id	sid	tid	token	lemma	pos
ejpam-4641	1	1	european	european	PROPN
ejpam-4641	1	2	journal	journal	PROPN
ejpam-4641	1	3	of	of	ADP
ejpam-4641	1	4	pure	pure	ADJ
ejpam-4641	1	5	and	and	CCONJ
ejpam-4641	1	6	applied	apply	VERB
ejpam-4641	1	7	mathematics	mathematic	NOUN
ejpam-4641	1	8	vol	vol	NOUN
ejpam-4641	1	9	.	.	PUNCT
ejpam-4641	2	1	16	16	NUM
ejpam-4641	2	2	,	,	PUNCT
ejpam-4641	2	3	no	no	INTJ
ejpam-4641	2	4	.	.	NOUN
ejpam-4641	2	5	1	1	NUM
ejpam-4641	2	6	,	,	PUNCT
ejpam-4641	2	7	2023	2023	NUM
ejpam-4641	2	8	,	,	PUNCT
ejpam-4641	2	9	97	97	NUM
ejpam-4641	2	10	-	-	SYM
ejpam-4641	2	11	111	111	NUM
ejpam-4641	2	12	issn	issn	PROPN
ejpam-4641	2	13	1307	1307	NUM
ejpam-4641	2	14	-	-	SYM
ejpam-4641	2	15	5543	5543	NUM
ejpam-4641	2	16	–	–	PUNCT
ejpam-4641	2	17	ejpam.com	ejpam.com	X
ejpam-4641	2	18	published	publish	VERB
ejpam-4641	2	19	by	by	ADP
ejpam-4641	2	20	new	new	PROPN
ejpam-4641	2	21	york	york	PROPN
ejpam-4641	2	22	business	business	PROPN
ejpam-4641	2	23	global	global	ADJ
ejpam-4641	2	24	moment	moment	NOUN
ejpam-4641	2	25	generating	generate	VERB
ejpam-4641	2	26	function	function	NOUN
ejpam-4641	2	27	of	of	ADP
ejpam-4641	2	28	current	current	ADJ
ejpam-4641	2	29	records	record	NOUN
ejpam-4641	2	30	based	base	VERB
ejpam-4641	2	31	on	on	ADP
ejpam-4641	2	32	generalized	generalized	ADJ
ejpam-4641	2	33	exponential	exponential	ADJ
ejpam-4641	2	34	distribution	distribution	NOUN
ejpam-4641	2	35	with	with	ADP
ejpam-4641	2	36	some	some	DET
ejpam-4641	2	37	recurrence	recurrence	NOUN
ejpam-4641	2	38	relations	relation	NOUN
ejpam-4641	2	39	ramy	ramy	PROPN
ejpam-4641	2	40	abdelhamid	abdelhamid	PROPN
ejpam-4641	2	41	aldallal	aldallal	PROPN
ejpam-4641	2	42	department	department	PROPN
ejpam-4641	2	43	of	of	ADP
ejpam-4641	2	44	accounting	accounting	PROPN
ejpam-4641	2	45	,	,	PUNCT
ejpam-4641	2	46	college	college	NOUN
ejpam-4641	2	47	of	of	ADP
ejpam-4641	2	48	business	business	PROPN
ejpam-4641	2	49	administration	administration	NOUN
ejpam-4641	2	50	in	in	ADP
ejpam-4641	2	51	hawtat	hawtat	PROPN
ejpam-4641	2	52	bani	bani	PROPN
ejpam-4641	2	53	tamim	tamim	PROPN
ejpam-4641	2	54	,	,	PUNCT
ejpam-4641	2	55	prince	prince	PROPN
ejpam-4641	2	56	sattam	sattam	PROPN
ejpam-4641	2	57	bin	bin	PROPN
ejpam-4641	2	58	abdulaziz	abdulaziz	PROPN
ejpam-4641	2	59	university	university	PROPN
ejpam-4641	2	60	,	,	PUNCT
ejpam-4641	2	61	saudi	saudi	PROPN
ejpam-4641	2	62	arabia	arabia	PROPN
ejpam-4641	2	63	abstract	abstract	NOUN
ejpam-4641	2	64	.	.	PUNCT
ejpam-4641	3	1	this	this	DET
ejpam-4641	3	2	paper	paper	NOUN
ejpam-4641	3	3	tries	try	VERB
ejpam-4641	3	4	to	to	PART
ejpam-4641	3	5	find	find	VERB
ejpam-4641	3	6	some	some	DET
ejpam-4641	3	7	formulas	formula	NOUN
ejpam-4641	3	8	for	for	ADP
ejpam-4641	3	9	calculating	calculate	VERB
ejpam-4641	3	10	the	the	DET
ejpam-4641	3	11	moment	moment	NOUN
ejpam-4641	3	12	generating	generate	VERB
ejpam-4641	3	13	function	function	NOUN
ejpam-4641	3	14	for	for	ADP
ejpam-4641	3	15	upper	upper	ADJ
ejpam-4641	3	16	and	and	CCONJ
ejpam-4641	3	17	lower	low	ADJ
ejpam-4641	3	18	current	current	ADJ
ejpam-4641	3	19	records	record	NOUN
ejpam-4641	3	20	picked	pick	VERB
ejpam-4641	3	21	from	from	ADP
ejpam-4641	3	22	generalized	generalized	ADJ
ejpam-4641	3	23	exponential	exponential	ADJ
ejpam-4641	3	24	distributed	distribute	VERB
ejpam-4641	3	25	data	datum	NOUN
ejpam-4641	3	26	and	and	CCONJ
ejpam-4641	3	27	the	the	DET
ejpam-4641	3	28	joint	joint	ADJ
ejpam-4641	3	29	moment	moment	NOUN
ejpam-4641	3	30	generating	generate	VERB
ejpam-4641	3	31	function	function	NOUN
ejpam-4641	3	32	between	between	ADP
ejpam-4641	3	33	them	they	PRON
ejpam-4641	3	34	.	.	PUNCT
ejpam-4641	4	1	after	after	ADP
ejpam-4641	4	2	that	that	PRON
ejpam-4641	4	3	,	,	PUNCT
ejpam-4641	4	4	some	some	DET
ejpam-4641	4	5	formulas	formula	NOUN
ejpam-4641	4	6	are	be	AUX
ejpam-4641	4	7	derived	derive	VERB
ejpam-4641	4	8	from	from	ADP
ejpam-4641	4	9	the	the	DET
ejpam-4641	4	10	previous	previous	ADJ
ejpam-4641	4	11	ones	one	NOUN
ejpam-4641	4	12	to	to	PART
ejpam-4641	4	13	find	find	VERB
ejpam-4641	4	14	the	the	DET
ejpam-4641	4	15	moments	moment	NOUN
ejpam-4641	4	16	of	of	ADP
ejpam-4641	4	17	each	each	DET
ejpam-4641	4	18	and	and	CCONJ
ejpam-4641	4	19	the	the	DET
ejpam-4641	4	20	product	product	NOUN
ejpam-4641	4	21	moments	moment	NOUN
ejpam-4641	4	22	of	of	ADP
ejpam-4641	4	23	both	both	CCONJ
ejpam-4641	4	24	upper	upper	ADJ
ejpam-4641	4	25	and	and	CCONJ
ejpam-4641	4	26	lower	low	ADJ
ejpam-4641	4	27	current	current	ADJ
ejpam-4641	4	28	records	record	NOUN
ejpam-4641	4	29	.	.	PUNCT
ejpam-4641	5	1	then	then	ADV
ejpam-4641	5	2	,	,	PUNCT
ejpam-4641	5	3	various	various	ADJ
ejpam-4641	5	4	recurrence	recurrence	NOUN
ejpam-4641	5	5	relations	relation	NOUN
ejpam-4641	5	6	are	be	AUX
ejpam-4641	5	7	established	establish	VERB
ejpam-4641	5	8	for	for	ADP
ejpam-4641	5	9	most	most	ADJ
ejpam-4641	5	10	of	of	ADP
ejpam-4641	5	11	the	the	DET
ejpam-4641	5	12	mentioned	mention	VERB
ejpam-4641	5	13	formulas	formula	NOUN
ejpam-4641	5	14	.	.	PUNCT
ejpam-4641	6	1	after	after	ADP
ejpam-4641	6	2	that	that	PRON
ejpam-4641	6	3	,	,	PUNCT
ejpam-4641	6	4	an	an	DET
ejpam-4641	6	5	integral	integral	ADJ
ejpam-4641	6	6	form	form	NOUN
ejpam-4641	6	7	of	of	ADP
ejpam-4641	6	8	the	the	DET
ejpam-4641	6	9	moments	moment	NOUN
ejpam-4641	6	10	of	of	ADP
ejpam-4641	6	11	record	record	NOUN
ejpam-4641	6	12	range	range	NOUN
ejpam-4641	6	13	is	be	AUX
ejpam-4641	6	14	founded	found	VERB
ejpam-4641	6	15	followed	follow	VERB
ejpam-4641	6	16	by	by	ADP
ejpam-4641	6	17	a	a	DET
ejpam-4641	6	18	numerical	numerical	ADJ
ejpam-4641	6	19	example	example	NOUN
ejpam-4641	6	20	with	with	ADP
ejpam-4641	6	21	simulated	simulated	ADJ
ejpam-4641	6	22	data	datum	NOUN
ejpam-4641	6	23	to	to	PART
ejpam-4641	6	24	clarify	clarify	VERB
ejpam-4641	6	25	the	the	DET
ejpam-4641	6	26	effectiveness	effectiveness	NOUN
ejpam-4641	6	27	of	of	ADP
ejpam-4641	6	28	the	the	DET
ejpam-4641	6	29	formulas	formula	NOUN
ejpam-4641	6	30	found	find	VERB
ejpam-4641	6	31	in	in	ADP
ejpam-4641	6	32	the	the	DET
ejpam-4641	6	33	study	study	NOUN
ejpam-4641	6	34	and	and	CCONJ
ejpam-4641	6	35	how	how	SCONJ
ejpam-4641	6	36	they	they	PRON
ejpam-4641	6	37	can	can	AUX
ejpam-4641	6	38	make	make	VERB
ejpam-4641	6	39	the	the	DET
ejpam-4641	6	40	calculation	calculation	NOUN
ejpam-4641	6	41	process	process	NOUN
ejpam-4641	6	42	easier	easy	ADJ
ejpam-4641	6	43	and	and	CCONJ
ejpam-4641	6	44	faster	fast	ADV
ejpam-4641	6	45	.	.	PUNCT
ejpam-4641	7	1	finally	finally	ADV
ejpam-4641	7	2	,	,	PUNCT
ejpam-4641	7	3	a	a	DET
ejpam-4641	7	4	conclusion	conclusion	NOUN
ejpam-4641	7	5	part	part	NOUN
ejpam-4641	7	6	is	be	AUX
ejpam-4641	7	7	added	add	VERB
ejpam-4641	7	8	,	,	PUNCT
ejpam-4641	7	9	to	to	PART
ejpam-4641	7	10	sum	sum	VERB
ejpam-4641	7	11	up	up	ADP
ejpam-4641	7	12	what	what	PRON
ejpam-4641	7	13	has	have	AUX
ejpam-4641	7	14	been	be	AUX
ejpam-4641	7	15	done	do	VERB
ejpam-4641	7	16	and	and	CCONJ
ejpam-4641	7	17	the	the	DET
ejpam-4641	7	18	results	result	NOUN
ejpam-4641	7	19	.	.	PUNCT
ejpam-4641	8	1	2020	2020	NUM
ejpam-4641	8	2	mathematics	mathematic	NOUN
ejpam-4641	8	3	subject	subject	NOUN
ejpam-4641	8	4	classifications	classification	NOUN
ejpam-4641	8	5	:	:	PUNCT
ejpam-4641	8	6	62g30	62g30	NUM
ejpam-4641	8	7	,	,	PUNCT
ejpam-4641	8	8	65q30	65q30	NUM
ejpam-4641	8	9	,	,	PUNCT
ejpam-4641	8	10	62e99	62e99	NUM
ejpam-4641	8	11	,	,	PUNCT
ejpam-4641	8	12	60e10	60e10	NUM
ejpam-4641	8	13	key	key	ADJ
ejpam-4641	8	14	words	word	NOUN
ejpam-4641	8	15	and	and	CCONJ
ejpam-4641	8	16	phrases	phrase	NOUN
ejpam-4641	8	17	:	:	PUNCT
ejpam-4641	8	18	record	record	NOUN
ejpam-4641	8	19	range	range	NOUN
ejpam-4641	8	20	,	,	PUNCT
ejpam-4641	8	21	lower	low	ADJ
ejpam-4641	8	22	and	and	CCONJ
ejpam-4641	8	23	upper	upper	ADJ
ejpam-4641	8	24	current	current	ADJ
ejpam-4641	8	25	records	record	NOUN
ejpam-4641	8	26	,	,	PUNCT
ejpam-4641	8	27	moment	moment	NOUN
ejpam-4641	8	28	generating	generate	VERB
ejpam-4641	8	29	function	function	NOUN
ejpam-4641	8	30	and	and	CCONJ
ejpam-4641	8	31	moments	moment	NOUN
ejpam-4641	8	32	,	,	PUNCT
ejpam-4641	8	33	recurrence	recurrence	NOUN
ejpam-4641	8	34	relations	relation	NOUN
ejpam-4641	8	35	,	,	PUNCT
ejpam-4641	8	36	generalized	generalize	VERB
ejpam-4641	8	37	exponential	exponential	ADJ
ejpam-4641	8	38	distribution	distribution	NOUN
ejpam-4641	8	39	1	1	NUM
ejpam-4641	8	40	.	.	PUNCT
ejpam-4641	9	1	introduction	introduction	NOUN
ejpam-4641	9	2	imagine	imagine	VERB
ejpam-4641	9	3	that	that	SCONJ
ejpam-4641	9	4	we	we	PRON
ejpam-4641	9	5	have	have	VERB
ejpam-4641	9	6	a	a	DET
ejpam-4641	9	7	sequence	sequence	NOUN
ejpam-4641	9	8	{	{	PUNCT
ejpam-4641	9	9	xj	xj	PROPN
ejpam-4641	9	10	}	}	PUNCT
ejpam-4641	9	11	that	that	PRON
ejpam-4641	9	12	consists	consist	VERB
ejpam-4641	9	13	of	of	ADP
ejpam-4641	9	14	identical	identical	ADJ
ejpam-4641	9	15	and	and	CCONJ
ejpam-4641	9	16	independent	independent	ADJ
ejpam-4641	9	17	random	random	ADJ
ejpam-4641	9	18	variables	variable	NOUN
ejpam-4641	9	19	such	such	ADJ
ejpam-4641	9	20	that	that	SCONJ
ejpam-4641	9	21	each	each	PRON
ejpam-4641	9	22	of	of	ADP
ejpam-4641	9	23	which	which	PRON
ejpam-4641	9	24	is	be	AUX
ejpam-4641	9	25	distributed	distribute	VERB
ejpam-4641	9	26	with	with	ADP
ejpam-4641	9	27	a	a	DET
ejpam-4641	9	28	probability	probability	NOUN
ejpam-4641	9	29	density	density	NOUN
ejpam-4641	9	30	function(pdf	function(pdf	NOUN
ejpam-4641	9	31	)	)	PUNCT
ejpam-4641	9	32	f(x	f(x	PROPN
ejpam-4641	9	33	)	)	PUNCT
ejpam-4641	9	34	and	and	CCONJ
ejpam-4641	9	35	a	a	DET
ejpam-4641	9	36	cumulative	cumulative	ADJ
ejpam-4641	9	37	distribution	distribution	NOUN
ejpam-4641	9	38	function(cdf	function(cdf	NOUN
ejpam-4641	9	39	)	)	PUNCT
ejpam-4641	10	1	f	f	PROPN
ejpam-4641	10	2	(	(	PUNCT
ejpam-4641	10	3	x	x	X
ejpam-4641	10	4	)	)	PUNCT
ejpam-4641	10	5	that	that	PRON
ejpam-4641	10	6	is	be	AUX
ejpam-4641	10	7	absolutely	absolutely	ADV
ejpam-4641	10	8	continuous	continuous	ADJ
ejpam-4641	10	9	.	.	PUNCT
ejpam-4641	11	1	xj	xj	PROPN
ejpam-4641	11	2	as	as	ADP
ejpam-4641	11	3	an	an	DET
ejpam-4641	11	4	observation	observation	NOUN
ejpam-4641	11	5	is	be	AUX
ejpam-4641	11	6	considered	consider	VERB
ejpam-4641	11	7	to	to	PART
ejpam-4641	11	8	be	be	AUX
ejpam-4641	11	9	an	an	DET
ejpam-4641	11	10	upper	upper	ADJ
ejpam-4641	11	11	record	record	NOUN
ejpam-4641	11	12	if	if	SCONJ
ejpam-4641	11	13	xj	xj	AUX
ejpam-4641	11	14	>	>	X
ejpam-4641	11	15	xi	xi	PROPN
ejpam-4641	11	16	for	for	ADP
ejpam-4641	11	17	every	every	DET
ejpam-4641	11	18	i	i	PRON
ejpam-4641	11	19	<	<	X
ejpam-4641	11	20	j.	j.	PROPN
ejpam-4641	11	21	a	a	DET
ejpam-4641	11	22	similar	similar	ADJ
ejpam-4641	11	23	definition	definition	NOUN
ejpam-4641	11	24	has	have	AUX
ejpam-4641	11	25	been	be	AUX
ejpam-4641	11	26	established	establish	VERB
ejpam-4641	11	27	for	for	ADP
ejpam-4641	11	28	the	the	DET
ejpam-4641	11	29	lower	low	ADJ
ejpam-4641	11	30	record	record	NOUN
ejpam-4641	11	31	values	value	NOUN
ejpam-4641	11	32	.	.	PUNCT
ejpam-4641	12	1	in	in	ADP
ejpam-4641	12	2	some	some	DET
ejpam-4641	12	3	situations	situation	NOUN
ejpam-4641	12	4	,	,	PUNCT
ejpam-4641	12	5	we	we	PRON
ejpam-4641	12	6	tend	tend	VERB
ejpam-4641	12	7	to	to	PART
ejpam-4641	12	8	pick	pick	VERB
ejpam-4641	12	9	the	the	DET
ejpam-4641	12	10	smallest	small	ADJ
ejpam-4641	12	11	and	and	CCONJ
ejpam-4641	12	12	largest	large	ADJ
ejpam-4641	13	1	x	x	ADJ
ejpam-4641	13	2	values	value	NOUN
ejpam-4641	13	3	detected	detect	VERB
ejpam-4641	13	4	as	as	ADP
ejpam-4641	13	5	new	new	ADJ
ejpam-4641	13	6	lower	low	ADJ
ejpam-4641	13	7	or	or	CCONJ
ejpam-4641	13	8	upper	upper	ADJ
ejpam-4641	13	9	record	record	NOUN
ejpam-4641	13	10	values	value	NOUN
ejpam-4641	13	11	of	of	ADP
ejpam-4641	13	12	either	either	DET
ejpam-4641	13	13	kind	kind	NOUN
ejpam-4641	13	14	take	take	VERB
ejpam-4641	13	15	place	place	NOUN
ejpam-4641	13	16	,	,	PUNCT
ejpam-4641	13	17	and	and	CCONJ
ejpam-4641	13	18	in	in	ADP
ejpam-4641	13	19	such	such	DET
ejpam-4641	13	20	a	a	DET
ejpam-4641	13	21	situation	situation	NOUN
ejpam-4641	13	22	,	,	PUNCT
ejpam-4641	13	23	we	we	PRON
ejpam-4641	13	24	name	name	VERB
ejpam-4641	13	25	it	it	PRON
ejpam-4641	13	26	current	current	ADJ
ejpam-4641	13	27	records	record	NOUN
ejpam-4641	13	28	.	.	PUNCT
ejpam-4641	14	1	we	we	PRON
ejpam-4641	14	2	will	will	AUX
ejpam-4641	14	3	symbolize	symbolize	VERB
ejpam-4641	14	4	u	u	PROPN
ejpam-4641	14	5	c	c	PROPN
ejpam-4641	14	6	n	n	PRON
ejpam-4641	14	7	as	as	ADP
ejpam-4641	14	8	the	the	DET
ejpam-4641	14	9	nth	nth	NOUN
ejpam-4641	14	10	upper	upper	ADJ
ejpam-4641	14	11	current	current	ADJ
ejpam-4641	14	12	records	record	NOUN
ejpam-4641	14	13	and	and	CCONJ
ejpam-4641	14	14	lc	lc	PROPN
ejpam-4641	14	15	n	n	PROPN
ejpam-4641	14	16	as	as	ADP
ejpam-4641	14	17	the	the	DET
ejpam-4641	14	18	nth	nth	NOUN
ejpam-4641	14	19	lower	low	ADJ
ejpam-4641	14	20	current	current	ADJ
ejpam-4641	14	21	records	record	NOUN
ejpam-4641	14	22	of	of	ADP
ejpam-4641	14	23	the	the	DET
ejpam-4641	14	24	sequence	sequence	NOUN
ejpam-4641	14	25	xn	xn	PROPN
ejpam-4641	14	26	,	,	PUNCT
ejpam-4641	14	27	when	when	SCONJ
ejpam-4641	14	28	any	any	DET
ejpam-4641	14	29	kind	kind	NOUN
ejpam-4641	14	30	o	o	NOUN
ejpam-4641	14	31	the	the	DET
ejpam-4641	14	32	nth	nth	NOUN
ejpam-4641	14	33	records	record	NOUN
ejpam-4641	14	34	appears	appear	VERB
ejpam-4641	14	35	.	.	PUNCT
ejpam-4641	15	1	so	so	ADV
ejpam-4641	15	2	,	,	PUNCT
ejpam-4641	15	3	u	u	NOUN
ejpam-4641	15	4	c	c	NOUN
ejpam-4641	15	5	n+1	n+1	PROPN
ejpam-4641	15	6	=	=	SYM
ejpam-4641	15	7	u	u	X
ejpam-4641	15	8	c	c	NOUN
ejpam-4641	15	9	n	n	ADV
ejpam-4641	15	10	if	if	SCONJ
ejpam-4641	15	11	lc	lc	PROPN
ejpam-4641	15	12	n+1	n+1	PROPN
ejpam-4641	15	13	<	<	X
ejpam-4641	15	14	lc	lc	PROPN
ejpam-4641	15	15	n	n	PROPN
ejpam-4641	15	16	and	and	CCONJ
ejpam-4641	15	17	lc	lc	PROPN
ejpam-4641	16	1	n+1	n+1	PROPN
ejpam-4641	16	2	=	=	SYM
ejpam-4641	16	3	lc	lc	PROPN
ejpam-4641	16	4	n	n	ADV
ejpam-4641	16	5	if	if	SCONJ
ejpam-4641	16	6	u	u	PROPN
ejpam-4641	16	7	c	c	NOUN
ejpam-4641	16	8	n+1	n+1	PUNCT
ejpam-4641	16	9	>	>	PUNCT
ejpam-4641	16	10	u	u	PROPN
ejpam-4641	16	11	c	c	NOUN
ejpam-4641	16	12	n	n	CCONJ
ejpam-4641	16	13	,	,	PUNCT
ejpam-4641	16	14	for	for	ADP
ejpam-4641	16	15	all	all	PRON
ejpam-4641	16	16	n	n	NOUN
ejpam-4641	16	17	=	=	SYM
ejpam-4641	16	18	1	1	NUM
ejpam-4641	16	19	,	,	PUNCT
ejpam-4641	16	20	2	2	NUM
ejpam-4641	16	21	,	,	PUNCT
ejpam-4641	16	22	...	...	PUNCT
ejpam-4641	16	23	where	where	SCONJ
ejpam-4641	16	24	by	by	ADP
ejpam-4641	16	25	definition	definition	NOUN
ejpam-4641	16	26	,	,	PUNCT
ejpam-4641	16	27	lc	lc	PROPN
ejpam-4641	16	28	0	0	NUM
ejpam-4641	17	1	=	=	SYM
ejpam-4641	17	2	u	u	X
ejpam-4641	17	3	c	c	NOUN
ejpam-4641	17	4	0	0	NUM
ejpam-4641	18	1	=	=	SYM
ejpam-4641	18	2	x1	x1	PROPN
ejpam-4641	18	3	.	.	PUNCT
ejpam-4641	19	1	we	we	PRON
ejpam-4641	19	2	can	can	AUX
ejpam-4641	19	3	define	define	VERB
ejpam-4641	19	4	the	the	DET
ejpam-4641	19	5	record	record	ADJ
ejpam-4641	19	6	range	range	NOUN
ejpam-4641	19	7	as	as	ADP
ejpam-4641	19	8	rc	rc	PROPN
ejpam-4641	19	9	n	n	PROPN
ejpam-4641	19	10	=	=	SYM
ejpam-4641	19	11	u	u	PROPN
ejpam-4641	19	12	c	c	PROPN
ejpam-4641	19	13	n	n	CCONJ
ejpam-4641	19	14	−	−	PROPN
ejpam-4641	19	15	lc	lc	NOUN
ejpam-4641	19	16	n.	n.	NOUN
ejpam-4641	19	17	and	and	CCONJ
ejpam-4641	19	18	of	of	ADP
ejpam-4641	19	19	doi	doi	NOUN
ejpam-4641	19	20	:	:	PUNCT
ejpam-4641	19	21	https://doi.org/10.29020/nybg.ejpam.v16i1.4641	https://doi.org/10.29020/nybg.ejpam.v16i1.4641	PROPN
ejpam-4641	19	22	email	email	NOUN
ejpam-4641	19	23	address	address	NOUN
ejpam-4641	19	24	:	:	PUNCT
ejpam-4641	19	25	dr.raldallal@gmail.com	dr.raldallal@gmail.com	PROPN
ejpam-4641	19	26	(	(	PUNCT
ejpam-4641	19	27	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	19	28	)	)	PUNCT
ejpam-4641	19	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4641	19	30	97	97	NUM
ejpam-4641	20	1	©	©	PROPN
ejpam-4641	20	2	2023	2023	NUM
ejpam-4641	20	3	ejpam	ejpam	NOUN
ejpam-4641	20	4	all	all	DET
ejpam-4641	20	5	rights	right	NOUN
ejpam-4641	20	6	reserved	reserve	VERB
ejpam-4641	20	7	.	.	PUNCT
ejpam-4641	21	1	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	21	2	/	/	SYM
ejpam-4641	21	3	eur	eur	PROPN
ejpam-4641	21	4	.	.	PUNCT
ejpam-4641	22	1	j.	j.	PROPN
ejpam-4641	22	2	pure	pure	PROPN
ejpam-4641	22	3	appl	appl	PROPN
ejpam-4641	22	4	.	.	PROPN
ejpam-4641	22	5	math	math	PROPN
ejpam-4641	22	6	,	,	PUNCT
ejpam-4641	22	7	16	16	NUM
ejpam-4641	22	8	(	(	PUNCT
ejpam-4641	22	9	1	1	NUM
ejpam-4641	22	10	)	)	PUNCT
ejpam-4641	22	11	(	(	PUNCT
ejpam-4641	22	12	2023	2023	NUM
ejpam-4641	22	13	)	)	PUNCT
ejpam-4641	22	14	,	,	PUNCT
ejpam-4641	22	15	97	97	NUM
ejpam-4641	22	16	-	-	SYM
ejpam-4641	22	17	111	111	NUM
ejpam-4641	22	18	98	98	NUM
ejpam-4641	22	19	course	course	NOUN
ejpam-4641	22	20	,	,	PUNCT
ejpam-4641	22	21	a	a	DET
ejpam-4641	22	22	new	new	ADJ
ejpam-4641	22	23	range	range	NOUN
ejpam-4641	22	24	is	be	AUX
ejpam-4641	22	25	recorded	record	VERB
ejpam-4641	22	26	at	at	ADP
ejpam-4641	22	27	the	the	DET
ejpam-4641	22	28	moment	moment	NOUN
ejpam-4641	22	29	a	a	DET
ejpam-4641	22	30	new	new	ADJ
ejpam-4641	22	31	upper	upper	ADJ
ejpam-4641	22	32	or	or	CCONJ
ejpam-4641	22	33	lower	low	ADJ
ejpam-4641	22	34	record	record	NOUN
ejpam-4641	22	35	has	have	AUX
ejpam-4641	22	36	occurred	occur	VERB
ejpam-4641	22	37	.	.	PUNCT
ejpam-4641	23	1	for	for	ADP
ejpam-4641	23	2	example	example	NOUN
ejpam-4641	23	3	,	,	PUNCT
ejpam-4641	23	4	let	let	VERB
ejpam-4641	23	5	’s	’s	NOUN
ejpam-4641	23	6	consider	consider	VERB
ejpam-4641	23	7	the	the	DET
ejpam-4641	23	8	following	follow	VERB
ejpam-4641	23	9	sequence	sequence	NOUN
ejpam-4641	23	10	of	of	ADP
ejpam-4641	23	11	observations	observation	NOUN
ejpam-4641	23	12	:	:	PUNCT
ejpam-4641	23	13	3	3	NUM
ejpam-4641	23	14	,	,	PUNCT
ejpam-4641	23	15	2	2	NUM
ejpam-4641	23	16	,	,	PUNCT
ejpam-4641	23	17	2.5	2.5	NUM
ejpam-4641	23	18	,	,	PUNCT
ejpam-4641	23	19	2.2	2.2	NUM
ejpam-4641	23	20	,	,	PUNCT
ejpam-4641	23	21	1	1	NUM
ejpam-4641	23	22	,	,	PUNCT
ejpam-4641	23	23	3.7	3.7	NUM
ejpam-4641	23	24	,	,	PUNCT
ejpam-4641	23	25	2.6	2.6	NUM
ejpam-4641	23	26	,	,	PUNCT
ejpam-4641	23	27	1.5	1.5	NUM
ejpam-4641	23	28	,	,	PUNCT
ejpam-4641	23	29	2.7	2.7	NUM
ejpam-4641	23	30	,	,	PUNCT
ejpam-4641	23	31	4	4	NUM
ejpam-4641	23	32	,	,	PUNCT
ejpam-4641	23	33	0.5	0.5	NUM
ejpam-4641	23	34	,	,	PUNCT
ejpam-4641	23	35	2.5	2.5	NUM
ejpam-4641	23	36	,	,	PUNCT
ejpam-4641	23	37	4.7	4.7	NUM
ejpam-4641	23	38	....	....	PUNCT
ejpam-4641	23	39	then	then	ADV
ejpam-4641	23	40	we	we	PRON
ejpam-4641	23	41	can	can	AUX
ejpam-4641	23	42	determine	determine	VERB
ejpam-4641	23	43	the	the	DET
ejpam-4641	23	44	upper	upper	ADJ
ejpam-4641	23	45	and	and	CCONJ
ejpam-4641	23	46	lower	low	ADJ
ejpam-4641	23	47	current	current	ADJ
ejpam-4641	23	48	records	record	NOUN
ejpam-4641	23	49	along	along	ADP
ejpam-4641	23	50	with	with	ADP
ejpam-4641	23	51	the	the	DET
ejpam-4641	23	52	current	current	ADJ
ejpam-4641	23	53	record	record	NOUN
ejpam-4641	23	54	range	range	NOUN
ejpam-4641	23	55	as	as	SCONJ
ejpam-4641	23	56	follows	follow	VERB
ejpam-4641	23	57	:	:	PUNCT
ejpam-4641	23	58	u	u	NOUN
ejpam-4641	23	59	c	c	NOUN
ejpam-4641	23	60	0	0	NUM
ejpam-4641	24	1	=	=	SYM
ejpam-4641	24	2	3	3	NUM
ejpam-4641	24	3	,	,	PUNCT
ejpam-4641	24	4	u	u	NOUN
ejpam-4641	24	5	c	c	NOUN
ejpam-4641	24	6	1	1	NUM
ejpam-4641	24	7	=	=	SYM
ejpam-4641	24	8	3	3	NUM
ejpam-4641	24	9	,	,	PUNCT
ejpam-4641	24	10	u	u	NOUN
ejpam-4641	24	11	c	c	PROPN
ejpam-4641	24	12	2	2	NUM
ejpam-4641	24	13	=	=	SYM
ejpam-4641	24	14	3	3	NUM
ejpam-4641	24	15	,	,	PUNCT
ejpam-4641	24	16	u	u	NOUN
ejpam-4641	24	17	c	c	NOUN
ejpam-4641	24	18	3	3	NUM
ejpam-4641	24	19	=	=	SYM
ejpam-4641	24	20	3.7	3.7	NUM
ejpam-4641	24	21	,	,	PUNCT
ejpam-4641	24	22	u	u	NOUN
ejpam-4641	24	23	c	c	NOUN
ejpam-4641	24	24	4	4	NUM
ejpam-4641	24	25	=	=	SYM
ejpam-4641	24	26	4	4	NUM
ejpam-4641	24	27	,	,	PUNCT
ejpam-4641	24	28	u	u	NOUN
ejpam-4641	24	29	c	c	NOUN
ejpam-4641	24	30	5	5	NUM
ejpam-4641	24	31	=	=	SYM
ejpam-4641	24	32	4	4	NUM
ejpam-4641	24	33	,	,	PUNCT
ejpam-4641	24	34	u	u	NOUN
ejpam-4641	24	35	c	c	PROPN
ejpam-4641	24	36	6	6	NUM
ejpam-4641	24	37	=	=	SYM
ejpam-4641	24	38	4.7	4.7	NUM
ejpam-4641	24	39	lc	lc	NOUN
ejpam-4641	24	40	0	0	NUM
ejpam-4641	25	1	=	=	SYM
ejpam-4641	25	2	3	3	NUM
ejpam-4641	25	3	,	,	PUNCT
ejpam-4641	25	4	lc	lc	PROPN
ejpam-4641	25	5	1	1	NUM
ejpam-4641	25	6	=	=	SYM
ejpam-4641	25	7	2	2	NUM
ejpam-4641	25	8	,	,	PUNCT
ejpam-4641	25	9	lc	lc	NOUN
ejpam-4641	25	10	2	2	NUM
ejpam-4641	25	11	=	=	SYM
ejpam-4641	25	12	1	1	NUM
ejpam-4641	25	13	,	,	PUNCT
ejpam-4641	25	14	lc	lc	PROPN
ejpam-4641	25	15	3	3	NUM
ejpam-4641	25	16	=	=	SYM
ejpam-4641	25	17	1	1	NUM
ejpam-4641	25	18	,	,	PUNCT
ejpam-4641	25	19	lc	lc	PROPN
ejpam-4641	25	20	4	4	NUM
ejpam-4641	25	21	=	=	SYM
ejpam-4641	25	22	1	1	NUM
ejpam-4641	25	23	,	,	PUNCT
ejpam-4641	25	24	lc	lc	PROPN
ejpam-4641	25	25	5	5	NUM
ejpam-4641	25	26	=	=	SYM
ejpam-4641	25	27	0.5	0.5	NUM
ejpam-4641	25	28	,	,	PUNCT
ejpam-4641	25	29	lc	lc	PROPN
ejpam-4641	25	30	6	6	NUM
ejpam-4641	25	31	=	=	SYM
ejpam-4641	25	32	0.5	0.5	NUM
ejpam-4641	25	33	rc	rc	NOUN
ejpam-4641	25	34	0	0	NUM
ejpam-4641	26	1	=	=	SYM
ejpam-4641	26	2	0	0	PROPN
ejpam-4641	26	3	,	,	PUNCT
ejpam-4641	26	4	rc	rc	PROPN
ejpam-4641	26	5	1	1	NUM
ejpam-4641	26	6	=	=	SYM
ejpam-4641	26	7	1	1	NUM
ejpam-4641	26	8	,	,	PUNCT
ejpam-4641	26	9	rc	rc	PROPN
ejpam-4641	26	10	2	2	NUM
ejpam-4641	26	11	=	=	SYM
ejpam-4641	26	12	2	2	NUM
ejpam-4641	26	13	,	,	PUNCT
ejpam-4641	26	14	rc	rc	PROPN
ejpam-4641	26	15	3	3	NUM
ejpam-4641	26	16	=	=	SYM
ejpam-4641	26	17	2.7	2.7	NUM
ejpam-4641	26	18	,	,	PUNCT
ejpam-4641	26	19	rc	rc	PROPN
ejpam-4641	26	20	4	4	NUM
ejpam-4641	26	21	=	=	SYM
ejpam-4641	26	22	3	3	NUM
ejpam-4641	26	23	,	,	PUNCT
ejpam-4641	26	24	rc	rc	PROPN
ejpam-4641	26	25	5	5	NUM
ejpam-4641	26	26	=	=	SYM
ejpam-4641	26	27	3.5	3.5	NUM
ejpam-4641	26	28	,	,	PUNCT
ejpam-4641	26	29	rc	rc	PROPN
ejpam-4641	26	30	6	6	NUM
ejpam-4641	26	31	=	=	SYM
ejpam-4641	26	32	4.2	4.2	NUM
ejpam-4641	26	33	there	there	PRON
ejpam-4641	26	34	are	be	VERB
ejpam-4641	26	35	cases	case	NOUN
ejpam-4641	26	36	in	in	ADP
ejpam-4641	26	37	which	which	PRON
ejpam-4641	26	38	it	it	PRON
ejpam-4641	26	39	is	be	AUX
ejpam-4641	26	40	interesting	interesting	ADJ
ejpam-4641	26	41	for	for	SCONJ
ejpam-4641	26	42	the	the	DET
ejpam-4641	26	43	current	current	ADJ
ejpam-4641	26	44	records	record	NOUN
ejpam-4641	26	45	to	to	PART
ejpam-4641	26	46	be	be	AUX
ejpam-4641	26	47	considered	consider	VERB
ejpam-4641	26	48	in	in	ADP
ejpam-4641	26	49	real	real	ADJ
ejpam-4641	26	50	life	life	NOUN
ejpam-4641	26	51	.	.	PUNCT
ejpam-4641	27	1	such	such	ADJ
ejpam-4641	27	2	as	as	ADP
ejpam-4641	27	3	whether	whether	SCONJ
ejpam-4641	27	4	data	datum	NOUN
ejpam-4641	27	5	where	where	SCONJ
ejpam-4641	27	6	lower	low	ADJ
ejpam-4641	27	7	and	and	CCONJ
ejpam-4641	27	8	upper	upper	ADJ
ejpam-4641	27	9	records	record	NOUN
ejpam-4641	27	10	are	be	AUX
ejpam-4641	27	11	being	be	AUX
ejpam-4641	27	12	taken	take	VERB
ejpam-4641	27	13	together	together	ADV
ejpam-4641	27	14	.	.	PUNCT
ejpam-4641	28	1	also	also	ADV
ejpam-4641	28	2	,	,	PUNCT
ejpam-4641	28	3	in	in	ADP
ejpam-4641	28	4	the	the	DET
ejpam-4641	28	5	case	case	NOUN
ejpam-4641	28	6	of	of	ADP
ejpam-4641	28	7	outlier	outlier	NOUN
ejpam-4641	28	8	detection	detection	NOUN
ejpam-4641	28	9	and	and	CCONJ
ejpam-4641	28	10	when	when	SCONJ
ejpam-4641	28	11	choosing	choose	VERB
ejpam-4641	28	12	a	a	DET
ejpam-4641	28	13	fitted	fit	VERB
ejpam-4641	28	14	model	model	NOUN
ejpam-4641	28	15	in	in	ADP
ejpam-4641	28	16	which	which	PRON
ejpam-4641	28	17	the	the	DET
ejpam-4641	28	18	record	record	NOUN
ejpam-4641	28	19	range	range	NOUN
ejpam-4641	28	20	plays	play	VERB
ejpam-4641	28	21	an	an	DET
ejpam-4641	28	22	important	important	ADJ
ejpam-4641	28	23	role	role	NOUN
ejpam-4641	28	24	in	in	ADP
ejpam-4641	28	25	it	it	PRON
ejpam-4641	28	26	(	(	PUNCT
ejpam-4641	28	27	see	see	PROPN
ejpam-4641	28	28	,	,	PUNCT
ejpam-4641	28	29	basak	basak	PROPN
ejpam-4641	29	1	[	[	X
ejpam-4641	29	2	10	10	NUM
ejpam-4641	29	3	]	]	NUM
ejpam-4641	29	4	)	)	PUNCT
ejpam-4641	29	5	.	.	PUNCT
ejpam-4641	30	1	again	again	ADV
ejpam-4641	30	2	,	,	PUNCT
ejpam-4641	30	3	it	it	PRON
ejpam-4641	30	4	is	be	AUX
ejpam-4641	30	5	very	very	ADV
ejpam-4641	30	6	substantial	substantial	ADJ
ejpam-4641	30	7	to	to	PART
ejpam-4641	30	8	be	be	AUX
ejpam-4641	30	9	used	use	VERB
ejpam-4641	30	10	when	when	SCONJ
ejpam-4641	30	11	we	we	PRON
ejpam-4641	30	12	want	want	VERB
ejpam-4641	30	13	to	to	PART
ejpam-4641	30	14	see	see	VERB
ejpam-4641	30	15	if	if	SCONJ
ejpam-4641	30	16	the	the	DET
ejpam-4641	30	17	production	production	NOUN
ejpam-4641	30	18	process	process	NOUN
ejpam-4641	30	19	is	be	AUX
ejpam-4641	30	20	good	good	ADJ
ejpam-4641	30	21	enough	enough	ADV
ejpam-4641	30	22	to	to	PART
ejpam-4641	30	23	fall	fall	VERB
ejpam-4641	30	24	within	within	ADP
ejpam-4641	30	25	the	the	DET
ejpam-4641	30	26	scope	scope	NOUN
ejpam-4641	30	27	of	of	ADP
ejpam-4641	30	28	the	the	DET
ejpam-4641	30	29	production	production	NOUN
ejpam-4641	30	30	’s	’s	PART
ejpam-4641	30	31	specifications	specification	NOUN
ejpam-4641	30	32	or	or	CCONJ
ejpam-4641	30	33	not	not	PART
ejpam-4641	30	34	.	.	PUNCT
ejpam-4641	31	1	meaning	mean	VERB
ejpam-4641	31	2	,	,	PUNCT
ejpam-4641	31	3	if	if	SCONJ
ejpam-4641	31	4	the	the	DET
ejpam-4641	31	5	record	record	NOUN
ejpam-4641	31	6	range	range	NOUN
ejpam-4641	31	7	is	be	AUX
ejpam-4641	31	8	greater	great	ADJ
ejpam-4641	31	9	than	than	ADP
ejpam-4641	31	10	a	a	DET
ejpam-4641	31	11	specific	specific	ADJ
ejpam-4641	31	12	value	value	NOUN
ejpam-4641	31	13	,	,	PUNCT
ejpam-4641	31	14	then	then	ADV
ejpam-4641	31	15	the	the	DET
ejpam-4641	31	16	products	product	NOUN
ejpam-4641	31	17	will	will	AUX
ejpam-4641	31	18	not	not	PART
ejpam-4641	31	19	fit	fit	VERB
ejpam-4641	31	20	the	the	DET
ejpam-4641	31	21	specifications	specification	NOUN
ejpam-4641	31	22	and	and	CCONJ
ejpam-4641	31	23	vice	vice	NOUN
ejpam-4641	31	24	versa	versa	ADV
ejpam-4641	31	25	.	.	PUNCT
ejpam-4641	32	1	and	and	CCONJ
ejpam-4641	32	2	you	you	PRON
ejpam-4641	32	3	can	can	AUX
ejpam-4641	32	4	see	see	VERB
ejpam-4641	32	5	it	it	PRON
ejpam-4641	32	6	also	also	ADV
ejpam-4641	32	7	in	in	ADP
ejpam-4641	32	8	any	any	DET
ejpam-4641	32	9	life	life	NOUN
ejpam-4641	32	10	test	test	NOUN
ejpam-4641	32	11	in	in	ADP
ejpam-4641	32	12	which	which	PRON
ejpam-4641	32	13	we	we	PRON
ejpam-4641	32	14	made	make	VERB
ejpam-4641	32	15	sequential	sequential	ADJ
ejpam-4641	32	16	measurements	measurement	NOUN
ejpam-4641	32	17	and	and	CCONJ
ejpam-4641	32	18	recorded	record	VERB
ejpam-4641	32	19	only	only	ADV
ejpam-4641	32	20	the	the	DET
ejpam-4641	32	21	values	value	NOUN
ejpam-4641	32	22	that	that	PRON
ejpam-4641	32	23	fall	fall	VERB
ejpam-4641	32	24	below	below	ADP
ejpam-4641	32	25	or	or	CCONJ
ejpam-4641	32	26	above	above	ADP
ejpam-4641	32	27	a	a	DET
ejpam-4641	32	28	current	current	ADJ
ejpam-4641	32	29	extreme	extreme	ADJ
ejpam-4641	32	30	value	value	NOUN
ejpam-4641	32	31	like	like	ADP
ejpam-4641	32	32	what	what	PRON
ejpam-4641	32	33	happens	happen	VERB
ejpam-4641	32	34	in	in	ADP
ejpam-4641	32	35	industrial	industrial	ADJ
ejpam-4641	32	36	stress	stress	NOUN
ejpam-4641	32	37	.	.	PUNCT
ejpam-4641	33	1	barakat	barakat	PROPN
ejpam-4641	33	2	et	et	PROPN
ejpam-4641	33	3	al	al	PROPN
ejpam-4641	33	4	.	.	PUNCT
ejpam-4641	34	1	[	[	X
ejpam-4641	34	2	8	8	NUM
ejpam-4641	34	3	]	]	PUNCT
ejpam-4641	34	4	obtained	obtain	VERB
ejpam-4641	34	5	some	some	DET
ejpam-4641	34	6	current	current	ADJ
ejpam-4641	34	7	record	record	NOUN
ejpam-4641	34	8	recurrence	recurrence	NOUN
ejpam-4641	34	9	relations	relation	NOUN
ejpam-4641	34	10	for	for	ADP
ejpam-4641	34	11	some	some	DET
ejpam-4641	34	12	distributions	distribution	NOUN
ejpam-4641	34	13	and	and	CCONJ
ejpam-4641	34	14	also	also	ADV
ejpam-4641	34	15	moments	moment	NOUN
ejpam-4641	34	16	recurrence	recurrence	NOUN
ejpam-4641	34	17	relations	relation	NOUN
ejpam-4641	34	18	for	for	ADP
ejpam-4641	34	19	record	record	NOUN
ejpam-4641	34	20	range	range	NOUN
ejpam-4641	34	21	when	when	SCONJ
ejpam-4641	34	22	the	the	DET
