id	sid	tid	token	lemma	pos
ejpam-5288	1	1	european	european	PROPN
ejpam-5288	1	2	journal	journal	PROPN
ejpam-5288	1	3	of	of	ADP
ejpam-5288	1	4	pure	pure	ADJ
ejpam-5288	1	5	and	and	CCONJ
ejpam-5288	1	6	applied	apply	VERB
ejpam-5288	1	7	mathematics	mathematic	NOUN
ejpam-5288	1	8	vol	vol	NOUN
ejpam-5288	1	9	.	.	PROPN
ejpam-5288	2	1	17	17	NUM
ejpam-5288	2	2	,	,	PUNCT
ejpam-5288	2	3	no	no	INTJ
ejpam-5288	2	4	.	.	NOUN
ejpam-5288	2	5	3	3	NUM
ejpam-5288	2	6	,	,	PUNCT
ejpam-5288	2	7	2024	2024	NUM
ejpam-5288	2	8	,	,	PUNCT
ejpam-5288	2	9	1385	1385	NUM
ejpam-5288	2	10	-	-	SYM
ejpam-5288	2	11	1402	1402	NUM
ejpam-5288	2	12	issn	issn	PROPN
ejpam-5288	2	13	1307	1307	NUM
ejpam-5288	2	14	-	-	SYM
ejpam-5288	2	15	5543	5543	NUM
ejpam-5288	2	16	–	–	PUNCT
ejpam-5288	2	17	ejpam.com	ejpam.com	X
ejpam-5288	2	18	published	publish	VERB
ejpam-5288	2	19	by	by	ADP
ejpam-5288	2	20	new	new	PROPN
ejpam-5288	2	21	york	york	PROPN
ejpam-5288	2	22	business	business	PROPN
ejpam-5288	2	23	global	global	ADJ
ejpam-5288	2	24	some	some	DET
ejpam-5288	2	25	identities	identity	NOUN
ejpam-5288	2	26	on	on	ADP
ejpam-5288	2	27	λ	λ	NOUN
ejpam-5288	2	28	-	-	NOUN
ejpam-5288	2	29	analogues	analogue	NOUN
ejpam-5288	2	30	of	of	ADP
ejpam-5288	2	31	lah	lah	NOUN
ejpam-5288	2	32	numbers	number	NOUN
ejpam-5288	2	33	and	and	CCONJ
ejpam-5288	2	34	lah	lah	NOUN
ejpam-5288	2	35	-	-	PUNCT
ejpam-5288	2	36	bell	bell	NOUN
ejpam-5288	2	37	polynomials	polynomial	NOUN
ejpam-5288	2	38	dae	dae	VERB
ejpam-5288	2	39	san	san	PROPN
ejpam-5288	2	40	kim1	kim1	PROPN
ejpam-5288	2	41	,	,	PUNCT
ejpam-5288	2	42	taekyun	taekyun	PROPN
ejpam-5288	2	43	kim2,∗	kim2,∗	PROPN
ejpam-5288	2	44	,	,	PUNCT
ejpam-5288	2	45	hyekyung	hyekyung	PROPN
ejpam-5288	2	46	kim3	kim3	PROPN
ejpam-5288	2	47	,	,	PUNCT
ejpam-5288	2	48	jongkyum	jongkyum	PROPN
ejpam-5288	2	49	kwon4	kwon4	PROPN
ejpam-5288	2	50	,	,	PUNCT
ejpam-5288	2	51	*	*	SYM
ejpam-5288	2	52	1	1	NUM
ejpam-5288	2	53	department	department	NOUN
ejpam-5288	2	54	of	of	ADP
ejpam-5288	2	55	mathematics	mathematics	PROPN
ejpam-5288	2	56	,	,	PUNCT
ejpam-5288	2	57	sogang	sogang	PROPN
ejpam-5288	2	58	university	university	PROPN
ejpam-5288	2	59	,	,	PUNCT
ejpam-5288	2	60	seoul	seoul	PROPN
ejpam-5288	2	61	121	121	NUM
ejpam-5288	2	62	-	-	SYM
ejpam-5288	2	63	742	742	NUM
ejpam-5288	2	64	,	,	PUNCT
ejpam-5288	2	65	republic	republic	NOUN
ejpam-5288	2	66	of	of	ADP
ejpam-5288	2	67	korea	korea	PROPN
ejpam-5288	2	68	2	2	PROPN
ejpam-5288	2	69	department	department	NOUN
ejpam-5288	2	70	of	of	ADP
ejpam-5288	2	71	mathematics	mathematic	NOUN
ejpam-5288	2	72	,	,	PUNCT
ejpam-5288	2	73	kwangwoon	kwangwoon	NOUN
ejpam-5288	2	74	university	university	NOUN
ejpam-5288	2	75	,	,	PUNCT
ejpam-5288	2	76	seoul	seoul	PROPN
ejpam-5288	2	77	139	139	NUM
ejpam-5288	2	78	-	-	SYM
ejpam-5288	2	79	701	701	NUM
ejpam-5288	2	80	,	,	PUNCT
ejpam-5288	2	81	republic	republic	NOUN
ejpam-5288	2	82	of	of	ADP
ejpam-5288	2	83	korea	korea	PROPN
ejpam-5288	2	84	3	3	PROPN
ejpam-5288	2	85	department	department	PROPN
ejpam-5288	2	86	of	of	ADP
ejpam-5288	2	87	mathematics	mathematics	PROPN
ejpam-5288	2	88	education	education	NOUN
ejpam-5288	2	89	,	,	PUNCT
ejpam-5288	2	90	daegu	daegu	PROPN
ejpam-5288	2	91	catholic	catholic	PROPN
ejpam-5288	2	92	university	university	PROPN
ejpam-5288	2	93	,	,	PUNCT
ejpam-5288	2	94	gyeongsan	gyeongsan	ADJ
ejpam-5288	2	95	38430	38430	NUM
ejpam-5288	2	96	,	,	PUNCT
ejpam-5288	2	97	republic	republic	NOUN
ejpam-5288	2	98	of	of	ADP
ejpam-5288	2	99	korea	korea	PROPN
ejpam-5288	2	100	4	4	NUM
ejpam-5288	2	101	department	department	PROPN
ejpam-5288	2	102	of	of	ADP
ejpam-5288	2	103	mathematics	mathematics	PROPN
ejpam-5288	2	104	education	education	NOUN
ejpam-5288	2	105	,	,	PUNCT
ejpam-5288	2	106	gyeongsang	gyeongsang	PROPN
ejpam-5288	2	107	national	national	PROPN
ejpam-5288	2	108	university	university	PROPN
ejpam-5288	2	109	,	,	PUNCT
ejpam-5288	2	110	jinju	jinju	NOUN
ejpam-5288	2	111	52828	52828	NUM
ejpam-5288	2	112	,	,	PUNCT
ejpam-5288	2	113	republic	republic	NOUN
ejpam-5288	2	114	of	of	ADP
ejpam-5288	2	115	korea	korea	PROPN
ejpam-5288	2	116	abstract	abstract	NOUN
ejpam-5288	2	117	.	.	PUNCT
ejpam-5288	3	1	in	in	ADP
ejpam-5288	3	2	recent	recent	ADJ
ejpam-5288	3	3	years	year	NOUN
ejpam-5288	3	4	,	,	PUNCT
ejpam-5288	3	5	some	some	DET
ejpam-5288	3	6	applications	application	NOUN
ejpam-5288	3	7	of	of	ADP
ejpam-5288	3	8	lah	lah	NOUN
ejpam-5288	3	9	numbers	number	NOUN
ejpam-5288	3	10	were	be	AUX
ejpam-5288	3	11	discovered	discover	VERB
ejpam-5288	3	12	in	in	ADP
ejpam-5288	3	13	the	the	DET
ejpam-5288	3	14	real	real	ADJ
ejpam-5288	3	15	world	world	NOUN
ejpam-5288	3	16	problem	problem	NOUN
ejpam-5288	3	17	of	of	ADP
ejpam-5288	3	18	telecommunications	telecommunication	NOUN
ejpam-5288	3	19	and	and	CCONJ
ejpam-5288	3	20	optics	optic	NOUN
ejpam-5288	3	21	.	.	PUNCT
ejpam-5288	4	1	the	the	DET
ejpam-5288	4	2	aim	aim	NOUN
ejpam-5288	4	3	of	of	ADP
ejpam-5288	4	4	this	this	DET
ejpam-5288	4	5	paper	paper	NOUN
ejpam-5288	4	6	is	be	AUX
ejpam-5288	4	7	to	to	PART
ejpam-5288	4	8	study	study	VERB
ejpam-5288	4	9	the	the	DET
ejpam-5288	4	10	λ	λ	NOUN
ejpam-5288	4	11	-	-	NOUN
ejpam-5288	4	12	analogues	analogue	NOUN
ejpam-5288	4	13	of	of	ADP
ejpam-5288	4	14	lah	lah	NOUN
ejpam-5288	4	15	numbers	number	NOUN
ejpam-5288	4	16	and	and	CCONJ
ejpam-5288	4	17	lah	lah	NOUN
ejpam-5288	4	18	-	-	PUNCT
ejpam-5288	4	19	bell	bell	NOUN
ejpam-5288	4	20	polynomials	polynomial	NOUN
ejpam-5288	4	21	which	which	PRON
ejpam-5288	4	22	are	be	AUX
ejpam-5288	4	23	λ	λ	NOUN
ejpam-5288	4	24	-	-	NOUN
ejpam-5288	4	25	analogues	analogue	NOUN
ejpam-5288	4	26	of	of	ADP
ejpam-5288	4	27	the	the	DET
ejpam-5288	4	28	lah	lah	NOUN
ejpam-5288	4	29	numbers	number	NOUN
ejpam-5288	4	30	and	and	CCONJ
ejpam-5288	4	31	and	and	CCONJ
ejpam-5288	4	32	lahbell	lahbell	NOUN
ejpam-5288	4	33	polynomials	polynomial	NOUN
ejpam-5288	4	34	.	.	PUNCT
ejpam-5288	5	1	here	here	ADV
ejpam-5288	5	2	we	we	PRON
ejpam-5288	5	3	note	note	VERB
ejpam-5288	5	4	that	that	SCONJ
ejpam-5288	5	5	λ	λ	NOUN
ejpam-5288	5	6	-	-	NOUN
ejpam-5288	5	7	analogues	analogue	NOUN
ejpam-5288	5	8	appear	appear	VERB
ejpam-5288	5	9	when	when	SCONJ
ejpam-5288	5	10	we	we	PRON
ejpam-5288	5	11	replace	replace	VERB
ejpam-5288	5	12	the	the	DET
ejpam-5288	5	13	falling	fall	VERB
ejpam-5288	5	14	factorials	factorial	NOUN
ejpam-5288	5	15	by	by	ADP
ejpam-5288	5	16	the	the	DET
ejpam-5288	5	17	generalized	generalized	ADJ
ejpam-5288	5	18	falling	fall	VERB
ejpam-5288	5	19	factorials	factorial	NOUN
ejpam-5288	5	20	in	in	ADP
ejpam-5288	5	21	the	the	DET
ejpam-5288	5	22	defining	define	VERB
ejpam-5288	5	23	equations	equation	NOUN
ejpam-5288	5	24	.	.	PUNCT
ejpam-5288	6	1	by	by	ADP
ejpam-5288	6	2	using	use	VERB
ejpam-5288	6	3	generating	generate	VERB
ejpam-5288	6	4	function	function	NOUN
ejpam-5288	6	5	method	method	NOUN
ejpam-5288	6	6	,	,	PUNCT
ejpam-5288	6	7	we	we	PRON
ejpam-5288	6	8	study	study	VERB
ejpam-5288	6	9	some	some	DET
ejpam-5288	6	10	properties	property	NOUN
ejpam-5288	6	11	,	,	PUNCT
ejpam-5288	6	12	explicit	explicit	ADJ
ejpam-5288	6	13	expressions	expression	NOUN
ejpam-5288	6	14	,	,	PUNCT
ejpam-5288	6	15	generating	generating	NOUN
ejpam-5288	6	16	functions	function	NOUN
ejpam-5288	6	17	and	and	CCONJ
ejpam-5288	6	18	dobinski	dobinski	ADJ
ejpam-5288	6	19	-	-	PUNCT
ejpam-5288	6	20	like	like	ADJ
ejpam-5288	6	21	formulas	formula	NOUN
ejpam-5288	6	22	for	for	ADP
ejpam-5288	6	23	those	those	DET
ejpam-5288	6	24	numbers	number	NOUN
ejpam-5288	6	25	and	and	CCONJ
ejpam-5288	6	26	polynomials	polynomial	NOUN
ejpam-5288	6	27	.	.	PUNCT
ejpam-5288	7	1	we	we	PRON
ejpam-5288	7	2	also	also	ADV
ejpam-5288	7	3	treat	treat	VERB
ejpam-5288	7	4	the	the	DET
ejpam-5288	7	5	more	more	ADV
ejpam-5288	7	6	general	general	ADJ
ejpam-5288	7	7	λ	λ	NOUN
ejpam-5288	7	8	-	-	NOUN
ejpam-5288	7	9	analogues	analogue	NOUN
ejpam-5288	7	10	of	of	ADP
ejpam-5288	7	11	r	r	NOUN
ejpam-5288	7	12	-	-	PUNCT
ejpam-5288	7	13	lah	lah	NOUN
ejpam-5288	7	14	numbers	number	NOUN
ejpam-5288	7	15	and	and	CCONJ
ejpam-5288	7	16	r	r	NOUN
ejpam-5288	7	17	-	-	PUNCT
ejpam-5288	7	18	extended	extend	VERB
ejpam-5288	7	19	λ	λ	NOUN
ejpam-5288	7	20	-	-	PUNCT
ejpam-5288	7	21	lah	lah	ADJ
ejpam-5288	7	22	-	-	PUNCT
ejpam-5288	7	23	bell	bell	NOUN
ejpam-5288	7	24	polynomials	polynomial	NOUN
ejpam-5288	7	25	.	.	PUNCT
ejpam-5288	8	1	in	in	ADP
ejpam-5288	8	2	addition	addition	NOUN
ejpam-5288	8	3	,	,	PUNCT
ejpam-5288	8	4	we	we	PRON
ejpam-5288	8	5	show	show	VERB
ejpam-5288	8	6	that	that	SCONJ
ejpam-5288	8	7	the	the	DET
ejpam-5288	8	8	expectations	expectation	NOUN
ejpam-5288	8	9	of	of	ADP
ejpam-5288	8	10	two	two	NUM
ejpam-5288	8	11	random	random	ADJ
ejpam-5288	8	12	variables	variable	NOUN
ejpam-5288	8	13	,	,	PUNCT
ejpam-5288	8	14	both	both	PRON
ejpam-5288	8	15	associated	associate	VERB
ejpam-5288	8	16	with	with	ADP
ejpam-5288	8	17	the	the	DET
ejpam-5288	8	18	poisson	poisson	NOUN
ejpam-5288	8	19	random	random	ADJ
ejpam-5288	8	20	variable	variable	NOUN
ejpam-5288	8	21	with	with	ADP
ejpam-5288	8	22	parameter	parameter	NOUN
ejpam-5288	8	23	α	α	PROPN
ejpam-5288	8	24	λ	λ	PROPN
ejpam-5288	8	25	,	,	PUNCT
ejpam-5288	8	26	are	be	AUX
ejpam-5288	8	27	equal	equal	ADJ
ejpam-5288	8	28	to	to	ADP
ejpam-5288	8	29	the	the	DET
ejpam-5288	8	30	λ	λ	NOUN
ejpam-5288	8	31	-	-	NOUN
ejpam-5288	8	32	analogue	analogue	NOUN
ejpam-5288	8	33	of	of	ADP
ejpam-5288	8	34	the	the	DET
ejpam-5288	8	35	lah	lah	PROPN
ejpam-5288	8	36	-	-	PUNCT
ejpam-5288	8	37	bell	bell	NOUN
ejpam-5288	8	38	polynomial	polynomial	ADJ
ejpam-5288	8	39	evaluated	evaluate	VERB
ejpam-5288	8	40	at	at	ADP
ejpam-5288	8	41	α	α	NOUN
ejpam-5288	8	42	for	for	ADP
ejpam-5288	8	43	one	one	NUM
ejpam-5288	8	44	and	and	CCONJ
ejpam-5288	8	45	the	the	DET
ejpam-5288	8	46	r	r	NOUN
ejpam-5288	8	47	-	-	PUNCT
ejpam-5288	8	48	extended	extend	VERB
ejpam-5288	8	49	λ	λ	NOUN
ejpam-5288	8	50	-	-	PUNCT
ejpam-5288	8	51	lah	lah	ADJ
ejpam-5288	8	52	-	-	PUNCT
ejpam-5288	8	53	bell	bell	NOUN
ejpam-5288	8	54	polynomial	polynomial	ADJ
ejpam-5288	8	55	evaluated	evaluate	VERB
ejpam-5288	8	56	at	at	ADP
ejpam-5288	8	57	α	α	NOUN
ejpam-5288	8	58	for	for	ADP
ejpam-5288	8	59	the	the	DET
ejpam-5288	8	60	other	other	ADJ
ejpam-5288	8	61	.	.	PUNCT
ejpam-5288	9	1	2020	2020	NUM
ejpam-5288	9	2	mathematics	mathematic	NOUN
ejpam-5288	9	3	subject	subject	NOUN
ejpam-5288	9	4	classifications	classification	NOUN
ejpam-5288	9	5	:	:	PUNCT
ejpam-5288	9	6	11b73	11b73	NUM
ejpam-5288	9	7	,	,	PUNCT
ejpam-5288	9	8	11b83	11b83	NUM
ejpam-5288	9	9	key	key	ADJ
ejpam-5288	9	10	words	word	NOUN
ejpam-5288	9	11	and	and	CCONJ
ejpam-5288	9	12	phrases	phrase	NOUN
ejpam-5288	9	13	:	:	PUNCT
ejpam-5288	9	14	λ	λ	NOUN
ejpam-5288	9	15	-	-	NOUN
ejpam-5288	9	16	analogues	analogue	NOUN
ejpam-5288	9	17	of	of	ADP
ejpam-5288	9	18	lah	lah	NOUN
ejpam-5288	9	19	numbers	number	NOUN
ejpam-5288	9	20	,	,	PUNCT
ejpam-5288	9	21	λ	λ	NOUN
ejpam-5288	9	22	-	-	NOUN
ejpam-5288	9	23	analogues	analogue	NOUN
ejpam-5288	9	24	of	of	ADP
ejpam-5288	9	25	lah	lah	PROPN
ejpam-5288	9	26	-	-	PUNCT
ejpam-5288	9	27	bell	bell	NOUN
ejpam-5288	9	28	polynomials	polynomial	NOUN
ejpam-5288	9	29	,	,	PUNCT
ejpam-5288	9	30	λanalogues	λanalogue	NOUN
ejpam-5288	9	31	of	of	ADP
ejpam-5288	9	32	laguerre	laguerre	NOUN
ejpam-5288	9	33	polynomials	polynomial	NOUN
ejpam-5288	9	34	,	,	PUNCT
ejpam-5288	9	35	λ	λ	NOUN
ejpam-5288	9	36	-	-	NOUN
ejpam-5288	9	37	analogues	analogue	NOUN
ejpam-5288	9	38	of	of	ADP
ejpam-5288	9	39	r	r	NOUN
ejpam-5288	9	40	-	-	PUNCT
ejpam-5288	9	41	numbers	number	NOUN
ejpam-5288	9	42	,	,	PUNCT
ejpam-5288	9	43	r	r	NOUN
ejpam-5288	9	44	-	-	PUNCT
ejpam-5288	9	45	extended	extend	VERB
ejpam-5288	9	46	λ	λ	NOUN
ejpam-5288	9	47	-	-	PUNCT
ejpam-5288	9	48	lah	lah	ADJ
ejpam-5288	9	49	-	-	PUNCT
ejpam-5288	9	50	bell	bell	NOUN
ejpam-5288	9	51	polynomials	polynomial	NOUN
ejpam-5288	9	52	1	1	NUM
ejpam-5288	9	53	.	.	PUNCT
ejpam-5288	9	54	introduction	introduction	NOUN
ejpam-5288	9	55	the	the	DET
ejpam-5288	9	56	unsigned	unsigned	ADJ
ejpam-5288	9	57	lah	lah	PROPN
ejpam-5288	9	58	number	number	NOUN
ejpam-5288	9	59	l(n	l(n	PROPN
ejpam-5288	9	60	,	,	PUNCT
ejpam-5288	9	61	k	k	NOUN
ejpam-5288	9	62	)	)	PUNCT
ejpam-5288	9	63	counts	count	VERB
ejpam-5288	9	64	the	the	DET
ejpam-5288	9	65	number	number	NOUN
ejpam-5288	9	66	of	of	ADP
ejpam-5288	9	67	ways	way	NOUN
ejpam-5288	9	68	that	that	PRON
ejpam-5288	9	69	a	a	DET
ejpam-5288	9	70	set	set	NOUN
ejpam-5288	9	71	of	of	ADP
ejpam-5288	9	72	n	n	PRON
ejpam-5288	9	73	elements	element	NOUN
ejpam-5288	9	74	can	can	AUX
ejpam-5288	9	75	be	be	AUX
ejpam-5288	9	76	partitioned	partition	VERB
ejpam-5288	9	77	into	into	ADP
ejpam-5288	9	78	k	k	PROPN
ejpam-5288	9	79	non	non	ADJ
ejpam-5288	9	80	-	-	ADJ
ejpam-5288	9	81	empty	empty	ADJ
ejpam-5288	9	82	linearly	linearly	ADV
ejpam-5288	9	83	ordered	order	VERB
ejpam-5288	9	84	susbsets	susbset	NOUN
ejpam-5288	9	85	,	,	PUNCT
ejpam-5288	9	86	while	while	SCONJ
ejpam-5288	9	87	the	the	DET
ejpam-5288	9	88	lah	lah	NOUN
ejpam-5288	9	89	-	-	PUNCT
ejpam-5288	9	90	bell	bell	NOUN
ejpam-5288	9	91	number	number	NOUN
ejpam-5288	9	92	bl	bl	PROPN
ejpam-5288	9	93	n	n	PROPN
ejpam-5288	9	94	is	be	AUX
ejpam-5288	9	95	the	the	DET
ejpam-5288	9	96	number	number	NOUN
ejpam-5288	9	97	of	of	ADP
ejpam-5288	9	98	ways	way	NOUN
ejpam-5288	9	99	that	that	PRON
ejpam-5288	9	100	a	a	DET
ejpam-5288	9	101	set	set	NOUN
ejpam-5288	9	102	of	of	ADP
ejpam-5288	9	103	n	n	PRON
ejpam-5288	9	104	elements	element	NOUN
ejpam-5288	9	105	can	can	AUX
ejpam-5288	9	106	be	be	AUX
ejpam-5288	9	107	partitioned	partition	VERB
ejpam-5288	9	108	into	into	ADP
ejpam-5288	9	109	nonempty	nonempty	NOUN
ejpam-5288	9	110	linearly	linearly	ADV
ejpam-5288	9	111	ordered	order	VERB
ejpam-5288	9	112	subsets	subset	NOUN
ejpam-5288	9	113	.	.	PUNCT
ejpam-5288	10	1	in	in	ADP
ejpam-5288	10	2	recent	recent	ADJ
ejpam-5288	10	3	years	year	NOUN
ejpam-5288	10	4	,	,	PUNCT
ejpam-5288	10	5	some	some	DET
ejpam-5288	10	6	practical	practical	ADJ
ejpam-5288	10	7	applications	application	NOUN
ejpam-5288	10	8	of	of	ADP
ejpam-5288	10	9	the	the	DET
ejpam-5288	10	10	lah	lah	NOUN
ejpam-5288	10	11	numbers	number	NOUN
ejpam-5288	10	12	were	be	AUX
ejpam-5288	10	13	found	find	VERB
ejpam-5288	10	14	in	in	ADP
ejpam-5288	10	15	telecommunications	telecommunication	NOUN
ejpam-5288	10	16	and	and	CCONJ
ejpam-5288	10	17	optics	optic	NOUN
ejpam-5288	10	18	.	.	PUNCT
ejpam-5288	11	1	indeed	indeed	ADV
ejpam-5288	11	2	,	,	PUNCT
ejpam-5288	11	3	lah	lah	PROPN
ejpam-5288	11	4	numbers	number	NOUN
ejpam-5288	11	5	have	have	AUX
ejpam-5288	11	6	been	be	AUX
ejpam-5288	11	7	used	use	VERB
ejpam-5288	11	8	in	in	ADP
ejpam-5288	11	9	∗corresponding	∗corresponde	VERB
ejpam-5288	11	10	author	author	NOUN
ejpam-5288	11	11	.	.	PUNCT
ejpam-5288	12	1	doi	doi	NOUN
ejpam-5288	12	2	:	:	PUNCT
ejpam-5288	12	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5288	https://doi.org/10.29020/nybg.ejpam.v17i3.5288	ADJ
ejpam-5288	12	4	email	email	NOUN
ejpam-5288	12	5	addresses	address	NOUN
ejpam-5288	12	6	:	:	PUNCT
ejpam-5288	12	7	dskim@sogang.ac.k	dskim@sogang.ac.k	X
ejpam-5288	12	8	(	(	PUNCT
ejpam-5288	12	9	d.	d.	PROPN
ejpam-5288	12	10	s.	s.	PROPN
ejpam-5288	12	11	kim	kim	PROPN
ejpam-5288	12	12	)	)	PUNCT
ejpam-5288	12	13	,	,	PUNCT
ejpam-5288	12	14	tkkim@kw.ac.kr	tkkim@kw.ac.kr	X
ejpam-5288	12	15	(	(	PUNCT
ejpam-5288	12	16	t.	t.	PROPN
ejpam-5288	12	17	kim	kim	PROPN
ejpam-5288	12	18	)	)	PUNCT
ejpam-5288	12	19	,	,	PUNCT
ejpam-5288	12	20	hkkim@cu.ac.kr	hkkim@cu.ac.kr	X
ejpam-5288	12	21	(	(	PUNCT
ejpam-5288	12	22	h.	h.	PROPN
ejpam-5288	12	23	kim	kim	PROPN
ejpam-5288	12	24	)	)	PUNCT
ejpam-5288	12	25	,	,	PUNCT
ejpam-5288	12	26	mathkjk26@gnu.ac.kr	mathkjk26@gnu.ac.kr	PROPN
ejpam-5288	12	27	(	(	PUNCT
ejpam-5288	12	28	j.	j.	PROPN
ejpam-5288	12	29	kwon	kwon	PROPN
ejpam-5288	12	30	)	)	PUNCT
ejpam-5288	12	31	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5288	12	32	1385	1385	NUM
ejpam-5288	12	33	©	©	ADP
ejpam-5288	12	34	2024	2024	NUM
ejpam-5288	12	35	ejpam	ejpam	NOUN
ejpam-5288	12	36	all	all	DET
ejpam-5288	12	37	rights	right	NOUN
ejpam-5288	12	38	reserved	reserve	VERB
ejpam-5288	12	39	.	.	PUNCT
ejpam-5288	13	1	j.	j.	PROPN
ejpam-5288	13	2	kwon	kwon	PROPN
ejpam-5288	13	3	et	et	PROPN
ejpam-5288	13	4	al	al	PROPN
ejpam-5288	13	5	.	.	PUNCT
ejpam-5288	13	6	/	/	SYM
ejpam-5288	13	7	eur	eur	PROPN
ejpam-5288	13	8	.	.	PUNCT
ejpam-5288	14	1	j.	j.	PROPN
ejpam-5288	14	2	pure	pure	PROPN
ejpam-5288	14	3	appl	appl	PROPN
ejpam-5288	14	4	.	.	PROPN
ejpam-5288	14	5	math	math	PROPN
ejpam-5288	14	6	,	,	PUNCT
ejpam-5288	14	7	17	17	NUM
ejpam-5288	14	8	(	(	PUNCT
ejpam-5288	14	9	3	3	NUM
ejpam-5288	14	10	)	)	PUNCT
ejpam-5288	14	11	(	(	PUNCT
ejpam-5288	14	12	2024	2024	NUM
ejpam-5288	14	13	)	)	PUNCT
ejpam-5288	14	14	,	,	PUNCT
ejpam-5288	14	15	1385	1385	NUM
ejpam-5288	14	16	-	-	SYM
ejpam-5288	14	17	1402	1402	NUM
ejpam-5288	14	18	1386	1386	NUM
ejpam-5288	14	19	steganography	steganography	NOUN
ejpam-5288	14	20	for	for	ADP
ejpam-5288	14	21	hiding	hiding	NOUN
ejpam-5288	14	22	data	datum	NOUN
ejpam-5288	14	23	in	in	ADP
ejpam-5288	14	24	images	image	NOUN
ejpam-5288	14	25	(	(	PUNCT
ejpam-5288	14	26	see	see	VERB
ejpam-5288	14	27	[	[	X
ejpam-5288	14	28	6	6	NUM
ejpam-5288	14	29	]	]	NUM
ejpam-5288	14	30	)	)	PUNCT
ejpam-5288	14	31	.	.	PUNCT
ejpam-5288	15	1	it	it	PRON
ejpam-5288	15	2	requires	require	VERB
ejpam-5288	15	3	lower	low	ADJ
ejpam-5288	15	4	complexity	complexity	NOUN
ejpam-5288	15	5	of	of	ADP
ejpam-5288	15	6	calculation	calculation	NOUN
ejpam-5288	15	7	,	,	PUNCT
ejpam-5288	15	8	compared	compare	VERB
ejpam-5288	15	9	to	to	ADP
ejpam-5288	15	10	alternatives	alternatives	PROPN
ejpam-5288	15	11	dft	dft	PROPN
ejpam-5288	15	12	(	(	PUNCT
ejpam-5288	15	13	discrete	discrete	ADJ
ejpam-5288	15	14	fourier	fourier	NOUN
ejpam-5288	15	15	transform	transform	NOUN
ejpam-5288	15	16	)	)	PUNCT
ejpam-5288	15	17	and	and	CCONJ
ejpam-5288	15	18	dwt	dwt	NOUN
ejpam-5288	15	19	(	(	PUNCT
ejpam-5288	15	20	discrete	discrete	ADJ
ejpam-5288	15	21	wavelet	wavelet	NOUN
ejpam-5288	15	22	transform	transform	NOUN
ejpam-5288	15	23	)	)	PUNCT
ejpam-5288	15	24	.	.	PUNCT
ejpam-5288	16	1	in	in	ADP
ejpam-5288	16	2	addition	addition	NOUN
ejpam-5288	16	3	,	,	PUNCT
ejpam-5288	16	4	the	the	DET
ejpam-5288	16	5	lah	lah	NOUN
ejpam-5288	16	6	transform	transform	NOUN
ejpam-5288	16	7	naturally	naturally	ADV
ejpam-5288	16	8	arises	arise	VERB
ejpam-5288	16	9	in	in	ADP
ejpam-5288	16	10	the	the	DET
ejpam-5288	16	11	perturbative	perturbative	ADJ
ejpam-5288	16	12	description	description	NOUN
ejpam-5288	16	13	of	of	ADP
ejpam-5288	16	14	the	the	DET
ejpam-5288	16	15	chromatic	chromatic	ADJ
ejpam-5288	16	16	dispersion	dispersion	NOUN
ejpam-5288	16	17	in	in	ADP
ejpam-5288	16	18	optics	optic	NOUN
ejpam-5288	16	19	(	(	PUNCT
ejpam-5288	16	20	see	see	VERB
ejpam-5288	16	21	[	[	X
ejpam-5288	16	22	22,23	22,23	NOUN
ejpam-5288	16	23	]	]	PUNCT
ejpam-5288	16	24	)	)	PUNCT
ejpam-5288	16	25	and	and	CCONJ
ejpam-5288	16	26	can	can	AUX
ejpam-5288	16	27	tremendously	tremendously	ADV
ejpam-5288	16	28	speeds	speed	VERB
ejpam-5288	16	29	up	up	ADP
ejpam-5288	16	30	optimization	optimization	NOUN
ejpam-5288	16	31	problems	problem	NOUN
ejpam-5288	16	32	.	.	PUNCT
ejpam-5288	17	1	the	the	DET
ejpam-5288	17	2	study	study	NOUN
ejpam-5288	17	3	of	of	ADP
ejpam-5288	17	4	degenerate	degenerate	ADJ
ejpam-5288	17	5	versions	version	NOUN
ejpam-5288	17	6	of	of	ADP
ejpam-5288	17	7	many	many	ADJ
ejpam-5288	17	8	special	special	ADJ
ejpam-5288	17	9	numbers	number	NOUN
ejpam-5288	17	10	and	and	CCONJ
ejpam-5288	17	11	polynomials	polynomial	NOUN
ejpam-5288	17	12	has	have	AUX
ejpam-5288	17	13	been	be	AUX
ejpam-5288	17	14	done	do	VERB
ejpam-5288	17	15	in	in	ADP
ejpam-5288	17	16	recent	recent	ADJ
ejpam-5288	17	17	years	year	NOUN
ejpam-5288	17	18	by	by	ADP
ejpam-5288	17	19	some	some	DET
ejpam-5288	17	20	mathematicians	mathematician	NOUN
ejpam-5288	17	21	for	for	ADP
ejpam-5288	17	22	their	their	PRON
ejpam-5288	17	23	regained	regain	VERB
ejpam-5288	17	24	interests	interest	NOUN
ejpam-5288	17	25	(	(	PUNCT
ejpam-5288	17	26	see	see	VERB
ejpam-5288	17	27	[	[	X
ejpam-5288	17	28	2,9,15,16,21	2,9,15,16,21	NUM
ejpam-5288	17	29	]	]	PUNCT
ejpam-5288	17	30	and	and	CCONJ
ejpam-5288	17	31	the	the	DET
ejpam-5288	17	32	references	reference	NOUN
ejpam-5288	17	33	therein	therein	ADV
ejpam-5288	17	34	)	)	PUNCT
ejpam-5288	17	35	.	.	PUNCT
ejpam-5288	18	1	a	a	DET
ejpam-5288	18	2	lot	lot	NOUN
ejpam-5288	18	3	of	of	ADP
ejpam-5288	18	4	fascinating	fascinating	ADJ
ejpam-5288	18	5	results	result	NOUN
ejpam-5288	18	6	have	have	AUX
ejpam-5288	18	7	been	be	AUX
ejpam-5288	18	8	discovered	discover	VERB
ejpam-5288	18	9	.	.	PUNCT
ejpam-5288	19	1	for	for	ADP
ejpam-5288	19	2	example	example	NOUN
ejpam-5288	19	3	,	,	PUNCT
ejpam-5288	19	4	the	the	DET
ejpam-5288	19	5	degenerate	degenerate	ADJ
ejpam-5288	19	6	stirling	stirling	NOUN
ejpam-5288	19	7	numbers	number	NOUN
ejpam-5288	19	8	of	of	ADP
ejpam-5288	19	9	the	the	DET
ejpam-5288	19	10	first	first	ADJ
ejpam-5288	19	11	kind	kind	NOUN
ejpam-5288	19	12	and	and	CCONJ
ejpam-5288	19	13	the	the	DET
ejpam-5288	19	14	second	second	ADJ
ejpam-5288	19	15	kind	kind	NOUN
ejpam-5288	19	16	,	,	PUNCT
ejpam-5288	19	17	which	which	PRON
ejpam-5288	19	18	are	be	AUX
ejpam-5288	19	19	degenerate	degenerate	ADJ
ejpam-5288	19	20	versions	version	NOUN
ejpam-5288	19	21	of	of	ADP
ejpam-5288	19	22	the	the	DET
ejpam-5288	19	23	ordinary	ordinary	ADJ
ejpam-5288	19	24	stirling	stirling	NOUN
ejpam-5288	19	25	numbers	number	NOUN
ejpam-5288	19	26	of	of	ADP
ejpam-5288	19	27	the	the	DET
ejpam-5288	19	28	first	first	ADJ
ejpam-5288	19	29	kind	kind	NOUN
ejpam-5288	19	30	and	and	CCONJ
ejpam-5288	19	31	the	the	DET
ejpam-5288	19	32	second	second	ADJ
ejpam-5288	19	33	kind	kind	NOUN
ejpam-5288	19	34	respectively	respectively	ADV
ejpam-5288	19	35	,	,	PUNCT
ejpam-5288	19	36	occur	occur	VERB
ejpam-5288	19	37	very	very	ADV
ejpam-5288	19	38	frequently	frequently	ADV
ejpam-5288	19	39	when	when	SCONJ
ejpam-5288	19	40	one	one	NUM
ejpam-5288	19	41	studies	study	NOUN
ejpam-5288	19	42	degenerate	degenerate	VERB
ejpam-5288	19	43	versions	version	NOUN
ejpam-5288	19	44	of	of	ADP
ejpam-5288	19	45	many	many	ADJ
ejpam-5288	19	46	special	special	ADJ
ejpam-5288	19	47	numbers	number	NOUN
ejpam-5288	19	48	and	and	CCONJ
ejpam-5288	19	49	polynomials	polynomial	NOUN
ejpam-5288	19	50	(	(	PUNCT
ejpam-5288	19	51	see	see	VERB
ejpam-5288	19	52	[	[	X
ejpam-5288	19	53	2,9,15,16,21	2,9,15,16,21	NUM
ejpam-5288	19	54	]	]	PUNCT
ejpam-5288	19	55	)	)	PUNCT
ejpam-5288	19	56	.	.	PUNCT
ejpam-5288	20	1	the	the	DET
ejpam-5288	20	2	λumbral	λumbral	ADJ
ejpam-5288	20	3	calculus	calculus	NOUN
ejpam-5288	20	4	,	,	PUNCT
ejpam-5288	20	5	which	which	PRON
ejpam-5288	20	6	is	be	AUX
ejpam-5288	20	7	more	more	ADV
ejpam-5288	20	8	convenient	convenient	ADJ
ejpam-5288	20	9	when	when	SCONJ
ejpam-5288	20	10	dealing	deal	VERB
ejpam-5288	20	11	with	with	ADP
ejpam-5288	20	12	degenerate	degenerate	ADJ
ejpam-5288	20	13	versions	version	NOUN
ejpam-5288	20	14	of	of	ADP
ejpam-5288	20	15	sheffer	sheffer	NOUN
ejpam-5288	20	16	polynomials	polynomial	NOUN
ejpam-5288	20	17	,	,	PUNCT
ejpam-5288	20	18	has	have	AUX
ejpam-5288	20	19	been	be	AUX
ejpam-5288	20	20	uncovered	uncover	VERB
ejpam-5288	20	21	as	as	ADP
ejpam-5288	20	22	a	a	DET
ejpam-5288	20	23	natural	natural	ADJ
ejpam-5288	20	24	degenerate	degenerate	ADJ
ejpam-5288	20	25	version	version	NOUN
ejpam-5288	20	26	of	of	ADP
ejpam-5288	20	27	the	the	DET
ejpam-5288	20	28	usual	usual	ADJ
ejpam-5288	20	29	umbral	umbral	ADJ
ejpam-5288	20	30	calculus	calculus	NOUN
ejpam-5288	20	31	(	(	PUNCT
ejpam-5288	20	32	see	see	VERB
ejpam-5288	20	33	[	[	X
ejpam-5288	20	34	13	13	NUM
ejpam-5288	20	35	]	]	NUM
ejpam-5288	20	36	)	)	PUNCT
ejpam-5288	20	37	.	.	PUNCT
ejpam-5288	21	1	in	in	ADP
ejpam-5288	21	2	addition	addition	NOUN
ejpam-5288	21	3	,	,	PUNCT
ejpam-5288	21	4	the	the	DET
ejpam-5288	21	5	degenerate	degenerate	ADJ
ejpam-5288	21	6	gamma	gamma	NOUN
ejpam-5288	21	7	functions	function	NOUN
ejpam-5288	21	8	were	be	AUX
ejpam-5288	21	9	found	find	VERB
ejpam-5288	21	10	as	as	ADP
ejpam-5288	21	11	a	a	DET
ejpam-5288	21	12	degenerate	degenerate	ADJ
ejpam-5288	21	13	version	version	NOUN
ejpam-5288	21	14	of	of	ADP
ejpam-5288	21	15	the	the	DET
ejpam-5288	21	16	ordinary	ordinary	ADJ
ejpam-5288	21	17	gamma	gamma	NOUN
ejpam-5288	21	18	functions	function	NOUN
ejpam-5288	21	19	(	(	PUNCT
ejpam-5288	21	20	see	see	VERB
ejpam-5288	21	21	[	[	X
ejpam-5288	21	22	14	14	NUM
ejpam-5288	21	23	]	]	NUM
ejpam-5288	21	24	)	)	PUNCT
ejpam-5288	21	25	.	.	PUNCT
ejpam-5288	22	1	the	the	DET
ejpam-5288	22	2	aim	aim	NOUN
ejpam-5288	22	3	of	of	ADP
ejpam-5288	22	4	this	this	DET
ejpam-5288	22	5	paper	paper	NOUN
ejpam-5288	22	6	is	be	AUX
ejpam-5288	22	7	to	to	PART
ejpam-5288	22	8	study	study	VERB
ejpam-5288	22	9	the	the	DET
ejpam-5288	22	10	λ	λ	NOUN
ejpam-5288	22	11	-	-	NOUN
ejpam-5288	22	12	analogues	analogue	NOUN
ejpam-5288	22	13	of	of	ADP
ejpam-5288	22	14	lah	lah	PROPN
ejpam-5288	22	15	numbers	number	NOUN
ejpam-5288	22	16	lλ(n	lλ(n	PUNCT
ejpam-5288	22	17	,	,	PUNCT
ejpam-5288	22	18	k	k	NOUN
ejpam-5288	22	19	)	)	PUNCT
ejpam-5288	22	20	(	(	PUNCT
ejpam-5288	22	21	see	see	VERB
ejpam-5288	22	22	(	(	PUNCT
ejpam-5288	22	23	14	14	NUM
ejpam-5288	22	24	)	)	PUNCT
ejpam-5288	22	25	)	)	PUNCT
ejpam-5288	22	26	and	and	CCONJ
ejpam-5288	22	27	lah	lah	PROPN
ejpam-5288	22	28	-	-	PUNCT
ejpam-5288	22	29	bell	bell	NOUN
ejpam-5288	22	30	polynomials	polynomial	NOUN
ejpam-5288	22	31	bl	bl	NOUN
ejpam-5288	22	32	n	n	PRON
ejpam-5288	22	33	,	,	PUNCT
ejpam-5288	22	34	λ(x	λ(x	PROPN
ejpam-5288	22	35	)	)	PUNCT
ejpam-5288	22	36	(	(	PUNCT
ejpam-5288	22	37	see	see	VERB
ejpam-5288	22	38	(	(	PUNCT
ejpam-5288	22	39	21	21	NUM
ejpam-5288	22	40	)	)	PUNCT
ejpam-5288	22	41	,	,	PUNCT
ejpam-5288	22	42	(	(	PUNCT
ejpam-5288	22	43	23	23	NUM
ejpam-5288	22	44	)	)	PUNCT
ejpam-5288	22	45	)	)	PUNCT
ejpam-5288	22	46	which	which	PRON
ejpam-5288	22	47	are	be	AUX
ejpam-5288	22	48	λanalogues	λanalogue	NOUN
ejpam-5288	22	49	of	of	ADP
ejpam-5288	22	50	the	the	DET
ejpam-5288	22	51	lah	lah	NOUN
ejpam-5288	22	52	numbers	number	NOUN
ejpam-5288	22	53	and	and	CCONJ
ejpam-5288	22	54	and	and	CCONJ
ejpam-5288	22	55	lah	lah	NOUN
ejpam-5288	22	56	-	-	PUNCT
ejpam-5288	22	57	bell	bell	NOUN
ejpam-5288	22	58	polynomials	polynomial	NOUN
ejpam-5288	22	59	.	.	PUNCT
ejpam-5288	23	1	we	we	PRON
ejpam-5288	23	2	investigate	investigate	VERB
ejpam-5288	23	3	some	some	DET
ejpam-5288	23	4	properties	property	NOUN
ejpam-5288	23	5	,	,	PUNCT
ejpam-5288	23	6	explicit	explicit	ADJ
ejpam-5288	23	7	expressions	expression	NOUN
ejpam-5288	23	8	,	,	PUNCT
ejpam-5288	23	9	dobinski	dobinski	ADJ
ejpam-5288	23	10	-	-	PUNCT
ejpam-5288	23	11	like	like	ADJ
ejpam-5288	23	12	formulas	formula	NOUN
ejpam-5288	23	13	and	and	CCONJ
ejpam-5288	23	14	generating	generating	NOUN
ejpam-5288	23	15	functions	function	NOUN
ejpam-5288	23	16	for	for	ADP
ejpam-5288	23	17	those	those	DET
ejpam-5288	23	18	numbers	number	NOUN
ejpam-5288	23	19	and	and	CCONJ
ejpam-5288	23	20	polynomials	polynomial	NOUN
ejpam-5288	23	21	.	.	PUNCT
ejpam-5288	24	1	we	we	PRON
ejpam-5288	24	2	also	also	ADV
ejpam-5288	24	3	treat	treat	VERB
ejpam-5288	24	4	the	the	DET
ejpam-5288	24	5	more	more	ADV
ejpam-5288	24	6	general	general	ADJ
ejpam-5288	24	7	λ	λ	NOUN
ejpam-5288	24	8	-	-	NOUN
ejpam-5288	24	9	analogues	analogue	NOUN
ejpam-5288	24	10	of	of	ADP
ejpam-5288	24	11	r	r	NOUN
ejpam-5288	24	12	-	-	PUNCT
ejpam-5288	24	13	lah	lah	NOUN
ejpam-5288	24	14	numbers	number	NOUN
ejpam-5288	24	15	lr	lr	NOUN
ejpam-5288	24	16	,	,	PUNCT
ejpam-5288	24	17	λ(n	λ(n	PROPN
ejpam-5288	24	18	,	,	PUNCT
ejpam-5288	24	19	k	k	NOUN
ejpam-5288	24	20	)	)	PUNCT
ejpam-5288	24	21	(	(	PUNCT
ejpam-5288	24	22	see	see	VERB
ejpam-5288	24	23	(	(	PUNCT
ejpam-5288	24	24	39	39	NUM
ejpam-5288	24	25	)	)	PUNCT
ejpam-5288	24	26	)	)	PUNCT
ejpam-5288	24	27	and	and	CCONJ
ejpam-5288	24	28	r	r	X
ejpam-5288	24	29	-	-	PUNCT
ejpam-5288	24	30	extended	extend	VERB
ejpam-5288	24	31	λ	λ	NOUN
ejpam-5288	24	32	-	-	PUNCT
ejpam-5288	24	33	lah	lah	ADJ
ejpam-5288	24	34	-	-	PUNCT
ejpam-5288	24	35	bell	bell	NOUN
ejpam-5288	24	36	polynomials	polynomial	NOUN
ejpam-5288	24	37	lb	lb	PRON
ejpam-5288	24	38	(	(	PUNCT
ejpam-5288	24	39	r	r	NOUN
ejpam-5288	24	40	)	)	PUNCT
ejpam-5288	24	41	n	n	CCONJ
ejpam-5288	24	42	,	,	PUNCT
ejpam-5288	24	43	λ(x	λ(x	PROPN
ejpam-5288	24	44	)	)	PUNCT
ejpam-5288	24	45	(	(	PUNCT
ejpam-5288	24	46	see	see	VERB
ejpam-5288	24	47	(	(	PUNCT
ejpam-5288	24	48	45	45	NUM
ejpam-5288	24	49	)	)	PUNCT
ejpam-5288	24	50	)	)	PUNCT
ejpam-5288	24	51	.	.	PUNCT
ejpam-5288	25	1	in	in	ADP
ejpam-5288	25	2	addition	addition	NOUN
ejpam-5288	25	3	,	,	PUNCT
ejpam-5288	25	4	we	we	PRON
ejpam-5288	25	5	show	show	VERB
ejpam-5288	25	6	the	the	DET
ejpam-5288	25	7	expectation	expectation	NOUN
ejpam-5288	25	8	of	of	ADP
ejpam-5288	25	9	one	one	NUM
ejpam-5288	25	10	random	random	ADJ
ejpam-5288	25	11	variable	variable	NOUN
ejpam-5288	25	12	and	and	CCONJ
ejpam-5288	25	13	that	that	PRON
ejpam-5288	25	14	of	of	ADP
ejpam-5288	25	15	another	another	DET
ejpam-5288	25	16	random	random	ADJ
ejpam-5288	25	17	variable	variable	NOUN
ejpam-5288	25	18	,	,	PUNCT
ejpam-5288	25	19	both	both	PRON
ejpam-5288	25	20	related	relate	VERB
ejpam-5288	25	21	to	to	ADP
ejpam-5288	25	22	the	the	DET
ejpam-5288	25	23	poisson	poisson	NOUN
ejpam-5288	25	24	random	random	ADJ
ejpam-5288	25	25	variable	variable	NOUN
ejpam-5288	25	26	with	with	ADP
ejpam-5288	25	27	parameter	parameter	NOUN
ejpam-5288	25	28	α	α	PROPN
ejpam-5288	25	29	λ	λ	PROPN
ejpam-5288	25	30	,	,	PUNCT
ejpam-5288	25	31	are	be	AUX
ejpam-5288	25	32	respectively	respectively	ADV
ejpam-5288	25	33	equal	equal	ADJ
ejpam-5288	25	34	to	to	PART
ejpam-5288	25	35	bl	bl	VERB
ejpam-5288	25	36	n	n	CCONJ
ejpam-5288	25	37	,	,	PUNCT
ejpam-5288	25	38	λ(α	λ(α	PROPN
ejpam-5288	25	39	)	)	PUNCT
ejpam-5288	25	40	and	and	CCONJ
ejpam-5288	25	41	lb	lb	X
ejpam-5288	25	42	(	(	PUNCT
ejpam-5288	25	43	r	r	NOUN
ejpam-5288	25	44	)	)	PUNCT
ejpam-5288	25	45	n	n	CCONJ
ejpam-5288	25	46	,	,	PUNCT
ejpam-5288	25	47	λ(α	λ(α	PROPN
ejpam-5288	25	48	)	)	PUNCT
ejpam-5288	25	49	.	.	PUNCT
ejpam-5288	26	1	here	here	ADV
ejpam-5288	26	2	we	we	PRON
ejpam-5288	26	3	note	note	VERB
ejpam-5288	26	4	that	that	SCONJ
ejpam-5288	26	5	the	the	DET
ejpam-5288	26	6	degenerate	degenerate	ADJ
ejpam-5288	26	7	versions	version	NOUN
ejpam-5288	26	8	arise	arise	VERB
ejpam-5288	26	9	naturally	naturally	ADV
ejpam-5288	26	10	when	when	SCONJ
ejpam-5288	26	11	we	we	PRON
ejpam-5288	26	12	replace	replace	VERB
ejpam-5288	26	13	the	the	DET
ejpam-5288	26	14	powers	power	NOUN
ejpam-5288	26	15	of	of	ADP
ejpam-5288	26	16	x	x	PUNCT
ejpam-5288	26	17	by	by	ADP
ejpam-5288	26	18	the	the	DET
ejpam-5288	26	19	generalized	generalized	ADJ
ejpam-5288	26	20	falling	fall	VERB
ejpam-5288	26	21	factorial	factorial	NOUN
ejpam-5288	26	22	polynomials	polynomial	NOUN
ejpam-5288	26	23	(	(	PUNCT
ejpam-5288	26	24	x)k	x)k	X
ejpam-5288	26	25	,	,	PUNCT
ejpam-5288	26	26	λ	λ	PROPN
ejpam-5288	26	27	(	(	PUNCT
ejpam-5288	26	28	see	see	VERB
ejpam-5288	26	29	(	(	PUNCT
ejpam-5288	26	30	1	1	NUM
ejpam-5288	26	31	)	)	PUNCT
ejpam-5288	26	32	)	)	PUNCT
ejpam-5288	26	33	in	in	ADP
ejpam-5288	26	34	the	the	DET
ejpam-5288	26	35	defining	define	VERB
ejpam-5288	26	36	equations	equation	NOUN
ejpam-5288	26	37	,	,	PUNCT
ejpam-5288	26	38	while	while	SCONJ
ejpam-5288	26	39	the	the	DET
ejpam-5288	26	40	λ	λ	NOUN
ejpam-5288	26	41	-	-	NOUN
ejpam-5288	26	42	analogues	analogue	NOUN
ejpam-5288	26	43	appear	appear	VERB
