id	sid	tid	token	lemma	pos
ejpam-5731	1	1	european	european	PROPN
ejpam-5731	1	2	journal	journal	PROPN
ejpam-5731	1	3	of	of	ADP
ejpam-5731	1	4	pure	pure	ADJ
ejpam-5731	1	5	and	and	CCONJ
ejpam-5731	1	6	applied	applied	ADJ
ejpam-5731	1	7	mathematics	mathematic	NOUN
ejpam-5731	1	8	2025	2025	NUM
ejpam-5731	1	9	,	,	PUNCT
ejpam-5731	1	10	vol	vol	NOUN
ejpam-5731	1	11	.	.	PROPN
ejpam-5731	1	12	18	18	NUM
ejpam-5731	1	13	,	,	PUNCT
ejpam-5731	1	14	issue	issue	NOUN
ejpam-5731	1	15	1	1	NUM
ejpam-5731	1	16	,	,	PUNCT
ejpam-5731	1	17	article	article	NOUN
ejpam-5731	1	18	number	number	NOUN
ejpam-5731	1	19	5731	5731	NUM
ejpam-5731	1	20	issn	issn	VERB
ejpam-5731	1	21	1307	1307	NUM
ejpam-5731	1	22	-	-	SYM
ejpam-5731	1	23	5543	5543	NUM
ejpam-5731	1	24	–	–	PUNCT
ejpam-5731	1	25	ejpam.com	ejpam.com	X
ejpam-5731	1	26	published	publish	VERB
ejpam-5731	1	27	by	by	ADP
ejpam-5731	1	28	new	new	PROPN
ejpam-5731	1	29	york	york	PROPN
ejpam-5731	1	30	business	business	PROPN
ejpam-5731	1	31	global	global	PROPN
ejpam-5731	1	32	an	an	DET
ejpam-5731	1	33	application	application	NOUN
ejpam-5731	1	34	of	of	ADP
ejpam-5731	1	35	legendre	legendre	PROPN
ejpam-5731	1	36	polynomials	polynomial	NOUN
ejpam-5731	1	37	to	to	ADP
ejpam-5731	1	38	bi	bi	ADJ
ejpam-5731	1	39	-	-	ADJ
ejpam-5731	1	40	bazilevic	bazilevic	ADJ
ejpam-5731	1	41	functions	function	NOUN
ejpam-5731	1	42	associated	associate	VERB
ejpam-5731	1	43	with	with	ADP
ejpam-5731	1	44	q	q	ADJ
ejpam-5731	1	45	-	-	PUNCT
ejpam-5731	1	46	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	1	47	operator	operator	NOUN
ejpam-5731	1	48	waleed	waleed	PROPN
ejpam-5731	1	49	al	al	PROPN
ejpam-5731	1	50	-	-	PUNCT
ejpam-5731	1	51	rawashdeh	rawashdeh	PROPN
ejpam-5731	1	52	department	department	NOUN
ejpam-5731	1	53	of	of	ADP
ejpam-5731	1	54	mathematics	mathematics	PROPN
ejpam-5731	1	55	,	,	PUNCT
ejpam-5731	1	56	zarqa	zarqa	PROPN
ejpam-5731	1	57	university	university	PROPN
ejpam-5731	1	58	,	,	PUNCT
ejpam-5731	1	59	2000	2000	NUM
ejpam-5731	1	60	zarqa	zarqa	NOUN
ejpam-5731	1	61	,	,	PUNCT
ejpam-5731	1	62	13110	13110	NUM
ejpam-5731	1	63	,	,	PUNCT
ejpam-5731	1	64	jordan	jordan	PROPN
ejpam-5731	1	65	abstract	abstract	PROPN
ejpam-5731	1	66	.	.	PUNCT
ejpam-5731	2	1	in	in	ADP
ejpam-5731	2	2	this	this	DET
ejpam-5731	2	3	paper	paper	NOUN
ejpam-5731	2	4	,	,	PUNCT
ejpam-5731	2	5	we	we	PRON
ejpam-5731	2	6	make	make	VERB
ejpam-5731	2	7	use	use	NOUN
ejpam-5731	2	8	of	of	ADP
ejpam-5731	2	9	the	the	DET
ejpam-5731	2	10	concept	concept	NOUN
ejpam-5731	2	11	of	of	ADP
ejpam-5731	2	12	fractional	fractional	ADJ
ejpam-5731	2	13	q	q	NOUN
ejpam-5731	2	14	-	-	NOUN
ejpam-5731	2	15	calculus	calculus	NOUN
ejpam-5731	2	16	to	to	PART
ejpam-5731	2	17	introduce	introduce	VERB
ejpam-5731	2	18	a	a	DET
ejpam-5731	2	19	novel	novel	ADJ
ejpam-5731	2	20	class	class	NOUN
ejpam-5731	2	21	of	of	ADP
ejpam-5731	2	22	bi	bi	ADJ
ejpam-5731	2	23	-	-	ADJ
ejpam-5731	2	24	bazilevic	bazilevic	ADJ
ejpam-5731	2	25	functions	function	NOUN
ejpam-5731	2	26	involving	involve	VERB
ejpam-5731	2	27	q	q	ADJ
ejpam-5731	2	28	-	-	PUNCT
ejpam-5731	2	29	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	2	30	differential	differential	ADJ
ejpam-5731	2	31	operator	operator	NOUN
ejpam-5731	2	32	that	that	PRON
ejpam-5731	2	33	are	be	AUX
ejpam-5731	2	34	subordinate	subordinate	ADJ
ejpam-5731	2	35	to	to	ADP
ejpam-5731	2	36	legendre	legendre	PROPN
ejpam-5731	2	37	polynomials	polynomial	NOUN
ejpam-5731	2	38	.	.	PUNCT
ejpam-5731	3	1	this	this	DET
ejpam-5731	3	2	study	study	NOUN
ejpam-5731	3	3	explores	explore	VERB
ejpam-5731	3	4	the	the	DET
ejpam-5731	3	5	characteristics	characteristic	NOUN
ejpam-5731	3	6	and	and	CCONJ
ejpam-5731	3	7	behaviors	behavior	NOUN
ejpam-5731	3	8	of	of	ADP
ejpam-5731	3	9	these	these	DET
ejpam-5731	3	10	functions	function	NOUN
ejpam-5731	3	11	,	,	PUNCT
ejpam-5731	3	12	providing	provide	VERB
ejpam-5731	3	13	estimates	estimate	NOUN
ejpam-5731	3	14	for	for	ADP
ejpam-5731	3	15	the	the	DET
ejpam-5731	3	16	modulus	modulus	NOUN
ejpam-5731	3	17	of	of	ADP
ejpam-5731	3	18	the	the	DET
ejpam-5731	3	19	initial	initial	ADJ
ejpam-5731	3	20	taylor	taylor	PROPN
ejpam-5731	3	21	series	series	PROPN
ejpam-5731	3	22	coefficients	coefficients	PROPN
ejpam-5731	3	23	a2	a2	PROPN
ejpam-5731	3	24	and	and	CCONJ
ejpam-5731	3	25	a3	a3	NOUN
ejpam-5731	3	26	within	within	ADP
ejpam-5731	3	27	this	this	DET
ejpam-5731	3	28	specific	specific	ADJ
ejpam-5731	3	29	class	class	NOUN
ejpam-5731	3	30	and	and	CCONJ
ejpam-5731	3	31	its	its	PRON
ejpam-5731	3	32	various	various	ADJ
ejpam-5731	3	33	subclasses	subclass	NOUN
ejpam-5731	3	34	.	.	PUNCT
ejpam-5731	4	1	additionally	additionally	ADV
ejpam-5731	4	2	,	,	PUNCT
ejpam-5731	4	3	the	the	DET
ejpam-5731	4	4	research	research	NOUN
ejpam-5731	4	5	delves	delve	VERB
ejpam-5731	4	6	into	into	ADP
ejpam-5731	4	7	the	the	DET
ejpam-5731	4	8	traditional	traditional	ADJ
ejpam-5731	4	9	fekete	fekete	PROPN
ejpam-5731	4	10	-	-	PUNCT
ejpam-5731	4	11	szegö	szegö	ADJ
ejpam-5731	4	12	functional	functional	ADJ
ejpam-5731	4	13	problem	problem	NOUN
ejpam-5731	4	14	of	of	ADP
ejpam-5731	4	15	functions	function	NOUN
ejpam-5731	4	16	f	f	PROPN
ejpam-5731	4	17	belong	belong	VERB
ejpam-5731	4	18	to	to	ADP
ejpam-5731	4	19	the	the	DET
ejpam-5731	4	20	newly	newly	ADV
ejpam-5731	4	21	defined	define	VERB
ejpam-5731	4	22	class	class	NOUN
ejpam-5731	4	23	and	and	CCONJ
ejpam-5731	4	24	several	several	ADJ
ejpam-5731	4	25	of	of	ADP
ejpam-5731	4	26	its	its	PRON
ejpam-5731	4	27	subclasses	subclass	NOUN
ejpam-5731	4	28	.	.	PUNCT
ejpam-5731	5	1	2020	2020	NUM
ejpam-5731	5	2	mathematics	mathematic	NOUN
ejpam-5731	5	3	subject	subject	NOUN
ejpam-5731	5	4	classifications	classification	NOUN
ejpam-5731	5	5	:	:	PUNCT
ejpam-5731	5	6	30c45	30c45	NUM
ejpam-5731	5	7	,	,	PUNCT
ejpam-5731	5	8	30c50	30c50	NUM
ejpam-5731	5	9	,	,	PUNCT
ejpam-5731	5	10	33c45	33c45	NUM
ejpam-5731	5	11	,	,	PUNCT
ejpam-5731	5	12	33c05	33c05	NUM
ejpam-5731	5	13	,	,	PUNCT
ejpam-5731	5	14	11b39	11b39	NUM
ejpam-5731	5	15	key	key	ADJ
ejpam-5731	5	16	words	word	NOUN
ejpam-5731	5	17	and	and	CCONJ
ejpam-5731	5	18	phrases	phrase	NOUN
ejpam-5731	5	19	:	:	PUNCT
ejpam-5731	5	20	bi	bi	ADJ
ejpam-5731	5	21	-	-	ADJ
ejpam-5731	5	22	univalent	univalent	ADJ
ejpam-5731	5	23	functions	function	NOUN
ejpam-5731	5	24	;	;	PUNCT
ejpam-5731	5	25	bi	bi	NOUN
ejpam-5731	5	26	-	-	ADJ
ejpam-5731	5	27	bazilevic	bazilevic	ADJ
ejpam-5731	5	28	;	;	PUNCT
ejpam-5731	5	29	q	q	X
ejpam-5731	5	30	-	-	PUNCT
ejpam-5731	5	31	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	5	32	differential	differential	ADJ
ejpam-5731	5	33	operator	operator	NOUN
ejpam-5731	5	34	;	;	PUNCT
ejpam-5731	5	35	jackson	jackson	PROPN
ejpam-5731	5	36	q	q	PROPN
ejpam-5731	5	37	-	-	PUNCT
ejpam-5731	5	38	derivative	derivative	ADJ
ejpam-5731	5	39	operator	operator	NOUN
ejpam-5731	5	40	;	;	PUNCT
ejpam-5731	5	41	q	q	ADJ
ejpam-5731	5	42	-	-	PUNCT
ejpam-5731	5	43	gamma	gamma	NOUN
ejpam-5731	5	44	function	function	NOUN
ejpam-5731	5	45	;	;	PUNCT
ejpam-5731	5	46	fractional	fractional	ADJ
ejpam-5731	5	47	q	q	ADJ
ejpam-5731	5	48	-	-	PUNCT
ejpam-5731	5	49	calculus	calculus	NOUN
ejpam-5731	5	50	operator	operator	NOUN
ejpam-5731	5	51	;	;	PUNCT
ejpam-5731	5	52	legendre	legendre	NOUN
ejpam-5731	5	53	polynomials	polynomial	NOUN
ejpam-5731	5	54	;	;	PUNCT
ejpam-5731	5	55	coefficient	coefficient	NOUN
ejpam-5731	5	56	estimates	estimate	NOUN
ejpam-5731	5	57	;	;	PUNCT
ejpam-5731	5	58	fekete	fekete	PROPN
ejpam-5731	5	59	-	-	PUNCT
ejpam-5731	5	60	szegö	szegö	ADJ
ejpam-5731	5	61	functional	functional	ADJ
ejpam-5731	5	62	problem	problem	NOUN
ejpam-5731	5	63	;	;	PUNCT
ejpam-5731	5	64	convolution	convolution	NOUN
ejpam-5731	5	65	;	;	PUNCT
ejpam-5731	5	66	hadamard	hadamard	ADJ
ejpam-5731	5	67	product	product	NOUN
ejpam-5731	5	68	1	1	NUM
ejpam-5731	5	69	.	.	PUNCT
ejpam-5731	5	70	introduction	introduction	NOUN
ejpam-5731	5	71	the	the	DET
ejpam-5731	5	72	q	q	NOUN
ejpam-5731	5	73	-	-	PUNCT
ejpam-5731	5	74	calculus	calculus	NOUN
ejpam-5731	5	75	offers	offer	VERB
ejpam-5731	5	76	essential	essential	ADJ
ejpam-5731	5	77	tools	tool	NOUN
ejpam-5731	5	78	that	that	PRON
ejpam-5731	5	79	are	be	AUX
ejpam-5731	5	80	widely	widely	ADV
ejpam-5731	5	81	utilized	utilize	VERB
ejpam-5731	5	82	to	to	PART
ejpam-5731	5	83	examine	examine	VERB
ejpam-5731	5	84	different	different	ADJ
ejpam-5731	5	85	categories	category	NOUN
ejpam-5731	5	86	of	of	ADP
ejpam-5731	5	87	analytic	analytic	ADJ
ejpam-5731	5	88	functions	function	NOUN
ejpam-5731	5	89	.	.	PUNCT
ejpam-5731	6	1	various	various	ADJ
ejpam-5731	6	2	geometric	geometric	ADJ
ejpam-5731	6	3	properties	property	NOUN
ejpam-5731	6	4	,	,	PUNCT
ejpam-5731	6	5	such	such	ADJ
ejpam-5731	6	6	as	as	ADP
ejpam-5731	6	7	coefficient	coefficient	NOUN
ejpam-5731	6	8	estimates	estimate	NOUN
ejpam-5731	6	9	,	,	PUNCT
ejpam-5731	6	10	convexity	convexity	NOUN
ejpam-5731	6	11	,	,	PUNCT
ejpam-5731	6	12	near	near	ADP
ejpam-5731	6	13	-	-	PUNCT
ejpam-5731	6	14	convexity	convexity	NOUN
ejpam-5731	6	15	,	,	PUNCT
ejpam-5731	6	16	distortion	distortion	NOUN
ejpam-5731	6	17	bounds	bound	NOUN
ejpam-5731	6	18	,	,	PUNCT
ejpam-5731	6	19	and	and	CCONJ
ejpam-5731	6	20	radii	radius	NOUN
ejpam-5731	6	21	of	of	ADP
ejpam-5731	6	22	starlikeness	starlikeness	NOUN
ejpam-5731	6	23	,	,	PUNCT
ejpam-5731	6	24	have	have	AUX
ejpam-5731	6	25	been	be	AUX
ejpam-5731	6	26	investigated	investigate	VERB
ejpam-5731	6	27	within	within	ADP
ejpam-5731	6	28	these	these	DET
ejpam-5731	6	29	classes	class	NOUN
ejpam-5731	6	30	of	of	ADP
ejpam-5731	6	31	functions	function	NOUN
ejpam-5731	6	32	.	.	PUNCT
ejpam-5731	7	1	moreover	moreover	ADV
ejpam-5731	7	2	,	,	PUNCT
ejpam-5731	7	3	q	q	X
ejpam-5731	7	4	-	-	PUNCT
ejpam-5731	7	5	analysis	analysis	NOUN
ejpam-5731	7	6	has	have	AUX
ejpam-5731	7	7	garnered	garner	VERB
ejpam-5731	7	8	considerable	considerable	ADJ
ejpam-5731	7	9	attention	attention	NOUN
ejpam-5731	7	10	in	in	ADP
ejpam-5731	7	11	operator	operator	NOUN
ejpam-5731	7	12	theory	theory	NOUN
ejpam-5731	7	13	,	,	PUNCT
ejpam-5731	7	14	as	as	SCONJ
ejpam-5731	7	15	highlighted	highlight	VERB
ejpam-5731	7	16	by	by	ADP
ejpam-5731	7	17	the	the	DET
ejpam-5731	7	18	extensive	extensive	ADJ
ejpam-5731	7	19	research	research	NOUN
ejpam-5731	7	20	documented	document	VERB
ejpam-5731	7	21	in	in	ADP
ejpam-5731	7	22	[	[	X
ejpam-5731	7	23	10	10	NUM
ejpam-5731	7	24	]	]	PUNCT
ejpam-5731	7	25	.	.	PUNCT
ejpam-5731	8	1	the	the	DET
ejpam-5731	8	2	progress	progress	NOUN
ejpam-5731	8	3	made	make	VERB
ejpam-5731	8	4	in	in	ADP
ejpam-5731	8	5	operator	operator	NOUN
ejpam-5731	8	6	theory	theory	NOUN
ejpam-5731	8	7	within	within	ADP
ejpam-5731	8	8	this	this	DET
ejpam-5731	8	9	domain	domain	NOUN
ejpam-5731	8	10	has	have	AUX
ejpam-5731	8	11	inspired	inspire	VERB
ejpam-5731	8	12	many	many	ADJ
ejpam-5731	8	13	researchers	researcher	NOUN
ejpam-5731	8	14	,	,	PUNCT
ejpam-5731	8	15	leading	lead	VERB
ejpam-5731	8	16	to	to	ADP
ejpam-5731	8	17	the	the	DET
ejpam-5731	8	18	publication	publication	NOUN
ejpam-5731	8	19	of	of	ADP
ejpam-5731	8	20	a	a	DET
ejpam-5731	8	21	variety	variety	NOUN
ejpam-5731	8	22	of	of	ADP
ejpam-5731	8	23	scholarly	scholarly	ADJ
ejpam-5731	8	24	articles	article	NOUN
ejpam-5731	8	25	.	.	PUNCT
ejpam-5731	9	1	recently	recently	ADV
ejpam-5731	9	2	,	,	PUNCT
ejpam-5731	9	3	srivastava	srivastava	PROPN
ejpam-5731	9	4	[	[	X
ejpam-5731	9	5	46	46	NUM
ejpam-5731	9	6	]	]	PUNCT
ejpam-5731	9	7	has	have	AUX
ejpam-5731	9	8	released	release	VERB
ejpam-5731	9	9	a	a	DET
ejpam-5731	9	10	comprehensive	comprehensive	ADJ
ejpam-5731	9	11	survey	survey	NOUN
ejpam-5731	9	12	and	and	CCONJ
ejpam-5731	9	13	expository	expository	ADJ
ejpam-5731	9	14	review	review	NOUN
ejpam-5731	9	15	paper	paper	NOUN
ejpam-5731	9	16	,	,	PUNCT
ejpam-5731	9	17	which	which	PRON
ejpam-5731	9	18	serves	serve	VERB
ejpam-5731	9	19	as	as	ADP
ejpam-5731	9	20	a	a	DET
ejpam-5731	9	21	significant	significant	ADJ
ejpam-5731	9	22	resource	resource	NOUN
ejpam-5731	9	23	for	for	ADP
ejpam-5731	9	24	researchers	researcher	NOUN
ejpam-5731	9	25	interested	interested	ADJ
ejpam-5731	9	26	in	in	ADP
ejpam-5731	9	27	the	the	DET
ejpam-5731	9	28	field	field	NOUN
ejpam-5731	9	29	of	of	ADP
ejpam-5731	9	30	geometric	geometric	ADJ
ejpam-5731	9	31	function	function	NOUN
ejpam-5731	9	32	theory	theory	NOUN
ejpam-5731	9	33	.	.	PUNCT
ejpam-5731	10	1	this	this	DET
ejpam-5731	10	2	survey	survey	NOUN
ejpam-5731	10	3	meticulously	meticulously	ADV
ejpam-5731	10	4	investigates	investigate	VERB
ejpam-5731	10	5	the	the	DET
ejpam-5731	10	6	mathematical	mathematical	ADJ
ejpam-5731	10	7	frameworks	framework	NOUN
ejpam-5731	10	8	and	and	CCONJ
ejpam-5731	10	9	applications	application	NOUN
ejpam-5731	10	10	of	of	ADP
ejpam-5731	10	11	fractional	fractional	ADJ
ejpam-5731	10	12	q	q	ADJ
ejpam-5731	10	13	-	-	ADJ
ejpam-5731	10	14	derivative	derivative	ADJ
ejpam-5731	10	15	operators	operator	NOUN
ejpam-5731	10	16	and	and	CCONJ
ejpam-5731	10	17	fractional	fractional	ADJ
ejpam-5731	10	18	q	q	NOUN
ejpam-5731	10	19	-	-	PUNCT
ejpam-5731	10	20	calculus	calculus	NOUN
ejpam-5731	10	21	,	,	PUNCT
ejpam-5731	10	22	particularly	particularly	ADV
ejpam-5731	10	23	in	in	ADP
ejpam-5731	10	24	relation	relation	NOUN
ejpam-5731	10	25	to	to	ADP
ejpam-5731	10	26	geometric	geometric	ADJ
ejpam-5731	10	27	function	function	NOUN
ejpam-5731	10	28	theory	theory	NOUN
ejpam-5731	10	29	.	.	PUNCT
ejpam-5731	11	1	it	it	PRON
ejpam-5731	11	2	addresses	address	VERB
ejpam-5731	11	3	the	the	DET
ejpam-5731	11	4	complexities	complexity	NOUN
ejpam-5731	11	5	involved	involve	VERB
ejpam-5731	11	6	in	in	ADP
ejpam-5731	11	7	utilizing	utilize	VERB
ejpam-5731	11	8	doi	doi	NOUN
ejpam-5731	11	9	:	:	PUNCT
ejpam-5731	11	10	https://doi.org/10.29020/nybg.ejpam.v18i1.5731	https://doi.org/10.29020/nybg.ejpam.v18i1.5731	NOUN
ejpam-5731	11	11	email	email	NOUN
ejpam-5731	11	12	address	address	NOUN
ejpam-5731	11	13	:	:	PUNCT
ejpam-5731	11	14	walrawashdeh@zu.edu.jo	walrawashdeh@zu.edu.jo	NOUN
ejpam-5731	11	15	(	(	PUNCT
ejpam-5731	11	16	w.	w.	PROPN
ejpam-5731	11	17	al	al	PROPN
ejpam-5731	11	18	-	-	PUNCT
ejpam-5731	11	19	rawashdeh	rawashdeh	NOUN
ejpam-5731	11	20	)	)	PUNCT
ejpam-5731	11	21	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5731	12	1	1	1	NUM
ejpam-5731	12	2	copyright	copyright	NOUN
ejpam-5731	12	3	:	:	PUNCT
ejpam-5731	12	4	©	©	PROPN
ejpam-5731	12	5	2025	2025	NUM
ejpam-5731	12	6	the	the	DET
ejpam-5731	12	7	author(s	author(s	NOUN
ejpam-5731	12	8	)	)	PUNCT
ejpam-5731	12	9	.	.	PUNCT
ejpam-5731	13	1	(	(	PUNCT
ejpam-5731	13	2	cc	cc	NOUN
ejpam-5731	13	3	by	by	ADP
ejpam-5731	13	4	-	-	PUNCT
ejpam-5731	13	5	nc	nc	PROPN
ejpam-5731	13	6	4.0	4.0	NUM
ejpam-5731	13	7	)	)	PUNCT
ejpam-5731	13	8	w.	w.	PROPN
ejpam-5731	13	9	al	al	PROPN
ejpam-5731	13	10	-	-	PUNCT
ejpam-5731	13	11	rawashdeh	rawashdeh	PROPN
ejpam-5731	13	12	/	/	SYM
ejpam-5731	13	13	eur	eur	PROPN
ejpam-5731	13	14	.	.	PUNCT
ejpam-5731	14	1	j.	j.	PROPN
ejpam-5731	14	2	pure	pure	PROPN
ejpam-5731	14	3	appl	appl	PROPN
ejpam-5731	14	4	.	.	PROPN
ejpam-5731	14	5	math	math	PROPN
ejpam-5731	14	6	,	,	PUNCT
ejpam-5731	14	7	18	18	NUM
ejpam-5731	14	8	(	(	PUNCT
ejpam-5731	14	9	1	1	NUM
ejpam-5731	14	10	)	)	PUNCT
ejpam-5731	14	11	(	(	PUNCT
ejpam-5731	14	12	2025	2025	NUM
ejpam-5731	14	13	)	)	PUNCT
ejpam-5731	14	14	,	,	PUNCT
ejpam-5731	14	15	5731	5731	NUM
ejpam-5731	14	16	2	2	NUM
ejpam-5731	14	17	of	of	ADP
ejpam-5731	14	18	20	20	NUM
ejpam-5731	14	19	these	these	DET
ejpam-5731	14	20	fractional	fractional	ADJ
ejpam-5731	14	21	operators	operator	NOUN
ejpam-5731	14	22	and	and	CCONJ
ejpam-5731	14	23	calculus	calculus	NOUN
ejpam-5731	14	24	concepts	concept	NOUN
ejpam-5731	14	25	to	to	PART
ejpam-5731	14	26	characterize	characterize	VERB
ejpam-5731	14	27	mathematical	mathematical	ADJ
ejpam-5731	14	28	functions	function	NOUN
ejpam-5731	14	29	and	and	CCONJ
ejpam-5731	14	30	their	their	PRON
ejpam-5731	14	31	geometric	geometric	ADJ
ejpam-5731	14	32	attributes	attribute	NOUN
ejpam-5731	14	33	.	.	PUNCT
ejpam-5731	15	1	furthermore	furthermore	ADV
ejpam-5731	15	2	,	,	PUNCT
ejpam-5731	15	3	the	the	DET
ejpam-5731	15	4	review	review	NOUN
ejpam-5731	15	5	highlights	highlight	VERB
ejpam-5731	15	6	the	the	DET
ejpam-5731	15	7	practical	practical	ADJ
ejpam-5731	15	8	applications	application	NOUN
ejpam-5731	15	9	and	and	CCONJ
ejpam-5731	15	10	ramifications	ramification	NOUN
ejpam-5731	15	11	of	of	ADP
ejpam-5731	15	12	fractional	fractional	ADJ
ejpam-5731	15	13	q	q	ADJ
ejpam-5731	15	14	-	-	ADJ
ejpam-5731	15	15	derivative	derivative	ADJ
ejpam-5731	15	16	operators	operator	NOUN
ejpam-5731	15	17	within	within	ADP
ejpam-5731	15	18	the	the	DET
ejpam-5731	15	19	expansive	expansive	ADJ
ejpam-5731	15	20	scope	scope	NOUN
ejpam-5731	15	21	of	of	ADP
ejpam-5731	15	22	geometric	geometric	ADJ
ejpam-5731	15	23	function	function	NOUN
ejpam-5731	15	24	theory	theory	NOUN
ejpam-5731	15	25	,	,	PUNCT
ejpam-5731	15	26	thereby	thereby	ADV
ejpam-5731	15	27	offering	offer	VERB
ejpam-5731	15	28	an	an	DET
ejpam-5731	15	29	in	in	ADP
ejpam-5731	15	30	-	-	PUNCT
ejpam-5731	15	31	depth	depth	NOUN
ejpam-5731	15	32	analysis	analysis	NOUN
ejpam-5731	15	33	of	of	ADP
ejpam-5731	15	34	both	both	CCONJ
ejpam-5731	15	35	the	the	DET
ejpam-5731	15	36	theoretical	theoretical	ADJ
ejpam-5731	15	37	underpinnings	underpinning	NOUN
ejpam-5731	15	38	and	and	CCONJ
ejpam-5731	15	39	practical	practical	ADJ
ejpam-5731	15	40	implementations	implementation	NOUN
ejpam-5731	15	41	of	of	ADP
ejpam-5731	15	42	these	these	DET
ejpam-5731	15	43	mathematical	mathematical	ADJ
ejpam-5731	15	44	instruments	instrument	NOUN
ejpam-5731	15	45	in	in	ADP
ejpam-5731	15	46	the	the	DET
ejpam-5731	15	47	relevant	relevant	ADJ
ejpam-5731	15	48	domain	domain	NOUN
ejpam-5731	15	49	.	.	PUNCT
ejpam-5731	16	1	many	many	ADJ
ejpam-5731	16	2	researchers	researcher	NOUN
ejpam-5731	16	3	have	have	AUX
ejpam-5731	16	4	employed	employ	VERB
ejpam-5731	16	5	the	the	DET
ejpam-5731	16	6	concept	concept	NOUN
ejpam-5731	16	7	of	of	ADP
ejpam-5731	16	8	q	q	NOUN
ejpam-5731	16	9	-	-	NOUN
ejpam-5731	16	10	calculus	calculus	NOUN
ejpam-5731	16	11	to	to	PART
ejpam-5731	16	12	establish	establish	VERB
ejpam-5731	16	13	novel	novel	ADJ
ejpam-5731	16	14	subclasses	subclass	NOUN
ejpam-5731	16	15	of	of	ADP
ejpam-5731	16	16	analytic	analytic	ADJ
ejpam-5731	16	17	and	and	CCONJ
ejpam-5731	16	18	univalent	univalent	ADJ
ejpam-5731	16	19	functions	function	NOUN
ejpam-5731	16	20	.	.	PUNCT
ejpam-5731	17	1	this	this	DET
ejpam-5731	17	2	investigation	investigation	NOUN
ejpam-5731	17	3	seeks	seek	VERB
ejpam-5731	17	4	to	to	PART
ejpam-5731	17	5	enhance	enhance	VERB
ejpam-5731	17	6	the	the	DET
ejpam-5731	17	7	comprehension	comprehension	NOUN
ejpam-5731	17	8	of	of	ADP
ejpam-5731	17	9	the	the	DET
ejpam-5731	17	10	properties	property	NOUN
ejpam-5731	17	11	and	and	CCONJ
ejpam-5731	17	12	attributes	attribute	NOUN
ejpam-5731	17	13	of	of	ADP
ejpam-5731	17	14	analytic	analytic	ADJ
ejpam-5731	17	15	and	and	CCONJ
ejpam-5731	17	16	univalent	univalent	ADJ
ejpam-5731	17	17	functions	function	NOUN
ejpam-5731	17	18	,	,	PUNCT
ejpam-5731	17	19	particularly	particularly	ADV
ejpam-5731	17	20	in	in	ADP
ejpam-5731	17	21	relation	relation	NOUN
ejpam-5731	17	22	to	to	ADP
ejpam-5731	17	23	the	the	DET
ejpam-5731	17	24	newly	newly	ADV
ejpam-5731	17	25	introduced	introduce	VERB
ejpam-5731	17	26	q	q	ADJ
ejpam-5731	17	27	-	-	NOUN
ejpam-5731	17	28	derivative	derivative	ADJ
ejpam-5731	17	29	,	,	PUNCT
ejpam-5731	17	30	thereby	thereby	ADV
ejpam-5731	17	31	elucidating	elucidate	VERB
ejpam-5731	17	32	the	the	DET
ejpam-5731	17	33	criteria	criterion	NOUN
ejpam-5731	17	34	that	that	PRON
ejpam-5731	17	35	determine	determine	VERB
ejpam-5731	17	36	membership	membership	NOUN
ejpam-5731	17	37	within	within	ADP
ejpam-5731	17	38	the	the	DET
ejpam-5731	17	39	specified	specify	VERB
ejpam-5731	17	40	subclasses	subclass	NOUN
ejpam-5731	17	41	,	,	PUNCT
ejpam-5731	17	42	see	see	VERB
ejpam-5731	17	43	,	,	PUNCT
ejpam-5731	17	44	for	for	ADP
ejpam-5731	17	45	example	example	NOUN
ejpam-5731	17	46	,	,	PUNCT
ejpam-5731	17	47	the	the	DET
ejpam-5731	17	48	articles	article	NOUN
ejpam-5731	17	49	[	[	X
ejpam-5731	17	50	9	9	NUM
ejpam-5731	17	51	]	]	PUNCT
ejpam-5731	17	52	,	,	PUNCT
ejpam-5731	17	53	[	[	X
ejpam-5731	17	54	22	22	NUM
ejpam-5731	17	55	]	]	PUNCT
ejpam-5731	17	56	,	,	PUNCT
ejpam-5731	17	57	[	[	X
ejpam-5731	17	58	28	28	NUM
ejpam-5731	17	59	]	]	PUNCT
ejpam-5731	17	60	,	,	PUNCT
ejpam-5731	18	1	[	[	X
ejpam-5731	18	2	38	38	NUM
ejpam-5731	18	3	]	]	PUNCT
ejpam-5731	18	4	,	,	PUNCT
ejpam-5731	19	1	[	[	X
ejpam-5731	19	2	40	40	NUM
ejpam-5731	19	3	]	]	PUNCT
ejpam-5731	19	4	,	,	PUNCT
ejpam-5731	19	5	[	[	X
ejpam-5731	19	6	47	47	NUM
ejpam-5731	19	7	]	]	PUNCT
ejpam-5731	19	8	,	,	PUNCT
ejpam-5731	20	1	[	[	X
ejpam-5731	20	2	51	51	NUM
ejpam-5731	20	3	]	]	PUNCT
ejpam-5731	20	4	and	and	CCONJ
ejpam-5731	20	5	the	the	DET
ejpam-5731	20	6	related	related	ADJ
ejpam-5731	20	7	references	reference	NOUN
ejpam-5731	20	8	included	include	VERB
ejpam-5731	20	9	therein	therein	ADV
ejpam-5731	20	10	.	.	PUNCT
ejpam-5731	21	1	in	in	ADP
ejpam-5731	21	2	this	this	DET
ejpam-5731	21	3	research	research	NOUN
ejpam-5731	21	4	paper	paper	NOUN
ejpam-5731	21	5	,	,	PUNCT
ejpam-5731	21	6	the	the	DET
ejpam-5731	21	7	central	central	ADJ
ejpam-5731	21	8	focus	focus	NOUN
ejpam-5731	21	9	lies	lie	VERB
ejpam-5731	21	10	in	in	ADP
ejpam-5731	21	11	the	the	DET
ejpam-5731	21	12	application	application	NOUN
ejpam-5731	21	13	of	of	ADP
ejpam-5731	21	14	the	the	DET
ejpam-5731	21	15	concept	concept	NOUN
ejpam-5731	21	16	of	of	ADP
ejpam-5731	21	17	the	the	DET
ejpam-5731	21	18	q	q	NOUN
ejpam-5731	21	19	-	-	NOUN
ejpam-5731	21	20	derivative	derivative	ADJ
ejpam-5731	21	21	to	to	PART
ejpam-5731	21	22	derive	derive	VERB
ejpam-5731	21	23	specific	specific	ADJ
ejpam-5731	21	24	differential	differential	NOUN
ejpam-5731	21	25	operator	operator	NOUN
ejpam-5731	21	26	.	.	PUNCT
ejpam-5731	22	1	this	this	DET
ejpam-5731	22	2	operator	operator	NOUN
ejpam-5731	22	3	is	be	AUX
ejpam-5731	22	4	introduced	introduce	VERB
ejpam-5731	22	5	with	with	ADP
ejpam-5731	22	6	the	the	DET
ejpam-5731	22	7	aim	aim	NOUN
ejpam-5731	22	8	of	of	ADP
ejpam-5731	22	9	generalizing	generalize	VERB
ejpam-5731	22	10	the	the	DET
ejpam-5731	22	11	class	class	NOUN
ejpam-5731	22	12	of	of	ADP
ejpam-5731	22	13	qanalogue	qanalogue	NOUN
ejpam-5731	22	14	of	of	ADP
ejpam-5731	22	15	the	the	DET
ejpam-5731	22	16	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	22	17	operator	operator	NOUN
ejpam-5731	22	18	within	within	ADP
ejpam-5731	22	19	the	the	DET
ejpam-5731	22	20	set	set	NOUN
ejpam-5731	22	21	of	of	ADP
ejpam-5731	22	22	univalent	univalent	ADJ
ejpam-5731	22	23	functions	function	NOUN
ejpam-5731	22	24	.	.	PUNCT
ejpam-5731	23	1	by	by	ADP
ejpam-5731	23	2	utilizing	utilize	VERB
ejpam-5731	23	3	the	the	DET
ejpam-5731	23	4	newly	newly	ADV
ejpam-5731	23	5	defined	define	VERB
ejpam-5731	23	6	operator	operator	NOUN
ejpam-5731	23	7	,	,	PUNCT
ejpam-5731	23	8	we	we	PRON
ejpam-5731	23	9	define	define	VERB
ejpam-5731	23	10	a	a	DET
ejpam-5731	23	11	novel	novel	ADJ
ejpam-5731	23	12	class	class	NOUN
ejpam-5731	23	13	of	of	ADP
ejpam-5731	23	14	bi	bi	ADJ
ejpam-5731	23	15	-	-	ADJ
ejpam-5731	23	16	bazilvic	bazilvic	ADJ
ejpam-5731	23	17	functions	function	NOUN
ejpam-5731	23	18	associated	associate	VERB
ejpam-5731	23	19	with	with	ADP
ejpam-5731	23	20	the	the	DET
ejpam-5731	23	21	legendre	legendre	PROPN
ejpam-5731	23	22	polynomials	polynomial	NOUN
ejpam-5731	23	23	.	.	PUNCT
ejpam-5731	24	1	now	now	ADV
ejpam-5731	24	2	,	,	PUNCT
ejpam-5731	24	3	consider	consider	VERB
ejpam-5731	24	4	the	the	DET
ejpam-5731	24	5	seth	seth	PROPN
ejpam-5731	24	6	,	,	PUNCT
ejpam-5731	24	7	which	which	PRON
ejpam-5731	24	8	consists	consist	VERB
ejpam-5731	24	9	of	of	ADP
ejpam-5731	24	10	all	all	DET
ejpam-5731	24	11	functions	function	NOUN
ejpam-5731	24	12	f(z	f(z	NOUN
ejpam-5731	24	13	)	)	PUNCT
ejpam-5731	24	14	that	that	PRON
ejpam-5731	24	15	are	be	AUX
ejpam-5731	24	16	analytic	analytic	ADJ
ejpam-5731	24	17	within	within	ADP
ejpam-5731	24	18	the	the	DET
ejpam-5731	24	19	open	open	ADJ
ejpam-5731	24	20	unit	unit	NOUN
ejpam-5731	24	21	disk	disk	NOUN
ejpam-5731	24	22	denoted	denote	VERB
ejpam-5731	24	23	as	as	ADP
ejpam-5731	24	24	d	d	X
ejpam-5731	24	25	=	=	PUNCT
ejpam-5731	24	26	{	{	PUNCT
ejpam-5731	24	27	z	z	NOUN
ejpam-5731	24	28	∈	∈	PROPN
ejpam-5731	24	29	c	c	NOUN
ejpam-5731	24	30	:	:	PUNCT
ejpam-5731	24	31	|z|	|z|	VERB
ejpam-5731	24	32	<	<	X
ejpam-5731	24	33	1	1	NUM
ejpam-5731	24	34	}	}	PUNCT
ejpam-5731	24	35	and	and	CCONJ
ejpam-5731	24	36	normalized	normalize	VERB
ejpam-5731	24	37	by	by	ADP
ejpam-5731	24	38	the	the	DET
ejpam-5731	24	39	conditions	condition	NOUN
ejpam-5731	24	40	f(0	f(0	NOUN
ejpam-5731	24	41	)	)	PUNCT
ejpam-5731	24	42	=	=	SYM
ejpam-5731	24	43	0	0	PUNCT
ejpam-5731	25	1	=	=	SYM
ejpam-5731	25	2	1	1	NUM
ejpam-5731	25	3	−	−	PROPN
ejpam-5731	25	4	f	f	PROPN
ejpam-5731	25	5	′(0	′(0	NOUN
ejpam-5731	25	6	)	)	PUNCT
ejpam-5731	25	7	.	.	PUNCT
ejpam-5731	26	1	the	the	DET
ejpam-5731	26	2	exploration	exploration	NOUN
ejpam-5731	26	3	of	of	ADP
ejpam-5731	26	4	such	such	ADJ
ejpam-5731	26	5	functions	function	NOUN
ejpam-5731	26	6	contributes	contribute	VERB
ejpam-5731	26	7	to	to	ADP
ejpam-5731	26	8	a	a	DET
ejpam-5731	26	9	deeper	deep	ADJ
ejpam-5731	26	10	comprehension	comprehension	NOUN
ejpam-5731	26	11	of	of	ADP
ejpam-5731	26	12	complex	complex	ADJ
ejpam-5731	26	13	analysis	analysis	NOUN
ejpam-5731	26	14	and	and	CCONJ
ejpam-5731	26	15	its	its	PRON
ejpam-5731	26	16	applications	application	NOUN
ejpam-5731	26	17	.	.	PUNCT
ejpam-5731	27	1	moreover	moreover	ADV
ejpam-5731	27	2	,	,	PUNCT
ejpam-5731	27	3	any	any	DET
ejpam-5731	27	4	function	function	NOUN
ejpam-5731	27	5	f	f	PROPN
ejpam-5731	27	6	belongs	belong	VERB
ejpam-5731	27	7	to	to	ADP
ejpam-5731	27	8	the	the	DET
ejpam-5731	27	9	set	set	NOUN
ejpam-5731	27	10	h	h	NOUN
ejpam-5731	27	11	can	can	AUX
ejpam-5731	27	12	be	be	AUX
ejpam-5731	27	13	written	write	VERB
ejpam-5731	27	14	as	as	ADP
ejpam-5731	27	15	f(z	f(z	NOUN
ejpam-5731	27	16	)	)	PUNCT
ejpam-5731	28	1	=	=	SYM
ejpam-5731	28	2	z	z	NOUN
ejpam-5731	29	1	+	+	NOUN
ejpam-5731	29	2	∞∑	∞∑	NUM
ejpam-5731	29	3	n=2	n=2	ADV
ejpam-5731	29	4	anz	anz	NOUN
ejpam-5731	29	5	n	n	CCONJ
ejpam-5731	29	6	,	,	PUNCT
ejpam-5731	29	7	where	where	SCONJ
ejpam-5731	29	8	z	z	PROPN
ejpam-5731	29	9	∈	∈	PROPN
ejpam-5731	29	10	d.	d.	PROPN
ejpam-5731	29	11	(	(	PUNCT
ejpam-5731	29	12	1	1	X
ejpam-5731	29	13	)	)	PUNCT
ejpam-5731	29	14	the	the	DET
ejpam-5731	29	15	hadamard	hadamard	ADJ
ejpam-5731	29	16	product	product	NOUN
ejpam-5731	29	17	(	(	PUNCT
ejpam-5731	29	18	or	or	CCONJ
ejpam-5731	29	19	convolution	convolution	NOUN
ejpam-5731	29	20	)	)	PUNCT
ejpam-5731	29	21	of	of	ADP
ejpam-5731	29	22	two	two	NUM
ejpam-5731	29	23	analytic	analytic	ADJ
ejpam-5731	29	24	functions	function	NOUN
ejpam-5731	29	25	f(z	f(z	NOUN
ejpam-5731	29	26	)	)	PUNCT
ejpam-5731	29	27	given	give	VERB
ejpam-5731	29	28	by	by	ADP
ejpam-5731	29	29	equation	equation	NOUN
ejpam-5731	29	30	(	(	PUNCT
ejpam-5731	29	31	1	1	NUM
ejpam-5731	29	32	)	)	PUNCT
ejpam-5731	29	33	and	and	CCONJ
ejpam-5731	29	34	h(z	h(z	NOUN
ejpam-5731	29	35	)	)	PUNCT
ejpam-5731	29	36	=	=	SYM
ejpam-5731	30	1	z	z	NOUN
ejpam-5731	30	2	+	+	NOUN
ejpam-5731	30	3	∞∑	∞∑	PROPN
ejpam-5731	30	4	n=2	n=2	X
ejpam-5731	30	5	bnz	bnz	NOUN
ejpam-5731	30	6	n	n	PART
ejpam-5731	30	7	is	be	AUX
ejpam-5731	30	8	defined	define	VERB
ejpam-5731	30	9	as	as	ADP
ejpam-5731	30	10	:	:	PUNCT
ejpam-5731	30	11	(	(	PUNCT
ejpam-5731	30	12	f	f	NOUN
ejpam-5731	30	13	∗	∗	NOUN
ejpam-5731	30	14	h)(z	h)(z	NOUN
ejpam-5731	30	15	)	)	PUNCT
ejpam-5731	31	1	=	=	PUNCT
ejpam-5731	32	1	z	z	NOUN
ejpam-5731	33	1	+	+	NOUN
ejpam-5731	33	2	∞∑	∞∑	NUM
ejpam-5731	33	3	n=2	n=2	ADV
ejpam-5731	33	4	anbnz	anbnz	NOUN
ejpam-5731	33	5	n.	n.	NOUN
ejpam-5731	33	6	the	the	DET
ejpam-5731	33	7	convolution	convolution	NOUN
ejpam-5731	33	8	facilitates	facilitate	VERB
ejpam-5731	33	9	deeper	deep	ADJ
ejpam-5731	33	10	mathematical	mathematical	ADJ
ejpam-5731	33	11	exploration	exploration	NOUN
ejpam-5731	33	12	and	and	CCONJ
ejpam-5731	33	13	enhances	enhance	VERB
ejpam-5731	33	14	better	well	ADJ
ejpam-5731	33	15	understanding	understanding	NOUN
ejpam-5731	33	16	of	of	ADP
ejpam-5731	33	17	the	the	DET
ejpam-5731	33	18	geometric	geometric	ADJ
ejpam-5731	33	19	and	and	CCONJ
ejpam-5731	33	20	symmetric	symmetric	ADJ
ejpam-5731	33	21	properties	property	NOUN
ejpam-5731	33	22	of	of	ADP
ejpam-5731	33	23	f	f	PROPN
ejpam-5731	33	24	∈	∈	PROPN
ejpam-5731	33	25	h.	h.	PROPN
ejpam-5731	33	26	the	the	DET
ejpam-5731	33	27	significance	significance	NOUN
ejpam-5731	33	28	of	of	ADP
ejpam-5731	33	29	convolution	convolution	NOUN
ejpam-5731	33	30	,	,	PUNCT
ejpam-5731	33	31	within	within	ADP
ejpam-5731	33	32	operator	operator	NOUN
ejpam-5731	33	33	theory	theory	NOUN
ejpam-5731	33	34	and	and	CCONJ
ejpam-5731	33	35	geometric	geometric	ADJ
ejpam-5731	33	36	function	function	NOUN
ejpam-5731	33	37	theory	theory	NOUN
ejpam-5731	33	38	,	,	PUNCT
ejpam-5731	33	39	is	be	AUX
ejpam-5731	33	40	well	well	ADV
ejpam-5731	33	41	-	-	PUNCT
ejpam-5731	33	42	documented	document	VERB
ejpam-5731	33	43	in	in	ADP
ejpam-5731	33	44	the	the	DET
ejpam-5731	33	45	literature	literature	NOUN
ejpam-5731	33	46	.	.	PUNCT
ejpam-5731	34	1	for	for	ADP
ejpam-5731	34	2	more	more	ADJ
ejpam-5731	34	3	information	information	NOUN
ejpam-5731	34	4	about	about	ADP
ejpam-5731	34	5	convolution	convolution	NOUN
ejpam-5731	34	6	in	in	ADP
ejpam-5731	34	7	the	the	DET
ejpam-5731	34	8	geometric	geometric	ADJ
ejpam-5731	34	9	function	function	NOUN
ejpam-5731	34	10	theory	theory	NOUN
ejpam-5731	34	11	,	,	PUNCT
ejpam-5731	34	12	we	we	PRON
ejpam-5731	34	13	invite	invite	VERB
ejpam-5731	34	14	the	the	DET
ejpam-5731	34	15	interested	interested	ADJ
ejpam-5731	34	16	reader	reader	NOUN
ejpam-5731	34	17	to	to	PART
ejpam-5731	34	18	see	see	VERB
ejpam-5731	34	19	the	the	DET
ejpam-5731	34	20	monograph	monograph	NOUN
ejpam-5731	35	1	[	[	X
ejpam-5731	35	2	10	10	NUM
ejpam-5731	35	3	]	]	PUNCT
ejpam-5731	35	4	,	,	PUNCT
ejpam-5731	35	5	the	the	DET
ejpam-5731	35	6	articles	article	NOUN
ejpam-5731	35	7	[	[	X
ejpam-5731	35	8	23	23	NUM
ejpam-5731	35	9	]	]	PUNCT
ejpam-5731	35	10	,	,	PUNCT
ejpam-5731	35	11	[	[	X
ejpam-5731	35	12	39	39	NUM
ejpam-5731	35	13	]	]	PUNCT
ejpam-5731	36	1	[	[	X
ejpam-5731	36	2	47	47	NUM
ejpam-5731	36	3	]	]	PUNCT
ejpam-5731	36	4	,	,	PUNCT
ejpam-5731	36	5	and	and	CCONJ
ejpam-5731	36	6	the	the	DET
ejpam-5731	36	7	related	related	ADJ
ejpam-5731	36	8	references	reference	NOUN
ejpam-5731	36	9	provided	provide	VERB
ejpam-5731	36	10	therein	therein	ADV
ejpam-5731	36	11	.	.	PUNCT
ejpam-5731	37	1	let	let	VERB
ejpam-5731	37	2	us	we	PRON
ejpam-5731	37	3	consider	consider	VERB
ejpam-5731	37	4	two	two	NUM
ejpam-5731	37	5	functions	function	NOUN
ejpam-5731	37	6	,	,	PUNCT
ejpam-5731	37	7	f	f	PROPN
ejpam-5731	37	8	and	and	CCONJ
ejpam-5731	37	9	g	g	PROPN
ejpam-5731	37	10	,	,	PUNCT
ejpam-5731	37	11	which	which	PRON
ejpam-5731	37	12	are	be	AUX
ejpam-5731	37	13	analytic	analytic	ADJ
ejpam-5731	37	14	within	within	ADP
ejpam-5731	37	15	the	the	DET
ejpam-5731	37	16	open	open	ADJ
ejpam-5731	37	17	unit	unit	NOUN
ejpam-5731	37	18	disk	disk	NOUN
ejpam-5731	37	19	d.	d.	NOUN
ejpam-5731	37	20	we	we	PRON
ejpam-5731	37	21	say	say	VERB
ejpam-5731	37	22	that	that	SCONJ
ejpam-5731	37	23	f	f	PROPN
ejpam-5731	37	24	is	be	AUX
ejpam-5731	37	25	subordinated	subordinate	VERB
ejpam-5731	37	26	to	to	ADP
ejpam-5731	37	27	g	g	NOUN
ejpam-5731	37	28	in	in	ADP
ejpam-5731	37	29	d	d	PROPN
ejpam-5731	37	30	,	,	PUNCT
ejpam-5731	37	31	denoted	denote	VERB
ejpam-5731	37	32	as	as	ADP
ejpam-5731	37	33	f(z	f(z	NOUN
ejpam-5731	37	34	)	)	PUNCT
ejpam-5731	37	35	≺	≺	NOUN
ejpam-5731	37	36	g(z	g(z	PROPN
ejpam-5731	37	37	)	)	PUNCT
ejpam-5731	37	38	for	for	ADP
ejpam-5731	37	39	every	every	DET
ejpam-5731	37	40	z	z	NOUN
ejpam-5731	37	41	in	in	ADP
ejpam-5731	37	42	d	d	PROPN
ejpam-5731	37	43	,	,	PUNCT
ejpam-5731	37	44	if	if	SCONJ
ejpam-5731	37	45	there	there	ADV
ejpam-5731	37	46	w.	w.	PROPN
ejpam-5731	37	47	al	al	PROPN
ejpam-5731	37	48	-	-	PUNCT
ejpam-5731	37	49	rawashdeh	rawashdeh	PROPN
ejpam-5731	37	50	/	/	SYM
ejpam-5731	37	51	eur	eur	PROPN
ejpam-5731	37	52	.	.	PUNCT
ejpam-5731	38	1	j.	j.	PROPN
ejpam-5731	38	2	pure	pure	PROPN
ejpam-5731	38	3	appl	appl	PROPN
ejpam-5731	38	4	.	.	PROPN
ejpam-5731	38	5	math	math	PROPN
ejpam-5731	38	6	,	,	PUNCT
ejpam-5731	38	7	18	18	NUM
ejpam-5731	38	8	(	(	PUNCT
ejpam-5731	38	9	1	1	NUM
ejpam-5731	38	10	)	)	PUNCT
ejpam-5731	38	11	(	(	PUNCT
ejpam-5731	38	12	2025	2025	NUM
ejpam-5731	38	13	)	)	PUNCT
ejpam-5731	38	14	,	,	PUNCT
ejpam-5731	38	15	5731	5731	NUM
ejpam-5731	38	16	3	3	NUM
ejpam-5731	38	17	of	of	ADP
ejpam-5731	38	18	20	20	NUM
ejpam-5731	38	19	exists	exist	VERB
ejpam-5731	38	20	a	a	DET
ejpam-5731	38	21	schwarz	schwarz	PROPN
ejpam-5731	38	22	function	function	NOUN
ejpam-5731	38	23	w	w	NOUN
ejpam-5731	38	24	that	that	PRON
ejpam-5731	38	25	meets	meet	VERB
ejpam-5731	38	26	the	the	DET
ejpam-5731	38	27	criteria	criterion	NOUN
ejpam-5731	38	28	of	of	ADP
ejpam-5731	38	29	w(0	w(0	PROPN
ejpam-5731	38	30	)	)	PUNCT
ejpam-5731	38	31	=	=	SYM
ejpam-5731	38	32	0	0	NUM
ejpam-5731	39	1	and	and	CCONJ
ejpam-5731	39	2	|w(z)|	|w(z)|	VERB
ejpam-5731	39	3	<	<	X
ejpam-5731	39	4	1	1	NUM
ejpam-5731	39	5	for	for	ADP
ejpam-5731	39	6	all	all	DET
ejpam-5731	39	7	z	z	NOUN
ejpam-5731	39	8	in	in	ADP
ejpam-5731	39	9	d.	d.	PROPN
ejpam-5731	39	10	this	this	PRON
ejpam-5731	39	11	means	mean	VERB
ejpam-5731	39	12	that	that	SCONJ
ejpam-5731	39	13	for	for	ADP
ejpam-5731	39	14	every	every	DET
ejpam-5731	39	15	z	z	NOUN
ejpam-5731	39	16	in	in	ADP
ejpam-5731	39	17	d	d	PROPN
ejpam-5731	39	18	,	,	PUNCT
ejpam-5731	39	19	the	the	DET
ejpam-5731	39	20	relationship	relationship	NOUN
ejpam-5731	39	21	f(z	f(z	VERB
ejpam-5731	39	22	)	)	PUNCT
ejpam-5731	39	23	=	=	SYM
ejpam-5731	39	24	g(w(z	g(w(z	PROPN
ejpam-5731	39	25	)	)	PUNCT
ejpam-5731	39	26	)	)	PUNCT
ejpam-5731	39	27	holds	hold	VERB
ejpam-5731	39	28	true	true	ADJ
ejpam-5731	39	29	.	.	PUNCT
ejpam-5731	40	1	this	this	DET
ejpam-5731	40	2	concept	concept	NOUN
ejpam-5731	40	3	of	of	ADP
ejpam-5731	40	4	subordination	subordination	NOUN
ejpam-5731	40	5	is	be	AUX
ejpam-5731	40	6	essential	essential	ADJ
ejpam-5731	40	7	in	in	ADP
ejpam-5731	40	8	complex	complex	ADJ
ejpam-5731	40	9	analysis	analysis	NOUN
ejpam-5731	40	10	,	,	PUNCT
ejpam-5731	40	11	as	as	SCONJ
ejpam-5731	40	12	it	it	PRON
ejpam-5731	40	13	allows	allow	VERB
ejpam-5731	40	14	us	we	PRON
ejpam-5731	40	15	to	to	PART
ejpam-5731	40	16	analyze	analyze	VERB
ejpam-5731	40	17	and	and	CCONJ
ejpam-5731	40	18	compare	compare	VERB
ejpam-5731	40	19	the	the	DET
ejpam-5731	40	20	behaviors	behavior	NOUN
ejpam-5731	40	21	of	of	ADP
ejpam-5731	40	22	two	two	NUM
ejpam-5731	40	23	analytic	analytic	ADJ
ejpam-5731	40	24	functions	function	NOUN
ejpam-5731	40	25	within	within	ADP
ejpam-5731	40	26	the	the	DET
ejpam-5731	40	27	unit	unit	NOUN
ejpam-5731	40	28	disk	disk	NOUN
ejpam-5731	40	29	.	.	PUNCT
ejpam-5731	41	1	importantly	importantly	ADV
ejpam-5731	41	2	,	,	PUNCT
ejpam-5731	41	3	when	when	SCONJ
ejpam-5731	41	4	g	g	PROPN
ejpam-5731	41	5	is	be	AUX
ejpam-5731	41	6	a	a	DET
ejpam-5731	41	7	univalent	univalent	ADJ
ejpam-5731	41	8	function	function	NOUN
ejpam-5731	41	9	in	in	ADP
ejpam-5731	41	10	d	d	PROPN
ejpam-5731	41	11	,	,	PUNCT
ejpam-5731	41	12	the	the	DET
ejpam-5731	41	13	condition	condition	NOUN
ejpam-5731	41	14	f(z	f(z	NOUN
ejpam-5731	41	15	)	)	PUNCT
ejpam-5731	41	16	≺	≺	NOUN
ejpam-5731	41	17	g(z	g(z	PROPN
ejpam-5731	41	18	)	)	PUNCT
ejpam-5731	41	19	translates	translate	VERB
ejpam-5731	41	20	to	to	ADP
ejpam-5731	41	21	the	the	DET
ejpam-5731	41	22	equivalence	equivalence	NOUN
ejpam-5731	41	23	of	of	ADP
ejpam-5731	41	24	f(0	f(0	NOUN
ejpam-5731	41	25	)	)	PUNCT
ejpam-5731	41	26	=	=	SYM
ejpam-5731	41	27	g(0	g(0	PROPN
ejpam-5731	41	28	)	)	PUNCT
ejpam-5731	41	29	and	and	CCONJ
ejpam-5731	41	30	the	the	DET
ejpam-5731	41	31	inclusion	inclusion	NOUN
ejpam-5731	41	32	f(d	f(d	PROPN
ejpam-5731	41	33	)	)	PUNCT
ejpam-5731	41	34	⊂	⊂	PROPN
ejpam-5731	41	35	g(d	g(d	PROPN
ejpam-5731	41	36	)	)	PUNCT
ejpam-5731	41	37	.	.	PUNCT
ejpam-5731	42	1	this	this	DET
ejpam-5731	42	2	equivalence	equivalence	NOUN
ejpam-5731	42	3	underscores	underscore	VERB
ejpam-5731	42	4	the	the	DET
ejpam-5731	42	5	importance	importance	NOUN
ejpam-5731	42	6	of	of	ADP
ejpam-5731	42	7	the	the	DET
ejpam-5731	42	8	subordination	subordination	NOUN
ejpam-5731	42	9	principle	principle	NOUN
ejpam-5731	42	10	in	in	ADP
ejpam-5731	42	11	elucidating	elucidate	VERB
ejpam-5731	42	12	the	the	DET
ejpam-5731	42	13	connections	connection	NOUN
ejpam-5731	42	14	between	between	ADP
ejpam-5731	42	15	analytic	analytic	ADJ
ejpam-5731	42	16	functions	function	NOUN
ejpam-5731	42	17	.	.	PUNCT
ejpam-5731	43	1	for	for	ADP
ejpam-5731	43	2	those	those	PRON
ejpam-5731	43	3	seeking	seek	VERB
ejpam-5731	43	4	a	a	DET
ejpam-5731	43	5	deeper	deep	ADJ
ejpam-5731	43	6	understanding	understanding	NOUN
ejpam-5731	43	7	and	and	CCONJ
ejpam-5731	43	8	more	more	ADV
ejpam-5731	43	9	detailed	detailed	ADJ
ejpam-5731	43	10	discussions	discussion	NOUN
ejpam-5731	43	11	on	on	ADP
ejpam-5731	43	12	the	the	DET
ejpam-5731	43	13	subordination	subordination	NOUN
ejpam-5731	43	14	principle	principle	NOUN
ejpam-5731	43	15	,	,	PUNCT
ejpam-5731	43	16	it	it	PRON
ejpam-5731	43	17	is	be	AUX
ejpam-5731	43	18	recommended	recommend	VERB
ejpam-5731	43	19	to	to	PART
ejpam-5731	43	20	consult	consult	VERB
ejpam-5731	43	21	the	the	DET
ejpam-5731	43	22	monographs	monograph	NOUN
ejpam-5731	44	1	[	[	X
ejpam-5731	44	2	18	18	NUM
ejpam-5731	44	3	]	]	PUNCT
ejpam-5731	44	4	,	,	PUNCT
ejpam-5731	44	5	[	[	X
ejpam-5731	44	6	17	17	NUM
ejpam-5731	44	7	]	]	PUNCT
ejpam-5731	44	8	,	,	PUNCT
ejpam-5731	45	1	[	[	X
ejpam-5731	45	2	34	34	NUM
ejpam-5731	45	3	]	]	PUNCT
ejpam-5731	45	4	,	,	PUNCT
ejpam-5731	45	5	and	and	CCONJ
ejpam-5731	45	6	[	[	X
ejpam-5731	45	7	36	36	NUM
ejpam-5731	45	8	]	]	X
ejpam-5731	45	9	,	,	PUNCT
ejpam-5731	45	10	which	which	PRON
ejpam-5731	45	11	offer	offer	VERB
ejpam-5731	45	12	thorough	thorough	ADJ
ejpam-5731	45	13	explanations	explanation	NOUN
ejpam-5731	45	14	and	and	CCONJ
ejpam-5731	45	15	applications	application	NOUN
ejpam-5731	45	16	of	of	ADP
ejpam-5731	45	17	this	this	DET
ejpam-5731	45	18	principle	principle	NOUN
ejpam-5731	45	19	within	within	ADP
ejpam-5731	45	20	the	the	DET
ejpam-5731	45	21	realms	realm	NOUN
ejpam-5731	45	22	of	of	ADP
ejpam-5731	45	23	complex	complex	ADJ
ejpam-5731	45	24	analysis	analysis	NOUN
ejpam-5731	45	25	and	and	CCONJ
ejpam-5731	45	26	geometric	geometric	ADJ
ejpam-5731	45	27	function	function	NOUN
ejpam-5731	45	28	theory	theory	NOUN
ejpam-5731	45	29	.	.	PUNCT
ejpam-5731	46	1	in	in	ADP
ejpam-5731	46	2	this	this	DET
ejpam-5731	46	3	context	context	NOUN
ejpam-5731	46	4	,	,	PUNCT
ejpam-5731	46	5	s	s	VERB
ejpam-5731	46	6	represents	represent	VERB
ejpam-5731	46	7	the	the	DET
ejpam-5731	46	8	set	set	NOUN
ejpam-5731	46	9	of	of	ADP
ejpam-5731	46	10	functions	function	NOUN
ejpam-5731	46	11	that	that	PRON
ejpam-5731	46	12	are	be	AUX
ejpam-5731	46	13	univalent	univalent	ADJ
ejpam-5731	46	14	in	in	ADP
ejpam-5731	46	15	the	the	DET
ejpam-5731	46	16	open	open	ADJ
ejpam-5731	46	17	unit	unit	NOUN
ejpam-5731	46	18	disk	disk	NOUN
ejpam-5731	46	19	d	d	PROPN
ejpam-5731	46	20	and	and	CCONJ
ejpam-5731	46	21	belong	belong	VERB
ejpam-5731	46	22	to	to	ADP
