id	sid	tid	token	lemma	pos
ejpam-5823	1	1	european	european	PROPN
ejpam-5823	1	2	journal	journal	PROPN
ejpam-5823	1	3	of	of	ADP
ejpam-5823	1	4	pure	pure	ADJ
ejpam-5823	1	5	and	and	CCONJ
ejpam-5823	1	6	applied	applied	ADJ
ejpam-5823	1	7	mathematics	mathematic	NOUN
ejpam-5823	1	8	2025	2025	NUM
ejpam-5823	1	9	,	,	PUNCT
ejpam-5823	1	10	vol	vol	NOUN
ejpam-5823	1	11	.	.	PROPN
ejpam-5823	1	12	18	18	NUM
ejpam-5823	1	13	,	,	PUNCT
ejpam-5823	1	14	issue	issue	NOUN
ejpam-5823	1	15	2	2	NUM
ejpam-5823	1	16	,	,	PUNCT
ejpam-5823	1	17	article	article	NOUN
ejpam-5823	1	18	number	number	NOUN
ejpam-5823	1	19	5823	5823	NUM
ejpam-5823	1	20	issn	issn	PROPN
ejpam-5823	1	21	1307	1307	NUM
ejpam-5823	1	22	-	-	SYM
ejpam-5823	1	23	5543	5543	NUM
ejpam-5823	1	24	–	–	PUNCT
ejpam-5823	1	25	ejpam.com	ejpam.com	X
ejpam-5823	1	26	published	publish	VERB
ejpam-5823	1	27	by	by	ADP
ejpam-5823	1	28	new	new	PROPN
ejpam-5823	1	29	york	york	PROPN
ejpam-5823	1	30	business	business	PROPN
ejpam-5823	1	31	global	global	ADJ
ejpam-5823	1	32	dual	dual	ADJ
ejpam-5823	1	33	approach	approach	NOUN
ejpam-5823	1	34	to	to	ADP
ejpam-5823	1	35	the	the	DET
ejpam-5823	1	36	generalization	generalization	NOUN
ejpam-5823	1	37	of	of	ADP
ejpam-5823	1	38	extended	extended	ADJ
ejpam-5823	1	39	bessel	bessel	NOUN
ejpam-5823	1	40	function	function	NOUN
ejpam-5823	1	41	syed	syed	PROPN
ejpam-5823	1	42	ali	ali	PROPN
ejpam-5823	1	43	haider	haider	PROPN
ejpam-5823	1	44	shah1	shah1	PROPN
ejpam-5823	1	45	,	,	PUNCT
ejpam-5823	1	46	hafsa1	hafsa1	PROPN
ejpam-5823	1	47	,	,	PUNCT
ejpam-5823	1	48	ahmad	ahmad	PROPN
ejpam-5823	1	49	alooaily2	alooaily2	NOUN
ejpam-5823	1	50	,	,	PUNCT
ejpam-5823	1	51	gauhar	gauhar	PROPN
ejpam-5823	1	52	rahman3,∗	rahman3,∗	PROPN
ejpam-5823	1	53	,	,	PUNCT
ejpam-5823	1	54	yasser	yasser	PROPN
ejpam-5823	1	55	elmasry4	elmasry4	PROPN
ejpam-5823	1	56	,	,	PUNCT
ejpam-5823	1	57	salma	salma	PROPN
ejpam-5823	1	58	haque2	haque2	PROPN
ejpam-5823	1	59	,	,	PUNCT
ejpam-5823	1	60	nabil	nabil	NOUN
ejpam-5823	1	61	mlaiki2	mlaiki2	PROPN
ejpam-5823	1	62	1	1	NUM
ejpam-5823	1	63	department	department	NOUN
ejpam-5823	1	64	of	of	ADP
ejpam-5823	1	65	mathematics	mathematics	PROPN
ejpam-5823	1	66	,	,	PUNCT
ejpam-5823	1	67	university	university	PROPN
ejpam-5823	1	68	of	of	ADP
ejpam-5823	1	69	sargodha	sargodha	PROPN
ejpam-5823	1	70	,	,	PUNCT
ejpam-5823	1	71	sargodha	sargodha	PROPN
ejpam-5823	1	72	,	,	PUNCT
ejpam-5823	1	73	pakistan	pakistan	PROPN
ejpam-5823	1	74	2	2	NUM
ejpam-5823	1	75	department	department	NOUN
ejpam-5823	1	76	of	of	ADP
ejpam-5823	1	77	mathematics	mathematic	NOUN
ejpam-5823	1	78	and	and	CCONJ
ejpam-5823	1	79	sciences	science	NOUN
ejpam-5823	1	80	,	,	PUNCT
ejpam-5823	1	81	prince	prince	PROPN
ejpam-5823	1	82	sultan	sultan	PROPN
ejpam-5823	1	83	university	university	PROPN
ejpam-5823	1	84	.	.	PUNCT
ejpam-5823	2	1	riyadh	riyadh	PROPN
ejpam-5823	2	2	,	,	PUNCT
ejpam-5823	2	3	11586	11586	NUM
ejpam-5823	2	4	saudi	saudi	PROPN
ejpam-5823	2	5	arabia	arabia	PROPN
ejpam-5823	2	6	3	3	NUM
ejpam-5823	2	7	department	department	NOUN
ejpam-5823	2	8	of	of	ADP
ejpam-5823	2	9	mathematics	mathematic	NOUN
ejpam-5823	2	10	and	and	CCONJ
ejpam-5823	2	11	statistics	statistic	NOUN
ejpam-5823	2	12	,	,	PUNCT
ejpam-5823	2	13	hazara	hazara	PROPN
ejpam-5823	2	14	university	university	PROPN
ejpam-5823	2	15	,	,	PUNCT
ejpam-5823	2	16	mansehra	mansehra	ADJ
ejpam-5823	2	17	,	,	PUNCT
ejpam-5823	2	18	pakistan	pakistan	PROPN
ejpam-5823	2	19	4	4	NUM
ejpam-5823	2	20	department	department	NOUN
ejpam-5823	2	21	of	of	ADP
ejpam-5823	2	22	mathematicsfaculty	mathematicsfaculty	NOUN
ejpam-5823	2	23	of	of	ADP
ejpam-5823	2	24	scienceking	scienceke	VERB
ejpam-5823	2	25	khalid	khalid	PROPN
ejpam-5823	2	26	university	university	PROPN
ejpam-5823	2	27	,	,	PUNCT
ejpam-5823	2	28	p.o	p.o	PROPN
ejpam-5823	2	29	.	.	PROPN
ejpam-5823	2	30	box	box	PROPN
ejpam-5823	2	31	9004	9004	NUM
ejpam-5823	2	32	,	,	PUNCT
ejpam-5823	2	33	abha	abha	NOUN
ejpam-5823	2	34	61466	61466	NUM
ejpam-5823	2	35	,	,	PUNCT
ejpam-5823	2	36	saudi	saudi	PROPN
ejpam-5823	2	37	arabia	arabia	PROPN
ejpam-5823	2	38	.	.	PUNCT
ejpam-5823	3	1	abstract	abstract	ADJ
ejpam-5823	3	2	.	.	PUNCT
ejpam-5823	4	1	in	in	ADP
ejpam-5823	4	2	this	this	DET
ejpam-5823	4	3	paper	paper	NOUN
ejpam-5823	4	4	,	,	PUNCT
ejpam-5823	4	5	we	we	PRON
ejpam-5823	4	6	will	will	AUX
ejpam-5823	4	7	discuss	discuss	VERB
ejpam-5823	4	8	the	the	DET
ejpam-5823	4	9	geometrical	geometrical	ADJ
ejpam-5823	4	10	interpretation	interpretation	NOUN
ejpam-5823	4	11	of	of	ADP
ejpam-5823	4	12	generalized	generalized	ADJ
ejpam-5823	4	13	bessel	bessel	NOUN
ejpam-5823	4	14	function	function	NOUN
ejpam-5823	4	15	,	,	PUNCT
ejpam-5823	4	16	which	which	PRON
ejpam-5823	4	17	is	be	AUX
ejpam-5823	4	18	defined	define	VERB
ejpam-5823	4	19	as	as	ADP
ejpam-5823	4	20	:	:	PUNCT
ejpam-5823	4	21	khξ	khξ	NOUN
ejpam-5823	4	22	,	,	PUNCT
ejpam-5823	4	23	b(z	b(z	NOUN
ejpam-5823	4	24	)	)	PUNCT
ejpam-5823	4	25	=	=	SYM
ejpam-5823	4	26	z	z	NOUN
ejpam-5823	4	27	.	.	PUNCT
ejpam-5823	5	1	khξ	khξ	NOUN
ejpam-5823	5	2	,	,	PUNCT
ejpam-5823	5	3	b(z	b(z	NOUN
ejpam-5823	5	4	)	)	PUNCT
ejpam-5823	5	5	=	=	SYM
ejpam-5823	6	1	z	z	NOUN
ejpam-5823	6	2	+	+	NOUN
ejpam-5823	6	3	∞∑	∞∑	NUM
ejpam-5823	6	4	r=1	r=1	NOUN
ejpam-5823	6	5	(	(	PUNCT
ejpam-5823	6	6	−b)r	−b)r	NOUN
ejpam-5823	6	7	zr+1	zr+1	NUM
ejpam-5823	7	1	r	r	NOUN
ejpam-5823	7	2	!	!	NOUN
ejpam-5823	7	3	4r	4r	PROPN
ejpam-5823	7	4	kr	kr	PROPN
ejpam-5823	7	5	(	(	PUNCT
ejpam-5823	7	6	ξ)r	ξ)r	NOUN
ejpam-5823	7	7	,	,	PUNCT
ejpam-5823	7	8	k	k	X
ejpam-5823	7	9	where	where	SCONJ
ejpam-5823	7	10	ξ	ξ	X
ejpam-5823	7	11	=	=	SYM
ejpam-5823	7	12	v	v	PROPN
ejpam-5823	7	13	+	+	CCONJ
ejpam-5823	7	14	k	k	PROPN
ejpam-5823	7	15	∈	∈	PROPN
ejpam-5823	7	16	(	(	PUNCT
ejpam-5823	7	17	0,+∞	0,+∞	NUM
ejpam-5823	7	18	)	)	PUNCT
ejpam-5823	7	19	,	,	PUNCT
ejpam-5823	7	20	k	k	PROPN
ejpam-5823	7	21	∈	∈	PROPN
ejpam-5823	7	22	r+	r+	ADV
ejpam-5823	7	23	,	,	PUNCT
ejpam-5823	7	24	v	v	X
ejpam-5823	7	25	>	>	X
ejpam-5823	7	26	−k	−k	PROPN
ejpam-5823	7	27	,	,	PUNCT
ejpam-5823	7	28	b	b	PROPN
ejpam-5823	7	29	∈	∈	PROPN
ejpam-5823	7	30	r.	r.	NOUN
ejpam-5823	7	31	the	the	DET
ejpam-5823	7	32	generalization	generalization	NOUN
ejpam-5823	7	33	of	of	ADP
ejpam-5823	7	34	pochammer	pochammer	NOUN
ejpam-5823	7	35	’s	’s	PART
ejpam-5823	7	36	symbol	symbol	NOUN
ejpam-5823	7	37	in	in	ADP
ejpam-5823	7	38	the	the	DET
ejpam-5823	7	39	form	form	NOUN
ejpam-5823	7	40	of	of	ADP
ejpam-5823	7	41	inequality	inequality	NOUN
ejpam-5823	7	42	:	:	PUNCT
ejpam-5823	7	43	(	(	PUNCT
ejpam-5823	7	44	q)r	q)r	X
ejpam-5823	7	45	,	,	PUNCT
ejpam-5823	7	46	k	k	PROPN
ejpam-5823	7	47	>	>	X
ejpam-5823	7	48	q(q	q(q	PROPN
ejpam-5823	7	49	+	+	CCONJ
ejpam-5823	7	50	β)r−1	β)r−1	PROPN
ejpam-5823	7	51	for	for	ADP
ejpam-5823	7	52	q	q	PROPN
ejpam-5823	7	53	>	>	X
ejpam-5823	7	54	0	0	PROPN
ejpam-5823	7	55	,	,	PUNCT
ejpam-5823	7	56	k	k	PROPN
ejpam-5823	7	57	∈	∈	PROPN
ejpam-5823	7	58	r+	r+	NOUN
ejpam-5823	7	59	,	,	PUNCT
ejpam-5823	7	60	0	0	NUM
ejpam-5823	7	61	≤	≤	NUM
ejpam-5823	7	62	β	β	X
ejpam-5823	7	63	≤	≤	ADJ
ejpam-5823	8	1	β0	β0	PROPN
ejpam-5823	8	2	=	=	NOUN
ejpam-5823	8	3	√	√	NUM
ejpam-5823	8	4	2	2	NUM
ejpam-5823	8	5	≃	≃	VERB
ejpam-5823	8	6	1.4142	1.4142	NUM
ejpam-5823	8	7	...	...	PUNCT
ejpam-5823	8	8	,	,	PUNCT
ejpam-5823	8	9	r	r	NOUN
ejpam-5823	8	10	∈	∈	PROPN
ejpam-5823	8	11	n\{1	n\{1	NOUN
ejpam-5823	8	12	,	,	PUNCT
ejpam-5823	8	13	2	2	NUM
ejpam-5823	8	14	}	}	PUNCT
ejpam-5823	8	15	,	,	PUNCT
ejpam-5823	8	16	which	which	PRON
ejpam-5823	8	17	is	be	AUX
ejpam-5823	8	18	proved	prove	VERB
ejpam-5823	8	19	by	by	ADP
ejpam-5823	8	20	using	use	VERB
ejpam-5823	8	21	the	the	DET
ejpam-5823	8	22	generalization	generalization	NOUN
ejpam-5823	8	23	of	of	ADP
ejpam-5823	8	24	lemma	lemma	PROPN
ejpam-5823	9	1	[	[	X
ejpam-5823	9	2	1	1	NUM
ejpam-5823	9	3	]	]	PUNCT
ejpam-5823	9	4	.	.	PUNCT
ejpam-5823	10	1	this	this	PRON
ejpam-5823	10	2	has	have	AUX
ejpam-5823	10	3	been	be	AUX
ejpam-5823	10	4	proved	prove	VERB
ejpam-5823	10	5	by	by	ADP
ejpam-5823	10	6	many	many	ADJ
ejpam-5823	10	7	authors	author	NOUN
ejpam-5823	10	8	by	by	ADP
ejpam-5823	10	9	using	use	VERB
ejpam-5823	10	10	different	different	ADJ
ejpam-5823	10	11	methods	method	NOUN
ejpam-5823	10	12	.	.	PUNCT
ejpam-5823	11	1	using	use	VERB
ejpam-5823	11	2	this	this	DET
ejpam-5823	11	3	inequality	inequality	NOUN
ejpam-5823	11	4	to	to	PART
ejpam-5823	11	5	analyse	analyse	VERB
ejpam-5823	11	6	the	the	DET
ejpam-5823	11	7	order	order	NOUN
ejpam-5823	11	8	of	of	ADP
ejpam-5823	11	9	starlikeness	starlikeness	NOUN
ejpam-5823	11	10	and	and	CCONJ
ejpam-5823	11	11	convexity	convexity	NOUN
ejpam-5823	11	12	.	.	PUNCT
ejpam-5823	12	1	we	we	PRON
ejpam-5823	12	2	will	will	AUX
ejpam-5823	12	3	prove	prove	VERB
ejpam-5823	12	4	this	this	DET
ejpam-5823	12	5	lemma	lemma	PROPN
ejpam-5823	12	6	by	by	ADP
ejpam-5823	12	7	the	the	DET
ejpam-5823	12	8	same	same	ADJ
ejpam-5823	12	9	technique	technique	NOUN
ejpam-5823	12	10	used	use	VERB
ejpam-5823	12	11	by	by	ADP
ejpam-5823	12	12	zayed	zayed	ADJ
ejpam-5823	12	13	and	and	CCONJ
ejpam-5823	12	14	bulboaca	bulboaca	ADJ
ejpam-5823	12	15	(	(	PUNCT
ejpam-5823	12	16	partial	partial	ADJ
ejpam-5823	12	17	derivative	derivative	ADJ
ejpam-5823	12	18	and	and	CCONJ
ejpam-5823	12	19	two	two	NUM
ejpam-5823	12	20	-	-	PUNCT
ejpam-5823	12	21	variable	variable	ADJ
ejpam-5823	12	22	extremum	extremum	ADJ
ejpam-5823	12	23	technique	technique	NOUN
ejpam-5823	12	24	)	)	PUNCT
ejpam-5823	12	25	.	.	PUNCT
ejpam-5823	13	1	we	we	PRON
ejpam-5823	13	2	will	will	AUX
ejpam-5823	13	3	give	give	VERB
ejpam-5823	13	4	the	the	DET
ejpam-5823	13	5	geometrical	geometrical	ADJ
ejpam-5823	13	6	interpretation	interpretation	NOUN
ejpam-5823	13	7	of	of	ADP
ejpam-5823	13	8	generalized	generalized	ADJ
ejpam-5823	13	9	bessel	bessel	NOUN
ejpam-5823	13	10	k	k	NOUN
ejpam-5823	13	11	-	-	NOUN
ejpam-5823	13	12	function	function	NOUN
ejpam-5823	13	13	for	for	ADP
ejpam-5823	13	14	different	different	ADJ
ejpam-5823	13	15	values	value	NOUN
ejpam-5823	13	16	of	of	ADP
ejpam-5823	13	17	k.	k.	NOUN
ejpam-5823	13	18	providing	provide	VERB
ejpam-5823	13	19	some	some	DET
ejpam-5823	13	20	examples	example	NOUN
ejpam-5823	13	21	for	for	ADP
ejpam-5823	13	22	better	well	ADJ
ejpam-5823	13	23	understanding	understanding	NOUN
ejpam-5823	13	24	of	of	ADP
ejpam-5823	13	25	the	the	DET
ejpam-5823	13	26	reader	reader	NOUN
ejpam-5823	13	27	regarding	regard	VERB
ejpam-5823	13	28	our	our	PRON
ejpam-5823	13	29	approach	approach	NOUN
ejpam-5823	13	30	.	.	PUNCT
ejpam-5823	14	1	2020	2020	NUM
ejpam-5823	14	2	mathematics	mathematic	NOUN
ejpam-5823	14	3	subject	subject	NOUN
ejpam-5823	14	4	classifications	classification	NOUN
ejpam-5823	14	5	:	:	PUNCT
ejpam-5823	14	6	30c45	30c45	NUM
ejpam-5823	14	7	,	,	PUNCT
ejpam-5823	14	8	33c10	33c10	NUM
ejpam-5823	14	9	,	,	PUNCT
ejpam-5823	14	10	33b15	33b15	NUM
ejpam-5823	14	11	key	key	ADJ
ejpam-5823	14	12	words	word	NOUN
ejpam-5823	14	13	and	and	CCONJ
ejpam-5823	14	14	phrases	phrase	NOUN
ejpam-5823	14	15	:	:	PUNCT
ejpam-5823	14	16	univalent	univalent	ADJ
ejpam-5823	14	17	,	,	PUNCT
ejpam-5823	14	18	starlikeness	starlikeness	NOUN
ejpam-5823	14	19	,	,	PUNCT
ejpam-5823	14	20	convexity	convexity	NOUN
ejpam-5823	14	21	,	,	PUNCT
ejpam-5823	14	22	pochammer	pochammer	NOUN
ejpam-5823	14	23	,	,	PUNCT
ejpam-5823	14	24	gamma	gamma	NOUN
ejpam-5823	14	25	function	function	PROPN
ejpam-5823	14	26	,	,	PUNCT
ejpam-5823	14	27	generalized	generalized	ADJ
ejpam-5823	14	28	bessel	bessel	NOUN
ejpam-5823	14	29	function	function	NOUN
ejpam-5823	14	30	∗corresponding	∗corresponde	VERB
ejpam-5823	14	31	author	author	NOUN
ejpam-5823	14	32	.	.	PUNCT
ejpam-5823	15	1	doi	doi	NOUN
ejpam-5823	15	2	:	:	PUNCT
ejpam-5823	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5823	https://doi.org/10.29020/nybg.ejpam.v18i2.5823	ADJ
ejpam-5823	15	4	email	email	NOUN
ejpam-5823	15	5	addresses	address	VERB
ejpam-5823	15	6	:	:	PUNCT
ejpam-5823	16	1	ali.bukhari78699@gmail.com	ali.bukhari78699@gmail.com	PROPN
ejpam-5823	16	2	(	(	PUNCT
ejpam-5823	16	3	s.	s.	PROPN
ejpam-5823	16	4	a.	a.	PROPN
ejpam-5823	16	5	h.	h.	PROPN
ejpam-5823	16	6	shah	shah	PROPN
ejpam-5823	16	7	)	)	PUNCT
ejpam-5823	16	8	,	,	PUNCT
ejpam-5823	16	9	hafsarehman3830@gmail.com	hafsarehman3830@gmail.com	X
ejpam-5823	16	10	(	(	PUNCT
ejpam-5823	16	11	hafsa	hafsa	PROPN
ejpam-5823	16	12	)	)	PUNCT
ejpam-5823	16	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5823	17	1	1	1	NUM
ejpam-5823	17	2	copyright	copyright	NOUN
ejpam-5823	17	3	:	:	PUNCT
ejpam-5823	17	4	©	©	PROPN
ejpam-5823	17	5	2025	2025	NUM
ejpam-5823	17	6	the	the	DET
ejpam-5823	17	7	author(s	author(s	NOUN
ejpam-5823	17	8	)	)	PUNCT
ejpam-5823	17	9	.	.	PUNCT
ejpam-5823	18	1	(	(	PUNCT
ejpam-5823	18	2	cc	cc	NOUN
ejpam-5823	18	3	by	by	ADP
ejpam-5823	18	4	-	-	PUNCT
ejpam-5823	18	5	nc	nc	PROPN
ejpam-5823	18	6	4.0	4.0	NUM
ejpam-5823	18	7	)	)	PUNCT
ejpam-5823	18	8	s.	s.	PROPN
ejpam-5823	18	9	a.	a.	PROPN
ejpam-5823	18	10	h.	h.	PROPN
ejpam-5823	18	11	shah	shah	PROPN
ejpam-5823	18	12	et	et	PROPN
ejpam-5823	18	13	al	al	PROPN
ejpam-5823	18	14	.	.	PUNCT
ejpam-5823	18	15	/	/	SYM
ejpam-5823	18	16	eur	eur	PROPN
ejpam-5823	18	17	.	.	PUNCT
ejpam-5823	19	1	j.	j.	PROPN
ejpam-5823	19	2	pure	pure	PROPN
ejpam-5823	19	3	appl	appl	PROPN
ejpam-5823	19	4	.	.	PROPN
ejpam-5823	19	5	math	math	PROPN
ejpam-5823	19	6	,	,	PUNCT
ejpam-5823	19	7	18	18	NUM
ejpam-5823	19	8	(	(	PUNCT
ejpam-5823	19	9	2	2	NUM
ejpam-5823	19	10	)	)	PUNCT
ejpam-5823	19	11	(	(	PUNCT
ejpam-5823	19	12	2025	2025	NUM
ejpam-5823	19	13	)	)	PUNCT
ejpam-5823	19	14	,	,	PUNCT
ejpam-5823	19	15	5823	5823	NUM
ejpam-5823	19	16	2	2	NUM
ejpam-5823	19	17	of	of	ADP
ejpam-5823	19	18	26	26	NUM
ejpam-5823	19	19	1	1	NUM
ejpam-5823	19	20	.	.	PUNCT
ejpam-5823	20	1	introduction	introduction	NOUN
ejpam-5823	20	2	mathematical	mathematical	ADJ
ejpam-5823	20	3	functions	function	NOUN
ejpam-5823	20	4	that	that	PRON
ejpam-5823	20	5	we	we	PRON
ejpam-5823	20	6	call	call	VERB
ejpam-5823	20	7	special	special	ADJ
ejpam-5823	20	8	functions	function	NOUN
ejpam-5823	20	9	are	be	AUX
ejpam-5823	20	10	very	very	ADV
ejpam-5823	20	11	important	important	ADJ
ejpam-5823	20	12	in	in	ADP
ejpam-5823	20	13	different	different	ADJ
ejpam-5823	20	14	fields	field	NOUN
ejpam-5823	20	15	like	like	ADP
ejpam-5823	20	16	applied	apply	VERB
ejpam-5823	20	17	mathematics	mathematic	NOUN
ejpam-5823	20	18	,	,	PUNCT
ejpam-5823	20	19	physics	physics	NOUN
ejpam-5823	20	20	,	,	PUNCT
ejpam-5823	20	21	economics	economic	NOUN
ejpam-5823	20	22	,	,	PUNCT
ejpam-5823	20	23	engineering	engineering	NOUN
ejpam-5823	20	24	,	,	PUNCT
ejpam-5823	20	25	statistics	statistic	NOUN
ejpam-5823	20	26	etc	etc	X
ejpam-5823	20	27	.	.	X
ejpam-5823	21	1	its	its	PRON
ejpam-5823	21	2	a	a	DET
ejpam-5823	21	3	fact	fact	NOUN
ejpam-5823	21	4	that	that	SCONJ
ejpam-5823	21	5	special	special	ADJ
ejpam-5823	21	6	functions	function	NOUN
ejpam-5823	21	7	have	have	AUX
ejpam-5823	21	8	an	an	DET
ejpam-5823	21	9	imperative	imperative	ADJ
ejpam-5823	21	10	space	space	NOUN
ejpam-5823	21	11	in	in	ADP
ejpam-5823	21	12	the	the	DET
ejpam-5823	21	13	solution	solution	NOUN
ejpam-5823	21	14	of	of	ADP
ejpam-5823	21	15	many	many	ADJ
ejpam-5823	21	16	problems	problem	NOUN
ejpam-5823	21	17	.	.	PUNCT
ejpam-5823	22	1	due	due	ADP
ejpam-5823	22	2	to	to	ADP
ejpam-5823	22	3	the	the	DET
ejpam-5823	22	4	unique	unique	ADJ
ejpam-5823	22	5	properties	property	NOUN
ejpam-5823	22	6	of	of	ADP
ejpam-5823	22	7	special	special	ADJ
ejpam-5823	22	8	functions	function	NOUN
ejpam-5823	22	9	,	,	PUNCT
ejpam-5823	22	10	these	these	DET
ejpam-5823	22	11	functions	function	NOUN
ejpam-5823	22	12	play	play	VERB
ejpam-5823	22	13	crucial	crucial	ADJ
ejpam-5823	22	14	role	role	NOUN
ejpam-5823	22	15	in	in	ADP
ejpam-5823	22	16	solving	solve	VERB
ejpam-5823	22	17	differential	differential	ADJ
ejpam-5823	22	18	equations	equation	NOUN
ejpam-5823	22	19	used	use	VERB
ejpam-5823	22	20	as	as	ADP
ejpam-5823	22	21	mathematical	mathematical	ADJ
ejpam-5823	22	22	models	model	NOUN
ejpam-5823	22	23	in	in	ADP
ejpam-5823	22	24	different	different	ADJ
ejpam-5823	22	25	fields	field	NOUN
ejpam-5823	22	26	.	.	PUNCT
ejpam-5823	23	1	it	it	PRON
ejpam-5823	23	2	is	be	AUX
ejpam-5823	23	3	linked	link	VERB
ejpam-5823	23	4	strongly	strongly	ADV
ejpam-5823	23	5	with	with	ADP
ejpam-5823	23	6	analytic	analytic	ADJ
ejpam-5823	23	7	functions	function	NOUN
ejpam-5823	23	8	series	series	NOUN
ejpam-5823	23	9	expansion	expansion	NOUN
ejpam-5823	23	10	for	for	ADP
ejpam-5823	23	11	real	real	ADJ
ejpam-5823	23	12	and	and	CCONJ
ejpam-5823	23	13	complex	complex	ADJ
ejpam-5823	23	14	variables	variable	NOUN
ejpam-5823	23	15	.	.	PUNCT
ejpam-5823	24	1	lots	lot	NOUN
ejpam-5823	24	2	of	of	ADP
ejpam-5823	24	3	work	work	NOUN
ejpam-5823	24	4	has	have	AUX
ejpam-5823	24	5	been	be	AUX
ejpam-5823	24	6	done	do	VERB
ejpam-5823	24	7	in	in	ADP
ejpam-5823	24	8	this	this	DET
ejpam-5823	24	9	field	field	NOUN
ejpam-5823	24	10	of	of	ADP
ejpam-5823	24	11	mathematics	mathematic	NOUN
ejpam-5823	24	12	such	such	ADJ
ejpam-5823	24	13	as	as	ADP
ejpam-5823	24	14	gamma	gamma	NOUN
ejpam-5823	24	15	functions	function	NOUN
ejpam-5823	24	16	,	,	PUNCT
ejpam-5823	24	17	pochammer	pochammer	NOUN
ejpam-5823	24	18	,	,	PUNCT
ejpam-5823	24	19	bessel	bessel	NOUN
ejpam-5823	24	20	functions	function	NOUN
ejpam-5823	24	21	,	,	PUNCT
ejpam-5823	24	22	hypergeometric	hypergeometric	ADJ
ejpam-5823	24	23	functions	function	NOUN
ejpam-5823	24	24	,	,	PUNCT
ejpam-5823	24	25	zeta	zeta	PROPN
ejpam-5823	24	26	function	function	PROPN
ejpam-5823	24	27	etc	etc	X
ejpam-5823	24	28	.	.	X
ejpam-5823	25	1	here	here	ADV
ejpam-5823	25	2	we	we	PRON
ejpam-5823	25	3	restrict	restrict	VERB
ejpam-5823	25	4	to	to	ADP
ejpam-5823	25	5	the	the	DET
ejpam-5823	25	6	study	study	NOUN
ejpam-5823	25	7	of	of	ADP
ejpam-5823	25	8	bessel	bessel	NOUN
ejpam-5823	25	9	functions	function	NOUN
ejpam-5823	25	10	which	which	PRON
ejpam-5823	25	11	also	also	ADV
ejpam-5823	25	12	have	have	VERB
ejpam-5823	25	13	important	important	ADJ
ejpam-5823	25	14	role	role	NOUN
ejpam-5823	25	15	in	in	ADP
ejpam-5823	25	16	mathematical	mathematical	ADJ
ejpam-5823	25	17	modeling	modeling	NOUN
ejpam-5823	25	18	.	.	PUNCT
ejpam-5823	26	1	friedrich	friedrich	PROPN
ejpam-5823	26	2	wilhelm	wilhelm	PROPN
ejpam-5823	26	3	bessel	bessel	PROPN
ejpam-5823	26	4	was	be	AUX
ejpam-5823	26	5	the	the	DET
ejpam-5823	26	6	first	first	ADJ
ejpam-5823	26	7	who	who	PRON
ejpam-5823	26	8	used	use	VERB
ejpam-5823	26	9	bessel	bessel	NOUN
ejpam-5823	26	10	functions	function	NOUN
ejpam-5823	26	11	to	to	PART
ejpam-5823	26	12	study	study	VERB
ejpam-5823	26	13	three	three	NUM
ejpam-5823	26	14	body	body	NOUN
ejpam-5823	26	15	motion	motion	NOUN
ejpam-5823	26	16	.	.	PUNCT
ejpam-5823	27	1	bessel	bessel	ADJ
ejpam-5823	27	2	functions	function	NOUN
ejpam-5823	27	3	are	be	AUX
ejpam-5823	27	4	usually	usually	ADV
ejpam-5823	27	5	used	use	VERB
ejpam-5823	27	6	in	in	ADP
ejpam-5823	27	7	solutions	solution	NOUN
ejpam-5823	27	8	of	of	ADP
ejpam-5823	27	9	cylindrical	cylindrical	ADJ
ejpam-5823	27	10	coordinates	coordinate	NOUN
ejpam-5823	27	11	boundary	boundary	ADJ
ejpam-5823	27	12	value	value	NOUN
ejpam-5823	27	13	problems	problem	NOUN
ejpam-5823	27	14	.	.	PUNCT
ejpam-5823	28	1	bessel	bessel	NOUN
ejpam-5823	28	2	functions	function	NOUN
ejpam-5823	28	3	are	be	AUX
ejpam-5823	28	4	originated	originate	VERB
ejpam-5823	28	5	as	as	ADP
ejpam-5823	28	6	solution	solution	NOUN
ejpam-5823	28	7	of	of	ADP
ejpam-5823	28	8	bessel	bessel	ADJ
ejpam-5823	28	9	equation	equation	NOUN
ejpam-5823	28	10	[	[	X
ejpam-5823	28	11	2	2	NUM
ejpam-5823	28	12	]	]	PUNCT
ejpam-5823	28	13	,	,	PUNCT
ejpam-5823	28	14	that	that	ADV
ejpam-5823	28	15	is	is	ADV
ejpam-5823	28	16	,	,	PUNCT
ejpam-5823	28	17	z2w′′(z	z2w′′(z	PRON
ejpam-5823	28	18	)	)	PUNCT
ejpam-5823	29	1	+	+	CCONJ
ejpam-5823	29	2	zw′(z	zw′(z	X
ejpam-5823	29	3	)	)	PUNCT
ejpam-5823	30	1	+	+	CCONJ
ejpam-5823	30	2	(	(	PUNCT
ejpam-5823	30	3	z2	z2	NOUN
ejpam-5823	30	4	−	−	NOUN
ejpam-5823	30	5	ν2)w	ν2)w	NOUN
ejpam-5823	30	6	=	=	PUNCT
ejpam-5823	30	7	0	0	NUM
ejpam-5823	30	8	,	,	PUNCT
ejpam-5823	30	9	where	where	SCONJ
ejpam-5823	30	10	ν	ν	PROPN
ejpam-5823	30	11	is	be	AUX
ejpam-5823	30	12	the	the	DET
ejpam-5823	30	13	order	order	NOUN
ejpam-5823	30	14	of	of	ADP
ejpam-5823	30	15	bessel	bessel	ADJ
ejpam-5823	30	16	equation	equation	NOUN
ejpam-5823	30	17	.	.	PUNCT
ejpam-5823	31	1	bessel	bessel	ADJ
ejpam-5823	31	2	functions	function	NOUN
ejpam-5823	31	3	are	be	AUX
ejpam-5823	31	4	of	of	ADP
ejpam-5823	31	5	various	various	ADJ
ejpam-5823	31	6	kinds	kind	NOUN
ejpam-5823	31	7	.	.	PUNCT
ejpam-5823	32	1	the	the	DET
ejpam-5823	32	2	bessel	bessel	ADJ
ejpam-5823	32	3	function	function	NOUN
ejpam-5823	32	4	of	of	ADP
ejpam-5823	32	5	1st	1st	ADJ
ejpam-5823	32	6	kind	kind	NOUN
ejpam-5823	32	7	is	be	AUX
ejpam-5823	32	8	defined	define	VERB
ejpam-5823	32	9	by	by	ADP
ejpam-5823	32	10	:	:	PUNCT
ejpam-5823	32	11	jν(z	jν(z	NOUN
ejpam-5823	32	12	)	)	PUNCT
ejpam-5823	33	1	=	=	PUNCT
ejpam-5823	33	2	∞∑	∞∑	NUM
ejpam-5823	33	3	ν=0	ν=0	NOUN
ejpam-5823	33	4	(	(	PUNCT
ejpam-5823	33	5	−1)ν	−1)ν	NOUN
ejpam-5823	33	6	γ(ν	γ(ν	PROPN
ejpam-5823	33	7	+	+	CCONJ
ejpam-5823	33	8	k	k	PROPN
ejpam-5823	34	1	+	+	CCONJ
ejpam-5823	34	2	1)γ(k	1)γ(k	NUM
ejpam-5823	34	3	+	+	CCONJ
ejpam-5823	34	4	1	1	NUM
ejpam-5823	34	5	)	)	PUNCT
ejpam-5823	34	6	(	(	PUNCT
ejpam-5823	34	7	z	z	NOUN
ejpam-5823	34	8	2	2	X
ejpam-5823	34	9	)	)	PUNCT
ejpam-5823	34	10	ν+2k	ν+2k	NOUN
ejpam-5823	34	11	.	.	PUNCT
ejpam-5823	34	12	bessel	bessel	ADJ
ejpam-5823	34	13	function	function	NOUN
ejpam-5823	34	14	of	of	ADP
ejpam-5823	34	15	2nd	2nd	ADJ
ejpam-5823	34	16	kind	kind	NOUN
ejpam-5823	34	17	is	be	AUX
ejpam-5823	34	18	also	also	ADV
ejpam-5823	34	19	reffered	reffere	VERB
ejpam-5823	34	20	as	as	ADP
ejpam-5823	34	21	weber	weber	PROPN
ejpam-5823	34	22	function	function	PROPN
ejpam-5823	34	23	or	or	CCONJ
ejpam-5823	34	24	neuman	neuman	ADJ
ejpam-5823	34	25	function	function	NOUN
ejpam-5823	34	26	,	,	PUNCT
ejpam-5823	34	27	defined	define	VERB
ejpam-5823	34	28	as	as	ADP
ejpam-5823	34	29	:	:	PUNCT
ejpam-5823	34	30	yν(x	yν(x	NUM
ejpam-5823	34	31	)	)	PUNCT
ejpam-5823	35	1	=	=	SYM
ejpam-5823	35	2	j−ν(z)cos(νπ)−	j−ν(z)cos(νπ)−	PROPN
ejpam-5823	35	3	j−ν(z	j−ν(z	NOUN
ejpam-5823	35	4	)	)	PUNCT
ejpam-5823	35	5	sin(νπ	sin(νπ	NOUN
ejpam-5823	35	6	)	)	PUNCT
ejpam-5823	35	7	.	.	PUNCT
ejpam-5823	36	1	here	here	ADV
ejpam-5823	36	2	is	be	AUX
ejpam-5823	36	3	a	a	DET
ejpam-5823	36	4	3rd	3rd	ADJ
ejpam-5823	36	5	kind	kind	NOUN
ejpam-5823	36	6	named	name	VERB
ejpam-5823	36	7	as	as	ADP
ejpam-5823	36	8	hankel	hankel	NOUN
ejpam-5823	36	9	function	function	NOUN
ejpam-5823	36	10	defined	define	VERB
ejpam-5823	36	11	as	as	ADP
ejpam-5823	36	12	:	:	PUNCT
ejpam-5823	36	13	h(1	h(1	PROPN
ejpam-5823	36	14	)	)	PUNCT
ejpam-5823	36	15	ν	ν	NOUN
ejpam-5823	36	16	(	(	PUNCT
ejpam-5823	36	17	z	z	NOUN
ejpam-5823	36	18	)	)	PUNCT
ejpam-5823	36	19	=	=	PUNCT
ejpam-5823	36	20	jν(z	jν(z	X
ejpam-5823	36	21	)	)	PUNCT
ejpam-5823	37	1	+	+	X
ejpam-5823	37	2	iyν(z	iyν(z	PROPN
ejpam-5823	37	3	)	)	PUNCT
ejpam-5823	37	4	h(2	h(2	NOUN
ejpam-5823	37	5	)	)	PUNCT
ejpam-5823	37	6	ν	ν	NOUN
ejpam-5823	37	7	(	(	PUNCT
ejpam-5823	37	8	z	z	NOUN
ejpam-5823	37	9	)	)	PUNCT
ejpam-5823	37	10	=	=	SYM
ejpam-5823	37	11	jν(z)−	jν(z)−	PROPN
ejpam-5823	37	12	iyν(z	iyν(z	PROPN
ejpam-5823	37	13	)	)	PUNCT
ejpam-5823	37	14	.	.	PUNCT
ejpam-5823	38	1	for	for	ADP
ejpam-5823	38	2	more	more	ADJ
ejpam-5823	38	3	details	detail	NOUN
ejpam-5823	38	4	about	about	ADP
ejpam-5823	38	5	bessel	bessel	NOUN
ejpam-5823	38	6	functions	function	NOUN
ejpam-5823	38	7	see	see	VERB
ejpam-5823	38	8	[	[	X
ejpam-5823	38	9	2	2	NUM
ejpam-5823	38	10	]	]	PUNCT
ejpam-5823	38	11	.	.	PUNCT
ejpam-5823	39	1	extending	extend	VERB
ejpam-5823	39	2	the	the	DET
ejpam-5823	39	3	bessel	bessel	ADJ
ejpam-5823	39	4	functions	function	NOUN
ejpam-5823	39	5	,	,	PUNCT
ejpam-5823	39	6	we	we	PRON
ejpam-5823	39	7	have	have	VERB
ejpam-5823	39	8	the	the	DET
ejpam-5823	39	9	generalized	generalize	VERB
ejpam-5823	39	10	bessel	bessel	NOUN
ejpam-5823	39	11	functions	function	NOUN
ejpam-5823	39	12	[	[	X
ejpam-5823	39	13	3	3	X
ejpam-5823	39	14	]	]	PUNCT
ejpam-5823	39	15	defined	define	VERB
ejpam-5823	39	16	as	as	ADP
ejpam-5823	39	17	:	:	PUNCT
ejpam-5823	39	18	τj1	τj1	NUM
ejpam-5823	39	19	ν	ν	NOUN
ejpam-5823	39	20	(	(	PUNCT
ejpam-5823	39	21	λz	λz	NOUN
ejpam-5823	39	22	)	)	PUNCT
ejpam-5823	39	23	=	=	SYM
ejpam-5823	39	24	e−τzx	e−τzx	NOUN
ejpam-5823	39	25	ν	ν	NOUN
ejpam-5823	39	26	2	2	NUM
ejpam-5823	39	27	jν(λ	jν(λ	NOUN
ejpam-5823	39	28	√	√	PROPN
ejpam-5823	39	29	z	z	NOUN
ejpam-5823	39	30	)	)	PUNCT
ejpam-5823	39	31	(	(	PUNCT
ejpam-5823	39	32	λ	λ	PROPN
ejpam-5823	39	33	,	,	PUNCT
ejpam-5823	39	34	τ	τ	PROPN
ejpam-5823	39	35	∈	∈	NOUN
ejpam-5823	39	36	r+	r+	NOUN
ejpam-5823	39	37	)	)	PUNCT
ejpam-5823	39	38	τj2	τj2	ADJ
ejpam-5823	39	39	ν	ν	X
ejpam-5823	39	40	(	(	PUNCT
ejpam-5823	39	41	λz	λz	NOUN
ejpam-5823	39	42	)	)	PUNCT
ejpam-5823	39	43	=	=	PRON
ejpam-5823	39	44	eτzx	eτzx	VERB
ejpam-5823	39	45	−ν	−ν	NOUN
ejpam-5823	39	46	2	2	NUM
ejpam-5823	39	47	jν(λ	jν(λ	NOUN
ejpam-5823	40	1	√	√	PROPN
ejpam-5823	40	2	z	z	NOUN
ejpam-5823	40	3	)	)	PUNCT
ejpam-5823	40	4	.	.	PUNCT
ejpam-5823	41	1	s.	s.	PROPN
ejpam-5823	41	2	a.	a.	PROPN
ejpam-5823	41	3	h.	h.	PROPN
ejpam-5823	41	4	shah	shah	PROPN
ejpam-5823	41	5	et	et	PROPN
ejpam-5823	41	6	al	al	PROPN
ejpam-5823	41	7	.	.	PUNCT
ejpam-5823	41	8	/	/	SYM
ejpam-5823	41	9	eur	eur	PROPN
ejpam-5823	41	10	.	.	PUNCT
ejpam-5823	42	1	j.	j.	PROPN
ejpam-5823	42	2	pure	pure	PROPN
ejpam-5823	42	3	appl	appl	PROPN
ejpam-5823	42	4	.	.	PROPN
ejpam-5823	42	5	math	math	PROPN
ejpam-5823	42	6	,	,	PUNCT
ejpam-5823	42	7	18	18	NUM
ejpam-5823	42	8	(	(	PUNCT
ejpam-5823	42	9	2	2	NUM
ejpam-5823	42	10	)	)	PUNCT
ejpam-5823	42	11	(	(	PUNCT
ejpam-5823	42	12	2025	2025	NUM
ejpam-5823	42	13	)	)	PUNCT
ejpam-5823	42	14	,	,	PUNCT
ejpam-5823	42	15	5823	5823	NUM
ejpam-5823	42	16	3	3	NUM
ejpam-5823	42	17	of	of	ADP
ejpam-5823	42	18	26	26	NUM
ejpam-5823	42	19	cesarano	cesarano	ADJ
ejpam-5823	42	20	and	and	CCONJ
ejpam-5823	42	21	assante	assante	NOUN
ejpam-5823	43	1	[	[	X
ejpam-5823	43	2	4	4	X
ejpam-5823	43	3	]	]	PUNCT
ejpam-5823	43	4	introduced	introduce	VERB
ejpam-5823	43	5	the	the	DET
ejpam-5823	43	6	two	two	NUM
ejpam-5823	43	7	-	-	PUNCT
ejpam-5823	43	8	index	index	NOUN
ejpam-5823	43	9	cylinder	cylinder	NOUN
ejpam-5823	43	10	generalized	generalize	VERB
ejpam-5823	43	11	bessel	bessel	NOUN
ejpam-5823	43	12	function	function	NOUN
ejpam-5823	43	13	jn	jn	PROPN
ejpam-5823	43	14	,	,	PUNCT
ejpam-5823	43	15	ν(z	ν(z	PROPN
ejpam-5823	43	16	)	)	PUNCT
ejpam-5823	44	1	=	=	PUNCT
ejpam-5823	45	1	∞∑	∞∑	NUM
ejpam-5823	45	2	s=−∞	s=−∞	NOUN
ejpam-5823	45	3	jn−s(z)jν−s(z)js(z	jn−s(z)jν−s(z)js(z	NOUN
ejpam-5823	45	4	)	)	PUNCT
ejpam-5823	45	5	.	.	PUNCT
ejpam-5823	45	6	bessel	bessel	ADJ
ejpam-5823	45	7	function	function	NOUN
ejpam-5823	45	8	has	have	VERB
ejpam-5823	45	9	a	a	DET
ejpam-5823	45	10	wide	wide	ADJ
ejpam-5823	45	11	variety	variety	NOUN
ejpam-5823	45	12	of	of	ADP
ejpam-5823	45	13	applications	application	NOUN
ejpam-5823	45	14	.	.	PUNCT
ejpam-5823	46	1	it	it	PRON
ejpam-5823	46	2	is	be	AUX
ejpam-5823	46	3	commonly	commonly	ADV
ejpam-5823	46	4	used	use	VERB
ejpam-5823	46	5	in	in	ADP
ejpam-5823	46	6	the	the	DET
ejpam-5823	46	7	solution	solution	NOUN
ejpam-5823	46	8	of	of	ADP
ejpam-5823	46	9	physical	physical	ADJ
ejpam-5823	46	10	2nd	2nd	ADJ
ejpam-5823	46	11	order	order	NOUN
ejpam-5823	46	12	differential	differential	ADJ
ejpam-5823	46	13	equation	equation	NOUN
ejpam-5823	46	14	problems	problem	NOUN
ejpam-5823	46	15	[	[	X
ejpam-5823	46	16	5	5	NUM
ejpam-5823	46	17	]	]	PUNCT
ejpam-5823	46	18	.	.	PUNCT
ejpam-5823	47	1	parand	parand	NOUN
ejpam-5823	47	2	and	and	CCONJ
ejpam-5823	47	3	nikarya	nikarya	ADJ
ejpam-5823	48	1	[	[	X
ejpam-5823	48	2	6	6	NUM
ejpam-5823	48	3	]	]	PUNCT
ejpam-5823	48	4	attempted	attempt	VERB
ejpam-5823	48	5	to	to	PART
ejpam-5823	48	6	solve	solve	VERB
ejpam-5823	48	7	fractional	fractional	ADJ
ejpam-5823	48	8	differential	differential	NOUN
ejpam-5823	48	9	equations	equation	NOUN
ejpam-5823	48	10	using	use	VERB
ejpam-5823	48	11	bessel	bessel	ADJ
ejpam-5823	48	12	function	function	NOUN
ejpam-5823	48	13	.	.	PUNCT
ejpam-5823	49	1	faisal	faisal	PROPN
ejpam-5823	49	2	et.al	et.al	PROPN
ejpam-5823	49	3	.	.	PUNCT
ejpam-5823	50	1	[	[	X
ejpam-5823	50	2	7	7	X
ejpam-5823	50	3	]	]	PUNCT
ejpam-5823	50	4	gives	give	VERB
ejpam-5823	50	5	the	the	DET
ejpam-5823	50	6	solution	solution	NOUN
ejpam-5823	50	7	of	of	ADP
ejpam-5823	50	8	schrodinger	schrodinger	ADJ
ejpam-5823	50	9	equation	equation	NOUN
ejpam-5823	50	10	in	in	ADP
ejpam-5823	50	11	a	a	DET
ejpam-5823	50	12	cylindrical	cylindrical	ADJ
ejpam-5823	50	13	function	function	NOUN
ejpam-5823	50	14	using	use	VERB
ejpam-5823	50	15	bessel	bessel	ADJ
ejpam-5823	50	16	function	function	NOUN
ejpam-5823	50	17	.	.	PUNCT
ejpam-5823	51	1	more	more	ADJ
ejpam-5823	51	2	applications	application	NOUN
ejpam-5823	51	3	of	of	ADP
ejpam-5823	51	4	bessel	bessel	NOUN
ejpam-5823	51	5	functions	function	NOUN
ejpam-5823	51	6	can	can	AUX
ejpam-5823	51	7	be	be	AUX
ejpam-5823	51	8	seen	see	VERB
ejpam-5823	51	9	in	in	ADP
ejpam-5823	51	10	[	[	X
ejpam-5823	51	11	8	8	NUM
ejpam-5823	51	12	,	,	PUNCT
ejpam-5823	51	13	9	9	NUM
ejpam-5823	51	14	]	]	PUNCT
ejpam-5823	51	15	.	.	PUNCT
ejpam-5823	52	1	researchers	researcher	NOUN
ejpam-5823	52	2	are	be	AUX
ejpam-5823	52	3	currently	currently	ADV
ejpam-5823	52	4	working	work	VERB
ejpam-5823	52	5	in	in	ADP
ejpam-5823	52	6	area	area	NOUN
ejpam-5823	52	7	of	of	ADP
ejpam-5823	52	8	generalized	generalized	ADJ
ejpam-5823	52	9	bessel	bessel	NOUN
ejpam-5823	52	10	functions	function	NOUN
ejpam-5823	52	11	including	include	VERB
ejpam-5823	52	12	k	k	PROPN
ejpam-5823	52	13	,	,	PUNCT
ejpam-5823	52	14	(	(	PUNCT
ejpam-5823	52	15	s	s	X
ejpam-5823	52	16	,	,	PUNCT
ejpam-5823	52	17	k	k	NOUN
ejpam-5823	52	18	)	)	PUNCT
ejpam-5823	52	19	,	,	PUNCT
ejpam-5823	52	20	(	(	PUNCT
ejpam-5823	52	21	p	p	X
ejpam-5823	52	22	,	,	PUNCT
ejpam-5823	52	23	k	k	NOUN
ejpam-5823	52	24	)	)	PUNCT
ejpam-5823	52	25	,	,	PUNCT
ejpam-5823	52	26	q	q	ADJ
ejpam-5823	52	27	-	-	PUNCT
ejpam-5823	52	28	bessel	bessel	ADJ
ejpam-5823	52	29	functions	function	NOUN
ejpam-5823	52	30	and	and	CCONJ
ejpam-5823	52	31	also	also	ADV
ejpam-5823	52	32	properties	property	NOUN
ejpam-5823	52	33	of	of	ADP
ejpam-5823	52	34	bessel	bessel	NOUN
ejpam-5823	52	35	,	,	PUNCT
ejpam-5823	52	36	modified	modified	ADJ
ejpam-5823	52	37	bessel	bessel	NOUN
ejpam-5823	52	38	functions	function	NOUN
ejpam-5823	52	39	and	and	CCONJ
ejpam-5823	52	40	generalized	generalized	ADJ
ejpam-5823	52	41	bessel	bessel	NOUN
ejpam-5823	52	42	functions	function	NOUN
ejpam-5823	52	43	.	.	PUNCT
ejpam-5823	53	1	one	one	PRON
ejpam-5823	53	2	can	can	AUX
ejpam-5823	53	3	refer	refer	VERB
ejpam-5823	53	4	for	for	ADP
ejpam-5823	53	5	the	the	DET
ejpam-5823	53	6	recent	recent	ADJ
ejpam-5823	53	7	researches	research	NOUN
ejpam-5823	53	8	on	on	ADP
ejpam-5823	53	9	generalized	generalized	ADJ
ejpam-5823	53	10	special	special	ADJ
ejpam-5823	53	11	functions	function	NOUN
ejpam-5823	53	12	to	to	ADP
ejpam-5823	53	13	[	[	X
ejpam-5823	53	14	10–16	10–16	NUM
ejpam-5823	53	15	]	]	SYM
ejpam-5823	53	16	.	.	PUNCT
ejpam-5823	54	1	univalent	univalent	ADJ
ejpam-5823	54	2	function	function	NOUN
ejpam-5823	54	3	is	be	AUX
ejpam-5823	54	4	defined	define	VERB
ejpam-5823	54	5	as	as	ADP
ejpam-5823	54	6	the	the	DET
ejpam-5823	54	7	function	function	NOUN
ejpam-5823	54	8	whose	whose	DET
ejpam-5823	54	9	domain	domain	NOUN
ejpam-5823	54	10	is	be	AUX
ejpam-5823	54	11	meromorphic	meromorphic	ADJ
ejpam-5823	54	12	and	and	CCONJ
ejpam-5823	54	13	injective	injective	ADJ
ejpam-5823	54	14	.	.	PUNCT
ejpam-5823	55	1	in	in	ADP
ejpam-5823	55	2	other	other	ADJ
ejpam-5823	55	3	words	word	NOUN
ejpam-5823	55	4	,	,	PUNCT
ejpam-5823	55	5	the	the	DET
ejpam-5823	55	6	function	function	NOUN
ejpam-5823	55	7	g	g	NOUN
ejpam-5823	55	8	:	:	PUNCT
ejpam-5823	55	9	d	d	X
ejpam-5823	55	10	→	→	SYM
ejpam-5823	55	11	c∗	c∗	PROPN
ejpam-5823	55	12	is	be	AUX
ejpam-5823	55	13	univalent	univalent	ADJ
ejpam-5823	55	14	in	in	ADP
ejpam-5823	55	15	d	d	PROPN
ejpam-5823	55	16	if	if	SCONJ
ejpam-5823	56	1	and	and	CCONJ
ejpam-5823	56	2	only	only	ADV
ejpam-5823	56	3	if	if	SCONJ
ejpam-5823	56	4	it	it	PRON
ejpam-5823	56	5	is	be	AUX
ejpam-5823	56	6	analytic	analytic	ADJ
ejpam-5823	56	7	in	in	ADP
ejpam-5823	56	8	domain	domain	NOUN
ejpam-5823	56	9	except	except	SCONJ
ejpam-5823	56	10	at	at	ADP
ejpam-5823	56	11	most	most	ADV
ejpam-5823	56	12	one	one	NUM
ejpam-5823	56	13	pole	pole	NOUN
ejpam-5823	56	14	and	and	CCONJ
ejpam-5823	56	15	g(x1	g(x1	NOUN
ejpam-5823	56	16	)	)	PUNCT
ejpam-5823	56	17	̸=	̸=	PROPN
ejpam-5823	56	18	g(x2	g(x2	NOUN
ejpam-5823	56	19	)	)	PUNCT
ejpam-5823	56	20	,	,	PUNCT
ejpam-5823	56	21	(	(	PUNCT
ejpam-5823	56	22	x1	x1	X
ejpam-5823	56	23	,	,	PUNCT
ejpam-5823	56	24	x2	x2	PROPN
ejpam-5823	56	25	∈	∈	PROPN
ejpam-5823	57	1	d	d	PROPN
ejpam-5823	57	2	,	,	PUNCT
ejpam-5823	57	3	x1	x1	PROPN
ejpam-5823	57	4	̸=	̸=	PROPN
ejpam-5823	57	5	x2	x2	PROPN
ejpam-5823	57	6	)	)	PUNCT
ejpam-5823	57	7	.	.	PUNCT
ejpam-5823	58	1	for	for	ADP
ejpam-5823	58	2	more	more	ADJ
ejpam-5823	58	3	details	detail	NOUN
ejpam-5823	58	4	about	about	ADP
ejpam-5823	58	5	univalent	univalent	ADJ
ejpam-5823	58	6	functions	function	NOUN
ejpam-5823	58	7	see	see	VERB
ejpam-5823	58	8	[	[	X
ejpam-5823	58	9	17	17	NUM
ejpam-5823	58	10	]	]	PUNCT
ejpam-5823	58	11	.	.	PUNCT
ejpam-5823	59	1	let	let	VERB
ejpam-5823	59	2	s	s	PRON
ejpam-5823	59	3	be	be	AUX
ejpam-5823	59	4	a	a	DET
ejpam-5823	59	5	set	set	NOUN
ejpam-5823	59	6	of	of	ADP
ejpam-5823	59	7	univalent	univalent	ADJ
ejpam-5823	59	8	(	(	PUNCT
ejpam-5823	59	9	meromorphic	meromorphic	ADJ
ejpam-5823	59	10	and	and	CCONJ
ejpam-5823	59	11	injective	injective	ADJ
ejpam-5823	59	12	domain	domain	NOUN
ejpam-5823	59	13	)	)	PUNCT
ejpam-5823	59	14	functions	function	NOUN
ejpam-5823	59	15	g	g	NOUN
ejpam-5823	59	16	in	in	ADP
ejpam-5823	59	17	u	u	PROPN
ejpam-5823	60	1	where	where	SCONJ
ejpam-5823	60	2	u	u	NOUN
ejpam-5823	60	3	:	:	PUNCT
ejpam-5823	60	4	=	=	SYM
ejpam-5823	60	5	{	{	PUNCT
ejpam-5823	60	6	y	y	PROPN
ejpam-5823	60	7	∈	∈	PROPN
ejpam-5823	60	8	c	c	NOUN
ejpam-5823	60	9	:	:	PUNCT
ejpam-5823	61	1	|y|	|y|	ADJ
ejpam-5823	61	2	<	<	X
ejpam-5823	61	3	1	1	NUM
ejpam-5823	61	4	}	}	PUNCT
ejpam-5823	61	5	with	with	ADP
ejpam-5823	61	6	g(0	g(0	NOUN
ejpam-5823	61	7	)	)	PUNCT
ejpam-5823	61	8	=	=	SYM
ejpam-5823	61	9	0	0	NUM
ejpam-5823	61	10	and	and	CCONJ
ejpam-5823	61	11	g′(0	g′(0	PROPN
ejpam-5823	61	12	)	)	PUNCT
ejpam-5823	61	13	=	=	SYM
ejpam-5823	61	14	1	1	X
ejpam-5823	61	15	.	.	PUNCT
ejpam-5823	61	16	power	power	NOUN
ejpam-5823	61	17	expansion	expansion	NOUN
ejpam-5823	61	18	series	series	NOUN
ejpam-5823	61	19	[	[	X
ejpam-5823	61	20	1	1	X
ejpam-5823	61	21	]	]	PUNCT
ejpam-5823	61	22	for	for	ADP
ejpam-5823	61	23	such	such	ADJ
ejpam-5823	61	24	functions	function	NOUN
ejpam-5823	61	25	is	be	AUX
ejpam-5823	61	26	of	of	ADP
ejpam-5823	61	27	the	the	DET
ejpam-5823	61	28	form	form	NOUN
ejpam-5823	61	29	:	:	PUNCT
ejpam-5823	61	30	g(x	g(x	NOUN
ejpam-5823	61	31	)	)	PUNCT
ejpam-5823	62	1	=	=	NOUN
ejpam-5823	63	1	∞∑	∞∑	NUM
ejpam-5823	63	2	k=1	k=1	ADV
ejpam-5823	63	3	gkx	gkx	VERB
ejpam-5823	63	4	k.	k.	PROPN
ejpam-5823	64	1	(	(	PUNCT
ejpam-5823	64	2	1	1	X
ejpam-5823	64	3	)	)	PUNCT
ejpam-5823	64	4	the	the	DET
ejpam-5823	64	5	class	class	NOUN
ejpam-5823	64	6	s	s	NOUN
ejpam-5823	64	7	is	be	AUX
ejpam-5823	64	8	compact	compact	ADJ
ejpam-5823	64	9	(	(	PUNCT
ejpam-5823	64	10	locally	locally	ADV
ejpam-5823	64	11	bounded	bound	VERB
ejpam-5823	64	12	and	and	CCONJ
ejpam-5823	64	13	closed	close	VERB
ejpam-5823	64	14	)	)	PUNCT
ejpam-5823	64	15	having	have	VERB
ejpam-5823	64	16	the	the	DET
ejpam-5823	64	17	most	most	ADV
ejpam-5823	64	18	classic	classic	ADJ
ejpam-5823	64	19	example	example	NOUN
ejpam-5823	64	20	is	be	AUX
ejpam-5823	64	21	koebe	koebe	NOUN
ejpam-5823	64	22	function	function	NOUN