ejpam-4641	34	23	data	datum	NOUN
ejpam-4641	34	24	follows	follow	VERB
ejpam-4641	34	25	the	the	DET
ejpam-4641	34	26	exponential	exponential	ADJ
ejpam-4641	34	27	distribution	distribution	NOUN
ejpam-4641	34	28	.	.	PUNCT
ejpam-4641	35	1	once	once	ADV
ejpam-4641	35	2	again	again	ADV
ejpam-4641	35	3	,	,	PUNCT
ejpam-4641	35	4	barakat	barakat	PROPN
ejpam-4641	35	5	et	et	PROPN
ejpam-4641	35	6	al	al	PROPN
ejpam-4641	35	7	.	.	PUNCT
ejpam-4641	36	1	[	[	X
ejpam-4641	36	2	9	9	NUM
ejpam-4641	36	3	]	]	PUNCT
ejpam-4641	36	4	worked	work	VERB
ejpam-4641	36	5	on	on	ADP
ejpam-4641	36	6	the	the	DET
ejpam-4641	36	7	current	current	ADJ
ejpam-4641	36	8	record	record	NOUN
ejpam-4641	36	9	and	and	CCONJ
ejpam-4641	36	10	record	record	NOUN
ejpam-4641	36	11	range	range	NOUN
ejpam-4641	36	12	,	,	PUNCT
ejpam-4641	36	13	but	but	CCONJ
ejpam-4641	36	14	at	at	ADP
ejpam-4641	36	15	this	this	DET
ejpam-4641	36	16	time	time	NOUN
ejpam-4641	36	17	,	,	PUNCT
ejpam-4641	36	18	they	they	PRON
ejpam-4641	36	19	established	establish	VERB
ejpam-4641	36	20	a	a	DET
ejpam-4641	36	21	prediction	prediction	NOUN
ejpam-4641	36	22	interval	interval	NOUN
ejpam-4641	36	23	for	for	ADP
ejpam-4641	36	24	a	a	DET
ejpam-4641	36	25	future	future	ADJ
ejpam-4641	36	26	value	value	NOUN
ejpam-4641	36	27	of	of	ADP
ejpam-4641	36	28	them	they	PRON
ejpam-4641	36	29	.	.	PUNCT
ejpam-4641	37	1	to	to	PART
ejpam-4641	37	2	read	read	VERB
ejpam-4641	37	3	more	more	ADJ
ejpam-4641	37	4	about	about	ADP
ejpam-4641	37	5	the	the	DET
ejpam-4641	37	6	record	record	NOUN
ejpam-4641	37	7	range	range	NOUN
ejpam-4641	37	8	and	and	CCONJ
ejpam-4641	37	9	current	current	ADJ
ejpam-4641	37	10	records	record	NOUN
ejpam-4641	37	11	and	and	CCONJ
ejpam-4641	37	12	the	the	DET
ejpam-4641	37	13	applications	application	NOUN
ejpam-4641	37	14	titled	title	VERB
ejpam-4641	37	15	to	to	ADP
ejpam-4641	37	16	them	they	PRON
ejpam-4641	37	17	,	,	PUNCT
ejpam-4641	37	18	we	we	PRON
ejpam-4641	37	19	pointed	point	VERB
ejpam-4641	37	20	to	to	ADP
ejpam-4641	37	21	raqab[20	raqab[20	PROPN
ejpam-4641	37	22	]	]	PUNCT
ejpam-4641	37	23	,	,	PUNCT
ejpam-4641	37	24	ahmadi	ahmadi	PROPN
ejpam-4641	37	25	et	et	PROPN
ejpam-4641	37	26	al.[3	al.[3	PROPN
ejpam-4641	37	27	]	]	PUNCT
ejpam-4641	37	28	and	and	CCONJ
ejpam-4641	37	29	ahmadi	ahmadi	PROPN
ejpam-4641	37	30	and	and	CCONJ
ejpam-4641	37	31	balakrishnan[1	balakrishnan[1	PROPN
ejpam-4641	37	32	]	]	X
ejpam-4641	37	33	and	and	CCONJ
ejpam-4641	37	34	[	[	X
ejpam-4641	37	35	2	2	NUM
ejpam-4641	37	36	]	]	PUNCT
ejpam-4641	37	37	.	.	PUNCT
ejpam-4641	38	1	but	but	CCONJ
ejpam-4641	38	2	to	to	PART
ejpam-4641	38	3	read	read	VERB
ejpam-4641	38	4	about	about	ADP
ejpam-4641	38	5	the	the	DET
ejpam-4641	38	6	record	record	NOUN
ejpam-4641	38	7	values	value	NOUN
ejpam-4641	38	8	themselves	themselves	PRON
ejpam-4641	38	9	,	,	PUNCT
ejpam-4641	38	10	you	you	PRON
ejpam-4641	38	11	can	can	AUX
ejpam-4641	38	12	check	check	VERB
ejpam-4641	38	13	aldallal	aldallal	NOUN
ejpam-4641	39	1	[	[	X
ejpam-4641	39	2	4	4	NUM
ejpam-4641	39	3	]	]	PUNCT
ejpam-4641	39	4	,	,	PUNCT
ejpam-4641	39	5	abd	abd	PROPN
ejpam-4641	39	6	elgawad	elgawad	PROPN
ejpam-4641	39	7	et	et	PROPN
ejpam-4641	39	8	al	al	PROPN
ejpam-4641	39	9	.	.	PUNCT
ejpam-4641	40	1	[	[	X
ejpam-4641	40	2	12	12	NUM
ejpam-4641	40	3	]	]	PUNCT
ejpam-4641	40	4	,	,	PUNCT
ejpam-4641	40	5	amany	amany	NOUN
ejpam-4641	40	6	et	et	PROPN
ejpam-4641	40	7	al	al	PROPN
ejpam-4641	40	8	.	.	PUNCT
ejpam-4641	41	1	[	[	X
ejpam-4641	41	2	5	5	NUM
ejpam-4641	41	3	]	]	PUNCT
ejpam-4641	41	4	,	,	PUNCT
ejpam-4641	41	5	husseiny	husseiny	ADJ
ejpam-4641	41	6	et	et	NOUN
ejpam-4641	41	7	al.[17	al.[17	PROPN
ejpam-4641	41	8	]	]	PUNCT
ejpam-4641	41	9	and	and	CCONJ
ejpam-4641	41	10	barakat	barakat	PROPN
ejpam-4641	41	11	and	and	CCONJ
ejpam-4641	41	12	harpy	harpy	ADJ
ejpam-4641	42	1	[	[	X
ejpam-4641	42	2	7	7	NUM
ejpam-4641	42	3	]	]	PUNCT
ejpam-4641	42	4	.	.	PUNCT
ejpam-4641	43	1	some	some	PRON
ejpam-4641	43	2	of	of	ADP
ejpam-4641	43	3	the	the	DET
ejpam-4641	43	4	data	datum	NOUN
ejpam-4641	43	5	in	in	ADP
ejpam-4641	43	6	the	the	DET
ejpam-4641	43	7	lifetime	lifetime	NOUN
ejpam-4641	43	8	examples	example	NOUN
ejpam-4641	43	9	mentioned	mention	VERB
ejpam-4641	43	10	above	above	ADV
ejpam-4641	43	11	can	can	AUX
ejpam-4641	43	12	be	be	AUX
ejpam-4641	43	13	distributed	distribute	VERB
ejpam-4641	43	14	using	use	VERB
ejpam-4641	43	15	a	a	DET
ejpam-4641	43	16	distribution	distribution	NOUN
ejpam-4641	43	17	introduced	introduce	VERB
ejpam-4641	43	18	by	by	ADP
ejpam-4641	43	19	gupta	gupta	PROPN
ejpam-4641	43	20	and	and	CCONJ
ejpam-4641	43	21	kundu[13	kundu[13	PROPN
ejpam-4641	43	22	]	]	PUNCT
ejpam-4641	43	23	called	call	VERB
ejpam-4641	43	24	the	the	DET
ejpam-4641	43	25	generalized	generalize	VERB
ejpam-4641	43	26	exponential	exponential	ADJ
ejpam-4641	43	27	distribution	distribution	NOUN
ejpam-4641	43	28	(	(	PUNCT
ejpam-4641	43	29	ged	ge	VERB
ejpam-4641	43	30	)	)	PUNCT
ejpam-4641	43	31	which	which	PRON
ejpam-4641	43	32	can	can	AUX
ejpam-4641	43	33	be	be	AUX
ejpam-4641	43	34	used	use	VERB
ejpam-4641	43	35	as	as	ADP
ejpam-4641	43	36	a	a	DET
ejpam-4641	43	37	good	good	ADJ
ejpam-4641	43	38	alternative	alternative	NOUN
ejpam-4641	43	39	for	for	ADP
ejpam-4641	43	40	gamma	gamma	NOUN
ejpam-4641	43	41	or	or	CCONJ
ejpam-4641	43	42	the	the	DET
ejpam-4641	43	43	weibull	weibull	PROPN
ejpam-4641	43	44	model	model	NOUN
ejpam-4641	43	45	(	(	PUNCT
ejpam-4641	43	46	see	see	PROPN
ejpam-4641	43	47	,	,	PUNCT
ejpam-4641	43	48	gupta	gupta	NOUN
ejpam-4641	43	49	and	and	CCONJ
ejpam-4641	43	50	kundu([13],[15	kundu([13],[15	NOUN
ejpam-4641	43	51	]	]	PUNCT
ejpam-4641	43	52	,	,	PUNCT
ejpam-4641	43	53	[	[	X
ejpam-4641	43	54	14	14	NUM
ejpam-4641	43	55	]	]	PUNCT
ejpam-4641	43	56	and	and	CCONJ
ejpam-4641	43	57	mohie	mohie	PROPN
ejpam-4641	43	58	el	el	PROPN
ejpam-4641	43	59	-	-	PUNCT
ejpam-4641	43	60	din	din	NOUN
ejpam-4641	43	61	and	and	CCONJ
ejpam-4641	43	62	sharawy	sharawy	PROPN
ejpam-4641	44	1	[	[	X
ejpam-4641	44	2	11	11	NUM
ejpam-4641	44	3	]	]	NUM
ejpam-4641	44	4	)	)	PUNCT
ejpam-4641	44	5	.	.	PUNCT
ejpam-4641	45	1	they	they	PRON
ejpam-4641	45	2	also	also	ADV
ejpam-4641	45	3	mentioned	mention	VERB
ejpam-4641	45	4	that	that	SCONJ
ejpam-4641	45	5	the	the	DET
ejpam-4641	45	6	ged	ge	VERB
ejpam-4641	45	7	has	have	VERB
ejpam-4641	45	8	more	more	ADJ
ejpam-4641	45	9	similarities	similarity	NOUN
ejpam-4641	45	10	to	to	ADP
ejpam-4641	45	11	a	a	DET
ejpam-4641	45	12	gamma	gamma	NOUN
ejpam-4641	45	13	family	family	NOUN
ejpam-4641	45	14	than	than	ADP
ejpam-4641	45	15	a	a	DET
ejpam-4641	45	16	weibull	weibull	PROPN
ejpam-4641	45	17	family	family	NOUN
ejpam-4641	45	18	regarding	regard	VERB
ejpam-4641	45	19	the	the	DET
ejpam-4641	45	20	hazard	hazard	NOUN
ejpam-4641	45	21	function	function	NOUN
ejpam-4641	45	22	.	.	PUNCT
ejpam-4641	46	1	in	in	ADP
ejpam-4641	46	2	this	this	DET
ejpam-4641	46	3	paper	paper	NOUN
ejpam-4641	46	4	,	,	PUNCT
ejpam-4641	46	5	we	we	PRON
ejpam-4641	46	6	will	will	AUX
ejpam-4641	46	7	introduce	introduce	VERB
ejpam-4641	46	8	some	some	DET
ejpam-4641	46	9	new	new	ADJ
ejpam-4641	46	10	moment	moment	NOUN
ejpam-4641	46	11	generating	generate	VERB
ejpam-4641	46	12	function	function	NOUN
ejpam-4641	46	13	(	(	PUNCT
ejpam-4641	46	14	mgf	mgf	NOUN
ejpam-4641	46	15	)	)	PUNCT
ejpam-4641	46	16	formulas	formula	NOUN
ejpam-4641	46	17	for	for	ADP
ejpam-4641	46	18	u	u	PROPN
ejpam-4641	46	19	c	c	PROPN
ejpam-4641	46	20	n	n	X
ejpam-4641	46	21	,	,	PUNCT
ejpam-4641	46	22	l	l	NOUN
ejpam-4641	46	23	c	c	NOUN
ejpam-4641	46	24	n	n	NOUN
ejpam-4641	46	25	and	and	CCONJ
ejpam-4641	46	26	the	the	DET
ejpam-4641	46	27	joint	joint	ADJ
ejpam-4641	46	28	mgf	mgf	PROPN
ejpam-4641	46	29	between	between	ADP
ejpam-4641	46	30	(	(	PUNCT
ejpam-4641	46	31	u	u	NOUN
ejpam-4641	46	32	c	c	NOUN
ejpam-4641	46	33	n	n	PROPN
ejpam-4641	46	34	and	and	CCONJ
ejpam-4641	46	35	lc	lc	PROPN
ejpam-4641	46	36	n	n	CCONJ
ejpam-4641	46	37	)	)	PUNCT
ejpam-4641	46	38	based	base	VERB
ejpam-4641	46	39	on	on	ADP
ejpam-4641	46	40	ged	ge	VERB
ejpam-4641	46	41	along	along	ADP
ejpam-4641	46	42	with	with	ADP
ejpam-4641	46	43	their	their	PRON
ejpam-4641	46	44	ith	ith	PROPN
ejpam-4641	46	45	moments	moment	NOUN
ejpam-4641	46	46	.	.	PUNCT
ejpam-4641	47	1	also	also	ADV
ejpam-4641	47	2	,	,	PUNCT
ejpam-4641	47	3	some	some	DET
ejpam-4641	47	4	recurrence	recurrence	NOUN
ejpam-4641	47	5	relations	relation	NOUN
ejpam-4641	47	6	are	be	AUX
ejpam-4641	47	7	introduced	introduce	VERB
ejpam-4641	47	8	for	for	ADP
ejpam-4641	47	9	the	the	DET
ejpam-4641	47	10	mgf	mgf	PROPN
ejpam-4641	47	11	of	of	ADP
ejpam-4641	47	12	them	they	PRON
ejpam-4641	47	13	beside	beside	ADP
ejpam-4641	47	14	the	the	DET
ejpam-4641	47	15	recurrence	recurrence	NOUN
ejpam-4641	47	16	relation	relation	NOUN
ejpam-4641	47	17	of	of	ADP
ejpam-4641	47	18	their	their	PRON
ejpam-4641	47	19	ith	ith	NOUN
ejpam-4641	47	20	moments	moment	NOUN
ejpam-4641	47	21	.	.	PUNCT
ejpam-4641	48	1	moreover	moreover	ADV
ejpam-4641	48	2	,	,	PUNCT
ejpam-4641	48	3	an	an	DET
ejpam-4641	48	4	integrated	integrate	VERB
ejpam-4641	48	5	form	form	NOUN
ejpam-4641	48	6	for	for	ADP
ejpam-4641	48	7	the	the	DET
ejpam-4641	48	8	mth	mth	NOUN
ejpam-4641	48	9	moments	moment	NOUN
ejpam-4641	48	10	for	for	ADP
ejpam-4641	48	11	the	the	DET
ejpam-4641	48	12	record	record	NOUN
ejpam-4641	48	13	range	range	NOUN
ejpam-4641	48	14	also	also	ADV
ejpam-4641	48	15	follows	follow	VERB
ejpam-4641	48	16	a	a	DET
ejpam-4641	48	17	ged	ge	VERB
ejpam-4641	48	18	has	have	AUX
ejpam-4641	48	19	been	be	AUX
ejpam-4641	48	20	driven	drive	VERB
ejpam-4641	48	21	.	.	PUNCT
ejpam-4641	49	1	these	these	DET
ejpam-4641	49	2	results	result	NOUN
ejpam-4641	49	3	can	can	AUX
ejpam-4641	49	4	help	help	VERB
ejpam-4641	49	5	minimize	minimize	VERB
ejpam-4641	49	6	the	the	DET
ejpam-4641	49	7	direct	direct	ADJ
ejpam-4641	49	8	computation	computation	NOUN
ejpam-4641	49	9	of	of	ADP
ejpam-4641	49	10	these	these	DET
ejpam-4641	49	11	mgfs	mgfs	NOUN
ejpam-4641	49	12	and	and	CCONJ
ejpam-4641	49	13	moments	moment	NOUN
ejpam-4641	49	14	since	since	SCONJ
ejpam-4641	49	15	numerical	numerical	ADJ
ejpam-4641	49	16	steps	step	NOUN
ejpam-4641	49	17	will	will	AUX
ejpam-4641	49	18	be	be	AUX
ejpam-4641	49	19	applied	apply	VERB
ejpam-4641	49	20	.	.	PUNCT
ejpam-4641	50	1	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	50	2	/	/	SYM
ejpam-4641	50	3	eur	eur	PROPN
ejpam-4641	50	4	.	.	PUNCT
ejpam-4641	51	1	j.	j.	PROPN
ejpam-4641	51	2	pure	pure	PROPN
ejpam-4641	51	3	appl	appl	PROPN
ejpam-4641	51	4	.	.	PROPN
ejpam-4641	51	5	math	math	PROPN
ejpam-4641	51	6	,	,	PUNCT
ejpam-4641	51	7	16	16	NUM
ejpam-4641	51	8	(	(	PUNCT
ejpam-4641	51	9	1	1	NUM
ejpam-4641	51	10	)	)	PUNCT
ejpam-4641	51	11	(	(	PUNCT
ejpam-4641	51	12	2023	2023	NUM
ejpam-4641	51	13	)	)	PUNCT
ejpam-4641	51	14	,	,	PUNCT
ejpam-4641	51	15	97	97	NUM
ejpam-4641	51	16	-	-	SYM
ejpam-4641	51	17	111	111	NUM
ejpam-4641	51	18	99	99	NUM
ejpam-4641	51	19	2	2	NUM
ejpam-4641	51	20	.	.	PUNCT
ejpam-4641	52	1	preliminaries	preliminary	NOUN
ejpam-4641	52	2	results	result	VERB
ejpam-4641	52	3	houchens	houchen	NOUN
ejpam-4641	53	1	[	[	X
ejpam-4641	53	2	16	16	NUM
ejpam-4641	53	3	]	]	PUNCT
ejpam-4641	53	4	concluded	conclude	VERB
ejpam-4641	53	5	the	the	DET
ejpam-4641	53	6	pdf	pdf	NOUN
ejpam-4641	53	7	of	of	ADP
ejpam-4641	53	8	u	u	PROPN
ejpam-4641	53	9	c	c	PROPN
ejpam-4641	53	10	n	n	X
ejpam-4641	53	11	,	,	PUNCT
ejpam-4641	53	12	l	l	PROPN
ejpam-4641	53	13	c	c	NOUN
ejpam-4641	53	14	n	n	X
ejpam-4641	53	15	,	,	PUNCT
ejpam-4641	53	16	r	r	NOUN
ejpam-4641	53	17	c	c	NOUN
ejpam-4641	53	18	n	n	CCONJ
ejpam-4641	53	19	,	,	PUNCT
ejpam-4641	53	20	and	and	CCONJ
ejpam-4641	53	21	the	the	DET
ejpam-4641	53	22	joint	joint	ADJ
ejpam-4641	53	23	pdf	pdf	NOUN
ejpam-4641	53	24	between	between	ADP
ejpam-4641	53	25	(	(	PUNCT
ejpam-4641	53	26	u	u	NOUN
ejpam-4641	53	27	c	c	NOUN
ejpam-4641	53	28	n	n	PROPN
ejpam-4641	53	29	and	and	CCONJ
ejpam-4641	53	30	lc	lc	PROPN
ejpam-4641	53	31	n	n	CCONJ
ejpam-4641	53	32	)	)	PUNCT
ejpam-4641	53	33	when	when	SCONJ
ejpam-4641	53	34	if	if	SCONJ
ejpam-4641	53	35	follows	follow	VERB
ejpam-4641	53	36	any	any	DET
ejpam-4641	53	37	cdf	cdf	PROPN
ejpam-4641	53	38	f	f	PROPN
ejpam-4641	53	39	(	(	PUNCT
ejpam-4641	53	40	x	x	NOUN
ejpam-4641	53	41	)	)	PUNCT
ejpam-4641	53	42	respectively	respectively	ADV
ejpam-4641	53	43	by	by	ADP
ejpam-4641	53	44	flc	flc	PROPN
ejpam-4641	53	45	n	n	PROPN
ejpam-4641	53	46	(	(	PUNCT
ejpam-4641	53	47	x	x	X
ejpam-4641	53	48	)	)	PUNCT
ejpam-4641	53	49	=	=	SYM
ejpam-4641	53	50	2nf(x	2nf(x	NUM
ejpam-4641	53	51	)	)	PUNCT
ejpam-4641	53	52	{	{	PUNCT
ejpam-4641	53	53	1−	1−	NUM
ejpam-4641	53	54	f	f	X
ejpam-4641	53	55	(	(	PUNCT
ejpam-4641	53	56	x	x	X
ejpam-4641	53	57	)	)	PUNCT
ejpam-4641	53	58	n−1∑	n−1∑	NOUN
ejpam-4641	53	59	k=0	k=0	PUNCT
ejpam-4641	54	1	[	[	X
ejpam-4641	54	2	−	−	X
ejpam-4641	54	3	logf	logf	NOUN
ejpam-4641	54	4	(	(	PUNCT
ejpam-4641	54	5	x)]k	x)]k	PROPN
ejpam-4641	54	6	k	k	PROPN
ejpam-4641	54	7	!	!	PUNCT
ejpam-4641	54	8	}	}	PUNCT
ejpam-4641	54	9	,	,	PUNCT
ejpam-4641	54	10	(	(	PUNCT
ejpam-4641	54	11	1	1	X
ejpam-4641	54	12	)	)	PUNCT
ejpam-4641	54	13	fuc	fuc	ADJ
ejpam-4641	54	14	n	n	CCONJ
ejpam-4641	54	15	(	(	PUNCT
ejpam-4641	54	16	x	x	X
ejpam-4641	54	17	)	)	PUNCT
ejpam-4641	54	18	=	=	SYM
ejpam-4641	54	19	2nf(x	2nf(x	NUM
ejpam-4641	54	20	)	)	PUNCT
ejpam-4641	54	21	{	{	PUNCT
ejpam-4641	54	22	1−	1−	NUM
ejpam-4641	54	23	f̄	f̄	PROPN
ejpam-4641	54	24	(	(	PUNCT
ejpam-4641	54	25	x	x	NOUN
ejpam-4641	54	26	)	)	PUNCT
ejpam-4641	54	27	n−1∑	n−1∑	NOUN
ejpam-4641	54	28	k=0	k=0	PUNCT
ejpam-4641	55	1	[	[	X
ejpam-4641	55	2	−	−	X
ejpam-4641	55	3	log	log	VERB
ejpam-4641	55	4	f̄	f̄	PROPN
ejpam-4641	55	5	(	(	PUNCT
ejpam-4641	55	6	x)]k	x)]k	PROPN
ejpam-4641	55	7	k	k	PROPN
ejpam-4641	55	8	!	!	PUNCT
ejpam-4641	55	9	}	}	PUNCT
ejpam-4641	55	10	,	,	PUNCT
ejpam-4641	55	11	(	(	PUNCT
ejpam-4641	55	12	2	2	X
ejpam-4641	55	13	)	)	PUNCT
ejpam-4641	55	14	frc	frc	NOUN
ejpam-4641	55	15	n	n	CCONJ
ejpam-4641	55	16	(	(	PUNCT
ejpam-4641	55	17	r)=	r)=	PROPN
ejpam-4641	55	18	2n	2n	NUM
ejpam-4641	55	19	(	(	PUNCT
ejpam-4641	55	20	n−	n−	NOUN
ejpam-4641	55	21	1	1	NUM
ejpam-4641	55	22	)	)	PUNCT
ejpam-4641	55	23	!	!	PUNCT
ejpam-4641	56	1	∫	∫	PROPN
ejpam-4641	57	1	∞	∞	PROPN
ejpam-4641	57	2	−∞	−∞	X
ejpam-4641	57	3	f(r	f(r	PROPN
ejpam-4641	57	4	+	+	NUM
ejpam-4641	57	5	x)f(x){−	x)f(x){−	NUM
ejpam-4641	57	6	log[1	log[1	PROPN
ejpam-4641	58	1	+	+	CCONJ
ejpam-4641	58	2	f	f	X
ejpam-4641	58	3	(	(	PUNCT
ejpam-4641	58	4	x)−	x)−	PROPN
ejpam-4641	58	5	f	f	PROPN
ejpam-4641	58	6	(	(	PUNCT
ejpam-4641	58	7	r	r	NOUN
ejpam-4641	58	8	+	+	PROPN
ejpam-4641	58	9	x)]}n−1dx	x)]}n−1dx	PROPN
ejpam-4641	58	10	,	,	PUNCT
ejpam-4641	58	11	0	0	PUNCT
ejpam-4641	58	12	<	<	X
ejpam-4641	58	13	r	r	X
ejpam-4641	58	14	<	<	X
ejpam-4641	58	15	∞	∞	PROPN
ejpam-4641	58	16	,	,	PUNCT
ejpam-4641	58	17	(	(	PUNCT
ejpam-4641	58	18	3	3	X
ejpam-4641	58	19	)	)	PUNCT
ejpam-4641	58	20	flc	flc	PROPN
ejpam-4641	58	21	n	n	SYM
ejpam-4641	58	22	,	,	PUNCT
ejpam-4641	58	23	u	u	PROPN
ejpam-4641	58	24	c	c	NOUN
ejpam-4641	58	25	n	n	PROPN
ejpam-4641	58	26	(	(	PUNCT
ejpam-4641	58	27	x	x	NOUN
ejpam-4641	58	28	,	,	PUNCT
ejpam-4641	58	29	y	y	NOUN
ejpam-4641	58	30	)	)	PUNCT
ejpam-4641	58	31	=	=	SYM
ejpam-4641	58	32	2n	2n	NUM
ejpam-4641	58	33	(	(	PUNCT
ejpam-4641	58	34	n−	n−	NOUN
ejpam-4641	58	35	1	1	NUM
ejpam-4641	58	36	)	)	PUNCT
ejpam-4641	58	37	!	!	PUNCT
ejpam-4641	59	1	f(x)f(y	f(x)f(y	X
ejpam-4641	59	2	)	)	PUNCT
ejpam-4641	59	3	{	{	PUNCT
ejpam-4641	60	1	−	−	PROPN
ejpam-4641	60	2	log[1	log[1	PROPN
ejpam-4641	61	1	+	+	CCONJ
ejpam-4641	61	2	f	f	X
ejpam-4641	61	3	(	(	PUNCT
ejpam-4641	61	4	x)−	x)−	PROPN
ejpam-4641	61	5	f	f	PROPN
ejpam-4641	61	6	(	(	PUNCT
ejpam-4641	61	7	y	y	PROPN
ejpam-4641	61	8	)	)	PUNCT
ejpam-4641	61	9	]	]	PUNCT
ejpam-4641	61	10	}	}	PUNCT
ejpam-4641	61	11	n−1	n−1	PROPN
ejpam-4641	61	12	,	,	PUNCT
ejpam-4641	61	13	(	(	PUNCT
ejpam-4641	61	14	4	4	X
ejpam-4641	61	15	)	)	PUNCT
ejpam-4641	62	1	where	where	SCONJ
ejpam-4641	62	2	f̄	f̄	PROPN
ejpam-4641	62	3	(	(	PUNCT
ejpam-4641	62	4	x	x	NOUN
ejpam-4641	62	5	)	)	PUNCT
ejpam-4641	62	6	=	=	SYM
ejpam-4641	62	7	1−	1−	NUM
ejpam-4641	62	8	f	f	X
ejpam-4641	62	9	(	(	PUNCT
ejpam-4641	62	10	x	x	NOUN
ejpam-4641	62	11	)	)	PUNCT
ejpam-4641	62	12	.	.	PUNCT
ejpam-4641	63	1	gupta	gupta	NOUN
ejpam-4641	63	2	and	and	CCONJ
ejpam-4641	63	3	kundu[13	kundu[13	PROPN
ejpam-4641	63	4	]	]	PUNCT
ejpam-4641	63	5	established	establish	VERB
ejpam-4641	63	6	ged	ge	VERB
ejpam-4641	63	7	with	with	ADP
ejpam-4641	63	8	the	the	DET
ejpam-4641	63	9	following	follow	VERB
ejpam-4641	63	10	pdf	pdf	PROPN
ejpam-4641	63	11	f(x;α	f(x;α	PROPN
ejpam-4641	63	12	,	,	PUNCT
ejpam-4641	63	13	λ	λ	NOUN
ejpam-4641	63	14	)	)	PUNCT
ejpam-4641	63	15	=	=	SYM
ejpam-4641	63	16	αλ(1−	αλ(1−	NUM
ejpam-4641	63	17	e−λx)α−1e−λx	e−λx)α−1e−λx	NOUN
ejpam-4641	63	18	,	,	PUNCT
ejpam-4641	63	19	(	(	PUNCT
ejpam-4641	63	20	5	5	NUM
ejpam-4641	63	21	)	)	PUNCT
ejpam-4641	63	22	and	and	CCONJ
ejpam-4641	63	23	the	the	DET
ejpam-4641	63	24	coming	come	VERB
ejpam-4641	63	25	cdf	cdf	PROPN
ejpam-4641	63	26	f	f	X
ejpam-4641	63	27	(	(	PUNCT
ejpam-4641	63	28	x	x	NOUN
ejpam-4641	63	29	)	)	PUNCT
ejpam-4641	63	30	=	=	SYM
ejpam-4641	63	31	(	(	PUNCT
ejpam-4641	63	32	1−	1−	NUM
ejpam-4641	63	33	e−λx)α	e−λx)α	ADV
ejpam-4641	63	34	.	.	PUNCT
ejpam-4641	64	1	(	(	PUNCT
ejpam-4641	64	2	6	6	NUM
ejpam-4641	64	3	)	)	PUNCT
ejpam-4641	64	4	where	where	SCONJ
ejpam-4641	64	5	α	α	NOUN
ejpam-4641	64	6	is	be	AUX
ejpam-4641	64	7	a	a	DET
ejpam-4641	64	8	shape	shape	NOUN
ejpam-4641	64	9	parameter	parameter	NOUN
ejpam-4641	64	10	,	,	PUNCT
ejpam-4641	64	11	λ	λ	PROPN
ejpam-4641	64	12	is	be	AUX
ejpam-4641	64	13	a	a	DET
ejpam-4641	64	14	scale	scale	NOUN
ejpam-4641	64	15	parameter	parameter	NOUN
ejpam-4641	64	16	and	and	CCONJ
ejpam-4641	64	17	a	a	DET
ejpam-4641	64	18	location	location	NOUN
ejpam-4641	64	19	parameter	parameter	NOUN
ejpam-4641	64	20	µ	µ	X
ejpam-4641	64	21	=	=	SYM
ejpam-4641	64	22	0	0	X
ejpam-4641	64	23	.	.	PUNCT
ejpam-4641	64	24	remark	remark	PROPN
ejpam-4641	64	25	1	1	NUM
ejpam-4641	64	26	.	.	PUNCT
ejpam-4641	65	1	the	the	DET
ejpam-4641	65	2	followings	following	NOUN
ejpam-4641	65	3	are	be	AUX
ejpam-4641	65	4	some	some	DET
ejpam-4641	65	5	previously	previously	ADV
ejpam-4641	65	6	introduced	introduce	VERB
ejpam-4641	65	7	expansions	expansion	NOUN
ejpam-4641	65	8	:	:	PUNCT
ejpam-4641	66	1	1	1	X
ejpam-4641	66	2	.	.	X
ejpam-4641	66	3	the	the	DET
ejpam-4641	66	4	logarithmic	logarithmic	ADJ
ejpam-4641	66	5	expansion	expansion	NOUN
ejpam-4641	66	6	introduced	introduce	VERB
ejpam-4641	66	7	by	by	ADP
ejpam-4641	66	8	balakrishnan	balakrishnan	PROPN
ejpam-4641	66	9	and	and	CCONJ
ejpam-4641	66	10	cohen	cohen	VERB
ejpam-4641	67	1	[	[	X
ejpam-4641	67	2	6	6	NUM
ejpam-4641	67	3	]	]	PUNCT
ejpam-4641	67	4	[	[	X
ejpam-4641	67	5	−ln(1−	−ln(1−	NOUN
ejpam-4641	67	6	t)]i	t)]i	NOUN
ejpam-4641	67	7	=	=	SYM
ejpam-4641	67	8	(	(	PUNCT
ejpam-4641	67	9	∞∑	∞∑	NUM
ejpam-4641	67	10	p=1	p=1	NOUN
ejpam-4641	67	11	tp	tp	ADP
ejpam-4641	67	12	p	p	NOUN
ejpam-4641	67	13	)	)	PUNCT
ejpam-4641	68	1	i	i	NOUN
ejpam-4641	68	2	=	=	SYM
ejpam-4641	69	1	∞∑	∞∑	NUM
ejpam-4641	69	2	p=0	p=0	PROPN
ejpam-4641	69	3	ap(i)t	ap(i)t	NUM
ejpam-4641	69	4	i+p	i+p	ADJ
ejpam-4641	69	5	,	,	PUNCT
ejpam-4641	69	6	|t|	|t|	VERB
ejpam-4641	69	7	<	<	X
ejpam-4641	69	8	1	1	NUM
ejpam-4641	69	9	(	(	PUNCT
ejpam-4641	69	10	7	7	NUM
ejpam-4641	69	11	)	)	PUNCT
ejpam-4641	69	12	where	where	SCONJ
ejpam-4641	69	13	ap(i	ap(i	NUM
ejpam-4641	69	14	)	)	PUNCT
ejpam-4641	69	15	is	be	AUX
ejpam-4641	69	16	the	the	DET
ejpam-4641	69	17	coefficient	coefficient	NOUN
ejpam-4641	69	18	of	of	ADP
ejpam-4641	69	19	ti+p	ti+p	PROPN
ejpam-4641	69	20	in	in	ADP
ejpam-4641	69	21	the	the	DET
ejpam-4641	69	22	expansion	expansion	NOUN
ejpam-4641	69	23	(	(	PUNCT
ejpam-4641	69	24	∑∞	∑∞	NOUN
ejpam-4641	69	25	p=1	p=1	X
ejpam-4641	69	26	tp	tp	X
ejpam-4641	69	27	p	p	NOUN
ejpam-4641	69	28	)	)	PUNCT
ejpam-4641	69	29	i	i	PRON
ejpam-4641	69	30	.	.	PUNCT
ejpam-4641	70	1	2	2	X
ejpam-4641	70	2	.	.	X
ejpam-4641	70	3	we	we	PRON
ejpam-4641	70	4	have	have	VERB
ejpam-4641	70	5	ix(a	ix(a	NOUN
ejpam-4641	70	6	,	,	PUNCT
ejpam-4641	70	7	b	b	NOUN
ejpam-4641	70	8	)	)	PUNCT
ejpam-4641	70	9	=	=	PUNCT
ejpam-4641	70	10	βx(a	βx(a	NOUN
ejpam-4641	70	11	,	,	PUNCT
ejpam-4641	70	12	b	b	NOUN
ejpam-4641	70	13	)	)	PUNCT
ejpam-4641	70	14	β(a	β(a	PROPN
ejpam-4641	70	15	,	,	PUNCT
ejpam-4641	70	16	b	b	NOUN
ejpam-4641	70	17	)	)	PUNCT
ejpam-4641	70	18	,	,	PUNCT
ejpam-4641	70	19	where	where	SCONJ
ejpam-4641	70	20	ix(a	ix(a	NOUN
ejpam-4641	70	21	,	,	PUNCT
ejpam-4641	70	22	b),βx(a	b),βx(a	NOUN
ejpam-4641	70	23	,	,	PUNCT
ejpam-4641	70	24	b	b	NOUN
ejpam-4641	70	25	)	)	PUNCT
ejpam-4641	70	26	and	and	CCONJ
ejpam-4641	70	27	β(a	β(a	PROPN
ejpam-4641	70	28	,	,	PUNCT
ejpam-4641	70	29	b	b	NOUN
ejpam-4641	70	30	)	)	PUNCT
ejpam-4641	70	31	represents	represent	VERB
ejpam-4641	70	32	the	the	DET
ejpam-4641	70	33	regularized	regularize	VERB
ejpam-4641	70	34	incomplete	incomplete	ADJ
ejpam-4641	70	35	beta	beta	NOUN
ejpam-4641	70	36	function	function	NOUN
ejpam-4641	70	37	,	,	PUNCT
ejpam-4641	70	38	the	the	DET
ejpam-4641	70	39	incomplete	incomplete	ADJ
ejpam-4641	70	40	beta	beta	NOUN
ejpam-4641	70	41	function	function	NOUN
ejpam-4641	70	42	and	and	CCONJ
ejpam-4641	70	43	the	the	DET
ejpam-4641	70	44	beta	beta	ADJ
ejpam-4641	70	45	function	function	NOUN
ejpam-4641	70	46	respectively	respectively	ADV
ejpam-4641	70	47	.	.	PUNCT
ejpam-4641	71	1	we	we	PRON
ejpam-4641	71	2	can	can	AUX
ejpam-4641	71	3	find	find	VERB
ejpam-4641	71	4	many	many	ADJ
ejpam-4641	71	5	series	series	NOUN
ejpam-4641	71	6	representations	representation	NOUN
ejpam-4641	71	7	for	for	ADP
ejpam-4641	71	8	ix(a	ix(a	NOUN
ejpam-4641	71	9	,	,	PUNCT
ejpam-4641	71	10	b	b	NOUN
ejpam-4641	71	11	)	)	PUNCT
ejpam-4641	71	12	in	in	ADP
ejpam-4641	71	13	many	many	ADJ
ejpam-4641	71	14	books	book	NOUN
ejpam-4641	71	15	and	and	CCONJ
ejpam-4641	71	16	journals	journal	NOUN
ejpam-4641	71	17	like	like	ADP
ejpam-4641	71	18	the	the	DET
ejpam-4641	71	19	following	following	NOUN
ejpam-4641	71	20	which	which	PRON
ejpam-4641	71	21	has	have	AUX
ejpam-4641	71	22	been	be	AUX
ejpam-4641	71	23	introduced	introduce	VERB
ejpam-4641	71	24	by	by	ADP
ejpam-4641	71	25	pearson	pearson	PROPN
ejpam-4641	72	1	[	[	X
ejpam-4641	72	2	18	18	NUM
ejpam-4641	72	3	]	]	PUNCT
ejpam-4641	72	4	ix(a	ix(a	NUM
ejpam-4641	72	5	,	,	PUNCT
ejpam-4641	72	6	b	b	NOUN
ejpam-4641	72	7	)	)	PUNCT
ejpam-4641	72	8	=	=	SYM
ejpam-4641	72	9	1−	1−	NUM
ejpam-4641	72	10	(	(	PUNCT
ejpam-4641	72	11	1−	1−	NUM
ejpam-4641	72	12	x)a+b−1	x)a+b−1	PROPN
ejpam-4641	72	13	a−1∑	a−1∑	PRON
ejpam-4641	72	14	i=0	i=0	PROPN
ejpam-4641	72	15	(	(	PUNCT
ejpam-4641	72	16	a+	a+	PUNCT
ejpam-4641	72	17	b−	b−	PROPN
ejpam-4641	72	18	1	1	NUM
ejpam-4641	72	19	i	i	NOUN
ejpam-4641	72	20	)	)	PUNCT
ejpam-4641	72	21	(	(	PUNCT
ejpam-4641	72	22	x	x	PROPN
ejpam-4641	72	23	1−	1−	NUM
ejpam-4641	72	24	x	x	X
ejpam-4641	72	25	)	)	PUNCT
ejpam-4641	73	1	i	i	PRON
ejpam-4641	73	2	,	,	PUNCT
ejpam-4641	73	3	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	73	4	/	/	SYM
ejpam-4641	73	5	eur	eur	PROPN
ejpam-4641	73	6	.	.	PUNCT
ejpam-4641	74	1	j.	j.	PROPN
ejpam-4641	74	2	pure	pure	PROPN
ejpam-4641	74	3	appl	appl	PROPN
ejpam-4641	74	4	.	.	PROPN
ejpam-4641	74	5	math	math	PROPN
ejpam-4641	74	6	,	,	PUNCT
ejpam-4641	74	7	16	16	NUM
ejpam-4641	74	8	(	(	PUNCT
ejpam-4641	74	9	1	1	NUM
ejpam-4641	74	10	)	)	PUNCT
ejpam-4641	74	11	(	(	PUNCT
ejpam-4641	74	12	2023	2023	NUM
ejpam-4641	74	13	)	)	PUNCT
ejpam-4641	74	14	,	,	PUNCT
ejpam-4641	74	15	97	97	NUM
ejpam-4641	74	16	-	-	SYM
ejpam-4641	74	17	111	111	NUM
ejpam-4641	74	18	100	100	NUM
ejpam-4641	74	19	from	from	ADP
ejpam-4641	74	20	which	which	PRON
ejpam-4641	74	21	we	we	PRON
ejpam-4641	74	22	conclude	conclude	VERB
ejpam-4641	74	23	that	that	PRON
ejpam-4641	74	24	βx(a	βx(a	NOUN
ejpam-4641	74	25	,	,	PUNCT
ejpam-4641	74	26	b	b	X
ejpam-4641	74	27	)	)	PUNCT
ejpam-4641	74	28	=	=	SYM
ejpam-4641	74	29	β(a	β(a	PROPN
ejpam-4641	74	30	,	,	PUNCT
ejpam-4641	74	31	b	b	NOUN
ejpam-4641	74	32	)	)	PUNCT
ejpam-4641	74	33	[	[	PUNCT
ejpam-4641	74	34	1−	1−	NUM
ejpam-4641	74	35	(	(	PUNCT
ejpam-4641	74	36	1−	1−	NUM
ejpam-4641	74	37	x)a+b−1	x)a+b−1	PROPN
ejpam-4641	74	38	a−1∑	a−1∑	PRON
ejpam-4641	74	39	i=0	i=0	PROPN
ejpam-4641	74	40	(	(	PUNCT
ejpam-4641	74	41	a+	a+	PUNCT
ejpam-4641	74	42	b−	b−	PROPN
ejpam-4641	74	43	1	1	NUM
ejpam-4641	74	44	i	i	NOUN
ejpam-4641	74	45	)	)	PUNCT
ejpam-4641	74	46	(	(	PUNCT
ejpam-4641	74	47	x	x	PROPN
ejpam-4641	74	48	1−	1−	NUM
ejpam-4641	74	49	x	x	X
ejpam-4641	74	50	)	)	PUNCT
ejpam-4641	74	51	i	i	NOUN
ejpam-4641	74	52	]	]	PUNCT
ejpam-4641	74	53	.	.	PUNCT
ejpam-4641	75	1	(	(	PUNCT
ejpam-4641	75	2	8)	8)	NUM
ejpam-4641	75	3	remark	remark	NOUN
ejpam-4641	75	4	2	2	NUM
ejpam-4641	75	5	.	.	PUNCT
ejpam-4641	76	1	we	we	PRON
ejpam-4641	76	2	can	can	AUX
ejpam-4641	76	3	conclude	conclude	VERB
ejpam-4641	76	4	the	the	DET
ejpam-4641	76	5	following	follow	VERB
ejpam-4641	76	6	characterized	characterize	VERB
ejpam-4641	76	7	differential	differential	NOUN
ejpam-4641	76	8	equation	equation	NOUN
ejpam-4641	76	9	f	f	X
ejpam-4641	76	10	(	(	PUNCT
ejpam-4641	76	11	x	x	X
ejpam-4641	76	12	)	)	PUNCT
ejpam-4641	76	13	=	=	SYM
ejpam-4641	76	14	1	1	NUM
ejpam-4641	76	15	λα	λα	NOUN
ejpam-4641	76	16	(	(	PUNCT
ejpam-4641	76	17	eλx	eλx	NOUN
ejpam-4641	76	18	−	−	PROPN
ejpam-4641	76	19	1)f(x	1)f(x	PROPN
ejpam-4641	76	20	)	)	PUNCT
ejpam-4641	76	21	,	,	PUNCT
ejpam-4641	76	22	(	(	PUNCT
ejpam-4641	76	23	9	9	X
ejpam-4641	76	24	)	)	PUNCT
ejpam-4641	76	25	which	which	PRON
ejpam-4641	76	26	will	will	AUX
ejpam-4641	76	27	be	be	AUX
ejpam-4641	76	28	used	use	VERB
ejpam-4641	76	29	in	in	ADP
ejpam-4641	76	30	some	some	PRON
ejpam-4641	76	31	of	of	ADP
ejpam-4641	76	32	the	the	DET
ejpam-4641	76	33	recurrence	recurrence	NOUN
ejpam-4641	76	34	relations	relation	NOUN
ejpam-4641	76	35	.	.	PUNCT
ejpam-4641	77	1	and	and	CCONJ
ejpam-4641	77	2	this	this	PRON
ejpam-4641	77	3	can	can	AUX
ejpam-4641	77	4	be	be	AUX
ejpam-4641	77	5	done	do	VERB
ejpam-4641	77	6	by	by	ADP
ejpam-4641	77	7	replacing	replace	VERB
ejpam-4641	77	8	the	the	DET
ejpam-4641	77	9	term	term	NOUN
ejpam-4641	77	10	(	(	PUNCT
ejpam-4641	77	11	1−	1−	NUM
ejpam-4641	77	12	e−λx)α	e−λx)α	ADV
ejpam-4641	77	13	from	from	ADP
ejpam-4641	77	14	(	(	PUNCT
ejpam-4641	77	15	5	5	NUM
ejpam-4641	77	16	)	)	PUNCT
ejpam-4641	77	17	by	by	ADP
ejpam-4641	77	18	f	f	PROPN
ejpam-4641	77	19	(	(	PUNCT
ejpam-4641	77	20	x	x	NOUN
ejpam-4641	77	21	)	)	PUNCT
ejpam-4641	77	22	,	,	PUNCT
ejpam-4641	77	23	which	which	PRON
ejpam-4641	77	24	will	will	AUX
ejpam-4641	77	25	lead	lead	VERB
ejpam-4641	77	26	to	to	ADP
ejpam-4641	77	27	f(x	f(x	PROPN
ejpam-4641	77	28	)	)	PUNCT
ejpam-4641	78	1	=	=	SYM
ejpam-4641	78	2	αλf	αλf	PROPN
ejpam-4641	78	3	(	(	PUNCT
ejpam-4641	78	4	x	x	NOUN
ejpam-4641	78	5	)	)	PUNCT
ejpam-4641	78	6	e−λx	e−λx	NOUN
ejpam-4641	78	7	1−	1−	NUM
ejpam-4641	78	8	e−λx	e−λx	NOUN
ejpam-4641	78	9	.	.	PUNCT
ejpam-4641	79	1	then	then	ADV
ejpam-4641	79	2	f	f	X
ejpam-4641	79	3	(	(	PUNCT
ejpam-4641	79	4	x	x	X
ejpam-4641	79	5	)	)	PUNCT
ejpam-4641	79	6	=	=	SYM
ejpam-4641	79	7	1	1	NUM
ejpam-4641	79	8	αλ	αλ	DET
ejpam-4641	79	9	1−	1−	NUM
ejpam-4641	79	10	e−λx	e−λx	NOUN
ejpam-4641	79	11	e−λx	e−λx	VERB
ejpam-4641	79	12	f(x	f(x	PROPN
ejpam-4641	79	13	)	)	PUNCT
ejpam-4641	79	14	=	=	PUNCT
ejpam-4641	80	1	1	1	NUM
ejpam-4641	80	2	αλ	αλ	PRON
ejpam-4641	80	3	(	(	PUNCT
ejpam-4641	80	4	1	1	NUM
ejpam-4641	80	5	e−λx	e−λx	NOUN
ejpam-4641	80	6	−	−	PROPN
ejpam-4641	80	7	1)f(x	1)f(x	NUM
ejpam-4641	80	8	)	)	PUNCT
ejpam-4641	80	9	=	=	PUNCT
ejpam-4641	80	10	.	.	PUNCT
ejpam-4641	81	1	remark	remark	PROPN
ejpam-4641	81	2	3	3	NUM
ejpam-4641	81	3	.	.	PUNCT
ejpam-4641	82	1	the	the	DET
ejpam-4641	82	2	following	follow	VERB
ejpam-4641	82	3	relations	relation	NOUN
ejpam-4641	82	4	will	will	AUX
ejpam-4641	82	5	be	be	AUX
ejpam-4641	82	6	used	use	VERB
ejpam-4641	82	7	in	in	ADP
ejpam-4641	82	8	the	the	DET
ejpam-4641	82	9	proof	proof	NOUN
ejpam-4641	82	10	of	of	ADP
