id	sid	tid	token	lemma	pos
ejpam-4779	1	1	european	european	PROPN
ejpam-4779	1	2	journal	journal	PROPN
ejpam-4779	1	3	of	of	ADP
ejpam-4779	1	4	pure	pure	ADJ
ejpam-4779	1	5	and	and	CCONJ
ejpam-4779	1	6	applied	apply	VERB
ejpam-4779	1	7	mathematics	mathematic	NOUN
ejpam-4779	1	8	vol	vol	NOUN
ejpam-4779	1	9	.	.	PUNCT
ejpam-4779	2	1	16	16	NUM
ejpam-4779	2	2	,	,	PUNCT
ejpam-4779	2	3	no	no	INTJ
ejpam-4779	2	4	.	.	NOUN
ejpam-4779	2	5	2	2	NUM
ejpam-4779	2	6	,	,	PUNCT
ejpam-4779	2	7	2023	2023	NUM
ejpam-4779	2	8	,	,	PUNCT
ejpam-4779	2	9	1167	1167	NUM
ejpam-4779	2	10	-	-	SYM
ejpam-4779	2	11	1179	1179	NUM
ejpam-4779	2	12	issn	issn	PROPN
ejpam-4779	2	13	1307	1307	NUM
ejpam-4779	2	14	-	-	SYM
ejpam-4779	2	15	5543	5543	NUM
ejpam-4779	2	16	–	–	PUNCT
ejpam-4779	2	17	ejpam.com	ejpam.com	X
ejpam-4779	2	18	published	publish	VERB
ejpam-4779	2	19	by	by	ADP
ejpam-4779	2	20	new	new	PROPN
ejpam-4779	2	21	york	york	PROPN
ejpam-4779	2	22	business	business	PROPN
ejpam-4779	2	23	global	global	ADJ
ejpam-4779	2	24	coefficient	coefficient	NOUN
ejpam-4779	2	25	problems	problem	NOUN
ejpam-4779	2	26	for	for	ADP
ejpam-4779	2	27	star	star	NOUN
ejpam-4779	2	28	-	-	PUNCT
ejpam-4779	2	29	like	like	ADJ
ejpam-4779	2	30	functions	function	NOUN
ejpam-4779	2	31	with	with	ADP
ejpam-4779	2	32	respect	respect	NOUN
ejpam-4779	2	33	to	to	ADP
ejpam-4779	2	34	symmetric	symmetric	ADJ
ejpam-4779	2	35	conjugate	conjugate	ADJ
ejpam-4779	2	36	points	point	NOUN
ejpam-4779	2	37	connected	connect	VERB
ejpam-4779	2	38	to	to	ADP
ejpam-4779	2	39	the	the	DET
ejpam-4779	2	40	sine	sine	ADJ
ejpam-4779	2	41	function	function	PROPN
ejpam-4779	2	42	daud	daud	PROPN
ejpam-4779	2	43	mohamad1	mohamad1	PROPN
ejpam-4779	2	44	,	,	PUNCT
ejpam-4779	2	45	nur	nur	VERB
ejpam-4779	2	46	hazwani	hazwani	PROPN
ejpam-4779	2	47	aqilah	aqilah	PROPN
ejpam-4779	2	48	abdul	abdul	PROPN
ejpam-4779	2	49	wahid1,∗	wahid1,∗	PROPN
ejpam-4779	2	50	,	,	PUNCT
ejpam-4779	2	51	nurul	nurul	NOUN
ejpam-4779	2	52	natasya	natasya	NOUN
ejpam-4779	2	53	hasni1	hasni1	PROPN
ejpam-4779	2	54	1	1	NUM
ejpam-4779	2	55	department	department	PROPN
ejpam-4779	2	56	of	of	ADP
ejpam-4779	2	57	mathematical	mathematical	ADJ
ejpam-4779	2	58	sciences	sciences	PROPN
ejpam-4779	2	59	,	,	PUNCT
ejpam-4779	2	60	college	college	NOUN
ejpam-4779	2	61	of	of	ADP
ejpam-4779	2	62	computing	computing	NOUN
ejpam-4779	2	63	,	,	PUNCT
ejpam-4779	2	64	informatics	informatic	NOUN
ejpam-4779	2	65	and	and	CCONJ
ejpam-4779	2	66	media	medium	NOUN
ejpam-4779	2	67	,	,	PUNCT
ejpam-4779	2	68	universiti	universiti	PROPN
ejpam-4779	2	69	teknologi	teknologi	PROPN
ejpam-4779	2	70	mara	mara	PROPN
ejpam-4779	2	71	,	,	PUNCT
ejpam-4779	2	72	40450	40450	NUM
ejpam-4779	2	73	shah	shah	PROPN
ejpam-4779	2	74	alam	alam	PROPN
ejpam-4779	2	75	,	,	PUNCT
ejpam-4779	2	76	selangor	selangor	PROPN
ejpam-4779	2	77	,	,	PUNCT
ejpam-4779	2	78	malaysia	malaysia	PROPN
ejpam-4779	2	79	abstract	abstract	NOUN
ejpam-4779	2	80	.	.	PUNCT
ejpam-4779	3	1	in	in	ADP
ejpam-4779	3	2	this	this	DET
ejpam-4779	3	3	paper	paper	NOUN
ejpam-4779	3	4	,	,	PUNCT
ejpam-4779	3	5	we	we	PRON
ejpam-4779	3	6	introduce	introduce	VERB
ejpam-4779	3	7	the	the	DET
ejpam-4779	3	8	subclass	subclass	NOUN
ejpam-4779	3	9	of	of	ADP
ejpam-4779	3	10	star	star	NOUN
ejpam-4779	3	11	-	-	PUNCT
ejpam-4779	3	12	like	like	ADJ
ejpam-4779	3	13	functions	function	NOUN
ejpam-4779	3	14	with	with	ADP
ejpam-4779	3	15	respect	respect	NOUN
ejpam-4779	3	16	to	to	ADP
ejpam-4779	3	17	symmetric	symmetric	ADJ
ejpam-4779	3	18	conjugate	conjugate	ADJ
ejpam-4779	3	19	points	point	NOUN
ejpam-4779	3	20	associated	associate	VERB
ejpam-4779	3	21	with	with	ADP
ejpam-4779	3	22	the	the	DET
ejpam-4779	3	23	sine	sine	ADJ
ejpam-4779	3	24	function	function	NOUN
ejpam-4779	3	25	.	.	PUNCT
ejpam-4779	4	1	some	some	DET
ejpam-4779	4	2	coefficient	coefficient	NOUN
ejpam-4779	4	3	functionals	functional	NOUN
ejpam-4779	4	4	for	for	ADP
ejpam-4779	4	5	this	this	DET
ejpam-4779	4	6	class	class	NOUN
ejpam-4779	4	7	are	be	AUX
ejpam-4779	4	8	considered	consider	VERB
ejpam-4779	4	9	.	.	PUNCT
ejpam-4779	5	1	bounds	bound	NOUN
ejpam-4779	5	2	of	of	ADP
ejpam-4779	5	3	taylor	taylor	PROPN
ejpam-4779	5	4	coefficients	coefficient	NOUN
ejpam-4779	5	5	,	,	PUNCT
ejpam-4779	5	6	logarithmic	logarithmic	ADJ
ejpam-4779	5	7	coefficients	coefficient	NOUN
ejpam-4779	5	8	,	,	PUNCT
ejpam-4779	5	9	and	and	CCONJ
ejpam-4779	5	10	the	the	DET
ejpam-4779	5	11	hankel	hankel	NOUN
ejpam-4779	5	12	and	and	CCONJ
ejpam-4779	5	13	toeplitz	toeplitz	NOUN
ejpam-4779	5	14	determinants	determinant	NOUN
ejpam-4779	5	15	whose	whose	DET
ejpam-4779	5	16	entries	entry	NOUN
ejpam-4779	5	17	are	be	AUX
ejpam-4779	5	18	logarithmic	logarithmic	ADJ
ejpam-4779	5	19	coefficients	coefficient	NOUN
ejpam-4779	5	20	are	be	AUX
ejpam-4779	5	21	provided	provide	VERB
ejpam-4779	5	22	.	.	PUNCT
ejpam-4779	6	1	2020	2020	NUM
ejpam-4779	6	2	mathematics	mathematic	NOUN
ejpam-4779	6	3	subject	subject	NOUN
ejpam-4779	6	4	classifications	classification	NOUN
ejpam-4779	6	5	:	:	PUNCT
ejpam-4779	6	6	30c45	30c45	NUM
ejpam-4779	6	7	,	,	PUNCT
ejpam-4779	6	8	30c50	30c50	DET
ejpam-4779	6	9	key	key	ADJ
ejpam-4779	6	10	words	word	NOUN
ejpam-4779	6	11	and	and	CCONJ
ejpam-4779	6	12	phrases	phrase	NOUN
ejpam-4779	6	13	:	:	PUNCT
ejpam-4779	6	14	star	star	NOUN
ejpam-4779	6	15	-	-	PUNCT
ejpam-4779	6	16	like	like	ADJ
ejpam-4779	6	17	functions	function	NOUN
ejpam-4779	6	18	with	with	ADP
ejpam-4779	6	19	respect	respect	NOUN
ejpam-4779	6	20	to	to	ADP
ejpam-4779	6	21	symmetric	symmetric	ADJ
ejpam-4779	6	22	conjugate	conjugate	ADJ
ejpam-4779	6	23	points	point	NOUN
ejpam-4779	6	24	,	,	PUNCT
ejpam-4779	6	25	sine	sine	ADJ
ejpam-4779	6	26	function	function	NOUN
ejpam-4779	6	27	,	,	PUNCT
ejpam-4779	6	28	coefficient	coefficient	NOUN
ejpam-4779	6	29	estimates	estimate	NOUN
ejpam-4779	6	30	,	,	PUNCT
ejpam-4779	6	31	logarithmic	logarithmic	ADJ
ejpam-4779	6	32	coefficients	coefficient	NOUN
ejpam-4779	6	33	,	,	PUNCT
ejpam-4779	6	34	hankel	hankel	NOUN
ejpam-4779	6	35	and	and	CCONJ
ejpam-4779	6	36	toeplitz	toeplitz	NOUN
ejpam-4779	6	37	determinants	determinant	NOUN
ejpam-4779	6	38	of	of	ADP
ejpam-4779	6	39	logarithmic	logarithmic	ADJ
ejpam-4779	6	40	coefficients	coefficient	NOUN
ejpam-4779	6	41	,	,	PUNCT
ejpam-4779	6	42	subordination	subordination	NOUN
ejpam-4779	6	43	1	1	NUM
ejpam-4779	6	44	.	.	PUNCT
ejpam-4779	7	1	introduction	introduction	NOUN
ejpam-4779	7	2	let	let	VERB
ejpam-4779	7	3	a	a	PRON
ejpam-4779	7	4	and	and	CCONJ
ejpam-4779	7	5	s	s	NOUN
ejpam-4779	7	6	denote	denote	VERB
ejpam-4779	7	7	the	the	DET
ejpam-4779	7	8	classes	class	NOUN
ejpam-4779	7	9	of	of	ADP
ejpam-4779	7	10	analytic	analytic	ADJ
ejpam-4779	7	11	and	and	CCONJ
ejpam-4779	7	12	univalent	univalent	ADJ
ejpam-4779	7	13	functions	function	NOUN
ejpam-4779	7	14	,	,	PUNCT
ejpam-4779	7	15	respectively	respectively	ADV
ejpam-4779	7	16	.	.	PUNCT
ejpam-4779	8	1	these	these	DET
ejpam-4779	8	2	classes	class	NOUN
ejpam-4779	8	3	are	be	AUX
ejpam-4779	8	4	defined	define	VERB
ejpam-4779	8	5	in	in	ADP
ejpam-4779	8	6	the	the	DET
ejpam-4779	8	7	form	form	NOUN
ejpam-4779	8	8	of	of	ADP
ejpam-4779	8	9	a	a	PRON
ejpam-4779	8	10	=	=	X
ejpam-4779	8	11	{	{	PUNCT
ejpam-4779	9	1	f	f	PROPN
ejpam-4779	9	2	∈	∈	PROPN
ejpam-4779	9	3	k	k	X
ejpam-4779	9	4	(	(	PUNCT
ejpam-4779	9	5	e	e	NOUN
ejpam-4779	9	6	)	)	PUNCT
ejpam-4779	9	7	:	:	PUNCT
ejpam-4779	10	1	f	f	X
ejpam-4779	10	2	(	(	PUNCT
ejpam-4779	10	3	0	0	NUM
ejpam-4779	10	4	)	)	PUNCT
ejpam-4779	10	5	=	=	SYM
ejpam-4779	11	1	f	f	X
ejpam-4779	12	1	′	′	NUM
ejpam-4779	12	2	(	(	PUNCT
ejpam-4779	12	3	0	0	NUM
ejpam-4779	12	4	)	)	PUNCT
ejpam-4779	12	5	−	−	NOUN
ejpam-4779	13	1	1	1	NUM
ejpam-4779	13	2	=	=	SYM
ejpam-4779	13	3	0	0	NUM
ejpam-4779	13	4	,	,	PUNCT
ejpam-4779	13	5	z	z	NOUN
ejpam-4779	13	6	∈	∈	PROPN
ejpam-4779	13	7	e	e	X
ejpam-4779	13	8	}	}	PUNCT
ejpam-4779	13	9	and	and	CCONJ
ejpam-4779	13	10	s	s	VERB
ejpam-4779	13	11	=	=	X
ejpam-4779	13	12	{	{	PUNCT
ejpam-4779	13	13	f	f	PROPN
ejpam-4779	13	14	∈	∈	PROPN
ejpam-4779	13	15	a	a	PRON
ejpam-4779	13	16	:	:	PUNCT
ejpam-4779	13	17	f	f	PROPN
ejpam-4779	13	18	is	be	AUX
ejpam-4779	13	19	univalent	univalent	ADJ
ejpam-4779	13	20	in	in	ADP
ejpam-4779	13	21	e	e	NOUN
ejpam-4779	13	22	}	}	PUNCT
ejpam-4779	13	23	,	,	PUNCT
ejpam-4779	13	24	where	where	SCONJ
ejpam-4779	13	25	k	k	PROPN
ejpam-4779	13	26	(	(	PUNCT
ejpam-4779	13	27	e	e	NOUN
ejpam-4779	13	28	)	)	PUNCT
ejpam-4779	13	29	is	be	AUX
ejpam-4779	13	30	the	the	DET
ejpam-4779	13	31	set	set	NOUN
ejpam-4779	13	32	of	of	ADP
ejpam-4779	13	33	analytic	analytic	ADJ
ejpam-4779	13	34	functions	function	NOUN
ejpam-4779	13	35	in	in	ADP
ejpam-4779	13	36	the	the	DET
ejpam-4779	13	37	open	open	ADJ
ejpam-4779	13	38	unit	unit	NOUN
ejpam-4779	13	39	disk	disk	NOUN
ejpam-4779	13	40	e	e	NOUN
ejpam-4779	14	1	=	=	PUNCT
ejpam-4779	14	2	{	{	PUNCT
ejpam-4779	14	3	z	z	NOUN
ejpam-4779	14	4	∈	∈	PROPN
ejpam-4779	14	5	c	c	NOUN
ejpam-4779	14	6	:	:	PUNCT
ejpam-4779	14	7	|z|	|z|	NOUN
ejpam-4779	14	8	<	<	X
ejpam-4779	14	9	1	1	NUM
ejpam-4779	14	10	}	}	PUNCT
ejpam-4779	14	11	.	.	PUNCT
ejpam-4779	15	1	if	if	SCONJ
ejpam-4779	15	2	f	f	PROPN
ejpam-4779	15	3	∈	∈	PROPN
ejpam-4779	15	4	a	a	PRON
ejpam-4779	15	5	,	,	PUNCT
ejpam-4779	15	6	then	then	ADV
ejpam-4779	15	7	it	it	PRON
ejpam-4779	15	8	can	can	AUX
ejpam-4779	15	9	be	be	AUX
ejpam-4779	15	10	expressed	express	VERB
ejpam-4779	15	11	in	in	ADP
ejpam-4779	15	12	the	the	DET
ejpam-4779	15	13	series	series	NOUN
ejpam-4779	15	14	representation	representation	NOUN
ejpam-4779	15	15	of	of	ADP
ejpam-4779	15	16	the	the	DET
ejpam-4779	15	17	form	form	NOUN
ejpam-4779	15	18	f	f	X
ejpam-4779	15	19	(	(	PUNCT
ejpam-4779	15	20	z	z	NOUN
ejpam-4779	15	21	)	)	PUNCT
ejpam-4779	15	22	=	=	SYM
ejpam-4779	16	1	z	z	NOUN
ejpam-4779	17	1	+	+	NOUN
ejpam-4779	17	2	∞∑	∞∑	NUM
ejpam-4779	17	3	n=2	n=2	ADV
ejpam-4779	17	4	anz	anz	NOUN
ejpam-4779	17	5	n	n	CCONJ
ejpam-4779	17	6	,	,	PUNCT
ejpam-4779	17	7	z	z	PROPN
ejpam-4779	17	8	∈	∈	PROPN
ejpam-4779	17	9	e.	e.	PROPN
ejpam-4779	17	10	(	(	PUNCT
ejpam-4779	17	11	1	1	X
ejpam-4779	17	12	)	)	PUNCT
ejpam-4779	17	13	∗corresponding	∗corresponde	VERB
ejpam-4779	17	14	author	author	NOUN
ejpam-4779	17	15	.	.	PUNCT
ejpam-4779	18	1	doi	doi	NOUN
ejpam-4779	18	2	:	:	PUNCT
ejpam-4779	18	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4779	https://doi.org/10.29020/nybg.ejpam.v16i2.4779	PROPN
ejpam-4779	18	4	email	email	NOUN
ejpam-4779	18	5	addresses	address	NOUN
ejpam-4779	18	6	:	:	PUNCT
ejpam-4779	18	7	daud201@uitm.edu.my	daud201@uitm.edu.my	X
ejpam-4779	18	8	(	(	PUNCT
ejpam-4779	18	9	d.	d.	PROPN
ejpam-4779	18	10	mohamad	mohamad	PROPN
ejpam-4779	18	11	)	)	PUNCT
ejpam-4779	18	12	,	,	PUNCT
ejpam-4779	18	13	hazwaniaqilah@uitm.edu.my	hazwaniaqilah@uitm.edu.my	NOUN
ejpam-4779	18	14	(	(	PUNCT
ejpam-4779	18	15	n.	n.	PROPN
ejpam-4779	18	16	h.	h.	PROPN
ejpam-4779	18	17	a.	a.	PROPN
ejpam-4779	18	18	a.	a.	PROPN
ejpam-4779	18	19	wahid	wahid	PROPN
ejpam-4779	18	20	)	)	PUNCT
ejpam-4779	18	21	,	,	PUNCT
ejpam-4779	18	22	nurulnatasya530@gmail.com	nurulnatasya530@gmail.com	NUM
ejpam-4779	18	23	(	(	PUNCT
ejpam-4779	18	24	n.	n.	PROPN
ejpam-4779	18	25	n.	n.	PROPN
ejpam-4779	18	26	hasni	hasni	PROPN
ejpam-4779	18	27	)	)	PUNCT
ejpam-4779	18	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4779	18	29	1167	1167	NUM
ejpam-4779	19	1	©	©	PROPN
ejpam-4779	19	2	2023	2023	NUM
ejpam-4779	19	3	ejpam	ejpam	NOUN
ejpam-4779	19	4	all	all	DET
ejpam-4779	19	5	rights	right	NOUN
ejpam-4779	19	6	reserved	reserve	VERB
ejpam-4779	19	7	.	.	PUNCT
ejpam-4779	20	1	d.	d.	PROPN
ejpam-4779	20	2	mohamad	mohamad	PROPN
ejpam-4779	20	3	,	,	PUNCT
ejpam-4779	20	4	n.	n.	PROPN
ejpam-4779	20	5	h.	h.	PROPN
ejpam-4779	20	6	a.	a.	PROPN
ejpam-4779	20	7	a.	a.	PROPN
ejpam-4779	20	8	wahid	wahid	PROPN
ejpam-4779	20	9	,	,	PUNCT
ejpam-4779	20	10	n.	n.	PROPN
ejpam-4779	20	11	n.	n.	PROPN
ejpam-4779	20	12	hasni	hasni	PROPN
ejpam-4779	20	13	/	/	SYM
ejpam-4779	20	14	eur	eur	PROPN
ejpam-4779	20	15	.	.	PUNCT
ejpam-4779	21	1	j.	j.	PROPN
ejpam-4779	21	2	pure	pure	PROPN
ejpam-4779	21	3	appl	appl	PROPN
ejpam-4779	21	4	.	.	PROPN
ejpam-4779	21	5	math	math	PROPN
ejpam-4779	21	6	,	,	PUNCT
ejpam-4779	21	7	16	16	NUM
ejpam-4779	21	8	(	(	PUNCT
ejpam-4779	21	9	2	2	NUM
ejpam-4779	21	10	)	)	PUNCT
ejpam-4779	21	11	(	(	PUNCT
ejpam-4779	21	12	2023	2023	NUM
ejpam-4779	21	13	)	)	PUNCT
ejpam-4779	21	14	,	,	PUNCT
ejpam-4779	21	15	1167	1167	NUM
ejpam-4779	21	16	-	-	SYM
ejpam-4779	21	17	1179	1179	NUM
ejpam-4779	21	18	1168	1168	NUM
ejpam-4779	21	19	let	let	VERB
ejpam-4779	21	20	h	h	PROPN
ejpam-4779	21	21	denotes	denote	VERB
ejpam-4779	21	22	the	the	DET
ejpam-4779	21	23	class	class	NOUN
ejpam-4779	21	24	of	of	ADP
ejpam-4779	21	25	schwarz	schwarz	PROPN
ejpam-4779	21	26	functions	function	NOUN
ejpam-4779	21	27	υ	υ	NOUN
ejpam-4779	21	28	which	which	PRON
ejpam-4779	21	29	are	be	AUX
ejpam-4779	21	30	analytic	analytic	ADJ
ejpam-4779	21	31	in	in	ADP
ejpam-4779	21	32	e	e	NOUN
ejpam-4779	21	33	given	give	VERB
ejpam-4779	21	34	by	by	ADP
ejpam-4779	21	35	υ	υ	PROPN
ejpam-4779	21	36	(	(	PUNCT
ejpam-4779	21	37	z	z	NOUN
ejpam-4779	21	38	)	)	PUNCT
ejpam-4779	21	39	=	=	NOUN
ejpam-4779	22	1	∞∑	∞∑	NUM
ejpam-4779	22	2	k=1	k=1	AUX
ejpam-4779	22	3	bkz	bkz	VERB
ejpam-4779	22	4	k	k	PROPN
ejpam-4779	22	5	,	,	PUNCT
ejpam-4779	22	6	z	z	PROPN
ejpam-4779	22	7	∈	∈	PROPN
ejpam-4779	22	8	e	e	X
ejpam-4779	22	9	and	and	CCONJ
ejpam-4779	22	10	satisfying	satisfy	VERB
ejpam-4779	22	11	υ	υ	PROPN
ejpam-4779	22	12	(	(	PUNCT
ejpam-4779	22	13	0	0	NUM
ejpam-4779	22	14	)	)	PUNCT
ejpam-4779	22	15	=	=	SYM
ejpam-4779	22	16	0	0	NUM
ejpam-4779	22	17	and	and	CCONJ
ejpam-4779	22	18	|υ	|υ	NOUN
ejpam-4779	22	19	(	(	PUNCT
ejpam-4779	22	20	z)|	z)|	X
ejpam-4779	22	21	<	<	X
ejpam-4779	22	22	1	1	NUM
ejpam-4779	22	23	.	.	PUNCT
ejpam-4779	22	24	given	give	VERB
ejpam-4779	22	25	two	two	NUM
ejpam-4779	22	26	functions	function	NOUN
ejpam-4779	22	27	f	f	NOUN
ejpam-4779	22	28	,	,	PUNCT
ejpam-4779	22	29	g	g	PROPN
ejpam-4779	22	30	∈	∈	PROPN
ejpam-4779	22	31	a.	a.	NOUN
ejpam-4779	22	32	we	we	PRON
ejpam-4779	22	33	let	let	VERB
ejpam-4779	22	34	≺	≺	NOUN
ejpam-4779	22	35	to	to	PART
ejpam-4779	22	36	denote	denote	VERB
ejpam-4779	22	37	the	the	DET
ejpam-4779	22	38	subordination	subordination	NOUN
ejpam-4779	22	39	.	.	PUNCT
ejpam-4779	23	1	the	the	DET
ejpam-4779	23	2	analytic	analytic	ADJ
ejpam-4779	23	3	function	function	NOUN
ejpam-4779	23	4	f	f	PROPN
ejpam-4779	23	5	is	be	AUX
ejpam-4779	23	6	subordinate	subordinate	ADJ
ejpam-4779	23	7	to	to	ADP
ejpam-4779	23	8	another	another	DET
ejpam-4779	23	9	analytic	analytic	ADJ
ejpam-4779	23	10	function	function	NOUN
ejpam-4779	23	11	g	g	NOUN
ejpam-4779	23	12	if	if	SCONJ
ejpam-4779	23	13	there	there	PRON
ejpam-4779	23	14	exists	exist	VERB
ejpam-4779	23	15	a	a	DET
ejpam-4779	23	16	schwarz	schwarz	NOUN
ejpam-4779	23	17	function	function	NOUN
ejpam-4779	23	18	υ	υ	PROPN
ejpam-4779	23	19	∈	∈	PROPN
ejpam-4779	23	20	h	h	NOUN
ejpam-4779	23	21	such	such	ADJ
ejpam-4779	24	1	that	that	SCONJ
ejpam-4779	24	2	f	f	PROPN
ejpam-4779	24	3	(	(	PUNCT
ejpam-4779	24	4	z	z	NOUN
ejpam-4779	24	5	)	)	PUNCT
ejpam-4779	24	6	=	=	SYM
ejpam-4779	24	7	g	g	PROPN
ejpam-4779	24	8	(	(	PUNCT
ejpam-4779	24	9	υ	υ	PROPN
ejpam-4779	24	10	(	(	PUNCT
ejpam-4779	24	11	z	z	NOUN
ejpam-4779	24	12	)	)	PUNCT
ejpam-4779	24	13	)	)	PUNCT
ejpam-4779	24	14	for	for	ADP
ejpam-4779	24	15	all	all	DET
ejpam-4779	24	16	z	z	PROPN
ejpam-4779	24	17	∈	∈	PROPN
ejpam-4779	24	18	e.	e.	PROPN
ejpam-4779	24	19	furthermore	furthermore	ADV
ejpam-4779	24	20	,	,	PUNCT
ejpam-4779	24	21	if	if	SCONJ
ejpam-4779	24	22	g	g	PROPN
ejpam-4779	24	23	is	be	AUX
ejpam-4779	24	24	univalent	univalent	ADJ
ejpam-4779	24	25	in	in	ADP
ejpam-4779	24	26	e	e	NOUN
ejpam-4779	24	27	,	,	PUNCT
ejpam-4779	24	28	then	then	ADV
ejpam-4779	24	29	we	we	PRON
ejpam-4779	24	30	have	have	VERB
ejpam-4779	24	31	the	the	DET
ejpam-4779	24	32	following	follow	VERB
ejpam-4779	24	33	equivalence	equivalence	NOUN
ejpam-4779	24	34	f	f	PROPN
ejpam-4779	24	35	≺	≺	NOUN
ejpam-4779	24	36	g	g	PROPN
ejpam-4779	24	37	⇔	⇔	PROPN
ejpam-4779	24	38	f	f	PROPN
ejpam-4779	24	39	(	(	PUNCT
ejpam-4779	24	40	0	0	NUM
ejpam-4779	24	41	)	)	PUNCT
ejpam-4779	24	42	=	=	SYM
ejpam-4779	24	43	g	g	PROPN
ejpam-4779	24	44	(	(	PUNCT
ejpam-4779	24	45	0	0	NUM
ejpam-4779	24	46	)	)	PUNCT
ejpam-4779	24	47	and	and	CCONJ
ejpam-4779	24	48	f	f	PROPN
ejpam-4779	24	49	(	(	PUNCT
ejpam-4779	24	50	e	e	NOUN
ejpam-4779	24	51	)	)	PUNCT
ejpam-4779	25	1	=	=	SYM
ejpam-4779	25	2	g	g	PROPN
ejpam-4779	25	3	(	(	PUNCT
ejpam-4779	25	4	e	e	NOUN
ejpam-4779	25	5	)	)	PUNCT
ejpam-4779	25	6	.	.	PUNCT
ejpam-4779	26	1	let	let	VERB
ejpam-4779	26	2	p	p	NOUN
ejpam-4779	26	3	(	(	PUNCT
ejpam-4779	26	4	a	a	DET
ejpam-4779	26	5	,	,	PUNCT
ejpam-4779	26	6	b	b	NOUN
ejpam-4779	26	7	)	)	PUNCT
ejpam-4779	26	8	denotes	denote	VERB
ejpam-4779	26	9	the	the	DET
ejpam-4779	26	10	class	class	NOUN
ejpam-4779	26	11	of	of	ADP
ejpam-4779	26	12	analytic	analytic	ADJ
ejpam-4779	26	13	functions	function	NOUN
ejpam-4779	26	14	defined	define	VERB
ejpam-4779	26	15	in	in	ADP
ejpam-4779	26	16	the	the	DET
ejpam-4779	26	17	form	form	NOUN
ejpam-4779	26	18	of	of	ADP
ejpam-4779	26	19	p	p	NOUN
ejpam-4779	26	20	(	(	PUNCT
ejpam-4779	26	21	a	a	DET
ejpam-4779	26	22	,	,	PUNCT
ejpam-4779	26	23	b	b	NOUN
ejpam-4779	26	24	)	)	PUNCT
ejpam-4779	27	1	=	=	NOUN
ejpam-4779	27	2	{	{	PUNCT
ejpam-4779	27	3	p	p	X
ejpam-4779	27	4	∈	∈	PROPN
ejpam-4779	27	5	a	a	PRON
ejpam-4779	27	6	:	:	PUNCT
ejpam-4779	27	7	p	p	X
ejpam-4779	27	8	(	(	PUNCT
ejpam-4779	27	9	z	z	NOUN
ejpam-4779	27	10	)	)	PUNCT
ejpam-4779	27	11	≺	≺	NOUN
ejpam-4779	27	12	1	1	NUM
ejpam-4779	28	1	+	+	NUM
ejpam-4779	28	2	az	az	PROPN
ejpam-4779	28	3	1	1	NUM
ejpam-4779	28	4	+	+	CCONJ
ejpam-4779	28	5	bz	bz	PROPN
ejpam-4779	28	6	,	,	PUNCT
ejpam-4779	28	7	−	−	PROPN
ejpam-4779	28	8	1	1	NUM
ejpam-4779	28	9	⩽	⩽	NOUN
ejpam-4779	28	10	b	b	ADP
ejpam-4779	28	11	<	<	X
ejpam-4779	28	12	a	a	DET
ejpam-4779	28	13	⩽	⩽	ADJ
ejpam-4779	28	14	1	1	NUM
ejpam-4779	28	15	,	,	PUNCT
ejpam-4779	28	16	z	z	NOUN
ejpam-4779	28	17	∈	∈	PROPN
ejpam-4779	28	18	e	e	X
ejpam-4779	28	19	}	}	PUNCT
ejpam-4779	28	20	,	,	PUNCT
ejpam-4779	28	21	where	where	SCONJ
ejpam-4779	28	22	p	p	NOUN
ejpam-4779	28	23	has	have	VERB
ejpam-4779	28	24	a	a	DET
ejpam-4779	28	25	series	series	NOUN
ejpam-4779	28	26	form	form	NOUN
ejpam-4779	28	27	given	give	VERB
ejpam-4779	28	28	by	by	ADP
ejpam-4779	28	29	p	p	PROPN
ejpam-4779	28	30	(	(	PUNCT
ejpam-4779	28	31	z	z	NOUN
ejpam-4779	28	32	)	)	PUNCT
ejpam-4779	28	33	=	=	SYM
ejpam-4779	28	34	1	1	NUM
ejpam-4779	28	35	+	+	CCONJ
ejpam-4779	28	36	∞∑	∞∑	NUM
ejpam-4779	28	37	n=1	n=1	PROPN
ejpam-4779	28	38	pnz	pnz	NOUN
ejpam-4779	28	39	n	n	CCONJ
ejpam-4779	28	40	,	,	PUNCT
ejpam-4779	28	41	z	z	PROPN
ejpam-4779	28	42	∈	∈	PROPN
ejpam-4779	28	43	e.	e.	PROPN
ejpam-4779	29	1	the	the	DET
ejpam-4779	29	2	class	class	NOUN
ejpam-4779	29	3	p	p	NOUN
ejpam-4779	29	4	(	(	PUNCT
ejpam-4779	29	5	a	a	DET
ejpam-4779	29	6	,	,	PUNCT
ejpam-4779	29	7	b	b	NOUN
ejpam-4779	29	8	)	)	PUNCT
ejpam-4779	29	9	is	be	AUX
ejpam-4779	29	10	known	know	VERB
ejpam-4779	29	11	as	as	ADP
ejpam-4779	29	12	the	the	DET
ejpam-4779	29	13	class	class	NOUN
ejpam-4779	29	14	of	of	ADP
ejpam-4779	29	15	janowski	janowski	NOUN
ejpam-4779	29	16	and	and	CCONJ
ejpam-4779	29	17	was	be	AUX
ejpam-4779	29	18	introduced	introduce	VERB
ejpam-4779	29	19	by	by	ADP
ejpam-4779	29	20	janowski	janowski	NOUN
ejpam-4779	30	1	[	[	X
ejpam-4779	30	2	13	13	NUM
ejpam-4779	30	3	]	]	PUNCT
ejpam-4779	30	4	.	.	PUNCT
ejpam-4779	31	1	if	if	SCONJ
ejpam-4779	31	2	p	p	PROPN
ejpam-4779	31	3	(	(	PUNCT
ejpam-4779	31	4	1,−1	1,−1	NUM
ejpam-4779	31	5	)	)	PUNCT
ejpam-4779	31	6	,	,	PUNCT
ejpam-4779	31	7	then	then	ADV
ejpam-4779	31	8	it	it	PRON
ejpam-4779	31	9	reduces	reduce	VERB
ejpam-4779	31	10	to	to	ADP
ejpam-4779	31	11	the	the	DET
ejpam-4779	31	12	class	class	NOUN
ejpam-4779	31	13	p	p	NOUN
ejpam-4779	31	14	,	,	PUNCT
ejpam-4779	31	15	the	the	DET
ejpam-4779	31	16	well	well	ADV
ejpam-4779	31	17	-	-	PUNCT
ejpam-4779	31	18	known	know	VERB
ejpam-4779	31	19	class	class	NOUN
ejpam-4779	31	20	of	of	ADP
ejpam-4779	31	21	functions	function	NOUN
ejpam-4779	31	22	with	with	ADP
ejpam-4779	31	23	positive	positive	ADJ
ejpam-4779	31	24	real	real	ADJ
ejpam-4779	31	25	part	part	NOUN
ejpam-4779	31	26	consists	consist	VERB
ejpam-4779	31	27	of	of	ADP
ejpam-4779	31	28	functions	function	NOUN
ejpam-4779	31	29	p	p	NOUN
ejpam-4779	31	30	that	that	DET
ejpam-4779	31	31	satisfy	satisfy	VERB
ejpam-4779	31	32	re	re	ADP
ejpam-4779	31	33	p	p	PROPN
ejpam-4779	31	34	(	(	PUNCT
ejpam-4779	31	35	z	z	NOUN
ejpam-4779	31	36	)	)	PUNCT
ejpam-4779	31	37	>	>	X
ejpam-4779	31	38	0	0	PUNCT
ejpam-4779	31	39	and	and	CCONJ
ejpam-4779	31	40	p	p	X
ejpam-4779	31	41	(	(	PUNCT
ejpam-4779	31	42	0	0	NUM
ejpam-4779	31	43	)	)	PUNCT
ejpam-4779	31	44	=	=	SYM
ejpam-4779	32	1	1	1	X
ejpam-4779	32	2	.	.	PUNCT
ejpam-4779	33	1	if	if	SCONJ
ejpam-4779	33	2	p	p	PROPN
ejpam-4779	33	3	∈	∈	PROPN
ejpam-4779	33	4	p	p	X
ejpam-4779	33	5	,	,	PUNCT
ejpam-4779	33	6	then	then	ADV
ejpam-4779	33	7	a	a	DET
ejpam-4779	33	8	schwarz	schwarz	NOUN
ejpam-4779	33	9	function	function	VERB
ejpam-4779	33	10	υ	υ	PROPN
ejpam-4779	33	11	∈	∈	PROPN
ejpam-4779	33	12	h	h	NOUN
ejpam-4779	33	13	exists	exist	VERB
ejpam-4779	33	14	with	with	ADP
ejpam-4779	33	15	υ	υ	PROPN
ejpam-4779	33	16	(	(	PUNCT
ejpam-4779	33	17	0	0	NUM
ejpam-4779	33	18	)	)	PUNCT
ejpam-4779	33	19	=	=	SYM
ejpam-4779	33	20	0	0	NUM
ejpam-4779	33	21	and	and	CCONJ
ejpam-4779	33	22	|υ	|υ	NOUN
ejpam-4779	33	23	(	(	PUNCT
ejpam-4779	33	24	z)|	z)|	X
ejpam-4779	33	25	<	<	X
ejpam-4779	33	26	1	1	NUM