ejpam-5823	64	23	,	,	PUNCT
ejpam-5823	64	24	defined	define	VERB
ejpam-5823	64	25	as	as	ADP
ejpam-5823	64	26	:	:	PUNCT
ejpam-5823	64	27	k(y	k(y	X
ejpam-5823	64	28	)	)	PUNCT
ejpam-5823	65	1	=	=	PUNCT
ejpam-5823	65	2	y(1−	y(1−	NOUN
ejpam-5823	65	3	y)−2	y)−2	NOUN
ejpam-5823	65	4	=	=	NOUN
ejpam-5823	65	5	1	1	NUM
ejpam-5823	65	6	4	4	NUM
ejpam-5823	65	7	[	[	X
ejpam-5823	65	8	(	(	PUNCT
ejpam-5823	65	9	1	1	NUM
ejpam-5823	65	10	+	+	NUM
ejpam-5823	65	11	y	y	PROPN
ejpam-5823	65	12	1−	1−	NUM
ejpam-5823	65	13	y	y	PROPN
ejpam-5823	65	14	)	)	PUNCT
ejpam-5823	65	15	2	2	NUM
ejpam-5823	65	16	−	−	NOUN
ejpam-5823	65	17	1	1	NUM
ejpam-5823	65	18	]	]	PUNCT
ejpam-5823	65	19	=	=	PUNCT
ejpam-5823	66	1	∞∑	∞∑	NUM
ejpam-5823	66	2	k=1	k=1	PROPN
ejpam-5823	66	3	kyk	kyk	PROPN
ejpam-5823	66	4	.	.	PUNCT
ejpam-5823	67	1	here	here	ADV
ejpam-5823	67	2	’s	’	VERB
ejpam-5823	67	3	involve	involve	VERB
ejpam-5823	67	4	the	the	DET
ejpam-5823	67	5	square	square	NOUN
ejpam-5823	67	6	of	of	ADP
ejpam-5823	67	7	cayley	cayley	ADJ
ejpam-5823	67	8	transformation	transformation	NOUN
ejpam-5823	68	1	y	y	PROPN
ejpam-5823	68	2	→	→	SYM
ejpam-5823	68	3	1+y	1+y	NUM
ejpam-5823	68	4	1−y	1−y	NUM
ejpam-5823	68	5	∈	∈	PROPN
ejpam-5823	68	6	s	s	NOUN
ejpam-5823	68	7	as	as	SCONJ
ejpam-5823	68	8	it	it	PRON
ejpam-5823	68	9	is	be	AUX
ejpam-5823	68	10	normalized	normalize	VERB
ejpam-5823	68	11	.	.	PUNCT
ejpam-5823	69	1	a	a	DET
ejpam-5823	69	2	function	function	NOUN
ejpam-5823	69	3	is	be	AUX
ejpam-5823	69	4	known	know	VERB
ejpam-5823	69	5	as	as	ADP
ejpam-5823	69	6	starlike	starlike	NOUN
ejpam-5823	69	7	if	if	SCONJ
ejpam-5823	69	8	its	its	PRON
ejpam-5823	69	9	mapping	mapping	NOUN
ejpam-5823	69	10	from	from	ADP
ejpam-5823	69	11	u	u	NOUN
ejpam-5823	69	12	onto	onto	ADP
ejpam-5823	69	13	domain	domain	NOUN
ejpam-5823	70	1	d	d	NOUN
ejpam-5823	70	2	is	be	AUX
ejpam-5823	70	3	starlike	starlike	NOUN
ejpam-5823	70	4	.	.	PUNCT
ejpam-5823	71	1	if	if	SCONJ
ejpam-5823	71	2	the	the	DET
ejpam-5823	71	3	domain	domain	NOUN
ejpam-5823	71	4	is	be	AUX
ejpam-5823	71	5	convex	convex	NOUN
ejpam-5823	71	6	,	,	PUNCT
ejpam-5823	71	7	we	we	PRON
ejpam-5823	71	8	can	can	AUX
ejpam-5823	71	9	simply	simply	ADV
ejpam-5823	71	10	say	say	VERB
ejpam-5823	71	11	it	it	PRON
ejpam-5823	71	12	a	a	DET
ejpam-5823	71	13	convex	convex	NOUN
ejpam-5823	71	14	function	function	NOUN
ejpam-5823	71	15	.	.	PUNCT
ejpam-5823	72	1	having	have	VERB
ejpam-5823	72	2	a	a	DET
ejpam-5823	72	3	convex	convex	ADJ
ejpam-5823	72	4	domain	domain	NOUN
ejpam-5823	72	5	means	mean	VERB
ejpam-5823	72	6	that	that	SCONJ
ejpam-5823	72	7	if	if	SCONJ
ejpam-5823	72	8	line	line	NOUN
ejpam-5823	72	9	segment	segment	NOUN
ejpam-5823	72	10	that	that	PRON
ejpam-5823	72	11	joins	join	VERB
ejpam-5823	72	12	any	any	DET
ejpam-5823	72	13	two	two	NUM
ejpam-5823	72	14	points	point	NOUN
ejpam-5823	72	15	must	must	AUX
ejpam-5823	72	16	lie	lie	VERB
ejpam-5823	72	17	in	in	ADP
ejpam-5823	72	18	domain	domain	NOUN
ejpam-5823	72	19	[	[	X
ejpam-5823	72	20	18	18	NUM
ejpam-5823	72	21	]	]	PUNCT
ejpam-5823	72	22	.	.	PUNCT
ejpam-5823	73	1	s.	s.	PROPN
ejpam-5823	73	2	a.	a.	PROPN
ejpam-5823	73	3	h.	h.	PROPN
ejpam-5823	73	4	shah	shah	PROPN
ejpam-5823	73	5	et	et	PROPN
ejpam-5823	73	6	al	al	PROPN
ejpam-5823	73	7	.	.	PUNCT
ejpam-5823	73	8	/	/	SYM
ejpam-5823	73	9	eur	eur	PROPN
ejpam-5823	73	10	.	.	PUNCT
ejpam-5823	74	1	j.	j.	PROPN
ejpam-5823	74	2	pure	pure	PROPN
ejpam-5823	74	3	appl	appl	PROPN
ejpam-5823	74	4	.	.	PROPN
ejpam-5823	74	5	math	math	PROPN
ejpam-5823	74	6	,	,	PUNCT
ejpam-5823	74	7	18	18	NUM
ejpam-5823	74	8	(	(	PUNCT
ejpam-5823	74	9	2	2	NUM
ejpam-5823	74	10	)	)	PUNCT
ejpam-5823	74	11	(	(	PUNCT
ejpam-5823	74	12	2025	2025	NUM
ejpam-5823	74	13	)	)	PUNCT
ejpam-5823	74	14	,	,	PUNCT
ejpam-5823	74	15	5823	5823	NUM
ejpam-5823	74	16	4	4	NUM
ejpam-5823	74	17	of	of	ADP
ejpam-5823	74	18	26	26	NUM
ejpam-5823	74	19	let	let	VERB
ejpam-5823	74	20	s∗	s∗	PROPN
ejpam-5823	74	21	and	and	CCONJ
ejpam-5823	74	22	k	k	PROPN
ejpam-5823	74	23	be	be	AUX
ejpam-5823	74	24	subclass	subclass	NOUN
ejpam-5823	74	25	of	of	ADP
ejpam-5823	74	26	s	s	PRON
ejpam-5823	74	27	where	where	SCONJ
ejpam-5823	74	28	domain	domain	NOUN
ejpam-5823	74	29	is	be	AUX
ejpam-5823	74	30	starlike	starlike	NOUN
ejpam-5823	74	31	and	and	CCONJ
ejpam-5823	74	32	convex	convex	VERB
ejpam-5823	74	33	with	with	ADP
ejpam-5823	74	34	respect	respect	NOUN
ejpam-5823	74	35	to	to	ADP
ejpam-5823	74	36	origin	origin	VERB
ejpam-5823	74	37	respectively	respectively	ADV
ejpam-5823	74	38	.	.	PUNCT
ejpam-5823	75	1	moreover	moreover	ADV
ejpam-5823	75	2	it	it	PRON
ejpam-5823	75	3	is	be	AUX
ejpam-5823	75	4	known	know	VERB
ejpam-5823	75	5	[	[	X
ejpam-5823	75	6	19	19	NUM
ejpam-5823	75	7	,	,	PUNCT
ejpam-5823	75	8	20	20	NUM
ejpam-5823	75	9	]	]	PUNCT
ejpam-5823	75	10	that	that	SCONJ
ejpam-5823	75	11	g(z	g(z	PROPN
ejpam-5823	75	12	)	)	PUNCT
ejpam-5823	75	13	∈	∈	PROPN
ejpam-5823	75	14	a	a	PRON
ejpam-5823	75	15	is	be	AUX
ejpam-5823	75	16	starlike	starlike	NOUN
ejpam-5823	75	17	if	if	SCONJ
ejpam-5823	75	18	and	and	CCONJ
ejpam-5823	75	19	only	only	ADV
ejpam-5823	75	20	if	if	SCONJ
ejpam-5823	75	21	re	re	X
ejpam-5823	75	22	(	(	PUNCT
ejpam-5823	75	23	zg′(z	zg′(z	PROPN
ejpam-5823	75	24	)	)	PUNCT
ejpam-5823	75	25	g(z	g(z	PROPN
ejpam-5823	75	26	)	)	PUNCT
ejpam-5823	75	27	)	)	PUNCT
ejpam-5823	76	1	>	>	X
ejpam-5823	76	2	0	0	NUM
ejpam-5823	76	3	,	,	PUNCT
ejpam-5823	76	4	z	z	PROPN
ejpam-5823	76	5	∈	∈	PROPN
ejpam-5823	76	6	u	u	NOUN
ejpam-5823	76	7	(	(	PUNCT
ejpam-5823	76	8	2	2	NUM
ejpam-5823	76	9	)	)	PUNCT
ejpam-5823	76	10	where	where	SCONJ
ejpam-5823	76	11	a	a	DET
ejpam-5823	76	12	be	be	AUX
ejpam-5823	76	13	the	the	DET
ejpam-5823	76	14	set	set	NOUN
ejpam-5823	76	15	of	of	ADP
ejpam-5823	76	16	analytic	analytic	NOUN
ejpam-5823	76	17	(	(	PUNCT
ejpam-5823	76	18	having	have	VERB
ejpam-5823	76	19	complex	complex	ADJ
ejpam-5823	76	20	derivatives	derivative	NOUN
ejpam-5823	76	21	)	)	PUNCT
ejpam-5823	76	22	functions	function	NOUN
ejpam-5823	76	23	.	.	PUNCT
ejpam-5823	77	1	taking	take	VERB
ejpam-5823	77	2	it	it	PRON
ejpam-5823	77	3	as	as	ADP
ejpam-5823	77	4	of	of	ADP
ejpam-5823	77	5	order	order	NOUN
ejpam-5823	77	6	η	η	PROPN
ejpam-5823	77	7	,	,	PUNCT
ejpam-5823	77	8	we	we	PRON
ejpam-5823	77	9	denote	denote	VERB
ejpam-5823	77	10	it	it	PRON
ejpam-5823	77	11	s∗(η	s∗(η	PROPN
ejpam-5823	77	12	)	)	PUNCT
ejpam-5823	77	13	satisfies	satisfy	VERB
ejpam-5823	77	14	the	the	DET
ejpam-5823	77	15	condition	condition	NOUN
ejpam-5823	77	16	:	:	PUNCT
ejpam-5823	77	17	re	re	X
ejpam-5823	77	18	(	(	PUNCT
ejpam-5823	77	19	zg′(z	zg′(z	PROPN
ejpam-5823	77	20	)	)	PUNCT
ejpam-5823	77	21	g(z	g(z	PROPN
ejpam-5823	77	22	)	)	PUNCT
ejpam-5823	77	23	)	)	PUNCT
ejpam-5823	77	24	>	>	X
ejpam-5823	78	1	η	η	PROPN
ejpam-5823	78	2	,	,	PUNCT
ejpam-5823	78	3	z	z	PROPN
ejpam-5823	78	4	∈	∈	PROPN
ejpam-5823	78	5	u	u	NOUN
ejpam-5823	78	6	,	,	PUNCT
ejpam-5823	78	7	0	0	NUM
ejpam-5823	78	8	≤	≤	NUM
ejpam-5823	78	9	η	η	PROPN
ejpam-5823	78	10	≤	≤	ADJ
ejpam-5823	78	11	1	1	NUM
ejpam-5823	78	12	.	.	PUNCT
ejpam-5823	78	13	(	(	PUNCT
ejpam-5823	78	14	3	3	X
ejpam-5823	78	15	)	)	PUNCT
ejpam-5823	78	16	also	also	ADV
ejpam-5823	78	17	convex	convex	VERB
ejpam-5823	78	18	function	function	NOUN
ejpam-5823	78	19	is	be	AUX
ejpam-5823	78	20	characterized	characterize	VERB
ejpam-5823	78	21	as	as	ADP
ejpam-5823	78	22	g(z	g(z	PROPN
ejpam-5823	78	23	)	)	PUNCT
ejpam-5823	78	24	∈	∈	PROPN
ejpam-5823	78	25	a	a	DET
ejpam-5823	78	26	satisfies	satisfie	NOUN
ejpam-5823	78	27	the	the	DET
ejpam-5823	78	28	condition	condition	NOUN
ejpam-5823	78	29	:	:	PUNCT
ejpam-5823	79	1	1	1	NUM
ejpam-5823	79	2	+	+	X
ejpam-5823	79	3	re	re	X
ejpam-5823	79	4	(	(	PUNCT
ejpam-5823	79	5	zg′′(z	zg′′(z	NOUN
ejpam-5823	79	6	)	)	PUNCT
ejpam-5823	79	7	g′(z	g′(z	NOUN
ejpam-5823	79	8	)	)	PUNCT
ejpam-5823	79	9	)	)	PUNCT
ejpam-5823	79	10	>	>	X
ejpam-5823	79	11	0	0	NUM
ejpam-5823	79	12	,	,	PUNCT
ejpam-5823	79	13	z	z	PROPN
ejpam-5823	79	14	∈	∈	PROPN
ejpam-5823	79	15	u.	u.	NOUN
ejpam-5823	79	16	(	(	PUNCT
ejpam-5823	79	17	4	4	NUM
ejpam-5823	79	18	)	)	PUNCT
ejpam-5823	79	19	similarly	similarly	ADV
ejpam-5823	79	20	for	for	ADP
ejpam-5823	79	21	order	order	NOUN
ejpam-5823	79	22	η	η	PROPN
ejpam-5823	79	23	,	,	PUNCT
ejpam-5823	79	24	we	we	PRON
ejpam-5823	79	25	can	can	AUX
ejpam-5823	79	26	say	say	VERB
ejpam-5823	79	27	1	1	NUM
ejpam-5823	79	28	+	+	NOUN
ejpam-5823	79	29	re	re	X
ejpam-5823	79	30	(	(	PUNCT
ejpam-5823	79	31	zg′′(z	zg′′(z	NOUN
ejpam-5823	79	32	)	)	PUNCT
ejpam-5823	79	33	g′(z	g′(z	NOUN
ejpam-5823	79	34	)	)	PUNCT
ejpam-5823	79	35	)	)	PUNCT
ejpam-5823	79	36	>	>	X
ejpam-5823	79	37	η	η	PROPN
ejpam-5823	79	38	,	,	PUNCT
ejpam-5823	79	39	z	z	PROPN
ejpam-5823	79	40	∈	∈	PROPN
ejpam-5823	79	41	u	u	NOUN
ejpam-5823	79	42	,	,	PUNCT
ejpam-5823	79	43	0	0	NUM
ejpam-5823	79	44	≤	≤	NUM
ejpam-5823	79	45	η	η	PROPN
ejpam-5823	79	46	≤	≤	ADJ
ejpam-5823	79	47	1	1	NUM
ejpam-5823	79	48	.	.	PUNCT
ejpam-5823	79	49	(	(	PUNCT
ejpam-5823	79	50	5	5	NUM
ejpam-5823	79	51	)	)	PUNCT
ejpam-5823	79	52	as	as	ADP
ejpam-5823	79	53	s∗(η	s∗(η	PROPN
ejpam-5823	79	54	)	)	PUNCT
ejpam-5823	79	55	⊂	⊂	PROPN
ejpam-5823	79	56	s∗(0	s∗(0	VERB
ejpam-5823	79	57	)	)	PUNCT
ejpam-5823	79	58	=	=	NOUN
ejpam-5823	79	59	:	:	PUNCT
ejpam-5823	79	60	s∗	s∗	PROPN
ejpam-5823	79	61	⊂	⊂	PROPN
ejpam-5823	79	62	s	s	PART
ejpam-5823	79	63	,	,	PUNCT
ejpam-5823	79	64	k(η	k(η	PROPN
ejpam-5823	79	65	)	)	PUNCT
ejpam-5823	79	66	⊂	⊂	PROPN
ejpam-5823	80	1	k(0	k(0	PROPN
ejpam-5823	80	2	)	)	PUNCT
ejpam-5823	81	1	=	=	NOUN
ejpam-5823	81	2	:	:	PUNCT
ejpam-5823	81	3	k	k	PROPN
ejpam-5823	81	4	⊂	⊂	PROPN
ejpam-5823	81	5	s	s	X
ejpam-5823	81	6	and	and	CCONJ
ejpam-5823	81	7	k(0	k(0	PROPN
ejpam-5823	81	8	)	)	PUNCT
ejpam-5823	81	9	⊂	⊂	PROPN
ejpam-5823	81	10	s∗(0	s∗(0	PROPN
ejpam-5823	81	11	)	)	PUNCT
ejpam-5823	81	12	⊂	⊂	PROPN
ejpam-5823	81	13	s.	s.	PROPN
ejpam-5823	81	14	for	for	ADP
ejpam-5823	81	15	β	β	X
ejpam-5823	81	16	<	<	X
ejpam-5823	81	17	0	0	NUM
ejpam-5823	81	18	,	,	PUNCT
ejpam-5823	81	19	k(η	k(η	PROPN
ejpam-5823	81	20	)	)	PUNCT
ejpam-5823	81	21	⊈	⊈	PRON
ejpam-5823	82	1	s∗.	s∗.	ADJ
ejpam-5823	82	2	teodor	teodor	NOUN
ejpam-5823	82	3	and	and	CCONJ
ejpam-5823	82	4	hanaa	hanaa	NOUN
ejpam-5823	83	1	[	[	X
ejpam-5823	83	2	1	1	NUM
ejpam-5823	83	3	]	]	PUNCT
ejpam-5823	83	4	proved	prove	VERB
ejpam-5823	83	5	the	the	DET
ejpam-5823	83	6	inequality	inequality	NOUN
ejpam-5823	83	7	(	(	PUNCT
ejpam-5823	83	8	a)m	a)m	X
ejpam-5823	83	9	>	>	X
ejpam-5823	83	10	a(a+	a(a+	PROPN
ejpam-5823	83	11	α)m−1	α)m−1	PROPN
ejpam-5823	83	12	,	,	PUNCT
ejpam-5823	83	13	a	a	DET
ejpam-5823	83	14	>	>	X
ejpam-5823	83	15	0	0	NUM
ejpam-5823	83	16	,	,	PUNCT
ejpam-5823	83	17	0	0	NUM
ejpam-5823	83	18	≤	≤	NUM
ejpam-5823	83	19	α	α	NOUN
ejpam-5823	83	20	≤	≤	NUM
ejpam-5823	83	21	√	√	ADP
ejpam-5823	83	22	2	2	NUM
ejpam-5823	83	23	by	by	ADP
ejpam-5823	83	24	partial	partial	ADJ
ejpam-5823	83	25	derivative	derivative	ADJ
ejpam-5823	83	26	and	and	CCONJ
ejpam-5823	83	27	variable	variable	ADJ
ejpam-5823	83	28	extremum	extremum	ADJ
ejpam-5823	83	29	method	method	NOUN
ejpam-5823	83	30	for	for	ADP
ejpam-5823	83	31	m	m	PROPN
ejpam-5823	83	32	∈	∈	PROPN
ejpam-5823	83	33	n\{1	n\{1	NOUN
ejpam-5823	83	34	,	,	PUNCT
ejpam-5823	83	35	2	2	NUM
ejpam-5823	83	36	}	}	PUNCT
ejpam-5823	83	37	and	and	CCONJ
ejpam-5823	83	38	used	use	VERB
ejpam-5823	83	39	the	the	DET
ejpam-5823	83	40	inequality	inequality	NOUN
ejpam-5823	83	41	to	to	PART
ejpam-5823	83	42	examine	examine	VERB
ejpam-5823	83	43	the	the	DET
ejpam-5823	83	44	order	order	NOUN
ejpam-5823	83	45	of	of	ADP
ejpam-5823	83	46	convexity	convexity	NOUN
ejpam-5823	83	47	as	as	ADV
ejpam-5823	83	48	well	well	ADV
ejpam-5823	83	49	as	as	ADP
ejpam-5823	83	50	starlikeness	starlikeness	NOUN
ejpam-5823	83	51	of	of	ADP
ejpam-5823	83	52	generalized	generalized	ADJ
ejpam-5823	83	53	bessel	bessel	NOUN
ejpam-5823	83	54	function	function	NOUN
ejpam-5823	83	55	.	.	PUNCT
ejpam-5823	84	1	many	many	ADJ
ejpam-5823	84	2	other	other	ADJ
ejpam-5823	84	3	researchers	researcher	NOUN
ejpam-5823	84	4	[	[	X
ejpam-5823	84	5	1	1	NUM
ejpam-5823	84	6	,	,	PUNCT
ejpam-5823	84	7	21	21	NUM
ejpam-5823	84	8	]	]	PUNCT
ejpam-5823	84	9	have	have	AUX
ejpam-5823	84	10	proved	prove	VERB
ejpam-5823	84	11	its	its	PRON
ejpam-5823	84	12	classical	classical	ADJ
ejpam-5823	84	13	form	form	NOUN
ejpam-5823	84	14	.	.	PUNCT
ejpam-5823	85	1	teodor	teodor	ADV
ejpam-5823	85	2	and	and	CCONJ
ejpam-5823	85	3	hanaa	hanaa	NOUN
ejpam-5823	86	1	[	[	X
ejpam-5823	86	2	1	1	NUM
ejpam-5823	86	3	]	]	PUNCT
ejpam-5823	86	4	gave	give	VERB
ejpam-5823	86	5	the	the	DET
ejpam-5823	86	6	graphical	graphical	ADJ
ejpam-5823	86	7	representations	representation	NOUN
ejpam-5823	86	8	of	of	ADP
ejpam-5823	86	9	generalized	generalized	ADJ
ejpam-5823	86	10	bessel	bessel	NOUN
ejpam-5823	86	11	function	function	NOUN
ejpam-5823	86	12	,	,	PUNCT
ejpam-5823	86	13	defined	define	VERB
ejpam-5823	86	14	by	by	ADP
ejpam-5823	86	15	:	:	PUNCT
ejpam-5823	86	16	wξ	wξ	NOUN
ejpam-5823	86	17	,	,	PUNCT
ejpam-5823	86	18	a	a	PRON
ejpam-5823	86	19	=	=	X
ejpam-5823	87	1	x+	x+	X
ejpam-5823	87	2	∞∑	∞∑	PROPN
ejpam-5823	87	3	m=1	m=1	X
ejpam-5823	87	4	(	(	PUNCT
ejpam-5823	87	5	−a)m	−a)m	NOUN
ejpam-5823	87	6	4m(1)m(ξ)m	4m(1)m(ξ)m	NUM
ejpam-5823	87	7	xm+1	xm+1	NUM
ejpam-5823	87	8	,	,	PUNCT
ejpam-5823	87	9	x	x	SYM
ejpam-5823	87	10	∈	∈	PROPN
ejpam-5823	87	11	u	u	NOUN
ejpam-5823	87	12	where	where	SCONJ
ejpam-5823	87	13	(	(	PUNCT
ejpam-5823	87	14	ξ	ξ	X
ejpam-5823	87	15	=	=	PRON
ejpam-5823	87	16	c+	c+	VERB
ejpam-5823	87	17	d+2	d+2	NOUN
ejpam-5823	87	18	2	2	NUM
ejpam-5823	87	19	)	)	PUNCT
ejpam-5823	87	20	/∈	/∈	PUNCT
ejpam-5823	87	21	{	{	PUNCT
ejpam-5823	87	22	0,−1,−2	0,−1,−2	NUM
ejpam-5823	87	23	,	,	PUNCT
ejpam-5823	87	24	...	...	PUNCT
ejpam-5823	87	25	}	}	PUNCT
ejpam-5823	87	26	and	and	CCONJ
ejpam-5823	87	27	pochhammer	pochhammer	NOUN
ejpam-5823	87	28	’s	’s	PART
ejpam-5823	87	29	symbol	symbol	NOUN
ejpam-5823	87	30	defined	define	VERB
ejpam-5823	87	31	by	by	ADP
ejpam-5823	87	32	:	:	PUNCT
ejpam-5823	87	33	(	(	PUNCT
ejpam-5823	87	34	a)p	a)p	X
ejpam-5823	87	35	=	=	SYM
ejpam-5823	87	36	(	(	PUNCT
ejpam-5823	87	37	a)(a+	a)(a+	NOUN
ejpam-5823	87	38	1)(a+	1)(a+	NUM
ejpam-5823	87	39	2)	2)	NUM
ejpam-5823	87	40	...	...	PUNCT
ejpam-5823	87	41	(a+	(a+	NOUN
ejpam-5823	87	42	p−	p−	NOUN
ejpam-5823	87	43	1	1	NUM
ejpam-5823	87	44	)	)	PUNCT
ejpam-5823	87	45	.	.	PUNCT
ejpam-5823	88	1	in	in	ADP
ejpam-5823	88	2	this	this	DET
ejpam-5823	88	3	research	research	NOUN
ejpam-5823	88	4	paper	paper	NOUN
ejpam-5823	88	5	,	,	PUNCT
ejpam-5823	88	6	we	we	PRON
ejpam-5823	88	7	discussed	discuss	VERB
ejpam-5823	88	8	the	the	DET
ejpam-5823	88	9	starlikeness	starlikeness	NOUN
ejpam-5823	88	10	and	and	CCONJ
ejpam-5823	88	11	convexity	convexity	NOUN
ejpam-5823	88	12	of	of	ADP
ejpam-5823	88	13	order	order	NOUN
ejpam-5823	88	14	η	η	PROPN
ejpam-5823	88	15	for	for	ADP
ejpam-5823	88	16	normalized	normalize	VERB
ejpam-5823	88	17	form	form	NOUN
ejpam-5823	88	18	of	of	ADP
ejpam-5823	88	19	generalized	generalized	ADJ
ejpam-5823	88	20	bessel	bessel	ADJ
ejpam-5823	88	21	function	function	NOUN
ejpam-5823	88	22	.	.	PUNCT
ejpam-5823	89	1	also	also	ADV
ejpam-5823	89	2	proved	prove	VERB
ejpam-5823	89	3	the	the	DET
ejpam-5823	89	4	following	follow	VERB
ejpam-5823	89	5	inequality	inequality	NOUN
ejpam-5823	89	6	by	by	ADP
ejpam-5823	89	7	partial	partial	ADJ
ejpam-5823	89	8	derivative	derivative	ADJ
ejpam-5823	89	9	and	and	CCONJ
ejpam-5823	89	10	variable	variable	ADJ
ejpam-5823	89	11	extremum	extremum	ADJ
ejpam-5823	89	12	method	method	NOUN
ejpam-5823	89	13	:	:	PUNCT
ejpam-5823	89	14	(	(	PUNCT
ejpam-5823	89	15	q)r	q)r	X
ejpam-5823	89	16	,	,	PUNCT
ejpam-5823	89	17	k	k	PROPN
ejpam-5823	89	18	>	>	X
ejpam-5823	89	19	q(q	q(q	PROPN
ejpam-5823	89	20	+	+	CCONJ
ejpam-5823	89	21	β)r−1	β)r−1	PROPN
ejpam-5823	89	22	.	.	PUNCT
ejpam-5823	90	1	s.	s.	PROPN
ejpam-5823	90	2	a.	a.	PROPN
ejpam-5823	90	3	h.	h.	PROPN
ejpam-5823	90	4	shah	shah	PROPN
ejpam-5823	90	5	et	et	PROPN
ejpam-5823	90	6	al	al	PROPN
ejpam-5823	90	7	.	.	PUNCT
ejpam-5823	90	8	/	/	SYM
ejpam-5823	90	9	eur	eur	PROPN
ejpam-5823	90	10	.	.	PUNCT
ejpam-5823	91	1	j.	j.	PROPN
ejpam-5823	91	2	pure	pure	PROPN
ejpam-5823	91	3	appl	appl	PROPN
ejpam-5823	91	4	.	.	PROPN
ejpam-5823	91	5	math	math	PROPN
ejpam-5823	91	6	,	,	PUNCT
ejpam-5823	91	7	18	18	NUM
ejpam-5823	91	8	(	(	PUNCT
ejpam-5823	91	9	2	2	NUM
ejpam-5823	91	10	)	)	PUNCT
ejpam-5823	91	11	(	(	PUNCT
ejpam-5823	91	12	2025	2025	NUM
ejpam-5823	91	13	)	)	PUNCT
ejpam-5823	91	14	,	,	PUNCT
ejpam-5823	91	15	5823	5823	NUM
ejpam-5823	91	16	5	5	NUM
ejpam-5823	91	17	of	of	ADP
ejpam-5823	91	18	26	26	NUM
ejpam-5823	91	19	we	we	PRON
ejpam-5823	91	20	also	also	ADV
ejpam-5823	91	21	discussed	discuss	VERB
ejpam-5823	91	22	some	some	DET
ejpam-5823	91	23	special	special	ADJ
ejpam-5823	91	24	cases	case	NOUN
ejpam-5823	91	25	and	and	CCONJ
ejpam-5823	91	26	examples	example	NOUN
ejpam-5823	91	27	related	relate	VERB
ejpam-5823	91	28	to	to	ADP
ejpam-5823	91	29	starlikeness	starlikeness	NOUN
ejpam-5823	91	30	and	and	CCONJ
ejpam-5823	91	31	convexity	convexity	NOUN
ejpam-5823	91	32	of	of	ADP
ejpam-5823	91	33	normalized	normalized	ADJ
ejpam-5823	91	34	form	form	NOUN
ejpam-5823	91	35	of	of	ADP
ejpam-5823	91	36	generalized	generalized	ADJ
ejpam-5823	91	37	bessel	bessel	NOUN
ejpam-5823	91	38	function	function	NOUN
ejpam-5823	91	39	and	and	CCONJ
ejpam-5823	91	40	also	also	ADV
ejpam-5823	91	41	discussed	discuss	VERB
ejpam-5823	91	42	starlikeness	starlikeness	NOUN
ejpam-5823	91	43	and	and	CCONJ
ejpam-5823	91	44	convexity	convexity	NOUN
ejpam-5823	91	45	conditons	conditon	NOUN
ejpam-5823	91	46	by	by	ADP
ejpam-5823	91	47	using	use	VERB
ejpam-5823	91	48	silverman	silverman	PROPN
ejpam-5823	91	49	’s	’s	PART
ejpam-5823	91	50	theorem	theorem	PROPN
ejpam-5823	91	51	.	.	PUNCT
ejpam-5823	92	1	a	a	DET
ejpam-5823	92	2	well	well	ADV
ejpam-5823	92	3	-	-	PUNCT
ejpam-5823	92	4	known	know	VERB
ejpam-5823	92	5	homogenous	homogenous	ADJ
ejpam-5823	92	6	differential	differential	NOUN
ejpam-5823	92	7	equation	equation	NOUN
ejpam-5823	92	8	given	give	VERB
ejpam-5823	92	9	explicitly	explicitly	ADV
ejpam-5823	92	10	by	by	ADP
ejpam-5823	92	11	[	[	PUNCT
ejpam-5823	92	12	22	22	NUM
ejpam-5823	92	13	]	]	PUNCT
ejpam-5823	92	14	z2y′′(z	z2y′′(z	PRON
ejpam-5823	92	15	)	)	PUNCT
ejpam-5823	93	1	+	+	CCONJ
ejpam-5823	93	2	zy′(z	zy′(z	NOUN
ejpam-5823	93	3	)	)	PUNCT
ejpam-5823	94	1	+	+	CCONJ
ejpam-5823	94	2	1	1	NUM
ejpam-5823	94	3	k2	k2	NOUN
ejpam-5823	94	4	(	(	PUNCT
ejpam-5823	94	5	bz2k	bz2k	NOUN
ejpam-5823	94	6	−	−	NUM
ejpam-5823	94	7	v2)y(z	v2)y(z	NOUN
ejpam-5823	94	8	)	)	PUNCT
ejpam-5823	94	9	=	=	SYM
ejpam-5823	94	10	0	0	NUM
ejpam-5823	94	11	,	,	PUNCT
ejpam-5823	94	12	gives	give	VERB
ejpam-5823	94	13	solution	solution	NOUN
ejpam-5823	94	14	as	as	ADP
ejpam-5823	94	15	generalized	generalized	ADJ
ejpam-5823	94	16	bessel	bessel	NOUN
ejpam-5823	94	17	k	k	NOUN
ejpam-5823	94	18	-	-	NOUN
ejpam-5823	94	19	function	function	NOUN
ejpam-5823	94	20	,	,	PUNCT
ejpam-5823	94	21	with	with	ADP
ejpam-5823	94	22	k	k	PROPN
ejpam-5823	94	23	∈	∈	PROPN
ejpam-5823	94	24	r+	r+	NOUN
ejpam-5823	94	25	and	and	CCONJ
ejpam-5823	94	26	v	v	ADP
ejpam-5823	94	27	>	>	X
ejpam-5823	94	28	−k	−k	NOUN
ejpam-5823	94	29	.	.	PUNCT
ejpam-5823	95	1	the	the	DET
ejpam-5823	95	2	generalized	generalized	ADJ
ejpam-5823	95	3	bessel	bessel	NOUN
ejpam-5823	95	4	function	function	NOUN
ejpam-5823	95	5	is	be	AUX
ejpam-5823	95	6	defined	define	VERB
ejpam-5823	95	7	as	as	ADP
ejpam-5823	95	8	:	:	PUNCT
ejpam-5823	95	9	kwr	kwr	NOUN
ejpam-5823	95	10	,	,	PUNCT
ejpam-5823	95	11	b(z	b(z	NOUN
ejpam-5823	95	12	)	)	PUNCT
ejpam-5823	95	13	=	=	PUNCT
ejpam-5823	96	1	∞∑	∞∑	NUM
ejpam-5823	96	2	r=0	r=0	PROPN
ejpam-5823	96	3	(	(	PUNCT
ejpam-5823	96	4	−b)r	−b)r	VERB
ejpam-5823	96	5	r!γk(rk	r!γk(rk	ADP
ejpam-5823	96	6	+	+	CCONJ
ejpam-5823	96	7	v	v	NOUN
ejpam-5823	96	8	+	+	CCONJ
ejpam-5823	96	9	k	k	NOUN
ejpam-5823	96	10	)	)	PUNCT
ejpam-5823	96	11	(	(	PUNCT
ejpam-5823	96	12	z	z	NOUN
ejpam-5823	96	13	2	2	NUM
ejpam-5823	96	14	)	)	PUNCT
ejpam-5823	96	15	2r+	2r+	NUM
ejpam-5823	96	16	v	v	ADP
ejpam-5823	96	17	k	k	NOUN
ejpam-5823	96	18	,	,	PUNCT
ejpam-5823	96	19	k	k	PROPN
ejpam-5823	96	20	∈	∈	PROPN
ejpam-5823	96	21	r+	r+	NOUN
ejpam-5823	96	22	,	,	PUNCT
ejpam-5823	96	23	v	v	X
ejpam-5823	96	24	>	>	X
ejpam-5823	96	25	−k	−k	PROPN
ejpam-5823	96	26	,	,	PUNCT
ejpam-5823	96	27	b	b	PROPN
ejpam-5823	96	28	∈	∈	PROPN
ejpam-5823	96	29	r.	r.	NOUN
ejpam-5823	96	30	(	(	PUNCT
ejpam-5823	96	31	6	6	NUM
ejpam-5823	96	32	)	)	PUNCT
ejpam-5823	96	33	γk	γk	PROPN
ejpam-5823	96	34	stands	stand	VERB
ejpam-5823	96	35	for	for	ADP
ejpam-5823	96	36	k	k	PROPN
ejpam-5823	96	37	-	-	PUNCT
ejpam-5823	96	38	gamma	gamma	NOUN
ejpam-5823	96	39	defined	define	VERB
ejpam-5823	96	40	as	as	ADP
ejpam-5823	96	41	:	:	PUNCT
ejpam-5823	96	42	γk(a	γk(a	NUM
ejpam-5823	96	43	)	)	PUNCT
ejpam-5823	96	44	=	=	SYM
ejpam-5823	97	1	∫	∫	PROPN
ejpam-5823	98	1	∞	∞	NUM
ejpam-5823	98	2	0	0	NUM
ejpam-5823	99	1	ta−1e	ta−1e	NUM
ejpam-5823	99	2	−tk	−tk	NOUN
ejpam-5823	99	3	k	k	PROPN
ejpam-5823	99	4	dt	dt	PROPN
ejpam-5823	99	5	,	,	PUNCT
ejpam-5823	99	6	re(a	re(a	NOUN
ejpam-5823	99	7	)	)	PUNCT
ejpam-5823	99	8	>	>	X
ejpam-5823	99	9	0	0	X
ejpam-5823	99	10	.	.	PUNCT
ejpam-5823	100	1	some	some	DET
ejpam-5823	100	2	basic	basic	ADJ
ejpam-5823	100	3	properties	property	NOUN
ejpam-5823	100	4	of	of	ADP
ejpam-5823	100	5	k	k	PROPN
ejpam-5823	100	6	-	-	PUNCT
ejpam-5823	100	7	gamma	gamma	NOUN
ejpam-5823	100	8	functions	function	NOUN
ejpam-5823	100	9	[	[	X
ejpam-5823	100	10	23	23	NUM
ejpam-5823	100	11	]	]	PUNCT
ejpam-5823	100	12	are	be	AUX
ejpam-5823	100	13	:	:	PUNCT
ejpam-5823	100	14	γk(a	γk(a	X
ejpam-5823	100	15	)	)	PUNCT
ejpam-5823	101	1	=	=	SYM
ejpam-5823	102	1	k	k	PROPN
ejpam-5823	102	2	a	a	DET
ejpam-5823	102	3	k	k	X
ejpam-5823	102	4	−1γ	−1γ	X
ejpam-5823	102	5	(	(	PUNCT
ejpam-5823	102	6	a	a	DET
ejpam-5823	102	7	k	k	NOUN
ejpam-5823	102	8	)	)	PUNCT
ejpam-5823	102	9	γk(a	γk(a	PUNCT
ejpam-5823	102	10	)	)	PUNCT
ejpam-5823	102	11	=	=	SYM
ejpam-5823	102	12	aγk(a	aγk(a	PROPN
ejpam-5823	102	13	)	)	PUNCT
ejpam-5823	102	14	γk(k	γk(k	NUM
ejpam-5823	102	15	)	)	PUNCT
ejpam-5823	102	16	=	=	SYM
ejpam-5823	103	1	1	1	X
ejpam-5823	103	2	.	.	X
ejpam-5823	103	3	observe	observe	VERB
ejpam-5823	103	4	that	that	SCONJ
ejpam-5823	103	5	if	if	SCONJ
ejpam-5823	103	6	k	k	PROPN
ejpam-5823	103	7	=	=	SYM
ejpam-5823	103	8	1	1	NUM
ejpam-5823	103	9	and	and	CCONJ
ejpam-5823	103	10	b	b	X
ejpam-5823	103	11	=	=	SYM
ejpam-5823	103	12	1	1	NUM
ejpam-5823	103	13	,	,	PUNCT
ejpam-5823	103	14	the	the	DET
ejpam-5823	103	15	function	function	NOUN
ejpam-5823	103	16	reduced	reduce	VERB
ejpam-5823	103	17	to	to	ADP
ejpam-5823	103	18	classic	classic	ADJ
ejpam-5823	103	19	bessel	bessel	NOUN
ejpam-5823	103	20	function	function	NOUN
ejpam-5823	103	21	jv	jv	NOUN
ejpam-5823	103	22	jv(z	jv(z	PUNCT
ejpam-5823	103	23	)	)	PUNCT
ejpam-5823	103	24	=	=	SYM
ejpam-5823	103	25	1wv,1(z	1wv,1(z	X
ejpam-5823	103	26	)	)	PUNCT
ejpam-5823	103	27	=	=	PUNCT
ejpam-5823	104	1	∞∑	∞∑	NUM
ejpam-5823	104	2	r=0	r=0	PROPN
ejpam-5823	104	3	(	(	PUNCT
ejpam-5823	104	4	−1)r	−1)r	ADJ
ejpam-5823	104	5	r!γ(r	r!γ(r	NOUN
ejpam-5823	104	6	+	+	X
ejpam-5823	104	7	v	v	X
ejpam-5823	104	8	+	+	NOUN
ejpam-5823	104	9	1	1	NUM
ejpam-5823	104	10	)	)	PUNCT
ejpam-5823	104	11	(	(	PUNCT
ejpam-5823	104	12	z	z	NOUN
ejpam-5823	104	13	2	2	NUM
ejpam-5823	104	14	)	)	PUNCT
ejpam-5823	104	15	2r+v	2r+v	NUM
ejpam-5823	104	16	.	.	PUNCT
ejpam-5823	105	1	if	if	SCONJ
ejpam-5823	105	2	k	k	PROPN
ejpam-5823	105	3	=	=	SYM
ejpam-5823	105	4	1	1	NUM
ejpam-5823	105	5	and	and	CCONJ
ejpam-5823	105	6	b	b	NOUN
ejpam-5823	105	7	=	=	SYM
ejpam-5823	105	8	−1	−1	NOUN
ejpam-5823	105	9	,	,	PUNCT
ejpam-5823	105	10	the	the	DET
ejpam-5823	105	11	function	function	NOUN
ejpam-5823	105	12	reduced	reduce	VERB
ejpam-5823	105	13	to	to	ADP
ejpam-5823	105	14	modified	modify	VERB
ejpam-5823	105	15	bessel	bessel	NOUN
ejpam-5823	105	16	function	function	NOUN
ejpam-5823	105	17	iv	iv	NUM
ejpam-5823	105	18	iv(z	iv(z	NOUN
ejpam-5823	105	19	)	)	PUNCT
ejpam-5823	105	20	=	=	SYM
ejpam-5823	105	21	1wv,−1(z	1wv,−1(z	X
ejpam-5823	105	22	)	)	PUNCT
ejpam-5823	105	23	=	=	PUNCT
ejpam-5823	106	1	∞∑	∞∑	NUM
ejpam-5823	106	2	r=0	r=0	NUM
ejpam-5823	106	3	1	1	NUM
ejpam-5823	106	4	r!γ(r	r!γ(r	NOUN
ejpam-5823	106	5	+	+	X
ejpam-5823	106	6	v	v	X
ejpam-5823	106	7	+	+	NOUN
ejpam-5823	106	8	1	1	NUM
ejpam-5823	106	9	)	)	PUNCT
ejpam-5823	106	10	(	(	PUNCT
ejpam-5823	106	11	z	z	NOUN
ejpam-5823	106	12	2	2	NUM
ejpam-5823	106	13	)	)	PUNCT
ejpam-5823	106	14	2r+v	2r+v	NUM
ejpam-5823	106	15	.	.	PUNCT
ejpam-5823	107	1	k	k	X
ejpam-5823	107	2	-	-	PUNCT
ejpam-5823	107	3	digamma	digamma	PROPN
ejpam-5823	107	4	function	function	NOUN
ejpam-5823	107	5	[	[	X
ejpam-5823	107	6	24	24	NUM
ejpam-5823	107	7	]	]	PUNCT
ejpam-5823	107	8	is	be	AUX
ejpam-5823	107	9	defined	define	VERB
ejpam-5823	107	10	as	as	ADP
ejpam-5823	107	11	the	the	DET
ejpam-5823	107	12	logarithmic	logarithmic	ADJ
ejpam-5823	107	13	derivative	derivative	NOUN
ejpam-5823	107	14	of	of	ADP
ejpam-5823	107	15	k	k	PROPN
ejpam-5823	107	16	-	-	PUNCT
ejpam-5823	107	17	gamma	gamma	NOUN
ejpam-5823	107	18	function	function	NOUN
ejpam-5823	107	19	,	,	PUNCT
ejpam-5823	107	20	which	which	PRON
ejpam-5823	107	21	is	be	AUX
ejpam-5823	107	22	given	give	VERB
ejpam-5823	107	23	as	as	ADP
ejpam-5823	107	24	:	:	PUNCT
ejpam-5823	107	25	ψk(a	ψk(a	NUM
ejpam-5823	107	26	)	)	PUNCT
ejpam-5823	107	27	=	=	SYM
ejpam-5823	107	28	∂	∂	NUM
ejpam-5823	108	1	∂a	∂a	NOUN
ejpam-5823	108	2	log	log	NOUN
ejpam-5823	108	3	γk(a	γk(a	PUNCT
ejpam-5823	108	4	)	)	PUNCT
ejpam-5823	108	5	=	=	SYM
ejpam-5823	108	6	γ′	γ′	PROPN
ejpam-5823	108	7	k(a	k(a	PROPN
ejpam-5823	108	8	)	)	PUNCT
ejpam-5823	108	9	γk(a	γk(a	NUM
ejpam-5823	108	10	)	)	PUNCT
ejpam-5823	108	11	.	.	PUNCT
ejpam-5823	109	1	(	(	PUNCT
ejpam-5823	109	2	7	7	X
ejpam-5823	109	3	)	)	PUNCT
ejpam-5823	109	4	s.	s.	PROPN
ejpam-5823	109	5	a.	a.	PROPN
ejpam-5823	109	6	h.	h.	PROPN
ejpam-5823	109	7	shah	shah	PROPN
ejpam-5823	109	8	et	et	PROPN
ejpam-5823	109	9	al	al	PROPN
ejpam-5823	109	10	.	.	PUNCT
ejpam-5823	109	11	/	/	SYM
ejpam-5823	109	12	eur	eur	PROPN
ejpam-5823	109	13	.	.	PUNCT
ejpam-5823	110	1	j.	j.	PROPN
ejpam-5823	110	2	pure	pure	PROPN
ejpam-5823	110	3	appl	appl	PROPN
ejpam-5823	110	4	.	.	PROPN
ejpam-5823	110	5	math	math	PROPN
ejpam-5823	110	6	,	,	PUNCT
ejpam-5823	110	7	18	18	NUM
ejpam-5823	110	8	(	(	PUNCT
ejpam-5823	110	9	2	2	NUM
ejpam-5823	110	10	)	)	PUNCT
ejpam-5823	110	11	(	(	PUNCT
ejpam-5823	110	12	2025	2025	NUM
ejpam-5823	110	13	)	)	PUNCT
ejpam-5823	110	14	,	,	PUNCT
ejpam-5823	110	15	5823	5823	NUM
ejpam-5823	110	16	6	6	NUM
ejpam-5823	110	17	of	of	ADP
ejpam-5823	110	18	26	26	NUM
ejpam-5823	110	19	some	some	DET
ejpam-5823	110	20	basic	basic	ADJ
ejpam-5823	110	21	properties	property	NOUN
ejpam-5823	110	22	of	of	ADP
ejpam-5823	110	23	k	k	PROPN
ejpam-5823	110	24	-	-	ADJ
ejpam-5823	110	25	digamma	digamma	PROPN
ejpam-5823	110	26	function	function	NOUN
ejpam-5823	110	27	[	[	X
ejpam-5823	110	28	24	24	NUM
ejpam-5823	110	29	,	,	PUNCT
ejpam-5823	110	30	25	25	NUM
ejpam-5823	110	31	]	]	PUNCT
ejpam-5823	110	32	are	be	AUX
ejpam-5823	110	33	:	:	PUNCT
ejpam-5823	110	34	ψk(a+	ψk(a+	PROPN
ejpam-5823	110	35	k	k	NOUN
ejpam-5823	110	36	)	)	PUNCT
ejpam-5823	110	37	=	=	PUNCT
ejpam-5823	110	38	ψk(a	ψk(a	PRON
ejpam-5823	110	39	)	)	PUNCT
ejpam-5823	111	1	+	+	CCONJ
ejpam-5823	111	2	1	1	NUM
ejpam-5823	111	3	a	a	PRON
ejpam-5823	111	4	ψk(a	ψk(a	NOUN
ejpam-5823	111	5	)	)	PUNCT
ejpam-5823	111	6	=	=	SYM
ejpam-5823	112	1	ln	ln	NOUN
ejpam-5823	113	1	k	k	PROPN
ejpam-5823	113	2	k	k	PROPN
ejpam-5823	114	1	+	+	PROPN
ejpam-5823	114	2	1	1	NUM
ejpam-5823	114	3	k	k	NOUN
ejpam-5823	114	4	ψ	ψ	X
ejpam-5823	114	5	(	(	PUNCT
ejpam-5823	114	6	x	x	X
ejpam-5823	114	7	k	k	PROPN
ejpam-5823	114	8	)	)	PUNCT
ejpam-5823	114	9	.	.	PUNCT
ejpam-5823	115	1	the	the	DET
ejpam-5823	115	2	function	function	NOUN
ejpam-5823	115	3	z	z	PROPN
ejpam-5823	115	4	→k	→k	PROPN
ejpam-5823	115	5	wv	wv	PROPN
ejpam-5823	115	6	,	,	PUNCT
ejpam-5823	115	7	b(z	b(z	PROPN
ejpam-5823	115	8	)	)	PUNCT
ejpam-5823	115	9	/∈	/∈	PUNCT
ejpam-5823	116	1	a.	a.	NOUN
ejpam-5823	117	1	so	so	ADV
ejpam-5823	117	2	,	,	PUNCT
ejpam-5823	117	3	we	we	PRON
ejpam-5823	117	4	define	define	VERB
ejpam-5823	117	5	a	a	DET
ejpam-5823	117	6	function	function	NOUN
ejpam-5823	117	7	originating	originate	VERB
ejpam-5823	117	8	from	from	ADP
ejpam-5823	117	9	kwv	kwv	PROPN
ejpam-5823	117	10	,	,	PUNCT
ejpam-5823	117	11	b(z	b(z	PROPN
ejpam-5823	117	12	)	)	PUNCT
ejpam-5823	117	13	as	as	ADP
ejpam-5823	117	14	:	:	PUNCT
ejpam-5823	117	15	khv	khv	NOUN
ejpam-5823	117	16	,	,	PUNCT
ejpam-5823	117	17	b(z	b(z	NOUN
ejpam-5823	117	18	)	)	PUNCT
ejpam-5823	117	19	=	=	PUNCT
ejpam-5823	118	1	(	(	PUNCT
ejpam-5823	118	2	2	2	NUM
ejpam-5823	118	3	√	√	PROPN
ejpam-5823	118	4	k	k	PROPN
ejpam-5823	118	5	)	)	PUNCT
ejpam-5823	118	6	v	v	PROPN
ejpam-5823	118	7	k	k	PROPN
ejpam-5823	118	8	γk(v	γk(v	PROPN
ejpam-5823	119	1	+	+	CCONJ
ejpam-5823	119	2	k	k	X
ejpam-5823	119	3	)	)	PUNCT
ejpam-5823	119	4	z−	z−	PROPN
ejpam-5823	119	5	v	v	ADP
ejpam-5823	119	6	2k	2k	NUM
ejpam-5823	119	7	kwv	kwv	PROPN
ejpam-5823	119	8	,	,	PUNCT
ejpam-5823	119	9	b	b	PROPN
ejpam-5823	119	10	(	(	PUNCT
ejpam-5823	119	11	√	√	PROPN
ejpam-5823	119	12	z	z	NOUN
ejpam-5823	119	13	k	k	NOUN
ejpam-5823	119	14	)	)	PUNCT
ejpam-5823	120	1	=	=	PUNCT
ejpam-5823	120	2	(	(	PUNCT
ejpam-5823	120	3	2	2	NUM
ejpam-5823	120	4	√	√	PROPN
ejpam-5823	120	5	k	k	PROPN
ejpam-5823	120	6	)	)	PUNCT
ejpam-5823	120	7	v	v	PROPN
ejpam-5823	120	8	k	k	PROPN
ejpam-5823	120	9	γk(v	γk(v	PROPN
ejpam-5823	121	1	+	+	CCONJ
ejpam-5823	121	2	k	k	X
ejpam-5823	121	3	)	)	PUNCT
ejpam-5823	121	4	z−	z−	PROPN
ejpam-5823	121	5	v	v	ADP
ejpam-5823	121	6	2k	2k	NUM
ejpam-5823	121	7			PUNCT
ejpam-5823	122	1	∞∑	∞∑	PRON
ejpam-5823	122	2	r=0	r=0	PROPN
ejpam-5823	122	3	(	(	PUNCT
ejpam-5823	122	4	−b)r	−b)r	NOUN
ejpam-5823	122	5	(	(	PUNCT
ejpam-5823	122	6	√	√	PROPN
ejpam-5823	122	7	z	z	NOUN
ejpam-5823	122	8	2	2	NUM
ejpam-5823	122	9	√	√	PROPN
ejpam-5823	122	10	k	k	PROPN
ejpam-5823	122	11	)	)	PUNCT
ejpam-5823	122	12	2r+	2r+	NUM
ejpam-5823	123	1	v	v	ADP
ejpam-5823	123	2	k	k	NOUN
ejpam-5823	123	3	r	r	NOUN
ejpam-5823	123	4	!	!	PUNCT
ejpam-5823	123	5	γk(rk	γk(rk	X
ejpam-5823	124	1	+	+	CCONJ
ejpam-5823	124	2	v	v	X
ejpam-5823	124	3	+	+	CCONJ
ejpam-5823	124	4	k	k	X
ejpam-5823	124	5	)	)	PUNCT
ejpam-5823	124	6			NOUN
ejpam-5823	124	7	=	=	SYM
ejpam-5823	125	1	∞∑	∞∑	NUM
ejpam-5823	125	2	r=0	r=0	PROPN
ejpam-5823	125	3	(	(	PUNCT
ejpam-5823	125	4	−b)r	−b)r	NOUN
ejpam-5823	125	5	zr	zr	NOUN
ejpam-5823	125	6	r	r	NOUN
ejpam-5823	125	7	!	!	PUNCT
ejpam-5823	125	8	4r	4r	PROPN
ejpam-5823	125	9	kr	kr	PROPN
ejpam-5823	125	10	(	(	PUNCT
ejpam-5823	125	11	v	v	NOUN
ejpam-5823	125	12	+	+	CCONJ
ejpam-5823	125	13	k)r	k)r	X
ejpam-5823	125	14	,	,	PUNCT
ejpam-5823	125	15	k	k	X
ejpam-5823	125	16	=	=	PUNCT
ejpam-5823	126	1	∞∑	∞∑	NUM
ejpam-5823	126	2	r=0	r=0	PROPN
ejpam-5823	126	3	(	(	PUNCT
ejpam-5823	126	4	−b)r	−b)r	NOUN
ejpam-5823	126	5	zr	zr	NOUN
ejpam-5823	126	6	r	r	NOUN
ejpam-5823	126	7	!	!	PUNCT
ejpam-5823	126	8	4r	4r	PROPN
ejpam-5823	126	9	kr	kr	PROPN
ejpam-5823	126	10	(	(	PUNCT
ejpam-5823	126	11	ξ)r	ξ)r	NOUN
ejpam-5823	126	12	,	,	PUNCT
ejpam-5823	126	13	k	k	PROPN
ejpam-5823	126	14	,	,	PUNCT
ejpam-5823	126	15	(	(	PUNCT
ejpam-5823	126	16	8)	8)	NUM
ejpam-5823	126	17	where	where	SCONJ
ejpam-5823	126	18	ξ	ξ	PROPN
ejpam-5823	126	19	=	=	SYM
ejpam-5823	126	20	v	v	PROPN
ejpam-5823	126	21	+	+	CCONJ
ejpam-5823	126	22	k	k	PROPN
ejpam-5823	126	23	/∈	/∈	PUNCT
ejpam-5823	126	24	{	{	PUNCT
ejpam-5823	126	25	0,−1,−2	0,−1,−2	NUM
ejpam-5823	126	26	,	,	PUNCT
ejpam-5823	126	27	...	...	PUNCT
ejpam-5823	126	28	}	}	PUNCT
ejpam-5823	126	29	.	.	PUNCT
ejpam-5823	127	1	2	2	X
ejpam-5823	127	2	.	.	X
ejpam-5823	127	3	main	main	ADJ
ejpam-5823	127	4	results	result	NOUN
ejpam-5823	127	5	keeping	keep	VERB
ejpam-5823	127	6	the	the	DET
ejpam-5823	127	7	above	above	ADJ
ejpam-5823	127	8	representations	representation	NOUN
ejpam-5823	127	9	in	in	ADP
ejpam-5823	127	10	mind	mind	NOUN
ejpam-5823	127	11	,	,	PUNCT
ejpam-5823	127	12	the	the	DET
ejpam-5823	127	13	normalized	normalize	VERB
ejpam-5823	127	14	form	form	NOUN
ejpam-5823	127	15	of	of	ADP
ejpam-5823	127	16	khξ	khξ	NOUN
ejpam-5823	127	17	,	,	PUNCT
ejpam-5823	127	18	b(z	b(z	PROPN
ejpam-5823	127	19	)	)	PUNCT
ejpam-5823	127	20	is	be	AUX
ejpam-5823	127	21	defined	define	VERB
ejpam-5823	127	22	as	as	ADP
ejpam-5823	127	23	:	:	PUNCT
ejpam-5823	127	24	definition	definition	NOUN
ejpam-5823	127	25	1	1	NUM
ejpam-5823	127	26	.	.	PUNCT
ejpam-5823	128	1	for	for	ADP
ejpam-5823	128	2	k	k	PROPN
ejpam-5823	128	3	∈	∈	PROPN
ejpam-5823	128	4	r+	r+	X
ejpam-5823	128	5	,	,	PUNCT
ejpam-5823	128	6	v	v	X
ejpam-5823	128	7	>	>	X
ejpam-5823	128	8	−k	−k	PROPN
ejpam-5823	128	9	,	,	PUNCT
ejpam-5823	128	10	b	b	X
ejpam-5823	128	11	∈	∈	PROPN
ejpam-5823	128	12	r	r	NOUN
ejpam-5823	128	13	,	,	PUNCT
ejpam-5823	128	14	the	the	DET
ejpam-5823	128	15	normalized	normalize	VERB
ejpam-5823	128	16	form	form	NOUN
ejpam-5823	128	17	of	of	ADP
ejpam-5823	128	18	khξ	khξ	NOUN
ejpam-5823	128	19	,	,	PUNCT
ejpam-5823	128	20	b(z	b(z	PROPN
ejpam-5823	128	21	)	)	PUNCT
ejpam-5823	128	22	is	be	AUX
ejpam-5823	128	23	given	give	VERB
ejpam-5823	128	24	by	by	ADP
ejpam-5823	128	25	:	:	PUNCT
ejpam-5823	128	26	khξ	khξ	PROPN
ejpam-5823	128	27	,	,	PUNCT
ejpam-5823	128	28	b(z	b(z	NOUN
ejpam-5823	128	29	)	)	PUNCT
ejpam-5823	128	30	=	=	SYM
ejpam-5823	128	31	z	z	NOUN
ejpam-5823	128	32	.	.	PUNCT
ejpam-5823	129	1	khξ	khξ	NOUN
ejpam-5823	129	2	,	,	PUNCT
ejpam-5823	129	3	b(z	b(z	NOUN
ejpam-5823	129	4	)	)	PUNCT
ejpam-5823	129	5	=	=	SYM
ejpam-5823	130	1	z	z	NOUN
ejpam-5823	130	2	+	+	NOUN
ejpam-5823	130	3	∞∑	∞∑	NUM
ejpam-5823	130	4	r=1	r=1	NOUN
ejpam-5823	130	5	(	(	PUNCT
ejpam-5823	130	6	−b)r	−b)r	NOUN
ejpam-5823	130	7	zr+1	zr+1	NUM
ejpam-5823	131	1	r	r	NOUN
ejpam-5823	131	2	!	!	NOUN
ejpam-5823	131	3	4r	4r	PROPN
ejpam-5823	131	4	kr	kr	PROPN
ejpam-5823	131	5	(	(	PUNCT
ejpam-5823	131	6	ξ)r	ξ)r	NOUN
ejpam-5823	131	7	,	,	PUNCT
ejpam-5823	131	8	k	k	PROPN
ejpam-5823	131	9	,	,	PUNCT
ejpam-5823	131	10	(	(	PUNCT
ejpam-5823	131	11	9	9	X
ejpam-5823	131	12	)	)	PUNCT
ejpam-5823	131	13	where	where	SCONJ
ejpam-5823	131	14	ξ	ξ	X
ejpam-5823	131	15	=	=	SYM
ejpam-5823	131	16	v	v	PROPN
ejpam-5823	131	17	+	+	CCONJ
ejpam-5823	131	18	k	k	PROPN
ejpam-5823	131	19	∈	∈	PROPN
ejpam-5823	131	20	(	(	PUNCT
ejpam-5823	131	21	0,+∞	0,+∞	NUM
ejpam-5823	131	22	)	)	PUNCT
ejpam-5823	131	23	.	.	PUNCT
ejpam-5823	132	1	we	we	PRON
ejpam-5823	132	2	will	will	AUX
ejpam-5823	132	3	be	be	AUX
ejpam-5823	132	4	in	in	ADP
ejpam-5823	132	5	need	need	NOUN
ejpam-5823	132	6	of	of	ADP
ejpam-5823	132	7	the	the	DET
ejpam-5823	132	8	following	follow	VERB
ejpam-5823	132	9	lemma	lemma	PROPN
ejpam-5823	132	10	in	in	ADP
ejpam-5823	132	11	our	our	PRON
ejpam-5823	132	12	research	research	NOUN
ejpam-5823	132	13	.	.	PUNCT
ejpam-5823	133	1	at	at	ADP
ejpam-5823	133	2	first	first	ADV
ejpam-5823	133	3	,	,	PUNCT
ejpam-5823	133	4	this	this	PRON
ejpam-5823	133	5	was	be	AUX
ejpam-5823	133	6	proved	prove	VERB
ejpam-5823	133	7	in	in	ADP
ejpam-5823	133	8	classical	classical	ADJ
ejpam-5823	133	9	form	form	NOUN
ejpam-5823	133	10	in	in	ADP
ejpam-5823	133	11	[	[	X
ejpam-5823	133	12	21	21	NUM
ejpam-5823	133	13	]	]	PUNCT
ejpam-5823	133	14	,	,	PUNCT
ejpam-5823	133	15	then	then	ADV
ejpam-5823	133	16	proved	prove	VERB
ejpam-5823	133	17	by	by	ADP
ejpam-5823	133	18	bulboaca	bulboaca	NOUN
ejpam-5823	133	19	and	and	CCONJ
ejpam-5823	133	20	zayed	zaye	VERB
ejpam-5823	133	21	in	in	ADP
ejpam-5823	133	22	[	[	X
ejpam-5823	133	23	1	1	NUM
ejpam-5823	133	24	]	]	PUNCT
ejpam-5823	133	25	by	by	ADP
ejpam-5823	133	26	partial	partial	ADJ
ejpam-5823	133	27	derivative	derivative	ADJ
ejpam-5823	133	28	and	and	CCONJ
ejpam-5823	133	29	variable	variable	ADJ
ejpam-5823	133	30	extremum	extremum	ADJ
ejpam-5823	133	31	technique	technique	NOUN
ejpam-5823	133	32	.	.	PUNCT
ejpam-5823	134	1	now	now	ADV