ejpam-5288	26	44	when	when	SCONJ
ejpam-5288	26	45	we	we	PRON
ejpam-5288	26	46	replace	replace	VERB
ejpam-5288	26	47	the	the	DET
ejpam-5288	26	48	falling	fall	VERB
ejpam-5288	26	49	factorials	factorial	NOUN
ejpam-5288	26	50	(	(	PUNCT
ejpam-5288	26	51	x)k	x)k	X
ejpam-5288	26	52	by	by	ADP
ejpam-5288	26	53	the	the	DET
ejpam-5288	26	54	generalized	generalized	ADJ
ejpam-5288	26	55	falling	fall	VERB
ejpam-5288	26	56	factorials	factorial	NOUN
ejpam-5288	26	57	.	.	PUNCT
ejpam-5288	27	1	in	in	ADP
ejpam-5288	27	2	more	more	ADJ
ejpam-5288	27	3	detail	detail	NOUN
ejpam-5288	27	4	,	,	PUNCT
ejpam-5288	27	5	the	the	DET
ejpam-5288	27	6	outline	outline	NOUN
ejpam-5288	27	7	of	of	ADP
ejpam-5288	27	8	this	this	DET
ejpam-5288	27	9	paper	paper	NOUN
ejpam-5288	27	10	is	be	AUX
ejpam-5288	27	11	as	as	SCONJ
ejpam-5288	27	12	follows	follow	VERB
ejpam-5288	27	13	.	.	PUNCT
ejpam-5288	28	1	in	in	ADP
ejpam-5288	28	2	section	section	NOUN
ejpam-5288	28	3	1	1	NUM
ejpam-5288	28	4	,	,	PUNCT
ejpam-5288	28	5	we	we	PRON
ejpam-5288	28	6	recall	recall	VERB
ejpam-5288	28	7	the	the	DET
ejpam-5288	28	8	generalized	generalized	ADJ
ejpam-5288	28	9	falling	fall	VERB
ejpam-5288	28	10	factorials	factorial	NOUN
ejpam-5288	28	11	(	(	PUNCT
ejpam-5288	28	12	x)n	x)n	PROPN
ejpam-5288	28	13	,	,	PUNCT
ejpam-5288	28	14	λ	λ	PROPN
ejpam-5288	28	15	and	and	CCONJ
ejpam-5288	28	16	the	the	DET
ejpam-5288	28	17	generalized	generalized	ADJ
ejpam-5288	28	18	rising	rise	VERB
ejpam-5288	28	19	factorials	factorial	NOUN
ejpam-5288	28	20	⟨x⟩n	⟨x⟩n	VERB
ejpam-5288	28	21	,	,	PUNCT
ejpam-5288	28	22	λ	λ	X
ejpam-5288	28	23	.	.	PUNCT
ejpam-5288	29	1	we	we	PRON
ejpam-5288	29	2	remind	remind	VERB
ejpam-5288	29	3	the	the	DET
ejpam-5288	29	4	reader	reader	NOUN
ejpam-5288	29	5	of	of	ADP
ejpam-5288	29	6	the	the	DET
ejpam-5288	29	7	unsigned	unsigned	ADJ
ejpam-5288	29	8	lah	lah	PROPN
ejpam-5288	29	9	numbers	number	NOUN
ejpam-5288	29	10	l(n	l(n	PROPN
ejpam-5288	29	11	,	,	PUNCT
ejpam-5288	29	12	k	k	NOUN
ejpam-5288	29	13	)	)	PUNCT
ejpam-5288	29	14	and	and	CCONJ
ejpam-5288	29	15	lah	lah	PROPN
ejpam-5288	29	16	-	-	PUNCT
ejpam-5288	29	17	bell	bell	NOUN
ejpam-5288	29	18	numbers	number	NOUN
ejpam-5288	29	19	bl	bl	VERB
ejpam-5288	29	20	n	n	ADV
ejpam-5288	29	21	.	.	PUNCT
ejpam-5288	30	1	we	we	PRON
ejpam-5288	30	2	recall	recall	VERB
ejpam-5288	30	3	the	the	DET
ejpam-5288	30	4	λ	λ	NOUN
ejpam-5288	30	5	-	-	NOUN
ejpam-5288	30	6	analogues	analogue	NOUN
ejpam-5288	30	7	of	of	ADP
ejpam-5288	30	8	the	the	DET
ejpam-5288	30	9	stirling	stirling	NOUN
ejpam-5288	30	10	numbers	number	NOUN
ejpam-5288	30	11	of	of	ADP
ejpam-5288	30	12	the	the	DET
ejpam-5288	30	13	first	first	ADJ
ejpam-5288	30	14	kind	kind	NOUN
ejpam-5288	30	15	s1,λ(n	s1,λ(n	PROPN
ejpam-5288	30	16	,	,	PUNCT
ejpam-5288	30	17	k	k	NOUN
ejpam-5288	30	18	)	)	PUNCT
ejpam-5288	30	19	and	and	CCONJ
ejpam-5288	30	20	the	the	DET
ejpam-5288	30	21	second	second	ADJ
ejpam-5288	30	22	kind	kind	NOUN
ejpam-5288	30	23	{	{	PUNCT
ejpam-5288	30	24	n	n	NOUN
ejpam-5288	30	25	k	k	ADJ
ejpam-5288	30	26	}	}	PUNCT
ejpam-5288	30	27	λ	λ	PROPN
ejpam-5288	30	28	.	.	PUNCT
ejpam-5288	31	1	we	we	PRON
ejpam-5288	31	2	remind	remind	VERB
ejpam-5288	31	3	the	the	DET
ejpam-5288	31	4	reader	reader	NOUN
ejpam-5288	31	5	of	of	ADP
ejpam-5288	31	6	the	the	DET
ejpam-5288	31	7	unsigned	unsigned	ADJ
ejpam-5288	31	8	λ	λ	PROPN
ejpam-5288	31	9	-	-	ADJ
ejpam-5288	31	10	stirling	stirling	ADJ
ejpam-5288	31	11	numbers	number	NOUN
ejpam-5288	31	12	of	of	ADP
ejpam-5288	31	13	the	the	DET
ejpam-5288	31	14	first	first	ADJ
ejpam-5288	31	15	kind	kind	NOUN
ejpam-5288	31	16	[	[	PUNCT
ejpam-5288	31	17	n	n	X
ejpam-5288	31	18	k	k	X
ejpam-5288	31	19	]	]	PUNCT
ejpam-5288	32	1	λ	λ	X
ejpam-5288	32	2	=	=	SYM
ejpam-5288	32	3	(	(	PUNCT
ejpam-5288	32	4	−1)n−ks1,λ(n	−1)n−ks1,λ(n	PROPN
ejpam-5288	32	5	,	,	PUNCT
ejpam-5288	32	6	k	k	PROPN
ejpam-5288	32	7	)	)	PUNCT
ejpam-5288	32	8	,	,	PUNCT
ejpam-5288	32	9	the	the	DET
ejpam-5288	32	10	λ	λ	NOUN
ejpam-5288	32	11	-	-	NOUN
ejpam-5288	32	12	analogues	analogue	NOUN
ejpam-5288	32	13	of	of	ADP
ejpam-5288	32	14	r	r	NOUN
ejpam-5288	32	15	-	-	PUNCT
ejpam-5288	32	16	stirling	stirling	NOUN
ejpam-5288	32	17	numbers	number	NOUN
ejpam-5288	32	18	of	of	ADP
ejpam-5288	32	19	the	the	DET
ejpam-5288	32	20	second	second	ADJ
ejpam-5288	32	21	{	{	PUNCT
ejpam-5288	32	22	n+r	n+r	X
ejpam-5288	32	23	k+r	k+r	X
ejpam-5288	32	24	}	}	PUNCT
ejpam-5288	32	25	r	r	PROPN
ejpam-5288	32	26	,	,	PUNCT
ejpam-5288	32	27	λ	λ	NOUN
ejpam-5288	32	28	,	,	PUNCT
ejpam-5288	32	29	and	and	CCONJ
ejpam-5288	32	30	the	the	DET
ejpam-5288	32	31	λ	λ	NOUN
ejpam-5288	32	32	-	-	ADJ
ejpam-5288	32	33	bell	bell	ADJ
ejpam-5288	32	34	polynomials	polynomial	NOUN
ejpam-5288	32	35	ϕn	ϕn	INTJ
ejpam-5288	32	36	,	,	PUNCT
ejpam-5288	32	37	λ(x	λ(x	PROPN
ejpam-5288	32	38	)	)	PUNCT
ejpam-5288	32	39	.	.	PUNCT
ejpam-5288	33	1	section	section	NOUN
ejpam-5288	33	2	2	2	NUM
ejpam-5288	33	3	is	be	AUX
ejpam-5288	33	4	the	the	DET
ejpam-5288	33	5	main	main	ADJ
ejpam-5288	33	6	result	result	NOUN
ejpam-5288	33	7	of	of	ADP
ejpam-5288	33	8	this	this	DET
ejpam-5288	33	9	paper	paper	NOUN
ejpam-5288	33	10	.	.	PUNCT
ejpam-5288	34	1	we	we	PRON
ejpam-5288	34	2	define	define	VERB
ejpam-5288	34	3	the	the	DET
ejpam-5288	34	4	λ	λ	NOUN
ejpam-5288	34	5	-	-	NOUN
ejpam-5288	34	6	analogues	analogue	NOUN
ejpam-5288	34	7	of	of	ADP
ejpam-5288	34	8	lah	lah	PROPN
ejpam-5288	34	9	numbers	number	NOUN
ejpam-5288	34	10	lλ(n	lλ(n	PUNCT
ejpam-5288	34	11	,	,	PUNCT
ejpam-5288	34	12	k	k	NOUN
ejpam-5288	34	13	)	)	PUNCT
ejpam-5288	34	14	,	,	PUNCT
ejpam-5288	34	15	and	and	CCONJ
ejpam-5288	34	16	express	express	VERB
ejpam-5288	34	17	it	it	PRON
ejpam-5288	34	18	as	as	ADP
ejpam-5288	34	19	finite	finite	ADJ
ejpam-5288	34	20	sums	sum	NOUN
ejpam-5288	34	21	of	of	ADP
ejpam-5288	34	22	products	product	NOUN
ejpam-5288	34	23	of	of	ADP
ejpam-5288	34	24	[	[	PUNCT
ejpam-5288	34	25	n	n	X
ejpam-5288	34	26	k	k	X
ejpam-5288	34	27	]	]	PUNCT
ejpam-5288	34	28	λ	λ	X
ejpam-5288	34	29	and	and	CCONJ
ejpam-5288	34	30	{	{	PUNCT
ejpam-5288	34	31	n	n	NOUN
ejpam-5288	34	32	k	k	ADJ
ejpam-5288	34	33	}	}	PUNCT
ejpam-5288	34	34	λ	λ	PROPN
ejpam-5288	34	35	in	in	ADP
ejpam-5288	34	36	theorem	theorem	NOUN
ejpam-5288	34	37	2.1	2.1	NUM
ejpam-5288	34	38	.	.	PUNCT
ejpam-5288	35	1	we	we	PRON
ejpam-5288	35	2	define	define	VERB
ejpam-5288	35	3	the	the	DET
ejpam-5288	35	4	λ	λ	NOUN
ejpam-5288	35	5	-	-	NOUN
ejpam-5288	35	6	analogues	analogue	NOUN
ejpam-5288	35	7	of	of	ADP
ejpam-5288	35	8	lah	lah	PROPN
ejpam-5288	35	9	-	-	PUNCT
ejpam-5288	35	10	bell	bell	NOUN
ejpam-5288	35	11	polynomials	polynomial	NOUN
ejpam-5288	35	12	bl	bl	NOUN
ejpam-5288	35	13	n	n	PRON
ejpam-5288	35	14	,	,	PUNCT
ejpam-5288	35	15	λ(x	λ(x	PROPN
ejpam-5288	35	16	)	)	PUNCT
ejpam-5288	35	17	and	and	CCONJ
ejpam-5288	35	18	numbers	number	NOUN
ejpam-5288	35	19	bl	bl	VERB
ejpam-5288	35	20	n	n	CCONJ
ejpam-5288	35	21	,	,	PUNCT
ejpam-5288	35	22	λ	λ	PROPN
ejpam-5288	35	23	,	,	PUNCT
ejpam-5288	35	24	and	and	CCONJ
ejpam-5288	35	25	find	find	VERB
ejpam-5288	35	26	explicit	explicit	ADJ
ejpam-5288	35	27	formulas	formula	NOUN
ejpam-5288	35	28	for	for	ADP
ejpam-5288	35	29	lλ(n	lλ(n	PRON
ejpam-5288	35	30	,	,	PUNCT
ejpam-5288	35	31	k	k	NOUN
ejpam-5288	35	32	)	)	PUNCT
ejpam-5288	35	33	in	in	ADP
ejpam-5288	35	34	theorem	theorem	ADJ
ejpam-5288	35	35	2.2	2.2	NUM
ejpam-5288	35	36	and	and	CCONJ
ejpam-5288	35	37	dobinski	dobinski	ADJ
ejpam-5288	35	38	-	-	PUNCT
ejpam-5288	35	39	like	like	ADJ
ejpam-5288	35	40	formulas	formula	NOUN
ejpam-5288	35	41	for	for	ADP
ejpam-5288	35	42	bl	bl	PROPN
ejpam-5288	35	43	n	n	CCONJ
ejpam-5288	35	44	,	,	PUNCT
ejpam-5288	35	45	λ(x	λ(x	PROPN
ejpam-5288	35	46	)	)	PUNCT
ejpam-5288	35	47	in	in	ADP
ejpam-5288	35	48	theorem	theorem	NOUN
ejpam-5288	35	49	2.3	2.3	NUM
ejpam-5288	35	50	.	.	PUNCT
ejpam-5288	36	1	in	in	ADP
ejpam-5288	36	2	theorem	theorem	ADJ
ejpam-5288	36	3	2.4	2.4	NUM
ejpam-5288	36	4	,	,	PUNCT
ejpam-5288	36	5	ϕn	ϕn	INTJ
ejpam-5288	36	6	,	,	PUNCT
ejpam-5288	36	7	λ(x	λ(x	PROPN
ejpam-5288	36	8	)	)	PUNCT
ejpam-5288	36	9	is	be	AUX
ejpam-5288	36	10	expressed	express	VERB
ejpam-5288	36	11	as	as	ADP
ejpam-5288	36	12	a	a	DET
ejpam-5288	36	13	finite	finite	ADJ
ejpam-5288	36	14	sum	sum	NOUN
ejpam-5288	36	15	involving	involve	VERB
ejpam-5288	36	16	bl	bl	PROPN
ejpam-5288	36	17	n	n	CCONJ
ejpam-5288	36	18	,	,	PUNCT
ejpam-5288	36	19	λ(x	λ(x	PROPN
ejpam-5288	36	20	)	)	PUNCT
ejpam-5288	36	21	and	and	CCONJ
ejpam-5288	36	22	{	{	PUNCT
ejpam-5288	36	23	n	n	NOUN
ejpam-5288	36	24	k	k	ADJ
ejpam-5288	36	25	}	}	PUNCT
ejpam-5288	36	26	λ	λ	PROPN
ejpam-5288	36	27	.	.	PUNCT
ejpam-5288	37	1	as	as	ADP
ejpam-5288	37	2	an	an	DET
ejpam-5288	37	3	inversion	inversion	NOUN
ejpam-5288	37	4	of	of	ADP
ejpam-5288	37	5	this	this	PRON
ejpam-5288	37	6	,	,	PUNCT
ejpam-5288	37	7	we	we	PRON
ejpam-5288	37	8	also	also	ADV
ejpam-5288	37	9	express	express	VERB
ejpam-5288	37	10	bl	bl	ADP
ejpam-5288	37	11	n	n	CCONJ
ejpam-5288	37	12	,	,	PUNCT
ejpam-5288	37	13	λ(x	λ(x	PROPN
ejpam-5288	37	14	)	)	PUNCT
ejpam-5288	37	15	as	as	ADP
ejpam-5288	37	16	a	a	DET
ejpam-5288	37	17	finite	finite	ADJ
ejpam-5288	37	18	sum	sum	NOUN
ejpam-5288	37	19	involving	involve	VERB
ejpam-5288	37	20	ϕn	ϕn	NUM
ejpam-5288	37	21	,	,	PUNCT
ejpam-5288	37	22	λ(x	λ(x	PROPN
ejpam-5288	37	23	)	)	PUNCT
ejpam-5288	37	24	and	and	CCONJ
ejpam-5288	37	25	[	[	PUNCT
ejpam-5288	37	26	n	n	X
ejpam-5288	37	27	k	k	X
ejpam-5288	37	28	]	]	X
ejpam-5288	38	1	λ	λ	X
ejpam-5288	38	2	.	.	PUNCT
ejpam-5288	39	1	we	we	PRON
ejpam-5288	39	2	define	define	VERB
ejpam-5288	39	3	the	the	DET
ejpam-5288	39	4	λ	λ	NOUN
ejpam-5288	39	5	-	-	NOUN
ejpam-5288	39	6	analogues	analogue	NOUN
ejpam-5288	39	7	of	of	ADP
ejpam-5288	39	8	laguerre	laguerre	NOUN
ejpam-5288	39	9	polynomials	polynomial	NOUN
ejpam-5288	39	10	l	l	PROPN
ejpam-5288	39	11	(	(	PUNCT
ejpam-5288	39	12	α	α	NOUN
ejpam-5288	39	13	)	)	PUNCT
ejpam-5288	39	14	n	n	CCONJ
ejpam-5288	39	15	,	,	PUNCT
ejpam-5288	39	16	λ(x	λ(x	PROPN
ejpam-5288	39	17	)	)	PUNCT
ejpam-5288	39	18	of	of	ADP
ejpam-5288	39	19	j.	j.	PROPN
ejpam-5288	39	20	kwon	kwon	PROPN
ejpam-5288	39	21	et	et	PROPN
ejpam-5288	39	22	al	al	PROPN
ejpam-5288	39	23	.	.	PUNCT
ejpam-5288	39	24	/	/	SYM
ejpam-5288	39	25	eur	eur	PROPN
ejpam-5288	39	26	.	.	PUNCT
ejpam-5288	40	1	j.	j.	PROPN
ejpam-5288	40	2	pure	pure	PROPN
ejpam-5288	40	3	appl	appl	PROPN
ejpam-5288	40	4	.	.	PROPN
ejpam-5288	40	5	math	math	PROPN
ejpam-5288	40	6	,	,	PUNCT
ejpam-5288	40	7	17	17	NUM
ejpam-5288	40	8	(	(	PUNCT
ejpam-5288	40	9	3	3	NUM
ejpam-5288	40	10	)	)	PUNCT
ejpam-5288	40	11	(	(	PUNCT
ejpam-5288	40	12	2024	2024	NUM
ejpam-5288	40	13	)	)	PUNCT
ejpam-5288	40	14	,	,	PUNCT
ejpam-5288	40	15	1385	1385	NUM
ejpam-5288	40	16	-	-	SYM
ejpam-5288	40	17	1402	1402	NUM
ejpam-5288	40	18	1387	1387	NUM
ejpam-5288	40	19	order	order	NOUN
ejpam-5288	40	20	α	α	NOUN
ejpam-5288	40	21	.	.	PUNCT
ejpam-5288	41	1	then	then	ADV
ejpam-5288	41	2	we	we	PRON
ejpam-5288	41	3	show	show	VERB
ejpam-5288	41	4	that	that	SCONJ
ejpam-5288	41	5	the	the	DET
ejpam-5288	41	6	convolution	convolution	NOUN
ejpam-5288	41	7	of	of	ADP
ejpam-5288	41	8	bl	bl	PROPN
ejpam-5288	41	9	n	n	CCONJ
ejpam-5288	41	10	,	,	PUNCT
ejpam-5288	41	11	λ(x	λ(x	PROPN
ejpam-5288	41	12	)	)	PUNCT
ejpam-5288	41	13	and	and	CCONJ
ejpam-5288	41	14	l	l	NOUN
ejpam-5288	41	15	(	(	PUNCT
ejpam-5288	41	16	α	α	NOUN
ejpam-5288	41	17	)	)	PUNCT
ejpam-5288	41	18	n	n	CCONJ
ejpam-5288	41	19	,	,	PUNCT
ejpam-5288	41	20	λ(x	λ(x	PROPN
ejpam-5288	41	21	)	)	PUNCT
ejpam-5288	41	22	is	be	AUX
ejpam-5288	41	23	equal	equal	ADJ
ejpam-5288	41	24	to	to	ADP
ejpam-5288	41	25	⟨α+1⟩n	⟨α+1⟩n	NUM
ejpam-5288	41	26	,	,	PUNCT
ejpam-5288	41	27	λ	λ	X
ejpam-5288	41	28	.	.	PUNCT
ejpam-5288	42	1	we	we	PRON
ejpam-5288	42	2	define	define	VERB
ejpam-5288	42	3	the	the	DET
ejpam-5288	42	4	λ	λ	NOUN
ejpam-5288	42	5	-	-	NOUN
ejpam-5288	42	6	analogues	analogue	NOUN
ejpam-5288	42	7	of	of	ADP
ejpam-5288	42	8	r	r	NOUN
ejpam-5288	42	9	-	-	PUNCT
ejpam-5288	42	10	lah	lah	NOUN
ejpam-5288	42	11	numbers	number	NOUN
ejpam-5288	42	12	lr	lr	NOUN
ejpam-5288	42	13	,	,	PUNCT
ejpam-5288	42	14	λ(n	λ(n	PROPN
ejpam-5288	42	15	,	,	PUNCT
ejpam-5288	42	16	k	k	NOUN
ejpam-5288	42	17	)	)	PUNCT
ejpam-5288	42	18	,	,	PUNCT
ejpam-5288	42	19	and	and	CCONJ
ejpam-5288	42	20	find	find	VERB
ejpam-5288	42	21	for	for	ADP
ejpam-5288	42	22	those	those	DET
ejpam-5288	42	23	numbers	number	NOUN
ejpam-5288	42	24	an	an	DET
ejpam-5288	42	25	explicit	explicit	ADJ
ejpam-5288	42	26	expression	expression	NOUN
ejpam-5288	42	27	in	in	ADP
ejpam-5288	42	28	theorem	theorem	ADJ
ejpam-5288	42	29	2.6	2.6	NUM
ejpam-5288	42	30	and	and	CCONJ
ejpam-5288	42	31	a	a	DET
ejpam-5288	42	32	recurrence	recurrence	NOUN
ejpam-5288	42	33	relation	relation	NOUN
ejpam-5288	42	34	in	in	ADP
ejpam-5288	42	35	theorem	theorem	NOUN
ejpam-5288	42	36	2.7	2.7	NUM
ejpam-5288	42	37	.	.	PUNCT
ejpam-5288	43	1	we	we	PRON
ejpam-5288	43	2	define	define	VERB
ejpam-5288	43	3	the	the	DET
ejpam-5288	43	4	r	r	NOUN
ejpam-5288	43	5	-	-	PUNCT
ejpam-5288	43	6	extended	extend	VERB
ejpam-5288	43	7	λ	λ	NOUN
ejpam-5288	43	8	-	-	PUNCT
ejpam-5288	43	9	lah	lah	ADJ
ejpam-5288	43	10	-	-	PUNCT
ejpam-5288	43	11	bell	bell	NOUN
ejpam-5288	43	12	polynomials	polynomial	NOUN
ejpam-5288	43	13	lb	lb	PRON
ejpam-5288	43	14	(	(	PUNCT
ejpam-5288	43	15	r	r	NOUN
ejpam-5288	43	16	)	)	PUNCT
ejpam-5288	43	17	n	n	CCONJ
ejpam-5288	43	18	,	,	PUNCT
ejpam-5288	43	19	λ(x	λ(x	PROPN
ejpam-5288	43	20	)	)	PUNCT
ejpam-5288	43	21	and	and	CCONJ
ejpam-5288	43	22	find	find	VERB
ejpam-5288	43	23	a	a	DET
ejpam-5288	43	24	dobinski	dobinski	ADJ
ejpam-5288	43	25	-	-	PUNCT
ejpam-5288	43	26	like	like	ADJ
ejpam-5288	43	27	formula	formula	NOUN
ejpam-5288	43	28	for	for	ADP
ejpam-5288	43	29	those	those	DET
ejpam-5288	43	30	polynomials	polynomial	NOUN
ejpam-5288	43	31	in	in	ADP
ejpam-5288	43	32	theorem	theorem	NOUN
ejpam-5288	43	33	2.8	2.8	NUM
ejpam-5288	43	34	.	.	PUNCT
ejpam-5288	44	1	in	in	ADP
ejpam-5288	44	2	theorem	theorem	NOUN
ejpam-5288	44	3	2.9	2.9	NUM
ejpam-5288	44	4	,	,	PUNCT
ejpam-5288	44	5	we	we	PRON
ejpam-5288	44	6	express	express	VERB
ejpam-5288	44	7	{	{	PUNCT
ejpam-5288	44	8	n+r	n+r	X
ejpam-5288	44	9	k+r	k+r	X
ejpam-5288	44	10	}	}	PUNCT
ejpam-5288	44	11	r	r	NOUN
ejpam-5288	44	12	,	,	PUNCT
ejpam-5288	44	13	λ	λ	PROPN
ejpam-5288	44	14	as	as	ADP
ejpam-5288	44	15	a	a	DET
ejpam-5288	44	16	finite	finite	ADJ
ejpam-5288	44	17	sum	sum	NOUN
ejpam-5288	44	18	of	of	ADP
ejpam-5288	44	19	the	the	DET
ejpam-5288	44	20	product	product	NOUN
ejpam-5288	44	21	of	of	ADP
ejpam-5288	44	22	lr	lr	NOUN
ejpam-5288	44	23	,	,	PUNCT
ejpam-5288	44	24	λ(n	λ(n	PROPN
ejpam-5288	44	25	,	,	PUNCT
ejpam-5288	44	26	k	k	NOUN
ejpam-5288	44	27	)	)	PUNCT
ejpam-5288	44	28	and	and	CCONJ
ejpam-5288	44	29	{	{	PUNCT
ejpam-5288	44	30	n	n	NOUN
ejpam-5288	44	31	m	m	VERB
ejpam-5288	44	32	}	}	PUNCT
ejpam-5288	44	33	−λ	−λ	ADJ
ejpam-5288	44	34	,	,	PUNCT
ejpam-5288	44	35	and	and	CCONJ
ejpam-5288	44	36	conversely	conversely	ADV
ejpam-5288	44	37	lr	lr	VERB
ejpam-5288	44	38	,	,	PUNCT
ejpam-5288	44	39	λ(n	λ(n	PROPN
ejpam-5288	44	40	,	,	PUNCT
ejpam-5288	44	41	k	k	NOUN
ejpam-5288	44	42	)	)	PUNCT
ejpam-5288	44	43	as	as	ADP
ejpam-5288	44	44	a	a	DET
ejpam-5288	44	45	finite	finite	ADJ
ejpam-5288	44	46	sum	sum	NOUN
ejpam-5288	44	47	of	of	ADP
ejpam-5288	44	48	the	the	DET
ejpam-5288	44	49	product	product	NOUN
ejpam-5288	44	50	of	of	ADP
ejpam-5288	44	51	{	{	PUNCT
ejpam-5288	44	52	m+r	m+r	X
ejpam-5288	44	53	k+r	k+r	X
ejpam-5288	44	54	}	}	PUNCT
ejpam-5288	44	55	r	r	NOUN
ejpam-5288	44	56	,	,	PUNCT
ejpam-5288	44	57	λ	λ	PROPN
ejpam-5288	44	58	and	and	CCONJ
ejpam-5288	44	59	[	[	PUNCT
ejpam-5288	44	60	n	n	X
ejpam-5288	44	61	m	m	VERB
ejpam-5288	44	62	]	]	X
ejpam-5288	45	1	λ	λ	X
ejpam-5288	45	2	.	.	PUNCT
ejpam-5288	46	1	let	let	VERB
ejpam-5288	46	2	x	x	PRON
ejpam-5288	46	3	be	be	AUX
ejpam-5288	46	4	the	the	DET
ejpam-5288	46	5	poisson	poisson	NOUN
ejpam-5288	46	6	distribution	distribution	NOUN
ejpam-5288	46	7	with	with	ADP
ejpam-5288	46	8	parameter	parameter	NOUN
ejpam-5288	46	9	α	α	PROPN
ejpam-5288	46	10	λ	λ	X
ejpam-5288	46	11	>	>	X
ejpam-5288	46	12	0	0	NUM
ejpam-5288	46	13	.	.	PUNCT
ejpam-5288	47	1	then	then	ADV
ejpam-5288	47	2	,	,	PUNCT
ejpam-5288	47	3	in	in	ADP
ejpam-5288	47	4	section	section	NOUN
ejpam-5288	47	5	3	3	NUM
ejpam-5288	47	6	,	,	PUNCT
ejpam-5288	47	7	we	we	PRON
ejpam-5288	47	8	show	show	VERB
ejpam-5288	47	9	that	that	SCONJ
ejpam-5288	47	10	the	the	DET
ejpam-5288	47	11	expectation	expectation	NOUN
ejpam-5288	47	12	of	of	ADP
ejpam-5288	47	13	the	the	DET
ejpam-5288	47	14	random	random	ADJ
ejpam-5288	47	15	variable	variable	ADJ
ejpam-5288	47	16	⟨xλ⟩n	⟨xλ⟩n	NOUN
ejpam-5288	47	17	,	,	PUNCT
ejpam-5288	47	18	λ	λ	PROPN
ejpam-5288	47	19	is	be	AUX
ejpam-5288	47	20	equal	equal	ADJ
ejpam-5288	47	21	to	to	PART
ejpam-5288	47	22	bl	bl	VERB
ejpam-5288	47	23	n	n	CCONJ
ejpam-5288	47	24	,	,	PUNCT
ejpam-5288	47	25	λ(α	λ(α	PROPN
ejpam-5288	47	26	)	)	PUNCT
ejpam-5288	47	27	and	and	CCONJ
ejpam-5288	47	28	that	that	PRON
ejpam-5288	47	29	of	of	ADP
ejpam-5288	47	30	the	the	DET
ejpam-5288	47	31	random	random	ADJ
ejpam-5288	47	32	variable	variable	NOUN
ejpam-5288	47	33	⟨xλ+	⟨xλ+	PROPN
ejpam-5288	47	34	r⟩n	r⟩n	NOUN
ejpam-5288	47	35	,	,	PUNCT
ejpam-5288	47	36	λ	λ	NOUN
ejpam-5288	47	37	is	be	AUX
ejpam-5288	47	38	equal	equal	ADJ
ejpam-5288	47	39	to	to	ADP
ejpam-5288	47	40	lb	lb	DET
ejpam-5288	47	41	(	(	PUNCT
ejpam-5288	47	42	r	r	NOUN
ejpam-5288	47	43	)	)	PUNCT
ejpam-5288	47	44	n	n	CCONJ
ejpam-5288	47	45	,	,	PUNCT
ejpam-5288	47	46	λ(α	λ(α	PROPN
ejpam-5288	47	47	)	)	PUNCT
ejpam-5288	47	48	.	.	PUNCT
ejpam-5288	48	1	in	in	ADP
ejpam-5288	48	2	the	the	DET
ejpam-5288	48	3	rest	rest	NOUN
ejpam-5288	48	4	of	of	ADP
ejpam-5288	48	5	this	this	DET
ejpam-5288	48	6	section	section	NOUN
ejpam-5288	48	7	,	,	PUNCT
ejpam-5288	48	8	we	we	PRON
ejpam-5288	48	9	recall	recall	VERB
ejpam-5288	48	10	the	the	DET
ejpam-5288	48	11	facts	fact	NOUN
ejpam-5288	48	12	that	that	PRON
ejpam-5288	48	13	are	be	AUX
ejpam-5288	48	14	needed	need	VERB
ejpam-5288	48	15	throughout	throughout	ADP
ejpam-5288	48	16	this	this	DET
ejpam-5288	48	17	paper	paper	NOUN
ejpam-5288	48	18	.	.	PUNCT
ejpam-5288	49	1	for	for	ADP
ejpam-5288	49	2	any	any	DET
ejpam-5288	49	3	nonzero	nonzero	NOUN
ejpam-5288	49	4	λ	λ	X
ejpam-5288	49	5	∈	∈	PROPN
ejpam-5288	49	6	r	r	NOUN
ejpam-5288	49	7	,	,	PUNCT
ejpam-5288	49	8	the	the	DET
ejpam-5288	49	9	generalized	generalized	ADJ
ejpam-5288	49	10	falling	fall	VERB
ejpam-5288	49	11	factorial	factorial	NOUN
ejpam-5288	49	12	sequence	sequence	NOUN
ejpam-5288	49	13	is	be	AUX
ejpam-5288	49	14	given	give	VERB
ejpam-5288	49	15	by	by	ADP
ejpam-5288	49	16	(	(	PUNCT
ejpam-5288	49	17	x)0,λ	x)0,λ	NOUN
ejpam-5288	49	18	=	=	SYM
ejpam-5288	49	19	1	1	NUM
ejpam-5288	49	20	,	,	PUNCT
ejpam-5288	49	21	(	(	PUNCT
ejpam-5288	49	22	x)n	x)n	PROPN
ejpam-5288	49	23	,	,	PUNCT
ejpam-5288	49	24	λ	λ	PROPN
ejpam-5288	49	25	=	=	SYM
ejpam-5288	49	26	x(x−λ)(x−2λ	x(x−λ)(x−2λ	PROPN
ejpam-5288	49	27	)	)	PUNCT
ejpam-5288	49	28	·	·	PUNCT
ejpam-5288	49	29	·	·	PUNCT
ejpam-5288	49	30	·	·	PUNCT
ejpam-5288	50	1	(	(	PUNCT
ejpam-5288	50	2	x−(n−1)λ	x−(n−1)λ	NUM
ejpam-5288	50	3	)	)	PUNCT
ejpam-5288	50	4	,	,	PUNCT
ejpam-5288	50	5	(	(	PUNCT
ejpam-5288	50	6	n	n	CCONJ
ejpam-5288	50	7	≥	≥	NOUN
ejpam-5288	50	8	1	1	NUM
ejpam-5288	50	9	)	)	PUNCT
ejpam-5288	50	10	,	,	PUNCT
ejpam-5288	50	11	(	(	PUNCT
ejpam-5288	50	12	see	see	VERB
ejpam-5288	50	13	[	[	X
ejpam-5288	50	14	1−5	1−5	NUM
ejpam-5288	50	15	,	,	PUNCT
ejpam-5288	50	16	7−26	7−26	PROPN
ejpam-5288	50	17	]	]	PUNCT
ejpam-5288	50	18	)	)	PUNCT
ejpam-5288	50	19	.	.	PUNCT
ejpam-5288	51	1	(	(	PUNCT
ejpam-5288	51	2	1	1	X
ejpam-5288	51	3	)	)	PUNCT
ejpam-5288	51	4	note	note	NOUN
ejpam-5288	51	5	that	that	SCONJ
ejpam-5288	51	6	lim	lim	PROPN
ejpam-5288	51	7	λ→1	λ→1	X
ejpam-5288	51	8	(	(	PUNCT
ejpam-5288	51	9	x)n	x)n	PROPN
ejpam-5288	51	10	,	,	PUNCT
ejpam-5288	51	11	λ	λ	PROPN
ejpam-5288	51	12	=	=	SYM
ejpam-5288	51	13	x(x−	x(x−	PROPN
ejpam-5288	51	14	1)(x−	1)(x−	NUM
ejpam-5288	51	15	2	2	NUM
ejpam-5288	51	16	)	)	PUNCT
ejpam-5288	51	17	·	·	PUNCT
ejpam-5288	51	18	·	·	PUNCT
ejpam-5288	51	19	·	·	PUNCT
ejpam-5288	51	20	(	(	PUNCT
ejpam-5288	51	21	x−	x−	X
ejpam-5288	51	22	(	(	PUNCT
ejpam-5288	51	23	n−	n−	NOUN
ejpam-5288	51	24	1	1	NUM
ejpam-5288	51	25	)	)	PUNCT
ejpam-5288	51	26	)	)	PUNCT
ejpam-5288	52	1	=	=	SYM
ejpam-5288	53	1	(	(	PUNCT
ejpam-5288	53	2	x)n	x)n	PROPN
ejpam-5288	53	3	,	,	PUNCT
ejpam-5288	53	4	(	(	PUNCT
ejpam-5288	53	5	n	n	CCONJ
ejpam-5288	53	6	≥	≥	NOUN
ejpam-5288	53	7	1	1	NUM
ejpam-5288	53	8	)	)	PUNCT
ejpam-5288	53	9	.	.	PUNCT
ejpam-5288	54	1	the	the	DET
ejpam-5288	54	2	generalized	generalized	ADJ
ejpam-5288	54	3	rising	rise	VERB
ejpam-5288	54	4	factorial	factorial	NOUN
ejpam-5288	54	5	sequence	sequence	NOUN
ejpam-5288	54	6	is	be	AUX
ejpam-5288	54	7	defined	define	VERB
ejpam-5288	54	8	by	by	ADP
ejpam-5288	54	9	⟨x⟩0,λ	⟨x⟩0,λ	NOUN
ejpam-5288	54	10	=	=	SYM
ejpam-5288	54	11	1	1	NUM
ejpam-5288	54	12	,	,	PUNCT
ejpam-5288	54	13	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5288	54	14	,	,	PUNCT
ejpam-5288	54	15	λ	λ	PROPN
ejpam-5288	54	16	=	=	SYM
ejpam-5288	55	1	x(x+	x(x+	PROPN
ejpam-5288	55	2	λ)(x+	λ)(x+	NOUN
ejpam-5288	55	3	2λ	2λ	NUM
ejpam-5288	55	4	)	)	PUNCT
ejpam-5288	55	5	·	·	PUNCT
ejpam-5288	55	6	·	·	PUNCT
ejpam-5288	55	7	·	·	PUNCT
ejpam-5288	56	1	(	(	PUNCT
ejpam-5288	56	2	x+	x+	X
ejpam-5288	56	3	(	(	PUNCT
ejpam-5288	56	4	n−	n−	NOUN
ejpam-5288	56	5	1)λ	1)λ	NUM
ejpam-5288	56	6	)	)	PUNCT
ejpam-5288	56	7	,	,	PUNCT
ejpam-5288	56	8	(	(	PUNCT
ejpam-5288	56	9	n	n	X
ejpam-5288	56	10	≥	≥	NOUN
ejpam-5288	56	11	1	1	NUM
ejpam-5288	56	12	)	)	PUNCT
ejpam-5288	56	13	.	.	PUNCT
ejpam-5288	57	1	note	note	VERB
ejpam-5288	57	2	that	that	SCONJ
ejpam-5288	57	3	lim	lim	PROPN
ejpam-5288	57	4	λ→1	λ→1	X
ejpam-5288	57	5	⟨x⟩n	⟨x⟩n	PROPN
ejpam-5288	57	6	,	,	PUNCT
ejpam-5288	57	7	λ	λ	PROPN
ejpam-5288	57	8	=	=	PUNCT
ejpam-5288	58	1	x(x+	x(x+	PROPN
ejpam-5288	58	2	1)(x+	1)(x+	NUM
ejpam-5288	58	3	2	2	NUM
ejpam-5288	58	4	)	)	PUNCT
ejpam-5288	58	5	·	·	PUNCT
ejpam-5288	58	6	·	·	PUNCT
ejpam-5288	58	7	·	·	PUNCT
ejpam-5288	58	8	(	(	PUNCT
ejpam-5288	58	9	x+	x+	X
ejpam-5288	58	10	(	(	PUNCT
ejpam-5288	58	11	n−	n−	NOUN
ejpam-5288	58	12	1	1	NUM
ejpam-5288	58	13	)	)	PUNCT
ejpam-5288	58	14	)	)	PUNCT
ejpam-5288	59	1	=	=	SYM
ejpam-5288	59	2	⟨x⟩n	⟨x⟩n	PROPN
ejpam-5288	59	3	,	,	PUNCT
ejpam-5288	59	4	(	(	PUNCT
ejpam-5288	59	5	n	n	CCONJ
ejpam-5288	59	6	≥	≥	NOUN
ejpam-5288	59	7	1	1	NUM
ejpam-5288	59	8	)	)	PUNCT
ejpam-5288	59	9	.	.	PUNCT
ejpam-5288	60	1	for	for	ADP
ejpam-5288	60	2	n	n	PRON
ejpam-5288	60	3	≥	≥	NOUN
ejpam-5288	60	4	0	0	NUM
ejpam-5288	60	5	,	,	PUNCT
ejpam-5288	60	6	the	the	DET
ejpam-5288	60	7	unsigned	unsigned	ADJ
ejpam-5288	60	8	lah	lah	PROPN
ejpam-5288	60	9	numbers	number	NOUN
ejpam-5288	60	10	are	be	AUX
ejpam-5288	60	11	defined	define	VERB
ejpam-5288	60	12	by	by	ADP
ejpam-5288	60	13	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5288	60	14	=	=	SYM
ejpam-5288	60	15	n∑	n∑	PROPN
ejpam-5288	60	16	k=0	k=0	PROPN
ejpam-5288	60	17	l(n	l(n	PROPN
ejpam-5288	60	18	,	,	PUNCT
ejpam-5288	60	19	k)(x)k	k)(x)k	PRON
ejpam-5288	60	20	,	,	PUNCT
ejpam-5288	60	21	(	(	PUNCT
ejpam-5288	60	22	see[5	see[5	ADJ
ejpam-5288	60	23	,	,	PUNCT
ejpam-5288	60	24	12	12	NUM
ejpam-5288	60	25	,	,	PUNCT
ejpam-5288	60	26	13	13	NUM
ejpam-5288	60	27	,	,	PUNCT
ejpam-5288	60	28	26	26	NUM
ejpam-5288	60	29	]	]	PUNCT
ejpam-5288	60	30	)	)	PUNCT
ejpam-5288	60	31	.	.	PUNCT
ejpam-5288	61	1	(	(	PUNCT
ejpam-5288	61	2	2	2	X
ejpam-5288	61	3	)	)	PUNCT
ejpam-5288	61	4	note	note	NOUN
ejpam-5288	61	5	that	that	SCONJ
ejpam-5288	61	6	l(n	l(n	NOUN
ejpam-5288	61	7	,	,	PUNCT
ejpam-5288	61	8	k	k	NOUN
ejpam-5288	61	9	)	)	PUNCT
ejpam-5288	61	10	=	=	SYM
ejpam-5288	61	11	n	n	X
ejpam-5288	61	12	!	!	PUNCT
ejpam-5288	62	1	k	k	X
ejpam-5288	62	2	!	!	PUNCT
ejpam-5288	63	1	(	(	PUNCT
ejpam-5288	63	2	n−1	n−1	PROPN
ejpam-5288	63	3	k−1	k−1	PROPN
ejpam-5288	63	4	)	)	PUNCT
ejpam-5288	63	5	,	,	PUNCT
ejpam-5288	63	6	(	(	PUNCT
ejpam-5288	63	7	n	n	CCONJ
ejpam-5288	63	8	≥	≥	NOUN
ejpam-5288	63	9	k	k	X
ejpam-5288	63	10	≥	≥	NUM
ejpam-5288	63	11	1	1	NUM
ejpam-5288	63	12	)	)	PUNCT
ejpam-5288	63	13	.	.	PUNCT
ejpam-5288	64	1	the	the	DET
ejpam-5288	64	2	lah	lah	PROPN
ejpam-5288	64	3	-	-	PUNCT
ejpam-5288	64	4	bell	bell	NOUN
ejpam-5288	64	5	number	number	NOUN
ejpam-5288	64	6	bl	bl	VERB
ejpam-5288	64	7	n	n	PRON
ejpam-5288	64	8	is	be	AUX
ejpam-5288	64	9	defined	define	VERB
ejpam-5288	64	10	by	by	ADP
ejpam-5288	64	11	bl	bl	PROPN
ejpam-5288	64	12	n	n	PROPN
ejpam-5288	64	13	=	=	PROPN
ejpam-5288	64	14	n∑	n∑	PROPN
ejpam-5288	64	15	k=0	k=0	PROPN
ejpam-5288	64	16	l(n	l(n	PROPN
ejpam-5288	64	17	,	,	PUNCT
ejpam-5288	64	18	k	k	NOUN
ejpam-5288	64	19	)	)	PUNCT
ejpam-5288	64	20	,	,	PUNCT
ejpam-5288	64	21	(	(	PUNCT
ejpam-5288	64	22	n	n	X
ejpam-5288	64	23	≥	≥	NOUN
ejpam-5288	64	24	0	0	NUM
ejpam-5288	64	25	)	)	PUNCT
ejpam-5288	64	26	,	,	PUNCT
ejpam-5288	64	27	(	(	PUNCT
ejpam-5288	64	28	see	see	VERB
ejpam-5288	64	29	[	[	X
ejpam-5288	64	30	12	12	NUM
ejpam-5288	64	31	,	,	PUNCT
ejpam-5288	64	32	13	13	NUM
ejpam-5288	64	33	]	]	PUNCT
ejpam-5288	64	34	)	)	PUNCT
ejpam-5288	64	35	.	.	PUNCT
ejpam-5288	65	1	(	(	PUNCT
ejpam-5288	65	2	3	3	X
ejpam-5288	65	3	)	)	PUNCT
ejpam-5288	65	4	the	the	DET
ejpam-5288	65	5	λ	λ	NOUN
ejpam-5288	65	6	-	-	NOUN
ejpam-5288	65	7	analogues	analogue	NOUN
ejpam-5288	65	8	of	of	ADP
ejpam-5288	65	9	the	the	DET
ejpam-5288	65	10	stirling	stirling	NOUN
ejpam-5288	65	11	numbers	number	NOUN
ejpam-5288	65	12	of	of	ADP
ejpam-5288	65	13	the	the	DET
ejpam-5288	65	14	first	first	ADJ
ejpam-5288	65	15	kind	kind	NOUN
ejpam-5288	65	16	are	be	AUX
ejpam-5288	65	17	defined	define	VERB
ejpam-5288	65	18	by	by	ADP
ejpam-5288	65	19	(	(	PUNCT
ejpam-5288	65	20	x)n	x)n	PROPN
ejpam-5288	65	21	,	,	PUNCT
ejpam-5288	65	22	λ	λ	PROPN
ejpam-5288	65	23	=	=	SYM
ejpam-5288	65	24	n∑	n∑	PROPN
ejpam-5288	65	25	k=0	k=0	X
ejpam-5288	65	26	s1,λ(n	s1,λ(n	PROPN
ejpam-5288	65	27	,	,	PUNCT
ejpam-5288	65	28	k)x	k)x	X
ejpam-5288	65	29	k	k	X
ejpam-5288	65	30	,	,	PUNCT
ejpam-5288	65	31	(	(	PUNCT
ejpam-5288	65	32	n	n	CCONJ
ejpam-5288	65	33	≥	≥	NOUN
ejpam-5288	65	34	0	0	NUM
ejpam-5288	65	35	)	)	PUNCT
ejpam-5288	65	36	.	.	PUNCT
ejpam-5288	66	1	(	(	PUNCT
ejpam-5288	66	2	4	4	X
ejpam-5288	66	3	)	)	PUNCT
ejpam-5288	66	4	j.	j.	PROPN
ejpam-5288	66	5	kwon	kwon	PROPN
ejpam-5288	66	6	et	et	PROPN
ejpam-5288	66	7	al	al	PROPN
ejpam-5288	66	8	.	.	PUNCT
ejpam-5288	66	9	/	/	SYM
ejpam-5288	66	10	eur	eur	PROPN
ejpam-5288	66	11	.	.	PUNCT
ejpam-5288	67	1	j.	j.	PROPN
ejpam-5288	67	2	pure	pure	PROPN
ejpam-5288	67	3	appl	appl	PROPN
ejpam-5288	67	4	.	.	PROPN
ejpam-5288	67	5	math	math	PROPN
ejpam-5288	67	6	,	,	PUNCT
ejpam-5288	67	7	17	17	NUM
ejpam-5288	67	8	(	(	PUNCT
ejpam-5288	67	9	3	3	NUM
ejpam-5288	67	10	)	)	PUNCT
ejpam-5288	67	11	(	(	PUNCT
ejpam-5288	67	12	2024	2024	NUM
ejpam-5288	67	13	)	)	PUNCT
ejpam-5288	67	14	,	,	PUNCT
ejpam-5288	67	15	1385	1385	NUM
ejpam-5288	67	16	-	-	SYM
ejpam-5288	67	17	1402	1402	NUM
ejpam-5288	67	18	1388	1388	NUM
ejpam-5288	67	19	from	from	ADP
ejpam-5288	67	20	(	(	PUNCT
ejpam-5288	67	21	4	4	NUM
ejpam-5288	67	22	)	)	PUNCT
ejpam-5288	68	1	,	,	PUNCT
ejpam-5288	68	2	we	we	PRON
ejpam-5288	68	3	get	get	VERB
ejpam-5288	68	4	1	1	NUM
ejpam-5288	68	5	λk	λk	ADP
ejpam-5288	68	6	1	1	NUM
ejpam-5288	68	7	k	k	NOUN
ejpam-5288	68	8	!	!	PUNCT
ejpam-5288	69	1	(	(	PUNCT
ejpam-5288	69	2	log(1	log(1	NOUN
ejpam-5288	69	3	+	+	CCONJ
ejpam-5288	70	1	λt	λt	X
ejpam-5288	70	2	)	)	PUNCT
ejpam-5288	70	3	)	)	PUNCT
ejpam-5288	71	1	k	k	X
ejpam-5288	72	1	=	=	PUNCT
ejpam-5288	72	2	∞∑	∞∑	NUM
ejpam-5288	72	3	n	n	CCONJ
ejpam-5288	72	4	=	=	X
ejpam-5288	72	5	k	k	X
ejpam-5288	72	6	s1,λ(n	s1,λ(n	X
ejpam-5288	72	7	,	,	PUNCT
ejpam-5288	72	8	k	k	NOUN
ejpam-5288	72	9	)	)	PUNCT
ejpam-5288	72	10	tn	tn	PROPN
ejpam-5288	72	11	n	n	PROPN
ejpam-5288	72	12	!	!	PROPN
ejpam-5288	72	13	,	,	PUNCT
ejpam-5288	72	14	(	(	PUNCT
ejpam-5288	72	15	k	k	X
ejpam-5288	72	16	≥	≥	PROPN
ejpam-5288	72	17	0	0	NUM
ejpam-5288	72	18	)	)	PUNCT
ejpam-5288	72	19	.	.	PUNCT
ejpam-5288	73	1	(	(	PUNCT
ejpam-5288	73	2	5	5	X
ejpam-5288	73	3	)	)	PUNCT
ejpam-5288	73	4	note	note	NOUN
ejpam-5288	73	5	that	that	SCONJ
ejpam-5288	73	6	limλ→1	limλ→1	PROPN
ejpam-5288	73	7	s1,λ(n	s1,λ(n	PRON
ejpam-5288	73	8	,	,	PUNCT
ejpam-5288	73	9	k	k	NOUN
ejpam-5288	73	10	)	)	PUNCT
ejpam-5288	73	11	=	=	SYM
ejpam-5288	73	12	s1(n	s1(n	PROPN
ejpam-5288	73	13	,	,	PUNCT
ejpam-5288	73	14	k	k	NOUN
ejpam-5288	73	15	)	)	PUNCT
ejpam-5288	73	16	are	be	AUX
ejpam-5288	73	17	the	the	DET
ejpam-5288	73	18	ordinary	ordinary	ADJ
ejpam-5288	73	19	stirling	stirling	NOUN
ejpam-5288	73	20	numbers	number	NOUN
ejpam-5288	73	21	of	of	ADP
ejpam-5288	73	22	the	the	DET
ejpam-5288	73	23	first	first	ADJ
ejpam-5288	73	24	kind	kind	NOUN
ejpam-5288	73	25	given	give	VERB
ejpam-5288	73	26	by	by	ADP
ejpam-5288	73	27	(	(	PUNCT
ejpam-5288	73	28	x)n	x)n	PUNCT
ejpam-5288	73	29	=	=	PUNCT
ejpam-5288	74	1	n∑	n∑	DET
ejpam-5288	74	2	k=0	k=0	PROPN
ejpam-5288	74	3	s1(n	s1(n	PROPN
ejpam-5288	74	4	,	,	PUNCT
ejpam-5288	74	5	k)x	k)x	X
ejpam-5288	74	6	k	k	X
ejpam-5288	74	7	,	,	PUNCT
ejpam-5288	74	8	(	(	PUNCT
ejpam-5288	74	9	see	see	VERB
ejpam-5288	74	10	[	[	X
ejpam-5288	74	11	1−	1−	NUM
ejpam-5288	74	12	5	5	NUM
ejpam-5288	74	13	,	,	PUNCT
ejpam-5288	74	14	7−	7−	NUM
ejpam-5288	74	15	13	13	NUM
ejpam-5288	74	16	,	,	PUNCT
ejpam-5288	74	17	15−	15−	PROPN
ejpam-5288	74	18	21	21	NUM
ejpam-5288	74	19	,	,	PUNCT
ejpam-5288	74	20	24−	24−	NOUN
ejpam-5288	74	21	26	26	NUM
ejpam-5288	74	22	]	]	PUNCT
ejpam-5288	74	23	)	)	PUNCT
ejpam-5288	74	24	.	.	PUNCT
ejpam-5288	75	1	(	(	PUNCT
ejpam-5288	75	2	6	6	X
ejpam-5288	75	3	)	)	PUNCT
ejpam-5288	75	4	the	the	DET
ejpam-5288	75	5	unsinged	unsinged	ADJ
ejpam-5288	75	6	λ	λ	PROPN
ejpam-5288	75	7	-	-	ADJ
ejpam-5288	75	8	stirling	stirling	ADJ
ejpam-5288	75	9	numbers	number	NOUN
ejpam-5288	75	10	of	of	ADP
ejpam-5288	75	11	the	the	DET
ejpam-5288	75	12	first	first	ADJ
ejpam-5288	75	13	kind	kind	NOUN
ejpam-5288	75	14	are	be	AUX
ejpam-5288	75	15	given	give	VERB
ejpam-5288	75	16	by	by	ADP
ejpam-5288	75	17	(	(	PUNCT
ejpam-5288	75	18	−1)n−ks1,λ(n	−1)n−ks1,λ(n	PROPN
ejpam-5288	75	19	,	,	PUNCT
ejpam-5288	75	20	k	k	NOUN
ejpam-5288	75	21	)	)	PUNCT
ejpam-5288	75	22	=	=	PUNCT
ejpam-5288	76	1	[	[	PUNCT
ejpam-5288	76	2	n	n	X
ejpam-5288	76	3	k	k	X
ejpam-5288	76	4	]	]	X
ejpam-5288	76	5	λ	λ	X
ejpam-5288	76	6	,	,	PUNCT
ejpam-5288	76	7	(	(	PUNCT
ejpam-5288	76	8	n	n	CCONJ
ejpam-5288	76	9	,	,	PUNCT
ejpam-5288	76	10	k	k	X
ejpam-5288	76	11	≥	≥	PROPN
ejpam-5288	76	12	0	0	NUM
ejpam-5288	76	13	)	)	PUNCT
ejpam-5288	76	14	,	,	PUNCT
ejpam-5288	76	15	and	and	CCONJ
ejpam-5288	76	16	hence	hence	ADV
ejpam-5288	76	17	we	we	PRON
ejpam-5288	76	18	see	see	VERB
ejpam-5288	76	19	from	from	ADP
ejpam-5288	76	20	(	(	PUNCT
ejpam-5288	76	21	4	4	NUM
ejpam-5288	76	22	)	)	PUNCT
ejpam-5288	76	23	and	and	CCONJ
ejpam-5288	76	24	(	(	PUNCT
ejpam-5288	76	25	5	5	NUM
ejpam-5288	76	26	)	)	PUNCT
ejpam-5288	76	27	that	that	PRON
ejpam-5288	76	28	⟨x⟩n	⟨x⟩n	VERB
ejpam-5288	76	29	,	,	PUNCT
ejpam-5288	76	30	λ	λ	PROPN
ejpam-5288	76	31	=	=	SYM
ejpam-5288	76	32	n∑	n∑	NOUN
ejpam-5288	76	33	k=0	k=0	PROPN
ejpam-5288	76	34	[	[	PUNCT
ejpam-5288	76	35	n	n	X
ejpam-5288	76	36	k	k	X
ejpam-5288	76	37	]	]	PUNCT
ejpam-5288	76	38	λ	λ	X
ejpam-5288	76	39	xk	xk	PROPN
ejpam-5288	76	40	,	,	PUNCT
ejpam-5288	76	41	(	(	PUNCT
ejpam-5288	76	42	n	n	CCONJ
ejpam-5288	76	43	≥	≥	NOUN
ejpam-5288	76	44	0	0	NUM
ejpam-5288	76	45	)	)	PUNCT
ejpam-5288	76	46	,	,	PUNCT
ejpam-5288	76	47	1	1	NUM
