id	sid	tid	token	lemma	pos
ejpam-5022	1	1	european	european	PROPN
ejpam-5022	1	2	journal	journal	PROPN
ejpam-5022	1	3	of	of	ADP
ejpam-5022	1	4	pure	pure	ADJ
ejpam-5022	1	5	and	and	CCONJ
ejpam-5022	1	6	applied	apply	VERB
ejpam-5022	1	7	mathematics	mathematic	NOUN
ejpam-5022	1	8	vol	vol	NOUN
ejpam-5022	1	9	.	.	PROPN
ejpam-5022	2	1	17	17	NUM
ejpam-5022	2	2	,	,	PUNCT
ejpam-5022	2	3	no	no	INTJ
ejpam-5022	2	4	.	.	NOUN
ejpam-5022	2	5	1	1	NUM
ejpam-5022	2	6	,	,	PUNCT
ejpam-5022	2	7	2024	2024	NUM
ejpam-5022	2	8	,	,	PUNCT
ejpam-5022	2	9	158	158	NUM
ejpam-5022	2	10	-	-	SYM
ejpam-5022	2	11	170	170	NUM
ejpam-5022	2	12	issn	issn	PROPN
ejpam-5022	2	13	1307	1307	NUM
ejpam-5022	2	14	-	-	SYM
ejpam-5022	2	15	5543	5543	NUM
ejpam-5022	2	16	–	–	PUNCT
ejpam-5022	2	17	ejpam.com	ejpam.com	X
ejpam-5022	2	18	published	publish	VERB
ejpam-5022	2	19	by	by	ADP
ejpam-5022	2	20	new	new	PROPN
ejpam-5022	2	21	york	york	PROPN
ejpam-5022	2	22	business	business	PROPN
ejpam-5022	2	23	global	global	PROPN
ejpam-5022	3	1	a	a	DET
ejpam-5022	3	2	family	family	NOUN
ejpam-5022	3	3	of	of	ADP
ejpam-5022	3	4	analytic	analytic	ADJ
ejpam-5022	3	5	functions	function	NOUN
ejpam-5022	3	6	subordinate	subordinate	VERB
ejpam-5022	3	7	to	to	PART
ejpam-5022	3	8	horadam	horadam	VERB
ejpam-5022	3	9	polynomials	polynomial	NOUN
ejpam-5022	3	10	waleed	waleed	PROPN
ejpam-5022	3	11	al	al	PROPN
ejpam-5022	3	12	-	-	PUNCT
ejpam-5022	3	13	rawashdeh	rawashdeh	PROPN
ejpam-5022	3	14	department	department	NOUN
ejpam-5022	3	15	of	of	ADP
ejpam-5022	3	16	mathematics	mathematics	PROPN
ejpam-5022	3	17	,	,	PUNCT
ejpam-5022	3	18	zarqa	zarqa	PROPN
ejpam-5022	3	19	university	university	PROPN
ejpam-5022	3	20	,	,	PUNCT
ejpam-5022	3	21	2000	2000	NUM
ejpam-5022	3	22	zarqa	zarqa	NOUN
ejpam-5022	3	23	,	,	PUNCT
ejpam-5022	3	24	13110	13110	NUM
ejpam-5022	3	25	,	,	PUNCT
ejpam-5022	3	26	jordan	jordan	PROPN
ejpam-5022	3	27	abstract	abstract	PROPN
ejpam-5022	3	28	.	.	PUNCT
ejpam-5022	4	1	in	in	ADP
ejpam-5022	4	2	this	this	DET
ejpam-5022	4	3	paper	paper	NOUN
ejpam-5022	4	4	,	,	PUNCT
ejpam-5022	4	5	we	we	PRON
ejpam-5022	4	6	introduce	introduce	VERB
ejpam-5022	4	7	and	and	CCONJ
ejpam-5022	4	8	investigate	investigate	VERB
ejpam-5022	4	9	a	a	DET
ejpam-5022	4	10	family	family	NOUN
ejpam-5022	4	11	of	of	ADP
ejpam-5022	4	12	analytic	analytic	ADJ
ejpam-5022	4	13	functions	function	NOUN
ejpam-5022	4	14	,	,	PUNCT
ejpam-5022	4	15	denoted	denote	VERB
ejpam-5022	4	16	by	by	ADP
ejpam-5022	4	17	f(π	f(π	PROPN
ejpam-5022	4	18	,	,	PUNCT
ejpam-5022	4	19	α	α	X
ejpam-5022	4	20	,	,	PUNCT
ejpam-5022	4	21	β	β	X
ejpam-5022	4	22	,	,	PUNCT
ejpam-5022	4	23	λ	λ	PROPN
ejpam-5022	4	24	,	,	PUNCT
ejpam-5022	4	25	δ	δ	PROPN
ejpam-5022	4	26	,	,	PUNCT
ejpam-5022	4	27	µ	µ	NOUN
ejpam-5022	4	28	)	)	PUNCT
ejpam-5022	4	29	,	,	PUNCT
ejpam-5022	4	30	defined	define	VERB
ejpam-5022	4	31	by	by	ADP
ejpam-5022	4	32	means	mean	NOUN
ejpam-5022	4	33	of	of	ADP
ejpam-5022	4	34	horadam	horadam	NOUN
ejpam-5022	4	35	polynomials	polynomial	NOUN
ejpam-5022	4	36	.	.	PUNCT
ejpam-5022	5	1	for	for	ADP
ejpam-5022	5	2	functions	function	NOUN
ejpam-5022	5	3	in	in	ADP
ejpam-5022	5	4	this	this	DET
ejpam-5022	5	5	family	family	NOUN
ejpam-5022	5	6	,	,	PUNCT
ejpam-5022	5	7	we	we	PRON
ejpam-5022	5	8	derive	derive	VERB
ejpam-5022	5	9	the	the	DET
ejpam-5022	5	10	estimations	estimation	NOUN
ejpam-5022	5	11	for	for	ADP
ejpam-5022	5	12	the	the	DET
ejpam-5022	5	13	initial	initial	ADJ
ejpam-5022	5	14	taylor	taylor	PROPN
ejpam-5022	5	15	-	-	PUNCT
ejpam-5022	5	16	maclaurin	maclaurin	NOUN
ejpam-5022	5	17	coefficients	coefficient	NOUN
ejpam-5022	5	18	|a2|	|a2|	NOUN
ejpam-5022	5	19	and	and	CCONJ
ejpam-5022	5	20	|a3|	|a3|	NOUN
ejpam-5022	5	21	.	.	PUNCT
ejpam-5022	6	1	moreover	moreover	ADV
ejpam-5022	6	2	,	,	PUNCT
ejpam-5022	6	3	we	we	PRON
ejpam-5022	6	4	obtain	obtain	VERB
ejpam-5022	6	5	the	the	DET
ejpam-5022	6	6	classical	classical	ADJ
ejpam-5022	6	7	fekete	fekete	PROPN
ejpam-5022	6	8	-	-	PUNCT
ejpam-5022	6	9	szegö	szegö	VERB
ejpam-5022	6	10	inequality	inequality	NOUN
ejpam-5022	6	11	of	of	ADP
ejpam-5022	6	12	functions	function	NOUN
ejpam-5022	6	13	belonging	belong	VERB
ejpam-5022	6	14	to	to	ADP
ejpam-5022	6	15	this	this	DET
ejpam-5022	6	16	family	family	NOUN
ejpam-5022	6	17	.	.	PUNCT
ejpam-5022	7	1	2020	2020	NUM
ejpam-5022	7	2	mathematics	mathematic	NOUN
ejpam-5022	7	3	subject	subject	NOUN
ejpam-5022	7	4	classifications	classification	NOUN
ejpam-5022	7	5	:	:	PUNCT
ejpam-5022	7	6	30c45	30c45	NUM
ejpam-5022	7	7	,	,	PUNCT
ejpam-5022	7	8	30c50	30c50	NUM
ejpam-5022	7	9	,	,	PUNCT
ejpam-5022	7	10	33c45	33c45	NUM
ejpam-5022	7	11	,	,	PUNCT
ejpam-5022	7	12	33c05	33c05	NUM
ejpam-5022	7	13	,	,	PUNCT
ejpam-5022	7	14	11b39	11b39	NUM
ejpam-5022	7	15	key	key	ADJ
ejpam-5022	7	16	words	word	NOUN
ejpam-5022	7	17	and	and	CCONJ
ejpam-5022	7	18	phrases	phrase	NOUN
ejpam-5022	7	19	:	:	PUNCT
ejpam-5022	7	20	analytic	analytic	ADJ
ejpam-5022	7	21	functions	function	NOUN
ejpam-5022	7	22	,	,	PUNCT
ejpam-5022	7	23	taylor	taylor	NOUN
ejpam-5022	7	24	-	-	PUNCT
ejpam-5022	7	25	maclaurin	maclaurin	NOUN
ejpam-5022	7	26	series	series	NOUN
ejpam-5022	7	27	,	,	PUNCT
ejpam-5022	7	28	principle	principle	NOUN
ejpam-5022	7	29	of	of	ADP
ejpam-5022	7	30	subordination	subordination	NOUN
ejpam-5022	7	31	,	,	PUNCT
ejpam-5022	7	32	horadam	horadam	PROPN
ejpam-5022	7	33	polynomials	polynomial	NOUN
ejpam-5022	7	34	,	,	PUNCT
ejpam-5022	7	35	chebyshev	chebyshev	NOUN
ejpam-5022	7	36	polynomials	polynomial	NOUN
ejpam-5022	7	37	,	,	PUNCT
ejpam-5022	7	38	coefficient	coefficient	NOUN
ejpam-5022	7	39	estimates	estimate	NOUN
ejpam-5022	7	40	,	,	PUNCT
ejpam-5022	7	41	fekete	fekete	PROPN
ejpam-5022	7	42	-	-	PUNCT
ejpam-5022	7	43	szegö	szegö	PROPN
ejpam-5022	7	44	inequality	inequality	NOUN
ejpam-5022	7	45	1	1	NUM
ejpam-5022	7	46	.	.	PUNCT
ejpam-5022	8	1	introduction	introduction	NOUN
ejpam-5022	8	2	let	let	VERB
ejpam-5022	8	3	a	a	PRON
ejpam-5022	8	4	be	be	AUX
ejpam-5022	8	5	the	the	DET
ejpam-5022	8	6	family	family	NOUN
ejpam-5022	8	7	of	of	ADP
ejpam-5022	8	8	all	all	DET
ejpam-5022	8	9	analytic	analytic	ADJ
ejpam-5022	8	10	functions	function	NOUN
ejpam-5022	8	11	f	f	PROPN
ejpam-5022	8	12	that	that	PRON
ejpam-5022	8	13	are	be	AUX
ejpam-5022	8	14	defined	define	VERB
ejpam-5022	8	15	on	on	ADP
ejpam-5022	8	16	the	the	DET
ejpam-5022	8	17	open	open	ADJ
ejpam-5022	8	18	unit	unit	NOUN
ejpam-5022	8	19	disk	disk	NOUN
ejpam-5022	8	20	d	d	NOUN
ejpam-5022	8	21	=	=	PUNCT
ejpam-5022	8	22	{	{	PUNCT
ejpam-5022	8	23	z	z	NOUN
ejpam-5022	8	24	∈	∈	PROPN
ejpam-5022	8	25	c	c	NOUN
ejpam-5022	8	26	:	:	PUNCT
ejpam-5022	8	27	|z|	|z|	VERB
ejpam-5022	8	28	<	<	X
ejpam-5022	8	29	1	1	NUM
ejpam-5022	8	30	}	}	PUNCT
ejpam-5022	8	31	and	and	CCONJ
ejpam-5022	8	32	normalized	normalize	VERB
ejpam-5022	8	33	by	by	ADP
ejpam-5022	8	34	the	the	DET
ejpam-5022	8	35	conditions	condition	NOUN
ejpam-5022	8	36	f(0	f(0	NOUN
ejpam-5022	8	37	)	)	PUNCT
ejpam-5022	8	38	=	=	SYM
ejpam-5022	9	1	1	1	NUM
ejpam-5022	9	2	−	−	PROPN
ejpam-5022	9	3	f	f	PROPN
ejpam-5022	9	4	′(0	′(0	PROPN
ejpam-5022	9	5	)	)	PUNCT
ejpam-5022	10	1	=	=	SYM
ejpam-5022	10	2	0	0	X
ejpam-5022	10	3	.	.	PUNCT
ejpam-5022	11	1	any	any	DET
ejpam-5022	11	2	function	function	NOUN
ejpam-5022	11	3	f	f	PROPN
ejpam-5022	11	4	∈	∈	PROPN
ejpam-5022	11	5	a	a	PRON
ejpam-5022	11	6	has	have	VERB
ejpam-5022	11	7	the	the	DET
ejpam-5022	11	8	following	follow	VERB
ejpam-5022	11	9	taylor	taylor	NOUN
ejpam-5022	11	10	-	-	PUNCT
ejpam-5022	11	11	maclarin	maclarin	PROPN
ejpam-5022	11	12	series	series	NOUN
ejpam-5022	11	13	expansion	expansion	NOUN
ejpam-5022	11	14	:	:	PUNCT
ejpam-5022	11	15	f(z	f(z	NUM
ejpam-5022	11	16	)	)	PUNCT
ejpam-5022	12	1	=	=	PUNCT
ejpam-5022	12	2	z	z	NOUN
ejpam-5022	13	1	+	+	NOUN
ejpam-5022	13	2	∞∑	∞∑	NUM
ejpam-5022	13	3	n=2	n=2	ADV
ejpam-5022	13	4	anz	anz	NOUN
ejpam-5022	13	5	n	n	CCONJ
ejpam-5022	13	6	,	,	PUNCT
ejpam-5022	13	7	where	where	SCONJ
ejpam-5022	13	8	z	z	PROPN
ejpam-5022	13	9	∈	∈	PROPN
ejpam-5022	13	10	d.	d.	PROPN
ejpam-5022	13	11	(	(	PUNCT
ejpam-5022	13	12	1	1	X
ejpam-5022	13	13	)	)	PUNCT
ejpam-5022	13	14	let	let	VERB
ejpam-5022	13	15	s	s	PRON
ejpam-5022	13	16	denote	denote	VERB
ejpam-5022	13	17	the	the	DET
ejpam-5022	13	18	class	class	NOUN
ejpam-5022	13	19	of	of	ADP
ejpam-5022	13	20	all	all	DET
ejpam-5022	13	21	functions	function	NOUN
ejpam-5022	13	22	f	f	PROPN
ejpam-5022	13	23	∈	∈	PROPN
ejpam-5022	13	24	a	a	PRON
ejpam-5022	13	25	that	that	PRON
ejpam-5022	13	26	are	be	AUX
ejpam-5022	13	27	univalent	univalent	ADJ
ejpam-5022	13	28	in	in	ADP
ejpam-5022	13	29	d.	d.	PROPN
ejpam-5022	13	30	let	let	VERB
ejpam-5022	13	31	the	the	DET
ejpam-5022	13	32	functions	function	NOUN
ejpam-5022	13	33	f	f	PROPN
ejpam-5022	13	34	and	and	CCONJ
ejpam-5022	13	35	g	g	PROPN
ejpam-5022	13	36	be	be	AUX
ejpam-5022	13	37	analytic	analytic	ADJ
ejpam-5022	13	38	in	in	ADP
ejpam-5022	13	39	d	d	PROPN
ejpam-5022	13	40	,	,	PUNCT
ejpam-5022	13	41	we	we	PRON
ejpam-5022	13	42	say	say	VERB
ejpam-5022	13	43	the	the	DET
ejpam-5022	13	44	function	function	NOUN
ejpam-5022	13	45	f	f	PROPN
ejpam-5022	13	46	is	be	AUX
ejpam-5022	13	47	subordinate	subordinate	ADJ
ejpam-5022	13	48	by	by	ADP
ejpam-5022	13	49	the	the	DET
ejpam-5022	13	50	function	function	NOUN
ejpam-5022	13	51	g	g	NOUN
ejpam-5022	13	52	in	in	ADP
ejpam-5022	13	53	d	d	PROPN
ejpam-5022	13	54	,	,	PUNCT
ejpam-5022	13	55	denoted	denote	VERB
ejpam-5022	13	56	by	by	ADP
ejpam-5022	13	57	f(z	f(z	NOUN
ejpam-5022	13	58	)	)	PUNCT
ejpam-5022	13	59	≺	≺	NOUN
ejpam-5022	13	60	g(z	g(z	PROPN
ejpam-5022	13	61	)	)	PUNCT
ejpam-5022	13	62	for	for	ADP
ejpam-5022	13	63	all	all	DET
ejpam-5022	13	64	z	z	NOUN
ejpam-5022	13	65	∈	∈	PROPN
ejpam-5022	14	1	d	d	NOUN
ejpam-5022	14	2	,	,	PUNCT
ejpam-5022	14	3	if	if	SCONJ
ejpam-5022	14	4	there	there	PRON
ejpam-5022	14	5	exists	exist	VERB
ejpam-5022	14	6	a	a	DET
ejpam-5022	14	7	schwarz	schwarz	PROPN
ejpam-5022	14	8	function	function	PROPN
ejpam-5022	14	9	w	w	PROPN
ejpam-5022	14	10	,	,	PUNCT
ejpam-5022	14	11	with	with	ADP
ejpam-5022	14	12	w(0	w(0	PROPN
ejpam-5022	14	13	)	)	PUNCT
ejpam-5022	14	14	=	=	SYM
ejpam-5022	14	15	0	0	NUM
ejpam-5022	14	16	and	and	CCONJ
ejpam-5022	14	17	|w(z)|	|w(z)|	VERB
ejpam-5022	14	18	<	<	X
ejpam-5022	14	19	1	1	NUM
ejpam-5022	14	20	for	for	ADP
ejpam-5022	14	21	all	all	DET
ejpam-5022	14	22	z	z	NOUN
ejpam-5022	14	23	∈	∈	PROPN
ejpam-5022	14	24	d	d	NOUN
ejpam-5022	14	25	,	,	PUNCT
ejpam-5022	14	26	such	such	ADJ
ejpam-5022	14	27	that	that	DET
ejpam-5022	14	28	f(z	f(z	PROPN
ejpam-5022	14	29	)	)	PUNCT
ejpam-5022	14	30	=	=	SYM
ejpam-5022	14	31	g(w(z	g(w(z	PROPN
ejpam-5022	14	32	)	)	PUNCT
ejpam-5022	14	33	)	)	PUNCT
ejpam-5022	14	34	for	for	ADP
ejpam-5022	14	35	all	all	DET
ejpam-5022	14	36	z	z	PROPN
ejpam-5022	14	37	∈	∈	PROPN
ejpam-5022	14	38	d.	d.	PROPN
ejpam-5022	14	39	in	in	ADP
ejpam-5022	14	40	particular	particular	ADJ
ejpam-5022	14	41	,	,	PUNCT
ejpam-5022	14	42	if	if	SCONJ
ejpam-5022	14	43	the	the	DET
ejpam-5022	14	44	function	function	NOUN
ejpam-5022	14	45	g	g	PROPN
ejpam-5022	14	46	is	be	AUX
ejpam-5022	14	47	univalent	univalent	ADJ
ejpam-5022	14	48	over	over	ADP
ejpam-5022	14	49	d	d	PROPN
ejpam-5022	14	50	then	then	ADV
ejpam-5022	14	51	f(z	f(z	PROPN
ejpam-5022	14	52	)	)	PUNCT
ejpam-5022	14	53	≺	≺	NOUN
ejpam-5022	14	54	g(z	g(z	PROPN
ejpam-5022	14	55	)	)	PUNCT
ejpam-5022	14	56	equivalent	equivalent	NOUN
ejpam-5022	14	57	to	to	ADP
ejpam-5022	14	58	f(0	f(0	NOUN
ejpam-5022	14	59	)	)	PUNCT
ejpam-5022	14	60	=	=	SYM
ejpam-5022	14	61	g(0	g(0	PROPN
ejpam-5022	14	62	)	)	PUNCT
ejpam-5022	14	63	and	and	CCONJ
ejpam-5022	14	64	f(d	f(d	PROPN
ejpam-5022	14	65	)	)	PUNCT
ejpam-5022	14	66	⊂	⊂	PROPN
ejpam-5022	15	1	g(d	g(d	PROPN
ejpam-5022	15	2	.	.	PUNCT
ejpam-5022	16	1	for	for	ADP
ejpam-5022	16	2	more	more	ADJ
ejpam-5022	16	3	information	information	NOUN
ejpam-5022	16	4	about	about	ADP
ejpam-5022	16	5	the	the	DET
ejpam-5022	16	6	subordination	subordination	NOUN
ejpam-5022	16	7	principle	principle	ADJ
ejpam-5022	16	8	and	and	CCONJ
ejpam-5022	16	9	univalent	univalent	ADJ
ejpam-5022	16	10	functions	function	NOUN
ejpam-5022	16	11	we	we	PRON
ejpam-5022	16	12	refer	refer	VERB
ejpam-5022	16	13	the	the	DET
ejpam-5022	16	14	readers	reader	NOUN
ejpam-5022	16	15	to	to	PART
ejpam-5022	16	16	to	to	ADP
ejpam-5022	16	17	the	the	DET
ejpam-5022	16	18	monographs	monograph	NOUN
ejpam-5022	17	1	[	[	X
ejpam-5022	17	2	11	11	NUM
ejpam-5022	17	3	]	]	PUNCT
ejpam-5022	17	4	,	,	PUNCT
ejpam-5022	17	5	[	[	X
ejpam-5022	17	6	10	10	NUM
ejpam-5022	17	7	]	]	PUNCT
ejpam-5022	17	8	,	,	PUNCT
ejpam-5022	17	9	[	[	X
ejpam-5022	17	10	14	14	NUM
ejpam-5022	17	11	]	]	PUNCT
ejpam-5022	17	12	,	,	PUNCT
ejpam-5022	18	1	[	[	X
ejpam-5022	18	2	23	23	NUM
ejpam-5022	18	3	]	]	PUNCT
ejpam-5022	18	4	,	,	PUNCT
ejpam-5022	18	5	[	[	X
ejpam-5022	18	6	25	25	NUM
ejpam-5022	18	7	]	]	PUNCT
ejpam-5022	18	8	and	and	CCONJ
ejpam-5022	18	9	the	the	DET
ejpam-5022	18	10	references	reference	NOUN
ejpam-5022	18	11	therein	therein	ADV
ejpam-5022	18	12	.	.	PUNCT
ejpam-5022	19	1	in	in	ADP
ejpam-5022	19	2	the	the	DET
ejpam-5022	19	3	year	year	NOUN
ejpam-5022	19	4	1965	1965	NUM
ejpam-5022	19	5	,	,	PUNCT
ejpam-5022	19	6	for	for	ADP
ejpam-5022	19	7	a	a	DET
ejpam-5022	19	8	,	,	PUNCT
ejpam-5022	19	9	b	b	NOUN
ejpam-5022	19	10	,	,	PUNCT
ejpam-5022	19	11	p	p	X
ejpam-5022	19	12	,	,	PUNCT
ejpam-5022	19	13	q	q	PUNCT
ejpam-5022	19	14	∈	∈	PROPN
ejpam-5022	19	15	r	r	NOUN
ejpam-5022	19	16	,	,	PUNCT
ejpam-5022	19	17	horadam	horadam	PROPN
ejpam-5022	19	18	[	[	X
ejpam-5022	19	19	17	17	NUM
ejpam-5022	19	20	]	]	PUNCT
ejpam-5022	19	21	introduced	introduce	VERB
ejpam-5022	19	22	the	the	DET
ejpam-5022	19	23	sequence	sequence	NOUN
ejpam-5022	19	24	wn	wn	NOUN
ejpam-5022	19	25	=	=	PUNCT
ejpam-5022	19	26	wn(a	wn(a	PROPN
ejpam-5022	19	27	,	,	PUNCT
ejpam-5022	19	28	b	b	X
ejpam-5022	19	29	;	;	PUNCT
ejpam-5022	19	30	p	p	X
ejpam-5022	19	31	,	,	PUNCT
ejpam-5022	19	32	q	q	NOUN
ejpam-5022	19	33	)	)	PUNCT
ejpam-5022	19	34	that	that	PRON
ejpam-5022	19	35	is	be	AUX
ejpam-5022	19	36	defined	define	VERB
ejpam-5022	19	37	by	by	ADP
ejpam-5022	19	38	the	the	DET
ejpam-5022	19	39	following	follow	VERB
ejpam-5022	19	40	recurrence	recurrence	NOUN
ejpam-5022	19	41	relation	relation	NOUN
ejpam-5022	19	42	wn+2	wn+2	AUX
ejpam-5022	19	43	=	=	SYM
ejpam-5022	19	44	pwn+1	pwn+1	NOUN
ejpam-5022	19	45	+	+	X
ejpam-5022	19	46	qwn	qwn	PROPN
ejpam-5022	19	47	,	,	PUNCT
ejpam-5022	19	48	for	for	ADP
ejpam-5022	19	49	n	n	PRON
ejpam-5022	19	50	≥	≥	NUM
ejpam-5022	19	51	2	2	NUM
ejpam-5022	19	52	,	,	PUNCT
ejpam-5022	19	53	doi	doi	NOUN
ejpam-5022	19	54	:	:	PUNCT
ejpam-5022	19	55	https://doi.org/10.29020/nybg.ejpam.v17i1.5022	https://doi.org/10.29020/nybg.ejpam.v17i1.5022	PROPN
ejpam-5022	19	56	email	email	NOUN
ejpam-5022	19	57	address	address	NOUN
ejpam-5022	19	58	:	:	PUNCT
ejpam-5022	19	59	walrawashdeh@zu.edu.jo	walrawashdeh@zu.edu.jo	NOUN
ejpam-5022	19	60	(	(	PUNCT
ejpam-5022	19	61	w.	w.	PROPN
ejpam-5022	19	62	al	al	PROPN
ejpam-5022	19	63	-	-	PUNCT
ejpam-5022	19	64	rawashdeh	rawashdeh	NOUN
ejpam-5022	19	65	)	)	PUNCT
ejpam-5022	19	66	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5022	19	67	158	158	NUM
ejpam-5022	20	1	©	©	ADP
ejpam-5022	20	2	2024	2024	NUM
ejpam-5022	20	3	ejpam	ejpam	NOUN
ejpam-5022	20	4	all	all	DET
ejpam-5022	20	5	rights	right	NOUN
ejpam-5022	20	6	reserved	reserve	VERB
ejpam-5022	20	7	.	.	PUNCT
ejpam-5022	21	1	w.	w.	PROPN
ejpam-5022	21	2	al	al	PROPN
ejpam-5022	21	3	-	-	PUNCT
ejpam-5022	21	4	rawashdeh	rawashdeh	PROPN
ejpam-5022	21	5	/	/	SYM
ejpam-5022	21	6	eur	eur	PROPN
ejpam-5022	21	7	.	.	PUNCT
ejpam-5022	22	1	j.	j.	PROPN
ejpam-5022	22	2	pure	pure	PROPN
ejpam-5022	22	3	appl	appl	PROPN
ejpam-5022	22	4	.	.	PROPN
ejpam-5022	22	5	math	math	PROPN
ejpam-5022	22	6	,	,	PUNCT
ejpam-5022	22	7	17	17	NUM
ejpam-5022	22	8	(	(	PUNCT
ejpam-5022	22	9	1	1	NUM
ejpam-5022	22	10	)	)	PUNCT
ejpam-5022	22	11	(	(	PUNCT
ejpam-5022	22	12	2024	2024	NUM
ejpam-5022	22	13	)	)	PUNCT
ejpam-5022	22	14	,	,	PUNCT
ejpam-5022	22	15	158	158	NUM
ejpam-5022	22	16	-	-	SYM
ejpam-5022	22	17	170	170	NUM
ejpam-5022	22	18	159	159	NUM
ejpam-5022	22	19	with	with	ADP
ejpam-5022	22	20	the	the	DET
ejpam-5022	22	21	initial	initial	ADJ
ejpam-5022	22	22	values	value	NOUN
ejpam-5022	22	23	w0	w0	PROPN
ejpam-5022	22	24	=	=	PROPN
ejpam-5022	22	25	a	a	PRON
ejpam-5022	22	26	and	and	CCONJ
ejpam-5022	22	27	w1	w1	NOUN
ejpam-5022	22	28	=	=	SYM
ejpam-5022	22	29	b.	b.	PROPN
ejpam-5022	23	1	the	the	DET
ejpam-5022	23	2	characteristic	characteristic	ADJ
ejpam-5022	23	3	equation	equation	NOUN
ejpam-5022	23	4	of	of	ADP
ejpam-5022	23	5	this	this	DET
ejpam-5022	23	6	sequence	sequence	NOUN
ejpam-5022	23	7	is	be	AUX
ejpam-5022	23	8	given	give	VERB
ejpam-5022	23	9	by	by	ADP
ejpam-5022	23	10	t2	t2	PROPN
ejpam-5022	23	11	−	−	PROPN
ejpam-5022	23	12	pt−	pt−	NUM
ejpam-5022	23	13	q	q	NOUN
ejpam-5022	24	1	=	=	NOUN
ejpam-5022	24	2	0	0	NUM
ejpam-5022	24	3	.	.	PUNCT
ejpam-5022	25	1	in	in	ADP
ejpam-5022	25	2	addition	addition	NOUN
ejpam-5022	25	3	,	,	PUNCT
ejpam-5022	25	4	the	the	DET
ejpam-5022	25	5	generating	generate	VERB
ejpam-5022	25	6	function	function	NOUN
ejpam-5022	25	7	of	of	ADP
ejpam-5022	25	8	horadam	horadam	PROPN
ejpam-5022	25	9	sequence	sequence	NOUN
ejpam-5022	25	10	is	be	AUX
ejpam-5022	25	11	f(t	f(t	NOUN
ejpam-5022	25	12	)	)	PUNCT
ejpam-5022	25	13	=	=	SYM
ejpam-5022	25	14	a+	a+	PUNCT
ejpam-5022	25	15	t(b−	t(b−	PROPN
ejpam-5022	25	16	ap	ap	PROPN
ejpam-5022	25	17	)	)	PUNCT
ejpam-5022	25	18	1−	1−	NUM
ejpam-5022	25	19	pt−	pt−	NUM
ejpam-5022	25	20	qt2	qt2	PROPN
ejpam-5022	25	21	.	.	PUNCT
ejpam-5022	26	1	the	the	DET
ejpam-5022	26	2	horadam	horadam	PROPN
ejpam-5022	26	3	sequences	sequence	NOUN
ejpam-5022	26	4	generalize	generalize	VERB
ejpam-5022	26	5	many	many	ADJ
ejpam-5022	26	6	famous	famous	ADJ
ejpam-5022	26	7	sequences	sequence	NOUN
ejpam-5022	26	8	such	such	ADJ
ejpam-5022	26	9	as	as	ADP
ejpam-5022	26	10	fibonacci	fibonacci	NOUN
ejpam-5022	26	11	,	,	PUNCT
ejpam-5022	26	12	lucas	lucas	PROPN
ejpam-5022	26	13	,	,	PUNCT
ejpam-5022	26	14	pell	pell	INTJ
ejpam-5022	26	15	,	,	PUNCT
ejpam-5022	26	16	pell	pell	NOUN
ejpam-5022	26	17	-	-	PUNCT
ejpam-5022	26	18	lucas	lucas	PROPN
ejpam-5022	26	19	and	and	CCONJ
ejpam-5022	26	20	jacobsthal	jacobsthal	ADJ
ejpam-5022	26	21	sequences	sequence	NOUN
ejpam-5022	26	22	.	.	PUNCT
ejpam-5022	27	1	these	these	DET
ejpam-5022	27	2	sequences	sequence	NOUN
ejpam-5022	27	3	have	have	AUX
ejpam-5022	27	4	been	be	AUX
ejpam-5022	27	5	studied	study	VERB
ejpam-5022	27	6	for	for	ADP
ejpam-5022	27	7	a	a	DET
ejpam-5022	27	8	long	long	ADJ
ejpam-5022	27	9	time	time	NOUN
ejpam-5022	27	10	.	.	PUNCT
ejpam-5022	28	1	for	for	ADP
ejpam-5022	28	2	more	more	ADJ
ejpam-5022	28	3	information	information	NOUN
ejpam-5022	28	4	about	about	ADP
ejpam-5022	28	5	these	these	DET
ejpam-5022	28	6	sequences	sequence	NOUN
ejpam-5022	28	7	,	,	PUNCT
ejpam-5022	28	8	we	we	PRON
ejpam-5022	28	9	refer	refer	VERB
ejpam-5022	28	10	the	the	DET
ejpam-5022	28	11	readers	reader	NOUN
ejpam-5022	28	12	to	to	ADP
ejpam-5022	28	13	the	the	DET
ejpam-5022	28	14	articles	article	NOUN
ejpam-5022	28	15	[	[	X
ejpam-5022	28	16	16	16	NUM
ejpam-5022	28	17	]	]	PUNCT
ejpam-5022	28	18	,	,	PUNCT
ejpam-5022	28	19	[	[	X
ejpam-5022	28	20	15	15	NUM
ejpam-5022	28	21	]	]	PUNCT
ejpam-5022	28	22	,	,	PUNCT
ejpam-5022	28	23	the	the	DET
ejpam-5022	28	24	monograph	monograph	NOUN
ejpam-5022	29	1	[	[	X
ejpam-5022	29	2	21	21	NUM
ejpam-5022	29	3	]	]	PUNCT
ejpam-5022	29	4	and	and	CCONJ
ejpam-5022	29	5	the	the	DET
ejpam-5022	29	6	references	reference	NOUN
ejpam-5022	29	7	therein	therein	ADV
ejpam-5022	29	8	.	.	PUNCT
ejpam-5022	30	1	in	in	ADP
ejpam-5022	30	2	the	the	DET
ejpam-5022	30	3	year	year	NOUN
ejpam-5022	30	4	1985	1985	NUM
ejpam-5022	30	5	,	,	PUNCT
ejpam-5022	30	6	horadam	horadam	PROPN
ejpam-5022	30	7	and	and	CCONJ
ejpam-5022	30	8	mahon	mahon	PROPN
ejpam-5022	31	1	[	[	X
ejpam-5022	31	2	16	16	NUM
ejpam-5022	31	3	]	]	PUNCT
ejpam-5022	31	4	defined	define	VERB
ejpam-5022	31	5	the	the	DET
ejpam-5022	31	6	horadam	horadam	PROPN
ejpam-5022	31	7	polynomials	polynomial	NOUN
ejpam-5022	31	8	hn(x	hn(x	X
ejpam-5022	31	9	)	)	PUNCT
ejpam-5022	31	10	=	=	PUNCT
ejpam-5022	32	1	hn(a	hn(a	NUM
ejpam-5022	32	2	,	,	PUNCT
ejpam-5022	32	3	b	b	NOUN
ejpam-5022	32	4	;	;	PUNCT
ejpam-5022	32	5	p	p	X
ejpam-5022	32	6	,	,	PUNCT
ejpam-5022	32	7	q	q	NOUN
ejpam-5022	32	8	)	)	PUNCT
ejpam-5022	32	9	by	by	ADP
ejpam-5022	32	10	the	the	DET
ejpam-5022	32	11	following	follow	VERB
ejpam-5022	32	12	recurrence	recurrence	NOUN
ejpam-5022	32	13	relation	relation	PROPN
ejpam-5022	32	14	:	:	PUNCT
ejpam-5022	32	15	hn(x	hn(x	X
ejpam-5022	32	16	)	)	PUNCT
ejpam-5022	32	17	=	=	SYM
ejpam-5022	32	18	pxhn−1(x	pxhn−1(x	NOUN
ejpam-5022	32	19	)	)	PUNCT
ejpam-5022	33	1	+	+	NUM
ejpam-5022	33	2	qhn−2(x	qhn−2(x	NOUN
ejpam-5022	33	3	)	)	PUNCT
ejpam-5022	33	4	,	,	PUNCT
ejpam-5022	33	5	for	for	ADP
ejpam-5022	33	6	n	n	PRON
ejpam-5022	33	7	∈	∈	PROPN
ejpam-5022	33	8	n	n	CCONJ
ejpam-5022	33	9	\	\	NOUN
ejpam-5022	33	10	{	{	PUNCT
ejpam-5022	33	11	1	1	NUM
ejpam-5022	33	12	,	,	PUNCT
ejpam-5022	33	13	2	2	NUM
ejpam-5022	33	14	}	}	PUNCT
ejpam-5022	33	15	,	,	PUNCT
ejpam-5022	33	16	(	(	PUNCT
ejpam-5022	33	17	2	2	X
ejpam-5022	33	18	)	)	PUNCT
ejpam-5022	33	19	with	with	ADP
ejpam-5022	33	20	initial	initial	ADJ
ejpam-5022	33	21	values	value	NOUN
ejpam-5022	33	22	,	,	PUNCT
ejpam-5022	33	23	h1(x	h1(x	NOUN
ejpam-5022	33	24	)	)	PUNCT
ejpam-5022	33	25	=	=	SYM
ejpam-5022	34	1	a	a	PROPN
ejpam-5022	34	2	,	,	PUNCT
ejpam-5022	34	3	h2(x	h2(x	X
ejpam-5022	34	4	)	)	PUNCT
ejpam-5022	34	5	=	=	SYM
ejpam-5022	34	6	bx	bx	PROPN
ejpam-5022	34	7	,	,	PUNCT
ejpam-5022	34	8	and	and	CCONJ
ejpam-5022	34	9	h3(x	h3(x	PROPN
ejpam-5022	34	10	)	)	PUNCT
ejpam-5022	34	11	=	=	VERB
ejpam-5022	34	12	pbx2	pbx2	VERB
ejpam-5022	34	13	+	+	CCONJ
ejpam-5022	34	14	qa	qa	PROPN
ejpam-5022	34	15	.	.	PUNCT
ejpam-5022	35	1	(	(	PUNCT
ejpam-5022	35	2	3	3	X
ejpam-5022	35	3	)	)	PUNCT
ejpam-5022	35	4	moreover	moreover	ADV
ejpam-5022	35	5	,	,	PUNCT
ejpam-5022	35	6	the	the	DET
ejpam-5022	35	7	generating	generate	VERB
ejpam-5022	35	8	function	function	NOUN
ejpam-5022	35	9	of	of	ADP
ejpam-5022	35	10	horadam	horadam	NOUN
ejpam-5022	35	11	ploynomials	ploynomial	NOUN
ejpam-5022	35	12	is	be	AUX
ejpam-5022	35	13	given	give	VERB
ejpam-5022	35	14	by	by	ADP
ejpam-5022	35	15	π(x	π(x	ADP
ejpam-5022	35	16	,	,	PUNCT
ejpam-5022	35	17	z	z	NOUN
ejpam-5022	35	18	)	)	PUNCT
ejpam-5022	35	19	=	=	NOUN