ejpam-5823	134	2	we	we	PRON
ejpam-5823	134	3	are	be	AUX
ejpam-5823	134	4	proving	prove	VERB
ejpam-5823	134	5	this	this	DET
ejpam-5823	134	6	lemma	lemma	PROPN
ejpam-5823	134	7	for	for	ADP
ejpam-5823	134	8	k	k	NOUN
ejpam-5823	134	9	-	-	NOUN
ejpam-5823	134	10	pochammer	pochammer	NOUN
ejpam-5823	134	11	by	by	ADP
ejpam-5823	134	12	the	the	DET
ejpam-5823	134	13	technique	technique	NOUN
ejpam-5823	134	14	as	as	ADP
ejpam-5823	134	15	bulboaca	bulboaca	NOUN
ejpam-5823	134	16	and	and	CCONJ
ejpam-5823	134	17	zayed	zayed	ADJ
ejpam-5823	134	18	.	.	PUNCT
ejpam-5823	135	1	it	it	PRON
ejpam-5823	135	2	is	be	AUX
ejpam-5823	135	3	shown	show	VERB
ejpam-5823	135	4	for	for	ADP
ejpam-5823	135	5	r	r	PROPN
ejpam-5823	135	6	∈	∈	PROPN
ejpam-5823	135	7	n\{1	n\{1	NOUN
ejpam-5823	135	8	,	,	PUNCT
ejpam-5823	135	9	2	2	NUM
ejpam-5823	135	10	}	}	PUNCT
ejpam-5823	135	11	,	,	PUNCT
ejpam-5823	135	12	q	q	X
ejpam-5823	135	13	>	>	X
ejpam-5823	135	14	0	0	PROPN
ejpam-5823	135	15	,	,	PUNCT
ejpam-5823	135	16	k	k	PROPN
ejpam-5823	135	17	∈	∈	PROPN
ejpam-5823	135	18	r+	r+	NOUN
ejpam-5823	135	19	,	,	PUNCT
ejpam-5823	135	20	0	0	NUM
ejpam-5823	135	21	≤	≤	NUM
ejpam-5823	135	22	β	β	X
ejpam-5823	135	23	≤	≤	NUM
ejpam-5823	135	24	√	√	ADP
ejpam-5823	135	25	2	2	NUM
ejpam-5823	135	26	,	,	PUNCT
ejpam-5823	135	27	the	the	DET
ejpam-5823	135	28	inequality	inequality	NOUN
ejpam-5823	135	29	satisfied	satisfied	ADJ
ejpam-5823	135	30	as	as	SCONJ
ejpam-5823	135	31	follows	follow	VERB
ejpam-5823	135	32	:	:	PUNCT
ejpam-5823	135	33	lemma	lemma	PROPN
ejpam-5823	136	1	1	1	X
ejpam-5823	136	2	.	.	PUNCT
ejpam-5823	137	1	if	if	SCONJ
ejpam-5823	137	2	q	q	PROPN
ejpam-5823	137	3	>	>	X
ejpam-5823	137	4	0	0	PROPN
ejpam-5823	137	5	,	,	PUNCT
ejpam-5823	137	6	k	k	PROPN
ejpam-5823	137	7	∈	∈	PROPN
ejpam-5823	137	8	r+	r+	NOUN
ejpam-5823	137	9	,	,	PUNCT
ejpam-5823	137	10	0	0	NUM
ejpam-5823	137	11	≤	≤	NUM
ejpam-5823	137	12	β	β	X
ejpam-5823	137	13	≤	≤	ADJ
ejpam-5823	137	14	β0	β0	PROPN
ejpam-5823	137	15	=	=	NOUN
ejpam-5823	137	16	√	√	NUM
ejpam-5823	137	17	2	2	NUM
ejpam-5823	137	18	≃	≃	VERB
ejpam-5823	137	19	1.4142	1.4142	NUM
ejpam-5823	137	20	...	...	PUNCT
ejpam-5823	137	21	,	,	PUNCT
ejpam-5823	137	22	and	and	CCONJ
ejpam-5823	137	23	r	r	NOUN
ejpam-5823	137	24	∈	∈	PROPN
ejpam-5823	137	25	n\{1	n\{1	NOUN
ejpam-5823	137	26	,	,	PUNCT
ejpam-5823	137	27	2	2	NUM
ejpam-5823	137	28	}	}	PUNCT
ejpam-5823	137	29	,	,	PUNCT
ejpam-5823	137	30	the	the	DET
ejpam-5823	137	31	results	result	NOUN
ejpam-5823	137	32	will	will	AUX
ejpam-5823	137	33	sharp	sharp	VERB
ejpam-5823	137	34	(	(	PUNCT
ejpam-5823	137	35	q)r	q)r	X
ejpam-5823	137	36	,	,	PUNCT
ejpam-5823	137	37	k	k	PROPN
ejpam-5823	137	38	>	>	X
ejpam-5823	137	39	q(q	q(q	PROPN
ejpam-5823	137	40	+	+	CCONJ
ejpam-5823	137	41	β)r−1	β)r−1	PROPN
ejpam-5823	137	42	.	.	PUNCT
ejpam-5823	138	1	(	(	PUNCT
ejpam-5823	138	2	10	10	NUM
ejpam-5823	138	3	)	)	PUNCT
ejpam-5823	138	4	s.	s.	PROPN
ejpam-5823	138	5	a.	a.	PROPN
ejpam-5823	138	6	h.	h.	PROPN
ejpam-5823	138	7	shah	shah	PROPN
ejpam-5823	138	8	et	et	PROPN
ejpam-5823	138	9	al	al	PROPN
ejpam-5823	138	10	.	.	PUNCT
ejpam-5823	138	11	/	/	SYM
ejpam-5823	138	12	eur	eur	PROPN
ejpam-5823	138	13	.	.	PUNCT
ejpam-5823	139	1	j.	j.	PROPN
ejpam-5823	139	2	pure	pure	PROPN
ejpam-5823	139	3	appl	appl	PROPN
ejpam-5823	139	4	.	.	PROPN
ejpam-5823	139	5	math	math	PROPN
ejpam-5823	139	6	,	,	PUNCT
ejpam-5823	139	7	18	18	NUM
ejpam-5823	139	8	(	(	PUNCT
ejpam-5823	139	9	2	2	NUM
ejpam-5823	139	10	)	)	PUNCT
ejpam-5823	139	11	(	(	PUNCT
ejpam-5823	139	12	2025	2025	NUM
ejpam-5823	139	13	)	)	PUNCT
ejpam-5823	139	14	,	,	PUNCT
ejpam-5823	139	15	5823	5823	NUM
ejpam-5823	139	16	7	7	NUM
ejpam-5823	139	17	of	of	ADP
ejpam-5823	139	18	26	26	NUM
ejpam-5823	139	19	proof	proof	NOUN
ejpam-5823	139	20	.	.	PUNCT
ejpam-5823	140	1	take	take	VERB
ejpam-5823	140	2	fk	fk	INTJ
ejpam-5823	140	3	:	:	PUNCT
ejpam-5823	140	4	(	(	PUNCT
ejpam-5823	140	5	0,+∞)×	0,+∞)×	X
ejpam-5823	141	1	[	[	X
ejpam-5823	141	2	3,+∞	3,+∞	NUM
ejpam-5823	141	3	)	)	PUNCT
ejpam-5823	141	4	→	→	SYM
ejpam-5823	141	5	r	r	NOUN
ejpam-5823	141	6	be	be	AUX
ejpam-5823	141	7	defined	define	VERB
ejpam-5823	141	8	by	by	ADP
ejpam-5823	141	9	:	:	PUNCT
ejpam-5823	141	10	fk(q	fk(q	NUM
ejpam-5823	141	11	,	,	PUNCT
ejpam-5823	141	12	rk	rk	NOUN
ejpam-5823	141	13	)	)	PUNCT
ejpam-5823	141	14	=	=	PUNCT
ejpam-5823	141	15	γk(q	γk(q	NOUN
ejpam-5823	141	16	+	+	CCONJ
ejpam-5823	141	17	rk	rk	NOUN
ejpam-5823	141	18	)	)	PUNCT
ejpam-5823	141	19	γk(q	γk(q	NOUN
ejpam-5823	142	1	+	+	CCONJ
ejpam-5823	143	1	k	k	X
ejpam-5823	143	2	)	)	PUNCT
ejpam-5823	143	3	(	(	PUNCT
ejpam-5823	143	4	q	q	NOUN
ejpam-5823	143	5	+	+	CCONJ
ejpam-5823	143	6	β)1−r	β)1−r	ADJ
ejpam-5823	143	7	−	−	NOUN
ejpam-5823	143	8	1	1	NUM
ejpam-5823	143	9	,	,	PUNCT
ejpam-5823	143	10	(	(	PUNCT
ejpam-5823	143	11	11	11	NUM
ejpam-5823	143	12	)	)	PUNCT
ejpam-5823	143	13	where	where	SCONJ
ejpam-5823	143	14	0	0	NUM
ejpam-5823	143	15	≤	≤	NUM
ejpam-5823	143	16	β	β	X
ejpam-5823	143	17	≤	≤	NUM
ejpam-5823	143	18	2	2	NUM
ejpam-5823	143	19	.	.	PUNCT
ejpam-5823	144	1	by	by	ADP
ejpam-5823	144	2	simple	simple	ADJ
ejpam-5823	144	3	computation	computation	NOUN
ejpam-5823	144	4	,	,	PUNCT
ejpam-5823	144	5	∂	∂	NOUN
ejpam-5823	144	6	∂r	∂r	PROPN
ejpam-5823	144	7	(	(	PUNCT
ejpam-5823	144	8	fk(q	fk(q	NOUN
ejpam-5823	144	9	,	,	PUNCT
ejpam-5823	144	10	rk	rk	NOUN
ejpam-5823	144	11	)	)	PUNCT
ejpam-5823	144	12	)	)	PUNCT
ejpam-5823	144	13	=	=	SYM
ejpam-5823	144	14	1	1	NUM
ejpam-5823	144	15	γk(q	γk(q	NOUN
ejpam-5823	144	16	+	+	CCONJ
ejpam-5823	144	17	k	k	X
ejpam-5823	144	18	)	)	PUNCT
ejpam-5823	144	19	[	[	PUNCT
ejpam-5823	144	20	∂	∂	NOUN
ejpam-5823	144	21	∂r	∂r	PROPN
ejpam-5823	144	22	(	(	PUNCT
ejpam-5823	144	23	γk(q	γk(q	NOUN
ejpam-5823	144	24	+	+	CCONJ
ejpam-5823	144	25	rk	rk	NOUN
ejpam-5823	144	26	)	)	PUNCT
ejpam-5823	144	27	(	(	PUNCT
ejpam-5823	144	28	q	q	NOUN
ejpam-5823	145	1	+	+	CCONJ
ejpam-5823	145	2	β)1−r	β)1−r	ADJ
ejpam-5823	145	3	−	−	NOUN
ejpam-5823	145	4	1	1	NUM
ejpam-5823	145	5	)	)	PUNCT
ejpam-5823	145	6	]	]	PUNCT
ejpam-5823	146	1	=	=	SYM
ejpam-5823	146	2	1	1	NUM
ejpam-5823	146	3	γk(q	γk(q	NOUN
ejpam-5823	146	4	+	+	CCONJ
ejpam-5823	146	5	k	k	X
ejpam-5823	146	6	)	)	PUNCT
ejpam-5823	146	7	[	[	PUNCT
ejpam-5823	146	8	γk(q	γk(q	NOUN
ejpam-5823	146	9	+	+	CCONJ
ejpam-5823	146	10	rk	rk	NOUN
ejpam-5823	146	11	)	)	PUNCT
ejpam-5823	146	12	∂	∂	NOUN
ejpam-5823	147	1	∂r	∂r	NOUN
ejpam-5823	147	2	(	(	PUNCT
ejpam-5823	147	3	q	q	NOUN
ejpam-5823	148	1	+	+	CCONJ
ejpam-5823	148	2	β)1−r	β)1−r	ADJ
ejpam-5823	149	1	+	+	CCONJ
ejpam-5823	149	2	(	(	PUNCT
ejpam-5823	149	3	q	q	X
ejpam-5823	149	4	+	+	CCONJ
ejpam-5823	149	5	β)1−r	β)1−r	ADJ
ejpam-5823	149	6	∂	∂	NOUN
ejpam-5823	149	7	∂r	∂r	NOUN
ejpam-5823	149	8	γk(q	γk(q	NOUN
ejpam-5823	149	9	+	+	CCONJ
ejpam-5823	149	10	rk	rk	NOUN
ejpam-5823	149	11	)	)	PUNCT
ejpam-5823	149	12	]	]	PUNCT
ejpam-5823	150	1	=	=	PUNCT
ejpam-5823	150	2	(	(	PUNCT
ejpam-5823	150	3	q	q	NOUN
ejpam-5823	150	4	+	+	CCONJ
ejpam-5823	150	5	β)1−r	β)1−r	ADJ
ejpam-5823	150	6	γk(q	γk(q	NOUN
ejpam-5823	150	7	+	+	X
ejpam-5823	150	8	k	k	X
ejpam-5823	150	9	)	)	PUNCT
ejpam-5823	151	1	[	[	X
ejpam-5823	151	2	−γk(q	−γk(q	X
ejpam-5823	151	3	+	+	CCONJ
ejpam-5823	151	4	rk	rk	NOUN
ejpam-5823	151	5	)	)	PUNCT
ejpam-5823	151	6	ln(q	ln(q	PUNCT
ejpam-5823	151	7	+	+	CCONJ
ejpam-5823	151	8	β	β	X
ejpam-5823	151	9	)	)	PUNCT
ejpam-5823	151	10	+	+	NUM
ejpam-5823	151	11	γk(q	γk(q	NOUN
ejpam-5823	151	12	+	+	CCONJ
ejpam-5823	151	13	rk	rk	NOUN
ejpam-5823	151	14	)	)	PUNCT
ejpam-5823	151	15	ψk(q	ψk(q	PUNCT
ejpam-5823	151	16	+	+	CCONJ
ejpam-5823	151	17	rk	rk	NOUN
ejpam-5823	151	18	)	)	PUNCT
ejpam-5823	151	19	]	]	PUNCT
ejpam-5823	151	20	,	,	PUNCT
ejpam-5823	151	21	where	where	SCONJ
ejpam-5823	151	22	ψk	ψk	NOUN
ejpam-5823	151	23	is	be	AUX
ejpam-5823	151	24	k	k	ADJ
ejpam-5823	151	25	-	-	ADJ
ejpam-5823	151	26	digamma	digamma	ADJ
ejpam-5823	151	27	function	function	NOUN
ejpam-5823	151	28	defined	define	VERB
ejpam-5823	151	29	in	in	ADP
ejpam-5823	151	30	eq	eq	ADJ
ejpam-5823	151	31	.	.	PROPN
ejpam-5823	151	32	7	7	NUM
ejpam-5823	151	33	.	.	NOUN
ejpam-5823	151	34	∂	∂	NUM
ejpam-5823	152	1	∂r	∂r	PROPN
ejpam-5823	152	2	(	(	PUNCT
ejpam-5823	152	3	fk(q	fk(q	NOUN
ejpam-5823	152	4	,	,	PUNCT
ejpam-5823	152	5	rk	rk	NOUN
ejpam-5823	152	6	)	)	PUNCT
ejpam-5823	152	7	)	)	PUNCT
ejpam-5823	153	1	=	=	PUNCT
ejpam-5823	153	2	γk(q	γk(q	X
ejpam-5823	153	3	+	+	CCONJ
ejpam-5823	153	4	rk	rk	NOUN
ejpam-5823	153	5	)	)	PUNCT
ejpam-5823	153	6	(	(	PUNCT
ejpam-5823	153	7	q	q	NOUN
ejpam-5823	153	8	+	+	CCONJ
ejpam-5823	153	9	β)1−r	β)1−r	ADJ
ejpam-5823	153	10	γk(q	γk(q	NOUN
ejpam-5823	153	11	+	+	CCONJ
ejpam-5823	153	12	k	k	X
ejpam-5823	153	13	)	)	PUNCT
ejpam-5823	153	14	[	[	PUNCT
ejpam-5823	153	15	ψk(q	ψk(q	PUNCT
ejpam-5823	153	16	+	+	CCONJ
ejpam-5823	153	17	rk)−	rk)−	ADJ
ejpam-5823	153	18	ln(q	ln(q	X
ejpam-5823	153	19	+	+	X
ejpam-5823	153	20	β	β	X
ejpam-5823	153	21	)	)	PUNCT
ejpam-5823	153	22	]	]	PUNCT
ejpam-5823	154	1	=	=	SYM
ejpam-5823	154	2	γk(q	γk(q	NOUN
ejpam-5823	154	3	+	+	CCONJ
ejpam-5823	154	4	rk	rk	NOUN
ejpam-5823	154	5	)	)	PUNCT
ejpam-5823	154	6	(	(	PUNCT
ejpam-5823	154	7	q	q	NOUN
ejpam-5823	154	8	+	+	CCONJ
ejpam-5823	154	9	β)1−r	β)1−r	ADJ
ejpam-5823	154	10	γk(q	γk(q	NOUN
ejpam-5823	154	11	+	+	X
ejpam-5823	154	12	k	k	X
ejpam-5823	154	13	)	)	PUNCT
ejpam-5823	154	14	gk(q	gk(q	NOUN
ejpam-5823	154	15	,	,	PUNCT
ejpam-5823	154	16	rk	rk	NOUN
ejpam-5823	154	17	)	)	PUNCT
ejpam-5823	154	18	,	,	PUNCT
ejpam-5823	154	19	(	(	PUNCT
ejpam-5823	154	20	12	12	NUM
ejpam-5823	154	21	)	)	PUNCT
ejpam-5823	154	22	where	where	SCONJ
ejpam-5823	154	23	(	(	PUNCT
ejpam-5823	154	24	q	q	NOUN
ejpam-5823	154	25	,	,	PUNCT
ejpam-5823	154	26	rk	rk	NOUN
ejpam-5823	154	27	)	)	PUNCT
ejpam-5823	154	28	∈	∈	PROPN
ejpam-5823	154	29	(	(	PUNCT
ejpam-5823	154	30	0,∞)×	0,∞)×	NUM
ejpam-5823	154	31	[	[	X
ejpam-5823	154	32	3,∞	3,∞	NOUN
ejpam-5823	154	33	)	)	PUNCT
ejpam-5823	154	34	and	and	CCONJ
ejpam-5823	154	35	gk(q	gk(q	NOUN
ejpam-5823	154	36	,	,	PUNCT
ejpam-5823	154	37	rk	rk	NOUN
ejpam-5823	154	38	)	)	PUNCT
ejpam-5823	154	39	=	=	PRON
ejpam-5823	154	40	ψk(q	ψk(q	X
ejpam-5823	154	41	+	+	X
ejpam-5823	154	42	rk)−	rk)−	ADJ
ejpam-5823	154	43	ln(q	ln(q	X
ejpam-5823	154	44	+	+	X
ejpam-5823	154	45	β	β	NOUN
ejpam-5823	154	46	)	)	PUNCT
ejpam-5823	154	47	.	.	PUNCT
ejpam-5823	155	1	(	(	PUNCT
ejpam-5823	155	2	13	13	NUM
ejpam-5823	155	3	)	)	PUNCT
ejpam-5823	155	4	using	use	VERB
ejpam-5823	155	5	γk(z	γk(z	X
ejpam-5823	155	6	)	)	PUNCT
ejpam-5823	155	7	=	=	PUNCT
ejpam-5823	156	1	+	+	NOUN
ejpam-5823	156	2	∞∫	∞∫	NOUN
ejpam-5823	156	3	0	0	NUM
ejpam-5823	156	4	tz−1	tz−1	PROPN
ejpam-5823	156	5	e−	e−	PROPN
ejpam-5823	156	6	tk	tk	PROPN
ejpam-5823	156	7	k	k	PROPN
ejpam-5823	156	8	dt	dt	PROPN
ejpam-5823	156	9	implies	imply	VERB
ejpam-5823	156	10	that	that	SCONJ
ejpam-5823	156	11	γk(q	γk(q	PUNCT
ejpam-5823	156	12	+	+	CCONJ
ejpam-5823	156	13	k	k	X
ejpam-5823	156	14	)	)	PUNCT
ejpam-5823	156	15	>	>	X
ejpam-5823	156	16	0	0	NUM
ejpam-5823	156	17	,	,	PUNCT
ejpam-5823	156	18	γk(q	γk(q	X
ejpam-5823	156	19	+	+	CCONJ
ejpam-5823	156	20	rk	rk	NOUN
ejpam-5823	156	21	)	)	PUNCT
ejpam-5823	156	22	>	>	X
ejpam-5823	156	23	0	0	PUNCT
ejpam-5823	156	24	for	for	ADP
ejpam-5823	156	25	all	all	PRON
ejpam-5823	156	26	(	(	PUNCT
ejpam-5823	156	27	q	q	ADJ
ejpam-5823	156	28	,	,	PUNCT
ejpam-5823	156	29	rk	rk	NOUN
ejpam-5823	156	30	)	)	PUNCT
ejpam-5823	156	31	∈	∈	PROPN
ejpam-5823	156	32	(	(	PUNCT
ejpam-5823	156	33	0,∞)×	0,∞)×	NUM
ejpam-5823	156	34	[	[	X
ejpam-5823	156	35	3,∞	3,∞	NOUN
ejpam-5823	156	36	)	)	PUNCT
ejpam-5823	156	37	.	.	PUNCT
ejpam-5823	157	1	as	as	ADP
ejpam-5823	157	2	β	β	X
ejpam-5823	157	3	>	>	X
ejpam-5823	157	4	0	0	NUM
ejpam-5823	157	5	,	,	PUNCT
ejpam-5823	157	6	then	then	ADV
ejpam-5823	157	7	by	by	ADP
ejpam-5823	157	8	eq	eq	NOUN
ejpam-5823	157	9	13	13	NUM
ejpam-5823	157	10	,	,	PUNCT
ejpam-5823	157	11	the	the	DET
ejpam-5823	157	12	sign	sign	NOUN
ejpam-5823	157	13	of	of	ADP
ejpam-5823	157	14	∂	∂	NUM
ejpam-5823	157	15	∂rfk(q	∂rfk(q	NOUN
ejpam-5823	157	16	+	+	CCONJ
ejpam-5823	157	17	rk	rk	NOUN
ejpam-5823	157	18	)	)	PUNCT
ejpam-5823	157	19	is	be	AUX
ejpam-5823	157	20	same	same	ADJ
ejpam-5823	157	21	as	as	ADP
ejpam-5823	157	22	of	of	ADP
ejpam-5823	157	23	gk(q	gk(q	NOUN
ejpam-5823	157	24	,	,	PUNCT
ejpam-5823	157	25	rk	rk	NOUN
ejpam-5823	157	26	)	)	PUNCT
ejpam-5823	157	27	.	.	PUNCT
ejpam-5823	158	1	as	as	SCONJ
ejpam-5823	158	2	it	it	PRON
ejpam-5823	158	3	is	be	AUX
ejpam-5823	158	4	well	well	ADV
ejpam-5823	158	5	known	know	VERB
ejpam-5823	158	6	by	by	ADP
ejpam-5823	158	7	[	[	X
ejpam-5823	158	8	26	26	NUM
ejpam-5823	158	9	]	]	PUNCT
ejpam-5823	158	10	,	,	PUNCT
ejpam-5823	158	11	for	for	ADP
ejpam-5823	158	12	x	x	X
ejpam-5823	158	13	>	>	X
ejpam-5823	158	14	0	0	NUM
ejpam-5823	159	1	and	and	CCONJ
ejpam-5823	159	2	0	0	NUM
ejpam-5823	159	3	<	<	X
ejpam-5823	159	4	k	k	X
ejpam-5823	159	5	≤	≤	NUM
ejpam-5823	159	6	1	1	NUM
ejpam-5823	159	7	,	,	PUNCT
ejpam-5823	159	8	we	we	PRON
ejpam-5823	159	9	have	have	VERB
ejpam-5823	159	10	1	1	NUM
ejpam-5823	159	11	k	k	PROPN
ejpam-5823	159	12	lny	lny	PROPN
ejpam-5823	159	13	−	−	PROPN
ejpam-5823	159	14	1	1	NUM
ejpam-5823	159	15	y	y	PROPN
ejpam-5823	159	16	<	<	X
ejpam-5823	159	17	ψk(y	ψk(y	X
ejpam-5823	159	18	)	)	PUNCT
ejpam-5823	159	19	<	<	X
ejpam-5823	159	20	1	1	NUM
ejpam-5823	159	21	k	k	PROPN
ejpam-5823	159	22	lny	lny	PROPN
ejpam-5823	159	23	.	.	PROPN
ejpam-5823	160	1	(	(	PUNCT
ejpam-5823	160	2	14	14	NUM
ejpam-5823	160	3	)	)	PUNCT
ejpam-5823	160	4	using	use	VERB
ejpam-5823	160	5	eq	eq	NOUN
ejpam-5823	160	6	.	.	PROPN
ejpam-5823	160	7	14	14	NUM
ejpam-5823	160	8	in	in	ADP
ejpam-5823	160	9	eq	eq	ADP
ejpam-5823	160	10	.	.	PROPN
ejpam-5823	160	11	13	13	NUM
ejpam-5823	160	12	,	,	PUNCT
ejpam-5823	160	13	we	we	PRON
ejpam-5823	160	14	get	get	VERB
ejpam-5823	160	15	gk(q	gk(q	ADV
ejpam-5823	160	16	,	,	PUNCT
ejpam-5823	160	17	rk	rk	NOUN
ejpam-5823	160	18	)	)	PUNCT
ejpam-5823	160	19	≥	≥	NOUN
ejpam-5823	160	20	1	1	NUM
ejpam-5823	160	21	k	k	X
ejpam-5823	160	22	ln(q+rk)−	ln(q+rk)−	NOUN
ejpam-5823	160	23	1	1	NUM
ejpam-5823	160	24	q	q	NOUN
ejpam-5823	160	25	+	+	NUM
ejpam-5823	160	26	rk	rk	VERB
ejpam-5823	160	27	−	−	PROPN
ejpam-5823	160	28	ln(q+β	ln(q+β	PROPN
ejpam-5823	160	29	)	)	PUNCT
ejpam-5823	161	1	=	=	SYM
ejpam-5823	161	2	ln	ln	ADJ
ejpam-5823	161	3	(	(	PUNCT
ejpam-5823	161	4	q	q	NOUN
ejpam-5823	161	5	+	+	NUM
ejpam-5823	161	6	rk	rk	NOUN
ejpam-5823	161	7	)	)	PUNCT
ejpam-5823	161	8	1	1	NUM
ejpam-5823	161	9	k	k	NOUN
ejpam-5823	161	10	q	q	X
ejpam-5823	162	1	+	+	CCONJ
ejpam-5823	162	2	β	β	X
ejpam-5823	162	3	−	−	NOUN
ejpam-5823	162	4	1	1	NUM
ejpam-5823	162	5	q	q	NOUN
ejpam-5823	163	1	+	+	NUM
ejpam-5823	163	2	rk	rk	NOUN
ejpam-5823	163	3	,	,	PUNCT
ejpam-5823	163	4	β	β	X
ejpam-5823	163	5	>	>	X
ejpam-5823	163	6	0	0	NUM
ejpam-5823	163	7	,	,	PUNCT
ejpam-5823	163	8	r	r	NOUN
ejpam-5823	163	9	≥	≥	NOUN
ejpam-5823	163	10	3	3	NUM
ejpam-5823	163	11	.	.	PUNCT
ejpam-5823	164	1	gk(q	gk(q	PROPN
ejpam-5823	164	2	,	,	PUNCT
ejpam-5823	164	3	rk	rk	NOUN
ejpam-5823	164	4	)	)	PUNCT
ejpam-5823	164	5	≥	≥	X
ejpam-5823	164	6	ln	ln	NOUN
ejpam-5823	164	7	(	(	PUNCT
ejpam-5823	164	8	q	q	NOUN
ejpam-5823	164	9	+	+	NUM
ejpam-5823	164	10	3k	3k	NUM
ejpam-5823	164	11	)	)	PUNCT
ejpam-5823	164	12	1	1	NUM
ejpam-5823	164	13	k	k	NOUN
ejpam-5823	164	14	q	q	X
ejpam-5823	165	1	+	+	CCONJ
ejpam-5823	165	2	β	β	X
ejpam-5823	165	3	−	−	NOUN
ejpam-5823	165	4	1	1	NUM
ejpam-5823	165	5	q	q	NOUN
ejpam-5823	165	6	+	+	NUM
ejpam-5823	165	7	3k	3k	NUM
ejpam-5823	165	8	=	=	PUNCT
ejpam-5823	165	9	ik(q	ik(q	NUM
ejpam-5823	165	10	)	)	PUNCT
ejpam-5823	165	11	,	,	PUNCT
ejpam-5823	165	12	(	(	PUNCT
ejpam-5823	165	13	15	15	X
ejpam-5823	165	14	)	)	PUNCT
ejpam-5823	165	15	s.	s.	PROPN
ejpam-5823	165	16	a.	a.	PROPN
ejpam-5823	165	17	h.	h.	PROPN
ejpam-5823	165	18	shah	shah	PROPN
ejpam-5823	165	19	et	et	PROPN
ejpam-5823	165	20	al	al	PROPN
ejpam-5823	165	21	.	.	PUNCT
ejpam-5823	165	22	/	/	SYM
ejpam-5823	165	23	eur	eur	PROPN
ejpam-5823	165	24	.	.	PUNCT
ejpam-5823	166	1	j.	j.	PROPN
ejpam-5823	166	2	pure	pure	PROPN
ejpam-5823	166	3	appl	appl	PROPN
ejpam-5823	166	4	.	.	PROPN
ejpam-5823	166	5	math	math	PROPN
ejpam-5823	166	6	,	,	PUNCT
ejpam-5823	166	7	18	18	NUM
ejpam-5823	166	8	(	(	PUNCT
ejpam-5823	166	9	2	2	NUM
ejpam-5823	166	10	)	)	PUNCT
ejpam-5823	166	11	(	(	PUNCT
ejpam-5823	166	12	2025	2025	NUM
ejpam-5823	166	13	)	)	PUNCT
ejpam-5823	166	14	,	,	PUNCT
ejpam-5823	166	15	5823	5823	NUM
ejpam-5823	166	16	8	8	NUM
ejpam-5823	166	17	of	of	ADP
ejpam-5823	166	18	26	26	NUM
ejpam-5823	166	19	where	where	SCONJ
ejpam-5823	166	20	ik(q	ik(q	NUM
ejpam-5823	166	21	)	)	PUNCT
ejpam-5823	166	22	=	=	SYM
ejpam-5823	166	23	ln	ln	ADJ
ejpam-5823	166	24	(	(	PUNCT
ejpam-5823	166	25	q+3k	q+3k	PROPN
ejpam-5823	166	26	)	)	PUNCT
ejpam-5823	166	27	1	1	NUM
ejpam-5823	167	1	k	k	NOUN
ejpam-5823	167	2	q+β	q+β	NUM
ejpam-5823	167	3	−	−	NUM
ejpam-5823	167	4	1	1	NUM
ejpam-5823	167	5	q+3k	q+3k	PROPN
ejpam-5823	167	6	.	.	PUNCT
ejpam-5823	168	1	by	by	ADP
ejpam-5823	168	2	taking	take	VERB
ejpam-5823	168	3	derivative	derivative	NOUN
ejpam-5823	168	4	of	of	ADP
ejpam-5823	168	5	ik(q	ik(q	NUM
ejpam-5823	168	6	)	)	PUNCT
ejpam-5823	168	7	,	,	PUNCT
ejpam-5823	168	8	i	i	PRON
ejpam-5823	168	9	′k(q	′k(q	NOUN
ejpam-5823	168	10	)	)	PUNCT
ejpam-5823	168	11	=	=	SYM
ejpam-5823	169	1	1	1	NUM
ejpam-5823	169	2	(	(	PUNCT
ejpam-5823	169	3	q+3k	q+3k	PROPN
ejpam-5823	169	4	)	)	PUNCT
ejpam-5823	169	5	1	1	NUM
ejpam-5823	170	1	k	k	NOUN
ejpam-5823	170	2	q+β	q+β	NUM
ejpam-5823	171	1	[	[	PUNCT
ejpam-5823	171	2	d	d	X
ejpam-5823	171	3	dq	dq	INTJ
ejpam-5823	171	4	(	(	PUNCT
ejpam-5823	171	5	(	(	PUNCT
ejpam-5823	171	6	q	q	X
ejpam-5823	171	7	+	+	NUM
ejpam-5823	171	8	3k	3k	NUM
ejpam-5823	171	9	)	)	PUNCT
ejpam-5823	172	1	1	1	NUM
ejpam-5823	172	2	k	k	NOUN
ejpam-5823	172	3	q	q	X
ejpam-5823	173	1	+	+	X
ejpam-5823	173	2	β	β	X
ejpam-5823	173	3	)	)	PUNCT
ejpam-5823	173	4	]	]	PUNCT
ejpam-5823	174	1	+	+	CCONJ
ejpam-5823	174	2	1	1	X
ejpam-5823	174	3	(	(	PUNCT
ejpam-5823	174	4	q	q	NOUN
ejpam-5823	174	5	+	+	NUM
ejpam-5823	174	6	3k)2	3k)2	NUM
ejpam-5823	174	7	=	=	SYM
ejpam-5823	174	8	q	q	PROPN
ejpam-5823	175	1	+	+	X
ejpam-5823	175	2	β	β	X
ejpam-5823	175	3	(	(	PUNCT
ejpam-5823	175	4	q	q	PROPN
ejpam-5823	175	5	+	+	NUM
ejpam-5823	175	6	3k	3k	NUM
ejpam-5823	175	7	)	)	PUNCT
ejpam-5823	175	8	1	1	NUM
ejpam-5823	175	9	k	k	X
ejpam-5823	175	10	[	[	PUNCT
ejpam-5823	175	11	(	(	PUNCT
ejpam-5823	175	12	q	q	X
ejpam-5823	175	13	+	+	NUM
ejpam-5823	175	14	β	β	X
ejpam-5823	175	15	)	)	PUNCT
ejpam-5823	175	16	1	1	NUM
ejpam-5823	175	17	k	k	NOUN
ejpam-5823	175	18	(	(	PUNCT
ejpam-5823	175	19	q	q	PROPN
ejpam-5823	175	20	+	+	NUM
ejpam-5823	175	21	3k	3k	NUM
ejpam-5823	175	22	)	)	PUNCT
ejpam-5823	175	23	1	1	NUM
ejpam-5823	175	24	k	k	NOUN
ejpam-5823	175	25	−1	−1	NOUN
ejpam-5823	175	26	−	−	PROPN
ejpam-5823	175	27	(	(	PUNCT
ejpam-5823	175	28	q	q	PROPN
ejpam-5823	175	29	+	+	NUM
ejpam-5823	175	30	3k	3k	NUM
ejpam-5823	175	31	)	)	PUNCT
ejpam-5823	175	32	1	1	NUM
ejpam-5823	175	33	k	k	NOUN
ejpam-5823	175	34	(	(	PUNCT
ejpam-5823	175	35	q	q	NOUN
ejpam-5823	175	36	+	+	PUNCT
ejpam-5823	175	37	β)2	β)2	X
ejpam-5823	175	38	]	]	X
ejpam-5823	175	39	+	+	CCONJ
ejpam-5823	175	40	1	1	NUM
ejpam-5823	175	41	(	(	PUNCT
ejpam-5823	175	42	q	q	NOUN
ejpam-5823	176	1	+	+	NUM
ejpam-5823	176	2	3k)2	3k)2	NUM
ejpam-5823	176	3	=	=	SYM
ejpam-5823	176	4	1	1	NUM
ejpam-5823	176	5	k(q	k(q	PROPN
ejpam-5823	176	6	+	+	CCONJ
ejpam-5823	176	7	3k	3k	NUM
ejpam-5823	176	8	)	)	PUNCT
ejpam-5823	176	9	−	−	PROPN
ejpam-5823	176	10	1	1	NUM
ejpam-5823	176	11	q	q	NOUN
ejpam-5823	176	12	+	+	NUM
ejpam-5823	176	13	β	β	X
ejpam-5823	176	14	+	+	ADJ
ejpam-5823	176	15	1	1	NUM
ejpam-5823	176	16	(	(	PUNCT
ejpam-5823	176	17	q	q	NOUN
ejpam-5823	176	18	+	+	NUM
ejpam-5823	176	19	3k)2	3k)2	NUM
ejpam-5823	176	20	=	=	SYM
ejpam-5823	176	21	1	1	NUM
ejpam-5823	176	22	q	q	NOUN
ejpam-5823	176	23	+	+	NUM
ejpam-5823	176	24	3k	3k	X
ejpam-5823	176	25	[	[	PUNCT
ejpam-5823	176	26	1	1	NUM
ejpam-5823	176	27	k	k	NOUN
ejpam-5823	176	28	−	−	PROPN
ejpam-5823	176	29	q	q	NOUN
ejpam-5823	177	1	+	+	NUM
ejpam-5823	177	2	3k	3k	PRON
ejpam-5823	177	3	q	q	X
ejpam-5823	178	1	+	+	NUM
ejpam-5823	178	2	β	β	X
ejpam-5823	178	3	+	+	NOUN
ejpam-5823	178	4	1	1	NUM
ejpam-5823	178	5	q	q	NOUN
ejpam-5823	178	6	+	+	NUM
ejpam-5823	178	7	3k	3k	X
ejpam-5823	178	8	]	]	PUNCT
ejpam-5823	178	9	,	,	PUNCT
ejpam-5823	178	10	q	q	X
ejpam-5823	178	11	>	>	X
ejpam-5823	178	12	0	0	NUM
ejpam-5823	178	13	,	,	PUNCT
ejpam-5823	178	14	0	0	NUM
ejpam-5823	178	15	≤	≤	NUM
ejpam-5823	178	16	β	β	X
ejpam-5823	178	17	≤	≤	NUM
ejpam-5823	178	18	2	2	NUM
ejpam-5823	178	19	.	.	PUNCT
ejpam-5823	179	1	(	(	PUNCT
ejpam-5823	179	2	16	16	NUM
ejpam-5823	179	3	)	)	PUNCT
ejpam-5823	179	4	and	and	CCONJ
ejpam-5823	179	5	we	we	PRON
ejpam-5823	179	6	have	have	VERB
ejpam-5823	179	7	the	the	DET
ejpam-5823	179	8	following	follow	VERB
ejpam-5823	179	9	equivalences	equivalence	NOUN
ejpam-5823	179	10	:	:	PUNCT
ejpam-5823	179	11	i	i	PROPN
ejpam-5823	179	12	′k(q	′k(q	NOUN
ejpam-5823	179	13	)	)	PUNCT
ejpam-5823	180	1	<	<	X
ejpam-5823	180	2	0	0	NUM
ejpam-5823	180	3	⇔	⇔	X
ejpam-5823	180	4	q	q	PROPN
ejpam-5823	181	1	+	+	NUM
ejpam-5823	181	2	3k	3k	PRON
ejpam-5823	181	3	q	q	X
ejpam-5823	182	1	+	+	X
ejpam-5823	182	2	β	β	X
ejpam-5823	182	3	>	>	X
ejpam-5823	182	4	1	1	NUM
ejpam-5823	182	5	k	k	X
ejpam-5823	183	1	+	+	CCONJ
ejpam-5823	183	2	1	1	NUM
ejpam-5823	183	3	q	q	NOUN
ejpam-5823	183	4	+	+	NUM
ejpam-5823	183	5	3k	3k	X
ejpam-5823	183	6	⇔	⇔	X
ejpam-5823	183	7	β	β	X
ejpam-5823	183	8	<	<	X
ejpam-5823	183	9	k(q	k(q	PROPN
ejpam-5823	183	10	+	+	CCONJ
ejpam-5823	183	11	3k)2	3k)2	NUM
ejpam-5823	183	12	q	q	NOUN
ejpam-5823	184	1	+	+	NUM
ejpam-5823	184	2	4k	4k	NUM
ejpam-5823	184	3	−	−	NOUN
ejpam-5823	184	4	q	q	X
ejpam-5823	184	5	(	(	PUNCT
ejpam-5823	184	6	17	17	NUM
ejpam-5823	184	7	)	)	PUNCT
ejpam-5823	184	8	because	because	SCONJ
ejpam-5823	184	9	inf	inf	PROPN
ejpam-5823	184	10	{	{	PUNCT
ejpam-5823	184	11	k(q	k(q	PROPN
ejpam-5823	184	12	+	+	CCONJ
ejpam-5823	184	13	3k)2	3k)2	NUM
ejpam-5823	184	14	q	q	NOUN
ejpam-5823	185	1	+	+	NUM
ejpam-5823	185	2	4k	4k	NUM
ejpam-5823	185	3	−	−	NOUN
ejpam-5823	185	4	q	q	NOUN
ejpam-5823	185	5	:	:	PUNCT
ejpam-5823	185	6	q	q	X
ejpam-5823	185	7	>	>	X
ejpam-5823	185	8	0	0	PUNCT
ejpam-5823	185	9	}	}	PUNCT
ejpam-5823	185	10	=	=	SYM
ejpam-5823	185	11	2	2	X
ejpam-5823	185	12	.	.	PUNCT
ejpam-5823	186	1	if	if	SCONJ
ejpam-5823	186	2	β	β	NOUN
ejpam-5823	186	3	≤	≤	ADV
ejpam-5823	186	4	2	2	NUM
ejpam-5823	186	5	,	,	PUNCT
ejpam-5823	186	6	the	the	DET
ejpam-5823	186	7	inequality	inequality	NOUN
ejpam-5823	186	8	i	i	PRON
ejpam-5823	186	9	′k(q	′k(q	NOUN
ejpam-5823	186	10	)	)	PUNCT
ejpam-5823	186	11	<	<	X
ejpam-5823	186	12	0	0	X
ejpam-5823	186	13	is	be	AUX
ejpam-5823	186	14	satisfied	satisfied	ADJ
ejpam-5823	186	15	,	,	PUNCT
ejpam-5823	186	16	for	for	ADP
ejpam-5823	186	17	all	all	DET
ejpam-5823	186	18	q	q	X
ejpam-5823	186	19	>	>	X
ejpam-5823	187	1	0	0	X
ejpam-5823	187	2	.	.	PUNCT
ejpam-5823	187	3	hence	hence	ADV
ejpam-5823	187	4	function	function	VERB
ejpam-5823	187	5	ik(q	ik(q	NUM
ejpam-5823	187	6	)	)	PUNCT
ejpam-5823	187	7	is	be	AUX
ejpam-5823	187	8	decreasing	decrease	VERB
ejpam-5823	187	9	strictly	strictly	ADV
ejpam-5823	187	10	on	on	ADP
ejpam-5823	187	11	(	(	PUNCT
ejpam-5823	187	12	0,+∞	0,+∞	NUM
ejpam-5823	187	13	)	)	PUNCT
ejpam-5823	187	14	,	,	PUNCT
ejpam-5823	187	15	⇒	⇒	NOUN
ejpam-5823	187	16	ik(q	ik(q	NUM
ejpam-5823	187	17	)	)	PUNCT
ejpam-5823	187	18	>	>	PUNCT
ejpam-5823	188	1	lim	lim	PROPN
ejpam-5823	188	2	x→+∞	x→+∞	PROPN
ejpam-5823	188	3	ik(y	ik(y	NUM
ejpam-5823	188	4	)	)	PUNCT
ejpam-5823	189	1	=	=	SYM
ejpam-5823	189	2	0	0	NUM
ejpam-5823	189	3	,	,	PUNCT
ejpam-5823	189	4	q	q	X
ejpam-5823	189	5	>	>	X
ejpam-5823	189	6	0	0	NUM
ejpam-5823	189	7	.	.	PUNCT
ejpam-5823	190	1	(	(	PUNCT
ejpam-5823	190	2	18	18	NUM
ejpam-5823	190	3	)	)	PUNCT
ejpam-5823	190	4	by	by	ADP
ejpam-5823	190	5	combining	combine	VERB
ejpam-5823	190	6	eqs	eqs	PROPN
ejpam-5823	190	7	.	.	PROPN
ejpam-5823	190	8	12	12	NUM
ejpam-5823	190	9	and	and	CCONJ
ejpam-5823	190	10	15	15	NUM
ejpam-5823	190	11	∂	∂	NUM
ejpam-5823	190	12	∂r	∂r	PROPN
ejpam-5823	190	13	(	(	PUNCT
ejpam-5823	190	14	fk(q	fk(q	NOUN
ejpam-5823	190	15	,	,	PUNCT
ejpam-5823	190	16	rk	rk	NOUN
ejpam-5823	190	17	)	)	PUNCT
ejpam-5823	190	18	)	)	PUNCT
ejpam-5823	190	19	>	>	X
ejpam-5823	191	1	0	0	NUM
ejpam-5823	191	2	,	,	PUNCT
ejpam-5823	191	3	(	(	PUNCT
ejpam-5823	191	4	q	q	X
ejpam-5823	191	5	,	,	PUNCT
ejpam-5823	191	6	rk	rk	NOUN
ejpam-5823	191	7	)	)	PUNCT
ejpam-5823	191	8	∈	∈	PROPN
ejpam-5823	191	9	(	(	PUNCT
ejpam-5823	191	10	0,∞)×	0,∞)×	NUM
ejpam-5823	191	11	[	[	X
ejpam-5823	191	12	3,∞	3,∞	NOUN
ejpam-5823	191	13	)	)	PUNCT
ejpam-5823	191	14	which	which	PRON
ejpam-5823	191	15	implies	imply	VERB
ejpam-5823	191	16	fk(q	fk(q	NUM
ejpam-5823	191	17	,	,	PUNCT
ejpam-5823	191	18	rk	rk	NOUN
ejpam-5823	191	19	)	)	PUNCT
ejpam-5823	191	20	is	be	AUX
ejpam-5823	191	21	strictly	strictly	ADV
ejpam-5823	191	22	increasing	increase	VERB
ejpam-5823	191	23	function	function	NOUN
ejpam-5823	191	24	on	on	ADP
ejpam-5823	191	25	r	r	NOUN
ejpam-5823	191	26	∈	∈	PROPN
ejpam-5823	192	1	[	[	X
ejpam-5823	192	2	3,+∞	3,+∞	NUM
ejpam-5823	192	3	)	)	PUNCT
ejpam-5823	192	4	,	,	PUNCT
ejpam-5823	192	5	q	q	X
ejpam-5823	192	6	>	>	X
ejpam-5823	192	7	0	0	NUM
ejpam-5823	192	8	.	.	X
ejpam-5823	192	9	fk(q	fk(q	PROPN
ejpam-5823	192	10	,	,	PUNCT
ejpam-5823	192	11	rk	rk	NOUN
ejpam-5823	192	12	)	)	PUNCT
ejpam-5823	192	13	≥	≥	NOUN
ejpam-5823	192	14	fk(q	fk(q	NUM
ejpam-5823	192	15	,	,	PUNCT
ejpam-5823	192	16	3k	3k	NUM
ejpam-5823	192	17	)	)	PUNCT
ejpam-5823	192	18	=	=	PUNCT
ejpam-5823	193	1	γk(q	γk(q	NOUN
ejpam-5823	193	2	+	+	CCONJ
ejpam-5823	193	3	3k	3k	NUM
ejpam-5823	193	4	)	)	PUNCT
ejpam-5823	193	5	γk(q	γk(q	NOUN
ejpam-5823	194	1	+	+	CCONJ
ejpam-5823	195	1	k	k	X
ejpam-5823	195	2	)	)	PUNCT
ejpam-5823	195	3	(	(	PUNCT
ejpam-5823	195	4	q	q	X
ejpam-5823	196	1	+	+	CCONJ
ejpam-5823	196	2	β)−2	β)−2	ADP
ejpam-5823	196	3	−	−	PROPN
ejpam-5823	196	4	1	1	NUM
ejpam-5823	196	5	=	=	SYM
ejpam-5823	196	6	γk(q	γk(q	NOUN
ejpam-5823	196	7	+	+	CCONJ
ejpam-5823	196	8	3k	3k	NUM
ejpam-5823	196	9	)	)	PUNCT
ejpam-5823	196	10	γk(q	γk(q	X
ejpam-5823	196	11	+	+	CCONJ
ejpam-5823	197	1	k)(q	k)(q	X
ejpam-5823	197	2	+	+	X
ejpam-5823	197	3	β)2	β)2	ADV
ejpam-5823	197	4	−	−	PROPN
ejpam-5823	197	5	1	1	NUM
ejpam-5823	197	6	s.	s.	PROPN
ejpam-5823	197	7	a.	a.	PROPN
ejpam-5823	197	8	h.	h.	PROPN
ejpam-5823	197	9	shah	shah	PROPN
ejpam-5823	197	10	et	et	PROPN
ejpam-5823	197	11	al	al	PROPN
ejpam-5823	197	12	.	.	PUNCT
ejpam-5823	197	13	/	/	SYM
ejpam-5823	197	14	eur	eur	PROPN
ejpam-5823	197	15	.	.	PUNCT
ejpam-5823	198	1	j.	j.	PROPN
ejpam-5823	198	2	pure	pure	PROPN
ejpam-5823	198	3	appl	appl	PROPN
ejpam-5823	198	4	.	.	PROPN
ejpam-5823	198	5	math	math	PROPN
ejpam-5823	198	6	,	,	PUNCT
ejpam-5823	198	7	18	18	NUM
ejpam-5823	198	8	(	(	PUNCT
ejpam-5823	198	9	2	2	NUM
ejpam-5823	198	10	)	)	PUNCT
ejpam-5823	198	11	(	(	PUNCT
ejpam-5823	198	12	2025	2025	NUM
ejpam-5823	198	13	)	)	PUNCT
ejpam-5823	198	14	,	,	PUNCT
ejpam-5823	198	15	5823	5823	NUM
ejpam-5823	198	16	9	9	NUM
ejpam-5823	198	17	of	of	ADP
ejpam-5823	198	18	26	26	NUM
ejpam-5823	198	19	=	=	SYM
ejpam-5823	198	20	(	(	PUNCT
ejpam-5823	198	21	q	q	PROPN
ejpam-5823	199	1	+	+	NUM
ejpam-5823	199	2	2k)(q	2k)(q	NUM
ejpam-5823	199	3	+	+	CCONJ
ejpam-5823	199	4	k)γk(q	k)γk(q	ADJ
ejpam-5823	199	5	+	+	CCONJ
ejpam-5823	199	6	k	k	NOUN
ejpam-5823	199	7	)	)	PUNCT
ejpam-5823	199	8	γk(q	γk(q	X
ejpam-5823	200	1	+	+	CCONJ
ejpam-5823	201	1	k)(q	k)(q	X
ejpam-5823	201	2	+	+	X
ejpam-5823	201	3	β)2	β)2	ADV
ejpam-5823	201	4	−	−	PROPN
ejpam-5823	201	5	1	1	NUM
ejpam-5823	201	6	=	=	SYM
ejpam-5823	201	7	(	(	PUNCT
ejpam-5823	201	8	q	q	PROPN
ejpam-5823	202	1	+	+	NUM
ejpam-5823	202	2	2k)(q	2k)(q	NUM
ejpam-5823	202	3	+	+	CCONJ
ejpam-5823	202	4	k	k	X
ejpam-5823	202	5	)	)	PUNCT
ejpam-5823	202	6	(	(	PUNCT
ejpam-5823	202	7	q	q	NOUN
ejpam-5823	202	8	+	+	PUNCT
ejpam-5823	202	9	β)2	β)2	ADV
ejpam-5823	202	10	−	−	NOUN
ejpam-5823	202	11	1	1	NUM
ejpam-5823	202	12	.	.	PUNCT
ejpam-5823	202	13	(	(	PUNCT
ejpam-5823	202	14	19	19	NUM
ejpam-5823	202	15	)	)	PUNCT
ejpam-5823	202	16	since	since	SCONJ
ejpam-5823	202	17	(	(	PUNCT
ejpam-5823	202	18	q+2k)(q+k	q+2k)(q+k	NOUN
ejpam-5823	202	19	)	)	PUNCT
ejpam-5823	202	20	(	(	PUNCT
ejpam-5823	202	21	q+β)2	q+β)2	NOUN
ejpam-5823	202	22	−	−	NOUN
ejpam-5823	202	23	1	1	NUM
ejpam-5823	202	24	>	>	SYM
ejpam-5823	202	25	0	0	PUNCT
ejpam-5823	202	26	under	under	ADP
ejpam-5823	202	27	conditions	condition	NOUN
ejpam-5823	202	28	q	q	X
ejpam-5823	202	29	>	>	X
ejpam-5823	202	30	0	0	NUM
ejpam-5823	202	31	,	,	PUNCT
ejpam-5823	202	32	β	β	X
ejpam-5823	202	33	>	>	X
ejpam-5823	202	34	0	0	NUM
ejpam-5823	202	35	,	,	PUNCT
ejpam-5823	202	36	therefore	therefore	ADV
ejpam-5823	202	37	,	,	PUNCT
ejpam-5823	202	38	we	we	PRON
ejpam-5823	202	39	have	have	VERB
ejpam-5823	202	40	(	(	PUNCT
ejpam-5823	202	41	q	q	X
ejpam-5823	203	1	+	+	NUM
ejpam-5823	203	2	2k)(q	2k)(q	NUM
ejpam-5823	203	3	+	+	CCONJ
ejpam-5823	203	4	k	k	X
ejpam-5823	203	5	)	)	PUNCT
ejpam-5823	203	6	>	>	X
ejpam-5823	204	1	(	(	PUNCT
ejpam-5823	204	2	q	q	NOUN
ejpam-5823	204	3	+	+	PUNCT
ejpam-5823	204	4	β)2	β)2	X
ejpam-5823	204	5	|q	|q	NOUN
ejpam-5823	204	6	+	+	CCONJ
ejpam-5823	204	7	β|	β|	X
ejpam-5823	204	8	<	<	X
ejpam-5823	204	9	√	√	X
ejpam-5823	204	10	(	(	PUNCT
ejpam-5823	204	11	q	q	PROPN
ejpam-5823	205	1	+	+	NUM
ejpam-5823	205	2	2k)(q	2k)(q	NUM
ejpam-5823	205	3	+	+	CCONJ
ejpam-5823	205	4	k	k	X
ejpam-5823	205	5	)	)	PUNCT
ejpam-5823	205	6	β	β	NOUN
ejpam-5823	205	7	<	<	X
ejpam-5823	205	8	√	√	X
ejpam-5823	205	9	(	(	PUNCT
ejpam-5823	205	10	q	q	PROPN
ejpam-5823	206	1	+	+	NUM
ejpam-5823	206	2	2k)(q	2k)(q	NUM
ejpam-5823	207	1	+	+	CCONJ
ejpam-5823	207	2	k)−	k)−	PROPN
ejpam-5823	207	3	q	q	PROPN
ejpam-5823	207	4	=	=	SYM
ejpam-5823	207	5	gk(q	gk(q	NOUN
ejpam-5823	207	6	)	)	PUNCT
ejpam-5823	207	7	.	.	PUNCT
ejpam-5823	208	1	(	(	PUNCT
ejpam-5823	208	2	20	20	X
ejpam-5823	208	3	)	)	PUNCT
ejpam-5823	208	4	taking	take	VERB
ejpam-5823	208	5	derivative	derivative	NOUN
ejpam-5823	208	6	of	of	ADP
ejpam-5823	208	7	gk(q	gk(q	NOUN
ejpam-5823	208	8	)	)	PUNCT
ejpam-5823	209	1	=	=	SYM
ejpam-5823	210	1	√	√	INTJ
ejpam-5823	210	2	(	(	PUNCT
ejpam-5823	210	3	q	q	PROPN
ejpam-5823	210	4	+	+	NUM
ejpam-5823	210	5	2k)(q	2k)(q	NUM
ejpam-5823	211	1	+	+	CCONJ
ejpam-5823	211	2	k)−	k)−	PROPN
ejpam-5823	211	3	q	q	PROPN
ejpam-5823	211	4	gives	give	VERB
ejpam-5823	211	5	g′k(q	g′k(q	NOUN
ejpam-5823	211	6	)	)	PUNCT
ejpam-5823	211	7	=	=	SYM
ejpam-5823	212	1	1	1	NUM
ejpam-5823	212	2	2	2	NUM
ejpam-5823	212	3	[	[	X
ejpam-5823	212	4	(	(	PUNCT
ejpam-5823	212	5	q	q	NOUN
ejpam-5823	212	6	+	+	NUM
ejpam-5823	212	7	2k)(q	2k)(q	NUM
ejpam-5823	213	1	+	+	CCONJ
ejpam-5823	213	2	k)]−	k)]−	NOUN
ejpam-5823	213	3	1	1	NUM
ejpam-5823	213	4	2	2	NUM
ejpam-5823	213	5	d	d	NOUN
ejpam-5823	213	6	da	da	X
ejpam-5823	214	1	[	[	X
ejpam-5823	214	2	(	(	PUNCT
ejpam-5823	214	3	q	q	NOUN
ejpam-5823	214	4	+	+	NUM
ejpam-5823	214	5	2k)(q	2k)(q	NUM
ejpam-5823	215	1	+	+	CCONJ
ejpam-5823	215	2	k)]−	k)]−	NOUN
ejpam-5823	215	3	1	1	NUM
ejpam-5823	215	4	=	=	SYM
ejpam-5823	215	5	(	(	PUNCT
ejpam-5823	215	6	q	q	PROPN
ejpam-5823	215	7	+	+	NUM
ejpam-5823	215	8	2k)(q	2k)(q	NUM
ejpam-5823	216	1	+	+	CCONJ
ejpam-5823	216	2	k	k	X
ejpam-5823	216	3	)	)	PUNCT
ejpam-5823	216	4	2	2	NUM
ejpam-5823	216	5	√	√	NOUN
ejpam-5823	216	6	(	(	PUNCT
ejpam-5823	216	7	q	q	PROPN
ejpam-5823	216	8	+	+	NUM
ejpam-5823	216	9	2k)(q	2k)(q	NUM
ejpam-5823	216	10	+	+	CCONJ
ejpam-5823	216	11	k	k	X
ejpam-5823	216	12	)	)	PUNCT
ejpam-5823	216	13	−	−	PROPN
ejpam-5823	217	1	1	1	X
ejpam-5823	217	2	.	.	PUNCT
ejpam-5823	217	3	by	by	ADP
ejpam-5823	217	4	easy	easy	ADJ
ejpam-5823	217	5	computation	computation	NOUN
ejpam-5823	217	6	,	,	PUNCT
ejpam-5823	217	7	we	we	PRON
ejpam-5823	217	8	have	have	VERB
ejpam-5823	217	9	g′k(q	g′k(q	NOUN
ejpam-5823	217	10	)	)	PUNCT
ejpam-5823	218	1	=	=	SYM
ejpam-5823	218	2	k2	k2	ADJ
ejpam-5823	218	3	2	2	NUM
ejpam-5823	218	4	√	√	PROPN
ejpam-5823	218	5	(	(	PUNCT
ejpam-5823	218	6	q	q	PROPN
ejpam-5823	218	7	+	+	NUM
ejpam-5823	218	8	2k)(q	2k)(q	NUM
ejpam-5823	219	1	+	+	CCONJ
ejpam-5823	219	2	k)(2q	k)(2q	PROPN
ejpam-5823	219	3	+	+	CCONJ
ejpam-5823	219	4	3k	3k	PRON
ejpam-5823	220	1	+	+	CCONJ
ejpam-5823	220	2	2	2	NUM
ejpam-5823	220	3	√	√	NOUN
ejpam-5823	220	4	(	(	PUNCT
ejpam-5823	220	5	q	q	PROPN
ejpam-5823	221	1	+	+	NUM
ejpam-5823	221	2	2k)(q	2k)(q	NUM
ejpam-5823	221	3	+	+	CCONJ
ejpam-5823	221	4	k	k	X
ejpam-5823	221	5	)	)	PUNCT
ejpam-5823	221	6	)	)	PUNCT
ejpam-5823	222	1	>	>	X
ejpam-5823	222	2	0	0	NUM
ejpam-5823	222	3	,	,	PUNCT
ejpam-5823	222	4	q	q	X
ejpam-5823	222	5	>	>	X
ejpam-5823	222	6	0	0	NUM
ejpam-5823	222	7	,	,	PUNCT
ejpam-5823	222	8	β	β	X
ejpam-5823	222	9	∈	∈	PROPN
ejpam-5823	222	10	r+	r+	PUNCT
ejpam-5823	222	11	gk	gk	NOUN
ejpam-5823	222	12	is	be	AUX
ejpam-5823	222	13	strictly	strictly	ADV
ejpam-5823	222	14	increasing	increase	VERB
ejpam-5823	222	15	on	on	ADP
ejpam-5823	222	16	(	(	PUNCT
ejpam-5823	222	17	0,+∞	0,+∞	NUM
ejpam-5823	222	18	)	)	PUNCT
ejpam-5823	222	19	,	,	PUNCT
ejpam-5823	222	20	hence	hence	ADV
ejpam-5823	222	21	lim	lim	PROPN
ejpam-5823	222	22	x→0	x→0	PROPN
ejpam-5823	222	23	+	+	X
ejpam-5823	222	24	gk(q	gk(q	X
ejpam-5823	222	25	)	)	PUNCT
ejpam-5823	222	26	=	=	SYM
ejpam-5823	223	1	√	√	ADP
ejpam-5823	223	2	2k	2k	NOUN
ejpam-5823	223	3	<	<	X
ejpam-5823	223	4	gk(q	gk(q	X
ejpam-5823	223	5	)	)	PUNCT
ejpam-5823	223	6	<	<	X
ejpam-5823	223	7	lim	lim	PROPN
ejpam-5823	223	8	x→+∞	x→+∞	PROPN
ejpam-5823	223	9	gk(q	gk(q	PROPN
ejpam-5823	223	10	)	)	PUNCT
ejpam-5823	223	11	=	=	PUNCT
ejpam-5823	223	12	3k	3k	X
ejpam-5823	223	13	2	2	NUM
ejpam-5823	223	14	.	.	PUNCT
ejpam-5823	224	1	(	(	PUNCT
ejpam-5823	224	2	21	21	NUM
ejpam-5823	224	3	)	)	PUNCT
ejpam-5823	224	4	consequently	consequently	ADV
ejpam-5823	224	5	if	if	SCONJ
ejpam-5823	224	6	β	β	X
ejpam-5823	224	7	≤	≤	NUM
ejpam-5823	224	8	√	√	NUM
ejpam-5823	224	9	2	2	NUM
ejpam-5823	224	10	fk(q	fk(q	NUM
ejpam-5823	224	11	,	,	PUNCT
ejpam-5823	224	12	rk	rk	NOUN
ejpam-5823	224	13	)	)	PUNCT
ejpam-5823	224	14	>	>	X
ejpam-5823	224	15	0	0	NUM
ejpam-5823	224	16	,	,	PUNCT
ejpam-5823	224	17	q	q	X
ejpam-5823	224	18	>	>	X
ejpam-5823	224	19	0	0	NUM
ejpam-5823	224	20	,	,	PUNCT
ejpam-5823	224	21	r	r	NOUN
ejpam-5823	224	22	≥	≥	NOUN
ejpam-5823	224	23	3	3	NUM
ejpam-5823	224	24	,	,	PUNCT
ejpam-5823	224	25	k	k	PROPN
ejpam-5823	224	26	∈	∈	PROPN
ejpam-5823	224	27	r+	r+	X
ejpam-5823	224	28	.	.	PUNCT
ejpam-5823	225	1	(	(	PUNCT
ejpam-5823	225	2	22	22	NUM
ejpam-5823	225	3	)	)	PUNCT
ejpam-5823	225	4	left	leave	VERB
ejpam-5823	225	5	side	side	NOUN
ejpam-5823	225	6	of	of	ADP
ejpam-5823	225	7	inequality	inequality	NOUN
ejpam-5823	225	8	14	14	NUM
ejpam-5823	225	9	could	could	AUX
ejpam-5823	225	10	be	be	AUX
ejpam-5823	225	11	improved	improve	VERB
ejpam-5823	225	12	as	as	ADP
ejpam-5823	225	13	:	:	PUNCT
ejpam-5823	225	14	inf	inf	PROPN
ejpam-5823	225	15	{	{	PUNCT
ejpam-5823	225	16	ψk(y)−	ψk(y)−	VERB
ejpam-5823	225	17	1	1	NUM
ejpam-5823	225	18	k	k	NOUN
ejpam-5823	225	19	ln(y	ln(y	PUNCT
ejpam-5823	225	20	)	)	PUNCT
ejpam-5823	226	1	+	+	CCONJ
ejpam-5823	226	2	1	1	NUM
ejpam-5823	226	3	y	y	NOUN
ejpam-5823	226	4	:	:	PUNCT
ejpam-5823	226	5	y	y	PROPN
ejpam-5823	226	6	>	>	X
ejpam-5823	226	7	0	0	PUNCT
ejpam-5823	226	8	}	}	PUNCT
ejpam-5823	226	9	=	=	SYM
ejpam-5823	226	10	0	0	X
ejpam-5823	226	11	.	.	PUNCT
ejpam-5823	227	1	as	as	SCONJ
ejpam-5823	227	2	y	y	PROPN
ejpam-5823	227	3	7−→	7−→	PROPN
ejpam-5823	227	4	ψk(y)−	ψk(y)−	VERB
ejpam-5823	227	5	1	1	NUM
ejpam-5823	227	6	k	k	NOUN
ejpam-5823	227	7	ln(y	ln(y	PUNCT
ejpam-5823	227	8	)	)	PUNCT
ejpam-5823	228	1	+	+	CCONJ
ejpam-5823	228	2	1	1	NUM
ejpam-5823	228	3	y	y	NOUN
ejpam-5823	228	4	is	be	AUX
ejpam-5823	228	5	decreasing	decrease	VERB
ejpam-5823	228	6	and	and	CCONJ
ejpam-5823	228	7	positive	positive	ADJ
ejpam-5823	228	8	on	on	ADP
ejpam-5823	228	9	(	(	PUNCT
ejpam-5823	228	10	0,+∞	0,+∞	NUM
ejpam-5823	228	11	)	)	PUNCT
