id	sid	tid	token	lemma	pos
ejpam-6081	1	1	european	european	PROPN
ejpam-6081	1	2	journal	journal	PROPN
ejpam-6081	1	3	of	of	ADP
ejpam-6081	1	4	pure	pure	ADJ
ejpam-6081	1	5	and	and	CCONJ
ejpam-6081	1	6	applied	applied	ADJ
ejpam-6081	1	7	mathematics	mathematic	NOUN
ejpam-6081	1	8	2025	2025	NUM
ejpam-6081	1	9	,	,	PUNCT
ejpam-6081	1	10	vol	vol	NOUN
ejpam-6081	1	11	.	.	PROPN
ejpam-6081	1	12	18	18	NUM
ejpam-6081	1	13	,	,	PUNCT
ejpam-6081	1	14	issue	issue	NOUN
ejpam-6081	1	15	2	2	NUM
ejpam-6081	1	16	,	,	PUNCT
ejpam-6081	1	17	article	article	NOUN
ejpam-6081	1	18	number	number	NOUN
ejpam-6081	1	19	6081	6081	NUM
ejpam-6081	1	20	issn	issn	PROPN
ejpam-6081	1	21	1307	1307	NUM
ejpam-6081	1	22	-	-	SYM
ejpam-6081	1	23	5543	5543	NUM
ejpam-6081	1	24	–	–	PUNCT
ejpam-6081	1	25	ejpam.com	ejpam.com	X
ejpam-6081	1	26	published	publish	VERB
ejpam-6081	1	27	by	by	ADP
ejpam-6081	1	28	new	new	PROPN
ejpam-6081	1	29	york	york	PROPN
ejpam-6081	1	30	business	business	PROPN
ejpam-6081	1	31	global	global	ADJ
ejpam-6081	1	32	vandermonde	vandermonde	NOUN
ejpam-6081	1	33	determinant	determinant	ADJ
ejpam-6081	1	34	for	for	ADP
ejpam-6081	1	35	the	the	DET
ejpam-6081	1	36	generalized	generalize	VERB
ejpam-6081	1	37	bounded	bounded	ADJ
ejpam-6081	1	38	turning	turning	NOUN
ejpam-6081	1	39	functions	function	NOUN
ejpam-6081	1	40	associated	associate	VERB
ejpam-6081	1	41	with	with	ADP
ejpam-6081	1	42	gregory	gregory	PROPN
ejpam-6081	1	43	coefficients	coefficients	PROPN
ejpam-6081	1	44	nur	nur	VERB
ejpam-6081	1	45	hazwani	hazwani	PROPN
ejpam-6081	1	46	aqilah	aqilah	PROPN
ejpam-6081	1	47	abdul	abdul	PROPN
ejpam-6081	1	48	wahid1,∗	wahid1,∗	PROPN
ejpam-6081	1	49	,	,	PUNCT
ejpam-6081	1	50	shaharuddin	shaharuddin	VERB
ejpam-6081	1	51	cik	cik	PROPN
ejpam-6081	1	52	soh1	soh1	PROPN
ejpam-6081	1	53	1	1	NUM
ejpam-6081	1	54	school	school	NOUN
ejpam-6081	1	55	of	of	ADP
ejpam-6081	1	56	mathematical	mathematical	ADJ
ejpam-6081	1	57	sciences	science	NOUN
ejpam-6081	1	58	,	,	PUNCT
ejpam-6081	1	59	college	college	NOUN
ejpam-6081	1	60	of	of	ADP
ejpam-6081	1	61	computing	computing	NOUN
ejpam-6081	1	62	,	,	PUNCT
ejpam-6081	1	63	informatics	informatic	NOUN
ejpam-6081	1	64	and	and	CCONJ
ejpam-6081	1	65	mathematics	mathematic	NOUN
ejpam-6081	1	66	,	,	PUNCT
ejpam-6081	1	67	universiti	universiti	PROPN
ejpam-6081	1	68	teknologi	teknologi	PROPN