ejpam-5022	36	1	∞∑	∞∑	NUM
ejpam-5022	36	2	n=1	n=1	NUM
ejpam-5022	36	3	hn(x)z	hn(x)z	PROPN
ejpam-5022	36	4	n−1	n−1	PROPN
ejpam-5022	36	5	=	=	SYM
ejpam-5022	36	6	a+	a+	PUNCT
ejpam-5022	36	7	(	(	PUNCT
ejpam-5022	36	8	b−	b−	NOUN
ejpam-5022	36	9	ap)xz	ap)xz	SYM
ejpam-5022	36	10	1−	1−	NUM
ejpam-5022	36	11	pxz	pxz	NOUN
ejpam-5022	36	12	−	−	PROPN
ejpam-5022	36	13	qz2	qz2	PROPN
ejpam-5022	36	14	.	.	PUNCT
ejpam-5022	37	1	in	in	ADP
ejpam-5022	37	2	this	this	DET
ejpam-5022	37	3	paper	paper	NOUN
ejpam-5022	37	4	,	,	PUNCT
ejpam-5022	37	5	the	the	DET
ejpam-5022	37	6	argument	argument	NOUN
ejpam-5022	37	7	of	of	ADP
ejpam-5022	37	8	x	x	SYM
ejpam-5022	37	9	∈	∈	NOUN
ejpam-5022	37	10	r	r	NOUN
ejpam-5022	37	11	is	be	AUX
ejpam-5022	37	12	independent	independent	ADJ
ejpam-5022	37	13	of	of	ADP
ejpam-5022	37	14	the	the	DET
ejpam-5022	37	15	argument	argument	NOUN
ejpam-5022	37	16	z	z	X
ejpam-5022	37	17	∈	∈	PROPN
ejpam-5022	37	18	c	c	NOUN
ejpam-5022	37	19	;	;	PUNCT
ejpam-5022	37	20	that	that	PRON
ejpam-5022	37	21	is	is	ADV
ejpam-5022	37	22	x	x	PUNCT
ejpam-5022	37	23	̸=	̸=	PROPN
ejpam-5022	37	24	r(z	r(z	NOUN
ejpam-5022	37	25	)	)	PUNCT
ejpam-5022	37	26	.	.	PUNCT
ejpam-5022	38	1	for	for	ADP
ejpam-5022	38	2	particular	particular	ADJ
ejpam-5022	38	3	values	value	NOUN
ejpam-5022	38	4	of	of	ADP
ejpam-5022	38	5	a	a	DET
ejpam-5022	38	6	,	,	PUNCT
ejpam-5022	38	7	b	b	NOUN
ejpam-5022	38	8	,	,	PUNCT
ejpam-5022	38	9	p	p	NOUN
ejpam-5022	38	10	and	and	CCONJ
ejpam-5022	38	11	q	q	PROPN
ejpam-5022	38	12	the	the	DET
ejpam-5022	38	13	horadam	horadam	PROPN
ejpam-5022	38	14	polynomials	polynomial	NOUN
ejpam-5022	38	15	leads	lead	VERB
ejpam-5022	38	16	to	to	ADP
ejpam-5022	38	17	many	many	ADJ
ejpam-5022	38	18	known	know	VERB
ejpam-5022	38	19	polynomials	polynomial	NOUN
ejpam-5022	38	20	.	.	PUNCT
ejpam-5022	39	1	below	below	ADV
ejpam-5022	39	2	,	,	PUNCT
ejpam-5022	39	3	we	we	PRON
ejpam-5022	39	4	list	list	VERB
ejpam-5022	39	5	some	some	DET
ejpam-5022	39	6	particular	particular	ADJ
ejpam-5022	39	7	cases	case	NOUN
ejpam-5022	39	8	of	of	ADP
ejpam-5022	39	9	horadam	horadam	NOUN
ejpam-5022	39	10	polynomials	polynomial	NOUN
ejpam-5022	39	11	.	.	PUNCT
ejpam-5022	40	1	•	•	INTJ
ejpam-5022	40	2	if	if	SCONJ
ejpam-5022	40	3	a	a	PRON
ejpam-5022	40	4	=	=	SYM
ejpam-5022	40	5	b	b	NOUN
ejpam-5022	40	6	=	=	SYM
ejpam-5022	41	1	p	p	NOUN
ejpam-5022	41	2	=	=	X
ejpam-5022	41	3	q	q	NOUN
ejpam-5022	41	4	=	=	NOUN
ejpam-5022	41	5	1	1	NUM
ejpam-5022	41	6	,	,	PUNCT
ejpam-5022	41	7	we	we	PRON
ejpam-5022	41	8	get	get	VERB
ejpam-5022	41	9	fibonacci	fibonacci	NOUN
ejpam-5022	41	10	polynomials	polynomial	NOUN
ejpam-5022	41	11	fn(x	fn(x	NOUN
ejpam-5022	41	12	)	)	PUNCT
ejpam-5022	41	13	whose	whose	DET
ejpam-5022	41	14	recurrence	recurrence	NOUN
ejpam-5022	41	15	relation	relation	NOUN
ejpam-5022	41	16	is	be	AUX
ejpam-5022	41	17	fn(x	fn(x	PRON
ejpam-5022	41	18	)	)	PUNCT
ejpam-5022	41	19	=	=	SYM
ejpam-5022	41	20	xfn−1(x	xfn−1(x	PRON
ejpam-5022	41	21	)	)	PUNCT
ejpam-5022	42	1	+	+	CCONJ
ejpam-5022	42	2	fn−2(x	fn−2(x	NOUN
ejpam-5022	42	3	)	)	PUNCT
ejpam-5022	42	4	;	;	PUNCT
ejpam-5022	42	5	with	with	ADP
ejpam-5022	42	6	f1(x	f1(x	NOUN
ejpam-5022	42	7	)	)	PUNCT
ejpam-5022	42	8	=	=	SYM
ejpam-5022	42	9	1	1	NUM
ejpam-5022	42	10	,	,	PUNCT
ejpam-5022	42	11	f2(x	f2(x	PROPN
ejpam-5022	42	12	)	)	PUNCT
ejpam-5022	42	13	=	=	PUNCT
ejpam-5022	43	1	x.	x.	NOUN
ejpam-5022	43	2	•	•	INTJ
ejpam-5022	43	3	if	if	SCONJ
ejpam-5022	43	4	a	a	PRON
ejpam-5022	43	5	=	=	SYM
ejpam-5022	43	6	2	2	NUM
ejpam-5022	43	7	and	and	CCONJ
ejpam-5022	43	8	b	b	NOUN
ejpam-5022	44	1	=	=	SYM
ejpam-5022	44	2	p	p	NOUN
ejpam-5022	44	3	=	=	X
ejpam-5022	44	4	q	q	NOUN
ejpam-5022	45	1	=	=	NOUN
ejpam-5022	45	2	1	1	NUM
ejpam-5022	45	3	,	,	PUNCT
ejpam-5022	45	4	we	we	PRON
ejpam-5022	45	5	get	get	VERB
ejpam-5022	45	6	lucas	lucas	NOUN
ejpam-5022	45	7	polynomials	polynomial	NOUN
ejpam-5022	45	8	ln(x	ln(x	X
ejpam-5022	45	9	)	)	PUNCT
ejpam-5022	45	10	whose	whose	DET
ejpam-5022	45	11	recurrence	recurrence	NOUN
ejpam-5022	45	12	relation	relation	NOUN
ejpam-5022	45	13	is	be	AUX
ejpam-5022	45	14	ln−1(x	ln−1(x	NOUN
ejpam-5022	45	15	)	)	PUNCT
ejpam-5022	46	1	=	=	SYM
ejpam-5022	46	2	xln−2(x	xln−2(x	X
ejpam-5022	46	3	)	)	PUNCT
ejpam-5022	46	4	+	+	NUM
ejpam-5022	46	5	ln−3(x	ln−3(x	PROPN
ejpam-5022	46	6	)	)	PUNCT
ejpam-5022	46	7	;	;	PUNCT
ejpam-5022	46	8	with	with	ADP
ejpam-5022	46	9	l0(x	l0(x	NOUN
ejpam-5022	46	10	)	)	PUNCT
ejpam-5022	46	11	=	=	SYM
ejpam-5022	46	12	2	2	NUM
ejpam-5022	46	13	,	,	PUNCT
ejpam-5022	46	14	l1(x	l1(x	NOUN
ejpam-5022	46	15	)	)	PUNCT
ejpam-5022	46	16	=	=	PUNCT
ejpam-5022	47	1	x.	x.	NOUN
ejpam-5022	47	2	•	•	INTJ
ejpam-5022	47	3	if	if	SCONJ
ejpam-5022	47	4	a	a	PRON
ejpam-5022	47	5	=	=	X
ejpam-5022	47	6	q	q	NOUN
ejpam-5022	47	7	=	=	SYM
ejpam-5022	47	8	1	1	NUM
ejpam-5022	47	9	and	and	CCONJ
ejpam-5022	47	10	b	b	X
ejpam-5022	48	1	=	=	SYM
ejpam-5022	48	2	p	p	NOUN
ejpam-5022	48	3	=	=	SYM
ejpam-5022	48	4	2	2	NUM
ejpam-5022	48	5	,	,	PUNCT
ejpam-5022	48	6	we	we	PRON
ejpam-5022	48	7	get	get	VERB
ejpam-5022	48	8	pell	pell	NOUN
ejpam-5022	48	9	polynomials	polynomial	NOUN
ejpam-5022	48	10	pn(x	pn(x	PRON
ejpam-5022	48	11	)	)	PUNCT
ejpam-5022	48	12	whose	whose	DET
ejpam-5022	48	13	recurrence	recurrence	NOUN
ejpam-5022	48	14	relation	relation	NOUN
ejpam-5022	48	15	is	be	AUX
ejpam-5022	48	16	pn(x	pn(x	PRON
ejpam-5022	48	17	)	)	PUNCT
ejpam-5022	48	18	=	=	SYM
ejpam-5022	48	19	2xpn−1(x	2xpn−1(x	NUM
ejpam-5022	48	20	)	)	PUNCT
ejpam-5022	49	1	+	+	NUM
ejpam-5022	49	2	pn−2(x	pn−2(x	NOUN
ejpam-5022	49	3	)	)	PUNCT
ejpam-5022	49	4	;	;	PUNCT
ejpam-5022	49	5	with	with	ADP
ejpam-5022	49	6	p1(x	p1(x	NOUN
ejpam-5022	49	7	)	)	PUNCT
ejpam-5022	49	8	=	=	SYM
ejpam-5022	49	9	1	1	NUM
ejpam-5022	49	10	,	,	PUNCT
ejpam-5022	49	11	p2(x	p2(x	NOUN
ejpam-5022	49	12	)	)	PUNCT
ejpam-5022	49	13	=	=	SYM
ejpam-5022	49	14	2x	2x	NUM
ejpam-5022	49	15	.	.	PUNCT
ejpam-5022	50	1	w.	w.	PROPN
ejpam-5022	50	2	al	al	PROPN
ejpam-5022	50	3	-	-	PUNCT
ejpam-5022	50	4	rawashdeh	rawashdeh	PROPN
ejpam-5022	50	5	/	/	SYM
ejpam-5022	50	6	eur	eur	PROPN
ejpam-5022	50	7	.	.	PUNCT
ejpam-5022	51	1	j.	j.	PROPN
ejpam-5022	51	2	pure	pure	PROPN
ejpam-5022	51	3	appl	appl	PROPN
ejpam-5022	51	4	.	.	PROPN
ejpam-5022	51	5	math	math	PROPN
ejpam-5022	51	6	,	,	PUNCT
ejpam-5022	51	7	17	17	NUM
ejpam-5022	51	8	(	(	PUNCT
ejpam-5022	51	9	1	1	NUM
ejpam-5022	51	10	)	)	PUNCT
ejpam-5022	51	11	(	(	PUNCT
ejpam-5022	51	12	2024	2024	NUM
ejpam-5022	51	13	)	)	PUNCT
ejpam-5022	51	14	,	,	PUNCT
ejpam-5022	51	15	158	158	NUM
ejpam-5022	51	16	-	-	SYM
ejpam-5022	51	17	170	170	NUM
ejpam-5022	51	18	160	160	NUM
ejpam-5022	51	19	•	•	NOUN
ejpam-5022	51	20	if	if	SCONJ
ejpam-5022	51	21	a	a	PRON
ejpam-5022	51	22	=	=	SYM
ejpam-5022	51	23	b	b	NOUN
ejpam-5022	51	24	=	=	SYM
ejpam-5022	51	25	p	p	NOUN
ejpam-5022	51	26	=	=	SYM
ejpam-5022	51	27	2	2	NUM
ejpam-5022	51	28	and	and	CCONJ
ejpam-5022	51	29	q	q	NOUN
ejpam-5022	52	1	=	=	NOUN
ejpam-5022	52	2	1	1	NUM
ejpam-5022	52	3	,	,	PUNCT
ejpam-5022	52	4	we	we	PRON
ejpam-5022	52	5	get	get	VERB
ejpam-5022	52	6	pell	pell	NOUN
ejpam-5022	52	7	-	-	PUNCT
ejpam-5022	52	8	lucas	lucas	NOUN
ejpam-5022	52	9	polynomials	polynomial	NOUN
ejpam-5022	52	10	qn(x	qn(x	NOUN
ejpam-5022	52	11	)	)	PUNCT
ejpam-5022	52	12	whose	whose	DET
ejpam-5022	52	13	recurrence	recurrence	NOUN
ejpam-5022	52	14	relation	relation	NOUN
ejpam-5022	52	15	is	be	AUX
ejpam-5022	52	16	qn−1(x	qn−1(x	NOUN
ejpam-5022	52	17	)	)	PUNCT
ejpam-5022	53	1	=	=	SYM
ejpam-5022	53	2	2xqn−2(x	2xqn−2(x	NUM
ejpam-5022	53	3	)	)	PUNCT
ejpam-5022	53	4	+	+	NOUN
ejpam-5022	53	5	qn−3(x	qn−3(x	PROPN
ejpam-5022	53	6	)	)	PUNCT
ejpam-5022	53	7	;	;	PUNCT
ejpam-5022	53	8	with	with	ADP
ejpam-5022	53	9	q0(x	q0(x	NOUN
ejpam-5022	53	10	)	)	PUNCT
ejpam-5022	53	11	=	=	SYM
ejpam-5022	53	12	2	2	NUM
ejpam-5022	53	13	,	,	PUNCT
ejpam-5022	53	14	q1(x	q1(x	NOUN
ejpam-5022	53	15	)	)	PUNCT
ejpam-5022	53	16	=	=	SYM
ejpam-5022	53	17	2x	2x	NUM
ejpam-5022	53	18	.	.	PUNCT
ejpam-5022	54	1	•	•	NOUN
ejpam-5022	54	2	if	if	SCONJ
ejpam-5022	54	3	a	a	PRON
ejpam-5022	54	4	=	=	SYM
ejpam-5022	54	5	b	b	NOUN
ejpam-5022	54	6	=	=	SYM
ejpam-5022	54	7	p	p	NOUN
ejpam-5022	54	8	=	=	PUNCT
ejpam-5022	54	9	x	x	SYM
ejpam-5022	54	10	=	=	SYM
ejpam-5022	54	11	1	1	NUM
ejpam-5022	54	12	and	and	CCONJ
ejpam-5022	54	13	q	q	NOUN
ejpam-5022	55	1	=	=	NOUN
ejpam-5022	55	2	2y	2y	NUM
ejpam-5022	55	3	,	,	PUNCT
ejpam-5022	55	4	we	we	PRON
ejpam-5022	55	5	get	get	VERB
ejpam-5022	55	6	jacobsthal	jacobsthal	ADJ
ejpam-5022	55	7	polynomials	polynomial	NOUN
ejpam-5022	55	8	jn(y	jn(y	NOUN
ejpam-5022	55	9	)	)	PUNCT
ejpam-5022	56	1	whose	whose	DET
ejpam-5022	56	2	recurrence	recurrence	NOUN
ejpam-5022	56	3	relation	relation	NOUN
ejpam-5022	56	4	is	be	AUX
ejpam-5022	56	5	jn(y	jn(y	X
ejpam-5022	56	6	)	)	PUNCT
ejpam-5022	57	1	=	=	SYM
ejpam-5022	57	2	jn−1(y	jn−1(y	ADV
ejpam-5022	57	3	)	)	PUNCT
ejpam-5022	58	1	+	+	CCONJ
ejpam-5022	59	1	2yjn−2(y	2yjn−2(y	NUM
ejpam-5022	59	2	)	)	PUNCT
ejpam-5022	59	3	;	;	PUNCT
ejpam-5022	59	4	with	with	ADP
ejpam-5022	59	5	j1(y	j1(y	PROPN
ejpam-5022	59	6	)	)	PUNCT
ejpam-5022	59	7	=	=	SYM
ejpam-5022	59	8	1	1	NUM
ejpam-5022	59	9	,	,	PUNCT
ejpam-5022	59	10	j2(y	j2(y	NOUN
ejpam-5022	59	11	)	)	PUNCT
ejpam-5022	59	12	=	=	SYM
ejpam-5022	60	1	1	1	X
ejpam-5022	60	2	.	.	NOUN
ejpam-5022	60	3	•	•	NOUN
ejpam-5022	60	4	if	if	SCONJ
ejpam-5022	60	5	a	a	PRON
ejpam-5022	60	6	=	=	SYM
ejpam-5022	60	7	2	2	NUM
ejpam-5022	60	8	,	,	PUNCT
ejpam-5022	60	9	b	b	NOUN
ejpam-5022	60	10	=	=	SYM
ejpam-5022	60	11	p	p	NOUN
ejpam-5022	60	12	=	=	PUNCT
ejpam-5022	60	13	x	x	SYM
ejpam-5022	60	14	=	=	SYM
ejpam-5022	60	15	1	1	NUM
ejpam-5022	60	16	and	and	CCONJ
ejpam-5022	60	17	q	q	NOUN
ejpam-5022	60	18	=	=	NOUN
ejpam-5022	60	19	2y	2y	NUM
ejpam-5022	60	20	,	,	PUNCT
ejpam-5022	60	21	we	we	PRON
ejpam-5022	60	22	get	get	VERB
ejpam-5022	60	23	jacobsthal	jacobsthal	ADJ
ejpam-5022	60	24	-	-	PUNCT
ejpam-5022	60	25	lucas	lucas	ADJ
ejpam-5022	60	26	polynomials	polynomial	NOUN
ejpam-5022	60	27	jn(y	jn(y	ADV
ejpam-5022	60	28	)	)	PUNCT
ejpam-5022	61	1	whose	whose	DET
ejpam-5022	61	2	recurrence	recurrence	NOUN
ejpam-5022	61	3	relation	relation	NOUN
ejpam-5022	61	4	is	be	AUX
ejpam-5022	61	5	jn−1(y	jn−1(y	ADJ
ejpam-5022	61	6	)	)	PUNCT
ejpam-5022	62	1	=	=	SYM
ejpam-5022	62	2	jn−2(y	jn−2(y	PROPN
ejpam-5022	62	3	)	)	PUNCT
ejpam-5022	62	4	+	+	CCONJ
ejpam-5022	62	5	2yjn−3(y	2yjn−3(y	NUM
ejpam-5022	62	6	)	)	PUNCT
ejpam-5022	62	7	;	;	PUNCT
ejpam-5022	62	8	with	with	ADP
ejpam-5022	62	9	j0(y	j0(y	PROPN
ejpam-5022	62	10	)	)	PUNCT
ejpam-5022	62	11	=	=	SYM
ejpam-5022	62	12	2	2	NUM
ejpam-5022	62	13	,	,	PUNCT
ejpam-5022	62	14	j1(y	j1(y	PROPN
ejpam-5022	62	15	)	)	PUNCT
ejpam-5022	62	16	=	=	SYM
ejpam-5022	63	1	1	1	X
ejpam-5022	63	2	.	.	NOUN
ejpam-5022	63	3	•	•	NOUN
ejpam-5022	63	4	if	if	SCONJ
ejpam-5022	63	5	a	a	PRON
ejpam-5022	63	6	=	=	SYM
ejpam-5022	63	7	1	1	NUM
ejpam-5022	63	8	and	and	CCONJ
ejpam-5022	63	9	b	b	X
ejpam-5022	63	10	=	=	SYM
ejpam-5022	64	1	p	p	NOUN
ejpam-5022	64	2	=	=	SYM
ejpam-5022	64	3	2	2	NUM
ejpam-5022	64	4	,	,	PUNCT
ejpam-5022	64	5	and	and	CCONJ
ejpam-5022	64	6	q	q	NOUN
ejpam-5022	64	7	=	=	SYM
ejpam-5022	64	8	−1	−1	NOUN
ejpam-5022	64	9	,	,	PUNCT
ejpam-5022	64	10	we	we	PRON
ejpam-5022	64	11	get	get	VERB
ejpam-5022	64	12	chebyshev	chebyshev	NOUN
ejpam-5022	64	13	polynomials	polynomial	NOUN
ejpam-5022	64	14	hn(x	hn(x	ADP
ejpam-5022	64	15	)	)	PUNCT
ejpam-5022	64	16	of	of	ADP
ejpam-5022	64	17	the	the	DET
ejpam-5022	64	18	second	second	ADJ
ejpam-5022	64	19	kind	kind	NOUN
ejpam-5022	64	20	whose	whose	DET
ejpam-5022	64	21	recurrence	recurrence	NOUN
ejpam-5022	64	22	relation	relation	NOUN
ejpam-5022	64	23	is	be	AUX
ejpam-5022	64	24	hn−1(x	hn−1(x	NOUN
ejpam-5022	64	25	)	)	PUNCT
ejpam-5022	65	1	=	=	SYM
ejpam-5022	65	2	2xhn−2(x)−hn−3(x	2xhn−2(x)−hn−3(x	NUM
ejpam-5022	65	3	)	)	PUNCT
ejpam-5022	65	4	;	;	PUNCT
ejpam-5022	65	5	with	with	ADP
ejpam-5022	65	6	h0(x	h0(x	NOUN
ejpam-5022	65	7	)	)	PUNCT
ejpam-5022	65	8	=	=	SYM
ejpam-5022	65	9	1	1	NUM
ejpam-5022	65	10	,	,	PUNCT
ejpam-5022	65	11	h1(x	h1(x	NOUN
ejpam-5022	65	12	)	)	PUNCT
ejpam-5022	65	13	=	=	SYM
ejpam-5022	65	14	2x	2x	NUM
ejpam-5022	65	15	.	.	PUNCT
ejpam-5022	66	1	•	•	NOUN
ejpam-5022	66	2	if	if	SCONJ
ejpam-5022	66	3	a	a	DET
ejpam-5022	66	4	=	=	SYM
ejpam-5022	66	5	b	b	NOUN
ejpam-5022	66	6	=	=	SYM
ejpam-5022	66	7	1	1	NUM
ejpam-5022	66	8	and	and	CCONJ
ejpam-5022	66	9	p	p	NOUN
ejpam-5022	66	10	=	=	PROPN
ejpam-5022	66	11	2	2	NUM
ejpam-5022	66	12	,	,	PUNCT
ejpam-5022	66	13	and	and	CCONJ
ejpam-5022	66	14	q	q	NOUN
ejpam-5022	66	15	=	=	SYM
ejpam-5022	66	16	−1	−1	NOUN
ejpam-5022	66	17	,	,	PUNCT
ejpam-5022	66	18	we	we	PRON
ejpam-5022	66	19	get	get	VERB
ejpam-5022	66	20	chebyshev	chebyshev	NOUN
ejpam-5022	66	21	polynomials	polynomial	NOUN
ejpam-5022	66	22	tn(x	tn(x	PUNCT
ejpam-5022	66	23	)	)	PUNCT
ejpam-5022	66	24	of	of	ADP
ejpam-5022	66	25	the	the	DET
ejpam-5022	66	26	first	first	ADJ
ejpam-5022	66	27	kind	kind	NOUN
ejpam-5022	66	28	whose	whose	DET
ejpam-5022	66	29	recurrence	recurrence	NOUN
ejpam-5022	66	30	relation	relation	NOUN
ejpam-5022	66	31	is	be	AUX
ejpam-5022	66	32	tn−1(x	tn−1(x	ADJ
ejpam-5022	66	33	)	)	PUNCT
ejpam-5022	67	1	=	=	PUNCT
ejpam-5022	67	2	2xtn−2(x)−	2xtn−2(x)−	NUM
ejpam-5022	67	3	tn−3(x	tn−3(x	PROPN
ejpam-5022	67	4	)	)	PUNCT
ejpam-5022	67	5	;	;	PUNCT
ejpam-5022	67	6	with	with	ADP
ejpam-5022	67	7	t0(x	t0(x	NOUN
ejpam-5022	67	8	)	)	PUNCT
ejpam-5022	67	9	=	=	SYM
ejpam-5022	67	10	1	1	NUM
ejpam-5022	67	11	,	,	PUNCT
ejpam-5022	67	12	t1(x	t1(x	NOUN
ejpam-5022	67	13	)	)	PUNCT
ejpam-5022	67	14	=	=	PUNCT
ejpam-5022	67	15	x.	x.	NOUN
ejpam-5022	67	16	for	for	ADP
ejpam-5022	67	17	more	more	ADJ
ejpam-5022	67	18	information	information	NOUN
ejpam-5022	67	19	about	about	ADP
ejpam-5022	67	20	horadam	horadam	NOUN
ejpam-5022	67	21	polynomials	polynomial	NOUN
ejpam-5022	67	22	and	and	CCONJ
ejpam-5022	67	23	its	its	PRON
ejpam-5022	67	24	special	special	ADJ
ejpam-5022	67	25	interesting	interesting	ADJ
ejpam-5022	67	26	cases	case	NOUN
ejpam-5022	67	27	,	,	PUNCT
ejpam-5022	67	28	we	we	PRON
ejpam-5022	67	29	refer	refer	VERB
ejpam-5022	67	30	the	the	DET
ejpam-5022	67	31	readers	reader	NOUN
ejpam-5022	67	32	to	to	ADP
ejpam-5022	67	33	the	the	DET
ejpam-5022	67	34	articles	article	NOUN
ejpam-5022	67	35	[	[	X
ejpam-5022	67	36	1	1	NUM
ejpam-5022	67	37	]	]	PUNCT
ejpam-5022	67	38	,	,	PUNCT
ejpam-5022	67	39	[	[	X
ejpam-5022	67	40	3	3	NUM
ejpam-5022	67	41	]	]	PUNCT
ejpam-5022	67	42	,	,	PUNCT
ejpam-5022	67	43	[	[	X
ejpam-5022	67	44	2	2	NUM
ejpam-5022	67	45	]	]	PUNCT
ejpam-5022	67	46	,	,	PUNCT
ejpam-5022	67	47	[	[	X
ejpam-5022	67	48	16	16	NUM
ejpam-5022	67	49	]	]	PUNCT
ejpam-5022	67	50	,	,	PUNCT
ejpam-5022	67	51	[	[	X
ejpam-5022	67	52	18	18	NUM
ejpam-5022	67	53	]	]	PUNCT
ejpam-5022	67	54	,	,	PUNCT
ejpam-5022	67	55	[	[	X
ejpam-5022	67	56	24	24	NUM
ejpam-5022	67	57	]	]	PUNCT
ejpam-5022	67	58	,	,	PUNCT
ejpam-5022	67	59	[	[	X
ejpam-5022	67	60	26	26	NUM
ejpam-5022	67	61	]	]	PUNCT
ejpam-5022	67	62	,	,	PUNCT
ejpam-5022	67	63	[	[	X
ejpam-5022	67	64	27	27	NUM
ejpam-5022	67	65	]	]	PUNCT
ejpam-5022	67	66	,	,	PUNCT
ejpam-5022	67	67	[	[	X
ejpam-5022	67	68	30	30	NUM
ejpam-5022	67	69	]	]	PUNCT
ejpam-5022	67	70	,	,	PUNCT
ejpam-5022	67	71	the	the	DET
ejpam-5022	67	72	monograph	monograph	NOUN
ejpam-5022	68	1	[	[	X
ejpam-5022	68	2	21	21	NUM
ejpam-5022	68	3	]	]	PUNCT
ejpam-5022	68	4	,	,	PUNCT
ejpam-5022	68	5	[	[	X
ejpam-5022	68	6	29	29	NUM
ejpam-5022	68	7	]	]	PUNCT
ejpam-5022	68	8	and	and	CCONJ
ejpam-5022	68	9	the	the	DET
ejpam-5022	68	10	references	reference	NOUN
ejpam-5022	68	11	therein	therein	ADV
ejpam-5022	68	12	.	.	PUNCT
ejpam-5022	69	1	recently	recently	ADV
ejpam-5022	69	2	,	,	PUNCT
ejpam-5022	69	3	many	many	ADJ
ejpam-5022	69	4	researchers	researcher	NOUN
ejpam-5022	69	5	have	have	AUX
ejpam-5022	69	6	been	be	AUX
ejpam-5022	69	7	studying	study	VERB
ejpam-5022	69	8	the	the	DET
ejpam-5022	69	9	geometric	geometric	ADJ
ejpam-5022	69	10	function	function	NOUN
ejpam-5022	69	11	theory	theory	NOUN
ejpam-5022	69	12	,	,	PUNCT
ejpam-5022	69	13	the	the	DET
ejpam-5022	69	14	typical	typical	ADJ
ejpam-5022	69	15	problem	problem	NOUN
ejpam-5022	69	16	in	in	ADP
ejpam-5022	69	17	this	this	DET
ejpam-5022	69	18	field	field	NOUN
ejpam-5022	69	19	is	be	AUX
ejpam-5022	69	20	studying	study	VERB
ejpam-5022	69	21	a	a	DET
ejpam-5022	69	22	functional	functional	ADJ
ejpam-5022	69	23	made	make	VERB
ejpam-5022	69	24	up	up	ADP
ejpam-5022	69	25	of	of	ADP
ejpam-5022	69	26	combinations	combination	NOUN
ejpam-5022	69	27	of	of	ADP
ejpam-5022	69	28	the	the	DET
ejpam-5022	69	29	initial	initial	ADJ
ejpam-5022	69	30	coefficients	coefficient	NOUN
ejpam-5022	69	31	of	of	ADP
ejpam-5022	69	32	the	the	DET
ejpam-5022	69	33	functions	function	NOUN
ejpam-5022	69	34	f	f	PROPN
ejpam-5022	69	35	∈	∈	PROPN
ejpam-5022	69	36	a.	a.	NOUN
ejpam-5022	69	37	for	for	ADP
ejpam-5022	69	38	a	a	DET
ejpam-5022	69	39	function	function	NOUN
ejpam-5022	69	40	in	in	ADP
ejpam-5022	69	41	the	the	DET
ejpam-5022	69	42	class	class	NOUN
ejpam-5022	69	43	s	s	PART
ejpam-5022	69	44	,	,	PUNCT
ejpam-5022	69	45	it	it	PRON
ejpam-5022	69	46	is	be	AUX
ejpam-5022	69	47	well	well	ADV
ejpam-5022	69	48	-	-	PUNCT
ejpam-5022	69	49	known	know	VERB
ejpam-5022	69	50	that	that	SCONJ
ejpam-5022	69	51	|an|	|an|	PROPN
ejpam-5022	69	52	is	be	AUX
ejpam-5022	69	53	bounded	bound	VERB
ejpam-5022	69	54	by	by	ADP
ejpam-5022	69	55	n.	n.	PROPN
ejpam-5022	69	56	moreover	moreover	ADV
ejpam-5022	69	57	,	,	PUNCT
ejpam-5022	69	58	the	the	DET
ejpam-5022	69	59	coefficient	coefficient	NOUN
ejpam-5022	69	60	bounds	bound	NOUN
ejpam-5022	69	61	give	give	VERB
ejpam-5022	69	62	information	information	NOUN
ejpam-5022	69	63	about	about	ADP
ejpam-5022	69	64	the	the	DET
ejpam-5022	69	65	geometric	geometric	ADJ
ejpam-5022	69	66	properties	property	NOUN
ejpam-5022	69	67	of	of	ADP
ejpam-5022	69	68	those	those	DET
ejpam-5022	69	69	functions	function	NOUN
ejpam-5022	69	70	.	.	PUNCT
ejpam-5022	70	1	for	for	ADP
ejpam-5022	70	2	instance	instance	NOUN
ejpam-5022	70	3	,	,	PUNCT
ejpam-5022	70	4	the	the	DET
ejpam-5022	70	5	bound	bind	VERB
ejpam-5022	70	6	for	for	ADP
ejpam-5022	70	7	the	the	DET
ejpam-5022	70	8	second	second	ADJ
ejpam-5022	70	9	coefficients	coefficient	NOUN
ejpam-5022	70	10	of	of	ADP
ejpam-5022	70	11	the	the	DET
ejpam-5022	70	12	class	class	NOUN
ejpam-5022	70	13	s	s	PART
ejpam-5022	70	14	gives	give	VERB
ejpam-5022	70	15	the	the	DET
ejpam-5022	70	16	growth	growth	NOUN
ejpam-5022	70	17	and	and	CCONJ
ejpam-5022	70	18	distortion	distortion	NOUN
ejpam-5022	70	19	bounds	bound	NOUN
ejpam-5022	70	20	for	for	ADP
ejpam-5022	70	21	the	the	DET
ejpam-5022	70	22	class	class	NOUN
ejpam-5022	70	23	.	.	PUNCT
ejpam-5022	71	1	in	in	ADP
ejpam-5022	71	2	addition	addition	NOUN
ejpam-5022	71	3	,	,	PUNCT
ejpam-5022	71	4	the	the	DET
ejpam-5022	71	5	fekete	fekete	PROPN
ejpam-5022	71	6	-	-	PUNCT
ejpam-5022	71	7	szegö	szegö	ADJ
ejpam-5022	71	8	functional	functional	NOUN
ejpam-5022	71	9	arises	arise	VERB
ejpam-5022	71	10	naturally	naturally	ADV
ejpam-5022	71	11	in	in	ADP
ejpam-5022	71	12	the	the	DET
ejpam-5022	71	13	investigation	investigation	NOUN
ejpam-5022	71	14	of	of	ADP
ejpam-5022	71	15	univalency	univalency	NOUN
ejpam-5022	71	16	of	of	ADP
ejpam-5022	71	17	analytic	analytic	ADJ
ejpam-5022	71	18	functions	function	NOUN
ejpam-5022	71	19	.	.	PUNCT
ejpam-5022	72	1	in	in	ADP
ejpam-5022	72	2	the	the	DET
ejpam-5022	72	3	year	year	NOUN
ejpam-5022	72	4	1933	1933	NUM
ejpam-5022	72	5	,	,	PUNCT
ejpam-5022	72	6	fekete	fekete	PROPN
ejpam-5022	72	7	and	and	CCONJ
ejpam-5022	72	8	szegö	szegö	VERB
ejpam-5022	73	1	[	[	X
ejpam-5022	73	2	13	13	NUM
ejpam-5022	73	3	]	]	PUNCT
ejpam-5022	73	4	found	find	VERB
ejpam-5022	73	5	the	the	DET
ejpam-5022	73	6	maximum	maximum	ADJ
ejpam-5022	73	7	value	value	NOUN
ejpam-5022	73	8	of	of	ADP
ejpam-5022	73	9	|a3	|a3	NOUN
ejpam-5022	73	10	−	−	PROPN
ejpam-5022	73	11	λa22|	λa22|	NOUN
ejpam-5022	73	12	,	,	PUNCT
ejpam-5022	73	13	as	as	ADP
ejpam-5022	73	14	a	a	DET
ejpam-5022	73	15	function	function	NOUN
ejpam-5022	73	16	of	of	ADP
ejpam-5022	73	17	the	the	DET
ejpam-5022	73	18	real	real	ADJ
ejpam-5022	73	19	parameter	parameter	NOUN
ejpam-5022	73	20	0	0	NUM
ejpam-5022	73	21	≤	≤	NUM
ejpam-5022	74	1	λ	λ	X
ejpam-5022	74	2	≤	≤	NOUN
ejpam-5022	74	3	1	1	NUM
ejpam-5022	74	4	for	for	ADP
ejpam-5022	74	5	a	a	DET
ejpam-5022	74	6	univalent	univalent	ADJ
ejpam-5022	74	7	function	function	NOUN
ejpam-5022	74	8	f	f	PROPN
ejpam-5022	74	9	.	.	PUNCT
ejpam-5022	75	1	since	since	SCONJ
ejpam-5022	75	2	then	then	ADV
ejpam-5022	75	3	,	,	PUNCT
ejpam-5022	75	4	the	the	DET
ejpam-5022	75	5	problem	problem	NOUN
ejpam-5022	75	6	of	of	ADP
ejpam-5022	75	7	dealing	deal	VERB
ejpam-5022	75	8	with	with	ADP
ejpam-5022	75	9	the	the	DET
ejpam-5022	75	10	fekete	fekete	NOUN
ejpam-5022	75	11	-	-	PUNCT
ejpam-5022	75	12	szegö	szegö	ADJ
ejpam-5022	75	13	functional	functional	NOUN
ejpam-5022	75	14	for	for	ADP
ejpam-5022	75	15	f	f	PROPN
ejpam-5022	75	16	∈	∈	PROPN
ejpam-5022	75	17	a	a	PRON
ejpam-5022	75	18	with	with	ADP
ejpam-5022	75	19	any	any	DET
ejpam-5022	75	20	complex	complex	ADJ
ejpam-5022	75	21	λ	λ	NOUN
ejpam-5022	75	22	is	be	AUX
ejpam-5022	75	23	known	know	VERB
ejpam-5022	75	24	as	as	ADP
ejpam-5022	75	25	the	the	DET
ejpam-5022	75	26	classical	classical	ADJ
ejpam-5022	75	27	fekete	fekete	PROPN
ejpam-5022	75	28	-	-	PUNCT
ejpam-5022	75	29	szegö	szegö	PROPN
ejpam-5022	75	30	problem	problem	NOUN
ejpam-5022	75	31	.	.	PUNCT
ejpam-5022	76	1	there	there	PRON
ejpam-5022	76	2	are	be	VERB
ejpam-5022	76	3	many	many	ADJ
ejpam-5022	76	4	researchers	researcher	NOUN
ejpam-5022	76	5	investigated	investigate	VERB
ejpam-5022	76	6	the	the	DET
ejpam-5022	76	7	fekete	fekete	PROPN
ejpam-5022	76	8	-	-	PUNCT
ejpam-5022	76	9	szegö	szegö	ADJ
ejpam-5022	76	10	functional	functional	ADJ
ejpam-5022	76	11	and	and	CCONJ
ejpam-5022	76	12	the	the	DET
ejpam-5022	76	13	other	other	ADJ
ejpam-5022	76	14	coefficient	coefficient	NOUN
ejpam-5022	76	15	estimates	estimate	VERB
ejpam-5022	76	16	problems	problem	NOUN
ejpam-5022	76	17	,	,	PUNCT
ejpam-5022	76	18	for	for	ADP
ejpam-5022	76	19	example	example	NOUN
ejpam-5022	76	20	see	see	VERB
ejpam-5022	76	21	the	the	DET
ejpam-5022	76	22	articles	article	NOUN
ejpam-5022	76	23	[	[	X
ejpam-5022	76	24	1	1	NUM
ejpam-5022	76	25	]	]	PUNCT
ejpam-5022	76	26	,	,	PUNCT
ejpam-5022	76	27	[	[	X
ejpam-5022	76	28	5	5	NUM
ejpam-5022	76	29	]	]	PUNCT
ejpam-5022	76	30	,	,	PUNCT
