1	PROPN
ejpam-6054	341	12	,	,	PUNCT
ejpam-6054	341	13	q2)j!s2(k	q2)j!s2(k	PROPN
ejpam-6054	341	14	,	,	PUNCT
ejpam-6054	341	15	j	j	PROPN
ejpam-6054	341	16	)	)	PUNCT
ejpam-6054	341	17	.	.	PUNCT
ejpam-6054	342	1	(	(	PUNCT
ejpam-6054	342	2	20	20	X
ejpam-6054	342	3	)	)	PUNCT
ejpam-6054	342	4	proof	proof	NOUN
ejpam-6054	342	5	.	.	PUNCT
ejpam-6054	343	1	(	(	PUNCT
ejpam-6054	343	2	see	see	VERB
ejpam-6054	343	3	(	(	PUNCT
ejpam-6054	343	4	19	19	NUM
ejpam-6054	343	5	)	)	PUNCT
ejpam-6054	343	6	)	)	PUNCT
ejpam-6054	343	7	.	.	PUNCT
ejpam-6054	344	1	when	when	SCONJ
ejpam-6054	344	2	we	we	PRON
ejpam-6054	344	3	partially	partially	ADV
ejpam-6054	344	4	differentiate	differentiate	VERB
ejpam-6054	344	5	both	both	DET
ejpam-6054	344	6	sides	side	NOUN
ejpam-6054	344	7	of	of	ADP
ejpam-6054	344	8	the	the	DET
ejpam-6054	344	9	equation	equation	NOUN
ejpam-6054	344	10	(	(	PUNCT
ejpam-6054	344	11	17	17	NUM
ejpam-6054	344	12	)	)	PUNCT
ejpam-6054	344	13	with	with	ADP
ejpam-6054	344	14	respect	respect	NOUN
ejpam-6054	344	15	to	to	ADP
ejpam-6054	344	16	the	the	DET
ejpam-6054	344	17	variable	variable	ADJ
ejpam-6054	344	18	q1	q1	PROPN
ejpam-6054	344	19	,	,	PUNCT
ejpam-6054	344	20	we	we	PRON
ejpam-6054	344	21	get	get	VERB
ejpam-6054	344	22	∂	∂	NOUN
ejpam-6054	344	23	∂q1	∂q1	NOUN
ejpam-6054	344	24	[	[	PUNCT
ejpam-6054	344	25	∞∑	∞∑	NUM
ejpam-6054	344	26	n=0	n=0	NUM
ejpam-6054	344	27	s	s	PART
ejpam-6054	345	1	[	[	X
ejpam-6054	345	2	j	j	X
ejpam-6054	345	3	]	]	X
ejpam-6054	345	4	2	2	NUM
ejpam-6054	345	5	(	(	PUNCT
ejpam-6054	345	6	n	n	CCONJ
ejpam-6054	345	7	,	,	PUNCT
ejpam-6054	345	8	ϵ	ϵ	X
ejpam-6054	345	9	;	;	PUNCT
ejpam-6054	345	10	q1	q1	PROPN
ejpam-6054	345	11	,	,	PUNCT
ejpam-6054	345	12	q2	q2	NOUN
ejpam-6054	345	13	)	)	PUNCT
ejpam-6054	345	14	ξn	ξn	NOUN
ejpam-6054	345	15	n	n	NOUN
ejpam-6054	345	16	!	!	PUNCT
ejpam-6054	345	17	]	]	PUNCT
ejpam-6054	346	1	=	=	SYM
ejpam-6054	346	2	∂	∂	NUM
ejpam-6054	346	3	∂q1	∂q1	NOUN
ejpam-6054	346	4	[	[	PUNCT
ejpam-6054	346	5	(	(	PUNCT
ejpam-6054	346	6	eξ	eξ	NOUN
ejpam-6054	346	7	−	−	PROPN
ejpam-6054	346	8	1)ϵ	1)ϵ	NUM
ejpam-6054	346	9	ϵ	ϵ	X
ejpam-6054	346	10	!	!	PUNCT
ejpam-6054	347	1	eq1(e	eq1(e	PROPN
ejpam-6054	347	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	PROPN
ejpam-6054	347	3	]	]	PUNCT
ejpam-6054	348	1	s.	s.	PROPN
ejpam-6054	348	2	a.	a.	PROPN
ejpam-6054	348	3	wani	wani	PROPN
ejpam-6054	348	4	et	et	PROPN
ejpam-6054	348	5	al	al	PROPN
ejpam-6054	348	6	.	.	PUNCT
ejpam-6054	348	7	/	/	SYM
ejpam-6054	348	8	eur	eur	PROPN
ejpam-6054	348	9	.	.	PUNCT
ejpam-6054	349	1	j.	j.	PROPN
ejpam-6054	349	2	pure	pure	PROPN
ejpam-6054	349	3	appl	appl	PROPN
ejpam-6054	349	4	.	.	PROPN
ejpam-6054	349	5	math	math	PROPN
ejpam-6054	349	6	,	,	PUNCT
ejpam-6054	349	7	18	18	NUM
ejpam-6054	349	8	(	(	PUNCT
ejpam-6054	349	9	3	3	NUM
ejpam-6054	349	10	)	)	PUNCT
ejpam-6054	349	11	(	(	PUNCT
ejpam-6054	349	12	2025	2025	NUM
ejpam-6054	349	13	)	)	PUNCT
ejpam-6054	349	14	,	,	PUNCT
ejpam-6054	349	15	6054	6054	NUM
ejpam-6054	349	16	14	14	NUM
ejpam-6054	349	17	of	of	ADP
ejpam-6054	349	18	16	16	NUM
ejpam-6054	349	19	=	=	SYM
ejpam-6054	349	20	(	(	PUNCT
ejpam-6054	349	21	eξ	eξ	PROPN
ejpam-6054	349	22	−	−	PROPN
ejpam-6054	349	23	1)ϵ	1)ϵ	NUM
ejpam-6054	349	24	ϵ	ϵ	X
ejpam-6054	349	25	!	!	PUNCT
ejpam-6054	350	1	eq1(e	eq1(e	PROPN
ejpam-6054	350	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	350	3	(	(	PUNCT
ejpam-6054	350	4	eξ	eξ	NOUN
ejpam-6054	350	5	−	−	PROPN
ejpam-6054	350	6	1	1	NUM
ejpam-6054	350	7	)	)	PUNCT
ejpam-6054	350	8	=	=	NOUN
ejpam-6054	351	1	∞∑	∞∑	NUM
ejpam-6054	351	2	n=0	n=0	NUM
ejpam-6054	351	3	s	s	PART
ejpam-6054	351	4	[	[	X
ejpam-6054	351	5	j	j	X
ejpam-6054	351	6	]	]	X
ejpam-6054	351	7	2	2	NUM
ejpam-6054	351	8	(	(	PUNCT
ejpam-6054	351	9	n	n	CCONJ
ejpam-6054	351	10	,	,	PUNCT
ejpam-6054	351	11	ϵ	ϵ	X
ejpam-6054	351	12	;	;	PUNCT
ejpam-6054	351	13	q1	q1	PROPN
ejpam-6054	351	14	,	,	PUNCT
ejpam-6054	351	15	q2	q2	NOUN
ejpam-6054	351	16	)	)	PUNCT
ejpam-6054	351	17	ξn	ξn	NOUN
ejpam-6054	351	18	n	n	NOUN
ejpam-6054	351	19	!	!	PUNCT
ejpam-6054	352	1	∞∑	∞∑	PRON
ejpam-6054	352	2	n=0	n=0	NUM
ejpam-6054	352	3	ξn	ξn	NOUN
ejpam-6054	352	4	n	n	NOUN
ejpam-6054	352	5	!	!	PUNCT
ejpam-6054	353	1	−	−	PROPN
ejpam-6054	354	1	∞∑	∞∑	PRON
ejpam-6054	354	2	n=0	n=0	NUM
ejpam-6054	354	3	s	s	PART
ejpam-6054	355	1	[	[	X
ejpam-6054	355	2	j	j	X
ejpam-6054	355	3	]	]	X
ejpam-6054	355	4	2	2	NUM
ejpam-6054	355	5	(	(	PUNCT
ejpam-6054	355	6	n	n	CCONJ
ejpam-6054	355	7	,	,	PUNCT
ejpam-6054	355	8	ϵ	ϵ	X
ejpam-6054	355	9	;	;	PUNCT
ejpam-6054	355	10	q1	q1	PROPN
ejpam-6054	355	11	,	,	PUNCT
ejpam-6054	355	12	q2	q2	NOUN
ejpam-6054	355	13	)	)	PUNCT
ejpam-6054	355	14	ξn	ξn	NOUN
ejpam-6054	355	15	n	n	NOUN
ejpam-6054	355	16	!	!	PUNCT
ejpam-6054	356	1	=	=	NOUN
ejpam-6054	357	1	∞∑	∞∑	NUM
ejpam-6054	357	2	n=0	n=0	PUNCT
ejpam-6054	357	3	[	[	PUNCT
ejpam-6054	357	4	n∑	n∑	NOUN
ejpam-6054	357	5	k=0	k=0	PROPN
ejpam-6054	357	6	(	(	PUNCT
ejpam-6054	357	7	n	n	X
ejpam-6054	357	8	k	k	NOUN
ejpam-6054	357	9	)	)	PUNCT
ejpam-6054	358	1	∞∑	∞∑	PRON
ejpam-6054	358	2	n=0	n=0	NUM
ejpam-6054	358	3	s	s	PART
ejpam-6054	358	4	[	[	X
ejpam-6054	358	5	j	j	X
ejpam-6054	358	6	]	]	X
ejpam-6054	358	7	2	2	NUM
ejpam-6054	358	8	(	(	PUNCT
ejpam-6054	358	9	n−	n−	NOUN
ejpam-6054	358	10	k	k	PROPN
ejpam-6054	358	11	,	,	PUNCT
ejpam-6054	358	12	ϵ	ϵ	X
ejpam-6054	358	13	;	;	PUNCT
ejpam-6054	358	14	q1	q1	PROPN
ejpam-6054	358	15	,	,	PUNCT
ejpam-6054	358	16	q2)−	q2)−	VERB
ejpam-6054	358	17	∞∑	∞∑	NUM
ejpam-6054	358	18	n=0	n=0	NUM
ejpam-6054	358	19	s	s	PART
ejpam-6054	359	1	[	[	X
ejpam-6054	359	2	j	j	X
ejpam-6054	359	3	]	]	X
ejpam-6054	359	4	2	2	NUM
ejpam-6054	359	5	(	(	PUNCT
ejpam-6054	359	6	n	n	CCONJ
ejpam-6054	359	7	,	,	PUNCT
ejpam-6054	359	8	ϵ	ϵ	X