ejpam-4641	82	11	some	some	DET
ejpam-4641	82	12	theorems	theorem	NOUN
ejpam-4641	82	13	(	(	PUNCT
ejpam-4641	82	14	see	see	VERB
ejpam-4641	82	15	,	,	PUNCT
ejpam-4641	82	16	raqab	raqab	NOUN
ejpam-4641	82	17	[	[	X
ejpam-4641	82	18	19	19	NUM
ejpam-4641	82	19	]	]	PUNCT
ejpam-4641	82	20	)	)	PUNCT
ejpam-4641	83	1	βx(a	βx(a	PUNCT
ejpam-4641	83	2	,	,	PUNCT
ejpam-4641	83	3	b	b	X
ejpam-4641	83	4	)	)	PUNCT
ejpam-4641	83	5	=	=	VERB
ejpam-4641	84	1	a−1xa	a−1xa	NOUN
ejpam-4641	84	2	2f1(a	2f1(a	NUM
ejpam-4641	84	3	,	,	PUNCT
ejpam-4641	84	4	1−	1−	NUM
ejpam-4641	84	5	b	b	NOUN
ejpam-4641	84	6	;	;	PUNCT
ejpam-4641	84	7	a+	a+	X
ejpam-4641	84	8	1;x	1;x	NOUN
ejpam-4641	84	9	)	)	PUNCT
ejpam-4641	84	10	,	,	PUNCT
ejpam-4641	84	11	(	(	PUNCT
ejpam-4641	84	12	10)∫	10)∫	NUM
ejpam-4641	84	13	1	1	NUM
ejpam-4641	84	14	0	0	NUM
ejpam-4641	84	15	ua−1(1−	ua−1(1−	ADJ
ejpam-4641	84	16	u)b−1	u)b−1	NOUN
ejpam-4641	84	17	2f1(c	2f1(c	NUM
ejpam-4641	84	18	,	,	PUNCT
ejpam-4641	84	19	d	d	X
ejpam-4641	84	20	;	;	PUNCT
ejpam-4641	84	21	ρ;u)du	ρ;u)du	PROPN
ejpam-4641	84	22	=	=	SYM
ejpam-4641	84	23	β(a	β(a	PROPN
ejpam-4641	84	24	,	,	PUNCT
ejpam-4641	84	25	b	b	NOUN
ejpam-4641	84	26	)	)	PUNCT
ejpam-4641	84	27	3f2(a	3f2(a	NOUN
ejpam-4641	84	28	,	,	PUNCT
ejpam-4641	84	29	c	c	X
ejpam-4641	84	30	,	,	PUNCT
ejpam-4641	84	31	d	d	NOUN
ejpam-4641	84	32	;	;	PUNCT
ejpam-4641	84	33	ρ	ρ	NUM
ejpam-4641	84	34	,	,	PUNCT
ejpam-4641	84	35	a+	a+	PUNCT
ejpam-4641	84	36	b	b	X
ejpam-4641	84	37	;	;	PUNCT
ejpam-4641	84	38	1	1	NUM
ejpam-4641	84	39	)	)	PUNCT
ejpam-4641	84	40	.	.	PUNCT
ejpam-4641	85	1	(	(	PUNCT
ejpam-4641	85	2	11	11	NUM
ejpam-4641	85	3	)	)	PUNCT
ejpam-4641	85	4	where	where	SCONJ
ejpam-4641	85	5	2f1	2f1	NUM
ejpam-4641	85	6	and	and	CCONJ
ejpam-4641	85	7	3f2	3f2	NUM
ejpam-4641	85	8	are	be	AUX
ejpam-4641	85	9	generalized	generalize	VERB
ejpam-4641	85	10	hypergeometric	hypergeometric	ADJ
ejpam-4641	85	11	function	function	NOUN
ejpam-4641	85	12	’s	’s	PART
ejpam-4641	85	13	special	special	ADJ
ejpam-4641	85	14	cases	case	NOUN
ejpam-4641	85	15	.	.	PUNCT
ejpam-4641	86	1	3	3	X
ejpam-4641	86	2	.	.	X
ejpam-4641	86	3	moment	moment	NOUN
ejpam-4641	86	4	generating	generating	NOUN
ejpam-4641	86	5	functions	function	NOUN
ejpam-4641	86	6	in	in	ADP
ejpam-4641	86	7	this	this	DET
ejpam-4641	86	8	section	section	NOUN
ejpam-4641	86	9	,	,	PUNCT
ejpam-4641	86	10	we	we	PRON
ejpam-4641	86	11	will	will	AUX
ejpam-4641	86	12	introduce	introduce	VERB
ejpam-4641	86	13	some	some	DET
ejpam-4641	86	14	new	new	ADJ
ejpam-4641	86	15	formulas	formula	NOUN
ejpam-4641	86	16	for	for	ADP
ejpam-4641	86	17	calculating	calculate	VERB
ejpam-4641	86	18	the	the	DET
ejpam-4641	86	19	mgf	mgf	NOUN
ejpam-4641	86	20	of	of	ADP
ejpam-4641	86	21	the	the	DET
ejpam-4641	86	22	lower	low	ADJ
ejpam-4641	86	23	current	current	ADJ
ejpam-4641	86	24	recordmlc	recordmlc	NOUN
ejpam-4641	86	25	n	n	PROPN
ejpam-4641	86	26	(	(	PUNCT
ejpam-4641	86	27	t	t	PROPN
ejpam-4641	86	28	)	)	PUNCT
ejpam-4641	86	29	,	,	PUNCT
ejpam-4641	86	30	mgf	mgf	PROPN
ejpam-4641	86	31	of	of	ADP
ejpam-4641	86	32	the	the	DET
ejpam-4641	86	33	upper	upper	ADJ
ejpam-4641	86	34	current	current	ADJ
ejpam-4641	86	35	recordmuc	recordmuc	ADJ
ejpam-4641	86	36	n	n	PROPN
ejpam-4641	86	37	(	(	PUNCT
ejpam-4641	86	38	t	t	PROPN
ejpam-4641	86	39	)	)	PUNCT
ejpam-4641	86	40	and	and	CCONJ
ejpam-4641	86	41	joint	joint	ADJ
ejpam-4641	86	42	mgf	mgf	NOUN
ejpam-4641	86	43	of	of	ADP
ejpam-4641	86	44	lower	low	ADJ
ejpam-4641	86	45	and	and	CCONJ
ejpam-4641	86	46	upper	upper	ADJ
ejpam-4641	86	47	current	current	ADJ
ejpam-4641	86	48	records	record	NOUN
ejpam-4641	86	49	mlc	mlc	PROPN
ejpam-4641	86	50	n	n	CCONJ
ejpam-4641	86	51	,	,	PUNCT
ejpam-4641	86	52	u	u	PROPN
ejpam-4641	86	53	c	c	PROPN
ejpam-4641	86	54	n	n	PROPN
ejpam-4641	86	55	(	(	PUNCT
ejpam-4641	86	56	t1	t1	PROPN
ejpam-4641	86	57	,	,	PUNCT
ejpam-4641	86	58	t2	t2	NOUN
ejpam-4641	86	59	)	)	PUNCT
ejpam-4641	86	60	all	all	PRON
ejpam-4641	86	61	based	base	VERB
ejpam-4641	86	62	on	on	ADP
ejpam-4641	86	63	ged	ge	VERB
ejpam-4641	86	64	.	.	PUNCT
ejpam-4641	87	1	theorem	theorem	NOUN
ejpam-4641	87	2	1	1	NUM
ejpam-4641	87	3	.	.	PUNCT
ejpam-4641	87	4	for	for	ADP
ejpam-4641	87	5	n	n	PROPN
ejpam-4641	87	6	≥	≥	NUM
ejpam-4641	87	7	2	2	NUM
ejpam-4641	87	8	mlc	mlc	PROPN
ejpam-4641	87	9	n	n	PROPN
ejpam-4641	87	10	(	(	PUNCT
ejpam-4641	87	11	t	t	PROPN
ejpam-4641	87	12	)	)	PUNCT
ejpam-4641	87	13	=	=	SYM
ejpam-4641	88	1	2nα	2nα	NOUN
ejpam-4641	88	2	[	[	PUNCT
ejpam-4641	88	3	β(α	β(α	PROPN
ejpam-4641	88	4	,	,	PUNCT
ejpam-4641	88	5	1−	1−	NUM
ejpam-4641	88	6	t	t	NOUN
ejpam-4641	88	7	λ	λ	PROPN
ejpam-4641	88	8	)	)	PUNCT
ejpam-4641	88	9	−	−	PROPN
ejpam-4641	88	10	β(2α	β(2α	ADP
ejpam-4641	88	11	,	,	PUNCT
ejpam-4641	88	12	1−	1−	NUM
ejpam-4641	88	13	t	t	NOUN
ejpam-4641	88	14	λ	λ	PROPN
ejpam-4641	88	15	)	)	PUNCT
ejpam-4641	88	16	−	−	PROPN
ejpam-4641	89	1	n−1∑	n−1∑	PROPN
ejpam-4641	89	2	k=1	k=1	INTJ
ejpam-4641	90	1	αk	αk	AUX
ejpam-4641	90	2	k	k	NOUN
ejpam-4641	90	3	!	!	PUNCT
ejpam-4641	91	1	∞∑	∞∑	NUM
ejpam-4641	91	2	p=0	p=0	PROPN
ejpam-4641	91	3	ap(k)β(2α	ap(k)β(2α	NOUN
ejpam-4641	91	4	,	,	PUNCT
ejpam-4641	91	5	1	1	NUM
ejpam-4641	92	1	+	+	CCONJ
ejpam-4641	92	2	k	k	NOUN
ejpam-4641	93	1	+	+	CCONJ
ejpam-4641	93	2	p−	p−	NOUN
ejpam-4641	93	3	t	t	NOUN
ejpam-4641	93	4	λ	λ	PROPN
ejpam-4641	93	5	)	)	PUNCT
ejpam-4641	93	6	]	]	PUNCT
ejpam-4641	93	7	.	.	PUNCT
ejpam-4641	94	1	(	(	PUNCT
ejpam-4641	94	2	12	12	NUM
ejpam-4641	94	3	)	)	PUNCT
ejpam-4641	94	4	while	while	SCONJ
ejpam-4641	94	5	muc	muc	PROPN
ejpam-4641	94	6	n	n	PROPN
ejpam-4641	94	7	(	(	PUNCT
ejpam-4641	94	8	t	t	PROPN
ejpam-4641	94	9	)	)	PUNCT
ejpam-4641	94	10	=	=	SYM
ejpam-4641	94	11	2nα	2nα	NOUN
ejpam-4641	94	12	[	[	PUNCT
ejpam-4641	94	13	β(2α	β(2α	NUM
ejpam-4641	94	14	,	,	PUNCT
ejpam-4641	94	15	1−	1−	NUM
ejpam-4641	94	16	t	t	NOUN
ejpam-4641	94	17	λ	λ	PROPN
ejpam-4641	94	18	)	)	PUNCT
ejpam-4641	94	19	−	−	PROPN
ejpam-4641	95	1	n−1∑	n−1∑	NUM
ejpam-4641	95	2	k=1	k=1	PROPN
ejpam-4641	95	3	1	1	NUM
ejpam-4641	95	4	k	k	NOUN
ejpam-4641	95	5	!	!	PUNCT
ejpam-4641	96	1	∞∑	∞∑	NUM
ejpam-4641	96	2	p=0	p=0	PROPN
ejpam-4641	96	3	ap(k	ap(k	NOUN
ejpam-4641	96	4	)	)	PUNCT
ejpam-4641	96	5	{	{	PUNCT
ejpam-4641	97	1	β((1	β((1	PROPN
ejpam-4641	98	1	+	+	NUM
ejpam-4641	98	2	k	k	X
ejpam-4641	98	3	+	+	CCONJ
ejpam-4641	98	4	p)α	p)α	NOUN
ejpam-4641	98	5	,	,	PUNCT
ejpam-4641	98	6	1−	1−	NUM
ejpam-4641	98	7	t	t	NOUN
ejpam-4641	98	8	λ	λ	PROPN
ejpam-4641	98	9	)	)	PUNCT
ejpam-4641	98	10	−	−	PROPN
ejpam-4641	99	1	β((2	β((2	PROPN
ejpam-4641	99	2	+	+	CCONJ
ejpam-4641	99	3	k	k	PROPN
ejpam-4641	99	4	+	+	CCONJ
ejpam-4641	99	5	p)α	p)α	NOUN
ejpam-4641	99	6	,	,	PUNCT
ejpam-4641	99	7	1−	1−	NUM
ejpam-4641	99	8	t	t	NOUN
ejpam-4641	99	9	λ	λ	PROPN
ejpam-4641	99	10	)	)	PUNCT
ejpam-4641	99	11	}	}	PUNCT
ejpam-4641	99	12	]	]	PUNCT
ejpam-4641	99	13	.	.	PUNCT
ejpam-4641	100	1	(	(	PUNCT
ejpam-4641	100	2	13	13	NUM
ejpam-4641	100	3	)	)	PUNCT
ejpam-4641	100	4	r.a.aldallal	r.a.aldallal	NOUN
ejpam-4641	100	5	/	/	SYM
ejpam-4641	100	6	eur	eur	PROPN
ejpam-4641	100	7	.	.	PUNCT
ejpam-4641	101	1	j.	j.	PROPN
ejpam-4641	101	2	pure	pure	PROPN
ejpam-4641	101	3	appl	appl	PROPN
ejpam-4641	101	4	.	.	PROPN
ejpam-4641	101	5	math	math	PROPN
ejpam-4641	101	6	,	,	PUNCT
ejpam-4641	101	7	16	16	NUM
ejpam-4641	101	8	(	(	PUNCT
ejpam-4641	101	9	1	1	NUM
ejpam-4641	101	10	)	)	PUNCT
ejpam-4641	101	11	(	(	PUNCT
ejpam-4641	101	12	2023	2023	NUM
ejpam-4641	101	13	)	)	PUNCT
ejpam-4641	101	14	,	,	PUNCT
ejpam-4641	101	15	97	97	NUM
ejpam-4641	101	16	-	-	SYM
ejpam-4641	101	17	111	111	NUM
ejpam-4641	101	18	101	101	NUM
ejpam-4641	101	19	and	and	CCONJ
ejpam-4641	101	20	mlc	mlc	PROPN
ejpam-4641	101	21	n	n	CCONJ
ejpam-4641	101	22	,	,	PUNCT
ejpam-4641	101	23	u	u	PROPN
ejpam-4641	101	24	c	c	PROPN
ejpam-4641	101	25	n	n	PROPN
ejpam-4641	101	26	(	(	PUNCT
ejpam-4641	101	27	t1	t1	PROPN
ejpam-4641	101	28	,	,	PUNCT
ejpam-4641	101	29	t2	t2	NOUN
ejpam-4641	101	30	)	)	PUNCT
ejpam-4641	101	31	=	=	SYM
ejpam-4641	101	32	2nα2	2nα2	NUM
ejpam-4641	101	33	(	(	PUNCT
ejpam-4641	101	34	n−	n−	NOUN
ejpam-4641	101	35	1	1	NUM
ejpam-4641	101	36	)	)	PUNCT
ejpam-4641	101	37	!	!	PUNCT
ejpam-4641	102	1	∞∑	∞∑	NUM
ejpam-4641	102	2	p=0	p=0	NOUN
ejpam-4641	102	3	ap(n−	ap(n−	VERB
ejpam-4641	102	4	1	1	X
ejpam-4641	102	5	)	)	PUNCT
ejpam-4641	102	6	n+p−1∑	n+p−1∑	ADJ
ejpam-4641	102	7	k=0	k=0	PROPN
ejpam-4641	102	8	(	(	PUNCT
ejpam-4641	102	9	n+	n+	X
ejpam-4641	102	10	p−	p−	NOUN
ejpam-4641	102	11	1	1	NUM
ejpam-4641	102	12	k	k	NOUN
ejpam-4641	102	13	)	)	PUNCT
ejpam-4641	102	14	(	(	PUNCT
ejpam-4641	102	15	−1)kβ(αk	−1)kβ(αk	PROPN
ejpam-4641	102	16	+	+	CCONJ
ejpam-4641	102	17	1	1	NUM
ejpam-4641	102	18	,	,	PUNCT
ejpam-4641	102	19	1−	1−	NUM
ejpam-4641	102	20	t1	t1	NOUN
ejpam-4641	102	21	λ	λ	PROPN
ejpam-4641	102	22	)	)	PUNCT
ejpam-4641	102	23	[	[	PUNCT
ejpam-4641	102	24	β(α	β(α	PROPN
ejpam-4641	102	25	,	,	PUNCT
ejpam-4641	102	26	1−	1−	NUM
ejpam-4641	102	27	t2	t2	PROPN
ejpam-4641	102	28	λ	λ	PROPN
ejpam-4641	102	29	)	)	PUNCT
ejpam-4641	102	30	−	−	PROPN
ejpam-4641	102	31	αk∑	αk∑	PROPN
ejpam-4641	102	32	i=0	i=0	PROPN
ejpam-4641	102	33	(	(	PUNCT
ejpam-4641	102	34	αk	αk	NOUN
ejpam-4641	102	35	−	−	PROPN
ejpam-4641	102	36	t1	t1	NOUN
ejpam-4641	102	37	λ	λ	PROPN
ejpam-4641	102	38	+	+	CCONJ
ejpam-4641	102	39	1	1	NUM
ejpam-4641	102	40	i	i	NOUN
ejpam-4641	102	41	)	)	PUNCT
ejpam-4641	102	42	β((n+	β((n+	PUNCT
ejpam-4641	103	1	p−	p−	NOUN
ejpam-4641	103	2	k)α−	k)α−	NOUN
ejpam-4641	103	3	1	1	NUM
ejpam-4641	103	4	+	+	CCONJ
ejpam-4641	103	5	i	i	PRON
ejpam-4641	103	6	,	,	PUNCT
ejpam-4641	103	7	2	2	NUM
ejpam-4641	103	8	+	+	NUM
ejpam-4641	103	9	i+	i+	NOUN
ejpam-4641	103	10	αk	αk	ADP
ejpam-4641	103	11	−	−	PROPN
ejpam-4641	103	12	t1	t1	NOUN
ejpam-4641	103	13	λ	λ	PROPN
ejpam-4641	103	14	−	−	PROPN
ejpam-4641	103	15	t2	t2	PROPN
ejpam-4641	103	16	λ	λ	PROPN
ejpam-4641	103	17	)	)	PUNCT
ejpam-4641	103	18	]	]	PUNCT
ejpam-4641	103	19	.	.	PUNCT
ejpam-4641	104	1	(	(	PUNCT
ejpam-4641	104	2	14	14	NUM
ejpam-4641	104	3	)	)	PUNCT
ejpam-4641	104	4	proof	proof	NOUN
ejpam-4641	104	5	.	.	PUNCT
ejpam-4641	105	1	by	by	ADP
ejpam-4641	105	2	substituting	substitute	VERB
ejpam-4641	105	3	(	(	PUNCT
ejpam-4641	105	4	5	5	NUM
ejpam-4641	105	5	)	)	PUNCT
ejpam-4641	105	6	and	and	CCONJ
ejpam-4641	105	7	(	(	PUNCT
ejpam-4641	105	8	6	6	NUM
ejpam-4641	105	9	)	)	PUNCT
ejpam-4641	105	10	in	in	ADP
ejpam-4641	105	11	(	(	PUNCT
ejpam-4641	105	12	1	1	NUM
ejpam-4641	105	13	)	)	PUNCT
ejpam-4641	105	14	,	,	PUNCT
ejpam-4641	105	15	we	we	PRON
ejpam-4641	105	16	get	get	VERB
ejpam-4641	105	17	flc	flc	PROPN
ejpam-4641	105	18	n	n	PROPN
ejpam-4641	105	19	(	(	PUNCT
ejpam-4641	105	20	x	x	X
ejpam-4641	105	21	)	)	PUNCT
ejpam-4641	105	22	=	=	SYM
ejpam-4641	105	23	2nαλ(1−	2nαλ(1−	NUM
ejpam-4641	105	24	e−λx)α−1e−λx	e−λx)α−1e−λx	NOUN
ejpam-4641	105	25	{	{	PUNCT
ejpam-4641	105	26	1−	1−	NUM
ejpam-4641	105	27	(	(	PUNCT
ejpam-4641	105	28	1−	1−	NUM
ejpam-4641	105	29	e−λx)α	e−λx)α	ADV
ejpam-4641	105	30	n−1∑	n−1∑	PROPN
ejpam-4641	105	31	k=0	k=0	PUNCT
ejpam-4641	106	1	[	[	X
ejpam-4641	106	2	−	−	X
ejpam-4641	106	3	log(1−	log(1−	PROPN
ejpam-4641	106	4	e−λx)α]k	e−λx)α]k	PROPN
ejpam-4641	106	5	k	k	X
ejpam-4641	106	6	!	!	PUNCT
ejpam-4641	106	7	}	}	PUNCT
ejpam-4641	107	1	=	=	SYM
ejpam-4641	107	2	2nαλ(1−	2nαλ(1−	NUM
ejpam-4641	107	3	e−λx)α−1e−λx	e−λx)α−1e−λx	NOUN
ejpam-4641	107	4	{	{	PUNCT
ejpam-4641	107	5	1−	1−	NUM
ejpam-4641	107	6	(	(	PUNCT
ejpam-4641	107	7	1−	1−	NUM
ejpam-4641	107	8	e−λx)α	e−λx)α	ADV
ejpam-4641	107	9	−	−	PROPN
ejpam-4641	107	10	(	(	PUNCT
ejpam-4641	107	11	1−	1−	NUM
ejpam-4641	107	12	e−λx)α	e−λx)α	ADV
ejpam-4641	107	13	n−1∑	n−1∑	NUM
ejpam-4641	107	14	k=1	k=1	PUNCT
ejpam-4641	108	1	[	[	X
ejpam-4641	108	2	−	−	X
ejpam-4641	108	3	log(1−	log(1−	PROPN
ejpam-4641	108	4	e−λx)α]k	e−λx)α]k	PROPN
ejpam-4641	108	5	k	k	PROPN
ejpam-4641	108	6	!	!	PUNCT
ejpam-4641	108	7	}	}	PUNCT
ejpam-4641	108	8	.	.	PUNCT
ejpam-4641	109	1	so	so	ADV
ejpam-4641	109	2	mlc	mlc	PROPN
ejpam-4641	109	3	n	n	PROPN
ejpam-4641	109	4	(	(	PUNCT
ejpam-4641	109	5	t	t	PROPN
ejpam-4641	109	6	)	)	PUNCT
ejpam-4641	109	7	=	=	PUNCT
ejpam-4641	110	1	2nαλ	2nαλ	NUM
ejpam-4641	110	2	∫	∫	NOUN
ejpam-4641	110	3	∞	∞	NOUN
ejpam-4641	110	4	0	0	NUM
ejpam-4641	110	5	e−(λ−t)x(1−	e−(λ−t)x(1−	X
ejpam-4641	110	6	e−λx)α−1dx−	e−λx)α−1dx−	X
ejpam-4641	110	7	2nαλ	2nαλ	NUM
ejpam-4641	110	8	∫	∫	NOUN
ejpam-4641	110	9	∞	∞	NOUN
ejpam-4641	110	10	0	0	NUM
ejpam-4641	110	11	e−(λ−t)x(1−	e−(λ−t)x(1−	PROPN
ejpam-4641	110	12	e−λx)2α−1dx	e−λx)2α−1dx	ADJ
ejpam-4641	110	13	−2nαλ	−2nαλ	NOUN
ejpam-4641	110	14	∫	∫	PROPN
ejpam-4641	110	15	∞	∞	NOUN
ejpam-4641	110	16	0	0	NUM
ejpam-4641	111	1	e−(λ−t)x(1−	e−(λ−t)x(1−	AUX
ejpam-4641	111	2	e−λx)2α−1	e−λx)2α−1	PROPN
ejpam-4641	111	3	n−1∑	n−1∑	NUM
ejpam-4641	111	4	k=1	k=1	PUNCT
ejpam-4641	111	5	αk[−	αk[−	PUNCT
ejpam-4641	111	6	log(1−	log(1−	PROPN
ejpam-4641	111	7	e−λx)]k	e−λx)]k	PROPN
ejpam-4641	111	8	k	k	PROPN
ejpam-4641	111	9	!	!	PUNCT
ejpam-4641	111	10	dx	dx	PROPN
ejpam-4641	112	1	=	=	SYM
ejpam-4641	112	2	2nα[β(α	2nα[β(α	NUM
ejpam-4641	112	3	,	,	PUNCT
ejpam-4641	112	4	1−	1−	NUM
ejpam-4641	112	5	t	t	NOUN
ejpam-4641	112	6	λ	λ	PROPN
ejpam-4641	112	7	)	)	PUNCT
ejpam-4641	112	8	−	−	PROPN
ejpam-4641	112	9	β(2α	β(2α	ADP
ejpam-4641	112	10	,	,	PUNCT
ejpam-4641	112	11	1−	1−	NUM
ejpam-4641	112	12	t	t	NOUN
ejpam-4641	112	13	λ	λ	PROPN
ejpam-4641	112	14	)	)	PUNCT
ejpam-4641	112	15	]	]	X
ejpam-4641	112	16	−k(t	−k(t	NOUN
ejpam-4641	112	17	)	)	PUNCT
ejpam-4641	112	18	.	.	PUNCT
ejpam-4641	113	1	upon	upon	SCONJ
ejpam-4641	113	2	using	use	VERB
ejpam-4641	113	3	the	the	DET
ejpam-4641	113	4	substitution	substitution	NOUN
ejpam-4641	113	5	a	a	DET
ejpam-4641	113	6	=	=	PUNCT
ejpam-4641	113	7	e−λx	e−λx	NOUN
ejpam-4641	113	8	ink(t	ink(t	NUM
ejpam-4641	113	9	)	)	PUNCT
ejpam-4641	113	10	and	and	CCONJ
ejpam-4641	113	11	then	then	ADV
ejpam-4641	113	12	applying	apply	VERB
ejpam-4641	113	13	the	the	DET
ejpam-4641	113	14	logarithmic	logarithmic	ADJ
ejpam-4641	113	15	expansion	expansion	NOUN
ejpam-4641	113	16	from	from	ADP
ejpam-4641	113	17	(	(	PUNCT
ejpam-4641	113	18	7	7	NUM
ejpam-4641	113	19	)	)	PUNCT
ejpam-4641	113	20	,	,	PUNCT
ejpam-4641	113	21	we	we	PRON
ejpam-4641	113	22	reach	reach	VERB
ejpam-4641	113	23	the	the	DET
ejpam-4641	113	24	following	follow	VERB
ejpam-4641	113	25	result	result	NOUN
ejpam-4641	113	26	k(t	k(t	X
ejpam-4641	113	27	)	)	PUNCT
ejpam-4641	114	1	=	=	SYM
ejpam-4641	114	2	2n	2n	NUM
ejpam-4641	115	1	n−1∑	n−1∑	PROPN
ejpam-4641	115	2	k=1	k=1	PROPN
ejpam-4641	115	3	αk+1	αk+1	NUM
ejpam-4641	115	4	k	k	NOUN
ejpam-4641	115	5	!	!	PUNCT
ejpam-4641	116	1	∞∑	∞∑	NUM
ejpam-4641	116	2	p=0	p=0	PROPN
ejpam-4641	116	3	ap(k)β(2α	ap(k)β(2α	NOUN
ejpam-4641	116	4	,	,	PUNCT
ejpam-4641	116	5	1	1	NUM
ejpam-4641	117	1	+	+	CCONJ
ejpam-4641	117	2	k	k	NOUN
ejpam-4641	118	1	+	+	X
ejpam-4641	118	2	p−	p−	NOUN
ejpam-4641	118	3	t	t	NOUN
ejpam-4641	118	4	λ	λ	PROPN
ejpam-4641	118	5	)	)	PUNCT
ejpam-4641	118	6	,	,	PUNCT
ejpam-4641	118	7	which	which	PRON
ejpam-4641	118	8	completes	complete	VERB
ejpam-4641	118	9	the	the	DET
ejpam-4641	118	10	proof	proof	NOUN
ejpam-4641	118	11	of	of	ADP
ejpam-4641	118	12	(	(	PUNCT
ejpam-4641	118	13	12	12	NUM
ejpam-4641	118	14	)	)	PUNCT
ejpam-4641	118	15	.	.	PUNCT
ejpam-4641	119	1	now	now	ADV
ejpam-4641	119	2	to	to	ADP
ejpam-4641	119	3	proof	proof	NOUN
ejpam-4641	119	4	(	(	PUNCT
ejpam-4641	119	5	13	13	NUM
ejpam-4641	119	6	)	)	PUNCT
ejpam-4641	119	7	,	,	PUNCT
ejpam-4641	119	8	we	we	PRON
ejpam-4641	119	9	will	will	AUX
ejpam-4641	119	10	substitute	substitute	VERB
ejpam-4641	119	11	(	(	PUNCT
ejpam-4641	119	12	5	5	NUM
ejpam-4641	119	13	)	)	PUNCT
ejpam-4641	119	14	and	and	CCONJ
ejpam-4641	119	15	(	(	PUNCT
ejpam-4641	119	16	6	6	NUM
ejpam-4641	119	17	)	)	PUNCT
ejpam-4641	119	18	in	in	ADP
ejpam-4641	119	19	(	(	PUNCT
ejpam-4641	119	20	2	2	NUM
ejpam-4641	119	21	)	)	PUNCT
ejpam-4641	119	22	and	and	CCONJ
ejpam-4641	119	23	with	with	ADP
ejpam-4641	119	24	a	a	DET
ejpam-4641	119	25	routine	routine	ADJ
ejpam-4641	119	26	calculation	calculation	NOUN
ejpam-4641	119	27	we	we	PRON
ejpam-4641	119	28	get	get	VERB
ejpam-4641	119	29	fuc	fuc	ADJ
ejpam-4641	119	30	n	n	CCONJ
ejpam-4641	119	31	(	(	PUNCT
ejpam-4641	119	32	x	x	X
ejpam-4641	119	33	)	)	PUNCT
ejpam-4641	119	34	=	=	SYM
ejpam-4641	119	35	2nαλ(1−	2nαλ(1−	NUM
ejpam-4641	119	36	e−λx)α−1e−λx	e−λx)α−1e−λx	NOUN
ejpam-4641	119	37	{	{	PUNCT
ejpam-4641	119	38	−	−	PROPN
ejpam-4641	119	39	n−1∑	n−1∑	PROPN
ejpam-4641	119	40	k=1	k=1	PUNCT
ejpam-4641	120	1	[	[	X
ejpam-4641	120	2	−	−	X
ejpam-4641	120	3	log(1−	log(1−	PROPN
ejpam-4641	120	4	(	(	PUNCT
ejpam-4641	120	5	1−	1−	NUM
ejpam-4641	120	6	e−λx)α)]k	e−λx)α)]k	PROPN
ejpam-4641	120	7	k	k	X
ejpam-4641	120	8	!	!	PUNCT
ejpam-4641	121	1	+	+	CCONJ
ejpam-4641	121	2	(	(	PUNCT
ejpam-4641	121	3	1−	1−	NUM
ejpam-4641	121	4	e−λx)α	e−λx)α	ADV
ejpam-4641	121	5	+	+	PROPN
ejpam-4641	121	6	(	(	PUNCT
ejpam-4641	121	7	1−	1−	NUM
ejpam-4641	121	8	e−λx)α	e−λx)α	ADV
ejpam-4641	121	9	n−1∑	n−1∑	NUM
ejpam-4641	121	10	k=1	k=1	PUNCT
ejpam-4641	122	1	[	[	X
ejpam-4641	122	2	−	−	X
ejpam-4641	122	3	log(1−	log(1−	PROPN
ejpam-4641	122	4	(	(	PUNCT
ejpam-4641	122	5	1−	1−	NUM
ejpam-4641	122	6	e−λx)α)]k	e−λx)α)]k	PROPN
ejpam-4641	122	7	k	k	X
ejpam-4641	122	8	!	!	PUNCT
ejpam-4641	122	9	}	}	PUNCT
ejpam-4641	122	10	.	.	PUNCT
ejpam-4641	123	1	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	123	2	/	/	SYM
ejpam-4641	123	3	eur	eur	PROPN
ejpam-4641	123	4	.	.	PUNCT
ejpam-4641	124	1	j.	j.	PROPN
ejpam-4641	124	2	pure	pure	PROPN
ejpam-4641	124	3	appl	appl	PROPN
ejpam-4641	124	4	.	.	PROPN
ejpam-4641	124	5	math	math	PROPN
ejpam-4641	124	6	,	,	PUNCT
ejpam-4641	124	7	16	16	NUM
ejpam-4641	124	8	(	(	PUNCT
ejpam-4641	124	9	1	1	NUM
ejpam-4641	124	10	)	)	PUNCT
ejpam-4641	124	11	(	(	PUNCT
ejpam-4641	124	12	2023	2023	NUM
ejpam-4641	124	13	)	)	PUNCT
ejpam-4641	124	14	,	,	PUNCT
ejpam-4641	124	15	97	97	NUM
ejpam-4641	124	16	-	-	SYM
ejpam-4641	124	17	111	111	NUM
ejpam-4641	124	18	102	102	NUM
ejpam-4641	124	19	then	then	ADV
ejpam-4641	124	20	muc	muc	PROPN
ejpam-4641	124	21	n	n	PROPN
ejpam-4641	124	22	(	(	PUNCT
ejpam-4641	124	23	t	t	PROPN
ejpam-4641	124	24	)	)	PUNCT
ejpam-4641	124	25	=	=	PUNCT
ejpam-4641	125	1	2nαλ	2nαλ	NUM
ejpam-4641	125	2	∫	∫	NOUN
ejpam-4641	125	3	∞	∞	NOUN
ejpam-4641	125	4	0	0	NUM
ejpam-4641	125	5	e−(λ−t)x(1−	e−(λ−t)x(1−	PROPN
ejpam-4641	125	6	e−λx)2α−1dx−	e−λx)2α−1dx−	PROPN
ejpam-4641	125	7	2nαλ	2nαλ	NUM
ejpam-4641	125	8	∫	∫	NOUN
ejpam-4641	125	9	∞	∞	NOUN
ejpam-4641	125	10	0	0	NUM
ejpam-4641	125	11	e−(λ−t)x(1−	e−(λ−t)x(1−	PROPN
ejpam-4641	125	12	e−λx)α−1	e−λx)α−1	NUM
ejpam-4641	125	13	n−1∑	n−1∑	NUM
ejpam-4641	125	14	k=1	k=1	PUNCT
ejpam-4641	126	1	[	[	X
ejpam-4641	126	2	−	−	X
ejpam-4641	126	3	log(1−	log(1−	PROPN
ejpam-4641	126	4	(	(	PUNCT
ejpam-4641	126	5	1−	1−	NUM
ejpam-4641	126	6	e−λx)α]k	e−λx)α]k	PROPN
ejpam-4641	126	7	k	k	AUX
ejpam-4641	126	8	!	!	PUNCT
ejpam-4641	126	9	dx+	dx+	PROPN
ejpam-4641	127	1	2nαλ	2nαλ	NUM
ejpam-4641	127	2	∫	∫	NOUN
ejpam-4641	127	3	∞	∞	NOUN
ejpam-4641	127	4	0	0	NUM
ejpam-4641	127	5	e−(λ−t)x(1−	e−(λ−t)x(1−	PROPN
ejpam-4641	127	6	e−λx)2α−1	e−λx)2α−1	PROPN
ejpam-4641	127	7	n−1∑	n−1∑	NUM
ejpam-4641	127	8	k=1	k=1	PUNCT
ejpam-4641	128	1	[	[	X
ejpam-4641	128	2	−	−	X
ejpam-4641	128	3	log(1−	log(1−	PROPN
ejpam-4641	128	4	(	(	PUNCT
ejpam-4641	128	5	1−	1−	NUM
ejpam-4641	128	6	e−λx)α]k	e−λx)α]k	PROPN
ejpam-4641	128	7	k	k	AUX
ejpam-4641	128	8	!	!	PUNCT
ejpam-4641	128	9	dx	dx	PROPN
ejpam-4641	128	10	=	=	SYM
ejpam-4641	128	11	2nαβ(2α	2nαβ(2α	PROPN
ejpam-4641	128	12	,	,	PUNCT
ejpam-4641	128	13	1−	1−	NUM
ejpam-4641	128	14	t	t	NOUN
ejpam-4641	128	15	λ	λ	PROPN
ejpam-4641	128	16	)	)	PUNCT
ejpam-4641	128	17	−	−	PROPN
ejpam-4641	128	18	v	v	INTJ
ejpam-4641	128	19	(	(	PUNCT
ejpam-4641	128	20	t	t	PROPN
ejpam-4641	128	21	)	)	PUNCT
ejpam-4641	128	22	+	+	NUM
ejpam-4641	128	23	z(t	z(t	NOUN
ejpam-4641	128	24	)	)	PUNCT
ejpam-4641	128	25	.	.	PUNCT
ejpam-4641	129	1	by	by	ADP
ejpam-4641	129	2	applying	apply	VERB
ejpam-4641	129	3	the	the	DET
ejpam-4641	129	4	substitution	substitution	NOUN
ejpam-4641	129	5	b	b	NOUN
ejpam-4641	129	6	=	=	SYM
ejpam-4641	129	7	(	(	PUNCT
ejpam-4641	129	8	1−	1−	NUM
ejpam-4641	129	9	e−λx)α	e−λx)α	ADV
ejpam-4641	129	10	then	then	ADV
ejpam-4641	129	11	using	use	VERB
ejpam-4641	129	12	the	the	DET
ejpam-4641	129	13	logarithmic	logarithmic	ADJ
ejpam-4641	129	14	expansion	expansion	NOUN
ejpam-4641	129	15	(	(	PUNCT
ejpam-4641	129	16	7	7	NUM
ejpam-4641	129	17	)	)	PUNCT
ejpam-4641	129	18	for	for	ADP
ejpam-4641	129	19	both	both	DET
ejpam-4641	129	20	v	v	NOUN
ejpam-4641	129	21	(	(	PUNCT
ejpam-4641	129	22	t	t	PROPN
ejpam-4641	129	23	)	)	PUNCT
ejpam-4641	129	24	and	and	CCONJ
ejpam-4641	129	25	z(t	z(t	NOUN
ejpam-4641	129	26	)	)	PUNCT
ejpam-4641	129	27	we	we	PRON
ejpam-4641	129	28	reach	reach	VERB
ejpam-4641	129	29	(	(	PUNCT
ejpam-4641	129	30	13	13	NUM
ejpam-4641	129	31	)	)	PUNCT
ejpam-4641	129	32	.	.	PUNCT
ejpam-4641	130	1	to	to	PART
ejpam-4641	130	2	prove	prove	VERB
ejpam-4641	130	3	(	(	PUNCT
ejpam-4641	130	4	14	14	NUM
ejpam-4641	130	5	)	)	PUNCT
ejpam-4641	130	6	,	,	PUNCT
ejpam-4641	130	7	we	we	PRON
ejpam-4641	130	8	will	will	AUX
ejpam-4641	130	9	apply	apply	VERB
ejpam-4641	130	10	(	(	PUNCT
ejpam-4641	130	11	5	5	NUM
ejpam-4641	130	12	)	)	PUNCT
ejpam-4641	130	13	and	and	CCONJ
ejpam-4641	130	14	(	(	PUNCT
ejpam-4641	130	15	6	6	NUM
ejpam-4641	130	16	)	)	PUNCT
ejpam-4641	130	17	into	into	ADP
ejpam-4641	130	18	(	(	PUNCT
ejpam-4641	130	19	4	4	NUM
ejpam-4641	130	20	)	)	PUNCT
ejpam-4641	130	21	and	and	CCONJ
ejpam-4641	130	22	this	this	PRON
ejpam-4641	130	23	will	will	AUX
ejpam-4641	130	24	lead	lead	VERB
ejpam-4641	130	25	to	to	ADP
ejpam-4641	130	26	flc	flc	PROPN
ejpam-4641	130	27	n	n	CCONJ
ejpam-4641	130	28	,	,	PUNCT
ejpam-4641	130	29	u	u	PROPN
ejpam-4641	130	30	c	c	NOUN
ejpam-4641	130	31	n	n	PROPN
ejpam-4641	130	32	(	(	PUNCT
ejpam-4641	130	33	x	x	NOUN
ejpam-4641	130	34	,	,	PUNCT
ejpam-4641	130	35	y	y	NOUN
ejpam-4641	130	36	)	)	PUNCT
ejpam-4641	130	37	=	=	SYM
ejpam-4641	130	38	2n	2n	NUM
ejpam-4641	130	39	(	(	PUNCT
ejpam-4641	130	40	n−	n−	NOUN
ejpam-4641	130	41	1	1	NUM
ejpam-4641	130	42	)	)	PUNCT
ejpam-4641	130	43	!	!	PUNCT
ejpam-4641	131	1	α2λ2(1−	α2λ2(1−	ADJ
ejpam-4641	131	2	e−λx)α−1e−λx(1−	e−λx)α−1e−λx(1−	ADJ
ejpam-4641	131	3	e−λy)α−1e−λy	e−λy)α−1e−λy	NOUN
ejpam-4641	131	4	{	{	PUNCT
ejpam-4641	131	5	−	−	PROPN
ejpam-4641	131	6	log[1−	log[1−	PUNCT
ejpam-4641	131	7	(	(	PUNCT
ejpam-4641	131	8	1−	1−	NUM
ejpam-4641	131	9	e−λy)α	e−λy)α	NOUN
ejpam-4641	131	10	+	+	CCONJ
ejpam-4641	131	11	(	(	PUNCT
ejpam-4641	131	12	1−	1−	NUM
ejpam-4641	131	13	e−λx)α	e−λx)α	ADV
ejpam-4641	131	14	]	]	PUNCT
ejpam-4641	131	15	}	}	PUNCT
ejpam-4641	131	16	n−1	n−1	PROPN
ejpam-4641	131	17	.	.	PUNCT
ejpam-4641	131	18	and	and	CCONJ
ejpam-4641	131	19	mlc	mlc	PROPN
ejpam-4641	131	20	n	n	CCONJ
ejpam-4641	131	21	,	,	PUNCT
ejpam-4641	131	22	u	u	PROPN
ejpam-4641	131	23	c	c	PROPN
ejpam-4641	131	24	n	n	PROPN
ejpam-4641	131	25	(	(	PUNCT
ejpam-4641	131	26	t1	t1	PROPN
ejpam-4641	131	27	,	,	PUNCT
ejpam-4641	131	28	t2	t2	NOUN
ejpam-4641	131	29	)	)	PUNCT
ejpam-4641	131	30	=	=	SYM
ejpam-4641	131	31	2nα2λ2	2nα2λ2	NUM
ejpam-4641	131	32	(	(	PUNCT
ejpam-4641	131	33	n−	n−	NOUN
ejpam-4641	131	34	1	1	NUM
ejpam-4641	131	35	)	)	PUNCT
ejpam-4641	131	36	!	!	PUNCT
ejpam-4641	132	1	∫	∫	PROPN
ejpam-4641	133	1	∞	∞	PROPN
ejpam-4641	133	2	0	0	NUM
ejpam-4641	133	3	e(t2−λ)y(1−	e(t2−λ)y(1−	PROPN
ejpam-4641	133	4	e−λy)α−1i(y)dy	e−λy)α−1i(y)dy	PROPN
ejpam-4641	133	5	,	,	PUNCT
ejpam-4641	133	6	where	where	SCONJ
ejpam-4641	133	7	i(y	i(y	NOUN
ejpam-4641	133	8	)	)	PUNCT
ejpam-4641	133	9	=	=	SYM
ejpam-4641	134	1	∫	∫	PROPN
ejpam-4641	134	2	y	y	PROPN
ejpam-4641	134	3	0	0	NUM
ejpam-4641	134	4	e(t1−λ)x(1−	e(t1−λ)x(1−	PROPN
ejpam-4641	134	5	e−λx)α−1	e−λx)α−1	NUM
ejpam-4641	134	6	{	{	PUNCT
ejpam-4641	134	7	−	−	PROPN
ejpam-4641	134	8	log[1−	log[1−	PUNCT
ejpam-4641	134	9	(	(	PUNCT
ejpam-4641	134	10	1−	1−	NUM
ejpam-4641	134	11	e−λy)α	e−λy)α	NOUN
ejpam-4641	134	12	+	+	CCONJ
ejpam-4641	134	13	(	(	PUNCT
ejpam-4641	134	14	1−	1−	NUM
ejpam-4641	134	15	e−λx)α	e−λx)α	ADV
ejpam-4641	134	16	]	]	PUNCT
ejpam-4641	134	17	}	}	PUNCT
ejpam-4641	134	18	n−1	n−1	PROPN
ejpam-4641	134	19	dx	dx	PROPN
ejpam-4641	134	20	.	.	PUNCT
ejpam-4641	135	1	let	let	VERB
ejpam-4641	135	2	u	u	PRON
ejpam-4641	135	3	=	=	X
ejpam-4641	135	4	(	(	PUNCT
ejpam-4641	135	5	1−	1−	NUM
ejpam-4641	135	6	e−λy)α	e−λy)α	NUM
ejpam-4641	135	7	−	−	PROPN
ejpam-4641	135	8	(	(	PUNCT
ejpam-4641	135	9	1−	1−	NUM
ejpam-4641	135	10	e−λx)α	e−λx)α	ADV
ejpam-4641	135	11	,	,	PUNCT
ejpam-4641	135	12	then	then	ADV
ejpam-4641	135	13	using	use	VERB
ejpam-4641	135	14	(	(	PUNCT
ejpam-4641	135	15	7	7	X
ejpam-4641	135	16	)	)	PUNCT
ejpam-4641	135	17	we	we	PRON
ejpam-4641	135	18	get	get	VERB
ejpam-4641	135	19	i(y	i(y	NOUN
ejpam-4641	135	20	)	)	PUNCT
ejpam-4641	135	21	=	=	SYM
ejpam-4641	136	1	1	1	NUM
ejpam-4641	136	2	αλ	αλ	PRON
ejpam-4641	136	3	∞∑	∞∑	NUM
ejpam-4641	136	4	p=0	p=0	NOUN
ejpam-4641	136	5	ap(n−	ap(n−	VERB
ejpam-4641	136	6	1	1	X
ejpam-4641	136	7	)	)	PUNCT
ejpam-4641	136	8	∫	∫	PROPN
ejpam-4641	136	9	(	(	PUNCT
ejpam-4641	136	10	1−e−λy)α	1−e−λy)α	NOUN
ejpam-4641	136	11	0	0	NUM
ejpam-4641	136	12	un+p−1	un+p−1	NOUN
ejpam-4641	136	13	{	{	PUNCT
ejpam-4641	137	1	1−	1−	NUM
ejpam-4641	137	2	[	[	X
ejpam-4641	137	3	(	(	PUNCT
ejpam-4641	137	4	1−	1−	NUM
ejpam-4641	137	5	e−λy)α	e−λy)α	NOUN
ejpam-4641	137	6	−	−	ADP
ejpam-4641	137	7	u	u	NOUN
ejpam-4641	137	8	]	]	X
ejpam-4641	137	9	1	1	NUM
ejpam-4641	137	10	α	α	NOUN
ejpam-4641	137	11	}	}	PUNCT
ejpam-4641	137	12	−t1	−t1	PROPN
ejpam-4641	137	13	λ	λ	X
ejpam-4641	137	14	du	du	X
ejpam-4641	137	15	,	,	PUNCT
ejpam-4641	137	16	again	again	ADV
ejpam-4641	137	17	using	use	VERB
ejpam-4641	137	18	another	another	DET
ejpam-4641	137	19	substitution	substitution	NOUN
ejpam-4641	137	20	w	w	NOUN
ejpam-4641	138	1	=	=	PUNCT
ejpam-4641	139	1	[	[	X
ejpam-4641	139	2	(	(	PUNCT
ejpam-4641	139	3	1−e−λy)α−u	1−e−λy)α−u	NUM
ejpam-4641	139	4	]	]	X
ejpam-4641	139	5	1	1	NUM
ejpam-4641	139	6	α	α	NOUN
ejpam-4641	139	7	then	then	ADV
ejpam-4641	139	8	a	a	DET
ejpam-4641	139	9	binomial	binomial	ADJ
ejpam-4641	139	10	expansion	expansion	NOUN
ejpam-4641	139	11	on	on	ADP
ejpam-4641	139	12	one	one	NUM
ejpam-4641	139	13	of	of	ADP
ejpam-4641	139	14	the	the	DET
ejpam-4641	139	15	terms	term	NOUN
ejpam-4641	139	16	,	,	PUNCT
ejpam-4641	139	17	we	we	PRON
ejpam-4641	139	18	get	get	VERB
ejpam-4641	139	19	i(y	i(y	NOUN
ejpam-4641	139	20	)	)	PUNCT
ejpam-4641	139	21	=	=	SYM
ejpam-4641	139	22	1	1	NUM
ejpam-4641	139	23	λ	λ	PROPN
ejpam-4641	139	24	∞∑	∞∑	NUM
ejpam-4641	139	25	p=0	p=0	NOUN
ejpam-4641	139	26	ap(n−	ap(n−	VERB
ejpam-4641	140	1	1	1	X
ejpam-4641	140	2	)	)	PUNCT
ejpam-4641	140	3	n+p−1∑	n+p−1∑	ADJ
ejpam-4641	140	4	k=0	k=0	PROPN
ejpam-4641	140	5	(	(	PUNCT
ejpam-4641	140	6	n+	n+	X
ejpam-4641	140	7	p−	p−	NOUN
ejpam-4641	140	8	1	1	NUM
ejpam-4641	140	9	k	k	NOUN
ejpam-4641	140	10	)	)	PUNCT
ejpam-4641	140	11	(	(	PUNCT
ejpam-4641	140	12	−1)k(1−	−1)k(1−	NOUN
ejpam-4641	140	13	e−λy)α(n+p−1−k)j(y	e−λy)α(n+p−1−k)j(y	PROPN
ejpam-4641	140	14	)	)	PUNCT
ejpam-4641	140	15	,	,	PUNCT
ejpam-4641	140	16	where	where	SCONJ
ejpam-4641	140	17	j(y	j(y	PROPN
ejpam-4641	140	18	)	)	PUNCT
ejpam-4641	140	19	=	=	SYM
ejpam-4641	141	1	∫	∫	PROPN
ejpam-4641	141	2	1−e−λy	1−e−λy	NUM
ejpam-4641	141	3	0	0	NUM
ejpam-4641	141	4	(	(	PUNCT
ejpam-4641	141	5	1−	1−	NUM
ejpam-4641	141	6	w	w	NOUN
ejpam-4641	141	7	)	)	PUNCT
ejpam-4641	141	8	−t1	−t1	PROPN
ejpam-4641	141	9	λ	λ	PROPN
ejpam-4641	141	10	wαkdw	wαkdw	NOUN
ejpam-4641	141	11	.	.	PUNCT
ejpam-4641	142	1	by	by	ADP
ejpam-4641	142	2	applying	apply	VERB
ejpam-4641	142	3	(	(	PUNCT
ejpam-4641	142	4	8)	8)	NUM
ejpam-4641	142	5	on	on	ADP
ejpam-4641	142	6	j(y	j(y	PROPN
ejpam-4641	142	7	)	)	PUNCT
ejpam-4641	142	8	,	,	PUNCT
ejpam-4641	142	9	we	we	PRON
ejpam-4641	142	10	get	get	VERB
ejpam-4641	142	11	i(y	i(y	NOUN
ejpam-4641	142	12	)	)	PUNCT
ejpam-4641	142	13	=	=	SYM
ejpam-4641	142	14	1	1	NUM
ejpam-4641	142	15	λ	λ	PROPN
ejpam-4641	142	16	∞∑	∞∑	NUM
ejpam-4641	142	17	p=0	p=0	NOUN