ejpam-5022	76	31	[	[	X
ejpam-5022	76	32	4	4	NUM
ejpam-5022	76	33	]	]	PUNCT
ejpam-5022	76	34	,	,	PUNCT
ejpam-5022	76	35	[	[	X
ejpam-5022	76	36	6	6	NUM
ejpam-5022	76	37	]	]	PUNCT
ejpam-5022	76	38	,	,	PUNCT
ejpam-5022	76	39	[	[	X
ejpam-5022	76	40	9	9	NUM
ejpam-5022	76	41	]	]	PUNCT
ejpam-5022	76	42	,	,	PUNCT
ejpam-5022	76	43	[	[	X
ejpam-5022	76	44	13	13	NUM
ejpam-5022	76	45	]	]	PUNCT
ejpam-5022	76	46	,	,	PUNCT
ejpam-5022	76	47	[	[	X
ejpam-5022	76	48	20	20	NUM
ejpam-5022	76	49	]	]	PUNCT
ejpam-5022	76	50	,	,	PUNCT
ejpam-5022	76	51	[	[	X
ejpam-5022	76	52	22	22	NUM
ejpam-5022	76	53	]	]	PUNCT
ejpam-5022	76	54	,	,	PUNCT
ejpam-5022	76	55	[	[	X
ejpam-5022	76	56	27	27	NUM
ejpam-5022	76	57	]	]	PUNCT
ejpam-5022	76	58	,	,	PUNCT
ejpam-5022	76	59	[	[	X
ejpam-5022	76	60	30	30	NUM
ejpam-5022	76	61	]	]	PUNCT
ejpam-5022	76	62	and	and	CCONJ
ejpam-5022	76	63	the	the	DET
ejpam-5022	76	64	references	reference	NOUN
ejpam-5022	76	65	therein	therein	ADV
ejpam-5022	76	66	.	.	PUNCT
ejpam-5022	77	1	motivated	motivate	VERB
ejpam-5022	77	2	by	by	ADP
ejpam-5022	77	3	the	the	DET
ejpam-5022	77	4	aforementioned	aforementioned	ADJ
ejpam-5022	77	5	research	research	NOUN
ejpam-5022	77	6	and	and	CCONJ
ejpam-5022	77	7	the	the	DET
ejpam-5022	77	8	papers	paper	NOUN
ejpam-5022	77	9	[	[	X
ejpam-5022	77	10	3	3	NUM
ejpam-5022	77	11	]	]	PUNCT
ejpam-5022	77	12	,	,	PUNCT
ejpam-5022	77	13	[	[	X
ejpam-5022	77	14	2	2	NUM
ejpam-5022	77	15	]	]	PUNCT
ejpam-5022	77	16	and	and	CCONJ
ejpam-5022	77	17	[	[	X
ejpam-5022	77	18	28	28	NUM
ejpam-5022	77	19	]	]	X
ejpam-5022	77	20	we	we	PRON
ejpam-5022	77	21	introduce	introduce	VERB
ejpam-5022	77	22	a	a	DET
ejpam-5022	77	23	novel	novel	ADJ
ejpam-5022	77	24	class	class	NOUN
ejpam-5022	77	25	of	of	ADP
ejpam-5022	77	26	analytic	analytic	ADJ
ejpam-5022	77	27	functions	function	NOUN
ejpam-5022	77	28	defined	define	VERB
ejpam-5022	77	29	using	use	VERB
ejpam-5022	77	30	horadam	horadam	NOUN
ejpam-5022	77	31	polynomials	polynomial	NOUN
ejpam-5022	77	32	.	.	PUNCT
ejpam-5022	78	1	for	for	SCONJ
ejpam-5022	78	2	functions	function	NOUN
ejpam-5022	78	3	belong	belong	VERB
ejpam-5022	78	4	to	to	ADP
ejpam-5022	78	5	this	this	DET
ejpam-5022	78	6	function	function	NOUN
ejpam-5022	78	7	class	class	NOUN
ejpam-5022	78	8	,	,	PUNCT
ejpam-5022	78	9	we	we	PRON
ejpam-5022	78	10	derive	derive	VERB
ejpam-5022	78	11	estimations	estimation	NOUN
ejpam-5022	78	12	for	for	ADP
ejpam-5022	78	13	the	the	DET
ejpam-5022	78	14	taylor	taylor	PROPN
ejpam-5022	78	15	-	-	PUNCT
ejpam-5022	78	16	maclaurin	maclaurin	NOUN
ejpam-5022	78	17	initial	initial	ADJ
ejpam-5022	78	18	coefficients	coefficient	NOUN
ejpam-5022	78	19	and	and	CCONJ
ejpam-5022	78	20	fekete	fekete	PROPN
ejpam-5022	78	21	-	-	PUNCT
ejpam-5022	78	22	szegö	szegö	ADJ
ejpam-5022	78	23	functional	functional	ADJ
ejpam-5022	78	24	problem	problem	NOUN
ejpam-5022	78	25	.	.	PUNCT
ejpam-5022	79	1	we	we	PRON
ejpam-5022	79	2	also	also	ADV
ejpam-5022	79	3	present	present	VERB
ejpam-5022	79	4	corollaries	corollary	NOUN
ejpam-5022	79	5	for	for	ADP
ejpam-5022	79	6	subclasses	subclass	NOUN
ejpam-5022	79	7	of	of	ADP
ejpam-5022	79	8	our	our	PRON
ejpam-5022	79	9	class	class	NOUN
ejpam-5022	79	10	defined	define	VERB
ejpam-5022	79	11	by	by	ADP
ejpam-5022	79	12	the	the	DET
ejpam-5022	79	13	means	mean	NOUN
ejpam-5022	79	14	of	of	ADP
ejpam-5022	79	15	special	special	ADJ
ejpam-5022	79	16	cases	case	NOUN
ejpam-5022	79	17	of	of	ADP
ejpam-5022	79	18	horadam	horadam	NOUN
ejpam-5022	79	19	polynomials	polynomial	NOUN
ejpam-5022	79	20	.	.	PUNCT
ejpam-5022	80	1	w.	w.	PROPN
ejpam-5022	80	2	al	al	PROPN
ejpam-5022	80	3	-	-	PUNCT
ejpam-5022	80	4	rawashdeh	rawashdeh	PROPN
ejpam-5022	80	5	/	/	SYM
ejpam-5022	80	6	eur	eur	PROPN
ejpam-5022	80	7	.	.	PUNCT
ejpam-5022	81	1	j.	j.	PROPN
ejpam-5022	81	2	pure	pure	PROPN
ejpam-5022	81	3	appl	appl	PROPN
ejpam-5022	81	4	.	.	PROPN
ejpam-5022	81	5	math	math	PROPN
ejpam-5022	81	6	,	,	PUNCT
ejpam-5022	81	7	17	17	NUM
ejpam-5022	81	8	(	(	PUNCT
ejpam-5022	81	9	1	1	NUM
ejpam-5022	81	10	)	)	PUNCT
ejpam-5022	81	11	(	(	PUNCT
ejpam-5022	81	12	2024	2024	NUM
ejpam-5022	81	13	)	)	PUNCT
ejpam-5022	81	14	,	,	PUNCT
ejpam-5022	81	15	158	158	NUM
ejpam-5022	81	16	-	-	SYM
ejpam-5022	81	17	170	170	NUM
ejpam-5022	81	18	161	161	NUM
ejpam-5022	81	19	2	2	NUM
ejpam-5022	81	20	.	.	PUNCT
ejpam-5022	81	21	preliminaries	preliminary	NOUN
ejpam-5022	81	22	in	in	ADP
ejpam-5022	81	23	this	this	DET
ejpam-5022	81	24	section	section	NOUN
ejpam-5022	81	25	we	we	PRON
ejpam-5022	81	26	present	present	VERB
ejpam-5022	81	27	some	some	DET
ejpam-5022	81	28	information	information	NOUN
ejpam-5022	81	29	that	that	PRON
ejpam-5022	81	30	are	be	AUX
ejpam-5022	81	31	curial	curial	ADJ
ejpam-5022	81	32	for	for	ADP
ejpam-5022	81	33	the	the	DET
ejpam-5022	81	34	main	main	ADJ
ejpam-5022	81	35	results	result	NOUN
ejpam-5022	81	36	of	of	ADP
ejpam-5022	81	37	this	this	DET
ejpam-5022	81	38	paper	paper	NOUN
ejpam-5022	81	39	.	.	PUNCT
ejpam-5022	82	1	first	first	ADV
ejpam-5022	82	2	,	,	PUNCT
ejpam-5022	82	3	we	we	PRON
ejpam-5022	82	4	define	define	VERB
ejpam-5022	82	5	our	our	PRON
ejpam-5022	82	6	family	family	NOUN
ejpam-5022	82	7	of	of	ADP
ejpam-5022	82	8	analytic	analytic	ADJ
ejpam-5022	82	9	functions	function	NOUN
ejpam-5022	82	10	subordinated	subordinate	VERB
ejpam-5022	82	11	by	by	ADP
ejpam-5022	82	12	horadam	horadam	PROPN
ejpam-5022	82	13	polynomials	polynomial	NOUN
ejpam-5022	82	14	,	,	PUNCT
ejpam-5022	82	15	which	which	PRON
ejpam-5022	82	16	we	we	PRON
ejpam-5022	82	17	denote	denote	VERB
ejpam-5022	82	18	by	by	ADP
ejpam-5022	82	19	f(π	f(π	PROPN
ejpam-5022	82	20	,	,	PUNCT
ejpam-5022	82	21	α	α	X
ejpam-5022	82	22	,	,	PUNCT
ejpam-5022	82	23	β	β	X
ejpam-5022	82	24	,	,	PUNCT
ejpam-5022	82	25	λ	λ	PROPN
ejpam-5022	82	26	,	,	PUNCT
ejpam-5022	82	27	δ	δ	PROPN
ejpam-5022	82	28	,	,	PUNCT
ejpam-5022	82	29	µ	µ	NOUN
ejpam-5022	82	30	)	)	PUNCT
ejpam-5022	82	31	.	.	PUNCT
ejpam-5022	83	1	definition	definition	NOUN
ejpam-5022	83	2	1	1	NUM
ejpam-5022	83	3	.	.	PUNCT
ejpam-5022	84	1	we	we	PRON
ejpam-5022	84	2	say	say	VERB
ejpam-5022	84	3	that	that	SCONJ
ejpam-5022	84	4	a	a	DET
ejpam-5022	84	5	function	function	NOUN
ejpam-5022	84	6	f	f	PROPN
ejpam-5022	84	7	∈	∈	PROPN
ejpam-5022	84	8	a	a	PRON
ejpam-5022	84	9	in	in	ADP
ejpam-5022	84	10	the	the	DET
ejpam-5022	84	11	class	class	NOUN
ejpam-5022	84	12	f(π	f(π	PROPN
ejpam-5022	84	13	,	,	PUNCT
ejpam-5022	84	14	α	α	X
ejpam-5022	84	15	,	,	PUNCT
ejpam-5022	84	16	β	β	X
ejpam-5022	84	17	,	,	PUNCT
ejpam-5022	84	18	λ	λ	PROPN
ejpam-5022	84	19	,	,	PUNCT
ejpam-5022	84	20	δ	δ	PROPN
ejpam-5022	84	21	,	,	PUNCT
ejpam-5022	84	22	µ	µ	NOUN
ejpam-5022	84	23	)	)	PUNCT
ejpam-5022	84	24	if	if	SCONJ
ejpam-5022	84	25	it	it	PRON
ejpam-5022	84	26	fulfills	fulfill	VERB
ejpam-5022	84	27	the	the	DET
ejpam-5022	84	28	subordination	subordination	NOUN
ejpam-5022	84	29	conditions	condition	NOUN
ejpam-5022	84	30	,	,	PUNCT
ejpam-5022	84	31	associated	associate	VERB
ejpam-5022	84	32	with	with	ADP
ejpam-5022	84	33	the	the	DET
ejpam-5022	84	34	horadam	horadam	PROPN
ejpam-5022	84	35	polynomials	polynomial	NOUN
ejpam-5022	84	36	,	,	PUNCT
ejpam-5022	84	37	for	for	ADP
ejpam-5022	84	38	all	all	DET
ejpam-5022	84	39	z	z	NOUN
ejpam-5022	84	40	∈	∈	PROPN
ejpam-5022	84	41	d	d	NOUN
ejpam-5022	84	42	:	:	PUNCT
ejpam-5022	84	43	β	β	X
ejpam-5022	84	44	(	(	PUNCT
ejpam-5022	84	45	zg′(z	zg′(z	PROPN
ejpam-5022	84	46	)	)	PUNCT
ejpam-5022	84	47	g(z	g(z	PROPN
ejpam-5022	84	48	)	)	PUNCT
ejpam-5022	84	49	)	)	PUNCT
ejpam-5022	85	1	α	α	PROPN
ejpam-5022	85	2	+	+	X
ejpam-5022	85	3	(	(	PUNCT
ejpam-5022	85	4	1−	1−	NUM
ejpam-5022	85	5	β	β	NOUN
ejpam-5022	85	6	)	)	PUNCT
ejpam-5022	85	7	(	(	PUNCT
ejpam-5022	85	8	zg′(z	zg′(z	PROPN
ejpam-5022	85	9	)	)	PUNCT
ejpam-5022	85	10	g(z	g(z	PROPN
ejpam-5022	85	11	)	)	PUNCT
ejpam-5022	85	12	)	)	PUNCT
ejpam-5022	86	1	λ	λ	NOUN
ejpam-5022	86	2	(	(	PUNCT
ejpam-5022	86	3	1	1	NUM
ejpam-5022	86	4	+	+	NUM
ejpam-5022	86	5	zg′′(z	zg′′(z	NOUN
ejpam-5022	86	6	)	)	PUNCT
ejpam-5022	86	7	g′(z	g′(z	VERB
ejpam-5022	86	8	)	)	PUNCT
ejpam-5022	86	9	)	)	PUNCT
ejpam-5022	86	10	1−λ	1−λ	NUM
ejpam-5022	86	11	≺	≺	NOUN
ejpam-5022	86	12	π(x	π(x	NOUN
ejpam-5022	86	13	,	,	PUNCT
ejpam-5022	86	14	z	z	NOUN
ejpam-5022	86	15	)	)	PUNCT
ejpam-5022	87	1	+	+	CCONJ
ejpam-5022	88	1	1−	1−	NUM
ejpam-5022	88	2	a	a	PRON
ejpam-5022	88	3	,	,	PUNCT
ejpam-5022	88	4	(	(	PUNCT
ejpam-5022	88	5	4	4	NUM
ejpam-5022	88	6	)	)	PUNCT
ejpam-5022	88	7	where	where	SCONJ
ejpam-5022	88	8	g(z	g(z	ADJ
ejpam-5022	88	9	)	)	PUNCT
ejpam-5022	88	10	=	=	SYM
ejpam-5022	88	11	δµz2f	δµz2f	X
ejpam-5022	88	12	′′(z	′′(z	NOUN
ejpam-5022	88	13	)	)	PUNCT
ejpam-5022	89	1	+	+	CCONJ
ejpam-5022	89	2	(	(	PUNCT
ejpam-5022	89	3	µ−	µ−	PROPN
ejpam-5022	89	4	δ)zf	δ)zf	PROPN
ejpam-5022	89	5	′(z	′(z	NOUN
ejpam-5022	89	6	)	)	PUNCT
ejpam-5022	90	1	+	+	CCONJ
ejpam-5022	90	2	(	(	PUNCT
ejpam-5022	90	3	1−	1−	NUM
ejpam-5022	90	4	µ+	µ+	ADJ
ejpam-5022	90	5	δ)f(z	δ)f(z	NUM
ejpam-5022	90	6	)	)	PUNCT
ejpam-5022	90	7	,	,	PUNCT
ejpam-5022	90	8	and	and	CCONJ
ejpam-5022	90	9	1	1	NUM
ejpam-5022	90	10	≤	≤	NUM
ejpam-5022	90	11	α	α	NOUN
ejpam-5022	90	12	≤	≤	NOUN
ejpam-5022	90	13	2	2	NUM
ejpam-5022	90	14	,	,	PUNCT
ejpam-5022	90	15	0	0	NUM
ejpam-5022	90	16	≤	≤	NUM
ejpam-5022	91	1	β	β	X
ejpam-5022	91	2	≤	≤	NUM
ejpam-5022	91	3	1	1	NUM
ejpam-5022	91	4	,	,	PUNCT
ejpam-5022	91	5	0	0	NUM
ejpam-5022	91	6	≤	≤	NUM
ejpam-5022	91	7	λ	λ	X
ejpam-5022	91	8	≤	≤	NUM
ejpam-5022	91	9	1	1	NUM
ejpam-5022	91	10	and	and	CCONJ
ejpam-5022	91	11	0	0	NUM
ejpam-5022	91	12	≤	≤	NUM
ejpam-5022	91	13	δ	δ	PROPN
ejpam-5022	91	14	≤	≤	PROPN
ejpam-5022	91	15	µ	µ	X
ejpam-5022	91	16	≤	≤	NOUN
ejpam-5022	91	17	1	1	NUM
ejpam-5022	91	18	.	.	PUNCT
ejpam-5022	92	1	the	the	DET
ejpam-5022	92	2	following	follow	VERB
ejpam-5022	92	3	are	be	AUX
ejpam-5022	92	4	interesting	interesting	ADJ
ejpam-5022	92	5	cases	case	NOUN
ejpam-5022	92	6	related	relate	VERB
ejpam-5022	92	7	to	to	ADP
ejpam-5022	92	8	our	our	PRON
ejpam-5022	92	9	presenting	present	VERB
ejpam-5022	92	10	class	class	NOUN
ejpam-5022	92	11	.	.	PUNCT
ejpam-5022	93	1	(	(	PUNCT
ejpam-5022	93	2	a	a	X
ejpam-5022	93	3	)	)	PUNCT
ejpam-5022	93	4	if	if	SCONJ
ejpam-5022	93	5	we	we	PRON
ejpam-5022	93	6	replace	replace	VERB
ejpam-5022	93	7	horadam	horadam	NOUN
ejpam-5022	93	8	polynomials	polynomial	NOUN
ejpam-5022	93	9	by	by	ADP
ejpam-5022	93	10	gegenbaure	gegenbaure	NOUN
ejpam-5022	93	11	polynomials	polynomial	NOUN
ejpam-5022	93	12	h	h	NOUN
ejpam-5022	93	13	(	(	PUNCT
ejpam-5022	93	14	γ	γ	NOUN
ejpam-5022	93	15	)	)	PUNCT
ejpam-5022	93	16	n	n	PROPN
ejpam-5022	93	17	(	(	PUNCT
ejpam-5022	93	18	z	z	PROPN
ejpam-5022	93	19	,	,	PUNCT
ejpam-5022	93	20	t	t	PROPN
ejpam-5022	93	21	)	)	PUNCT
ejpam-5022	93	22	,	,	PUNCT
ejpam-5022	93	23	we	we	PRON
ejpam-5022	93	24	obtain	obtain	VERB
ejpam-5022	93	25	the	the	DET
ejpam-5022	93	26	class	class	NOUN
ejpam-5022	93	27	f(h	f(h	PROPN
ejpam-5022	93	28	(	(	PUNCT
ejpam-5022	93	29	γ	γ	NOUN
ejpam-5022	93	30	)	)	PUNCT
ejpam-5022	93	31	n	n	PROPN
ejpam-5022	93	32	(	(	PUNCT
ejpam-5022	93	33	z	z	PROPN
ejpam-5022	93	34	,	,	PUNCT
ejpam-5022	93	35	t	t	PROPN
ejpam-5022	93	36	)	)	PUNCT
ejpam-5022	93	37	,	,	PUNCT
ejpam-5022	93	38	α	α	X
ejpam-5022	93	39	,	,	PUNCT
ejpam-5022	93	40	β	β	X
ejpam-5022	93	41	,	,	PUNCT
ejpam-5022	93	42	λ	λ	PROPN
ejpam-5022	93	43	,	,	PUNCT
ejpam-5022	93	44	δ	δ	PROPN
ejpam-5022	93	45	,	,	PUNCT
ejpam-5022	93	46	µ	µ	NOUN
ejpam-5022	93	47	)	)	PUNCT
ejpam-5022	93	48	which	which	PRON
ejpam-5022	93	49	was	be	AUX
ejpam-5022	93	50	investigated	investigate	VERB
ejpam-5022	93	51	by	by	ADP
ejpam-5022	93	52	sirvastava	sirvastava	NOUN
ejpam-5022	93	53	et	et	PROPN
ejpam-5022	93	54	al	al	PROPN
ejpam-5022	93	55	.	.	PUNCT
ejpam-5022	94	1	[	[	X
ejpam-5022	94	2	28	28	NUM
ejpam-5022	94	3	]	]	PUNCT
ejpam-5022	94	4	.	.	PUNCT
ejpam-5022	95	1	for	for	ADP
ejpam-5022	95	2	z	z	PROPN
ejpam-5022	95	3	∈	∈	PROPN
ejpam-5022	95	4	d	d	PROPN
ejpam-5022	95	5	,	,	PUNCT
ejpam-5022	95	6	t	t	PROPN
ejpam-5022	95	7	∈	∈	PROPN
ejpam-5022	95	8	(	(	PUNCT
ejpam-5022	95	9	12	12	NUM
ejpam-5022	95	10	,	,	PUNCT
ejpam-5022	95	11	1	1	NUM
ejpam-5022	95	12	]	]	PUNCT
ejpam-5022	95	13	,	,	PUNCT
ejpam-5022	95	14	and	and	CCONJ
ejpam-5022	95	15	γ	γ	X
ejpam-5022	95	16	≥	≥	X
ejpam-5022	95	17	0	0	NUM
ejpam-5022	95	18	the	the	DET
ejpam-5022	95	19	generating	generate	VERB
ejpam-5022	95	20	function	function	NOUN
ejpam-5022	95	21	of	of	ADP
ejpam-5022	95	22	gegenbauer	gegenbauer	NOUN
ejpam-5022	95	23	polynomials	polynomial	NOUN
ejpam-5022	95	24	is	be	AUX
ejpam-5022	95	25	given	give	VERB
ejpam-5022	95	26	by	by	ADP
ejpam-5022	95	27	h(γ	h(γ	NOUN
ejpam-5022	95	28	)	)	PUNCT
ejpam-5022	95	29	n	n	CCONJ
ejpam-5022	95	30	(	(	PUNCT
ejpam-5022	95	31	z	z	PROPN
ejpam-5022	95	32	,	,	PUNCT
ejpam-5022	95	33	t	t	PROPN
ejpam-5022	95	34	)	)	PUNCT
ejpam-5022	95	35	=	=	PUNCT
ejpam-5022	96	1	(	(	PUNCT
ejpam-5022	96	2	z2	z2	NOUN
ejpam-5022	96	3	−	−	PROPN
ejpam-5022	96	4	2tz	2tz	NOUN
ejpam-5022	97	1	+	+	CCONJ
ejpam-5022	97	2	1)−γ	1)−γ	NUM
ejpam-5022	97	3	.	.	PUNCT
ejpam-5022	98	1	(	(	PUNCT
ejpam-5022	98	2	b	b	X
ejpam-5022	98	3	)	)	PUNCT
ejpam-5022	98	4	if	if	SCONJ
ejpam-5022	98	5	we	we	PRON
ejpam-5022	98	6	replace	replace	VERB
ejpam-5022	98	7	horadam	horadam	NOUN
ejpam-5022	98	8	polynomials	polynomial	NOUN
ejpam-5022	98	9	by	by	ADP
ejpam-5022	98	10	chebyshev	chebyshev	NOUN
ejpam-5022	98	11	polynomials	polynomial	NOUN
ejpam-5022	98	12	hn(z	hn(z	NOUN
ejpam-5022	98	13	,	,	PUNCT
ejpam-5022	98	14	t	t	PROPN
ejpam-5022	98	15	)	)	PUNCT
ejpam-5022	98	16	of	of	ADP
ejpam-5022	98	17	the	the	DET
ejpam-5022	98	18	second	second	ADJ
ejpam-5022	98	19	kind	kind	NOUN
ejpam-5022	98	20	,	,	PUNCT
ejpam-5022	98	21	where	where	SCONJ
ejpam-5022	98	22	γ	γ	X
ejpam-5022	98	23	=	=	SYM
ejpam-5022	98	24	1	1	NUM
ejpam-5022	98	25	,	,	PUNCT
ejpam-5022	98	26	we	we	PRON
ejpam-5022	98	27	obtain	obtain	VERB
ejpam-5022	98	28	the	the	DET
ejpam-5022	98	29	class	class	NOUN
ejpam-5022	98	30	f(hn(z	f(hn(z	PROPN
ejpam-5022	98	31	,	,	PUNCT
ejpam-5022	98	32	t	t	PROPN
ejpam-5022	98	33	)	)	PUNCT
ejpam-5022	98	34	,	,	PUNCT
ejpam-5022	98	35	α	α	X
ejpam-5022	98	36	,	,	PUNCT
ejpam-5022	98	37	β	β	X
ejpam-5022	98	38	,	,	PUNCT
ejpam-5022	98	39	λ	λ	PROPN
ejpam-5022	98	40	,	,	PUNCT
ejpam-5022	98	41	δ	δ	PROPN
ejpam-5022	98	42	,	,	PUNCT
ejpam-5022	98	43	µ	µ	NOUN
ejpam-5022	98	44	)	)	PUNCT
ejpam-5022	98	45	which	which	PRON
ejpam-5022	98	46	was	be	AUX
ejpam-5022	98	47	introduced	introduce	VERB
ejpam-5022	98	48	and	and	CCONJ
ejpam-5022	98	49	studied	study	VERB
ejpam-5022	98	50	by	by	ADP
ejpam-5022	98	51	kamali	kamali	PROPN
ejpam-5022	98	52	et	et	PROPN
ejpam-5022	98	53	al	al	PROPN
ejpam-5022	98	54	.	.	PUNCT
ejpam-5022	99	1	[	[	X
ejpam-5022	99	2	19	19	NUM
ejpam-5022	99	3	]	]	PUNCT
ejpam-5022	99	4	.	.	PUNCT
ejpam-5022	100	1	now	now	ADV
ejpam-5022	100	2	,	,	PUNCT
ejpam-5022	100	3	we	we	PRON
ejpam-5022	100	4	present	present	VERB
ejpam-5022	100	5	some	some	DET
ejpam-5022	100	6	particular	particular	ADJ
ejpam-5022	100	7	special	special	ADJ
ejpam-5022	100	8	subclasses	subclass	NOUN
ejpam-5022	100	9	which	which	PRON
ejpam-5022	100	10	obtained	obtain	VERB
ejpam-5022	100	11	by	by	ADP
ejpam-5022	100	12	taking	take	VERB
ejpam-5022	100	13	specific	specific	ADJ
ejpam-5022	100	14	values	value	NOUN
ejpam-5022	100	15	of	of	ADP
ejpam-5022	100	16	the	the	DET
ejpam-5022	100	17	parameters	parameter	NOUN
ejpam-5022	100	18	involved	involve	VERB
ejpam-5022	100	19	in	in	ADP
ejpam-5022	100	20	our	our	PRON
ejpam-5022	100	21	class	class	NOUN
ejpam-5022	100	22	f(π	f(π	PROPN
ejpam-5022	100	23	,	,	PUNCT
ejpam-5022	100	24	α	α	X
ejpam-5022	100	25	,	,	PUNCT
ejpam-5022	100	26	β	β	X
ejpam-5022	100	27	,	,	PUNCT
ejpam-5022	100	28	λ	λ	PROPN
ejpam-5022	100	29	,	,	PUNCT
ejpam-5022	100	30	δ	δ	PROPN
ejpam-5022	100	31	,	,	PUNCT
ejpam-5022	100	32	µ	µ	NOUN
ejpam-5022	100	33	)	)	PUNCT
ejpam-5022	100	34	.	.	PUNCT
ejpam-5022	101	1	•	•	INTJ
ejpam-5022	102	1	if	if	SCONJ
ejpam-5022	102	2	λ	λ	NOUN
ejpam-5022	102	3	=	=	SYM
ejpam-5022	102	4	δ	δ	X
ejpam-5022	102	5	=	=	SYM
ejpam-5022	102	6	µ	µ	X
ejpam-5022	102	7	=	=	SYM
ejpam-5022	102	8	0	0	PROPN
ejpam-5022	102	9	,	,	PUNCT
ejpam-5022	102	10	α	α	NOUN
ejpam-5022	102	11	=	=	SYM
ejpam-5022	102	12	1	1	NUM
ejpam-5022	102	13	,	,	PUNCT
ejpam-5022	102	14	and	and	CCONJ
ejpam-5022	102	15	β	β	X
ejpam-5022	102	16	=	=	SYM
ejpam-5022	102	17	1	1	NUM
ejpam-5022	102	18	−	−	PROPN
ejpam-5022	102	19	η	η	PROPN
ejpam-5022	102	20	where	where	SCONJ
ejpam-5022	102	21	0	0	NUM
ejpam-5022	102	22	≤	≤	NUM
ejpam-5022	102	23	η	η	PROPN
ejpam-5022	102	24	≤	≤	PROPN
ejpam-5022	102	25	1	1	NUM
ejpam-5022	102	26	,	,	PUNCT
ejpam-5022	102	27	then	then	ADV
ejpam-5022	102	28	we	we	PRON
ejpam-5022	102	29	get	get	VERB
ejpam-5022	102	30	the	the	DET
ejpam-5022	102	31	class	class	NOUN
ejpam-5022	102	32	f(π	f(π	PROPN
ejpam-5022	102	33	,	,	PUNCT
ejpam-5022	102	34	1	1	NUM
ejpam-5022	102	35	,	,	PUNCT
ejpam-5022	102	36	1	1	NUM
ejpam-5022	102	37	−	−	PROPN
ejpam-5022	102	38	η	η	PROPN
ejpam-5022	102	39	,	,	PUNCT
ejpam-5022	102	40	0	0	NUM
ejpam-5022	102	41	,	,	PUNCT
ejpam-5022	102	42	0	0	NUM
ejpam-5022	102	43	,	,	PUNCT
ejpam-5022	102	44	0	0	NUM
ejpam-5022	102	45	)	)	PUNCT
ejpam-5022	102	46	.	.	PUNCT
ejpam-5022	103	1	we	we	PRON
ejpam-5022	103	2	say	say	VERB
ejpam-5022	103	3	f	f	PROPN
ejpam-5022	103	4	∈	∈	PROPN
ejpam-5022	103	5	a	a	DET
ejpam-5022	103	6	belong	belong	NOUN
ejpam-5022	103	7	to	to	ADP
ejpam-5022	103	8	this	this	DET
ejpam-5022	103	9	class	class	NOUN
ejpam-5022	103	10	if	if	SCONJ
ejpam-5022	103	11	it	it	PRON
ejpam-5022	103	12	satisfies	satisfy	VERB
ejpam-5022	103	13	the	the	DET
ejpam-5022	103	14	following	follow	VERB
ejpam-5022	103	15	subordination	subordination	NOUN
ejpam-5022	103	16	:	:	PUNCT
ejpam-5022	103	17	(	(	PUNCT
ejpam-5022	103	18	1−	1−	NUM
ejpam-5022	103	19	η	η	NOUN
ejpam-5022	103	20	)	)	PUNCT
ejpam-5022	103	21	(	(	PUNCT
ejpam-5022	103	22	zf	zf	PROPN
ejpam-5022	103	23	′(z	′(z	NOUN
ejpam-5022	103	24	)	)	PUNCT
ejpam-5022	103	25	f(z	f(z	PROPN
ejpam-5022	103	26	)	)	PUNCT
ejpam-5022	103	27	)	)	PUNCT
ejpam-5022	104	1	+	+	CCONJ
ejpam-5022	104	2	η	η	X
ejpam-5022	104	3	(	(	PUNCT
ejpam-5022	104	4	1	1	NUM
ejpam-5022	104	5	+	+	NUM
ejpam-5022	104	6	zf	zf	PROPN
ejpam-5022	104	7	′′(z	′′(z	PROPN
ejpam-5022	104	8	)	)	PUNCT
ejpam-5022	104	9	f	f	PROPN
ejpam-5022	104	10	′(z	′(z	NOUN
ejpam-5022	104	11	)	)	PUNCT
ejpam-5022	104	12	)	)	PUNCT
ejpam-5022	104	13	≺	≺	NOUN
ejpam-5022	104	14	π(x	π(x	NOUN
ejpam-5022	104	15	,	,	PUNCT
ejpam-5022	104	16	z	z	NOUN
ejpam-5022	104	17	)	)	PUNCT
ejpam-5022	105	1	+	+	CCONJ
ejpam-5022	105	2	1−	1−	NUM
ejpam-5022	105	3	a.	a.	NOUN
ejpam-5022	105	4	(	(	PUNCT
ejpam-5022	105	5	5	5	X
ejpam-5022	105	6	)	)	PUNCT
ejpam-5022	105	7	this	this	DET
ejpam-5022	105	8	class	class	NOUN
ejpam-5022	105	9	investigated	investigate	VERB
ejpam-5022	105	10	by	by	ADP
ejpam-5022	105	11	abrami	abrami	PROPN
ejpam-5022	105	12	et	et	PROPN
ejpam-5022	105	13	al	al	PROPN
ejpam-5022	105	14	.	.	PUNCT
ejpam-5022	106	1	[	[	X
ejpam-5022	106	2	1	1	NUM
ejpam-5022	106	3	]	]	PUNCT
ejpam-5022	106	4	.	.	PUNCT
ejpam-5022	107	1	•	•	INTJ
ejpam-5022	107	2	if	if	SCONJ
ejpam-5022	107	3	β	β	X
ejpam-5022	107	4	=	=	SYM
ejpam-5022	107	5	0	0	NUM
ejpam-5022	107	6	and	and	CCONJ
ejpam-5022	107	7	δ	δ	PROPN
ejpam-5022	107	8	=	=	SYM
ejpam-5022	107	9	µ	µ	X
ejpam-5022	107	10	=	=	SYM
ejpam-5022	107	11	0	0	NUM
ejpam-5022	107	12	,	,	PUNCT
ejpam-5022	107	13	we	we	PRON
ejpam-5022	107	14	get	get	VERB
ejpam-5022	107	15	the	the	DET
ejpam-5022	107	16	class	class	NOUN
ejpam-5022	107	17	f(π	f(π	PROPN
ejpam-5022	107	18	,	,	PUNCT
ejpam-5022	107	19	α	α	NOUN
ejpam-5022	107	20	,	,	PUNCT
ejpam-5022	107	21	0	0	NUM
ejpam-5022	107	22	,	,	PUNCT
ejpam-5022	107	23	λ	λ	NOUN
ejpam-5022	107	24	,	,	PUNCT
ejpam-5022	107	25	0	0	NUM
ejpam-5022	107	26	,	,	PUNCT
ejpam-5022	107	27	0	0	NUM
ejpam-5022	107	28	)	)	PUNCT
ejpam-5022	107	29	.	.	PUNCT
ejpam-5022	108	1	we	we	PRON
ejpam-5022	108	2	say	say	VERB
ejpam-5022	108	3	f	f	PROPN
ejpam-5022	108	4	∈	∈	PROPN
ejpam-5022	108	5	a	a	DET
ejpam-5022	108	6	belong	belong	NOUN
ejpam-5022	108	7	to	to	ADP
ejpam-5022	108	8	this	this	DET
ejpam-5022	108	9	class	class	NOUN
ejpam-5022	108	10	if	if	SCONJ
ejpam-5022	108	11	it	it	PRON
ejpam-5022	108	12	satisfies	satisfy	VERB
ejpam-5022	108	13	the	the	DET
ejpam-5022	108	14	following	follow	VERB
ejpam-5022	108	15	subordination	subordination	NOUN
ejpam-5022	108	16	:(	:(	PROPN
ejpam-5022	108	17	zf	zf	PROPN
ejpam-5022	108	18	′(z	′(z	NOUN
ejpam-5022	108	19	)	)	PUNCT
ejpam-5022	108	20	f(z	f(z	PROPN
ejpam-5022	108	21	)	)	PUNCT
ejpam-5022	108	22	)	)	PUNCT
ejpam-5022	109	1	λ	λ	NOUN
ejpam-5022	109	2	(	(	PUNCT
ejpam-5022	109	3	1	1	NUM
ejpam-5022	109	4	+	+	NUM
ejpam-5022	109	5	zf	zf	PROPN
ejpam-5022	109	6	′′(z	′′(z	PROPN
ejpam-5022	109	7	)	)	PUNCT
ejpam-5022	109	8	f	f	PROPN
ejpam-5022	109	9	′(z	′(z	NOUN
ejpam-5022	109	10	)	)	PUNCT
ejpam-5022	109	11	)	)	PUNCT
ejpam-5022	110	1	1−λ	1−λ	NUM
ejpam-5022	110	2	≺	≺	NOUN
ejpam-5022	110	3	π(x	π(x	NOUN
ejpam-5022	110	4	,	,	PUNCT
ejpam-5022	110	5	z	z	NOUN
ejpam-5022	110	6	)	)	PUNCT
ejpam-5022	111	1	+	+	CCONJ
ejpam-5022	111	2	1−	1−	NUM
ejpam-5022	111	3	a.	a.	NOUN
ejpam-5022	111	4	(	(	PUNCT
ejpam-5022	111	5	6	6	NUM
ejpam-5022	111	6	)	)	PUNCT
ejpam-5022	111	7	this	this	DET
ejpam-5022	111	8	class	class	NOUN
ejpam-5022	111	9	investigated	investigate	VERB
ejpam-5022	111	10	by	by	ADP
ejpam-5022	111	11	abrami	abrami	PROPN
ejpam-5022	111	12	et	et	PROPN
ejpam-5022	111	13	al	al	PROPN
ejpam-5022	111	14	.	.	PUNCT
ejpam-5022	112	1	[	[	X
ejpam-5022	112	2	1	1	NUM
ejpam-5022	112	3	]	]	PUNCT
ejpam-5022	112	4	.	.	PUNCT
ejpam-5022	113	1	w.	w.	PROPN
ejpam-5022	113	2	al	al	PROPN
ejpam-5022	113	3	-	-	PUNCT
ejpam-5022	113	4	rawashdeh	rawashdeh	PROPN
ejpam-5022	113	5	/	/	SYM
ejpam-5022	113	6	eur	eur	PROPN
ejpam-5022	113	7	.	.	PUNCT
ejpam-5022	114	1	j.	j.	PROPN
ejpam-5022	114	2	pure	pure	PROPN
ejpam-5022	114	3	appl	appl	PROPN
ejpam-5022	114	4	.	.	PROPN
ejpam-5022	114	5	math	math	PROPN
ejpam-5022	114	6	,	,	PUNCT
ejpam-5022	114	7	17	17	NUM
ejpam-5022	114	8	(	(	PUNCT
ejpam-5022	114	9	1	1	NUM
ejpam-5022	114	10	)	)	PUNCT
ejpam-5022	114	11	(	(	PUNCT
ejpam-5022	114	12	2024	2024	NUM
ejpam-5022	114	13	)	)	PUNCT
ejpam-5022	114	14	,	,	PUNCT
ejpam-5022	114	15	158	158	NUM
ejpam-5022	114	16	-	-	SYM
ejpam-5022	114	17	170	170	NUM
ejpam-5022	114	18	162	162	NUM
ejpam-5022	114	19	•	•	NOUN
ejpam-5022	114	20	if	if	SCONJ
ejpam-5022	114	21	α	α	NOUN
ejpam-5022	114	22	=	=	PUNCT