ejpam-6054	359	9	;	;	PUNCT
ejpam-6054	359	10	q1	q1	PROPN
ejpam-6054	359	11	,	,	PUNCT
ejpam-6054	359	12	q2	q2	NOUN
ejpam-6054	359	13	)	)	PUNCT
ejpam-6054	359	14	]	]	PUNCT
ejpam-6054	359	15	ξn	ξn	PROPN
ejpam-6054	359	16	n	n	X
ejpam-6054	359	17	!	!	PUNCT
ejpam-6054	359	18	.	.	PUNCT
ejpam-6054	360	1	so	so	ADV
ejpam-6054	360	2	,	,	PUNCT
ejpam-6054	360	3	∂	∂	NUM
ejpam-6054	360	4	∂q1	∂q1	NOUN
ejpam-6054	360	5	s	s	PART
ejpam-6054	360	6	[	[	X
ejpam-6054	360	7	j	j	X
ejpam-6054	360	8	]	]	X
ejpam-6054	360	9	2	2	NUM
ejpam-6054	360	10	(	(	PUNCT
ejpam-6054	360	11	n	n	CCONJ
ejpam-6054	360	12	,	,	PUNCT
ejpam-6054	360	13	ϵ	ϵ	X
ejpam-6054	360	14	;	;	PUNCT
ejpam-6054	360	15	q1	q1	PROPN
ejpam-6054	360	16	,	,	PUNCT
ejpam-6054	360	17	q2	q2	NOUN
ejpam-6054	360	18	)	)	PUNCT
ejpam-6054	361	1	=	=	SYM
ejpam-6054	362	1	n∑	n∑	NOUN
ejpam-6054	362	2	k=0	k=0	PROPN
ejpam-6054	362	3	(	(	PUNCT
ejpam-6054	362	4	n	n	X
ejpam-6054	362	5	k	k	NOUN
ejpam-6054	362	6	)	)	PUNCT
ejpam-6054	362	7	s	s	PART
ejpam-6054	363	1	[	[	X
ejpam-6054	363	2	j	j	X
ejpam-6054	363	3	]	]	X
ejpam-6054	363	4	2	2	NUM
ejpam-6054	363	5	(	(	PUNCT
ejpam-6054	363	6	n−	n−	NOUN
ejpam-6054	363	7	k	k	PROPN
ejpam-6054	363	8	,	,	PUNCT
ejpam-6054	363	9	ϵ	ϵ	X
ejpam-6054	363	10	;	;	PUNCT
ejpam-6054	363	11	q1	q1	NOUN
ejpam-6054	363	12	,	,	PUNCT
ejpam-6054	363	13	q2)−	q2)−	PROPN
ejpam-6054	363	14	s	s	PROPN
ejpam-6054	364	1	[	[	X
ejpam-6054	364	2	j	j	X
ejpam-6054	364	3	]	]	X
ejpam-6054	364	4	2	2	NUM
ejpam-6054	364	5	(	(	PUNCT
ejpam-6054	364	6	n	n	CCONJ
ejpam-6054	364	7	,	,	PUNCT
ejpam-6054	364	8	ϵ	ϵ	X
ejpam-6054	364	9	;	;	PUNCT
ejpam-6054	364	10	q1	q1	PROPN
ejpam-6054	364	11	,	,	PUNCT
ejpam-6054	364	12	q2	q2	NOUN
ejpam-6054	364	13	)	)	PUNCT
ejpam-6054	364	14	.	.	PUNCT
ejpam-6054	365	1	proof	proof	NOUN
ejpam-6054	365	2	.	.	PUNCT
ejpam-6054	366	1	(	(	PUNCT
ejpam-6054	366	2	see	see	VERB
ejpam-6054	366	3	(	(	PUNCT
ejpam-6054	366	4	20	20	NUM
ejpam-6054	366	5	)	)	PUNCT
ejpam-6054	366	6	)	)	PUNCT
ejpam-6054	366	7	.	.	PUNCT
ejpam-6054	367	1	when	when	SCONJ
ejpam-6054	367	2	we	we	PRON
ejpam-6054	367	3	take	take	VERB
ejpam-6054	367	4	the	the	DET
ejpam-6054	367	5	partial	partial	ADJ
ejpam-6054	367	6	derivative	derivative	NOUN
ejpam-6054	367	7	with	with	ADP
ejpam-6054	367	8	respect	respect	NOUN
ejpam-6054	367	9	to	to	ADP
ejpam-6054	367	10	the	the	DET
ejpam-6054	367	11	variable	variable	ADJ
ejpam-6054	367	12	q2	q2	NOUN
ejpam-6054	367	13	of	of	ADP
ejpam-6054	367	14	both	both	DET
ejpam-6054	367	15	sides	side	NOUN
ejpam-6054	367	16	of	of	ADP
ejpam-6054	367	17	the	the	DET
ejpam-6054	367	18	equation	equation	NOUN
ejpam-6054	367	19	(	(	PUNCT
ejpam-6054	367	20	17	17	NUM
ejpam-6054	367	21	)	)	PUNCT
ejpam-6054	367	22	,	,	PUNCT
ejpam-6054	367	23	we	we	PRON
ejpam-6054	367	24	get	get	VERB
ejpam-6054	367	25	∂	∂	NOUN
ejpam-6054	367	26	∂q2	∂q2	NOUN
ejpam-6054	367	27	[	[	PUNCT
ejpam-6054	367	28	∞∑	∞∑	PROPN
ejpam-6054	367	29	n=0	n=0	NUM
ejpam-6054	367	30	s	s	PART
ejpam-6054	368	1	[	[	X
ejpam-6054	368	2	j	j	X
ejpam-6054	368	3	]	]	X
ejpam-6054	368	4	2	2	NUM
ejpam-6054	368	5	(	(	PUNCT
ejpam-6054	368	6	n	n	CCONJ
ejpam-6054	368	7	,	,	PUNCT
ejpam-6054	368	8	ϵ	ϵ	X
ejpam-6054	368	9	;	;	PUNCT
ejpam-6054	368	10	q1	q1	PROPN
ejpam-6054	368	11	,	,	PUNCT
ejpam-6054	368	12	q2	q2	NOUN
ejpam-6054	368	13	)	)	PUNCT
ejpam-6054	368	14	ξn	ξn	NOUN
ejpam-6054	368	15	n	n	NOUN
ejpam-6054	368	16	!	!	PUNCT
ejpam-6054	368	17	]	]	PUNCT
ejpam-6054	369	1	=	=	SYM
ejpam-6054	369	2	∂	∂	NUM
ejpam-6054	369	3	∂q1	∂q1	NOUN
ejpam-6054	369	4	[	[	PUNCT
ejpam-6054	369	5	(	(	PUNCT
ejpam-6054	369	6	eξ	eξ	NOUN
ejpam-6054	369	7	−	−	PROPN
ejpam-6054	369	8	1)ϵ	1)ϵ	NUM
ejpam-6054	369	9	ϵ	ϵ	X
ejpam-6054	369	10	!	!	PUNCT
ejpam-6054	370	1	eq1(e	eq1(e	PROPN
ejpam-6054	370	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	370	3	]	]	PUNCT
ejpam-6054	371	1	=	=	SYM
ejpam-6054	371	2	(	(	PUNCT
ejpam-6054	371	3	eξ	eξ	PROPN
ejpam-6054	371	4	−	−	PROPN
ejpam-6054	371	5	1)ϵ	1)ϵ	NUM
ejpam-6054	371	6	ϵ	ϵ	X
ejpam-6054	371	7	!	!	PUNCT
ejpam-6054	372	1	eq1(e	eq1(e	PROPN
ejpam-6054	372	2	ξ−1)+q2(eξ−1)j	ξ−1)+q2(eξ−1)j	NOUN
ejpam-6054	372	3	(	(	PUNCT
ejpam-6054	372	4	eξ	eξ	NOUN
ejpam-6054	372	5	−	−	PROPN
ejpam-6054	372	6	1)j	1)j	NUM
ejpam-6054	372	7	=	=	PUNCT
ejpam-6054	373	1	∞∑	∞∑	DET
ejpam-6054	373	2	n=0	n=0	NUM
ejpam-6054	373	3	s	s	PART
ejpam-6054	373	4	[	[	X
ejpam-6054	373	5	j	j	X
ejpam-6054	373	6	]	]	X
ejpam-6054	373	7	2	2	NUM
ejpam-6054	373	8	(	(	PUNCT
ejpam-6054	373	9	n	n	CCONJ
ejpam-6054	373	10	,	,	PUNCT
ejpam-6054	373	11	ϵ	ϵ	X
ejpam-6054	373	12	;	;	PUNCT
ejpam-6054	373	13	q1	q1	PROPN
ejpam-6054	373	14	,	,	PUNCT
ejpam-6054	373	15	q2	q2	NOUN
ejpam-6054	373	16	)	)	PUNCT
ejpam-6054	373	17	ξn	ξn	NOUN
ejpam-6054	373	18	n	n	NOUN
ejpam-6054	373	19	!	!	PUNCT
ejpam-6054	374	1	∞∑	∞∑	PRON
ejpam-6054	374	2	n=0	n=0	NUM
ejpam-6054	374	3	j!s2(n	j!s2(n	NOUN
ejpam-6054	374	4	,	,	PUNCT
ejpam-6054	374	5	j	j	NOUN
ejpam-6054	374	6	)	)	PUNCT
ejpam-6054	374	7	ξn	ξn	PROPN
ejpam-6054	374	8	n	n	NOUN
ejpam-6054	374	9	!	!	PUNCT
ejpam-6054	374	10	=	=	NOUN
ejpam-6054	375	1	∞∑	∞∑	PRON
ejpam-6054	375	2	n=0	n=0	NUM
ejpam-6054	375	3	n∑	n∑	NOUN
ejpam-6054	375	4	k=0	k=0	PROPN
ejpam-6054	375	5	(	(	PUNCT
ejpam-6054	375	6	n	n	X
ejpam-6054	375	7	k	k	NOUN
ejpam-6054	375	8	)	)	PUNCT
ejpam-6054	375	9	s	s	PART
ejpam-6054	376	1	[	[	X
ejpam-6054	376	2	j	j	X
ejpam-6054	376	3	]	]	X
ejpam-6054	376	4	2	2	NUM
ejpam-6054	376	5	(	(	PUNCT
ejpam-6054	376	6	n	n	CCONJ
ejpam-6054	376	7	,	,	PUNCT
ejpam-6054	376	8	ϵ	ϵ	X
ejpam-6054	376	9	;	;	PUNCT
ejpam-6054	376	10	q1	q1	PROPN
ejpam-6054	376	11	,	,	PUNCT
ejpam-6054	376	12	q2)j!s2(k	q2)j!s2(k	PROPN
ejpam-6054	376	13	,	,	PUNCT
ejpam-6054	376	14	j	j	PROPN
ejpam-6054	376	15	)	)	PUNCT
ejpam-6054	376	16	ξn	ξn	PROPN