ejpam-4641	142	18	ap(n−	ap(n−	VERB
ejpam-4641	143	1	1	1	X
ejpam-4641	143	2	)	)	PUNCT
ejpam-4641	143	3	n+p−1∑	n+p−1∑	ADJ
ejpam-4641	143	4	k=0	k=0	PROPN
ejpam-4641	143	5	(	(	PUNCT
ejpam-4641	143	6	n+	n+	X
ejpam-4641	143	7	p−	p−	NOUN
ejpam-4641	143	8	1	1	NUM
ejpam-4641	143	9	k	k	NOUN
ejpam-4641	143	10	)	)	PUNCT
ejpam-4641	143	11	(	(	PUNCT
ejpam-4641	143	12	−1)k(1−	−1)k(1−	NOUN
ejpam-4641	143	13	e−λy)α(n+p−1−k)β(αk	e−λy)α(n+p−1−k)β(αk	PROPN
ejpam-4641	143	14	+	+	CCONJ
ejpam-4641	143	15	1	1	NUM
ejpam-4641	143	16	,	,	PUNCT
ejpam-4641	143	17	−t1	−t1	NOUN
ejpam-4641	143	18	λ	λ	NOUN
ejpam-4641	143	19	+	+	NOUN
ejpam-4641	143	20	1	1	NUM
ejpam-4641	143	21	)	)	PUNCT
ejpam-4641	143	22	[	[	PUNCT
ejpam-4641	143	23	1−	1−	NUM
ejpam-4641	143	24	(	(	PUNCT
ejpam-4641	143	25	e−λy)αk−	e−λy)αk−	PROPN
ejpam-4641	143	26	t1	t1	NOUN
ejpam-4641	143	27	λ	λ	PROPN
ejpam-4641	143	28	+1	+1	PROPN
ejpam-4641	143	29	αk∑	αk∑	NOUN
ejpam-4641	143	30	i=0	i=0	PROPN
ejpam-4641	143	31	(	(	PUNCT
ejpam-4641	143	32	αk	αk	NOUN
ejpam-4641	143	33	−	−	PROPN
ejpam-4641	143	34	t1	t1	NOUN
ejpam-4641	143	35	λ	λ	PROPN
ejpam-4641	143	36	+	+	CCONJ
ejpam-4641	143	37	1	1	NUM
ejpam-4641	143	38	i	i	NOUN
ejpam-4641	143	39	)	)	PUNCT
ejpam-4641	143	40	(	(	PUNCT
ejpam-4641	143	41	1−	1−	NUM
ejpam-4641	143	42	e−λy)i	e−λy)i	PROPN
ejpam-4641	143	43	(	(	PUNCT
ejpam-4641	143	44	e−λy)i	e−λy)i	PROPN
ejpam-4641	143	45	]	]	PUNCT
ejpam-4641	143	46	.	.	PUNCT
ejpam-4641	144	1	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	144	2	/	/	SYM
ejpam-4641	144	3	eur	eur	PROPN
ejpam-4641	144	4	.	.	PUNCT
ejpam-4641	145	1	j.	j.	PROPN
ejpam-4641	145	2	pure	pure	PROPN
ejpam-4641	145	3	appl	appl	PROPN
ejpam-4641	145	4	.	.	PROPN
ejpam-4641	145	5	math	math	PROPN
ejpam-4641	145	6	,	,	PUNCT
ejpam-4641	145	7	16	16	NUM
ejpam-4641	145	8	(	(	PUNCT
ejpam-4641	145	9	1	1	NUM
ejpam-4641	145	10	)	)	PUNCT
ejpam-4641	145	11	(	(	PUNCT
ejpam-4641	145	12	2023	2023	NUM
ejpam-4641	145	13	)	)	PUNCT
ejpam-4641	145	14	,	,	PUNCT
ejpam-4641	145	15	97	97	NUM
ejpam-4641	145	16	-	-	SYM
ejpam-4641	145	17	111	111	NUM
ejpam-4641	145	18	103	103	NUM
ejpam-4641	145	19	now	now	ADV
ejpam-4641	145	20	mlc	mlc	PROPN
ejpam-4641	145	21	n	n	CCONJ
ejpam-4641	145	22	,	,	PUNCT
ejpam-4641	145	23	u	u	PROPN
ejpam-4641	145	24	c	c	PROPN
ejpam-4641	145	25	n	n	PROPN
ejpam-4641	145	26	(	(	PUNCT
ejpam-4641	145	27	t1	t1	PROPN
ejpam-4641	145	28	,	,	PUNCT
ejpam-4641	145	29	t2	t2	NOUN
ejpam-4641	145	30	)	)	PUNCT
ejpam-4641	145	31	=	=	SYM
ejpam-4641	145	32	2nα2λ	2nα2λ	NUM
ejpam-4641	145	33	(	(	PUNCT
ejpam-4641	145	34	n−	n−	NOUN
ejpam-4641	145	35	1	1	NUM
ejpam-4641	145	36	)	)	PUNCT
ejpam-4641	145	37	!	!	PUNCT
ejpam-4641	146	1	∞∑	∞∑	NUM
ejpam-4641	146	2	p=0	p=0	NOUN
ejpam-4641	146	3	ap(n−	ap(n−	VERB
ejpam-4641	146	4	1	1	X
ejpam-4641	146	5	)	)	PUNCT
ejpam-4641	146	6	n+p−1∑	n+p−1∑	ADJ
ejpam-4641	146	7	k=0	k=0	PROPN
ejpam-4641	146	8	(	(	PUNCT
ejpam-4641	146	9	n+	n+	X
ejpam-4641	146	10	p−	p−	NOUN
ejpam-4641	146	11	1	1	NUM
ejpam-4641	146	12	k	k	NOUN
ejpam-4641	146	13	)	)	PUNCT
ejpam-4641	146	14	(	(	PUNCT
ejpam-4641	146	15	−1)k(1−	−1)k(1−	NOUN
ejpam-4641	146	16	e−λy)α(n+p−1−k	e−λy)α(n+p−1−k	PROPN
ejpam-4641	146	17	)	)	PUNCT
ejpam-4641	146	18	β(αk	β(αk	PROPN
ejpam-4641	146	19	+	+	CCONJ
ejpam-4641	146	20	1	1	NUM
ejpam-4641	146	21	,	,	PUNCT
ejpam-4641	146	22	−t1	−t1	NOUN
ejpam-4641	146	23	λ	λ	NOUN
ejpam-4641	146	24	+	+	NOUN
ejpam-4641	146	25	1	1	X
ejpam-4641	146	26	)	)	PUNCT
ejpam-4641	146	27	[	[	PUNCT
ejpam-4641	146	28	q(t2)−	q(t2)−	PROPN
ejpam-4641	146	29	αk∑	αk∑	X
ejpam-4641	146	30	i=0	i=0	PROPN
ejpam-4641	146	31	(	(	PUNCT
ejpam-4641	146	32	αk	αk	NOUN
ejpam-4641	146	33	−	−	PROPN
ejpam-4641	146	34	t1	t1	NOUN
ejpam-4641	146	35	λ	λ	PROPN
ejpam-4641	146	36	+	+	CCONJ
ejpam-4641	146	37	1	1	NUM
ejpam-4641	146	38	i	i	NOUN
ejpam-4641	146	39	)	)	PUNCT
ejpam-4641	146	40	r(t2	r(t2	NOUN
ejpam-4641	146	41	)	)	PUNCT
ejpam-4641	146	42	]	]	PUNCT
ejpam-4641	146	43	,	,	PUNCT
ejpam-4641	146	44	where	where	SCONJ
ejpam-4641	146	45	q(t2	q(t2	NOUN
ejpam-4641	146	46	)	)	PUNCT
ejpam-4641	146	47	=	=	SYM
ejpam-4641	147	1	∫	∫	PROPN
ejpam-4641	147	2	∞	∞	PROPN
ejpam-4641	147	3	0	0	NUM
ejpam-4641	147	4	e(t2−λ)y(1−	e(t2−λ)y(1−	PROPN
ejpam-4641	147	5	e−λy)α(n+p−k)−1dy	e−λy)α(n+p−k)−1dy	PROPN
ejpam-4641	147	6	,	,	PUNCT
ejpam-4641	147	7	and	and	CCONJ
ejpam-4641	147	8	r(t2	r(t2	NOUN
ejpam-4641	147	9	)	)	PUNCT
ejpam-4641	147	10	=	=	SYM
ejpam-4641	148	1	∫	∫	PROPN
ejpam-4641	148	2	∞	∞	PROPN
ejpam-4641	148	3	0	0	NUM
ejpam-4641	149	1	et2y(e−λy)2+i+αk−	et2y(e−λy)2+i+αk−	PROPN
ejpam-4641	149	2	t1	t1	NOUN
ejpam-4641	149	3	λ	λ	PROPN
ejpam-4641	149	4	(	(	PUNCT
ejpam-4641	149	5	1−	1−	NUM
ejpam-4641	149	6	e−λy)α(n+p−k)−1+idy	e−λy)α(n+p−k)−1+idy	NOUN
ejpam-4641	149	7	.	.	PUNCT
ejpam-4641	150	1	substituting	substitute	VERB
ejpam-4641	150	2	z	z	NOUN
ejpam-4641	150	3	=	=	SYM
ejpam-4641	150	4	e−λy	e−λy	X
ejpam-4641	150	5	in	in	ADP
ejpam-4641	150	6	q(t2	q(t2	NOUN
ejpam-4641	150	7	)	)	PUNCT
ejpam-4641	150	8	and	and	CCONJ
ejpam-4641	150	9	r(t2	r(t2	NOUN
ejpam-4641	150	10	)	)	PUNCT
ejpam-4641	150	11	,	,	PUNCT
ejpam-4641	150	12	and	and	CCONJ
ejpam-4641	150	13	with	with	ADP
ejpam-4641	150	14	some	some	DET
ejpam-4641	150	15	routine	routine	ADJ
ejpam-4641	150	16	calculations	calculation	NOUN
ejpam-4641	150	17	,	,	PUNCT
ejpam-4641	150	18	we	we	PRON
ejpam-4641	150	19	reach	reach	VERB
ejpam-4641	150	20	(	(	PUNCT
ejpam-4641	150	21	14	14	NUM
ejpam-4641	150	22	)	)	PUNCT
ejpam-4641	150	23	.	.	PUNCT
ejpam-4641	151	1	and	and	CCONJ
ejpam-4641	151	2	this	this	PRON
ejpam-4641	151	3	completes	complete	VERB
ejpam-4641	151	4	the	the	DET
ejpam-4641	151	5	proof	proof	NOUN
ejpam-4641	151	6	.	.	PUNCT
ejpam-4641	152	1	corollary	corollary	ADJ
ejpam-4641	152	2	1	1	NUM
ejpam-4641	152	3	.	.	PUNCT
ejpam-4641	153	1	the	the	DET
ejpam-4641	153	2	following	follow	VERB
ejpam-4641	153	3	recurrence	recurrence	NOUN
ejpam-4641	153	4	relation	relation	NOUN
ejpam-4641	153	5	evaluated	evaluate	VERB
ejpam-4641	153	6	from	from	ADP
ejpam-4641	153	7	recursively	recursively	ADV
ejpam-4641	153	8	differentiating	differentiate	VERB
ejpam-4641	153	9	β(α	β(α	PROPN
ejpam-4641	153	10	,	,	PUNCT
ejpam-4641	153	11	1−	1−	NUM
ejpam-4641	153	12	t	t	PROPN
ejpam-4641	153	13	λ	λ	PROPN
ejpam-4641	153	14	)	)	PUNCT
ejpam-4641	153	15	with	with	ADP
ejpam-4641	153	16	respect	respect	NOUN
ejpam-4641	153	17	to	to	ADP
ejpam-4641	153	18	t	t	PROPN
ejpam-4641	153	19	for	for	ADP
ejpam-4641	153	20	(	(	PUNCT
ejpam-4641	153	21	i	i	NOUN
ejpam-4641	153	22	)	)	PUNCT
ejpam-4641	153	23	times	times	PROPN
ejpam-4641	153	24	β(i)(α	β(i)(α	NOUN
ejpam-4641	153	25	,	,	PUNCT
ejpam-4641	153	26	1−	1−	NUM
ejpam-4641	153	27	t	t	NOUN
ejpam-4641	153	28	λ	λ	PROPN
ejpam-4641	153	29	)	)	PUNCT
ejpam-4641	153	30	=	=	SYM
ejpam-4641	153	31	i−1∑	i−1∑	NUM
ejpam-4641	153	32	k=0	k=0	PROPN
ejpam-4641	153	33	(	(	PUNCT
ejpam-4641	153	34	−1)i−k−1	−1)i−k−1	PROPN
ejpam-4641	153	35	(	(	PUNCT
ejpam-4641	153	36	1	1	NUM
ejpam-4641	153	37	λ	λ	NOUN
ejpam-4641	153	38	)	)	PUNCT
ejpam-4641	153	39	i−k	i−k	NOUN
ejpam-4641	153	40	(	(	PUNCT
ejpam-4641	153	41	i−	i−	PROPN
ejpam-4641	153	42	1	1	NUM
ejpam-4641	153	43	j	j	NOUN
ejpam-4641	153	44	)	)	PUNCT
ejpam-4641	153	45	β(k)(α	β(k)(α	ADP
ejpam-4641	153	46	,	,	PUNCT
ejpam-4641	153	47	1−	1−	NUM
ejpam-4641	153	48	t	t	NOUN
ejpam-4641	153	49	λ	λ	PROPN
ejpam-4641	153	50	)	)	PUNCT
ejpam-4641	153	51	[	[	PUNCT
ejpam-4641	153	52	ψ(i−k−1)(α+1−	ψ(i−k−1)(α+1−	X
ejpam-4641	153	53	t	t	NOUN
ejpam-4641	153	54	λ	λ	PROPN
ejpam-4641	153	55	)	)	PUNCT
ejpam-4641	153	56	−ψ(i−k−1)(1−	−ψ(i−k−1)(1−	NOUN
ejpam-4641	153	57	t	t	NOUN
ejpam-4641	153	58	λ	λ	PROPN
ejpam-4641	153	59	)	)	PUNCT
ejpam-4641	153	60	]	]	PUNCT
ejpam-4641	153	61	.	.	PUNCT
ejpam-4641	154	1	(	(	PUNCT
ejpam-4641	154	2	15	15	NUM
ejpam-4641	154	3	)	)	PUNCT
ejpam-4641	154	4	where	where	SCONJ
ejpam-4641	154	5	β(i)(α	β(i)(α	NOUN
ejpam-4641	154	6	,	,	PUNCT
ejpam-4641	154	7	1−	1−	NUM
ejpam-4641	154	8	t	t	PROPN
ejpam-4641	154	9	λ	λ	PROPN
ejpam-4641	154	10	)	)	PUNCT
ejpam-4641	154	11	is	be	AUX
ejpam-4641	154	12	the	the	DET
ejpam-4641	154	13	i	i	PROPN
ejpam-4641	154	14	th	th	X
ejpam-4641	154	15	derivative	derivative	NOUN
ejpam-4641	154	16	of	of	ADP
ejpam-4641	154	17	β(α	β(α	PROPN
ejpam-4641	154	18	,	,	PUNCT
ejpam-4641	154	19	1−	1−	NUM
ejpam-4641	154	20	t	t	PROPN
ejpam-4641	154	21	λ	λ	PROPN
ejpam-4641	154	22	)	)	PUNCT
ejpam-4641	154	23	and	and	CCONJ
ejpam-4641	155	1	ψ	ψ	X
ejpam-4641	155	2	(	(	PUNCT
ejpam-4641	155	3	i)(α	i)(α	NOUN
ejpam-4641	155	4	)	)	PUNCT
ejpam-4641	155	5	is	be	AUX
ejpam-4641	155	6	the	the	DET
ejpam-4641	155	7	ith	ith	PROPN
ejpam-4641	155	8	derivative	derivative	NOUN
ejpam-4641	155	9	of	of	ADP
ejpam-4641	155	10	the	the	DET
ejpam-4641	155	11	poly	poly	ADJ
ejpam-4641	155	12	-	-	PUNCT
ejpam-4641	155	13	gamma	gamma	NOUN
ejpam-4641	155	14	function	function	NOUN
ejpam-4641	155	15	ψ(α	ψ(α	PROPN
ejpam-4641	155	16	)	)	PUNCT
ejpam-4641	155	17	.	.	PUNCT
ejpam-4641	156	1	corollary	corollary	ADJ
ejpam-4641	156	2	2	2	NUM
ejpam-4641	156	3	.	.	PUNCT
ejpam-4641	156	4	by	by	ADP
ejpam-4641	156	5	differentiating	differentiate	VERB
ejpam-4641	156	6	(	(	PUNCT
ejpam-4641	156	7	12	12	NUM
ejpam-4641	156	8	)	)	PUNCT
ejpam-4641	156	9	and	and	CCONJ
ejpam-4641	156	10	(	(	PUNCT
ejpam-4641	156	11	13	13	NUM
ejpam-4641	156	12	)	)	PUNCT
ejpam-4641	156	13	i	i	PRON
ejpam-4641	156	14	times	time	NOUN
ejpam-4641	156	15	and	and	CCONJ
ejpam-4641	156	16	substituting	substitute	VERB
ejpam-4641	156	17	t	t	PROPN
ejpam-4641	156	18	=	=	SYM
ejpam-4641	156	19	0	0	NUM
ejpam-4641	156	20	,	,	PUNCT
ejpam-4641	156	21	we	we	PRON
ejpam-4641	156	22	get	get	VERB
ejpam-4641	156	23	the	the	DET
ejpam-4641	156	24	ith	ith	ADJ
ejpam-4641	156	25	moment	moment	NOUN
ejpam-4641	156	26	of	of	ADP
ejpam-4641	156	27	lower	low	ADJ
ejpam-4641	156	28	current	current	ADJ
ejpam-4641	156	29	record	record	NOUN
ejpam-4641	156	30	µ	µ	X
ejpam-4641	156	31	(	(	PUNCT
ejpam-4641	156	32	i	i	NOUN
ejpam-4641	156	33	)	)	PUNCT
ejpam-4641	156	34	lc	lc	PROPN
ejpam-4641	156	35	n	n	PROPN
ejpam-4641	156	36	and	and	CCONJ
ejpam-4641	156	37	ith	ith	PROPN
ejpam-4641	156	38	moment	moment	NOUN
ejpam-4641	156	39	of	of	ADP
ejpam-4641	156	40	upper	upper	ADJ
ejpam-4641	156	41	current	current	ADJ
ejpam-4641	156	42	record	record	NOUN
ejpam-4641	156	43	µ	µ	X
ejpam-4641	156	44	(	(	PUNCT
ejpam-4641	156	45	i	i	NOUN
ejpam-4641	156	46	)	)	PUNCT
ejpam-4641	156	47	uc	uc	PROPN
ejpam-4641	156	48	n	n	PRON
ejpam-4641	156	49	respectively	respectively	ADV
ejpam-4641	156	50	.	.	PUNCT
ejpam-4641	157	1	also	also	ADV
ejpam-4641	157	2	,	,	PUNCT
ejpam-4641	157	3	by	by	ADP
ejpam-4641	157	4	differentiating	differentiate	VERB
ejpam-4641	157	5	(	(	PUNCT
ejpam-4641	157	6	14	14	NUM
ejpam-4641	157	7	)	)	PUNCT
ejpam-4641	157	8	j	j	PROPN
ejpam-4641	157	9	times	time	NOUN
ejpam-4641	157	10	with	with	ADP
ejpam-4641	157	11	respect	respect	NOUN
ejpam-4641	157	12	to	to	ADP
ejpam-4641	157	13	t2	t2	NOUN
ejpam-4641	157	14	and	and	CCONJ
ejpam-4641	157	15	i	i	PRON
ejpam-4641	157	16	times	time	NOUN
ejpam-4641	157	17	with	with	ADP
ejpam-4641	157	18	respect	respect	NOUN
ejpam-4641	157	19	to	to	ADP
ejpam-4641	157	20	t1	t1	NOUN
ejpam-4641	157	21	and	and	CCONJ
ejpam-4641	157	22	then	then	ADV
ejpam-4641	157	23	substituting	substitute	VERB
ejpam-4641	157	24	t1	t1	NOUN
ejpam-4641	157	25	=	=	SYM
ejpam-4641	157	26	t2	t2	PROPN
ejpam-4641	157	27	=	=	SYM
ejpam-4641	157	28	0	0	NUM
ejpam-4641	157	29	we	we	PRON
ejpam-4641	157	30	get	get	VERB
ejpam-4641	157	31	the	the	DET
ejpam-4641	157	32	product	product	NOUN
ejpam-4641	157	33	moment	moment	NOUN
ejpam-4641	157	34	of	of	ADP
ejpam-4641	157	35	the	the	DET
ejpam-4641	157	36	lower	low	ADJ
ejpam-4641	157	37	and	and	CCONJ
ejpam-4641	157	38	upper	upper	ADJ
ejpam-4641	157	39	current	current	ADJ
ejpam-4641	157	40	record	record	NOUN
ejpam-4641	157	41	µ	µ	X
ejpam-4641	157	42	(	(	PUNCT
ejpam-4641	157	43	i	i	PROPN
ejpam-4641	157	44	,	,	PUNCT
ejpam-4641	157	45	j	j	PROPN
ejpam-4641	157	46	)	)	PUNCT
ejpam-4641	157	47	lc	lc	PROPN
ejpam-4641	157	48	n	n	CCONJ
ejpam-4641	157	49	,	,	PUNCT
ejpam-4641	157	50	u	u	NOUN
ejpam-4641	157	51	c	c	NOUN
ejpam-4641	157	52	n	n	NOUN
ejpam-4641	157	53	.	.	PUNCT
ejpam-4641	158	1	µ	µ	X
ejpam-4641	158	2	(	(	PUNCT
ejpam-4641	158	3	i	i	NOUN
ejpam-4641	158	4	)	)	PUNCT
ejpam-4641	158	5	lc	lc	PROPN
ejpam-4641	158	6	n	n	NOUN
ejpam-4641	158	7	=	=	SYM
ejpam-4641	158	8	2nα	2nα	ADJ
ejpam-4641	158	9	[	[	PUNCT
ejpam-4641	158	10	β(i)(α	β(i)(α	NUM
ejpam-4641	158	11	,	,	PUNCT
ejpam-4641	158	12	1−	1−	NUM
ejpam-4641	158	13	t	t	PROPN
ejpam-4641	158	14	λ	λ	PROPN
ejpam-4641	158	15	)	)	PUNCT
ejpam-4641	158	16	−	−	PROPN
ejpam-4641	159	1	β(i)(2α	β(i)(2α	PROPN
ejpam-4641	159	2	,	,	PUNCT
ejpam-4641	159	3	1−	1−	NUM
ejpam-4641	159	4	t	t	NOUN
ejpam-4641	159	5	λ	λ	PROPN
ejpam-4641	159	6	)	)	PUNCT
ejpam-4641	159	7	−	−	PROPN
ejpam-4641	160	1	n−1∑	n−1∑	PROPN
ejpam-4641	160	2	k=1	k=1	INTJ
ejpam-4641	161	1	αk	αk	AUX
ejpam-4641	161	2	k	k	NOUN
ejpam-4641	161	3	!	!	PUNCT
ejpam-4641	162	1	∞∑	∞∑	NUM
ejpam-4641	162	2	p=0	p=0	PROPN
ejpam-4641	162	3	ap(k)β	ap(k)β	PUNCT
ejpam-4641	162	4	(	(	PUNCT
ejpam-4641	162	5	i)(2α	i)(2α	PROPN
ejpam-4641	162	6	,	,	PUNCT
ejpam-4641	162	7	1	1	NUM
ejpam-4641	162	8	+	+	CCONJ
ejpam-4641	162	9	k	k	NOUN
ejpam-4641	163	1	+	+	CCONJ
ejpam-4641	163	2	p−	p−	NOUN
ejpam-4641	163	3	t	t	NOUN
ejpam-4641	163	4	λ	λ	PROPN
ejpam-4641	163	5	)	)	PUNCT
ejpam-4641	164	1	]	]	PUNCT
ejpam-4641	164	2	∣∣∣	∣∣∣	X
ejpam-4641	164	3	t=0	t=0	ADJ
ejpam-4641	164	4	∣∣∣	∣∣∣	ADJ
ejpam-4641	164	5	t=0	t=0	X
ejpam-4641	164	6	∣∣∣	∣∣∣	NOUN
ejpam-4641	164	7	t=0	t=0	X
ejpam-4641	164	8	.	.	PUNCT
ejpam-4641	165	1	(	(	PUNCT
ejpam-4641	165	2	16	16	NUM
ejpam-4641	165	3	)	)	PUNCT
ejpam-4641	165	4	while	while	SCONJ
ejpam-4641	165	5	µ	µ	X
ejpam-4641	165	6	(	(	PUNCT
ejpam-4641	165	7	i	i	NOUN
ejpam-4641	165	8	)	)	PUNCT
ejpam-4641	165	9	uc	uc	PROPN
ejpam-4641	165	10	n	n	NOUN
ejpam-4641	165	11	=	=	SYM
ejpam-4641	165	12	2nα	2nα	ADJ
ejpam-4641	165	13	[	[	PUNCT
ejpam-4641	165	14	β(i)(2α	β(i)(2α	PROPN
ejpam-4641	165	15	,	,	PUNCT
ejpam-4641	165	16	1−	1−	NUM
ejpam-4641	165	17	t	t	NOUN
ejpam-4641	165	18	λ	λ	PROPN
ejpam-4641	165	19	)	)	PUNCT
ejpam-4641	165	20	−	−	PROPN
ejpam-4641	166	1	n−1∑	n−1∑	NUM
ejpam-4641	166	2	k=1	k=1	PROPN
ejpam-4641	166	3	1	1	NUM
ejpam-4641	166	4	k	k	NOUN
ejpam-4641	166	5	!	!	PUNCT
ejpam-4641	167	1	∞∑	∞∑	NUM
ejpam-4641	167	2	p=0	p=0	PROPN
ejpam-4641	167	3	ap(k	ap(k	PUNCT
ejpam-4641	167	4	)	)	PUNCT
ejpam-4641	167	5	{	{	PUNCT
ejpam-4641	167	6	β(i)((1	β(i)((1	PROPN
ejpam-4641	167	7	+	+	CCONJ
ejpam-4641	167	8	k	k	X
ejpam-4641	167	9	+	+	CCONJ
ejpam-4641	167	10	p)α	p)α	NOUN
ejpam-4641	167	11	,	,	PUNCT
ejpam-4641	167	12	1−	1−	NUM
ejpam-4641	167	13	t	t	NOUN
ejpam-4641	167	14	λ	λ	PROPN
ejpam-4641	167	15	)	)	PUNCT
ejpam-4641	168	1	−β(i)((2	−β(i)((2	PROPN
ejpam-4641	169	1	+	+	CCONJ
ejpam-4641	169	2	k	k	X
ejpam-4641	169	3	+	+	CCONJ
ejpam-4641	169	4	p)α	p)α	NOUN
ejpam-4641	169	5	,	,	PUNCT
ejpam-4641	169	6	1−	1−	NUM
ejpam-4641	169	7	t	t	NOUN
ejpam-4641	169	8	λ	λ	PROPN
ejpam-4641	169	9	)	)	PUNCT
ejpam-4641	169	10	}	}	PUNCT
ejpam-4641	169	11	]	]	PUNCT
ejpam-4641	169	12	∣∣∣	∣∣∣	X
ejpam-4641	169	13	t=0	t=0	X
ejpam-4641	169	14	∣∣∣	∣∣∣	ADJ
ejpam-4641	169	15	t=0	t=0	X
ejpam-4641	169	16	∣∣∣	∣∣∣	NOUN
ejpam-4641	169	17	t=0	t=0	PROPN
ejpam-4641	169	18	.	.	PUNCT
ejpam-4641	170	1	(	(	PUNCT
ejpam-4641	170	2	17	17	NUM
ejpam-4641	170	3	)	)	PUNCT
ejpam-4641	170	4	r.a.aldallal	r.a.aldallal	NOUN
ejpam-4641	170	5	/	/	SYM
ejpam-4641	170	6	eur	eur	PROPN
ejpam-4641	170	7	.	.	PUNCT
ejpam-4641	171	1	j.	j.	PROPN
ejpam-4641	171	2	pure	pure	PROPN
ejpam-4641	171	3	appl	appl	PROPN
ejpam-4641	171	4	.	.	PROPN
ejpam-4641	171	5	math	math	PROPN
ejpam-4641	171	6	,	,	PUNCT
ejpam-4641	171	7	16	16	NUM
ejpam-4641	171	8	(	(	PUNCT
ejpam-4641	171	9	1	1	NUM
ejpam-4641	171	10	)	)	PUNCT
ejpam-4641	171	11	(	(	PUNCT
ejpam-4641	171	12	2023	2023	NUM
ejpam-4641	171	13	)	)	PUNCT
ejpam-4641	171	14	,	,	PUNCT
ejpam-4641	171	15	97	97	NUM
ejpam-4641	171	16	-	-	SYM
ejpam-4641	171	17	111	111	NUM
ejpam-4641	171	18	104	104	NUM
ejpam-4641	171	19	4	4	NUM
ejpam-4641	171	20	.	.	PUNCT
ejpam-4641	172	1	some	some	DET
ejpam-4641	172	2	recurrence	recurrence	NOUN
ejpam-4641	172	3	relations	relation	NOUN
ejpam-4641	172	4	here	here	ADV
ejpam-4641	172	5	we	we	PRON
ejpam-4641	172	6	tried	try	VERB
ejpam-4641	172	7	to	to	PART
ejpam-4641	172	8	find	find	VERB
ejpam-4641	172	9	recurrence	recurrence	NOUN
ejpam-4641	172	10	relations	relation	NOUN
ejpam-4641	172	11	for	for	ADP
ejpam-4641	172	12	mlc	mlc	PROPN
ejpam-4641	172	13	n+1	n+1	PROPN
ejpam-4641	172	14	(	(	PUNCT
ejpam-4641	172	15	t	t	PROPN
ejpam-4641	172	16	)	)	PUNCT
ejpam-4641	172	17	and	and	CCONJ
ejpam-4641	172	18	muc	muc	VERB
ejpam-4641	172	19	n+1	n+1	PROPN
ejpam-4641	172	20	(	(	PUNCT
ejpam-4641	172	21	t	t	NOUN
ejpam-4641	172	22	)	)	PUNCT
ejpam-4641	172	23	based	base	VERB
ejpam-4641	172	24	on	on	ADP
ejpam-4641	172	25	previous	previous	ADJ
ejpam-4641	172	26	terms	term	NOUN
ejpam-4641	172	27	mlc	mlc	X
ejpam-4641	172	28	n	n	CCONJ
ejpam-4641	172	29	(	(	PUNCT
ejpam-4641	172	30	t	t	PROPN
ejpam-4641	172	31	)	)	PUNCT
ejpam-4641	172	32	and	and	CCONJ
ejpam-4641	172	33	mlc	mlc	PROPN
ejpam-4641	172	34	n	n	PROPN
ejpam-4641	172	35	(	(	PUNCT
ejpam-4641	172	36	t	t	PROPN
ejpam-4641	172	37	)	)	PUNCT
ejpam-4641	172	38	along	along	ADP
ejpam-4641	172	39	with	with	ADP
ejpam-4641	172	40	some	some	DET
ejpam-4641	172	41	additional	additional	ADJ
ejpam-4641	172	42	terms	term	NOUN
ejpam-4641	172	43	.	.	PUNCT
ejpam-4641	173	1	also	also	ADV
ejpam-4641	173	2	,	,	PUNCT
ejpam-4641	173	3	the	the	DET
ejpam-4641	173	4	same	same	ADJ
ejpam-4641	173	5	has	have	AUX
ejpam-4641	173	6	been	be	AUX
ejpam-4641	173	7	done	do	VERB
ejpam-4641	173	8	for	for	ADP
ejpam-4641	173	9	µ	µ	X
ejpam-4641	173	10	(	(	PUNCT
ejpam-4641	173	11	i	i	NOUN
ejpam-4641	173	12	)	)	PUNCT
ejpam-4641	173	13	lc	lc	PROPN
ejpam-4641	173	14	n+1	n+1	PROPN
ejpam-4641	173	15	and	and	CCONJ
ejpam-4641	173	16	µ	µ	PROPN
ejpam-4641	173	17	(	(	PUNCT
ejpam-4641	173	18	i	i	NOUN
ejpam-4641	173	19	)	)	PUNCT
ejpam-4641	173	20	uc	uc	PROPN
ejpam-4641	173	21	n+1	n+1	PROPN
ejpam-4641	173	22	.	.	PUNCT
ejpam-4641	174	1	again	again	ADV
ejpam-4641	174	2	,	,	PUNCT
ejpam-4641	174	3	the	the	DET
ejpam-4641	174	4	same	same	ADJ
ejpam-4641	174	5	has	have	AUX
ejpam-4641	174	6	been	be	AUX
ejpam-4641	174	7	done	do	VERB
ejpam-4641	174	8	for	for	ADP
ejpam-4641	174	9	mlc	mlc	PROPN
ejpam-4641	174	10	n+1,u	n+1,u	PROPN
ejpam-4641	174	11	c	c	PROPN
ejpam-4641	174	12	n+1	n+1	PROPN
ejpam-4641	174	13	(	(	PUNCT
ejpam-4641	174	14	t1	t1	NOUN
ejpam-4641	174	15	,	,	PUNCT
ejpam-4641	174	16	t2	t2	NOUN
ejpam-4641	174	17	)	)	PUNCT
ejpam-4641	174	18	based	base	VERB
ejpam-4641	174	19	on	on	ADP
ejpam-4641	174	20	previous	previous	ADJ
ejpam-4641	174	21	function	function	NOUN
ejpam-4641	174	22	mlc	mlc	NOUN
ejpam-4641	174	23	n	n	CCONJ
ejpam-4641	174	24	,	,	PUNCT
ejpam-4641	174	25	u	u	PROPN
ejpam-4641	174	26	c	c	PROPN
ejpam-4641	174	27	n	n	PROPN
ejpam-4641	174	28	(	(	PUNCT
ejpam-4641	174	29	t1	t1	PROPN
ejpam-4641	174	30	,	,	PUNCT
ejpam-4641	174	31	t2	t2	NOUN
ejpam-4641	174	32	)	)	PUNCT
ejpam-4641	174	33	with	with	ADP
ejpam-4641	174	34	some	some	DET
ejpam-4641	174	35	added	add	VERB
ejpam-4641	174	36	terms	term	NOUN
ejpam-4641	174	37	and	and	CCONJ
ejpam-4641	174	38	for	for	ADP
ejpam-4641	174	39	the	the	DET
ejpam-4641	174	40	product	product	NOUN
ejpam-4641	175	1	moments	moment	NOUN
ejpam-4641	175	2	µ	µ	X
ejpam-4641	175	3	(	(	PUNCT
ejpam-4641	175	4	i	i	PROPN
ejpam-4641	175	5	,	,	PUNCT
ejpam-4641	175	6	j	j	PROPN
ejpam-4641	175	7	)	)	PUNCT
ejpam-4641	175	8	lc	lc	PROPN
ejpam-4641	176	1	n+1,u	n+1,u	PROPN
ejpam-4641	176	2	c	c	PROPN
ejpam-4641	176	3	n+1	n+1	PROPN
ejpam-4641	176	4	.	.	PUNCT
ejpam-4641	177	1	theorem	theorem	NOUN
ejpam-4641	177	2	2	2	NUM
ejpam-4641	177	3	.	.	X
ejpam-4641	177	4	for	for	ADP
ejpam-4641	177	5	n	n	PROPN
ejpam-4641	177	6	≥	≥	NUM
ejpam-4641	177	7	2	2	NUM
ejpam-4641	177	8	mlc	mlc	X
ejpam-4641	177	9	n+1	n+1	PROPN
ejpam-4641	177	10	(	(	PUNCT
ejpam-4641	177	11	t	t	NOUN
ejpam-4641	177	12	)	)	PUNCT
ejpam-4641	177	13	=	=	PUNCT
ejpam-4641	178	1	2mlc	2mlc	NUM
ejpam-4641	178	2	n	n	X
ejpam-4641	178	3	(	(	PUNCT
ejpam-4641	178	4	t)−	t)−	PROPN
ejpam-4641	178	5	(	(	PUNCT
ejpam-4641	178	6	2α)n+1	2α)n+1	NOUN
ejpam-4641	178	7	n	n	X
ejpam-4641	178	8	!	!	PUNCT
ejpam-4641	179	1	∞∑	∞∑	NUM
ejpam-4641	179	2	p=0	p=0	PROPN
ejpam-4641	179	3	ap(n)β(2α,−	ap(n)β(2α,−	VERB
ejpam-4641	179	4	t	t	PROPN
ejpam-4641	179	5	λ	λ	PROPN
ejpam-4641	179	6	+	+	PROPN
ejpam-4641	179	7	n+	n+	PROPN
ejpam-4641	179	8	p+	p+	NOUN
ejpam-4641	179	9	1	1	NUM
ejpam-4641	179	10	)	)	PUNCT
ejpam-4641	179	11	(	(	PUNCT
ejpam-4641	179	12	18	18	NUM
ejpam-4641	179	13	)	)	PUNCT
ejpam-4641	179	14	muc	muc	NOUN
ejpam-4641	180	1	n+1	n+1	PROPN
ejpam-4641	180	2	(	(	PUNCT
ejpam-4641	180	3	t	t	NOUN
ejpam-4641	180	4	)	)	PUNCT
ejpam-4641	180	5	=	=	SYM
ejpam-4641	181	1	2muc	2muc	NUM
ejpam-4641	181	2	n	n	PRON
ejpam-4641	181	3	(	(	PUNCT
ejpam-4641	181	4	t)−	t)−	PROPN
ejpam-4641	181	5	2n+1α	2n+1α	NUM
ejpam-4641	181	6	n	n	CCONJ
ejpam-4641	181	7	!	!	PUNCT
ejpam-4641	182	1	∞∑	∞∑	NUM
ejpam-4641	182	2	p=0	p=0	PROPN
ejpam-4641	182	3	ap(n	ap(n	PUNCT
ejpam-4641	182	4	)	)	PUNCT
ejpam-4641	182	5	[	[	PUNCT
ejpam-4641	182	6	β((1+n+p)α	β((1+n+p)α	NOUN
ejpam-4641	182	7	,	,	PUNCT
ejpam-4641	182	8	1−	1−	NUM
ejpam-4641	182	9	t	t	NOUN
ejpam-4641	182	10	λ	λ	PROPN
ejpam-4641	182	11	)	)	PUNCT
ejpam-4641	182	12	−β((2+n+p)α	−β((2+n+p)α	PROPN
ejpam-4641	182	13	,	,	PUNCT
ejpam-4641	182	14	1−	1−	NUM
ejpam-4641	182	15	t	t	PROPN
ejpam-4641	182	16	λ	λ	PROPN
ejpam-4641	182	17	)	)	PUNCT
ejpam-4641	182	18	]	]	PUNCT
ejpam-4641	182	19	(	(	PUNCT
ejpam-4641	182	20	19	19	NUM
ejpam-4641	182	21	)	)	PUNCT
ejpam-4641	182	22	proof	proof	NOUN
ejpam-4641	182	23	.	.	PUNCT
ejpam-4641	183	1	by	by	ADP
ejpam-4641	183	2	replacing	replace	VERB
ejpam-4641	183	3	n	n	ADV
ejpam-4641	183	4	by	by	ADP
ejpam-4641	183	5	n+	n+	ADP
ejpam-4641	183	6	1	1	NUM
ejpam-4641	183	7	in	in	ADP
ejpam-4641	183	8	(	(	PUNCT
ejpam-4641	183	9	12	12	NUM
ejpam-4641	183	10	)	)	PUNCT
ejpam-4641	183	11	and	and	CCONJ
ejpam-4641	183	12	(	(	PUNCT
ejpam-4641	183	13	13	13	NUM
ejpam-4641	183	14	)	)	PUNCT
ejpam-4641	183	15	,	,	PUNCT
ejpam-4641	183	16	and	and	CCONJ
ejpam-4641	183	17	by	by	ADP
ejpam-4641	183	18	some	some	DET
ejpam-4641	183	19	routine	routine	ADJ
ejpam-4641	183	20	calculations	calculation	NOUN
ejpam-4641	183	21	we	we	PRON
ejpam-4641	183	22	reach	reach	VERB
ejpam-4641	183	23	(	(	PUNCT
ejpam-4641	183	24	18	18	NUM
ejpam-4641	183	25	)	)	PUNCT
ejpam-4641	183	26	and	and	CCONJ
ejpam-4641	183	27	(	(	PUNCT
ejpam-4641	183	28	19	19	NUM
ejpam-4641	183	29	)	)	PUNCT
ejpam-4641	183	30	respectively	respectively	ADV
ejpam-4641	183	31	.	.	PUNCT
ejpam-4641	184	1	theorem	theorem	VERB
ejpam-4641	184	2	3	3	NUM
ejpam-4641	184	3	.	.	PUNCT
ejpam-4641	184	4	knowing	know	VERB
ejpam-4641	184	5	mlc	mlc	PROPN
ejpam-4641	184	6	n	n	CCONJ
ejpam-4641	184	7	,	,	PUNCT
ejpam-4641	184	8	u	u	PROPN
ejpam-4641	184	9	c	c	PROPN
ejpam-4641	184	10	n	n	PROPN
ejpam-4641	184	11	(	(	PUNCT
ejpam-4641	184	12	t1	t1	PROPN
ejpam-4641	184	13	,	,	PUNCT
ejpam-4641	184	14	t2	t2	NOUN
ejpam-4641	184	15	)	)	PUNCT
ejpam-4641	184	16	and	and	CCONJ
ejpam-4641	184	17	for	for	ADP
ejpam-4641	184	18	n	n	PRON
ejpam-4641	184	19	≥	≥	NUM
ejpam-4641	184	20	2	2	NUM
ejpam-4641	184	21	,	,	PUNCT
ejpam-4641	184	22	we	we	PRON
ejpam-4641	184	23	can	can	AUX
ejpam-4641	184	24	calculate	calculate	VERB
ejpam-4641	184	25	mlc	mlc	PROPN
ejpam-4641	184	26	n+1,u	n+1,u	PROPN
ejpam-4641	184	27	c	c	PROPN
ejpam-4641	184	28	n+1	n+1	PROPN
ejpam-4641	185	1	(	(	PUNCT
ejpam-4641	185	2	t1	t1	NOUN
ejpam-4641	185	3	,	,	PUNCT
ejpam-4641	185	4	t2	t2	NOUN
ejpam-4641	185	5	)	)	PUNCT
ejpam-4641	185	6	using	use	VERB
ejpam-4641	185	7	the	the	DET
ejpam-4641	185	8	following	follow	VERB
ejpam-4641	185	9	mlc	mlc	PROPN
ejpam-4641	185	10	n+1,u	n+1,u	PROPN
ejpam-4641	185	11	c	c	PROPN
ejpam-4641	185	12	n+1	n+1	PROPN
ejpam-4641	186	1	(	(	PUNCT
ejpam-4641	186	2	t1	t1	NOUN
ejpam-4641	186	3	,	,	PUNCT
ejpam-4641	186	4	t2	t2	NOUN
ejpam-4641	186	5	)	)	PUNCT
ejpam-4641	187	1	=	=	SYM
ejpam-4641	187	2	2mlc	2mlc	NOUN
ejpam-4641	187	3	n	n	CCONJ
ejpam-4641	187	4	,	,	PUNCT
ejpam-4641	187	5	u	u	PROPN
ejpam-4641	187	6	c	c	PROPN
ejpam-4641	187	7	n	n	PROPN
ejpam-4641	187	8	(	(	PUNCT
ejpam-4641	187	9	t1	t1	PROPN
ejpam-4641	187	10	,	,	PUNCT
ejpam-4641	187	11	t2	t2	NOUN
ejpam-4641	187	12	)	)	PUNCT
ejpam-4641	188	1	+	+	CCONJ
ejpam-4641	188	2	2n+1	2n+1	NOUN
ejpam-4641	188	3	(	(	PUNCT
ejpam-4641	188	4	n−	n−	NOUN
ejpam-4641	188	5	1	1	NUM
ejpam-4641	188	6	)	)	PUNCT
ejpam-4641	188	7	!	!	PUNCT
ejpam-4641	189	1	∞∑	∞∑	NUM
ejpam-4641	189	2	p=0	p=0	PROPN
ejpam-4641	189	3	ap(n	ap(n	PRON
ejpam-4641	189	4	)	)	PUNCT
ejpam-4641	189	5	{	{	PUNCT
ejpam-4641	189	6	α2	α2	ADV
ejpam-4641	189	7	∞∑	∞∑	PROPN
ejpam-4641	189	8	k=0	k=0	PUNCT
ejpam-4641	189	9	n+p+k−1∑	n+p+k−1∑	PROPN
ejpam-4641	189	10	ω=0	ω=0	X
ejpam-4641	189	11	(	(	PUNCT
ejpam-4641	189	12	−1)ω	−1)ω	X
ejpam-4641	189	13	(	(	PUNCT
ejpam-4641	189	14	n+	n+	X
ejpam-4641	189	15	p+	p+	VERB
ejpam-4641	189	16	k	k	X
ejpam-4641	189	17	−	−	PROPN
ejpam-4641	189	18	1	1	NUM
ejpam-4641	189	19	ω	ω	NOUN
ejpam-4641	189	20	)	)	PUNCT
ejpam-4641	190	1	[	[	PUNCT
ejpam-4641	190	2	α(n+p+k−ω+1)−1∑	α(n+p+k−ω+1)−1∑	PROPN
ejpam-4641	190	3	i=0	i=0	PROPN
ejpam-4641	190	4	(	(	PUNCT
ejpam-4641	190	5	−1)i	−1)i	X
ejpam-4641	190	6	(	(	PUNCT
ejpam-4641	190	7	α(n+	α(n+	NUM
ejpam-4641	190	8	p+	p+	NOUN
ejpam-4641	190	9	k	k	PROPN
ejpam-4641	190	10	−	−	PROPN
ejpam-4641	190	11	ω	ω	PROPN
ejpam-4641	190	12	+	+	PROPN
ejpam-4641	191	1	1)−	1)−	NUM
ejpam-4641	191	2	1	1	NUM
ejpam-4641	191	3	i	i	NOUN
ejpam-4641	191	4	)	)	PUNCT
ejpam-4641	191	5	β(α(ω	β(α(ω	PROPN
ejpam-4641	192	1	+	+	CCONJ
ejpam-4641	192	2	1	1	NUM
ejpam-4641	192	3	)	)	PUNCT
ejpam-4641	192	4	+	+	NUM
ejpam-4641	192	5	1	1	NUM
ejpam-4641	192	6	,	,	PUNCT
ejpam-4641	192	7	i−	i−	ADJ
ejpam-4641	192	8	t2	t2	NOUN
ejpam-4641	192	9	λ	λ	PROPN
ejpam-4641	192	10	+	+	CCONJ
ejpam-4641	192	11	1	1	NUM
ejpam-4641	192	12	)	)	PUNCT
ejpam-4641	192	13	3f2	3f2	NUM
ejpam-4641	192	14	(	(	PUNCT
ejpam-4641	192	15	α(ω	α(ω	NOUN
ejpam-4641	192	16	+	+	NOUN
ejpam-4641	192	17	1	1	NUM
ejpam-4641	192	18	)	)	PUNCT
ejpam-4641	192	19	+	+	NUM
ejpam-4641	192	20	1	1	NUM
ejpam-4641	192	21	,	,	PUNCT
ejpam-4641	192	22	α(ω	α(ω	PROPN
ejpam-4641	192	23	+	+	NOUN
ejpam-4641	192	24	1	1	NUM
ejpam-4641	192	25	)	)	PUNCT
ejpam-4641	192	26	,	,	PUNCT
ejpam-4641	192	27	1−	1−	NUM
ejpam-4641	192	28	t1	t1	NOUN
ejpam-4641	192	29	λ	λ	PROPN
ejpam-4641	192	30	;	;	PUNCT
ejpam-4641	192	31	α(ω	α(ω	PROPN
ejpam-4641	192	32	+	+	SYM
ejpam-4641	192	33	1	1	NUM
ejpam-4641	192	34	)	)	PUNCT
ejpam-4641	192	35	+	+	NUM
ejpam-4641	192	36	1	1	NUM
ejpam-4641	192	37	,	,	PUNCT
ejpam-4641	192	38	α(ω	α(ω	PROPN
ejpam-4641	192	39	+	+	NOUN
ejpam-4641	192	40	1	1	NUM
ejpam-4641	192	41	)	)	PUNCT
ejpam-4641	192	42	+	+	CCONJ
ejpam-4641	192	43	i−	i−	PROPN
ejpam-4641	192	44	t2	t2	NOUN
ejpam-4641	192	45	λ	λ	PROPN
ejpam-4641	192	46	+	+	PROPN
ejpam-4641	192	47	2	2	NUM
ejpam-4641	192	48	;	;	PUNCT
ejpam-4641	192	49	1	1	NUM
ejpam-4641	192	50	)	)	PUNCT
ejpam-4641	192	51	−	−	NOUN
ejpam-4641	193	1	α(n+p+k−ω)−1∑	α(n+p+k−ω)−1∑	NUM
ejpam-4641	193	2	l=0	l=0	PROPN
ejpam-4641	193	3	(	(	PUNCT
ejpam-4641	193	4	−1)l	−1)l	PROPN
ejpam-4641	193	5	(	(	PUNCT
ejpam-4641	193	6	α(n+	α(n+	NUM
ejpam-4641	193	7	p+	p+	NOUN
ejpam-4641	193	8	k	k	PROPN
ejpam-4641	193	9	−	−	PROPN
ejpam-4641	193	10	ω)−	ω)−	PROPN
ejpam-4641	193	11	1	1	NUM
ejpam-4641	193	12	l	l	NOUN
ejpam-4641	193	13	)	)	PUNCT
ejpam-4641	193	14	β(α(ω	β(α(ω	PROPN
ejpam-4641	194	1	+	+	CCONJ
ejpam-4641	194	2	1	1	NUM
ejpam-4641	194	3	)	)	PUNCT
ejpam-4641	194	4	+	+	NUM
ejpam-4641	194	5	1	1	NUM
ejpam-4641	194	6	,	,	PUNCT
ejpam-4641	194	7	l	l	NOUN
ejpam-4641	194	8	−	−	PROPN
ejpam-4641	194	9	t2	t2	NOUN
ejpam-4641	194	10	λ	λ	NOUN
ejpam-4641	194	11	+	+	NOUN
ejpam-4641	194	12	1	1	NUM
ejpam-4641	194	13	)	)	PUNCT
ejpam-4641	194	14	3f2	3f2	NUM
ejpam-4641	194	15	(	(	PUNCT
