id	sid	tid	token	lemma	pos
ejpam-5011	1	1	european	european	PROPN
ejpam-5011	1	2	journal	journal	PROPN
ejpam-5011	1	3	of	of	ADP
ejpam-5011	1	4	pure	pure	ADJ
ejpam-5011	1	5	and	and	CCONJ
ejpam-5011	1	6	applied	apply	VERB
ejpam-5011	1	7	mathematics	mathematic	NOUN
ejpam-5011	1	8	vol	vol	NOUN
ejpam-5011	1	9	.	.	PROPN
ejpam-5011	2	1	17	17	NUM
ejpam-5011	2	2	,	,	PUNCT
ejpam-5011	2	3	no	no	INTJ
ejpam-5011	2	4	.	.	NOUN
ejpam-5011	2	5	1	1	NUM
ejpam-5011	2	6	,	,	PUNCT
ejpam-5011	2	7	2024	2024	NUM
ejpam-5011	2	8	,	,	PUNCT
ejpam-5011	2	9	1	1	NUM
ejpam-5011	2	10	-	-	SYM
ejpam-5011	2	11	10	10	NUM
ejpam-5011	2	12	issn	issn	PROPN
ejpam-5011	2	13	1307	1307	NUM
ejpam-5011	2	14	-	-	SYM
ejpam-5011	2	15	5543	5543	NUM
ejpam-5011	2	16	–	–	PUNCT
ejpam-5011	2	17	ejpam.com	ejpam.com	X
ejpam-5011	2	18	published	publish	VERB
ejpam-5011	2	19	by	by	ADP
ejpam-5011	2	20	new	new	PROPN
ejpam-5011	2	21	york	york	PROPN
ejpam-5011	2	22	business	business	PROPN
ejpam-5011	2	23	global	global	ADJ
ejpam-5011	2	24	study	study	NOUN
ejpam-5011	2	25	on	on	ADP
ejpam-5011	2	26	degenerate	degenerate	ADJ
ejpam-5011	2	27	stirling	stirling	NOUN
ejpam-5011	2	28	numbers	number	NOUN
ejpam-5011	2	29	dae	dae	VERB
ejpam-5011	2	30	san	san	PROPN
ejpam-5011	2	31	kim1	kim1	PROPN
ejpam-5011	2	32	,	,	PUNCT
ejpam-5011	2	33	taekyun	taekyun	VERB
ejpam-5011	2	34	kim2	kim2	PROPN
ejpam-5011	2	35	,	,	PUNCT
ejpam-5011	2	36	*	*	PUNCT
ejpam-5011	2	37	,	,	PUNCT
ejpam-5011	2	38	jongkyum	jongkyum	PROPN
ejpam-5011	2	39	kwon3	kwon3	PROPN
ejpam-5011	2	40	,	,	PUNCT
ejpam-5011	2	41	*	*	PROPN
ejpam-5011	2	42	1	1	NUM
ejpam-5011	2	43	department	department	NOUN
ejpam-5011	2	44	of	of	ADP
ejpam-5011	2	45	mathematics	mathematics	PROPN
ejpam-5011	2	46	,	,	PUNCT
ejpam-5011	2	47	sogang	sogang	PROPN
ejpam-5011	2	48	university	university	PROPN
ejpam-5011	2	49	,	,	PUNCT
ejpam-5011	2	50	seoul	seoul	PROPN
ejpam-5011	2	51	121	121	NUM
ejpam-5011	2	52	-	-	SYM
ejpam-5011	2	53	742	742	NUM
ejpam-5011	2	54	,	,	PUNCT
ejpam-5011	2	55	republic	republic	NOUN
ejpam-5011	2	56	of	of	ADP
ejpam-5011	2	57	korea	korea	PROPN
ejpam-5011	2	58	2	2	PROPN
ejpam-5011	2	59	department	department	NOUN
ejpam-5011	2	60	of	of	ADP
ejpam-5011	2	61	mathematics	mathematic	NOUN
ejpam-5011	2	62	,	,	PUNCT
ejpam-5011	2	63	kwangwoon	kwangwoon	NOUN
ejpam-5011	2	64	university	university	NOUN
ejpam-5011	2	65	,	,	PUNCT
ejpam-5011	2	66	seoul	seoul	PROPN
ejpam-5011	2	67	139	139	NUM
ejpam-5011	2	68	-	-	SYM
ejpam-5011	2	69	701	701	NUM
ejpam-5011	2	70	,	,	PUNCT
ejpam-5011	2	71	republic	republic	NOUN
ejpam-5011	2	72	of	of	ADP
ejpam-5011	2	73	korea	korea	PROPN
ejpam-5011	2	74	3	3	PROPN
ejpam-5011	2	75	department	department	PROPN
ejpam-5011	2	76	of	of	ADP
ejpam-5011	2	77	mathematics	mathematics	PROPN
ejpam-5011	2	78	education	education	NOUN
ejpam-5011	2	79	,	,	PUNCT
ejpam-5011	2	80	gyeongsang	gyeongsang	PROPN
ejpam-5011	2	81	national	national	PROPN
ejpam-5011	2	82	university	university	PROPN
ejpam-5011	2	83	,	,	PUNCT
ejpam-5011	2	84	jinju	jinju	NOUN
ejpam-5011	2	85	52828	52828	NUM
ejpam-5011	2	86	,	,	PUNCT
ejpam-5011	2	87	republic	republic	NOUN
ejpam-5011	2	88	of	of	ADP
ejpam-5011	2	89	korea	korea	PROPN
ejpam-5011	2	90	abstract	abstract	NOUN
ejpam-5011	2	91	.	.	PUNCT
ejpam-5011	3	1	in	in	ADP
ejpam-5011	3	2	this	this	DET
ejpam-5011	3	3	paper	paper	NOUN
ejpam-5011	3	4	,	,	PUNCT
ejpam-5011	3	5	we	we	PRON
ejpam-5011	3	6	consider	consider	VERB
ejpam-5011	3	7	various	various	ADJ
ejpam-5011	3	8	stirling	stirling	NOUN
ejpam-5011	3	9	numbers	number	NOUN
ejpam-5011	3	10	of	of	ADP
ejpam-5011	3	11	both	both	DET
ejpam-5011	3	12	kinds	kind	NOUN
ejpam-5011	3	13	,	,	PUNCT
ejpam-5011	3	14	including	include	VERB
ejpam-5011	3	15	the	the	DET
ejpam-5011	3	16	unsigned	unsigned	ADJ
ejpam-5011	3	17	degenerate	degenerate	ADJ
ejpam-5011	3	18	stirling	stirling	NOUN
ejpam-5011	3	19	numbers	number	NOUN
ejpam-5011	3	20	of	of	ADP
ejpam-5011	3	21	the	the	DET
ejpam-5011	3	22	first	first	ADJ
ejpam-5011	3	23	kind	kind	NOUN
ejpam-5011	3	24	,	,	PUNCT
ejpam-5011	3	25	the	the	DET
ejpam-5011	3	26	degenerate	degenerate	ADJ
ejpam-5011	3	27	stirling	stirling	NOUN
ejpam-5011	3	28	numbers	number	NOUN
ejpam-5011	3	29	of	of	ADP
ejpam-5011	3	30	the	the	DET
ejpam-5011	3	31	second	second	ADJ
ejpam-5011	3	32	kind	kind	NOUN
ejpam-5011	3	33	,	,	PUNCT
ejpam-5011	3	34	the	the	DET
ejpam-5011	3	35	unsigned	unsigned	ADJ
ejpam-5011	3	36	degenerate	degenerate	ADJ
ejpam-5011	3	37	r	r	NOUN
ejpam-5011	3	38	-	-	PUNCT
ejpam-5011	3	39	stirling	stirling	NOUN
ejpam-5011	3	40	numbers	number	NOUN
ejpam-5011	3	41	of	of	ADP
ejpam-5011	3	42	the	the	DET
ejpam-5011	3	43	first	first	ADJ
ejpam-5011	3	44	kind	kind	NOUN
ejpam-5011	3	45	and	and	CCONJ
ejpam-5011	3	46	the	the	DET
ejpam-5011	3	47	degenerate	degenerate	ADJ
ejpam-5011	3	48	r	r	NOUN
ejpam-5011	3	49	-	-	PUNCT
ejpam-5011	3	50	stirling	stirling	NOUN
ejpam-5011	3	51	numbers	number	NOUN
ejpam-5011	3	52	of	of	ADP
ejpam-5011	3	53	the	the	DET
ejpam-5011	3	54	second	second	ADJ
ejpam-5011	3	55	kind	kind	NOUN
ejpam-5011	3	56	.	.	PUNCT
ejpam-5011	4	1	the	the	DET
ejpam-5011	4	2	aim	aim	NOUN
ejpam-5011	4	3	of	of	ADP
ejpam-5011	4	4	this	this	DET
ejpam-5011	4	5	paper	paper	NOUN
ejpam-5011	4	6	is	be	AUX
ejpam-5011	4	7	by	by	ADP
ejpam-5011	4	8	using	use	VERB
ejpam-5011	4	9	generating	generating	NOUN
ejpam-5011	4	10	functions	function	NOUN
ejpam-5011	4	11	to	to	PART
ejpam-5011	4	12	further	far	ADV
ejpam-5011	4	13	study	study	VERB
ejpam-5011	4	14	explicit	explicit	ADJ
ejpam-5011	4	15	expressions	expression	NOUN
ejpam-5011	4	16	,	,	PUNCT
ejpam-5011	4	17	some	some	DET
ejpam-5011	4	18	identities	identity	NOUN
ejpam-5011	4	19	and	and	CCONJ
ejpam-5011	4	20	equivalent	equivalent	ADJ
ejpam-5011	4	21	relations	relation	NOUN
ejpam-5011	4	22	for	for	ADP
ejpam-5011	4	23	those	those	DET
ejpam-5011	4	24	stirling	stirling	NOUN
ejpam-5011	4	25	numbers	number	NOUN
ejpam-5011	4	26	.	.	PUNCT
ejpam-5011	5	1	2020	2020	NUM
ejpam-5011	5	2	mathematics	mathematic	NOUN
ejpam-5011	5	3	subject	subject	NOUN
ejpam-5011	5	4	classifications	classification	NOUN
ejpam-5011	5	5	:	:	PUNCT
ejpam-5011	5	6	11b73	11b73	NUM
ejpam-5011	5	7	,	,	PUNCT
ejpam-5011	5	8	11b83	11b83	NUM
ejpam-5011	5	9	key	key	ADJ
ejpam-5011	5	10	words	word	NOUN
ejpam-5011	5	11	and	and	CCONJ
ejpam-5011	5	12	phrases	phrase	NOUN
ejpam-5011	5	13	:	:	PUNCT
ejpam-5011	5	14	unsigned	unsigned	ADJ
ejpam-5011	5	15	degenerate	degenerate	ADJ
ejpam-5011	5	16	stirling	stirling	NOUN
ejpam-5011	5	17	numbers	number	NOUN
ejpam-5011	5	18	of	of	ADP
ejpam-5011	5	19	the	the	DET
ejpam-5011	5	20	first	first	ADJ
ejpam-5011	5	21	kind	kind	NOUN
ejpam-5011	5	22	,	,	PUNCT
ejpam-5011	5	23	unsigned	unsigned	ADJ
ejpam-5011	5	24	degenerate	degenerate	ADJ
ejpam-5011	5	25	r	r	NOUN
ejpam-5011	5	26	-	-	PUNCT
ejpam-5011	5	27	stirling	stirling	NOUN
ejpam-5011	5	28	numbers	number	NOUN
ejpam-5011	5	29	of	of	ADP
ejpam-5011	5	30	the	the	DET
ejpam-5011	5	31	first	first	ADJ
ejpam-5011	5	32	kind	kind	NOUN
ejpam-5011	5	33	,	,	PUNCT
ejpam-5011	5	34	degenerate	degenerate	ADJ
ejpam-5011	5	35	stirling	stirling	NOUN
ejpam-5011	5	36	numbers	number	NOUN
ejpam-5011	5	37	of	of	ADP
ejpam-5011	5	38	the	the	DET
ejpam-5011	5	39	second	second	ADJ
ejpam-5011	5	40	kind	kind	NOUN
ejpam-5011	5	41	,	,	PUNCT
ejpam-5011	5	42	degenerate	degenerate	ADJ
ejpam-5011	5	43	r	r	NOUN
ejpam-5011	5	44	-	-	PUNCT
ejpam-5011	5	45	stirling	stirling	NOUN
ejpam-5011	5	46	numbers	number	NOUN
ejpam-5011	5	47	of	of	ADP
ejpam-5011	5	48	the	the	DET
ejpam-5011	5	49	second	second	ADJ
ejpam-5011	5	50	kind	kind	NOUN
ejpam-5011	5	51	1	1	NUM
ejpam-5011	5	52	.	.	PUNCT
ejpam-5011	5	53	introduction	introduction	NOUN
ejpam-5011	5	54	the	the	DET
ejpam-5011	5	55	stirling	stirling	NOUN
ejpam-5011	5	56	number	number	NOUN
ejpam-5011	5	57	of	of	ADP
ejpam-5011	5	58	the	the	DET
ejpam-5011	5	59	second	second	ADJ
ejpam-5011	5	60	kind	kind	NOUN
ejpam-5011	5	61	{	{	PUNCT
ejpam-5011	5	62	n	n	X
ejpam-5011	5	63	k	k	X
ejpam-5011	5	64	}	}	PUNCT
ejpam-5011	5	65	enumerates	enumerate	VERB
ejpam-5011	5	66	the	the	DET
ejpam-5011	5	67	number	number	NOUN
ejpam-5011	5	68	of	of	ADP
ejpam-5011	5	69	partitions	partition	NOUN
ejpam-5011	5	70	of	of	ADP
ejpam-5011	5	71	the	the	DET
ejpam-5011	5	72	set	set	NOUN
ejpam-5011	5	73	[	[	X
ejpam-5011	5	74	n	n	X
ejpam-5011	5	75	]	]	X
ejpam-5011	5	76	=	=	PUNCT
ejpam-5011	5	77	{	{	PUNCT
ejpam-5011	5	78	1,2	1,2	NUM
ejpam-5011	5	79	,	,	PUNCT
ejpam-5011	5	80	.	.	PUNCT
ejpam-5011	5	81	.	.	PUNCT
ejpam-5011	6	1	.	.	PUNCT
ejpam-5011	7	1	,	,	PUNCT
ejpam-5011	7	2	n	n	CCONJ
ejpam-5011	7	3	}	}	PUNCT
ejpam-5011	7	4	into	into	ADP
ejpam-5011	7	5	k	k	PROPN
ejpam-5011	7	6	nonempty	nonempty	X
ejpam-5011	7	7	disjoint	disjoint	NOUN
ejpam-5011	7	8	subsets	subset	NOUN
ejpam-5011	7	9	,	,	PUNCT
ejpam-5011	7	10	while	while	SCONJ
ejpam-5011	7	11	the	the	DET
ejpam-5011	7	12	unsigned	unsigned	ADJ
ejpam-5011	7	13	stirling	stirling	NOUN
ejpam-5011	7	14	number	number	NOUN
ejpam-5011	7	15	of	of	ADP
ejpam-5011	7	16	the	the	DET
ejpam-5011	7	17	first	first	ADJ
ejpam-5011	7	18	kind	kind	NOUN
ejpam-5011	7	19	[	[	X
ejpam-5011	7	20	n	n	X
ejpam-5011	7	21	k	k	X
ejpam-5011	7	22	]	]	PUNCT
ejpam-5011	7	23	counts	count	VERB
ejpam-5011	7	24	the	the	DET
ejpam-5011	7	25	number	number	NOUN
ejpam-5011	7	26	of	of	ADP
ejpam-5011	7	27	permutations	permutation	NOUN
ejpam-5011	7	28	of	of	ADP
ejpam-5011	7	29	the	the	DET
ejpam-5011	7	30	set	set	NOUN
ejpam-5011	7	31	[	[	X
ejpam-5011	7	32	n	n	X
ejpam-5011	7	33	]	]	X
ejpam-5011	7	34	having	have	VERB
ejpam-5011	7	35	k	k	PROPN
ejpam-5011	7	36	disjoint	disjoint	PROPN
ejpam-5011	7	37	cycles	cycle	NOUN
ejpam-5011	7	38	.	.	PUNCT
ejpam-5011	8	1	let	let	VERB
ejpam-5011	8	2	r	r	PRON
ejpam-5011	8	3	be	be	AUX
ejpam-5011	8	4	a	a	DET
ejpam-5011	8	5	positive	positive	ADJ
ejpam-5011	8	6	integer	integer	NOUN
ejpam-5011	8	7	.	.	PUNCT
ejpam-5011	9	1	then	then	ADV
ejpam-5011	9	2	the	the	DET
ejpam-5011	9	3	stirling	stirling	NOUN
ejpam-5011	9	4	numbers	number	NOUN
ejpam-5011	9	5	of	of	ADP
ejpam-5011	9	6	both	both	DET
ejpam-5011	9	7	kinds	kind	NOUN
ejpam-5011	9	8	are	be	AUX
ejpam-5011	9	9	generalized	generalize	VERB
ejpam-5011	9	10	as	as	SCONJ
ejpam-5011	9	11	follows	follow	VERB
ejpam-5011	9	12	.	.	PUNCT
ejpam-5011	10	1	the	the	DET
ejpam-5011	10	2	r	r	NOUN
ejpam-5011	10	3	-	-	PUNCT
ejpam-5011	10	4	stirling	stirling	NOUN
ejpam-5011	10	5	number	number	NOUN
ejpam-5011	10	6	of	of	ADP
ejpam-5011	10	7	the	the	DET
ejpam-5011	10	8	second	second	ADJ
ejpam-5011	10	9	kind	kind	NOUN
ejpam-5011	10	10	{	{	PUNCT
ejpam-5011	10	11	n	n	NOUN
ejpam-5011	10	12	k	k	NOUN
ejpam-5011	10	13	}	}	PUNCT
ejpam-5011	10	14	r	r	NOUN
ejpam-5011	10	15	enumerates	enumerate	VERB
ejpam-5011	10	16	the	the	DET
ejpam-5011	10	17	number	number	NOUN
ejpam-5011	10	18	of	of	ADP
ejpam-5011	10	19	partitions	partition	NOUN
ejpam-5011	10	20	of	of	ADP
ejpam-5011	10	21	the	the	DET
ejpam-5011	10	22	set	set	NOUN
ejpam-5011	10	23	[	[	X
ejpam-5011	10	24	n	n	X
ejpam-5011	10	25	]	]	PUNCT
ejpam-5011	10	26	into	into	ADP
ejpam-5011	10	27	k	k	PROPN
ejpam-5011	10	28	nonempty	nonempty	X
ejpam-5011	10	29	disjoint	disjoint	NOUN
ejpam-5011	10	30	subsets	subset	NOUN
ejpam-5011	10	31	in	in	ADP
ejpam-5011	10	32	such	such	DET
ejpam-5011	10	33	a	a	DET
ejpam-5011	10	34	way	way	NOUN
ejpam-5011	10	35	that	that	SCONJ
ejpam-5011	10	36	1,2	1,2	NUM
ejpam-5011	10	37	,	,	PUNCT
ejpam-5011	10	38	.	.	PUNCT
ejpam-5011	10	39	.	.	PUNCT
ejpam-5011	11	1	.	.	PUNCT
ejpam-5011	12	1	,	,	PUNCT
ejpam-5011	12	2	r	r	NOUN
ejpam-5011	12	3	are	be	AUX
ejpam-5011	12	4	in	in	ADP
ejpam-5011	12	5	distinct	distinct	ADJ
ejpam-5011	12	6	subsets	subset	NOUN
ejpam-5011	12	7	,	,	PUNCT
ejpam-5011	12	8	while	while	SCONJ
ejpam-5011	12	9	the	the	DET
ejpam-5011	12	10	unsigned	unsigned	ADJ
ejpam-5011	12	11	r	r	NOUN
ejpam-5011	12	12	-	-	PUNCT
ejpam-5011	12	13	stirling	stirling	NOUN
ejpam-5011	12	14	number	number	NOUN
ejpam-5011	12	15	of	of	ADP
ejpam-5011	12	16	the	the	DET
ejpam-5011	12	17	first	first	ADJ
ejpam-5011	12	18	kind	kind	NOUN
ejpam-5011	12	19	[	[	X
ejpam-5011	12	20	n	n	X
ejpam-5011	12	21	k	k	X
ejpam-5011	12	22	]	]	X
ejpam-5011	12	23	r	r	NOUN
ejpam-5011	12	24	counts	count	VERB
ejpam-5011	12	25	the	the	DET
ejpam-5011	12	26	number	number	NOUN
ejpam-5011	12	27	of	of	ADP
ejpam-5011	12	28	permutations	permutation	NOUN
ejpam-5011	12	29	of	of	ADP
ejpam-5011	12	30	the	the	DET
ejpam-5011	12	31	set	set	NOUN
ejpam-5011	12	32	[	[	X
ejpam-5011	12	33	n	n	X
ejpam-5011	12	34	]	]	X
ejpam-5011	12	35	having	have	VERB
ejpam-5011	12	36	k	k	PROPN
ejpam-5011	12	37	disjoint	disjoint	PROPN
ejpam-5011	12	38	cycles	cycle	NOUN
ejpam-5011	12	39	in	in	ADP
ejpam-5011	12	40	such	such	DET
ejpam-5011	12	41	a	a	DET
ejpam-5011	12	42	way	way	NOUN
ejpam-5011	12	43	that	that	SCONJ
ejpam-5011	12	44	1,2	1,2	NUM
ejpam-5011	12	45	,	,	PUNCT
ejpam-5011	12	46	.	.	PUNCT
ejpam-5011	12	47	.	.	PUNCT
ejpam-5011	13	1	.r	.r	PROPN
ejpam-5011	13	2	are	be	AUX
ejpam-5011	13	3	in	in	ADP
ejpam-5011	13	4	distinct	distinct	ADJ
ejpam-5011	13	5	cycles	cycle	NOUN
ejpam-5011	13	6	.	.	PUNCT
ejpam-5011	14	1	carlitz	carlitz	PROPN
ejpam-5011	14	2	initiated	initiate	VERB
ejpam-5011	14	3	an	an	DET
ejpam-5011	14	4	investigation	investigation	NOUN
ejpam-5011	14	5	of	of	ADP
ejpam-5011	14	6	degenerate	degenerate	ADJ
ejpam-5011	14	7	versions	version	NOUN
ejpam-5011	14	8	of	of	ADP
ejpam-5011	14	9	some	some	DET
ejpam-5011	14	10	special	special	ADJ
ejpam-5011	14	11	numbers	number	NOUN
ejpam-5011	14	12	and	and	CCONJ
ejpam-5011	14	13	polynomials	polynomial	NOUN
ejpam-5011	14	14	.	.	PUNCT
ejpam-5011	15	1	indeed	indeed	ADV
ejpam-5011	15	2	,	,	PUNCT
ejpam-5011	15	3	in	in	ADP
ejpam-5011	15	4	[	[	X
ejpam-5011	15	5	5	5	X
ejpam-5011	15	6	]	]	PUNCT
ejpam-5011	15	7	he	he	PRON
ejpam-5011	15	8	studied	study	VERB
ejpam-5011	15	9	degenerate	degenerate	ADJ
ejpam-5011	15	10	versions	version	NOUN
ejpam-5011	15	11	of	of	ADP
ejpam-5011	15	12	bernoulli	bernoulli	PROPN
ejpam-5011	15	13	and	and	CCONJ
ejpam-5011	15	14	euler	euler	NOUN
ejpam-5011	15	15	polynomials	polynomial	NOUN
ejpam-5011	15	16	,	,	PUNCT
ejpam-5011	15	17	namely	namely	ADV
ejpam-5011	15	18	the	the	DET
ejpam-5011	15	19	degenerate	degenerate	ADJ
ejpam-5011	15	20	bernoulli	bernoulli	NOUN
ejpam-5011	15	21	and	and	CCONJ
ejpam-5011	15	22	degenerate	degenerate	ADJ
ejpam-5011	15	23	euler	euler	NOUN
ejpam-5011	15	24	polynomials	polynomial	NOUN
ejpam-5011	15	25	.	.	PUNCT
ejpam-5011	16	1	in	in	ADP
ejpam-5011	16	2	recent	recent	ADJ
ejpam-5011	16	3	years	year	NOUN
ejpam-5011	16	4	,	,	PUNCT
ejpam-5011	16	5	this	this	DET
ejpam-5011	16	6	exploration	exploration	NOUN
ejpam-5011	16	7	for	for	ADP
ejpam-5011	16	8	degenerate	degenerate	ADJ
ejpam-5011	16	9	versions	version	NOUN
ejpam-5011	16	10	have	have	AUX
ejpam-5011	16	11	regained	regain	VERB
ejpam-5011	16	12	interests	interest	NOUN
ejpam-5011	16	13	of	of	ADP
ejpam-5011	16	14	some	some	DET
ejpam-5011	16	15	mathematicians	mathematician	NOUN
ejpam-5011	16	16	and	and	CCONJ
ejpam-5011	16	17	a	a	DET
ejpam-5011	16	18	lot	lot	NOUN
ejpam-5011	16	19	of	of	ADP
ejpam-5011	16	20	interesting	interesting	ADJ
ejpam-5011	16	21	results	result	NOUN
ejpam-5011	16	22	on	on	ADP
ejpam-5011	16	23	degenerate	degenerate	ADJ
ejpam-5011	16	24	versions	version	NOUN
ejpam-5011	16	25	of	of	ADP
ejpam-5011	16	26	many	many	ADJ
ejpam-5011	16	27	special	special	ADJ
ejpam-5011	16	28	polynomials	polynomial	NOUN
ejpam-5011	16	29	and	and	CCONJ
ejpam-5011	16	30	numbers	number	NOUN
ejpam-5011	16	31	were	be	AUX
ejpam-5011	16	32	obtained	obtain	VERB
ejpam-5011	16	33	during	during	ADP
ejpam-5011	16	34	the	the	DET
ejpam-5011	16	35	∗corresponding	∗corresponde	VERB
ejpam-5011	16	36	author	author	NOUN
ejpam-5011	16	37	.	.	PUNCT
ejpam-5011	17	1	∗corresponding	∗corresponde	VERB
ejpam-5011	17	2	author	author	NOUN
ejpam-5011	17	3	.	.	PUNCT
ejpam-5011	18	1	doi	doi	NOUN
ejpam-5011	18	2	:	:	PUNCT
ejpam-5011	18	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5011	https://doi.org/10.29020/nybg.ejpam.v17i1.5011	PROPN
ejpam-5011	18	4	email	email	NOUN
ejpam-5011	18	5	addresses	address	NOUN
ejpam-5011	18	6	:	:	PUNCT
ejpam-5011	18	7	dskim@sogang.ac.kr	dskim@sogang.ac.kr	PROPN
ejpam-5011	18	8	(	(	PUNCT
ejpam-5011	18	9	d.	d.	PROPN
ejpam-5011	18	10	s.	s.	PROPN
ejpam-5011	18	11	kim	kim	PROPN
ejpam-5011	18	12	)	)	PUNCT
ejpam-5011	18	13	,	,	PUNCT
ejpam-5011	18	14	tkkim@kw.ac.kr	tkkim@kw.ac.kr	X
ejpam-5011	18	15	(	(	PUNCT
ejpam-5011	18	16	t.	t.	PROPN
ejpam-5011	18	17	kim	kim	PROPN
ejpam-5011	18	18	)	)	PUNCT
ejpam-5011	18	19	,	,	PUNCT
ejpam-5011	18	20	mathkjk26@gnu.ac.kr	mathkjk26@gnu.ac.kr	PROPN
ejpam-5011	18	21	(	(	PUNCT
ejpam-5011	18	22	j.	j.	PROPN
ejpam-5011	18	23	kwon	kwon	PROPN
ejpam-5011	18	24	)	)	PUNCT
ejpam-5011	18	25	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5011	19	1	1	1	NUM
ejpam-5011	20	1	©	©	ADP
ejpam-5011	20	2	2024	2024	NUM
ejpam-5011	20	3	ejpam	ejpam	NOUN
ejpam-5011	20	4	all	all	DET
ejpam-5011	20	5	rights	right	NOUN
ejpam-5011	20	6	reserved	reserve	VERB
ejpam-5011	20	7	.	.	PUNCT
ejpam-5011	21	1	d.	d.	PROPN
ejpam-5011	21	2	kim	kim	PROPN
ejpam-5011	21	3	,	,	PUNCT
ejpam-5011	21	4	t.	t.	PROPN
ejpam-5011	21	5	kim	kim	PROPN
ejpam-5011	21	6	,	,	PUNCT
ejpam-5011	21	7	j.	j.	PROPN
ejpam-5011	21	8	kwon	kwon	PROPN
ejpam-5011	21	9	/	/	SYM
ejpam-5011	21	10	eur	eur	PROPN
ejpam-5011	21	11	.	.	PUNCT
ejpam-5011	22	1	j.	j.	PROPN
ejpam-5011	22	2	pure	pure	PROPN
ejpam-5011	22	3	appl	appl	PROPN
ejpam-5011	22	4	.	.	PROPN
ejpam-5011	22	5	math	math	PROPN
ejpam-5011	22	6	,	,	PUNCT
ejpam-5011	22	7	17	17	NUM
ejpam-5011	22	8	(	(	PUNCT
ejpam-5011	22	9	1	1	NUM
ejpam-5011	22	10	)	)	PUNCT
ejpam-5011	22	11	(	(	PUNCT
ejpam-5011	22	12	2024	2024	NUM
ejpam-5011	22	13	)	)	PUNCT
ejpam-5011	22	14	,	,	PUNCT
ejpam-5011	22	15	1	1	NUM
ejpam-5011	22	16	-	-	SYM
ejpam-5011	22	17	10	10	NUM
ejpam-5011	22	18	2	2	NUM
ejpam-5011	22	19	course	course	NOUN
ejpam-5011	22	20	of	of	ADP
ejpam-5011	22	21	this	this	DET
ejpam-5011	22	22	quest	quest	NOUN
ejpam-5011	22	23	(	(	PUNCT
ejpam-5011	22	24	see	see	VERB
ejpam-5011	22	25	[	[	X
ejpam-5011	22	26	12	12	NUM
ejpam-5011	22	27	,	,	PUNCT
ejpam-5011	22	28	14	14	NUM
ejpam-5011	22	29	,	,	PUNCT
ejpam-5011	22	30	15	15	NUM
ejpam-5011	22	31	]	]	PUNCT
ejpam-5011	22	32	and	and	CCONJ
ejpam-5011	22	33	the	the	DET
ejpam-5011	22	34	references	reference	NOUN
ejpam-5011	22	35	therein	therein	ADV
ejpam-5011	22	36	)	)	PUNCT
ejpam-5011	22	37	.	.	PUNCT
ejpam-5011	23	1	for	for	ADP
ejpam-5011	23	2	instance	instance	NOUN
ejpam-5011	23	3	,	,	PUNCT
ejpam-5011	23	4	the	the	DET
ejpam-5011	23	5	unsigned	unsigned	ADJ
ejpam-5011	23	6	degenerate	degenerate	ADJ
ejpam-5011	23	7	stirling	stirling	NOUN
ejpam-5011	23	8	number	number	NOUN
ejpam-5011	23	9	of	of	ADP
ejpam-5011	23	10	the	the	DET
ejpam-5011	23	11	first	first	ADJ
ejpam-5011	23	12	kind	kind	NOUN
ejpam-5011	24	1	[	[	X
ejpam-5011	24	2	n	n	X