ejpam-5288	76	48	λk	λk	ADP
ejpam-5288	76	49	1	1	NUM
ejpam-5288	76	50	k	k	NOUN
ejpam-5288	76	51	!	!	PUNCT
ejpam-5288	77	1	(	(	PUNCT
ejpam-5288	77	2	−	−	PROPN
ejpam-5288	77	3	log(1−	log(1−	PROPN
ejpam-5288	77	4	λt	λt	ADP
ejpam-5288	77	5	)	)	PUNCT
ejpam-5288	77	6	)	)	PUNCT
ejpam-5288	78	1	k	k	X
ejpam-5288	79	1	=	=	PUNCT
ejpam-5288	80	1	∞∑	∞∑	NUM
ejpam-5288	80	2	n	n	CCONJ
ejpam-5288	80	3	=	=	SYM
ejpam-5288	80	4	k	k	X
ejpam-5288	80	5	[	[	PUNCT
ejpam-5288	80	6	n	n	X
ejpam-5288	80	7	k	k	X
ejpam-5288	80	8	]	]	PUNCT
ejpam-5288	81	1	λ	λ	X
ejpam-5288	81	2	tn	tn	NOUN
ejpam-5288	81	3	n	n	X
ejpam-5288	81	4	!	!	PUNCT
ejpam-5288	81	5	,	,	PUNCT
ejpam-5288	81	6	(	(	PUNCT
ejpam-5288	81	7	k	k	X
ejpam-5288	81	8	≥	≥	PROPN
ejpam-5288	81	9	0	0	NUM
ejpam-5288	81	10	)	)	PUNCT
ejpam-5288	81	11	.	.	PUNCT
ejpam-5288	82	1	(	(	PUNCT
ejpam-5288	82	2	7	7	X
ejpam-5288	82	3	)	)	PUNCT
ejpam-5288	82	4	the	the	DET
ejpam-5288	82	5	λ	λ	NOUN
ejpam-5288	82	6	-	-	NOUN
ejpam-5288	82	7	analogues	analogue	NOUN
ejpam-5288	82	8	of	of	ADP
ejpam-5288	82	9	stirling	stirling	NOUN
ejpam-5288	82	10	numbers	number	NOUN
ejpam-5288	82	11	of	of	ADP
ejpam-5288	82	12	the	the	DET
ejpam-5288	82	13	second	second	ADJ
ejpam-5288	82	14	kind	kind	NOUN
ejpam-5288	82	15	are	be	AUX
ejpam-5288	82	16	defined	define	VERB
ejpam-5288	82	17	by	by	ADP
ejpam-5288	82	18	xn	xn	PROPN
ejpam-5288	82	19	=	=	SYM
ejpam-5288	82	20	n∑	n∑	PROPN
ejpam-5288	82	21	k=0	k=0	PROPN
ejpam-5288	82	22	{	{	PUNCT
ejpam-5288	82	23	n	n	NOUN
ejpam-5288	82	24	k	k	ADJ
ejpam-5288	82	25	}	}	PUNCT
ejpam-5288	82	26	λ	λ	PROPN
ejpam-5288	82	27	(	(	PUNCT
ejpam-5288	82	28	x)k	x)k	NOUN
ejpam-5288	82	29	,	,	PUNCT
ejpam-5288	82	30	λ	λ	PROPN
ejpam-5288	82	31	,	,	PUNCT
ejpam-5288	82	32	(	(	PUNCT
ejpam-5288	82	33	n	n	CCONJ
ejpam-5288	82	34	≥	≥	NOUN
ejpam-5288	82	35	0	0	NUM
ejpam-5288	82	36	)	)	PUNCT
ejpam-5288	82	37	,	,	PUNCT
ejpam-5288	82	38	(	(	PUNCT
ejpam-5288	82	39	see	see	VERB
ejpam-5288	82	40	[	[	X
ejpam-5288	82	41	10	10	NUM
ejpam-5288	82	42	]	]	NUM
ejpam-5288	82	43	)	)	PUNCT
ejpam-5288	82	44	.	.	PUNCT
ejpam-5288	83	1	(	(	PUNCT
ejpam-5288	83	2	8)	8)	NUM
ejpam-5288	83	3	from	from	ADP
ejpam-5288	83	4	(	(	PUNCT
ejpam-5288	83	5	8)	8)	NUM
ejpam-5288	83	6	,	,	PUNCT
ejpam-5288	83	7	we	we	PRON
ejpam-5288	83	8	have	have	VERB
ejpam-5288	83	9	1	1	NUM
ejpam-5288	83	10	λk	λk	ADP
ejpam-5288	83	11	1	1	NUM
ejpam-5288	83	12	k	k	NOUN
ejpam-5288	83	13	!	!	PUNCT
ejpam-5288	84	1	(	(	PUNCT
ejpam-5288	84	2	eλt	eλt	PROPN
ejpam-5288	84	3	−	−	PROPN
ejpam-5288	84	4	1	1	X
ejpam-5288	84	5	)	)	PUNCT
ejpam-5288	84	6	k	k	NOUN
ejpam-5288	85	1	=	=	PUNCT
ejpam-5288	86	1	∞∑	∞∑	NUM
ejpam-5288	86	2	n	n	CCONJ
ejpam-5288	86	3	=	=	SYM
ejpam-5288	86	4	k	k	X
ejpam-5288	86	5	{	{	PUNCT
ejpam-5288	86	6	n	n	NOUN
ejpam-5288	86	7	k	k	ADJ
ejpam-5288	86	8	}	}	PUNCT
ejpam-5288	86	9	λ	λ	PROPN
ejpam-5288	86	10	tn	tn	NOUN
ejpam-5288	86	11	n	n	X
ejpam-5288	86	12	!	!	PROPN
ejpam-5288	86	13	,	,	PUNCT
ejpam-5288	86	14	(	(	PUNCT
ejpam-5288	86	15	see	see	VERB
ejpam-5288	86	16	[	[	X
ejpam-5288	86	17	10	10	NUM
ejpam-5288	86	18	]	]	NUM
ejpam-5288	86	19	)	)	PUNCT
ejpam-5288	86	20	.	.	PUNCT
ejpam-5288	87	1	(	(	PUNCT
ejpam-5288	87	2	9	9	X
ejpam-5288	87	3	)	)	PUNCT
ejpam-5288	87	4	note	note	NOUN
ejpam-5288	87	5	that	that	SCONJ
ejpam-5288	87	6	limλ→1	limλ→1	PROPN
ejpam-5288	87	7	{	{	PUNCT
ejpam-5288	87	8	n	n	NOUN
ejpam-5288	87	9	k	k	PROPN
ejpam-5288	87	10	}	}	PUNCT
ejpam-5288	87	11	λ	λ	PROPN
ejpam-5288	87	12	=	=	SYM
ejpam-5288	87	13	{	{	PUNCT
ejpam-5288	87	14	n	n	CCONJ
ejpam-5288	87	15	k	k	PROPN
ejpam-5288	87	16	}	}	PUNCT
ejpam-5288	87	17	are	be	AUX
ejpam-5288	87	18	the	the	DET
ejpam-5288	87	19	ordinary	ordinary	ADJ
ejpam-5288	87	20	stirling	stirling	NOUN
ejpam-5288	87	21	numbers	number	NOUN
ejpam-5288	87	22	of	of	ADP
ejpam-5288	87	23	the	the	DET
ejpam-5288	87	24	second	second	ADJ
ejpam-5288	87	25	kind	kind	NOUN
ejpam-5288	87	26	defined	define	VERB
ejpam-5288	87	27	by	by	ADP
ejpam-5288	87	28	xn	xn	PROPN
ejpam-5288	88	1	=	=	SYM
ejpam-5288	88	2	n∑	n∑	PROPN
ejpam-5288	88	3	k=0	k=0	PROPN
ejpam-5288	88	4	{	{	PUNCT
ejpam-5288	88	5	n	n	NOUN
ejpam-5288	88	6	k	k	NOUN
ejpam-5288	88	7	}	}	PUNCT
ejpam-5288	88	8	(	(	PUNCT
ejpam-5288	88	9	x)k	x)k	X
ejpam-5288	88	10	,	,	PUNCT
ejpam-5288	88	11	(	(	PUNCT
ejpam-5288	88	12	n	n	X
ejpam-5288	88	13	≥	≥	NOUN
ejpam-5288	88	14	0	0	NUM
ejpam-5288	88	15	)	)	PUNCT
ejpam-5288	88	16	,	,	PUNCT
ejpam-5288	88	17	(	(	PUNCT
ejpam-5288	88	18	see	see	VERB
ejpam-5288	88	19	[	[	X
ejpam-5288	88	20	1−	1−	NUM
ejpam-5288	88	21	5	5	NUM
ejpam-5288	88	22	,	,	PUNCT
ejpam-5288	88	23	7−	7−	NUM
ejpam-5288	88	24	13	13	NUM
ejpam-5288	88	25	,	,	PUNCT
ejpam-5288	88	26	15−	15−	PROPN
ejpam-5288	88	27	32	32	NUM
ejpam-5288	88	28	]	]	PUNCT
ejpam-5288	88	29	)	)	PUNCT
ejpam-5288	88	30	.	.	PUNCT
ejpam-5288	89	1	for	for	SCONJ
ejpam-5288	89	2	r	r	NOUN
ejpam-5288	89	3	∈	∈	PROPN
ejpam-5288	89	4	n	n	NOUN
ejpam-5288	89	5	∪	∪	X
ejpam-5288	89	6	{	{	PUNCT
ejpam-5288	89	7	0	0	NUM
ejpam-5288	89	8	}	}	PUNCT
ejpam-5288	89	9	,	,	PUNCT
ejpam-5288	89	10	the	the	DET
ejpam-5288	89	11	λ	λ	NOUN
ejpam-5288	89	12	-	-	NOUN
ejpam-5288	89	13	analogues	analogue	NOUN
ejpam-5288	89	14	of	of	ADP
ejpam-5288	89	15	r	r	NOUN
ejpam-5288	89	16	-	-	PUNCT
ejpam-5288	89	17	stirling	stirling	NOUN
ejpam-5288	89	18	numbers	number	NOUN
ejpam-5288	89	19	of	of	ADP
ejpam-5288	89	20	the	the	DET
ejpam-5288	89	21	second	second	ADJ
ejpam-5288	89	22	kind	kind	NOUN
ejpam-5288	89	23	are	be	AUX
ejpam-5288	89	24	given	give	VERB
ejpam-5288	89	25	by	by	ADP
ejpam-5288	89	26	(	(	PUNCT
ejpam-5288	89	27	x+	x+	X
ejpam-5288	89	28	r)n	r)n	X
ejpam-5288	89	29	=	=	SYM
ejpam-5288	89	30	n∑	n∑	X
ejpam-5288	89	31	k=0	k=0	PROPN
ejpam-5288	89	32	{	{	PUNCT
ejpam-5288	89	33	n+	n+	ADP
ejpam-5288	89	34	r	r	NOUN
ejpam-5288	89	35	k	k	NOUN
ejpam-5288	90	1	+	+	CCONJ
ejpam-5288	90	2	r	r	NOUN
ejpam-5288	90	3	}	}	PUNCT
ejpam-5288	90	4	r	r	NOUN
ejpam-5288	90	5	,	,	PUNCT
ejpam-5288	90	6	λ	λ	PROPN
ejpam-5288	90	7	(	(	PUNCT
ejpam-5288	90	8	x)k	x)k	NOUN
ejpam-5288	90	9	,	,	PUNCT
ejpam-5288	90	10	λ	λ	PROPN
ejpam-5288	90	11	,	,	PUNCT
ejpam-5288	90	12	(	(	PUNCT
ejpam-5288	90	13	n	n	CCONJ
ejpam-5288	90	14	≥	≥	NOUN
ejpam-5288	90	15	0	0	NUM
ejpam-5288	90	16	)	)	PUNCT
ejpam-5288	90	17	,	,	PUNCT
ejpam-5288	90	18	(	(	PUNCT
ejpam-5288	90	19	see	see	VERB
ejpam-5288	90	20	[	[	X
ejpam-5288	90	21	10	10	NUM
ejpam-5288	90	22	,	,	PUNCT
ejpam-5288	90	23	11	11	NUM
ejpam-5288	90	24	,	,	PUNCT
ejpam-5288	90	25	15	15	NUM
ejpam-5288	90	26	]	]	NUM
ejpam-5288	90	27	)	)	PUNCT
ejpam-5288	90	28	.	.	PUNCT
ejpam-5288	91	1	(	(	PUNCT
ejpam-5288	91	2	10	10	NUM
ejpam-5288	91	3	)	)	PUNCT
ejpam-5288	91	4	thus	thus	ADV
ejpam-5288	91	5	,	,	PUNCT
ejpam-5288	91	6	by	by	ADP
ejpam-5288	91	7	(	(	PUNCT
ejpam-5288	91	8	10	10	NUM
ejpam-5288	91	9	)	)	PUNCT
ejpam-5288	91	10	,	,	PUNCT
ejpam-5288	91	11	we	we	PRON
ejpam-5288	91	12	get	get	VERB
ejpam-5288	91	13	1	1	NUM
ejpam-5288	91	14	λk	λk	ADP
ejpam-5288	91	15	1	1	NUM
ejpam-5288	91	16	k	k	NOUN
ejpam-5288	91	17	!	!	PUNCT
ejpam-5288	92	1	(	(	PUNCT
ejpam-5288	92	2	eλt	eλt	PROPN
ejpam-5288	92	3	−	−	PROPN
ejpam-5288	92	4	1	1	NUM
ejpam-5288	92	5	)	)	PUNCT
ejpam-5288	92	6	k	k	PROPN
ejpam-5288	92	7	ert	ert	NOUN
ejpam-5288	92	8	=	=	NOUN
ejpam-5288	93	1	∞∑	∞∑	NUM
ejpam-5288	93	2	n	n	CCONJ
ejpam-5288	93	3	=	=	SYM
ejpam-5288	93	4	k	k	X
ejpam-5288	93	5	{	{	PUNCT
ejpam-5288	93	6	n+	n+	ADP
ejpam-5288	93	7	r	r	NOUN
ejpam-5288	93	8	k	k	NOUN
ejpam-5288	94	1	+	+	CCONJ
ejpam-5288	94	2	r	r	NOUN
ejpam-5288	94	3	}	}	PUNCT
ejpam-5288	94	4	r	r	NOUN
ejpam-5288	94	5	,	,	PUNCT
ejpam-5288	94	6	λ	λ	PROPN
ejpam-5288	94	7	tn	tn	NOUN
ejpam-5288	94	8	n	n	X
ejpam-5288	94	9	!	!	PUNCT
ejpam-5288	94	10	,	,	PUNCT
ejpam-5288	94	11	(	(	PUNCT
ejpam-5288	94	12	k	k	X
ejpam-5288	94	13	≥	≥	PROPN
ejpam-5288	94	14	0	0	NUM
ejpam-5288	94	15	)	)	PUNCT
ejpam-5288	94	16	,	,	PUNCT
ejpam-5288	94	17	(	(	PUNCT
ejpam-5288	94	18	see	see	VERB
ejpam-5288	94	19	[	[	X
ejpam-5288	94	20	10	10	NUM
ejpam-5288	94	21	,	,	PUNCT
ejpam-5288	94	22	11	11	NUM
ejpam-5288	94	23	]	]	NUM
ejpam-5288	94	24	)	)	PUNCT
ejpam-5288	94	25	.	.	PUNCT
ejpam-5288	95	1	(	(	PUNCT
ejpam-5288	95	2	11	11	NUM
ejpam-5288	95	3	)	)	PUNCT
ejpam-5288	95	4	j.	j.	PROPN
ejpam-5288	95	5	kwon	kwon	PROPN
ejpam-5288	95	6	et	et	PROPN
ejpam-5288	95	7	al	al	PROPN
ejpam-5288	95	8	.	.	PUNCT
ejpam-5288	95	9	/	/	SYM
ejpam-5288	95	10	eur	eur	PROPN
ejpam-5288	95	11	.	.	PUNCT
ejpam-5288	96	1	j.	j.	PROPN
ejpam-5288	96	2	pure	pure	PROPN
ejpam-5288	96	3	appl	appl	PROPN
ejpam-5288	96	4	.	.	PROPN
ejpam-5288	96	5	math	math	PROPN
ejpam-5288	96	6	,	,	PUNCT
ejpam-5288	96	7	17	17	NUM
ejpam-5288	96	8	(	(	PUNCT
ejpam-5288	96	9	3	3	NUM
ejpam-5288	96	10	)	)	PUNCT
ejpam-5288	96	11	(	(	PUNCT
ejpam-5288	96	12	2024	2024	NUM
ejpam-5288	96	13	)	)	PUNCT
ejpam-5288	96	14	,	,	PUNCT
ejpam-5288	96	15	1385	1385	NUM
ejpam-5288	96	16	-	-	SYM
ejpam-5288	96	17	1402	1402	NUM
ejpam-5288	96	18	1389	1389	NUM
ejpam-5288	96	19	the	the	DET
ejpam-5288	96	20	λ	λ	PROPN
ejpam-5288	96	21	-	-	ADJ
ejpam-5288	96	22	bell	bell	ADJ
ejpam-5288	96	23	polynomials	polynomial	NOUN
ejpam-5288	96	24	are	be	AUX
ejpam-5288	96	25	given	give	VERB
ejpam-5288	96	26	by	by	ADP
ejpam-5288	96	27	e	e	PROPN
ejpam-5288	96	28	x	x	SYM
ejpam-5288	96	29	λ	λ	PROPN
ejpam-5288	96	30	(	(	PUNCT
ejpam-5288	96	31	eλt−1	eλt−1	PROPN
ejpam-5288	96	32	)	)	PUNCT
ejpam-5288	96	33	=	=	PUNCT
ejpam-5288	97	1	∞∑	∞∑	PROPN
ejpam-5288	97	2	n=0	n=0	NUM
ejpam-5288	97	3	ϕn	ϕn	INTJ
ejpam-5288	97	4	,	,	PUNCT
ejpam-5288	97	5	λ(x	λ(x	PROPN
ejpam-5288	97	6	)	)	PUNCT
ejpam-5288	97	7	tn	tn	PROPN
ejpam-5288	97	8	n	n	PROPN
ejpam-5288	97	9	!	!	PROPN
ejpam-5288	97	10	,	,	PUNCT
ejpam-5288	97	11	(	(	PUNCT
ejpam-5288	97	12	see	see	VERB
ejpam-5288	97	13	[	[	X
ejpam-5288	97	14	10	10	NUM
ejpam-5288	97	15	]	]	NUM
ejpam-5288	97	16	)	)	PUNCT
ejpam-5288	97	17	.	.	PUNCT
ejpam-5288	98	1	(	(	PUNCT
ejpam-5288	98	2	12	12	NUM
ejpam-5288	98	3	)	)	PUNCT
ejpam-5288	98	4	note	note	NOUN
ejpam-5288	98	5	that	that	SCONJ
ejpam-5288	98	6	lim	lim	PROPN
ejpam-5288	98	7	λ→1	λ→1	X
ejpam-5288	98	8	ϕn	ϕn	INTJ
ejpam-5288	98	9	,	,	PUNCT
ejpam-5288	98	10	λ(x	λ(x	PROPN
ejpam-5288	98	11	)	)	PUNCT
ejpam-5288	98	12	=	=	SYM
ejpam-5288	98	13	ϕn(x	ϕn(x	X
ejpam-5288	98	14	)	)	PUNCT
ejpam-5288	99	1	=	=	SYM
ejpam-5288	99	2	n∑	n∑	NOUN
ejpam-5288	99	3	k=0	k=0	PROPN
ejpam-5288	99	4	{	{	PUNCT
ejpam-5288	99	5	n	n	NOUN
ejpam-5288	99	6	k	k	PROPN
ejpam-5288	99	7	}	}	PUNCT
ejpam-5288	99	8	xk	xk	PROPN
ejpam-5288	99	9	are	be	AUX
ejpam-5288	99	10	the	the	DET
ejpam-5288	99	11	ordinary	ordinary	ADJ
ejpam-5288	99	12	bell	bell	NOUN
ejpam-5288	99	13	polynomials	polynomial	NOUN
ejpam-5288	99	14	.	.	PUNCT
ejpam-5288	100	1	here	here	ADV
ejpam-5288	100	2	we	we	PRON
ejpam-5288	100	3	note	note	VERB
ejpam-5288	100	4	that	that	SCONJ
ejpam-5288	100	5	ϕn	ϕn	INTJ
ejpam-5288	100	6	,	,	PUNCT
ejpam-5288	100	7	λ(x	λ(x	PROPN
ejpam-5288	100	8	)	)	PUNCT
ejpam-5288	100	9	=	=	PUNCT
ejpam-5288	101	1	λne−	λne−	PROPN
ejpam-5288	101	2	x	x	PUNCT
ejpam-5288	101	3	λ	λ	PROPN
ejpam-5288	101	4	∞∑	∞∑	PROPN
ejpam-5288	101	5	k=0	k=0	PROPN
ejpam-5288	101	6	kn	kn	PROPN
ejpam-5288	101	7	k	k	PROPN
ejpam-5288	101	8	!	!	PUNCT
ejpam-5288	102	1	(	(	PUNCT
ejpam-5288	102	2	x	x	PUNCT
ejpam-5288	102	3	λ	λ	X
ejpam-5288	102	4	)	)	PUNCT
ejpam-5288	102	5	k	k	NOUN
ejpam-5288	102	6	,	,	PUNCT
ejpam-5288	102	7	ϕn(x	ϕn(x	PUNCT
ejpam-5288	102	8	)	)	PUNCT
ejpam-5288	102	9	=	=	PUNCT
ejpam-5288	102	10	e−x	e−x	NOUN
ejpam-5288	102	11	∞∑	∞∑	PRON
ejpam-5288	102	12	k=0	k=0	PROPN
ejpam-5288	102	13	kn	kn	PROPN
ejpam-5288	102	14	k	k	PROPN
ejpam-5288	102	15	!	!	PUNCT
ejpam-5288	103	1	xk	xk	PROPN
ejpam-5288	103	2	,	,	PUNCT
ejpam-5288	103	3	ϕn	ϕn	INTJ
ejpam-5288	103	4	,	,	PUNCT
ejpam-5288	103	5	λ(x	λ(x	PROPN
ejpam-5288	103	6	)	)	PUNCT
ejpam-5288	103	7	=	=	SYM
ejpam-5288	103	8	λnϕn	λnϕn	NOUN
ejpam-5288	103	9	(	(	PUNCT
ejpam-5288	103	10	x	x	NOUN
ejpam-5288	103	11	λ	λ	PROPN
ejpam-5288	103	12	)	)	PUNCT
ejpam-5288	103	13	.	.	PUNCT
ejpam-5288	104	1	(	(	PUNCT
ejpam-5288	104	2	13	13	NUM
ejpam-5288	104	3	)	)	PUNCT
ejpam-5288	104	4	from	from	ADP
ejpam-5288	104	5	(	(	PUNCT
ejpam-5288	104	6	9	9	NUM
ejpam-5288	104	7	)	)	PUNCT
ejpam-5288	104	8	and	and	CCONJ
ejpam-5288	104	9	(	(	PUNCT
ejpam-5288	104	10	12	12	NUM
ejpam-5288	104	11	)	)	PUNCT
ejpam-5288	104	12	,	,	PUNCT
ejpam-5288	104	13	we	we	PRON
ejpam-5288	104	14	have	have	VERB
ejpam-5288	104	15	ϕn	ϕn	INTJ
ejpam-5288	104	16	,	,	PUNCT
ejpam-5288	104	17	λ(x	λ(x	PROPN
ejpam-5288	104	18	)	)	PUNCT
ejpam-5288	105	1	=	=	SYM
ejpam-5288	106	1	n∑	n∑	NOUN
ejpam-5288	106	2	k=0	k=0	PROPN
ejpam-5288	106	3	{	{	PUNCT
ejpam-5288	106	4	n	n	NOUN
ejpam-5288	106	5	k	k	ADJ
ejpam-5288	106	6	}	}	PUNCT
ejpam-5288	106	7	λ	λ	PROPN
ejpam-5288	106	8	xk	xk	PROPN
ejpam-5288	106	9	.	.	PROPN
ejpam-5288	107	1	in	in	ADP
ejpam-5288	107	2	particular	particular	ADJ
ejpam-5288	107	3	,	,	PUNCT
ejpam-5288	107	4	for	for	ADP
ejpam-5288	107	5	x	x	SYM
ejpam-5288	107	6	=	=	SYM
ejpam-5288	107	7	1	1	NUM
ejpam-5288	107	8	,	,	PUNCT
ejpam-5288	107	9	ϕn	ϕn	INTJ
ejpam-5288	107	10	,	,	PUNCT
ejpam-5288	107	11	λ	λ	PROPN
ejpam-5288	107	12	=	=	SYM
ejpam-5288	107	13	ϕn	ϕn	PROPN
ejpam-5288	107	14	,	,	PUNCT
ejpam-5288	107	15	λ(1	λ(1	PROPN
ejpam-5288	107	16	)	)	PUNCT
ejpam-5288	107	17	are	be	AUX
ejpam-5288	107	18	called	call	VERB
ejpam-5288	107	19	the	the	DET
ejpam-5288	107	20	λ	λ	NOUN
ejpam-5288	107	21	-	-	ADJ
ejpam-5288	107	22	bell	bell	ADJ
ejpam-5288	107	23	numbers	number	NOUN
ejpam-5288	107	24	.	.	PUNCT
ejpam-5288	108	1	2	2	X
ejpam-5288	108	2	.	.	X
ejpam-5288	108	3	identities	identity	NOUN
ejpam-5288	108	4	on	on	ADP
ejpam-5288	108	5	λ	λ	NOUN
ejpam-5288	108	6	-	-	NOUN
ejpam-5288	108	7	analogues	analogue	NOUN
ejpam-5288	108	8	of	of	ADP
ejpam-5288	108	9	lah	lah	NOUN
ejpam-5288	108	10	numbers	number	NOUN
ejpam-5288	108	11	and	and	CCONJ
ejpam-5288	108	12	lah	lah	NOUN
ejpam-5288	108	13	-	-	PUNCT
ejpam-5288	108	14	bell	bell	NOUN
ejpam-5288	108	15	polynomials	polynomial	NOUN
ejpam-5288	108	16	in	in	ADP
ejpam-5288	108	17	view	view	NOUN
ejpam-5288	108	18	of	of	ADP
ejpam-5288	108	19	(	(	PUNCT
ejpam-5288	108	20	2	2	NUM
ejpam-5288	108	21	)	)	PUNCT
ejpam-5288	108	22	,	,	PUNCT
ejpam-5288	108	23	we	we	PRON
ejpam-5288	108	24	consider	consider	VERB
ejpam-5288	108	25	the	the	DET
ejpam-5288	108	26	λ	λ	NOUN
ejpam-5288	108	27	-	-	NOUN
ejpam-5288	108	28	analogues	analogue	NOUN
ejpam-5288	108	29	of	of	ADP
ejpam-5288	108	30	lah	lah	NOUN
ejpam-5288	108	31	numbers	number	NOUN
ejpam-5288	108	32	defined	define	VERB
ejpam-5288	108	33	by	by	ADP
ejpam-5288	108	34	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5288	108	35	,	,	PUNCT
ejpam-5288	108	36	λ	λ	PROPN
ejpam-5288	108	37	=	=	SYM
ejpam-5288	109	1	n∑	n∑	ADJ
ejpam-5288	109	2	k=0	k=0	PROPN
ejpam-5288	109	3	lλ(n	lλ(n	VERB
ejpam-5288	109	4	,	,	PUNCT
ejpam-5288	109	5	k)(x)k	k)(x)k	NOUN
ejpam-5288	109	6	,	,	PUNCT
ejpam-5288	109	7	λ	λ	PROPN
ejpam-5288	109	8	,	,	PUNCT
ejpam-5288	109	9	(	(	PUNCT
ejpam-5288	109	10	n	n	CCONJ
ejpam-5288	109	11	≥	≥	NOUN
ejpam-5288	109	12	0	0	NUM
ejpam-5288	109	13	)	)	PUNCT
ejpam-5288	109	14	.	.	PUNCT
ejpam-5288	110	1	(	(	PUNCT
ejpam-5288	110	2	14	14	NUM
ejpam-5288	110	3	)	)	PUNCT
ejpam-5288	110	4	from	from	ADP
ejpam-5288	110	5	(	(	PUNCT
ejpam-5288	110	6	2	2	NUM
ejpam-5288	110	7	)	)	PUNCT
ejpam-5288	110	8	,	,	PUNCT
ejpam-5288	110	9	we	we	PRON
ejpam-5288	110	10	note	note	VERB
ejpam-5288	110	11	that	that	SCONJ
ejpam-5288	110	12	limλ→1	limλ→1	PROPN
ejpam-5288	110	13	lλ(n	lλ(n	NUM
ejpam-5288	110	14	,	,	PUNCT
ejpam-5288	110	15	k	k	X
ejpam-5288	110	16	)	)	PUNCT
ejpam-5288	110	17	=	=	SYM
ejpam-5288	110	18	l(n	l(n	PROPN
ejpam-5288	110	19	,	,	PUNCT
ejpam-5288	110	20	k	k	NOUN
ejpam-5288	110	21	)	)	PUNCT
ejpam-5288	110	22	,	,	PUNCT
ejpam-5288	110	23	(	(	PUNCT
ejpam-5288	110	24	n	n	CCONJ
ejpam-5288	110	25	,	,	PUNCT
ejpam-5288	110	26	k	k	X
ejpam-5288	110	27	≥	≥	PROPN
ejpam-5288	110	28	0	0	NUM
ejpam-5288	110	29	)	)	PUNCT
ejpam-5288	110	30	.	.	PUNCT
ejpam-5288	111	1	by	by	ADP
ejpam-5288	111	2	(	(	PUNCT
ejpam-5288	111	3	14	14	NUM
ejpam-5288	111	4	)	)	PUNCT
ejpam-5288	111	5	,	,	PUNCT
ejpam-5288	111	6	we	we	PRON
ejpam-5288	111	7	get	get	VERB
ejpam-5288	111	8	n∑	n∑	ADJ
ejpam-5288	111	9	k=0	k=0	PROPN
ejpam-5288	111	10	lλ(n	lλ(n	X
ejpam-5288	111	11	,	,	PUNCT
ejpam-5288	111	12	k)(x)k	k)(x)k	NOUN
ejpam-5288	111	13	,	,	PUNCT
ejpam-5288	111	14	λ	λ	NOUN
ejpam-5288	111	15	=	=	SYM
ejpam-5288	111	16	⟨x⟩n	⟨x⟩n	PROPN
ejpam-5288	111	17	,	,	PUNCT
ejpam-5288	111	18	λ	λ	PROPN
ejpam-5288	112	1	=	=	SYM
ejpam-5288	112	2	n∑	n∑	X
ejpam-5288	112	3	j=0	j=0	PROPN
ejpam-5288	112	4	[	[	PUNCT
ejpam-5288	112	5	n	n	X
ejpam-5288	112	6	j	j	NOUN
ejpam-5288	112	7	]	]	PUNCT
ejpam-5288	112	8	λ	λ	X
ejpam-5288	112	9	xj	xj	PROPN
ejpam-5288	112	10	=	=	SYM
ejpam-5288	112	11	n∑	n∑	PROPN
ejpam-5288	112	12	j=0	j=0	PROPN
ejpam-5288	112	13	[	[	PUNCT
ejpam-5288	112	14	n	n	X
ejpam-5288	112	15	j	j	NOUN
ejpam-5288	112	16	]	]	X
ejpam-5288	113	1	λ	λ	X
ejpam-5288	113	2	j∑	j∑	PROPN
ejpam-5288	113	3	k=0	k=0	PROPN
ejpam-5288	113	4	{	{	PUNCT
ejpam-5288	113	5	j	j	PROPN
ejpam-5288	113	6	k	k	PROPN
ejpam-5288	113	7	}	}	PUNCT
ejpam-5288	113	8	λ	λ	PROPN
ejpam-5288	113	9	(	(	PUNCT
ejpam-5288	113	10	x)k	x)k	X
ejpam-5288	113	11	,	,	PUNCT
ejpam-5288	113	12	λ	λ	PROPN
ejpam-5288	113	13	(	(	PUNCT
ejpam-5288	113	14	15	15	NUM
ejpam-5288	113	15	)	)	PUNCT
ejpam-5288	113	16	=	=	SYM
ejpam-5288	113	17	n∑	n∑	NOUN
ejpam-5288	113	18	k=0	k=0	PROPN
ejpam-5288	113	19	(	(	PUNCT
ejpam-5288	113	20	n∑	n∑	NOUN
ejpam-5288	113	21	j	j	PROPN
ejpam-5288	113	22	=	=	PROPN
ejpam-5288	113	23	k	k	X
ejpam-5288	113	24	[	[	PUNCT
ejpam-5288	113	25	n	n	X
ejpam-5288	113	26	j	j	NOUN
ejpam-5288	113	27	]	]	X
ejpam-5288	114	1	λ	λ	X
ejpam-5288	114	2	{	{	PUNCT
ejpam-5288	114	3	j	j	PROPN
ejpam-5288	114	4	k	k	PROPN
ejpam-5288	114	5	}	}	PUNCT
ejpam-5288	114	6	λ	λ	PROPN
ejpam-5288	114	7	)	)	PUNCT
ejpam-5288	114	8	(	(	PUNCT
ejpam-5288	114	9	x)k	x)k	X
ejpam-5288	114	10	,	,	PUNCT
ejpam-5288	114	11	λ	λ	PROPN
ejpam-5288	114	12	.	.	PUNCT
ejpam-5288	114	13	theorem	theorem	PROPN
ejpam-5288	114	14	1	1	NUM
ejpam-5288	114	15	.	.	PUNCT
ejpam-5288	114	16	for	for	ADP
ejpam-5288	114	17	n	n	PRON
ejpam-5288	114	18	,	,	PUNCT
ejpam-5288	114	19	k	k	PROPN
ejpam-5288	114	20	≥	≥	PROPN
ejpam-5288	114	21	0	0	NUM
ejpam-5288	114	22	,	,	PUNCT
ejpam-5288	114	23	we	we	PRON
ejpam-5288	114	24	have	have	VERB
ejpam-5288	114	25	lλ(n	lλ(n	NUM
ejpam-5288	114	26	,	,	PUNCT
ejpam-5288	114	27	k	k	NOUN
ejpam-5288	114	28	)	)	PUNCT
ejpam-5288	114	29	=	=	SYM
ejpam-5288	115	1	n∑	n∑	PROPN
ejpam-5288	115	2	j	j	PROPN
ejpam-5288	115	3	=	=	VERB
ejpam-5288	115	4	k	k	X
ejpam-5288	115	5	[	[	PUNCT
ejpam-5288	115	6	n	n	X
ejpam-5288	115	7	j	j	NOUN
ejpam-5288	116	1	]	]	X
ejpam-5288	116	2	λ	λ	X
ejpam-5288	116	3	{	{	PUNCT
ejpam-5288	116	4	j	j	PROPN
ejpam-5288	116	5	k	k	PROPN
ejpam-5288	116	6	}	}	PUNCT
ejpam-5288	116	7	λ	λ	PROPN
ejpam-5288	116	8	.	.	PUNCT
ejpam-5288	117	1	j.	j.	PROPN
ejpam-5288	117	2	kwon	kwon	PROPN
ejpam-5288	117	3	et	et	PROPN
ejpam-5288	117	4	al	al	PROPN
ejpam-5288	117	5	.	.	PUNCT
ejpam-5288	117	6	/	/	SYM
ejpam-5288	117	7	eur	eur	PROPN
ejpam-5288	117	8	.	.	PUNCT
ejpam-5288	118	1	j.	j.	PROPN
ejpam-5288	118	2	pure	pure	PROPN
ejpam-5288	118	3	appl	appl	PROPN
ejpam-5288	118	4	.	.	PROPN
ejpam-5288	118	5	math	math	PROPN
ejpam-5288	118	6	,	,	PUNCT
ejpam-5288	118	7	17	17	NUM
ejpam-5288	118	8	(	(	PUNCT
ejpam-5288	118	9	3	3	NUM
ejpam-5288	118	10	)	)	PUNCT
ejpam-5288	118	11	(	(	PUNCT
ejpam-5288	118	12	2024	2024	NUM
ejpam-5288	118	13	)	)	PUNCT
ejpam-5288	118	14	,	,	PUNCT
ejpam-5288	118	15	1385	1385	NUM
ejpam-5288	118	16	-	-	SYM
ejpam-5288	118	17	1402	1402	NUM
ejpam-5288	118	18	1390	1390	NUM
ejpam-5288	118	19	we	we	PRON
ejpam-5288	118	20	note	note	VERB
ejpam-5288	118	21	from	from	ADP
ejpam-5288	118	22	(	(	PUNCT
ejpam-5288	118	23	14	14	NUM
ejpam-5288	118	24	)	)	PUNCT
ejpam-5288	118	25	that	that	PRON
ejpam-5288	118	26	(	(	PUNCT
ejpam-5288	118	27	x)n	x)n	PROPN
ejpam-5288	118	28	,	,	PUNCT
ejpam-5288	118	29	λ	λ	X
ejpam-5288	118	30	=	=	SYM
ejpam-5288	118	31	(	(	PUNCT
ejpam-5288	118	32	−1)n⟨−x⟩n	−1)n⟨−x⟩n	PROPN
ejpam-5288	118	33	,	,	PUNCT
ejpam-5288	118	34	λ	λ	X
ejpam-5288	118	35	=	=	SYM
ejpam-5288	118	36	(	(	PUNCT
ejpam-5288	118	37	−1)n	−1)n	PROPN
ejpam-5288	118	38	n∑	n∑	PROPN
ejpam-5288	118	39	k=0	k=0	PROPN
ejpam-5288	118	40	lλ(n	lλ(n	NUM
ejpam-5288	118	41	,	,	PUNCT
ejpam-5288	118	42	k)(−x)k	k)(−x)k	X
ejpam-5288	118	43	,	,	PUNCT
ejpam-5288	118	44	λ	λ	PROPN
ejpam-5288	118	45	=	=	SYM
ejpam-5288	118	46	n∑	n∑	PROPN
ejpam-5288	118	47	k=0	k=0	PROPN
ejpam-5288	118	48	(	(	PUNCT
ejpam-5288	118	49	−1)n−klλ(n	−1)n−klλ(n	X
ejpam-5288	118	50	,	,	PUNCT
ejpam-5288	118	51	k)⟨x⟩k	k)⟨x⟩k	NOUN
ejpam-5288	118	52	,	,	PUNCT
ejpam-5288	118	53	λ	λ	PROPN
ejpam-5288	118	54	.	.	PROPN
ejpam-5288	118	55	for	for	ADP
ejpam-5288	118	56	any	any	DET
ejpam-5288	118	57	nonzero	nonzero	NOUN
ejpam-5288	118	58	λ	λ	X
ejpam-5288	118	59	∈	∈	PROPN
ejpam-5288	118	60	r	r	NOUN
ejpam-5288	118	61	,	,	PUNCT
ejpam-5288	118	62	the	the	DET
ejpam-5288	118	63	λ	λ	NOUN
ejpam-5288	118	64	-	-	NOUN
ejpam-5288	118	65	exponentials	exponential	NOUN
ejpam-5288	118	66	are	be	AUX
ejpam-5288	118	67	defined	define	VERB
ejpam-5288	118	68	by	by	ADP
ejpam-5288	118	69	exλ(t	exλ(t	NOUN
ejpam-5288	118	70	)	)	PUNCT
ejpam-5288	118	71	=	=	PUNCT
ejpam-5288	119	1	(	(	PUNCT
ejpam-5288	119	2	1	1	NUM
ejpam-5288	119	3	+	+	CCONJ
ejpam-5288	119	4	λt	λt	X
ejpam-5288	119	5	)	)	PUNCT
ejpam-5288	119	6	x	x	SYM
ejpam-5288	120	1	λ	λ	NOUN
ejpam-5288	120	2	=	=	SYM
ejpam-5288	120	3	∞∑	∞∑	NUM
ejpam-5288	120	4	k=0	k=0	PROPN
ejpam-5288	120	5	(	(	PUNCT
ejpam-5288	120	6	x)k	x)k	X
ejpam-5288	120	7	,	,	PUNCT
ejpam-5288	120	8	λ	λ	PROPN
ejpam-5288	120	9	k	k	PROPN
ejpam-5288	120	10	!	!	PROPN
ejpam-5288	120	11	tk	tk	PROPN
ejpam-5288	120	12	,	,	PUNCT
ejpam-5288	120	13	(	(	PUNCT
ejpam-5288	120	14	see	see	VERB
ejpam-5288	120	15	[	[	X
ejpam-5288	120	16	11	11	NUM
ejpam-5288	120	17	,	,	PUNCT
ejpam-5288	120	18	15−	15−	PROPN
ejpam-5288	120	19	22	22	NUM
ejpam-5288	120	20	]	]	PUNCT
ejpam-5288	120	21	)	)	PUNCT
ejpam-5288	120	22	.	.	PUNCT
ejpam-5288	121	1	(	(	PUNCT
ejpam-5288	121	2	16	16	NUM
ejpam-5288	121	3	)	)	PUNCT
ejpam-5288	121	4	from	from	ADP
ejpam-5288	121	5	(	(	PUNCT
ejpam-5288	121	6	16	16	NUM
ejpam-5288	121	7	)	)	PUNCT
ejpam-5288	121	8	,	,	PUNCT
ejpam-5288	121	9	we	we	PRON
ejpam-5288	121	10	have	have	VERB
ejpam-5288	121	11	e−x	e−x	PROPN
ejpam-5288	121	12	λ	λ	PROPN
ejpam-5288	121	13	(	(	PUNCT
ejpam-5288	121	14	−t	−t	NOUN
ejpam-5288	121	15	)	)	PUNCT
ejpam-5288	121	16	=	=	PUNCT
ejpam-5288	122	1	∞∑	∞∑	NUM
ejpam-5288	122	2	n=0	n=0	NUM
ejpam-5288	122	3	(	(	PUNCT
ejpam-5288	122	4	−x)n	−x)n	NOUN
ejpam-5288	122	5	,	,	PUNCT
ejpam-5288	122	6	λ	λ	PROPN
ejpam-5288	122	7	(	(	PUNCT
ejpam-5288	122	8	−t)n	−t)n	PROPN
ejpam-5288	122	9	n	n	X
ejpam-5288	122	10	!	!	PUNCT
ejpam-5288	122	11	=	=	PUNCT
ejpam-5288	123	1	∞∑	∞∑	PRON
ejpam-5288	123	2	n=0	n=0	NUM
ejpam-5288	123	3	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5288	123	4	,	,	PUNCT
ejpam-5288	123	5	λ	λ	PROPN
ejpam-5288	123	6	tn	tn	NOUN
ejpam-5288	123	7	n	n	X
ejpam-5288	123	8	!	!	PUNCT
ejpam-5288	124	1	(	(	PUNCT
ejpam-5288	124	2	17	17	NUM
ejpam-5288	124	3	)	)	PUNCT
ejpam-5288	124	4	=	=	PUNCT
ejpam-5288	125	1	∞∑	∞∑	NUM
ejpam-5288	125	2	n=0	n=0	NUM
ejpam-5288	125	3	(	(	PUNCT
ejpam-5288	125	4	n∑	n∑	ADV
ejpam-5288	125	5	k=0	k=0	PROPN
ejpam-5288	125	6	lλ(n	lλ(n	VERB
ejpam-5288	125	7	,	,	PUNCT
ejpam-5288	125	8	k)(x)k	k)(x)k	NOUN
ejpam-5288	125	9	,	,	PUNCT
ejpam-5288	125	10	λ	λ	PROPN
ejpam-5288	125	11	)	)	PUNCT
ejpam-5288	125	12	tn	tn	PROPN
ejpam-5288	125	13	n	n	ADV
ejpam-5288	125	14	!	!	PUNCT
ejpam-5288	125	15	=	=	NOUN
ejpam-5288	126	1	∞∑	∞∑	NUM
ejpam-5288	126	2	k=0	k=0	PROPN
ejpam-5288	126	3	(	(	PUNCT
ejpam-5288	126	4	∞∑	∞∑	NUM
ejpam-5288	126	5	n	n	CCONJ
ejpam-5288	126	6	=	=	SYM
ejpam-5288	126	7	k	k	PROPN
ejpam-5288	126	8	lk(n	lk(n	X
ejpam-5288	126	9	,	,	PUNCT
ejpam-5288	126	10	k	k	NOUN
ejpam-5288	126	11	)	)	PUNCT
ejpam-5288	126	12	tn	tn	PROPN
ejpam-5288	126	13	n	n	PROPN
ejpam-5288	126	14	!	!	PUNCT
ejpam-5288	126	15	)	)	PUNCT
ejpam-5288	127	1	(	(	PUNCT
ejpam-5288	127	2	x)k	x)k	NOUN
ejpam-5288	127	3	,	,	PUNCT
ejpam-5288	127	4	λ	λ	PROPN
ejpam-5288	127	5	.	.	PROPN
ejpam-5288	127	6	on	on	ADP
ejpam-5288	127	7	the	the	DET
ejpam-5288	127	8	other	other	ADJ
ejpam-5288	127	9	hand	hand	NOUN
ejpam-5288	127	10	,	,	PUNCT
ejpam-5288	127	11	by	by	ADP
ejpam-5288	127	12	(	(	PUNCT
ejpam-5288	127	13	16	16	NUM
ejpam-5288	127	14	)	)	PUNCT
ejpam-5288	127	15	,	,	PUNCT
ejpam-5288	127	16	we	we	PRON
ejpam-5288	127	17	get	get	VERB
ejpam-5288	127	18	e−x	e−x	PROPN
ejpam-5288	127	19	λ	λ	PROPN
ejpam-5288	127	20	(	(	PUNCT
ejpam-5288	127	21	−t	−t	NOUN
ejpam-5288	127	22	)	)	PUNCT
ejpam-5288	127	23	=	=	PUNCT
ejpam-5288	128	1	(	(	PUNCT
ejpam-5288	128	2	1−	1−	NUM
ejpam-5288	128	3	λt)−	λt)−	PUNCT
ejpam-5288	129	1	x	x	PUNCT
ejpam-5288	129	2	λ	λ	NOUN
ejpam-5288	129	3	=	=	SYM
ejpam-5288	129	4	(	(	PUNCT
ejpam-5288	129	5	1	1	NUM
ejpam-5288	129	6	1−	1−	NUM
ejpam-5288	129	7	λt	λt	ADP
ejpam-5288	129	8	)	)	PUNCT
ejpam-5288	129	9	x	x	PUNCT
ejpam-5288	129	10	λ	λ	NOUN
ejpam-5288	129	11	=	=	SYM
ejpam-5288	129	12	(	(	PUNCT
ejpam-5288	129	13	1	1	NUM
ejpam-5288	129	14	+	+	CCONJ
ejpam-5288	129	15	λt	λt	ADP
ejpam-5288	129	16	1−	1−	NUM
ejpam-5288	129	17	λt	λt	ADP
ejpam-5288	129	18	)	)	PUNCT
ejpam-5288	129	19	x	x	PUNCT
ejpam-5288	129	20	λ	λ	X
ejpam-5288	129	21	(	(	PUNCT
ejpam-5288	129	22	18	18	NUM
ejpam-5288	129	23	)	)	PUNCT
ejpam-5288	129	24	=	=	NOUN
ejpam-5288	130	1	∞∑	∞∑	NUM
ejpam-5288	130	2	k=0	k=0	PROPN
ejpam-5288	130	3	1	1	NUM
ejpam-5288	130	4	k	k	NOUN
ejpam-5288	130	5	!	!	PUNCT
ejpam-5288	131	1	(	(	PUNCT
ejpam-5288	131	2	t	t	PROPN
ejpam-5288	131	3	1−	1−	NUM
ejpam-5288	131	4	λt	λt	ADP
ejpam-5288	131	5	)	)	PUNCT
ejpam-5288	131	6	k	k	PROPN
ejpam-5288	131	7	(	(	PUNCT
ejpam-5288	131	8	x)k	x)k	NOUN
ejpam-5288	131	9	,	,	PUNCT
ejpam-5288	131	10	λ	λ	X
ejpam-5288	131	11	.	.	PUNCT
ejpam-5288	131	12	by	by	ADP
ejpam-5288	131	13	(	(	PUNCT
ejpam-5288	131	14	17	17	NUM
ejpam-5288	131	15	)	)	PUNCT
ejpam-5288	131	16	and	and	CCONJ
ejpam-5288	131	17	(	(	PUNCT
ejpam-5288	131	18	18	18	NUM
ejpam-5288	131	19	)	)	PUNCT
ejpam-5288	131	20	,	,	PUNCT
ejpam-5288	131	21	we	we	PRON
ejpam-5288	131	22	get	get	VERB
ejpam-5288	131	23	1	1	NUM
ejpam-5288	131	24	k	k	NOUN
ejpam-5288	131	25	!	!	PUNCT
ejpam-5288	132	1	(	(	PUNCT
ejpam-5288	132	2	t	t	PROPN
ejpam-5288	132	3	1−	1−	NUM
ejpam-5288	132	4	λt	λt	ADP
ejpam-5288	132	5	)	)	PUNCT
ejpam-5288	132	6	k	k	NOUN
ejpam-5288	133	1	=	=	PUNCT
ejpam-5288	133	2	1	1	NUM
ejpam-5288	133	3	λk	λk	ADP
ejpam-5288	133	4	1	1	NUM
ejpam-5288	133	5	k	k	NOUN
ejpam-5288	133	6	!	!	PUNCT
ejpam-5288	134	1	(	(	PUNCT
ejpam-5288	134	2	1	1	NUM
ejpam-5288	134	3	1−	1−	NUM
ejpam-5288	134	4	λt	λt	ADP
ejpam-5288	134	5	−	−	PROPN
ejpam-5288	134	6	1	1	NUM
ejpam-5288	134	7	)	)	PUNCT
ejpam-5288	134	8	k	k	NOUN
ejpam-5288	135	1	=	=	PUNCT
ejpam-5288	135	2	∞∑	∞∑	NUM
ejpam-5288	135	3	n	n	CCONJ
ejpam-5288	135	4	=	=	X
ejpam-5288	135	5	k	k	NOUN
ejpam-5288	135	6	lλ(n	lλ(n	X
ejpam-5288	135	7	,	,	PUNCT
ejpam-5288	135	8	k	k	NOUN
ejpam-5288	135	9	)	)	PUNCT
ejpam-5288	135	10	tn	tn	PROPN
ejpam-5288	135	11	n	n	PROPN
ejpam-5288	135	12	!	!	PROPN
ejpam-5288	135	13	,	,	PUNCT
ejpam-5288	135	14	(	(	PUNCT
ejpam-5288	135	15	k	k	X
ejpam-5288	135	16	≥	≥	PROPN
ejpam-5288	135	17	0	0	NUM
ejpam-5288	135	18	)	)	PUNCT
ejpam-5288	135	19	.	.	PUNCT
ejpam-5288	136	1	(	(	PUNCT
ejpam-5288	136	2	19	19	NUM
ejpam-5288	136	3	)	)	PUNCT
ejpam-5288	136	4	the	the	DET
ejpam-5288	136	5	left	left	ADJ
ejpam-5288	136	6	hand	hand	NOUN
ejpam-5288	136	7	side	side	NOUN
ejpam-5288	136	8	of	of	ADP
ejpam-5288	136	9	(	(	PUNCT
ejpam-5288	136	10	19	19	NUM
ejpam-5288	136	11	)	)	PUNCT
ejpam-5288	136	12	can	can	AUX
ejpam-5288	136	13	be	be	AUX
ejpam-5288	136	14	written	write	VERB
ejpam-5288	136	15	as	as	ADP
ejpam-5288	136	16	1	1	NUM
ejpam-5288	136	17	k	k	NOUN
ejpam-5288	136	18	!	!	PUNCT
ejpam-5288	137	1	(	(	PUNCT
ejpam-5288	137	2	t	t	PROPN
ejpam-5288	137	3	1−	1−	NUM
ejpam-5288	137	4	λt	λt	ADP
ejpam-5288	137	5	)	)	PUNCT
ejpam-5288	137	6	k	k	NOUN
ejpam-5288	138	1	=	=	PUNCT
ejpam-5288	138	2	1	1	NUM
ejpam-5288	138	3	λk	λk	ADP
ejpam-5288	138	4	1	1	NUM
ejpam-5288	138	5	k	k	X
ejpam-5288	138	6	!	!	PUNCT
ejpam-5288	138	7	k∑	k∑	PROPN
ejpam-5288	139	1	l=0	l=0	PROPN
ejpam-5288	139	2	(	(	PUNCT
ejpam-5288	139	3	k	k	NOUN
ejpam-5288	139	4	l	l	NOUN
ejpam-5288	139	5	)	)	PUNCT
ejpam-5288	140	1	(	(	PUNCT
ejpam-5288	140	2	−1)k−l(1−	−1)k−l(1−	PROPN
ejpam-5288	140	3	λt)−	λt)−	X
ejpam-5288	140	4	λl	λl	PROPN
ejpam-5288	140	5	λ	λ	X
ejpam-5288	140	6	(	(	PUNCT
ejpam-5288	140	7	20	20	NUM
ejpam-5288	140	8	)	)	PUNCT
ejpam-5288	140	9	=	=	NOUN
ejpam-5288	141	1	∞∑	∞∑	NUM
ejpam-5288	141	2	n=0	n=0	NUM
ejpam-5288	141	3	(	(	PUNCT
ejpam-5288	141	4	1	1	NUM
ejpam-5288	141	5	λk	λk	ADP
ejpam-5288	141	6	1	1	NUM
ejpam-5288	141	7	k	k	X
ejpam-5288	141	8	!	!	PUNCT
ejpam-5288	141	9	k∑	k∑	PROPN
ejpam-5288	142	1	l=0	l=0	PROPN
ejpam-5288	142	2	(	(	PUNCT
ejpam-5288	142	3	k	k	NOUN
ejpam-5288	142	4	l	l	NOUN
ejpam-5288	142	5	)	)	PUNCT
ejpam-5288	142	6	(	(	PUNCT
ejpam-5288	142	7	−1)k−l⟨λl⟩n	−1)k−l⟨λl⟩n	INTJ
ejpam-5288	142	8	,	,	PUNCT
ejpam-5288	142	9	λ	λ	PROPN
ejpam-5288	142	10	)	)	PUNCT
ejpam-5288	142	11	tn	tn	PROPN
ejpam-5288	142	12	n	n	PROPN
ejpam-5288	142	13	!	!	PUNCT
ejpam-5288	142	14	.	.	PUNCT
ejpam-5288	143	1	therefore	therefore	ADV
ejpam-5288	143	2	,	,	PUNCT
ejpam-5288	143	3	by	by	ADP
ejpam-5288	143	4	(	(	PUNCT
ejpam-5288	143	5	19	19	NUM
ejpam-5288	143	6	)	)	PUNCT
ejpam-5288	143	7	and	and	CCONJ
ejpam-5288	143	8	(	(	PUNCT
ejpam-5288	143	9	20	20	NUM
ejpam-5288	143	10	)	)	PUNCT
ejpam-5288	143	11	,	,	PUNCT
ejpam-5288	143	12	we	we	PRON
ejpam-5288	143	13	obtain	obtain	VERB
ejpam-5288	143	14	the	the	DET
ejpam-5288	143	15	following	follow	VERB
ejpam-5288	143	16	theorem	theorem	PROPN
ejpam-5288	143	17	.	.	PUNCT
ejpam-5288	144	1	j.	j.	PROPN
ejpam-5288	144	2	kwon	kwon	PROPN
ejpam-5288	144	3	et	et	PROPN
ejpam-5288	144	4	al	al	PROPN
ejpam-5288	144	5	.	.	PUNCT
ejpam-5288	144	6	/	/	SYM
ejpam-5288	144	7	eur	eur	PROPN
ejpam-5288	144	8	.	.	PUNCT
ejpam-5288	145	1	j.	j.	PROPN
ejpam-5288	145	2	pure	pure	PROPN
ejpam-5288	145	3	appl	appl	PROPN
ejpam-5288	145	4	.	.	PROPN
ejpam-5288	145	5	math	math	PROPN
ejpam-5288	145	6	,	,	PUNCT
ejpam-5288	145	7	17	17	NUM
ejpam-5288	145	8	(	(	PUNCT
ejpam-5288	145	9	3	3	NUM
ejpam-5288	145	10	)	)	PUNCT
ejpam-5288	145	11	(	(	PUNCT
ejpam-5288	145	12	2024	2024	NUM
ejpam-5288	145	13	)	)	PUNCT
ejpam-5288	145	14	,	,	PUNCT
ejpam-5288	145	15	1385	1385	NUM
ejpam-5288	145	16	-	-	SYM
ejpam-5288	145	17	1402	1402	NUM
ejpam-5288	145	18	1391	1391	NUM
ejpam-5288	145	19	theorem	theorem	NOUN
ejpam-5288	145	20	2	2	NUM
ejpam-5288	145	21	.	.	NOUN
ejpam-5288	145	22	for	for	ADP
ejpam-5288	145	23	n	n	PRON
ejpam-5288	145	24	,	,	PUNCT
ejpam-5288	145	25	k	k	X
ejpam-5288	145	26	≥	≥	PROPN
ejpam-5288	145	27	0	0	NUM
ejpam-5288	145	28	,	,	PUNCT
ejpam-5288	145	29	with	with	ADP
ejpam-5288	145	30	n	n	PRON
ejpam-5288	145	31	≥	≥	NOUN
ejpam-5288	145	32	k	k	NOUN
ejpam-5288	145	33	,	,	PUNCT
ejpam-5288	145	34	we	we	PRON
ejpam-5288	145	35	have	have	VERB
ejpam-5288	145	36	lλ(n	lλ(n	NUM
ejpam-5288	145	37	,	,	PUNCT
ejpam-5288	145	38	k	k	NOUN
ejpam-5288	145	39	)	)	PUNCT
ejpam-5288	145	40	=	=	SYM
ejpam-5288	146	1	1	1	NUM
ejpam-5288	146	2	λk	λk	ADP
ejpam-5288	146	3	1	1	NUM
ejpam-5288	146	4	k	k	X
ejpam-5288	146	5	!	!	PUNCT
ejpam-5288	146	6	k∑	k∑	PROPN
ejpam-5288	147	1	l=0	l=0	PROPN
ejpam-5288	147	2	(	(	PUNCT
ejpam-5288	147	3	k	k	NOUN