ejpam-4641	194	16	α(ω	α(ω	NOUN
ejpam-4641	194	17	+	+	NOUN
ejpam-4641	194	18	1	1	NUM
ejpam-4641	194	19	)	)	PUNCT
ejpam-4641	194	20	+	+	NUM
ejpam-4641	194	21	1	1	NUM
ejpam-4641	194	22	,	,	PUNCT
ejpam-4641	194	23	α(ω	α(ω	PROPN
ejpam-4641	194	24	+	+	NOUN
ejpam-4641	194	25	1	1	NUM
ejpam-4641	194	26	)	)	PUNCT
ejpam-4641	194	27	,	,	PUNCT
ejpam-4641	194	28	1−	1−	NUM
ejpam-4641	194	29	t1	t1	NOUN
ejpam-4641	194	30	λ	λ	PROPN
ejpam-4641	194	31	;	;	PUNCT
ejpam-4641	194	32	α(ω	α(ω	PROPN
ejpam-4641	194	33	+	+	SYM
ejpam-4641	194	34	1	1	NUM
ejpam-4641	194	35	)	)	PUNCT
ejpam-4641	194	36	+	+	NUM
ejpam-4641	194	37	1	1	NUM
ejpam-4641	194	38	,	,	PUNCT
ejpam-4641	194	39	α(ω	α(ω	PROPN
ejpam-4641	194	40	+	+	NOUN
ejpam-4641	194	41	1	1	NUM
ejpam-4641	194	42	)	)	PUNCT
ejpam-4641	195	1	+	+	NOUN
ejpam-4641	195	2	l	l	NOUN
ejpam-4641	195	3	−	−	PROPN
ejpam-4641	195	4	t2	t2	NOUN
ejpam-4641	195	5	λ	λ	NOUN
ejpam-4641	195	6	+	+	PROPN
ejpam-4641	195	7	2	2	NUM
ejpam-4641	195	8	;	;	PUNCT
ejpam-4641	195	9	1	1	NUM
ejpam-4641	195	10	]	]	PUNCT
ejpam-4641	195	11	+	+	CCONJ
ejpam-4641	195	12	t1	t1	NOUN
ejpam-4641	195	13	nλ(λ+	nλ(λ+	ADJ
ejpam-4641	195	14	1	1	NUM
ejpam-4641	195	15	)	)	PUNCT
ejpam-4641	195	16	p+n∑	p+n∑	NOUN
ejpam-4641	195	17	h=0	h=0	PUNCT
ejpam-4641	195	18	(	(	PUNCT
ejpam-4641	195	19	n+	n+	ADP
ejpam-4641	195	20	p	p	NOUN
ejpam-4641	195	21	h	h	NOUN
ejpam-4641	195	22	)	)	PUNCT
ejpam-4641	195	23	(	(	PUNCT
ejpam-4641	195	24	−1)hβ(α(p+	−1)hβ(α(p+	NOUN
ejpam-4641	195	25	n+	n+	PUNCT
ejpam-4641	195	26	2	2	NUM
ejpam-4641	195	27	)	)	PUNCT
ejpam-4641	195	28	,	,	PUNCT
ejpam-4641	195	29	−t2	−t2	PROPN
ejpam-4641	195	30	λ	λ	PROPN
ejpam-4641	195	31	+	+	PROPN
ejpam-4641	195	32	1	1	NUM
ejpam-4641	195	33	)	)	PUNCT
ejpam-4641	195	34	[	[	PUNCT
ejpam-4641	195	35	3f2	3f2	NUM
ejpam-4641	195	36	(	(	PUNCT
ejpam-4641	195	37	α(p+	α(p+	NUM
ejpam-4641	195	38	n+	n+	PUNCT
ejpam-4641	195	39	2	2	NUM
ejpam-4641	195	40	)	)	PUNCT
ejpam-4641	195	41	)	)	PUNCT
ejpam-4641	195	42	,	,	PUNCT
ejpam-4641	195	43	α(h+	α(h+	NOUN
ejpam-4641	195	44	1	1	NUM
ejpam-4641	195	45	)	)	PUNCT
ejpam-4641	195	46	,	,	PUNCT
ejpam-4641	195	47	1	1	NUM
ejpam-4641	195	48	+	+	NUM
ejpam-4641	195	49	t1	t1	NUM
ejpam-4641	195	50	λ	λ	PROPN
ejpam-4641	195	51	;	;	PUNCT
ejpam-4641	195	52	α(h+	α(h+	NOUN
ejpam-4641	195	53	1	1	NUM
ejpam-4641	195	54	)	)	PUNCT
ejpam-4641	195	55	+	+	NUM
ejpam-4641	195	56	1	1	NUM
ejpam-4641	195	57	,	,	PUNCT
ejpam-4641	195	58	α(p+	α(p+	NUM
ejpam-4641	195	59	n+	n+	PUNCT
ejpam-4641	195	60	2	2	NUM
ejpam-4641	195	61	)	)	PUNCT
ejpam-4641	195	62	+	+	SYM
ejpam-4641	195	63	1−	1−	NUM
ejpam-4641	195	64	t2	t2	NOUN
ejpam-4641	195	65	λ	λ	NOUN
ejpam-4641	195	66	;	;	PUNCT
ejpam-4641	195	67	1	1	X
ejpam-4641	195	68	)	)	PUNCT
ejpam-4641	195	69	−	−	ADP
ejpam-4641	196	1	3f2	3f2	NUM
ejpam-4641	196	2	(	(	PUNCT
ejpam-4641	196	3	α(p+	α(p+	NUM
ejpam-4641	196	4	n+	n+	PUNCT
ejpam-4641	196	5	2	2	NUM
ejpam-4641	196	6	)	)	PUNCT
ejpam-4641	196	7	)	)	PUNCT
ejpam-4641	196	8	,	,	PUNCT
ejpam-4641	196	9	α(h+	α(h+	NOUN
ejpam-4641	196	10	1	1	NUM
ejpam-4641	196	11	)	)	PUNCT
ejpam-4641	196	12	,	,	PUNCT
ejpam-4641	196	13	t1	t1	PROPN
ejpam-4641	196	14	λ	λ	PROPN
ejpam-4641	196	15	;	;	PUNCT
ejpam-4641	196	16	α(h+	α(h+	NOUN
ejpam-4641	196	17	1	1	NUM
ejpam-4641	196	18	)	)	PUNCT
ejpam-4641	196	19	+	+	NUM
ejpam-4641	196	20	1	1	NUM
ejpam-4641	196	21	,	,	PUNCT
ejpam-4641	196	22	α(p+	α(p+	NUM
ejpam-4641	196	23	n+	n+	PUNCT
ejpam-4641	196	24	2	2	NUM
ejpam-4641	196	25	)	)	PUNCT
ejpam-4641	196	26	+	+	SYM
ejpam-4641	196	27	1−	1−	NUM
ejpam-4641	196	28	t2	t2	NOUN
ejpam-4641	196	29	λ	λ	NOUN
ejpam-4641	196	30	;	;	PUNCT
ejpam-4641	196	31	1	1	NUM
ejpam-4641	196	32	)	)	PUNCT
ejpam-4641	196	33	]	]	PUNCT
ejpam-4641	196	34	}	}	PUNCT
ejpam-4641	196	35	.	.	PUNCT
ejpam-4641	197	1	(	(	PUNCT
ejpam-4641	197	2	20	20	X
ejpam-4641	197	3	)	)	PUNCT
ejpam-4641	197	4	r.a.aldallal	r.a.aldallal	NOUN
ejpam-4641	197	5	/	/	SYM
ejpam-4641	197	6	eur	eur	PROPN
ejpam-4641	197	7	.	.	PUNCT
ejpam-4641	198	1	j.	j.	PROPN
ejpam-4641	198	2	pure	pure	PROPN
ejpam-4641	198	3	appl	appl	PROPN
ejpam-4641	198	4	.	.	PROPN
ejpam-4641	198	5	math	math	PROPN
ejpam-4641	198	6	,	,	PUNCT
ejpam-4641	198	7	16	16	NUM
ejpam-4641	198	8	(	(	PUNCT
ejpam-4641	198	9	1	1	NUM
ejpam-4641	198	10	)	)	PUNCT
ejpam-4641	198	11	(	(	PUNCT
ejpam-4641	198	12	2023	2023	NUM
ejpam-4641	198	13	)	)	PUNCT
ejpam-4641	198	14	,	,	PUNCT
ejpam-4641	198	15	97	97	NUM
ejpam-4641	198	16	-	-	SYM
ejpam-4641	198	17	111	111	NUM
ejpam-4641	198	18	105	105	NUM
ejpam-4641	198	19	proof	proof	NOUN
ejpam-4641	198	20	.	.	PUNCT
ejpam-4641	199	1	we	we	PRON
ejpam-4641	199	2	already	already	ADV
ejpam-4641	199	3	know	know	VERB
ejpam-4641	199	4	that	that	SCONJ
ejpam-4641	199	5	mlc	mlc	PROPN
ejpam-4641	200	1	n+1,u	n+1,u	PROPN
ejpam-4641	200	2	c	c	PROPN
ejpam-4641	200	3	n+1	n+1	PROPN
ejpam-4641	200	4	(	(	PUNCT
ejpam-4641	200	5	t1	t1	NOUN
ejpam-4641	200	6	,	,	PUNCT
ejpam-4641	200	7	t2	t2	NOUN
ejpam-4641	200	8	)	)	PUNCT
ejpam-4641	200	9	=	=	SYM
ejpam-4641	200	10	2n+1	2n+1	PROPN
ejpam-4641	200	11	n	n	NUM
ejpam-4641	200	12	!	!	PUNCT
ejpam-4641	200	13	∫	∫	PROPN
ejpam-4641	201	1	∞	∞	PROPN
ejpam-4641	201	2	0	0	NUM
ejpam-4641	202	1	∫	∫	PROPN
ejpam-4641	202	2	y	y	PROPN
ejpam-4641	202	3	0	0	PROPN
ejpam-4641	203	1	et1x+t2yf(x)f(y)−	et1x+t2yf(x)f(y)−	PRON
ejpam-4641	203	2	log[1	log[1	PROPN
ejpam-4641	203	3	+	+	CCONJ
ejpam-4641	203	4	f	f	X
ejpam-4641	203	5	(	(	PUNCT
ejpam-4641	203	6	x)−	x)−	PROPN
ejpam-4641	203	7	f	f	PROPN
ejpam-4641	203	8	(	(	PUNCT
ejpam-4641	203	9	y)]ndxdy	y)]ndxdy	PROPN
ejpam-4641	203	10	.	.	PUNCT
ejpam-4641	204	1	let	let	VERB
ejpam-4641	204	2	i(y	i(y	NOUN
ejpam-4641	204	3	)	)	PUNCT
ejpam-4641	205	1	=	=	SYM
ejpam-4641	205	2	∫	∫	PROPN
ejpam-4641	205	3	y	y	NOUN
ejpam-4641	205	4	0	0	NUM
ejpam-4641	205	5	et1xf(x){−	et1xf(x){−	NUM
ejpam-4641	206	1	log[1	log[1	PROPN
ejpam-4641	206	2	+	+	CCONJ
ejpam-4641	206	3	f	f	X
ejpam-4641	206	4	(	(	PUNCT
ejpam-4641	206	5	x)−	x)−	PROPN
ejpam-4641	206	6	f	f	PROPN
ejpam-4641	206	7	(	(	PUNCT
ejpam-4641	206	8	y)]}ndx	y)]}ndx	PROPN
ejpam-4641	206	9	,	,	PUNCT
ejpam-4641	206	10	using	use	VERB
ejpam-4641	206	11	integration	integration	NOUN
ejpam-4641	206	12	by	by	ADP
ejpam-4641	206	13	parts	part	NOUN
ejpam-4641	206	14	by	by	ADP
ejpam-4641	206	15	putting	put	VERB
ejpam-4641	206	16	the	the	DET
ejpam-4641	206	17	deferential	deferential	ADJ
ejpam-4641	206	18	part	part	NOUN
ejpam-4641	206	19	to	to	PART
ejpam-4641	206	20	be	be	AUX
ejpam-4641	206	21	et1x{−	et1x{−	ADJ
ejpam-4641	206	22	log[1+f	log[1+f	NOUN
ejpam-4641	206	23	(	(	PUNCT
ejpam-4641	206	24	x)−f	x)−f	PROPN
ejpam-4641	206	25	(	(	PUNCT
ejpam-4641	206	26	y)]}n	y)]}n	PROPN
ejpam-4641	206	27	and	and	CCONJ
ejpam-4641	206	28	the	the	DET
ejpam-4641	206	29	rest	rest	NOUN
ejpam-4641	206	30	as	as	ADP
ejpam-4641	206	31	the	the	DET
ejpam-4641	206	32	integral	integral	ADJ
ejpam-4641	206	33	part	part	NOUN
ejpam-4641	206	34	we	we	PRON
ejpam-4641	206	35	reach	reach	VERB
ejpam-4641	206	36	mlc	mlc	PROPN
ejpam-4641	206	37	n+1,u	n+1,u	PROPN
ejpam-4641	206	38	c	c	PROPN
ejpam-4641	206	39	n+1	n+1	PROPN
ejpam-4641	207	1	(	(	PUNCT
ejpam-4641	207	2	t1	t1	NOUN
ejpam-4641	207	3	,	,	PUNCT
ejpam-4641	207	4	t2	t2	NOUN
ejpam-4641	207	5	)	)	PUNCT
ejpam-4641	207	6	=	=	SYM
ejpam-4641	207	7	2n+1	2n+1	PROPN
ejpam-4641	207	8	(	(	PUNCT
ejpam-4641	207	9	n−	n−	NOUN
ejpam-4641	207	10	1	1	NUM
ejpam-4641	207	11	)	)	PUNCT
ejpam-4641	207	12	!	!	PUNCT
ejpam-4641	208	1	∫	∫	PROPN
ejpam-4641	209	1	∞	∞	PROPN
ejpam-4641	209	2	0	0	NUM
ejpam-4641	210	1	∫	∫	PROPN
ejpam-4641	210	2	y	y	NOUN
ejpam-4641	210	3	0	0	NUM
ejpam-4641	211	1	et1x+t2y	et1x+t2y	ADJ
ejpam-4641	211	2	f	f	X
ejpam-4641	211	3	(	(	PUNCT
ejpam-4641	211	4	x	x	X
ejpam-4641	211	5	)	)	PUNCT
ejpam-4641	211	6	1	1	NUM
ejpam-4641	212	1	+	+	NUM
ejpam-4641	212	2	f	f	X
ejpam-4641	212	3	(	(	PUNCT
ejpam-4641	212	4	x)−	x)−	PROPN
ejpam-4641	212	5	f	f	PROPN
ejpam-4641	212	6	(	(	PUNCT
ejpam-4641	212	7	y	y	NOUN
ejpam-4641	212	8	)	)	PUNCT
ejpam-4641	212	9	f(x)f(y	f(x)f(y	NOUN
ejpam-4641	212	10	)	)	PUNCT
ejpam-4641	212	11	{	{	PUNCT
ejpam-4641	212	12	−	−	PROPN
ejpam-4641	212	13	log[1	log[1	PROPN
ejpam-4641	212	14	+	+	CCONJ
ejpam-4641	212	15	f	f	X
ejpam-4641	212	16	(	(	PUNCT
ejpam-4641	212	17	x)−	x)−	PROPN
ejpam-4641	212	18	f	f	PROPN
ejpam-4641	212	19	(	(	PUNCT
ejpam-4641	212	20	y)]}n−1dxdy	y)]}n−1dxdy	PROPN
ejpam-4641	212	21	−	−	PROPN
ejpam-4641	212	22	2n+1	2n+1	PROPN
ejpam-4641	212	23	n	n	CCONJ
ejpam-4641	212	24	!	!	PUNCT
ejpam-4641	213	1	t1	t1	NOUN
ejpam-4641	213	2	∫	∫	PROPN
ejpam-4641	214	1	∞	∞	PROPN
ejpam-4641	214	2	0	0	NUM
ejpam-4641	215	1	∫	∫	PROPN
ejpam-4641	215	2	y	y	PROPN
ejpam-4641	215	3	0	0	NUM
ejpam-4641	215	4	et1x+t2yf(y)f	et1x+t2yf(y)f	NOUN
ejpam-4641	215	5	(	(	PUNCT
ejpam-4641	215	6	x	x	X
ejpam-4641	215	7	)	)	PUNCT
ejpam-4641	215	8	{	{	PUNCT
ejpam-4641	215	9	−	−	PROPN
ejpam-4641	215	10	log[1	log[1	PROPN
ejpam-4641	216	1	+	+	CCONJ
ejpam-4641	216	2	f	f	X
ejpam-4641	216	3	(	(	PUNCT
ejpam-4641	216	4	x)−	x)−	PROPN
ejpam-4641	216	5	f	f	PROPN
ejpam-4641	216	6	(	(	PUNCT
ejpam-4641	216	7	y)]}ndxdy	y)]}ndxdy	PROPN
ejpam-4641	216	8	,	,	PUNCT
ejpam-4641	216	9	from	from	ADP
ejpam-4641	216	10	which	which	PRON
ejpam-4641	216	11	,	,	PUNCT
ejpam-4641	216	12	we	we	PRON
ejpam-4641	216	13	can	can	AUX
ejpam-4641	216	14	simply	simply	ADV
ejpam-4641	216	15	conclude	conclude	VERB
ejpam-4641	216	16	that	that	SCONJ
ejpam-4641	216	17	it	it	PRON
ejpam-4641	216	18	will	will	AUX
ejpam-4641	216	19	became	become	VERB
ejpam-4641	216	20	mlc	mlc	PROPN
ejpam-4641	216	21	n+1,u	n+1,u	PROPN
ejpam-4641	216	22	c	c	PROPN
ejpam-4641	216	23	n+1	n+1	PROPN
ejpam-4641	217	1	(	(	PUNCT
ejpam-4641	217	2	t1	t1	NOUN
ejpam-4641	217	3	,	,	PUNCT
ejpam-4641	217	4	t2	t2	NOUN
ejpam-4641	217	5	)	)	PUNCT
ejpam-4641	218	1	=	=	SYM
ejpam-4641	218	2	2mlc	2mlc	NOUN
ejpam-4641	218	3	n	n	CCONJ
ejpam-4641	218	4	,	,	PUNCT
ejpam-4641	218	5	u	u	PROPN
ejpam-4641	218	6	c	c	PROPN
ejpam-4641	218	7	n	n	PROPN
ejpam-4641	218	8	(	(	PUNCT
ejpam-4641	218	9	t1	t1	PROPN
ejpam-4641	218	10	,	,	PUNCT
ejpam-4641	218	11	t2	t2	NOUN
ejpam-4641	218	12	)	)	PUNCT
ejpam-4641	219	1	+	+	CCONJ
ejpam-4641	219	2	2n+1	2n+1	NOUN
ejpam-4641	219	3	(	(	PUNCT
ejpam-4641	219	4	n−	n−	NOUN
ejpam-4641	219	5	1	1	NUM
ejpam-4641	219	6	)	)	PUNCT
ejpam-4641	219	7	!	!	PUNCT
ejpam-4641	220	1	∫	∫	PROPN
ejpam-4641	221	1	∞	∞	PROPN
ejpam-4641	221	2	0	0	NUM
ejpam-4641	222	1	∫	∫	PROPN
ejpam-4641	222	2	y	y	NOUN
ejpam-4641	222	3	0	0	NUM
ejpam-4641	223	1	et1x+t2y	et1x+t2y	ADJ
ejpam-4641	223	2	f	f	X
ejpam-4641	223	3	(	(	PUNCT
ejpam-4641	223	4	y)−	y)−	PROPN
ejpam-4641	223	5	1	1	NUM
ejpam-4641	223	6	1	1	NUM
ejpam-4641	223	7	+	+	NUM
ejpam-4641	223	8	f	f	X
ejpam-4641	223	9	(	(	PUNCT
ejpam-4641	223	10	x)−	x)−	PROPN
ejpam-4641	223	11	f	f	PROPN
ejpam-4641	223	12	(	(	PUNCT
ejpam-4641	223	13	y	y	NOUN
ejpam-4641	223	14	)	)	PUNCT
ejpam-4641	223	15	f(x)f(y	f(x)f(y	NOUN
ejpam-4641	223	16	)	)	PUNCT
ejpam-4641	223	17	{	{	PUNCT
ejpam-4641	223	18	−	−	PROPN
ejpam-4641	223	19	log[1	log[1	PROPN
ejpam-4641	224	1	+	+	CCONJ
ejpam-4641	224	2	f	f	X
ejpam-4641	224	3	(	(	PUNCT
ejpam-4641	224	4	x)−	x)−	PROPN
ejpam-4641	224	5	f	f	PROPN
ejpam-4641	224	6	(	(	PUNCT
ejpam-4641	224	7	y)]}n−1dxdy	y)]}n−1dxdy	PROPN
ejpam-4641	224	8	−	−	PROPN
ejpam-4641	224	9	2n+1	2n+1	PROPN
ejpam-4641	224	10	n	n	CCONJ
ejpam-4641	224	11	!	!	PUNCT
ejpam-4641	225	1	t1	t1	NOUN
ejpam-4641	225	2	∫	∫	PROPN
ejpam-4641	226	1	∞	∞	PROPN
ejpam-4641	226	2	0	0	NUM
ejpam-4641	227	1	∫	∫	PROPN
ejpam-4641	227	2	y	y	PROPN
ejpam-4641	227	3	0	0	NUM
ejpam-4641	227	4	et1x+t2yf(y)f	et1x+t2yf(y)f	NOUN
ejpam-4641	227	5	(	(	PUNCT
ejpam-4641	227	6	x	x	X
ejpam-4641	227	7	)	)	PUNCT
ejpam-4641	227	8	{	{	PUNCT
ejpam-4641	227	9	−	−	PROPN
ejpam-4641	227	10	log[1	log[1	PROPN
ejpam-4641	228	1	+	+	CCONJ
ejpam-4641	228	2	f	f	X
ejpam-4641	228	3	(	(	PUNCT
ejpam-4641	228	4	x)−	x)−	PROPN
ejpam-4641	228	5	f	f	PROPN
ejpam-4641	228	6	(	(	PUNCT
ejpam-4641	228	7	y)]}ndxdy	y)]}ndxdy	PROPN
ejpam-4641	228	8	.	.	PROPN
ejpam-4641	228	9	(	(	PUNCT
ejpam-4641	228	10	21	21	NUM
ejpam-4641	228	11	)	)	PUNCT
ejpam-4641	228	12	now	now	ADV
ejpam-4641	228	13	choose	choose	VERB
ejpam-4641	228	14	j(t1	j(t1	PROPN
ejpam-4641	228	15	,	,	PUNCT
ejpam-4641	228	16	t2	t2	NOUN
ejpam-4641	228	17	)	)	PUNCT
ejpam-4641	228	18	=	=	SYM
ejpam-4641	229	1	∫	∫	PROPN
ejpam-4641	230	1	∞	∞	NUM
ejpam-4641	230	2	0	0	NUM
ejpam-4641	231	1	∫	∫	PROPN
ejpam-4641	231	2	y	y	NOUN
ejpam-4641	231	3	0	0	NUM
ejpam-4641	232	1	et1x+t2y	et1x+t2y	ADJ
ejpam-4641	232	2	f	f	X
ejpam-4641	232	3	(	(	PUNCT
ejpam-4641	232	4	y)−	y)−	PROPN
ejpam-4641	232	5	1	1	NUM
ejpam-4641	232	6	1	1	NUM
ejpam-4641	232	7	+	+	NUM
ejpam-4641	232	8	f	f	X
ejpam-4641	232	9	(	(	PUNCT
ejpam-4641	232	10	x)−	x)−	PROPN
ejpam-4641	232	11	f	f	PROPN
ejpam-4641	232	12	(	(	PUNCT
ejpam-4641	232	13	y	y	PROPN
ejpam-4641	232	14	)	)	PUNCT
ejpam-4641	232	15	f(x)f(y){−	f(x)f(y){−	NUM
ejpam-4641	233	1	log[1	log[1	PROPN
ejpam-4641	234	1	+	+	CCONJ
ejpam-4641	234	2	f	f	X
ejpam-4641	234	3	(	(	PUNCT
ejpam-4641	234	4	x)−	x)−	PROPN
ejpam-4641	234	5	f	f	PROPN
ejpam-4641	234	6	(	(	PUNCT
ejpam-4641	234	7	y)]}n−1dxdy	y)]}n−1dxdy	PROPN
ejpam-4641	234	8	,	,	PUNCT
ejpam-4641	234	9	and	and	CCONJ
ejpam-4641	234	10	ζ(t1	ζ(t1	NOUN
ejpam-4641	234	11	,	,	PUNCT
ejpam-4641	234	12	t2	t2	NOUN
ejpam-4641	234	13	)	)	PUNCT
ejpam-4641	234	14	=	=	SYM
ejpam-4641	235	1	∫	∫	PROPN
ejpam-4641	236	1	∞	∞	NUM
ejpam-4641	236	2	0	0	NUM
ejpam-4641	237	1	∫	∫	PROPN
ejpam-4641	237	2	y	y	PROPN
ejpam-4641	237	3	0	0	NUM
ejpam-4641	237	4	et1x+t2yf(y)f	et1x+t2yf(y)f	NOUN
ejpam-4641	237	5	(	(	PUNCT
ejpam-4641	237	6	x){−	x){−	PROPN
ejpam-4641	237	7	log[1	log[1	PROPN
ejpam-4641	238	1	+	+	CCONJ
ejpam-4641	238	2	f	f	X
ejpam-4641	238	3	(	(	PUNCT
ejpam-4641	238	4	x)−	x)−	PROPN
ejpam-4641	238	5	f	f	PROPN
ejpam-4641	238	6	(	(	PUNCT
ejpam-4641	238	7	y)]}ndxdy	y)]}ndxdy	PROPN
ejpam-4641	238	8	.	.	PROPN
ejpam-4641	238	9	from	from	ADP
ejpam-4641	238	10	j(t1	j(t1	PROPN
ejpam-4641	238	11	,	,	PUNCT
ejpam-4641	238	12	t2	t2	PROPN
ejpam-4641	238	13	)	)	PUNCT
ejpam-4641	238	14	,	,	PUNCT
ejpam-4641	238	15	let	let	VERB
ejpam-4641	238	16	k(y	k(y	PRON
ejpam-4641	238	17	)	)	PUNCT
ejpam-4641	239	1	=	=	SYM
ejpam-4641	239	2	∫	∫	PROPN
ejpam-4641	240	1	∞	∞	NOUN
ejpam-4641	240	2	0	0	NUM
ejpam-4641	241	1	et1x	et1x	ADJ
ejpam-4641	241	2	f(x	f(x	PROPN
ejpam-4641	241	3	)	)	PUNCT
ejpam-4641	241	4	1	1	NUM
ejpam-4641	242	1	+	+	NUM
ejpam-4641	242	2	f	f	X
ejpam-4641	242	3	(	(	PUNCT
ejpam-4641	242	4	x)−	x)−	PROPN
ejpam-4641	242	5	f	f	PROPN
ejpam-4641	242	6	(	(	PUNCT
ejpam-4641	242	7	y	y	NOUN
ejpam-4641	242	8	)	)	PUNCT
ejpam-4641	242	9	{	{	PUNCT
ejpam-4641	242	10	−	−	PROPN
ejpam-4641	242	11	log[1	log[1	PROPN
ejpam-4641	242	12	+	+	CCONJ
ejpam-4641	242	13	f	f	X
ejpam-4641	242	14	(	(	PUNCT
ejpam-4641	242	15	x)−	x)−	PROPN
ejpam-4641	242	16	f	f	PROPN
ejpam-4641	242	17	(	(	PUNCT
ejpam-4641	242	18	y)]}n−1dx	y)]}n−1dx	PROPN
ejpam-4641	242	19	,	,	PUNCT
ejpam-4641	242	20	now	now	ADV
ejpam-4641	242	21	,	,	PUNCT
ejpam-4641	242	22	substituting	substitute	VERB
ejpam-4641	242	23	u	u	NOUN
ejpam-4641	242	24	=	=	X
ejpam-4641	242	25	f	f	PROPN
ejpam-4641	242	26	(	(	PUNCT
ejpam-4641	242	27	y)−f	y)−f	PROPN
ejpam-4641	242	28	(	(	PUNCT
ejpam-4641	242	29	x	x	NOUN
ejpam-4641	242	30	)	)	PUNCT
ejpam-4641	242	31	and	and	CCONJ
ejpam-4641	242	32	then	then	ADV
ejpam-4641	242	33	using	use	VERB
ejpam-4641	242	34	the	the	DET
ejpam-4641	242	35	logarithmic	logarithmic	ADJ
ejpam-4641	242	36	expansion	expansion	NOUN
ejpam-4641	242	37	from	from	ADP
ejpam-4641	242	38	(	(	PUNCT
ejpam-4641	242	39	7	7	X
ejpam-4641	242	40	)	)	PUNCT
ejpam-4641	242	41	we	we	PRON
ejpam-4641	242	42	reach	reach	VERB
ejpam-4641	242	43	k(y	k(y	NOUN
ejpam-4641	242	44	)	)	PUNCT
ejpam-4641	242	45	=	=	PUNCT
ejpam-4641	243	1	∞∑	∞∑	NUM
ejpam-4641	243	2	p=0	p=0	PROPN
ejpam-4641	243	3	ap(n	ap(n	PUNCT
ejpam-4641	243	4	)	)	PUNCT
ejpam-4641	244	1	∫	∫	PROPN
ejpam-4641	244	2	f	f	PROPN
ejpam-4641	244	3	(	(	PUNCT
ejpam-4641	244	4	y	y	PROPN
ejpam-4641	244	5	)	)	PUNCT
ejpam-4641	244	6	0	0	NUM
ejpam-4641	245	1	un−1+p	un−1+p	PROPN
ejpam-4641	245	2	1−	1−	NUM
ejpam-4641	245	3	u	u	NOUN
ejpam-4641	245	4	[	[	X
ejpam-4641	245	5	1−	1−	NUM
ejpam-4641	245	6	(	(	PUNCT
ejpam-4641	245	7	f	f	X
ejpam-4641	245	8	(	(	PUNCT
ejpam-4641	245	9	y)−	y)−	PROPN
ejpam-4641	245	10	u	u	NOUN
ejpam-4641	245	11	)	)	PUNCT
ejpam-4641	245	12	1	1	NUM
ejpam-4641	245	13	α	α	NOUN
ejpam-4641	245	14	]	]	PUNCT
ejpam-4641	245	15	−t1	−t1	PROPN
ejpam-4641	245	16	λ	λ	X
ejpam-4641	245	17	du	du	PROPN
ejpam-4641	245	18	,	,	PUNCT
ejpam-4641	245	19	since	since	SCONJ
ejpam-4641	245	20	−1	−1	NOUN
ejpam-4641	245	21	<	<	X
ejpam-4641	245	22	u	u	X
ejpam-4641	245	23	<	<	X
ejpam-4641	245	24	1	1	NUM
ejpam-4641	245	25	,	,	PUNCT
ejpam-4641	245	26	we	we	PRON
ejpam-4641	245	27	can	can	AUX
ejpam-4641	245	28	use	use	VERB
ejpam-4641	245	29	the	the	DET
ejpam-4641	245	30	well	well	ADV
ejpam-4641	245	31	known	know	VERB
ejpam-4641	245	32	expansion	expansion	NOUN
ejpam-4641	245	33	1	1	NUM
ejpam-4641	245	34	1−u	1−u	NUM
ejpam-4641	245	35	=	=	NOUN
ejpam-4641	245	36	∑∞	∑∞	NOUN
ejpam-4641	245	37	k=0	k=0	PROPN
ejpam-4641	245	38	u	u	PROPN
ejpam-4641	245	39	k	k	PROPN
ejpam-4641	245	40	,	,	PUNCT
ejpam-4641	245	41	then	then	ADV
ejpam-4641	245	42	make	make	VERB
ejpam-4641	245	43	a	a	DET
ejpam-4641	245	44	substitution	substitution	NOUN
ejpam-4641	245	45	of	of	ADP
ejpam-4641	245	46	w	w	NOUN
ejpam-4641	245	47	=	=	PUNCT
ejpam-4641	245	48	(	(	PUNCT
ejpam-4641	245	49	f	f	X
ejpam-4641	245	50	(	(	PUNCT
ejpam-4641	245	51	y)−	y)−	PROPN
ejpam-4641	245	52	u	u	NOUN
ejpam-4641	245	53	)	)	PUNCT
ejpam-4641	245	54	1	1	NUM
ejpam-4641	245	55	α	α	NOUN
ejpam-4641	245	56	to	to	PART
ejpam-4641	245	57	reach	reach	VERB
ejpam-4641	245	58	k(y	k(y	NOUN
ejpam-4641	245	59	)	)	PUNCT
ejpam-4641	245	60	=	=	PUNCT
ejpam-4641	246	1	α	α	PROPN
ejpam-4641	246	2	∞∑	∞∑	PROPN
ejpam-4641	246	3	p=0	p=0	PROPN
ejpam-4641	246	4	ap(n	ap(n	NOUN
ejpam-4641	246	5	)	)	PUNCT
ejpam-4641	247	1	∞∑	∞∑	PRON
ejpam-4641	247	2	k=0	k=0	PUNCT
ejpam-4641	247	3	n+p+k−1∑	n+p+k−1∑	PROPN
ejpam-4641	247	4	ω=0	ω=0	X
ejpam-4641	247	5	(	(	PUNCT
ejpam-4641	247	6	−1)ω	−1)ω	X
ejpam-4641	247	7	(	(	PUNCT
ejpam-4641	247	8	n+	n+	X
ejpam-4641	247	9	p+	p+	VERB
ejpam-4641	247	10	k	k	X
ejpam-4641	247	11	−	−	PROPN
ejpam-4641	247	12	1	1	NUM
ejpam-4641	247	13	ω	ω	NOUN
ejpam-4641	247	14	)	)	PUNCT
ejpam-4641	247	15	(	(	PUNCT
ejpam-4641	247	16	f	f	X
ejpam-4641	247	17	(	(	PUNCT
ejpam-4641	247	18	y))n+p+k−ω−1β	y))n+p+k−ω−1β	NOUN
ejpam-4641	247	19	(	(	PUNCT
ejpam-4641	247	20	f	f	PROPN
ejpam-4641	247	21	(	(	PUNCT
ejpam-4641	247	22	y	y	NOUN
ejpam-4641	247	23	)	)	PUNCT
ejpam-4641	247	24	)	)	PUNCT
ejpam-4641	247	25	1	1	NUM
ejpam-4641	247	26	α	α	NOUN
ejpam-4641	247	27	(	(	PUNCT
ejpam-4641	247	28	α(ω	α(ω	NOUN
ejpam-4641	247	29	+	+	NOUN
ejpam-4641	247	30	1	1	NUM
ejpam-4641	247	31	)	)	PUNCT
ejpam-4641	247	32	,	,	PUNCT
ejpam-4641	247	33	1−	1−	NUM
ejpam-4641	247	34	t1	t1	NOUN
ejpam-4641	247	35	λ	λ	PROPN
ejpam-4641	247	36	)	)	PUNCT
ejpam-4641	247	37	.	.	PUNCT
ejpam-4641	248	1	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	248	2	/	/	SYM
ejpam-4641	248	3	eur	eur	PROPN
ejpam-4641	248	4	.	.	PUNCT
ejpam-4641	249	1	j.	j.	PROPN
ejpam-4641	249	2	pure	pure	PROPN
ejpam-4641	249	3	appl	appl	PROPN
ejpam-4641	249	4	.	.	PROPN
ejpam-4641	249	5	math	math	PROPN
ejpam-4641	249	6	,	,	PUNCT
ejpam-4641	249	7	16	16	NUM
ejpam-4641	249	8	(	(	PUNCT
ejpam-4641	249	9	1	1	NUM
ejpam-4641	249	10	)	)	PUNCT
ejpam-4641	249	11	(	(	PUNCT
ejpam-4641	249	12	2023	2023	NUM
ejpam-4641	249	13	)	)	PUNCT
ejpam-4641	249	14	,	,	PUNCT
ejpam-4641	249	15	97	97	NUM
ejpam-4641	249	16	-	-	SYM
ejpam-4641	249	17	111	111	NUM
ejpam-4641	249	18	106	106	NUM
ejpam-4641	249	19	now	now	ADV
ejpam-4641	249	20	j(t1	j(t1	PROPN
ejpam-4641	249	21	,	,	PUNCT
ejpam-4641	249	22	t2	t2	NOUN
ejpam-4641	249	23	)	)	PUNCT
ejpam-4641	249	24	has	have	AUX
ejpam-4641	249	25	became	become	VERB
ejpam-4641	249	26	j(t1	j(t1	PROPN
ejpam-4641	249	27	,	,	PUNCT
ejpam-4641	249	28	t2	t2	NOUN
ejpam-4641	249	29	)	)	PUNCT
ejpam-4641	250	1	=	=	PUNCT
ejpam-4641	250	2	α	α	PROPN
ejpam-4641	250	3	∞∑	∞∑	PROPN
ejpam-4641	250	4	p=0	p=0	PROPN
ejpam-4641	250	5	ap(n	ap(n	NOUN
ejpam-4641	250	6	)	)	PUNCT
ejpam-4641	251	1	∞∑	∞∑	DET
ejpam-4641	251	2	k=0	k=0	PUNCT
ejpam-4641	251	3	n+p+k−1∑	n+p+k−1∑	PROPN
ejpam-4641	251	4	ω=0	ω=0	X
ejpam-4641	251	5	(	(	PUNCT
ejpam-4641	251	6	−1)ω	−1)ω	X
ejpam-4641	251	7	(	(	PUNCT
ejpam-4641	251	8	n+	n+	X
ejpam-4641	251	9	p+	p+	VERB
ejpam-4641	251	10	k	k	X
ejpam-4641	251	11	−	−	PROPN
ejpam-4641	251	12	1	1	NUM
ejpam-4641	251	13	ω	ω	NUM
ejpam-4641	251	14	)	)	PUNCT
ejpam-4641	251	15	∫	∫	PROPN
ejpam-4641	252	1	∞	∞	PROPN
ejpam-4641	252	2	0	0	NUM
ejpam-4641	252	3	f(y)(f	f(y)(f	PUNCT
ejpam-4641	252	4	(	(	PUNCT
ejpam-4641	252	5	y)−	y)−	PROPN
ejpam-4641	252	6	1)(f	1)(f	NUM
ejpam-4641	252	7	(	(	PUNCT
ejpam-4641	252	8	y))n+p+k−ω−1et2y	y))n+p+k−ω−1et2y	NOUN
ejpam-4641	252	9	β	β	X
ejpam-4641	252	10	(	(	PUNCT
ejpam-4641	252	11	f	f	PROPN
ejpam-4641	252	12	(	(	PUNCT
ejpam-4641	252	13	y	y	NOUN
ejpam-4641	252	14	)	)	PUNCT
ejpam-4641	252	15	)	)	PUNCT
ejpam-4641	252	16	1	1	NUM
ejpam-4641	252	17	α	α	NOUN
ejpam-4641	252	18	(	(	PUNCT
ejpam-4641	252	19	α(ω	α(ω	NOUN
ejpam-4641	252	20	+	+	NOUN
ejpam-4641	252	21	1	1	NUM
ejpam-4641	252	22	)	)	PUNCT
ejpam-4641	252	23	,	,	PUNCT
ejpam-4641	252	24	1−	1−	NUM
ejpam-4641	252	25	t1	t1	NOUN
ejpam-4641	252	26	λ	λ	PROPN
ejpam-4641	252	27	)	)	PUNCT
ejpam-4641	252	28	dy	dy	X
ejpam-4641	252	29	.	.	PUNCT
ejpam-4641	253	1	by	by	ADP
ejpam-4641	253	2	replacing	replace	VERB
ejpam-4641	253	3	f(y	f(y	NOUN
ejpam-4641	253	4	)	)	PUNCT
ejpam-4641	253	5	and	and	CCONJ
ejpam-4641	253	6	f	f	PROPN
ejpam-4641	253	7	(	(	PUNCT
ejpam-4641	253	8	y	y	NOUN
ejpam-4641	253	9	)	)	PUNCT
ejpam-4641	253	10	by	by	ADP
ejpam-4641	253	11	their	their	PRON
ejpam-4641	253	12	original	original	ADJ
ejpam-4641	253	13	formulas	formula	NOUN
ejpam-4641	253	14	from	from	ADP
ejpam-4641	253	15	(	(	PUNCT
ejpam-4641	253	16	5	5	NUM
ejpam-4641	253	17	)	)	PUNCT
ejpam-4641	253	18	and	and	CCONJ
ejpam-4641	253	19	(	(	PUNCT
ejpam-4641	253	20	6	6	NUM
ejpam-4641	253	21	)	)	PUNCT
ejpam-4641	253	22	and	and	CCONJ
ejpam-4641	253	23	after	after	ADP
ejpam-4641	253	24	that	that	PRON
ejpam-4641	253	25	we	we	PRON
ejpam-4641	253	26	made	make	VERB
ejpam-4641	253	27	a	a	DET
ejpam-4641	253	28	substituting	substitute	VERB
ejpam-4641	253	29	e−λy	e−λy	NOUN
ejpam-4641	253	30	=	=	SYM
ejpam-4641	253	31	u	u	NOUN
ejpam-4641	253	32	,	,	PUNCT
ejpam-4641	253	33	we	we	PRON
ejpam-4641	253	34	get	get	VERB
ejpam-4641	253	35	j(t1	j(t1	NOUN
ejpam-4641	253	36	,	,	PUNCT
ejpam-4641	253	37	t2	t2	NOUN
ejpam-4641	253	38	)	)	PUNCT
ejpam-4641	253	39	=	=	VERB
ejpam-4641	254	1	α2	α2	ADJ
ejpam-4641	254	2	∞∑	∞∑	PROPN
ejpam-4641	254	3	p=0	p=0	PROPN
ejpam-4641	254	4	ap(n	ap(n	NOUN
ejpam-4641	254	5	)	)	PUNCT
ejpam-4641	255	1	∞∑	∞∑	DET
ejpam-4641	255	2	k=0	k=0	PUNCT
ejpam-4641	255	3	n+p+k−1∑	n+p+k−1∑	PROPN
ejpam-4641	255	4	ω=0	ω=0	X
ejpam-4641	255	5	(	(	PUNCT
ejpam-4641	255	6	−1)ω	−1)ω	X
ejpam-4641	255	7	(	(	PUNCT
ejpam-4641	255	8	n+	n+	X
ejpam-4641	255	9	p+	p+	VERB
ejpam-4641	255	10	k	k	X
ejpam-4641	255	11	−	−	PROPN
ejpam-4641	255	12	1	1	NUM
ejpam-4641	255	13	ω	ω	NOUN
ejpam-4641	255	14	)	)	PUNCT
ejpam-4641	255	15	[	[	PUNCT
ejpam-4641	255	16	α(n+p+k−ω+1)−1∑	α(n+p+k−ω+1)−1∑	PROPN
ejpam-4641	255	17	i=0	i=0	PROPN
ejpam-4641	255	18	(	(	PUNCT
ejpam-4641	255	19	−1)i	−1)i	X
ejpam-4641	255	20	(	(	PUNCT
ejpam-4641	255	21	α(n+	α(n+	NUM
ejpam-4641	255	22	p+	p+	NOUN
ejpam-4641	255	23	k	k	PROPN
ejpam-4641	255	24	−	−	PROPN
ejpam-4641	255	25	ω	ω	PROPN
ejpam-4641	255	26	+	+	PROPN
ejpam-4641	256	1	1)−	1)−	NUM
ejpam-4641	256	2	1	1	NUM
ejpam-4641	256	3	i	i	NOUN
ejpam-4641	256	4	)	)	PUNCT
ejpam-4641	256	5	∫	∫	PROPN
ejpam-4641	257	1	1	1	NUM
ejpam-4641	257	2	0	0	NUM
ejpam-4641	257	3	ui−	ui−	NUM
ejpam-4641	257	4	t2	t2	NOUN
ejpam-4641	257	5	λ	λ	X
ejpam-4641	257	6	β1−u(α(ω	β1−u(α(ω	PROPN
ejpam-4641	257	7	+	+	PROPN
ejpam-4641	257	8	1	1	NUM
ejpam-4641	257	9	)	)	PUNCT
ejpam-4641	257	10	,	,	PUNCT
ejpam-4641	257	11	1−	1−	NUM
ejpam-4641	257	12	t1	t1	NOUN
ejpam-4641	257	13	λ	λ	PROPN
ejpam-4641	257	14	)	)	PUNCT
ejpam-4641	257	15	du	du	PROPN
ejpam-4641	257	16	−	−	PROPN
ejpam-4641	257	17	α(n+p+k−ω)−1∑	α(n+p+k−ω)−1∑	NUM
ejpam-4641	257	18	l=0	l=0	PROPN
ejpam-4641	257	19	(	(	PUNCT
ejpam-4641	257	20	−1)l	−1)l	PROPN
ejpam-4641	257	21	(	(	PUNCT
ejpam-4641	257	22	α(n+	α(n+	NUM
ejpam-4641	257	23	p+	p+	NOUN
ejpam-4641	257	24	k	k	PROPN
ejpam-4641	257	25	−	−	PROPN
ejpam-4641	257	26	ω)−	ω)−	PROPN
ejpam-4641	257	27	1	1	NUM
ejpam-4641	257	28	l	l	NOUN
ejpam-4641	257	29	)	)	PUNCT
ejpam-4641	257	30	∫	∫	PROPN
ejpam-4641	257	31	1	1	NUM
ejpam-4641	257	32	0	0	X
ejpam-4641	257	33	ul−	ul−	PROPN
ejpam-4641	257	34	t2	t2	NOUN
ejpam-4641	257	35	λ	λ	X
ejpam-4641	257	36	β1−u(α(ω	β1−u(α(ω	PROPN
ejpam-4641	257	37	+	+	PROPN
ejpam-4641	257	38	1	1	NUM
ejpam-4641	257	39	)	)	PUNCT
ejpam-4641	257	40	,	,	PUNCT
ejpam-4641	257	41	1−	1−	NUM
ejpam-4641	257	42	t1	t1	NOUN
ejpam-4641	257	43	λ	λ	PROPN
ejpam-4641	257	44	)	)	PUNCT
ejpam-4641	257	45	du	du	X
ejpam-4641	257	46	]	]	PUNCT
ejpam-4641	257	47	,	,	PUNCT
ejpam-4641	257	48	upon	upon	SCONJ
ejpam-4641	257	49	using	use	VERB
ejpam-4641	257	50	(	(	PUNCT
ejpam-4641	257	51	10	10	NUM
ejpam-4641	257	52	)	)	PUNCT
ejpam-4641	257	53	and	and	CCONJ
ejpam-4641	257	54	(	(	PUNCT
ejpam-4641	257	55	11	11	NUM
ejpam-4641	257	56	)	)	PUNCT
ejpam-4641	257	57	in	in	ADP
ejpam-4641	257	58	the	the	DET
ejpam-4641	257	59	last	last	ADJ
ejpam-4641	257	60	integral	integral	NOUN
ejpam-4641	257	61	we	we	PRON
ejpam-4641	257	62	reach	reach	VERB
ejpam-4641	257	63	the	the	DET
ejpam-4641	257	64	final	final	ADJ
ejpam-4641	257	65	form	form	NOUN
ejpam-4641	257	66	of	of	ADP
ejpam-4641	257	67	the	the	DET
ejpam-4641	257	68	function	function	NOUN
ejpam-4641	257	69	j(t1	j(t1	PROPN
ejpam-4641	257	70	,	,	PUNCT
ejpam-4641	257	71	t2	t2	PROPN
ejpam-4641	257	72	)	)	PUNCT
ejpam-4641	257	73	as	as	SCONJ
ejpam-4641	257	74	follows	follow	VERB
ejpam-4641	257	75	j(t1	j(t1	PROPN
ejpam-4641	257	76	,	,	PUNCT
ejpam-4641	257	77	t2	t2	NOUN
ejpam-4641	257	78	)	)	PUNCT
ejpam-4641	257	79	=	=	VERB
ejpam-4641	258	1	α2	α2	ADJ
ejpam-4641	258	2	∞∑	∞∑	PROPN
ejpam-4641	258	3	p=0	p=0	PROPN
ejpam-4641	258	4	ap(n	ap(n	NOUN
ejpam-4641	258	5	)	)	PUNCT
ejpam-4641	259	1	∞∑	∞∑	DET
ejpam-4641	259	2	k=0	k=0	PUNCT
ejpam-4641	259	3	n+p+k−1∑	n+p+k−1∑	PROPN
ejpam-4641	259	4	ω=0	ω=0	X
ejpam-4641	259	5	(	(	PUNCT
ejpam-4641	259	6	−1)ω	−1)ω	X
ejpam-4641	259	7	(	(	PUNCT
ejpam-4641	259	8	n+	n+	X
ejpam-4641	259	9	p+	p+	VERB
ejpam-4641	259	10	k	k	X
ejpam-4641	259	11	−	−	PROPN
ejpam-4641	259	12	1	1	NUM
ejpam-4641	259	13	ω	ω	NOUN
ejpam-4641	259	14	)	)	PUNCT
ejpam-4641	259	15	[	[	PUNCT
ejpam-4641	259	16	α(n+p+k−ω+1)−1∑	α(n+p+k−ω+1)−1∑	PROPN
ejpam-4641	259	17	i=0	i=0	PROPN
ejpam-4641	259	18	(	(	PUNCT
ejpam-4641	259	19	−1)i	−1)i	X
ejpam-4641	259	20	(	(	PUNCT
ejpam-4641	259	21	α(n+	α(n+	NUM
ejpam-4641	259	22	p+	p+	NOUN
ejpam-4641	259	23	k	k	PROPN
ejpam-4641	259	24	−	−	PROPN
ejpam-4641	259	25	ω	ω	PROPN
ejpam-4641	259	26	+	+	PROPN
ejpam-4641	259	27	1)−	1)−	NUM
ejpam-4641	259	28	1	1	NUM
ejpam-4641	259	29	i	i	NOUN
ejpam-4641	259	30	)	)	PUNCT
ejpam-4641	259	31	β(α(ω	β(α(ω	PROPN
ejpam-4641	260	1	+	+	CCONJ
ejpam-4641	260	2	1	1	NUM
ejpam-4641	260	3	)	)	PUNCT
ejpam-4641	260	4	+	+	NUM
ejpam-4641	260	5	1	1	NUM
ejpam-4641	260	6	,	,	PUNCT
ejpam-4641	260	7	i−	i−	ADJ
ejpam-4641	260	8	t2	t2	NOUN
ejpam-4641	260	9	λ	λ	PROPN
ejpam-4641	260	10	+	+	CCONJ
ejpam-4641	260	11	1	1	NUM
ejpam-4641	260	12	)	)	PUNCT
ejpam-4641	260	13	3f2	3f2	NUM
ejpam-4641	260	14	(	(	PUNCT
ejpam-4641	260	15	α(ω	α(ω	NOUN
ejpam-4641	260	16	+	+	NOUN
ejpam-4641	260	17	1	1	NUM
ejpam-4641	260	18	)	)	PUNCT
ejpam-4641	260	19	+	+	NUM
ejpam-4641	260	20	1	1	NUM
ejpam-4641	260	21	,	,	PUNCT
ejpam-4641	260	22	α(ω	α(ω	PROPN
ejpam-4641	260	23	+	+	NOUN
ejpam-4641	260	24	1	1	NUM
ejpam-4641	260	25	)	)	PUNCT
ejpam-4641	260	26	,	,	PUNCT
ejpam-4641	260	27	1−	1−	NUM
ejpam-4641	260	28	t1	t1	NOUN