ejpam-5011	24	3	k	k	X
ejpam-5011	24	4	]	]	PUNCT
ejpam-5011	24	5	λ	λ	X
ejpam-5011	24	6	and	and	CCONJ
ejpam-5011	24	7	the	the	DET
ejpam-5011	24	8	degenerate	degenerate	ADJ
ejpam-5011	24	9	stirling	stirling	NOUN
ejpam-5011	24	10	number	number	NOUN
ejpam-5011	24	11	of	of	ADP
ejpam-5011	24	12	the	the	DET
ejpam-5011	24	13	second	second	ADJ
ejpam-5011	24	14	kind	kind	NOUN
ejpam-5011	24	15	{	{	PUNCT
ejpam-5011	24	16	n	n	NOUN
ejpam-5011	24	17	k	k	ADJ
ejpam-5011	24	18	}	}	PUNCT
ejpam-5011	24	19	λ	λ	NOUN
ejpam-5011	24	20	are	be	AUX
ejpam-5011	24	21	respectively	respectively	ADV
ejpam-5011	24	22	degenerate	degenerate	ADJ
ejpam-5011	24	23	versions	version	NOUN
ejpam-5011	24	24	of	of	ADP
ejpam-5011	24	25	[	[	X
ejpam-5011	24	26	n	n	X
ejpam-5011	24	27	k	k	X
ejpam-5011	24	28	]	]	PUNCT
ejpam-5011	24	29	and	and	CCONJ
ejpam-5011	24	30	{	{	PUNCT
ejpam-5011	24	31	n	n	X
ejpam-5011	24	32	k	k	PROPN
ejpam-5011	24	33	}	}	PUNCT
ejpam-5011	24	34	.	.	PUNCT
ejpam-5011	25	1	further	far	ADV
ejpam-5011	25	2	,	,	PUNCT
ejpam-5011	25	3	the	the	DET
ejpam-5011	25	4	unsigned	unsigned	ADJ
ejpam-5011	25	5	degenerate	degenerate	ADJ
ejpam-5011	25	6	r	r	NOUN
ejpam-5011	25	7	-	-	PUNCT
ejpam-5011	25	8	stirling	stirling	NOUN
ejpam-5011	25	9	number	number	NOUN
ejpam-5011	25	10	of	of	ADP
ejpam-5011	25	11	the	the	DET
ejpam-5011	25	12	first	first	ADJ
ejpam-5011	25	13	kind	kind	NOUN
ejpam-5011	26	1	[	[	X
ejpam-5011	26	2	n	n	X
ejpam-5011	26	3	k	k	X
ejpam-5011	26	4	]	]	X
ejpam-5011	26	5	r	r	X
ejpam-5011	26	6	,	,	PUNCT
ejpam-5011	26	7	λ	λ	PROPN
ejpam-5011	26	8	and	and	CCONJ
ejpam-5011	26	9	the	the	DET
ejpam-5011	26	10	degenerate	degenerate	ADJ
ejpam-5011	26	11	r	r	NOUN
ejpam-5011	26	12	-	-	PUNCT
ejpam-5011	26	13	stirling	stirling	NOUN
ejpam-5011	26	14	number	number	NOUN
ejpam-5011	26	15	of	of	ADP
ejpam-5011	26	16	the	the	DET
ejpam-5011	26	17	second	second	ADJ
ejpam-5011	26	18	kind{n	kind{n	PROPN
ejpam-5011	26	19	k	k	NOUN
ejpam-5011	26	20	}	}	PUNCT
ejpam-5011	26	21	r	r	NOUN
ejpam-5011	26	22	,	,	PUNCT
ejpam-5011	26	23	λ	λ	NOUN
ejpam-5011	26	24	are	be	AUX
ejpam-5011	26	25	respectively	respectively	ADV
ejpam-5011	26	26	degenerate	degenerate	ADJ
ejpam-5011	26	27	versions	version	NOUN
ejpam-5011	26	28	of	of	ADP
ejpam-5011	26	29	[	[	X
ejpam-5011	26	30	n	n	X
ejpam-5011	26	31	k	k	NOUN
ejpam-5011	26	32	]	]	X
ejpam-5011	26	33	r	r	NOUN
ejpam-5011	26	34	and	and	CCONJ
ejpam-5011	26	35	{	{	PUNCT
ejpam-5011	26	36	n	n	CCONJ
ejpam-5011	26	37	k	k	PROPN
ejpam-5011	26	38	}	}	PUNCT
ejpam-5011	26	39	r.	r.	VERB
ejpam-5011	26	40	these	these	DET
ejpam-5011	26	41	investigations	investigation	NOUN
ejpam-5011	26	42	about	about	ADP
ejpam-5011	26	43	degenerate	degenerate	ADJ
ejpam-5011	26	44	versions	version	NOUN
ejpam-5011	26	45	have	have	AUX
ejpam-5011	26	46	been	be	AUX
ejpam-5011	26	47	carried	carry	VERB
ejpam-5011	26	48	out	out	ADP
ejpam-5011	26	49	by	by	ADP
ejpam-5011	26	50	employing	employ	VERB
ejpam-5011	26	51	such	such	ADJ
ejpam-5011	26	52	diverse	diverse	ADJ
ejpam-5011	26	53	tools	tool	NOUN
ejpam-5011	26	54	as	as	ADP
ejpam-5011	26	55	generating	generating	NOUN
ejpam-5011	26	56	functions	function	NOUN
ejpam-5011	26	57	,	,	PUNCT
ejpam-5011	26	58	combinatorial	combinatorial	ADJ
ejpam-5011	26	59	methods	method	NOUN
ejpam-5011	26	60	,	,	PUNCT
ejpam-5011	26	61	p	p	NOUN
ejpam-5011	26	62	-	-	PUNCT
ejpam-5011	26	63	adic	adic	ADJ
ejpam-5011	26	64	analysis	analysis	NOUN
ejpam-5011	26	65	,	,	PUNCT
ejpam-5011	26	66	p	p	NOUN
ejpam-5011	26	67	-	-	PUNCT
ejpam-5011	26	68	adic	adic	ADJ
ejpam-5011	26	69	q	q	NOUN
ejpam-5011	26	70	-	-	PUNCT
ejpam-5011	26	71	analysis	analysis	NOUN
ejpam-5011	26	72	,	,	PUNCT
ejpam-5011	26	73	umbral	umbral	ADJ
ejpam-5011	26	74	calculus	calculus	NOUN
ejpam-5011	26	75	,	,	PUNCT
ejpam-5011	26	76	probability	probability	NOUN
ejpam-5011	26	77	theory	theory	NOUN
ejpam-5011	26	78	,	,	PUNCT
ejpam-5011	26	79	differential	differential	ADJ
ejpam-5011	26	80	equations	equation	NOUN
ejpam-5011	26	81	,	,	PUNCT
ejpam-5011	26	82	analytic	analytic	ADJ
ejpam-5011	26	83	number	number	NOUN
ejpam-5011	26	84	theory	theory	NOUN
ejpam-5011	26	85	,	,	PUNCT
ejpam-5011	26	86	operator	operator	NOUN
ejpam-5011	26	87	theory	theory	NOUN
ejpam-5011	26	88	,	,	PUNCT
ejpam-5011	26	89	and	and	CCONJ
ejpam-5011	26	90	quantum	quantum	NOUN
ejpam-5011	26	91	mechanics	mechanic	NOUN
ejpam-5011	26	92	.	.	PUNCT
ejpam-5011	27	1	the	the	DET
ejpam-5011	27	2	aim	aim	NOUN
ejpam-5011	27	3	of	of	ADP
ejpam-5011	27	4	this	this	DET
ejpam-5011	27	5	paper	paper	NOUN
ejpam-5011	27	6	is	be	AUX
ejpam-5011	27	7	by	by	ADP
ejpam-5011	27	8	using	use	VERB
ejpam-5011	27	9	generating	generating	NOUN
ejpam-5011	27	10	functions	function	NOUN
ejpam-5011	27	11	to	to	PART
ejpam-5011	27	12	further	far	ADV
ejpam-5011	27	13	study	study	VERB
ejpam-5011	27	14	explicit	explicit	ADJ
ejpam-5011	27	15	expressions	expression	NOUN
ejpam-5011	27	16	,	,	PUNCT
ejpam-5011	27	17	some	some	DET
ejpam-5011	27	18	identities	identity	NOUN
ejpam-5011	27	19	and	and	CCONJ
ejpam-5011	27	20	equivalent	equivalent	ADJ
ejpam-5011	27	21	relations	relation	NOUN
ejpam-5011	27	22	for	for	ADP
ejpam-5011	27	23	the	the	DET
ejpam-5011	27	24	aforementioned	aforementioned	ADJ
ejpam-5011	27	25	stirling	stirling	NOUN
ejpam-5011	27	26	numbers	number	NOUN
ejpam-5011	27	27	of	of	ADP
ejpam-5011	27	28	both	both	DET
ejpam-5011	27	29	kinds	kind	NOUN
ejpam-5011	27	30	.	.	PUNCT
ejpam-5011	28	1	the	the	DET
ejpam-5011	28	2	outline	outline	NOUN
ejpam-5011	28	3	of	of	ADP
ejpam-5011	28	4	this	this	DET
ejpam-5011	28	5	paper	paper	NOUN
ejpam-5011	28	6	is	be	AUX
ejpam-5011	28	7	as	as	SCONJ
ejpam-5011	28	8	follows	follow	VERB
ejpam-5011	28	9	.	.	PUNCT
ejpam-5011	29	1	in	in	ADP
ejpam-5011	29	2	section	section	NOUN
ejpam-5011	29	3	1	1	NUM
ejpam-5011	29	4	,	,	PUNCT
ejpam-5011	29	5	we	we	PRON
ejpam-5011	29	6	recall	recall	VERB
ejpam-5011	29	7	the	the	DET
ejpam-5011	29	8	degenerate	degenerate	ADJ
ejpam-5011	29	9	exponentials	exponential	NOUN
ejpam-5011	29	10	and	and	CCONJ
ejpam-5011	29	11	degenerate	degenerate	ADJ
ejpam-5011	29	12	logarithms	logarithm	NOUN
ejpam-5011	29	13	.	.	PUNCT
ejpam-5011	30	1	we	we	PRON
ejpam-5011	30	2	remind	remind	VERB
ejpam-5011	30	3	the	the	DET
ejpam-5011	30	4	reader	reader	NOUN
ejpam-5011	30	5	of	of	ADP
ejpam-5011	30	6	the	the	DET
ejpam-5011	30	7	unsigned	unsigned	ADJ
ejpam-5011	30	8	stirling	stirling	NOUN
ejpam-5011	30	9	numbers	number	NOUN
ejpam-5011	30	10	of	of	ADP
ejpam-5011	30	11	the	the	DET
ejpam-5011	30	12	first	first	ADJ
ejpam-5011	30	13	kind	kind	NOUN
ejpam-5011	30	14	and	and	CCONJ
ejpam-5011	30	15	its	its	PRON
ejpam-5011	30	16	generalization	generalization	NOUN
ejpam-5011	30	17	the	the	DET
ejpam-5011	30	18	unsigned	unsigned	ADJ
ejpam-5011	30	19	r	r	NOUN
ejpam-5011	30	20	-	-	PUNCT
ejpam-5011	30	21	stirling	stirling	NOUN
ejpam-5011	30	22	numbers	number	NOUN
ejpam-5011	30	23	of	of	ADP
ejpam-5011	30	24	the	the	DET
ejpam-5011	30	25	first	first	ADJ
ejpam-5011	30	26	kind	kind	NOUN
ejpam-5011	30	27	,	,	PUNCT
ejpam-5011	30	28	and	and	CCONJ
ejpam-5011	30	29	the	the	DET
ejpam-5011	30	30	stirling	stirling	NOUN
ejpam-5011	30	31	numbers	number	NOUN
ejpam-5011	30	32	of	of	ADP
ejpam-5011	30	33	the	the	DET
ejpam-5011	30	34	second	second	ADJ
ejpam-5011	30	35	kind	kind	NOUN
ejpam-5011	30	36	and	and	CCONJ
ejpam-5011	30	37	its	its	PRON
ejpam-5011	30	38	generalization	generalization	NOUN
ejpam-5011	30	39	the	the	DET
ejpam-5011	30	40	r	r	NOUN
ejpam-5011	30	41	-	-	PUNCT
ejpam-5011	30	42	stirling	stirling	NOUN
ejpam-5011	30	43	numbers	number	NOUN
ejpam-5011	30	44	of	of	ADP
ejpam-5011	30	45	the	the	DET
ejpam-5011	30	46	second	second	ADJ
ejpam-5011	30	47	kind	kind	NOUN
ejpam-5011	30	48	.	.	PUNCT
ejpam-5011	31	1	then	then	ADV
ejpam-5011	31	2	we	we	PRON
ejpam-5011	31	3	recall	recall	VERB
ejpam-5011	31	4	their	their	PRON
ejpam-5011	31	5	degenerate	degenerate	ADJ
ejpam-5011	31	6	versions	version	NOUN
ejpam-5011	31	7	,	,	PUNCT
ejpam-5011	31	8	namely	namely	ADV
ejpam-5011	31	9	the	the	DET
ejpam-5011	31	10	unsigned	unsigned	ADJ
ejpam-5011	31	11	degenerate	degenerate	ADJ
ejpam-5011	31	12	stirling	stirling	NOUN
ejpam-5011	31	13	numbers	number	NOUN
ejpam-5011	31	14	of	of	ADP
ejpam-5011	31	15	the	the	DET
ejpam-5011	31	16	first	first	ADJ
ejpam-5011	31	17	kind	kind	NOUN
ejpam-5011	31	18	and	and	CCONJ
ejpam-5011	31	19	its	its	PRON
ejpam-5011	31	20	generalization	generalization	NOUN
ejpam-5011	31	21	the	the	DET
ejpam-5011	31	22	unsigned	unsigned	ADJ
ejpam-5011	31	23	degenerate	degenerate	ADJ
ejpam-5011	31	24	r	r	NOUN
ejpam-5011	31	25	-	-	PUNCT
ejpam-5011	31	26	stirling	stirling	NOUN
ejpam-5011	31	27	numbers	number	NOUN
ejpam-5011	31	28	of	of	ADP
ejpam-5011	31	29	the	the	DET
ejpam-5011	31	30	first	first	ADJ
ejpam-5011	31	31	kind	kind	NOUN
ejpam-5011	31	32	,	,	PUNCT
ejpam-5011	31	33	and	and	CCONJ
ejpam-5011	31	34	the	the	DET
ejpam-5011	31	35	degenerate	degenerate	ADJ
ejpam-5011	31	36	stirling	stirling	NOUN
ejpam-5011	31	37	numbers	number	NOUN
ejpam-5011	31	38	of	of	ADP
ejpam-5011	31	39	the	the	DET
ejpam-5011	31	40	second	second	ADJ
ejpam-5011	31	41	kind	kind	NOUN
ejpam-5011	31	42	and	and	CCONJ
ejpam-5011	31	43	its	its	PRON
ejpam-5011	31	44	generalization	generalization	NOUN
ejpam-5011	31	45	the	the	DET
ejpam-5011	31	46	degenerate	degenerate	ADJ
ejpam-5011	31	47	r	r	NOUN
ejpam-5011	31	48	-	-	PUNCT
ejpam-5011	31	49	stirling	stirling	NOUN
ejpam-5011	31	50	numbers	number	NOUN
ejpam-5011	31	51	of	of	ADP
ejpam-5011	31	52	the	the	DET
ejpam-5011	31	53	second	second	ADJ
ejpam-5011	31	54	kind	kind	NOUN
ejpam-5011	31	55	.	.	PUNCT
ejpam-5011	32	1	section	section	NOUN
ejpam-5011	32	2	2	2	NUM
ejpam-5011	32	3	is	be	AUX
ejpam-5011	32	4	the	the	DET
ejpam-5011	32	5	main	main	ADJ
ejpam-5011	32	6	result	result	NOUN
ejpam-5011	32	7	of	of	ADP
ejpam-5011	32	8	this	this	DET
ejpam-5011	32	9	paper	paper	NOUN
ejpam-5011	32	10	.	.	PUNCT
ejpam-5011	33	1	we	we	PRON
ejpam-5011	33	2	find	find	VERB
ejpam-5011	33	3	an	an	DET
ejpam-5011	33	4	explicit	explicit	ADJ
ejpam-5011	33	5	expression	expression	NOUN
ejpam-5011	33	6	for{n	for{n	NOUN
ejpam-5011	33	7	k	k	PROPN
ejpam-5011	33	8	}	}	PUNCT
ejpam-5011	33	9	λ	λ	PROPN
ejpam-5011	33	10	as	as	ADP
ejpam-5011	33	11	a	a	DET
ejpam-5011	33	12	finite	finite	ADJ
ejpam-5011	33	13	sum	sum	NOUN
ejpam-5011	33	14	involving	involve	VERB
ejpam-5011	33	15	(	(	PUNCT
ejpam-5011	33	16	l)n	l)n	X
ejpam-5011	33	17	,	,	PUNCT
ejpam-5011	33	18	λ	λ	NOUN
ejpam-5011	33	19	and	and	CCONJ
ejpam-5011	33	20	an	an	DET
ejpam-5011	33	21	equivalent	equivalent	ADJ
ejpam-5011	33	22	inverse	inverse	NOUN
ejpam-5011	33	23	relation	relation	NOUN
ejpam-5011	33	24	expressing	express	VERB
ejpam-5011	33	25	(	(	PUNCT
ejpam-5011	33	26	k)n	k)n	X
ejpam-5011	33	27	,	,	PUNCT
ejpam-5011	33	28	λ	λ	NOUN
ejpam-5011	33	29	in	in	ADP
ejpam-5011	33	30	terms	term	NOUN
ejpam-5011	33	31	of	of	ADP
ejpam-5011	33	32	{	{	PUNCT
ejpam-5011	33	33	n	n	PRON
ejpam-5011	33	34	j	j	PROPN
ejpam-5011	33	35	}	}	PUNCT
ejpam-5011	33	36	λ	λ	PROPN
ejpam-5011	33	37	in	in	ADP
ejpam-5011	33	38	theorem	theorem	NOUN
ejpam-5011	33	39	2.1	2.1	NUM
ejpam-5011	33	40	.	.	PUNCT
ejpam-5011	34	1	in	in	ADP
ejpam-5011	34	2	theorem	theorem	NOUN
ejpam-5011	34	3	2.2	2.2	NUM
ejpam-5011	34	4	,	,	PUNCT
ejpam-5011	34	5	we	we	PRON
ejpam-5011	34	6	express	express	VERB
ejpam-5011	34	7	the	the	DET
ejpam-5011	34	8	finite	finite	ADJ
ejpam-5011	34	9	sum	sum	NOUN
ejpam-5011	34	10	∑	∑	PROPN
ejpam-5011	34	11	m	m	PROPN
ejpam-5011	34	12	k=1(k)n	k=1(k)n	NUM
ejpam-5011	34	13	,	,	PUNCT
ejpam-5011	34	14	λ	λ	PROPN
ejpam-5011	34	15	hk	hk	NOUN
ejpam-5011	34	16	as	as	ADP
ejpam-5011	34	17	a	a	DET
ejpam-5011	34	18	finite	finite	ADJ
ejpam-5011	34	19	sum	sum	NOUN
ejpam-5011	34	20	involving	involve	VERB
ejpam-5011	34	21	{	{	PUNCT
ejpam-5011	34	22	n	n	CCONJ
ejpam-5011	34	23	k	k	ADJ
ejpam-5011	34	24	}	}	PUNCT
ejpam-5011	34	25	λ	λ	PROPN
ejpam-5011	34	26	.	.	PUNCT
ejpam-5011	35	1	here	here	ADV
ejpam-5011	35	2	hk	hk	PROPN
ejpam-5011	35	3	are	be	AUX
ejpam-5011	35	4	the	the	DET
ejpam-5011	35	5	usual	usual	ADJ
ejpam-5011	35	6	harmonic	harmonic	ADJ
ejpam-5011	35	7	numbers	number	NOUN
ejpam-5011	35	8	.	.	PUNCT
ejpam-5011	36	1	in	in	ADP
ejpam-5011	36	2	theorem	theorem	NOUN
ejpam-5011	36	3	2.3	2.3	NUM
ejpam-5011	36	4	,	,	PUNCT
ejpam-5011	36	5	we	we	PRON
ejpam-5011	36	6	find	find	VERB
ejpam-5011	36	7	an	an	DET
ejpam-5011	36	8	explicit	explicit	ADJ
ejpam-5011	36	9	expression	expression	NOUN
ejpam-5011	36	10	of	of	ADP
ejpam-5011	36	11	[	[	X
ejpam-5011	36	12	n+r	n+r	X
ejpam-5011	36	13	k+r	k+r	X
ejpam-5011	36	14	]	]	PUNCT
ejpam-5011	37	1	r	r	X
ejpam-5011	37	2	,	,	PUNCT
ejpam-5011	37	3	λ	λ	PROPN
ejpam-5011	37	4	as	as	ADP
ejpam-5011	37	5	a	a	DET
ejpam-5011	37	6	finite	finite	ADJ
ejpam-5011	37	7	sum	sum	NOUN
ejpam-5011	37	8	involving	involve	VERB
ejpam-5011	37	9	[	[	X
ejpam-5011	37	10	n	n	X
ejpam-5011	37	11	l	l	NOUN
ejpam-5011	37	12	]	]	PUNCT
ejpam-5011	38	1	λ	λ	X
ejpam-5011	38	2	.	.	PUNCT
ejpam-5011	39	1	in	in	ADP
ejpam-5011	39	2	theorem	theorem	ADJ
ejpam-5011	39	3	2.4	2.4	NUM
ejpam-5011	39	4	,	,	PUNCT
ejpam-5011	39	5	we	we	PRON
ejpam-5011	39	6	derive	derive	VERB
ejpam-5011	39	7	finite	finite	ADJ
ejpam-5011	39	8	sum	sum	NOUN
ejpam-5011	39	9	identities	identity	NOUN
ejpam-5011	39	10	involving	involve	VERB
ejpam-5011	39	11	the	the	DET
ejpam-5011	39	12	unsigned	unsigned	ADJ
ejpam-5011	39	13	stirling	stirling	NOUN
ejpam-5011	39	14	numbers	number	NOUN
ejpam-5011	39	15	of	of	ADP
ejpam-5011	39	16	the	the	DET
ejpam-5011	39	17	first	first	ADJ
ejpam-5011	39	18	kind	kind	NOUN
ejpam-5011	39	19	,	,	PUNCT
ejpam-5011	39	20	the	the	DET
ejpam-5011	39	21	degenerate	degenerate	ADJ
ejpam-5011	39	22	stirling	stirling	NOUN
ejpam-5011	39	23	numbers	number	NOUN
ejpam-5011	39	24	of	of	ADP
ejpam-5011	39	25	the	the	DET
ejpam-5011	39	26	second	second	ADJ
ejpam-5011	39	27	kind	kind	NOUN
ejpam-5011	39	28	and	and	CCONJ
ejpam-5011	39	29	the	the	DET
ejpam-5011	39	30	generalized	generalized	ADJ
ejpam-5011	39	31	falling	fall	VERB
ejpam-5011	39	32	factorials	factorial	NOUN
ejpam-5011	39	33	.	.	PUNCT
ejpam-5011	40	1	an	an	DET
ejpam-5011	40	2	explicit	explicit	ADJ
ejpam-5011	40	3	expression	expression	NOUN
ejpam-5011	40	4	for{n+r	for{n+r	PROPN
ejpam-5011	40	5	k+r	k+r	X
ejpam-5011	40	6	}	}	PUNCT
ejpam-5011	40	7	r	r	NOUN
ejpam-5011	40	8	,	,	PUNCT
ejpam-5011	40	9	λ	λ	NOUN
ejpam-5011	40	10	is	be	AUX
ejpam-5011	40	11	found	find	VERB
ejpam-5011	40	12	as	as	ADP
ejpam-5011	40	13	a	a	DET
ejpam-5011	40	14	finite	finite	ADJ
ejpam-5011	40	15	sum	sum	NOUN
ejpam-5011	40	16	involving	involve	VERB
ejpam-5011	40	17	(	(	PUNCT
ejpam-5011	40	18	l	l	NOUN
ejpam-5011	40	19	+	+	X
ejpam-5011	40	20	r)n	r)n	ADJ
ejpam-5011	40	21	,	,	PUNCT
ejpam-5011	40	22	λ	λ	INTJ
ejpam-5011	40	23	,	,	PUNCT
ejpam-5011	40	24	as	as	ADP
ejpam-5011	40	25	a	a	DET
ejpam-5011	40	26	generalization	generalization	NOUN
ejpam-5011	40	27	of	of	ADP
ejpam-5011	40	28	the	the	DET
ejpam-5011	40	29	corresponding	corresponding	ADJ
ejpam-5011	40	30	result	result	NOUN
ejpam-5011	40	31	.	.	PUNCT
ejpam-5011	41	1	theorem	theorem	VERB
ejpam-5011	41	2	2.5	2.5	NUM
ejpam-5011	41	3	is	be	AUX
ejpam-5011	41	4	a	a	DET
ejpam-5011	41	5	generalization	generalization	NOUN
ejpam-5011	41	6	of	of	ADP
ejpam-5011	41	7	theorem	theorem	ADJ
ejpam-5011	41	8	2.1	2.1	NUM
ejpam-5011	41	9	,	,	PUNCT
ejpam-5011	41	10	while	while	SCONJ
ejpam-5011	41	11	theorem	theorem	VERB
ejpam-5011	41	12	2.6	2.6	NUM
ejpam-5011	41	13	is	be	AUX
ejpam-5011	41	14	that	that	PRON
ejpam-5011	41	15	of	of	ADP
ejpam-5011	41	16	theorems	theorem	NOUN
ejpam-5011	41	17	2.2	2.2	NUM
ejpam-5011	41	18	and	and	CCONJ
ejpam-5011	41	19	2.4	2.4	NUM
ejpam-5011	41	20	.	.	PUNCT
ejpam-5011	42	1	for	for	ADP
ejpam-5011	42	2	the	the	DET
ejpam-5011	42	3	rest	rest	NOUN
ejpam-5011	42	4	of	of	ADP
ejpam-5011	42	5	this	this	DET
ejpam-5011	42	6	section	section	NOUN
ejpam-5011	42	7	,	,	PUNCT
ejpam-5011	42	8	we	we	PRON
ejpam-5011	42	9	recall	recall	VERB
ejpam-5011	42	10	the	the	DET
ejpam-5011	42	11	facts	fact	NOUN
ejpam-5011	42	12	that	that	PRON
ejpam-5011	42	13	are	be	AUX
ejpam-5011	42	14	needed	need	VERB
ejpam-5011	42	15	throughout	throughout	ADP
ejpam-5011	42	16	this	this	DET
ejpam-5011	42	17	paper	paper	NOUN
ejpam-5011	42	18	.	.	PUNCT
ejpam-5011	43	1	for	for	ADP
ejpam-5011	43	2	any	any	DET
ejpam-5011	43	3	nonzero	nonzero	NOUN
ejpam-5011	43	4	λ	λ	X
ejpam-5011	43	5	∈	∈	PROPN
ejpam-5011	43	6	r	r	NOUN
ejpam-5011	43	7	,	,	PUNCT
ejpam-5011	43	8	the	the	DET
ejpam-5011	43	9	degenerate	degenerate	ADJ
ejpam-5011	43	10	exponentials	exponential	NOUN
ejpam-5011	43	11	are	be	AUX
ejpam-5011	43	12	defined	define	VERB
ejpam-5011	43	13	by	by	ADP
ejpam-5011	43	14	ex	ex	ADJ
ejpam-5011	43	15	λ	λ	PROPN
ejpam-5011	43	16	(	(	PUNCT
ejpam-5011	43	17	t	t	PROPN
ejpam-5011	43	18	)	)	PUNCT
ejpam-5011	43	19	=	=	SYM
ejpam-5011	44	1	∞	∞	PROPN
ejpam-5011	44	2	∑	∑	PUNCT
ejpam-5011	44	3	k=0	k=0	PROPN
ejpam-5011	44	4	(	(	PUNCT
ejpam-5011	44	5	x)k	x)k	X
ejpam-5011	44	6	,	,	PUNCT
ejpam-5011	44	7	λ	λ	PROPN
ejpam-5011	44	8	tk	tk	PROPN
ejpam-5011	44	9	k	k	PROPN
ejpam-5011	44	10	!	!	PROPN
ejpam-5011	44	11	,	,	PUNCT
ejpam-5011	44	12	(	(	PUNCT
ejpam-5011	44	13	see	see	VERB
ejpam-5011	44	14	[	[	X
ejpam-5011	44	15	9	9	NUM
ejpam-5011	44	16	,	,	PUNCT
ejpam-5011	44	17	10	10	NUM
ejpam-5011	44	18	,	,	PUNCT
ejpam-5011	44	19	13	13	NUM
ejpam-5011	44	20	,	,	PUNCT
ejpam-5011	44	21	16	16	NUM
ejpam-5011	44	22	]	]	PUNCT
ejpam-5011	44	23	)	)	PUNCT
ejpam-5011	44	24	,	,	PUNCT
ejpam-5011	44	25	(	(	PUNCT
ejpam-5011	44	26	1	1	X
ejpam-5011	44	27	)	)	PUNCT
ejpam-5011	44	28	where	where	SCONJ
ejpam-5011	44	29	the	the	DET
ejpam-5011	44	30	generalized	generalized	ADJ
ejpam-5011	44	31	falling	fall	VERB
ejpam-5011	44	32	factorials	factorial	NOUN
ejpam-5011	44	33	are	be	AUX
ejpam-5011	44	34	given	give	VERB
ejpam-5011	44	35	by	by	ADP
ejpam-5011	44	36	(	(	PUNCT
ejpam-5011	44	37	x)0,λ	x)0,λ	NOUN
ejpam-5011	44	38	=	=	SYM
ejpam-5011	44	39	1	1	NUM
ejpam-5011	44	40	,	,	PUNCT
ejpam-5011	44	41	(	(	PUNCT
ejpam-5011	44	42	x)n	x)n	PROPN
ejpam-5011	44	43	,	,	PUNCT
ejpam-5011	44	44	λ	λ	PROPN
ejpam-5011	44	45	=	=	PUNCT
ejpam-5011	44	46	x(x−λ	x(x−λ	PROPN
ejpam-5011	44	47	)	)	PUNCT
ejpam-5011	44	48	·	·	PUNCT
ejpam-5011	44	49	·	·	PUNCT
ejpam-5011	45	1	·	·	PUNCT
ejpam-5011	45	2	(	(	PUNCT
ejpam-5011	45	3	x−	x−	PROPN
ejpam-5011	45	4	(	(	PUNCT
ejpam-5011	45	5	n−1)λ	n−1)λ	PROPN
ejpam-5011	45	6	)	)	PUNCT
ejpam-5011	45	7	,	,	PUNCT
ejpam-5011	45	8	(	(	PUNCT
ejpam-5011	45	9	n	n	X
ejpam-5011	45	10	≥	≥	NOUN
ejpam-5011	45	11	1	1	NUM
ejpam-5011	45	12	)	)	PUNCT
ejpam-5011	45	13	.	.	PUNCT
ejpam-5011	46	1	(	(	PUNCT
ejpam-5011	46	2	2	2	X
ejpam-5011	46	3	)	)	PUNCT
ejpam-5011	46	4	for	for	ADP
ejpam-5011	46	5	x	x	SYM
ejpam-5011	46	6	=	=	SYM
ejpam-5011	46	7	1	1	NUM
ejpam-5011	46	8	,	,	PUNCT
ejpam-5011	46	9	for	for	ADP
ejpam-5011	46	10	brevity	brevity	NOUN