ejpam-5731	46	23	the	the	DET
ejpam-5731	46	24	set	set	NOUN
ejpam-5731	46	25	h.	h.	PROPN
ejpam-5731	46	26	as	as	SCONJ
ejpam-5731	46	27	known	know	VERB
ejpam-5731	46	28	univalent	univalent	ADJ
ejpam-5731	46	29	functions	function	NOUN
ejpam-5731	46	30	are	be	AUX
ejpam-5731	46	31	injective	injective	ADJ
ejpam-5731	46	32	functions	function	NOUN
ejpam-5731	46	33	.	.	PUNCT
ejpam-5731	47	1	hence	hence	ADV
ejpam-5731	47	2	,	,	PUNCT
ejpam-5731	47	3	they	they	PRON
ejpam-5731	47	4	are	be	AUX
ejpam-5731	47	5	invertible	invertible	ADJ
ejpam-5731	47	6	and	and	CCONJ
ejpam-5731	47	7	the	the	DET
ejpam-5731	47	8	inverse	inverse	NOUN
ejpam-5731	47	9	functions	function	NOUN
ejpam-5731	47	10	may	may	AUX
ejpam-5731	47	11	not	not	PART
ejpam-5731	47	12	be	be	AUX
ejpam-5731	47	13	defined	define	VERB
ejpam-5731	47	14	on	on	ADP
ejpam-5731	47	15	the	the	DET
ejpam-5731	47	16	entire	entire	ADJ
ejpam-5731	47	17	unit	unit	NOUN
ejpam-5731	47	18	disk	disk	NOUN
ejpam-5731	47	19	d.	d.	NOUN
ejpam-5731	47	20	in	in	ADP
ejpam-5731	47	21	fact	fact	NOUN
ejpam-5731	47	22	,	,	PUNCT
ejpam-5731	47	23	according	accord	VERB
ejpam-5731	47	24	to	to	AUX
ejpam-5731	47	25	koebe	koebe	VERB
ejpam-5731	47	26	one	one	NUM
ejpam-5731	47	27	-	-	PUNCT
ejpam-5731	47	28	quarter	quarter	NOUN
ejpam-5731	47	29	theorem	theorem	NOUN
ejpam-5731	47	30	,	,	PUNCT
ejpam-5731	47	31	the	the	DET
ejpam-5731	47	32	image	image	NOUN
ejpam-5731	47	33	of	of	ADP
ejpam-5731	47	34	d	d	PROPN
ejpam-5731	47	35	under	under	ADP
ejpam-5731	47	36	any	any	DET
ejpam-5731	47	37	function	function	NOUN
ejpam-5731	47	38	f	f	PROPN
ejpam-5731	47	39	∈	∈	PROPN
ejpam-5731	47	40	s	s	PART
ejpam-5731	47	41	contains	contain	VERB
ejpam-5731	47	42	the	the	DET
ejpam-5731	47	43	disk	disk	NOUN
ejpam-5731	47	44	d(0	d(0	NOUN
ejpam-5731	47	45	,	,	PUNCT
ejpam-5731	47	46	1/4	1/4	NUM
ejpam-5731	47	47	)	)	PUNCT
ejpam-5731	47	48	of	of	ADP
ejpam-5731	47	49	center	center	NOUN
ejpam-5731	47	50	0	0	PUNCT
ejpam-5731	47	51	and	and	CCONJ
ejpam-5731	47	52	radius	radius	PROPN
ejpam-5731	47	53	1/4	1/4	NUM
ejpam-5731	47	54	.	.	PUNCT
ejpam-5731	48	1	accordingly	accordingly	ADV
ejpam-5731	48	2	,	,	PUNCT
ejpam-5731	48	3	every	every	DET
ejpam-5731	48	4	function	function	NOUN
ejpam-5731	48	5	f	f	PROPN
ejpam-5731	48	6	∈	∈	PROPN
ejpam-5731	49	1	s	s	PART
ejpam-5731	49	2	has	have	VERB
ejpam-5731	49	3	an	an	DET
ejpam-5731	49	4	inverse	inverse	NOUN
ejpam-5731	49	5	f−1	f−1	PROPN
ejpam-5731	49	6	=	=	PUNCT
ejpam-5731	49	7	g	g	NOUN
ejpam-5731	49	8	which	which	PRON
ejpam-5731	49	9	is	be	AUX
ejpam-5731	49	10	defined	define	VERB
ejpam-5731	49	11	as	as	ADP
ejpam-5731	49	12	g(f(z	g(f(z	PROPN
ejpam-5731	49	13	)	)	PUNCT
ejpam-5731	49	14	)	)	PUNCT
ejpam-5731	50	1	=	=	PUNCT
ejpam-5731	51	1	z	z	X
ejpam-5731	51	2	,	,	PUNCT
ejpam-5731	51	3	z	z	PROPN
ejpam-5731	51	4	∈	∈	PROPN
ejpam-5731	51	5	d	d	X
ejpam-5731	51	6	f(g(w	f(g(w	PROPN
ejpam-5731	51	7	)	)	PUNCT
ejpam-5731	51	8	)	)	PUNCT
ejpam-5731	52	1	=	=	SYM
ejpam-5731	52	2	w	w	X
ejpam-5731	52	3	,	,	PUNCT
ejpam-5731	52	4	|w|	|w|	VERB
ejpam-5731	52	5	<	<	X
ejpam-5731	52	6	r(f	r(f	PROPN
ejpam-5731	52	7	)	)	PUNCT
ejpam-5731	52	8	;	;	PUNCT
ejpam-5731	52	9	r(f	r(f	PROPN
ejpam-5731	52	10	)	)	PUNCT
ejpam-5731	52	11	≥	≥	NOUN
ejpam-5731	52	12	1/4	1/4	NUM
ejpam-5731	52	13	.	.	PUNCT
ejpam-5731	53	1	moreover	moreover	ADV
ejpam-5731	53	2	,	,	PUNCT
ejpam-5731	53	3	the	the	DET
ejpam-5731	53	4	inverse	inverse	NOUN
ejpam-5731	53	5	function	function	NOUN
ejpam-5731	53	6	is	be	AUX
ejpam-5731	53	7	given	give	VERB
ejpam-5731	53	8	by	by	ADP
ejpam-5731	53	9	g(w	g(w	PROPN
ejpam-5731	53	10	)	)	PUNCT
ejpam-5731	53	11	=	=	PUNCT
ejpam-5731	54	1	w	w	PROPN
ejpam-5731	54	2	−	−	NOUN
ejpam-5731	54	3	a2w	a2w	PROPN
ejpam-5731	54	4	2	2	NUM
ejpam-5731	54	5	+	+	CCONJ
ejpam-5731	54	6	(	(	PUNCT
ejpam-5731	54	7	2a22	2a22	NUM
ejpam-5731	54	8	−	−	PROPN
ejpam-5731	54	9	a3)w	a3)w	NOUN
ejpam-5731	54	10	3	3	NUM
ejpam-5731	54	11	−	−	NOUN
ejpam-5731	54	12	(	(	PUNCT
ejpam-5731	54	13	5a32	5a32	NUM
ejpam-5731	54	14	−	−	NOUN
ejpam-5731	55	1	5a2a3	5a2a3	PROPN
ejpam-5731	56	1	+	+	CCONJ
ejpam-5731	56	2	a4)w	a4)w	PROPN
ejpam-5731	56	3	4	4	NUM
ejpam-5731	56	4	+	+	CCONJ
ejpam-5731	56	5	·	·	PUNCT
ejpam-5731	56	6	·	·	PUNCT
ejpam-5731	56	7	·	·	PUNCT
ejpam-5731	56	8	·	·	PUNCT
ejpam-5731	56	9	(	(	PUNCT
ejpam-5731	56	10	2	2	X
ejpam-5731	56	11	)	)	PUNCT
ejpam-5731	56	12	now	now	ADV
ejpam-5731	56	13	,	,	PUNCT
ejpam-5731	56	14	we	we	PRON
ejpam-5731	56	15	introduce	introduce	VERB
ejpam-5731	56	16	the	the	DET
ejpam-5731	56	17	class	class	NOUN
ejpam-5731	56	18	σ	σ	NOUN
ejpam-5731	56	19	in	in	ADP
ejpam-5731	56	20	the	the	DET
ejpam-5731	56	21	following	following	ADJ
ejpam-5731	56	22	manner	manner	NOUN
ejpam-5731	56	23	.	.	PUNCT
ejpam-5731	57	1	a	a	DET
ejpam-5731	57	2	function	function	NOUN
ejpam-5731	57	3	f	f	PROPN
ejpam-5731	57	4	∈	∈	PROPN
ejpam-5731	57	5	h	h	NOUN
ejpam-5731	57	6	is	be	AUX
ejpam-5731	57	7	considered	consider	VERB
ejpam-5731	57	8	bi	bi	ADJ
ejpam-5731	57	9	-	-	ADJ
ejpam-5731	57	10	univalent	univalent	ADJ
ejpam-5731	57	11	if	if	SCONJ
ejpam-5731	57	12	both	both	CCONJ
ejpam-5731	57	13	the	the	DET
ejpam-5731	57	14	function	function	NOUN
ejpam-5731	57	15	itself	itself	PRON
ejpam-5731	57	16	and	and	CCONJ
ejpam-5731	57	17	its	its	PRON
ejpam-5731	57	18	inverse	inverse	NOUN
ejpam-5731	57	19	,	,	PUNCT
ejpam-5731	57	20	f−1	f−1	PROPN
ejpam-5731	57	21	,	,	PUNCT
ejpam-5731	57	22	are	be	AUX
ejpam-5731	57	23	univalent	univalent	ADJ
ejpam-5731	57	24	within	within	ADP
ejpam-5731	57	25	the	the	DET
ejpam-5731	57	26	unit	unit	NOUN
ejpam-5731	57	27	disk	disk	NOUN
ejpam-5731	57	28	d.	d.	PROPN
ejpam-5731	57	29	consequently	consequently	ADV
ejpam-5731	57	30	,	,	PUNCT
ejpam-5731	57	31	we	we	PRON
ejpam-5731	57	32	define	define	VERB
ejpam-5731	57	33	σ	σ	NOUN
ejpam-5731	57	34	as	as	ADP
ejpam-5731	57	35	the	the	DET
ejpam-5731	57	36	collection	collection	NOUN
ejpam-5731	57	37	of	of	ADP
ejpam-5731	57	38	all	all	DET
ejpam-5731	57	39	bi	bi	ADJ
ejpam-5731	57	40	-	-	ADJ
ejpam-5731	57	41	univalent	univalent	ADJ
ejpam-5731	57	42	functions	function	NOUN
ejpam-5731	57	43	in	in	ADP
ejpam-5731	57	44	h	h	NOUN
ejpam-5731	57	45	that	that	PRON
ejpam-5731	57	46	are	be	AUX
ejpam-5731	57	47	represented	represent	VERB
ejpam-5731	57	48	by	by	ADP
ejpam-5731	57	49	equation	equation	NOUN
ejpam-5731	57	50	(	(	PUNCT
ejpam-5731	57	51	1	1	NUM
ejpam-5731	57	52	)	)	PUNCT
ejpam-5731	57	53	.	.	PUNCT
ejpam-5731	58	1	for	for	ADP
ejpam-5731	58	2	more	more	ADJ
ejpam-5731	58	3	information	information	NOUN
ejpam-5731	58	4	about	about	ADP
ejpam-5731	58	5	univalent	univalent	ADJ
ejpam-5731	58	6	and	and	CCONJ
ejpam-5731	58	7	bi	bi	ADJ
ejpam-5731	58	8	-	-	ADJ
ejpam-5731	58	9	univalent	univalent	ADJ
ejpam-5731	58	10	functions	function	NOUN
ejpam-5731	58	11	we	we	PRON
ejpam-5731	58	12	refer	refer	VERB
ejpam-5731	58	13	the	the	DET
ejpam-5731	58	14	readers	reader	NOUN
ejpam-5731	58	15	to	to	ADP
ejpam-5731	58	16	the	the	DET
ejpam-5731	58	17	articles	article	NOUN
ejpam-5731	58	18	[	[	X
ejpam-5731	58	19	30	30	NUM
ejpam-5731	58	20	]	]	PUNCT
ejpam-5731	58	21	,	,	PUNCT
ejpam-5731	58	22	[	[	X
ejpam-5731	58	23	32	32	NUM
ejpam-5731	58	24	]	]	PUNCT
ejpam-5731	58	25	,	,	PUNCT
ejpam-5731	58	26	[	[	X
ejpam-5731	58	27	37	37	NUM
ejpam-5731	58	28	]	]	PUNCT
ejpam-5731	58	29	the	the	DET
ejpam-5731	58	30	monograph	monograph	NOUN
ejpam-5731	59	1	[	[	X
ejpam-5731	59	2	18	18	NUM
ejpam-5731	59	3	]	]	PUNCT
ejpam-5731	59	4	,	,	PUNCT
ejpam-5731	59	5	[	[	X
ejpam-5731	59	6	21	21	NUM
ejpam-5731	59	7	]	]	PUNCT
ejpam-5731	59	8	and	and	CCONJ
ejpam-5731	59	9	the	the	DET
ejpam-5731	59	10	references	reference	NOUN
ejpam-5731	59	11	provided	provide	VERB
ejpam-5731	59	12	therein	therein	ADV
ejpam-5731	59	13	.	.	PUNCT
ejpam-5731	60	1	research	research	NOUN
ejpam-5731	60	2	in	in	ADP
ejpam-5731	60	3	geometric	geometric	ADJ
ejpam-5731	60	4	function	function	NOUN
ejpam-5731	60	5	theory	theory	NOUN
ejpam-5731	60	6	illuminates	illuminate	VERB
ejpam-5731	60	7	the	the	DET
ejpam-5731	60	8	complex	complex	ADJ
ejpam-5731	60	9	connections	connection	NOUN
ejpam-5731	60	10	between	between	ADP
ejpam-5731	60	11	coefficients	coefficient	NOUN
ejpam-5731	60	12	and	and	CCONJ
ejpam-5731	60	13	the	the	DET
ejpam-5731	60	14	geometric	geometric	ADJ
ejpam-5731	60	15	properties	property	NOUN
ejpam-5731	60	16	of	of	ADP
ejpam-5731	60	17	functions	function	NOUN
ejpam-5731	60	18	.	.	PUNCT
ejpam-5731	61	1	by	by	ADP
ejpam-5731	61	2	analyzing	analyze	VERB
ejpam-5731	61	3	the	the	DET
ejpam-5731	61	4	constraints	constraint	NOUN
ejpam-5731	61	5	on	on	ADP
ejpam-5731	61	6	the	the	DET
ejpam-5731	61	7	modulus	modulus	NOUN
ejpam-5731	61	8	of	of	ADP
ejpam-5731	61	9	a	a	DET
ejpam-5731	61	10	function	function	NOUN
ejpam-5731	61	11	’s	’s	PART
ejpam-5731	61	12	coefficients	coefficient	NOUN
ejpam-5731	61	13	,	,	PUNCT
ejpam-5731	61	14	we	we	PRON
ejpam-5731	61	15	can	can	AUX
ejpam-5731	61	16	better	well	ADV
ejpam-5731	61	17	understand	understand	VERB
ejpam-5731	61	18	the	the	DET
ejpam-5731	61	19	behavior	behavior	NOUN
ejpam-5731	61	20	and	and	CCONJ
ejpam-5731	61	21	interactions	interaction	NOUN
ejpam-5731	61	22	of	of	ADP
ejpam-5731	61	23	these	these	DET
ejpam-5731	61	24	functions	function	NOUN
ejpam-5731	61	25	within	within	ADP
ejpam-5731	61	26	the	the	DET
ejpam-5731	61	27	mathematical	mathematical	ADJ
ejpam-5731	61	28	landscape	landscape	NOUN
ejpam-5731	61	29	.	.	PUNCT
ejpam-5731	62	1	this	this	DET
ejpam-5731	62	2	analytical	analytical	ADJ
ejpam-5731	62	3	perspective	perspective	NOUN
ejpam-5731	62	4	not	not	PART
ejpam-5731	62	5	only	only	ADV
ejpam-5731	62	6	deepens	deepen	VERB
ejpam-5731	62	7	our	our	PRON
ejpam-5731	62	8	grasp	grasp	NOUN
ejpam-5731	62	9	of	of	ADP
ejpam-5731	62	10	the	the	DET
ejpam-5731	62	11	fundamental	fundamental	ADJ
ejpam-5731	62	12	principles	principle	NOUN
ejpam-5731	62	13	of	of	ADP
ejpam-5731	62	14	geometric	geometric	ADJ
ejpam-5731	62	15	function	function	NOUN
ejpam-5731	62	16	theory	theory	NOUN
ejpam-5731	62	17	but	but	CCONJ
ejpam-5731	62	18	also	also	ADV
ejpam-5731	62	19	opens	open	VERB
ejpam-5731	62	20	avenues	avenue	NOUN
ejpam-5731	62	21	for	for	ADP
ejpam-5731	62	22	further	further	ADJ
ejpam-5731	62	23	investigation	investigation	NOUN
ejpam-5731	62	24	and	and	CCONJ
ejpam-5731	62	25	innovation	innovation	NOUN
ejpam-5731	62	26	in	in	ADP
ejpam-5731	62	27	this	this	DET
ejpam-5731	62	28	vibrant	vibrant	ADJ
ejpam-5731	62	29	area	area	NOUN
ejpam-5731	62	30	of	of	ADP
ejpam-5731	62	31	study	study	NOUN
ejpam-5731	62	32	.	.	PUNCT
ejpam-5731	63	1	for	for	ADP
ejpam-5731	63	2	instance	instance	NOUN
ejpam-5731	63	3	,	,	PUNCT
ejpam-5731	63	4	within	within	ADP
ejpam-5731	63	5	the	the	DET
ejpam-5731	63	6	class	class	NOUN
ejpam-5731	63	7	s	s	PART
ejpam-5731	63	8	,	,	PUNCT
ejpam-5731	63	9	it	it	PRON
ejpam-5731	63	10	is	be	AUX
ejpam-5731	63	11	shown	show	VERB
ejpam-5731	63	12	that	that	SCONJ
ejpam-5731	63	13	the	the	DET
ejpam-5731	63	14	modulus	modulus	NOUN
ejpam-5731	63	15	of	of	ADP
ejpam-5731	63	16	the	the	DET
ejpam-5731	63	17	coefficient	coefficient	NOUN
ejpam-5731	63	18	an	an	PRON
ejpam-5731	63	19	is	be	AUX
ejpam-5731	63	20	limited	limit	VERB
ejpam-5731	63	21	by	by	ADP
ejpam-5731	63	22	the	the	DET
ejpam-5731	63	23	value	value	NOUN
ejpam-5731	63	24	of	of	ADP
ejpam-5731	63	25	n.	n.	NOUN
ejpam-5731	63	26	these	these	DET
ejpam-5731	63	27	constraints	constraint	NOUN
ejpam-5731	63	28	on	on	ADP
ejpam-5731	63	29	the	the	DET
ejpam-5731	63	30	modulus	modulus	NOUN
ejpam-5731	63	31	of	of	ADP
ejpam-5731	63	32	coefficients	coefficient	NOUN
ejpam-5731	63	33	yield	yield	VERB
ejpam-5731	63	34	important	important	ADJ
ejpam-5731	63	35	insights	insight	NOUN
ejpam-5731	63	36	into	into	ADP
ejpam-5731	63	37	the	the	DET
ejpam-5731	63	38	geometric	geometric	ADJ
ejpam-5731	63	39	features	feature	NOUN
ejpam-5731	63	40	of	of	ADP
ejpam-5731	63	41	these	these	DET
ejpam-5731	63	42	functions	function	NOUN
ejpam-5731	63	43	.	.	PUNCT
ejpam-5731	64	1	in	in	ADP
ejpam-5731	64	2	particular	particular	ADJ
ejpam-5731	64	3	,	,	PUNCT
ejpam-5731	64	4	the	the	DET
ejpam-5731	64	5	bounds	bound	NOUN
ejpam-5731	64	6	on	on	ADP
ejpam-5731	64	7	the	the	DET
ejpam-5731	64	8	second	second	ADJ
ejpam-5731	64	9	coefficients	coefficient	NOUN
ejpam-5731	64	10	of	of	ADP
ejpam-5731	64	11	functions	function	NOUN
ejpam-5731	64	12	in	in	ADP
ejpam-5731	64	13	the	the	DET
ejpam-5731	64	14	class	class	NOUN
ejpam-5731	64	15	s	s	AUX
ejpam-5731	64	16	provide	provide	VERB
ejpam-5731	64	17	essential	essential	ADJ
ejpam-5731	64	18	information	information	NOUN
ejpam-5731	64	19	about	about	ADP
ejpam-5731	64	20	the	the	DET
ejpam-5731	64	21	growth	growth	NOUN
ejpam-5731	64	22	and	and	CCONJ
ejpam-5731	64	23	w.	w.	PROPN
ejpam-5731	64	24	al	al	PROPN
ejpam-5731	64	25	-	-	PUNCT
ejpam-5731	64	26	rawashdeh	rawashdeh	PROPN
ejpam-5731	64	27	/	/	SYM
ejpam-5731	64	28	eur	eur	PROPN
ejpam-5731	64	29	.	.	PUNCT
ejpam-5731	65	1	j.	j.	PROPN
ejpam-5731	65	2	pure	pure	PROPN
ejpam-5731	65	3	appl	appl	PROPN
ejpam-5731	65	4	.	.	PROPN
ejpam-5731	65	5	math	math	PROPN
ejpam-5731	65	6	,	,	PUNCT
ejpam-5731	65	7	18	18	NUM
ejpam-5731	65	8	(	(	PUNCT
ejpam-5731	65	9	1	1	NUM
ejpam-5731	65	10	)	)	PUNCT
ejpam-5731	65	11	(	(	PUNCT
ejpam-5731	65	12	2025	2025	NUM
ejpam-5731	65	13	)	)	PUNCT
ejpam-5731	65	14	,	,	PUNCT
ejpam-5731	65	15	5731	5731	NUM
ejpam-5731	65	16	4	4	NUM
ejpam-5731	65	17	of	of	ADP
ejpam-5731	65	18	20	20	NUM
ejpam-5731	65	19	distortion	distortion	NOUN
ejpam-5731	65	20	bounds	bound	VERB
ejpam-5731	65	21	relevant	relevant	ADJ
ejpam-5731	65	22	to	to	ADP
ejpam-5731	65	23	this	this	DET
ejpam-5731	65	24	class	class	NOUN
ejpam-5731	65	25	.	.	PUNCT
ejpam-5731	66	1	the	the	DET
ejpam-5731	66	2	study	study	NOUN
ejpam-5731	66	3	of	of	ADP
ejpam-5731	66	4	coefficient	coefficient	NOUN
ejpam-5731	66	5	-	-	PUNCT
ejpam-5731	66	6	related	relate	VERB
ejpam-5731	66	7	characteristics	characteristic	NOUN
ejpam-5731	66	8	of	of	ADP
ejpam-5731	66	9	functions	function	NOUN
ejpam-5731	66	10	within	within	ADP
ejpam-5731	66	11	the	the	DET
ejpam-5731	66	12	bi	bi	ADJ
ejpam-5731	66	13	-	-	ADJ
ejpam-5731	66	14	univalent	univalent	ADJ
ejpam-5731	66	15	class	class	NOUN
ejpam-5731	66	16	σ	σ	PROPN
ejpam-5731	66	17	began	begin	VERB
ejpam-5731	66	18	in	in	ADP
ejpam-5731	66	19	the	the	DET
ejpam-5731	66	20	1970s	1970s	NUM
ejpam-5731	66	21	.	.	PUNCT
ejpam-5731	67	1	a	a	DET
ejpam-5731	67	2	pivotal	pivotal	ADJ
ejpam-5731	67	3	moment	moment	NOUN
ejpam-5731	67	4	occurred	occur	VERB
ejpam-5731	67	5	in	in	ADP
ejpam-5731	67	6	1967	1967	NUM
ejpam-5731	67	7	when	when	SCONJ
ejpam-5731	67	8	lewin	lewin	PROPN
ejpam-5731	67	9	[	[	X
ejpam-5731	67	10	30	30	NUM
ejpam-5731	67	11	]	]	PUNCT
ejpam-5731	67	12	investigated	investigate	VERB
ejpam-5731	67	13	the	the	DET
ejpam-5731	67	14	bi	bi	ADJ
ejpam-5731	67	15	-	-	ADJ
ejpam-5731	67	16	univalent	univalent	ADJ
ejpam-5731	67	17	function	function	NOUN
ejpam-5731	67	18	class	class	NOUN
ejpam-5731	67	19	and	and	CCONJ
ejpam-5731	67	20	set	set	VERB
ejpam-5731	67	21	a	a	DET
ejpam-5731	67	22	limit	limit	NOUN
ejpam-5731	67	23	for	for	ADP
ejpam-5731	67	24	the	the	DET
ejpam-5731	67	25	coefficient	coefficient	NOUN
ejpam-5731	67	26	|a2|	|a2|	NOUN
ejpam-5731	67	27	.	.	PUNCT
ejpam-5731	68	1	in	in	ADP
ejpam-5731	68	2	1969	1969	NUM
ejpam-5731	68	3	,	,	PUNCT
ejpam-5731	68	4	netanyahu	netanyahu	PROPN
ejpam-5731	68	5	[	[	X
ejpam-5731	68	6	37	37	NUM
ejpam-5731	68	7	]	]	PUNCT
ejpam-5731	68	8	furthered	further	VERB
ejpam-5731	68	9	this	this	DET
ejpam-5731	68	10	research	research	NOUN
ejpam-5731	68	11	by	by	ADP
ejpam-5731	68	12	establishing	establish	VERB
ejpam-5731	68	13	that	that	SCONJ
ejpam-5731	68	14	the	the	DET
ejpam-5731	68	15	maximum	maximum	ADJ
ejpam-5731	68	16	value	value	NOUN
ejpam-5731	68	17	of	of	ADP
ejpam-5731	68	18	|a2|	|a2|	NOUN
ejpam-5731	68	19	for	for	ADP
ejpam-5731	68	20	functions	function	NOUN
ejpam-5731	68	21	in	in	ADP
ejpam-5731	68	22	σ	σ	PROPN
ejpam-5731	68	23	is	be	AUX
ejpam-5731	68	24	4	4	NUM
ejpam-5731	68	25	3	3	NUM
ejpam-5731	68	26	.	.	PUNCT
ejpam-5731	69	1	later	later	ADV
ejpam-5731	69	2	,	,	PUNCT
ejpam-5731	69	3	in	in	ADP
ejpam-5731	69	4	1979	1979	NUM
ejpam-5731	69	5	,	,	PUNCT
ejpam-5731	69	6	brannan	brannan	PROPN
ejpam-5731	69	7	and	and	CCONJ
ejpam-5731	69	8	clunie	clunie	NOUN
ejpam-5731	69	9	[	[	X
ejpam-5731	69	10	11	11	NUM
ejpam-5731	69	11	]	]	PUNCT
ejpam-5731	69	12	proved	prove	VERB
ejpam-5731	69	13	that	that	SCONJ
ejpam-5731	69	14	for	for	ADP
ejpam-5731	69	15	functions	function	NOUN
ejpam-5731	69	16	belonging	belong	VERB
ejpam-5731	69	17	to	to	ADP
ejpam-5731	69	18	this	this	DET
ejpam-5731	69	19	class	class	NOUN
ejpam-5731	69	20	,	,	PUNCT
ejpam-5731	69	21	the	the	DET
ejpam-5731	69	22	inequality	inequality	NOUN
ejpam-5731	69	23	|a2|	|a2|	VERB
ejpam-5731	69	24	≤	≤	NOUN
ejpam-5731	69	25	√	√	NUM
ejpam-5731	69	26	2	2	NUM
ejpam-5731	69	27	is	be	AUX
ejpam-5731	69	28	valid	valid	ADJ
ejpam-5731	69	29	.	.	PUNCT
ejpam-5731	70	1	this	this	DET
ejpam-5731	70	2	foundational	foundational	ADJ
ejpam-5731	70	3	research	research	NOUN
ejpam-5731	70	4	has	have	AUX
ejpam-5731	70	5	led	lead	VERB
ejpam-5731	70	6	to	to	ADP
ejpam-5731	70	7	a	a	DET
ejpam-5731	70	8	multitude	multitude	NOUN
ejpam-5731	70	9	of	of	ADP
ejpam-5731	70	10	studies	study	NOUN
ejpam-5731	70	11	focused	focus	VERB
ejpam-5731	70	12	on	on	ADP
ejpam-5731	70	13	the	the	DET
ejpam-5731	70	14	coefficient	coefficient	NOUN
ejpam-5731	70	15	bounds	bound	VERB
ejpam-5731	70	16	for	for	ADP
ejpam-5731	70	17	various	various	ADJ
ejpam-5731	70	18	subclasses	subclass	NOUN
ejpam-5731	70	19	of	of	ADP
ejpam-5731	70	20	bi	bi	ADJ
ejpam-5731	70	21	-	-	ADJ
ejpam-5731	70	22	univalent	univalent	ADJ
ejpam-5731	70	23	functions	function	NOUN
ejpam-5731	70	24	.	.	PUNCT
ejpam-5731	71	1	however	however	ADV
ejpam-5731	71	2	,	,	PUNCT
ejpam-5731	71	3	despite	despite	SCONJ
ejpam-5731	71	4	the	the	DET
ejpam-5731	71	5	extensive	extensive	ADJ
ejpam-5731	71	6	investigations	investigation	NOUN
ejpam-5731	71	7	into	into	ADP
ejpam-5731	71	8	coefficient	coefficient	NOUN
ejpam-5731	71	9	bounds	bound	NOUN
ejpam-5731	71	10	,	,	PUNCT
ejpam-5731	71	11	there	there	PRON
ejpam-5731	71	12	is	be	VERB
ejpam-5731	71	13	still	still	ADV
ejpam-5731	71	14	a	a	DET
ejpam-5731	71	15	considerable	considerable	ADJ
ejpam-5731	71	16	lack	lack	NOUN
ejpam-5731	71	17	of	of	ADP
ejpam-5731	71	18	understanding	understanding	NOUN
ejpam-5731	71	19	regarding	regard	VERB
ejpam-5731	71	20	the	the	DET
ejpam-5731	71	21	general	general	ADJ
ejpam-5731	71	22	coefficients	coefficient	NOUN
ejpam-5731	71	23	|a2|	|a2|	VERB
ejpam-5731	71	24	when	when	SCONJ
ejpam-5731	71	25	n	n	X
ejpam-5731	71	26	≥	≥	NOUN
ejpam-5731	71	27	4	4	NUM
ejpam-5731	71	28	.	.	PUNCT
ejpam-5731	72	1	the	the	DET
ejpam-5731	72	2	difficulty	difficulty	NOUN
ejpam-5731	72	3	in	in	ADP
ejpam-5731	72	4	estimating	estimate	VERB
ejpam-5731	72	5	these	these	DET
ejpam-5731	72	6	coefficients	coefficient	NOUN
ejpam-5731	72	7	,	,	PUNCT
ejpam-5731	72	8	especially	especially	ADV
ejpam-5731	72	9	the	the	DET
ejpam-5731	72	10	general	general	ADJ
ejpam-5731	72	11	coefficient	coefficient	NOUN
ejpam-5731	72	12	|an|	|an|	PROPN
ejpam-5731	72	13	,	,	PUNCT
ejpam-5731	72	14	remains	remain	VERB
ejpam-5731	72	15	an	an	DET
ejpam-5731	72	16	open	open	ADJ
ejpam-5731	72	17	question	question	NOUN
ejpam-5731	72	18	in	in	ADP
ejpam-5731	72	19	the	the	DET
ejpam-5731	72	20	field	field	NOUN
ejpam-5731	72	21	,	,	PUNCT
ejpam-5731	72	22	underscoring	underscore	VERB
ejpam-5731	72	23	the	the	DET
ejpam-5731	72	24	complexity	complexity	NOUN
ejpam-5731	72	25	and	and	CCONJ
ejpam-5731	72	26	depth	depth	NOUN
ejpam-5731	72	27	of	of	ADP
ejpam-5731	72	28	the	the	DET
ejpam-5731	72	29	bi	bi	ADJ
ejpam-5731	72	30	-	-	ADJ
ejpam-5731	72	31	univalent	univalent	ADJ
ejpam-5731	72	32	function	function	NOUN
ejpam-5731	72	33	class	class	NOUN
ejpam-5731	72	34	and	and	CCONJ
ejpam-5731	72	35	indicating	indicate	VERB
ejpam-5731	72	36	that	that	SCONJ
ejpam-5731	72	37	further	further	ADJ
ejpam-5731	72	38	research	research	NOUN
ejpam-5731	72	39	is	be	AUX
ejpam-5731	72	40	essential	essential	ADJ
ejpam-5731	72	41	to	to	PART
ejpam-5731	72	42	grasp	grasp	VERB
ejpam-5731	72	43	the	the	DET
ejpam-5731	72	44	behavior	behavior	NOUN
ejpam-5731	72	45	of	of	ADP
ejpam-5731	72	46	these	these	DET
ejpam-5731	72	47	coefficients	coefficient	NOUN
ejpam-5731	72	48	in	in	ADP
ejpam-5731	72	49	higher	high	ADJ
ejpam-5731	72	50	dimensions	dimension	NOUN
ejpam-5731	72	51	.	.	PUNCT
ejpam-5731	73	1	in	in	ADP
ejpam-5731	73	2	1933	1933	NUM
ejpam-5731	73	3	,	,	PUNCT
ejpam-5731	73	4	fekete	fekete	PROPN
ejpam-5731	73	5	and	and	CCONJ
ejpam-5731	73	6	szegö	szegö	VERB
ejpam-5731	74	1	[	[	X
ejpam-5731	74	2	19	19	NUM
ejpam-5731	74	3	]	]	PUNCT
ejpam-5731	74	4	established	establish	VERB
ejpam-5731	74	5	the	the	DET
ejpam-5731	74	6	upper	upper	ADJ
ejpam-5731	74	7	bound	bound	NOUN
ejpam-5731	74	8	of	of	ADP
ejpam-5731	74	9	the	the	DET
ejpam-5731	74	10	expression	expression	NOUN
ejpam-5731	74	11	|a3−λa22|	|a3−λa22|	ADP
ejpam-5731	74	12	for	for	ADP
ejpam-5731	74	13	univalent	univalent	ADJ
ejpam-5731	74	14	functions	function	NOUN
ejpam-5731	74	15	f	f	NOUN
ejpam-5731	74	16	,	,	PUNCT
ejpam-5731	74	17	where	where	SCONJ
ejpam-5731	74	18	the	the	DET
ejpam-5731	74	19	0	0	NUM
ejpam-5731	74	20	≤	≤	NUM
ejpam-5731	74	21	λ	λ	NOUN
ejpam-5731	74	22	≤	≤	NOUN
ejpam-5731	74	23	1	1	NUM
ejpam-5731	74	24	.	.	PUNCT
ejpam-5731	75	1	this	this	DET
ejpam-5731	75	2	pivotal	pivotal	ADJ
ejpam-5731	75	3	finding	finding	NOUN
ejpam-5731	75	4	gave	give	VERB
ejpam-5731	75	5	rise	rise	NOUN
ejpam-5731	75	6	to	to	ADP
ejpam-5731	75	7	the	the	DET
ejpam-5731	75	8	fekete	fekete	PROPN
ejpam-5731	75	9	-	-	PUNCT
ejpam-5731	75	10	szegö	szegö	PROPN
ejpam-5731	75	11	problem	problem	NOUN
ejpam-5731	75	12	,	,	PUNCT
ejpam-5731	75	13	which	which	PRON
ejpam-5731	75	14	focuses	focus	VERB
ejpam-5731	75	15	on	on	ADP
ejpam-5731	75	16	maximizing	maximize	VERB
ejpam-5731	75	17	the	the	DET
ejpam-5731	75	18	modulus	modulus	NOUN
ejpam-5731	75	19	of	of	ADP
ejpam-5731	75	20	the	the	DET
ejpam-5731	75	21	functional	functional	ADJ
ejpam-5731	75	22	ψλ(f	ψλ(f	NOUN
ejpam-5731	75	23	)	)	PUNCT
ejpam-5731	75	24	=	=	SYM
ejpam-5731	75	25	a3	a3	NOUN
ejpam-5731	75	26	−	−	PROPN
ejpam-5731	75	27	λa22	λa22	PROPN
ejpam-5731	75	28	for	for	ADP
ejpam-5731	75	29	functions	function	NOUN
ejpam-5731	75	30	f	f	NOUN
ejpam-5731	75	31	belonging	belong	VERB
ejpam-5731	75	32	to	to	ADP
ejpam-5731	75	33	the	the	DET
ejpam-5731	75	34	class	class	NOUN
ejpam-5731	75	35	h	h	NOUN
ejpam-5731	75	36	,	,	PUNCT
ejpam-5731	75	37	with	with	ADP
ejpam-5731	75	38	λ	λ	NOUN
ejpam-5731	75	39	being	be	AUX
ejpam-5731	75	40	any	any	DET
ejpam-5731	75	41	complex	complex	ADJ
ejpam-5731	75	42	number	number	NOUN
ejpam-5731	75	43	.	.	PUNCT
ejpam-5731	76	1	a	a	DET
ejpam-5731	76	2	significant	significant	ADJ
ejpam-5731	76	3	body	body	NOUN
ejpam-5731	76	4	of	of	ADP
ejpam-5731	76	5	research	research	NOUN
ejpam-5731	76	6	has	have	AUX
ejpam-5731	76	7	since	since	ADV
ejpam-5731	76	8	been	be	AUX
ejpam-5731	76	9	dedicated	dedicate	VERB
ejpam-5731	76	10	to	to	ADP
ejpam-5731	76	11	exploring	explore	VERB
ejpam-5731	76	12	the	the	DET
ejpam-5731	76	13	feketeszegö	feketeszegö	ADJ
ejpam-5731	76	14	functional	functional	ADJ
ejpam-5731	76	15	and	and	CCONJ
ejpam-5731	76	16	related	related	ADJ
ejpam-5731	76	17	coefficient	coefficient	NOUN
ejpam-5731	76	18	estimation	estimation	NOUN
ejpam-5731	76	19	issues	issue	NOUN
ejpam-5731	76	20	.	.	PUNCT
ejpam-5731	77	1	noteworthy	noteworthy	ADJ
ejpam-5731	77	2	contributions	contribution	NOUN
ejpam-5731	77	3	to	to	ADP
ejpam-5731	77	4	this	this	DET
ejpam-5731	77	5	area	area	NOUN
ejpam-5731	77	6	can	can	AUX
ejpam-5731	77	7	be	be	AUX
ejpam-5731	77	8	found	find	VERB
ejpam-5731	77	9	in	in	ADP
ejpam-5731	77	10	various	various	ADJ
ejpam-5731	77	11	publications	publication	NOUN
ejpam-5731	77	12	,	,	PUNCT
ejpam-5731	77	13	including	include	VERB
ejpam-5731	77	14	[	[	X
ejpam-5731	77	15	3	3	NUM
ejpam-5731	77	16	]	]	PUNCT
ejpam-5731	77	17	,	,	PUNCT
ejpam-5731	77	18	[	[	X
ejpam-5731	77	19	4	4	NUM
ejpam-5731	77	20	]	]	PUNCT
ejpam-5731	77	21	,	,	PUNCT
ejpam-5731	77	22	[	[	X
ejpam-5731	77	23	6	6	NUM
ejpam-5731	77	24	]	]	PUNCT
ejpam-5731	77	25	,	,	PUNCT
ejpam-5731	77	26	[	[	X
ejpam-5731	77	27	12	12	NUM
ejpam-5731	77	28	]	]	PUNCT
ejpam-5731	77	29	,	,	PUNCT
ejpam-5731	77	30	[	[	X
ejpam-5731	77	31	15	15	NUM
ejpam-5731	77	32	]	]	PUNCT
ejpam-5731	77	33	,	,	PUNCT
ejpam-5731	77	34	[	[	X
ejpam-5731	77	35	24	24	NUM
ejpam-5731	77	36	]	]	PUNCT
ejpam-5731	77	37	,	,	PUNCT
ejpam-5731	77	38	[	[	X
ejpam-5731	77	39	26	26	NUM
ejpam-5731	77	40	]	]	PUNCT
ejpam-5731	77	41	,	,	PUNCT
ejpam-5731	77	42	[	[	X
ejpam-5731	77	43	31	31	NUM
ejpam-5731	77	44	]	]	PUNCT
ejpam-5731	77	45	,	,	PUNCT
ejpam-5731	77	46	[	[	X
ejpam-5731	77	47	32	32	NUM
ejpam-5731	77	48	]	]	PUNCT
ejpam-5731	77	49	,	,	PUNCT
ejpam-5731	77	50	[	[	X
ejpam-5731	77	51	48	48	NUM
ejpam-5731	77	52	]	]	PUNCT
ejpam-5731	77	53	and	and	CCONJ
ejpam-5731	77	54	the	the	DET
ejpam-5731	77	55	references	reference	NOUN
ejpam-5731	77	56	provided	provide	VERB
ejpam-5731	77	57	therein	therein	ADV
ejpam-5731	77	58	.	.	PUNCT
ejpam-5731	78	1	these	these	DET
ejpam-5731	78	2	investigations	investigation	NOUN
ejpam-5731	78	3	have	have	AUX
ejpam-5731	78	4	significantly	significantly	ADV
ejpam-5731	78	5	enhanced	enhance	VERB
ejpam-5731	78	6	the	the	DET
ejpam-5731	78	7	comprehension	comprehension	NOUN
ejpam-5731	78	8	of	of	ADP
ejpam-5731	78	9	the	the	DET
ejpam-5731	78	10	fekete	fekete	PROPN
ejpam-5731	78	11	-	-	PUNCT
ejpam-5731	78	12	szegö	szegö	ADJ
ejpam-5731	78	13	problem	problem	NOUN
ejpam-5731	78	14	and	and	CCONJ
ejpam-5731	78	15	its	its	PRON
ejpam-5731	78	16	relevance	relevance	NOUN
ejpam-5731	78	17	within	within	ADP
ejpam-5731	78	18	the	the	DET
ejpam-5731	78	19	domain	domain	NOUN
ejpam-5731	78	20	of	of	ADP
ejpam-5731	78	21	geometric	geometric	ADJ
ejpam-5731	78	22	function	function	NOUN
ejpam-5731	78	23	theory	theory	NOUN
ejpam-5731	78	24	.	.	PUNCT
ejpam-5731	79	1	2	2	X
ejpam-5731	79	2	.	.	NUM
ejpam-5731	79	3	preliminaries	preliminary	NOUN
ejpam-5731	79	4	and	and	CCONJ
ejpam-5731	79	5	lemmas	lemma	VERB
ejpam-5731	79	6	the	the	DET
ejpam-5731	79	7	information	information	NOUN
ejpam-5731	79	8	provided	provide	VERB
ejpam-5731	79	9	in	in	ADP
ejpam-5731	79	10	this	this	DET
ejpam-5731	79	11	section	section	NOUN
ejpam-5731	79	12	is	be	AUX
ejpam-5731	79	13	crucial	crucial	ADJ
ejpam-5731	79	14	for	for	ADP
ejpam-5731	79	15	comprehending	comprehend	VERB
ejpam-5731	79	16	the	the	DET
ejpam-5731	79	17	key	key	ADJ
ejpam-5731	79	18	findings	finding	NOUN
ejpam-5731	79	19	of	of	ADP
ejpam-5731	79	20	this	this	DET
ejpam-5731	79	21	study	study	NOUN
ejpam-5731	79	22	.	.	PUNCT
ejpam-5731	80	1	in	in	ADP
ejpam-5731	80	2	1975	1975	NUM
ejpam-5731	80	3	,	,	PUNCT
ejpam-5731	80	4	ruscheweyh	ruscheweyh	VERB
ejpam-5731	80	5	[	[	X
ejpam-5731	80	6	43	43	NUM
ejpam-5731	80	7	]	]	PUNCT
ejpam-5731	80	8	introduced	introduce	VERB
ejpam-5731	80	9	the	the	DET
ejpam-5731	80	10	operator	operator	NOUN
ejpam-5731	80	11	r	r	NOUN
ejpam-5731	80	12	,	,	PUNCT
ejpam-5731	80	13	which	which	PRON
ejpam-5731	80	14	is	be	AUX
ejpam-5731	80	15	defined	define	VERB
ejpam-5731	80	16	through	through	ADP
ejpam-5731	80	17	the	the	DET
ejpam-5731	80	18	convolution	convolution	NOUN
ejpam-5731	80	19	(	(	PUNCT
ejpam-5731	80	20	hadamard	hadamard	ADJ
ejpam-5731	80	21	product	product	NOUN
ejpam-5731	80	22	)	)	PUNCT
ejpam-5731	80	23	of	of	ADP
ejpam-5731	80	24	two	two	NUM
ejpam-5731	80	25	power	power	NOUN
ejpam-5731	80	26	series	series	NOUN
ejpam-5731	80	27	.	.	PUNCT
ejpam-5731	81	1	in	in	ADP
ejpam-5731	81	2	particular	particular	ADJ
ejpam-5731	81	3	,	,	PUNCT
ejpam-5731	81	4	for	for	ADP
ejpam-5731	81	5	a	a	DET
ejpam-5731	81	6	function	function	NOUN
ejpam-5731	81	7	f	f	PROPN
ejpam-5731	81	8	∈	∈	PROPN
ejpam-5731	81	9	h	h	NOUN
ejpam-5731	81	10	,	,	PUNCT
ejpam-5731	81	11	a	a	DET
ejpam-5731	81	12	variable	variable	ADJ
ejpam-5731	81	13	z	z	NOUN
ejpam-5731	81	14	∈	∈	PROPN
ejpam-5731	81	15	d	d	NOUN
ejpam-5731	81	16	,	,	PUNCT
ejpam-5731	81	17	and	and	CCONJ
ejpam-5731	81	18	a	a	DET
ejpam-5731	81	19	real	real	ADJ
ejpam-5731	81	20	number	number	NOUN
ejpam-5731	81	21	α	α	PROPN
ejpam-5731	81	22	>	>	X
ejpam-5731	81	23	−1	−1	NOUN
ejpam-5731	81	24	,	,	PUNCT
ejpam-5731	81	25	the	the	DET
ejpam-5731	81	26	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	81	27	operator	operator	NOUN
ejpam-5731	81	28	is	be	AUX
ejpam-5731	81	29	articulated	articulate	VERB
ejpam-5731	81	30	as	as	SCONJ
ejpam-5731	81	31	follows	follow	VERB
ejpam-5731	81	32	:	:	PUNCT
ejpam-5731	81	33	rαf(z	rαf(z	VERB
ejpam-5731	81	34	)	)	PUNCT
ejpam-5731	81	35	=	=	SYM
ejpam-5731	81	36	f(z	f(z	PROPN
ejpam-5731	81	37	)	)	PUNCT
ejpam-5731	81	38	∗	∗	NOUN
ejpam-5731	81	39	z	z	NOUN
ejpam-5731	81	40	(	(	PUNCT
ejpam-5731	81	41	1−	1−	NUM
ejpam-5731	81	42	z)α+1	z)α+1	PROPN
ejpam-5731	81	43	.	.	PUNCT
ejpam-5731	82	1	for	for	ADP
ejpam-5731	82	2	α	α	NOUN
ejpam-5731	82	3	=	=	SYM
ejpam-5731	82	4	n	n	CCONJ
ejpam-5731	82	5	∈	∈	PROPN
ejpam-5731	82	6	n0	n0	X
ejpam-5731	82	7	=	=	SYM
ejpam-5731	82	8	n	n	PRON
ejpam-5731	82	9	∪	∪	X
ejpam-5731	82	10	{	{	PUNCT
ejpam-5731	82	11	0	0	NUM
ejpam-5731	82	12	}	}	PUNCT
ejpam-5731	82	13	,	,	PUNCT
ejpam-5731	82	14	we	we	PRON
ejpam-5731	82	15	get	get	VERB
ejpam-5731	82	16	the	the	DET
ejpam-5731	82	17	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	82	18	derivative	derivative	NOUN
ejpam-5731	82	19	rα	rα	ADP
ejpam-5731	82	20	of	of	ADP
ejpam-5731	82	21	the	the	DET
ejpam-5731	82	22	function	function	NOUN
ejpam-5731	82	23	f	f	NOUN
ejpam-5731	82	24	:	:	PUNCT
ejpam-5731	82	25	rαf(z	rαf(z	PROPN
ejpam-5731	82	26	)	)	PUNCT
ejpam-5731	83	1	=	=	SYM
ejpam-5731	83	2	z	z	NOUN
ejpam-5731	83	3	(	(	PUNCT
ejpam-5731	83	4	zα−1f(z	zα−1f(z	NUM
ejpam-5731	83	5	)	)	PUNCT
ejpam-5731	83	6	)	)	PUNCT
ejpam-5731	83	7	(	(	PUNCT
ejpam-5731	83	8	α	α	X
ejpam-5731	83	9	)	)	PUNCT
ejpam-5731	83	10	γ(α+	γ(α+	DET
ejpam-5731	83	11	1	1	NUM
ejpam-5731	83	12	)	)	PUNCT
ejpam-5731	83	13	.	.	PUNCT
ejpam-5731	84	1	w.	w.	PROPN
ejpam-5731	84	2	al	al	PROPN
ejpam-5731	84	3	-	-	PUNCT
ejpam-5731	84	4	rawashdeh	rawashdeh	PROPN
ejpam-5731	84	5	/	/	SYM
ejpam-5731	84	6	eur	eur	PROPN
ejpam-5731	84	7	.	.	PUNCT
ejpam-5731	85	1	j.	j.	PROPN
ejpam-5731	85	2	pure	pure	PROPN
ejpam-5731	85	3	appl	appl	PROPN
ejpam-5731	85	4	.	.	PROPN
ejpam-5731	85	5	math	math	PROPN
ejpam-5731	85	6	,	,	PUNCT
ejpam-5731	85	7	18	18	NUM
ejpam-5731	85	8	(	(	PUNCT
ejpam-5731	85	9	1	1	NUM
ejpam-5731	85	10	)	)	PUNCT
ejpam-5731	85	11	(	(	PUNCT
ejpam-5731	85	12	2025	2025	NUM
ejpam-5731	85	13	)	)	PUNCT
ejpam-5731	85	14	,	,	PUNCT
ejpam-5731	85	15	5731	5731	NUM
ejpam-5731	85	16	5	5	NUM
ejpam-5731	85	17	of	of	ADP
ejpam-5731	85	18	20	20	NUM
ejpam-5731	85	19	moreover	moreover	ADV
ejpam-5731	85	20	,	,	PUNCT
ejpam-5731	85	21	the	the	DET
ejpam-5731	85	22	taylor	taylor	PROPN
ejpam-5731	85	23	-	-	PUNCT
ejpam-5731	85	24	maclaurin	maclaurin	PROPN
ejpam-5731	85	25	series	series	NOUN
ejpam-5731	85	26	(	(	PUNCT
ejpam-5731	85	27	see	see	VERB
ejpam-5731	85	28	,	,	PUNCT
ejpam-5731	85	29	for	for	ADP
ejpam-5731	85	30	example	example	NOUN
ejpam-5731	86	1	[	[	X
ejpam-5731	86	2	27	27	NUM
ejpam-5731	86	3	]	]	PUNCT
ejpam-5731	86	4	)	)	PUNCT
ejpam-5731	86	5	of	of	ADP
ejpam-5731	86	6	rαf	rαf	NOUN
ejpam-5731	86	7	is	be	AUX
ejpam-5731	86	8	given	give	VERB
ejpam-5731	86	9	by	by	ADP
ejpam-5731	86	10	rαf(z	rαf(z	PROPN
ejpam-5731	86	11	)	)	PUNCT
ejpam-5731	86	12	=	=	SYM
ejpam-5731	87	1	z	z	NOUN
ejpam-5731	88	1	+	+	NOUN
ejpam-5731	88	2	∞∑	∞∑	NUM
ejpam-5731	88	3	n=2	n=2	PRON
ejpam-5731	88	4	γ(α+	γ(α+	PRON
ejpam-5731	88	5	n	n	CCONJ
ejpam-5731	88	6	)	)	PUNCT
ejpam-5731	88	7	γ(n)γ(α+	γ(n)γ(α+	X
ejpam-5731	88	8	1	1	X
ejpam-5731	88	9	)	)	PUNCT
ejpam-5731	88	10	anz	anz	PROPN
ejpam-5731	88	11	n.	n.	NOUN
ejpam-5731	88	12	in	in	ADP
ejpam-5731	88	13	this	this	DET
ejpam-5731	88	14	framework	framework	NOUN
ejpam-5731	88	15	,	,	PUNCT
ejpam-5731	88	16	we	we	PRON
ejpam-5731	88	17	revisit	revisit	VERB
ejpam-5731	88	18	the	the	DET
ejpam-5731	88	19	concept	concept	NOUN
ejpam-5731	88	20	of	of	ADP
ejpam-5731	88	21	q	q	ADJ
ejpam-5731	88	22	-	-	PUNCT
ejpam-5731	88	23	difference	difference	NOUN
ejpam-5731	88	24	operators	operator	NOUN
ejpam-5731	88	25	,	,	PUNCT
ejpam-5731	88	26	which	which	PRON
ejpam-5731	88	27	play	play	VERB
ejpam-5731	88	28	a	a	DET
ejpam-5731	88	29	crucial	crucial	ADJ
ejpam-5731	88	30	role	role	NOUN
ejpam-5731	88	31	in	in	ADP
ejpam-5731	88	32	the	the	DET
ejpam-5731	88	33	fields	field	NOUN
ejpam-5731	88	34	of	of	ADP
ejpam-5731	88	35	hypergeometric	hypergeometric	ADJ
ejpam-5731	88	36	series	series	NOUN
ejpam-5731	88	37	,	,	PUNCT
ejpam-5731	88	38	quantum	quantum	NOUN
ejpam-5731	88	39	mechanics	mechanic	NOUN
ejpam-5731	88	40	,	,	PUNCT
ejpam-5731	88	41	and	and	CCONJ
ejpam-5731	88	42	the	the	DET
ejpam-5731	88	43	theory	theory	NOUN
ejpam-5731	88	44	of	of	ADP
ejpam-5731	88	45	geometric	geometric	ADJ
ejpam-5731	88	46	functions	function	NOUN
ejpam-5731	88	47	.	.	PUNCT
ejpam-5731	89	1	the	the	DET
ejpam-5731	89	2	introduction	introduction	NOUN
ejpam-5731	89	3	of	of	ADP
ejpam-5731	89	4	q	q	NOUN
ejpam-5731	89	5	-	-	PUNCT
ejpam-5731	89	6	calculus	calculus	NOUN
ejpam-5731	89	7	can	can	AUX
ejpam-5731	89	8	be	be	AUX
ejpam-5731	89	9	traced	trace	VERB
ejpam-5731	89	10	back	back	ADV
ejpam-5731	89	11	to	to	ADP
ejpam-5731	89	12	jackson	jackson	PROPN
ejpam-5731	90	1	[	[	X
ejpam-5731	90	2	23	23	NUM
ejpam-5731	90	3	]	]	PUNCT
ejpam-5731	90	4	.	.	PUNCT
ejpam-5731	91	1	following	follow	VERB
ejpam-5731	91	2	this	this	PRON
ejpam-5731	91	3	,	,	PUNCT
ejpam-5731	91	4	kanas	kanas	PROPN
ejpam-5731	91	5	and	and	CCONJ
ejpam-5731	91	6	răducanu	răducanu	PROPN
ejpam-5731	91	7	[	[	X
ejpam-5731	91	8	25	25	NUM
ejpam-5731	91	9	]	]	PUNCT
ejpam-5731	91	10	utilized	utilize	VERB
ejpam-5731	91	11	fractional	fractional	ADJ
ejpam-5731	91	12	q	q	ADJ
ejpam-5731	91	13	-	-	PUNCT
ejpam-5731	91	14	calculus	calculus	ADJ
ejpam-5731	91	15	operators	operator	NOUN
ejpam-5731	91	16	to	to	PART
ejpam-5731	91	17	explore	explore	VERB
ejpam-5731	91	18	particular	particular	ADJ
ejpam-5731	91	19	categories	category	NOUN
ejpam-5731	91	20	of	of	ADP
ejpam-5731	91	21	analytic	analytic	ADJ
ejpam-5731	91	22	functions	function	NOUN
ejpam-5731	91	23	associated	associate	VERB
ejpam-5731	91	24	with	with	ADP
ejpam-5731	91	25	conic	conic	ADJ
ejpam-5731	91	26	domains	domain	NOUN
ejpam-5731	91	27	.	.	PUNCT
ejpam-5731	92	1	the	the	DET
ejpam-5731	92	2	q	q	ADJ
ejpam-5731	92	3	-	-	PUNCT
ejpam-5731	92	4	integer	integer	NOUN
ejpam-5731	92	5	number	number	NOUN
ejpam-5731	92	6	,	,	PUNCT
ejpam-5731	92	7	for	for	ADP
ejpam-5731	92	8	0	0	NUM
ejpam-5731	92	9	<	<	X
ejpam-5731	92	10	q	q	X
ejpam-5731	92	11	<	<	X
ejpam-5731	92	12	1	1	NUM
ejpam-5731	92	13	and	and	CCONJ
ejpam-5731	92	14	non	non	ADJ
ejpam-5731	92	15	-	-	ADJ
ejpam-5731	92	16	negative	negative	ADJ
ejpam-5731	92	17	integer	integer	NOUN
ejpam-5731	92	18	n	n	CCONJ
ejpam-5731	92	19	,	,	PUNCT
ejpam-5731	92	20	is	be	AUX
ejpam-5731	92	21	defined	define	VERB
ejpam-5731	92	22	as	as	SCONJ
ejpam-5731	92	23	follows	follow	VERB
ejpam-5731	92	24	[	[	PRON
ejpam-5731	92	25	n]q	n]q	X
ejpam-5731	93	1	=	=	SYM
ejpam-5731	93	2	1−	1−	NUM
ejpam-5731	93	3	qn	qn	NOUN
ejpam-5731	93	4	1−	1−	NUM
ejpam-5731	93	5	q	q	NOUN
ejpam-5731	93	6	=	=	PUNCT
ejpam-5731	93	7	n−1∑	n−1∑	PROPN
ejpam-5731	93	8	k=0	k=0	PROPN
ejpam-5731	93	9	qk	qk	NOUN
ejpam-5731	93	10	,	,	PUNCT
ejpam-5731	93	11	with	with	ADP
ejpam-5731	93	12	[	[	X
ejpam-5731	93	13	0]q	0]q	X
ejpam-5731	93	14	=	=	SYM
ejpam-5731	93	15	0	0	X
ejpam-5731	93	16	.	.	PUNCT
ejpam-5731	94	1	in	in	ADP
ejpam-5731	94	2	general	general	ADJ
ejpam-5731	94	3	,	,	PUNCT
ejpam-5731	94	4	for	for	ADP
ejpam-5731	94	5	any	any	DET
ejpam-5731	94	6	non	non	ADJ
ejpam-5731	94	7	-	-	ADJ
ejpam-5731	94	8	negative	negative	ADJ
ejpam-5731	94	9	real	real	ADJ
ejpam-5731	94	10	number	number	NOUN
ejpam-5731	94	11	x	x	NOUN
ejpam-5731	94	12	,	,	PUNCT
ejpam-5731	94	13	we	we	PRON
ejpam-5731	94	14	have	have	VERB
ejpam-5731	94	15	[	[	X
ejpam-5731	94	16	x]q	x]q	ADJ
ejpam-5731	94	17	=	=	SYM
ejpam-5731	94	18	1−	1−	NUM
ejpam-5731	94	19	qx	qx	INTJ
ejpam-5731	94	20	1−	1−	NUM
ejpam-5731	94	21	q	q	NOUN
ejpam-5731	94	22	.	.	PUNCT
ejpam-5731	95	1	moreover	moreover	ADV
ejpam-5731	95	2	,	,	PUNCT
ejpam-5731	95	3	the	the	DET
ejpam-5731	95	4	q	q	ADJ
ejpam-5731	95	5	-	-	PUNCT
ejpam-5731	95	6	shifted	shift	VERB
ejpam-5731	95	7	factorial	factorial	NOUN
ejpam-5731	95	8	is	be	AUX
ejpam-5731	95	9	defined	define	VERB
ejpam-5731	95	10	by	by	ADP
ejpam-5731	95	11	[	[	X
ejpam-5731	95	12	n]q	n]q	X
ejpam-5731	95	13	!	!	PUNCT
ejpam-5731	95	14	=	=	PUNCT
ejpam-5731	96	1	[	[	X
ejpam-5731	96	2	n]q[n−	n]q[n−	ADP
ejpam-5731	96	3	1]q[n−	1]q[n−	NUM
ejpam-5731	96	4	2]q	2]q	NUM
ejpam-5731	96	5	·	·	PUNCT
ejpam-5731	96	6	·	·	PUNCT
ejpam-5731	96	7	·	·	PUNCT
ejpam-5731	97	1	[	[	X
ejpam-5731	97	2	2]q[1]q	2]q[1]q	NUM
ejpam-5731	97	3	,	,	PUNCT
ejpam-5731	97	4	with	with	ADP
ejpam-5731	97	5	[	[	X
ejpam-5731	97	6	0]q	0]q	NOUN
ejpam-5731	97	7	!	!	PUNCT
ejpam-5731	98	1	=	=	PUNCT
ejpam-5731	99	1	1	1	X
ejpam-5731	99	2	.	.	PUNCT
ejpam-5731	100	1	it	it	PRON
ejpam-5731	100	2	is	be	AUX
ejpam-5731	100	3	obvious	obvious	ADJ
ejpam-5731	100	4	that	that	SCONJ
ejpam-5731	100	5	lim	lim	PROPN
ejpam-5731	100	6	q→1−	q→1−	PROPN
ejpam-5731	101	1	[	[	X
ejpam-5731	101	2	n]q	n]q	X
ejpam-5731	101	3	=	=	SYM
ejpam-5731	101	4	n	n	NOUN
ejpam-5731	101	5	and	and	CCONJ
ejpam-5731	101	6	lim	lim	PROPN
ejpam-5731	101	7	q→1−	q→1−	PROPN
ejpam-5731	102	1	[	[	X
ejpam-5731	103	1	n]q	n]q	X
ejpam-5731	103	2	!	!	PUNCT
ejpam-5731	104	1	=	=	PRON
ejpam-5731	105	1	n	n	CCONJ
ejpam-5731	105	2	!	!	PUNCT
ejpam-5731	105	3	.	.	PUNCT
ejpam-5731	106	1	let	let	VERB
ejpam-5731	106	2	the	the	DET
ejpam-5731	106	3	function	function	NOUN
ejpam-5731	106	4	f	f	PROPN
ejpam-5731	106	5	belong	belong	VERB
ejpam-5731	106	6	to	to	ADP
ejpam-5731	106	7	the	the	DET
ejpam-5731	106	8	set	set	ADJ
ejpam-5731	106	9	h	h	NOUN
ejpam-5731	106	10	and	and	CCONJ
ejpam-5731	106	11	represented	represent	VERB
ejpam-5731	106	12	by	by	ADP
ejpam-5731	106	13	equation	equation	NOUN
ejpam-5731	106	14	(	(	PUNCT
ejpam-5731	106	15	1	1	NUM
ejpam-5731	106	16	)	)	PUNCT
ejpam-5731	106	17	.	.	PUNCT
ejpam-5731	107	1	the	the	DET
ejpam-5731	107	2	q	q	PROPN
ejpam-5731	107	3	-	-	PUNCT
ejpam-5731	107	4	jackson	jackson	PROPN
ejpam-5731	107	5	derivative	derivative	ADJ
ejpam-5731	107	6	operator	operator	NOUN
ejpam-5731	107	7	(	(	PUNCT
ejpam-5731	107	8	or	or	CCONJ
ejpam-5731	107	9	q	q	ADJ
ejpam-5731	107	10	-	-	PUNCT
ejpam-5731	107	11	difference	difference	NOUN
ejpam-5731	107	12	operator	operator	NOUN
ejpam-5731	107	13	)	)	PUNCT
ejpam-5731	107	14	is	be	AUX
ejpam-5731	107	15	defined	define	VERB
ejpam-5731	107	16	by	by	ADP
ejpam-5731	107	17	dqf(z	dqf(z	PROPN
ejpam-5731	107	18	)	)	PUNCT
ejpam-5731	107	19	=	=	SYM
ejpam-5731	108	1			PRON
ejpam-5731	108	2	f(qz)−f(z	f(qz)−f(z	X
ejpam-5731	108	3	)	)	PUNCT
ejpam-5731	108	4	(	(	PUNCT
ejpam-5731	108	5	q−1)z	q−1)z	INTJ
ejpam-5731	108	6	,	,	PUNCT
ejpam-5731	108	7	if	if	SCONJ
ejpam-5731	108	8	z	z	PROPN
ejpam-5731	108	9	̸=	̸=	PROPN
ejpam-5731	108	10	0	0	NUM
ejpam-5731	108	11	f	f	PROPN
ejpam-5731	108	12	′(0	′(0	NOUN
ejpam-5731	108	13	)	)	PUNCT
ejpam-5731	108	14	,	,	PUNCT
ejpam-5731	108	15	if	if	SCONJ
ejpam-5731	108	16	z	z	NOUN
ejpam-5731	108	17	=	=	SYM
ejpam-5731	108	18	0	0	NUM
ejpam-5731	108	19	f	f	PROPN