ejpam-4779	33	27	such	such	ADJ
ejpam-4779	33	28	that	that	SCONJ
ejpam-4779	33	29	p	p	X
ejpam-4779	33	30	(	(	PUNCT
ejpam-4779	33	31	z	z	NOUN
ejpam-4779	33	32	)	)	PUNCT
ejpam-4779	33	33	=	=	SYM
ejpam-4779	34	1	1	1	NUM
ejpam-4779	34	2	+	+	NUM
ejpam-4779	34	3	υ	υ	PROPN
ejpam-4779	34	4	(	(	PUNCT
ejpam-4779	34	5	z	z	NOUN
ejpam-4779	34	6	)	)	PUNCT
ejpam-4779	34	7	1	1	NUM
ejpam-4779	34	8	−	−	NOUN
ejpam-4779	34	9	υ	υ	PROPN
ejpam-4779	34	10	(	(	PUNCT
ejpam-4779	34	11	z	z	NOUN
ejpam-4779	34	12	)	)	PUNCT
ejpam-4779	34	13	,	,	PUNCT
ejpam-4779	34	14	z	z	PROPN
ejpam-4779	34	15	∈	∈	PROPN
ejpam-4779	34	16	e.	e.	PROPN
ejpam-4779	35	1	we	we	PRON
ejpam-4779	35	2	now	now	ADV
ejpam-4779	35	3	introduce	introduce	VERB
ejpam-4779	35	4	the	the	DET
ejpam-4779	35	5	subclass	subclass	NOUN
ejpam-4779	35	6	of	of	ADP
ejpam-4779	35	7	star	star	NOUN
ejpam-4779	35	8	-	-	PUNCT
ejpam-4779	35	9	like	like	ADJ
ejpam-4779	35	10	functions	function	NOUN
ejpam-4779	35	11	with	with	ADP
ejpam-4779	35	12	respect	respect	NOUN
ejpam-4779	35	13	to	to	ADP
ejpam-4779	35	14	symmetric	symmetric	ADJ
ejpam-4779	35	15	conjugate	conjugate	ADJ
ejpam-4779	35	16	points	point	NOUN
ejpam-4779	35	17	connected	connect	VERB
ejpam-4779	35	18	to	to	ADP
ejpam-4779	35	19	the	the	DET
ejpam-4779	35	20	sine	sine	ADJ
ejpam-4779	35	21	function	function	NOUN
ejpam-4779	35	22	as	as	SCONJ
ejpam-4779	35	23	follows	follow	VERB
ejpam-4779	35	24	:	:	PUNCT
ejpam-4779	35	25	definition	definition	NOUN
ejpam-4779	35	26	1	1	NUM
ejpam-4779	35	27	.	.	PUNCT
ejpam-4779	36	1	let	let	VERB
ejpam-4779	36	2	s∗	s∗	PROPN
ejpam-4779	36	3	sc	sc	PROPN
ejpam-4779	36	4	(	(	PUNCT
ejpam-4779	36	5	sin	sin	PROPN
ejpam-4779	36	6	z	z	NOUN
ejpam-4779	36	7	)	)	PUNCT
ejpam-4779	36	8	be	be	AUX
ejpam-4779	36	9	the	the	DET
ejpam-4779	36	10	class	class	NOUN
ejpam-4779	36	11	of	of	ADP
ejpam-4779	36	12	functions	function	NOUN
ejpam-4779	36	13	defined	define	VERB
ejpam-4779	36	14	by	by	ADP
ejpam-4779	36	15	zf	zf	PROPN
ejpam-4779	37	1	′	′	NUM
ejpam-4779	38	1	(	(	PUNCT
ejpam-4779	38	2	z	z	X
ejpam-4779	38	3	)	)	PUNCT
ejpam-4779	38	4	h	h	NOUN
ejpam-4779	38	5	(	(	PUNCT
ejpam-4779	38	6	z	z	NOUN
ejpam-4779	38	7	)	)	PUNCT
ejpam-4779	38	8	≺	≺	NOUN
ejpam-4779	38	9	φ	φ	X
ejpam-4779	38	10	(	(	PUNCT
ejpam-4779	38	11	z	z	NOUN
ejpam-4779	38	12	)	)	PUNCT
ejpam-4779	38	13	,	,	PUNCT
ejpam-4779	38	14	z	z	NOUN
ejpam-4779	38	15	∈	∈	PROPN
ejpam-4779	39	1	e	e	NOUN
ejpam-4779	39	2	,	,	PUNCT
ejpam-4779	39	3	(	(	PUNCT
ejpam-4779	39	4	2	2	X
ejpam-4779	39	5	)	)	PUNCT
ejpam-4779	39	6	where	where	SCONJ
ejpam-4779	39	7	h	h	NOUN
ejpam-4779	39	8	(	(	PUNCT
ejpam-4779	39	9	z	z	NOUN
ejpam-4779	39	10	)	)	PUNCT
ejpam-4779	39	11	=	=	SYM
ejpam-4779	39	12	f(z)−f(−z	f(z)−f(−z	VERB
ejpam-4779	39	13	)	)	PUNCT
ejpam-4779	39	14	2	2	NUM
ejpam-4779	39	15	and	and	CCONJ
ejpam-4779	39	16	φ	φ	NUM
ejpam-4779	39	17	(	(	PUNCT
ejpam-4779	39	18	z	z	NOUN
ejpam-4779	39	19	)	)	PUNCT
ejpam-4779	39	20	=	=	SYM
ejpam-4779	39	21	1	1	NUM
ejpam-4779	39	22	+	+	NUM
ejpam-4779	39	23	sin	sin	NOUN
ejpam-4779	39	24	z.	z.	PROPN
ejpam-4779	40	1	it	it	PRON
ejpam-4779	40	2	is	be	AUX
ejpam-4779	40	3	observed	observe	VERB
ejpam-4779	40	4	that	that	SCONJ
ejpam-4779	40	5	the	the	DET
ejpam-4779	40	6	classes	class	NOUN
ejpam-4779	40	7	s∗	s∗	VERB
ejpam-4779	40	8	sc	sc	PROPN
ejpam-4779	40	9	and	and	CCONJ
ejpam-4779	40	10	s∗	s∗	PROPN
ejpam-4779	40	11	sc	sc	PROPN
ejpam-4779	40	12	(	(	PUNCT
ejpam-4779	40	13	a	a	DET
ejpam-4779	40	14	,	,	PUNCT
ejpam-4779	40	15	b	b	NOUN
ejpam-4779	40	16	)	)	PUNCT
ejpam-4779	40	17	consisting	consist	VERB
ejpam-4779	40	18	of	of	ADP
ejpam-4779	40	19	star	star	NOUN
ejpam-4779	40	20	-	-	PUNCT
ejpam-4779	40	21	like	like	ADJ
ejpam-4779	40	22	functions	function	NOUN
ejpam-4779	40	23	with	with	ADP
ejpam-4779	40	24	respect	respect	NOUN
ejpam-4779	40	25	to	to	ADP
ejpam-4779	40	26	symmetric	symmetric	ADJ
ejpam-4779	40	27	conjugate	conjugate	ADJ
ejpam-4779	40	28	points	point	NOUN
ejpam-4779	40	29	defined	define	VERB
ejpam-4779	40	30	by	by	ADP
ejpam-4779	40	31	el	el	PROPN
ejpam-4779	40	32	-	-	NOUN
ejpam-4779	40	33	ashwah	ashwah	NOUN
ejpam-4779	40	34	and	and	CCONJ
ejpam-4779	40	35	thomas	thomas	PROPN
ejpam-4779	41	1	[	[	X
ejpam-4779	41	2	11	11	NUM
ejpam-4779	41	3	]	]	PUNCT
ejpam-4779	41	4	and	and	CCONJ
ejpam-4779	41	5	ping	ping	NOUN
ejpam-4779	41	6	and	and	CCONJ
ejpam-4779	41	7	janteng	janteng	PROPN
ejpam-4779	41	8	[	[	X
ejpam-4779	41	9	26	26	NUM
ejpam-4779	41	10	]	]	PUNCT
ejpam-4779	41	11	,	,	PUNCT
ejpam-4779	41	12	respectively	respectively	ADV
ejpam-4779	41	13	,	,	PUNCT
ejpam-4779	41	14	are	be	AUX
ejpam-4779	41	15	obtained	obtain	VERB
ejpam-4779	41	16	if	if	SCONJ
ejpam-4779	41	17	the	the	DET
ejpam-4779	41	18	right	right	ADJ
ejpam-4779	41	19	-	-	PUNCT
ejpam-4779	41	20	hand	hand	NOUN
ejpam-4779	41	21	side	side	NOUN
ejpam-4779	41	22	of	of	ADP
ejpam-4779	41	23	(	(	PUNCT
ejpam-4779	41	24	2	2	NUM
ejpam-4779	41	25	)	)	PUNCT
ejpam-4779	41	26	is	be	AUX
ejpam-4779	41	27	changed	change	VERB
ejpam-4779	41	28	to	to	ADP
ejpam-4779	41	29	φ	φ	PROPN
ejpam-4779	41	30	(	(	PUNCT
ejpam-4779	41	31	z	z	NOUN
ejpam-4779	41	32	)	)	PUNCT
ejpam-4779	42	1	=	=	SYM
ejpam-4779	42	2	1+z	1+z	NUM
ejpam-4779	42	3	1−z	1−z	NUM
ejpam-4779	42	4	and	and	CCONJ
ejpam-4779	42	5	φ	φ	PROPN
ejpam-4779	42	6	(	(	PUNCT
ejpam-4779	42	7	z	z	NOUN
ejpam-4779	42	8	)	)	PUNCT
ejpam-4779	42	9	=	=	SYM
ejpam-4779	43	1	1+az	1+az	NUM
ejpam-4779	43	2	1+bz	1+bz	NUM
ejpam-4779	43	3	,	,	PUNCT
ejpam-4779	43	4	i.e.	i.e.	X
ejpam-4779	43	5	,	,	PUNCT
ejpam-4779	43	6	s∗	s∗	PROPN
ejpam-4779	43	7	sc	sc	PROPN
ejpam-4779	43	8	=	=	PUNCT
ejpam-4779	43	9	{	{	PUNCT
ejpam-4779	43	10	f	f	PROPN
ejpam-4779	43	11	∈	∈	PROPN
ejpam-4779	43	12	a	a	PRON
ejpam-4779	43	13	:	:	PUNCT
ejpam-4779	43	14	re	re	X
ejpam-4779	43	15	(	(	PUNCT
ejpam-4779	43	16	zf	zf	PROPN
ejpam-4779	43	17	′	′	NUM
ejpam-4779	43	18	(	(	PUNCT
ejpam-4779	43	19	z	z	X
ejpam-4779	43	20	)	)	PUNCT
ejpam-4779	43	21	h	h	NOUN
ejpam-4779	43	22	(	(	PUNCT
ejpam-4779	43	23	z	z	NOUN
ejpam-4779	43	24	)	)	PUNCT
ejpam-4779	43	25	)	)	PUNCT
ejpam-4779	43	26	>	>	X
ejpam-4779	44	1	0	0	NUM
ejpam-4779	44	2	,	,	PUNCT
ejpam-4779	44	3	z	z	NOUN
ejpam-4779	44	4	∈	∈	PROPN
ejpam-4779	44	5	e	e	X
ejpam-4779	44	6	}	}	PUNCT
ejpam-4779	44	7	d.	d.	PROPN
ejpam-4779	44	8	mohamad	mohamad	PROPN
ejpam-4779	44	9	,	,	PUNCT
ejpam-4779	44	10	n.	n.	PROPN
ejpam-4779	44	11	h.	h.	PROPN
ejpam-4779	44	12	a.	a.	PROPN
ejpam-4779	44	13	a.	a.	PROPN
ejpam-4779	44	14	wahid	wahid	PROPN
ejpam-4779	44	15	,	,	PUNCT
ejpam-4779	44	16	n.	n.	PROPN
ejpam-4779	44	17	n.	n.	PROPN
ejpam-4779	44	18	hasni	hasni	PROPN
ejpam-4779	44	19	/	/	SYM
ejpam-4779	44	20	eur	eur	PROPN
ejpam-4779	44	21	.	.	PUNCT
ejpam-4779	45	1	j.	j.	PROPN
ejpam-4779	45	2	pure	pure	PROPN
ejpam-4779	45	3	appl	appl	PROPN
ejpam-4779	45	4	.	.	PROPN
ejpam-4779	45	5	math	math	PROPN
ejpam-4779	45	6	,	,	PUNCT
ejpam-4779	45	7	16	16	NUM
ejpam-4779	45	8	(	(	PUNCT
ejpam-4779	45	9	2	2	NUM
ejpam-4779	45	10	)	)	PUNCT
ejpam-4779	45	11	(	(	PUNCT
ejpam-4779	45	12	2023	2023	NUM
ejpam-4779	45	13	)	)	PUNCT
ejpam-4779	45	14	,	,	PUNCT
ejpam-4779	45	15	1167	1167	NUM
ejpam-4779	45	16	-	-	SYM
ejpam-4779	45	17	1179	1179	NUM
ejpam-4779	45	18	1169	1169	NUM
ejpam-4779	45	19	and	and	CCONJ
ejpam-4779	45	20	s∗	s∗	PROPN
ejpam-4779	45	21	sc	sc	PROPN
ejpam-4779	45	22	(	(	PUNCT
ejpam-4779	45	23	a	a	DET
ejpam-4779	45	24	,	,	PUNCT
ejpam-4779	45	25	b	b	NOUN
ejpam-4779	45	26	)	)	PUNCT
ejpam-4779	45	27	=	=	NOUN
ejpam-4779	45	28	{	{	PUNCT
ejpam-4779	45	29	f	f	PROPN
ejpam-4779	45	30	∈	∈	PROPN
ejpam-4779	46	1	a	a	PRON
ejpam-4779	46	2	:	:	PUNCT
ejpam-4779	46	3	zf	zf	PROPN
ejpam-4779	46	4	′	′	NUM
ejpam-4779	46	5	(	(	PUNCT
ejpam-4779	46	6	z	z	X
ejpam-4779	46	7	)	)	PUNCT
ejpam-4779	46	8	h	h	NOUN
ejpam-4779	46	9	(	(	PUNCT
ejpam-4779	46	10	z	z	NOUN
ejpam-4779	46	11	)	)	PUNCT
ejpam-4779	46	12	≺	≺	NOUN
ejpam-4779	46	13	1	1	NUM
ejpam-4779	46	14	+	+	NUM
ejpam-4779	46	15	az	az	PROPN
ejpam-4779	46	16	1	1	NUM
ejpam-4779	46	17	+	+	CCONJ
ejpam-4779	46	18	bz	bz	PROPN
ejpam-4779	46	19	,	,	PUNCT
ejpam-4779	46	20	−	−	PROPN
ejpam-4779	46	21	1	1	NUM
ejpam-4779	46	22	⩽	⩽	NOUN
ejpam-4779	46	23	b	b	ADP
ejpam-4779	46	24	<	<	X
ejpam-4779	46	25	a	a	DET
ejpam-4779	46	26	⩽	⩽	ADJ
ejpam-4779	46	27	1	1	NUM
ejpam-4779	46	28	,	,	PUNCT
ejpam-4779	46	29	z	z	NOUN
ejpam-4779	46	30	∈	∈	PROPN
ejpam-4779	46	31	e	e	X
ejpam-4779	46	32	}	}	PUNCT
ejpam-4779	46	33	,	,	PUNCT
ejpam-4779	46	34	where	where	SCONJ
ejpam-4779	46	35	h	h	NOUN
ejpam-4779	46	36	(	(	PUNCT
ejpam-4779	46	37	z	z	NOUN
ejpam-4779	46	38	)	)	PUNCT
ejpam-4779	46	39	=	=	SYM
ejpam-4779	46	40	f(z)−f(−z	f(z)−f(−z	VERB
ejpam-4779	46	41	)	)	PUNCT
ejpam-4779	46	42	2	2	NUM
ejpam-4779	46	43	.	.	PUNCT
ejpam-4779	47	1	besides	besides	SCONJ
ejpam-4779	47	2	that	that	PRON
ejpam-4779	47	3	,	,	PUNCT
ejpam-4779	47	4	some	some	DET
ejpam-4779	47	5	subclasses	subclass	NOUN
ejpam-4779	47	6	of	of	ADP
ejpam-4779	47	7	star	star	NOUN
ejpam-4779	47	8	-	-	PUNCT
ejpam-4779	47	9	like	like	ADJ
ejpam-4779	47	10	functions	function	NOUN
ejpam-4779	47	11	with	with	ADP
ejpam-4779	47	12	respect	respect	NOUN
ejpam-4779	47	13	to	to	ADP
ejpam-4779	47	14	symmetric	symmetric	ADJ
ejpam-4779	47	15	conjugate	conjugate	ADJ
ejpam-4779	47	16	points	point	NOUN
ejpam-4779	47	17	are	be	AUX
ejpam-4779	47	18	also	also	ADV
ejpam-4779	47	19	studied	study	VERB
ejpam-4779	47	20	from	from	ADP
ejpam-4779	47	21	a	a	DET
ejpam-4779	47	22	different	different	ADJ
ejpam-4779	47	23	perspective	perspective	NOUN
ejpam-4779	47	24	by	by	ADP
ejpam-4779	47	25	halim	halim	PROPN
ejpam-4779	48	1	[	[	X
ejpam-4779	48	2	1	1	X
ejpam-4779	48	3	]	]	PUNCT
ejpam-4779	48	4	and	and	CCONJ
ejpam-4779	48	5	mohamad	mohamad	PROPN
ejpam-4779	48	6	et	et	PROPN
ejpam-4779	48	7	al	al	PROPN
ejpam-4779	48	8	.	.	PUNCT
ejpam-4779	49	1	[	[	X
ejpam-4779	49	2	24	24	NUM
ejpam-4779	49	3	]	]	PUNCT
ejpam-4779	49	4	.	.	PUNCT
ejpam-4779	50	1	these	these	DET
ejpam-4779	50	2	subclasses	subclass	NOUN
ejpam-4779	50	3	are	be	AUX
ejpam-4779	50	4	defined	define	VERB
ejpam-4779	50	5	as	as	SCONJ
ejpam-4779	50	6	follows	follow	VERB
ejpam-4779	50	7	:	:	PUNCT
ejpam-4779	50	8	s∗	s∗	PROPN
ejpam-4779	50	9	sc	sc	PROPN
ejpam-4779	50	10	(	(	PUNCT
ejpam-4779	50	11	δ	δ	PROPN
ejpam-4779	50	12	)	)	PUNCT
ejpam-4779	50	13	=	=	PRON
ejpam-4779	50	14	{	{	PUNCT
ejpam-4779	50	15	re	re	X
ejpam-4779	50	16	(	(	PUNCT
ejpam-4779	50	17	zf	zf	PROPN
ejpam-4779	50	18	′	′	NUM
ejpam-4779	50	19	(	(	PUNCT
ejpam-4779	50	20	z	z	X
ejpam-4779	50	21	)	)	PUNCT
ejpam-4779	50	22	h	h	NOUN
ejpam-4779	50	23	(	(	PUNCT
ejpam-4779	50	24	z	z	NOUN
ejpam-4779	50	25	)	)	PUNCT
ejpam-4779	50	26	)	)	PUNCT
ejpam-4779	50	27	>	>	X
ejpam-4779	51	1	δ	δ	PROPN
ejpam-4779	51	2	,	,	PUNCT
ejpam-4779	51	3	0	0	NUM
ejpam-4779	51	4	⩽	⩽	PROPN
ejpam-4779	51	5	δ	δ	PROPN
ejpam-4779	51	6	<	<	X
ejpam-4779	51	7	1	1	NUM
ejpam-4779	51	8	,	,	PUNCT
ejpam-4779	51	9	z	z	NOUN
ejpam-4779	51	10	∈	∈	PROPN
ejpam-4779	51	11	e	e	X
ejpam-4779	51	12	}	}	PUNCT
ejpam-4779	51	13	(	(	PUNCT
ejpam-4779	51	14	3	3	NUM
ejpam-4779	51	15	)	)	PUNCT
ejpam-4779	51	16	and	and	CCONJ
ejpam-4779	51	17	s∗	s∗	PROPN
ejpam-4779	51	18	sc	sc	PROPN
ejpam-4779	51	19	(	(	PUNCT
ejpam-4779	51	20	α	α	PROPN
ejpam-4779	51	21	,	,	PUNCT
ejpam-4779	51	22	δ	δ	PROPN
ejpam-4779	51	23	,	,	PUNCT
ejpam-4779	51	24	a	a	DET
ejpam-4779	51	25	,	,	PUNCT
ejpam-4779	51	26	b	b	NOUN
ejpam-4779	51	27	)	)	PUNCT
ejpam-4779	51	28	=	=	NOUN
ejpam-4779	51	29	{	{	PUNCT
ejpam-4779	51	30	f	f	PROPN
ejpam-4779	51	31	∈	∈	PROPN
ejpam-4779	51	32	a	a	PRON
ejpam-4779	51	33	:	:	PUNCT
ejpam-4779	51	34	(	(	PUNCT
ejpam-4779	51	35	eiα	eiα	NOUN
ejpam-4779	51	36	zf	zf	PROPN
ejpam-4779	51	37	′	′	NUM
ejpam-4779	52	1	(	(	PUNCT
ejpam-4779	52	2	z	z	X
ejpam-4779	52	3	)	)	PUNCT
ejpam-4779	52	4	h	h	NOUN
ejpam-4779	52	5	(	(	PUNCT
ejpam-4779	52	6	z	z	NOUN
ejpam-4779	52	7	)	)	PUNCT
ejpam-4779	52	8	−	−	PROPN
ejpam-4779	53	1	δ	δ	INTJ
ejpam-4779	53	2	−	−	PROPN
ejpam-4779	54	1	i	i	PRON
ejpam-4779	54	2	sinα	sinα	VERB
ejpam-4779	54	3	)	)	PUNCT
ejpam-4779	54	4	1	1	NUM
ejpam-4779	54	5	ταδ	ταδ	NOUN
ejpam-4779	54	6	≺	≺	NOUN
ejpam-4779	54	7	1	1	NUM
ejpam-4779	54	8	+	+	NUM
ejpam-4779	54	9	az	az	PROPN
ejpam-4779	54	10	1	1	NUM
ejpam-4779	54	11	+	+	CCONJ
ejpam-4779	54	12	bz	bz	PROPN
ejpam-4779	54	13	}	}	PUNCT
ejpam-4779	54	14	,	,	PUNCT
ejpam-4779	54	15	(	(	PUNCT
ejpam-4779	54	16	4	4	X
ejpam-4779	54	17	)	)	PUNCT
ejpam-4779	54	18	where	where	SCONJ
ejpam-4779	54	19	h	h	NOUN
ejpam-4779	54	20	(	(	PUNCT
ejpam-4779	54	21	z	z	NOUN
ejpam-4779	54	22	)	)	PUNCT
ejpam-4779	54	23	=	=	SYM
ejpam-4779	54	24	f(z)−f(−z	f(z)−f(−z	VERB
ejpam-4779	54	25	)	)	PUNCT
ejpam-4779	54	26	2	2	NUM
ejpam-4779	54	27	,	,	PUNCT
ejpam-4779	54	28	ταδ	ταδ	ADV
ejpam-4779	54	29	=	=	SYM
ejpam-4779	54	30	cosα−	cosα−	PROPN
ejpam-4779	54	31	δ	δ	PROPN
ejpam-4779	54	32	,	,	PUNCT
ejpam-4779	54	33	0	0	NUM
ejpam-4779	54	34	⩽	⩽	PROPN
ejpam-4779	54	35	δ	δ	PROPN
ejpam-4779	54	36	<	<	X
ejpam-4779	54	37	1	1	NUM
ejpam-4779	54	38	,	,	PUNCT
ejpam-4779	54	39	and	and	CCONJ
ejpam-4779	54	40	|α|	|α|	X
ejpam-4779	54	41	<	<	X
ejpam-4779	54	42	π	π	PROPN
ejpam-4779	54	43	2	2	NUM
ejpam-4779	54	44	.	.	PUNCT
ejpam-4779	55	1	the	the	DET
ejpam-4779	55	2	problem	problem	NOUN
ejpam-4779	55	3	of	of	ADP
ejpam-4779	55	4	computing	compute	VERB
ejpam-4779	55	5	the	the	DET
ejpam-4779	55	6	bounds	bound	NOUN
ejpam-4779	55	7	of	of	ADP
ejpam-4779	55	8	the	the	DET
ejpam-4779	55	9	hankel	hankel	NOUN
ejpam-4779	55	10	determinant	determinant	ADJ
ejpam-4779	55	11	has	have	AUX
ejpam-4779	55	12	been	be	AUX
ejpam-4779	55	13	studied	study	VERB
ejpam-4779	55	14	in	in	ADP
ejpam-4779	55	15	almost	almost	ADV
ejpam-4779	55	16	every	every	PRON
ejpam-4779	55	17	subclass	subclass	NOUN
ejpam-4779	55	18	of	of	ADP
ejpam-4779	55	19	a	a	PRON
ejpam-4779	55	20	and	and	CCONJ
ejpam-4779	55	21	has	have	AUX
ejpam-4779	55	22	consistently	consistently	ADV
ejpam-4779	55	23	piqued	pique	VERB
ejpam-4779	55	24	the	the	DET
ejpam-4779	55	25	interest	interest	NOUN
ejpam-4779	55	26	of	of	ADP
ejpam-4779	55	27	geometric	geometric	ADJ
ejpam-4779	55	28	functions	function	NOUN
ejpam-4779	55	29	theory	theory	NOUN
ejpam-4779	55	30	researchers	researcher	NOUN
ejpam-4779	55	31	.	.	PUNCT
ejpam-4779	56	1	the	the	DET
ejpam-4779	56	2	hankel	hankel	NOUN
ejpam-4779	56	3	determinant	determinant	ADJ
ejpam-4779	56	4	of	of	ADP
ejpam-4779	56	5	a	a	DET
ejpam-4779	56	6	function	function	NOUN
ejpam-4779	56	7	f	f	PROPN
ejpam-4779	56	8	∈	∈	PROPN
ejpam-4779	56	9	a	a	PRON
ejpam-4779	56	10	whose	whose	DET
ejpam-4779	56	11	elements	element	NOUN
ejpam-4779	56	12	are	be	AUX
ejpam-4779	56	13	taylor	taylor	PROPN
ejpam-4779	56	14	coefficients	coefficient	NOUN
ejpam-4779	56	15	of	of	ADP
ejpam-4779	56	16	f	f	PROPN
ejpam-4779	56	17	∈	∈	PROPN
ejpam-4779	56	18	a	a	PRON
ejpam-4779	56	19	is	be	AUX
ejpam-4779	56	20	defined	define	VERB
ejpam-4779	56	21	as	as	ADP
ejpam-4779	56	22	[	[	X
ejpam-4779	56	23	27	27	NUM
ejpam-4779	56	24	,	,	PUNCT
ejpam-4779	56	25	28	28	NUM
ejpam-4779	56	26	]	]	PUNCT
ejpam-4779	56	27	hq	hq	NOUN
ejpam-4779	56	28	,	,	PUNCT
ejpam-4779	56	29	n	n	PROPN
ejpam-4779	56	30	(	(	PUNCT
ejpam-4779	56	31	f	f	X
ejpam-4779	56	32	)	)	PUNCT
ejpam-4779	57	1	=	=	SYM
ejpam-4779	57	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	57	3	an	an	DET
ejpam-4779	57	4	an+1	an+1	NOUN
ejpam-4779	57	5	·	·	PUNCT
ejpam-4779	57	6	·	·	PUNCT
ejpam-4779	57	7	·	·	PUNCT
ejpam-4779	58	1	an+q−1	an+q−1	PRON
ejpam-4779	58	2	an+1	an+1	VERB
ejpam-4779	58	3	an+2	an+2	X
ejpam-4779	58	4	·	·	PUNCT
ejpam-4779	58	5	·	·	PUNCT
ejpam-4779	58	6	·	·	PUNCT
ejpam-4779	58	7	an+q	an+q	PROPN
ejpam-4779	58	8	...	...	PUNCT
ejpam-4779	58	9	...	...	PUNCT
ejpam-4779	58	10	...	...	PUNCT
ejpam-4779	58	11	...	...	PUNCT
ejpam-4779	59	1	an+q−1	an+q−1	PRON
ejpam-4779	59	2	an+q	an+q	PROPN
ejpam-4779	59	3	·	·	PUNCT
ejpam-4779	59	4	·	·	PUNCT
ejpam-4779	59	5	·	·	PUNCT
ejpam-4779	59	6	an+2q−2	an+2q−2	X
ejpam-4779	59	7	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	59	8	,	,	PUNCT
ejpam-4779	59	9	where	where	SCONJ
ejpam-4779	59	10	q	q	X
ejpam-4779	59	11	,	,	PUNCT
ejpam-4779	59	12	n	n	PRON
ejpam-4779	59	13	∈	∈	PROPN
ejpam-4779	59	14	n	n	NOUN
ejpam-4779	59	15	and	and	CCONJ
ejpam-4779	59	16	a1	a1	NOUN
ejpam-4779	59	17	=	=	NOUN
ejpam-4779	59	18	1	1	X
ejpam-4779	59	19	.	.	PUNCT
ejpam-4779	59	20	it	it	PRON
ejpam-4779	59	21	plays	play	VERB
ejpam-4779	59	22	an	an	DET
ejpam-4779	59	23	important	important	ADJ
ejpam-4779	59	24	role	role	NOUN
ejpam-4779	59	25	in	in	ADP
ejpam-4779	59	26	the	the	DET
ejpam-4779	59	27	study	study	NOUN
ejpam-4779	59	28	of	of	ADP
ejpam-4779	59	29	singularities	singularity	NOUN
ejpam-4779	59	30	and	and	CCONJ
ejpam-4779	59	31	power	power	NOUN
ejpam-4779	59	32	series	series	NOUN
ejpam-4779	59	33	with	with	ADP
ejpam-4779	59	34	integral	integral	ADJ
ejpam-4779	59	35	coefficients	coefficient	NOUN
ejpam-4779	59	36	[	[	X
ejpam-4779	59	37	7	7	NUM
ejpam-4779	59	38	,	,	PUNCT
ejpam-4779	59	39	8	8	NUM
ejpam-4779	59	40	]	]	PUNCT
ejpam-4779	59	41	.	.	PUNCT
ejpam-4779	60	1	on	on	ADP
ejpam-4779	60	2	the	the	DET
ejpam-4779	60	3	other	other	ADJ
ejpam-4779	60	4	hand	hand	NOUN
ejpam-4779	60	5	,	,	PUNCT
ejpam-4779	60	6	it	it	PRON
ejpam-4779	60	7	is	be	AUX
ejpam-4779	60	8	known	know	VERB
ejpam-4779	60	9	that	that	SCONJ
ejpam-4779	60	10	the	the	DET
ejpam-4779	60	11	toeplitz	toeplitz	NOUN
ejpam-4779	60	12	matrices	matrix	NOUN
ejpam-4779	60	13	are	be	AUX
ejpam-4779	60	14	closely	closely	ADV
ejpam-4779	60	15	related	relate	VERB
ejpam-4779	60	16	to	to	ADP
ejpam-4779	60	17	the	the	DET
ejpam-4779	60	18	hankel	hankel	NOUN
ejpam-4779	60	19	matrices	matrix	NOUN
ejpam-4779	60	20	and	and	CCONJ
ejpam-4779	60	21	one	one	NUM
ejpam-4779	60	22	of	of	ADP
ejpam-4779	60	23	the	the	DET
ejpam-4779	60	24	well	well	ADV
ejpam-4779	60	25	-	-	PUNCT
ejpam-4779	60	26	studied	study	VERB
ejpam-4779	60	27	classes	class	NOUN
ejpam-4779	60	28	of	of	ADP
ejpam-4779	60	29	structured	structured	ADJ
ejpam-4779	60	30	matrices	matrix	NOUN
ejpam-4779	60	31	.	.	PUNCT
ejpam-4779	61	1	unlike	unlike	ADP
ejpam-4779	61	2	the	the	DET
ejpam-4779	61	3	hankel	hankel	NOUN
ejpam-4779	61	4	matrices	matrix	NOUN
ejpam-4779	61	5	,	,	PUNCT
ejpam-4779	61	6	which	which	PRON
ejpam-4779	61	7	have	have	VERB
ejpam-4779	61	8	constant	constant	ADJ
ejpam-4779	61	9	entries	entry	NOUN
ejpam-4779	61	10	along	along	ADP
ejpam-4779	61	11	the	the	DET
ejpam-4779	61	12	reverse	reverse	ADJ
ejpam-4779	61	13	diagonals	diagonal	NOUN
ejpam-4779	61	14	,	,	PUNCT
ejpam-4779	61	15	toeplitz	toeplitz	NOUN
ejpam-4779	61	16	matrices	matrix	NOUN
ejpam-4779	61	17	have	have	VERB
ejpam-4779	61	18	constant	constant	ADJ
ejpam-4779	61	19	entries	entry	NOUN
ejpam-4779	61	20	along	along	ADP
ejpam-4779	61	21	the	the	DET
ejpam-4779	61	22	diagonals	diagonal	NOUN
ejpam-4779	61	23	.	.	PUNCT
ejpam-4779	62	1	toeplitz	toeplitz	NOUN
ejpam-4779	62	2	matrices	matrix	NOUN
ejpam-4779	62	3	have	have	VERB
ejpam-4779	62	4	a	a	DET
ejpam-4779	62	5	wide	wide	ADJ
ejpam-4779	62	6	range	range	NOUN
ejpam-4779	62	7	of	of	ADP
ejpam-4779	62	8	uses	use	NOUN
ejpam-4779	62	9	in	in	ADP
ejpam-4779	62	10	both	both	CCONJ
ejpam-4779	62	11	pure	pure	ADJ
ejpam-4779	62	12	and	and	CCONJ
ejpam-4779	62	13	applied	applied	ADJ
ejpam-4779	62	14	mathematics	mathematic	NOUN
ejpam-4779	62	15	,	,	PUNCT
ejpam-4779	62	16	which	which	PRON
ejpam-4779	62	17	has	have	AUX
ejpam-4779	62	18	sparked	spark	VERB
ejpam-4779	62	19	some	some	PRON
ejpam-4779	62	20	of	of	ADP
ejpam-4779	62	21	the	the	DET
ejpam-4779	62	22	most	most	ADV
ejpam-4779	62	23	important	important	ADJ
ejpam-4779	62	24	advances	advance	NOUN
ejpam-4779	62	25	in	in	ADP
ejpam-4779	62	26	research	research	NOUN
ejpam-4779	62	27	on	on	ADP
ejpam-4779	62	28	the	the	DET
ejpam-4779	62	29	toeplitz	toeplitz	NOUN
ejpam-4779	62	30	determinants	determinant	NOUN
ejpam-4779	62	31	,	,	PUNCT
ejpam-4779	62	32	kernel	kernel	NOUN
ejpam-4779	62	33	,	,	PUNCT
ejpam-4779	62	34	operators	operator	NOUN
ejpam-4779	62	35	,	,	PUNCT
ejpam-4779	62	36	and	and	CCONJ
ejpam-4779	62	37	q	q	X
ejpam-4779	62	38	-	-	PUNCT
ejpam-4779	62	39	deformed	deform	VERB
ejpam-4779	62	40	toeplitz	toeplitz	NOUN
ejpam-4779	62	41	matrices	matrix	NOUN
ejpam-4779	62	42	(	(	PUNCT
ejpam-4779	62	43	see	see	VERB
ejpam-4779	62	44	ye	ye	PRON
ejpam-4779	62	45	and	and	CCONJ
ejpam-4779	62	46	lim	lim	PROPN
ejpam-4779	63	1	[	[	X
ejpam-4779	63	2	35	35	NUM
ejpam-4779	63	3	]	]	SYM
ejpam-4779	63	4	)	)	PUNCT
ejpam-4779	63	5	.	.	PUNCT
ejpam-4779	64	1	thomas	thomas	PROPN
ejpam-4779	64	2	and	and	CCONJ
ejpam-4779	64	3	halim	halim	PROPN
ejpam-4779	65	1	[	[	X
ejpam-4779	65	2	32	32	NUM
ejpam-4779	65	3	]	]	PUNCT
ejpam-4779	65	4	introduced	introduce	VERB
ejpam-4779	65	5	the	the	DET
ejpam-4779	65	6	symmetric	symmetric	ADJ
ejpam-4779	65	7	toeplitz	toeplitz	NOUN
ejpam-4779	65	8	determinant	determinant	ADJ
ejpam-4779	65	9	of	of	ADP
ejpam-4779	65	10	a	a	DET
ejpam-4779	65	11	function	function	NOUN
ejpam-4779	65	12	f	f	PROPN
ejpam-4779	65	13	∈	∈	PROPN
ejpam-4779	65	14	a	a	DET
ejpam-4779	65	15	whose	whose	DET
ejpam-4779	65	16	elements	element	NOUN
ejpam-4779	65	17	are	be	AUX
ejpam-4779	65	18	taylor	taylor	PROPN
ejpam-4779	65	19	coefficients	coefficient	NOUN
ejpam-4779	65	20	of	of	ADP
ejpam-4779	65	21	f	f	PROPN
ejpam-4779	65	22	∈	∈	PROPN
ejpam-4779	65	23	a	a	PRON
ejpam-4779	66	1	and	and	CCONJ
ejpam-4779	66	2	it	it	PRON
ejpam-4779	66	3	is	be	AUX
ejpam-4779	66	4	defined	define	VERB
ejpam-4779	66	5	as	as	ADP
ejpam-4779	66	6	tq	tq	ADP
ejpam-4779	66	7	,	,	PUNCT
ejpam-4779	66	8	n	n	PROPN
ejpam-4779	66	9	(	(	PUNCT
ejpam-4779	66	10	f	f	X
ejpam-4779	66	11	)	)	PUNCT
ejpam-4779	67	1	=	=	SYM
ejpam-4779	67	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	67	3	an	an	DET