ejpam-6081	1	69	mara	mara	PROPN
ejpam-6081	1	70	,	,	PUNCT
ejpam-6081	1	71	40450	40450	NUM
ejpam-6081	1	72	shah	shah	PROPN
ejpam-6081	1	73	alam	alam	PROPN
ejpam-6081	1	74	,	,	PUNCT
ejpam-6081	1	75	selangor	selangor	PROPN
ejpam-6081	1	76	,	,	PUNCT
ejpam-6081	1	77	malaysia	malaysia	PROPN
ejpam-6081	1	78	abstract	abstract	NOUN
ejpam-6081	1	79	.	.	PUNCT
ejpam-6081	2	1	this	this	DET
ejpam-6081	2	2	paper	paper	NOUN
ejpam-6081	2	3	explores	explore	VERB
ejpam-6081	2	4	the	the	DET
ejpam-6081	2	5	class	class	NOUN
ejpam-6081	2	6	gg	gg	NOUN
ejpam-6081	2	7	(	(	PUNCT
ejpam-6081	2	8	α	α	PROPN
ejpam-6081	2	9	,	,	PUNCT
ejpam-6081	2	10	δ	δ	PROPN
ejpam-6081	2	11	)	)	PUNCT
ejpam-6081	2	12	of	of	ADP
ejpam-6081	2	13	analytic	analytic	ADJ
ejpam-6081	2	14	functions	function	NOUN
ejpam-6081	2	15	,	,	PUNCT
ejpam-6081	2	16	which	which	PRON
ejpam-6081	2	17	is	be	AUX
ejpam-6081	2	18	associated	associate	VERB
ejpam-6081	2	19	with	with	ADP
ejpam-6081	2	20	generalized	generalized	ADJ
ejpam-6081	2	21	bounded	bounded	ADJ
ejpam-6081	2	22	turning	turning	NOUN
ejpam-6081	2	23	and	and	CCONJ
ejpam-6081	2	24	the	the	DET
ejpam-6081	2	25	generating	generating	NOUN
ejpam-6081	2	26	functions	function	NOUN
ejpam-6081	2	27	of	of	ADP
ejpam-6081	2	28	gregory	gregory	PROPN
ejpam-6081	2	29	coefficients	coefficient	NOUN
ejpam-6081	2	30	.	.	PUNCT
ejpam-6081	3	1	by	by	ADP
ejpam-6081	3	2	using	use	VERB
ejpam-6081	3	3	bounds	bound	NOUN
ejpam-6081	3	4	on	on	ADP
ejpam-6081	3	5	certain	certain	ADJ
ejpam-6081	3	6	coefficient	coefficient	NOUN
ejpam-6081	3	7	functionals	functional	NOUN
ejpam-6081	3	8	for	for	ADP
ejpam-6081	3	9	functions	function	NOUN
ejpam-6081	3	10	with	with	ADP
ejpam-6081	3	11	a	a	DET
ejpam-6081	3	12	positive	positive	ADJ
ejpam-6081	3	13	real	real	ADJ
ejpam-6081	3	14	part	part	NOUN
ejpam-6081	3	15	,	,	PUNCT
ejpam-6081	3	16	we	we	PRON
ejpam-6081	3	17	obtain	obtain	VERB
ejpam-6081	3	18	initial	initial	ADJ
ejpam-6081	3	19	taylor	taylor	PROPN
ejpam-6081	3	20	coefficient	coefficient	NOUN
ejpam-6081	3	21	bounds	bound	NOUN
ejpam-6081	3	22	and	and	CCONJ
ejpam-6081	3	23	logarithmic	logarithmic	ADJ
ejpam-6081	3	24	coefficient	coefficient	NOUN
ejpam-6081	3	25	bounds	bound	NOUN
ejpam-6081	3	26	of	of	ADP
ejpam-6081	3	27	functions	function	NOUN
ejpam-6081	3	28	and	and	CCONJ
ejpam-6081	3	29	inverse	inverse	NOUN