ejpam-5011	46	11	we	we	PRON
ejpam-5011	46	12	write	write	VERB
ejpam-5011	46	13	eλ	eλ	PROPN
ejpam-5011	46	14	(	(	PUNCT
ejpam-5011	46	15	t	t	NOUN
ejpam-5011	46	16	)	)	PUNCT
ejpam-5011	47	1	=	=	SYM
ejpam-5011	47	2	e1	e1	PROPN
ejpam-5011	47	3	λ	λ	PROPN
ejpam-5011	47	4	(	(	PUNCT
ejpam-5011	47	5	t	t	PROPN
ejpam-5011	47	6	)	)	PUNCT
ejpam-5011	47	7	=	=	PUNCT
ejpam-5011	48	1	∑	∑	PUNCT
ejpam-5011	48	2	∞	∞	NUM
ejpam-5011	48	3	k=0(1)k	k=0(1)k	PROPN
ejpam-5011	48	4	,	,	PUNCT
ejpam-5011	48	5	λ	λ	PROPN
ejpam-5011	48	6	tk	tk	PROPN
ejpam-5011	48	7	k	k	PROPN
ejpam-5011	48	8	!	!	PUNCT
ejpam-5011	48	9	.	.	PUNCT
ejpam-5011	49	1	as	as	ADP
ejpam-5011	49	2	the	the	DET
ejpam-5011	49	3	compositional	compositional	ADJ
ejpam-5011	49	4	inverse	inverse	NOUN
ejpam-5011	49	5	of	of	ADP
ejpam-5011	49	6	eλ	eλ	PROPN
ejpam-5011	49	7	(	(	PUNCT
ejpam-5011	49	8	t	t	PROPN
ejpam-5011	49	9	)	)	PUNCT
ejpam-5011	49	10	,	,	PUNCT
ejpam-5011	49	11	the	the	DET
ejpam-5011	49	12	degenerate	degenerate	ADJ
ejpam-5011	49	13	logarithm	logarithm	NOUN
ejpam-5011	49	14	is	be	AUX
ejpam-5011	49	15	given	give	VERB
ejpam-5011	49	16	by	by	ADP
ejpam-5011	49	17	logλ	logλ	PROPN
ejpam-5011	49	18	(	(	PUNCT
ejpam-5011	49	19	t	t	NOUN
ejpam-5011	49	20	)	)	PUNCT
ejpam-5011	49	21	=	=	SYM
ejpam-5011	49	22	1	1	NUM
ejpam-5011	49	23	λ	λ	NOUN
ejpam-5011	49	24	(	(	PUNCT
ejpam-5011	49	25	tλ	tλ	NOUN
ejpam-5011	49	26	−1	−1	NOUN
ejpam-5011	49	27	)	)	PUNCT
ejpam-5011	49	28	,	,	PUNCT
ejpam-5011	49	29	(	(	PUNCT
ejpam-5011	49	30	see	see	VERB
ejpam-5011	49	31	[	[	X
ejpam-5011	49	32	10	10	NUM
ejpam-5011	49	33	]	]	NUM
ejpam-5011	49	34	)	)	PUNCT
ejpam-5011	49	35	.	.	PUNCT
ejpam-5011	50	1	(	(	PUNCT
ejpam-5011	50	2	3	3	X
ejpam-5011	50	3	)	)	PUNCT
ejpam-5011	50	4	note	note	NOUN
ejpam-5011	50	5	that	that	SCONJ
ejpam-5011	50	6	limλ→0	limλ→0	PROPN
ejpam-5011	50	7	logλ	logλ	PROPN
ejpam-5011	50	8	(	(	PUNCT
ejpam-5011	50	9	t	t	NOUN
ejpam-5011	50	10	)	)	PUNCT
ejpam-5011	50	11	=	=	SYM
ejpam-5011	51	1	log	log	VERB
ejpam-5011	51	2	t.	t.	PROPN
ejpam-5011	51	3	d.	d.	PROPN
ejpam-5011	51	4	kim	kim	PROPN
ejpam-5011	51	5	,	,	PUNCT
ejpam-5011	51	6	t.	t.	PROPN
ejpam-5011	51	7	kim	kim	PROPN
ejpam-5011	51	8	,	,	PUNCT
ejpam-5011	51	9	j.	j.	PROPN
ejpam-5011	51	10	kwon	kwon	PROPN
ejpam-5011	51	11	/	/	SYM
ejpam-5011	51	12	eur	eur	PROPN
ejpam-5011	51	13	.	.	PUNCT
ejpam-5011	52	1	j.	j.	PROPN
ejpam-5011	52	2	pure	pure	PROPN
ejpam-5011	52	3	appl	appl	PROPN
ejpam-5011	52	4	.	.	PROPN
ejpam-5011	52	5	math	math	PROPN
ejpam-5011	52	6	,	,	PUNCT
ejpam-5011	52	7	17	17	NUM
ejpam-5011	52	8	(	(	PUNCT
ejpam-5011	52	9	1	1	NUM
ejpam-5011	52	10	)	)	PUNCT
ejpam-5011	52	11	(	(	PUNCT
ejpam-5011	52	12	2024	2024	NUM
ejpam-5011	52	13	)	)	PUNCT
ejpam-5011	52	14	,	,	PUNCT
ejpam-5011	52	15	1	1	NUM
ejpam-5011	52	16	-	-	SYM
ejpam-5011	52	17	10	10	NUM
ejpam-5011	52	18	3	3	NUM
ejpam-5011	52	19	for	for	ADP
ejpam-5011	52	20	n	n	PRON
ejpam-5011	52	21	≥	≥	NOUN
ejpam-5011	52	22	0	0	NUM
ejpam-5011	52	23	,	,	PUNCT
ejpam-5011	52	24	the	the	DET
ejpam-5011	52	25	unsigned	unsigned	ADJ
ejpam-5011	52	26	stirling	stirling	NOUN
ejpam-5011	52	27	numbers	number	NOUN
ejpam-5011	52	28	of	of	ADP
ejpam-5011	52	29	the	the	DET
ejpam-5011	52	30	first	first	ADJ
ejpam-5011	52	31	kind	kind	NOUN
ejpam-5011	52	32	are	be	AUX
ejpam-5011	52	33	defined	define	VERB
ejpam-5011	52	34	by	by	ADP
ejpam-5011	52	35	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5011	52	36	=	=	SYM
ejpam-5011	52	37	n	n	PROPN
ejpam-5011	52	38	∑	∑	ADV
ejpam-5011	52	39	k=0	k=0	PROPN
ejpam-5011	52	40	[	[	PUNCT
ejpam-5011	52	41	n	n	X
ejpam-5011	52	42	k	k	X
ejpam-5011	52	43	]	]	PUNCT
ejpam-5011	52	44	xk	xk	PROPN
ejpam-5011	52	45	,	,	PUNCT
ejpam-5011	52	46	(	(	PUNCT
ejpam-5011	52	47	see	see	VERB
ejpam-5011	52	48	[	[	X
ejpam-5011	52	49	1	1	NUM
ejpam-5011	52	50	,	,	PUNCT
ejpam-5011	52	51	3	3	NUM
ejpam-5011	52	52	,	,	PUNCT
ejpam-5011	52	53	4	4	NUM
ejpam-5011	52	54	,	,	PUNCT
ejpam-5011	52	55	8	8	NUM
ejpam-5011	52	56	,	,	PUNCT
ejpam-5011	52	57	17	17	NUM
ejpam-5011	52	58	,	,	PUNCT
ejpam-5011	52	59	18	18	NUM
ejpam-5011	52	60	]	]	PUNCT
ejpam-5011	52	61	)	)	PUNCT
ejpam-5011	52	62	,	,	PUNCT
ejpam-5011	52	63	(	(	PUNCT
ejpam-5011	52	64	4	4	X
ejpam-5011	52	65	)	)	PUNCT
ejpam-5011	52	66	where	where	SCONJ
ejpam-5011	52	67	the	the	DET
ejpam-5011	52	68	rising	rise	VERB
ejpam-5011	52	69	factorials	factorial	NOUN
ejpam-5011	52	70	are	be	AUX
ejpam-5011	52	71	given	give	VERB
ejpam-5011	52	72	by	by	ADP
ejpam-5011	52	73	⟨x⟩0	⟨x⟩0	PROPN
ejpam-5011	52	74	=	=	SYM
ejpam-5011	52	75	1	1	NUM
ejpam-5011	52	76	,	,	PUNCT
ejpam-5011	52	77	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5011	52	78	=	=	SYM
ejpam-5011	52	79	x(x+1	x(x+1	X
ejpam-5011	52	80	)	)	PUNCT
ejpam-5011	52	81	·	·	PUNCT
ejpam-5011	52	82	·	·	PUNCT
ejpam-5011	53	1	·	·	PUNCT
ejpam-5011	53	2	(	(	PUNCT
ejpam-5011	53	3	x+n−1	x+n−1	PROPN
ejpam-5011	53	4	)	)	PUNCT
ejpam-5011	53	5	,	,	PUNCT
ejpam-5011	53	6	(	(	PUNCT
ejpam-5011	53	7	n	n	X
ejpam-5011	53	8	≥	≥	NOUN
ejpam-5011	53	9	1	1	NUM
ejpam-5011	53	10	)	)	PUNCT
ejpam-5011	53	11	.	.	PUNCT
ejpam-5011	54	1	the	the	DET
ejpam-5011	54	2	stirling	stirling	NOUN
ejpam-5011	54	3	numbers	number	NOUN
ejpam-5011	54	4	of	of	ADP
ejpam-5011	54	5	the	the	DET
ejpam-5011	54	6	second	second	ADJ
ejpam-5011	54	7	kind	kind	NOUN
ejpam-5011	54	8	are	be	AUX
ejpam-5011	54	9	given	give	VERB
ejpam-5011	54	10	by	by	ADP
ejpam-5011	54	11	xn	xn	PROPN
ejpam-5011	54	12	=	=	PROPN
ejpam-5011	54	13	n	n	PROPN
ejpam-5011	54	14	∑	∑	PUNCT
ejpam-5011	54	15	k=0	k=0	PROPN
ejpam-5011	54	16	{	{	PUNCT
ejpam-5011	54	17	n	n	NOUN
ejpam-5011	54	18	k	k	NOUN
ejpam-5011	54	19	}	}	PUNCT
ejpam-5011	54	20	(	(	PUNCT
ejpam-5011	54	21	x)k	x)k	X
ejpam-5011	54	22	,	,	PUNCT
ejpam-5011	54	23	(	(	PUNCT
ejpam-5011	54	24	n	n	X
ejpam-5011	54	25	≥	≥	NOUN
ejpam-5011	54	26	0	0	NUM
ejpam-5011	54	27	)	)	PUNCT
ejpam-5011	54	28	,	,	PUNCT
ejpam-5011	54	29	(	(	PUNCT
ejpam-5011	54	30	see	see	VERB
ejpam-5011	54	31	[	[	X
ejpam-5011	54	32	2	2	NUM
ejpam-5011	54	33	,	,	PUNCT
ejpam-5011	54	34	6	6	NUM
ejpam-5011	54	35	,	,	PUNCT
ejpam-5011	54	36	7	7	NUM
ejpam-5011	54	37	]	]	NUM
ejpam-5011	54	38	)	)	PUNCT
ejpam-5011	54	39	,	,	PUNCT
ejpam-5011	54	40	(	(	PUNCT
ejpam-5011	54	41	5	5	X
ejpam-5011	54	42	)	)	PUNCT
ejpam-5011	54	43	where	where	SCONJ
ejpam-5011	54	44	the	the	DET
ejpam-5011	54	45	falling	fall	VERB
ejpam-5011	54	46	factorials	factorial	NOUN
ejpam-5011	54	47	are	be	AUX
ejpam-5011	54	48	given	give	VERB
ejpam-5011	54	49	by	by	ADP
ejpam-5011	54	50	(	(	PUNCT
ejpam-5011	54	51	x)0	x)0	X
ejpam-5011	54	52	=	=	SYM
ejpam-5011	54	53	1	1	NUM
ejpam-5011	54	54	,	,	PUNCT
ejpam-5011	54	55	(	(	PUNCT
ejpam-5011	54	56	x)n	x)n	PUNCT
ejpam-5011	54	57	=	=	SYM
ejpam-5011	54	58	x(x−1	x(x−1	X
ejpam-5011	54	59	)	)	PUNCT
ejpam-5011	54	60	·	·	PUNCT
ejpam-5011	54	61	·	·	PUNCT
ejpam-5011	54	62	·	·	PUNCT
ejpam-5011	54	63	(	(	PUNCT
ejpam-5011	54	64	x−n+1	x−n+1	PROPN
ejpam-5011	54	65	)	)	PUNCT
ejpam-5011	54	66	,	,	PUNCT
ejpam-5011	54	67	(	(	PUNCT
ejpam-5011	54	68	n	n	X
ejpam-5011	54	69	≥	≥	NOUN
ejpam-5011	54	70	1	1	NUM
ejpam-5011	54	71	)	)	PUNCT
ejpam-5011	54	72	.	.	PUNCT
ejpam-5011	55	1	for	for	ADP
ejpam-5011	55	2	n	n	PRON
ejpam-5011	55	3	,	,	PUNCT
ejpam-5011	55	4	r	r	NOUN
ejpam-5011	55	5	≥	≥	NOUN
ejpam-5011	55	6	0	0	NUM
ejpam-5011	55	7	,	,	PUNCT
ejpam-5011	55	8	the	the	DET
ejpam-5011	55	9	unsigned	unsigned	ADJ
ejpam-5011	55	10	r	r	NOUN
ejpam-5011	55	11	-	-	PUNCT
ejpam-5011	55	12	stirling	stirling	NOUN
ejpam-5011	55	13	numbers	number	NOUN
ejpam-5011	55	14	of	of	ADP
ejpam-5011	55	15	the	the	DET
ejpam-5011	55	16	first	first	ADJ
ejpam-5011	55	17	kind	kind	NOUN
ejpam-5011	55	18	are	be	AUX
ejpam-5011	55	19	defined	define	VERB
ejpam-5011	55	20	by	by	ADP
ejpam-5011	55	21	⟨x+	⟨x+	NOUN
ejpam-5011	55	22	r⟩n	r⟩n	NUM
ejpam-5011	55	23	=	=	SYM
ejpam-5011	55	24	n	n	PRON
ejpam-5011	55	25	∑	∑	ADV
ejpam-5011	55	26	k=0	k=0	PUNCT
ejpam-5011	55	27	[	[	PUNCT
ejpam-5011	55	28	n+	n+	ADP
ejpam-5011	55	29	r	r	NOUN
ejpam-5011	55	30	k+	k+	NOUN
ejpam-5011	55	31	r	r	NOUN
ejpam-5011	55	32	]	]	PUNCT
ejpam-5011	55	33	r	r	NOUN
ejpam-5011	55	34	xk	xk	PROPN
ejpam-5011	55	35	,	,	PUNCT
ejpam-5011	55	36	(	(	PUNCT
ejpam-5011	55	37	see	see	VERB
ejpam-5011	55	38	[	[	X
ejpam-5011	55	39	11	11	NUM
ejpam-5011	55	40	,	,	PUNCT
ejpam-5011	55	41	12	12	NUM
ejpam-5011	55	42	,	,	PUNCT
ejpam-5011	55	43	14	14	NUM
ejpam-5011	55	44	]	]	PUNCT
ejpam-5011	55	45	)	)	PUNCT
ejpam-5011	55	46	.	.	PUNCT
ejpam-5011	56	1	(	(	PUNCT
ejpam-5011	56	2	6	6	NUM
ejpam-5011	56	3	)	)	PUNCT
ejpam-5011	56	4	the	the	DET
ejpam-5011	56	5	r	r	NOUN
ejpam-5011	56	6	-	-	PUNCT
ejpam-5011	56	7	stirling	stirling	NOUN
ejpam-5011	56	8	numbers	number	NOUN
ejpam-5011	56	9	of	of	ADP
ejpam-5011	56	10	the	the	DET
ejpam-5011	56	11	second	second	ADJ
ejpam-5011	56	12	kind	kind	NOUN
ejpam-5011	56	13	are	be	AUX
ejpam-5011	56	14	defined	define	VERB
ejpam-5011	56	15	by	by	ADP
ejpam-5011	56	16	(	(	PUNCT
ejpam-5011	56	17	x+	x+	X
ejpam-5011	56	18	r)n	r)n	X
ejpam-5011	56	19	=	=	SYM
ejpam-5011	56	20	n	n	X
ejpam-5011	56	21	∑	∑	PUNCT
ejpam-5011	56	22	k=0	k=0	PROPN
ejpam-5011	56	23	{	{	PUNCT
ejpam-5011	56	24	n+	n+	ADP
ejpam-5011	56	25	r	r	NOUN
ejpam-5011	56	26	k+	k+	NOUN
ejpam-5011	56	27	r	r	NOUN
ejpam-5011	56	28	}	}	PUNCT
ejpam-5011	56	29	r	r	NOUN
ejpam-5011	56	30	(	(	PUNCT
ejpam-5011	56	31	x)k	x)k	NOUN
ejpam-5011	56	32	,	,	PUNCT
ejpam-5011	56	33	(	(	PUNCT
ejpam-5011	56	34	see	see	VERB
ejpam-5011	56	35	[	[	X
ejpam-5011	56	36	12	12	NUM
ejpam-5011	56	37	,	,	PUNCT
ejpam-5011	56	38	14	14	NUM
ejpam-5011	56	39	]	]	PUNCT
ejpam-5011	56	40	)	)	PUNCT
ejpam-5011	56	41	.	.	PUNCT
ejpam-5011	57	1	(	(	PUNCT
ejpam-5011	57	2	7	7	X
ejpam-5011	57	3	)	)	PUNCT
ejpam-5011	57	4	for	for	ADP
ejpam-5011	57	5	any	any	DET
ejpam-5011	57	6	λ	λ	PROPN
ejpam-5011	57	7	∈	∈	PROPN
ejpam-5011	57	8	r	r	NOUN
ejpam-5011	57	9	,	,	PUNCT
ejpam-5011	57	10	the	the	DET
ejpam-5011	57	11	unsigned	unsigned	ADJ
ejpam-5011	57	12	degenerate	degenerate	ADJ
ejpam-5011	57	13	stirling	stirling	NOUN
ejpam-5011	57	14	numbers	number	NOUN
ejpam-5011	57	15	of	of	ADP
ejpam-5011	57	16	the	the	DET
ejpam-5011	57	17	first	first	ADJ
ejpam-5011	57	18	kind	kind	NOUN
ejpam-5011	57	19	are	be	AUX
ejpam-5011	57	20	defined	define	VERB
ejpam-5011	57	21	by	by	ADP
ejpam-5011	57	22	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5011	57	23	=	=	SYM
ejpam-5011	57	24	n	n	PROPN
ejpam-5011	57	25	∑	∑	ADV
ejpam-5011	57	26	k=0	k=0	PROPN
ejpam-5011	57	27	[	[	PUNCT
ejpam-5011	57	28	n	n	X
ejpam-5011	57	29	k	k	X
ejpam-5011	57	30	]	]	PUNCT
ejpam-5011	57	31	λ	λ	X
ejpam-5011	57	32	⟨x⟩k	⟨x⟩k	NOUN
ejpam-5011	57	33	,	,	PUNCT
ejpam-5011	57	34	λ	λ	X
ejpam-5011	57	35	,	,	PUNCT
ejpam-5011	57	36	(	(	PUNCT
ejpam-5011	57	37	n	n	CCONJ
ejpam-5011	57	38	≥	≥	NOUN
ejpam-5011	57	39	0	0	NUM
ejpam-5011	57	40	)	)	PUNCT
ejpam-5011	57	41	,	,	PUNCT
ejpam-5011	57	42	(	(	PUNCT
ejpam-5011	57	43	see	see	VERB
ejpam-5011	57	44	[	[	X
ejpam-5011	57	45	10	10	NUM
ejpam-5011	57	46	,	,	PUNCT
ejpam-5011	57	47	14	14	NUM
ejpam-5011	57	48	,	,	PUNCT
ejpam-5011	57	49	15	15	NUM
ejpam-5011	57	50	]	]	NUM
ejpam-5011	57	51	)	)	PUNCT
ejpam-5011	57	52	,	,	PUNCT
ejpam-5011	57	53	(	(	PUNCT
ejpam-5011	57	54	8)	8)	NUM
ejpam-5011	57	55	where	where	SCONJ
ejpam-5011	57	56	the	the	DET
ejpam-5011	57	57	generalized	generalized	ADJ
ejpam-5011	57	58	rising	rise	VERB
ejpam-5011	57	59	factorials	factorial	NOUN
ejpam-5011	57	60	are	be	AUX
ejpam-5011	57	61	given	give	VERB
ejpam-5011	57	62	by	by	ADP
ejpam-5011	57	63	⟨x⟩0,λ	⟨x⟩0,λ	NOUN
ejpam-5011	57	64	=	=	SYM
ejpam-5011	57	65	1	1	NUM
ejpam-5011	57	66	⟨x⟩n	⟨x⟩n	NOUN
ejpam-5011	57	67	,	,	PUNCT
ejpam-5011	57	68	λ	λ	PROPN
ejpam-5011	57	69	=	=	PUNCT
ejpam-5011	57	70	x(x+λ	x(x+λ	PROPN
ejpam-5011	57	71	)	)	PUNCT
ejpam-5011	57	72	·	·	PUNCT
ejpam-5011	58	1	·	·	PUNCT
ejpam-5011	58	2	·	·	PUNCT
ejpam-5011	58	3	(	(	PUNCT
ejpam-5011	58	4	x+(n−1)λ	x+(n−1)λ	NOUN
ejpam-5011	58	5	)	)	PUNCT
ejpam-5011	58	6	,	,	PUNCT
ejpam-5011	58	7	(	(	PUNCT
ejpam-5011	58	8	n	n	CCONJ
ejpam-5011	58	9	≥	≥	NOUN
ejpam-5011	58	10	1	1	NUM
ejpam-5011	58	11	)	)	PUNCT
ejpam-5011	58	12	.	.	PUNCT
ejpam-5011	59	1	in	in	ADP
ejpam-5011	59	2	view	view	NOUN
ejpam-5011	59	3	of	of	ADP
ejpam-5011	59	4	(	(	PUNCT
ejpam-5011	59	5	5	5	NUM
ejpam-5011	59	6	)	)	PUNCT
ejpam-5011	59	7	,	,	PUNCT
ejpam-5011	59	8	the	the	DET
ejpam-5011	59	9	degenerate	degenerate	ADJ
ejpam-5011	59	10	stirling	stirling	NOUN
ejpam-5011	59	11	numbers	number	NOUN
ejpam-5011	59	12	of	of	ADP
ejpam-5011	59	13	the	the	DET
ejpam-5011	59	14	second	second	ADJ
ejpam-5011	59	15	kind	kind	NOUN
ejpam-5011	59	16	are	be	AUX
ejpam-5011	59	17	defined	define	VERB
ejpam-5011	59	18	by	by	ADP
ejpam-5011	59	19	(	(	PUNCT
ejpam-5011	59	20	x)n	x)n	PROPN
ejpam-5011	59	21	,	,	PUNCT
ejpam-5011	59	22	λ	λ	X
ejpam-5011	59	23	=	=	SYM
ejpam-5011	59	24	n	n	PROPN
ejpam-5011	59	25	∑	∑	ADP
ejpam-5011	59	26	k=0	k=0	PROPN
ejpam-5011	59	27	{	{	PUNCT
ejpam-5011	59	28	n	n	NOUN
ejpam-5011	59	29	k	k	ADJ
ejpam-5011	59	30	}	}	PUNCT
ejpam-5011	59	31	λ	λ	PROPN
ejpam-5011	59	32	(	(	PUNCT
ejpam-5011	59	33	x)k	x)k	X
ejpam-5011	59	34	,	,	PUNCT
ejpam-5011	59	35	(	(	PUNCT
ejpam-5011	59	36	see	see	VERB
ejpam-5011	59	37	[	[	X
ejpam-5011	59	38	10	10	NUM
ejpam-5011	59	39	]	]	NUM
ejpam-5011	59	40	)	)	PUNCT
ejpam-5011	59	41	.	.	PUNCT
ejpam-5011	60	1	(	(	PUNCT
ejpam-5011	60	2	9	9	X
ejpam-5011	60	3	)	)	PUNCT
ejpam-5011	60	4	for	for	ADP
ejpam-5011	60	5	n	n	X
ejpam-5011	60	6	,	,	PUNCT
ejpam-5011	60	7	r	r	NOUN
ejpam-5011	60	8	≥	≥	NOUN
ejpam-5011	60	9	0	0	NUM
ejpam-5011	60	10	,	,	PUNCT
ejpam-5011	60	11	the	the	DET
ejpam-5011	60	12	unsigned	unsigned	ADJ
ejpam-5011	60	13	degenerate	degenerate	ADJ
ejpam-5011	60	14	r	r	NOUN
ejpam-5011	60	15	-	-	PUNCT
ejpam-5011	60	16	stirling	stirling	NOUN
ejpam-5011	60	17	numbers	number	NOUN
ejpam-5011	60	18	of	of	ADP
ejpam-5011	60	19	the	the	DET
ejpam-5011	60	20	first	first	ADJ
ejpam-5011	60	21	kind	kind	NOUN
ejpam-5011	60	22	are	be	AUX
ejpam-5011	60	23	given	give	VERB
ejpam-5011	60	24	by	by	ADP
ejpam-5011	60	25	⟨x+	⟨x+	NOUN
ejpam-5011	60	26	r⟩n	r⟩n	NUM
ejpam-5011	60	27	=	=	SYM
ejpam-5011	60	28	n	n	DET
ejpam-5011	60	29	∑	∑	ADV
ejpam-5011	60	30	k=0	k=0	PUNCT
ejpam-5011	60	31	[	[	PUNCT
ejpam-5011	60	32	n+	n+	ADP
ejpam-5011	60	33	r	r	NOUN
ejpam-5011	60	34	k+	k+	NOUN
ejpam-5011	60	35	r	r	NOUN
ejpam-5011	60	36	]	]	PUNCT
ejpam-5011	60	37	r	r	NOUN
ejpam-5011	60	38	,	,	PUNCT
ejpam-5011	60	39	λ	λ	NOUN
ejpam-5011	60	40	⟨x⟩k	⟨x⟩k	NOUN
ejpam-5011	60	41	,	,	PUNCT
ejpam-5011	60	42	λ	λ	PROPN
ejpam-5011	60	43	(	(	PUNCT
ejpam-5011	60	44	n	n	CCONJ
ejpam-5011	60	45	≥	≥	NOUN
ejpam-5011	60	46	0	0	NUM
ejpam-5011	60	47	)	)	PUNCT
ejpam-5011	60	48	,	,	PUNCT
ejpam-5011	60	49	(	(	PUNCT
ejpam-5011	60	50	see	see	VERB
ejpam-5011	60	51	[	[	X
ejpam-5011	60	52	11	11	NUM
ejpam-5011	60	53	,	,	PUNCT
ejpam-5011	60	54	13−−15	13−−15	NUM
ejpam-5011	60	55	]	]	PUNCT
ejpam-5011	60	56	)	)	PUNCT
ejpam-5011	60	57	.	.	PUNCT
ejpam-5011	61	1	(	(	PUNCT
ejpam-5011	61	2	10	10	NUM
ejpam-5011	61	3	)	)	PUNCT
ejpam-5011	61	4	in	in	ADP
ejpam-5011	61	5	[	[	X
ejpam-5011	61	6	14	14	NUM
ejpam-5011	61	7	]	]	PUNCT
ejpam-5011	61	8	,	,	PUNCT
ejpam-5011	61	9	the	the	DET
ejpam-5011	61	10	degenerate	degenerate	ADJ
ejpam-5011	61	11	r	r	NOUN
ejpam-5011	61	12	-	-	PUNCT
ejpam-5011	61	13	stirling	stirling	NOUN
ejpam-5011	61	14	numbers	number	NOUN
ejpam-5011	61	15	of	of	ADP
ejpam-5011	61	16	the	the	DET
ejpam-5011	61	17	second	second	ADJ
ejpam-5011	61	18	kind	kind	NOUN
ejpam-5011	61	19	are	be	AUX
ejpam-5011	61	20	defined	define	VERB
ejpam-5011	61	21	by	by	ADP
ejpam-5011	61	22	(	(	PUNCT
ejpam-5011	61	23	x+	x+	ADJ
ejpam-5011	61	24	r)n	r)n	NOUN
ejpam-5011	61	25	,	,	PUNCT
ejpam-5011	61	26	λ	λ	PROPN
ejpam-5011	61	27	=	=	SYM
ejpam-5011	61	28	n	n	PROPN
ejpam-5011	61	29	∑	∑	ADP
ejpam-5011	61	30	k=0	k=0	PROPN
ejpam-5011	61	31	{	{	PUNCT
ejpam-5011	61	32	n+	n+	ADP
ejpam-5011	61	33	r	r	NOUN
ejpam-5011	61	34	k+	k+	NOUN
ejpam-5011	61	35	r	r	NOUN
ejpam-5011	61	36	}	}	PUNCT
ejpam-5011	61	37	r	r	NOUN
ejpam-5011	61	38	,	,	PUNCT
ejpam-5011	61	39	λ	λ	PROPN
ejpam-5011	61	40	(	(	PUNCT
ejpam-5011	61	41	x)k	x)k	X
ejpam-5011	61	42	,	,	PUNCT
ejpam-5011	61	43	(	(	PUNCT
ejpam-5011	61	44	n	n	X
ejpam-5011	61	45	≥	≥	NOUN
ejpam-5011	61	46	0	0	NUM
ejpam-5011	61	47	)	)	PUNCT
ejpam-5011	61	48	.	.	PUNCT
ejpam-5011	62	1	(	(	PUNCT
ejpam-5011	62	2	11	11	NUM
ejpam-5011	62	3	)	)	PUNCT
ejpam-5011	62	4	d.	d.	PROPN
ejpam-5011	62	5	kim	kim	PROPN
ejpam-5011	62	6	,	,	PUNCT
ejpam-5011	62	7	t.	t.	PROPN
ejpam-5011	62	8	kim	kim	PROPN
ejpam-5011	62	9	,	,	PUNCT
ejpam-5011	62	10	j.	j.	PROPN
ejpam-5011	62	11	kwon	kwon	PROPN
ejpam-5011	62	12	/	/	SYM
ejpam-5011	62	13	eur	eur	PROPN
ejpam-5011	62	14	.	.	PUNCT
ejpam-5011	63	1	j.	j.	PROPN
ejpam-5011	63	2	pure	pure	PROPN
ejpam-5011	63	3	appl	appl	PROPN
ejpam-5011	63	4	.	.	PROPN
ejpam-5011	63	5	math	math	PROPN
ejpam-5011	63	6	,	,	PUNCT
ejpam-5011	63	7	17	17	NUM
ejpam-5011	63	8	(	(	PUNCT
ejpam-5011	63	9	1	1	NUM
ejpam-5011	63	10	)	)	PUNCT
ejpam-5011	63	11	(	(	PUNCT
ejpam-5011	63	12	2024	2024	NUM
ejpam-5011	63	13	)	)	PUNCT
ejpam-5011	63	14	,	,	PUNCT
ejpam-5011	63	15	1	1	NUM
ejpam-5011	63	16	-	-	SYM
ejpam-5011	63	17	10	10	NUM
ejpam-5011	63	18	4	4	NUM
ejpam-5011	63	19	2	2	NUM
ejpam-5011	63	20	.	.	PUNCT
ejpam-5011	64	1	some	some	DET
ejpam-5011	64	2	formulas	formula	NOUN
ejpam-5011	64	3	for	for	ADP
ejpam-5011	64	4	degenerate	degenerate	ADJ
ejpam-5011	64	5	stirling	stirling	NOUN
ejpam-5011	64	6	numbers	number	NOUN
ejpam-5011	64	7	for	for	ADP
ejpam-5011	64	8	(	(	PUNCT
ejpam-5011	64	9	9	9	NUM
ejpam-5011	64	10	)	)	PUNCT
ejpam-5011	64	11	,	,	PUNCT
ejpam-5011	64	12	we	we	PRON
ejpam-5011	64	13	note	note	VERB
ejpam-5011	64	14	that	that	SCONJ
ejpam-5011	64	15	1	1	NUM
ejpam-5011	64	16	k	k	X
ejpam-5011	64	17	!	!	PUNCT
ejpam-5011	65	1	(	(	PUNCT
ejpam-5011	65	2	eλ	eλ	X
ejpam-5011	65	3	(	(	PUNCT
ejpam-5011	65	4	t)−1	t)−1	NOUN
ejpam-5011	65	5	)	)	PUNCT
ejpam-5011	65	6	k	k	NOUN
ejpam-5011	66	1	=	=	SYM
ejpam-5011	66	2	∞	∞	NUM
ejpam-5011	66	3	∑	∑	PUNCT
ejpam-5011	66	4	n	n	CCONJ
ejpam-5011	66	5	=	=	SYM
ejpam-5011	66	6	k	k	X
ejpam-5011	66	7	{	{	PUNCT
ejpam-5011	66	8	n	n	NOUN
ejpam-5011	66	9	k	k	ADJ
ejpam-5011	66	10	}	}	PUNCT
ejpam-5011	66	11	λ	λ	PROPN
ejpam-5011	66	12	tn	tn	NOUN
ejpam-5011	66	13	n	n	X
ejpam-5011	66	14	!	!	PUNCT
ejpam-5011	66	15	,	,	PUNCT
ejpam-5011	66	16	(	(	PUNCT
ejpam-5011	66	17	k	k	X
ejpam-5011	66	18	≥	≥	PROPN
ejpam-5011	66	19	0	0	NUM
ejpam-5011	66	20	)	)	PUNCT
ejpam-5011	66	21	,	,	PUNCT
ejpam-5011	66	22	(	(	PUNCT
ejpam-5011	66	23	see	see	VERB
ejpam-5011	66	24	[	[	X
ejpam-5011	66	25	10	10	NUM
ejpam-5011	66	26	,	,	PUNCT
ejpam-5011	66	27	14	14	NUM
ejpam-5011	66	28	]	]	PUNCT
ejpam-5011	66	29	)	)	PUNCT
ejpam-5011	66	30	.	.	PUNCT
ejpam-5011	67	1	(	(	PUNCT
ejpam-5011	67	2	12	12	NUM
ejpam-5011	67	3	)	)	PUNCT
ejpam-5011	67	4	by	by	ADP
ejpam-5011	67	5	(	(	PUNCT
ejpam-5011	67	6	12	12	NUM