ejpam-5022	114	23	β	β	X
ejpam-5022	114	24	=	=	SYM
ejpam-5022	114	25	1	1	NUM
ejpam-5022	114	26	,	,	PUNCT
ejpam-5022	114	27	we	we	PRON
ejpam-5022	114	28	get	get	VERB
ejpam-5022	114	29	the	the	DET
ejpam-5022	114	30	class	class	NOUN
ejpam-5022	114	31	f(π	f(π	PROPN
ejpam-5022	114	32	,	,	PUNCT
ejpam-5022	114	33	1	1	NUM
ejpam-5022	114	34	,	,	PUNCT
ejpam-5022	114	35	1	1	NUM
ejpam-5022	114	36	,	,	PUNCT
ejpam-5022	114	37	λ	λ	PROPN
ejpam-5022	114	38	,	,	PUNCT
ejpam-5022	114	39	δ	δ	PROPN
ejpam-5022	114	40	,	,	PUNCT
ejpam-5022	114	41	µ	µ	NOUN
ejpam-5022	114	42	)	)	PUNCT
ejpam-5022	114	43	.	.	PUNCT
ejpam-5022	115	1	we	we	PRON
ejpam-5022	115	2	say	say	VERB
ejpam-5022	115	3	f	f	PROPN
ejpam-5022	115	4	∈	∈	PROPN
ejpam-5022	115	5	a	a	DET
ejpam-5022	115	6	belong	belong	NOUN
ejpam-5022	115	7	to	to	ADP
ejpam-5022	115	8	this	this	DET
ejpam-5022	115	9	class	class	NOUN
ejpam-5022	115	10	if	if	SCONJ
ejpam-5022	115	11	it	it	PRON
ejpam-5022	115	12	satisfies	satisfy	VERB
ejpam-5022	115	13	the	the	DET
ejpam-5022	115	14	following	follow	VERB
ejpam-5022	115	15	subordination	subordination	NOUN
ejpam-5022	115	16	:	:	PUNCT
ejpam-5022	115	17	µδz3f	µδz3f	PROPN
ejpam-5022	115	18	′′′(z	′′′(z	PROPN
ejpam-5022	115	19	)	)	PUNCT
ejpam-5022	115	20	+	+	CCONJ
ejpam-5022	115	21	(	(	PUNCT
ejpam-5022	115	22	2µδ	2µδ	ADJ
ejpam-5022	115	23	+	+	CCONJ
ejpam-5022	115	24	µ−	µ−	PROPN
ejpam-5022	115	25	δ)z2f	δ)z2f	ADJ
ejpam-5022	115	26	′′(z	′′(z	NOUN
ejpam-5022	115	27	)	)	PUNCT
ejpam-5022	116	1	+	+	CCONJ
ejpam-5022	116	2	zf	zf	PROPN
ejpam-5022	116	3	′(z	′(z	NOUN
ejpam-5022	116	4	)	)	PUNCT
ejpam-5022	116	5	µδz2f	µδz2f	NUM
ejpam-5022	116	6	′′(z	′′(z	NOUN
ejpam-5022	116	7	)	)	PUNCT
ejpam-5022	117	1	+	+	CCONJ
ejpam-5022	117	2	(	(	PUNCT
ejpam-5022	117	3	µ−	µ−	PROPN
ejpam-5022	117	4	δ)zf	δ)zf	PROPN
ejpam-5022	117	5	′(z	′(z	NOUN
ejpam-5022	117	6	)	)	PUNCT
ejpam-5022	118	1	+	+	CCONJ
ejpam-5022	118	2	(	(	PUNCT
ejpam-5022	118	3	1−	1−	NUM
ejpam-5022	118	4	µ+	µ+	X
ejpam-5022	118	5	δ)f(z	δ)f(z	X
ejpam-5022	118	6	)	)	PUNCT
ejpam-5022	118	7	≺	≺	NOUN
ejpam-5022	118	8	π(x	π(x	NOUN
ejpam-5022	118	9	,	,	PUNCT
ejpam-5022	118	10	z	z	NOUN
ejpam-5022	118	11	)	)	PUNCT
ejpam-5022	119	1	+	+	CCONJ
ejpam-5022	119	2	1−	1−	NUM
ejpam-5022	119	3	a.	a.	NOUN
ejpam-5022	119	4	(	(	PUNCT
ejpam-5022	119	5	7	7	NUM
ejpam-5022	119	6	)	)	PUNCT
ejpam-5022	119	7	if	if	SCONJ
ejpam-5022	119	8	we	we	PRON
ejpam-5022	119	9	replace	replace	VERB
ejpam-5022	119	10	π(x	π(x	ADP
ejpam-5022	119	11	,	,	PUNCT
ejpam-5022	119	12	z	z	NOUN
ejpam-5022	119	13	)	)	PUNCT
ejpam-5022	120	1	+	+	CCONJ
ejpam-5022	120	2	1	1	NUM
ejpam-5022	120	3	−	−	NOUN
ejpam-5022	120	4	a	a	NOUN
ejpam-5022	120	5	by	by	ADP
ejpam-5022	120	6	the	the	DET
ejpam-5022	120	7	chebyshev	chebyshev	NOUN
ejpam-5022	120	8	polynomials	polynomial	NOUN
ejpam-5022	120	9	hn(z	hn(z	NOUN
ejpam-5022	120	10	,	,	PUNCT
ejpam-5022	120	11	t	t	PROPN
ejpam-5022	120	12	)	)	PUNCT
ejpam-5022	120	13	of	of	ADP
ejpam-5022	120	14	the	the	DET
ejpam-5022	120	15	second	second	ADJ
ejpam-5022	120	16	kind	kind	NOUN
ejpam-5022	120	17	,	,	PUNCT
ejpam-5022	120	18	we	we	PRON
ejpam-5022	120	19	get	get	VERB
ejpam-5022	120	20	the	the	DET
ejpam-5022	120	21	class	class	NOUN
ejpam-5022	120	22	f(hn(z	f(hn(z	PROPN
ejpam-5022	120	23	,	,	PUNCT
ejpam-5022	120	24	t	t	PROPN
ejpam-5022	120	25	)	)	PUNCT
ejpam-5022	120	26	,	,	PUNCT
ejpam-5022	120	27	1	1	NUM
ejpam-5022	120	28	,	,	PUNCT
ejpam-5022	120	29	1	1	NUM
ejpam-5022	120	30	,	,	PUNCT
ejpam-5022	120	31	λ	λ	PROPN
ejpam-5022	120	32	,	,	PUNCT
ejpam-5022	120	33	δ	δ	PROPN
ejpam-5022	120	34	,	,	PUNCT
ejpam-5022	120	35	µ	µ	NOUN
ejpam-5022	120	36	)	)	PUNCT
ejpam-5022	120	37	which	which	PRON
ejpam-5022	120	38	introduced	introduce	VERB
ejpam-5022	120	39	and	and	CCONJ
ejpam-5022	120	40	studied	study	VERB
ejpam-5022	120	41	by	by	ADP
ejpam-5022	120	42	çağlar	çağlar	PROPN
ejpam-5022	120	43	et	et	PROPN
ejpam-5022	120	44	al	al	PROPN
ejpam-5022	120	45	.	.	PUNCT
ejpam-5022	121	1	[	[	X
ejpam-5022	121	2	8	8	NUM
ejpam-5022	121	3	]	]	PUNCT
ejpam-5022	121	4	.	.	PUNCT
ejpam-5022	122	1	•	•	INTJ
ejpam-5022	122	2	if	if	SCONJ
ejpam-5022	122	3	µ	µ	X
ejpam-5022	122	4	=	=	SYM
ejpam-5022	122	5	δ	δ	X
ejpam-5022	122	6	=	=	SYM
ejpam-5022	122	7	0	0	PROPN
ejpam-5022	122	8	,	,	PUNCT
ejpam-5022	122	9	we	we	PRON
ejpam-5022	122	10	get	get	VERB
ejpam-5022	122	11	the	the	DET
ejpam-5022	122	12	class	class	NOUN
ejpam-5022	122	13	f(π	f(π	PROPN
ejpam-5022	122	14	,	,	PUNCT
ejpam-5022	122	15	α	α	X
ejpam-5022	122	16	,	,	PUNCT
ejpam-5022	122	17	β	β	X
ejpam-5022	122	18	,	,	PUNCT
ejpam-5022	122	19	λ	λ	PROPN
ejpam-5022	122	20	,	,	PUNCT
ejpam-5022	122	21	0	0	NUM
ejpam-5022	122	22	,	,	PUNCT
ejpam-5022	122	23	0	0	NUM
ejpam-5022	122	24	)	)	PUNCT
ejpam-5022	122	25	.	.	PUNCT
ejpam-5022	123	1	we	we	PRON
ejpam-5022	123	2	say	say	VERB
ejpam-5022	123	3	f	f	PROPN
ejpam-5022	123	4	∈	∈	PROPN
ejpam-5022	123	5	a	a	DET
ejpam-5022	123	6	belong	belong	NOUN
ejpam-5022	123	7	to	to	ADP
ejpam-5022	123	8	this	this	DET
ejpam-5022	123	9	class	class	NOUN
ejpam-5022	123	10	if	if	SCONJ
ejpam-5022	123	11	it	it	PRON
ejpam-5022	123	12	satisfies	satisfy	VERB
ejpam-5022	123	13	the	the	DET
ejpam-5022	123	14	following	follow	VERB
ejpam-5022	123	15	subordination	subordination	NOUN
ejpam-5022	123	16	:	:	PUNCT
ejpam-5022	123	17	β	β	X
ejpam-5022	123	18	(	(	PUNCT
ejpam-5022	123	19	zf	zf	PROPN
ejpam-5022	123	20	′(z	′(z	NOUN
ejpam-5022	123	21	)	)	PUNCT
ejpam-5022	123	22	f(z	f(z	PROPN
ejpam-5022	123	23	)	)	PUNCT
ejpam-5022	123	24	)	)	PUNCT
ejpam-5022	124	1	α	α	PROPN
ejpam-5022	124	2	+	+	X
ejpam-5022	124	3	(	(	PUNCT
ejpam-5022	124	4	1−	1−	NUM
ejpam-5022	124	5	β	β	NOUN
ejpam-5022	124	6	)	)	PUNCT
ejpam-5022	124	7	(	(	PUNCT
ejpam-5022	124	8	zf	zf	PROPN
ejpam-5022	124	9	′(z	′(z	NOUN
ejpam-5022	124	10	)	)	PUNCT
ejpam-5022	124	11	f(z	f(z	PROPN
ejpam-5022	124	12	)	)	PUNCT
ejpam-5022	124	13	)	)	PUNCT
ejpam-5022	125	1	λ	λ	NOUN
ejpam-5022	125	2	(	(	PUNCT
ejpam-5022	125	3	1	1	NUM
ejpam-5022	125	4	+	+	NUM
ejpam-5022	125	5	zf	zf	PROPN
ejpam-5022	125	6	′′(z	′′(z	PROPN
ejpam-5022	125	7	)	)	PUNCT
ejpam-5022	125	8	f	f	PROPN
ejpam-5022	125	9	′(z	′(z	NOUN
ejpam-5022	125	10	)	)	PUNCT
ejpam-5022	125	11	)	)	PUNCT
ejpam-5022	126	1	1−λ	1−λ	NUM
ejpam-5022	126	2	≺	≺	NOUN
ejpam-5022	126	3	π(x	π(x	NOUN
ejpam-5022	126	4	,	,	PUNCT
ejpam-5022	126	5	z	z	NOUN
ejpam-5022	126	6	)	)	PUNCT
ejpam-5022	126	7	+	+	CCONJ
ejpam-5022	126	8	1−	1−	NUM
ejpam-5022	126	9	a.	a.	NOUN
ejpam-5022	126	10	(	(	PUNCT
ejpam-5022	126	11	8)	8)	NUM
ejpam-5022	126	12	if	if	SCONJ
ejpam-5022	126	13	we	we	PRON
ejpam-5022	126	14	replace	replace	VERB
ejpam-5022	126	15	π(x	π(x	ADP
ejpam-5022	126	16	,	,	PUNCT
ejpam-5022	126	17	z)+1−a	z)+1−a	NUM
ejpam-5022	126	18	by	by	ADP
ejpam-5022	126	19	the	the	DET
ejpam-5022	126	20	chebyshev	chebyshev	PROPN
ejpam-5022	126	21	polynomialshn(z	polynomialshn(z	PROPN
ejpam-5022	126	22	,	,	PUNCT
ejpam-5022	126	23	t	t	PROPN
ejpam-5022	126	24	)	)	PUNCT
ejpam-5022	126	25	of	of	ADP
ejpam-5022	126	26	the	the	DET
ejpam-5022	126	27	second	second	ADJ
ejpam-5022	126	28	kind	kind	NOUN
ejpam-5022	126	29	,	,	PUNCT
ejpam-5022	126	30	we	we	PRON
ejpam-5022	126	31	get	get	VERB
ejpam-5022	126	32	the	the	DET
ejpam-5022	126	33	class	class	NOUN
ejpam-5022	126	34	f(hn(z	f(hn(z	PROPN
ejpam-5022	126	35	,	,	PUNCT
ejpam-5022	126	36	t	t	PROPN
ejpam-5022	126	37	)	)	PUNCT
ejpam-5022	126	38	,	,	PUNCT
ejpam-5022	126	39	α	α	X
ejpam-5022	126	40	,	,	PUNCT
ejpam-5022	126	41	β	β	X
ejpam-5022	126	42	,	,	PUNCT
ejpam-5022	126	43	λ	λ	PROPN
ejpam-5022	126	44	,	,	PUNCT
ejpam-5022	126	45	0	0	NUM
ejpam-5022	126	46	,	,	PUNCT
ejpam-5022	126	47	0	0	NUM
ejpam-5022	126	48	)	)	PUNCT
ejpam-5022	126	49	which	which	PRON
ejpam-5022	126	50	introduced	introduce	VERB
ejpam-5022	126	51	and	and	CCONJ
ejpam-5022	126	52	studied	study	VERB
ejpam-5022	126	53	by	by	ADP
ejpam-5022	126	54	szatmari	szatmari	PROPN
ejpam-5022	126	55	et	et	PROPN
ejpam-5022	126	56	al	al	PROPN
ejpam-5022	126	57	.	.	PUNCT
ejpam-5022	127	1	[	[	X
ejpam-5022	127	2	31	31	NUM
ejpam-5022	127	3	]	]	PUNCT
ejpam-5022	127	4	.	.	PUNCT
ejpam-5022	128	1	•	•	INTJ
ejpam-5022	128	2	if	if	SCONJ
ejpam-5022	128	3	δ	δ	PROPN
ejpam-5022	128	4	=	=	SYM
ejpam-5022	128	5	λ	λ	X
ejpam-5022	128	6	=	=	SYM
ejpam-5022	128	7	0	0	PROPN
ejpam-5022	128	8	,	,	PUNCT
ejpam-5022	128	9	α	α	NOUN
ejpam-5022	128	10	=	=	SYM
ejpam-5022	128	11	1	1	NUM
ejpam-5022	128	12	and	and	CCONJ
ejpam-5022	128	13	β	β	X
ejpam-5022	128	14	=	=	SYM
ejpam-5022	129	1	1	1	NUM
ejpam-5022	129	2	−	−	PROPN
ejpam-5022	129	3	η	η	PROPN
ejpam-5022	129	4	,	,	PUNCT
ejpam-5022	129	5	we	we	PRON
ejpam-5022	129	6	get	get	VERB
ejpam-5022	129	7	the	the	DET
ejpam-5022	129	8	class	class	NOUN
ejpam-5022	129	9	f(π	f(π	PROPN
ejpam-5022	129	10	,	,	PUNCT
ejpam-5022	129	11	1	1	NUM
ejpam-5022	129	12	,	,	PUNCT
ejpam-5022	129	13	1	1	NUM
ejpam-5022	129	14	−	−	PROPN
ejpam-5022	129	15	η	η	PROPN
ejpam-5022	129	16	,	,	PUNCT
ejpam-5022	129	17	0	0	NUM
ejpam-5022	129	18	,	,	PUNCT
ejpam-5022	129	19	0	0	NUM
ejpam-5022	129	20	,	,	PUNCT
ejpam-5022	129	21	µ).we	µ).we	NOUN
ejpam-5022	129	22	say	say	VERB
ejpam-5022	129	23	f	f	PROPN
ejpam-5022	129	24	∈	∈	PROPN
ejpam-5022	129	25	a	a	DET
ejpam-5022	129	26	belong	belong	NOUN
ejpam-5022	129	27	to	to	ADP
ejpam-5022	129	28	this	this	DET
ejpam-5022	129	29	class	class	NOUN
ejpam-5022	129	30	if	if	SCONJ
ejpam-5022	129	31	it	it	PRON
ejpam-5022	129	32	satisfies	satisfy	VERB
ejpam-5022	129	33	the	the	DET
ejpam-5022	129	34	following	follow	VERB
ejpam-5022	129	35	subordination	subordination	NOUN
ejpam-5022	129	36	:	:	PUNCT
ejpam-5022	129	37	(	(	PUNCT
ejpam-5022	129	38	1−	1−	NUM
ejpam-5022	129	39	η	η	NOUN
ejpam-5022	129	40	)	)	PUNCT
ejpam-5022	129	41	(	(	PUNCT
ejpam-5022	129	42	zg′(z	zg′(z	PROPN
ejpam-5022	129	43	)	)	PUNCT
ejpam-5022	129	44	g(z	g(z	PROPN
ejpam-5022	129	45	)	)	PUNCT
ejpam-5022	129	46	)	)	PUNCT
ejpam-5022	130	1	+	+	CCONJ
ejpam-5022	130	2	η	η	X
ejpam-5022	130	3	(	(	PUNCT
ejpam-5022	130	4	1	1	NUM
ejpam-5022	130	5	+	+	NUM
ejpam-5022	130	6	zg′′(z	zg′′(z	NOUN
ejpam-5022	130	7	)	)	PUNCT
ejpam-5022	130	8	g′(z	g′(z	NOUN
ejpam-5022	130	9	)	)	PUNCT
ejpam-5022	130	10	)	)	PUNCT
ejpam-5022	130	11	≺	≺	NOUN
ejpam-5022	130	12	π(x	π(x	NOUN
ejpam-5022	130	13	,	,	PUNCT
ejpam-5022	130	14	z	z	NOUN
ejpam-5022	130	15	)	)	PUNCT
ejpam-5022	131	1	+	+	CCONJ
ejpam-5022	131	2	1−	1−	NUM
ejpam-5022	131	3	a	a	PRON
ejpam-5022	131	4	,	,	PUNCT
ejpam-5022	131	5	(	(	PUNCT
ejpam-5022	131	6	9	9	NUM
ejpam-5022	131	7	)	)	PUNCT
ejpam-5022	131	8	where	where	SCONJ
ejpam-5022	131	9	g(z	g(z	ADJ
ejpam-5022	131	10	)	)	PUNCT
ejpam-5022	131	11	=	=	PUNCT
ejpam-5022	131	12	µzf	µzf	PROPN
ejpam-5022	131	13	′(z	′(z	NOUN
ejpam-5022	131	14	)	)	PUNCT
ejpam-5022	132	1	+	+	CCONJ
ejpam-5022	132	2	(	(	PUNCT
ejpam-5022	132	3	1−µ)f(z	1−µ)f(z	NUM
ejpam-5022	132	4	)	)	PUNCT
ejpam-5022	132	5	.	.	PUNCT
ejpam-5022	133	1	if	if	SCONJ
ejpam-5022	133	2	we	we	PRON
ejpam-5022	133	3	replace	replace	VERB
ejpam-5022	133	4	π(x	π(x	ADP
ejpam-5022	133	5	,	,	PUNCT
ejpam-5022	133	6	z	z	NOUN
ejpam-5022	133	7	)	)	PUNCT
ejpam-5022	134	1	+	+	CCONJ
ejpam-5022	134	2	1−	1−	NUM
ejpam-5022	134	3	a	a	PRON
ejpam-5022	134	4	by	by	ADP
ejpam-5022	134	5	the	the	DET
ejpam-5022	134	6	chebyshev	chebyshev	NOUN
ejpam-5022	134	7	polynomials	polynomial	NOUN
ejpam-5022	134	8	hn(z	hn(z	NOUN
ejpam-5022	134	9	,	,	PUNCT
ejpam-5022	134	10	t	t	PROPN
ejpam-5022	134	11	)	)	PUNCT
ejpam-5022	134	12	of	of	ADP
ejpam-5022	134	13	the	the	DET
ejpam-5022	134	14	second	second	ADJ
ejpam-5022	134	15	kind	kind	NOUN
ejpam-5022	134	16	,	,	PUNCT
ejpam-5022	134	17	we	we	PRON
ejpam-5022	134	18	get	get	VERB
ejpam-5022	134	19	the	the	DET
ejpam-5022	134	20	class	class	NOUN
ejpam-5022	134	21	f(hn(z	f(hn(z	PROPN
ejpam-5022	134	22	,	,	PUNCT
ejpam-5022	134	23	t	t	PROPN
ejpam-5022	134	24	)	)	PUNCT
ejpam-5022	134	25	,	,	PUNCT
ejpam-5022	134	26	α	α	X
ejpam-5022	134	27	,	,	PUNCT
ejpam-5022	134	28	1−	1−	NUM
ejpam-5022	134	29	η	η	PROPN
ejpam-5022	134	30	,	,	PUNCT
ejpam-5022	134	31	λ	λ	PROPN
ejpam-5022	134	32	,	,	PUNCT
ejpam-5022	134	33	0	0	NUM
ejpam-5022	134	34	,	,	PUNCT
ejpam-5022	134	35	0	0	NUM
ejpam-5022	134	36	)	)	PUNCT
ejpam-5022	134	37	which	which	PRON
ejpam-5022	134	38	introduced	introduce	VERB
ejpam-5022	134	39	and	and	CCONJ
ejpam-5022	134	40	studied	study	VERB
ejpam-5022	134	41	by	by	ADP
ejpam-5022	134	42	bulut	bulut	NOUN
ejpam-5022	134	43	et	et	PROPN
ejpam-5022	134	44	al	al	PROPN
ejpam-5022	134	45	.	.	PUNCT
ejpam-5022	135	1	[	[	X
ejpam-5022	135	2	7	7	NUM
ejpam-5022	135	3	]	]	PUNCT
ejpam-5022	135	4	.	.	PUNCT
ejpam-5022	136	1	•	•	INTJ
ejpam-5022	136	2	if	if	SCONJ
ejpam-5022	136	3	δ	δ	PROPN
ejpam-5022	136	4	=	=	SYM
ejpam-5022	136	5	µ	µ	X
ejpam-5022	136	6	=	=	X
ejpam-5022	136	7	β	β	X
ejpam-5022	136	8	=	=	PUNCT
ejpam-5022	136	9	λ	λ	X
ejpam-5022	136	10	=	=	SYM
ejpam-5022	136	11	0	0	NUM
ejpam-5022	136	12	,	,	PUNCT
ejpam-5022	136	13	we	we	PRON
ejpam-5022	136	14	get	get	VERB
ejpam-5022	136	15	the	the	DET
ejpam-5022	136	16	class	class	NOUN
ejpam-5022	136	17	f(π	f(π	PROPN
ejpam-5022	136	18	,	,	PUNCT
ejpam-5022	136	19	α	α	NOUN
ejpam-5022	136	20	,	,	PUNCT
ejpam-5022	136	21	0	0	NUM
ejpam-5022	136	22	,	,	PUNCT
ejpam-5022	136	23	0	0	NUM
ejpam-5022	136	24	,	,	PUNCT
ejpam-5022	136	25	0	0	NUM
ejpam-5022	136	26	,	,	PUNCT
ejpam-5022	136	27	0	0	NUM
ejpam-5022	136	28	)	)	PUNCT
ejpam-5022	136	29	.	.	PUNCT
ejpam-5022	137	1	we	we	PRON
ejpam-5022	137	2	say	say	VERB
ejpam-5022	137	3	f	f	PROPN
ejpam-5022	137	4	∈	∈	PROPN
ejpam-5022	137	5	a	a	DET
ejpam-5022	137	6	belong	belong	NOUN
ejpam-5022	137	7	to	to	ADP
ejpam-5022	137	8	this	this	DET
ejpam-5022	137	9	class	class	NOUN
ejpam-5022	137	10	if	if	SCONJ
ejpam-5022	137	11	it	it	PRON
ejpam-5022	137	12	satisfies	satisfy	VERB
ejpam-5022	137	13	the	the	DET
ejpam-5022	137	14	following	follow	VERB
ejpam-5022	137	15	subordination	subordination	NOUN
ejpam-5022	137	16	:	:	PUNCT
ejpam-5022	137	17	1	1	NUM
ejpam-5022	137	18	+	+	CCONJ
ejpam-5022	137	19	zf	zf	PROPN
ejpam-5022	137	20	′′(z	′′(z	PROPN
ejpam-5022	137	21	)	)	PUNCT
ejpam-5022	137	22	f	f	PROPN
ejpam-5022	137	23	′(z	′(z	NOUN
ejpam-5022	137	24	)	)	PUNCT
ejpam-5022	137	25	≺	≺	NOUN
ejpam-5022	137	26	π(x	π(x	NOUN
ejpam-5022	137	27	,	,	PUNCT
ejpam-5022	137	28	z	z	NOUN
ejpam-5022	137	29	)	)	PUNCT
ejpam-5022	138	1	+	+	CCONJ
ejpam-5022	138	2	1−	1−	NUM
ejpam-5022	138	3	a.	a.	NOUN
ejpam-5022	138	4	(	(	PUNCT
ejpam-5022	138	5	10	10	NUM
ejpam-5022	138	6	)	)	PUNCT
ejpam-5022	138	7	if	if	SCONJ
ejpam-5022	138	8	we	we	PRON
ejpam-5022	138	9	replace	replace	VERB
ejpam-5022	138	10	π(x	π(x	ADP
ejpam-5022	138	11	,	,	PUNCT
ejpam-5022	138	12	z	z	NOUN
ejpam-5022	138	13	)	)	PUNCT
ejpam-5022	139	1	+	+	CCONJ
ejpam-5022	139	2	1	1	NUM
ejpam-5022	139	3	−	−	NOUN
ejpam-5022	139	4	a	a	NOUN
ejpam-5022	139	5	by	by	ADP
ejpam-5022	139	6	the	the	DET
ejpam-5022	139	7	chebyshev	chebyshev	NOUN
ejpam-5022	139	8	polynomials	polynomial	NOUN
ejpam-5022	139	9	hn(z	hn(z	NOUN
ejpam-5022	139	10	,	,	PUNCT
ejpam-5022	139	11	t	t	PROPN
ejpam-5022	139	12	)	)	PUNCT
ejpam-5022	139	13	of	of	ADP
ejpam-5022	139	14	the	the	DET
ejpam-5022	139	15	second	second	ADJ
ejpam-5022	139	16	kind	kind	NOUN
ejpam-5022	139	17	,	,	PUNCT
ejpam-5022	139	18	we	we	PRON
ejpam-5022	139	19	get	get	VERB
ejpam-5022	139	20	the	the	DET
ejpam-5022	139	21	class	class	NOUN
ejpam-5022	139	22	f(hn(z	f(hn(z	PROPN
ejpam-5022	139	23	,	,	PUNCT
ejpam-5022	139	24	t	t	PROPN
ejpam-5022	139	25	)	)	PUNCT
ejpam-5022	139	26	,	,	PUNCT
ejpam-5022	139	27	α	α	NOUN
ejpam-5022	139	28	,	,	PUNCT
ejpam-5022	139	29	0	0	NUM
ejpam-5022	139	30	,	,	PUNCT
ejpam-5022	139	31	0	0	NUM
ejpam-5022	139	32	,	,	PUNCT
ejpam-5022	139	33	0	0	NUM
ejpam-5022	139	34	,	,	PUNCT
ejpam-5022	139	35	0	0	NUM
ejpam-5022	139	36	)	)	PUNCT
ejpam-5022	139	37	which	which	PRON
ejpam-5022	139	38	introduced	introduce	VERB
ejpam-5022	139	39	and	and	CCONJ
ejpam-5022	139	40	studied	study	VERB
ejpam-5022	139	41	by	by	ADP
ejpam-5022	139	42	dziok	dziok	NOUN
ejpam-5022	139	43	et	et	PROPN
ejpam-5022	139	44	al	al	PROPN
ejpam-5022	139	45	.	.	PUNCT
ejpam-5022	140	1	[	[	X
ejpam-5022	140	2	12	12	NUM
ejpam-5022	140	3	]	]	PUNCT
ejpam-5022	140	4	.	.	PUNCT
ejpam-5022	141	1	the	the	DET
ejpam-5022	141	2	following	follow	VERB
ejpam-5022	141	3	lemma	lemma	PROPN
ejpam-5022	141	4	(	(	PUNCT
ejpam-5022	141	5	see	see	VERB
ejpam-5022	141	6	,	,	PUNCT
ejpam-5022	141	7	for	for	ADP
ejpam-5022	141	8	details	detail	NOUN
ejpam-5022	141	9	[	[	X
ejpam-5022	141	10	20	20	NUM
ejpam-5022	141	11	]	]	PUNCT
ejpam-5022	141	12	)	)	PUNCT
ejpam-5022	141	13	is	be	AUX
ejpam-5022	141	14	a	a	DET
ejpam-5022	141	15	well	well	ADV
ejpam-5022	141	16	-	-	PUNCT
ejpam-5022	141	17	known	know	VERB
ejpam-5022	141	18	fact	fact	NOUN
ejpam-5022	141	19	,	,	PUNCT
ejpam-5022	141	20	but	but	CCONJ
ejpam-5022	141	21	it	it	PRON
ejpam-5022	141	22	is	be	AUX
ejpam-5022	141	23	crucial	crucial	ADJ
ejpam-5022	141	24	for	for	ADP
ejpam-5022	141	25	the	the	DET
ejpam-5022	141	26	main	main	ADJ
ejpam-5022	141	27	results	result	NOUN
ejpam-5022	141	28	of	of	ADP
ejpam-5022	141	29	this	this	DET
ejpam-5022	141	30	paper	paper	NOUN
ejpam-5022	141	31	.	.	PUNCT
ejpam-5022	142	1	lemma	lemma	PROPN
ejpam-5022	142	2	1	1	X
ejpam-5022	142	3	.	.	PUNCT
ejpam-5022	143	1	let	let	VERB
ejpam-5022	143	2	the	the	DET
ejpam-5022	143	3	schwarz	schwarz	PROPN
ejpam-5022	143	4	function	function	VERB
ejpam-5022	143	5	w(z	w(z	PROPN
ejpam-5022	143	6	)	)	PUNCT
ejpam-5022	143	7	be	be	AUX
ejpam-5022	143	8	given	give	VERB
ejpam-5022	143	9	by	by	ADP
ejpam-5022	143	10	:	:	PUNCT
ejpam-5022	143	11	w(z	w(z	PROPN
ejpam-5022	143	12	)	)	PUNCT
ejpam-5022	144	1	=	=	SYM
ejpam-5022	145	1	w1z	w1z	NOUN
ejpam-5022	145	2	+	+	CCONJ
ejpam-5022	145	3	w2z	w2z	NOUN
ejpam-5022	145	4	2	2	NUM
ejpam-5022	145	5	+	+	CCONJ
ejpam-5022	145	6	w3z	w3z	PROPN
ejpam-5022	145	7	3	3	NUM
ejpam-5022	145	8	+	+	NOUN
ejpam-5022	145	9	·	·	PUNCT
ejpam-5022	145	10	·	·	PUNCT
ejpam-5022	145	11	·	·	PUNCT
ejpam-5022	146	1	where	where	SCONJ
ejpam-5022	146	2	z	z	PROPN
ejpam-5022	146	3	∈	∈	PROPN
ejpam-5022	147	1	d	d	NOUN
ejpam-5022	147	2	,	,	PUNCT
ejpam-5022	147	3	then	then	ADV
ejpam-5022	147	4	|w1|	|w1|	NOUN
ejpam-5022	147	5	≤	≤	NUM
ejpam-5022	147	6	1	1	NUM
ejpam-5022	147	7	and	and	CCONJ
ejpam-5022	147	8	for	for	ADP
ejpam-5022	147	9	t	t	PROPN
ejpam-5022	147	10	∈	∈	PROPN
ejpam-5022	147	11	c	c	PROPN
ejpam-5022	147	12	|w2	|w2	NOUN
ejpam-5022	148	1	−	−	PROPN
ejpam-5022	148	2	tw2	tw2	PROPN
ejpam-5022	148	3	1|	1|	NUM
ejpam-5022	148	4	≤	≤	NUM
ejpam-5022	148	5	1	1	NUM
ejpam-5022	148	6	+	+	CCONJ
ejpam-5022	148	7	(	(	PUNCT
ejpam-5022	148	8	|t|	|t|	PROPN
ejpam-5022	148	9	−	−	PROPN
ejpam-5022	148	10	1)|w1|2	1)|w1|2	PROPN
ejpam-5022	148	11	≤	≤	PROPN
ejpam-5022	148	12	max{1	max{1	NOUN
ejpam-5022	148	13	,	,	PUNCT
ejpam-5022	148	14	|t|	|t|	PROPN
ejpam-5022	148	15	}	}	PUNCT
ejpam-5022	148	16	.	.	PUNCT
ejpam-5022	149	1	the	the	DET
ejpam-5022	149	2	result	result	NOUN
ejpam-5022	149	3	is	be	AUX
ejpam-5022	149	4	sharp	sharp	ADJ
ejpam-5022	149	5	for	for	SCONJ
ejpam-5022	149	6	the	the	DET
ejpam-5022	149	7	functions	function	NOUN
ejpam-5022	149	8	w(z	w(z	PROPN
ejpam-5022	149	9	)	)	PUNCT
ejpam-5022	149	10	=	=	SYM
ejpam-5022	149	11	z	z	NOUN
ejpam-5022	149	12	and	and	CCONJ
ejpam-5022	149	13	w(z	w(z	PROPN
ejpam-5022	149	14	)	)	PUNCT
ejpam-5022	149	15	=	=	SYM
ejpam-5022	149	16	z2	z2	PROPN
ejpam-5022	149	17	.	.	PUNCT
ejpam-5022	150	1	w.	w.	PROPN
ejpam-5022	150	2	al	al	PROPN
ejpam-5022	150	3	-	-	PUNCT
ejpam-5022	150	4	rawashdeh	rawashdeh	PROPN
ejpam-5022	150	5	/	/	SYM
ejpam-5022	150	6	eur	eur	PROPN
ejpam-5022	150	7	.	.	PUNCT
ejpam-5022	151	1	j.	j.	PROPN
ejpam-5022	151	2	pure	pure	PROPN
ejpam-5022	151	3	appl	appl	PROPN
ejpam-5022	151	4	.	.	PROPN
ejpam-5022	151	5	math	math	PROPN
ejpam-5022	151	6	,	,	PUNCT
ejpam-5022	151	7	17	17	NUM
ejpam-5022	151	8	(	(	PUNCT
ejpam-5022	151	9	1	1	NUM
ejpam-5022	151	10	)	)	PUNCT
ejpam-5022	151	11	(	(	PUNCT
ejpam-5022	151	12	2024	2024	NUM
ejpam-5022	151	13	)	)	PUNCT
ejpam-5022	151	14	,	,	PUNCT
ejpam-5022	151	15	158	158	NUM
ejpam-5022	151	16	-	-	SYM
ejpam-5022	151	17	170	170	NUM
ejpam-5022	151	18	163	163	NUM
ejpam-5022	151	19	in	in	ADP
ejpam-5022	151	20	this	this	DET
ejpam-5022	151	21	presenting	presenting	NOUN
ejpam-5022	151	22	paper	paper	NOUN
ejpam-5022	152	1	,	,	PUNCT
ejpam-5022	152	2	we	we	PRON
ejpam-5022	152	3	investigate	investigate	VERB
ejpam-5022	152	4	a	a	DET
ejpam-5022	152	5	family	family	NOUN
ejpam-5022	152	6	of	of	ADP
ejpam-5022	152	7	analytic	analytic	ADJ
ejpam-5022	152	8	functions	function	NOUN
ejpam-5022	152	9	on	on	ADP
ejpam-5022	152	10	the	the	DET
ejpam-5022	152	11	open	open	ADJ
ejpam-5022	152	12	unit	unit	NOUN
ejpam-5022	152	13	disk	disk	NOUN
ejpam-5022	152	14	d	d	PROPN
ejpam-5022	152	15	,	,	PUNCT
ejpam-5022	152	16	which	which	PRON
ejpam-5022	152	17	we	we	PRON
ejpam-5022	152	18	denoted	denote	VERB
ejpam-5022	152	19	by	by	ADP
ejpam-5022	152	20	f(π	f(π	PROPN
ejpam-5022	152	21	,	,	PUNCT
ejpam-5022	152	22	α	α	X
ejpam-5022	152	23	,	,	PUNCT
ejpam-5022	152	24	β	β	X
ejpam-5022	152	25	,	,	PUNCT
ejpam-5022	152	26	λ	λ	PROPN
ejpam-5022	152	27	,	,	PUNCT
ejpam-5022	152	28	δ	δ	PROPN
ejpam-5022	152	29	,	,	PUNCT
ejpam-5022	152	30	µ	µ	NOUN
ejpam-5022	152	31	)	)	PUNCT
ejpam-5022	152	32	subordinate	subordinate	NOUN
ejpam-5022	152	33	to	to	ADP
ejpam-5022	152	34	horadam	horadam	NOUN
ejpam-5022	152	35	polynomials	polynomial	NOUN
ejpam-5022	152	36	.	.	PUNCT
ejpam-5022	153	1	for	for	ADP
ejpam-5022	153	2	functions	function	NOUN
ejpam-5022	153	3	in	in	ADP
ejpam-5022	153	4	this	this	DET
ejpam-5022	153	5	family	family	NOUN
ejpam-5022	153	6	,	,	PUNCT
ejpam-5022	153	7	we	we	PRON
ejpam-5022	153	8	derive	derive	VERB
ejpam-5022	153	9	upper	upper	ADJ
ejpam-5022	153	10	bounds	bound	NOUN
ejpam-5022	153	11	for	for	ADP
ejpam-5022	153	12	the	the	DET
ejpam-5022	153	13	initial	initial	ADJ
ejpam-5022	153	14	taylor	taylor	NOUN
ejpam-5022	153	15	-	-	PUNCT
ejpam-5022	153	16	maclarin	maclarin	NOUN
ejpam-5022	153	17	coefficients	coefficient	NOUN
ejpam-5022	153	18	|a2|	|a2|	NOUN
ejpam-5022	153	19	and	and	CCONJ
ejpam-5022	153	20	|a3|	|a3|	NOUN
ejpam-5022	153	21	.	.	PUNCT
ejpam-5022	154	1	furthermore	furthermore	ADV
ejpam-5022	154	2	,	,	PUNCT
ejpam-5022	154	3	we	we	PRON
ejpam-5022	154	4	examine	examine	VERB
ejpam-5022	154	5	the	the	DET
ejpam-5022	154	6	corresponding	corresponding	PROPN
ejpam-5022	154	7	fekete	fekete	PROPN
ejpam-5022	154	8	-	-	PUNCT
ejpam-5022	154	9	szegö	szegö	ADJ
ejpam-5022	154	10	functional	functional	ADJ
ejpam-5022	154	11	problem	problem	NOUN