ejpam-6081	3	30	functions	function	NOUN
ejpam-6081	3	31	within	within	ADP
ejpam-6081	3	32	this	this	DET
ejpam-6081	3	33	class	class	NOUN
ejpam-6081	3	34	.	.	PUNCT
ejpam-6081	4	1	consequently	consequently	ADV
ejpam-6081	4	2	,	,	PUNCT
ejpam-6081	4	3	we	we	PRON
ejpam-6081	4	4	establish	establish	VERB
ejpam-6081	4	5	upper	upper	ADJ
ejpam-6081	4	6	bounds	bound	NOUN
ejpam-6081	4	7	of	of	ADP
ejpam-6081	4	8	the	the	DET
ejpam-6081	4	9	second	second	ADJ
ejpam-6081	4	10	-	-	PUNCT
ejpam-6081	4	11	order	order	NOUN
ejpam-6081	4	12	for	for	ADP
ejpam-6081	4	13	the	the	DET
ejpam-6081	4	14	vandermonde	vandermonde	NOUN
ejpam-6081	4	15	determinant	determinant	ADJ
ejpam-6081	4	16	,	,	PUNCT
ejpam-6081	4	17	where	where	SCONJ
ejpam-6081	4	18	the	the	DET
ejpam-6081	4	19	entries	entry	NOUN
ejpam-6081	4	20	are	be	AUX
ejpam-6081	4	21	taylor	taylor	PROPN
ejpam-6081	4	22	coefficients	coefficient	NOUN
ejpam-6081	4	23	and	and	CCONJ
ejpam-6081	4	24	logarithmic	logarithmic	ADJ
ejpam-6081	4	25	coefficients	coefficient	NOUN
ejpam-6081	4	26	of	of	ADP
ejpam-6081	4	27	functions	function	NOUN
ejpam-6081	4	28	and	and	CCONJ
ejpam-6081	4	29	inverse	inverse	NOUN
ejpam-6081	4	30	functions	function	NOUN
ejpam-6081	4	31	.	.	PUNCT
ejpam-6081	5	1	additionally	additionally	ADV
ejpam-6081	5	2	,	,	PUNCT
ejpam-6081	5	3	we	we	PRON
ejpam-6081	5	4	highlight	highlight	VERB
ejpam-6081	5	5	several	several	ADJ
ejpam-6081	5	6	interesting	interesting	ADJ
ejpam-6081	5	7	implications	implication	NOUN
ejpam-6081	5	8	of	of	ADP
ejpam-6081	5	9	these	these	DET
ejpam-6081	5	10	results	result	NOUN
ejpam-6081	5	11	,	,	PUNCT
ejpam-6081	5	12	contributing	contribute	VERB
ejpam-6081	5	13	new	new	ADJ
ejpam-6081	5	14	insights	insight	NOUN
ejpam-6081	5	15	to	to	ADP
ejpam-6081	5	16	this	this	DET
ejpam-6081	5	17	generalized	generalized	ADJ
ejpam-6081	5	18	class	class	NOUN
ejpam-6081	5	19	.	.	PUNCT
ejpam-6081	6	1	2020	2020	NUM
ejpam-6081	6	2	mathematics	mathematic	NOUN
ejpam-6081	6	3	subject	subject	NOUN
ejpam-6081	6	4	classifications	classification	NOUN
ejpam-6081	6	5	:	:	PUNCT
ejpam-6081	6	6	30c45	30c45	NUM
ejpam-6081	6	7	,	,	PUNCT
ejpam-6081	6	8	30c50	30c50	DET
ejpam-6081	6	9	key	key	ADJ
ejpam-6081	6	10	words	word	NOUN
ejpam-6081	6	11	and	and	CCONJ
ejpam-6081	6	12	phrases	phrase	NOUN
ejpam-6081	6	13	:	:	PUNCT
ejpam-6081	6	14	univalent	univalent	ADJ