ejpam-5288	147	4	l	l	NOUN
ejpam-5288	147	5	)	)	PUNCT
ejpam-5288	147	6	(	(	PUNCT
ejpam-5288	147	7	−1)k−l⟨λl⟩n	−1)k−l⟨λl⟩n	INTJ
ejpam-5288	147	8	,	,	PUNCT
ejpam-5288	147	9	λ	λ	PROPN
ejpam-5288	147	10	.	.	PUNCT
ejpam-5288	147	11	note	note	VERB
ejpam-5288	147	12	that	that	SCONJ
ejpam-5288	147	13	l(n	l(n	NOUN
ejpam-5288	147	14	,	,	PUNCT
ejpam-5288	147	15	k	k	NOUN
ejpam-5288	147	16	)	)	PUNCT
ejpam-5288	147	17	=	=	SYM
ejpam-5288	147	18	lim	lim	PROPN
ejpam-5288	147	19	λ→1	λ→1	X
ejpam-5288	147	20	lλ(n	lλ(n	PROPN
ejpam-5288	147	21	,	,	PUNCT
ejpam-5288	147	22	k	k	X
ejpam-5288	147	23	)	)	PUNCT
ejpam-5288	147	24	=	=	SYM
ejpam-5288	147	25	1	1	NUM
ejpam-5288	147	26	k	k	X
ejpam-5288	147	27	!	!	PUNCT
ejpam-5288	147	28	k∑	k∑	PROPN
ejpam-5288	148	1	l=0	l=0	PROPN
ejpam-5288	148	2	(	(	PUNCT
ejpam-5288	148	3	k	k	NOUN
ejpam-5288	148	4	l	l	NOUN
ejpam-5288	148	5	)	)	PUNCT
ejpam-5288	148	6	(	(	PUNCT
ejpam-5288	148	7	−1)k−l⟨l⟩n	−1)k−l⟨l⟩n	X
ejpam-5288	148	8	.	.	PUNCT
ejpam-5288	149	1	in	in	ADP
ejpam-5288	149	2	view	view	NOUN
ejpam-5288	149	3	of	of	ADP
ejpam-5288	149	4	(	(	PUNCT
ejpam-5288	149	5	3	3	NUM
ejpam-5288	149	6	)	)	PUNCT
ejpam-5288	149	7	,	,	PUNCT
ejpam-5288	149	8	we	we	PRON
ejpam-5288	149	9	define	define	VERB
ejpam-5288	149	10	the	the	DET
ejpam-5288	149	11	λ	λ	NOUN
ejpam-5288	149	12	-	-	NOUN
ejpam-5288	149	13	analogues	analogue	NOUN
ejpam-5288	149	14	of	of	ADP
ejpam-5288	149	15	lah	lah	PROPN
ejpam-5288	149	16	-	-	PUNCT
ejpam-5288	149	17	bell	bell	NOUN
ejpam-5288	149	18	numbers	number	NOUN
ejpam-5288	149	19	as	as	ADP
ejpam-5288	149	20	bl	bl	NOUN
ejpam-5288	149	21	n	n	CCONJ
ejpam-5288	149	22	,	,	PUNCT
ejpam-5288	149	23	λ	λ	PROPN
ejpam-5288	149	24	=	=	SYM
ejpam-5288	150	1	n∑	n∑	ADJ
ejpam-5288	150	2	k=0	k=0	PROPN
ejpam-5288	150	3	lλ(n	lλ(n	X
ejpam-5288	150	4	,	,	PUNCT
ejpam-5288	150	5	k	k	NOUN
ejpam-5288	150	6	)	)	PUNCT
ejpam-5288	150	7	,	,	PUNCT
ejpam-5288	150	8	(	(	PUNCT
ejpam-5288	150	9	n	n	X
ejpam-5288	150	10	≥	≥	NOUN
ejpam-5288	150	11	0	0	NUM
ejpam-5288	150	12	)	)	PUNCT
ejpam-5288	150	13	.	.	PUNCT
ejpam-5288	151	1	(	(	PUNCT
ejpam-5288	151	2	21	21	NUM
ejpam-5288	151	3	)	)	PUNCT
ejpam-5288	151	4	from	from	ADP
ejpam-5288	151	5	(	(	PUNCT
ejpam-5288	151	6	19	19	NUM
ejpam-5288	151	7	)	)	PUNCT
ejpam-5288	151	8	and	and	CCONJ
ejpam-5288	151	9	(	(	PUNCT
ejpam-5288	151	10	21	21	NUM
ejpam-5288	151	11	)	)	PUNCT
ejpam-5288	151	12	,	,	PUNCT
ejpam-5288	151	13	we	we	PRON
ejpam-5288	151	14	can	can	AUX
ejpam-5288	151	15	easily	easily	ADV
ejpam-5288	151	16	derive	derive	VERB
ejpam-5288	151	17	the	the	DET
ejpam-5288	151	18	following	follow	VERB
ejpam-5288	151	19	equation	equation	NOUN
ejpam-5288	151	20	:	:	PUNCT
ejpam-5288	151	21	e	e	PROPN
ejpam-5288	151	22	t	t	PROPN
ejpam-5288	151	23	1−λt	1−λt	PROPN
ejpam-5288	151	24	=	=	PUNCT
ejpam-5288	152	1	∞∑	∞∑	PROPN
ejpam-5288	152	2	n=0	n=0	NUM
ejpam-5288	152	3	bl	bl	NOUN
ejpam-5288	152	4	n	n	CCONJ
ejpam-5288	152	5	,	,	PUNCT
ejpam-5288	152	6	λ	λ	PROPN
ejpam-5288	152	7	tn	tn	NOUN
ejpam-5288	152	8	n	n	X
ejpam-5288	152	9	!	!	PUNCT
ejpam-5288	152	10	.	.	PUNCT
ejpam-5288	153	1	(	(	PUNCT
ejpam-5288	153	2	22	22	NUM
ejpam-5288	153	3	)	)	PUNCT
ejpam-5288	153	4	now	now	ADV
ejpam-5288	153	5	,	,	PUNCT
ejpam-5288	153	6	we	we	PRON
ejpam-5288	153	7	define	define	VERB
ejpam-5288	153	8	the	the	DET
ejpam-5288	153	9	λ	λ	NOUN
ejpam-5288	153	10	-	-	NOUN
ejpam-5288	153	11	analogues	analogue	NOUN
ejpam-5288	153	12	of	of	ADP
ejpam-5288	153	13	lah	lah	PROPN
ejpam-5288	153	14	-	-	PUNCT
ejpam-5288	153	15	bell	bell	NOUN
ejpam-5288	153	16	polynomials	polynomial	NOUN
ejpam-5288	153	17	as	as	ADP
ejpam-5288	153	18	bl	bl	NOUN
ejpam-5288	153	19	n	n	CCONJ
ejpam-5288	153	20	,	,	PUNCT
ejpam-5288	153	21	λ(x	λ(x	PROPN
ejpam-5288	153	22	)	)	PUNCT
ejpam-5288	154	1	=	=	SYM
ejpam-5288	154	2	n∑	n∑	PROPN
ejpam-5288	154	3	k=0	k=0	PROPN
ejpam-5288	154	4	lλ(n	lλ(n	PUNCT
ejpam-5288	154	5	,	,	PUNCT
ejpam-5288	154	6	k)x	k)x	X
ejpam-5288	154	7	k	k	X
ejpam-5288	154	8	,	,	PUNCT
ejpam-5288	154	9	(	(	PUNCT
ejpam-5288	154	10	n	n	CCONJ
ejpam-5288	154	11	≥	≥	NOUN
ejpam-5288	154	12	0	0	NUM
ejpam-5288	154	13	)	)	PUNCT
ejpam-5288	154	14	.	.	PUNCT
ejpam-5288	155	1	(	(	PUNCT
ejpam-5288	155	2	23	23	X
ejpam-5288	155	3	)	)	PUNCT
ejpam-5288	155	4	note	note	NOUN
ejpam-5288	155	5	that	that	SCONJ
ejpam-5288	155	6	bl	bl	PROPN
ejpam-5288	155	7	n	n	CCONJ
ejpam-5288	155	8	,	,	PUNCT
ejpam-5288	155	9	λ(1	λ(1	PROPN
ejpam-5288	155	10	)	)	PUNCT
ejpam-5288	155	11	=	=	SYM
ejpam-5288	155	12	bl	bl	PROPN
ejpam-5288	155	13	n	n	CCONJ
ejpam-5288	155	14	,	,	PUNCT
ejpam-5288	155	15	λ	λ	PROPN
ejpam-5288	155	16	,	,	PUNCT
ejpam-5288	155	17	(	(	PUNCT
ejpam-5288	155	18	n	n	CCONJ
ejpam-5288	155	19	≥	≥	NOUN
ejpam-5288	155	20	0	0	NUM
ejpam-5288	155	21	)	)	PUNCT
ejpam-5288	155	22	.	.	PUNCT
ejpam-5288	156	1	by	by	ADP
ejpam-5288	156	2	(	(	PUNCT
ejpam-5288	156	3	22	22	NUM
ejpam-5288	156	4	)	)	PUNCT
ejpam-5288	156	5	and	and	CCONJ
ejpam-5288	156	6	(	(	PUNCT
ejpam-5288	156	7	23	23	NUM
ejpam-5288	156	8	)	)	PUNCT
ejpam-5288	156	9	,	,	PUNCT
ejpam-5288	156	10	we	we	PRON
ejpam-5288	156	11	get	get	VERB
ejpam-5288	156	12	e	e	NOUN
ejpam-5288	156	13	x	x	PART
ejpam-5288	156	14	λ	λ	X
ejpam-5288	156	15	(	(	PUNCT
ejpam-5288	156	16	1	1	NUM
ejpam-5288	156	17	1−λt	1−λt	NUM
ejpam-5288	156	18	−1	−1	NOUN
ejpam-5288	156	19	)	)	PUNCT
ejpam-5288	156	20	=	=	PUNCT
ejpam-5288	157	1	∞∑	∞∑	PROPN
ejpam-5288	157	2	n=0	n=0	NUM
ejpam-5288	157	3	bl	bl	NOUN
ejpam-5288	157	4	n	n	CCONJ
ejpam-5288	157	5	,	,	PUNCT
ejpam-5288	157	6	λ(x	λ(x	PROPN
ejpam-5288	157	7	)	)	PUNCT
ejpam-5288	157	8	tn	tn	PROPN
ejpam-5288	157	9	n	n	PROPN
ejpam-5288	157	10	!	!	PUNCT
ejpam-5288	157	11	.	.	PUNCT
ejpam-5288	158	1	(	(	PUNCT
ejpam-5288	158	2	24	24	NUM
ejpam-5288	158	3	)	)	PUNCT
ejpam-5288	158	4	from	from	ADP
ejpam-5288	158	5	(	(	PUNCT
ejpam-5288	158	6	24	24	NUM
ejpam-5288	158	7	)	)	PUNCT
ejpam-5288	158	8	,	,	PUNCT
ejpam-5288	158	9	we	we	PRON
ejpam-5288	158	10	have	have	VERB
ejpam-5288	158	11	e	e	NOUN
ejpam-5288	158	12	x	x	PART
ejpam-5288	158	13	λ	λ	X
ejpam-5288	158	14	(	(	PUNCT
ejpam-5288	158	15	1	1	NUM
ejpam-5288	158	16	1−λt	1−λt	NUM
ejpam-5288	158	17	−1	−1	NOUN
ejpam-5288	158	18	)	)	PUNCT
ejpam-5288	158	19	=	=	PUNCT
ejpam-5288	159	1	e−	e−	NOUN
ejpam-5288	159	2	x	x	PUNCT
ejpam-5288	159	3	λ	λ	X
ejpam-5288	159	4	e	e	NOUN
ejpam-5288	159	5	x	x	X
ejpam-5288	159	6	λ	λ	X
ejpam-5288	159	7	(	(	PUNCT
ejpam-5288	159	8	1	1	NUM
ejpam-5288	159	9	1−λt	1−λt	NOUN
ejpam-5288	159	10	)	)	PUNCT
ejpam-5288	159	11	=	=	PUNCT
ejpam-5288	160	1	e−	e−	NOUN
ejpam-5288	160	2	x	x	PUNCT
ejpam-5288	160	3	λ	λ	PROPN
ejpam-5288	160	4	∞∑	∞∑	PROPN
ejpam-5288	160	5	k=0	k=0	PUNCT
ejpam-5288	160	6	xk	xk	PROPN
ejpam-5288	161	1	k	k	PROPN
ejpam-5288	161	2	!	!	PROPN
ejpam-5288	161	3	1	1	NUM
ejpam-5288	161	4	λk	λk	NOUN
ejpam-5288	161	5	(	(	PUNCT
ejpam-5288	161	6	1	1	NUM
ejpam-5288	161	7	1−	1−	NUM
ejpam-5288	161	8	λt	λt	ADP
ejpam-5288	161	9	)	)	PUNCT
ejpam-5288	161	10	k	k	PROPN
ejpam-5288	161	11	(	(	PUNCT
ejpam-5288	161	12	25	25	NUM
ejpam-5288	161	13	)	)	PUNCT
ejpam-5288	161	14	=	=	PUNCT
ejpam-5288	161	15	e−	e−	NOUN
ejpam-5288	161	16	x	x	PUNCT
ejpam-5288	161	17	λ	λ	PROPN
ejpam-5288	161	18	∞∑	∞∑	PROPN
ejpam-5288	161	19	k=0	k=0	PUNCT
ejpam-5288	161	20	xk	xk	PROPN
ejpam-5288	161	21	λkk	λkk	NOUN
ejpam-5288	161	22	!	!	PUNCT
ejpam-5288	162	1	∞∑	∞∑	DET
ejpam-5288	162	2	n=0	n=0	PROPN
ejpam-5288	162	3	⟨λk⟩n	⟨λk⟩n	ADV
ejpam-5288	162	4	,	,	PUNCT
ejpam-5288	162	5	λ	λ	PROPN
ejpam-5288	162	6	tn	tn	NOUN
ejpam-5288	162	7	n	n	ADV
ejpam-5288	162	8	!	!	PUNCT
ejpam-5288	162	9	=	=	PUNCT
ejpam-5288	163	1	e−	e−	NOUN
ejpam-5288	163	2	x	x	PUNCT
ejpam-5288	163	3	λ	λ	PROPN
ejpam-5288	163	4	∞∑	∞∑	PROPN
ejpam-5288	163	5	n=0	n=0	NUM
ejpam-5288	163	6	(	(	PUNCT
ejpam-5288	163	7	∞∑	∞∑	NUM
ejpam-5288	163	8	k=0	k=0	PROPN
ejpam-5288	163	9	1	1	NUM
ejpam-5288	163	10	λkk	λkk	NOUN
ejpam-5288	163	11	!	!	PUNCT
ejpam-5288	164	1	⟨λk⟩n	⟨λk⟩n	ADV
ejpam-5288	164	2	,	,	PUNCT
ejpam-5288	164	3	λxk	λxk	PROPN
ejpam-5288	164	4	)	)	PUNCT
ejpam-5288	164	5	tn	tn	PROPN
ejpam-5288	165	1	n	n	PROPN
ejpam-5288	165	2	!	!	PUNCT
ejpam-5288	165	3	.	.	PUNCT
ejpam-5288	166	1	therefore	therefore	ADV
ejpam-5288	166	2	,	,	PUNCT
ejpam-5288	166	3	by	by	ADP
ejpam-5288	166	4	comparing	compare	VERB
ejpam-5288	166	5	the	the	DET
ejpam-5288	166	6	coefficients	coefficient	NOUN
ejpam-5288	166	7	on	on	ADP
ejpam-5288	166	8	both	both	DET
ejpam-5288	166	9	sides	side	NOUN
ejpam-5288	166	10	of	of	ADP
ejpam-5288	166	11	(	(	PUNCT
ejpam-5288	166	12	25	25	NUM
ejpam-5288	166	13	)	)	PUNCT
ejpam-5288	166	14	,	,	PUNCT
ejpam-5288	166	15	we	we	PRON
ejpam-5288	166	16	obtain	obtain	VERB
ejpam-5288	166	17	the	the	DET
ejpam-5288	166	18	following	follow	VERB
ejpam-5288	166	19	theorem	theorem	VERB
ejpam-5288	166	20	.	.	PUNCT
ejpam-5288	166	21	theorem	theorem	NOUN
ejpam-5288	166	22	3	3	NUM
ejpam-5288	166	23	.	.	X
ejpam-5288	166	24	for	for	ADP
ejpam-5288	166	25	n	n	PRON
ejpam-5288	166	26	≥	≥	NOUN
ejpam-5288	166	27	0	0	NUM
ejpam-5288	166	28	,	,	PUNCT
ejpam-5288	166	29	we	we	PRON
ejpam-5288	166	30	have	have	VERB
ejpam-5288	166	31	bl	bl	PROPN
ejpam-5288	166	32	n	n	CCONJ
ejpam-5288	166	33	,	,	PUNCT
ejpam-5288	166	34	λ(x	λ(x	PROPN
ejpam-5288	166	35	)	)	PUNCT
ejpam-5288	166	36	=	=	PUNCT
ejpam-5288	167	1	e−	e−	NOUN
ejpam-5288	167	2	x	x	PUNCT
ejpam-5288	167	3	λ	λ	PROPN
ejpam-5288	167	4	∞∑	∞∑	PROPN
ejpam-5288	167	5	k=0	k=0	PROPN
ejpam-5288	167	6	1	1	NUM
ejpam-5288	167	7	λk	λk	ADP
ejpam-5288	167	8	⟨λk⟩n	⟨λk⟩n	ADV
ejpam-5288	167	9	,	,	PUNCT
ejpam-5288	167	10	λ	λ	PROPN
ejpam-5288	167	11	k	k	X
ejpam-5288	167	12	!	!	PUNCT
ejpam-5288	167	13	xk	xk	PROPN
ejpam-5288	167	14	.	.	PROPN
ejpam-5288	167	15	j.	j.	PROPN
ejpam-5288	167	16	kwon	kwon	PROPN
ejpam-5288	167	17	et	et	PROPN
ejpam-5288	167	18	al	al	PROPN
ejpam-5288	167	19	.	.	PUNCT
ejpam-5288	167	20	/	/	SYM
ejpam-5288	167	21	eur	eur	PROPN
ejpam-5288	167	22	.	.	PUNCT
ejpam-5288	168	1	j.	j.	PROPN
ejpam-5288	168	2	pure	pure	PROPN
ejpam-5288	168	3	appl	appl	PROPN
ejpam-5288	168	4	.	.	PROPN
ejpam-5288	168	5	math	math	PROPN
ejpam-5288	168	6	,	,	PUNCT
ejpam-5288	168	7	17	17	NUM
ejpam-5288	168	8	(	(	PUNCT
ejpam-5288	168	9	3	3	NUM
ejpam-5288	168	10	)	)	PUNCT
ejpam-5288	168	11	(	(	PUNCT
ejpam-5288	168	12	2024	2024	NUM
ejpam-5288	168	13	)	)	PUNCT
ejpam-5288	168	14	,	,	PUNCT
ejpam-5288	168	15	1385	1385	NUM
ejpam-5288	168	16	-	-	SYM
ejpam-5288	168	17	1402	1402	NUM
ejpam-5288	168	18	1392	1392	NUM
ejpam-5288	168	19	we	we	PRON
ejpam-5288	168	20	observe	observe	VERB
ejpam-5288	168	21	that	that	SCONJ
ejpam-5288	168	22	bl	bl	PROPN
ejpam-5288	168	23	n	n	INTJ
ejpam-5288	168	24	(	(	PUNCT
ejpam-5288	168	25	x	x	X
ejpam-5288	168	26	)	)	PUNCT
ejpam-5288	169	1	=	=	SYM
ejpam-5288	169	2	lim	lim	PROPN
ejpam-5288	169	3	λ→1	λ→1	X
ejpam-5288	169	4	bl	bl	PROPN
ejpam-5288	169	5	n	n	CCONJ
ejpam-5288	169	6	,	,	PUNCT
ejpam-5288	169	7	λ(x	λ(x	PROPN
ejpam-5288	169	8	)	)	PUNCT
ejpam-5288	169	9	=	=	PUNCT
ejpam-5288	170	1	e−x	e−x	NOUN
ejpam-5288	170	2	∞∑	∞∑	DET
ejpam-5288	170	3	k=0	k=0	PROPN
ejpam-5288	170	4	⟨k⟩n	⟨k⟩n	PROPN
ejpam-5288	170	5	k	k	X
ejpam-5288	170	6	!	!	PUNCT
ejpam-5288	171	1	xk	xk	PROPN
ejpam-5288	171	2	,	,	PUNCT
ejpam-5288	171	3	where	where	SCONJ
ejpam-5288	171	4	bl	bl	VERB
ejpam-5288	171	5	n	n	CCONJ
ejpam-5288	171	6	(	(	PUNCT
ejpam-5288	171	7	x	x	X
ejpam-5288	171	8	)	)	PUNCT
ejpam-5288	171	9	are	be	AUX
ejpam-5288	171	10	the	the	DET
ejpam-5288	171	11	ordinary	ordinary	ADJ
ejpam-5288	171	12	lah	lah	ADJ
ejpam-5288	171	13	-	-	PUNCT
ejpam-5288	171	14	bell	bell	NOUN
ejpam-5288	171	15	polynomials	polynomial	NOUN
ejpam-5288	171	16	given	give	VERB
ejpam-5288	171	17	by	by	ADP
ejpam-5288	171	18	bl	bl	INTJ
ejpam-5288	171	19	n	n	PROPN
ejpam-5288	171	20	(	(	PUNCT
ejpam-5288	171	21	x	x	X
ejpam-5288	171	22	)	)	PUNCT
ejpam-5288	171	23	=	=	SYM
ejpam-5288	171	24	n∑	n∑	PROPN
ejpam-5288	171	25	k=0	k=0	PROPN
ejpam-5288	171	26	l(n	l(n	PROPN
ejpam-5288	171	27	,	,	PUNCT
ejpam-5288	171	28	k)xk	k)xk	PROPN
ejpam-5288	171	29	,	,	PUNCT
ejpam-5288	171	30	(	(	PUNCT
ejpam-5288	171	31	n	n	CCONJ
ejpam-5288	171	32	≥	≥	NOUN
ejpam-5288	171	33	0	0	NUM
ejpam-5288	171	34	)	)	PUNCT
ejpam-5288	171	35	.	.	PUNCT
ejpam-5288	172	1	replacing	replace	VERB
ejpam-5288	172	2	t	t	NOUN
ejpam-5288	172	3	by	by	ADP
ejpam-5288	172	4	1	1	NUM
ejpam-5288	172	5	λ(1−	λ(1−	PROPN
ejpam-5288	172	6	e−λt	e−λt	NOUN
ejpam-5288	172	7	)	)	PUNCT
ejpam-5288	172	8	in	in	ADP
ejpam-5288	172	9	(	(	PUNCT
ejpam-5288	172	10	24	24	NUM
ejpam-5288	172	11	)	)	PUNCT
ejpam-5288	172	12	and	and	CCONJ
ejpam-5288	172	13	from	from	ADP
ejpam-5288	172	14	(	(	PUNCT
ejpam-5288	172	15	9	9	NUM
ejpam-5288	172	16	)	)	PUNCT
ejpam-5288	172	17	,	,	PUNCT
ejpam-5288	172	18	we	we	PRON
ejpam-5288	172	19	get	get	VERB
ejpam-5288	172	20	e	e	NOUN
ejpam-5288	172	21	x	x	PART
ejpam-5288	172	22	λ	λ	X
ejpam-5288	172	23	(	(	PUNCT
ejpam-5288	172	24	eλt−1	eλt−1	PROPN
ejpam-5288	172	25	)	)	PUNCT
ejpam-5288	172	26	=	=	PROPN
ejpam-5288	173	1	∞∑	∞∑	NUM
ejpam-5288	173	2	k=0	k=0	PROPN
ejpam-5288	173	3	bl	bl	PROPN
ejpam-5288	173	4	k	k	PROPN
ejpam-5288	173	5	,	,	PUNCT
ejpam-5288	173	6	λ(x	λ(x	PROPN
ejpam-5288	173	7	)	)	PUNCT
ejpam-5288	173	8	1	1	NUM
ejpam-5288	174	1	k	k	NOUN
ejpam-5288	174	2	!	!	PROPN
ejpam-5288	174	3	1	1	NUM
ejpam-5288	174	4	λk	λk	PROPN
ejpam-5288	174	5	(	(	PUNCT
ejpam-5288	174	6	1−	1−	NUM
ejpam-5288	174	7	e−λt	e−λt	NOUN
ejpam-5288	174	8	)	)	PUNCT
ejpam-5288	174	9	k	k	PROPN
ejpam-5288	174	10	(	(	PUNCT
ejpam-5288	174	11	26	26	NUM
ejpam-5288	174	12	)	)	PUNCT
ejpam-5288	174	13	=	=	NOUN
ejpam-5288	175	1	∞∑	∞∑	NUM
ejpam-5288	175	2	k=0	k=0	PROPN
ejpam-5288	175	3	bl	bl	PROPN
ejpam-5288	175	4	k	k	PROPN
ejpam-5288	175	5	,	,	PUNCT
ejpam-5288	175	6	λ(x	λ(x	PROPN
ejpam-5288	175	7	)	)	PUNCT
ejpam-5288	175	8	∞∑	∞∑	NUM
ejpam-5288	175	9	n	n	X
ejpam-5288	175	10	=	=	SYM
ejpam-5288	175	11	k	k	X
ejpam-5288	175	12	{	{	PUNCT
ejpam-5288	175	13	n	n	NOUN
ejpam-5288	175	14	k	k	ADJ
ejpam-5288	175	15	}	}	PUNCT
ejpam-5288	175	16	λ	λ	PROPN
ejpam-5288	175	17	(	(	PUNCT
ejpam-5288	175	18	−1)n−k	−1)n−k	PROPN
ejpam-5288	175	19	t	t	NOUN
ejpam-5288	175	20	n	n	NOUN
ejpam-5288	175	21	n	n	CCONJ
ejpam-5288	175	22	!	!	PUNCT
ejpam-5288	176	1	=	=	NOUN
ejpam-5288	177	1	∞∑	∞∑	PRON
ejpam-5288	177	2	n=0	n=0	NUM
ejpam-5288	177	3	(	(	PUNCT
ejpam-5288	177	4	n∑	n∑	NOUN
ejpam-5288	177	5	k=0	k=0	PROPN
ejpam-5288	177	6	(	(	PUNCT
ejpam-5288	177	7	−1)n−kbl	−1)n−kbl	NOUN
ejpam-5288	177	8	k	k	X
ejpam-5288	177	9	,	,	PUNCT
ejpam-5288	177	10	λ(x	λ(x	PROPN
ejpam-5288	177	11	)	)	PUNCT
ejpam-5288	177	12	{	{	PUNCT
ejpam-5288	177	13	n	n	NOUN
ejpam-5288	177	14	k	k	ADJ
ejpam-5288	177	15	}	}	PUNCT
ejpam-5288	177	16	λ	λ	PROPN
ejpam-5288	177	17	)	)	PUNCT
ejpam-5288	177	18	tn	tn	PROPN
ejpam-5288	177	19	n	n	PROPN
ejpam-5288	177	20	!	!	PUNCT
ejpam-5288	177	21	.	.	PUNCT
ejpam-5288	178	1	from	from	ADP
ejpam-5288	178	2	(	(	PUNCT
ejpam-5288	178	3	12	12	NUM
ejpam-5288	178	4	)	)	PUNCT
ejpam-5288	178	5	and	and	CCONJ
ejpam-5288	178	6	(	(	PUNCT
ejpam-5288	178	7	26	26	NUM
ejpam-5288	178	8	)	)	PUNCT
ejpam-5288	178	9	,	,	PUNCT
ejpam-5288	178	10	we	we	PRON
ejpam-5288	178	11	have	have	VERB
ejpam-5288	178	12	ϕn	ϕn	INTJ
ejpam-5288	178	13	,	,	PUNCT
ejpam-5288	178	14	λ(x	λ(x	PROPN
ejpam-5288	178	15	)	)	PUNCT
ejpam-5288	179	1	=	=	SYM
ejpam-5288	179	2	n∑	n∑	NOUN
ejpam-5288	179	3	k=0	k=0	PROPN
ejpam-5288	179	4	(	(	PUNCT
ejpam-5288	179	5	−1)n−k	−1)n−k	X
ejpam-5288	179	6	{	{	PUNCT
ejpam-5288	179	7	n	n	NOUN
ejpam-5288	179	8	k	k	ADJ
ejpam-5288	179	9	}	}	PUNCT
ejpam-5288	179	10	λ	λ	PROPN
ejpam-5288	179	11	bl	bl	X
ejpam-5288	179	12	k	k	X
ejpam-5288	179	13	,	,	PUNCT
ejpam-5288	179	14	λ(x	λ(x	PROPN
ejpam-5288	179	15	)	)	PUNCT
ejpam-5288	179	16	.	.	PUNCT
ejpam-5288	180	1	(	(	PUNCT
ejpam-5288	180	2	27	27	NUM
ejpam-5288	180	3	)	)	PUNCT
ejpam-5288	180	4	replacing	replace	VERB
ejpam-5288	180	5	t	t	NOUN
ejpam-5288	180	6	by	by	ADP
ejpam-5288	180	7	1	1	NUM
ejpam-5288	180	8	λ	λ	NOUN
ejpam-5288	180	9	log	log	NOUN
ejpam-5288	180	10	(	(	PUNCT
ejpam-5288	180	11	1	1	NUM
ejpam-5288	180	12	1−λt	1−λt	NOUN
ejpam-5288	180	13	)	)	PUNCT
ejpam-5288	180	14	in	in	ADP
ejpam-5288	180	15	(	(	PUNCT
ejpam-5288	180	16	12	12	NUM
ejpam-5288	180	17	)	)	PUNCT
ejpam-5288	180	18	and	and	CCONJ
ejpam-5288	180	19	from	from	ADP
ejpam-5288	180	20	(	(	PUNCT
ejpam-5288	180	21	7	7	NUM
ejpam-5288	180	22	)	)	PUNCT
ejpam-5288	180	23	,	,	PUNCT
ejpam-5288	180	24	we	we	PRON
ejpam-5288	180	25	get	get	VERB
ejpam-5288	180	26	e	e	NOUN
ejpam-5288	180	27	x	x	PART
ejpam-5288	180	28	λ	λ	X
ejpam-5288	180	29	(	(	PUNCT
ejpam-5288	180	30	1	1	NUM
ejpam-5288	180	31	1−λt	1−λt	NUM
ejpam-5288	180	32	−1	−1	NOUN
ejpam-5288	180	33	)	)	PUNCT
ejpam-5288	180	34	=	=	PUNCT
ejpam-5288	181	1	∞∑	∞∑	NUM
ejpam-5288	181	2	k=0	k=0	PROPN
ejpam-5288	181	3	ϕk	ϕk	NUM
ejpam-5288	181	4	,	,	PUNCT
ejpam-5288	181	5	λ(x	λ(x	PROPN
ejpam-5288	181	6	)	)	PUNCT
ejpam-5288	181	7	1	1	NUM
ejpam-5288	182	1	k	k	NOUN
ejpam-5288	182	2	!	!	PUNCT
ejpam-5288	183	1	(	(	PUNCT
ejpam-5288	183	2	1	1	NUM
ejpam-5288	183	3	λ	λ	NOUN
ejpam-5288	183	4	log	log	NOUN
ejpam-5288	183	5	(	(	PUNCT
ejpam-5288	183	6	1	1	NUM
ejpam-5288	183	7	1−	1−	NUM
ejpam-5288	183	8	λt	λt	ADP
ejpam-5288	183	9	)	)	PUNCT
ejpam-5288	183	10	)	)	PUNCT
ejpam-5288	184	1	k	k	PROPN
ejpam-5288	184	2	(	(	PUNCT
ejpam-5288	184	3	28	28	NUM
ejpam-5288	184	4	)	)	PUNCT
ejpam-5288	184	5	=	=	PUNCT
ejpam-5288	185	1	∞∑	∞∑	NUM
ejpam-5288	185	2	k=0	k=0	PROPN
ejpam-5288	185	3	ϕk	ϕk	PROPN
ejpam-5288	185	4	,	,	PUNCT
ejpam-5288	185	5	λ(x)(−1)k	λ(x)(−1)k	PROPN
ejpam-5288	185	6	1	1	NUM
ejpam-5288	185	7	k	k	X
ejpam-5288	185	8	!	!	PUNCT
ejpam-5288	186	1	(	(	PUNCT
ejpam-5288	186	2	log(1−	log(1−	PROPN
ejpam-5288	186	3	λt	λt	ADP
ejpam-5288	186	4	)	)	PUNCT
ejpam-5288	186	5	λ	λ	NOUN
ejpam-5288	186	6	)	)	PUNCT
ejpam-5288	186	7	k	k	X
ejpam-5288	187	1	=	=	PUNCT
ejpam-5288	188	1	∞∑	∞∑	NUM
ejpam-5288	188	2	k=0	k=0	PUNCT
ejpam-5288	188	3	ϕn	ϕn	INTJ
ejpam-5288	188	4	,	,	PUNCT
ejpam-5288	188	5	λ(x	λ(x	PROPN
ejpam-5288	188	6	)	)	PUNCT
ejpam-5288	189	1	∞∑	∞∑	NUM
ejpam-5288	189	2	n	n	NOUN
ejpam-5288	189	3	=	=	SYM
ejpam-5288	189	4	k	k	X
ejpam-5288	189	5	[	[	PUNCT
ejpam-5288	189	6	n	n	X
ejpam-5288	189	7	k	k	X
ejpam-5288	189	8	]	]	PUNCT
ejpam-5288	189	9	λ	λ	X
ejpam-5288	189	10	tn	tn	NOUN
ejpam-5288	189	11	n	n	NOUN
ejpam-5288	189	12	!	!	PUNCT
ejpam-5288	190	1	=	=	NOUN
ejpam-5288	191	1	∞∑	∞∑	PRON
ejpam-5288	191	2	n=0	n=0	NUM
ejpam-5288	191	3	(	(	PUNCT
ejpam-5288	191	4	n∑	n∑	PROPN
ejpam-5288	191	5	k=0	k=0	PROPN
ejpam-5288	191	6	ϕk	ϕk	PROPN
ejpam-5288	191	7	,	,	PUNCT
ejpam-5288	191	8	λ(x	λ(x	X
ejpam-5288	191	9	)	)	PUNCT
ejpam-5288	191	10	[	[	PUNCT
ejpam-5288	191	11	n	n	X
ejpam-5288	191	12	k	k	X
ejpam-5288	191	13	]	]	X
ejpam-5288	191	14	λ	λ	X
ejpam-5288	191	15	)	)	PUNCT
ejpam-5288	191	16	tn	tn	PROPN
ejpam-5288	191	17	n	n	PROPN
ejpam-5288	191	18	!	!	PUNCT
ejpam-5288	191	19	.	.	PUNCT
ejpam-5288	192	1	thus	thus	ADV
ejpam-5288	192	2	,	,	PUNCT
ejpam-5288	192	3	by	by	ADP
ejpam-5288	192	4	(	(	PUNCT
ejpam-5288	192	5	24	24	NUM
ejpam-5288	192	6	)	)	PUNCT
ejpam-5288	192	7	and	and	CCONJ
ejpam-5288	192	8	(	(	PUNCT
ejpam-5288	192	9	28	28	NUM
ejpam-5288	192	10	)	)	PUNCT
ejpam-5288	192	11	,	,	PUNCT
ejpam-5288	192	12	we	we	PRON
ejpam-5288	192	13	get	get	VERB
ejpam-5288	192	14	bl	bl	INTJ
ejpam-5288	192	15	n	n	PRON
ejpam-5288	192	16	,	,	PUNCT
ejpam-5288	192	17	λ(x	λ(x	PROPN
ejpam-5288	192	18	)	)	PUNCT
ejpam-5288	193	1	=	=	PUNCT
ejpam-5288	194	1	n∑	n∑	PROPN
ejpam-5288	194	2	k=0	k=0	PROPN
ejpam-5288	194	3	ϕk	ϕk	PROPN
ejpam-5288	194	4	,	,	PUNCT
ejpam-5288	194	5	λ(x	λ(x	X
ejpam-5288	194	6	)	)	PUNCT
ejpam-5288	195	1	[	[	PUNCT
ejpam-5288	195	2	n	n	X
ejpam-5288	195	3	k	k	X
ejpam-5288	195	4	]	]	X
ejpam-5288	195	5	λ	λ	X
ejpam-5288	195	6	,	,	PUNCT
ejpam-5288	195	7	(	(	PUNCT
ejpam-5288	195	8	n	n	CCONJ
ejpam-5288	195	9	≥	≥	NOUN
ejpam-5288	195	10	0	0	NUM
ejpam-5288	195	11	)	)	PUNCT
ejpam-5288	195	12	.	.	PUNCT
ejpam-5288	196	1	(	(	PUNCT
ejpam-5288	196	2	29	29	NUM
ejpam-5288	196	3	)	)	PUNCT
ejpam-5288	196	4	therefore	therefore	ADV
ejpam-5288	196	5	,	,	PUNCT
ejpam-5288	196	6	by	by	ADP
ejpam-5288	196	7	(	(	PUNCT
ejpam-5288	196	8	27	27	NUM
ejpam-5288	196	9	)	)	PUNCT
ejpam-5288	196	10	and	and	CCONJ
ejpam-5288	196	11	(	(	PUNCT
ejpam-5288	196	12	29	29	NUM
ejpam-5288	196	13	)	)	PUNCT
ejpam-5288	196	14	,	,	PUNCT
ejpam-5288	196	15	we	we	PRON
ejpam-5288	196	16	obtain	obtain	VERB
ejpam-5288	196	17	the	the	DET
ejpam-5288	196	18	following	follow	VERB
ejpam-5288	196	19	theorem	theorem	PROPN
ejpam-5288	196	20	.	.	PUNCT
ejpam-5288	197	1	j.	j.	PROPN
ejpam-5288	197	2	kwon	kwon	PROPN
ejpam-5288	197	3	et	et	PROPN
ejpam-5288	197	4	al	al	PROPN
ejpam-5288	197	5	.	.	PUNCT
ejpam-5288	197	6	/	/	SYM
ejpam-5288	197	7	eur	eur	PROPN
ejpam-5288	197	8	.	.	PUNCT
ejpam-5288	198	1	j.	j.	PROPN
ejpam-5288	198	2	pure	pure	PROPN
ejpam-5288	198	3	appl	appl	PROPN
ejpam-5288	198	4	.	.	PROPN
ejpam-5288	198	5	math	math	PROPN
ejpam-5288	198	6	,	,	PUNCT
ejpam-5288	198	7	17	17	NUM
ejpam-5288	198	8	(	(	PUNCT
ejpam-5288	198	9	3	3	NUM
ejpam-5288	198	10	)	)	PUNCT
ejpam-5288	198	11	(	(	PUNCT
ejpam-5288	198	12	2024	2024	NUM
ejpam-5288	198	13	)	)	PUNCT
ejpam-5288	198	14	,	,	PUNCT
ejpam-5288	198	15	1385	1385	NUM
ejpam-5288	198	16	-	-	SYM
ejpam-5288	198	17	1402	1402	NUM
ejpam-5288	198	18	1393	1393	NUM
ejpam-5288	198	19	theorem	theorem	NOUN
ejpam-5288	198	20	4	4	NUM
ejpam-5288	198	21	.	.	NOUN
ejpam-5288	198	22	for	for	ADP
ejpam-5288	198	23	n	n	PRON
ejpam-5288	198	24	≥	≥	NOUN
ejpam-5288	198	25	0	0	NUM
ejpam-5288	198	26	,	,	PUNCT
ejpam-5288	198	27	we	we	PRON
ejpam-5288	198	28	have	have	VERB
ejpam-5288	198	29	ϕn	ϕn	INTJ
ejpam-5288	198	30	,	,	PUNCT
ejpam-5288	198	31	λ(x	λ(x	PROPN
ejpam-5288	198	32	)	)	PUNCT
ejpam-5288	199	1	=	=	SYM
ejpam-5288	199	2	n∑	n∑	NOUN
ejpam-5288	199	3	k=0	k=0	PROPN
ejpam-5288	199	4	(	(	PUNCT
ejpam-5288	199	5	−1)n−k	−1)n−k	X
ejpam-5288	199	6	{	{	PUNCT
ejpam-5288	199	7	n	n	NOUN
ejpam-5288	199	8	k	k	ADJ
ejpam-5288	199	9	}	}	PUNCT
ejpam-5288	199	10	λ	λ	PROPN
ejpam-5288	199	11	bl	bl	NOUN
ejpam-5288	199	12	n	n	CCONJ
ejpam-5288	199	13	,	,	PUNCT
ejpam-5288	199	14	λ(x	λ(x	PROPN
ejpam-5288	199	15	)	)	PUNCT
ejpam-5288	199	16	,	,	PUNCT
ejpam-5288	199	17	and	and	CCONJ
ejpam-5288	199	18	bl	bl	X
ejpam-5288	199	19	n	n	CCONJ
ejpam-5288	199	20	,	,	PUNCT
ejpam-5288	199	21	λ(x	λ(x	PROPN
ejpam-5288	199	22	)	)	PUNCT
ejpam-5288	199	23	=	=	SYM
ejpam-5288	200	1	n∑	n∑	NOUN
ejpam-5288	200	2	k=0	k=0	PROPN
ejpam-5288	200	3	[	[	PUNCT
ejpam-5288	200	4	n	n	X
ejpam-5288	200	5	k	k	X
ejpam-5288	200	6	]	]	PUNCT
ejpam-5288	200	7	λ	λ	X
ejpam-5288	200	8	ϕn	ϕn	INTJ
ejpam-5288	200	9	,	,	PUNCT
ejpam-5288	200	10	λ(x	λ(x	PROPN
ejpam-5288	200	11	)	)	PUNCT
ejpam-5288	200	12	.	.	PUNCT
ejpam-5288	201	1	it	it	PRON
ejpam-5288	201	2	is	be	AUX
ejpam-5288	201	3	well	well	ADV
ejpam-5288	201	4	known	know	VERB
ejpam-5288	201	5	that	that	SCONJ
ejpam-5288	201	6	the	the	DET
ejpam-5288	201	7	laguerre	laguerre	NOUN
ejpam-5288	201	8	polynomials	polynomial	VERB
ejpam-5288	201	9	l	l	PROPN
ejpam-5288	201	10	(	(	PUNCT
ejpam-5288	201	11	α	α	NOUN
ejpam-5288	201	12	)	)	PUNCT
ejpam-5288	201	13	n	n	PROPN
ejpam-5288	201	14	(	(	PUNCT
ejpam-5288	201	15	x	x	X
ejpam-5288	201	16	)	)	PUNCT
ejpam-5288	201	17	of	of	ADP
ejpam-5288	201	18	order	order	NOUN
ejpam-5288	201	19	α	α	NOUN
ejpam-5288	201	20	,	,	PUNCT
ejpam-5288	201	21	(	(	PUNCT
ejpam-5288	201	22	α	α	X
ejpam-5288	201	23	>	>	X
ejpam-5288	201	24	−1	−1	NOUN
ejpam-5288	201	25	)	)	PUNCT
ejpam-5288	201	26	,	,	PUNCT
ejpam-5288	201	27	are	be	AUX
ejpam-5288	201	28	given	give	VERB
ejpam-5288	201	29	by	by	ADP
ejpam-5288	201	30	(	(	PUNCT
ejpam-5288	201	31	1−	1−	NUM
ejpam-5288	201	32	t)−α−1ex	t)−α−1ex	NOUN
ejpam-5288	201	33	(	(	PUNCT
ejpam-5288	201	34	t	t	PROPN
ejpam-5288	201	35	t−1	t−1	PROPN
ejpam-5288	201	36	)	)	PUNCT
ejpam-5288	202	1	=	=	PUNCT
ejpam-5288	203	1	∞∑	∞∑	PRON
ejpam-5288	203	2	n=0	n=0	NUM
ejpam-5288	203	3	l(α	l(α	PROPN
ejpam-5288	203	4	)	)	PUNCT
ejpam-5288	203	5	n	n	CCONJ
ejpam-5288	203	6	(	(	PUNCT
ejpam-5288	203	7	x	x	X
ejpam-5288	203	8	)	)	PUNCT
ejpam-5288	203	9	tn	tn	PROPN
ejpam-5288	203	10	n	n	NUM
ejpam-5288	203	11	!	!	PUNCT
ejpam-5288	203	12	.	.	PUNCT
ejpam-5288	204	1	(	(	PUNCT
ejpam-5288	204	2	30	30	NUM
ejpam-5288	204	3	)	)	PUNCT
ejpam-5288	204	4	now	now	ADV
ejpam-5288	204	5	,	,	PUNCT
ejpam-5288	204	6	we	we	PRON
ejpam-5288	204	7	consider	consider	VERB
ejpam-5288	204	8	the	the	DET
ejpam-5288	204	9	λ	λ	NOUN
ejpam-5288	204	10	-	-	NOUN
ejpam-5288	204	11	analogues	analogue	NOUN
ejpam-5288	204	12	of	of	ADP
ejpam-5288	204	13	laguerre	laguerre	NOUN
ejpam-5288	204	14	polynomials	polynomial	NOUN
ejpam-5288	204	15	l	l	PROPN
ejpam-5288	204	16	(	(	PUNCT
ejpam-5288	204	17	α	α	NOUN
ejpam-5288	204	18	)	)	PUNCT
ejpam-5288	204	19	n	n	CCONJ
ejpam-5288	204	20	,	,	PUNCT
ejpam-5288	204	21	λ(x	λ(x	PROPN
ejpam-5288	204	22	)	)	PUNCT
ejpam-5288	204	23	of	of	ADP
ejpam-5288	204	24	order	order	NOUN
ejpam-5288	204	25	α	α	NOUN
ejpam-5288	204	26	,	,	PUNCT
ejpam-5288	204	27	(	(	PUNCT
ejpam-5288	204	28	α	α	X
ejpam-5288	204	29	>	>	X
ejpam-5288	204	30	−1	−1	NOUN
ejpam-5288	204	31	)	)	PUNCT
ejpam-5288	204	32	,	,	PUNCT
ejpam-5288	204	33	which	which	PRON
ejpam-5288	204	34	are	be	AUX
ejpam-5288	204	35	given	give	VERB
ejpam-5288	204	36	by	by	ADP
ejpam-5288	204	37	(	(	PUNCT
ejpam-5288	204	38	1−	1−	NUM
ejpam-5288	204	39	λt)−	λt)−	PUNCT
ejpam-5288	205	1	α+1	α+1	NUM
ejpam-5288	206	1	λ	λ	X
ejpam-5288	206	2	ex	ex	X
ejpam-5288	206	3	(	(	PUNCT
ejpam-5288	206	4	t	t	X
ejpam-5288	206	5	λt−1	λt−1	PROPN
ejpam-5288	206	6	)	)	PUNCT
ejpam-5288	207	1	=	=	PUNCT
ejpam-5288	208	1	∞∑	∞∑	PRON
ejpam-5288	208	2	n=0	n=0	NUM
ejpam-5288	208	3	l	l	NOUN
ejpam-5288	208	4	(	(	PUNCT
ejpam-5288	208	5	α	α	NOUN
ejpam-5288	208	6	)	)	PUNCT
ejpam-5288	208	7	n	n	CCONJ
ejpam-5288	208	8	,	,	PUNCT
ejpam-5288	208	9	λ(x	λ(x	PROPN
ejpam-5288	208	10	)	)	PUNCT
ejpam-5288	208	11	tn	tn	PROPN
ejpam-5288	208	12	n	n	PROPN
ejpam-5288	208	13	!	!	PUNCT
ejpam-5288	208	14	.	.	PUNCT
ejpam-5288	209	1	(	(	PUNCT
ejpam-5288	209	2	31	31	NUM
ejpam-5288	209	3	)	)	PUNCT
ejpam-5288	209	4	note	note	NOUN
ejpam-5288	209	5	that	that	SCONJ
ejpam-5288	209	6	lim	lim	PROPN
ejpam-5288	209	7	λ→1	λ→1	PROPN
ejpam-5288	209	8	l	l	PROPN
ejpam-5288	209	9	(	(	PUNCT
ejpam-5288	209	10	α	α	NOUN
ejpam-5288	209	11	)	)	PUNCT
ejpam-5288	209	12	n	n	CCONJ
ejpam-5288	209	13	,	,	PUNCT
ejpam-5288	209	14	λ(x	λ(x	X
ejpam-5288	209	15	)	)	PUNCT
ejpam-5288	209	16	=	=	SYM
ejpam-5288	209	17	l(α	l(α	PROPN
ejpam-5288	209	18	)	)	PUNCT
ejpam-5288	210	1	n	n	CCONJ
ejpam-5288	210	2	(	(	PUNCT
ejpam-5288	210	3	x	x	NOUN
ejpam-5288	210	4	)	)	PUNCT
ejpam-5288	210	5	,	,	PUNCT
ejpam-5288	210	6	(	(	PUNCT
ejpam-5288	210	7	n	n	X
ejpam-5288	210	8	≥	≥	NOUN
ejpam-5288	210	9	0	0	NUM
ejpam-5288	210	10	)	)	PUNCT
ejpam-5288	210	11	.	.	PUNCT
ejpam-5288	211	1	from	from	ADP
ejpam-5288	211	2	(	(	PUNCT
ejpam-5288	211	3	31	31	NUM
ejpam-5288	211	4	)	)	PUNCT
ejpam-5288	211	5	,	,	PUNCT
ejpam-5288	211	6	we	we	PRON
ejpam-5288	211	7	have	have	VERB
ejpam-5288	211	8	(	(	PUNCT
ejpam-5288	211	9	1−	1−	NUM
ejpam-5288	211	10	λt)−	λt)−	PUNCT
ejpam-5288	211	11	α+1	α+1	NUM
ejpam-5288	212	1	λ	λ	X
ejpam-5288	212	2	=	=	SYM
ejpam-5288	212	3	ex	ex	X
ejpam-5288	212	4	(	(	PUNCT
ejpam-5288	212	5	t	t	PROPN
ejpam-5288	212	6	1−λt	1−λt	PROPN
ejpam-5288	212	7	)	)	PUNCT
ejpam-5288	213	1	∞∑	∞∑	DET
ejpam-5288	213	2	k=0	k=0	PROPN
ejpam-5288	213	3	l	l	NOUN
ejpam-5288	213	4	(	(	PUNCT
ejpam-5288	213	5	α	α	NOUN
ejpam-5288	213	6	)	)	PUNCT
ejpam-5288	213	7	k	k	NOUN
ejpam-5288	213	8	,	,	PUNCT
ejpam-5288	213	9	λ(x	λ(x	PROPN
ejpam-5288	213	10	)	)	PUNCT
ejpam-5288	213	11	tk	tk	PROPN
ejpam-5288	214	1	k	k	PROPN
ejpam-5288	214	2	!	!	PUNCT
ejpam-5288	215	1	(	(	PUNCT
ejpam-5288	215	2	32	32	NUM
ejpam-5288	215	3	)	)	PUNCT
ejpam-5288	215	4	=	=	NOUN
ejpam-5288	216	1	∞∑	∞∑	NUM
ejpam-5288	216	2	m=0	m=0	PROPN
ejpam-5288	216	3	bl	bl	PROPN
ejpam-5288	216	4	m	m	PROPN
ejpam-5288	216	5	,	,	PUNCT
ejpam-5288	216	6	λ(x	λ(x	PROPN
ejpam-5288	216	7	)	)	PUNCT
ejpam-5288	216	8	tm	tm	PROPN
ejpam-5288	216	9	m	m	PROPN
ejpam-5288	216	10	!	!	PUNCT
ejpam-5288	217	1	∞∑	∞∑	NUM
ejpam-5288	217	2	k=0	k=0	PROPN
ejpam-5288	217	3	l	l	NOUN
ejpam-5288	217	4	(	(	PUNCT
ejpam-5288	217	5	α	α	NOUN
ejpam-5288	217	6	)	)	PUNCT
ejpam-5288	217	7	k	k	NOUN
ejpam-5288	217	8	,	,	PUNCT
ejpam-5288	217	9	λ(x	λ(x	PROPN
ejpam-5288	217	10	)	)	PUNCT
ejpam-5288	217	11	tk	tk	PROPN
ejpam-5288	218	1	k	k	NOUN
ejpam-5288	218	2	!	!	PUNCT
ejpam-5288	218	3	=	=	PUNCT
ejpam-5288	219	1	∞∑	∞∑	PRON
ejpam-5288	219	2	n=0	n=0	NUM
ejpam-5288	219	3	(	(	PUNCT
ejpam-5288	219	4	n∑	n∑	PROPN
ejpam-5288	219	5	m=0	m=0	PROPN
ejpam-5288	219	6	(	(	PUNCT
ejpam-5288	219	7	n	n	NOUN
ejpam-5288	219	8	m	m	PROPN
ejpam-5288	219	9	)	)	PUNCT
ejpam-5288	219	10	bl	bl	PROPN
ejpam-5288	219	11	m	m	PROPN
ejpam-5288	219	12	,	,	PUNCT
ejpam-5288	219	13	λ(x)l	λ(x)l	PROPN
ejpam-5288	219	14	(	(	PUNCT
ejpam-5288	219	15	α	α	NOUN
ejpam-5288	219	16	)	)	PUNCT
ejpam-5288	219	17	n−m	n−m	PROPN
ejpam-5288	219	18	,	,	PUNCT
ejpam-5288	219	19	λ(x	λ(x	PROPN
ejpam-5288	219	20	)	)	PUNCT
ejpam-5288	219	21	)	)	PUNCT
ejpam-5288	219	22	tn	tn	PROPN
ejpam-5288	219	23	n	n	PROPN
ejpam-5288	219	24	!	!	PUNCT
ejpam-5288	219	25	.	.	PUNCT
ejpam-5288	220	1	on	on	ADP
ejpam-5288	220	2	the	the	DET
ejpam-5288	220	3	other	other	ADJ
ejpam-5288	220	4	hand	hand	NOUN
ejpam-5288	220	5	,	,	PUNCT
ejpam-5288	220	6	by	by	ADP
ejpam-5288	220	7	binomial	binomial	ADJ
ejpam-5288	220	8	expansion	expansion	NOUN
ejpam-5288	220	9	,	,	PUNCT
ejpam-5288	220	10	we	we	PRON
ejpam-5288	220	11	get	get	VERB
ejpam-5288	220	12	(	(	PUNCT
ejpam-5288	220	13	1−	1−	NUM
ejpam-5288	220	14	λt)−	λt)−	PUNCT
ejpam-5288	220	15	α+1	α+1	NUM
ejpam-5288	221	1	λ	λ	NOUN
ejpam-5288	221	2	=	=	SYM
ejpam-5288	221	3	∞∑	∞∑	ADJ
ejpam-5288	221	4	n=0	n=0	PUNCT
ejpam-5288	221	5	⟨α+	⟨α+	NOUN
ejpam-5288	221	6	1⟩n	1⟩n	NUM
ejpam-5288	221	7	,	,	PUNCT
ejpam-5288	221	8	λ	λ	PROPN
ejpam-5288	221	9	tn	tn	NOUN
ejpam-5288	221	10	n	n	X
ejpam-5288	221	11	!	!	PUNCT
ejpam-5288	221	12	.	.	PUNCT
ejpam-5288	222	1	(	(	PUNCT
ejpam-5288	222	2	33	33	NUM
ejpam-5288	222	3	)	)	PUNCT
ejpam-5288	222	4	therefore	therefore	ADV
ejpam-5288	222	5	,	,	PUNCT
ejpam-5288	222	6	by	by	ADP
ejpam-5288	222	7	(	(	PUNCT
ejpam-5288	222	8	32	32	NUM
ejpam-5288	222	9	)	)	PUNCT
ejpam-5288	222	10	and	and	CCONJ
ejpam-5288	222	11	(	(	PUNCT
ejpam-5288	222	12	33	33	NUM
ejpam-5288	222	13	)	)	PUNCT
ejpam-5288	222	14	,	,	PUNCT
ejpam-5288	222	15	we	we	PRON
ejpam-5288	222	16	obtain	obtain	VERB
ejpam-5288	222	17	the	the	DET
ejpam-5288	222	18	following	follow	VERB
ejpam-5288	222	19	theorem	theorem	VERB
ejpam-5288	222	20	.	.	PUNCT
ejpam-5288	222	21	theorem	theorem	NOUN
ejpam-5288	222	22	5	5	NUM
ejpam-5288	222	23	.	.	PUNCT
ejpam-5288	222	24	for	for	ADP
ejpam-5288	222	25	n	n	PRON
ejpam-5288	222	26	≥	≥	NOUN
ejpam-5288	222	27	0	0	NUM
ejpam-5288	222	28	,	,	PUNCT
ejpam-5288	222	29	we	we	PRON
ejpam-5288	222	30	have	have	VERB
ejpam-5288	222	31	⟨α+	⟨α+	NOUN
ejpam-5288	222	32	1⟩n	1⟩n	NUM
ejpam-5288	222	33	,	,	PUNCT
ejpam-5288	222	34	λ	λ	PROPN
ejpam-5288	222	35	=	=	SYM
ejpam-5288	223	1	n∑	n∑	PROPN
ejpam-5288	223	2	m=0	m=0	PROPN
ejpam-5288	223	3	(	(	PUNCT
ejpam-5288	223	4	n	n	X
ejpam-5288	223	5	m	m	PROPN
ejpam-5288	223	6	)	)	PUNCT
ejpam-5288	223	7	bl	bl	PROPN
ejpam-5288	223	8	m	m	PROPN
ejpam-5288	223	9	,	,	PUNCT
ejpam-5288	223	10	λ(x)l	λ(x)l	PROPN
ejpam-5288	223	11	(	(	PUNCT
ejpam-5288	223	12	α	α	NOUN
ejpam-5288	223	13	)	)	PUNCT
ejpam-5288	223	14	n−m	n−m	PROPN
ejpam-5288	223	15	,	,	PUNCT
ejpam-5288	223	16	λ(x	λ(x	PROPN
ejpam-5288	223	17	)	)	PUNCT
ejpam-5288	223	18	.	.	PUNCT
ejpam-5288	224	1	(	(	PUNCT
ejpam-5288	224	2	34	34	NUM