ejpam-5731	108	20	′(z	′(z	NOUN
ejpam-5731	108	21	)	)	PUNCT
ejpam-5731	108	22	,	,	PUNCT
ejpam-5731	108	23	as	as	ADP
ejpam-5731	108	24	q	q	PROPN
ejpam-5731	108	25	→	→	SYM
ejpam-5731	108	26	1−.	1−.	PROPN
ejpam-5731	108	27	therefore	therefore	ADV
ejpam-5731	108	28	,	,	PUNCT
ejpam-5731	108	29	for	for	ADP
ejpam-5731	108	30	a	a	DET
ejpam-5731	108	31	function	function	NOUN
ejpam-5731	108	32	f	f	PROPN
ejpam-5731	108	33	∈	∈	PROPN
ejpam-5731	108	34	h	h	NOUN
ejpam-5731	108	35	that	that	PRON
ejpam-5731	108	36	is	be	AUX
ejpam-5731	108	37	given	give	VERB
ejpam-5731	108	38	by	by	ADP
ejpam-5731	108	39	equation	equation	NOUN
ejpam-5731	108	40	(	(	PUNCT
ejpam-5731	108	41	1	1	NUM
ejpam-5731	108	42	)	)	PUNCT
ejpam-5731	108	43	,	,	PUNCT
ejpam-5731	108	44	it	it	PRON
ejpam-5731	108	45	is	be	AUX
ejpam-5731	108	46	easy	easy	ADJ
ejpam-5731	108	47	to	to	PART
ejpam-5731	108	48	see	see	VERB
ejpam-5731	108	49	that	that	DET
ejpam-5731	108	50	dqf(z	dqf(z	NOUN
ejpam-5731	108	51	)	)	PUNCT
ejpam-5731	108	52	=	=	SYM
ejpam-5731	108	53	1	1	NUM
ejpam-5731	108	54	+	+	NUM
ejpam-5731	108	55	∞∑	∞∑	NUM
ejpam-5731	108	56	n=2	n=2	PRON
ejpam-5731	109	1	[	[	X
ejpam-5731	109	2	n]qanz	n]qanz	PROPN
ejpam-5731	109	3	n−1	n−1	PROPN
ejpam-5731	109	4	.	.	PROPN
ejpam-5731	110	1	for	for	ADP
ejpam-5731	110	2	example	example	NOUN
ejpam-5731	110	3	,	,	PUNCT
ejpam-5731	110	4	if	if	SCONJ
ejpam-5731	110	5	n	n	PRON
ejpam-5731	110	6	∈	∈	PROPN
ejpam-5731	110	7	n	n	NOUN
ejpam-5731	110	8	=	=	SYM
ejpam-5731	110	9	{	{	PUNCT
ejpam-5731	110	10	1	1	NUM
ejpam-5731	110	11	,	,	PUNCT
ejpam-5731	110	12	2	2	NUM
ejpam-5731	110	13	,	,	PUNCT
ejpam-5731	110	14	·	·	PUNCT
ejpam-5731	110	15	·	·	PUNCT
ejpam-5731	110	16	·	·	PUNCT
ejpam-5731	110	17	}	}	PUNCT
ejpam-5731	110	18	and	and	CCONJ
ejpam-5731	110	19	z	z	NOUN
ejpam-5731	110	20	∈	∈	PROPN
ejpam-5731	110	21	d	d	NOUN
ejpam-5731	110	22	,	,	PUNCT
ejpam-5731	110	23	then	then	ADV
ejpam-5731	110	24	dq	dq	PROPN
ejpam-5731	110	25	(	(	PUNCT
ejpam-5731	110	26	z	z	NOUN
ejpam-5731	110	27	n	n	CCONJ
ejpam-5731	110	28	)	)	PUNCT
ejpam-5731	110	29	=	=	PUNCT
ejpam-5731	110	30	(	(	PUNCT
ejpam-5731	110	31	qn	qn	INTJ
ejpam-5731	110	32	−	−	PROPN
ejpam-5731	110	33	1)zn−1	1)zn−1	PROPN
ejpam-5731	110	34	(	(	PUNCT
ejpam-5731	110	35	q	q	NOUN
ejpam-5731	110	36	−	−	PROPN
ejpam-5731	110	37	1	1	NUM
ejpam-5731	110	38	)	)	PUNCT
ejpam-5731	110	39	=	=	NOUN
ejpam-5731	111	1	[	[	PUNCT
ejpam-5731	111	2	n]qz	n]qz	PROPN
ejpam-5731	111	3	n−1	n−1	PROPN
ejpam-5731	111	4	.	.	PUNCT
ejpam-5731	112	1	also	also	ADV
ejpam-5731	112	2	,	,	PUNCT
ejpam-5731	112	3	lim	lim	PROPN
ejpam-5731	112	4	q→1−	q→1−	PROPN
ejpam-5731	112	5	dq	dq	INTJ
ejpam-5731	112	6	(	(	PUNCT
ejpam-5731	112	7	z	z	NOUN
ejpam-5731	112	8	n	n	CCONJ
ejpam-5731	112	9	)	)	PUNCT
ejpam-5731	113	1	=	=	SYM
ejpam-5731	113	2	lim	lim	PROPN
ejpam-5731	113	3	q→1−	q→1−	PROPN
ejpam-5731	114	1	[	[	X
ejpam-5731	114	2	n]qz	n]qz	PROPN
ejpam-5731	114	3	n−1	n−1	PROPN
ejpam-5731	114	4	=	=	SYM
ejpam-5731	114	5	nzn−1	nzn−1	PROPN
ejpam-5731	114	6	,	,	PUNCT
ejpam-5731	114	7	which	which	PRON
ejpam-5731	114	8	is	be	AUX
ejpam-5731	114	9	the	the	DET
ejpam-5731	114	10	ordinary	ordinary	ADJ
ejpam-5731	114	11	derivative	derivative	NOUN
ejpam-5731	114	12	of	of	ADP
ejpam-5731	114	13	the	the	DET
ejpam-5731	114	14	function	function	NOUN
ejpam-5731	114	15	zn	zn	PROPN
ejpam-5731	114	16	.	.	PUNCT
ejpam-5731	115	1	w.	w.	PROPN
ejpam-5731	115	2	al	al	PROPN
ejpam-5731	115	3	-	-	PUNCT
ejpam-5731	115	4	rawashdeh	rawashdeh	PROPN
ejpam-5731	115	5	/	/	SYM
ejpam-5731	115	6	eur	eur	PROPN
ejpam-5731	115	7	.	.	PUNCT
ejpam-5731	116	1	j.	j.	PROPN
ejpam-5731	116	2	pure	pure	PROPN
ejpam-5731	116	3	appl	appl	PROPN
ejpam-5731	116	4	.	.	PROPN
ejpam-5731	116	5	math	math	PROPN
ejpam-5731	116	6	,	,	PUNCT
ejpam-5731	116	7	18	18	NUM
ejpam-5731	116	8	(	(	PUNCT
ejpam-5731	116	9	1	1	NUM
ejpam-5731	116	10	)	)	PUNCT
ejpam-5731	116	11	(	(	PUNCT
ejpam-5731	116	12	2025	2025	NUM
ejpam-5731	116	13	)	)	PUNCT
ejpam-5731	116	14	,	,	PUNCT
ejpam-5731	116	15	5731	5731	NUM
ejpam-5731	116	16	6	6	NUM
ejpam-5731	116	17	of	of	ADP
ejpam-5731	116	18	20	20	NUM
ejpam-5731	116	19	moreover	moreover	ADV
ejpam-5731	116	20	,	,	PUNCT
ejpam-5731	116	21	for	for	ADP
ejpam-5731	116	22	m	m	PROPN
ejpam-5731	116	23	∈	∈	PROPN
ejpam-5731	116	24	n	n	CCONJ
ejpam-5731	116	25	,	,	PUNCT
ejpam-5731	116	26	we	we	PRON
ejpam-5731	116	27	have	have	VERB
ejpam-5731	116	28	the	the	DET
ejpam-5731	116	29	following	follow	VERB
ejpam-5731	116	30	d0	d0	NOUN
ejpam-5731	116	31	qf(z	qf(z	NUM
ejpam-5731	116	32	)	)	PUNCT
ejpam-5731	116	33	=	=	SYM
ejpam-5731	116	34	f(z	f(z	PROPN
ejpam-5731	116	35	)	)	PUNCT
ejpam-5731	116	36	,	,	PUNCT
ejpam-5731	116	37	and	and	CCONJ
ejpam-5731	116	38	dm	dm	PRON
ejpam-5731	116	39	q	q	NOUN
ejpam-5731	116	40	f(z	f(z	PROPN
ejpam-5731	116	41	)	)	PUNCT
ejpam-5731	117	1	=	=	SYM
ejpam-5731	117	2	dq	dq	PROPN
ejpam-5731	117	3	(	(	PUNCT
ejpam-5731	117	4	dm−1	dm−1	PROPN
ejpam-5731	117	5	q	q	PROPN
ejpam-5731	117	6	f(z	f(z	PROPN
ejpam-5731	117	7	)	)	PUNCT
ejpam-5731	117	8	)	)	PUNCT
ejpam-5731	117	9	.	.	PUNCT
ejpam-5731	118	1	it	it	PRON
ejpam-5731	118	2	is	be	AUX
ejpam-5731	118	3	known	know	VERB
ejpam-5731	118	4	that	that	SCONJ
ejpam-5731	118	5	,	,	PUNCT
ejpam-5731	118	6	for	for	ADP
ejpam-5731	118	7	f	f	PROPN
ejpam-5731	118	8	,	,	PUNCT
ejpam-5731	118	9	g	g	PROPN
ejpam-5731	118	10	∈	∈	PROPN
ejpam-5731	118	11	h	h	NOUN
ejpam-5731	118	12	,	,	PUNCT
ejpam-5731	118	13	we	we	PRON
ejpam-5731	118	14	have	have	VERB
ejpam-5731	118	15	the	the	DET
ejpam-5731	118	16	following	follow	VERB
ejpam-5731	118	17	rules	rule	NOUN
ejpam-5731	118	18	for	for	ADP
ejpam-5731	118	19	the	the	DET
ejpam-5731	118	20	q	q	ADJ
ejpam-5731	118	21	-	-	PUNCT
ejpam-5731	118	22	difference	difference	NOUN
ejpam-5731	118	23	operator	operator	NOUN
ejpam-5731	118	24	(	(	PUNCT
ejpam-5731	118	25	i	i	NOUN
ejpam-5731	118	26	)	)	PUNCT
ejpam-5731	118	27	dq(mf(z)±	dq(mf(z)±	PROPN
ejpam-5731	118	28	ng(z	ng(z	NUM
ejpam-5731	118	29	)	)	PUNCT
ejpam-5731	118	30	)	)	PUNCT
ejpam-5731	119	1	=	=	PUNCT
ejpam-5731	119	2	mdqf(z)±	mdqf(z)±	NOUN
ejpam-5731	119	3	ndqg(z	ndqg(z	NOUN
ejpam-5731	119	4	)	)	PUNCT
ejpam-5731	119	5	,	,	PUNCT
ejpam-5731	119	6	for	for	ADP
ejpam-5731	119	7	m	m	PROPN
ejpam-5731	119	8	,	,	PUNCT
ejpam-5731	119	9	n	n	PROPN
ejpam-5731	119	10	∈	∈	PROPN
ejpam-5731	119	11	c.	c.	PROPN
ejpam-5731	119	12	(	(	PUNCT
ejpam-5731	119	13	ii	ii	PROPN
ejpam-5731	119	14	)	)	PUNCT
ejpam-5731	119	15	dq(fg)(z	dq(fg)(z	NOUN
ejpam-5731	119	16	)	)	PUNCT
ejpam-5731	119	17	=	=	SYM
ejpam-5731	119	18	f(z)dqg(z	f(z)dqg(z	NOUN
ejpam-5731	119	19	)	)	PUNCT
ejpam-5731	120	1	+	+	CCONJ
ejpam-5731	120	2	g(z)dqf(z	g(z)dqf(z	NOUN
ejpam-5731	120	3	)	)	PUNCT
ejpam-5731	120	4	.	.	PUNCT
ejpam-5731	121	1	(	(	PUNCT
ejpam-5731	121	2	iii	iii	X
ejpam-5731	121	3	)	)	PUNCT
ejpam-5731	121	4	dq	dq	PROPN
ejpam-5731	121	5	(	(	PUNCT
ejpam-5731	121	6	f(z	f(z	PROPN
ejpam-5731	121	7	)	)	PUNCT
ejpam-5731	121	8	g(z	g(z	PROPN
ejpam-5731	121	9	)	)	PUNCT
ejpam-5731	121	10	)	)	PUNCT
ejpam-5731	122	1	=	=	SYM
ejpam-5731	122	2	g(z)dqf(z)−f(z)dqg(z	g(z)dqf(z)−f(z)dqg(z	PROPN
ejpam-5731	122	3	)	)	PUNCT
ejpam-5731	122	4	g(z)g(qz	g(z)g(qz	PROPN
ejpam-5731	122	5	)	)	PUNCT
ejpam-5731	122	6	,	,	PUNCT
ejpam-5731	122	7	where	where	SCONJ
ejpam-5731	122	8	g(z)g(qz	g(z)g(qz	NOUN
ejpam-5731	122	9	)	)	PUNCT
ejpam-5731	122	10	̸=	̸=	PROPN
ejpam-5731	122	11	0	0	NUM
ejpam-5731	122	12	.	.	PUNCT
ejpam-5731	123	1	for	for	ADP
ejpam-5731	123	2	any	any	DET
ejpam-5731	123	3	real	real	ADJ
ejpam-5731	123	4	number	number	NOUN
ejpam-5731	123	5	x	x	PUNCT
ejpam-5731	123	6	and	and	CCONJ
ejpam-5731	123	7	natural	natural	ADJ
ejpam-5731	123	8	number	number	NOUN
ejpam-5731	123	9	n	n	CCONJ
ejpam-5731	123	10	,	,	PUNCT
ejpam-5731	123	11	the	the	DET
ejpam-5731	123	12	q	q	ADJ
ejpam-5731	123	13	-	-	PUNCT
ejpam-5731	123	14	generalized	generalize	VERB
ejpam-5731	123	15	pochhammer	pochhammer	NOUN
ejpam-5731	123	16	symbol	symbol	NOUN
ejpam-5731	123	17	is	be	AUX
ejpam-5731	123	18	defined	define	VERB
ejpam-5731	123	19	as	as	SCONJ
ejpam-5731	123	20	follows	follow	VERB
ejpam-5731	123	21	[	[	X
ejpam-5731	123	22	x;n]q	x;n]q	X
ejpam-5731	123	23	=	=	PUNCT
ejpam-5731	124	1	[	[	X
ejpam-5731	124	2	x]q[x+	x]q[x+	PROPN
ejpam-5731	124	3	1]q[x+	1]q[x+	PROPN
ejpam-5731	124	4	2]q	2]q	NUM
ejpam-5731	124	5	·	·	PUNCT
ejpam-5731	124	6	·	·	PUNCT
ejpam-5731	124	7	·	·	PUNCT
ejpam-5731	125	1	[	[	X
ejpam-5731	125	2	x+	x+	ADJ
ejpam-5731	125	3	n−	n−	PROPN
ejpam-5731	125	4	1]q	1]q	NUM
ejpam-5731	125	5	.	.	PUNCT
ejpam-5731	126	1	moreover	moreover	ADV
ejpam-5731	126	2	,	,	PUNCT
ejpam-5731	126	3	for	for	ADP
ejpam-5731	126	4	x	x	SYM
ejpam-5731	126	5	>	>	X
ejpam-5731	126	6	0	0	PROPN
ejpam-5731	126	7	,	,	PUNCT
ejpam-5731	126	8	the	the	DET
ejpam-5731	126	9	q	q	ADJ
ejpam-5731	126	10	-	-	PUNCT
ejpam-5731	126	11	gamman	gamman	NOUN
ejpam-5731	126	12	function	function	NOUN
ejpam-5731	126	13	is	be	AUX
ejpam-5731	126	14	defined	define	VERB
ejpam-5731	126	15	as	as	SCONJ
ejpam-5731	126	16	follows	follow	VERB
ejpam-5731	126	17	γq(x+	γq(x+	PROPN
ejpam-5731	126	18	1	1	X
ejpam-5731	126	19	)	)	PUNCT
ejpam-5731	126	20	=	=	NOUN
ejpam-5731	127	1	[	[	X
ejpam-5731	127	2	x]qγq(x	x]qγq(x	NOUN
ejpam-5731	127	3	)	)	PUNCT
ejpam-5731	127	4	,	,	PUNCT
ejpam-5731	127	5	with	with	ADP
ejpam-5731	127	6	γq(1	γq(1	NOUN
ejpam-5731	127	7	)	)	PUNCT
ejpam-5731	127	8	=	=	SYM
ejpam-5731	128	1	1	1	X
ejpam-5731	128	2	.	.	PUNCT
ejpam-5731	128	3	now	now	ADV
ejpam-5731	128	4	,	,	PUNCT
ejpam-5731	128	5	we	we	PRON
ejpam-5731	128	6	present	present	VERB
ejpam-5731	128	7	a	a	DET
ejpam-5731	128	8	q	q	NOUN
ejpam-5731	128	9	-	-	PUNCT
ejpam-5731	128	10	analogue	analogue	NOUN
ejpam-5731	128	11	of	of	ADP
ejpam-5731	128	12	the	the	DET
ejpam-5731	128	13	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	128	14	differential	differential	ADJ
ejpam-5731	128	15	operator	operator	NOUN
ejpam-5731	128	16	by	by	ADP
ejpam-5731	128	17	employing	employ	VERB
ejpam-5731	128	18	the	the	DET
ejpam-5731	128	19	convolution	convolution	NOUN
ejpam-5731	128	20	alongside	alongside	ADP
ejpam-5731	128	21	the	the	DET
ejpam-5731	128	22	q	q	ADJ
ejpam-5731	128	23	-	-	PUNCT
ejpam-5731	128	24	difference	difference	NOUN
ejpam-5731	128	25	operator	operator	NOUN
ejpam-5731	128	26	rαq	rαq	NOUN
ejpam-5731	128	27	:	:	PUNCT
ejpam-5731	128	28	h	h	PROPN
ejpam-5731	128	29	→	→	SYM
ejpam-5731	128	30	h.	h.	PROPN
ejpam-5731	128	31	thus	thus	ADV
ejpam-5731	128	32	,	,	PUNCT
ejpam-5731	128	33	for	for	ADP
ejpam-5731	128	34	any	any	DET
ejpam-5731	128	35	f	f	PROPN
ejpam-5731	128	36	∈	∈	PROPN
ejpam-5731	128	37	h	h	NOUN
ejpam-5731	128	38	and	and	CCONJ
ejpam-5731	128	39	α	α	NOUN
ejpam-5731	128	40	>	>	X
ejpam-5731	128	41	−1	−1	NOUN
ejpam-5731	128	42	,	,	PUNCT
ejpam-5731	128	43	this	this	DET
ejpam-5731	128	44	linear	linear	ADJ
ejpam-5731	128	45	operator	operator	NOUN
ejpam-5731	128	46	is	be	AUX
ejpam-5731	128	47	defined	define	VERB
ejpam-5731	128	48	as	as	ADP
ejpam-5731	128	49	rαq	rαq	PROPN
ejpam-5731	128	50	f(z	f(z	PROPN
ejpam-5731	128	51	)	)	PUNCT
ejpam-5731	129	1	=	=	SYM
ejpam-5731	129	2	fq	fq	PROPN
ejpam-5731	129	3	,	,	PUNCT
ejpam-5731	129	4	α+1(z	α+1(z	NUM
ejpam-5731	129	5	)	)	PUNCT
ejpam-5731	129	6	∗	∗	NOUN
ejpam-5731	129	7	f(z	f(z	PROPN
ejpam-5731	129	8	)	)	PUNCT
ejpam-5731	129	9	,	,	PUNCT
ejpam-5731	129	10	where	where	SCONJ
ejpam-5731	129	11	fq	fq	PROPN
ejpam-5731	129	12	,	,	PUNCT
ejpam-5731	129	13	α+1(z	α+1(z	NUM
ejpam-5731	129	14	)	)	PUNCT
ejpam-5731	129	15	=	=	SYM
ejpam-5731	130	1	z	z	NOUN
ejpam-5731	131	1	+	+	NOUN
ejpam-5731	131	2	∞∑	∞∑	NUM
ejpam-5731	131	3	n=2	n=2	ADV
ejpam-5731	131	4	γq(n+	γq(n+	NOUN
ejpam-5731	131	5	α	α	NOUN
ejpam-5731	131	6	)	)	PUNCT
ejpam-5731	132	1	[	[	X
ejpam-5731	132	2	n−	n−	NOUN
ejpam-5731	132	3	1]q!γq(α+	1]q!γq(α+	NOUN
ejpam-5731	132	4	1	1	NUM
ejpam-5731	132	5	)	)	PUNCT
ejpam-5731	132	6	zn	zn	NOUN
ejpam-5731	132	7	.	.	PUNCT
ejpam-5731	133	1	more	more	ADV
ejpam-5731	133	2	precisely	precisely	ADV
ejpam-5731	133	3	,	,	PUNCT
ejpam-5731	133	4	the	the	DET
ejpam-5731	133	5	q	q	ADJ
ejpam-5731	133	6	-	-	PUNCT
ejpam-5731	133	7	rucheweyh	rucheweyh	NOUN
ejpam-5731	133	8	differential	differential	NOUN
ejpam-5731	133	9	operator	operator	NOUN
ejpam-5731	133	10	can	can	AUX
ejpam-5731	133	11	be	be	AUX
ejpam-5731	133	12	written	write	VERB
ejpam-5731	133	13	as	as	SCONJ
ejpam-5731	133	14	follows	follow	VERB
ejpam-5731	133	15	rαq	rαq	PROPN
ejpam-5731	133	16	f(z	f(z	PROPN
ejpam-5731	133	17	)	)	PUNCT
ejpam-5731	134	1	=	=	PUNCT
ejpam-5731	134	2	z	z	NOUN
ejpam-5731	135	1	+	+	NOUN
ejpam-5731	135	2	∞∑	∞∑	NUM
ejpam-5731	135	3	n=2	n=2	PRON
ejpam-5731	135	4	ψn(q	ψn(q	NOUN
ejpam-5731	135	5	,	,	PUNCT
ejpam-5731	135	6	α)anz	α)anz	PROPN
ejpam-5731	135	7	n	n	CCONJ
ejpam-5731	135	8	,	,	PUNCT
ejpam-5731	135	9	where	where	SCONJ
ejpam-5731	135	10	ψn	ψn	ADV
ejpam-5731	135	11	=	=	SYM
ejpam-5731	135	12	ψn(q	ψn(q	X
ejpam-5731	135	13	,	,	PUNCT
ejpam-5731	135	14	α	α	X
ejpam-5731	135	15	)	)	PUNCT
ejpam-5731	135	16	=	=	SYM
ejpam-5731	135	17	γq(α+	γq(α+	PROPN
ejpam-5731	135	18	n	n	CCONJ
ejpam-5731	135	19	)	)	PUNCT
ejpam-5731	136	1	[	[	X
ejpam-5731	136	2	n−	n−	NOUN
ejpam-5731	136	3	1]q!γq(α+	1]q!γq(α+	NOUN
ejpam-5731	136	4	1	1	NUM
ejpam-5731	136	5	)	)	PUNCT
ejpam-5731	136	6	.	.	PUNCT
ejpam-5731	137	1	it	it	PRON
ejpam-5731	137	2	is	be	AUX
ejpam-5731	137	3	clear	clear	ADJ
ejpam-5731	137	4	that	that	SCONJ
ejpam-5731	137	5	,	,	PUNCT
ejpam-5731	137	6	r0	r0	NOUN
ejpam-5731	137	7	qf(z	qf(z	NUM
ejpam-5731	137	8	)	)	PUNCT
ejpam-5731	137	9	=	=	SYM
ejpam-5731	137	10	f(z	f(z	PROPN
ejpam-5731	137	11	)	)	PUNCT
ejpam-5731	137	12	,	,	PUNCT
ejpam-5731	137	13	r1	r1	PROPN
ejpam-5731	137	14	qf(z	qf(z	NUM
ejpam-5731	137	15	)	)	PUNCT
ejpam-5731	137	16	=	=	SYM
ejpam-5731	137	17	zdqf(z	zdqf(z	NUM
ejpam-5731	137	18	)	)	PUNCT
ejpam-5731	137	19	,	,	PUNCT
ejpam-5731	137	20	and	and	CCONJ
ejpam-5731	137	21	rnq	rnq	PROPN
ejpam-5731	137	22	f(z	f(z	PROPN
ejpam-5731	137	23	)	)	PUNCT
ejpam-5731	138	1	=	=	NOUN
ejpam-5731	138	2	zdn	zdn	NOUN
ejpam-5731	138	3	q	q	PROPN
ejpam-5731	138	4	(	(	PUNCT
ejpam-5731	138	5	zn−1f(z	zn−1f(z	NUM
ejpam-5731	138	6	)	)	PUNCT
ejpam-5731	138	7	)	)	PUNCT
ejpam-5731	139	1	[	[	X
ejpam-5731	139	2	n]q	n]q	X
ejpam-5731	139	3	!	!	NOUN
ejpam-5731	139	4	,	,	PUNCT
ejpam-5731	139	5	n	n	X
ejpam-5731	139	6	∈	∈	PROPN
ejpam-5731	139	7	n	n	CCONJ
ejpam-5731	139	8	it	it	PRON
ejpam-5731	139	9	is	be	AUX
ejpam-5731	139	10	worth	worth	ADJ
ejpam-5731	139	11	mention	mention	ADP
ejpam-5731	139	12	that	that	PRON
ejpam-5731	139	13	,	,	PUNCT
ejpam-5731	139	14	lim	lim	PROPN
ejpam-5731	139	15	q→1−	q→1−	PROPN
ejpam-5731	139	16	fq	fq	PROPN
ejpam-5731	139	17	,	,	PUNCT
ejpam-5731	139	18	α+1(z	α+1(z	NUM
ejpam-5731	139	19	)	)	PUNCT
ejpam-5731	139	20	=	=	SYM
ejpam-5731	140	1	z	z	NOUN
ejpam-5731	140	2	(	(	PUNCT
ejpam-5731	140	3	1−	1−	NUM
ejpam-5731	140	4	z)α+1	z)α+1	NOUN
ejpam-5731	140	5	,	,	PUNCT
ejpam-5731	140	6	w.	w.	PROPN
ejpam-5731	140	7	al	al	PROPN
ejpam-5731	140	8	-	-	PUNCT
ejpam-5731	140	9	rawashdeh	rawashdeh	PROPN
ejpam-5731	140	10	/	/	SYM
ejpam-5731	140	11	eur	eur	PROPN
ejpam-5731	140	12	.	.	PUNCT
ejpam-5731	141	1	j.	j.	PROPN
ejpam-5731	141	2	pure	pure	PROPN
ejpam-5731	141	3	appl	appl	PROPN
ejpam-5731	141	4	.	.	PROPN
ejpam-5731	141	5	math	math	PROPN
ejpam-5731	141	6	,	,	PUNCT
ejpam-5731	141	7	18	18	NUM
ejpam-5731	141	8	(	(	PUNCT
ejpam-5731	141	9	1	1	NUM
ejpam-5731	141	10	)	)	PUNCT
ejpam-5731	141	11	(	(	PUNCT
ejpam-5731	141	12	2025	2025	NUM
ejpam-5731	141	13	)	)	PUNCT
ejpam-5731	141	14	,	,	PUNCT
ejpam-5731	141	15	5731	5731	NUM
ejpam-5731	141	16	7	7	NUM
ejpam-5731	141	17	of	of	ADP
ejpam-5731	141	18	20	20	NUM
ejpam-5731	141	19	and	and	CCONJ
ejpam-5731	141	20	lim	lim	PROPN
ejpam-5731	141	21	q→1−	q→1−	PROPN
ejpam-5731	141	22	rαq	rαq	PROPN
ejpam-5731	141	23	f(z	f(z	PROPN
ejpam-5731	141	24	)	)	PUNCT
ejpam-5731	141	25	=	=	SYM
ejpam-5731	141	26	f(z	f(z	PROPN
ejpam-5731	141	27	)	)	PUNCT
ejpam-5731	141	28	∗	∗	NOUN
ejpam-5731	141	29	z	z	NOUN
ejpam-5731	141	30	(	(	PUNCT
ejpam-5731	141	31	1−	1−	NUM
ejpam-5731	141	32	z)α+1	z)α+1	NOUN
ejpam-5731	141	33	=	=	PUNCT
ejpam-5731	141	34	rαf(z	rαf(z	VERB
ejpam-5731	141	35	)	)	PUNCT
ejpam-5731	141	36	.	.	PUNCT
ejpam-5731	142	1	for	for	ADP
ejpam-5731	142	2	more	more	ADJ
ejpam-5731	142	3	information	information	NOUN
ejpam-5731	142	4	about	about	ADP
ejpam-5731	142	5	q	q	ADJ
ejpam-5731	142	6	-	-	PUNCT
ejpam-5731	142	7	rucheweyh	rucheweyh	NOUN
ejpam-5731	142	8	differential	differential	NOUN
ejpam-5731	142	9	operator	operator	NOUN
ejpam-5731	142	10	and	and	CCONJ
ejpam-5731	142	11	q	q	ADJ
ejpam-5731	142	12	-	-	ADJ
ejpam-5731	142	13	derivative	derivative	ADJ
ejpam-5731	142	14	operator	operator	NOUN
ejpam-5731	142	15	,	,	PUNCT
ejpam-5731	142	16	we	we	PRON
ejpam-5731	142	17	refer	refer	VERB
ejpam-5731	142	18	the	the	DET
ejpam-5731	142	19	interested	interested	ADJ
ejpam-5731	142	20	readers	reader	NOUN
ejpam-5731	142	21	to	to	PART
ejpam-5731	142	22	consult	consult	VERB
ejpam-5731	142	23	the	the	DET
ejpam-5731	142	24	articles	article	NOUN
ejpam-5731	142	25	[	[	X
ejpam-5731	142	26	8	8	NUM
ejpam-5731	142	27	]	]	PUNCT
ejpam-5731	142	28	,	,	PUNCT
ejpam-5731	142	29	[	[	X
ejpam-5731	142	30	9	9	NUM
ejpam-5731	142	31	]	]	PUNCT
ejpam-5731	142	32	,	,	PUNCT
ejpam-5731	142	33	[	[	X
ejpam-5731	142	34	13	13	NUM
ejpam-5731	142	35	]	]	PUNCT
ejpam-5731	142	36	,	,	PUNCT
ejpam-5731	142	37	[	[	X
ejpam-5731	142	38	16	16	NUM
ejpam-5731	142	39	]	]	PUNCT
ejpam-5731	142	40	,	,	PUNCT
ejpam-5731	142	41	[	[	X
ejpam-5731	142	42	23	23	NUM
ejpam-5731	142	43	]	]	PUNCT
ejpam-5731	142	44	,	,	PUNCT
ejpam-5731	142	45	[	[	X
ejpam-5731	142	46	25	25	NUM
ejpam-5731	142	47	]	]	PUNCT
ejpam-5731	142	48	,	,	PUNCT
ejpam-5731	142	49	[	[	X
ejpam-5731	142	50	27	27	NUM
ejpam-5731	142	51	]	]	PUNCT
ejpam-5731	142	52	,	,	PUNCT
ejpam-5731	142	53	[	[	X
ejpam-5731	142	54	44	44	NUM
ejpam-5731	142	55	]	]	PUNCT
ejpam-5731	142	56	,	,	PUNCT
ejpam-5731	142	57	[	[	X
ejpam-5731	142	58	46	46	NUM
ejpam-5731	142	59	]	]	PUNCT
ejpam-5731	142	60	,	,	PUNCT
ejpam-5731	142	61	[	[	X
ejpam-5731	142	62	50	50	NUM
ejpam-5731	142	63	]	]	PUNCT
ejpam-5731	142	64	,	,	PUNCT
ejpam-5731	142	65	[	[	X
ejpam-5731	142	66	51	51	NUM
ejpam-5731	142	67	]	]	PUNCT
ejpam-5731	142	68	,	,	PUNCT
ejpam-5731	142	69	[	[	X
ejpam-5731	142	70	52	52	NUM
ejpam-5731	142	71	]	]	PUNCT
ejpam-5731	142	72	and	and	CCONJ
ejpam-5731	142	73	the	the	DET
ejpam-5731	142	74	references	reference	NOUN
ejpam-5731	142	75	provided	provide	VERB
ejpam-5731	142	76	therein	therein	ADV
ejpam-5731	142	77	.	.	PUNCT
ejpam-5731	143	1	legendre	legendre	PROPN
ejpam-5731	143	2	polynomials	polynomial	NOUN
ejpam-5731	143	3	belong	belong	VERB
ejpam-5731	143	4	to	to	ADP
ejpam-5731	143	5	a	a	DET
ejpam-5731	143	6	well	well	ADV
ejpam-5731	143	7	-	-	PUNCT
ejpam-5731	143	8	established	establish	VERB
ejpam-5731	143	9	family	family	NOUN
ejpam-5731	143	10	of	of	ADP
ejpam-5731	143	11	classical	classical	ADJ
ejpam-5731	143	12	orthogonal	orthogonal	ADJ
ejpam-5731	143	13	polynomials	polynomial	NOUN
ejpam-5731	143	14	.	.	PUNCT
ejpam-5731	144	1	they	they	PRON
ejpam-5731	144	2	are	be	AUX
ejpam-5731	144	3	defined	define	VERB
ejpam-5731	144	4	by	by	ADP
ejpam-5731	144	5	their	their	PRON
ejpam-5731	144	6	compliance	compliance	NOUN
ejpam-5731	144	7	with	with	ADP
ejpam-5731	144	8	a	a	DET
ejpam-5731	144	9	second	second	ADJ
ejpam-5731	144	10	-	-	PUNCT
ejpam-5731	144	11	order	order	NOUN
ejpam-5731	144	12	linear	linear	ADJ
ejpam-5731	144	13	differential	differential	NOUN
ejpam-5731	144	14	equation	equation	NOUN
ejpam-5731	144	15	,	,	PUNCT
ejpam-5731	144	16	which	which	PRON
ejpam-5731	144	17	emerges	emerge	VERB
ejpam-5731	144	18	naturally	naturally	ADV
ejpam-5731	144	19	in	in	ADP
ejpam-5731	144	20	the	the	DET
ejpam-5731	144	21	context	context	NOUN
ejpam-5731	144	22	of	of	ADP
ejpam-5731	144	23	solving	solve	VERB
ejpam-5731	144	24	initial	initial	ADJ
ejpam-5731	144	25	value	value	NOUN
ejpam-5731	144	26	problems	problem	NOUN
ejpam-5731	144	27	in	in	ADP
ejpam-5731	144	28	threedimensional	threedimensional	ADJ
ejpam-5731	144	29	spaces	space	NOUN
ejpam-5731	144	30	exhibiting	exhibit	VERB
ejpam-5731	144	31	spherical	spherical	ADJ
ejpam-5731	144	32	symmetry	symmetry	NOUN
ejpam-5731	144	33	.	.	PUNCT
ejpam-5731	145	1	the	the	DET
ejpam-5731	145	2	equation	equation	NOUN
ejpam-5731	145	3	associated	associate	VERB
ejpam-5731	145	4	with	with	ADP
ejpam-5731	145	5	legendre	legendre	PROPN
ejpam-5731	145	6	polynomials	polynomial	NOUN
ejpam-5731	145	7	is	be	AUX
ejpam-5731	145	8	classified	classify	VERB
ejpam-5731	145	9	as	as	ADP
ejpam-5731	145	10	a	a	DET
ejpam-5731	145	11	legendre	legendre	PROPN
ejpam-5731	145	12	second	second	ADJ
ejpam-5731	145	13	-	-	PUNCT
ejpam-5731	145	14	order	order	NOUN
ejpam-5731	145	15	differential	differential	ADJ
ejpam-5731	145	16	equation	equation	NOUN
ejpam-5731	145	17	:	:	PUNCT
ejpam-5731	145	18	(	(	PUNCT
ejpam-5731	145	19	1−	1−	NUM
ejpam-5731	145	20	x2)y′′	x2)y′′	NOUN
ejpam-5731	146	1	−	−	PROPN
ejpam-5731	146	2	2xy′	2xy′	NUM
ejpam-5731	146	3	+	+	CCONJ
ejpam-5731	146	4	λy	λy	PROPN
ejpam-5731	146	5	=	=	SYM
ejpam-5731	146	6	0	0	NUM
ejpam-5731	146	7	,	,	PUNCT
ejpam-5731	146	8	−1	−1	NOUN
ejpam-5731	146	9	<	<	X
ejpam-5731	146	10	x	x	X
ejpam-5731	146	11	<	<	X
ejpam-5731	146	12	1	1	NUM
ejpam-5731	146	13	.	.	PUNCT
ejpam-5731	147	1	(	(	PUNCT
ejpam-5731	147	2	3	3	X
ejpam-5731	147	3	)	)	PUNCT
ejpam-5731	147	4	the	the	DET
ejpam-5731	147	5	process	process	NOUN
ejpam-5731	147	6	of	of	ADP
ejpam-5731	147	7	identifying	identify	VERB
ejpam-5731	147	8	the	the	DET
ejpam-5731	147	9	parameters	parameter	NOUN
ejpam-5731	147	10	λ	λ	X
ejpam-5731	147	11	∈	∈	NOUN
ejpam-5731	147	12	r	r	NOUN
ejpam-5731	147	13	that	that	PRON
ejpam-5731	147	14	allows	allow	VERB
ejpam-5731	147	15	equation	equation	NOUN
ejpam-5731	147	16	(	(	PUNCT
ejpam-5731	147	17	3	3	NUM
ejpam-5731	147	18	)	)	PUNCT
ejpam-5731	147	19	to	to	PART
ejpam-5731	147	20	possess	possess	VERB
ejpam-5731	147	21	a	a	DET
ejpam-5731	147	22	bounded	bounded	ADJ
ejpam-5731	147	23	solution	solution	NOUN
ejpam-5731	147	24	is	be	AUX
ejpam-5731	147	25	referred	refer	VERB
ejpam-5731	147	26	to	to	ADP
ejpam-5731	147	27	as	as	ADP
ejpam-5731	147	28	a	a	DET
ejpam-5731	147	29	singular	singular	ADJ
ejpam-5731	147	30	sturm	sturm	NOUN
ejpam-5731	147	31	-	-	PUNCT
ejpam-5731	147	32	liouville	liouville	NOUN
ejpam-5731	147	33	problem	problem	NOUN
ejpam-5731	147	34	.	.	PUNCT
ejpam-5731	148	1	the	the	DET
ejpam-5731	148	2	significance	significance	NOUN
ejpam-5731	148	3	of	of	ADP
ejpam-5731	148	4	these	these	PRON
ejpam-5731	148	5	eigenvalues	eigenvalue	VERB
ejpam-5731	148	6	λ	λ	NOUN
ejpam-5731	148	7	lies	lie	NOUN
ejpam-5731	148	8	in	in	ADP
ejpam-5731	148	9	their	their	PRON
ejpam-5731	148	10	role	role	NOUN
ejpam-5731	148	11	in	in	ADP
ejpam-5731	148	12	determining	determine	VERB
ejpam-5731	148	13	the	the	DET
ejpam-5731	148	14	nature	nature	NOUN
ejpam-5731	148	15	of	of	ADP
ejpam-5731	148	16	the	the	DET
ejpam-5731	148	17	solutions	solution	NOUN
ejpam-5731	148	18	to	to	ADP
ejpam-5731	148	19	the	the	DET
ejpam-5731	148	20	differential	differential	ADJ
ejpam-5731	148	21	equation	equation	NOUN
ejpam-5731	148	22	.	.	PUNCT
ejpam-5731	149	1	in	in	ADP
ejpam-5731	149	2	this	this	DET
ejpam-5731	149	3	context	context	NOUN
ejpam-5731	149	4	,	,	PUNCT
ejpam-5731	149	5	the	the	DET
ejpam-5731	149	6	necessity	necessity	NOUN
ejpam-5731	149	7	for	for	ADP
ejpam-5731	149	8	boundary	boundary	ADJ
ejpam-5731	149	9	conditions	condition	NOUN
ejpam-5731	149	10	is	be	AUX
ejpam-5731	149	11	eliminated	eliminate	VERB
ejpam-5731	149	12	,	,	PUNCT
ejpam-5731	149	13	as	as	SCONJ
ejpam-5731	149	14	the	the	DET
ejpam-5731	149	15	boundedness	boundedness	NOUN
ejpam-5731	149	16	of	of	ADP
ejpam-5731	149	17	the	the	DET
ejpam-5731	149	18	solution	solution	NOUN
ejpam-5731	149	19	itself	itself	PRON
ejpam-5731	149	20	serves	serve	VERB
ejpam-5731	149	21	as	as	ADP
ejpam-5731	149	22	a	a	DET
ejpam-5731	149	23	substitute	substitute	NOUN
ejpam-5731	149	24	for	for	ADP
ejpam-5731	149	25	these	these	DET
ejpam-5731	149	26	conditions	condition	NOUN
ejpam-5731	149	27	.	.	PUNCT
ejpam-5731	150	1	it	it	PRON
ejpam-5731	150	2	has	have	AUX
ejpam-5731	150	3	been	be	AUX
ejpam-5731	150	4	established	establish	VERB
ejpam-5731	150	5	that	that	SCONJ
ejpam-5731	150	6	the	the	DET
ejpam-5731	150	7	only	only	ADJ
ejpam-5731	150	8	permissible	permissible	ADJ
ejpam-5731	150	9	values	value	NOUN
ejpam-5731	150	10	of	of	ADP
ejpam-5731	150	11	λ	λ	PROPN
ejpam-5731	150	12	that	that	PRON
ejpam-5731	150	13	yield	yield	VERB
ejpam-5731	150	14	bounded	bounded	ADJ
ejpam-5731	150	15	solutions	solution	NOUN
ejpam-5731	150	16	are	be	AUX
ejpam-5731	150	17	of	of	ADP
ejpam-5731	150	18	the	the	DET
ejpam-5731	150	19	form	form	NOUN
ejpam-5731	150	20	λ	λ	X
ejpam-5731	150	21	=	=	PUNCT
ejpam-5731	150	22	n(n	n(n	PROPN
ejpam-5731	150	23	+	+	CCONJ
ejpam-5731	150	24	1	1	NUM
ejpam-5731	150	25	)	)	PUNCT
ejpam-5731	150	26	,	,	PUNCT
ejpam-5731	150	27	where	where	SCONJ
ejpam-5731	150	28	n	n	PRON
ejpam-5731	150	29	is	be	AUX
ejpam-5731	150	30	a	a	DET
ejpam-5731	150	31	natural	natural	ADJ
ejpam-5731	150	32	number	number	NOUN
ejpam-5731	150	33	.	.	PUNCT
ejpam-5731	151	1	these	these	DET
ejpam-5731	151	2	values	value	NOUN
ejpam-5731	151	3	of	of	ADP
ejpam-5731	151	4	λ	λ	NOUN
ejpam-5731	151	5	are	be	AUX
ejpam-5731	151	6	called	call	VERB
ejpam-5731	151	7	the	the	DET
ejpam-5731	151	8	eigenvalues	eigenvalue	NOUN
ejpam-5731	151	9	of	of	ADP
ejpam-5731	151	10	the	the	DET
ejpam-5731	151	11	sturm	sturm	NOUN
ejpam-5731	151	12	-	-	PUNCT
ejpam-5731	151	13	liouville	liouville	NOUN
ejpam-5731	151	14	problem	problem	NOUN
ejpam-5731	151	15	.	.	PUNCT
ejpam-5731	152	1	the	the	DET
ejpam-5731	152	2	polynomial	polynomial	ADJ
ejpam-5731	152	3	solutions	solution	NOUN
ejpam-5731	152	4	of	of	ADP
ejpam-5731	152	5	legendre	legendre	PROPN
ejpam-5731	152	6	’s	’s	PART
ejpam-5731	152	7	differential	differential	ADJ
ejpam-5731	152	8	equation	equation	NOUN
ejpam-5731	152	9	can	can	AUX
ejpam-5731	152	10	be	be	AUX
ejpam-5731	152	11	explicitly	explicitly	ADV
ejpam-5731	152	12	expressed	express	VERB
ejpam-5731	152	13	as	as	SCONJ
ejpam-5731	152	14	follows	follow	VERB
ejpam-5731	152	15	.	.	PUNCT
ejpam-5731	153	1	these	these	DET
ejpam-5731	153	2	solutions	solution	NOUN
ejpam-5731	153	3	play	play	VERB
ejpam-5731	153	4	a	a	DET
ejpam-5731	153	5	significant	significant	ADJ
ejpam-5731	153	6	role	role	NOUN
ejpam-5731	153	7	in	in	ADP
ejpam-5731	153	8	various	various	ADJ
ejpam-5731	153	9	applications	application	NOUN
ejpam-5731	153	10	,	,	PUNCT
ejpam-5731	153	11	particularly	particularly	ADV
ejpam-5731	153	12	in	in	ADP
ejpam-5731	153	13	mathematical	mathematical	ADJ
ejpam-5731	153	14	physics	physics	NOUN
ejpam-5731	153	15	and	and	CCONJ
ejpam-5731	153	16	engineering	engineering	NOUN
ejpam-5731	153	17	,	,	PUNCT
ejpam-5731	153	18	where	where	SCONJ
ejpam-5731	153	19	they	they	PRON
ejpam-5731	153	20	are	be	AUX
ejpam-5731	153	21	utilized	utilize	VERB
ejpam-5731	153	22	to	to	PART
ejpam-5731	153	23	solve	solve	VERB
ejpam-5731	153	24	problems	problem	NOUN
ejpam-5731	153	25	involving	involve	VERB
ejpam-5731	153	26	spherical	spherical	ADJ
ejpam-5731	153	27	symmetry	symmetry	NOUN
ejpam-5731	153	28	.	.	PUNCT
ejpam-5731	154	1	pn(x	pn(x	PUNCT
ejpam-5731	154	2	)	)	PUNCT
ejpam-5731	154	3	=	=	SYM
ejpam-5731	154	4	1	1	NUM
ejpam-5731	154	5	2n	2n	NUM
ejpam-5731	154	6	⌊n/2⌋∑	⌊n/2⌋∑	NOUN
ejpam-5731	154	7	k=0	k=0	PROPN
ejpam-5731	154	8	(	(	PUNCT
ejpam-5731	154	9	−1)k	−1)k	PROPN
ejpam-5731	154	10	(	(	PUNCT
ejpam-5731	154	11	n	n	X
ejpam-5731	154	12	k	k	NOUN
ejpam-5731	154	13	)	)	PUNCT
ejpam-5731	154	14	(	(	PUNCT
ejpam-5731	154	15	2n−	2n−	PROPN
ejpam-5731	154	16	2k	2k	NUM
ejpam-5731	154	17	n	n	CCONJ
ejpam-5731	154	18	)	)	PUNCT
ejpam-5731	154	19	xn−2k	xn−2k	PROPN
ejpam-5731	154	20	,	,	PUNCT
ejpam-5731	154	21	(	(	PUNCT
ejpam-5731	154	22	4	4	X
ejpam-5731	154	23	)	)	PUNCT
ejpam-5731	154	24	where	where	SCONJ
ejpam-5731	154	25	⌊z⌋	⌊z⌋	PUNCT
ejpam-5731	154	26	is	be	AUX
ejpam-5731	154	27	the	the	DET
ejpam-5731	154	28	floor	floor	NOUN
ejpam-5731	154	29	of	of	ADP
ejpam-5731	154	30	z	z	PROPN
ejpam-5731	154	31	,	,	PUNCT
ejpam-5731	155	1	i.e.	i.e.	X
ejpam-5731	155	2	the	the	DET
ejpam-5731	155	3	greatest	great	ADJ
ejpam-5731	155	4	integerm	integerm	ADJ
ejpam-5731	155	5	≤	≤	PROPN
ejpam-5731	155	6	z.	z.	PROPN
ejpam-5731	156	1	it	it	PRON
ejpam-5731	156	2	is	be	AUX
ejpam-5731	156	3	worth	worth	ADJ
ejpam-5731	156	4	to	to	PART
ejpam-5731	156	5	mention	mention	VERB
ejpam-5731	156	6	that	that	SCONJ
ejpam-5731	156	7	when	when	SCONJ
ejpam-5731	156	8	n	n	PRON
ejpam-5731	156	9	is	be	AUX
ejpam-5731	156	10	even	even	ADV
ejpam-5731	156	11	,	,	PUNCT
ejpam-5731	156	12	the	the	DET
ejpam-5731	156	13	polynomial	polynomial	ADJ
ejpam-5731	156	14	pn(x	pn(x	X
ejpam-5731	156	15	)	)	PUNCT
ejpam-5731	156	16	exclusively	exclusively	ADV
ejpam-5731	156	17	comprises	comprise	VERB
ejpam-5731	156	18	even	even	ADV
ejpam-5731	156	19	powers	power	NOUN
ejpam-5731	156	20	of	of	ADP
ejpam-5731	156	21	x	x	PRON
ejpam-5731	156	22	,	,	PUNCT
ejpam-5731	156	23	while	while	SCONJ
ejpam-5731	156	24	for	for	ADP
ejpam-5731	156	25	odd	odd	ADJ
ejpam-5731	156	26	n	n	PRON
ejpam-5731	156	27	it	it	PRON
ejpam-5731	156	28	contains	contain	VERB
ejpam-5731	156	29	only	only	ADV
ejpam-5731	156	30	odd	odd	ADJ
ejpam-5731	156	31	powers	power	NOUN
ejpam-5731	156	32	.	.	PUNCT
ejpam-5731	157	1	consequently	consequently	ADV
ejpam-5731	157	2	,	,	PUNCT
ejpam-5731	157	3	pn(x	pn(x	X
ejpam-5731	157	4	)	)	PUNCT
ejpam-5731	157	5	is	be	AUX
ejpam-5731	157	6	classified	classify	VERB
ejpam-5731	157	7	as	as	ADP
ejpam-5731	157	8	an	an	DET
ejpam-5731	157	9	even	even	ADJ
ejpam-5731	157	10	function	function	NOUN
ejpam-5731	157	11	for	for	ADP
ejpam-5731	157	12	even	even	ADV
ejpam-5731	157	13	n	n	ADV
ejpam-5731	157	14	and	and	CCONJ
ejpam-5731	157	15	as	as	ADP
ejpam-5731	157	16	an	an	DET
ejpam-5731	157	17	odd	odd	ADJ
ejpam-5731	157	18	function	function	NOUN
ejpam-5731	157	19	for	for	ADP
ejpam-5731	157	20	odd	odd	ADJ
ejpam-5731	157	21	n.	n.	NOUN
ejpam-5731	157	22	their	their	PRON
ejpam-5731	157	23	unique	unique	ADJ
ejpam-5731	157	24	properties	property	NOUN
ejpam-5731	157	25	,	,	PUNCT
ejpam-5731	157	26	such	such	ADJ
ejpam-5731	157	27	as	as	ADP
ejpam-5731	157	28	orthogonality	orthogonality	NOUN
ejpam-5731	157	29	and	and	CCONJ
ejpam-5731	157	30	recurrence	recurrence	NOUN
ejpam-5731	157	31	relations	relation	NOUN
ejpam-5731	157	32	,	,	PUNCT
ejpam-5731	157	33	further	far	ADV
ejpam-5731	157	34	enhance	enhance	VERB
ejpam-5731	157	35	their	their	PRON
ejpam-5731	157	36	utility	utility	NOUN
ejpam-5731	157	37	in	in	ADP
ejpam-5731	157	38	both	both	CCONJ
ejpam-5731	157	39	theoretical	theoretical	ADJ
ejpam-5731	157	40	and	and	CCONJ
ejpam-5731	157	41	applied	applied	ADJ
ejpam-5731	157	42	mathematics	mathematic	NOUN
ejpam-5731	157	43	.	.	PUNCT
ejpam-5731	158	1	the	the	DET
ejpam-5731	158	2	first	first	ADJ
ejpam-5731	158	3	few	few	ADJ
ejpam-5731	158	4	of	of	ADP
ejpam-5731	158	5	them	they	PRON
ejpam-5731	158	6	are	be	AUX
ejpam-5731	158	7	:	:	PUNCT
ejpam-5731	158	8	p0(x	p0(x	X
ejpam-5731	158	9	)	)	PUNCT
ejpam-5731	158	10	=	=	SYM
ejpam-5731	158	11	1	1	NUM
ejpam-5731	158	12	,	,	PUNCT
ejpam-5731	158	13	p1(x	p1(x	NOUN
ejpam-5731	158	14	)	)	PUNCT
ejpam-5731	158	15	=	=	SYM
ejpam-5731	159	1	x	x	X
ejpam-5731	159	2	,	,	PUNCT
ejpam-5731	159	3	p2(x	p2(x	X
ejpam-5731	159	4	)	)	PUNCT
ejpam-5731	159	5	=	=	SYM
ejpam-5731	159	6	1	1	NUM
ejpam-5731	159	7	2	2	NUM
ejpam-5731	159	8	(	(	PUNCT
ejpam-5731	159	9	3x2	3x2	NUM
ejpam-5731	159	10	−	−	NOUN
ejpam-5731	159	11	1	1	NUM
ejpam-5731	159	12	)	)	PUNCT
ejpam-5731	159	13	,	,	PUNCT
ejpam-5731	159	14	p3(x	p3(x	PROPN
ejpam-5731	159	15	)	)	PUNCT
ejpam-5731	159	16	=	=	SYM
ejpam-5731	159	17	1	1	NUM
ejpam-5731	159	18	2	2	NUM
ejpam-5731	159	19	(	(	PUNCT
ejpam-5731	159	20	5x3	5x3	NUM
ejpam-5731	159	21	−	−	NOUN
ejpam-5731	159	22	3x	3x	NUM
ejpam-5731	159	23	)	)	PUNCT
ejpam-5731	159	24	,	,	PUNCT
ejpam-5731	159	25	p4(x	p4(x	X
ejpam-5731	159	26	)	)	PUNCT
ejpam-5731	159	27	=	=	SYM
ejpam-5731	159	28	1	1	NUM
ejpam-5731	159	29	8	8	NUM
ejpam-5731	159	30	(	(	PUNCT
ejpam-5731	159	31	35x4	35x4	NUM
ejpam-5731	159	32	−	−	NUM
ejpam-5731	159	33	30x2	30x2	NUM
ejpam-5731	159	34	+	+	CCONJ
ejpam-5731	159	35	3	3	NUM
ejpam-5731	159	36	)	)	PUNCT
ejpam-5731	159	37	,	,	PUNCT
ejpam-5731	159	38	p5(x	p5(x	NUM
ejpam-5731	159	39	)	)	PUNCT
ejpam-5731	159	40	=	=	SYM
ejpam-5731	159	41	1	1	NUM
ejpam-5731	159	42	8	8	NUM
ejpam-5731	159	43	(	(	PUNCT
ejpam-5731	159	44	63x5	63x5	NUM
ejpam-5731	159	45	−	−	NUM
ejpam-5731	159	46	70x3	70x3	NUM
ejpam-5731	159	47	+	+	NUM
ejpam-5731	159	48	15x	15x	NOUN
ejpam-5731	159	49	)	)	PUNCT
ejpam-5731	159	50	.	.	PUNCT
ejpam-5731	160	1	it	it	PRON
ejpam-5731	160	2	is	be	AUX
ejpam-5731	160	3	important	important	ADJ
ejpam-5731	160	4	to	to	PART
ejpam-5731	160	5	highlight	highlight	VERB
ejpam-5731	160	6	that	that	SCONJ
ejpam-5731	160	7	the	the	DET
ejpam-5731	160	8	legendre	legendre	PROPN
ejpam-5731	160	9	polynomials	polynomial	NOUN
ejpam-5731	160	10	can	can	AUX
ejpam-5731	160	11	be	be	AUX
ejpam-5731	160	12	represented	represent	VERB
ejpam-5731	160	13	in	in	ADP
ejpam-5731	160	14	a	a	DET
ejpam-5731	160	15	more	more	ADV
ejpam-5731	160	16	concise	concise	ADJ
ejpam-5731	160	17	manner	manner	NOUN
ejpam-5731	160	18	.	.	PUNCT
ejpam-5731	161	1	specifically	specifically	ADV
ejpam-5731	161	2	,	,	PUNCT
ejpam-5731	161	3	the	the	DET
ejpam-5731	161	4	nth	nth	NOUN
ejpam-5731	161	5	legendre	legendre	PROPN
ejpam-5731	161	6	polynomial	polynomial	PROPN
ejpam-5731	161	7	,	,	PUNCT
ejpam-5731	161	8	denoted	denote	VERB
ejpam-5731	161	9	as	as	ADP
ejpam-5731	161	10	pn	pn	PROPN
ejpam-5731	161	11	,	,	PUNCT
ejpam-5731	161	12	can	can	AUX
ejpam-5731	161	13	be	be	AUX
ejpam-5731	161	14	w.	w.	PROPN
ejpam-5731	161	15	al	al	PROPN
ejpam-5731	161	16	-	-	PUNCT
ejpam-5731	161	17	rawashdeh	rawashdeh	PROPN
ejpam-5731	161	18	/	/	SYM
ejpam-5731	161	19	eur	eur	PROPN
ejpam-5731	161	20	.	.	PUNCT
ejpam-5731	162	1	j.	j.	PROPN
ejpam-5731	162	2	pure	pure	PROPN
ejpam-5731	162	3	appl	appl	PROPN
ejpam-5731	162	4	.	.	PROPN
ejpam-5731	162	5	math	math	PROPN
ejpam-5731	162	6	,	,	PUNCT
ejpam-5731	162	7	18	18	NUM
ejpam-5731	162	8	(	(	PUNCT
ejpam-5731	162	9	1	1	NUM
ejpam-5731	162	10	)	)	PUNCT
ejpam-5731	162	11	(	(	PUNCT
ejpam-5731	162	12	2025	2025	NUM
ejpam-5731	162	13	)	)	PUNCT
ejpam-5731	162	14	,	,	PUNCT
ejpam-5731	162	15	5731	5731	NUM
ejpam-5731	162	16	8	8	NUM
ejpam-5731	162	17	of	of	ADP
ejpam-5731	162	18	20	20	NUM
ejpam-5731	162	19	formulated	formulated	ADJ
ejpam-5731	162	20	using	using	NOUN
ejpam-5731	162	21	rodrigues	rodrigue	NOUN
ejpam-5731	162	22	’	'	PUNCT
ejpam-5731	162	23	formula	formula	NOUN
ejpam-5731	162	24	(	(	PUNCT
ejpam-5731	162	25	5	5	NUM
ejpam-5731	162	26	)	)	PUNCT
ejpam-5731	162	27	,	,	PUNCT
ejpam-5731	162	28	which	which	PRON
ejpam-5731	162	29	serves	serve	VERB
ejpam-5731	162	30	as	as	ADP
ejpam-5731	162	31	a	a	DET
ejpam-5731	162	32	foundational	foundational	ADJ
ejpam-5731	162	33	tool	tool	NOUN
ejpam-5731	162	34	in	in	ADP
ejpam-5731	162	35	the	the	DET
ejpam-5731	162	36	study	study	NOUN
ejpam-5731	162	37	of	of	ADP
ejpam-5731	162	38	these	these	DET
ejpam-5731	162	39	polynomials	polynomial	NOUN
ejpam-5731	162	40	.	.	PUNCT
ejpam-5731	163	1	pn(x	pn(x	PUNCT
ejpam-5731	163	2	)	)	PUNCT
ejpam-5731	163	3	=	=	SYM
ejpam-5731	163	4	1	1	NUM
ejpam-5731	163	5	2nn	2nn	NOUN
ejpam-5731	163	6	!	!	PUNCT
ejpam-5731	164	1	dn	dn	PROPN
ejpam-5731	164	2	dxn	dxn	PROPN
ejpam-5731	164	3	(	(	PUNCT
ejpam-5731	164	4	x2	x2	INTJ
ejpam-5731	164	5	−	−	PROPN
ejpam-5731	164	6	1)n	1)n	NUM
ejpam-5731	164	7	.	.	PUNCT
ejpam-5731	165	1	(	(	PUNCT
ejpam-5731	165	2	5	5	NUM
ejpam-5731	165	3	)	)	PUNCT
ejpam-5731	165	4	as	as	ADP
ejpam-5731	165	5	a	a	DET
ejpam-5731	165	6	result	result	NOUN
ejpam-5731	165	7	of	of	ADP
ejpam-5731	165	8	rodrigue	rodrigue	NOUN
ejpam-5731	165	9	’s	’s	PART
ejpam-5731	165	10	formula	formula	NOUN
ejpam-5731	165	11	,	,	PUNCT
ejpam-5731	165	12	one	one	PRON
ejpam-5731	165	13	can	can	AUX
ejpam-5731	165	14	observe	observe	VERB
ejpam-5731	165	15	a	a	DET
ejpam-5731	165	16	specific	specific	ADJ
ejpam-5731	165	17	connection	connection	NOUN
ejpam-5731	165	18	that	that	PRON
ejpam-5731	165	19	exists	exist	VERB
ejpam-5731	165	20	between	between	ADP
ejpam-5731	165	21	three	three	NUM
ejpam-5731	165	22	consecutive	consecutive	ADJ
ejpam-5731	165	23	legendre	legendre	NOUN
ejpam-5731	165	24	polynomials	polynomial	NOUN
ejpam-5731	165	25	.	.	PUNCT
ejpam-5731	166	1	this	this	DET
ejpam-5731	166	2	relationship	relationship	NOUN
ejpam-5731	166	3	plays	play	VERB
ejpam-5731	166	4	a	a	DET
ejpam-5731	166	5	crucial	crucial	ADJ
ejpam-5731	166	6	role	role	NOUN
ejpam-5731	166	7	in	in	ADP
ejpam-5731	166	8	understanding	understand	VERB
ejpam-5731	166	9	the	the	DET
ejpam-5731	166	10	properties	property	NOUN
ejpam-5731	166	11	and	and	CCONJ
ejpam-5731	166	12	behaviors	behavior	NOUN
ejpam-5731	166	13	of	of	ADP
ejpam-5731	166	14	these	these	DET
ejpam-5731	166	15	polynomials	polynomial	NOUN
ejpam-5731	166	16	and	and	CCONJ
ejpam-5731	166	17	their	their	PRON
ejpam-5731	166	18	applications	application	NOUN
ejpam-5731	166	19	in	in	ADP
ejpam-5731	166	20	mathematical	mathematical	ADJ
ejpam-5731	166	21	physics	physics	NOUN
ejpam-5731	166	22	.	.	PUNCT
ejpam-5731	167	1	(	(	PUNCT
ejpam-5731	167	2	2n+	2n+	NUM
ejpam-5731	167	3	1)xpn(x	1)xpn(x	NUM
ejpam-5731	167	4	)	)	PUNCT
ejpam-5731	167	5	=	=	PUNCT
ejpam-5731	167	6	(	(	PUNCT
ejpam-5731	167	7	n+	n+	NOUN
ejpam-5731	167	8	1)pn+1(x	1)pn+1(x	NOUN
ejpam-5731	167	9	)	)	PUNCT
ejpam-5731	167	10	+	+	NUM
ejpam-5731	167	11	npn−1(x	npn−1(x	NUM
ejpam-5731	167	12	)	)	PUNCT
ejpam-5731	167	13	.	.	PUNCT
ejpam-5731	168	1	it	it	PRON
ejpam-5731	168	2	can	can	AUX
ejpam-5731	168	3	be	be	AUX
ejpam-5731	168	4	demonstrated	demonstrate	VERB
ejpam-5731	168	5	that	that	SCONJ
ejpam-5731	168	6	the	the	DET
ejpam-5731	168	7	legendre	legendre	PROPN
ejpam-5731	168	8	polynomials	polynomial	NOUN
ejpam-5731	168	9	are	be	AUX
ejpam-5731	168	10	produced	produce	VERB
ejpam-5731	168	11	by	by	ADP
ejpam-5731	168	12	the	the	DET
ejpam-5731	168	13	generating	generate	VERB
ejpam-5731	168	14	function	function	NOUN
ejpam-5731	168	15	g(x	g(x	PROPN
ejpam-5731	168	16	,	,	PUNCT
ejpam-5731	168	17	t	t	PROPN
ejpam-5731	168	18	)	)	PUNCT
ejpam-5731	168	19	=	=	SYM
ejpam-5731	168	20	1√	1√	PROPN
ejpam-5731	168	21	t2	t2	PROPN
ejpam-5731	168	22	−	−	PROPN
ejpam-5731	168	23	2xt+	2xt+	NOUN
ejpam-5731	168	24	1	1	NUM
ejpam-5731	168	25	.	.	PUNCT
ejpam-5731	169	1	this	this	DET
ejpam-5731	169	2	relationship	relationship	NOUN
ejpam-5731	169	3	highlights	highlight	VERB
ejpam-5731	169	4	the	the	DET
ejpam-5731	169	5	significance	significance	NOUN
ejpam-5731	169	6	of	of	ADP
ejpam-5731	169	7	this	this	DET
ejpam-5731	169	8	function	function	NOUN
ejpam-5731	169	9	in	in	ADP
ejpam-5731	169	10	generating	generate	VERB
ejpam-5731	169	11	these	these	DET
ejpam-5731	169	12	important	important	ADJ
ejpam-5731	169	13	polynomials	polynomial	NOUN
ejpam-5731	169	14	,	,	PUNCT
ejpam-5731	169	15	which	which	PRON
ejpam-5731	169	16	have	have	VERB
ejpam-5731	169	17	numerous	numerous	ADJ
ejpam-5731	169	18	applications	application	NOUN
ejpam-5731	169	19	in	in	ADP
ejpam-5731	169	20	physics	physics	NOUN
ejpam-5731	169	21	and	and	CCONJ
ejpam-5731	169	22	engineering	engineering	NOUN
ejpam-5731	169	23	.	.	PUNCT
ejpam-5731	170	1	additionally	additionally	ADV
ejpam-5731	170	2	,	,	PUNCT
ejpam-5731	170	3	when	when	SCONJ