ejpam-6081	6	15	functions	function	NOUN
ejpam-6081	6	16	,	,	PUNCT
ejpam-6081	6	17	inverse	inverse	NOUN
ejpam-6081	6	18	functions	function	NOUN
ejpam-6081	6	19	,	,	PUNCT
ejpam-6081	6	20	bounded	bound	VERB
ejpam-6081	6	21	turning	turning	NOUN
ejpam-6081	6	22	functions	function	NOUN
ejpam-6081	6	23	,	,	PUNCT
ejpam-6081	6	24	gregory	gregory	PROPN
ejpam-6081	6	25	coefficients	coefficients	PROPN
ejpam-6081	6	26	,	,	PUNCT
ejpam-6081	6	27	taylor	taylor	PROPN
ejpam-6081	6	28	coefficients	coefficient	NOUN
ejpam-6081	6	29	,	,	PUNCT
ejpam-6081	6	30	logarithmic	logarithmic	ADJ
ejpam-6081	6	31	coefficients	coefficient	NOUN
ejpam-6081	6	32	,	,	PUNCT
ejpam-6081	6	33	vandermonde	vandermonde	VERB
ejpam-6081	6	34	determinant	determinant	ADJ
ejpam-6081	6	35	1	1	NUM
ejpam-6081	6	36	.	.	PUNCT
ejpam-6081	7	1	introduction	introduction	NOUN
ejpam-6081	7	2	let	let	VERB
ejpam-6081	7	3	a	a	DET
ejpam-6081	7	4	denote	denote	NOUN
ejpam-6081	7	5	the	the	DET
ejpam-6081	7	6	class	class	NOUN
ejpam-6081	7	7	of	of	ADP
ejpam-6081	7	8	analytic	analytic	ADJ
ejpam-6081	7	9	functions	function	NOUN
ejpam-6081	7	10	f	f	X
ejpam-6081	7	11	(	(	PUNCT
ejpam-6081	7	12	z	z	NOUN
ejpam-6081	7	13	)	)	PUNCT
ejpam-6081	7	14	that	that	PRON
ejpam-6081	7	15	can	can	AUX
ejpam-6081	7	16	be	be	AUX
ejpam-6081	7	17	expressed	express	VERB
ejpam-6081	7	18	as	as	ADP
ejpam-6081	7	19	a	a	DET
ejpam-6081	7	20	taylor	taylor	PROPN
ejpam-6081	7	21	series	series	NOUN
ejpam-6081	7	22	expansion	expansion	NOUN
ejpam-6081	7	23	in	in	ADP
ejpam-6081	7	24	the	the	DET
ejpam-6081	7	25	open	open	ADJ
ejpam-6081	7	26	unit	unit	NOUN
ejpam-6081	7	27	disk	disk	NOUN
ejpam-6081	7	28	e	e	NOUN
ejpam-6081	7	29	=	=	PUNCT
ejpam-6081	7	30	{	{	PUNCT
ejpam-6081	7	31	z	z	NOUN
ejpam-6081	7	32	∈	∈	PROPN
ejpam-6081	7	33	c	c	NOUN
ejpam-6081	7	34	:	:	PUNCT
ejpam-6081	7	35	|z|	|z|	NOUN
ejpam-6081	7	36	<	<	X
ejpam-6081	7	37	1	1	NUM
ejpam-6081	7	38	}	}	PUNCT
ejpam-6081	7	39	,	,	PUNCT
ejpam-6081	7	40	given	give	VERB
ejpam-6081	7	41	by	by	ADP
ejpam-6081	7	42	f	f	PROPN
ejpam-6081	7	43	(	(	PUNCT
ejpam-6081	7	44	z	z	NOUN
ejpam-6081	7	45	)	)	PUNCT
ejpam-6081	7	46	=	=	SYM
ejpam-6081	8	1	z	z	NOUN
ejpam-6081	9	1	+	+	NOUN
ejpam-6081	9	2	∞∑	∞∑	NUM
ejpam-6081	9	3	n=2	n=2	VERB
ejpam-6081	9	4	anz	anz	NOUN
ejpam-6081	9	5	n	n	PRON
ejpam-6081	9	6	,	,	PUNCT
ejpam-6081	9	7	z	z	PROPN