ejpam-5288	224	3	)	)	PUNCT
ejpam-5288	224	4	we	we	PRON
ejpam-5288	224	5	observe	observe	VERB
ejpam-5288	224	6	that	that	SCONJ
ejpam-5288	224	7	⟨α+	⟨α+	PROPN
ejpam-5288	224	8	1⟩n	1⟩n	NUM
ejpam-5288	224	9	,	,	PUNCT
ejpam-5288	224	10	λ	λ	X
ejpam-5288	224	11	=	=	SYM
ejpam-5288	224	12	n∑	n∑	ADJ
ejpam-5288	224	13	k=0	k=0	PROPN
ejpam-5288	224	14	lλ(n	lλ(n	NUM
ejpam-5288	224	15	,	,	PUNCT
ejpam-5288	224	16	k)(α+	k)(α+	NOUN
ejpam-5288	224	17	1)k	1)k	NUM
ejpam-5288	224	18	,	,	PUNCT
ejpam-5288	224	19	λ	λ	PROPN
ejpam-5288	224	20	=	=	SYM
ejpam-5288	225	1	n∑	n∑	ADJ
ejpam-5288	225	2	k=0	k=0	PROPN
ejpam-5288	225	3	lλ(n	lλ(n	X
ejpam-5288	225	4	,	,	PUNCT
ejpam-5288	225	5	k	k	X
ejpam-5288	225	6	)	)	PUNCT
ejpam-5288	225	7	k∑	k∑	NOUN
ejpam-5288	225	8	j=0	j=0	PROPN
ejpam-5288	226	1	(	(	PUNCT
ejpam-5288	226	2	k	k	PROPN
ejpam-5288	226	3	j	j	PROPN
ejpam-5288	226	4	)	)	PUNCT
ejpam-5288	226	5	(	(	PUNCT
ejpam-5288	226	6	α)j	α)j	ADJ
ejpam-5288	226	7	,	,	PUNCT
ejpam-5288	226	8	λ(1)k−j	λ(1)k−j	INTJ
ejpam-5288	226	9	,	,	PUNCT
ejpam-5288	226	10	λ	λ	PROPN
ejpam-5288	226	11	(	(	PUNCT
ejpam-5288	226	12	35	35	NUM
ejpam-5288	226	13	)	)	PUNCT
ejpam-5288	226	14	j.	j.	PROPN
ejpam-5288	226	15	kwon	kwon	PROPN
ejpam-5288	226	16	et	et	PROPN
ejpam-5288	226	17	al	al	PROPN
ejpam-5288	226	18	.	.	PUNCT
ejpam-5288	226	19	/	/	SYM
ejpam-5288	226	20	eur	eur	PROPN
ejpam-5288	226	21	.	.	PUNCT
ejpam-5288	227	1	j.	j.	PROPN
ejpam-5288	227	2	pure	pure	PROPN
ejpam-5288	227	3	appl	appl	PROPN
ejpam-5288	227	4	.	.	PROPN
ejpam-5288	227	5	math	math	PROPN
ejpam-5288	227	6	,	,	PUNCT
ejpam-5288	227	7	17	17	NUM
ejpam-5288	227	8	(	(	PUNCT
ejpam-5288	227	9	3	3	NUM
ejpam-5288	227	10	)	)	PUNCT
ejpam-5288	227	11	(	(	PUNCT
ejpam-5288	227	12	2024	2024	NUM
ejpam-5288	227	13	)	)	PUNCT
ejpam-5288	227	14	,	,	PUNCT
ejpam-5288	227	15	1385	1385	NUM
ejpam-5288	227	16	-	-	SYM
ejpam-5288	227	17	1402	1402	NUM
ejpam-5288	227	18	1394	1394	NUM
ejpam-5288	227	19	=	=	SYM
ejpam-5288	227	20	n∑	n∑	PROPN
ejpam-5288	227	21	j=0	j=0	PROPN
ejpam-5288	227	22	n∑	n∑	PROPN
ejpam-5288	227	23	k	k	PROPN
ejpam-5288	228	1	=	=	PROPN
ejpam-5288	228	2	j	j	PROPN
ejpam-5288	228	3	(	(	PUNCT
ejpam-5288	228	4	k	k	PROPN
ejpam-5288	228	5	j	j	PROPN
ejpam-5288	228	6	)	)	PUNCT
ejpam-5288	228	7	lλ(n	lλ(n	NUM
ejpam-5288	228	8	,	,	PUNCT
ejpam-5288	228	9	k)(α)j	k)(α)j	X
ejpam-5288	228	10	,	,	PUNCT
ejpam-5288	228	11	λ(1)k−j	λ(1)k−j	INTJ
ejpam-5288	228	12	,	,	PUNCT
ejpam-5288	228	13	λ	λ	X
ejpam-5288	228	14	.	.	PUNCT
ejpam-5288	228	15	hence	hence	ADV
ejpam-5288	228	16	,	,	PUNCT
ejpam-5288	228	17	by	by	ADP
ejpam-5288	228	18	(	(	PUNCT
ejpam-5288	228	19	34	34	NUM
ejpam-5288	228	20	)	)	PUNCT
ejpam-5288	228	21	and	and	CCONJ
ejpam-5288	228	22	(	(	PUNCT
ejpam-5288	228	23	35	35	NUM
ejpam-5288	228	24	)	)	PUNCT
ejpam-5288	228	25	,	,	PUNCT
ejpam-5288	228	26	we	we	PRON
ejpam-5288	228	27	get	get	VERB
ejpam-5288	228	28	n∑	n∑	PROPN
ejpam-5288	228	29	m=0	m=0	PROPN
ejpam-5288	228	30	n∑	n∑	PROPN
ejpam-5288	229	1	k	k	PROPN
ejpam-5288	230	1	=	=	NOUN
ejpam-5288	230	2	m	m	X
ejpam-5288	230	3	(	(	PUNCT
ejpam-5288	230	4	k	k	NOUN
ejpam-5288	230	5	m	m	PROPN
ejpam-5288	230	6	)	)	PUNCT
ejpam-5288	230	7	lλ(n	lλ(n	NUM
ejpam-5288	230	8	,	,	PUNCT
ejpam-5288	230	9	k)(α)m	k)(α)m	NOUN
ejpam-5288	230	10	,	,	PUNCT
ejpam-5288	230	11	λ(1)k−m	λ(1)k−m	NOUN
ejpam-5288	230	12	,	,	PUNCT
ejpam-5288	230	13	λ	λ	PROPN
ejpam-5288	230	14	=	=	SYM
ejpam-5288	230	15	n∑	n∑	PROPN
ejpam-5288	230	16	m=0	m=0	PROPN
ejpam-5288	230	17	(	(	PUNCT
ejpam-5288	230	18	n	n	X
ejpam-5288	230	19	m	m	PROPN
ejpam-5288	230	20	)	)	PUNCT
ejpam-5288	230	21	bl	bl	PROPN
ejpam-5288	230	22	m	m	PROPN
ejpam-5288	230	23	,	,	PUNCT
ejpam-5288	230	24	λ(x)l	λ(x)l	PROPN
ejpam-5288	230	25	(	(	PUNCT
ejpam-5288	230	26	α	α	NOUN
ejpam-5288	230	27	)	)	PUNCT
ejpam-5288	230	28	n−m	n−m	PROPN
ejpam-5288	230	29	,	,	PUNCT
ejpam-5288	230	30	λ(x	λ(x	PROPN
ejpam-5288	230	31	)	)	PUNCT
ejpam-5288	230	32	.	.	PUNCT
ejpam-5288	231	1	(	(	PUNCT
ejpam-5288	231	2	36	36	NUM
ejpam-5288	231	3	)	)	PUNCT
ejpam-5288	231	4	now	now	ADV
ejpam-5288	231	5	,	,	PUNCT
ejpam-5288	231	6	we	we	PRON
ejpam-5288	231	7	consider	consider	VERB
ejpam-5288	231	8	the	the	DET
ejpam-5288	231	9	bivariate	bivariate	ADJ
ejpam-5288	231	10	λ	λ	PROPN
ejpam-5288	231	11	-	-	PUNCT
ejpam-5288	231	12	lah	lah	ADJ
ejpam-5288	231	13	-	-	PUNCT
ejpam-5288	231	14	bell	bell	NOUN
ejpam-5288	231	15	polynomials	polynomial	NOUN
ejpam-5288	231	16	given	give	VERB
ejpam-5288	231	17	by	by	ADP
ejpam-5288	231	18	(	(	PUNCT
ejpam-5288	231	19	1	1	NUM
ejpam-5288	231	20	+	+	NUM
ejpam-5288	231	21	y	y	PROPN
ejpam-5288	231	22	t	t	NOUN
ejpam-5288	231	23	1−	1−	NUM
ejpam-5288	231	24	λt	λt	ADP
ejpam-5288	231	25	)	)	PUNCT
ejpam-5288	231	26	x	x	X
ejpam-5288	232	1	=	=	PUNCT
ejpam-5288	232	2	∞∑	∞∑	PROPN
ejpam-5288	232	3	n=0	n=0	NUM
ejpam-5288	232	4	bl	bl	NOUN
ejpam-5288	232	5	n	n	CCONJ
ejpam-5288	232	6	,	,	PUNCT
ejpam-5288	232	7	λ(x	λ(x	PROPN
ejpam-5288	232	8	,	,	PUNCT
ejpam-5288	232	9	y	y	PROPN
ejpam-5288	232	10	)	)	PUNCT
ejpam-5288	232	11	tn	tn	PROPN
ejpam-5288	232	12	n	n	PROPN
ejpam-5288	232	13	!	!	PUNCT
ejpam-5288	232	14	.	.	PUNCT
ejpam-5288	233	1	(	(	PUNCT
ejpam-5288	233	2	37	37	NUM
ejpam-5288	233	3	)	)	PUNCT
ejpam-5288	233	4	thus	thus	ADV
ejpam-5288	233	5	,	,	PUNCT
ejpam-5288	233	6	by	by	ADP
ejpam-5288	233	7	(	(	PUNCT
ejpam-5288	233	8	37	37	NUM
ejpam-5288	233	9	)	)	PUNCT
ejpam-5288	233	10	and	and	CCONJ
ejpam-5288	233	11	(	(	PUNCT
ejpam-5288	233	12	19	19	NUM
ejpam-5288	233	13	)	)	PUNCT
ejpam-5288	233	14	,	,	PUNCT
ejpam-5288	233	15	we	we	PRON
ejpam-5288	233	16	get	get	VERB
ejpam-5288	233	17	(	(	PUNCT
ejpam-5288	233	18	1	1	NUM
ejpam-5288	233	19	+	+	NUM
ejpam-5288	233	20	y	y	PROPN
ejpam-5288	233	21	t	t	NOUN
ejpam-5288	233	22	1−	1−	NUM
ejpam-5288	233	23	λt	λt	ADP
ejpam-5288	233	24	)	)	PUNCT
ejpam-5288	233	25	x	x	X
ejpam-5288	234	1	=	=	PUNCT
ejpam-5288	234	2	∞∑	∞∑	NUM
ejpam-5288	234	3	k=0	k=0	PROPN
ejpam-5288	234	4	(	(	PUNCT
ejpam-5288	234	5	x	x	SYM
ejpam-5288	234	6	k	k	X
ejpam-5288	234	7	)	)	PUNCT
ejpam-5288	234	8	yk	yk	PROPN
ejpam-5288	234	9	(	(	PUNCT
ejpam-5288	234	10	t	t	PROPN
ejpam-5288	234	11	1−	1−	NUM
ejpam-5288	234	12	λt	λt	ADP
ejpam-5288	234	13	)	)	PUNCT
ejpam-5288	234	14	k	k	PROPN
ejpam-5288	234	15	=	=	PUNCT
ejpam-5288	235	1	∞∑	∞∑	NUM
ejpam-5288	235	2	k=0	k=0	PROPN
ejpam-5288	235	3	(	(	PUNCT
ejpam-5288	235	4	x)ky	x)ky	PROPN
ejpam-5288	235	5	k	k	PROPN
ejpam-5288	235	6	1	1	NUM
ejpam-5288	235	7	k	k	NOUN
ejpam-5288	235	8	!	!	PUNCT
ejpam-5288	236	1	(	(	PUNCT
ejpam-5288	236	2	t	t	PROPN
ejpam-5288	236	3	1−	1−	NUM
ejpam-5288	236	4	λt	λt	ADP
ejpam-5288	236	5	)	)	PUNCT
ejpam-5288	236	6	k	k	PROPN
ejpam-5288	236	7	(	(	PUNCT
ejpam-5288	236	8	38	38	NUM
ejpam-5288	236	9	)	)	PUNCT
ejpam-5288	236	10	=	=	NOUN
ejpam-5288	237	1	∞∑	∞∑	NUM
ejpam-5288	237	2	k=0	k=0	PROPN
ejpam-5288	237	3	(	(	PUNCT
ejpam-5288	237	4	x)ky	x)ky	PROPN
ejpam-5288	237	5	k	k	PROPN
ejpam-5288	237	6	∞∑	∞∑	NUM
ejpam-5288	237	7	n	n	X
ejpam-5288	237	8	=	=	X
ejpam-5288	237	9	k	k	NOUN
ejpam-5288	237	10	lλ(n	lλ(n	X
ejpam-5288	237	11	,	,	PUNCT
ejpam-5288	237	12	k	k	NOUN
ejpam-5288	237	13	)	)	PUNCT
ejpam-5288	237	14	tn	tn	PROPN
ejpam-5288	237	15	n	n	ADV
ejpam-5288	237	16	!	!	PUNCT
ejpam-5288	237	17	=	=	NOUN
ejpam-5288	238	1	∞∑	∞∑	PRON
ejpam-5288	238	2	n=0	n=0	NUM
ejpam-5288	238	3	(	(	PUNCT
ejpam-5288	238	4	n∑	n∑	ADV
ejpam-5288	238	5	k=0	k=0	PROPN
ejpam-5288	238	6	lλ(n	lλ(n	PUNCT
ejpam-5288	238	7	,	,	PUNCT
ejpam-5288	238	8	k)(x)ky	k)(x)ky	X
ejpam-5288	238	9	k	k	X
ejpam-5288	238	10	)	)	PUNCT
ejpam-5288	238	11	tn	tn	PROPN
ejpam-5288	238	12	n	n	PROPN
ejpam-5288	238	13	!	!	PUNCT
ejpam-5288	238	14	.	.	PUNCT
ejpam-5288	239	1	by	by	ADP
ejpam-5288	239	2	(	(	PUNCT
ejpam-5288	239	3	37	37	NUM
ejpam-5288	239	4	)	)	PUNCT
ejpam-5288	239	5	and	and	CCONJ
ejpam-5288	239	6	(	(	PUNCT
ejpam-5288	239	7	38	38	NUM
ejpam-5288	239	8	)	)	PUNCT
ejpam-5288	239	9	,	,	PUNCT
ejpam-5288	239	10	we	we	PRON
ejpam-5288	239	11	get	get	VERB
ejpam-5288	239	12	bl	bl	INTJ
ejpam-5288	239	13	n	n	PRON
ejpam-5288	239	14	,	,	PUNCT
ejpam-5288	239	15	λ(x	λ(x	PROPN
ejpam-5288	239	16	,	,	PUNCT
ejpam-5288	239	17	y	y	NOUN
ejpam-5288	239	18	)	)	PUNCT
ejpam-5288	240	1	=	=	SYM
ejpam-5288	240	2	n∑	n∑	PROPN
ejpam-5288	240	3	k=0	k=0	PROPN
ejpam-5288	240	4	lλ(n	lλ(n	PUNCT
ejpam-5288	240	5	,	,	PUNCT
ejpam-5288	240	6	k)(x)ky	k)(x)ky	X
ejpam-5288	240	7	k	k	X
ejpam-5288	240	8	,	,	PUNCT
ejpam-5288	240	9	(	(	PUNCT
ejpam-5288	240	10	n	n	CCONJ
ejpam-5288	240	11	≥	≥	NOUN
ejpam-5288	240	12	0	0	NUM
ejpam-5288	240	13	)	)	PUNCT
ejpam-5288	240	14	.	.	PUNCT
ejpam-5288	241	1	replacing	replace	VERB
ejpam-5288	241	2	y	y	PRON
ejpam-5288	241	3	by	by	ADP
ejpam-5288	241	4	y	y	PROPN
ejpam-5288	241	5	x	x	PROPN
ejpam-5288	241	6	and	and	CCONJ
ejpam-5288	241	7	letting	let	VERB
ejpam-5288	241	8	x	x	PRON
ejpam-5288	241	9	→	→	SYM
ejpam-5288	241	10	∞	∞	PROPN
ejpam-5288	241	11	,	,	PUNCT
ejpam-5288	241	12	we	we	PRON
ejpam-5288	241	13	see	see	VERB
ejpam-5288	241	14	that	that	DET
ejpam-5288	241	15	bl	bl	PROPN
ejpam-5288	241	16	n	n	CCONJ
ejpam-5288	241	17	,	,	PUNCT
ejpam-5288	241	18	λ(y	λ(y	NUM
ejpam-5288	241	19	)	)	PUNCT
ejpam-5288	241	20	=	=	SYM
ejpam-5288	241	21	limx→∞bl	limx→∞bl	NOUN
ejpam-5288	241	22	n	n	CCONJ
ejpam-5288	241	23	,	,	PUNCT
ejpam-5288	241	24	λ(x	λ(x	PROPN
ejpam-5288	241	25	,	,	PUNCT
ejpam-5288	241	26	y	y	PROPN
ejpam-5288	241	27	x	x	PROPN
ejpam-5288	241	28	)	)	PUNCT
ejpam-5288	241	29	.	.	PUNCT
ejpam-5288	242	1	for	for	ADP
ejpam-5288	242	2	r	r	NOUN
ejpam-5288	242	3	∈	∈	PROPN
ejpam-5288	242	4	n	n	NOUN
ejpam-5288	242	5	∪	∪	X
ejpam-5288	242	6	{	{	PUNCT
ejpam-5288	242	7	0	0	NUM
ejpam-5288	242	8	}	}	PUNCT
ejpam-5288	242	9	,	,	PUNCT
ejpam-5288	242	10	we	we	PRON
ejpam-5288	242	11	define	define	VERB
ejpam-5288	242	12	the	the	DET
ejpam-5288	242	13	λ	λ	NOUN
ejpam-5288	242	14	-	-	NOUN
ejpam-5288	242	15	analogues	analogue	NOUN
ejpam-5288	242	16	of	of	ADP
ejpam-5288	242	17	r	r	NOUN
ejpam-5288	242	18	-	-	PUNCT
ejpam-5288	242	19	lah	lah	NOUN
ejpam-5288	242	20	numbers	number	NOUN
ejpam-5288	242	21	by	by	ADP
ejpam-5288	242	22	⟨x+	⟨x+	NOUN
ejpam-5288	242	23	r⟩n	r⟩n	NOUN
ejpam-5288	242	24	,	,	PUNCT
ejpam-5288	242	25	λ	λ	PROPN
ejpam-5288	242	26	=	=	SYM
ejpam-5288	242	27	n∑	n∑	PROPN
ejpam-5288	242	28	k=0	k=0	PROPN
ejpam-5288	242	29	lr	lr	PROPN
ejpam-5288	242	30	,	,	PUNCT
ejpam-5288	242	31	λ(n	λ(n	PROPN
ejpam-5288	242	32	,	,	PUNCT
ejpam-5288	242	33	k)(x)k	k)(x)k	NOUN
ejpam-5288	242	34	,	,	PUNCT
ejpam-5288	242	35	λ	λ	PROPN
ejpam-5288	242	36	,	,	PUNCT
ejpam-5288	242	37	(	(	PUNCT
ejpam-5288	242	38	n	n	CCONJ
ejpam-5288	242	39	≥	≥	NOUN
ejpam-5288	242	40	0	0	NUM
ejpam-5288	242	41	)	)	PUNCT
ejpam-5288	242	42	.	.	PUNCT
ejpam-5288	243	1	(	(	PUNCT
ejpam-5288	243	2	39	39	NUM
ejpam-5288	243	3	)	)	PUNCT
ejpam-5288	243	4	from	from	ADP
ejpam-5288	243	5	(	(	PUNCT
ejpam-5288	243	6	39	39	NUM
ejpam-5288	243	7	)	)	PUNCT
ejpam-5288	243	8	,	,	PUNCT
ejpam-5288	243	9	we	we	PRON
ejpam-5288	243	10	note	note	VERB
ejpam-5288	244	1	that	that	SCONJ
ejpam-5288	244	2	e	e	PROPN
ejpam-5288	244	3	−(x+r	−(x+r	NOUN
ejpam-5288	244	4	)	)	PUNCT
ejpam-5288	244	5	λ	λ	PROPN
ejpam-5288	244	6	(	(	PUNCT
ejpam-5288	244	7	−t	−t	NOUN
ejpam-5288	244	8	)	)	PUNCT
ejpam-5288	244	9	=	=	PUNCT
ejpam-5288	245	1	∞∑	∞∑	ADJ
ejpam-5288	245	2	n=0	n=0	PROPN
ejpam-5288	245	3	⟨x+	⟨x+	NOUN
ejpam-5288	245	4	r⟩n	r⟩n	NOUN
ejpam-5288	245	5	,	,	PUNCT
ejpam-5288	245	6	λ	λ	PROPN
ejpam-5288	245	7	tn	tn	NOUN
ejpam-5288	245	8	n	n	ADV
ejpam-5288	245	9	!	!	PUNCT
ejpam-5288	245	10	=	=	NOUN
ejpam-5288	246	1	∞∑	∞∑	PRON
ejpam-5288	246	2	n=0	n=0	NUM
ejpam-5288	246	3	(	(	PUNCT
ejpam-5288	246	4	n∑	n∑	PROPN
ejpam-5288	246	5	k=0	k=0	PROPN
ejpam-5288	246	6	lr	lr	PROPN
ejpam-5288	246	7	,	,	PUNCT
ejpam-5288	246	8	λ(n	λ(n	PROPN
ejpam-5288	246	9	,	,	PUNCT
ejpam-5288	246	10	k)(x)k	k)(x)k	NOUN
ejpam-5288	246	11	,	,	PUNCT
ejpam-5288	246	12	λ	λ	PROPN
ejpam-5288	246	13	)	)	PUNCT
ejpam-5288	246	14	tn	tn	PROPN
ejpam-5288	246	15	n	n	PROPN
ejpam-5288	246	16	!	!	PUNCT
ejpam-5288	247	1	(	(	PUNCT
ejpam-5288	247	2	40	40	NUM
ejpam-5288	247	3	)	)	PUNCT
ejpam-5288	247	4	=	=	NOUN
ejpam-5288	248	1	∞∑	∞∑	NUM
ejpam-5288	248	2	k=0	k=0	PROPN
ejpam-5288	248	3	(	(	PUNCT
ejpam-5288	248	4	∞∑	∞∑	NUM
ejpam-5288	248	5	n	n	CCONJ
ejpam-5288	248	6	=	=	SYM
ejpam-5288	248	7	k	k	X
ejpam-5288	248	8	lr	lr	PROPN
ejpam-5288	248	9	,	,	PUNCT
ejpam-5288	248	10	λ(n	λ(n	PROPN
ejpam-5288	248	11	,	,	PUNCT
ejpam-5288	248	12	k	k	NOUN
ejpam-5288	248	13	)	)	PUNCT
ejpam-5288	248	14	tn	tn	PROPN
ejpam-5288	248	15	n	n	PROPN
ejpam-5288	248	16	!	!	PUNCT
ejpam-5288	248	17	)	)	PUNCT
ejpam-5288	249	1	(	(	PUNCT
ejpam-5288	249	2	x)k	x)k	NOUN
ejpam-5288	249	3	,	,	PUNCT
ejpam-5288	249	4	λ	λ	PROPN
ejpam-5288	249	5	.	.	PROPN
ejpam-5288	249	6	on	on	ADP
ejpam-5288	249	7	the	the	DET
ejpam-5288	249	8	other	other	ADJ
ejpam-5288	249	9	hand	hand	NOUN
ejpam-5288	249	10	,	,	PUNCT
ejpam-5288	249	11	by	by	ADP
ejpam-5288	249	12	binomial	binomial	ADJ
ejpam-5288	249	13	expansion	expansion	NOUN
ejpam-5288	249	14	,	,	PUNCT
ejpam-5288	249	15	we	we	PRON
ejpam-5288	249	16	get	get	VERB
ejpam-5288	249	17	e	e	NOUN
ejpam-5288	249	18	−(x+r	−(x+r	NOUN
ejpam-5288	249	19	)	)	PUNCT
ejpam-5288	250	1	λ	λ	PROPN
ejpam-5288	250	2	(	(	PUNCT
ejpam-5288	250	3	−t	−t	NOUN
ejpam-5288	250	4	)	)	PUNCT
ejpam-5288	250	5	=	=	PUNCT
ejpam-5288	250	6	(	(	PUNCT
ejpam-5288	250	7	1	1	NUM
ejpam-5288	250	8	1−	1−	NUM
ejpam-5288	250	9	λt	λt	ADP
ejpam-5288	250	10	)	)	PUNCT
ejpam-5288	250	11	r	r	NOUN
ejpam-5288	250	12	λ	λ	PROPN
ejpam-5288	250	13	(	(	PUNCT
ejpam-5288	250	14	1−	1−	NUM
ejpam-5288	250	15	λt)−	λt)−	NOUN
ejpam-5288	250	16	x	x	PUNCT
ejpam-5288	251	1	λ	λ	NOUN
ejpam-5288	251	2	=	=	SYM
ejpam-5288	251	3	(	(	PUNCT
ejpam-5288	251	4	1	1	NUM
ejpam-5288	251	5	1−	1−	NUM
ejpam-5288	251	6	λt	λt	ADP
ejpam-5288	251	7	)	)	PUNCT
ejpam-5288	251	8	r	r	NOUN
ejpam-5288	251	9	λ	λ	NOUN
ejpam-5288	251	10	(	(	PUNCT
ejpam-5288	251	11	1	1	NUM
ejpam-5288	251	12	+	+	CCONJ
ejpam-5288	251	13	λt	λt	ADP
ejpam-5288	251	14	1−	1−	NUM
ejpam-5288	251	15	λt	λt	ADP
ejpam-5288	251	16	)	)	PUNCT
ejpam-5288	251	17	x	x	PUNCT
ejpam-5288	251	18	λ	λ	X
ejpam-5288	251	19	(	(	PUNCT
ejpam-5288	251	20	41	41	NUM
ejpam-5288	251	21	)	)	PUNCT
ejpam-5288	251	22	j.	j.	PROPN
ejpam-5288	251	23	kwon	kwon	PROPN
ejpam-5288	251	24	et	et	PROPN
ejpam-5288	251	25	al	al	PROPN
ejpam-5288	251	26	.	.	PUNCT
ejpam-5288	251	27	/	/	SYM
ejpam-5288	251	28	eur	eur	PROPN
ejpam-5288	251	29	.	.	PUNCT
ejpam-5288	252	1	j.	j.	PROPN
ejpam-5288	252	2	pure	pure	PROPN
ejpam-5288	252	3	appl	appl	PROPN
ejpam-5288	252	4	.	.	PROPN
ejpam-5288	252	5	math	math	PROPN
ejpam-5288	252	6	,	,	PUNCT
ejpam-5288	252	7	17	17	NUM
ejpam-5288	252	8	(	(	PUNCT
ejpam-5288	252	9	3	3	NUM
ejpam-5288	252	10	)	)	PUNCT
ejpam-5288	252	11	(	(	PUNCT
ejpam-5288	252	12	2024	2024	NUM
ejpam-5288	252	13	)	)	PUNCT
ejpam-5288	252	14	,	,	PUNCT
ejpam-5288	252	15	1385	1385	NUM
ejpam-5288	252	16	-	-	SYM
ejpam-5288	252	17	1402	1402	NUM
ejpam-5288	252	18	1395	1395	NUM
ejpam-5288	252	19	=	=	PUNCT
ejpam-5288	253	1	∞∑	∞∑	NUM
ejpam-5288	253	2	k=0	k=0	PROPN
ejpam-5288	253	3	1	1	NUM
ejpam-5288	253	4	k	k	NOUN
ejpam-5288	253	5	!	!	PUNCT
ejpam-5288	254	1	(	(	PUNCT
ejpam-5288	254	2	t	t	PROPN
ejpam-5288	254	3	1−	1−	NUM
ejpam-5288	254	4	λt	λt	ADP
ejpam-5288	254	5	)	)	PUNCT
ejpam-5288	255	1	k	k	NOUN
ejpam-5288	255	2	(	(	PUNCT
ejpam-5288	255	3	1	1	NUM
ejpam-5288	255	4	1−	1−	NUM
ejpam-5288	255	5	λt	λt	ADP
ejpam-5288	255	6	)	)	PUNCT
ejpam-5288	255	7	r	r	NOUN
ejpam-5288	255	8	λ	λ	PROPN
ejpam-5288	255	9	(	(	PUNCT
ejpam-5288	255	10	x)k	x)k	NOUN
ejpam-5288	255	11	,	,	PUNCT
ejpam-5288	255	12	λ	λ	X
ejpam-5288	255	13	.	.	PUNCT
ejpam-5288	256	1	by	by	ADP
ejpam-5288	256	2	(	(	PUNCT
ejpam-5288	256	3	40	40	NUM
ejpam-5288	256	4	)	)	PUNCT
ejpam-5288	256	5	and	and	CCONJ
ejpam-5288	256	6	(	(	PUNCT
ejpam-5288	256	7	41	41	NUM
ejpam-5288	256	8	)	)	PUNCT
ejpam-5288	256	9	,	,	PUNCT
ejpam-5288	256	10	we	we	PRON
ejpam-5288	256	11	get	get	VERB
ejpam-5288	256	12	1	1	NUM
ejpam-5288	256	13	k	k	NOUN
ejpam-5288	256	14	!	!	PUNCT
ejpam-5288	257	1	(	(	PUNCT
ejpam-5288	257	2	t	t	PROPN
ejpam-5288	257	3	1−	1−	NUM
ejpam-5288	257	4	λt	λt	ADP
ejpam-5288	257	5	)	)	PUNCT
ejpam-5288	258	1	k	k	NOUN
ejpam-5288	258	2	(	(	PUNCT
ejpam-5288	258	3	1	1	NUM
ejpam-5288	258	4	1−	1−	NUM
ejpam-5288	258	5	λt	λt	ADP
ejpam-5288	258	6	)	)	PUNCT
ejpam-5288	258	7	r	r	NOUN
ejpam-5288	258	8	λ	λ	NOUN
ejpam-5288	258	9	=	=	SYM
ejpam-5288	259	1	∞∑	∞∑	NUM
ejpam-5288	259	2	n	n	CCONJ
ejpam-5288	259	3	=	=	SYM
ejpam-5288	259	4	k	k	X
ejpam-5288	259	5	lr	lr	PROPN
ejpam-5288	259	6	,	,	PUNCT
ejpam-5288	259	7	λ(n	λ(n	PROPN
ejpam-5288	259	8	,	,	PUNCT
ejpam-5288	259	9	k	k	NOUN
ejpam-5288	259	10	)	)	PUNCT
ejpam-5288	259	11	tn	tn	PROPN
ejpam-5288	259	12	n	n	PROPN
ejpam-5288	259	13	!	!	PROPN
ejpam-5288	259	14	,	,	PUNCT
ejpam-5288	259	15	(	(	PUNCT
ejpam-5288	259	16	k	k	X
ejpam-5288	259	17	≥	≥	PROPN
ejpam-5288	259	18	0	0	NUM
ejpam-5288	259	19	)	)	PUNCT
ejpam-5288	259	20	.	.	PUNCT
ejpam-5288	260	1	(	(	PUNCT
ejpam-5288	260	2	42	42	X
ejpam-5288	260	3	)	)	PUNCT
ejpam-5288	260	4	the	the	DET
ejpam-5288	260	5	left	left	ADJ
ejpam-5288	260	6	hand	hand	NOUN
ejpam-5288	260	7	side	side	NOUN
ejpam-5288	260	8	of	of	ADP
ejpam-5288	260	9	(	(	PUNCT
ejpam-5288	260	10	42	42	NUM
ejpam-5288	260	11	)	)	PUNCT
ejpam-5288	260	12	can	can	AUX
ejpam-5288	260	13	be	be	AUX
ejpam-5288	260	14	written	write	VERB
ejpam-5288	260	15	as	as	ADP
ejpam-5288	260	16	1	1	NUM
ejpam-5288	260	17	k	k	NOUN
ejpam-5288	260	18	!	!	PUNCT
ejpam-5288	261	1	(	(	PUNCT
ejpam-5288	261	2	t	t	PROPN
ejpam-5288	261	3	1−	1−	NUM
ejpam-5288	261	4	λt	λt	ADP
ejpam-5288	261	5	)	)	PUNCT
ejpam-5288	262	1	k	k	NOUN
ejpam-5288	262	2	(	(	PUNCT
ejpam-5288	262	3	1	1	NUM
ejpam-5288	262	4	1−	1−	NUM
ejpam-5288	262	5	λt	λt	ADP
ejpam-5288	262	6	)	)	PUNCT
ejpam-5288	262	7	r	r	NOUN
ejpam-5288	262	8	λ	λ	NOUN
ejpam-5288	262	9	=	=	NOUN
ejpam-5288	262	10	1	1	NUM
ejpam-5288	262	11	λk	λk	ADP
ejpam-5288	262	12	1	1	NUM
ejpam-5288	262	13	k	k	NOUN
ejpam-5288	262	14	!	!	PUNCT
ejpam-5288	263	1	(	(	PUNCT
ejpam-5288	263	2	1	1	NUM
ejpam-5288	263	3	1−	1−	NUM
ejpam-5288	263	4	λt	λt	ADP
ejpam-5288	263	5	−	−	PROPN
ejpam-5288	263	6	1	1	NUM
ejpam-5288	263	7	)	)	PUNCT
ejpam-5288	263	8	k	k	NOUN
ejpam-5288	263	9	(	(	PUNCT
ejpam-5288	263	10	1	1	NUM
ejpam-5288	263	11	1−	1−	NUM
ejpam-5288	263	12	λt	λt	ADP
ejpam-5288	263	13	)	)	PUNCT
ejpam-5288	263	14	r	r	NOUN
ejpam-5288	263	15	λ	λ	PROPN
ejpam-5288	263	16	(	(	PUNCT
ejpam-5288	263	17	43	43	NUM
ejpam-5288	263	18	)	)	PUNCT
ejpam-5288	263	19	=	=	VERB
ejpam-5288	264	1	k∑	k∑	PROPN
ejpam-5288	265	1	l=0	l=0	PROPN
ejpam-5288	265	2	(	(	PUNCT
ejpam-5288	265	3	k	k	NOUN
ejpam-5288	265	4	l	l	NOUN
ejpam-5288	265	5	)	)	PUNCT
ejpam-5288	265	6	(	(	PUNCT
ejpam-5288	265	7	−1)k−l	−1)k−l	NOUN
ejpam-5288	265	8	1	1	NUM
ejpam-5288	265	9	λk	λk	PROPN
ejpam-5288	265	10	1	1	NUM
ejpam-5288	265	11	k	k	NOUN
ejpam-5288	265	12	!	!	PUNCT
ejpam-5288	266	1	(	(	PUNCT
ejpam-5288	266	2	1	1	NUM
ejpam-5288	266	3	1−	1−	NUM
ejpam-5288	266	4	λt	λt	ADP
ejpam-5288	266	5	)	)	PUNCT
ejpam-5288	266	6	r+lλ	r+lλ	PROPN
ejpam-5288	266	7	λ	λ	X
ejpam-5288	267	1	=	=	SYM
ejpam-5288	268	1	k∑	k∑	PROPN
ejpam-5288	269	1	l=0	l=0	PROPN
ejpam-5288	269	2	(	(	PUNCT
ejpam-5288	269	3	k	k	NOUN
ejpam-5288	269	4	l	l	NOUN
ejpam-5288	269	5	)	)	PUNCT
ejpam-5288	269	6	(	(	PUNCT
ejpam-5288	269	7	−1)k−l	−1)k−l	NOUN
ejpam-5288	269	8	1	1	NUM
ejpam-5288	269	9	λkk	λkk	NOUN
ejpam-5288	269	10	!	!	PUNCT
ejpam-5288	270	1	∞∑	∞∑	PRON
ejpam-5288	270	2	n=0	n=0	NUM
ejpam-5288	270	3	⟨r	⟨r	NOUN
ejpam-5288	270	4	+	+	NUM
ejpam-5288	270	5	lλ⟩n	lλ⟩n	NOUN
ejpam-5288	270	6	,	,	PUNCT
ejpam-5288	270	7	λ	λ	PROPN
ejpam-5288	270	8	tn	tn	NOUN
ejpam-5288	270	9	n	n	ADV
ejpam-5288	270	10	!	!	PUNCT
ejpam-5288	270	11	=	=	NOUN
ejpam-5288	271	1	∞∑	∞∑	NUM
ejpam-5288	271	2	n=0	n=0	NUM
ejpam-5288	271	3	(	(	PUNCT
ejpam-5288	271	4	1	1	NUM
ejpam-5288	271	5	λkk	λkk	NOUN
ejpam-5288	271	6	!	!	PUNCT
ejpam-5288	271	7	k∑	k∑	VERB
ejpam-5288	272	1	l=0	l=0	PROPN
ejpam-5288	272	2	(	(	PUNCT
ejpam-5288	272	3	k	k	NOUN
ejpam-5288	272	4	l	l	NOUN
ejpam-5288	272	5	)	)	PUNCT
ejpam-5288	272	6	(	(	PUNCT
ejpam-5288	272	7	−1)k−l⟨r	−1)k−l⟨r	NUM
ejpam-5288	272	8	+	+	CCONJ
ejpam-5288	272	9	lλ⟩n	lλ⟩n	NOUN
ejpam-5288	272	10	,	,	PUNCT
ejpam-5288	272	11	λ	λ	PROPN
ejpam-5288	272	12	)	)	PUNCT
ejpam-5288	272	13	tn	tn	PROPN
ejpam-5288	272	14	n	n	PROPN
ejpam-5288	272	15	!	!	PUNCT
ejpam-5288	272	16	.	.	PUNCT
ejpam-5288	273	1	therefore	therefore	ADV
ejpam-5288	273	2	,	,	PUNCT
ejpam-5288	273	3	by	by	ADP
ejpam-5288	273	4	(	(	PUNCT
ejpam-5288	273	5	42	42	NUM
ejpam-5288	273	6	)	)	PUNCT
ejpam-5288	273	7	and	and	CCONJ
ejpam-5288	273	8	(	(	PUNCT
ejpam-5288	273	9	43	43	NUM
ejpam-5288	273	10	)	)	PUNCT
ejpam-5288	273	11	,	,	PUNCT
ejpam-5288	273	12	we	we	PRON
ejpam-5288	273	13	obtain	obtain	VERB
ejpam-5288	273	14	the	the	DET
ejpam-5288	273	15	following	follow	VERB
ejpam-5288	273	16	theorem	theorem	VERB
ejpam-5288	273	17	.	.	PUNCT
ejpam-5288	273	18	theorem	theorem	PROPN
ejpam-5288	273	19	6	6	NUM
ejpam-5288	273	20	.	.	PUNCT
ejpam-5288	273	21	for	for	ADP
ejpam-5288	273	22	n	n	PRON
ejpam-5288	273	23	,	,	PUNCT
ejpam-5288	273	24	k	k	X
ejpam-5288	273	25	≥	≥	PROPN
ejpam-5288	273	26	0	0	NUM
ejpam-5288	273	27	,	,	PUNCT
ejpam-5288	273	28	with	with	ADP
ejpam-5288	273	29	n	n	PRON
ejpam-5288	273	30	≥	≥	NOUN
ejpam-5288	273	31	k	k	NOUN
ejpam-5288	273	32	,	,	PUNCT
ejpam-5288	273	33	we	we	PRON
ejpam-5288	273	34	have	have	VERB
ejpam-5288	273	35	lr	lr	NOUN
ejpam-5288	273	36	,	,	PUNCT
ejpam-5288	273	37	λ(n	λ(n	PROPN
ejpam-5288	273	38	,	,	PUNCT
ejpam-5288	273	39	k	k	NOUN
ejpam-5288	273	40	)	)	PUNCT
ejpam-5288	273	41	=	=	SYM
ejpam-5288	273	42	1	1	NUM
ejpam-5288	273	43	λk	λk	ADP
ejpam-5288	273	44	1	1	NUM
ejpam-5288	273	45	k	k	X
ejpam-5288	273	46	!	!	PUNCT
ejpam-5288	273	47	k∑	k∑	PROPN
ejpam-5288	274	1	l=0	l=0	PROPN
ejpam-5288	274	2	(	(	PUNCT
ejpam-5288	274	3	k	k	NOUN
ejpam-5288	274	4	l	l	NOUN
ejpam-5288	274	5	)	)	PUNCT
ejpam-5288	274	6	(	(	PUNCT
ejpam-5288	274	7	−1)k−l⟨r	−1)k−l⟨r	NUM
ejpam-5288	274	8	+	+	CCONJ
ejpam-5288	274	9	lλ⟩n	lλ⟩n	NOUN
ejpam-5288	274	10	,	,	PUNCT
ejpam-5288	274	11	λ	λ	NOUN
ejpam-5288	274	12	.	.	PROPN
ejpam-5288	274	13	from	from	ADP
ejpam-5288	274	14	(	(	PUNCT
ejpam-5288	274	15	39	39	NUM
ejpam-5288	274	16	)	)	PUNCT
ejpam-5288	274	17	,	,	PUNCT
ejpam-5288	274	18	we	we	PRON
ejpam-5288	274	19	note	note	VERB
ejpam-5288	274	20	that	that	SCONJ
ejpam-5288	274	21	n+1∑	n+1∑	PROPN
ejpam-5288	274	22	k=0	k=0	PUNCT
ejpam-5288	274	23	lr	lr	PROPN
ejpam-5288	274	24	,	,	PUNCT
ejpam-5288	274	25	λ(n+	λ(n+	NOUN
ejpam-5288	274	26	1	1	NUM
ejpam-5288	274	27	,	,	PUNCT
ejpam-5288	274	28	k)(x)k	k)(x)k	NOUN
ejpam-5288	274	29	,	,	PUNCT
ejpam-5288	274	30	λ	λ	NOUN
ejpam-5288	274	31	=	=	SYM
ejpam-5288	275	1	⟨x+	⟨x+	NOUN
ejpam-5288	275	2	r⟩n+1,λ	r⟩n+1,λ	NOUN
ejpam-5288	275	3	=	=	NOUN
ejpam-5288	275	4	⟨x+	⟨x+	NOUN
ejpam-5288	275	5	r⟩n	r⟩n	NOUN
ejpam-5288	275	6	,	,	PUNCT
ejpam-5288	275	7	λ(x+	λ(x+	PRON
ejpam-5288	275	8	r	r	NOUN
ejpam-5288	275	9	+	+	NUM
ejpam-5288	275	10	nλ	nλ	NUM
ejpam-5288	275	11	)	)	PUNCT
ejpam-5288	275	12	(	(	PUNCT
ejpam-5288	275	13	44	44	NUM
ejpam-5288	275	14	)	)	PUNCT
ejpam-5288	275	15	=	=	SYM
ejpam-5288	276	1	n∑	n∑	PROPN
ejpam-5288	276	2	k=0	k=0	PROPN
ejpam-5288	276	3	lr	lr	PROPN
ejpam-5288	276	4	,	,	PUNCT
ejpam-5288	276	5	λ(x)k	λ(x)k	PROPN
ejpam-5288	276	6	,	,	PUNCT
ejpam-5288	276	7	λ	λ	PROPN
ejpam-5288	276	8	(	(	PUNCT
ejpam-5288	276	9	x−	x−	PROPN
ejpam-5288	276	10	kλ+	kλ+	PROPN
ejpam-5288	276	11	r	r	NOUN
ejpam-5288	276	12	+	+	NUM
ejpam-5288	276	13	(	(	PUNCT
ejpam-5288	276	14	n+	n+	X
ejpam-5288	276	15	k)λ	k)λ	X
ejpam-5288	276	16	)	)	PUNCT
ejpam-5288	277	1	=	=	SYM
ejpam-5288	277	2	n∑	n∑	PROPN
ejpam-5288	277	3	k=0	k=0	PROPN
ejpam-5288	277	4	lr	lr	PROPN
ejpam-5288	277	5	,	,	PUNCT
ejpam-5288	277	6	λ(n	λ(n	PROPN
ejpam-5288	277	7	,	,	PUNCT
ejpam-5288	277	8	k)(x)k+1,λ	k)(x)k+1,λ	X
ejpam-5288	278	1	+	+	CCONJ
ejpam-5288	278	2	n∑	n∑	PROPN
ejpam-5288	278	3	k=0	k=0	PROPN
ejpam-5288	278	4	lr	lr	PROPN
ejpam-5288	278	5	,	,	PUNCT
ejpam-5288	278	6	λ(n	λ(n	PROPN
ejpam-5288	278	7	,	,	PUNCT
ejpam-5288	278	8	k	k	NOUN
ejpam-5288	278	9	)	)	PUNCT
ejpam-5288	278	10	(	(	PUNCT
ejpam-5288	278	11	r	r	NOUN
ejpam-5288	278	12	+	+	CCONJ
ejpam-5288	278	13	(	(	PUNCT
ejpam-5288	278	14	n+	n+	X
ejpam-5288	278	15	k)λ	k)λ	X
ejpam-5288	278	16	)	)	PUNCT
ejpam-5288	278	17	(	(	PUNCT
ejpam-5288	278	18	x)k	x)k	X
ejpam-5288	278	19	,	,	PUNCT
ejpam-5288	278	20	λ	λ	X
ejpam-5288	278	21	=	=	PROPN
ejpam-5288	278	22	n+1∑	n+1∑	PROPN
ejpam-5288	278	23	k=0	k=0	PROPN
ejpam-5288	278	24	(	(	PUNCT
ejpam-5288	278	25	lr	lr	INTJ
ejpam-5288	278	26	,	,	PUNCT
ejpam-5288	278	27	λ(n	λ(n	PROPN
ejpam-5288	278	28	,	,	PUNCT
ejpam-5288	278	29	k	k	PROPN
ejpam-5288	278	30	−	−	PROPN
ejpam-5288	278	31	1	1	NUM
ejpam-5288	278	32	)	)	PUNCT
ejpam-5288	278	33	+	+	CCONJ
ejpam-5288	278	34	(	(	PUNCT
ejpam-5288	278	35	r	r	NOUN
ejpam-5288	278	36	+	+	CCONJ
ejpam-5288	278	37	(	(	PUNCT
ejpam-5288	278	38	n+	n+	X
ejpam-5288	278	39	k)λ	k)λ	X
ejpam-5288	278	40	)	)	PUNCT
ejpam-5288	278	41	lr	lr	NOUN
ejpam-5288	278	42	,	,	PUNCT
ejpam-5288	278	43	λ(n	λ(n	PROPN
ejpam-5288	278	44	,	,	PUNCT
ejpam-5288	278	45	k	k	NOUN
ejpam-5288	278	46	)	)	PUNCT
ejpam-5288	278	47	)	)	PUNCT
ejpam-5288	278	48	(	(	PUNCT
ejpam-5288	278	49	x)k	x)k	NOUN
ejpam-5288	278	50	,	,	PUNCT
ejpam-5288	278	51	λ	λ	X
ejpam-5288	278	52	.	.	NOUN
ejpam-5288	278	53	comparing	compare	VERB
ejpam-5288	278	54	the	the	DET
ejpam-5288	278	55	coefficients	coefficient	NOUN
ejpam-5288	278	56	on	on	ADP
ejpam-5288	278	57	both	both	DET
ejpam-5288	278	58	sides	side	NOUN
ejpam-5288	278	59	of	of	ADP
ejpam-5288	278	60	(	(	PUNCT
ejpam-5288	278	61	44	44	NUM
ejpam-5288	278	62	)	)	PUNCT
ejpam-5288	278	63	,	,	PUNCT
ejpam-5288	278	64	we	we	PRON
ejpam-5288	278	65	obtain	obtain	VERB
ejpam-5288	278	66	the	the	DET
ejpam-5288	278	67	following	follow	VERB
ejpam-5288	278	68	theorem	theorem	PROPN
ejpam-5288	278	69	.	.	PUNCT
ejpam-5288	279	1	j.	j.	PROPN
ejpam-5288	279	2	kwon	kwon	PROPN
ejpam-5288	279	3	et	et	PROPN
ejpam-5288	279	4	al	al	PROPN
ejpam-5288	279	5	.	.	PUNCT
ejpam-5288	279	6	/	/	SYM
ejpam-5288	279	7	eur	eur	PROPN
ejpam-5288	279	8	.	.	PUNCT
ejpam-5288	280	1	j.	j.	PROPN
ejpam-5288	280	2	pure	pure	PROPN
ejpam-5288	280	3	appl	appl	PROPN
ejpam-5288	280	4	.	.	PROPN
ejpam-5288	280	5	math	math	PROPN
ejpam-5288	280	6	,	,	PUNCT
ejpam-5288	280	7	17	17	NUM
ejpam-5288	280	8	(	(	PUNCT
ejpam-5288	280	9	3	3	NUM
ejpam-5288	280	10	)	)	PUNCT
ejpam-5288	280	11	(	(	PUNCT
ejpam-5288	280	12	2024	2024	NUM
ejpam-5288	280	13	)	)	PUNCT
ejpam-5288	280	14	,	,	PUNCT
ejpam-5288	280	15	1385	1385	NUM
ejpam-5288	280	16	-	-	SYM
ejpam-5288	280	17	1402	1402	NUM
ejpam-5288	280	18	1396	1396	NUM
ejpam-5288	280	19	theorem	theorem	VERB
ejpam-5288	280	20	7	7	NUM
ejpam-5288	280	21	.	.	NOUN
ejpam-5288	280	22	for	for	ADP
ejpam-5288	280	23	n	n	PRON
ejpam-5288	280	24	,	,	PUNCT
ejpam-5288	280	25	k	k	PROPN
ejpam-5288	280	26	∈	∈	PROPN
ejpam-5288	280	27	n	n	CCONJ
ejpam-5288	280	28	,	,	PUNCT
ejpam-5288	280	29	with	with	ADP
ejpam-5288	280	30	n	n	PRON
ejpam-5288	280	31	≥	≥	NOUN
ejpam-5288	280	32	k	k	NOUN
ejpam-5288	280	33	,	,	PUNCT
ejpam-5288	280	34	we	we	PRON
ejpam-5288	280	35	have	have	VERB
ejpam-5288	280	36	lr	lr	NOUN
ejpam-5288	280	37	,	,	PUNCT
ejpam-5288	280	38	λ(n+	λ(n+	NOUN
ejpam-5288	280	39	1	1	NUM
ejpam-5288	280	40	,	,	PUNCT
ejpam-5288	280	41	k	k	NOUN
ejpam-5288	280	42	)	)	PUNCT
ejpam-5288	280	43	=	=	SYM
ejpam-5288	281	1	lr	lr	NOUN
ejpam-5288	281	2	,	,	PUNCT
ejpam-5288	281	3	λ(n	λ(n	PROPN
ejpam-5288	281	4	,	,	PUNCT
ejpam-5288	281	5	k	k	PROPN
ejpam-5288	281	6	−	−	PROPN
ejpam-5288	281	7	1	1	NUM
ejpam-5288	281	8	)	)	PUNCT
ejpam-5288	281	9	+	+	CCONJ
ejpam-5288	282	1	(	(	PUNCT
ejpam-5288	282	2	r	r	NOUN
ejpam-5288	282	3	+	+	CCONJ
ejpam-5288	282	4	(	(	PUNCT
ejpam-5288	282	5	n+	n+	X
ejpam-5288	282	6	k)λ	k)λ	X
ejpam-5288	282	7	)	)	PUNCT
ejpam-5288	282	8	lr	lr	NOUN
ejpam-5288	282	9	,	,	PUNCT
ejpam-5288	282	10	λ(n	λ(n	PROPN
ejpam-5288	282	11	,	,	PUNCT
ejpam-5288	282	12	k	k	NOUN
ejpam-5288	282	13	)	)	PUNCT
ejpam-5288	282	14	.	.	PUNCT
ejpam-5288	283	1	now	now	ADV
ejpam-5288	283	2	,	,	PUNCT
ejpam-5288	283	3	we	we	PRON
ejpam-5288	283	4	consider	consider	VERB
ejpam-5288	283	5	the	the	DET
ejpam-5288	283	6	r	r	NOUN
ejpam-5288	283	7	-	-	PUNCT
ejpam-5288	283	8	extended	extend	VERB
ejpam-5288	283	9	λ	λ	NOUN
ejpam-5288	283	10	-	-	PUNCT
ejpam-5288	283	11	lah	lah	ADJ
ejpam-5288	283	12	-	-	PUNCT
ejpam-5288	283	13	bell	bell	NOUN
ejpam-5288	283	14	polynomials	polynomial	NOUN
ejpam-5288	283	15	defined	define	VERB
ejpam-5288	283	16	by	by	ADP
ejpam-5288	283	17	lb	lb	DET
ejpam-5288	283	18	(	(	PUNCT
ejpam-5288	283	19	r	r	NOUN
ejpam-5288	283	20	)	)	PUNCT
ejpam-5288	283	21	n	n	CCONJ
ejpam-5288	283	22	,	,	PUNCT
ejpam-5288	283	23	λ(x	λ(x	PROPN
ejpam-5288	283	24	)	)	PUNCT
ejpam-5288	284	1	=	=	SYM
ejpam-5288	284	2	n∑	n∑	PROPN
ejpam-5288	284	3	k=0	k=0	PROPN
ejpam-5288	285	1	lr	lr	PROPN
ejpam-5288	285	2	,	,	PUNCT
ejpam-5288	285	3	λ(n	λ(n	PROPN
ejpam-5288	285	4	,	,	PUNCT
ejpam-5288	285	5	k)x	k)x	X
ejpam-5288	285	6	k	k	X
ejpam-5288	285	7	,	,	PUNCT
ejpam-5288	285	8	(	(	PUNCT
ejpam-5288	285	9	n	n	CCONJ
ejpam-5288	285	10	≥	≥	NOUN
ejpam-5288	285	11	0	0	NUM
ejpam-5288	285	12	)	)	PUNCT
ejpam-5288	285	13	.	.	PUNCT
ejpam-5288	286	1	(	(	PUNCT
ejpam-5288	286	2	45	45	NUM
ejpam-5288	286	3	)	)	PUNCT
ejpam-5288	286	4	thus	thus	ADV
ejpam-5288	286	5	,	,	PUNCT
ejpam-5288	286	6	by	by	ADP
ejpam-5288	286	7	(	(	PUNCT
ejpam-5288	286	8	42	42	NUM
ejpam-5288	286	9	)	)	PUNCT
ejpam-5288	286	10	and	and	CCONJ
ejpam-5288	286	11	(	(	PUNCT
ejpam-5288	286	12	45	45	NUM
ejpam-5288	286	13	)	)	PUNCT
ejpam-5288	286	14	,	,	PUNCT
ejpam-5288	286	15	we	we	PRON
ejpam-5288	286	16	easily	easily	ADV
ejpam-5288	286	17	get	get	VERB
ejpam-5288	286	18	e	e	NOUN
ejpam-5288	286	19	x	x	PART
ejpam-5288	286	20	λ	λ	X
ejpam-5288	286	21	(	(	PUNCT
ejpam-5288	286	22	1	1	NUM
ejpam-5288	286	23	1−λt	1−λt	NUM
ejpam-5288	286	24	−1	−1	NOUN
ejpam-5288	286	25	)	)	PUNCT
ejpam-5288	286	26	(	(	PUNCT
ejpam-5288	286	27	1	1	NUM
ejpam-5288	286	28	1−	1−	NUM
ejpam-5288	286	29	λt	λt	ADP
ejpam-5288	286	30	)	)	PUNCT
ejpam-5288	286	31	r	r	NOUN
ejpam-5288	286	32	λ	λ	NOUN
ejpam-5288	286	33	=	=	PUNCT
ejpam-5288	287	1	∞∑	∞∑	PROPN
ejpam-5288	287	2	n=0	n=0	NUM
ejpam-5288	287	3	lb	lb	ADP
ejpam-5288	287	4	(	(	PUNCT
ejpam-5288	287	5	r	r	NOUN
ejpam-5288	287	6	)	)	PUNCT
ejpam-5288	287	7	n	n	CCONJ
ejpam-5288	287	8	,	,	PUNCT
ejpam-5288	287	9	λ(x	λ(x	PROPN
ejpam-5288	287	10	)	)	PUNCT
ejpam-5288	287	11	tn	tn	PROPN
ejpam-5288	287	12	n	n	PROPN
ejpam-5288	287	13	!	!	PUNCT
ejpam-5288	287	14	.	.	PUNCT
ejpam-5288	288	1	(	(	PUNCT
ejpam-5288	288	2	46	46	NUM
ejpam-5288	288	3	)	)	PUNCT
ejpam-5288	288	4	in	in	ADP
ejpam-5288	288	5	particular	particular	ADJ
ejpam-5288	288	6	,	,	PUNCT
ejpam-5288	288	7	for	for	ADP
ejpam-5288	288	8	x	x	SYM
ejpam-5288	288	9	=	=	SYM
ejpam-5288	288	10	1	1	NUM
ejpam-5288	288	11	,	,	PUNCT
ejpam-5288	288	12	lb	lb	PRON
ejpam-5288	288	13	(	(	PUNCT
ejpam-5288	288	14	r	r	NOUN
ejpam-5288	288	15	)	)	PUNCT
ejpam-5288	288	16	n	n	CCONJ
ejpam-5288	288	17	,	,	PUNCT
ejpam-5288	288	18	λ	λ	X
ejpam-5288	288	19	=	=	VERB
ejpam-5288	288	20	lb	lb	X
ejpam-5288	288	21	(	(	PUNCT
ejpam-5288	288	22	r	r	NOUN
ejpam-5288	288	23	)	)	PUNCT
ejpam-5288	288	24	n	n	CCONJ
ejpam-5288	288	25	,	,	PUNCT
ejpam-5288	288	26	λ(1	λ(1	PROPN
ejpam-5288	288	27	)	)	PUNCT
ejpam-5288	288	28	are	be	AUX
ejpam-5288	288	29	called	call	VERB
ejpam-5288	288	30	the	the	DET
ejpam-5288	288	31	r	r	NOUN
ejpam-5288	288	32	-	-	PUNCT