ejpam-5011	67	7	)	)	PUNCT
ejpam-5011	67	8	,	,	PUNCT
ejpam-5011	67	9	we	we	PRON
ejpam-5011	67	10	get	get	VERB
ejpam-5011	67	11	k	k	PROPN
ejpam-5011	67	12	∑	∑	PUNCT
ejpam-5011	67	13	l=0	l=0	PROPN
ejpam-5011	67	14	(	(	PUNCT
ejpam-5011	67	15	k	k	NOUN
ejpam-5011	67	16	l	l	NOUN
ejpam-5011	67	17	)	)	PUNCT
ejpam-5011	67	18	(	(	PUNCT
ejpam-5011	67	19	−1)k−l(l)n	−1)k−l(l)n	PROPN
ejpam-5011	67	20	,	,	PUNCT
ejpam-5011	67	21	λ	λ	PROPN
ejpam-5011	67	22	=	=	SYM
ejpam-5011	67	23	k	k	X
ejpam-5011	67	24	!	!	PUNCT
ejpam-5011	67	25	{	{	PUNCT
ejpam-5011	68	1	n	n	NOUN
ejpam-5011	68	2	k	k	X
ejpam-5011	68	3	}	}	PUNCT
ejpam-5011	68	4	λ	λ	PROPN
ejpam-5011	68	5	,	,	PUNCT
ejpam-5011	68	6	(	(	PUNCT
ejpam-5011	68	7	n	n	CCONJ
ejpam-5011	68	8	,	,	PUNCT
ejpam-5011	68	9	k	k	PROPN
ejpam-5011	68	10	≥	≥	PROPN
ejpam-5011	68	11	0	0	NUM
ejpam-5011	68	12	)	)	PUNCT
ejpam-5011	68	13	.	.	PUNCT
ejpam-5011	69	1	(	(	PUNCT
ejpam-5011	69	2	13	13	NUM
ejpam-5011	69	3	)	)	PUNCT
ejpam-5011	69	4	theorem	theorem	NOUN
ejpam-5011	69	5	1	1	NUM
ejpam-5011	69	6	.	.	X
ejpam-5011	70	1	for	for	ADP
ejpam-5011	70	2	any	any	DET
ejpam-5011	70	3	nonnegative	nonnegative	ADJ
ejpam-5011	70	4	integers	integer	NOUN
ejpam-5011	70	5	n	n	CCONJ
ejpam-5011	70	6	,	,	PUNCT
ejpam-5011	70	7	k	k	PROPN
ejpam-5011	70	8	,	,	PUNCT
ejpam-5011	70	9	we	we	PRON
ejpam-5011	70	10	have	have	VERB
ejpam-5011	70	11	k	k	NOUN
ejpam-5011	70	12	!	!	PUNCT
ejpam-5011	70	13	{	{	PUNCT
ejpam-5011	71	1	n	n	NOUN
ejpam-5011	71	2	k	k	X
ejpam-5011	71	3	}	}	PUNCT
ejpam-5011	71	4	λ	λ	PROPN
ejpam-5011	71	5	=	=	SYM
ejpam-5011	71	6	k	k	X
ejpam-5011	71	7	∑	∑	PUNCT
ejpam-5011	71	8	j=0	j=0	PROPN
ejpam-5011	71	9	(	(	PUNCT
ejpam-5011	71	10	k	k	PROPN
ejpam-5011	71	11	j	j	PROPN
ejpam-5011	71	12	)	)	PUNCT
ejpam-5011	71	13	(	(	PUNCT
ejpam-5011	71	14	−1)k−	−1)k−	X
ejpam-5011	71	15	j	j	X
ejpam-5011	71	16	(	(	PUNCT
ejpam-5011	71	17	j)n	j)n	PROPN
ejpam-5011	71	18	,	,	PUNCT
ejpam-5011	71	19	λ	λ	X
ejpam-5011	71	20	⇐	⇐	ADJ
ejpam-5011	71	21	⇒	⇒	PROPN
ejpam-5011	71	22	(	(	PUNCT
ejpam-5011	71	23	k)n	k)n	ADJ
ejpam-5011	71	24	,	,	PUNCT
ejpam-5011	71	25	λ	λ	PROPN
ejpam-5011	71	26	=	=	SYM
ejpam-5011	71	27	k	k	X
ejpam-5011	71	28	∑	∑	PUNCT
ejpam-5011	71	29	j=0	j=0	PROPN
ejpam-5011	71	30	(	(	PUNCT
ejpam-5011	71	31	k	k	PROPN
ejpam-5011	71	32	j	j	PROPN
ejpam-5011	71	33	)	)	PUNCT
ejpam-5011	71	34	j	j	PROPN
ejpam-5011	71	35	!	!	PUNCT
ejpam-5011	71	36	{	{	PUNCT
ejpam-5011	72	1	n	n	PRON
ejpam-5011	72	2	j	j	PROPN
ejpam-5011	72	3	}	}	PUNCT
ejpam-5011	72	4	λ	λ	PROPN
ejpam-5011	72	5	.	.	PUNCT
ejpam-5011	73	1	(	(	PUNCT
ejpam-5011	73	2	14	14	NUM
ejpam-5011	73	3	)	)	PUNCT
ejpam-5011	73	4	proof	proof	NOUN
ejpam-5011	73	5	.	.	PUNCT
ejpam-5011	74	1	(=	(=	X
ejpam-5011	74	2	⇒	⇒	NOUN
ejpam-5011	74	3	)	)	PUNCT
ejpam-5011	74	4	assume	assume	VERB
ejpam-5011	74	5	that	that	SCONJ
ejpam-5011	74	6	k	k	X
ejpam-5011	74	7	!	!	PUNCT
ejpam-5011	74	8	{	{	PUNCT
ejpam-5011	74	9	n	n	NOUN
ejpam-5011	74	10	k	k	X
ejpam-5011	74	11	}	}	PUNCT
ejpam-5011	74	12	λ	λ	PROPN
ejpam-5011	74	13	=	=	SYM
ejpam-5011	74	14	k	k	X
ejpam-5011	74	15	∑	∑	PUNCT
ejpam-5011	74	16	j=0	j=0	PROPN
ejpam-5011	74	17	(	(	PUNCT
ejpam-5011	74	18	k	k	PROPN
ejpam-5011	74	19	j	j	PROPN
ejpam-5011	74	20	)	)	PUNCT
ejpam-5011	74	21	(	(	PUNCT
ejpam-5011	74	22	−1)k−	−1)k−	X
ejpam-5011	74	23	j	j	X
ejpam-5011	74	24	(	(	PUNCT
ejpam-5011	74	25	j)n	j)n	NOUN
ejpam-5011	74	26	,	,	PUNCT
ejpam-5011	74	27	λ	λ	INTJ
ejpam-5011	74	28	.	.	PUNCT
ejpam-5011	75	1	then	then	ADV
ejpam-5011	75	2	we	we	PRON
ejpam-5011	75	3	have	have	VERB
ejpam-5011	75	4	k	k	PROPN
ejpam-5011	75	5	∑	∑	PUNCT
ejpam-5011	75	6	j=0	j=0	PROPN
ejpam-5011	75	7	(	(	PUNCT
ejpam-5011	75	8	k	k	PROPN
ejpam-5011	75	9	j	j	PROPN
ejpam-5011	75	10	)	)	PUNCT
ejpam-5011	75	11	j	j	PROPN
ejpam-5011	75	12	!	!	PUNCT
ejpam-5011	75	13	{	{	PUNCT
ejpam-5011	76	1	n	n	PRON
ejpam-5011	76	2	j	j	NOUN
ejpam-5011	76	3	}	}	PUNCT
ejpam-5011	76	4	λ	λ	PROPN
ejpam-5011	76	5	=	=	SYM
ejpam-5011	76	6	k	k	X
ejpam-5011	76	7	∑	∑	PUNCT
ejpam-5011	76	8	j=0	j=0	PROPN
ejpam-5011	76	9	(	(	PUNCT
ejpam-5011	77	1	k	k	PROPN
ejpam-5011	77	2	j	j	PROPN
ejpam-5011	77	3	)	)	PUNCT
ejpam-5011	77	4	j	j	PROPN
ejpam-5011	77	5	∑	∑	PUNCT
ejpam-5011	77	6	l=0	l=0	PROPN
ejpam-5011	77	7	(	(	PUNCT
ejpam-5011	77	8	j	j	PROPN
ejpam-5011	77	9	l	l	NOUN
ejpam-5011	77	10	)	)	PUNCT
ejpam-5011	77	11	(	(	PUNCT
ejpam-5011	77	12	−1	−1	NOUN
ejpam-5011	77	13	)	)	PUNCT
ejpam-5011	77	14	j−l(l)n	j−l(l)n	NOUN
ejpam-5011	77	15	,	,	PUNCT
ejpam-5011	77	16	λ	λ	X
ejpam-5011	77	17	=	=	SYM
ejpam-5011	77	18	k	k	PROPN
ejpam-5011	77	19	∑	∑	PUNCT
ejpam-5011	77	20	l=0	l=0	PROPN
ejpam-5011	77	21	(	(	PUNCT
ejpam-5011	77	22	l)n	l)n	PROPN
ejpam-5011	77	23	,	,	PUNCT
ejpam-5011	77	24	λ	λ	X
ejpam-5011	77	25	k	k	PROPN
ejpam-5011	77	26	∑	∑	PUNCT
ejpam-5011	77	27	j	j	PROPN
ejpam-5011	77	28	=	=	PROPN
ejpam-5011	77	29	l	l	PROPN
ejpam-5011	77	30	(	(	PUNCT
ejpam-5011	77	31	k	k	PROPN
ejpam-5011	77	32	j	j	PROPN
ejpam-5011	77	33	)	)	PUNCT
ejpam-5011	77	34	(	(	PUNCT
ejpam-5011	77	35	j	j	PROPN
ejpam-5011	77	36	l	l	NOUN
ejpam-5011	77	37	)	)	PUNCT
ejpam-5011	77	38	(	(	PUNCT
ejpam-5011	77	39	−1	−1	NOUN
ejpam-5011	77	40	)	)	PUNCT
ejpam-5011	77	41	j−l	j−l	NOUN
ejpam-5011	77	42	=	=	SYM
ejpam-5011	78	1	k	k	PROPN
ejpam-5011	78	2	∑	∑	PUNCT
ejpam-5011	78	3	l=0	l=0	PROPN
ejpam-5011	78	4	(	(	PUNCT
ejpam-5011	78	5	l)n	l)n	X
ejpam-5011	78	6	,	,	PUNCT
ejpam-5011	78	7	λ	λ	PROPN
ejpam-5011	78	8	(	(	PUNCT
ejpam-5011	78	9	k	k	NOUN
ejpam-5011	78	10	l	l	NOUN
ejpam-5011	78	11	)	)	PUNCT
ejpam-5011	78	12	k−l	k−l	NOUN
ejpam-5011	78	13	∑	∑	PUNCT
ejpam-5011	78	14	j=0	j=0	PROPN
ejpam-5011	78	15	(	(	PUNCT
ejpam-5011	78	16	−1)k−l−	−1)k−l−	NUM
ejpam-5011	78	17	j	j	PROPN
ejpam-5011	78	18	(	(	PUNCT
ejpam-5011	78	19	k−	k−	PROPN
ejpam-5011	78	20	l	l	PROPN
ejpam-5011	78	21	j	j	PROPN
ejpam-5011	78	22	)	)	PUNCT
ejpam-5011	79	1	=	=	PUNCT
ejpam-5011	80	1	k	k	X
ejpam-5011	80	2	∑	∑	PUNCT
ejpam-5011	80	3	l=0	l=0	PROPN
ejpam-5011	80	4	(	(	PUNCT
ejpam-5011	80	5	l)n	l)n	X
ejpam-5011	80	6	,	,	PUNCT
ejpam-5011	80	7	λ	λ	PROPN
ejpam-5011	80	8	(	(	PUNCT
ejpam-5011	80	9	k	k	NOUN
ejpam-5011	80	10	l	l	NOUN
ejpam-5011	80	11	)	)	PUNCT
ejpam-5011	81	1	(	(	PUNCT
ejpam-5011	81	2	1−1)k−l	1−1)k−l	X
ejpam-5011	81	3	=	=	SYM
ejpam-5011	81	4	(	(	PUNCT
ejpam-5011	81	5	k)n	k)n	X
ejpam-5011	81	6	,	,	PUNCT
ejpam-5011	81	7	λ	λ	INTJ
ejpam-5011	81	8	.	.	PUNCT
ejpam-5011	82	1	(	(	PUNCT
ejpam-5011	82	2	⇐	⇐	ADJ
ejpam-5011	82	3	=)	=)	PROPN
ejpam-5011	82	4	suppose	suppose	VERB
ejpam-5011	82	5	that	that	SCONJ
ejpam-5011	82	6	(	(	PUNCT
ejpam-5011	82	7	k)n	k)n	X
ejpam-5011	82	8	,	,	PUNCT
ejpam-5011	82	9	λ	λ	PROPN
ejpam-5011	82	10	=	=	SYM
ejpam-5011	82	11	k	k	X
ejpam-5011	82	12	∑	∑	PUNCT
ejpam-5011	82	13	j=0	j=0	PROPN
ejpam-5011	82	14	(	(	PUNCT
ejpam-5011	82	15	k	k	PROPN
ejpam-5011	82	16	j	j	PROPN
ejpam-5011	82	17	)	)	PUNCT
ejpam-5011	82	18	j	j	PROPN
ejpam-5011	82	19	!	!	PUNCT
ejpam-5011	82	20	{	{	PUNCT
ejpam-5011	83	1	n	n	PRON
ejpam-5011	83	2	j	j	PROPN
ejpam-5011	83	3	}	}	PUNCT
ejpam-5011	83	4	λ	λ	PROPN
ejpam-5011	83	5	.	.	PUNCT
ejpam-5011	84	1	then	then	ADV
ejpam-5011	84	2	we	we	PRON
ejpam-5011	84	3	have	have	VERB
ejpam-5011	84	4	k	k	PROPN
ejpam-5011	84	5	∑	∑	PUNCT
ejpam-5011	84	6	j=0	j=0	PROPN
ejpam-5011	84	7	(	(	PUNCT
ejpam-5011	84	8	k	k	PROPN
ejpam-5011	84	9	j	j	PROPN
ejpam-5011	84	10	)	)	PUNCT
ejpam-5011	84	11	(	(	PUNCT
ejpam-5011	84	12	−1)k−	−1)k−	X
ejpam-5011	84	13	j	j	X
ejpam-5011	84	14	(	(	PUNCT
ejpam-5011	84	15	j)n	j)n	NOUN
ejpam-5011	84	16	,	,	PUNCT
ejpam-5011	84	17	λ	λ	PROPN
ejpam-5011	84	18	=	=	SYM
ejpam-5011	84	19	k	k	X
ejpam-5011	84	20	∑	∑	PUNCT
ejpam-5011	84	21	j=0	j=0	PROPN
ejpam-5011	84	22	(	(	PUNCT
ejpam-5011	84	23	k	k	PROPN
ejpam-5011	84	24	j	j	PROPN
ejpam-5011	84	25	)	)	PUNCT
ejpam-5011	84	26	(	(	PUNCT
ejpam-5011	84	27	−1)k−	−1)k−	PUNCT
ejpam-5011	84	28	j	j	PROPN
ejpam-5011	84	29	j	j	PROPN
ejpam-5011	84	30	∑	∑	PUNCT
ejpam-5011	84	31	l=0	l=0	PROPN
ejpam-5011	84	32	(	(	PUNCT
ejpam-5011	84	33	j	j	PROPN
ejpam-5011	84	34	l	l	NOUN
ejpam-5011	84	35	)	)	PUNCT
ejpam-5011	85	1	l	l	NOUN
ejpam-5011	85	2	!	!	PUNCT
ejpam-5011	85	3	{	{	PUNCT
ejpam-5011	85	4	n	n	ADV
ejpam-5011	85	5	l	l	NOUN
ejpam-5011	85	6	}	}	PUNCT
ejpam-5011	85	7	λ	λ	PROPN
ejpam-5011	85	8	=	=	SYM
ejpam-5011	85	9	k	k	PROPN
ejpam-5011	85	10	∑	∑	PUNCT
ejpam-5011	85	11	l=0	l=0	PROPN
ejpam-5011	85	12	l	l	PROPN
ejpam-5011	85	13	!	!	PUNCT
ejpam-5011	85	14	{	{	PUNCT
ejpam-5011	86	1	n	n	ADV
ejpam-5011	86	2	l	l	NOUN
ejpam-5011	86	3	}	}	PUNCT
ejpam-5011	87	1	λ	λ	X
ejpam-5011	87	2	k	k	NOUN
ejpam-5011	87	3	∑	∑	PUNCT
ejpam-5011	87	4	j	j	PROPN
ejpam-5011	87	5	=	=	PROPN
ejpam-5011	87	6	l	l	PROPN
ejpam-5011	87	7	(	(	PUNCT
ejpam-5011	87	8	k	k	PROPN
ejpam-5011	87	9	j	j	PROPN
ejpam-5011	87	10	)	)	PUNCT
ejpam-5011	87	11	(	(	PUNCT
ejpam-5011	87	12	j	j	PROPN
ejpam-5011	87	13	l	l	NOUN
ejpam-5011	87	14	)	)	PUNCT
ejpam-5011	87	15	(	(	PUNCT
ejpam-5011	87	16	−1)k−	−1)k−	PUNCT
ejpam-5011	87	17	j	j	PROPN
ejpam-5011	87	18	d.	d.	PROPN
ejpam-5011	87	19	kim	kim	PROPN
ejpam-5011	87	20	,	,	PUNCT
ejpam-5011	87	21	t.	t.	PROPN
ejpam-5011	87	22	kim	kim	PROPN
ejpam-5011	87	23	,	,	PUNCT
ejpam-5011	87	24	j.	j.	PROPN
ejpam-5011	87	25	kwon	kwon	PROPN
ejpam-5011	87	26	/	/	SYM
ejpam-5011	87	27	eur	eur	PROPN
ejpam-5011	87	28	.	.	PUNCT
ejpam-5011	88	1	j.	j.	PROPN
ejpam-5011	88	2	pure	pure	PROPN
ejpam-5011	88	3	appl	appl	PROPN
ejpam-5011	88	4	.	.	PROPN
ejpam-5011	88	5	math	math	PROPN
ejpam-5011	88	6	,	,	PUNCT
ejpam-5011	88	7	17	17	NUM
ejpam-5011	88	8	(	(	PUNCT
ejpam-5011	88	9	1	1	NUM
ejpam-5011	88	10	)	)	PUNCT
ejpam-5011	88	11	(	(	PUNCT
ejpam-5011	88	12	2024	2024	NUM
ejpam-5011	88	13	)	)	PUNCT
ejpam-5011	88	14	,	,	PUNCT
ejpam-5011	88	15	1	1	NUM
ejpam-5011	88	16	-	-	SYM
ejpam-5011	88	17	10	10	NUM
ejpam-5011	88	18	5	5	NUM
ejpam-5011	88	19	=	=	SYM
ejpam-5011	88	20	k	k	X
ejpam-5011	88	21	∑	∑	PUNCT
ejpam-5011	88	22	l=0	l=0	PROPN
ejpam-5011	88	23	l	l	PROPN
ejpam-5011	88	24	!	!	PUNCT
ejpam-5011	88	25	{	{	PUNCT
ejpam-5011	89	1	n	n	ADV
ejpam-5011	89	2	l	l	NOUN
ejpam-5011	89	3	}	}	PUNCT
ejpam-5011	89	4	λ	λ	PROPN
ejpam-5011	89	5	(	(	PUNCT
ejpam-5011	89	6	k	k	NOUN
ejpam-5011	89	7	l	l	NOUN
ejpam-5011	89	8	)	)	PUNCT
ejpam-5011	89	9	k−l	k−l	NOUN
ejpam-5011	89	10	∑	∑	PUNCT
ejpam-5011	89	11	j=0	j=0	PROPN
ejpam-5011	89	12	(	(	PUNCT
ejpam-5011	89	13	−1)k−l−	−1)k−l−	NUM
ejpam-5011	89	14	j	j	PROPN
ejpam-5011	89	15	(	(	PUNCT
ejpam-5011	89	16	k−	k−	PROPN
ejpam-5011	89	17	l	l	PROPN
ejpam-5011	89	18	j	j	PROPN
ejpam-5011	89	19	)	)	PUNCT
ejpam-5011	90	1	=	=	PUNCT
ejpam-5011	91	1	k	k	X
ejpam-5011	91	2	∑	∑	PUNCT
ejpam-5011	91	3	l=0	l=0	PROPN
ejpam-5011	91	4	{	{	PUNCT
ejpam-5011	91	5	n	n	ADP
ejpam-5011	91	6	l	l	NOUN
ejpam-5011	91	7	}	}	PUNCT
ejpam-5011	91	8	λ	λ	PROPN
ejpam-5011	91	9	(	(	PUNCT
ejpam-5011	91	10	k	k	NOUN
ejpam-5011	91	11	l	l	NOUN
ejpam-5011	91	12	)	)	PUNCT
ejpam-5011	92	1	l!(1−1)k−l	l!(1−1)k−l	NOUN
ejpam-5011	92	2	=	=	SYM
ejpam-5011	93	1	k	k	X
ejpam-5011	93	2	!	!	PUNCT
ejpam-5011	93	3	{	{	PUNCT
ejpam-5011	93	4	n	n	NOUN
ejpam-5011	93	5	k	k	X
ejpam-5011	93	6	}	}	PUNCT
ejpam-5011	93	7	λ	λ	PROPN
ejpam-5011	93	8	.	.	PUNCT
ejpam-5011	94	1	the	the	DET
ejpam-5011	94	2	harmonic	harmonic	ADJ
ejpam-5011	94	3	numbers	number	NOUN
ejpam-5011	94	4	are	be	AUX
ejpam-5011	94	5	defined	define	VERB
ejpam-5011	94	6	by	by	ADP
ejpam-5011	94	7	h0	h0	NOUN
ejpam-5011	94	8	=	=	PROPN
ejpam-5011	94	9	0	0	PROPN
ejpam-5011	94	10	,	,	PUNCT
ejpam-5011	94	11	hk	hk	NOUN
ejpam-5011	94	12	=	=	VERB
ejpam-5011	95	1	1	1	NUM
ejpam-5011	95	2	+	+	NUM
ejpam-5011	95	3	1	1	NUM
ejpam-5011	95	4	2	2	NUM
ejpam-5011	95	5	+	+	CCONJ
ejpam-5011	95	6	1	1	NUM
ejpam-5011	95	7	3	3	NUM
ejpam-5011	95	8	+	+	NUM
ejpam-5011	95	9	·	·	PUNCT
ejpam-5011	95	10	·	·	PUNCT
ejpam-5011	95	11	·	·	PUNCT
ejpam-5011	96	1	+	+	NUM
ejpam-5011	96	2	1	1	NUM
ejpam-5011	96	3	k	k	NOUN
ejpam-5011	96	4	,	,	PUNCT
ejpam-5011	96	5	(	(	PUNCT
ejpam-5011	96	6	k	k	PROPN
ejpam-5011	96	7	∈	∈	PROPN
ejpam-5011	96	8	n	n	CCONJ
ejpam-5011	96	9	)	)	PUNCT
ejpam-5011	96	10	.	.	PUNCT
ejpam-5011	97	1	(	(	PUNCT
ejpam-5011	97	2	15	15	NUM
ejpam-5011	97	3	)	)	PUNCT
ejpam-5011	97	4	theorem	theorem	NOUN
ejpam-5011	97	5	2	2	NUM
ejpam-5011	97	6	.	.	NOUN
ejpam-5011	97	7	for	for	ADP
ejpam-5011	97	8	n	n	CCONJ
ejpam-5011	97	9	,	,	PUNCT
ejpam-5011	97	10	m	m	PROPN
ejpam-5011	97	11	∈	∈	PROPN
ejpam-5011	98	1	n	n	CCONJ
ejpam-5011	98	2	,	,	PUNCT
ejpam-5011	98	3	we	we	PRON
ejpam-5011	98	4	have	have	VERB
ejpam-5011	98	5	m	m	PROPN
ejpam-5011	98	6	∑	∑	PROPN
ejpam-5011	98	7	k=1	k=1	X
ejpam-5011	98	8	(	(	PUNCT
ejpam-5011	98	9	k)n	k)n	ADJ
ejpam-5011	98	10	,	,	PUNCT
ejpam-5011	98	11	λ	λ	PROPN
ejpam-5011	98	12	hk	hk	NOUN
ejpam-5011	99	1	=	=	PUNCT
ejpam-5011	99	2	m	m	VERB
ejpam-5011	99	3	∑	∑	VERB
ejpam-5011	99	4	j=1	j=1	PROPN
ejpam-5011	99	5	j	j	PROPN
ejpam-5011	99	6	!	!	PUNCT
ejpam-5011	99	7	{	{	PUNCT
ejpam-5011	99	8	n	n	PRON
ejpam-5011	99	9	j	j	PROPN
ejpam-5011	99	10	}	}	PUNCT
ejpam-5011	99	11	λ	λ	PROPN
ejpam-5011	99	12	(	(	PUNCT
ejpam-5011	99	13	m+1	m+1	PROPN
ejpam-5011	99	14	j+1	j+1	NUM
ejpam-5011	99	15	)	)	PUNCT
ejpam-5011	99	16	(	(	PUNCT
ejpam-5011	99	17	hm+1	hm+1	X
ejpam-5011	99	18	−	−	PROPN
ejpam-5011	99	19	1	1	NUM
ejpam-5011	99	20	j+1	j+1	NOUN
ejpam-5011	99	21	)	)	PUNCT
ejpam-5011	99	22	.	.	PUNCT
ejpam-5011	100	1	proof	proof	NOUN
ejpam-5011	100	2	.	.	PUNCT
ejpam-5011	101	1	from	from	ADP
ejpam-5011	101	2	theorem	theorem	ADJ
ejpam-5011	101	3	2.1	2.1	NUM
ejpam-5011	101	4	and	and	CCONJ
ejpam-5011	101	5	noting	note	VERB
ejpam-5011	101	6	that	that	SCONJ
ejpam-5011	101	7	{	{	PUNCT
ejpam-5011	101	8	n	n	NOUN
ejpam-5011	101	9	0	0	NUM
ejpam-5011	101	10	}	}	PUNCT
ejpam-5011	101	11	λ	λ	X
ejpam-5011	101	12	=	=	SYM
ejpam-5011	101	13	0	0	NUM
ejpam-5011	101	14	,	,	PUNCT
ejpam-5011	101	15	for	for	ADP
ejpam-5011	101	16	n	n	PRON
ejpam-5011	101	17	≥	≥	NOUN
ejpam-5011	101	18	1	1	NUM
ejpam-5011	101	19	,	,	PUNCT
ejpam-5011	101	20	we	we	PRON
ejpam-5011	101	21	see	see	VERB
ejpam-5011	101	22	that	that	SCONJ
ejpam-5011	101	23	m	m	VERB
ejpam-5011	101	24	∑	∑	ADV
ejpam-5011	101	25	k=1	k=1	X
ejpam-5011	101	26	(	(	PUNCT
ejpam-5011	101	27	k)n	k)n	ADJ
ejpam-5011	101	28	,	,	PUNCT
ejpam-5011	101	29	λ	λ	PROPN
ejpam-5011	101	30	hk	hk	NOUN
ejpam-5011	102	1	=	=	PUNCT
ejpam-5011	102	2	m	m	VERB
ejpam-5011	102	3	∑	∑	PUNCT
ejpam-5011	102	4	k=1	k=1	PROPN
ejpam-5011	102	5	hk	hk	PROPN
ejpam-5011	103	1	k	k	INTJ
ejpam-5011	103	2	∑	∑	PUNCT
ejpam-5011	103	3	j=1	j=1	PROPN
ejpam-5011	103	4	(	(	PUNCT
ejpam-5011	103	5	k	k	PROPN
ejpam-5011	103	6	j	j	PROPN
ejpam-5011	103	7	)	)	PUNCT
ejpam-5011	103	8	j	j	PROPN
ejpam-5011	103	9	!	!	PUNCT
ejpam-5011	103	10	{	{	PUNCT
ejpam-5011	104	1	n	n	PRON
ejpam-5011	104	2	j	j	PROPN
ejpam-5011	104	3	}	}	PUNCT
ejpam-5011	104	4	λ	λ	PROPN
ejpam-5011	104	5	(	(	PUNCT
ejpam-5011	104	6	16	16	NUM
ejpam-5011	104	7	)	)	PUNCT
ejpam-5011	104	8	=	=	PUNCT
ejpam-5011	105	1	m	m	VERB
ejpam-5011	105	2	∑	∑	PUNCT
ejpam-5011	105	3	j=1	j=1	PROPN
ejpam-5011	105	4	j	j	PROPN
ejpam-5011	105	5	!	!	PUNCT
ejpam-5011	105	6	{	{	PUNCT
ejpam-5011	106	1	n	n	PRON
ejpam-5011	106	2	j	j	NOUN
ejpam-5011	106	3	}	}	PUNCT
ejpam-5011	106	4	λ	λ	PROPN
ejpam-5011	106	5	m	m	VERB
ejpam-5011	106	6	∑	∑	PROPN
ejpam-5011	106	7	k=	k=	PROPN
ejpam-5011	107	1	j	j	PROPN
ejpam-5011	107	2	hk	hk	PROPN
ejpam-5011	107	3	(	(	PUNCT
ejpam-5011	107	4	k	k	PROPN
ejpam-5011	107	5	j	j	PROPN
ejpam-5011	107	6	)	)	PUNCT
ejpam-5011	107	7	.	.	PUNCT
ejpam-5011	108	1	the	the	DET
ejpam-5011	108	2	forward	forward	ADJ
ejpam-5011	108	3	difference	difference	NOUN
ejpam-5011	108	4	operator	operator	NOUN
ejpam-5011	108	5	△	△	X
ejpam-5011	108	6	is	be	AUX
ejpam-5011	108	7	defined	define	VERB
ejpam-5011	108	8	by	by	ADP
ejpam-5011	108	9	△	△	PROPN
ejpam-5011	108	10	f	f	PROPN
ejpam-5011	108	11	(	(	PUNCT
ejpam-5011	108	12	x	x	X
ejpam-5011	108	13	)	)	PUNCT
ejpam-5011	108	14	=	=	SYM
ejpam-5011	108	15	f	f	PROPN
ejpam-5011	108	16	(	(	PUNCT
ejpam-5011	108	17	x+1)−	x+1)−	PROPN
ejpam-5011	108	18	f	f	PROPN
ejpam-5011	108	19	(	(	PUNCT
ejpam-5011	108	20	x	x	NOUN
ejpam-5011	108	21	)	)	PUNCT
ejpam-5011	108	22	.	.	PUNCT
ejpam-5011	109	1	from	from	ADP
ejpam-5011	109	2	the	the	DET
ejpam-5011	109	3	definition	definition	NOUN
ejpam-5011	109	4	of	of	ADP
ejpam-5011	109	5	the	the	DET
ejpam-5011	109	6	forward	forward	ADJ
ejpam-5011	109	7	difference	difference	NOUN
ejpam-5011	109	8	operator	operator	NOUN
ejpam-5011	109	9	,	,	PUNCT
ejpam-5011	109	10	we	we	PRON
ejpam-5011	109	11	get	get	VERB
ejpam-5011	109	12	f	f	PROPN
ejpam-5011	109	13	(	(	PUNCT
ejpam-5011	109	14	x)	x)	PROPN
ejpam-5011	109	15	△	△	X
ejpam-5011	109	16	g(x	g(x	NOUN
ejpam-5011	109	17	)	)	PUNCT
ejpam-5011	110	1	=	=	NOUN
ejpam-5011	110	2	△	△	X
ejpam-5011	110	3	(	(	PUNCT
ejpam-5011	110	4	f	f	X
ejpam-5011	110	5	(	(	PUNCT
ejpam-5011	110	6	x)g(x	x)g(x	PROPN
ejpam-5011	110	7	)	)	PUNCT
ejpam-5011	110	8	)	)	PUNCT
ejpam-5011	110	9	−	−	PROPN
ejpam-5011	111	1	(	(	PUNCT
ejpam-5011	111	2	△	△	PROPN
ejpam-5011	111	3	f	f	X
ejpam-5011	111	4	(	(	PUNCT
ejpam-5011	111	5	x	x	NOUN
ejpam-5011	111	6	)	)	PUNCT
ejpam-5011	111	7	)	)	PUNCT
ejpam-5011	111	8	g(x+1	g(x+1	PROPN
ejpam-5011	111	9	)	)	PUNCT
ejpam-5011	111	10	.	.	PUNCT
ejpam-5011	112	1	(	(	PUNCT
ejpam-5011	112	2	17	17	NUM
ejpam-5011	112	3	)	)	PUNCT
ejpam-5011	112	4	thus	thus	ADV
ejpam-5011	112	5	,	,	PUNCT
ejpam-5011	112	6	by	by	ADP
ejpam-5011	112	7	(	(	PUNCT
ejpam-5011	112	8	17	17	NUM
ejpam-5011	112	9	)	)	PUNCT
ejpam-5011	112	10	,	,	PUNCT
ejpam-5011	112	11	we	we	PRON
ejpam-5011	112	12	get	get	VERB
ejpam-5011	112	13	m−1	m−1	PROPN
ejpam-5011	112	14	∑	∑	PUNCT
ejpam-5011	112	15	k=0	k=0	PROPN
ejpam-5011	112	16	f	f	PROPN
ejpam-5011	112	17	(	(	PUNCT
ejpam-5011	112	18	k	k	NOUN
ejpam-5011	112	19	)	)	PUNCT
ejpam-5011	112	20	(	(	PUNCT
ejpam-5011	112	21	△	△	NOUN
ejpam-5011	112	22	g(k	g(k	NOUN
ejpam-5011	112	23	)	)	PUNCT
ejpam-5011	112	24	)	)	PUNCT
ejpam-5011	113	1	=	=	PUNCT
ejpam-5011	113	2	m−1	m−1	PROPN
ejpam-5011	113	3	∑	∑	PUNCT
ejpam-5011	113	4	k=0	k=0	PROPN
ejpam-5011	113	5	△	△	X
ejpam-5011	113	6	(	(	PUNCT
ejpam-5011	113	7	f	f	PROPN
ejpam-5011	113	8	(	(	PUNCT
ejpam-5011	113	9	k)g(k	k)g(k	PROPN
ejpam-5011	113	10	)	)	PUNCT
ejpam-5011	113	11	)	)	PUNCT
ejpam-5011	114	1	−	−	PROPN
ejpam-5011	115	1	m−1	m−1	PROPN
ejpam-5011	115	2	∑	∑	PUNCT
ejpam-5011	115	3	k=0	k=0	PROPN
ejpam-5011	115	4	(	(	PUNCT
ejpam-5011	115	5	△	△	PROPN
ejpam-5011	115	6	f	f	X
ejpam-5011	115	7	(	(	PUNCT
ejpam-5011	115	8	k	k	NOUN
ejpam-5011	115	9	)	)	PUNCT
ejpam-5011	115	10	)	)	PUNCT
ejpam-5011	115	11	g(k+1	g(k+1	VERB
ejpam-5011	115	12	)	)	PUNCT
ejpam-5011	115	13	(	(	PUNCT
ejpam-5011	115	14	18	18	NUM
ejpam-5011	115	15	)	)	PUNCT
ejpam-5011	115	16	=	=	SYM
ejpam-5011	116	1	m−1	m−1	PROPN
ejpam-5011	116	2	∑	∑	PUNCT
ejpam-5011	116	3	k=0	k=0	PROPN
ejpam-5011	116	4	(	(	PUNCT
ejpam-5011	116	5	f	f	PROPN
ejpam-5011	116	6	(	(	PUNCT
ejpam-5011	116	7	k+1)g(k+1)−	k+1)g(k+1)−	PROPN
ejpam-5011	116	8	f	f	PROPN