ejpam-4779	67	4	an+1	an+1	NOUN
ejpam-4779	67	5	...	...	PUNCT
ejpam-4779	68	1	an+q−1	an+q−1	PRON
ejpam-4779	68	2	an+1	an+1	VERB
ejpam-4779	68	3	an	an	PRON
ejpam-4779	68	4	...	...	PUNCT
ejpam-4779	68	5	an+q−2	an+q−2	NOUN
ejpam-4779	68	6	·	·	PUNCT
ejpam-4779	68	7	·	·	PUNCT
ejpam-4779	68	8	·	·	PUNCT
ejpam-4779	68	9	·	·	PUNCT
ejpam-4779	68	10	·	·	PUNCT
ejpam-4779	68	11	·	·	PUNCT
ejpam-4779	68	12	...	...	PUNCT
ejpam-4779	68	13	·	·	PUNCT
ejpam-4779	68	14	·	·	PUNCT
ejpam-4779	68	15	·	·	PUNCT
ejpam-4779	69	1	an+q−1	an+q−1	PRON
ejpam-4779	69	2	an+q−2	an+q−2	VERB
ejpam-4779	69	3	...	...	PUNCT
ejpam-4779	69	4	an	an	DET
ejpam-4779	69	5	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	69	6	,	,	PUNCT
ejpam-4779	69	7	where	where	SCONJ
ejpam-4779	69	8	q	q	X
ejpam-4779	69	9	,	,	PUNCT
ejpam-4779	69	10	n	n	PRON
ejpam-4779	69	11	∈	∈	PROPN
ejpam-4779	69	12	n	n	NOUN
ejpam-4779	69	13	and	and	CCONJ
ejpam-4779	69	14	a1	a1	NOUN
ejpam-4779	69	15	=	=	NOUN
ejpam-4779	69	16	1	1	X
ejpam-4779	69	17	.	.	PUNCT
ejpam-4779	70	1	it	it	PRON
ejpam-4779	70	2	is	be	AUX
ejpam-4779	70	3	worth	worth	ADJ
ejpam-4779	70	4	noting	note	VERB
ejpam-4779	70	5	that	that	SCONJ
ejpam-4779	70	6	the	the	DET
ejpam-4779	70	7	exact	exact	ADJ
ejpam-4779	70	8	bounds	bound	NOUN
ejpam-4779	70	9	of	of	ADP
ejpam-4779	70	10	the	the	DET
ejpam-4779	70	11	hankel	hankel	NOUN
ejpam-4779	70	12	and	and	CCONJ
ejpam-4779	70	13	toeplitz	toeplitz	NOUN
ejpam-4779	70	14	determinants	determinant	NOUN
ejpam-4779	70	15	for	for	ADP
ejpam-4779	70	16	some	some	DET
ejpam-4779	70	17	subclasses	subclass	NOUN
ejpam-4779	70	18	of	of	ADP
ejpam-4779	70	19	s	s	NOUN
ejpam-4779	70	20	are	be	AUX
ejpam-4779	70	21	still	still	ADV
ejpam-4779	70	22	not	not	PART
ejpam-4779	70	23	sharp	sharp	ADJ
ejpam-4779	70	24	and	and	CCONJ
ejpam-4779	70	25	are	be	AUX
ejpam-4779	70	26	yet	yet	ADV
ejpam-4779	70	27	undiscovered	undiscovered	ADJ
ejpam-4779	70	28	.	.	PUNCT
ejpam-4779	71	1	for	for	ADP
ejpam-4779	71	2	recent	recent	ADJ
ejpam-4779	71	3	work	work	NOUN
ejpam-4779	71	4	especially	especially	ADV
ejpam-4779	71	5	related	relate	VERB
ejpam-4779	71	6	to	to	ADP
ejpam-4779	71	7	the	the	DET
ejpam-4779	71	8	class	class	NOUN
ejpam-4779	71	9	consisting	consist	VERB
ejpam-4779	71	10	of	of	ADP
ejpam-4779	71	11	star	star	NOUN
ejpam-4779	71	12	-	-	PUNCT
ejpam-4779	71	13	like	like	ADJ
ejpam-4779	71	14	functions	function	NOUN
ejpam-4779	71	15	with	with	ADP
ejpam-4779	71	16	respect	respect	PROPN
ejpam-4779	71	17	d.	d.	PROPN
ejpam-4779	71	18	mohamad	mohamad	PROPN
ejpam-4779	71	19	,	,	PUNCT
ejpam-4779	71	20	n.	n.	PROPN
ejpam-4779	71	21	h.	h.	PROPN
ejpam-4779	71	22	a.	a.	PROPN
ejpam-4779	71	23	a.	a.	PROPN
ejpam-4779	71	24	wahid	wahid	PROPN
ejpam-4779	71	25	,	,	PUNCT
ejpam-4779	71	26	n.	n.	PROPN
ejpam-4779	71	27	n.	n.	PROPN
ejpam-4779	71	28	hasni	hasni	PROPN
ejpam-4779	71	29	/	/	SYM
ejpam-4779	71	30	eur	eur	PROPN
ejpam-4779	71	31	.	.	PUNCT
ejpam-4779	72	1	j.	j.	PROPN
ejpam-4779	72	2	pure	pure	PROPN
ejpam-4779	72	3	appl	appl	PROPN
ejpam-4779	72	4	.	.	PROPN
ejpam-4779	72	5	math	math	PROPN
ejpam-4779	72	6	,	,	PUNCT
ejpam-4779	72	7	16	16	NUM
ejpam-4779	72	8	(	(	PUNCT
ejpam-4779	72	9	2	2	NUM
ejpam-4779	72	10	)	)	PUNCT
ejpam-4779	72	11	(	(	PUNCT
ejpam-4779	72	12	2023	2023	NUM
ejpam-4779	72	13	)	)	PUNCT
ejpam-4779	72	14	,	,	PUNCT
ejpam-4779	72	15	1167	1167	NUM
ejpam-4779	72	16	-	-	SYM
ejpam-4779	72	17	1179	1179	NUM
ejpam-4779	72	18	1170	1170	NUM
ejpam-4779	72	19	to	to	ADP
ejpam-4779	72	20	other	other	ADJ
ejpam-4779	72	21	points	point	NOUN
ejpam-4779	72	22	,	,	PUNCT
ejpam-4779	72	23	i.e.	i.e.	X
ejpam-4779	72	24	,	,	PUNCT
ejpam-4779	72	25	symmetric	symmetric	ADJ
ejpam-4779	72	26	points	point	NOUN
ejpam-4779	72	27	,	,	PUNCT
ejpam-4779	72	28	conjugate	conjugate	ADJ
ejpam-4779	72	29	points	point	NOUN
ejpam-4779	72	30	,	,	PUNCT
ejpam-4779	72	31	and	and	CCONJ
ejpam-4779	72	32	symmetric	symmetric	ADJ
ejpam-4779	72	33	conjugate	conjugate	ADJ
ejpam-4779	72	34	points	point	NOUN
ejpam-4779	72	35	,	,	PUNCT
ejpam-4779	72	36	see	see	VERB
ejpam-4779	72	37	(	(	PUNCT
ejpam-4779	72	38	[	[	X
ejpam-4779	72	39	2	2	NUM
ejpam-4779	72	40	,	,	PUNCT
ejpam-4779	72	41	16	16	NUM
ejpam-4779	72	42	,	,	PUNCT
ejpam-4779	72	43	22	22	NUM
ejpam-4779	72	44	,	,	PUNCT
ejpam-4779	72	45	24	24	NUM
ejpam-4779	72	46	,	,	PUNCT
ejpam-4779	72	47	30	30	NUM
ejpam-4779	72	48	,	,	PUNCT
ejpam-4779	72	49	31	31	NUM
ejpam-4779	72	50	,	,	PUNCT
ejpam-4779	72	51	34	34	NUM
ejpam-4779	72	52	]	]	PUNCT
ejpam-4779	72	53	and	and	CCONJ
ejpam-4779	72	54	reference	reference	NOUN
ejpam-4779	72	55	therein	therein	ADV
ejpam-4779	72	56	)	)	PUNCT
ejpam-4779	72	57	.	.	PUNCT
ejpam-4779	73	1	recently	recently	ADV
ejpam-4779	73	2	,	,	PUNCT
ejpam-4779	73	3	the	the	DET
ejpam-4779	73	4	hankel	hankel	NOUN
ejpam-4779	73	5	and	and	CCONJ
ejpam-4779	73	6	toeplitz	toeplitz	NOUN
ejpam-4779	73	7	determinants	determinant	NOUN
ejpam-4779	73	8	of	of	ADP
ejpam-4779	73	9	a	a	DET
ejpam-4779	73	10	function	function	NOUN
ejpam-4779	73	11	f	f	PROPN
ejpam-4779	73	12	∈	∈	PROPN
ejpam-4779	73	13	a	a	PRON
ejpam-4779	73	14	whose	whose	DET
ejpam-4779	73	15	elements	element	NOUN
ejpam-4779	73	16	are	be	AUX
ejpam-4779	73	17	logarithmic	logarithmic	ADJ
ejpam-4779	73	18	coefficients	coefficient	NOUN
ejpam-4779	73	19	of	of	ADP
ejpam-4779	73	20	f	f	PROPN
ejpam-4779	73	21	∈	∈	PROPN
ejpam-4779	73	22	a	a	PRON
ejpam-4779	73	23	have	have	AUX
ejpam-4779	73	24	been	be	AUX
ejpam-4779	73	25	introduced	introduce	VERB
ejpam-4779	73	26	by	by	ADP
ejpam-4779	73	27	kowalczyk	kowalczyk	NOUN
ejpam-4779	73	28	and	and	CCONJ
ejpam-4779	73	29	lecko	lecko	NOUN
ejpam-4779	73	30	[	[	X
ejpam-4779	73	31	17	17	NUM
ejpam-4779	73	32	,	,	PUNCT
ejpam-4779	73	33	18	18	NUM
ejpam-4779	73	34	]	]	PUNCT
ejpam-4779	73	35	and	and	CCONJ
ejpam-4779	73	36	giri	giri	PROPN
ejpam-4779	73	37	and	and	CCONJ
ejpam-4779	73	38	kumar	kumar	PROPN
ejpam-4779	74	1	[	[	X
ejpam-4779	74	2	12	12	NUM
ejpam-4779	74	3	]	]	PUNCT
ejpam-4779	74	4	,	,	PUNCT
ejpam-4779	74	5	respectively	respectively	ADV
ejpam-4779	74	6	,	,	PUNCT
ejpam-4779	74	7	as	as	SCONJ
ejpam-4779	74	8	follows	follow	VERB
ejpam-4779	74	9	:	:	PUNCT
ejpam-4779	75	1	hq	hq	NOUN
ejpam-4779	75	2	,	,	PUNCT
ejpam-4779	75	3	n	n	CCONJ
ejpam-4779	75	4	(	(	PUNCT
ejpam-4779	75	5	ff/2	ff/2	PROPN
ejpam-4779	75	6	)	)	PUNCT
ejpam-4779	75	7	=	=	PUNCT
ejpam-4779	76	1	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	76	2	γn	γn	X
ejpam-4779	76	3	γn+1	γn+1	NUM
ejpam-4779	77	1	...	...	PUNCT
ejpam-4779	77	2	γn+q−1	γn+q−1	PROPN
ejpam-4779	77	3	γn+1	γn+1	ADP
ejpam-4779	77	4	γn+2	γn+2	NUM
ejpam-4779	77	5	...	...	PUNCT
ejpam-4779	78	1	γn+q	γn+q	PROPN
ejpam-4779	78	2	·	·	PUNCT
ejpam-4779	78	3	·	·	PUNCT
ejpam-4779	78	4	·	·	PUNCT
ejpam-4779	78	5	·	·	PUNCT
ejpam-4779	78	6	·	·	PUNCT
ejpam-4779	78	7	·	·	PUNCT
ejpam-4779	78	8	...	...	PUNCT
ejpam-4779	78	9	·	·	PUNCT
ejpam-4779	79	1	·	·	PUNCT
ejpam-4779	79	2	·	·	PUNCT
ejpam-4779	79	3	γn+q−1	γn+q−1	PROPN
ejpam-4779	79	4	γn+q	γn+q	PROPN
ejpam-4779	79	5	...	...	PUNCT
ejpam-4779	80	1	γn+2q−2	γn+2q−2	PROPN
ejpam-4779	80	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	80	3	,	,	PUNCT
ejpam-4779	80	4	and	and	CCONJ
ejpam-4779	80	5	tq	tq	INTJ
ejpam-4779	80	6	,	,	PUNCT
ejpam-4779	80	7	n	n	CCONJ
ejpam-4779	80	8	(	(	PUNCT
ejpam-4779	80	9	γf	γf	ADJ
ejpam-4779	80	10	)	)	PUNCT
ejpam-4779	80	11	=	=	PUNCT
ejpam-4779	80	12	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	80	13	γn	γn	X
ejpam-4779	80	14	γn+1	γn+1	NUM
ejpam-4779	80	15	...	...	PUNCT
ejpam-4779	81	1	γn+q−1	γn+q−1	PROPN
ejpam-4779	81	2	γn+1	γn+1	NUM
ejpam-4779	81	3	γn	γn	NOUN
ejpam-4779	81	4	...	...	PUNCT
ejpam-4779	82	1	γn+q−2	γn+q−2	X
ejpam-4779	82	2	·	·	PUNCT
ejpam-4779	82	3	·	·	PUNCT
ejpam-4779	82	4	·	·	PUNCT
ejpam-4779	82	5	·	·	PUNCT
ejpam-4779	82	6	·	·	PUNCT
ejpam-4779	82	7	·	·	PUNCT
ejpam-4779	82	8	...	...	PUNCT
ejpam-4779	82	9	·	·	PUNCT
ejpam-4779	82	10	·	·	PUNCT
ejpam-4779	82	11	·	·	PUNCT
ejpam-4779	83	1	γn+q−1	γn+q−1	PROPN
ejpam-4779	83	2	γn+q−2	γn+q−2	PROPN
ejpam-4779	83	3	...	...	PUNCT
ejpam-4779	83	4	γn	γn	X
ejpam-4779	83	5	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4779	83	6	,	,	PUNCT
ejpam-4779	83	7	where	where	SCONJ
ejpam-4779	83	8	γn	γn	NOUN
ejpam-4779	83	9	,	,	PUNCT
ejpam-4779	83	10	n	n	CCONJ
ejpam-4779	83	11	⩾	⩾	NOUN
ejpam-4779	83	12	1	1	NUM
ejpam-4779	83	13	,	,	PUNCT
ejpam-4779	83	14	the	the	DET
ejpam-4779	83	15	logarithmic	logarithmic	ADJ
ejpam-4779	83	16	coefficients	coefficient	NOUN
ejpam-4779	83	17	,	,	PUNCT
ejpam-4779	83	18	are	be	AUX
ejpam-4779	83	19	defined	define	VERB
ejpam-4779	83	20	in	in	ADP
ejpam-4779	83	21	the	the	DET
ejpam-4779	83	22	series	series	NOUN
ejpam-4779	83	23	form	form	NOUN
ejpam-4779	83	24	log	log	PROPN
ejpam-4779	83	25	f	f	PROPN
ejpam-4779	83	26	(	(	PUNCT
ejpam-4779	83	27	z	z	NOUN
ejpam-4779	83	28	)	)	PUNCT
ejpam-4779	83	29	z	z	NOUN
ejpam-4779	84	1	=	=	SYM
ejpam-4779	84	2	2	2	NUM
ejpam-4779	84	3	∞∑	∞∑	NUM
ejpam-4779	84	4	n=1	n=1	NUM
ejpam-4779	84	5	γnz	γnz	VERB
ejpam-4779	84	6	n.	n.	NOUN
ejpam-4779	84	7	in	in	ADP
ejpam-4779	84	8	particular	particular	ADJ
ejpam-4779	84	9	,	,	PUNCT
ejpam-4779	84	10	for	for	ADP
ejpam-4779	84	11	a	a	DET
ejpam-4779	84	12	function	function	NOUN
ejpam-4779	84	13	given	give	VERB
ejpam-4779	84	14	in	in	ADP
ejpam-4779	84	15	(	(	PUNCT
ejpam-4779	84	16	1	1	NUM
ejpam-4779	84	17	)	)	PUNCT
ejpam-4779	84	18	,	,	PUNCT
ejpam-4779	84	19	the	the	DET
ejpam-4779	84	20	logarithmic	logarithmic	ADJ
ejpam-4779	84	21	coefficients	coefficient	NOUN
ejpam-4779	84	22	γn	γn	ADP
ejpam-4779	84	23	,	,	PUNCT
ejpam-4779	84	24	n	n	NOUN
ejpam-4779	84	25	=	=	SYM
ejpam-4779	84	26	1	1	NUM
ejpam-4779	84	27	,	,	PUNCT
ejpam-4779	84	28	2	2	NUM
ejpam-4779	84	29	,	,	PUNCT
ejpam-4779	84	30	3	3	NUM
ejpam-4779	84	31	,	,	PUNCT
ejpam-4779	84	32	4	4	NUM
ejpam-4779	84	33	are	be	AUX
ejpam-4779	84	34	given	give	VERB
ejpam-4779	84	35	as	as	SCONJ
ejpam-4779	84	36	follows	follow	VERB
ejpam-4779	84	37	:	:	PUNCT
ejpam-4779	84	38	γ1	γ1	NOUN
ejpam-4779	84	39	=	=	NOUN
ejpam-4779	84	40	1	1	NUM
ejpam-4779	84	41	2	2	NUM
ejpam-4779	84	42	a2	a2	NOUN
ejpam-4779	84	43	,	,	PUNCT
ejpam-4779	84	44	(	(	PUNCT
ejpam-4779	84	45	5	5	X
ejpam-4779	84	46	)	)	PUNCT
ejpam-4779	84	47	γ2	γ2	NOUN
ejpam-4779	84	48	=	=	SYM
ejpam-4779	84	49	1	1	NUM
ejpam-4779	84	50	2	2	NUM
ejpam-4779	84	51	(	(	PUNCT
ejpam-4779	84	52	a3	a3	NOUN
ejpam-4779	84	53	−	−	NOUN
ejpam-4779	84	54	1	1	NUM
ejpam-4779	84	55	2	2	NUM
ejpam-4779	84	56	a2	a2	PROPN
ejpam-4779	84	57	2	2	NUM
ejpam-4779	84	58	)	)	PUNCT
ejpam-4779	84	59	,	,	PUNCT
ejpam-4779	84	60	(	(	PUNCT
ejpam-4779	84	61	6	6	X
ejpam-4779	84	62	)	)	PUNCT
ejpam-4779	84	63	γ3	γ3	NOUN
ejpam-4779	84	64	=	=	NOUN
ejpam-4779	84	65	1	1	NUM
ejpam-4779	84	66	2	2	NUM
ejpam-4779	84	67	(	(	PUNCT
ejpam-4779	84	68	a4	a4	NOUN
ejpam-4779	84	69	−	−	NOUN
ejpam-4779	85	1	a2a3	a2a3	NOUN
ejpam-4779	85	2	+	+	NUM
ejpam-4779	85	3	1	1	NUM
ejpam-4779	85	4	3	3	NUM
ejpam-4779	85	5	a2	a2	PROPN
ejpam-4779	85	6	3	3	NUM
ejpam-4779	85	7	)	)	PUNCT
ejpam-4779	85	8	,	,	PUNCT
ejpam-4779	85	9	(	(	PUNCT
ejpam-4779	85	10	7	7	X
ejpam-4779	85	11	)	)	PUNCT
ejpam-4779	85	12	and	and	CCONJ
ejpam-4779	86	1	γ4	γ4	NOUN
ejpam-4779	86	2	=	=	SYM
ejpam-4779	86	3	1	1	NUM
ejpam-4779	86	4	2	2	NUM
ejpam-4779	86	5	(	(	PUNCT
ejpam-4779	86	6	a5	a5	NOUN
ejpam-4779	86	7	−	−	PROPN
ejpam-4779	86	8	a2a4	a2a4	PROPN
ejpam-4779	86	9	+	+	NUM
ejpam-4779	86	10	a2	a2	PROPN
ejpam-4779	86	11	2a3	2a3	NUM
ejpam-4779	86	12	−	−	NOUN
ejpam-4779	86	13	1	1	NUM
ejpam-4779	86	14	2	2	NUM
ejpam-4779	86	15	a3	a3	NOUN
ejpam-4779	86	16	2	2	NUM
ejpam-4779	86	17	−	−	NOUN
ejpam-4779	86	18	1	1	NUM
ejpam-4779	86	19	4	4	NUM
ejpam-4779	86	20	a2	a2	PROPN
ejpam-4779	86	21	4	4	NUM
ejpam-4779	86	22	)	)	PUNCT
ejpam-4779	86	23	.	.	PUNCT
ejpam-4779	87	1	(	(	PUNCT
ejpam-4779	87	2	8)	8)	NUM
ejpam-4779	87	3	the	the	DET
ejpam-4779	87	4	logarithmic	logarithmic	ADJ
ejpam-4779	87	5	coefficients	coefficient	NOUN
ejpam-4779	87	6	have	have	VERB
ejpam-4779	87	7	great	great	ADJ
ejpam-4779	87	8	importance	importance	NOUN
ejpam-4779	87	9	,	,	PUNCT
ejpam-4779	87	10	for	for	ADP
ejpam-4779	87	11	instance	instance	NOUN
ejpam-4779	87	12	,	,	PUNCT
ejpam-4779	87	13	these	these	DET
ejpam-4779	87	14	coefficients	coefficient	NOUN
ejpam-4779	87	15	helped	help	VERB
ejpam-4779	87	16	kayumov	kayumov	ADJ
ejpam-4779	87	17	[	[	X
ejpam-4779	87	18	14	14	NUM
ejpam-4779	87	19	]	]	PUNCT
ejpam-4779	87	20	to	to	PART
ejpam-4779	87	21	solve	solve	VERB
ejpam-4779	87	22	brennan	brennan	PROPN
ejpam-4779	87	23	’s	’s	PART
ejpam-4779	87	24	conjecture	conjecture	NOUN
ejpam-4779	87	25	for	for	ADP
ejpam-4779	87	26	conformal	conformal	ADJ
ejpam-4779	87	27	mapping	mapping	NOUN
ejpam-4779	87	28	and	and	CCONJ
ejpam-4779	87	29	estimation	estimation	NOUN
ejpam-4779	87	30	of	of	ADP
ejpam-4779	87	31	the	the	DET
ejpam-4779	87	32	logarithmic	logarithmic	ADJ
ejpam-4779	87	33	coefficients	coefficient	NOUN
ejpam-4779	87	34	can	can	AUX
ejpam-4779	87	35	be	be	AUX
ejpam-4779	87	36	transferred	transfer	VERB
ejpam-4779	87	37	to	to	ADP
ejpam-4779	87	38	the	the	DET
ejpam-4779	87	39	taylor	taylor	PROPN
ejpam-4779	87	40	coefficients	coefficient	NOUN
ejpam-4779	87	41	of	of	ADP
ejpam-4779	87	42	univalent	univalent	ADJ
ejpam-4779	87	43	functions	function	NOUN
ejpam-4779	87	44	via	via	ADP
ejpam-4779	87	45	the	the	DET
ejpam-4779	87	46	lebedev	lebedev	PROPN
ejpam-4779	87	47	–	–	PUNCT
ejpam-4779	87	48	milin	milin	PROPN
ejpam-4779	87	49	inequalities	inequality	NOUN
ejpam-4779	87	50	(	(	PUNCT
ejpam-4779	87	51	see	see	VERB
ejpam-4779	87	52	[	[	X
ejpam-4779	87	53	9	9	NUM
ejpam-4779	87	54	,	,	PUNCT
ejpam-4779	87	55	19–21	19–21	NUM
ejpam-4779	87	56	]	]	PUNCT
ejpam-4779	87	57	for	for	ADP
ejpam-4779	87	58	details	detail	NOUN
ejpam-4779	87	59	)	)	PUNCT
ejpam-4779	87	60	.	.	PUNCT
ejpam-4779	88	1	due	due	ADP
ejpam-4779	88	2	to	to	ADP
ejpam-4779	88	3	the	the	DET
ejpam-4779	88	4	great	great	ADJ
ejpam-4779	88	5	importance	importance	NOUN
ejpam-4779	88	6	of	of	ADP
ejpam-4779	88	7	logarithmic	logarithmic	ADJ
ejpam-4779	88	8	coefficients	coefficient	NOUN
ejpam-4779	88	9	and	and	CCONJ
ejpam-4779	88	10	the	the	DET
ejpam-4779	88	11	hankel	hankel	NOUN
ejpam-4779	88	12	and	and	CCONJ
ejpam-4779	88	13	toeplitz	toeplitz	NOUN
ejpam-4779	88	14	determinants	determinant	NOUN
ejpam-4779	88	15	,	,	PUNCT
ejpam-4779	88	16	some	some	DET
ejpam-4779	88	17	recent	recent	ADJ
ejpam-4779	88	18	works	work	NOUN
ejpam-4779	88	19	on	on	ADP
ejpam-4779	88	20	this	this	DET
ejpam-4779	88	21	problem	problem	NOUN
ejpam-4779	88	22	that	that	PRON
ejpam-4779	88	23	relate	relate	VERB
ejpam-4779	88	24	to	to	ADP
ejpam-4779	88	25	the	the	DET
ejpam-4779	88	26	theory	theory	NOUN
ejpam-4779	88	27	of	of	ADP
ejpam-4779	88	28	univalent	univalent	ADJ
ejpam-4779	88	29	functions	function	NOUN
ejpam-4779	88	30	have	have	AUX
ejpam-4779	88	31	been	be	AUX
ejpam-4779	88	32	studied	study	VERB
ejpam-4779	88	33	in	in	ADP
ejpam-4779	88	34	[	[	X
ejpam-4779	88	35	3–5	3–5	NOUN
ejpam-4779	88	36	,	,	PUNCT
ejpam-4779	88	37	12	12	NUM
ejpam-4779	88	38	,	,	PUNCT
ejpam-4779	88	39	15	15	NUM
ejpam-4779	88	40	,	,	PUNCT
ejpam-4779	88	41	16	16	NUM
ejpam-4779	88	42	,	,	PUNCT
ejpam-4779	88	43	18	18	NUM
ejpam-4779	88	44	,	,	PUNCT
ejpam-4779	88	45	23	23	NUM
ejpam-4779	88	46	,	,	PUNCT
ejpam-4779	88	47	25	25	NUM
ejpam-4779	88	48	,	,	PUNCT
ejpam-4779	88	49	29	29	NUM
ejpam-4779	88	50	,	,	PUNCT
ejpam-4779	88	51	33	33	NUM
ejpam-4779	88	52	,	,	PUNCT
ejpam-4779	88	53	36	36	NUM
ejpam-4779	88	54	]	]	PUNCT
ejpam-4779	88	55	but	but	CCONJ
ejpam-4779	88	56	only	only	ADV
ejpam-4779	88	57	a	a	DET
ejpam-4779	88	58	few	few	ADJ
ejpam-4779	88	59	papers	paper	NOUN
ejpam-4779	88	60	have	have	AUX
ejpam-4779	88	61	been	be	AUX
ejpam-4779	88	62	published	publish	VERB
ejpam-4779	88	63	for	for	ADP
ejpam-4779	88	64	the	the	DET
ejpam-4779	88	65	class	class	NOUN
ejpam-4779	88	66	of	of	ADP
ejpam-4779	88	67	star	star	NOUN
ejpam-4779	88	68	-	-	PUNCT
ejpam-4779	88	69	like	like	ADJ
ejpam-4779	88	70	functions	function	NOUN
ejpam-4779	88	71	with	with	ADP
ejpam-4779	88	72	respect	respect	NOUN
ejpam-4779	88	73	to	to	ADP
ejpam-4779	88	74	other	other	ADJ
ejpam-4779	88	75	points	point	NOUN
ejpam-4779	88	76	.	.	PUNCT
ejpam-4779	89	1	motivated	motivate	VERB
ejpam-4779	89	2	by	by	ADP
ejpam-4779	89	3	these	these	DET
ejpam-4779	89	4	works	work	NOUN
ejpam-4779	89	5	,	,	PUNCT
ejpam-4779	89	6	in	in	ADP
ejpam-4779	89	7	this	this	DET
ejpam-4779	89	8	paper	paper	NOUN
ejpam-4779	89	9	,	,	PUNCT
ejpam-4779	89	10	we	we	PRON
ejpam-4779	89	11	obtain	obtain	VERB
ejpam-4779	89	12	the	the	DET
ejpam-4779	89	13	upper	upper	ADJ
ejpam-4779	89	14	bounds	bound	NOUN
ejpam-4779	89	15	of	of	ADP
ejpam-4779	89	16	the	the	DET
ejpam-4779	89	17	taylor	taylor	PROPN
ejpam-4779	89	18	coefficients	coefficient	NOUN
ejpam-4779	89	19	|an|	|an|	PROPN
ejpam-4779	89	20	,	,	PUNCT
ejpam-4779	89	21	n	n	NOUN
ejpam-4779	89	22	=	=	SYM
ejpam-4779	89	23	2	2	NUM
ejpam-4779	89	24	,	,	PUNCT
ejpam-4779	89	25	3	3	NUM
ejpam-4779	89	26	,	,	PUNCT
ejpam-4779	89	27	4	4	NUM
ejpam-4779	89	28	,	,	PUNCT
ejpam-4779	89	29	5	5	NUM
ejpam-4779	89	30	,	,	PUNCT
ejpam-4779	89	31	d.	d.	PROPN
ejpam-4779	89	32	mohamad	mohamad	PROPN
ejpam-4779	89	33	,	,	PUNCT
ejpam-4779	89	34	n.	n.	PROPN
ejpam-4779	89	35	h.	h.	PROPN
ejpam-4779	89	36	a.	a.	PROPN
ejpam-4779	89	37	a.	a.	PROPN
ejpam-4779	89	38	wahid	wahid	PROPN
ejpam-4779	89	39	,	,	PUNCT
ejpam-4779	89	40	n.	n.	PROPN
ejpam-4779	89	41	n.	n.	PROPN
ejpam-4779	89	42	hasni	hasni	PROPN
ejpam-4779	89	43	/	/	SYM
ejpam-4779	89	44	eur	eur	PROPN
ejpam-4779	89	45	.	.	PUNCT
ejpam-4779	90	1	j.	j.	PROPN
ejpam-4779	90	2	pure	pure	PROPN
ejpam-4779	90	3	appl	appl	PROPN
ejpam-4779	90	4	.	.	PROPN
ejpam-4779	90	5	math	math	PROPN
ejpam-4779	90	6	,	,	PUNCT
ejpam-4779	90	7	16	16	NUM
ejpam-4779	90	8	(	(	PUNCT
ejpam-4779	90	9	2	2	NUM
ejpam-4779	90	10	)	)	PUNCT
ejpam-4779	90	11	(	(	PUNCT
ejpam-4779	90	12	2023	2023	NUM
ejpam-4779	90	13	)	)	PUNCT
ejpam-4779	90	14	,	,	PUNCT
ejpam-4779	90	15	1167	1167	NUM
ejpam-4779	90	16	-	-	SYM
ejpam-4779	90	17	1179	1179	NUM
ejpam-4779	90	18	1171	1171	NUM
ejpam-4779	90	19	logarithmic	logarithmic	ADJ
ejpam-4779	90	20	coefficients	coefficient	NOUN
ejpam-4779	90	21	|γn|	|γn|	PROPN
ejpam-4779	90	22	,	,	PUNCT
ejpam-4779	90	23	n	n	NOUN
ejpam-4779	90	24	=	=	SYM
ejpam-4779	90	25	1	1	NUM
ejpam-4779	90	26	,	,	PUNCT
ejpam-4779	90	27	2	2	NUM
ejpam-4779	90	28	,	,	PUNCT
ejpam-4779	90	29	3	3	NUM
ejpam-4779	90	30	,	,	PUNCT
ejpam-4779	90	31	4	4	NUM
ejpam-4779	90	32	,	,	PUNCT
ejpam-4779	90	33	and	and	CCONJ
ejpam-4779	90	34	hence	hence	ADV
ejpam-4779	90	35	some	some	DET
ejpam-4779	90	36	cases	case	NOUN
ejpam-4779	90	37	of	of	ADP
ejpam-4779	90	38	the	the	DET
ejpam-4779	90	39	hankel	hankel	NOUN
ejpam-4779	90	40	determinant	determinant	ADJ
ejpam-4779	90	41	as	as	ADV
ejpam-4779	90	42	well	well	ADV
ejpam-4779	90	43	as	as	ADP
ejpam-4779	90	44	toeplitz	toeplitz	NOUN
ejpam-4779	90	45	determinant	determinant	ADJ
ejpam-4779	90	46	,	,	PUNCT
ejpam-4779	90	47	whose	whose	DET
ejpam-4779	90	48	both	both	DET
ejpam-4779	90	49	entries	entry	NOUN
ejpam-4779	90	50	are	be	AUX
ejpam-4779	90	51	logarithmic	logarithmic	ADJ
ejpam-4779	90	52	coefficients	coefficient	NOUN
ejpam-4779	90	53	,	,	PUNCT
ejpam-4779	90	54	i.e.	i.e.	X
ejpam-4779	90	55	,	,	PUNCT
ejpam-4779	90	56	|h2,1	|h2,1	ADJ
ejpam-4779	90	57	(	(	PUNCT
ejpam-4779	90	58	ff/2)|	ff/2)|	ADJ
ejpam-4779	90	59	,	,	PUNCT
ejpam-4779	90	60	|h2,2	|h2,2	NOUN
ejpam-4779	90	61	(	(	PUNCT
ejpam-4779	90	62	ff/2)|	ff/2)|	NOUN
ejpam-4779	90	63	,	,	PUNCT
ejpam-4779	90	64	|t2,1	|t2,1	INTJ
ejpam-4779	90	65	(	(	PUNCT
ejpam-4779	90	66	γn)|	γn)|	ADV
ejpam-4779	90	67	,	,	PUNCT
ejpam-4779	90	68	and	and	CCONJ
ejpam-4779	90	69	|t2,2	|t2,2	NOUN
ejpam-4779	90	70	(	(	PUNCT
ejpam-4779	90	71	γn)|	γn)|	ADV
ejpam-4779	90	72	for	for	ADP
ejpam-4779	90	73	the	the	DET
ejpam-4779	90	74	functions	function	NOUN
ejpam-4779	90	75	in	in	ADP
ejpam-4779	90	76	the	the	DET
ejpam-4779	90	77	class	class	NOUN
ejpam-4779	90	78	s∗	s∗	PROPN
ejpam-4779	90	79	sc	sc	PROPN
ejpam-4779	90	80	(	(	PUNCT
ejpam-4779	90	81	sin	sin	PROPN
ejpam-4779	90	82	z	z	NOUN
ejpam-4779	90	83	)	)	PUNCT
ejpam-4779	90	84	as	as	SCONJ
ejpam-4779	90	85	defined	define	VERB
ejpam-4779	90	86	in	in	ADP
ejpam-4779	90	87	definition	definition	NOUN
ejpam-4779	90	88	1	1	NUM
ejpam-4779	90	89	.	.	NOUN
ejpam-4779	90	90	2	2	NUM
ejpam-4779	90	91	.	.	X
ejpam-4779	90	92	preliminary	preliminary	ADJ
ejpam-4779	90	93	results	result	NOUN
ejpam-4779	90	94	in	in	ADP
ejpam-4779	90	95	this	this	DET
ejpam-4779	90	96	section	section	NOUN
ejpam-4779	90	97	,	,	PUNCT
ejpam-4779	90	98	we	we	PRON
ejpam-4779	90	99	give	give	VERB
ejpam-4779	90	100	some	some	DET
ejpam-4779	90	101	lemmas	lemma	NOUN
ejpam-4779	90	102	to	to	PART
ejpam-4779	90	103	prove	prove	VERB
ejpam-4779	90	104	our	our	PRON
ejpam-4779	90	105	main	main	ADJ
ejpam-4779	90	106	results	result	NOUN
ejpam-4779	90	107	.	.	PUNCT
ejpam-4779	91	1	lemma	lemma	PROPN
ejpam-4779	91	2	1	1	NUM
ejpam-4779	91	3	.	.	PUNCT
ejpam-4779	92	1	(	(	PUNCT
ejpam-4779	92	2	[	[	X
ejpam-4779	92	3	9	9	NUM
ejpam-4779	92	4	]	]	PUNCT
ejpam-4779	92	5	)	)	PUNCT
ejpam-4779	92	6	for	for	ADP
ejpam-4779	92	7	a	a	DET
ejpam-4779	92	8	function	function	NOUN
ejpam-4779	92	9	p	p	X
ejpam-4779	92	10	∈	∈	PROPN
ejpam-4779	92	11	p	p	NOUN
ejpam-4779	92	12	of	of	ADP
ejpam-4779	92	13	the	the	DET
ejpam-4779	92	14	form	form	NOUN
ejpam-4779	92	15	p	p	X
ejpam-4779	92	16	(	(	PUNCT
ejpam-4779	92	17	z	z	NOUN
ejpam-4779	92	18	)	)	PUNCT
ejpam-4779	92	19	=	=	SYM
ejpam-4779	93	1	1	1	NUM
ejpam-4779	93	2	+	+	CCONJ
ejpam-4779	93	3	∞∑	∞∑	NUM
ejpam-4779	93	4	n=1	n=1	PROPN