ejpam-5288	288	33	extended	extend	VERB
ejpam-5288	288	34	λ	λ	NOUN
ejpam-5288	288	35	-	-	PUNCT
ejpam-5288	288	36	lah	lah	ADJ
ejpam-5288	288	37	-	-	PUNCT
ejpam-5288	288	38	bell	bell	NOUN
ejpam-5288	288	39	numbers	number	NOUN
ejpam-5288	288	40	.	.	PUNCT
ejpam-5288	289	1	the	the	DET
ejpam-5288	289	2	left	left	ADJ
ejpam-5288	289	3	hand	hand	NOUN
ejpam-5288	289	4	side	side	NOUN
ejpam-5288	289	5	of	of	ADP
ejpam-5288	289	6	(	(	PUNCT
ejpam-5288	289	7	46	46	NUM
ejpam-5288	289	8	)	)	PUNCT
ejpam-5288	289	9	can	can	AUX
ejpam-5288	289	10	be	be	AUX
ejpam-5288	289	11	written	write	VERB
ejpam-5288	289	12	as	as	ADP
ejpam-5288	289	13	e	e	X
ejpam-5288	289	14	x	x	PROPN
ejpam-5288	289	15	λ	λ	X
ejpam-5288	289	16	(	(	PUNCT
ejpam-5288	289	17	1	1	NUM
ejpam-5288	289	18	1−λt	1−λt	NUM
ejpam-5288	289	19	−1	−1	NOUN
ejpam-5288	289	20	)	)	PUNCT
ejpam-5288	289	21	(	(	PUNCT
ejpam-5288	289	22	1	1	NUM
ejpam-5288	289	23	1−	1−	NUM
ejpam-5288	289	24	λt	λt	ADP
ejpam-5288	289	25	)	)	PUNCT
ejpam-5288	289	26	r	r	NOUN
ejpam-5288	289	27	λ	λ	NOUN
ejpam-5288	289	28	=	=	PUNCT
ejpam-5288	289	29	e−	e−	PROPN
ejpam-5288	289	30	x	x	PUNCT
ejpam-5288	290	1	λ	λ	PROPN
ejpam-5288	290	2	∞∑	∞∑	PROPN
ejpam-5288	290	3	k=0	k=0	PROPN
ejpam-5288	290	4	xk	xk	PROPN
ejpam-5288	290	5	λk!k	λk!k	PROPN
ejpam-5288	290	6	!	!	PUNCT
ejpam-5288	291	1	(	(	PUNCT
ejpam-5288	291	2	1	1	NUM
ejpam-5288	291	3	1−	1−	NUM
ejpam-5288	291	4	λt	λt	ADP
ejpam-5288	291	5	)	)	PUNCT
ejpam-5288	291	6	λk+r	λk+r	PROPN
ejpam-5288	291	7	λ	λ	PROPN
ejpam-5288	291	8	(	(	PUNCT
ejpam-5288	291	9	47	47	NUM
ejpam-5288	291	10	)	)	PUNCT
ejpam-5288	291	11	=	=	PUNCT
ejpam-5288	292	1	e−	e−	NOUN
ejpam-5288	292	2	x	x	PUNCT
ejpam-5288	292	3	λ	λ	PROPN
ejpam-5288	292	4	∞∑	∞∑	PROPN
ejpam-5288	292	5	k=0	k=0	PUNCT
ejpam-5288	292	6	xk	xk	PROPN
ejpam-5288	292	7	λkk	λkk	NOUN
ejpam-5288	292	8	!	!	PUNCT
ejpam-5288	293	1	∞∑	∞∑	PRON
ejpam-5288	293	2	n=0	n=0	NUM
ejpam-5288	293	3	⟨λk	⟨λk	X
ejpam-5288	294	1	+	+	PUNCT
ejpam-5288	294	2	r⟩n	r⟩n	NOUN
ejpam-5288	294	3	,	,	PUNCT
ejpam-5288	294	4	λ	λ	PROPN
ejpam-5288	294	5	tn	tn	NOUN
ejpam-5288	294	6	n	n	ADV
ejpam-5288	294	7	!	!	PUNCT
ejpam-5288	294	8	=	=	NOUN
ejpam-5288	295	1	∞∑	∞∑	PRON
ejpam-5288	295	2	n=0	n=0	NUM
ejpam-5288	295	3	(	(	PUNCT
ejpam-5288	295	4	e−	e−	PROPN
ejpam-5288	295	5	x	x	SYM
ejpam-5288	295	6	λ	λ	PROPN
ejpam-5288	295	7	∞∑	∞∑	PROPN
ejpam-5288	295	8	k=0	k=0	PROPN
ejpam-5288	295	9	⟨λk	⟨λk	X
ejpam-5288	296	1	+	+	CCONJ
ejpam-5288	296	2	r⟩n	r⟩n	NOUN
ejpam-5288	296	3	,	,	PUNCT
ejpam-5288	296	4	λ	λ	X
ejpam-5288	296	5	λkk	λkk	NOUN
ejpam-5288	296	6	!	!	PUNCT
ejpam-5288	296	7	xk	xk	PROPN
ejpam-5288	296	8	)	)	PUNCT
ejpam-5288	296	9	tn	tn	PROPN
ejpam-5288	297	1	n	n	PROPN
ejpam-5288	297	2	!	!	PUNCT
ejpam-5288	297	3	.	.	PUNCT
ejpam-5288	298	1	therefore	therefore	ADV
ejpam-5288	298	2	,	,	PUNCT
ejpam-5288	298	3	by	by	ADP
ejpam-5288	298	4	(	(	PUNCT
ejpam-5288	298	5	46	46	NUM
ejpam-5288	298	6	)	)	PUNCT
ejpam-5288	298	7	and	and	CCONJ
ejpam-5288	298	8	(	(	PUNCT
ejpam-5288	298	9	47	47	NUM
ejpam-5288	298	10	)	)	PUNCT
ejpam-5288	298	11	,	,	PUNCT
ejpam-5288	298	12	we	we	PRON
ejpam-5288	298	13	obtain	obtain	VERB
ejpam-5288	298	14	the	the	DET
ejpam-5288	298	15	following	follow	VERB
ejpam-5288	298	16	theorem	theorem	VERB
ejpam-5288	298	17	.	.	PUNCT
ejpam-5288	298	18	theorem	theorem	ADJ
ejpam-5288	298	19	8	8	NUM
ejpam-5288	298	20	.	.	PUNCT
ejpam-5288	298	21	for	for	ADP
ejpam-5288	298	22	n	n	PRON
ejpam-5288	298	23	≥	≥	NOUN
ejpam-5288	298	24	0	0	NUM
ejpam-5288	298	25	,	,	PUNCT
ejpam-5288	298	26	we	we	PRON
ejpam-5288	298	27	have	have	VERB
ejpam-5288	298	28	lb	lb	NUM
ejpam-5288	298	29	(	(	PUNCT
ejpam-5288	298	30	r	r	NOUN
ejpam-5288	298	31	)	)	PUNCT
ejpam-5288	298	32	n	n	CCONJ
ejpam-5288	298	33	,	,	PUNCT
ejpam-5288	298	34	λ(x	λ(x	X
ejpam-5288	298	35	)	)	PUNCT
ejpam-5288	298	36	=	=	PUNCT
ejpam-5288	299	1	e−	e−	NOUN
ejpam-5288	299	2	x	x	PUNCT
ejpam-5288	299	3	λ	λ	PROPN
ejpam-5288	299	4	∞∑	∞∑	PROPN
ejpam-5288	299	5	k=0	k=0	PROPN
ejpam-5288	299	6	⟨λk	⟨λk	X
ejpam-5288	300	1	+	+	CCONJ
ejpam-5288	300	2	r⟩n	r⟩n	NOUN
ejpam-5288	300	3	,	,	PUNCT
ejpam-5288	300	4	λ	λ	PROPN
ejpam-5288	300	5	k!λk	k!λk	PROPN
ejpam-5288	300	6	xk	xk	PROPN
ejpam-5288	300	7	.	.	PROPN
ejpam-5288	300	8	for	for	ADP
ejpam-5288	300	9	r	r	PROPN
ejpam-5288	300	10	≥	≥	NOUN
ejpam-5288	300	11	0	0	NUM
ejpam-5288	300	12	,	,	PUNCT
ejpam-5288	300	13	the	the	DET
ejpam-5288	300	14	λ	λ	NOUN
ejpam-5288	300	15	-	-	NOUN
ejpam-5288	300	16	analogues	analogue	NOUN
ejpam-5288	300	17	of	of	ADP
ejpam-5288	300	18	r	r	NOUN
ejpam-5288	300	19	-	-	PUNCT
ejpam-5288	300	20	stirling	stirling	NOUN
ejpam-5288	300	21	numbers	number	NOUN
ejpam-5288	300	22	of	of	ADP
ejpam-5288	300	23	the	the	DET
ejpam-5288	300	24	second	second	ADJ
ejpam-5288	300	25	kind	kind	NOUN
ejpam-5288	300	26	are	be	AUX
ejpam-5288	300	27	defined	define	VERB
ejpam-5288	300	28	by	by	ADP
ejpam-5288	300	29	∞∑	∞∑	NUM
ejpam-5288	300	30	n	n	X
ejpam-5288	300	31	=	=	SYM
ejpam-5288	300	32	k	k	X
ejpam-5288	300	33	{	{	PUNCT
ejpam-5288	301	1	n+	n+	ADP
ejpam-5288	301	2	r	r	NOUN
ejpam-5288	301	3	k	k	NOUN
ejpam-5288	302	1	+	+	CCONJ
ejpam-5288	302	2	r	r	NOUN
ejpam-5288	302	3	}	}	PUNCT
ejpam-5288	302	4	r	r	NOUN
ejpam-5288	302	5	,	,	PUNCT
ejpam-5288	302	6	λ	λ	PROPN
ejpam-5288	302	7	tn	tn	NOUN
ejpam-5288	302	8	n	n	NOUN
ejpam-5288	302	9	!	!	PUNCT
ejpam-5288	303	1	=	=	SYM
ejpam-5288	303	2	1	1	NUM
ejpam-5288	303	3	λk	λk	ADP
ejpam-5288	303	4	1	1	NUM
ejpam-5288	303	5	k	k	NOUN
ejpam-5288	303	6	!	!	PUNCT
ejpam-5288	304	1	(	(	PUNCT
ejpam-5288	304	2	eλt	eλt	PROPN
ejpam-5288	304	3	−	−	PROPN
ejpam-5288	304	4	1	1	NUM
ejpam-5288	304	5	)	)	PUNCT
ejpam-5288	305	1	k	k	PROPN
ejpam-5288	305	2	ert	ert	PROPN
ejpam-5288	305	3	,	,	PUNCT
ejpam-5288	305	4	(	(	PUNCT
ejpam-5288	305	5	k	k	X
ejpam-5288	305	6	≥	≥	NOUN
ejpam-5288	305	7	0	0	NUM
ejpam-5288	305	8	)	)	PUNCT
ejpam-5288	305	9	,	,	PUNCT
ejpam-5288	305	10	(	(	PUNCT
ejpam-5288	305	11	see	see	VERB
ejpam-5288	305	12	[	[	X
ejpam-5288	305	13	13	13	NUM
ejpam-5288	305	14	]	]	NUM
ejpam-5288	305	15	)	)	PUNCT
ejpam-5288	305	16	.	.	PUNCT
ejpam-5288	306	1	(	(	PUNCT
ejpam-5288	306	2	48	48	NUM
ejpam-5288	306	3	)	)	PUNCT
ejpam-5288	306	4	replacing	replace	VERB
ejpam-5288	306	5	t	t	NOUN
ejpam-5288	306	6	by	by	ADP
ejpam-5288	306	7	1	1	NUM
ejpam-5288	306	8	λ(1−	λ(1−	PROPN
ejpam-5288	306	9	e−λt	e−λt	NOUN
ejpam-5288	306	10	)	)	PUNCT
ejpam-5288	306	11	in	in	ADP
ejpam-5288	306	12	(	(	PUNCT
ejpam-5288	306	13	42	42	NUM
ejpam-5288	306	14	)	)	PUNCT
ejpam-5288	306	15	and	and	CCONJ
ejpam-5288	306	16	using	use	VERB
ejpam-5288	306	17	(	(	PUNCT
ejpam-5288	306	18	9	9	NUM
ejpam-5288	306	19	)	)	PUNCT
ejpam-5288	306	20	,	,	PUNCT
ejpam-5288	306	21	we	we	PRON
ejpam-5288	306	22	get	get	VERB
ejpam-5288	306	23	1	1	NUM
ejpam-5288	306	24	k	k	NOUN
ejpam-5288	306	25	!	!	PROPN
ejpam-5288	306	26	1	1	NUM
ejpam-5288	307	1	λk	λk	PROPN
ejpam-5288	307	2	(	(	PUNCT
ejpam-5288	307	3	eλt	eλt	PROPN
ejpam-5288	307	4	−	−	PROPN
ejpam-5288	307	5	1	1	NUM
ejpam-5288	307	6	)	)	PUNCT
ejpam-5288	307	7	k	k	PROPN
ejpam-5288	307	8	ert	ert	NOUN
ejpam-5288	307	9	=	=	NOUN
ejpam-5288	307	10	∞∑	∞∑	NUM
ejpam-5288	307	11	m	m	NOUN
ejpam-5288	307	12	=	=	PROPN
ejpam-5288	307	13	k	k	X
ejpam-5288	307	14	lr	lr	PROPN
ejpam-5288	307	15	,	,	PUNCT
ejpam-5288	307	16	λ(m	λ(m	PROPN
ejpam-5288	307	17	,	,	PUNCT
ejpam-5288	307	18	k	k	NOUN
ejpam-5288	307	19	)	)	PUNCT
ejpam-5288	307	20	1	1	NUM
ejpam-5288	307	21	m	m	NOUN
ejpam-5288	307	22	!	!	PUNCT
ejpam-5288	308	1	(	(	PUNCT
ejpam-5288	308	2	e−λt	e−λt	NOUN
ejpam-5288	308	3	−	−	PROPN
ejpam-5288	308	4	1	1	NUM
ejpam-5288	308	5	−λ	−λ	NOUN
ejpam-5288	308	6	)	)	PUNCT
ejpam-5288	308	7	m	m	PROPN
ejpam-5288	308	8	(	(	PUNCT
ejpam-5288	308	9	49	49	NUM
ejpam-5288	308	10	)	)	PUNCT
ejpam-5288	308	11	=	=	NOUN
ejpam-5288	309	1	∞∑	∞∑	NUM
ejpam-5288	309	2	m	m	NOUN
ejpam-5288	309	3	=	=	PROPN
ejpam-5288	309	4	k	k	X
ejpam-5288	309	5	lr	lr	PROPN
ejpam-5288	309	6	,	,	PUNCT
ejpam-5288	309	7	λ(m	λ(m	PROPN
ejpam-5288	309	8	,	,	PUNCT
ejpam-5288	309	9	k	k	NOUN
ejpam-5288	309	10	)	)	PUNCT
ejpam-5288	309	11	∞∑	∞∑	NUM
ejpam-5288	309	12	n	n	NOUN
ejpam-5288	309	13	=	=	NOUN
ejpam-5288	309	14	m	m	PROPN
ejpam-5288	309	15	{	{	PUNCT
ejpam-5288	309	16	n	n	ADV
ejpam-5288	309	17	m	m	VERB
ejpam-5288	309	18	}	}	PUNCT
ejpam-5288	309	19	−λ	−λ	PROPN
ejpam-5288	309	20	tn	tn	PROPN
ejpam-5288	309	21	n	n	PROPN
ejpam-5288	309	22	!	!	PUNCT
ejpam-5288	310	1	j.	j.	PROPN
ejpam-5288	310	2	kwon	kwon	PROPN
ejpam-5288	310	3	et	et	PROPN
ejpam-5288	310	4	al	al	PROPN
ejpam-5288	310	5	.	.	PUNCT
ejpam-5288	310	6	/	/	SYM
ejpam-5288	310	7	eur	eur	PROPN
ejpam-5288	310	8	.	.	PUNCT
ejpam-5288	311	1	j.	j.	PROPN
ejpam-5288	311	2	pure	pure	PROPN
ejpam-5288	311	3	appl	appl	PROPN
ejpam-5288	311	4	.	.	PROPN
ejpam-5288	311	5	math	math	PROPN
ejpam-5288	311	6	,	,	PUNCT
ejpam-5288	311	7	17	17	NUM
ejpam-5288	311	8	(	(	PUNCT
ejpam-5288	311	9	3	3	NUM
ejpam-5288	311	10	)	)	PUNCT
ejpam-5288	311	11	(	(	PUNCT
ejpam-5288	311	12	2024	2024	NUM
ejpam-5288	311	13	)	)	PUNCT
ejpam-5288	311	14	,	,	PUNCT
ejpam-5288	311	15	1385	1385	NUM
ejpam-5288	311	16	-	-	SYM
ejpam-5288	311	17	1402	1402	NUM
ejpam-5288	311	18	1397	1397	NUM
ejpam-5288	311	19	=	=	PUNCT
ejpam-5288	312	1	∞∑	∞∑	NUM
ejpam-5288	312	2	n	n	CCONJ
ejpam-5288	312	3	=	=	SYM
ejpam-5288	312	4	k	k	PROPN
ejpam-5288	312	5	(	(	PUNCT
ejpam-5288	312	6	n∑	n∑	NOUN
ejpam-5288	312	7	m	m	PROPN
ejpam-5288	312	8	=	=	PROPN
ejpam-5288	312	9	k	k	X
ejpam-5288	312	10	lr	lr	PROPN
ejpam-5288	312	11	,	,	PUNCT
ejpam-5288	312	12	λ(m	λ(m	PROPN
ejpam-5288	312	13	,	,	PUNCT
ejpam-5288	312	14	k	k	NOUN
ejpam-5288	312	15	)	)	PUNCT
ejpam-5288	312	16	{	{	PUNCT
ejpam-5288	312	17	n	n	NOUN
ejpam-5288	312	18	m	m	VERB
ejpam-5288	312	19	}	}	PUNCT
ejpam-5288	312	20	−λ	−λ	ADJ
ejpam-5288	312	21	)	)	PUNCT
ejpam-5288	312	22	tn	tn	PROPN
ejpam-5288	312	23	n	n	PROPN
ejpam-5288	312	24	!	!	PUNCT
ejpam-5288	312	25	.	.	PUNCT
ejpam-5288	313	1	thus	thus	ADV
ejpam-5288	313	2	,	,	PUNCT
ejpam-5288	313	3	by	by	ADP
ejpam-5288	313	4	(	(	PUNCT
ejpam-5288	313	5	48	48	NUM
ejpam-5288	313	6	)	)	PUNCT
ejpam-5288	313	7	and	and	CCONJ
ejpam-5288	313	8	(	(	PUNCT
ejpam-5288	313	9	49	49	NUM
ejpam-5288	313	10	)	)	PUNCT
ejpam-5288	313	11	,	,	PUNCT
ejpam-5288	313	12	we	we	PRON
ejpam-5288	313	13	have	have	VERB
ejpam-5288	313	14	{	{	PUNCT
ejpam-5288	313	15	n+	n+	ADP
ejpam-5288	313	16	r	r	NOUN
ejpam-5288	313	17	k	k	NOUN
ejpam-5288	314	1	+	+	CCONJ
ejpam-5288	314	2	r	r	NOUN
ejpam-5288	314	3	}	}	PUNCT
ejpam-5288	314	4	r	r	NOUN
ejpam-5288	314	5	,	,	PUNCT
ejpam-5288	314	6	λ	λ	NOUN
ejpam-5288	314	7	=	=	SYM
ejpam-5288	314	8	n∑	n∑	PROPN
ejpam-5288	314	9	m	m	PROPN
ejpam-5288	314	10	=	=	PROPN
ejpam-5288	314	11	k	k	X
ejpam-5288	314	12	lr	lr	PROPN
ejpam-5288	314	13	,	,	PUNCT
ejpam-5288	314	14	λ(m	λ(m	PROPN
ejpam-5288	314	15	,	,	PUNCT
ejpam-5288	314	16	k	k	NOUN
ejpam-5288	314	17	)	)	PUNCT
ejpam-5288	314	18	{	{	PUNCT
ejpam-5288	315	1	n	n	NOUN
ejpam-5288	315	2	m	m	VERB
ejpam-5288	315	3	}	}	PUNCT
ejpam-5288	315	4	−λ	−λ	ADJ
ejpam-5288	315	5	,	,	PUNCT
ejpam-5288	315	6	(	(	PUNCT
ejpam-5288	315	7	k	k	X
ejpam-5288	315	8	≥	≥	NOUN
ejpam-5288	315	9	0	0	NUM
ejpam-5288	315	10	)	)	PUNCT
ejpam-5288	315	11	.	.	PUNCT
ejpam-5288	316	1	(	(	PUNCT
ejpam-5288	316	2	50	50	X
ejpam-5288	316	3	)	)	PUNCT
ejpam-5288	316	4	replacing	replace	VERB
ejpam-5288	316	5	t	t	NOUN
ejpam-5288	316	6	by	by	ADP
ejpam-5288	316	7	1	1	NUM
ejpam-5288	316	8	λ	λ	NOUN
ejpam-5288	316	9	log	log	NOUN
ejpam-5288	316	10	(	(	PUNCT
ejpam-5288	316	11	1	1	NUM
ejpam-5288	316	12	1−λt	1−λt	NOUN
ejpam-5288	316	13	)	)	PUNCT
ejpam-5288	316	14	in	in	ADP
ejpam-5288	316	15	(	(	PUNCT
ejpam-5288	316	16	48	48	NUM
ejpam-5288	316	17	)	)	PUNCT
ejpam-5288	316	18	and	and	CCONJ
ejpam-5288	316	19	using	use	VERB
ejpam-5288	316	20	(	(	PUNCT
ejpam-5288	316	21	7	7	NUM
ejpam-5288	316	22	)	)	PUNCT
ejpam-5288	316	23	,	,	PUNCT
ejpam-5288	316	24	we	we	PRON
ejpam-5288	316	25	see	see	VERB
ejpam-5288	316	26	that	that	SCONJ
ejpam-5288	316	27	1	1	NUM
ejpam-5288	316	28	λk	λk	ADP
ejpam-5288	316	29	1	1	NUM
ejpam-5288	316	30	k	k	NOUN
ejpam-5288	316	31	!	!	PUNCT
ejpam-5288	317	1	(	(	PUNCT
ejpam-5288	317	2	1	1	NUM
ejpam-5288	317	3	1−	1−	NUM
ejpam-5288	317	4	λt	λt	ADP
ejpam-5288	317	5	−	−	PROPN
ejpam-5288	317	6	1	1	NUM
ejpam-5288	317	7	)	)	PUNCT
ejpam-5288	317	8	k	k	NOUN
ejpam-5288	317	9	(	(	PUNCT
ejpam-5288	317	10	1	1	NUM
ejpam-5288	317	11	1−	1−	NUM
ejpam-5288	317	12	λt	λt	ADP
ejpam-5288	317	13	)	)	PUNCT
ejpam-5288	317	14	r	r	NOUN
ejpam-5288	317	15	λ	λ	NOUN
ejpam-5288	317	16	=	=	NOUN
ejpam-5288	318	1	∞∑	∞∑	NUM
ejpam-5288	318	2	m	m	NOUN
ejpam-5288	318	3	=	=	VERB
ejpam-5288	318	4	k	k	X
ejpam-5288	318	5	{	{	PUNCT
ejpam-5288	318	6	m+	m+	NOUN
ejpam-5288	318	7	r	r	NOUN
ejpam-5288	318	8	k	k	PROPN
ejpam-5288	318	9	+	+	CCONJ
ejpam-5288	318	10	r	r	NOUN
ejpam-5288	318	11	}	}	PUNCT
ejpam-5288	318	12	r	r	NOUN
ejpam-5288	318	13	,	,	PUNCT
ejpam-5288	318	14	λ	λ	PROPN
ejpam-5288	318	15	1	1	NUM
ejpam-5288	318	16	m	m	NOUN
ejpam-5288	318	17	!	!	PUNCT
ejpam-5288	319	1	(	(	PUNCT
ejpam-5288	319	2	1	1	NUM
ejpam-5288	319	3	λ	λ	NOUN
ejpam-5288	319	4	log	log	NOUN
ejpam-5288	319	5	(	(	PUNCT
ejpam-5288	319	6	1	1	NUM
ejpam-5288	319	7	1−	1−	NUM
ejpam-5288	319	8	λt	λt	ADP
ejpam-5288	319	9	)	)	PUNCT
ejpam-5288	319	10	)	)	PUNCT
ejpam-5288	319	11	m	m	PROPN
ejpam-5288	319	12	(	(	PUNCT
ejpam-5288	319	13	51	51	NUM
ejpam-5288	319	14	)	)	PUNCT
ejpam-5288	319	15	=	=	NOUN
ejpam-5288	320	1	∞∑	∞∑	NUM
ejpam-5288	320	2	m	m	NOUN
ejpam-5288	320	3	=	=	VERB
ejpam-5288	320	4	k	k	X
ejpam-5288	320	5	{	{	PUNCT
ejpam-5288	320	6	m+	m+	NOUN
ejpam-5288	320	7	r	r	NOUN
ejpam-5288	320	8	k	k	PROPN
ejpam-5288	320	9	+	+	CCONJ
ejpam-5288	320	10	r	r	NOUN
ejpam-5288	320	11	}	}	PUNCT
ejpam-5288	320	12	r	r	NOUN
ejpam-5288	320	13	,	,	PUNCT
ejpam-5288	320	14	λ	λ	X
ejpam-5288	320	15	∞∑	∞∑	NUM
ejpam-5288	320	16	n	n	NOUN
ejpam-5288	320	17	=	=	NOUN
ejpam-5288	320	18	m	m	PROPN
ejpam-5288	320	19	[	[	PUNCT
ejpam-5288	320	20	n	n	NOUN
ejpam-5288	320	21	m	m	PRON
ejpam-5288	320	22	]	]	PUNCT
ejpam-5288	320	23	λ	λ	X
ejpam-5288	320	24	tn	tn	NOUN
ejpam-5288	320	25	n	n	NOUN
ejpam-5288	320	26	!	!	PUNCT
ejpam-5288	321	1	=	=	NOUN
ejpam-5288	322	1	∞∑	∞∑	NUM
ejpam-5288	322	2	n	n	CCONJ
ejpam-5288	322	3	=	=	SYM
ejpam-5288	322	4	k	k	PROPN
ejpam-5288	322	5	(	(	PUNCT
ejpam-5288	322	6	n∑	n∑	NOUN
ejpam-5288	322	7	m	m	PROPN
ejpam-5288	322	8	=	=	PROPN
ejpam-5288	322	9	k	k	X
ejpam-5288	322	10	{	{	PUNCT
ejpam-5288	322	11	m+	m+	NOUN
ejpam-5288	322	12	r	r	NOUN
ejpam-5288	322	13	k	k	PROPN
ejpam-5288	323	1	+	+	CCONJ
ejpam-5288	323	2	r	r	NOUN
ejpam-5288	323	3	}	}	PUNCT
ejpam-5288	323	4	r	r	NOUN
ejpam-5288	323	5	,	,	PUNCT
ejpam-5288	323	6	λ	λ	X
ejpam-5288	323	7	[	[	PUNCT
ejpam-5288	323	8	n	n	NOUN
ejpam-5288	323	9	m	m	PRON
ejpam-5288	323	10	]	]	X
ejpam-5288	323	11	λ	λ	X
ejpam-5288	323	12	)	)	PUNCT
ejpam-5288	323	13	tn	tn	PROPN
ejpam-5288	323	14	n	n	PROPN
ejpam-5288	323	15	!	!	PUNCT
ejpam-5288	323	16	.	.	PUNCT
ejpam-5288	324	1	by	by	ADP
ejpam-5288	324	2	(	(	PUNCT
ejpam-5288	324	3	42	42	NUM
ejpam-5288	324	4	)	)	PUNCT
ejpam-5288	324	5	and	and	CCONJ
ejpam-5288	324	6	(	(	PUNCT
ejpam-5288	324	7	51	51	NUM
ejpam-5288	324	8	)	)	PUNCT
ejpam-5288	324	9	,	,	PUNCT
ejpam-5288	324	10	we	we	PRON
ejpam-5288	324	11	get	get	VERB
ejpam-5288	324	12	lr	lr	NOUN
ejpam-5288	324	13	,	,	PUNCT
ejpam-5288	324	14	λ(n	λ(n	PROPN
ejpam-5288	324	15	,	,	PUNCT
ejpam-5288	324	16	k	k	NOUN
ejpam-5288	324	17	)	)	PUNCT
ejpam-5288	324	18	=	=	SYM
ejpam-5288	325	1	n∑	n∑	NOUN
ejpam-5288	325	2	m	m	PROPN
ejpam-5288	325	3	=	=	VERB
ejpam-5288	325	4	k	k	X
ejpam-5288	325	5	{	{	PUNCT
ejpam-5288	325	6	m+	m+	NOUN
ejpam-5288	326	1	r	r	NOUN
ejpam-5288	326	2	k	k	PROPN
ejpam-5288	327	1	+	+	CCONJ
ejpam-5288	327	2	r	r	NOUN
ejpam-5288	327	3	}	}	PUNCT
ejpam-5288	327	4	r	r	NOUN
ejpam-5288	327	5	,	,	PUNCT
ejpam-5288	327	6	λ	λ	X
ejpam-5288	327	7	[	[	PUNCT
ejpam-5288	327	8	n	n	NOUN
ejpam-5288	327	9	m	m	PRON
ejpam-5288	327	10	]	]	X
ejpam-5288	327	11	λ	λ	X
ejpam-5288	327	12	,	,	PUNCT
ejpam-5288	327	13	(	(	PUNCT
ejpam-5288	327	14	k	k	X
ejpam-5288	327	15	≥	≥	PROPN
ejpam-5288	327	16	0	0	NUM
ejpam-5288	327	17	)	)	PUNCT
ejpam-5288	327	18	.	.	PUNCT
ejpam-5288	328	1	(	(	PUNCT
ejpam-5288	328	2	52	52	NUM
ejpam-5288	328	3	)	)	PUNCT
ejpam-5288	328	4	therefore	therefore	ADV
ejpam-5288	328	5	,	,	PUNCT
ejpam-5288	328	6	by	by	ADP
ejpam-5288	328	7	(	(	PUNCT
ejpam-5288	328	8	50	50	NUM
ejpam-5288	328	9	)	)	PUNCT
ejpam-5288	328	10	and	and	CCONJ
ejpam-5288	328	11	(	(	PUNCT
ejpam-5288	328	12	52	52	NUM
ejpam-5288	328	13	)	)	PUNCT
ejpam-5288	328	14	,	,	PUNCT
ejpam-5288	328	15	we	we	PRON
ejpam-5288	328	16	obtain	obtain	VERB
ejpam-5288	328	17	the	the	DET
ejpam-5288	328	18	following	follow	VERB
ejpam-5288	328	19	theorem	theorem	VERB
ejpam-5288	328	20	.	.	PUNCT
ejpam-5288	328	21	theorem	theorem	NOUN
ejpam-5288	328	22	9	9	NUM
ejpam-5288	328	23	.	.	PUNCT
ejpam-5288	328	24	for	for	ADP
ejpam-5288	328	25	n	n	PRON
ejpam-5288	328	26	,	,	PUNCT
ejpam-5288	328	27	k	k	X
ejpam-5288	328	28	≥	≥	X
ejpam-5288	328	29	0	0	NUM
ejpam-5288	328	30	with	with	ADP
ejpam-5288	328	31	n	n	PRON
ejpam-5288	328	32	≥	≥	NOUN
ejpam-5288	328	33	k	k	NOUN
ejpam-5288	328	34	,	,	PUNCT
ejpam-5288	328	35	we	we	PRON
ejpam-5288	328	36	have	have	VERB
ejpam-5288	328	37	{	{	PUNCT
ejpam-5288	328	38	n+	n+	ADP
ejpam-5288	328	39	r	r	NOUN
ejpam-5288	328	40	k	k	NOUN
ejpam-5288	329	1	+	+	CCONJ
ejpam-5288	329	2	r	r	NOUN
ejpam-5288	329	3	}	}	PUNCT
ejpam-5288	329	4	r	r	NOUN
ejpam-5288	329	5	,	,	PUNCT
ejpam-5288	329	6	λ	λ	NOUN
ejpam-5288	329	7	=	=	SYM
ejpam-5288	329	8	n∑	n∑	PROPN
ejpam-5288	329	9	m	m	PROPN
ejpam-5288	329	10	=	=	PROPN
ejpam-5288	329	11	k	k	X
ejpam-5288	329	12	lr	lr	PROPN
ejpam-5288	329	13	,	,	PUNCT
ejpam-5288	329	14	λ(n	λ(n	PROPN
ejpam-5288	329	15	,	,	PUNCT
ejpam-5288	329	16	k	k	NOUN
ejpam-5288	329	17	)	)	PUNCT
ejpam-5288	329	18	{	{	PUNCT
ejpam-5288	330	1	n	n	NOUN
ejpam-5288	330	2	m	m	VERB
ejpam-5288	330	3	}	}	PUNCT
ejpam-5288	330	4	−λ	−λ	ADJ
ejpam-5288	330	5	,	,	PUNCT
ejpam-5288	330	6	and	and	CCONJ
ejpam-5288	330	7	lr	lr	INTJ
ejpam-5288	330	8	,	,	PUNCT
ejpam-5288	330	9	λ(n	λ(n	PROPN
ejpam-5288	330	10	,	,	PUNCT
ejpam-5288	330	11	k	k	NOUN
ejpam-5288	330	12	)	)	PUNCT
ejpam-5288	331	1	=	=	SYM
ejpam-5288	331	2	n∑	n∑	NOUN
ejpam-5288	331	3	m	m	PROPN
ejpam-5288	331	4	=	=	VERB
ejpam-5288	331	5	k	k	X
ejpam-5288	331	6	{	{	PUNCT
ejpam-5288	331	7	m+	m+	NOUN
ejpam-5288	332	1	r	r	NOUN
ejpam-5288	332	2	k	k	PROPN
ejpam-5288	333	1	+	+	CCONJ
ejpam-5288	333	2	r	r	NOUN
ejpam-5288	333	3	}	}	PUNCT
ejpam-5288	333	4	r	r	NOUN
ejpam-5288	333	5	,	,	PUNCT
ejpam-5288	333	6	λ	λ	X
ejpam-5288	333	7	[	[	PUNCT
ejpam-5288	333	8	n	n	NOUN
ejpam-5288	333	9	m	m	PRON
ejpam-5288	333	10	]	]	X
ejpam-5288	334	1	λ	λ	X
ejpam-5288	334	2	.	.	PUNCT
ejpam-5288	335	1	3	3	X
ejpam-5288	335	2	.	.	X
ejpam-5288	335	3	further	further	ADJ
ejpam-5288	335	4	remarks	remark	VERB
ejpam-5288	335	5	a	a	DET
ejpam-5288	335	6	poisson	poisson	NOUN
ejpam-5288	335	7	random	random	ADJ
ejpam-5288	335	8	variable	variable	NOUN
ejpam-5288	335	9	indicates	indicate	VERB
ejpam-5288	335	10	how	how	SCONJ
ejpam-5288	335	11	many	many	ADJ
ejpam-5288	335	12	events	event	NOUN
ejpam-5288	335	13	occured	occur	VERB
ejpam-5288	335	14	within	within	ADP
ejpam-5288	335	15	a	a	DET
ejpam-5288	335	16	given	give	VERB
ejpam-5288	335	17	period	period	NOUN
ejpam-5288	335	18	of	of	ADP
ejpam-5288	335	19	time	time	NOUN
ejpam-5288	335	20	.	.	PUNCT
ejpam-5288	336	1	a	a	DET
ejpam-5288	336	2	random	random	ADJ
ejpam-5288	336	3	variable	variable	NOUN
ejpam-5288	336	4	x	x	NOUN
ejpam-5288	336	5	,	,	PUNCT
ejpam-5288	336	6	taking	take	VERB
ejpam-5288	336	7	on	on	ADP
ejpam-5288	336	8	one	one	NUM
ejpam-5288	336	9	of	of	ADP
ejpam-5288	336	10	the	the	DET
ejpam-5288	336	11	variables	variable	NOUN
ejpam-5288	336	12	0	0	NUM
ejpam-5288	336	13	,	,	PUNCT
ejpam-5288	336	14	1	1	NUM
ejpam-5288	336	15	,	,	PUNCT
ejpam-5288	336	16	2	2	NUM
ejpam-5288	336	17	,	,	PUNCT
ejpam-5288	336	18	.	.	PUNCT
ejpam-5288	336	19	.	.	PUNCT
ejpam-5288	336	20	.	.	PUNCT
ejpam-5288	337	1	,	,	PUNCT
ejpam-5288	337	2	is	be	AUX
ejpam-5288	337	3	said	say	VERB
ejpam-5288	337	4	to	to	PART
ejpam-5288	337	5	be	be	AUX
ejpam-5288	337	6	the	the	DET
ejpam-5288	337	7	poisson	poisson	NOUN
ejpam-5288	337	8	random	random	ADJ
ejpam-5288	337	9	variable	variable	NOUN
ejpam-5288	337	10	with	with	ADP
ejpam-5288	337	11	parameter	parameter	PROPN
ejpam-5288	337	12	α	α	PROPN
ejpam-5288	337	13	>	>	X
ejpam-5288	337	14	0	0	PUNCT
ejpam-5288	338	1	if	if	SCONJ
ejpam-5288	338	2	the	the	DET
ejpam-5288	338	3	probability	probability	NOUN
ejpam-5288	338	4	mass	mass	NOUN
ejpam-5288	338	5	function	function	NOUN
ejpam-5288	338	6	of	of	ADP
ejpam-5288	338	7	x	x	PROPN
ejpam-5288	338	8	is	be	AUX
ejpam-5288	338	9	given	give	VERB
ejpam-5288	338	10	by	by	ADP
ejpam-5288	338	11	p(i	p(i	PROPN
ejpam-5288	338	12	)	)	PUNCT
ejpam-5288	339	1	=	=	NOUN
ejpam-5288	339	2	p{x	p{x	NOUN
ejpam-5288	340	1	=	=	PUNCT
ejpam-5288	340	2	i	i	NOUN
ejpam-5288	340	3	}	}	PUNCT
ejpam-5288	340	4	=	=	PUNCT
ejpam-5288	340	5	e−αα	e−αα	PROPN
ejpam-5288	340	6	i	i	PRON
ejpam-5288	340	7	i	i	PROPN
ejpam-5288	340	8	!	!	PUNCT
ejpam-5288	340	9	,	,	PUNCT
ejpam-5288	340	10	(	(	PUNCT
ejpam-5288	340	11	see	see	VERB
ejpam-5288	340	12	[	[	X
ejpam-5288	340	13	16	16	NUM
ejpam-5288	340	14	,	,	PUNCT
ejpam-5288	340	15	25	25	NUM
ejpam-5288	340	16	]	]	PUNCT
ejpam-5288	340	17	)	)	PUNCT
ejpam-5288	340	18	.	.	PUNCT
ejpam-5288	341	1	(	(	PUNCT
ejpam-5288	341	2	53	53	NUM
ejpam-5288	341	3	)	)	PUNCT
ejpam-5288	341	4	j.	j.	PROPN
ejpam-5288	341	5	kwon	kwon	PROPN
ejpam-5288	341	6	et	et	PROPN
ejpam-5288	341	7	al	al	PROPN
ejpam-5288	341	8	.	.	PUNCT
ejpam-5288	341	9	/	/	SYM
ejpam-5288	341	10	eur	eur	PROPN
ejpam-5288	341	11	.	.	PUNCT
ejpam-5288	342	1	j.	j.	PROPN
ejpam-5288	342	2	pure	pure	PROPN
ejpam-5288	342	3	appl	appl	PROPN
ejpam-5288	342	4	.	.	PROPN
ejpam-5288	342	5	math	math	PROPN
ejpam-5288	342	6	,	,	PUNCT
ejpam-5288	342	7	17	17	NUM
ejpam-5288	342	8	(	(	PUNCT
ejpam-5288	342	9	3	3	NUM
ejpam-5288	342	10	)	)	PUNCT
ejpam-5288	342	11	(	(	PUNCT
ejpam-5288	342	12	2024	2024	NUM
ejpam-5288	342	13	)	)	PUNCT
ejpam-5288	342	14	,	,	PUNCT
ejpam-5288	342	15	1385	1385	NUM
ejpam-5288	342	16	-	-	SYM
ejpam-5288	342	17	1402	1402	NUM
ejpam-5288	342	18	1398	1398	NUM
ejpam-5288	342	19	let	let	VERB
ejpam-5288	342	20	f	f	PRON
ejpam-5288	342	21	be	be	AUX
ejpam-5288	342	22	a	a	DET
ejpam-5288	342	23	real	real	ADV
ejpam-5288	342	24	valued	value	VERB
ejpam-5288	342	25	function	function	NOUN
ejpam-5288	342	26	,	,	PUNCT
ejpam-5288	342	27	and	and	CCONJ
ejpam-5288	342	28	let	let	VERB
ejpam-5288	342	29	x	x	PRON
ejpam-5288	342	30	be	be	AUX
ejpam-5288	342	31	a	a	DET
ejpam-5288	342	32	random	random	ADJ
ejpam-5288	342	33	variable	variable	NOUN
ejpam-5288	342	34	.	.	PUNCT
ejpam-5288	343	1	then	then	ADV
ejpam-5288	343	2	we	we	PRON
ejpam-5288	343	3	define	define	VERB
ejpam-5288	343	4	e[f(x	e[f(x	NOUN
ejpam-5288	343	5	)	)	PUNCT
ejpam-5288	343	6	]	]	PUNCT
ejpam-5288	344	1	=	=	PUNCT
ejpam-5288	344	2	∞∑	∞∑	NUM
ejpam-5288	344	3	i=0	i=0	PROPN
ejpam-5288	344	4	f(i)p(i	f(i)p(i	NUM
ejpam-5288	344	5	)	)	PUNCT
ejpam-5288	344	6	,	,	PUNCT
ejpam-5288	344	7	(	(	PUNCT
ejpam-5288	344	8	see	see	VERB
ejpam-5288	344	9	[	[	X
ejpam-5288	344	10	25	25	NUM
ejpam-5288	344	11	]	]	PUNCT
ejpam-5288	344	12	)	)	PUNCT
ejpam-5288	344	13	.	.	PUNCT
ejpam-5288	345	1	(	(	PUNCT
ejpam-5288	345	2	54	54	NUM
ejpam-5288	345	3	)	)	PUNCT
ejpam-5288	345	4	for	for	ADP
ejpam-5288	345	5	λ	λ	PROPN
ejpam-5288	345	6	∈	∈	PROPN
ejpam-5288	345	7	r	r	NOUN
ejpam-5288	345	8	with	with	ADP
ejpam-5288	345	9	0	0	NUM
ejpam-5288	345	10	<	<	X
ejpam-5288	345	11	λ	λ	X
ejpam-5288	345	12	<	<	X
ejpam-5288	345	13	1	1	NUM
ejpam-5288	345	14	,	,	PUNCT
ejpam-5288	345	15	assume	assume	VERB
ejpam-5288	345	16	that	that	SCONJ
ejpam-5288	345	17	x	x	PRON
ejpam-5288	345	18	is	be	AUX
ejpam-5288	345	19	the	the	DET
ejpam-5288	345	20	poisson	poisson	NOUN
ejpam-5288	345	21	random	random	ADJ
ejpam-5288	345	22	variable	variable	NOUN
ejpam-5288	345	23	with	with	ADP
ejpam-5288	345	24	parameter	parameter	NOUN
ejpam-5288	345	25	α	α	PROPN
ejpam-5288	345	26	λ	λ	PROPN
ejpam-5288	345	27	(	(	PUNCT
ejpam-5288	345	28	>	>	X
ejpam-5288	345	29	0	0	NUM
ejpam-5288	345	30	)	)	PUNCT
ejpam-5288	345	31	.	.	PUNCT
ejpam-5288	346	1	then	then	ADV
ejpam-5288	346	2	we	we	PRON
ejpam-5288	346	3	note	note	VERB
ejpam-5288	346	4	from	from	ADP
ejpam-5288	346	5	(	(	PUNCT
ejpam-5288	346	6	54	54	NUM
ejpam-5288	346	7	)	)	PUNCT
ejpam-5288	346	8	that	that	PRON
ejpam-5288	347	1	e	e	X
ejpam-5288	348	1	[	[	X
ejpam-5288	348	2	(	(	PUNCT
ejpam-5288	348	3	1	1	NUM
ejpam-5288	348	4	1−	1−	NUM
ejpam-5288	348	5	λt	λt	ADP
ejpam-5288	348	6	)	)	PUNCT
ejpam-5288	348	7	x	x	X
ejpam-5288	348	8	]	]	X
ejpam-5288	348	9	=	=	PUNCT
ejpam-5288	348	10	∞∑	∞∑	NUM
ejpam-5288	348	11	i=0	i=0	PROPN
ejpam-5288	348	12	(	(	PUNCT
ejpam-5288	348	13	1	1	NUM
ejpam-5288	348	14	1−	1−	NUM
ejpam-5288	348	15	λt	λt	ADP
ejpam-5288	348	16	)	)	PUNCT
ejpam-5288	348	17	i	i	PRON
ejpam-5288	348	18	p(i	p(i	PROPN
ejpam-5288	348	19	)	)	PUNCT
ejpam-5288	348	20	(	(	PUNCT
ejpam-5288	348	21	55	55	NUM
ejpam-5288	348	22	)	)	PUNCT
ejpam-5288	348	23	=	=	NOUN
ejpam-5288	349	1	∞∑	∞∑	NUM
ejpam-5288	349	2	i=0	i=0	PROPN
ejpam-5288	349	3	(	(	PUNCT
ejpam-5288	349	4	1	1	NUM
ejpam-5288	349	5	1−	1−	NUM
ejpam-5288	349	6	λt	λt	ADP
ejpam-5288	349	7	)	)	PUNCT
ejpam-5288	349	8	i	i	PROPN
ejpam-5288	349	9	1	1	NUM
ejpam-5288	349	10	i	i	PRON
ejpam-5288	349	11	!	!	PUNCT
ejpam-5288	349	12	(	(	PUNCT
ejpam-5288	349	13	α	α	NOUN
ejpam-5288	349	14	λ	λ	PROPN
ejpam-5288	349	15	)	)	PUNCT
ejpam-5288	349	16	i	i	PRON
ejpam-5288	349	17	e−	e−	PROPN
ejpam-5288	349	18	α	α	NOUN
ejpam-5288	349	19	λ	λ	X
ejpam-5288	349	20	=	=	SYM
ejpam-5288	349	21	e	e	X
ejpam-5288	349	22	1	1	NUM
ejpam-5288	349	23	λ	λ	SYM
ejpam-5288	349	24	α	α	NOUN
ejpam-5288	349	25	1−λt	1−λt	NUM
ejpam-5288	350	1	e−	e−	PROPN
ejpam-5288	350	2	α	α	NOUN
ejpam-5288	350	3	λ	λ	X
ejpam-5288	350	4	=	=	SYM
ejpam-5288	350	5	e	e	X
ejpam-5288	350	6	α	α	PROPN
ejpam-5288	350	7	λ	λ	X
ejpam-5288	350	8	(	(	PUNCT
ejpam-5288	350	9	1	1	NUM
ejpam-5288	350	10	1−λt	1−λt	NUM
ejpam-5288	350	11	−1	−1	NOUN
ejpam-5288	350	12	)	)	PUNCT
ejpam-5288	350	13	=	=	PUNCT
ejpam-5288	351	1	∞∑	∞∑	PROPN
ejpam-5288	351	2	n=0	n=0	NUM
ejpam-5288	351	3	bl	bl	NOUN
ejpam-5288	351	4	n	n	CCONJ
ejpam-5288	351	5	,	,	PUNCT
ejpam-5288	351	6	λ(α	λ(α	NUM
ejpam-5288	351	7	)	)	PUNCT
ejpam-5288	351	8	tn	tn	PROPN
ejpam-5288	351	9	n	n	PROPN
ejpam-5288	351	10	!	!	PUNCT
ejpam-5288	351	11	.	.	PUNCT
ejpam-5288	352	1	on	on	ADP
ejpam-5288	352	2	the	the	DET
ejpam-5288	352	3	other	other	ADJ
ejpam-5288	352	4	hand	hand	NOUN
ejpam-5288	352	5	,	,	PUNCT
ejpam-5288	352	6	by	by	ADP
ejpam-5288	352	7	binomial	binomial	ADJ
ejpam-5288	352	8	expansion	expansion	NOUN
ejpam-5288	352	9	,	,	PUNCT
ejpam-5288	352	10	we	we	PRON
ejpam-5288	352	11	get	get	VERB
ejpam-5288	352	12	e	e	NOUN
ejpam-5288	352	13	[	[	X
ejpam-5288	352	14	(	(	PUNCT
ejpam-5288	352	15	1	1	NUM
ejpam-5288	352	16	1−	1−	NUM
ejpam-5288	352	17	λt	λt	ADP
ejpam-5288	352	18	)	)	PUNCT
ejpam-5288	352	19	x	x	X
ejpam-5288	352	20	]	]	X
ejpam-5288	353	1	=	=	PUNCT
ejpam-5288	353	2	e	e	X
ejpam-5288	353	3	[	[	X
ejpam-5288	353	4	(	(	PUNCT
ejpam-5288	353	5	1	1	NUM
ejpam-5288	353	6	1−	1−	NUM
ejpam-5288	353	7	λt	λt	ADP
ejpam-5288	353	8	)	)	PUNCT
ejpam-5288	353	9	λx	λx	PROPN
ejpam-5288	353	10	λ	λ	X
ejpam-5288	353	11	]	]	X
ejpam-5288	353	12	=	=	PUNCT
ejpam-5288	354	1	∞∑	∞∑	NUM
ejpam-5288	354	2	n=0	n=0	NUM
ejpam-5288	354	3	e	e	NOUN
ejpam-5288	354	4	[	[	PUNCT
ejpam-5288	354	5	⟨xλ⟩n	⟨xλ⟩n	NOUN
ejpam-5288	354	6	,	,	PUNCT
ejpam-5288	354	7	λ	λ	PROPN
ejpam-5288	354	8	]	]	PUNCT
ejpam-5288	354	9	tn	tn	PROPN
ejpam-5288	354	10	n	n	X
ejpam-5288	354	11	!	!	PUNCT
ejpam-5288	354	12	.	.	PUNCT
ejpam-5288	355	1	(	(	PUNCT
ejpam-5288	355	2	56	56	NUM
ejpam-5288	355	3	)	)	PUNCT
ejpam-5288	355	4	hence	hence	ADV
ejpam-5288	355	5	,	,	PUNCT
ejpam-5288	355	6	by	by	ADP
ejpam-5288	355	7	(	(	PUNCT
ejpam-5288	355	8	55	55	NUM
ejpam-5288	355	9	)	)	PUNCT
ejpam-5288	355	10	and	and	CCONJ
ejpam-5288	355	11	(	(	PUNCT
ejpam-5288	355	12	56	56	NUM
ejpam-5288	355	13	)	)	PUNCT
ejpam-5288	355	14	,	,	PUNCT
ejpam-5288	355	15	we	we	PRON
ejpam-5288	355	16	get	get	VERB
ejpam-5288	355	17	e	e	NOUN
ejpam-5288	355	18	[	[	PUNCT
ejpam-5288	355	19	⟨xλ⟩n	⟨xλ⟩n	NOUN
ejpam-5288	355	20	,	,	PUNCT
ejpam-5288	355	21	λ	λ	X
ejpam-5288	355	22	]	]	X
ejpam-5288	355	23	=	=	PUNCT
ejpam-5288	355	24	bl	bl	PROPN
ejpam-5288	355	25	n	n	CCONJ
ejpam-5288	355	26	,	,	PUNCT
ejpam-5288	355	27	λ(α	λ(α	PROPN
ejpam-5288	355	28	)	)	PUNCT
ejpam-5288	355	29	,	,	PUNCT
ejpam-5288	355	30	(	(	PUNCT
ejpam-5288	355	31	n	n	X
ejpam-5288	355	32	≥	≥	NOUN
ejpam-5288	355	33	0	0	NUM
ejpam-5288	355	34	)	)	PUNCT
ejpam-5288	355	35	.	.	PUNCT
ejpam-5288	356	1	(	(	PUNCT
ejpam-5288	356	2	57	57	NUM
ejpam-5288	356	3	)	)	PUNCT
ejpam-5288	356	4	for	for	ADP
ejpam-5288	356	5	r	r	NOUN
ejpam-5288	356	6	≥	≥	NOUN
ejpam-5288	356	7	0	0	NUM
ejpam-5288	356	8	,	,	PUNCT
ejpam-5288	356	9	from	from	ADP
ejpam-5288	356	10	(	(	PUNCT
ejpam-5288	356	11	46	46	NUM
ejpam-5288	356	12	)	)	PUNCT
ejpam-5288	356	13	and	and	CCONJ
ejpam-5288	356	14	(	(	PUNCT
ejpam-5288	356	15	55	55	NUM
ejpam-5288	356	16	)	)	PUNCT
ejpam-5288	356	17	,	,	PUNCT
ejpam-5288	356	18	we	we	PRON
ejpam-5288	356	19	observe	observe	VERB
ejpam-5288	356	20	that	that	SCONJ
ejpam-5288	356	21	e	e	PROPN
ejpam-5288	357	1	[	[	X
ejpam-5288	357	2	(	(	PUNCT
ejpam-5288	357	3	1	1	NUM
ejpam-5288	357	4	1−	1−	NUM
ejpam-5288	357	5	λt	λt	ADP
ejpam-5288	357	6	)	)	PUNCT
ejpam-5288	357	7	x+	x+	PROPN
ejpam-5288	357	8	r	r	NOUN
ejpam-5288	357	9	λ	λ	X
ejpam-5288	357	10	]	]	X
ejpam-5288	357	11	=	=	PUNCT
ejpam-5288	357	12	e	e	X
ejpam-5288	357	13	[	[	X
ejpam-5288	357	14	(	(	PUNCT
ejpam-5288	357	15	1	1	NUM
ejpam-5288	357	16	1−	1−	NUM
ejpam-5288	357	17	λt	λt	ADP
ejpam-5288	357	18	)	)	PUNCT
ejpam-5288	357	19	x	x	X
ejpam-5288	357	20	]	]	X
ejpam-5288	357	21	(	(	PUNCT
ejpam-5288	357	22	1	1	NUM
ejpam-5288	357	23	1−	1−	NUM
ejpam-5288	357	24	λt	λt	ADP
ejpam-5288	357	25	)	)	PUNCT
ejpam-5288	357	26	r	r	NOUN
ejpam-5288	357	27	λ	λ	PROPN
ejpam-5288	357	28	(	(	PUNCT
ejpam-5288	357	29	58	58	NUM
ejpam-5288	357	30	)	)	PUNCT
ejpam-5288	357	31	=	=	PUNCT
ejpam-5288	357	32	e	e	X
ejpam-5288	357	33	α	α	X
ejpam-5288	357	34	λ	λ	X
ejpam-5288	357	35	(	(	PUNCT
ejpam-5288	357	36	1	1	NUM
ejpam-5288	357	37	1−λt	1−λt	NUM
ejpam-5288	357	38	−1	−1	NOUN
ejpam-5288	357	39	)	)	PUNCT
ejpam-5288	357	40	(	(	PUNCT
ejpam-5288	357	41	1	1	NUM
ejpam-5288	357	42	1−	1−	NUM
ejpam-5288	357	43	λt	λt	ADP
ejpam-5288	357	44	)	)	PUNCT
ejpam-5288	357	45	r	r	NOUN
ejpam-5288	357	46	λ	λ	NOUN
ejpam-5288	357	47	=	=	PUNCT
ejpam-5288	357	48	∞∑	∞∑	PROPN
ejpam-5288	357	49	n=0	n=0	NUM
ejpam-5288	357	50	lb	lb	ADP
ejpam-5288	357	51	(	(	PUNCT
ejpam-5288	357	52	r	r	NOUN
ejpam-5288	357	53	)	)	PUNCT
ejpam-5288	357	54	n	n	CCONJ
ejpam-5288	357	55	,	,	PUNCT
ejpam-5288	357	56	λ(α	λ(α	NUM
ejpam-5288	357	57	)	)	PUNCT
ejpam-5288	357	58	tn	tn	PROPN
ejpam-5288	357	59	n	n	PROPN
ejpam-5288	357	60	!	!	PUNCT
ejpam-5288	357	61	.	.	PUNCT
ejpam-5288	358	1	on	on	ADP
ejpam-5288	358	2	the	the	DET
ejpam-5288	358	3	other	other	ADJ
ejpam-5288	358	4	hand	hand	NOUN
ejpam-5288	358	5	,	,	PUNCT
ejpam-5288	358	6	by	by	ADP
ejpam-5288	358	7	binomial	binomial	ADJ
ejpam-5288	358	8	expansion	expansion	NOUN
ejpam-5288	358	9	,	,	PUNCT
ejpam-5288	358	10	we	we	PRON
ejpam-5288	358	11	get	get	VERB
ejpam-5288	358	12	e	e	NOUN
ejpam-5288	358	13	[	[	X
ejpam-5288	358	14	(	(	PUNCT
ejpam-5288	358	15	1	1	NUM
ejpam-5288	358	16	1−	1−	NUM
ejpam-5288	358	17	λt	λt	ADP