ejpam-5011	116	9	(	(	PUNCT
ejpam-5011	116	10	k)g(k	k)g(k	PROPN
ejpam-5011	116	11	)	)	PUNCT
ejpam-5011	116	12	)	)	PUNCT
ejpam-5011	117	1	−	−	PROPN
ejpam-5011	118	1	m−1	m−1	PROPN
ejpam-5011	118	2	∑	∑	PUNCT
ejpam-5011	118	3	k=0	k=0	PROPN
ejpam-5011	118	4	(	(	PUNCT
ejpam-5011	118	5	△	△	PROPN
ejpam-5011	118	6	f	f	X
ejpam-5011	118	7	(	(	PUNCT
ejpam-5011	118	8	k	k	NOUN
ejpam-5011	118	9	)	)	PUNCT
ejpam-5011	118	10	)	)	PUNCT
ejpam-5011	118	11	g(k+1	g(k+1	VERB
ejpam-5011	118	12	)	)	PUNCT
ejpam-5011	119	1	=	=	SYM
ejpam-5011	119	2	f	f	PROPN
ejpam-5011	119	3	(	(	PUNCT
ejpam-5011	119	4	m)g(m)−	m)g(m)−	PROPN
ejpam-5011	119	5	f	f	X
ejpam-5011	119	6	(	(	PUNCT
ejpam-5011	119	7	0)g(0)−	0)g(0)−	PROPN
ejpam-5011	119	8	m−1	m−1	PROPN
ejpam-5011	119	9	∑	∑	PUNCT
ejpam-5011	119	10	k=0	k=0	PROPN
ejpam-5011	119	11	(	(	PUNCT
ejpam-5011	119	12	△	△	PROPN
ejpam-5011	119	13	f	f	X
ejpam-5011	119	14	(	(	PUNCT
ejpam-5011	119	15	k	k	NOUN
ejpam-5011	119	16	)	)	PUNCT
ejpam-5011	119	17	)	)	PUNCT
ejpam-5011	119	18	g(k+1	g(k+1	NOUN
ejpam-5011	119	19	)	)	PUNCT
ejpam-5011	119	20	.	.	PUNCT
ejpam-5011	120	1	let	let	VERB
ejpam-5011	120	2	f	f	PROPN
ejpam-5011	120	3	(	(	PUNCT
ejpam-5011	120	4	k	k	NOUN
ejpam-5011	120	5	)	)	PUNCT
ejpam-5011	120	6	=	=	SYM
ejpam-5011	120	7	hk	hk	PROPN
ejpam-5011	120	8	and	and	CCONJ
ejpam-5011	120	9	g(k	g(k	VERB
ejpam-5011	120	10	)	)	PUNCT
ejpam-5011	120	11	=	=	PUNCT
ejpam-5011	121	1	(	(	PUNCT
ejpam-5011	121	2	k	k	NOUN
ejpam-5011	121	3	j+1	j+1	ADJ
ejpam-5011	121	4	)	)	PUNCT
ejpam-5011	121	5	.	.	PUNCT
ejpam-5011	122	1	then	then	ADV
ejpam-5011	122	2	we	we	PRON
ejpam-5011	122	3	have	have	VERB
ejpam-5011	122	4	△	△	NOUN
ejpam-5011	122	5	g(k	g(k	NOUN
ejpam-5011	122	6	)	)	PUNCT
ejpam-5011	122	7	=	=	SYM
ejpam-5011	122	8	g(k+1)−g(k	g(k+1)−g(k	NOUN
ejpam-5011	122	9	)	)	PUNCT
ejpam-5011	122	10	=	=	PUNCT
ejpam-5011	122	11	(	(	PUNCT
ejpam-5011	122	12	k+1	k+1	X
ejpam-5011	122	13	j+1	j+1	PROPN
ejpam-5011	122	14	)	)	PUNCT
ejpam-5011	123	1	−	−	PROPN
ejpam-5011	124	1	(	(	PUNCT
ejpam-5011	124	2	k	k	NOUN
ejpam-5011	124	3	j+1	j+1	ADJ
ejpam-5011	124	4	)	)	PUNCT
ejpam-5011	124	5	=	=	SYM
ejpam-5011	125	1	(	(	PUNCT
ejpam-5011	125	2	k	k	X
ejpam-5011	125	3	j	j	PROPN
ejpam-5011	125	4	)	)	PUNCT
ejpam-5011	125	5	,	,	PUNCT
ejpam-5011	125	6	△	△	X
ejpam-5011	125	7	f	f	X
ejpam-5011	125	8	(	(	PUNCT
ejpam-5011	125	9	x	x	X
ejpam-5011	125	10	)	)	PUNCT
ejpam-5011	125	11	=	=	SYM
ejpam-5011	125	12	f	f	PROPN
ejpam-5011	125	13	(	(	PUNCT
ejpam-5011	125	14	k+1)−	k+1)−	PROPN
ejpam-5011	125	15	f	f	PROPN
ejpam-5011	125	16	(	(	PUNCT
ejpam-5011	125	17	k	k	NOUN
ejpam-5011	125	18	)	)	PUNCT
ejpam-5011	125	19	=	=	SYM
ejpam-5011	125	20	hk+1	hk+1	X
ejpam-5011	125	21	−hk	−hk	NOUN
ejpam-5011	125	22	=	=	SYM
ejpam-5011	125	23	1	1	NUM
ejpam-5011	125	24	k+1	k+1	NOUN
ejpam-5011	125	25	.	.	PUNCT
ejpam-5011	126	1	(	(	PUNCT
ejpam-5011	126	2	19	19	NUM
ejpam-5011	126	3	)	)	PUNCT
ejpam-5011	126	4	d.	d.	PROPN
ejpam-5011	126	5	kim	kim	PROPN
ejpam-5011	126	6	,	,	PUNCT
ejpam-5011	126	7	t.	t.	PROPN
ejpam-5011	126	8	kim	kim	PROPN
ejpam-5011	126	9	,	,	PUNCT
ejpam-5011	126	10	j.	j.	PROPN
ejpam-5011	126	11	kwon	kwon	PROPN
ejpam-5011	126	12	/	/	SYM
ejpam-5011	126	13	eur	eur	PROPN
ejpam-5011	126	14	.	.	PUNCT
ejpam-5011	127	1	j.	j.	PROPN
ejpam-5011	127	2	pure	pure	PROPN
ejpam-5011	127	3	appl	appl	PROPN
ejpam-5011	127	4	.	.	PROPN
ejpam-5011	127	5	math	math	PROPN
ejpam-5011	127	6	,	,	PUNCT
ejpam-5011	127	7	17	17	NUM
ejpam-5011	127	8	(	(	PUNCT
ejpam-5011	127	9	1	1	NUM
ejpam-5011	127	10	)	)	PUNCT
ejpam-5011	127	11	(	(	PUNCT
ejpam-5011	127	12	2024	2024	NUM
ejpam-5011	127	13	)	)	PUNCT
ejpam-5011	127	14	,	,	PUNCT
ejpam-5011	127	15	1	1	NUM
ejpam-5011	127	16	-	-	SYM
ejpam-5011	127	17	10	10	NUM
ejpam-5011	127	18	6	6	NUM
ejpam-5011	127	19	from	from	ADP
ejpam-5011	127	20	(	(	PUNCT
ejpam-5011	127	21	18	18	NUM
ejpam-5011	127	22	)	)	PUNCT
ejpam-5011	127	23	and	and	CCONJ
ejpam-5011	127	24	(	(	PUNCT
ejpam-5011	127	25	19	19	NUM
ejpam-5011	127	26	)	)	PUNCT
ejpam-5011	127	27	,	,	PUNCT
ejpam-5011	127	28	we	we	PRON
ejpam-5011	127	29	note	note	VERB
ejpam-5011	127	30	taht	taht	ADV
ejpam-5011	127	31	m−1	m−1	PROPN
ejpam-5011	127	32	∑	∑	PUNCT
ejpam-5011	127	33	k=0	k=0	PROPN
ejpam-5011	127	34	(	(	PUNCT
ejpam-5011	127	35	k	k	PROPN
ejpam-5011	127	36	j	j	PROPN
ejpam-5011	127	37	)	)	PUNCT
ejpam-5011	128	1	hk	hk	PROPN
ejpam-5011	128	2	=	=	PUNCT
ejpam-5011	128	3	m−1	m−1	PROPN
ejpam-5011	128	4	∑	∑	PUNCT
ejpam-5011	128	5	k=0	k=0	PROPN
ejpam-5011	128	6	(	(	PUNCT
ejpam-5011	128	7	△	△	NOUN
ejpam-5011	128	8	g(k	g(k	NOUN
ejpam-5011	128	9	)	)	PUNCT
ejpam-5011	128	10	)	)	PUNCT
ejpam-5011	129	1	f	f	X
ejpam-5011	129	2	(	(	PUNCT
ejpam-5011	129	3	k	k	NOUN
ejpam-5011	129	4	)	)	PUNCT
ejpam-5011	129	5	=	=	SYM
ejpam-5011	129	6	f	f	PROPN
ejpam-5011	129	7	(	(	PUNCT
ejpam-5011	129	8	m)g(m)−	m)g(m)−	ADJ
ejpam-5011	129	9	m−1	m−1	PROPN
ejpam-5011	129	10	∑	∑	PUNCT
ejpam-5011	129	11	k=0	k=0	PROPN
ejpam-5011	129	12	(	(	PUNCT
ejpam-5011	129	13	△	△	PROPN
ejpam-5011	129	14	f	f	X
ejpam-5011	129	15	(	(	PUNCT
ejpam-5011	129	16	k	k	NOUN
ejpam-5011	129	17	)	)	PUNCT
ejpam-5011	129	18	)	)	PUNCT
ejpam-5011	129	19	g(k+1	g(k+1	VERB
ejpam-5011	129	20	)	)	PUNCT
ejpam-5011	129	21	(	(	PUNCT
ejpam-5011	129	22	20	20	NUM
ejpam-5011	129	23	)	)	PUNCT
ejpam-5011	129	24	=	=	VERB
ejpam-5011	130	1	hm	hm	INTJ
ejpam-5011	130	2	(	(	PUNCT
ejpam-5011	130	3	m	m	VERB
ejpam-5011	130	4	j+1	j+1	ADJ
ejpam-5011	130	5	)	)	PUNCT
ejpam-5011	131	1	−	−	PROPN
ejpam-5011	132	1	m−1	m−1	PROPN
ejpam-5011	132	2	∑	∑	PUNCT
ejpam-5011	132	3	k=0	k=0	PROPN
ejpam-5011	132	4	1	1	NUM
ejpam-5011	132	5	k+1	k+1	X
ejpam-5011	132	6	(	(	PUNCT
ejpam-5011	132	7	k+1	k+1	X
ejpam-5011	132	8	j+1	j+1	X
ejpam-5011	132	9	)	)	PUNCT
ejpam-5011	132	10	=	=	SYM
ejpam-5011	133	1	hm	hm	INTJ
ejpam-5011	133	2	(	(	PUNCT
ejpam-5011	133	3	m	m	VERB
ejpam-5011	133	4	j+1	j+1	ADJ
ejpam-5011	133	5	)	)	PUNCT
ejpam-5011	133	6	−	−	NOUN
ejpam-5011	134	1	1	1	NUM
ejpam-5011	134	2	j+1	j+1	ADJ
ejpam-5011	134	3	m−1	m−1	PROPN
ejpam-5011	134	4	∑	∑	PUNCT
ejpam-5011	134	5	k=0	k=0	PROPN
ejpam-5011	134	6	(	(	PUNCT
ejpam-5011	134	7	k	k	X
ejpam-5011	134	8	j	j	PROPN
ejpam-5011	134	9	)	)	PUNCT
ejpam-5011	135	1	=	=	PUNCT
ejpam-5011	135	2	hm	hm	INTJ
ejpam-5011	135	3	(	(	PUNCT
ejpam-5011	135	4	m	m	VERB
ejpam-5011	135	5	j+1	j+1	ADJ
ejpam-5011	135	6	)	)	PUNCT
ejpam-5011	136	1	−	−	NOUN
ejpam-5011	136	2	1	1	NUM
ejpam-5011	137	1	j+1	j+1	ADJ
ejpam-5011	137	2	m−1	m−1	PROPN
ejpam-5011	137	3	∑	∑	PUNCT
ejpam-5011	137	4	k=0	k=0	PUNCT
ejpam-5011	138	1	[	[	X
ejpam-5011	138	2	(	(	PUNCT
ejpam-5011	138	3	k+1	k+1	X
ejpam-5011	138	4	j+1	j+1	PROPN
ejpam-5011	138	5	)	)	PUNCT
ejpam-5011	138	6	−	−	PROPN
ejpam-5011	138	7	(	(	PUNCT
ejpam-5011	138	8	k	k	NOUN
ejpam-5011	138	9	j+1	j+1	NOUN
ejpam-5011	138	10	)	)	PUNCT
ejpam-5011	138	11	]	]	PUNCT
ejpam-5011	139	1	=	=	PUNCT
ejpam-5011	139	2	hm	hm	INTJ
ejpam-5011	139	3	(	(	PUNCT
ejpam-5011	139	4	m	m	VERB
ejpam-5011	139	5	j+1	j+1	ADJ
ejpam-5011	139	6	)	)	PUNCT
ejpam-5011	139	7	−	−	NOUN
ejpam-5011	140	1	1	1	NUM
ejpam-5011	140	2	j+1	j+1	PROPN
ejpam-5011	140	3	(	(	PUNCT
ejpam-5011	140	4	m	m	VERB
ejpam-5011	140	5	j+1	j+1	ADJ
ejpam-5011	140	6	)	)	PUNCT
ejpam-5011	140	7	=	=	PUNCT
ejpam-5011	140	8	(	(	PUNCT
ejpam-5011	140	9	m	m	VERB
ejpam-5011	140	10	j+1	j+1	ADJ
ejpam-5011	140	11	)	)	PUNCT
ejpam-5011	140	12	(	(	PUNCT
ejpam-5011	140	13	hm	hm	INTJ
ejpam-5011	140	14	−	−	PROPN
ejpam-5011	140	15	1	1	NUM
ejpam-5011	140	16	j+1	j+1	NOUN
ejpam-5011	140	17	)	)	PUNCT
ejpam-5011	140	18	.	.	PUNCT
ejpam-5011	141	1	thus	thus	ADV
ejpam-5011	141	2	,	,	PUNCT
ejpam-5011	141	3	by	by	ADP
ejpam-5011	141	4	(	(	PUNCT
ejpam-5011	141	5	16	16	NUM
ejpam-5011	141	6	)	)	PUNCT
ejpam-5011	141	7	and	and	CCONJ
ejpam-5011	141	8	(	(	PUNCT
ejpam-5011	141	9	20	20	NUM
ejpam-5011	141	10	)	)	PUNCT
ejpam-5011	141	11	,	,	PUNCT
ejpam-5011	141	12	we	we	PRON
ejpam-5011	141	13	get	get	VERB
ejpam-5011	141	14	m	m	PRON
ejpam-5011	141	15	∑	∑	ADJ
ejpam-5011	141	16	k=1	k=1	X
ejpam-5011	141	17	(	(	PUNCT
ejpam-5011	141	18	k)n	k)n	ADJ
ejpam-5011	141	19	,	,	PUNCT
ejpam-5011	141	20	λ	λ	PROPN
ejpam-5011	141	21	hk	hk	NOUN
ejpam-5011	142	1	=	=	PUNCT
ejpam-5011	142	2	m	m	VERB
ejpam-5011	142	3	∑	∑	VERB
ejpam-5011	142	4	j=1	j=1	PROPN
ejpam-5011	142	5	j	j	PROPN
ejpam-5011	142	6	!	!	PUNCT
ejpam-5011	142	7	{	{	PUNCT
ejpam-5011	142	8	n	n	PRON
ejpam-5011	142	9	j	j	NOUN
ejpam-5011	142	10	}	}	PUNCT
ejpam-5011	142	11	λ	λ	PROPN
ejpam-5011	142	12	m	m	VERB
ejpam-5011	142	13	∑	∑	PROPN
ejpam-5011	142	14	k=	k=	PROPN
ejpam-5011	143	1	j	j	PROPN
ejpam-5011	143	2	hk	hk	PROPN
ejpam-5011	143	3	(	(	PUNCT
ejpam-5011	143	4	k	k	PROPN
ejpam-5011	143	5	j	j	PROPN
ejpam-5011	143	6	)	)	PUNCT
ejpam-5011	144	1	=	=	PUNCT
ejpam-5011	145	1	m	m	VERB
ejpam-5011	145	2	∑	∑	VERB
ejpam-5011	145	3	j=1	j=1	PROPN
ejpam-5011	145	4	j	j	PROPN
ejpam-5011	145	5	!	!	PUNCT
ejpam-5011	145	6	{	{	PUNCT
ejpam-5011	145	7	n	n	PRON
ejpam-5011	145	8	j	j	PROPN
ejpam-5011	145	9	}	}	PUNCT
ejpam-5011	145	10	λ	λ	PROPN
ejpam-5011	145	11	(	(	PUNCT
ejpam-5011	145	12	m+1	m+1	PROPN
ejpam-5011	145	13	j+1	j+1	NUM
ejpam-5011	145	14	)	)	PUNCT
ejpam-5011	145	15	(	(	PUNCT
ejpam-5011	145	16	hm+1	hm+1	X
ejpam-5011	145	17	−	−	PROPN
ejpam-5011	145	18	1	1	NUM
ejpam-5011	145	19	j+1	j+1	NUM
ejpam-5011	145	20	)	)	PUNCT
ejpam-5011	145	21	.	.	PUNCT
ejpam-5011	146	1	from	from	ADP
ejpam-5011	146	2	(	(	PUNCT
ejpam-5011	146	3	10	10	NUM
ejpam-5011	146	4	)	)	PUNCT
ejpam-5011	146	5	,	,	PUNCT
ejpam-5011	146	6	we	we	PRON
ejpam-5011	146	7	note	note	VERB
ejpam-5011	146	8	that	that	SCONJ
ejpam-5011	146	9	(	(	PUNCT
ejpam-5011	146	10	1	1	NUM
ejpam-5011	146	11	1−	1−	NUM
ejpam-5011	146	12	t	t	NOUN
ejpam-5011	146	13	)	)	PUNCT
ejpam-5011	147	1	r	r	NOUN
ejpam-5011	147	2	(	(	PUNCT
ejpam-5011	147	3	1	1	NUM
ejpam-5011	147	4	1−	1−	NUM
ejpam-5011	147	5	t	t	NOUN
ejpam-5011	147	6	)	)	PUNCT
ejpam-5011	147	7	x	x	PUNCT
ejpam-5011	147	8	=	=	SYM
ejpam-5011	147	9	∞	∞	NUM
ejpam-5011	147	10	∑	∑	PUNCT
ejpam-5011	147	11	n=0	n=0	X
ejpam-5011	147	12	⟨x+	⟨x+	NOUN
ejpam-5011	147	13	r⟩n	r⟩n	NUM
ejpam-5011	147	14	tn	tn	NOUN
ejpam-5011	147	15	n	n	NOUN
ejpam-5011	147	16	!	!	PUNCT
ejpam-5011	147	17	=	=	SYM
ejpam-5011	148	1	∞	∞	NUM
ejpam-5011	148	2	∑	∑	PUNCT
ejpam-5011	148	3	n=0	n=0	PROPN
ejpam-5011	148	4	n	n	CCONJ
ejpam-5011	148	5	∑	∑	PUNCT
ejpam-5011	148	6	k=0	k=0	PUNCT
ejpam-5011	148	7	[	[	PUNCT
ejpam-5011	148	8	n+	n+	ADP
ejpam-5011	148	9	r	r	NOUN
ejpam-5011	148	10	k+	k+	NOUN
ejpam-5011	148	11	r	r	NOUN
ejpam-5011	148	12	]	]	PUNCT
ejpam-5011	148	13	r	r	NOUN
ejpam-5011	148	14	,	,	PUNCT
ejpam-5011	148	15	λ	λ	NOUN
ejpam-5011	148	16	⟨x⟩k	⟨x⟩k	NOUN
ejpam-5011	148	17	,	,	PUNCT
ejpam-5011	148	18	λ	λ	PROPN
ejpam-5011	148	19	tn	tn	NOUN
ejpam-5011	148	20	n	n	X
ejpam-5011	148	21	!	!	PUNCT
ejpam-5011	149	1	(	(	PUNCT
ejpam-5011	149	2	21	21	NUM
ejpam-5011	149	3	)	)	PUNCT
ejpam-5011	149	4	=	=	SYM
ejpam-5011	150	1	∞	∞	PROPN
ejpam-5011	150	2	∑	∑	PUNCT
ejpam-5011	150	3	k=0	k=0	PROPN
ejpam-5011	150	4	(	(	PUNCT
ejpam-5011	150	5	∞	∞	PROPN
ejpam-5011	150	6	∑	∑	PUNCT
ejpam-5011	150	7	n	n	PROPN
ejpam-5011	150	8	=	=	SYM
ejpam-5011	150	9	k	k	X
ejpam-5011	150	10	[	[	PUNCT
ejpam-5011	150	11	n+	n+	ADP
ejpam-5011	150	12	r	r	NOUN
ejpam-5011	150	13	k+	k+	NOUN
ejpam-5011	150	14	r	r	NOUN
ejpam-5011	150	15	]	]	PUNCT
ejpam-5011	150	16	r	r	X
ejpam-5011	150	17	,	,	PUNCT
ejpam-5011	150	18	λ	λ	PROPN
ejpam-5011	150	19	tn	tn	NOUN
ejpam-5011	150	20	n	n	NOUN
ejpam-5011	150	21	!	!	PUNCT
ejpam-5011	150	22	)	)	PUNCT
ejpam-5011	150	23	⟨x⟩k	⟨x⟩k	NOUN
ejpam-5011	150	24	,	,	PUNCT
ejpam-5011	150	25	λ	λ	INTJ
ejpam-5011	150	26	.	.	PUNCT
ejpam-5011	151	1	on	on	ADP
ejpam-5011	151	2	the	the	DET
ejpam-5011	151	3	other	other	ADJ
ejpam-5011	151	4	hand	hand	NOUN
ejpam-5011	151	5	,	,	PUNCT
ejpam-5011	151	6	by	by	ADP
ejpam-5011	151	7	(	(	PUNCT
ejpam-5011	151	8	1	1	NUM
ejpam-5011	151	9	)	)	PUNCT
ejpam-5011	151	10	and	and	CCONJ
ejpam-5011	151	11	(	(	PUNCT
ejpam-5011	151	12	3	3	NUM
ejpam-5011	151	13	)	)	PUNCT
ejpam-5011	151	14	,	,	PUNCT
ejpam-5011	151	15	we	we	PRON
ejpam-5011	151	16	get	get	VERB
ejpam-5011	151	17	(	(	PUNCT
ejpam-5011	151	18	1	1	NUM
ejpam-5011	151	19	1−	1−	NUM
ejpam-5011	151	20	t	t	NOUN
ejpam-5011	151	21	)	)	PUNCT
ejpam-5011	152	1	r	r	NOUN
ejpam-5011	152	2	(	(	PUNCT
ejpam-5011	152	3	1	1	NUM
ejpam-5011	152	4	1−	1−	NUM
ejpam-5011	152	5	t	t	NOUN
ejpam-5011	152	6	)	)	PUNCT
ejpam-5011	152	7	x	x	X
ejpam-5011	152	8	=	=	SYM
ejpam-5011	152	9	e−x	e−x	PROPN
ejpam-5011	152	10	λ	λ	PROPN
ejpam-5011	152	11	(	(	PUNCT
ejpam-5011	152	12	logλ	logλ	PROPN
ejpam-5011	152	13	(	(	PUNCT
ejpam-5011	152	14	1−	1−	NUM
ejpam-5011	152	15	t	t	PROPN
ejpam-5011	152	16	)	)	PUNCT
ejpam-5011	152	17	)	)	PUNCT
ejpam-5011	152	18	(	(	PUNCT
ejpam-5011	152	19	1	1	NUM
ejpam-5011	152	20	1−	1−	NUM
ejpam-5011	152	21	t	t	NOUN
ejpam-5011	152	22	)	)	PUNCT
ejpam-5011	152	23	r	r	NOUN
ejpam-5011	152	24	=	=	SYM
ejpam-5011	152	25	∞	∞	NUM
ejpam-5011	152	26	∑	∑	PUNCT
ejpam-5011	152	27	k=0	k=0	PROPN
ejpam-5011	152	28	(	(	PUNCT
ejpam-5011	152	29	−	−	PROPN
ejpam-5011	152	30	logλ	logλ	ADJ
ejpam-5011	152	31	(	(	PUNCT
ejpam-5011	152	32	1−	1−	NUM
ejpam-5011	152	33	t))k	t))k	PROPN
ejpam-5011	152	34	k	k	PROPN
ejpam-5011	152	35	!	!	PUNCT
ejpam-5011	153	1	(	(	PUNCT
ejpam-5011	153	2	1	1	NUM
ejpam-5011	153	3	1−	1−	NUM
ejpam-5011	153	4	t	t	NOUN
ejpam-5011	153	5	)	)	PUNCT
ejpam-5011	153	6	r	r	NOUN
ejpam-5011	153	7	⟨x⟩k	⟨x⟩k	NOUN
ejpam-5011	153	8	,	,	PUNCT
ejpam-5011	153	9	λ	λ	PROPN
ejpam-5011	153	10	(	(	PUNCT
ejpam-5011	153	11	22	22	NUM
ejpam-5011	153	12	)	)	PUNCT
ejpam-5011	153	13	=	=	SYM
ejpam-5011	154	1	∞	∞	NUM
ejpam-5011	154	2	∑	∑	PUNCT
ejpam-5011	154	3	k=0	k=0	PROPN
ejpam-5011	154	4	1	1	NUM
ejpam-5011	154	5	k	k	NOUN
ejpam-5011	154	6	!	!	PUNCT
ejpam-5011	155	1	(	(	PUNCT
ejpam-5011	155	2	log−λ	log−λ	NUM
ejpam-5011	155	3	(	(	PUNCT
ejpam-5011	155	4	1	1	NUM
ejpam-5011	155	5	1−	1−	NUM
ejpam-5011	155	6	t	t	NOUN
ejpam-5011	155	7	)	)	PUNCT
ejpam-5011	155	8	)	)	PUNCT
ejpam-5011	156	1	k	k	X
ejpam-5011	156	2	(	(	PUNCT
ejpam-5011	156	3	1	1	NUM
ejpam-5011	156	4	1−	1−	NUM
ejpam-5011	156	5	t	t	NOUN
ejpam-5011	156	6	)	)	PUNCT
ejpam-5011	156	7	r	r	NOUN
ejpam-5011	156	8	⟨x⟩k	⟨x⟩k	NOUN
ejpam-5011	156	9	,	,	PUNCT
ejpam-5011	156	10	λ	λ	INTJ
ejpam-5011	156	11	.	.	PUNCT
ejpam-5011	157	1	by	by	ADP
ejpam-5011	157	2	(	(	PUNCT
ejpam-5011	157	3	21	21	NUM
ejpam-5011	157	4	)	)	PUNCT
ejpam-5011	157	5	and	and	CCONJ
ejpam-5011	157	6	(	(	PUNCT
ejpam-5011	157	7	22	22	NUM
ejpam-5011	157	8	)	)	PUNCT
ejpam-5011	157	9	,	,	PUNCT
ejpam-5011	157	10	we	we	PRON
ejpam-5011	157	11	get	get	VERB
ejpam-5011	157	12	1	1	NUM
ejpam-5011	157	13	k	k	NOUN
ejpam-5011	157	14	!	!	PUNCT
ejpam-5011	158	1	(	(	PUNCT
ejpam-5011	158	2	log−λ	log−λ	NUM
ejpam-5011	158	3	(	(	PUNCT
ejpam-5011	158	4	1	1	NUM
ejpam-5011	158	5	1−	1−	NUM
ejpam-5011	158	6	t	t	NOUN
ejpam-5011	158	7	)	)	PUNCT
ejpam-5011	158	8	)	)	PUNCT
ejpam-5011	159	1	k	k	X
ejpam-5011	159	2	(	(	PUNCT
ejpam-5011	159	3	1	1	NUM
ejpam-5011	159	4	1−	1−	NUM
ejpam-5011	159	5	t	t	NOUN
ejpam-5011	159	6	)	)	PUNCT
ejpam-5011	159	7	r	r	NOUN
ejpam-5011	159	8	=	=	SYM
ejpam-5011	159	9	∞	∞	NUM
ejpam-5011	159	10	∑	∑	PUNCT
ejpam-5011	159	11	n	n	CCONJ
ejpam-5011	159	12	=	=	SYM
ejpam-5011	159	13	k	k	X
ejpam-5011	159	14	[	[	PUNCT
ejpam-5011	159	15	n+	n+	ADP
ejpam-5011	159	16	r	r	NOUN
ejpam-5011	159	17	k+	k+	NOUN
ejpam-5011	159	18	r	r	NOUN
ejpam-5011	159	19	]	]	PUNCT
ejpam-5011	159	20	r	r	X
ejpam-5011	159	21	,	,	PUNCT
ejpam-5011	159	22	λ	λ	PROPN
ejpam-5011	159	23	tn	tn	NOUN
ejpam-5011	159	24	n	n	X
ejpam-5011	159	25	!	!	PUNCT
ejpam-5011	159	26	,	,	PUNCT
ejpam-5011	159	27	(	(	PUNCT
ejpam-5011	159	28	k	k	X
ejpam-5011	159	29	≥	≥	PROPN
ejpam-5011	159	30	0	0	NUM
ejpam-5011	159	31	)	)	PUNCT
ejpam-5011	159	32	.	.	PUNCT
ejpam-5011	160	1	(	(	PUNCT
ejpam-5011	160	2	23	23	NUM
ejpam-5011	160	3	)	)	PUNCT
ejpam-5011	160	4	from	from	ADP
ejpam-5011	160	5	(	(	PUNCT
ejpam-5011	160	6	8)	8)	NUM
ejpam-5011	160	7	or	or	CCONJ
ejpam-5011	160	8	(	(	PUNCT
ejpam-5011	160	9	23	23	NUM
ejpam-5011	160	10	)	)	PUNCT
ejpam-5011	160	11	,	,	PUNCT
ejpam-5011	160	12	we	we	PRON
ejpam-5011	160	13	see	see	VERB
ejpam-5011	160	14	that	that	SCONJ
ejpam-5011	160	15	1	1	NUM
ejpam-5011	160	16	k	k	NOUN
ejpam-5011	160	17	!	!	PUNCT
ejpam-5011	161	1	(	(	PUNCT
ejpam-5011	161	2	log−λ	log−λ	NUM
ejpam-5011	161	3	(	(	PUNCT
ejpam-5011	161	4	1	1	NUM
ejpam-5011	161	5	1−	1−	NUM
ejpam-5011	161	6	t	t	NOUN
ejpam-5011	161	7	)	)	PUNCT
ejpam-5011	161	8	)	)	PUNCT
ejpam-5011	162	1	k	k	X
ejpam-5011	162	2	=	=	SYM
ejpam-5011	162	3	∞	∞	NUM
ejpam-5011	162	4	∑	∑	PUNCT
ejpam-5011	162	5	n	n	PROPN
ejpam-5011	162	6	=	=	SYM
ejpam-5011	162	7	k	k	X
ejpam-5011	162	8	[	[	PUNCT
ejpam-5011	162	9	n	n	X
ejpam-5011	162	10	k	k	X
ejpam-5011	162	11	]	]	PUNCT
ejpam-5011	163	1	λ	λ	X
ejpam-5011	163	2	tn	tn	NOUN
ejpam-5011	163	3	n	n	X
ejpam-5011	163	4	!	!	PUNCT
ejpam-5011	163	5	.	.	PUNCT
ejpam-5011	164	1	(	(	PUNCT
ejpam-5011	164	2	24	24	NUM
ejpam-5011	164	3	)	)	PUNCT
ejpam-5011	164	4	theorem	theorem	NOUN
ejpam-5011	164	5	3	3	NUM
ejpam-5011	164	6	.	.	X
ejpam-5011	165	1	for	for	ADP
ejpam-5011	165	2	any	any	DET
ejpam-5011	165	3	nonnegative	nonnegative	ADJ
ejpam-5011	165	4	integers	integer	NOUN
ejpam-5011	165	5	n	n	CCONJ
ejpam-5011	165	6	,	,	PUNCT
ejpam-5011	165	7	k	k	PROPN
ejpam-5011	165	8	,	,	PUNCT
ejpam-5011	165	9	we	we	PRON
ejpam-5011	165	10	have	have	VERB
ejpam-5011	165	11	[	[	PUNCT
ejpam-5011	165	12	n+1	n+1	PROPN
ejpam-5011	165	13	k+1	k+1	X
ejpam-5011	165	14	]	]	PUNCT
ejpam-5011	166	1	1,λ	1,λ	NUM
ejpam-5011	166	2	=	=	PUNCT
ejpam-5011	166	3	n	n	CCONJ
ejpam-5011	166	4	∑	∑	PROPN
ejpam-5011	166	5	l	l	X
ejpam-5011	166	6	=	=	X
ejpam-5011	166	7	k	k	X
ejpam-5011	166	8	(	(	PUNCT
ejpam-5011	166	9	l	l	NOUN
ejpam-5011	166	10	k	k	X
ejpam-5011	166	11	)	)	PUNCT
ejpam-5011	166	12	[	[	PUNCT
ejpam-5011	166	13	n	n	X
ejpam-5011	166	14	l	l	NOUN
ejpam-5011	166	15	]	]	PUNCT
ejpam-5011	166	16	λ	λ	X
ejpam-5011	166	17	⟨1⟩l−k	⟨1⟩l−k	NOUN
ejpam-5011	166	18	,	,	PUNCT
ejpam-5011	166	19	λ	λ	PROPN
ejpam-5011	166	20	.	.	PUNCT
ejpam-5011	167	1	d.	d.	PROPN
ejpam-5011	167	2	kim	kim	PROPN
ejpam-5011	167	3	,	,	PUNCT
ejpam-5011	167	4	t.	t.	PROPN
ejpam-5011	167	5	kim	kim	PROPN
ejpam-5011	167	6	,	,	PUNCT
ejpam-5011	167	7	j.	j.	PROPN
ejpam-5011	167	8	kwon	kwon	PROPN
ejpam-5011	167	9	/	/	SYM
ejpam-5011	167	10	eur	eur	PROPN
ejpam-5011	167	11	.	.	PUNCT
ejpam-5011	168	1	j.	j.	PROPN
ejpam-5011	168	2	pure	pure	PROPN
ejpam-5011	168	3	appl	appl	PROPN
ejpam-5011	168	4	.	.	PROPN
ejpam-5011	168	5	math	math	PROPN
ejpam-5011	168	6	,	,	PUNCT
ejpam-5011	168	7	17	17	NUM
ejpam-5011	168	8	(	(	PUNCT
ejpam-5011	168	9	1	1	NUM
ejpam-5011	168	10	)	)	PUNCT
ejpam-5011	168	11	(	(	PUNCT
ejpam-5011	168	12	2024	2024	NUM
ejpam-5011	168	13	)	)	PUNCT
ejpam-5011	168	14	,	,	PUNCT
ejpam-5011	168	15	1	1	NUM
ejpam-5011	168	16	-	-	SYM
ejpam-5011	168	17	10	10	NUM
ejpam-5011	168	18	7	7	NUM