ejpam-5022	154	12	for	for	ADP
ejpam-5022	154	13	functions	function	NOUN
ejpam-5022	154	14	belong	belong	VERB
ejpam-5022	154	15	to	to	ADP
ejpam-5022	154	16	this	this	DET
ejpam-5022	154	17	family	family	NOUN
ejpam-5022	154	18	.	.	PUNCT
ejpam-5022	155	1	3	3	X
ejpam-5022	155	2	.	.	X
ejpam-5022	155	3	coefficient	coefficient	NOUN
ejpam-5022	155	4	estimates	estimate	NOUN
ejpam-5022	155	5	for	for	ADP
ejpam-5022	155	6	the	the	DET
ejpam-5022	155	7	function	function	NOUN
ejpam-5022	155	8	class	class	NOUN
ejpam-5022	155	9	f(π	f(π	PROPN
ejpam-5022	155	10	,	,	PUNCT
ejpam-5022	155	11	α	α	X
ejpam-5022	155	12	,	,	PUNCT
ejpam-5022	155	13	β	β	X
ejpam-5022	155	14	,	,	PUNCT
ejpam-5022	155	15	λ	λ	PROPN
ejpam-5022	155	16	,	,	PUNCT
ejpam-5022	155	17	δ	δ	PROPN
ejpam-5022	155	18	,	,	PUNCT
ejpam-5022	155	19	µ	µ	NOUN
ejpam-5022	155	20	)	)	PUNCT
ejpam-5022	155	21	in	in	ADP
ejpam-5022	155	22	this	this	DET
ejpam-5022	155	23	section	section	NOUN
ejpam-5022	155	24	,	,	PUNCT
ejpam-5022	155	25	we	we	PRON
ejpam-5022	155	26	provide	provide	VERB
ejpam-5022	155	27	bounds	bound	NOUN
ejpam-5022	155	28	for	for	ADP
ejpam-5022	155	29	the	the	DET
ejpam-5022	155	30	initial	initial	ADJ
ejpam-5022	155	31	taylor	taylor	PROPN
ejpam-5022	155	32	-	-	PUNCT
ejpam-5022	155	33	maclaurin	maclaurin	NOUN
ejpam-5022	155	34	coefficients	coefficient	NOUN
ejpam-5022	155	35	for	for	ADP
ejpam-5022	155	36	the	the	DET
ejpam-5022	155	37	functions	function	NOUN
ejpam-5022	155	38	belong	belong	VERB
ejpam-5022	155	39	to	to	ADP
ejpam-5022	155	40	the	the	DET
ejpam-5022	155	41	class	class	NOUN
ejpam-5022	155	42	f(π	f(π	PROPN
ejpam-5022	155	43	,	,	PUNCT
ejpam-5022	155	44	α	α	X
ejpam-5022	155	45	,	,	PUNCT
ejpam-5022	155	46	β	β	X
ejpam-5022	155	47	,	,	PUNCT
ejpam-5022	155	48	λ	λ	PROPN
ejpam-5022	155	49	,	,	PUNCT
ejpam-5022	155	50	δ	δ	PROPN
ejpam-5022	155	51	,	,	PUNCT
ejpam-5022	155	52	µ	µ	NOUN
ejpam-5022	155	53	)	)	PUNCT
ejpam-5022	155	54	which	which	PRON
ejpam-5022	155	55	are	be	AUX
ejpam-5022	155	56	given	give	VERB
ejpam-5022	155	57	by	by	ADP
ejpam-5022	155	58	equation	equation	NOUN
ejpam-5022	155	59	(	(	PUNCT
ejpam-5022	155	60	1	1	NUM
ejpam-5022	155	61	)	)	PUNCT
ejpam-5022	155	62	.	.	PUNCT
ejpam-5022	156	1	theorem	theorem	NOUN
ejpam-5022	156	2	1	1	NUM
ejpam-5022	156	3	.	.	PUNCT
ejpam-5022	157	1	let	let	VERB
ejpam-5022	157	2	the	the	DET
ejpam-5022	157	3	function	function	NOUN
ejpam-5022	157	4	f(z	f(z	PROPN
ejpam-5022	157	5	)	)	PUNCT
ejpam-5022	157	6	given	give	VERB
ejpam-5022	157	7	by	by	ADP
ejpam-5022	157	8	(	(	PUNCT
ejpam-5022	157	9	1	1	X
ejpam-5022	157	10	)	)	PUNCT
ejpam-5022	157	11	be	be	AUX
ejpam-5022	157	12	in	in	ADP
ejpam-5022	157	13	the	the	DET
ejpam-5022	157	14	class	class	NOUN
ejpam-5022	157	15	f(π	f(π	PROPN
ejpam-5022	157	16	,	,	PUNCT
ejpam-5022	157	17	α	α	X
ejpam-5022	157	18	,	,	PUNCT
ejpam-5022	157	19	β	β	X
ejpam-5022	157	20	,	,	PUNCT
ejpam-5022	157	21	λ	λ	PROPN
ejpam-5022	157	22	,	,	PUNCT
ejpam-5022	157	23	δ	δ	PROPN
ejpam-5022	157	24	,	,	PUNCT
ejpam-5022	157	25	µ	µ	NOUN
ejpam-5022	157	26	)	)	PUNCT
ejpam-5022	157	27	.	.	PUNCT
ejpam-5022	158	1	then	then	ADV
ejpam-5022	158	2	|a2|	|a2|	VERB
ejpam-5022	158	3	≤	≤	ADJ
ejpam-5022	158	4	|bx|	|bx|	NOUN
ejpam-5022	159	1	a(1	a(1	PROPN
ejpam-5022	159	2	+	+	NUM
ejpam-5022	159	3	2µδ	2µδ	ADJ
ejpam-5022	159	4	+	+	CCONJ
ejpam-5022	159	5	µ−	µ−	PROPN
ejpam-5022	159	6	δ	δ	PROPN
ejpam-5022	159	7	)	)	PUNCT
ejpam-5022	159	8	,	,	PUNCT
ejpam-5022	159	9	(	(	PUNCT
ejpam-5022	159	10	11	11	X
ejpam-5022	159	11	)	)	PUNCT
ejpam-5022	159	12	|a3|	|a3|	VERB
ejpam-5022	159	13	≤	≤	ADJ
ejpam-5022	159	14	|bx|	|bx|	PROPN
ejpam-5022	159	15	2b	2b	NUM
ejpam-5022	159	16	max	max	PROPN
ejpam-5022	159	17	{	{	PUNCT
ejpam-5022	159	18	1	1	NUM
ejpam-5022	159	19	,	,	PUNCT
ejpam-5022	159	20	∣∣∣∣bxk2a2	∣∣∣∣bxk2a2	PROPN
ejpam-5022	159	21	−	−	PROPN
ejpam-5022	159	22	pbx2	pbx2	VERB
ejpam-5022	159	23	+	+	CCONJ
ejpam-5022	159	24	qa	qa	PROPN
ejpam-5022	159	25	bx	bx	NOUN
ejpam-5022	159	26	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5022	159	27	}	}	PUNCT
ejpam-5022	159	28	,	,	PUNCT
ejpam-5022	159	29	(	(	PUNCT
ejpam-5022	159	30	12	12	NUM
ejpam-5022	159	31	)	)	PUNCT
ejpam-5022	159	32	where	where	SCONJ
ejpam-5022	159	33	a	a	PRON
ejpam-5022	159	34	=	=	NOUN
ejpam-5022	160	1	αβ	αβ	NOUN
ejpam-5022	160	2	+	+	CCONJ
ejpam-5022	160	3	(	(	PUNCT
ejpam-5022	160	4	1−	1−	NUM
ejpam-5022	160	5	β)(2−	β)(2−	PROPN
ejpam-5022	160	6	λ	λ	PROPN
ejpam-5022	160	7	)	)	PUNCT
ejpam-5022	160	8	,	,	PUNCT
ejpam-5022	160	9	b	b	X
ejpam-5022	160	10	=	=	PUNCT
ejpam-5022	160	11	(	(	PUNCT
ejpam-5022	160	12	αβ	αβ	INTJ
ejpam-5022	161	1	+	+	CCONJ
ejpam-5022	161	2	(	(	PUNCT
ejpam-5022	161	3	1−	1−	NUM
ejpam-5022	161	4	β)(3−	β)(3−	ADP
ejpam-5022	161	5	2λ))(1	2λ))(1	NUM
ejpam-5022	162	1	+	+	CCONJ
ejpam-5022	162	2	2(3µδ	2(3µδ	NUM
ejpam-5022	162	3	+	+	CCONJ
ejpam-5022	162	4	µ−	µ−	PROPN
ejpam-5022	162	5	δ	δ	PROPN
ejpam-5022	162	6	)	)	PUNCT
ejpam-5022	162	7	)	)	PUNCT
ejpam-5022	162	8	,	,	PUNCT
ejpam-5022	162	9	and	and	CCONJ
ejpam-5022	162	10	k	k	PROPN
ejpam-5022	162	11	=	=	X
ejpam-5022	162	12	αβ(α−	αβ(α−	NOUN
ejpam-5022	162	13	3	3	X
ejpam-5022	162	14	)	)	PUNCT
ejpam-5022	162	15	+	+	CCONJ
ejpam-5022	162	16	(	(	PUNCT
ejpam-5022	162	17	1−	1−	NUM
ejpam-5022	162	18	β)(λ2	β)(λ2	NOUN
ejpam-5022	163	1	+	+	CCONJ
ejpam-5022	163	2	5λ−	5λ−	NUM
ejpam-5022	163	3	8)	8)	NUM
ejpam-5022	163	4	.	.	PUNCT
ejpam-5022	164	1	proof	proof	NOUN
ejpam-5022	164	2	.	.	PUNCT
ejpam-5022	165	1	let	let	VERB
ejpam-5022	165	2	f	f	PRON
ejpam-5022	165	3	belong	belong	VERB
ejpam-5022	165	4	to	to	ADP
ejpam-5022	165	5	the	the	DET
ejpam-5022	165	6	class	class	NOUN
ejpam-5022	165	7	f(π	f(π	PROPN
ejpam-5022	165	8	,	,	PUNCT
ejpam-5022	165	9	α	α	X
ejpam-5022	165	10	,	,	PUNCT
ejpam-5022	165	11	β	β	X
ejpam-5022	165	12	,	,	PUNCT
ejpam-5022	165	13	λ	λ	PROPN
ejpam-5022	165	14	,	,	PUNCT
ejpam-5022	165	15	δ	δ	PROPN
ejpam-5022	165	16	,	,	PUNCT
ejpam-5022	165	17	µ	µ	NOUN
ejpam-5022	165	18	)	)	PUNCT
ejpam-5022	165	19	.	.	PUNCT
ejpam-5022	166	1	then	then	ADV
ejpam-5022	166	2	,	,	PUNCT
ejpam-5022	166	3	using	use	VERB
ejpam-5022	166	4	definition	definition	NOUN
ejpam-5022	166	5	1	1	NUM
ejpam-5022	166	6	,	,	PUNCT
ejpam-5022	166	7	we	we	PRON
ejpam-5022	166	8	can	can	AUX
ejpam-5022	166	9	find	find	VERB
ejpam-5022	166	10	an	an	DET
ejpam-5022	166	11	analytic	analytic	ADJ
ejpam-5022	166	12	function	function	NOUN
ejpam-5022	166	13	u	u	NOUN
ejpam-5022	167	1	such	such	ADJ
ejpam-5022	167	2	that	that	SCONJ
ejpam-5022	167	3	β	β	X
ejpam-5022	167	4	(	(	PUNCT
ejpam-5022	167	5	zg′(z	zg′(z	PROPN
ejpam-5022	167	6	)	)	PUNCT
ejpam-5022	167	7	g(z	g(z	PROPN
ejpam-5022	167	8	)	)	PUNCT
ejpam-5022	167	9	)	)	PUNCT
ejpam-5022	167	10	α	α	PROPN
ejpam-5022	167	11	+	+	X
ejpam-5022	167	12	(	(	PUNCT
ejpam-5022	167	13	1−	1−	NUM
ejpam-5022	167	14	β	β	NOUN
ejpam-5022	167	15	)	)	PUNCT
ejpam-5022	167	16	(	(	PUNCT
ejpam-5022	167	17	zg′(z	zg′(z	PROPN
ejpam-5022	167	18	)	)	PUNCT
ejpam-5022	167	19	g(z	g(z	PROPN
ejpam-5022	167	20	)	)	PUNCT
ejpam-5022	167	21	)	)	PUNCT
ejpam-5022	168	1	λ	λ	NOUN
ejpam-5022	168	2	(	(	PUNCT
ejpam-5022	168	3	1	1	NUM
ejpam-5022	168	4	+	+	NUM
ejpam-5022	168	5	zg′′(z	zg′′(z	NOUN
ejpam-5022	168	6	)	)	PUNCT
ejpam-5022	168	7	g′(z	g′(z	VERB
ejpam-5022	168	8	)	)	PUNCT
ejpam-5022	168	9	)	)	PUNCT
ejpam-5022	168	10	1−λ	1−λ	NUM
ejpam-5022	168	11	≺	≺	NOUN
ejpam-5022	168	12	π(x	π(x	NOUN
ejpam-5022	168	13	,	,	PUNCT
ejpam-5022	168	14	u(z	u(z	NOUN
ejpam-5022	168	15	)	)	PUNCT
ejpam-5022	168	16	)	)	PUNCT
ejpam-5022	169	1	+	+	CCONJ
ejpam-5022	169	2	1−	1−	NUM
ejpam-5022	169	3	a	a	DET
ejpam-5022	169	4	(	(	PUNCT
ejpam-5022	169	5	13	13	NUM
ejpam-5022	169	6	)	)	PUNCT
ejpam-5022	169	7	where	where	SCONJ
ejpam-5022	169	8	u	u	NOUN
ejpam-5022	169	9	:	:	PUNCT
ejpam-5022	169	10	d	d	X
ejpam-5022	169	11	→	→	PUNCT
ejpam-5022	169	12	d	d	X
ejpam-5022	169	13	is	be	AUX
ejpam-5022	169	14	given	give	VERB
ejpam-5022	169	15	by	by	ADP
ejpam-5022	169	16	u(z	u(z	NOUN
ejpam-5022	169	17	)	)	PUNCT
ejpam-5022	169	18	=	=	NOUN
ejpam-5022	170	1	∞∑	∞∑	NUM
ejpam-5022	170	2	n=1	n=1	NUM
ejpam-5022	170	3	unz	unz	PROPN
ejpam-5022	170	4	n	n	X
ejpam-5022	170	5	for	for	ADP
ejpam-5022	170	6	z	z	PROPN
ejpam-5022	170	7	∈	∈	PROPN
ejpam-5022	170	8	d	d	NOUN
ejpam-5022	170	9	,	,	PUNCT
ejpam-5022	170	10	such	such	ADJ
ejpam-5022	170	11	that	that	SCONJ
ejpam-5022	170	12	u(0	u(0	NOUN
ejpam-5022	170	13	)	)	PUNCT
ejpam-5022	170	14	=	=	SYM
ejpam-5022	170	15	0	0	NUM
ejpam-5022	170	16	and	and	CCONJ
ejpam-5022	170	17	|u(z)|	|u(z)|	VERB
ejpam-5022	170	18	<	<	X
ejpam-5022	170	19	1	1	NUM
ejpam-5022	170	20	for	for	ADP
ejpam-5022	170	21	all	all	DET
ejpam-5022	170	22	z	z	NOUN
ejpam-5022	170	23	∈	∈	PROPN
ejpam-5022	170	24	d.	d.	PROPN
ejpam-5022	170	25	moreover	moreover	ADV
ejpam-5022	170	26	,	,	PUNCT
ejpam-5022	170	27	it	it	PRON
ejpam-5022	170	28	is	be	AUX
ejpam-5022	170	29	well	well	ADV
ejpam-5022	170	30	-	-	PUNCT
ejpam-5022	170	31	known	know	VERB
ejpam-5022	170	32	that	that	SCONJ
ejpam-5022	170	33	(	(	PUNCT
ejpam-5022	170	34	see	see	VERB
ejpam-5022	170	35	,	,	PUNCT
ejpam-5022	170	36	for	for	ADP
ejpam-5022	170	37	details	detail	NOUN
ejpam-5022	170	38	[	[	X
ejpam-5022	170	39	11	11	NUM
ejpam-5022	170	40	]	]	NUM
ejpam-5022	170	41	)	)	PUNCT
ejpam-5022	170	42	,	,	PUNCT
ejpam-5022	170	43	|uj	|uj	PROPN
ejpam-5022	170	44	|	|	ADV
ejpam-5022	170	45	≤	≤	NUM
ejpam-5022	170	46	for	for	ADP
ejpam-5022	170	47	all	all	DET
ejpam-5022	170	48	j	j	PROPN
ejpam-5022	170	49	∈	∈	PROPN
ejpam-5022	170	50	n.	n.	NOUN
ejpam-5022	170	51	now	now	ADV
ejpam-5022	170	52	,	,	PUNCT
ejpam-5022	170	53	upon	upon	SCONJ
ejpam-5022	170	54	comparing	compare	VERB
ejpam-5022	170	55	the	the	DET
ejpam-5022	170	56	coefficients	coefficient	NOUN
ejpam-5022	170	57	in	in	ADP
ejpam-5022	170	58	both	both	DET
ejpam-5022	170	59	sides	side	NOUN
ejpam-5022	170	60	of	of	ADP
ejpam-5022	170	61	equation	equation	NOUN
ejpam-5022	170	62	(	(	PUNCT
ejpam-5022	170	63	13	13	NUM
ejpam-5022	170	64	)	)	PUNCT
ejpam-5022	170	65	,	,	PUNCT
ejpam-5022	170	66	we	we	PRON
ejpam-5022	170	67	obtain	obtain	VERB
ejpam-5022	170	68	the	the	DET
ejpam-5022	170	69	following	follow	VERB
ejpam-5022	170	70	equations	equation	NOUN
ejpam-5022	170	71	,	,	PUNCT
ejpam-5022	170	72	where	where	SCONJ
ejpam-5022	170	73	γ	γ	X
ejpam-5022	170	74	=	=	SYM
ejpam-5022	170	75	2µδ	2µδ	PROPN
ejpam-5022	170	76	+	+	CCONJ
ejpam-5022	170	77	µ−	µ−	PROPN
ejpam-5022	170	78	δ	δ	PROPN
ejpam-5022	170	79	,	,	PUNCT
ejpam-5022	170	80	(	(	PUNCT
ejpam-5022	170	81	αβ	αβ	INTJ
ejpam-5022	171	1	+	+	CCONJ
ejpam-5022	171	2	(	(	PUNCT
ejpam-5022	171	3	1−	1−	NUM
ejpam-5022	171	4	β)(2−	β)(2−	NOUN
ejpam-5022	171	5	λ))(γ	λ))(γ	NOUN
ejpam-5022	171	6	+	+	CCONJ
ejpam-5022	171	7	1)a2	1)a2	NUM
ejpam-5022	171	8	=	=	SYM
ejpam-5022	171	9	h2(x)u1	h2(x)u1	PROPN
ejpam-5022	171	10	.	.	PUNCT
ejpam-5022	172	1	(	(	PUNCT
ejpam-5022	172	2	14	14	NUM
ejpam-5022	172	3	)	)	PUNCT
ejpam-5022	173	1	[	[	X
ejpam-5022	173	2	αβ(α−	αβ(α−	NUM
ejpam-5022	173	3	3	3	X
ejpam-5022	173	4	)	)	PUNCT
ejpam-5022	173	5	+	+	CCONJ
ejpam-5022	173	6	(	(	PUNCT
ejpam-5022	173	7	1−	1−	NUM
ejpam-5022	173	8	β)(λ2	β)(λ2	NOUN
ejpam-5022	174	1	+	+	CCONJ
ejpam-5022	174	2	5λ−	5λ−	NUM
ejpam-5022	174	3	8)](γ	8)](γ	NUM
ejpam-5022	174	4	+	+	NUM
ejpam-5022	174	5	1)2a22	1)2a22	NUM
ejpam-5022	174	6	+	+	SYM
ejpam-5022	174	7	(	(	PUNCT
ejpam-5022	174	8	15	15	NUM
ejpam-5022	174	9	)	)	PUNCT
ejpam-5022	174	10	w.	w.	PROPN
ejpam-5022	174	11	al	al	PROPN
ejpam-5022	174	12	-	-	PUNCT
ejpam-5022	174	13	rawashdeh	rawashdeh	PROPN
ejpam-5022	174	14	/	/	SYM
ejpam-5022	174	15	eur	eur	PROPN
ejpam-5022	174	16	.	.	PUNCT
ejpam-5022	175	1	j.	j.	PROPN
ejpam-5022	175	2	pure	pure	PROPN
ejpam-5022	175	3	appl	appl	PROPN
ejpam-5022	175	4	.	.	PROPN
ejpam-5022	175	5	math	math	PROPN
ejpam-5022	175	6	,	,	PUNCT
ejpam-5022	175	7	17	17	NUM
ejpam-5022	175	8	(	(	PUNCT
ejpam-5022	175	9	1	1	NUM
ejpam-5022	175	10	)	)	PUNCT
ejpam-5022	175	11	(	(	PUNCT
ejpam-5022	175	12	2024	2024	NUM
ejpam-5022	175	13	)	)	PUNCT
ejpam-5022	175	14	,	,	PUNCT
ejpam-5022	175	15	158	158	NUM
ejpam-5022	175	16	-	-	SYM
ejpam-5022	175	17	170	170	NUM
ejpam-5022	175	18	164	164	NUM
ejpam-5022	175	19	+4(αβ	+4(αβ	NOUN
ejpam-5022	175	20	+	+	CCONJ
ejpam-5022	175	21	(	(	PUNCT
ejpam-5022	175	22	1−	1−	NUM
ejpam-5022	175	23	β)(3−	β)(3−	ADP
ejpam-5022	175	24	2λ))(2(γ	2λ))(2(γ	NUM
ejpam-5022	175	25	+	+	CCONJ
ejpam-5022	175	26	µδ	µδ	NOUN
ejpam-5022	175	27	)	)	PUNCT
ejpam-5022	176	1	+	+	CCONJ
ejpam-5022	176	2	1)a3	1)a3	NUM
ejpam-5022	176	3	=	=	SYM
ejpam-5022	176	4	2h2(x)u2	2h2(x)u2	NOUN
ejpam-5022	176	5	+	+	CCONJ
ejpam-5022	176	6	2h3(x)u	2h3(x)u	NUM
ejpam-5022	176	7	2	2	NUM
ejpam-5022	176	8	1	1	NUM
ejpam-5022	176	9	.	.	PUNCT
ejpam-5022	177	1	using	use	VERB
ejpam-5022	177	2	equation	equation	NOUN
ejpam-5022	177	3	(	(	PUNCT
ejpam-5022	177	4	14	14	NUM
ejpam-5022	177	5	)	)	PUNCT
ejpam-5022	177	6	,	,	PUNCT
ejpam-5022	177	7	|u1|	|u1|	ADJ
ejpam-5022	177	8	≤	≤	NUM
ejpam-5022	177	9	1	1	NUM
ejpam-5022	177	10	and	and	CCONJ
ejpam-5022	177	11	h2(x	h2(x	NUM
ejpam-5022	177	12	)	)	PUNCT
ejpam-5022	177	13	=	=	SYM
ejpam-5022	177	14	bx	bx	PROPN
ejpam-5022	177	15	,	,	PUNCT
ejpam-5022	177	16	we	we	PRON
ejpam-5022	177	17	get	get	VERB
ejpam-5022	177	18	the	the	DET
ejpam-5022	177	19	desired	desire	VERB
ejpam-5022	177	20	bound	bind	VERB
ejpam-5022	177	21	of	of	ADP
ejpam-5022	177	22	|a2|	|a2|	NOUN
ejpam-5022	177	23	:	:	PUNCT
ejpam-5022	177	24	|a2|	|a2|	NOUN
ejpam-5022	177	25	≤	≤	ADJ
ejpam-5022	177	26	|bx|	|bx|	NOUN
ejpam-5022	178	1	[	[	X
ejpam-5022	178	2	αβ	αβ	X
ejpam-5022	178	3	+	+	X
ejpam-5022	178	4	(	(	PUNCT
ejpam-5022	178	5	1−	1−	NUM
ejpam-5022	178	6	β)(2−	β)(2−	NOUN
ejpam-5022	178	7	λ)](γ	λ)](γ	NOUN
ejpam-5022	178	8	+	+	CCONJ
ejpam-5022	178	9	1	1	NUM
ejpam-5022	178	10	)	)	PUNCT
ejpam-5022	178	11	.	.	PUNCT
ejpam-5022	179	1	in	in	ADP
ejpam-5022	179	2	view	view	NOUN
ejpam-5022	179	3	of	of	ADP
ejpam-5022	179	4	equation	equation	NOUN
ejpam-5022	179	5	(	(	PUNCT
ejpam-5022	179	6	14	14	NUM
ejpam-5022	179	7	)	)	PUNCT
ejpam-5022	179	8	,	,	PUNCT
ejpam-5022	179	9	we	we	PRON
ejpam-5022	179	10	can	can	AUX
ejpam-5022	179	11	write	write	VERB
ejpam-5022	179	12	equation	equation	NOUN
ejpam-5022	179	13	(	(	PUNCT
ejpam-5022	179	14	15	15	NUM
ejpam-5022	179	15	)	)	PUNCT
ejpam-5022	179	16	as	as	ADP
ejpam-5022	179	17	:	:	PUNCT
ejpam-5022	179	18	a3	a3	PROPN
ejpam-5022	179	19	=	=	SYM
ejpam-5022	179	20	h2(x	h2(x	PROPN
ejpam-5022	179	21	)	)	PUNCT
ejpam-5022	179	22	2b	2b	NOUN
ejpam-5022	179	23	(	(	PUNCT
ejpam-5022	179	24	u2	u2	NOUN
ejpam-5022	179	25	−	−	PROPN
ejpam-5022	179	26	1	1	NUM
ejpam-5022	179	27	h2(x	h2(x	NOUN
ejpam-5022	179	28	)	)	PUNCT
ejpam-5022	179	29	(	(	PUNCT
ejpam-5022	179	30	k[h2(x	k[h2(x	PROPN
ejpam-5022	179	31	)	)	PUNCT
ejpam-5022	179	32	]	]	PUNCT
ejpam-5022	180	1	2	2	NUM
ejpam-5022	180	2	2a2	2a2	NUM
ejpam-5022	180	3	−	−	ADP
ejpam-5022	180	4	h3(x	h3(x	PROPN
ejpam-5022	180	5	)	)	PUNCT
ejpam-5022	180	6	)	)	PUNCT
ejpam-5022	180	7	u21	u21	PROPN
ejpam-5022	180	8	)	)	PUNCT
ejpam-5022	180	9	.	.	PUNCT
ejpam-5022	181	1	using	use	VERB
ejpam-5022	181	2	lemma	lemma	PROPN
ejpam-5022	181	3	1	1	NUM
ejpam-5022	181	4	,	,	PUNCT
ejpam-5022	181	5	we	we	PRON
ejpam-5022	181	6	obtain	obtain	AUX
ejpam-5022	181	7	|a3|	|a3|	NOUN
ejpam-5022	181	8	≤	≤	PUNCT
ejpam-5022	181	9	|h2(x)|	|h2(x)|	PART
ejpam-5022	181	10	2b	2b	NUM
ejpam-5022	181	11	max	max	PROPN
ejpam-5022	181	12	{	{	PUNCT
ejpam-5022	181	13	1	1	NUM
ejpam-5022	181	14	,	,	PUNCT
ejpam-5022	181	15	∣∣∣∣k[h2(x	∣∣∣∣k[h2(x	NOUN
ejpam-5022	181	16	)	)	PUNCT
ejpam-5022	181	17	]	]	PUNCT
ejpam-5022	181	18	2	2	NUM
ejpam-5022	181	19	−	−	PROPN
ejpam-5022	181	20	2a2h3(x	2a2h3(x	NUM
ejpam-5022	181	21	)	)	PUNCT
ejpam-5022	181	22	2a2h2(x	2a2h2(x	PROPN
ejpam-5022	181	23	)	)	PUNCT
ejpam-5022	181	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5022	181	25	}	}	PUNCT
ejpam-5022	181	26	.	.	PUNCT
ejpam-5022	182	1	using	use	VERB
ejpam-5022	182	2	the	the	DET
ejpam-5022	182	3	initial	initial	ADJ
ejpam-5022	182	4	values	value	NOUN
ejpam-5022	182	5	(	(	PUNCT
ejpam-5022	182	6	3	3	NUM
ejpam-5022	182	7	)	)	PUNCT
ejpam-5022	182	8	,	,	PUNCT
ejpam-5022	182	9	we	we	PRON
ejpam-5022	182	10	get	get	VERB
ejpam-5022	182	11	the	the	DET
ejpam-5022	182	12	desired	desire	VERB
ejpam-5022	182	13	estimate	estimate	NOUN
ejpam-5022	182	14	of	of	ADP
ejpam-5022	182	15	|a3|	|a3|	PROPN
ejpam-5022	182	16	.	.	PUNCT
ejpam-5022	183	1	this	this	PRON
ejpam-5022	183	2	complete	complete	VERB
ejpam-5022	183	3	the	the	DET
ejpam-5022	183	4	proof	proof	NOUN
ejpam-5022	183	5	.	.	PUNCT
ejpam-5022	184	1	the	the	DET
ejpam-5022	184	2	following	follow	VERB
ejpam-5022	184	3	corollaries	corollary	NOUN
ejpam-5022	184	4	are	be	AUX
ejpam-5022	184	5	just	just	ADV
ejpam-5022	184	6	consequences	consequence	NOUN
ejpam-5022	184	7	of	of	ADP
ejpam-5022	184	8	theorem	theorem	ADJ
ejpam-5022	184	9	1	1	NUM
ejpam-5022	184	10	.	.	PUNCT
ejpam-5022	184	11	corollary	corollary	ADJ
ejpam-5022	184	12	1	1	NUM
ejpam-5022	184	13	.	.	PUNCT
ejpam-5022	185	1	if	if	SCONJ
ejpam-5022	185	2	the	the	DET
ejpam-5022	185	3	function	function	NOUN
ejpam-5022	185	4	f	f	PROPN
ejpam-5022	185	5	∈	∈	PROPN
ejpam-5022	185	6	a	a	DET
ejpam-5022	185	7	satisfies	satisfie	NOUN
ejpam-5022	185	8	the	the	DET
ejpam-5022	185	9	subordination	subordination	NOUN
ejpam-5022	185	10	(	(	PUNCT
ejpam-5022	185	11	5	5	NUM
ejpam-5022	185	12	)	)	PUNCT
ejpam-5022	185	13	,	,	PUNCT
ejpam-5022	185	14	then	then	ADV
ejpam-5022	185	15	|a2|	|a2|	VERB
ejpam-5022	185	16	≤	≤	ADJ
ejpam-5022	185	17	|bx|	|bx|	NOUN
ejpam-5022	185	18	1	1	NUM
ejpam-5022	185	19	+	+	SYM
ejpam-5022	185	20	η	η	PROPN
ejpam-5022	185	21	,	,	PUNCT
ejpam-5022	185	22	and	and	CCONJ
ejpam-5022	185	23	|a3|	|a3|	VERB
ejpam-5022	185	24	≤	≤	ADJ
ejpam-5022	185	25	|bx|	|bx|	PROPN
ejpam-5022	185	26	2(1	2(1	NUM
ejpam-5022	185	27	+	+	CCONJ
ejpam-5022	185	28	2η	2η	NUM
ejpam-5022	185	29	)	)	PUNCT
ejpam-5022	185	30	max	max	PROPN
ejpam-5022	185	31	{	{	PUNCT
ejpam-5022	185	32	1	1	NUM
ejpam-5022	185	33	,	,	PUNCT
ejpam-5022	185	34	∣∣∣∣bx(1	∣∣∣∣bx(1	NOUN
ejpam-5022	185	35	+	+	SYM
ejpam-5022	185	36	3η	3η	NUM
ejpam-5022	185	37	)	)	PUNCT
ejpam-5022	185	38	(	(	PUNCT
ejpam-5022	185	39	1	1	NUM
ejpam-5022	185	40	+	+	CCONJ
ejpam-5022	185	41	η)2	η)2	NOUN
ejpam-5022	185	42	+	+	CCONJ
ejpam-5022	185	43	pbx2	pbx2	VERB
ejpam-5022	185	44	+	+	CCONJ
ejpam-5022	185	45	qa	qa	PROPN
ejpam-5022	185	46	bx	bx	NOUN
ejpam-5022	185	47	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5022	185	48	}	}	PUNCT
ejpam-5022	185	49	.	.	PUNCT
ejpam-5022	186	1	corollary	corollary	ADJ
ejpam-5022	186	2	2	2	NUM
ejpam-5022	186	3	.	.	PUNCT
ejpam-5022	187	1	if	if	SCONJ
ejpam-5022	187	2	the	the	DET
ejpam-5022	187	3	function	function	NOUN
ejpam-5022	187	4	f	f	PROPN
ejpam-5022	187	5	∈	∈	PROPN
ejpam-5022	187	6	a	a	DET
ejpam-5022	187	7	satisfies	satisfie	NOUN
ejpam-5022	187	8	the	the	DET
ejpam-5022	187	9	subordination	subordination	NOUN
ejpam-5022	187	10	(	(	PUNCT
ejpam-5022	187	11	6	6	NUM
ejpam-5022	187	12	)	)	PUNCT
ejpam-5022	187	13	,	,	PUNCT
ejpam-5022	187	14	then	then	ADV
ejpam-5022	187	15	|a2|	|a2|	VERB
ejpam-5022	187	16	≤	≤	ADJ
ejpam-5022	187	17	|bx|	|bx|	NOUN
ejpam-5022	187	18	2−	2−	NUM
ejpam-5022	187	19	λ	λ	NOUN
ejpam-5022	187	20	,	,	PUNCT
ejpam-5022	187	21	and	and	CCONJ
ejpam-5022	187	22	|a3|	|a3|	VERB
ejpam-5022	187	23	≤	≤	ADJ
ejpam-5022	187	24	|bx|	|bx|	PROPN
ejpam-5022	187	25	2(3−	2(3−	ADP
ejpam-5022	187	26	2λ	2λ	PROPN
ejpam-5022	187	27	)	)	PUNCT
ejpam-5022	188	1	max	max	PROPN
ejpam-5022	188	2	{	{	PUNCT
ejpam-5022	188	3	1	1	NUM
ejpam-5022	188	4	,	,	PUNCT
ejpam-5022	188	5	∣∣∣∣bx(λ2	∣∣∣∣bx(λ2	PROPN
ejpam-5022	188	6	+	+	CCONJ
ejpam-5022	189	1	5λ−	5λ−	NUM
ejpam-5022	189	2	8)	8)	NUM
ejpam-5022	189	3	2(2−	2(2−	NUM
ejpam-5022	189	4	λ)2	λ)2	NOUN
ejpam-5022	189	5	−	−	PROPN
ejpam-5022	189	6	pbx2	pbx2	NOUN
ejpam-5022	189	7	+	+	CCONJ
ejpam-5022	189	8	qa	qa	PROPN
ejpam-5022	189	9	bx	bx	NOUN
ejpam-5022	189	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5022	189	11	}	}	PUNCT
ejpam-5022	189	12	.	.	PUNCT
ejpam-5022	190	1	corollary	corollary	ADJ
ejpam-5022	190	2	3	3	X
ejpam-5022	190	3	.	.	PUNCT
ejpam-5022	191	1	if	if	SCONJ
ejpam-5022	191	2	the	the	DET
ejpam-5022	191	3	function	function	NOUN
ejpam-5022	191	4	f	f	PROPN
ejpam-5022	191	5	∈	∈	PROPN
ejpam-5022	191	6	a	a	DET
ejpam-5022	191	7	satisfies	satisfie	NOUN
ejpam-5022	191	8	the	the	DET
ejpam-5022	191	9	subordination	subordination	NOUN
ejpam-5022	191	10	(	(	PUNCT
ejpam-5022	191	11	7	7	NUM
ejpam-5022	191	12	)	)	PUNCT
ejpam-5022	191	13	,	,	PUNCT
ejpam-5022	191	14	then	then	ADV
ejpam-5022	191	15	|a2|	|a2|	VERB
ejpam-5022	191	16	≤	≤	ADJ
ejpam-5022	191	17	|bx|	|bx|	NOUN
ejpam-5022	191	18	1	1	NUM
ejpam-5022	192	1	+	+	CCONJ
ejpam-5022	192	2	2µδ	2µδ	ADJ
ejpam-5022	192	3	+	+	CCONJ
ejpam-5022	192	4	µ−	µ−	PROPN
ejpam-5022	192	5	δ	δ	NOUN
ejpam-5022	192	6	,	,	PUNCT
ejpam-5022	192	7	and	and	CCONJ
ejpam-5022	192	8	|a3|	|a3|	VERB
ejpam-5022	192	9	≤	≤	ADJ
ejpam-5022	192	10	|bx|	|bx|	PROPN
ejpam-5022	192	11	2(1	2(1	NUM
ejpam-5022	193	1	+	+	CCONJ
ejpam-5022	193	2	2(3µδ	2(3µδ	NUM
ejpam-5022	193	3	+	+	NUM
ejpam-5022	193	4	µ−	µ−	PROPN
ejpam-5022	193	5	δ	δ	PROPN
ejpam-5022	193	6	)	)	PUNCT
ejpam-5022	193	7	)	)	PUNCT
ejpam-5022	194	1	max	max	PROPN
ejpam-5022	194	2	{	{	PUNCT
ejpam-5022	194	3	1	1	NUM
ejpam-5022	194	4	,	,	PUNCT
ejpam-5022	194	5	∣∣∣∣b2x2	∣∣∣∣b2x2	VERB
ejpam-5022	194	6	+	+	CCONJ
ejpam-5022	194	7	pbx2	pbx2	VERB
ejpam-5022	194	8	+	+	CCONJ
ejpam-5022	194	9	qa	qa	PROPN
ejpam-5022	194	10	bx	bx	NOUN
ejpam-5022	194	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5022	194	12	}	}	PUNCT
ejpam-5022	194	13	.	.	PUNCT
ejpam-5022	195	1	w.	w.	PROPN
ejpam-5022	195	2	al	al	PROPN
ejpam-5022	195	3	-	-	PUNCT
ejpam-5022	195	4	rawashdeh	rawashdeh	PROPN
ejpam-5022	195	5	/	/	SYM
ejpam-5022	195	6	eur	eur	PROPN
ejpam-5022	195	7	.	.	PUNCT
ejpam-5022	196	1	j.	j.	PROPN
ejpam-5022	196	2	pure	pure	PROPN
ejpam-5022	196	3	appl	appl	PROPN
ejpam-5022	196	4	.	.	PROPN
ejpam-5022	196	5	math	math	PROPN
ejpam-5022	196	6	,	,	PUNCT
ejpam-5022	196	7	17	17	NUM
ejpam-5022	196	8	(	(	PUNCT
ejpam-5022	196	9	1	1	NUM
ejpam-5022	196	10	)	)	PUNCT
ejpam-5022	196	11	(	(	PUNCT
ejpam-5022	196	12	2024	2024	NUM
ejpam-5022	196	13	)	)	PUNCT
ejpam-5022	196	14	,	,	PUNCT
ejpam-5022	196	15	158	158	NUM
ejpam-5022	196	16	-	-	SYM
ejpam-5022	196	17	170	170	NUM
ejpam-5022	196	18	165	165	NUM
ejpam-5022	196	19	corollary	corollary	ADJ
ejpam-5022	196	20	4	4	NUM
ejpam-5022	196	21	.	.	PUNCT
ejpam-5022	197	1	if	if	SCONJ