ejpam-5823	228	12	and	and	CCONJ
ejpam-5823	228	13	by	by	ADP
ejpam-5823	228	14	inequality	inequality	NOUN
ejpam-5823	228	15	14	14	NUM
ejpam-5823	228	16	,	,	PUNCT
ejpam-5823	228	17	we	we	PRON
ejpam-5823	228	18	have	have	VERB
ejpam-5823	228	19	lim	lim	PROPN
ejpam-5823	228	20	y→+∞	y→+∞	PROPN
ejpam-5823	228	21	(	(	PUNCT
ejpam-5823	228	22	ψk(y)−	ψk(y)−	NOUN
ejpam-5823	228	23	1	1	NUM
ejpam-5823	228	24	k	k	NOUN
ejpam-5823	228	25	ln(y	ln(y	PUNCT
ejpam-5823	228	26	)	)	PUNCT
ejpam-5823	229	1	+	+	CCONJ
ejpam-5823	229	2	1	1	NUM
ejpam-5823	229	3	y	y	NOUN
ejpam-5823	229	4	)	)	PUNCT
ejpam-5823	230	1	=	=	PUNCT
ejpam-5823	230	2	0	0	X
ejpam-5823	230	3	.	.	PUNCT
ejpam-5823	231	1	(	(	PUNCT
ejpam-5823	231	2	23	23	NUM
ejpam-5823	231	3	)	)	PUNCT
ejpam-5823	231	4	using	use	VERB
ejpam-5823	231	5	eqs	eqs	PROPN
ejpam-5823	231	6	.	.	PROPN
ejpam-5823	231	7	15	15	NUM
ejpam-5823	231	8	,	,	PUNCT
ejpam-5823	231	9	19	19	NUM
ejpam-5823	231	10	and	and	CCONJ
ejpam-5823	231	11	21	21	NUM
ejpam-5823	231	12	,	,	PUNCT
ejpam-5823	231	13	we	we	PRON
ejpam-5823	231	14	conclude	conclude	VERB
ejpam-5823	231	15	that	that	SCONJ
ejpam-5823	231	16	the	the	DET
ejpam-5823	231	17	value	value	NOUN
ejpam-5823	231	18	√	√	NOUN
ejpam-5823	231	19	2k	2k	NOUN
ejpam-5823	231	20	is	be	AUX
ejpam-5823	231	21	maximum	maximum	ADJ
ejpam-5823	231	22	possible	possible	ADJ
ejpam-5823	231	23	to	to	PART
ejpam-5823	231	24	holds	hold	VERB
ejpam-5823	231	25	the	the	DET
ejpam-5823	231	26	inequality	inequality	NOUN
ejpam-5823	231	27	22	22	NUM
ejpam-5823	231	28	for	for	ADP
ejpam-5823	231	29	sharp	sharp	ADJ
ejpam-5823	231	30	results	result	NOUN
ejpam-5823	231	31	that	that	PRON
ejpam-5823	231	32	completes	complete	VERB
ejpam-5823	231	33	the	the	DET
ejpam-5823	231	34	proof	proof	NOUN
ejpam-5823	231	35	.	.	PUNCT
ejpam-5823	232	1	s.	s.	PROPN
ejpam-5823	232	2	a.	a.	PROPN
ejpam-5823	232	3	h.	h.	PROPN
ejpam-5823	232	4	shah	shah	PROPN
ejpam-5823	232	5	et	et	PROPN
ejpam-5823	232	6	al	al	PROPN
ejpam-5823	232	7	.	.	PUNCT
ejpam-5823	232	8	/	/	SYM
ejpam-5823	232	9	eur	eur	PROPN
ejpam-5823	232	10	.	.	PUNCT
ejpam-5823	233	1	j.	j.	PROPN
ejpam-5823	233	2	pure	pure	PROPN
ejpam-5823	233	3	appl	appl	PROPN
ejpam-5823	233	4	.	.	PROPN
ejpam-5823	233	5	math	math	PROPN
ejpam-5823	233	6	,	,	PUNCT
ejpam-5823	233	7	18	18	NUM
ejpam-5823	233	8	(	(	PUNCT
ejpam-5823	233	9	2	2	NUM
ejpam-5823	233	10	)	)	PUNCT
ejpam-5823	233	11	(	(	PUNCT
ejpam-5823	233	12	2025	2025	NUM
ejpam-5823	233	13	)	)	PUNCT
ejpam-5823	233	14	,	,	PUNCT
ejpam-5823	233	15	5823	5823	NUM
ejpam-5823	233	16	10	10	NUM
ejpam-5823	233	17	of	of	ADP
ejpam-5823	233	18	26	26	NUM
ejpam-5823	233	19	3	3	NUM
ejpam-5823	233	20	.	.	PUNCT
ejpam-5823	234	1	starlikeness	starlikeness	NOUN
ejpam-5823	234	2	and	and	CCONJ
ejpam-5823	234	3	convexity	convexity	NOUN
ejpam-5823	234	4	of	of	ADP
ejpam-5823	234	5	order	order	NOUN
ejpam-5823	234	6	η	η	PROPN
ejpam-5823	234	7	in	in	ADP
ejpam-5823	234	8	this	this	DET
ejpam-5823	234	9	section	section	NOUN
ejpam-5823	234	10	,	,	PUNCT
ejpam-5823	234	11	the	the	DET
ejpam-5823	234	12	following	follow	VERB
ejpam-5823	234	13	theorems	theorem	NOUN
ejpam-5823	234	14	provide	provide	VERB
ejpam-5823	234	15	the	the	DET
ejpam-5823	234	16	starlikeness	starlikeness	NOUN
ejpam-5823	234	17	and	and	CCONJ
ejpam-5823	234	18	convexity	convexity	NOUN
ejpam-5823	234	19	of	of	ADP
ejpam-5823	234	20	order	order	NOUN
ejpam-5823	234	21	η	η	PROPN
ejpam-5823	234	22	with	with	ADP
ejpam-5823	234	23	improved	improved	ADJ
ejpam-5823	234	24	results	result	NOUN
ejpam-5823	234	25	for	for	ADP
ejpam-5823	234	26	generalized	generalized	ADJ
ejpam-5823	234	27	bessel	bessel	NOUN
ejpam-5823	234	28	function	function	NOUN
ejpam-5823	234	29	khξ	khξ	PROPN
ejpam-5823	234	30	,	,	PUNCT
ejpam-5823	234	31	b.	b.	PROPN
ejpam-5823	234	32	theorem	theorem	PROPN
ejpam-5823	234	33	1	1	X
ejpam-5823	234	34	.	.	PUNCT
ejpam-5823	234	35	assume	assume	VERB
ejpam-5823	234	36	ξ	ξ	X
ejpam-5823	234	37	>	>	PUNCT
ejpam-5823	234	38	0	0	PUNCT
ejpam-5823	235	1	and	and	CCONJ
ejpam-5823	235	2	let	let	VERB
ejpam-5823	235	3	b	b	PROPN
ejpam-5823	235	4	∈	∈	PROPN
ejpam-5823	235	5	c∗	c∗	NOUN
ejpam-5823	235	6	,	,	PUNCT
ejpam-5823	235	7	k	k	PROPN
ejpam-5823	235	8	∈	∈	PROPN
ejpam-5823	235	9	r+	r+	NOUN
ejpam-5823	235	10	with	with	ADP
ejpam-5823	235	11	0	0	NUM
ejpam-5823	235	12	<	<	X
ejpam-5823	235	13	|b|	|b|	PROPN
ejpam-5823	235	14	<	<	X
ejpam-5823	235	15	4kξ	4kξ	NOUN
ejpam-5823	235	16	1	1	NUM
ejpam-5823	236	1	+	+	SYM
ejpam-5823	236	2	ξ	ξ	X
ejpam-5823	236	3	=	=	NOUN
ejpam-5823	236	4	:	:	PUNCT
ejpam-5823	236	5	b∗.	b∗.	NOUN
ejpam-5823	236	6	(	(	PUNCT
ejpam-5823	236	7	24	24	NUM
ejpam-5823	236	8	)	)	PUNCT
ejpam-5823	236	9	if	if	SCONJ
ejpam-5823	236	10	η	η	PROPN
ejpam-5823	236	11	≤	≤	X
ejpam-5823	236	12	1−	1−	NUM
ejpam-5823	236	13	|b|	|b|	X
ejpam-5823	236	14	ξ(4k	ξ(4k	NUM
ejpam-5823	236	15	−	−	PROPN
ejpam-5823	236	16	|b|)−	|b|)−	NOUN
ejpam-5823	236	17	|b|	|b|	PROPN
ejpam-5823	236	18	=	=	NOUN
ejpam-5823	236	19	:	:	PUNCT
ejpam-5823	236	20	η∗	η∗	NOUN
ejpam-5823	236	21	(	(	PUNCT
ejpam-5823	236	22	25	25	NUM
ejpam-5823	236	23	)	)	PUNCT
ejpam-5823	236	24	then	then	ADV
ejpam-5823	236	25	khξ	khξ	PROPN
ejpam-5823	236	26	,	,	PUNCT
ejpam-5823	236	27	b	b	PROPN
ejpam-5823	236	28	∈	∈	PROPN
ejpam-5823	236	29	s∗(η	s∗(η	PROPN
ejpam-5823	236	30	)	)	PUNCT
ejpam-5823	236	31	.	.	PUNCT
ejpam-5823	237	1	proof	proof	NOUN
ejpam-5823	237	2	.	.	PUNCT
ejpam-5823	238	1	by	by	ADP
ejpam-5823	238	2	considering	consider	VERB
ejpam-5823	238	3	k	k	NOUN
ejpam-5823	238	4	-	-	NOUN
ejpam-5823	238	5	form	form	NOUN
ejpam-5823	238	6	of	of	ADP
ejpam-5823	238	7	the	the	DET
ejpam-5823	238	8	condition	condition	NOUN
ejpam-5823	238	9	in	in	ADP
ejpam-5823	238	10	[	[	X
ejpam-5823	238	11	20	20	NUM
ejpam-5823	238	12	]	]	PUNCT
ejpam-5823	238	13	,	,	PUNCT
ejpam-5823	238	14	we	we	PRON
ejpam-5823	238	15	have∣∣∣∣z(khξ	have∣∣∣∣z(khξ	VERB
ejpam-5823	238	16	,	,	PUNCT
ejpam-5823	238	17	b(z	b(z	NOUN
ejpam-5823	238	18	)	)	PUNCT
ejpam-5823	238	19	)	)	PUNCT
ejpam-5823	239	1	′	′	NUM
ejpam-5823	240	1	khξ	khξ	NOUN
ejpam-5823	240	2	,	,	PUNCT
ejpam-5823	240	3	b(z	b(z	NOUN
ejpam-5823	240	4	)	)	PUNCT
ejpam-5823	240	5	−	−	PROPN
ejpam-5823	240	6	1	1	NUM
ejpam-5823	240	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	240	8	<	<	X
ejpam-5823	240	9	1−	1−	NUM
ejpam-5823	240	10	η	η	PROPN
ejpam-5823	240	11	,	,	PUNCT
ejpam-5823	240	12	η	η	PROPN
ejpam-5823	240	13	≤	≤	ADJ
ejpam-5823	240	14	1	1	NUM
ejpam-5823	240	15	.	.	PUNCT
ejpam-5823	241	1	(	(	PUNCT
ejpam-5823	241	2	26	26	NUM
ejpam-5823	241	3	)	)	PUNCT
ejpam-5823	241	4	taking	take	VERB
ejpam-5823	241	5	∣∣∣∣(khξ	∣∣∣∣(khξ	ADJ
ejpam-5823	241	6	,	,	PUNCT
ejpam-5823	241	7	b(z	b(z	NOUN
ejpam-5823	241	8	)	)	PUNCT
ejpam-5823	241	9	)	)	PUNCT
ejpam-5823	242	1	′	′	NUM
ejpam-5823	243	1	−	−	PROPN
ejpam-5823	243	2	khξ	khξ	NOUN
ejpam-5823	243	3	,	,	PUNCT
ejpam-5823	243	4	b(z	b(z	NOUN
ejpam-5823	243	5	)	)	PUNCT
ejpam-5823	243	6	z	z	NOUN
ejpam-5823	243	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	243	8	=	=	SYM
ejpam-5823	243	9	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5823	243	10	(	(	PUNCT
ejpam-5823	243	11	z	z	X
ejpam-5823	243	12	+	+	NUM
ejpam-5823	243	13	∞∑	∞∑	NUM
ejpam-5823	243	14	r=1	r=1	NOUN
ejpam-5823	243	15	(	(	PUNCT
ejpam-5823	243	16	−b)r	−b)r	NOUN
ejpam-5823	243	17	zr+1	zr+1	NUM
ejpam-5823	243	18	r	r	NOUN
ejpam-5823	243	19	!	!	NOUN
ejpam-5823	243	20	4r	4r	PROPN
ejpam-5823	243	21	kr	kr	PROPN
ejpam-5823	243	22	(	(	PUNCT
ejpam-5823	243	23	ξ)r	ξ)r	NOUN
ejpam-5823	243	24	,	,	PUNCT
ejpam-5823	243	25	k	k	PROPN
ejpam-5823	243	26	)	)	PUNCT
ejpam-5823	243	27	′	′	NUM
ejpam-5823	244	1	−	−	NOUN
ejpam-5823	244	2	z	z	NOUN
ejpam-5823	245	1	+	+	CCONJ
ejpam-5823	245	2	∞∑	∞∑	NUM
ejpam-5823	245	3	r=1	r=1	NOUN
ejpam-5823	245	4	(	(	PUNCT
ejpam-5823	245	5	−b)r	−b)r	NOUN
ejpam-5823	245	6	zr+1	zr+1	NUM
ejpam-5823	245	7	r	r	NOUN
ejpam-5823	245	8	!	!	NOUN
ejpam-5823	245	9	4r	4r	PROPN
ejpam-5823	245	10	kr	kr	PROPN
ejpam-5823	245	11	(	(	PUNCT
ejpam-5823	245	12	ξ)r	ξ)r	NOUN
ejpam-5823	245	13	,	,	PUNCT
ejpam-5823	245	14	k	k	PROPN
ejpam-5823	245	15	z	z	NOUN
ejpam-5823	245	16	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5823	245	17	=	=	PUNCT
ejpam-5823	245	18	∣∣∣∣∣∣∣∣1	∣∣∣∣∣∣∣∣1	VERB
ejpam-5823	245	19	+	+	CCONJ
ejpam-5823	245	20	∞∑	∞∑	NUM
ejpam-5823	245	21	r=1	r=1	NOUN
ejpam-5823	245	22	(	(	PUNCT
ejpam-5823	245	23	r	r	NOUN
ejpam-5823	245	24	+	+	NUM
ejpam-5823	245	25	1)(−b)r	1)(−b)r	NUM
ejpam-5823	245	26	zr	zr	NOUN
ejpam-5823	245	27	r	r	NOUN
ejpam-5823	245	28	!	!	NOUN
ejpam-5823	245	29	4r	4r	PROPN
ejpam-5823	245	30	kr	kr	PROPN
ejpam-5823	245	31	(	(	PUNCT
ejpam-5823	245	32	ξ)r	ξ)r	NOUN
ejpam-5823	245	33	,	,	PUNCT
ejpam-5823	245	34	k	k	PROPN
ejpam-5823	245	35	−	−	PROPN
ejpam-5823	245	36	z	z	NOUN
ejpam-5823	245	37	[	[	PUNCT
ejpam-5823	245	38	1	1	NUM
ejpam-5823	245	39	+	+	NUM
ejpam-5823	245	40	∞∑	∞∑	NUM
ejpam-5823	245	41	r=1	r=1	NOUN
ejpam-5823	245	42	(	(	PUNCT
ejpam-5823	245	43	−b)r	−b)r	VERB
ejpam-5823	245	44	zr	zr	PROPN
ejpam-5823	245	45	4r	4r	NOUN
ejpam-5823	245	46	kr	kr	PROPN
ejpam-5823	245	47	r	r	X
ejpam-5823	245	48	!	!	PUNCT
ejpam-5823	245	49	(	(	PUNCT
ejpam-5823	245	50	ξ)r	ξ)r	PROPN
ejpam-5823	245	51	,	,	PUNCT
ejpam-5823	245	52	k	k	X
ejpam-5823	245	53	]	]	X
ejpam-5823	245	54	z	z	X
ejpam-5823	245	55	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5823	245	56	=	=	SYM
ejpam-5823	246	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5823	246	2	∞∑	∞∑	NUM
ejpam-5823	246	3	r=1	r=1	NOUN
ejpam-5823	246	4	(	(	PUNCT
ejpam-5823	246	5	r	r	NOUN
ejpam-5823	246	6	+	+	NOUN
ejpam-5823	246	7	1	1	NUM
ejpam-5823	246	8	)	)	PUNCT
ejpam-5823	246	9	(	(	PUNCT
ejpam-5823	246	10	−b)r	−b)r	VERB
ejpam-5823	246	11	zr	zr	NOUN
ejpam-5823	246	12	4r	4r	NOUN
ejpam-5823	246	13	kr	kr	PROPN
ejpam-5823	246	14	r	r	X
ejpam-5823	246	15	!	!	PUNCT
ejpam-5823	246	16	(	(	PUNCT
ejpam-5823	246	17	ξ)r	ξ)r	NOUN
ejpam-5823	246	18	,	,	PUNCT
ejpam-5823	247	1	k	k	PROPN
ejpam-5823	247	2	−	−	PROPN
ejpam-5823	247	3	∞∑	∞∑	NUM
ejpam-5823	247	4	r=1	r=1	NOUN
ejpam-5823	247	5	(	(	PUNCT
ejpam-5823	247	6	−b)r	−b)r	VERB
ejpam-5823	247	7	zr	zr	PROPN
ejpam-5823	247	8	4r	4r	NOUN
ejpam-5823	247	9	kr	kr	PROPN
ejpam-5823	247	10	r	r	X
ejpam-5823	247	11	!	!	PUNCT
ejpam-5823	247	12	(	(	PUNCT
ejpam-5823	247	13	ξ)r	ξ)r	NOUN
ejpam-5823	247	14	,	,	PUNCT
ejpam-5823	247	15	k	k	PROPN
ejpam-5823	247	16	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	247	17	=	=	SYM
ejpam-5823	248	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	248	2	∞∑	∞∑	NUM
ejpam-5823	248	3	r=1	r=1	NOUN
ejpam-5823	248	4	(	(	PUNCT
ejpam-5823	248	5	r	r	NOUN
ejpam-5823	248	6	)	)	PUNCT
ejpam-5823	248	7	(	(	PUNCT
ejpam-5823	248	8	−b)r	−b)r	VERB
ejpam-5823	248	9	zr	zr	NOUN
ejpam-5823	248	10	4r	4r	NOUN
ejpam-5823	248	11	kr	kr	PROPN
ejpam-5823	248	12	r	r	X
ejpam-5823	248	13	!	!	PUNCT
ejpam-5823	248	14	(	(	PUNCT
ejpam-5823	248	15	ξ)r	ξ)r	NOUN
ejpam-5823	248	16	,	,	PUNCT
ejpam-5823	248	17	k	k	PROPN
ejpam-5823	248	18	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	248	19	<	<	X
ejpam-5823	248	20	sup	sup	X
ejpam-5823	248	21	θ∈2π	θ∈2π	X
ejpam-5823	248	22	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5823	248	23	∞∑	∞∑	NUM
ejpam-5823	248	24	r=1	r=1	NOUN
ejpam-5823	248	25	(	(	PUNCT
ejpam-5823	248	26	r	r	NOUN
ejpam-5823	248	27	)	)	PUNCT
ejpam-5823	248	28	(	(	PUNCT
ejpam-5823	248	29	−b)r	−b)r	VERB
ejpam-5823	248	30	eiθr	eiθr	NOUN
ejpam-5823	248	31	4r	4r	NUM
ejpam-5823	248	32	kr	kr	PROPN
ejpam-5823	248	33	r	r	X
ejpam-5823	248	34	!	!	PUNCT
ejpam-5823	248	35	(	(	PUNCT
ejpam-5823	248	36	ξ)r	ξ)r	NOUN
ejpam-5823	248	37	,	,	PUNCT
ejpam-5823	248	38	k	k	PROPN
ejpam-5823	248	39	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	248	40	≤	≤	X
ejpam-5823	248	41	∞∑	∞∑	NUM
ejpam-5823	248	42	r=1	r=1	ADJ
ejpam-5823	248	43	(	(	PUNCT
ejpam-5823	248	44	r	r	NOUN
ejpam-5823	248	45	)	)	PUNCT
ejpam-5823	248	46	|b|r	|b|r	PROPN
ejpam-5823	248	47	4r	4r	NOUN
ejpam-5823	248	48	kr	kr	PROPN
ejpam-5823	248	49	r	r	X
ejpam-5823	248	50	!	!	PUNCT
ejpam-5823	249	1	γk(ξ+rk	γk(ξ+rk	ADV
ejpam-5823	249	2	)	)	PUNCT
ejpam-5823	250	1	γk(ξ	γk(ξ	NUM
ejpam-5823	250	2	)	)	PUNCT
ejpam-5823	251	1	,	,	PUNCT
ejpam-5823	251	2	|z|	|z|	VERB
ejpam-5823	251	3	≤	≤	NUM
ejpam-5823	251	4	1	1	NUM
ejpam-5823	251	5	≤	≤	NOUN
ejpam-5823	251	6	γk(ξ	γk(ξ	ADV
ejpam-5823	251	7	+	+	SYM
ejpam-5823	251	8	k	k	X
ejpam-5823	251	9	)	)	PUNCT
ejpam-5823	251	10	ξ	ξ	VERB
ejpam-5823	251	11	∞∑	∞∑	NUM
ejpam-5823	251	12	r=1	r=1	NOUN
ejpam-5823	251	13	|b|r	|b|r	X
ejpam-5823	251	14	(	(	PUNCT
ejpam-5823	251	15	r	r	NOUN
ejpam-5823	251	16	)	)	PUNCT
ejpam-5823	251	17	4r	4r	NOUN
ejpam-5823	251	18	kr	kr	NOUN
ejpam-5823	251	19	γk(r	γk(r	NOUN
ejpam-5823	252	1	+	+	CCONJ
ejpam-5823	252	2	k)γk(ξ	k)γk(ξ	X
ejpam-5823	252	3	+	+	CCONJ
ejpam-5823	252	4	rk	rk	NOUN
ejpam-5823	252	5	)	)	PUNCT
ejpam-5823	252	6	.	.	PUNCT
ejpam-5823	253	1	(	(	PUNCT
ejpam-5823	253	2	27	27	NUM
ejpam-5823	253	3	)	)	PUNCT
ejpam-5823	253	4	letting	let	VERB
ejpam-5823	253	5	the	the	DET
ejpam-5823	253	6	function	function	NOUN
ejpam-5823	253	7	σk(a	σk(a	PUNCT
ejpam-5823	253	8	)	)	PUNCT
ejpam-5823	253	9	=	=	PUNCT
ejpam-5823	253	10	a	a	DET
ejpam-5823	253	11	γk(a+	γk(a+	PROPN
ejpam-5823	253	12	k)γk(ξ	k)γk(ξ	X
ejpam-5823	253	13	+	+	CCONJ
ejpam-5823	253	14	ak	ak	PROPN
ejpam-5823	253	15	)	)	PUNCT
ejpam-5823	253	16	,	,	PUNCT
ejpam-5823	253	17	r	r	NOUN
ejpam-5823	253	18	∈	∈	PROPN
ejpam-5823	253	19	n.	n.	NOUN
ejpam-5823	253	20	(	(	PUNCT
ejpam-5823	253	21	28	28	NUM
ejpam-5823	253	22	)	)	PUNCT
ejpam-5823	253	23	s.	s.	PROPN
ejpam-5823	253	24	a.	a.	PROPN
ejpam-5823	253	25	h.	h.	PROPN
ejpam-5823	253	26	shah	shah	PROPN
ejpam-5823	253	27	et	et	PROPN
ejpam-5823	253	28	al	al	PROPN
ejpam-5823	253	29	.	.	PUNCT
ejpam-5823	253	30	/	/	SYM
ejpam-5823	253	31	eur	eur	PROPN
ejpam-5823	253	32	.	.	PUNCT
ejpam-5823	254	1	j.	j.	PROPN
ejpam-5823	254	2	pure	pure	PROPN
ejpam-5823	254	3	appl	appl	PROPN
ejpam-5823	254	4	.	.	PROPN
ejpam-5823	254	5	math	math	PROPN
ejpam-5823	254	6	,	,	PUNCT
ejpam-5823	254	7	18	18	NUM
ejpam-5823	254	8	(	(	PUNCT
ejpam-5823	254	9	2	2	NUM
ejpam-5823	254	10	)	)	PUNCT
ejpam-5823	254	11	(	(	PUNCT
ejpam-5823	254	12	2025	2025	NUM
ejpam-5823	254	13	)	)	PUNCT
ejpam-5823	254	14	,	,	PUNCT
ejpam-5823	254	15	5823	5823	NUM
ejpam-5823	254	16	11	11	NUM
ejpam-5823	254	17	of	of	ADP
ejpam-5823	254	18	26	26	NUM
ejpam-5823	254	19	by	by	ADP
ejpam-5823	254	20	easy	easy	ADJ
ejpam-5823	254	21	computation	computation	NOUN
ejpam-5823	254	22	σk(r	σk(r	PUNCT
ejpam-5823	255	1	+	+	PROPN
ejpam-5823	255	2	1)−	1)−	NUM
ejpam-5823	255	3	σk(r	σk(r	NUM
ejpam-5823	255	4	)	)	PUNCT
ejpam-5823	256	1	=	=	PUNCT
ejpam-5823	257	1	r	r	NOUN
ejpam-5823	257	2	+	+	NUM
ejpam-5823	257	3	1	1	NUM
ejpam-5823	257	4	γk(r	γk(r	NOUN
ejpam-5823	257	5	+	+	NOUN
ejpam-5823	257	6	1	1	NUM
ejpam-5823	257	7	+	+	NUM
ejpam-5823	257	8	k)γk(ξ	k)γk(ξ	NOUN
ejpam-5823	257	9	+	+	CCONJ
ejpam-5823	257	10	(	(	PUNCT
ejpam-5823	257	11	r	r	NOUN
ejpam-5823	257	12	+	+	NUM
ejpam-5823	257	13	1)k	1)k	NUM
ejpam-5823	257	14	)	)	PUNCT
ejpam-5823	258	1	−	−	NOUN
ejpam-5823	258	2	r	r	NOUN
ejpam-5823	258	3	γk(r	γk(r	NOUN
ejpam-5823	258	4	+	+	CCONJ
ejpam-5823	258	5	k)γk(ξ	k)γk(ξ	X
ejpam-5823	258	6	+	+	CCONJ
ejpam-5823	258	7	rk	rk	NOUN
ejpam-5823	258	8	)	)	PUNCT
ejpam-5823	258	9	=	=	SYM
ejpam-5823	258	10	r	r	NOUN
ejpam-5823	258	11	+	+	NUM
ejpam-5823	258	12	1−	1−	NUM
ejpam-5823	258	13	(	(	PUNCT
ejpam-5823	258	14	r)(r	r)(r	NOUN
ejpam-5823	258	15	+	+	CCONJ
ejpam-5823	258	16	k)(ξ	k)(ξ	NOUN
ejpam-5823	258	17	+	+	CCONJ
ejpam-5823	258	18	rk	rk	NOUN
ejpam-5823	258	19	)	)	PUNCT
ejpam-5823	258	20	(	(	PUNCT
ejpam-5823	258	21	r	r	NOUN
ejpam-5823	258	22	+	+	NUM
ejpam-5823	258	23	k)(ξ	k)(ξ	NOUN
ejpam-5823	258	24	+	+	CCONJ
ejpam-5823	258	25	rk)γk(r	rk)γk(r	NOUN
ejpam-5823	258	26	+	+	CCONJ
ejpam-5823	258	27	k)γk(ξ	k)γk(ξ	X
ejpam-5823	258	28	+	+	CCONJ
ejpam-5823	258	29	rk	rk	NOUN
ejpam-5823	258	30	)	)	PUNCT
ejpam-5823	258	31	=	=	SYM
ejpam-5823	258	32	1	1	NUM
ejpam-5823	258	33	+	+	NUM
ejpam-5823	258	34	r	r	NOUN
ejpam-5823	258	35	−	−	NOUN
ejpam-5823	258	36	rk(r2	rk(r2	NOUN
ejpam-5823	258	37	−	−	X
ejpam-5823	258	38	ξ)−	ξ)−	PROPN
ejpam-5823	258	39	r2(k2	r2(k2	NOUN
ejpam-5823	258	40	+	+	CCONJ
ejpam-5823	258	41	ξ	ξ	X
ejpam-5823	258	42	)	)	PUNCT
ejpam-5823	258	43	γk(r	γk(r	PUNCT
ejpam-5823	259	1	+	+	CCONJ
ejpam-5823	259	2	k	k	X
ejpam-5823	259	3	+	+	CCONJ
ejpam-5823	259	4	1)γk(ξ	1)γk(ξ	NUM
ejpam-5823	259	5	+	+	CCONJ
ejpam-5823	259	6	rk	rk	NOUN
ejpam-5823	259	7	+	+	CCONJ
ejpam-5823	259	8	k	k	NOUN
ejpam-5823	259	9	)	)	PUNCT
ejpam-5823	259	10	(	(	PUNCT
ejpam-5823	259	11	29	29	NUM
ejpam-5823	259	12	)	)	PUNCT
ejpam-5823	259	13	which	which	PRON
ejpam-5823	259	14	implies	imply	VERB
ejpam-5823	259	15	that	that	PRON
ejpam-5823	259	16	σk(r	σk(r	PUNCT
ejpam-5823	260	1	+	+	PROPN
ejpam-5823	260	2	1)−	1)−	NUM
ejpam-5823	260	3	σk(r	σk(r	NUM
ejpam-5823	260	4	)	)	PUNCT
ejpam-5823	261	1	<	<	X
ejpam-5823	261	2	0	0	NUM
ejpam-5823	261	3	,	,	PUNCT
ejpam-5823	261	4	r	r	NOUN
ejpam-5823	261	5	∈	∈	PROPN
ejpam-5823	261	6	n.	n.	NOUN
ejpam-5823	261	7	(	(	PUNCT
ejpam-5823	261	8	30	30	NUM
ejpam-5823	261	9	)	)	PUNCT
ejpam-5823	261	10	hence	hence	ADV
ejpam-5823	261	11	the	the	DET
ejpam-5823	261	12	function	function	NOUN
ejpam-5823	261	13	is	be	AUX
ejpam-5823	261	14	strictly	strictly	ADV
ejpam-5823	261	15	decreasing	decrease	VERB
ejpam-5823	261	16	,	,	PUNCT
ejpam-5823	261	17	so	so	ADV
ejpam-5823	261	18	:	:	PUNCT
ejpam-5823	261	19	a	a	DET
ejpam-5823	261	20	γk(a+	γk(a+	PROPN
ejpam-5823	261	21	k)γk(ξ	k)γk(ξ	X
ejpam-5823	261	22	+	+	CCONJ
ejpam-5823	261	23	ak	ak	NOUN
ejpam-5823	261	24	)	)	PUNCT
ejpam-5823	261	25	≤	≤	NOUN
ejpam-5823	261	26	σk(1	σk(1	NOUN
ejpam-5823	261	27	)	)	PUNCT
ejpam-5823	261	28	=	=	SYM
ejpam-5823	261	29	1	1	NUM
ejpam-5823	261	30	γk(1	γk(1	NOUN
ejpam-5823	261	31	+	+	CCONJ
ejpam-5823	261	32	k)γk(ξ	k)γk(ξ	NOUN
ejpam-5823	261	33	+	+	CCONJ
ejpam-5823	261	34	k	k	NOUN
ejpam-5823	261	35	)	)	PUNCT
ejpam-5823	261	36	.	.	PUNCT
ejpam-5823	262	1	by	by	ADP
ejpam-5823	262	2	the	the	DET
ejpam-5823	262	3	inequality	inequality	NOUN
ejpam-5823	262	4	27	27	NUM
ejpam-5823	262	5	,	,	PUNCT
ejpam-5823	262	6	we	we	PRON
ejpam-5823	262	7	get:∣∣∣∣(khξ	get:∣∣∣∣(khξ	NOUN
ejpam-5823	262	8	,	,	PUNCT
ejpam-5823	262	9	b(z	b(z	NOUN
ejpam-5823	262	10	)	)	PUNCT
ejpam-5823	262	11	)	)	PUNCT
ejpam-5823	262	12	′	′	NUM
ejpam-5823	263	1	−	−	PROPN
ejpam-5823	263	2	khξ	khξ	NOUN
ejpam-5823	263	3	,	,	PUNCT
ejpam-5823	263	4	b(z	b(z	NOUN
ejpam-5823	263	5	)	)	PUNCT
ejpam-5823	263	6	z	z	NOUN
ejpam-5823	263	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	263	8	≤	≤	NOUN
ejpam-5823	263	9	γk(ξ	γk(ξ	ADV
ejpam-5823	263	10	+	+	SYM
ejpam-5823	263	11	k	k	X
ejpam-5823	263	12	)	)	PUNCT
ejpam-5823	263	13	ξ	ξ	VERB
ejpam-5823	263	14	∞∑	∞∑	NUM
ejpam-5823	263	15	r=1	r=1	NOUN
ejpam-5823	263	16	|b|r	|b|r	PROPN
ejpam-5823	263	17	4r	4r	NUM
ejpam-5823	263	18	kr	kr	PROPN
ejpam-5823	263	19	γk(1	γk(1	PROPN
ejpam-5823	263	20	+	+	CCONJ
ejpam-5823	263	21	k)γk(ξ	k)γk(ξ	X
ejpam-5823	263	22	+	+	CCONJ
ejpam-5823	263	23	k	k	X
ejpam-5823	263	24	)	)	PUNCT
ejpam-5823	263	25	=	=	SYM
ejpam-5823	263	26	1	1	NUM
ejpam-5823	263	27	ξ	ξ	X
ejpam-5823	263	28	∞∑	∞∑	NUM
ejpam-5823	263	29	r=1	r=1	NOUN
ejpam-5823	263	30	(	(	PUNCT
ejpam-5823	263	31	|b|	|b|	X
ejpam-5823	263	32	4k	4k	NOUN
ejpam-5823	263	33	)	)	PUNCT
ejpam-5823	263	34	r	r	NOUN
ejpam-5823	263	35	=	=	PUNCT
ejpam-5823	263	36	|b|	|b|	X
ejpam-5823	263	37	ξ(4k	ξ(4k	NUM
ejpam-5823	263	38	−	−	PROPN
ejpam-5823	263	39	|b|	|b|	PROPN
ejpam-5823	263	40	)	)	PUNCT
ejpam-5823	263	41	⇒	⇒	PROPN
ejpam-5823	263	42	∣∣∣∣(khξ	∣∣∣∣(khξ	PROPN
ejpam-5823	263	43	,	,	PUNCT
ejpam-5823	263	44	b(z	b(z	NOUN
ejpam-5823	263	45	)	)	PUNCT
ejpam-5823	263	46	)	)	PUNCT
ejpam-5823	264	1	′	′	NUM
ejpam-5823	265	1	−	−	PROPN
ejpam-5823	265	2	khξ	khξ	NOUN
ejpam-5823	265	3	,	,	PUNCT
ejpam-5823	265	4	b(z	b(z	NOUN
ejpam-5823	265	5	)	)	PUNCT
ejpam-5823	265	6	z	z	NOUN
ejpam-5823	265	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	265	8	≤	≤	NOUN
ejpam-5823	265	9	|b|	|b|	VERB
ejpam-5823	265	10	ξ(4k	ξ(4k	NUM
ejpam-5823	265	11	−	−	PROPN
ejpam-5823	265	12	|b|	|b|	PROPN
ejpam-5823	265	13	)	)	PUNCT
ejpam-5823	265	14	,	,	PUNCT
ejpam-5823	265	15	z	z	PROPN
ejpam-5823	265	16	∈	∈	PROPN
ejpam-5823	265	17	u	u	NOUN
ejpam-5823	265	18	,	,	PUNCT
ejpam-5823	265	19	k	k	PROPN
ejpam-5823	265	20	∈	∈	PROPN
ejpam-5823	265	21	r+	r+	X
ejpam-5823	265	22	.	.	PUNCT
ejpam-5823	266	1	(	(	PUNCT
ejpam-5823	266	2	31	31	NUM
ejpam-5823	266	3	)	)	PUNCT
ejpam-5823	266	4	now	now	ADV
ejpam-5823	266	5	by	by	ADP
ejpam-5823	266	6	assuming	assume	VERB
ejpam-5823	266	7	the	the	DET
ejpam-5823	266	8	above	above	ADJ
ejpam-5823	266	9	inequality	inequality	NOUN
ejpam-5823	266	10	|b|	|b|	PROPN
ejpam-5823	266	11	ξ(4k−|b|	ξ(4k−|b|	PROPN
ejpam-5823	266	12	)	)	PUNCT
ejpam-5823	266	13	>	>	X
ejpam-5823	266	14	0	0	NUM
ejpam-5823	266	15	,	,	PUNCT
ejpam-5823	266	16	equivalence	equivalence	NOUN
ejpam-5823	266	17	to	to	ADP
ejpam-5823	266	18	0	0	NUM
ejpam-5823	266	19	<	<	X
ejpam-5823	266	20	|b|	|b|	PROPN
ejpam-5823	266	21	<	<	X
ejpam-5823	266	22	4k	4k	NUM
ejpam-5823	266	23	which	which	PRON
ejpam-5823	266	24	holds	hold	VERB
ejpam-5823	266	25	according	accord	VERB
ejpam-5823	266	26	to	to	ADP
ejpam-5823	266	27	35	35	NUM
ejpam-5823	266	28	and	and	CCONJ
ejpam-5823	266	29	the	the	DET
ejpam-5823	266	30	assumption	assumption	NOUN
ejpam-5823	266	31	0	0	PUNCT
ejpam-5823	266	32	<	<	X
ejpam-5823	266	33	|b|	|b|	X
ejpam-5823	266	34	<	<	X
ejpam-5823	266	35	4kξ	4kξ	NOUN
ejpam-5823	266	36	1	1	NUM
ejpam-5823	266	37	+	+	SYM
ejpam-5823	266	38	ξ	ξ	PROPN
ejpam-5823	266	39	(	(	PUNCT
ejpam-5823	266	40	32	32	NUM
ejpam-5823	266	41	)	)	PUNCT
ejpam-5823	266	42	the	the	DET
ejpam-5823	266	43	case	case	NOUN
ejpam-5823	266	44	|b|	|b|	VERB
ejpam-5823	266	45	=	=	SYM
ejpam-5823	266	46	0	0	NUM
ejpam-5823	266	47	is	be	AUX
ejpam-5823	266	48	the	the	DET
ejpam-5823	266	49	trivial	trivial	ADJ
ejpam-5823	266	50	case	case	NOUN
ejpam-5823	266	51	gives	give	VERB
ejpam-5823	266	52	the	the	DET
ejpam-5823	266	53	identity	identity	NOUN
ejpam-5823	266	54	function	function	NOUN
ejpam-5823	266	55	.	.	PUNCT
ejpam-5823	267	1	now	now	ADV
ejpam-5823	267	2	taking	take	VERB
ejpam-5823	267	3	the	the	DET
ejpam-5823	267	4	other	other	ADJ
ejpam-5823	267	5	part	part	NOUN
ejpam-5823	267	6	,	,	PUNCT
ejpam-5823	267	7	we	we	PRON
ejpam-5823	267	8	have∣∣∣∣khξ	have∣∣∣∣khξ	NOUN
ejpam-5823	267	9	,	,	PUNCT
ejpam-5823	267	10	b(z	b(z	NOUN
ejpam-5823	267	11	)	)	PUNCT
ejpam-5823	267	12	z	z	NOUN
ejpam-5823	267	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	267	14	=	=	NOUN
ejpam-5823	267	15	∣∣∣∣∣1	∣∣∣∣∣1	VERB
ejpam-5823	267	16	+	+	CCONJ
ejpam-5823	267	17	∞∑	∞∑	NUM
ejpam-5823	267	18	r=1	r=1	NOUN
ejpam-5823	267	19	(	(	PUNCT
ejpam-5823	267	20	−b)r	−b)r	VERB
ejpam-5823	267	21	zr	zr	NOUN
ejpam-5823	267	22	r	r	NOUN
ejpam-5823	267	23	!	!	PUNCT
ejpam-5823	267	24	4r	4r	PROPN
ejpam-5823	267	25	kr	kr	PROPN
ejpam-5823	267	26	(	(	PUNCT
ejpam-5823	267	27	ξ)r	ξ)r	NOUN
ejpam-5823	267	28	,	,	PUNCT
ejpam-5823	267	29	k	k	PROPN
ejpam-5823	267	30	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	267	31	.	.	PUNCT
ejpam-5823	268	1	by	by	ADP
ejpam-5823	268	2	using	use	VERB
ejpam-5823	268	3	triangular	triangular	NOUN
ejpam-5823	268	4	inequality	inequality	NOUN
ejpam-5823	268	5	and	and	CCONJ
ejpam-5823	268	6	the	the	DET
ejpam-5823	268	7	modulus	modulus	ADJ
ejpam-5823	268	8	theorem:∣∣∣∣khξ	theorem:∣∣∣∣khξ	NOUN
ejpam-5823	268	9	,	,	PUNCT
ejpam-5823	268	10	b(z	b(z	NOUN
ejpam-5823	268	11	)	)	PUNCT
ejpam-5823	268	12	z	z	NOUN
ejpam-5823	268	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	268	14	>	>	X
ejpam-5823	268	15	1−	1−	NUM
ejpam-5823	268	16	sup	sup	NOUN
ejpam-5823	268	17	θ∈2π	θ∈2π	PROPN
ejpam-5823	268	18	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5823	268	19	∞∑	∞∑	NUM
ejpam-5823	268	20	r=1	r=1	NOUN
ejpam-5823	268	21	(	(	PUNCT
ejpam-5823	268	22	−b)r	−b)r	NOUN
ejpam-5823	268	23	eiθr	eiθr	NOUN
ejpam-5823	268	24	4r	4r	NUM
ejpam-5823	268	25	kr	kr	PROPN
ejpam-5823	268	26	r	r	X
ejpam-5823	268	27	!	!	PUNCT
ejpam-5823	268	28	(	(	PUNCT
ejpam-5823	268	29	ξ)r	ξ)r	NOUN
ejpam-5823	268	30	,	,	PUNCT
ejpam-5823	268	31	k	k	PROPN
ejpam-5823	268	32	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	268	33	s.	s.	PROPN
ejpam-5823	268	34	a.	a.	PROPN
ejpam-5823	268	35	h.	h.	PROPN
ejpam-5823	268	36	shah	shah	PROPN
ejpam-5823	268	37	et	et	PROPN
ejpam-5823	268	38	al	al	PROPN
ejpam-5823	268	39	.	.	PUNCT
ejpam-5823	268	40	/	/	SYM
ejpam-5823	268	41	eur	eur	PROPN
ejpam-5823	268	42	.	.	PUNCT
ejpam-5823	269	1	j.	j.	PROPN
ejpam-5823	269	2	pure	pure	PROPN
ejpam-5823	269	3	appl	appl	PROPN
ejpam-5823	269	4	.	.	PROPN
ejpam-5823	269	5	math	math	PROPN
ejpam-5823	269	6	,	,	PUNCT
ejpam-5823	269	7	18	18	NUM
ejpam-5823	269	8	(	(	PUNCT
ejpam-5823	269	9	2	2	NUM
ejpam-5823	269	10	)	)	PUNCT
ejpam-5823	269	11	(	(	PUNCT
ejpam-5823	269	12	2025	2025	NUM
ejpam-5823	269	13	)	)	PUNCT
ejpam-5823	269	14	,	,	PUNCT
ejpam-5823	269	15	5823	5823	NUM
ejpam-5823	269	16	12	12	NUM
ejpam-5823	269	17	of	of	ADP
ejpam-5823	269	18	26	26	NUM
ejpam-5823	269	19	≥	≥	NOUN
ejpam-5823	269	20	1−	1−	NUM
ejpam-5823	269	21	∞∑	∞∑	NUM
ejpam-5823	269	22	r=1	r=1	NOUN
ejpam-5823	269	23	|b|r	|b|r	PROPN
ejpam-5823	269	24	4r	4r	NOUN
ejpam-5823	269	25	kr	kr	PROPN
ejpam-5823	269	26	r	r	X
ejpam-5823	269	27	!	!	PUNCT
ejpam-5823	269	28	(	(	PUNCT
ejpam-5823	269	29	ξ)r	ξ)r	NOUN
ejpam-5823	269	30	,	,	PUNCT
ejpam-5823	269	31	k	k	PROPN
ejpam-5823	269	32	=	=	SYM
ejpam-5823	269	33	1−	1−	NUM
ejpam-5823	270	1	∞∑	∞∑	NUM
ejpam-5823	270	2	r=1	r=1	NOUN
ejpam-5823	270	3	|b|r	|b|r	X
ejpam-5823	270	4	γk(ξ	γk(ξ	NOUN
ejpam-5823	270	5	)	)	PUNCT
ejpam-5823	270	6	4r	4r	NUM
ejpam-5823	270	7	kr	kr	PROPN
ejpam-5823	270	8	γk(ξ	γk(ξ	X
ejpam-5823	270	9	+	+	ADJ
ejpam-5823	270	10	rk	rk	NOUN
ejpam-5823	270	11	)	)	PUNCT
ejpam-5823	270	12	γk(r	γk(r	PUNCT
ejpam-5823	271	1	+	+	SYM
ejpam-5823	271	2	k	k	X
ejpam-5823	271	3	)	)	PUNCT
ejpam-5823	271	4	=	=	SYM
ejpam-5823	271	5	1−	1−	NUM
ejpam-5823	271	6	γk(ξ	γk(ξ	X
ejpam-5823	271	7	+	+	SYM
ejpam-5823	271	8	k	k	X
ejpam-5823	271	9	)	)	PUNCT
ejpam-5823	271	10	ξ	ξ	VERB
ejpam-5823	272	1	∞∑	∞∑	NUM
ejpam-5823	272	2	r=1	r=1	NOUN
ejpam-5823	272	3	|b|r	|b|r	PROPN
ejpam-5823	272	4	4r	4r	NUM
ejpam-5823	272	5	kr	kr	NOUN
ejpam-5823	272	6	γk(ξ	γk(ξ	X
ejpam-5823	272	7	+	+	ADJ
ejpam-5823	272	8	rk	rk	NOUN
ejpam-5823	272	9	)	)	PUNCT
ejpam-5823	272	10	γk(r	γk(r	PUNCT
ejpam-5823	272	11	+	+	CCONJ
ejpam-5823	272	12	k	k	X
ejpam-5823	272	13	)	)	PUNCT
ejpam-5823	272	14	.	.	PUNCT
ejpam-5823	273	1	as	as	SCONJ
ejpam-5823	273	2	we	we	PRON
ejpam-5823	273	3	know	know	VERB
ejpam-5823	273	4	that	that	SCONJ
ejpam-5823	273	5	1	1	NUM
ejpam-5823	273	6	γk(ξ+rk	γk(ξ+rk	ADV
ejpam-5823	273	7	)	)	PUNCT
ejpam-5823	274	1	γk(r+k	γk(r+k	X
ejpam-5823	274	2	)	)	PUNCT
ejpam-5823	274	3	is	be	AUX
ejpam-5823	274	4	strictly	strictly	ADV
ejpam-5823	274	5	decreasing	decrease	VERB
ejpam-5823	274	6	,	,	PUNCT
ejpam-5823	274	7	we	we	PRON
ejpam-5823	274	8	have∣∣∣∣khξ	have∣∣∣∣khξ	NUM
ejpam-5823	274	9	,	,	PUNCT
ejpam-5823	274	10	b(z	b(z	NOUN
ejpam-5823	274	11	)	)	PUNCT
ejpam-5823	274	12	z	z	NOUN
ejpam-5823	274	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	274	14	>	>	X
ejpam-5823	274	15	1−	1−	NUM
ejpam-5823	274	16	γk(ξ	γk(ξ	X
ejpam-5823	274	17	+	+	SYM
ejpam-5823	274	18	k	k	X
ejpam-5823	274	19	)	)	PUNCT
ejpam-5823	274	20	ξ	ξ	VERB
ejpam-5823	274	21	∞∑	∞∑	NUM
ejpam-5823	274	22	r=1	r=1	NOUN
ejpam-5823	274	23	|b|r	|b|r	PROPN
ejpam-5823	274	24	4r	4r	NUM
ejpam-5823	274	25	kr	kr	NOUN
ejpam-5823	274	26	γk(ξ	γk(ξ	X
ejpam-5823	274	27	+	+	SYM
ejpam-5823	274	28	k	k	X
ejpam-5823	274	29	)	)	PUNCT
ejpam-5823	274	30	γk(1	γk(1	NOUN
ejpam-5823	274	31	+	+	CCONJ
ejpam-5823	274	32	k	k	NOUN
ejpam-5823	274	33	)	)	PUNCT
ejpam-5823	274	34	=	=	SYM
ejpam-5823	275	1	1−	1−	NUM
ejpam-5823	275	2	1	1	NUM
ejpam-5823	275	3	ξ	ξ	X
ejpam-5823	275	4	∞∑	∞∑	NUM
ejpam-5823	275	5	r=1	r=1	NOUN
ejpam-5823	275	6	(	(	PUNCT
ejpam-5823	275	7	|b|	|b|	X
ejpam-5823	275	8	4k	4k	NOUN
ejpam-5823	275	9	)	)	PUNCT
ejpam-5823	275	10	r	r	NOUN
ejpam-5823	275	11	=	=	SYM
ejpam-5823	275	12	1−	1−	NUM
ejpam-5823	275	13	|b|	|b|	PROPN
ejpam-5823	275	14	ξ(4k	ξ(4k	NUM
ejpam-5823	275	15	−	−	PROPN
ejpam-5823	275	16	|b|	|b|	PROPN
ejpam-5823	275	17	)	)	PUNCT
ejpam-5823	275	18	=	=	SYM
ejpam-5823	275	19	ξ(4k	ξ(4k	NUM
ejpam-5823	275	20	−	−	PROPN
ejpam-5823	275	21	|b|)−	|b|)−	NOUN
ejpam-5823	275	22	|b|	|b|	PROPN
ejpam-5823	275	23	ξ(4k	ξ(4k	NUM
ejpam-5823	275	24	−	−	PROPN
ejpam-5823	275	25	|b|	|b|	PROPN
ejpam-5823	275	26	)	)	PUNCT
ejpam-5823	275	27	(	(	PUNCT
ejpam-5823	275	28	33	33	NUM
ejpam-5823	275	29	)	)	PUNCT
ejpam-5823	275	30	where	where	SCONJ
ejpam-5823	275	31	ξ(4k	ξ(4k	NOUN
ejpam-5823	275	32	−	−	PROPN
ejpam-5823	275	33	|b|)−	|b|)−	NOUN
ejpam-5823	275	34	|b|	|b|	PROPN
ejpam-5823	275	35	ξ(4k	ξ(4k	NUM
ejpam-5823	275	36	−	−	PROPN
ejpam-5823	275	37	|b|	|b|	PROPN
ejpam-5823	275	38	)	)	PUNCT
ejpam-5823	275	39	>	>	X
ejpam-5823	275	40	0	0	X
ejpam-5823	275	41	.	.	PUNCT
ejpam-5823	275	42	(	(	PUNCT
ejpam-5823	275	43	34	34	NUM
ejpam-5823	275	44	)	)	PUNCT
ejpam-5823	275	45	above	above	ADP
ejpam-5823	275	46	equation	equation	NOUN
ejpam-5823	275	47	holds	hold	VERB
ejpam-5823	275	48	because	because	SCONJ
ejpam-5823	275	49	ξ	ξ	PROPN
ejpam-5823	275	50	>	>	SYM
ejpam-5823	275	51	0	0	PUNCT
ejpam-5823	275	52	and	and	CCONJ
ejpam-5823	275	53	|b|	|b|	PROPN
ejpam-5823	275	54	<	<	X
ejpam-5823	275	55	min	min	PROPN
ejpam-5823	275	56	{	{	PUNCT
ejpam-5823	275	57	4	4	NUM
ejpam-5823	275	58	;	;	PUNCT
ejpam-5823	275	59	4kξ	4kξ	NOUN
ejpam-5823	275	60	1	1	NUM
ejpam-5823	275	61	+	+	SYM
ejpam-5823	275	62	ξ	ξ	X
ejpam-5823	275	63	}	}	PUNCT
ejpam-5823	275	64	=	=	PUNCT
ejpam-5823	275	65	4kξ	4kξ	NOUN
ejpam-5823	275	66	1	1	NUM
ejpam-5823	276	1	+	+	SYM
ejpam-5823	276	2	ξ	ξ	PROPN
ejpam-5823	276	3	.	.	PUNCT
ejpam-5823	277	1	(	(	PUNCT
ejpam-5823	277	2	35	35	NUM
ejpam-5823	277	3	)	)	PUNCT
ejpam-5823	277	4	since	since	SCONJ
ejpam-5823	277	5	∣∣∣∣z(khξ	∣∣∣∣z(khξ	NOUN
ejpam-5823	277	6	,	,	PUNCT
ejpam-5823	277	7	b(z	b(z	NOUN
ejpam-5823	277	8	)	)	PUNCT
ejpam-5823	277	9	)	)	PUNCT
ejpam-5823	278	1	′	′	NUM
ejpam-5823	279	1	khξ	khξ	NOUN
ejpam-5823	279	2	,	,	PUNCT
ejpam-5823	279	3	b(z	b(z	NOUN
ejpam-5823	279	4	)	)	PUNCT
ejpam-5823	279	5	−	−	PROPN
ejpam-5823	279	6	1	1	NUM
ejpam-5823	279	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	279	8	=	=	SYM
ejpam-5823	279	9	∣∣∣∣(khξ	∣∣∣∣(khξ	NOUN
ejpam-5823	279	10	,	,	PUNCT
ejpam-5823	279	11	b(z	b(z	NOUN
ejpam-5823	279	12	)	)	PUNCT
ejpam-5823	279	13	)	)	PUNCT
ejpam-5823	280	1	′	′	NUM
ejpam-5823	281	1	−	−	PROPN
ejpam-5823	281	2	khξ	khξ	NOUN
ejpam-5823	281	3	,	,	PUNCT
ejpam-5823	281	4	b(z	b(z	NOUN
ejpam-5823	281	5	)	)	PUNCT
ejpam-5823	281	6	z	z	NOUN
ejpam-5823	281	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	281	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	281	9	z	z	PROPN
ejpam-5823	281	10	khξ	khξ	PROPN
ejpam-5823	281	11	,	,	PUNCT
ejpam-5823	281	12	b(z	b(z	NOUN
ejpam-5823	281	13	)	)	PUNCT
ejpam-5823	281	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	281	15	<	<	X
ejpam-5823	281	16	|b|	|b|	PROPN
ejpam-5823	281	17	ξ(4k	ξ(4k	NUM
ejpam-5823	281	18	−	−	PROPN
ejpam-5823	281	19	|b|	|b|	PROPN
ejpam-5823	281	20	)	)	PUNCT
ejpam-5823	281	21	×	×	NOUN
ejpam-5823	281	22	ξ(4k	ξ(4k	NUM
ejpam-5823	281	23	−	−	NUM
ejpam-5823	281	24	|b|	|b|	PROPN
ejpam-5823	281	25	)	)	PUNCT
ejpam-5823	281	26	ξ(4k	ξ(4k	NUM
ejpam-5823	281	27	−	−	PROPN
ejpam-5823	281	28	|b|)−	|b|)−	NOUN
ejpam-5823	281	29	|b|	|b|	PROPN
ejpam-5823	281	30	<	<	X
ejpam-5823	281	31	|b|	|b|	PROPN
ejpam-5823	281	32	ξ(4k	ξ(4k	X
ejpam-5823	281	33	−	−	PROPN
ejpam-5823	281	34	|b|)−	|b|)−	NOUN
ejpam-5823	281	35	|b|	|b|	VERB
ejpam-5823	281	36	≤	≤	PROPN
ejpam-5823	281	37	1−	1−	NUM
ejpam-5823	281	38	η	η	NOUN
ejpam-5823	281	39	which	which	PRON
ejpam-5823	281	40	gives	give	VERB
ejpam-5823	281	41	η	η	PROPN
ejpam-5823	281	42	≤	≤	NOUN
ejpam-5823	281	43	1−	1−	NUM
ejpam-5823	281	44	|b|	|b|	X
ejpam-5823	281	45	ξ(4k	ξ(4k	NUM
ejpam-5823	281	46	−	−	PROPN
ejpam-5823	281	47	|b|)−	|b|)−	NOUN
ejpam-5823	281	48	|b|	|b|	PROPN
ejpam-5823	281	49	.	.	PUNCT
ejpam-5823	282	1	(	(	PUNCT
ejpam-5823	282	2	36	36	NUM
ejpam-5823	282	3	)	)	PUNCT
ejpam-5823	282	4	finally	finally	ADV
ejpam-5823	282	5	from	from	ADP
ejpam-5823	282	6	inequality	inequality	NOUN
ejpam-5823	282	7	26	26	NUM
ejpam-5823	282	8	,	,	PUNCT
ejpam-5823	282	9	it	it	PRON
ejpam-5823	282	10	is	be	AUX
ejpam-5823	282	11	proved	prove	VERB
ejpam-5823	282	12	that	that	SCONJ
ejpam-5823	282	13	khξ	khξ	NOUN
ejpam-5823	282	14	,	,	PUNCT
ejpam-5823	282	15	b	b	PROPN
ejpam-5823	282	16	∈	∈	PROPN
ejpam-5823	282	17	s∗(η	s∗(η	PROPN
ejpam-5823	282	18	)	)	PUNCT
ejpam-5823	282	19	.	.	PUNCT
ejpam-5823	283	1	s.	s.	PROPN
ejpam-5823	283	2	a.	a.	PROPN
ejpam-5823	283	3	h.	h.	PROPN
ejpam-5823	283	4	shah	shah	PROPN
ejpam-5823	283	5	et	et	PROPN
ejpam-5823	283	6	al	al	PROPN
ejpam-5823	283	7	.	.	PUNCT
ejpam-5823	283	8	/	/	SYM
ejpam-5823	283	9	eur	eur	PROPN
ejpam-5823	283	10	.	.	PUNCT
ejpam-5823	284	1	j.	j.	PROPN
ejpam-5823	284	2	pure	pure	PROPN
ejpam-5823	284	3	appl	appl	PROPN
ejpam-5823	284	4	.	.	PROPN
ejpam-5823	284	5	math	math	PROPN
ejpam-5823	284	6	,	,	PUNCT
ejpam-5823	284	7	18	18	NUM
ejpam-5823	284	8	(	(	PUNCT
ejpam-5823	284	9	2	2	NUM
ejpam-5823	284	10	)	)	PUNCT
ejpam-5823	284	11	(	(	PUNCT
ejpam-5823	284	12	2025	2025	NUM
ejpam-5823	284	13	)	)	PUNCT
ejpam-5823	284	14	,	,	PUNCT
ejpam-5823	284	15	5823	5823	NUM
ejpam-5823	284	16	13	13	NUM
ejpam-5823	284	17	of	of	ADP
ejpam-5823	284	18	26	26	NUM
ejpam-5823	284	19	theorem	theorem	NOUN
ejpam-5823	284	20	2	2	NUM
ejpam-5823	284	21	.	.	X
ejpam-5823	284	22	assume	assume	VERB
ejpam-5823	284	23	ξ	ξ	X
ejpam-5823	284	24	>	>	SYM
ejpam-5823	284	25	1	1	NUM
ejpam-5823	284	26	2	2	NUM
ejpam-5823	284	27	and	and	CCONJ
ejpam-5823	284	28	let	let	VERB
ejpam-5823	284	29	b	b	PROPN
ejpam-5823	284	30	∈	∈	PROPN
ejpam-5823	284	31	c∗	c∗	NOUN
ejpam-5823	284	32	,	,	PUNCT
ejpam-5823	284	33	k	k	PROPN
ejpam-5823	284	34	∈	∈	PROPN
ejpam-5823	284	35	r+	r+	NOUN
ejpam-5823	284	36	with	with	ADP
ejpam-5823	284	37	0	0	NUM
ejpam-5823	284	38	<	<	X
ejpam-5823	284	39	|b|	|b|	PROPN
ejpam-5823	284	40	<	<	X
ejpam-5823	284	41	4kξ	4kξ	NOUN
ejpam-5823	284	42	2	2	NUM
ejpam-5823	285	1	+	+	SYM
ejpam-5823	285	2	ξ	ξ	X
ejpam-5823	285	3	=	=	X
ejpam-5823	285	4	:	:	PUNCT
ejpam-5823	285	5	bc	bc	PROPN
ejpam-5823	285	6	.	.	PROPN
ejpam-5823	286	1	(	(	PUNCT
ejpam-5823	286	2	37	37	NUM
ejpam-5823	286	3	)	)	PUNCT
ejpam-5823	286	4	if	if	SCONJ
ejpam-5823	286	5	η	η	PROPN
ejpam-5823	286	6	≤	≤	X
ejpam-5823	286	7	1−	1−	NUM
ejpam-5823	286	8	2|b|	2|b|	NUM
ejpam-5823	286	9	ξ(4k	ξ(4k	NUM
ejpam-5823	286	10	−	−	PROPN
ejpam-5823	286	11	|b|)−	|b|)−	NOUN
ejpam-5823	286	12	2|b|	2|b|	NUM
ejpam-5823	287	1	=	=	NOUN
ejpam-5823	287	2	:	:	PUNCT
ejpam-5823	287	3	η∗	η∗	NOUN
ejpam-5823	287	4	(	(	PUNCT
ejpam-5823	287	5	38	38	NUM
ejpam-5823	287	6	)	)	PUNCT
ejpam-5823	287	7	then	then	ADV
ejpam-5823	287	8	khξ	khξ	PROPN
ejpam-5823	287	9	,	,	PUNCT
ejpam-5823	287	10	b	b	PROPN
ejpam-5823	287	11	∈	∈	PROPN
ejpam-5823	287	12	k(η	k(η	PROPN
ejpam-5823	287	13	)	)	PUNCT
ejpam-5823	287	14	.	.	PUNCT
ejpam-5823	288	1	proof	proof	NOUN
ejpam-5823	288	2	.	.	PUNCT
ejpam-5823	289	1	by	by	ADP
ejpam-5823	289	2	considering	consider	VERB
ejpam-5823	289	3	k	k	NOUN
ejpam-5823	289	4	-	-	NOUN
ejpam-5823	289	5	form	form	NOUN
ejpam-5823	289	6	of	of	ADP
ejpam-5823	289	7	the	the	DET
ejpam-5823	289	8	condition	condition	NOUN
ejpam-5823	289	9	in	in	ADP
ejpam-5823	289	10	[	[	X
ejpam-5823	289	11	20	20	NUM
ejpam-5823	289	12	]	]	PUNCT
ejpam-5823	289	13	,	,	PUNCT
ejpam-5823	289	14	we	we	PRON
ejpam-5823	289	15	have∣∣∣∣z(khξ	have∣∣∣∣z(khξ	VERB
ejpam-5823	289	16	,	,	PUNCT
ejpam-5823	289	17	b(z	b(z	NOUN
ejpam-5823	289	18	)	)	PUNCT
ejpam-5823	289	19	)	)	PUNCT
ejpam-5823	290	1	′′	′′	PROPN
ejpam-5823	290	2	(	(	PUNCT
ejpam-5823	290	3	khξ	khξ	PROPN
ejpam-5823	290	4	,	,	PUNCT
ejpam-5823	290	5	b(z))′	b(z))′	PROPN
ejpam-5823	290	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	290	7	<	<	X