ejpam-4641	260	29	λ	λ	PROPN
ejpam-4641	260	30	;	;	PUNCT
ejpam-4641	260	31	α(ω	α(ω	PROPN
ejpam-4641	260	32	+	+	SYM
ejpam-4641	260	33	1	1	NUM
ejpam-4641	260	34	)	)	PUNCT
ejpam-4641	260	35	+	+	NUM
ejpam-4641	260	36	1	1	NUM
ejpam-4641	260	37	,	,	PUNCT
ejpam-4641	260	38	α(ω	α(ω	PROPN
ejpam-4641	260	39	+	+	NOUN
ejpam-4641	260	40	1	1	NUM
ejpam-4641	260	41	)	)	PUNCT
ejpam-4641	260	42	+	+	CCONJ
ejpam-4641	260	43	i−	i−	PROPN
ejpam-4641	260	44	t2	t2	NOUN
ejpam-4641	260	45	λ	λ	PROPN
ejpam-4641	260	46	+	+	PROPN
ejpam-4641	260	47	2	2	NUM
ejpam-4641	260	48	;	;	PUNCT
ejpam-4641	260	49	1	1	NUM
ejpam-4641	260	50	)	)	PUNCT
ejpam-4641	260	51	−	−	NOUN
ejpam-4641	261	1	α(n+p+k−ω)−1∑	α(n+p+k−ω)−1∑	NUM
ejpam-4641	261	2	l=0	l=0	PROPN
ejpam-4641	261	3	(	(	PUNCT
ejpam-4641	261	4	−1)l	−1)l	PROPN
ejpam-4641	261	5	(	(	PUNCT
ejpam-4641	261	6	α(n+	α(n+	NUM
ejpam-4641	261	7	p+	p+	NOUN
ejpam-4641	261	8	k	k	PROPN
ejpam-4641	261	9	−	−	PROPN
ejpam-4641	261	10	ω)−	ω)−	PROPN
ejpam-4641	261	11	1	1	NUM
ejpam-4641	261	12	l	l	NOUN
ejpam-4641	261	13	)	)	PUNCT
ejpam-4641	261	14	β(α(ω	β(α(ω	PROPN
ejpam-4641	262	1	+	+	CCONJ
ejpam-4641	262	2	1	1	NUM
ejpam-4641	262	3	)	)	PUNCT
ejpam-4641	262	4	+	+	NUM
ejpam-4641	262	5	1	1	NUM
ejpam-4641	262	6	,	,	PUNCT
ejpam-4641	262	7	l	l	NOUN
ejpam-4641	262	8	−	−	PROPN
ejpam-4641	262	9	t2	t2	NOUN
ejpam-4641	262	10	λ	λ	NOUN
ejpam-4641	262	11	+	+	NOUN
ejpam-4641	262	12	1	1	NUM
ejpam-4641	262	13	)	)	PUNCT
ejpam-4641	262	14	3f2	3f2	NUM
ejpam-4641	262	15	(	(	PUNCT
ejpam-4641	262	16	α(ω	α(ω	NOUN
ejpam-4641	262	17	+	+	NOUN
ejpam-4641	262	18	1	1	NUM
ejpam-4641	262	19	)	)	PUNCT
ejpam-4641	262	20	+	+	NUM
ejpam-4641	262	21	1	1	NUM
ejpam-4641	262	22	,	,	PUNCT
ejpam-4641	262	23	α(ω	α(ω	PROPN
ejpam-4641	262	24	+	+	NOUN
ejpam-4641	262	25	1	1	NUM
ejpam-4641	262	26	)	)	PUNCT
ejpam-4641	262	27	,	,	PUNCT
ejpam-4641	262	28	1−	1−	NUM
ejpam-4641	262	29	t1	t1	NOUN
ejpam-4641	262	30	λ	λ	PROPN
ejpam-4641	262	31	;	;	PUNCT
ejpam-4641	262	32	α(ω	α(ω	PROPN
ejpam-4641	262	33	+	+	SYM
ejpam-4641	262	34	1	1	NUM
ejpam-4641	262	35	)	)	PUNCT
ejpam-4641	262	36	+	+	NUM
ejpam-4641	262	37	1	1	NUM
ejpam-4641	262	38	,	,	PUNCT
ejpam-4641	262	39	α(ω	α(ω	PROPN
ejpam-4641	262	40	+	+	NOUN
ejpam-4641	262	41	1	1	NUM
ejpam-4641	262	42	)	)	PUNCT
ejpam-4641	263	1	+	+	NOUN
ejpam-4641	263	2	l	l	NOUN
ejpam-4641	263	3	−	−	PROPN
ejpam-4641	263	4	t2	t2	NOUN
ejpam-4641	263	5	λ	λ	NOUN
ejpam-4641	263	6	+	+	PROPN
ejpam-4641	263	7	2	2	NUM
ejpam-4641	263	8	;	;	PUNCT
ejpam-4641	263	9	1	1	NUM
ejpam-4641	263	10	]	]	PUNCT
ejpam-4641	263	11	.	.	PUNCT
ejpam-4641	264	1	(	(	PUNCT
ejpam-4641	264	2	22	22	NUM
ejpam-4641	264	3	)	)	PUNCT
ejpam-4641	264	4	and	and	CCONJ
ejpam-4641	264	5	for	for	ADP
ejpam-4641	264	6	ζ(t1	ζ(t1	NOUN
ejpam-4641	264	7	,	,	PUNCT
ejpam-4641	264	8	t2	t2	PROPN
ejpam-4641	264	9	)	)	PUNCT
ejpam-4641	264	10	we	we	PRON
ejpam-4641	264	11	begin	begin	VERB
ejpam-4641	264	12	by	by	ADP
ejpam-4641	264	13	taking	take	VERB
ejpam-4641	264	14	the	the	DET
ejpam-4641	264	15	following	follow	VERB
ejpam-4641	264	16	integration	integration	NOUN
ejpam-4641	264	17	out	out	ADP
ejpam-4641	264	18	of	of	ADP
ejpam-4641	264	19	it	it	PRON
ejpam-4641	264	20	z(y	z(y	PROPN
ejpam-4641	264	21	)	)	PUNCT
ejpam-4641	265	1	=	=	PUNCT
ejpam-4641	265	2	∫	∫	PROPN
ejpam-4641	265	3	y	y	PROPN
ejpam-4641	265	4	0	0	PROPN
ejpam-4641	265	5	et1xf	et1xf	PROPN
ejpam-4641	265	6	(	(	PUNCT
ejpam-4641	265	7	x){−	x){−	PROPN
ejpam-4641	265	8	log[1	log[1	PROPN
ejpam-4641	265	9	+	+	CCONJ
ejpam-4641	265	10	f	f	X
ejpam-4641	265	11	(	(	PUNCT
ejpam-4641	265	12	x)−	x)−	PROPN
ejpam-4641	265	13	f	f	PROPN
ejpam-4641	265	14	(	(	PUNCT
ejpam-4641	265	15	y)]}ndx	y)]}ndx	PROPN
ejpam-4641	265	16	,	,	PUNCT
ejpam-4641	265	17	then	then	ADV
ejpam-4641	265	18	making	make	VERB
ejpam-4641	265	19	a	a	DET
ejpam-4641	265	20	substitution	substitution	NOUN
ejpam-4641	265	21	of	of	ADP
ejpam-4641	265	22	u	u	NOUN
ejpam-4641	265	23	=	=	PROPN
ejpam-4641	265	24	f	f	PROPN
ejpam-4641	265	25	(	(	PUNCT
ejpam-4641	265	26	y)−	y)−	PROPN
ejpam-4641	265	27	f	f	X
ejpam-4641	265	28	(	(	PUNCT
ejpam-4641	265	29	x	x	NOUN
ejpam-4641	265	30	)	)	PUNCT
ejpam-4641	265	31	,	,	PUNCT
ejpam-4641	265	32	after	after	ADP
ejpam-4641	265	33	that	that	PRON
ejpam-4641	265	34	we	we	PRON
ejpam-4641	265	35	used	use	VERB
ejpam-4641	265	36	equation	equation	NOUN
ejpam-4641	265	37	(	(	PUNCT
ejpam-4641	265	38	9	9	NUM
ejpam-4641	265	39	)	)	PUNCT
ejpam-4641	265	40	followed	follow	VERB
ejpam-4641	265	41	by	by	ADP
ejpam-4641	265	42	the	the	DET
ejpam-4641	265	43	logarithmic	logarithmic	ADJ
ejpam-4641	265	44	expansion	expansion	NOUN
ejpam-4641	265	45	from	from	ADP
ejpam-4641	265	46	(	(	PUNCT
ejpam-4641	265	47	7	7	NUM
ejpam-4641	265	48	)	)	PUNCT
ejpam-4641	265	49	.	.	PUNCT
ejpam-4641	266	1	another	another	DET
ejpam-4641	266	2	substitution	substitution	NOUN
ejpam-4641	266	3	made	make	VERB
ejpam-4641	266	4	by	by	ADP
ejpam-4641	266	5	w	w	PROPN
ejpam-4641	266	6	=	=	SYM
ejpam-4641	266	7	(	(	PUNCT
ejpam-4641	266	8	(	(	PUNCT
ejpam-4641	266	9	f	f	X
ejpam-4641	266	10	(	(	PUNCT
ejpam-4641	266	11	y)−	y)−	PROPN
ejpam-4641	266	12	u	u	NOUN
ejpam-4641	266	13	)	)	PUNCT
ejpam-4641	266	14	1	1	NUM
ejpam-4641	266	15	α	α	NOUN
ejpam-4641	266	16	and	and	CCONJ
ejpam-4641	266	17	some	some	DET
ejpam-4641	266	18	routine	routine	ADJ
ejpam-4641	266	19	calculations	calculation	NOUN
ejpam-4641	266	20	leads	lead	VERB
ejpam-4641	266	21	to	to	ADP
ejpam-4641	266	22	the	the	DET
ejpam-4641	266	23	following	follow	VERB
ejpam-4641	266	24	z(y	z(y	PROPN
ejpam-4641	266	25	)	)	PUNCT
ejpam-4641	267	1	=	=	SYM
ejpam-4641	267	2	1	1	NUM
ejpam-4641	267	3	λ	λ	PROPN
ejpam-4641	267	4	∞∑	∞∑	NUM
ejpam-4641	267	5	q=0	q=0	ADV
ejpam-4641	267	6	aq(n	aq(n	PUNCT
ejpam-4641	267	7	)	)	PUNCT
ejpam-4641	267	8	q+n∑	q+n∑	PROPN
ejpam-4641	267	9	h=0	h=0	PROPN
ejpam-4641	267	10	(	(	PUNCT
ejpam-4641	267	11	n+	n+	ADP
ejpam-4641	267	12	q	q	NOUN
ejpam-4641	267	13	h	h	NOUN
ejpam-4641	267	14	)	)	PUNCT
ejpam-4641	267	15	(	(	PUNCT
ejpam-4641	267	16	−1)h(f	−1)h(f	NOUN
ejpam-4641	267	17	(	(	PUNCT
ejpam-4641	267	18	y))q+n−h	y))q+n−h	PROPN
ejpam-4641	267	19	{	{	PUNCT
ejpam-4641	267	20	β	β	X
ejpam-4641	267	21	(	(	PUNCT
ejpam-4641	267	22	f	f	PROPN
ejpam-4641	267	23	(	(	PUNCT
ejpam-4641	267	24	y	y	NOUN
ejpam-4641	267	25	)	)	PUNCT
ejpam-4641	267	26	)	)	PUNCT
ejpam-4641	267	27	1	1	NUM
ejpam-4641	267	28	α	α	NOUN
ejpam-4641	267	29	(	(	PUNCT
ejpam-4641	267	30	α(h+	α(h+	NOUN
ejpam-4641	267	31	1	1	NUM
ejpam-4641	267	32	)	)	PUNCT
ejpam-4641	267	33	,	,	PUNCT
ejpam-4641	267	34	−t1	−t1	PROPN
ejpam-4641	267	35	λ	λ	PROPN
ejpam-4641	267	36	)	)	PUNCT
ejpam-4641	267	37	−	−	PROPN
ejpam-4641	267	38	β	β	X
ejpam-4641	267	39	(	(	PUNCT
ejpam-4641	267	40	f	f	PROPN
ejpam-4641	267	41	(	(	PUNCT
ejpam-4641	267	42	y	y	NOUN
ejpam-4641	267	43	)	)	PUNCT
ejpam-4641	267	44	)	)	PUNCT
ejpam-4641	267	45	1	1	NUM
ejpam-4641	267	46	α	α	NOUN
ejpam-4641	267	47	(	(	PUNCT
ejpam-4641	267	48	α(h+	α(h+	NOUN
ejpam-4641	267	49	1	1	NUM
ejpam-4641	267	50	)	)	PUNCT
ejpam-4641	267	51	,	,	PUNCT
ejpam-4641	267	52	−t1	−t1	NOUN
ejpam-4641	267	53	λ	λ	NOUN
ejpam-4641	267	54	+	+	NOUN
ejpam-4641	267	55	1	1	NUM
ejpam-4641	267	56	)	)	PUNCT
ejpam-4641	267	57	}	}	PUNCT
ejpam-4641	267	58	.	.	PUNCT
ejpam-4641	268	1	r.a.aldallal	r.a.aldallal	PROPN
ejpam-4641	268	2	/	/	SYM
ejpam-4641	268	3	eur	eur	PROPN
ejpam-4641	268	4	.	.	PUNCT
ejpam-4641	269	1	j.	j.	PROPN
ejpam-4641	269	2	pure	pure	PROPN
ejpam-4641	269	3	appl	appl	PROPN
ejpam-4641	269	4	.	.	PROPN
ejpam-4641	269	5	math	math	PROPN
ejpam-4641	269	6	,	,	PUNCT
ejpam-4641	269	7	16	16	NUM
ejpam-4641	269	8	(	(	PUNCT
ejpam-4641	269	9	1	1	NUM
ejpam-4641	269	10	)	)	PUNCT
ejpam-4641	269	11	(	(	PUNCT
ejpam-4641	269	12	2023	2023	NUM
ejpam-4641	269	13	)	)	PUNCT
ejpam-4641	269	14	,	,	PUNCT
ejpam-4641	269	15	97	97	NUM
ejpam-4641	269	16	-	-	SYM
ejpam-4641	269	17	111	111	NUM
ejpam-4641	269	18	107	107	NUM
ejpam-4641	269	19	now	now	ADV
ejpam-4641	269	20	,	,	PUNCT
ejpam-4641	269	21	we	we	PRON
ejpam-4641	269	22	return	return	VERB
ejpam-4641	269	23	to	to	ADP
ejpam-4641	269	24	the	the	DET
ejpam-4641	269	25	original	original	ADJ
ejpam-4641	269	26	ζ(t1	ζ(t1	NOUN
ejpam-4641	269	27	,	,	PUNCT
ejpam-4641	269	28	t2	t2	NOUN
ejpam-4641	269	29	)	)	PUNCT
ejpam-4641	269	30	double	double	ADJ
ejpam-4641	269	31	integral	integral	ADJ
ejpam-4641	269	32	and	and	CCONJ
ejpam-4641	269	33	put	put	VERB
ejpam-4641	269	34	the	the	DET
ejpam-4641	269	35	final	final	ADJ
ejpam-4641	269	36	form	form	NOUN
ejpam-4641	269	37	of	of	ADP
ejpam-4641	269	38	z(y	z(y	PROPN
ejpam-4641	269	39	)	)	PUNCT
ejpam-4641	269	40	function	function	NOUN
ejpam-4641	269	41	in	in	ADP
ejpam-4641	269	42	it	it	PRON
ejpam-4641	269	43	.	.	PUNCT
ejpam-4641	270	1	after	after	ADP
ejpam-4641	270	2	that	that	PRON
ejpam-4641	270	3	,	,	PUNCT
ejpam-4641	270	4	we	we	PRON
ejpam-4641	270	5	replace	replace	VERB
ejpam-4641	270	6	f	f	PROPN
ejpam-4641	270	7	(	(	PUNCT
ejpam-4641	270	8	y	y	NOUN
ejpam-4641	270	9	)	)	PUNCT
ejpam-4641	270	10	and	and	CCONJ
ejpam-4641	270	11	f(y	f(y	NOUN
ejpam-4641	270	12	)	)	PUNCT
ejpam-4641	270	13	as	as	ADP
ejpam-4641	270	14	in	in	ADP
ejpam-4641	270	15	(	(	PUNCT
ejpam-4641	270	16	5	5	NUM
ejpam-4641	270	17	)	)	PUNCT
ejpam-4641	270	18	and	and	CCONJ
ejpam-4641	270	19	(	(	PUNCT
ejpam-4641	270	20	6	6	NUM
ejpam-4641	270	21	)	)	PUNCT
ejpam-4641	270	22	respectively	respectively	ADV
ejpam-4641	270	23	and	and	CCONJ
ejpam-4641	270	24	by	by	ADP
ejpam-4641	270	25	the	the	DET
ejpam-4641	270	26	substitution	substitution	NOUN
ejpam-4641	270	27	u	u	NOUN
ejpam-4641	270	28	=	=	NOUN
ejpam-4641	270	29	1	1	NUM
ejpam-4641	270	30	−	−	NOUN
ejpam-4641	270	31	e−λy	e−λy	NOUN
ejpam-4641	270	32	we	we	PRON
ejpam-4641	270	33	reach	reach	VERB
ejpam-4641	270	34	an	an	DET
ejpam-4641	270	35	integral	integral	ADJ
ejpam-4641	270	36	in	in	ADP
ejpam-4641	270	37	which	which	PRON
ejpam-4641	270	38	we	we	PRON
ejpam-4641	270	39	can	can	AUX
ejpam-4641	270	40	use	use	VERB
ejpam-4641	270	41	(	(	PUNCT
ejpam-4641	270	42	10	10	NUM
ejpam-4641	270	43	)	)	PUNCT
ejpam-4641	270	44	and	and	CCONJ
ejpam-4641	270	45	(	(	PUNCT
ejpam-4641	270	46	11	11	NUM
ejpam-4641	270	47	)	)	PUNCT
ejpam-4641	270	48	to	to	PART
ejpam-4641	270	49	solve	solve	VERB
ejpam-4641	270	50	it	it	PRON
ejpam-4641	270	51	and	and	CCONJ
ejpam-4641	270	52	reach	reach	VERB
ejpam-4641	270	53	that	that	DET
ejpam-4641	270	54	final	final	ADJ
ejpam-4641	270	55	formula	formula	NOUN
ejpam-4641	270	56	of	of	ADP
ejpam-4641	270	57	ζ(t1	ζ(t1	NOUN
ejpam-4641	270	58	,	,	PUNCT
ejpam-4641	270	59	t2	t2	PROPN
ejpam-4641	270	60	)	)	PUNCT
ejpam-4641	270	61	which	which	PRON
ejpam-4641	270	62	is	be	AUX
ejpam-4641	270	63	going	go	VERB
ejpam-4641	270	64	to	to	PART
ejpam-4641	270	65	be	be	AUX
ejpam-4641	270	66	ζ(t1	ζ(t1	NOUN
ejpam-4641	270	67	,	,	PUNCT
ejpam-4641	270	68	t2	t2	NOUN
ejpam-4641	270	69	)	)	PUNCT
ejpam-4641	270	70	=	=	SYM
ejpam-4641	271	1	−1	−1	NOUN
ejpam-4641	271	2	λ(λ+	λ(λ+	NOUN
ejpam-4641	271	3	1	1	X
ejpam-4641	271	4	)	)	PUNCT
ejpam-4641	271	5	∞∑	∞∑	NUM
ejpam-4641	271	6	q=0	q=0	NOUN
ejpam-4641	271	7	aq(n	aq(n	PUNCT
ejpam-4641	271	8	)	)	PUNCT
ejpam-4641	271	9	q+n∑	q+n∑	PROPN
ejpam-4641	271	10	h=0	h=0	PROPN
ejpam-4641	271	11	(	(	PUNCT
ejpam-4641	271	12	n+	n+	ADP
ejpam-4641	271	13	q	q	NOUN
ejpam-4641	271	14	h	h	NOUN
ejpam-4641	271	15	)	)	PUNCT
ejpam-4641	271	16	(	(	PUNCT
ejpam-4641	271	17	−1)hβ(α(q	−1)hβ(α(q	PUNCT
ejpam-4641	271	18	+	+	NUM
ejpam-4641	271	19	n+	n+	NUM
ejpam-4641	271	20	2	2	NUM
ejpam-4641	271	21	)	)	PUNCT
ejpam-4641	271	22	,	,	PUNCT
ejpam-4641	271	23	−t2	−t2	PROPN
ejpam-4641	271	24	λ	λ	PROPN
ejpam-4641	271	25	+	+	PROPN
ejpam-4641	271	26	1	1	NUM
ejpam-4641	271	27	)	)	PUNCT
ejpam-4641	271	28	{	{	PUNCT
ejpam-4641	271	29	3f2	3f2	NUM
ejpam-4641	271	30	(	(	PUNCT
ejpam-4641	271	31	α(q	α(q	PROPN
ejpam-4641	271	32	+	+	CCONJ
ejpam-4641	271	33	n+	n+	NUM
ejpam-4641	271	34	2	2	NUM
ejpam-4641	271	35	)	)	PUNCT
ejpam-4641	271	36	)	)	PUNCT
ejpam-4641	271	37	,	,	PUNCT
ejpam-4641	271	38	α(h+	α(h+	NOUN
ejpam-4641	271	39	1	1	NUM
ejpam-4641	271	40	)	)	PUNCT
ejpam-4641	271	41	,	,	PUNCT
ejpam-4641	271	42	1	1	NUM
ejpam-4641	271	43	+	+	NUM
ejpam-4641	271	44	t1	t1	NUM
ejpam-4641	271	45	λ	λ	PROPN
ejpam-4641	271	46	;	;	PUNCT
ejpam-4641	271	47	α(h+	α(h+	NOUN
ejpam-4641	271	48	1	1	NUM
ejpam-4641	271	49	)	)	PUNCT
ejpam-4641	271	50	+	+	NUM
ejpam-4641	271	51	1	1	NUM
ejpam-4641	271	52	,	,	PUNCT
ejpam-4641	271	53	α(q	α(q	PROPN
ejpam-4641	271	54	+	+	CCONJ
ejpam-4641	271	55	n+	n+	NUM
ejpam-4641	271	56	2	2	NUM
ejpam-4641	271	57	)	)	PUNCT
ejpam-4641	271	58	+	+	SYM
ejpam-4641	271	59	1−	1−	NUM
ejpam-4641	271	60	t2	t2	NOUN
ejpam-4641	271	61	λ	λ	NOUN
ejpam-4641	271	62	;	;	PUNCT
ejpam-4641	271	63	1	1	X
ejpam-4641	271	64	)	)	PUNCT
ejpam-4641	271	65	−	−	ADP
ejpam-4641	272	1	3f2	3f2	NUM
ejpam-4641	272	2	(	(	PUNCT
ejpam-4641	272	3	α(q	α(q	PROPN
ejpam-4641	272	4	+	+	CCONJ
ejpam-4641	272	5	n+	n+	NUM
ejpam-4641	272	6	2	2	NUM
ejpam-4641	272	7	)	)	PUNCT
ejpam-4641	272	8	)	)	PUNCT
ejpam-4641	272	9	,	,	PUNCT
ejpam-4641	272	10	α(h+	α(h+	NOUN
ejpam-4641	272	11	1	1	NUM
ejpam-4641	272	12	)	)	PUNCT
ejpam-4641	272	13	,	,	PUNCT
ejpam-4641	272	14	t1	t1	PROPN
ejpam-4641	272	15	λ	λ	PROPN
ejpam-4641	272	16	;	;	PUNCT
ejpam-4641	272	17	α(h+	α(h+	NOUN
ejpam-4641	272	18	1	1	NUM
ejpam-4641	272	19	)	)	PUNCT
ejpam-4641	272	20	+	+	NUM
ejpam-4641	272	21	1	1	NUM
ejpam-4641	272	22	,	,	PUNCT
ejpam-4641	272	23	α(q	α(q	PROPN
ejpam-4641	272	24	+	+	CCONJ
ejpam-4641	272	25	n+	n+	NUM
ejpam-4641	272	26	2	2	NUM
ejpam-4641	272	27	)	)	PUNCT
ejpam-4641	272	28	+	+	SYM
ejpam-4641	272	29	1−	1−	NUM
ejpam-4641	272	30	t2	t2	NOUN
ejpam-4641	272	31	λ	λ	NOUN
ejpam-4641	272	32	;	;	PUNCT
ejpam-4641	272	33	1	1	NUM
ejpam-4641	272	34	)	)	PUNCT
ejpam-4641	272	35	}	}	PUNCT
ejpam-4641	272	36	.	.	PUNCT
ejpam-4641	273	1	(	(	PUNCT
ejpam-4641	273	2	23	23	X
ejpam-4641	273	3	)	)	PUNCT
ejpam-4641	273	4	exchanging	exchange	VERB
ejpam-4641	273	5	(	(	PUNCT
ejpam-4641	273	6	22	22	NUM
ejpam-4641	273	7	)	)	PUNCT
ejpam-4641	273	8	and	and	CCONJ
ejpam-4641	273	9	(	(	PUNCT
ejpam-4641	273	10	23	23	NUM
ejpam-4641	273	11	)	)	PUNCT
ejpam-4641	273	12	by	by	ADP
ejpam-4641	273	13	their	their	PRON
ejpam-4641	273	14	equal	equal	ADJ
ejpam-4641	273	15	parts	part	NOUN
ejpam-4641	273	16	from	from	ADP
ejpam-4641	273	17	(	(	PUNCT
ejpam-4641	273	18	21	21	NUM
ejpam-4641	273	19	)	)	PUNCT
ejpam-4641	273	20	,	,	PUNCT
ejpam-4641	273	21	we	we	PRON
ejpam-4641	273	22	get	get	VERB
ejpam-4641	273	23	(	(	PUNCT
ejpam-4641	273	24	20	20	NUM
ejpam-4641	273	25	)	)	PUNCT
ejpam-4641	273	26	.	.	PUNCT
ejpam-4641	274	1	lemma	lemma	PROPN
ejpam-4641	274	2	1	1	NUM
ejpam-4641	274	3	.	.	PUNCT
ejpam-4641	275	1	another	another	DET
ejpam-4641	275	2	recurrence	recurrence	NOUN
ejpam-4641	275	3	relation	relation	NOUN
ejpam-4641	275	4	for	for	ADP
ejpam-4641	275	5	of	of	ADP
ejpam-4641	275	6	mlc	mlc	PROPN
ejpam-4641	275	7	n+1,u	n+1,u	PROPN
ejpam-4641	275	8	c	c	PROPN
ejpam-4641	275	9	n+1	n+1	PROPN
ejpam-4641	276	1	(	(	PUNCT
ejpam-4641	277	1	t1	t1	NOUN
ejpam-4641	277	2	,	,	PUNCT
ejpam-4641	277	3	t2	t2	NOUN
ejpam-4641	277	4	)	)	PUNCT
ejpam-4641	277	5	can	can	AUX
ejpam-4641	277	6	be	be	AUX
ejpam-4641	277	7	found	find	VERB
ejpam-4641	277	8	by	by	ADP
ejpam-4641	277	9	using	use	VERB
ejpam-4641	277	10	analogs	analog	NOUN
ejpam-4641	277	11	steps	step	NOUN
ejpam-4641	277	12	used	use	VERB
ejpam-4641	277	13	in	in	ADP
ejpam-4641	277	14	theorem	theorem	ADJ
ejpam-4641	277	15	3	3	NUM
ejpam-4641	277	16	but	but	CCONJ
ejpam-4641	277	17	leads	lead	VERB
ejpam-4641	277	18	to	to	ADP
ejpam-4641	277	19	the	the	DET
ejpam-4641	277	20	following	follow	VERB
ejpam-4641	277	21	relation	relation	NOUN
ejpam-4641	277	22	(	(	PUNCT
ejpam-4641	277	23	1−	1−	NUM
ejpam-4641	277	24	t1	t1	NOUN
ejpam-4641	277	25	αλ	αλ	NUM
ejpam-4641	277	26	)	)	PUNCT
ejpam-4641	277	27	mlc	mlc	PROPN
ejpam-4641	277	28	n+1,u	n+1,u	PROPN
ejpam-4641	277	29	c	c	PROPN
ejpam-4641	277	30	n+1	n+1	PROPN
ejpam-4641	278	1	(	(	PUNCT
ejpam-4641	278	2	t1	t1	NOUN
ejpam-4641	278	3	,	,	PUNCT
ejpam-4641	278	4	t2	t2	NOUN
ejpam-4641	278	5	)	)	PUNCT
ejpam-4641	279	1	+	+	CCONJ
ejpam-4641	279	2	t1	t1	NOUN
ejpam-4641	279	3	αλ	αλ	NUM
ejpam-4641	279	4	mlc	mlc	NOUN
ejpam-4641	279	5	n+1,u	n+1,u	PROPN
ejpam-4641	279	6	c	c	PROPN
ejpam-4641	279	7	n+1	n+1	PROPN
ejpam-4641	279	8	(	(	PUNCT
ejpam-4641	279	9	t1	t1	NOUN
ejpam-4641	279	10	+	+	PROPN
ejpam-4641	279	11	λ	λ	PROPN
ejpam-4641	279	12	,	,	PUNCT
ejpam-4641	279	13	t2	t2	NOUN
ejpam-4641	279	14	)	)	PUNCT
ejpam-4641	280	1	=	=	SYM
ejpam-4641	280	2	2mlc	2mlc	NOUN
ejpam-4641	280	3	n	n	CCONJ
ejpam-4641	280	4	,	,	PUNCT
ejpam-4641	280	5	u	u	PROPN
ejpam-4641	280	6	c	c	PROPN
ejpam-4641	280	7	n	n	PROPN
ejpam-4641	280	8	(	(	PUNCT
ejpam-4641	280	9	t1	t1	PROPN
ejpam-4641	280	10	,	,	PUNCT
ejpam-4641	280	11	t2	t2	NOUN
ejpam-4641	280	12	)	)	PUNCT
ejpam-4641	281	1	+	+	CCONJ
ejpam-4641	281	2	2n+1	2n+1	NOUN
ejpam-4641	281	3	(	(	PUNCT
ejpam-4641	281	4	n−	n−	NOUN
ejpam-4641	281	5	1	1	NUM
ejpam-4641	281	6	)	)	PUNCT
ejpam-4641	281	7	!	!	PUNCT
ejpam-4641	282	1	α2	α2	PROPN
ejpam-4641	283	1	∞∑	∞∑	PRON
ejpam-4641	283	2	p=0	p=0	PROPN
ejpam-4641	283	3	ap(n	ap(n	PUNCT
ejpam-4641	283	4	)	)	PUNCT
ejpam-4641	283	5	∞∑	∞∑	DET
ejpam-4641	283	6	k=0	k=0	PUNCT
ejpam-4641	283	7	n+p+k−1∑	n+p+k−1∑	PROPN
ejpam-4641	283	8	ω=0	ω=0	X
ejpam-4641	283	9	(	(	PUNCT
ejpam-4641	283	10	−1)ω	−1)ω	X
ejpam-4641	283	11	(	(	PUNCT
ejpam-4641	283	12	n+	n+	X
ejpam-4641	283	13	p+	p+	VERB
ejpam-4641	283	14	k	k	X
ejpam-4641	283	15	−	−	PROPN
ejpam-4641	283	16	1	1	NUM
ejpam-4641	283	17	ω	ω	NOUN
ejpam-4641	283	18	)	)	PUNCT
ejpam-4641	284	1	[	[	PUNCT
ejpam-4641	284	2	α(n+p+k−ω+1)−1∑	α(n+p+k−ω+1)−1∑	PROPN
ejpam-4641	284	3	i=0	i=0	PROPN
ejpam-4641	284	4	(	(	PUNCT
ejpam-4641	284	5	−1)i	−1)i	X
ejpam-4641	284	6	(	(	PUNCT
ejpam-4641	284	7	α(n+	α(n+	NUM
ejpam-4641	284	8	p+	p+	NOUN
ejpam-4641	284	9	k	k	PROPN
ejpam-4641	284	10	−	−	PROPN
ejpam-4641	284	11	ω	ω	PROPN
ejpam-4641	284	12	+	+	PROPN
ejpam-4641	285	1	1)−	1)−	NUM
ejpam-4641	285	2	1	1	NUM
ejpam-4641	285	3	i	i	NOUN
ejpam-4641	285	4	)	)	PUNCT
ejpam-4641	285	5	β(α(ω	β(α(ω	PROPN
ejpam-4641	286	1	+	+	CCONJ
ejpam-4641	286	2	1	1	NUM
ejpam-4641	286	3	)	)	PUNCT
ejpam-4641	286	4	+	+	NUM
ejpam-4641	286	5	1	1	NUM
ejpam-4641	286	6	,	,	PUNCT
ejpam-4641	286	7	i−	i−	ADJ
ejpam-4641	286	8	t2	t2	NOUN
ejpam-4641	286	9	λ	λ	PROPN
ejpam-4641	286	10	+	+	CCONJ
ejpam-4641	286	11	1	1	NUM
ejpam-4641	286	12	)	)	PUNCT
ejpam-4641	286	13	3f2	3f2	NUM
ejpam-4641	286	14	(	(	PUNCT
ejpam-4641	286	15	α(ω	α(ω	NOUN
ejpam-4641	286	16	+	+	NOUN
ejpam-4641	286	17	1	1	NUM
ejpam-4641	286	18	)	)	PUNCT
ejpam-4641	286	19	+	+	NUM
ejpam-4641	286	20	1	1	NUM
ejpam-4641	286	21	,	,	PUNCT
ejpam-4641	286	22	α(ω	α(ω	PROPN
ejpam-4641	286	23	+	+	NOUN
ejpam-4641	286	24	1	1	NUM
ejpam-4641	286	25	)	)	PUNCT
ejpam-4641	286	26	,	,	PUNCT
ejpam-4641	286	27	1−	1−	NUM
ejpam-4641	286	28	t1	t1	NOUN
ejpam-4641	286	29	λ	λ	PROPN
ejpam-4641	286	30	;	;	PUNCT
ejpam-4641	286	31	α(ω	α(ω	PROPN
ejpam-4641	286	32	+	+	SYM
ejpam-4641	286	33	1	1	NUM
ejpam-4641	286	34	)	)	PUNCT
ejpam-4641	286	35	+	+	NUM
ejpam-4641	286	36	1	1	NUM
ejpam-4641	286	37	,	,	PUNCT
ejpam-4641	286	38	α(ω	α(ω	PROPN
ejpam-4641	286	39	+	+	NOUN
ejpam-4641	286	40	1	1	NUM
ejpam-4641	286	41	)	)	PUNCT
ejpam-4641	286	42	+	+	CCONJ
ejpam-4641	286	43	i−	i−	PROPN
ejpam-4641	286	44	t2	t2	NOUN
ejpam-4641	286	45	λ	λ	PROPN
ejpam-4641	286	46	+	+	PROPN
ejpam-4641	286	47	2	2	NUM
ejpam-4641	286	48	;	;	PUNCT
ejpam-4641	286	49	1	1	NUM
ejpam-4641	286	50	)	)	PUNCT
ejpam-4641	286	51	−	−	NOUN
ejpam-4641	287	1	α(n+p+k−ω)−1∑	α(n+p+k−ω)−1∑	NUM
ejpam-4641	287	2	l=0	l=0	PROPN
ejpam-4641	287	3	(	(	PUNCT
ejpam-4641	287	4	−1)l	−1)l	PROPN
ejpam-4641	287	5	(	(	PUNCT
ejpam-4641	287	6	α(n+	α(n+	NUM
ejpam-4641	287	7	p+	p+	NOUN
ejpam-4641	287	8	k	k	PROPN
ejpam-4641	287	9	−	−	PROPN
ejpam-4641	287	10	ω)−	ω)−	PROPN
ejpam-4641	287	11	1	1	NUM
ejpam-4641	287	12	l	l	NOUN
ejpam-4641	287	13	)	)	PUNCT
ejpam-4641	287	14	β(α(ω	β(α(ω	PROPN
ejpam-4641	288	1	+	+	CCONJ
ejpam-4641	288	2	1	1	NUM
ejpam-4641	288	3	)	)	PUNCT
ejpam-4641	288	4	+	+	NUM
ejpam-4641	288	5	1	1	NUM
ejpam-4641	288	6	,	,	PUNCT
ejpam-4641	288	7	l	l	NOUN
ejpam-4641	288	8	−	−	PROPN
ejpam-4641	288	9	t2	t2	NOUN
ejpam-4641	288	10	λ	λ	NOUN
ejpam-4641	288	11	+	+	NOUN
ejpam-4641	288	12	1	1	NUM
ejpam-4641	288	13	)	)	PUNCT
ejpam-4641	288	14	3f2	3f2	NUM
ejpam-4641	288	15	(	(	PUNCT
ejpam-4641	288	16	α(ω	α(ω	NOUN
ejpam-4641	288	17	+	+	NOUN
ejpam-4641	288	18	1	1	NUM
ejpam-4641	288	19	)	)	PUNCT
ejpam-4641	288	20	+	+	NUM
ejpam-4641	288	21	1	1	NUM
ejpam-4641	288	22	,	,	PUNCT
ejpam-4641	288	23	α(ω	α(ω	PROPN
ejpam-4641	288	24	+	+	NOUN
ejpam-4641	288	25	1	1	NUM
ejpam-4641	288	26	)	)	PUNCT
ejpam-4641	288	27	,	,	PUNCT
ejpam-4641	288	28	1−	1−	NUM
ejpam-4641	288	29	t1	t1	NOUN
ejpam-4641	288	30	λ	λ	PROPN
ejpam-4641	288	31	;	;	PUNCT
ejpam-4641	288	32	α(ω	α(ω	PROPN
ejpam-4641	288	33	+	+	SYM
ejpam-4641	288	34	1	1	NUM
ejpam-4641	288	35	)	)	PUNCT
ejpam-4641	288	36	+	+	NUM
ejpam-4641	288	37	1	1	NUM
ejpam-4641	288	38	,	,	PUNCT
ejpam-4641	288	39	α(ω	α(ω	PROPN
ejpam-4641	288	40	+	+	NOUN
ejpam-4641	288	41	1	1	NUM
ejpam-4641	288	42	)	)	PUNCT
ejpam-4641	289	1	+	+	NOUN
ejpam-4641	289	2	l	l	NOUN
ejpam-4641	289	3	−	−	PROPN
ejpam-4641	289	4	t2	t2	NOUN
ejpam-4641	289	5	λ	λ	NOUN
ejpam-4641	289	6	+	+	PROPN
ejpam-4641	289	7	2	2	NUM
ejpam-4641	289	8	;	;	PUNCT
ejpam-4641	289	9	1	1	NUM
ejpam-4641	289	10	]	]	PUNCT
ejpam-4641	289	11	.	.	PUNCT
ejpam-4641	290	1	(	(	PUNCT
ejpam-4641	290	2	24	24	NUM
ejpam-4641	290	3	)	)	PUNCT
ejpam-4641	290	4	corollary	corollary	NOUN
ejpam-4641	290	5	3	3	NUM
ejpam-4641	290	6	.	.	X
ejpam-4641	291	1	for	for	ADP
ejpam-4641	291	2	i	i	PRON
ejpam-4641	291	3	=	=	NOUN
ejpam-4641	291	4	1	1	NUM
ejpam-4641	291	5	,	,	PUNCT
ejpam-4641	291	6	2	2	NUM
ejpam-4641	291	7	,	,	PUNCT
ejpam-4641	291	8	3	3	NUM
ejpam-4641	291	9	,	,	PUNCT
ejpam-4641	291	10	...	...	PUNCT
ejpam-4641	291	11	,	,	PUNCT
ejpam-4641	291	12	and	and	CCONJ
ejpam-4641	291	13	n	n	PRON
ejpam-4641	291	14	≥	≥	NOUN
ejpam-4641	291	15	2	2	NUM
ejpam-4641	291	16	,	,	PUNCT
ejpam-4641	291	17	by	by	ADP
ejpam-4641	291	18	taking	take	VERB
ejpam-4641	291	19	the	the	DET
ejpam-4641	291	20	ith	ith	PROPN
ejpam-4641	291	21	derivative	derivative	NOUN
ejpam-4641	291	22	of	of	ADP
ejpam-4641	291	23	(	(	PUNCT
ejpam-4641	291	24	18	18	NUM
ejpam-4641	291	25	)	)	PUNCT
ejpam-4641	291	26	and	and	CCONJ
ejpam-4641	291	27	(	(	PUNCT
ejpam-4641	291	28	19	19	NUM
ejpam-4641	291	29	)	)	PUNCT
ejpam-4641	291	30	and	and	CCONJ
ejpam-4641	291	31	substituting	substitute	VERB
ejpam-4641	291	32	t	t	NOUN
ejpam-4641	291	33	=	=	SYM
ejpam-4641	291	34	0	0	NUM
ejpam-4641	291	35	we	we	PRON
ejpam-4641	291	36	reach	reach	VERB
ejpam-4641	291	37	the	the	DET
ejpam-4641	291	38	following	follow	VERB
ejpam-4641	291	39	relations	relation	NOUN
ejpam-4641	291	40	.	.	PUNCT
ejpam-4641	292	1	also	also	ADV
ejpam-4641	292	2	,	,	PUNCT
ejpam-4641	292	3	by	by	ADP
ejpam-4641	292	4	differentiating	differentiate	VERB
ejpam-4641	292	5	(	(	PUNCT
ejpam-4641	292	6	20	20	NUM
ejpam-4641	292	7	)	)	PUNCT
ejpam-4641	292	8	i	i	PRON
ejpam-4641	292	9	times	time	VERB
ejpam-4641	292	10	with	with	ADP
ejpam-4641	292	11	respect	respect	NOUN
ejpam-4641	292	12	to	to	ADP
ejpam-4641	292	13	t1	t1	NOUN
ejpam-4641	292	14	and	and	CCONJ
ejpam-4641	292	15	j	j	PROPN
ejpam-4641	292	16	times	time	NOUN
ejpam-4641	292	17	with	with	ADP
ejpam-4641	292	18	respect	respect	NOUN
ejpam-4641	292	19	to	to	ADP
ejpam-4641	292	20	t2	t2	NOUN
ejpam-4641	292	21	and	and	CCONJ
ejpam-4641	292	22	then	then	ADV
ejpam-4641	292	23	substituting	substitute	VERB
ejpam-4641	292	24	t1	t1	NOUN
ejpam-4641	292	25	=	=	SYM
ejpam-4641	292	26	t2	t2	PROPN
ejpam-4641	292	27	=	=	SYM
ejpam-4641	292	28	0	0	NUM
ejpam-4641	292	29	we	we	PRON
ejpam-4641	292	30	get	get	VERB
ejpam-4641	292	31	the	the	DET
ejpam-4641	292	32	recurrence	recurrence	NOUN
ejpam-4641	292	33	relation	relation	NOUN
ejpam-4641	292	34	of	of	ADP
ejpam-4641	292	35	the	the	DET
ejpam-4641	292	36	product	product	NOUN
ejpam-4641	292	37	moment	moment	NOUN
ejpam-4641	292	38	between	between	ADP
ejpam-4641	292	39	lower	low	ADJ
ejpam-4641	292	40	and	and	CCONJ
ejpam-4641	292	41	upper	upper	ADJ
ejpam-4641	292	42	current	current	ADJ
ejpam-4641	292	43	record	record	NOUN
ejpam-4641	292	44	µ	µ	X
ejpam-4641	292	45	(	(	PUNCT
ejpam-4641	292	46	i	i	PROPN
ejpam-4641	292	47	,	,	PUNCT
ejpam-4641	292	48	j	j	PROPN
ejpam-4641	292	49	)	)	PUNCT
ejpam-4641	292	50	lc	lc	PROPN
ejpam-4641	293	1	n+1,u	n+1,u	PROPN
ejpam-4641	293	2	c	c	PROPN
ejpam-4641	293	3	n+1	n+1	PROPN
ejpam-4641	293	4	.	.	PUNCT
ejpam-4641	294	1	µ	µ	X
ejpam-4641	294	2	(	(	PUNCT
ejpam-4641	294	3	i	i	NOUN
ejpam-4641	294	4	)	)	PUNCT
ejpam-4641	294	5	lc	lc	PROPN
ejpam-4641	295	1	n+1	n+1	NUM
ejpam-4641	295	2	=	=	SYM
ejpam-4641	295	3	2µ	2µ	NUM
ejpam-4641	295	4	(	(	PUNCT
ejpam-4641	295	5	i	i	NOUN
ejpam-4641	295	6	)	)	PUNCT
ejpam-4641	295	7	lc	lc	PROPN
ejpam-4641	296	1	n	n	PROPN
ejpam-4641	296	2	(	(	PUNCT
ejpam-4641	296	3	t)−	t)−	PROPN
ejpam-4641	296	4	(	(	PUNCT
ejpam-4641	296	5	2α)n+1	2α)n+1	NOUN
ejpam-4641	296	6	n	n	X
ejpam-4641	296	7	!	!	PUNCT
ejpam-4641	297	1	∞∑	∞∑	NUM
ejpam-4641	297	2	p=0	p=0	PROPN
ejpam-4641	297	3	ap(n)β	ap(n)β	PROPN
ejpam-4641	297	4	(	(	PUNCT
ejpam-4641	297	5	i)(2α,−	i)(2α,−	NOUN
ejpam-4641	297	6	t	t	PROPN
ejpam-4641	297	7	λ	λ	PROPN
ejpam-4641	297	8	+	+	PROPN
ejpam-4641	297	9	n+	n+	PROPN
ejpam-4641	297	10	p+	p+	ADJ
ejpam-4641	297	11	1	1	NUM
ejpam-4641	297	12	)	)	PUNCT
ejpam-4641	297	13	∣∣∣	∣∣∣	ADJ
ejpam-4641	297	14	t=0	t=0	ADJ
ejpam-4641	297	15	∣∣∣	∣∣∣	ADJ
ejpam-4641	297	16	t=0	t=0	X
ejpam-4641	297	17	∣∣∣	∣∣∣	PROPN
ejpam-4641	297	18	t=0	t=0	X
ejpam-4641	297	19	.	.	PUNCT
ejpam-4641	298	1	(	(	PUNCT
ejpam-4641	298	2	25	25	NUM
ejpam-4641	298	3	)	)	PUNCT
ejpam-4641	298	4	µ	µ	X
ejpam-4641	298	5	(	(	PUNCT
ejpam-4641	298	6	i	i	NOUN
ejpam-4641	298	7	)	)	PUNCT
ejpam-4641	298	8	uc	uc	PROPN
ejpam-4641	298	9	n+1	n+1	X
ejpam-4641	298	10	=	=	SYM
ejpam-4641	298	11	2µ	2µ	NUM
ejpam-4641	298	12	(	(	PUNCT
ejpam-4641	298	13	i	i	NOUN
ejpam-4641	298	14	)	)	PUNCT
ejpam-4641	298	15	uc	uc	PROPN
ejpam-4641	298	16	n	n	INTJ
ejpam-4641	298	17	(	(	PUNCT
ejpam-4641	298	18	t)−	t)−	PROPN
ejpam-4641	298	19	2n+1α	2n+1α	NUM
ejpam-4641	298	20	n	n	CCONJ
ejpam-4641	298	21	!	!	PUNCT
ejpam-4641	299	1	∞∑	∞∑	NUM
ejpam-4641	299	2	p=0	p=0	PROPN
ejpam-4641	299	3	ap(n	ap(n	PUNCT
ejpam-4641	299	4	)	)	PUNCT
ejpam-4641	299	5	[	[	PUNCT
ejpam-4641	299	6	β(i)((1+n+p)α	β(i)((1+n+p)α	NOUN
ejpam-4641	299	7	,	,	PUNCT
ejpam-4641	299	8	1−	1−	NUM
ejpam-4641	299	9	t	t	NOUN
ejpam-4641	299	10	λ	λ	PROPN
ejpam-4641	299	11	)	)	PUNCT
ejpam-4641	299	12	−β(i)((2+n+p)α	−β(i)((2+n+p)α	PROPN
ejpam-4641	299	13	,	,	PUNCT
ejpam-4641	299	14	1−	1−	NUM
ejpam-4641	299	15	t	t	PROPN
ejpam-4641	299	16	λ	λ	PROPN
ejpam-4641	299	17	)	)	PUNCT
ejpam-4641	299	18	]	]	PUNCT
ejpam-4641	299	19	∣∣∣	∣∣∣	X
ejpam-4641	299	20	t=0	t=0	ADJ
ejpam-4641	299	21	∣∣∣	∣∣∣	ADJ
ejpam-4641	299	22	t=0	t=0	X
ejpam-4641	299	23	∣∣∣	∣∣∣	NOUN
ejpam-4641	299	24	t=0	t=0	X
ejpam-4641	299	25	.	.	PUNCT
ejpam-4641	300	1	(	(	PUNCT
ejpam-4641	300	2	26	26	NUM
ejpam-4641	300	3	)	)	PUNCT
ejpam-4641	300	4	r.a.aldallal	r.a.aldallal	NOUN
ejpam-4641	300	5	/	/	SYM
ejpam-4641	300	6	eur	eur	PROPN
ejpam-4641	300	7	.	.	PUNCT
ejpam-4641	301	1	j.	j.	PROPN
ejpam-4641	301	2	pure	pure	PROPN
ejpam-4641	301	3	appl	appl	PROPN
ejpam-4641	301	4	.	.	PROPN
ejpam-4641	301	5	math	math	PROPN
ejpam-4641	301	6	,	,	PUNCT
ejpam-4641	301	7	16	16	NUM
ejpam-4641	301	8	(	(	PUNCT
ejpam-4641	301	9	1	1	NUM
ejpam-4641	301	10	)	)	PUNCT
ejpam-4641	301	11	(	(	PUNCT
ejpam-4641	301	12	2023	2023	NUM
ejpam-4641	301	13	)	)	PUNCT
ejpam-4641	301	14	,	,	PUNCT
ejpam-4641	301	15	97	97	NUM
ejpam-4641	301	16	-	-	SYM
ejpam-4641	301	17	111	111	NUM
ejpam-4641	301	18	108	108	NUM
ejpam-4641	301	19	5	5	NUM
ejpam-4641	301	20	.	.	PUNCT
ejpam-4641	302	1	moments	moment	NOUN
ejpam-4641	302	2	of	of	ADP
ejpam-4641	302	3	record	record	NOUN
ejpam-4641	302	4	range	range	NOUN
ejpam-4641	302	5	a	a	DET
ejpam-4641	302	6	calculable	calculable	ADJ
ejpam-4641	302	7	formula	formula	NOUN
ejpam-4641	302	8	for	for	ADP