ejpam-5011	168	19	in	in	ADP
ejpam-5011	168	20	general	general	ADJ
ejpam-5011	168	21	,	,	PUNCT
ejpam-5011	168	22	for	for	ADP
ejpam-5011	168	23	r	r	NOUN
ejpam-5011	168	24	≥	≥	NOUN
ejpam-5011	168	25	0	0	NUM
ejpam-5011	168	26	,	,	PUNCT
ejpam-5011	168	27	we	we	PRON
ejpam-5011	168	28	have	have	VERB
ejpam-5011	168	29	[	[	PUNCT
ejpam-5011	168	30	n+	n+	ADP
ejpam-5011	168	31	r	r	NOUN
ejpam-5011	168	32	k+	k+	NOUN
ejpam-5011	168	33	r	r	NOUN
ejpam-5011	168	34	]	]	PUNCT
ejpam-5011	168	35	r	r	NOUN
ejpam-5011	168	36	,	,	PUNCT
ejpam-5011	168	37	λ	λ	NOUN
ejpam-5011	168	38	=	=	SYM
ejpam-5011	168	39	n	n	PROPN
ejpam-5011	168	40	∑	∑	PROPN
ejpam-5011	168	41	l	l	X
ejpam-5011	169	1	=	=	X
ejpam-5011	169	2	k	k	X
ejpam-5011	169	3	(	(	PUNCT
ejpam-5011	169	4	l	l	NOUN
ejpam-5011	169	5	k	k	X
ejpam-5011	169	6	)	)	PUNCT
ejpam-5011	169	7	[	[	PUNCT
ejpam-5011	169	8	n	n	X
ejpam-5011	169	9	l	l	NOUN
ejpam-5011	169	10	]	]	PUNCT
ejpam-5011	169	11	λ	λ	X
ejpam-5011	169	12	⟨r⟩l−k	⟨r⟩l−k	NOUN
ejpam-5011	169	13	,	,	PUNCT
ejpam-5011	169	14	λ	λ	X
ejpam-5011	169	15	.	.	PUNCT
ejpam-5011	170	1	proof	proof	NOUN
ejpam-5011	170	2	.	.	PUNCT
ejpam-5011	171	1	from	from	ADP
ejpam-5011	171	2	(	(	PUNCT
ejpam-5011	171	3	23	23	NUM
ejpam-5011	171	4	)	)	PUNCT
ejpam-5011	171	5	,	,	PUNCT
ejpam-5011	171	6	we	we	PRON
ejpam-5011	171	7	note	note	VERB
ejpam-5011	171	8	that	that	SCONJ
ejpam-5011	171	9	1	1	NUM
ejpam-5011	171	10	1−	1−	NUM
ejpam-5011	171	11	t	t	PROPN
ejpam-5011	171	12	1	1	NUM
ejpam-5011	171	13	k	k	NOUN
ejpam-5011	171	14	!	!	PUNCT
ejpam-5011	172	1	(	(	PUNCT
ejpam-5011	172	2	log−λ	log−λ	NUM
ejpam-5011	172	3	(	(	PUNCT
ejpam-5011	172	4	1	1	NUM
ejpam-5011	172	5	1−	1−	NUM
ejpam-5011	172	6	t	t	NOUN
ejpam-5011	172	7	)	)	PUNCT
ejpam-5011	172	8	)	)	PUNCT
ejpam-5011	173	1	k	k	X
ejpam-5011	173	2	=	=	SYM
ejpam-5011	173	3	∞	∞	NUM
ejpam-5011	173	4	∑	∑	PUNCT
ejpam-5011	173	5	n	n	PROPN
ejpam-5011	173	6	=	=	SYM
ejpam-5011	173	7	k	k	X
ejpam-5011	173	8	[	[	PUNCT
ejpam-5011	173	9	n+1	n+1	X
ejpam-5011	173	10	k+1	k+1	X
ejpam-5011	173	11	]	]	PUNCT
ejpam-5011	173	12	1,λ	1,λ	NUM
ejpam-5011	173	13	tn	tn	PROPN
ejpam-5011	173	14	n	n	X
ejpam-5011	173	15	!	!	PUNCT
ejpam-5011	173	16	.	.	PUNCT
ejpam-5011	174	1	(	(	PUNCT
ejpam-5011	174	2	25	25	NUM
ejpam-5011	174	3	)	)	PUNCT
ejpam-5011	174	4	on	on	ADP
ejpam-5011	174	5	the	the	DET
ejpam-5011	174	6	other	other	ADJ
ejpam-5011	174	7	hand	hand	NOUN
ejpam-5011	174	8	,	,	PUNCT
ejpam-5011	174	9	by	by	ADP
ejpam-5011	174	10	(	(	PUNCT
ejpam-5011	174	11	3	3	NUM
ejpam-5011	174	12	)	)	PUNCT
ejpam-5011	174	13	and	and	CCONJ
ejpam-5011	174	14	(	(	PUNCT
ejpam-5011	174	15	24	24	NUM
ejpam-5011	174	16	)	)	PUNCT
ejpam-5011	174	17	,	,	PUNCT
ejpam-5011	174	18	we	we	PRON
ejpam-5011	174	19	get	get	VERB
ejpam-5011	174	20	1	1	NUM
ejpam-5011	174	21	k	k	NOUN
ejpam-5011	174	22	!	!	PUNCT
ejpam-5011	175	1	(	(	PUNCT
ejpam-5011	175	2	log−λ	log−λ	NUM
ejpam-5011	175	3	(	(	PUNCT
ejpam-5011	175	4	1	1	NUM
ejpam-5011	175	5	1−	1−	NUM
ejpam-5011	175	6	t	t	NOUN
ejpam-5011	175	7	)	)	PUNCT
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ejpam-5011	176	1	k	k	X
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ejpam-5011	176	3	1−	1−	NUM
ejpam-5011	176	4	t	t	NOUN
ejpam-5011	176	5	=	=	SYM
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ejpam-5011	176	7	k	k	NOUN
ejpam-5011	176	8	!	!	PUNCT
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ejpam-5011	177	2	log−λ	log−λ	NUM
ejpam-5011	177	3	(	(	PUNCT
ejpam-5011	177	4	1	1	NUM
ejpam-5011	177	5	1−	1−	NUM
ejpam-5011	177	6	t	t	NOUN
ejpam-5011	177	7	)	)	PUNCT
ejpam-5011	177	8	)	)	PUNCT
ejpam-5011	178	1	k	k	X
ejpam-5011	179	1	∞	∞	NUM
ejpam-5011	179	2	∑	∑	PUNCT
ejpam-5011	179	3	l=0	l=0	PROPN
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ejpam-5011	179	5	,	,	PUNCT
ejpam-5011	179	6	λ	λ	X
ejpam-5011	179	7	l	l	NOUN
ejpam-5011	179	8	!	!	PUNCT
ejpam-5011	180	1	(	(	PUNCT
ejpam-5011	180	2	log−λ	log−λ	NUM
ejpam-5011	180	3	(	(	PUNCT
ejpam-5011	180	4	1	1	NUM
ejpam-5011	180	5	1−	1−	NUM
ejpam-5011	180	6	t	t	NOUN
ejpam-5011	180	7	)	)	PUNCT
ejpam-5011	180	8	)	)	PUNCT
ejpam-5011	181	1	l	l	NOUN
ejpam-5011	181	2	(	(	PUNCT
ejpam-5011	181	3	26	26	NUM
ejpam-5011	181	4	)	)	PUNCT
ejpam-5011	181	5	=	=	SYM
ejpam-5011	181	6	∞	∞	NUM
ejpam-5011	181	7	∑	∑	PUNCT
ejpam-5011	181	8	l=0	l=0	PROPN
ejpam-5011	181	9	⟨1⟩l	⟨1⟩l	NOUN
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ejpam-5011	181	11	λ	λ	PROPN
ejpam-5011	181	12	(	(	PUNCT
ejpam-5011	181	13	k+1	k+1	NOUN
ejpam-5011	181	14	)	)	PUNCT
ejpam-5011	181	15	!	!	PUNCT
ejpam-5011	182	1	l!k	l!k	PROPN
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ejpam-5011	182	4	(	(	PUNCT
ejpam-5011	182	5	k+1	k+1	NOUN
ejpam-5011	182	6	)	)	PUNCT
ejpam-5011	182	7	!	!	PUNCT
ejpam-5011	183	1	(	(	PUNCT
ejpam-5011	183	2	log−λ	log−λ	X
ejpam-5011	183	3	(	(	PUNCT
ejpam-5011	183	4	1	1	NUM
ejpam-5011	183	5	1−	1−	NUM
ejpam-5011	183	6	t	t	NOUN
ejpam-5011	183	7	)	)	PUNCT
ejpam-5011	183	8	)	)	PUNCT
ejpam-5011	183	9	k+l	k+l	PUNCT
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ejpam-5011	184	2	∞	∞	NUM
ejpam-5011	184	3	∑	∑	PROPN
ejpam-5011	184	4	l=0	l=0	PROPN
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ejpam-5011	184	6	,	,	PUNCT
ejpam-5011	184	7	λ	λ	PROPN
ejpam-5011	184	8	(	(	PUNCT
ejpam-5011	184	9	k+	k+	PROPN
ejpam-5011	184	10	l	l	NOUN
ejpam-5011	184	11	)	)	PUNCT
ejpam-5011	184	12	!	!	PUNCT
ejpam-5011	185	1	k!l	k!l	X
ejpam-5011	185	2	!	!	PUNCT
ejpam-5011	185	3	∞	∞	NUM
ejpam-5011	185	4	∑	∑	PUNCT
ejpam-5011	185	5	n	n	CCONJ
ejpam-5011	185	6	=	=	X
ejpam-5011	185	7	k+l	k+l	X
ejpam-5011	185	8	[	[	PUNCT
ejpam-5011	185	9	n	n	X
ejpam-5011	185	10	k+	k+	X
ejpam-5011	185	11	l	l	NOUN
ejpam-5011	185	12	]	]	PUNCT
ejpam-5011	186	1	λ	λ	X
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ejpam-5011	186	3	n	n	NOUN
ejpam-5011	186	4	!	!	PUNCT
ejpam-5011	186	5	=	=	SYM
ejpam-5011	187	1	∞	∞	NUM
ejpam-5011	187	2	∑	∑	PUNCT
ejpam-5011	187	3	l=0	l=0	PROPN
ejpam-5011	187	4	(	(	PUNCT
ejpam-5011	187	5	k+	k+	X
ejpam-5011	187	6	l	l	PROPN
ejpam-5011	187	7	k	k	PROPN
ejpam-5011	187	8	)	)	PUNCT
ejpam-5011	187	9	⟨1⟩l	⟨1⟩l	NOUN
ejpam-5011	187	10	,	,	PUNCT
ejpam-5011	187	11	λ	λ	PROPN
ejpam-5011	187	12	∞	∞	NUM
ejpam-5011	187	13	∑	∑	PUNCT
ejpam-5011	187	14	n	n	CCONJ
ejpam-5011	187	15	=	=	X
ejpam-5011	187	16	k+l	k+l	X
ejpam-5011	187	17	[	[	PUNCT
ejpam-5011	187	18	n	n	X
ejpam-5011	187	19	k+	k+	X
ejpam-5011	187	20	l	l	NOUN
ejpam-5011	187	21	]	]	PUNCT
ejpam-5011	188	1	λ	λ	X
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ejpam-5011	188	3	n	n	NOUN
ejpam-5011	188	4	!	!	PUNCT
ejpam-5011	188	5	=	=	SYM
ejpam-5011	189	1	∞	∞	NUM
ejpam-5011	189	2	∑	∑	PUNCT
ejpam-5011	189	3	l	l	X
ejpam-5011	189	4	=	=	SYM
ejpam-5011	189	5	k	k	X
ejpam-5011	189	6	(	(	PUNCT
ejpam-5011	189	7	l	l	NOUN
ejpam-5011	189	8	k	k	X
ejpam-5011	189	9	)	)	PUNCT
ejpam-5011	189	10	⟨1⟩l−k	⟨1⟩l−k	NOUN
ejpam-5011	189	11	,	,	PUNCT
ejpam-5011	189	12	λ	λ	PROPN
ejpam-5011	189	13	∞	∞	NUM
ejpam-5011	189	14	∑	∑	PUNCT
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ejpam-5011	189	16	=	=	PROPN
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ejpam-5011	189	18	[	[	PUNCT
ejpam-5011	189	19	n	n	X
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ejpam-5011	189	21	]	]	PUNCT
ejpam-5011	190	1	λ	λ	X
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ejpam-5011	190	4	!	!	PUNCT
ejpam-5011	190	5	=	=	SYM
ejpam-5011	191	1	∞	∞	NUM
ejpam-5011	191	2	∑	∑	PUNCT
ejpam-5011	191	3	n	n	PROPN
ejpam-5011	191	4	=	=	SYM
ejpam-5011	191	5	k	k	X
ejpam-5011	191	6	(	(	PUNCT
ejpam-5011	191	7	n	n	CCONJ
ejpam-5011	191	8	∑	∑	PROPN
ejpam-5011	191	9	l	l	X
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ejpam-5011	191	11	k	k	X
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ejpam-5011	191	13	l	l	NOUN
ejpam-5011	191	14	k	k	X
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ejpam-5011	191	16	[	[	PUNCT
ejpam-5011	191	17	n	n	X
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ejpam-5011	191	19	]	]	PUNCT
ejpam-5011	192	1	λ	λ	X
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ejpam-5011	192	3	,	,	PUNCT
ejpam-5011	192	4	λ	λ	PROPN
ejpam-5011	192	5	)	)	PUNCT
ejpam-5011	192	6	tn	tn	PROPN
ejpam-5011	192	7	n	n	PROPN
ejpam-5011	192	8	!	!	PUNCT
ejpam-5011	192	9	.	.	PUNCT
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ejpam-5011	193	2	,	,	PUNCT
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ejpam-5011	193	4	(	(	PUNCT
ejpam-5011	193	5	25	25	NUM
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ejpam-5011	193	7	and	and	CCONJ
ejpam-5011	193	8	(	(	PUNCT
ejpam-5011	193	9	26	26	NUM
ejpam-5011	193	10	)	)	PUNCT
ejpam-5011	193	11	,	,	PUNCT
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ejpam-5011	193	14	[	[	PUNCT
ejpam-5011	193	15	n+1	n+1	X
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ejpam-5011	193	17	]	]	X
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ejpam-5011	194	2	=	=	SYM
ejpam-5011	194	3	n	n	PROPN
ejpam-5011	194	4	∑	∑	PROPN
ejpam-5011	194	5	l	l	X
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ejpam-5011	194	7	k	k	X
ejpam-5011	194	8	(	(	PUNCT
ejpam-5011	194	9	l	l	NOUN
ejpam-5011	194	10	k	k	X
ejpam-5011	194	11	)	)	PUNCT
ejpam-5011	194	12	[	[	PUNCT
ejpam-5011	194	13	n	n	X
ejpam-5011	194	14	l	l	NOUN
ejpam-5011	194	15	]	]	PUNCT
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ejpam-5011	195	3	,	,	PUNCT
ejpam-5011	195	4	λ	λ	X
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ejpam-5011	196	2	27	27	NUM
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ejpam-5011	196	15	∞	∞	PROPN
ejpam-5011	196	16	∑	∑	PUNCT
ejpam-5011	196	17	n	n	PROPN
ejpam-5011	196	18	=	=	SYM
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ejpam-5011	197	1	[	[	PUNCT
ejpam-5011	197	2	n+	n+	ADP
ejpam-5011	197	3	r	r	NOUN
ejpam-5011	197	4	k+	k+	NOUN
ejpam-5011	197	5	r	r	NOUN
ejpam-5011	197	6	]	]	PUNCT
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ejpam-5011	197	9	λ	λ	PROPN
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ejpam-5011	198	4	(	(	PUNCT
ejpam-5011	198	5	logλ	logλ	PROPN
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ejpam-5011	198	7	1−	1−	NUM
ejpam-5011	198	8	t	t	PROPN
ejpam-5011	198	9	)	)	PUNCT
ejpam-5011	198	10	)	)	PUNCT
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ejpam-5011	200	1	(	(	PUNCT
ejpam-5011	200	2	log−λ	log−λ	NUM
ejpam-5011	200	3	(	(	PUNCT
ejpam-5011	200	4	1	1	NUM
ejpam-5011	200	5	1−	1−	NUM
ejpam-5011	200	6	t	t	NOUN
ejpam-5011	200	7	)	)	PUNCT
ejpam-5011	200	8	)	)	PUNCT
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ejpam-5011	201	2	(	(	PUNCT
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ejpam-5011	201	4	)	)	PUNCT
ejpam-5011	201	5	=	=	SYM
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ejpam-5011	202	2	∑	∑	PUNCT
ejpam-5011	202	3	l=0	l=0	PROPN
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ejpam-5011	202	5	,	,	PUNCT
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ejpam-5011	202	8	l	l	NOUN
ejpam-5011	202	9	!	!	PUNCT
ejpam-5011	203	1	(	(	PUNCT
ejpam-5011	203	2	log−λ	log−λ	NUM
ejpam-5011	203	3	(	(	PUNCT
ejpam-5011	203	4	1	1	NUM
ejpam-5011	203	5	1−	1−	NUM
ejpam-5011	203	6	t	t	NOUN
ejpam-5011	203	7	)	)	PUNCT
ejpam-5011	203	8	)	)	PUNCT
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ejpam-5011	204	4	!	!	PUNCT
ejpam-5011	205	1	(	(	PUNCT
ejpam-5011	205	2	log−λ	log−λ	NUM
ejpam-5011	205	3	(	(	PUNCT
ejpam-5011	205	4	1	1	NUM
ejpam-5011	205	5	1−	1−	NUM
ejpam-5011	205	6	t	t	NOUN
ejpam-5011	205	7	)	)	PUNCT
ejpam-5011	205	8	)	)	PUNCT
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ejpam-5011	207	3	∑	∑	PUNCT
ejpam-5011	207	4	l=0	l=0	PROPN
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ejpam-5011	207	6	,	,	PUNCT
ejpam-5011	207	7	λ	λ	PROPN
ejpam-5011	207	8	(	(	PUNCT
ejpam-5011	207	9	k+	k+	X
ejpam-5011	207	10	l	l	PROPN
ejpam-5011	207	11	l	l	NOUN
ejpam-5011	207	12	)	)	PUNCT
ejpam-5011	207	13	1	1	NUM
ejpam-5011	207	14	(	(	PUNCT
ejpam-5011	207	15	k+	k+	NOUN
ejpam-5011	207	16	l	l	NOUN
ejpam-5011	207	17	)	)	PUNCT
ejpam-5011	207	18	!	!	PUNCT
ejpam-5011	208	1	(	(	PUNCT
ejpam-5011	208	2	log−λ	log−λ	X
ejpam-5011	208	3	(	(	PUNCT
ejpam-5011	208	4	1	1	NUM
ejpam-5011	208	5	1−	1−	NUM
ejpam-5011	208	6	t	t	NOUN
ejpam-5011	208	7	)	)	PUNCT
ejpam-5011	208	8	)	)	PUNCT
ejpam-5011	208	9	k+l	k+l	PUNCT
ejpam-5011	209	1	=	=	SYM
ejpam-5011	209	2	∞	∞	NUM
ejpam-5011	209	3	∑	∑	PUNCT
ejpam-5011	209	4	l	l	X
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ejpam-5011	209	6	k	k	X
ejpam-5011	209	7	⟨r⟩l−k	⟨r⟩l−k	NOUN
ejpam-5011	209	8	,	,	PUNCT
ejpam-5011	209	9	λ	λ	PROPN
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ejpam-5011	209	11	l	l	NOUN
ejpam-5011	209	12	k	k	X
ejpam-5011	209	13	)	)	PUNCT
ejpam-5011	209	14	1	1	NUM
ejpam-5011	209	15	l	l	NOUN
ejpam-5011	209	16	!	!	PUNCT
ejpam-5011	210	1	(	(	PUNCT
ejpam-5011	210	2	log−λ	log−λ	NUM
ejpam-5011	210	3	(	(	PUNCT
ejpam-5011	210	4	1	1	NUM
ejpam-5011	210	5	1−	1−	NUM
ejpam-5011	210	6	t	t	NOUN
ejpam-5011	210	7	)	)	PUNCT
ejpam-5011	210	8	)	)	PUNCT
ejpam-5011	210	9	l	l	NOUN
ejpam-5011	211	1	=	=	SYM
ejpam-5011	211	2	∞	∞	NUM
ejpam-5011	211	3	∑	∑	PUNCT
ejpam-5011	211	4	l	l	X
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ejpam-5011	211	6	k	k	X
ejpam-5011	211	7	⟨r⟩l−k	⟨r⟩l−k	NOUN
ejpam-5011	211	8	,	,	PUNCT
ejpam-5011	211	9	λ	λ	PROPN
ejpam-5011	211	10	(	(	PUNCT
ejpam-5011	211	11	l	l	NOUN
ejpam-5011	211	12	k	k	X
ejpam-5011	211	13	)	)	PUNCT
ejpam-5011	211	14	∞	∞	PROPN
ejpam-5011	211	15	∑	∑	PUNCT
ejpam-5011	211	16	n	n	CCONJ
ejpam-5011	211	17	=	=	PROPN
ejpam-5011	211	18	l	l	NOUN
ejpam-5011	211	19	[	[	PUNCT
ejpam-5011	211	20	n	n	X
ejpam-5011	211	21	l	l	NOUN
ejpam-5011	211	22	]	]	PUNCT
ejpam-5011	212	1	λ	λ	X
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ejpam-5011	212	3	n	n	NOUN
ejpam-5011	212	4	!	!	PUNCT
ejpam-5011	212	5	=	=	SYM
ejpam-5011	213	1	∞	∞	NUM
ejpam-5011	213	2	∑	∑	PUNCT
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ejpam-5011	213	4	=	=	SYM
ejpam-5011	213	5	k	k	X
ejpam-5011	213	6	(	(	PUNCT
ejpam-5011	213	7	n	n	CCONJ
ejpam-5011	213	8	∑	∑	PROPN
ejpam-5011	213	9	l	l	X
ejpam-5011	213	10	=	=	X
ejpam-5011	213	11	k	k	X
ejpam-5011	213	12	(	(	PUNCT
ejpam-5011	213	13	l	l	NOUN
ejpam-5011	213	14	k	k	X
ejpam-5011	213	15	)	)	PUNCT
ejpam-5011	213	16	[	[	PUNCT
ejpam-5011	213	17	n	n	X
ejpam-5011	213	18	l	l	NOUN
ejpam-5011	213	19	]	]	PUNCT
ejpam-5011	213	20	λ	λ	X
ejpam-5011	213	21	⟨r⟩l−k	⟨r⟩l−k	NOUN
ejpam-5011	213	22	,	,	PUNCT
ejpam-5011	213	23	λ	λ	PROPN
ejpam-5011	213	24	)	)	PUNCT
ejpam-5011	213	25	tn	tn	PROPN
ejpam-5011	213	26	n	n	PROPN
ejpam-5011	213	27	!	!	PUNCT
ejpam-5011	213	28	.	.	PUNCT
ejpam-5011	214	1	d.	d.	PROPN
ejpam-5011	214	2	kim	kim	PROPN
ejpam-5011	214	3	,	,	PUNCT
ejpam-5011	214	4	t.	t.	PROPN
ejpam-5011	214	5	kim	kim	PROPN
ejpam-5011	214	6	,	,	PUNCT
ejpam-5011	214	7	j.	j.	PROPN
ejpam-5011	214	8	kwon	kwon	PROPN
ejpam-5011	214	9	/	/	SYM
ejpam-5011	214	10	eur	eur	PROPN
ejpam-5011	214	11	.	.	PUNCT
ejpam-5011	215	1	j.	j.	PROPN
ejpam-5011	215	2	pure	pure	PROPN
ejpam-5011	215	3	appl	appl	PROPN
ejpam-5011	215	4	.	.	PROPN
ejpam-5011	215	5	math	math	PROPN
ejpam-5011	215	6	,	,	PUNCT
ejpam-5011	215	7	17	17	NUM
ejpam-5011	215	8	(	(	PUNCT
ejpam-5011	215	9	1	1	NUM
ejpam-5011	215	10	)	)	PUNCT
ejpam-5011	215	11	(	(	PUNCT
ejpam-5011	215	12	2024	2024	NUM
ejpam-5011	215	13	)	)	PUNCT
ejpam-5011	215	14	,	,	PUNCT
ejpam-5011	215	15	1	1	NUM
ejpam-5011	215	16	-	-	SYM
ejpam-5011	215	17	10	10	NUM
ejpam-5011	215	18	8	8	NUM
ejpam-5011	215	19	by	by	ADP
ejpam-5011	215	20	comparing	compare	VERB
ejpam-5011	215	21	the	the	DET
ejpam-5011	215	22	coefficients	coefficient	NOUN
ejpam-5011	215	23	on	on	ADP
ejpam-5011	215	24	both	both	DET
ejpam-5011	215	25	sides	side	NOUN
ejpam-5011	215	26	of	of	ADP
ejpam-5011	215	27	(	(	PUNCT
ejpam-5011	215	28	28	28	NUM
ejpam-5011	215	29	)	)	PUNCT
ejpam-5011	215	30	,	,	PUNCT
ejpam-5011	215	31	we	we	PRON
ejpam-5011	215	32	get	get	VERB
ejpam-5011	215	33	[	[	PUNCT
ejpam-5011	215	34	n+	n+	ADP
ejpam-5011	215	35	r	r	NOUN
ejpam-5011	215	36	k+	k+	NOUN
ejpam-5011	215	37	r	r	NOUN
ejpam-5011	215	38	]	]	PUNCT
ejpam-5011	216	1	r	r	NOUN
ejpam-5011	216	2	,	,	PUNCT
ejpam-5011	216	3	λ	λ	NOUN
ejpam-5011	216	4	=	=	SYM
ejpam-5011	216	5	n	n	PROPN
ejpam-5011	216	6	∑	∑	PROPN
ejpam-5011	216	7	l	l	X
ejpam-5011	216	8	=	=	X
ejpam-5011	216	9	k	k	X
ejpam-5011	216	10	(	(	PUNCT
ejpam-5011	216	11	l	l	NOUN
ejpam-5011	216	12	k	k	X
ejpam-5011	216	13	)	)	PUNCT
ejpam-5011	216	14	[	[	PUNCT
ejpam-5011	216	15	n	n	X
ejpam-5011	216	16	l	l	NOUN
ejpam-5011	216	17	]	]	PUNCT
ejpam-5011	217	1	λ	λ	X
ejpam-5011	217	2	⟨r⟩l−k	⟨r⟩l−k	NOUN
ejpam-5011	217	3	,	,	PUNCT
ejpam-5011	217	4	λ	λ	X
ejpam-5011	217	5	,	,	PUNCT
ejpam-5011	217	6	(	(	PUNCT
ejpam-5011	217	7	n	n	CCONJ
ejpam-5011	217	8	,	,	PUNCT
ejpam-5011	217	9	k	k	PROPN
ejpam-5011	217	10	≥	≥	PROPN
ejpam-5011	217	11	0	0	NUM
ejpam-5011	217	12	)	)	PUNCT
ejpam-5011	217	13	.	.	PUNCT
ejpam-5011	218	1	note	note	VERB
ejpam-5011	218	2	that	that	SCONJ
ejpam-5011	218	3	[	[	PUNCT
ejpam-5011	218	4	n+1	n+1	X
ejpam-5011	218	5	k+1	k+1	X
ejpam-5011	218	6	]	]	PUNCT
ejpam-5011	218	7	1	1	X
ejpam-5011	218	8	=	=	SYM
ejpam-5011	218	9	lim	lim	PROPN
ejpam-5011	218	10	λ→0	λ→0	PUNCT
ejpam-5011	218	11	[	[	PUNCT
ejpam-5011	218	12	n+1	n+1	PUNCT
ejpam-5011	218	13	k+1	k+1	X
ejpam-5011	218	14	]	]	PUNCT
ejpam-5011	219	1	1,λ	1,λ	NUM
ejpam-5011	219	2	=	=	SYM
ejpam-5011	219	3	lim	lim	PROPN
ejpam-5011	219	4	λ→0	λ→0	PROPN
ejpam-5011	219	5	n	n	PROPN
ejpam-5011	219	6	∑	∑	PROPN
ejpam-5011	219	7	l	l	X
ejpam-5011	219	8	=	=	X
ejpam-5011	219	9	k	k	X
ejpam-5011	219	10	(	(	PUNCT
ejpam-5011	219	11	l	l	NOUN
ejpam-5011	219	12	k	k	X
ejpam-5011	219	13	)	)	PUNCT
ejpam-5011	219	14	[	[	PUNCT
ejpam-5011	219	15	n	n	X
ejpam-5011	219	16	l	l	NOUN
ejpam-5011	219	17	]	]	PUNCT
ejpam-5011	219	18	λ	λ	X
ejpam-5011	219	19	⟨1⟩l−k	⟨1⟩l−k	NOUN
ejpam-5011	219	20	,	,	PUNCT
ejpam-5011	219	21	λ	λ	PROPN
ejpam-5011	219	22	=	=	SYM
ejpam-5011	219	23	n	n	PROPN
ejpam-5011	219	24	∑	∑	PROPN
ejpam-5011	219	25	l	l	X
ejpam-5011	219	26	=	=	X
ejpam-5011	219	27	k	k	X
ejpam-5011	219	28	(	(	PUNCT
ejpam-5011	219	29	l	l	NOUN
ejpam-5011	219	30	k	k	X
ejpam-5011	219	31	)	)	PUNCT
ejpam-5011	219	32	[	[	PUNCT
ejpam-5011	219	33	n	n	X
ejpam-5011	219	34	l	l	NOUN
ejpam-5011	219	35	]	]	PUNCT
ejpam-5011	219	36	,	,	PUNCT
ejpam-5011	219	37	and	and	CCONJ
ejpam-5011	219	38	[	[	PUNCT
ejpam-5011	219	39	n+	n+	NOUN
ejpam-5011	219	40	r	r	NOUN
ejpam-5011	219	41	k+	k+	NOUN
ejpam-5011	219	42	r	r	NOUN
ejpam-5011	219	43	]	]	PUNCT
ejpam-5011	219	44	r	r	NOUN
ejpam-5011	219	45	=	=	SYM
ejpam-5011	219	46	lim	lim	PROPN
ejpam-5011	219	47	λ→0	λ→0	PUNCT
ejpam-5011	219	48	[	[	PUNCT
ejpam-5011	219	49	n+	n+	ADP
ejpam-5011	219	50	r	r	NOUN
ejpam-5011	219	51	k+	k+	NOUN
ejpam-5011	219	52	r	r	NOUN
ejpam-5011	219	53	]	]	PUNCT
ejpam-5011	219	54	r	r	NOUN
ejpam-5011	219	55	,	,	PUNCT
ejpam-5011	219	56	λ	λ	NOUN