ejpam-6054	376	17	n	n	X
ejpam-6054	376	18	!	!	PUNCT
ejpam-6054	376	19	.	.	PUNCT
ejpam-6054	377	1	so	so	ADV
ejpam-6054	377	2	,	,	PUNCT
ejpam-6054	377	3	∂	∂	NUM
ejpam-6054	377	4	∂q2	∂q2	NOUN
ejpam-6054	377	5	s	s	PART
ejpam-6054	378	1	[	[	X
ejpam-6054	378	2	j	j	X
ejpam-6054	378	3	]	]	X
ejpam-6054	378	4	2	2	NUM
ejpam-6054	378	5	(	(	PUNCT
ejpam-6054	378	6	n	n	CCONJ
ejpam-6054	378	7	,	,	PUNCT
ejpam-6054	378	8	ϵ	ϵ	X
ejpam-6054	378	9	;	;	PUNCT
ejpam-6054	378	10	q1	q1	PROPN
ejpam-6054	378	11	,	,	PUNCT
ejpam-6054	378	12	q2	q2	NOUN
ejpam-6054	378	13	)	)	PUNCT
ejpam-6054	378	14	=	=	SYM
ejpam-6054	378	15	n∑	n∑	NOUN
ejpam-6054	378	16	k=0	k=0	PROPN
ejpam-6054	378	17	(	(	PUNCT
ejpam-6054	378	18	n	n	X
ejpam-6054	378	19	k	k	NOUN
ejpam-6054	378	20	)	)	PUNCT
ejpam-6054	378	21	s	s	PART
ejpam-6054	379	1	[	[	X
ejpam-6054	379	2	j	j	X
ejpam-6054	379	3	]	]	X
ejpam-6054	379	4	2	2	NUM
ejpam-6054	379	5	(	(	PUNCT
ejpam-6054	379	6	n−	n−	NOUN
ejpam-6054	379	7	k	k	PROPN
ejpam-6054	379	8	,	,	PUNCT
ejpam-6054	379	9	ϵ	ϵ	X
ejpam-6054	379	10	;	;	PUNCT
ejpam-6054	379	11	q1	q1	PROPN
ejpam-6054	379	12	,	,	PUNCT
ejpam-6054	379	13	q2)j!s2(k	q2)j!s2(k	PROPN
ejpam-6054	379	14	,	,	PUNCT
ejpam-6054	379	15	j	j	PROPN
ejpam-6054	379	16	)	)	PUNCT
ejpam-6054	379	17	.	.	PUNCT
ejpam-6054	380	1	4	4	X
ejpam-6054	380	2	.	.	X
ejpam-6054	380	3	conclusion	conclusion	NOUN
ejpam-6054	380	4	in	in	ADP
ejpam-6054	380	5	this	this	DET
ejpam-6054	380	6	article	article	NOUN
ejpam-6054	380	7	,	,	PUNCT
ejpam-6054	380	8	we	we	PRON
ejpam-6054	380	9	present	present	VERB
ejpam-6054	380	10	2d	2d	NUM
ejpam-6054	380	11	bell	bell	NOUN
ejpam-6054	380	12	polynomials	polynomial	NOUN
ejpam-6054	380	13	using	use	VERB
ejpam-6054	380	14	generating	generating	NOUN
ejpam-6054	380	15	functions	function	NOUN
ejpam-6054	380	16	and	and	CCONJ
ejpam-6054	380	17	thoroughly	thoroughly	ADV
ejpam-6054	380	18	examine	examine	VERB
ejpam-6054	380	19	their	their	PRON
ejpam-6054	380	20	various	various	ADJ
ejpam-6054	380	21	associated	associated	ADJ
ejpam-6054	380	22	properties	property	NOUN
ejpam-6054	380	23	.	.	PUNCT
ejpam-6054	381	1	our	our	PRON
ejpam-6054	381	2	exploration	exploration	NOUN
ejpam-6054	381	3	includes	include	VERB
ejpam-6054	381	4	explicit	explicit	ADJ
ejpam-6054	381	5	representations	representation	NOUN
ejpam-6054	381	6	,	,	PUNCT
ejpam-6054	381	7	summation	summation	NOUN
ejpam-6054	381	8	formulae	formulae	NOUN
ejpam-6054	381	9	,	,	PUNCT
ejpam-6054	381	10	recurrence	recurrence	NOUN
ejpam-6054	381	11	relations	relation	NOUN
ejpam-6054	381	12	,	,	PUNCT
ejpam-6054	381	13	and	and	CCONJ
ejpam-6054	381	14	addition	addition	NOUN
ejpam-6054	381	15	formulas	formula	NOUN
ejpam-6054	381	16	,	,	PUNCT
ejpam-6054	381	17	providing	provide	VERB
ejpam-6054	381	18	valuable	valuable	ADJ
ejpam-6054	381	19	insights	insight	NOUN
ejpam-6054	381	20	into	into	ADP
ejpam-6054	381	21	their	their	PRON
ejpam-6054	381	22	mathematical	mathematical	ADJ
ejpam-6054	381	23	foundations	foundation	NOUN
ejpam-6054	381	24	.	.	PUNCT
ejpam-6054	382	1	lastly	lastly	ADV
ejpam-6054	382	2	,	,	PUNCT
ejpam-6054	382	3	we	we	PRON
ejpam-6054	382	4	have	have	AUX
ejpam-6054	382	5	introduced	introduce	VERB
ejpam-6054	382	6	the	the	DET
ejpam-6054	382	7	2d	2d	NUM
ejpam-6054	382	8	bell	bell	NOUN
ejpam-6054	382	9	-	-	PUNCT
ejpam-6054	382	10	based	base	VERB
ejpam-6054	382	11	stirling	stirling	NOUN
ejpam-6054	382	12	polynomials	polynomial	NOUN
ejpam-6054	382	13	of	of	ADP
ejpam-6054	382	14	the	the	DET
ejpam-6054	382	15	second	second	ADJ
ejpam-6054	382	16	kind	kind	NOUN
ejpam-6054	382	17	,	,	PUNCT
ejpam-6054	382	18	broadening	broaden	VERB
ejpam-6054	382	19	the	the	DET
ejpam-6054	382	20	scope	scope	NOUN
ejpam-6054	382	21	of	of	ADP
ejpam-6054	382	22	our	our	PRON
ejpam-6054	382	23	study	study	NOUN
ejpam-6054	382	24	to	to	PART
ejpam-6054	382	25	include	include	VERB
ejpam-6054	382	26	related	related	ADJ
ejpam-6054	382	27	concepts	concept	NOUN
ejpam-6054	382	28	and	and	CCONJ
ejpam-6054	382	29	results	result	NOUN
ejpam-6054	382	30	.	.	PUNCT
ejpam-6054	383	1	through	through	ADP
ejpam-6054	383	2	this	this	DET
ejpam-6054	383	3	comprehensive	comprehensive	ADJ
ejpam-6054	383	4	analysis	analysis	NOUN
ejpam-6054	383	5	,	,	PUNCT
ejpam-6054	383	6	our	our	PRON
ejpam-6054	383	7	research	research	NOUN
ejpam-6054	383	8	contributes	contribute	VERB
ejpam-6054	383	9	to	to	ADP
ejpam-6054	383	10	a	a	DET
ejpam-6054	383	11	deeper	deep	ADJ
ejpam-6054	383	12	comprehension	comprehension	NOUN
ejpam-6054	383	13	of	of	ADP
ejpam-6054	383	14	the	the	DET
ejpam-6054	383	15	properties	property	NOUN
ejpam-6054	383	16	and	and	CCONJ
ejpam-6054	383	17	applications	application	NOUN
ejpam-6054	383	18	of	of	ADP
ejpam-6054	383	19	bell	bell	NOUN
ejpam-6054	383	20	polynomials	polynomial	NOUN
ejpam-6054	383	21	in	in	ADP
ejpam-6054	383	22	mathematical	mathematical	ADJ
ejpam-6054	383	23	analysis	analysis	NOUN
ejpam-6054	383	24	.	.	PUNCT
ejpam-6054	384	1	this	this	PRON
ejpam-6054	384	2	lays	lay	VERB
ejpam-6054	384	3	a	a	DET
ejpam-6054	384	4	solid	solid	ADJ
ejpam-6054	384	5	groundwork	groundwork	NOUN
ejpam-6054	384	6	for	for	ADP
ejpam-6054	384	7	further	further	ADJ
ejpam-6054	384	8	exploration	exploration	NOUN
ejpam-6054	384	9	and	and	CCONJ
ejpam-6054	384	10	practical	practical	ADJ
ejpam-6054	384	11	use	use	NOUN
ejpam-6054	384	12	in	in	ADP
ejpam-6054	384	13	diverse	diverse	ADJ
ejpam-6054	384	14	fields	field	NOUN
ejpam-6054	384	15	.	.	PUNCT
ejpam-6054	385	1	future	future	ADJ
ejpam-6054	385	2	research	research	NOUN
ejpam-6054	385	3	in	in	ADP
ejpam-6054	385	4	the	the	DET
ejpam-6054	385	5	realm	realm	NOUN
ejpam-6054	385	6	of	of	ADP
ejpam-6054	385	7	2d	2d	NUM
ejpam-6054	385	8	bell	bell	NOUN
ejpam-6054	385	9	polynomials	polynomial	NOUN