ejpam-4641	302	9	the	the	DET
ejpam-4641	302	10	mth	mth	NOUN
ejpam-4641	302	11	moments	moment	NOUN
ejpam-4641	302	12	of	of	ADP
ejpam-4641	302	13	record	record	ADJ
ejpam-4641	302	14	range	range	NOUN
ejpam-4641	302	15	µ	µ	X
ejpam-4641	302	16	(	(	PUNCT
ejpam-4641	302	17	m	m	NOUN
ejpam-4641	302	18	)	)	PUNCT
ejpam-4641	302	19	rc	rc	PROPN
ejpam-4641	302	20	n	n	PRON
ejpam-4641	302	21	will	will	AUX
ejpam-4641	302	22	be	be	AUX
ejpam-4641	302	23	provided	provide	VERB
ejpam-4641	302	24	in	in	ADP
ejpam-4641	302	25	the	the	DET
ejpam-4641	302	26	next	next	ADJ
ejpam-4641	302	27	theorem	theorem	NOUN
ejpam-4641	302	28	along	along	ADP
ejpam-4641	302	29	with	with	ADP
ejpam-4641	302	30	its	its	PRON
ejpam-4641	302	31	proof	proof	NOUN
ejpam-4641	302	32	.	.	PUNCT
ejpam-4641	303	1	the	the	DET
ejpam-4641	303	2	formula	formula	NOUN
ejpam-4641	303	3	contains	contain	VERB
ejpam-4641	303	4	an	an	DET
ejpam-4641	303	5	integrated	integrated	ADJ
ejpam-4641	303	6	part	part	NOUN
ejpam-4641	303	7	that	that	PRON
ejpam-4641	303	8	can	can	AUX
ejpam-4641	303	9	be	be	AUX
ejpam-4641	303	10	easily	easily	ADV
ejpam-4641	303	11	calculated	calculate	VERB
ejpam-4641	303	12	using	use	VERB
ejpam-4641	303	13	any	any	DET
ejpam-4641	303	14	mathematical	mathematical	ADJ
ejpam-4641	303	15	package	package	NOUN
ejpam-4641	303	16	such	such	ADJ
ejpam-4641	303	17	as	as	ADP
ejpam-4641	303	18	mathematica	mathematica	PROPN
ejpam-4641	303	19	.	.	PUNCT
ejpam-4641	304	1	theorem	theorem	VERB
ejpam-4641	304	2	4	4	NUM
ejpam-4641	304	3	.	.	PUNCT
ejpam-4641	304	4	for	for	ADP
ejpam-4641	304	5	n	n	PROPN
ejpam-4641	304	6	>	>	SYM
ejpam-4641	304	7	2	2	NUM
ejpam-4641	304	8	µ	µ	X
ejpam-4641	304	9	(	(	PUNCT
ejpam-4641	304	10	m	m	NOUN
ejpam-4641	304	11	)	)	PUNCT
ejpam-4641	304	12	rc	rc	PROPN
ejpam-4641	304	13	n	n	PROPN
ejpam-4641	304	14	=	=	SYM
ejpam-4641	304	15	2nα2λ	2nα2λ	NUM
ejpam-4641	304	16	(	(	PUNCT
ejpam-4641	304	17	n−	n−	NOUN
ejpam-4641	304	18	1	1	NUM
ejpam-4641	304	19	)	)	PUNCT
ejpam-4641	304	20	!	!	PUNCT
ejpam-4641	305	1	α−1∑	α−1∑	NUM
ejpam-4641	306	1	v=0	v=0	X
ejpam-4641	306	2	α−1∑	α−1∑	NUM
ejpam-4641	306	3	w=0	w=0	PROPN
ejpam-4641	306	4	∞∑	∞∑	NUM
ejpam-4641	306	5	j=0	j=0	PROPN
ejpam-4641	306	6	(	(	PUNCT
ejpam-4641	306	7	α−	α−	ADP
ejpam-4641	306	8	1	1	NUM
ejpam-4641	306	9	v	v	NOUN
ejpam-4641	306	10	)	)	PUNCT
ejpam-4641	306	11	(	(	PUNCT
ejpam-4641	306	12	α−	α−	ADP
ejpam-4641	306	13	1	1	NUM
ejpam-4641	306	14	w	w	NOUN
ejpam-4641	306	15	)	)	PUNCT
ejpam-4641	306	16	(	(	PUNCT
ejpam-4641	306	17	−1)v+w	−1)v+w	NUM
ejpam-4641	306	18	v	v	NOUN
ejpam-4641	306	19	+	+	CCONJ
ejpam-4641	306	20	w	w	PROPN
ejpam-4641	306	21	+	+	PROPN
ejpam-4641	306	22	n+	n+	PROPN
ejpam-4641	306	23	j	j	PROPN
ejpam-4641	306	24	+	+	CCONJ
ejpam-4641	306	25	1	1	NUM
ejpam-4641	306	26	∫	∫	NUM
ejpam-4641	306	27	∞	∞	PROPN
ejpam-4641	306	28	0	0	NUM
ejpam-4641	306	29	rme−λ(w+1)r	rme−λ(w+1)r	NOUN
ejpam-4641	306	30	aj(n−	aj(n−	NUM
ejpam-4641	306	31	1	1	NUM
ejpam-4641	306	32	,	,	PUNCT
ejpam-4641	306	33	e−λr	e−λr	ADJ
ejpam-4641	306	34	,	,	PUNCT
ejpam-4641	306	35	α)dr	α)dr	PROPN
ejpam-4641	306	36	.	.	PUNCT
ejpam-4641	307	1	(	(	PUNCT
ejpam-4641	307	2	27	27	NUM
ejpam-4641	307	3	)	)	PUNCT
ejpam-4641	307	4	proof	proof	NOUN
ejpam-4641	307	5	.	.	PUNCT
ejpam-4641	308	1	by	by	ADP
ejpam-4641	308	2	substituting	substitute	VERB
ejpam-4641	308	3	(	(	PUNCT
ejpam-4641	308	4	5	5	NUM
ejpam-4641	308	5	)	)	PUNCT
ejpam-4641	308	6	and	and	CCONJ
ejpam-4641	308	7	(	(	PUNCT
ejpam-4641	308	8	6	6	NUM
ejpam-4641	308	9	)	)	PUNCT
ejpam-4641	308	10	in	in	ADP
ejpam-4641	308	11	(	(	PUNCT
ejpam-4641	308	12	3	3	NUM
ejpam-4641	308	13	)	)	PUNCT
ejpam-4641	308	14	,	,	PUNCT
ejpam-4641	308	15	we	we	PRON
ejpam-4641	308	16	get	get	VERB
ejpam-4641	308	17	frc	frc	PROPN
ejpam-4641	308	18	n	n	CCONJ
ejpam-4641	308	19	(	(	PUNCT
ejpam-4641	308	20	r	r	NOUN
ejpam-4641	308	21	)	)	PUNCT
ejpam-4641	308	22	=	=	SYM
ejpam-4641	309	1	2nα2λe−λr	2nα2λe−λr	NUM
ejpam-4641	309	2	(	(	PUNCT
ejpam-4641	309	3	n−	n−	NOUN
ejpam-4641	309	4	1	1	NUM
ejpam-4641	309	5	)	)	PUNCT
ejpam-4641	309	6	!	!	PUNCT
ejpam-4641	310	1	λi(r	λi(r	PUNCT
ejpam-4641	310	2	)	)	PUNCT
ejpam-4641	310	3	,	,	PUNCT
ejpam-4641	310	4	(	(	PUNCT
ejpam-4641	310	5	28	28	NUM
ejpam-4641	310	6	)	)	PUNCT
ejpam-4641	310	7	where	where	SCONJ
ejpam-4641	310	8	i(r	i(r	NOUN
ejpam-4641	310	9	)	)	PUNCT
ejpam-4641	310	10	=	=	PUNCT
ejpam-4641	311	1	λ	λ	X
ejpam-4641	311	2	∫	∫	PROPN
ejpam-4641	311	3	∞	∞	NUM
ejpam-4641	311	4	0	0	NUM
ejpam-4641	312	1	(	(	PUNCT
ejpam-4641	312	2	e−λx)2(1−	e−λx)2(1−	PROPN
ejpam-4641	312	3	e−λx)α−1(1−	e−λx)α−1(1−	X
ejpam-4641	312	4	e−λre−λx)α−1	e−λre−λx)α−1	NOUN
ejpam-4641	312	5	{	{	PUNCT
ejpam-4641	312	6	−	−	X
ejpam-4641	312	7	log[1−	log[1−	PUNCT
ejpam-4641	312	8	(	(	PUNCT
ejpam-4641	312	9	1−	1−	NUM
ejpam-4641	312	10	e−λre−λx)α	e−λre−λx)α	NUM
ejpam-4641	313	1	+	+	ADJ
ejpam-4641	313	2	(	(	PUNCT
ejpam-4641	313	3	1−	1−	NUM
ejpam-4641	313	4	e−λx)α	e−λx)α	ADV
ejpam-4641	313	5	]	]	PUNCT
ejpam-4641	313	6	}	}	PUNCT
ejpam-4641	313	7	n−1	n−1	PROPN
ejpam-4641	313	8	dx	dx	PROPN
ejpam-4641	313	9	.	.	PUNCT
ejpam-4641	313	10	by	by	ADP
ejpam-4641	313	11	making	make	VERB
ejpam-4641	313	12	the	the	DET
ejpam-4641	313	13	substitution	substitution	NOUN
ejpam-4641	313	14	u	u	NOUN
ejpam-4641	313	15	=	=	NOUN
ejpam-4641	313	16	eλx	eλx	NOUN
ejpam-4641	313	17	and	and	CCONJ
ejpam-4641	313	18	then	then	ADV
ejpam-4641	313	19	using	use	VERB
ejpam-4641	313	20	the	the	DET
ejpam-4641	313	21	binomial	binomial	ADJ
ejpam-4641	313	22	expansion	expansion	NOUN
ejpam-4641	313	23	on	on	ADP
ejpam-4641	313	24	some	some	PRON
ejpam-4641	313	25	of	of	ADP
ejpam-4641	313	26	the	the	DET
ejpam-4641	313	27	terms	term	NOUN
ejpam-4641	313	28	,	,	PUNCT
ejpam-4641	313	29	we	we	PRON
ejpam-4641	313	30	reach	reach	VERB
ejpam-4641	313	31	i(r	i(r	PROPN
ejpam-4641	313	32	)	)	PUNCT
ejpam-4641	313	33	=	=	SYM
ejpam-4641	314	1	α−1∑	α−1∑	NUM
ejpam-4641	314	2	v=0	v=0	X
ejpam-4641	314	3	α−1∑	α−1∑	NUM
ejpam-4641	314	4	w=0	w=0	PROPN
ejpam-4641	314	5	(	(	PUNCT
ejpam-4641	314	6	α−	α−	ADP
ejpam-4641	314	7	1	1	NUM
ejpam-4641	314	8	v	v	NOUN
ejpam-4641	314	9	)	)	PUNCT
ejpam-4641	314	10	(	(	PUNCT
ejpam-4641	314	11	α−	α−	ADP
ejpam-4641	314	12	1	1	NUM
ejpam-4641	314	13	w	w	NOUN
ejpam-4641	314	14	)	)	PUNCT
ejpam-4641	314	15	(	(	PUNCT
ejpam-4641	314	16	−1)v+w(e−λr)w	−1)v+w(e−λr)w	NOUN
ejpam-4641	314	17	∫	∫	PROPN
ejpam-4641	314	18	1	1	NUM
ejpam-4641	314	19	0	0	NUM
ejpam-4641	314	20	uv+w+1	uv+w+1	ADJ
ejpam-4641	314	21	{	{	PUNCT
ejpam-4641	314	22	−log[1−(1−e−λru)α+(1−u)α	−log[1−(1−e−λru)α+(1−u)α	NOUN
ejpam-4641	314	23	]	]	X
ejpam-4641	314	24	}	}	PUNCT
ejpam-4641	314	25	n−1	n−1	PROPN
ejpam-4641	314	26	du	du	X
ejpam-4641	314	27	.	.	PUNCT
ejpam-4641	315	1	the	the	DET
ejpam-4641	315	2	following	follow	VERB
ejpam-4641	315	3	expansion	expansion	NOUN
ejpam-4641	315	4	was	be	AUX
ejpam-4641	315	5	created	create	VERB
ejpam-4641	315	6	in	in	ADP
ejpam-4641	315	7	the	the	DET
ejpam-4641	315	8	same	same	ADJ
ejpam-4641	315	9	way	way	NOUN
ejpam-4641	315	10	balakrishnan	balakrishnan	PROPN
ejpam-4641	315	11	and	and	CCONJ
ejpam-4641	315	12	cohen	cohen	VERB
ejpam-4641	316	1	[	[	X
ejpam-4641	316	2	6	6	NUM
ejpam-4641	316	3	]	]	PUNCT
ejpam-4641	316	4	did	do	AUX
ejpam-4641	316	5	in	in	ADP
ejpam-4641	316	6	(	(	PUNCT
ejpam-4641	316	7	7	7	NUM
ejpam-4641	316	8	)	)	PUNCT
ejpam-4641	316	9	{	{	PUNCT
ejpam-4641	316	10	−	−	PROPN
ejpam-4641	316	11	log[1−	log[1−	PUNCT
ejpam-4641	316	12	(	(	PUNCT
ejpam-4641	316	13	1−	1−	NUM
ejpam-4641	316	14	e−λru)α	e−λru)α	NOUN
ejpam-4641	316	15	+	+	CCONJ
ejpam-4641	316	16	(	(	PUNCT
ejpam-4641	316	17	1−	1−	NUM
ejpam-4641	316	18	u)α	u)α	NOUN
ejpam-4641	316	19	]	]	PUNCT
ejpam-4641	316	20	}	}	PUNCT
ejpam-4641	316	21	n−1	n−1	PROPN
ejpam-4641	316	22	=	=	SYM
ejpam-4641	316	23	∞∑	∞∑	PROPN
ejpam-4641	316	24	j=0	j=0	PROPN
ejpam-4641	316	25	aj(n−	aj(n−	PROPN
ejpam-4641	316	26	1	1	NUM
ejpam-4641	316	27	,	,	PUNCT
ejpam-4641	316	28	e−λr	e−λr	ADJ
ejpam-4641	316	29	,	,	PUNCT
ejpam-4641	316	30	α)un−1+j	α)un−1+j	NOUN
ejpam-4641	316	31	,	,	PUNCT
ejpam-4641	316	32	where	where	SCONJ
ejpam-4641	316	33	aj(n−	aj(n−	PRON
ejpam-4641	316	34	1	1	NUM
ejpam-4641	316	35	,	,	PUNCT
ejpam-4641	316	36	e−λr	e−λr	ADJ
ejpam-4641	316	37	,	,	PUNCT
ejpam-4641	316	38	α	α	NOUN
ejpam-4641	316	39	)	)	PUNCT
ejpam-4641	316	40	is	be	AUX
ejpam-4641	316	41	the	the	DET
ejpam-4641	316	42	coefficient	coefficient	NOUN
ejpam-4641	316	43	of	of	ADP
ejpam-4641	316	44	the	the	DET
ejpam-4641	316	45	expansion	expansion	NOUN
ejpam-4641	316	46	.	.	PUNCT
ejpam-4641	317	1	then	then	ADV
ejpam-4641	317	2	i(r	i(r	PROPN
ejpam-4641	317	3	)	)	PUNCT
ejpam-4641	317	4	=	=	SYM
ejpam-4641	318	1	α−1∑	α−1∑	NUM
ejpam-4641	318	2	v=0	v=0	X
ejpam-4641	318	3	α−1∑	α−1∑	NUM
ejpam-4641	318	4	w=0	w=0	PROPN
ejpam-4641	318	5	∞∑	∞∑	NUM
ejpam-4641	318	6	j=0	j=0	PROPN
ejpam-4641	318	7	(	(	PUNCT
ejpam-4641	318	8	α−	α−	ADP
ejpam-4641	318	9	1	1	NUM
ejpam-4641	318	10	v	v	NOUN
ejpam-4641	318	11	)	)	PUNCT
ejpam-4641	318	12	(	(	PUNCT
ejpam-4641	318	13	α−	α−	ADP
ejpam-4641	318	14	1	1	NUM
ejpam-4641	318	15	w	w	NOUN
ejpam-4641	318	16	)	)	PUNCT
ejpam-4641	318	17	(	(	PUNCT
ejpam-4641	318	18	−1)v+w(e−λr)waj(n−	−1)v+w(e−λr)waj(n−	PROPN
ejpam-4641	318	19	1	1	NUM
ejpam-4641	318	20	,	,	PUNCT
ejpam-4641	318	21	e−λr	e−λr	ADJ
ejpam-4641	318	22	,	,	PUNCT
ejpam-4641	318	23	α	α	X
ejpam-4641	318	24	)	)	PUNCT
ejpam-4641	318	25	∫	∫	PROPN
ejpam-4641	318	26	1	1	NUM
ejpam-4641	318	27	0	0	NUM
ejpam-4641	318	28	uv+w+1un−1+jdu	uv+w+1un−1+jdu	NOUN
ejpam-4641	318	29	=	=	SYM
ejpam-4641	318	30	α−1∑	α−1∑	NUM
ejpam-4641	318	31	v=0	v=0	X
ejpam-4641	318	32	α−1∑	α−1∑	NUM
ejpam-4641	318	33	w=0	w=0	PROPN
ejpam-4641	318	34	∞∑	∞∑	NUM
ejpam-4641	318	35	j=0	j=0	PROPN
ejpam-4641	318	36	(	(	PUNCT
ejpam-4641	318	37	α−	α−	ADP
ejpam-4641	318	38	1	1	NUM
ejpam-4641	318	39	v	v	NOUN
ejpam-4641	318	40	)	)	PUNCT
ejpam-4641	318	41	(	(	PUNCT
ejpam-4641	318	42	α−	α−	ADP
ejpam-4641	318	43	1	1	NUM
ejpam-4641	318	44	w	w	NOUN
ejpam-4641	318	45	)	)	PUNCT
ejpam-4641	318	46	(	(	PUNCT
ejpam-4641	318	47	−1)v+waj(n−	−1)v+waj(n−	PROPN
ejpam-4641	318	48	1	1	NUM
ejpam-4641	318	49	,	,	PUNCT
ejpam-4641	318	50	e−λr	e−λr	ADJ
ejpam-4641	318	51	,	,	PUNCT
ejpam-4641	318	52	α	α	X
ejpam-4641	318	53	)	)	PUNCT
ejpam-4641	318	54	e−λwr	e−λwr	NOUN
ejpam-4641	318	55	v	v	ADP
ejpam-4641	318	56	+	+	CCONJ
ejpam-4641	318	57	w	w	PROPN
ejpam-4641	318	58	+	+	PROPN
ejpam-4641	318	59	n+	n+	PROPN
ejpam-4641	318	60	j	j	NOUN
ejpam-4641	318	61	+	+	NOUN
ejpam-4641	318	62	1	1	NUM
ejpam-4641	318	63	.	.	PUNCT
ejpam-4641	319	1	(	(	PUNCT
ejpam-4641	319	2	29	29	NUM
ejpam-4641	319	3	)	)	PUNCT
ejpam-4641	319	4	now	now	ADV
ejpam-4641	319	5	,	,	PUNCT
ejpam-4641	319	6	substitute	substitute	NOUN
ejpam-4641	319	7	(	(	PUNCT
ejpam-4641	319	8	29	29	NUM
ejpam-4641	319	9	)	)	PUNCT
ejpam-4641	319	10	in	in	ADP
ejpam-4641	319	11	(	(	PUNCT
ejpam-4641	319	12	28	28	NUM
ejpam-4641	319	13	)	)	PUNCT
ejpam-4641	319	14	we	we	PRON
ejpam-4641	319	15	get	get	VERB
ejpam-4641	319	16	r.a.aldallal	r.a.aldallal	NOUN
ejpam-4641	319	17	/	/	SYM
ejpam-4641	319	18	eur	eur	PROPN
ejpam-4641	319	19	.	.	PUNCT
ejpam-4641	320	1	j.	j.	PROPN
ejpam-4641	320	2	pure	pure	PROPN
ejpam-4641	320	3	appl	appl	PROPN
ejpam-4641	320	4	.	.	PROPN
ejpam-4641	320	5	math	math	PROPN
ejpam-4641	320	6	,	,	PUNCT
ejpam-4641	320	7	16	16	NUM
ejpam-4641	320	8	(	(	PUNCT
ejpam-4641	320	9	1	1	NUM
ejpam-4641	320	10	)	)	PUNCT
ejpam-4641	320	11	(	(	PUNCT
ejpam-4641	320	12	2023	2023	NUM
ejpam-4641	320	13	)	)	PUNCT
ejpam-4641	320	14	,	,	PUNCT
ejpam-4641	320	15	97	97	NUM
ejpam-4641	320	16	-	-	SYM
ejpam-4641	320	17	111	111	NUM
ejpam-4641	320	18	109	109	NUM
ejpam-4641	320	19	frc	frc	NOUN
ejpam-4641	320	20	n	n	CCONJ
ejpam-4641	320	21	(	(	PUNCT
ejpam-4641	320	22	r	r	NOUN
ejpam-4641	320	23	)	)	PUNCT
ejpam-4641	320	24	=	=	SYM
ejpam-4641	320	25	2nα2λ	2nα2λ	NUM
ejpam-4641	320	26	(	(	PUNCT
ejpam-4641	320	27	n−	n−	NOUN
ejpam-4641	320	28	1	1	NUM
ejpam-4641	320	29	)	)	PUNCT
ejpam-4641	320	30	!	!	PUNCT
ejpam-4641	321	1	α−1∑	α−1∑	NUM
ejpam-4641	322	1	v=0	v=0	X
ejpam-4641	322	2	α−1∑	α−1∑	NUM
ejpam-4641	322	3	w=0	w=0	PROPN
ejpam-4641	322	4	∞∑	∞∑	NUM
ejpam-4641	322	5	j=0	j=0	PROPN
ejpam-4641	322	6	(	(	PUNCT
ejpam-4641	322	7	α−	α−	ADP
ejpam-4641	322	8	1	1	NUM
ejpam-4641	322	9	v	v	NOUN
ejpam-4641	322	10	)	)	PUNCT
ejpam-4641	322	11	(	(	PUNCT
ejpam-4641	322	12	α−	α−	ADP
ejpam-4641	322	13	1	1	NUM
ejpam-4641	322	14	w	w	NOUN
ejpam-4641	322	15	)	)	PUNCT
ejpam-4641	322	16	(	(	PUNCT
ejpam-4641	322	17	−1)v+waj(n−1	−1)v+waj(n−1	ADJ
ejpam-4641	322	18	,	,	PUNCT
ejpam-4641	322	19	e−λr	e−λr	ADJ
ejpam-4641	322	20	,	,	PUNCT
ejpam-4641	322	21	α	α	X
ejpam-4641	322	22	)	)	PUNCT
ejpam-4641	322	23	e−λ(w+1)r	e−λ(w+1)r	PROPN
ejpam-4641	322	24	v	v	ADP
ejpam-4641	322	25	+	+	CCONJ
ejpam-4641	322	26	w	w	PROPN
ejpam-4641	322	27	+	+	PROPN
ejpam-4641	322	28	n+	n+	PROPN
ejpam-4641	322	29	j	j	NOUN
ejpam-4641	322	30	+	+	NOUN
ejpam-4641	322	31	1	1	NUM
ejpam-4641	322	32	.	.	PUNCT
ejpam-4641	322	33	(	(	PUNCT
ejpam-4641	322	34	30	30	NUM
ejpam-4641	322	35	)	)	PUNCT
ejpam-4641	322	36	to	to	PART
ejpam-4641	322	37	find	find	VERB
ejpam-4641	322	38	the	the	DET
ejpam-4641	322	39	moments	moment	NOUN
ejpam-4641	322	40	of	of	ADP
ejpam-4641	322	41	the	the	DET
ejpam-4641	322	42	record	record	NOUN
ejpam-4641	322	43	range	range	NOUN
ejpam-4641	322	44	we	we	PRON
ejpam-4641	322	45	will	will	AUX
ejpam-4641	322	46	use	use	VERB
ejpam-4641	322	47	the	the	DET
ejpam-4641	322	48	well	well	ADV
ejpam-4641	322	49	-	-	PUNCT
ejpam-4641	322	50	known	know	VERB
ejpam-4641	322	51	formula	formula	NOUN
ejpam-4641	322	52	µ	µ	X
ejpam-4641	322	53	(	(	PUNCT
ejpam-4641	322	54	m	m	NOUN
ejpam-4641	322	55	)	)	PUNCT
ejpam-4641	322	56	rc	rc	PROPN
ejpam-4641	322	57	n	n	NOUN
ejpam-4641	322	58	=	=	SYM
ejpam-4641	322	59	∫	∫	PROPN
ejpam-4641	322	60	∞	∞	NUM
ejpam-4641	322	61	0	0	NUM
ejpam-4641	322	62	rmfrc	rmfrc	PROPN
ejpam-4641	322	63	n	n	PROPN
ejpam-4641	322	64	(	(	PUNCT
ejpam-4641	322	65	r)dr	r)dr	PROPN
ejpam-4641	322	66	.	.	PROPN
ejpam-4641	322	67	(	(	PUNCT
ejpam-4641	322	68	31	31	NUM
ejpam-4641	322	69	)	)	PUNCT
ejpam-4641	322	70	substituting	substituting	NOUN
ejpam-4641	322	71	(	(	PUNCT
ejpam-4641	322	72	30	30	NUM
ejpam-4641	322	73	)	)	PUNCT
ejpam-4641	322	74	in	in	ADP
ejpam-4641	322	75	(	(	PUNCT
ejpam-4641	322	76	31	31	NUM
ejpam-4641	322	77	)	)	PUNCT
ejpam-4641	322	78	we	we	PRON
ejpam-4641	322	79	get	get	VERB
ejpam-4641	322	80	reach	reach	NOUN
ejpam-4641	322	81	(	(	PUNCT
ejpam-4641	322	82	27	27	NUM
ejpam-4641	322	83	)	)	PUNCT
ejpam-4641	322	84	.	.	PUNCT
ejpam-4641	323	1	6	6	X
ejpam-4641	323	2	.	.	X
ejpam-4641	323	3	numerical	numerical	ADJ
ejpam-4641	323	4	example	example	NOUN
ejpam-4641	323	5	to	to	PART
ejpam-4641	323	6	prove	prove	VERB
ejpam-4641	323	7	the	the	DET
ejpam-4641	323	8	benefits	benefit	NOUN
ejpam-4641	323	9	and	and	CCONJ
ejpam-4641	323	10	motivations	motivation	NOUN
ejpam-4641	323	11	of	of	ADP
ejpam-4641	323	12	using	use	VERB
ejpam-4641	323	13	the	the	DET
ejpam-4641	323	14	previous	previous	ADJ
ejpam-4641	323	15	formulas	formula	NOUN
ejpam-4641	323	16	,	,	PUNCT
ejpam-4641	323	17	a	a	DET
ejpam-4641	323	18	numerical	numerical	PROPN
ejpam-4641	323	19	simulation	simulation	NOUN
ejpam-4641	323	20	study	study	NOUN
ejpam-4641	323	21	was	be	AUX
ejpam-4641	323	22	conducted	conduct	VERB
ejpam-4641	323	23	to	to	PART
ejpam-4641	323	24	illustrate	illustrate	VERB
ejpam-4641	323	25	that	that	PRON
ejpam-4641	323	26	.	.	PUNCT
ejpam-4641	324	1	simulation	simulation	NOUN
ejpam-4641	324	2	study	study	PROPN
ejpam-4641	324	3	.	.	PUNCT
ejpam-4641	325	1	samples	sample	NOUN
ejpam-4641	325	2	of	of	ADP
ejpam-4641	325	3	size	size	NOUN
ejpam-4641	325	4	20	20	NUM
ejpam-4641	325	5	from	from	ADP
ejpam-4641	325	6	the	the	DET
ejpam-4641	325	7	pdf	pdf	NOUN
ejpam-4641	325	8	of	of	ADP
ejpam-4641	325	9	the	the	DET
ejpam-4641	325	10	upper	upper	ADJ
ejpam-4641	325	11	current	current	ADJ
ejpam-4641	325	12	records	record	NOUN
ejpam-4641	325	13	(	(	PUNCT
ejpam-4641	325	14	2	2	NUM
ejpam-4641	325	15	)	)	PUNCT
ejpam-4641	325	16	for	for	ADP
ejpam-4641	325	17	ged	ge	VERB
ejpam-4641	325	18	cdf	cdf	PROPN
ejpam-4641	325	19	when	when	SCONJ
ejpam-4641	325	20	α	α	PROPN
ejpam-4641	325	21	=	=	SYM
ejpam-4641	325	22	5	5	NUM
ejpam-4641	325	23	and	and	CCONJ
ejpam-4641	325	24	λ	λ	X
ejpam-4641	325	25	=	=	SYM
ejpam-4641	325	26	2	2	NUM
ejpam-4641	325	27	and	and	CCONJ
ejpam-4641	325	28	at	at	ADP
ejpam-4641	325	29	different	different	ADJ
ejpam-4641	325	30	values	value	NOUN
ejpam-4641	325	31	of	of	ADP
ejpam-4641	325	32	n	n	NOUN
ejpam-4641	325	33	=	=	SYM
ejpam-4641	325	34	2	2	NUM
ejpam-4641	325	35	,	,	PUNCT
ejpam-4641	325	36	3	3	NUM
ejpam-4641	325	37	,	,	PUNCT
ejpam-4641	325	38	4	4	NUM
ejpam-4641	325	39	,	,	PUNCT
ejpam-4641	325	40	5	5	NUM
ejpam-4641	325	41	and	and	CCONJ
ejpam-4641	325	42	6	6	NUM
ejpam-4641	325	43	was	be	AUX
ejpam-4641	325	44	simulated	simulate	VERB
ejpam-4641	325	45	using	use	VERB
ejpam-4641	325	46	mathematica	mathematica	PROPN
ejpam-4641	325	47	12.0	12.0	NUM
ejpam-4641	325	48	and	and	CCONJ
ejpam-4641	325	49	the	the	DET
ejpam-4641	325	50	true	true	ADJ
ejpam-4641	325	51	mean	mean	NOUN
ejpam-4641	325	52	for	for	SCONJ
ejpam-4641	325	53	each	each	DET
ejpam-4641	325	54	sample	sample	NOUN
ejpam-4641	325	55	was	be	AUX
ejpam-4641	325	56	calculated	calculate	VERB
ejpam-4641	325	57	.	.	PUNCT
ejpam-4641	326	1	after	after	ADP
ejpam-4641	326	2	that	that	PRON
ejpam-4641	326	3	,	,	PUNCT
ejpam-4641	326	4	we	we	PRON
ejpam-4641	326	5	used	use	VERB
ejpam-4641	326	6	formula	formula	NOUN
ejpam-4641	326	7	(	(	PUNCT
ejpam-4641	326	8	17	17	NUM
ejpam-4641	326	9	)	)	PUNCT
ejpam-4641	326	10	to	to	PART
ejpam-4641	326	11	estimate	estimate	VERB
ejpam-4641	326	12	the	the	DET
ejpam-4641	326	13	value	value	NOUN
ejpam-4641	326	14	of	of	ADP
ejpam-4641	326	15	the	the	DET
ejpam-4641	326	16	mean	mean	NOUN
ejpam-4641	326	17	at	at	ADP
ejpam-4641	326	18	the	the	DET
ejpam-4641	326	19	same	same	ADJ
ejpam-4641	326	20	values	value	NOUN
ejpam-4641	326	21	of	of	ADP
ejpam-4641	326	22	α	α	NOUN
ejpam-4641	326	23	,	,	PUNCT
ejpam-4641	326	24	λ	λ	X
ejpam-4641	326	25	andn	andn	VERB
ejpam-4641	326	26	when	when	SCONJ
ejpam-4641	326	27	i	i	PRON
ejpam-4641	326	28	=	=	NOUN
ejpam-4641	326	29	1	1	X
ejpam-4641	326	30	.	.	PUNCT
ejpam-4641	327	1	then	then	ADV
ejpam-4641	327	2	,	,	PUNCT
ejpam-4641	327	3	from	from	ADP
ejpam-4641	327	4	(	(	PUNCT
ejpam-4641	327	5	23	23	NUM
ejpam-4641	327	6	)	)	PUNCT
ejpam-4641	327	7	we	we	PRON
ejpam-4641	327	8	calculated	calculate	VERB
ejpam-4641	327	9	the	the	DET
ejpam-4641	327	10	predicted	predict	VERB
ejpam-4641	327	11	mean	mean	NOUN
ejpam-4641	327	12	at	at	ADP
ejpam-4641	327	13	also	also	ADV
ejpam-4641	327	14	the	the	DET
ejpam-4641	327	15	same	same	ADJ
ejpam-4641	327	16	α	α	NOUN
ejpam-4641	327	17	,	,	PUNCT
ejpam-4641	327	18	λ	λ	PROPN
ejpam-4641	327	19	,	,	PUNCT
ejpam-4641	327	20	n	n	NOUN
ejpam-4641	327	21	and	and	CCONJ
ejpam-4641	327	22	i.	i.	NOUN
ejpam-4641	327	23	as	as	SCONJ
ejpam-4641	327	24	we	we	PRON
ejpam-4641	327	25	can	can	AUX
ejpam-4641	327	26	see	see	VERB
ejpam-4641	327	27	from	from	ADP
ejpam-4641	327	28	the	the	DET
ejpam-4641	327	29	results	result	NOUN
ejpam-4641	327	30	listed	list	VERB
ejpam-4641	327	31	in	in	ADP
ejpam-4641	327	32	table	table	NOUN
ejpam-4641	327	33	1	1	NUM
ejpam-4641	327	34	,	,	PUNCT
ejpam-4641	327	35	the	the	DET
ejpam-4641	327	36	true	true	ADJ
ejpam-4641	327	37	mean	mean	NOUN
ejpam-4641	327	38	is	be	AUX
ejpam-4641	327	39	very	very	ADV
ejpam-4641	327	40	close	close	ADJ
ejpam-4641	327	41	to	to	ADP
ejpam-4641	327	42	the	the	DET
ejpam-4641	327	43	estimated	estimate	VERB
ejpam-4641	327	44	mean	mean	NOUN
ejpam-4641	327	45	and	and	CCONJ
ejpam-4641	327	46	the	the	DET
ejpam-4641	327	47	predicted	predict	VERB
ejpam-4641	327	48	mean	mean	NOUN
ejpam-4641	327	49	is	be	AUX
ejpam-4641	327	50	even	even	ADV
ejpam-4641	327	51	closer	close	ADJ
ejpam-4641	327	52	to	to	ADP
ejpam-4641	327	53	the	the	DET
ejpam-4641	327	54	estimated	estimate	VERB
ejpam-4641	327	55	mean	mean	NOUN
ejpam-4641	327	56	indicating	indicate	VERB
ejpam-4641	327	57	the	the	DET
ejpam-4641	327	58	efficiency	efficiency	NOUN
ejpam-4641	327	59	of	of	ADP
ejpam-4641	327	60	the	the	DET
ejpam-4641	327	61	formulas	formula	NOUN
ejpam-4641	327	62	created	create	VERB
ejpam-4641	327	63	in	in	ADP
ejpam-4641	327	64	this	this	DET
ejpam-4641	327	65	paper	paper	NOUN
ejpam-4641	327	66	.	.	PUNCT
ejpam-4641	328	1	analogies	analogy	NOUN
ejpam-4641	328	2	work	work	NOUN
ejpam-4641	328	3	has	have	AUX
ejpam-4641	328	4	been	be	AUX
ejpam-4641	328	5	done	do	VERB
ejpam-4641	328	6	for	for	ADP
ejpam-4641	328	7	the	the	DET
ejpam-4641	328	8	lower	low	ADJ
ejpam-4641	328	9	current	current	ADJ
ejpam-4641	328	10	records	record	NOUN
ejpam-4641	328	11	formulas	formula	NOUN
ejpam-4641	328	12	and	and	CCONJ
ejpam-4641	328	13	the	the	DET
ejpam-4641	328	14	same	same	ADJ
ejpam-4641	328	15	good	good	ADJ
ejpam-4641	328	16	results	result	NOUN
ejpam-4641	328	17	were	be	AUX
ejpam-4641	328	18	found	find	VERB
ejpam-4641	328	19	.	.	PUNCT
ejpam-4641	329	1	note	note	VERB
ejpam-4641	329	2	:	:	PUNCT
ejpam-4641	329	3	most	most	ADJ
ejpam-4641	329	4	of	of	ADP
ejpam-4641	329	5	the	the	DET
ejpam-4641	329	6	results	result	NOUN
ejpam-4641	329	7	calculated	calculate	VERB
ejpam-4641	329	8	from	from	ADP
ejpam-4641	329	9	the	the	DET
ejpam-4641	329	10	formulas	formula	NOUN
ejpam-4641	329	11	(	(	PUNCT
ejpam-4641	329	12	16),(17),(18	16),(17),(18	NOUN
ejpam-4641	329	13	)	)	PUNCT
ejpam-4641	329	14	,	,	PUNCT
ejpam-4641	329	15	and	and	CCONJ
ejpam-4641	329	16	(	(	PUNCT
ejpam-4641	329	17	19	19	NUM
ejpam-4641	329	18	)	)	PUNCT
ejpam-4641	329	19	were	be	AUX
ejpam-4641	329	20	conducted	conduct	VERB
ejpam-4641	329	21	to	to	ADP
ejpam-4641	329	22	a	a	DET
ejpam-4641	329	23	maximum	maximum	NOUN
ejpam-4641	329	24	of	of	ADP
ejpam-4641	329	25	2000	2000	NUM
ejpam-4641	329	26	iterations	iteration	NOUN
ejpam-4641	329	27	.	.	PUNCT
ejpam-4641	330	1	and	and	CCONJ
ejpam-4641	330	2	after	after	ADP
ejpam-4641	330	3	that	that	PRON
ejpam-4641	330	4	,	,	PUNCT
ejpam-4641	330	5	the	the	DET
ejpam-4641	330	6	results	result	NOUN
ejpam-4641	330	7	did	do	AUX
ejpam-4641	330	8	not	not	PART
ejpam-4641	330	9	change	change	VERB
ejpam-4641	330	10	.	.	PUNCT
ejpam-4641	331	1	table	table	NOUN
ejpam-4641	331	2	1	1	NUM
ejpam-4641	331	3	:	:	PUNCT
ejpam-4641	331	4	true	true	ADJ
ejpam-4641	331	5	,	,	PUNCT
ejpam-4641	331	6	estimate	estimate	VERB
ejpam-4641	331	7	and	and	CCONJ
ejpam-4641	331	8	predicted	predict	VERB
ejpam-4641	331	9	mean	mean	ADJ
ejpam-4641	331	10	upper	upper	ADJ
ejpam-4641	331	11	current	current	ADJ
ejpam-4641	331	12	record	record	NOUN
ejpam-4641	331	13	n	n	NOUN
ejpam-4641	331	14	=	=	SYM
ejpam-4641	331	15	2	2	NUM
ejpam-4641	331	16	n	n	NOUN
ejpam-4641	331	17	=	=	SYM
ejpam-4641	331	18	3	3	NUM
ejpam-4641	331	19	n	n	NOUN
ejpam-4641	331	20	=	=	SYM
ejpam-4641	331	21	4	4	NUM
ejpam-4641	331	22	n	n	NOUN
ejpam-4641	331	23	=	=	SYM
ejpam-4641	331	24	5	5	NUM
ejpam-4641	331	25	n	n	NOUN
ejpam-4641	331	26	=	=	SYM
ejpam-4641	331	27	6	6	NUM
ejpam-4641	331	28	true	true	ADJ
ejpam-4641	331	29	mean	mean	VERB
ejpam-4641	331	30	1.73759	1.73759	NUM
ejpam-4641	332	1	2.03974	2.03974	NUM
ejpam-4641	332	2	2.32234	2.32234	NUM
ejpam-4641	332	3	2.52788	2.52788	NUM
ejpam-4641	332	4	2.78866	2.78866	NUM
ejpam-4641	332	5	estimated	estimate	VERB
ejpam-4641	332	6	mean	mean	PROPN
ejpam-4641	332	7	1.75027	1.75027	NUM
ejpam-4641	332	8	2.02074	2.02074	NUM
ejpam-4641	332	9	2.28374	2.28374	NUM
ejpam-4641	332	10	2.54529	2.54529	NUM
ejpam-4641	332	11	2.81821	2.81821	NUM
ejpam-4641	332	12	predicted	predict	VERB
ejpam-4641	332	13	mean	mean	NOUN
ejpam-4641	332	14	2.02066	2.02066	NUM
ejpam-4641	332	15	2.28373	2.28373	NUM
ejpam-4641	332	16	2.5453	2.5453	NUM
ejpam-4641	332	17	2.81863	2.81863	NUM
ejpam-4641	332	18	lower	low	ADJ
ejpam-4641	332	19	current	current	ADJ
ejpam-4641	332	20	record	record	NOUN
ejpam-4641	332	21	n	n	NOUN
ejpam-4641	332	22	=	=	SYM
ejpam-4641	332	23	2	2	NUM
ejpam-4641	332	24	n	n	NOUN
ejpam-4641	332	25	=	=	SYM
ejpam-4641	332	26	3	3	NUM
ejpam-4641	332	27	n	n	NOUN
ejpam-4641	332	28	=	=	SYM
ejpam-4641	332	29	4	4	NUM
ejpam-4641	332	30	n	n	NOUN
ejpam-4641	332	31	=	=	SYM
ejpam-4641	332	32	5	5	NUM
ejpam-4641	332	33	n	n	NOUN
ejpam-4641	332	34	=	=	SYM
ejpam-4641	332	35	6	6	NUM
ejpam-4641	332	36	true	true	ADJ
ejpam-4641	332	37	mean	mean	VERB
ejpam-4641	333	1	0.649044	0.649044	NUM
ejpam-4641	333	2	0.52386	0.52386	NUM
ejpam-4641	333	3	0.474306	0.474306	NUM
ejpam-4641	333	4	0.403313	0.403313	NUM
ejpam-4641	333	5	0.326389	0.326389	NUM
ejpam-4641	333	6	estimated	estimate	VERB
ejpam-4641	333	7	mean	mean	VERB
ejpam-4641	333	8	0.649046	0.649046	NUM
ejpam-4641	333	9	0.535685	0.535685	NUM
ejpam-4641	333	10	0.452289	0.452289	NUM
ejpam-4641	333	11	0.387566	0.387566	NUM
ejpam-4641	333	12	0.335597	0.335597	NUM
ejpam-4641	333	13	predicted	predict	VERB
ejpam-4641	333	14	mean	mean	NOUN
ejpam-4641	333	15	0.535681	0.535681	NUM
ejpam-4641	333	16	0.452289	0.452289	NUM
ejpam-4641	333	17	0.387566	0.387566	NUM
ejpam-4641	334	1	0.335597	0.335597	NUM
ejpam-4641	334	2	7	7	NUM
ejpam-4641	334	3	.	.	PUNCT
ejpam-4641	334	4	conclusion	conclusion	NOUN
ejpam-4641	334	5	it	it	PRON
ejpam-4641	334	6	is	be	AUX
ejpam-4641	334	7	difficult	difficult	ADJ
ejpam-4641	334	8	to	to	PART
ejpam-4641	334	9	calculate	calculate	VERB
ejpam-4641	334	10	the	the	DET
ejpam-4641	334	11	mgf	mgf	PROPN
ejpam-4641	334	12	of	of	ADP
ejpam-4641	334	13	the	the	DET
ejpam-4641	334	14	lower	low	ADJ
ejpam-4641	334	15	or	or	CCONJ
ejpam-4641	334	16	the	the	DET
ejpam-4641	334	17	upper	upper	ADJ
ejpam-4641	334	18	current	current	ADJ
ejpam-4641	334	19	record	record	NOUN
ejpam-4641	334	20	or	or	CCONJ
ejpam-4641	334	21	the	the	DET
ejpam-4641	334	22	joint	joint	ADJ
ejpam-4641	334	23	mgf	mgf	PROPN
ejpam-4641	334	24	of	of	ADP
ejpam-4641	334	25	the	the	DET
ejpam-4641	334	26	lower	low	ADJ
ejpam-4641	334	27	and	and	CCONJ
ejpam-4641	334	28	upper	upper	ADJ
ejpam-4641	334	29	current	current	ADJ
ejpam-4641	334	30	record	record	NOUN
ejpam-4641	334	31	especially	especially	ADV
ejpam-4641	334	32	when	when	SCONJ
ejpam-4641	334	33	it	it	PRON
ejpam-4641	334	34	follows	follow	VERB
ejpam-4641	334	35	a	a	DET
ejpam-4641	334	36	distribution	distribution	NOUN
ejpam-4641	334	37	such	such	ADJ
ejpam-4641	334	38	references	reference	NOUN
ejpam-4641	334	39	110	110	NUM
ejpam-4641	334	40	as	as	SCONJ
ejpam-4641	334	41	ged	ge	VERB
ejpam-4641	334	42	.	.	PUNCT
ejpam-4641	335	1	the	the	DET
ejpam-4641	335	2	author	author	NOUN
ejpam-4641	335	3	tries	try	VERB
ejpam-4641	335	4	to	to	PART
ejpam-4641	335	5	solve	solve	VERB
ejpam-4641	335	6	this	this	PRON
ejpam-4641	335	7	by	by	ADP
ejpam-4641	335	8	finding	find	VERB
ejpam-4641	335	9	the	the	DET
ejpam-4641	335	10	simplest	simple	ADJ
ejpam-4641	335	11	formulas	formula	NOUN
ejpam-4641	335	12	to	to	PART
ejpam-4641	335	13	achieve	achieve	VERB
ejpam-4641	335	14	that	that	PRON
ejpam-4641	335	15	.	.	PUNCT
ejpam-4641	336	1	although	although	SCONJ
ejpam-4641	336	2	,	,	PUNCT
ejpam-4641	336	3	the	the	DET
ejpam-4641	336	4	author	author	NOUN
ejpam-4641	336	5	establishes	establish	VERB
ejpam-4641	336	6	some	some	DET
ejpam-4641	336	7	formulas	formula	NOUN
ejpam-4641	336	8	to	to	PART
ejpam-4641	336	9	find	find	VERB
ejpam-4641	336	10	the	the	DET
ejpam-4641	336	11	moments	moment	NOUN
ejpam-4641	336	12	of	of	ADP
ejpam-4641	336	13	the	the	DET
ejpam-4641	336	14	lower	low	ADJ
ejpam-4641	336	15	current	current	ADJ
ejpam-4641	336	16	record	record	NOUN
ejpam-4641	336	17	,	,	PUNCT
ejpam-4641	336	18	upper	upper	ADJ
ejpam-4641	336	19	current	current	ADJ
ejpam-4641	336	20	record	record	NOUN
ejpam-4641	336	21	,	,	PUNCT
ejpam-4641	336	22	record	record	NOUN
ejpam-4641	336	23	range	range	NOUN
ejpam-4641	336	24	,	,	PUNCT
ejpam-4641	336	25	and	and	CCONJ
ejpam-4641	336	26	product	product	NOUN
ejpam-4641	336	27	moments	moment	NOUN
ejpam-4641	336	28	of	of	ADP
ejpam-4641	336	29	the	the	DET
ejpam-4641	336	30	lower	low	ADJ
ejpam-4641	336	31	and	and	CCONJ
ejpam-4641	336	32	upper	upper	ADJ
ejpam-4641	336	33	current	current	ADJ