ejpam-5823	290	8	1−	1−	NUM
ejpam-5823	290	9	η	η	PROPN
ejpam-5823	290	10	,	,	PUNCT
ejpam-5823	290	11	η	η	PROPN
ejpam-5823	290	12	≤	≤	ADJ
ejpam-5823	290	13	1	1	NUM
ejpam-5823	290	14	.	.	PUNCT
ejpam-5823	290	15	(	(	PUNCT
ejpam-5823	290	16	39	39	NUM
ejpam-5823	290	17	)	)	PUNCT
ejpam-5823	290	18	taking	take	VERB
ejpam-5823	290	19	the	the	DET
ejpam-5823	290	20	part	part	NOUN
ejpam-5823	290	21	:	:	PUNCT
ejpam-5823	290	22	∣∣z(khξ	∣∣z(khξ	NOUN
ejpam-5823	290	23	,	,	PUNCT
ejpam-5823	290	24	b(z	b(z	NOUN
ejpam-5823	290	25	)	)	PUNCT
ejpam-5823	290	26	)	)	PUNCT
ejpam-5823	290	27	′′∣∣	′′∣∣	PROPN
ejpam-5823	290	28	=	=	SYM
ejpam-5823	290	29	∣∣∣∣∣z	∣∣∣∣∣z	NOUN
ejpam-5823	290	30	(	(	PUNCT
ejpam-5823	290	31	z	z	NOUN
ejpam-5823	290	32	+	+	NOUN
ejpam-5823	290	33	∞∑	∞∑	NUM
ejpam-5823	290	34	r=1	r=1	NOUN
ejpam-5823	290	35	(	(	PUNCT
ejpam-5823	290	36	−b)r	−b)r	NOUN
ejpam-5823	290	37	zr+1	zr+1	NUM
ejpam-5823	290	38	r	r	NOUN
ejpam-5823	290	39	!	!	NOUN
ejpam-5823	290	40	4r	4r	PROPN
ejpam-5823	290	41	kr	kr	PROPN
ejpam-5823	290	42	(	(	PUNCT
ejpam-5823	290	43	ξ)r	ξ)r	NOUN
ejpam-5823	290	44	,	,	PUNCT
ejpam-5823	290	45	k	k	NOUN
ejpam-5823	290	46	)	)	PUNCT
ejpam-5823	290	47	′′∣∣∣∣∣	′′∣∣∣∣∣	ADJ
ejpam-5823	290	48	=	=	PUNCT
ejpam-5823	290	49	∣∣∣∣∣z	∣∣∣∣∣z	NOUN
ejpam-5823	290	50	(	(	PUNCT
ejpam-5823	290	51	1	1	NUM
ejpam-5823	290	52	+	+	NUM
ejpam-5823	290	53	∞∑	∞∑	NUM
ejpam-5823	290	54	r=1	r=1	NOUN
ejpam-5823	290	55	(	(	PUNCT
ejpam-5823	290	56	r	r	NOUN
ejpam-5823	290	57	+	+	NUM
ejpam-5823	290	58	1)(−b)r	1)(−b)r	NUM
ejpam-5823	290	59	zr	zr	NOUN
ejpam-5823	290	60	r	r	NOUN
ejpam-5823	290	61	!	!	NOUN
ejpam-5823	290	62	4r	4r	PROPN
ejpam-5823	290	63	kr	kr	PROPN
ejpam-5823	290	64	(	(	PUNCT
ejpam-5823	290	65	ξ)r	ξ)r	NOUN
ejpam-5823	290	66	,	,	PUNCT
ejpam-5823	290	67	k	k	NOUN
ejpam-5823	290	68	)	)	PUNCT
ejpam-5823	290	69	′∣∣∣∣∣	′∣∣∣∣∣	PROPN
ejpam-5823	290	70	=	=	SYM
ejpam-5823	290	71	∣∣∣∣∣z	∣∣∣∣∣z	NOUN
ejpam-5823	290	72	(	(	PUNCT
ejpam-5823	290	73	∞∑	∞∑	NUM
ejpam-5823	290	74	r=1	r=1	ADJ
ejpam-5823	290	75	(	(	PUNCT
ejpam-5823	290	76	r	r	NOUN
ejpam-5823	290	77	+	+	NOUN
ejpam-5823	290	78	1	1	NUM
ejpam-5823	290	79	)	)	PUNCT
ejpam-5823	290	80	(	(	PUNCT
ejpam-5823	290	81	r	r	NOUN
ejpam-5823	290	82	)	)	PUNCT
ejpam-5823	290	83	(	(	PUNCT
ejpam-5823	290	84	−b)r	−b)r	VERB
ejpam-5823	290	85	kr	kr	PROPN
ejpam-5823	290	86	zr−1	zr−1	PROPN
ejpam-5823	290	87	4r	4r	NOUN
ejpam-5823	290	88	kr	kr	PROPN
ejpam-5823	290	89	r	r	X
ejpam-5823	290	90	!	!	PUNCT
ejpam-5823	291	1	(	(	PUNCT
ejpam-5823	292	1	ξ)r	ξ)r	NOUN
ejpam-5823	292	2	,	,	PUNCT
ejpam-5823	292	3	k	k	PROPN
ejpam-5823	292	4	)	)	PUNCT
ejpam-5823	292	5	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	292	6	=	=	SYM
ejpam-5823	293	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	293	2	∞∑	∞∑	NUM
ejpam-5823	293	3	r=1	r=1	NOUN
ejpam-5823	293	4	(	(	PUNCT
ejpam-5823	293	5	r	r	NOUN
ejpam-5823	293	6	+	+	NOUN
ejpam-5823	293	7	1	1	NUM
ejpam-5823	293	8	)	)	PUNCT
ejpam-5823	293	9	(	(	PUNCT
ejpam-5823	293	10	r	r	NOUN
ejpam-5823	293	11	)	)	PUNCT
ejpam-5823	293	12	(	(	PUNCT
ejpam-5823	293	13	−b)r	−b)r	VERB
ejpam-5823	293	14	zr	zr	NOUN
ejpam-5823	293	15	4r	4r	NOUN
ejpam-5823	293	16	kr	kr	PROPN
ejpam-5823	293	17	r	r	X
ejpam-5823	293	18	!	!	PUNCT
ejpam-5823	293	19	(	(	PUNCT
ejpam-5823	293	20	ξ)r	ξ)r	NOUN
ejpam-5823	293	21	,	,	PUNCT
ejpam-5823	293	22	k	k	PROPN
ejpam-5823	293	23	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	293	24	.	.	PUNCT
ejpam-5823	294	1	by	by	ADP
ejpam-5823	294	2	using	use	VERB
ejpam-5823	294	3	maximum	maximum	ADJ
ejpam-5823	294	4	modulus	modulus	ADJ
ejpam-5823	294	5	theorem	theorem	NOUN
ejpam-5823	294	6	:	:	PUNCT
ejpam-5823	294	7	∣∣z(khξ	∣∣z(khξ	ADJ
ejpam-5823	294	8	,	,	PUNCT
ejpam-5823	294	9	b(z	b(z	NOUN
ejpam-5823	294	10	)	)	PUNCT
ejpam-5823	294	11	)	)	PUNCT
ejpam-5823	294	12	′′∣∣	′′∣∣	NOUN
ejpam-5823	294	13	=	=	PUNCT
ejpam-5823	294	14	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	294	15	∞∑	∞∑	NUM
ejpam-5823	294	16	r=1	r=1	NOUN
ejpam-5823	294	17	(	(	PUNCT
ejpam-5823	294	18	r	r	NOUN
ejpam-5823	294	19	+	+	NOUN
ejpam-5823	294	20	1)(r)(−b)r	1)(r)(−b)r	NOUN
ejpam-5823	294	21	zr	zr	PROPN
ejpam-5823	294	22	4rkrr!(ξ)r	4rkrr!(ξ)r	PROPN
ejpam-5823	294	23	,	,	PUNCT
ejpam-5823	294	24	k	k	PROPN
ejpam-5823	294	25	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	294	26	<	<	X
ejpam-5823	294	27	sup	sup	X
ejpam-5823	294	28	θ∈2π	θ∈2π	X
ejpam-5823	294	29	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5823	294	30	∞∑	∞∑	NUM
ejpam-5823	294	31	r=1	r=1	NOUN
ejpam-5823	294	32	(	(	PUNCT
ejpam-5823	294	33	r	r	NOUN
ejpam-5823	294	34	+	+	NOUN
ejpam-5823	294	35	1)(r)(−b)r	1)(r)(−b)r	NUM
ejpam-5823	294	36	eiθr	eiθr	PROPN
ejpam-5823	294	37	4r	4r	PROPN
ejpam-5823	294	38	krr!(ξ)r	krr!(ξ)r	PROPN
ejpam-5823	294	39	,	,	PUNCT
ejpam-5823	294	40	k	k	PROPN
ejpam-5823	294	41	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-5823	294	42	≤	≤	X
ejpam-5823	294	43	∞∑	∞∑	NUM
ejpam-5823	294	44	r=1	r=1	NOUN
ejpam-5823	294	45	(	(	PUNCT
ejpam-5823	294	46	r	r	NOUN
ejpam-5823	294	47	+	+	SYM
ejpam-5823	294	48	1)(r)|b|r	1)(r)|b|r	NUM
ejpam-5823	294	49	4rkrr!γk(ξ+rk	4rkrr!γk(ξ+rk	NUM
ejpam-5823	294	50	)	)	PUNCT
ejpam-5823	294	51	γk(ξ	γk(ξ	NUM
ejpam-5823	294	52	)	)	PUNCT
ejpam-5823	294	53	,	,	PUNCT
ejpam-5823	294	54	|z|	|z|	VERB
ejpam-5823	294	55	≤	≤	NOUN
ejpam-5823	294	56	1	1	NUM
ejpam-5823	294	57	=	=	NOUN
ejpam-5823	294	58	γk(ξ	γk(ξ	X
ejpam-5823	294	59	+	+	SYM
ejpam-5823	294	60	k	k	X
ejpam-5823	294	61	)	)	PUNCT
ejpam-5823	294	62	ξ	ξ	VERB
ejpam-5823	294	63	∞∑	∞∑	NUM
ejpam-5823	294	64	r=1	r=1	NOUN
ejpam-5823	294	65	|b|r(r)(r	|b|r(r)(r	NOUN
ejpam-5823	294	66	+	+	CCONJ
ejpam-5823	294	67	1	1	X
ejpam-5823	294	68	)	)	PUNCT
ejpam-5823	294	69	4rkrγk(r	4rkrγk(r	NOUN
ejpam-5823	295	1	+	+	CCONJ
ejpam-5823	295	2	k)γk(ξ	k)γk(ξ	X
ejpam-5823	295	3	+	+	CCONJ
ejpam-5823	295	4	rk	rk	NOUN
ejpam-5823	295	5	)	)	PUNCT
ejpam-5823	295	6	.	.	PUNCT
ejpam-5823	296	1	(	(	PUNCT
ejpam-5823	296	2	40	40	NUM
ejpam-5823	296	3	)	)	PUNCT
ejpam-5823	296	4	letting	let	VERB
ejpam-5823	296	5	the	the	DET
ejpam-5823	296	6	function	function	NOUN
ejpam-5823	296	7	ϱk(a	ϱk(a	PUNCT
ejpam-5823	296	8	)	)	PUNCT
ejpam-5823	297	1	=	=	SYM
ejpam-5823	297	2	(	(	PUNCT
ejpam-5823	297	3	a)(a+	a)(a+	NOUN
ejpam-5823	297	4	1	1	NUM
ejpam-5823	297	5	)	)	PUNCT
ejpam-5823	297	6	γk(a+	γk(a+	NOUN
ejpam-5823	297	7	k)γk(ξ	k)γk(ξ	X
ejpam-5823	297	8	+	+	CCONJ
ejpam-5823	297	9	ak	ak	PROPN
ejpam-5823	297	10	)	)	PUNCT
ejpam-5823	297	11	,	,	PUNCT
ejpam-5823	297	12	r	r	NOUN
ejpam-5823	297	13	∈	∈	PROPN
ejpam-5823	297	14	n.	n.	NOUN
ejpam-5823	297	15	(	(	PUNCT
ejpam-5823	297	16	41	41	NUM
ejpam-5823	297	17	)	)	PUNCT
ejpam-5823	297	18	s.	s.	PROPN
ejpam-5823	297	19	a.	a.	PROPN
ejpam-5823	297	20	h.	h.	PROPN
ejpam-5823	297	21	shah	shah	PROPN
ejpam-5823	297	22	et	et	PROPN
ejpam-5823	297	23	al	al	PROPN
ejpam-5823	297	24	.	.	PUNCT
ejpam-5823	297	25	/	/	SYM
ejpam-5823	297	26	eur	eur	PROPN
ejpam-5823	297	27	.	.	PUNCT
ejpam-5823	298	1	j.	j.	PROPN
ejpam-5823	298	2	pure	pure	PROPN
ejpam-5823	298	3	appl	appl	PROPN
ejpam-5823	298	4	.	.	PROPN
ejpam-5823	298	5	math	math	PROPN
ejpam-5823	298	6	,	,	PUNCT
ejpam-5823	298	7	18	18	NUM
ejpam-5823	298	8	(	(	PUNCT
ejpam-5823	298	9	2	2	NUM
ejpam-5823	298	10	)	)	PUNCT
ejpam-5823	298	11	(	(	PUNCT
ejpam-5823	298	12	2025	2025	NUM
ejpam-5823	298	13	)	)	PUNCT
ejpam-5823	298	14	,	,	PUNCT
ejpam-5823	298	15	5823	5823	NUM
ejpam-5823	298	16	14	14	NUM
ejpam-5823	298	17	of	of	ADP
ejpam-5823	298	18	26	26	NUM
ejpam-5823	298	19	by	by	ADP
ejpam-5823	298	20	easy	easy	ADJ
ejpam-5823	298	21	computation	computation	NOUN
ejpam-5823	298	22	ϱk(r	ϱk(r	NOUN
ejpam-5823	298	23	+	+	PROPN
ejpam-5823	298	24	1)−	1)−	NUM
ejpam-5823	298	25	ϱk(r	ϱk(r	NOUN
ejpam-5823	298	26	)	)	PUNCT
ejpam-5823	298	27	=	=	SYM
ejpam-5823	298	28	(	(	PUNCT
ejpam-5823	298	29	r	r	NOUN
ejpam-5823	298	30	+	+	NUM
ejpam-5823	298	31	1)(r	1)(r	NUM
ejpam-5823	298	32	+	+	CCONJ
ejpam-5823	298	33	2	2	NUM
ejpam-5823	298	34	)	)	PUNCT
ejpam-5823	298	35	γk(r	γk(r	PUNCT
ejpam-5823	299	1	+	+	CCONJ
ejpam-5823	299	2	1	1	NUM
ejpam-5823	300	1	+	+	NUM
ejpam-5823	300	2	k)γk(ξ	k)γk(ξ	NOUN
ejpam-5823	300	3	+	+	CCONJ
ejpam-5823	300	4	(	(	PUNCT
ejpam-5823	300	5	r	r	NOUN
ejpam-5823	300	6	+	+	NUM
ejpam-5823	300	7	1)k	1)k	NUM
ejpam-5823	300	8	)	)	PUNCT
ejpam-5823	301	1	−	−	PROPN
ejpam-5823	301	2	(	(	PUNCT
ejpam-5823	301	3	r)(r	r)(r	NOUN
ejpam-5823	301	4	+	+	CCONJ
ejpam-5823	301	5	1	1	NUM
ejpam-5823	301	6	)	)	PUNCT
ejpam-5823	301	7	γk(r	γk(r	PUNCT
ejpam-5823	302	1	+	+	CCONJ
ejpam-5823	302	2	k)γk(ξ	k)γk(ξ	X
ejpam-5823	302	3	+	+	CCONJ
ejpam-5823	302	4	rk	rk	NOUN
ejpam-5823	302	5	)	)	PUNCT
ejpam-5823	302	6	=	=	SYM
ejpam-5823	303	1	r	r	NOUN
ejpam-5823	303	2	+	+	NUM
ejpam-5823	303	3	1	1	NUM
ejpam-5823	303	4	γk(r	γk(r	NOUN
ejpam-5823	303	5	+	+	CCONJ
ejpam-5823	303	6	k)γk(ξ	k)γk(ξ	X
ejpam-5823	303	7	+	+	CCONJ
ejpam-5823	303	8	rk	rk	NOUN
ejpam-5823	303	9	)	)	PUNCT
ejpam-5823	303	10	[	[	PUNCT
ejpam-5823	303	11	r	r	NOUN
ejpam-5823	303	12	+	+	NOUN
ejpam-5823	303	13	2	2	NUM
ejpam-5823	303	14	(	(	PUNCT
ejpam-5823	303	15	r	r	NOUN
ejpam-5823	303	16	+	+	NUM
ejpam-5823	303	17	k)(ξ	k)(ξ	NOUN
ejpam-5823	303	18	+	+	CCONJ
ejpam-5823	303	19	rk	rk	NOUN
ejpam-5823	303	20	)	)	PUNCT
ejpam-5823	303	21	−	−	NOUN
ejpam-5823	303	22	r	r	NOUN
ejpam-5823	303	23	]	]	PUNCT
ejpam-5823	304	1	=	=	PUNCT
ejpam-5823	304	2	r	r	NOUN
ejpam-5823	304	3	+	+	NOUN
ejpam-5823	304	4	1	1	NUM
ejpam-5823	304	5	γk(r	γk(r	NOUN
ejpam-5823	304	6	+	+	CCONJ
ejpam-5823	304	7	k)γk(ξ	k)γk(ξ	X
ejpam-5823	304	8	+	+	CCONJ
ejpam-5823	304	9	rk	rk	NOUN
ejpam-5823	304	10	)	)	PUNCT
ejpam-5823	304	11	[	[	PUNCT
ejpam-5823	304	12	r	r	NOUN
ejpam-5823	304	13	+	+	NUM
ejpam-5823	304	14	2−	2−	NUM
ejpam-5823	304	15	(	(	PUNCT
ejpam-5823	304	16	r)(r	r)(r	NOUN
ejpam-5823	304	17	+	+	CCONJ
ejpam-5823	304	18	k)(ξ	k)(ξ	NOUN
ejpam-5823	304	19	+	+	CCONJ
ejpam-5823	304	20	rk	rk	NOUN
ejpam-5823	304	21	)	)	PUNCT
ejpam-5823	304	22	(	(	PUNCT
ejpam-5823	304	23	r	r	NOUN
ejpam-5823	304	24	+	+	NUM
ejpam-5823	304	25	k)(ξ	k)(ξ	NOUN
ejpam-5823	304	26	+	+	CCONJ
ejpam-5823	304	27	rk	rk	NOUN
ejpam-5823	304	28	)	)	PUNCT
ejpam-5823	304	29	]	]	PUNCT
ejpam-5823	305	1	=	=	PUNCT
ejpam-5823	305	2	−	−	PROPN
ejpam-5823	305	3	r2	r2	NOUN
ejpam-5823	305	4	(	(	PUNCT
ejpam-5823	305	5	ξ	ξ	X
ejpam-5823	305	6	+	+	X
ejpam-5823	305	7	k2	k2	ADJ
ejpam-5823	305	8	)	)	PUNCT
ejpam-5823	306	1	+	+	NUM
ejpam-5823	306	2	ξkr	ξkr	NOUN
ejpam-5823	306	3	+	+	CCONJ
ejpam-5823	306	4	kr3	kr3	NOUN
ejpam-5823	306	5	−	−	NOUN
ejpam-5823	306	6	r	r	NOUN
ejpam-5823	306	7	−	−	NOUN
ejpam-5823	306	8	2	2	NUM
ejpam-5823	306	9	γk(r	γk(r	NOUN
ejpam-5823	306	10	+	+	NOUN
ejpam-5823	306	11	1	1	NUM
ejpam-5823	306	12	+	+	NUM
ejpam-5823	306	13	k)γk(ξ	k)γk(ξ	X
ejpam-5823	306	14	+	+	CCONJ
ejpam-5823	306	15	rk	rk	NOUN
ejpam-5823	306	16	+	+	CCONJ
ejpam-5823	306	17	k	k	NOUN
ejpam-5823	306	18	)	)	PUNCT
ejpam-5823	306	19	(	(	PUNCT
ejpam-5823	306	20	42	42	NUM
ejpam-5823	306	21	)	)	PUNCT
ejpam-5823	306	22	which	which	PRON
ejpam-5823	306	23	implies	imply	VERB
ejpam-5823	306	24	that	that	PRON
ejpam-5823	306	25	:	:	PUNCT
ejpam-5823	306	26	ϱk(r	ϱk(r	NOUN
ejpam-5823	306	27	+	+	PROPN
ejpam-5823	306	28	1)−	1)−	NUM
ejpam-5823	306	29	ϱk(r	ϱk(r	NOUN
ejpam-5823	306	30	)	)	PUNCT
ejpam-5823	306	31	<	<	X
ejpam-5823	306	32	0	0	NUM
ejpam-5823	306	33	,	,	PUNCT
ejpam-5823	306	34	r	r	NOUN
ejpam-5823	306	35	∈	∈	PROPN
ejpam-5823	306	36	n.	n.	NOUN
ejpam-5823	306	37	(	(	PUNCT
ejpam-5823	306	38	43	43	NUM
ejpam-5823	306	39	)	)	PUNCT
ejpam-5823	306	40	hence	hence	ADV
ejpam-5823	306	41	the	the	DET
ejpam-5823	306	42	function	function	NOUN
ejpam-5823	306	43	is	be	AUX
ejpam-5823	306	44	decreasing	decrease	VERB
ejpam-5823	306	45	strictly	strictly	ADV
ejpam-5823	306	46	,	,	PUNCT
ejpam-5823	306	47	so	so	ADV
ejpam-5823	306	48	:	:	PUNCT
ejpam-5823	306	49	(	(	PUNCT
ejpam-5823	306	50	a)(a+	a)(a+	NOUN
ejpam-5823	306	51	1	1	NUM
ejpam-5823	306	52	)	)	PUNCT
ejpam-5823	306	53	γk(a+	γk(a+	NOUN
ejpam-5823	306	54	k)γk(ξ	k)γk(ξ	X
ejpam-5823	306	55	+	+	CCONJ
ejpam-5823	306	56	ak	ak	PROPN
ejpam-5823	306	57	)	)	PUNCT
ejpam-5823	306	58	≤	≤	NOUN
ejpam-5823	306	59	ϱk(1	ϱk(1	NOUN
ejpam-5823	306	60	)	)	PUNCT
ejpam-5823	306	61	=	=	SYM
ejpam-5823	306	62	2	2	NUM
ejpam-5823	306	63	γk(1	γk(1	NOUN
ejpam-5823	306	64	+	+	CCONJ
ejpam-5823	306	65	k)γk(ξ	k)γk(ξ	NOUN
ejpam-5823	306	66	+	+	CCONJ
ejpam-5823	306	67	k	k	NOUN
ejpam-5823	306	68	)	)	PUNCT
ejpam-5823	306	69	.	.	PUNCT
ejpam-5823	307	1	by	by	ADP
ejpam-5823	307	2	the	the	DET
ejpam-5823	307	3	inequality	inequality	NOUN
ejpam-5823	307	4	40	40	NUM
ejpam-5823	307	5	,	,	PUNCT
ejpam-5823	307	6	we	we	PRON
ejpam-5823	307	7	get	get	VERB
ejpam-5823	307	8	:	:	PUNCT
ejpam-5823	307	9	∣∣z(khξ	∣∣z(khξ	ADJ
ejpam-5823	307	10	,	,	PUNCT
ejpam-5823	307	11	b(z	b(z	NOUN
ejpam-5823	307	12	)	)	PUNCT
ejpam-5823	307	13	)	)	PUNCT
ejpam-5823	308	1	′′∣∣	′′∣∣	ADJ
ejpam-5823	308	2	<	<	X
ejpam-5823	308	3	γk(ξ	γk(ξ	X
ejpam-5823	308	4	+	+	SYM
ejpam-5823	308	5	k	k	X
ejpam-5823	308	6	)	)	PUNCT
ejpam-5823	308	7	ξ	ξ	VERB
ejpam-5823	308	8	∞∑	∞∑	NUM
ejpam-5823	308	9	r=1	r=1	NOUN
ejpam-5823	308	10	2	2	NUM
ejpam-5823	308	11	|b|r	|b|r	PROPN
ejpam-5823	308	12	4r	4r	NOUN
ejpam-5823	308	13	kr	kr	PROPN
ejpam-5823	308	14	γk(1	γk(1	PROPN
ejpam-5823	308	15	+	+	CCONJ
ejpam-5823	308	16	k)γk(ξ	k)γk(ξ	X
ejpam-5823	308	17	+	+	CCONJ
ejpam-5823	308	18	k	k	X
ejpam-5823	308	19	)	)	PUNCT
ejpam-5823	308	20	=	=	SYM
ejpam-5823	308	21	2	2	NUM
ejpam-5823	308	22	ξ	ξ	X
ejpam-5823	308	23	∞∑	∞∑	NUM
ejpam-5823	308	24	r=1	r=1	NOUN
ejpam-5823	308	25	(	(	PUNCT
ejpam-5823	308	26	|b|	|b|	X
ejpam-5823	308	27	4k	4k	NOUN
ejpam-5823	308	28	)	)	PUNCT
ejpam-5823	309	1	r	r	NOUN
ejpam-5823	309	2	=	=	SYM
ejpam-5823	309	3	2|b|	2|b|	NUM
ejpam-5823	309	4	ξ(4k	ξ(4k	NUM
ejpam-5823	309	5	−	−	PROPN
ejpam-5823	309	6	|b|)∣∣z(khξ	|b|)∣∣z(khξ	PROPN
ejpam-5823	309	7	,	,	PUNCT
ejpam-5823	309	8	b(z	b(z	NOUN
ejpam-5823	309	9	)	)	PUNCT
ejpam-5823	309	10	)	)	PUNCT
ejpam-5823	310	1	′′∣∣	′′∣∣	ADV
ejpam-5823	310	2	<	<	X
ejpam-5823	310	3	2|b|	2|b|	NUM
ejpam-5823	310	4	ξ(4k	ξ(4k	NUM
ejpam-5823	310	5	−	−	PROPN
ejpam-5823	310	6	|b|	|b|	PROPN
ejpam-5823	310	7	)	)	PUNCT
ejpam-5823	310	8	,	,	PUNCT
ejpam-5823	310	9	z	z	PROPN
ejpam-5823	310	10	∈	∈	PROPN
ejpam-5823	310	11	u	u	NOUN
ejpam-5823	310	12	,	,	PUNCT
ejpam-5823	310	13	k	k	PROPN
ejpam-5823	310	14	∈	∈	PROPN
ejpam-5823	310	15	r+	r+	X
ejpam-5823	310	16	.	.	PUNCT
ejpam-5823	311	1	(	(	PUNCT
ejpam-5823	311	2	44	44	NUM
ejpam-5823	311	3	)	)	PUNCT
ejpam-5823	311	4	now	now	ADV
ejpam-5823	311	5	by	by	ADP
ejpam-5823	311	6	assuming	assume	VERB
ejpam-5823	311	7	the	the	DET
ejpam-5823	311	8	above	above	ADJ
ejpam-5823	311	9	inequality	inequality	NOUN
ejpam-5823	311	10	44	44	NUM
ejpam-5823	311	11	is	be	AUX
ejpam-5823	311	12	greater	great	ADJ
ejpam-5823	311	13	than	than	ADP
ejpam-5823	311	14	0	0	NUM
ejpam-5823	311	15	,	,	PUNCT
ejpam-5823	311	16	gives	give	VERB
ejpam-5823	311	17	0	0	PUNCT
ejpam-5823	311	18	<	<	X
ejpam-5823	311	19	|b|	|b|	PROPN
ejpam-5823	311	20	<	<	X
ejpam-5823	311	21	4k	4k	NUM
ejpam-5823	311	22	,	,	PUNCT
ejpam-5823	311	23	(	(	PUNCT
ejpam-5823	311	24	45	45	NUM
ejpam-5823	311	25	)	)	PUNCT
ejpam-5823	311	26	which	which	PRON
ejpam-5823	311	27	holds	hold	VERB
ejpam-5823	311	28	because	because	SCONJ
ejpam-5823	311	29	of	of	ADP
ejpam-5823	311	30	our	our	PRON
ejpam-5823	311	31	assumption	assumption	NOUN
ejpam-5823	311	32	.	.	PUNCT
ejpam-5823	312	1	the	the	DET
ejpam-5823	312	2	case	case	NOUN
ejpam-5823	312	3	|b|	|b|	VERB
ejpam-5823	312	4	=	=	SYM
ejpam-5823	312	5	0	0	NUM
ejpam-5823	312	6	is	be	AUX
ejpam-5823	312	7	the	the	DET
ejpam-5823	312	8	trivial	trivial	ADJ
ejpam-5823	312	9	case	case	NOUN
ejpam-5823	312	10	gives	give	VERB
ejpam-5823	312	11	the	the	DET
ejpam-5823	312	12	identity	identity	NOUN
ejpam-5823	312	13	function	function	NOUN
ejpam-5823	312	14	.	.	PUNCT
ejpam-5823	313	1	now	now	ADV
ejpam-5823	313	2	the	the	DET
ejpam-5823	313	3	other	other	ADJ
ejpam-5823	313	4	part	part	NOUN
ejpam-5823	313	5	,	,	PUNCT
ejpam-5823	313	6	we	we	PRON
ejpam-5823	313	7	have	have	VERB
ejpam-5823	313	8	∣∣(khξ	∣∣(khξ	NOUN
ejpam-5823	313	9	,	,	PUNCT
ejpam-5823	313	10	b(z	b(z	NOUN
ejpam-5823	313	11	)	)	PUNCT
ejpam-5823	313	12	)	)	PUNCT
ejpam-5823	314	1	′∣∣	′∣∣	PROPN
ejpam-5823	314	2	=	=	PUNCT
ejpam-5823	315	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5823	315	2	(	(	PUNCT
ejpam-5823	315	3	z	z	NOUN
ejpam-5823	315	4	+	+	CCONJ
ejpam-5823	315	5	∞∑	∞∑	NUM
ejpam-5823	315	6	r=1	r=1	NOUN
ejpam-5823	315	7	(	(	PUNCT
ejpam-5823	315	8	−b)r	−b)r	NOUN
ejpam-5823	315	9	zr+1γk(ξ	zr+1γk(ξ	NOUN
ejpam-5823	315	10	)	)	PUNCT
ejpam-5823	315	11	kr	kr	PROPN
ejpam-5823	315	12	4r	4r	NUM
ejpam-5823	315	13	γk(r	γk(r	PUNCT
ejpam-5823	315	14	+	+	SYM
ejpam-5823	315	15	k	k	X
ejpam-5823	315	16	)	)	PUNCT
ejpam-5823	315	17	γk(ξ	γk(ξ	X
ejpam-5823	315	18	+	+	CCONJ
ejpam-5823	315	19	rk	rk	NOUN
ejpam-5823	315	20	)	)	PUNCT
ejpam-5823	315	21	)	)	PUNCT
ejpam-5823	315	22	′∣∣∣∣∣	′∣∣∣∣∣	PROPN
ejpam-5823	315	23	s.	s.	PROPN
ejpam-5823	315	24	a.	a.	PROPN
ejpam-5823	315	25	h.	h.	PROPN
ejpam-5823	315	26	shah	shah	PROPN
ejpam-5823	315	27	et	et	PROPN
ejpam-5823	315	28	al	al	PROPN
ejpam-5823	315	29	.	.	PUNCT
ejpam-5823	315	30	/	/	SYM
ejpam-5823	315	31	eur	eur	PROPN
ejpam-5823	315	32	.	.	PUNCT
ejpam-5823	316	1	j.	j.	PROPN
ejpam-5823	316	2	pure	pure	PROPN
ejpam-5823	316	3	appl	appl	PROPN
ejpam-5823	316	4	.	.	PROPN
ejpam-5823	316	5	math	math	PROPN
ejpam-5823	316	6	,	,	PUNCT
ejpam-5823	316	7	18	18	NUM
ejpam-5823	316	8	(	(	PUNCT
ejpam-5823	316	9	2	2	NUM
ejpam-5823	316	10	)	)	PUNCT
ejpam-5823	316	11	(	(	PUNCT
ejpam-5823	316	12	2025	2025	NUM
ejpam-5823	316	13	)	)	PUNCT
ejpam-5823	316	14	,	,	PUNCT
ejpam-5823	316	15	5823	5823	NUM
ejpam-5823	316	16	15	15	NUM
ejpam-5823	316	17	of	of	ADP
ejpam-5823	316	18	26	26	NUM
ejpam-5823	316	19	=	=	NUM
ejpam-5823	316	20	∣∣∣∣∣1	∣∣∣∣∣1	VERB
ejpam-5823	316	21	+	+	CCONJ
ejpam-5823	316	22	∞∑	∞∑	NUM
ejpam-5823	316	23	r=1	r=1	NOUN
ejpam-5823	316	24	(	(	PUNCT
ejpam-5823	316	25	−b)r	−b)r	NOUN
ejpam-5823	316	26	zr	zr	NOUN
ejpam-5823	316	27	(	(	PUNCT
ejpam-5823	316	28	r	r	NOUN
ejpam-5823	316	29	+	+	NUM
ejpam-5823	316	30	1)γk(ξ	1)γk(ξ	NUM
ejpam-5823	316	31	+	+	CCONJ
ejpam-5823	316	32	k	k	X
ejpam-5823	316	33	)	)	PUNCT
ejpam-5823	317	1	ξ	ξ	PROPN
ejpam-5823	317	2	kr	kr	PROPN
ejpam-5823	317	3	4r	4r	NUM
ejpam-5823	317	4	γk(r	γk(r	PUNCT
ejpam-5823	318	1	+	+	SYM
ejpam-5823	318	2	k	k	X
ejpam-5823	318	3	)	)	PUNCT
ejpam-5823	318	4	γk(ξ	γk(ξ	X
ejpam-5823	319	1	+	+	CCONJ
ejpam-5823	319	2	rk	rk	NOUN
ejpam-5823	319	3	)	)	PUNCT
ejpam-5823	319	4	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-5823	319	5	.	.	PUNCT
ejpam-5823	320	1	by	by	ADP
ejpam-5823	320	2	using	use	VERB
ejpam-5823	320	3	triangular	triangular	NOUN
ejpam-5823	320	4	inequality	inequality	NOUN
ejpam-5823	320	5	and	and	CCONJ
ejpam-5823	320	6	the	the	DET
ejpam-5823	320	7	modulus	modulus	ADJ
ejpam-5823	320	8	theorem:∣∣(khξ	theorem:∣∣(khξ	NOUN
ejpam-5823	320	9	,	,	PUNCT
ejpam-5823	320	10	b(z	b(z	NOUN
ejpam-5823	320	11	)	)	PUNCT
ejpam-5823	320	12	)	)	PUNCT
ejpam-5823	321	1	′∣∣	′∣∣	PROPN
ejpam-5823	321	2	>	>	PUNCT
ejpam-5823	321	3	|eiθr|	|eiθr|	PROPN
ejpam-5823	321	4	−	−	PROPN
ejpam-5823	321	5	sup	sup	NOUN
ejpam-5823	321	6	θ∈2π	θ∈2π	PUNCT
ejpam-5823	321	7	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5823	321	8	∞∑	∞∑	NUM
ejpam-5823	321	9	r=1	r=1	NOUN
ejpam-5823	321	10	(	(	PUNCT
ejpam-5823	321	11	r	r	NOUN
ejpam-5823	321	12	+	+	NOUN
ejpam-5823	321	13	1	1	NUM
ejpam-5823	321	14	)	)	PUNCT
ejpam-5823	321	15	(	(	PUNCT
ejpam-5823	321	16	−b)r	−b)r	VERB
ejpam-5823	321	17	eiθr	eiθr	VERB
ejpam-5823	321	18	γk(ξ	γk(ξ	X
ejpam-5823	321	19	+	+	SYM
ejpam-5823	321	20	k	k	X
ejpam-5823	321	21	)	)	PUNCT
ejpam-5823	321	22	4r	4r	NUM
ejpam-5823	321	23	kr	kr	NOUN
ejpam-5823	321	24	γk(r	γk(r	PROPN
ejpam-5823	321	25	+	+	CCONJ
ejpam-5823	321	26	k	k	X
ejpam-5823	321	27	)	)	PUNCT
ejpam-5823	321	28	γk(ξ	γk(ξ	X
ejpam-5823	321	29	+	+	CCONJ
ejpam-5823	321	30	rk	rk	NOUN
ejpam-5823	321	31	)	)	PUNCT
ejpam-5823	321	32	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5823	321	33	≥	≥	NOUN
ejpam-5823	321	34	1−	1−	NUM
ejpam-5823	321	35	γk(ξ	γk(ξ	X
ejpam-5823	321	36	+	+	SYM
ejpam-5823	321	37	k	k	X
ejpam-5823	321	38	)	)	PUNCT
ejpam-5823	321	39	ξ	ξ	VERB
ejpam-5823	321	40	∞∑	∞∑	NUM
ejpam-5823	321	41	r=1	r=1	NOUN
ejpam-5823	321	42	(	(	PUNCT
ejpam-5823	321	43	r	r	NOUN
ejpam-5823	321	44	+	+	NOUN
ejpam-5823	321	45	1	1	X
ejpam-5823	321	46	)	)	PUNCT
ejpam-5823	321	47	|b|r	|b|r	PROPN
ejpam-5823	321	48	4r	4r	NUM
ejpam-5823	321	49	kr	kr	NOUN
ejpam-5823	321	50	γk(ξ	γk(ξ	X
ejpam-5823	321	51	+	+	ADJ
ejpam-5823	321	52	rk	rk	NOUN
ejpam-5823	321	53	)	)	PUNCT
ejpam-5823	321	54	γk(r	γk(r	PUNCT
ejpam-5823	322	1	+	+	CCONJ
ejpam-5823	322	2	k	k	X
ejpam-5823	322	3	)	)	PUNCT
ejpam-5823	322	4	.	.	PUNCT
ejpam-5823	323	1	as	as	SCONJ
ejpam-5823	323	2	we	we	PRON
ejpam-5823	323	3	know	know	VERB
ejpam-5823	323	4	that	that	SCONJ
ejpam-5823	323	5	1	1	NUM
ejpam-5823	323	6	γk(ξ+rk	γk(ξ+rk	ADV
ejpam-5823	323	7	)	)	PUNCT
ejpam-5823	324	1	γk(r+k	γk(r+k	X
ejpam-5823	324	2	)	)	PUNCT
ejpam-5823	324	3	is	be	AUX
ejpam-5823	324	4	strictly	strictly	ADV
ejpam-5823	324	5	decreasing	decrease	VERB
ejpam-5823	324	6	,	,	PUNCT
ejpam-5823	324	7	we	we	PRON
ejpam-5823	324	8	have	have	VERB
ejpam-5823	324	9	∣∣(khξ	∣∣(khξ	NOUN
ejpam-5823	324	10	,	,	PUNCT
ejpam-5823	324	11	b(z	b(z	NOUN
ejpam-5823	324	12	)	)	PUNCT
ejpam-5823	324	13	)	)	PUNCT
ejpam-5823	325	1	′∣∣	′∣∣	PROPN
ejpam-5823	325	2	>	>	X
ejpam-5823	325	3	1−	1−	NUM
ejpam-5823	325	4	γk(ξ	γk(ξ	X
ejpam-5823	325	5	+	+	SYM
ejpam-5823	325	6	k	k	X
ejpam-5823	325	7	)	)	PUNCT
ejpam-5823	325	8	ξ	ξ	VERB
ejpam-5823	326	1	∞∑	∞∑	NUM
ejpam-5823	326	2	r=1	r=1	NOUN
ejpam-5823	326	3	2	2	NUM
ejpam-5823	326	4	|b|r	|b|r	PROPN
ejpam-5823	326	5	4r	4r	NUM
ejpam-5823	326	6	kr	kr	NOUN
ejpam-5823	326	7	γk(ξ	γk(ξ	X
ejpam-5823	326	8	+	+	SYM
ejpam-5823	326	9	k	k	X
ejpam-5823	326	10	)	)	PUNCT
ejpam-5823	326	11	γk(1	γk(1	NOUN
ejpam-5823	326	12	+	+	CCONJ
ejpam-5823	326	13	k	k	NOUN
ejpam-5823	326	14	)	)	PUNCT
ejpam-5823	326	15	=	=	SYM
ejpam-5823	327	1	1−	1−	NUM
ejpam-5823	327	2	2	2	NUM
ejpam-5823	327	3	ξ	ξ	X
ejpam-5823	327	4	∞∑	∞∑	NUM
ejpam-5823	327	5	r=1	r=1	NOUN
ejpam-5823	327	6	(	(	PUNCT
ejpam-5823	327	7	|b|	|b|	X
ejpam-5823	327	8	4k	4k	NOUN
ejpam-5823	327	9	)	)	PUNCT
ejpam-5823	328	1	r	r	NOUN
ejpam-5823	328	2	=	=	SYM
ejpam-5823	328	3	1−	1−	NUM
ejpam-5823	328	4	2|b|	2|b|	NUM
ejpam-5823	328	5	ξ(4k	ξ(4k	NUM
ejpam-5823	328	6	−	−	PROPN
ejpam-5823	328	7	|b|	|b|	PROPN
ejpam-5823	328	8	)	)	PUNCT
ejpam-5823	328	9	=	=	SYM
ejpam-5823	328	10	ξ(4k	ξ(4k	NUM
ejpam-5823	328	11	−	−	PROPN
ejpam-5823	328	12	|b|)−	|b|)−	NOUN
ejpam-5823	328	13	2|b|	2|b|	NUM
ejpam-5823	328	14	ξ(4k	ξ(4k	NUM
ejpam-5823	328	15	−	−	PROPN
ejpam-5823	328	16	|b|	|b|	PROPN
ejpam-5823	328	17	)	)	PUNCT
ejpam-5823	328	18	(	(	PUNCT
ejpam-5823	328	19	46	46	NUM
ejpam-5823	328	20	)	)	PUNCT
ejpam-5823	328	21	where	where	SCONJ
ejpam-5823	328	22	ξ(4k	ξ(4k	NUM
ejpam-5823	328	23	−	−	PROPN
ejpam-5823	328	24	|b|)−	|b|)−	NOUN
ejpam-5823	328	25	2|b|	2|b|	NUM
ejpam-5823	328	26	ξ(4k	ξ(4k	NUM
ejpam-5823	328	27	−	−	PROPN
ejpam-5823	328	28	|b|	|b|	PROPN
ejpam-5823	328	29	)	)	PUNCT
ejpam-5823	328	30	>	>	X
ejpam-5823	328	31	0	0	X
ejpam-5823	328	32	.	.	PUNCT
ejpam-5823	329	1	(	(	PUNCT
ejpam-5823	329	2	47	47	NUM
ejpam-5823	329	3	)	)	PUNCT
ejpam-5823	329	4	above	above	ADP
ejpam-5823	329	5	equation	equation	NOUN
ejpam-5823	329	6	holds	hold	VERB
ejpam-5823	330	1	because	because	SCONJ
ejpam-5823	330	2	ξ	ξ	PROPN
ejpam-5823	330	3	≥	≥	NOUN
ejpam-5823	330	4	0	0	NUM
ejpam-5823	330	5	and	and	CCONJ
ejpam-5823	330	6	|b|	|b|	PROPN
ejpam-5823	330	7	<	<	X
ejpam-5823	330	8	min	min	PROPN
ejpam-5823	330	9	{	{	PUNCT
ejpam-5823	330	10	4	4	NUM
ejpam-5823	330	11	;	;	PUNCT
ejpam-5823	330	12	4kξ	4kξ	NOUN
ejpam-5823	330	13	2	2	NUM
ejpam-5823	330	14	+	+	SYM
ejpam-5823	330	15	ξ	ξ	X
ejpam-5823	330	16	}	}	PUNCT
ejpam-5823	330	17	=	=	SYM
ejpam-5823	330	18	4kξ	4kξ	NOUN
ejpam-5823	330	19	2	2	NUM
ejpam-5823	330	20	+	+	SYM
ejpam-5823	330	21	ξ	ξ	PROPN
ejpam-5823	330	22	.	.	PUNCT
ejpam-5823	331	1	(	(	PUNCT
ejpam-5823	331	2	48	48	NUM
ejpam-5823	331	3	)	)	PUNCT
ejpam-5823	331	4	since	since	SCONJ
ejpam-5823	331	5	∣∣∣∣z(khξ	∣∣∣∣z(khξ	NOUN
ejpam-5823	331	6	,	,	PUNCT
ejpam-5823	331	7	b(z	b(z	NOUN
ejpam-5823	331	8	)	)	PUNCT
ejpam-5823	331	9	)	)	PUNCT
ejpam-5823	332	1	′′	′′	PROPN
ejpam-5823	332	2	(	(	PUNCT
ejpam-5823	332	3	khξ	khξ	PROPN
ejpam-5823	332	4	,	,	PUNCT
ejpam-5823	332	5	b(z))′	b(z))′	PROPN
ejpam-5823	332	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	332	7	=	=	PUNCT
ejpam-5823	332	8	∣∣z(khξ	∣∣z(khξ	NOUN
ejpam-5823	332	9	,	,	PUNCT
ejpam-5823	332	10	b(z	b(z	NOUN
ejpam-5823	332	11	)	)	PUNCT
ejpam-5823	332	12	)	)	PUNCT
ejpam-5823	332	13	′′∣∣	′′∣∣	ADJ
ejpam-5823	332	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	332	15	1	1	NUM
ejpam-5823	332	16	(	(	PUNCT
ejpam-5823	332	17	khξ	khξ	NOUN
ejpam-5823	332	18	,	,	PUNCT
ejpam-5823	332	19	b(z))′	b(z))′	PROPN
ejpam-5823	332	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5823	332	21	<	<	X
ejpam-5823	332	22	2|b|	2|b|	NUM
ejpam-5823	332	23	ξ(4k	ξ(4k	NUM
ejpam-5823	332	24	−	−	PROPN
ejpam-5823	332	25	|b|	|b|	PROPN
ejpam-5823	332	26	)	)	PUNCT
ejpam-5823	332	27	×	×	NOUN
ejpam-5823	332	28	ξ(4k	ξ(4k	NUM
ejpam-5823	332	29	−	−	NUM
ejpam-5823	332	30	|b|	|b|	PROPN
ejpam-5823	332	31	)	)	PUNCT
ejpam-5823	332	32	ξ(4k	ξ(4k	NUM
ejpam-5823	332	33	−	−	PROPN
ejpam-5823	332	34	|b|)−	|b|)−	NOUN
ejpam-5823	332	35	2|b|	2|b|	NUM
ejpam-5823	332	36	<	<	X
ejpam-5823	332	37	2|b|	2|b|	NUM
ejpam-5823	332	38	ξ(4k	ξ(4k	NUM
ejpam-5823	332	39	−	−	PROPN
ejpam-5823	332	40	|b|)−	|b|)−	NOUN
ejpam-5823	332	41	2|b|	2|b|	NUM
ejpam-5823	332	42	≤	≤	NUM
ejpam-5823	332	43	1−	1−	NUM
ejpam-5823	332	44	η	η	NOUN
ejpam-5823	332	45	which	which	PRON
ejpam-5823	332	46	gives	give	VERB
ejpam-5823	332	47	η	η	PROPN
ejpam-5823	332	48	≤	≤	NOUN
ejpam-5823	332	49	1−	1−	NUM
ejpam-5823	332	50	2|b|	2|b|	NUM
ejpam-5823	332	51	ξ(4k	ξ(4k	NUM
ejpam-5823	332	52	−	−	PROPN
ejpam-5823	332	53	|b|)−	|b|)−	NOUN
ejpam-5823	332	54	2|b|	2|b|	NUM
ejpam-5823	332	55	.	.	PUNCT
ejpam-5823	333	1	(	(	PUNCT
ejpam-5823	333	2	49	49	NUM
ejpam-5823	333	3	)	)	PUNCT
ejpam-5823	333	4	finally	finally	ADV
ejpam-5823	333	5	from	from	ADP
ejpam-5823	333	6	inequality	inequality	NOUN
ejpam-5823	333	7	39	39	NUM
ejpam-5823	333	8	,	,	PUNCT
ejpam-5823	333	9	it	it	PRON
ejpam-5823	333	10	is	be	AUX
ejpam-5823	333	11	proved	prove	VERB
ejpam-5823	333	12	that	that	SCONJ
ejpam-5823	333	13	khξ	khξ	NOUN
ejpam-5823	333	14	,	,	PUNCT
ejpam-5823	333	15	b	b	PROPN
ejpam-5823	333	16	∈	∈	PROPN
ejpam-5823	333	17	k(η	k(η	PROPN
ejpam-5823	333	18	)	)	PUNCT
ejpam-5823	333	19	.	.	PUNCT
ejpam-5823	334	1	s.	s.	PROPN
ejpam-5823	334	2	a.	a.	PROPN
ejpam-5823	334	3	h.	h.	PROPN
ejpam-5823	334	4	shah	shah	PROPN
ejpam-5823	334	5	et	et	PROPN
ejpam-5823	334	6	al	al	PROPN
ejpam-5823	334	7	.	.	PUNCT
ejpam-5823	334	8	/	/	SYM
ejpam-5823	334	9	eur	eur	PROPN
ejpam-5823	334	10	.	.	PUNCT
ejpam-5823	335	1	j.	j.	PROPN
ejpam-5823	335	2	pure	pure	PROPN
ejpam-5823	335	3	appl	appl	PROPN
ejpam-5823	335	4	.	.	PROPN
ejpam-5823	335	5	math	math	PROPN
ejpam-5823	335	6	,	,	PUNCT
ejpam-5823	335	7	18	18	NUM
ejpam-5823	335	8	(	(	PUNCT
ejpam-5823	335	9	2	2	NUM
ejpam-5823	335	10	)	)	PUNCT
ejpam-5823	335	11	(	(	PUNCT
ejpam-5823	335	12	2025	2025	NUM
ejpam-5823	335	13	)	)	PUNCT
ejpam-5823	335	14	,	,	PUNCT
ejpam-5823	335	15	5823	5823	NUM
ejpam-5823	335	16	16	16	NUM
ejpam-5823	335	17	of	of	ADP
ejpam-5823	335	18	26	26	NUM
ejpam-5823	335	19	4	4	NUM
ejpam-5823	335	20	.	.	PUNCT
ejpam-5823	336	1	examples	example	NOUN
ejpam-5823	336	2	this	this	DET
ejpam-5823	336	3	section	section	NOUN
ejpam-5823	336	4	illustrates	illustrate	VERB
ejpam-5823	336	5	some	some	DET
ejpam-5823	336	6	examples	example	NOUN
ejpam-5823	336	7	to	to	PART
ejpam-5823	336	8	check	check	VERB
ejpam-5823	336	9	convexity	convexity	NOUN
ejpam-5823	336	10	and	and	CCONJ
ejpam-5823	336	11	starlikeness	starlikeness	NOUN
ejpam-5823	336	12	of	of	ADP
ejpam-5823	336	13	different	different	ADJ
ejpam-5823	336	14	orders	order	NOUN
ejpam-5823	336	15	:	:	PUNCT
ejpam-5823	336	16	example	example	NOUN
ejpam-5823	336	17	1	1	X
ejpam-5823	336	18	.	.	PUNCT
ejpam-5823	337	1	taking	take	VERB
ejpam-5823	337	2	ξ	ξ	PROPN
ejpam-5823	337	3	=	=	SYM
ejpam-5823	337	4	2.2565	2.2565	NUM
ejpam-5823	337	5	,	,	PUNCT
ejpam-5823	337	6	b	b	NOUN
ejpam-5823	337	7	=	=	SYM
ejpam-5823	337	8	0.0253	0.0253	NUM
ejpam-5823	337	9	,	,	PUNCT
ejpam-5823	337	10	η	η	PROPN
ejpam-5823	337	11	=	=	SYM
ejpam-5823	337	12	0	0	PROPN
ejpam-5823	337	13	and	and	CCONJ
ejpam-5823	337	14	k	k	X
ejpam-5823	337	15	=	=	NOUN
ejpam-5823	337	16	0.1	0.1	NUM
ejpam-5823	337	17	.	.	PUNCT
ejpam-5823	337	18	to	to	PART
ejpam-5823	337	19	check	check	VERB
ejpam-5823	337	20	0.1h2.2565,0.0253	0.1h2.2565,0.0253	NUM
ejpam-5823	337	21	∈	∈	PROPN
ejpam-5823	337	22	s∗(0	s∗(0	NOUN
ejpam-5823	337	23	)	)	PUNCT
ejpam-5823	337	24	or	or	CCONJ
ejpam-5823	337	25	0.1h2.2565,0.0253	0.1h2.2565,0.0253	NUM
ejpam-5823	337	26	∈	∈	PROPN
ejpam-5823	337	27	k(0	k(0	PROPN
ejpam-5823	337	28	)	)	PUNCT
ejpam-5823	337	29	,	,	PUNCT
ejpam-5823	337	30	we	we	PRON
ejpam-5823	337	31	will	will	AUX
ejpam-5823	337	32	check	check	VERB
ejpam-5823	337	33	the	the	DET
ejpam-5823	337	34	sufficient	sufficient	ADJ
ejpam-5823	337	35	conditions	condition	NOUN
ejpam-5823	337	36	for	for	ADP
ejpam-5823	337	37	starlikeness	starlikeness	NOUN
ejpam-5823	337	38	and	and	CCONJ
ejpam-5823	337	39	convexity	convexity	NOUN
ejpam-5823	337	40	,	,	PUNCT
ejpam-5823	337	41	that	that	PRON
ejpam-5823	337	42	is	be	AUX
ejpam-5823	337	43	:	:	PUNCT
ejpam-5823	337	44	for	for	ADP
ejpam-5823	337	45	ξ	ξ	PROPN
ejpam-5823	337	46	>	>	SYM
ejpam-5823	337	47	0	0	PUNCT
ejpam-5823	338	1	and	and	CCONJ
ejpam-5823	338	2	let	let	VERB
ejpam-5823	338	3	b	b	PROPN
ejpam-5823	338	4	∈	∈	PROPN
ejpam-5823	338	5	c∗	c∗	NOUN
ejpam-5823	338	6	,	,	PUNCT
ejpam-5823	338	7	k	k	PROPN
ejpam-5823	338	8	∈	∈	PROPN
ejpam-5823	338	9	r+	r+	NOUN
ejpam-5823	338	10	with	with	ADP
ejpam-5823	338	11	0	0	NUM
ejpam-5823	338	12	<	<	X
ejpam-5823	338	13	|b|	|b|	PROPN
ejpam-5823	338	14	<	<	X
ejpam-5823	338	15	4kξ	4kξ	NOUN
ejpam-5823	338	16	1	1	NUM
ejpam-5823	339	1	+	+	SYM
ejpam-5823	339	2	ξ	ξ	X
ejpam-5823	339	3	=	=	NOUN
ejpam-5823	339	4	:	:	PUNCT
ejpam-5823	339	5	b∗.	b∗.	NOUN
ejpam-5823	339	6	(	(	PUNCT
ejpam-5823	339	7	50	50	NUM
ejpam-5823	339	8	)	)	PUNCT
ejpam-5823	339	9	if	if	SCONJ
ejpam-5823	339	10	η	η	PROPN
ejpam-5823	339	11	≤	≤	X
ejpam-5823	339	12	1−	1−	NUM
ejpam-5823	339	13	|b|	|b|	X
ejpam-5823	339	14	ξ(4k	ξ(4k	NUM
ejpam-5823	339	15	−	−	PROPN
ejpam-5823	339	16	|b|)−	|b|)−	NOUN
ejpam-5823	339	17	|b|	|b|	PROPN
ejpam-5823	339	18	=	=	NOUN
ejpam-5823	339	19	:	:	PUNCT
ejpam-5823	339	20	η∗	η∗	NOUN
ejpam-5823	339	21	(	(	PUNCT
ejpam-5823	339	22	51	51	NUM
ejpam-5823	339	23	)	)	PUNCT
ejpam-5823	339	24	then	then	ADV
ejpam-5823	339	25	khξ	khξ	PROPN
ejpam-5823	339	26	,	,	PUNCT
ejpam-5823	339	27	b	b	PROPN
ejpam-5823	339	28	∈	∈	PROPN
ejpam-5823	339	29	s∗(η	s∗(η	PROPN
ejpam-5823	339	30	)	)	PUNCT
ejpam-5823	339	31	.	.	PUNCT
ejpam-5823	340	1	above	above	ADP
ejpam-5823	340	2	parameter	parameter	NOUN
ejpam-5823	340	3	values	value	NOUN
ejpam-5823	340	4	satisfy	satisfy	VERB
ejpam-5823	340	5	the	the	DET
ejpam-5823	340	6	condition	condition	NOUN
ejpam-5823	340	7	;	;	PUNCT
ejpam-5823	340	8	0	0	PUNCT
ejpam-5823	340	9	<	<	X
ejpam-5823	340	10	|0.0253|	|0.0253|	ADJ
ejpam-5823	340	11	<	<	X
ejpam-5823	340	12	4×	4×	NOUN
ejpam-5823	340	13	0.1(2.2565	0.1(2.2565	NUM
ejpam-5823	340	14	)	)	PUNCT
ejpam-5823	340	15	2.2565	2.2565	NUM
ejpam-5823	340	16	+	+	CCONJ
ejpam-5823	340	17	1	1	NUM
ejpam-5823	340	18	=	=	SYM
ejpam-5823	340	19	0.277169	0.277169	NUM
ejpam-5823	340	20	.	.	PUNCT
ejpam-5823	341	1	and	and	CCONJ
ejpam-5823	341	2	0	0	NUM
ejpam-5823	341	3	≤	≤	NOUN
ejpam-5823	341	4	1−	1−	NUM
ejpam-5823	341	5	|0.0253|	|0.0253|	ADJ
ejpam-5823	341	6	2.2565(4×	2.2565(4×	NUM
ejpam-5823	341	7	0.1−	0.1−	NOUN
ejpam-5823	341	8	|0.0253|)−	|0.0253|)−	PUNCT
ejpam-5823	341	9	|0.0253|	|0.0253|	ADJ
ejpam-5823	341	10	=	=	SYM
ejpam-5823	341	11	0.969154	0.969154	NUM
ejpam-5823	341	12	.	.	PUNCT
ejpam-5823	342	1	both	both	DET
ejpam-5823	342	2	conditions	condition	NOUN
ejpam-5823	342	3	satisfied	satisfied	ADJ
ejpam-5823	342	4	,	,	PUNCT
ejpam-5823	342	5	hence	hence	ADV
ejpam-5823	342	6	0.1h2.2565,0.0253	0.1h2.2565,0.0253	NUM
ejpam-5823	342	7	∈	∈	PROPN
ejpam-5823	342	8	s∗(0	s∗(0	NOUN
ejpam-5823	342	9	)	)	PUNCT
ejpam-5823	342	10	.	.	PUNCT
ejpam-5823	343	1	now	now	ADV
ejpam-5823	343	2	check	check	VERB
ejpam-5823	343	3	the	the	DET
ejpam-5823	343	4	conditions	condition	NOUN
ejpam-5823	343	5	for	for	ADP
ejpam-5823	343	6	convexity	convexity	NOUN
ejpam-5823	343	7	:	:	PUNCT
ejpam-5823	343	8	for	for	ADP
ejpam-5823	343	9	ξ	ξ	PROPN
ejpam-5823	343	10	>	>	SYM
ejpam-5823	343	11	1	1	NUM
ejpam-5823	343	12	2	2	NUM
ejpam-5823	343	13	and	and	CCONJ
ejpam-5823	343	14	let	let	VERB
ejpam-5823	343	15	b	b	PROPN
ejpam-5823	343	16	∈	∈	PROPN
ejpam-5823	343	17	c∗	c∗	NOUN
ejpam-5823	343	18	,	,	PUNCT
ejpam-5823	343	19	k	k	PROPN
ejpam-5823	343	20	∈	∈	PROPN
ejpam-5823	343	21	r+	r+	NOUN
ejpam-5823	343	22	with	with	ADP
ejpam-5823	343	23	0	0	NUM
ejpam-5823	343	24	<	<	X
ejpam-5823	343	25	|b|	|b|	PROPN
ejpam-5823	343	26	<	<	X
ejpam-5823	343	27	4kξ	4kξ	NOUN
ejpam-5823	343	28	2	2	NUM
ejpam-5823	343	29	+	+	SYM
ejpam-5823	343	30	ξ	ξ	X
ejpam-5823	343	31	=	=	X
ejpam-5823	343	32	:	:	PUNCT
ejpam-5823	343	33	bc	bc	PROPN
ejpam-5823	343	34	.	.	PROPN
ejpam-5823	344	1	(	(	PUNCT
ejpam-5823	344	2	52	52	NUM
ejpam-5823	344	3	)	)	PUNCT
ejpam-5823	344	4	if	if	SCONJ
ejpam-5823	344	5	η	η	PROPN
ejpam-5823	344	6	≤	≤	X
ejpam-5823	344	7	1−	1−	NUM
ejpam-5823	344	8	2|b|	2|b|	NUM
ejpam-5823	344	9	ξ(4k	ξ(4k	NUM
ejpam-5823	344	10	−	−	PROPN
ejpam-5823	344	11	|b|)−	|b|)−	NOUN
ejpam-5823	344	12	2|b|	2|b|	NUM
ejpam-5823	345	1	=	=	NOUN
ejpam-5823	345	2	:	:	PUNCT
ejpam-5823	345	3	η∗	η∗	NOUN
ejpam-5823	345	4	(	(	PUNCT
ejpam-5823	345	5	53	53	NUM
ejpam-5823	345	6	)	)	PUNCT
ejpam-5823	345	7	then	then	ADV
ejpam-5823	345	8	khξ	khξ	PROPN
ejpam-5823	345	9	,	,	PUNCT
ejpam-5823	345	10	b	b	PROPN
ejpam-5823	345	11	∈	∈	PROPN
ejpam-5823	345	12	k(η	k(η	PROPN
ejpam-5823	345	13	)	)	PUNCT
ejpam-5823	345	14	.	.	PUNCT
ejpam-5823	346	1	above	above	ADP
ejpam-5823	346	2	parameter	parameter	NOUN
ejpam-5823	346	3	values	value	NOUN
ejpam-5823	346	4	satisfy	satisfy	VERB
ejpam-5823	346	5	the	the	DET
ejpam-5823	346	6	condition	condition	NOUN
ejpam-5823	346	7	;	;	PUNCT
ejpam-5823	346	8	0	0	PUNCT
ejpam-5823	346	9	<	<	X
ejpam-5823	346	10	|0.0253|	|0.0253|	ADJ
ejpam-5823	346	11	<	<	X
ejpam-5823	346	12	4×	4×	NOUN
ejpam-5823	346	13	0.1(2.2565	0.1(2.2565	NUM
ejpam-5823	346	14	)	)	PUNCT
ejpam-5823	346	15	2.2565	2.2565	NUM
ejpam-5823	346	16	+	+	CCONJ
ejpam-5823	346	17	2	2	NUM
ejpam-5823	346	18	=	=	SYM
ejpam-5823	346	19	0.212052	0.212052	NUM
ejpam-5823	346	20	.	.	PUNCT
ejpam-5823	347	1	and	and	CCONJ
ejpam-5823	347	2	0	0	NUM
ejpam-5823	347	3	≤	≤	NUM
ejpam-5823	347	4	1−	1−	NUM
ejpam-5823	347	5	2|0.0253|	2|0.0253|	NUM
ejpam-5823	347	6	2.2565(4(0.1)−	2.2565(4(0.1)−	PROPN
ejpam-5823	347	7	|0.0253|)−	|0.0253|)−	PROPN
ejpam-5823	347	8	2|0.0253|	2|0.0253|	NUM
ejpam-5823	347	9	=	=	SYM
ejpam-5823	347	10	0.936345	0.936345	NUM
ejpam-5823	347	11	.	.	PUNCT
ejpam-5823	348	1	both	both	DET
ejpam-5823	348	2	conditions	condition	NOUN
ejpam-5823	348	3	satisfied	satisfied	ADJ
ejpam-5823	348	4	,	,	PUNCT
ejpam-5823	348	5	hence	hence	ADV
ejpam-5823	348	6	0.1h2.2565,0.0253	0.1h2.2565,0.0253	NUM
ejpam-5823	349	1	∈	∈	PROPN
ejpam-5823	349	2	k(0	k(0	PROPN
ejpam-5823	349	3	)	)	PUNCT
ejpam-5823	349	4	.	.	PUNCT
ejpam-5823	350	1	s.	s.	PROPN
ejpam-5823	350	2	a.	a.	PROPN
ejpam-5823	350	3	h.	h.	PROPN
ejpam-5823	350	4	shah	shah	PROPN
ejpam-5823	350	5	et	et	PROPN
ejpam-5823	350	6	al	al	PROPN
ejpam-5823	350	7	.	.	PUNCT
ejpam-5823	350	8	/	/	SYM
ejpam-5823	350	9	eur	eur	PROPN
ejpam-5823	350	10	.	.	PUNCT