ejpam-5288	358	18	)	)	PUNCT
ejpam-5288	358	19	x+	x+	PROPN
ejpam-5288	358	20	r	r	NOUN
ejpam-5288	358	21	λ	λ	X
ejpam-5288	358	22	]	]	X
ejpam-5288	358	23	=	=	PUNCT
ejpam-5288	359	1	e	e	X
ejpam-5288	359	2	[	[	X
ejpam-5288	359	3	(	(	PUNCT
ejpam-5288	359	4	1	1	NUM
ejpam-5288	359	5	1−	1−	NUM
ejpam-5288	359	6	λt	λt	ADP
ejpam-5288	359	7	)	)	PUNCT
ejpam-5288	359	8	λx+r	λx+r	PROPN
ejpam-5288	359	9	λ	λ	X
ejpam-5288	359	10	]	]	X
ejpam-5288	359	11	=	=	PUNCT
ejpam-5288	360	1	∞∑	∞∑	NUM
ejpam-5288	360	2	n=0	n=0	NUM
ejpam-5288	360	3	e[⟨λx	e[⟨λx	PROPN
ejpam-5288	360	4	+	+	NUM
ejpam-5288	360	5	r⟩n	r⟩n	NOUN
ejpam-5288	360	6	,	,	PUNCT
ejpam-5288	360	7	λ	λ	NOUN
ejpam-5288	360	8	]	]	X
ejpam-5288	360	9	tn	tn	PROPN
ejpam-5288	360	10	n	n	X
ejpam-5288	360	11	!	!	PUNCT
ejpam-5288	360	12	.	.	PUNCT
ejpam-5288	361	1	(	(	PUNCT
ejpam-5288	361	2	59	59	NUM
ejpam-5288	361	3	)	)	PUNCT
ejpam-5288	361	4	thus	thus	ADV
ejpam-5288	361	5	,	,	PUNCT
ejpam-5288	361	6	by	by	ADP
ejpam-5288	361	7	(	(	PUNCT
ejpam-5288	361	8	58	58	NUM
ejpam-5288	361	9	)	)	PUNCT
ejpam-5288	361	10	and	and	CCONJ
ejpam-5288	361	11	(	(	PUNCT
ejpam-5288	361	12	59	59	NUM
ejpam-5288	361	13	)	)	PUNCT
ejpam-5288	361	14	,	,	PUNCT
ejpam-5288	361	15	we	we	PRON
ejpam-5288	361	16	get	get	VERB
ejpam-5288	361	17	lb	lb	DET
ejpam-5288	361	18	(	(	PUNCT
ejpam-5288	361	19	r	r	NOUN
ejpam-5288	361	20	)	)	PUNCT
ejpam-5288	361	21	n	n	CCONJ
ejpam-5288	361	22	,	,	PUNCT
ejpam-5288	361	23	λ(α	λ(α	PROPN
ejpam-5288	361	24	)	)	PUNCT
ejpam-5288	362	1	=	=	SYM
ejpam-5288	362	2	e	e	X
ejpam-5288	362	3	[	[	PUNCT
ejpam-5288	362	4	⟨λx	⟨λx	NOUN
ejpam-5288	362	5	+	+	CCONJ
ejpam-5288	362	6	r⟩n	r⟩n	NOUN
ejpam-5288	362	7	,	,	PUNCT
ejpam-5288	362	8	λ	λ	X
ejpam-5288	362	9	]	]	PUNCT
ejpam-5288	362	10	,	,	PUNCT
ejpam-5288	362	11	(	(	PUNCT
ejpam-5288	362	12	n	n	X
ejpam-5288	362	13	≥	≥	NOUN
ejpam-5288	362	14	0	0	NUM
ejpam-5288	362	15	)	)	PUNCT
ejpam-5288	362	16	.	.	PUNCT
ejpam-5288	363	1	(	(	PUNCT
ejpam-5288	363	2	60	60	NUM
ejpam-5288	363	3	)	)	PUNCT
ejpam-5288	363	4	from	from	ADP
ejpam-5288	363	5	(	(	PUNCT
ejpam-5288	363	6	4	4	NUM
ejpam-5288	363	7	)	)	PUNCT
ejpam-5288	363	8	,	,	PUNCT
ejpam-5288	363	9	(	(	PUNCT
ejpam-5288	363	10	39	39	NUM
ejpam-5288	363	11	)	)	PUNCT
ejpam-5288	363	12	,	,	PUNCT
ejpam-5288	363	13	and	and	CCONJ
ejpam-5288	363	14	(	(	PUNCT
ejpam-5288	363	15	60	60	NUM
ejpam-5288	363	16	)	)	PUNCT
ejpam-5288	363	17	,	,	PUNCT
ejpam-5288	363	18	we	we	PRON
ejpam-5288	363	19	note	note	VERB
ejpam-5288	363	20	that	that	SCONJ
ejpam-5288	364	1	lb	lb	X
ejpam-5288	364	2	(	(	PUNCT
ejpam-5288	364	3	r	r	NOUN
ejpam-5288	364	4	)	)	PUNCT
ejpam-5288	364	5	n	n	CCONJ
ejpam-5288	364	6	,	,	PUNCT
ejpam-5288	364	7	λ(α	λ(α	PROPN
ejpam-5288	364	8	)	)	PUNCT
ejpam-5288	364	9	=	=	SYM
ejpam-5288	365	1	e	e	X
ejpam-5288	365	2	[	[	PUNCT
ejpam-5288	365	3	⟨xλ+	⟨xλ+	PROPN
ejpam-5288	365	4	r⟩n	r⟩n	NOUN
ejpam-5288	365	5	,	,	PUNCT
ejpam-5288	365	6	λ	λ	X
ejpam-5288	365	7	]	]	PUNCT
ejpam-5288	365	8	=	=	SYM
ejpam-5288	365	9	n∑	n∑	PROPN
ejpam-5288	365	10	k=0	k=0	PROPN
ejpam-5288	365	11	lr	lr	PROPN
ejpam-5288	365	12	,	,	PUNCT
ejpam-5288	365	13	λ(n	λ(n	PROPN
ejpam-5288	365	14	,	,	PUNCT
ejpam-5288	365	15	k)e[(λx)k	k)e[(λx)k	NOUN
ejpam-5288	365	16	,	,	PUNCT
ejpam-5288	365	17	λ	λ	NOUN
ejpam-5288	365	18	]	]	X
ejpam-5288	365	19	.	.	PUNCT
ejpam-5288	366	1	(	(	PUNCT
ejpam-5288	366	2	61	61	NUM
ejpam-5288	366	3	)	)	PUNCT
ejpam-5288	366	4	j.	j.	PROPN
ejpam-5288	366	5	kwon	kwon	PROPN
ejpam-5288	366	6	et	et	PROPN
ejpam-5288	366	7	al	al	PROPN
ejpam-5288	366	8	.	.	PUNCT
ejpam-5288	366	9	/	/	SYM
ejpam-5288	366	10	eur	eur	PROPN
ejpam-5288	366	11	.	.	PUNCT
ejpam-5288	367	1	j.	j.	PROPN
ejpam-5288	367	2	pure	pure	PROPN
ejpam-5288	367	3	appl	appl	PROPN
ejpam-5288	367	4	.	.	PROPN
ejpam-5288	367	5	math	math	PROPN
ejpam-5288	367	6	,	,	PUNCT
ejpam-5288	367	7	17	17	NUM
ejpam-5288	367	8	(	(	PUNCT
ejpam-5288	367	9	3	3	NUM
ejpam-5288	367	10	)	)	PUNCT
ejpam-5288	367	11	(	(	PUNCT
ejpam-5288	367	12	2024	2024	NUM
ejpam-5288	367	13	)	)	PUNCT
ejpam-5288	367	14	,	,	PUNCT
ejpam-5288	367	15	1385	1385	NUM
ejpam-5288	367	16	-	-	SYM
ejpam-5288	367	17	1402	1402	NUM
ejpam-5288	367	18	1399	1399	NUM
ejpam-5288	367	19	=	=	SYM
ejpam-5288	367	20	n∑	n∑	PROPN
ejpam-5288	367	21	k=0	k=0	PROPN
ejpam-5288	367	22	lr	lr	PROPN
ejpam-5288	367	23	,	,	PUNCT
ejpam-5288	367	24	λ(n	λ(n	PROPN
ejpam-5288	367	25	,	,	PUNCT
ejpam-5288	367	26	k	k	NOUN
ejpam-5288	367	27	)	)	PUNCT
ejpam-5288	367	28	k∑	k∑	NOUN
ejpam-5288	367	29	j=0	j=0	PROPN
ejpam-5288	367	30	s1,λ(k	s1,λ(k	PROPN
ejpam-5288	367	31	,	,	PUNCT
ejpam-5288	367	32	j)λ	j)λ	X
ejpam-5288	367	33	je[xj	je[xj	X
ejpam-5288	367	34	]	]	PUNCT
ejpam-5288	367	35	.	.	PUNCT
ejpam-5288	368	1	from	from	ADP
ejpam-5288	368	2	(	(	PUNCT
ejpam-5288	368	3	13	13	NUM
ejpam-5288	368	4	)	)	PUNCT
ejpam-5288	368	5	,	,	PUNCT
ejpam-5288	368	6	we	we	PRON
ejpam-5288	368	7	have	have	VERB
ejpam-5288	368	8	e[xj	e[xj	PROPN
ejpam-5288	368	9	]	]	PUNCT
ejpam-5288	369	1	=	=	PUNCT
ejpam-5288	370	1	∞∑	∞∑	NUM
ejpam-5288	370	2	k=0	k=0	PROPN
ejpam-5288	370	3	kjp(k	kjp(k	PROPN
ejpam-5288	370	4	)	)	PUNCT
ejpam-5288	370	5	=	=	NOUN
ejpam-5288	371	1	∞∑	∞∑	NUM
ejpam-5288	371	2	k=0	k=0	PROPN
ejpam-5288	371	3	(	(	PUNCT
ejpam-5288	371	4	αλ	αλ	NUM
ejpam-5288	371	5	)	)	PUNCT
ejpam-5288	371	6	k	k	PROPN
ejpam-5288	372	1	k	k	X
ejpam-5288	372	2	!	!	PUNCT
ejpam-5288	373	1	e−	e−	PROPN
ejpam-5288	373	2	α	α	PROPN
ejpam-5288	373	3	λ	λ	X
ejpam-5288	373	4	kj	kj	PROPN
ejpam-5288	373	5	(	(	PUNCT
ejpam-5288	373	6	62	62	NUM
ejpam-5288	373	7	)	)	PUNCT
ejpam-5288	373	8	=	=	PUNCT
ejpam-5288	374	1	e−	e−	NUM
ejpam-5288	374	2	α	α	NOUN
ejpam-5288	374	3	λ	λ	PROPN
ejpam-5288	374	4	∞∑	∞∑	PRON
ejpam-5288	374	5	k=0	k=0	PROPN
ejpam-5288	374	6	kj	kj	PROPN
ejpam-5288	374	7	k	k	PROPN
ejpam-5288	374	8	!	!	PUNCT
ejpam-5288	375	1	(	(	PUNCT
ejpam-5288	375	2	α	α	NOUN
ejpam-5288	375	3	λ	λ	PROPN
ejpam-5288	375	4	)	)	PUNCT
ejpam-5288	375	5	k	k	X
ejpam-5288	376	1	=	=	PUNCT
ejpam-5288	376	2	ϕj	ϕj	PROPN
ejpam-5288	376	3	(	(	PUNCT
ejpam-5288	376	4	α	α	NOUN
ejpam-5288	376	5	λ	λ	PROPN
ejpam-5288	376	6	)	)	PUNCT
ejpam-5288	376	7	.	.	PUNCT
ejpam-5288	377	1	hence	hence	ADV
ejpam-5288	377	2	,	,	PUNCT
ejpam-5288	377	3	by	by	ADP
ejpam-5288	377	4	(	(	PUNCT
ejpam-5288	377	5	13	13	NUM
ejpam-5288	377	6	)	)	PUNCT
ejpam-5288	377	7	,	,	PUNCT
ejpam-5288	377	8	(	(	PUNCT
ejpam-5288	377	9	61	61	NUM
ejpam-5288	377	10	)	)	PUNCT
ejpam-5288	377	11	,	,	PUNCT
ejpam-5288	377	12	and	and	CCONJ
ejpam-5288	377	13	(	(	PUNCT
ejpam-5288	377	14	62	62	NUM
ejpam-5288	377	15	)	)	PUNCT
ejpam-5288	377	16	,	,	PUNCT
ejpam-5288	377	17	we	we	PRON
ejpam-5288	377	18	get	get	VERB
ejpam-5288	377	19	lb	lb	DET
ejpam-5288	377	20	(	(	PUNCT
ejpam-5288	377	21	r	r	NOUN
ejpam-5288	377	22	)	)	PUNCT
ejpam-5288	377	23	n	n	CCONJ
ejpam-5288	377	24	,	,	PUNCT
ejpam-5288	377	25	λ(α	λ(α	PROPN
ejpam-5288	377	26	)	)	PUNCT
ejpam-5288	377	27	=	=	SYM
ejpam-5288	378	1	n∑	n∑	NOUN
ejpam-5288	378	2	j=0	j=0	PROPN
ejpam-5288	378	3	n∑	n∑	PROPN
ejpam-5288	378	4	k	k	PROPN
ejpam-5288	379	1	=	=	PROPN
ejpam-5288	379	2	j	j	X
ejpam-5288	379	3	lr	lr	NOUN
ejpam-5288	379	4	,	,	PUNCT
ejpam-5288	379	5	λ(n	λ(n	PROPN
ejpam-5288	379	6	,	,	PUNCT
ejpam-5288	379	7	k)s1,λ(k	k)s1,λ(k	NOUN
ejpam-5288	379	8	,	,	PUNCT
ejpam-5288	379	9	j)ϕj	j)ϕj	PROPN
ejpam-5288	379	10	,	,	PUNCT
ejpam-5288	379	11	λ(α	λ(α	PROPN
ejpam-5288	379	12	)	)	PUNCT
ejpam-5288	379	13	,	,	PUNCT
ejpam-5288	379	14	(	(	PUNCT
ejpam-5288	379	15	n	n	X
ejpam-5288	379	16	≥	≥	NOUN
ejpam-5288	379	17	0	0	NUM
ejpam-5288	379	18	)	)	PUNCT
ejpam-5288	379	19	.	.	PUNCT
ejpam-5288	380	1	(	(	PUNCT
ejpam-5288	380	2	63	63	NUM
ejpam-5288	380	3	)	)	PUNCT
ejpam-5288	380	4	we	we	PRON
ejpam-5288	380	5	obtain	obtain	VERB
ejpam-5288	380	6	the	the	DET
ejpam-5288	380	7	following	following	NOUN
ejpam-5288	380	8	theorem	theorem	NOUN
ejpam-5288	380	9	from	from	ADP
ejpam-5288	380	10	(	(	PUNCT
ejpam-5288	380	11	57	57	NUM
ejpam-5288	380	12	)	)	PUNCT
ejpam-5288	380	13	,	,	PUNCT
ejpam-5288	380	14	(	(	PUNCT
ejpam-5288	380	15	60	60	NUM
ejpam-5288	380	16	)	)	PUNCT
ejpam-5288	380	17	,	,	PUNCT
ejpam-5288	380	18	and	and	CCONJ
ejpam-5288	380	19	(	(	PUNCT
ejpam-5288	380	20	63	63	NUM
ejpam-5288	380	21	)	)	PUNCT
ejpam-5288	380	22	.	.	PUNCT
ejpam-5288	381	1	theorem	theorem	ADJ
ejpam-5288	381	2	10	10	NUM
ejpam-5288	381	3	.	.	PUNCT
ejpam-5288	382	1	assume	assume	VERB
ejpam-5288	382	2	that	that	SCONJ
ejpam-5288	382	3	x	x	PRON
ejpam-5288	382	4	is	be	AUX
ejpam-5288	382	5	the	the	DET
ejpam-5288	382	6	poisson	poisson	NOUN
ejpam-5288	382	7	random	random	ADJ
ejpam-5288	382	8	variable	variable	NOUN
ejpam-5288	382	9	with	with	ADP
ejpam-5288	382	10	parameter	parameter	NOUN
ejpam-5288	382	11	α	α	PROPN
ejpam-5288	382	12	λ	λ	PROPN
ejpam-5288	382	13	(	(	PUNCT
ejpam-5288	382	14	>	>	X
ejpam-5288	382	15	0	0	NUM
ejpam-5288	382	16	)	)	PUNCT
ejpam-5288	382	17	,	,	PUNCT
ejpam-5288	382	18	for	for	ADP
ejpam-5288	382	19	λ	λ	PROPN
ejpam-5288	382	20	with	with	ADP
ejpam-5288	382	21	0	0	NUM
ejpam-5288	382	22	<	<	X
ejpam-5288	382	23	λ	λ	X
ejpam-5288	382	24	<	<	X
ejpam-5288	382	25	1	1	NUM
ejpam-5288	382	26	.	.	PUNCT
ejpam-5288	383	1	e	e	X
ejpam-5288	383	2	[	[	PUNCT
ejpam-5288	383	3	⟨xλ⟩n	⟨xλ⟩n	NOUN
ejpam-5288	383	4	,	,	PUNCT
ejpam-5288	383	5	λ	λ	X
ejpam-5288	383	6	]	]	X
ejpam-5288	383	7	=	=	PUNCT
ejpam-5288	383	8	bl	bl	PROPN
ejpam-5288	383	9	n	n	CCONJ
ejpam-5288	383	10	,	,	PUNCT
ejpam-5288	383	11	λ(α	λ(α	PROPN
ejpam-5288	383	12	)	)	PUNCT
ejpam-5288	383	13	,	,	PUNCT
ejpam-5288	383	14	lb	lb	X
ejpam-5288	383	15	(	(	PUNCT
ejpam-5288	383	16	r	r	NOUN
ejpam-5288	383	17	)	)	PUNCT
ejpam-5288	383	18	n	n	CCONJ
ejpam-5288	383	19	,	,	PUNCT
ejpam-5288	383	20	λ(α	λ(α	PROPN
ejpam-5288	383	21	)	)	PUNCT
ejpam-5288	383	22	=	=	SYM
ejpam-5288	383	23	e	e	X
ejpam-5288	383	24	[	[	PUNCT
ejpam-5288	383	25	⟨λx	⟨λx	NOUN
ejpam-5288	383	26	+	+	CCONJ
ejpam-5288	383	27	r⟩n	r⟩n	NOUN
ejpam-5288	383	28	,	,	PUNCT
ejpam-5288	383	29	λ	λ	X
ejpam-5288	383	30	]	]	PUNCT
ejpam-5288	384	1	=	=	SYM
ejpam-5288	384	2	n∑	n∑	NOUN
ejpam-5288	384	3	j=0	j=0	PROPN
ejpam-5288	384	4	n∑	n∑	PROPN
ejpam-5288	384	5	k	k	PROPN
ejpam-5288	385	1	=	=	PROPN
ejpam-5288	385	2	j	j	X
ejpam-5288	385	3	lr	lr	NOUN
ejpam-5288	385	4	,	,	PUNCT
ejpam-5288	385	5	λ(n	λ(n	PROPN
ejpam-5288	385	6	,	,	PUNCT
ejpam-5288	385	7	k)s1,λ(k	k)s1,λ(k	NOUN
ejpam-5288	385	8	,	,	PUNCT
ejpam-5288	385	9	j)ϕj	j)ϕj	PROPN
ejpam-5288	385	10	,	,	PUNCT
ejpam-5288	385	11	λ(α	λ(α	PROPN
ejpam-5288	385	12	)	)	PUNCT
ejpam-5288	385	13	,	,	PUNCT
ejpam-5288	385	14	(	(	PUNCT
ejpam-5288	385	15	n	n	X
ejpam-5288	385	16	≥	≥	NOUN
ejpam-5288	385	17	0	0	NUM
ejpam-5288	385	18	)	)	PUNCT
ejpam-5288	385	19	.	.	PUNCT
ejpam-5288	386	1	4	4	X
ejpam-5288	386	2	.	.	X
ejpam-5288	386	3	conclusion	conclusion	NOUN
ejpam-5288	386	4	the	the	DET
ejpam-5288	386	5	degenerate	degenerate	ADJ
ejpam-5288	386	6	versions	version	NOUN
ejpam-5288	386	7	arise	arise	VERB
ejpam-5288	386	8	when	when	SCONJ
ejpam-5288	386	9	we	we	PRON
ejpam-5288	386	10	replace	replace	VERB
ejpam-5288	386	11	the	the	DET
ejpam-5288	386	12	powers	power	NOUN
ejpam-5288	386	13	of	of	ADP
ejpam-5288	386	14	x	x	PUNCT
ejpam-5288	386	15	by	by	ADP
ejpam-5288	386	16	the	the	DET
ejpam-5288	386	17	generalized	generalized	ADJ
ejpam-5288	386	18	falling	fall	VERB
ejpam-5288	386	19	factorial	factorial	NOUN
ejpam-5288	386	20	polynomials	polynomial	NOUN
ejpam-5288	386	21	(	(	PUNCT
ejpam-5288	386	22	x)k	x)k	X
ejpam-5288	386	23	,	,	PUNCT
ejpam-5288	386	24	λ	λ	NOUN
ejpam-5288	386	25	in	in	ADP
ejpam-5288	386	26	the	the	DET
ejpam-5288	386	27	defining	define	VERB
ejpam-5288	386	28	equations	equation	NOUN
ejpam-5288	386	29	,	,	PUNCT
ejpam-5288	386	30	whereas	whereas	SCONJ
ejpam-5288	386	31	the	the	DET
ejpam-5288	386	32	λ	λ	NOUN
ejpam-5288	386	33	-	-	NOUN
ejpam-5288	386	34	analogues	analogue	NOUN
ejpam-5288	386	35	appear	appear	VERB
ejpam-5288	386	36	when	when	SCONJ
ejpam-5288	386	37	we	we	PRON
ejpam-5288	386	38	replace	replace	VERB
ejpam-5288	386	39	the	the	DET
ejpam-5288	386	40	falling	fall	VERB
ejpam-5288	386	41	factorials	factorial	NOUN
ejpam-5288	386	42	(	(	PUNCT
ejpam-5288	386	43	x)k	x)k	X
ejpam-5288	386	44	by	by	ADP
ejpam-5288	386	45	the	the	DET
ejpam-5288	386	46	generalized	generalized	ADJ
ejpam-5288	386	47	falling	fall	VERB
ejpam-5288	386	48	factorials	factorial	NOUN
ejpam-5288	386	49	.	.	PUNCT
ejpam-5288	387	1	in	in	ADP
ejpam-5288	387	2	this	this	DET
ejpam-5288	387	3	paper	paper	NOUN
ejpam-5288	387	4	,	,	PUNCT
ejpam-5288	387	5	as	as	ADP
ejpam-5288	387	6	λanalogues	λanalogue	NOUN
ejpam-5288	387	7	of	of	ADP
ejpam-5288	387	8	the	the	DET
ejpam-5288	387	9	lah	lah	NOUN
ejpam-5288	387	10	numbers	number	NOUN
ejpam-5288	387	11	and	and	CCONJ
ejpam-5288	387	12	lah	lah	NOUN
ejpam-5288	387	13	-	-	PUNCT
ejpam-5288	387	14	bell	bell	NOUN
ejpam-5288	387	15	polynomials	polynomial	NOUN
ejpam-5288	387	16	,	,	PUNCT
ejpam-5288	387	17	we	we	PRON
ejpam-5288	387	18	studied	study	VERB
ejpam-5288	387	19	the	the	DET
ejpam-5288	387	20	λ	λ	NOUN
ejpam-5288	387	21	-	-	NOUN
ejpam-5288	387	22	analogues	analogue	NOUN
ejpam-5288	387	23	of	of	ADP
ejpam-5288	387	24	lah	lah	PROPN
ejpam-5288	387	25	numbers	number	NOUN
ejpam-5288	387	26	lλ(n	lλ(n	PUNCT
ejpam-5288	387	27	,	,	PUNCT
ejpam-5288	387	28	k	k	NOUN
ejpam-5288	387	29	)	)	PUNCT
ejpam-5288	387	30	and	and	CCONJ
ejpam-5288	387	31	lah	lah	PROPN
ejpam-5288	387	32	-	-	PUNCT
ejpam-5288	387	33	bell	bell	NOUN
ejpam-5288	387	34	polynomials	polynomial	NOUN
ejpam-5288	387	35	bl	bl	NOUN
ejpam-5288	387	36	n	n	PRON
ejpam-5288	387	37	,	,	PUNCT
ejpam-5288	387	38	λ(x	λ(x	PROPN
ejpam-5288	387	39	)	)	PUNCT
ejpam-5288	387	40	.	.	PUNCT
ejpam-5288	388	1	for	for	ADP
ejpam-5288	388	2	those	those	DET
ejpam-5288	388	3	numbers	number	NOUN
ejpam-5288	388	4	and	and	CCONJ
ejpam-5288	388	5	polynomials	polynomial	NOUN
ejpam-5288	388	6	,	,	PUNCT
ejpam-5288	388	7	we	we	PRON
ejpam-5288	388	8	investigated	investigate	VERB
ejpam-5288	388	9	some	some	DET
ejpam-5288	388	10	properties	property	NOUN
ejpam-5288	388	11	,	,	PUNCT
ejpam-5288	388	12	explicit	explicit	ADJ
ejpam-5288	388	13	expressions	expression	NOUN
ejpam-5288	388	14	,	,	PUNCT
ejpam-5288	388	15	generating	generating	NOUN
ejpam-5288	388	16	functions	function	NOUN
ejpam-5288	388	17	and	and	CCONJ
ejpam-5288	388	18	dobinski	dobinski	ADJ
ejpam-5288	388	19	-	-	PUNCT
ejpam-5288	388	20	like	like	ADJ
ejpam-5288	388	21	formulas	formula	NOUN
ejpam-5288	388	22	.	.	PUNCT
ejpam-5288	389	1	we	we	PRON
ejpam-5288	389	2	also	also	ADV
ejpam-5288	389	3	considered	consider	VERB
ejpam-5288	389	4	the	the	DET
ejpam-5288	389	5	more	more	ADV
ejpam-5288	389	6	general	general	ADJ
ejpam-5288	389	7	λ	λ	NOUN
ejpam-5288	389	8	-	-	NOUN
ejpam-5288	389	9	analogues	analogue	NOUN
ejpam-5288	389	10	of	of	ADP
ejpam-5288	389	11	r	r	NOUN
ejpam-5288	389	12	-	-	PUNCT
ejpam-5288	389	13	lah	lah	NOUN
ejpam-5288	389	14	numbers	number	NOUN
ejpam-5288	389	15	lr	lr	NOUN
ejpam-5288	389	16	,	,	PUNCT
ejpam-5288	389	17	λ(n	λ(n	PROPN
ejpam-5288	389	18	,	,	PUNCT
ejpam-5288	389	19	k	k	NOUN
ejpam-5288	389	20	)	)	PUNCT
ejpam-5288	389	21	and	and	CCONJ
ejpam-5288	389	22	r	r	NOUN
ejpam-5288	389	23	-	-	PUNCT
ejpam-5288	389	24	extended	extend	VERB
ejpam-5288	389	25	λ	λ	NOUN
ejpam-5288	389	26	-	-	PUNCT
ejpam-5288	389	27	lah	lah	ADJ
ejpam-5288	389	28	-	-	PUNCT
ejpam-5288	389	29	bell	bell	NOUN
ejpam-5288	389	30	polynomials	polynomial	NOUN
ejpam-5288	389	31	lb	lb	PRON
ejpam-5288	389	32	(	(	PUNCT
ejpam-5288	389	33	r	r	NOUN
ejpam-5288	389	34	)	)	PUNCT
ejpam-5288	389	35	n	n	CCONJ
ejpam-5288	389	36	,	,	PUNCT
ejpam-5288	389	37	λ(x	λ(x	PROPN
ejpam-5288	389	38	)	)	PUNCT
ejpam-5288	389	39	and	and	CCONJ
ejpam-5288	389	40	similar	similar	ADJ
ejpam-5288	389	41	results	result	NOUN
ejpam-5288	389	42	to	to	ADP
ejpam-5288	389	43	lλ(n	lλ(n	PROPN
ejpam-5288	389	44	,	,	PUNCT
ejpam-5288	389	45	k	k	NOUN
ejpam-5288	389	46	)	)	PUNCT
ejpam-5288	389	47	and	and	CCONJ
ejpam-5288	389	48	bl	bl	VERB
ejpam-5288	389	49	n	n	CCONJ
ejpam-5288	389	50	,	,	PUNCT
ejpam-5288	389	51	λ(x	λ(x	PROPN
ejpam-5288	389	52	)	)	PUNCT
ejpam-5288	389	53	were	be	AUX
ejpam-5288	389	54	derived	derive	VERB
ejpam-5288	389	55	.	.	PUNCT
ejpam-5288	390	1	in	in	ADP
ejpam-5288	390	2	addition	addition	NOUN
ejpam-5288	390	3	,	,	PUNCT
ejpam-5288	390	4	we	we	PRON
ejpam-5288	390	5	showed	show	VERB
ejpam-5288	390	6	the	the	DET
ejpam-5288	390	7	expectation	expectation	NOUN
ejpam-5288	390	8	of	of	ADP
ejpam-5288	390	9	one	one	NUM
ejpam-5288	390	10	random	random	ADJ
ejpam-5288	390	11	variable	variable	NOUN
ejpam-5288	390	12	and	and	CCONJ
ejpam-5288	390	13	that	that	PRON
ejpam-5288	390	14	of	of	ADP
ejpam-5288	390	15	another	another	DET
ejpam-5288	390	16	random	random	ADJ
ejpam-5288	390	17	variable	variable	NOUN
ejpam-5288	390	18	,	,	PUNCT
ejpam-5288	390	19	both	both	PRON
ejpam-5288	390	20	related	relate	VERB
ejpam-5288	390	21	to	to	ADP
ejpam-5288	390	22	the	the	DET
ejpam-5288	390	23	poisson	poisson	NOUN
ejpam-5288	390	24	random	random	ADJ
ejpam-5288	390	25	variable	variable	NOUN
ejpam-5288	390	26	with	with	ADP
ejpam-5288	390	27	parameter	parameter	NOUN
ejpam-5288	390	28	α	α	PROPN
ejpam-5288	390	29	λ	λ	PROPN
ejpam-5288	390	30	,	,	PUNCT
ejpam-5288	390	31	are	be	AUX
ejpam-5288	390	32	respectively	respectively	ADV
ejpam-5288	390	33	equal	equal	ADJ
ejpam-5288	390	34	to	to	PART
ejpam-5288	390	35	bl	bl	VERB
ejpam-5288	390	36	n	n	CCONJ
ejpam-5288	390	37	,	,	PUNCT
ejpam-5288	390	38	λ(α	λ(α	PROPN
ejpam-5288	390	39	)	)	PUNCT
ejpam-5288	390	40	and	and	CCONJ
ejpam-5288	390	41	lb	lb	X
ejpam-5288	390	42	(	(	PUNCT
ejpam-5288	390	43	r	r	NOUN
ejpam-5288	390	44	)	)	PUNCT
ejpam-5288	390	45	n	n	CCONJ
ejpam-5288	390	46	,	,	PUNCT
ejpam-5288	390	47	λ(α	λ(α	PROPN
ejpam-5288	390	48	)	)	PUNCT
ejpam-5288	390	49	.	.	PUNCT
ejpam-5288	391	1	as	as	ADP
ejpam-5288	391	2	one	one	NUM
ejpam-5288	391	3	of	of	ADP
ejpam-5288	391	4	our	our	PRON
ejpam-5288	391	5	future	future	ADJ
ejpam-5288	391	6	research	research	NOUN
ejpam-5288	391	7	projects	project	NOUN
ejpam-5288	391	8	,	,	PUNCT
ejpam-5288	391	9	we	we	PRON
ejpam-5288	391	10	would	would	AUX
ejpam-5288	391	11	like	like	VERB
ejpam-5288	391	12	to	to	PART
ejpam-5288	391	13	continue	continue	VERB
ejpam-5288	391	14	to	to	PART
ejpam-5288	391	15	explore	explore	VERB
ejpam-5288	391	16	λ	λ	NOUN
ejpam-5288	391	17	-	-	NOUN
ejpam-5288	391	18	analogues	analogue	NOUN
ejpam-5288	391	19	of	of	ADP
ejpam-5288	391	20	some	some	DET
ejpam-5288	391	21	special	special	ADJ
ejpam-5288	391	22	numbers	number	NOUN
ejpam-5288	391	23	and	and	CCONJ
ejpam-5288	391	24	polynomials	polynomial	NOUN
ejpam-5288	391	25	and	and	CCONJ
ejpam-5288	391	26	their	their	PRON
ejpam-5288	391	27	applications	application	NOUN
ejpam-5288	391	28	to	to	ADP
ejpam-5288	391	29	physics	physics	NOUN
ejpam-5288	391	30	,	,	PUNCT
ejpam-5288	391	31	science	science	NOUN
ejpam-5288	391	32	and	and	CCONJ
ejpam-5288	391	33	engineering	engineering	NOUN
ejpam-5288	391	34	as	as	ADV
ejpam-5288	391	35	well	well	ADV
ejpam-5288	391	36	as	as	ADP
ejpam-5288	391	37	to	to	ADP
ejpam-5288	391	38	mathematics	mathematic	NOUN
ejpam-5288	391	39	.	.	PUNCT
ejpam-5288	392	1	references	reference	NOUN
ejpam-5288	392	2	1400	1400	NUM
ejpam-5288	392	3	acknowledgements	acknowledgement	NOUN
ejpam-5288	392	4	we	we	PRON
ejpam-5288	392	5	would	would	AUX
ejpam-5288	392	6	like	like	VERB
ejpam-5288	392	7	to	to	PART
ejpam-5288	392	8	thank	thank	VERB
ejpam-5288	392	9	jangjeon	jangjeon	PROPN
ejpam-5288	392	10	institute	institute	PROPN
ejpam-5288	392	11	for	for	ADP
ejpam-5288	392	12	mathematical	mathematical	ADJ
ejpam-5288	392	13	science	science	NOUN
ejpam-5288	392	14	for	for	ADP
ejpam-5288	392	15	its	its	PRON
ejpam-5288	392	16	support	support	NOUN
ejpam-5288	392	17	during	during	ADP
ejpam-5288	392	18	the	the	DET
ejpam-5288	392	19	preparation	preparation	NOUN
ejpam-5288	392	20	of	of	ADP
ejpam-5288	392	21	this	this	DET
ejpam-5288	392	22	paper	paper	NOUN
ejpam-5288	392	23	.	.	PUNCT
ejpam-5288	393	1	conflict	conflict	NOUN
ejpam-5288	393	2	of	of	ADP
ejpam-5288	393	3	interest	interest	NOUN
ejpam-5288	393	4	the	the	DET
ejpam-5288	393	5	authors	author	NOUN
ejpam-5288	393	6	declare	declare	VERB
ejpam-5288	393	7	that	that	SCONJ
ejpam-5288	393	8	they	they	PRON
ejpam-5288	393	9	have	have	VERB
ejpam-5288	393	10	no	no	DET
ejpam-5288	393	11	competing	compete	VERB
ejpam-5288	393	12	interests	interest	NOUN
ejpam-5288	393	13	in	in	ADP
ejpam-5288	393	14	this	this	DET
ejpam-5288	393	15	paper	paper	NOUN
ejpam-5288	393	16	.	.	PUNCT
ejpam-5288	394	1	references	reference	NOUN
ejpam-5288	394	2	[	[	X
ejpam-5288	394	3	1	1	NUM
ejpam-5288	394	4	]	]	PUNCT
ejpam-5288	394	5	s.	s.	PROPN
ejpam-5288	394	6	araci	araci	PROPN
ejpam-5288	394	7	,	,	PUNCT
ejpam-5288	394	8	m.	m.	NOUN
ejpam-5288	394	9	acikgoz	acikgoz	PROPN
ejpam-5288	394	10	,	,	PUNCT
ejpam-5288	394	11	a	a	DET
ejpam-5288	394	12	note	note	NOUN
ejpam-5288	394	13	on	on	ADP
ejpam-5288	394	14	the	the	DET
ejpam-5288	394	15	frobenius	frobenius	NOUN
ejpam-5288	394	16	-	-	PUNCT
ejpam-5288	394	17	euler	euler	NOUN
ejpam-5288	394	18	numbers	number	NOUN
ejpam-5288	394	19	and	and	CCONJ
ejpam-5288	394	20	polynomials	polynomial	NOUN
ejpam-5288	394	21	associated	associate	VERB
ejpam-5288	394	22	with	with	ADP
ejpam-5288	394	23	bernstein	bernstein	PROPN
ejpam-5288	394	24	polynomials	polynomials	PROPN
ejpam-5288	394	25	,	,	PUNCT
ejpam-5288	394	26	adv	adv	PROPN
ejpam-5288	394	27	.	.	PUNCT
ejpam-5288	394	28	stud	stud	PROPN
ejpam-5288	394	29	.	.	PUNCT
ejpam-5288	395	1	contemp	contemp	NOUN
ejpam-5288	395	2	.	.	PUNCT
ejpam-5288	396	1	math	math	NOUN
ejpam-5288	396	2	.	.	PUNCT
ejpam-5288	396	3	,	,	PUNCT
ejpam-5288	397	1	kyungshang	kyungshang	PROPN
ejpam-5288	397	2	,	,	PUNCT
ejpam-5288	397	3	22	22	NUM
ejpam-5288	397	4	(	(	PUNCT
ejpam-5288	397	5	2012	2012	NUM
ejpam-5288	397	6	)	)	PUNCT
ejpam-5288	397	7	,	,	PUNCT
ejpam-5288	397	8	no	no	INTJ
ejpam-5288	397	9	.	.	NOUN
ejpam-5288	397	10	3	3	NUM
ejpam-5288	397	11	,	,	PUNCT
ejpam-5288	397	12	399	399	NUM
ejpam-5288	397	13	-	-	SYM
ejpam-5288	397	14	406	406	NUM
ejpam-5288	397	15	.	.	PUNCT
ejpam-5288	398	1	[	[	X
ejpam-5288	398	2	2	2	X
ejpam-5288	398	3	]	]	PUNCT
ejpam-5288	398	4	m.	m.	NOUN
ejpam-5288	398	5	s.	s.	PROPN
ejpam-5288	398	6	aydin	aydin	PROPN
ejpam-5288	398	7	,	,	PUNCT
ejpam-5288	398	8	m.	m.	NOUN
ejpam-5288	398	9	acikgoz	acikgoz	PROPN
ejpam-5288	398	10	,	,	PUNCT
ejpam-5288	398	11	s.	s.	PROPN
ejpam-5288	398	12	a.	a.	PROPN
ejpam-5288	398	13	araci	araci	PROPN
ejpam-5288	398	14	,	,	PUNCT
ejpam-5288	398	15	new	new	ADJ
ejpam-5288	398	16	construction	construction	NOUN
ejpam-5288	398	17	on	on	ADP
ejpam-5288	398	18	the	the	DET
ejpam-5288	398	19	degenerate	degenerate	ADJ
ejpam-5288	398	20	hurwitzzeta	hurwitzzeta	NOUN
ejpam-5288	398	21	function	function	NOUN
ejpam-5288	398	22	associated	associate	VERB
ejpam-5288	398	23	with	with	ADP
ejpam-5288	398	24	certain	certain	ADJ
ejpam-5288	398	25	applications	application	NOUN
ejpam-5288	398	26	,	,	PUNCT
ejpam-5288	398	27	proc	proc	NOUN
ejpam-5288	398	28	.	.	PUNCT
ejpam-5288	399	1	jangjeon	jangjeon	PROPN
ejpam-5288	399	2	math	math	PROPN
ejpam-5288	399	3	.	.	PUNCT
ejpam-5288	400	1	soc	soc	PROPN
ejpam-5288	400	2	.	.	PROPN
ejpam-5288	400	3	,	,	PUNCT
ejpam-5288	400	4	25	25	NUM
ejpam-5288	400	5	(	(	PUNCT
ejpam-5288	400	6	2022	2022	NUM
ejpam-5288	400	7	)	)	PUNCT
ejpam-5288	400	8	,	,	PUNCT
ejpam-5288	400	9	no	no	INTJ
ejpam-5288	400	10	.	.	NOUN
ejpam-5288	400	11	2	2	NUM
ejpam-5288	400	12	,	,	PUNCT
ejpam-5288	400	13	195	195	NUM
ejpam-5288	400	14	-	-	SYM
ejpam-5288	400	15	203	203	NUM
ejpam-5288	400	16	.	.	PUNCT
ejpam-5288	401	1	[	[	X
ejpam-5288	401	2	3	3	X
ejpam-5288	401	3	]	]	PUNCT
ejpam-5288	401	4	k.	k.	PROPN
ejpam-5288	401	5	boubellouta	boubellouta	PROPN
ejpam-5288	401	6	,	,	PUNCT
ejpam-5288	401	7	a.	a.	PROPN
ejpam-5288	401	8	boussayoud	boussayoud	PROPN
ejpam-5288	401	9	,	,	PUNCT
ejpam-5288	401	10	s.	s.	PROPN
ejpam-5288	401	11	araci	araci	PROPN
ejpam-5288	401	12	,	,	PUNCT
ejpam-5288	401	13	m.	m.	PROPN
ejpam-5288	401	14	kerada	kerada	PROPN
ejpam-5288	401	15	,	,	PUNCT
ejpam-5288	401	16	some	some	DET
ejpam-5288	401	17	theorems	theorem	NOUN
ejpam-5288	401	18	on	on	ADP
ejpam-5288	401	19	generating	generating	NOUN
ejpam-5288	401	20	functions	function	NOUN
ejpam-5288	401	21	and	and	CCONJ
ejpam-5288	401	22	their	their	PRON
ejpam-5288	401	23	applications	application	NOUN
ejpam-5288	401	24	,	,	PUNCT
ejpam-5288	401	25	adv	adv	PROPN
ejpam-5288	401	26	.	.	PUNCT
ejpam-5288	401	27	stud	stud	PROPN
ejpam-5288	401	28	.	.	PUNCT
ejpam-5288	402	1	contemp	contemp	NOUN
ejpam-5288	402	2	.	.	PUNCT
ejpam-5288	403	1	math	math	NOUN
ejpam-5288	403	2	.	.	PUNCT
ejpam-5288	403	3	,	,	PUNCT
ejpam-5288	404	1	kyungshang	kyungshang	PROPN
ejpam-5288	404	2	,	,	PUNCT
ejpam-5288	404	3	30	30	NUM
ejpam-5288	404	4	(	(	PUNCT
ejpam-5288	404	5	2020	2020	NUM
ejpam-5288	404	6	)	)	PUNCT
ejpam-5288	404	7	,	,	PUNCT
ejpam-5288	404	8	no	no	INTJ
ejpam-5288	404	9	.	.	NOUN
ejpam-5288	404	10	3	3	NUM
ejpam-5288	404	11	,	,	PUNCT
ejpam-5288	404	12	307	307	NUM
ejpam-5288	404	13	-	-	SYM
ejpam-5288	404	14	324	324	NUM
ejpam-5288	404	15	.	.	PUNCT
ejpam-5288	405	1	[	[	X
ejpam-5288	405	2	4	4	NUM
ejpam-5288	405	3	]	]	PUNCT
ejpam-5288	405	4	l.	l.	PROPN
ejpam-5288	405	5	carlitz	carlitz	PROPN
ejpam-5288	405	6	,	,	PUNCT
ejpam-5288	405	7	weighted	weight	VERB
ejpam-5288	405	8	stirling	stirling	NOUN
ejpam-5288	405	9	numbers	number	NOUN
ejpam-5288	405	10	of	of	ADP
ejpam-5288	405	11	the	the	DET
ejpam-5288	405	12	first	first	ADJ
ejpam-5288	405	13	and	and	CCONJ
ejpam-5288	405	14	second	second	ADJ
ejpam-5288	405	15	kind	kind	NOUN
ejpam-5288	405	16	i	i	PROPN
ejpam-5288	405	17	,	,	PUNCT
ejpam-5288	405	18	fibonacci	fibonacci	NOUN
ejpam-5288	405	19	quart	quart	NOUN
ejpam-5288	405	20	.	.	PUNCT
ejpam-5288	406	1	,	,	PUNCT
ejpam-5288	406	2	18	18	NUM
ejpam-5288	406	3	(	(	PUNCT
ejpam-5288	406	4	1980	1980	NUM
ejpam-5288	406	5	)	)	PUNCT
ejpam-5288	406	6	,	,	PUNCT
ejpam-5288	406	7	no	no	INTJ
ejpam-5288	406	8	.	.	NOUN
ejpam-5288	406	9	2	2	NUM
ejpam-5288	406	10	,	,	PUNCT
ejpam-5288	406	11	147	147	NUM
ejpam-5288	406	12	-	-	SYM
ejpam-5288	406	13	162	162	NUM
ejpam-5288	406	14	.	.	PUNCT
ejpam-5288	407	1	[	[	X
ejpam-5288	407	2	5	5	X
ejpam-5288	407	3	]	]	PUNCT
ejpam-5288	407	4	l.	l.	PROPN
ejpam-5288	407	5	comtet	comtet	PROPN
ejpam-5288	407	6	,	,	PUNCT
ejpam-5288	407	7	advanced	advanced	ADJ
ejpam-5288	407	8	combinatorics	combinatoric	NOUN
ejpam-5288	407	9	:	:	PUNCT
ejpam-5288	407	10	the	the	DET
ejpam-5288	407	11	art	art	NOUN
ejpam-5288	407	12	of	of	ADP
ejpam-5288	407	13	finite	finite	NOUN
ejpam-5288	407	14	and	and	CCONJ
ejpam-5288	407	15	infinite	infinite	ADJ
ejpam-5288	407	16	expansions	expansion	NOUN
ejpam-5288	407	17	,	,	PUNCT
ejpam-5288	407	18	new	new	PROPN
ejpam-5288	407	19	york	york	PROPN
ejpam-5288	407	20	:	:	PUNCT
ejpam-5288	407	21	american	american	PROPN
ejpam-5288	407	22	mathematical	mathematical	PROPN
ejpam-5288	407	23	society	society	NOUN
ejpam-5288	407	24	,	,	PUNCT
ejpam-5288	407	25	1974	1974	NUM
ejpam-5288	407	26	.	.	PUNCT
ejpam-5288	408	1	https://doi.org/10.2307/2005450	https://doi.org/10.2307/2005450	NOUN
ejpam-5288	409	1	[	[	X
ejpam-5288	409	2	6	6	NUM
ejpam-5288	409	3	]	]	PUNCT
ejpam-5288	409	4	s.	s.	PROPN
ejpam-5288	409	5	k.	k.	PROPN
ejpam-5288	409	6	ghosal	ghosal	PROPN
ejpam-5288	409	7	,	,	PUNCT
ejpam-5288	409	8	s.	s.	PROPN
ejpam-5288	409	9	mukhopadhyay	mukhopadhyay	PROPN
ejpam-5288	409	10	,	,	PUNCT
ejpam-5288	409	11	s.	s.	PROPN
ejpam-5288	409	12	hossain	hossain	PROPN
ejpam-5288	409	13	,	,	PUNCT
ejpam-5288	409	14	r.	r.	PROPN
ejpam-5288	409	15	sarkar	sarkar	PROPN
ejpam-5288	409	16	,	,	PUNCT
ejpam-5288	409	17	application	application	NOUN
ejpam-5288	409	18	of	of	ADP
ejpam-5288	409	19	lah	lah	PROPN
ejpam-5288	409	20	transform	transform	NOUN
ejpam-5288	409	21	for	for	ADP
ejpam-5288	409	22	security	security	NOUN
ejpam-5288	409	23	and	and	CCONJ
ejpam-5288	409	24	privacy	privacy	NOUN
ejpam-5288	409	25	of	of	ADP
ejpam-5288	409	26	data	datum	NOUN
ejpam-5288	409	27	through	through	ADP
ejpam-5288	409	28	information	information	NOUN
ejpam-5288	409	29	hiding	hide	VERB
ejpam-5288	409	30	in	in	ADP
ejpam-5288	409	31	telecommunication	telecommunication	NOUN
ejpam-5288	409	32	,	,	PUNCT
ejpam-5288	409	33	t.	t.	PROPN
ejpam-5288	409	34	on	on	ADP
ejpam-5288	409	35	emerg	emerg	PROPN
ejpam-5288	409	36	.	.	PUNCT
ejpam-5288	410	1	telecommun	telecommun	PROPN
ejpam-5288	410	2	.	.	PUNCT
ejpam-5288	411	1	t.	t.	PROPN
ejpam-5288	411	2	,	,	PUNCT
ejpam-5288	411	3	32	32	NUM
ejpam-5288	411	4	(	(	PUNCT
ejpam-5288	411	5	2020	2020	NUM
ejpam-5288	411	6	)	)	PUNCT
ejpam-5288	411	7	,	,	PUNCT
ejpam-5288	411	8	no	no	INTJ
ejpam-5288	411	9	.	.	NOUN
ejpam-5288	411	10	2	2	NUM
ejpam-5288	411	11	,	,	PUNCT
ejpam-5288	411	12	e3984	e3984	PROPN
ejpam-5288	411	13	.	.	PUNCT
ejpam-5288	411	14	https://doi:10.1002	https://doi:10.1002	PROPN
ejpam-5288	411	15	/	/	SYM
ejpam-5288	411	16	ett.3984	ett.3984	PROPN
ejpam-5288	411	17	[	[	X
ejpam-5288	411	18	7	7	X
ejpam-5288	411	19	]	]	X
ejpam-5288	411	20	d.	d.	PROPN
ejpam-5288	411	21	gun	gun	PROPN
ejpam-5288	411	22	,	,	PUNCT
ejpam-5288	411	23	y.	y.	PROPN
ejpam-5288	411	24	simsek	simsek	PROPN
ejpam-5288	411	25	,	,	PUNCT
ejpam-5288	411	26	combinatorial	combinatorial	ADJ
ejpam-5288	411	27	sums	sum	NOUN
ejpam-5288	411	28	involving	involve	VERB
ejpam-5288	411	29	stirling	stirling	NOUN
ejpam-5288	411	30	,	,	PUNCT
ejpam-5288	411	31	fubini	fubini	NOUN
ejpam-5288	411	32	,	,	PUNCT
ejpam-5288	411	33	bernoulli	bernoulli	NOUN
ejpam-5288	411	34	numbers	number	NOUN
ejpam-5288	411	35	and	and	CCONJ
ejpam-5288	411	36	approximate	approximate	ADJ
ejpam-5288	411	37	values	value	NOUN
ejpam-5288	411	38	of	of	ADP
ejpam-5288	411	39	catalan	catalan	NOUN
ejpam-5288	411	40	numbers	number	NOUN
ejpam-5288	411	41	,	,	PUNCT
ejpam-5288	411	42	adv	adv	PROPN
ejpam-5288	411	43	.	.	PUNCT
ejpam-5288	411	44	stud	stud	PROPN
ejpam-5288	411	45	.	.	PUNCT
ejpam-5288	412	1	contemp	contemp	NOUN
ejpam-5288	412	2	.	.	PUNCT
ejpam-5288	413	1	math	math	NOUN
ejpam-5288	413	2	.	.	PUNCT
ejpam-5288	413	3	,	,	PUNCT
ejpam-5288	414	1	kyungshang	kyungshang	PROPN
ejpam-5288	414	2	,	,	PUNCT
ejpam-5288	414	3	30	30	NUM
ejpam-5288	414	4	(	(	PUNCT
ejpam-5288	414	5	2020	2020	NUM
ejpam-5288	414	6	)	)	PUNCT
ejpam-5288	414	7	,	,	PUNCT
ejpam-5288	414	8	no	no	INTJ
ejpam-5288	414	9	.	.	NOUN
ejpam-5288	414	10	4	4	NUM
ejpam-5288	414	11	,	,	PUNCT
ejpam-5288	414	12	503	503	NUM
ejpam-5288	414	13	-	-	SYM
ejpam-5288	414	14	513	513	NUM
ejpam-5288	414	15	.	.	PUNCT
ejpam-5288	415	1	[	[	X
ejpam-5288	415	2	8	8	NUM
ejpam-5288	415	3	]	]	X
ejpam-5288	415	4	l.	l.	PROPN
ejpam-5288	415	5	c.	c.	PROPN
ejpam-5288	415	6	hsu	hsu	PROPN
ejpam-5288	415	7	,	,	PUNCT
ejpam-5288	415	8	p.	p.	PROPN
ejpam-5288	415	9	j.-s	j.-s	PROPN
ejpam-5288	415	10	.	.	PUNCT
ejpam-5288	416	1	shiue	shiue	PROPN
ejpam-5288	416	2	,	,	PUNCT
ejpam-5288	416	3	a	a	DET
ejpam-5288	416	4	unified	unified	ADJ
ejpam-5288	416	5	approach	approach	NOUN
ejpam-5288	416	6	to	to	ADP
ejpam-5288	416	7	generalized	generalize	VERB
ejpam-5288	416	8	stirling	stirling	NOUN
ejpam-5288	416	9	numbers	number	NOUN
ejpam-5288	416	10	,	,	PUNCT
ejpam-5288	416	11	adv	adv	PROPN
ejpam-5288	416	12	.	.	PUNCT
ejpam-5288	416	13	appl	appl	PROPN
ejpam-5288	416	14	.	.	PROPN
ejpam-5288	416	15	math	math	PROPN
ejpam-5288	416	16	.	.	PUNCT
ejpam-5288	417	1	,	,	PUNCT
ejpam-5288	417	2	20	20	NUM
ejpam-5288	417	3	(	(	PUNCT
ejpam-5288	417	4	1998	1998	NUM
ejpam-5288	417	5	)	)	PUNCT
ejpam-5288	417	6	,	,	PUNCT
ejpam-5288	417	7	no	no	INTJ
ejpam-5288	417	8	.	.	NOUN
ejpam-5288	417	9	3	3	NUM