ejpam-4641	336	34	record	record	NOUN
ejpam-4641	336	35	based	base	VERB
ejpam-4641	336	36	on	on	ADP
ejpam-4641	336	37	the	the	DET
ejpam-4641	336	38	same	same	ADJ
ejpam-4641	336	39	distribution	distribution	NOUN
ejpam-4641	336	40	.	.	PUNCT
ejpam-4641	337	1	also	also	ADV
ejpam-4641	337	2	,	,	PUNCT
ejpam-4641	337	3	the	the	PRON
ejpam-4641	337	4	larger	large	ADJ
ejpam-4641	337	5	the	the	DET
ejpam-4641	337	6	value	value	NOUN
ejpam-4641	337	7	n	n	PRON
ejpam-4641	337	8	grows	grow	VERB
ejpam-4641	337	9	,	,	PUNCT
ejpam-4641	337	10	the	the	DET
ejpam-4641	337	11	more	more	ADJ
ejpam-4641	337	12	time	time	NOUN
ejpam-4641	337	13	it	it	PRON
ejpam-4641	337	14	takes	take	VERB
ejpam-4641	337	15	and	and	CCONJ
ejpam-4641	337	16	the	the	DET
ejpam-4641	337	17	more	more	ADV
ejpam-4641	337	18	difficult	difficult	ADJ
ejpam-4641	337	19	it	it	PRON
ejpam-4641	337	20	becomes	become	VERB
ejpam-4641	337	21	to	to	PART
ejpam-4641	337	22	be	be	AUX
ejpam-4641	337	23	calculated	calculate	VERB
ejpam-4641	337	24	.	.	PUNCT
ejpam-4641	338	1	and	and	CCONJ
ejpam-4641	338	2	here	here	ADV
ejpam-4641	338	3	comes	come	VERB
ejpam-4641	338	4	the	the	DET
ejpam-4641	338	5	role	role	NOUN
ejpam-4641	338	6	of	of	ADP
ejpam-4641	338	7	the	the	DET
ejpam-4641	338	8	recurrence	recurrence	NOUN
ejpam-4641	338	9	relation	relation	NOUN
ejpam-4641	338	10	formulas	formula	NOUN
ejpam-4641	338	11	created	create	VERB
ejpam-4641	338	12	for	for	ADP
ejpam-4641	338	13	the	the	DET
ejpam-4641	338	14	moments	moment	NOUN
ejpam-4641	338	15	and	and	CCONJ
ejpam-4641	338	16	mgfs	mgfs	NOUN
ejpam-4641	338	17	in	in	ADP
ejpam-4641	338	18	this	this	DET
ejpam-4641	338	19	paper	paper	NOUN
ejpam-4641	338	20	to	to	PART
ejpam-4641	338	21	make	make	VERB
ejpam-4641	338	22	it	it	PRON
ejpam-4641	338	23	easier	easy	ADJ
ejpam-4641	338	24	and	and	CCONJ
ejpam-4641	338	25	faster	fast	ADV
ejpam-4641	338	26	.	.	PUNCT
ejpam-4641	339	1	to	to	PART
ejpam-4641	339	2	demonstrate	demonstrate	VERB
ejpam-4641	339	3	that	that	SCONJ
ejpam-4641	339	4	,	,	PUNCT
ejpam-4641	339	5	a	a	DET
ejpam-4641	339	6	numerical	numerical	ADJ
ejpam-4641	339	7	example	example	NOUN
ejpam-4641	339	8	is	be	AUX
ejpam-4641	339	9	added	add	VERB
ejpam-4641	339	10	and	and	CCONJ
ejpam-4641	339	11	most	most	ADJ
ejpam-4641	339	12	of	of	ADP
ejpam-4641	339	13	the	the	DET
ejpam-4641	339	14	formulas	formula	NOUN
ejpam-4641	339	15	are	be	AUX
ejpam-4641	339	16	used	use	VERB
ejpam-4641	339	17	in	in	ADP
ejpam-4641	339	18	it	it	PRON
ejpam-4641	339	19	and	and	CCONJ
ejpam-4641	339	20	the	the	DET
ejpam-4641	339	21	desired	desire	VERB
ejpam-4641	339	22	result	result	NOUN
ejpam-4641	339	23	occurred	occur	VERB
ejpam-4641	339	24	by	by	ADP
ejpam-4641	339	25	finding	find	VERB
ejpam-4641	339	26	that	that	SCONJ
ejpam-4641	339	27	the	the	DET
ejpam-4641	339	28	formulas	formula	NOUN
ejpam-4641	339	29	of	of	ADP
ejpam-4641	339	30	the	the	DET
ejpam-4641	339	31	mgf	mgf	PROPN
ejpam-4641	339	32	and	and	CCONJ
ejpam-4641	339	33	the	the	DET
ejpam-4641	339	34	moments	moment	NOUN
ejpam-4641	339	35	give	give	VERB
ejpam-4641	339	36	values	value	NOUN
ejpam-4641	339	37	very	very	ADV
ejpam-4641	339	38	close	close	ADV
ejpam-4641	339	39	to	to	ADP
ejpam-4641	339	40	the	the	DET
ejpam-4641	339	41	actual	actual	ADJ
ejpam-4641	339	42	ones	one	NOUN
ejpam-4641	339	43	.	.	PUNCT
ejpam-4641	340	1	and	and	CCONJ
ejpam-4641	340	2	also	also	ADV
ejpam-4641	340	3	,	,	PUNCT
ejpam-4641	340	4	the	the	DET
ejpam-4641	340	5	values	value	NOUN
ejpam-4641	340	6	that	that	PRON
ejpam-4641	340	7	result	result	VERB
ejpam-4641	340	8	from	from	ADP
ejpam-4641	340	9	the	the	DET
ejpam-4641	340	10	recurrence	recurrence	NOUN
ejpam-4641	340	11	relations	relation	NOUN
ejpam-4641	340	12	are	be	AUX
ejpam-4641	340	13	almost	almost	ADV
ejpam-4641	340	14	the	the	DET
ejpam-4641	340	15	same	same	ADJ
ejpam-4641	340	16	values	value	NOUN
ejpam-4641	340	17	as	as	ADP
ejpam-4641	340	18	the	the	DET
ejpam-4641	340	19	ones	one	NOUN
ejpam-4641	340	20	from	from	ADP
ejpam-4641	340	21	its	its	PRON
ejpam-4641	340	22	opposite	opposite	ADJ
ejpam-4641	340	23	mgf	mgf	NOUN
ejpam-4641	340	24	or	or	CCONJ
ejpam-4641	340	25	moments	moment	NOUN
ejpam-4641	340	26	but	but	CCONJ
ejpam-4641	340	27	calculated	calculate	VERB
ejpam-4641	340	28	faster	fast	ADV
ejpam-4641	340	29	.	.	PUNCT
ejpam-4641	341	1	acknowledgements	acknowledgement	NOUN
ejpam-4641	341	2	this	this	DET
ejpam-4641	341	3	publication	publication	NOUN
ejpam-4641	341	4	was	be	AUX
ejpam-4641	341	5	supported	support	VERB
ejpam-4641	341	6	by	by	ADP
ejpam-4641	341	7	deanship	deanship	NOUN
ejpam-4641	341	8	of	of	ADP
ejpam-4641	341	9	scientific	scientific	ADJ
ejpam-4641	341	10	research	research	NOUN
ejpam-4641	341	11	,	,	PUNCT
ejpam-4641	341	12	prince	prince	PROPN
ejpam-4641	341	13	sattam	sattam	PROPN
ejpam-4641	341	14	bin	bin	PROPN
ejpam-4641	341	15	abdul	abdul	PROPN
ejpam-4641	341	16	-	-	PUNCT
ejpam-4641	341	17	aziz	aziz	PROPN
ejpam-4641	341	18	university	university	PROPN
ejpam-4641	341	19	,	,	PUNCT
ejpam-4641	341	20	alkharj	alkharj	VERB
ejpam-4641	341	21	,	,	PUNCT
ejpam-4641	341	22	saudi	saudi	PROPN
ejpam-4641	341	23	arabia	arabia	PROPN
ejpam-4641	341	24	.	.	PUNCT
ejpam-4641	342	1	our	our	PRON
ejpam-4641	342	2	special	special	ADJ
ejpam-4641	342	3	thanks	thank	NOUN
ejpam-4641	342	4	for	for	ADP
ejpam-4641	342	5	their	their	PRON
ejpam-4641	342	6	encouragement	encouragement	NOUN
ejpam-4641	342	7	and	and	CCONJ
ejpam-4641	342	8	supporting	support	VERB
ejpam-4641	342	9	of	of	ADP
ejpam-4641	342	10	this	this	DET
ejpam-4641	342	11	research	research	NOUN
ejpam-4641	342	12	.	.	PUNCT
ejpam-4641	343	1	also	also	ADV
ejpam-4641	343	2	,	,	PUNCT
ejpam-4641	343	3	i	i	PRON
ejpam-4641	343	4	would	would	AUX
ejpam-4641	343	5	like	like	VERB
ejpam-4641	343	6	to	to	PART
ejpam-4641	343	7	thank	thank	VERB
ejpam-4641	343	8	prof	prof	PROPN
ejpam-4641	343	9	.	.	PUNCT
ejpam-4641	344	1	haroon	haroon	PROPN
ejpam-4641	344	2	barakat	barakat	PROPN
ejpam-4641	344	3	for	for	ADP
ejpam-4641	344	4	his	his	PRON
ejpam-4641	344	5	valuable	valuable	ADJ
ejpam-4641	344	6	ideas	idea	NOUN
ejpam-4641	344	7	that	that	PRON
ejpam-4641	344	8	were	be	AUX
ejpam-4641	344	9	very	very	ADV
ejpam-4641	344	10	helpful	helpful	ADJ
ejpam-4641	344	11	in	in	ADP
ejpam-4641	344	12	creating	create	VERB
ejpam-4641	344	13	this	this	DET
ejpam-4641	344	14	paper	paper	NOUN
ejpam-4641	344	15	.	.	PUNCT
ejpam-4641	345	1	references	reference	NOUN
ejpam-4641	345	2	[	[	X
ejpam-4641	345	3	1	1	X
ejpam-4641	345	4	]	]	PUNCT
ejpam-4641	345	5	j.	j.	PROPN
ejpam-4641	345	6	ahmadi	ahmadi	PROPN
ejpam-4641	345	7	and	and	CCONJ
ejpam-4641	345	8	n.	n.	PROPN
ejpam-4641	345	9	balakrishnan	balakrishnan	PROPN
ejpam-4641	345	10	.	.	PUNCT
ejpam-4641	346	1	distribution	distribution	NOUN
ejpam-4641	346	2	-	-	PUNCT
ejpam-4641	346	3	free	free	ADJ
ejpam-4641	346	4	confidence	confidence	NOUN
ejpam-4641	346	5	intervals	interval	NOUN
ejpam-4641	346	6	for	for	ADP
ejpam-4641	346	7	quantile	quantile	ADJ
ejpam-4641	346	8	intervals	interval	NOUN
ejpam-4641	346	9	based	base	VERB
ejpam-4641	346	10	on	on	ADP
ejpam-4641	346	11	current	current	ADJ
ejpam-4641	346	12	records	record	NOUN
ejpam-4641	346	13	.	.	PUNCT
ejpam-4641	347	1	statistics	statistic	NOUN
ejpam-4641	347	2	and	and	CCONJ
ejpam-4641	347	3	probability	probability	NOUN
ejpam-4641	347	4	letters	letter	NOUN
ejpam-4641	347	5	,	,	PUNCT
ejpam-4641	347	6	75(3):190–202	75(3):190–202	NOUN
ejpam-4641	347	7	,	,	PUNCT
ejpam-4641	347	8	2005	2005	NUM
ejpam-4641	347	9	.	.	PUNCT
ejpam-4641	348	1	[	[	X
ejpam-4641	348	2	2	2	X
ejpam-4641	348	3	]	]	PUNCT
ejpam-4641	348	4	j.	j.	PROPN
ejpam-4641	348	5	ahmadi	ahmadi	PROPN
ejpam-4641	348	6	and	and	CCONJ
ejpam-4641	348	7	n.	n.	PROPN
ejpam-4641	348	8	balakrishnan	balakrishnan	PROPN
ejpam-4641	348	9	.	.	PUNCT
ejpam-4641	349	1	preservation	preservation	NOUN
ejpam-4641	349	2	of	of	ADP
ejpam-4641	349	3	some	some	DET
ejpam-4641	349	4	reliability	reliability	NOUN
ejpam-4641	349	5	properties	property	NOUN
ejpam-4641	349	6	by	by	ADP
ejpam-4641	349	7	certain	certain	ADJ
ejpam-4641	349	8	record	record	NOUN
ejpam-4641	349	9	statistics	statistic	NOUN
ejpam-4641	349	10	.	.	PUNCT
ejpam-4641	350	1	statistics	statistic	NOUN
ejpam-4641	350	2	,	,	PUNCT
ejpam-4641	350	3	39(4):347–354	39(4):347–354	PROPN
ejpam-4641	350	4	,	,	PUNCT
ejpam-4641	350	5	2005	2005	NUM
ejpam-4641	350	6	.	.	PUNCT
ejpam-4641	351	1	[	[	X
ejpam-4641	351	2	3	3	X
ejpam-4641	351	3	]	]	X
ejpam-4641	351	4	j.	j.	PROPN
ejpam-4641	351	5	ahmadi	ahmadi	PROPN
ejpam-4641	351	6	,	,	PUNCT
ejpam-4641	351	7	m.	m.	NOUN
ejpam-4641	351	8	razmkhah	razmkhah	NOUN
ejpam-4641	351	9	,	,	PUNCT
ejpam-4641	351	10	and	and	CCONJ
ejpam-4641	351	11	n.	n.	PROPN
ejpam-4641	351	12	balakrishnan	balakrishnan	PROPN
ejpam-4641	351	13	.	.	PUNCT
ejpam-4641	352	1	current	current	ADJ
ejpam-4641	352	2	k	k	NOUN
ejpam-4641	352	3	-	-	PUNCT
ejpam-4641	352	4	records	record	NOUN
ejpam-4641	352	5	and	and	CCONJ
ejpam-4641	352	6	their	their	PRON
ejpam-4641	352	7	use	use	NOUN
ejpam-4641	352	8	in	in	ADP
ejpam-4641	352	9	distribution	distribution	NOUN
ejpam-4641	352	10	-	-	PUNCT
ejpam-4641	352	11	free	free	ADJ
ejpam-4641	352	12	confidence	confidence	NOUN
ejpam-4641	352	13	intervals	interval	NOUN
ejpam-4641	352	14	.	.	PUNCT
ejpam-4641	353	1	statistics	statistic	NOUN
ejpam-4641	353	2	and	and	CCONJ
ejpam-4641	353	3	probability	probability	NOUN
ejpam-4641	353	4	letters	letter	NOUN
ejpam-4641	353	5	,	,	PUNCT
ejpam-4641	353	6	79(1):29–37	79(1):29–37	NUM
ejpam-4641	353	7	,	,	PUNCT
ejpam-4641	353	8	2009	2009	NUM
ejpam-4641	353	9	.	.	PUNCT
ejpam-4641	354	1	[	[	X
ejpam-4641	354	2	4	4	X
ejpam-4641	354	3	]	]	X
ejpam-4641	354	4	r.	r.	PROPN
ejpam-4641	354	5	a.	a.	PROPN
ejpam-4641	354	6	aldallal	aldallal	PROPN
ejpam-4641	354	7	.	.	PUNCT
ejpam-4641	355	1	best	good	ADJ
ejpam-4641	355	2	linear	linear	ADJ
ejpam-4641	355	3	unbiased	unbiased	ADJ
ejpam-4641	355	4	estimation	estimation	NOUN
ejpam-4641	355	5	and	and	CCONJ
ejpam-4641	355	6	prediction	prediction	NOUN
ejpam-4641	355	7	of	of	ADP
ejpam-4641	355	8	record	record	NOUN
ejpam-4641	355	9	values	value	NOUN
ejpam-4641	355	10	based	base	VERB
ejpam-4641	355	11	on	on	ADP
ejpam-4641	355	12	kumaraswamy	kumaraswamy	ADJ
ejpam-4641	355	13	distributed	distribute	VERB
ejpam-4641	355	14	data	datum	NOUN
ejpam-4641	355	15	.	.	PUNCT
ejpam-4641	356	1	statistics	statistic	NOUN
ejpam-4641	356	2	,	,	PUNCT
ejpam-4641	356	3	optimization	optimization	NOUN
ejpam-4641	356	4	&	&	CCONJ
ejpam-4641	356	5	information	information	NOUN
ejpam-4641	356	6	computing	computing	PROPN
ejpam-4641	356	7	,	,	PUNCT
ejpam-4641	356	8	10(4):1250–1266	10(4):1250–1266	NUM
ejpam-4641	356	9	,	,	PUNCT
ejpam-4641	356	10	2022	2022	NUM
ejpam-4641	356	11	.	.	PUNCT
ejpam-4641	357	1	[	[	X
ejpam-4641	357	2	5	5	X
ejpam-4641	357	3	]	]	PUNCT
ejpam-4641	357	4	e.	e.	PROPN
ejpam-4641	357	5	a.	a.	PROPN
ejpam-4641	357	6	amany	amany	PROPN
ejpam-4641	357	7	,	,	PUNCT
ejpam-4641	357	8	h.	h.	PROPN
ejpam-4641	357	9	m.	m.	PROPN
ejpam-4641	357	10	barakat	barakat	PROPN
ejpam-4641	357	11	,	,	PUNCT
ejpam-4641	357	12	and	and	CCONJ
ejpam-4641	357	13	m.	m.	PROPN
ejpam-4641	357	14	e.	e.	PROPN
ejpam-4641	357	15	el	el	PROPN
ejpam-4641	357	16	-	-	PUNCT
ejpam-4641	357	17	adll	adll	PROPN
ejpam-4641	357	18	.	.	PUNCT
ejpam-4641	358	1	prediction	prediction	NOUN
ejpam-4641	358	2	intervals	interval	NOUN
ejpam-4641	358	3	of	of	ADP
ejpam-4641	358	4	the	the	DET
ejpam-4641	358	5	recordvalues	recordvalue	NOUN
ejpam-4641	358	6	process	process	NOUN
ejpam-4641	358	7	.	.	PUNCT
ejpam-4641	359	1	revstat	revstat	PROPN
ejpam-4641	359	2	statistical	statistical	ADJ
ejpam-4641	359	3	journal	journal	NOUN
ejpam-4641	359	4	,	,	PUNCT
ejpam-4641	359	5	17(3):401–427	17(3):401–427	NUM
ejpam-4641	359	6	,	,	PUNCT
ejpam-4641	359	7	2019	2019	NUM
ejpam-4641	359	8	.	.	PUNCT
ejpam-4641	360	1	[	[	X
ejpam-4641	360	2	6	6	NUM
ejpam-4641	360	3	]	]	X
ejpam-4641	360	4	n.	n.	PROPN
ejpam-4641	360	5	balakrishnan	balakrishnan	PROPN
ejpam-4641	360	6	and	and	CCONJ
ejpam-4641	360	7	a.	a.	PROPN
ejpam-4641	360	8	c.	c.	PROPN
ejpam-4641	360	9	cohen	cohen	PROPN
ejpam-4641	360	10	.	.	PUNCT
ejpam-4641	361	1	order	order	NOUN
ejpam-4641	361	2	statistics	statistic	NOUN
ejpam-4641	361	3	and	and	CCONJ
ejpam-4641	361	4	inference	inference	NOUN
ejpam-4641	361	5	:	:	PUNCT
ejpam-4641	361	6	estimation	estimation	NOUN
ejpam-4641	361	7	methods	method	NOUN
ejpam-4641	361	8	.	.	PUNCT
ejpam-4641	362	1	academic	academic	ADJ
ejpam-4641	362	2	press	press	NOUN
ejpam-4641	362	3	,	,	PUNCT
ejpam-4641	362	4	san	san	PROPN
ejpam-4641	362	5	diego	diego	PROPN
ejpam-4641	362	6	,	,	PUNCT
ejpam-4641	362	7	1991	1991	NUM
ejpam-4641	362	8	.	.	PUNCT
ejpam-4641	363	1	[	[	X
ejpam-4641	363	2	7	7	X
ejpam-4641	363	3	]	]	X
ejpam-4641	363	4	h.	h.	PROPN
ejpam-4641	363	5	m.	m.	PROPN
ejpam-4641	363	6	barakat	barakat	PROPN
ejpam-4641	363	7	and	and	CCONJ
ejpam-4641	363	8	m.	m.	PROPN
ejpam-4641	363	9	h.	h.	PROPN
ejpam-4641	363	10	harpy	harpy	PROPN
ejpam-4641	363	11	.	.	PUNCT
ejpam-4641	364	1	asymptotic	asymptotic	ADJ
ejpam-4641	364	2	behavior	behavior	NOUN
ejpam-4641	364	3	of	of	ADP
ejpam-4641	364	4	the	the	DET
ejpam-4641	364	5	records	record	NOUN
ejpam-4641	364	6	of	of	ADP
ejpam-4641	364	7	multivariate	multivariate	NOUN
ejpam-4641	364	8	random	random	ADJ
ejpam-4641	364	9	sequences	sequence	NOUN
ejpam-4641	364	10	in	in	ADP
ejpam-4641	364	11	a	a	DET
ejpam-4641	364	12	norm	norm	NOUN
ejpam-4641	364	13	sense	sense	NOUN
ejpam-4641	364	14	.	.	PUNCT
ejpam-4641	365	1	math	math	NOUN
ejpam-4641	365	2	.	.	PUNCT
ejpam-4641	366	1	slovaca	slovaca	PROPN
ejpam-4641	366	2	,	,	PUNCT
ejpam-4641	366	3	70(6):1457–1468	70(6):1457–1468	NOUN
ejpam-4641	366	4	,	,	PUNCT
ejpam-4641	366	5	2020	2020	NUM
ejpam-4641	366	6	.	.	PUNCT
ejpam-4641	367	1	references	reference	NOUN
ejpam-4641	367	2	111	111	NUM
ejpam-4641	367	3	[	[	SYM
ejpam-4641	367	4	8	8	NUM
ejpam-4641	367	5	]	]	X
ejpam-4641	367	6	h.	h.	PROPN
ejpam-4641	367	7	m.	m.	PROPN
ejpam-4641	367	8	barakat	barakat	PROPN
ejpam-4641	367	9	,	,	PUNCT
ejpam-4641	367	10	e.	e.	PROPN
ejpam-4641	367	11	m.	m.	PROPN
ejpam-4641	367	12	nigm	nigm	PROPN
ejpam-4641	367	13	,	,	PUNCT
ejpam-4641	367	14	and	and	CCONJ
ejpam-4641	367	15	r.	r.	PROPN
ejpam-4641	367	16	a.	a.	PROPN
ejpam-4641	367	17	aldallal	aldallal	PROPN
ejpam-4641	367	18	.	.	PUNCT
ejpam-4641	368	1	current	current	ADJ
ejpam-4641	368	2	records	record	NOUN
ejpam-4641	368	3	and	and	CCONJ
ejpam-4641	368	4	record	record	NOUN
ejpam-4641	368	5	range	range	NOUN
ejpam-4641	368	6	with	with	ADP
ejpam-4641	368	7	some	some	DET
ejpam-4641	368	8	applications	application	NOUN
ejpam-4641	368	9	.	.	PUNCT
ejpam-4641	369	1	journal	journal	NOUN
ejpam-4641	369	2	of	of	ADP
ejpam-4641	369	3	the	the	DET
ejpam-4641	369	4	korean	korean	ADJ
ejpam-4641	369	5	statistical	statistical	ADJ
ejpam-4641	369	6	society	society	NOUN
ejpam-4641	369	7	,	,	PUNCT
ejpam-4641	369	8	43(2):263–273	43(2):263–273	PROPN
ejpam-4641	369	9	,	,	PUNCT
ejpam-4641	369	10	2014	2014	NUM
ejpam-4641	369	11	.	.	PUNCT
ejpam-4641	370	1	[	[	X
ejpam-4641	370	2	9	9	NUM
ejpam-4641	370	3	]	]	X
ejpam-4641	370	4	h.	h.	PROPN
ejpam-4641	370	5	m.	m.	PROPN
ejpam-4641	370	6	barakat	barakat	PROPN
ejpam-4641	370	7	,	,	PUNCT
ejpam-4641	370	8	e.	e.	PROPN
ejpam-4641	370	9	m.	m.	PROPN
ejpam-4641	370	10	nigm	nigm	PROPN
ejpam-4641	370	11	,	,	PUNCT
ejpam-4641	370	12	and	and	CCONJ
ejpam-4641	370	13	r.	r.	PROPN
ejpam-4641	370	14	a.	a.	PROPN
ejpam-4641	370	15	aldallal	aldallal	PROPN
ejpam-4641	370	16	.	.	PUNCT
ejpam-4641	371	1	exact	exact	ADJ
ejpam-4641	371	2	prediction	prediction	NOUN
ejpam-4641	371	3	intervals	interval	NOUN
ejpam-4641	371	4	for	for	ADP
ejpam-4641	371	5	future	future	ADJ
ejpam-4641	371	6	current	current	ADJ
ejpam-4641	371	7	records	record	NOUN
ejpam-4641	371	8	and	and	CCONJ
ejpam-4641	371	9	record	record	NOUN
ejpam-4641	371	10	range	range	NOUN
ejpam-4641	371	11	from	from	ADP
ejpam-4641	371	12	any	any	DET
ejpam-4641	371	13	continuous	continuous	ADJ
ejpam-4641	371	14	distribution	distribution	NOUN
ejpam-4641	371	15	.	.	PUNCT
ejpam-4641	372	1	sort	sort	NOUN
ejpam-4641	372	2	,	,	PUNCT
ejpam-4641	372	3	38(2):251	38(2):251	NUM
ejpam-4641	372	4	–	–	PUNCT
ejpam-4641	372	5	270	270	NUM
ejpam-4641	372	6	,	,	PUNCT
ejpam-4641	372	7	2014	2014	NUM
ejpam-4641	372	8	.	.	PUNCT
ejpam-4641	373	1	[	[	X
ejpam-4641	373	2	10	10	NUM
ejpam-4641	373	3	]	]	X
ejpam-4641	373	4	p.	p.	PROPN
ejpam-4641	373	5	basak	basak	PROPN
ejpam-4641	373	6	.	.	PUNCT
ejpam-4641	374	1	an	an	DET
ejpam-4641	374	2	application	application	NOUN
ejpam-4641	374	3	of	of	ADP
ejpam-4641	374	4	record	record	NOUN
ejpam-4641	374	5	range	range	NOUN
ejpam-4641	374	6	and	and	CCONJ
ejpam-4641	374	7	some	some	DET
ejpam-4641	374	8	characterization	characterization	NOUN
ejpam-4641	374	9	results	result	NOUN
ejpam-4641	374	10	.	.	PUNCT
ejpam-4641	375	1	in	in	ADP
ejpam-4641	375	2	advances	advance	NOUN
ejpam-4641	375	3	on	on	ADP
ejpam-4641	375	4	theoretical	theoretical	ADJ
ejpam-4641	375	5	and	and	CCONJ
ejpam-4641	375	6	methodological	methodological	ADJ
ejpam-4641	375	7	a	a	DET
ejpam-4641	375	8	spects	spect	NOUN
ejpam-4641	375	9	of	of	ADP
ejpam-4641	375	10	probability	probability	NOUN
ejpam-4641	375	11	and	and	CCONJ
ejpam-4641	375	12	statistics	statistic	NOUN
ejpam-4641	375	13	,	,	PUNCT
ejpam-4641	375	14	pages	page	NOUN
ejpam-4641	375	15	83–95	83–95	NUM
ejpam-4641	375	16	.	.	PUNCT
ejpam-4641	376	1	crc	crc	PROPN
ejpam-4641	376	2	press	press	PROPN
ejpam-4641	376	3	,	,	PUNCT
ejpam-4641	376	4	2019	2019	NUM
ejpam-4641	376	5	.	.	PUNCT
ejpam-4641	377	1	[	[	X
ejpam-4641	377	2	11	11	NUM
ejpam-4641	377	3	]	]	PUNCT
ejpam-4641	377	4	m.	m.	NOUN
ejpam-4641	377	5	m.	m.	PROPN
ejpam-4641	377	6	mohie	mohie	PROPN
ejpam-4641	377	7	el	el	PROPN
ejpam-4641	377	8	-	-	PUNCT
ejpam-4641	377	9	din	din	PROPN
ejpam-4641	377	10	and	and	CCONJ
ejpam-4641	377	11	a.	a.	NOUN
ejpam-4641	377	12	m.	m.	NOUN
ejpam-4641	377	13	sharawy	sharawy	PROPN
ejpam-4641	377	14	.	.	PUNCT
ejpam-4641	378	1	characterization	characterization	NOUN
ejpam-4641	378	2	for	for	ADP
ejpam-4641	378	3	generalized	generalized	ADJ
ejpam-4641	378	4	exponential	exponential	ADJ
ejpam-4641	378	5	distribution	distribution	NOUN
ejpam-4641	378	6	.	.	PUNCT
ejpam-4641	379	1	mathematical	mathematical	ADJ
ejpam-4641	379	2	sciences	science	NOUN
ejpam-4641	379	3	letters	letter	NOUN
ejpam-4641	379	4	,	,	PUNCT
ejpam-4641	379	5	10(1):15–21	10(1):15–21	NUM
ejpam-4641	379	6	,	,	PUNCT
ejpam-4641	379	7	2021	2021	NUM
ejpam-4641	379	8	.	.	PUNCT
ejpam-4641	380	1	[	[	X
ejpam-4641	380	2	12	12	NUM
ejpam-4641	380	3	]	]	PUNCT
ejpam-4641	380	4	m.	m.	NOUN
ejpam-4641	380	5	a.	a.	PROPN
ejpam-4641	380	6	abd	abd	PROPN
ejpam-4641	380	7	elgawad	elgawad	PROPN
ejpam-4641	380	8	,	,	PUNCT
ejpam-4641	380	9	h.	h.	PROPN
ejpam-4641	380	10	m.	m.	PROPN
ejpam-4641	380	11	barakat	barakat	PROPN
ejpam-4641	380	12	,	,	PUNCT
ejpam-4641	380	13	and	and	CCONJ
ejpam-4641	380	14	y.	y.	PROPN
ejpam-4641	380	15	ting	ting	PROPN
ejpam-4641	380	16	.	.	PUNCT
ejpam-4641	381	1	bivariate	bivariate	ADJ
ejpam-4641	381	2	limit	limit	NOUN
ejpam-4641	381	3	theorems	theorem	NOUN
ejpam-4641	381	4	for	for	ADP
ejpam-4641	381	5	record	record	NOUN
ejpam-4641	381	6	values	value	NOUN
ejpam-4641	381	7	based	base	VERB
ejpam-4641	381	8	on	on	ADP
ejpam-4641	381	9	random	random	ADJ
ejpam-4641	381	10	sample	sample	NOUN
ejpam-4641	381	11	sizes	size	NOUN
ejpam-4641	381	12	.	.	PUNCT
ejpam-4641	382	1	sankhya	sankhya	PROPN
ejpam-4641	382	2	a	a	PRON
ejpam-4641	382	3	:	:	PUNCT
ejpam-4641	382	4	the	the	DET
ejpam-4641	382	5	indian	indian	PROPN
ejpam-4641	382	6	journal	journal	PROPN
ejpam-4641	382	7	of	of	ADP
ejpam-4641	382	8	statistics	statistic	NOUN
ejpam-4641	382	9	,	,	PUNCT
ejpam-4641	382	10	82(1):50–67	82(1):50–67	NUM
ejpam-4641	382	11	,	,	PUNCT
ejpam-4641	382	12	2020	2020	NUM
ejpam-4641	382	13	.	.	PUNCT
ejpam-4641	383	1	[	[	X
ejpam-4641	383	2	13	13	NUM
ejpam-4641	383	3	]	]	PUNCT
ejpam-4641	383	4	r.	r.	PROPN
ejpam-4641	383	5	d.	d.	PROPN
ejpam-4641	383	6	gupta	gupta	PROPN
ejpam-4641	383	7	and	and	CCONJ
ejpam-4641	383	8	d.	d.	PROPN
ejpam-4641	383	9	kundu	kundu	PROPN
ejpam-4641	383	10	.	.	PUNCT
ejpam-4641	384	1	theory	theory	NOUN
ejpam-4641	384	2	and	and	CCONJ
ejpam-4641	384	3	methods	method	NOUN
ejpam-4641	384	4	:	:	PUNCT
ejpam-4641	384	5	generalized	generalize	VERB
ejpam-4641	384	6	exponential	exponential	ADJ
ejpam-4641	384	7	distributions	distribution	NOUN
ejpam-4641	384	8	.	.	PUNCT
ejpam-4641	385	1	australian	australian	ADJ
ejpam-4641	385	2	and	and	CCONJ
ejpam-4641	385	3	new	new	PROPN
ejpam-4641	385	4	zealand	zealand	PROPN
ejpam-4641	385	5	journal	journal	PROPN
ejpam-4641	385	6	of	of	ADP
ejpam-4641	385	7	statistics	statistic	NOUN
ejpam-4641	385	8	,	,	PUNCT
ejpam-4641	385	9	41(2):173–188	41(2):173–188	NOUN
ejpam-4641	385	10	,	,	PUNCT
ejpam-4641	385	11	1999	1999	NUM
ejpam-4641	385	12	.	.	PUNCT
ejpam-4641	386	1	[	[	X
ejpam-4641	386	2	14	14	NUM
ejpam-4641	386	3	]	]	X
ejpam-4641	386	4	r.	r.	PROPN
ejpam-4641	386	5	d.	d.	PROPN
ejpam-4641	386	6	gupta	gupta	PROPN
ejpam-4641	386	7	and	and	CCONJ
ejpam-4641	386	8	d.	d.	PROPN
ejpam-4641	386	9	kundu	kundu	PROPN
ejpam-4641	386	10	.	.	PUNCT
ejpam-4641	387	1	exponentiated	exponentiate	VERB
ejpam-4641	387	2	exponential	exponential	ADJ
ejpam-4641	387	3	family	family	NOUN
ejpam-4641	387	4	:	:	PUNCT
ejpam-4641	387	5	an	an	DET
ejpam-4641	387	6	alternative	alternative	NOUN
ejpam-4641	387	7	to	to	ADP
ejpam-4641	387	8	gamma	gamma	NOUN
ejpam-4641	387	9	and	and	CCONJ
ejpam-4641	387	10	weibull	weibull	PROPN
ejpam-4641	387	11	distributions	distribution	NOUN
ejpam-4641	387	12	.	.	PUNCT
ejpam-4641	388	1	biometrical	biometrical	ADJ
ejpam-4641	388	2	journal	journal	PROPN
ejpam-4641	388	3	:	:	PUNCT
ejpam-4641	388	4	journal	journal	PROPN
ejpam-4641	388	5	of	of	ADP
ejpam-4641	388	6	mathematical	mathematical	ADJ
ejpam-4641	388	7	methods	method	NOUN
ejpam-4641	388	8	in	in	ADP
ejpam-4641	388	9	biosciences	bioscience	NOUN
ejpam-4641	388	10	,	,	PUNCT
ejpam-4641	388	11	43(1):117–130	43(1):117–130	PROPN
ejpam-4641	388	12	,	,	PUNCT
ejpam-4641	388	13	2001	2001	NUM
ejpam-4641	388	14	.	.	PUNCT
ejpam-4641	389	1	[	[	X
ejpam-4641	389	2	15	15	NUM
ejpam-4641	389	3	]	]	X
ejpam-4641	389	4	r.	r.	PROPN
ejpam-4641	389	5	d.	d.	PROPN
ejpam-4641	389	6	gupta	gupta	PROPN
ejpam-4641	389	7	and	and	CCONJ
ejpam-4641	389	8	d.	d.	PROPN
ejpam-4641	389	9	kundu	kundu	PROPN
ejpam-4641	389	10	.	.	PUNCT
ejpam-4641	390	1	generalized	generalize	VERB
ejpam-4641	390	2	exponential	exponential	ADJ
ejpam-4641	390	3	distribution	distribution	NOUN
ejpam-4641	390	4	:	:	PUNCT
ejpam-4641	390	5	different	different	ADJ
ejpam-4641	390	6	method	method	NOUN
ejpam-4641	390	7	of	of	ADP
ejpam-4641	390	8	estimations	estimation	NOUN
ejpam-4641	390	9	.	.	PUNCT
ejpam-4641	391	1	journal	journal	NOUN
ejpam-4641	391	2	of	of	ADP
ejpam-4641	391	3	statistical	statistical	ADJ
ejpam-4641	391	4	computation	computation	NOUN
ejpam-4641	391	5	and	and	CCONJ
ejpam-4641	391	6	simulation	simulation	NOUN
ejpam-4641	391	7	,	,	PUNCT
ejpam-4641	391	8	69(4):315–337	69(4):315–337	PROPN
ejpam-4641	391	9	,	,	PUNCT
ejpam-4641	391	10	2001	2001	NUM
ejpam-4641	391	11	.	.	PUNCT
ejpam-4641	392	1	[	[	X
ejpam-4641	392	2	16	16	NUM
ejpam-4641	392	3	]	]	X
ejpam-4641	392	4	r.	r.	PROPN
ejpam-4641	392	5	l.	l.	PROPN
ejpam-4641	392	6	houchens	houchens	PROPN
ejpam-4641	392	7	.	.	PUNCT
ejpam-4641	392	8	record	record	NOUN
ejpam-4641	392	9	value	value	NOUN
ejpam-4641	392	10	theory	theory	NOUN
ejpam-4641	392	11	and	and	CCONJ
ejpam-4641	392	12	inference	inference	NOUN
ejpam-4641	392	13	.	.	PUNCT
ejpam-4641	393	1	phd	phd	NOUN
ejpam-4641	393	2	thesis	thesis	PROPN
ejpam-4641	393	3	,	,	PUNCT
ejpam-4641	393	4	university	university	PROPN
ejpam-4641	393	5	of	of	ADP
ejpam-4641	393	6	california	california	PROPN
ejpam-4641	393	7	,	,	PUNCT
ejpam-4641	393	8	riverside	riverside	PROPN
ejpam-4641	393	9	,	,	PUNCT
ejpam-4641	393	10	1984	1984	NUM
ejpam-4641	393	11	.	.	PUNCT
ejpam-4641	394	1	[	[	X
ejpam-4641	394	2	17	17	NUM
ejpam-4641	394	3	]	]	X
ejpam-4641	394	4	i.	i.	PROPN
ejpam-4641	394	5	a.	a.	PROPN
ejpam-4641	394	6	husseiny	husseiny	PROPN
ejpam-4641	394	7	,	,	PUNCT
ejpam-4641	394	8	h.	h.	PROPN
ejpam-4641	394	9	m.	m.	PROPN
ejpam-4641	394	10	barakat	barakat	PROPN
ejpam-4641	394	11	,	,	PUNCT
ejpam-4641	394	12	g.	g.	PROPN
ejpam-4641	394	13	m.	m.	PROPN
ejpam-4641	394	14	mansour	mansour	PROPN
ejpam-4641	394	15	,	,	PUNCT
ejpam-4641	394	16	and	and	CCONJ
ejpam-4641	394	17	m.	m.	NOUN
ejpam-4641	394	18	a.	a.	PROPN
ejpam-4641	394	19	alawady	alawady	PROPN
ejpam-4641	394	20	.	.	PUNCT
ejpam-4641	395	1	information	information	NOUN
ejpam-4641	395	2	measures	measure	NOUN
ejpam-4641	395	3	in	in	ADP
ejpam-4641	395	4	records	record	NOUN
ejpam-4641	395	5	and	and	CCONJ
ejpam-4641	395	6	their	their	PRON
ejpam-4641	395	7	concomitants	concomitant	NOUN
ejpam-4641	395	8	arising	arise	VERB
ejpam-4641	395	9	from	from	ADP
ejpam-4641	395	10	sarmanov	sarmanov	NOUN
ejpam-4641	395	11	family	family	NOUN
ejpam-4641	395	12	of	of	ADP
ejpam-4641	395	13	bivariate	bivariate	ADJ
ejpam-4641	395	14	distributions	distribution	NOUN
ejpam-4641	395	15	.	.	PUNCT
ejpam-4641	396	1	journal	journal	NOUN
ejpam-4641	396	2	of	of	ADP
ejpam-4641	396	3	computational	computational	ADJ
ejpam-4641	396	4	and	and	CCONJ
ejpam-4641	396	5	applied	applied	ADJ
ejpam-4641	396	6	mathematics	mathematic	NOUN
ejpam-4641	396	7	,	,	PUNCT
ejpam-4641	396	8	408:114–120	408:114–120	NUM
ejpam-4641	396	9	,	,	PUNCT
ejpam-4641	396	10	2022	2022	NUM
ejpam-4641	396	11	.	.	PUNCT
ejpam-4641	397	1	[	[	X
ejpam-4641	397	2	18	18	NUM
ejpam-4641	397	3	]	]	PUNCT
ejpam-4641	397	4	k.	k.	PROPN
ejpam-4641	397	5	pearson	pearson	PROPN
ejpam-4641	397	6	.	.	PUNCT
ejpam-4641	398	1	tables	table	NOUN
ejpam-4641	398	2	of	of	ADP
ejpam-4641	398	3	the	the	DET
ejpam-4641	398	4	incomplete	incomplete	ADJ
ejpam-4641	398	5	beta	beta	NOUN
ejpam-4641	398	6	function	function	NOUN
ejpam-4641	398	7	.	.	PUNCT
ejpam-4641	399	1	cambridge	cambridge	PROPN
ejpam-4641	399	2	university	university	PROPN
ejpam-4641	399	3	press	press	PROPN
ejpam-4641	399	4	,	,	PUNCT
ejpam-4641	399	5	london	london	PROPN
ejpam-4641	399	6	,	,	PUNCT
ejpam-4641	399	7	1968	1968	NUM
ejpam-4641	399	8	.	.	PUNCT
ejpam-4641	400	1	[	[	X
ejpam-4641	400	2	19	19	NUM
ejpam-4641	400	3	]	]	PUNCT
ejpam-4641	400	4	m.	m.	NOUN
ejpam-4641	400	5	z.	z.	PROPN
ejpam-4641	400	6	raqab	raqab	PROPN
ejpam-4641	400	7	.	.	PUNCT
ejpam-4641	401	1	generalized	generalize	VERB
ejpam-4641	401	2	exponential	exponential	ADJ
ejpam-4641	401	3	distribution	distribution	NOUN
ejpam-4641	401	4	:	:	PUNCT
ejpam-4641	401	5	moments	moment	NOUN
ejpam-4641	401	6	of	of	ADP
ejpam-4641	401	7	order	order	NOUN
ejpam-4641	401	8	statistics	statistic	NOUN
ejpam-4641	401	9	.	.	PUNCT
ejpam-4641	402	1	statistics	statistic	NOUN
ejpam-4641	402	2	,	,	PUNCT
ejpam-4641	402	3	38(1):29–41	38(1):29–41	NUM
ejpam-4641	402	4	,	,	PUNCT
ejpam-4641	402	5	2004	2004	NUM
ejpam-4641	402	6	.	.	PUNCT
ejpam-4641	403	1	[	[	X
ejpam-4641	403	2	20	20	NUM
ejpam-4641	403	3	]	]	PUNCT
ejpam-4641	403	4	m.	m.	NOUN
ejpam-4641	403	5	z.	z.	PROPN
ejpam-4641	403	6	raqab	raqab	PROPN
ejpam-4641	403	7	.	.	PUNCT
ejpam-4641	404	1	bounds	bound	NOUN
ejpam-4641	404	2	on	on	ADP
ejpam-4641	404	3	expectations	expectation	NOUN
ejpam-4641	404	4	of	of	ADP
ejpam-4641	404	5	record	record	NOUN
ejpam-4641	404	6	range	range	NOUN
ejpam-4641	404	7	and	and	CCONJ
ejpam-4641	404	8	record	record	NOUN
ejpam-4641	404	9	increment	increment	NOUN
ejpam-4641	404	10	from	from	ADP
ejpam-4641	404	11	distributions	distribution	NOUN
ejpam-4641	404	12	with	with	ADP
ejpam-4641	404	13	bounded	bounded	ADJ
ejpam-4641	404	14	support	support	NOUN
ejpam-4641	404	15	.	.	PUNCT
ejpam-4641	405	1	j	j	PROPN
ejpam-4641	405	2	inequalities	inequalitie	VERB
ejpam-4641	405	3	pure	pure	ADJ
ejpam-4641	405	4	appl	appl	PROPN
ejpam-4641	405	5	math	math	NOUN
ejpam-4641	405	6	,	,	PUNCT
ejpam-4641	405	7	8(1	8(1	NOUN
ejpam-4641	405	8	)	)	PUNCT
ejpam-4641	405	9	,	,	PUNCT
ejpam-4641	405	10	2007	2007	NUM
ejpam-4641	405	11	.	.	PUNCT