ejpam-6081	9	8	∈	∈	PROPN
ejpam-6081	9	9	e.	e.	PROPN
ejpam-6081	9	10	(	(	PUNCT
ejpam-6081	9	11	1	1	X
ejpam-6081	9	12	)	)	PUNCT
ejpam-6081	9	13	we	we	PRON
ejpam-6081	9	14	denote	denote	VERB
ejpam-6081	9	15	by	by	ADP
ejpam-6081	9	16	s	s	PRON
ejpam-6081	9	17	the	the	DET
ejpam-6081	9	18	subclass	subclass	NOUN
ejpam-6081	9	19	of	of	ADP
ejpam-6081	9	20	a	a	DET
ejpam-6081	9	21	consisting	consisting	NOUN
ejpam-6081	9	22	of	of	ADP
ejpam-6081	9	23	univalent	univalent	ADJ
ejpam-6081	9	24	functions	function	NOUN
ejpam-6081	9	25	in	in	ADP
ejpam-6081	9	26	e.	e.	PROPN
ejpam-6081	9	27	the	the	DET
ejpam-6081	9	28	inverse	inverse	NOUN
ejpam-6081	9	29	of	of	ADP
ejpam-6081	9	30	a	a	DET
ejpam-6081	9	31	function	function	NOUN
ejpam-6081	9	32	f	f	X
ejpam-6081	9	33	(	(	PUNCT
ejpam-6081	9	34	z	z	NOUN
ejpam-6081	9	35	)	)	PUNCT
ejpam-6081	9	36	∈	∈	PROPN
ejpam-6081	9	37	s	s	NOUN
ejpam-6081	9	38	of	of	ADP
ejpam-6081	9	39	the	the	DET
ejpam-6081	9	40	form	form	NOUN
ejpam-6081	9	41	(	(	PUNCT
ejpam-6081	9	42	1	1	X
ejpam-6081	9	43	)	)	PUNCT
ejpam-6081	9	44	has	have	VERB
ejpam-6081	9	45	a	a	DET
ejpam-6081	9	46	series	series	NOUN
ejpam-6081	9	47	expansion	expansion	NOUN
ejpam-6081	9	48	given	give	VERB
ejpam-6081	9	49	by	by	ADP
ejpam-6081	9	50	f−1	f−1	PROPN
ejpam-6081	9	51	(	(	PUNCT
ejpam-6081	9	52	w	w	NOUN
ejpam-6081	9	53	)	)	PUNCT
ejpam-6081	9	54	=	=	SYM
ejpam-6081	10	1	w	w	PROPN
ejpam-6081	11	1	+	+	PUNCT
ejpam-6081	11	2	∞∑	∞∑	NUM
ejpam-6081	11	3	n=2	n=2	PRON
ejpam-6081	11	4	anw	anw	NOUN
ejpam-6081	11	5	n	n	CCONJ
ejpam-6081	11	6	,	,	PUNCT
ejpam-6081	11	7	|w|	|w|	VERB
ejpam-6081	11	8	<	<	X
ejpam-6081	11	9	r0	r0	NOUN
ejpam-6081	11	10	(	(	PUNCT
ejpam-6081	11	11	f	f	PROPN
ejpam-6081	11	12	)	)	PUNCT
ejpam-6081	11	13	,	,	PUNCT
ejpam-6081	11	14	r0	r0	NOUN
ejpam-6081	11	15	(	(	PUNCT
ejpam-6081	11	16	f	f	X
ejpam-6081	11	17	)	)	PUNCT
ejpam-6081	11	18	≥	≥	NOUN
ejpam-6081	11	19	1	1	NUM
ejpam-6081	11	20	4	4	NUM
ejpam-6081	11	21	,	,	PUNCT
ejpam-6081	11	22	(	(	PUNCT
ejpam-6081	11	23	2	2	X
ejpam-6081	11	24	)	)	PUNCT
ejpam-6081	11	25	∗corresponding	∗corresponde	VERB
ejpam-6081	11	26	author	author	NOUN
ejpam-6081	11	27	.	.	PUNCT
ejpam-6081	12	1	doi	doi	NOUN
ejpam-6081	12	2	:	:	PUNCT
ejpam-6081	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6081	https://doi.org/10.29020/nybg.ejpam.v18i2.6081	PROPN
ejpam-6081	12	4	email	email	NOUN