ejpam-4779	93	5	pnz	pnz	NOUN
ejpam-4779	93	6	n	n	CCONJ
ejpam-4779	93	7	,	,	PUNCT
ejpam-4779	93	8	z	z	PROPN
ejpam-4779	93	9	∈	∈	PROPN
ejpam-4779	93	10	e	e	NOUN
ejpam-4779	93	11	,	,	PUNCT
ejpam-4779	93	12	the	the	DET
ejpam-4779	93	13	sharp	sharp	ADJ
ejpam-4779	93	14	inequality	inequality	NOUN
ejpam-4779	93	15	|pn|	|pn|	ADJ
ejpam-4779	93	16	⩽	⩽	ADJ
ejpam-4779	93	17	2	2	NUM
ejpam-4779	93	18	holds	hold	VERB
ejpam-4779	93	19	for	for	ADP
ejpam-4779	93	20	each	each	DET
ejpam-4779	93	21	n	n	CCONJ
ejpam-4779	93	22	⩾	⩾	NOUN
ejpam-4779	93	23	1	1	X
ejpam-4779	93	24	.	.	X
ejpam-4779	94	1	equality	equality	NOUN
ejpam-4779	94	2	holds	hold	VERB
ejpam-4779	94	3	for	for	ADP
ejpam-4779	94	4	the	the	DET
ejpam-4779	94	5	function	function	NOUN
ejpam-4779	94	6	p	p	NOUN
ejpam-4779	94	7	(	(	PUNCT
ejpam-4779	94	8	z	z	NOUN
ejpam-4779	94	9	)	)	PUNCT
ejpam-4779	94	10	=	=	SYM
ejpam-4779	95	1	1+z	1+z	NUM
ejpam-4779	95	2	1−z	1−z	NUM
ejpam-4779	95	3	.	.	PUNCT
ejpam-4779	96	1	lemma	lemma	PROPN
ejpam-4779	96	2	2	2	NUM
ejpam-4779	96	3	.	.	PUNCT
ejpam-4779	97	1	(	(	PUNCT
ejpam-4779	97	2	[	[	X
ejpam-4779	97	3	10	10	NUM
ejpam-4779	97	4	]	]	PUNCT
ejpam-4779	97	5	)	)	PUNCT
ejpam-4779	97	6	let	let	VERB
ejpam-4779	97	7	p	p	PRON
ejpam-4779	97	8	∈	∈	PROPN
ejpam-4779	97	9	p	p	NOUN
ejpam-4779	97	10	of	of	ADP
ejpam-4779	97	11	the	the	DET
ejpam-4779	97	12	form	form	NOUN
ejpam-4779	97	13	p	p	X
ejpam-4779	97	14	(	(	PUNCT
ejpam-4779	97	15	z	z	NOUN
ejpam-4779	97	16	)	)	PUNCT
ejpam-4779	97	17	=	=	SYM
ejpam-4779	98	1	1	1	NUM
ejpam-4779	98	2	+	+	CCONJ
ejpam-4779	98	3	∞∑	∞∑	NUM
ejpam-4779	98	4	n=1	n=1	ADJ
ejpam-4779	98	5	pnz	pnz	NOUN
ejpam-4779	98	6	n	n	ADJ
ejpam-4779	98	7	and	and	CCONJ
ejpam-4779	98	8	µ	µ	PROPN
ejpam-4779	98	9	∈	∈	PROPN
ejpam-4779	98	10	c.	c.	NOUN
ejpam-4779	99	1	then	then	ADV
ejpam-4779	99	2	|pn	|pn	X
ejpam-4779	99	3	−	−	PROPN
ejpam-4779	99	4	µpkpn−k|	µpkpn−k|	PROPN
ejpam-4779	99	5	⩽	⩽	NOUN
ejpam-4779	99	6	2max	2max	NUM
ejpam-4779	99	7	{	{	PUNCT
ejpam-4779	99	8	1	1	NUM
ejpam-4779	99	9	,	,	PUNCT
ejpam-4779	99	10	|2µ−	|2µ−	NOUN
ejpam-4779	99	11	1|	1|	NUM
ejpam-4779	99	12	}	}	PUNCT
ejpam-4779	99	13	,	,	PUNCT
ejpam-4779	99	14	1	1	NUM
ejpam-4779	99	15	⩽	⩽	NOUN
ejpam-4779	99	16	k	k	PROPN
ejpam-4779	99	17	⩽	⩽	ADJ
ejpam-4779	99	18	n−	n−	PROPN
ejpam-4779	99	19	1	1	NUM
ejpam-4779	99	20	.	.	PUNCT
ejpam-4779	100	1	if	if	SCONJ
ejpam-4779	100	2	|2µ−	|2µ−	NOUN
ejpam-4779	100	3	1|	1|	NUM
ejpam-4779	100	4	⩾	⩾	NOUN
ejpam-4779	100	5	1	1	NUM
ejpam-4779	100	6	,	,	PUNCT
ejpam-4779	100	7	then	then	ADV
ejpam-4779	100	8	the	the	DET
ejpam-4779	100	9	inequality	inequality	NOUN
ejpam-4779	100	10	is	be	AUX
ejpam-4779	100	11	sharp	sharp	ADJ
ejpam-4779	100	12	for	for	ADP
ejpam-4779	100	13	the	the	DET
ejpam-4779	100	14	function	function	NOUN
ejpam-4779	100	15	p	p	NOUN
ejpam-4779	100	16	(	(	PUNCT
ejpam-4779	100	17	z	z	NOUN
ejpam-4779	100	18	)	)	PUNCT
ejpam-4779	101	1	=	=	SYM
ejpam-4779	101	2	1+z	1+z	NUM
ejpam-4779	101	3	1−z	1−z	NUM
ejpam-4779	101	4	or	or	CCONJ
ejpam-4779	101	5	its	its	PRON
ejpam-4779	101	6	rotations	rotation	NOUN
ejpam-4779	101	7	.	.	PUNCT
ejpam-4779	102	1	if	if	SCONJ
ejpam-4779	102	2	|2µ−	|2µ−	NOUN
ejpam-4779	102	3	1|	1|	X
ejpam-4779	102	4	<	<	X
ejpam-4779	102	5	1	1	NUM
ejpam-4779	102	6	,	,	PUNCT
ejpam-4779	102	7	then	then	ADV
ejpam-4779	102	8	the	the	DET
ejpam-4779	102	9	inequality	inequality	NOUN
ejpam-4779	102	10	is	be	AUX
ejpam-4779	102	11	sharp	sharp	ADJ
ejpam-4779	102	12	for	for	ADP
ejpam-4779	102	13	the	the	DET
ejpam-4779	102	14	function	function	NOUN
ejpam-4779	102	15	p	p	NOUN
ejpam-4779	102	16	(	(	PUNCT
ejpam-4779	102	17	z	z	NOUN
ejpam-4779	102	18	)	)	PUNCT
ejpam-4779	102	19	=	=	PUNCT
ejpam-4779	103	1	1+zn	1+zn	NUM
ejpam-4779	103	2	1−zn	1−zn	NUM
ejpam-4779	103	3	or	or	CCONJ
ejpam-4779	103	4	its	its	PRON
ejpam-4779	103	5	rotations	rotation	NOUN
ejpam-4779	103	6	.	.	PUNCT
ejpam-4779	104	1	lemma	lemma	PROPN
ejpam-4779	104	2	3	3	NUM
ejpam-4779	104	3	.	.	PUNCT
ejpam-4779	105	1	(	(	PUNCT
ejpam-4779	105	2	[	[	X
ejpam-4779	105	3	6	6	NUM
ejpam-4779	105	4	]	]	PUNCT
ejpam-4779	105	5	)	)	PUNCT
ejpam-4779	105	6	let	let	VERB
ejpam-4779	105	7	p	p	PRON
ejpam-4779	105	8	∈	∈	PROPN
ejpam-4779	105	9	p	p	NOUN
ejpam-4779	105	10	of	of	ADP
ejpam-4779	105	11	the	the	DET
ejpam-4779	105	12	form	form	NOUN
ejpam-4779	105	13	p	p	X
ejpam-4779	105	14	(	(	PUNCT
ejpam-4779	105	15	z	z	NOUN
ejpam-4779	105	16	)	)	PUNCT
ejpam-4779	105	17	=	=	SYM
ejpam-4779	105	18	1	1	NUM
ejpam-4779	105	19	+	+	CCONJ
ejpam-4779	105	20	∞∑	∞∑	NUM
ejpam-4779	105	21	n=1	n=1	PROPN
ejpam-4779	105	22	pnz	pnz	NOUN
ejpam-4779	105	23	n	n	CCONJ
ejpam-4779	105	24	,	,	PUNCT
ejpam-4779	105	25	z	z	PROPN
ejpam-4779	105	26	∈	∈	PROPN
ejpam-4779	105	27	e	e	X
ejpam-4779	105	28	and	and	CCONJ
ejpam-4779	105	29	α	α	NOUN
ejpam-4779	105	30	,	,	PUNCT
ejpam-4779	105	31	β	β	X
ejpam-4779	105	32	,	,	PUNCT
ejpam-4779	105	33	γ	γ	PROPN
ejpam-4779	105	34	∈	∈	PROPN
ejpam-4779	105	35	ℜ.	ℜ.	PROPN
ejpam-4779	105	36	then	then	ADV
ejpam-4779	105	37	∣∣αp13	∣∣αp13	VERB
ejpam-4779	105	38	−	−	ADP
ejpam-4779	105	39	βp1p2	βp1p2	PROPN
ejpam-4779	106	1	+	+	NUM
ejpam-4779	106	2	γp3	γp3	X
ejpam-4779	106	3	∣∣	∣∣	NUM
ejpam-4779	106	4	⩽	⩽	ADJ
ejpam-4779	106	5	2	2	NUM
ejpam-4779	106	6	|α|	|α|	NOUN
ejpam-4779	106	7	+	+	CCONJ
ejpam-4779	106	8	2	2	NUM
ejpam-4779	106	9	|β	|β	VERB
ejpam-4779	106	10	−	−	NOUN
ejpam-4779	106	11	2α|	2α|	NUM
ejpam-4779	106	12	+	+	SYM
ejpam-4779	106	13	2	2	NUM
ejpam-4779	106	14	|α−	|α−	NOUN
ejpam-4779	106	15	β	β	X
ejpam-4779	106	16	+	+	X
ejpam-4779	106	17	γ|	γ|	PROPN
ejpam-4779	106	18	.	.	PUNCT
ejpam-4779	107	1	3	3	X
ejpam-4779	107	2	.	.	X
ejpam-4779	107	3	main	main	ADJ
ejpam-4779	107	4	results	result	NOUN
ejpam-4779	107	5	this	this	DET
ejpam-4779	107	6	section	section	NOUN
ejpam-4779	107	7	is	be	AUX
ejpam-4779	107	8	devoted	devote	VERB
ejpam-4779	107	9	to	to	ADP
ejpam-4779	107	10	the	the	DET
ejpam-4779	107	11	proof	proof	NOUN
ejpam-4779	107	12	of	of	ADP
ejpam-4779	107	13	our	our	PRON
ejpam-4779	107	14	main	main	ADJ
ejpam-4779	107	15	results	result	NOUN
ejpam-4779	107	16	.	.	PUNCT
ejpam-4779	108	1	we	we	PRON
ejpam-4779	108	2	will	will	AUX
ejpam-4779	108	3	now	now	ADV
ejpam-4779	108	4	determine	determine	VERB
ejpam-4779	108	5	the	the	DET
ejpam-4779	108	6	upper	upper	ADJ
ejpam-4779	108	7	bounds	bound	NOUN
ejpam-4779	108	8	of	of	ADP
ejpam-4779	108	9	the	the	DET
ejpam-4779	108	10	taylor	taylor	PROPN
ejpam-4779	108	11	coefficients	coefficient	NOUN
ejpam-4779	108	12	,	,	PUNCT
ejpam-4779	108	13	logarithmic	logarithmic	ADJ
ejpam-4779	108	14	coefficients	coefficient	NOUN
ejpam-4779	108	15	,	,	PUNCT
ejpam-4779	108	16	and	and	CCONJ
ejpam-4779	108	17	hankel	hankel	NOUN
ejpam-4779	108	18	and	and	CCONJ
ejpam-4779	108	19	toeplitz	toeplitz	NOUN
ejpam-4779	108	20	determinants	determinant	NOUN
ejpam-4779	108	21	of	of	ADP
ejpam-4779	108	22	logarithmic	logarithmic	ADJ
ejpam-4779	108	23	coefficients	coefficient	NOUN
ejpam-4779	108	24	,	,	PUNCT
ejpam-4779	108	25	respectively	respectively	ADV
ejpam-4779	108	26	,	,	PUNCT
ejpam-4779	108	27	as	as	SCONJ
ejpam-4779	108	28	follows	follow	VERB
ejpam-4779	108	29	:	:	PUNCT
ejpam-4779	108	30	3.1	3.1	NUM
ejpam-4779	108	31	.	.	PUNCT
ejpam-4779	109	1	taylor	taylor	PROPN
ejpam-4779	109	2	coefficients	coefficient	NOUN
ejpam-4779	109	3	theorem	theorem	VERB
ejpam-4779	109	4	1	1	X
ejpam-4779	109	5	.	.	PUNCT
ejpam-4779	110	1	if	if	SCONJ
ejpam-4779	110	2	f	f	PROPN
ejpam-4779	110	3	is	be	AUX
ejpam-4779	110	4	of	of	ADP
ejpam-4779	110	5	the	the	DET
ejpam-4779	110	6	form	form	NOUN
ejpam-4779	110	7	(	(	PUNCT
ejpam-4779	110	8	1	1	X
ejpam-4779	110	9	)	)	PUNCT
ejpam-4779	110	10	belongs	belong	VERB
ejpam-4779	110	11	to	to	PART
ejpam-4779	110	12	s∗	s∗	PROPN
ejpam-4779	110	13	sc	sc	PROPN
ejpam-4779	110	14	(	(	PUNCT
ejpam-4779	110	15	sin	sin	PROPN
ejpam-4779	110	16	z	z	PROPN
ejpam-4779	110	17	)	)	PUNCT
ejpam-4779	110	18	,	,	PUNCT
ejpam-4779	110	19	then	then	ADV
ejpam-4779	110	20	|a2|	|a2|	VERB
ejpam-4779	110	21	⩽	⩽	ADJ
ejpam-4779	110	22	1	1	NUM
ejpam-4779	110	23	2	2	NUM
ejpam-4779	110	24	,	,	PUNCT
ejpam-4779	110	25	|a3|	|a3|	VERB
ejpam-4779	110	26	⩽	⩽	ADJ
ejpam-4779	110	27	1	1	NUM
ejpam-4779	110	28	2	2	NUM
ejpam-4779	110	29	,	,	PUNCT
ejpam-4779	110	30	|a4|	|a4|	ADJ
ejpam-4779	110	31	⩽	⩽	ADJ
ejpam-4779	110	32	1	1	NUM
ejpam-4779	110	33	4	4	NUM
ejpam-4779	110	34	,	,	PUNCT
ejpam-4779	110	35	and	and	CCONJ
ejpam-4779	110	36	|a5|	|a5|	VERB
ejpam-4779	110	37	⩽	⩽	ADJ
ejpam-4779	110	38	1	1	NUM
ejpam-4779	110	39	2	2	NUM
ejpam-4779	110	40	.	.	PUNCT
ejpam-4779	111	1	d.	d.	PROPN
ejpam-4779	111	2	mohamad	mohamad	PROPN
ejpam-4779	111	3	,	,	PUNCT
ejpam-4779	111	4	n.	n.	PROPN
ejpam-4779	111	5	h.	h.	PROPN
ejpam-4779	111	6	a.	a.	PROPN
ejpam-4779	111	7	a.	a.	PROPN
ejpam-4779	111	8	wahid	wahid	PROPN
ejpam-4779	111	9	,	,	PUNCT
ejpam-4779	111	10	n.	n.	PROPN
ejpam-4779	111	11	n.	n.	PROPN
ejpam-4779	111	12	hasni	hasni	PROPN
ejpam-4779	111	13	/	/	SYM
ejpam-4779	111	14	eur	eur	PROPN
ejpam-4779	111	15	.	.	PUNCT
ejpam-4779	112	1	j.	j.	PROPN
ejpam-4779	112	2	pure	pure	PROPN
ejpam-4779	112	3	appl	appl	PROPN
ejpam-4779	112	4	.	.	PROPN
ejpam-4779	112	5	math	math	PROPN
ejpam-4779	112	6	,	,	PUNCT
ejpam-4779	112	7	16	16	NUM
ejpam-4779	112	8	(	(	PUNCT
ejpam-4779	112	9	2	2	NUM
ejpam-4779	112	10	)	)	PUNCT
ejpam-4779	112	11	(	(	PUNCT
ejpam-4779	112	12	2023	2023	NUM
ejpam-4779	112	13	)	)	PUNCT
ejpam-4779	112	14	,	,	PUNCT
ejpam-4779	112	15	1167	1167	NUM
ejpam-4779	112	16	-	-	SYM
ejpam-4779	112	17	1179	1179	NUM
ejpam-4779	112	18	1172	1172	NUM
ejpam-4779	112	19	proof	proof	NOUN
ejpam-4779	112	20	.	.	PUNCT
ejpam-4779	113	1	since	since	SCONJ
ejpam-4779	113	2	f	f	PROPN
ejpam-4779	113	3	∈	∈	PROPN
ejpam-4779	113	4	s∗	s∗	PROPN
ejpam-4779	113	5	sc	sc	PROPN
ejpam-4779	113	6	(	(	PUNCT
ejpam-4779	113	7	sin	sin	PROPN
ejpam-4779	113	8	z	z	PROPN
ejpam-4779	113	9	)	)	PUNCT
ejpam-4779	113	10	,	,	PUNCT
ejpam-4779	113	11	from	from	ADP
ejpam-4779	113	12	definition	definition	NOUN
ejpam-4779	113	13	of	of	ADP
ejpam-4779	113	14	subordination	subordination	NOUN
ejpam-4779	113	15	,	,	PUNCT
ejpam-4779	113	16	there	there	PRON
ejpam-4779	113	17	exists	exist	VERB
ejpam-4779	113	18	a	a	DET
ejpam-4779	113	19	schwarz	schwarz	NOUN
ejpam-4779	113	20	function	function	NOUN
ejpam-4779	113	21	υ	υ	NOUN
ejpam-4779	113	22	with	with	ADP
ejpam-4779	113	23	υ	υ	PROPN
ejpam-4779	113	24	(	(	PUNCT
ejpam-4779	113	25	0	0	NUM
ejpam-4779	113	26	)	)	PUNCT
ejpam-4779	113	27	=	=	SYM
ejpam-4779	113	28	0	0	NUM
ejpam-4779	113	29	and	and	CCONJ
ejpam-4779	113	30	|υ	|υ	NOUN
ejpam-4779	113	31	(	(	PUNCT
ejpam-4779	113	32	z)|	z)|	X
ejpam-4779	113	33	<	<	X
ejpam-4779	113	34	1	1	NUM
ejpam-4779	113	35	,	,	PUNCT
ejpam-4779	113	36	and	and	CCONJ
ejpam-4779	113	37	from	from	ADP
ejpam-4779	113	38	(	(	PUNCT
ejpam-4779	113	39	2	2	X
ejpam-4779	113	40	)	)	PUNCT
ejpam-4779	113	41	we	we	PRON
ejpam-4779	113	42	have	have	VERB
ejpam-4779	113	43	zf	zf	PROPN
ejpam-4779	113	44	′	′	NUM
ejpam-4779	114	1	(	(	PUNCT
ejpam-4779	114	2	z	z	NOUN
ejpam-4779	114	3	)	)	PUNCT
ejpam-4779	114	4	h	h	NOUN
ejpam-4779	114	5	(	(	PUNCT
ejpam-4779	114	6	z	z	NOUN
ejpam-4779	114	7	)	)	PUNCT
ejpam-4779	114	8	=	=	SYM
ejpam-4779	114	9	1	1	NUM
ejpam-4779	115	1	+	+	CCONJ
ejpam-4779	115	2	sin	sin	NOUN
ejpam-4779	115	3	υ	υ	NOUN
ejpam-4779	115	4	(	(	PUNCT
ejpam-4779	115	5	z	z	NOUN
ejpam-4779	115	6	)	)	PUNCT
ejpam-4779	115	7	,	,	PUNCT
ejpam-4779	115	8	z	z	NOUN
ejpam-4779	115	9	∈	∈	PROPN
ejpam-4779	115	10	e	e	NOUN
ejpam-4779	115	11	,	,	PUNCT
ejpam-4779	115	12	(	(	PUNCT
ejpam-4779	115	13	9	9	X
ejpam-4779	115	14	)	)	PUNCT
ejpam-4779	115	15	where	where	SCONJ
ejpam-4779	115	16	h	h	NOUN
ejpam-4779	115	17	(	(	PUNCT
ejpam-4779	115	18	z	z	NOUN
ejpam-4779	115	19	)	)	PUNCT
ejpam-4779	115	20	=	=	SYM
ejpam-4779	115	21	f(z)−f(−z	f(z)−f(−z	VERB
ejpam-4779	115	22	)	)	PUNCT
ejpam-4779	115	23	2	2	NUM
ejpam-4779	115	24	.	.	PUNCT
ejpam-4779	115	25	assuming	assume	VERB
ejpam-4779	115	26	that	that	SCONJ
ejpam-4779	115	27	p	p	PROPN
ejpam-4779	115	28	(	(	PUNCT
ejpam-4779	115	29	z	z	NOUN
ejpam-4779	115	30	)	)	PUNCT
ejpam-4779	115	31	=	=	SYM
ejpam-4779	115	32	1	1	NUM
ejpam-4779	115	33	+	+	NUM
ejpam-4779	115	34	υ	υ	PROPN
ejpam-4779	115	35	(	(	PUNCT
ejpam-4779	115	36	z	z	NOUN
ejpam-4779	115	37	)	)	PUNCT
ejpam-4779	115	38	1	1	NUM
ejpam-4779	115	39	−	−	NOUN
ejpam-4779	115	40	υ	υ	NOUN
ejpam-4779	115	41	(	(	PUNCT
ejpam-4779	115	42	z	z	NOUN
ejpam-4779	115	43	)	)	PUNCT
ejpam-4779	115	44	=	=	SYM
ejpam-4779	115	45	1	1	NUM
ejpam-4779	115	46	+	+	CCONJ
ejpam-4779	115	47	∞∑	∞∑	NUM
ejpam-4779	115	48	n=1	n=1	PROPN
ejpam-4779	115	49	knz	knz	NOUN
ejpam-4779	115	50	n	n	CCONJ
ejpam-4779	115	51	∈	∈	PROPN
ejpam-4779	115	52	p.	p.	NOUN
ejpam-4779	115	53	this	this	PRON
ejpam-4779	115	54	leads	lead	VERB
ejpam-4779	115	55	to	to	ADP
ejpam-4779	115	56	υ	υ	PROPN
ejpam-4779	115	57	(	(	PUNCT
ejpam-4779	115	58	z	z	NOUN
ejpam-4779	115	59	)	)	PUNCT
ejpam-4779	116	1	=	=	SYM
ejpam-4779	116	2	p	p	X
ejpam-4779	116	3	(	(	PUNCT
ejpam-4779	116	4	z	z	NOUN
ejpam-4779	116	5	)	)	PUNCT
ejpam-4779	116	6	−	−	PROPN
ejpam-4779	116	7	1	1	NUM
ejpam-4779	116	8	p(z	p(z	NOUN
ejpam-4779	116	9	)	)	PUNCT
ejpam-4779	117	1	+	+	CCONJ
ejpam-4779	117	2	1	1	X
ejpam-4779	117	3	.	.	PUNCT
ejpam-4779	118	1	hence	hence	ADV
ejpam-4779	118	2	,	,	PUNCT
ejpam-4779	118	3	from	from	ADP
ejpam-4779	118	4	the	the	DET
ejpam-4779	118	5	right	right	ADJ
ejpam-4779	118	6	-	-	PUNCT
ejpam-4779	118	7	hand	hand	NOUN
ejpam-4779	118	8	side	side	NOUN
ejpam-4779	118	9	of	of	ADP
ejpam-4779	118	10	(	(	PUNCT
ejpam-4779	118	11	9	9	NUM
ejpam-4779	118	12	)	)	PUNCT
ejpam-4779	118	13	,	,	PUNCT
ejpam-4779	118	14	we	we	PRON
ejpam-4779	118	15	obtain	obtain	VERB
ejpam-4779	118	16	1	1	NUM
ejpam-4779	118	17	+	+	CCONJ
ejpam-4779	118	18	sin	sin	NOUN
ejpam-4779	118	19	υ	υ	NOUN
ejpam-4779	118	20	(	(	PUNCT
ejpam-4779	118	21	z	z	NOUN
ejpam-4779	118	22	)	)	PUNCT
ejpam-4779	118	23	=	=	SYM
ejpam-4779	119	1	1	1	NUM
ejpam-4779	119	2	+	+	CCONJ
ejpam-4779	119	3	1	1	NUM
ejpam-4779	119	4	2	2	NUM
ejpam-4779	119	5	k1z	k1z	PROPN
ejpam-4779	119	6	+	+	CCONJ
ejpam-4779	119	7	(	(	PUNCT
ejpam-4779	119	8	k2	k2	ADJ
ejpam-4779	119	9	2	2	NUM
ejpam-4779	119	10	−	−	NOUN
ejpam-4779	119	11	k1	k1	NOUN
ejpam-4779	119	12	2	2	NUM
ejpam-4779	119	13	4	4	NUM
ejpam-4779	119	14	)	)	PUNCT
ejpam-4779	119	15	z2	z2	NOUN
ejpam-4779	119	16	+	+	CCONJ
ejpam-4779	119	17	(	(	PUNCT
ejpam-4779	119	18	5k1	5k1	NUM
ejpam-4779	119	19	3	3	NUM
ejpam-4779	119	20	48	48	NUM
ejpam-4779	119	21	−	−	NOUN
ejpam-4779	119	22	k1k2	k1k2	PROPN
ejpam-4779	119	23	2	2	NUM
ejpam-4779	119	24	+	+	CCONJ
ejpam-4779	119	25	k3	k3	VERB
ejpam-4779	119	26	2	2	NUM
ejpam-4779	119	27	)	)	PUNCT
ejpam-4779	119	28	z3	z3	PROPN
ejpam-4779	120	1	+	+	CCONJ
ejpam-4779	120	2	(	(	PUNCT
ejpam-4779	120	3	k4	k4	NOUN
ejpam-4779	120	4	2	2	NUM
ejpam-4779	120	5	+	+	CCONJ
ejpam-4779	120	6	5k1	5k1	NUM
ejpam-4779	120	7	2k2	2k2	NUM
ejpam-4779	120	8	16	16	NUM
ejpam-4779	120	9	−	−	PROPN
ejpam-4779	120	10	k2	k2	ADJ
ejpam-4779	120	11	2	2	NUM
ejpam-4779	120	12	4	4	NUM
ejpam-4779	120	13	−	−	NOUN
ejpam-4779	120	14	k1k3	k1k3	PROPN
ejpam-4779	120	15	2	2	NUM
ejpam-4779	120	16	−	−	NOUN
ejpam-4779	120	17	k1	k1	NOUN
ejpam-4779	120	18	4	4	NUM
ejpam-4779	120	19	32	32	NUM
ejpam-4779	120	20	)	)	PUNCT
ejpam-4779	120	21	z4	z4	PROPN
ejpam-4779	120	22	+	+	CCONJ
ejpam-4779	120	23	·	·	PUNCT
ejpam-4779	120	24	·	·	PUNCT
ejpam-4779	120	25	·	·	PUNCT
ejpam-4779	120	26	.	.	PUNCT
ejpam-4779	121	1	on	on	ADP
ejpam-4779	121	2	the	the	DET
ejpam-4779	121	3	other	other	ADJ
ejpam-4779	121	4	hand	hand	NOUN
ejpam-4779	121	5	,	,	PUNCT
ejpam-4779	121	6	since	since	SCONJ
ejpam-4779	121	7	f	f	PROPN
ejpam-4779	121	8	of	of	ADP
ejpam-4779	121	9	the	the	DET
ejpam-4779	121	10	form	form	NOUN
ejpam-4779	121	11	(	(	PUNCT
ejpam-4779	121	12	1	1	NUM
ejpam-4779	121	13	)	)	PUNCT
ejpam-4779	121	14	,	,	PUNCT
ejpam-4779	121	15	this	this	PRON
ejpam-4779	121	16	gives	give	VERB
ejpam-4779	121	17	zf	zf	PROPN
ejpam-4779	121	18	′	′	NUM
ejpam-4779	121	19	(	(	PUNCT
ejpam-4779	121	20	z	z	X
ejpam-4779	121	21	)	)	PUNCT
ejpam-4779	121	22	=	=	SYM
ejpam-4779	122	1	z	z	NOUN
ejpam-4779	123	1	+	+	CCONJ
ejpam-4779	123	2	2a2z	2a2z	NOUN
ejpam-4779	123	3	2	2	NUM
ejpam-4779	123	4	+	+	NUM
ejpam-4779	123	5	3a3z	3a3z	NOUN
ejpam-4779	123	6	3	3	NUM
ejpam-4779	123	7	+	+	CCONJ
ejpam-4779	123	8	4a4z	4a4z	ADJ
ejpam-4779	123	9	4	4	NUM
ejpam-4779	123	10	+	+	NUM
ejpam-4779	123	11	5a5z	5a5z	NUM
ejpam-4779	123	12	5	5	NUM
ejpam-4779	123	13	+	+	NUM
ejpam-4779	123	14	·	·	PUNCT
ejpam-4779	123	15	·	·	PUNCT
ejpam-4779	123	16	·	·	PUNCT
ejpam-4779	123	17	and	and	CCONJ
ejpam-4779	123	18	h	h	NOUN
ejpam-4779	123	19	(	(	PUNCT
ejpam-4779	123	20	z	z	NOUN
ejpam-4779	123	21	)	)	PUNCT
ejpam-4779	123	22	=	=	SYM
ejpam-4779	123	23	z	z	X
ejpam-4779	124	1	+	+	CCONJ
ejpam-4779	124	2	a3z	a3z	VERB
ejpam-4779	124	3	3	3	NUM
ejpam-4779	125	1	+	+	CCONJ
ejpam-4779	125	2	a5z	a5z	PROPN
ejpam-4779	125	3	5	5	NUM
ejpam-4779	125	4	+	+	NUM
ejpam-4779	125	5	·	·	PUNCT
ejpam-4779	125	6	·	·	PUNCT
ejpam-4779	125	7	·	·	PUNCT
ejpam-4779	125	8	.	.	PUNCT
ejpam-4779	126	1	further	far	ADV
ejpam-4779	126	2	,	,	PUNCT
ejpam-4779	126	3	we	we	PRON
ejpam-4779	126	4	have	have	VERB
ejpam-4779	126	5	from	from	ADP
ejpam-4779	126	6	(	(	PUNCT
ejpam-4779	126	7	9	9	NUM
ejpam-4779	126	8	)	)	PUNCT
ejpam-4779	126	9	that	that	SCONJ
ejpam-4779	126	10	z	z	VERB
ejpam-4779	127	1	+	+	CCONJ
ejpam-4779	127	2	2a2z	2a2z	NOUN
ejpam-4779	127	3	2	2	NUM
ejpam-4779	127	4	+	+	NUM
ejpam-4779	127	5	3a3z	3a3z	NOUN
ejpam-4779	127	6	3	3	NUM
ejpam-4779	127	7	+	+	CCONJ
ejpam-4779	127	8	4a4z	4a4z	ADJ
ejpam-4779	127	9	4	4	NUM
ejpam-4779	127	10	+	+	NUM
ejpam-4779	127	11	5a5z	5a5z	NUM
ejpam-4779	127	12	5	5	NUM
ejpam-4779	127	13	+	+	NUM
ejpam-4779	127	14	·	·	PUNCT
ejpam-4779	127	15	·	·	PUNCT
ejpam-4779	127	16	·	·	PUNCT
ejpam-4779	128	1	=	=	PUNCT
ejpam-4779	128	2	(	(	PUNCT
ejpam-4779	128	3	z	z	X
ejpam-4779	128	4	+	+	CCONJ
ejpam-4779	128	5	a3z	a3z	VERB
ejpam-4779	128	6	3	3	NUM
ejpam-4779	128	7	+	+	CCONJ
ejpam-4779	128	8	a5z	a5z	PROPN
ejpam-4779	128	9	5	5	NUM
ejpam-4779	128	10	+	+	NUM
ejpam-4779	128	11	·	·	PUNCT
ejpam-4779	128	12	·	·	PUNCT
ejpam-4779	128	13	·	·	PUNCT
ejpam-4779	128	14	)	)	PUNCT
ejpam-4779	129	1	[	[	PUNCT
ejpam-4779	129	2	1	1	NUM
ejpam-4779	129	3	+	+	SYM
ejpam-4779	129	4	1	1	NUM
ejpam-4779	129	5	2	2	NUM
ejpam-4779	129	6	k1z	k1z	PROPN
ejpam-4779	129	7	+	+	CCONJ
ejpam-4779	129	8	(	(	PUNCT
ejpam-4779	129	9	k2	k2	ADJ
ejpam-4779	129	10	2	2	NUM
ejpam-4779	129	11	−	−	NOUN
ejpam-4779	129	12	k1	k1	NOUN
ejpam-4779	129	13	2	2	NUM
ejpam-4779	129	14	4	4	NUM
ejpam-4779	129	15	)	)	PUNCT
ejpam-4779	129	16	z2	z2	NOUN
ejpam-4779	129	17	+	+	CCONJ
ejpam-4779	129	18	(	(	PUNCT
ejpam-4779	129	19	5k1	5k1	NUM
ejpam-4779	129	20	3	3	NUM
ejpam-4779	129	21	48	48	NUM
ejpam-4779	129	22	−	−	NOUN
ejpam-4779	129	23	k1k2	k1k2	PROPN
ejpam-4779	129	24	2	2	NUM
ejpam-4779	129	25	+	+	CCONJ
ejpam-4779	129	26	k3	k3	VERB
ejpam-4779	129	27	2	2	NUM
ejpam-4779	129	28	)	)	PUNCT
ejpam-4779	129	29	z3	z3	PROPN
ejpam-4779	130	1	+	+	CCONJ
ejpam-4779	130	2	(	(	PUNCT
ejpam-4779	130	3	k4	k4	NOUN
ejpam-4779	130	4	2	2	NUM
ejpam-4779	130	5	+	+	CCONJ
ejpam-4779	130	6	5k1	5k1	NUM
ejpam-4779	130	7	2k2	2k2	NUM
ejpam-4779	130	8	16	16	NUM
ejpam-4779	130	9	−	−	PROPN
ejpam-4779	130	10	k2	k2	ADJ
ejpam-4779	130	11	2	2	NUM
ejpam-4779	130	12	4	4	NUM
ejpam-4779	130	13	−	−	NOUN
ejpam-4779	130	14	k1k3	k1k3	PROPN
ejpam-4779	130	15	2	2	NUM
ejpam-4779	130	16	−	−	NOUN
ejpam-4779	130	17	k1	k1	NOUN
ejpam-4779	130	18	4	4	NUM
ejpam-4779	130	19	32	32	NUM
ejpam-4779	130	20	)	)	PUNCT
ejpam-4779	130	21	z4	z4	PROPN
ejpam-4779	130	22	+	+	CCONJ
ejpam-4779	130	23	·	·	PUNCT
ejpam-4779	130	24	·	·	PUNCT
ejpam-4779	130	25	·	·	PUNCT
ejpam-4779	130	26	]	]	PUNCT
ejpam-4779	130	27	.	.	PUNCT
ejpam-4779	131	1	(	(	PUNCT
ejpam-4779	131	2	10	10	NUM
ejpam-4779	131	3	)	)	PUNCT
ejpam-4779	131	4	expanding	expand	VERB
ejpam-4779	131	5	the	the	DET
ejpam-4779	131	6	series	series	NOUN
ejpam-4779	131	7	and	and	CCONJ
ejpam-4779	131	8	comparing	compare	VERB
ejpam-4779	131	9	the	the	DET
ejpam-4779	131	10	coefficients	coefficient	NOUN
ejpam-4779	131	11	of	of	ADP
ejpam-4779	131	12	zn	zn	PROPN
ejpam-4779	131	13	,	,	PUNCT
ejpam-4779	131	14	n	n	PROPN
ejpam-4779	131	15	=	=	SYM
ejpam-4779	131	16	1	1	NUM
ejpam-4779	131	17	,	,	PUNCT
ejpam-4779	131	18	2	2	NUM
ejpam-4779	131	19	,	,	PUNCT
ejpam-4779	131	20	3	3	NUM
ejpam-4779	131	21	,	,	PUNCT
ejpam-4779	131	22	4	4	NUM
ejpam-4779	131	23	,	,	PUNCT
ejpam-4779	131	24	5	5	NUM
ejpam-4779	131	25	on	on	ADP
ejpam-4779	131	26	both	both	DET
ejpam-4779	131	27	sides	side	NOUN
ejpam-4779	131	28	of	of	ADP
ejpam-4779	131	29	(	(	PUNCT
ejpam-4779	131	30	10	10	NUM
ejpam-4779	131	31	)	)	PUNCT
ejpam-4779	131	32	yields	yield	NOUN
ejpam-4779	131	33	a2	a2	NOUN
ejpam-4779	131	34	=	=	SYM
ejpam-4779	131	35	k1	k1	PROPN
ejpam-4779	131	36	4	4	NUM
ejpam-4779	131	37	,	,	PUNCT
ejpam-4779	131	38	(	(	PUNCT
ejpam-4779	131	39	11	11	NUM
ejpam-4779	131	40	)	)	PUNCT
ejpam-4779	131	41	a3	a3	NOUN
ejpam-4779	131	42	=	=	NOUN
ejpam-4779	131	43	1	1	NUM
ejpam-4779	131	44	8	8	NUM
ejpam-4779	131	45	(	(	PUNCT
ejpam-4779	131	46	2k2	2k2	NUM
ejpam-4779	131	47	−	−	PRON
ejpam-4779	131	48	k1	k1	NOUN
ejpam-4779	131	49	2	2	NUM
ejpam-4779	131	50	)	)	PUNCT
ejpam-4779	131	51	,	,	PUNCT
ejpam-4779	131	52	(	(	PUNCT
ejpam-4779	131	53	12	12	NUM
ejpam-4779	131	54	)	)	PUNCT
ejpam-4779	131	55	a4	a4	NOUN
ejpam-4779	131	56	=	=	SYM
ejpam-4779	131	57	1	1	NUM
ejpam-4779	131	58	96	96	NUM
ejpam-4779	131	59	(	(	PUNCT
ejpam-4779	131	60	k1	k1	PROPN
ejpam-4779	131	61	3	3	NUM
ejpam-4779	131	62	−	−	PROPN
ejpam-4779	131	63	9k1k2	9k1k2	PROPN
ejpam-4779	132	1	+	+	CCONJ
ejpam-4779	133	1	12k3	12k3	NUM