ejpam-5731	170	4	the	the	DET
ejpam-5731	170	5	function	function	NOUN
ejpam-5731	170	6	g(x	g(x	PROPN
ejpam-5731	170	7	,	,	PUNCT
ejpam-5731	170	8	t	t	PROPN
ejpam-5731	170	9	)	)	PUNCT
ejpam-5731	170	10	is	be	AUX
ejpam-5731	170	11	expanded	expand	VERB
ejpam-5731	170	12	as	as	ADP
ejpam-5731	170	13	a	a	DET
ejpam-5731	170	14	taylor	taylor	PROPN
ejpam-5731	170	15	series	series	NOUN
ejpam-5731	170	16	in	in	ADP
ejpam-5731	170	17	terms	term	NOUN
ejpam-5731	170	18	of	of	ADP
ejpam-5731	170	19	t	t	PROPN
ejpam-5731	170	20	,	,	PUNCT
ejpam-5731	170	21	the	the	DET
ejpam-5731	170	22	coefficient	coefficient	NOUN
ejpam-5731	170	23	corresponding	correspond	VERB
ejpam-5731	170	24	to	to	ADP
ejpam-5731	170	25	tn	tn	PROPN
ejpam-5731	170	26	is	be	AUX
ejpam-5731	170	27	the	the	DET
ejpam-5731	170	28	legendre	legendre	PROPN
ejpam-5731	170	29	polynomial	polynomial	ADJ
ejpam-5731	170	30	pn(x	pn(x	X
ejpam-5731	170	31	):	):	PUNCT
ejpam-5731	170	32	g(x	g(x	PROPN
ejpam-5731	170	33	,	,	PUNCT
ejpam-5731	170	34	t	t	PROPN
ejpam-5731	170	35	)	)	PUNCT
ejpam-5731	170	36	=	=	PUNCT
ejpam-5731	171	1	∞∑	∞∑	NUM
ejpam-5731	171	2	n=0	n=0	SYM
ejpam-5731	171	3	pn(x)t	pn(x)t	PROPN
ejpam-5731	171	4	n	n	CCONJ
ejpam-5731	171	5	,	,	PUNCT
ejpam-5731	171	6	where	where	SCONJ
ejpam-5731	171	7	|x|	|x|	PROPN
ejpam-5731	171	8	<	<	X
ejpam-5731	171	9	1	1	NUM
ejpam-5731	171	10	and	and	CCONJ
ejpam-5731	171	11	t	t	PROPN
ejpam-5731	171	12	∈	∈	PROPN
ejpam-5731	171	13	d.	d.	PROPN
ejpam-5731	171	14	(	(	PUNCT
ejpam-5731	171	15	6	6	NUM
ejpam-5731	171	16	)	)	PUNCT
ejpam-5731	171	17	in	in	ADP
ejpam-5731	171	18	this	this	DET
ejpam-5731	171	19	paper	paper	NOUN
ejpam-5731	171	20	,	,	PUNCT
ejpam-5731	171	21	the	the	DET
ejpam-5731	171	22	symbol	symbol	NOUN
ejpam-5731	171	23	p	p	NOUN
ejpam-5731	171	24	denotes	denote	VERB
ejpam-5731	171	25	the	the	DET
ejpam-5731	171	26	caratheodory	caratheodory	ADJ
ejpam-5731	171	27	class	class	NOUN
ejpam-5731	171	28	,	,	PUNCT
ejpam-5731	171	29	which	which	PRON
ejpam-5731	171	30	is	be	AUX
ejpam-5731	171	31	formally	formally	ADV
ejpam-5731	171	32	defined	define	VERB
ejpam-5731	171	33	as	as	ADP
ejpam-5731	171	34	p	p	NOUN
ejpam-5731	171	35	=	=	PUNCT
ejpam-5731	171	36	{	{	PUNCT
ejpam-5731	171	37	ω	ω	NUM
ejpam-5731	171	38	∈	∈	PROPN
ejpam-5731	171	39	h	h	NOUN
ejpam-5731	171	40	:	:	PUNCT
ejpam-5731	171	41	ω(0	ω(0	X
ejpam-5731	171	42	)	)	PUNCT
ejpam-5731	171	43	=	=	SYM
ejpam-5731	171	44	1	1	NUM
ejpam-5731	171	45	,	,	PUNCT
ejpam-5731	171	46	r(ω(z	r(ω(z	ADJ
ejpam-5731	171	47	)	)	PUNCT
ejpam-5731	171	48	)	)	PUNCT
ejpam-5731	172	1	>	>	X
ejpam-5731	172	2	0	0	NUM
ejpam-5731	172	3	,	,	PUNCT
ejpam-5731	172	4	z	z	NOUN
ejpam-5731	172	5	∈	∈	PROPN
ejpam-5731	172	6	d	d	NOUN
ejpam-5731	172	7	}	}	PUNCT
ejpam-5731	172	8	.	.	PUNCT
ejpam-5731	173	1	it	it	PRON
ejpam-5731	173	2	is	be	AUX
ejpam-5731	173	3	established	establish	VERB
ejpam-5731	173	4	in	in	ADP
ejpam-5731	173	5	the	the	DET
ejpam-5731	173	6	literature	literature	NOUN
ejpam-5731	173	7	(	(	PUNCT
ejpam-5731	173	8	for	for	ADP
ejpam-5731	173	9	example	example	NOUN
ejpam-5731	173	10	,	,	PUNCT
ejpam-5731	173	11	see	see	VERB
ejpam-5731	173	12	[	[	X
ejpam-5731	173	13	21	21	NUM
ejpam-5731	173	14	]	]	PUNCT
ejpam-5731	173	15	,	,	PUNCT
ejpam-5731	173	16	page	page	NOUN
ejpam-5731	173	17	102	102	NUM
ejpam-5731	173	18	)	)	PUNCT
ejpam-5731	173	19	that	that	SCONJ
ejpam-5731	173	20	the	the	DET
ejpam-5731	173	21	function	function	NOUN
ejpam-5731	173	22	ϕ(z	ϕ(z	PROPN
ejpam-5731	173	23	)	)	PUNCT
ejpam-5731	173	24	is	be	AUX
ejpam-5731	173	25	a	a	DET
ejpam-5731	173	26	member	member	NOUN
ejpam-5731	173	27	of	of	ADP
ejpam-5731	173	28	the	the	DET
ejpam-5731	173	29	class	class	NOUN
ejpam-5731	173	30	p	p	NOUN
ejpam-5731	173	31	for	for	ADP
ejpam-5731	173	32	any	any	DET
ejpam-5731	173	33	real	real	ADJ
ejpam-5731	173	34	number	number	NOUN
ejpam-5731	173	35	θ	θ	NOUN
ejpam-5731	173	36	,	,	PUNCT
ejpam-5731	173	37	with	with	ADP
ejpam-5731	173	38	ϕ	ϕ	NOUN
ejpam-5731	173	39	expressed	express	VERB
ejpam-5731	173	40	as	as	ADP
ejpam-5731	173	41	ϕ(z	ϕ(z	NOUN
ejpam-5731	173	42	)	)	PUNCT
ejpam-5731	173	43	=	=	SYM
ejpam-5731	173	44	1−	1−	NUM
ejpam-5731	173	45	z√	z√	PROPN
ejpam-5731	173	46	1−	1−	NUM
ejpam-5731	173	47	(	(	PUNCT
ejpam-5731	173	48	2	2	NUM
ejpam-5731	173	49	cos	cos	PROPN
ejpam-5731	173	50	θ)z	θ)z	PROPN
ejpam-5731	174	1	+	+	X
ejpam-5731	174	2	z2	z2	PROPN
ejpam-5731	174	3	.	.	PUNCT
ejpam-5731	175	1	notably	notably	ADV
ejpam-5731	175	2	,	,	PUNCT
ejpam-5731	175	3	the	the	DET
ejpam-5731	175	4	function	function	NOUN
ejpam-5731	175	5	ϕ(z	ϕ(z	PROPN
ejpam-5731	175	6	)	)	PUNCT
ejpam-5731	175	7	transforms	transform	VERB
ejpam-5731	175	8	the	the	DET
ejpam-5731	175	9	open	open	ADJ
ejpam-5731	175	10	unit	unit	NOUN
ejpam-5731	175	11	disk	disk	NOUN
ejpam-5731	175	12	d	d	PROPN
ejpam-5731	175	13	onto	onto	ADP
ejpam-5731	175	14	the	the	DET
ejpam-5731	175	15	right	right	ADJ
ejpam-5731	175	16	half	half	ADJ
ejpam-5731	175	17	-	-	PUNCT
ejpam-5731	175	18	plane	plane	NOUN
ejpam-5731	175	19	r(w	r(w	PROPN
ejpam-5731	175	20	)	)	PUNCT
ejpam-5731	175	21	>	>	X
ejpam-5731	175	22	0	0	NUM
ejpam-5731	175	23	,	,	PUNCT
ejpam-5731	175	24	with	with	ADP
ejpam-5731	175	25	the	the	DET
ejpam-5731	175	26	exception	exception	NOUN
ejpam-5731	175	27	of	of	ADP
ejpam-5731	175	28	the	the	DET
ejpam-5731	175	29	slit	slit	NOUN
ejpam-5731	175	30	along	along	ADP
ejpam-5731	175	31	the	the	DET
ejpam-5731	175	32	positive	positive	ADJ
ejpam-5731	175	33	real	real	ADJ
ejpam-5731	175	34	axis	axis	NOUN
ejpam-5731	175	35	extending	extend	VERB
ejpam-5731	175	36	from	from	ADP
ejpam-5731	175	37	|cos(α/2)|−1	|cos(α/2)|−1	VERB
ejpam-5731	175	38	to	to	ADP
ejpam-5731	175	39	infinity	infinity	NOUN
ejpam-5731	175	40	.	.	PUNCT
ejpam-5731	176	1	consequently	consequently	ADV
ejpam-5731	176	2	,	,	PUNCT
ejpam-5731	176	3	ϕ	ϕ	PROPN
ejpam-5731	176	4	exhibits	exhibit	VERB
ejpam-5731	176	5	starlikeness	starlikeness	NOUN
ejpam-5731	176	6	with	with	ADP
ejpam-5731	176	7	respect	respect	NOUN
ejpam-5731	176	8	to	to	ADP
ejpam-5731	176	9	the	the	DET
ejpam-5731	176	10	point	point	NOUN
ejpam-5731	176	11	1	1	NUM
ejpam-5731	176	12	.	.	PUNCT
ejpam-5731	176	13	by	by	ADP
ejpam-5731	176	14	consulting	consult	VERB
ejpam-5731	176	15	equation	equation	NOUN
ejpam-5731	176	16	(	(	PUNCT
ejpam-5731	176	17	6	6	NUM
ejpam-5731	176	18	)	)	PUNCT
ejpam-5731	176	19	,	,	PUNCT
ejpam-5731	176	20	it	it	PRON
ejpam-5731	176	21	is	be	AUX
ejpam-5731	176	22	straightforward	straightforward	ADJ
ejpam-5731	176	23	to	to	PART
ejpam-5731	176	24	verify	verify	VERB
ejpam-5731	176	25	the	the	DET
ejpam-5731	176	26	following	follow	VERB
ejpam-5731	176	27	equation	equation	NOUN
ejpam-5731	176	28	,	,	PUNCT
ejpam-5731	176	29	for	for	ADP
ejpam-5731	176	30	any	any	DET
ejpam-5731	176	31	z	z	NOUN
ejpam-5731	176	32	within	within	ADP
ejpam-5731	176	33	the	the	DET
ejpam-5731	176	34	open	open	ADJ
ejpam-5731	176	35	unit	unit	NOUN
ejpam-5731	176	36	disk	disk	NOUN
ejpam-5731	176	37	d.	d.	PROPN
ejpam-5731	176	38	l(z	l(z	PROPN
ejpam-5731	176	39	)	)	PUNCT
ejpam-5731	177	1	=	=	SYM
ejpam-5731	177	2	1	1	NUM
ejpam-5731	177	3	+	+	NUM
ejpam-5731	177	4	∞∑	∞∑	NUM
ejpam-5731	177	5	n=1	n=1	PUNCT
ejpam-5731	178	1	[	[	X
ejpam-5731	178	2	pn(cos	pn(cos	PROPN
ejpam-5731	178	3	θ)−	θ)−	PROPN
ejpam-5731	178	4	pn−1(cos	pn−1(cos	PROPN
ejpam-5731	178	5	θ	θ	PROPN
ejpam-5731	178	6	)	)	PUNCT
ejpam-5731	178	7	]	]	PUNCT
ejpam-5731	179	1	z	z	NOUN
ejpam-5731	179	2	n	n	CCONJ
ejpam-5731	179	3	(	(	PUNCT
ejpam-5731	179	4	7	7	X
ejpam-5731	179	5	)	)	PUNCT
ejpam-5731	179	6	=	=	NOUN
ejpam-5731	179	7	1	1	NUM
ejpam-5731	179	8	+	+	NUM
ejpam-5731	179	9	∞∑	∞∑	NUM
ejpam-5731	179	10	n=1	n=1	PROPN
ejpam-5731	179	11	βn(θ)z	βn(θ)z	PROPN
ejpam-5731	179	12	n.	n.	PROPN
ejpam-5731	179	13	(	(	PUNCT
ejpam-5731	179	14	8)	8)	NUM
ejpam-5731	179	15	w.	w.	PROPN
ejpam-5731	179	16	al	al	PROPN
ejpam-5731	179	17	-	-	PUNCT
ejpam-5731	179	18	rawashdeh	rawashdeh	PROPN
ejpam-5731	179	19	/	/	SYM
ejpam-5731	179	20	eur	eur	PROPN
ejpam-5731	179	21	.	.	PUNCT
ejpam-5731	180	1	j.	j.	PROPN
ejpam-5731	180	2	pure	pure	PROPN
ejpam-5731	180	3	appl	appl	PROPN
ejpam-5731	180	4	.	.	PROPN
ejpam-5731	180	5	math	math	PROPN
ejpam-5731	180	6	,	,	PUNCT
ejpam-5731	180	7	18	18	NUM
ejpam-5731	180	8	(	(	PUNCT
ejpam-5731	180	9	1	1	NUM
ejpam-5731	180	10	)	)	PUNCT
ejpam-5731	180	11	(	(	PUNCT
ejpam-5731	180	12	2025	2025	NUM
ejpam-5731	180	13	)	)	PUNCT
ejpam-5731	180	14	,	,	PUNCT
ejpam-5731	180	15	5731	5731	NUM
ejpam-5731	180	16	9	9	NUM
ejpam-5731	180	17	of	of	ADP
ejpam-5731	180	18	20	20	NUM
ejpam-5731	180	19	using	use	VERB
ejpam-5731	180	20	the	the	DET
ejpam-5731	180	21	rodregue	rodregue	NOUN
ejpam-5731	180	22	’s	’s	PART
ejpam-5731	180	23	formula	formula	NOUN
ejpam-5731	180	24	(	(	PUNCT
ejpam-5731	180	25	5	5	NUM
ejpam-5731	180	26	)	)	PUNCT
ejpam-5731	180	27	,	,	PUNCT
ejpam-5731	180	28	we	we	PRON
ejpam-5731	180	29	easily	easily	ADV
ejpam-5731	180	30	obtain	obtain	VERB
ejpam-5731	180	31	the	the	DET
ejpam-5731	180	32	following	following	ADJ
ejpam-5731	180	33	initial	initial	ADJ
ejpam-5731	180	34	values	value	NOUN
ejpam-5731	180	35	of	of	ADP
ejpam-5731	180	36	βn(θ	βn(θ	PUNCT
ejpam-5731	180	37	)	)	PUNCT
ejpam-5731	180	38	=	=	SYM
ejpam-5731	180	39	pn(cos	pn(co	NOUN
ejpam-5731	180	40	θ)−	θ)−	PROPN
ejpam-5731	180	41	pn−1(cos	pn−1(cos	PROPN
ejpam-5731	180	42	θ	θ	PROPN
ejpam-5731	180	43	)	)	PUNCT
ejpam-5731	180	44	which	which	PRON
ejpam-5731	180	45	are	be	AUX
ejpam-5731	180	46	listed	list	VERB
ejpam-5731	180	47	below	below	ADP
ejpam-5731	180	48	:	:	PUNCT
ejpam-5731	180	49	β1(θ	β1(θ	X
ejpam-5731	180	50	)	)	PUNCT
ejpam-5731	180	51	=	=	PUNCT
ejpam-5731	181	1	cos	cos	ADP
ejpam-5731	181	2	θ	θ	PROPN
ejpam-5731	181	3	−	−	PROPN
ejpam-5731	181	4	1	1	NUM
ejpam-5731	181	5	,	,	PUNCT
ejpam-5731	181	6	β2(θ	β2(θ	NUM
ejpam-5731	181	7	)	)	PUNCT
ejpam-5731	181	8	=	=	SYM
ejpam-5731	181	9	1	1	NUM
ejpam-5731	181	10	2	2	NUM
ejpam-5731	181	11	(	(	PUNCT
ejpam-5731	181	12	cos	cos	PROPN
ejpam-5731	181	13	θ	θ	PROPN
ejpam-5731	181	14	−	−	NUM
ejpam-5731	181	15	1)(1	1)(1	NUM
ejpam-5731	181	16	+	+	CCONJ
ejpam-5731	181	17	3	3	NUM
ejpam-5731	181	18	cos	cos	NOUN
ejpam-5731	181	19	θ	θ	PROPN
ejpam-5731	181	20	)	)	PUNCT
ejpam-5731	181	21	.	.	PUNCT
ejpam-5731	182	1	additional	additional	ADJ
ejpam-5731	182	2	information	information	NOUN
ejpam-5731	182	3	regarding	regard	VERB
ejpam-5731	182	4	the	the	DET
ejpam-5731	182	5	legengre	legengre	NOUN
ejpam-5731	182	6	polynomials	polynomial	NOUN
ejpam-5731	182	7	readers	reader	NOUN
ejpam-5731	182	8	are	be	AUX
ejpam-5731	182	9	encouraged	encourage	VERB
ejpam-5731	182	10	to	to	PART
ejpam-5731	182	11	consult	consult	VERB
ejpam-5731	182	12	the	the	DET
ejpam-5731	182	13	articles	article	NOUN
ejpam-5731	182	14	referenced	reference	VERB
ejpam-5731	182	15	as	as	ADP
ejpam-5731	182	16	[	[	X
ejpam-5731	182	17	1	1	NUM
ejpam-5731	182	18	]	]	PUNCT
ejpam-5731	182	19	,	,	PUNCT
ejpam-5731	182	20	[	[	X
ejpam-5731	182	21	2	2	NUM
ejpam-5731	182	22	]	]	PUNCT
ejpam-5731	182	23	,	,	PUNCT
ejpam-5731	182	24	[	[	X
ejpam-5731	182	25	5	5	NUM
ejpam-5731	182	26	]	]	PUNCT
ejpam-5731	182	27	,	,	PUNCT
ejpam-5731	182	28	[	[	X
ejpam-5731	182	29	7	7	NUM
ejpam-5731	182	30	]	]	PUNCT
ejpam-5731	182	31	,	,	PUNCT
ejpam-5731	182	32	[	[	X
ejpam-5731	182	33	13	13	NUM
ejpam-5731	182	34	]	]	PUNCT
ejpam-5731	182	35	,	,	PUNCT
ejpam-5731	182	36	[	[	X
ejpam-5731	182	37	35	35	NUM
ejpam-5731	182	38	]	]	PUNCT
ejpam-5731	182	39	and	and	CCONJ
ejpam-5731	182	40	[	[	X
ejpam-5731	182	41	41	41	NUM
ejpam-5731	182	42	]	]	PUNCT
ejpam-5731	182	43	,	,	PUNCT
ejpam-5731	182	44	as	as	ADV
ejpam-5731	182	45	well	well	ADV
ejpam-5731	182	46	as	as	ADP
ejpam-5731	182	47	the	the	DET
ejpam-5731	182	48	monographs	monograph	NOUN
ejpam-5731	182	49	[	[	X
ejpam-5731	182	50	18	18	NUM
ejpam-5731	182	51	]	]	PUNCT
ejpam-5731	182	52	,	,	PUNCT
ejpam-5731	182	53	[	[	X
ejpam-5731	182	54	21	21	NUM
ejpam-5731	182	55	]	]	PUNCT
ejpam-5731	182	56	,	,	PUNCT
ejpam-5731	182	57	[	[	X
ejpam-5731	182	58	42	42	NUM
ejpam-5731	182	59	]	]	PUNCT
ejpam-5731	182	60	,	,	PUNCT
ejpam-5731	182	61	[	[	X
ejpam-5731	182	62	49	49	NUM
ejpam-5731	182	63	]	]	PUNCT
ejpam-5731	182	64	,	,	PUNCT
ejpam-5731	182	65	and	and	CCONJ
ejpam-5731	182	66	the	the	DET
ejpam-5731	182	67	related	related	ADJ
ejpam-5731	182	68	sources	source	NOUN
ejpam-5731	182	69	.	.	PUNCT
ejpam-5731	183	1	expanding	expand	VERB
ejpam-5731	183	2	on	on	ADP
ejpam-5731	183	3	these	these	DET
ejpam-5731	183	4	foundational	foundational	ADJ
ejpam-5731	183	5	concepts	concept	NOUN
ejpam-5731	183	6	,	,	PUNCT
ejpam-5731	183	7	our	our	PRON
ejpam-5731	183	8	objective	objective	NOUN
ejpam-5731	183	9	is	be	AUX
ejpam-5731	183	10	to	to	PART
ejpam-5731	183	11	introduce	introduce	VERB
ejpam-5731	183	12	a	a	DET
ejpam-5731	183	13	novel	novel	ADJ
ejpam-5731	183	14	class	class	NOUN
ejpam-5731	183	15	.	.	PUNCT
ejpam-5731	184	1	this	this	DET
ejpam-5731	184	2	class	class	NOUN
ejpam-5731	184	3	is	be	AUX
ejpam-5731	184	4	comprised	comprise	VERB
ejpam-5731	184	5	of	of	ADP
ejpam-5731	184	6	bi	bi	ADJ
ejpam-5731	184	7	-	-	ADJ
ejpam-5731	184	8	bazilevic	bazilevic	ADJ
ejpam-5731	184	9	functions	function	NOUN
ejpam-5731	184	10	characterized	characterize	VERB
ejpam-5731	184	11	by	by	ADP
ejpam-5731	184	12	the	the	DET
ejpam-5731	184	13	q	q	NOUN
ejpam-5731	184	14	-	-	PUNCT
ejpam-5731	184	15	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	184	16	differential	differential	ADJ
ejpam-5731	184	17	operator	operator	NOUN
ejpam-5731	184	18	associated	associate	VERB
ejpam-5731	184	19	with	with	ADP
ejpam-5731	184	20	legendre	legendre	PROPN
ejpam-5731	184	21	polynomials	polynomial	NOUN
ejpam-5731	184	22	.	.	PUNCT
ejpam-5731	185	1	we	we	PRON
ejpam-5731	185	2	denote	denote	VERB
ejpam-5731	185	3	this	this	DET
ejpam-5731	185	4	class	class	NOUN
ejpam-5731	185	5	asbλ(δ	asbλ(δ	PROPN
ejpam-5731	185	6	,	,	PUNCT
ejpam-5731	185	7	rαq	rαq	PROPN
ejpam-5731	185	8	,	,	PUNCT
ejpam-5731	185	9	ϕ	ϕ	NOUN
ejpam-5731	185	10	)	)	PUNCT
ejpam-5731	185	11	,	,	PUNCT
ejpam-5731	185	12	and	and	CCONJ
ejpam-5731	185	13	we	we	PRON
ejpam-5731	185	14	next	next	ADV
ejpam-5731	185	15	provide	provide	VERB
ejpam-5731	185	16	a	a	DET
ejpam-5731	185	17	formal	formal	ADJ
ejpam-5731	185	18	definition	definition	NOUN
ejpam-5731	185	19	for	for	ADP
ejpam-5731	185	20	this	this	DET
ejpam-5731	185	21	class	class	NOUN
ejpam-5731	185	22	.	.	PUNCT
ejpam-5731	186	1	definition	definition	NOUN
ejpam-5731	186	2	1	1	NUM
ejpam-5731	186	3	.	.	PUNCT
ejpam-5731	187	1	a	a	DET
ejpam-5731	187	2	function	function	NOUN
ejpam-5731	187	3	f(z	f(z	PROPN
ejpam-5731	187	4	)	)	PUNCT
ejpam-5731	187	5	belongs	belong	VERB
ejpam-5731	187	6	to	to	ADP
ejpam-5731	187	7	the	the	DET
ejpam-5731	187	8	family	family	NOUN
ejpam-5731	187	9	σ	σ	PROPN
ejpam-5731	187	10	is	be	AUX
ejpam-5731	187	11	considered	consider	VERB
ejpam-5731	187	12	to	to	PART
ejpam-5731	187	13	be	be	AUX
ejpam-5731	187	14	part	part	NOUN
ejpam-5731	187	15	of	of	ADP
ejpam-5731	187	16	the	the	DET
ejpam-5731	187	17	class	class	NOUN
ejpam-5731	187	18	bλ(δ	bλ(δ	NOUN
ejpam-5731	187	19	,	,	PUNCT
ejpam-5731	187	20	rαq	rαq	NOUN
ejpam-5731	187	21	,	,	PUNCT
ejpam-5731	187	22	ϕ	ϕ	PROPN
ejpam-5731	187	23	)	)	PUNCT
ejpam-5731	187	24	if	if	SCONJ
ejpam-5731	187	25	it	it	PRON
ejpam-5731	187	26	obeys	obey	VERB
ejpam-5731	187	27	the	the	DET
ejpam-5731	187	28	following	follow	VERB
ejpam-5731	187	29	subordination	subordination	NOUN
ejpam-5731	187	30	conditions	condition	NOUN
ejpam-5731	187	31	:	:	PUNCT
ejpam-5731	187	32	eiδz1−λ	eiδz1−λ	PROPN
ejpam-5731	187	33	(	(	PUNCT
ejpam-5731	187	34	rαq	rαq	PROPN
ejpam-5731	187	35	f(z	f(z	PROPN
ejpam-5731	187	36	)	)	PUNCT
ejpam-5731	187	37	)	)	PUNCT
ejpam-5731	188	1	′	′	NUM
ejpam-5731	188	2	(	(	PUNCT
ejpam-5731	188	3	rαq	rαq	PROPN
ejpam-5731	188	4	f(z	f(z	PROPN
ejpam-5731	188	5	)	)	PUNCT
ejpam-5731	188	6	)	)	PUNCT
ejpam-5731	189	1	1−λ	1−λ	NUM
ejpam-5731	189	2	≺	≺	NOUN
ejpam-5731	189	3	ϕ(z	ϕ(z	NOUN
ejpam-5731	189	4	)	)	PUNCT
ejpam-5731	189	5	cos	cos	ADP
ejpam-5731	189	6	δ	δ	PROPN
ejpam-5731	190	1	+	+	CCONJ
ejpam-5731	190	2	i	i	PRON
ejpam-5731	190	3	sin	sin	VERB
ejpam-5731	190	4	δ	δ	PROPN
ejpam-5731	190	5	,	,	PUNCT
ejpam-5731	190	6	and	and	CCONJ
ejpam-5731	190	7	eiδw1−λ	eiδw1−λ	PROPN
ejpam-5731	190	8	(	(	PUNCT
ejpam-5731	190	9	rαq	rαq	PROPN
ejpam-5731	190	10	g(w))′	g(w))′	PROPN
ejpam-5731	190	11	(	(	PUNCT
ejpam-5731	190	12	rαq	rαq	PROPN
ejpam-5731	190	13	g(w	g(w	PROPN
ejpam-5731	190	14	)	)	PUNCT
ejpam-5731	190	15	)	)	PUNCT
ejpam-5731	191	1	1−λ	1−λ	NUM
ejpam-5731	191	2	≺	≺	NOUN
ejpam-5731	191	3	ϕ(w	ϕ(w	NOUN
ejpam-5731	191	4	)	)	PUNCT
ejpam-5731	191	5	cos	cos	ADP
ejpam-5731	191	6	δ	δ	PROPN
ejpam-5731	192	1	+	+	CCONJ
ejpam-5731	192	2	i	i	PRON
ejpam-5731	192	3	sin	sin	VERB
ejpam-5731	192	4	δ	δ	PROPN
ejpam-5731	192	5	,	,	PUNCT
ejpam-5731	192	6	where	where	SCONJ
ejpam-5731	192	7	the	the	DET
ejpam-5731	192	8	function	function	NOUN
ejpam-5731	192	9	g(w	g(w	PROPN
ejpam-5731	192	10	)	)	PUNCT
ejpam-5731	192	11	=	=	SYM
ejpam-5731	192	12	f−1(w	f−1(w	PROPN
ejpam-5731	192	13	)	)	PUNCT
ejpam-5731	192	14	is	be	AUX
ejpam-5731	192	15	given	give	VERB
ejpam-5731	192	16	by	by	ADP
ejpam-5731	192	17	the	the	DET
ejpam-5731	192	18	equation	equation	NOUN
ejpam-5731	192	19	(	(	PUNCT
ejpam-5731	192	20	2	2	NUM
ejpam-5731	192	21	)	)	PUNCT
ejpam-5731	192	22	,	,	PUNCT
ejpam-5731	192	23	the	the	DET
ejpam-5731	192	24	parameters	parameter	NOUN
ejpam-5731	192	25	λ	λ	X
ejpam-5731	192	26	≥	≥	NOUN
ejpam-5731	192	27	0	0	NUM
ejpam-5731	192	28	,	,	PUNCT
ejpam-5731	192	29	0	0	PUNCT
ejpam-5731	192	30	<	<	X
ejpam-5731	192	31	q	q	X
ejpam-5731	192	32	<	<	X
ejpam-5731	192	33	1	1	NUM
ejpam-5731	192	34	,	,	PUNCT
ejpam-5731	192	35	α	α	NOUN
ejpam-5731	192	36	>	>	X
ejpam-5731	192	37	−1	−1	NOUN
ejpam-5731	192	38	,	,	PUNCT
ejpam-5731	192	39	and	and	CCONJ
ejpam-5731	192	40	δ	δ	PROPN
ejpam-5731	192	41	∈	∈	PROPN
ejpam-5731	192	42	(	(	PUNCT
ejpam-5731	192	43	−π	−π	ADV
ejpam-5731	192	44	2	2	NUM
ejpam-5731	192	45	,	,	PUNCT
ejpam-5731	192	46	π	π	PROPN
ejpam-5731	192	47	2	2	NUM
ejpam-5731	192	48	)	)	PUNCT
ejpam-5731	192	49	.	.	PUNCT
ejpam-5731	193	1	the	the	DET
ejpam-5731	193	2	following	follow	VERB
ejpam-5731	193	3	lemma	lemma	PROPN
ejpam-5731	193	4	,	,	PUNCT
ejpam-5731	193	5	extensively	extensively	ADV
ejpam-5731	193	6	elaborated	elaborate	VERB
ejpam-5731	193	7	upon	upon	SCONJ
ejpam-5731	193	8	in	in	ADP
ejpam-5731	193	9	existing	exist	VERB
ejpam-5731	193	10	literature	literature	NOUN
ejpam-5731	193	11	,	,	PUNCT
ejpam-5731	193	12	represents	represent	VERB
ejpam-5731	193	13	well	well	ADV
ejpam-5731	193	14	-	-	PUNCT
ejpam-5731	193	15	established	establish	VERB
ejpam-5731	193	16	principles	principle	NOUN
ejpam-5731	193	17	that	that	PRON
ejpam-5731	193	18	hold	hold	VERB
ejpam-5731	193	19	significant	significant	ADJ
ejpam-5731	193	20	importance	importance	NOUN
ejpam-5731	193	21	for	for	ADP
ejpam-5731	193	22	the	the	DET
ejpam-5731	193	23	research	research	NOUN
ejpam-5731	193	24	we	we	PRON
ejpam-5731	193	25	are	be	AUX
ejpam-5731	193	26	currently	currently	ADV
ejpam-5731	193	27	presenting	present	VERB
ejpam-5731	193	28	.	.	PUNCT
ejpam-5731	194	1	lemma	lemma	PROPN
ejpam-5731	194	2	1	1	NUM
ejpam-5731	194	3	.	.	PUNCT
ejpam-5731	195	1	[	[	X
ejpam-5731	195	2	26	26	NUM
ejpam-5731	195	3	]	]	X
ejpam-5731	195	4	if	if	SCONJ
ejpam-5731	195	5	ω	ω	NOUN
ejpam-5731	195	6	belongs	belong	VERB
ejpam-5731	195	7	to	to	ADP
ejpam-5731	195	8	the	the	DET
ejpam-5731	195	9	caratheodory	caratheodory	ADJ
ejpam-5731	195	10	class	class	NOUN
ejpam-5731	195	11	,	,	PUNCT
ejpam-5731	195	12	then	then	ADV
ejpam-5731	195	13	for	for	ADP
ejpam-5731	195	14	z	z	PROPN
ejpam-5731	195	15	∈	∈	PROPN
ejpam-5731	195	16	d	d	X
ejpam-5731	195	17	the	the	DET
ejpam-5731	195	18	function	function	NOUN
ejpam-5731	195	19	ω	ω	NOUN
ejpam-5731	195	20	can	can	AUX
ejpam-5731	195	21	be	be	AUX
ejpam-5731	195	22	written	write	VERB
ejpam-5731	195	23	as	as	ADP
ejpam-5731	195	24	ω(z	ω(z	ADJ
ejpam-5731	195	25	)	)	PUNCT
ejpam-5731	195	26	=	=	SYM
ejpam-5731	196	1	1	1	NUM
ejpam-5731	197	1	+	+	CCONJ
ejpam-5731	197	2	c1z	c1z	PROPN
ejpam-5731	198	1	+	+	CCONJ
ejpam-5731	198	2	c2z	c2z	PROPN
ejpam-5731	198	3	2	2	NUM
ejpam-5731	198	4	+	+	CCONJ
ejpam-5731	198	5	c3z	c3z	X
ejpam-5731	198	6	3	3	NUM
ejpam-5731	198	7	+	+	NOUN
ejpam-5731	198	8	·	·	PUNCT
ejpam-5731	198	9	·	·	PUNCT
ejpam-5731	198	10	·	·	PUNCT
ejpam-5731	198	11	moreover	moreover	ADV
ejpam-5731	198	12	,	,	PUNCT
ejpam-5731	198	13	|cn|	|cn|	ADJ
ejpam-5731	198	14	≤	≤	ADV
ejpam-5731	198	15	2	2	NUM
ejpam-5731	198	16	for	for	ADP
ejpam-5731	198	17	each	each	DET
ejpam-5731	198	18	natural	natural	ADJ
ejpam-5731	198	19	number	number	NOUN
ejpam-5731	198	20	n.	n.	NOUN
ejpam-5731	198	21	the	the	DET
ejpam-5731	198	22	lemma	lemma	PROPN
ejpam-5731	198	23	presented	present	VERB
ejpam-5731	198	24	in	in	ADP
ejpam-5731	198	25	the	the	DET
ejpam-5731	198	26	following	follow	VERB
ejpam-5731	198	27	discussion	discussion	NOUN
ejpam-5731	198	28	is	be	AUX
ejpam-5731	198	29	extensively	extensively	ADV
ejpam-5731	198	30	referenced	reference	VERB
ejpam-5731	198	31	in	in	ADP
ejpam-5731	198	32	existing	exist	VERB
ejpam-5731	198	33	literature	literature	NOUN
ejpam-5731	198	34	and	and	CCONJ
ejpam-5731	198	35	is	be	AUX
ejpam-5731	198	36	regarded	regard	VERB
ejpam-5731	198	37	as	as	ADP
ejpam-5731	198	38	a	a	DET
ejpam-5731	198	39	foundational	foundational	ADJ
ejpam-5731	198	40	principle	principle	NOUN
ejpam-5731	198	41	that	that	PRON
ejpam-5731	198	42	significantly	significantly	ADV
ejpam-5731	198	43	influences	influence	VERB
ejpam-5731	198	44	the	the	DET
ejpam-5731	198	45	research	research	NOUN
ejpam-5731	198	46	we	we	PRON
ejpam-5731	198	47	are	be	AUX
ejpam-5731	198	48	conducting	conduct	VERB
ejpam-5731	198	49	.	.	PUNCT
ejpam-5731	199	1	lemma	lemma	PROPN
ejpam-5731	199	2	2	2	NUM
ejpam-5731	199	3	.	.	PUNCT
ejpam-5731	200	1	[	[	X
ejpam-5731	200	2	26	26	NUM
ejpam-5731	200	3	]	]	X
ejpam-5731	200	4	let	let	VERB
ejpam-5731	200	5	k	k	NOUN
ejpam-5731	200	6	and	and	CCONJ
ejpam-5731	200	7	l	l	NOUN
ejpam-5731	200	8	be	be	AUX
ejpam-5731	200	9	real	real	ADJ
ejpam-5731	200	10	numbers	number	NOUN
ejpam-5731	200	11	.	.	PUNCT
ejpam-5731	201	1	let	let	VERB
ejpam-5731	201	2	p	p	NOUN
ejpam-5731	201	3	and	and	CCONJ
ejpam-5731	201	4	q	q	AUX
ejpam-5731	201	5	be	be	AUX
ejpam-5731	201	6	complex	complex	ADJ
ejpam-5731	201	7	numbers	number	NOUN
ejpam-5731	201	8	.	.	PUNCT
ejpam-5731	202	1	if	if	SCONJ
ejpam-5731	202	2	|p|	|p|	PRON
ejpam-5731	202	3	<	<	X
ejpam-5731	202	4	r	r	NOUN
ejpam-5731	202	5	and	and	CCONJ
ejpam-5731	202	6	|q|	|q|	VERB
ejpam-5731	202	7	<	<	X
ejpam-5731	202	8	r	r	NOUN
ejpam-5731	202	9	,	,	PUNCT
ejpam-5731	202	10	|(k	|(k	NOUN
ejpam-5731	203	1	+	+	CCONJ
ejpam-5731	203	2	l)p+	l)p+	NUM
ejpam-5731	203	3	(	(	PUNCT
ejpam-5731	203	4	k	k	PROPN
ejpam-5731	203	5	−	−	PROPN
ejpam-5731	203	6	l)q|	l)q|	PROPN
ejpam-5731	203	7	≤	≤	PROPN
ejpam-5731	203	8	{	{	PUNCT
ejpam-5731	203	9	2r|k|	2r|k|	NUM
ejpam-5731	203	10	,	,	PUNCT
ejpam-5731	203	11	if	if	SCONJ
ejpam-5731	203	12	|k|	|k|	PRON
ejpam-5731	203	13	≥	≥	VERB
ejpam-5731	203	14	|l|	|l|	VERB
ejpam-5731	203	15	2r|l|	2r|l|	NUM
ejpam-5731	203	16	,	,	PUNCT
ejpam-5731	203	17	if	if	SCONJ
ejpam-5731	203	18	|k|	|k|	PRON
ejpam-5731	203	19	≤	≤	VERB
ejpam-5731	203	20	|l|	|l|	VERB
ejpam-5731	203	21	.	.	PUNCT
ejpam-5731	204	1	w.	w.	PROPN
ejpam-5731	204	2	al	al	PROPN
ejpam-5731	204	3	-	-	PUNCT
ejpam-5731	204	4	rawashdeh	rawashdeh	PROPN
ejpam-5731	204	5	/	/	SYM
ejpam-5731	204	6	eur	eur	PROPN
ejpam-5731	204	7	.	.	PUNCT
ejpam-5731	205	1	j.	j.	PROPN
ejpam-5731	205	2	pure	pure	PROPN
ejpam-5731	205	3	appl	appl	PROPN
ejpam-5731	205	4	.	.	PROPN
ejpam-5731	205	5	math	math	PROPN
ejpam-5731	205	6	,	,	PUNCT
ejpam-5731	205	7	18	18	NUM
ejpam-5731	205	8	(	(	PUNCT
ejpam-5731	205	9	1	1	NUM
ejpam-5731	205	10	)	)	PUNCT
ejpam-5731	205	11	(	(	PUNCT
ejpam-5731	205	12	2025	2025	NUM
ejpam-5731	205	13	)	)	PUNCT
ejpam-5731	205	14	,	,	PUNCT
ejpam-5731	205	15	5731	5731	NUM
ejpam-5731	205	16	10	10	NUM
ejpam-5731	205	17	of	of	ADP
ejpam-5731	205	18	20	20	NUM
ejpam-5731	206	1	this	this	DET
ejpam-5731	206	2	paper	paper	NOUN
ejpam-5731	206	3	seeks	seek	VERB
ejpam-5731	206	4	to	to	PART
ejpam-5731	206	5	explore	explore	VERB
ejpam-5731	206	6	two	two	NUM
ejpam-5731	206	7	novel	novel	ADJ
ejpam-5731	206	8	categories	category	NOUN
ejpam-5731	206	9	of	of	ADP
ejpam-5731	206	10	bi	bi	ADJ
ejpam-5731	206	11	-	-	ADJ
ejpam-5731	206	12	bazilevic	bazilevic	ADJ
ejpam-5731	206	13	functions	function	NOUN
ejpam-5731	206	14	that	that	PRON
ejpam-5731	206	15	are	be	AUX
ejpam-5731	206	16	defined	define	VERB
ejpam-5731	206	17	through	through	ADP
ejpam-5731	206	18	the	the	DET
ejpam-5731	206	19	q	q	NOUN
ejpam-5731	206	20	-	-	PUNCT
ejpam-5731	206	21	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	206	22	operator	operator	NOUN
ejpam-5731	206	23	within	within	ADP
ejpam-5731	206	24	the	the	DET
ejpam-5731	206	25	open	open	ADJ
ejpam-5731	206	26	unit	unit	NOUN
ejpam-5731	206	27	disk	disk	NOUN
ejpam-5731	206	28	d	d	NOUN
ejpam-5731	206	29	,	,	PUNCT
ejpam-5731	206	30	with	with	ADP
ejpam-5731	206	31	a	a	DET
ejpam-5731	206	32	particular	particular	ADJ
ejpam-5731	206	33	connection	connection	NOUN
ejpam-5731	206	34	to	to	ADP
ejpam-5731	206	35	legendre	legendre	PROPN
ejpam-5731	206	36	polynomials	polynomial	NOUN
ejpam-5731	206	37	.	.	PUNCT
ejpam-5731	207	1	the	the	DET
ejpam-5731	207	2	central	central	ADJ
ejpam-5731	207	3	objective	objective	NOUN
ejpam-5731	207	4	is	be	AUX
ejpam-5731	207	5	to	to	PART
ejpam-5731	207	6	establish	establish	VERB
ejpam-5731	207	7	estimates	estimate	NOUN
ejpam-5731	207	8	for	for	ADP
ejpam-5731	207	9	the	the	DET
ejpam-5731	207	10	magnitudes	magnitude	NOUN
ejpam-5731	207	11	of	of	ADP
ejpam-5731	207	12	the	the	DET
ejpam-5731	207	13	initial	initial	ADJ
ejpam-5731	207	14	coefficients	coefficient	NOUN
ejpam-5731	207	15	|a2|	|a2|	VERB
ejpam-5731	207	16	and	and	CCONJ
ejpam-5731	207	17	|a3|	|a3|	NOUN
ejpam-5731	207	18	that	that	PRON
ejpam-5731	207	19	are	be	AUX
ejpam-5731	207	20	linked	link	VERB
ejpam-5731	207	21	to	to	ADP
ejpam-5731	207	22	the	the	DET
ejpam-5731	207	23	taylor	taylor	PROPN
ejpam-5731	207	24	-	-	PUNCT
ejpam-5731	207	25	maclaurin	maclaurin	PROPN
ejpam-5731	207	26	series	series	NOUN
ejpam-5731	207	27	representation	representation	NOUN
ejpam-5731	207	28	of	of	ADP
ejpam-5731	207	29	functions	function	NOUN
ejpam-5731	207	30	belonging	belong	VERB
ejpam-5731	207	31	to	to	ADP
ejpam-5731	207	32	this	this	DET
ejpam-5731	207	33	class	class	NOUN
ejpam-5731	207	34	.	.	PUNCT
ejpam-5731	208	1	additionally	additionally	ADV
ejpam-5731	208	2	,	,	PUNCT
ejpam-5731	208	3	the	the	DET
ejpam-5731	208	4	research	research	NOUN
ejpam-5731	208	5	delves	delve	VERB
ejpam-5731	208	6	into	into	ADP
ejpam-5731	208	7	the	the	DET
ejpam-5731	208	8	fekete	fekete	PROPN
ejpam-5731	208	9	-	-	PUNCT
ejpam-5731	208	10	szegö	szegö	ADJ
ejpam-5731	208	11	functional	functional	ADJ
ejpam-5731	208	12	problem	problem	NOUN
ejpam-5731	208	13	pertinent	pertinent	ADJ
ejpam-5731	208	14	to	to	ADP
ejpam-5731	208	15	these	these	DET
ejpam-5731	208	16	functions	function	NOUN
ejpam-5731	208	17	,	,	PUNCT
ejpam-5731	208	18	thereby	thereby	ADV
ejpam-5731	208	19	enhancing	enhance	VERB
ejpam-5731	208	20	the	the	DET
ejpam-5731	208	21	comprehension	comprehension	NOUN
ejpam-5731	208	22	of	of	ADP
ejpam-5731	208	23	their	their	PRON
ejpam-5731	208	24	inherent	inherent	ADJ
ejpam-5731	208	25	characteristics	characteristic	NOUN
ejpam-5731	208	26	.	.	PUNCT
ejpam-5731	209	1	moreover	moreover	ADV
ejpam-5731	209	2	,	,	PUNCT
ejpam-5731	209	3	some	some	DET
ejpam-5731	209	4	known	know	VERB
ejpam-5731	209	5	corollaries	corollary	NOUN
ejpam-5731	209	6	are	be	AUX
ejpam-5731	209	7	presented	present	VERB
ejpam-5731	209	8	based	base	VERB
ejpam-5731	209	9	on	on	ADP
ejpam-5731	209	10	the	the	DET
ejpam-5731	209	11	choices	choice	NOUN
ejpam-5731	209	12	of	of	ADP
ejpam-5731	209	13	the	the	DET
ejpam-5731	209	14	parameters	parameter	NOUN
ejpam-5731	209	15	involved	involve	VERB
ejpam-5731	209	16	in	in	ADP
ejpam-5731	209	17	defining	define	VERB
ejpam-5731	209	18	our	our	PRON
ejpam-5731	209	19	specific	specific	ADJ
ejpam-5731	209	20	class	class	NOUN
ejpam-5731	209	21	.	.	PUNCT
ejpam-5731	210	1	3	3	X
ejpam-5731	210	2	.	.	X
ejpam-5731	210	3	coefficient	coefficient	NOUN
ejpam-5731	210	4	bounds	bound	NOUN
ejpam-5731	210	5	of	of	ADP
ejpam-5731	210	6	the	the	DET
ejpam-5731	210	7	function	function	NOUN
ejpam-5731	210	8	class	class	NOUN
ejpam-5731	210	9	this	this	DET
ejpam-5731	210	10	section	section	NOUN
ejpam-5731	210	11	of	of	ADP
ejpam-5731	210	12	the	the	DET
ejpam-5731	210	13	paper	paper	NOUN
ejpam-5731	210	14	focuses	focus	VERB
ejpam-5731	210	15	on	on	ADP
ejpam-5731	210	16	investigating	investigate	VERB
ejpam-5731	210	17	the	the	DET
ejpam-5731	210	18	bounds	bound	NOUN
ejpam-5731	210	19	pertaining	pertain	VERB
ejpam-5731	210	20	to	to	ADP
ejpam-5731	210	21	the	the	DET
ejpam-5731	210	22	modulus	modulus	NOUN
ejpam-5731	210	23	of	of	ADP
ejpam-5731	210	24	the	the	DET
ejpam-5731	210	25	initial	initial	ADJ
ejpam-5731	210	26	coefficients	coefficient	NOUN
ejpam-5731	210	27	of	of	ADP
ejpam-5731	210	28	functions	function	NOUN
ejpam-5731	210	29	belonging	belong	VERB
ejpam-5731	210	30	to	to	ADP
ejpam-5731	210	31	the	the	DET
ejpam-5731	210	32	class	class	NOUN
ejpam-5731	210	33	bλ(δ	bλ(δ	NOUN
ejpam-5731	210	34	,	,	PUNCT
ejpam-5731	210	35	rαq	rαq	NOUN
ejpam-5731	210	36	,	,	PUNCT
ejpam-5731	210	37	ϕ	ϕ	PROPN
ejpam-5731	210	38	)	)	PUNCT
ejpam-5731	210	39	,	,	PUNCT
ejpam-5731	210	40	along	along	ADP
ejpam-5731	210	41	with	with	ADP
ejpam-5731	210	42	several	several	ADJ
ejpam-5731	210	43	of	of	ADP
ejpam-5731	210	44	its	its	PRON
ejpam-5731	210	45	distinct	distinct	ADJ
ejpam-5731	210	46	subclasses	subclass	NOUN
ejpam-5731	210	47	,	,	PUNCT
ejpam-5731	210	48	as	as	SCONJ
ejpam-5731	210	49	delineated	delineated	ADJ
ejpam-5731	210	50	in	in	ADP
ejpam-5731	210	51	equation	equation	NOUN
ejpam-5731	210	52	(	(	PUNCT
ejpam-5731	210	53	1	1	NUM
ejpam-5731	210	54	)	)	PUNCT
ejpam-5731	210	55	.	.	PUNCT
ejpam-5731	211	1	theorem	theorem	NOUN
ejpam-5731	211	2	1	1	NUM
ejpam-5731	211	3	.	.	PUNCT
ejpam-5731	212	1	let	let	VERB
ejpam-5731	212	2	a	a	DET
ejpam-5731	212	3	function	function	NOUN
ejpam-5731	212	4	f	f	X
ejpam-5731	212	5	be	be	AUX
ejpam-5731	212	6	in	in	ADP
ejpam-5731	212	7	the	the	DET
ejpam-5731	212	8	family	family	NOUN
ejpam-5731	212	9	σ	σ	PROPN
ejpam-5731	212	10	.	.	PUNCT
ejpam-5731	213	1	if	if	SCONJ
ejpam-5731	213	2	the	the	DET
ejpam-5731	213	3	function	function	NOUN
ejpam-5731	213	4	f	f	PROPN
ejpam-5731	213	5	belongs	belong	VERB
ejpam-5731	213	6	to	to	ADP
ejpam-5731	213	7	the	the	DET
ejpam-5731	213	8	class	class	NOUN
ejpam-5731	213	9	bλ(δ	bλ(δ	NOUN
ejpam-5731	213	10	,	,	PUNCT
ejpam-5731	213	11	rαq	rαq	NOUN
ejpam-5731	213	12	,	,	PUNCT
ejpam-5731	213	13	ϕ	ϕ	PROPN
ejpam-5731	213	14	)	)	PUNCT
ejpam-5731	213	15	and	and	CCONJ
ejpam-5731	213	16	is	be	AUX
ejpam-5731	213	17	represented	represent	VERB
ejpam-5731	213	18	by	by	ADP
ejpam-5731	213	19	the	the	DET
ejpam-5731	213	20	equation	equation	NOUN
ejpam-5731	213	21	(	(	PUNCT
ejpam-5731	213	22	1	1	NUM
ejpam-5731	213	23	)	)	PUNCT
ejpam-5731	213	24	,	,	PUNCT
ejpam-5731	213	25	then	then	ADV
ejpam-5731	213	26	the	the	DET
ejpam-5731	213	27	following	follow	VERB
ejpam-5731	213	28	inequalities	inequality	NOUN
ejpam-5731	213	29	hold	hold	VERB
ejpam-5731	213	30	:	:	PUNCT
ejpam-5731	213	31	|a2|	|a2|	NOUN
ejpam-5731	213	32	≤	≤	NUM
ejpam-5731	214	1	√	√	ADP
ejpam-5731	214	2	2|1−	2|1−	NUM
ejpam-5731	214	3	cos	cos	ADP
ejpam-5731	214	4	θ|	θ|	PROPN
ejpam-5731	214	5	cos	co	NOUN
ejpam-5731	214	6	δ√	δ√	PROPN
ejpam-5731	214	7	|a	|a	X
ejpam-5731	214	8	cos	cos	ADP
ejpam-5731	214	9	δ(cos	δ(cos	PROPN
ejpam-5731	214	10	θ	θ	PROPN
ejpam-5731	215	1	−	−	NOUN
ejpam-5731	215	2	1	1	NUM
ejpam-5731	215	3	)	)	PUNCT
ejpam-5731	215	4	+	+	CCONJ
ejpam-5731	215	5	(	(	PUNCT
ejpam-5731	215	6	1−	1−	NUM
ejpam-5731	215	7	3	3	NUM
ejpam-5731	215	8	cos	cos	X
ejpam-5731	215	9	θ)(λ+	θ)(λ+	NOUN
ejpam-5731	215	10	1)2ψ2	1)2ψ2	NUM
ejpam-5731	215	11	2e	2e	NOUN
ejpam-5731	215	12	iδ|	iδ|	PROPN
ejpam-5731	215	13	,	,	PUNCT
ejpam-5731	215	14	(	(	PUNCT
ejpam-5731	215	15	9	9	NUM
ejpam-5731	215	16	)	)	PUNCT
ejpam-5731	215	17	and	and	CCONJ
ejpam-5731	215	18	|a3|	|a3|	VERB
ejpam-5731	215	19	≤	≤	PROPN
ejpam-5731	215	20	|1−	|1−	PROPN
ejpam-5731	215	21	cos	cos	ADP
ejpam-5731	215	22	θ|	θ|	PROPN
ejpam-5731	215	23	cos	cos	PROPN
ejpam-5731	215	24	δ	δ	PROPN
ejpam-5731	215	25	(	(	PUNCT
ejpam-5731	215	26	λ+	λ+	PUNCT
ejpam-5731	215	27	2)ψ3	2)ψ3	NOUN
ejpam-5731	215	28	+	+	CCONJ
ejpam-5731	215	29	(	(	PUNCT
ejpam-5731	215	30	1−	1−	NUM
ejpam-5731	215	31	cos	cos	PROPN
ejpam-5731	215	32	θ)2	θ)2	PROPN
ejpam-5731	215	33	cos2	cos2	PROPN
ejpam-5731	215	34	δ	δ	PROPN
ejpam-5731	215	35	(	(	PUNCT
ejpam-5731	215	36	λ+	λ+	PUNCT
ejpam-5731	215	37	1)2ψ2	1)2ψ2	NUM
ejpam-5731	215	38	2	2	NUM
ejpam-5731	215	39	,	,	PUNCT
ejpam-5731	215	40	(	(	PUNCT
ejpam-5731	215	41	10	10	NUM
ejpam-5731	215	42	)	)	PUNCT
ejpam-5731	215	43	where	where	SCONJ
ejpam-5731	215	44	a	a	DET
ejpam-5731	215	45	=	=	SYM
ejpam-5731	215	46	2(λ+	2(λ+	PROPN
ejpam-5731	215	47	2)ψ3	2)ψ3	NOUN
ejpam-5731	215	48	+	+	CCONJ
ejpam-5731	215	49	(	(	PUNCT
ejpam-5731	215	50	λ−	λ−	PROPN
ejpam-5731	215	51	1)(λ+	1)(λ+	NUM
ejpam-5731	215	52	2)ψ2	2)ψ2	NUM
ejpam-5731	215	53	2	2	NUM
ejpam-5731	215	54	.	.	PUNCT
ejpam-5731	216	1	proof	proof	NOUN
ejpam-5731	216	2	.	.	PUNCT
ejpam-5731	217	1	suppose	suppose	VERB
ejpam-5731	217	2	a	a	DET
ejpam-5731	217	3	function	function	NOUN
ejpam-5731	217	4	f	f	PROPN
ejpam-5731	217	5	belongs	belong	VERB
ejpam-5731	217	6	to	to	ADP
ejpam-5731	217	7	the	the	DET
ejpam-5731	217	8	class	class	NOUN
ejpam-5731	217	9	b(λ	b(λ	PROPN
ejpam-5731	217	10	,	,	PUNCT
ejpam-5731	217	11	δ	δ	PROPN
ejpam-5731	217	12	,	,	PUNCT
ejpam-5731	217	13	rαη	rαη	VERB
ejpam-5731	217	14	,	,	PUNCT
ejpam-5731	217	15	β(t	β(t	PROPN
ejpam-5731	217	16	)	)	PUNCT
ejpam-5731	217	17	)	)	PUNCT
ejpam-5731	217	18	.	.	PUNCT
ejpam-5731	218	1	consulting	consult	VERB
ejpam-5731	218	2	the	the	DET
ejpam-5731	218	3	definition	definition	NOUN
ejpam-5731	218	4	1	1	NUM
ejpam-5731	218	5	and	and	CCONJ
ejpam-5731	218	6	subordination	subordination	NOUN
ejpam-5731	218	7	principle	principle	NOUN
ejpam-5731	218	8	,	,	PUNCT
ejpam-5731	218	9	we	we	PRON
ejpam-5731	218	10	can	can	AUX
ejpam-5731	218	11	find	find	VERB
ejpam-5731	218	12	two	two	NUM
ejpam-5731	218	13	schwarz	schwarz	PROPN
ejpam-5731	218	14	functions	function	NOUN
ejpam-5731	218	15	k(z	k(z	PROPN
ejpam-5731	218	16	)	)	PUNCT
ejpam-5731	218	17	and	and	CCONJ
ejpam-5731	218	18	h(w	h(w	PROPN
ejpam-5731	218	19	)	)	PUNCT
ejpam-5731	218	20	defined	define	VERB
ejpam-5731	218	21	on	on	ADP
ejpam-5731	218	22	the	the	DET
ejpam-5731	218	23	open	open	ADJ
ejpam-5731	218	24	unit	unit	NOUN
ejpam-5731	218	25	disk	disk	NOUN
ejpam-5731	218	26	d	d	NOUN
ejpam-5731	218	27	such	such	ADJ
ejpam-5731	218	28	that	that	PRON
ejpam-5731	218	29	eiδz1−λ	eiδz1−λ	PROPN
ejpam-5731	218	30	(	(	PUNCT
ejpam-5731	218	31	rαq	rαq	PROPN
ejpam-5731	218	32	f(z	f(z	PROPN
ejpam-5731	218	33	)	)	PUNCT
ejpam-5731	218	34	)	)	PUNCT
ejpam-5731	219	1	′	′	NUM
ejpam-5731	219	2	(	(	PUNCT
ejpam-5731	219	3	rαq	rαq	PROPN
ejpam-5731	219	4	f(z	f(z	PROPN
ejpam-5731	219	5	)	)	PUNCT
ejpam-5731	219	6	)	)	PUNCT
ejpam-5731	220	1	1−λ	1−λ	NUM
ejpam-5731	220	2	=	=	SYM
ejpam-5731	220	3	ϕ(k(z	ϕ(k(z	PROPN
ejpam-5731	220	4	)	)	PUNCT
ejpam-5731	220	5	)	)	PUNCT
ejpam-5731	221	1	cos	cos	PROPN
ejpam-5731	221	2	δ	δ	PROPN
ejpam-5731	222	1	+	+	CCONJ
ejpam-5731	222	2	i	i	PRON
ejpam-5731	222	3	sin	sin	VERB
ejpam-5731	222	4	δ	δ	PROPN
ejpam-5731	222	5	,	,	PUNCT
ejpam-5731	222	6	(	(	PUNCT
ejpam-5731	222	7	11	11	NUM
ejpam-5731	222	8	)	)	PUNCT
ejpam-5731	222	9	and	and	CCONJ
ejpam-5731	222	10	eiδw1−λ	eiδw1−λ	PROPN
ejpam-5731	222	11	(	(	PUNCT
ejpam-5731	222	12	rαq	rαq	PROPN
ejpam-5731	222	13	g(w))′	g(w))′	PROPN
ejpam-5731	222	14	(	(	PUNCT
ejpam-5731	222	15	rαq	rαq	PROPN
ejpam-5731	222	16	g(w	g(w	PROPN
ejpam-5731	222	17	)	)	PUNCT
ejpam-5731	222	18	)	)	PUNCT
ejpam-5731	222	19	1−λ	1−λ	NUM
ejpam-5731	222	20	=	=	SYM
ejpam-5731	222	21	ϕ(h(w	ϕ(h(w	PROPN
ejpam-5731	222	22	)	)	PUNCT
ejpam-5731	222	23	)	)	PUNCT
ejpam-5731	222	24	cos	cos	PROPN
ejpam-5731	223	1	δ	δ	PROPN
ejpam-5731	223	2	+	+	CCONJ
ejpam-5731	223	3	i	i	PRON
ejpam-5731	223	4	sin	sin	VERB
ejpam-5731	223	5	δ	δ	PROPN
ejpam-5731	223	6	.	.	PUNCT
ejpam-5731	224	1	(	(	PUNCT
ejpam-5731	224	2	12	12	NUM
ejpam-5731	224	3	)	)	PUNCT
ejpam-5731	224	4	now	now	ADV
ejpam-5731	224	5	,	,	PUNCT
ejpam-5731	224	6	using	use	VERB
ejpam-5731	224	7	those	those	DET
ejpam-5731	224	8	schwarz	schwarz	PROPN
ejpam-5731	224	9	functions	function	NOUN
ejpam-5731	224	10	,	,	PUNCT
ejpam-5731	224	11	we	we	PRON
ejpam-5731	224	12	define	define	VERB
ejpam-5731	224	13	two	two	NUM
ejpam-5731	224	14	new	new	ADJ
ejpam-5731	224	15	analytic	analytic	ADJ
ejpam-5731	224	16	functions	function	NOUN
ejpam-5731	224	17	η(z	η(z	PROPN
ejpam-5731	224	18	)	)	PUNCT
ejpam-5731	224	19	and	and	CCONJ
ejpam-5731	224	20	ζ(w	ζ(w	PROPN
ejpam-5731	224	21	)	)	PUNCT
ejpam-5731	224	22	as	as	SCONJ
ejpam-5731	224	23	follow	follow	VERB
ejpam-5731	224	24	:	:	PUNCT
ejpam-5731	224	25	η(z	η(z	PROPN
ejpam-5731	224	26	)	)	PUNCT
ejpam-5731	224	27	=	=	PUNCT
ejpam-5731	225	1	1	1	NUM
ejpam-5731	225	2	+	+	NUM
ejpam-5731	225	3	k(z	k(z	PROPN
ejpam-5731	225	4	)	)	PUNCT
ejpam-5731	226	1	1−	1−	NUM
ejpam-5731	226	2	k(z	k(z	PROPN
ejpam-5731	226	3	)	)	PUNCT
ejpam-5731	226	4	and	and	CCONJ
ejpam-5731	226	5	ζ(w	ζ(w	PROPN
ejpam-5731	226	6	)	)	PUNCT
ejpam-5731	226	7	=	=	SYM
ejpam-5731	226	8	1	1	NUM
ejpam-5731	226	9	+	+	CCONJ
ejpam-5731	226	10	h(w	h(w	PROPN
ejpam-5731	226	11	)	)	PUNCT
ejpam-5731	226	12	1−	1−	NUM
ejpam-5731	226	13	h(w	h(w	NOUN
ejpam-5731	226	14	)	)	PUNCT
ejpam-5731	226	15	.	.	PUNCT
ejpam-5731	227	1	it	it	PRON
ejpam-5731	227	2	is	be	AUX
ejpam-5731	227	3	clear	clear	ADJ
ejpam-5731	227	4	that	that	SCONJ
ejpam-5731	227	5	,	,	PUNCT
ejpam-5731	227	6	these	these	DET
ejpam-5731	227	7	functions	function	NOUN
ejpam-5731	227	8	η(z	η(z	PROPN
ejpam-5731	227	9	)	)	PUNCT
ejpam-5731	227	10	and	and	CCONJ
ejpam-5731	227	11	ζ(w	ζ(w	PROPN
ejpam-5731	227	12	)	)	PUNCT
ejpam-5731	227	13	are	be	AUX
ejpam-5731	227	14	analytic	analytic	ADJ
ejpam-5731	227	15	in	in	ADP
ejpam-5731	227	16	the	the	DET
ejpam-5731	227	17	open	open	ADJ
ejpam-5731	227	18	unit	unit	NOUN
ejpam-5731	227	19	disk	disk	NOUN
ejpam-5731	227	20	d	d	PROPN
ejpam-5731	227	21	and	and	CCONJ
ejpam-5731	227	22	belong	belong	VERB
ejpam-5731	227	23	to	to	ADP
ejpam-5731	227	24	the	the	DET
ejpam-5731	227	25	caratheodory	caratheodory	ADJ
ejpam-5731	227	26	class	class	NOUN
ejpam-5731	227	27	.	.	PUNCT
ejpam-5731	228	1	therefore	therefore	ADV
ejpam-5731	228	2	,	,	PUNCT
ejpam-5731	228	3	they	they	PRON
ejpam-5731	228	4	can	can	AUX
ejpam-5731	228	5	be	be	AUX
ejpam-5731	228	6	written	write	VERB
ejpam-5731	228	7	as	as	SCONJ
ejpam-5731	228	8	follows	follow	VERB
ejpam-5731	228	9	η(z	η(z	PROPN
ejpam-5731	228	10	)	)	PUNCT
ejpam-5731	228	11	=	=	SYM
ejpam-5731	229	1	1	1	NUM
ejpam-5731	229	2	+	+	NUM
ejpam-5731	229	3	k(z	k(z	PROPN
ejpam-5731	229	4	)	)	PUNCT
ejpam-5731	229	5	1−	1−	NUM
ejpam-5731	229	6	k(z	k(z	PROPN
ejpam-5731	229	7	)	)	PUNCT
ejpam-5731	229	8	=	=	PUNCT
ejpam-5731	230	1	1	1	NUM
ejpam-5731	230	2	+	+	CCONJ
ejpam-5731	230	3	η1z	η1z	PROPN
ejpam-5731	231	1	+	+	CCONJ
ejpam-5731	231	2	η2z	η2z	ADP
ejpam-5731	231	3	2	2	NUM
ejpam-5731	231	4	+	+	NUM