ejpam-5823	351	1	j.	j.	PROPN
ejpam-5823	351	2	pure	pure	PROPN
ejpam-5823	351	3	appl	appl	PROPN
ejpam-5823	351	4	.	.	PROPN
ejpam-5823	351	5	math	math	PROPN
ejpam-5823	351	6	,	,	PUNCT
ejpam-5823	351	7	18	18	NUM
ejpam-5823	351	8	(	(	PUNCT
ejpam-5823	351	9	2	2	NUM
ejpam-5823	351	10	)	)	PUNCT
ejpam-5823	351	11	(	(	PUNCT
ejpam-5823	351	12	2025	2025	NUM
ejpam-5823	351	13	)	)	PUNCT
ejpam-5823	351	14	,	,	PUNCT
ejpam-5823	351	15	5823	5823	NUM
ejpam-5823	351	16	17	17	NUM
ejpam-5823	351	17	of	of	ADP
ejpam-5823	351	18	26	26	NUM
ejpam-5823	351	19	(	(	PUNCT
ejpam-5823	351	20	a	a	NOUN
ejpam-5823	351	21	)	)	PUNCT
ejpam-5823	351	22	0.1h2.2565,0.0253	0.1h2.2565,0.0253	NOUN
ejpam-5823	351	23	(	(	PUNCT
ejpam-5823	351	24	b	b	X
ejpam-5823	351	25	)	)	PUNCT
ejpam-5823	351	26	0.4h2.2565,0.0253	0.4h2.2565,0.0253	NOUN
ejpam-5823	352	1	(	(	PUNCT
ejpam-5823	352	2	c	c	NOUN
ejpam-5823	352	3	)	)	PUNCT
ejpam-5823	352	4	0.8h2.2565,0.0253	0.8h2.2565,0.0253	X
ejpam-5823	353	1	(	(	PUNCT
ejpam-5823	353	2	d	d	X
ejpam-5823	353	3	)	)	PUNCT
ejpam-5823	353	4	1h2.2565,0.0253	1h2.2565,0.0253	NUM
ejpam-5823	353	5	(	(	PUNCT
ejpam-5823	353	6	e	e	NOUN
ejpam-5823	353	7	)	)	PUNCT
ejpam-5823	353	8	h2.2565,0.0253	h2.2565,0.0253	NUM
ejpam-5823	353	9	figures	figure	NOUN
ejpam-5823	353	10	are	be	AUX
ejpam-5823	353	11	the	the	DET
ejpam-5823	353	12	illustrations	illustration	NOUN
ejpam-5823	353	13	of	of	ADP
ejpam-5823	353	14	the	the	DET
ejpam-5823	353	15	example	example	NOUN
ejpam-5823	353	16	1	1	NUM
ejpam-5823	353	17	which	which	PRON
ejpam-5823	353	18	show	show	VERB
ejpam-5823	353	19	the	the	DET
ejpam-5823	353	20	contour	contour	NOUN
ejpam-5823	353	21	plot	plot	NOUN
ejpam-5823	353	22	of	of	ADP
ejpam-5823	353	23	generalized	generalized	ADJ
ejpam-5823	353	24	bessel	bessel	NOUN
ejpam-5823	353	25	k	k	NOUN
ejpam-5823	353	26	-	-	NOUN
ejpam-5823	353	27	function	function	NOUN
ejpam-5823	353	28	for	for	ADP
ejpam-5823	353	29	different	different	ADJ
ejpam-5823	353	30	values	value	NOUN
ejpam-5823	353	31	of	of	ADP
ejpam-5823	353	32	k.	k.	PROPN
ejpam-5823	353	33	it	it	PRON
ejpam-5823	353	34	can	can	AUX
ejpam-5823	353	35	be	be	AUX
ejpam-5823	353	36	observed	observe	VERB
ejpam-5823	353	37	that	that	SCONJ
ejpam-5823	353	38	the	the	DET
ejpam-5823	353	39	graphs	graph	NOUN
ejpam-5823	353	40	show	show	VERB
ejpam-5823	353	41	the	the	DET
ejpam-5823	353	42	symmetrical	symmetrical	ADJ
ejpam-5823	353	43	behaviour	behaviour	NOUN
ejpam-5823	353	44	and	and	CCONJ
ejpam-5823	353	45	provide	provide	VERB
ejpam-5823	353	46	a	a	DET
ejpam-5823	353	47	way	way	NOUN
ejpam-5823	353	48	to	to	PART
ejpam-5823	353	49	check	check	VERB
ejpam-5823	353	50	the	the	DET
ejpam-5823	353	51	accuracy	accuracy	NOUN
ejpam-5823	353	52	of	of	ADP
ejpam-5823	353	53	our	our	PRON
ejpam-5823	353	54	results	result	NOUN
ejpam-5823	353	55	i.e.	i.e.	ADV
ejpam-5823	353	56	,	,	PUNCT
ejpam-5823	353	57	as	as	SCONJ
ejpam-5823	353	58	k	k	PROPN
ejpam-5823	353	59	approaches	approach	VERB
ejpam-5823	353	60	to	to	ADP
ejpam-5823	353	61	1	1	NUM
ejpam-5823	353	62	,	,	PUNCT
ejpam-5823	353	63	the	the	DET
ejpam-5823	353	64	graphical	graphical	ADJ
ejpam-5823	353	65	behaviour	behaviour	NOUN
ejpam-5823	353	66	will	will	AUX
ejpam-5823	353	67	approach	approach	VERB
ejpam-5823	353	68	the	the	DET
ejpam-5823	353	69	classical	classical	ADJ
ejpam-5823	353	70	form	form	NOUN
ejpam-5823	353	71	of	of	ADP
ejpam-5823	353	72	generalized	generalized	ADJ
ejpam-5823	353	73	bessel	bessel	ADJ
ejpam-5823	353	74	function	function	NOUN
ejpam-5823	353	75	.	.	PUNCT
ejpam-5823	354	1	exactly	exactly	ADV
ejpam-5823	354	2	at	at	ADP
ejpam-5823	354	3	k	k	PROPN
ejpam-5823	354	4	=	=	SYM
ejpam-5823	354	5	1	1	NUM
ejpam-5823	354	6	,	,	PUNCT
ejpam-5823	354	7	the	the	DET
ejpam-5823	354	8	graphs	graph	NOUN
ejpam-5823	354	9	are	be	AUX
ejpam-5823	354	10	same	same	ADJ
ejpam-5823	354	11	.	.	PUNCT
ejpam-5823	354	12	example	example	NOUN
ejpam-5823	355	1	2	2	NUM
ejpam-5823	355	2	.	.	PUNCT
ejpam-5823	355	3	taking	take	VERB
ejpam-5823	355	4	ξ	ξ	PROPN
ejpam-5823	355	5	=	=	SYM
ejpam-5823	355	6	2.5	2.5	NUM
ejpam-5823	355	7	,	,	PUNCT
ejpam-5823	355	8	b	b	NOUN
ejpam-5823	355	9	=	=	SYM
ejpam-5823	355	10	1.2	1.2	NUM
ejpam-5823	355	11	,	,	PUNCT
ejpam-5823	355	12	η	η	X
ejpam-5823	355	13	=	=	PROPN
ejpam-5823	355	14	0.32	0.32	NUM
ejpam-5823	355	15	and	and	CCONJ
ejpam-5823	355	16	k	k	NOUN
ejpam-5823	355	17	=	=	NOUN
ejpam-5823	355	18	0.6	0.6	NUM
ejpam-5823	355	19	.	.	PUNCT
ejpam-5823	355	20	to	to	PART
ejpam-5823	355	21	check	check	VERB
ejpam-5823	355	22	0.6h2.5,1.2	0.6h2.5,1.2	X
ejpam-5823	355	23	∈	∈	PROPN
ejpam-5823	355	24	s∗(0.32	s∗(0.32	NOUN
ejpam-5823	355	25	)	)	PUNCT
ejpam-5823	355	26	or	or	CCONJ
ejpam-5823	355	27	0.6h2.5,1.2	0.6h2.5,1.2	X
ejpam-5823	355	28	∈	∈	PROPN
ejpam-5823	355	29	k(0.32	k(0.32	PROPN
ejpam-5823	355	30	)	)	PUNCT
ejpam-5823	355	31	.	.	PUNCT
ejpam-5823	356	1	we	we	PRON
ejpam-5823	356	2	will	will	AUX
ejpam-5823	356	3	check	check	VERB
ejpam-5823	356	4	the	the	DET
ejpam-5823	356	5	sufficient	sufficient	ADJ
ejpam-5823	356	6	conditions	condition	NOUN
ejpam-5823	356	7	for	for	ADP
ejpam-5823	356	8	starlikeness	starlikeness	NOUN
ejpam-5823	356	9	and	and	CCONJ
ejpam-5823	356	10	convexity	convexity	NOUN
ejpam-5823	356	11	,	,	PUNCT
ejpam-5823	356	12	that	that	PRON
ejpam-5823	356	13	is	be	AUX
ejpam-5823	356	14	:	:	PUNCT
ejpam-5823	356	15	for	for	ADP
ejpam-5823	356	16	ξ	ξ	PROPN
ejpam-5823	356	17	>	>	SYM
ejpam-5823	356	18	0	0	PUNCT
ejpam-5823	357	1	and	and	CCONJ
ejpam-5823	357	2	let	let	VERB
ejpam-5823	357	3	b	b	PROPN
ejpam-5823	357	4	∈	∈	PROPN
ejpam-5823	357	5	c∗	c∗	NOUN
ejpam-5823	357	6	,	,	PUNCT
ejpam-5823	357	7	k	k	PROPN
ejpam-5823	357	8	∈	∈	PROPN
ejpam-5823	357	9	r+	r+	NOUN
ejpam-5823	357	10	with	with	ADP
ejpam-5823	357	11	0	0	NUM
ejpam-5823	357	12	<	<	X
ejpam-5823	357	13	|b|	|b|	PROPN
ejpam-5823	357	14	<	<	X
ejpam-5823	357	15	4kξ	4kξ	NOUN
ejpam-5823	357	16	1	1	NUM
ejpam-5823	358	1	+	+	SYM
ejpam-5823	358	2	ξ	ξ	X
ejpam-5823	358	3	=	=	NOUN
ejpam-5823	358	4	:	:	PUNCT
ejpam-5823	358	5	b∗.	b∗.	NOUN
ejpam-5823	358	6	(	(	PUNCT
ejpam-5823	358	7	54	54	NUM
ejpam-5823	358	8	)	)	PUNCT
ejpam-5823	358	9	if	if	SCONJ
ejpam-5823	358	10	η	η	PROPN
ejpam-5823	358	11	≤	≤	X
ejpam-5823	358	12	1−	1−	NUM
ejpam-5823	358	13	|b|	|b|	X
ejpam-5823	358	14	ξ(4k	ξ(4k	NUM
ejpam-5823	358	15	−	−	PROPN
ejpam-5823	358	16	|b|)−	|b|)−	NOUN
ejpam-5823	358	17	|b|	|b|	PROPN
ejpam-5823	358	18	=	=	NOUN
ejpam-5823	358	19	:	:	PUNCT
ejpam-5823	358	20	η∗	η∗	NOUN
ejpam-5823	358	21	(	(	PUNCT
ejpam-5823	358	22	55	55	NUM
ejpam-5823	358	23	)	)	PUNCT
ejpam-5823	358	24	then	then	ADV
ejpam-5823	358	25	khξ	khξ	PROPN
ejpam-5823	358	26	,	,	PUNCT
ejpam-5823	358	27	b	b	PROPN
ejpam-5823	358	28	∈	∈	PROPN
ejpam-5823	358	29	s∗(η	s∗(η	PROPN
ejpam-5823	358	30	)	)	PUNCT
ejpam-5823	358	31	.	.	PUNCT
ejpam-5823	359	1	above	above	ADP
ejpam-5823	359	2	parameter	parameter	NOUN
ejpam-5823	359	3	values	value	NOUN
ejpam-5823	359	4	satisfy	satisfy	VERB
ejpam-5823	359	5	the	the	DET
ejpam-5823	359	6	condition	condition	NOUN
ejpam-5823	359	7	;	;	PUNCT
ejpam-5823	359	8	0	0	NUM
ejpam-5823	359	9	<	<	X
ejpam-5823	359	10	|1.2|	|1.2|	PROPN
ejpam-5823	359	11	<	<	X
ejpam-5823	359	12	4×	4×	NOUN
ejpam-5823	359	13	0.6(2.5	0.6(2.5	NOUN
ejpam-5823	359	14	)	)	PUNCT
ejpam-5823	359	15	2.5	2.5	NUM
ejpam-5823	360	1	+	+	SYM
ejpam-5823	360	2	1	1	NUM
ejpam-5823	360	3	=	=	SYM
ejpam-5823	360	4	1.71429	1.71429	NUM
ejpam-5823	360	5	.	.	PUNCT
ejpam-5823	361	1	now	now	ADV
ejpam-5823	361	2	check	check	VERB
ejpam-5823	361	3	for	for	ADP
ejpam-5823	361	4	:	:	PUNCT
ejpam-5823	361	5	0.32	0.32	NUM
ejpam-5823	361	6	≤	≤	NUM
ejpam-5823	361	7	1−	1−	NUM
ejpam-5823	362	1	|1.2|	|1.2|	PROPN
ejpam-5823	362	2	2.5(4×	2.5(4×	NUM
ejpam-5823	362	3	0.6−	0.6−	NOUN
ejpam-5823	362	4	|1.2|)−	|1.2|)−	PROPN
ejpam-5823	362	5	|1.2|	|1.2|	PROPN
ejpam-5823	362	6	=	=	NOUN
ejpam-5823	362	7	0.333333	0.333333	NUM
ejpam-5823	362	8	.	.	PUNCT
ejpam-5823	363	1	s.	s.	PROPN
ejpam-5823	363	2	a.	a.	PROPN
ejpam-5823	363	3	h.	h.	PROPN
ejpam-5823	363	4	shah	shah	PROPN
ejpam-5823	363	5	et	et	PROPN
ejpam-5823	363	6	al	al	PROPN
ejpam-5823	363	7	.	.	PUNCT
ejpam-5823	363	8	/	/	SYM
ejpam-5823	363	9	eur	eur	PROPN
ejpam-5823	363	10	.	.	PUNCT
ejpam-5823	364	1	j.	j.	PROPN
ejpam-5823	364	2	pure	pure	PROPN
ejpam-5823	364	3	appl	appl	PROPN
ejpam-5823	364	4	.	.	PROPN
ejpam-5823	364	5	math	math	PROPN
ejpam-5823	364	6	,	,	PUNCT
ejpam-5823	364	7	18	18	NUM
ejpam-5823	364	8	(	(	PUNCT
ejpam-5823	364	9	2	2	NUM
ejpam-5823	364	10	)	)	PUNCT
ejpam-5823	364	11	(	(	PUNCT
ejpam-5823	364	12	2025	2025	NUM
ejpam-5823	364	13	)	)	PUNCT
ejpam-5823	364	14	,	,	PUNCT
ejpam-5823	364	15	5823	5823	NUM
ejpam-5823	364	16	18	18	NUM
ejpam-5823	364	17	of	of	ADP
ejpam-5823	364	18	26	26	NUM
ejpam-5823	364	19	both	both	DET
ejpam-5823	364	20	conditions	condition	NOUN
ejpam-5823	364	21	satisfied	satisfied	ADJ
ejpam-5823	364	22	,	,	PUNCT
ejpam-5823	364	23	hence	hence	ADV
ejpam-5823	364	24	0.6h2.5,1.2	0.6h2.5,1.2	X
ejpam-5823	364	25	∈	∈	NOUN
ejpam-5823	364	26	s∗(0.32	s∗(0.32	NOUN
ejpam-5823	364	27	)	)	PUNCT
ejpam-5823	364	28	.	.	PUNCT
ejpam-5823	365	1	now	now	ADV
ejpam-5823	365	2	check	check	VERB
ejpam-5823	365	3	the	the	DET
ejpam-5823	365	4	conditions	condition	NOUN
ejpam-5823	365	5	for	for	ADP
ejpam-5823	365	6	convexity	convexity	NOUN
ejpam-5823	365	7	:	:	PUNCT
ejpam-5823	365	8	for	for	ADP
ejpam-5823	365	9	ξ	ξ	PROPN
ejpam-5823	365	10	>	>	SYM
ejpam-5823	365	11	1	1	NUM
ejpam-5823	365	12	2	2	NUM
ejpam-5823	365	13	and	and	CCONJ
ejpam-5823	365	14	let	let	VERB
ejpam-5823	365	15	b	b	PROPN
ejpam-5823	365	16	∈	∈	PROPN
ejpam-5823	365	17	c∗	c∗	NOUN
ejpam-5823	365	18	,	,	PUNCT
ejpam-5823	365	19	k	k	PROPN
ejpam-5823	365	20	∈	∈	PROPN
ejpam-5823	365	21	r+	r+	NOUN
ejpam-5823	365	22	with	with	ADP
ejpam-5823	365	23	0	0	NUM
ejpam-5823	365	24	<	<	X
ejpam-5823	365	25	|b|	|b|	PROPN
ejpam-5823	365	26	<	<	X
ejpam-5823	365	27	4kξ	4kξ	NOUN
ejpam-5823	365	28	2	2	NUM
ejpam-5823	365	29	+	+	SYM
ejpam-5823	365	30	ξ	ξ	X
ejpam-5823	365	31	=	=	X
ejpam-5823	365	32	:	:	PUNCT
ejpam-5823	365	33	bc	bc	PROPN
ejpam-5823	365	34	.	.	PROPN
ejpam-5823	366	1	(	(	PUNCT
ejpam-5823	366	2	56	56	NUM
ejpam-5823	366	3	)	)	PUNCT
ejpam-5823	366	4	if	if	SCONJ
ejpam-5823	366	5	η	η	PROPN
ejpam-5823	366	6	≤	≤	X
ejpam-5823	366	7	1−	1−	NUM
ejpam-5823	366	8	2|b|	2|b|	NUM
ejpam-5823	366	9	ξ(4k	ξ(4k	NUM
ejpam-5823	366	10	−	−	PROPN
ejpam-5823	366	11	|b|)−	|b|)−	NOUN
ejpam-5823	366	12	2|b|	2|b|	NUM
ejpam-5823	367	1	=	=	NOUN
ejpam-5823	367	2	:	:	PUNCT
ejpam-5823	367	3	η∗	η∗	NOUN
ejpam-5823	367	4	(	(	PUNCT
ejpam-5823	367	5	57	57	NUM
ejpam-5823	367	6	)	)	PUNCT
ejpam-5823	367	7	then	then	ADV
ejpam-5823	367	8	khξ	khξ	PROPN
ejpam-5823	367	9	,	,	PUNCT
ejpam-5823	367	10	b	b	PROPN
ejpam-5823	367	11	∈	∈	PROPN
ejpam-5823	367	12	k(η	k(η	PROPN
ejpam-5823	367	13	)	)	PUNCT
ejpam-5823	367	14	.	.	PUNCT
ejpam-5823	368	1	above	above	ADP
ejpam-5823	368	2	parameter	parameter	NOUN
ejpam-5823	368	3	values	value	NOUN
ejpam-5823	368	4	do	do	AUX
ejpam-5823	368	5	not	not	PART
ejpam-5823	368	6	satisfy	satisfy	VERB
ejpam-5823	368	7	the	the	DET
ejpam-5823	368	8	conditions	condition	NOUN
ejpam-5823	368	9	;	;	PUNCT
ejpam-5823	368	10	0	0	PUNCT
ejpam-5823	368	11	<	<	X
ejpam-5823	368	12	|1.2|	|1.2|	PROPN
ejpam-5823	368	13	<	<	X
ejpam-5823	368	14	4×	4×	NOUN
ejpam-5823	368	15	0.6(2.5	0.6(2.5	NOUN
ejpam-5823	368	16	)	)	PUNCT
ejpam-5823	368	17	2.5	2.5	NUM
ejpam-5823	369	1	+	+	CCONJ
ejpam-5823	369	2	2	2	NUM
ejpam-5823	369	3	=	=	SYM
ejpam-5823	369	4	1.3333	1.3333	NUM
ejpam-5823	369	5	.	.	PUNCT
ejpam-5823	370	1	0.32	0.32	NUM
ejpam-5823	370	2	≰	≰	PROPN
ejpam-5823	370	3	1−	1−	NUM
ejpam-5823	370	4	2×	2×	NUM
ejpam-5823	370	5	2.5	2.5	NUM
ejpam-5823	370	6	2.5(4×	2.5(4×	NUM
ejpam-5823	370	7	0.6−	0.6−	NOUN
ejpam-5823	370	8	|1.2|)−	|1.2|)−	NOUN
ejpam-5823	370	9	2|1.2|	2|1.2|	NUM
ejpam-5823	370	10	=	=	SYM
ejpam-5823	370	11	−3	−3	ADJ
ejpam-5823	370	12	.	.	PUNCT
ejpam-5823	371	1	hence	hence	ADV
ejpam-5823	371	2	0.6h2.5,1.2	0.6h2.5,1.2	X
ejpam-5823	371	3	/∈	/∈	PUNCT
ejpam-5823	372	1	k(0.32	k(0.32	PROPN
ejpam-5823	372	2	)	)	PUNCT
ejpam-5823	372	3	.	.	PUNCT
ejpam-5823	373	1	(	(	PUNCT
ejpam-5823	373	2	f	f	X
ejpam-5823	373	3	)	)	PUNCT
ejpam-5823	373	4	0.6h2.5,1.2	0.6h2.5,1.2	NOUN
ejpam-5823	373	5	(	(	PUNCT
ejpam-5823	373	6	g	g	NOUN
ejpam-5823	373	7	)	)	PUNCT
ejpam-5823	373	8	0.8h2.5,1.2	0.8h2.5,1.2	NOUN
ejpam-5823	373	9	(	(	PUNCT
ejpam-5823	373	10	h	h	NOUN
ejpam-5823	373	11	)	)	PUNCT
ejpam-5823	373	12	0.9h2.5,1.2	0.9h2.5,1.2	NOUN
ejpam-5823	373	13	(	(	PUNCT
ejpam-5823	373	14	i	i	NOUN
ejpam-5823	373	15	)	)	PUNCT
ejpam-5823	373	16	1h2.5,1.2	1h2.5,1.2	NUM
ejpam-5823	373	17	(	(	PUNCT
ejpam-5823	373	18	j	j	NOUN
ejpam-5823	373	19	)	)	PUNCT
ejpam-5823	373	20	h2.5,1.2	h2.5,1.2	VERB
ejpam-5823	373	21	figures	figure	NOUN
ejpam-5823	373	22	are	be	AUX
ejpam-5823	373	23	the	the	DET
ejpam-5823	373	24	illustrations	illustration	NOUN
ejpam-5823	373	25	of	of	ADP
ejpam-5823	373	26	the	the	DET
ejpam-5823	373	27	example	example	NOUN
ejpam-5823	373	28	2	2	NUM
ejpam-5823	373	29	which	which	PRON
ejpam-5823	373	30	show	show	VERB
ejpam-5823	373	31	the	the	DET
ejpam-5823	373	32	contour	contour	NOUN
ejpam-5823	373	33	plot	plot	NOUN
ejpam-5823	373	34	of	of	ADP
ejpam-5823	373	35	generalized	generalized	ADJ
ejpam-5823	373	36	bessel	bessel	NOUN
ejpam-5823	373	37	k	k	NOUN
ejpam-5823	373	38	-	-	NOUN
ejpam-5823	373	39	function	function	NOUN
ejpam-5823	373	40	for	for	ADP
ejpam-5823	373	41	different	different	ADJ
ejpam-5823	373	42	values	value	NOUN
ejpam-5823	373	43	of	of	ADP
ejpam-5823	373	44	k.	k.	PROPN
ejpam-5823	373	45	it	it	PRON
ejpam-5823	373	46	can	can	AUX
ejpam-5823	373	47	be	be	AUX
ejpam-5823	373	48	observed	observe	VERB
ejpam-5823	373	49	that	that	SCONJ
ejpam-5823	373	50	the	the	DET
ejpam-5823	373	51	graphs	graph	NOUN
ejpam-5823	373	52	show	show	VERB
ejpam-5823	373	53	the	the	DET
ejpam-5823	373	54	symmetrical	symmetrical	ADJ
ejpam-5823	373	55	domains	domain	NOUN
ejpam-5823	373	56	with	with	ADP
ejpam-5823	373	57	respect	respect	NOUN
ejpam-5823	373	58	to	to	ADP
ejpam-5823	373	59	real	real	ADJ
ejpam-5823	373	60	axis	axis	NOUN
ejpam-5823	373	61	and	and	CCONJ
ejpam-5823	373	62	provide	provide	VERB
ejpam-5823	373	63	a	a	DET
ejpam-5823	373	64	way	way	NOUN
ejpam-5823	373	65	to	to	PART
ejpam-5823	373	66	check	check	VERB
ejpam-5823	373	67	the	the	DET
ejpam-5823	373	68	accuracy	accuracy	NOUN
ejpam-5823	373	69	of	of	ADP
ejpam-5823	373	70	our	our	PRON
ejpam-5823	373	71	results	result	NOUN
ejpam-5823	373	72	i.e.	i.e.	ADV
ejpam-5823	373	73	,	,	PUNCT
ejpam-5823	373	74	as	as	SCONJ
ejpam-5823	373	75	k	k	PROPN
ejpam-5823	373	76	approaches	approach	VERB
ejpam-5823	373	77	to	to	ADP
ejpam-5823	373	78	1	1	NUM
ejpam-5823	373	79	,	,	PUNCT
ejpam-5823	373	80	the	the	DET
ejpam-5823	373	81	graphical	graphical	ADJ
ejpam-5823	373	82	behaviour	behaviour	NOUN
ejpam-5823	373	83	will	will	AUX
ejpam-5823	373	84	approach	approach	VERB
ejpam-5823	373	85	the	the	DET
ejpam-5823	373	86	classical	classical	ADJ
ejpam-5823	373	87	form	form	NOUN
ejpam-5823	373	88	of	of	ADP
ejpam-5823	373	89	generalized	generalized	ADJ
ejpam-5823	373	90	bessel	bessel	ADJ
ejpam-5823	373	91	function	function	NOUN
ejpam-5823	373	92	.	.	PUNCT
ejpam-5823	374	1	exactly	exactly	ADV
ejpam-5823	374	2	at	at	ADP
ejpam-5823	374	3	k	k	PROPN
ejpam-5823	374	4	=	=	SYM
ejpam-5823	374	5	1	1	NUM
ejpam-5823	374	6	,	,	PUNCT
ejpam-5823	374	7	the	the	DET
ejpam-5823	374	8	graphs	graph	NOUN
ejpam-5823	374	9	are	be	AUX
ejpam-5823	374	10	same	same	ADJ
ejpam-5823	374	11	.	.	PUNCT
ejpam-5823	375	1	s.	s.	PROPN
ejpam-5823	375	2	a.	a.	PROPN
ejpam-5823	375	3	h.	h.	PROPN
ejpam-5823	375	4	shah	shah	PROPN
ejpam-5823	375	5	et	et	PROPN
ejpam-5823	375	6	al	al	PROPN
ejpam-5823	375	7	.	.	PUNCT
ejpam-5823	375	8	/	/	SYM
ejpam-5823	375	9	eur	eur	PROPN
ejpam-5823	375	10	.	.	PUNCT
ejpam-5823	376	1	j.	j.	PROPN
ejpam-5823	376	2	pure	pure	PROPN
ejpam-5823	376	3	appl	appl	PROPN
ejpam-5823	376	4	.	.	PROPN
ejpam-5823	376	5	math	math	PROPN
ejpam-5823	376	6	,	,	PUNCT
ejpam-5823	376	7	18	18	NUM
ejpam-5823	376	8	(	(	PUNCT
ejpam-5823	376	9	2	2	NUM
ejpam-5823	376	10	)	)	PUNCT
ejpam-5823	376	11	(	(	PUNCT
ejpam-5823	376	12	2025	2025	NUM
ejpam-5823	376	13	)	)	PUNCT
ejpam-5823	376	14	,	,	PUNCT
ejpam-5823	376	15	5823	5823	NUM
ejpam-5823	376	16	19	19	NUM
ejpam-5823	376	17	of	of	ADP
ejpam-5823	376	18	26	26	NUM
ejpam-5823	376	19	5	5	NUM
ejpam-5823	376	20	.	.	PUNCT
ejpam-5823	377	1	order	order	NOUN
ejpam-5823	377	2	of	of	ADP
ejpam-5823	377	3	starlikeness	starlikeness	NOUN
ejpam-5823	377	4	and	and	CCONJ
ejpam-5823	377	5	convexity	convexity	NOUN
ejpam-5823	377	6	by	by	ADP
ejpam-5823	377	7	silverman	silverman	PROPN
ejpam-5823	377	8	’s	’s	PART
ejpam-5823	377	9	theorem	theorem	NOUN
ejpam-5823	377	10	in	in	ADP
ejpam-5823	377	11	this	this	DET
ejpam-5823	377	12	section	section	NOUN
ejpam-5823	377	13	,	,	PUNCT
ejpam-5823	377	14	the	the	DET
ejpam-5823	377	15	theorem	theorem	NOUN
ejpam-5823	377	16	describes	describe	VERB
ejpam-5823	377	17	the	the	DET
ejpam-5823	377	18	sufficient	sufficient	ADJ
ejpam-5823	377	19	condition	condition	NOUN
ejpam-5823	377	20	for	for	ADP
ejpam-5823	377	21	starlikeness	starlikeness	NOUN
ejpam-5823	377	22	and	and	CCONJ
ejpam-5823	377	23	convexity	convexity	NOUN
ejpam-5823	377	24	of	of	ADP
ejpam-5823	377	25	order	order	NOUN
ejpam-5823	377	26	η	η	X
ejpam-5823	377	27	by	by	ADP
ejpam-5823	377	28	using	use	VERB
ejpam-5823	377	29	the	the	DET
ejpam-5823	377	30	lemma	lemma	PROPN
ejpam-5823	377	31	1	1	NUM
ejpam-5823	377	32	and	and	CCONJ
ejpam-5823	377	33	a	a	DET
ejpam-5823	377	34	result	result	NOUN
ejpam-5823	377	35	from	from	ADP
ejpam-5823	377	36	by	by	ADP
ejpam-5823	377	37	silverman	silverman	NOUN
ejpam-5823	377	38	(	(	PUNCT
ejpam-5823	377	39	[	[	X
ejpam-5823	377	40	27	27	NUM
ejpam-5823	377	41	]	]	PUNCT
ejpam-5823	377	42	,	,	PUNCT
ejpam-5823	377	43	theorem	theorem	VERB
ejpam-5823	377	44	1	1	NUM
ejpam-5823	377	45	)	)	PUNCT
ejpam-5823	377	46	.	.	PUNCT
ejpam-5823	378	1	theorem	theorem	NOUN
ejpam-5823	378	2	3	3	X
ejpam-5823	378	3	.	.	PUNCT
ejpam-5823	379	1	let	let	VERB
ejpam-5823	379	2	kxξ	kxξ	PROPN
ejpam-5823	379	3	,	,	PUNCT
ejpam-5823	379	4	b	b	X
ejpam-5823	379	5	=	=	PRON
ejpam-5823	379	6	(	(	PUNCT
ejpam-5823	379	7	1−	1−	NUM
ejpam-5823	379	8	|b|	|b|	VERB
ejpam-5823	379	9	4ξ	4ξ	NOUN
ejpam-5823	379	10	−	−	X
ejpam-5823	380	1	|b|2	|b|2	PROPN
ejpam-5823	380	2	32ξ(ξ	32ξ(ξ	NUM
ejpam-5823	380	3	+	+	CCONJ
ejpam-5823	380	4	k	k	X
ejpam-5823	380	5	)	)	PUNCT
ejpam-5823	381	1	−	−	NOUN
ejpam-5823	382	1	|b|3	|b|3	PROPN
ejpam-5823	382	2	16ξ(1	16ξ(1	NUM
ejpam-5823	382	3	+	+	CCONJ
ejpam-5823	382	4	√	√	NUM
ejpam-5823	382	5	2)(ξ	2)(ξ	NUM
ejpam-5823	382	6	+	+	CCONJ
ejpam-5823	382	7	√	√	PROPN
ejpam-5823	382	8	2k)(4ξ	2k)(4ξ	NOUN
ejpam-5823	383	1	+	+	CCONJ
ejpam-5823	383	2	4	4	NUM
ejpam-5823	383	3	√	√	NUM
ejpam-5823	383	4	2ξ	2ξ	NUM
ejpam-5823	383	5	+	+	CCONJ
ejpam-5823	383	6	4	4	NUM
ejpam-5823	383	7	√	√	NOUN
ejpam-5823	383	8	2k	2k	NOUN
ejpam-5823	383	9	+	+	CCONJ
ejpam-5823	383	10	8k	8k	PROPN
ejpam-5823	383	11	−	−	PROPN
ejpam-5823	383	12	|b|	|b|	PROPN
ejpam-5823	383	13	)	)	PUNCT
ejpam-5823	383	14	)	)	PUNCT
ejpam-5823	384	1	η	η	PROPN
ejpam-5823	384	2	+	+	PROPN
ejpam-5823	384	3	|b|	|b|	PROPN
ejpam-5823	384	4	2ξ	2ξ	NUM
ejpam-5823	384	5	+	+	CCONJ
ejpam-5823	384	6	3|b|2	3|b|2	NUM
ejpam-5823	384	7	32ξ(ξ	32ξ(ξ	NUM
ejpam-5823	384	8	+	+	CCONJ
ejpam-5823	384	9	k	k	X
ejpam-5823	384	10	)	)	PUNCT
ejpam-5823	385	1	+	+	CCONJ
ejpam-5823	385	2	3|b|3	3|b|3	NUM
ejpam-5823	385	3	64ξ(1	64ξ(1	NUM
ejpam-5823	385	4	+	+	CCONJ
ejpam-5823	385	5	√	√	NUM
ejpam-5823	385	6	2)(ξ	2)(ξ	NUM
ejpam-5823	385	7	+	+	CCONJ
ejpam-5823	385	8	√	√	PROPN
ejpam-5823	385	9	2k)(ξ	2k)(ξ	NUM
ejpam-5823	385	10	+	+	CCONJ
ejpam-5823	385	11	√	√	ADP
ejpam-5823	385	12	2ξ	2ξ	NUM
ejpam-5823	385	13	+	+	CCONJ
ejpam-5823	385	14	√	√	ADP
ejpam-5823	385	15	2k	2k	NOUN
ejpam-5823	385	16	+	+	CCONJ
ejpam-5823	385	17	2k	2k	NOUN
ejpam-5823	385	18	−	−	PROPN
ejpam-5823	385	19	|b|	|b|	PROPN
ejpam-5823	385	20	)	)	PUNCT
ejpam-5823	385	21	+	+	CCONJ
ejpam-5823	385	22	|b|3	|b|3	PROPN
ejpam-5823	385	23	16ξ(1	16ξ(1	NUM
ejpam-5823	385	24	+	+	CCONJ
ejpam-5823	385	25	√	√	NUM
ejpam-5823	385	26	2)(ξ	2)(ξ	NUM
ejpam-5823	385	27	+	+	CCONJ
ejpam-5823	385	28	√	√	PROPN
ejpam-5823	385	29	2k)(4ξ	2k)(4ξ	NOUN
ejpam-5823	386	1	+	+	CCONJ
ejpam-5823	386	2	4	4	NUM
ejpam-5823	386	3	√	√	NUM
ejpam-5823	386	4	2ξ	2ξ	NUM
ejpam-5823	386	5	+	+	CCONJ
ejpam-5823	386	6	4	4	NUM
ejpam-5823	386	7	√	√	NOUN
ejpam-5823	386	8	2k	2k	NOUN
ejpam-5823	386	9	+	+	CCONJ
ejpam-5823	386	10	8k	8k	PROPN
ejpam-5823	386	11	−	−	PROPN
ejpam-5823	386	12	|b|	|b|	PROPN
ejpam-5823	386	13	)	)	PUNCT
ejpam-5823	386	14	−	−	PROPN
ejpam-5823	386	15	1	1	NUM
ejpam-5823	386	16	where	where	SCONJ
ejpam-5823	386	17	ξ	ξ	X
ejpam-5823	386	18	>	>	SYM
ejpam-5823	386	19	2	2	NUM
ejpam-5823	386	20	and	and	CCONJ
ejpam-5823	386	21	b	b	PROPN
ejpam-5823	386	22	∈	∈	PROPN
ejpam-5823	386	23	c∗	c∗	NOUN
ejpam-5823	386	24	.	.	PUNCT
ejpam-5823	387	1	if	if	SCONJ
ejpam-5823	387	2	there	there	PRON
ejpam-5823	387	3	exists	exist	VERB
ejpam-5823	387	4	η	η	PROPN
ejpam-5823	387	5	<	<	X
ejpam-5823	387	6	1	1	NUM
ejpam-5823	387	7	such	such	ADJ
ejpam-5823	387	8	that	that	SCONJ
ejpam-5823	387	9	kxξ	kxξ	PROPN
ejpam-5823	387	10	,	,	PUNCT
ejpam-5823	387	11	b	b	PROPN
ejpam-5823	387	12	≤	≤	NUM
ejpam-5823	387	13	0	0	NUM
ejpam-5823	387	14	,	,	PUNCT
ejpam-5823	387	15	(	(	PUNCT
ejpam-5823	387	16	58	58	NUM
ejpam-5823	387	17	)	)	PUNCT
ejpam-5823	387	18	then	then	ADV
ejpam-5823	387	19	khξ	khξ	PROPN
ejpam-5823	387	20	,	,	PUNCT
ejpam-5823	387	21	b	b	PROPN
ejpam-5823	387	22	∈	∈	PROPN
ejpam-5823	387	23	s∗(η	s∗(η	PROPN
ejpam-5823	387	24	)	)	PUNCT
ejpam-5823	387	25	.	.	PUNCT
ejpam-5823	388	1	proof	proof	NOUN
ejpam-5823	388	2	.	.	PUNCT
ejpam-5823	389	1	from	from	ADP
ejpam-5823	389	2	silverman	silverman	PROPN
ejpam-5823	389	3	’s	’s	PART
ejpam-5823	389	4	[	[	X
ejpam-5823	389	5	27	27	NUM
ejpam-5823	389	6	]	]	X
ejpam-5823	389	7	well	well	ADV
ejpam-5823	389	8	-	-	PUNCT
ejpam-5823	389	9	known	know	VERB
ejpam-5823	389	10	result	result	NOUN
ejpam-5823	389	11	,	,	PUNCT
ejpam-5823	389	12	if	if	SCONJ
ejpam-5823	389	13	f	f	PROPN
ejpam-5823	389	14	is	be	AUX
ejpam-5823	389	15	in	in	ADP
ejpam-5823	389	16	form	form	NOUN
ejpam-5823	389	17	of	of	ADP
ejpam-5823	389	18	eq	eq	NOUN
ejpam-5823	389	19	.	.	PROPN
ejpam-5823	389	20	1	1	NUM
ejpam-5823	389	21	and	and	CCONJ
ejpam-5823	389	22	satisfies	satisfy	VERB
ejpam-5823	389	23	∞∑	∞∑	NUM
ejpam-5823	389	24	r=2	r=2	X
ejpam-5823	389	25	(	(	PUNCT
ejpam-5823	389	26	r	r	NOUN
ejpam-5823	389	27	−	−	PROPN
ejpam-5823	389	28	η)|fk|	η)|fk|	NOUN
ejpam-5823	389	29	≤	≤	PROPN
ejpam-5823	389	30	1−	1−	NUM
ejpam-5823	389	31	η	η	NOUN
ejpam-5823	389	32	,	,	PUNCT
ejpam-5823	389	33	then	then	ADV
ejpam-5823	389	34	f	f	PROPN
ejpam-5823	389	35	∈	∈	PROPN
ejpam-5823	389	36	s∗(η	s∗(η	PROPN
ejpam-5823	389	37	)	)	PUNCT
ejpam-5823	389	38	.	.	PUNCT
ejpam-5823	390	1	according	accord	VERB
ejpam-5823	390	2	to	to	ADP
ejpam-5823	390	3	eq	eq	PROPN
ejpam-5823	390	4	.	.	PROPN
ejpam-5823	390	5	9	9	NUM
ejpam-5823	390	6	,	,	PUNCT
ejpam-5823	390	7	it	it	PRON
ejpam-5823	390	8	is	be	AUX
ejpam-5823	390	9	sufficient	sufficient	ADJ
ejpam-5823	390	10	to	to	PART
ejpam-5823	390	11	show	show	VERB
ejpam-5823	390	12	:	:	PUNCT
ejpam-5823	390	13	b1	b1	NOUN
ejpam-5823	390	14	:	:	PUNCT
ejpam-5823	390	15	=	=	SYM
ejpam-5823	390	16	∞∑	∞∑	NUM
ejpam-5823	390	17	r=2	r=2	X
ejpam-5823	390	18	(	(	PUNCT
ejpam-5823	390	19	r	r	NOUN
ejpam-5823	390	20	−	−	PROPN
ejpam-5823	390	21	η	η	PROPN
ejpam-5823	390	22	)	)	PUNCT
ejpam-5823	390	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	390	24	(	(	PUNCT
ejpam-5823	390	25	−b)r−1	−b)r−1	PRON
ejpam-5823	390	26	4r−1(1)r−1,k(ξ)r−1,k	4r−1(1)r−1,k(ξ)r−1,k	PROPN
ejpam-5823	390	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	390	28	≤	≤	PROPN
ejpam-5823	390	29	1−	1−	NUM
ejpam-5823	390	30	η	η	PROPN
ejpam-5823	390	31	,	,	PUNCT
ejpam-5823	390	32	ξ	ξ	PROPN
ejpam-5823	390	33	>	>	X
ejpam-5823	390	34	0	0	NUM
ejpam-5823	390	35	,	,	PUNCT
ejpam-5823	390	36	b	b	X
ejpam-5823	390	37	∈	∈	PROPN
ejpam-5823	390	38	c∗	c∗	NOUN
ejpam-5823	390	39	=	=	PUNCT
ejpam-5823	391	1	∞∑	∞∑	NUM
ejpam-5823	391	2	r=2	r=2	X
ejpam-5823	391	3	(	(	PUNCT
ejpam-5823	391	4	r	r	NOUN
ejpam-5823	391	5	−	−	PROPN
ejpam-5823	391	6	η)|b|r−1	η)|b|r−1	X
ejpam-5823	391	7	4r−1(1)r−1,k(ξ)r−1,k	4r−1(1)r−1,k(ξ)r−1,k	NOUN
ejpam-5823	391	8	=	=	SYM
ejpam-5823	392	1	∞∑	∞∑	NUM
ejpam-5823	392	2	r=1	r=1	NOUN
ejpam-5823	392	3	(	(	PUNCT
ejpam-5823	392	4	r	r	NOUN
ejpam-5823	392	5	+	+	SYM
ejpam-5823	392	6	1−	1−	NUM
ejpam-5823	392	7	η)|b|r	η)|b|r	NUM
ejpam-5823	392	8	4r(1)r(ξ)r	4r(1)r(ξ)r	NUM
ejpam-5823	392	9	,	,	PUNCT
ejpam-5823	392	10	k	k	X
ejpam-5823	392	11	=	=	PUNCT
ejpam-5823	392	12	(	(	PUNCT
ejpam-5823	392	13	2−	2−	NUM
ejpam-5823	392	14	η)|b|	η)|b|	PROPN
ejpam-5823	392	15	4ξ	4ξ	NOUN
ejpam-5823	392	16	+	+	CCONJ
ejpam-5823	392	17	(	(	PUNCT
ejpam-5823	392	18	3−	3−	NUM
ejpam-5823	392	19	η)|b|2	η)|b|2	PROPN
ejpam-5823	392	20	8(ξ)2,k(1)2,k	8(ξ)2,k(1)2,k	NUM
ejpam-5823	392	21	+	+	CCONJ
ejpam-5823	392	22	∞∑	∞∑	PROPN
ejpam-5823	392	23	r=3	r=3	VERB
ejpam-5823	392	24	(	(	PUNCT
ejpam-5823	392	25	1−	1−	NUM
ejpam-5823	392	26	η)|b|r	η)|b|r	NUM
ejpam-5823	392	27	4r(1)r	4r(1)r	PROPN
ejpam-5823	392	28	,	,	PUNCT
ejpam-5823	392	29	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	392	30	,	,	PUNCT
ejpam-5823	392	31	k	k	PROPN
ejpam-5823	392	32	+	+	CCONJ
ejpam-5823	392	33	∞∑	∞∑	PROPN
ejpam-5823	392	34	r=3	r=3	PUNCT
ejpam-5823	392	35	(	(	PUNCT
ejpam-5823	392	36	r)|b|r	r)|b|r	PROPN
ejpam-5823	392	37	4r(1)r	4r(1)r	PROPN
ejpam-5823	392	38	,	,	PUNCT
ejpam-5823	392	39	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	392	40	,	,	PUNCT
ejpam-5823	392	41	k	k	PROPN
ejpam-5823	392	42	=	=	PUNCT
ejpam-5823	392	43	(	(	PUNCT
ejpam-5823	392	44	2−	2−	NUM
ejpam-5823	392	45	η)|b|	η)|b|	PROPN
ejpam-5823	392	46	4ξ	4ξ	NOUN
ejpam-5823	392	47	+	+	CCONJ
ejpam-5823	392	48	(	(	PUNCT
ejpam-5823	392	49	3−	3−	NUM
ejpam-5823	392	50	η)|b|2	η)|b|2	PROPN
ejpam-5823	392	51	8(ξ)2,k(1)2,k	8(ξ)2,k(1)2,k	NUM
ejpam-5823	392	52	+	+	CCONJ
ejpam-5823	392	53	(	(	PUNCT
ejpam-5823	392	54	1−	1−	NUM
ejpam-5823	392	55	η	η	NOUN
ejpam-5823	392	56	)	)	PUNCT
ejpam-5823	392	57	∞∑	∞∑	PROPN
ejpam-5823	392	58	r=3	r=3	PROPN
ejpam-5823	392	59	|b|r	|b|r	PROPN
ejpam-5823	392	60	4r(1)r	4r(1)r	PROPN
ejpam-5823	392	61	,	,	PUNCT
ejpam-5823	392	62	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	392	63	,	,	PUNCT
ejpam-5823	392	64	k	k	PROPN
ejpam-5823	392	65	+	+	CCONJ
ejpam-5823	392	66	∞∑	∞∑	PROPN
ejpam-5823	392	67	r=3	r=3	PUNCT
ejpam-5823	392	68	(	(	PUNCT
ejpam-5823	392	69	r)|b|r	r)|b|r	PROPN
ejpam-5823	392	70	4r(1)r	4r(1)r	PROPN
ejpam-5823	392	71	,	,	PUNCT
ejpam-5823	392	72	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	392	73	,	,	PUNCT
ejpam-5823	392	74	k	k	PROPN
ejpam-5823	392	75	.	.	PUNCT
ejpam-5823	393	1	by	by	ADP
ejpam-5823	393	2	simple	simple	ADJ
ejpam-5823	393	3	mathematical	mathematical	ADJ
ejpam-5823	393	4	induction	induction	NOUN
ejpam-5823	393	5	,	,	PUNCT
ejpam-5823	393	6	we	we	PRON
ejpam-5823	393	7	have	have	VERB
ejpam-5823	393	8	r	r	NOUN
ejpam-5823	393	9	≤	≤	NUM
ejpam-5823	393	10	(	(	PUNCT
ejpam-5823	393	11	3	3	NUM
ejpam-5823	393	12	64	64	NUM
ejpam-5823	393	13	)	)	PUNCT
ejpam-5823	393	14	4r	4r	NOUN
ejpam-5823	393	15	for	for	ADP
ejpam-5823	393	16	all	all	DET
ejpam-5823	393	17	r	r	NOUN
ejpam-5823	393	18	∈	∈	NOUN
ejpam-5823	393	19	n\[1	n\[1	NOUN
ejpam-5823	393	20	,	,	PUNCT
ejpam-5823	393	21	2	2	NUM
ejpam-5823	393	22	]	]	PUNCT
ejpam-5823	393	23	.	.	PUNCT
ejpam-5823	394	1	by	by	ADP
ejpam-5823	394	2	using	use	VERB
ejpam-5823	394	3	lemma	lemma	PROPN
ejpam-5823	394	4	,	,	PUNCT
ejpam-5823	394	5	we	we	PRON
ejpam-5823	394	6	have	have	VERB
ejpam-5823	394	7	(	(	PUNCT
ejpam-5823	394	8	1)r	1)r	NUM
ejpam-5823	394	9	,	,	PUNCT
ejpam-5823	394	10	k	k	X
ejpam-5823	394	11	>	>	X
ejpam-5823	394	12	(	(	PUNCT
ejpam-5823	394	13	1	1	NUM
ejpam-5823	394	14	+	+	NUM
ejpam-5823	394	15	β)r−1	β)r−1	NOUN
ejpam-5823	394	16	,	,	PUNCT
ejpam-5823	394	17	r	r	NOUN
ejpam-5823	394	18	∈	∈	PROPN
ejpam-5823	394	19	n\[1	n\[1	NOUN
ejpam-5823	394	20	,	,	PUNCT
ejpam-5823	394	21	2	2	NUM
ejpam-5823	394	22	]	]	PUNCT
ejpam-5823	394	23	,	,	PUNCT
ejpam-5823	394	24	0	0	NUM
ejpam-5823	394	25	≤	≤	NUM
ejpam-5823	394	26	β	β	X
ejpam-5823	394	27	≤	≤	NUM
ejpam-5823	394	28	√	√	ADP
ejpam-5823	394	29	2	2	NUM
ejpam-5823	394	30	.	.	PUNCT
ejpam-5823	395	1	since	since	SCONJ
ejpam-5823	395	2	max(1	max(1	NOUN
ejpam-5823	395	3	+	+	CCONJ
ejpam-5823	395	4	β)r−1	β)r−1	PROPN
ejpam-5823	395	5	:	:	PUNCT
ejpam-5823	395	6	0	0	NUM
ejpam-5823	395	7	≤	≤	NUM
ejpam-5823	395	8	β	β	X
ejpam-5823	395	9	≤	≤	NUM
ejpam-5823	395	10	√	√	ADV
ejpam-5823	395	11	2	2	NUM
ejpam-5823	395	12	=	=	SYM
ejpam-5823	395	13	(	(	PUNCT
ejpam-5823	395	14	1	1	NUM
ejpam-5823	395	15	+	+	CCONJ
ejpam-5823	395	16	√	√	PROPN
ejpam-5823	395	17	2)r−1	2)r−1	NUM
ejpam-5823	395	18	s.	s.	PROPN
ejpam-5823	395	19	a.	a.	PROPN
ejpam-5823	395	20	h.	h.	PROPN
ejpam-5823	395	21	shah	shah	PROPN
ejpam-5823	395	22	et	et	PROPN
ejpam-5823	395	23	al	al	PROPN
ejpam-5823	395	24	.	.	PUNCT
ejpam-5823	395	25	/	/	SYM
ejpam-5823	395	26	eur	eur	PROPN
ejpam-5823	395	27	.	.	PUNCT
ejpam-5823	396	1	j.	j.	PROPN
ejpam-5823	396	2	pure	pure	PROPN
ejpam-5823	396	3	appl	appl	PROPN
ejpam-5823	396	4	.	.	PROPN
ejpam-5823	396	5	math	math	PROPN
ejpam-5823	396	6	,	,	PUNCT
ejpam-5823	396	7	18	18	NUM
ejpam-5823	396	8	(	(	PUNCT
ejpam-5823	396	9	2	2	NUM
ejpam-5823	396	10	)	)	PUNCT
ejpam-5823	396	11	(	(	PUNCT
ejpam-5823	396	12	2025	2025	NUM
ejpam-5823	396	13	)	)	PUNCT
ejpam-5823	396	14	,	,	PUNCT
ejpam-5823	396	15	5823	5823	NUM
ejpam-5823	396	16	20	20	NUM
ejpam-5823	396	17	of	of	ADP
ejpam-5823	396	18	26	26	NUM
ejpam-5823	396	19	follows	follow	VERB
ejpam-5823	396	20	that	that	PRON
ejpam-5823	396	21	:	:	PUNCT
ejpam-5823	396	22	(	(	PUNCT
ejpam-5823	396	23	ξ)r	ξ)r	NOUN
ejpam-5823	396	24	,	,	PUNCT
ejpam-5823	396	25	k	k	PROPN
ejpam-5823	396	26	≥	≥	X
ejpam-5823	396	27	ξ(ξ	ξ(ξ	PROPN
ejpam-5823	396	28	+	+	CCONJ
ejpam-5823	396	29	√	√	NUM
ejpam-5823	396	30	2)r−1	2)r−1	NUM
ejpam-5823	396	31	,	,	PUNCT
ejpam-5823	396	32	ξ	ξ	PROPN
ejpam-5823	396	33	>	>	X
ejpam-5823	396	34	0	0	NUM
ejpam-5823	396	35	.	.	PUNCT
ejpam-5823	397	1	(	(	PUNCT
ejpam-5823	397	2	59	59	NUM
ejpam-5823	397	3	)	)	PUNCT
ejpam-5823	397	4	as	as	ADP
ejpam-5823	397	5	by	by	ADP
ejpam-5823	397	6	eq	eq	NOUN
ejpam-5823	397	7	.	.	PROPN
ejpam-5823	397	8	58	58	NUM
ejpam-5823	397	9	,	,	PUNCT
ejpam-5823	397	10	kxξ	kxξ	PROPN
ejpam-5823	397	11	,	,	PUNCT
ejpam-5823	397	12	b(η	b(η	NOUN
ejpam-5823	397	13	)	)	PUNCT
ejpam-5823	397	14	≤	≤	NOUN
ejpam-5823	397	15	0	0	NUM
ejpam-5823	397	16	,	,	PUNCT
ejpam-5823	397	17	we	we	PRON
ejpam-5823	397	18	have	have	VERB
ejpam-5823	397	19	b1	b1	NOUN
ejpam-5823	397	20	≤	≤	NOUN
ejpam-5823	397	21	(	(	PUNCT
ejpam-5823	397	22	2−	2−	NUM
ejpam-5823	397	23	η)|b|	η)|b|	PROPN
ejpam-5823	397	24	4ξ	4ξ	NOUN
ejpam-5823	397	25	+	+	CCONJ
ejpam-5823	397	26	(	(	PUNCT
ejpam-5823	397	27	3−	3−	NUM
ejpam-5823	397	28	η)|b|2	η)|b|2	PROPN
ejpam-5823	397	29	32ξ(ξ	32ξ(ξ	PROPN
ejpam-5823	397	30	+	+	CCONJ
ejpam-5823	397	31	k	k	X
ejpam-5823	397	32	)	)	PUNCT
ejpam-5823	398	1	+	+	CCONJ
ejpam-5823	398	2	3|b|	3|b|	NUM
ejpam-5823	398	3	64ξ	64ξ	NUM
ejpam-5823	399	1	∞∑	∞∑	NUM
ejpam-5823	399	2	r=3	r=3	ADJ
ejpam-5823	399	3	|b|r−1	|b|r−1	X
ejpam-5823	399	4	(	(	PUNCT
ejpam-5823	399	5	1	1	NUM
ejpam-5823	399	6	+	+	CCONJ
ejpam-5823	399	7	√	√	NUM
ejpam-5823	399	8	2)r−1(ξ	2)r−1(ξ	NUM
ejpam-5823	399	9	+	+	CCONJ
ejpam-5823	399	10	√	√	PROPN
ejpam-5823	399	11	2k)r−1	2k)r−1	NUM
ejpam-5823	399	12	+	+	CCONJ
ejpam-5823	399	13	(	(	PUNCT
ejpam-5823	399	14	1−	1−	NUM
ejpam-5823	399	15	η)|b|	η)|b|	PROPN
ejpam-5823	399	16	4ξ	4ξ	NOUN
ejpam-5823	399	17	∞∑	∞∑	PROPN
ejpam-5823	399	18	r=3	r=3	PROPN
ejpam-5823	399	19	|b|r−1	|b|r−1	X
ejpam-5823	399	20	4r−1(1	4r−1(1	NUM
ejpam-5823	399	21	+	+	NOUN
ejpam-5823	399	22	√	√	NUM
ejpam-5823	399	23	2)r−1(ξ	2)r−1(ξ	NUM
ejpam-5823	399	24	+	+	CCONJ
ejpam-5823	399	25	√	√	PROPN
ejpam-5823	399	26	2k)r−1	2k)r−1	PROPN
ejpam-5823	399	27	.	.	PUNCT
ejpam-5823	400	1	after	after	ADP
ejpam-5823	400	2	simplifications	simplification	NOUN
ejpam-5823	400	3	,	,	PUNCT
ejpam-5823	400	4	we	we	PRON
ejpam-5823	400	5	get	get	VERB
ejpam-5823	400	6	:	:	PUNCT
ejpam-5823	400	7	b1	b1	NOUN
ejpam-5823	400	8	=	=	PUNCT
ejpam-5823	400	9	(	(	PUNCT
ejpam-5823	400	10	2−	2−	NUM
ejpam-5823	400	11	η)|b|	η)|b|	PROPN
ejpam-5823	400	12	4ξ	4ξ	NOUN
ejpam-5823	400	13	+	+	CCONJ
ejpam-5823	400	14	(	(	PUNCT
ejpam-5823	400	15	3−	3−	NUM
ejpam-5823	400	16	η)|b|2	η)|b|2	PROPN
ejpam-5823	400	17	32ξ(ξ	32ξ(ξ	PROPN
ejpam-5823	400	18	+	+	CCONJ
ejpam-5823	400	19	k	k	X
ejpam-5823	400	20	)	)	PUNCT
ejpam-5823	401	1	+	+	CCONJ
ejpam-5823	401	2	3|b|3	3|b|3	NUM
ejpam-5823	401	3	64ξ(1	64ξ(1	NUM
ejpam-5823	401	4	+	+	CCONJ
ejpam-5823	401	5	√	√	NUM
ejpam-5823	401	6	2)(ξ	2)(ξ	NUM
ejpam-5823	401	7	+	+	CCONJ
ejpam-5823	401	8	√	√	PROPN
ejpam-5823	401	9	2k)((1	2k)((1	NUM
ejpam-5823	401	10	+	+	CCONJ
ejpam-5823	401	11	√	√	NUM
ejpam-5823	401	12	2)(ξ	2)(ξ	NUM
ejpam-5823	401	13	+	+	CCONJ
ejpam-5823	401	14	√	√	PROPN
ejpam-5823	401	15	2k)−	2k)−	NUM
ejpam-5823	401	16	|b|	|b|	PROPN
ejpam-5823	401	17	)	)	PUNCT
ejpam-5823	401	18	+	+	CCONJ
ejpam-5823	401	19	(	(	PUNCT
ejpam-5823	401	20	1−	1−	NUM
ejpam-5823	401	21	η)|b|3	η)|b|3	X
ejpam-5823	401	22	16ξ(1	16ξ(1	NUM
ejpam-5823	401	23	+	+	CCONJ
ejpam-5823	401	24	√	√	NUM
ejpam-5823	401	25	2)(ξ	2)(ξ	NUM
ejpam-5823	401	26	+	+	CCONJ
ejpam-5823	401	27	√	√	ADV
ejpam-5823	401	28	2k)(4(1	2k)(4(1	NUM
ejpam-5823	401	29	+	+	CCONJ
ejpam-5823	401	30	√	√	NUM
ejpam-5823	401	31	2)(ξ	2)(ξ	NUM
ejpam-5823	401	32	+	+	CCONJ
ejpam-5823	401	33	√	√	PROPN
ejpam-5823	401	34	2k)−	2k)−	NUM
ejpam-5823	401	35	|b|	|b|	PROPN
ejpam-5823	401	36	)	)	PUNCT
ejpam-5823	401	37	=	=	PUNCT
ejpam-5823	401	38	(	(	PUNCT
ejpam-5823	401	39	2−	2−	NUM
ejpam-5823	401	40	η)|b|	η)|b|	PROPN
ejpam-5823	401	41	4ξ	4ξ	NOUN
ejpam-5823	401	42	+	+	CCONJ
ejpam-5823	401	43	(	(	PUNCT
ejpam-5823	401	44	3−	3−	NUM
ejpam-5823	401	45	η)|b|2	η)|b|2	PROPN
ejpam-5823	401	46	32ξ(ξ	32ξ(ξ	PROPN
ejpam-5823	401	47	+	+	CCONJ
ejpam-5823	401	48	k	k	X
ejpam-5823	401	49	)	)	PUNCT
ejpam-5823	402	1	+	+	CCONJ
ejpam-5823	402	2	3|b|3	3|b|3	NUM
ejpam-5823	402	3	64ξ(1	64ξ(1	NUM
ejpam-5823	402	4	+	+	CCONJ
ejpam-5823	402	5	√	√	NUM
ejpam-5823	402	6	2)(ξ	2)(ξ	NUM
ejpam-5823	402	7	+	+	CCONJ
ejpam-5823	402	8	√	√	PROPN
ejpam-5823	402	9	2k)(ξ	2k)(ξ	NUM
ejpam-5823	402	10	+	+	SYM
ejpam-5823	402	11	ξ	ξ	NOUN
ejpam-5823	402	12	√	√	NUM
ejpam-5823	402	13	2	2	NUM
ejpam-5823	402	14	+	+	CCONJ
ejpam-5823	402	15	√	√	NOUN
ejpam-5823	402	16	2k	2k	NOUN
ejpam-5823	402	17	+	+	CCONJ
ejpam-5823	402	18	2k	2k	NOUN
ejpam-5823	402	19	−	−	PROPN
ejpam-5823	402	20	|b|	|b|	PROPN
ejpam-5823	402	21	)	)	PUNCT
ejpam-5823	402	22	+	+	CCONJ
ejpam-5823	402	23	(	(	PUNCT
ejpam-5823	402	24	1−	1−	NUM
ejpam-5823	402	25	η)|b|3	η)|b|3	X
ejpam-5823	402	26	16ξ(1	16ξ(1	NUM
ejpam-5823	402	27	+	+	CCONJ
ejpam-5823	402	28	√	√	NUM
ejpam-5823	402	29	2)(ξ	2)(ξ	NUM
ejpam-5823	402	30	+	+	CCONJ
ejpam-5823	402	31	√	√	PROPN
ejpam-5823	402	32	2k)(4ξ	2k)(4ξ	NOUN
ejpam-5823	402	33	+	+	CCONJ
ejpam-5823	402	34	4	4	NUM
ejpam-5823	402	35	√	√	NUM
ejpam-5823	402	36	2ξ	2ξ	NUM
ejpam-5823	402	37	+	+	CCONJ
ejpam-5823	402	38	4	4	NUM
ejpam-5823	402	39	√	√	NOUN
ejpam-5823	402	40	2k	2k	NOUN
ejpam-5823	402	41	+	+	CCONJ
ejpam-5823	402	42	8k	8k	PROPN
ejpam-5823	402	43	−	−	PROPN
ejpam-5823	402	44	|b|	|b|	PROPN
ejpam-5823	402	45	)	)	PUNCT
ejpam-5823	402	46	≤	≤	NOUN
ejpam-5823	402	47	1−	1−	NUM
ejpam-5823	402	48	η	η	PROPN
ejpam-5823	402	49	.	.	PROPN
ejpam-5823	402	50	(	(	PUNCT
ejpam-5823	402	51	60	60	NUM
ejpam-5823	402	52	)	)	PUNCT
ejpam-5823	402	53	this	this	PRON
ejpam-5823	402	54	completes	complete	VERB
ejpam-5823	402	55	the	the	DET
ejpam-5823	402	56	proof	proof	NOUN
ejpam-5823	402	57	.	.	PUNCT
ejpam-5823	403	1	example	example	NOUN
ejpam-5823	404	1	3	3	NUM
ejpam-5823	404	2	.	.	PUNCT
ejpam-5823	405	1	some	some	DET