ejpam-5022	197	2	the	the	DET
ejpam-5022	197	3	function	function	NOUN
ejpam-5022	197	4	f	f	PROPN
ejpam-5022	197	5	∈	∈	PROPN
ejpam-5022	197	6	a	a	DET
ejpam-5022	197	7	satisfies	satisfie	NOUN
ejpam-5022	197	8	the	the	DET
ejpam-5022	197	9	subordination	subordination	NOUN
ejpam-5022	197	10	(	(	PUNCT
ejpam-5022	197	11	8)	8)	NUM
ejpam-5022	197	12	,	,	PUNCT
ejpam-5022	197	13	then	then	ADV
ejpam-5022	197	14	|a2|	|a2|	VERB
ejpam-5022	197	15	≤	≤	ADJ
ejpam-5022	197	16	|bx|	|bx|	NOUN
ejpam-5022	198	1	αβ	αβ	INTJ
ejpam-5022	198	2	+	+	CCONJ
ejpam-5022	198	3	(	(	PUNCT
ejpam-5022	198	4	1−	1−	NUM
ejpam-5022	198	5	β)(2−	β)(2−	PROPN
ejpam-5022	198	6	λ	λ	PROPN
ejpam-5022	198	7	)	)	PUNCT
ejpam-5022	198	8	,	,	PUNCT
ejpam-5022	198	9	and	and	CCONJ
ejpam-5022	198	10	|a3|	|a3|	VERB
ejpam-5022	198	11	≤	≤	ADJ
ejpam-5022	198	12	|bx|	|bx|	NOUN
ejpam-5022	198	13	2(αβ	2(αβ	NUM
ejpam-5022	198	14	+	+	CCONJ
ejpam-5022	198	15	(	(	PUNCT
ejpam-5022	198	16	1−	1−	NUM
ejpam-5022	198	17	β)(3−	β)(3−	ADP
ejpam-5022	198	18	2λ	2λ	NUM
ejpam-5022	198	19	)	)	PUNCT
ejpam-5022	198	20	)	)	PUNCT
ejpam-5022	199	1	max	max	PROPN
ejpam-5022	199	2	{	{	PUNCT
ejpam-5022	199	3	1	1	NUM
ejpam-5022	199	4	,	,	PUNCT
ejpam-5022	199	5	∣∣∣∣bxk2a2	∣∣∣∣bxk2a2	PROPN
ejpam-5022	199	6	−	−	PROPN
ejpam-5022	199	7	pbx2	pbx2	VERB
ejpam-5022	199	8	+	+	CCONJ
ejpam-5022	199	9	qa	qa	PROPN
ejpam-5022	199	10	bx	bx	NOUN
ejpam-5022	199	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5022	199	12	}	}	PUNCT
ejpam-5022	199	13	,	,	PUNCT
ejpam-5022	199	14	corollary	corollary	ADJ
ejpam-5022	199	15	5	5	NUM
ejpam-5022	199	16	.	.	PUNCT
ejpam-5022	200	1	if	if	SCONJ
ejpam-5022	200	2	the	the	DET
ejpam-5022	200	3	function	function	NOUN
ejpam-5022	200	4	f	f	PROPN
ejpam-5022	200	5	∈	∈	PROPN
ejpam-5022	200	6	a	a	DET
ejpam-5022	200	7	satisfies	satisfie	NOUN
ejpam-5022	200	8	the	the	DET
ejpam-5022	200	9	subordination	subordination	NOUN
ejpam-5022	200	10	(	(	PUNCT
ejpam-5022	200	11	9	9	NUM
ejpam-5022	200	12	)	)	PUNCT
ejpam-5022	200	13	,	,	PUNCT
ejpam-5022	200	14	then	then	ADV
ejpam-5022	200	15	|a2|	|a2|	VERB
ejpam-5022	200	16	≤	≤	ADJ
ejpam-5022	200	17	|bx|	|bx|	NOUN
ejpam-5022	200	18	(	(	PUNCT
ejpam-5022	200	19	1	1	NUM
ejpam-5022	200	20	+	+	NUM
ejpam-5022	200	21	η)(1	η)(1	NUM
ejpam-5022	200	22	+	+	SYM
ejpam-5022	200	23	µ	µ	X
ejpam-5022	200	24	)	)	PUNCT
ejpam-5022	200	25	,	,	PUNCT
ejpam-5022	200	26	and	and	CCONJ
ejpam-5022	200	27	|a3|	|a3|	VERB
ejpam-5022	200	28	≤	≤	ADJ
ejpam-5022	200	29	|bx|	|bx|	PROPN
ejpam-5022	200	30	2(1	2(1	NUM
ejpam-5022	200	31	+	+	CCONJ
ejpam-5022	200	32	2η)(1	2η)(1	NUM
ejpam-5022	200	33	+	+	SYM
ejpam-5022	200	34	2µ	2µ	NUM
ejpam-5022	200	35	)	)	PUNCT
ejpam-5022	200	36	max	max	PROPN
ejpam-5022	200	37	{	{	PUNCT
ejpam-5022	200	38	1	1	NUM
ejpam-5022	200	39	,	,	PUNCT
ejpam-5022	200	40	∣∣∣∣bx(1	∣∣∣∣bx(1	NOUN
ejpam-5022	200	41	+	+	SYM
ejpam-5022	200	42	3η	3η	NUM
ejpam-5022	200	43	)	)	PUNCT
ejpam-5022	200	44	(	(	PUNCT
ejpam-5022	200	45	1	1	NUM
ejpam-5022	200	46	+	+	CCONJ
ejpam-5022	200	47	η)2	η)2	NOUN
ejpam-5022	200	48	+	+	CCONJ
ejpam-5022	200	49	pbx2	pbx2	VERB
ejpam-5022	200	50	+	+	CCONJ
ejpam-5022	200	51	qa	qa	PROPN
ejpam-5022	200	52	bx	bx	NOUN
ejpam-5022	200	53	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5022	200	54	}	}	PUNCT
ejpam-5022	200	55	.	.	PUNCT
ejpam-5022	201	1	4	4	X
ejpam-5022	201	2	.	.	X
ejpam-5022	201	3	fekete	fekete	NOUN
ejpam-5022	201	4	-	-	PUNCT
ejpam-5022	201	5	szegö	szegö	ADJ
ejpam-5022	201	6	functional	functional	NOUN
ejpam-5022	201	7	of	of	ADP
ejpam-5022	201	8	the	the	DET
ejpam-5022	201	9	class	class	NOUN
ejpam-5022	201	10	f(π	f(π	PROPN
ejpam-5022	201	11	,	,	PUNCT
ejpam-5022	201	12	α	α	X
ejpam-5022	201	13	,	,	PUNCT
ejpam-5022	201	14	β	β	X
ejpam-5022	201	15	,	,	PUNCT
ejpam-5022	201	16	λ	λ	PROPN
ejpam-5022	201	17	,	,	PUNCT
ejpam-5022	201	18	δ	δ	PROPN
ejpam-5022	201	19	,	,	PUNCT
ejpam-5022	201	20	µ	µ	NOUN
ejpam-5022	201	21	)	)	PUNCT
ejpam-5022	201	22	in	in	ADP
ejpam-5022	201	23	this	this	DET
ejpam-5022	201	24	section	section	NOUN
ejpam-5022	201	25	,	,	PUNCT
ejpam-5022	201	26	we	we	PRON
ejpam-5022	201	27	consider	consider	VERB
ejpam-5022	201	28	the	the	DET
ejpam-5022	201	29	classical	classical	ADJ
ejpam-5022	201	30	fekete	fekete	PROPN
ejpam-5022	201	31	-	-	PUNCT
ejpam-5022	201	32	szegö	szegö	ADJ
ejpam-5022	201	33	problem	problem	NOUN
ejpam-5022	201	34	for	for	ADP
ejpam-5022	201	35	our	our	PRON
ejpam-5022	201	36	presenting	present	VERB
ejpam-5022	201	37	class	class	NOUN
ejpam-5022	201	38	f(π	f(π	PROPN
ejpam-5022	201	39	,	,	PUNCT
ejpam-5022	201	40	α	α	X
ejpam-5022	201	41	,	,	PUNCT
ejpam-5022	201	42	β	β	X
ejpam-5022	201	43	,	,	PUNCT
ejpam-5022	201	44	λ	λ	PROPN
ejpam-5022	201	45	,	,	PUNCT
ejpam-5022	201	46	δ	δ	PROPN
ejpam-5022	201	47	,	,	PUNCT
ejpam-5022	201	48	µ	µ	NOUN
ejpam-5022	201	49	)	)	PUNCT
ejpam-5022	201	50	.	.	PUNCT
ejpam-5022	202	1	theorem	theorem	NOUN
ejpam-5022	202	2	2	2	NUM
ejpam-5022	202	3	.	.	PUNCT
ejpam-5022	203	1	let	let	VERB
ejpam-5022	203	2	the	the	DET
ejpam-5022	203	3	function	function	NOUN
ejpam-5022	203	4	f	f	NOUN
ejpam-5022	203	5	given	give	VERB
ejpam-5022	203	6	by	by	ADP
ejpam-5022	203	7	(	(	PUNCT
ejpam-5022	203	8	1	1	X
ejpam-5022	203	9	)	)	PUNCT
ejpam-5022	203	10	be	be	AUX
ejpam-5022	203	11	in	in	ADP
ejpam-5022	203	12	the	the	DET
ejpam-5022	203	13	class	class	NOUN
ejpam-5022	203	14	f(π	f(π	PROPN
ejpam-5022	203	15	,	,	PUNCT
ejpam-5022	203	16	α	α	X
ejpam-5022	203	17	,	,	PUNCT
ejpam-5022	203	18	β	β	X
ejpam-5022	203	19	,	,	PUNCT
ejpam-5022	203	20	λ	λ	PROPN
ejpam-5022	203	21	,	,	PUNCT
ejpam-5022	203	22	δ	δ	PROPN
ejpam-5022	203	23	,	,	PUNCT
ejpam-5022	203	24	µ	µ	NOUN
ejpam-5022	203	25	)	)	PUNCT
ejpam-5022	203	26	.	.	PUNCT
ejpam-5022	204	1	then	then	ADV
ejpam-5022	204	2	for	for	ADP
ejpam-5022	204	3	bx	bx	PROPN
ejpam-5022	204	4	>	>	X
ejpam-5022	204	5	0	0	PUNCT
ejpam-5022	205	1	and	and	CCONJ
ejpam-5022	205	2	for	for	ADP
ejpam-5022	205	3	some	some	DET
ejpam-5022	205	4	ζ	ζ	NOUN
ejpam-5022	205	5	∈	∈	NOUN
ejpam-5022	205	6	r	r	NOUN
ejpam-5022	205	7	,	,	PUNCT
ejpam-5022	205	8	|a3	|a3	NOUN
ejpam-5022	205	9	−	−	PROPN
ejpam-5022	205	10	ζa22|	ζa22|	NOUN
ejpam-5022	205	11	≤	≤	PROPN
ejpam-5022	205	12	{	{	PUNCT
ejpam-5022	205	13	bx	bx	NOUN
ejpam-5022	205	14	2b	2b	NOUN
ejpam-5022	205	15	,	,	PUNCT
ejpam-5022	205	16	if	if	SCONJ
ejpam-5022	205	17	ζ	ζ	PROPN
ejpam-5022	205	18	∈	∈	PROPN
ejpam-5022	205	19	[	[	X
ejpam-5022	205	20	ζ1	ζ1	NOUN
ejpam-5022	205	21	,	,	PUNCT
ejpam-5022	205	22	ζ2	ζ2	NOUN
ejpam-5022	205	23	]	]	PUNCT
ejpam-5022	205	24	|2(pbx2+qa)ba2(γ+1)2−b2x2(k(γ+1)2	|2(pbx2+qa)ba2(γ+1)2−b2x2(k(γ+1)2	X
ejpam-5022	205	25	+	+	PROPN
ejpam-5022	205	26	4ζb)|	4ζb)|	NUM
ejpam-5022	205	27	4ba2(γ+1)2	4ba2(γ+1)2	NUM
ejpam-5022	205	28	,	,	PUNCT
ejpam-5022	205	29	if	if	SCONJ
ejpam-5022	205	30	ζ	ζ	NOUN
ejpam-5022	205	31	/∈	/∈	PUNCT
ejpam-5022	206	1	[	[	X
ejpam-5022	206	2	ζ1	ζ1	NOUN
ejpam-5022	206	3	,	,	PUNCT
ejpam-5022	206	4	ζ2	ζ2	NOUN
ejpam-5022	206	5	]	]	PUNCT
ejpam-5022	206	6	,	,	PUNCT
ejpam-5022	206	7	(	(	PUNCT
ejpam-5022	206	8	16	16	NUM
ejpam-5022	206	9	)	)	PUNCT
ejpam-5022	207	1	where	where	SCONJ
ejpam-5022	207	2	ζ1	ζ1	NOUN
ejpam-5022	207	3	=	=	SYM
ejpam-5022	207	4	(	(	PUNCT
ejpam-5022	207	5	γ	γ	X
ejpam-5022	207	6	+	+	PROPN
ejpam-5022	207	7	1)2(2a2(pbx2	1)2(2a2(pbx2	NUM
ejpam-5022	207	8	−	−	NOUN
ejpam-5022	207	9	bx+	bx+	NOUN
ejpam-5022	207	10	qa)−	qa)−	NOUN
ejpam-5022	207	11	b2x2k	b2x2k	NOUN
ejpam-5022	207	12	)	)	PUNCT
ejpam-5022	207	13	4bb2x2	4bb2x2	NUM
ejpam-5022	207	14	,	,	PUNCT
ejpam-5022	207	15	and	and	CCONJ
ejpam-5022	207	16	ζ2	ζ2	NOUN
ejpam-5022	207	17	=	=	SYM
ejpam-5022	207	18	(	(	PUNCT
ejpam-5022	207	19	γ	γ	X
ejpam-5022	207	20	+	+	PROPN
ejpam-5022	207	21	1)2(2a2(pbx2	1)2(2a2(pbx2	NUM
ejpam-5022	207	22	+	+	CCONJ
ejpam-5022	207	23	bx+	bx+	NOUN
ejpam-5022	207	24	qa)−	qa)−	NOUN
ejpam-5022	207	25	b2x2k	b2x2k	NOUN
ejpam-5022	207	26	)	)	PUNCT
ejpam-5022	208	1	4bb2x2	4bb2x2	NUM
ejpam-5022	208	2	.	.	PUNCT
ejpam-5022	209	1	proof	proof	NOUN
ejpam-5022	209	2	.	.	PUNCT
ejpam-5022	210	1	in	in	ADP
ejpam-5022	210	2	view	view	NOUN
ejpam-5022	210	3	of	of	ADP
ejpam-5022	210	4	equations	equation	NOUN
ejpam-5022	210	5	(	(	PUNCT
ejpam-5022	210	6	14	14	NUM
ejpam-5022	210	7	)	)	PUNCT
ejpam-5022	210	8	and	and	CCONJ
ejpam-5022	210	9	(	(	PUNCT
ejpam-5022	210	10	15	15	NUM
ejpam-5022	210	11	)	)	PUNCT
ejpam-5022	210	12	,	,	PUNCT
ejpam-5022	210	13	we	we	PRON
ejpam-5022	210	14	get	get	VERB
ejpam-5022	210	15	the	the	DET
ejpam-5022	210	16	following	follow	VERB
ejpam-5022	210	17	a3	a3	NOUN
ejpam-5022	210	18	=	=	NOUN
ejpam-5022	210	19	h2(x)u2	h2(x)u2	NOUN
ejpam-5022	210	20	2b	2b	NOUN
ejpam-5022	210	21	+	+	CCONJ
ejpam-5022	210	22	h3(x)u	h3(x)u	ADP
ejpam-5022	210	23	2	2	NUM
ejpam-5022	210	24	1	1	NUM
ejpam-5022	210	25	2b	2b	NUM
ejpam-5022	210	26	−	−	PROPN
ejpam-5022	210	27	k[h2(x	k[h2(x	PROPN
ejpam-5022	210	28	)	)	PUNCT
ejpam-5022	210	29	]	]	PUNCT
ejpam-5022	211	1	2u21	2u21	NUM
ejpam-5022	211	2	4ba2	4ba2	NUM
ejpam-5022	211	3	.	.	PUNCT
ejpam-5022	212	1	for	for	ADP
ejpam-5022	212	2	some	some	DET
ejpam-5022	212	3	real	real	ADJ
ejpam-5022	212	4	number	number	NOUN
ejpam-5022	212	5	ζ	ζ	NOUN
ejpam-5022	212	6	,	,	PUNCT
ejpam-5022	212	7	using	use	VERB
ejpam-5022	212	8	equation	equation	NOUN
ejpam-5022	212	9	(	(	PUNCT
ejpam-5022	212	10	15	15	NUM
ejpam-5022	212	11	)	)	PUNCT
ejpam-5022	212	12	,	,	PUNCT
ejpam-5022	212	13	we	we	PRON
ejpam-5022	212	14	have	have	AUX
ejpam-5022	212	15	a3	a3	VERB
ejpam-5022	212	16	−	−	PROPN
ejpam-5022	213	1	ζa22	ζa22	PROPN
ejpam-5022	213	2	=	=	PROPN
ejpam-5022	213	3	h2(x)u2	h2(x)u2	NOUN
ejpam-5022	213	4	2b	2b	NOUN
ejpam-5022	213	5	+	+	CCONJ
ejpam-5022	213	6	h3(x)u	h3(x)u	ADP
ejpam-5022	213	7	2	2	NUM
ejpam-5022	213	8	1	1	NUM
ejpam-5022	213	9	2b	2b	NUM
ejpam-5022	213	10	−	−	PROPN
ejpam-5022	213	11	k[h2(x	k[h2(x	PROPN
ejpam-5022	213	12	)	)	PUNCT
ejpam-5022	213	13	]	]	PUNCT
ejpam-5022	214	1	2u21	2u21	NUM
ejpam-5022	214	2	4ba2	4ba2	NUM
ejpam-5022	214	3	−	−	PROPN
ejpam-5022	214	4	ζ[h2(x	ζ[h2(x	PROPN
ejpam-5022	214	5	)	)	PUNCT
ejpam-5022	214	6	]	]	PUNCT
ejpam-5022	215	1	2u21	2u21	NUM
ejpam-5022	215	2	(	(	PUNCT
ejpam-5022	215	3	γ	γ	X
ejpam-5022	215	4	+	+	PROPN
ejpam-5022	215	5	1)2a2	1)2a2	PROPN
ejpam-5022	215	6	=	=	SYM
ejpam-5022	215	7	h2(x	h2(x	PROPN
ejpam-5022	215	8	)	)	PUNCT
ejpam-5022	215	9	2b	2b	NOUN
ejpam-5022	215	10	{	{	PUNCT
ejpam-5022	215	11	u2	u2	NOUN
ejpam-5022	215	12	+	+	CCONJ
ejpam-5022	215	13	(	(	PUNCT
ejpam-5022	215	14	h3(x	h3(x	PROPN
ejpam-5022	215	15	)	)	PUNCT
ejpam-5022	215	16	h2(x	h2(x	NOUN
ejpam-5022	215	17	)	)	PUNCT
ejpam-5022	215	18	−	−	PROPN
ejpam-5022	215	19	kh2(x	kh2(x	PROPN
ejpam-5022	215	20	)	)	PUNCT
ejpam-5022	215	21	2a2	2a2	NUM
ejpam-5022	216	1	−	−	PROPN
ejpam-5022	216	2	2ζbh2(x	2ζbh2(x	NUM
ejpam-5022	216	3	)	)	PUNCT
ejpam-5022	216	4	(	(	PUNCT
ejpam-5022	216	5	γ	γ	X
ejpam-5022	216	6	+	+	PROPN
ejpam-5022	216	7	1)2a2	1)2a2	PROPN
ejpam-5022	216	8	)	)	PUNCT
ejpam-5022	216	9	u21	u21	PROPN
ejpam-5022	216	10	}	}	PUNCT
ejpam-5022	216	11	w.	w.	PROPN
ejpam-5022	216	12	al	al	PROPN
ejpam-5022	216	13	-	-	PUNCT
ejpam-5022	216	14	rawashdeh	rawashdeh	PROPN
ejpam-5022	216	15	/	/	SYM
ejpam-5022	216	16	eur	eur	PROPN
ejpam-5022	216	17	.	.	PUNCT
ejpam-5022	217	1	j.	j.	PROPN
ejpam-5022	217	2	pure	pure	PROPN
ejpam-5022	217	3	appl	appl	PROPN
ejpam-5022	217	4	.	.	PROPN
ejpam-5022	217	5	math	math	PROPN
ejpam-5022	217	6	,	,	PUNCT
ejpam-5022	217	7	17	17	NUM
ejpam-5022	217	8	(	(	PUNCT
ejpam-5022	217	9	1	1	NUM
ejpam-5022	217	10	)	)	PUNCT
ejpam-5022	217	11	(	(	PUNCT
ejpam-5022	217	12	2024	2024	NUM
ejpam-5022	217	13	)	)	PUNCT
ejpam-5022	217	14	,	,	PUNCT
ejpam-5022	217	15	158	158	NUM
ejpam-5022	217	16	-	-	SYM
ejpam-5022	217	17	170	170	NUM
ejpam-5022	217	18	166	166	NUM
ejpam-5022	217	19	using	use	VERB
ejpam-5022	217	20	lemma	lemma	PROPN
ejpam-5022	217	21	1	1	NUM
ejpam-5022	217	22	and	and	CCONJ
ejpam-5022	217	23	the	the	DET
ejpam-5022	217	24	initial	initial	ADJ
ejpam-5022	217	25	values	value	NOUN
ejpam-5022	217	26	(	(	PUNCT
ejpam-5022	217	27	3	3	NUM
ejpam-5022	217	28	)	)	PUNCT
ejpam-5022	217	29	,	,	PUNCT
ejpam-5022	217	30	we	we	PRON
ejpam-5022	217	31	obtain	obtain	VERB
ejpam-5022	217	32	|a3	|a3	NOUN
ejpam-5022	217	33	−	−	PROPN
ejpam-5022	217	34	ζa22|	ζa22|	NOUN
ejpam-5022	217	35	≤	≤	NUM
ejpam-5022	217	36	|bx|	|bx|	PROPN
ejpam-5022	217	37	2b	2b	NUM
ejpam-5022	217	38	max	max	PROPN
ejpam-5022	217	39	{	{	PUNCT
ejpam-5022	217	40	1	1	NUM
ejpam-5022	217	41	,	,	PUNCT
ejpam-5022	217	42	∣∣∣∣pbx2	∣∣∣∣pbx2	PUNCT
ejpam-5022	217	43	+	+	CCONJ
ejpam-5022	217	44	qa	qa	PROPN
ejpam-5022	217	45	bx	bx	NOUN
ejpam-5022	217	46	−	−	PROPN
ejpam-5022	217	47	bxk	bxk	NOUN
ejpam-5022	217	48	2a2	2a2	NUM
ejpam-5022	218	1	−	−	NOUN
ejpam-5022	219	1	2ζbbx	2ζbbx	NUM
ejpam-5022	219	2	(	(	PUNCT
ejpam-5022	219	3	γ	γ	X
ejpam-5022	219	4	+	+	PROPN
ejpam-5022	219	5	1)2a2	1)2a2	PROPN
ejpam-5022	219	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5022	219	7	}	}	PUNCT
ejpam-5022	219	8	(	(	PUNCT
ejpam-5022	219	9	17	17	NUM
ejpam-5022	219	10	)	)	PUNCT
ejpam-5022	219	11	since	since	SCONJ
ejpam-5022	219	12	bx	bx	PROPN
ejpam-5022	219	13	>	>	X
ejpam-5022	219	14	0	0	PROPN
ejpam-5022	219	15	,	,	PUNCT
ejpam-5022	219	16	we	we	PRON
ejpam-5022	219	17	have	have	AUX
ejpam-5022	219	18	∣∣∣∣pbx2	∣∣∣∣pbx2	VERB
ejpam-5022	220	1	+	+	CCONJ
ejpam-5022	220	2	qa	qa	PROPN
ejpam-5022	220	3	bx	bx	NOUN
ejpam-5022	220	4	−	−	PROPN
ejpam-5022	220	5	bxk	bxk	NOUN
ejpam-5022	220	6	2a2	2a2	NUM
ejpam-5022	221	1	−	−	NOUN
ejpam-5022	221	2	2ζbbx	2ζbbx	NUM
ejpam-5022	221	3	(	(	PUNCT
ejpam-5022	221	4	γ	γ	X
ejpam-5022	221	5	+	+	PROPN
ejpam-5022	221	6	1)2a2	1)2a2	PROPN
ejpam-5022	221	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5022	221	8	≤	≤	NUM
ejpam-5022	221	9	1	1	NUM
ejpam-5022	221	10	.	.	PUNCT
ejpam-5022	222	1	solving	solve	VERB
ejpam-5022	222	2	for	for	ADP
ejpam-5022	222	3	ζ	ζ	NOUN
ejpam-5022	222	4	we	we	PRON
ejpam-5022	222	5	get	get	VERB
ejpam-5022	222	6	:	:	PUNCT
ejpam-5022	222	7	(	(	PUNCT
ejpam-5022	222	8	γ	γ	X
ejpam-5022	222	9	+	+	PROPN
ejpam-5022	222	10	1)2(2a2(pbx2	1)2(2a2(pbx2	NUM
ejpam-5022	222	11	−	−	NOUN
ejpam-5022	222	12	bx+	bx+	NOUN
ejpam-5022	222	13	qa)−	qa)−	NOUN
ejpam-5022	222	14	b2x2k	b2x2k	NOUN
ejpam-5022	222	15	)	)	PUNCT
ejpam-5022	223	1	4bb2x2	4bb2x2	NUM
ejpam-5022	223	2	≤	≤	NUM
ejpam-5022	223	3	ζ	ζ	NOUN
ejpam-5022	223	4	≤	≤	NOUN
ejpam-5022	223	5	(	(	PUNCT
ejpam-5022	223	6	γ	γ	X
ejpam-5022	223	7	+	+	PROPN
ejpam-5022	223	8	1)2(2a2(pbx2	1)2(2a2(pbx2	NUM
ejpam-5022	223	9	+	+	CCONJ
ejpam-5022	223	10	bx+	bx+	NOUN
ejpam-5022	223	11	qa)−	qa)−	NOUN
ejpam-5022	223	12	b2x2k	b2x2k	NOUN
ejpam-5022	223	13	)	)	PUNCT
ejpam-5022	224	1	4bb2x2	4bb2x2	NUM
ejpam-5022	224	2	hence	hence	ADV
ejpam-5022	224	3	,	,	PUNCT
ejpam-5022	224	4	inequality	inequality	NOUN
ejpam-5022	224	5	(	(	PUNCT
ejpam-5022	224	6	17	17	NUM
ejpam-5022	224	7	)	)	PUNCT
ejpam-5022	224	8	becomes	become	VERB
ejpam-5022	224	9	|a3	|a3	NOUN
ejpam-5022	224	10	−	−	PROPN
ejpam-5022	224	11	ζa22|	ζa22|	NOUN
ejpam-5022	224	12	≤	≤	PROPN
ejpam-5022	224	13			PUNCT
ejpam-5022	224	14	bx	bx	NOUN
ejpam-5022	224	15	2b	2b	NOUN
ejpam-5022	224	16	,	,	PUNCT
ejpam-5022	224	17	if	if	SCONJ
ejpam-5022	224	18	ζ	ζ	PROPN
ejpam-5022	224	19	∈	∈	PROPN
ejpam-5022	224	20	[	[	X
ejpam-5022	224	21	ζ1	ζ1	NOUN
ejpam-5022	224	22	,	,	PUNCT
ejpam-5022	224	23	ζ2]∣∣∣∣pbx2+qa	ζ2]∣∣∣∣pbx2+qa	PROPN
ejpam-5022	224	24	2b	2b	NUM
ejpam-5022	224	25	−	−	PROPN
ejpam-5022	224	26	b2x2k	b2x2k	NOUN
ejpam-5022	224	27	4ba2	4ba2	NUM
ejpam-5022	224	28	−	−	NOUN
ejpam-5022	224	29	ζ	ζ	PROPN
ejpam-5022	224	30	(	(	PUNCT
ejpam-5022	224	31	bx	bx	NOUN
ejpam-5022	224	32	a(γ+1	a(γ+1	NOUN
ejpam-5022	224	33	)	)	PUNCT
ejpam-5022	224	34	)	)	PUNCT
ejpam-5022	224	35	2	2	NUM
ejpam-5022	224	36	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5022	224	37	,	,	PUNCT
ejpam-5022	224	38	if	if	SCONJ
ejpam-5022	224	39	ζ	ζ	NOUN
ejpam-5022	224	40	/∈	/∈	PUNCT
ejpam-5022	225	1	[	[	X
ejpam-5022	225	2	ζ1	ζ1	NOUN
ejpam-5022	225	3	,	,	PUNCT
ejpam-5022	225	4	ζ2	ζ2	NOUN
ejpam-5022	225	5	]	]	PUNCT
ejpam-5022	225	6	.	.	PUNCT
ejpam-5022	226	1	simplifying	simplify	VERB
ejpam-5022	226	2	the	the	DET
ejpam-5022	226	3	last	last	ADJ
ejpam-5022	226	4	inequality	inequality	NOUN
ejpam-5022	226	5	,	,	PUNCT
ejpam-5022	226	6	we	we	PRON
ejpam-5022	226	7	get	get	VERB
ejpam-5022	226	8	the	the	DET
ejpam-5022	226	9	desired	desire	VERB
ejpam-5022	226	10	inequality	inequality	NOUN
ejpam-5022	226	11	(	(	PUNCT
ejpam-5022	226	12	16	16	NUM
ejpam-5022	226	13	)	)	PUNCT
ejpam-5022	226	14	,	,	PUNCT
ejpam-5022	226	15	this	this	PRON
ejpam-5022	226	16	completes	complete	VERB
ejpam-5022	226	17	the	the	DET
ejpam-5022	226	18	proof	proof	NOUN
ejpam-5022	226	19	of	of	ADP
ejpam-5022	226	20	theorem	theorem	NOUN
ejpam-5022	226	21	2	2	NUM
ejpam-5022	226	22	.	.	PUNCT
ejpam-5022	227	1	the	the	DET
ejpam-5022	227	2	following	follow	VERB
ejpam-5022	227	3	corollaries	corollary	NOUN
ejpam-5022	227	4	are	be	AUX
ejpam-5022	227	5	just	just	ADV
ejpam-5022	227	6	consequences	consequence	NOUN
ejpam-5022	227	7	of	of	ADP
ejpam-5022	227	8	theorem	theorem	ADJ
ejpam-5022	227	9	2	2	NUM
ejpam-5022	227	10	.	.	PUNCT
ejpam-5022	227	11	corollary	corollary	ADJ
ejpam-5022	227	12	6	6	NUM
ejpam-5022	227	13	.	.	PUNCT
ejpam-5022	228	1	if	if	SCONJ
ejpam-5022	228	2	the	the	DET
ejpam-5022	228	3	function	function	NOUN
ejpam-5022	228	4	f	f	PROPN
ejpam-5022	228	5	∈	∈	PROPN
ejpam-5022	228	6	a	a	DET
ejpam-5022	228	7	satisfies	satisfie	NOUN
ejpam-5022	228	8	the	the	DET
ejpam-5022	228	9	subordination	subordination	NOUN
ejpam-5022	228	10	(	(	PUNCT
ejpam-5022	228	11	5	5	NUM
ejpam-5022	228	12	)	)	PUNCT
ejpam-5022	228	13	,	,	PUNCT
ejpam-5022	228	14	then	then	ADV
ejpam-5022	228	15	for	for	ADP
ejpam-5022	228	16	bx	bx	PROPN
ejpam-5022	228	17	>	>	X
ejpam-5022	228	18	0	0	PUNCT
ejpam-5022	229	1	and	and	CCONJ
ejpam-5022	229	2	for	for	ADP
ejpam-5022	229	3	some	some	DET
ejpam-5022	229	4	ζ	ζ	NOUN
ejpam-5022	229	5	∈	∈	NOUN
ejpam-5022	229	6	r	r	NOUN
ejpam-5022	229	7	|a3	|a3	NOUN
ejpam-5022	229	8	−	−	PROPN
ejpam-5022	229	9	ζa22|	ζa22|	NOUN
ejpam-5022	229	10	≤	≤	NUM
ejpam-5022	229	11			PUNCT
ejpam-5022	229	12	bx	bx	PROPN
ejpam-5022	229	13	2(1	2(1	NUM
ejpam-5022	229	14	+	+	NOUN
ejpam-5022	229	15	2η	2η	NUM
ejpam-5022	229	16	)	)	PUNCT
ejpam-5022	229	17	,	,	PUNCT
ejpam-5022	229	18	if	if	SCONJ
ejpam-5022	229	19	ζ	ζ	PROPN
ejpam-5022	229	20	∈	∈	PROPN
ejpam-5022	229	21	[	[	X
ejpam-5022	229	22	ζ1	ζ1	NOUN
ejpam-5022	229	23	,	,	PUNCT
ejpam-5022	229	24	ζ2]∣∣∣pbx2+qa	ζ2]∣∣∣pbx2+qa	PROPN
ejpam-5022	229	25	2(1	2(1	NUM
ejpam-5022	229	26	+	+	NOUN
ejpam-5022	229	27	2η	2η	NUM
ejpam-5022	229	28	)	)	PUNCT
ejpam-5022	229	29	+	+	NUM
ejpam-5022	229	30	b2x2(1	b2x2(1	NOUN
ejpam-5022	229	31	+	+	PROPN
ejpam-5022	229	32	3η−2ζ(1	3η−2ζ(1	PROPN
ejpam-5022	229	33	+	+	NOUN
ejpam-5022	229	34	2η	2η	NUM
ejpam-5022	229	35	)	)	PUNCT
ejpam-5022	229	36	)	)	PUNCT
ejpam-5022	230	1	2(1	2(1	NUM
ejpam-5022	231	1	+	+	NOUN
ejpam-5022	231	2	2η)(1+η)2	2η)(1+η)2	NUM
ejpam-5022	231	3	∣∣∣	∣∣∣	NOUN
ejpam-5022	231	4	,	,	PUNCT
ejpam-5022	231	5	if	if	SCONJ
ejpam-5022	231	6	ζ	ζ	NOUN
ejpam-5022	231	7	/∈	/∈	PUNCT
ejpam-5022	232	1	[	[	X
ejpam-5022	232	2	ζ1	ζ1	NOUN
ejpam-5022	232	3	,	,	PUNCT
ejpam-5022	232	4	ζ2	ζ2	NOUN
ejpam-5022	232	5	]	]	PUNCT
ejpam-5022	232	6	,	,	PUNCT
ejpam-5022	232	7	where	where	SCONJ
ejpam-5022	232	8	ζ1	ζ1	NOUN
ejpam-5022	232	9	=	=	SYM
ejpam-5022	232	10	(	(	PUNCT
ejpam-5022	232	11	1	1	NUM
ejpam-5022	232	12	+	+	CCONJ
ejpam-5022	232	13	η)2(pbx2	η)2(pbx2	NOUN
ejpam-5022	232	14	−	−	PROPN
ejpam-5022	232	15	bx+	bx+	PROPN
ejpam-5022	232	16	qa	qa	PROPN
ejpam-5022	232	17	)	)	PUNCT
ejpam-5022	233	1	+	+	NUM
ejpam-5022	233	2	b2x2(1	b2x2(1	NOUN
ejpam-5022	233	3	+	+	CCONJ
ejpam-5022	233	4	3η	3η	NUM
ejpam-5022	233	5	)	)	PUNCT
ejpam-5022	233	6	2(1	2(1	NUM
ejpam-5022	234	1	+	+	CCONJ
ejpam-5022	234	2	2η)b2x2	2η)b2x2	NUM
ejpam-5022	234	3	,	,	PUNCT
ejpam-5022	234	4	and	and	CCONJ
ejpam-5022	234	5	ζ2	ζ2	NOUN
ejpam-5022	234	6	=	=	SYM
ejpam-5022	234	7	(	(	PUNCT
ejpam-5022	234	8	1	1	NUM
ejpam-5022	234	9	+	+	CCONJ
ejpam-5022	234	10	η)2(pbx2	η)2(pbx2	NOUN
ejpam-5022	234	11	+	+	CCONJ
ejpam-5022	234	12	bx+	bx+	PROPN
ejpam-5022	234	13	qa	qa	PROPN
ejpam-5022	234	14	)	)	PUNCT
ejpam-5022	235	1	+	+	NUM
ejpam-5022	235	2	b2x2(1	b2x2(1	NOUN
ejpam-5022	235	3	+	+	CCONJ
ejpam-5022	235	4	3η	3η	NUM
ejpam-5022	235	5	)	)	PUNCT
ejpam-5022	235	6	2(1	2(1	NUM
ejpam-5022	236	1	+	+	CCONJ
ejpam-5022	236	2	2η)b2x2	2η)b2x2	NUM
ejpam-5022	236	3	.	.	PUNCT
ejpam-5022	237	1	corollary	corollary	ADJ
ejpam-5022	237	2	7	7	NUM
ejpam-5022	237	3	.	.	PUNCT
ejpam-5022	238	1	if	if	SCONJ
ejpam-5022	238	2	the	the	DET
ejpam-5022	238	3	function	function	NOUN
ejpam-5022	238	4	f	f	PROPN
ejpam-5022	238	5	∈	∈	PROPN
ejpam-5022	238	6	a	a	DET
ejpam-5022	238	7	satisfies	satisfie	NOUN
ejpam-5022	238	8	the	the	DET
ejpam-5022	238	9	subordination	subordination	NOUN
ejpam-5022	238	10	(	(	PUNCT
ejpam-5022	238	11	6	6	NUM
ejpam-5022	238	12	)	)	PUNCT
ejpam-5022	238	13	,	,	PUNCT
ejpam-5022	238	14	then	then	ADV
ejpam-5022	238	15	for	for	ADP
ejpam-5022	238	16	bx	bx	PROPN
ejpam-5022	238	17	>	>	X
ejpam-5022	238	18	0	0	PUNCT
ejpam-5022	239	1	and	and	CCONJ
ejpam-5022	239	2	for	for	ADP
ejpam-5022	239	3	some	some	DET
ejpam-5022	239	4	ζ	ζ	NOUN
ejpam-5022	239	5	∈	∈	NOUN
ejpam-5022	239	6	r	r	NOUN
ejpam-5022	239	7	|a3	|a3	NOUN
ejpam-5022	239	8	−	−	PROPN
ejpam-5022	239	9	ζa22|	ζa22|	NOUN
ejpam-5022	239	10	≤	≤	PROPN
ejpam-5022	239	11	{	{	PUNCT
ejpam-5022	239	12	bx	bx	NOUN
ejpam-5022	239	13	2(3−2λ	2(3−2λ	NUM
ejpam-5022	239	14	)	)	PUNCT
ejpam-5022	239	15	,	,	PUNCT
ejpam-5022	239	16	if	if	SCONJ
ejpam-5022	239	17	ζ	ζ	PROPN
ejpam-5022	239	18	∈	∈	PROPN
ejpam-5022	239	19	[	[	X
ejpam-5022	239	20	ζ1	ζ1	NOUN
ejpam-5022	239	21	,	,	PUNCT
ejpam-5022	239	22	ζ2	ζ2	NOUN
ejpam-5022	239	23	]	]	PUNCT
ejpam-5022	239	24	|2(pbx2+qa)(3−2λ)(2−λ)2−b2x2(λ2	|2(pbx2+qa)(3−2λ)(2−λ)2−b2x2(λ2	PROPN
ejpam-5022	239	25	+	+	PROPN
ejpam-5022	239	26	5λ+4ζ(3−2λ)−8)|	5λ+4ζ(3−2λ)−8)|	PROPN
ejpam-5022	239	27	4(3−2λ)(2−λ)2	4(3−2λ)(2−λ)2	NOUN
ejpam-5022	239	28	,	,	PUNCT
ejpam-5022	239	29	if	if	SCONJ
ejpam-5022	239	30	ζ	ζ	NOUN
ejpam-5022	239	31	/∈	/∈	PUNCT
ejpam-5022	240	1	[	[	X
ejpam-5022	240	2	ζ1	ζ1	NOUN
ejpam-5022	240	3	,	,	PUNCT
ejpam-5022	240	4	ζ2	ζ2	NOUN
ejpam-5022	240	5	]	]	PUNCT
ejpam-5022	240	6	,	,	PUNCT
ejpam-5022	240	7	w.	w.	PROPN
ejpam-5022	240	8	al	al	PROPN
ejpam-5022	240	9	-	-	PUNCT
ejpam-5022	240	10	rawashdeh	rawashdeh	PROPN
ejpam-5022	240	11	/	/	SYM