ejpam-5731	231	5	·	·	PUNCT
ejpam-5731	231	6	·	·	PUNCT
ejpam-5731	231	7	·	·	PUNCT
ejpam-5731	231	8	w.	w.	PROPN
ejpam-5731	231	9	al	al	PROPN
ejpam-5731	231	10	-	-	PUNCT
ejpam-5731	231	11	rawashdeh	rawashdeh	PROPN
ejpam-5731	231	12	/	/	SYM
ejpam-5731	231	13	eur	eur	PROPN
ejpam-5731	231	14	.	.	PUNCT
ejpam-5731	232	1	j.	j.	PROPN
ejpam-5731	232	2	pure	pure	PROPN
ejpam-5731	232	3	appl	appl	PROPN
ejpam-5731	232	4	.	.	PROPN
ejpam-5731	232	5	math	math	PROPN
ejpam-5731	232	6	,	,	PUNCT
ejpam-5731	232	7	18	18	NUM
ejpam-5731	232	8	(	(	PUNCT
ejpam-5731	232	9	1	1	NUM
ejpam-5731	232	10	)	)	PUNCT
ejpam-5731	232	11	(	(	PUNCT
ejpam-5731	232	12	2025	2025	NUM
ejpam-5731	232	13	)	)	PUNCT
ejpam-5731	232	14	,	,	PUNCT
ejpam-5731	232	15	5731	5731	NUM
ejpam-5731	232	16	11	11	NUM
ejpam-5731	232	17	of	of	ADP
ejpam-5731	232	18	20	20	NUM
ejpam-5731	232	19	and	and	CCONJ
ejpam-5731	232	20	ζ(w	ζ(w	NOUN
ejpam-5731	232	21	)	)	PUNCT
ejpam-5731	232	22	=	=	SYM
ejpam-5731	232	23	1	1	NUM
ejpam-5731	232	24	+	+	CCONJ
ejpam-5731	232	25	h(w	h(w	PROPN
ejpam-5731	232	26	)	)	PUNCT
ejpam-5731	232	27	1−	1−	NUM
ejpam-5731	232	28	h(w	h(w	NOUN
ejpam-5731	232	29	)	)	PUNCT
ejpam-5731	232	30	=	=	SYM
ejpam-5731	232	31	1	1	NUM
ejpam-5731	233	1	+	+	CCONJ
ejpam-5731	233	2	ζ1w	ζ1w	NOUN
ejpam-5731	233	3	+	+	CCONJ
ejpam-5731	233	4	ζ2w	ζ2w	NOUN
ejpam-5731	233	5	2	2	NUM
ejpam-5731	233	6	+	+	CCONJ
ejpam-5731	233	7	·	·	PUNCT
ejpam-5731	233	8	·	·	PUNCT
ejpam-5731	233	9	·	·	PUNCT
ejpam-5731	233	10	moreover	moreover	ADV
ejpam-5731	233	11	,	,	PUNCT
ejpam-5731	233	12	η(0	η(0	PROPN
ejpam-5731	233	13	)	)	PUNCT
ejpam-5731	233	14	=	=	SYM
ejpam-5731	233	15	1	1	NUM
ejpam-5731	233	16	=	=	SYM
ejpam-5731	233	17	ζ(0	ζ(0	NOUN
ejpam-5731	233	18	)	)	PUNCT
ejpam-5731	233	19	,	,	PUNCT
ejpam-5731	233	20	ℜ(η	ℜ(η	PROPN
ejpam-5731	233	21	)	)	PUNCT
ejpam-5731	233	22	>	>	X
ejpam-5731	233	23	0	0	NUM
ejpam-5731	233	24	,	,	PUNCT
ejpam-5731	233	25	ℜ(ζ	ℜ(ζ	PRON
ejpam-5731	233	26	)	)	PUNCT
ejpam-5731	233	27	>	>	X
ejpam-5731	233	28	0	0	NUM
ejpam-5731	233	29	,	,	PUNCT
ejpam-5731	233	30	|ηj	|ηj	PROPN
ejpam-5731	233	31	|	|	ADV
ejpam-5731	233	32	≤	≤	NUM
ejpam-5731	233	33	2	2	NUM
ejpam-5731	233	34	and	and	CCONJ
ejpam-5731	233	35	|ζj	|ζj	PRON
ejpam-5731	233	36	|	|	ADV
ejpam-5731	233	37	≤	≤	ADV
ejpam-5731	233	38	2	2	NUM
ejpam-5731	233	39	for	for	ADP
ejpam-5731	233	40	all	all	DET
ejpam-5731	233	41	natural	natural	ADJ
ejpam-5731	233	42	numbers	number	NOUN
ejpam-5731	233	43	j.	j.	PROPN
ejpam-5731	233	44	equivalently	equivalently	PROPN
ejpam-5731	233	45	,	,	PUNCT
ejpam-5731	233	46	we	we	PRON
ejpam-5731	233	47	get	get	VERB
ejpam-5731	233	48	the	the	DET
ejpam-5731	233	49	following	follow	VERB
ejpam-5731	233	50	representations	representation	NOUN
ejpam-5731	233	51	of	of	ADP
ejpam-5731	233	52	k(z	k(z	PROPN
ejpam-5731	233	53	)	)	PUNCT
ejpam-5731	233	54	and	and	CCONJ
ejpam-5731	233	55	h(w	h(w	PROPN
ejpam-5731	233	56	)	)	PUNCT
ejpam-5731	233	57	k(z	k(z	PROPN
ejpam-5731	233	58	)	)	PUNCT
ejpam-5731	234	1	=	=	PUNCT
ejpam-5731	234	2	η(z)−	η(z)−	PROPN
ejpam-5731	234	3	1	1	NUM
ejpam-5731	234	4	η(z	η(z	PROPN
ejpam-5731	234	5	)	)	PUNCT
ejpam-5731	235	1	+	+	CCONJ
ejpam-5731	235	2	1	1	NUM
ejpam-5731	235	3	=	=	SYM
ejpam-5731	235	4	η1	η1	NOUN
ejpam-5731	235	5	2	2	NUM
ejpam-5731	235	6	z	z	NOUN
ejpam-5731	235	7	+	+	CCONJ
ejpam-5731	235	8	(	(	PUNCT
ejpam-5731	235	9	η2	η2	X
ejpam-5731	235	10	2	2	NUM
ejpam-5731	235	11	−	−	PROPN
ejpam-5731	235	12	η21	η21	NOUN
ejpam-5731	235	13	4	4	NUM
ejpam-5731	235	14	)	)	PUNCT
ejpam-5731	235	15	z2	z2	PROPN
ejpam-5731	235	16	+	+	CCONJ
ejpam-5731	235	17	·	·	PUNCT
ejpam-5731	235	18	·	·	PUNCT
ejpam-5731	236	1	·	·	PUNCT
ejpam-5731	236	2	,	,	PUNCT
ejpam-5731	236	3	(	(	PUNCT
ejpam-5731	236	4	13	13	NUM
ejpam-5731	236	5	)	)	PUNCT
ejpam-5731	236	6	and	and	CCONJ
ejpam-5731	236	7	h(w	h(w	PROPN
ejpam-5731	236	8	)	)	PUNCT
ejpam-5731	236	9	=	=	SYM
ejpam-5731	236	10	ζ(w)−	ζ(w)−	PROPN
ejpam-5731	236	11	1	1	NUM
ejpam-5731	236	12	ζ(w	ζ(w	PROPN
ejpam-5731	236	13	)	)	PUNCT
ejpam-5731	237	1	+	+	CCONJ
ejpam-5731	237	2	1	1	NUM
ejpam-5731	237	3	=	=	SYM
ejpam-5731	237	4	ζ1	ζ1	NOUN
ejpam-5731	237	5	2	2	NUM
ejpam-5731	237	6	w	w	NOUN
ejpam-5731	237	7	+	+	CCONJ
ejpam-5731	237	8	(	(	PUNCT
ejpam-5731	237	9	ζ2	ζ2	NOUN
ejpam-5731	237	10	2	2	NUM
ejpam-5731	237	11	−	−	NOUN
ejpam-5731	237	12	ζ21	ζ21	VERB
ejpam-5731	237	13	4	4	NUM
ejpam-5731	237	14	)	)	PUNCT
ejpam-5731	237	15	w2	w2	NOUN
ejpam-5731	237	16	+	+	CCONJ
ejpam-5731	237	17	·	·	PUNCT
ejpam-5731	237	18	·	·	PUNCT
ejpam-5731	237	19	·	·	PUNCT
ejpam-5731	237	20	.	.	PUNCT
ejpam-5731	238	1	(	(	PUNCT
ejpam-5731	238	2	14	14	NUM
ejpam-5731	238	3	)	)	PUNCT
ejpam-5731	238	4	therefore	therefore	ADV
ejpam-5731	238	5	,	,	PUNCT
ejpam-5731	238	6	by	by	ADP
ejpam-5731	238	7	consulting	consult	VERB
ejpam-5731	238	8	equation	equation	NOUN
ejpam-5731	238	9	(	(	PUNCT
ejpam-5731	238	10	7	7	NUM
ejpam-5731	238	11	)	)	PUNCT
ejpam-5731	238	12	and	and	CCONJ
ejpam-5731	238	13	equation	equation	NOUN
ejpam-5731	238	14	(	(	PUNCT
ejpam-5731	238	15	13	13	NUM
ejpam-5731	238	16	)	)	PUNCT
ejpam-5731	238	17	the	the	DET
ejpam-5731	238	18	right	right	ADJ
ejpam-5731	238	19	-	-	PUNCT
ejpam-5731	238	20	hand	hand	NOUN
ejpam-5731	238	21	side	side	NOUN
ejpam-5731	238	22	of	of	ADP
ejpam-5731	238	23	equation	equation	NOUN
ejpam-5731	238	24	(	(	PUNCT
ejpam-5731	238	25	11	11	NUM
ejpam-5731	238	26	)	)	PUNCT
ejpam-5731	238	27	can	can	AUX
ejpam-5731	238	28	be	be	AUX
ejpam-5731	238	29	written	write	VERB
ejpam-5731	238	30	as	as	ADP
ejpam-5731	238	31	:	:	PUNCT
ejpam-5731	238	32	ϕ(k(z	ϕ(k(z	PROPN
ejpam-5731	238	33	)	)	PUNCT
ejpam-5731	238	34	)	)	PUNCT
ejpam-5731	239	1	cos	cos	PROPN
ejpam-5731	239	2	δ	δ	PROPN
ejpam-5731	240	1	+	+	CCONJ
ejpam-5731	240	2	i	i	PRON
ejpam-5731	240	3	sin	sin	VERB
ejpam-5731	240	4	δ	δ	X
ejpam-5731	240	5	=	=	PUNCT
ejpam-5731	240	6	(	(	PUNCT
ejpam-5731	240	7	1	1	NUM
ejpam-5731	240	8	+	+	CCONJ
ejpam-5731	240	9	β1η1	β1η1	SYM
ejpam-5731	240	10	2	2	NUM
ejpam-5731	240	11	z	z	NOUN
ejpam-5731	240	12	+	+	CCONJ
ejpam-5731	240	13	[	[	PUNCT
ejpam-5731	240	14	β1	β1	X
ejpam-5731	240	15	(	(	PUNCT
ejpam-5731	240	16	η2	η2	X
ejpam-5731	240	17	2	2	NUM
ejpam-5731	240	18	−	−	PROPN
ejpam-5731	240	19	η21	η21	NOUN
ejpam-5731	240	20	4	4	NUM
ejpam-5731	240	21	)	)	PUNCT
ejpam-5731	240	22	+	+	CCONJ
ejpam-5731	240	23	β2η	β2η	SYM
ejpam-5731	240	24	2	2	NUM
ejpam-5731	240	25	1	1	NUM
ejpam-5731	240	26	4	4	NUM
ejpam-5731	240	27	]	]	PUNCT
ejpam-5731	240	28	z2	z2	PROPN
ejpam-5731	240	29	+	+	CCONJ
ejpam-5731	240	30	·	·	PUNCT
ejpam-5731	240	31	·	·	PUNCT
ejpam-5731	240	32	·	·	PUNCT
ejpam-5731	240	33	)	)	PUNCT
ejpam-5731	241	1	cos	cos	PROPN
ejpam-5731	241	2	δ	δ	PROPN
ejpam-5731	242	1	+	+	CCONJ
ejpam-5731	242	2	i	i	PRON
ejpam-5731	242	3	sin	sin	VERB
ejpam-5731	242	4	δ	δ	PROPN
ejpam-5731	242	5	.	.	PUNCT
ejpam-5731	243	1	(	(	PUNCT
ejpam-5731	243	2	15	15	NUM
ejpam-5731	243	3	)	)	PUNCT
ejpam-5731	243	4	moreover	moreover	ADV
ejpam-5731	243	5	,	,	PUNCT
ejpam-5731	243	6	the	the	DET
ejpam-5731	243	7	left	leave	VERB
ejpam-5731	243	8	-	-	PUNCT
ejpam-5731	243	9	hand	hand	NOUN
ejpam-5731	243	10	side	side	NOUN
ejpam-5731	243	11	of	of	ADP
ejpam-5731	243	12	equation	equation	NOUN
ejpam-5731	243	13	(	(	PUNCT
ejpam-5731	243	14	11	11	NUM
ejpam-5731	243	15	)	)	PUNCT
ejpam-5731	243	16	can	can	AUX
ejpam-5731	243	17	be	be	AUX
ejpam-5731	243	18	written	write	VERB
ejpam-5731	243	19	as	as	ADP
ejpam-5731	243	20	:	:	PUNCT
ejpam-5731	243	21	eiδz1−λ	eiδz1−λ	PROPN
ejpam-5731	243	22	(	(	PUNCT
ejpam-5731	243	23	rαq	rαq	PROPN
ejpam-5731	243	24	f(z	f(z	PROPN
ejpam-5731	243	25	)	)	PUNCT
ejpam-5731	243	26	)	)	PUNCT
ejpam-5731	244	1	′	′	NUM
ejpam-5731	244	2	(	(	PUNCT
ejpam-5731	244	3	rαq	rαq	PROPN
ejpam-5731	244	4	f(z	f(z	PROPN
ejpam-5731	244	5	)	)	PUNCT
ejpam-5731	244	6	)	)	PUNCT
ejpam-5731	244	7	1−λ	1−λ	X
ejpam-5731	245	1	=	=	PUNCT
ejpam-5731	245	2	eiδ(λ+	eiδ(λ+	PROPN
ejpam-5731	245	3	1)ψ2a2z	1)ψ2a2z	NUM
ejpam-5731	245	4	+	+	CCONJ
ejpam-5731	245	5	eiδ	eiδ	VERB
ejpam-5731	245	6	[	[	PUNCT
ejpam-5731	245	7	(	(	PUNCT
ejpam-5731	245	8	λ−	λ−	PROPN
ejpam-5731	245	9	1)(λ+	1)(λ+	NUM
ejpam-5731	245	10	2	2	NUM
ejpam-5731	245	11	)	)	PUNCT
ejpam-5731	245	12	2	2	NUM
ejpam-5731	245	13	ψ2	ψ2	NOUN
ejpam-5731	245	14	2a	2a	NUM
ejpam-5731	245	15	2	2	NUM
ejpam-5731	245	16	2	2	NUM
ejpam-5731	245	17	+	+	CCONJ
ejpam-5731	245	18	(	(	PUNCT
ejpam-5731	245	19	λ+	λ+	NUM
ejpam-5731	245	20	2)ψ3a3	2)ψ3a3	PROPN
ejpam-5731	245	21	]	]	X
ejpam-5731	245	22	z2	z2	PROPN
ejpam-5731	245	23	+	+	CCONJ
ejpam-5731	245	24	·	·	PUNCT
ejpam-5731	245	25	·	·	PUNCT
ejpam-5731	245	26	·	·	PUNCT
ejpam-5731	246	1	(	(	PUNCT
ejpam-5731	246	2	16	16	NUM
ejpam-5731	246	3	)	)	PUNCT
ejpam-5731	246	4	now	now	ADV
ejpam-5731	246	5	,	,	PUNCT
ejpam-5731	246	6	consulting	consult	VERB
ejpam-5731	246	7	equation	equation	NOUN
ejpam-5731	246	8	(	(	PUNCT
ejpam-5731	246	9	11	11	NUM
ejpam-5731	246	10	)	)	PUNCT
ejpam-5731	246	11	,	,	PUNCT
ejpam-5731	246	12	we	we	PRON
ejpam-5731	246	13	get	get	VERB
ejpam-5731	246	14	the	the	DET
ejpam-5731	246	15	right	right	ADJ
ejpam-5731	246	16	-	-	PUNCT
ejpam-5731	246	17	hand	hand	NOUN
ejpam-5731	246	18	sides	side	NOUN
ejpam-5731	246	19	of	of	ADP
ejpam-5731	246	20	equation	equation	NOUN
ejpam-5731	246	21	(	(	PUNCT
ejpam-5731	246	22	15	15	NUM
ejpam-5731	246	23	)	)	PUNCT
ejpam-5731	246	24	and	and	CCONJ
ejpam-5731	246	25	equation	equation	NOUN
ejpam-5731	246	26	(	(	PUNCT
ejpam-5731	246	27	16	16	NUM
ejpam-5731	246	28	)	)	PUNCT
ejpam-5731	246	29	are	be	AUX
ejpam-5731	246	30	equal	equal	ADJ
ejpam-5731	246	31	.	.	PUNCT
ejpam-5731	247	1	therefore	therefore	ADV
ejpam-5731	247	2	comparing	compare	VERB
ejpam-5731	247	3	these	these	DET
ejpam-5731	247	4	equations	equation	NOUN
ejpam-5731	247	5	coefficients	coefficient	NOUN
ejpam-5731	247	6	we	we	PRON
ejpam-5731	247	7	get	get	VERB
ejpam-5731	247	8	the	the	DET
ejpam-5731	247	9	following	follow	VERB
ejpam-5731	247	10	two	two	NUM
ejpam-5731	247	11	equations	equation	NOUN
ejpam-5731	247	12	:	:	PUNCT
ejpam-5731	247	13	2eiδ(λ+	2eiδ(λ+	NUM
ejpam-5731	247	14	1)ψ2a2	1)ψ2a2	NOUN
ejpam-5731	247	15	=	=	PUNCT
ejpam-5731	247	16	β1η1	β1η1	PUNCT
ejpam-5731	247	17	cos	cos	PROPN
ejpam-5731	247	18	δ	δ	PROPN
ejpam-5731	247	19	,	,	PUNCT
ejpam-5731	247	20	(	(	PUNCT
ejpam-5731	247	21	17	17	NUM
ejpam-5731	247	22	)	)	PUNCT
ejpam-5731	247	23	and	and	CCONJ
ejpam-5731	247	24	eiδ	eiδ	X
ejpam-5731	247	25	[	[	PUNCT
ejpam-5731	247	26	2(λ−	2(λ−	NUM
ejpam-5731	247	27	1)(λ+	1)(λ+	NUM
ejpam-5731	247	28	2)ψ2	2)ψ2	NUM
ejpam-5731	247	29	2a	2a	NUM
ejpam-5731	247	30	2	2	NUM
ejpam-5731	247	31	2	2	NUM
ejpam-5731	247	32	+	+	NUM
ejpam-5731	247	33	4(λ+	4(λ+	NOUN
ejpam-5731	247	34	2)ψ3a3	2)ψ3a3	PROPN
ejpam-5731	247	35	]	]	PUNCT
ejpam-5731	248	1	=	=	PUNCT
ejpam-5731	249	1	[	[	X
ejpam-5731	249	2	2β1η2	2β1η2	NUM
ejpam-5731	249	3	+	+	CCONJ
ejpam-5731	249	4	(	(	PUNCT
ejpam-5731	249	5	β2	β2	NOUN
ejpam-5731	249	6	−	−	PROPN
ejpam-5731	249	7	β1)η	β1)η	NOUN
ejpam-5731	249	8	2	2	NUM
ejpam-5731	249	9	1	1	NUM
ejpam-5731	249	10	]	]	PUNCT
ejpam-5731	249	11	cos	cos	PROPN
ejpam-5731	249	12	δ	δ	PROPN
ejpam-5731	249	13	.	.	PUNCT
ejpam-5731	250	1	(	(	PUNCT
ejpam-5731	250	2	18	18	NUM
ejpam-5731	250	3	)	)	PUNCT
ejpam-5731	250	4	on	on	ADP
ejpam-5731	250	5	the	the	DET
ejpam-5731	250	6	other	other	ADJ
ejpam-5731	250	7	hand	hand	NOUN
ejpam-5731	250	8	,	,	PUNCT
ejpam-5731	250	9	by	by	ADP
ejpam-5731	250	10	consulting	consult	VERB
ejpam-5731	250	11	equation	equation	NOUN
ejpam-5731	250	12	(	(	PUNCT
ejpam-5731	250	13	7	7	NUM
ejpam-5731	250	14	)	)	PUNCT
ejpam-5731	250	15	and	and	CCONJ
ejpam-5731	250	16	equation	equation	NOUN
ejpam-5731	250	17	(	(	PUNCT
ejpam-5731	250	18	14	14	NUM
ejpam-5731	250	19	)	)	PUNCT
ejpam-5731	250	20	the	the	DET
ejpam-5731	250	21	right	right	ADJ
ejpam-5731	250	22	-	-	PUNCT
ejpam-5731	250	23	hand	hand	NOUN
ejpam-5731	250	24	side	side	NOUN
ejpam-5731	250	25	of	of	ADP
ejpam-5731	250	26	equation	equation	NOUN
ejpam-5731	250	27	(	(	PUNCT
ejpam-5731	250	28	12	12	NUM
ejpam-5731	250	29	)	)	PUNCT
ejpam-5731	250	30	can	can	AUX
ejpam-5731	250	31	be	be	AUX
ejpam-5731	250	32	written	write	VERB
ejpam-5731	250	33	as	as	ADP
ejpam-5731	250	34	:	:	PUNCT
ejpam-5731	250	35	ϕ(h(w	ϕ(h(w	PROPN
ejpam-5731	250	36	)	)	PUNCT
ejpam-5731	250	37	)	)	PUNCT
ejpam-5731	251	1	=	=	SYM
ejpam-5731	251	2	1	1	NUM
ejpam-5731	251	3	+	+	NUM
ejpam-5731	251	4	β1ζ1	β1ζ1	X
ejpam-5731	251	5	2	2	NUM
ejpam-5731	251	6	w	w	NOUN
ejpam-5731	251	7	+	+	CCONJ
ejpam-5731	251	8	[	[	PUNCT
ejpam-5731	251	9	β1	β1	X
ejpam-5731	251	10	(	(	PUNCT
ejpam-5731	251	11	ζ2	ζ2	NOUN
ejpam-5731	251	12	2	2	NUM
ejpam-5731	251	13	−	−	NOUN
ejpam-5731	251	14	ζ21	ζ21	VERB
ejpam-5731	251	15	4	4	NUM
ejpam-5731	251	16	)	)	PUNCT
ejpam-5731	251	17	+	+	CCONJ
ejpam-5731	251	18	β2ζ	β2ζ	SYM
ejpam-5731	251	19	2	2	NUM
ejpam-5731	251	20	1	1	NUM
ejpam-5731	251	21	4	4	NUM
ejpam-5731	251	22	]	]	PUNCT
ejpam-5731	251	23	w2	w2	NOUN
ejpam-5731	251	24	+	+	CCONJ
ejpam-5731	251	25	·	·	PUNCT
ejpam-5731	251	26	·	·	PUNCT
ejpam-5731	251	27	·	·	PUNCT
ejpam-5731	251	28	(	(	PUNCT
ejpam-5731	251	29	19	19	NUM
ejpam-5731	251	30	)	)	PUNCT
ejpam-5731	251	31	w.	w.	PROPN
ejpam-5731	251	32	al	al	PROPN
ejpam-5731	251	33	-	-	PUNCT
ejpam-5731	251	34	rawashdeh	rawashdeh	PROPN
ejpam-5731	251	35	/	/	SYM
ejpam-5731	251	36	eur	eur	PROPN
ejpam-5731	251	37	.	.	PUNCT
ejpam-5731	252	1	j.	j.	PROPN
ejpam-5731	252	2	pure	pure	PROPN
ejpam-5731	252	3	appl	appl	PROPN
ejpam-5731	252	4	.	.	PROPN
ejpam-5731	252	5	math	math	PROPN
ejpam-5731	252	6	,	,	PUNCT
ejpam-5731	252	7	18	18	NUM
ejpam-5731	252	8	(	(	PUNCT
ejpam-5731	252	9	1	1	NUM
ejpam-5731	252	10	)	)	PUNCT
ejpam-5731	252	11	(	(	PUNCT
ejpam-5731	252	12	2025	2025	NUM
ejpam-5731	252	13	)	)	PUNCT
ejpam-5731	252	14	,	,	PUNCT
ejpam-5731	252	15	5731	5731	NUM
ejpam-5731	252	16	12	12	NUM
ejpam-5731	252	17	of	of	ADP
ejpam-5731	252	18	20	20	NUM
ejpam-5731	252	19	moreover	moreover	ADV
ejpam-5731	252	20	,	,	PUNCT
ejpam-5731	252	21	the	the	DET
ejpam-5731	252	22	left	leave	VERB
ejpam-5731	252	23	-	-	PUNCT
ejpam-5731	252	24	hand	hand	NOUN
ejpam-5731	252	25	side	side	NOUN
ejpam-5731	252	26	of	of	ADP
ejpam-5731	252	27	equation	equation	NOUN
ejpam-5731	252	28	(	(	PUNCT
ejpam-5731	252	29	12	12	NUM
ejpam-5731	252	30	)	)	PUNCT
ejpam-5731	252	31	can	can	AUX
ejpam-5731	252	32	be	be	AUX
ejpam-5731	252	33	written	write	VERB
ejpam-5731	252	34	as	as	ADP
ejpam-5731	252	35	:	:	PUNCT
ejpam-5731	252	36	eiδw1−λ	eiδw1−λ	PROPN
ejpam-5731	252	37	(	(	PUNCT
ejpam-5731	252	38	rαq	rαq	PROPN
ejpam-5731	252	39	g(w))′	g(w))′	PROPN
ejpam-5731	252	40	(	(	PUNCT
ejpam-5731	252	41	rαq	rαq	PROPN
ejpam-5731	252	42	g(w	g(w	PROPN
ejpam-5731	252	43	)	)	PUNCT
ejpam-5731	252	44	)	)	PUNCT
ejpam-5731	252	45	1−λ	1−λ	NUM
ejpam-5731	253	1	=	=	PUNCT
ejpam-5731	253	2	−eiδ(λ+	−eiδ(λ+	ADP
ejpam-5731	253	3	1)ψ2a2w	1)ψ2a2w	PROPN
ejpam-5731	253	4	+	+	CCONJ
ejpam-5731	253	5	eiδ	eiδ	VERB
ejpam-5731	253	6	2(λ+	2(λ+	PROPN
ejpam-5731	253	7	2)ψ3	2)ψ3	PROPN
ejpam-5731	253	8	+	+	CCONJ
ejpam-5731	253	9	(	(	PUNCT
ejpam-5731	253	10	λ−	λ−	PROPN
ejpam-5731	253	11	1)(λ+	1)(λ+	NUM
ejpam-5731	253	12	2	2	NUM
ejpam-5731	253	13	)	)	SYM
ejpam-5731	253	14	2	2	NUM
ejpam-5731	253	15	ψ2	ψ2	NOUN
ejpam-5731	253	16	2	2	NUM
ejpam-5731	253	17			PROPN
ejpam-5731	253	18	a22	a22	NOUN
ejpam-5731	253	19	−	−	PROPN
ejpam-5731	253	20	(	(	PUNCT
ejpam-5731	253	21	λ+	λ+	NUM
ejpam-5731	253	22	2)ψ3a3	2)ψ3a3	PROPN
ejpam-5731	253	23	w2	w2	PROPN
ejpam-5731	253	24	+	+	CCONJ
ejpam-5731	253	25	·	·	PUNCT
ejpam-5731	253	26	·	·	PUNCT
ejpam-5731	253	27	·	·	PUNCT
ejpam-5731	253	28	(	(	PUNCT
ejpam-5731	253	29	20	20	NUM
ejpam-5731	253	30	)	)	PUNCT
ejpam-5731	253	31	now	now	ADV
ejpam-5731	253	32	,	,	PUNCT
ejpam-5731	253	33	considering	consider	VERB
ejpam-5731	253	34	equation	equation	NOUN
ejpam-5731	253	35	(	(	PUNCT
ejpam-5731	253	36	12	12	NUM
ejpam-5731	253	37	)	)	PUNCT
ejpam-5731	253	38	and	and	CCONJ
ejpam-5731	253	39	comparing	compare	VERB
ejpam-5731	253	40	coefficients	coefficient	NOUN
ejpam-5731	253	41	on	on	ADP
ejpam-5731	253	42	bothsides	bothside	NOUN
ejpam-5731	253	43	of	of	ADP
ejpam-5731	253	44	equation	equation	NOUN
ejpam-5731	253	45	(	(	PUNCT
ejpam-5731	253	46	19	19	NUM
ejpam-5731	253	47	)	)	PUNCT
ejpam-5731	253	48	and	and	CCONJ
ejpam-5731	253	49	equation(20	equation(20	NOUN
ejpam-5731	253	50	)	)	PUNCT
ejpam-5731	253	51	we	we	PRON
ejpam-5731	253	52	get	get	VERB
ejpam-5731	253	53	the	the	DET
ejpam-5731	253	54	following	follow	VERB
ejpam-5731	253	55	two	two	NUM
ejpam-5731	253	56	equations	equation	NOUN
ejpam-5731	253	57	:	:	PUNCT
ejpam-5731	254	1	−2eiδ(λ+	−2eiδ(λ+	PROPN
ejpam-5731	254	2	1)ψ2a2	1)ψ2a2	NUM
ejpam-5731	254	3	=	=	SYM
ejpam-5731	254	4	β1ζ1	β1ζ1	PROPN
ejpam-5731	254	5	cos	cos	PROPN
ejpam-5731	254	6	δ	δ	PROPN
ejpam-5731	254	7	,	,	PUNCT
ejpam-5731	254	8	(	(	PUNCT
ejpam-5731	254	9	21	21	NUM
ejpam-5731	254	10	)	)	PUNCT
ejpam-5731	254	11	and	and	CCONJ
ejpam-5731	254	12	eiδ	eiδ	X
ejpam-5731	254	13	(	(	PUNCT
ejpam-5731	254	14	[	[	PUNCT
ejpam-5731	254	15	8(λ+	8(λ+	NUM
ejpam-5731	254	16	2)ψ3	2)ψ3	NOUN
ejpam-5731	254	17	+	+	CCONJ
ejpam-5731	254	18	2(λ−	2(λ−	NUM
ejpam-5731	254	19	1)(λ+	1)(λ+	NUM
ejpam-5731	254	20	2)ψ2	2)ψ2	NUM
ejpam-5731	254	21	2	2	NUM
ejpam-5731	254	22	]	]	PUNCT
ejpam-5731	254	23	a22	a22	PROPN
ejpam-5731	254	24	−	−	NOUN
ejpam-5731	254	25	4(λ+	4(λ+	NOUN
ejpam-5731	254	26	2)ψ3a3	2)ψ3a3	PROPN
ejpam-5731	254	27	)	)	PUNCT
ejpam-5731	255	1	=	=	PUNCT
ejpam-5731	256	1	[	[	X
ejpam-5731	256	2	2β1ζ2	2β1ζ2	NUM
ejpam-5731	256	3	+	+	CCONJ
ejpam-5731	256	4	(	(	PUNCT
ejpam-5731	256	5	β2	β2	NOUN
ejpam-5731	256	6	−	−	PROPN
ejpam-5731	256	7	β1)ζ	β1)ζ	NOUN
ejpam-5731	256	8	2	2	NUM
ejpam-5731	256	9	1	1	NUM
ejpam-5731	256	10	]	]	PUNCT
ejpam-5731	256	11	cos	cos	PROPN
ejpam-5731	256	12	δ	δ	PROPN
ejpam-5731	256	13	.	.	PUNCT
ejpam-5731	257	1	(	(	PUNCT
ejpam-5731	257	2	22	22	NUM
ejpam-5731	257	3	)	)	PUNCT
ejpam-5731	257	4	therefore	therefore	ADV
ejpam-5731	257	5	,	,	PUNCT
ejpam-5731	257	6	using	use	VERB
ejpam-5731	257	7	equation	equation	NOUN
ejpam-5731	257	8	(	(	PUNCT
ejpam-5731	257	9	17	17	NUM
ejpam-5731	257	10	)	)	PUNCT
ejpam-5731	257	11	and	and	CCONJ
ejpam-5731	257	12	equation	equation	NOUN
ejpam-5731	257	13	(	(	PUNCT
ejpam-5731	257	14	21	21	NUM
ejpam-5731	257	15	)	)	PUNCT
ejpam-5731	257	16	,	,	PUNCT
ejpam-5731	257	17	we	we	PRON
ejpam-5731	257	18	easily	easily	ADV
ejpam-5731	257	19	derive	derive	VERB
ejpam-5731	257	20	the	the	DET
ejpam-5731	257	21	following	follow	VERB
ejpam-5731	257	22	equation	equation	NOUN
ejpam-5731	257	23	eiδa2	eiδa2	NOUN
ejpam-5731	258	1	=	=	PUNCT
ejpam-5731	258	2	β1η1	β1η1	PUNCT
ejpam-5731	258	3	cos	cos	ADP
ejpam-5731	258	4	δ	δ	PROPN
ejpam-5731	258	5	2(λ+	2(λ+	PROPN
ejpam-5731	258	6	1)ψ2	1)ψ2	PROPN
ejpam-5731	258	7	=	=	SYM
ejpam-5731	258	8	−β1ζ1	−β1ζ1	PROPN
ejpam-5731	258	9	cos	cos	PROPN
ejpam-5731	258	10	δ	δ	PROPN
ejpam-5731	258	11	2(λ+	2(λ+	PROPN
ejpam-5731	258	12	1)ψ2	1)ψ2	PROPN
ejpam-5731	258	13	.	.	PUNCT
ejpam-5731	259	1	(	(	PUNCT
ejpam-5731	259	2	23	23	NUM
ejpam-5731	259	3	)	)	PUNCT
ejpam-5731	259	4	on	on	ADP
ejpam-5731	259	5	one	one	NUM
ejpam-5731	259	6	hand	hand	NOUN
ejpam-5731	259	7	,	,	PUNCT
ejpam-5731	259	8	adding	add	VERB
ejpam-5731	259	9	equation	equation	NOUN
ejpam-5731	259	10	(	(	PUNCT
ejpam-5731	259	11	18	18	NUM
ejpam-5731	259	12	)	)	PUNCT
ejpam-5731	259	13	to	to	ADP
ejpam-5731	259	14	equation	equation	NOUN
ejpam-5731	259	15	(	(	PUNCT
ejpam-5731	259	16	22	22	NUM
ejpam-5731	259	17	)	)	PUNCT
ejpam-5731	259	18	,	,	PUNCT
ejpam-5731	259	19	we	we	PRON
ejpam-5731	259	20	obtain	obtain	VERB
ejpam-5731	259	21	the	the	DET
ejpam-5731	259	22	following	follow	VERB
ejpam-5731	259	23	equation	equation	NOUN
ejpam-5731	259	24	eiδ	eiδ	NOUN
ejpam-5731	259	25	[	[	PUNCT
ejpam-5731	259	26	4(λ−	4(λ−	NUM
ejpam-5731	259	27	1)(λ+	1)(λ+	NUM
ejpam-5731	259	28	2)ψ2	2)ψ2	NUM
ejpam-5731	259	29	2	2	NUM
ejpam-5731	259	30	+	+	CCONJ
ejpam-5731	259	31	8(λ+	8(λ+	NUM
ejpam-5731	259	32	2)ψ3	2)ψ3	NOUN
ejpam-5731	259	33	]	]	PUNCT
ejpam-5731	259	34	a22	a22	X
ejpam-5731	259	35	=	=	PUNCT
ejpam-5731	260	1	[	[	X
ejpam-5731	260	2	2β1(η2	2β1(η2	NUM
ejpam-5731	260	3	+	+	CCONJ
ejpam-5731	260	4	ζ2	ζ2	NOUN
ejpam-5731	260	5	)	)	PUNCT
ejpam-5731	260	6	+	+	CCONJ
ejpam-5731	260	7	(	(	PUNCT
ejpam-5731	260	8	β2	β2	NOUN
ejpam-5731	260	9	−	−	PROPN
ejpam-5731	260	10	β1)(η	β1)(η	ADP
ejpam-5731	260	11	2	2	NUM
ejpam-5731	260	12	1	1	NUM
ejpam-5731	260	13	+	+	CCONJ
ejpam-5731	260	14	ζ21	ζ21	VERB
ejpam-5731	260	15	)	)	PUNCT
ejpam-5731	260	16	]	]	PUNCT
ejpam-5731	260	17	cos	cos	PROPN
ejpam-5731	260	18	δ	δ	PROPN
ejpam-5731	260	19	.	.	PUNCT
ejpam-5731	261	1	(	(	PUNCT
ejpam-5731	261	2	24	24	NUM
ejpam-5731	261	3	)	)	PUNCT
ejpam-5731	261	4	on	on	ADP
ejpam-5731	261	5	the	the	DET
ejpam-5731	261	6	other	other	ADJ
ejpam-5731	261	7	hand	hand	NOUN
ejpam-5731	261	8	,	,	PUNCT
ejpam-5731	261	9	consulting	consult	VERB
ejpam-5731	261	10	equation	equation	NOUN
ejpam-5731	261	11	(	(	PUNCT
ejpam-5731	261	12	23	23	NUM
ejpam-5731	261	13	)	)	PUNCT
ejpam-5731	261	14	,	,	PUNCT
ejpam-5731	261	15	we	we	PRON
ejpam-5731	261	16	obtain	obtain	VERB
ejpam-5731	261	17	the	the	DET
ejpam-5731	261	18	following	follow	VERB
ejpam-5731	261	19	equation	equation	NOUN
ejpam-5731	261	20	:	:	PUNCT
ejpam-5731	261	21	η21	η21	PROPN
ejpam-5731	261	22	+	+	CCONJ
ejpam-5731	261	23	ζ21	ζ21	VERB
ejpam-5731	261	24	=	=	SYM
ejpam-5731	261	25	8(λ+	8(λ+	NUM
ejpam-5731	261	26	1)2ψ2	1)2ψ2	NUM
ejpam-5731	262	1	2e	2e	NOUN
ejpam-5731	263	1	i(2δ	i(2δ	ADJ
ejpam-5731	263	2	)	)	PUNCT
ejpam-5731	263	3	β21	β21	ADP
ejpam-5731	263	4	cos	cos	PROPN
ejpam-5731	263	5	2	2	NUM
ejpam-5731	263	6	δ	δ	PROPN
ejpam-5731	263	7	a22	a22	PROPN
ejpam-5731	263	8	.	.	PUNCT
ejpam-5731	264	1	(	(	PUNCT
ejpam-5731	264	2	25	25	NUM
ejpam-5731	264	3	)	)	PUNCT
ejpam-5731	264	4	now	now	ADV
ejpam-5731	264	5	,	,	PUNCT
ejpam-5731	264	6	using	use	VERB
ejpam-5731	264	7	equation	equation	NOUN
ejpam-5731	264	8	(	(	PUNCT
ejpam-5731	264	9	24	24	NUM
ejpam-5731	264	10	)	)	PUNCT
ejpam-5731	264	11	and	and	CCONJ
ejpam-5731	264	12	equation	equation	NOUN
ejpam-5731	264	13	(	(	PUNCT
ejpam-5731	264	14	25	25	NUM
ejpam-5731	264	15	)	)	PUNCT
ejpam-5731	264	16	,	,	PUNCT
ejpam-5731	264	17	we	we	PRON
ejpam-5731	264	18	easily	easily	ADV
ejpam-5731	264	19	derive	derive	VERB
ejpam-5731	264	20	the	the	DET
ejpam-5731	264	21	following	follow	VERB
ejpam-5731	264	22	equations	equation	NOUN
ejpam-5731	264	23	β21	β21	PROPN
ejpam-5731	265	1	cos	cos	PROPN
ejpam-5731	265	2	δe	δe	ADP
ejpam-5731	265	3	iδ	iδ	PROPN
ejpam-5731	266	1	[	[	PUNCT
ejpam-5731	266	2	4(λ−	4(λ−	NUM
ejpam-5731	266	3	1)(λ+	1)(λ+	NUM
ejpam-5731	266	4	2)ψ2	2)ψ2	NUM
ejpam-5731	266	5	2	2	NUM
ejpam-5731	266	6	+	+	CCONJ
ejpam-5731	266	7	8(λ+	8(λ+	NUM
ejpam-5731	266	8	2)ψ3	2)ψ3	NOUN
ejpam-5731	266	9	]	]	PUNCT
ejpam-5731	266	10	a22	a22	PROPN
ejpam-5731	266	11	=	=	SYM
ejpam-5731	266	12	2β31	2β31	PROPN
ejpam-5731	266	13	cos	cos	PROPN
ejpam-5731	266	14	2	2	NUM
ejpam-5731	266	15	δ(η2	δ(η2	NOUN
ejpam-5731	266	16	+	+	CCONJ
ejpam-5731	266	17	ζ2	ζ2	NOUN
ejpam-5731	266	18	)	)	PUNCT
ejpam-5731	266	19	+	+	NOUN
ejpam-5731	267	1	8(β2	8(β2	NUM
ejpam-5731	267	2	−	−	NOUN
ejpam-5731	267	3	β1)(λ+	β1)(λ+	NOUN
ejpam-5731	267	4	1)2ψ2	1)2ψ2	NUM
ejpam-5731	267	5	2e	2e	PROPN
ejpam-5731	267	6	i(2δ)a22	i(2δ)a22	PROPN
ejpam-5731	267	7	.	.	PUNCT
ejpam-5731	268	1	therefore	therefore	ADV
ejpam-5731	268	2	,	,	PUNCT
ejpam-5731	268	3	considering	consider	VERB
ejpam-5731	268	4	the	the	DET
ejpam-5731	268	5	initial	initial	ADJ
ejpam-5731	268	6	values	value	NOUN
ejpam-5731	268	7	β1	β1	NOUN
ejpam-5731	268	8	=	=	PUNCT
ejpam-5731	268	9	cos	cos	PROPN
ejpam-5731	268	10	θ	θ	PROPN
ejpam-5731	268	11	−	−	PROPN
ejpam-5731	268	12	1	1	NUM
ejpam-5731	268	13	and	and	CCONJ
ejpam-5731	268	14	2(δ2	2(δ2	NUM
ejpam-5731	268	15	−	−	PROPN
ejpam-5731	268	16	δ1	δ1	NOUN
ejpam-5731	268	17	)	)	PUNCT
ejpam-5731	268	18	=	=	PUNCT
ejpam-5731	269	1	(	(	PUNCT
ejpam-5731	269	2	3	3	NUM
ejpam-5731	269	3	cos	cos	NOUN
ejpam-5731	269	4	θ	θ	PROPN
ejpam-5731	269	5	−	−	PROPN
ejpam-5731	269	6	1)(cos	1)(cos	NUM
ejpam-5731	269	7	θ	θ	NOUN
ejpam-5731	269	8	−	−	NOUN
ejpam-5731	269	9	1	1	NUM
ejpam-5731	269	10	)	)	PUNCT
ejpam-5731	269	11	,	,	PUNCT
ejpam-5731	269	12	we	we	PRON
ejpam-5731	269	13	easily	easily	ADV
ejpam-5731	269	14	get	get	VERB
ejpam-5731	269	15	the	the	DET
ejpam-5731	269	16	following	follow	VERB
ejpam-5731	269	17	equation	equation	NOUN
ejpam-5731	269	18	a22	a22	NOUN
ejpam-5731	269	19	=	=	PUNCT
ejpam-5731	269	20	β21	β21	NOUN
ejpam-5731	269	21	cos	cos	PROPN
ejpam-5731	269	22	2	2	NUM
ejpam-5731	269	23	δ(η2	δ(η2	NOUN
ejpam-5731	269	24	+	+	CCONJ
ejpam-5731	269	25	ζ2)e	ζ2)e	VERB
ejpam-5731	269	26	−iδ	−iδ	ADP
ejpam-5731	269	27	β1	β1	PROPN
ejpam-5731	269	28	cos	cos	PROPN
ejpam-5731	269	29	δ[2(λ−	δ[2(λ−	PROPN
ejpam-5731	270	1	1)(λ+	1)(λ+	NUM
ejpam-5731	270	2	2)ψ2	2)ψ2	NUM
ejpam-5731	270	3	2	2	NUM
ejpam-5731	270	4	+	+	NUM
ejpam-5731	270	5	4(λ+	4(λ+	NOUN
ejpam-5731	270	6	2)ψ3	2)ψ3	NOUN
ejpam-5731	270	7	]	]	X
ejpam-5731	271	1	+	+	CCONJ
ejpam-5731	271	2	2(1−	2(1−	NUM
ejpam-5731	271	3	3	3	NUM
ejpam-5731	271	4	cos	cos	X
ejpam-5731	271	5	θ)(λ+	θ)(λ+	NOUN
ejpam-5731	271	6	1)2ψ2	1)2ψ2	NUM
ejpam-5731	271	7	2e	2e	NOUN
ejpam-5731	271	8	iδ	iδ	INTJ
ejpam-5731	271	9	.	.	PUNCT
ejpam-5731	272	1	(	(	PUNCT
ejpam-5731	272	2	26	26	NUM
ejpam-5731	272	3	)	)	PUNCT
ejpam-5731	272	4	w.	w.	PROPN
ejpam-5731	272	5	al	al	PROPN
ejpam-5731	272	6	-	-	PUNCT
ejpam-5731	272	7	rawashdeh	rawashdeh	PROPN
ejpam-5731	272	8	/	/	SYM
ejpam-5731	272	9	eur	eur	PROPN
ejpam-5731	272	10	.	.	PUNCT
ejpam-5731	273	1	j.	j.	PROPN
ejpam-5731	273	2	pure	pure	PROPN
ejpam-5731	273	3	appl	appl	PROPN
ejpam-5731	273	4	.	.	PROPN
ejpam-5731	273	5	math	math	PROPN
ejpam-5731	273	6	,	,	PUNCT
ejpam-5731	273	7	18	18	NUM
ejpam-5731	273	8	(	(	PUNCT
ejpam-5731	273	9	1	1	NUM
ejpam-5731	273	10	)	)	PUNCT
ejpam-5731	273	11	(	(	PUNCT
ejpam-5731	273	12	2025	2025	NUM
ejpam-5731	273	13	)	)	PUNCT
ejpam-5731	273	14	,	,	PUNCT
ejpam-5731	273	15	5731	5731	NUM
ejpam-5731	273	16	13	13	NUM
ejpam-5731	273	17	of	of	ADP
ejpam-5731	273	18	20	20	NUM
ejpam-5731	273	19	thus	thus	ADV
ejpam-5731	273	20	,	,	PUNCT
ejpam-5731	273	21	using	use	VERB
ejpam-5731	273	22	the	the	DET
ejpam-5731	273	23	constraints	constraint	NOUN
ejpam-5731	273	24	|η2|	|η2|	NOUN
ejpam-5731	273	25	≤	≤	ADV
ejpam-5731	273	26	2	2	NUM
ejpam-5731	273	27	and	and	CCONJ
ejpam-5731	273	28	|ζ2|	|ζ2|	NOUN
ejpam-5731	273	29	≤	≤	ADJ
ejpam-5731	273	30	2	2	NUM
ejpam-5731	273	31	,	,	PUNCT
ejpam-5731	273	32	then	then	ADV
ejpam-5731	273	33	simple	simple	ADJ
ejpam-5731	273	34	calculations	calculation	NOUN
ejpam-5731	273	35	give	give	VERB
ejpam-5731	273	36	the	the	DET
ejpam-5731	273	37	desired	desire	VERB
ejpam-5731	273	38	estimation	estimation	NOUN
ejpam-5731	273	39	of	of	ADP
ejpam-5731	273	40	|a2|	|a2|	NOUN
ejpam-5731	273	41	presented	present	VERB
ejpam-5731	273	42	in	in	ADP
ejpam-5731	273	43	equation	equation	NOUN
ejpam-5731	273	44	(	(	PUNCT
ejpam-5731	273	45	9	9	NUM
ejpam-5731	273	46	)	)	PUNCT
ejpam-5731	273	47	.	.	PUNCT
ejpam-5731	274	1	in	in	ADP
ejpam-5731	274	2	the	the	DET
ejpam-5731	274	3	next	next	ADJ
ejpam-5731	274	4	step	step	NOUN
ejpam-5731	274	5	,	,	PUNCT
ejpam-5731	274	6	we	we	PRON
ejpam-5731	274	7	seek	seek	VERB
ejpam-5731	274	8	to	to	PART
ejpam-5731	274	9	determine	determine	VERB
ejpam-5731	274	10	the	the	DET
ejpam-5731	274	11	coefficient	coefficient	ADJ
ejpam-5731	274	12	estimate	estimate	NOUN
ejpam-5731	274	13	for	for	ADP
ejpam-5731	274	14	|a3|	|a3|	NOUN
ejpam-5731	274	15	.	.	PUNCT
ejpam-5731	275	1	by	by	ADP
ejpam-5731	275	2	substituting	substitute	VERB
ejpam-5731	275	3	equation	equation	NOUN
ejpam-5731	275	4	(	(	PUNCT
ejpam-5731	275	5	22	22	NUM
ejpam-5731	275	6	)	)	PUNCT
ejpam-5731	275	7	from	from	ADP
ejpam-5731	275	8	equation	equation	NOUN
ejpam-5731	275	9	(	(	PUNCT
ejpam-5731	275	10	18	18	NUM
ejpam-5731	275	11	)	)	PUNCT
ejpam-5731	275	12	,	,	PUNCT
ejpam-5731	275	13	we	we	PRON
ejpam-5731	275	14	can	can	AUX
ejpam-5731	275	15	derive	derive	VERB
ejpam-5731	275	16	the	the	DET
ejpam-5731	275	17	following	follow	VERB
ejpam-5731	275	18	equation	equation	NOUN
ejpam-5731	275	19	:	:	PUNCT
ejpam-5731	276	1	8eiδ(λ+	8eiδ(λ+	NUM
ejpam-5731	276	2	2)ψ3(a3	2)ψ3(a3	NUM
ejpam-5731	276	3	−	−	NUM
ejpam-5731	276	4	a22	a22	NOUN
ejpam-5731	276	5	)	)	PUNCT
ejpam-5731	276	6	=	=	PUNCT
ejpam-5731	277	1	[	[	X
ejpam-5731	277	2	2β1(η2	2β1(η2	NUM
ejpam-5731	277	3	−	−	NOUN
ejpam-5731	277	4	ζ2	ζ2	NOUN
ejpam-5731	277	5	)	)	PUNCT
ejpam-5731	278	1	+	+	CCONJ
ejpam-5731	278	2	(	(	PUNCT
ejpam-5731	278	3	β2	β2	NOUN
ejpam-5731	278	4	−	−	PROPN
ejpam-5731	278	5	β1)(η	β1)(η	ADP
ejpam-5731	278	6	2	2	NUM
ejpam-5731	278	7	1	1	NUM
ejpam-5731	278	8	−	−	NOUN
ejpam-5731	278	9	ζ21	ζ21	VERB
ejpam-5731	278	10	)	)	PUNCT
ejpam-5731	278	11	]	]	PUNCT
ejpam-5731	279	1	cos	cos	PROPN
ejpam-5731	279	2	δ	δ	PROPN
ejpam-5731	279	3	.	.	PUNCT
ejpam-5731	280	1	now	now	ADV
ejpam-5731	280	2	,	,	PUNCT
ejpam-5731	280	3	consulting	consult	VERB
ejpam-5731	280	4	equation	equation	NOUN
ejpam-5731	280	5	(	(	PUNCT
ejpam-5731	280	6	23	23	NUM
ejpam-5731	280	7	)	)	PUNCT
ejpam-5731	280	8	,	,	PUNCT
ejpam-5731	280	9	we	we	PRON
ejpam-5731	280	10	get	get	VERB
ejpam-5731	280	11	η1	η1	NOUN
ejpam-5731	280	12	=	=	SYM
ejpam-5731	280	13	−ζ1	−ζ1	PROPN
ejpam-5731	280	14	.	.	PUNCT
ejpam-5731	281	1	hence	hence	ADV
ejpam-5731	281	2	,	,	PUNCT
ejpam-5731	281	3	the	the	DET
ejpam-5731	281	4	last	last	ADJ
ejpam-5731	281	5	equation	equation	NOUN
ejpam-5731	281	6	can	can	AUX
ejpam-5731	281	7	be	be	AUX
ejpam-5731	281	8	written	write	VERB
ejpam-5731	281	9	as	as	ADP
ejpam-5731	281	10	a3	a3	NOUN
ejpam-5731	281	11	=	=	PROPN
ejpam-5731	281	12	β1(η2	β1(η2	NUM
ejpam-5731	281	13	−	−	NOUN
ejpam-5731	281	14	ζ2	ζ2	NOUN
ejpam-5731	281	15	)	)	PUNCT
ejpam-5731	281	16	cos	cos	ADP
ejpam-5731	281	17	δ	δ	PROPN
ejpam-5731	281	18	4eiδ(λ+	4eiδ(λ+	PROPN
ejpam-5731	282	1	2)ψ3	2)ψ3	PROPN
ejpam-5731	282	2	+	+	CCONJ
ejpam-5731	282	3	a22	a22	PROPN
ejpam-5731	282	4	.	.	PUNCT
ejpam-5731	283	1	(	(	PUNCT
ejpam-5731	283	2	27	27	NUM
ejpam-5731	283	3	)	)	PUNCT
ejpam-5731	283	4	moreover	moreover	ADV
ejpam-5731	283	5	,	,	PUNCT
ejpam-5731	283	6	using	use	VERB
ejpam-5731	283	7	equation	equation	NOUN
ejpam-5731	283	8	(	(	PUNCT
ejpam-5731	283	9	25	25	NUM
ejpam-5731	283	10	)	)	PUNCT
ejpam-5731	283	11	,	,	PUNCT
ejpam-5731	283	12	the	the	DET
ejpam-5731	283	13	last	last	ADJ
ejpam-5731	283	14	equation	equation	NOUN
ejpam-5731	283	15	can	can	AUX
ejpam-5731	283	16	be	be	AUX
ejpam-5731	283	17	written	write	VERB
ejpam-5731	283	18	as	as	ADP
ejpam-5731	283	19	:	:	PUNCT
ejpam-5731	283	20	a3	a3	NOUN
ejpam-5731	283	21	=	=	PUNCT
ejpam-5731	283	22	β1(η2	β1(η2	NUM
ejpam-5731	283	23	−	−	NOUN
ejpam-5731	283	24	ζ2	ζ2	NOUN
ejpam-5731	283	25	)	)	PUNCT
ejpam-5731	283	26	cos	cos	ADP
ejpam-5731	284	1	δ	δ	PROPN
ejpam-5731	284	2	4eiδ(λ+	4eiδ(λ+	PROPN
ejpam-5731	284	3	2)ψ3	2)ψ3	NOUN
ejpam-5731	284	4	+	+	CCONJ
ejpam-5731	284	5	β21(η	β21(η	NUM
ejpam-5731	284	6	2	2	NUM
ejpam-5731	284	7	1	1	NUM
ejpam-5731	284	8	+	+	CCONJ
ejpam-5731	284	9	ζ21	ζ21	VERB
ejpam-5731	284	10	)	)	PUNCT
ejpam-5731	284	11	cos	cos	PROPN
ejpam-5731	284	12	2	2	NUM
ejpam-5731	284	13	δ	δ	NOUN
ejpam-5731	284	14	8δei(2δ)(λ+	8δei(2δ)(λ+	NOUN
ejpam-5731	284	15	1)2ψ2	1)2ψ2	NUM
ejpam-5731	284	16	2	2	NUM
ejpam-5731	284	17	.	.	PUNCT
ejpam-5731	285	1	(	(	PUNCT
ejpam-5731	285	2	28	28	NUM
ejpam-5731	285	3	)	)	PUNCT
ejpam-5731	285	4	finally	finally	ADV
ejpam-5731	285	5	,	,	PUNCT
ejpam-5731	285	6	considering	consider	VERB
ejpam-5731	285	7	the	the	DET
ejpam-5731	285	8	value	value	NOUN
ejpam-5731	285	9	β1	β1	PROPN
ejpam-5731	285	10	=	=	PUNCT
ejpam-5731	285	11	cos	cos	PROPN
ejpam-5731	285	12	θ	θ	PROPN
ejpam-5731	285	13	−	−	PROPN
ejpam-5731	285	14	1	1	NUM
ejpam-5731	285	15	,	,	PUNCT
ejpam-5731	285	16	then	then	ADV
ejpam-5731	285	17	using	use	VERB
ejpam-5731	285	18	the	the	DET
ejpam-5731	285	19	constraints	constraint	NOUN
ejpam-5731	285	20	|ηj	|ηj	ADP
ejpam-5731	285	21	|	|	ADV
ejpam-5731	285	22	≤	≤	NUM
ejpam-5731	285	23	2	2	NUM
ejpam-5731	285	24	and	and	CCONJ
ejpam-5731	285	25	|ζj	|ζj	PRON
ejpam-5731	285	26	|	|	ADV
ejpam-5731	285	27	≤	≤	ADV
ejpam-5731	285	28	2	2	NUM
ejpam-5731	285	29	for	for	ADP
ejpam-5731	285	30	all	all	DET
ejpam-5731	285	31	j	j	PROPN
ejpam-5731	285	32	∈	∈	PROPN
ejpam-5731	285	33	n	n	CCONJ
ejpam-5731	285	34	,	,	PUNCT
ejpam-5731	285	35	the	the	DET
ejpam-5731	285	36	last	last	ADJ
ejpam-5731	285	37	equation	equation	NOUN
ejpam-5731	285	38	gives	give	VERB
ejpam-5731	285	39	the	the	DET
ejpam-5731	285	40	required	require	VERB
ejpam-5731	285	41	estimation	estimation	NOUN
ejpam-5731	285	42	of	of	ADP
ejpam-5731	285	43	|a3|	|a3|	NOUN
ejpam-5731	285	44	that	that	PRON
ejpam-5731	285	45	is	be	AUX
ejpam-5731	285	46	represented	represent	VERB
ejpam-5731	285	47	by	by	ADP
ejpam-5731	285	48	the	the	DET
ejpam-5731	285	49	inequality	inequality	NOUN
ejpam-5731	285	50	(	(	PUNCT
ejpam-5731	285	51	10	10	NUM
ejpam-5731	285	52	)	)	PUNCT
ejpam-5731	285	53	.	.	PUNCT
ejpam-5731	286	1	consequently	consequently	ADV
ejpam-5731	286	2	,	,	PUNCT
ejpam-5731	286	3	the	the	DET
ejpam-5731	286	4	proof	proof	NOUN
ejpam-5731	286	5	of	of	ADP
ejpam-5731	286	6	theorem	theorem	NOUN
ejpam-5731	286	7	1	1	NUM
ejpam-5731	286	8	is	be	AUX
ejpam-5731	286	9	now	now	ADV
ejpam-5731	286	10	concluded	conclude	VERB
ejpam-5731	286	11	.	.	PUNCT
ejpam-5731	287	1	by	by	ADP
ejpam-5731	287	2	selecting	select	VERB
ejpam-5731	287	3	particular	particular	ADJ
ejpam-5731	287	4	values	value	NOUN
ejpam-5731	287	5	of	of	ADP
ejpam-5731	287	6	λ	λ	PROPN
ejpam-5731	287	7	in	in	ADP
ejpam-5731	287	8	definition	definition	NOUN
ejpam-5731	287	9	1	1	NUM
ejpam-5731	287	10	,	,	PUNCT
ejpam-5731	287	11	it	it	PRON
ejpam-5731	287	12	is	be	AUX
ejpam-5731	287	13	possible	possible	ADJ
ejpam-5731	287	14	to	to	PART
ejpam-5731	287	15	obtain	obtain	VERB
ejpam-5731	287	16	the	the	DET
ejpam-5731	287	17	subsequent	subsequent	ADJ
ejpam-5731	287	18	subclasses	subclass	NOUN
ejpam-5731	287	19	.	.	PUNCT
ejpam-5731	287	20	example	example	NOUN
ejpam-5731	288	1	1	1	NUM
ejpam-5731	288	2	.	.	PUNCT
ejpam-5731	288	3	a	a	DET
ejpam-5731	288	4	bi	bi	ADJ
ejpam-5731	288	5	-	-	ADJ
ejpam-5731	288	6	univalent	univalent	ADJ
ejpam-5731	288	7	function	function	NOUN
ejpam-5731	288	8	f	f	PROPN
ejpam-5731	288	9	that	that	PRON
ejpam-5731	288	10	represented	represent	VERB
ejpam-5731	288	11	as	as	ADP
ejpam-5731	288	12	(	(	PUNCT
ejpam-5731	288	13	1	1	NUM
ejpam-5731	288	14	)	)	PUNCT
ejpam-5731	288	15	belongs	belong	VERB
ejpam-5731	288	16	to	to	ADP
ejpam-5731	288	17	the	the	DET
ejpam-5731	288	18	subclass	subclass	NOUN
ejpam-5731	288	19	b0(δ	b0(δ	PROPN
ejpam-5731	288	20	,	,	PUNCT
ejpam-5731	288	21	rαq	rαq	NOUN
ejpam-5731	288	22	,	,	PUNCT
ejpam-5731	288	23	ϕ	ϕ	PROPN
ejpam-5731	288	24	)	)	PUNCT
ejpam-5731	288	25	if	if	SCONJ
ejpam-5731	288	26	the	the	DET
ejpam-5731	288	27	following	follow	VERB
ejpam-5731	288	28	subordinations	subordination	NOUN
ejpam-5731	288	29	hold	hold	VERB
ejpam-5731	288	30	:	:	PUNCT
ejpam-5731	288	31	eiδz	eiδz	NOUN
ejpam-5731	288	32	(	(	PUNCT
ejpam-5731	288	33	rαq	rαq	PROPN
ejpam-5731	288	34	f(z	f(z	PROPN
ejpam-5731	288	35	)	)	PUNCT
ejpam-5731	288	36	)	)	PUNCT
ejpam-5731	289	1	′	′	NUM
ejpam-5731	289	2	rαq	rαq	NOUN
ejpam-5731	289	3	f(z	f(z	PROPN
ejpam-5731	289	4	)	)	PUNCT
ejpam-5731	289	5	≺	≺	NOUN
ejpam-5731	289	6	ϕ(z	ϕ(z	NOUN
ejpam-5731	289	7	)	)	PUNCT
ejpam-5731	289	8	cos	cos	ADP
ejpam-5731	289	9	δ	δ	PROPN
ejpam-5731	290	1	+	+	CCONJ
ejpam-5731	290	2	i	i	PRON
ejpam-5731	290	3	sin	sin	VERB
ejpam-5731	290	4	δ	δ	PROPN
ejpam-5731	290	5	,	,	PUNCT
ejpam-5731	290	6	(	(	PUNCT
ejpam-5731	290	7	29	29	NUM
ejpam-5731	290	8	)	)	PUNCT
ejpam-5731	290	9	and	and	CCONJ
ejpam-5731	290	10	eiδw	eiδw	NOUN
ejpam-5731	290	11	(	(	PUNCT
ejpam-5731	290	12	rαq	rαq	PROPN
ejpam-5731	290	13	g(w	g(w	PROPN
ejpam-5731	290	14	)	)	PUNCT
ejpam-5731	290	15	)	)	PUNCT
ejpam-5731	291	1	′	′	NUM
ejpam-5731	291	2	rαq	rαq	NOUN
ejpam-5731	291	3	g(w	g(w	PROPN
ejpam-5731	291	4	)	)	PUNCT
ejpam-5731	291	5	≺	≺	NOUN
ejpam-5731	291	6	ϕ(w	ϕ(w	NOUN
ejpam-5731	291	7	)	)	PUNCT
ejpam-5731	291	8	cos	cos	ADP
ejpam-5731	291	9	δ	δ	PROPN
ejpam-5731	292	1	+	+	CCONJ
ejpam-5731	292	2	i	i	PRON
ejpam-5731	292	3	sin	sin	VERB
ejpam-5731	292	4	δ	δ	PROPN
ejpam-5731	292	5	,	,	PUNCT
ejpam-5731	292	6	(	(	PUNCT
ejpam-5731	292	7	30	30	NUM
ejpam-5731	292	8	)	)	PUNCT
ejpam-5731	292	9	where	where	SCONJ
ejpam-5731	292	10	the	the	DET
ejpam-5731	292	11	function	function	NOUN
ejpam-5731	292	12	g(w	g(w	PROPN
ejpam-5731	292	13	)	)	PUNCT
ejpam-5731	292	14	=	=	SYM
ejpam-5731	292	15	f−1(w	f−1(w	PROPN
ejpam-5731	292	16	)	)	PUNCT
ejpam-5731	292	17	is	be	AUX
ejpam-5731	292	18	given	give	VERB
ejpam-5731	292	19	by	by	ADP
ejpam-5731	292	20	the	the	DET
ejpam-5731	292	21	equation	equation	NOUN
ejpam-5731	292	22	(	(	PUNCT
ejpam-5731	292	23	2	2	NUM
ejpam-5731	292	24	)	)	PUNCT
ejpam-5731	292	25	,	,	PUNCT
ejpam-5731	292	26	the	the	DET
ejpam-5731	292	27	parameters	parameter	NOUN
ejpam-5731	292	28	0	0	PUNCT
ejpam-5731	292	29	<	<	X
ejpam-5731	292	30	q	q	X
ejpam-5731	292	31	<	<	X
ejpam-5731	292	32	1	1	NUM
ejpam-5731	292	33	,	,	PUNCT
ejpam-5731	292	34	α	α	NOUN
ejpam-5731	292	35	>	>	X
ejpam-5731	292	36	−1	−1	NOUN
ejpam-5731	292	37	,	,	PUNCT
ejpam-5731	292	38	and	and	CCONJ
ejpam-5731	292	39	δ	δ	PROPN
ejpam-5731	292	40	∈	∈	PROPN
ejpam-5731	292	41	(	(	PUNCT
ejpam-5731	292	42	−π	−π	ADV
ejpam-5731	292	43	2	2	NUM
ejpam-5731	292	44	,	,	PUNCT
ejpam-5731	292	45	π	π	PROPN
ejpam-5731	292	46	2	2	NUM
ejpam-5731	292	47	)	)	PUNCT
ejpam-5731	292	48	.	.	PUNCT
ejpam-5731	293	1	example	example	NOUN
ejpam-5731	294	1	2	2	NUM
ejpam-5731	294	2	.	.	X
ejpam-5731	294	3	a	a	DET
ejpam-5731	294	4	bi	bi	ADJ
ejpam-5731	294	5	-	-	ADJ
ejpam-5731	294	6	univalent	univalent	ADJ
ejpam-5731	294	7	function	function	NOUN
ejpam-5731	294	8	f	f	PROPN
ejpam-5731	294	9	that	that	PRON
ejpam-5731	294	10	represented	represent	VERB
ejpam-5731	294	11	as	as	ADP
ejpam-5731	294	12	(	(	PUNCT
ejpam-5731	294	13	1	1	NUM
ejpam-5731	294	14	)	)	PUNCT
ejpam-5731	294	15	belongs	belong	VERB
ejpam-5731	294	16	to	to	ADP
ejpam-5731	294	17	the	the	DET
ejpam-5731	294	18	subclass	subclass	NOUN
ejpam-5731	294	19	b1(δ	b1(δ	PROPN
ejpam-5731	294	20	,	,	PUNCT
ejpam-5731	294	21	rαq	rαq	NOUN
ejpam-5731	294	22	,	,	PUNCT
ejpam-5731	294	23	ϕ	ϕ	PROPN
ejpam-5731	294	24	)	)	PUNCT
ejpam-5731	294	25	if	if	SCONJ
ejpam-5731	294	26	the	the	DET
ejpam-5731	294	27	following	follow	VERB
ejpam-5731	294	28	subordinations	subordination	NOUN
ejpam-5731	294	29	hold	hold	VERB
ejpam-5731	294	30	:	:	PUNCT
ejpam-5731	294	31	eiδ	eiδ	PROPN
ejpam-5731	294	32	(	(	PUNCT
ejpam-5731	294	33	rαq	rαq	PROPN
ejpam-5731	294	34	f(z	f(z	PROPN
ejpam-5731	294	35	)	)	PUNCT
ejpam-5731	294	36	)	)	PUNCT
ejpam-5731	294	37	′	′	NUM
ejpam-5731	294	38	≺	≺	NOUN
ejpam-5731	294	39	ϕ(z	ϕ(z	NOUN
ejpam-5731	294	40	)	)	PUNCT
ejpam-5731	294	41	cos	cos	ADP
ejpam-5731	294	42	δ	δ	PROPN
ejpam-5731	295	1	+	+	CCONJ
ejpam-5731	295	2	i	i	PRON
ejpam-5731	295	3	sin	sin	VERB
ejpam-5731	295	4	δ	δ	PROPN
ejpam-5731	295	5	,	,	PUNCT
ejpam-5731	295	6	(	(	PUNCT
ejpam-5731	295	7	31	31	NUM
ejpam-5731	295	8	)	)	PUNCT
ejpam-5731	295	9	and	and	CCONJ
ejpam-5731	295	10	eiδ	eiδ	NOUN
ejpam-5731	295	11	(	(	PUNCT
ejpam-5731	295	12	rαq	rαq	NOUN
ejpam-5731	295	13	g(w	g(w	PROPN
ejpam-5731	295	14	)	)	PUNCT
ejpam-5731	295	15	)	)	PUNCT
ejpam-5731	295	16	′	′	NUM
ejpam-5731	295	17	≺	≺	NOUN
ejpam-5731	295	18	ϕ(w	ϕ(w	NOUN
ejpam-5731	295	19	)	)	PUNCT
ejpam-5731	295	20	cos	cos	ADP
ejpam-5731	295	21	δ	δ	PROPN