ejpam-6081	12	5	addresses	address	NOUN
ejpam-6081	12	6	:	:	PUNCT
ejpam-6081	12	7	hazwaniaqilah@uitm.edu.my	hazwaniaqilah@uitm.edu.my	PROPN
ejpam-6081	12	8	(	(	PUNCT
ejpam-6081	12	9	n.	n.	PROPN
ejpam-6081	12	10	h.	h.	PROPN
ejpam-6081	12	11	a.	a.	PROPN
ejpam-6081	12	12	a.	a.	PROPN
ejpam-6081	12	13	wahid	wahid	PROPN
ejpam-6081	12	14	)	)	PUNCT
ejpam-6081	12	15	,	,	PUNCT
ejpam-6081	12	16	haruddin@uitm.edu.my	haruddin@uitm.edu.my	NOUN
ejpam-6081	12	17	(	(	PUNCT
ejpam-6081	12	18	s.	s.	PROPN
ejpam-6081	12	19	cik	cik	PROPN
ejpam-6081	12	20	soh	soh	PROPN
ejpam-6081	12	21	)	)	PUNCT
ejpam-6081	12	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6081	13	1	1	1	NUM
ejpam-6081	13	2	copyright	copyright	NOUN
ejpam-6081	13	3	:	:	PUNCT
ejpam-6081	13	4	©	©	PROPN
ejpam-6081	13	5	2025	2025	NUM
ejpam-6081	13	6	the	the	DET
ejpam-6081	13	7	author(s	author(s	NOUN
ejpam-6081	13	8	)	)	PUNCT
ejpam-6081	13	9	.	.	PUNCT
ejpam-6081	14	1	(	(	PUNCT
ejpam-6081	14	2	cc	cc	NOUN
ejpam-6081	14	3	by	by	ADP
ejpam-6081	14	4	-	-	PUNCT
ejpam-6081	14	5	nc	nc	PROPN
ejpam-6081	14	6	4.0	4.0	NUM
ejpam-6081	14	7	)	)	PUNCT
ejpam-6081	14	8	n.	n.	PROPN
ejpam-6081	14	9	h.	h.	PROPN
ejpam-6081	14	10	a.	a.	PROPN
ejpam-6081	14	11	a.	a.	PROPN
ejpam-6081	14	12	wahid	wahid	PROPN
ejpam-6081	14	13	,	,	PUNCT
ejpam-6081	15	1	s.	s.	PROPN
ejpam-6081	15	2	c.	c.	PROPN
ejpam-6081	15	3	soh	soh	PROPN
ejpam-6081	15	4	/	/	SYM
ejpam-6081	15	5	eur	eur	PROPN
ejpam-6081	15	6	.	.	PUNCT
ejpam-6081	16	1	j.	j.	PROPN
ejpam-6081	16	2	pure	pure	PROPN
ejpam-6081	16	3	appl	appl	PROPN
ejpam-6081	16	4	.	.	PROPN
ejpam-6081	16	5	math	math	PROPN
ejpam-6081	16	6	,	,	PUNCT
ejpam-6081	16	7	18	18	NUM
ejpam-6081	16	8	(	(	PUNCT
ejpam-6081	16	9	2	2	NUM
ejpam-6081	16	10	)	)	PUNCT
ejpam-6081	16	11	(	(	PUNCT
ejpam-6081	16	12	2025	2025	NUM
ejpam-6081	16	13	)	)	PUNCT
ejpam-6081	16	14	,	,	PUNCT
ejpam-6081	16	15	6081	6081	NUM
ejpam-6081	16	16	2	2	NUM
ejpam-6081	16	17	of	of	ADP
ejpam-6081	16	18	16	16	NUM
ejpam-6081	16	19	where	where	SCONJ
ejpam-6081	16	20	,	,	PUNCT
ejpam-6081	16	21	in	in	ADP
ejpam-6081	16	22	particular	particular	ADJ
ejpam-6081	16	23	,	,	PUNCT
ejpam-6081	16	24	the	the	DET
ejpam-6081	16	25	coefficients	coefficient	NOUN
ejpam-6081	16	26	an	an	PRON
ejpam-6081	16	27	for	for	ADP
ejpam-6081	16	28	n	n	NOUN
ejpam-6081	16	29	=	=	SYM
ejpam-6081	16	30	2	2	NUM