ejpam-5011	219	57	=	=	SYM
ejpam-5011	219	58	n	n	PROPN
ejpam-5011	219	59	∑	∑	PROPN
ejpam-5011	219	60	l	l	X
ejpam-5011	219	61	=	=	X
ejpam-5011	219	62	k	k	X
ejpam-5011	219	63	(	(	PUNCT
ejpam-5011	219	64	l	l	NOUN
ejpam-5011	219	65	k	k	X
ejpam-5011	219	66	)	)	PUNCT
ejpam-5011	219	67	[	[	PUNCT
ejpam-5011	219	68	n	n	X
ejpam-5011	219	69	l	l	NOUN
ejpam-5011	219	70	]	]	PUNCT
ejpam-5011	219	71	rl−k	rl−k	NOUN
ejpam-5011	219	72	.	.	PUNCT
ejpam-5011	220	1	theorem	theorem	NOUN
ejpam-5011	220	2	4	4	NUM
ejpam-5011	220	3	.	.	NOUN
ejpam-5011	220	4	for	for	ADP
ejpam-5011	220	5	n	n	CCONJ
ejpam-5011	220	6	,	,	PUNCT
ejpam-5011	220	7	m	m	PROPN
ejpam-5011	220	8	∈	∈	PROPN
ejpam-5011	221	1	n	n	CCONJ
ejpam-5011	221	2	,	,	PUNCT
ejpam-5011	221	3	we	we	PRON
ejpam-5011	221	4	have	have	VERB
ejpam-5011	221	5	m	m	PROPN
ejpam-5011	221	6	∑	∑	PROPN
ejpam-5011	221	7	k=1	k=1	PUNCT
ejpam-5011	222	1	[	[	PUNCT
ejpam-5011	222	2	m	m	VERB
ejpam-5011	222	3	k	k	X
ejpam-5011	222	4	]	]	X
ejpam-5011	222	5	(	(	PUNCT
ejpam-5011	222	6	k)n	k)n	X
ejpam-5011	222	7	,	,	PUNCT
ejpam-5011	222	8	λ	λ	X
ejpam-5011	222	9	=	=	VERB
ejpam-5011	222	10	m	m	VERB
ejpam-5011	222	11	∑	∑	PROPN
ejpam-5011	223	1	j=1	j=1	PROPN
ejpam-5011	223	2	j	j	PROPN
ejpam-5011	223	3	!	!	PUNCT
ejpam-5011	223	4	{	{	PUNCT
ejpam-5011	223	5	n	n	PRON
ejpam-5011	223	6	j	j	PROPN
ejpam-5011	223	7	}	}	PUNCT
ejpam-5011	223	8	λ	λ	PROPN
ejpam-5011	223	9	[	[	PUNCT
ejpam-5011	223	10	m+1	m+1	PROPN
ejpam-5011	223	11	j+1	j+1	PROPN
ejpam-5011	223	12	]	]	PUNCT
ejpam-5011	223	13	1	1	NUM
ejpam-5011	223	14	.	.	PUNCT
ejpam-5011	224	1	proof	proof	NOUN
ejpam-5011	224	2	.	.	PUNCT
ejpam-5011	225	1	by	by	ADP
ejpam-5011	225	2	(	(	PUNCT
ejpam-5011	225	3	14	14	NUM
ejpam-5011	225	4	)	)	PUNCT
ejpam-5011	225	5	,	,	PUNCT
ejpam-5011	225	6	we	we	PRON
ejpam-5011	225	7	get	get	VERB
ejpam-5011	225	8	m	m	PRON
ejpam-5011	225	9	∑	∑	PUNCT
ejpam-5011	225	10	k=1	k=1	PUNCT
ejpam-5011	226	1	[	[	PUNCT
ejpam-5011	226	2	m	m	VERB
ejpam-5011	226	3	k	k	X
ejpam-5011	226	4	]	]	X
ejpam-5011	226	5	(	(	PUNCT
ejpam-5011	226	6	k)n	k)n	X
ejpam-5011	226	7	,	,	PUNCT
ejpam-5011	226	8	λ	λ	X
ejpam-5011	226	9	=	=	VERB
ejpam-5011	226	10	m	m	VERB
ejpam-5011	226	11	∑	∑	PUNCT
ejpam-5011	226	12	k=1	k=1	PUNCT
ejpam-5011	226	13	[	[	PUNCT
ejpam-5011	226	14	m	m	VERB
ejpam-5011	226	15	k	k	X
ejpam-5011	226	16	]	]	PUNCT
ejpam-5011	227	1	k	k	X
ejpam-5011	227	2	∑	∑	PUNCT
ejpam-5011	227	3	j=1	j=1	PROPN
ejpam-5011	227	4	(	(	PUNCT
ejpam-5011	227	5	k	k	PROPN
ejpam-5011	227	6	j	j	PROPN
ejpam-5011	227	7	)	)	PUNCT
ejpam-5011	227	8	j	j	PROPN
ejpam-5011	227	9	!	!	PUNCT
ejpam-5011	227	10	{	{	PUNCT
ejpam-5011	228	1	n	n	PRON
ejpam-5011	228	2	j	j	PROPN
ejpam-5011	228	3	}	}	PUNCT
ejpam-5011	228	4	λ	λ	PROPN
ejpam-5011	228	5	(	(	PUNCT
ejpam-5011	228	6	29	29	NUM
ejpam-5011	228	7	)	)	PUNCT
ejpam-5011	228	8	=	=	PUNCT
ejpam-5011	229	1	m	m	VERB
ejpam-5011	229	2	∑	∑	PUNCT
ejpam-5011	229	3	j=1	j=1	PROPN
ejpam-5011	229	4	j	j	PROPN
ejpam-5011	229	5	!	!	PUNCT
ejpam-5011	229	6	{	{	PUNCT
ejpam-5011	230	1	n	n	PRON
ejpam-5011	230	2	j	j	NOUN
ejpam-5011	230	3	}	}	PUNCT
ejpam-5011	230	4	λ	λ	PROPN
ejpam-5011	230	5	m	m	VERB
ejpam-5011	230	6	∑	∑	PROPN
ejpam-5011	230	7	k=	k=	INTJ
ejpam-5011	230	8	j	j	PROPN
ejpam-5011	231	1	(	(	PUNCT
ejpam-5011	231	2	k	k	PROPN
ejpam-5011	231	3	j	j	PROPN
ejpam-5011	231	4	)	)	PUNCT
ejpam-5011	232	1	[	[	PUNCT
ejpam-5011	232	2	m	m	VERB
ejpam-5011	232	3	k	k	X
ejpam-5011	232	4	]	]	X
ejpam-5011	233	1	=	=	PUNCT
ejpam-5011	233	2	m	m	VERB
ejpam-5011	233	3	∑	∑	VERB
ejpam-5011	233	4	j=1	j=1	PROPN
ejpam-5011	233	5	j	j	PROPN
ejpam-5011	233	6	!	!	PUNCT
ejpam-5011	233	7	{	{	PUNCT
ejpam-5011	233	8	n	n	PRON
ejpam-5011	233	9	j	j	PROPN
ejpam-5011	233	10	}	}	PUNCT
ejpam-5011	233	11	λ	λ	PROPN
ejpam-5011	233	12	[	[	PUNCT
ejpam-5011	233	13	m+1	m+1	PROPN
ejpam-5011	233	14	j+1	j+1	PROPN
ejpam-5011	233	15	]	]	PUNCT
ejpam-5011	233	16	1	1	X
ejpam-5011	233	17	.	.	PUNCT
ejpam-5011	234	1	(	(	PUNCT
ejpam-5011	234	2	30	30	NUM
ejpam-5011	234	3	)	)	PUNCT
ejpam-5011	234	4	from	from	ADP
ejpam-5011	234	5	(	(	PUNCT
ejpam-5011	234	6	11	11	NUM
ejpam-5011	234	7	)	)	PUNCT
ejpam-5011	234	8	,	,	PUNCT
ejpam-5011	234	9	we	we	PRON
ejpam-5011	234	10	note	note	VERB
ejpam-5011	234	11	that	that	SCONJ
ejpam-5011	234	12	1	1	NUM
ejpam-5011	234	13	k	k	X
ejpam-5011	234	14	!	!	PUNCT
ejpam-5011	235	1	(	(	PUNCT
ejpam-5011	235	2	eλ	eλ	X
ejpam-5011	235	3	(	(	PUNCT
ejpam-5011	235	4	t)−1	t)−1	NOUN
ejpam-5011	235	5	)	)	PUNCT
ejpam-5011	235	6	ker	ker	NOUN
ejpam-5011	235	7	λ	λ	PROPN
ejpam-5011	235	8	(	(	PUNCT
ejpam-5011	235	9	t	t	PROPN
ejpam-5011	235	10	)	)	PUNCT
ejpam-5011	235	11	=	=	SYM
ejpam-5011	236	1	∞	∞	NUM
ejpam-5011	236	2	∑	∑	PUNCT
ejpam-5011	236	3	n	n	CCONJ
ejpam-5011	236	4	=	=	SYM
ejpam-5011	236	5	k	k	X
ejpam-5011	236	6	{	{	PUNCT
ejpam-5011	236	7	n+	n+	ADP
ejpam-5011	236	8	r	r	NOUN
ejpam-5011	236	9	k+	k+	NOUN
ejpam-5011	236	10	r	r	NOUN
ejpam-5011	236	11	}	}	PUNCT
ejpam-5011	236	12	r	r	NOUN
ejpam-5011	236	13	,	,	PUNCT
ejpam-5011	236	14	λ	λ	PROPN
ejpam-5011	236	15	tn	tn	NOUN
ejpam-5011	236	16	n	n	X
ejpam-5011	236	17	!	!	PROPN
ejpam-5011	236	18	,	,	PUNCT
ejpam-5011	236	19	(	(	PUNCT
ejpam-5011	236	20	k	k	X
ejpam-5011	236	21	,	,	PUNCT
ejpam-5011	236	22	r	r	NOUN
ejpam-5011	236	23	≥	≥	NOUN
ejpam-5011	236	24	0	0	NUM
ejpam-5011	236	25	)	)	PUNCT
ejpam-5011	236	26	.	.	PUNCT
ejpam-5011	237	1	(	(	PUNCT
ejpam-5011	237	2	31	31	NUM
ejpam-5011	237	3	)	)	PUNCT
ejpam-5011	237	4	by	by	ADP
ejpam-5011	237	5	(	(	PUNCT
ejpam-5011	237	6	31	31	NUM
ejpam-5011	237	7	)	)	PUNCT
ejpam-5011	237	8	,	,	PUNCT
ejpam-5011	237	9	we	we	PRON
ejpam-5011	237	10	get	get	VERB
ejpam-5011	237	11	∞	∞	PROPN
ejpam-5011	237	12	∑	∑	PUNCT
ejpam-5011	237	13	n	n	PROPN
ejpam-5011	237	14	=	=	SYM
ejpam-5011	237	15	k	k	X
ejpam-5011	237	16	{	{	PUNCT
ejpam-5011	237	17	n+	n+	ADP
ejpam-5011	237	18	r	r	NOUN
ejpam-5011	237	19	k+	k+	NOUN
ejpam-5011	237	20	r	r	NOUN
ejpam-5011	237	21	}	}	PUNCT
ejpam-5011	237	22	r	r	NOUN
ejpam-5011	237	23	,	,	PUNCT
ejpam-5011	237	24	λ	λ	PROPN
ejpam-5011	237	25	tn	tn	NOUN
ejpam-5011	237	26	n	n	NOUN
ejpam-5011	237	27	!	!	PUNCT
ejpam-5011	238	1	=	=	SYM
ejpam-5011	238	2	1	1	NUM
ejpam-5011	238	3	k	k	NOUN
ejpam-5011	238	4	!	!	PUNCT
ejpam-5011	239	1	(	(	PUNCT
ejpam-5011	239	2	eλ	eλ	X
ejpam-5011	239	3	(	(	PUNCT
ejpam-5011	239	4	t)−1	t)−1	NOUN
ejpam-5011	239	5	)	)	PUNCT
ejpam-5011	239	6	ker	ker	NOUN
ejpam-5011	239	7	λ	λ	PROPN
ejpam-5011	239	8	(	(	PUNCT
ejpam-5011	239	9	t	t	PROPN
ejpam-5011	239	10	)	)	PUNCT
ejpam-5011	239	11	=	=	SYM
ejpam-5011	239	12	1	1	NUM
ejpam-5011	239	13	k	k	NOUN
ejpam-5011	239	14	!	!	PUNCT
ejpam-5011	240	1	k	k	X
ejpam-5011	241	1	∑	∑	PUNCT
ejpam-5011	241	2	l=0	l=0	PROPN
ejpam-5011	241	3	(	(	PUNCT
ejpam-5011	241	4	k	k	NOUN
ejpam-5011	241	5	l	l	NOUN
ejpam-5011	241	6	)	)	PUNCT
ejpam-5011	241	7	(	(	PUNCT
ejpam-5011	241	8	−1)k−lel+r	−1)k−lel+r	PROPN
ejpam-5011	241	9	λ	λ	PROPN
ejpam-5011	241	10	(	(	PUNCT
ejpam-5011	241	11	t	t	PROPN
ejpam-5011	241	12	)	)	PUNCT
ejpam-5011	241	13	(	(	PUNCT
ejpam-5011	241	14	32	32	NUM
ejpam-5011	241	15	)	)	PUNCT
ejpam-5011	241	16	=	=	SYM
ejpam-5011	242	1	∞	∞	NUM
ejpam-5011	242	2	∑	∑	PROPN
ejpam-5011	242	3	n=0	n=0	PROPN
ejpam-5011	242	4	1	1	NUM
ejpam-5011	242	5	k	k	NOUN
ejpam-5011	242	6	!	!	PUNCT
ejpam-5011	243	1	k	k	X
ejpam-5011	244	1	∑	∑	PUNCT
ejpam-5011	244	2	l=0	l=0	PROPN
ejpam-5011	244	3	(	(	PUNCT
ejpam-5011	244	4	k	k	NOUN
ejpam-5011	244	5	l	l	NOUN
ejpam-5011	244	6	)	)	PUNCT
ejpam-5011	244	7	(	(	PUNCT
ejpam-5011	244	8	−1)k−l(l	−1)k−l(l	ADV
ejpam-5011	244	9	+	+	X
ejpam-5011	244	10	r)n	r)n	ADJ
ejpam-5011	244	11	,	,	PUNCT
ejpam-5011	244	12	λ	λ	PROPN
ejpam-5011	244	13	tn	tn	NOUN
ejpam-5011	244	14	n	n	X
ejpam-5011	244	15	!	!	PUNCT
ejpam-5011	244	16	.	.	PUNCT
ejpam-5011	245	1	thus	thus	ADV
ejpam-5011	245	2	,	,	PUNCT
ejpam-5011	245	3	by	by	ADP
ejpam-5011	245	4	comparing	compare	VERB
ejpam-5011	245	5	the	the	DET
ejpam-5011	245	6	coefficients	coefficient	NOUN
ejpam-5011	245	7	on	on	ADP
ejpam-5011	245	8	both	both	DET
ejpam-5011	245	9	sides	side	NOUN
ejpam-5011	245	10	of	of	ADP
ejpam-5011	245	11	(	(	PUNCT
ejpam-5011	245	12	32	32	NUM
ejpam-5011	245	13	)	)	PUNCT
ejpam-5011	245	14	,	,	PUNCT
ejpam-5011	245	15	we	we	PRON
ejpam-5011	245	16	get	get	VERB
ejpam-5011	245	17	k	k	X
ejpam-5011	245	18	!	!	PUNCT
ejpam-5011	245	19	{	{	PUNCT
ejpam-5011	246	1	n+	n+	ADP
ejpam-5011	246	2	r	r	NOUN
ejpam-5011	246	3	k+	k+	NOUN
ejpam-5011	246	4	r	r	NOUN
ejpam-5011	246	5	}	}	PUNCT
ejpam-5011	246	6	r	r	NOUN
ejpam-5011	246	7	,	,	PUNCT
ejpam-5011	246	8	λ	λ	X
ejpam-5011	246	9	=	=	SYM
ejpam-5011	246	10	k	k	X
ejpam-5011	246	11	∑	∑	PUNCT
ejpam-5011	246	12	l=0	l=0	PROPN
ejpam-5011	246	13	(	(	PUNCT
ejpam-5011	246	14	k	k	NOUN
ejpam-5011	246	15	l	l	NOUN
ejpam-5011	246	16	)	)	PUNCT
ejpam-5011	246	17	(	(	PUNCT
ejpam-5011	246	18	−1)k−l(l	−1)k−l(l	ADV
ejpam-5011	246	19	+	+	X
ejpam-5011	246	20	r)n	r)n	ADJ
ejpam-5011	246	21	,	,	PUNCT
ejpam-5011	246	22	λ	λ	INTJ
ejpam-5011	246	23	,	,	PUNCT
ejpam-5011	246	24	(	(	PUNCT
ejpam-5011	246	25	n	n	CCONJ
ejpam-5011	246	26	≥	≥	NOUN
ejpam-5011	246	27	k	k	NOUN
ejpam-5011	246	28	)	)	PUNCT
ejpam-5011	246	29	.	.	PUNCT
ejpam-5011	247	1	(	(	PUNCT
ejpam-5011	247	2	33	33	NUM
ejpam-5011	247	3	)	)	PUNCT
ejpam-5011	247	4	theorem	theorem	NOUN
ejpam-5011	247	5	5	5	NUM
ejpam-5011	247	6	.	.	PUNCT
ejpam-5011	247	7	for	for	ADP
ejpam-5011	247	8	n	n	PRON
ejpam-5011	247	9	,	,	PUNCT
ejpam-5011	247	10	r	r	NOUN
ejpam-5011	247	11	≥	≥	NOUN
ejpam-5011	247	12	0	0	NUM
ejpam-5011	247	13	,	,	PUNCT
ejpam-5011	247	14	we	we	PRON
ejpam-5011	247	15	have	have	VERB
ejpam-5011	247	16	k	k	NOUN
ejpam-5011	247	17	!	!	PUNCT
ejpam-5011	247	18	{	{	PUNCT
ejpam-5011	248	1	n+	n+	ADP
ejpam-5011	248	2	r	r	NOUN
ejpam-5011	248	3	k+	k+	NOUN
ejpam-5011	248	4	r	r	NOUN
ejpam-5011	248	5	}	}	PUNCT
ejpam-5011	248	6	r	r	NOUN
ejpam-5011	248	7	,	,	PUNCT
ejpam-5011	248	8	λ	λ	X
ejpam-5011	248	9	=	=	SYM
ejpam-5011	248	10	k	k	X
ejpam-5011	248	11	∑	∑	PUNCT
ejpam-5011	248	12	l=0	l=0	PROPN
ejpam-5011	248	13	(	(	PUNCT
ejpam-5011	248	14	k	k	NOUN
ejpam-5011	248	15	l	l	NOUN
ejpam-5011	248	16	)	)	PUNCT
ejpam-5011	248	17	(	(	PUNCT
ejpam-5011	248	18	−1)k−l(l	−1)k−l(l	ADV
ejpam-5011	248	19	+	+	X
ejpam-5011	248	20	r)n	r)n	ADJ
ejpam-5011	248	21	,	,	PUNCT
ejpam-5011	248	22	λ	λ	PROPN
ejpam-5011	248	23	⇐	⇐	ADJ
ejpam-5011	248	24	⇒	⇒	PROPN
ejpam-5011	248	25	(	(	PUNCT
ejpam-5011	248	26	k+	k+	NOUN
ejpam-5011	248	27	r)n	r)n	NOUN
ejpam-5011	248	28	,	,	PUNCT
ejpam-5011	248	29	λ	λ	PROPN
ejpam-5011	248	30	=	=	SYM
ejpam-5011	248	31	k	k	X
ejpam-5011	248	32	∑	∑	PUNCT
ejpam-5011	248	33	l=0	l=0	PROPN
ejpam-5011	248	34	(	(	PUNCT
ejpam-5011	248	35	k	k	NOUN
ejpam-5011	248	36	l	l	NOUN
ejpam-5011	248	37	)	)	PUNCT
ejpam-5011	249	1	l	l	NOUN
ejpam-5011	249	2	!	!	PUNCT
ejpam-5011	249	3	{	{	PUNCT
ejpam-5011	250	1	n+	n+	INTJ
ejpam-5011	250	2	r	r	NOUN
ejpam-5011	250	3	l	l	NOUN
ejpam-5011	251	1	+	+	CCONJ
ejpam-5011	251	2	r	r	NOUN
ejpam-5011	251	3	}	}	PUNCT
ejpam-5011	251	4	r	r	NOUN
ejpam-5011	251	5	,	,	PUNCT
ejpam-5011	251	6	λ	λ	PROPN
ejpam-5011	251	7	.	.	PUNCT
ejpam-5011	252	1	references	reference	NOUN
ejpam-5011	252	2	9	9	NUM
ejpam-5011	252	3	proof	proof	NOUN
ejpam-5011	252	4	.	.	PUNCT
ejpam-5011	253	1	this	this	PRON
ejpam-5011	253	2	can	can	AUX
ejpam-5011	253	3	be	be	AUX
ejpam-5011	253	4	shown	show	VERB
ejpam-5011	253	5	just	just	ADV
ejpam-5011	253	6	as	as	ADP
ejpam-5011	253	7	the	the	DET
ejpam-5011	253	8	proof	proof	NOUN
ejpam-5011	253	9	of	of	ADP
ejpam-5011	253	10	theorem	theorem	ADJ
ejpam-5011	253	11	2.1	2.1	NUM
ejpam-5011	253	12	.	.	PUNCT
ejpam-5011	254	1	theorem	theorem	VERB
ejpam-5011	254	2	6	6	NUM
ejpam-5011	254	3	.	.	PUNCT
ejpam-5011	254	4	for	for	ADP
ejpam-5011	254	5	n	n	CCONJ
ejpam-5011	254	6	,	,	PUNCT
ejpam-5011	254	7	m	m	PROPN
ejpam-5011	254	8	∈	∈	PROPN
ejpam-5011	255	1	n	n	CCONJ
ejpam-5011	255	2	,	,	PUNCT
ejpam-5011	255	3	we	we	PRON
ejpam-5011	255	4	have	have	VERB
ejpam-5011	255	5	m	m	PROPN
ejpam-5011	255	6	∑	∑	PROPN
ejpam-5011	255	7	k=1	k=1	X
ejpam-5011	255	8	(	(	PUNCT
ejpam-5011	255	9	k+	k+	NOUN
ejpam-5011	255	10	r)n	r)n	NOUN
ejpam-5011	255	11	,	,	PUNCT
ejpam-5011	255	12	λ	λ	PROPN
ejpam-5011	255	13	hk	hk	NOUN
ejpam-5011	256	1	=	=	PUNCT
ejpam-5011	256	2	m	m	VERB
ejpam-5011	256	3	∑	∑	VERB
ejpam-5011	256	4	j=1	j=1	PROPN
ejpam-5011	256	5	j	j	PROPN
ejpam-5011	256	6	!	!	PUNCT
ejpam-5011	256	7	{	{	PUNCT
ejpam-5011	257	1	n+	n+	PRON
ejpam-5011	257	2	r	r	NOUN
ejpam-5011	257	3	j+	j+	NUM
ejpam-5011	257	4	r	r	NOUN
ejpam-5011	257	5	}	}	PUNCT
ejpam-5011	257	6	r	r	NOUN
ejpam-5011	257	7	,	,	PUNCT
ejpam-5011	257	8	λ	λ	X
ejpam-5011	257	9	(	(	PUNCT
ejpam-5011	257	10	m+1	m+1	PROPN
ejpam-5011	257	11	j+1	j+1	NUM
ejpam-5011	257	12	)	)	PUNCT
ejpam-5011	257	13	(	(	PUNCT
ejpam-5011	257	14	hm+1	hm+1	X
ejpam-5011	257	15	−	−	PROPN
ejpam-5011	257	16	1	1	NUM
ejpam-5011	257	17	j+1	j+1	NUM
ejpam-5011	257	18	)	)	PUNCT
ejpam-5011	257	19	,	,	PUNCT
ejpam-5011	257	20	and	and	CCONJ
ejpam-5011	257	21	m	m	VERB
ejpam-5011	257	22	∑	∑	NOUN
ejpam-5011	257	23	k=1	k=1	X
ejpam-5011	257	24	[	[	PUNCT
ejpam-5011	257	25	m	m	VERB
ejpam-5011	257	26	k	k	X
ejpam-5011	257	27	]	]	X
ejpam-5011	257	28	(	(	PUNCT
ejpam-5011	257	29	k+	k+	X
ejpam-5011	257	30	r)n	r)n	NOUN
ejpam-5011	257	31	,	,	PUNCT
ejpam-5011	257	32	λ	λ	X
ejpam-5011	257	33	=	=	VERB
ejpam-5011	257	34	m	m	VERB
ejpam-5011	257	35	∑	∑	PROPN
ejpam-5011	257	36	j=1	j=1	PROPN
ejpam-5011	257	37	j	j	PROPN
ejpam-5011	257	38	!	!	PUNCT
ejpam-5011	257	39	{	{	PUNCT
ejpam-5011	258	1	n+	n+	PRON
ejpam-5011	258	2	r	r	NOUN
ejpam-5011	258	3	j+	j+	NUM
ejpam-5011	258	4	r	r	NOUN
ejpam-5011	258	5	}	}	PUNCT
ejpam-5011	258	6	r	r	NOUN
ejpam-5011	258	7	,	,	PUNCT
ejpam-5011	258	8	λ	λ	X
ejpam-5011	258	9	[	[	PUNCT
ejpam-5011	258	10	m+1	m+1	PROPN
ejpam-5011	258	11	j+1	j+1	PROPN
ejpam-5011	258	12	]	]	PUNCT
ejpam-5011	258	13	1	1	NUM
ejpam-5011	258	14	.	.	PUNCT
ejpam-5011	259	1	proof	proof	NOUN
ejpam-5011	259	2	.	.	PUNCT
ejpam-5011	260	1	by	by	ADP
ejpam-5011	260	2	using	use	VERB
ejpam-5011	260	3	(	(	PUNCT
ejpam-5011	260	4	33	33	NUM
ejpam-5011	260	5	)	)	PUNCT
ejpam-5011	260	6	,	,	PUNCT
ejpam-5011	260	7	this	this	PRON
ejpam-5011	260	8	can	can	AUX
ejpam-5011	260	9	be	be	AUX
ejpam-5011	260	10	proved	prove	VERB
ejpam-5011	260	11	just	just	ADV
ejpam-5011	260	12	as	as	SCONJ
ejpam-5011	260	13	the	the	DET
ejpam-5011	260	14	proofs	proof	NOUN
ejpam-5011	260	15	of	of	ADP
ejpam-5011	260	16	theorem	theorem	ADJ
ejpam-5011	260	17	2.2	2.2	NUM
ejpam-5011	260	18	and	and	CCONJ
ejpam-5011	260	19	theorem	theorem	VERB
ejpam-5011	260	20	2.4	2.4	NUM
ejpam-5011	260	21	.	.	PUNCT
ejpam-5011	261	1	the	the	DET
ejpam-5011	261	2	details	detail	NOUN
ejpam-5011	261	3	are	be	AUX
ejpam-5011	261	4	left	leave	VERB
ejpam-5011	261	5	to	to	ADP
ejpam-5011	261	6	the	the	DET
ejpam-5011	261	7	reader	reader	NOUN
ejpam-5011	261	8	.	.	PUNCT
ejpam-5011	262	1	3	3	X
ejpam-5011	262	2	.	.	X
ejpam-5011	262	3	conclusion	conclusion	VERB
ejpam-5011	262	4	various	various	ADJ
ejpam-5011	262	5	degenerate	degenerate	ADJ
ejpam-5011	262	6	stirling	stirling	NOUN
ejpam-5011	262	7	numbers	number	NOUN
ejpam-5011	262	8	of	of	ADP
ejpam-5011	262	9	both	both	DET
ejpam-5011	262	10	kinds	kind	NOUN
ejpam-5011	262	11	appear	appear	VERB
ejpam-5011	262	12	very	very	ADV
ejpam-5011	262	13	frequently	frequently	ADV
ejpam-5011	262	14	when	when	SCONJ
ejpam-5011	262	15	we	we	PRON
ejpam-5011	262	16	study	study	VERB
ejpam-5011	262	17	degenerate	degenerate	ADJ
ejpam-5011	262	18	versions	version	NOUN
ejpam-5011	262	19	of	of	ADP
ejpam-5011	262	20	many	many	ADJ
ejpam-5011	262	21	special	special	ADJ
ejpam-5011	262	22	numbers	number	NOUN
ejpam-5011	262	23	and	and	CCONJ
ejpam-5011	262	24	polynomials	polynomial	NOUN
ejpam-5011	262	25	.	.	PUNCT
ejpam-5011	263	1	in	in	ADP
ejpam-5011	263	2	this	this	DET
ejpam-5011	263	3	paper	paper	NOUN
ejpam-5011	263	4	,	,	PUNCT
ejpam-5011	263	5	we	we	PRON
ejpam-5011	263	6	investigated	investigate	VERB
ejpam-5011	263	7	several	several	ADJ
ejpam-5011	263	8	degenerate	degenerate	ADJ
ejpam-5011	263	9	stirling	stirling	NOUN
ejpam-5011	263	10	numbers	number	NOUN
ejpam-5011	263	11	like	like	ADP
ejpam-5011	263	12	the	the	DET
ejpam-5011	263	13	unsigned	unsigned	ADJ
ejpam-5011	263	14	degenerate	degenerate	ADJ
ejpam-5011	263	15	stirling	stirling	NOUN
ejpam-5011	263	16	numbers	number	NOUN
ejpam-5011	263	17	of	of	ADP
ejpam-5011	263	18	the	the	DET
ejpam-5011	263	19	first	first	ADJ
ejpam-5011	263	20	kind	kind	NOUN
ejpam-5011	263	21	,	,	PUNCT
ejpam-5011	263	22	the	the	DET
ejpam-5011	263	23	degenerate	degenerate	ADJ
ejpam-5011	263	24	stirling	stirling	NOUN
ejpam-5011	263	25	numbers	number	NOUN
ejpam-5011	263	26	of	of	ADP
ejpam-5011	263	27	the	the	DET
ejpam-5011	263	28	second	second	ADJ
ejpam-5011	263	29	kind	kind	NOUN
ejpam-5011	263	30	,	,	PUNCT
ejpam-5011	263	31	the	the	DET
ejpam-5011	263	32	unsigned	unsigned	ADJ
ejpam-5011	263	33	degenerate	degenerate	ADJ
ejpam-5011	263	34	r	r	NOUN
ejpam-5011	263	35	-	-	PUNCT
ejpam-5011	263	36	stirling	stirling	NOUN
ejpam-5011	263	37	numbers	number	NOUN
ejpam-5011	263	38	of	of	ADP
ejpam-5011	263	39	the	the	DET
ejpam-5011	263	40	first	first	ADJ
ejpam-5011	263	41	kind	kind	NOUN
ejpam-5011	263	42	and	and	CCONJ
ejpam-5011	263	43	the	the	DET
ejpam-5011	263	44	degenerate	degenerate	ADJ
ejpam-5011	263	45	r	r	NOUN
ejpam-5011	263	46	-	-	PUNCT
ejpam-5011	263	47	stirling	stirling	NOUN
ejpam-5011	263	48	numbers	number	NOUN
ejpam-5011	263	49	of	of	ADP
ejpam-5011	263	50	the	the	DET
ejpam-5011	263	51	second	second	ADJ
ejpam-5011	263	52	kind	kind	NOUN
ejpam-5011	263	53	.	.	PUNCT
ejpam-5011	264	1	we	we	PRON
ejpam-5011	264	2	found	find	VERB
ejpam-5011	264	3	some	some	DET
ejpam-5011	264	4	identities	identity	NOUN
ejpam-5011	264	5	,	,	PUNCT
ejpam-5011	264	6	explicit	explicit	ADJ
ejpam-5011	264	7	expressions	expression	NOUN
ejpam-5011	264	8	and	and	CCONJ
ejpam-5011	264	9	some	some	DET
ejpam-5011	264	10	equivalent	equivalent	ADJ
ejpam-5011	264	11	relations	relation	NOUN
ejpam-5011	264	12	among	among	ADP
ejpam-5011	264	13	them	they	PRON
ejpam-5011	264	14	.	.	PUNCT
ejpam-5011	265	1	it	it	PRON
ejpam-5011	265	2	is	be	AUX
ejpam-5011	265	3	one	one	NUM
ejpam-5011	265	4	of	of	ADP
ejpam-5011	265	5	our	our	PRON
ejpam-5011	265	6	future	future	ADJ
ejpam-5011	265	7	projects	project	NOUN
ejpam-5011	265	8	to	to	PART
ejpam-5011	265	9	continue	continue	VERB
ejpam-5011	265	10	to	to	PART
ejpam-5011	265	11	explore	explore	VERB
ejpam-5011	265	12	degenerate	degenerate	ADJ
ejpam-5011	265	13	versions	version	NOUN
ejpam-5011	265	14	of	of	ADP
ejpam-5011	265	15	some	some	DET
ejpam-5011	265	16	special	special	ADJ
ejpam-5011	265	17	numbers	number	NOUN
ejpam-5011	265	18	and	and	CCONJ
ejpam-5011	265	19	polynomials	polynomial	NOUN
ejpam-5011	265	20	and	and	CCONJ
ejpam-5011	265	21	their	their	PRON
ejpam-5011	265	22	applications	application	NOUN
ejpam-5011	265	23	to	to	ADP