ejpam-5022	240	12	eur	eur	PROPN
ejpam-5022	240	13	.	.	PUNCT
ejpam-5022	241	1	j.	j.	PROPN
ejpam-5022	241	2	pure	pure	PROPN
ejpam-5022	241	3	appl	appl	PROPN
ejpam-5022	241	4	.	.	PROPN
ejpam-5022	241	5	math	math	PROPN
ejpam-5022	241	6	,	,	PUNCT
ejpam-5022	241	7	17	17	NUM
ejpam-5022	241	8	(	(	PUNCT
ejpam-5022	241	9	1	1	NUM
ejpam-5022	241	10	)	)	PUNCT
ejpam-5022	241	11	(	(	PUNCT
ejpam-5022	241	12	2024	2024	NUM
ejpam-5022	241	13	)	)	PUNCT
ejpam-5022	241	14	,	,	PUNCT
ejpam-5022	241	15	158	158	NUM
ejpam-5022	241	16	-	-	SYM
ejpam-5022	241	17	170	170	NUM
ejpam-5022	241	18	167	167	NUM
ejpam-5022	241	19	where	where	SCONJ
ejpam-5022	241	20	ζ1	ζ1	NOUN
ejpam-5022	241	21	=	=	SYM
ejpam-5022	241	22	2(2−	2(2−	NUM
ejpam-5022	241	23	λ)2(pbx2	λ)2(pbx2	NOUN
ejpam-5022	241	24	−	−	PROPN
ejpam-5022	241	25	bx+	bx+	PROPN
ejpam-5022	241	26	qa)−	qa)−	NOUN
ejpam-5022	241	27	b2x2(λ2	b2x2(λ2	NOUN
ejpam-5022	242	1	+	+	CCONJ
ejpam-5022	242	2	5λ−	5λ−	NUM
ejpam-5022	242	3	8)	8)	NUM
ejpam-5022	242	4	)	)	PUNCT
ejpam-5022	242	5	4(3−	4(3−	NUM
ejpam-5022	242	6	2λ)b2x2	2λ)b2x2	NUM
ejpam-5022	242	7	,	,	PUNCT
ejpam-5022	242	8	and	and	CCONJ
ejpam-5022	242	9	ζ2	ζ2	NOUN
ejpam-5022	242	10	=	=	SYM
ejpam-5022	242	11	2(2−	2(2−	NUM
ejpam-5022	242	12	λ)2(pbx2	λ)2(pbx2	NOUN
ejpam-5022	242	13	+	+	CCONJ
ejpam-5022	242	14	bx+	bx+	NOUN
ejpam-5022	242	15	qa)−	qa)−	NOUN
ejpam-5022	242	16	b2x2(λ2	b2x2(λ2	VERB
ejpam-5022	243	1	+	+	CCONJ
ejpam-5022	243	2	5λ−	5λ−	NUM
ejpam-5022	243	3	8)	8)	NUM
ejpam-5022	243	4	)	)	PUNCT
ejpam-5022	243	5	4(3−	4(3−	NUM
ejpam-5022	243	6	2λ)b2x2	2λ)b2x2	NUM
ejpam-5022	243	7	.	.	PUNCT
ejpam-5022	244	1	corollary	corollary	ADJ
ejpam-5022	244	2	8	8	NUM
ejpam-5022	244	3	.	.	PUNCT
ejpam-5022	245	1	if	if	SCONJ
ejpam-5022	245	2	the	the	DET
ejpam-5022	245	3	function	function	NOUN
ejpam-5022	245	4	f	f	PROPN
ejpam-5022	245	5	∈	∈	PROPN
ejpam-5022	245	6	a	a	DET
ejpam-5022	245	7	satisfies	satisfie	NOUN
ejpam-5022	245	8	the	the	DET
ejpam-5022	245	9	subordination	subordination	NOUN
ejpam-5022	245	10	(	(	PUNCT
ejpam-5022	245	11	7	7	NUM
ejpam-5022	245	12	)	)	PUNCT
ejpam-5022	245	13	,	,	PUNCT
ejpam-5022	245	14	then	then	ADV
ejpam-5022	245	15	for	for	ADP
ejpam-5022	245	16	bx	bx	PROPN
ejpam-5022	245	17	>	>	X
ejpam-5022	245	18	0	0	PUNCT
ejpam-5022	246	1	and	and	CCONJ
ejpam-5022	246	2	for	for	ADP
ejpam-5022	246	3	some	some	DET
ejpam-5022	246	4	ζ	ζ	NOUN
ejpam-5022	246	5	∈	∈	NOUN
ejpam-5022	246	6	r	r	NOUN
ejpam-5022	246	7	|a3	|a3	NOUN
ejpam-5022	246	8	−	−	PROPN
ejpam-5022	246	9	ζa22|	ζa22|	NOUN
ejpam-5022	246	10	≤	≤	NUM
ejpam-5022	246	11			PUNCT
ejpam-5022	246	12	bx	bx	PROPN
ejpam-5022	246	13	2(1	2(1	NUM
ejpam-5022	246	14	+	+	NOUN
ejpam-5022	246	15	2(3µδ+µ−δ	2(3µδ+µ−δ	NUM
ejpam-5022	246	16	)	)	PUNCT
ejpam-5022	246	17	)	)	PUNCT
ejpam-5022	246	18	,	,	PUNCT
ejpam-5022	246	19	if	if	SCONJ
ejpam-5022	246	20	ζ	ζ	PROPN
ejpam-5022	246	21	∈	∈	PROPN
ejpam-5022	246	22	[	[	X
ejpam-5022	246	23	ζ1	ζ1	NOUN
ejpam-5022	246	24	,	,	PUNCT
ejpam-5022	246	25	ζ2]∣∣∣∣	ζ2]∣∣∣∣	PROPN
ejpam-5022	246	26	pbx2+qa+b2x2	pbx2+qa+b2x2	PROPN
ejpam-5022	246	27	2(1	2(1	NUM
ejpam-5022	246	28	+	+	NOUN
ejpam-5022	246	29	2(3µδ+µ−δ	2(3µδ+µ−δ	NUM
ejpam-5022	246	30	)	)	PUNCT
ejpam-5022	246	31	)	)	PUNCT
ejpam-5022	247	1	−	−	PROPN
ejpam-5022	247	2	ζ	ζ	NOUN
ejpam-5022	247	3	(	(	PUNCT
ejpam-5022	247	4	bx	bx	NOUN
ejpam-5022	247	5	1	1	NUM
ejpam-5022	247	6	+	+	PROPN
ejpam-5022	247	7	2µδ+µ−δ	2µδ+µ−δ	NUM
ejpam-5022	247	8	)	)	PUNCT
ejpam-5022	247	9	2	2	NUM
ejpam-5022	247	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5022	247	11	,	,	PUNCT
ejpam-5022	247	12	if	if	SCONJ
ejpam-5022	247	13	ζ	ζ	NOUN
ejpam-5022	247	14	/∈	/∈	PUNCT
ejpam-5022	248	1	[	[	X
ejpam-5022	248	2	ζ1	ζ1	NOUN
ejpam-5022	248	3	,	,	PUNCT
ejpam-5022	248	4	ζ2	ζ2	NOUN
ejpam-5022	248	5	]	]	PUNCT
ejpam-5022	248	6	,	,	PUNCT
ejpam-5022	248	7	where	where	SCONJ
ejpam-5022	248	8	ζ1	ζ1	NOUN
ejpam-5022	248	9	=	=	SYM
ejpam-5022	248	10	(	(	PUNCT
ejpam-5022	248	11	1	1	NUM
ejpam-5022	248	12	+	+	NUM
ejpam-5022	248	13	2µδ	2µδ	ADJ
ejpam-5022	248	14	+	+	CCONJ
ejpam-5022	248	15	µ−	µ−	PROPN
ejpam-5022	248	16	δ)2(pbx2	δ)2(pbx2	NOUN
ejpam-5022	248	17	−	−	PROPN
ejpam-5022	248	18	bx+	bx+	PROPN
ejpam-5022	248	19	qa+	qa+	PROPN
ejpam-5022	248	20	b2x2	b2x2	ADP
ejpam-5022	248	21	)	)	PUNCT
ejpam-5022	248	22	2(1	2(1	NUM
ejpam-5022	249	1	+	+	CCONJ
ejpam-5022	249	2	2(3µδ	2(3µδ	NUM
ejpam-5022	249	3	+	+	NUM
ejpam-5022	249	4	µ−	µ−	PROPN
ejpam-5022	249	5	δ))b2x2	δ))b2x2	NUM
ejpam-5022	249	6	,	,	PUNCT
ejpam-5022	249	7	and	and	CCONJ
ejpam-5022	249	8	ζ2	ζ2	NOUN
ejpam-5022	249	9	=	=	SYM
ejpam-5022	249	10	(	(	PUNCT
ejpam-5022	249	11	1	1	NUM
ejpam-5022	249	12	+	+	NUM
ejpam-5022	249	13	2µδ	2µδ	ADJ
ejpam-5022	249	14	+	+	CCONJ
ejpam-5022	249	15	µ−	µ−	PROPN
ejpam-5022	249	16	δ)2(pbx2	δ)2(pbx2	NOUN
ejpam-5022	249	17	+	+	NUM
ejpam-5022	249	18	bx+	bx+	PROPN
ejpam-5022	249	19	qa+	qa+	PROPN
ejpam-5022	249	20	b2x2	b2x2	ADP
ejpam-5022	249	21	)	)	PUNCT
ejpam-5022	249	22	2(1	2(1	NUM
ejpam-5022	250	1	+	+	CCONJ
ejpam-5022	250	2	2(3µδ	2(3µδ	NUM
ejpam-5022	250	3	+	+	NUM
ejpam-5022	250	4	µ−	µ−	PROPN
ejpam-5022	250	5	δ))b2x2	δ))b2x2	NUM
ejpam-5022	250	6	.	.	PUNCT
ejpam-5022	251	1	corollary	corollary	ADJ
ejpam-5022	251	2	9	9	NUM
ejpam-5022	251	3	.	.	PUNCT
ejpam-5022	252	1	if	if	SCONJ
ejpam-5022	252	2	the	the	DET
ejpam-5022	252	3	function	function	NOUN
ejpam-5022	252	4	f	f	PROPN
ejpam-5022	252	5	∈	∈	PROPN
ejpam-5022	252	6	a	a	DET
ejpam-5022	252	7	satisfies	satisfie	NOUN
ejpam-5022	252	8	the	the	DET
ejpam-5022	252	9	subordination	subordination	NOUN
ejpam-5022	252	10	(	(	PUNCT
ejpam-5022	252	11	8)	8)	NUM
ejpam-5022	252	12	,	,	PUNCT
ejpam-5022	252	13	then	then	ADV
ejpam-5022	252	14	for	for	ADP
ejpam-5022	252	15	bx	bx	PROPN
ejpam-5022	252	16	>	>	X
ejpam-5022	252	17	0	0	PUNCT
ejpam-5022	252	18	and	and	CCONJ
ejpam-5022	252	19	for	for	ADP
ejpam-5022	252	20	some	some	DET
ejpam-5022	252	21	ζ	ζ	NOUN
ejpam-5022	252	22	∈	∈	NOUN
ejpam-5022	252	23	r	r	NOUN
ejpam-5022	252	24	|a3	|a3	NOUN
ejpam-5022	252	25	−	−	PROPN
ejpam-5022	252	26	ζa22|	ζa22|	NOUN
ejpam-5022	252	27	≤	≤	PROPN
ejpam-5022	252	28			PUNCT
ejpam-5022	252	29	bx	bx	PROPN
ejpam-5022	252	30	2(αβ+(1−β)(3−2λ	2(αβ+(1−β)(3−2λ	NUM
ejpam-5022	252	31	)	)	PUNCT
ejpam-5022	252	32	)	)	PUNCT
ejpam-5022	252	33	,	,	PUNCT
ejpam-5022	252	34	if	if	SCONJ
ejpam-5022	252	35	ζ	ζ	PROPN
ejpam-5022	252	36	∈	∈	PROPN
ejpam-5022	252	37	[	[	X
ejpam-5022	252	38	ζ1	ζ1	NOUN
ejpam-5022	252	39	,	,	PUNCT
ejpam-5022	252	40	ζ2]∣∣∣	ζ2]∣∣∣	VERB
ejpam-5022	252	41	pbx2+qa	pbx2+qa	NOUN
ejpam-5022	252	42	2(αβ+(1−β)(3−2λ	2(αβ+(1−β)(3−2λ	NUM
ejpam-5022	252	43	)	)	PUNCT
ejpam-5022	252	44	)	)	PUNCT
ejpam-5022	253	1	−	−	ADP
ejpam-5022	253	2	b2x2k	b2x2k	NUM
ejpam-5022	253	3	4(αβ+(1−β)(3−2λ))a2	4(αβ+(1−β)(3−2λ))a2	NUM
ejpam-5022	253	4	−	−	NOUN
ejpam-5022	253	5	ζ	ζ	NOUN
ejpam-5022	253	6	(	(	PUNCT
ejpam-5022	253	7	bx	bx	NOUN
ejpam-5022	253	8	a	a	PRON
ejpam-5022	253	9	)	)	PUNCT
ejpam-5022	253	10	2∣∣∣	2∣∣∣	PROPN
ejpam-5022	253	11	,	,	PUNCT
ejpam-5022	253	12	if	if	SCONJ
ejpam-5022	253	13	ζ	ζ	NOUN
ejpam-5022	253	14	/∈	/∈	PUNCT
ejpam-5022	254	1	[	[	X
ejpam-5022	254	2	ζ1	ζ1	NOUN
ejpam-5022	254	3	,	,	PUNCT
ejpam-5022	254	4	ζ2	ζ2	NOUN
ejpam-5022	254	5	]	]	PUNCT
ejpam-5022	254	6	.	.	PUNCT
ejpam-5022	255	1	where	where	SCONJ
ejpam-5022	255	2	ζ1	ζ1	NOUN
ejpam-5022	255	3	=	=	SYM
ejpam-5022	255	4	2a2(pbx2	2a2(pbx2	NUM
ejpam-5022	255	5	−	−	PROPN
ejpam-5022	255	6	bx+	bx+	NOUN
ejpam-5022	255	7	qa)−	qa)−	NOUN
ejpam-5022	255	8	b2x2k	b2x2k	NUM
ejpam-5022	255	9	4(αβ	4(αβ	NOUN
ejpam-5022	255	10	+	+	CCONJ
ejpam-5022	255	11	(	(	PUNCT
ejpam-5022	255	12	1−	1−	NUM
ejpam-5022	255	13	β)(3−	β)(3−	ADP
ejpam-5022	255	14	2λ)b2x2	2λ)b2x2	NUM
ejpam-5022	255	15	,	,	PUNCT
ejpam-5022	255	16	and	and	CCONJ
ejpam-5022	255	17	ζ2	ζ2	NOUN
ejpam-5022	255	18	=	=	SYM
ejpam-5022	255	19	2a2(pbx2	2a2(pbx2	NUM
ejpam-5022	255	20	+	+	NUM
ejpam-5022	255	21	bx+	bx+	NOUN
ejpam-5022	255	22	qa)−	qa)−	NOUN
ejpam-5022	255	23	b2x2k	b2x2k	PUNCT
ejpam-5022	255	24	4(αβ	4(αβ	NOUN
ejpam-5022	255	25	+	+	CCONJ
ejpam-5022	255	26	(	(	PUNCT
ejpam-5022	255	27	1−	1−	NUM
ejpam-5022	255	28	β)(3−	β)(3−	ADP
ejpam-5022	255	29	2λ)b2x2	2λ)b2x2	NUM
ejpam-5022	255	30	.	.	PUNCT
ejpam-5022	256	1	corollary	corollary	ADJ
ejpam-5022	256	2	10	10	NUM
ejpam-5022	256	3	.	.	PUNCT
ejpam-5022	257	1	if	if	SCONJ
ejpam-5022	257	2	the	the	DET
ejpam-5022	257	3	function	function	NOUN
ejpam-5022	257	4	f	f	PROPN
ejpam-5022	257	5	∈	∈	PROPN
ejpam-5022	257	6	a	a	DET
ejpam-5022	257	7	satisfies	satisfie	NOUN
ejpam-5022	257	8	the	the	DET
ejpam-5022	257	9	subordination	subordination	NOUN
ejpam-5022	257	10	(	(	PUNCT
ejpam-5022	257	11	9	9	NUM
ejpam-5022	257	12	)	)	PUNCT
ejpam-5022	257	13	,	,	PUNCT
ejpam-5022	257	14	then	then	ADV
ejpam-5022	257	15	for	for	ADP
ejpam-5022	257	16	bx	bx	PROPN
ejpam-5022	257	17	>	>	X
ejpam-5022	257	18	0	0	PUNCT
ejpam-5022	258	1	and	and	CCONJ
ejpam-5022	258	2	for	for	ADP
ejpam-5022	258	3	some	some	DET
ejpam-5022	258	4	ζ	ζ	NOUN
ejpam-5022	258	5	∈	∈	NOUN
ejpam-5022	258	6	r	r	NOUN
ejpam-5022	258	7	|a3	|a3	NOUN
ejpam-5022	258	8	−	−	PROPN
ejpam-5022	258	9	ζa22|	ζa22|	NOUN
ejpam-5022	258	10	≤	≤	NUM
ejpam-5022	258	11			PUNCT
ejpam-5022	258	12	bx	bx	NOUN
ejpam-5022	258	13	2(1	2(1	PRON
ejpam-5022	258	14	+	+	NOUN
ejpam-5022	258	15	2η)(1	2η)(1	NUM
ejpam-5022	258	16	+	+	SYM
ejpam-5022	258	17	2µ	2µ	NUM
ejpam-5022	258	18	)	)	PUNCT
ejpam-5022	258	19	,	,	PUNCT
ejpam-5022	258	20	if	if	SCONJ
ejpam-5022	258	21	ζ	ζ	PROPN
ejpam-5022	258	22	∈	∈	PROPN
ejpam-5022	258	23	[	[	X
ejpam-5022	258	24	ζ1	ζ1	NOUN
ejpam-5022	258	25	,	,	PUNCT
ejpam-5022	258	26	ζ2]∣∣∣	ζ2]∣∣∣	ADJ
ejpam-5022	258	27	(	(	PUNCT
ejpam-5022	258	28	pbx2+qa)(1+η)2+b2x2(1	pbx2+qa)(1+η)2+b2x2(1	NOUN
ejpam-5022	258	29	+	+	NOUN
ejpam-5022	258	30	3η	3η	NUM
ejpam-5022	258	31	)	)	PUNCT
ejpam-5022	258	32	2(1	2(1	NUM
ejpam-5022	258	33	+	+	NOUN
ejpam-5022	258	34	2η)(1	2η)(1	NUM
ejpam-5022	258	35	+	+	NOUN
ejpam-5022	258	36	2µ)(1+η)2	2µ)(1+η)2	NUM
ejpam-5022	258	37	−	−	NOUN
ejpam-5022	258	38	ζb2x2	ζb2x2	PUNCT
ejpam-5022	258	39	(	(	PUNCT
ejpam-5022	258	40	1+η)2(1+µ)2	1+η)2(1+µ)2	NUM
ejpam-5022	258	41	∣∣∣	∣∣∣	NOUN
ejpam-5022	258	42	,	,	PUNCT
ejpam-5022	258	43	if	if	SCONJ
ejpam-5022	258	44	ζ	ζ	NOUN
ejpam-5022	258	45	/∈	/∈	PUNCT
ejpam-5022	259	1	[	[	X
ejpam-5022	259	2	ζ1	ζ1	NOUN
ejpam-5022	259	3	,	,	PUNCT
ejpam-5022	259	4	ζ2	ζ2	NOUN
ejpam-5022	259	5	]	]	PUNCT
ejpam-5022	259	6	.	.	PUNCT
ejpam-5022	260	1	where	where	SCONJ
ejpam-5022	260	2	ζ1	ζ1	NOUN
ejpam-5022	260	3	=	=	SYM
ejpam-5022	260	4	(	(	PUNCT
ejpam-5022	260	5	1	1	NUM
ejpam-5022	260	6	+	+	NUM
ejpam-5022	260	7	µ)2[(1	µ)2[(1	PRON
ejpam-5022	260	8	+	+	CCONJ
ejpam-5022	260	9	η)2(pbx2	η)2(pbx2	NOUN
ejpam-5022	260	10	−	−	PROPN
ejpam-5022	260	11	bx+	bx+	PROPN
ejpam-5022	260	12	qa	qa	PROPN
ejpam-5022	260	13	)	)	PUNCT
ejpam-5022	260	14	+	+	NUM
ejpam-5022	260	15	b2x2(1	b2x2(1	NOUN
ejpam-5022	260	16	+	+	CCONJ
ejpam-5022	260	17	3η	3η	NUM
ejpam-5022	260	18	)	)	PUNCT
ejpam-5022	260	19	]	]	PUNCT
ejpam-5022	261	1	2(1	2(1	NUM
ejpam-5022	261	2	+	+	CCONJ
ejpam-5022	261	3	2η)(1	2η)(1	NUM
ejpam-5022	261	4	+	+	CCONJ
ejpam-5022	261	5	2µ)b2x2	2µ)b2x2	NUM
ejpam-5022	261	6	,	,	PUNCT
ejpam-5022	261	7	and	and	CCONJ
ejpam-5022	261	8	ζ2	ζ2	NOUN
ejpam-5022	261	9	=	=	SYM
ejpam-5022	261	10	(	(	PUNCT
ejpam-5022	261	11	1	1	NUM
ejpam-5022	261	12	+	+	NUM
ejpam-5022	261	13	µ)2[(1	µ)2[(1	PRON
ejpam-5022	261	14	+	+	CCONJ
ejpam-5022	261	15	η)2(pbx2	η)2(pbx2	NOUN
ejpam-5022	261	16	+	+	CCONJ
ejpam-5022	261	17	bx+	bx+	PROPN
ejpam-5022	261	18	qa	qa	PROPN
ejpam-5022	261	19	)	)	PUNCT
ejpam-5022	262	1	+	+	NUM
ejpam-5022	262	2	b2x2(1	b2x2(1	NOUN
ejpam-5022	262	3	+	+	CCONJ
ejpam-5022	262	4	3η	3η	NUM
ejpam-5022	262	5	)	)	PUNCT
ejpam-5022	262	6	]	]	PUNCT
ejpam-5022	263	1	2(1	2(1	NUM
ejpam-5022	263	2	+	+	CCONJ
ejpam-5022	263	3	2η)(1	2η)(1	NUM
ejpam-5022	263	4	+	+	CCONJ
ejpam-5022	263	5	2µ)b2x2	2µ)b2x2	NUM
ejpam-5022	263	6	.	.	PUNCT
ejpam-5022	264	1	references	reference	NOUN
ejpam-5022	264	2	168	168	NUM
ejpam-5022	264	3	references	reference	NOUN
ejpam-5022	264	4	[	[	X
ejpam-5022	264	5	1	1	NUM
ejpam-5022	264	6	]	]	PUNCT
ejpam-5022	264	7	c.	c.	PROPN
ejpam-5022	264	8	abirami	abirami	PROPN
ejpam-5022	264	9	,	,	PUNCT
ejpam-5022	264	10	n.	n.	PROPN
ejpam-5022	264	11	magesh	magesh	PROPN
ejpam-5022	264	12	,	,	PUNCT
ejpam-5022	264	13	and	and	CCONJ
ejpam-5022	264	14	j.	j.	PROPN
ejpam-5022	264	15	yamini	yamini	PROPN
ejpam-5022	264	16	.	.	PROPN
ejpam-5022	265	1	initial	initial	ADJ
ejpam-5022	265	2	bounds	bound	NOUN
ejpam-5022	265	3	for	for	ADP
ejpam-5022	265	4	certain	certain	ADJ
ejpam-5022	265	5	classes	class	NOUN
ejpam-5022	265	6	of	of	ADP
ejpam-5022	265	7	biunivalent	biunivalent	NOUN
ejpam-5022	265	8	functions	function	NOUN
ejpam-5022	265	9	defined	define	VERB
ejpam-5022	265	10	by	by	ADP
ejpam-5022	265	11	horadam	horadam	NOUN
ejpam-5022	265	12	polynomials	polynomial	NOUN
ejpam-5022	265	13	.	.	PUNCT
ejpam-5022	266	1	abstract	abstract	ADJ
ejpam-5022	266	2	and	and	CCONJ
ejpam-5022	266	3	applied	apply	VERB
ejpam-5022	266	4	analysis	analysis	NOUN
ejpam-5022	266	5	,	,	PUNCT
ejpam-5022	266	6	article	article	NOUN
ejpam-5022	266	7	i	i	NOUN
ejpam-5022	266	8	d	d	PROPN
ejpam-5022	266	9	7391058:8	7391058:8	NUM
ejpam-5022	266	10	pages	page	NOUN
ejpam-5022	266	11	,	,	PUNCT
ejpam-5022	266	12	2020	2020	NUM
ejpam-5022	266	13	.	.	PUNCT
ejpam-5022	267	1	[	[	X
ejpam-5022	267	2	2	2	X
ejpam-5022	267	3	]	]	PUNCT
ejpam-5022	267	4	w.	w.	PROPN
ejpam-5022	267	5	al	al	PROPN
ejpam-5022	267	6	-	-	PUNCT
ejpam-5022	267	7	rawashdeh	rawashdeh	PROPN
ejpam-5022	267	8	.	.	PUNCT
ejpam-5022	268	1	applications	application	NOUN
ejpam-5022	268	2	of	of	ADP
ejpam-5022	268	3	horadam	horadam	NOUN
ejpam-5022	268	4	polynomials	polynomial	NOUN
ejpam-5022	268	5	to	to	ADP
ejpam-5022	268	6	a	a	DET
ejpam-5022	268	7	class	class	NOUN
ejpam-5022	268	8	of	of	ADP
ejpam-5022	268	9	close	close	NOUN
ejpam-5022	268	10	-	-	PUNCT
ejpam-5022	268	11	to	to	ADP
ejpam-5022	268	12	-	-	PUNCT
ejpam-5022	268	13	convex	convex	NOUN
ejpam-5022	268	14	functions	function	NOUN
ejpam-5022	268	15	.	.	PUNCT
ejpam-5022	269	1	preprint	preprint	NOUN
ejpam-5022	269	2	.	.	PUNCT
ejpam-5022	270	1	[	[	X
ejpam-5022	270	2	3	3	X
ejpam-5022	270	3	]	]	PUNCT
ejpam-5022	270	4	w.	w.	PROPN
ejpam-5022	270	5	al	al	PROPN
ejpam-5022	270	6	-	-	PUNCT
ejpam-5022	270	7	rawashdeh	rawashdeh	PROPN
ejpam-5022	270	8	.	.	PUNCT
ejpam-5022	271	1	horadam	horadam	PROPN
ejpam-5022	271	2	polynomials	polynomial	NOUN
ejpam-5022	271	3	and	and	CCONJ
ejpam-5022	271	4	a	a	DET
ejpam-5022	271	5	class	class	NOUN
ejpam-5022	271	6	of	of	ADP
ejpam-5022	271	7	binivalent	binivalent	NOUN
ejpam-5022	271	8	functions	function	NOUN
ejpam-5022	271	9	defined	define	VERB
ejpam-5022	271	10	by	by	ADP
ejpam-5022	271	11	ruscheweyh	ruscheweyh	NOUN
ejpam-5022	271	12	operator	operator	NOUN
ejpam-5022	271	13	.	.	PUNCT
ejpam-5022	272	1	international	international	ADJ
ejpam-5022	272	2	journal	journal	PROPN
ejpam-5022	272	3	of	of	ADP
ejpam-5022	272	4	mathematics	mathematics	PROPN
ejpam-5022	272	5	and	and	CCONJ
ejpam-5022	272	6	mathematical	mathematical	ADJ
ejpam-5022	272	7	sciences	science	NOUN
ejpam-5022	272	8	,	,	PUNCT
ejpam-5022	272	9	article	article	NOUN
ejpam-5022	272	10	i	i	NOUN
ejpam-5022	272	11	d	d	PROPN
ejpam-5022	272	12	2573044:7	2573044:7	NUM
ejpam-5022	272	13	pages	page	NOUN
ejpam-5022	272	14	,	,	PUNCT
ejpam-5022	272	15	2023	2023	NUM
ejpam-5022	272	16	.	.	PUNCT
ejpam-5022	273	1	[	[	X
ejpam-5022	273	2	4	4	X
ejpam-5022	273	3	]	]	PUNCT
ejpam-5022	273	4	w.	w.	PROPN
ejpam-5022	273	5	al	al	PROPN
ejpam-5022	273	6	-	-	PUNCT
ejpam-5022	273	7	rawashdeh	rawashdeh	PROPN
ejpam-5022	273	8	.	.	PUNCT
ejpam-5022	274	1	coefficient	coefficient	NOUN
ejpam-5022	274	2	bounds	bound	NOUN
ejpam-5022	274	3	of	of	ADP
ejpam-5022	274	4	a	a	DET
ejpam-5022	274	5	class	class	NOUN
ejpam-5022	274	6	of	of	ADP
ejpam-5022	274	7	bi	bi	ADJ
ejpam-5022	274	8	-	-	ADJ
ejpam-5022	274	9	univalent	univalent	ADJ
ejpam-5022	274	10	functions	function	NOUN
ejpam-5022	274	11	related	relate	VERB
ejpam-5022	274	12	to	to	ADP
ejpam-5022	274	13	gegenbauer	gegenbauer	NOUN
ejpam-5022	274	14	polynomials	polynomial	NOUN
ejpam-5022	274	15	.	.	PUNCT
ejpam-5022	275	1	international	international	ADJ
ejpam-5022	275	2	journal	journal	PROPN
ejpam-5022	275	3	of	of	ADP
ejpam-5022	275	4	mathematics	mathematic	NOUN
ejpam-5022	275	5	and	and	CCONJ
ejpam-5022	275	6	computer	computer	NOUN
ejpam-5022	275	7	science	science	NOUN
ejpam-5022	275	8	,	,	PUNCT
ejpam-5022	275	9	19:635–642	19:635–642	NUM
ejpam-5022	275	10	,	,	PUNCT
ejpam-5022	275	11	2024	2024	NUM
ejpam-5022	275	12	.	.	PUNCT
ejpam-5022	276	1	[	[	X
ejpam-5022	276	2	5	5	X
ejpam-5022	276	3	]	]	PUNCT
ejpam-5022	276	4	w.	w.	PROPN
ejpam-5022	276	5	al	al	PROPN
ejpam-5022	276	6	-	-	PUNCT
ejpam-5022	276	7	rawashdeh	rawashdeh	PROPN
ejpam-5022	276	8	.	.	PUNCT
ejpam-5022	277	1	fekete	fekete	PROPN
ejpam-5022	277	2	-	-	PUNCT
ejpam-5022	277	3	szegö	szegö	VERB
ejpam-5022	277	4	functional	functional	NOUN
ejpam-5022	277	5	of	of	ADP
ejpam-5022	277	6	a	a	DET
ejpam-5022	277	7	subclass	subclass	NOUN
ejpam-5022	277	8	of	of	ADP
ejpam-5022	277	9	bi	bi	ADJ
ejpam-5022	277	10	-	-	ADJ
ejpam-5022	277	11	univalent	univalent	ADJ
ejpam-5022	277	12	functions	function	NOUN
ejpam-5022	277	13	associated	associate	VERB
ejpam-5022	277	14	with	with	ADP
ejpam-5022	277	15	gegenbauer	gegenbauer	NOUN
ejpam-5022	277	16	polynomials	polynomial	NOUN
ejpam-5022	277	17	.	.	PUNCT
ejpam-5022	278	1	european	european	PROPN
ejpam-5022	278	2	journal	journal	PROPN
ejpam-5022	278	3	of	of	ADP
ejpam-5022	278	4	pure	pure	ADJ
ejpam-5022	278	5	and	and	CCONJ
ejpam-5022	278	6	applied	applied	ADJ
ejpam-5022	278	7	mathematics	mathematic	NOUN
ejpam-5022	278	8	,	,	PUNCT
ejpam-5022	278	9	in	in	ADP
ejpam-5022	278	10	press	press	NOUN
ejpam-5022	278	11	,	,	PUNCT
ejpam-5022	278	12	2024	2024	NUM
ejpam-5022	278	13	.	.	PUNCT
ejpam-5022	279	1	https://doi.org/10.29020/nybg.ejpam.v17i1.5022	https://doi.org/10.29020/nybg.ejpam.v17i1.5022	X
ejpam-5022	279	2	.	.	PUNCT
ejpam-5022	280	1	[	[	X
ejpam-5022	280	2	6	6	NUM
ejpam-5022	280	3	]	]	PUNCT
ejpam-5022	280	4	s.	s.	PROPN
ejpam-5022	280	5	altınkaya	altınkaya	PROPN
ejpam-5022	280	6	and	and	CCONJ
ejpam-5022	280	7	s.	s.	PROPN
ejpam-5022	280	8	yalcin	yalcin	PROPN
ejpam-5022	280	9	.	.	PUNCT
ejpam-5022	281	1	on	on	ADP
ejpam-5022	281	2	the	the	DET
ejpam-5022	281	3	chebyshev	chebyshev	NOUN
ejpam-5022	281	4	polynomial	polynomial	ADJ
ejpam-5022	281	5	bounds	bound	NOUN
ejpam-5022	281	6	for	for	ADP
ejpam-5022	281	7	classes	class	NOUN
ejpam-5022	281	8	of	of	ADP
ejpam-5022	281	9	univalent	univalent	ADJ
ejpam-5022	281	10	functions	function	NOUN
ejpam-5022	281	11	.	.	PUNCT
ejpam-5022	282	1	khayyam	khayyam	PROPN
ejpam-5022	282	2	journal	journal	PROPN
ejpam-5022	282	3	mathematics	mathematics	PROPN
ejpam-5022	282	4	,	,	PUNCT
ejpam-5022	282	5	2(1):1–5	2(1):1–5	NUM
ejpam-5022	282	6	,	,	PUNCT
ejpam-5022	282	7	2016	2016	NUM
ejpam-5022	282	8	.	.	PUNCT
ejpam-5022	283	1	[	[	X
ejpam-5022	283	2	7	7	X
ejpam-5022	283	3	]	]	X
ejpam-5022	283	4	s.	s.	PROPN
ejpam-5022	283	5	bulut	bulut	PROPN
ejpam-5022	283	6	,	,	PUNCT
ejpam-5022	283	7	n.	n.	PROPN
ejpam-5022	283	8	magesh	magesh	PROPN
ejpam-5022	283	9	,	,	PUNCT
ejpam-5022	283	10	and	and	CCONJ
ejpam-5022	283	11	v.k	v.k	PROPN
ejpam-5022	283	12	.	.	PROPN
ejpam-5022	283	13	balaji	balaji	PROPN
ejpam-5022	283	14	.	.	PUNCT
ejpam-5022	284	1	certain	certain	ADJ
ejpam-5022	284	2	subclasses	subclass	NOUN
ejpam-5022	284	3	of	of	ADP
ejpam-5022	284	4	analytic	analytic	ADJ
ejpam-5022	284	5	functions	function	NOUN
ejpam-5022	284	6	associated	associate	VERB
ejpam-5022	284	7	with	with	ADP
ejpam-5022	284	8	the	the	DET
ejpam-5022	284	9	chebyshev	chebyshev	NOUN
ejpam-5022	284	10	polynomials	polynomial	NOUN
ejpam-5022	284	11	.	.	PUNCT
ejpam-5022	285	1	honam	honam	PROPN
ejpam-5022	285	2	mathematical	mathematical	PROPN
ejpam-5022	285	3	journal	journal	PROPN
ejpam-5022	285	4	,	,	PUNCT
ejpam-5022	285	5	40(4):611–619	40(4):611–619	PROPN
ejpam-5022	285	6	,	,	PUNCT
ejpam-5022	285	7	2018	2018	NUM
ejpam-5022	285	8	.	.	PUNCT
ejpam-5022	286	1	[	[	X
ejpam-5022	286	2	8	8	NUM
ejpam-5022	286	3	]	]	PUNCT
ejpam-5022	286	4	m.	m.	NOUN
ejpam-5022	286	5	cağlar	cağlar	PROPN
ejpam-5022	286	6	,	,	PUNCT
ejpam-5022	286	7	h.	h.	PROPN
ejpam-5022	286	8	orhan	orhan	PROPN
ejpam-5022	286	9	,	,	PUNCT
ejpam-5022	286	10	and	and	CCONJ
ejpam-5022	286	11	m.	m.	PROPN
ejpam-5022	286	12	kamali	kamali	PROPN
ejpam-5022	286	13	.	.	PUNCT
ejpam-5022	287	1	fekete	fekete	PROPN
ejpam-5022	287	2	-	-	PUNCT
ejpam-5022	287	3	szegö	szegö	PROPN
ejpam-5022	287	4	problem	problem	NOUN
ejpam-5022	287	5	for	for	ADP
ejpam-5022	287	6	a	a	DET
ejpam-5022	287	7	subclass	subclass	NOUN
ejpam-5022	287	8	of	of	ADP
ejpam-5022	287	9	analytic	analytic	ADJ
ejpam-5022	287	10	functions	function	NOUN
ejpam-5022	287	11	associated	associate	VERB
ejpam-5022	287	12	with	with	ADP
ejpam-5022	287	13	chebyshev	chebyshev	NOUN
ejpam-5022	287	14	polynomials	polynomial	NOUN
ejpam-5022	287	15	.	.	PUNCT
ejpam-5022	288	1	bol	bol	NOUN
ejpam-5022	288	2	.	.	PUNCT
ejpam-5022	289	1	soc	soc	PROPN
ejpam-5022	289	2	.	.	PUNCT
ejpam-5022	290	1	paran	paran	PROPN
ejpam-5022	290	2	.	.	PUNCT
ejpam-5022	291	1	mat	mat	PROPN
ejpam-5022	291	2	.	.	PROPN
ejpam-5022	291	3	,	,	PUNCT
ejpam-5022	291	4	40	40	NUM
ejpam-5022	291	5	,	,	PUNCT
ejpam-5022	291	6	2022	2022	NUM
ejpam-5022	291	7	.	.	PUNCT
ejpam-5022	292	1	[	[	X
ejpam-5022	292	2	9	9	NUM
ejpam-5022	292	3	]	]	X
ejpam-5022	292	4	j.h	j.h	PROPN
ejpam-5022	292	5	.	.	PROPN
ejpam-5022	292	6	choi	choi	PROPN
ejpam-5022	292	7	,	,	PUNCT
ejpam-5022	292	8	y.c	y.c	PROPN
ejpam-5022	292	9	.	.	PROPN
ejpam-5022	292	10	kim	kim	PROPN
ejpam-5022	292	11	,	,	PUNCT
ejpam-5022	292	12	and	and	CCONJ
ejpam-5022	292	13	t.	t.	PROPN
ejpam-5022	292	14	sugawa	sugawa	PROPN
ejpam-5022	292	15	.	.	PUNCT
ejpam-5022	293	1	a	a	DET
ejpam-5022	293	2	general	general	ADJ
ejpam-5022	293	3	approach	approach	NOUN
ejpam-5022	293	4	to	to	ADP
ejpam-5022	293	5	the	the	DET
ejpam-5022	293	6	fekete	fekete	PROPN
ejpam-5022	293	7	-	-	PUNCT
ejpam-5022	293	8	szegö	szegö	PROPN
ejpam-5022	293	9	problem	problem	NOUN
ejpam-5022	293	10	.	.	PUNCT
ejpam-5022	294	1	journal	journal	NOUN
ejpam-5022	294	2	of	of	ADP
ejpam-5022	294	3	the	the	DET
ejpam-5022	294	4	mathematical	mathematical	ADJ
ejpam-5022	294	5	society	society	NOUN
ejpam-5022	294	6	of	of	ADP
ejpam-5022	294	7	japan	japan	PROPN