ejpam-6081	16	31	,	,	PUNCT
ejpam-6081	16	32	3	3	NUM
ejpam-6081	16	33	,	,	PUNCT
ejpam-6081	16	34	4	4	NUM
ejpam-6081	16	35	are	be	AUX
ejpam-6081	16	36	expressed	express	VERB
ejpam-6081	16	37	in	in	ADP
ejpam-6081	16	38	terms	term	NOUN
ejpam-6081	16	39	of	of	ADP
ejpam-6081	16	40	the	the	DET
ejpam-6081	16	41	taylor	taylor	PROPN
ejpam-6081	16	42	coefficients	coefficient	NOUN
ejpam-6081	16	43	of	of	ADP
ejpam-6081	16	44	f	f	PROPN
ejpam-6081	16	45	(	(	PUNCT
ejpam-6081	16	46	z	z	NOUN
ejpam-6081	16	47	)	)	PUNCT
ejpam-6081	16	48	∈	∈	PROPN
ejpam-6081	16	49	s	s	NOUN
ejpam-6081	16	50	as	as	SCONJ
ejpam-6081	16	51	follows	follow	VERB
ejpam-6081	16	52	:	:	PUNCT
ejpam-6081	16	53	a2	a2	PROPN
ejpam-6081	16	54	=	=	PROPN
ejpam-6081	16	55	−a2	−a2	PROPN
ejpam-6081	16	56	,	,	PUNCT
ejpam-6081	16	57	(	(	PUNCT
ejpam-6081	16	58	3	3	X
ejpam-6081	16	59	)	)	PUNCT
ejpam-6081	16	60	a3	a3	NOUN
ejpam-6081	16	61	=	=	PUNCT
ejpam-6081	16	62	−a3	−a3	PROPN
ejpam-6081	16	63	+	+	CCONJ
ejpam-6081	16	64	2a2	2a2	NUM
ejpam-6081	16	65	2	2	NUM
ejpam-6081	16	66	,	,	PUNCT
ejpam-6081	16	67	(	(	PUNCT
ejpam-6081	16	68	4	4	NUM
ejpam-6081	16	69	)	)	PUNCT
ejpam-6081	16	70	and	and	CCONJ
ejpam-6081	16	71	a4	a4	NOUN
ejpam-6081	17	1	=	=	SYM
ejpam-6081	17	2	−a4	−a4	PROPN
ejpam-6081	17	3	+	+	NOUN
ejpam-6081	18	1	5a2a3	5a2a3	NUM
ejpam-6081	18	2	−	−	NOUN
ejpam-6081	19	1	5a2	5a2	NOUN
ejpam-6081	19	2	3	3	X
ejpam-6081	19	3	.	.	PUNCT
ejpam-6081	20	1	(	(	PUNCT
ejpam-6081	20	2	5	5	X
ejpam-6081	20	3	)	)	PUNCT
ejpam-6081	20	4	let	let	VERB
ejpam-6081	20	5	p	p	PRON
ejpam-6081	20	6	denote	denote	VERB
ejpam-6081	20	7	the	the	DET
ejpam-6081	20	8	class	class	NOUN
ejpam-6081	20	9	of	of	ADP
ejpam-6081	20	10	functions	function	NOUN
ejpam-6081	20	11	with	with	ADP
ejpam-6081	20	12	a	a	DET
ejpam-6081	20	13	positive	positive	ADJ
ejpam-6081	20	14	real	real	ADJ
ejpam-6081	20	15	part	part	NOUN
ejpam-6081	20	16	in	in	ADP
ejpam-6081	20	17	the	the	DET
ejpam-6081	20	18	open	open	ADJ
ejpam-6081	20	19	unit	unit	NOUN
ejpam-6081	20	20	disk	disk	NOUN
ejpam-6081	20	21	e.	e.	PROPN
ejpam-6081	20	22	a	a	DET
ejpam-6081	20	23	function	function	NOUN
ejpam-6081	20	24	p	p	X
ejpam-6081	20	25	(	(	PUNCT
ejpam-6081	20	26	z	z	NOUN
ejpam-6081	20	27	)	)	PUNCT
ejpam-6081	20	28	in	in	ADP
ejpam-6081	20	29	p	p	NOUN
ejpam-6081	20	30	has	have	VERB
ejpam-6081	20	31	the	the	DET