ejpam-5011	265	24	statistics	statistic	NOUN
ejpam-5011	265	25	,	,	PUNCT
ejpam-5011	265	26	physics	physics	NOUN
ejpam-5011	265	27	,	,	PUNCT
ejpam-5011	265	28	science	science	NOUN
ejpam-5011	265	29	,	,	PUNCT
ejpam-5011	265	30	engineering	engineering	NOUN
ejpam-5011	265	31	,	,	PUNCT
ejpam-5011	265	32	and	and	CCONJ
ejpam-5011	265	33	social	social	ADJ
ejpam-5011	265	34	sciences	science	NOUN
ejpam-5011	265	35	as	as	ADV
ejpam-5011	265	36	well	well	ADV
ejpam-5011	265	37	as	as	ADP
ejpam-5011	265	38	to	to	ADP
ejpam-5011	265	39	mathematics	mathematic	NOUN
ejpam-5011	265	40	.	.	PUNCT
ejpam-5011	266	1	references	reference	NOUN
ejpam-5011	266	2	[	[	X
ejpam-5011	266	3	1	1	X
ejpam-5011	266	4	]	]	X
ejpam-5011	266	5	ms	ms	ADJ
ejpam-5011	266	6	aydin	aydin	PROPN
ejpam-5011	266	7	,	,	PUNCT
ejpam-5011	266	8	m	m	VERB
ejpam-5011	266	9	acikgoz	acikgoz	ADJ
ejpam-5011	266	10	,	,	PUNCT
ejpam-5011	266	11	and	and	CCONJ
ejpam-5011	266	12	s	s	VERB
ejpam-5011	266	13	araci	araci	NOUN
ejpam-5011	266	14	.	.	PUNCT
ejpam-5011	267	1	a	a	DET
ejpam-5011	267	2	new	new	ADJ
ejpam-5011	267	3	construction	construction	NOUN
ejpam-5011	267	4	on	on	ADP
ejpam-5011	267	5	the	the	DET
ejpam-5011	267	6	degenerate	degenerate	ADJ
ejpam-5011	267	7	hurwitz	hurwitz	PROPN
ejpam-5011	267	8	-	-	PUNCT
ejpam-5011	267	9	zeta	zeta	PROPN
ejpam-5011	267	10	function	function	NOUN
ejpam-5011	267	11	associated	associate	VERB
ejpam-5011	267	12	with	with	ADP
ejpam-5011	267	13	certain	certain	ADJ
ejpam-5011	267	14	applications	application	NOUN
ejpam-5011	267	15	.	.	PUNCT
ejpam-5011	268	1	in	in	ADP
ejpam-5011	268	2	proceedings	proceeding	NOUN
ejpam-5011	268	3	of	of	ADP
ejpam-5011	268	4	the	the	DET
ejpam-5011	268	5	jangjeon	jangjeon	PROPN
ejpam-5011	268	6	mathematical	mathematical	PROPN
ejpam-5011	268	7	society	society	NOUN
ejpam-5011	268	8	,	,	PUNCT
ejpam-5011	268	9	volume	volume	NOUN
ejpam-5011	268	10	25	25	NUM
ejpam-5011	268	11	,	,	PUNCT
ejpam-5011	268	12	pages	page	NOUN
ejpam-5011	268	13	195–203	195–203	NUM
ejpam-5011	268	14	,	,	PUNCT
ejpam-5011	268	15	2022	2022	NUM
ejpam-5011	268	16	.	.	PUNCT
ejpam-5011	269	1	[	[	X
ejpam-5011	269	2	2	2	NUM
ejpam-5011	269	3	]	]	PUNCT
ejpam-5011	269	4	khadidja	khadidja	NOUN
ejpam-5011	269	5	boubellouta	boubellouta	PROPN
ejpam-5011	269	6	,	,	PUNCT
ejpam-5011	269	7	ali	ali	PROPN
ejpam-5011	269	8	boussayoud	boussayoud	PROPN
ejpam-5011	269	9	,	,	PUNCT
ejpam-5011	269	10	serkan	serkan	ADJ
ejpam-5011	269	11	araci	araci	NOUN
ejpam-5011	269	12	,	,	PUNCT
ejpam-5011	269	13	and	and	CCONJ
ejpam-5011	269	14	mohamed	mohamed	PROPN
ejpam-5011	269	15	kerada	kerada	PROPN
ejpam-5011	269	16	.	.	PUNCT
ejpam-5011	270	1	some	some	DET
ejpam-5011	270	2	theorems	theorem	NOUN
ejpam-5011	270	3	on	on	ADP
ejpam-5011	270	4	generating	generating	NOUN
ejpam-5011	270	5	functions	function	NOUN
ejpam-5011	270	6	and	and	CCONJ
ejpam-5011	270	7	their	their	PRON
ejpam-5011	270	8	applications	application	NOUN
ejpam-5011	270	9	.	.	PUNCT
ejpam-5011	271	1	advanced	advanced	ADJ
ejpam-5011	271	2	studies	study	NOUN
ejpam-5011	271	3	in	in	ADP
ejpam-5011	271	4	contemporary	contemporary	ADJ
ejpam-5011	271	5	mathematics	mathematic	NOUN
ejpam-5011	271	6	,	,	PUNCT
ejpam-5011	271	7	30(3):307–324	30(3):307–324	NUM
ejpam-5011	271	8	,	,	PUNCT
ejpam-5011	271	9	2020	2020	NUM
ejpam-5011	271	10	.	.	PUNCT
ejpam-5011	272	1	[	[	X
ejpam-5011	272	2	3	3	X
ejpam-5011	272	3	]	]	X
ejpam-5011	272	4	khristo	khristo	NOUN
ejpam-5011	272	5	n	n	PRON
ejpam-5011	272	6	boyadzhiev	boyadzhiev	NOUN
ejpam-5011	272	7	.	.	PUNCT
ejpam-5011	273	1	power	power	NOUN
ejpam-5011	273	2	sum	sum	NOUN
ejpam-5011	273	3	identities	identity	NOUN
ejpam-5011	273	4	with	with	ADP
ejpam-5011	273	5	generalized	generalized	ADJ
ejpam-5011	273	6	stirling	stirling	NOUN
ejpam-5011	273	7	numbers	number	NOUN
ejpam-5011	273	8	.	.	PUNCT
ejpam-5011	274	1	arxiv	arxiv	PROPN
ejpam-5011	274	2	preprint	preprint	PROPN
ejpam-5011	274	3	arxiv:0909.1852	arxiv:0909.1852	PROPN
ejpam-5011	274	4	,	,	PUNCT
ejpam-5011	274	5	2009	2009	NUM
ejpam-5011	274	6	.	.	PUNCT
ejpam-5011	275	1	[	[	X
ejpam-5011	275	2	4	4	NUM
ejpam-5011	275	3	]	]	X
ejpam-5011	275	4	paul	paul	PROPN
ejpam-5011	275	5	l	l	PROPN
ejpam-5011	275	6	butzer	butzer	NOUN
ejpam-5011	275	7	,	,	PUNCT
ejpam-5011	275	8	anatoly	anatoly	PROPN
ejpam-5011	275	9	a	a	DET
ejpam-5011	275	10	kilbas	kilbas	PROPN
ejpam-5011	275	11	,	,	PUNCT
ejpam-5011	275	12	and	and	CCONJ
ejpam-5011	275	13	juan	juan	PROPN
ejpam-5011	275	14	j	j	PROPN
ejpam-5011	275	15	trujillo	trujillo	PROPN
ejpam-5011	275	16	.	.	PUNCT
ejpam-5011	276	1	stirling	stirling	NOUN
ejpam-5011	276	2	functions	function	NOUN
ejpam-5011	276	3	of	of	ADP
ejpam-5011	276	4	the	the	DET
ejpam-5011	276	5	second	second	ADJ
ejpam-5011	276	6	kind	kind	NOUN
ejpam-5011	276	7	in	in	ADP
ejpam-5011	276	8	the	the	DET
ejpam-5011	276	9	setting	setting	NOUN
ejpam-5011	276	10	of	of	ADP
ejpam-5011	276	11	difference	difference	NOUN
ejpam-5011	276	12	and	and	CCONJ
ejpam-5011	276	13	fractional	fractional	ADJ
ejpam-5011	276	14	calculus	calculus	NOUN
ejpam-5011	276	15	.	.	PUNCT
ejpam-5011	276	16	2003	2003	NUM
ejpam-5011	276	17	.	.	PUNCT
ejpam-5011	277	1	[	[	X
ejpam-5011	277	2	5	5	NUM
ejpam-5011	277	3	]	]	SYM
ejpam-5011	277	4	l	l	NOUN
ejpam-5011	277	5	catlitz	catlitz	PROPN
ejpam-5011	277	6	.	.	PUNCT
ejpam-5011	278	1	degenerate	degenerate	ADJ
ejpam-5011	278	2	stirling	stirling	PROPN
ejpam-5011	278	3	,	,	PUNCT
ejpam-5011	278	4	bernoulli	bernoulli	PROPN
ejpam-5011	278	5	and	and	CCONJ
ejpam-5011	278	6	eulerian	eulerian	ADJ
ejpam-5011	278	7	numbers	number	NOUN
ejpam-5011	278	8	.	.	PUNCT
ejpam-5011	279	1	util	util	NOUN
ejpam-5011	279	2	.	.	PUNCT
ejpam-5011	280	1	math	math	PROPN
ejpam-5011	280	2	,	,	PUNCT
ejpam-5011	280	3	15:51–88	15:51–88	NUM
ejpam-5011	280	4	,	,	PUNCT
ejpam-5011	280	5	1979	1979	NUM
ejpam-5011	280	6	.	.	PUNCT
ejpam-5011	281	1	[	[	X
ejpam-5011	281	2	6	6	NUM
ejpam-5011	281	3	]	]	SYM
ejpam-5011	281	4	louis	louis	NOUN
ejpam-5011	281	5	comtet	comtet	NOUN
ejpam-5011	281	6	.	.	PUNCT
ejpam-5011	282	1	advanced	advanced	ADJ
ejpam-5011	282	2	combinatorics	combinatoric	NOUN
ejpam-5011	282	3	:	:	PUNCT
ejpam-5011	282	4	the	the	DET
ejpam-5011	282	5	art	art	NOUN
ejpam-5011	282	6	of	of	ADP
ejpam-5011	282	7	finite	finite	NOUN
ejpam-5011	282	8	and	and	CCONJ
ejpam-5011	282	9	infinite	infinite	ADJ
ejpam-5011	282	10	expansions	expansion	NOUN
ejpam-5011	282	11	.	.	PUNCT
ejpam-5011	283	1	springer	springer	NOUN
ejpam-5011	283	2	science	science	PROPN
ejpam-5011	283	3	&	&	CCONJ
ejpam-5011	283	4	business	business	NOUN
ejpam-5011	283	5	media	medium	NOUN
ejpam-5011	283	6	,	,	PUNCT
ejpam-5011	283	7	1974	1974	NUM
ejpam-5011	283	8	.	.	PUNCT
ejpam-5011	284	1	references	reference	NOUN
ejpam-5011	284	2	10	10	NUM
ejpam-5011	284	3	[	[	X
ejpam-5011	284	4	7	7	NUM
ejpam-5011	284	5	]	]	X
ejpam-5011	284	6	ronald	ronald	PROPN
ejpam-5011	284	7	l	l	PROPN
ejpam-5011	284	8	graham	graham	PROPN
ejpam-5011	284	9	,	,	PUNCT
ejpam-5011	284	10	donald	donald	PROPN
ejpam-5011	284	11	e	e	PROPN
ejpam-5011	284	12	knuth	knuth	PROPN
ejpam-5011	284	13	,	,	PUNCT
ejpam-5011	284	14	oren	oren	PROPN
ejpam-5011	284	15	patashnik	patashnik	X
ejpam-5011	284	16	,	,	PUNCT
ejpam-5011	284	17	and	and	CCONJ
ejpam-5011	284	18	stanley	stanley	PROPN
ejpam-5011	284	19	liu	liu	PROPN
ejpam-5011	284	20	.	.	PUNCT
ejpam-5011	285	1	concrete	concrete	ADJ
ejpam-5011	285	2	mathematics	mathematic	NOUN
ejpam-5011	285	3	:	:	PUNCT
ejpam-5011	285	4	a	a	DET
ejpam-5011	285	5	foundation	foundation	NOUN
ejpam-5011	285	6	for	for	ADP
ejpam-5011	285	7	computer	computer	NOUN
ejpam-5011	285	8	science	science	NOUN
ejpam-5011	285	9	.	.	PUNCT
ejpam-5011	286	1	computers	computer	NOUN
ejpam-5011	286	2	in	in	ADP
ejpam-5011	286	3	physics	physics	PROPN
ejpam-5011	286	4	,	,	PUNCT
ejpam-5011	286	5	3(5):106–107	3(5):106–107	PROPN
ejpam-5011	286	6	,	,	PUNCT
ejpam-5011	286	7	1989	1989	NUM
ejpam-5011	286	8	.	.	PUNCT
ejpam-5011	287	1	[	[	X
ejpam-5011	287	2	8	8	NUM
ejpam-5011	287	3	]	]	PUNCT
ejpam-5011	287	4	damla	damla	NOUN
ejpam-5011	287	5	gun	gun	NOUN
ejpam-5011	287	6	and	and	CCONJ
ejpam-5011	287	7	yilmaz	yilmaz	PROPN
ejpam-5011	287	8	simsek	simsek	NOUN
ejpam-5011	287	9	.	.	PUNCT
ejpam-5011	288	1	combinatorial	combinatorial	ADJ
ejpam-5011	288	2	sums	sum	NOUN
ejpam-5011	288	3	involving	involve	VERB
ejpam-5011	288	4	stirling	stirling	NOUN
ejpam-5011	288	5	,	,	PUNCT
ejpam-5011	288	6	fubini	fubini	NOUN
ejpam-5011	288	7	,	,	PUNCT
ejpam-5011	288	8	bernoulli	bernoulli	NOUN
ejpam-5011	288	9	numbers	number	NOUN
ejpam-5011	288	10	and	and	CCONJ
ejpam-5011	288	11	approximate	approximate	ADJ
ejpam-5011	288	12	values	value	NOUN
ejpam-5011	288	13	of	of	ADP
ejpam-5011	288	14	catalan	catalan	NOUN
ejpam-5011	288	15	numbers	number	NOUN
ejpam-5011	288	16	.	.	PUNCT
ejpam-5011	289	1	advanced	advanced	ADJ
ejpam-5011	289	2	studies	study	NOUN
ejpam-5011	289	3	in	in	ADP
ejpam-5011	289	4	contemporary	contemporary	ADJ
ejpam-5011	289	5	mathematics	mathematic	NOUN
ejpam-5011	289	6	,	,	PUNCT
ejpam-5011	289	7	30(4):505–515	30(4):505–515	NUM
ejpam-5011	289	8	,	,	PUNCT
ejpam-5011	289	9	2020	2020	NUM
ejpam-5011	289	10	.	.	PUNCT
ejpam-5011	290	1	[	[	X
ejpam-5011	290	2	9	9	NUM
ejpam-5011	290	3	]	]	PUNCT
ejpam-5011	290	4	dae	dae	NOUN
ejpam-5011	290	5	san	san	PROPN
ejpam-5011	290	6	kim	kim	PROPN
ejpam-5011	290	7	et	et	PROPN
ejpam-5011	290	8	al	al	PROPN
ejpam-5011	290	9	.	.	PUNCT
ejpam-5011	291	1	stirling	stirling	NOUN
ejpam-5011	291	2	numbers	number	NOUN
ejpam-5011	291	3	associated	associate	VERB
ejpam-5011	291	4	with	with	ADP
ejpam-5011	291	5	sequences	sequence	NOUN
ejpam-5011	291	6	of	of	ADP
ejpam-5011	291	7	polynomials	polynomial	NOUN
ejpam-5011	291	8	.	.	PUNCT
ejpam-5011	292	1	arxiv	arxiv	PROPN
ejpam-5011	292	2	preprint	preprint	VERB
ejpam-5011	292	3	arxiv:2202.11306	arxiv:2202.11306	PROPN
ejpam-5011	292	4	,	,	PUNCT
ejpam-5011	292	5	2022	2022	NUM
ejpam-5011	292	6	.	.	PUNCT
ejpam-5011	293	1	[	[	X
ejpam-5011	293	2	10	10	NUM
ejpam-5011	293	3	]	]	X
ejpam-5011	293	4	ds	ds	PROPN
ejpam-5011	293	5	kim	kim	PROPN
ejpam-5011	293	6	and	and	CCONJ
ejpam-5011	293	7	t	t	PROPN
ejpam-5011	293	8	kim	kim	PROPN
ejpam-5011	293	9	.	.	PUNCT
ejpam-5011	294	1	a	a	DET
ejpam-5011	294	2	note	note	NOUN
ejpam-5011	294	3	on	on	ADP
ejpam-5011	294	4	a	a	DET
ejpam-5011	294	5	new	new	ADJ
ejpam-5011	294	6	type	type	NOUN
ejpam-5011	294	7	of	of	ADP
ejpam-5011	294	8	degenerate	degenerate	ADJ
ejpam-5011	294	9	bernoulli	bernoulli	NOUN
ejpam-5011	294	10	numbers	number	NOUN
ejpam-5011	294	11	.	.	PUNCT
ejpam-5011	295	1	russian	russian	ADJ
ejpam-5011	295	2	journal	journal	PROPN
ejpam-5011	295	3	of	of	ADP
ejpam-5011	295	4	mathematical	mathematical	ADJ
ejpam-5011	295	5	physics	physics	NOUN
ejpam-5011	295	6	,	,	PUNCT
ejpam-5011	295	7	27:227–235	27:227–235	NUM
ejpam-5011	295	8	,	,	PUNCT
ejpam-5011	295	9	2020	2020	NUM
ejpam-5011	295	10	.	.	PUNCT
ejpam-5011	296	1	[	[	X
ejpam-5011	296	2	11	11	NUM
ejpam-5011	296	3	]	]	X
ejpam-5011	296	4	ds	ds	PROPN
ejpam-5011	296	5	kim	kim	PROPN
ejpam-5011	296	6	and	and	CCONJ
ejpam-5011	296	7	tk	tk	PROPN
ejpam-5011	296	8	kim	kim	PROPN
ejpam-5011	296	9	.	.	PUNCT
ejpam-5011	297	1	normal	normal	ADJ
ejpam-5011	297	2	ordering	ordering	NOUN
ejpam-5011	297	3	associated	associate	VERB
ejpam-5011	297	4	with	with	ADP
ejpam-5011	297	5	-	-	PUNCT
ejpam-5011	297	6	whitney	whitney	NOUN
ejpam-5011	297	7	numbers	number	NOUN
ejpam-5011	297	8	of	of	ADP
ejpam-5011	297	9	the	the	DET
ejpam-5011	297	10	first	first	ADJ
ejpam-5011	297	11	kind	kind	NOUN
ejpam-5011	297	12	in	in	ADP
ejpam-5011	297	13	-	-	PUNCT
ejpam-5011	297	14	shift	shift	NOUN
ejpam-5011	297	15	algebra	algebra	NOUN
ejpam-5011	297	16	.	.	PUNCT
ejpam-5011	298	1	russian	russian	ADJ
ejpam-5011	298	2	journal	journal	PROPN
ejpam-5011	298	3	of	of	ADP
ejpam-5011	298	4	mathematical	mathematical	ADJ
ejpam-5011	298	5	physics	physics	NOUN
ejpam-5011	298	6	,	,	PUNCT
ejpam-5011	298	7	30(3):310–319	30(3):310–319	PROPN
ejpam-5011	298	8	,	,	PUNCT
ejpam-5011	298	9	2023	2023	NUM
ejpam-5011	298	10	.	.	PUNCT
ejpam-5011	299	1	[	[	X
ejpam-5011	299	2	12	12	NUM
ejpam-5011	299	3	]	]	PUNCT
ejpam-5011	299	4	taekyun	taekyun	VERB
ejpam-5011	299	5	kim	kim	PROPN
ejpam-5011	299	6	and	and	CCONJ
ejpam-5011	299	7	dae	dae	VERB
ejpam-5011	299	8	san	san	PROPN
ejpam-5011	299	9	kim	kim	PROPN
ejpam-5011	299	10	.	.	PUNCT
ejpam-5011	300	1	some	some	DET
ejpam-5011	300	2	identities	identity	NOUN
ejpam-5011	300	3	involving	involve	VERB
ejpam-5011	300	4	degenerate	degenerate	ADJ
ejpam-5011	300	5	r	r	NOUN
ejpam-5011	300	6	-	-	PUNCT
ejpam-5011	300	7	stirling	stirling	NOUN
ejpam-5011	300	8	numbers	number	NOUN
ejpam-5011	300	9	.	.	PUNCT
ejpam-5011	301	1	arxiv	arxiv	PROPN
ejpam-5011	301	2	preprint	preprint	VERB
ejpam-5011	301	3	arxiv:2202.08421	arxiv:2202.08421	NOUN
ejpam-5011	301	4	,	,	PUNCT
ejpam-5011	301	5	2022	2022	NUM
ejpam-5011	301	6	.	.	PUNCT
ejpam-5011	302	1	[	[	X
ejpam-5011	302	2	13	13	NUM
ejpam-5011	302	3	]	]	PUNCT
ejpam-5011	302	4	taekyun	taekyun	VERB
ejpam-5011	302	5	kim	kim	PROPN
ejpam-5011	302	6	and	and	CCONJ
ejpam-5011	302	7	dae	dae	VERB
ejpam-5011	302	8	san	san	PROPN
ejpam-5011	302	9	kim	kim	PROPN
ejpam-5011	302	10	.	.	PUNCT
ejpam-5011	303	1	some	some	DET
ejpam-5011	303	2	identities	identity	NOUN
ejpam-5011	303	3	on	on	ADP
ejpam-5011	303	4	degenerate	degenerate	ADJ
ejpam-5011	303	5	-	-	PUNCT
ejpam-5011	303	6	stirling	stirling	NOUN
ejpam-5011	303	7	numbers	number	NOUN
ejpam-5011	303	8	via	via	ADP
ejpam-5011	303	9	boson	boson	NOUN
ejpam-5011	303	10	operators	operator	NOUN
ejpam-5011	303	11	.	.	PUNCT
ejpam-5011	304	1	russian	russian	ADJ
ejpam-5011	304	2	journal	journal	PROPN
ejpam-5011	304	3	of	of	ADP
ejpam-5011	304	4	mathematical	mathematical	ADJ
ejpam-5011	304	5	physics	physics	PROPN
ejpam-5011	304	6	,	,	PUNCT
ejpam-5011	304	7	29(4):508–517	29(4):508–517	PROPN
ejpam-5011	304	8	,	,	PUNCT
ejpam-5011	304	9	2022	2022	NUM
ejpam-5011	304	10	.	.	PUNCT
ejpam-5011	305	1	[	[	X
ejpam-5011	305	2	14	14	NUM
ejpam-5011	305	3	]	]	PUNCT
ejpam-5011	305	4	taekyun	taekyun	NOUN
ejpam-5011	305	5	kim	kim	PROPN
ejpam-5011	305	6	,	,	PUNCT
ejpam-5011	305	7	dae	dae	VERB
ejpam-5011	305	8	san	san	PROPN
ejpam-5011	305	9	kim	kim	PROPN
ejpam-5011	305	10	,	,	PUNCT
ejpam-5011	305	11	hyunseok	hyunseok	PROPN
ejpam-5011	305	12	lee	lee	PROPN
ejpam-5011	305	13	,	,	PUNCT
ejpam-5011	305	14	and	and	CCONJ
ejpam-5011	305	15	jin	jin	NOUN
ejpam-5011	305	16	-	-	PUNCT
ejpam-5011	305	17	woo	woo	NOUN
ejpam-5011	305	18	park	park	NOUN
ejpam-5011	305	19	.	.	PUNCT
ejpam-5011	306	1	a	a	DET
ejpam-5011	306	2	note	note	NOUN
ejpam-5011	306	3	on	on	ADP
ejpam-5011	306	4	degenerate	degenerate	ADJ
ejpam-5011	306	5	rstirling	rstirling	NOUN
ejpam-5011	306	6	numbers	number	NOUN
ejpam-5011	306	7	.	.	PUNCT
ejpam-5011	307	1	journal	journal	PROPN
ejpam-5011	307	2	of	of	ADP
ejpam-5011	307	3	inequalities	inequality	NOUN
ejpam-5011	307	4	and	and	CCONJ
ejpam-5011	307	5	applications	application	NOUN
ejpam-5011	307	6	,	,	PUNCT
ejpam-5011	307	7	2020:1–12	2020:1–12	NUM
ejpam-5011	307	8	,	,	PUNCT
ejpam-5011	307	9	2020	2020	NUM
ejpam-5011	307	10	.	.	PUNCT
ejpam-5011	308	1	[	[	X
ejpam-5011	308	2	15	15	NUM
ejpam-5011	308	3	]	]	AUX
ejpam-5011	308	4	taekyun	taekyun	NOUN
ejpam-5011	308	5	kim	kim	PROPN
ejpam-5011	308	6	and	and	CCONJ
ejpam-5011	308	7	dae	dae	VERB
ejpam-5011	308	8	san	san	PROPN
ejpam-5011	308	9	kim	kim	PROPN
ejpam-5011	308	10	.	.	PUNCT
ejpam-5011	309	1	combinatorial	combinatorial	ADJ
ejpam-5011	309	2	identities	identity	NOUN
ejpam-5011	309	3	involving	involve	VERB
ejpam-5011	309	4	degenerate	degenerate	ADJ
ejpam-5011	309	5	harmonic	harmonic	ADJ
ejpam-5011	309	6	and	and	CCONJ
ejpam-5011	309	7	hyperharmonic	hyperharmonic	ADJ
ejpam-5011	309	8	numbers	number	NOUN
ejpam-5011	309	9	.	.	PUNCT
ejpam-5011	310	1	advances	advance	NOUN
ejpam-5011	310	2	in	in	ADP
ejpam-5011	310	3	applied	apply	VERB
ejpam-5011	310	4	mathematics	mathematic	NOUN
ejpam-5011	310	5	,	,	PUNCT
ejpam-5011	310	6	148:102535	148:102535	NUM
ejpam-5011	310	7	,	,	PUNCT
ejpam-5011	310	8	2023	2023	NUM
ejpam-5011	310	9	.	.	PUNCT
ejpam-5011	311	1	[	[	X
ejpam-5011	311	2	16	16	NUM
ejpam-5011	311	3	]	]	X
ejpam-5011	311	4	tk	tk	PROPN
ejpam-5011	311	5	kim	kim	PROPN
ejpam-5011	311	6	and	and	CCONJ
ejpam-5011	311	7	dae	dae	VERB
ejpam-5011	311	8	san	san	PROPN
ejpam-5011	311	9	kim	kim	PROPN
ejpam-5011	311	10	.	.	PUNCT
ejpam-5011	312	1	some	some	DET
ejpam-5011	312	2	identities	identity	NOUN
ejpam-5011	312	3	involving	involve	VERB
ejpam-5011	312	4	degenerate	degenerate	ADJ
ejpam-5011	312	5	stirling	stirling	NOUN
ejpam-5011	312	6	numbers	number	NOUN
ejpam-5011	312	7	associated	associate	VERB
ejpam-5011	312	8	with	with	ADP
ejpam-5011	312	9	several	several	ADJ
ejpam-5011	312	10	degenerate	degenerate	ADJ
ejpam-5011	312	11	polynomials	polynomial	NOUN
ejpam-5011	312	12	and	and	CCONJ
ejpam-5011	312	13	numbers	number	NOUN
ejpam-5011	312	14	.	.	PUNCT
ejpam-5011	313	1	russian	russian	ADJ
ejpam-5011	313	2	journal	journal	PROPN
ejpam-5011	313	3	of	of	ADP
ejpam-5011	313	4	mathematical	mathematical	ADJ
ejpam-5011	313	5	physics	physics	NOUN
ejpam-5011	313	6	,	,	PUNCT
ejpam-5011	313	7	30(1):62–75	30(1):62–75	NUM
ejpam-5011	313	8	,	,	PUNCT
ejpam-5011	313	9	2023	2023	NUM
ejpam-5011	313	10	.	.	PUNCT
ejpam-5011	314	1	[	[	X
ejpam-5011	314	2	17	17	NUM
ejpam-5011	314	3	]	]	X
ejpam-5011	314	4	yilmaz	yilmaz	PROPN
ejpam-5011	314	5	simsek	simsek	NOUN
ejpam-5011	314	6	.	.	PUNCT
ejpam-5011	315	1	construction	construction	NOUN
ejpam-5011	315	2	of	of	ADP
ejpam-5011	315	3	generalized	generalized	ADJ
ejpam-5011	315	4	leibnitz	leibnitz	NOUN
ejpam-5011	315	5	type	type	NOUN
ejpam-5011	315	6	numbers	number	NOUN
ejpam-5011	315	7	and	and	CCONJ
ejpam-5011	315	8	their	their	PRON
ejpam-5011	315	9	properties	property	NOUN
ejpam-5011	315	10	.	.	PUNCT
ejpam-5011	316	1	advanced	advanced	ADJ
ejpam-5011	316	2	studies	study	NOUN
ejpam-5011	316	3	in	in	ADP
ejpam-5011	316	4	contemporary	contemporary	ADJ
ejpam-5011	316	5	mathematics	mathematic	NOUN
ejpam-5011	316	6	,	,	PUNCT
ejpam-5011	316	7	31(3):311–323	31(3):311–323	PROPN
ejpam-5011	316	8	,	,	PUNCT
ejpam-5011	316	9	2021	2021	NUM
ejpam-5011	316	10	.	.	PUNCT
ejpam-5011	317	1	[	[	X
ejpam-5011	317	2	18	18	NUM
ejpam-5011	317	3	]	]	X
ejpam-5011	317	4	michael	michael	PROPN
ejpam-5011	317	5	z	z	PROPN
ejpam-5011	317	6	spivey	spivey	PROPN
ejpam-5011	317	7	.	.	PUNCT
ejpam-5011	318	1	combinatorial	combinatorial	ADJ
ejpam-5011	318	2	sums	sum	NOUN
ejpam-5011	318	3	and	and	CCONJ
ejpam-5011	318	4	finite	finite	ADJ
ejpam-5011	318	5	differences	difference	NOUN
ejpam-5011	318	6	.	.	PUNCT
ejpam-5011	319	1	discrete	discrete	ADJ
ejpam-5011	319	2	mathematics	mathematic	NOUN
ejpam-5011	319	3	,	,	PUNCT
ejpam-5011	319	4	307(24):3130–3146	307(24):3130–3146	NUM
ejpam-5011	319	5	,	,	PUNCT
ejpam-5011	319	6	2007	2007	NUM
ejpam-5011	319	7	.	.	PUNCT