ejpam-6054	385	10	could	could	AUX
ejpam-6054	385	11	focus	focus	VERB
ejpam-6054	385	12	on	on	ADP
ejpam-6054	385	13	several	several	ADJ
ejpam-6054	385	14	avenues	avenue	NOUN
ejpam-6054	385	15	to	to	PART
ejpam-6054	385	16	further	far	ADV
ejpam-6054	385	17	expand	expand	VERB
ejpam-6054	385	18	our	our	PRON
ejpam-6054	385	19	understanding	understanding	NOUN
ejpam-6054	385	20	and	and	CCONJ
ejpam-6054	385	21	applications	application	NOUN
ejpam-6054	385	22	of	of	ADP
ejpam-6054	385	23	these	these	DET
ejpam-6054	385	24	mathematical	mathematical	ADJ
ejpam-6054	385	25	entities	entity	NOUN
ejpam-6054	385	26	.	.	PUNCT
ejpam-6054	386	1	one	one	NUM
ejpam-6054	386	2	s.	s.	PROPN
ejpam-6054	386	3	a.	a.	PROPN
ejpam-6054	386	4	wani	wani	PROPN
ejpam-6054	386	5	et	et	PROPN
ejpam-6054	386	6	al	al	PROPN
ejpam-6054	386	7	.	.	PUNCT
ejpam-6054	386	8	/	/	SYM
ejpam-6054	386	9	eur	eur	PROPN
ejpam-6054	386	10	.	.	PUNCT
ejpam-6054	387	1	j.	j.	PROPN
ejpam-6054	387	2	pure	pure	PROPN
ejpam-6054	387	3	appl	appl	PROPN
ejpam-6054	387	4	.	.	PROPN
ejpam-6054	387	5	math	math	PROPN
ejpam-6054	387	6	,	,	PUNCT
ejpam-6054	387	7	18	18	NUM
ejpam-6054	387	8	(	(	PUNCT
ejpam-6054	387	9	3	3	NUM
ejpam-6054	387	10	)	)	PUNCT
ejpam-6054	387	11	(	(	PUNCT
ejpam-6054	387	12	2025	2025	NUM
ejpam-6054	387	13	)	)	PUNCT
ejpam-6054	387	14	,	,	PUNCT
ejpam-6054	387	15	6054	6054	NUM
ejpam-6054	387	16	15	15	NUM
ejpam-6054	387	17	of	of	ADP
ejpam-6054	387	18	16	16	NUM
ejpam-6054	387	19	potential	potential	ADJ
ejpam-6054	387	20	direction	direction	NOUN
ejpam-6054	387	21	is	be	AUX
ejpam-6054	387	22	the	the	DET
ejpam-6054	387	23	exploration	exploration	NOUN
ejpam-6054	387	24	of	of	ADP
ejpam-6054	387	25	higher	high	ADJ
ejpam-6054	387	26	-	-	PUNCT
ejpam-6054	387	27	dimensional	dimensional	ADJ
ejpam-6054	387	28	generalizations	generalization	NOUN
ejpam-6054	387	29	beyond	beyond	ADP
ejpam-6054	387	30	the	the	DET
ejpam-6054	387	31	2d	2d	NUM
ejpam-6054	387	32	case	case	NOUN
ejpam-6054	387	33	,	,	PUNCT
ejpam-6054	387	34	investigating	investigate	VERB
ejpam-6054	387	35	how	how	SCONJ
ejpam-6054	387	36	bell	bell	NOUN
ejpam-6054	387	37	polynomials	polynomial	NOUN
ejpam-6054	387	38	can	can	AUX
ejpam-6054	387	39	be	be	AUX
ejpam-6054	387	40	extended	extend	VERB
ejpam-6054	387	41	to	to	ADP
ejpam-6054	387	42	three	three	NUM
ejpam-6054	387	43	or	or	CCONJ
ejpam-6054	387	44	more	more	ADJ
ejpam-6054	387	45	variables	variable	NOUN
ejpam-6054	387	46	and	and	CCONJ
ejpam-6054	387	47	uncovering	uncover	VERB
ejpam-6054	387	48	their	their	PRON
ejpam-6054	387	49	properties	property	NOUN
ejpam-6054	387	50	and	and	CCONJ
ejpam-6054	387	51	relationships	relationship	NOUN
ejpam-6054	387	52	in	in	ADP
ejpam-6054	387	53	multi	multi	ADJ
ejpam-6054	387	54	-	-	ADJ
ejpam-6054	387	55	dimensional	dimensional	ADJ
ejpam-6054	387	56	spaces	space	NOUN
ejpam-6054	387	57	.	.	PUNCT
ejpam-6054	388	1	additionally	additionally	ADV
ejpam-6054	388	2	,	,	PUNCT
ejpam-6054	388	3	there	there	PRON
ejpam-6054	388	4	is	be	VERB
ejpam-6054	388	5	room	room	NOUN
ejpam-6054	388	6	for	for	ADP
ejpam-6054	388	7	research	research	NOUN
ejpam-6054	388	8	into	into	ADP
ejpam-6054	388	9	the	the	DET
ejpam-6054	388	10	development	development	NOUN
ejpam-6054	388	11	of	of	ADP
ejpam-6054	388	12	more	more	ADV
ejpam-6054	388	13	efficient	efficient	ADJ
ejpam-6054	388	14	computational	computational	ADJ
ejpam-6054	388	15	algorithms	algorithm	NOUN
ejpam-6054	388	16	and	and	CCONJ
ejpam-6054	388	17	numerical	numerical	ADJ
ejpam-6054	388	18	techniques	technique	NOUN
ejpam-6054	388	19	for	for	ADP
ejpam-6054	388	20	handling	handle	VERB
ejpam-6054	388	21	2d	2d	NUM
ejpam-6054	388	22	bell	bell	NOUN
ejpam-6054	388	23	polynomials	polynomial	NOUN
ejpam-6054	388	24	,	,	PUNCT
ejpam-6054	388	25	especially	especially	ADV
ejpam-6054	388	26	in	in	ADP
ejpam-6054	388	27	scenarios	scenario	NOUN
ejpam-6054	388	28	involving	involve	VERB
ejpam-6054	388	29	large	large	ADJ
ejpam-6054	388	30	datasets	dataset	NOUN
ejpam-6054	388	31	or	or	CCONJ
ejpam-6054	388	32	complex	complex	ADJ
ejpam-6054	388	33	systems	system	NOUN
ejpam-6054	388	34	.	.	PUNCT
ejpam-6054	389	1	improving	improve	VERB
ejpam-6054	389	2	computational	computational	ADJ
ejpam-6054	389	3	efficiency	efficiency	NOUN
ejpam-6054	389	4	could	could	AUX
ejpam-6054	389	5	open	open	VERB
ejpam-6054	389	6	up	up	ADP
ejpam-6054	389	7	new	new	ADJ
ejpam-6054	389	8	possibilities	possibility	NOUN
ejpam-6054	389	9	for	for	ADP
ejpam-6054	389	10	applying	apply	VERB
ejpam-6054	389	11	bell	bell	NOUN
ejpam-6054	389	12	polynomials	polynomial	NOUN
ejpam-6054	389	13	in	in	ADP
ejpam-6054	389	14	practical	practical	ADJ
ejpam-6054	389	15	fields	field	NOUN
ejpam-6054	389	16	such	such	ADJ
ejpam-6054	389	17	as	as	ADP
ejpam-6054	389	18	data	datum	NOUN
ejpam-6054	389	19	analysis	analysis	NOUN
ejpam-6054	389	20	,	,	PUNCT
ejpam-6054	389	21	optimization	optimization	NOUN
ejpam-6054	389	22	,	,	PUNCT
ejpam-6054	389	23	and	and	CCONJ
ejpam-6054	389	24	machine	machine	NOUN
ejpam-6054	389	25	learning	learning	NOUN
ejpam-6054	389	26	.	.	PUNCT
ejpam-6054	390	1	references	reference	NOUN
ejpam-6054	390	2	[	[	X
ejpam-6054	390	3	1	1	NUM
ejpam-6054	390	4	]	]	PUNCT
ejpam-6054	390	5	carlitz	carlitz	PROPN
ejpam-6054	390	6	l.	l.	PROPN
ejpam-6054	390	7	,	,	PUNCT
ejpam-6054	390	8	some	some	DET
ejpam-6054	390	9	remarks	remark	NOUN
ejpam-6054	390	10	on	on	ADP
ejpam-6054	390	11	the	the	DET
ejpam-6054	390	12	bell	bell	NOUN
ejpam-6054	390	13	numbers	number	NOUN
ejpam-6054	390	14	,	,	PUNCT
ejpam-6054	390	15	fibonacci	fibonacci	PROPN
ejpam-6054	390	16	quarterly	quarterly	ADV
ejpam-6054	390	17	,	,	PUNCT
ejpam-6054	390	18	18	18	NUM
ejpam-6054	390	19	(	(	PUNCT
ejpam-6054	390	20	1	1	NUM
ejpam-6054	390	21	)	)	PUNCT