ejpam-5731	296	1	+	+	CCONJ
ejpam-5731	296	2	i	i	PRON
ejpam-5731	296	3	sin	sin	VERB
ejpam-5731	296	4	δ	δ	PROPN
ejpam-5731	296	5	,	,	PUNCT
ejpam-5731	296	6	(	(	PUNCT
ejpam-5731	296	7	32	32	NUM
ejpam-5731	296	8	)	)	PUNCT
ejpam-5731	296	9	where	where	SCONJ
ejpam-5731	296	10	the	the	DET
ejpam-5731	296	11	function	function	NOUN
ejpam-5731	296	12	g(w	g(w	PROPN
ejpam-5731	296	13	)	)	PUNCT
ejpam-5731	296	14	=	=	SYM
ejpam-5731	296	15	f−1(w	f−1(w	PROPN
ejpam-5731	296	16	)	)	PUNCT
ejpam-5731	296	17	is	be	AUX
ejpam-5731	296	18	given	give	VERB
ejpam-5731	296	19	by	by	ADP
ejpam-5731	296	20	the	the	DET
ejpam-5731	296	21	equation	equation	NOUN
ejpam-5731	296	22	(	(	PUNCT
ejpam-5731	296	23	2	2	NUM
ejpam-5731	296	24	)	)	PUNCT
ejpam-5731	296	25	,	,	PUNCT
ejpam-5731	296	26	the	the	DET
ejpam-5731	296	27	parameters	parameter	NOUN
ejpam-5731	296	28	0	0	PUNCT
ejpam-5731	296	29	<	<	X
ejpam-5731	296	30	q	q	X
ejpam-5731	296	31	<	<	X
ejpam-5731	296	32	1	1	NUM
ejpam-5731	296	33	,	,	PUNCT
ejpam-5731	296	34	α	α	NOUN
ejpam-5731	296	35	>	>	X
ejpam-5731	296	36	−1	−1	NOUN
ejpam-5731	296	37	,	,	PUNCT
ejpam-5731	296	38	and	and	CCONJ
ejpam-5731	296	39	δ	δ	PROPN
ejpam-5731	296	40	∈	∈	PROPN
ejpam-5731	296	41	(	(	PUNCT
ejpam-5731	296	42	−π	−π	ADV
ejpam-5731	296	43	2	2	NUM
ejpam-5731	296	44	,	,	PUNCT
ejpam-5731	296	45	π	π	PROPN
ejpam-5731	296	46	2	2	NUM
ejpam-5731	296	47	)	)	PUNCT
ejpam-5731	296	48	.	.	PUNCT
ejpam-5731	297	1	w.	w.	PROPN
ejpam-5731	297	2	al	al	PROPN
ejpam-5731	297	3	-	-	PUNCT
ejpam-5731	297	4	rawashdeh	rawashdeh	PROPN
ejpam-5731	297	5	/	/	SYM
ejpam-5731	297	6	eur	eur	PROPN
ejpam-5731	297	7	.	.	PUNCT
ejpam-5731	298	1	j.	j.	PROPN
ejpam-5731	298	2	pure	pure	PROPN
ejpam-5731	298	3	appl	appl	PROPN
ejpam-5731	298	4	.	.	PROPN
ejpam-5731	298	5	math	math	PROPN
ejpam-5731	298	6	,	,	PUNCT
ejpam-5731	298	7	18	18	NUM
ejpam-5731	298	8	(	(	PUNCT
ejpam-5731	298	9	1	1	NUM
ejpam-5731	298	10	)	)	PUNCT
ejpam-5731	298	11	(	(	PUNCT
ejpam-5731	298	12	2025	2025	NUM
ejpam-5731	298	13	)	)	PUNCT
ejpam-5731	298	14	,	,	PUNCT
ejpam-5731	298	15	5731	5731	NUM
ejpam-5731	298	16	14	14	NUM
ejpam-5731	298	17	of	of	ADP
ejpam-5731	298	18	20	20	NUM
ejpam-5731	298	19	moreover	moreover	ADV
ejpam-5731	298	20	,	,	PUNCT
ejpam-5731	298	21	as	as	ADP
ejpam-5731	298	22	q	q	PROPN
ejpam-5731	298	23	→	→	SYM
ejpam-5731	298	24	1−	1−	NUM
ejpam-5731	298	25	and	and	CCONJ
ejpam-5731	298	26	taking	take	VERB
ejpam-5731	298	27	α	α	NOUN
ejpam-5731	298	28	=	=	SYM
ejpam-5731	298	29	0	0	NUM
ejpam-5731	298	30	,	,	PUNCT
ejpam-5731	298	31	we	we	PRON
ejpam-5731	298	32	get	get	VERB
ejpam-5731	298	33	r0	r0	NOUN
ejpam-5731	298	34	qf(z	qf(z	NUM
ejpam-5731	298	35	)	)	PUNCT
ejpam-5731	298	36	=	=	SYM
ejpam-5731	298	37	f(z	f(z	PROPN
ejpam-5731	298	38	)	)	PUNCT
ejpam-5731	298	39	.	.	PUNCT
ejpam-5731	299	1	therefore	therefore	ADV
ejpam-5731	299	2	,	,	PUNCT
ejpam-5731	299	3	we	we	PRON
ejpam-5731	299	4	get	get	VERB
ejpam-5731	299	5	the	the	DET
ejpam-5731	299	6	following	follow	VERB
ejpam-5731	299	7	close	close	VERB
ejpam-5731	299	8	-	-	PUNCT
ejpam-5731	299	9	to	to	ADP
ejpam-5731	299	10	-	-	PUNCT
ejpam-5731	299	11	starlike	starlike	NOUN
ejpam-5731	299	12	subclasses	subclass	NOUN
ejpam-5731	299	13	.	.	PUNCT
ejpam-5731	300	1	example	example	NOUN
ejpam-5731	301	1	3	3	NUM
ejpam-5731	301	2	.	.	PUNCT
ejpam-5731	301	3	a	a	DET
ejpam-5731	301	4	bi	bi	ADJ
ejpam-5731	301	5	-	-	ADJ
ejpam-5731	301	6	univalent	univalent	ADJ
ejpam-5731	301	7	function	function	NOUN
ejpam-5731	301	8	f	f	PROPN
ejpam-5731	301	9	that	that	PRON
ejpam-5731	301	10	represented	represent	VERB
ejpam-5731	301	11	as	as	ADP
ejpam-5731	301	12	(	(	PUNCT
ejpam-5731	301	13	1	1	NUM
ejpam-5731	301	14	)	)	PUNCT
ejpam-5731	301	15	belongs	belong	VERB
ejpam-5731	301	16	to	to	ADP
ejpam-5731	301	17	the	the	DET
ejpam-5731	301	18	subclass	subclass	NOUN
ejpam-5731	301	19	s∗(δ	s∗(δ	PROPN
ejpam-5731	301	20	,	,	PUNCT
ejpam-5731	301	21	ϕ	ϕ	NOUN
ejpam-5731	301	22	)	)	PUNCT
ejpam-5731	301	23	if	if	SCONJ
ejpam-5731	301	24	the	the	DET
ejpam-5731	301	25	following	follow	VERB
ejpam-5731	301	26	subordinations	subordination	NOUN
ejpam-5731	301	27	hold	hold	VERB
ejpam-5731	301	28	:	:	PUNCT
ejpam-5731	301	29	eiδ	eiδ	PROPN
ejpam-5731	301	30	(	(	PUNCT
ejpam-5731	301	31	zf	zf	PROPN
ejpam-5731	301	32	′(z	′(z	NOUN
ejpam-5731	301	33	)	)	PUNCT
ejpam-5731	301	34	f(z	f(z	PROPN
ejpam-5731	301	35	)	)	PUNCT
ejpam-5731	301	36	)	)	PUNCT
ejpam-5731	301	37	≺	≺	NOUN
ejpam-5731	301	38	ϕ(z	ϕ(z	NOUN
ejpam-5731	301	39	)	)	PUNCT
ejpam-5731	301	40	cos	cos	ADP
ejpam-5731	301	41	δ	δ	PROPN
ejpam-5731	302	1	+	+	CCONJ
ejpam-5731	302	2	i	i	PRON
ejpam-5731	302	3	sin	sin	VERB
ejpam-5731	302	4	δ	δ	PROPN
ejpam-5731	302	5	,	,	PUNCT
ejpam-5731	302	6	(	(	PUNCT
ejpam-5731	302	7	33	33	NUM
ejpam-5731	302	8	)	)	PUNCT
ejpam-5731	302	9	and	and	CCONJ
ejpam-5731	302	10	eiδ	eiδ	ADJ
ejpam-5731	302	11	(	(	PUNCT
ejpam-5731	302	12	wg′(w	wg′(w	PROPN
ejpam-5731	302	13	)	)	PUNCT
ejpam-5731	302	14	g(w	g(w	PROPN
ejpam-5731	302	15	)	)	PUNCT
ejpam-5731	302	16	)	)	PUNCT
ejpam-5731	302	17	≺	≺	NOUN
ejpam-5731	302	18	ϕ(w	ϕ(w	NOUN
ejpam-5731	302	19	)	)	PUNCT
ejpam-5731	302	20	cos	cos	ADP
ejpam-5731	302	21	δ	δ	PROPN
ejpam-5731	303	1	+	+	CCONJ
ejpam-5731	303	2	i	i	PRON
ejpam-5731	303	3	sin	sin	VERB
ejpam-5731	303	4	δ	δ	PROPN
ejpam-5731	303	5	(	(	PUNCT
ejpam-5731	303	6	34	34	NUM
ejpam-5731	303	7	)	)	PUNCT
ejpam-5731	303	8	where	where	SCONJ
ejpam-5731	303	9	g(w	g(w	ADJ
ejpam-5731	303	10	)	)	PUNCT
ejpam-5731	303	11	=	=	SYM
ejpam-5731	303	12	f−1(w	f−1(w	PROPN
ejpam-5731	303	13	)	)	PUNCT
ejpam-5731	303	14	is	be	AUX
ejpam-5731	303	15	given	give	VERB
ejpam-5731	303	16	by	by	ADP
ejpam-5731	303	17	the	the	DET
ejpam-5731	303	18	equation	equation	NOUN
ejpam-5731	303	19	(	(	PUNCT
ejpam-5731	303	20	2	2	NUM
ejpam-5731	303	21	)	)	PUNCT
ejpam-5731	303	22	and	and	CCONJ
ejpam-5731	303	23	δ	δ	PROPN
ejpam-5731	303	24	∈	∈	PROPN
ejpam-5731	303	25	(	(	PUNCT
ejpam-5731	303	26	−π	−π	ADV
ejpam-5731	303	27	2	2	NUM
ejpam-5731	303	28	,	,	PUNCT
ejpam-5731	303	29	π	π	PROPN
ejpam-5731	303	30	2	2	NUM
ejpam-5731	303	31	)	)	PUNCT
ejpam-5731	303	32	.	.	PUNCT
ejpam-5731	304	1	example	example	NOUN
ejpam-5731	305	1	4	4	NUM
ejpam-5731	305	2	.	.	PUNCT
ejpam-5731	305	3	a	a	DET
ejpam-5731	305	4	bi	bi	ADJ
ejpam-5731	305	5	-	-	ADJ
ejpam-5731	305	6	univalent	univalent	ADJ
ejpam-5731	305	7	function	function	NOUN
ejpam-5731	305	8	f	f	PROPN
ejpam-5731	305	9	that	that	PRON
ejpam-5731	305	10	represented	represent	VERB
ejpam-5731	305	11	as	as	ADP
ejpam-5731	305	12	(	(	PUNCT
ejpam-5731	305	13	1	1	NUM
ejpam-5731	305	14	)	)	PUNCT
ejpam-5731	305	15	belongs	belong	VERB
ejpam-5731	305	16	to	to	ADP
ejpam-5731	305	17	the	the	DET
ejpam-5731	305	18	subclass	subclass	NOUN
ejpam-5731	305	19	g∗(δ	g∗(δ	PROPN
ejpam-5731	305	20	,	,	PUNCT
ejpam-5731	305	21	ϕ	ϕ	NOUN
ejpam-5731	305	22	)	)	PUNCT
ejpam-5731	305	23	if	if	SCONJ
ejpam-5731	305	24	the	the	DET
ejpam-5731	305	25	following	follow	VERB
ejpam-5731	305	26	subordinations	subordination	NOUN
ejpam-5731	305	27	hold	hold	VERB
ejpam-5731	305	28	:	:	PUNCT
ejpam-5731	305	29	eiδ	eiδ	PROPN
ejpam-5731	305	30	(	(	PUNCT
ejpam-5731	305	31	f	f	NOUN
ejpam-5731	305	32	′(z	′(z	NOUN
ejpam-5731	305	33	)	)	PUNCT
ejpam-5731	305	34	)	)	PUNCT
ejpam-5731	305	35	≺	≺	NOUN
ejpam-5731	305	36	ϕ(z	ϕ(z	NOUN
ejpam-5731	305	37	)	)	PUNCT
ejpam-5731	305	38	cos	cos	ADP
ejpam-5731	305	39	δ	δ	PROPN
ejpam-5731	306	1	+	+	CCONJ
ejpam-5731	306	2	i	i	PRON
ejpam-5731	306	3	sin	sin	VERB
ejpam-5731	306	4	δ	δ	PROPN
ejpam-5731	306	5	,	,	PUNCT
ejpam-5731	306	6	(	(	PUNCT
ejpam-5731	306	7	35	35	NUM
ejpam-5731	306	8	)	)	PUNCT
ejpam-5731	306	9	and	and	CCONJ
ejpam-5731	306	10	eiδ	eiδ	X
ejpam-5731	306	11	(	(	PUNCT
ejpam-5731	306	12	g′(w	g′(w	NOUN
ejpam-5731	306	13	)	)	PUNCT
ejpam-5731	306	14	)	)	PUNCT
ejpam-5731	306	15	≺	≺	NOUN
ejpam-5731	306	16	ϕ(w	ϕ(w	NOUN
ejpam-5731	306	17	)	)	PUNCT
ejpam-5731	306	18	cos	cos	ADP
ejpam-5731	306	19	δ	δ	PROPN
ejpam-5731	307	1	+	+	CCONJ
ejpam-5731	307	2	i	i	PRON
ejpam-5731	307	3	sin	sin	VERB
ejpam-5731	307	4	δ	δ	PROPN
ejpam-5731	307	5	,	,	PUNCT
ejpam-5731	307	6	(	(	PUNCT
ejpam-5731	307	7	36	36	NUM
ejpam-5731	307	8	)	)	PUNCT
ejpam-5731	307	9	where	where	SCONJ
ejpam-5731	307	10	g(w	g(w	ADJ
ejpam-5731	307	11	)	)	PUNCT
ejpam-5731	307	12	=	=	SYM
ejpam-5731	307	13	f−1(w	f−1(w	PROPN
ejpam-5731	307	14	)	)	PUNCT
ejpam-5731	307	15	is	be	AUX
ejpam-5731	307	16	given	give	VERB
ejpam-5731	307	17	by	by	ADP
ejpam-5731	307	18	the	the	DET
ejpam-5731	307	19	equation	equation	NOUN
ejpam-5731	307	20	(	(	PUNCT
ejpam-5731	307	21	2	2	NUM
ejpam-5731	307	22	)	)	PUNCT
ejpam-5731	307	23	and	and	CCONJ
ejpam-5731	307	24	δ	δ	PROPN
ejpam-5731	307	25	∈	∈	PROPN
ejpam-5731	307	26	(	(	PUNCT
ejpam-5731	307	27	−π	−π	ADV
ejpam-5731	307	28	2	2	NUM
ejpam-5731	307	29	,	,	PUNCT
ejpam-5731	307	30	π	π	PROPN
ejpam-5731	307	31	2	2	NUM
ejpam-5731	307	32	)	)	PUNCT
ejpam-5731	307	33	.	.	PUNCT
ejpam-5731	308	1	the	the	DET
ejpam-5731	308	2	subsequent	subsequent	ADJ
ejpam-5731	308	3	corollaries	corollary	NOUN
ejpam-5731	308	4	are	be	AUX
ejpam-5731	308	5	directly	directly	ADV
ejpam-5731	308	6	obtained	obtain	VERB
ejpam-5731	308	7	from	from	ADP
ejpam-5731	308	8	theorem	theorem	ADJ
ejpam-5731	308	9	1	1	NUM
ejpam-5731	308	10	,	,	PUNCT
ejpam-5731	308	11	contingent	contingent	ADJ
ejpam-5731	308	12	upon	upon	SCONJ
ejpam-5731	308	13	the	the	DET
ejpam-5731	308	14	conditions	condition	NOUN
ejpam-5731	308	15	specified	specify	VERB
ejpam-5731	308	16	in	in	ADP
ejpam-5731	308	17	the	the	DET
ejpam-5731	308	18	earlier	early	ADJ
ejpam-5731	308	19	examples	example	NOUN
ejpam-5731	308	20	.	.	PUNCT
ejpam-5731	309	1	the	the	DET
ejpam-5731	309	2	techniques	technique	NOUN
ejpam-5731	309	3	employed	employ	VERB
ejpam-5731	309	4	in	in	ADP
ejpam-5731	309	5	deriving	derive	VERB
ejpam-5731	309	6	these	these	DET
ejpam-5731	309	7	corollaries	corollary	NOUN
ejpam-5731	309	8	closely	closely	ADV
ejpam-5731	309	9	mirror	mirror	VERB
ejpam-5731	309	10	those	those	PRON
ejpam-5731	309	11	applied	apply	VERB
ejpam-5731	309	12	in	in	ADP
ejpam-5731	309	13	the	the	DET
ejpam-5731	309	14	proof	proof	NOUN
ejpam-5731	309	15	of	of	ADP
ejpam-5731	309	16	theorem	theorem	NOUN
ejpam-5731	309	17	1	1	NUM
ejpam-5731	309	18	,	,	PUNCT
ejpam-5731	309	19	which	which	PRON
ejpam-5731	309	20	is	be	AUX
ejpam-5731	309	21	the	the	DET
ejpam-5731	309	22	rationale	rationale	NOUN
ejpam-5731	309	23	behind	behind	ADP
ejpam-5731	309	24	our	our	PRON
ejpam-5731	309	25	decision	decision	NOUN
ejpam-5731	309	26	to	to	PART
ejpam-5731	309	27	exclude	exclude	VERB
ejpam-5731	309	28	the	the	DET
ejpam-5731	309	29	detailed	detailed	ADJ
ejpam-5731	309	30	proofs	proof	NOUN
ejpam-5731	309	31	.	.	PUNCT
ejpam-5731	310	1	corollary	corollary	ADJ
ejpam-5731	310	2	1	1	NUM
ejpam-5731	310	3	.	.	PUNCT
ejpam-5731	311	1	if	if	SCONJ
ejpam-5731	311	2	a	a	DET
ejpam-5731	311	3	function	function	NOUN
ejpam-5731	311	4	f	f	PROPN
ejpam-5731	311	5	∈	∈	PROPN
ejpam-5731	311	6	σ	σ	PROPN
ejpam-5731	311	7	is	be	AUX
ejpam-5731	311	8	represented	represent	VERB
ejpam-5731	311	9	by	by	ADP
ejpam-5731	311	10	(	(	PUNCT
ejpam-5731	311	11	1	1	NUM
ejpam-5731	311	12	)	)	PUNCT
ejpam-5731	311	13	and	and	CCONJ
ejpam-5731	311	14	belong	belong	VERB
ejpam-5731	311	15	to	to	ADP
ejpam-5731	311	16	the	the	DET
ejpam-5731	311	17	class	class	NOUN
ejpam-5731	311	18	b0(δ	b0(δ	PROPN
ejpam-5731	311	19	,	,	PUNCT
ejpam-5731	311	20	rαq	rαq	NOUN
ejpam-5731	311	21	,	,	PUNCT
ejpam-5731	311	22	ϕ	ϕ	PROPN
ejpam-5731	311	23	)	)	PUNCT
ejpam-5731	311	24	,	,	PUNCT
ejpam-5731	311	25	then	then	ADV
ejpam-5731	311	26	it	it	PRON
ejpam-5731	311	27	can	can	AUX
ejpam-5731	311	28	be	be	AUX
ejpam-5731	311	29	concluded	conclude	VERB
ejpam-5731	311	30	that	that	SCONJ
ejpam-5731	311	31	|a2|	|a2|	NOUN
ejpam-5731	311	32	≤	≤	NUM
ejpam-5731	311	33	√	√	ADP
ejpam-5731	311	34	2|1−	2|1−	NUM
ejpam-5731	311	35	cos	cos	ADP
ejpam-5731	311	36	θ|	θ|	PROPN
ejpam-5731	311	37	cos	co	NOUN
ejpam-5731	311	38	δ√	δ√	PROPN
ejpam-5731	311	39	|	|	NOUN
ejpam-5731	311	40	cos	cos	ADP
ejpam-5731	311	41	δ(cos	δ(cos	PROPN
ejpam-5731	311	42	θ	θ	PROPN
ejpam-5731	312	1	−	−	PROPN
ejpam-5731	312	2	1)(4ψ3	1)(4ψ3	NUM
ejpam-5731	313	1	−	−	NUM
ejpam-5731	313	2	2ψ2	2ψ2	NUM
ejpam-5731	313	3	2	2	NUM
ejpam-5731	313	4	)	)	PUNCT
ejpam-5731	313	5	+	+	CCONJ
ejpam-5731	313	6	(	(	PUNCT
ejpam-5731	313	7	1−	1−	NUM
ejpam-5731	313	8	3	3	NUM
ejpam-5731	313	9	cos	cos	ADP
ejpam-5731	313	10	θ)ψ2	θ)ψ2	PROPN
ejpam-5731	313	11	2e	2e	NOUN
ejpam-5731	313	12	iδ|	iδ|	ADV
ejpam-5731	313	13	,	,	PUNCT
ejpam-5731	313	14	and	and	CCONJ
ejpam-5731	313	15	|a3|	|a3|	VERB
ejpam-5731	313	16	≤	≤	PROPN
ejpam-5731	313	17	|1−	|1−	PROPN
ejpam-5731	314	1	cos	cos	ADP
ejpam-5731	314	2	θ|	θ|	PROPN
ejpam-5731	314	3	cos	cos	ADP
ejpam-5731	314	4	δ	δ	PROPN
ejpam-5731	314	5	2ψ3	2ψ3	NUM
ejpam-5731	314	6	+	+	CCONJ
ejpam-5731	314	7	(	(	PUNCT
ejpam-5731	314	8	1−	1−	NUM
ejpam-5731	314	9	cos	cos	PROPN
ejpam-5731	314	10	θ)2	θ)2	PROPN
ejpam-5731	314	11	cos2	cos2	PROPN
ejpam-5731	314	12	δ	δ	PROPN
ejpam-5731	314	13	ψ2	ψ2	VERB
ejpam-5731	314	14	2	2	NUM
ejpam-5731	314	15	.	.	PUNCT
ejpam-5731	315	1	corollary	corollary	ADJ
ejpam-5731	315	2	2	2	NUM
ejpam-5731	315	3	.	.	PUNCT
ejpam-5731	316	1	if	if	SCONJ
ejpam-5731	316	2	a	a	DET
ejpam-5731	316	3	function	function	NOUN
ejpam-5731	316	4	f	f	PROPN
ejpam-5731	316	5	∈	∈	PROPN
ejpam-5731	316	6	σ	σ	PROPN
ejpam-5731	316	7	is	be	AUX
ejpam-5731	316	8	represented	represent	VERB
ejpam-5731	316	9	by	by	ADP
ejpam-5731	316	10	(	(	PUNCT
ejpam-5731	316	11	1	1	NUM
ejpam-5731	316	12	)	)	PUNCT
ejpam-5731	316	13	and	and	CCONJ
ejpam-5731	316	14	belong	belong	VERB
ejpam-5731	316	15	to	to	ADP
ejpam-5731	316	16	the	the	DET
ejpam-5731	316	17	class	class	NOUN
ejpam-5731	316	18	b1(δ	b1(δ	PROPN
ejpam-5731	316	19	,	,	PUNCT
ejpam-5731	316	20	rαq	rαq	NOUN
ejpam-5731	316	21	,	,	PUNCT
ejpam-5731	316	22	ϕ	ϕ	PROPN
ejpam-5731	316	23	)	)	PUNCT
ejpam-5731	316	24	,	,	PUNCT
ejpam-5731	316	25	then	then	ADV
ejpam-5731	316	26	it	it	PRON
ejpam-5731	316	27	can	can	AUX
ejpam-5731	316	28	be	be	AUX
ejpam-5731	316	29	concluded	conclude	VERB
ejpam-5731	316	30	that	that	SCONJ
ejpam-5731	316	31	|a2|	|a2|	NOUN
ejpam-5731	316	32	≤	≤	NUM
ejpam-5731	316	33	|1−	|1−	NOUN
ejpam-5731	316	34	cos	cos	ADP
ejpam-5731	316	35	θ|	θ|	PROPN
ejpam-5731	316	36	cos	co	NOUN
ejpam-5731	316	37	δ√	δ√	NOUN
ejpam-5731	316	38	|2	|2	NUM
ejpam-5731	316	39	cos	cos	X
ejpam-5731	316	40	δ(cos	δ(cos	PROPN
ejpam-5731	316	41	θ	θ	PROPN
ejpam-5731	317	1	−	−	PROPN
ejpam-5731	318	1	1)ψ3	1)ψ3	NUM
ejpam-5731	318	2	+	+	CCONJ
ejpam-5731	318	3	2(1−	2(1−	NUM
ejpam-5731	318	4	3	3	NUM
ejpam-5731	318	5	cos	cos	X
ejpam-5731	318	6	θ)ψ2	θ)ψ2	PROPN
ejpam-5731	318	7	2e	2e	NOUN
ejpam-5731	318	8	iδ|	iδ|	ADV
ejpam-5731	318	9	,	,	PUNCT
ejpam-5731	318	10	and	and	CCONJ
ejpam-5731	318	11	|a3|	|a3|	VERB
ejpam-5731	318	12	≤	≤	PROPN
ejpam-5731	318	13	|1−	|1−	PROPN
ejpam-5731	318	14	cos	cos	ADP
ejpam-5731	318	15	θ|	θ|	PROPN
ejpam-5731	318	16	cos	cos	ADP
ejpam-5731	318	17	δ	δ	PROPN
ejpam-5731	318	18	3ψ3	3ψ3	NUM
ejpam-5731	318	19	+	+	CCONJ
ejpam-5731	318	20	(	(	PUNCT
ejpam-5731	318	21	1−	1−	NUM
ejpam-5731	318	22	cos	cos	PROPN
ejpam-5731	318	23	θ)2	θ)2	PROPN
ejpam-5731	318	24	cos2	cos2	PROPN
ejpam-5731	318	25	δ	δ	PROPN
ejpam-5731	318	26	4ψ2	4ψ2	NUM
ejpam-5731	318	27	2	2	NUM
ejpam-5731	318	28	.	.	PUNCT
ejpam-5731	319	1	w.	w.	PROPN
ejpam-5731	319	2	al	al	PROPN
ejpam-5731	319	3	-	-	PUNCT
ejpam-5731	319	4	rawashdeh	rawashdeh	PROPN
ejpam-5731	319	5	/	/	SYM
ejpam-5731	319	6	eur	eur	PROPN
ejpam-5731	319	7	.	.	PUNCT
ejpam-5731	320	1	j.	j.	PROPN
ejpam-5731	320	2	pure	pure	PROPN
ejpam-5731	320	3	appl	appl	PROPN
ejpam-5731	320	4	.	.	PROPN
ejpam-5731	320	5	math	math	PROPN
ejpam-5731	320	6	,	,	PUNCT
ejpam-5731	320	7	18	18	NUM
ejpam-5731	320	8	(	(	PUNCT
ejpam-5731	320	9	1	1	NUM
ejpam-5731	320	10	)	)	PUNCT
ejpam-5731	320	11	(	(	PUNCT
ejpam-5731	320	12	2025	2025	NUM
ejpam-5731	320	13	)	)	PUNCT
ejpam-5731	320	14	,	,	PUNCT
ejpam-5731	320	15	5731	5731	NUM
ejpam-5731	320	16	15	15	NUM
ejpam-5731	320	17	of	of	ADP
ejpam-5731	320	18	20	20	NUM
ejpam-5731	320	19	corollary	corollary	ADJ
ejpam-5731	320	20	3	3	NUM
ejpam-5731	320	21	.	.	PUNCT
ejpam-5731	321	1	if	if	SCONJ
ejpam-5731	321	2	a	a	DET
ejpam-5731	321	3	function	function	NOUN
ejpam-5731	321	4	f	f	PROPN
ejpam-5731	321	5	∈	∈	PROPN
ejpam-5731	321	6	σ	σ	PROPN
ejpam-5731	321	7	is	be	AUX
ejpam-5731	321	8	represented	represent	VERB
ejpam-5731	321	9	by	by	ADP
ejpam-5731	321	10	(	(	PUNCT
ejpam-5731	321	11	1	1	NUM
ejpam-5731	321	12	)	)	PUNCT
ejpam-5731	321	13	and	and	CCONJ
ejpam-5731	321	14	belong	belong	VERB
ejpam-5731	321	15	to	to	ADP
ejpam-5731	321	16	the	the	DET
ejpam-5731	321	17	class	class	NOUN
ejpam-5731	321	18	s∗(δ	s∗(δ	PROPN
ejpam-5731	321	19	,	,	PUNCT
ejpam-5731	321	20	ϕ	ϕ	NOUN
ejpam-5731	321	21	)	)	PUNCT
ejpam-5731	321	22	,	,	PUNCT
ejpam-5731	321	23	then	then	ADV
ejpam-5731	321	24	it	it	PRON
ejpam-5731	321	25	can	can	AUX
ejpam-5731	321	26	be	be	AUX
ejpam-5731	321	27	concluded	conclude	VERB
ejpam-5731	321	28	that	that	SCONJ
ejpam-5731	321	29	|a2|	|a2|	NOUN
ejpam-5731	321	30	≤	≤	NUM
ejpam-5731	321	31	√	√	ADP
ejpam-5731	321	32	2|1−	2|1−	NUM
ejpam-5731	321	33	cos	cos	ADP
ejpam-5731	321	34	θ|	θ|	PROPN
ejpam-5731	321	35	cos	co	NOUN
ejpam-5731	321	36	δ√	δ√	NOUN
ejpam-5731	321	37	|2	|2	NUM
ejpam-5731	321	38	cos	cos	X
ejpam-5731	321	39	δ(cos	δ(cos	PROPN
ejpam-5731	321	40	θ	θ	PROPN
ejpam-5731	322	1	−	−	NOUN
ejpam-5731	322	2	1	1	NUM
ejpam-5731	322	3	)	)	PUNCT
ejpam-5731	322	4	+	+	CCONJ
ejpam-5731	322	5	(	(	PUNCT
ejpam-5731	322	6	1−	1−	NUM
ejpam-5731	322	7	3	3	NUM
ejpam-5731	322	8	cos	cos	PROPN
ejpam-5731	322	9	θ)eiδ|	θ)eiδ|	PROPN
ejpam-5731	322	10	,	,	PUNCT
ejpam-5731	322	11	and	and	CCONJ
ejpam-5731	322	12	|a3|	|a3|	VERB
ejpam-5731	322	13	≤	≤	PROPN
ejpam-5731	322	14	|1−	|1−	PROPN
ejpam-5731	322	15	cos	cos	ADP
ejpam-5731	322	16	θ|	θ|	PROPN
ejpam-5731	322	17	cos	cos	ADP
ejpam-5731	322	18	δ	δ	PROPN
ejpam-5731	322	19	2	2	NUM
ejpam-5731	322	20	+	+	CCONJ
ejpam-5731	322	21	(	(	PUNCT
ejpam-5731	322	22	1−	1−	NUM
ejpam-5731	322	23	cos	cos	PROPN
ejpam-5731	322	24	θ)2	θ)2	PROPN
ejpam-5731	322	25	cos2	cos2	PROPN
ejpam-5731	322	26	δ	δ	PROPN
ejpam-5731	322	27	.	.	PUNCT
ejpam-5731	322	28	corollary	corollary	ADJ
ejpam-5731	323	1	4	4	NUM
ejpam-5731	323	2	.	.	PUNCT
ejpam-5731	324	1	if	if	SCONJ
ejpam-5731	324	2	a	a	DET
ejpam-5731	324	3	function	function	NOUN
ejpam-5731	324	4	f	f	PROPN
ejpam-5731	324	5	∈	∈	PROPN
ejpam-5731	324	6	σ	σ	PROPN
ejpam-5731	324	7	is	be	AUX
ejpam-5731	324	8	represented	represent	VERB
ejpam-5731	324	9	by	by	ADP
ejpam-5731	324	10	(	(	PUNCT
ejpam-5731	324	11	1	1	NUM
ejpam-5731	324	12	)	)	PUNCT
ejpam-5731	324	13	and	and	CCONJ
ejpam-5731	324	14	belong	belong	VERB
ejpam-5731	324	15	to	to	ADP
ejpam-5731	324	16	the	the	DET
ejpam-5731	324	17	class	class	NOUN
ejpam-5731	324	18	g∗(δ	g∗(δ	PROPN
ejpam-5731	324	19	,	,	PUNCT
ejpam-5731	324	20	ϕ	ϕ	NOUN
ejpam-5731	324	21	)	)	PUNCT
ejpam-5731	324	22	,	,	PUNCT
ejpam-5731	324	23	then	then	ADV
ejpam-5731	324	24	it	it	PRON
ejpam-5731	324	25	can	can	AUX
ejpam-5731	324	26	be	be	AUX
ejpam-5731	324	27	concluded	conclude	VERB
ejpam-5731	324	28	that	that	SCONJ
ejpam-5731	324	29	|a2|	|a2|	NOUN
ejpam-5731	324	30	≤	≤	NUM
ejpam-5731	324	31	|1−	|1−	NOUN
ejpam-5731	324	32	cos	cos	ADP
ejpam-5731	324	33	θ|	θ|	PROPN
ejpam-5731	324	34	cos	co	NOUN
ejpam-5731	324	35	δ√	δ√	NOUN
ejpam-5731	324	36	|2	|2	NUM
ejpam-5731	324	37	cos	cos	X
ejpam-5731	324	38	δ(cos	δ(cos	PROPN
ejpam-5731	324	39	θ	θ	PROPN
ejpam-5731	324	40	−	−	NOUN
ejpam-5731	324	41	1	1	NUM
ejpam-5731	324	42	)	)	PUNCT
ejpam-5731	324	43	+	+	CCONJ
ejpam-5731	324	44	2(1−	2(1−	NUM
ejpam-5731	324	45	3	3	NUM
ejpam-5731	324	46	cos	cos	ADP
ejpam-5731	324	47	θ)eiδ|	θ)eiδ|	PROPN
ejpam-5731	324	48	,	,	PUNCT
ejpam-5731	324	49	and	and	CCONJ
ejpam-5731	324	50	|a3|	|a3|	VERB
ejpam-5731	324	51	≤	≤	PROPN
ejpam-5731	324	52	|1−	|1−	PROPN
ejpam-5731	324	53	cos	cos	ADP
ejpam-5731	324	54	θ|	θ|	PROPN
ejpam-5731	324	55	cos	cos	ADP
ejpam-5731	324	56	δ	δ	PROPN
ejpam-5731	324	57	3	3	NUM
ejpam-5731	325	1	+	+	CCONJ
ejpam-5731	325	2	(	(	PUNCT
ejpam-5731	325	3	1−	1−	NUM
ejpam-5731	325	4	cos	cos	PROPN
ejpam-5731	325	5	θ)2	θ)2	PROPN
ejpam-5731	325	6	cos2	cos2	PROPN
ejpam-5731	325	7	δ	δ	PROPN
ejpam-5731	325	8	4	4	NUM
ejpam-5731	325	9	.	.	PUNCT
ejpam-5731	326	1	4	4	X
ejpam-5731	326	2	.	.	X
ejpam-5731	326	3	fekete	fekete	NOUN
ejpam-5731	326	4	-	-	PUNCT
ejpam-5731	326	5	szegö	szegö	ADJ
ejpam-5731	326	6	problem	problem	NOUN
ejpam-5731	326	7	of	of	ADP
ejpam-5731	326	8	the	the	DET
ejpam-5731	326	9	function	function	NOUN
ejpam-5731	326	10	class	class	NOUN
ejpam-5731	326	11	bλ(α	bλ(α	PROPN
ejpam-5731	326	12	,	,	PUNCT
ejpam-5731	326	13	rα	rα	ADJ
ejpam-5731	326	14	q	q	NOUN
ejpam-5731	326	15	,	,	PUNCT
ejpam-5731	326	16	ϕ	ϕ	NOUN
ejpam-5731	326	17	)	)	PUNCT
ejpam-5731	326	18	in	in	ADP
ejpam-5731	326	19	this	this	DET
ejpam-5731	326	20	section	section	NOUN
ejpam-5731	327	1	,	,	PUNCT
ejpam-5731	327	2	we	we	PRON
ejpam-5731	327	3	will	will	AUX
ejpam-5731	327	4	derive	derive	VERB
ejpam-5731	327	5	the	the	DET
ejpam-5731	327	6	fekete	fekete	PROPN
ejpam-5731	327	7	-	-	PUNCT
ejpam-5731	327	8	szegö	szegö	ADJ
ejpam-5731	327	9	inequalities	inequality	NOUN
ejpam-5731	327	10	for	for	ADP
ejpam-5731	327	11	functions	function	NOUN
ejpam-5731	327	12	belonging	belong	VERB
ejpam-5731	327	13	to	to	ADP
ejpam-5731	327	14	the	the	DET
ejpam-5731	327	15	class	class	NOUN
ejpam-5731	327	16	bλ(α	bλ(α	PROPN
ejpam-5731	327	17	,	,	PUNCT
ejpam-5731	327	18	rαq	rαq	NOUN
ejpam-5731	327	19	,	,	PUNCT
ejpam-5731	327	20	ϕ	ϕ	PROPN
ejpam-5731	327	21	)	)	PUNCT
ejpam-5731	327	22	,	,	PUNCT
ejpam-5731	327	23	which	which	PRON
ejpam-5731	327	24	encompasses	encompass	VERB
ejpam-5731	327	25	bi	bi	ADJ
ejpam-5731	327	26	-	-	ADJ
ejpam-5731	327	27	bazilevic	bazilevic	ADJ
ejpam-5731	327	28	functions	function	NOUN
ejpam-5731	327	29	defined	define	VERB
ejpam-5731	327	30	through	through	ADP
ejpam-5731	327	31	the	the	DET
ejpam-5731	327	32	qruscheweyh	qruscheweyh	NOUN
ejpam-5731	327	33	differential	differential	NOUN
ejpam-5731	327	34	operator	operator	NOUN
ejpam-5731	327	35	and	and	CCONJ
ejpam-5731	327	36	associated	associate	VERB
ejpam-5731	327	37	with	with	ADP
ejpam-5731	327	38	legendre	legendre	PROPN
ejpam-5731	327	39	polynomials	polynomial	NOUN
ejpam-5731	327	40	.	.	PUNCT
ejpam-5731	328	1	additionally	additionally	ADV
ejpam-5731	328	2	,	,	PUNCT
ejpam-5731	328	3	we	we	PRON
ejpam-5731	328	4	aim	aim	VERB
ejpam-5731	328	5	to	to	PART
ejpam-5731	328	6	establish	establish	VERB
ejpam-5731	328	7	fekete	fekete	PROPN
ejpam-5731	328	8	-	-	PUNCT
ejpam-5731	328	9	szegö	szegö	ADJ
ejpam-5731	328	10	inequalities	inequality	NOUN
ejpam-5731	328	11	for	for	ADP
ejpam-5731	328	12	several	several	ADJ
ejpam-5731	328	13	subclasses	subclass	NOUN
ejpam-5731	328	14	within	within	ADP
ejpam-5731	328	15	our	our	PRON
ejpam-5731	328	16	defined	define	VERB
ejpam-5731	328	17	class	class	NOUN
ejpam-5731	328	18	.	.	PUNCT
ejpam-5731	329	1	theorem	theorem	NOUN
ejpam-5731	329	2	2	2	NUM
ejpam-5731	329	3	.	.	PUNCT
ejpam-5731	330	1	if	if	SCONJ
ejpam-5731	330	2	a	a	DET
ejpam-5731	330	3	function	function	NOUN
ejpam-5731	330	4	f	f	PROPN
ejpam-5731	330	5	is	be	AUX
ejpam-5731	330	6	a	a	DET
ejpam-5731	330	7	member	member	NOUN
ejpam-5731	330	8	of	of	ADP
ejpam-5731	330	9	the	the	DET
ejpam-5731	330	10	class	class	NOUN
ejpam-5731	330	11	bλ(α	bλ(α	PROPN
ejpam-5731	330	12	,	,	PUNCT
ejpam-5731	330	13	rαq	rαq	NOUN
ejpam-5731	330	14	,	,	PUNCT
ejpam-5731	330	15	ϕ	ϕ	PROPN
ejpam-5731	330	16	)	)	PUNCT
ejpam-5731	330	17	and	and	CCONJ
ejpam-5731	330	18	is	be	AUX
ejpam-5731	330	19	represented	represent	VERB
ejpam-5731	330	20	by	by	ADP
ejpam-5731	330	21	equation	equation	NOUN
ejpam-5731	330	22	(	(	PUNCT
ejpam-5731	330	23	1	1	NUM
ejpam-5731	330	24	)	)	PUNCT
ejpam-5731	330	25	,	,	PUNCT
ejpam-5731	330	26	then	then	ADV
ejpam-5731	330	27	for	for	ADP
ejpam-5731	330	28	a	a	DET
ejpam-5731	330	29	real	real	ADJ
ejpam-5731	330	30	number	number	NOUN
ejpam-5731	330	31	γ	γ	NOUN
ejpam-5731	330	32	the	the	DET
ejpam-5731	330	33	following	follow	VERB
ejpam-5731	330	34	inequality	inequality	NOUN
ejpam-5731	330	35	holds	hold	VERB
ejpam-5731	330	36	|a3	|a3	NOUN
ejpam-5731	330	37	−	−	PROPN
ejpam-5731	330	38	γa22|	γa22|	NOUN
ejpam-5731	330	39	≤	≤	NOUN
ejpam-5731	330	40	{	{	PUNCT
ejpam-5731	330	41	|1−cos	|1−cos	NUM
ejpam-5731	330	42	θ|	θ|	PROPN
ejpam-5731	330	43	cos	cos	PRON
ejpam-5731	330	44	δ	δ	PROPN
ejpam-5731	330	45	2(λ+2)ψ3	2(λ+2)ψ3	NOUN
ejpam-5731	330	46	,	,	PUNCT
ejpam-5731	330	47	if	if	SCONJ
ejpam-5731	330	48	|1−	|1−	VERB
ejpam-5731	330	49	ζ|	ζ|	PROPN
ejpam-5731	330	50	≤	≤	PUNCT
ejpam-5731	331	1	|∆|	|∆|	PROPN
ejpam-5731	331	2	|1−cos	|1−cos	NUM
ejpam-5731	331	3	θ||1−γ|	θ||1−γ|	PROPN
ejpam-5731	331	4	cos	cos	ADP
ejpam-5731	331	5	δ	δ	PROPN
ejpam-5731	331	6	|aβ1	|aβ1	PROPN
ejpam-5731	331	7	cos	cos	PROPN
ejpam-5731	331	8	δ+b2(1−3	δ+b2(1−3	PROPN
ejpam-5731	331	9	cos	cos	PROPN
ejpam-5731	331	10	θ)eiδ|	θ)eiδ|	PROPN
ejpam-5731	331	11	,	,	PUNCT
ejpam-5731	331	12	if	if	SCONJ
ejpam-5731	331	13	|1−	|1−	VERB
ejpam-5731	331	14	ζ|	ζ|	PROPN
ejpam-5731	331	15	≥	≥	NUM
ejpam-5731	331	16	|∆|	|∆|	NUM
ejpam-5731	331	17	,	,	PUNCT
ejpam-5731	331	18	(	(	PUNCT
ejpam-5731	331	19	37	37	NUM
ejpam-5731	331	20	)	)	PUNCT
ejpam-5731	332	1	where	where	SCONJ
ejpam-5731	332	2	a	a	DET
ejpam-5731	332	3	=	=	SYM
ejpam-5731	332	4	2(λ+	2(λ+	PROPN
ejpam-5731	332	5	2)ψ3	2)ψ3	NOUN
ejpam-5731	332	6	+	+	CCONJ
ejpam-5731	332	7	(	(	PUNCT
ejpam-5731	332	8	λ−	λ−	PROPN
ejpam-5731	332	9	1)(λ+	1)(λ+	NUM
ejpam-5731	332	10	2)ψ2	2)ψ2	NUM
ejpam-5731	332	11	2	2	NUM
ejpam-5731	332	12	,	,	PUNCT
ejpam-5731	332	13	b	b	X
ejpam-5731	333	1	=	=	PUNCT
ejpam-5731	334	1	(	(	PUNCT
ejpam-5731	334	2	λ+	λ+	NUM
ejpam-5731	334	3	1)ψ2	1)ψ2	NUM
ejpam-5731	334	4	,	,	PUNCT
ejpam-5731	334	5	and	and	CCONJ
ejpam-5731	334	6	∆	∆	X
ejpam-5731	334	7	=	=	SYM
ejpam-5731	335	1	|a(cos	|a(cos	NUM
ejpam-5731	335	2	θ	θ	NOUN
ejpam-5731	335	3	−	−	PROPN
ejpam-5731	335	4	1	1	NUM
ejpam-5731	335	5	)	)	PUNCT
ejpam-5731	335	6	cos	cos	ADP
ejpam-5731	335	7	δ	δ	PROPN
ejpam-5731	335	8	+	+	PROPN
ejpam-5731	335	9	b2(1−	b2(1−	PROPN
ejpam-5731	335	10	3	3	NUM
ejpam-5731	335	11	cos	cos	PROPN
ejpam-5731	335	12	θ)eiδ|	θ)eiδ|	PROPN
ejpam-5731	335	13	2|1−	2|1−	PROPN
ejpam-5731	335	14	cos	cos	ADP
ejpam-5731	335	15	θ|	θ|	PROPN
ejpam-5731	335	16	cos	cos	ADP
ejpam-5731	335	17	δ(λ+	δ(λ+	ADJ
ejpam-5731	335	18	2)ψ3	2)ψ3	NOUN
ejpam-5731	335	19	.	.	PUNCT
ejpam-5731	336	1	proof	proof	NOUN
ejpam-5731	336	2	.	.	PUNCT
ejpam-5731	337	1	for	for	ADP
ejpam-5731	337	2	any	any	DET
ejpam-5731	337	3	real	real	ADJ
ejpam-5731	337	4	number	number	NOUN
ejpam-5731	337	5	γ	γ	NOUN
ejpam-5731	337	6	,	,	PUNCT
ejpam-5731	337	7	using	use	VERB
ejpam-5731	337	8	equation	equation	NOUN
ejpam-5731	337	9	(	(	PUNCT
ejpam-5731	337	10	26	26	NUM
ejpam-5731	337	11	)	)	PUNCT
ejpam-5731	337	12	and	and	CCONJ
ejpam-5731	337	13	equation	equation	NOUN
ejpam-5731	337	14	(	(	PUNCT
ejpam-5731	337	15	27	27	NUM
ejpam-5731	337	16	)	)	PUNCT
ejpam-5731	337	17	,	,	PUNCT
ejpam-5731	337	18	we	we	PRON
ejpam-5731	337	19	easily	easily	ADV
ejpam-5731	337	20	derive	derive	VERB
ejpam-5731	337	21	the	the	DET
ejpam-5731	337	22	following	follow	VERB
ejpam-5731	337	23	equations	equation	NOUN
ejpam-5731	337	24	a3	a3	VERB
ejpam-5731	337	25	−	−	PROPN
ejpam-5731	338	1	γa22	γa22	PROPN
ejpam-5731	338	2	=	=	SYM
ejpam-5731	338	3	β1	β1	PROPN
ejpam-5731	338	4	cos	cos	PROPN
ejpam-5731	338	5	δe	δe	PRON
ejpam-5731	338	6	−iδ(η2	−iδ(η2	ADJ
ejpam-5731	338	7	−	−	PROPN
ejpam-5731	338	8	ζ2	ζ2	NOUN
ejpam-5731	338	9	)	)	PUNCT
ejpam-5731	338	10	4(λ+	4(λ+	NOUN
ejpam-5731	339	1	2)ψ3	2)ψ3	NOUN
ejpam-5731	339	2	+	+	CCONJ
ejpam-5731	339	3	β21	β21	NOUN
ejpam-5731	339	4	cos	cos	PROPN
ejpam-5731	339	5	2	2	NUM
ejpam-5731	339	6	δe−iδ(η2	δe−iδ(η2	PROPN
ejpam-5731	339	7	+	+	CCONJ
ejpam-5731	339	8	ζ2)(1−	ζ2)(1−	PROPN
ejpam-5731	339	9	γ	γ	X
ejpam-5731	339	10	)	)	PUNCT
ejpam-5731	339	11	β1	β1	PROPN
ejpam-5731	339	12	cos	cos	PROPN
ejpam-5731	339	13	δ[4(λ+	δ[4(λ+	PROPN
ejpam-5731	339	14	2)ψ3	2)ψ3	PROPN
ejpam-5731	339	15	+	+	CCONJ
ejpam-5731	339	16	2(λ−	2(λ−	NUM
ejpam-5731	339	17	1)(λ+	1)(λ+	NUM
ejpam-5731	339	18	2)ψ2	2)ψ2	NUM
ejpam-5731	339	19	2	2	NUM
ejpam-5731	339	20	]	]	PUNCT
ejpam-5731	339	21	+	+	CCONJ
ejpam-5731	339	22	2(1−	2(1−	NUM
ejpam-5731	339	23	cos	cos	X
ejpam-5731	339	24	θ)(λ+	θ)(λ+	NOUN
ejpam-5731	339	25	1)2ψ2	1)2ψ2	NUM
ejpam-5731	339	26	2e	2e	NOUN
ejpam-5731	339	27	iδ	iδ	PROPN
ejpam-5731	339	28	w.	w.	PROPN
ejpam-5731	339	29	al	al	PROPN
ejpam-5731	339	30	-	-	PUNCT
ejpam-5731	339	31	rawashdeh	rawashdeh	PROPN
ejpam-5731	339	32	/	/	SYM
ejpam-5731	339	33	eur	eur	PROPN
ejpam-5731	339	34	.	.	PUNCT
ejpam-5731	340	1	j.	j.	PROPN
ejpam-5731	340	2	pure	pure	PROPN
ejpam-5731	340	3	appl	appl	PROPN
ejpam-5731	340	4	.	.	PROPN
ejpam-5731	340	5	math	math	PROPN
ejpam-5731	340	6	,	,	PUNCT
ejpam-5731	340	7	18	18	NUM
ejpam-5731	340	8	(	(	PUNCT
ejpam-5731	340	9	1	1	NUM
ejpam-5731	340	10	)	)	PUNCT
ejpam-5731	340	11	(	(	PUNCT
ejpam-5731	340	12	2025	2025	NUM
ejpam-5731	340	13	)	)	PUNCT
ejpam-5731	340	14	,	,	PUNCT
ejpam-5731	340	15	5731	5731	NUM
ejpam-5731	340	16	16	16	NUM
ejpam-5731	340	17	of	of	ADP
ejpam-5731	340	18	20	20	NUM
ejpam-5731	340	19	=	=	SYM
ejpam-5731	340	20	(	(	PUNCT
ejpam-5731	340	21	β1	β1	PROPN
ejpam-5731	340	22	cos	cos	PROPN
ejpam-5731	340	23	δe	δe	ADP
ejpam-5731	340	24	−iδ	−iδ	PROPN
ejpam-5731	340	25	)	)	PUNCT
ejpam-5731	340	26	{	{	PUNCT
ejpam-5731	340	27	(	(	PUNCT
ejpam-5731	340	28	µ+	µ+	X
ejpam-5731	340	29	1	1	NUM
ejpam-5731	340	30	4(λ+	4(λ+	NOUN
ejpam-5731	340	31	2)ψ3	2)ψ3	NOUN
ejpam-5731	340	32	)	)	PUNCT
ejpam-5731	340	33	η2	η2	PROPN
ejpam-5731	340	34	+	+	CCONJ
ejpam-5731	340	35	(	(	PUNCT
ejpam-5731	340	36	µ−	µ−	PROPN
ejpam-5731	340	37	1	1	NUM
ejpam-5731	340	38	4(λ+	4(λ+	NOUN
ejpam-5731	340	39	2)ψ3	2)ψ3	ADJ
ejpam-5731	340	40	)	)	PUNCT
ejpam-5731	340	41	ζ2	ζ2	NOUN
ejpam-5731	340	42	}	}	PUNCT
ejpam-5731	340	43	,	,	PUNCT
ejpam-5731	340	44	where	where	SCONJ
ejpam-5731	340	45	µ	µ	X
ejpam-5731	340	46	=	=	SYM
ejpam-5731	340	47	(	(	PUNCT
ejpam-5731	340	48	1−	1−	NUM
ejpam-5731	340	49	γ)β1	γ)β1	PROPN
ejpam-5731	340	50	cos	cos	PROPN
ejpam-5731	340	51	δe	δe	PRON
ejpam-5731	340	52	−iδ	−iδ	NOUN
ejpam-5731	340	53	2aβ1	2aβ1	NUM
ejpam-5731	340	54	cos	cos	PROPN
ejpam-5731	340	55	δ	δ	PROPN
ejpam-5731	340	56	+	+	PROPN
ejpam-5731	340	57	2b2(1−	2b2(1−	NUM
ejpam-5731	340	58	cos	cos	ADP
ejpam-5731	340	59	θ)eiδ	θ)eiδ	ADJ
ejpam-5731	340	60	.	.	PUNCT
ejpam-5731	341	1	therefore	therefore	ADV
ejpam-5731	341	2	,	,	PUNCT
ejpam-5731	341	3	with	with	ADP
ejpam-5731	341	4	the	the	DET
ejpam-5731	341	5	assistance	assistance	NOUN
ejpam-5731	341	6	of	of	ADP
ejpam-5731	341	7	lemma	lemma	PROPN
ejpam-5731	341	8	2	2	NUM
ejpam-5731	341	9	,	,	PUNCT
ejpam-5731	341	10	we	we	PRON
ejpam-5731	341	11	are	be	AUX
ejpam-5731	341	12	able	able	ADJ
ejpam-5731	341	13	to	to	PART
ejpam-5731	341	14	achieve	achieve	VERB
ejpam-5731	341	15	the	the	DET
ejpam-5731	341	16	following	follow	VERB
ejpam-5731	341	17	inequality	inequality	NOUN
ejpam-5731	341	18	|a3	|a3	NOUN
ejpam-5731	341	19	−	−	PROPN
ejpam-5731	341	20	γa22|	γa22|	NOUN
ejpam-5731	341	21	≤	≤	NUM
ejpam-5731	341	22			PUNCT
ejpam-5731	341	23	2|β1	2|β1	NUM
ejpam-5731	341	24	cos	cos	ADP
ejpam-5731	341	25	δe−iδ|	δe−iδ|	PROPN
ejpam-5731	341	26	4(λ+2)ψ3	4(λ+2)ψ3	PROPN
ejpam-5731	341	27	,	,	PUNCT
ejpam-5731	341	28	if	if	SCONJ
ejpam-5731	341	29	|µ|	|µ|	PROPN
ejpam-5731	341	30	≤	≤	NOUN
ejpam-5731	341	31	1	1	NUM
ejpam-5731	341	32	4(λ+2)ψ3	4(λ+2)ψ3	NUM
ejpam-5731	341	33	2	2	NUM
ejpam-5731	341	34	∣∣β1	∣∣β1	NOUN
ejpam-5731	341	35	cos	cos	ADP
ejpam-5731	341	36	δe−iδ∣∣	δe−iδ∣∣	PROPN
ejpam-5731	341	37	|µ|	|µ|	PROPN
ejpam-5731	341	38	,	,	PUNCT
ejpam-5731	341	39	if	if	SCONJ
ejpam-5731	341	40	|µ|	|µ|	PROPN
ejpam-5731	341	41	≥	≥	VERB
ejpam-5731	341	42	1	1	NUM
ejpam-5731	341	43	4(λ+2)ψ3	4(λ+2)ψ3	NUM
ejpam-5731	341	44	.	.	PUNCT
ejpam-5731	342	1	finally	finally	ADV
ejpam-5731	342	2	,	,	PUNCT
ejpam-5731	342	3	by	by	ADP
ejpam-5731	342	4	streamlining	streamline	VERB
ejpam-5731	342	5	the	the	DET
ejpam-5731	342	6	right	right	ADJ
ejpam-5731	342	7	-	-	PUNCT
ejpam-5731	342	8	hand	hand	NOUN
ejpam-5731	342	9	side	side	NOUN
ejpam-5731	342	10	of	of	ADP
ejpam-5731	342	11	the	the	DET
ejpam-5731	342	12	final	final	ADJ
ejpam-5731	342	13	inequality	inequality	NOUN
ejpam-5731	342	14	,	,	PUNCT
ejpam-5731	342	15	we	we	PRON
ejpam-5731	342	16	arrive	arrive	VERB
ejpam-5731	342	17	at	at	ADP
ejpam-5731	342	18	the	the	DET
ejpam-5731	342	19	expected	expect	VERB
ejpam-5731	342	20	result	result	NOUN
ejpam-5731	342	21	as	as	SCONJ
ejpam-5731	342	22	presented	present	VERB
ejpam-5731	342	23	in	in	ADP
ejpam-5731	342	24	inequality	inequality	NOUN
ejpam-5731	342	25	(	(	PUNCT
ejpam-5731	342	26	37	37	NUM
ejpam-5731	342	27	)	)	PUNCT
ejpam-5731	342	28	.	.	PUNCT
ejpam-5731	343	1	this	this	PRON
ejpam-5731	343	2	signifies	signify	VERB
ejpam-5731	343	3	the	the	DET
ejpam-5731	343	4	completion	completion	NOUN
ejpam-5731	343	5	of	of	ADP
ejpam-5731	343	6	the	the	DET
ejpam-5731	343	7	proof	proof	NOUN
ejpam-5731	343	8	.	.	PUNCT
ejpam-5731	344	1	the	the	DET
ejpam-5731	344	2	subsequent	subsequent	ADJ
ejpam-5731	344	3	corollaries	corollary	NOUN
ejpam-5731	344	4	emerge	emerge	VERB
ejpam-5731	344	5	as	as	ADP
ejpam-5731	344	6	logical	logical	ADJ
ejpam-5731	344	7	extensions	extension	NOUN
ejpam-5731	344	8	of	of	ADP
ejpam-5731	344	9	theorem	theorem	NOUN
ejpam-5731	344	10	2	2	NUM
ejpam-5731	344	11	,	,	PUNCT
ejpam-5731	344	12	given	give	VERB
ejpam-5731	344	13	the	the	DET
ejpam-5731	344	14	conditions	condition	NOUN
ejpam-5731	344	15	outlined	outline	VERB
ejpam-5731	344	16	in	in	ADP
ejpam-5731	344	17	the	the	DET
ejpam-5731	344	18	preceding	precede	VERB
ejpam-5731	344	19	examples	example	NOUN
ejpam-5731	344	20	.	.	PUNCT
ejpam-5731	345	1	the	the	DET
ejpam-5731	345	2	methodology	methodology	NOUN
ejpam-5731	345	3	employed	employ	VERB
ejpam-5731	345	4	to	to	PART
ejpam-5731	345	5	derive	derive	VERB
ejpam-5731	345	6	this	this	DET
ejpam-5731	345	7	corollary	corollary	NOUN
ejpam-5731	345	8	closely	closely	ADV
ejpam-5731	345	9	resembles	resemble	VERB
ejpam-5731	345	10	that	that	PRON
ejpam-5731	345	11	utilized	utilize	VERB
ejpam-5731	345	12	in	in	ADP
ejpam-5731	345	13	the	the	DET
ejpam-5731	345	14	earlier	early	ADJ
ejpam-5731	345	15	theorem	theorem	ADJ
ejpam-5731	345	16	;	;	PUNCT
ejpam-5731	345	17	therefore	therefore	ADV
ejpam-5731	345	18	,	,	PUNCT
ejpam-5731	345	19	we	we	PRON
ejpam-5731	345	20	have	have	AUX
ejpam-5731	345	21	opted	opt	VERB
ejpam-5731	345	22	to	to	PART
ejpam-5731	345	23	forgo	forgo	VERB
ejpam-5731	345	24	a	a	DET
ejpam-5731	345	25	detailed	detailed	ADJ
ejpam-5731	345	26	proof	proof	NOUN
ejpam-5731	345	27	for	for	ADP
ejpam-5731	345	28	this	this	DET
ejpam-5731	345	29	corollary	corollary	NOUN
ejpam-5731	345	30	.	.	PUNCT
ejpam-5731	346	1	corollary	corollary	ADJ
ejpam-5731	346	2	5	5	NUM
ejpam-5731	346	3	.	.	PUNCT
ejpam-5731	347	1	if	if	SCONJ
ejpam-5731	347	2	a	a	DET
ejpam-5731	347	3	function	function	NOUN
ejpam-5731	347	4	f	f	PROPN
ejpam-5731	347	5	∈	∈	PROPN
ejpam-5731	347	6	σ	σ	PROPN
ejpam-5731	347	7	is	be	AUX
ejpam-5731	347	8	represented	represent	VERB
ejpam-5731	347	9	by	by	ADP
ejpam-5731	347	10	equation	equation	NOUN
ejpam-5731	347	11	(	(	PUNCT
ejpam-5731	347	12	1	1	NUM
ejpam-5731	347	13	)	)	PUNCT
ejpam-5731	347	14	and	and	CCONJ
ejpam-5731	347	15	is	be	AUX
ejpam-5731	347	16	obeying	obey	VERB
ejpam-5731	347	17	the	the	DET
ejpam-5731	347	18	subordination	subordination	NOUN
ejpam-5731	347	19	conditions	condition	NOUN
ejpam-5731	347	20	(	(	PUNCT
ejpam-5731	347	21	29	29	NUM
ejpam-5731	347	22	)	)	PUNCT
ejpam-5731	347	23	and	and	CCONJ
ejpam-5731	347	24	(	(	PUNCT
ejpam-5731	347	25	30	30	NUM
ejpam-5731	347	26	)	)	PUNCT
ejpam-5731	347	27	,	,	PUNCT
ejpam-5731	347	28	then	then	ADV
ejpam-5731	347	29	for	for	ADP
ejpam-5731	347	30	a	a	DET
ejpam-5731	347	31	real	real	ADJ
ejpam-5731	347	32	number	number	NOUN
ejpam-5731	347	33	γ	γ	NOUN
ejpam-5731	347	34	the	the	DET
ejpam-5731	347	35	following	following	NOUN
ejpam-5731	347	36	holds	hold	VERB
ejpam-5731	347	37	|a3	|a3	NOUN
ejpam-5731	347	38	−	−	PROPN
ejpam-5731	347	39	γa22|	γa22|	NOUN
ejpam-5731	347	40	≤	≤	NOUN
ejpam-5731	347	41	{	{	PUNCT
ejpam-5731	347	42	|1−cos	|1−cos	NUM
ejpam-5731	347	43	θ|	θ|	PROPN
ejpam-5731	347	44	cos	cos	ADP
ejpam-5731	347	45	δ	δ	PROPN
ejpam-5731	347	46	4ψ3	4ψ3	NOUN
ejpam-5731	347	47	,	,	PUNCT
ejpam-5731	347	48	if	if	SCONJ
ejpam-5731	347	49	|1−	|1−	PROPN
ejpam-5731	347	50	ζ|	ζ|	PROPN
ejpam-5731	347	51	≤	≤	NUM
ejpam-5731	347	52	|∆1|	|∆1|	NOUN
ejpam-5731	347	53	|1−cos	|1−cos	NUM
ejpam-5731	347	54	θ||1−γ|	θ||1−γ|	PROPN
ejpam-5731	347	55	cos	cos	ADP
ejpam-5731	347	56	δ	δ	PROPN
ejpam-5731	347	57	|β1	|β1	X
ejpam-5731	347	58	cos	cos	X
ejpam-5731	347	59	δ(4ψ3−2ψ2	δ(4ψ3−2ψ2	PROPN
ejpam-5731	347	60	2)+(1−3	2)+(1−3	NUM
ejpam-5731	347	61	cos	cos	X
ejpam-5731	347	62	θ)ψ2	θ)ψ2	PROPN
ejpam-5731	347	63	2e	2e	NOUN
ejpam-5731	347	64	iδ|	iδ|	ADV
ejpam-5731	347	65	,	,	PUNCT
ejpam-5731	347	66	if	if	SCONJ
ejpam-5731	347	67	|1−	|1−	PROPN
ejpam-5731	347	68	ζ|	ζ|	PROPN
ejpam-5731	347	69	≥	≥	PUNCT
ejpam-5731	347	70	|∆1|	|∆1|	NOUN
ejpam-5731	347	71	,	,	PUNCT
ejpam-5731	347	72	where	where	SCONJ
ejpam-5731	347	73	∆1	∆1	NOUN
ejpam-5731	347	74	=	=	SYM
ejpam-5731	347	75	|β1	|β1	X
ejpam-5731	347	76	cos	cos	INTJ
ejpam-5731	347	77	δ(4ψ3	δ(4ψ3	NOUN
ejpam-5731	347	78	−	−	NUM
ejpam-5731	347	79	2ψ2	2ψ2	NUM
ejpam-5731	347	80	2	2	NUM
ejpam-5731	347	81	)	)	PUNCT
ejpam-5731	347	82	+	+	CCONJ
ejpam-5731	347	83	(	(	PUNCT
ejpam-5731	347	84	1−	1−	NUM
ejpam-5731	347	85	3	3	NUM
ejpam-5731	347	86	cos	cos	X
ejpam-5731	347	87	θ)ψ2	θ)ψ2	PROPN
ejpam-5731	347	88	2e	2e	NOUN
ejpam-5731	347	89	iδ|	iδ|	PROPN
ejpam-5731	347	90	4|1−	4|1−	PROPN
ejpam-5731	347	91	cos	cos	ADP
ejpam-5731	347	92	θ|	θ|	PROPN
ejpam-5731	347	93	cos	cos	PROPN
ejpam-5731	347	94	δψ3	δψ3	PROPN
ejpam-5731	347	95	.	.	PUNCT
ejpam-5731	348	1	corollary	corollary	ADJ
ejpam-5731	348	2	6	6	NUM
ejpam-5731	348	3	.	.	PUNCT
ejpam-5731	349	1	if	if	SCONJ
ejpam-5731	349	2	a	a	DET
ejpam-5731	349	3	function	function	NOUN
ejpam-5731	349	4	f	f	PROPN
ejpam-5731	349	5	∈	∈	PROPN
ejpam-5731	349	6	σ	σ	PROPN
ejpam-5731	349	7	is	be	AUX
ejpam-5731	349	8	represented	represent	VERB
ejpam-5731	349	9	by	by	ADP
ejpam-5731	349	10	equation	equation	NOUN
ejpam-5731	349	11	(	(	PUNCT
ejpam-5731	349	12	1	1	NUM
ejpam-5731	349	13	)	)	PUNCT
ejpam-5731	349	14	and	and	CCONJ
ejpam-5731	349	15	is	be	AUX
ejpam-5731	349	16	obeying	obey	VERB
ejpam-5731	349	17	the	the	DET
ejpam-5731	349	18	subordination	subordination	NOUN
ejpam-5731	349	19	conditions	condition	NOUN
ejpam-5731	349	20	(	(	PUNCT
ejpam-5731	349	21	31	31	NUM
ejpam-5731	349	22	)	)	PUNCT
ejpam-5731	349	23	and	and	CCONJ
ejpam-5731	349	24	(	(	PUNCT
ejpam-5731	349	25	32	32	NUM
ejpam-5731	349	26	)	)	PUNCT
ejpam-5731	349	27	,	,	PUNCT
ejpam-5731	349	28	then	then	ADV
ejpam-5731	349	29	for	for	ADP
ejpam-5731	349	30	a	a	DET
ejpam-5731	349	31	real	real	ADJ
ejpam-5731	349	32	number	number	NOUN
ejpam-5731	349	33	ζ	ζ	NOUN
ejpam-5731	349	34	the	the	DET
ejpam-5731	349	35	following	following	NOUN
ejpam-5731	349	36	holds	hold	VERB
ejpam-5731	349	37	|a3	|a3	NOUN
ejpam-5731	349	38	−	−	PROPN
ejpam-5731	349	39	γa22|	γa22|	NOUN
ejpam-5731	349	40	≤	≤	NOUN
ejpam-5731	349	41	{	{	PUNCT
ejpam-5731	349	42	|1−cos	|1−cos	NUM
ejpam-5731	349	43	θ|	θ|	PROPN
ejpam-5731	349	44	cos	cos	ADP
ejpam-5731	349	45	δ	δ	PROPN