ejpam-5823	405	2	special	special	ADJ
ejpam-5823	405	3	cases	case	NOUN
ejpam-5823	405	4	of	of	ADP
ejpam-5823	405	5	theorem	theorem	NOUN
ejpam-5823	405	6	3	3	NUM
ejpam-5823	405	7	gives	give	VERB
ejpam-5823	405	8	the	the	DET
ejpam-5823	405	9	following	follow	VERB
ejpam-5823	405	10	different	different	ADJ
ejpam-5823	405	11	situations	situation	NOUN
ejpam-5823	405	12	:	:	PUNCT
ejpam-5823	405	13	case-1	case-1	NOUN
ejpam-5823	405	14	for	for	ADP
ejpam-5823	405	15	b	b	NOUN
ejpam-5823	405	16	=	=	SYM
ejpam-5823	405	17	0.1	0.1	NUM
ejpam-5823	405	18	,	,	PUNCT
ejpam-5823	405	19	η	η	X
ejpam-5823	405	20	=	=	SYM
ejpam-5823	405	21	0.1	0.1	NUM
ejpam-5823	405	22	and	and	CCONJ
ejpam-5823	405	23	ξ	ξ	X
ejpam-5823	405	24	=	=	SYM
ejpam-5823	405	25	2.05166	2.05166	NUM
ejpam-5823	405	26	.	.	PUNCT
ejpam-5823	406	1	(	(	PUNCT
ejpam-5823	406	2	k	k	X
ejpam-5823	406	3	)	)	PUNCT
ejpam-5823	406	4	0.8h2.05166,0.1	0.8h2.05166,0.1	NOUN
ejpam-5823	406	5	(	(	PUNCT
ejpam-5823	406	6	l	l	NOUN
ejpam-5823	406	7	)	)	PUNCT
ejpam-5823	406	8	0.9h2.05166,0.1	0.9h2.05166,0.1	NOUN
ejpam-5823	406	9	this	this	PRON
ejpam-5823	406	10	shows	show	VERB
ejpam-5823	406	11	that	that	SCONJ
ejpam-5823	406	12	the	the	DET
ejpam-5823	406	13	behaviour	behaviour	NOUN
ejpam-5823	406	14	of	of	ADP
ejpam-5823	406	15	the	the	DET
ejpam-5823	406	16	graph	graph	NOUN
ejpam-5823	406	17	is	be	AUX
ejpam-5823	406	18	same	same	ADJ
ejpam-5823	406	19	whether	whether	SCONJ
ejpam-5823	406	20	we	we	PRON
ejpam-5823	406	21	change	change	VERB
ejpam-5823	406	22	the	the	DET
ejpam-5823	406	23	values	value	NOUN
ejpam-5823	406	24	of	of	ADP
ejpam-5823	406	25	k.	k.	NOUN
ejpam-5823	406	26	exactly	exactly	ADV
ejpam-5823	406	27	at	at	ADP
ejpam-5823	406	28	k	k	PROPN
ejpam-5823	406	29	=	=	SYM
ejpam-5823	406	30	1	1	NUM
ejpam-5823	406	31	,	,	PUNCT
ejpam-5823	406	32	the	the	DET
ejpam-5823	406	33	conditions	condition	NOUN
ejpam-5823	406	34	and	and	CCONJ
ejpam-5823	406	35	graph	graph	NOUN
ejpam-5823	406	36	approaches	approach	NOUN
ejpam-5823	406	37	to	to	ADP
ejpam-5823	406	38	classical	classical	ADJ
ejpam-5823	406	39	form	form	NOUN
ejpam-5823	406	40	which	which	PRON
ejpam-5823	406	41	gives	give	VERB
ejpam-5823	406	42	the	the	DET
ejpam-5823	406	43	accuracy	accuracy	NOUN
ejpam-5823	406	44	of	of	ADP
ejpam-5823	406	45	our	our	PRON
ejpam-5823	406	46	results	result	NOUN
ejpam-5823	406	47	.	.	PUNCT
ejpam-5823	407	1	s.	s.	PROPN
ejpam-5823	407	2	a.	a.	PROPN
ejpam-5823	407	3	h.	h.	PROPN
ejpam-5823	407	4	shah	shah	PROPN
ejpam-5823	407	5	et	et	PROPN
ejpam-5823	407	6	al	al	PROPN
ejpam-5823	407	7	.	.	PUNCT
ejpam-5823	407	8	/	/	SYM
ejpam-5823	407	9	eur	eur	PROPN
ejpam-5823	407	10	.	.	PUNCT
ejpam-5823	408	1	j.	j.	PROPN
ejpam-5823	408	2	pure	pure	PROPN
ejpam-5823	408	3	appl	appl	PROPN
ejpam-5823	408	4	.	.	PROPN
ejpam-5823	408	5	math	math	PROPN
ejpam-5823	408	6	,	,	PUNCT
ejpam-5823	408	7	18	18	NUM
ejpam-5823	408	8	(	(	PUNCT
ejpam-5823	408	9	2	2	NUM
ejpam-5823	408	10	)	)	PUNCT
ejpam-5823	408	11	(	(	PUNCT
ejpam-5823	408	12	2025	2025	NUM
ejpam-5823	408	13	)	)	PUNCT
ejpam-5823	408	14	,	,	PUNCT
ejpam-5823	408	15	5823	5823	NUM
ejpam-5823	408	16	21	21	NUM
ejpam-5823	408	17	of	of	ADP
ejpam-5823	408	18	26	26	NUM
ejpam-5823	408	19	case-2	case-2	NUM
ejpam-5823	408	20	for	for	ADP
ejpam-5823	408	21	b	b	NOUN
ejpam-5823	408	22	=	=	SYM
ejpam-5823	408	23	1.2	1.2	NUM
ejpam-5823	408	24	,	,	PUNCT
ejpam-5823	408	25	η	η	PROPN
ejpam-5823	408	26	=	=	PROPN
ejpam-5823	408	27	0.2	0.2	NUM
ejpam-5823	408	28	and	and	CCONJ
ejpam-5823	408	29	ξ	ξ	X
ejpam-5823	408	30	=	=	SYM
ejpam-5823	408	31	2.8566	2.8566	NUM
ejpam-5823	408	32	.	.	PUNCT
ejpam-5823	409	1	(	(	PUNCT
ejpam-5823	409	2	m	m	NOUN
ejpam-5823	409	3	)	)	PUNCT
ejpam-5823	409	4	0.8h2.8566,1.2	0.8h2.8566,1.2	NOUN
ejpam-5823	409	5	(	(	PUNCT
ejpam-5823	409	6	n	n	CCONJ
ejpam-5823	409	7	)	)	PUNCT
ejpam-5823	409	8	0.9h2.8566,1.2	0.9h2.8566,1.2	NOUN
ejpam-5823	409	9	this	this	PRON
ejpam-5823	409	10	shows	show	VERB
ejpam-5823	409	11	that	that	SCONJ
ejpam-5823	409	12	the	the	DET
ejpam-5823	409	13	behaviour	behaviour	NOUN
ejpam-5823	409	14	of	of	ADP
ejpam-5823	409	15	the	the	DET
ejpam-5823	409	16	graph	graph	NOUN
ejpam-5823	409	17	is	be	AUX
ejpam-5823	409	18	same	same	ADJ
ejpam-5823	409	19	whether	whether	SCONJ
ejpam-5823	409	20	we	we	PRON
ejpam-5823	409	21	change	change	VERB
ejpam-5823	409	22	the	the	DET
ejpam-5823	409	23	values	value	NOUN
ejpam-5823	409	24	of	of	ADP
ejpam-5823	409	25	k.	k.	NOUN
ejpam-5823	409	26	exactly	exactly	ADV
ejpam-5823	409	27	at	at	ADP
ejpam-5823	409	28	k	k	PROPN
ejpam-5823	409	29	=	=	SYM
ejpam-5823	409	30	1	1	NUM
ejpam-5823	409	31	,	,	PUNCT
ejpam-5823	409	32	the	the	DET
ejpam-5823	409	33	conditions	condition	NOUN
ejpam-5823	409	34	and	and	CCONJ
ejpam-5823	409	35	graph	graph	NOUN
ejpam-5823	409	36	approaches	approach	NOUN
ejpam-5823	409	37	to	to	ADP
ejpam-5823	409	38	classical	classical	ADJ
ejpam-5823	409	39	form	form	NOUN
ejpam-5823	409	40	which	which	PRON
ejpam-5823	409	41	gives	give	VERB
ejpam-5823	409	42	the	the	DET
ejpam-5823	409	43	accuracy	accuracy	NOUN
ejpam-5823	409	44	of	of	ADP
ejpam-5823	409	45	our	our	PRON
ejpam-5823	409	46	results	result	NOUN
ejpam-5823	409	47	.	.	PUNCT
ejpam-5823	410	1	theorem	theorem	ADJ
ejpam-5823	410	2	4	4	NUM
ejpam-5823	410	3	.	.	PUNCT
ejpam-5823	411	1	let	let	VERB
ejpam-5823	411	2	kyξ	kyξ	NOUN
ejpam-5823	411	3	,	,	PUNCT
ejpam-5823	411	4	b	b	X
ejpam-5823	411	5	=	=	SYM
ejpam-5823	411	6	(	(	PUNCT
ejpam-5823	411	7	1−	1−	NUM
ejpam-5823	411	8	|b|	|b|	VERB
ejpam-5823	411	9	2ξ	2ξ	NUM
ejpam-5823	411	10	−	−	PROPN
ejpam-5823	411	11	3|b|2	3|b|2	NUM
ejpam-5823	412	1	32ξ(ξ	32ξ(ξ	NUM
ejpam-5823	412	2	+	+	CCONJ
ejpam-5823	412	3	k	k	X
ejpam-5823	412	4	)	)	PUNCT
ejpam-5823	412	5	−	−	NOUN
ejpam-5823	413	1	3|b|3	3|b|3	NUM
ejpam-5823	413	2	64ξ(1	64ξ(1	NUM
ejpam-5823	413	3	+	+	CCONJ
ejpam-5823	413	4	√	√	NUM
ejpam-5823	413	5	2)(ξ	2)(ξ	NUM
ejpam-5823	413	6	+	+	CCONJ
ejpam-5823	413	7	√	√	PROPN
ejpam-5823	413	8	2k)(ξ	2k)(ξ	NUM
ejpam-5823	413	9	+	+	CCONJ
ejpam-5823	413	10	√	√	ADP
ejpam-5823	413	11	2ξ	2ξ	NUM
ejpam-5823	413	12	+	+	CCONJ
ejpam-5823	414	1	√	√	ADP
ejpam-5823	414	2	2k	2k	NOUN
ejpam-5823	414	3	+	+	CCONJ
ejpam-5823	414	4	2k	2k	NOUN
ejpam-5823	414	5	−	−	PROPN
ejpam-5823	414	6	|b|	|b|	PROPN
ejpam-5823	414	7	)	)	PUNCT
ejpam-5823	414	8	−	−	NOUN
ejpam-5823	414	9	|b|3	|b|3	PROPN
ejpam-5823	414	10	16ξ(1	16ξ(1	NUM
ejpam-5823	414	11	+	+	CCONJ
ejpam-5823	414	12	√	√	NUM
ejpam-5823	414	13	2)(ξ	2)(ξ	NUM
ejpam-5823	414	14	+	+	CCONJ
ejpam-5823	414	15	√	√	PROPN
ejpam-5823	414	16	2k)(4ξ	2k)(4ξ	NOUN
ejpam-5823	415	1	+	+	CCONJ
ejpam-5823	415	2	4	4	NUM
ejpam-5823	415	3	√	√	NUM
ejpam-5823	415	4	2ξ	2ξ	NUM
ejpam-5823	415	5	+	+	CCONJ
ejpam-5823	415	6	4	4	NUM
ejpam-5823	415	7	√	√	NOUN
ejpam-5823	415	8	2k	2k	NOUN
ejpam-5823	415	9	+	+	CCONJ
ejpam-5823	415	10	8k	8k	PROPN
ejpam-5823	415	11	−	−	PROPN
ejpam-5823	415	12	|b|	|b|	PROPN
ejpam-5823	415	13	)	)	PUNCT
ejpam-5823	415	14	)	)	PUNCT
ejpam-5823	416	1	η	η	PROPN
ejpam-5823	417	1	+	+	PROPN
ejpam-5823	417	2	|b|	|b|	PROPN
ejpam-5823	417	3	ξ	ξ	PROPN
ejpam-5823	417	4	+	+	NOUN
ejpam-5823	417	5	9|b|2	9|b|2	NUM
ejpam-5823	418	1	32ξ(ξ	32ξ(ξ	NUM
ejpam-5823	418	2	+	+	CCONJ
ejpam-5823	418	3	k	k	X
ejpam-5823	418	4	)	)	PUNCT
ejpam-5823	419	1	+	+	CCONJ
ejpam-5823	419	2	15|b|3	15|b|3	NUM
ejpam-5823	419	3	64ξ(1	64ξ(1	NUM
ejpam-5823	419	4	+	+	CCONJ
ejpam-5823	419	5	√	√	NUM
ejpam-5823	419	6	2)(ξ	2)(ξ	NUM
ejpam-5823	419	7	+	+	CCONJ
ejpam-5823	419	8	√	√	PROPN
ejpam-5823	419	9	2k)(ξ	2k)(ξ	NUM
ejpam-5823	419	10	+	+	CCONJ
ejpam-5823	419	11	√	√	ADP
ejpam-5823	419	12	2ξ	2ξ	NUM
ejpam-5823	419	13	+	+	CCONJ
ejpam-5823	419	14	√	√	ADP
ejpam-5823	419	15	2k	2k	NOUN
ejpam-5823	419	16	+	+	CCONJ
ejpam-5823	419	17	2k	2k	NOUN
ejpam-5823	419	18	−	−	PROPN
ejpam-5823	419	19	|b|	|b|	PROPN
ejpam-5823	419	20	)	)	PUNCT
ejpam-5823	419	21	+	+	CCONJ
ejpam-5823	419	22	|b|3	|b|3	PROPN
ejpam-5823	419	23	16ξ(1	16ξ(1	NUM
ejpam-5823	419	24	+	+	CCONJ
ejpam-5823	419	25	√	√	NUM
ejpam-5823	419	26	2)(ξ	2)(ξ	NUM
ejpam-5823	419	27	+	+	CCONJ
ejpam-5823	419	28	√	√	PROPN
ejpam-5823	419	29	2k)(4ξ	2k)(4ξ	NOUN
ejpam-5823	420	1	+	+	CCONJ
ejpam-5823	420	2	4	4	NUM
ejpam-5823	420	3	√	√	NUM
ejpam-5823	420	4	2ξ	2ξ	NUM
ejpam-5823	420	5	+	+	CCONJ
ejpam-5823	420	6	4	4	NUM
ejpam-5823	420	7	√	√	NOUN
ejpam-5823	420	8	2k	2k	NOUN
ejpam-5823	420	9	+	+	CCONJ
ejpam-5823	420	10	8k	8k	PROPN
ejpam-5823	420	11	−	−	PROPN
ejpam-5823	420	12	|b|	|b|	PROPN
ejpam-5823	420	13	)	)	PUNCT
ejpam-5823	420	14	−	−	PROPN
ejpam-5823	420	15	1	1	NUM
ejpam-5823	420	16	where	where	SCONJ
ejpam-5823	420	17	ξ	ξ	X
ejpam-5823	420	18	>	>	SYM
ejpam-5823	420	19	3	3	NUM
ejpam-5823	420	20	and	and	CCONJ
ejpam-5823	420	21	b	b	PROPN
ejpam-5823	420	22	∈	∈	PROPN
ejpam-5823	420	23	c∗	c∗	NOUN
ejpam-5823	420	24	.	.	PUNCT
ejpam-5823	421	1	if	if	SCONJ
ejpam-5823	421	2	η	η	PROPN
ejpam-5823	421	3	<	<	X
ejpam-5823	421	4	1	1	NUM
ejpam-5823	421	5	then	then	ADV
ejpam-5823	421	6	kyξ	kyξ	PROPN
ejpam-5823	421	7	,	,	PUNCT
ejpam-5823	421	8	b	b	PROPN
ejpam-5823	421	9	≤	≤	NOUN
ejpam-5823	421	10	0	0	NUM
ejpam-5823	421	11	,	,	PUNCT
ejpam-5823	421	12	(	(	PUNCT
ejpam-5823	421	13	61	61	NUM
ejpam-5823	421	14	)	)	PUNCT
ejpam-5823	421	15	hence	hence	ADV
ejpam-5823	421	16	khξ	khξ	PROPN
ejpam-5823	421	17	,	,	PUNCT
ejpam-5823	421	18	b	b	PROPN
ejpam-5823	421	19	∈	∈	PROPN
ejpam-5823	421	20	k(η	k(η	PROPN
ejpam-5823	421	21	)	)	PUNCT
ejpam-5823	421	22	.	.	PUNCT
ejpam-5823	422	1	proof	proof	NOUN
ejpam-5823	422	2	.	.	PUNCT
ejpam-5823	423	1	from	from	ADP
ejpam-5823	423	2	silverman	silverman	PROPN
ejpam-5823	423	3	’s	’s	PART
ejpam-5823	423	4	[	[	X
ejpam-5823	423	5	27	27	NUM
ejpam-5823	423	6	]	]	X
ejpam-5823	423	7	well	well	ADV
ejpam-5823	423	8	-	-	PUNCT
ejpam-5823	423	9	known	know	VERB
ejpam-5823	423	10	result	result	NOUN
ejpam-5823	423	11	,	,	PUNCT
ejpam-5823	423	12	if	if	SCONJ
ejpam-5823	423	13	f	f	PROPN
ejpam-5823	423	14	is	be	AUX
ejpam-5823	423	15	in	in	ADP
ejpam-5823	423	16	form	form	NOUN
ejpam-5823	423	17	of	of	ADP
ejpam-5823	423	18	eq	eq	NOUN
ejpam-5823	423	19	.	.	PROPN
ejpam-5823	423	20	1	1	NUM
ejpam-5823	423	21	and	and	CCONJ
ejpam-5823	423	22	satisfies	satisfy	VERB
ejpam-5823	423	23	∞∑	∞∑	NUM
ejpam-5823	423	24	r=2	r=2	X
ejpam-5823	423	25	r(r	r(r	NOUN
ejpam-5823	423	26	−	−	PROPN
ejpam-5823	423	27	η)|fk|	η)|fk|	NOUN
ejpam-5823	423	28	≤	≤	PROPN
ejpam-5823	423	29	1−	1−	NUM
ejpam-5823	423	30	η	η	NOUN
ejpam-5823	423	31	,	,	PUNCT
ejpam-5823	423	32	then	then	ADV
ejpam-5823	423	33	f	f	PROPN
ejpam-5823	423	34	∈	∈	PROPN
ejpam-5823	423	35	k(η	k(η	PROPN
ejpam-5823	423	36	)	)	PUNCT
ejpam-5823	423	37	.	.	PUNCT
ejpam-5823	424	1	according	accord	VERB
ejpam-5823	424	2	to	to	ADP
ejpam-5823	424	3	eq	eq	PROPN
ejpam-5823	424	4	.	.	PROPN
ejpam-5823	424	5	9	9	NUM
ejpam-5823	424	6	,	,	PUNCT
ejpam-5823	424	7	it	it	PRON
ejpam-5823	424	8	is	be	AUX
ejpam-5823	424	9	sufficient	sufficient	ADJ
ejpam-5823	424	10	to	to	PART
ejpam-5823	424	11	show	show	VERB
ejpam-5823	424	12	:	:	PUNCT
ejpam-5823	424	13	b2	b2	NOUN
ejpam-5823	424	14	:	:	PUNCT
ejpam-5823	424	15	=	=	SYM
ejpam-5823	424	16	∞∑	∞∑	NUM
ejpam-5823	424	17	r=2	r=2	X
ejpam-5823	424	18	r(r	r(r	PROPN
ejpam-5823	424	19	−	−	PROPN
ejpam-5823	424	20	η	η	PROPN
ejpam-5823	424	21	)	)	PUNCT
ejpam-5823	424	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	424	23	(	(	PUNCT
ejpam-5823	424	24	−b)r−1	−b)r−1	PRON
ejpam-5823	424	25	4r−1(1)r−1,k(ξ)r−1,k	4r−1(1)r−1,k(ξ)r−1,k	PROPN
ejpam-5823	424	26	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5823	424	27	≤	≤	PROPN
ejpam-5823	424	28	1−	1−	NUM
ejpam-5823	424	29	η	η	PROPN
ejpam-5823	424	30	,	,	PUNCT
ejpam-5823	424	31	ξ	ξ	PROPN
ejpam-5823	424	32	>	>	X
ejpam-5823	424	33	0	0	NUM
ejpam-5823	424	34	,	,	PUNCT
ejpam-5823	424	35	b	b	X
ejpam-5823	424	36	∈	∈	PROPN
ejpam-5823	424	37	c∗	c∗	NOUN
ejpam-5823	424	38	=	=	PUNCT
ejpam-5823	424	39	∞∑	∞∑	NUM
ejpam-5823	424	40	r=2	r=2	X
ejpam-5823	424	41	r(r	r(r	NOUN
ejpam-5823	424	42	−	−	PROPN
ejpam-5823	424	43	η)|b|r−1	η)|b|r−1	ADP
ejpam-5823	424	44	4r−1(1)r−1,k(ξ)r−1,k	4r−1(1)r−1,k(ξ)r−1,k	PROPN
ejpam-5823	424	45	s.	s.	PROPN
ejpam-5823	424	46	a.	a.	PROPN
ejpam-5823	424	47	h.	h.	PROPN
ejpam-5823	424	48	shah	shah	PROPN
ejpam-5823	424	49	et	et	PROPN
ejpam-5823	424	50	al	al	PROPN
ejpam-5823	424	51	.	.	PUNCT
ejpam-5823	424	52	/	/	SYM
ejpam-5823	424	53	eur	eur	PROPN
ejpam-5823	424	54	.	.	PUNCT
ejpam-5823	425	1	j.	j.	PROPN
ejpam-5823	425	2	pure	pure	PROPN
ejpam-5823	425	3	appl	appl	PROPN
ejpam-5823	425	4	.	.	PROPN
ejpam-5823	425	5	math	math	PROPN
ejpam-5823	425	6	,	,	PUNCT
ejpam-5823	425	7	18	18	NUM
ejpam-5823	425	8	(	(	PUNCT
ejpam-5823	425	9	2	2	NUM
ejpam-5823	425	10	)	)	PUNCT
ejpam-5823	425	11	(	(	PUNCT
ejpam-5823	425	12	2025	2025	NUM
ejpam-5823	425	13	)	)	PUNCT
ejpam-5823	425	14	,	,	PUNCT
ejpam-5823	425	15	5823	5823	NUM
ejpam-5823	425	16	22	22	NUM
ejpam-5823	425	17	of	of	ADP
ejpam-5823	425	18	26	26	NUM
ejpam-5823	425	19	=	=	SYM
ejpam-5823	425	20	∞∑	∞∑	NUM
ejpam-5823	425	21	r=1	r=1	NOUN
ejpam-5823	425	22	(	(	PUNCT
ejpam-5823	425	23	r	r	NOUN
ejpam-5823	425	24	+	+	NUM
ejpam-5823	425	25	1)(r	1)(r	NUM
ejpam-5823	425	26	+	+	SYM
ejpam-5823	425	27	1−	1−	NUM
ejpam-5823	425	28	η)|b|r	η)|b|r	NUM
ejpam-5823	425	29	4r(1)r	4r(1)r	PROPN
ejpam-5823	425	30	,	,	PUNCT
ejpam-5823	425	31	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	425	32	,	,	PUNCT
ejpam-5823	425	33	k	k	PROPN
ejpam-5823	425	34	=	=	PUNCT
ejpam-5823	426	1	2(2−	2(2−	NUM
ejpam-5823	426	2	η)|b|	η)|b|	PROPN
ejpam-5823	426	3	4ξ	4ξ	NOUN
ejpam-5823	426	4	+	+	CCONJ
ejpam-5823	426	5	3(3−	3(3−	NUM
ejpam-5823	426	6	η)|b|2	η)|b|2	PROPN
ejpam-5823	426	7	16(ξ)2,k(1)2,k	16(ξ)2,k(1)2,k	PROPN
ejpam-5823	426	8	+	+	CCONJ
ejpam-5823	426	9	∞∑	∞∑	PROPN
ejpam-5823	426	10	r=3	r=3	PUNCT
ejpam-5823	426	11	(	(	PUNCT
ejpam-5823	427	1	r	r	NOUN
ejpam-5823	427	2	+	+	NUM
ejpam-5823	427	3	1)(r	1)(r	NUM
ejpam-5823	427	4	+	+	SYM
ejpam-5823	427	5	1−	1−	NUM
ejpam-5823	427	6	η)|b|r	η)|b|r	NUM
ejpam-5823	427	7	4r(1)r	4r(1)r	PROPN
ejpam-5823	427	8	,	,	PUNCT
ejpam-5823	427	9	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	427	10	,	,	PUNCT
ejpam-5823	427	11	k	k	PROPN
ejpam-5823	427	12	=	=	PUNCT
ejpam-5823	427	13	(	(	PUNCT
ejpam-5823	427	14	2−	2−	NUM
ejpam-5823	427	15	η)|b|	η)|b|	PROPN
ejpam-5823	427	16	2ξ	2ξ	NUM
ejpam-5823	427	17	+	+	CCONJ
ejpam-5823	427	18	3(3−	3(3−	NUM
ejpam-5823	427	19	η)|b|2	η)|b|2	PROPN
ejpam-5823	427	20	32ξ(ξ	32ξ(ξ	NUM
ejpam-5823	427	21	+	+	CCONJ
ejpam-5823	427	22	1	1	NUM
ejpam-5823	427	23	)	)	PUNCT
ejpam-5823	427	24	+	+	CCONJ
ejpam-5823	428	1	∞∑	∞∑	NUM
ejpam-5823	428	2	r=3	r=3	PROPN
ejpam-5823	428	3	r2|b|r	r2|b|r	NUM
ejpam-5823	428	4	4r(1)r	4r(1)r	NUM
ejpam-5823	428	5	,	,	PUNCT
ejpam-5823	428	6	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	428	7	,	,	PUNCT
ejpam-5823	428	8	k	k	PROPN
ejpam-5823	428	9	+	+	X
ejpam-5823	428	10	(	(	PUNCT
ejpam-5823	428	11	2−	2−	NUM
ejpam-5823	428	12	η	η	NOUN
ejpam-5823	428	13	)	)	PUNCT
ejpam-5823	428	14	∞∑	∞∑	NUM
ejpam-5823	428	15	r=3	r=3	VERB
ejpam-5823	428	16	r|b|r	r|b|r	PROPN
ejpam-5823	428	17	4r(1)r	4r(1)r	PROPN
ejpam-5823	428	18	,	,	PUNCT
ejpam-5823	428	19	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	428	20	,	,	PUNCT
ejpam-5823	428	21	k	k	PROPN
ejpam-5823	428	22	+	+	CCONJ
ejpam-5823	428	23	(	(	PUNCT
ejpam-5823	428	24	1−	1−	NUM
ejpam-5823	428	25	η	η	NOUN
ejpam-5823	428	26	)	)	PUNCT
ejpam-5823	428	27	∞∑	∞∑	PROPN
ejpam-5823	428	28	r=3	r=3	PROPN
ejpam-5823	428	29	|b|r	|b|r	PROPN
ejpam-5823	428	30	4r(1)r	4r(1)r	PROPN
ejpam-5823	428	31	,	,	PUNCT
ejpam-5823	428	32	k(ξ)r	k(ξ)r	PROPN
ejpam-5823	428	33	,	,	PUNCT
ejpam-5823	428	34	k	k	PROPN
ejpam-5823	428	35	.	.	PUNCT
ejpam-5823	429	1	by	by	ADP
ejpam-5823	429	2	simple	simple	ADJ
ejpam-5823	429	3	mathematical	mathematical	ADJ
ejpam-5823	429	4	induction	induction	NOUN
ejpam-5823	429	5	,	,	PUNCT
ejpam-5823	429	6	we	we	PRON
ejpam-5823	429	7	have	have	VERB
ejpam-5823	429	8	r2	r2	PROPN
ejpam-5823	429	9	≤	≤	NUM
ejpam-5823	429	10	(	(	PUNCT
ejpam-5823	429	11	9	9	NUM
ejpam-5823	429	12	64	64	NUM
ejpam-5823	429	13	)	)	PUNCT
ejpam-5823	429	14	4r	4r	NOUN
ejpam-5823	429	15	and	and	CCONJ
ejpam-5823	429	16	r	r	NOUN
ejpam-5823	429	17	≤	≤	NUM
ejpam-5823	429	18	(	(	PUNCT
ejpam-5823	429	19	9	9	NUM
ejpam-5823	429	20	64	64	NUM
ejpam-5823	429	21	)	)	PUNCT
ejpam-5823	429	22	4r	4r	NOUN
ejpam-5823	429	23	for	for	ADP
ejpam-5823	429	24	all	all	DET
ejpam-5823	429	25	r	r	NOUN
ejpam-5823	429	26	∈	∈	NOUN
ejpam-5823	429	27	n\[1	n\[1	NOUN
ejpam-5823	429	28	,	,	PUNCT
ejpam-5823	429	29	2	2	NUM
ejpam-5823	429	30	]	]	PUNCT
ejpam-5823	429	31	.	.	PUNCT
ejpam-5823	430	1	by	by	ADP
ejpam-5823	430	2	using	use	VERB
ejpam-5823	430	3	lemma	lemma	PROPN
ejpam-5823	430	4	,	,	PUNCT
ejpam-5823	430	5	we	we	PRON
ejpam-5823	430	6	have	have	VERB
ejpam-5823	430	7	(	(	PUNCT
ejpam-5823	430	8	1)r	1)r	NUM
ejpam-5823	430	9	,	,	PUNCT
ejpam-5823	430	10	k	k	X
ejpam-5823	430	11	>	>	X
ejpam-5823	430	12	(	(	PUNCT
ejpam-5823	430	13	1	1	NUM
ejpam-5823	430	14	+	+	NUM
ejpam-5823	430	15	β)r−1	β)r−1	NOUN
ejpam-5823	430	16	,	,	PUNCT
ejpam-5823	430	17	r	r	NOUN
ejpam-5823	430	18	∈	∈	PROPN
ejpam-5823	430	19	n\[1	n\[1	NOUN
ejpam-5823	430	20	,	,	PUNCT
ejpam-5823	430	21	2	2	NUM
ejpam-5823	430	22	]	]	PUNCT
ejpam-5823	430	23	,	,	PUNCT
ejpam-5823	430	24	0	0	NUM
ejpam-5823	430	25	≤	≤	NUM
ejpam-5823	430	26	β	β	X
ejpam-5823	430	27	≤	≤	NUM
ejpam-5823	430	28	√	√	ADP
ejpam-5823	430	29	2	2	NUM
ejpam-5823	430	30	.	.	PUNCT
ejpam-5823	431	1	since	since	SCONJ
ejpam-5823	431	2	max(1	max(1	NOUN
ejpam-5823	431	3	+	+	CCONJ
ejpam-5823	431	4	β)r−1	β)r−1	PROPN
ejpam-5823	431	5	:	:	PUNCT
ejpam-5823	431	6	0	0	NUM
ejpam-5823	431	7	≤	≤	NUM
ejpam-5823	431	8	β	β	X
ejpam-5823	431	9	≤	≤	NUM
ejpam-5823	431	10	√	√	ADV
ejpam-5823	431	11	2	2	NUM
ejpam-5823	431	12	=	=	SYM
ejpam-5823	431	13	(	(	PUNCT
ejpam-5823	431	14	1	1	NUM
ejpam-5823	431	15	+	+	CCONJ
ejpam-5823	431	16	√	√	PROPN
ejpam-5823	431	17	2)r−1	2)r−1	NUM
ejpam-5823	431	18	follows	follow	VERB
ejpam-5823	431	19	that	that	SCONJ
ejpam-5823	431	20	:	:	PUNCT
ejpam-5823	431	21	(	(	PUNCT
ejpam-5823	431	22	ξ)r	ξ)r	NOUN
ejpam-5823	431	23	,	,	PUNCT
ejpam-5823	431	24	k	k	PROPN
ejpam-5823	431	25	≥	≥	X
ejpam-5823	431	26	ξ(ξ	ξ(ξ	PROPN
ejpam-5823	431	27	+	+	CCONJ
ejpam-5823	431	28	√	√	NUM
ejpam-5823	431	29	2)r−1	2)r−1	NUM
ejpam-5823	431	30	,	,	PUNCT
ejpam-5823	431	31	ξ	ξ	PROPN
ejpam-5823	431	32	>	>	X
ejpam-5823	431	33	0	0	NUM
ejpam-5823	431	34	.	.	PUNCT
ejpam-5823	432	1	(	(	PUNCT
ejpam-5823	432	2	62	62	NUM
ejpam-5823	432	3	)	)	PUNCT
ejpam-5823	432	4	as	as	ADP
ejpam-5823	432	5	by	by	ADP
ejpam-5823	432	6	eq	eq	PROPN
ejpam-5823	432	7	.	.	PROPN
ejpam-5823	432	8	61	61	NUM
ejpam-5823	432	9	,	,	PUNCT
ejpam-5823	432	10	kyξ	kyξ	NOUN
ejpam-5823	432	11	,	,	PUNCT
ejpam-5823	432	12	b(η	b(η	NOUN
ejpam-5823	432	13	)	)	PUNCT
ejpam-5823	432	14	≤	≤	NOUN
ejpam-5823	432	15	0	0	NUM
ejpam-5823	432	16	,	,	PUNCT
ejpam-5823	432	17	we	we	PRON
ejpam-5823	432	18	have	have	AUX
ejpam-5823	432	19	b2	b2	VERB
ejpam-5823	432	20	≤	≤	NOUN
ejpam-5823	432	21	(	(	PUNCT
ejpam-5823	432	22	2−	2−	NUM
ejpam-5823	432	23	η)|b|	η)|b|	PROPN
ejpam-5823	432	24	2ξ	2ξ	NUM
ejpam-5823	432	25	+	+	CCONJ
ejpam-5823	432	26	3(3−	3(3−	NUM
ejpam-5823	432	27	η)|b|2	η)|b|2	PROPN
ejpam-5823	432	28	32ξ(ξ	32ξ(ξ	PROPN
ejpam-5823	432	29	+	+	CCONJ
ejpam-5823	432	30	k	k	NOUN
ejpam-5823	432	31	)	)	PUNCT
ejpam-5823	433	1	+	+	CCONJ
ejpam-5823	433	2	(	(	PUNCT
ejpam-5823	433	3	9	9	NUM
ejpam-5823	433	4	+	+	NUM
ejpam-5823	433	5	3(2−	3(2−	NUM
ejpam-5823	433	6	η))|b|	η))|b|	NOUN
ejpam-5823	433	7	64ξ	64ξ	NUM
ejpam-5823	434	1	∞∑	∞∑	NUM
ejpam-5823	434	2	r=3	r=3	ADJ
ejpam-5823	434	3	|b|r−1	|b|r−1	X
ejpam-5823	434	4	(	(	PUNCT
ejpam-5823	434	5	1	1	NUM
ejpam-5823	434	6	+	+	CCONJ
ejpam-5823	434	7	√	√	NUM
ejpam-5823	434	8	2)r−1(ξ	2)r−1(ξ	NUM
ejpam-5823	434	9	+	+	CCONJ
ejpam-5823	434	10	√	√	PROPN
ejpam-5823	434	11	2k)r−1	2k)r−1	NUM
ejpam-5823	434	12	+	+	CCONJ
ejpam-5823	434	13	(	(	PUNCT
ejpam-5823	434	14	1−	1−	NUM
ejpam-5823	434	15	η)|b|	η)|b|	PROPN
ejpam-5823	434	16	4ξ	4ξ	NOUN
ejpam-5823	434	17	∞∑	∞∑	PROPN
ejpam-5823	434	18	r=3	r=3	PROPN
ejpam-5823	434	19	|b|r−1	|b|r−1	X
ejpam-5823	434	20	4r−1(1	4r−1(1	NUM
ejpam-5823	434	21	+	+	NOUN
ejpam-5823	434	22	√	√	NUM
ejpam-5823	434	23	2)r−1(ξ	2)r−1(ξ	NUM
ejpam-5823	434	24	+	+	CCONJ
ejpam-5823	434	25	√	√	PROPN
ejpam-5823	434	26	2k)r−1	2k)r−1	PROPN
ejpam-5823	434	27	.	.	PUNCT
ejpam-5823	435	1	after	after	ADP
ejpam-5823	435	2	simplifications	simplification	NOUN
ejpam-5823	435	3	,	,	PUNCT
ejpam-5823	435	4	we	we	PRON
ejpam-5823	435	5	get	get	VERB
ejpam-5823	435	6	:	:	PUNCT
ejpam-5823	435	7	b2	b2	NOUN
ejpam-5823	435	8	=	=	SYM
ejpam-5823	435	9	(	(	PUNCT
ejpam-5823	435	10	2−	2−	NUM
ejpam-5823	435	11	η)|b|	η)|b|	PROPN
ejpam-5823	435	12	2ξ	2ξ	NUM
ejpam-5823	435	13	+	+	CCONJ
ejpam-5823	435	14	3(3−	3(3−	NUM
ejpam-5823	435	15	η)|b|2	η)|b|2	PROPN
ejpam-5823	435	16	32ξ(ξ	32ξ(ξ	PROPN
ejpam-5823	435	17	+	+	CCONJ
ejpam-5823	435	18	k	k	X
ejpam-5823	435	19	)	)	PUNCT
ejpam-5823	436	1	+	+	CCONJ
ejpam-5823	436	2	3(5−	3(5−	NUM
ejpam-5823	436	3	η	η	NOUN
ejpam-5823	436	4	)	)	PUNCT
ejpam-5823	436	5	64ξ	64ξ	NUM
ejpam-5823	436	6	.	.	PUNCT
ejpam-5823	437	1	|b|3	|b|3	PROPN
ejpam-5823	437	2	(	(	PUNCT
ejpam-5823	437	3	1	1	NUM
ejpam-5823	437	4	+	+	CCONJ
ejpam-5823	437	5	√	√	NUM
ejpam-5823	437	6	2)(ξ	2)(ξ	NUM
ejpam-5823	437	7	+	+	CCONJ
ejpam-5823	437	8	√	√	PROPN
ejpam-5823	437	9	2k)(2k	2k)(2k	NUM
ejpam-5823	437	10	+	+	CCONJ
ejpam-5823	437	11	√	√	NOUN
ejpam-5823	437	12	2k	2k	NUM
ejpam-5823	437	13	+	+	SYM
ejpam-5823	437	14	ξ	ξ	PROPN
ejpam-5823	437	15	+	+	SYM
ejpam-5823	437	16	ξ	ξ	NOUN
ejpam-5823	437	17	√	√	NUM
ejpam-5823	437	18	2−	2−	NUM
ejpam-5823	437	19	|b|	|b|	PROPN
ejpam-5823	437	20	+	+	CCONJ
ejpam-5823	437	21	(	(	PUNCT
ejpam-5823	437	22	1−	1−	NUM
ejpam-5823	437	23	η)|b|3	η)|b|3	X
ejpam-5823	437	24	16ξ(1	16ξ(1	NUM
ejpam-5823	437	25	+	+	CCONJ
ejpam-5823	437	26	√	√	NUM
ejpam-5823	437	27	2)(ξ	2)(ξ	NUM
ejpam-5823	437	28	+	+	CCONJ
ejpam-5823	437	29	√	√	NUM
ejpam-5823	437	30	2k)(8k	2k)(8k	NUM
ejpam-5823	437	31	+	+	CCONJ
ejpam-5823	437	32	4	4	NUM
ejpam-5823	437	33	√	√	NOUN
ejpam-5823	437	34	2k	2k	NOUN
ejpam-5823	437	35	+	+	CCONJ
ejpam-5823	437	36	4ξ	4ξ	NOUN
ejpam-5823	437	37	+	+	CCONJ
ejpam-5823	437	38	4ξ	4ξ	NOUN
ejpam-5823	437	39	√	√	PROPN
ejpam-5823	437	40	2−	2−	NUM
ejpam-5823	437	41	|b|	|b|	PROPN
ejpam-5823	437	42	=	=	PUNCT
ejpam-5823	437	43	(	(	PUNCT
ejpam-5823	437	44	2−	2−	NUM
ejpam-5823	437	45	η)|b|	η)|b|	PROPN
ejpam-5823	437	46	2ξ	2ξ	NUM
ejpam-5823	437	47	+	+	CCONJ
ejpam-5823	437	48	3(3−	3(3−	NUM
ejpam-5823	437	49	η)|b|2	η)|b|2	PROPN
ejpam-5823	437	50	32ξ(ξ	32ξ(ξ	PROPN
ejpam-5823	437	51	+	+	CCONJ
ejpam-5823	437	52	k	k	X
ejpam-5823	437	53	)	)	PUNCT
ejpam-5823	437	54	+	+	CCONJ
ejpam-5823	437	55	3(5−	3(5−	NUM
ejpam-5823	437	56	η	η	NOUN
ejpam-5823	437	57	)	)	PUNCT
ejpam-5823	437	58	64ξ	64ξ	NUM
ejpam-5823	437	59	.	.	PUNCT
ejpam-5823	438	1	|b|3	|b|3	PROPN
ejpam-5823	438	2	(	(	PUNCT
ejpam-5823	438	3	1	1	NUM
ejpam-5823	438	4	+	+	CCONJ
ejpam-5823	438	5	√	√	NUM
ejpam-5823	438	6	2)(ξ	2)(ξ	NUM
ejpam-5823	438	7	+	+	CCONJ
ejpam-5823	438	8	√	√	PROPN
ejpam-5823	438	9	2k)(2k	2k)(2k	NUM
ejpam-5823	438	10	+	+	CCONJ
ejpam-5823	438	11	√	√	NOUN
ejpam-5823	438	12	2k	2k	NUM
ejpam-5823	438	13	+	+	SYM
ejpam-5823	438	14	ξ	ξ	PROPN
ejpam-5823	438	15	+	+	SYM
ejpam-5823	438	16	ξ	ξ	NOUN
ejpam-5823	438	17	√	√	NUM
ejpam-5823	438	18	2−	2−	NUM
ejpam-5823	438	19	|b|	|b|	PROPN
ejpam-5823	438	20	+	+	CCONJ
ejpam-5823	438	21	(	(	PUNCT
ejpam-5823	438	22	1−	1−	NUM
ejpam-5823	438	23	η)|b|3	η)|b|3	X
ejpam-5823	438	24	16ξ(1	16ξ(1	NUM
ejpam-5823	438	25	+	+	CCONJ
ejpam-5823	438	26	√	√	NUM
ejpam-5823	438	27	2)(ξ	2)(ξ	NUM
ejpam-5823	438	28	+	+	CCONJ
ejpam-5823	438	29	√	√	NUM
ejpam-5823	438	30	2k)(8k	2k)(8k	NUM
ejpam-5823	438	31	+	+	CCONJ
ejpam-5823	438	32	4	4	NUM
ejpam-5823	438	33	√	√	NOUN
ejpam-5823	438	34	2k	2k	NOUN
ejpam-5823	438	35	+	+	CCONJ
ejpam-5823	438	36	4ξ	4ξ	NOUN
ejpam-5823	438	37	+	+	CCONJ
ejpam-5823	438	38	4ξ	4ξ	NOUN
ejpam-5823	438	39	√	√	PROPN
ejpam-5823	438	40	2−	2−	NUM
ejpam-5823	438	41	|b|	|b|	PROPN
ejpam-5823	438	42	≤	≤	PROPN
ejpam-5823	438	43	1−	1−	NUM
ejpam-5823	438	44	η	η	PROPN
ejpam-5823	438	45	.	.	PROPN
ejpam-5823	438	46	(	(	PUNCT
ejpam-5823	438	47	63	63	NUM
ejpam-5823	438	48	)	)	PUNCT
ejpam-5823	438	49	this	this	PRON
ejpam-5823	438	50	completes	complete	VERB
ejpam-5823	438	51	the	the	DET
ejpam-5823	438	52	proof	proof	NOUN
ejpam-5823	438	53	,	,	PUNCT
ejpam-5823	438	54	hence	hence	ADV
ejpam-5823	438	55	khξ	khξ	PROPN
ejpam-5823	438	56	,	,	PUNCT
ejpam-5823	438	57	b	b	PROPN
ejpam-5823	438	58	∈	∈	PROPN
ejpam-5823	438	59	k(η	k(η	PROPN
ejpam-5823	438	60	)	)	PUNCT
ejpam-5823	438	61	.	.	PUNCT
ejpam-5823	439	1	example	example	NOUN
ejpam-5823	440	1	4	4	NUM
ejpam-5823	440	2	.	.	PUNCT
ejpam-5823	441	1	some	some	DET
ejpam-5823	441	2	special	special	ADJ
ejpam-5823	441	3	cases	case	NOUN
ejpam-5823	441	4	of	of	ADP
ejpam-5823	441	5	theorem	theorem	NOUN
ejpam-5823	441	6	4	4	NUM
ejpam-5823	441	7	gives	give	VERB
ejpam-5823	441	8	the	the	DET
ejpam-5823	441	9	following	follow	VERB
ejpam-5823	441	10	different	different	ADJ
ejpam-5823	441	11	situations	situation	NOUN
ejpam-5823	441	12	:	:	PUNCT
ejpam-5823	441	13	case-1	case-1	NOUN
ejpam-5823	441	14	for	for	ADP
ejpam-5823	441	15	b	b	NOUN
ejpam-5823	441	16	=	=	SYM
ejpam-5823	441	17	1.2	1.2	NUM
ejpam-5823	441	18	,	,	PUNCT
ejpam-5823	441	19	η	η	PROPN
ejpam-5823	441	20	=	=	SYM
ejpam-5823	441	21	0.3	0.3	NUM
ejpam-5823	441	22	and	and	CCONJ
ejpam-5823	441	23	ξ	ξ	X
ejpam-5823	441	24	=	=	SYM
ejpam-5823	441	25	5.87545	5.87545	NUM
ejpam-5823	441	26	.	.	PUNCT
ejpam-5823	442	1	s.	s.	PROPN
ejpam-5823	442	2	a.	a.	PROPN
ejpam-5823	442	3	h.	h.	PROPN
ejpam-5823	442	4	shah	shah	PROPN
ejpam-5823	442	5	et	et	PROPN
ejpam-5823	442	6	al	al	PROPN
ejpam-5823	442	7	.	.	PUNCT
ejpam-5823	442	8	/	/	SYM
ejpam-5823	442	9	eur	eur	PROPN
ejpam-5823	442	10	.	.	PUNCT
ejpam-5823	443	1	j.	j.	PROPN
ejpam-5823	443	2	pure	pure	PROPN
ejpam-5823	443	3	appl	appl	PROPN
ejpam-5823	443	4	.	.	PROPN
ejpam-5823	443	5	math	math	PROPN
ejpam-5823	443	6	,	,	PUNCT
ejpam-5823	443	7	18	18	NUM
ejpam-5823	443	8	(	(	PUNCT
ejpam-5823	443	9	2	2	NUM
ejpam-5823	443	10	)	)	PUNCT
ejpam-5823	443	11	(	(	PUNCT
ejpam-5823	443	12	2025	2025	NUM
ejpam-5823	443	13	)	)	PUNCT
ejpam-5823	443	14	,	,	PUNCT
ejpam-5823	443	15	5823	5823	NUM
ejpam-5823	443	16	23	23	NUM
ejpam-5823	443	17	of	of	ADP
ejpam-5823	443	18	26	26	NUM
ejpam-5823	443	19	(	(	PUNCT
ejpam-5823	443	20	o	o	NOUN
ejpam-5823	443	21	)	)	PUNCT
ejpam-5823	443	22	0.8h5.87545,1.2	0.8h5.87545,1.2	NOUN
ejpam-5823	443	23	(	(	PUNCT
ejpam-5823	443	24	p	p	NOUN
ejpam-5823	443	25	)	)	PUNCT
ejpam-5823	443	26	0.9h5.87545,1.2	0.9h5.87545,1.2	NOUN
ejpam-5823	443	27	this	this	PRON
ejpam-5823	443	28	shows	show	VERB
ejpam-5823	443	29	that	that	SCONJ
ejpam-5823	443	30	the	the	DET
ejpam-5823	443	31	behaviour	behaviour	NOUN
ejpam-5823	443	32	of	of	ADP
ejpam-5823	443	33	the	the	DET
ejpam-5823	443	34	graph	graph	NOUN
ejpam-5823	443	35	is	be	AUX
ejpam-5823	443	36	same	same	ADJ
ejpam-5823	443	37	whether	whether	SCONJ
ejpam-5823	443	38	we	we	PRON
ejpam-5823	443	39	change	change	VERB
ejpam-5823	443	40	the	the	DET
ejpam-5823	443	41	values	value	NOUN
ejpam-5823	443	42	of	of	ADP
ejpam-5823	443	43	k.	k.	NOUN
ejpam-5823	443	44	exactly	exactly	ADV
ejpam-5823	443	45	at	at	ADP
ejpam-5823	443	46	k	k	PROPN
ejpam-5823	443	47	=	=	SYM
ejpam-5823	443	48	1	1	NUM
ejpam-5823	443	49	,	,	PUNCT
ejpam-5823	443	50	the	the	DET
ejpam-5823	443	51	conditions	condition	NOUN
ejpam-5823	443	52	and	and	CCONJ
ejpam-5823	443	53	graph	graph	NOUN
ejpam-5823	443	54	approaches	approach	NOUN
ejpam-5823	443	55	to	to	ADP
ejpam-5823	443	56	classical	classical	ADJ
ejpam-5823	443	57	form	form	NOUN
ejpam-5823	443	58	which	which	PRON
ejpam-5823	443	59	shows	show	VERB
ejpam-5823	443	60	the	the	DET
ejpam-5823	443	61	accuracy	accuracy	NOUN
ejpam-5823	443	62	of	of	ADP
ejpam-5823	443	63	our	our	PRON
ejpam-5823	443	64	results	result	NOUN
ejpam-5823	443	65	.	.	PUNCT
ejpam-5823	444	1	case-2	case-2	NUM
ejpam-5823	444	2	for	for	ADP
ejpam-5823	444	3	b	b	NOUN
ejpam-5823	444	4	=	=	SYM
ejpam-5823	444	5	1.2	1.2	NUM
ejpam-5823	444	6	,	,	PUNCT
ejpam-5823	444	7	η	η	PROPN
ejpam-5823	444	8	=	=	PROPN
ejpam-5823	444	9	0.4	0.4	NUM
ejpam-5823	444	10	and	and	CCONJ
ejpam-5823	444	11	ξ	ξ	X
ejpam-5823	444	12	=	=	SYM
ejpam-5823	444	13	4.7998	4.7998	NUM
ejpam-5823	444	14	.	.	PUNCT
ejpam-5823	445	1	(	(	PUNCT
ejpam-5823	445	2	q	q	X
ejpam-5823	445	3	)	)	PUNCT
ejpam-5823	445	4	0.9h4.7998,1.2	0.9h4.7998,1.2	NOUN
ejpam-5823	445	5	(	(	PUNCT
ejpam-5823	445	6	r	r	NOUN
ejpam-5823	445	7	)	)	PUNCT
ejpam-5823	445	8	0.9h4.7998,1.2	0.9h4.7998,1.2	NOUN
ejpam-5823	445	9	this	this	PRON
ejpam-5823	445	10	shows	show	VERB
ejpam-5823	445	11	that	that	SCONJ
ejpam-5823	445	12	the	the	DET
ejpam-5823	445	13	behaviour	behaviour	NOUN
ejpam-5823	445	14	of	of	ADP
ejpam-5823	445	15	the	the	DET
ejpam-5823	445	16	graph	graph	NOUN
ejpam-5823	445	17	is	be	AUX
ejpam-5823	445	18	same	same	ADJ
ejpam-5823	445	19	whether	whether	SCONJ
ejpam-5823	445	20	we	we	PRON
ejpam-5823	445	21	change	change	VERB
ejpam-5823	445	22	the	the	DET
ejpam-5823	445	23	values	value	NOUN
ejpam-5823	445	24	of	of	ADP
ejpam-5823	445	25	k.	k.	NOUN
ejpam-5823	445	26	exactly	exactly	ADV
ejpam-5823	445	27	at	at	ADP
ejpam-5823	445	28	k	k	PROPN
ejpam-5823	445	29	=	=	SYM
ejpam-5823	445	30	1	1	NUM
ejpam-5823	445	31	,	,	PUNCT
ejpam-5823	445	32	the	the	DET
ejpam-5823	445	33	conditions	condition	NOUN
ejpam-5823	445	34	and	and	CCONJ
ejpam-5823	445	35	graph	graph	NOUN
ejpam-5823	445	36	approaches	approach	NOUN
ejpam-5823	445	37	to	to	ADP
ejpam-5823	445	38	classical	classical	ADJ
ejpam-5823	445	39	form	form	NOUN
ejpam-5823	445	40	which	which	PRON
ejpam-5823	445	41	shows	show	VERB
ejpam-5823	445	42	the	the	DET
ejpam-5823	445	43	accuracy	accuracy	NOUN
ejpam-5823	445	44	of	of	ADP
ejpam-5823	445	45	our	our	PRON
ejpam-5823	445	46	results	result	NOUN
ejpam-5823	445	47	.	.	PUNCT
ejpam-5823	446	1	conclusions	conclusion	NOUN
ejpam-5823	446	2	in	in	ADP
ejpam-5823	446	3	our	our	PRON
ejpam-5823	446	4	current	current	ADJ
ejpam-5823	446	5	findings	finding	NOUN
ejpam-5823	446	6	,	,	PUNCT
ejpam-5823	446	7	we	we	PRON
ejpam-5823	446	8	have	have	AUX
ejpam-5823	446	9	discussed	discuss	VERB
ejpam-5823	446	10	the	the	DET
ejpam-5823	446	11	geometrical	geometrical	ADJ
ejpam-5823	446	12	interpretation	interpretation	NOUN
ejpam-5823	446	13	for	for	ADP
ejpam-5823	446	14	different	different	ADJ
ejpam-5823	446	15	values	value	NOUN
ejpam-5823	446	16	of	of	ADP
ejpam-5823	446	17	k.	k.	PROPN
ejpam-5823	446	18	(	(	PUNCT
ejpam-5823	446	19	i	i	NOUN
ejpam-5823	446	20	)	)	PUNCT
ejpam-5823	446	21	the	the	DET
ejpam-5823	446	22	generalization	generalization	NOUN
ejpam-5823	446	23	of	of	ADP
ejpam-5823	446	24	pochammer	pochammer	NOUN
ejpam-5823	446	25	’s	’s	PART
ejpam-5823	446	26	symbol	symbol	NOUN
ejpam-5823	446	27	in	in	ADP
ejpam-5823	446	28	the	the	DET
ejpam-5823	446	29	form	form	NOUN
ejpam-5823	446	30	of	of	ADP
ejpam-5823	446	31	inequality	inequality	NOUN
ejpam-5823	446	32	(	(	PUNCT
ejpam-5823	446	33	q)r	q)r	NOUN
ejpam-5823	446	34	,	,	PUNCT
ejpam-5823	446	35	k	k	PROPN
ejpam-5823	446	36	>	>	X
ejpam-5823	446	37	q(q	q(q	PROPN
ejpam-5823	446	38	+	+	CCONJ
ejpam-5823	446	39	β)r−1	β)r−1	PROPN
ejpam-5823	446	40	is	be	AUX
ejpam-5823	446	41	proved	prove	VERB
ejpam-5823	446	42	by	by	ADP
ejpam-5823	446	43	using	use	VERB
ejpam-5823	446	44	the	the	DET
ejpam-5823	446	45	generalization	generalization	NOUN
ejpam-5823	446	46	of	of	ADP
ejpam-5823	446	47	lemma	lemma	PROPN
ejpam-5823	447	1	[	[	X
ejpam-5823	447	2	1	1	NUM
ejpam-5823	447	3	]	]	PUNCT
ejpam-5823	447	4	(	(	PUNCT
ejpam-5823	447	5	ii	ii	NOUN
ejpam-5823	447	6	)	)	PUNCT
ejpam-5823	447	7	convexity	convexity	NOUN
ejpam-5823	447	8	and	and	CCONJ
ejpam-5823	447	9	starlikeness	starlikeness	NOUN
ejpam-5823	447	10	of	of	ADP
ejpam-5823	447	11	order	order	NOUN
ejpam-5823	447	12	η	η	PROPN
ejpam-5823	447	13	for	for	ADP
ejpam-5823	447	14	generalized	generalized	ADJ
ejpam-5823	447	15	bessel	bessel	ADJ
ejpam-5823	447	16	function	function	NOUN
ejpam-5823	447	17	.	.	PUNCT
ejpam-5823	448	1	theorem	theorem	NOUN
ejpam-5823	448	2	1	1	NUM
ejpam-5823	448	3	in	in	ADP
ejpam-5823	448	4	our	our	PRON
ejpam-5823	448	5	paper	paper	NOUN
ejpam-5823	448	6	is	be	AUX
ejpam-5823	448	7	the	the	DET
ejpam-5823	448	8	generalized	generalized	ADJ
ejpam-5823	448	9	form	form	NOUN
ejpam-5823	448	10	of	of	ADP
ejpam-5823	448	11	theorem	theorem	NOUN
ejpam-5823	448	12	2.1	2.1	NUM
ejpam-5823	448	13	from	from	ADP
ejpam-5823	448	14	[	[	X
ejpam-5823	448	15	1	1	NUM
ejpam-5823	448	16	]	]	PUNCT
ejpam-5823	448	17	,	,	PUNCT
ejpam-5823	448	18	and	and	CCONJ
ejpam-5823	448	19	theorem	theorem	VERB
ejpam-5823	448	20	2	2	NUM
ejpam-5823	448	21	is	be	AUX
ejpam-5823	448	22	generalization	generalization	NOUN
ejpam-5823	448	23	of	of	ADP
ejpam-5823	448	24	theorem	theorem	NOUN
ejpam-5823	448	25	2.2	2.2	NUM
ejpam-5823	448	26	in	in	ADP
ejpam-5823	448	27	[	[	X
ejpam-5823	448	28	1	1	NUM
ejpam-5823	448	29	]	]	PUNCT
ejpam-5823	448	30	.	.	PUNCT
ejpam-5823	449	1	it	it	PRON
ejpam-5823	449	2	has	have	AUX
ejpam-5823	449	3	given	give	VERB
ejpam-5823	449	4	the	the	DET
ejpam-5823	449	5	sufficient	sufficient	ADJ
ejpam-5823	449	6	conditions	condition	NOUN
ejpam-5823	449	7	for	for	ADP
ejpam-5823	449	8	finding	find	VERB
ejpam-5823	449	9	the	the	DET
ejpam-5823	449	10	s.	s.	PROPN
ejpam-5823	449	11	a.	a.	PROPN
ejpam-5823	449	12	h.	h.	PROPN
ejpam-5823	449	13	shah	shah	PROPN
ejpam-5823	449	14	et	et	PROPN
ejpam-5823	449	15	al	al	PROPN
ejpam-5823	449	16	.	.	PUNCT
ejpam-5823	449	17	/	/	SYM
ejpam-5823	449	18	eur	eur	PROPN
ejpam-5823	449	19	.	.	PUNCT
ejpam-5823	450	1	j.	j.	PROPN
ejpam-5823	450	2	pure	pure	PROPN
ejpam-5823	450	3	appl	appl	PROPN
ejpam-5823	450	4	.	.	PROPN
ejpam-5823	450	5	math	math	PROPN
ejpam-5823	450	6	,	,	PUNCT
ejpam-5823	450	7	18	18	NUM
ejpam-5823	450	8	(	(	PUNCT
ejpam-5823	450	9	2	2	NUM
ejpam-5823	450	10	)	)	PUNCT
ejpam-5823	450	11	(	(	PUNCT
ejpam-5823	450	12	2025	2025	NUM
ejpam-5823	450	13	)	)	PUNCT
ejpam-5823	450	14	,	,	PUNCT
ejpam-5823	450	15	5823	5823	NUM
ejpam-5823	450	16	24	24	NUM
ejpam-5823	450	17	of	of	ADP
ejpam-5823	450	18	26	26	NUM
ejpam-5823	450	19	order	order	NOUN
ejpam-5823	450	20	of	of	ADP
ejpam-5823	450	21	starlikeness	starlikeness	NOUN
ejpam-5823	450	22	and	and	CCONJ
ejpam-5823	450	23	convexity	convexity	NOUN
ejpam-5823	450	24	respectively	respectively	ADV
ejpam-5823	450	25	.	.	PUNCT
ejpam-5823	451	1	(	(	PUNCT
ejpam-5823	451	2	iii	iii	X
ejpam-5823	451	3	)	)	PUNCT
ejpam-5823	451	4	convexity	convexity	NOUN
ejpam-5823	451	5	and	and	CCONJ
ejpam-5823	451	6	starlikeness	starlikeness	NOUN
ejpam-5823	451	7	of	of	ADP
ejpam-5823	451	8	order	order	NOUN
ejpam-5823	451	9	η	η	PROPN
ejpam-5823	451	10	by	by	ADP
ejpam-5823	451	11	silverman	silverman	PROPN
ejpam-5823	451	12	’s	’s	PART
ejpam-5823	451	13	theorem	theorem	NOUN
ejpam-5823	451	14	for	for	ADP
ejpam-5823	451	15	generalized	generalized	ADJ
ejpam-5823	451	16	bessel	bessel	NOUN
ejpam-5823	451	17	function	function	NOUN
ejpam-5823	451	18	is	be	AUX
ejpam-5823	451	19	proved	prove	VERB
ejpam-5823	451	20	.	.	PUNCT
ejpam-5823	452	1	theorem	theorem	VERB
ejpam-5823	452	2	3	3	NUM
ejpam-5823	452	3	in	in	ADP
ejpam-5823	452	4	our	our	PRON
ejpam-5823	452	5	paper	paper	NOUN
ejpam-5823	452	6	is	be	AUX
ejpam-5823	452	7	the	the	DET
ejpam-5823	452	8	extended	extended	ADJ
ejpam-5823	452	9	form	form	NOUN
ejpam-5823	452	10	of	of	ADP
ejpam-5823	452	11	theorem	theorem	NOUN
ejpam-5823	452	12	4.1	4.1	NUM
ejpam-5823	452	13	from	from	ADP
ejpam-5823	452	14	[	[	X
ejpam-5823	452	15	1	1	NUM
ejpam-5823	452	16	]	]	PUNCT
ejpam-5823	452	17	,	,	PUNCT
ejpam-5823	452	18	and	and	CCONJ
ejpam-5823	452	19	theorem	theorem	VERB
ejpam-5823	452	20	4	4	NUM
ejpam-5823	452	21	is	be	AUX
ejpam-5823	452	22	generalization	generalization	NOUN
ejpam-5823	452	23	of	of	ADP
ejpam-5823	452	24	theorem	theorem	ADJ
ejpam-5823	452	25	4.2	4.2	NUM
ejpam-5823	452	26	in	in	ADP