ejpam-5288	417	10	,	,	PUNCT
ejpam-5288	417	11	366	366	NUM
ejpam-5288	417	12	-	-	SYM
ejpam-5288	417	13	384	384	NUM
ejpam-5288	417	14	.	.	PUNCT
ejpam-5288	418	1	https://doi.org/10.1006/aama.1998.0586	https://doi.org/10.1006/aama.1998.0586	PROPN
ejpam-5288	418	2	[	[	X
ejpam-5288	418	3	9	9	NUM
ejpam-5288	418	4	]	]	X
ejpam-5288	418	5	b.	b.	PROPN
ejpam-5288	418	6	m.	m.	PROPN
ejpam-5288	418	7	kim	kim	PROPN
ejpam-5288	418	8	,	,	PUNCT
ejpam-5288	418	9	y.	y.	PROPN
ejpam-5288	418	10	kim	kim	PROPN
ejpam-5288	418	11	,	,	PUNCT
ejpam-5288	418	12	j.-w	j.-w	PROPN
ejpam-5288	418	13	.	.	PUNCT
ejpam-5288	419	1	park	park	PROPN
ejpam-5288	419	2	,	,	PUNCT
ejpam-5288	419	3	on	on	ADP
ejpam-5288	419	4	the	the	DET
ejpam-5288	419	5	reciprocal	reciprocal	ADJ
ejpam-5288	419	6	degenerate	degenerate	ADJ
ejpam-5288	419	7	lah	lah	ADJ
ejpam-5288	419	8	-	-	PUNCT
ejpam-5288	419	9	bell	bell	NOUN
ejpam-5288	419	10	polynomials	polynomial	NOUN
ejpam-5288	419	11	and	and	CCONJ
ejpam-5288	419	12	numbers	number	NOUN
ejpam-5288	419	13	,	,	PUNCT
ejpam-5288	419	14	adv	adv	PROPN
ejpam-5288	419	15	.	.	PUNCT
ejpam-5288	419	16	stud	stud	PROPN
ejpam-5288	419	17	.	.	PUNCT
ejpam-5288	420	1	contemp	contemp	NOUN
ejpam-5288	420	2	.	.	PUNCT
ejpam-5288	421	1	math	math	NOUN
ejpam-5288	421	2	.	.	PUNCT
ejpam-5288	421	3	,	,	PUNCT
ejpam-5288	422	1	kyungshang	kyungshang	PROPN
ejpam-5288	422	2	,	,	PUNCT
ejpam-5288	422	3	32	32	NUM
ejpam-5288	422	4	,	,	PUNCT
ejpam-5288	422	5	no	no	INTJ
ejpam-5288	422	6	.	.	NOUN
ejpam-5288	422	7	1	1	NUM
ejpam-5288	422	8	,	,	PUNCT
ejpam-5288	422	9	63	63	NUM
ejpam-5288	422	10	-	-	SYM
ejpam-5288	422	11	70	70	NUM
ejpam-5288	422	12	(	(	PUNCT
ejpam-5288	422	13	2022	2022	NUM
ejpam-5288	422	14	)	)	PUNCT
ejpam-5288	422	15	.	.	PUNCT
ejpam-5288	423	1	[	[	X
ejpam-5288	423	2	10	10	NUM
ejpam-5288	423	3	]	]	X
ejpam-5288	423	4	d.	d.	PROPN
ejpam-5288	423	5	s.	s.	PROPN
ejpam-5288	423	6	kim	kim	PROPN
ejpam-5288	423	7	,	,	PUNCT
ejpam-5288	423	8	h.	h.	PROPN
ejpam-5288	423	9	k.	k.	PROPN
ejpam-5288	423	10	kim	kim	PROPN
ejpam-5288	423	11	,	,	PUNCT
ejpam-5288	423	12	t.	t.	PROPN
ejpam-5288	423	13	kim	kim	PROPN
ejpam-5288	423	14	,	,	PUNCT
ejpam-5288	423	15	some	some	DET
ejpam-5288	423	16	identities	identity	NOUN
ejpam-5288	423	17	on	on	ADP
ejpam-5288	423	18	λ	λ	NOUN
ejpam-5288	423	19	-	-	NOUN
ejpam-5288	423	20	analogues	analogue	NOUN
ejpam-5288	423	21	of	of	ADP
ejpam-5288	423	22	r	r	NOUN
ejpam-5288	423	23	-	-	PUNCT
ejpam-5288	423	24	stirling	stirling	NOUN
ejpam-5288	423	25	numbers	number	NOUN
ejpam-5288	423	26	of	of	ADP
ejpam-5288	423	27	the	the	DET
ejpam-5288	423	28	second	second	ADJ
ejpam-5288	423	29	kind	kind	NOUN
ejpam-5288	423	30	,	,	PUNCT
ejpam-5288	423	31	eur	eur	PROPN
ejpam-5288	423	32	.	.	PUNCT
ejpam-5288	424	1	j.	j.	PROPN
ejpam-5288	424	2	pure	pure	PROPN
ejpam-5288	424	3	appl	appl	PROPN
ejpam-5288	424	4	.	.	PUNCT
ejpam-5288	424	5	math	math	PROPN
ejpam-5288	424	6	.	.	PUNCT
ejpam-5288	425	1	,	,	PUNCT
ejpam-5288	425	2	15	15	NUM
ejpam-5288	425	3	(	(	PUNCT
ejpam-5288	425	4	2022	2022	NUM
ejpam-5288	425	5	)	)	PUNCT
ejpam-5288	425	6	,	,	PUNCT
ejpam-5288	425	7	no	no	INTJ
ejpam-5288	425	8	.	.	NOUN
ejpam-5288	425	9	3	3	NUM
ejpam-5288	425	10	,	,	PUNCT
ejpam-5288	425	11	1054	1054	NUM
ejpam-5288	425	12	-	-	SYM
ejpam-5288	425	13	1066	1066	NUM
ejpam-5288	425	14	.	.	PUNCT
ejpam-5288	426	1	https://doi.org/10.29020/nybg.ejpam.v15i3.4441	https://doi.org/10.29020/nybg.ejpam.v15i3.4441	ADP
ejpam-5288	426	2	references	reference	NOUN
ejpam-5288	426	3	1401	1401	NUM
ejpam-5288	426	4	[	[	X
ejpam-5288	426	5	11	11	NUM
ejpam-5288	426	6	]	]	X
ejpam-5288	426	7	d.	d.	PROPN
ejpam-5288	426	8	s.	s.	PROPN
ejpam-5288	426	9	kim	kim	PROPN
ejpam-5288	426	10	,	,	PUNCT
ejpam-5288	426	11	t.	t.	PROPN
ejpam-5288	426	12	kim	kim	PROPN
ejpam-5288	426	13	,	,	PUNCT
ejpam-5288	426	14	normal	normal	ADJ
ejpam-5288	426	15	ordering	ordering	NOUN
ejpam-5288	426	16	associated	associate	VERB
ejpam-5288	426	17	with	with	ADP
ejpam-5288	426	18	λ	λ	PROPN
ejpam-5288	426	19	-	-	PROPN
ejpam-5288	426	20	whitney	whitney	NOUN
ejpam-5288	426	21	numbers	number	NOUN
ejpam-5288	426	22	of	of	ADP
ejpam-5288	426	23	the	the	DET
ejpam-5288	426	24	first	first	ADJ
ejpam-5288	426	25	kind	kind	NOUN
ejpam-5288	426	26	in	in	ADP
ejpam-5288	426	27	λ	λ	NOUN
ejpam-5288	426	28	-	-	NOUN
ejpam-5288	426	29	shift	shift	NOUN
ejpam-5288	426	30	algebra	algebra	NOUN
ejpam-5288	426	31	,	,	PUNCT
ejpam-5288	426	32	russ	russ	PROPN
ejpam-5288	426	33	.	.	PUNCT
ejpam-5288	427	1	j.	j.	PROPN
ejpam-5288	427	2	math	math	PROPN
ejpam-5288	427	3	.	.	PUNCT
ejpam-5288	428	1	phys	phy	NOUN
ejpam-5288	428	2	.	.	PUNCT
ejpam-5288	428	3	,	,	PUNCT
ejpam-5288	428	4	30	30	NUM
ejpam-5288	428	5	(	(	PUNCT
ejpam-5288	428	6	2023	2023	NUM
ejpam-5288	428	7	)	)	PUNCT
ejpam-5288	428	8	,	,	PUNCT
ejpam-5288	428	9	no	no	INTJ
ejpam-5288	428	10	.	.	NOUN
ejpam-5288	428	11	3	3	NUM
ejpam-5288	428	12	,	,	PUNCT
ejpam-5288	428	13	310	310	NUM
ejpam-5288	428	14	-	-	SYM
ejpam-5288	428	15	319	319	NUM
ejpam-5288	428	16	.	.	PUNCT
ejpam-5288	429	1	https://doi.org/10.1134/s1061920823030044	https://doi.org/10.1134/s1061920823030044	PRON
ejpam-5288	430	1	[	[	X
ejpam-5288	430	2	12	12	NUM
ejpam-5288	430	3	]	]	X
ejpam-5288	430	4	d.	d.	PROPN
ejpam-5288	430	5	s.	s.	PROPN
ejpam-5288	430	6	kim	kim	PROPN
ejpam-5288	430	7	,	,	PUNCT
ejpam-5288	430	8	t.	t.	PROPN
ejpam-5288	430	9	kim	kim	PROPN
ejpam-5288	430	10	,	,	PUNCT
ejpam-5288	430	11	r	r	NOUN
ejpam-5288	430	12	-	-	PUNCT
ejpam-5288	430	13	extended	extend	VERB
ejpam-5288	430	14	lah	lah	NOUN
ejpam-5288	430	15	-	-	PUNCT
ejpam-5288	430	16	bell	bell	NOUN
ejpam-5288	430	17	numbers	number	NOUN
ejpam-5288	430	18	and	and	CCONJ
ejpam-5288	430	19	polynomials	polynomial	NOUN
ejpam-5288	430	20	associated	associate	VERB
ejpam-5288	430	21	with	with	ADP
ejpam-5288	430	22	r	r	NOUN
ejpam-5288	430	23	-	-	PUNCT
ejpam-5288	430	24	lah	lah	NOUN
ejpam-5288	430	25	numbers	number	NOUN
ejpam-5288	430	26	,	,	PUNCT
ejpam-5288	430	27	proc	proc	NOUN
ejpam-5288	430	28	.	.	PUNCT
ejpam-5288	431	1	jangjeon	jangjeon	PROPN
ejpam-5288	431	2	math	math	PROPN
ejpam-5288	431	3	.	.	PUNCT
ejpam-5288	432	1	soc	soc	PROPN
ejpam-5288	432	2	.	.	PROPN
ejpam-5288	432	3	,	,	PUNCT
ejpam-5288	432	4	24	24	NUM
ejpam-5288	432	5	(	(	PUNCT
ejpam-5288	432	6	2021	2021	NUM
ejpam-5288	432	7	)	)	PUNCT
ejpam-5288	432	8	,	,	PUNCT
ejpam-5288	432	9	no	no	INTJ
ejpam-5288	432	10	.	.	NOUN
ejpam-5288	432	11	1	1	NUM
ejpam-5288	432	12	,	,	PUNCT
ejpam-5288	432	13	1	1	NUM
ejpam-5288	432	14	-	-	SYM
ejpam-5288	432	15	10	10	NUM
ejpam-5288	432	16	.	.	PUNCT
ejpam-5288	433	1	[	[	X
ejpam-5288	433	2	13	13	NUM
ejpam-5288	433	3	]	]	X
ejpam-5288	433	4	d.	d.	PROPN
ejpam-5288	433	5	s.	s.	PROPN
ejpam-5288	433	6	kim	kim	PROPN
ejpam-5288	433	7	,	,	PUNCT
ejpam-5288	433	8	t.	t.	PROPN
ejpam-5288	433	9	kim	kim	PROPN
ejpam-5288	433	10	,	,	PUNCT
ejpam-5288	433	11	degenerate	degenerate	ADJ
ejpam-5288	433	12	sheffer	sheffer	NOUN
ejpam-5288	433	13	sequences	sequence	NOUN
ejpam-5288	433	14	and	and	CCONJ
ejpam-5288	433	15	λ	λ	NOUN
ejpam-5288	433	16	-	-	NOUN
ejpam-5288	433	17	sheffer	sheffer	NOUN
ejpam-5288	433	18	sequences	sequence	NOUN
ejpam-5288	433	19	,	,	PUNCT
ejpam-5288	433	20	j.	j.	PROPN
ejpam-5288	433	21	math	math	PROPN
ejpam-5288	433	22	.	.	PUNCT
ejpam-5288	434	1	anal	anal	PROPN
ejpam-5288	434	2	.	.	PUNCT
ejpam-5288	435	1	appl	appl	PROPN
ejpam-5288	435	2	.	.	PROPN
ejpam-5288	435	3	,	,	PUNCT
ejpam-5288	435	4	493	493	NUM
ejpam-5288	435	5	(	(	PUNCT
ejpam-5288	435	6	2021	2021	NUM
ejpam-5288	435	7	)	)	PUNCT
ejpam-5288	435	8	,	,	PUNCT
ejpam-5288	435	9	no	no	INTJ
ejpam-5288	435	10	.	.	NOUN
ejpam-5288	435	11	1	1	NUM
ejpam-5288	435	12	,	,	PUNCT
ejpam-5288	435	13	124521	124521	NUM
ejpam-5288	435	14	.	.	PUNCT
ejpam-5288	436	1	https://doi.org/10.1016/j.jmaa.2020.124521	https://doi.org/10.1016/j.jmaa.2020.124521	NOUN
ejpam-5288	436	2	[	[	X
ejpam-5288	436	3	14	14	NUM
ejpam-5288	436	4	]	]	PUNCT
ejpam-5288	436	5	t.	t.	PROPN
ejpam-5288	436	6	kim	kim	PROPN
ejpam-5288	436	7	,	,	PUNCT
ejpam-5288	436	8	d.	d.	PROPN
ejpam-5288	436	9	s.	s.	PROPN
ejpam-5288	436	10	kim	kim	PROPN
ejpam-5288	436	11	,	,	PUNCT
ejpam-5288	436	12	degenerate	degenerate	ADJ
ejpam-5288	436	13	laplace	laplace	NOUN
ejpam-5288	436	14	transform	transform	NOUN
ejpam-5288	436	15	and	and	CCONJ
ejpam-5288	436	16	degenerate	degenerate	ADJ
ejpam-5288	436	17	gamma	gamma	NOUN
ejpam-5288	436	18	function	function	NOUN
ejpam-5288	436	19	,	,	PUNCT
ejpam-5288	436	20	russ	russ	PROPN
ejpam-5288	436	21	.	.	PUNCT
ejpam-5288	437	1	j.	j.	PROPN
ejpam-5288	437	2	math	math	PROPN
ejpam-5288	437	3	.	.	PUNCT
ejpam-5288	438	1	phys	phy	NOUN
ejpam-5288	438	2	.	.	PUNCT
ejpam-5288	438	3	,	,	PUNCT
ejpam-5288	438	4	24	24	NUM
ejpam-5288	438	5	(	(	PUNCT
ejpam-5288	438	6	2017	2017	NUM
ejpam-5288	438	7	)	)	PUNCT
ejpam-5288	438	8	,	,	PUNCT
ejpam-5288	438	9	241–248	241–248	NUM
ejpam-5288	438	10	.	.	PUNCT
ejpam-5288	439	1	https://doi.org/10.1134/s1061920817020091	https://doi.org/10.1134/s1061920817020091	PRON
ejpam-5288	440	1	[	[	X
ejpam-5288	440	2	15	15	NUM
ejpam-5288	440	3	]	]	PUNCT
ejpam-5288	440	4	t.	t.	PROPN
ejpam-5288	440	5	kim	kim	PROPN
ejpam-5288	440	6	,	,	PUNCT
ejpam-5288	440	7	d.	d.	PROPN
ejpam-5288	440	8	s.	s.	PROPN
ejpam-5288	440	9	kim	kim	PROPN
ejpam-5288	440	10	,	,	PUNCT
ejpam-5288	440	11	combinatorial	combinatorial	ADJ
ejpam-5288	440	12	identities	identity	NOUN
ejpam-5288	440	13	involving	involve	VERB
ejpam-5288	440	14	degenerate	degenerate	ADJ
ejpam-5288	440	15	harmonic	harmonic	ADJ
ejpam-5288	440	16	and	and	CCONJ
ejpam-5288	440	17	hyperharmonic	hyperharmonic	ADJ
ejpam-5288	440	18	numbers	number	NOUN
ejpam-5288	440	19	,	,	PUNCT
ejpam-5288	440	20	adv	adv	PROPN
ejpam-5288	440	21	.	.	PUNCT
ejpam-5288	440	22	appl	appl	PROPN
ejpam-5288	440	23	.	.	PROPN
ejpam-5288	440	24	math	math	PROPN
ejpam-5288	440	25	.	.	PUNCT
ejpam-5288	441	1	,	,	PUNCT
ejpam-5288	441	2	148	148	NUM
ejpam-5288	441	3	(	(	PUNCT
ejpam-5288	441	4	2023	2023	NUM
ejpam-5288	441	5	)	)	PUNCT
ejpam-5288	441	6	,	,	PUNCT
ejpam-5288	441	7	paper	paper	NOUN
ejpam-5288	441	8	no	no	NOUN
ejpam-5288	441	9	.	.	PROPN
ejpam-5288	442	1	102535	102535	NUM
ejpam-5288	442	2	.	.	PUNCT
ejpam-5288	443	1	https://doi.org/10.1016/j.aam.2023.102535	https://doi.org/10.1016/j.aam.2023.102535	PROPN
ejpam-5288	444	1	[	[	X
ejpam-5288	444	2	16	16	NUM
ejpam-5288	444	3	]	]	PUNCT
ejpam-5288	444	4	t.	t.	PROPN
ejpam-5288	444	5	kim	kim	PROPN
ejpam-5288	444	6	,	,	PUNCT
ejpam-5288	444	7	d.	d.	PROPN
ejpam-5288	444	8	s.	s.	PROPN
ejpam-5288	444	9	kim	kim	PROPN
ejpam-5288	444	10	,	,	PUNCT
ejpam-5288	444	11	d.	d.	PROPN
ejpam-5288	444	12	v.	v.	PROPN
ejpam-5288	444	13	dolgy	dolgy	PROPN
ejpam-5288	444	14	,	,	PUNCT
ejpam-5288	444	15	j.-w	j.-w	PROPN
ejpam-5288	444	16	.	.	PUNCT
ejpam-5288	445	1	park	park	NOUN
ejpam-5288	445	2	,	,	PUNCT
ejpam-5288	445	3	degenerate	degenerate	ADJ
ejpam-5288	445	4	binomial	binomial	NOUN
ejpam-5288	445	5	and	and	CCONJ
ejpam-5288	445	6	poisson	poisson	PROPN
ejpam-5288	445	7	random	random	ADJ
ejpam-5288	445	8	variables	variable	NOUN
ejpam-5288	445	9	associated	associate	VERB
ejpam-5288	445	10	with	with	ADP
ejpam-5288	445	11	degenerate	degenerate	ADJ
ejpam-5288	445	12	lah	lah	NOUN
ejpam-5288	445	13	-	-	PUNCT
ejpam-5288	445	14	bell	bell	NOUN
ejpam-5288	445	15	polynomials	polynomial	NOUN
ejpam-5288	445	16	,	,	PUNCT
ejpam-5288	445	17	open	open	ADJ
ejpam-5288	445	18	math	math	NOUN
ejpam-5288	445	19	.	.	PUNCT
ejpam-5288	445	20	,	,	PUNCT
ejpam-5288	445	21	19	19	NUM
ejpam-5288	445	22	(	(	PUNCT
ejpam-5288	445	23	2021	2021	NUM
ejpam-5288	445	24	)	)	PUNCT
ejpam-5288	445	25	,	,	PUNCT
ejpam-5288	445	26	no	no	INTJ
ejpam-5288	445	27	.	.	NOUN
ejpam-5288	445	28	1	1	NUM
ejpam-5288	445	29	,	,	PUNCT
ejpam-5288	445	30	1588	1588	NUM
ejpam-5288	445	31	-	-	SYM
ejpam-5288	445	32	1597	1597	NUM
ejpam-5288	445	33	.	.	PUNCT
ejpam-5288	446	1	https://doi.org/10.1515/math-2021-0116	https://doi.org/10.1515/math-2021-0116	PROPN
ejpam-5288	447	1	[	[	X
ejpam-5288	447	2	17	17	NUM
ejpam-5288	447	3	]	]	PUNCT
ejpam-5288	447	4	t.	t.	PROPN
ejpam-5288	447	5	kim	kim	PROPN
ejpam-5288	447	6	,	,	PUNCT
ejpam-5288	447	7	d.	d.	PROPN
ejpam-5288	447	8	s.	s.	PROPN
ejpam-5288	447	9	kim	kim	PROPN
ejpam-5288	447	10	,	,	PUNCT
ejpam-5288	447	11	h.	h.	PROPN
ejpam-5288	447	12	k.	k.	PROPN
ejpam-5288	447	13	kim	kim	PROPN
ejpam-5288	447	14	,	,	PUNCT
ejpam-5288	447	15	normal	normal	ADJ
ejpam-5288	447	16	ordering	ordering	NOUN
ejpam-5288	447	17	associated	associate	VERB
ejpam-5288	447	18	with	with	ADP
ejpam-5288	447	19	λ	λ	PROPN
ejpam-5288	447	20	-	-	ADJ
ejpam-5288	447	21	stirling	stirling	ADJ
ejpam-5288	447	22	numbers	number	NOUN
ejpam-5288	447	23	in	in	ADP
ejpam-5288	447	24	λ	λ	NOUN
ejpam-5288	447	25	-	-	NOUN
ejpam-5288	447	26	shift	shift	NOUN
ejpam-5288	447	27	algebra	algebra	NOUN
ejpam-5288	447	28	,	,	PUNCT
ejpam-5288	447	29	demonstr	demonstr	NOUN
ejpam-5288	447	30	.	.	PUNCT
ejpam-5288	447	31	math	math	NOUN
ejpam-5288	447	32	.	.	PUNCT
ejpam-5288	447	33	,	,	PUNCT
ejpam-5288	447	34	56	56	NUM
ejpam-5288	447	35	(	(	PUNCT
ejpam-5288	447	36	2023	2023	NUM
ejpam-5288	447	37	)	)	PUNCT
ejpam-5288	447	38	,	,	PUNCT
ejpam-5288	447	39	no	no	INTJ
ejpam-5288	447	40	.	.	NOUN
ejpam-5288	447	41	1	1	NUM
ejpam-5288	447	42	,	,	PUNCT
ejpam-5288	447	43	paper	paper	NOUN
ejpam-5288	447	44	no	no	NOUN
ejpam-5288	447	45	.	.	PUNCT
ejpam-5288	447	46	20220250	20220250	NUM
ejpam-5288	447	47	.	.	PUNCT
ejpam-5288	448	1	https://doi.org/10.1515/dema-2022-0250	https://doi.org/10.1515/dema-2022-0250	PROPN
ejpam-5288	449	1	[	[	X
ejpam-5288	449	2	18	18	NUM
ejpam-5288	449	3	]	]	PUNCT
ejpam-5288	449	4	t.	t.	PROPN
ejpam-5288	449	5	kim	kim	PROPN
ejpam-5288	449	6	,	,	PUNCT
ejpam-5288	449	7	d.	d.	PROPN
ejpam-5288	449	8	s.	s.	PROPN
ejpam-5288	449	9	kim	kim	PROPN
ejpam-5288	449	10	,	,	PUNCT
ejpam-5288	449	11	h.	h.	PROPN
ejpam-5288	449	12	lee	lee	PROPN
ejpam-5288	449	13	,	,	PUNCT
ejpam-5288	449	14	j.	j.	PROPN
ejpam-5288	449	15	kwon	kwon	PROPN
ejpam-5288	449	16	,	,	PUNCT
ejpam-5288	449	17	representations	representation	NOUN
ejpam-5288	449	18	by	by	ADP
ejpam-5288	449	19	degenerate	degenerate	ADJ
ejpam-5288	449	20	daehee	daehee	NOUN
ejpam-5288	449	21	polynomials	polynomial	NOUN
ejpam-5288	449	22	,	,	PUNCT
ejpam-5288	449	23	open	open	ADJ
ejpam-5288	449	24	math	math	NOUN
ejpam-5288	449	25	.	.	PUNCT
ejpam-5288	449	26	,	,	PUNCT
ejpam-5288	449	27	20	20	NUM
ejpam-5288	449	28	(	(	PUNCT
ejpam-5288	449	29	2022	2022	NUM
ejpam-5288	449	30	)	)	PUNCT
ejpam-5288	449	31	,	,	PUNCT
ejpam-5288	449	32	no	no	INTJ
ejpam-5288	449	33	.	.	NOUN
ejpam-5288	449	34	1	1	NUM
ejpam-5288	449	35	,	,	PUNCT
ejpam-5288	449	36	179–194	179–194	NUM
ejpam-5288	449	37	.	.	PUNCT
ejpam-5288	450	1	[	[	X
ejpam-5288	450	2	19	19	NUM
ejpam-5288	450	3	]	]	PUNCT
ejpam-5288	450	4	t.	t.	PROPN
ejpam-5288	450	5	kim	kim	PROPN
ejpam-5288	450	6	,	,	PUNCT
ejpam-5288	450	7	d.	d.	PROPN
ejpam-5288	450	8	s.	s.	PROPN
ejpam-5288	450	9	kim	kim	PROPN
ejpam-5288	450	10	,	,	PUNCT
ejpam-5288	450	11	d.	d.	PROPN
ejpam-5288	450	12	v.	v.	PROPN
ejpam-5288	450	13	dolgy	dolgy	PROPN
ejpam-5288	450	14	,	,	PUNCT
ejpam-5288	450	15	h.	h.	PROPN
ejpam-5288	450	16	k.	k.	PROPN
ejpam-5288	450	17	kim	kim	PROPN
ejpam-5288	450	18	,	,	PUNCT
ejpam-5288	450	19	h.	h.	PROPN
ejpam-5288	450	20	lee	lee	PROPN
ejpam-5288	450	21	,	,	PUNCT
ejpam-5288	450	22	a	a	DET
ejpam-5288	450	23	new	new	ADJ
ejpam-5288	450	24	approach	approach	NOUN
ejpam-5288	450	25	to	to	ADP
ejpam-5288	450	26	bell	bell	NOUN
ejpam-5288	450	27	and	and	CCONJ
ejpam-5288	450	28	poly	poly	ADJ
ejpam-5288	450	29	-	-	PUNCT
ejpam-5288	450	30	bell	bell	NOUN
ejpam-5288	450	31	numbers	number	NOUN
ejpam-5288	450	32	and	and	CCONJ
ejpam-5288	450	33	polynomials	polynomial	NOUN
ejpam-5288	450	34	,	,	PUNCT
ejpam-5288	450	35	aims	aim	VERB
ejpam-5288	450	36	math	math	NOUN
ejpam-5288	450	37	.	.	PUNCT
ejpam-5288	451	1	,	,	PUNCT
ejpam-5288	451	2	7	7	NUM
ejpam-5288	451	3	(	(	PUNCT
ejpam-5288	451	4	2022	2022	NUM
ejpam-5288	451	5	)	)	PUNCT
ejpam-5288	451	6	,	,	PUNCT
ejpam-5288	452	1	no	no	INTJ
ejpam-5288	452	2	.	.	NOUN
ejpam-5288	452	3	3	3	NUM
ejpam-5288	452	4	,	,	PUNCT
ejpam-5288	452	5	4004–4016	4004–4016	NUM
ejpam-5288	452	6	.	.	PUNCT
ejpam-5288	453	1	[	[	X
ejpam-5288	453	2	20	20	NUM
ejpam-5288	453	3	]	]	PUNCT
ejpam-5288	453	4	t.	t.	PROPN
ejpam-5288	453	5	kim	kim	PROPN
ejpam-5288	453	6	,	,	PUNCT
ejpam-5288	453	7	d.	d.	PROPN
ejpam-5288	453	8	s.	s.	PROPN
ejpam-5288	453	9	kim	kim	PROPN
ejpam-5288	453	10	,	,	PUNCT
ejpam-5288	453	11	probabilistic	probabilistic	ADJ
ejpam-5288	453	12	degenerate	degenerate	ADJ
ejpam-5288	453	13	bell	bell	NOUN
ejpam-5288	453	14	polynomials	polynomial	NOUN
ejpam-5288	453	15	associated	associate	VERB
ejpam-5288	453	16	with	with	ADP
ejpam-5288	453	17	random	random	ADJ
ejpam-5288	453	18	variables	variable	NOUN
ejpam-5288	453	19	,	,	PUNCT
ejpam-5288	453	20	russ	russ	PROPN
ejpam-5288	453	21	.	.	PUNCT
ejpam-5288	454	1	j.	j.	PROPN
ejpam-5288	454	2	math	math	PROPN
ejpam-5288	454	3	.	.	PUNCT
ejpam-5288	455	1	phys	phy	NOUN
ejpam-5288	455	2	.	.	PUNCT
ejpam-5288	455	3	,	,	PUNCT
ejpam-5288	455	4	30	30	NUM
ejpam-5288	455	5	(	(	PUNCT
ejpam-5288	455	6	2023	2023	NUM
ejpam-5288	455	7	)	)	PUNCT
ejpam-5288	455	8	,	,	PUNCT
ejpam-5288	455	9	no	no	INTJ
ejpam-5288	455	10	.	.	PUNCT
ejpam-5288	456	1	4,528–542	4,528–542	NUM
ejpam-5288	456	2	.	.	PUNCT
ejpam-5288	457	1	[	[	X
ejpam-5288	457	2	21	21	NUM
ejpam-5288	457	3	]	]	PUNCT
ejpam-5288	457	4	t.	t.	PROPN
ejpam-5288	457	5	kim	kim	PROPN
ejpam-5288	457	6	,	,	PUNCT
ejpam-5288	457	7	d.	d.	PROPN
ejpam-5288	457	8	s.	s.	PROPN
ejpam-5288	457	9	kim	kim	PROPN
ejpam-5288	457	10	,	,	PUNCT
ejpam-5288	457	11	probabilistic	probabilistic	ADJ
ejpam-5288	457	12	bernoulli	bernoulli	NOUN
ejpam-5288	457	13	and	and	CCONJ
ejpam-5288	457	14	euler	euler	NOUN
ejpam-5288	457	15	polynomials	polynomial	NOUN
ejpam-5288	457	16	,	,	PUNCT
ejpam-5288	457	17	russ	russ	PROPN
ejpam-5288	457	18	.	.	PUNCT
ejpam-5288	458	1	j.	j.	PROPN
ejpam-5288	458	2	math	math	PROPN
ejpam-5288	458	3	.	.	PUNCT
ejpam-5288	459	1	phys	phy	NOUN
ejpam-5288	459	2	.	.	PUNCT
ejpam-5288	459	3	,	,	PUNCT
ejpam-5288	459	4	31	31	NUM
ejpam-5288	459	5	(	(	PUNCT
ejpam-5288	459	6	2024	2024	NUM
ejpam-5288	459	7	)	)	PUNCT
ejpam-5288	459	8	,	,	PUNCT
ejpam-5288	459	9	no	no	INTJ
ejpam-5288	459	10	.	.	NOUN
ejpam-5288	459	11	1	1	NUM
ejpam-5288	459	12	,	,	PUNCT
ejpam-5288	459	13	94–105	94–105	NOUN
ejpam-5288	459	14	.	.	PUNCT
ejpam-5288	460	1	[	[	X
ejpam-5288	460	2	22	22	NUM
ejpam-5288	460	3	]	]	X
ejpam-5288	460	4	d.	d.	PROPN
ejpam-5288	460	5	s.	s.	PROPN
ejpam-5288	460	6	kim	kim	PROPN
ejpam-5288	460	7	,	,	PUNCT
ejpam-5288	460	8	t.	t.	PROPN
ejpam-5288	460	9	kim	kim	PROPN
ejpam-5288	460	10	,	,	PUNCT
ejpam-5288	460	11	stirling	stirling	NOUN
ejpam-5288	460	12	numbers	number	NOUN
ejpam-5288	460	13	associated	associate	VERB
ejpam-5288	460	14	with	with	ADP
ejpam-5288	460	15	sequences	sequence	NOUN
ejpam-5288	460	16	of	of	ADP
ejpam-5288	460	17	polynomials	polynomial	NOUN
ejpam-5288	460	18	,	,	PUNCT
ejpam-5288	460	19	appl	appl	PROPN
ejpam-5288	460	20	.	.	PUNCT
ejpam-5288	461	1	comput	comput	PROPN
ejpam-5288	461	2	.	.	PUNCT
ejpam-5288	462	1	math	math	NOUN
ejpam-5288	462	2	,	,	PUNCT
ejpam-5288	462	3	22	22	NUM
ejpam-5288	462	4	(	(	PUNCT
ejpam-5288	462	5	2023	2023	NUM
ejpam-5288	462	6	)	)	PUNCT
ejpam-5288	462	7	,	,	PUNCT
ejpam-5288	462	8	no	no	INTJ
ejpam-5288	462	9	.	.	NOUN
ejpam-5288	462	10	1	1	NUM
ejpam-5288	462	11	,	,	PUNCT
ejpam-5288	462	12	80–115	80–115	NUM
ejpam-5288	462	13	.	.	PUNCT
ejpam-5288	463	1	[	[	X
ejpam-5288	463	2	23	23	NUM
ejpam-5288	463	3	]	]	PUNCT
ejpam-5288	463	4	t.	t.	PROPN
ejpam-5288	463	5	kim	kim	PROPN
ejpam-5288	463	6	,	,	PUNCT
ejpam-5288	463	7	d.	d.	PROPN
ejpam-5288	463	8	s.	s.	PROPN
ejpam-5288	463	9	kim	kim	PROPN
ejpam-5288	463	10	,	,	PUNCT
ejpam-5288	463	11	generalization	generalization	NOUN
ejpam-5288	463	12	of	of	ADP
ejpam-5288	463	13	spivey	spivey	PROPN
ejpam-5288	463	14	’s	’s	PART
ejpam-5288	463	15	recurrence	recurrence	PROPN
ejpam-5288	463	16	relation	relation	PROPN
ejpam-5288	463	17	,	,	PUNCT
ejpam-5288	463	18	russ	russ	PROPN
ejpam-5288	463	19	.	.	PUNCT
ejpam-5288	464	1	j.	j.	PROPN
ejpam-5288	464	2	math	math	PROPN
ejpam-5288	464	3	.	.	PUNCT
ejpam-5288	465	1	phys	phy	NOUN
ejpam-5288	465	2	.	.	PUNCT
ejpam-5288	465	3	,	,	PUNCT
ejpam-5288	465	4	31	31	NUM
ejpam-5288	465	5	(	(	PUNCT
ejpam-5288	465	6	2024	2024	NUM
ejpam-5288	465	7	)	)	PUNCT
ejpam-5288	465	8	,	,	PUNCT
ejpam-5288	465	9	no	no	INTJ
ejpam-5288	465	10	.	.	NOUN
ejpam-5288	465	11	2	2	NUM
ejpam-5288	465	12	,	,	PUNCT
ejpam-5288	465	13	218–226	218–226	NUM
ejpam-5288	465	14	.	.	PUNCT
ejpam-5288	466	1	[	[	X
ejpam-5288	466	2	24	24	NUM
ejpam-5288	466	3	]	]	PUNCT
ejpam-5288	466	4	b.	b.	PROPN
ejpam-5288	466	5	kurt	kurt	PROPN
ejpam-5288	466	6	,	,	PUNCT
ejpam-5288	466	7	y.	y.	PROPN
ejpam-5288	466	8	simsek	simsek	PROPN
ejpam-5288	466	9	,	,	PUNCT
ejpam-5288	466	10	on	on	ADP
ejpam-5288	466	11	the	the	DET
ejpam-5288	466	12	hermite	hermite	ADJ
ejpam-5288	466	13	base	base	NOUN
ejpam-5288	466	14	genocchi	genocchi	PROPN
ejpam-5288	466	15	polynomials	polynomial	VERB
ejpam-5288	466	16	,	,	PUNCT
ejpam-5288	466	17	adv	adv	PROPN
ejpam-5288	466	18	.	.	PUNCT
ejpam-5288	466	19	stud	stud	PROPN
ejpam-5288	466	20	.	.	PUNCT
ejpam-5288	467	1	contemp	contemp	NOUN
ejpam-5288	467	2	.	.	PUNCT
ejpam-5288	468	1	math	math	NOUN
ejpam-5288	468	2	.	.	PUNCT
ejpam-5288	468	3	,	,	PUNCT
ejpam-5288	469	1	kyungshang	kyungshang	PROPN
ejpam-5288	469	2	,	,	PUNCT
ejpam-5288	469	3	23	23	NUM
ejpam-5288	469	4	(	(	PUNCT
ejpam-5288	469	5	2013	2013	NUM
ejpam-5288	469	6	)	)	PUNCT
ejpam-5288	469	7	,	,	PUNCT
ejpam-5288	469	8	no	no	INTJ
ejpam-5288	469	9	.	.	NOUN
ejpam-5288	469	10	1	1	NUM
ejpam-5288	469	11	,	,	PUNCT
ejpam-5288	469	12	13	13	NUM
ejpam-5288	469	13	-	-	SYM
ejpam-5288	469	14	17	17	NUM
ejpam-5288	469	15	(	(	PUNCT
ejpam-5288	469	16	2013	2013	NUM
ejpam-5288	469	17	)	)	PUNCT
ejpam-5288	469	18	.	.	PUNCT
ejpam-5288	470	1	references	reference	NOUN
ejpam-5288	470	2	1402	1402	NUM
ejpam-5288	471	1	[	[	X
ejpam-5288	471	2	25	25	NUM
ejpam-5288	471	3	]	]	X
ejpam-5288	471	4	l.	l.	PROPN
ejpam-5288	471	5	luo	luo	PROPN
ejpam-5288	471	6	,	,	PUNCT
ejpam-5288	471	7	y.	y.	PROPN
ejpam-5288	471	8	ma	ma	PROPN
ejpam-5288	471	9	,	,	PUNCT
ejpam-5288	471	10	t.	t.	PROPN
ejpam-5288	471	11	kim	kim	PROPN
ejpam-5288	471	12	,	,	PUNCT
ejpam-5288	471	13	w.	w.	PROPN
ejpam-5288	471	14	liu	liu	PROPN
ejpam-5288	471	15	,	,	PUNCT
ejpam-5288	471	16	some	some	DET
ejpam-5288	471	17	identities	identity	NOUN
ejpam-5288	471	18	on	on	ADP
ejpam-5288	471	19	truncated	truncated	ADJ
ejpam-5288	471	20	polynomials	polynomial	NOUN
ejpam-5288	471	21	associated	associate	VERB
ejpam-5288	471	22	with	with	ADP
ejpam-5288	471	23	lah	lah	PROPN
ejpam-5288	471	24	-	-	PUNCT
ejpam-5288	471	25	bell	bell	NOUN
ejpam-5288	471	26	polynomials	polynomial	NOUN
ejpam-5288	471	27	,	,	PUNCT
ejpam-5288	471	28	appl	appl	PROPN
ejpam-5288	471	29	.	.	PROPN
ejpam-5288	471	30	math	math	PROPN
ejpam-5288	471	31	.	.	PUNCT
ejpam-5288	472	1	sci	sci	PROPN
ejpam-5288	472	2	.	.	PUNCT
ejpam-5288	473	1	eng	eng	PROPN
ejpam-5288	473	2	.	.	PROPN
ejpam-5288	473	3	,	,	PUNCT
ejpam-5288	473	4	31	31	NUM
ejpam-5288	473	5	(	(	PUNCT
ejpam-5288	473	6	2023	2023	NUM
ejpam-5288	473	7	)	)	PUNCT
ejpam-5288	473	8	,	,	PUNCT
ejpam-5288	473	9	no	no	INTJ
ejpam-5288	473	10	.	.	NOUN
ejpam-5288	473	11	1	1	NUM
ejpam-5288	473	12	,	,	PUNCT
ejpam-5288	473	13	2245539	2245539	NUM
ejpam-5288	473	14	.	.	PUNCT
ejpam-5288	473	15	https://doi.org/10.1080/27690911.2023.2245539	https://doi.org/10.1080/27690911.2023.2245539	X
ejpam-5288	474	1	[	[	X
ejpam-5288	474	2	26	26	NUM
ejpam-5288	474	3	]	]	PUNCT
ejpam-5288	474	4	m.	m.	NOUN
ejpam-5288	474	5	m.	m.	NOUN
ejpam-5288	474	6	mangontarum	mangontarum	PROPN
ejpam-5288	474	7	,	,	PUNCT
ejpam-5288	474	8	a.	a.	NOUN
ejpam-5288	474	9	p.	p.	NOUN
ejpam-5288	474	10	macodi	macodi	NOUN
ejpam-5288	474	11	-	-	PUNCT
ejpam-5288	474	12	ringia	ringia	ADJ
ejpam-5288	474	13	,	,	PUNCT
ejpam-5288	474	14	n.	n.	PROPN
ejpam-5288	474	15	s.	s.	PROPN
ejpam-5288	474	16	abdulcarim	abdulcarim	PROPN
ejpam-5288	474	17	,	,	PUNCT
ejpam-5288	474	18	the	the	DET
ejpam-5288	474	19	translated	translate	VERB
ejpam-5288	474	20	dowling	dowling	NOUN
ejpam-5288	474	21	polynomials	polynomial	NOUN
ejpam-5288	474	22	and	and	CCONJ
ejpam-5288	474	23	numbers	number	NOUN
ejpam-5288	474	24	,	,	PUNCT
ejpam-5288	474	25	int	int	NOUN
ejpam-5288	474	26	.	.	PUNCT
ejpam-5288	475	1	sch	sch	PROPN
ejpam-5288	475	2	.	.	PUNCT
ejpam-5288	476	1	res	re	NOUN
ejpam-5288	476	2	.	.	PUNCT
ejpam-5288	477	1	not	not	PART
ejpam-5288	477	2	.	.	PUNCT
ejpam-5288	478	1	,	,	PUNCT
ejpam-5288	478	2	2014	2014	NUM
ejpam-5288	478	3	(	(	PUNCT
ejpam-5288	478	4	2014	2014	NUM
ejpam-5288	478	5	)	)	PUNCT
ejpam-5288	478	6	,	,	PUNCT
ejpam-5288	478	7	article	article	NOUN
ejpam-5288	478	8	i	i	PROPN
ejpam-5288	478	9	d	d	PROPN
ejpam-5288	478	10	678408	678408	NUM
ejpam-5288	478	11	.	.	PUNCT
ejpam-5288	479	1	https://doi.org/10.1155/2014/678408	https://doi.org/10.1155/2014/678408	VERB
ejpam-5288	479	2	[	[	X
ejpam-5288	479	3	27	27	NUM
ejpam-5288	479	4	]	]	PUNCT
ejpam-5288	479	5	j.-w	j.-w	PROPN
ejpam-5288	479	6	.	.	PUNCT
ejpam-5288	480	1	park	park	NOUN
ejpam-5288	480	2	,	,	PUNCT
ejpam-5288	480	3	s.-s	s.-	NOUN
ejpam-5288	480	4	.	.	PUNCT
ejpam-5288	481	1	pyo	pyo	PROPN
ejpam-5288	481	2	,	,	PUNCT
ejpam-5288	481	3	a	a	DET
ejpam-5288	481	4	note	note	NOUN
ejpam-5288	481	5	on	on	ADP
ejpam-5288	481	6	degenerate	degenerate	ADJ
ejpam-5288	481	7	bernoulli	bernoulli	NOUN
ejpam-5288	481	8	polynomials	polynomial	NOUN
ejpam-5288	481	9	arising	arise	VERB
ejpam-5288	481	10	from	from	ADP
ejpam-5288	481	11	umbral	umbral	ADJ
ejpam-5288	481	12	calculus	calculus	NOUN
ejpam-5288	481	13	,	,	PUNCT
ejpam-5288	481	14	adv	adv	PROPN
ejpam-5288	481	15	.	.	PUNCT
ejpam-5288	481	16	stud	stud	PROPN
ejpam-5288	481	17	.	.	PUNCT
ejpam-5288	482	1	contemp	contemp	NOUN
ejpam-5288	482	2	.	.	PUNCT
ejpam-5288	483	1	math	math	NOUN
ejpam-5288	483	2	.	.	PUNCT
ejpam-5288	483	3	,	,	PUNCT
ejpam-5288	484	1	kyungshang	kyungshang	PROPN
ejpam-5288	484	2	,	,	PUNCT
ejpam-5288	484	3	32(2022	32(2022	NUM
ejpam-5288	484	4	)	)	PUNCT
ejpam-5288	484	5	,	,	PUNCT
ejpam-5288	484	6	no	no	INTJ
ejpam-5288	484	7	.	.	NOUN
ejpam-5288	484	8	4	4	NUM
ejpam-5288	484	9	,	,	PUNCT
ejpam-5288	484	10	509	509	NUM
ejpam-5288	484	11	-	-	SYM
ejpam-5288	484	12	525	525	NUM
ejpam-5288	484	13	.	.	PUNCT
ejpam-5288	485	1	[	[	X
ejpam-5288	485	2	28	28	NUM
ejpam-5288	485	3	]	]	X
ejpam-5288	485	4	d.	d.	PROPN
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ejpam-5288	485	6	,	,	PUNCT
ejpam-5288	485	7	s.	s.	PROPN
ejpam-5288	485	8	wang	wang	PROPN
ejpam-5288	485	9	,	,	PUNCT
ejpam-5288	485	10	x.	x.	PROPN
ejpam-5288	485	11	zhang	zhang	PROPN
ejpam-5288	485	12	,	,	PUNCT
ejpam-5288	485	13	v.	v.	ADP
ejpam-5288	485	14	stoev	stoev	NOUN
ejpam-5288	485	15	,	,	PUNCT
ejpam-5288	485	16	t.	t.	NOUN
ejpam-5288	485	17	popmintchev	popmintchev	PROPN
ejpam-5288	485	18	,	,	PUNCT
ejpam-5288	485	19	analytical	analytical	ADJ
ejpam-5288	485	20	lahlaguerre	lahlaguerre	NOUN
ejpam-5288	485	21	optical	optical	ADJ
ejpam-5288	485	22	formalism	formalism	NOUN
ejpam-5288	485	23	for	for	ADP
ejpam-5288	485	24	perturbative	perturbative	ADJ
ejpam-5288	485	25	chromatic	chromatic	ADJ
ejpam-5288	485	26	dispersion	dispersion	NOUN
ejpam-5288	485	27	,	,	PUNCT
ejpam-5288	485	28	opti	opti	PROPN
ejpam-5288	485	29	.	.	PUNCT
ejpam-5288	486	1	express	express	VERB
ejpam-5288	486	2	30	30	NUM
ejpam-5288	486	3	(	(	PUNCT
ejpam-5288	486	4	2022	2022	NUM
ejpam-5288	486	5	)	)	PUNCT
ejpam-5288	486	6	,	,	PUNCT
ejpam-5288	486	7	no	no	INTJ
ejpam-5288	486	8	.	.	NOUN
ejpam-5288	487	1	22/24	22/24	NUM
ejpam-5288	487	2	,	,	PUNCT
ejpam-5288	487	3	40779	40779	NUM
ejpam-5288	487	4	-	-	SYM
ejpam-5288	487	5	40808	40808	NUM
ejpam-5288	487	6	.	.	PUNCT
ejpam-5288	488	1	https://	https://	PROPN
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ejpam-5288	488	3	/	/	SYM
ejpam-5288	489	1	oe.457139	oe.457139	PROPN
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ejpam-5288	489	3	29	29	NUM
ejpam-5288	489	4	]	]	PUNCT
ejpam-5288	489	5	d.	d.	PROPN
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ejpam-5288	489	7	,	,	PUNCT
ejpam-5288	489	8	s.	s.	PROPN
ejpam-5288	489	9	wang	wang	PROPN
ejpam-5288	489	10	,	,	PUNCT
ejpam-5288	489	11	z.	z.	PROPN
ejpam-5288	489	12	xiaoshi	xiaoshi	PROPN
ejpam-5288	489	13	,	,	PUNCT
ejpam-5288	489	14	v.	v.	ADP
ejpam-5288	489	15	stoev	stoev	NOUN
ejpam-5288	489	16	,	,	PUNCT
ejpam-5288	489	17	t.	t.	NOUN
ejpam-5288	489	18	popmintchev	popmintchev	PROPN
ejpam-5288	489	19	,	,	PUNCT
ejpam-5288	489	20	theory	theory	NOUN
ejpam-5288	489	21	of	of	ADP
ejpam-5288	489	22	the	the	DET
ejpam-5288	489	23	chromatic	chromatic	ADJ
ejpam-5288	489	24	dispersion	dispersion	NOUN
ejpam-5288	489	25	,	,	PUNCT
ejpam-5288	489	26	revisited	revisit	VERB
ejpam-5288	489	27	,	,	PUNCT
ejpam-5288	489	28	arxiv:2011.00066	arxiv:2011.00066	NOUN
ejpam-5288	489	29	[	[	X
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ejpam-5288	489	31	]	]	PUNCT
ejpam-5288	489	32	.	.	PUNCT
ejpam-5288	490	1	[	[	X
ejpam-5288	490	2	30	30	NUM
ejpam-5288	490	3	]	]	X
ejpam-5288	490	4	s.	s.	PROPN
ejpam-5288	490	5	roman	roman	PROPN
ejpam-5288	490	6	,	,	PUNCT
ejpam-5288	490	7	the	the	DET
ejpam-5288	490	8	umbral	umbral	ADJ
ejpam-5288	490	9	calculus	calculus	NOUN
ejpam-5288	490	10	,	,	PUNCT
ejpam-5288	490	11	berlin	berlin	PROPN
ejpam-5288	490	12	:	:	PUNCT
ejpam-5288	490	13	springer	springer	NOUN
ejpam-5288	490	14	,	,	PUNCT
ejpam-5288	490	15	2005	2005	NUM
ejpam-5288	490	16	.	.	PUNCT
ejpam-5288	491	1	[	[	X
ejpam-5288	491	2	31	31	NUM
ejpam-5288	491	3	]	]	PUNCT
ejpam-5288	491	4	s.	s.	PROPN
ejpam-5288	491	5	m.	m.	PROPN
ejpam-5288	491	6	ross	ross	PROPN
ejpam-5288	491	7	,	,	PUNCT
ejpam-5288	491	8	introduction	introduction	NOUN
ejpam-5288	491	9	to	to	ADP
ejpam-5288	491	10	probability	probability	NOUN
ejpam-5288	491	11	models	model	NOUN
ejpam-5288	491	12	,	,	PUNCT
ejpam-5288	491	13	12th	12th	ADJ
ejpam-5288	491	14	ed	ed	NOUN
ejpam-5288	491	15	.	.	PROPN
ejpam-5288	491	16	,	,	PUNCT
ejpam-5288	491	17	london	london	PROPN
ejpam-5288	491	18	:	:	PUNCT
ejpam-5288	491	19	academic	academic	ADJ
ejpam-5288	491	20	press	press	NOUN
ejpam-5288	491	21	,	,	PUNCT
ejpam-5288	491	22	2019	2019	NUM
ejpam-5288	491	23	.	.	PUNCT
ejpam-5288	492	1	[	[	X
ejpam-5288	492	2	32	32	NUM
ejpam-5288	492	3	]	]	X
ejpam-5288	492	4	y.	y.	NOUN
ejpam-5288	492	5	simsek	simsek	PROPN
ejpam-5288	492	6	,	,	PUNCT
ejpam-5288	492	7	identities	identity	NOUN
ejpam-5288	492	8	and	and	CCONJ
ejpam-5288	492	9	relations	relation	NOUN
ejpam-5288	492	10	related	relate	VERB
ejpam-5288	492	11	to	to	ADP
ejpam-5288	492	12	combinatorial	combinatorial	ADJ
ejpam-5288	492	13	numbers	number	NOUN
ejpam-5288	492	14	and	and	CCONJ
ejpam-5288	492	15	polynomials	polynomial	NOUN
ejpam-5288	492	16	,	,	PUNCT
ejpam-5288	492	17	proc	proc	NOUN
ejpam-5288	492	18	.	.	PUNCT
ejpam-5288	493	1	jangjeon	jangjeon	PROPN
ejpam-5288	493	2	math	math	PROPN
ejpam-5288	493	3	.	.	PUNCT
ejpam-5288	494	1	soc	soc	PROPN
ejpam-5288	494	2	.	.	PUNCT
ejpam-5288	494	3	,	,	PUNCT
ejpam-5288	494	4	20	20	NUM
ejpam-5288	494	5	(	(	PUNCT
ejpam-5288	494	6	2017	2017	NUM
ejpam-5288	494	7	)	)	PUNCT
ejpam-5288	494	8	,	,	PUNCT
ejpam-5288	494	9	no	no	INTJ
ejpam-5288	494	10	.	.	NOUN
ejpam-5288	494	11	1	1	NUM
ejpam-5288	494	12	,	,	PUNCT
ejpam-5288	494	13	127	127	NUM
ejpam-5288	494	14	-	-	SYM
ejpam-5288	494	15	135	135	NUM
ejpam-5288	494	16	.	.	PUNCT