ejpam-4779	133	2	)	)	PUNCT
ejpam-4779	133	3	,	,	PUNCT
ejpam-4779	133	4	(	(	PUNCT
ejpam-4779	133	5	13	13	X
ejpam-4779	133	6	)	)	PUNCT
ejpam-4779	133	7	d.	d.	PROPN
ejpam-4779	133	8	mohamad	mohamad	PROPN
ejpam-4779	133	9	,	,	PUNCT
ejpam-4779	133	10	n.	n.	PROPN
ejpam-4779	133	11	h.	h.	PROPN
ejpam-4779	133	12	a.	a.	PROPN
ejpam-4779	133	13	a.	a.	PROPN
ejpam-4779	133	14	wahid	wahid	PROPN
ejpam-4779	133	15	,	,	PUNCT
ejpam-4779	133	16	n.	n.	PROPN
ejpam-4779	133	17	n.	n.	PROPN
ejpam-4779	133	18	hasni	hasni	PROPN
ejpam-4779	133	19	/	/	SYM
ejpam-4779	133	20	eur	eur	PROPN
ejpam-4779	133	21	.	.	PUNCT
ejpam-4779	134	1	j.	j.	PROPN
ejpam-4779	134	2	pure	pure	PROPN
ejpam-4779	134	3	appl	appl	PROPN
ejpam-4779	134	4	.	.	PROPN
ejpam-4779	134	5	math	math	PROPN
ejpam-4779	134	6	,	,	PUNCT
ejpam-4779	134	7	16	16	NUM
ejpam-4779	134	8	(	(	PUNCT
ejpam-4779	134	9	2	2	NUM
ejpam-4779	134	10	)	)	PUNCT
ejpam-4779	134	11	(	(	PUNCT
ejpam-4779	134	12	2023	2023	NUM
ejpam-4779	134	13	)	)	PUNCT
ejpam-4779	134	14	,	,	PUNCT
ejpam-4779	134	15	1167	1167	NUM
ejpam-4779	134	16	-	-	SYM
ejpam-4779	134	17	1179	1179	NUM
ejpam-4779	134	18	1173	1173	NUM
ejpam-4779	134	19	and	and	CCONJ
ejpam-4779	134	20	a5	a5	PROPN
ejpam-4779	134	21	=	=	PUNCT
ejpam-4779	134	22	1	1	NUM
ejpam-4779	134	23	64	64	NUM
ejpam-4779	134	24	(	(	PUNCT
ejpam-4779	134	25	8k4	8k4	NUM
ejpam-4779	134	26	+	+	CCONJ
ejpam-4779	134	27	3k1	3k1	NUM
ejpam-4779	134	28	2k2	2k2	NUM
ejpam-4779	134	29	−	−	NOUN
ejpam-4779	134	30	2k2	2k2	NUM
ejpam-4779	134	31	2	2	NUM
ejpam-4779	134	32	−	−	NOUN
ejpam-4779	134	33	8k1k3	8k1k3	NUM
ejpam-4779	134	34	)	)	PUNCT
ejpam-4779	134	35	.	.	PUNCT
ejpam-4779	135	1	(	(	PUNCT
ejpam-4779	135	2	14	14	NUM
ejpam-4779	135	3	)	)	PUNCT
ejpam-4779	135	4	using	use	VERB
ejpam-4779	135	5	triangle	triangle	NOUN
ejpam-4779	135	6	inequality	inequality	NOUN
ejpam-4779	135	7	and	and	CCONJ
ejpam-4779	135	8	lemma	lemma	PROPN
ejpam-4779	135	9	1	1	NUM
ejpam-4779	135	10	in	in	ADP
ejpam-4779	135	11	(	(	PUNCT
ejpam-4779	135	12	11	11	NUM
ejpam-4779	135	13	)	)	PUNCT
ejpam-4779	135	14	,	,	PUNCT
ejpam-4779	135	15	we	we	PRON
ejpam-4779	135	16	get	get	AUX
ejpam-4779	135	17	|a2|	|a2|	NOUN
ejpam-4779	135	18	⩽	⩽	ADJ
ejpam-4779	135	19	1	1	NUM
ejpam-4779	135	20	2	2	NUM
ejpam-4779	135	21	.	.	PUNCT
ejpam-4779	136	1	now	now	ADV
ejpam-4779	136	2	,	,	PUNCT
ejpam-4779	136	3	applying	apply	VERB
ejpam-4779	136	4	lemma	lemma	PROPN
ejpam-4779	136	5	2	2	NUM
ejpam-4779	136	6	in	in	ADP
ejpam-4779	136	7	(	(	PUNCT
ejpam-4779	136	8	12	12	NUM
ejpam-4779	136	9	)	)	PUNCT
ejpam-4779	136	10	and	and	CCONJ
ejpam-4779	136	11	lemma	lemma	PROPN
ejpam-4779	136	12	3	3	NUM
ejpam-4779	136	13	in	in	ADP
ejpam-4779	136	14	(	(	PUNCT
ejpam-4779	136	15	13	13	NUM
ejpam-4779	136	16	)	)	PUNCT
ejpam-4779	136	17	,	,	PUNCT
ejpam-4779	136	18	respectively	respectively	ADV
ejpam-4779	136	19	,	,	PUNCT
ejpam-4779	136	20	implies	imply	VERB
ejpam-4779	136	21	that	that	SCONJ
ejpam-4779	136	22	|a3|	|a3|	VERB
ejpam-4779	136	23	=	=	NOUN
ejpam-4779	136	24	1	1	NUM
ejpam-4779	136	25	8	8	NUM
ejpam-4779	136	26	∣∣2k2	∣∣2k2	NOUN
ejpam-4779	136	27	−	−	PROPN
ejpam-4779	136	28	k1	k1	NOUN
ejpam-4779	136	29	2	2	NUM
ejpam-4779	136	30	∣∣	∣∣	NUM
ejpam-4779	136	31	⩽	⩽	ADJ
ejpam-4779	136	32	1	1	NUM
ejpam-4779	136	33	4	4	NUM
ejpam-4779	136	34	[	[	PUNCT
ejpam-4779	136	35	2max	2max	NUM
ejpam-4779	136	36	{	{	PUNCT
ejpam-4779	136	37	1	1	NUM
ejpam-4779	136	38	,	,	PUNCT
ejpam-4779	136	39	∣∣∣∣2(1	∣∣∣∣2(1	PROPN
ejpam-4779	136	40	2	2	NUM
ejpam-4779	136	41	)	)	PUNCT
ejpam-4779	136	42	−	−	PROPN
ejpam-4779	136	43	1	1	NUM
ejpam-4779	136	44	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4779	136	45	}	}	PUNCT
ejpam-4779	136	46	]	]	PUNCT
ejpam-4779	137	1	=	=	SYM
ejpam-4779	137	2	1	1	NUM
ejpam-4779	137	3	2	2	NUM
ejpam-4779	137	4	and	and	CCONJ
ejpam-4779	137	5	|a4|	|a4|	PRON
ejpam-4779	137	6	=	=	SYM
ejpam-4779	137	7	1	1	NUM
ejpam-4779	137	8	96	96	NUM
ejpam-4779	137	9	∣∣k13	∣∣k13	PROPN
ejpam-4779	137	10	−	−	PROPN
ejpam-4779	137	11	9k1k2	9k1k2	PROPN
ejpam-4779	138	1	+	+	CCONJ
ejpam-4779	139	1	12k3	12k3	NUM
ejpam-4779	139	2	∣∣	∣∣	NUM
ejpam-4779	139	3	⩽	⩽	ADJ
ejpam-4779	139	4	1	1	NUM
ejpam-4779	139	5	96	96	NUM
ejpam-4779	139	6	[	[	SYM
ejpam-4779	139	7	2	2	NUM
ejpam-4779	139	8	|1|	|1|	NOUN
ejpam-4779	139	9	+	+	NUM
ejpam-4779	139	10	2	2	NUM
ejpam-4779	139	11	|9	|9	NUM
ejpam-4779	139	12	−	−	PROPN
ejpam-4779	139	13	2	2	NUM
ejpam-4779	139	14	(	(	PUNCT
ejpam-4779	139	15	1)|	1)|	NUM
ejpam-4779	139	16	+	+	CCONJ
ejpam-4779	139	17	2	2	NUM
ejpam-4779	139	18	|1	|1	NUM
ejpam-4779	139	19	−	−	NUM
ejpam-4779	139	20	9	9	NUM
ejpam-4779	139	21	+	+	CCONJ
ejpam-4779	139	22	12|	12|	NUM
ejpam-4779	139	23	]	]	X
ejpam-4779	139	24	=	=	SYM
ejpam-4779	139	25	1	1	NUM
ejpam-4779	139	26	4	4	NUM
ejpam-4779	139	27	.	.	PUNCT
ejpam-4779	140	1	rearranging	rearrange	VERB
ejpam-4779	140	2	the	the	DET
ejpam-4779	140	3	terms	term	NOUN
ejpam-4779	140	4	in	in	ADP
ejpam-4779	140	5	(	(	PUNCT
ejpam-4779	140	6	14	14	NUM
ejpam-4779	140	7	)	)	PUNCT
ejpam-4779	140	8	,	,	PUNCT
ejpam-4779	140	9	we	we	PRON
ejpam-4779	140	10	can	can	AUX
ejpam-4779	140	11	rewrite	rewrite	VERB
ejpam-4779	140	12	it	it	PRON
ejpam-4779	140	13	as	as	SCONJ
ejpam-4779	140	14	|a5|	|a5|	VERB
ejpam-4779	140	15	=	=	SYM
ejpam-4779	140	16	1	1	NUM
ejpam-4779	140	17	64	64	NUM
ejpam-4779	140	18	∣∣8	∣∣8	PROPN
ejpam-4779	140	19	(	(	PUNCT
ejpam-4779	140	20	k4	k4	VERB
ejpam-4779	140	21	−	−	PROPN
ejpam-4779	140	22	ν1k1k3	ν1k1k3	NOUN
ejpam-4779	140	23	)	)	PUNCT
ejpam-4779	140	24	−	−	PROPN
ejpam-4779	141	1	2k2	2k2	NUM
ejpam-4779	141	2	(	(	PUNCT
ejpam-4779	141	3	k2	k2	ADJ
ejpam-4779	141	4	−	−	PROPN
ejpam-4779	141	5	ν2k1	ν2k1	NOUN
ejpam-4779	141	6	2	2	NUM
ejpam-4779	141	7	)	)	PUNCT
ejpam-4779	141	8	∣∣	∣∣	NUM
ejpam-4779	141	9	,	,	PUNCT
ejpam-4779	141	10	where	where	SCONJ
ejpam-4779	141	11	ν1	ν1	NOUN
ejpam-4779	141	12	=	=	SYM
ejpam-4779	141	13	1	1	NUM
ejpam-4779	141	14	and	and	CCONJ
ejpam-4779	141	15	ν2	ν2	NOUN
ejpam-4779	141	16	=	=	SYM
ejpam-4779	141	17	3	3	NUM
ejpam-4779	141	18	2	2	NUM
ejpam-4779	141	19	.	.	PUNCT
ejpam-4779	142	1	consequently	consequently	ADV
ejpam-4779	142	2	,	,	PUNCT
ejpam-4779	142	3	by	by	ADP
ejpam-4779	142	4	applying	apply	VERB
ejpam-4779	142	5	lemma	lemma	PROPN
ejpam-4779	142	6	1	1	NUM
ejpam-4779	142	7	and	and	CCONJ
ejpam-4779	142	8	lemma	lemma	PROPN
ejpam-4779	142	9	2	2	NUM
ejpam-4779	142	10	as	as	ADV
ejpam-4779	142	11	well	well	ADV
ejpam-4779	142	12	as	as	ADP
ejpam-4779	142	13	the	the	DET
ejpam-4779	142	14	triangle	triangle	NOUN
ejpam-4779	142	15	inequality	inequality	NOUN
ejpam-4779	142	16	,	,	PUNCT
ejpam-4779	142	17	we	we	PRON
ejpam-4779	142	18	obtain	obtain	AUX
ejpam-4779	142	19	|a5|	|a5|	VERB
ejpam-4779	142	20	⩽	⩽	ADJ
ejpam-4779	142	21	1	1	NUM
ejpam-4779	142	22	2	2	NUM
ejpam-4779	142	23	.	.	PUNCT
ejpam-4779	143	1	this	this	PRON
ejpam-4779	143	2	completes	complete	VERB
ejpam-4779	143	3	the	the	DET
ejpam-4779	143	4	proof	proof	NOUN
ejpam-4779	143	5	of	of	ADP
ejpam-4779	143	6	theorem	theorem	NOUN
ejpam-4779	143	7	1	1	NUM
ejpam-4779	143	8	.	.	NOUN
ejpam-4779	143	9	3.2	3.2	NUM
ejpam-4779	143	10	.	.	PUNCT
ejpam-4779	144	1	logarithmic	logarithmic	ADJ
ejpam-4779	144	2	coefficients	coefficient	NOUN
ejpam-4779	144	3	theorem	theorem	VERB
ejpam-4779	144	4	2	2	NUM
ejpam-4779	144	5	.	.	PUNCT
ejpam-4779	145	1	if	if	SCONJ
ejpam-4779	145	2	f	f	PROPN
ejpam-4779	145	3	is	be	AUX
ejpam-4779	145	4	of	of	ADP
ejpam-4779	145	5	the	the	DET
ejpam-4779	145	6	form	form	NOUN
ejpam-4779	145	7	(	(	PUNCT
ejpam-4779	145	8	1	1	X
ejpam-4779	145	9	)	)	PUNCT
ejpam-4779	145	10	belongs	belong	VERB
ejpam-4779	145	11	to	to	PART
ejpam-4779	145	12	s∗	s∗	PROPN
ejpam-4779	145	13	sc	sc	PROPN
ejpam-4779	145	14	(	(	PUNCT
ejpam-4779	145	15	sin	sin	PROPN
ejpam-4779	145	16	z	z	PROPN
ejpam-4779	145	17	)	)	PUNCT
ejpam-4779	145	18	,	,	PUNCT
ejpam-4779	145	19	then	then	ADV
ejpam-4779	145	20	|γ1|	|γ1|	X
ejpam-4779	145	21	⩽	⩽	NOUN
ejpam-4779	145	22	1	1	NUM
ejpam-4779	145	23	4	4	NUM
ejpam-4779	145	24	,	,	PUNCT
ejpam-4779	145	25	|γ2|	|γ2|	ADJ
ejpam-4779	145	26	⩽	⩽	ADJ
ejpam-4779	145	27	1	1	NUM
ejpam-4779	145	28	4	4	NUM
ejpam-4779	145	29	,	,	PUNCT
ejpam-4779	145	30	|γ3|	|γ3|	ADJ
ejpam-4779	145	31	⩽	⩽	ADJ
ejpam-4779	145	32	1	1	NUM
ejpam-4779	145	33	8	8	NUM
ejpam-4779	145	34	,	,	PUNCT
ejpam-4779	145	35	and	and	CCONJ
ejpam-4779	145	36	|γ4|	|γ4|	NOUN
ejpam-4779	145	37	⩽	⩽	NOUN
ejpam-4779	145	38	7	7	NUM
ejpam-4779	145	39	16	16	NUM
ejpam-4779	145	40	.	.	PUNCT
ejpam-4779	146	1	proof	proof	NOUN
ejpam-4779	146	2	.	.	PUNCT
ejpam-4779	147	1	putting	put	VERB
ejpam-4779	147	2	(	(	PUNCT
ejpam-4779	147	3	11)-(14	11)-(14	NOUN
ejpam-4779	147	4	)	)	PUNCT
ejpam-4779	147	5	in	in	ADP
ejpam-4779	147	6	(	(	PUNCT
ejpam-4779	147	7	5)-(8	5)-(8	NUM
ejpam-4779	147	8	)	)	PUNCT
ejpam-4779	147	9	,	,	PUNCT
ejpam-4779	147	10	we	we	PRON
ejpam-4779	147	11	obtain	obtain	VERB
ejpam-4779	147	12	γ1	γ1	NOUN
ejpam-4779	147	13	=	=	SYM
ejpam-4779	147	14	k1	k1	PROPN
ejpam-4779	147	15	8	8	NUM
ejpam-4779	147	16	,	,	PUNCT
ejpam-4779	147	17	(	(	PUNCT
ejpam-4779	147	18	15	15	NUM
ejpam-4779	147	19	)	)	PUNCT
ejpam-4779	147	20	d.	d.	PROPN
ejpam-4779	147	21	mohamad	mohamad	PROPN
ejpam-4779	147	22	,	,	PUNCT
ejpam-4779	147	23	n.	n.	PROPN
ejpam-4779	147	24	h.	h.	PROPN
ejpam-4779	147	25	a.	a.	PROPN
ejpam-4779	147	26	a.	a.	PROPN
ejpam-4779	147	27	wahid	wahid	PROPN
ejpam-4779	147	28	,	,	PUNCT
ejpam-4779	147	29	n.	n.	PROPN
ejpam-4779	147	30	n.	n.	PROPN
ejpam-4779	147	31	hasni	hasni	PROPN
ejpam-4779	147	32	/	/	SYM
ejpam-4779	147	33	eur	eur	PROPN
ejpam-4779	147	34	.	.	PUNCT
ejpam-4779	148	1	j.	j.	PROPN
ejpam-4779	148	2	pure	pure	PROPN
ejpam-4779	148	3	appl	appl	PROPN
ejpam-4779	148	4	.	.	PROPN
ejpam-4779	148	5	math	math	PROPN
ejpam-4779	148	6	,	,	PUNCT
ejpam-4779	148	7	16	16	NUM
ejpam-4779	148	8	(	(	PUNCT
ejpam-4779	148	9	2	2	NUM
ejpam-4779	148	10	)	)	PUNCT
ejpam-4779	148	11	(	(	PUNCT
ejpam-4779	148	12	2023	2023	NUM
ejpam-4779	148	13	)	)	PUNCT
ejpam-4779	148	14	,	,	PUNCT
ejpam-4779	148	15	1167	1167	NUM
ejpam-4779	148	16	-	-	SYM
ejpam-4779	148	17	1179	1179	NUM
ejpam-4779	148	18	1174	1174	NUM
ejpam-4779	148	19	γ2	γ2	NOUN
ejpam-4779	148	20	=	=	NOUN
ejpam-4779	148	21	1	1	NUM
ejpam-4779	148	22	2	2	NUM
ejpam-4779	148	23	[	[	PUNCT
ejpam-4779	148	24	1	1	NUM
ejpam-4779	148	25	8	8	NUM
ejpam-4779	148	26	(	(	PUNCT
ejpam-4779	148	27	2k2	2k2	NUM
ejpam-4779	148	28	−	−	PRON
ejpam-4779	148	29	k1	k1	NOUN
ejpam-4779	148	30	2	2	NUM
ejpam-4779	148	31	)	)	PUNCT
ejpam-4779	148	32	−	−	NOUN
ejpam-4779	148	33	1	1	NUM
ejpam-4779	148	34	2	2	NUM
ejpam-4779	148	35	(	(	PUNCT
ejpam-4779	148	36	k1	k1	PROPN
ejpam-4779	148	37	4	4	NUM
ejpam-4779	148	38	)	)	PUNCT
ejpam-4779	148	39	2	2	NUM
ejpam-4779	148	40	]	]	PUNCT
ejpam-4779	148	41	=	=	SYM
ejpam-4779	148	42	1	1	NUM
ejpam-4779	148	43	8	8	NUM
ejpam-4779	148	44	(	(	PUNCT
ejpam-4779	148	45	k2	k2	ADJ
ejpam-4779	148	46	−	−	PROPN
ejpam-4779	148	47	5	5	NUM
ejpam-4779	148	48	8	8	NUM
ejpam-4779	148	49	k1	k1	NOUN
ejpam-4779	148	50	2	2	NUM
ejpam-4779	148	51	)	)	PUNCT
ejpam-4779	148	52	,	,	PUNCT
ejpam-4779	148	53	(	(	PUNCT
ejpam-4779	148	54	16	16	X
ejpam-4779	148	55	)	)	PUNCT
ejpam-4779	148	56	γ3	γ3	NOUN
ejpam-4779	148	57	=	=	NOUN
ejpam-4779	148	58	1	1	NUM
ejpam-4779	148	59	2	2	NUM
ejpam-4779	148	60	[	[	PUNCT
ejpam-4779	148	61	1	1	NUM
ejpam-4779	148	62	96	96	NUM
ejpam-4779	148	63	(	(	PUNCT
ejpam-4779	148	64	k1	k1	PROPN
ejpam-4779	148	65	3	3	NUM
ejpam-4779	148	66	−	−	PROPN
ejpam-4779	148	67	9k1k2	9k1k2	PROPN
ejpam-4779	148	68	+	+	CCONJ
ejpam-4779	148	69	12k3	12k3	NUM
ejpam-4779	148	70	)	)	PUNCT
ejpam-4779	148	71	−	−	PROPN
ejpam-4779	149	1	(	(	PUNCT
ejpam-4779	149	2	k1	k1	PROPN
ejpam-4779	149	3	4	4	NUM
ejpam-4779	149	4	)	)	PUNCT
ejpam-4779	149	5	(	(	PUNCT
ejpam-4779	149	6	1	1	NUM
ejpam-4779	149	7	8	8	NUM
ejpam-4779	149	8	(	(	PUNCT
ejpam-4779	149	9	2k2	2k2	NUM
ejpam-4779	149	10	−	−	PRON
ejpam-4779	149	11	k1	k1	NOUN
ejpam-4779	149	12	2	2	NUM
ejpam-4779	149	13	)	)	PUNCT
ejpam-4779	149	14	)	)	PUNCT
ejpam-4779	150	1	+	+	CCONJ
ejpam-4779	150	2	1	1	NUM
ejpam-4779	150	3	3	3	NUM
ejpam-4779	150	4	(	(	PUNCT
ejpam-4779	150	5	k1	k1	PROPN
ejpam-4779	150	6	4	4	NUM
ejpam-4779	150	7	)	)	PUNCT
ejpam-4779	150	8	3	3	NUM
ejpam-4779	150	9	]	]	PUNCT
ejpam-4779	150	10	=	=	SYM
ejpam-4779	150	11	1	1	NUM
ejpam-4779	150	12	128	128	NUM
ejpam-4779	150	13	(	(	PUNCT
ejpam-4779	150	14	3k1	3k1	NUM
ejpam-4779	150	15	3	3	NUM
ejpam-4779	150	16	−	−	PROPN
ejpam-4779	150	17	10k1k2	10k1k2	NOUN
ejpam-4779	150	18	+	+	CCONJ
ejpam-4779	150	19	8k3	8k3	NUM
ejpam-4779	150	20	)	)	PUNCT
ejpam-4779	150	21	,	,	PUNCT
ejpam-4779	150	22	(	(	PUNCT
ejpam-4779	150	23	17	17	NUM
ejpam-4779	150	24	)	)	PUNCT
ejpam-4779	150	25	and	and	CCONJ
ejpam-4779	150	26	γ4	γ4	NOUN
ejpam-4779	150	27	=	=	SYM
ejpam-4779	150	28	1	1	NUM
ejpam-4779	150	29	2	2	NUM
ejpam-4779	150	30	[	[	PUNCT
ejpam-4779	150	31	1	1	NUM
ejpam-4779	150	32	64	64	NUM
ejpam-4779	150	33	(	(	PUNCT
ejpam-4779	150	34	8k4	8k4	NUM
ejpam-4779	150	35	+	+	CCONJ
ejpam-4779	150	36	3k1	3k1	NUM
ejpam-4779	150	37	2k2	2k2	NUM
ejpam-4779	150	38	−	−	NOUN
ejpam-4779	150	39	2k2	2k2	NUM
ejpam-4779	150	40	2	2	NUM
ejpam-4779	150	41	−	−	NOUN
ejpam-4779	150	42	8k1k3	8k1k3	NUM
ejpam-4779	150	43	)	)	PUNCT
ejpam-4779	151	1	−	−	ADP
ejpam-4779	151	2	k1	k1	NOUN
ejpam-4779	151	3	4	4	NUM
ejpam-4779	151	4	(	(	PUNCT
ejpam-4779	151	5	1	1	NUM
ejpam-4779	151	6	96	96	NUM
ejpam-4779	151	7	(	(	PUNCT
ejpam-4779	151	8	k1	k1	PROPN
ejpam-4779	151	9	3	3	NUM
ejpam-4779	151	10	−	−	PROPN
ejpam-4779	151	11	9k1k2	9k1k2	PROPN
ejpam-4779	151	12	+	+	CCONJ
ejpam-4779	151	13	12k3	12k3	NUM
ejpam-4779	151	14	)	)	PUNCT
ejpam-4779	151	15	)	)	PUNCT
ejpam-4779	152	1	+	+	CCONJ
ejpam-4779	152	2	(	(	PUNCT
ejpam-4779	152	3	k1	k1	PROPN
ejpam-4779	152	4	4	4	NUM
ejpam-4779	152	5	)	)	PUNCT
ejpam-4779	152	6	2(1	2(1	NUM
ejpam-4779	152	7	8	8	NUM
ejpam-4779	152	8	(	(	PUNCT
ejpam-4779	152	9	2k2	2k2	NUM
ejpam-4779	152	10	−	−	PRON
ejpam-4779	152	11	k1	k1	NOUN
ejpam-4779	152	12	2	2	NUM
ejpam-4779	152	13	)	)	PUNCT
ejpam-4779	152	14	)	)	PUNCT
ejpam-4779	153	1	−	−	NOUN
ejpam-4779	153	2	1	1	NUM
ejpam-4779	153	3	2	2	NUM
ejpam-4779	153	4	(	(	PUNCT
ejpam-4779	153	5	1	1	NUM
ejpam-4779	153	6	8	8	NUM
ejpam-4779	153	7	(	(	PUNCT
ejpam-4779	153	8	2k2	2k2	NUM
ejpam-4779	153	9	−	−	PRON
ejpam-4779	153	10	k1	k1	NOUN
ejpam-4779	153	11	2	2	NUM
ejpam-4779	153	12	)	)	PUNCT
ejpam-4779	153	13	)	)	PUNCT
ejpam-4779	153	14	2	2	NUM
ejpam-4779	153	15	−	−	NOUN
ejpam-4779	153	16	1	1	NUM
ejpam-4779	153	17	4	4	NUM
ejpam-4779	153	18	(	(	PUNCT
ejpam-4779	153	19	k1	k1	PROPN
ejpam-4779	153	20	4	4	NUM
ejpam-4779	153	21	)	)	PUNCT
ejpam-4779	153	22	4	4	NUM
ejpam-4779	153	23	]	]	PUNCT
ejpam-4779	153	24	=	=	SYM
ejpam-4779	153	25	1	1	NUM
ejpam-4779	153	26	6144	6144	NUM
ejpam-4779	153	27	(	(	PUNCT
ejpam-4779	153	28	384k4	384k4	NUM
ejpam-4779	153	29	+	+	SYM
ejpam-4779	153	30	360k1	360k1	NUM
ejpam-4779	153	31	2k2	2k2	NUM
ejpam-4779	153	32	−	−	NUM
ejpam-4779	153	33	192k2	192k2	NUM
ejpam-4779	153	34	2	2	NUM
ejpam-4779	153	35	−	−	PROPN
ejpam-4779	153	36	480k1k3	480k1k3	NOUN
ejpam-4779	153	37	−	−	PROPN
ejpam-4779	153	38	59k1	59k1	NUM
ejpam-4779	153	39	4	4	NUM
ejpam-4779	153	40	)	)	PUNCT
ejpam-4779	153	41	.	.	PUNCT
ejpam-4779	154	1	(	(	PUNCT
ejpam-4779	154	2	18	18	NUM
ejpam-4779	154	3	)	)	PUNCT
ejpam-4779	154	4	the	the	DET
ejpam-4779	154	5	bounds	bound	NOUN
ejpam-4779	154	6	of	of	ADP
ejpam-4779	154	7	|γ1|	|γ1|	NOUN
ejpam-4779	154	8	,	,	PUNCT
ejpam-4779	154	9	|γ2|	|γ2|	INTJ
ejpam-4779	154	10	,	,	PUNCT
ejpam-4779	154	11	and	and	CCONJ
ejpam-4779	154	12	|γ3|	|γ3|	ADP
ejpam-4779	154	13	follow	follow	NOUN
ejpam-4779	154	14	from	from	ADP
ejpam-4779	154	15	lemma	lemma	PROPN
ejpam-4779	154	16	1	1	NUM
ejpam-4779	154	17	,	,	PUNCT
ejpam-4779	154	18	lemma	lemma	PROPN
ejpam-4779	154	19	2	2	NUM
ejpam-4779	154	20	,	,	PUNCT
ejpam-4779	154	21	and	and	CCONJ
ejpam-4779	154	22	lemma	lemma	PROPN
ejpam-4779	154	23	3	3	NUM
ejpam-4779	154	24	,	,	PUNCT
ejpam-4779	154	25	respectively	respectively	ADV
ejpam-4779	154	26	.	.	PUNCT
ejpam-4779	155	1	on	on	ADP
ejpam-4779	155	2	the	the	DET
ejpam-4779	155	3	other	other	ADJ
ejpam-4779	155	4	hand	hand	NOUN
ejpam-4779	155	5	,	,	PUNCT
ejpam-4779	155	6	rearranging	rearrange	VERB
ejpam-4779	155	7	the	the	DET
ejpam-4779	155	8	terms	term	NOUN
ejpam-4779	155	9	in	in	ADP
ejpam-4779	155	10	(	(	PUNCT
ejpam-4779	155	11	18	18	NUM
ejpam-4779	155	12	)	)	PUNCT
ejpam-4779	155	13	,	,	PUNCT
ejpam-4779	155	14	we	we	PRON
ejpam-4779	155	15	get	get	VERB
ejpam-4779	155	16	γ4	γ4	NOUN
ejpam-4779	155	17	=	=	SYM
ejpam-4779	155	18	1	1	NUM
ejpam-4779	155	19	6144	6144	NUM
ejpam-4779	155	20	(	(	PUNCT
ejpam-4779	155	21	384	384	NUM
ejpam-4779	155	22	(	(	PUNCT
ejpam-4779	155	23	k4	k4	NOUN
ejpam-4779	155	24	−	−	PROPN
ejpam-4779	155	25	µk2	µk2	NOUN
ejpam-4779	155	26	2	2	NUM
ejpam-4779	155	27	)	)	PUNCT
ejpam-4779	156	1	−	−	PROPN
ejpam-4779	156	2	k1	k1	NOUN
ejpam-4779	157	1	(	(	PUNCT
ejpam-4779	157	2	αk1	αk1	NOUN
ejpam-4779	157	3	3	3	NUM
ejpam-4779	157	4	−	−	NOUN
ejpam-4779	158	1	βk1k2	βk1k2	PUNCT
ejpam-4779	158	2	+	+	NUM
ejpam-4779	158	3	γk3	γk3	NOUN
ejpam-4779	158	4	)	)	PUNCT
ejpam-4779	158	5	)	)	PUNCT
ejpam-4779	158	6	,	,	PUNCT
ejpam-4779	159	1	where	where	SCONJ
ejpam-4779	159	2	µ	µ	X
ejpam-4779	159	3	=	=	SYM
ejpam-4779	159	4	1	1	NUM
ejpam-4779	159	5	2	2	NUM
ejpam-4779	159	6	,	,	PUNCT
ejpam-4779	159	7	α	α	NOUN
ejpam-4779	159	8	=	=	SYM
ejpam-4779	159	9	59	59	NUM
ejpam-4779	159	10	,	,	PUNCT
ejpam-4779	159	11	β	β	X
ejpam-4779	159	12	=	=	SYM
ejpam-4779	159	13	360	360	NUM
ejpam-4779	159	14	,	,	PUNCT
ejpam-4779	159	15	and	and	CCONJ
ejpam-4779	159	16	γ	γ	X
ejpam-4779	159	17	=	=	SYM
ejpam-4779	159	18	480	480	NUM
ejpam-4779	159	19	.	.	PUNCT
ejpam-4779	159	20	hence	hence	ADV
ejpam-4779	159	21	,	,	PUNCT
ejpam-4779	159	22	implementing	implement	VERB
ejpam-4779	159	23	lemma	lemma	PROPN
ejpam-4779	159	24	2	2	NUM
ejpam-4779	159	25	and	and	CCONJ
ejpam-4779	159	26	lemma	lemma	PROPN
ejpam-4779	159	27	3	3	NUM
ejpam-4779	159	28	,	,	PUNCT
ejpam-4779	159	29	we	we	PRON
ejpam-4779	159	30	get	get	VERB
ejpam-4779	159	31	the	the	DET
ejpam-4779	159	32	desired	desire	VERB
ejpam-4779	159	33	bound	bind	VERB
ejpam-4779	159	34	of	of	ADP
ejpam-4779	159	35	|γ4|	|γ4|	NOUN
ejpam-4779	159	36	.	.	PUNCT
ejpam-4779	160	1	this	this	PRON
ejpam-4779	160	2	completes	complete	VERB
ejpam-4779	160	3	the	the	DET
ejpam-4779	160	4	proof	proof	NOUN
ejpam-4779	160	5	of	of	ADP
ejpam-4779	160	6	theorem	theorem	ADJ
ejpam-4779	160	7	2	2	NUM
ejpam-4779	160	8	.	.	NOUN
ejpam-4779	160	9	3.3	3.3	NUM
ejpam-4779	160	10	.	.	PUNCT
ejpam-4779	161	1	hankel	hankel	NOUN
ejpam-4779	161	2	determinant	determinant	ADJ
ejpam-4779	161	3	of	of	ADP
ejpam-4779	161	4	logarithmic	logarithmic	ADJ
ejpam-4779	161	5	coefficients	coefficient	NOUN
ejpam-4779	161	6	theorem	theorem	VERB
ejpam-4779	161	7	3	3	X
ejpam-4779	161	8	.	.	PUNCT
ejpam-4779	162	1	if	if	SCONJ
ejpam-4779	162	2	f	f	PROPN
ejpam-4779	162	3	∈	∈	PROPN
ejpam-4779	162	4	s∗	s∗	PROPN
ejpam-4779	162	5	sc	sc	PROPN
ejpam-4779	162	6	(	(	PUNCT
ejpam-4779	162	7	sin	sin	PROPN
ejpam-4779	162	8	z	z	NOUN
ejpam-4779	162	9	)	)	PUNCT
ejpam-4779	162	10	and	and	CCONJ
ejpam-4779	162	11	has	have	VERB
ejpam-4779	162	12	the	the	DET
ejpam-4779	162	13	series	series	NOUN
ejpam-4779	162	14	representation	representation	NOUN
ejpam-4779	162	15	(	(	PUNCT
ejpam-4779	162	16	1	1	NUM
ejpam-4779	162	17	)	)	PUNCT
ejpam-4779	162	18	,	,	PUNCT
ejpam-4779	162	19	then	then	ADV
ejpam-4779	162	20	|h2,1	|h2,1	VERB
ejpam-4779	162	21	(	(	PUNCT
ejpam-4779	162	22	ff/2)|	ff/2)|	PROPN
ejpam-4779	162	23	⩽	⩽	NOUN
ejpam-4779	162	24	87	87	NUM
ejpam-4779	162	25	1024	1024	NUM
ejpam-4779	162	26	.	.	PUNCT
ejpam-4779	163	1	proof	proof	NOUN
ejpam-4779	163	2	.	.	PUNCT
ejpam-4779	164	1	in	in	ADP
ejpam-4779	164	2	view	view	NOUN
ejpam-4779	164	3	of	of	ADP
ejpam-4779	164	4	(	(	PUNCT
ejpam-4779	164	5	15)-(17	15)-(17	NUM
ejpam-4779	164	6	)	)	PUNCT
ejpam-4779	164	7	,	,	PUNCT
ejpam-4779	164	8	we	we	PRON
ejpam-4779	164	9	have	have	VERB
ejpam-4779	164	10	h2,1	h2,1	PROPN
ejpam-4779	164	11	(	(	PUNCT
ejpam-4779	164	12	ff/2	ff/2	PROPN
ejpam-4779	164	13	)	)	PUNCT
ejpam-4779	164	14	=	=	SYM
ejpam-4779	165	1	γ1γ3	γ1γ3	ADP
ejpam-4779	165	2	−	−	NOUN
ejpam-4779	165	3	γ2	γ2	NOUN
ejpam-4779	165	4	2	2	NUM
ejpam-4779	165	5	=	=	SYM
ejpam-4779	165	6	k1	k1	NOUN
ejpam-4779	165	7	8	8	NUM
ejpam-4779	165	8	(	(	PUNCT
ejpam-4779	165	9	1	1	NUM
ejpam-4779	165	10	128	128	NUM
ejpam-4779	165	11	(	(	PUNCT
ejpam-4779	165	12	3k1	3k1	NUM
ejpam-4779	165	13	3	3	NUM
ejpam-4779	165	14	−	−	PROPN
ejpam-4779	165	15	10k1k2	10k1k2	NOUN
ejpam-4779	165	16	+	+	CCONJ
ejpam-4779	165	17	8k3	8k3	NUM
ejpam-4779	165	18	)	)	PUNCT
ejpam-4779	165	19	)	)	PUNCT
ejpam-4779	166	1	−	−	PROPN
ejpam-4779	166	2	(	(	PUNCT
ejpam-4779	166	3	1	1	NUM
ejpam-4779	166	4	8	8	NUM
ejpam-4779	166	5	(	(	PUNCT
ejpam-4779	166	6	k2	k2	ADJ
ejpam-4779	166	7	−	−	PROPN
ejpam-4779	166	8	5	5	NUM
ejpam-4779	166	9	8	8	NUM
ejpam-4779	166	10	k1	k1	NOUN
ejpam-4779	166	11	2	2	NUM
ejpam-4779	166	12	)	)	PUNCT
ejpam-4779	166	13	)	)	PUNCT
ejpam-4779	166	14	2	2	NUM
ejpam-4779	166	15	=	=	SYM
ejpam-4779	166	16	1	1	NUM
ejpam-4779	166	17	64	64	NUM
ejpam-4779	166	18	(	(	PUNCT
ejpam-4779	166	19	3	3	NUM
ejpam-4779	166	20	16	16	NUM
ejpam-4779	166	21	k1	k1	NOUN
ejpam-4779	166	22	4	4	NUM
ejpam-4779	166	23	−	−	PROPN
ejpam-4779	166	24	10	10	NUM
ejpam-4779	166	25	16	16	NUM
ejpam-4779	166	26	k1	k1	NOUN
ejpam-4779	166	27	2k2	2k2	NUM
ejpam-4779	166	28	+	+	CCONJ
ejpam-4779	166	29	1	1	NUM
ejpam-4779	166	30	2	2	NUM
ejpam-4779	166	31	k1k3	k1k3	NOUN
ejpam-4779	166	32	−	−	PROPN
ejpam-4779	166	33	k2	k2	NOUN
ejpam-4779	166	34	2	2	NUM