ejpam-5731	349	46	6ψ3	6ψ3	NUM
ejpam-5731	349	47	,	,	PUNCT
ejpam-5731	349	48	if	if	SCONJ
ejpam-5731	349	49	|1−	|1−	PRON
ejpam-5731	349	50	ζ|	ζ|	PROPN
ejpam-5731	349	51	≤	≤	PUNCT
ejpam-5731	349	52	|∆2|	|∆2|	ADJ
ejpam-5731	349	53	|1−cos	|1−cos	NUM
ejpam-5731	349	54	θ||1−γ|	θ||1−γ|	PROPN
ejpam-5731	349	55	cos	cos	SCONJ
ejpam-5731	349	56	δ	δ	PROPN
ejpam-5731	349	57	|6β1	|6β1	VERB
ejpam-5731	349	58	cos	cos	ADP
ejpam-5731	349	59	δψ3	δψ3	PROPN
ejpam-5731	349	60	+	+	PROPN
ejpam-5731	349	61	4(1−3	4(1−3	NOUN
ejpam-5731	349	62	cos	cos	ADP
ejpam-5731	350	1	θ)ψ2	θ)ψ2	PROPN
ejpam-5731	350	2	2e	2e	NOUN
ejpam-5731	351	1	iδ|	iδ|	ADV
ejpam-5731	351	2	,	,	PUNCT
ejpam-5731	351	3	if	if	SCONJ
ejpam-5731	351	4	|1−	|1−	PROPN
ejpam-5731	351	5	ζ|	ζ|	PROPN
ejpam-5731	351	6	≥	≥	AUX
ejpam-5731	351	7	|∆2|	|∆2|	ADJ
ejpam-5731	351	8	,	,	PUNCT
ejpam-5731	351	9	where	where	SCONJ
ejpam-5731	351	10	∆2	∆2	PROPN
ejpam-5731	351	11	=	=	SYM
ejpam-5731	351	12	|3(cos	|3(cos	X
ejpam-5731	351	13	θ	θ	X
ejpam-5731	351	14	−	−	NOUN
ejpam-5731	351	15	1	1	X
ejpam-5731	351	16	)	)	PUNCT
ejpam-5731	351	17	cos	cos	NOUN
ejpam-5731	351	18	δψ3	δψ3	NOUN
ejpam-5731	351	19	+	+	CCONJ
ejpam-5731	351	20	2(1−	2(1−	NUM
ejpam-5731	351	21	3	3	NUM
ejpam-5731	351	22	cos	cos	X
ejpam-5731	351	23	θ)ψ2	θ)ψ2	PROPN
ejpam-5731	351	24	2e	2e	NOUN
ejpam-5731	351	25	iδ|	iδ|	PROPN
ejpam-5731	351	26	3|1−	3|1−	PROPN
ejpam-5731	351	27	cos	cos	PROPN
ejpam-5731	351	28	θ|	θ|	PROPN
ejpam-5731	351	29	cos	cos	PROPN
ejpam-5731	351	30	δψ3	δψ3	PROPN
ejpam-5731	351	31	.	.	PUNCT
ejpam-5731	352	1	corollary	corollary	ADJ
ejpam-5731	352	2	7	7	NUM
ejpam-5731	352	3	.	.	PUNCT
ejpam-5731	353	1	if	if	SCONJ
ejpam-5731	353	2	a	a	DET
ejpam-5731	353	3	function	function	NOUN
ejpam-5731	353	4	f	f	PROPN
ejpam-5731	353	5	∈	∈	PROPN
ejpam-5731	353	6	σ	σ	PROPN
ejpam-5731	353	7	is	be	AUX
ejpam-5731	353	8	represented	represent	VERB
ejpam-5731	353	9	by	by	ADP
ejpam-5731	353	10	equation	equation	NOUN
ejpam-5731	353	11	(	(	PUNCT
ejpam-5731	353	12	1	1	NUM
ejpam-5731	353	13	)	)	PUNCT
ejpam-5731	353	14	and	and	CCONJ
ejpam-5731	353	15	is	be	AUX
ejpam-5731	353	16	obeying	obey	VERB
ejpam-5731	353	17	the	the	DET
ejpam-5731	353	18	subordination	subordination	NOUN
ejpam-5731	353	19	conditions	condition	NOUN
ejpam-5731	353	20	(	(	PUNCT
ejpam-5731	353	21	33	33	NUM
ejpam-5731	353	22	)	)	PUNCT
ejpam-5731	353	23	and	and	CCONJ
ejpam-5731	353	24	(	(	PUNCT
ejpam-5731	353	25	34	34	NUM
ejpam-5731	353	26	)	)	PUNCT
ejpam-5731	353	27	,	,	PUNCT
ejpam-5731	353	28	then	then	ADV
ejpam-5731	353	29	for	for	ADP
ejpam-5731	353	30	a	a	DET
ejpam-5731	353	31	real	real	ADJ
ejpam-5731	353	32	number	number	NOUN
ejpam-5731	353	33	ζ	ζ	NOUN
ejpam-5731	353	34	the	the	DET
ejpam-5731	353	35	following	following	NOUN
ejpam-5731	353	36	holds	hold	VERB
ejpam-5731	353	37	|a3	|a3	NOUN
ejpam-5731	353	38	−	−	PROPN
ejpam-5731	353	39	γa22|	γa22|	NOUN
ejpam-5731	353	40	≤	≤	NOUN
ejpam-5731	353	41	{	{	PUNCT
ejpam-5731	353	42	|1−cos	|1−cos	NUM
ejpam-5731	353	43	θ|	θ|	PROPN
ejpam-5731	353	44	cos	cos	ADP
ejpam-5731	353	45	δ	δ	PROPN
ejpam-5731	353	46	4	4	NUM
ejpam-5731	353	47	,	,	PUNCT
ejpam-5731	353	48	if	if	SCONJ
ejpam-5731	353	49	|1−	|1−	PRON
ejpam-5731	353	50	ζ|	ζ|	PROPN
ejpam-5731	353	51	≤	≤	NUM
ejpam-5731	353	52	|∆3|	|∆3|	NOUN
ejpam-5731	353	53	|1−cos	|1−cos	PRON
ejpam-5731	353	54	θ||1−γ|	θ||1−γ|	PROPN
ejpam-5731	353	55	cos	cos	PROPN
ejpam-5731	353	56	δ	δ	PROPN
ejpam-5731	353	57	|2β1	|2β1	PROPN
ejpam-5731	354	1	cos	cos	PROPN
ejpam-5731	354	2	δ+(1−3	δ+(1−3	PROPN
ejpam-5731	354	3	cos	cos	PROPN
ejpam-5731	354	4	θ)2eiδ|	θ)2eiδ|	PROPN
ejpam-5731	354	5	,	,	PUNCT
ejpam-5731	354	6	if	if	SCONJ
ejpam-5731	354	7	|1−	|1−	PROPN
ejpam-5731	354	8	ζ|	ζ|	PROPN
ejpam-5731	354	9	≥	≥	NUM
ejpam-5731	354	10	|∆3|	|∆3|	NOUN
ejpam-5731	354	11	,	,	PUNCT
ejpam-5731	354	12	where	where	SCONJ
ejpam-5731	354	13	∆3	∆3	PROPN
ejpam-5731	354	14	=	=	SYM
ejpam-5731	354	15	|2β1	|2β1	PROPN
ejpam-5731	354	16	cos	cos	PROPN
ejpam-5731	354	17	δ	δ	PROPN
ejpam-5731	354	18	+	+	X
ejpam-5731	354	19	(	(	PUNCT
ejpam-5731	354	20	1−	1−	NUM
ejpam-5731	354	21	3	3	NUM
ejpam-5731	354	22	cos	cos	PROPN
ejpam-5731	354	23	θ)eiδ|	θ)eiδ|	PROPN
ejpam-5731	354	24	4|1−	4|1−	NUM
ejpam-5731	354	25	cos	cos	ADP
ejpam-5731	354	26	θ|	θ|	PROPN
ejpam-5731	354	27	cos	cos	PROPN
ejpam-5731	354	28	δ	δ	PROPN
ejpam-5731	354	29	.	.	PUNCT
ejpam-5731	355	1	w.	w.	PROPN
ejpam-5731	355	2	al	al	PROPN
ejpam-5731	355	3	-	-	PUNCT
ejpam-5731	355	4	rawashdeh	rawashdeh	PROPN
ejpam-5731	355	5	/	/	SYM
ejpam-5731	355	6	eur	eur	PROPN
ejpam-5731	355	7	.	.	PUNCT
ejpam-5731	356	1	j.	j.	PROPN
ejpam-5731	356	2	pure	pure	PROPN
ejpam-5731	356	3	appl	appl	PROPN
ejpam-5731	356	4	.	.	PROPN
ejpam-5731	356	5	math	math	PROPN
ejpam-5731	356	6	,	,	PUNCT
ejpam-5731	356	7	18	18	NUM
ejpam-5731	356	8	(	(	PUNCT
ejpam-5731	356	9	1	1	NUM
ejpam-5731	356	10	)	)	PUNCT
ejpam-5731	356	11	(	(	PUNCT
ejpam-5731	356	12	2025	2025	NUM
ejpam-5731	356	13	)	)	PUNCT
ejpam-5731	356	14	,	,	PUNCT
ejpam-5731	356	15	5731	5731	NUM
ejpam-5731	356	16	17	17	NUM
ejpam-5731	356	17	of	of	ADP
ejpam-5731	356	18	20	20	NUM
ejpam-5731	356	19	corollary	corollary	ADJ
ejpam-5731	356	20	8	8	NUM
ejpam-5731	356	21	.	.	PUNCT
ejpam-5731	357	1	if	if	SCONJ
ejpam-5731	357	2	a	a	DET
ejpam-5731	357	3	function	function	NOUN
ejpam-5731	357	4	f	f	PROPN
ejpam-5731	357	5	∈	∈	PROPN
ejpam-5731	357	6	σ	σ	PROPN
ejpam-5731	357	7	is	be	AUX
ejpam-5731	357	8	represented	represent	VERB
ejpam-5731	357	9	by	by	ADP
ejpam-5731	357	10	equation	equation	NOUN
ejpam-5731	357	11	(	(	PUNCT
ejpam-5731	357	12	1	1	NUM
ejpam-5731	357	13	)	)	PUNCT
ejpam-5731	357	14	and	and	CCONJ
ejpam-5731	357	15	is	be	AUX
ejpam-5731	357	16	obeying	obey	VERB
ejpam-5731	357	17	the	the	DET
ejpam-5731	357	18	subordination	subordination	NOUN
ejpam-5731	357	19	conditions	condition	NOUN
ejpam-5731	357	20	(	(	PUNCT
ejpam-5731	357	21	35	35	NUM
ejpam-5731	357	22	)	)	PUNCT
ejpam-5731	357	23	and	and	CCONJ
ejpam-5731	357	24	(	(	PUNCT
ejpam-5731	357	25	36	36	NUM
ejpam-5731	357	26	)	)	PUNCT
ejpam-5731	357	27	,	,	PUNCT
ejpam-5731	357	28	then	then	ADV
ejpam-5731	357	29	for	for	ADP
ejpam-5731	357	30	a	a	DET
ejpam-5731	357	31	real	real	ADJ
ejpam-5731	357	32	number	number	NOUN
ejpam-5731	357	33	ζ	ζ	NOUN
ejpam-5731	357	34	the	the	DET
ejpam-5731	357	35	following	following	NOUN
ejpam-5731	357	36	holds	hold	VERB
ejpam-5731	357	37	|a3	|a3	NOUN
ejpam-5731	357	38	−	−	PROPN
ejpam-5731	357	39	γa22|	γa22|	NOUN
ejpam-5731	357	40	≤	≤	NOUN
ejpam-5731	357	41	{	{	PUNCT
ejpam-5731	357	42	|1−cos	|1−cos	NUM
ejpam-5731	357	43	θ|	θ|	PROPN
ejpam-5731	357	44	cos	cos	PRON
ejpam-5731	357	45	δ	δ	PROPN
ejpam-5731	357	46	6	6	NUM
ejpam-5731	357	47	,	,	PUNCT
ejpam-5731	357	48	if	if	SCONJ
ejpam-5731	357	49	|1−	|1−	PRON
ejpam-5731	357	50	ζ|	ζ|	PROPN
ejpam-5731	357	51	≤	≤	NUM
ejpam-5731	357	52	|∆4|	|∆4|	NOUN
ejpam-5731	357	53	|1−cos	|1−cos	PRON
ejpam-5731	357	54	θ||1−γ|	θ||1−γ|	PROPN
ejpam-5731	357	55	cos	cos	SCONJ
ejpam-5731	357	56	δ	δ	PROPN
ejpam-5731	357	57	|6β1	|6β1	VERB
ejpam-5731	357	58	cos	cos	PROPN
ejpam-5731	357	59	δ+4(1−3	δ+4(1−3	PROPN
ejpam-5731	357	60	cos	cos	PROPN
ejpam-5731	357	61	θ)eiδ|	θ)eiδ|	PROPN
ejpam-5731	357	62	,	,	PUNCT
ejpam-5731	357	63	if	if	SCONJ
ejpam-5731	357	64	|1−	|1−	PROPN
ejpam-5731	357	65	ζ|	ζ|	PROPN
ejpam-5731	357	66	≥	≥	PRON
ejpam-5731	357	67	|∆4|	|∆4|	NOUN
ejpam-5731	357	68	,	,	PUNCT
ejpam-5731	357	69	where	where	SCONJ
ejpam-5731	357	70	∆4	∆4	NOUN
ejpam-5731	357	71	=	=	SYM
ejpam-5731	357	72	|3(cos	|3(co	NOUN
ejpam-5731	358	1	θ	θ	X
ejpam-5731	359	1	−	−	NOUN
ejpam-5731	359	2	1	1	X
ejpam-5731	359	3	)	)	PUNCT
ejpam-5731	359	4	cos	cos	ADP
ejpam-5731	359	5	δ	δ	PROPN
ejpam-5731	359	6	+	+	CCONJ
ejpam-5731	359	7	2(1−	2(1−	NUM
ejpam-5731	359	8	3	3	NUM
ejpam-5731	359	9	cos	cos	PROPN
ejpam-5731	359	10	θ)eiδ|	θ)eiδ|	PROPN
ejpam-5731	359	11	3|1−	3|1−	PROPN
ejpam-5731	359	12	cos	cos	PROPN
ejpam-5731	359	13	θ|	θ|	PROPN
ejpam-5731	359	14	cos	cos	PROPN
ejpam-5731	359	15	δ	δ	PROPN
ejpam-5731	359	16	.	.	PUNCT
ejpam-5731	360	1	remark	remark	PROPN
ejpam-5731	360	2	1	1	NUM
ejpam-5731	360	3	.	.	PUNCT
ejpam-5731	360	4	assuming	assume	VERB
ejpam-5731	360	5	δ	δ	PROPN
ejpam-5731	360	6	=	=	SYM
ejpam-5731	360	7	0	0	PROPN
ejpam-5731	360	8	,	,	PUNCT
ejpam-5731	360	9	the	the	DET
ejpam-5731	360	10	results	result	NOUN
ejpam-5731	360	11	presented	present	VERB
ejpam-5731	360	12	in	in	ADP
ejpam-5731	360	13	this	this	DET
ejpam-5731	360	14	paper	paper	NOUN
ejpam-5731	360	15	would	would	AUX
ejpam-5731	360	16	give	give	VERB
ejpam-5731	360	17	various	various	ADJ
ejpam-5731	360	18	new	new	ADJ
ejpam-5731	360	19	and	and	CCONJ
ejpam-5731	360	20	known	known	ADJ
ejpam-5731	360	21	results	result	NOUN
ejpam-5731	360	22	.	.	PUNCT
ejpam-5731	361	1	moreover	moreover	ADV
ejpam-5731	361	2	,	,	PUNCT
ejpam-5731	361	3	taking	take	VERB
ejpam-5731	361	4	δ	δ	X
ejpam-5731	361	5	=	=	PUNCT
ejpam-5731	361	6	0	0	NUM
ejpam-5731	361	7	in	in	ADP
ejpam-5731	361	8	example	example	NOUN
ejpam-5731	361	9	3	3	NUM
ejpam-5731	361	10	,	,	PUNCT
ejpam-5731	361	11	would	would	AUX
ejpam-5731	361	12	lead	lead	VERB
ejpam-5731	361	13	to	to	ADP
ejpam-5731	361	14	the	the	DET
ejpam-5731	361	15	known	know	VERB
ejpam-5731	361	16	classes	class	NOUN
ejpam-5731	361	17	of	of	ADP
ejpam-5731	361	18	starlike	starlike	ADJ
ejpam-5731	361	19	bi	bi	ADJ
ejpam-5731	361	20	-	-	ADJ
ejpam-5731	361	21	univalent	univalent	ADJ
ejpam-5731	361	22	functions	function	NOUN
ejpam-5731	361	23	that	that	PRON
ejpam-5731	361	24	studied	study	VERB
ejpam-5731	361	25	by	by	ADP
ejpam-5731	361	26	many	many	ADJ
ejpam-5731	361	27	researchers	researcher	NOUN
ejpam-5731	361	28	see	see	VERB
ejpam-5731	361	29	,	,	PUNCT
ejpam-5731	361	30	for	for	ADP
ejpam-5731	361	31	example	example	NOUN
ejpam-5731	361	32	,	,	PUNCT
ejpam-5731	361	33	[	[	X
ejpam-5731	361	34	7	7	NUM
ejpam-5731	361	35	]	]	PUNCT
ejpam-5731	361	36	,	,	PUNCT
ejpam-5731	361	37	[	[	X
ejpam-5731	361	38	14	14	NUM
ejpam-5731	361	39	]	]	PUNCT
ejpam-5731	361	40	,	,	PUNCT
ejpam-5731	361	41	[	[	X
ejpam-5731	361	42	20	20	NUM
ejpam-5731	361	43	]	]	PUNCT
ejpam-5731	361	44	,	,	PUNCT
ejpam-5731	361	45	[	[	X
ejpam-5731	361	46	29	29	NUM
ejpam-5731	361	47	]	]	PUNCT
ejpam-5731	361	48	,	,	PUNCT
ejpam-5731	361	49	[	[	X
ejpam-5731	361	50	33	33	NUM
ejpam-5731	361	51	]	]	PUNCT
ejpam-5731	361	52	,	,	PUNCT
ejpam-5731	361	53	and	and	CCONJ
ejpam-5731	361	54	[	[	X
ejpam-5731	361	55	45	45	NUM
ejpam-5731	361	56	]	]	PUNCT
ejpam-5731	361	57	.	.	PUNCT
ejpam-5731	362	1	more	more	ADV
ejpam-5731	362	2	precisely	precisely	ADV
ejpam-5731	362	3	,	,	PUNCT
ejpam-5731	362	4	the	the	DET
ejpam-5731	362	5	results	result	NOUN
ejpam-5731	362	6	presented	present	VERB
ejpam-5731	362	7	in	in	ADP
ejpam-5731	362	8	those	those	DET
ejpam-5731	362	9	papers	paper	NOUN
ejpam-5731	362	10	are	be	AUX
ejpam-5731	362	11	just	just	ADV
ejpam-5731	362	12	special	special	ADJ
ejpam-5731	362	13	case	case	NOUN
ejpam-5731	362	14	of	of	ADP
ejpam-5731	362	15	the	the	DET
ejpam-5731	362	16	class	class	NOUN
ejpam-5731	362	17	mentioned	mention	VERB
ejpam-5731	362	18	in	in	ADP
ejpam-5731	362	19	example	example	NOUN
ejpam-5731	362	20	3	3	NUM
ejpam-5731	362	21	.	.	NOUN
ejpam-5731	362	22	5	5	NUM
ejpam-5731	362	23	.	.	X
ejpam-5731	362	24	conclusion	conclusion	NOUN
ejpam-5731	362	25	this	this	DET
ejpam-5731	362	26	research	research	NOUN
ejpam-5731	362	27	paper	paper	NOUN
ejpam-5731	362	28	investigates	investigate	VERB
ejpam-5731	362	29	a	a	DET
ejpam-5731	362	30	new	new	ADJ
ejpam-5731	362	31	category	category	NOUN
ejpam-5731	362	32	of	of	ADP
ejpam-5731	362	33	bi	bi	ADJ
ejpam-5731	362	34	-	-	ADJ
ejpam-5731	362	35	bazilevic	bazilevic	ADJ
ejpam-5731	362	36	functions	function	NOUN
ejpam-5731	362	37	that	that	PRON
ejpam-5731	362	38	are	be	AUX
ejpam-5731	362	39	defined	define	VERB
ejpam-5731	362	40	through	through	ADP
ejpam-5731	362	41	the	the	DET
ejpam-5731	362	42	q	q	NOUN
ejpam-5731	362	43	-	-	PUNCT
ejpam-5731	362	44	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	362	45	differential	differential	ADJ
ejpam-5731	362	46	operator	operator	NOUN
ejpam-5731	362	47	and	and	CCONJ
ejpam-5731	362	48	are	be	AUX
ejpam-5731	362	49	linked	link	VERB
ejpam-5731	362	50	to	to	ADP
ejpam-5731	362	51	legendre	legendre	PROPN
ejpam-5731	362	52	polynomials	polynomial	NOUN
ejpam-5731	362	53	.	.	PUNCT
ejpam-5731	363	1	the	the	DET
ejpam-5731	363	2	author	author	NOUN
ejpam-5731	363	3	has	have	VERB
ejpam-5731	363	4	derived	derive	VERB
ejpam-5731	363	5	estimates	estimate	NOUN
ejpam-5731	363	6	for	for	ADP
ejpam-5731	363	7	the	the	DET
ejpam-5731	363	8	initial	initial	ADJ
ejpam-5731	363	9	coefficients	coefficient	NOUN
ejpam-5731	363	10	and	and	CCONJ
ejpam-5731	363	11	examined	examine	VERB
ejpam-5731	363	12	the	the	DET
ejpam-5731	363	13	fekete	fekete	PROPN
ejpam-5731	363	14	-	-	PUNCT
ejpam-5731	363	15	szegö	szegö	ADJ
ejpam-5731	363	16	functional	functional	ADJ
ejpam-5731	363	17	problem	problem	NOUN
ejpam-5731	363	18	concerning	concern	VERB
ejpam-5731	363	19	functions	function	NOUN
ejpam-5731	363	20	within	within	ADP
ejpam-5731	363	21	these	these	DET
ejpam-5731	363	22	specific	specific	ADJ
ejpam-5731	363	23	classes	class	NOUN
ejpam-5731	363	24	.	.	PUNCT
ejpam-5731	364	1	in	in	ADP
ejpam-5731	364	2	conclusion	conclusion	NOUN
ejpam-5731	364	3	,	,	PUNCT
ejpam-5731	364	4	potential	potential	ADJ
ejpam-5731	364	5	avenues	avenue	NOUN
ejpam-5731	364	6	for	for	ADP
ejpam-5731	364	7	future	future	ADJ
ejpam-5731	364	8	research	research	NOUN
ejpam-5731	364	9	are	be	AUX
ejpam-5731	364	10	suggested	suggest	VERB
ejpam-5731	364	11	,	,	PUNCT
ejpam-5731	364	12	particularly	particularly	ADV
ejpam-5731	364	13	the	the	DET
ejpam-5731	364	14	exploration	exploration	NOUN
ejpam-5731	364	15	of	of	ADP
ejpam-5731	364	16	substituting	substitute	VERB
ejpam-5731	364	17	legendre	legendre	PROPN
ejpam-5731	364	18	polynomials	polynomial	NOUN
ejpam-5731	364	19	with	with	ADP
ejpam-5731	364	20	other	other	ADJ
ejpam-5731	364	21	types	type	NOUN
ejpam-5731	364	22	of	of	ADP
ejpam-5731	364	23	orthogonal	orthogonal	ADJ
ejpam-5731	364	24	polynomials	polynomial	NOUN
ejpam-5731	364	25	,	,	PUNCT
ejpam-5731	364	26	such	such	ADJ
ejpam-5731	364	27	as	as	ADP
ejpam-5731	364	28	gegenbauer	gegenbauer	NOUN
ejpam-5731	364	29	polynomials	polynomial	NOUN
ejpam-5731	364	30	.	.	PUNCT
ejpam-5731	365	1	furthermore	furthermore	ADV
ejpam-5731	365	2	,	,	PUNCT
ejpam-5731	365	3	the	the	DET
ejpam-5731	365	4	findings	finding	NOUN
ejpam-5731	365	5	presented	present	VERB
ejpam-5731	365	6	in	in	ADP
ejpam-5731	365	7	this	this	DET
ejpam-5731	365	8	study	study	NOUN
ejpam-5731	365	9	are	be	AUX
ejpam-5731	365	10	anticipated	anticipate	VERB
ejpam-5731	365	11	to	to	PART
ejpam-5731	365	12	motivate	motivate	VERB
ejpam-5731	365	13	researchers	researcher	NOUN
ejpam-5731	365	14	to	to	PART
ejpam-5731	365	15	expand	expand	VERB
ejpam-5731	365	16	the	the	DET
ejpam-5731	365	17	scope	scope	NOUN
ejpam-5731	365	18	of	of	ADP
ejpam-5731	365	19	this	this	DET
ejpam-5731	365	20	investigation	investigation	NOUN
ejpam-5731	365	21	to	to	PART
ejpam-5731	365	22	include	include	VERB
ejpam-5731	365	23	meromorphic	meromorphic	ADJ
ejpam-5731	365	24	bi	bi	ADJ
ejpam-5731	365	25	-	-	ADJ
ejpam-5731	365	26	univalent	univalent	ADJ
ejpam-5731	365	27	functions	function	NOUN
ejpam-5731	365	28	.	.	PUNCT
ejpam-5731	366	1	acknowledgements	acknowledgement	NOUN
ejpam-5731	366	2	this	this	DET
ejpam-5731	366	3	research	research	NOUN
ejpam-5731	366	4	is	be	AUX
ejpam-5731	366	5	partially	partially	ADV
ejpam-5731	366	6	funded	fund	VERB
ejpam-5731	366	7	by	by	ADP
ejpam-5731	366	8	zarqa	zarqa	PROPN
ejpam-5731	366	9	university	university	PROPN
ejpam-5731	366	10	.	.	PUNCT
ejpam-5731	367	1	the	the	DET
ejpam-5731	367	2	author	author	NOUN
ejpam-5731	367	3	would	would	AUX
ejpam-5731	367	4	like	like	VERB
ejpam-5731	367	5	to	to	PART
ejpam-5731	367	6	express	express	VERB
ejpam-5731	367	7	his	his	PRON
ejpam-5731	367	8	sincerest	sincere	ADJ
ejpam-5731	367	9	thanks	thank	NOUN
ejpam-5731	367	10	to	to	ADP
ejpam-5731	367	11	zarqa	zarqa	PROPN
ejpam-5731	367	12	university	university	PROPN
ejpam-5731	367	13	for	for	ADP
ejpam-5731	367	14	the	the	DET
ejpam-5731	367	15	financial	financial	ADJ
ejpam-5731	367	16	support	support	NOUN
ejpam-5731	367	17	.	.	PUNCT
ejpam-5731	368	1	the	the	DET
ejpam-5731	368	2	author	author	NOUN
ejpam-5731	368	3	expresses	express	VERB
ejpam-5731	368	4	sincere	sincere	ADJ
ejpam-5731	368	5	gratitude	gratitude	NOUN
ejpam-5731	368	6	to	to	ADP
ejpam-5731	368	7	the	the	DET
ejpam-5731	368	8	anonymous	anonymous	ADJ
ejpam-5731	368	9	referees	referee	NOUN
ejpam-5731	368	10	for	for	ADP
ejpam-5731	368	11	their	their	PRON
ejpam-5731	368	12	insightful	insightful	ADJ
ejpam-5731	368	13	comments	comment	NOUN
ejpam-5731	368	14	and	and	CCONJ
ejpam-5731	368	15	recommendations	recommendation	NOUN
ejpam-5731	368	16	,	,	PUNCT
ejpam-5731	368	17	which	which	PRON
ejpam-5731	368	18	significantly	significantly	ADV
ejpam-5731	368	19	enhanced	enhance	VERB
ejpam-5731	368	20	the	the	DET
ejpam-5731	368	21	quality	quality	NOUN
ejpam-5731	368	22	of	of	ADP
ejpam-5731	368	23	this	this	DET
ejpam-5731	368	24	paper	paper	NOUN
ejpam-5731	368	25	’s	’s	PART
ejpam-5731	368	26	presentation	presentation	NOUN
ejpam-5731	368	27	.	.	PUNCT
ejpam-5731	369	1	6	6	X
ejpam-5731	369	2	.	.	X
ejpam-5731	369	3	conflicts	conflict	NOUN
ejpam-5731	369	4	of	of	ADP
ejpam-5731	369	5	interest	interest	NOUN
ejpam-5731	369	6	the	the	DET
ejpam-5731	369	7	author	author	NOUN
ejpam-5731	369	8	confirms	confirm	VERB
ejpam-5731	369	9	that	that	SCONJ
ejpam-5731	369	10	there	there	PRON
ejpam-5731	369	11	are	be	VERB
ejpam-5731	369	12	no	no	DET
ejpam-5731	369	13	relevant	relevant	ADJ
ejpam-5731	369	14	conflicts	conflict	NOUN
ejpam-5731	369	15	of	of	ADP
ejpam-5731	369	16	interest	interest	NOUN
ejpam-5731	369	17	that	that	PRON
ejpam-5731	369	18	are	be	AUX
ejpam-5731	369	19	pertinent	pertinent	ADJ
ejpam-5731	369	20	to	to	ADP
ejpam-5731	369	21	the	the	DET
ejpam-5731	369	22	content	content	NOUN
ejpam-5731	369	23	of	of	ADP
ejpam-5731	369	24	this	this	DET
ejpam-5731	369	25	article	article	NOUN
ejpam-5731	369	26	.	.	PUNCT
ejpam-5731	370	1	references	reference	NOUN
ejpam-5731	370	2	[	[	X
ejpam-5731	370	3	1	1	X
ejpam-5731	370	4	]	]	PUNCT
ejpam-5731	370	5	v.	v.	ADP
ejpam-5731	370	6	aboites	aboite	NOUN
ejpam-5731	370	7	.	.	PUNCT
ejpam-5731	371	1	easy	easy	ADJ
ejpam-5731	371	2	route	route	NOUN
ejpam-5731	371	3	to	to	ADP
ejpam-5731	371	4	tchebycheff	tchebycheff	NOUN
ejpam-5731	371	5	polynomials	polynomial	NOUN
ejpam-5731	371	6	.	.	PUNCT
ejpam-5731	372	1	revista	revista	VERB
ejpam-5731	372	2	mexicana	mexicana	PROPN
ejpam-5731	372	3	de	de	PROPN
ejpam-5731	372	4	fisica	fisica	PROPN
ejpam-5731	372	5	,	,	PUNCT
ejpam-5731	372	6	65:12–14	65:12–14	PROPN
ejpam-5731	372	7	,	,	PUNCT
ejpam-5731	372	8	2019	2019	NUM
ejpam-5731	372	9	.	.	PUNCT
ejpam-5731	373	1	w.	w.	PROPN
ejpam-5731	373	2	al	al	PROPN
ejpam-5731	373	3	-	-	PUNCT
ejpam-5731	373	4	rawashdeh	rawashdeh	PROPN
ejpam-5731	373	5	/	/	SYM
ejpam-5731	373	6	eur	eur	PROPN
ejpam-5731	373	7	.	.	PUNCT
ejpam-5731	374	1	j.	j.	PROPN
ejpam-5731	374	2	pure	pure	PROPN
ejpam-5731	374	3	appl	appl	PROPN
ejpam-5731	374	4	.	.	PROPN
ejpam-5731	374	5	math	math	PROPN
ejpam-5731	374	6	,	,	PUNCT
ejpam-5731	374	7	18	18	NUM
ejpam-5731	374	8	(	(	PUNCT
ejpam-5731	374	9	1	1	NUM
ejpam-5731	374	10	)	)	PUNCT
ejpam-5731	374	11	(	(	PUNCT
ejpam-5731	374	12	2025	2025	NUM
ejpam-5731	374	13	)	)	PUNCT
ejpam-5731	374	14	,	,	PUNCT
ejpam-5731	374	15	5731	5731	NUM
ejpam-5731	374	16	18	18	NUM
ejpam-5731	374	17	of	of	ADP
ejpam-5731	374	18	20	20	NUM
ejpam-5731	374	19	[	[	SYM
ejpam-5731	374	20	2	2	NUM
ejpam-5731	374	21	]	]	PUNCT
ejpam-5731	374	22	m.	m.	NOUN
ejpam-5731	374	23	ahsan	ahsan	PROPN
ejpam-5731	374	24	,	,	PUNCT
ejpam-5731	374	25	m.	m.	NOUN
ejpam-5731	374	26	ahmad	ahmad	PROPN
ejpam-5731	374	27	,	,	PUNCT
ejpam-5731	374	28	w.	w.	PROPN
ejpam-5731	374	29	khan	khan	PROPN
ejpam-5731	374	30	,	,	PUNCT
ejpam-5731	374	31	e.e	e.e	PROPN
ejpam-5731	374	32	.	.	PROPN
ejpam-5731	374	33	mahmoud	mahmoud	PROPN
ejpam-5731	374	34	,	,	PUNCT
ejpam-5731	374	35	and	and	CCONJ
ejpam-5731	374	36	a.h	a.h	PROPN
ejpam-5731	374	37	.	.	PROPN
ejpam-5731	374	38	abdel	abdel	PROPN
ejpam-5731	374	39	-	-	PUNCT
ejpam-5731	374	40	aty	aty	PROPN
ejpam-5731	374	41	.	.	PUNCT
ejpam-5731	375	1	meshless	meshless	ADJ
ejpam-5731	375	2	analysis	analysis	NOUN
ejpam-5731	375	3	of	of	ADP
ejpam-5731	375	4	nonlocal	nonlocal	ADJ
ejpam-5731	375	5	boundary	boundary	ADJ
ejpam-5731	375	6	value	value	NOUN
ejpam-5731	375	7	problems	problem	NOUN
ejpam-5731	375	8	in	in	ADP
ejpam-5731	375	9	anisotropic	anisotropic	NOUN
ejpam-5731	375	10	and	and	CCONJ
ejpam-5731	375	11	inhomogeneous	inhomogeneous	ADJ
ejpam-5731	375	12	media	medium	NOUN
ejpam-5731	375	13	.	.	PUNCT
ejpam-5731	376	1	mathemaics	mathemaic	NOUN
ejpam-5731	376	2	,	,	PUNCT
ejpam-5731	376	3	11(8):2045	11(8):2045	NUM
ejpam-5731	376	4	,	,	PUNCT
ejpam-5731	376	5	2020	2020	NUM
ejpam-5731	376	6	.	.	PUNCT
ejpam-5731	377	1	[	[	X
ejpam-5731	377	2	3	3	X
ejpam-5731	377	3	]	]	PUNCT
ejpam-5731	377	4	w.	w.	PROPN
ejpam-5731	377	5	al	al	PROPN
ejpam-5731	377	6	-	-	PUNCT
ejpam-5731	377	7	rawashdeh	rawashdeh	PROPN
ejpam-5731	377	8	.	.	PUNCT
ejpam-5731	378	1	applications	application	NOUN
ejpam-5731	378	2	of	of	ADP
ejpam-5731	378	3	gegenbauer	gegenbauer	NOUN
ejpam-5731	378	4	polynomials	polynomial	VERB
ejpam-5731	378	5	to	to	ADP
ejpam-5731	378	6	a	a	DET
ejpam-5731	378	7	certain	certain	ADJ
ejpam-5731	378	8	subclass	subclass	NOUN
ejpam-5731	378	9	of	of	ADP
ejpam-5731	378	10	p	p	NOUN
ejpam-5731	378	11	-	-	PUNCT
ejpam-5731	378	12	valent	valent	NOUN
ejpam-5731	378	13	functions	function	NOUN
ejpam-5731	378	14	.	.	PUNCT
ejpam-5731	379	1	wseas	wseas	VERB
ejpam-5731	379	2	transactions	transaction	NOUN
ejpam-5731	379	3	on	on	ADP
ejpam-5731	379	4	mathematics	mathematic	NOUN
ejpam-5731	379	5	,	,	PUNCT
ejpam-5731	379	6	22:1025–1030	22:1025–1030	NUM
ejpam-5731	379	7	,	,	PUNCT
ejpam-5731	379	8	2023	2023	NUM
ejpam-5731	379	9	.	.	PUNCT
ejpam-5731	380	1	[	[	X
ejpam-5731	380	2	4	4	X
ejpam-5731	380	3	]	]	PUNCT
ejpam-5731	380	4	w.	w.	PROPN
ejpam-5731	380	5	al	al	PROPN
ejpam-5731	380	6	-	-	PUNCT
ejpam-5731	380	7	rawashdeh	rawashdeh	PROPN
ejpam-5731	380	8	.	.	PUNCT
ejpam-5731	381	1	horadam	horadam	PROPN
ejpam-5731	381	2	polynomials	polynomial	NOUN
ejpam-5731	381	3	and	and	CCONJ
ejpam-5731	381	4	a	a	DET
ejpam-5731	381	5	class	class	NOUN
ejpam-5731	381	6	of	of	ADP
ejpam-5731	381	7	binivalent	binivalent	NOUN
ejpam-5731	381	8	functions	function	NOUN
ejpam-5731	381	9	defined	define	VERB
ejpam-5731	381	10	by	by	ADP
ejpam-5731	381	11	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	381	12	operator	operator	NOUN
ejpam-5731	381	13	.	.	PUNCT
ejpam-5731	382	1	international	international	ADJ
ejpam-5731	382	2	journal	journal	PROPN
ejpam-5731	382	3	of	of	ADP
ejpam-5731	382	4	mathematics	mathematics	PROPN
ejpam-5731	382	5	and	and	CCONJ
ejpam-5731	382	6	mathematical	mathematical	ADJ
ejpam-5731	382	7	sciences	science	NOUN
ejpam-5731	382	8	,	,	PUNCT
ejpam-5731	382	9	article	article	NOUN
ejpam-5731	382	10	i	i	NOUN
ejpam-5731	382	11	d	d	PROPN
ejpam-5731	382	12	2573044:7	2573044:7	NUM
ejpam-5731	382	13	pages	page	NOUN
ejpam-5731	382	14	,	,	PUNCT
ejpam-5731	382	15	2023	2023	NUM
ejpam-5731	382	16	.	.	PUNCT
ejpam-5731	383	1	[	[	X
ejpam-5731	383	2	5	5	X
ejpam-5731	383	3	]	]	PUNCT
ejpam-5731	383	4	w.	w.	PROPN
ejpam-5731	383	5	al	al	PROPN
ejpam-5731	383	6	-	-	PUNCT
ejpam-5731	383	7	rawashdeh	rawashdeh	PROPN
ejpam-5731	383	8	.	.	PUNCT
ejpam-5731	384	1	a	a	DET
ejpam-5731	384	2	class	class	NOUN
ejpam-5731	384	3	of	of	ADP
ejpam-5731	384	4	non	non	ADJ
ejpam-5731	384	5	-	-	ADJ
ejpam-5731	384	6	bazilevic	bazilevic	ADJ
ejpam-5731	384	7	functions	function	NOUN
ejpam-5731	384	8	subordinate	subordinate	VERB
ejpam-5731	384	9	to	to	ADP
ejpam-5731	384	10	gegenbauer	gegenbauer	NOUN
ejpam-5731	384	11	polynomials	polynomial	NOUN
ejpam-5731	384	12	.	.	PUNCT
ejpam-5731	385	1	int	int	NOUN
ejpam-5731	385	2	.	.	PUNCT
ejpam-5731	386	1	j.	j.	PROPN
ejpam-5731	386	2	of	of	ADP
ejpam-5731	386	3	analysis	analysis	NOUN
ejpam-5731	386	4	and	and	CCONJ
ejpam-5731	386	5	applications	application	NOUN
ejpam-5731	386	6	,	,	PUNCT
ejpam-5731	386	7	22(29):1–9	22(29):1–9	NUM
ejpam-5731	386	8	,	,	PUNCT
ejpam-5731	386	9	2024	2024	NUM
ejpam-5731	386	10	.	.	PUNCT
ejpam-5731	387	1	[	[	X
ejpam-5731	387	2	6	6	NUM
ejpam-5731	387	3	]	]	PUNCT
ejpam-5731	387	4	w.	w.	PROPN
ejpam-5731	387	5	al	al	PROPN
ejpam-5731	387	6	-	-	PUNCT
ejpam-5731	387	7	rawashdeh	rawashdeh	PROPN
ejpam-5731	387	8	.	.	PUNCT
ejpam-5731	388	1	fekete	fekete	PROPN
ejpam-5731	388	2	-	-	PUNCT
ejpam-5731	388	3	szegö	szegö	VERB
ejpam-5731	388	4	functional	functional	NOUN
ejpam-5731	388	5	of	of	ADP
ejpam-5731	388	6	a	a	DET
ejpam-5731	388	7	subclass	subclass	NOUN
ejpam-5731	388	8	of	of	ADP
ejpam-5731	388	9	bi	bi	ADJ
ejpam-5731	388	10	-	-	ADJ
ejpam-5731	388	11	univalent	univalent	ADJ
ejpam-5731	388	12	functions	function	NOUN
ejpam-5731	388	13	associated	associate	VERB
ejpam-5731	388	14	with	with	ADP
ejpam-5731	388	15	gegenbauer	gegenbauer	NOUN
ejpam-5731	388	16	polynomials	polynomial	NOUN
ejpam-5731	388	17	.	.	PUNCT
ejpam-5731	389	1	european	european	PROPN
ejpam-5731	389	2	journal	journal	PROPN
ejpam-5731	389	3	of	of	ADP
ejpam-5731	389	4	pure	pure	ADJ
ejpam-5731	389	5	and	and	CCONJ
ejpam-5731	389	6	applied	applied	ADJ
ejpam-5731	389	7	mathematics	mathematic	NOUN
ejpam-5731	389	8	,	,	PUNCT
ejpam-5731	389	9	17(1):105–115	17(1):105–115	PROPN
ejpam-5731	389	10	,	,	PUNCT
ejpam-5731	389	11	2024	2024	NUM
ejpam-5731	389	12	.	.	PUNCT
ejpam-5731	390	1	[	[	X
ejpam-5731	390	2	7	7	X
ejpam-5731	390	3	]	]	PUNCT
ejpam-5731	390	4	w.	w.	PROPN
ejpam-5731	390	5	al	al	PROPN
ejpam-5731	390	6	-	-	PUNCT
ejpam-5731	390	7	rawashdeh	rawashdeh	PROPN
ejpam-5731	390	8	.	.	PUNCT
ejpam-5731	391	1	on	on	ADP
ejpam-5731	391	2	the	the	DET
ejpam-5731	391	3	study	study	NOUN
ejpam-5731	391	4	of	of	ADP
ejpam-5731	391	5	bi	bi	ADJ
ejpam-5731	391	6	-	-	ADJ
ejpam-5731	391	7	univalent	univalent	ADJ
ejpam-5731	391	8	functions	function	NOUN
ejpam-5731	391	9	defined	define	VERB
ejpam-5731	391	10	by	by	ADP
ejpam-5731	391	11	the	the	DET
ejpam-5731	391	12	generalized	generalized	ADJ
ejpam-5731	391	13	sălăgean	sălăgean	ADJ
ejpam-5731	391	14	differential	differential	NOUN
ejpam-5731	391	15	operator	operator	NOUN
ejpam-5731	391	16	.	.	PUNCT
ejpam-5731	392	1	european	european	PROPN
ejpam-5731	392	2	journal	journal	PROPN
ejpam-5731	392	3	of	of	ADP
ejpam-5731	392	4	pure	pure	ADJ
ejpam-5731	392	5	and	and	CCONJ
ejpam-5731	392	6	applied	applied	ADJ
ejpam-5731	392	7	mathematics	mathematic	NOUN
ejpam-5731	392	8	,	,	PUNCT
ejpam-5731	392	9	17(4):3899–3914	17(4):3899–3914	NUM
ejpam-5731	392	10	,	,	PUNCT
ejpam-5731	392	11	2024	2024	NUM
ejpam-5731	392	12	.	.	PUNCT
ejpam-5731	393	1	[	[	X
ejpam-5731	393	2	8	8	X
ejpam-5731	393	3	]	]	X
ejpam-5731	393	4	h.	h.	NOUN
ejpam-5731	393	5	aldweby	aldweby	PROPN
ejpam-5731	393	6	and	and	CCONJ
ejpam-5731	393	7	m.	m.	NOUN
ejpam-5731	393	8	darus	darus	NOUN
ejpam-5731	393	9	.	.	PUNCT
ejpam-5731	394	1	some	some	DET
ejpam-5731	394	2	subordination	subordination	NOUN
ejpam-5731	394	3	results	result	VERB
ejpam-5731	394	4	on	on	ADP
ejpam-5731	394	5	q	q	NOUN
ejpam-5731	394	6	-	-	NOUN
ejpam-5731	394	7	analogue	analogue	NOUN
ejpam-5731	394	8	of	of	ADP
ejpam-5731	394	9	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	394	10	differential	differential	ADJ
ejpam-5731	394	11	operator	operator	NOUN
ejpam-5731	394	12	.	.	PUNCT
ejpam-5731	395	1	abst	abst	PROPN
ejpam-5731	395	2	.	.	PROPN
ejpam-5731	395	3	appl	appl	PROPN
ejpam-5731	395	4	.	.	PUNCT
ejpam-5731	396	1	anal	anal	PROPN
ejpam-5731	396	2	.	.	PUNCT
ejpam-5731	396	3	,	,	PUNCT
ejpam-5731	396	4	article	article	NOUN
ejpam-5731	396	5	i	i	PROPN
ejpam-5731	396	6	d	d	PROPN
ejpam-5731	396	7	985563:1–6	985563:1–6	PROPN
ejpam-5731	396	8	,	,	PUNCT
ejpam-5731	396	9	2014	2014	NUM
ejpam-5731	396	10	.	.	PUNCT
ejpam-5731	397	1	[	[	X
ejpam-5731	397	2	9	9	NUM
ejpam-5731	397	3	]	]	PUNCT
ejpam-5731	397	4	l.	l.	PROPN
ejpam-5731	397	5	andrei	andrei	PROPN
ejpam-5731	397	6	and	and	CCONJ
ejpam-5731	397	7	v.a	v.a	PROPN
ejpam-5731	397	8	.	.	PROPN
ejpam-5731	397	9	caus	caus	PROPN
ejpam-5731	397	10	.	.	PUNCT
ejpam-5731	398	1	subordinations	subordination	NOUN
ejpam-5731	398	2	results	result	VERB
ejpam-5731	398	3	on	on	ADP
ejpam-5731	398	4	a	a	DET
ejpam-5731	398	5	q	q	ADJ
ejpam-5731	398	6	-	-	ADJ
ejpam-5731	398	7	derivative	derivative	ADJ
ejpam-5731	398	8	differential	differential	NOUN
ejpam-5731	398	9	operator	operator	NOUN
ejpam-5731	398	10	.	.	PUNCT
ejpam-5731	399	1	mathematics	mathematic	NOUN
ejpam-5731	399	2	,	,	PUNCT
ejpam-5731	399	3	12:208	12:208	NUM
ejpam-5731	399	4	,	,	PUNCT
ejpam-5731	399	5	2024	2024	NUM
ejpam-5731	399	6	.	.	PUNCT
ejpam-5731	400	1	[	[	X
ejpam-5731	400	2	10	10	NUM
ejpam-5731	400	3	]	]	X
ejpam-5731	400	4	a.	a.	NOUN
ejpam-5731	400	5	aral	aral	PROPN
ejpam-5731	400	6	,	,	PUNCT
ejpam-5731	400	7	v.	v.	PROPN
ejpam-5731	400	8	gupta	gupta	PROPN
ejpam-5731	400	9	,	,	PUNCT
ejpam-5731	400	10	and	and	CCONJ
ejpam-5731	400	11	r.p	r.p	PROPN
ejpam-5731	400	12	.	.	PROPN
ejpam-5731	400	13	agarwal	agarwal	PROPN
ejpam-5731	400	14	.	.	PUNCT
ejpam-5731	401	1	applications	application	NOUN
ejpam-5731	401	2	of	of	ADP
ejpam-5731	401	3	q	q	NOUN
ejpam-5731	401	4	-	-	NOUN
ejpam-5731	401	5	calculus	calculus	NOUN
ejpam-5731	401	6	in	in	ADP
ejpam-5731	401	7	operator	operator	NOUN
ejpam-5731	401	8	theory	theory	NOUN
ejpam-5731	401	9	.	.	PUNCT
ejpam-5731	402	1	springer	springer	NOUN
ejpam-5731	402	2	,	,	PUNCT
ejpam-5731	402	3	new	new	PROPN
ejpam-5731	402	4	york	york	PROPN
ejpam-5731	402	5	,	,	PUNCT
ejpam-5731	402	6	us	we	PRON
ejpam-5731	402	7	,	,	PUNCT
ejpam-5731	402	8	2013	2013	NUM
ejpam-5731	402	9	.	.	PUNCT
ejpam-5731	403	1	[	[	X
ejpam-5731	403	2	11	11	NUM
ejpam-5731	403	3	]	]	X
ejpam-5731	403	4	d.a	d.a	PROPN
ejpam-5731	403	5	.	.	PROPN
ejpam-5731	403	6	brannan	brannan	PROPN
ejpam-5731	403	7	and	and	CCONJ
ejpam-5731	403	8	j.g	j.g	PROPN
ejpam-5731	403	9	.	.	PROPN
ejpam-5731	403	10	clunie	clunie	PROPN
ejpam-5731	403	11	.	.	PUNCT
ejpam-5731	404	1	aspects	aspect	NOUN
ejpam-5731	404	2	of	of	ADP
ejpam-5731	404	3	contemporary	contemporary	ADJ
ejpam-5731	404	4	complex	complex	ADJ
ejpam-5731	404	5	analysis	analysis	NOUN
ejpam-5731	404	6	,	,	PUNCT
ejpam-5731	404	7	proceedings	proceeding	NOUN
ejpam-5731	404	8	of	of	ADP
ejpam-5731	404	9	the	the	DET
ejpam-5731	404	10	nato	nato	PROPN
ejpam-5731	404	11	advanced	advanced	ADJ
ejpam-5731	404	12	study	study	PROPN
ejpam-5731	404	13	institute	institute	PROPN
ejpam-5731	404	14	(	(	PUNCT
ejpam-5731	404	15	university	university	PROPN
ejpam-5731	404	16	of	of	ADP
ejpam-5731	404	17	durham	durham	PROPN
ejpam-5731	404	18	,	,	PUNCT
ejpam-5731	404	19	durham	durham	PROPN
ejpam-5731	404	20	;	;	PUNCT
ejpam-5731	404	21	july	july	PROPN
ejpam-5731	404	22	1–20	1–20	PROPN
ejpam-5731	404	23	,	,	PUNCT
ejpam-5731	404	24	1979	1979	NUM
ejpam-5731	404	25	)	)	PUNCT
ejpam-5731	404	26	.	.	PUNCT
ejpam-5731	405	1	academic	academic	ADJ
ejpam-5731	405	2	press	press	NOUN
ejpam-5731	405	3	,	,	PUNCT
ejpam-5731	405	4	new	new	PROPN
ejpam-5731	405	5	york	york	PROPN
ejpam-5731	405	6	and	and	CCONJ
ejpam-5731	405	7	london	london	PROPN
ejpam-5731	405	8	,	,	PUNCT
ejpam-5731	405	9	1979	1979	NUM
ejpam-5731	405	10	.	.	PUNCT
ejpam-5731	406	1	[	[	X
ejpam-5731	406	2	12	12	NUM
ejpam-5731	406	3	]	]	PUNCT
ejpam-5731	406	4	m.	m.	NOUN
ejpam-5731	406	5	cağlar	cağlar	PROPN
ejpam-5731	406	6	,	,	PUNCT
ejpam-5731	406	7	h.	h.	PROPN
ejpam-5731	406	8	orhan	orhan	PROPN
ejpam-5731	406	9	,	,	PUNCT
ejpam-5731	406	10	and	and	CCONJ
ejpam-5731	406	11	m.	m.	PROPN
ejpam-5731	406	12	kamali	kamali	PROPN
ejpam-5731	406	13	.	.	PUNCT
ejpam-5731	407	1	fekete	fekete	PROPN
ejpam-5731	407	2	-	-	PUNCT
ejpam-5731	407	3	szegö	szegö	PROPN
ejpam-5731	407	4	problem	problem	NOUN
ejpam-5731	407	5	for	for	ADP
ejpam-5731	407	6	a	a	DET
ejpam-5731	407	7	subclass	subclass	NOUN
ejpam-5731	407	8	of	of	ADP
ejpam-5731	407	9	analytic	analytic	ADJ
ejpam-5731	407	10	functions	function	NOUN
ejpam-5731	407	11	associated	associate	VERB
ejpam-5731	407	12	with	with	ADP
ejpam-5731	407	13	chebyshev	chebyshev	NOUN
ejpam-5731	407	14	polynomials	polynomial	NOUN
ejpam-5731	407	15	.	.	PUNCT
ejpam-5731	408	1	boletim	boletim	PROPN
ejpam-5731	408	2	da	da	PROPN
ejpam-5731	408	3	sociedade	sociedade	PROPN
ejpam-5731	408	4	paranaense	paranaense	PROPN
ejpam-5731	408	5	de	de	PROPN
ejpam-5731	408	6	matemática	matemática	PROPN
ejpam-5731	408	7	,	,	PUNCT
ejpam-5731	408	8	40:1–6	40:1–6	NOUN
ejpam-5731	408	9	,	,	PUNCT
ejpam-5731	408	10	2022	2022	NUM
ejpam-5731	408	11	.	.	PUNCT
ejpam-5731	409	1	[	[	X
ejpam-5731	409	2	13	13	NUM
ejpam-5731	409	3	]	]	X
ejpam-5731	409	4	y.	y.	PROPN
ejpam-5731	409	5	cheng	cheng	PROPN
ejpam-5731	409	6	,	,	PUNCT
ejpam-5731	409	7	r.	r.	PROPN
ejpam-5731	409	8	srivastava	srivastava	PROPN
ejpam-5731	409	9	,	,	PUNCT
ejpam-5731	409	10	and	and	CCONJ
ejpam-5731	409	11	j.l	j.l	PROPN
ejpam-5731	409	12	.	.	PROPN
ejpam-5731	409	13	liu	liu	PROPN
ejpam-5731	409	14	.	.	PUNCT
ejpam-5731	410	1	applications	application	NOUN
ejpam-5731	410	2	of	of	ADP
ejpam-5731	410	3	the	the	DET
ejpam-5731	410	4	q−derivative	q−derivative	ADJ
ejpam-5731	410	5	operator	operator	NOUN
ejpam-5731	410	6	to	to	ADP
ejpam-5731	410	7	new	new	ADJ
ejpam-5731	410	8	families	family	NOUN
ejpam-5731	410	9	of	of	ADP
ejpam-5731	410	10	bi	bi	ADJ
ejpam-5731	410	11	-	-	ADJ
ejpam-5731	410	12	univalent	univalent	ADJ
ejpam-5731	410	13	functions	function	NOUN
ejpam-5731	410	14	related	relate	VERB
ejpam-5731	410	15	to	to	ADP
ejpam-5731	410	16	the	the	DET
ejpam-5731	410	17	legendre	legendre	PROPN
ejpam-5731	410	18	polynomials	polynomial	NOUN
ejpam-5731	410	19	.	.	PUNCT
ejpam-5731	411	1	axioms	axiom	NOUN
ejpam-5731	411	2	,	,	PUNCT
ejpam-5731	411	3	11(595):1–13	11(595):1–13	NOUN
ejpam-5731	411	4	,	,	PUNCT
ejpam-5731	411	5	2022	2022	NUM
ejpam-5731	411	6	.	.	PUNCT
ejpam-5731	412	1	[	[	X
ejpam-5731	412	2	14	14	NUM
ejpam-5731	412	3	]	]	X
ejpam-5731	412	4	n.	n.	PROPN
ejpam-5731	412	5	e.	e.	PROPN
ejpam-5731	412	6	cho	cho	PROPN
ejpam-5731	412	7	,	,	PUNCT
ejpam-5731	412	8	v.	v.	PROPN
ejpam-5731	412	9	kumar	kumar	PROPN
ejpam-5731	412	10	,	,	PUNCT
ejpam-5731	412	11	s.	s.	PROPN
ejpam-5731	412	12	kumar	kumar	PROPN
ejpam-5731	412	13	,	,	PUNCT
ejpam-5731	412	14	and	and	CCONJ
ejpam-5731	412	15	v.	v.	ADP
ejpam-5731	412	16	ravichandran	ravichandran	NOUN
ejpam-5731	412	17	.	.	PUNCT
ejpam-5731	413	1	radius	radius	NOUN
ejpam-5731	413	2	problems	problem	NOUN
ejpam-5731	413	3	for	for	ADP
ejpam-5731	413	4	starlike	starlike	NOUN
ejpam-5731	413	5	functions	function	NOUN
ejpam-5731	413	6	associated	associate	VERB
ejpam-5731	413	7	with	with	ADP
ejpam-5731	413	8	the	the	DET
ejpam-5731	413	9	sine	sine	ADJ
ejpam-5731	413	10	function	function	NOUN
ejpam-5731	413	11	.	.	PUNCT
ejpam-5731	414	1	bull	bull	NOUN
ejpam-5731	414	2	.	.	PUNCT
ejpam-5731	415	1	iranian	iranian	ADJ
ejpam-5731	415	2	math	math	PROPN
ejpam-5731	415	3	.	.	PUNCT
ejpam-5731	416	1	society	society	NOUN
ejpam-5731	416	2	,	,	PUNCT
ejpam-5731	416	3	45:213–232	45:213–232	PROPN
ejpam-5731	416	4	,	,	PUNCT
ejpam-5731	416	5	2019	2019	NUM
ejpam-5731	416	6	.	.	PUNCT
ejpam-5731	417	1	[	[	X
ejpam-5731	417	2	15	15	NUM
ejpam-5731	417	3	]	]	X
ejpam-5731	417	4	j.h	j.h	PROPN
ejpam-5731	417	5	.	.	PROPN
ejpam-5731	417	6	choi	choi	PROPN
ejpam-5731	417	7	,	,	PUNCT
ejpam-5731	417	8	y.c	y.c	PROPN
ejpam-5731	417	9	.	.	PROPN
ejpam-5731	417	10	kim	kim	PROPN
ejpam-5731	417	11	,	,	PUNCT
ejpam-5731	417	12	and	and	CCONJ
ejpam-5731	417	13	t.	t.	PROPN
ejpam-5731	417	14	sugawa	sugawa	PROPN
ejpam-5731	417	15	.	.	PUNCT
ejpam-5731	418	1	a	a	DET
ejpam-5731	418	2	general	general	ADJ
ejpam-5731	418	3	approach	approach	NOUN
ejpam-5731	418	4	to	to	ADP
ejpam-5731	418	5	the	the	DET
ejpam-5731	418	6	fekete	fekete	PROPN
ejpam-5731	418	7	-	-	PUNCT
ejpam-5731	418	8	szegö	szegö	PROPN
ejpam-5731	418	9	problem	problem	NOUN
ejpam-5731	418	10	.	.	PUNCT
ejpam-5731	419	1	journal	journal	NOUN
ejpam-5731	419	2	of	of	ADP
ejpam-5731	419	3	the	the	DET
ejpam-5731	419	4	mathematical	mathematical	ADJ
ejpam-5731	419	5	society	society	NOUN
ejpam-5731	419	6	of	of	ADP
ejpam-5731	419	7	japan	japan	PROPN
ejpam-5731	419	8	,	,	PUNCT
ejpam-5731	419	9	59:707–727	59:707–727	PROPN
ejpam-5731	419	10	,	,	PUNCT
ejpam-5731	419	11	2007	2007	NUM
ejpam-5731	419	12	.	.	PUNCT
ejpam-5731	420	1	[	[	X
ejpam-5731	420	2	16	16	NUM
ejpam-5731	420	3	]	]	X
ejpam-5731	420	4	l.i	l.i	PROPN
ejpam-5731	420	5	.	.	PROPN
ejpam-5731	420	6	cot̆irlă	cot̆irlă	PROPN
ejpam-5731	420	7	and	and	CCONJ
ejpam-5731	420	8	g.	g.	PROPN
ejpam-5731	420	9	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-5731	420	10	.	.	PUNCT
ejpam-5731	421	1	starlike	starlike	NOUN
ejpam-5731	421	2	functions	function	NOUN
ejpam-5731	421	3	based	base	VERB
ejpam-5731	421	4	on	on	ADP
ejpam-5731	421	5	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	421	6	q−differential	q−differential	ADJ
ejpam-5731	421	7	operator	operator	NOUN
ejpam-5731	421	8	defined	define	VERB
ejpam-5731	421	9	in	in	ADP
ejpam-5731	421	10	janowski	janowski	ADJ
ejpam-5731	421	11	domain	domain	NOUN
ejpam-5731	421	12	.	.	PUNCT
ejpam-5731	422	1	fractal	fractal	ADJ
ejpam-5731	422	2	fractional	fractional	ADJ
ejpam-5731	422	3	,	,	PUNCT
ejpam-5731	422	4	7(148	7(148	NUM
ejpam-5731	422	5	)	)	PUNCT
ejpam-5731	422	6	,	,	PUNCT
ejpam-5731	422	7	2023	2023	NUM
ejpam-5731	422	8	.	.	PUNCT
ejpam-5731	423	1	[	[	X
ejpam-5731	423	2	17	17	NUM
ejpam-5731	423	3	]	]	PUNCT
ejpam-5731	423	4	p.	p.	PROPN
ejpam-5731	423	5	duren	duren	PROPN
ejpam-5731	423	6	.	.	PUNCT
ejpam-5731	423	7	subordination	subordination	NOUN
ejpam-5731	423	8	in	in	ADP
ejpam-5731	423	9	complex	complex	ADJ
ejpam-5731	423	10	analysis	analysis	NOUN
ejpam-5731	423	11	,	,	PUNCT
ejpam-5731	423	12	lecture	lecture	NOUN
ejpam-5731	423	13	notes	note	NOUN
ejpam-5731	423	14	in	in	ADP
ejpam-5731	423	15	mathematics	mathematic	NOUN
ejpam-5731	423	16	.	.	PUNCT
ejpam-5731	424	1	springer	springer	PROPN
ejpam-5731	424	2	,	,	PUNCT
ejpam-5731	424	3	berlin	berlin	PROPN
ejpam-5731	424	4	,	,	PUNCT
ejpam-5731	424	5	germany	germany	PROPN
ejpam-5731	424	6	,	,	PUNCT
ejpam-5731	424	7	599:22–29	599:22–29	NUM
ejpam-5731	424	8	,	,	PUNCT
ejpam-5731	424	9	1977	1977	NUM
ejpam-5731	424	10	.	.	PUNCT
ejpam-5731	425	1	[	[	X
ejpam-5731	425	2	18	18	NUM
ejpam-5731	425	3	]	]	PUNCT
ejpam-5731	425	4	p.	p.	PROPN
ejpam-5731	425	5	duren	duren	PROPN
ejpam-5731	425	6	.	.	PUNCT
ejpam-5731	425	7	univalent	univalent	ADJ
ejpam-5731	425	8	functions	function	NOUN
ejpam-5731	425	9	.	.	PUNCT
ejpam-5731	426	1	grundlehren	grundlehren	PROPN
ejpam-5731	426	2	der	der	PROPN
ejpam-5731	426	3	mathematischen	mathematischen	PROPN
ejpam-5731	426	4	wissenschaften	wissenschaften	VERB
ejpam-5731	426	5	259	259	NUM
ejpam-5731	426	6	,	,	PUNCT
ejpam-5731	426	7	springer	springer	NOUN
ejpam-5731	426	8	-	-	PUNCT
ejpam-5731	426	9	verlag	verlag	PROPN
ejpam-5731	426	10	,	,	PUNCT
ejpam-5731	426	11	new	new	PROPN
ejpam-5731	426	12	york	york	PROPN
ejpam-5731	426	13	,	,	PUNCT
ejpam-5731	426	14	1983	1983	NUM
ejpam-5731	426	15	.	.	PUNCT
ejpam-5731	427	1	[	[	X
ejpam-5731	427	2	19	19	NUM
ejpam-5731	427	3	]	]	PUNCT
ejpam-5731	427	4	m.	m.	NOUN
ejpam-5731	427	5	fekete	fekete	PROPN
ejpam-5731	427	6	and	and	CCONJ
ejpam-5731	427	7	g.	g.	PROPN
ejpam-5731	427	8	szegö.	szegö.	PROPN