ejpam-5022	294	8	,	,	PUNCT
ejpam-5022	294	9	59(3):707–727	59(3):707–727	NUM
ejpam-5022	294	10	,	,	PUNCT
ejpam-5022	294	11	2007	2007	NUM
ejpam-5022	294	12	.	.	PUNCT
ejpam-5022	295	1	[	[	X
ejpam-5022	295	2	10	10	NUM
ejpam-5022	295	3	]	]	X
ejpam-5022	295	4	p.	p.	PROPN
ejpam-5022	295	5	duren	duren	PROPN
ejpam-5022	295	6	.	.	PUNCT
ejpam-5022	295	7	subordination	subordination	NOUN
ejpam-5022	295	8	in	in	ADP
ejpam-5022	295	9	complex	complex	ADJ
ejpam-5022	295	10	analysis	analysis	NOUN
ejpam-5022	295	11	,	,	PUNCT
ejpam-5022	295	12	lecture	lecture	NOUN
ejpam-5022	295	13	notes	note	NOUN
ejpam-5022	295	14	in	in	ADP
ejpam-5022	295	15	mathematics	mathematic	NOUN
ejpam-5022	295	16	.	.	PUNCT
ejpam-5022	296	1	springer	springer	PROPN
ejpam-5022	296	2	,	,	PUNCT
ejpam-5022	296	3	berlin	berlin	PROPN
ejpam-5022	296	4	,	,	PUNCT
ejpam-5022	296	5	germany	germany	PROPN
ejpam-5022	296	6	,	,	PUNCT
ejpam-5022	296	7	599(3):22–29	599(3):22–29	NUM
ejpam-5022	296	8	,	,	PUNCT
ejpam-5022	296	9	1977	1977	NUM
ejpam-5022	296	10	.	.	PUNCT
ejpam-5022	297	1	[	[	X
ejpam-5022	297	2	11	11	NUM
ejpam-5022	297	3	]	]	PUNCT
ejpam-5022	297	4	p.	p.	PROPN
ejpam-5022	297	5	duren	duren	PROPN
ejpam-5022	297	6	.	.	PUNCT
ejpam-5022	298	1	univalent	univalent	ADJ
ejpam-5022	298	2	functions	function	NOUN
ejpam-5022	298	3	.	.	PUNCT
ejpam-5022	299	1	grundlehren	grundlehren	PROPN
ejpam-5022	299	2	der	der	PROPN
ejpam-5022	299	3	mathematischen	mathematischen	PROPN
ejpam-5022	299	4	wissenschaften	wissenschaften	VERB
ejpam-5022	299	5	259	259	NUM
ejpam-5022	299	6	,	,	PUNCT
ejpam-5022	299	7	springer	springer	NOUN
ejpam-5022	299	8	-	-	PUNCT
ejpam-5022	299	9	verlag	verlag	PROPN
ejpam-5022	299	10	,	,	PUNCT
ejpam-5022	299	11	new	new	PROPN
ejpam-5022	299	12	york	york	PROPN
ejpam-5022	299	13	,	,	PUNCT
ejpam-5022	299	14	1983	1983	NUM
ejpam-5022	299	15	.	.	PUNCT
ejpam-5022	300	1	[	[	X
ejpam-5022	300	2	12	12	NUM
ejpam-5022	300	3	]	]	PUNCT
ejpam-5022	300	4	j.	j.	PROPN
ejpam-5022	300	5	dziok	dziok	PROPN
ejpam-5022	300	6	,	,	PUNCT
ejpam-5022	300	7	r.k	r.k	PROPN
ejpam-5022	300	8	.	.	PROPN
ejpam-5022	300	9	raina	raina	PROPN
ejpam-5022	300	10	rk	rk	PROPN
ejpam-5022	300	11	,	,	PUNCT
ejpam-5022	300	12	and	and	CCONJ
ejpam-5022	300	13	j.	j.	PROPN
ejpam-5022	300	14	sokol	sokol	PROPN
ejpam-5022	300	15	j.	j.	PROPN
ejpam-5022	300	16	application	application	PROPN
ejpam-5022	300	17	of	of	ADP
ejpam-5022	300	18	chebyshev	chebyshev	NOUN
ejpam-5022	300	19	polynomials	polynomial	NOUN
ejpam-5022	300	20	to	to	ADP
ejpam-5022	300	21	classes	class	NOUN
ejpam-5022	300	22	of	of	ADP
ejpam-5022	300	23	analytic	analytic	ADJ
ejpam-5022	300	24	functions	function	NOUN
ejpam-5022	300	25	.	.	PUNCT
ejpam-5022	301	1	comptes	compte	VERB
ejpam-5022	301	2	rendus	rendus	PROPN
ejpam-5022	301	3	de	de	PROPN
ejpam-5022	301	4	ĺacadémie	ĺacadémie	X
ejpam-5022	301	5	des	des	PROPN
ejpam-5022	301	6	sciences	sciences	PROPN
ejpam-5022	301	7	paris	paris	PROPN
ejpam-5022	301	8	,	,	PUNCT
ejpam-5022	301	9	353(3):433–438	353(3):433–438	NUM
ejpam-5022	301	10	,	,	PUNCT
ejpam-5022	301	11	2015	2015	NUM
ejpam-5022	301	12	.	.	PUNCT
ejpam-5022	302	1	[	[	X
ejpam-5022	302	2	13	13	NUM
ejpam-5022	302	3	]	]	PUNCT
ejpam-5022	302	4	m.	m.	NOUN
ejpam-5022	302	5	fekete	fekete	PROPN
ejpam-5022	302	6	and	and	CCONJ
ejpam-5022	302	7	g.	g.	PROPN
ejpam-5022	302	8	szegö.	szegö.	PROPN
ejpam-5022	302	9	eine	eine	PROPN
ejpam-5022	302	10	bemerkung	bemerkung	PROPN
ejpam-5022	302	11	über	über	PROPN
ejpam-5022	302	12	ungerade	ungerade	PROPN
ejpam-5022	302	13	schlichte	schlichte	PROPN
ejpam-5022	302	14	funktionen	funktionen	PROPN
ejpam-5022	302	15	.	.	PROPN
ejpam-5022	303	1	journal	journal	PROPN
ejpam-5022	303	2	of	of	ADP
ejpam-5022	303	3	london	london	PROPN
ejpam-5022	303	4	mathematical	mathematical	ADJ
ejpam-5022	303	5	society	society	NOUN
ejpam-5022	303	6	,	,	PUNCT
ejpam-5022	303	7	s1	s1	NOUN
ejpam-5022	303	8	-	-	PUNCT
ejpam-5022	303	9	8(3):85–89	8(3):85–89	NUM
ejpam-5022	303	10	,	,	PUNCT
ejpam-5022	303	11	1933	1933	NUM
ejpam-5022	303	12	.	.	PUNCT
ejpam-5022	304	1	[	[	X
ejpam-5022	304	2	14	14	NUM
ejpam-5022	304	3	]	]	PUNCT
ejpam-5022	304	4	a.	a.	PROPN
ejpam-5022	304	5	w.	w.	PROPN
ejpam-5022	304	6	goodman	goodman	PROPN
ejpam-5022	304	7	.	.	PUNCT
ejpam-5022	305	1	univalent	univalent	ADJ
ejpam-5022	305	2	functions	function	NOUN
ejpam-5022	305	3	.	.	PUNCT
ejpam-5022	306	1	mariner	mariner	PROPN
ejpam-5022	306	2	publishing	publishing	PROPN
ejpam-5022	306	3	co.	co.	PROPN
ejpam-5022	306	4	inc	inc	PROPN
ejpam-5022	306	5	.	.	PROPN
ejpam-5022	306	6	,	,	PUNCT
ejpam-5022	306	7	boston	boston	PROPN
ejpam-5022	306	8	,	,	PUNCT
ejpam-5022	306	9	1983	1983	NUM
ejpam-5022	306	10	.	.	PUNCT
ejpam-5022	307	1	references	reference	NOUN
ejpam-5022	307	2	169	169	NUM
ejpam-5022	308	1	[	[	X
ejpam-5022	308	2	15	15	NUM
ejpam-5022	308	3	]	]	X
ejpam-5022	308	4	a.	a.	NOUN
ejpam-5022	308	5	f.	f.	PROPN
ejpam-5022	308	6	horadam	horadam	PROPN
ejpam-5022	308	7	.	.	PUNCT
ejpam-5022	309	1	jacobsthal	jacobsthal	ADJ
ejpam-5022	309	2	representation	representation	NOUN
ejpam-5022	309	3	polynomials	polynomial	NOUN
ejpam-5022	309	4	.	.	PUNCT
ejpam-5022	310	1	the	the	DET
ejpam-5022	310	2	fibonacci	fibonacci	NOUN
ejpam-5022	310	3	quarterly	quarterly	ADV
ejpam-5022	310	4	,	,	PUNCT
ejpam-5022	310	5	35(3):137–148	35(3):137–148	PROPN
ejpam-5022	310	6	,	,	PUNCT
ejpam-5022	310	7	1997	1997	NUM
ejpam-5022	310	8	.	.	PUNCT
ejpam-5022	311	1	[	[	X
ejpam-5022	311	2	16	16	NUM
ejpam-5022	311	3	]	]	PUNCT
ejpam-5022	311	4	a.	a.	PROPN
ejpam-5022	311	5	f.	f.	PROPN
ejpam-5022	311	6	horadam	horadam	PROPN
ejpam-5022	311	7	and	and	CCONJ
ejpam-5022	311	8	j.	j.	PROPN
ejpam-5022	311	9	m.	m.	PROPN
ejpam-5022	311	10	mahon	mahon	PROPN
ejpam-5022	311	11	.	.	PUNCT
ejpam-5022	312	1	pell	pell	VERB
ejpam-5022	312	2	and	and	CCONJ
ejpam-5022	312	3	pell	pell	NOUN
ejpam-5022	312	4	-	-	PUNCT
ejpam-5022	312	5	lucas	lucas	NOUN
ejpam-5022	312	6	polynomials	polynomial	NOUN
ejpam-5022	312	7	.	.	PUNCT
ejpam-5022	313	1	the	the	DET
ejpam-5022	313	2	fibonacci	fibonacci	NOUN
ejpam-5022	313	3	quarterly	quarterly	ADV
ejpam-5022	313	4	,	,	PUNCT
ejpam-5022	313	5	23(3):7–20	23(3):7–20	NUM
ejpam-5022	313	6	,	,	PUNCT
ejpam-5022	313	7	1985	1985	NUM
ejpam-5022	313	8	.	.	PUNCT
ejpam-5022	314	1	[	[	X
ejpam-5022	314	2	17	17	NUM
ejpam-5022	314	3	]	]	X
ejpam-5022	314	4	a.f	a.f	PROPN
ejpam-5022	314	5	.	.	PUNCT
ejpam-5022	314	6	horadam	horadam	PROPN
ejpam-5022	314	7	.	.	PUNCT
ejpam-5022	315	1	basic	basic	ADJ
ejpam-5022	315	2	properties	property	NOUN
ejpam-5022	315	3	of	of	ADP
ejpam-5022	315	4	a	a	DET
ejpam-5022	315	5	certain	certain	ADJ
ejpam-5022	315	6	generalized	generalized	ADJ
ejpam-5022	315	7	sequence	sequence	NOUN
ejpam-5022	315	8	of	of	ADP
ejpam-5022	315	9	numbers	number	NOUN
ejpam-5022	315	10	.	.	PUNCT
ejpam-5022	316	1	the	the	DET
ejpam-5022	316	2	fibonacci	fibonacci	PROPN
ejpam-5022	316	3	quarterly	quarterly	PROPN
ejpam-5022	316	4	,	,	PUNCT
ejpam-5022	316	5	3(3):161–176	3(3):161–176	PROPN
ejpam-5022	316	6	,	,	PUNCT
ejpam-5022	316	7	1965	1965	NUM
ejpam-5022	316	8	.	.	PUNCT
ejpam-5022	317	1	[	[	X
ejpam-5022	317	2	18	18	NUM
ejpam-5022	317	3	]	]	PUNCT
ejpam-5022	317	4	t.	t.	NOUN
ejpam-5022	317	5	horzum	horzum	NOUN
ejpam-5022	317	6	and	and	CCONJ
ejpam-5022	317	7	e.g.	e.g.	ADV
ejpam-5022	317	8	kocer	kocer	NOUN
ejpam-5022	317	9	.	.	PUNCT
ejpam-5022	318	1	on	on	ADP
ejpam-5022	318	2	some	some	DET
ejpam-5022	318	3	properties	property	NOUN
ejpam-5022	318	4	of	of	ADP
ejpam-5022	318	5	horadam	horadam	NOUN
ejpam-5022	318	6	polynomials	polynomial	NOUN
ejpam-5022	318	7	.	.	PUNCT
ejpam-5022	319	1	international	international	ADJ
ejpam-5022	319	2	mathematics	mathematics	PROPN
ejpam-5022	319	3	forum	forum	PROPN
ejpam-5022	319	4	,	,	PUNCT
ejpam-5022	319	5	4(3):1243–1252	4(3):1243–1252	PROPN
ejpam-5022	319	6	,	,	PUNCT
ejpam-5022	319	7	2009	2009	NUM
ejpam-5022	319	8	.	.	PUNCT
ejpam-5022	320	1	[	[	X
ejpam-5022	320	2	19	19	NUM
ejpam-5022	320	3	]	]	X
ejpam-5022	320	4	m.	m.	NOUN
ejpam-5022	320	5	kamali	kamali	PROPN
ejpam-5022	320	6	,	,	PUNCT
ejpam-5022	320	7	m.	m.	NOUN
ejpam-5022	320	8	cağlar	cağlar	PROPN
ejpam-5022	320	9	,	,	PUNCT
ejpam-5022	320	10	e.	e.	PROPN
ejpam-5022	320	11	deniz	deniz	PROPN
ejpam-5022	320	12	,	,	PUNCT
ejpam-5022	320	13	and	and	CCONJ
ejpam-5022	320	14	m.	m.	PROPN
ejpam-5022	320	15	turabaev	turabaev	PROPN
ejpam-5022	320	16	.	.	PUNCT
ejpam-5022	321	1	fekete	fekete	PROPN
ejpam-5022	321	2	szegö	szegö	PROPN
ejpam-5022	321	3	problem	problem	NOUN
ejpam-5022	321	4	for	for	ADP
ejpam-5022	321	5	a	a	DET
ejpam-5022	321	6	new	new	ADJ
ejpam-5022	321	7	subclass	subclass	NOUN
ejpam-5022	321	8	of	of	ADP
ejpam-5022	321	9	analytic	analytic	ADJ
ejpam-5022	321	10	functions	function	NOUN
ejpam-5022	321	11	satisfying	satisfy	VERB
ejpam-5022	321	12	subordinate	subordinate	ADJ
ejpam-5022	321	13	condition	condition	NOUN
ejpam-5022	321	14	associated	associate	VERB
ejpam-5022	321	15	with	with	ADP
ejpam-5022	321	16	chebyshev	chebyshev	NOUN
ejpam-5022	321	17	polynomials	polynomial	NOUN
ejpam-5022	321	18	.	.	PUNCT
ejpam-5022	322	1	turkish	turkish	ADJ
ejpam-5022	322	2	j.	j.	PROPN
ejpam-5022	322	3	math	math	PROPN
ejpam-5022	322	4	.	.	PUNCT
ejpam-5022	322	5	,	,	PUNCT
ejpam-5022	322	6	45(3):1195–1208	45(3):1195–1208	NUM
ejpam-5022	322	7	,	,	PUNCT
ejpam-5022	322	8	2012	2012	NUM
ejpam-5022	322	9	.	.	PUNCT
ejpam-5022	323	1	[	[	X
ejpam-5022	323	2	20	20	NUM
ejpam-5022	323	3	]	]	SYM
ejpam-5022	323	4	f.r	f.r	PROPN
ejpam-5022	323	5	.	.	PROPN
ejpam-5022	323	6	keogh	keogh	PROPN
ejpam-5022	323	7	and	and	CCONJ
ejpam-5022	323	8	e.p	e.p	PROPN
ejpam-5022	323	9	.	.	PROPN
ejpam-5022	323	10	merkes	merke	NOUN
ejpam-5022	323	11	.	.	PUNCT
ejpam-5022	324	1	a	a	DET
ejpam-5022	324	2	coefficient	coefficient	NOUN
ejpam-5022	324	3	inequality	inequality	NOUN
ejpam-5022	324	4	for	for	ADP
ejpam-5022	324	5	certain	certain	ADJ
ejpam-5022	324	6	classes	class	NOUN
ejpam-5022	324	7	of	of	ADP
ejpam-5022	324	8	analytic	analytic	ADJ
ejpam-5022	324	9	functions	function	NOUN
ejpam-5022	324	10	.	.	PUNCT
ejpam-5022	325	1	proceedings	proceeding	NOUN
ejpam-5022	325	2	of	of	ADP
ejpam-5022	325	3	the	the	DET
ejpam-5022	325	4	american	american	PROPN
ejpam-5022	325	5	mathematical	mathematical	PROPN
ejpam-5022	325	6	society	society	NOUN
ejpam-5022	325	7	,	,	PUNCT
ejpam-5022	325	8	20(3):8–12	20(3):8–12	NUM
ejpam-5022	325	9	,	,	PUNCT
ejpam-5022	325	10	1969	1969	NUM
ejpam-5022	325	11	.	.	PUNCT
ejpam-5022	326	1	[	[	X
ejpam-5022	326	2	21	21	NUM
ejpam-5022	326	3	]	]	X
ejpam-5022	326	4	t.	t.	PROPN
ejpam-5022	326	5	koshy	koshy	PROPN
ejpam-5022	326	6	.	.	PUNCT
ejpam-5022	326	7	jacobsthal	jacobsthal	ADJ
ejpam-5022	326	8	representation	representation	NOUN
ejpam-5022	326	9	polynomials	polynomial	NOUN
ejpam-5022	326	10	,	,	PUNCT
ejpam-5022	326	11	second	second	ADJ
ejpam-5022	326	12	edition	edition	NOUN
ejpam-5022	326	13	;	;	PUNCT
ejpam-5022	326	14	pure	pure	ADJ
ejpam-5022	326	15	and	and	CCONJ
ejpam-5022	326	16	applied	applied	ADJ
ejpam-5022	326	17	mathematics	mathematic	NOUN
ejpam-5022	326	18	.	.	PUNCT
ejpam-5022	327	1	2018	2018	NUM
ejpam-5022	327	2	.	.	PUNCT
ejpam-5022	328	1	[	[	X
ejpam-5022	328	2	22	22	NUM
ejpam-5022	328	3	]	]	PUNCT
ejpam-5022	328	4	m.	m.	NOUN
ejpam-5022	328	5	lewin	lewin	PROPN
ejpam-5022	328	6	.	.	PUNCT
ejpam-5022	329	1	on	on	ADP
ejpam-5022	329	2	a	a	DET
ejpam-5022	329	3	coefficient	coefficient	NOUN
ejpam-5022	329	4	problem	problem	NOUN
ejpam-5022	329	5	for	for	ADP
ejpam-5022	329	6	bi	bi	ADJ
ejpam-5022	329	7	-	-	ADJ
ejpam-5022	329	8	univalent	univalent	ADJ
ejpam-5022	329	9	functions	function	NOUN
ejpam-5022	329	10	.	.	PUNCT
ejpam-5022	330	1	proceedings	proceeding	NOUN
ejpam-5022	330	2	of	of	ADP
ejpam-5022	330	3	the	the	DET
ejpam-5022	330	4	american	american	PROPN
ejpam-5022	330	5	mathematical	mathematical	PROPN
ejpam-5022	330	6	society	society	NOUN
ejpam-5022	330	7	,	,	PUNCT
ejpam-5022	330	8	18(1):63–68	18(1):63–68	NUM
ejpam-5022	330	9	,	,	PUNCT
ejpam-5022	330	10	1967	1967	NUM
ejpam-5022	330	11	.	.	PUNCT
ejpam-5022	331	1	[	[	X
ejpam-5022	331	2	23	23	NUM
ejpam-5022	331	3	]	]	X
ejpam-5022	331	4	s.	s.	PROPN
ejpam-5022	331	5	miller	miller	PROPN
ejpam-5022	331	6	and	and	CCONJ
ejpam-5022	331	7	p.	p.	NOUN
ejpam-5022	331	8	mocabu	mocabu	NOUN
ejpam-5022	331	9	.	.	PUNCT
ejpam-5022	332	1	differential	differential	ADJ
ejpam-5022	332	2	subordination	subordination	NOUN
ejpam-5022	332	3	:	:	PUNCT
ejpam-5022	332	4	theory	theory	NOUN
ejpam-5022	332	5	and	and	CCONJ
ejpam-5022	332	6	applications	application	NOUN
ejpam-5022	332	7	.	.	PUNCT
ejpam-5022	333	1	crc	crc	PROPN
ejpam-5022	333	2	press	press	PROPN
ejpam-5022	333	3	,	,	PUNCT
ejpam-5022	333	4	new	new	PROPN
ejpam-5022	333	5	york	york	PROPN
ejpam-5022	333	6	,	,	PUNCT
ejpam-5022	333	7	2000	2000	NUM
ejpam-5022	333	8	.	.	PUNCT
ejpam-5022	334	1	[	[	X
ejpam-5022	334	2	24	24	NUM
ejpam-5022	334	3	]	]	PUNCT
ejpam-5022	334	4	k.	k.	PROPN
ejpam-5022	334	5	muthunagai	muthunagai	PROPN
ejpam-5022	334	6	,	,	PUNCT
ejpam-5022	334	7	g.	g.	PROPN
ejpam-5022	334	8	saravanan	saravanan	PROPN
ejpam-5022	334	9	,	,	PUNCT
ejpam-5022	334	10	and	and	CCONJ
ejpam-5022	334	11	s.	s.	PROPN
ejpam-5022	334	12	baskaran	baskaran	VERB
ejpam-5022	334	13	.	.	PUNCT
ejpam-5022	335	1	a	a	DET
ejpam-5022	335	2	subclass	subclass	NOUN
ejpam-5022	335	3	with	with	ADP
ejpam-5022	335	4	bi	bi	NOUN
ejpam-5022	335	5	-	-	NOUN
ejpam-5022	335	6	univalence	univalence	NOUN
ejpam-5022	335	7	involving	involve	VERB
ejpam-5022	335	8	horadam	horadam	PROPN
ejpam-5022	335	9	polynomials	polynomial	NOUN
ejpam-5022	335	10	and	and	CCONJ
ejpam-5022	335	11	its	its	PRON
ejpam-5022	335	12	coefficient	coefficient	NOUN
ejpam-5022	335	13	bounds	bound	NOUN
ejpam-5022	335	14	.	.	PUNCT
ejpam-5022	336	1	proyecciones	proyecciones	PROPN
ejpam-5022	336	2	journal	journal	PROPN
ejpam-5022	336	3	of	of	ADP
ejpam-5022	336	4	mathematics	mathematics	PROPN
ejpam-5022	336	5	,	,	PUNCT
ejpam-5022	336	6	40(3):721–730	40(3):721–730	NOUN
ejpam-5022	336	7	,	,	PUNCT
ejpam-5022	336	8	2021	2021	NUM
ejpam-5022	336	9	.	.	PUNCT
ejpam-5022	337	1	[	[	X
ejpam-5022	337	2	25	25	NUM
ejpam-5022	337	3	]	]	PUNCT
ejpam-5022	337	4	z.	z.	PROPN
ejpam-5022	337	5	nehari	nehari	PROPN
ejpam-5022	337	6	.	.	PUNCT
ejpam-5022	338	1	conformal	conformal	ADJ
ejpam-5022	338	2	mappings	mapping	NOUN
ejpam-5022	338	3	.	.	PUNCT
ejpam-5022	339	1	mcgraw	mcgraw	PROPN
ejpam-5022	339	2	-	-	PUNCT
ejpam-5022	339	3	hill	hill	PROPN
ejpam-5022	339	4	,	,	PUNCT
ejpam-5022	339	5	new	new	PROPN
ejpam-5022	339	6	york	york	PROPN
ejpam-5022	339	7	,	,	PUNCT
ejpam-5022	339	8	1952	1952	NUM
ejpam-5022	339	9	.	.	PUNCT
ejpam-5022	340	1	[	[	X
ejpam-5022	340	2	26	26	NUM
ejpam-5022	340	3	]	]	X
ejpam-5022	340	4	f.	f.	PROPN
ejpam-5022	340	5	qi	qi	PROPN
ejpam-5022	340	6	,	,	PUNCT
ejpam-5022	340	7	c.	c.	PROPN
ejpam-5022	340	8	kizilateş	kizilateş	PROPN
ejpam-5022	340	9	,	,	PUNCT
ejpam-5022	340	10	and	and	CCONJ
ejpam-5022	340	11	w.s	w.s	PROPN
ejpam-5022	340	12	.	.	PROPN
ejpam-5022	340	13	du	du	PROPN
ejpam-5022	340	14	.	.	PUNCT
ejpam-5022	341	1	a	a	DET
ejpam-5022	341	2	cloed	cloed	NOUN
ejpam-5022	341	3	formula	formula	NOUN
ejpam-5022	341	4	for	for	ADP
ejpam-5022	341	5	the	the	DET
ejpam-5022	341	6	horadam	horadam	PROPN
ejpam-5022	341	7	polynomials	polynomial	NOUN
ejpam-5022	341	8	in	in	ADP
ejpam-5022	341	9	terms	term	NOUN
ejpam-5022	341	10	of	of	ADP
ejpam-5022	341	11	a	a	DET
ejpam-5022	341	12	tridiagonal	tridiagonal	ADJ
ejpam-5022	341	13	determinant	determinant	ADJ
ejpam-5022	341	14	.	.	PUNCT
ejpam-5022	341	15	symmetry	symmetry	PROPN
ejpam-5022	341	16	,	,	PUNCT
ejpam-5022	341	17	11(782	11(782	PROPN
ejpam-5022	341	18	)	)	PUNCT
ejpam-5022	341	19	,	,	PUNCT
ejpam-5022	341	20	2019	2019	NUM
ejpam-5022	341	21	.	.	PUNCT
ejpam-5022	342	1	[	[	X
ejpam-5022	342	2	27	27	NUM
ejpam-5022	342	3	]	]	X
ejpam-5022	342	4	h.m	h.m	PROPN
ejpam-5022	342	5	.	.	PROPN
ejpam-5022	342	6	srivastava	srivastava	PROPN
ejpam-5022	342	7	,	,	PUNCT
ejpam-5022	342	8	s.	s.	PROPN
ejpam-5022	342	9	altınkaya	altınkaya	PROPN
ejpam-5022	342	10	,	,	PUNCT
ejpam-5022	342	11	and	and	CCONJ
ejpam-5022	342	12	s.	s.	PROPN
ejpam-5022	342	13	yalcin	yalcin	PROPN
ejpam-5022	342	14	.	.	PUNCT
ejpam-5022	343	1	certain	certain	ADJ
ejpam-5022	343	2	subclasses	subclass	NOUN
ejpam-5022	343	3	of	of	ADP
ejpam-5022	343	4	bi	bi	ADJ
ejpam-5022	343	5	-	-	ADJ
ejpam-5022	343	6	univalent	univalent	ADJ
ejpam-5022	343	7	functions	function	NOUN
ejpam-5022	343	8	associated	associate	VERB
ejpam-5022	343	9	with	with	ADP
ejpam-5022	343	10	the	the	DET
ejpam-5022	343	11	horadam	horadam	PROPN
ejpam-5022	343	12	polynomials	polynomial	NOUN
ejpam-5022	343	13	.	.	PUNCT
ejpam-5022	344	1	iranian	iranian	ADJ
ejpam-5022	344	2	journal	journal	PROPN
ejpam-5022	344	3	of	of	ADP
ejpam-5022	344	4	science	science	NOUN
ejpam-5022	344	5	and	and	CCONJ
ejpam-5022	344	6	technology	technology	NOUN
ejpam-5022	344	7	,	,	PUNCT
ejpam-5022	344	8	transaction	transaction	NOUN
ejpam-5022	344	9	a	a	DET
ejpam-5022	344	10	:	:	PUNCT
ejpam-5022	344	11	science	science	NOUN
ejpam-5022	344	12	,	,	PUNCT
ejpam-5022	344	13	34(2):1873–1879	34(2):1873–1879	NUM
ejpam-5022	344	14	,	,	PUNCT
ejpam-5022	344	15	2019	2019	NUM
ejpam-5022	344	16	.	.	PUNCT
ejpam-5022	345	1	[	[	X
ejpam-5022	345	2	28	28	NUM
ejpam-5022	345	3	]	]	X
ejpam-5022	345	4	h.m	h.m	PROPN
ejpam-5022	345	5	.	.	PROPN
ejpam-5022	345	6	srivastava	srivastava	PROPN
ejpam-5022	345	7	,	,	PUNCT
ejpam-5022	345	8	m.	m.	NOUN
ejpam-5022	345	9	kamali	kamali	PROPN
ejpam-5022	345	10	,	,	PUNCT
ejpam-5022	345	11	and	and	CCONJ
ejpam-5022	345	12	a.	a.	NOUN
ejpam-5022	345	13	urdaletova	urdaletova	PROPN
ejpam-5022	345	14	.	.	PUNCT
ejpam-5022	346	1	a	a	DET
ejpam-5022	346	2	study	study	NOUN
ejpam-5022	346	3	of	of	ADP
ejpam-5022	346	4	the	the	DET
ejpam-5022	346	5	fekete	fekete	PROPN
ejpam-5022	346	6	-	-	PUNCT
ejpam-5022	346	7	szegö	szegö	ADJ
ejpam-5022	346	8	functional	functional	ADJ
ejpam-5022	346	9	and	and	CCONJ
ejpam-5022	346	10	coefficient	coefficient	NOUN
ejpam-5022	346	11	estimates	estimate	VERB
ejpam-5022	346	12	forvsubclasses	forvsubclasse	NOUN
ejpam-5022	346	13	of	of	ADP
ejpam-5022	346	14	analytic	analytic	ADJ
ejpam-5022	346	15	functions	function	NOUN
ejpam-5022	346	16	satisfying	satisfy	VERB
ejpam-5022	346	17	a	a	DET
ejpam-5022	346	18	certain	certain	ADJ
ejpam-5022	346	19	subordination	subordination	NOUN
ejpam-5022	346	20	conditionv	conditionv	NOUN
ejpam-5022	346	21	and	and	CCONJ
ejpam-5022	346	22	associated	associate	VERB
ejpam-5022	346	23	with	with	ADP
ejpam-5022	346	24	the	the	DET
ejpam-5022	346	25	gegenbauer	gegenbauer	NOUN
ejpam-5022	346	26	polynomials	polynomial	NOUN
ejpam-5022	346	27	.	.	PUNCT
ejpam-5022	347	1	aims	aim	VERB
ejpam-5022	347	2	mathematics	mathematic	NOUN
ejpam-5022	347	3	,	,	PUNCT
ejpam-5022	347	4	7(2):2568–2584	7(2):2568–2584	PROPN
ejpam-5022	347	5	,	,	PUNCT
ejpam-5022	347	6	2021	2021	NUM
ejpam-5022	347	7	.	.	PUNCT
ejpam-5022	348	1	[	[	X
ejpam-5022	348	2	29	29	NUM
ejpam-5022	348	3	]	]	X
ejpam-5022	348	4	h.m	h.m	PROPN
ejpam-5022	348	5	.	.	PROPN
ejpam-5022	348	6	srivastava	srivastava	PROPN
ejpam-5022	348	7	and	and	CCONJ
ejpam-5022	348	8	h.l	h.l	PROPN
ejpam-5022	348	9	.	.	PROPN
ejpam-5022	348	10	manocha	manocha	PROPN
ejpam-5022	348	11	.	.	PUNCT
ejpam-5022	349	1	a	a	DET
ejpam-5022	349	2	treatise	treatise	NOUN
ejpam-5022	349	3	on	on	ADP
ejpam-5022	349	4	generating	generating	NOUN
ejpam-5022	349	5	functions	function	NOUN
ejpam-5022	349	6	.	.	PUNCT
ejpam-5022	350	1	halsted	halsted	ADJ
ejpam-5022	350	2	press	press	PROPN
ejpam-5022	350	3	,	,	PUNCT
ejpam-5022	350	4	john	john	PROPN
ejpam-5022	350	5	wiley	wiley	PROPN
ejpam-5022	350	6	and	and	CCONJ
ejpam-5022	350	7	sons	son	NOUN
ejpam-5022	350	8	,	,	PUNCT
ejpam-5022	350	9	new	new	PROPN
ejpam-5022	350	10	york	york	PROPN
ejpam-5022	350	11	,	,	PUNCT
ejpam-5022	350	12	chichester	chichester	PROPN
ejpam-5022	350	13	,	,	PUNCT
ejpam-5022	350	14	brisbane	brisbane	NOUN
ejpam-5022	350	15	and	and	CCONJ
ejpam-5022	350	16	toronto	toronto	PROPN
ejpam-5022	350	17	,	,	PUNCT
ejpam-5022	350	18	1984	1984	NUM
ejpam-5022	350	19	.	.	PUNCT
ejpam-5022	351	1	references	reference	NOUN
ejpam-5022	351	2	170	170	NUM
ejpam-5022	351	3	[	[	X
ejpam-5022	351	4	30	30	NUM
ejpam-5022	351	5	]	]	X
ejpam-5022	351	6	s.r	s.r	PROPN
ejpam-5022	351	7	.	.	PROPN
ejpam-5022	351	8	swamy	swamy	PROPN
ejpam-5022	351	9	.	.	PUNCT
ejpam-5022	352	1	bi	bi	ADJ
ejpam-5022	352	2	-	-	ADJ
ejpam-5022	352	3	univalent	univalent	ADJ
ejpam-5022	352	4	function	function	NOUN
ejpam-5022	352	5	subclasses	subclass	NOUN
ejpam-5022	352	6	subordinate	subordinate	VERB
ejpam-5022	352	7	to	to	ADP
ejpam-5022	352	8	horadam	horadam	NOUN
ejpam-5022	352	9	polynomials	polynomial	NOUN
ejpam-5022	352	10	.	.	PUNCT
ejpam-5022	353	1	earthline	earthline	PROPN
ejpam-5022	353	2	journal	journal	PROPN
ejpam-5022	353	3	of	of	ADP
ejpam-5022	353	4	mathematical	mathematical	ADJ
ejpam-5022	353	5	sciences	science	NOUN
ejpam-5022	353	6	,	,	PUNCT
ejpam-5022	353	7	11	11	NUM
ejpam-5022	353	8	,	,	PUNCT
ejpam-5022	353	9	2023	2023	NUM
ejpam-5022	353	10	.	.	PUNCT
ejpam-5022	354	1	[	[	X
ejpam-5022	354	2	31	31	NUM
ejpam-5022	354	3	]	]	X
ejpam-5022	354	4	e.	e.	PROPN
ejpam-5022	354	5	szatmari	szatmari	PROPN
ejpam-5022	354	6	and	and	CCONJ
ejpam-5022	354	7	ş.	ş.	PROPN
ejpam-5022	354	8	altınkaya	altınkaya	PROPN
ejpam-5022	354	9	.	.	PUNCT
ejpam-5022	355	1	coefficient	coefficient	NOUN
ejpam-5022	355	2	estimates	estimate	NOUN
ejpam-5022	355	3	and	and	CCONJ
ejpam-5022	355	4	fekete	fekete	PROPN
ejpam-5022	355	5	-	-	PUNCT
ejpam-5022	355	6	szegö	szegö	PROPN
ejpam-5022	355	7	inequality	inequality	NOUN
ejpam-5022	355	8	for	for	ADP
ejpam-5022	355	9	a	a	DET
ejpam-5022	355	10	class	class	NOUN
ejpam-5022	355	11	of	of	ADP
ejpam-5022	355	12	analytic	analytic	ADJ
ejpam-5022	355	13	functions	function	NOUN
ejpam-5022	355	14	satisfying	satisfy	VERB
ejpam-5022	355	15	subordinate	subordinate	ADJ
ejpam-5022	355	16	condition	condition	NOUN
ejpam-5022	355	17	associated	associate	VERB
ejpam-5022	355	18	with	with	ADP
ejpam-5022	355	19	chebyshev	chebyshev	NOUN
ejpam-5022	355	20	polynomials	polynomial	NOUN
ejpam-5022	355	21	.	.	PUNCT
ejpam-5022	356	1	acta	acta	PROPN
ejpam-5022	356	2	universitatis	universitatis	PROPN
ejpam-5022	356	3	sapientiae	sapientiae	PROPN
ejpam-5022	356	4	mathematica	mathematica	PROPN
ejpam-5022	356	5	,	,	PUNCT
ejpam-5022	356	6	11	11	NUM
ejpam-5022	356	7	,	,	PUNCT
ejpam-5022	356	8	2019	2019	NUM
ejpam-5022	356	9	.	.	PUNCT