ejpam-4779	166	35	+	+	CCONJ
ejpam-4779	166	36	5	5	NUM
ejpam-4779	166	37	4	4	NUM
ejpam-4779	166	38	k1	k1	NOUN
ejpam-4779	166	39	2k2	2k2	NUM
ejpam-4779	166	40	−	−	NUM
ejpam-4779	166	41	25	25	NUM
ejpam-4779	166	42	64	64	NUM
ejpam-4779	166	43	k1	k1	NOUN
ejpam-4779	166	44	4	4	NUM
ejpam-4779	166	45	)	)	PUNCT
ejpam-4779	166	46	=	=	SYM
ejpam-4779	166	47	1	1	NUM
ejpam-4779	166	48	4096	4096	NUM
ejpam-4779	166	49	(	(	PUNCT
ejpam-4779	166	50	−13k1	−13k1	NOUN
ejpam-4779	166	51	4	4	NUM
ejpam-4779	166	52	+	+	SYM
ejpam-4779	166	53	40k1	40k1	NUM
ejpam-4779	166	54	2k2	2k2	NUM
ejpam-4779	167	1	+	+	CCONJ
ejpam-4779	167	2	32k1k3	32k1k3	PROPN
ejpam-4779	167	3	−	−	PROPN
ejpam-4779	167	4	k2	k2	PROPN
ejpam-4779	167	5	2	2	NUM
ejpam-4779	167	6	)	)	PUNCT
ejpam-4779	167	7	.	.	PUNCT
ejpam-4779	168	1	(	(	PUNCT
ejpam-4779	168	2	19	19	NUM
ejpam-4779	168	3	)	)	PUNCT
ejpam-4779	168	4	d.	d.	PROPN
ejpam-4779	168	5	mohamad	mohamad	PROPN
ejpam-4779	168	6	,	,	PUNCT
ejpam-4779	168	7	n.	n.	PROPN
ejpam-4779	168	8	h.	h.	PROPN
ejpam-4779	168	9	a.	a.	PROPN
ejpam-4779	168	10	a.	a.	PROPN
ejpam-4779	168	11	wahid	wahid	PROPN
ejpam-4779	168	12	,	,	PUNCT
ejpam-4779	168	13	n.	n.	PROPN
ejpam-4779	168	14	n.	n.	PROPN
ejpam-4779	168	15	hasni	hasni	PROPN
ejpam-4779	168	16	/	/	SYM
ejpam-4779	168	17	eur	eur	PROPN
ejpam-4779	168	18	.	.	PUNCT
ejpam-4779	169	1	j.	j.	PROPN
ejpam-4779	169	2	pure	pure	PROPN
ejpam-4779	169	3	appl	appl	PROPN
ejpam-4779	169	4	.	.	PROPN
ejpam-4779	169	5	math	math	PROPN
ejpam-4779	169	6	,	,	PUNCT
ejpam-4779	169	7	16	16	NUM
ejpam-4779	169	8	(	(	PUNCT
ejpam-4779	169	9	2	2	NUM
ejpam-4779	169	10	)	)	PUNCT
ejpam-4779	169	11	(	(	PUNCT
ejpam-4779	169	12	2023	2023	NUM
ejpam-4779	169	13	)	)	PUNCT
ejpam-4779	169	14	,	,	PUNCT
ejpam-4779	169	15	1167	1167	NUM
ejpam-4779	169	16	-	-	SYM
ejpam-4779	169	17	1179	1179	NUM
ejpam-4779	169	18	1175	1175	NUM
ejpam-4779	169	19	rearranging	rearrange	VERB
ejpam-4779	169	20	the	the	DET
ejpam-4779	169	21	terms	term	NOUN
ejpam-4779	169	22	in	in	ADP
ejpam-4779	169	23	(	(	PUNCT
ejpam-4779	169	24	19	19	NUM
ejpam-4779	169	25	)	)	PUNCT
ejpam-4779	169	26	,	,	PUNCT
ejpam-4779	169	27	it	it	PRON
ejpam-4779	169	28	becomes	become	VERB
ejpam-4779	169	29	h2,1	h2,1	PROPN
ejpam-4779	169	30	(	(	PUNCT
ejpam-4779	169	31	ff/2	ff/2	PROPN
ejpam-4779	169	32	)	)	PUNCT
ejpam-4779	169	33	=	=	SYM
ejpam-4779	169	34	1	1	NUM
ejpam-4779	169	35	4096	4096	NUM
ejpam-4779	169	36	(	(	PUNCT
ejpam-4779	169	37	−k1	−k1	NOUN
ejpam-4779	169	38	(	(	PUNCT
ejpam-4779	169	39	χk1	χk1	PROPN
ejpam-4779	169	40	3	3	NUM
ejpam-4779	169	41	−	−	PROPN
ejpam-4779	169	42	λk1k2	λk1k2	PROPN
ejpam-4779	169	43	+	+	PROPN
ejpam-4779	169	44	η32k3	η32k3	PROPN
ejpam-4779	169	45	)	)	PUNCT
ejpam-4779	169	46	−	−	PROPN
ejpam-4779	170	1	k2	k2	PROPN
ejpam-4779	170	2	2	2	NUM
ejpam-4779	170	3	)	)	PUNCT
ejpam-4779	170	4	,	,	PUNCT
ejpam-4779	170	5	where	where	SCONJ
ejpam-4779	170	6	χ	χ	ADJ
ejpam-4779	170	7	=	=	SYM
ejpam-4779	170	8	13	13	NUM
ejpam-4779	170	9	,	,	PUNCT
ejpam-4779	170	10	λ	λ	X
ejpam-4779	170	11	=	=	NOUN
ejpam-4779	170	12	40	40	NUM
ejpam-4779	170	13	,	,	PUNCT
ejpam-4779	170	14	and	and	CCONJ
ejpam-4779	170	15	η	η	X
ejpam-4779	170	16	=	=	SYM
ejpam-4779	170	17	−32	−32	PROPN
ejpam-4779	170	18	.	.	PUNCT
ejpam-4779	171	1	by	by	ADP
ejpam-4779	171	2	applying	apply	VERB
ejpam-4779	171	3	the	the	DET
ejpam-4779	171	4	triangle	triangle	NOUN
ejpam-4779	171	5	inequality	inequality	NOUN
ejpam-4779	171	6	as	as	ADV
ejpam-4779	171	7	well	well	ADV
ejpam-4779	171	8	as	as	ADP
ejpam-4779	171	9	lemma	lemma	PROPN
ejpam-4779	171	10	1	1	NUM
ejpam-4779	171	11	and	and	CCONJ
ejpam-4779	171	12	lemma	lemma	PROPN
ejpam-4779	171	13	3	3	NUM
ejpam-4779	171	14	,	,	PUNCT
ejpam-4779	171	15	we	we	PRON
ejpam-4779	171	16	get	get	VERB
ejpam-4779	171	17	the	the	DET
ejpam-4779	171	18	desired	desire	VERB
ejpam-4779	171	19	inequality	inequality	NOUN
ejpam-4779	171	20	.	.	PUNCT
ejpam-4779	172	1	theorem	theorem	VERB
ejpam-4779	172	2	4	4	NUM
ejpam-4779	172	3	.	.	PUNCT
ejpam-4779	173	1	if	if	SCONJ
ejpam-4779	173	2	f	f	PROPN
ejpam-4779	173	3	∈	∈	PROPN
ejpam-4779	173	4	s∗	s∗	PROPN
ejpam-4779	173	5	sc	sc	PROPN
ejpam-4779	173	6	(	(	PUNCT
ejpam-4779	173	7	sin	sin	PROPN
ejpam-4779	173	8	z	z	NOUN
ejpam-4779	173	9	)	)	PUNCT
ejpam-4779	173	10	and	and	CCONJ
ejpam-4779	173	11	has	have	VERB
ejpam-4779	173	12	the	the	DET
ejpam-4779	173	13	series	series	NOUN
ejpam-4779	173	14	representation	representation	NOUN
ejpam-4779	173	15	(	(	PUNCT
ejpam-4779	173	16	1	1	NUM
ejpam-4779	173	17	)	)	PUNCT
ejpam-4779	173	18	,	,	PUNCT
ejpam-4779	173	19	then	then	ADV
ejpam-4779	173	20	|h2,2	|h2,2	VERB
ejpam-4779	173	21	(	(	PUNCT
ejpam-4779	173	22	ff/2)|	ff/2)|	PROPN
ejpam-4779	173	23	⩽	⩽	NOUN
ejpam-4779	173	24	33	33	NUM
ejpam-4779	173	25	256	256	NUM
ejpam-4779	173	26	.	.	PUNCT
ejpam-4779	174	1	proof	proof	NOUN
ejpam-4779	174	2	.	.	PUNCT
ejpam-4779	175	1	in	in	ADP
ejpam-4779	175	2	view	view	NOUN
ejpam-4779	175	3	of	of	ADP
ejpam-4779	175	4	(	(	PUNCT
ejpam-4779	175	5	16)-(18	16)-(18	NOUN
ejpam-4779	175	6	)	)	PUNCT
ejpam-4779	175	7	,	,	PUNCT
ejpam-4779	175	8	we	we	PRON
ejpam-4779	175	9	can	can	AUX
ejpam-4779	175	10	establish	establish	VERB
ejpam-4779	175	11	h2,2	h2,2	PROPN
ejpam-4779	175	12	(	(	PUNCT
ejpam-4779	175	13	ff/2	ff/2	PROPN
ejpam-4779	175	14	)	)	PUNCT
ejpam-4779	175	15	=	=	PUNCT
ejpam-4779	176	1	γ2γ4	γ2γ4	PUNCT
ejpam-4779	176	2	−	−	PROPN
ejpam-4779	176	3	γ3	γ3	NOUN
ejpam-4779	176	4	2	2	NUM
ejpam-4779	176	5	=	=	SYM
ejpam-4779	176	6	1	1	NUM
ejpam-4779	176	7	8	8	NUM
ejpam-4779	176	8	(	(	PUNCT
ejpam-4779	176	9	k2	k2	ADJ
ejpam-4779	176	10	−	−	PROPN
ejpam-4779	176	11	5	5	NUM
ejpam-4779	176	12	8	8	NUM
ejpam-4779	176	13	k1	k1	NOUN
ejpam-4779	176	14	2	2	NUM
ejpam-4779	176	15	)	)	PUNCT
ejpam-4779	176	16	(	(	PUNCT
ejpam-4779	176	17	1	1	NUM
ejpam-4779	176	18	6144	6144	NUM
ejpam-4779	176	19	(	(	PUNCT
ejpam-4779	176	20	384k4	384k4	NUM
ejpam-4779	176	21	+	+	SYM
ejpam-4779	176	22	360k1	360k1	NUM
ejpam-4779	176	23	2k2	2k2	NUM
ejpam-4779	176	24	−	−	NUM
ejpam-4779	176	25	192k2	192k2	NUM
ejpam-4779	176	26	2	2	NUM
ejpam-4779	176	27	−	−	PROPN
ejpam-4779	176	28	480k1k3	480k1k3	NOUN
ejpam-4779	176	29	−	−	PROPN
ejpam-4779	176	30	59k1	59k1	NUM
ejpam-4779	176	31	4	4	NUM
ejpam-4779	176	32	)	)	PUNCT
ejpam-4779	176	33	)	)	PUNCT
ejpam-4779	177	1	−	−	PROPN
ejpam-4779	177	2	(	(	PUNCT
ejpam-4779	177	3	1	1	NUM
ejpam-4779	177	4	128	128	NUM
ejpam-4779	177	5	(	(	PUNCT
ejpam-4779	177	6	3k1	3k1	NUM
ejpam-4779	177	7	3	3	NUM
ejpam-4779	177	8	−	−	PROPN
ejpam-4779	177	9	10k1k2	10k1k2	NOUN
ejpam-4779	177	10	+	+	CCONJ
ejpam-4779	177	11	8k3	8k3	NUM
ejpam-4779	177	12	)	)	PUNCT
ejpam-4779	177	13	)	)	PUNCT
ejpam-4779	177	14	2	2	NUM
ejpam-4779	178	1	=	=	SYM
ejpam-4779	178	2	1	1	NUM
ejpam-4779	178	3	393216	393216	NUM
ejpam-4779	178	4	(	(	PUNCT
ejpam-4779	178	5	3072k2k4	3072k2k4	NUM
ejpam-4779	178	6	+	+	NUM
ejpam-4779	178	7	1440k1	1440k1	NUM
ejpam-4779	178	8	2k2	2k2	NUM
ejpam-4779	178	9	2	2	NUM
ejpam-4779	178	10	−	−	PROPN
ejpam-4779	178	11	1536k2	1536k2	NUM
ejpam-4779	178	12	3	3	NUM
ejpam-4779	178	13	−	−	PROPN
ejpam-4779	178	14	832k1	832k1	NUM
ejpam-4779	178	15	4k2	4k2	NUM
ejpam-4779	178	16	−	−	NOUN
ejpam-4779	178	17	1920k1	1920k1	NUM
ejpam-4779	178	18	2k4	2k4	NUM
ejpam-4779	178	19	+1248k1	+1248k1	NOUN
ejpam-4779	178	20	3k3	3k3	NUM
ejpam-4779	179	1	+	+	CCONJ
ejpam-4779	179	2	79k1	79k1	NUM
ejpam-4779	179	3	6	6	NUM
ejpam-4779	179	4	−	−	NOUN
ejpam-4779	179	5	1536k3	1536k3	NOUN
ejpam-4779	179	6	2	2	NUM
ejpam-4779	179	7	)	)	PUNCT
ejpam-4779	179	8	.	.	PUNCT
ejpam-4779	180	1	(	(	PUNCT
ejpam-4779	180	2	20	20	NUM
ejpam-4779	180	3	)	)	PUNCT
ejpam-4779	180	4	further	far	ADV
ejpam-4779	180	5	,	,	PUNCT
ejpam-4779	180	6	rearranging	rearrange	VERB
ejpam-4779	180	7	the	the	DET
ejpam-4779	180	8	terms	term	NOUN
ejpam-4779	180	9	in	in	ADP
ejpam-4779	180	10	(	(	PUNCT
ejpam-4779	180	11	20	20	NUM
ejpam-4779	180	12	)	)	PUNCT
ejpam-4779	180	13	,	,	PUNCT
ejpam-4779	180	14	we	we	PRON
ejpam-4779	180	15	can	can	AUX
ejpam-4779	180	16	rewrite	rewrite	VERB
ejpam-4779	180	17	it	it	PRON
ejpam-4779	180	18	in	in	ADP
ejpam-4779	180	19	the	the	DET
ejpam-4779	180	20	following	follow	VERB
ejpam-4779	180	21	expression	expression	NOUN
ejpam-4779	180	22	:	:	PUNCT
ejpam-4779	181	1	h2,2	h2,2	PROPN
ejpam-4779	181	2	(	(	PUNCT
ejpam-4779	181	3	ff/2	ff/2	PROPN
ejpam-4779	181	4	)	)	PUNCT
ejpam-4779	181	5	=	=	SYM
ejpam-4779	181	6	1	1	NUM
ejpam-4779	181	7	393216	393216	NUM
ejpam-4779	181	8	[	[	X
ejpam-4779	181	9	(	(	PUNCT
ejpam-4779	181	10	3072k4	3072k4	PROPN
ejpam-4779	181	11	(	(	PUNCT
ejpam-4779	181	12	k2	k2	ADJ
ejpam-4779	181	13	−	−	PROPN
ejpam-4779	181	14	5	5	NUM
ejpam-4779	181	15	8	8	NUM
ejpam-4779	181	16	k1	k1	NOUN
ejpam-4779	181	17	2	2	NUM
ejpam-4779	181	18	)	)	PUNCT
ejpam-4779	181	19	−	−	PROPN
ejpam-4779	181	20	1536k2	1536k2	NUM
ejpam-4779	181	21	2	2	NUM
ejpam-4779	181	22	(	(	PUNCT
ejpam-4779	181	23	k2	k2	ADJ
ejpam-4779	181	24	−	−	PROPN
ejpam-4779	181	25	15	15	NUM
ejpam-4779	181	26	16	16	NUM
ejpam-4779	181	27	k1	k1	NOUN
ejpam-4779	181	28	2	2	NUM
ejpam-4779	181	29	)	)	PUNCT
ejpam-4779	181	30	+	+	NOUN
ejpam-4779	181	31	k1	k1	NOUN
ejpam-4779	181	32	3	3	NUM
ejpam-4779	181	33	(	(	PUNCT
ejpam-4779	181	34	79k1	79k1	NUM
ejpam-4779	181	35	3	3	NUM
ejpam-4779	181	36	−	−	PROPN
ejpam-4779	181	37	832k1k2	832k1k2	NUM
ejpam-4779	181	38	+	+	CCONJ
ejpam-4779	181	39	1248k3	1248k3	NUM
ejpam-4779	181	40	)	)	PUNCT
ejpam-4779	181	41	−	−	PROPN
ejpam-4779	181	42	1536k3	1536k3	NOUN
ejpam-4779	181	43	2	2	NUM
ejpam-4779	181	44	)	)	PUNCT
ejpam-4779	181	45	]	]	PUNCT
ejpam-4779	181	46	.	.	PUNCT
ejpam-4779	182	1	hence	hence	ADV
ejpam-4779	182	2	,	,	PUNCT
ejpam-4779	182	3	making	make	VERB
ejpam-4779	182	4	use	use	NOUN
ejpam-4779	182	5	of	of	ADP
ejpam-4779	182	6	lemma	lemma	PROPN
ejpam-4779	182	7	1	1	NUM
ejpam-4779	182	8	,	,	PUNCT
ejpam-4779	182	9	lemma	lemma	PROPN
ejpam-4779	182	10	2	2	NUM
ejpam-4779	182	11	,	,	PUNCT
ejpam-4779	182	12	and	and	CCONJ
ejpam-4779	182	13	lemma	lemma	PROPN
ejpam-4779	182	14	3	3	NUM
ejpam-4779	182	15	yields	yield	NOUN
ejpam-4779	182	16	the	the	DET
ejpam-4779	182	17	desired	desire	VERB
ejpam-4779	182	18	bound	bind	VERB
ejpam-4779	182	19	.	.	PUNCT
ejpam-4779	183	1	3.4	3.4	NUM
ejpam-4779	183	2	.	.	PUNCT
ejpam-4779	183	3	toeplitz	toeplitz	NOUN
ejpam-4779	183	4	determinant	determinant	ADJ
ejpam-4779	183	5	of	of	ADP
ejpam-4779	183	6	logarithmic	logarithmic	ADJ
ejpam-4779	183	7	coefficients	coefficient	NOUN
ejpam-4779	183	8	theorem	theorem	VERB
ejpam-4779	183	9	5	5	NUM
ejpam-4779	183	10	.	.	PUNCT
ejpam-4779	184	1	if	if	SCONJ
ejpam-4779	184	2	f	f	PROPN
ejpam-4779	184	3	∈	∈	PROPN
ejpam-4779	184	4	s∗	s∗	PROPN
ejpam-4779	184	5	sc	sc	PROPN
ejpam-4779	184	6	(	(	PUNCT
ejpam-4779	184	7	sin	sin	PROPN
ejpam-4779	184	8	z	z	PROPN
ejpam-4779	184	9	)	)	PUNCT
ejpam-4779	184	10	,	,	PUNCT
ejpam-4779	184	11	then∣∣γ12	then∣∣γ12	DET
ejpam-4779	184	12	−	−	NOUN
ejpam-4779	184	13	γ2	γ2	NOUN
ejpam-4779	184	14	2	2	NUM
ejpam-4779	184	15	∣∣	∣∣	NUM
ejpam-4779	184	16	⩽	⩽	NOUN
ejpam-4779	184	17	65	65	NUM
ejpam-4779	184	18	256	256	NUM
ejpam-4779	184	19	.	.	PUNCT
ejpam-4779	185	1	proof	proof	NOUN
ejpam-4779	185	2	.	.	PUNCT
ejpam-4779	186	1	using	use	VERB
ejpam-4779	186	2	(	(	PUNCT
ejpam-4779	186	3	15	15	NUM
ejpam-4779	186	4	)	)	PUNCT
ejpam-4779	186	5	and	and	CCONJ
ejpam-4779	186	6	(	(	PUNCT
ejpam-4779	186	7	16	16	NUM
ejpam-4779	186	8	)	)	PUNCT
ejpam-4779	186	9	,	,	PUNCT
ejpam-4779	186	10	we	we	PRON
ejpam-4779	186	11	obtain	obtain	VERB
ejpam-4779	186	12	γ1	γ1	NOUN
ejpam-4779	186	13	2	2	NUM
ejpam-4779	186	14	−	−	NOUN
ejpam-4779	186	15	γ2	γ2	NOUN
ejpam-4779	186	16	2	2	NUM
ejpam-4779	186	17	=	=	SYM
ejpam-4779	186	18	k1	k1	NOUN
ejpam-4779	186	19	2	2	NUM
ejpam-4779	186	20	64	64	NUM
ejpam-4779	186	21	−	−	NUM
ejpam-4779	186	22	1	1	NUM
ejpam-4779	186	23	64	64	NUM
ejpam-4779	186	24	(	(	PUNCT
ejpam-4779	186	25	k2	k2	ADJ
ejpam-4779	186	26	−	−	PROPN
ejpam-4779	186	27	5	5	NUM
ejpam-4779	186	28	8	8	NUM
ejpam-4779	186	29	k1	k1	NOUN
ejpam-4779	186	30	2	2	NUM
ejpam-4779	186	31	)	)	PUNCT
ejpam-4779	186	32	2	2	NUM
ejpam-4779	186	33	=	=	SYM
ejpam-4779	186	34	1	1	NUM
ejpam-4779	186	35	64	64	NUM
ejpam-4779	186	36	(	(	PUNCT
ejpam-4779	186	37	5	5	NUM
ejpam-4779	186	38	4	4	NUM
ejpam-4779	186	39	k1	k1	NOUN
ejpam-4779	186	40	2	2	NUM
ejpam-4779	186	41	(	(	PUNCT
ejpam-4779	186	42	k2	k2	NOUN
ejpam-4779	186	43	−	−	PROPN
ejpam-4779	186	44	25	25	NUM
ejpam-4779	186	45	80	80	NUM
ejpam-4779	186	46	k1	k1	NOUN
ejpam-4779	186	47	2	2	NUM
ejpam-4779	186	48	)	)	PUNCT
ejpam-4779	186	49	+	+	CCONJ
ejpam-4779	186	50	k1	k1	NOUN
ejpam-4779	186	51	2	2	NUM
ejpam-4779	186	52	−	−	NOUN
ejpam-4779	186	53	k2	k2	NOUN
ejpam-4779	186	54	2	2	NUM
ejpam-4779	186	55	)	)	PUNCT
ejpam-4779	186	56	.	.	PUNCT
ejpam-4779	187	1	(	(	PUNCT
ejpam-4779	187	2	21	21	NUM
ejpam-4779	187	3	)	)	PUNCT
ejpam-4779	187	4	applying	apply	VERB
ejpam-4779	187	5	the	the	DET
ejpam-4779	187	6	triangle	triangle	NOUN
ejpam-4779	187	7	inequality	inequality	NOUN
ejpam-4779	187	8	and	and	CCONJ
ejpam-4779	187	9	lemma	lemma	PROPN
ejpam-4779	187	10	1	1	NUM
ejpam-4779	187	11	and	and	CCONJ
ejpam-4779	187	12	lemma	lemma	PROPN
ejpam-4779	187	13	2	2	NUM
ejpam-4779	187	14	,	,	PUNCT
ejpam-4779	187	15	we	we	PRON
ejpam-4779	187	16	get	get	VERB
ejpam-4779	187	17	the	the	DET
ejpam-4779	187	18	desired	desire	VERB
ejpam-4779	187	19	inequality	inequality	NOUN
ejpam-4779	187	20	.	.	PUNCT
ejpam-4779	188	1	references	reference	NOUN
ejpam-4779	188	2	1176	1176	NUM
ejpam-4779	188	3	theorem	theorem	NOUN
ejpam-4779	188	4	6	6	NUM
ejpam-4779	188	5	.	.	PUNCT
ejpam-4779	189	1	if	if	SCONJ
ejpam-4779	189	2	f	f	PROPN
ejpam-4779	189	3	∈	∈	PROPN
ejpam-4779	189	4	s∗	s∗	PROPN
ejpam-4779	189	5	sc	sc	PROPN
ejpam-4779	189	6	(	(	PUNCT
ejpam-4779	189	7	sin	sin	PROPN
ejpam-4779	189	8	z	z	PROPN
ejpam-4779	189	9	)	)	PUNCT
ejpam-4779	189	10	,	,	PUNCT
ejpam-4779	189	11	then	then	ADV
ejpam-4779	189	12	|t2,2	|t2,2	NOUN
ejpam-4779	189	13	(	(	PUNCT
ejpam-4779	189	14	γn)|	γn)|	PROPN
ejpam-4779	189	15	⩽	⩽	ADJ
ejpam-4779	189	16	11	11	NUM
ejpam-4779	189	17	32	32	NUM
ejpam-4779	189	18	.	.	PUNCT
ejpam-4779	190	1	proof	proof	NOUN
ejpam-4779	190	2	.	.	PUNCT
ejpam-4779	191	1	making	make	VERB
ejpam-4779	191	2	use	use	NOUN
ejpam-4779	191	3	of	of	ADP
ejpam-4779	191	4	(	(	PUNCT
ejpam-4779	191	5	16	16	NUM
ejpam-4779	191	6	)	)	PUNCT
ejpam-4779	191	7	and	and	CCONJ
ejpam-4779	191	8	(	(	PUNCT
ejpam-4779	191	9	17	17	NUM
ejpam-4779	191	10	)	)	PUNCT
ejpam-4779	191	11	,	,	PUNCT
ejpam-4779	191	12	upon	upon	SCONJ
ejpam-4779	191	13	simplification	simplification	NOUN
ejpam-4779	191	14	,	,	PUNCT
ejpam-4779	191	15	we	we	PRON
ejpam-4779	191	16	have	have	VERB
ejpam-4779	191	17	t2,2	t2,2	NUM
ejpam-4779	191	18	(	(	PUNCT
ejpam-4779	191	19	γn	γn	NOUN
ejpam-4779	191	20	)	)	PUNCT
ejpam-4779	192	1	=	=	SYM
ejpam-4779	193	1	γ2	γ2	ADJ
ejpam-4779	193	2	2	2	NUM
ejpam-4779	193	3	−	−	NOUN
ejpam-4779	193	4	γ3	γ3	NOUN
ejpam-4779	193	5	2	2	NUM
ejpam-4779	193	6	=	=	SYM
ejpam-4779	193	7	1	1	NUM
ejpam-4779	193	8	64	64	NUM
ejpam-4779	193	9	(	(	PUNCT
ejpam-4779	193	10	k2	k2	ADJ
ejpam-4779	193	11	−	−	PROPN
ejpam-4779	193	12	5	5	NUM
ejpam-4779	193	13	8	8	NUM
ejpam-4779	193	14	k1	k1	NOUN
ejpam-4779	193	15	2	2	NUM
ejpam-4779	193	16	)	)	PUNCT
ejpam-4779	193	17	2	2	NUM
ejpam-4779	193	18	−	−	PROPN
ejpam-4779	193	19	1	1	NUM
ejpam-4779	193	20	16384	16384	NUM
ejpam-4779	193	21	(	(	PUNCT
ejpam-4779	193	22	3k1	3k1	NUM
ejpam-4779	193	23	3	3	NUM
ejpam-4779	193	24	−	−	PROPN
ejpam-4779	194	1	10k1k2	10k1k2	NOUN
ejpam-4779	194	2	+	+	CCONJ
ejpam-4779	194	3	8k3	8k3	NUM
ejpam-4779	194	4	)	)	PUNCT
ejpam-4779	194	5	2	2	NUM
ejpam-4779	194	6	=	=	SYM
ejpam-4779	194	7	1	1	NUM
ejpam-4779	194	8	16384	16384	NUM
ejpam-4779	194	9	(	(	PUNCT
ejpam-4779	194	10	256k2	256k2	NUM
ejpam-4779	194	11	2	2	NUM
ejpam-4779	194	12	−	−	NOUN
ejpam-4779	194	13	320k1	320k1	NUM
ejpam-4779	194	14	2k2	2k2	NUM
ejpam-4779	195	1	+	+	CCONJ
ejpam-4779	195	2	100k1	100k1	NUM
ejpam-4779	195	3	4	4	NUM
ejpam-4779	195	4	−	−	NOUN
ejpam-4779	195	5	9k1	9k1	NUM
ejpam-4779	195	6	6	6	NUM
ejpam-4779	195	7	+	+	NUM
ejpam-4779	196	1	60k1	60k1	NUM
ejpam-4779	196	2	4k2	4k2	NUM
ejpam-4779	196	3	−	−	NOUN
ejpam-4779	196	4	100k1	100k1	NUM
ejpam-4779	196	5	2k2	2k2	NUM
ejpam-4779	196	6	2	2	NUM
ejpam-4779	196	7	−	−	PROPN
ejpam-4779	196	8	48k1	48k1	NUM
ejpam-4779	196	9	3k3	3k3	NUM
ejpam-4779	196	10	+160k1k2k3	+160k1k2k3	ADV
ejpam-4779	196	11	−	−	PROPN
ejpam-4779	197	1	64k3	64k3	NUM
ejpam-4779	197	2	2	2	NUM
ejpam-4779	197	3	)	)	PUNCT
ejpam-4779	197	4	and	and	CCONJ
ejpam-4779	197	5	equivalently	equivalently	ADV
ejpam-4779	197	6	,	,	PUNCT
ejpam-4779	197	7	t2,2	t2,2	NUM
ejpam-4779	197	8	(	(	PUNCT
ejpam-4779	197	9	γn	γn	NOUN
ejpam-4779	197	10	)	)	PUNCT
ejpam-4779	197	11	=	=	SYM
ejpam-4779	197	12	1	1	NUM
ejpam-4779	197	13	16384	16384	NUM
ejpam-4779	197	14	[	[	PUNCT
ejpam-4779	197	15	256k2	256k2	NUM
ejpam-4779	197	16	(	(	PUNCT
ejpam-4779	197	17	k2	k2	ADJ
ejpam-4779	197	18	−	−	PROPN
ejpam-4779	197	19	5	5	NUM
ejpam-4779	197	20	4	4	NUM
ejpam-4779	197	21	k1	k1	NOUN
ejpam-4779	197	22	2	2	NUM
ejpam-4779	197	23	)	)	PUNCT
ejpam-4779	197	24	−	−	PROPN
ejpam-4779	198	1	100k1	100k1	NUM
ejpam-4779	198	2	2k2	2k2	NUM
ejpam-4779	198	3	(	(	PUNCT
ejpam-4779	198	4	k2	k2	ADJ
ejpam-4779	198	5	−	−	PROPN
ejpam-4779	198	6	3	3	NUM
ejpam-4779	198	7	5	5	NUM
ejpam-4779	198	8	k1	k1	NOUN
ejpam-4779	198	9	2	2	NUM
ejpam-4779	198	10	)	)	PUNCT
ejpam-4779	198	11	+	+	CCONJ
ejpam-4779	198	12	100k1	100k1	NUM
ejpam-4779	198	13	4	4	NUM
ejpam-4779	198	14	−	−	NOUN
ejpam-4779	198	15	9k1	9k1	NUM
ejpam-4779	198	16	6	6	NUM
ejpam-4779	198	17	+	+	ADV
ejpam-4779	198	18	k3	k3	ADJ
ejpam-4779	198	19	(	(	PUNCT
ejpam-4779	198	20	−48k1	−48k1	X
ejpam-4779	198	21	3	3	NUM
ejpam-4779	198	22	+	+	SYM
ejpam-4779	198	23	160k1k2	160k1k2	NUM
ejpam-4779	198	24	−	−	NUM
ejpam-4779	198	25	64k3	64k3	NUM
ejpam-4779	198	26	)	)	PUNCT
ejpam-4779	198	27	]	]	PUNCT
ejpam-4779	198	28	.	.	PUNCT
ejpam-4779	199	1	(	(	PUNCT
ejpam-4779	199	2	22	22	X
ejpam-4779	199	3	)	)	PUNCT
ejpam-4779	199	4	applying	apply	VERB
ejpam-4779	199	5	lemma	lemma	PROPN
ejpam-4779	199	6	1	1	NUM
ejpam-4779	199	7	,	,	PUNCT
ejpam-4779	199	8	lemma	lemma	PROPN
ejpam-4779	199	9	2	2	NUM
ejpam-4779	199	10	,	,	PUNCT
ejpam-4779	199	11	and	and	CCONJ
ejpam-4779	199	12	lemma	lemma	PROPN
ejpam-4779	199	13	3	3	NUM
ejpam-4779	199	14	on	on	ADP
ejpam-4779	199	15	(	(	PUNCT
ejpam-4779	199	16	22	22	NUM
ejpam-4779	199	17	)	)	PUNCT
ejpam-4779	199	18	,	,	PUNCT
ejpam-4779	199	19	we	we	PRON
ejpam-4779	199	20	can	can	AUX
ejpam-4779	199	21	obtain	obtain	VERB
ejpam-4779	199	22	the	the	DET
ejpam-4779	199	23	desired	desire	VERB
ejpam-4779	199	24	bound	bind	VERB
ejpam-4779	199	25	.	.	PUNCT
ejpam-4779	200	1	4	4	X
ejpam-4779	200	2	.	.	X
ejpam-4779	200	3	conclusion	conclusion	NOUN
ejpam-4779	200	4	this	this	DET
ejpam-4779	200	5	study	study	NOUN
ejpam-4779	200	6	was	be	AUX
ejpam-4779	200	7	inspired	inspire	VERB
ejpam-4779	200	8	by	by	ADP
ejpam-4779	200	9	a	a	DET
ejpam-4779	200	10	number	number	NOUN
ejpam-4779	200	11	of	of	ADP
ejpam-4779	200	12	previous	previous	ADJ
ejpam-4779	200	13	studies	study	NOUN
ejpam-4779	200	14	.	.	PUNCT
ejpam-4779	201	1	in	in	ADP
ejpam-4779	201	2	this	this	DET
ejpam-4779	201	3	paper	paper	NOUN
ejpam-4779	201	4	,	,	PUNCT
ejpam-4779	201	5	we	we	PRON
ejpam-4779	201	6	have	have	AUX
ejpam-4779	201	7	obtained	obtain	VERB
ejpam-4779	201	8	the	the	DET
ejpam-4779	201	9	upper	upper	ADJ
ejpam-4779	201	10	bounds	bound	NOUN
ejpam-4779	201	11	of	of	ADP
ejpam-4779	201	12	some	some	DET
ejpam-4779	201	13	coefficient	coefficient	NOUN
ejpam-4779	201	14	problems	problem	NOUN
ejpam-4779	201	15	for	for	ADP
ejpam-4779	201	16	functions	function	NOUN
ejpam-4779	201	17	in	in	ADP
ejpam-4779	201	18	the	the	DET
ejpam-4779	201	19	class	class	NOUN
ejpam-4779	201	20	s∗	s∗	PROPN
ejpam-4779	201	21	sc	sc	PROPN
ejpam-4779	201	22	(	(	PUNCT
ejpam-4779	201	23	sin	sin	PROPN
ejpam-4779	201	24	z	z	NOUN
ejpam-4779	201	25	)	)	PUNCT
ejpam-4779	201	26	including	include	VERB
ejpam-4779	201	27	taylor	taylor	PROPN
ejpam-4779	201	28	coefficients	coefficient	NOUN
ejpam-4779	201	29	,	,	PUNCT
ejpam-4779	201	30	logarithmic	logarithmic	ADJ
ejpam-4779	201	31	coefficients	coefficient	NOUN
ejpam-4779	201	32	,	,	PUNCT
ejpam-4779	201	33	and	and	CCONJ
ejpam-4779	201	34	hankel	hankel	NOUN
ejpam-4779	201	35	and	and	CCONJ
ejpam-4779	201	36	toeplitz	toeplitz	NOUN
ejpam-4779	201	37	determinants	determinant	NOUN
ejpam-4779	201	38	of	of	ADP
ejpam-4779	201	39	logarithmic	logarithmic	ADJ
ejpam-4779	201	40	coefficients	coefficient	NOUN
ejpam-4779	201	41	.	.	PUNCT
ejpam-4779	202	1	the	the	DET
ejpam-4779	202	2	results	result	NOUN
ejpam-4779	202	3	provided	provide	VERB
ejpam-4779	202	4	in	in	ADP
ejpam-4779	202	5	this	this	DET
ejpam-4779	202	6	paper	paper	NOUN
ejpam-4779	202	7	perhaps	perhaps	ADV
ejpam-4779	202	8	could	could	AUX
ejpam-4779	202	9	be	be	AUX
ejpam-4779	202	10	the	the	DET
ejpam-4779	202	11	subject	subject	NOUN
ejpam-4779	202	12	of	of	ADP
ejpam-4779	202	13	further	further	ADJ
ejpam-4779	202	14	research	research	NOUN
ejpam-4779	202	15	related	relate	VERB
ejpam-4779	202	16	to	to	ADP
ejpam-4779	202	17	the	the	DET
ejpam-4779	202	18	higher	high	ADJ
ejpam-4779	202	19	-	-	PUNCT
ejpam-4779	202	20	order	order	NOUN
ejpam-4779	202	21	hankel	hankel	NOUN
ejpam-4779	202	22	and	and	CCONJ
ejpam-4779	202	23	toeplitz	toeplitz	NOUN
ejpam-4779	202	24	determinants	determinant	NOUN
ejpam-4779	202	25	of	of	ADP
ejpam-4779	202	26	logarithmic	logarithmic	ADJ
ejpam-4779	202	27	coefficients	coefficient	NOUN
ejpam-4779	202	28	and	and	CCONJ
ejpam-4779	202	29	other	other	ADJ
ejpam-4779	202	30	coefficient	coefficient	NOUN