ejpam-5823	452	27	[	[	X
ejpam-5823	452	28	1	1	NUM
ejpam-5823	452	29	]	]	PUNCT
ejpam-5823	452	30	.	.	PUNCT
ejpam-5823	453	1	it	it	PRON
ejpam-5823	453	2	gives	give	VERB
ejpam-5823	453	3	sufficient	sufficient	ADJ
ejpam-5823	453	4	condition	condition	NOUN
ejpam-5823	453	5	on	on	ADP
ejpam-5823	453	6	ξ	ξ	PROPN
ejpam-5823	453	7	,	,	PUNCT
ejpam-5823	453	8	b	b	PROPN
ejpam-5823	453	9	and	and	CCONJ
ejpam-5823	453	10	its	its	PRON
ejpam-5823	453	11	proof	proof	NOUN
ejpam-5823	453	12	uses	use	VERB
ejpam-5823	453	13	the	the	DET
ejpam-5823	453	14	lemma	lemma	PROPN
ejpam-5823	453	15	1	1	NUM
ejpam-5823	453	16	.	.	PUNCT
ejpam-5823	453	17	(	(	PUNCT
ejpam-5823	453	18	iv	iv	X
ejpam-5823	453	19	)	)	PUNCT
ejpam-5823	453	20	for	for	ADP
ejpam-5823	453	21	the	the	DET
ejpam-5823	453	22	reader	reader	NOUN
ejpam-5823	453	23	’s	’s	PART
ejpam-5823	453	24	help	help	NOUN
ejpam-5823	453	25	,	,	PUNCT
ejpam-5823	453	26	illustrated	illustrate	VERB
ejpam-5823	453	27	some	some	DET
ejpam-5823	453	28	examples	example	NOUN
ejpam-5823	453	29	with	with	ADP
ejpam-5823	453	30	graphs	graph	NOUN
ejpam-5823	453	31	to	to	PART
ejpam-5823	453	32	estimate	estimate	VERB
ejpam-5823	453	33	our	our	PRON
ejpam-5823	453	34	approach	approach	NOUN
ejpam-5823	453	35	.	.	PUNCT
ejpam-5823	454	1	there	there	PRON
ejpam-5823	454	2	is	be	VERB
ejpam-5823	454	3	a	a	DET
ejpam-5823	454	4	comparison	comparison	NOUN
ejpam-5823	454	5	between	between	ADP
ejpam-5823	454	6	different	different	ADJ
ejpam-5823	454	7	graphs	graph	NOUN
ejpam-5823	454	8	with	with	ADP
ejpam-5823	454	9	different	different	ADJ
ejpam-5823	454	10	values	value	NOUN
ejpam-5823	454	11	of	of	ADP
ejpam-5823	454	12	k.	k.	NOUN
ejpam-5823	454	13	by	by	ADP
ejpam-5823	454	14	observing	observe	VERB
ejpam-5823	454	15	them	they	PRON
ejpam-5823	454	16	,	,	PUNCT
ejpam-5823	454	17	it	it	PRON
ejpam-5823	454	18	is	be	AUX
ejpam-5823	454	19	concluded	conclude	VERB
ejpam-5823	454	20	that	that	SCONJ
ejpam-5823	454	21	the	the	DET
ejpam-5823	454	22	behaviour	behaviour	NOUN
ejpam-5823	454	23	of	of	ADP
ejpam-5823	454	24	the	the	DET
ejpam-5823	454	25	graphs	graph	NOUN
ejpam-5823	454	26	is	be	AUX
ejpam-5823	454	27	same	same	ADJ
ejpam-5823	454	28	whether	whether	SCONJ
ejpam-5823	454	29	the	the	DET
ejpam-5823	454	30	values	value	NOUN
ejpam-5823	454	31	of	of	ADP
ejpam-5823	454	32	k	k	PROPN
ejpam-5823	454	33	changes	change	NOUN
ejpam-5823	454	34	and	and	CCONJ
ejpam-5823	454	35	approaches	approach	NOUN
ejpam-5823	454	36	to	to	ADP
ejpam-5823	454	37	the	the	DET
ejpam-5823	454	38	graph	graph	NOUN
ejpam-5823	454	39	of	of	ADP
ejpam-5823	454	40	classical	classical	ADJ
ejpam-5823	454	41	function	function	NOUN
ejpam-5823	454	42	as	as	SCONJ
ejpam-5823	454	43	k	k	PROPN
ejpam-5823	454	44	approaches	approach	NOUN
ejpam-5823	454	45	to	to	ADP
ejpam-5823	454	46	1	1	NUM
ejpam-5823	454	47	.	.	PUNCT
ejpam-5823	455	1	acknowledgements	acknowledgement	NOUN
ejpam-5823	455	2	the	the	DET
ejpam-5823	455	3	authors	author	NOUN
ejpam-5823	455	4	extend	extend	VERB
ejpam-5823	455	5	their	their	PRON
ejpam-5823	455	6	appreciation	appreciation	NOUN
ejpam-5823	455	7	to	to	ADP
ejpam-5823	455	8	the	the	DET
ejpam-5823	455	9	deanship	deanship	NOUN
ejpam-5823	455	10	of	of	ADP
ejpam-5823	455	11	research	research	NOUN
ejpam-5823	455	12	and	and	CCONJ
ejpam-5823	455	13	graduate	graduate	NOUN
ejpam-5823	455	14	studies	study	NOUN
ejpam-5823	455	15	at	at	ADP
ejpam-5823	455	16	king	king	PROPN
ejpam-5823	455	17	khalid	khalid	PROPN
ejpam-5823	455	18	university	university	PROPN
ejpam-5823	455	19	for	for	ADP
ejpam-5823	455	20	funding	fund	VERB
ejpam-5823	455	21	this	this	DET
ejpam-5823	455	22	work	work	NOUN
ejpam-5823	455	23	through	through	ADP
ejpam-5823	455	24	large	large	ADJ
ejpam-5823	455	25	research	research	NOUN
ejpam-5823	455	26	project	project	NOUN
ejpam-5823	455	27	under	under	ADP
ejpam-5823	455	28	grant	grant	NOUN
ejpam-5823	455	29	number	number	NOUN
ejpam-5823	455	30	rgp2/588/45	rgp2/588/45	PROPN
ejpam-5823	455	31	.	.	PUNCT
ejpam-5823	456	1	the	the	DET
ejpam-5823	456	2	authors	author	NOUN
ejpam-5823	456	3	a.	a.	VERB
ejpam-5823	456	4	aloqaily	aloqaily	ADV
ejpam-5823	456	5	,	,	PUNCT
ejpam-5823	456	6	s.	s.	PROPN
ejpam-5823	456	7	haque	haque	PROPN
ejpam-5823	456	8	,	,	PUNCT
ejpam-5823	456	9	n.	n.	PROPN
ejpam-5823	456	10	mlaiki	mlaiki	PROPN
ejpam-5823	456	11	would	would	AUX
ejpam-5823	456	12	like	like	VERB
ejpam-5823	456	13	to	to	PART
ejpam-5823	456	14	thank	thank	VERB
ejpam-5823	456	15	prince	prince	PROPN
ejpam-5823	456	16	sultan	sultan	PROPN
ejpam-5823	456	17	university	university	PROPN
ejpam-5823	456	18	for	for	ADP
ejpam-5823	456	19	paying	pay	VERB
ejpam-5823	456	20	the	the	DET
ejpam-5823	456	21	apc	apc	NOUN
ejpam-5823	456	22	and	and	CCONJ
ejpam-5823	456	23	for	for	ADP
ejpam-5823	456	24	the	the	DET
ejpam-5823	456	25	support	support	NOUN
ejpam-5823	456	26	through	through	ADP
ejpam-5823	456	27	the	the	DET
ejpam-5823	456	28	tas	tas	PROPN
ejpam-5823	456	29	research	research	NOUN
ejpam-5823	456	30	lab	lab	NOUN
ejpam-5823	456	31	.	.	PUNCT
ejpam-5823	457	1	references	reference	NOUN
ejpam-5823	457	2	[	[	X
ejpam-5823	457	3	1	1	NUM
ejpam-5823	457	4	]	]	PUNCT
ejpam-5823	457	5	t	t	PROPN
ejpam-5823	457	6	bulboacă	bulboacă	NOUN
ejpam-5823	457	7	and	and	CCONJ
ejpam-5823	457	8	h	h	NOUN
ejpam-5823	457	9	m	m	VERB
ejpam-5823	457	10	zayed	zayed	ADJ
ejpam-5823	457	11	.	.	PUNCT
ejpam-5823	458	1	analytical	analytical	ADJ
ejpam-5823	458	2	and	and	CCONJ
ejpam-5823	458	3	geometrical	geometrical	ADJ
ejpam-5823	458	4	approach	approach	NOUN
ejpam-5823	458	5	to	to	ADP
ejpam-5823	458	6	the	the	DET
ejpam-5823	458	7	generalized	generalized	ADJ
ejpam-5823	458	8	bessel	bessel	NOUN
ejpam-5823	458	9	function	function	NOUN
ejpam-5823	458	10	.	.	PUNCT
ejpam-5823	459	1	journal	journal	PROPN
ejpam-5823	459	2	of	of	ADP
ejpam-5823	459	3	inequalities	inequality	NOUN
ejpam-5823	459	4	and	and	CCONJ
ejpam-5823	459	5	applications	application	NOUN
ejpam-5823	459	6	,	,	PUNCT
ejpam-5823	459	7	2024(1):51	2024(1):51	NUM
ejpam-5823	459	8	,	,	PUNCT
ejpam-5823	459	9	2024	2024	NUM
ejpam-5823	459	10	.	.	PUNCT
ejpam-5823	460	1	[	[	X
ejpam-5823	460	2	2	2	X
ejpam-5823	460	3	]	]	PUNCT
ejpam-5823	460	4	g	g	NOUN
ejpam-5823	460	5	dattoli	dattoli	NOUN
ejpam-5823	460	6	and	and	CCONJ
ejpam-5823	460	7	a	a	DET
ejpam-5823	460	8	torre	torre	PROPN
ejpam-5823	460	9	.	.	PUNCT
ejpam-5823	461	1	theory	theory	NOUN
ejpam-5823	461	2	and	and	CCONJ
ejpam-5823	461	3	applications	application	NOUN
ejpam-5823	461	4	of	of	ADP
ejpam-5823	461	5	generalized	generalized	ADJ
ejpam-5823	461	6	bessel	bessel	NOUN
ejpam-5823	461	7	functions	function	NOUN
ejpam-5823	461	8	.	.	PUNCT
ejpam-5823	462	1	aracne	aracne	PROPN
ejpam-5823	462	2	rome	rome	PROPN
ejpam-5823	462	3	,	,	PUNCT
ejpam-5823	462	4	1996	1996	NUM
ejpam-5823	462	5	.	.	PUNCT
ejpam-5823	463	1	[	[	X
ejpam-5823	463	2	3	3	NUM
ejpam-5823	463	3	]	]	X
ejpam-5823	463	4	h	h	PROPN
ejpam-5823	463	5	khosravian	khosravian	PROPN
ejpam-5823	463	6	-	-	PUNCT
ejpam-5823	463	7	arab	arab	PROPN
ejpam-5823	463	8	,	,	PUNCT
ejpam-5823	463	9	m	m	VERB
ejpam-5823	463	10	dehghan	dehghan	ADJ
ejpam-5823	463	11	,	,	PUNCT
ejpam-5823	463	12	and	and	CCONJ
ejpam-5823	463	13	m	m	PROPN
ejpam-5823	463	14	r	r	NOUN
ejpam-5823	463	15	eslahchi	eslahchi	ADJ
ejpam-5823	463	16	.	.	PUNCT
ejpam-5823	463	17	generalized	generalized	ADJ
ejpam-5823	463	18	bessel	bessel	NOUN
ejpam-5823	463	19	functions	function	NOUN
ejpam-5823	463	20	:	:	PUNCT
ejpam-5823	463	21	theory	theory	NOUN
ejpam-5823	463	22	and	and	CCONJ
ejpam-5823	463	23	their	their	PRON
ejpam-5823	463	24	applications	application	NOUN
ejpam-5823	463	25	.	.	PUNCT
ejpam-5823	464	1	mathematical	mathematical	ADJ
ejpam-5823	464	2	methods	method	NOUN
ejpam-5823	464	3	in	in	ADP
ejpam-5823	464	4	the	the	DET
ejpam-5823	464	5	applied	apply	VERB
ejpam-5823	464	6	sciences	science	NOUN
ejpam-5823	464	7	,	,	PUNCT
ejpam-5823	464	8	40(18):6389–6410	40(18):6389–6410	NUM
ejpam-5823	464	9	,	,	PUNCT
ejpam-5823	464	10	2017	2017	NUM
ejpam-5823	464	11	.	.	PUNCT
ejpam-5823	465	1	[	[	X
ejpam-5823	465	2	4	4	X
ejpam-5823	465	3	]	]	X
ejpam-5823	465	4	c	c	X
ejpam-5823	465	5	cesarano	cesarano	PROPN
ejpam-5823	465	6	and	and	CCONJ
ejpam-5823	465	7	d	d	X
ejpam-5823	465	8	assante	assante	PROPN
ejpam-5823	465	9	.	.	PUNCT
ejpam-5823	466	1	a	a	DET
ejpam-5823	466	2	note	note	NOUN
ejpam-5823	466	3	on	on	ADP
ejpam-5823	466	4	generalized	generalized	ADJ
ejpam-5823	466	5	bessel	bessel	NOUN
ejpam-5823	466	6	functions	function	NOUN
ejpam-5823	466	7	.	.	PUNCT
ejpam-5823	467	1	international	international	ADJ
ejpam-5823	467	2	journal	journal	PROPN
ejpam-5823	467	3	of	of	ADP
ejpam-5823	467	4	mathematical	mathematical	ADJ
ejpam-5823	467	5	models	model	NOUN
ejpam-5823	467	6	and	and	CCONJ
ejpam-5823	467	7	methods	method	NOUN
ejpam-5823	467	8	in	in	ADP
ejpam-5823	467	9	applied	applied	ADJ
ejpam-5823	467	10	sciences	science	NOUN
ejpam-5823	467	11	,	,	PUNCT
ejpam-5823	467	12	7(6):625–629	7(6):625–629	NUM
ejpam-5823	467	13	,	,	PUNCT
ejpam-5823	467	14	2013	2013	NUM
ejpam-5823	467	15	.	.	PUNCT
ejpam-5823	468	1	[	[	X
ejpam-5823	468	2	5	5	NUM
ejpam-5823	468	3	]	]	PUNCT
ejpam-5823	468	4	j	j	PROPN
ejpam-5823	468	5	niedziela	niedziela	PROPN
ejpam-5823	468	6	.	.	PUNCT
ejpam-5823	468	7	bessel	bessel	ADJ
ejpam-5823	468	8	functions	function	NOUN
ejpam-5823	468	9	and	and	CCONJ
ejpam-5823	468	10	their	their	PRON
ejpam-5823	468	11	applications	application	NOUN
ejpam-5823	468	12	.	.	PUNCT
ejpam-5823	469	1	university	university	NOUN
ejpam-5823	469	2	of	of	ADP
ejpam-5823	469	3	tennesseeknoxville,(dated	tennesseeknoxville,(dated	PROPN
ejpam-5823	469	4	:	:	PUNCT
ejpam-5823	469	5	october	october	PROPN
ejpam-5823	469	6	29	29	NUM
ejpam-5823	469	7	,	,	PUNCT
ejpam-5823	469	8	2008	2008	NUM
ejpam-5823	469	9	)	)	PUNCT
ejpam-5823	469	10	,	,	PUNCT
ejpam-5823	469	11	2008	2008	NUM
ejpam-5823	469	12	.	.	PUNCT
ejpam-5823	470	1	[	[	X
ejpam-5823	470	2	6	6	NUM
ejpam-5823	470	3	]	]	PUNCT
ejpam-5823	470	4	k	k	PROPN
ejpam-5823	470	5	parand	parand	PROPN
ejpam-5823	470	6	and	and	CCONJ
ejpam-5823	470	7	m	m	PRON
ejpam-5823	470	8	nikarya	nikarya	ADJ
ejpam-5823	470	9	.	.	PUNCT
ejpam-5823	471	1	application	application	NOUN
ejpam-5823	471	2	of	of	ADP
ejpam-5823	471	3	bessel	bessel	NOUN
ejpam-5823	471	4	functions	function	NOUN
ejpam-5823	471	5	for	for	ADP
ejpam-5823	471	6	solving	solve	VERB
ejpam-5823	471	7	differential	differential	NOUN
ejpam-5823	471	8	and	and	CCONJ
ejpam-5823	471	9	integro	integro	ADJ
ejpam-5823	471	10	-	-	PUNCT
ejpam-5823	471	11	differential	differential	NOUN
ejpam-5823	471	12	equations	equation	NOUN
ejpam-5823	471	13	of	of	ADP
ejpam-5823	471	14	the	the	DET
ejpam-5823	471	15	fractional	fractional	ADJ
ejpam-5823	471	16	order	order	NOUN
ejpam-5823	471	17	.	.	PUNCT
ejpam-5823	472	1	applied	apply	VERB
ejpam-5823	472	2	mathematical	mathematical	ADJ
ejpam-5823	472	3	modelling	modelling	NOUN
ejpam-5823	472	4	,	,	PUNCT
ejpam-5823	472	5	38(15	38(15	PROPN
ejpam-5823	472	6	-	-	SYM
ejpam-5823	472	7	16):4137–4147	16):4137–4147	NUM
ejpam-5823	472	8	,	,	PUNCT
ejpam-5823	472	9	2014	2014	NUM
ejpam-5823	472	10	.	.	PUNCT
ejpam-5823	473	1	[	[	X
ejpam-5823	473	2	7	7	X
ejpam-5823	473	3	]	]	X
ejpam-5823	473	4	f	f	PROPN
ejpam-5823	473	5	a	a	DET
ejpam-5823	473	6	idris	idris	PROPN
ejpam-5823	473	7	,	,	PUNCT
ejpam-5823	473	8	a	a	DET
ejpam-5823	473	9	l	l	NOUN
ejpam-5823	473	10	buhari	buhari	X
ejpam-5823	473	11	,	,	PUNCT
ejpam-5823	473	12	and	and	CCONJ
ejpam-5823	473	13	t	t	PROPN
ejpam-5823	473	14	u	u	PROPN
ejpam-5823	473	15	adamu	adamu	PROPN
ejpam-5823	473	16	.	.	PUNCT
ejpam-5823	473	17	bessel	bessel	ADJ
ejpam-5823	473	18	functions	function	NOUN
ejpam-5823	473	19	and	and	CCONJ
ejpam-5823	473	20	their	their	PRON
ejpam-5823	473	21	applications	application	NOUN
ejpam-5823	473	22	:	:	PUNCT
ejpam-5823	473	23	solution	solution	NOUN
ejpam-5823	473	24	to	to	ADP
ejpam-5823	473	25	schrödinger	schrödinger	NOUN
ejpam-5823	473	26	equation	equation	NOUN
ejpam-5823	473	27	in	in	ADP
ejpam-5823	473	28	a	a	DET
ejpam-5823	473	29	cylindrical	cylindrical	ADJ
ejpam-5823	473	30	function	function	NOUN
ejpam-5823	473	31	of	of	ADP
ejpam-5823	473	32	the	the	DET
ejpam-5823	473	33	second	second	ADJ
ejpam-5823	473	34	kind	kind	NOUN
ejpam-5823	473	35	and	and	CCONJ
ejpam-5823	473	36	hankel	hankel	NOUN
ejpam-5823	473	37	functions	function	NOUN
ejpam-5823	473	38	.	.	PUNCT
ejpam-5823	474	1	international	international	ADJ
ejpam-5823	474	2	journal	journal	PROPN
ejpam-5823	474	3	novel	novel	NOUN
ejpam-5823	474	4	research	research	NOUN
ejpam-5823	474	5	in	in	ADP
ejpam-5823	474	6	physics	physics	NOUN
ejpam-5823	474	7	chemistry	chemistry	PROPN
ejpam-5823	474	8	&	&	CCONJ
ejpam-5823	474	9	mathematics	mathematic	NOUN
ejpam-5823	474	10	,	,	PUNCT
ejpam-5823	474	11	3:17–31	3:17–31	NUM
ejpam-5823	474	12	,	,	PUNCT
ejpam-5823	474	13	2016	2016	NUM
ejpam-5823	474	14	.	.	PUNCT
ejpam-5823	475	1	s.	s.	PROPN
ejpam-5823	475	2	a.	a.	PROPN
ejpam-5823	475	3	h.	h.	PROPN
ejpam-5823	475	4	shah	shah	PROPN
ejpam-5823	475	5	et	et	PROPN
ejpam-5823	475	6	al	al	PROPN
ejpam-5823	475	7	.	.	PUNCT
ejpam-5823	475	8	/	/	SYM
ejpam-5823	475	9	eur	eur	PROPN
ejpam-5823	475	10	.	.	PUNCT
ejpam-5823	476	1	j.	j.	PROPN
ejpam-5823	476	2	pure	pure	PROPN
ejpam-5823	476	3	appl	appl	PROPN
ejpam-5823	476	4	.	.	PROPN
ejpam-5823	476	5	math	math	PROPN
ejpam-5823	476	6	,	,	PUNCT
ejpam-5823	476	7	18	18	NUM
ejpam-5823	476	8	(	(	PUNCT
ejpam-5823	476	9	2	2	NUM
ejpam-5823	476	10	)	)	PUNCT
ejpam-5823	476	11	(	(	PUNCT
ejpam-5823	476	12	2025	2025	NUM
ejpam-5823	476	13	)	)	PUNCT
ejpam-5823	476	14	,	,	PUNCT
ejpam-5823	476	15	5823	5823	NUM
ejpam-5823	476	16	25	25	NUM
ejpam-5823	476	17	of	of	ADP
ejpam-5823	476	18	26	26	NUM
ejpam-5823	477	1	[	[	SYM
ejpam-5823	477	2	8	8	NUM
ejpam-5823	477	3	]	]	X
ejpam-5823	477	4	robert	robert	PROPN
ejpam-5823	477	5	reynolds	reynolds	PROPN
ejpam-5823	477	6	and	and	CCONJ
ejpam-5823	477	7	allan	allan	PROPN
ejpam-5823	477	8	stauffer	stauffer	PROPN
ejpam-5823	477	9	.	.	PUNCT
ejpam-5823	478	1	double	double	ADJ
ejpam-5823	478	2	integral	integral	ADJ
ejpam-5823	478	3	involving	involve	VERB
ejpam-5823	478	4	the	the	DET
ejpam-5823	478	5	product	product	NOUN
ejpam-5823	478	6	of	of	ADP
ejpam-5823	478	7	the	the	DET
ejpam-5823	478	8	bessel	bessel	ADJ
ejpam-5823	478	9	function	function	NOUN
ejpam-5823	478	10	of	of	ADP
ejpam-5823	478	11	the	the	DET
ejpam-5823	478	12	first	first	ADJ
ejpam-5823	478	13	kind	kind	NOUN
ejpam-5823	478	14	and	and	CCONJ
ejpam-5823	478	15	modified	modified	ADJ
ejpam-5823	478	16	bessel	bessel	NOUN
ejpam-5823	478	17	function	function	NOUN
ejpam-5823	478	18	of	of	ADP
ejpam-5823	478	19	the	the	DET
ejpam-5823	478	20	second	second	ADJ
ejpam-5823	478	21	kind	kind	NOUN
ejpam-5823	478	22	:	:	PUNCT
ejpam-5823	478	23	derivation	derivation	NOUN
ejpam-5823	478	24	and	and	CCONJ
ejpam-5823	478	25	evaluation	evaluation	NOUN
ejpam-5823	478	26	.	.	PUNCT
ejpam-5823	479	1	european	european	ADJ
ejpam-5823	479	2	journal	journal	PROPN
ejpam-5823	479	3	of	of	ADP
ejpam-5823	479	4	pure	pure	ADJ
ejpam-5823	479	5	and	and	CCONJ
ejpam-5823	479	6	applied	applied	ADJ
ejpam-5823	479	7	mathematics	mathematic	NOUN
ejpam-5823	479	8	,	,	PUNCT
ejpam-5823	479	9	15(3):856–863	15(3):856–863	NOUN
ejpam-5823	479	10	,	,	PUNCT
ejpam-5823	479	11	2022	2022	NUM
ejpam-5823	479	12	.	.	PUNCT
ejpam-5823	480	1	[	[	X
ejpam-5823	480	2	9	9	NUM
ejpam-5823	480	3	]	]	X
ejpam-5823	480	4	robert	robert	PROPN
ejpam-5823	480	5	reynolds	reynolds	PROPN
ejpam-5823	480	6	and	and	CCONJ
ejpam-5823	480	7	allan	allan	PROPN
ejpam-5823	480	8	stauffer	stauffer	PROPN
ejpam-5823	480	9	.	.	PUNCT
ejpam-5823	481	1	triple	triple	ADJ
ejpam-5823	481	2	integral	integral	ADJ
ejpam-5823	481	3	involving	involve	VERB
ejpam-5823	481	4	the	the	DET
ejpam-5823	481	5	bessel	bessel	NOUN
ejpam-5823	481	6	-	-	PUNCT
ejpam-5823	481	7	integral	integral	ADJ
ejpam-5823	481	8	function	function	NOUN
ejpam-5823	481	9	jiv	jiv	PROPN
ejpam-5823	481	10	(	(	PUNCT
ejpam-5823	481	11	z	z	NOUN
ejpam-5823	481	12	):	):	PUNCT
ejpam-5823	481	13	derivation	derivation	NOUN
ejpam-5823	481	14	and	and	CCONJ
ejpam-5823	481	15	evaluation	evaluation	NOUN
ejpam-5823	481	16	.	.	PUNCT
ejpam-5823	482	1	european	european	ADJ
ejpam-5823	482	2	journal	journal	PROPN
ejpam-5823	482	3	of	of	ADP
ejpam-5823	482	4	pure	pure	ADJ
ejpam-5823	482	5	and	and	CCONJ
ejpam-5823	482	6	applied	applied	ADJ
ejpam-5823	482	7	mathematics	mathematic	NOUN
ejpam-5823	482	8	,	,	PUNCT
ejpam-5823	482	9	15(3):916–923	15(3):916–923	PROPN
ejpam-5823	482	10	,	,	PUNCT
ejpam-5823	482	11	2022	2022	NUM
ejpam-5823	482	12	.	.	PUNCT
ejpam-5823	483	1	[	[	X
ejpam-5823	483	2	10	10	NUM
ejpam-5823	483	3	]	]	X
ejpam-5823	483	4	b	b	NOUN
ejpam-5823	483	5	a	a	DET
ejpam-5823	483	6	frasin	frasin	NOUN
ejpam-5823	484	1	and	and	CCONJ
ejpam-5823	484	2	i	i	PRON
ejpam-5823	484	3	aldawish	aldawish	VERB
ejpam-5823	484	4	.	.	PUNCT
ejpam-5823	485	1	on	on	ADP
ejpam-5823	485	2	subclasses	subclass	NOUN
ejpam-5823	485	3	of	of	ADP
ejpam-5823	485	4	uniformly	uniformly	ADV
ejpam-5823	485	5	spiral	spiral	ADJ
ejpam-5823	485	6	-	-	PUNCT
ejpam-5823	485	7	like	like	ADJ
ejpam-5823	485	8	functions	function	NOUN
ejpam-5823	485	9	associated	associate	VERB
ejpam-5823	485	10	with	with	ADP
ejpam-5823	485	11	generalized	generalized	ADJ
ejpam-5823	485	12	bessel	bessel	NOUN
ejpam-5823	485	13	functions	function	NOUN
ejpam-5823	485	14	.	.	PUNCT
ejpam-5823	486	1	journal	journal	NOUN
ejpam-5823	486	2	of	of	ADP
ejpam-5823	486	3	function	function	NOUN
ejpam-5823	486	4	spaces	space	NOUN
ejpam-5823	486	5	,	,	PUNCT
ejpam-5823	486	6	2019(1):1329462	2019(1):1329462	NOUN
ejpam-5823	486	7	,	,	PUNCT
ejpam-5823	486	8	2019	2019	NUM
ejpam-5823	486	9	.	.	PUNCT
ejpam-5823	487	1	[	[	X
ejpam-5823	487	2	11	11	NUM
ejpam-5823	487	3	]	]	PUNCT
ejpam-5823	487	4	syed	syed	PROPN
ejpam-5823	487	5	ali	ali	PROPN
ejpam-5823	487	6	haider	haider	PROPN
ejpam-5823	487	7	shah	shah	PROPN
ejpam-5823	487	8	and	and	CCONJ
ejpam-5823	487	9	shahid	shahid	PROPN
ejpam-5823	487	10	mubeen	mubeen	PROPN
ejpam-5823	487	11	.	.	PUNCT
ejpam-5823	487	12	expressions	expression	NOUN
ejpam-5823	487	13	of	of	ADP
ejpam-5823	487	14	the	the	DET
ejpam-5823	487	15	laguerre	laguerre	NOUN
ejpam-5823	487	16	polynomial	polynomial	ADJ
ejpam-5823	487	17	and	and	CCONJ
ejpam-5823	487	18	some	some	DET
ejpam-5823	487	19	other	other	ADJ
ejpam-5823	487	20	special	special	ADJ
ejpam-5823	487	21	functions	function	NOUN
ejpam-5823	487	22	in	in	ADP
ejpam-5823	487	23	terms	term	NOUN
ejpam-5823	487	24	of	of	ADP
ejpam-5823	487	25	the	the	DET
ejpam-5823	487	26	generalized	generalized	ADJ
ejpam-5823	487	27	meijer	meijer	NOUN
ejpam-5823	487	28	g	g	NOUN
ejpam-5823	487	29	-	-	PUNCT
ejpam-5823	487	30	functions	function	NOUN
ejpam-5823	487	31	.	.	PUNCT
ejpam-5823	488	1	aims	aim	VERB
ejpam-5823	488	2	math	math	NOUN
ejpam-5823	488	3	,	,	PUNCT
ejpam-5823	488	4	6:11631–11641	6:11631–11641	NUM
ejpam-5823	488	5	,	,	PUNCT
ejpam-5823	488	6	2021	2021	NUM
ejpam-5823	488	7	.	.	PUNCT
ejpam-5823	489	1	[	[	X
ejpam-5823	489	2	12	12	NUM
ejpam-5823	489	3	]	]	X
ejpam-5823	489	4	r	r	NOUN
ejpam-5823	489	5	m	m	VERB
ejpam-5823	489	6	ali	ali	PROPN
ejpam-5823	489	7	,	,	PUNCT
ejpam-5823	489	8	s	s	PART
ejpam-5823	489	9	k	k	PROPN
ejpam-5823	489	10	lee	lee	PROPN
ejpam-5823	489	11	,	,	PUNCT
ejpam-5823	489	12	and	and	CCONJ
ejpam-5823	489	13	s	s	NOUN
ejpam-5823	489	14	r	r	NOUN
ejpam-5823	489	15	mondal	mondal	NOUN
ejpam-5823	489	16	.	.	PUNCT
ejpam-5823	490	1	inequalities	inequality	NOUN
ejpam-5823	490	2	on	on	ADP
ejpam-5823	490	3	an	an	DET
ejpam-5823	490	4	extended	extended	ADJ
ejpam-5823	490	5	bessel	bessel	NOUN
ejpam-5823	490	6	function	function	NOUN
ejpam-5823	490	7	.	.	PUNCT
ejpam-5823	491	1	journal	journal	PROPN
ejpam-5823	491	2	of	of	ADP
ejpam-5823	491	3	inequalities	inequality	NOUN
ejpam-5823	491	4	and	and	CCONJ
ejpam-5823	491	5	applications	application	NOUN
ejpam-5823	491	6	,	,	PUNCT
ejpam-5823	491	7	2018:1–22	2018:1–22	NUM
ejpam-5823	491	8	,	,	PUNCT
ejpam-5823	491	9	2018	2018	NUM
ejpam-5823	491	10	.	.	PUNCT
ejpam-5823	492	1	[	[	X
ejpam-5823	492	2	13	13	NUM
ejpam-5823	492	3	]	]	PUNCT
ejpam-5823	492	4	á	á	NOUN
ejpam-5823	492	5	baricz	baricz	NOUN
ejpam-5823	492	6	.	.	PUNCT
ejpam-5823	493	1	generalized	generalized	ADJ
ejpam-5823	493	2	bessel	bessel	NOUN
ejpam-5823	493	3	functions	function	NOUN
ejpam-5823	493	4	of	of	ADP
ejpam-5823	493	5	the	the	DET
ejpam-5823	493	6	first	first	ADJ
ejpam-5823	493	7	kind	kind	NOUN
ejpam-5823	493	8	.	.	PUNCT
ejpam-5823	494	1	lecture	lecture	NOUN
ejpam-5823	494	2	notes	note	NOUN
ejpam-5823	494	3	in	in	ADP
ejpam-5823	494	4	mathematics	mathematics	NOUN
ejpam-5823	494	5	/	/	SYM
ejpam-5823	494	6	springer	springer	NOUN
ejpam-5823	494	7	-	-	PUNCT
ejpam-5823	494	8	verlag	verlag	PROPN
ejpam-5823	494	9	,	,	PUNCT
ejpam-5823	494	10	2010	2010	NUM
ejpam-5823	494	11	.	.	PUNCT
ejpam-5823	495	1	[	[	X
ejpam-5823	495	2	14	14	NUM
ejpam-5823	495	3	]	]	PUNCT
ejpam-5823	495	4	á	á	NOUN
ejpam-5823	495	5	baricz	baricz	NOUN
ejpam-5823	495	6	.	.	PUNCT
ejpam-5823	496	1	functional	functional	ADJ
ejpam-5823	496	2	inequalities	inequality	NOUN
ejpam-5823	496	3	for	for	ADP
ejpam-5823	496	4	galué	galué	NOUN
ejpam-5823	496	5	’s	’s	PART
ejpam-5823	496	6	generalized	generalize	VERB
ejpam-5823	496	7	modified	modify	VERB
ejpam-5823	496	8	bessel	bessel	NOUN
ejpam-5823	496	9	functions	function	NOUN
ejpam-5823	496	10	.	.	PUNCT
ejpam-5823	497	1	journal	journal	PROPN
ejpam-5823	497	2	of	of	ADP
ejpam-5823	497	3	mathematical	mathematical	ADJ
ejpam-5823	497	4	inequalities	inequality	NOUN
ejpam-5823	497	5	,	,	PUNCT
ejpam-5823	497	6	1(2):183–193	1(2):183–193	NUM
ejpam-5823	497	7	,	,	PUNCT
ejpam-5823	497	8	2007	2007	NUM
ejpam-5823	497	9	.	.	PUNCT
ejpam-5823	498	1	[	[	X
ejpam-5823	498	2	15	15	NUM
ejpam-5823	498	3	]	]	X
ejpam-5823	498	4	r	r	X
ejpam-5823	498	5	ali	ali	PROPN
ejpam-5823	498	6	,	,	PUNCT
ejpam-5823	498	7	m	m	PROPN
ejpam-5823	498	8	kamran	kamran	PROPN
ejpam-5823	498	9	,	,	PUNCT
ejpam-5823	498	10	and	and	CCONJ
ejpam-5823	498	11	i	i	PRON
ejpam-5823	498	12	nayab	nayab	VERB
ejpam-5823	498	13	.	.	PUNCT
ejpam-5823	499	1	some	some	DET
ejpam-5823	499	2	results	result	NOUN
ejpam-5823	499	3	of	of	ADP
ejpam-5823	499	4	generalized	generalized	ADJ
ejpam-5823	499	5	k	k	ADJ
ejpam-5823	499	6	-	-	ADJ
ejpam-5823	499	7	fractional	fractional	ADJ
ejpam-5823	499	8	integral	integral	ADJ
ejpam-5823	499	9	operator	operator	NOUN
ejpam-5823	499	10	with	with	ADP
ejpam-5823	499	11	k	k	ADJ
ejpam-5823	499	12	-	-	ADJ
ejpam-5823	499	13	bessel	bessel	ADJ
ejpam-5823	499	14	function	function	NOUN
ejpam-5823	499	15	.	.	PUNCT
ejpam-5823	500	1	turkish	turkish	ADJ
ejpam-5823	500	2	journal	journal	PROPN
ejpam-5823	500	3	of	of	ADP
ejpam-5823	500	4	science	science	NOUN
ejpam-5823	500	5	,	,	PUNCT
ejpam-5823	500	6	5(3):157–169	5(3):157–169	NUM
ejpam-5823	500	7	,	,	PUNCT
ejpam-5823	500	8	2020	2020	NUM
ejpam-5823	500	9	.	.	PUNCT
ejpam-5823	501	1	[	[	X
ejpam-5823	501	2	16	16	NUM
ejpam-5823	501	3	]	]	X
ejpam-5823	501	4	h	h	PROPN
ejpam-5823	501	5	m	m	PROPN
ejpam-5823	501	6	srivastava	srivastava	PROPN
ejpam-5823	501	7	.	.	PUNCT
ejpam-5823	502	1	an	an	DET
ejpam-5823	502	2	introductory	introductory	ADJ
ejpam-5823	502	3	overview	overview	NOUN
ejpam-5823	502	4	of	of	ADP
ejpam-5823	502	5	bessel	bessel	ADJ
ejpam-5823	502	6	polynomials	polynomial	NOUN
ejpam-5823	502	7	,	,	PUNCT
ejpam-5823	502	8	the	the	DET
ejpam-5823	502	9	generalized	generalized	ADJ
ejpam-5823	502	10	bessel	bessel	ADJ
ejpam-5823	502	11	polynomials	polynomial	NOUN
ejpam-5823	502	12	and	and	CCONJ
ejpam-5823	502	13	the	the	DET
ejpam-5823	502	14	q	q	ADJ
ejpam-5823	502	15	-	-	PUNCT
ejpam-5823	502	16	bessel	bessel	ADJ
ejpam-5823	502	17	polynomials	polynomial	NOUN
ejpam-5823	502	18	.	.	PUNCT
ejpam-5823	503	1	symmetry	symmetry	NOUN
ejpam-5823	503	2	,	,	PUNCT
ejpam-5823	503	3	15(4):822	15(4):822	NUM
ejpam-5823	503	4	,	,	PUNCT
ejpam-5823	503	5	2023	2023	NUM
ejpam-5823	503	6	.	.	PUNCT
ejpam-5823	504	1	[	[	X
ejpam-5823	504	2	17	17	NUM
ejpam-5823	504	3	]	]	X
ejpam-5823	504	4	d	d	X
ejpam-5823	504	5	girela	girela	NOUN
ejpam-5823	504	6	.	.	PUNCT
ejpam-5823	505	1	basic	basic	ADJ
ejpam-5823	505	2	theory	theory	NOUN
ejpam-5823	505	3	of	of	ADP
ejpam-5823	505	4	univalent	univalent	ADJ
ejpam-5823	505	5	functions	function	NOUN
ejpam-5823	505	6	.	.	PUNCT
ejpam-5823	506	1	in	in	ADP
ejpam-5823	506	2	conference	conference	NOUN
ejpam-5823	506	3	paper	paper	NOUN
ejpam-5823	506	4	.	.	PUNCT
ejpam-5823	507	1	universidad	universidad	PROPN
ejpam-5823	507	2	de	de	PROPN
ejpam-5823	507	3	málaga	málaga	PROPN
ejpam-5823	507	4	,	,	PUNCT
ejpam-5823	507	5	2013	2013	NUM
ejpam-5823	507	6	.	.	PUNCT
ejpam-5823	508	1	[	[	X
ejpam-5823	508	2	18	18	NUM
ejpam-5823	508	3	]	]	X
ejpam-5823	508	4	d	d	PROPN
ejpam-5823	508	5	k	k	PROPN
ejpam-5823	508	6	thomas	thomas	PROPN
ejpam-5823	508	7	,	,	PUNCT
ejpam-5823	508	8	n	n	CCONJ
ejpam-5823	508	9	tuneski	tuneski	ADJ
ejpam-5823	508	10	,	,	PUNCT
ejpam-5823	508	11	and	and	CCONJ
ejpam-5823	508	12	a	a	DET
ejpam-5823	508	13	vasudevarao	vasudevarao	NOUN
ejpam-5823	508	14	.	.	PUNCT
ejpam-5823	509	1	univalent	univalent	ADJ
ejpam-5823	509	2	functions	function	NOUN
ejpam-5823	509	3	:	:	PUNCT
ejpam-5823	509	4	a	a	DET
ejpam-5823	509	5	primer	primer	NOUN
ejpam-5823	509	6	,	,	PUNCT
ejpam-5823	509	7	volume	volume	NOUN
ejpam-5823	509	8	69	69	NUM
ejpam-5823	509	9	.	.	PUNCT
ejpam-5823	510	1	walter	walter	PROPN
ejpam-5823	510	2	de	de	PROPN
ejpam-5823	510	3	gruyter	gruyter	PROPN
ejpam-5823	510	4	gmbh	gmbh	PROPN
ejpam-5823	510	5	&	&	CCONJ
ejpam-5823	510	6	co	co	X
ejpam-5823	510	7	kg	kg	PROPN
ejpam-5823	510	8	,	,	PUNCT
ejpam-5823	510	9	2018	2018	NUM
ejpam-5823	510	10	.	.	PUNCT
ejpam-5823	511	1	[	[	X
ejpam-5823	511	2	19	19	NUM
ejpam-5823	511	3	]	]	SYM
ejpam-5823	511	4	s	s	NOUN
ejpam-5823	511	5	r	r	NOUN
ejpam-5823	511	6	mondal	mondal	NOUN
ejpam-5823	511	7	and	and	CCONJ
ejpam-5823	511	8	a	a	DET
ejpam-5823	511	9	swaminathan	swaminathan	NOUN
ejpam-5823	511	10	.	.	PUNCT
ejpam-5823	512	1	geometric	geometric	ADJ
ejpam-5823	512	2	properties	property	NOUN
ejpam-5823	512	3	of	of	ADP
ejpam-5823	512	4	generalized	generalized	ADJ
ejpam-5823	512	5	bessel	bessel	NOUN
ejpam-5823	512	6	functions	function	NOUN
ejpam-5823	512	7	.	.	PUNCT
ejpam-5823	513	1	bulletin	bulletin	NOUN
ejpam-5823	513	2	of	of	ADP
ejpam-5823	513	3	the	the	DET
ejpam-5823	513	4	malaysian	malaysian	PROPN
ejpam-5823	513	5	mathematical	mathematical	PROPN
ejpam-5823	513	6	sciences	sciences	PROPN
ejpam-5823	513	7	society	society	NOUN
ejpam-5823	513	8	,	,	PUNCT
ejpam-5823	513	9	35(1	35(1	NUM
ejpam-5823	513	10	)	)	PUNCT
ejpam-5823	513	11	,	,	PUNCT
ejpam-5823	513	12	2012	2012	NUM
ejpam-5823	513	13	.	.	PUNCT
ejpam-5823	514	1	[	[	X
ejpam-5823	514	2	20	20	NUM
ejpam-5823	514	3	]	]	X
ejpam-5823	514	4	h	h	NOUN
ejpam-5823	514	5	m	m	VERB
ejpam-5823	514	6	zayed	zayed	ADJ
ejpam-5823	514	7	and	and	CCONJ
ejpam-5823	514	8	t	t	PROPN
ejpam-5823	514	9	bulboacă.	bulboacă.	PROPN
ejpam-5823	514	10	normalized	normalize	VERB
ejpam-5823	514	11	generalized	generalized	ADJ
ejpam-5823	514	12	bessel	bessel	NOUN
ejpam-5823	514	13	function	function	NOUN
ejpam-5823	514	14	and	and	CCONJ
ejpam-5823	514	15	its	its	PRON
ejpam-5823	514	16	geometric	geometric	ADJ
ejpam-5823	514	17	properties	property	NOUN
ejpam-5823	514	18	.	.	PUNCT
ejpam-5823	515	1	journal	journal	PROPN
ejpam-5823	515	2	of	of	ADP
ejpam-5823	515	3	inequalities	inequality	NOUN
ejpam-5823	515	4	and	and	CCONJ
ejpam-5823	515	5	applications	application	NOUN
ejpam-5823	515	6	,	,	PUNCT
ejpam-5823	515	7	2022(1):158	2022(1):158	NUM
ejpam-5823	515	8	,	,	PUNCT
ejpam-5823	515	9	2022	2022	NUM
ejpam-5823	515	10	.	.	PUNCT
ejpam-5823	516	1	[	[	X
ejpam-5823	516	2	21	21	NUM
ejpam-5823	516	3	]	]	PUNCT
ejpam-5823	516	4	á	á	NOUN
ejpam-5823	516	5	baricz	baricz	NOUN
ejpam-5823	516	6	and	and	CCONJ
ejpam-5823	516	7	s	s	NOUN
ejpam-5823	516	8	ponnusamy	ponnusamy	NOUN
ejpam-5823	516	9	.	.	PUNCT
ejpam-5823	517	1	starlikeness	starlikeness	NOUN
ejpam-5823	517	2	and	and	CCONJ
ejpam-5823	517	3	convexity	convexity	NOUN
ejpam-5823	517	4	of	of	ADP
ejpam-5823	517	5	generalized	generalized	ADJ
ejpam-5823	517	6	bessel	bessel	NOUN
ejpam-5823	517	7	functions	function	NOUN
ejpam-5823	517	8	.	.	PUNCT
ejpam-5823	518	1	integral	integral	ADJ
ejpam-5823	518	2	transforms	transform	NOUN
ejpam-5823	518	3	and	and	CCONJ
ejpam-5823	518	4	special	special	ADJ
ejpam-5823	518	5	functions	function	NOUN
ejpam-5823	518	6	,	,	PUNCT
ejpam-5823	518	7	21(9):641–653	21(9):641–653	PROPN
ejpam-5823	518	8	,	,	PUNCT
ejpam-5823	518	9	2010	2010	NUM
ejpam-5823	518	10	.	.	PUNCT
ejpam-5823	519	1	[	[	X
ejpam-5823	519	2	22	22	NUM
ejpam-5823	519	3	]	]	SYM
ejpam-5823	519	4	s	s	NOUN
ejpam-5823	519	5	r	r	NOUN
ejpam-5823	519	6	mondal	mondal	NOUN
ejpam-5823	519	7	and	and	CCONJ
ejpam-5823	519	8	m	m	PROPN
ejpam-5823	519	9	s	s	PROPN
ejpam-5823	519	10	akel	akel	PROPN
ejpam-5823	519	11	.	.	PUNCT
ejpam-5823	519	12	differential	differential	ADJ
ejpam-5823	519	13	equation	equation	NOUN
ejpam-5823	519	14	and	and	CCONJ
ejpam-5823	519	15	inequalities	inequality	NOUN
ejpam-5823	519	16	of	of	ADP
ejpam-5823	519	17	the	the	DET
ejpam-5823	519	18	generalized	generalized	ADJ
ejpam-5823	519	19	k	k	ADJ
ejpam-5823	519	20	-	-	ADJ
ejpam-5823	519	21	bessel	bessel	ADJ
ejpam-5823	519	22	functions	function	NOUN
ejpam-5823	519	23	.	.	PUNCT
ejpam-5823	520	1	journal	journal	PROPN
ejpam-5823	520	2	of	of	ADP
ejpam-5823	520	3	inequalities	inequality	NOUN
ejpam-5823	520	4	and	and	CCONJ
ejpam-5823	520	5	applications	application	NOUN
ejpam-5823	520	6	,	,	PUNCT
ejpam-5823	520	7	2018:1–14	2018:1–14	NOUN
ejpam-5823	520	8	,	,	PUNCT
ejpam-5823	520	9	2018	2018	NUM
ejpam-5823	520	10	.	.	PUNCT
ejpam-5823	521	1	[	[	X
ejpam-5823	521	2	23	23	NUM
ejpam-5823	521	3	]	]	X
ejpam-5823	521	4	r	r	NOUN
ejpam-5823	521	5	diaz	diaz	PROPN
ejpam-5823	521	6	and	and	CCONJ
ejpam-5823	521	7	e	e	PROPN
ejpam-5823	521	8	pariguan	pariguan	PROPN
ejpam-5823	521	9	.	.	PUNCT
ejpam-5823	522	1	on	on	ADP
ejpam-5823	522	2	hypergeometric	hypergeometric	ADJ
ejpam-5823	522	3	functions	function	NOUN
ejpam-5823	522	4	and	and	CCONJ
ejpam-5823	522	5	pochhammer	pochhammer	NOUN
ejpam-5823	522	6	k	k	NOUN
ejpam-5823	522	7	-	-	NOUN
ejpam-5823	522	8	symbol	symbol	NOUN
ejpam-5823	522	9	.	.	PUNCT
ejpam-5823	523	1	arxiv	arxiv	PROPN
ejpam-5823	523	2	preprint	preprint	PROPN
ejpam-5823	523	3	math/0405596	math/0405596	PROPN
ejpam-5823	523	4	,	,	PUNCT
ejpam-5823	523	5	2004	2004	NUM
ejpam-5823	523	6	.	.	PUNCT
ejpam-5823	524	1	[	[	X
ejpam-5823	524	2	24	24	NUM
ejpam-5823	524	3	]	]	X
ejpam-5823	524	4	s	s	AUX
ejpam-5823	524	5	ahmed	ahme	VERB
ejpam-5823	524	6	.	.	PUNCT
ejpam-5823	525	1	some	some	DET
ejpam-5823	525	2	integrals	integral	NOUN
ejpam-5823	525	3	involving	involve	VERB
ejpam-5823	525	4	k	k	PROPN
ejpam-5823	525	5	-	-	NOUN
ejpam-5823	525	6	gamma	gamma	NOUN
ejpam-5823	525	7	and	and	CCONJ
ejpam-5823	525	8	k	k	PROPN
ejpam-5823	525	9	-	-	ADJ
ejpam-5823	525	10	digamma	digamma	PROPN
ejpam-5823	525	11	function	function	NOUN
ejpam-5823	525	12	.	.	PUNCT
ejpam-5823	526	1	journal	journal	NOUN
ejpam-5823	526	2	of	of	ADP
ejpam-5823	526	3	the	the	DET
ejpam-5823	526	4	egyptian	egyptian	PROPN
ejpam-5823	526	5	mathematical	mathematical	PROPN
ejpam-5823	526	6	society	society	NOUN
ejpam-5823	526	7	,	,	PUNCT
ejpam-5823	526	8	28(1):39	28(1):39	NUM
ejpam-5823	526	9	,	,	PUNCT
ejpam-5823	526	10	2020	2020	NUM
ejpam-5823	526	11	.	.	PUNCT
ejpam-5823	527	1	[	[	X
ejpam-5823	527	2	25	25	NUM
ejpam-5823	527	3	]	]	X
ejpam-5823	527	4	e	e	NOUN
ejpam-5823	527	5	m	m	PROPN
ejpam-5823	527	6	r	r	VERB
ejpam-5823	527	7	a	a	DET
ejpam-5823	527	8	h	h	NOUN
ejpam-5823	527	9	yildirim	yildirim	NOUN
ejpam-5823	528	1	and	and	CCONJ
ejpam-5823	528	2	i	i	PRON
ejpam-5823	528	3	n	n	VERB
ejpam-5823	528	4	c	c	VERB
ejpam-5823	528	5	i	i	PRON
ejpam-5823	528	6	ege	ege	PROPN
ejpam-5823	528	7	.	.	PUNCT
ejpam-5823	529	1	on	on	ADP
ejpam-5823	529	2	k	k	NOUN
ejpam-5823	529	3	-	-	PUNCT
ejpam-5823	529	4	analogues	analogue	NOUN
ejpam-5823	529	5	of	of	ADP
ejpam-5823	529	6	digamma	digamma	PROPN
ejpam-5823	529	7	and	and	CCONJ
ejpam-5823	529	8	polygamma	polygamma	PROPN
ejpam-5823	529	9	functions	function	NOUN
ejpam-5823	529	10	.	.	PUNCT
ejpam-5823	530	1	journal	journal	NOUN
ejpam-5823	530	2	of	of	ADP
ejpam-5823	530	3	classical	classical	ADJ
ejpam-5823	530	4	analysis	analysis	NOUN
ejpam-5823	530	5	,	,	PUNCT
ejpam-5823	530	6	13(2):123–131	13(2):123–131	NUM
ejpam-5823	530	7	,	,	PUNCT
ejpam-5823	530	8	2018	2018	NUM
ejpam-5823	530	9	.	.	PUNCT
ejpam-5823	531	1	[	[	X
ejpam-5823	531	2	26	26	NUM
ejpam-5823	531	3	]	]	X
ejpam-5823	531	4	k	k	PROPN
ejpam-5823	531	5	nantomah	nantomah	PROPN
ejpam-5823	531	6	,	,	PUNCT
ejpam-5823	531	7	f	f	PROPN
ejpam-5823	531	8	merovci	merovci	NOUN
ejpam-5823	531	9	,	,	PUNCT
ejpam-5823	531	10	and	and	CCONJ
ejpam-5823	531	11	s	s	VERB
ejpam-5823	531	12	nasiru	nasiru	NOUN
ejpam-5823	531	13	.	.	PUNCT
ejpam-5823	532	1	some	some	DET
ejpam-5823	532	2	monotonicity	monotonicity	NOUN
ejpam-5823	532	3	properties	property	NOUN
ejpam-5823	532	4	and	and	CCONJ
ejpam-5823	532	5	inequalities	inequality	NOUN
ejpam-5823	532	6	for	for	ADP
ejpam-5823	532	7	the	the	DET
ejpam-5823	532	8	(	(	PUNCT
ejpam-5823	532	9	p	p	NOUN
ejpam-5823	532	10	,	,	PUNCT
ejpam-5823	532	11	k)-gamma	k)-gamma	PROPN
ejpam-5823	532	12	function	function	NOUN
ejpam-5823	532	13	.	.	PUNCT
ejpam-5823	533	1	kragujevac	kragujevac	PROPN
ejpam-5823	533	2	journal	journal	PROPN
ejpam-5823	533	3	of	of	ADP
ejpam-5823	533	4	mathematics	mathematic	NOUN
ejpam-5823	533	5	,	,	PUNCT
ejpam-5823	533	6	42(2):287–297	42(2):287–297	PROPN
ejpam-5823	533	7	,	,	PUNCT
ejpam-5823	533	8	2018	2018	NUM
ejpam-5823	533	9	.	.	PUNCT
ejpam-5823	534	1	s.	s.	PROPN
ejpam-5823	534	2	a.	a.	PROPN
ejpam-5823	534	3	h.	h.	PROPN
ejpam-5823	534	4	shah	shah	PROPN
ejpam-5823	534	5	et	et	PROPN
ejpam-5823	534	6	al	al	PROPN
ejpam-5823	534	7	.	.	PUNCT
ejpam-5823	534	8	/	/	SYM
ejpam-5823	534	9	eur	eur	PROPN
ejpam-5823	534	10	.	.	PUNCT
ejpam-5823	535	1	j.	j.	PROPN
ejpam-5823	535	2	pure	pure	PROPN
ejpam-5823	535	3	appl	appl	PROPN
ejpam-5823	535	4	.	.	PROPN
ejpam-5823	535	5	math	math	PROPN
ejpam-5823	535	6	,	,	PUNCT
ejpam-5823	535	7	18	18	NUM
ejpam-5823	535	8	(	(	PUNCT
ejpam-5823	535	9	2	2	NUM
ejpam-5823	535	10	)	)	PUNCT
ejpam-5823	535	11	(	(	PUNCT
ejpam-5823	535	12	2025	2025	NUM
ejpam-5823	535	13	)	)	PUNCT
ejpam-5823	535	14	,	,	PUNCT
ejpam-5823	535	15	5823	5823	NUM
ejpam-5823	535	16	26	26	NUM
ejpam-5823	535	17	of	of	ADP
ejpam-5823	535	18	26	26	NUM
ejpam-5823	535	19	[	[	X
ejpam-5823	535	20	27	27	NUM
ejpam-5823	535	21	]	]	X
ejpam-5823	535	22	h	h	NOUN
ejpam-5823	535	23	silverman	silverman	NOUN
ejpam-5823	535	24	.	.	PUNCT
ejpam-5823	536	1	univalent	univalent	ADJ
ejpam-5823	536	2	functions	function	NOUN
ejpam-5823	536	3	with	with	ADP
ejpam-5823	536	4	negative	negative	ADJ
ejpam-5823	536	5	coefficients	coefficient	NOUN
ejpam-5823	536	6	.	.	PUNCT
ejpam-5823	537	1	proceedings	proceeding	NOUN
ejpam-5823	537	2	of	of	ADP
ejpam-5823	537	3	the	the	DET
ejpam-5823	537	4	american	american	PROPN
ejpam-5823	537	5	mathematical	mathematical	PROPN
ejpam-5823	537	6	society	society	NOUN
ejpam-5823	537	7	,	,	PUNCT
ejpam-5823	537	8	51(1):109–116	51(1):109–116	PROPN
ejpam-5823	537	9	,	,	PUNCT
ejpam-5823	537	10	1975	1975	NUM
ejpam-5823	537	11	.	.	PUNCT
ejpam-5823	538	1	introduction	introduction	NOUN
ejpam-5823	538	2	main	main	ADJ
ejpam-5823	538	3	results	result	NOUN
ejpam-5823	538	4	starlikeness	starlikeness	NOUN
ejpam-5823	538	5	and	and	CCONJ
ejpam-5823	538	6	convexity	convexity	NOUN
ejpam-5823	538	7	of	of	ADP
ejpam-5823	538	8	order	order	NOUN
ejpam-5823	538	9	examples	example	NOUN
ejpam-5823	538	10	order	order	NOUN
ejpam-5823	538	11	of	of	ADP
ejpam-5823	538	12	starlikeness	starlikeness	NOUN
ejpam-5823	538	13	and	and	CCONJ
ejpam-5823	538	14	convexity	convexity	NOUN
ejpam-5823	538	15	by	by	ADP
ejpam-5823	538	16	silverman	silverman	PROPN
ejpam-5823	538	17	's	's	PART
ejpam-5823	538	18	theorem	theorem	NOUN