ejpam-6054	390	22	,	,	PUNCT
ejpam-6054	390	23	(	(	PUNCT
ejpam-6054	390	24	1980	1980	NUM
ejpam-6054	390	25	)	)	PUNCT
ejpam-6054	390	26	66	66	NUM
ejpam-6054	390	27	-	-	SYM
ejpam-6054	390	28	73	73	NUM
ejpam-6054	390	29	.	.	PUNCT
ejpam-6054	391	1	[	[	X
ejpam-6054	391	2	2	2	NUM
ejpam-6054	391	3	]	]	SYM
ejpam-6054	391	4	dattoli	dattoli	NOUN
ejpam-6054	391	5	g.	g.	PROPN
ejpam-6054	391	6	,	,	PUNCT
ejpam-6054	391	7	ottaviani	ottaviani	PROPN
ejpam-6054	391	8	p.l	p.l	PROPN
ejpam-6054	391	9	.	.	PROPN
ejpam-6054	391	10	,	,	PUNCT
ejpam-6054	391	11	torre	torre	PROPN
ejpam-6054	391	12	a.	a.	PROPN
ejpam-6054	391	13	,	,	PUNCT
ejpam-6054	391	14	vazquez	vazquez	PROPN
ejpam-6054	391	15	l.	l.	PROPN
ejpam-6054	391	16	,	,	PUNCT
ejpam-6054	391	17	evolution	evolution	NOUN
ejpam-6054	391	18	operator	operator	NOUN
ejpam-6054	391	19	equations	equation	NOUN
ejpam-6054	391	20	:	:	PUNCT
ejpam-6054	391	21	integration	integration	NOUN
ejpam-6054	391	22	with	with	ADP
ejpam-6054	391	23	algebraic	algebraic	ADJ
ejpam-6054	391	24	and	and	CCONJ
ejpam-6054	391	25	finite	finite	ADJ
ejpam-6054	391	26	difference	difference	NOUN
ejpam-6054	391	27	methods	method	NOUN
ejpam-6054	391	28	,	,	PUNCT
ejpam-6054	391	29	applications	application	NOUN
ejpam-6054	391	30	to	to	ADP
ejpam-6054	391	31	physical	physical	ADJ
ejpam-6054	391	32	problems	problem	NOUN
ejpam-6054	391	33	in	in	ADP
ejpam-6054	391	34	classical	classical	ADJ
ejpam-6054	391	35	and	and	CCONJ
ejpam-6054	391	36	quantum	quantum	ADJ
ejpam-6054	391	37	mechanics	mechanic	NOUN
ejpam-6054	391	38	and	and	CCONJ
ejpam-6054	391	39	quantum	quantum	NOUN
ejpam-6054	391	40	field	field	NOUN
ejpam-6054	391	41	theory	theory	NOUN
ejpam-6054	391	42	.	.	PUNCT
ejpam-6054	392	1	riv	riv	PROPN
ejpam-6054	392	2	.	.	PROPN
ejpam-6054	392	3	nuovo	nuovo	PROPN
ejpam-6054	392	4	cim	cim	PROPN
ejpam-6054	392	5	.	.	PROPN
ejpam-6054	392	6	20	20	NUM
ejpam-6054	392	7	,	,	PUNCT
ejpam-6054	392	8	(	(	PUNCT
ejpam-6054	392	9	1997	1997	NUM
ejpam-6054	392	10	)	)	PUNCT
ejpam-6054	392	11	.	.	PUNCT
ejpam-6054	393	1	[	[	X
ejpam-6054	393	2	3	3	X
ejpam-6054	393	3	]	]	X
ejpam-6054	393	4	srivastava	srivastava	PROPN
ejpam-6054	393	5	,	,	PUNCT
ejpam-6054	393	6	h.m	h.m	PROPN
ejpam-6054	393	7	.	.	PROPN
ejpam-6054	393	8	;	;	PUNCT
ejpam-6054	393	9	manocha	manocha	PROPN
ejpam-6054	393	10	,	,	PUNCT
ejpam-6054	393	11	h.l	h.l	PROPN
ejpam-6054	393	12	.	.	PROPN
ejpam-6054	393	13	a	a	DET
ejpam-6054	393	14	treatise	treatise	NOUN
ejpam-6054	393	15	on	on	ADP
ejpam-6054	393	16	generating	generating	NOUN
ejpam-6054	393	17	functions	function	NOUN
ejpam-6054	393	18	;	;	PUNCT
ejpam-6054	393	19	ellis	ellis	PROPN
ejpam-6054	393	20	horwood	horwood	PROPN
ejpam-6054	393	21	limited	limited	PROPN
ejpam-6054	393	22	.	.	PUNCT
ejpam-6054	394	1	co.	co.	PROPN
ejpam-6054	394	2	:	:	PUNCT
ejpam-6054	394	3	new	new	PROPN
ejpam-6054	394	4	york	york	PROPN
ejpam-6054	394	5	,	,	PUNCT
ejpam-6054	394	6	ny	ny	PROPN
ejpam-6054	394	7	,	,	PUNCT
ejpam-6054	394	8	usa	usa	PROPN
ejpam-6054	394	9	,	,	PUNCT
ejpam-6054	394	10	1984	1984	NUM
ejpam-6054	394	11	.	.	PUNCT
ejpam-6054	395	1	[	[	X
ejpam-6054	395	2	4	4	NUM
ejpam-6054	395	3	]	]	X
ejpam-6054	395	4	wang	wang	PROPN
ejpam-6054	395	5	,	,	PUNCT
ejpam-6054	395	6	w.	w.	PROPN
ejpam-6054	395	7	;	;	PUNCT
ejpam-6054	395	8	wang	wang	PROPN
ejpam-6054	395	9	,	,	PUNCT
ejpam-6054	395	10	t.	t.	PROPN
ejpam-6054	395	11	identities	identity	NOUN
ejpam-6054	395	12	on	on	ADP
ejpam-6054	395	13	bell	bell	NOUN
ejpam-6054	395	14	polynomials	polynomial	NOUN
ejpam-6054	395	15	and	and	CCONJ
ejpam-6054	395	16	sheffer	sheffer	VERB
ejpam-6054	395	17	sequences	sequence	NOUN
ejpam-6054	395	18	.	.	PUNCT
ejpam-6054	396	1	discret	discret	PROPN
ejpam-6054	396	2	.	.	PUNCT
ejpam-6054	396	3	math	math	PROPN
ejpam-6054	396	4	.	.	PUNCT
ejpam-6054	397	1	2009	2009	NUM
ejpam-6054	397	2	,	,	PUNCT
ejpam-6054	397	3	309	309	NUM
ejpam-6054	397	4	,	,	PUNCT
ejpam-6054	397	5	1637	1637	NUM
ejpam-6054	397	6	-	-	SYM
ejpam-6054	397	7	1648	1648	NUM
ejpam-6054	397	8	.	.	PUNCT
ejpam-6054	398	1	[	[	X
ejpam-6054	398	2	5	5	NUM
ejpam-6054	398	3	]	]	X
ejpam-6054	398	4	bell	bell	PROPN
ejpam-6054	398	5	,	,	PUNCT
ejpam-6054	398	6	e.t	e.t	PROPN
ejpam-6054	398	7	.	.	PROPN
ejpam-6054	398	8	exponential	exponential	ADJ
ejpam-6054	398	9	polynomials	polynomial	NOUN
ejpam-6054	398	10	.	.	PUNCT
ejpam-6054	399	1	ann	ann	PROPN
ejpam-6054	399	2	.	.	PUNCT
ejpam-6054	399	3	math	math	PROPN
ejpam-6054	399	4	.	.	PUNCT
ejpam-6054	400	1	1934	1934	NUM
ejpam-6054	400	2	,	,	PUNCT
ejpam-6054	400	3	35	35	NUM
ejpam-6054	400	4	,	,	PUNCT
ejpam-6054	400	5	258	258	NUM
ejpam-6054	400	6	-	-	SYM
ejpam-6054	400	7	277	277	NUM
ejpam-6054	400	8	.	.	PUNCT
ejpam-6054	401	1	[	[	X
ejpam-6054	401	2	6	6	NUM
ejpam-6054	401	3	]	]	PUNCT
ejpam-6054	401	4	boas	boa	NOUN
ejpam-6054	401	5	,	,	PUNCT
ejpam-6054	401	6	r.p	r.p	PROPN
ejpam-6054	401	7	.	.	PROPN
ejpam-6054	401	8	;	;	PUNCT
ejpam-6054	401	9	buck	buck	NOUN
ejpam-6054	401	10	,	,	PUNCT
ejpam-6054	401	11	r.c	r.c	PROPN
ejpam-6054	401	12	.	.	PROPN
ejpam-6054	401	13	polynomial	polynomial	ADJ
ejpam-6054	401	14	expansions	expansion	NOUN
ejpam-6054	401	15	of	of	ADP
ejpam-6054	401	16	analytic	analytic	ADJ
ejpam-6054	401	17	functions	function	NOUN
ejpam-6054	401	18	;	;	PUNCT
ejpam-6054	401	19	springer	springer	NOUN
ejpam-6054	401	20	:	:	PUNCT
ejpam-6054	401	21	berlin	berlin	PROPN
ejpam-6054	401	22	/	/	SYM
ejpam-6054	401	23	gottingen	gottingen	PROPN
ejpam-6054	401	24	/	/	SYM
ejpam-6054	401	25	heidelberg	heidelberg	PROPN
ejpam-6054	401	26	,	,	PUNCT
ejpam-6054	401	27	germany	germany	PROPN
ejpam-6054	401	28	,	,	PUNCT
ejpam-6054	401	29	1958	1958	NUM
ejpam-6054	401	30	.	.	PUNCT
ejpam-6054	402	1	[	[	X
ejpam-6054	402	2	7	7	NUM
ejpam-6054	402	3	]	]	X