ejpam-4779	202	31	problems	problem	NOUN
ejpam-4779	202	32	,	,	PUNCT
ejpam-4779	202	33	for	for	ADP
ejpam-4779	202	34	instance	instance	NOUN
ejpam-4779	202	35	,	,	PUNCT
ejpam-4779	202	36	the	the	DET
ejpam-4779	202	37	fekete	fekete	PROPN
ejpam-4779	202	38	-	-	PUNCT
ejpam-4779	202	39	szegö	szegö	VERB
ejpam-4779	202	40	functional	functional	NOUN
ejpam-4779	202	41	,	,	PUNCT
ejpam-4779	202	42	the	the	DET
ejpam-4779	202	43	toeplitz	toeplitz	NOUN
ejpam-4779	202	44	and	and	CCONJ
ejpam-4779	202	45	hermitian	hermitian	ADJ
ejpam-4779	202	46	-	-	PUNCT
ejpam-4779	202	47	toeplitz	toeplitz	NOUN
ejpam-4779	202	48	determinants	determinant	NOUN
ejpam-4779	202	49	,	,	PUNCT
ejpam-4779	202	50	and	and	CCONJ
ejpam-4779	202	51	the	the	DET
ejpam-4779	202	52	krushkal	krushkal	ADJ
ejpam-4779	202	53	inequality	inequality	NOUN
ejpam-4779	202	54	for	for	ADP
ejpam-4779	202	55	functions	function	NOUN
ejpam-4779	202	56	from	from	ADP
ejpam-4779	202	57	the	the	DET
ejpam-4779	202	58	subclass	subclass	NOUN
ejpam-4779	202	59	of	of	ADP
ejpam-4779	202	60	star	star	NOUN
ejpam-4779	202	61	-	-	PUNCT
ejpam-4779	202	62	like	like	ADJ
ejpam-4779	202	63	functions	function	NOUN
ejpam-4779	202	64	with	with	ADP
ejpam-4779	202	65	respect	respect	NOUN
ejpam-4779	202	66	to	to	ADP
ejpam-4779	202	67	other	other	ADJ
ejpam-4779	202	68	points	point	NOUN
ejpam-4779	202	69	.	.	PUNCT
ejpam-4779	203	1	additionally	additionally	ADV
ejpam-4779	203	2	,	,	PUNCT
ejpam-4779	203	3	for	for	ADP
ejpam-4779	203	4	another	another	DET
ejpam-4779	203	5	particular	particular	ADJ
ejpam-4779	203	6	value	value	NOUN
ejpam-4779	203	7	of	of	ADP
ejpam-4779	203	8	φ	φ	PROPN
ejpam-4779	203	9	,	,	PUNCT
ejpam-4779	203	10	several	several	ADJ
ejpam-4779	203	11	other	other	ADJ
ejpam-4779	203	12	classes	class	NOUN
ejpam-4779	203	13	of	of	ADP
ejpam-4779	203	14	functions	function	NOUN
ejpam-4779	203	15	that	that	PRON
ejpam-4779	203	16	are	be	AUX
ejpam-4779	203	17	star	star	NOUN
ejpam-4779	203	18	-	-	PUNCT
ejpam-4779	203	19	like	like	ADJ
ejpam-4779	203	20	with	with	ADP
ejpam-4779	203	21	respect	respect	NOUN
ejpam-4779	203	22	to	to	ADP
ejpam-4779	203	23	symmetric	symmetric	ADJ
ejpam-4779	203	24	conjugate	conjugate	ADJ
ejpam-4779	203	25	points	point	NOUN
ejpam-4779	203	26	can	can	AUX
ejpam-4779	203	27	also	also	ADV
ejpam-4779	203	28	be	be	AUX
ejpam-4779	203	29	studied	study	VERB
ejpam-4779	203	30	.	.	PUNCT
ejpam-4779	204	1	acknowledgements	acknowledgement	NOUN
ejpam-4779	204	2	the	the	DET
ejpam-4779	204	3	authors	author	NOUN
ejpam-4779	204	4	truly	truly	ADV
ejpam-4779	204	5	appreciate	appreciate	VERB
ejpam-4779	204	6	the	the	DET
ejpam-4779	204	7	referees	referee	NOUN
ejpam-4779	204	8	’	’	PART
ejpam-4779	204	9	insightful	insightful	ADJ
ejpam-4779	204	10	comments	comment	NOUN
ejpam-4779	204	11	.	.	PUNCT
ejpam-4779	205	1	a	a	DET
ejpam-4779	205	2	special	special	ADJ
ejpam-4779	205	3	thanks	thank	NOUN
ejpam-4779	205	4	to	to	ADP
ejpam-4779	205	5	universiti	universiti	PROPN
ejpam-4779	205	6	teknologi	teknologi	PROPN
ejpam-4779	205	7	mara	mara	PROPN
ejpam-4779	205	8	for	for	ADP
ejpam-4779	205	9	supporting	support	VERB
ejpam-4779	205	10	the	the	DET
ejpam-4779	205	11	publication	publication	NOUN
ejpam-4779	205	12	of	of	ADP
ejpam-4779	205	13	this	this	DET
ejpam-4779	205	14	paper	paper	NOUN
ejpam-4779	205	15	.	.	PUNCT
ejpam-4779	206	1	references	reference	NOUN
ejpam-4779	206	2	[	[	X
ejpam-4779	206	3	1	1	NUM
ejpam-4779	206	4	]	]	X
ejpam-4779	206	5	s	s	PART
ejpam-4779	206	6	abdul	abdul	PROPN
ejpam-4779	206	7	halim	halim	PROPN
ejpam-4779	206	8	.	.	PUNCT
ejpam-4779	207	1	functions	function	NOUN
ejpam-4779	207	2	starlike	starlike	NOUN
ejpam-4779	207	3	with	with	ADP
ejpam-4779	207	4	respect	respect	NOUN
ejpam-4779	207	5	to	to	ADP
ejpam-4779	207	6	other	other	ADJ
ejpam-4779	207	7	points	point	NOUN
ejpam-4779	207	8	.	.	PUNCT
ejpam-4779	208	1	international	international	ADJ
ejpam-4779	208	2	journal	journal	NOUN
ejpam-4779	208	3	of	of	ADP
ejpam-4779	208	4	mathematics	mathematics	PROPN
ejpam-4779	208	5	and	and	CCONJ
ejpam-4779	208	6	mathematical	mathematical	ADJ
ejpam-4779	208	7	sciences	science	NOUN
ejpam-4779	208	8	,	,	PUNCT
ejpam-4779	208	9	14(3):451–456	14(3):451–456	PROPN
ejpam-4779	208	10	,	,	PUNCT
ejpam-4779	208	11	1991	1991	NUM
ejpam-4779	208	12	.	.	PUNCT
ejpam-4779	209	1	references	reference	NOUN
ejpam-4779	209	2	1177	1177	NUM
ejpam-4779	209	3	[	[	X
ejpam-4779	209	4	2	2	NUM
ejpam-4779	209	5	]	]	PUNCT
ejpam-4779	209	6	nur	nur	PROPN
ejpam-4779	209	7	hazwani	hazwani	PROPN
ejpam-4779	209	8	aqilah	aqilah	PROPN
ejpam-4779	209	9	abdul	abdul	PROPN
ejpam-4779	209	10	wahid	wahid	PROPN
ejpam-4779	209	11	and	and	CCONJ
ejpam-4779	209	12	daud	daud	PROPN
ejpam-4779	209	13	mohamad	mohamad	PROPN
ejpam-4779	209	14	.	.	PROPN
ejpam-4779	209	15	bounds	bound	VERB
ejpam-4779	209	16	on	on	ADP
ejpam-4779	209	17	hankel	hankel	NOUN
ejpam-4779	209	18	determinant	determinant	ADJ
ejpam-4779	209	19	for	for	ADP
ejpam-4779	209	20	starlike	starlike	NOUN
ejpam-4779	209	21	functions	function	NOUN
ejpam-4779	209	22	with	with	ADP
ejpam-4779	209	23	respect	respect	NOUN
ejpam-4779	209	24	to	to	ADP
ejpam-4779	209	25	conjugate	conjugate	ADJ
ejpam-4779	209	26	points	point	NOUN
ejpam-4779	209	27	.	.	PUNCT
ejpam-4779	210	1	j.	j.	PROPN
ejpam-4779	210	2	math	math	PROPN
ejpam-4779	210	3	.	.	PUNCT
ejpam-4779	211	1	comput	comput	NOUN
ejpam-4779	211	2	.	.	PUNCT
ejpam-4779	212	1	sci	sci	PROPN
ejpam-4779	212	2	.	.	PROPN
ejpam-4779	212	3	,	,	PUNCT
ejpam-4779	212	4	11(3):3347–3360	11(3):3347–3360	NUM
ejpam-4779	212	5	,	,	PUNCT
ejpam-4779	212	6	2021	2021	NUM
ejpam-4779	212	7	.	.	PUNCT
ejpam-4779	213	1	[	[	X
ejpam-4779	213	2	3	3	X
ejpam-4779	213	3	]	]	X
ejpam-4779	213	4	davood	davood	ADJ
ejpam-4779	213	5	alimohammadi	alimohammadi	NOUN
ejpam-4779	213	6	,	,	PUNCT
ejpam-4779	213	7	ebrahim	ebrahim	PROPN
ejpam-4779	213	8	analouei	analouei	PROPN
ejpam-4779	213	9	adegani	adegani	NOUN
ejpam-4779	213	10	,	,	PUNCT
ejpam-4779	213	11	teodor	teodor	NOUN
ejpam-4779	213	12	bulboacă	bulboacă	NOUN
ejpam-4779	213	13	,	,	PUNCT
ejpam-4779	213	14	and	and	CCONJ
ejpam-4779	213	15	nak	nak	PROPN
ejpam-4779	213	16	eun	eun	PROPN
ejpam-4779	213	17	cho	cho	PROPN
ejpam-4779	213	18	.	.	PUNCT
ejpam-4779	214	1	logarithmic	logarithmic	ADJ
ejpam-4779	214	2	coefficient	coefficient	NOUN
ejpam-4779	214	3	bounds	bound	NOUN
ejpam-4779	214	4	and	and	CCONJ
ejpam-4779	214	5	coefficient	coefficient	NOUN
ejpam-4779	214	6	conjectures	conjecture	VERB
ejpam-4779	214	7	for	for	ADP
ejpam-4779	214	8	classes	class	NOUN
ejpam-4779	214	9	associated	associate	VERB
ejpam-4779	214	10	with	with	ADP
ejpam-4779	214	11	convex	convex	NOUN
ejpam-4779	214	12	functions	function	NOUN
ejpam-4779	214	13	.	.	PUNCT
ejpam-4779	215	1	journal	journal	NOUN
ejpam-4779	215	2	of	of	ADP
ejpam-4779	215	3	function	function	NOUN
ejpam-4779	215	4	spaces	space	NOUN
ejpam-4779	215	5	,	,	PUNCT
ejpam-4779	215	6	2021:1–7	2021:1–7	PROPN
ejpam-4779	215	7	,	,	PUNCT
ejpam-4779	215	8	2021	2021	NUM
ejpam-4779	215	9	.	.	PUNCT
ejpam-4779	216	1	[	[	X
ejpam-4779	216	2	4	4	X
ejpam-4779	216	3	]	]	PUNCT
ejpam-4779	216	4	vasudevarao	vasudevarao	VERB
ejpam-4779	216	5	allu	allu	NOUN
ejpam-4779	216	6	and	and	CCONJ
ejpam-4779	216	7	vibhuti	vibhuti	PROPN
ejpam-4779	216	8	arora	arora	PROPN
ejpam-4779	216	9	.	.	PUNCT
ejpam-4779	217	1	second	second	ADJ
ejpam-4779	217	2	hankel	hankel	NOUN
ejpam-4779	217	3	determinant	determinant	ADJ
ejpam-4779	217	4	of	of	ADP
ejpam-4779	217	5	logarithmic	logarithmic	ADJ
ejpam-4779	217	6	coefficients	coefficient	NOUN
ejpam-4779	217	7	of	of	ADP
ejpam-4779	217	8	certain	certain	ADJ
ejpam-4779	217	9	analytic	analytic	ADJ
ejpam-4779	217	10	functions	function	NOUN
ejpam-4779	217	11	.	.	PUNCT
ejpam-4779	218	1	arxiv	arxiv	PROPN
ejpam-4779	218	2	preprint	preprint	NOUN
ejpam-4779	218	3	arxiv:2110.05161	arxiv:2110.05161	ADJ
ejpam-4779	218	4	,	,	PUNCT
ejpam-4779	218	5	2021	2021	NUM
ejpam-4779	218	6	.	.	PUNCT
ejpam-4779	219	1	[	[	X
ejpam-4779	219	2	5	5	NUM
ejpam-4779	219	3	]	]	PUNCT
ejpam-4779	219	4	vasudevarao	vasudevarao	VERB
ejpam-4779	219	5	allu	allu	NOUN
ejpam-4779	219	6	,	,	PUNCT
ejpam-4779	219	7	vibhuti	vibhuti	PROPN
ejpam-4779	219	8	arora	arora	PROPN
ejpam-4779	219	9	,	,	PUNCT
ejpam-4779	219	10	and	and	CCONJ
ejpam-4779	219	11	amal	amal	PROPN
ejpam-4779	219	12	shaji	shaji	PROPN
ejpam-4779	219	13	.	.	PROPN
ejpam-4779	220	1	on	on	ADP
ejpam-4779	220	2	the	the	DET
ejpam-4779	220	3	second	second	ADJ
ejpam-4779	220	4	hankel	hankel	NOUN
ejpam-4779	220	5	determinant	determinant	ADJ
ejpam-4779	220	6	of	of	ADP
ejpam-4779	220	7	logarithmic	logarithmic	ADJ
ejpam-4779	220	8	coefficients	coefficient	NOUN
ejpam-4779	220	9	for	for	ADP
ejpam-4779	220	10	certain	certain	ADJ
ejpam-4779	220	11	univalent	univalent	ADJ
ejpam-4779	220	12	functions	function	NOUN
ejpam-4779	220	13	.	.	PUNCT
ejpam-4779	221	1	mediterranean	mediterranean	PROPN
ejpam-4779	221	2	journal	journal	PROPN
ejpam-4779	221	3	of	of	ADP
ejpam-4779	221	4	mathematics	mathematic	NOUN
ejpam-4779	221	5	,	,	PUNCT
ejpam-4779	221	6	20(2):81	20(2):81	NUM
ejpam-4779	221	7	,	,	PUNCT
ejpam-4779	221	8	2023	2023	NUM
ejpam-4779	221	9	.	.	PUNCT
ejpam-4779	222	1	[	[	X
ejpam-4779	222	2	6	6	X
ejpam-4779	222	3	]	]	X
ejpam-4779	222	4	muhammad	muhammad	PROPN
ejpam-4779	222	5	arif	arif	PROPN
ejpam-4779	222	6	,	,	PUNCT
ejpam-4779	222	7	mohsan	mohsan	PROPN
ejpam-4779	222	8	raza	raza	PROPN
ejpam-4779	222	9	,	,	PUNCT
ejpam-4779	222	10	huo	huo	PROPN
ejpam-4779	222	11	tang	tang	PROPN
ejpam-4779	222	12	,	,	PUNCT
ejpam-4779	222	13	shehzad	shehzad	PROPN
ejpam-4779	222	14	hussain	hussain	PROPN
ejpam-4779	222	15	,	,	PUNCT
ejpam-4779	222	16	and	and	CCONJ
ejpam-4779	222	17	hassan	hassan	PROPN
ejpam-4779	222	18	khan	khan	PROPN
ejpam-4779	222	19	.	.	PUNCT
ejpam-4779	223	1	hankel	hankel	NOUN
ejpam-4779	223	2	determinant	determinant	ADJ
ejpam-4779	223	3	of	of	ADP
ejpam-4779	223	4	order	order	NOUN
ejpam-4779	223	5	three	three	NUM
ejpam-4779	223	6	for	for	ADP
ejpam-4779	223	7	familiar	familiar	ADJ
ejpam-4779	223	8	subsets	subset	NOUN
ejpam-4779	223	9	of	of	ADP
ejpam-4779	223	10	analytic	analytic	ADJ
ejpam-4779	223	11	functions	function	NOUN
ejpam-4779	223	12	related	relate	VERB
ejpam-4779	223	13	with	with	ADP
ejpam-4779	223	14	sine	sine	ADJ
ejpam-4779	223	15	function	function	NOUN
ejpam-4779	223	16	.	.	PUNCT
ejpam-4779	224	1	open	open	ADJ
ejpam-4779	224	2	mathematics	mathematic	NOUN
ejpam-4779	224	3	,	,	PUNCT
ejpam-4779	224	4	17(1):1615–1630	17(1):1615–1630	PROPN
ejpam-4779	224	5	,	,	PUNCT
ejpam-4779	224	6	2019	2019	NUM
ejpam-4779	224	7	.	.	PUNCT
ejpam-4779	225	1	[	[	X
ejpam-4779	225	2	7	7	X
ejpam-4779	225	3	]	]	X
ejpam-4779	225	4	david	david	PROPN
ejpam-4779	225	5	g	g	PROPN
ejpam-4779	225	6	cantor	cantor	PROPN
ejpam-4779	225	7	.	.	PUNCT
ejpam-4779	226	1	power	power	NOUN
ejpam-4779	226	2	series	series	PROPN
ejpam-4779	226	3	with	with	ADP
ejpam-4779	226	4	integral	integral	ADJ
ejpam-4779	226	5	coefficients	coefficient	NOUN
ejpam-4779	226	6	.	.	PUNCT
ejpam-4779	227	1	1963	1963	NUM
ejpam-4779	227	2	.	.	PUNCT
ejpam-4779	228	1	[	[	X
ejpam-4779	228	2	8	8	NUM
ejpam-4779	228	3	]	]	X
ejpam-4779	228	4	paul	paul	PROPN
ejpam-4779	228	5	dienes	dienes	PROPN
ejpam-4779	228	6	.	.	PUNCT
ejpam-4779	229	1	the	the	DET
ejpam-4779	229	2	taylor	taylor	PROPN
ejpam-4779	229	3	series	series	PROPN
ejpam-4779	229	4	.	.	PUNCT
ejpam-4779	230	1	an	an	DET
ejpam-4779	230	2	introduction	introduction	NOUN
ejpam-4779	230	3	to	to	ADP
ejpam-4779	230	4	the	the	DET
ejpam-4779	230	5	theory	theory	NOUN
ejpam-4779	230	6	of	of	ADP
ejpam-4779	230	7	functions	function	NOUN
ejpam-4779	230	8	of	of	ADP
ejpam-4779	230	9	a	a	DET
ejpam-4779	230	10	complex	complex	ADJ
ejpam-4779	230	11	variable	variable	NOUN
ejpam-4779	230	12	.	.	PUNCT
ejpam-4779	231	1	dover	dover	PROPN
ejpam-4779	231	2	books	book	NOUN
ejpam-4779	231	3	on	on	ADP
ejpam-4779	231	4	science	science	NOUN
ejpam-4779	231	5	s	s	PROPN
ejpam-4779	231	6	,	,	PUNCT
ejpam-4779	231	7	1957	1957	NUM
ejpam-4779	231	8	.	.	PUNCT
ejpam-4779	232	1	[	[	X
ejpam-4779	232	2	9	9	NUM
ejpam-4779	232	3	]	]	SYM
ejpam-4779	232	4	pl	pl	PROPN
ejpam-4779	232	5	duren	duren	PROPN
ejpam-4779	232	6	.	.	PUNCT
ejpam-4779	232	7	univalent	univalent	ADJ
ejpam-4779	232	8	functions	function	NOUN
ejpam-4779	232	9	,	,	PUNCT
ejpam-4779	232	10	vol	vol	NOUN
ejpam-4779	232	11	.	.	PUNCT
ejpam-4779	232	12	259,(1983	259,(1983	NUM
ejpam-4779	232	13	)	)	PUNCT
ejpam-4779	232	14	.	.	PUNCT
ejpam-4779	233	1	[	[	X
ejpam-4779	233	2	10	10	NUM
ejpam-4779	233	3	]	]	X
ejpam-4779	233	4	iason	iason	NOUN
ejpam-4779	233	5	efraimidis	efraimidis	NOUN
ejpam-4779	233	6	.	.	PUNCT
ejpam-4779	234	1	a	a	DET
ejpam-4779	234	2	generalization	generalization	NOUN
ejpam-4779	234	3	of	of	ADP
ejpam-4779	234	4	livingston	livingston	PROPN
ejpam-4779	234	5	’s	’s	PART
ejpam-4779	234	6	coefficient	coefficient	NOUN
ejpam-4779	234	7	inequalities	inequality	NOUN
ejpam-4779	234	8	for	for	ADP
ejpam-4779	234	9	functions	function	NOUN
ejpam-4779	234	10	with	with	ADP
ejpam-4779	234	11	positive	positive	ADJ
ejpam-4779	234	12	real	real	ADJ
ejpam-4779	234	13	part	part	NOUN
ejpam-4779	234	14	.	.	PUNCT
ejpam-4779	235	1	journal	journal	PROPN
ejpam-4779	235	2	of	of	ADP
ejpam-4779	235	3	mathematical	mathematical	ADJ
ejpam-4779	235	4	analysis	analysis	NOUN
ejpam-4779	235	5	and	and	CCONJ
ejpam-4779	235	6	applications	application	NOUN
ejpam-4779	235	7	,	,	PUNCT
ejpam-4779	235	8	435(1):369–379	435(1):369–379	PROPN
ejpam-4779	235	9	,	,	PUNCT
ejpam-4779	235	10	2016	2016	NUM
ejpam-4779	235	11	.	.	PUNCT
ejpam-4779	236	1	[	[	X
ejpam-4779	236	2	11	11	NUM
ejpam-4779	236	3	]	]	X
ejpam-4779	236	4	rabha	rabha	PROPN
ejpam-4779	236	5	md	md	PROPN
ejpam-4779	236	6	el	el	PROPN
ejpam-4779	236	7	-	-	PROPN
ejpam-4779	236	8	ashwah	ashwah	NOUN
ejpam-4779	236	9	and	and	CCONJ
ejpam-4779	236	10	dk	dk	PROPN
ejpam-4779	236	11	thomas	thomas	PROPN
ejpam-4779	236	12	.	.	PUNCT
ejpam-4779	237	1	some	some	DET
ejpam-4779	237	2	subclasses	subclass	NOUN
ejpam-4779	237	3	of	of	ADP
ejpam-4779	237	4	close	close	NOUN
ejpam-4779	237	5	-	-	PUNCT
ejpam-4779	237	6	to	to	ADP
ejpam-4779	237	7	-	-	PUNCT
ejpam-4779	237	8	convex	convex	NOUN
ejpam-4779	237	9	functions	function	NOUN
ejpam-4779	237	10	.	.	PUNCT
ejpam-4779	238	1	j.	j.	PROPN
ejpam-4779	238	2	ramanujan	ramanujan	PROPN
ejpam-4779	238	3	math	math	PROPN
ejpam-4779	238	4	.	.	PUNCT
ejpam-4779	239	1	soc	soc	PROPN
ejpam-4779	239	2	,	,	PUNCT
ejpam-4779	239	3	2(1):85–100	2(1):85–100	NUM
ejpam-4779	239	4	,	,	PUNCT
ejpam-4779	239	5	1987	1987	NUM
ejpam-4779	239	6	.	.	PUNCT
ejpam-4779	240	1	[	[	X
ejpam-4779	240	2	12	12	NUM
ejpam-4779	240	3	]	]	X
ejpam-4779	240	4	surya	surya	PROPN
ejpam-4779	240	5	giri	giri	PROPN
ejpam-4779	240	6	and	and	CCONJ
ejpam-4779	240	7	s	s	PROPN
ejpam-4779	240	8	sivaprasad	sivaprasad	PROPN
ejpam-4779	240	9	kumar	kumar	PROPN
ejpam-4779	240	10	.	.	PUNCT
ejpam-4779	241	1	toeplitz	toeplitz	NOUN
ejpam-4779	241	2	determinants	determinant	NOUN
ejpam-4779	241	3	of	of	ADP
ejpam-4779	241	4	logarithmic	logarithmic	ADJ
ejpam-4779	241	5	coefficients	coefficient	NOUN
ejpam-4779	241	6	for	for	ADP
ejpam-4779	241	7	starlike	starlike	NOUN
ejpam-4779	241	8	and	and	CCONJ
ejpam-4779	241	9	convex	convex	NOUN
ejpam-4779	241	10	functions	function	NOUN
ejpam-4779	241	11	.	.	PUNCT
ejpam-4779	242	1	arxiv	arxiv	PROPN
ejpam-4779	242	2	preprint	preprint	PROPN
ejpam-4779	242	3	arxiv:2303.14712	arxiv:2303.14712	NOUN
ejpam-4779	242	4	,	,	PUNCT
ejpam-4779	242	5	2023	2023	NUM
ejpam-4779	242	6	.	.	PUNCT
ejpam-4779	243	1	[	[	X
ejpam-4779	243	2	13	13	NUM
ejpam-4779	243	3	]	]	PUNCT
ejpam-4779	243	4	w	w	PROPN
ejpam-4779	243	5	janowski	janowski	PROPN
ejpam-4779	243	6	.	.	PUNCT
ejpam-4779	244	1	some	some	DET
ejpam-4779	244	2	extremal	extremal	ADJ
ejpam-4779	244	3	problems	problem	NOUN
ejpam-4779	244	4	for	for	ADP
ejpam-4779	244	5	certain	certain	ADJ
ejpam-4779	244	6	families	family	NOUN
ejpam-4779	244	7	of	of	ADP
ejpam-4779	244	8	analytic	analytic	ADJ
ejpam-4779	244	9	functions	function	NOUN
ejpam-4779	244	10	i.	i.	NOUN
ejpam-4779	244	11	in	in	ADP
ejpam-4779	244	12	annales	annales	PROPN
ejpam-4779	244	13	polonici	polonici	PROPN
ejpam-4779	244	14	mathematici	mathematici	NOUN
ejpam-4779	244	15	,	,	PUNCT
ejpam-4779	244	16	volume	volume	NOUN
ejpam-4779	244	17	3	3	NUM
ejpam-4779	244	18	,	,	PUNCT
ejpam-4779	244	19	pages	page	NOUN
ejpam-4779	244	20	297–326	297–326	NUM
ejpam-4779	244	21	,	,	PUNCT
ejpam-4779	244	22	1973	1973	NUM
ejpam-4779	244	23	.	.	PUNCT
ejpam-4779	245	1	[	[	X
ejpam-4779	245	2	14	14	NUM
ejpam-4779	245	3	]	]	PUNCT
ejpam-4779	245	4	ip	ip	NOUN
ejpam-4779	245	5	kayumov	kayumov	ADJ
ejpam-4779	245	6	.	.	PUNCT
ejpam-4779	246	1	on	on	ADP
ejpam-4779	246	2	brennan	brennan	PROPN
ejpam-4779	246	3	’s	’s	PART
ejpam-4779	246	4	conjecture	conjecture	NOUN
ejpam-4779	246	5	for	for	ADP
ejpam-4779	246	6	a	a	DET
ejpam-4779	246	7	special	special	ADJ
ejpam-4779	246	8	class	class	NOUN
ejpam-4779	246	9	of	of	ADP
ejpam-4779	246	10	functions	function	NOUN
ejpam-4779	246	11	.	.	PUNCT
ejpam-4779	247	1	mathematical	mathematical	ADJ
ejpam-4779	247	2	notes	note	NOUN
ejpam-4779	247	3	,	,	PUNCT
ejpam-4779	247	4	78:498–502	78:498–502	PROPN
ejpam-4779	247	5	,	,	PUNCT
ejpam-4779	247	6	2005	2005	NUM
ejpam-4779	247	7	.	.	PUNCT
ejpam-4779	248	1	[	[	X
ejpam-4779	248	2	15	15	NUM
ejpam-4779	248	3	]	]	X
ejpam-4779	248	4	bilal	bilal	PROPN
ejpam-4779	248	5	khan	khan	PROPN
ejpam-4779	248	6	,	,	PUNCT
ejpam-4779	248	7	ibtisam	ibtisam	PROPN
ejpam-4779	248	8	aldawish	aldawish	PROPN
ejpam-4779	248	9	,	,	PUNCT
ejpam-4779	248	10	serkan	serkan	ADJ
ejpam-4779	248	11	araci	araci	NOUN
ejpam-4779	248	12	,	,	PUNCT
ejpam-4779	248	13	and	and	CCONJ
ejpam-4779	248	14	muhammad	muhammad	PROPN
ejpam-4779	248	15	ghaffar	ghaffar	PROPN
ejpam-4779	248	16	khan	khan	PROPN
ejpam-4779	248	17	.	.	PUNCT
ejpam-4779	249	1	third	third	ADJ
ejpam-4779	249	2	hankel	hankel	NOUN
ejpam-4779	249	3	determinant	determinant	ADJ
ejpam-4779	249	4	for	for	ADP
ejpam-4779	249	5	the	the	DET
ejpam-4779	249	6	logarithmic	logarithmic	ADJ
ejpam-4779	249	7	coefficients	coefficient	NOUN
ejpam-4779	249	8	of	of	ADP
ejpam-4779	249	9	starlike	starlike	NOUN
ejpam-4779	249	10	functions	function	NOUN
ejpam-4779	249	11	associated	associate	VERB
ejpam-4779	249	12	with	with	ADP
ejpam-4779	249	13	sine	sine	ADJ
ejpam-4779	249	14	function	function	NOUN
ejpam-4779	249	15	.	.	PUNCT
ejpam-4779	250	1	fractal	fractal	ADJ
ejpam-4779	250	2	and	and	CCONJ
ejpam-4779	250	3	fractional	fractional	ADJ
ejpam-4779	250	4	,	,	PUNCT
ejpam-4779	250	5	6(5):261	6(5):261	NUM
ejpam-4779	250	6	,	,	PUNCT
ejpam-4779	250	7	2022	2022	NUM
ejpam-4779	250	8	.	.	PUNCT
ejpam-4779	251	1	references	reference	NOUN
ejpam-4779	251	2	1178	1178	NUM
ejpam-4779	252	1	[	[	X
ejpam-4779	252	2	16	16	NUM
ejpam-4779	252	3	]	]	X
ejpam-4779	252	4	mg	mg	PROPN
ejpam-4779	252	5	khan	khan	PROPN
ejpam-4779	252	6	,	,	PUNCT
ejpam-4779	252	7	b	b	PROPN
ejpam-4779	252	8	ahmad	ahmad	PROPN
ejpam-4779	252	9	,	,	PUNCT
ejpam-4779	252	10	g	g	PROPN
ejpam-4779	252	11	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-4779	252	12	,	,	PUNCT
ejpam-4779	252	13	wk	wk	X
ejpam-4779	252	14	mashwani	mashwani	PROPN
ejpam-4779	252	15	,	,	PUNCT
ejpam-4779	252	16	s	s	VERB
ejpam-4779	252	17	yalcin	yalcin	PROPN
ejpam-4779	252	18	,	,	PUNCT
ejpam-4779	252	19	tg	tg	PROPN
ejpam-4779	252	20	shaba	shaba	PROPN
ejpam-4779	252	21	,	,	PUNCT
ejpam-4779	252	22	and	and	CCONJ
ejpam-4779	252	23	z	z	PROPN
ejpam-4779	252	24	salleh	salleh	PROPN
ejpam-4779	252	25	.	.	PUNCT
ejpam-4779	253	1	third	third	ADJ
ejpam-4779	253	2	hankel	hankel	NOUN
ejpam-4779	253	3	determinant	determinant	ADJ
ejpam-4779	253	4	and	and	CCONJ
ejpam-4779	253	5	zalcman	zalcman	NOUN
ejpam-4779	253	6	functional	functional	PROPN
ejpam-4779	253	7	for	for	ADP
ejpam-4779	253	8	a	a	DET
ejpam-4779	253	9	class	class	NOUN
ejpam-4779	253	10	of	of	ADP
ejpam-4779	253	11	starlike	starlike	NOUN
ejpam-4779	253	12	functions	function	NOUN
ejpam-4779	253	13	with	with	ADP
ejpam-4779	253	14	respect	respect	NOUN
ejpam-4779	253	15	to	to	ADP
ejpam-4779	253	16	symmetric	symmetric	ADJ
ejpam-4779	253	17	points	point	NOUN
ejpam-4779	253	18	related	relate	VERB
ejpam-4779	253	19	with	with	ADP
ejpam-4779	253	20	sine	sine	ADJ
ejpam-4779	253	21	function	function	NOUN
ejpam-4779	253	22	.	.	PUNCT
ejpam-4779	254	1	j.	j.	PROPN
ejpam-4779	254	2	math	math	PROPN
ejpam-4779	254	3	.	.	PUNCT
ejpam-4779	255	1	comput	comput	NOUN
ejpam-4779	255	2	.	.	PUNCT
ejpam-4779	256	1	sci	sci	PROPN
ejpam-4779	256	2	,	,	PUNCT
ejpam-4779	256	3	25:29–36	25:29–36	NUM
ejpam-4779	256	4	,	,	PUNCT
ejpam-4779	256	5	2022	2022	NUM
ejpam-4779	256	6	.	.	PUNCT
ejpam-4779	257	1	[	[	X
ejpam-4779	257	2	17	17	NUM
ejpam-4779	257	3	]	]	X
ejpam-4779	257	4	bogumi	bogumi	NOUN
ejpam-4779	257	5	la	la	PROPN
ejpam-4779	257	6	kowalczyk	kowalczyk	PROPN
ejpam-4779	257	7	and	and	CCONJ
ejpam-4779	257	8	adam	adam	PROPN
ejpam-4779	257	9	lecko	lecko	PROPN
ejpam-4779	257	10	.	.	PUNCT
ejpam-4779	258	1	second	second	ADJ
ejpam-4779	258	2	hankel	hankel	NOUN
ejpam-4779	258	3	determinant	determinant	ADJ
ejpam-4779	258	4	of	of	ADP
ejpam-4779	258	5	logarithmic	logarithmic	ADJ
ejpam-4779	258	6	coefficients	coefficient	NOUN
ejpam-4779	258	7	of	of	ADP
ejpam-4779	258	8	convex	convex	NOUN
ejpam-4779	258	9	and	and	CCONJ
ejpam-4779	258	10	starlike	starlike	NOUN
ejpam-4779	258	11	functions	function	NOUN
ejpam-4779	258	12	.	.	PUNCT
ejpam-4779	259	1	bulletin	bulletin	NOUN
ejpam-4779	259	2	of	of	ADP
ejpam-4779	259	3	the	the	DET
ejpam-4779	259	4	australian	australian	ADJ
ejpam-4779	259	5	mathematical	mathematical	ADJ