ejpam-5731	427	9	eine	eine	PROPN
ejpam-5731	427	10	bemerkung	bemerkung	PROPN
ejpam-5731	427	11	über	über	PROPN
ejpam-5731	427	12	ungerade	ungerade	PROPN
ejpam-5731	427	13	schlichte	schlichte	PROPN
ejpam-5731	427	14	funktionen	funktionen	PROPN
ejpam-5731	427	15	.	.	PUNCT
ejpam-5731	428	1	journal	journal	PROPN
ejpam-5731	428	2	w.	w.	PROPN
ejpam-5731	428	3	al	al	PROPN
ejpam-5731	428	4	-	-	PUNCT
ejpam-5731	428	5	rawashdeh	rawashdeh	PROPN
ejpam-5731	428	6	/	/	SYM
ejpam-5731	428	7	eur	eur	PROPN
ejpam-5731	428	8	.	.	PUNCT
ejpam-5731	429	1	j.	j.	PROPN
ejpam-5731	429	2	pure	pure	PROPN
ejpam-5731	429	3	appl	appl	PROPN
ejpam-5731	429	4	.	.	PROPN
ejpam-5731	429	5	math	math	PROPN
ejpam-5731	429	6	,	,	PUNCT
ejpam-5731	429	7	18	18	NUM
ejpam-5731	429	8	(	(	PUNCT
ejpam-5731	429	9	1	1	NUM
ejpam-5731	429	10	)	)	PUNCT
ejpam-5731	429	11	(	(	PUNCT
ejpam-5731	429	12	2025	2025	NUM
ejpam-5731	429	13	)	)	PUNCT
ejpam-5731	429	14	,	,	PUNCT
ejpam-5731	429	15	5731	5731	NUM
ejpam-5731	429	16	19	19	NUM
ejpam-5731	429	17	of	of	ADP
ejpam-5731	429	18	20	20	NUM
ejpam-5731	429	19	of	of	ADP
ejpam-5731	429	20	london	london	PROPN
ejpam-5731	429	21	mathematical	mathematical	ADJ
ejpam-5731	429	22	society	society	NOUN
ejpam-5731	429	23	,	,	PUNCT
ejpam-5731	429	24	s1	s1	NOUN
ejpam-5731	429	25	-	-	PUNCT
ejpam-5731	429	26	8:85–89	8:85–89	NUM
ejpam-5731	429	27	,	,	PUNCT
ejpam-5731	429	28	1933	1933	NUM
ejpam-5731	429	29	.	.	PUNCT
ejpam-5731	430	1	[	[	X
ejpam-5731	430	2	20	20	NUM
ejpam-5731	430	3	]	]	PUNCT
ejpam-5731	430	4	p.	p.	NOUN
ejpam-5731	430	5	goel	goel	PROPN
ejpam-5731	430	6	and	and	CCONJ
ejpam-5731	430	7	s.	s.	PROPN
ejpam-5731	430	8	kumar	kumar	PROPN
ejpam-5731	430	9	.	.	PUNCT
ejpam-5731	431	1	certain	certain	ADJ
ejpam-5731	431	2	class	class	NOUN
ejpam-5731	431	3	of	of	ADP
ejpam-5731	431	4	starlike	starlike	NOUN
ejpam-5731	431	5	functions	function	NOUN
ejpam-5731	431	6	associated	associate	VERB
ejpam-5731	431	7	with	with	ADP
ejpam-5731	431	8	modified	modify	VERB
ejpam-5731	431	9	sigmoid	sigmoid	NOUN
ejpam-5731	431	10	function	function	NOUN
ejpam-5731	431	11	.	.	PUNCT
ejpam-5731	432	1	bull	bull	NOUN
ejpam-5731	432	2	.	.	PUNCT
ejpam-5731	433	1	malaysian	malaysian	ADJ
ejpam-5731	433	2	math	math	PROPN
ejpam-5731	433	3	.	.	PUNCT
ejpam-5731	434	1	sci	sci	PROPN
ejpam-5731	434	2	.	.	PUNCT
ejpam-5731	434	3	society	society	PROPN
ejpam-5731	434	4	,	,	PUNCT
ejpam-5731	434	5	43:957–991	43:957–991	PROPN
ejpam-5731	434	6	,	,	PUNCT
ejpam-5731	434	7	2020	2020	NUM
ejpam-5731	434	8	.	.	PUNCT
ejpam-5731	435	1	[	[	X
ejpam-5731	435	2	21	21	NUM
ejpam-5731	435	3	]	]	PUNCT
ejpam-5731	435	4	a.	a.	PROPN
ejpam-5731	435	5	w.	w.	PROPN
ejpam-5731	435	6	goodman	goodman	PROPN
ejpam-5731	435	7	.	.	PUNCT
ejpam-5731	436	1	univalent	univalent	ADJ
ejpam-5731	436	2	functions	function	NOUN
ejpam-5731	436	3	.	.	PUNCT
ejpam-5731	437	1	mariner	mariner	PROPN
ejpam-5731	437	2	publishing	publishing	PROPN
ejpam-5731	437	3	co.	co.	PROPN
ejpam-5731	437	4	inc	inc	PROPN
ejpam-5731	437	5	.	.	PROPN
ejpam-5731	437	6	,	,	PUNCT
ejpam-5731	437	7	boston	boston	PROPN
ejpam-5731	437	8	,	,	PUNCT
ejpam-5731	437	9	1983	1983	NUM
ejpam-5731	438	1	.	.	PUNCT
ejpam-5731	439	1	[	[	X
ejpam-5731	439	2	22	22	NUM
ejpam-5731	439	3	]	]	PUNCT
ejpam-5731	439	4	r.	r.	PROPN
ejpam-5731	439	5	ibrahim	ibrahim	PROPN
ejpam-5731	439	6	,	,	PUNCT
ejpam-5731	439	7	j.	j.	PROPN
ejpam-5731	439	8	suzan	suzan	PROPN
ejpam-5731	439	9	,	,	PUNCT
ejpam-5731	439	10	and	and	CCONJ
ejpam-5731	439	11	m.d	m.d	PROPN
ejpam-5731	439	12	.	.	PROPN
ejpam-5731	439	13	obaiys	obaiys	PROPN
ejpam-5731	439	14	.	.	PUNCT
ejpam-5731	440	1	studies	study	NOUN
ejpam-5731	440	2	on	on	ADP
ejpam-5731	440	3	generalized	generalized	ADJ
ejpam-5731	440	4	differential	differential	ADJ
ejpam-5731	440	5	-	-	PUNCT
ejpam-5731	440	6	difference	difference	NOUN
ejpam-5731	440	7	operator	operator	NOUN
ejpam-5731	440	8	of	of	ADP
ejpam-5731	440	9	normalized	normalize	VERB
ejpam-5731	440	10	analytic	analytic	ADJ
ejpam-5731	440	11	functions	function	NOUN
ejpam-5731	440	12	.	.	PUNCT
ejpam-5731	441	1	southeast	southeast	ADJ
ejpam-5731	441	2	asian	asian	ADJ
ejpam-5731	441	3	bull	bull	PROPN
ejpam-5731	441	4	.	.	PUNCT
ejpam-5731	442	1	math	math	NOUN
ejpam-5731	442	2	.	.	PUNCT
ejpam-5731	442	3	,	,	PUNCT
ejpam-5731	442	4	45:43–55	45:43–55	PROPN
ejpam-5731	442	5	,	,	PUNCT
ejpam-5731	442	6	2021	2021	NUM
ejpam-5731	442	7	.	.	PUNCT
ejpam-5731	443	1	[	[	X
ejpam-5731	443	2	23	23	NUM
ejpam-5731	443	3	]	]	X
ejpam-5731	443	4	f.h	f.h	PROPN
ejpam-5731	443	5	.	.	PROPN
ejpam-5731	443	6	jackson	jackson	PROPN
ejpam-5731	443	7	.	.	PUNCT
ejpam-5731	444	1	on	on	ADP
ejpam-5731	444	2	q	q	NOUN
ejpam-5731	444	3	-	-	PUNCT
ejpam-5731	444	4	functions	function	NOUN
ejpam-5731	444	5	and	and	CCONJ
ejpam-5731	444	6	a	a	DET
ejpam-5731	444	7	certain	certain	ADJ
ejpam-5731	444	8	difference	difference	NOUN
ejpam-5731	444	9	operator	operator	NOUN
ejpam-5731	444	10	.	.	PUNCT
ejpam-5731	445	1	trans	trans	PROPN
ejpam-5731	445	2	.	.	PUNCT
ejpam-5731	445	3	r.	r.	PROPN
ejpam-5731	445	4	soc	soc	PROPN
ejpam-5731	445	5	.	.	PUNCT
ejpam-5731	446	1	edinb	edinb	PROPN
ejpam-5731	446	2	.	.	PUNCT
ejpam-5731	446	3	,	,	PUNCT
ejpam-5731	447	1	46:253–281	46:253–281	NUM
ejpam-5731	447	2	,	,	PUNCT
ejpam-5731	447	3	1908	1908	NUM
ejpam-5731	447	4	.	.	PUNCT
ejpam-5731	448	1	[	[	X
ejpam-5731	448	2	24	24	NUM
ejpam-5731	448	3	]	]	PUNCT
ejpam-5731	448	4	m.	m.	NOUN
ejpam-5731	448	5	kamali	kamali	PROPN
ejpam-5731	448	6	,	,	PUNCT
ejpam-5731	448	7	m.	m.	NOUN
ejpam-5731	448	8	cağlar	cağlar	PROPN
ejpam-5731	448	9	,	,	PUNCT
ejpam-5731	448	10	e.	e.	PROPN
ejpam-5731	448	11	deniz	deniz	PROPN
ejpam-5731	448	12	,	,	PUNCT
ejpam-5731	448	13	and	and	CCONJ
ejpam-5731	448	14	m.	m.	PROPN
ejpam-5731	448	15	turabaev	turabaev	PROPN
ejpam-5731	448	16	.	.	PUNCT
ejpam-5731	449	1	fekete	fekete	PROPN
ejpam-5731	449	2	szegö	szegö	PROPN
ejpam-5731	449	3	problem	problem	NOUN
ejpam-5731	449	4	for	for	ADP
ejpam-5731	449	5	a	a	DET
ejpam-5731	449	6	new	new	ADJ
ejpam-5731	449	7	subclass	subclass	NOUN
ejpam-5731	449	8	of	of	ADP
ejpam-5731	449	9	analytic	analytic	ADJ
ejpam-5731	449	10	functions	function	NOUN
ejpam-5731	449	11	satisfying	satisfy	VERB
ejpam-5731	449	12	subordinate	subordinate	ADJ
ejpam-5731	449	13	condition	condition	NOUN
ejpam-5731	449	14	associated	associate	VERB
ejpam-5731	449	15	with	with	ADP
ejpam-5731	449	16	chebyshev	chebyshev	NOUN
ejpam-5731	449	17	polynomials	polynomial	NOUN
ejpam-5731	449	18	.	.	PUNCT
ejpam-5731	450	1	turkish	turkish	ADJ
ejpam-5731	450	2	j.	j.	PROPN
ejpam-5731	450	3	math	math	PROPN
ejpam-5731	450	4	.	.	PUNCT
ejpam-5731	450	5	,	,	PUNCT
ejpam-5731	450	6	45:1195–1208	45:1195–1208	NOUN
ejpam-5731	450	7	,	,	PUNCT
ejpam-5731	450	8	2012	2012	NUM
ejpam-5731	450	9	.	.	PUNCT
ejpam-5731	451	1	[	[	X
ejpam-5731	451	2	25	25	NUM
ejpam-5731	451	3	]	]	X
ejpam-5731	451	4	s.	s.	PROPN
ejpam-5731	451	5	kanas	kanas	PROPN
ejpam-5731	451	6	and	and	CCONJ
ejpam-5731	451	7	d.	d.	PROPN
ejpam-5731	451	8	răducanu	răducanu	PROPN
ejpam-5731	451	9	.	.	PUNCT
ejpam-5731	452	1	some	some	DET
ejpam-5731	452	2	subclass	subclass	NOUN
ejpam-5731	452	3	of	of	ADP
ejpam-5731	452	4	analytic	analytic	ADJ
ejpam-5731	452	5	functions	function	NOUN
ejpam-5731	452	6	related	relate	VERB
ejpam-5731	452	7	to	to	ADP
ejpam-5731	452	8	conic	conic	ADJ
ejpam-5731	452	9	domains	domain	NOUN
ejpam-5731	452	10	.	.	PUNCT
ejpam-5731	452	11	math	math	NOUN
ejpam-5731	452	12	.	.	PUNCT
ejpam-5731	453	1	slovaca	slovaca	PROPN
ejpam-5731	453	2	,	,	PUNCT
ejpam-5731	453	3	64:1183–1196	64:1183–1196	NUM
ejpam-5731	453	4	,	,	PUNCT
ejpam-5731	453	5	2014	2014	NUM
ejpam-5731	453	6	.	.	PUNCT
ejpam-5731	454	1	[	[	X
ejpam-5731	454	2	26	26	NUM
ejpam-5731	454	3	]	]	X
ejpam-5731	454	4	f.r	f.r	PROPN
ejpam-5731	454	5	.	.	PROPN
ejpam-5731	454	6	keogh	keogh	PROPN
ejpam-5731	454	7	and	and	CCONJ
ejpam-5731	454	8	e.p	e.p	PROPN
ejpam-5731	454	9	.	.	PROPN
ejpam-5731	454	10	merkes	merke	NOUN
ejpam-5731	454	11	.	.	PUNCT
ejpam-5731	455	1	a	a	DET
ejpam-5731	455	2	coefficient	coefficient	NOUN
ejpam-5731	455	3	inequality	inequality	NOUN
ejpam-5731	455	4	for	for	ADP
ejpam-5731	455	5	certain	certain	ADJ
ejpam-5731	455	6	classes	class	NOUN
ejpam-5731	455	7	of	of	ADP
ejpam-5731	455	8	analytic	analytic	ADJ
ejpam-5731	455	9	functions	function	NOUN
ejpam-5731	455	10	.	.	PUNCT
ejpam-5731	456	1	proceedings	proceeding	NOUN
ejpam-5731	456	2	of	of	ADP
ejpam-5731	456	3	the	the	DET
ejpam-5731	456	4	american	american	PROPN
ejpam-5731	456	5	mathematical	mathematical	PROPN
ejpam-5731	456	6	society	society	NOUN
ejpam-5731	456	7	,	,	PUNCT
ejpam-5731	456	8	20:8–12	20:8–12	NUM
ejpam-5731	456	9	,	,	PUNCT
ejpam-5731	456	10	1969	1969	NUM
ejpam-5731	456	11	.	.	PUNCT
ejpam-5731	457	1	[	[	X
ejpam-5731	457	2	27	27	NUM
ejpam-5731	457	3	]	]	X
ejpam-5731	457	4	b.	b.	PROPN
ejpam-5731	457	5	khan	khan	PROPN
ejpam-5731	457	6	,	,	PUNCT
ejpam-5731	457	7	h.m	h.m	PROPN
ejpam-5731	457	8	.	.	PROPN
ejpam-5731	457	9	srivastava	srivastava	PROPN
ejpam-5731	457	10	,	,	PUNCT
ejpam-5731	457	11	and	and	CCONJ
ejpam-5731	457	12	s.	s.	PROPN
ejpam-5731	457	13	arjika	arjika	PROPN
ejpam-5731	457	14	.	.	PUNCT
ejpam-5731	458	1	a	a	DET
ejpam-5731	458	2	certain	certain	ADJ
ejpam-5731	458	3	q	q	NOUN
ejpam-5731	458	4	-	-	PUNCT
ejpam-5731	458	5	ruscheweyh	ruscheweyh	NOUN
ejpam-5731	458	6	type	type	VERB
ejpam-5731	458	7	derivative	derivative	ADJ
ejpam-5731	458	8	operator	operator	NOUN
ejpam-5731	458	9	and	and	CCONJ
ejpam-5731	458	10	its	its	PRON
ejpam-5731	458	11	applications	application	NOUN
ejpam-5731	458	12	involving	involve	VERB
ejpam-5731	458	13	multivalent	multivalent	NOUN
ejpam-5731	458	14	functions	function	NOUN
ejpam-5731	458	15	.	.	PUNCT
ejpam-5731	459	1	adv	adv	PROPN
ejpam-5731	459	2	.	.	PROPN
ejpam-5731	459	3	differ	differ	VERB
ejpam-5731	459	4	.	.	PUNCT
ejpam-5731	460	1	equ	equ	PROPN
ejpam-5731	460	2	.	.	PROPN
ejpam-5731	460	3	,	,	PUNCT
ejpam-5731	460	4	2012(279	2012(279	NUM
ejpam-5731	460	5	)	)	PUNCT
ejpam-5731	460	6	,	,	PUNCT
ejpam-5731	460	7	2021	2021	NUM
ejpam-5731	460	8	.	.	PUNCT
ejpam-5731	461	1	[	[	X
ejpam-5731	461	2	28	28	NUM
ejpam-5731	461	3	]	]	X
ejpam-5731	461	4	m.f	m.f	PROPN
ejpam-5731	461	5	.	.	PROPN
ejpam-5731	461	6	khan	khan	PROPN
ejpam-5731	461	7	,	,	PUNCT
ejpam-5731	461	8	i.	i.	PROPN
ejpam-5731	461	9	al	al	PROPN
ejpam-5731	461	10	-	-	PUNCT
ejpam-5731	461	11	shbeil	shbeil	PROPN
ejpam-5731	461	12	,	,	PUNCT
ejpam-5731	461	13	s.	s.	PROPN
ejpam-5731	461	14	khan	khan	PROPN
ejpam-5731	461	15	,	,	PUNCT
ejpam-5731	461	16	n.	n.	PROPN
ejpam-5731	461	17	khan	khan	PROPN
ejpam-5731	461	18	,	,	PUNCT
ejpam-5731	461	19	w.u	w.u	PROPN
ejpam-5731	461	20	.	.	PROPN
ejpam-5731	461	21	haq	haq	PROPN
ejpam-5731	461	22	,	,	PUNCT
ejpam-5731	461	23	and	and	CCONJ
ejpam-5731	461	24	j.	j.	PROPN
ejpam-5731	461	25	gong	gong	PROPN
ejpam-5731	461	26	.	.	PUNCT
ejpam-5731	462	1	applications	application	NOUN
ejpam-5731	462	2	of	of	ADP
ejpam-5731	462	3	a	a	DET
ejpam-5731	462	4	q	q	ADJ
ejpam-5731	462	5	-	-	PUNCT
ejpam-5731	462	6	differential	differential	ADJ
ejpam-5731	462	7	operator	operator	NOUN
ejpam-5731	462	8	to	to	ADP
ejpam-5731	462	9	a	a	DET
ejpam-5731	462	10	class	class	NOUN
ejpam-5731	462	11	of	of	ADP
ejpam-5731	462	12	harmonic	harmonic	ADJ
ejpam-5731	462	13	mappings	mapping	NOUN
ejpam-5731	462	14	defined	define	VERB
ejpam-5731	462	15	by	by	ADP
ejpam-5731	462	16	q	q	ADJ
ejpam-5731	462	17	-	-	PUNCT
ejpam-5731	462	18	mittag	mittag	ADJ
ejpam-5731	462	19	–	–	PUNCT
ejpam-5731	462	20	leffler	leffler	NOUN
ejpam-5731	462	21	functions	function	NOUN
ejpam-5731	462	22	.	.	PUNCT
ejpam-5731	463	1	symmetry	symmetry	NOUN
ejpam-5731	463	2	,	,	PUNCT
ejpam-5731	463	3	14:1905	14:1905	NUM
ejpam-5731	463	4	,	,	PUNCT
ejpam-5731	463	5	2022	2022	NUM
ejpam-5731	463	6	.	.	PUNCT
ejpam-5731	464	1	[	[	X
ejpam-5731	464	2	29	29	NUM
ejpam-5731	464	3	]	]	PUNCT
ejpam-5731	464	4	s.	s.	PROPN
ejpam-5731	464	5	kumar	kumar	PROPN
ejpam-5731	464	6	and	and	CCONJ
ejpam-5731	464	7	s.	s.	PROPN
ejpam-5731	464	8	banga	banga	PROPN
ejpam-5731	464	9	.	.	PUNCT
ejpam-5731	465	1	on	on	ADP
ejpam-5731	465	2	a	a	DET
ejpam-5731	465	3	special	special	ADJ
ejpam-5731	465	4	type	type	NOUN
ejpam-5731	465	5	of	of	ADP
ejpam-5731	465	6	ma	ma	PROPN
ejpam-5731	465	7	-	-	PUNCT
ejpam-5731	465	8	minda	minda	PROPN
ejpam-5731	465	9	function	function	PROPN
ejpam-5731	465	10	.	.	PUNCT
ejpam-5731	466	1	arxiv	arxiv	PROPN
ejpam-5731	466	2	preprint	preprint	PROPN
ejpam-5731	466	3	arxiv:2006.02111	arxiv:2006.02111	PROPN
ejpam-5731	466	4	,	,	PUNCT
ejpam-5731	466	5	2020	2020	NUM
ejpam-5731	466	6	.	.	PUNCT
ejpam-5731	467	1	[	[	X
ejpam-5731	467	2	30	30	NUM
ejpam-5731	467	3	]	]	X
ejpam-5731	467	4	m.	m.	NOUN
ejpam-5731	467	5	lewin	lewin	PROPN
ejpam-5731	467	6	.	.	PUNCT
ejpam-5731	468	1	on	on	ADP
ejpam-5731	468	2	a	a	DET
ejpam-5731	468	3	coefficient	coefficient	NOUN
ejpam-5731	468	4	problem	problem	NOUN
ejpam-5731	468	5	for	for	ADP
ejpam-5731	468	6	bi	bi	ADJ
ejpam-5731	468	7	-	-	ADJ
ejpam-5731	468	8	univalent	univalent	ADJ
ejpam-5731	468	9	functions	function	NOUN
ejpam-5731	468	10	.	.	PUNCT
ejpam-5731	469	1	proceedings	proceeding	NOUN
ejpam-5731	469	2	of	of	ADP
ejpam-5731	469	3	the	the	DET
ejpam-5731	469	4	american	american	PROPN
ejpam-5731	469	5	mathematical	mathematical	PROPN
ejpam-5731	469	6	society	society	NOUN
ejpam-5731	469	7	,	,	PUNCT
ejpam-5731	469	8	18(1):63–68	18(1):63–68	NUM
ejpam-5731	469	9	,	,	PUNCT
ejpam-5731	469	10	1967	1967	NUM
ejpam-5731	469	11	.	.	PUNCT
ejpam-5731	470	1	[	[	X
ejpam-5731	470	2	31	31	NUM
ejpam-5731	470	3	]	]	PUNCT
ejpam-5731	470	4	w.	w.	PROPN
ejpam-5731	470	5	ma	ma	PROPN
ejpam-5731	470	6	and	and	CCONJ
ejpam-5731	470	7	d.	d.	PROPN
ejpam-5731	470	8	minda	minda	PROPN
ejpam-5731	470	9	.	.	PUNCT
ejpam-5731	471	1	a	a	DET
ejpam-5731	471	2	unified	unified	ADJ
ejpam-5731	471	3	treatment	treatment	NOUN
ejpam-5731	471	4	of	of	ADP
ejpam-5731	471	5	some	some	DET
ejpam-5731	471	6	special	special	ADJ
ejpam-5731	471	7	classes	class	NOUN
ejpam-5731	471	8	of	of	ADP
ejpam-5731	471	9	univalent	univalent	ADJ
ejpam-5731	471	10	functions	function	NOUN
ejpam-5731	471	11	.	.	PUNCT
ejpam-5731	472	1	in	in	ADP
ejpam-5731	472	2	i	i	PROPN
ejpam-5731	472	3	conf	conf	NOUN
ejpam-5731	472	4	.	.	PUNCT
ejpam-5731	473	1	proc	proc	PROPN
ejpam-5731	473	2	.	.	PUNCT
ejpam-5731	474	1	lecture	lecture	NOUN
ejpam-5731	474	2	notes	note	VERB
ejpam-5731	474	3	anal	anal	ADJ
ejpam-5731	474	4	.	.	PUNCT
ejpam-5731	474	5	,	,	PUNCT
ejpam-5731	474	6	editor	editor	NOUN
ejpam-5731	474	7	,	,	PUNCT
ejpam-5731	474	8	proceedings	proceeding	NOUN
ejpam-5731	474	9	of	of	ADP
ejpam-5731	474	10	the	the	DET
ejpam-5731	474	11	conference	conference	NOUN
ejpam-5731	474	12	on	on	ADP
ejpam-5731	474	13	complex	complex	ADJ
ejpam-5731	474	14	analysis	analysis	NOUN
ejpam-5731	474	15	,	,	PUNCT
ejpam-5731	474	16	pages	page	NOUN
ejpam-5731	474	17	157–169	157–169	NUM
ejpam-5731	474	18	.	.	PUNCT
ejpam-5731	475	1	int	int	NOUN
ejpam-5731	475	2	.	.	PUNCT
ejpam-5731	476	1	press	press	PROPN
ejpam-5731	476	2	,	,	PUNCT
ejpam-5731	476	3	cambridge	cambridge	PROPN
ejpam-5731	476	4	,	,	PUNCT
ejpam-5731	476	5	ma	ma	PROPN
ejpam-5731	476	6	,	,	PUNCT
ejpam-5731	476	7	1992	1992	NUM
ejpam-5731	476	8	.	.	PUNCT
ejpam-5731	477	1	[	[	X
ejpam-5731	477	2	32	32	NUM
ejpam-5731	477	3	]	]	X
ejpam-5731	477	4	n.	n.	NOUN
ejpam-5731	477	5	magesh	magesh	PROPN
ejpam-5731	477	6	and	and	CCONJ
ejpam-5731	477	7	s.	s.	PROPN
ejpam-5731	477	8	bulut	bulut	PROPN
ejpam-5731	477	9	.	.	PUNCT
ejpam-5731	478	1	chebyshev	chebyshev	PROPN
ejpam-5731	478	2	polynomial	polynomial	ADJ
ejpam-5731	478	3	coefficient	coefficient	NOUN
ejpam-5731	478	4	estimates	estimate	NOUN
ejpam-5731	478	5	for	for	ADP
ejpam-5731	478	6	a	a	DET
ejpam-5731	478	7	class	class	NOUN
ejpam-5731	478	8	of	of	ADP
ejpam-5731	478	9	analytic	analytic	ADJ
ejpam-5731	478	10	bi	bi	ADJ
ejpam-5731	478	11	-	-	ADJ
ejpam-5731	478	12	univalent	univalent	ADJ
ejpam-5731	478	13	functions	function	NOUN
ejpam-5731	478	14	related	relate	VERB
ejpam-5731	478	15	to	to	ADP
ejpam-5731	478	16	pseudo	pseudo	NOUN
ejpam-5731	478	17	-	-	ADJ
ejpam-5731	478	18	starlike	starlike	ADJ
ejpam-5731	478	19	functions	function	NOUN
ejpam-5731	478	20	.	.	PUNCT
ejpam-5731	479	1	afrika	afrika	PROPN
ejpam-5731	479	2	matematika	matematika	PROPN
ejpam-5731	479	3	,	,	PUNCT
ejpam-5731	479	4	29(1	29(1	NUM
ejpam-5731	479	5	-	-	PUNCT
ejpam-5731	479	6	2):203–209	2):203–209	NOUN
ejpam-5731	479	7	,	,	PUNCT
ejpam-5731	479	8	2018	2018	NUM
ejpam-5731	479	9	.	.	PUNCT
ejpam-5731	480	1	[	[	X
ejpam-5731	480	2	33	33	NUM
ejpam-5731	480	3	]	]	PUNCT
ejpam-5731	480	4	r.	r.	PROPN
ejpam-5731	480	5	mendiratta	mendiratta	PROPN
ejpam-5731	480	6	,	,	PUNCT
ejpam-5731	480	7	s.	s.	PROPN
ejpam-5731	480	8	nagpal	nagpal	PROPN
ejpam-5731	480	9	,	,	PUNCT
ejpam-5731	480	10	and	and	CCONJ
ejpam-5731	480	11	v.	v.	ADP
ejpam-5731	480	12	ravichandran	ravichandran	NOUN
ejpam-5731	480	13	.	.	PUNCT
ejpam-5731	481	1	on	on	ADP
ejpam-5731	481	2	a	a	DET
ejpam-5731	481	3	subclass	subclass	NOUN
ejpam-5731	481	4	of	of	ADP
ejpam-5731	481	5	strongly	strongly	ADV
ejpam-5731	481	6	starlike	starlike	NOUN
ejpam-5731	481	7	functions	function	NOUN
ejpam-5731	481	8	associated	associate	VERB
ejpam-5731	481	9	with	with	ADP
ejpam-5731	481	10	exponential	exponential	ADJ
ejpam-5731	481	11	function	function	NOUN
ejpam-5731	481	12	.	.	PUNCT
ejpam-5731	482	1	bull	bull	NOUN
ejpam-5731	482	2	.	.	PUNCT
ejpam-5731	483	1	malays	malays	PROPN
ejpam-5731	483	2	.	.	PUNCT
ejpam-5731	484	1	math	math	NOUN
ejpam-5731	484	2	.	.	PUNCT
ejpam-5731	485	1	sci	sci	PROPN
ejpam-5731	485	2	.	.	PUNCT
ejpam-5731	485	3	society	society	PROPN
ejpam-5731	485	4	,	,	PUNCT
ejpam-5731	485	5	38:365–386	38:365–386	NUM
ejpam-5731	485	6	,	,	PUNCT
ejpam-5731	485	7	2015	2015	NUM
ejpam-5731	485	8	.	.	PUNCT
ejpam-5731	486	1	[	[	X
ejpam-5731	486	2	34	34	NUM
ejpam-5731	486	3	]	]	X
ejpam-5731	486	4	s.	s.	PROPN
ejpam-5731	486	5	miller	miller	PROPN
ejpam-5731	486	6	and	and	CCONJ
ejpam-5731	486	7	p.	p.	NOUN
ejpam-5731	486	8	mocabu	mocabu	NOUN
ejpam-5731	486	9	.	.	PUNCT
ejpam-5731	487	1	differential	differential	ADJ
ejpam-5731	487	2	subordination	subordination	NOUN
ejpam-5731	487	3	:	:	PUNCT
ejpam-5731	487	4	theory	theory	NOUN
ejpam-5731	487	5	and	and	CCONJ
ejpam-5731	487	6	applications	application	NOUN
ejpam-5731	487	7	.	.	PUNCT
ejpam-5731	488	1	crc	crc	PROPN
ejpam-5731	488	2	press	press	PROPN
ejpam-5731	488	3	,	,	PUNCT
ejpam-5731	488	4	new	new	PROPN
ejpam-5731	488	5	york	york	PROPN
ejpam-5731	488	6	,	,	PUNCT
ejpam-5731	488	7	2000	2000	NUM
ejpam-5731	488	8	.	.	PUNCT
ejpam-5731	489	1	[	[	X
ejpam-5731	489	2	35	35	NUM
ejpam-5731	489	3	]	]	X
ejpam-5731	489	4	e.	e.	PROPN
ejpam-5731	489	5	muthaiyan	muthaiyan	PROPN
ejpam-5731	489	6	and	and	CCONJ
ejpam-5731	489	7	a.	a.	NOUN
ejpam-5731	489	8	wanas	wanas	PROPN
ejpam-5731	489	9	.	.	PUNCT
ejpam-5731	490	1	on	on	ADP
ejpam-5731	490	2	some	some	DET
ejpam-5731	490	3	coefficient	coefficient	NOUN
ejpam-5731	490	4	inequalities	inequality	NOUN
ejpam-5731	490	5	involving	involve	VERB
ejpam-5731	490	6	legendre	legendre	NOUN
ejpam-5731	490	7	polynomials	polynomial	NOUN
ejpam-5731	490	8	in	in	ADP
ejpam-5731	490	9	the	the	DET
ejpam-5731	490	10	class	class	NOUN
ejpam-5731	490	11	of	of	ADP
ejpam-5731	490	12	bi	bi	ADJ
ejpam-5731	490	13	-	-	ADJ
ejpam-5731	490	14	univalent	univalent	ADJ
ejpam-5731	490	15	functions	function	NOUN
ejpam-5731	490	16	.	.	PUNCT
ejpam-5731	491	1	turkish	turkish	ADJ
ejpam-5731	491	2	journal	journal	PROPN
ejpam-5731	491	3	of	of	ADP
ejpam-5731	491	4	inequalities	inequality	NOUN
ejpam-5731	491	5	,	,	PUNCT
ejpam-5731	491	6	7(2):39–46	7(2):39–46	NUM
ejpam-5731	491	7	,	,	PUNCT
ejpam-5731	491	8	2023	2023	NUM
ejpam-5731	491	9	.	.	PUNCT
ejpam-5731	492	1	[	[	X
ejpam-5731	492	2	36	36	NUM
ejpam-5731	492	3	]	]	PUNCT
ejpam-5731	492	4	z.	z.	PROPN
ejpam-5731	492	5	nehari	nehari	PROPN
ejpam-5731	492	6	.	.	PUNCT
ejpam-5731	493	1	conformal	conformal	ADJ
ejpam-5731	493	2	mappings	mapping	NOUN
ejpam-5731	493	3	.	.	PUNCT
ejpam-5731	494	1	mcgraw	mcgraw	PROPN
ejpam-5731	494	2	-	-	PUNCT
ejpam-5731	494	3	hill	hill	PROPN
ejpam-5731	494	4	,	,	PUNCT
ejpam-5731	494	5	new	new	PROPN
ejpam-5731	494	6	york	york	PROPN
ejpam-5731	494	7	,	,	PUNCT
ejpam-5731	494	8	1952	1952	NUM
ejpam-5731	494	9	.	.	PUNCT
ejpam-5731	495	1	[	[	X
ejpam-5731	495	2	37	37	NUM
ejpam-5731	495	3	]	]	PUNCT
ejpam-5731	495	4	e.	e.	PROPN
ejpam-5731	495	5	netanyahu	netanyahu	PROPN
ejpam-5731	495	6	.	.	PUNCT
ejpam-5731	496	1	the	the	DET
ejpam-5731	496	2	minimal	minimal	ADJ
ejpam-5731	496	3	distance	distance	NOUN
ejpam-5731	496	4	of	of	ADP
ejpam-5731	496	5	the	the	DET
ejpam-5731	496	6	image	image	NOUN
ejpam-5731	496	7	boundary	boundary	ADJ
ejpam-5731	496	8	from	from	ADP
ejpam-5731	496	9	the	the	DET
ejpam-5731	496	10	origin	origin	NOUN
ejpam-5731	496	11	and	and	CCONJ
ejpam-5731	496	12	the	the	DET
ejpam-5731	496	13	second	second	ADJ
ejpam-5731	496	14	coefficient	coefficient	NOUN
ejpam-5731	496	15	of	of	ADP
ejpam-5731	496	16	a	a	DET
ejpam-5731	496	17	univalent	univalent	ADJ
ejpam-5731	496	18	function	function	NOUN
ejpam-5731	496	19	in	in	ADP
ejpam-5731	496	20	|z|	|z|	NOUN
ejpam-5731	496	21	<	<	X
ejpam-5731	496	22	1	1	NUM
ejpam-5731	496	23	.	.	X
ejpam-5731	496	24	archive	archive	NOUN
ejpam-5731	496	25	for	for	ADP
ejpam-5731	496	26	rational	rational	ADJ
ejpam-5731	496	27	mechanics	mechanic	NOUN
ejpam-5731	496	28	w.	w.	PROPN
ejpam-5731	496	29	al	al	PROPN
ejpam-5731	496	30	-	-	PUNCT
ejpam-5731	496	31	rawashdeh	rawashdeh	PROPN
ejpam-5731	496	32	/	/	SYM
ejpam-5731	496	33	eur	eur	PROPN
ejpam-5731	496	34	.	.	PUNCT
ejpam-5731	497	1	j.	j.	PROPN
ejpam-5731	497	2	pure	pure	PROPN
ejpam-5731	497	3	appl	appl	PROPN
ejpam-5731	497	4	.	.	PROPN
ejpam-5731	497	5	math	math	PROPN
ejpam-5731	497	6	,	,	PUNCT
ejpam-5731	497	7	18	18	NUM
ejpam-5731	497	8	(	(	PUNCT
ejpam-5731	497	9	1	1	NUM
ejpam-5731	497	10	)	)	PUNCT
ejpam-5731	497	11	(	(	PUNCT
ejpam-5731	497	12	2025	2025	NUM
ejpam-5731	497	13	)	)	PUNCT
ejpam-5731	497	14	,	,	PUNCT
ejpam-5731	497	15	5731	5731	NUM
ejpam-5731	497	16	20	20	NUM
ejpam-5731	497	17	of	of	ADP
ejpam-5731	497	18	20	20	NUM
ejpam-5731	497	19	and	and	CCONJ
ejpam-5731	497	20	analysis	analysis	NOUN
ejpam-5731	497	21	,	,	PUNCT
ejpam-5731	497	22	32(2):100–112	32(2):100–112	PROPN
ejpam-5731	497	23	,	,	PUNCT
ejpam-5731	497	24	1969	1969	NUM
ejpam-5731	497	25	.	.	PUNCT
ejpam-5731	498	1	[	[	X
ejpam-5731	498	2	38	38	NUM
ejpam-5731	498	3	]	]	PUNCT
ejpam-5731	498	4	v.	v.	CCONJ
ejpam-5731	498	5	nezir	nezir	NOUN
ejpam-5731	498	6	and	and	CCONJ
ejpam-5731	498	7	n.	n.	PROPN
ejpam-5731	498	8	mustafa	mustafa	PROPN
ejpam-5731	498	9	.	.	PUNCT
ejpam-5731	499	1	analytic	analytic	ADJ
ejpam-5731	499	2	functions	function	NOUN
ejpam-5731	499	3	expressed	express	VERB
ejpam-5731	499	4	with	with	ADP
ejpam-5731	499	5	q	q	ADJ
ejpam-5731	499	6	-	-	PUNCT
ejpam-5731	499	7	poisson	poisson	NOUN
ejpam-5731	499	8	distribution	distribution	NOUN
ejpam-5731	499	9	series	series	NOUN
ejpam-5731	499	10	.	.	PUNCT
ejpam-5731	500	1	turk	turk	PROPN
ejpam-5731	500	2	.	.	PUNCT
ejpam-5731	501	1	j.	j.	PROPN
ejpam-5731	501	2	sci	sci	PROPN
ejpam-5731	501	3	.	.	PROPN
ejpam-5731	501	4	,	,	PUNCT
ejpam-5731	501	5	6:24–30	6:24–30	PROPN
ejpam-5731	501	6	,	,	PUNCT
ejpam-5731	501	7	2021	2021	NUM
ejpam-5731	501	8	.	.	PUNCT
ejpam-5731	502	1	[	[	X
ejpam-5731	502	2	39	39	NUM
ejpam-5731	502	3	]	]	X
ejpam-5731	502	4	s.d	s.d	PROPN
ejpam-5731	502	5	.	.	PROPN
ejpam-5731	502	6	purohit	purohit	PROPN
ejpam-5731	502	7	and	and	CCONJ
ejpam-5731	502	8	r.k	r.k	PROPN
ejpam-5731	502	9	.	.	PROPN
ejpam-5731	502	10	raina	raina	PROPN
ejpam-5731	502	11	.	.	PUNCT
ejpam-5731	503	1	fractional	fractional	ADJ
ejpam-5731	503	2	q	q	ADJ
ejpam-5731	503	3	-	-	PUNCT
ejpam-5731	503	4	calculus	calculus	NOUN
ejpam-5731	503	5	and	and	CCONJ
ejpam-5731	503	6	certain	certain	ADJ
ejpam-5731	503	7	subclasses	subclass	NOUN
ejpam-5731	503	8	of	of	ADP
ejpam-5731	503	9	univalent	univalent	ADJ
ejpam-5731	503	10	analytic	analytic	ADJ
ejpam-5731	503	11	functions	function	NOUN
ejpam-5731	503	12	.	.	PUNCT
ejpam-5731	504	1	mathematica	mathematica	PROPN
ejpam-5731	504	2	,	,	PUNCT
ejpam-5731	504	3	55:6274	55:6274	NOUN
ejpam-5731	504	4	,	,	PUNCT
ejpam-5731	504	5	2013	2013	NUM
ejpam-5731	504	6	.	.	PUNCT
ejpam-5731	505	1	[	[	X
ejpam-5731	505	2	40	40	NUM
ejpam-5731	505	3	]	]	PUNCT
ejpam-5731	505	4	c.	c.	PROPN
ejpam-5731	505	5	ramachandran	ramachandran	PROPN
ejpam-5731	505	6	and	and	CCONJ
ejpam-5731	505	7	d.	d.	PROPN
ejpam-5731	505	8	kavitha	kavitha	PROPN
ejpam-5731	505	9	.	.	PUNCT
ejpam-5731	506	1	coefficient	coefficient	NOUN
ejpam-5731	506	2	estimates	estimate	NOUN
ejpam-5731	506	3	for	for	ADP
ejpam-5731	506	4	a	a	DET
ejpam-5731	506	5	subclass	subclass	NOUN
ejpam-5731	506	6	of	of	ADP
ejpam-5731	506	7	bi	bi	ADJ
ejpam-5731	506	8	-	-	ADJ
ejpam-5731	506	9	univalent	univalent	ADJ
ejpam-5731	506	10	functions	function	NOUN
ejpam-5731	506	11	defined	define	VERB
ejpam-5731	506	12	by	by	ADP
ejpam-5731	506	13	sălăgean	sălăgean	ADJ
ejpam-5731	506	14	operator	operator	NOUN
ejpam-5731	506	15	using	use	VERB
ejpam-5731	506	16	quasi	quasi	NOUN
ejpam-5731	506	17	-	-	NOUN
ejpam-5731	506	18	subordination	subordination	NOUN
ejpam-5731	506	19	.	.	PUNCT
ejpam-5731	507	1	applied	apply	VERB
ejpam-5731	507	2	mathematical	mathematical	ADJ
ejpam-5731	507	3	sciences	science	NOUN
ejpam-5731	507	4	,	,	PUNCT
ejpam-5731	507	5	11:1725–1732	11:1725–1732	NUM
ejpam-5731	507	6	,	,	PUNCT
ejpam-5731	507	7	2017	2017	NUM
ejpam-5731	507	8	.	.	PUNCT
ejpam-5731	508	1	[	[	X
ejpam-5731	508	2	41	41	NUM
ejpam-5731	508	3	]	]	PUNCT
ejpam-5731	508	4	a.	a.	NOUN
ejpam-5731	508	5	raposo	raposo	NOUN
ejpam-5731	508	6	,	,	PUNCT
ejpam-5731	508	7	h.	h.	PROPN
ejpam-5731	508	8	weber	weber	PROPN
ejpam-5731	508	9	,	,	PUNCT
ejpam-5731	508	10	d.	d.	PROPN
ejpam-5731	508	11	alvarez	alvarez	PROPN
ejpam-5731	508	12	-	-	PUNCT
ejpam-5731	508	13	castillo	castillo	PROPN
ejpam-5731	508	14	,	,	PUNCT
ejpam-5731	508	15	and	and	CCONJ
ejpam-5731	508	16	m.	m.	NOUN
ejpam-5731	508	17	kirchbach	kirchbach	NOUN
ejpam-5731	508	18	.	.	PUNCT
ejpam-5731	509	1	romanovski	romanovski	ADJ
ejpam-5731	509	2	polynomials	polynomial	NOUN
ejpam-5731	509	3	in	in	ADP
ejpam-5731	509	4	selected	select	VERB
ejpam-5731	509	5	physics	physics	NOUN
ejpam-5731	509	6	problems	problem	NOUN
ejpam-5731	509	7	.	.	PUNCT
ejpam-5731	510	1	central	central	ADJ
ejpam-5731	510	2	european	european	PROPN
ejpam-5731	510	3	journal	journal	PROPN
ejpam-5731	510	4	of	of	ADP
ejpam-5731	510	5	physics	physics	PROPN
ejpam-5731	510	6	,	,	PUNCT
ejpam-5731	510	7	5(3):253–284	5(3):253–284	NUM
ejpam-5731	510	8	,	,	PUNCT
ejpam-5731	510	9	2007	2007	NUM
ejpam-5731	510	10	.	.	PUNCT
ejpam-5731	511	1	[	[	X
ejpam-5731	511	2	42	42	NUM
ejpam-5731	511	3	]	]	PUNCT
ejpam-5731	511	4	k.	k.	PROPN
ejpam-5731	511	5	riley	riley	PROPN
ejpam-5731	511	6	,	,	PUNCT
ejpam-5731	511	7	m.	m.	PROPN
ejpam-5731	511	8	hobson	hobson	PROPN
ejpam-5731	511	9	,	,	PUNCT
ejpam-5731	511	10	and	and	CCONJ
ejpam-5731	511	11	s.	s.	PROPN
ejpam-5731	511	12	bence	bence	NOUN
ejpam-5731	511	13	.	.	PUNCT
ejpam-5731	512	1	mathematical	mathematical	ADJ
ejpam-5731	512	2	methods	method	NOUN
ejpam-5731	512	3	for	for	ADP
ejpam-5731	512	4	physics	physics	NOUN
ejpam-5731	512	5	and	and	CCONJ
ejpam-5731	512	6	engineering	engineering	NOUN
ejpam-5731	512	7	,	,	PUNCT
ejpam-5731	512	8	third	third	ADJ
ejpam-5731	512	9	edition	edition	NOUN
ejpam-5731	512	10	.	.	PUNCT
ejpam-5731	513	1	cambridge	cambridge	PROPN
ejpam-5731	513	2	university	university	PROPN
ejpam-5731	513	3	press	press	PROPN
ejpam-5731	513	4	,	,	PUNCT
ejpam-5731	513	5	cambridge	cambridge	PROPN
ejpam-5731	513	6	,	,	PUNCT
ejpam-5731	513	7	uk	uk	PROPN
ejpam-5731	513	8	,	,	PUNCT
ejpam-5731	513	9	2006	2006	NUM
ejpam-5731	513	10	.	.	PUNCT
ejpam-5731	514	1	[	[	X
ejpam-5731	514	2	43	43	NUM
ejpam-5731	514	3	]	]	X
ejpam-5731	514	4	s.	s.	PROPN
ejpam-5731	514	5	ruscheweyh	ruscheweyh	PROPN
ejpam-5731	514	6	.	.	PUNCT
ejpam-5731	515	1	new	new	ADJ
ejpam-5731	515	2	criteria	criterion	NOUN
ejpam-5731	515	3	for	for	ADP
ejpam-5731	515	4	univalent	univalent	ADJ
ejpam-5731	515	5	functions	function	NOUN
ejpam-5731	515	6	.	.	PUNCT
ejpam-5731	516	1	proceedings	proceeding	NOUN
ejpam-5731	516	2	of	of	ADP
ejpam-5731	516	3	the	the	DET
ejpam-5731	516	4	american	american	PROPN
ejpam-5731	516	5	mathematical	mathematical	PROPN
ejpam-5731	516	6	society	society	NOUN
ejpam-5731	516	7	,	,	PUNCT
ejpam-5731	516	8	49:109–115	49:109–115	PROPN
ejpam-5731	516	9	,	,	PUNCT
ejpam-5731	516	10	1975	1975	NUM
ejpam-5731	516	11	.	.	PUNCT
ejpam-5731	517	1	[	[	X
ejpam-5731	517	2	44	44	NUM
ejpam-5731	517	3	]	]	X
ejpam-5731	517	4	t.m	t.m	PROPN
ejpam-5731	517	5	.	.	PROPN
ejpam-5731	517	6	seoudy	seoudy	PROPN
ejpam-5731	517	7	and	and	CCONJ
ejpam-5731	517	8	m.k	m.k	PROPN
ejpam-5731	517	9	.	.	PROPN
ejpam-5731	517	10	aouf	aouf	PROPN
ejpam-5731	517	11	.	.	PUNCT
ejpam-5731	518	1	coefficient	coefficient	NOUN
ejpam-5731	518	2	estimates	estimate	NOUN
ejpam-5731	518	3	of	of	ADP
ejpam-5731	518	4	new	new	ADJ
ejpam-5731	518	5	classes	class	NOUN
ejpam-5731	518	6	q−starlike	q−starlike	ADJ
ejpam-5731	518	7	and	and	CCONJ
ejpam-5731	518	8	q−convex	q−convex	NOUN
ejpam-5731	518	9	functions	function	NOUN
ejpam-5731	518	10	of	of	ADP
ejpam-5731	518	11	complex	complex	ADJ
ejpam-5731	518	12	order	order	NOUN
ejpam-5731	518	13	.	.	PUNCT
ejpam-5731	519	1	journal	journal	NOUN
ejpam-5731	519	2	of	of	ADP
ejpam-5731	519	3	mathematical	mathematical	ADJ
ejpam-5731	519	4	inequalities	inequality	NOUN
ejpam-5731	519	5	,	,	PUNCT
ejpam-5731	519	6	10(1):130–145	10(1):130–145	PROPN
ejpam-5731	519	7	,	,	PUNCT
ejpam-5731	519	8	2016	2016	NUM
ejpam-5731	519	9	.	.	PUNCT
ejpam-5731	520	1	[	[	X
ejpam-5731	520	2	45	45	NUM
ejpam-5731	520	3	]	]	PUNCT
ejpam-5731	520	4	j.	j.	PROPN
ejpam-5731	520	5	sokól	sokól	PROPN
ejpam-5731	520	6	and	and	CCONJ
ejpam-5731	520	7	j.	j.	PROPN
ejpam-5731	520	8	stankiewicz	stankiewicz	PROPN
ejpam-5731	520	9	.	.	PUNCT
ejpam-5731	521	1	radius	radius	NOUN
ejpam-5731	521	2	of	of	ADP
ejpam-5731	521	3	convexity	convexity	NOUN
ejpam-5731	521	4	of	of	ADP
ejpam-5731	521	5	some	some	DET
ejpam-5731	521	6	subclasses	subclass	NOUN
ejpam-5731	521	7	of	of	ADP
ejpam-5731	521	8	strongly	strongly	ADV
ejpam-5731	521	9	starlike	starlike	NOUN
ejpam-5731	521	10	functions	function	NOUN
ejpam-5731	521	11	.	.	PUNCT
ejpam-5731	522	1	zeszyty	zeszyty	PROPN
ejpam-5731	522	2	nauk	nauk	PROPN
ejpam-5731	522	3	.	.	PROPN
ejpam-5731	522	4	politech	politech	PROPN
ejpam-5731	522	5	.	.	PUNCT
ejpam-5731	523	1	rzeszowskiej	rzeszowskiej	NOUN
ejpam-5731	523	2	mathematics	mathematic	NOUN
ejpam-5731	523	3	,	,	PUNCT
ejpam-5731	523	4	19:101–105	19:101–105	PROPN
ejpam-5731	523	5	,	,	PUNCT
ejpam-5731	523	6	1996	1996	NUM
ejpam-5731	523	7	.	.	PUNCT
ejpam-5731	524	1	[	[	X
ejpam-5731	524	2	46	46	NUM
ejpam-5731	524	3	]	]	X
ejpam-5731	524	4	h.m	h.m	PROPN
ejpam-5731	524	5	.	.	PROPN
ejpam-5731	524	6	srivastava	srivastava	PROPN
ejpam-5731	524	7	.	.	PUNCT
ejpam-5731	525	1	operators	operator	NOUN
ejpam-5731	525	2	of	of	ADP
ejpam-5731	525	3	basic	basic	ADJ
ejpam-5731	525	4	(	(	PUNCT
ejpam-5731	525	5	or	or	CCONJ
ejpam-5731	525	6	q−	q−	PROPN
ejpam-5731	525	7	)	)	PUNCT
ejpam-5731	525	8	calculus	calculus	NOUN
ejpam-5731	525	9	and	and	CCONJ
ejpam-5731	525	10	fractional	fractional	ADJ
ejpam-5731	525	11	q−calculus	q−calculus	ADJ
ejpam-5731	525	12	and	and	CCONJ
ejpam-5731	525	13	their	their	PRON
ejpam-5731	525	14	applications	application	NOUN
ejpam-5731	525	15	in	in	ADP
ejpam-5731	525	16	geometric	geometric	ADJ
ejpam-5731	525	17	function	function	NOUN
ejpam-5731	525	18	theory	theory	NOUN
ejpam-5731	525	19	of	of	ADP
ejpam-5731	525	20	complex	complex	ADJ
ejpam-5731	525	21	analysis	analysis	NOUN
ejpam-5731	525	22	.	.	PUNCT
ejpam-5731	526	1	iran	iran	PROPN
ejpam-5731	526	2	.	.	PUNCT
ejpam-5731	527	1	j.	j.	PROPN
ejpam-5731	527	2	sci	sci	PROPN
ejpam-5731	527	3	technol	technol	PROPN
ejpam-5731	527	4	trans	trans	PROPN
ejpam-5731	527	5	.	.	PUNCT
ejpam-5731	528	1	sci	sci	PROPN
ejpam-5731	528	2	.	.	PROPN
ejpam-5731	528	3	,	,	PUNCT
ejpam-5731	528	4	44:327–344	44:327–344	PROPN
ejpam-5731	528	5	,	,	PUNCT
ejpam-5731	528	6	2020	2020	NUM
ejpam-5731	528	7	.	.	PUNCT
ejpam-5731	529	1	[	[	X
ejpam-5731	529	2	47	47	NUM
ejpam-5731	529	3	]	]	X
ejpam-5731	529	4	h.m	h.m	PROPN
ejpam-5731	529	5	.	.	PROPN
ejpam-5731	529	6	srivastava	srivastava	PROPN
ejpam-5731	529	7	,	,	PUNCT
ejpam-5731	529	8	q.z	q.z	PROPN
ejpam-5731	529	9	.	.	PROPN
ejpam-5731	529	10	ahmad	ahmad	PROPN
ejpam-5731	529	11	,	,	PUNCT
ejpam-5731	529	12	m.	m.	PROPN
ejpam-5731	529	13	tahir	tahir	PROPN
ejpam-5731	529	14	,	,	PUNCT
ejpam-5731	529	15	b.	b.	PROPN
ejpam-5731	529	16	khan	khan	PROPN
ejpam-5731	529	17	,	,	PUNCT
ejpam-5731	529	18	m.	m.	NOUN
ejpam-5731	529	19	darus	darus	NOUN
ejpam-5731	529	20	,	,	PUNCT
ejpam-5731	529	21	and	and	CCONJ
ejpam-5731	529	22	n.	n.	PROPN
ejpam-5731	529	23	khan	khan	PROPN
ejpam-5731	529	24	.	.	PUNCT
ejpam-5731	530	1	certain	certain	ADJ
ejpam-5731	530	2	subclasses	subclass	NOUN
ejpam-5731	530	3	of	of	ADP
ejpam-5731	530	4	meromorphically	meromorphically	ADV
ejpam-5731	530	5	-	-	PUNCT
ejpam-5731	530	6	starlike	starlike	NOUN
ejpam-5731	530	7	functions	function	NOUN
ejpam-5731	530	8	associated	associate	VERB
ejpam-5731	530	9	with	with	ADP
ejpam-5731	530	10	the	the	DET
ejpam-5731	530	11	q	q	ADJ
ejpam-5731	530	12	-	-	ADJ
ejpam-5731	530	13	derivative	derivative	ADJ
ejpam-5731	530	14	operators	operator	NOUN
ejpam-5731	530	15	.	.	PUNCT
ejpam-5731	531	1	ukr	ukr	PROPN
ejpam-5731	531	2	.	.	PROPN
ejpam-5731	531	3	math	math	PROPN
ejpam-5731	531	4	.	.	PUNCT
ejpam-5731	532	1	j.	j.	PROPN
ejpam-5731	532	2	,	,	PUNCT
ejpam-5731	532	3	73:1260–1273	73:1260–1273	PROPN
ejpam-5731	532	4	,	,	PUNCT
ejpam-5731	532	5	2021	2021	NUM
ejpam-5731	532	6	.	.	PUNCT
ejpam-5731	533	1	[	[	X
ejpam-5731	533	2	48	48	NUM
ejpam-5731	533	3	]	]	X
ejpam-5731	533	4	h.m	h.m	PROPN
ejpam-5731	533	5	.	.	PROPN
ejpam-5731	533	6	srivastava	srivastava	PROPN
ejpam-5731	533	7	,	,	PUNCT
ejpam-5731	533	8	m.	m.	NOUN
ejpam-5731	533	9	kamali	kamali	PROPN
ejpam-5731	533	10	,	,	PUNCT
ejpam-5731	533	11	and	and	CCONJ
ejpam-5731	533	12	a.	a.	NOUN
ejpam-5731	533	13	urdaletova	urdaletova	PROPN
ejpam-5731	533	14	.	.	PUNCT
ejpam-5731	534	1	a	a	DET
ejpam-5731	534	2	study	study	NOUN
ejpam-5731	534	3	of	of	ADP
ejpam-5731	534	4	the	the	DET
ejpam-5731	534	5	fekete	fekete	PROPN
ejpam-5731	534	6	-	-	PUNCT
ejpam-5731	534	7	szegö	szegö	ADJ
ejpam-5731	534	8	functional	functional	ADJ
ejpam-5731	534	9	and	and	CCONJ
ejpam-5731	534	10	coefficient	coefficient	ADJ
ejpam-5731	534	11	estimates	estimate	NOUN
ejpam-5731	534	12	for	for	ADP
ejpam-5731	534	13	subclasses	subclass	NOUN
ejpam-5731	534	14	of	of	ADP
ejpam-5731	534	15	analytic	analytic	ADJ
ejpam-5731	534	16	functions	function	NOUN
ejpam-5731	534	17	satisfying	satisfy	VERB
ejpam-5731	534	18	a	a	DET
ejpam-5731	534	19	certain	certain	ADJ
ejpam-5731	534	20	subordination	subordination	NOUN
ejpam-5731	534	21	condition	condition	NOUN
ejpam-5731	534	22	and	and	CCONJ
ejpam-5731	534	23	associated	associate	VERB
ejpam-5731	534	24	with	with	ADP
ejpam-5731	534	25	the	the	DET
ejpam-5731	534	26	gegenbauer	gegenbauer	NOUN
ejpam-5731	534	27	polynomials	polynomial	NOUN
ejpam-5731	534	28	.	.	PUNCT
ejpam-5731	535	1	aims	aim	VERB
ejpam-5731	535	2	mathematics	mathematic	NOUN
ejpam-5731	535	3	,	,	PUNCT
ejpam-5731	535	4	7(2):2568–2584	7(2):2568–2584	PROPN
ejpam-5731	535	5	,	,	PUNCT
ejpam-5731	535	6	2021	2021	NUM
ejpam-5731	535	7	.	.	PUNCT
ejpam-5731	536	1	[	[	X
ejpam-5731	536	2	49	49	NUM
ejpam-5731	536	3	]	]	X
ejpam-5731	536	4	h.m	h.m	PROPN
ejpam-5731	536	5	.	.	PROPN
ejpam-5731	536	6	srivastava	srivastava	PROPN
ejpam-5731	536	7	and	and	CCONJ
ejpam-5731	536	8	h.l	h.l	PROPN
ejpam-5731	536	9	.	.	PROPN
ejpam-5731	536	10	manocha	manocha	PROPN
ejpam-5731	536	11	.	.	PUNCT
ejpam-5731	537	1	a	a	DET
ejpam-5731	537	2	treatise	treatise	NOUN
ejpam-5731	537	3	on	on	ADP
ejpam-5731	537	4	generating	generating	NOUN
ejpam-5731	537	5	functions	function	NOUN
ejpam-5731	537	6	.	.	PUNCT
ejpam-5731	538	1	halsted	halsted	ADJ
ejpam-5731	538	2	press	press	PROPN
ejpam-5731	538	3	,	,	PUNCT
ejpam-5731	538	4	john	john	PROPN
ejpam-5731	538	5	wiley	wiley	PROPN
ejpam-5731	538	6	and	and	CCONJ
ejpam-5731	538	7	sons	son	NOUN
ejpam-5731	538	8	,	,	PUNCT
ejpam-5731	538	9	1984	1984	NUM
ejpam-5731	538	10	.	.	PUNCT
ejpam-5731	539	1	[	[	X
ejpam-5731	539	2	50	50	NUM
ejpam-5731	539	3	]	]	X
ejpam-5731	539	4	h.e	h.e	PROPN
ejpam-5731	539	5	.	.	PUNCT
ejpam-5731	539	6	uçar	uçar	PROPN
ejpam-5731	539	7	.	.	PROPN
ejpam-5731	540	1	coefficient	coefficient	NOUN
ejpam-5731	540	2	inequality	inequality	NOUN
ejpam-5731	540	3	for	for	ADP
ejpam-5731	540	4	q−starlike	q−starlike	NOUN
ejpam-5731	540	5	functions	function	NOUN
ejpam-5731	540	6	.	.	PUNCT
ejpam-5731	541	1	applied	apply	VERB
ejpam-5731	541	2	mathematical	mathematical	ADJ
ejpam-5731	541	3	comput	comput	NOUN
ejpam-5731	541	4	.	.	PUNCT
ejpam-5731	541	5	,	,	PUNCT
ejpam-5731	541	6	276:122–126	276:122–126	NUM
ejpam-5731	541	7	,	,	PUNCT
ejpam-5731	541	8	2016	2016	NUM
ejpam-5731	541	9	.	.	PUNCT
ejpam-5731	542	1	[	[	X
ejpam-5731	542	2	51	51	NUM
ejpam-5731	542	3	]	]	PUNCT
ejpam-5731	542	4	m.	m.	NOUN
ejpam-5731	542	5	ul	ul	INTJ
ejpam-5731	542	6	-	-	PUNCT
ejpam-5731	542	7	haq	haq	PROPN
ejpam-5731	542	8	,	,	PUNCT
ejpam-5731	542	9	m.	m.	NOUN
ejpam-5731	542	10	raza	raza	PROPN
ejpam-5731	542	11	,	,	PUNCT
ejpam-5731	542	12	m.	m.	PROPN
ejpam-5731	542	13	arif	arif	PROPN
ejpam-5731	542	14	,	,	PUNCT
ejpam-5731	542	15	q.	q.	PROPN
ejpam-5731	542	16	khan	khan	PROPN
ejpam-5731	542	17	,	,	PUNCT
ejpam-5731	542	18	and	and	CCONJ
ejpam-5731	542	19	h.	h.	PROPN
ejpam-5731	542	20	tang	tang	PROPN
ejpam-5731	542	21	.	.	PUNCT
ejpam-5731	543	1	q−analogue	q−analogue	NOUN
ejpam-5731	543	2	of	of	ADP
ejpam-5731	543	3	differential	differential	ADJ
ejpam-5731	543	4	subordinations	subordination	NOUN
ejpam-5731	543	5	.	.	PUNCT
ejpam-5731	544	1	mathematics	mathematic	NOUN
ejpam-5731	544	2	,	,	PUNCT
ejpam-5731	544	3	7(724	7(724	NUM
ejpam-5731	544	4	)	)	PUNCT
ejpam-5731	544	5	,	,	PUNCT
ejpam-5731	544	6	2019	2019	NUM
ejpam-5731	544	7	.	.	PUNCT
ejpam-5731	545	1	[	[	X
ejpam-5731	545	2	52	52	NUM
ejpam-5731	545	3	]	]	PUNCT
ejpam-5731	545	4	k.	k.	PROPN
ejpam-5731	545	5	vijaya	vijaya	PROPN
ejpam-5731	545	6	.	.	PUNCT
ejpam-5731	546	1	coefficient	coefficient	NOUN
ejpam-5731	546	2	estimates	estimate	NOUN
ejpam-5731	546	3	of	of	ADP
ejpam-5731	546	4	bi	bi	ADJ
ejpam-5731	546	5	-	-	ADJ
ejpam-5731	546	6	univalent	univalent	ADJ
ejpam-5731	546	7	bi	bi	ADJ
ejpam-5731	546	8	-	-	ADJ
ejpam-5731	546	9	bazilevic	bazilevic	ADJ
ejpam-5731	546	10	functions	function	NOUN
ejpam-5731	546	11	defined	define	VERB
ejpam-5731	546	12	by	by	ADP
ejpam-5731	546	13	q−ruscheweyh	q−ruscheweyh	VERB
ejpam-5731	546	14	differential	differential	ADJ
ejpam-5731	546	15	operator	operator	NOUN
ejpam-5731	546	16	associated	associate	VERB
ejpam-5731	546	17	with	with	ADP
ejpam-5731	546	18	haradam	haradam	ADJ
ejpam-5731	546	19	polynomials	polynomial	NOUN
ejpam-5731	546	20	.	.	PUNCT
ejpam-5731	547	1	palestine	palestine	PROPN
ejpam-5731	547	2	journal	journal	PROPN
ejpam-5731	547	3	of	of	ADP
ejpam-5731	547	4	mathematics	mathematic	NOUN
ejpam-5731	547	5	,	,	PUNCT
ejpam-5731	547	6	11(2):352–361	11(2):352–361	NOUN
ejpam-5731	547	7	,	,	PUNCT
ejpam-5731	547	8	2022	2022	NUM
ejpam-5731	547	9	.	.	PUNCT