ejpam-6054	402	4	khan	khan	PROPN
ejpam-6054	402	5	,	,	PUNCT
ejpam-6054	402	6	s.	s.	PROPN
ejpam-6054	402	7	;	;	PUNCT
ejpam-6054	402	8	pathan	pathan	PROPN
ejpam-6054	402	9	,	,	PUNCT
ejpam-6054	402	10	m.a	m.a	PROPN
ejpam-6054	402	11	.	.	PROPN
ejpam-6054	402	12	;	;	PUNCT
ejpam-6054	402	13	hassan	hassan	PROPN
ejpam-6054	402	14	,	,	PUNCT
ejpam-6054	402	15	n.a.m	n.a.m	PROPN
ejpam-6054	402	16	.	.	PROPN
ejpam-6054	402	17	;	;	PUNCT
ejpam-6054	402	18	yasmin	yasmin	PROPN
ejpam-6054	402	19	,	,	PUNCT
ejpam-6054	402	20	g.	g.	PROPN
ejpam-6054	402	21	implicit	implicit	ADJ
ejpam-6054	402	22	summation	summation	NOUN
ejpam-6054	402	23	formulae	formulae	NOUN
ejpam-6054	402	24	for	for	ADP
ejpam-6054	402	25	hermite	hermite	ADJ
ejpam-6054	402	26	and	and	CCONJ
ejpam-6054	402	27	related	related	ADJ
ejpam-6054	402	28	polynomials	polynomial	NOUN
ejpam-6054	402	29	.	.	PUNCT
ejpam-6054	403	1	j.	j.	PROPN
ejpam-6054	403	2	math	math	PROPN
ejpam-6054	403	3	.	.	PUNCT
ejpam-6054	404	1	anal	anal	PROPN
ejpam-6054	404	2	.	.	PUNCT
ejpam-6054	404	3	appl	appl	PROPN
ejpam-6054	404	4	.	.	PROPN
ejpam-6054	404	5	2008	2008	NUM
ejpam-6054	404	6	,	,	PUNCT
ejpam-6054	404	7	344	344	NUM
ejpam-6054	404	8	,	,	PUNCT
ejpam-6054	404	9	408	408	NUM
ejpam-6054	404	10	-	-	SYM
ejpam-6054	404	11	416	416	NUM
ejpam-6054	404	12	.	.	PUNCT
ejpam-6054	405	1	[	[	X
ejpam-6054	405	2	8	8	NUM
ejpam-6054	405	3	]	]	X
ejpam-6054	405	4	m.	m.	NOUN
ejpam-6054	405	5	fadel	fadel	PROPN
ejpam-6054	405	6	,	,	PUNCT
ejpam-6054	405	7	w.	w.	PROPN
ejpam-6054	405	8	ramı́rez	ramı́rez	PROPN
ejpam-6054	405	9	,	,	PUNCT
ejpam-6054	405	10	c.cesarano	c.cesarano	PROPN
ejpam-6054	405	11	,	,	PUNCT
ejpam-6054	405	12	s.	s.	PROPN
ejpam-6054	405	13	dı́az	dı́az	PROPN
ejpam-6054	405	14	.	.	PROPN
ejpam-6054	405	15	,	,	PUNCT
ejpam-6054	405	16	the	the	DET
ejpam-6054	405	17	2	2	NUM
ejpam-6054	405	18	-	-	PUNCT
ejpam-6054	405	19	variable	variable	ADJ
ejpam-6054	405	20	truncated	truncated	ADJ
ejpam-6054	405	21	tricomi	tricomi	NOUN
ejpam-6054	405	22	functions	function	NOUN
ejpam-6054	405	23	.	.	PUNCT
ejpam-6054	406	1	dolomites	dolomite	NOUN
ejpam-6054	406	2	research	research	NOUN
ejpam-6054	406	3	notes	note	NOUN
ejpam-6054	406	4	on	on	ADP
ejpam-6054	406	5	approximation	approximation	NOUN
ejpam-6054	406	6	,	,	PUNCT
ejpam-6054	406	7	18(1	18(1	NUM
ejpam-6054	406	8	)	)	PUNCT
ejpam-6054	406	9	,	,	PUNCT
ejpam-6054	406	10	49–45	49–45	NUM
ejpam-6054	406	11	,	,	PUNCT
ejpam-6054	406	12	(	(	PUNCT
ejpam-6054	406	13	2025	2025	NUM
ejpam-6054	406	14	)	)	PUNCT
ejpam-6054	406	15	.	.	PUNCT
ejpam-6054	407	1	[	[	X
ejpam-6054	407	2	9	9	NUM
ejpam-6054	407	3	]	]	X
ejpam-6054	407	4	n.	n.	PROPN
ejpam-6054	407	5	raza	raza	PROPN
ejpam-6054	407	6	,	,	PUNCT
ejpam-6054	407	7	m.	m.	PROPN
ejpam-6054	407	8	fadel	fadel	PROPN
ejpam-6054	407	9	,	,	PUNCT
ejpam-6054	407	10	c.cesarano	c.cesarano	PROPN
ejpam-6054	407	11	.	.	PUNCT
ejpam-6054	407	12	,	,	PUNCT
ejpam-6054	407	13	on	on	ADP
ejpam-6054	407	14	2	2	NUM
ejpam-6054	407	15	-	-	PUNCT
ejpam-6054	407	16	variable	variable	ADJ
ejpam-6054	407	17	q	q	ADJ
ejpam-6054	407	18	-	-	PUNCT
ejpam-6054	407	19	legendre	legendre	NOUN
ejpam-6054	407	20	polynomials	polynomial	NOUN
ejpam-6054	407	21	:	:	PUNCT
ejpam-6054	407	22	the	the	DET
ejpam-6054	407	23	view	view	NOUN
ejpam-6054	407	24	point	point	NOUN
ejpam-6054	407	25	of	of	ADP
ejpam-6054	407	26	the	the	DET
ejpam-6054	407	27	q	q	ADJ
ejpam-6054	407	28	-	-	ADJ
ejpam-6054	407	29	operational	operational	ADJ
ejpam-6054	407	30	technique	technique	NOUN
ejpam-6054	407	31	.	.	PUNCT
ejpam-6054	408	1	carpathian	carpathian	ADJ
ejpam-6054	408	2	math	math	PROPN
ejpam-6054	408	3	.	.	PUNCT
ejpam-6054	409	1	publ	publ	PROPN
ejpam-6054	409	2	,	,	PUNCT
ejpam-6054	409	3	117	117	NUM
ejpam-6054	409	4	-	-	SYM
ejpam-6054	409	5	141	141	NUM
ejpam-6054	409	6	,	,	PUNCT
ejpam-6054	409	7	17(1	17(1	NUM
ejpam-6054	409	8	)	)	PUNCT
ejpam-6054	409	9	(	(	PUNCT
ejpam-6054	409	10	2024	2024	NUM
ejpam-6054	409	11	)	)	PUNCT
ejpam-6054	409	12	.	.	PUNCT
ejpam-6054	410	1	[	[	X
ejpam-6054	410	2	10	10	NUM
ejpam-6054	410	3	]	]	X
ejpam-6054	410	4	n.	n.	PROPN
ejpam-6054	410	5	raza	raza	PROPN
ejpam-6054	410	6	,	,	PUNCT
ejpam-6054	410	7	m.	m.	PROPN
ejpam-6054	410	8	fadel	fadel	PROPN
ejpam-6054	410	9	,	,	PUNCT
ejpam-6054	410	10	k.s	k.s	PROPN
ejpam-6054	410	11	.	.	PROPN
ejpam-6054	410	12	nisar	nisar	PROPN
ejpam-6054	410	13	,	,	PUNCT
ejpam-6054	410	14	m.	m.	NOUN
ejpam-6054	410	15	zakarya	zakarya	NOUN
ejpam-6054	410	16	.	.	PUNCT
ejpam-6054	411	1	on	on	ADP
ejpam-6054	411	2	2	2	NUM
ejpam-6054	411	3	-	-	PUNCT
ejpam-6054	411	4	variable	variable	ADJ
ejpam-6054	411	5	q	q	ADJ
ejpam-6054	411	6	-	-	PUNCT
ejpam-6054	411	7	hermite	hermite	ADJ
ejpam-6054	411	8	polynomials	polynomial	NOUN
ejpam-6054	411	9	.	.	PUNCT
ejpam-6054	412	1	aims	aim	VERB
ejpam-6054	412	2	math	math	NOUN
ejpam-6054	412	3	.	.	PUNCT
ejpam-6054	412	4	,	,	PUNCT
ejpam-6054	412	5	8(2021	8(2021	NUM
ejpam-6054	412	6	)	)	PUNCT
ejpam-6054	412	7	.	.	PUNCT
ejpam-6054	413	1	[	[	X
ejpam-6054	413	2	11	11	NUM
ejpam-6054	413	3	]	]	PUNCT
ejpam-6054	413	4	w.	w.	PROPN
ejpam-6054	413	5	ramı́rez	ramı́rez	PROPN
ejpam-6054	413	6	,	,	PUNCT
ejpam-6054	413	7	c.	c.	PROPN
ejpam-6054	413	8	cesarano	cesarano	PROPN
ejpam-6054	413	9	,	,	PUNCT
ejpam-6054	413	10	s.a	s.a	PROPN
ejpam-6054	413	11	.	.	PROPN
ejpam-6054	413	12	wani	wani	PROPN
ejpam-6054	413	13	,	,	PUNCT
ejpam-6054	413	14	s.	s.	PROPN
ejpam-6054	413	15	yousuf	yousuf	PROPN
ejpam-6054	413	16	,	,	PUNCT
ejpam-6054	413	17	d.	d.	PROPN
ejpam-6054	413	18	bedoya	bedoya	PROPN
ejpam-6054	413	19	.	.	PUNCT
ejpam-6054	414	1	about	about	ADP
ejpam-6054	414	2	properties	property	NOUN
ejpam-6054	414	3	and	and	CCONJ
ejpam-6054	414	4	the	the	DET
ejpam-6054	414	5	monomiality	monomiality	NOUN