ejpam-4779	259	6	society	society	NOUN
ejpam-4779	259	7	,	,	PUNCT
ejpam-4779	259	8	105(3):458–467	105(3):458–467	NUM
ejpam-4779	259	9	,	,	PUNCT
ejpam-4779	259	10	2022	2022	NUM
ejpam-4779	259	11	.	.	PUNCT
ejpam-4779	260	1	[	[	X
ejpam-4779	260	2	18	18	NUM
ejpam-4779	260	3	]	]	X
ejpam-4779	260	4	bogumi	bogumi	NOUN
ejpam-4779	260	5	la	la	PROPN
ejpam-4779	260	6	kowalczyk	kowalczyk	PROPN
ejpam-4779	260	7	and	and	CCONJ
ejpam-4779	260	8	adam	adam	PROPN
ejpam-4779	260	9	lecko	lecko	PROPN
ejpam-4779	260	10	.	.	PUNCT
ejpam-4779	261	1	second	second	ADJ
ejpam-4779	261	2	hankel	hankel	NOUN
ejpam-4779	261	3	determinant	determinant	ADJ
ejpam-4779	261	4	of	of	ADP
ejpam-4779	261	5	logarithmic	logarithmic	ADJ
ejpam-4779	261	6	coefficients	coefficient	NOUN
ejpam-4779	261	7	of	of	ADP
ejpam-4779	261	8	convex	convex	NOUN
ejpam-4779	261	9	and	and	CCONJ
ejpam-4779	261	10	starlike	starlike	NOUN
ejpam-4779	261	11	functions	function	NOUN
ejpam-4779	261	12	of	of	ADP
ejpam-4779	261	13	order	order	NOUN
ejpam-4779	261	14	alpha	alpha	NOUN
ejpam-4779	261	15	.	.	PUNCT
ejpam-4779	262	1	bulletin	bulletin	NOUN
ejpam-4779	262	2	of	of	ADP
ejpam-4779	262	3	the	the	DET
ejpam-4779	262	4	malaysian	malaysian	PROPN
ejpam-4779	262	5	mathematical	mathematical	PROPN
ejpam-4779	262	6	sciences	sciences	PROPN
ejpam-4779	262	7	society	society	NOUN
ejpam-4779	262	8	,	,	PUNCT
ejpam-4779	262	9	45(2):727–740	45(2):727–740	NOUN
ejpam-4779	262	10	,	,	PUNCT
ejpam-4779	262	11	2022	2022	NUM
ejpam-4779	262	12	.	.	PUNCT
ejpam-4779	263	1	[	[	X
ejpam-4779	263	2	19	19	NUM
ejpam-4779	263	3	]	]	X
ejpam-4779	263	4	i	i	NOUN
ejpam-4779	263	5	m	m	PROPN
ejpam-4779	263	6	milin	milin	PROPN
ejpam-4779	263	7	.	.	PUNCT
ejpam-4779	264	1	on	on	ADP
ejpam-4779	264	2	a	a	DET
ejpam-4779	264	3	property	property	NOUN
ejpam-4779	264	4	of	of	ADP
ejpam-4779	264	5	the	the	DET
ejpam-4779	264	6	logarithmic	logarithmic	ADJ
ejpam-4779	264	7	coefficients	coefficient	NOUN
ejpam-4779	264	8	of	of	ADP
ejpam-4779	264	9	univalent	univalent	ADJ
ejpam-4779	264	10	functions	function	NOUN
ejpam-4779	264	11	.	.	PUNCT
ejpam-4779	265	1	metric	metric	ADJ
ejpam-4779	265	2	questions	question	NOUN
ejpam-4779	265	3	in	in	ADP
ejpam-4779	265	4	the	the	DET
ejpam-4779	265	5	theory	theory	NOUN
ejpam-4779	265	6	of	of	ADP
ejpam-4779	265	7	functions	function	NOUN
ejpam-4779	265	8	,	,	PUNCT
ejpam-4779	265	9	naukova	naukova	PROPN
ejpam-4779	265	10	dumka	dumka	PROPN
ejpam-4779	265	11	,	,	PUNCT
ejpam-4779	265	12	kiev	kiev	PROPN
ejpam-4779	265	13	,	,	PUNCT
ejpam-4779	265	14	pages	page	NOUN
ejpam-4779	265	15	86–90	86–90	NUM
ejpam-4779	265	16	,	,	PUNCT
ejpam-4779	265	17	1980	1980	NUM
ejpam-4779	265	18	.	.	PUNCT
ejpam-4779	266	1	[	[	X
ejpam-4779	266	2	20	20	NUM
ejpam-4779	266	3	]	]	PUNCT
ejpam-4779	266	4	isaak	isaak	PROPN
ejpam-4779	266	5	moiseevich	moiseevich	PROPN
ejpam-4779	266	6	milin	milin	PROPN
ejpam-4779	266	7	.	.	PUNCT
ejpam-4779	267	1	univalent	univalent	ADJ
ejpam-4779	267	2	functions	function	NOUN
ejpam-4779	267	3	and	and	CCONJ
ejpam-4779	267	4	orthonormal	orthonormal	ADJ
ejpam-4779	267	5	systems	system	NOUN
ejpam-4779	267	6	,	,	PUNCT
ejpam-4779	267	7	volume	volume	NOUN
ejpam-4779	267	8	49	49	NUM
ejpam-4779	267	9	.	.	PUNCT
ejpam-4779	268	1	amer	amer	PROPN
ejpam-4779	268	2	mathematical	mathematical	PROPN
ejpam-4779	268	3	society	society	NOUN
ejpam-4779	268	4	,	,	PUNCT
ejpam-4779	268	5	1977	1977	NUM
ejpam-4779	268	6	.	.	PUNCT
ejpam-4779	269	1	[	[	X
ejpam-4779	269	2	21	21	NUM
ejpam-4779	269	3	]	]	X
ejpam-4779	269	4	isaak	isaak	PROPN
ejpam-4779	269	5	moiseevich	moiseevich	PROPN
ejpam-4779	269	6	milin	milin	PROPN
ejpam-4779	269	7	.	.	PUNCT
ejpam-4779	270	1	on	on	ADP
ejpam-4779	270	2	one	one	NUM
ejpam-4779	270	3	conjecture	conjecture	NOUN
ejpam-4779	270	4	for	for	ADP
ejpam-4779	270	5	the	the	DET
ejpam-4779	270	6	logariphmic	logariphmic	ADJ
ejpam-4779	270	7	coefficients	coefficient	NOUN
ejpam-4779	270	8	of	of	ADP
ejpam-4779	270	9	univalent	univalent	ADJ
ejpam-4779	270	10	functions	function	NOUN
ejpam-4779	270	11	.	.	PUNCT
ejpam-4779	271	1	zapiski	zapiski	PROPN
ejpam-4779	271	2	nauchnykh	nauchnykh	PROPN
ejpam-4779	271	3	seminarov	seminarov	PROPN
ejpam-4779	271	4	pomi	pomi	NOUN
ejpam-4779	271	5	,	,	PUNCT
ejpam-4779	271	6	125:135–143	125:135–143	NUM
ejpam-4779	271	7	,	,	PUNCT
ejpam-4779	271	8	1983	1983	NUM
ejpam-4779	271	9	.	.	PUNCT
ejpam-4779	272	1	[	[	X
ejpam-4779	272	2	22	22	NUM
ejpam-4779	272	3	]	]	X
ejpam-4779	272	4	ambuj	ambuj	PROPN
ejpam-4779	272	5	k	k	PROPN
ejpam-4779	272	6	mishra	mishra	PROPN
ejpam-4779	272	7	,	,	PUNCT
ejpam-4779	272	8	jugal	jugal	PROPN
ejpam-4779	272	9	k	k	PROPN
ejpam-4779	272	10	prajapat	prajapat	PROPN
ejpam-4779	272	11	,	,	PUNCT
ejpam-4779	272	12	and	and	CCONJ
ejpam-4779	272	13	sudhananda	sudhananda	ADV
ejpam-4779	272	14	maharana	maharana	PROPN
ejpam-4779	272	15	.	.	PUNCT
ejpam-4779	273	1	bounds	bound	VERB
ejpam-4779	273	2	on	on	ADP
ejpam-4779	273	3	hankel	hankel	NOUN
ejpam-4779	273	4	determinant	determinant	ADJ
ejpam-4779	273	5	for	for	ADP
ejpam-4779	273	6	starlike	starlike	NOUN
ejpam-4779	273	7	and	and	CCONJ
ejpam-4779	273	8	convex	convex	NOUN
ejpam-4779	273	9	functions	function	NOUN
ejpam-4779	273	10	with	with	ADP
ejpam-4779	273	11	respect	respect	NOUN
ejpam-4779	273	12	to	to	ADP
ejpam-4779	273	13	symmetric	symmetric	ADJ
ejpam-4779	273	14	points	point	NOUN
ejpam-4779	273	15	.	.	PUNCT
ejpam-4779	274	1	cogent	cogent	NOUN
ejpam-4779	274	2	mathematics	mathematic	NOUN
ejpam-4779	274	3	,	,	PUNCT
ejpam-4779	274	4	3(1):1160557	3(1):1160557	NUM
ejpam-4779	274	5	,	,	PUNCT
ejpam-4779	274	6	2016	2016	NUM
ejpam-4779	274	7	.	.	PUNCT
ejpam-4779	275	1	[	[	X
ejpam-4779	275	2	23	23	NUM
ejpam-4779	275	3	]	]	PUNCT
ejpam-4779	275	4	daud	daud	PROPN
ejpam-4779	275	5	mohamad	mohamad	PROPN
ejpam-4779	275	6	and	and	CCONJ
ejpam-4779	275	7	nur	nur	VERB
ejpam-4779	275	8	hazwani	hazwani	PROPN
ejpam-4779	275	9	aqilah	aqilah	PROPN
ejpam-4779	275	10	abdul	abdul	PROPN
ejpam-4779	275	11	wahid	wahid	PROPN
ejpam-4779	275	12	.	.	PUNCT
ejpam-4779	276	1	hankel	hankel	NOUN
ejpam-4779	276	2	determinant	determinant	ADJ
ejpam-4779	276	3	of	of	ADP
ejpam-4779	276	4	logarithmic	logarithmic	ADJ
ejpam-4779	276	5	coefficients	coefficient	NOUN
ejpam-4779	276	6	for	for	ADP
ejpam-4779	276	7	tilted	tilted	ADJ
ejpam-4779	276	8	starlike	starlike	NOUN
ejpam-4779	276	9	functions	function	NOUN
ejpam-4779	276	10	with	with	ADP
ejpam-4779	276	11	respect	respect	NOUN
ejpam-4779	276	12	to	to	ADP
ejpam-4779	276	13	conjugate	conjugate	ADJ
ejpam-4779	276	14	points	point	NOUN
ejpam-4779	276	15	.	.	PUNCT
ejpam-4779	277	1	international	international	ADJ
ejpam-4779	277	2	journal	journal	NOUN
ejpam-4779	277	3	of	of	ADP
ejpam-4779	277	4	analysis	analysis	NOUN
ejpam-4779	277	5	and	and	CCONJ
ejpam-4779	277	6	applications	application	NOUN
ejpam-4779	277	7	,	,	PUNCT
ejpam-4779	277	8	21:10–10	21:10–10	NUM
ejpam-4779	277	9	,	,	PUNCT
ejpam-4779	277	10	2023	2023	NUM
ejpam-4779	277	11	.	.	PUNCT
ejpam-4779	278	1	[	[	X
ejpam-4779	278	2	24	24	NUM
ejpam-4779	278	3	]	]	SYM
ejpam-4779	278	4	daud	daud	PROPN
ejpam-4779	278	5	mohamad	mohamad	PROPN
ejpam-4779	278	6	,	,	PUNCT
ejpam-4779	278	7	nur	nur	PROPN
ejpam-4779	278	8	hazwani	hazwani	PROPN
ejpam-4779	278	9	aqilah	aqilah	PROPN
ejpam-4779	278	10	abdul	abdul	PROPN
ejpam-4779	278	11	wahid	wahid	PROPN
ejpam-4779	278	12	,	,	PUNCT
ejpam-4779	278	13	and	and	CCONJ
ejpam-4779	278	14	nurfatin	nurfatin	PROPN
ejpam-4779	278	15	nabilah	nabilah	PROPN
ejpam-4779	278	16	md	md	PROPN
ejpam-4779	278	17	fauzi	fauzi	PROPN
ejpam-4779	278	18	.	.	PUNCT
ejpam-4779	279	1	some	some	DET
ejpam-4779	279	2	properties	property	NOUN
ejpam-4779	279	3	of	of	ADP
ejpam-4779	279	4	a	a	DET
ejpam-4779	279	5	new	new	ADJ
ejpam-4779	279	6	subclass	subclass	NOUN
ejpam-4779	279	7	of	of	ADP
ejpam-4779	279	8	tilted	tilted	ADJ
ejpam-4779	279	9	star	star	NOUN
ejpam-4779	279	10	-	-	PUNCT
ejpam-4779	279	11	like	like	ADJ
ejpam-4779	279	12	functions	function	NOUN
ejpam-4779	279	13	with	with	ADP
ejpam-4779	279	14	respect	respect	NOUN
ejpam-4779	279	15	to	to	ADP
ejpam-4779	279	16	symmetric	symmetric	ADJ
ejpam-4779	279	17	conjugate	conjugate	ADJ
ejpam-4779	279	18	points	point	NOUN
ejpam-4779	279	19	.	.	PUNCT
ejpam-4779	280	1	aims	aim	VERB
ejpam-4779	280	2	mathematics	mathematic	NOUN
ejpam-4779	280	3	,	,	PUNCT
ejpam-4779	280	4	8(1):1889–1900	8(1):1889–1900	NUM
ejpam-4779	280	5	,	,	PUNCT
ejpam-4779	280	6	2023	2023	NUM
ejpam-4779	280	7	.	.	PUNCT
ejpam-4779	281	1	[	[	X
ejpam-4779	281	2	25	25	NUM
ejpam-4779	281	3	]	]	PUNCT
ejpam-4779	281	4	milutin	milutin	NOUN
ejpam-4779	281	5	obradović	obradović	NOUN
ejpam-4779	281	6	,	,	PUNCT
ejpam-4779	281	7	saminathan	saminathan	NOUN
ejpam-4779	281	8	ponnusamy	ponnusamy	NOUN
ejpam-4779	281	9	,	,	PUNCT
ejpam-4779	281	10	and	and	CCONJ
ejpam-4779	281	11	karl	karl	PROPN
ejpam-4779	281	12	-	-	PUNCT
ejpam-4779	281	13	joachim	joachim	PROPN
ejpam-4779	281	14	wirths	wirth	NOUN
ejpam-4779	281	15	.	.	PUNCT
ejpam-4779	282	1	logarithmic	logarithmic	ADJ
ejpam-4779	282	2	coefficients	coefficient	NOUN
ejpam-4779	282	3	and	and	CCONJ
ejpam-4779	282	4	a	a	DET
ejpam-4779	282	5	coefficient	coefficient	NOUN
ejpam-4779	282	6	conjecture	conjecture	NOUN
ejpam-4779	282	7	for	for	ADP
ejpam-4779	282	8	univalent	univalent	ADJ
ejpam-4779	282	9	functions	function	NOUN
ejpam-4779	282	10	.	.	PUNCT
ejpam-4779	283	1	monatshefte	monatshefte	PROPN
ejpam-4779	283	2	für	für	PROPN
ejpam-4779	283	3	mathematik	mathematik	PROPN
ejpam-4779	283	4	,	,	PUNCT
ejpam-4779	283	5	185:489–501	185:489–501	NUM
ejpam-4779	283	6	,	,	PUNCT
ejpam-4779	283	7	2018	2018	NUM
ejpam-4779	283	8	.	.	PUNCT
ejpam-4779	284	1	[	[	X
ejpam-4779	284	2	26	26	NUM
ejpam-4779	284	3	]	]	X
ejpam-4779	284	4	loo	loo	PROPN
ejpam-4779	284	5	chien	chien	PROPN
ejpam-4779	284	6	ping	ping	PROPN
ejpam-4779	284	7	and	and	CCONJ
ejpam-4779	284	8	aini	aini	PROPN
ejpam-4779	284	9	janteng	janteng	PROPN
ejpam-4779	284	10	.	.	PUNCT
ejpam-4779	285	1	subclass	subclass	NOUN
ejpam-4779	285	2	of	of	ADP
ejpam-4779	285	3	starlike	starlike	NOUN
ejpam-4779	285	4	functions	function	NOUN
ejpam-4779	285	5	with	with	ADP
ejpam-4779	285	6	respect	respect	NOUN
ejpam-4779	285	7	to	to	ADP
ejpam-4779	285	8	symmetric	symmetric	ADJ
ejpam-4779	285	9	conjugate	conjugate	ADJ
ejpam-4779	285	10	points	point	NOUN
ejpam-4779	285	11	.	.	PUNCT
ejpam-4779	286	1	international	international	ADJ
ejpam-4779	286	2	journal	journal	NOUN
ejpam-4779	286	3	of	of	ADP
ejpam-4779	286	4	algebra	algebra	PROPN
ejpam-4779	286	5	,	,	PUNCT
ejpam-4779	286	6	5(16):755–762	5(16):755–762	NUM
ejpam-4779	286	7	,	,	PUNCT
ejpam-4779	286	8	2011	2011	NUM
ejpam-4779	286	9	.	.	PUNCT
ejpam-4779	287	1	[	[	X
ejpam-4779	287	2	27	27	NUM
ejpam-4779	287	3	]	]	SYM
ejpam-4779	287	4	ch	ch	NOUN
ejpam-4779	287	5	pommerenke	pommerenke	NOUN
ejpam-4779	287	6	.	.	PUNCT
ejpam-4779	288	1	on	on	ADP
ejpam-4779	288	2	the	the	DET
ejpam-4779	288	3	coefficients	coefficient	NOUN
ejpam-4779	288	4	and	and	CCONJ
ejpam-4779	288	5	hankel	hankel	NOUN
ejpam-4779	288	6	determinants	determinant	NOUN
ejpam-4779	288	7	of	of	ADP
ejpam-4779	288	8	univalent	univalent	ADJ
ejpam-4779	288	9	functions	function	NOUN
ejpam-4779	288	10	.	.	PUNCT
ejpam-4779	289	1	journal	journal	NOUN
ejpam-4779	289	2	of	of	ADP
ejpam-4779	289	3	the	the	DET
ejpam-4779	289	4	london	london	PROPN
ejpam-4779	289	5	mathematical	mathematical	ADJ
ejpam-4779	289	6	society	society	NOUN
ejpam-4779	289	7	,	,	PUNCT
ejpam-4779	289	8	1(1):111–122	1(1):111–122	NUM
ejpam-4779	289	9	,	,	PUNCT
ejpam-4779	289	10	1966	1966	NUM
ejpam-4779	289	11	.	.	PUNCT
ejpam-4779	290	1	[	[	X
ejpam-4779	290	2	28	28	NUM
ejpam-4779	290	3	]	]	X
ejpam-4779	290	4	ch	ch	NOUN
ejpam-4779	290	5	pommerenke	pommerenke	NOUN
ejpam-4779	290	6	.	.	PUNCT
ejpam-4779	291	1	on	on	ADP
ejpam-4779	291	2	the	the	DET
ejpam-4779	291	3	hankel	hankel	NOUN
ejpam-4779	291	4	determinants	determinant	NOUN
ejpam-4779	291	5	of	of	ADP
ejpam-4779	291	6	univalent	univalent	ADJ
ejpam-4779	291	7	functions	function	NOUN
ejpam-4779	291	8	.	.	PUNCT
ejpam-4779	291	9	mathematika	mathematika	NOUN
ejpam-4779	291	10	,	,	PUNCT
ejpam-4779	291	11	14(1):108–112	14(1):108–112	PROPN
ejpam-4779	291	12	,	,	PUNCT
ejpam-4779	291	13	1967	1967	NUM
ejpam-4779	291	14	.	.	PUNCT
ejpam-4779	292	1	references	reference	NOUN
ejpam-4779	292	2	1179	1179	NUM
ejpam-4779	292	3	[	[	X
ejpam-4779	292	4	29	29	NUM
ejpam-4779	292	5	]	]	X
ejpam-4779	292	6	lei	lei	PROPN
ejpam-4779	292	7	shi	shi	PROPN
ejpam-4779	292	8	,	,	PUNCT
ejpam-4779	292	9	muhammad	muhammad	PROPN
ejpam-4779	292	10	arif	arif	PROPN
ejpam-4779	292	11	,	,	PUNCT
ejpam-4779	292	12	ayesha	ayesha	PROPN
ejpam-4779	292	13	rafiq	rafiq	PROPN
ejpam-4779	292	14	,	,	PUNCT
ejpam-4779	292	15	muhammad	muhammad	PROPN
ejpam-4779	292	16	abbas	abbas	PROPN
ejpam-4779	292	17	,	,	PUNCT
ejpam-4779	292	18	and	and	CCONJ
ejpam-4779	292	19	javed	javed	PROPN
ejpam-4779	292	20	iqbal	iqbal	PROPN
ejpam-4779	292	21	.	.	PUNCT
ejpam-4779	293	1	sharp	sharp	ADJ
ejpam-4779	293	2	bounds	bound	NOUN
ejpam-4779	293	3	of	of	ADP
ejpam-4779	293	4	hankel	hankel	NOUN
ejpam-4779	293	5	determinant	determinant	ADJ
ejpam-4779	293	6	on	on	ADP
ejpam-4779	293	7	logarithmic	logarithmic	ADJ
ejpam-4779	293	8	coefficients	coefficient	NOUN
ejpam-4779	293	9	for	for	ADP
ejpam-4779	293	10	functions	function	NOUN
ejpam-4779	293	11	of	of	ADP
ejpam-4779	293	12	bounded	bounded	ADJ
ejpam-4779	293	13	turning	turning	NOUN
ejpam-4779	293	14	associated	associate	VERB
ejpam-4779	293	15	with	with	ADP
ejpam-4779	293	16	petal	petal	ADJ
ejpam-4779	293	17	-	-	PUNCT
ejpam-4779	293	18	shaped	shape	VERB
ejpam-4779	293	19	domain	domain	NOUN
ejpam-4779	293	20	.	.	PUNCT
ejpam-4779	294	1	mathematics	mathematic	NOUN
ejpam-4779	294	2	,	,	PUNCT
ejpam-4779	294	3	10(11):1939	10(11):1939	NUM
ejpam-4779	294	4	,	,	PUNCT
ejpam-4779	294	5	2022	2022	NUM
ejpam-4779	294	6	.	.	PUNCT
ejpam-4779	295	1	[	[	X
ejpam-4779	295	2	30	30	NUM
ejpam-4779	295	3	]	]	PUNCT
ejpam-4779	295	4	gagandeep	gagandeep	NOUN
ejpam-4779	295	5	singh	singh	PROPN
ejpam-4779	295	6	.	.	PUNCT
ejpam-4779	296	1	hankel	hankel	PROPN
ejpam-4779	296	2	determinant	determinant	ADJ
ejpam-4779	296	3	for	for	ADP
ejpam-4779	296	4	analytic	analytic	ADJ
ejpam-4779	296	5	functions	function	NOUN
ejpam-4779	296	6	with	with	ADP
ejpam-4779	296	7	respect	respect	NOUN
ejpam-4779	296	8	to	to	ADP
ejpam-4779	296	9	other	other	ADJ
ejpam-4779	296	10	points	point	NOUN
ejpam-4779	296	11	.	.	PUNCT
ejpam-4779	297	1	eng	eng	PROPN
ejpam-4779	297	2	.	.	PROPN
ejpam-4779	297	3	math	math	PROPN
ejpam-4779	297	4	.	.	PUNCT
ejpam-4779	298	1	lett	lett	PROPN
ejpam-4779	298	2	.	.	PROPN
ejpam-4779	298	3	,	,	PUNCT
ejpam-4779	298	4	2(1):115–123	2(1):115–123	NUM
ejpam-4779	298	5	,	,	PUNCT
ejpam-4779	298	6	2013	2013	NUM
ejpam-4779	298	7	.	.	PUNCT
ejpam-4779	299	1	[	[	X
ejpam-4779	299	2	31	31	NUM
ejpam-4779	299	3	]	]	PUNCT
ejpam-4779	299	4	gagandeep	gagandeep	NOUN
ejpam-4779	299	5	singh	singh	ADJ
ejpam-4779	299	6	and	and	CCONJ
ejpam-4779	299	7	gurcharanjit	gurcharanjit	ADJ
ejpam-4779	299	8	singh	singh	PROPN
ejpam-4779	299	9	.	.	PUNCT
ejpam-4779	300	1	coefficient	coefficient	NOUN
ejpam-4779	300	2	inequality	inequality	NOUN
ejpam-4779	300	3	for	for	ADP
ejpam-4779	300	4	subclasses	subclass	NOUN
ejpam-4779	300	5	of	of	ADP
ejpam-4779	300	6	starlike	starlike	NOUN
ejpam-4779	300	7	functions	function	NOUN
ejpam-4779	300	8	with	with	ADP
ejpam-4779	300	9	respect	respect	NOUN
ejpam-4779	300	10	to	to	ADP
ejpam-4779	300	11	conjugate	conjugate	ADJ
ejpam-4779	300	12	points	point	NOUN
ejpam-4779	300	13	.	.	PUNCT
ejpam-4779	301	1	international	international	ADJ
ejpam-4779	301	2	journal	journal	NOUN
ejpam-4779	301	3	of	of	ADP
ejpam-4779	301	4	modern	modern	ADJ
ejpam-4779	301	5	mathematical	mathematical	ADJ
ejpam-4779	301	6	sciences	science	NOUN
ejpam-4779	301	7	,	,	PUNCT
ejpam-4779	301	8	8:48–56	8:48–56	NUM
ejpam-4779	301	9	,	,	PUNCT
ejpam-4779	301	10	2013	2013	NUM
ejpam-4779	301	11	.	.	PUNCT
ejpam-4779	302	1	[	[	X
ejpam-4779	302	2	32	32	NUM
ejpam-4779	302	3	]	]	PUNCT
ejpam-4779	302	4	dk	dk	PROPN
ejpam-4779	302	5	thomas	thomas	PROPN
ejpam-4779	302	6	and	and	CCONJ
ejpam-4779	302	7	s	s	PROPN
ejpam-4779	302	8	abdul	abdul	PROPN
ejpam-4779	302	9	halim	halim	PROPN
ejpam-4779	302	10	.	.	PUNCT
ejpam-4779	303	1	retracted	retracted	ADJ
ejpam-4779	303	2	article	article	NOUN
ejpam-4779	303	3	:	:	PUNCT
ejpam-4779	303	4	toeplitz	toeplitz	NOUN
ejpam-4779	303	5	matrices	matrix	NOUN
ejpam-4779	303	6	whose	whose	DET
ejpam-4779	303	7	elements	element	NOUN
ejpam-4779	303	8	are	be	AUX
ejpam-4779	303	9	the	the	DET
ejpam-4779	303	10	coefficients	coefficient	NOUN
ejpam-4779	303	11	of	of	ADP
ejpam-4779	303	12	starlike	starlike	NOUN
ejpam-4779	303	13	and	and	CCONJ
ejpam-4779	303	14	close	close	NOUN
ejpam-4779	303	15	-	-	PUNCT
ejpam-4779	303	16	to	to	ADP
ejpam-4779	303	17	-	-	PUNCT
ejpam-4779	303	18	convex	convex	NOUN
ejpam-4779	303	19	functions	function	NOUN
ejpam-4779	303	20	.	.	PUNCT
ejpam-4779	304	1	bulletin	bulletin	NOUN
ejpam-4779	304	2	of	of	ADP
ejpam-4779	304	3	the	the	DET
ejpam-4779	304	4	malaysian	malaysian	PROPN
ejpam-4779	304	5	mathematical	mathematical	PROPN
ejpam-4779	304	6	sciences	sciences	PROPN
ejpam-4779	304	7	society	society	NOUN
ejpam-4779	304	8	,	,	PUNCT
ejpam-4779	304	9	40:1781–1790	40:1781–1790	NUM
ejpam-4779	304	10	,	,	PUNCT
ejpam-4779	304	11	2017	2017	NUM
ejpam-4779	304	12	.	.	PUNCT
ejpam-4779	305	1	[	[	X
ejpam-4779	305	2	33	33	NUM
ejpam-4779	305	3	]	]	PUNCT
ejpam-4779	305	4	katarzyna	katarzyna	PROPN
ejpam-4779	305	5	trabka	trabka	PROPN
ejpam-4779	305	6	-	-	PUNCT
ejpam-4779	305	7	wiec	wiec	PROPN
ejpam-4779	305	8	law	law	NOUN
ejpam-4779	305	9	.	.	PUNCT
ejpam-4779	306	1	on	on	ADP
ejpam-4779	306	2	coefficient	coefficient	NOUN
ejpam-4779	306	3	problems	problem	NOUN
ejpam-4779	306	4	for	for	ADP
ejpam-4779	306	5	functions	function	NOUN
ejpam-4779	306	6	connected	connect	VERB
ejpam-4779	306	7	with	with	ADP
ejpam-4779	306	8	the	the	DET
ejpam-4779	306	9	sine	sine	ADJ
ejpam-4779	306	10	function	function	NOUN
ejpam-4779	306	11	.	.	PUNCT
ejpam-4779	307	1	symmetry	symmetry	NOUN
ejpam-4779	307	2	,	,	PUNCT
ejpam-4779	307	3	13(7):1179	13(7):1179	NUM
ejpam-4779	307	4	,	,	PUNCT
ejpam-4779	307	5	2021	2021	NUM
ejpam-4779	307	6	.	.	PUNCT
ejpam-4779	308	1	[	[	X
ejpam-4779	308	2	34	34	NUM
ejpam-4779	308	3	]	]	PUNCT
ejpam-4779	308	4	nur	nur	PROPN
ejpam-4779	308	5	hazwani	hazwani	PROPN
ejpam-4779	308	6	aqilah	aqilah	PROPN
ejpam-4779	308	7	abdul	abdul	PROPN
ejpam-4779	308	8	wahid	wahid	PROPN
ejpam-4779	308	9	.	.	PUNCT
ejpam-4779	309	1	second	second	ADJ
ejpam-4779	309	2	hankel	hankel	NOUN
ejpam-4779	309	3	determinant	determinant	ADJ
ejpam-4779	309	4	for	for	ADP
ejpam-4779	309	5	a	a	DET
ejpam-4779	309	6	subclass	subclass	NOUN
ejpam-4779	309	7	of	of	ADP
ejpam-4779	309	8	tilted	tilted	ADJ
ejpam-4779	309	9	starlike	starlike	NOUN
ejpam-4779	309	10	functions	function	NOUN
ejpam-4779	309	11	with	with	ADP
ejpam-4779	309	12	respect	respect	NOUN
ejpam-4779	309	13	to	to	ADP
ejpam-4779	309	14	conjugate	conjugate	ADJ
ejpam-4779	309	15	points	point	NOUN
ejpam-4779	309	16	.	.	PUNCT
ejpam-4779	310	1	matematika	matematika	ADJ
ejpam-4779	310	2	:	:	PUNCT
ejpam-4779	310	3	malaysian	malaysian	ADJ
ejpam-4779	310	4	journal	journal	PROPN
ejpam-4779	310	5	of	of	ADP
ejpam-4779	310	6	industrial	industrial	ADJ
ejpam-4779	310	7	and	and	CCONJ
ejpam-4779	310	8	applied	apply	VERB
ejpam-4779	310	9	mathematics	mathematic	NOUN
ejpam-4779	310	10	,	,	PUNCT
ejpam-4779	310	11	pages	page	NOUN
ejpam-4779	310	12	111–119	111–119	NUM
ejpam-4779	310	13	,	,	PUNCT
ejpam-4779	310	14	2015	2015	NUM
ejpam-4779	310	15	.	.	PUNCT
ejpam-4779	311	1	[	[	X
ejpam-4779	311	2	35	35	NUM
ejpam-4779	311	3	]	]	X
ejpam-4779	311	4	ke	ke	NOUN
ejpam-4779	311	5	ye	ye	NOUN
ejpam-4779	311	6	and	and	CCONJ
ejpam-4779	311	7	lek	lek	PROPN
ejpam-4779	311	8	-	-	PUNCT
ejpam-4779	311	9	heng	heng	PROPN
ejpam-4779	311	10	lim	lim	PROPN
ejpam-4779	311	11	.	.	PUNCT
ejpam-4779	312	1	every	every	DET
ejpam-4779	312	2	matrix	matrix	NOUN
ejpam-4779	312	3	is	be	AUX
ejpam-4779	312	4	a	a	DET
ejpam-4779	312	5	product	product	NOUN
ejpam-4779	312	6	of	of	ADP
ejpam-4779	312	7	toeplitz	toeplitz	NOUN
ejpam-4779	312	8	matrices	matrix	NOUN
ejpam-4779	312	9	.	.	PUNCT
ejpam-4779	313	1	foundations	foundation	NOUN
ejpam-4779	313	2	of	of	ADP
ejpam-4779	313	3	computational	computational	ADJ
ejpam-4779	313	4	mathematics	mathematic	NOUN
ejpam-4779	313	5	,	,	PUNCT
ejpam-4779	313	6	16:577–598	16:577–598	NUM
ejpam-4779	313	7	,	,	PUNCT
ejpam-4779	313	8	2016	2016	NUM
ejpam-4779	313	9	.	.	PUNCT
ejpam-4779	314	1	[	[	X
ejpam-4779	314	2	36	36	NUM
ejpam-4779	314	3	]	]	X
ejpam-4779	314	4	zhongqiu	zhongqiu	PROPN
ejpam-4779	314	5	ye	ye	PROPN
ejpam-4779	314	6	.	.	PUNCT
ejpam-4779	315	1	the	the	DET
ejpam-4779	315	2	logarithmic	logarithmic	ADJ
ejpam-4779	315	3	coefficients	coefficient	NOUN
ejpam-4779	315	4	of	of	ADP
ejpam-4779	315	5	close	close	NOUN
ejpam-4779	315	6	-	-	PUNCT
ejpam-4779	315	7	to	to	ADP
ejpam-4779	315	8	-	-	PUNCT
ejpam-4779	315	9	convex	convex	NOUN
ejpam-4779	315	10	functions	function	NOUN
ejpam-4779	315	11	.	.	PUNCT
ejpam-4779	316	1	bull	bull	NOUN
ejpam-4779	316	2	.	.	PUNCT
ejpam-4779	316	3	inst	inst	PROPN
ejpam-4779	316	4	.	.	PUNCT
ejpam-4779	317	1	math	math	NOUN
ejpam-4779	317	2	.	.	PUNCT
ejpam-4779	318	1	acad	acad	PROPN
ejpam-4779	318	2	.	.	PUNCT
ejpam-4779	319	1	sin.(ns	sin.(ns	ADP
ejpam-4779	319	2	)	)	PUNCT
ejpam-4779	319	3	,	,	PUNCT
ejpam-4779	319	4	3(3):445–452	3(3):445–452	NOUN
ejpam-4779	319	5	,	,	PUNCT
ejpam-4779	319	6	2008	2008	NUM
ejpam-4779	319	7	.	.	PUNCT