ejpam-6054	414	6	principle	principle	NOUN
ejpam-6054	414	7	of	of	ADP
ejpam-6054	414	8	bell	bell	NOUN
ejpam-6054	414	9	-	-	PUNCT
ejpam-6054	414	10	based	base	VERB
ejpam-6054	414	11	apostol	apostol	NOUN
ejpam-6054	414	12	-	-	PUNCT
ejpam-6054	414	13	bernoulli	bernoulli	NOUN
ejpam-6054	414	14	-	-	PUNCT
ejpam-6054	414	15	type	type	NOUN
ejpam-6054	414	16	polynomials	polynomial	NOUN
ejpam-6054	414	17	.	.	PUNCT
ejpam-6054	415	1	carpathian	carpathian	ADJ
ejpam-6054	415	2	math	math	PROPN
ejpam-6054	415	3	.	.	PUNCT
ejpam-6054	416	1	publ	publ	NOUN
ejpam-6054	416	2	.	.	PUNCT
ejpam-6054	417	1	16	16	NUM
ejpam-6054	417	2	(	(	PUNCT
ejpam-6054	417	3	2	2	NUM
ejpam-6054	417	4	)	)	PUNCT
ejpam-6054	417	5	(	(	PUNCT
ejpam-6054	417	6	2024	2024	NUM
ejpam-6054	417	7	)	)	PUNCT
ejpam-6054	417	8	,	,	PUNCT
ejpam-6054	417	9	379	379	NUM
ejpam-6054	417	10	-	-	SYM
ejpam-6054	417	11	390	390	NUM
ejpam-6054	417	12	.	.	PUNCT
ejpam-6054	418	1	[	[	X
ejpam-6054	418	2	12	12	NUM
ejpam-6054	418	3	]	]	X
ejpam-6054	418	4	w.	w.	PROPN
ejpam-6054	418	5	ramı́rez	ramı́rez	PROPN
ejpam-6054	418	6	,	,	PUNCT
ejpam-6054	418	7	z.	z.	PROPN
ejpam-6054	418	8	mohra	mohra	PROPN
ejpam-6054	418	9	,	,	PUNCT
ejpam-6054	418	10	w.	w.	PROPN
ejpam-6054	418	11	shahid	shahid	PROPN
ejpam-6054	418	12	,	,	PUNCT
ejpam-6054	418	13	a.	a.	NOUN
ejpam-6054	418	14	mohammad	mohammad	PROPN
ejpam-6054	418	15	,	,	PUNCT
ejpam-6054	418	16	f.	f.	PROPN
ejpam-6054	418	17	fuente	fuente	PROPN
ejpam-6054	418	18	.	.	PUNCT
ejpam-6054	419	1	properties	property	NOUN
ejpam-6054	419	2	and	and	CCONJ
ejpam-6054	419	3	applications	application	NOUN
ejpam-6054	419	4	of	of	ADP
ejpam-6054	419	5	bell	bell	NOUN
ejpam-6054	419	6	polynomials	polynomial	NOUN
ejpam-6054	419	7	of	of	ADP
ejpam-6054	419	8	two	two	NUM
ejpam-6054	419	9	variables	variable	NOUN
ejpam-6054	419	10	.	.	PUNCT
ejpam-6054	420	1	j.	j.	PROPN
ejpam-6054	420	2	math	math	PROPN
ejpam-6054	420	3	.	.	PUNCT
ejpam-6054	421	1	computer	computer	PROPN
ejpam-6054	421	2	sci	sci	PROPN
ejpam-6054	421	3	,	,	PUNCT
ejpam-6054	421	4	35	35	NUM
ejpam-6054	421	5	(	(	PUNCT
ejpam-6054	421	6	2024	2024	NUM
ejpam-6054	421	7	)	)	PUNCT
ejpam-6054	421	8	,	,	PUNCT
ejpam-6054	421	9	291	291	NUM
ejpam-6054	421	10	-	-	SYM
ejpam-6054	421	11	303	303	NUM
ejpam-6054	421	12	.	.	PUNCT
ejpam-6054	422	1	[	[	X
ejpam-6054	422	2	13	13	NUM
ejpam-6054	422	3	]	]	PUNCT
ejpam-6054	422	4	m.	m.	NOUN
ejpam-6054	422	5	fadel	fadel	PROPN
ejpam-6054	422	6	,	,	PUNCT
ejpam-6054	422	7	n.	n.	PROPN
ejpam-6054	422	8	raza	raza	PROPN
ejpam-6054	422	9	,	,	PUNCT
ejpam-6054	422	10	w.-s	w.-	NOUN
ejpam-6054	422	11	.	.	PUNCT
ejpam-6054	423	1	du	du	PROPN
ejpam-6054	423	2	.	.	PROPN
ejpam-6054	423	3	,	,	PUNCT
ejpam-6054	423	4	on	on	ADP
ejpam-6054	423	5	q	q	ADJ
ejpam-6054	423	6	-	-	ADJ
ejpam-6054	423	7	hermite	hermite	ADJ
ejpam-6054	423	8	polynomials	polynomial	NOUN
ejpam-6054	423	9	with	with	ADP
ejpam-6054	423	10	three	three	NUM
ejpam-6054	423	11	variables	variable	NOUN
ejpam-6054	423	12	:	:	PUNCT
ejpam-6054	423	13	recurrence	recurrence	NOUN
ejpam-6054	423	14	relations	relation	NOUN
ejpam-6054	423	15	,	,	PUNCT
ejpam-6054	423	16	q	q	ADJ
ejpam-6054	423	17	-	-	PUNCT
ejpam-6054	423	18	differential	differential	ADJ
ejpam-6054	423	19	equations	equation	NOUN
ejpam-6054	423	20	,	,	PUNCT
ejpam-6054	423	21	summation	summation	NOUN
ejpam-6054	423	22	and	and	CCONJ
ejpam-6054	423	23	operational	operational	ADJ
ejpam-6054	423	24	formulas	formula	NOUN
ejpam-6054	423	25	.	.	PUNCT
ejpam-6054	424	1	symmetry	symmetry	NOUN
ejpam-6054	424	2	.	.	PUNCT
ejpam-6054	425	1	16	16	NUM
ejpam-6054	425	2	,	,	PUNCT
ejpam-6054	425	3	(	(	PUNCT
ejpam-6054	425	4	2024	2024	NUM
ejpam-6054	425	5	)	)	PUNCT
ejpam-6054	425	6	.	.	PUNCT
ejpam-6054	426	1	[	[	X
ejpam-6054	426	2	14	14	NUM
ejpam-6054	426	3	]	]	X
ejpam-6054	426	4	d.s	d.s	PROPN
ejpam-6054	426	5	.	.	PROPN
ejpam-6054	426	6	kim	kim	PROPN
ejpam-6054	426	7	,	,	PUNCT
ejpam-6054	426	8	t.	t.	PROPN
ejpam-6054	426	9	kim	kim	PROPN
ejpam-6054	426	10	,	,	PUNCT
ejpam-6054	426	11	some	some	DET
ejpam-6054	426	12	new	new	ADJ
ejpam-6054	426	13	identities	identity	NOUN
ejpam-6054	426	14	of	of	ADP
ejpam-6054	426	15	frobenius	frobenius	NOUN
ejpam-6054	426	16	-	-	PUNCT
ejpam-6054	426	17	euler	euler	NOUN
ejpam-6054	426	18	numbers	number	NOUN
ejpam-6054	426	19	and	and	CCONJ
ejpam-6054	426	20	polynomials	polynomial	NOUN
ejpam-6054	426	21	,	,	PUNCT
ejpam-6054	426	22	j.	j.	PROPN
ejpam-6054	426	23	inequal	inequal	PROPN
ejpam-6054	426	24	.	.	PUNCT
ejpam-6054	427	1	appl	appl	PROPN
ejpam-6054	427	2	.	.	PUNCT
ejpam-6054	428	1	307	307	NUM
ejpam-6054	428	2	(	(	PUNCT
ejpam-6054	428	3	2012	2012	NUM
ejpam-6054	428	4	)	)	PUNCT
ejpam-6054	428	5	1	1	NUM
ejpam-6054	428	6	-	-	SYM
ejpam-6054	428	7	10	10	NUM
ejpam-6054	428	8	.	.	PUNCT
ejpam-6054	429	1	s.	s.	PROPN
ejpam-6054	429	2	a.	a.	PROPN
ejpam-6054	429	3	wani	wani	PROPN
ejpam-6054	429	4	et	et	PROPN
ejpam-6054	429	5	al	al	PROPN
ejpam-6054	429	6	.	.	PUNCT
ejpam-6054	429	7	/	/	SYM
ejpam-6054	429	8	eur	eur	PROPN
ejpam-6054	429	9	.	.	PUNCT
ejpam-6054	430	1	j.	j.	PROPN
ejpam-6054	430	2	pure	pure	PROPN
ejpam-6054	430	3	appl	appl	PROPN
ejpam-6054	430	4	.	.	PROPN
ejpam-6054	430	5	math	math	PROPN
ejpam-6054	430	6	,	,	PUNCT
ejpam-6054	430	7	18	18	NUM
ejpam-6054	430	8	(	(	PUNCT
ejpam-6054	430	9	3	3	NUM
ejpam-6054	430	10	)	)	PUNCT
ejpam-6054	430	11	(	(	PUNCT
ejpam-6054	430	12	2025	2025	NUM
ejpam-6054	430	13	)	)	PUNCT
ejpam-6054	430	14	,	,	PUNCT
ejpam-6054	430	15	6054	6054	NUM
ejpam-6054	430	16	16	16	NUM
ejpam-6054	430	17	of	of	ADP
ejpam-6054	430	18	16	16	NUM
ejpam-6054	431	1	[	[	X
ejpam-6054	431	2	15	15	NUM
ejpam-6054	431	3	]	]	PUNCT
ejpam-6054	431	4	t.	t.	PROPN
ejpam-6054	431	5	kim	kim	PROPN
ejpam-6054	431	6	,	,	PUNCT
ejpam-6054	431	7	identities	identity	NOUN
ejpam-6054	431	8	involving	involve	VERB
ejpam-6054	431	9	frobenius	frobenius	NOUN
ejpam-6054	431	10	-	-	PUNCT
ejpam-6054	431	11	euler	euler	NOUN
ejpam-6054	431	12	polynomials	polynomial	NOUN
ejpam-6054	431	13	arising	arise	VERB
ejpam-6054	431	14	from	from	ADP
ejpam-6054	431	15	non	non	ADJ
ejpam-6054	431	16	-	-	ADJ
ejpam-6054	431	17	linear	linear	ADJ
ejpam-6054	431	18	differential	differential	ADJ
ejpam-6054	431	19	equations	equation	NOUN
ejpam-6054	431	20	,	,	PUNCT
ejpam-6054	431	21	j.	j.	PROPN
ejpam-6054	431	22	number	number	PROPN
ejpam-6054	431	23	theory	theory	NOUN
ejpam-6054	431	24	132(12	132(12	NUM
ejpam-6054	431	25	)	)	PUNCT
ejpam-6054	431	26	(	(	PUNCT
ejpam-6054	431	27	2012	2012	NUM
ejpam-6054	431	28	)	)	PUNCT
ejpam-6054	431	29	2854	2854	NUM
ejpam-6054	431	30	-	-	SYM
ejpam-6054	431	31	2865	2865	NUM
ejpam-6054	431	32	.	.	PUNCT
ejpam-6054	432	1	[	[	X
ejpam-6054	432	2	16	16	NUM
ejpam-6054	432	3	]	]	PUNCT
ejpam-6054	432	4	t.	t.	PROPN
ejpam-6054	432	5	kim	kim	PROPN
ejpam-6054	432	6	,	,	PUNCT
ejpam-6054	432	7	b.-j	b.-j	PROPN
ejpam-6054	432	8	.	.	PUNCT
ejpam-6054	433	1	lee	lee	PROPN
ejpam-6054	433	2	,	,	PUNCT
ejpam-6054	433	3	some	some	DET
ejpam-6054	433	4	identities	identity	NOUN
ejpam-6054	433	5	of	of	ADP
ejpam-6054	433	6	the	the	DET
ejpam-6054	433	7	frobenius	frobenius	NOUN
ejpam-6054	433	8	-	-	PUNCT
ejpam-6054	433	9	euler	euler	NOUN
ejpam-6054	433	10	polynomials	polynomial	NOUN
ejpam-6054	433	11	,	,	PUNCT
ejpam-6054	433	12	abstr	abstr	PROPN
ejpam-6054	433	13	.	.	PUNCT
ejpam-6054	434	1	appl	appl	PROPN
ejpam-6054	434	2	.	.	PUNCT
ejpam-6054	435	1	anal	anal	PROPN
ejpam-6054	435	2	.	.	PUNCT
ejpam-6054	436	1	(	(	PUNCT
ejpam-6054	436	2	2009	2009	NUM
ejpam-6054	436	3	)	)	PUNCT
ejpam-6054	436	4	1	1	NUM
ejpam-6054	436	5	-	-	SYM
ejpam-6054	436	6	7	7	NUM
ejpam-6054	436	7	.	.	PUNCT
ejpam-6054	437	1	[	[	X
ejpam-6054	437	2	17	17	NUM
ejpam-6054	437	3	]	]	PUNCT
ejpam-6054	437	4	t.	t.	PROPN
ejpam-6054	437	5	kim	kim	PROPN
ejpam-6054	437	6	,	,	PUNCT
ejpam-6054	437	7	j.j	j.j	PROPN
ejpam-6054	437	8	.	.	PROPN
ejpam-6054	437	9	seo	seo	PROPN
ejpam-6054	437	10	,	,	PUNCT
ejpam-6054	437	11	some	some	DET
ejpam-6054	437	12	identities	identity	NOUN
ejpam-6054	437	13	involving	involve	VERB
ejpam-6054	437	14	frobenius	frobenius	NOUN
ejpam-6054	437	15	-	-	PUNCT
ejpam-6054	437	16	euler	euler	NOUN
ejpam-6054	437	17	polynomials	polynomial	NOUN
ejpam-6054	437	18	and	and	CCONJ
ejpam-6054	437	19	numbers	number	NOUN
ejpam-6054	437	20	,	,	PUNCT
ejpam-6054	437	21	proc	proc	NOUN
ejpam-6054	437	22	.	.	PUNCT
ejpam-6054	438	1	jangjeon	jangjeon	PROPN
ejpam-6054	438	2	math	math	PROPN
ejpam-6054	438	3	.	.	PUNCT
ejpam-6054	439	1	soc	soc	PROPN
ejpam-6054	439	2	.	.	PUNCT
ejpam-6054	440	1	19	19	NUM
ejpam-6054	440	2	(	(	PUNCT
ejpam-6054	440	3	2016	2016	NUM
ejpam-6054	440	4	)	)	PUNCT
ejpam-6054	440	5	39	39	NUM
ejpam-6054	440	6	-	-	SYM
ejpam-6054	440	7	46	46	NUM
ejpam-6054	440	8	.	.	PUNCT
ejpam-6054	441	1	[	[	X
ejpam-6054	441	2	18	18	NUM
ejpam-6054	441	3	]	]	PUNCT
ejpam-6054	441	4	a.	a.	NOUN
ejpam-6054	441	5	bayad	bayad	PROPN
ejpam-6054	441	6	,	,	PUNCT
ejpam-6054	441	7	t.	t.	PROPN
ejpam-6054	441	8	kim	kim	PROPN
ejpam-6054	441	9	,	,	PUNCT
ejpam-6054	441	10	identities	identity	NOUN
ejpam-6054	441	11	for	for	ADP
ejpam-6054	441	12	apostol	apostol	NOUN
ejpam-6054	441	13	-	-	PUNCT
ejpam-6054	441	14	type	type	NOUN
ejpam-6054	441	15	frobenius	frobenius	NOUN
ejpam-6054	441	16	-	-	PUNCT
ejpam-6054	441	17	euler	euler	NOUN
ejpam-6054	441	18	polynomials	polynomial	NOUN
ejpam-6054	441	19	resulting	result	VERB
ejpam-6054	441	20	from	from	ADP
ejpam-6054	441	21	the	the	DET
ejpam-6054	441	22	study	study	NOUN
ejpam-6054	441	23	of	of	ADP
ejpam-6054	441	24	a	a	DET
ejpam-6054	441	25	nonlinear	nonlinear	ADJ
ejpam-6054	441	26	operator	operator	NOUN
ejpam-6054	441	27	,	,	PUNCT
ejpam-6054	441	28	russ	russ	PROPN
ejpam-6054	441	29	.	.	PUNCT
ejpam-6054	442	1	j.	j.	PROPN
ejpam-6054	442	2	math	math	PROPN
ejpam-6054	442	3	.	.	PUNCT
ejpam-6054	443	1	phys	phy	NOUN
ejpam-6054	443	2	.	.	PUNCT
ejpam-6054	444	1	23	23	NUM
ejpam-6054	444	2	(	(	PUNCT
ejpam-6054	444	3	2016	2016	NUM
ejpam-6054	444	4	)	)	PUNCT
ejpam-6054	444	5	164	164	NUM
ejpam-6054	444	6	-	-	SYM
ejpam-6054	444	7	171	171	NUM
ejpam-6054	444	8	.	.	PUNCT
ejpam-6054	445	1	[	[	X
ejpam-6054	445	2	19	19	NUM
ejpam-6054	445	3	]	]	PUNCT
ejpam-6054	445	4	t.	t.	PROPN
ejpam-6054	445	5	kim	kim	PROPN
ejpam-6054	445	6	,	,	PUNCT
ejpam-6054	445	7	an	an	DET
ejpam-6054	445	8	identity	identity	NOUN
ejpam-6054	445	9	of	of	ADP
ejpam-6054	445	10	the	the	DET
ejpam-6054	445	11	symmetry	symmetry	NOUN
ejpam-6054	445	12	for	for	ADP
ejpam-6054	445	13	the	the	DET
ejpam-6054	445	14	frobenius	frobenius	NOUN
ejpam-6054	445	15	-	-	PUNCT
ejpam-6054	445	16	euler	euler	NOUN
ejpam-6054	445	17	polynomials	polynomial	NOUN
ejpam-6054	445	18	associated	associate	VERB
ejpam-6054	445	19	with	with	ADP
ejpam-6054	445	20	the	the	DET
ejpam-6054	445	21	fermionic	fermionic	NOUN
ejpam-6054	445	22	p	p	NOUN
ejpam-6054	445	23	-	-	PUNCT
ejpam-6054	445	24	adic	adic	ADJ
ejpam-6054	445	25	invariant	invariant	ADJ
ejpam-6054	445	26	q	q	NOUN
ejpam-6054	445	27	-	-	PUNCT
ejpam-6054	445	28	integrals	integral	NOUN
ejpam-6054	445	29	on	on	ADP
ejpam-6054	445	30	zp	zp	PROPN
ejpam-6054	445	31	,	,	PUNCT
ejpam-6054	445	32	rocky	rocky	PROPN
ejpam-6054	445	33	mt	mt	PROPN
ejpam-6054	445	34	.	.	PROPN
ejpam-6054	445	35	j.	j.	PROPN
ejpam-6054	445	36	math	math	PROPN
ejpam-6054	445	37	.	.	PUNCT
ejpam-6054	446	1	41	41	NUM
ejpam-6054	446	2	(	(	PUNCT
ejpam-6054	446	3	2011	2011	NUM
ejpam-6054	446	4	)	)	PUNCT
ejpam-6054	446	5	239	239	NUM
ejpam-6054	446	6	-	-	SYM
ejpam-6054	446	7	247	247	NUM
ejpam-6054	446	8	.	.	PUNCT