ejpam-6081	20	32	series	series	NOUN
ejpam-6081	20	33	expansion	expansion	NOUN
ejpam-6081	20	34	p	p	X
ejpam-6081	20	35	(	(	PUNCT
ejpam-6081	20	36	z	z	NOUN
ejpam-6081	20	37	)	)	PUNCT
ejpam-6081	20	38	=	=	SYM
ejpam-6081	21	1	1	1	NUM
ejpam-6081	21	2	+	+	CCONJ
ejpam-6081	21	3	∞∑	∞∑	NUM
ejpam-6081	21	4	n=1	n=1	PROPN
ejpam-6081	21	5	pnz	pnz	NOUN
ejpam-6081	21	6	n	n	CCONJ
ejpam-6081	21	7	,	,	PUNCT
ejpam-6081	21	8	z	z	PROPN
ejpam-6081	21	9	∈	∈	PROPN
ejpam-6081	21	10	e	e	NOUN
ejpam-6081	21	11	,	,	PUNCT
ejpam-6081	21	12	(	(	PUNCT
ejpam-6081	21	13	6	6	NUM
ejpam-6081	21	14	)	)	PUNCT
ejpam-6081	21	15	that	that	PRON
ejpam-6081	21	16	is	be	AUX
ejpam-6081	21	17	analytic	analytic	ADJ
ejpam-6081	21	18	in	in	ADP
ejpam-6081	21	19	e	e	NOUN
ejpam-6081	21	20	and	and	CCONJ
ejpam-6081	21	21	satisfying	satisfy	VERB
ejpam-6081	21	22	the	the	DET
ejpam-6081	21	23	condition	condition	NOUN
ejpam-6081	22	1	re	re	ADP
ejpam-6081	22	2	(	(	PUNCT
ejpam-6081	22	3	p	p	X
ejpam-6081	22	4	(	(	PUNCT
ejpam-6081	22	5	z	z	NOUN
ejpam-6081	22	6	)	)	PUNCT
ejpam-6081	22	7	)	)	PUNCT
ejpam-6081	22	8	>	>	X
ejpam-6081	22	9	0	0	X
ejpam-6081	22	10	.	.	PUNCT
ejpam-6081	22	11	functions	function	NOUN
ejpam-6081	22	12	in	in	ADP
ejpam-6081	22	13	p	p	PROPN
ejpam-6081	22	14	have	have	AUX
ejpam-6081	22	15	often	often	ADV
ejpam-6081	22	16	been	be	AUX
ejpam-6081	22	17	used	use	VERB
ejpam-6081	22	18	to	to	PART
ejpam-6081	22	19	describe	describe	VERB
ejpam-6081	22	20	geometric	geometric	ADJ
ejpam-6081	22	21	properties	property	NOUN
ejpam-6081	22	22	of	of	ADP
ejpam-6081	22	23	functions	function	NOUN
ejpam-6081	22	24	in	in	ADP
ejpam-6081	22	25	a	a	PRON
ejpam-6081	22	26	,	,	PUNCT
ejpam-6081	22	27	and	and	CCONJ
ejpam-6081	22	28	to	to	PART
ejpam-6081	22	29	define	define	VERB
ejpam-6081	22	30	subclasses	subclass	NOUN
ejpam-6081	22	31	in	in	ADP
ejpam-6081	22	32	s.	s.	PROPN
ejpam-6081	22	33	let	let	VERB
ejpam-6081	22	34	h	h	NOUN
ejpam-6081	22	35	denote	denote	VERB
ejpam-6081	22	36	the	the	DET
ejpam-6081	22	37	class	class	NOUN
ejpam-6081	22	38	of	of	ADP
ejpam-6081	22	39	schwarz	schwarz	PROPN
ejpam-6081	22	40	functions	function	NOUN
ejpam-6081	22	41	υ	υ	PROPN
ejpam-6081	22	42	(	(	PUNCT
ejpam-6081	22	43	z	z	NOUN
ejpam-6081	22	44	)	)	PUNCT
ejpam-6081	22	45	which	which	PRON
ejpam-6081	22	46	are	be	AUX
ejpam-6081	22	47	analytic	analytic	ADJ
ejpam-6081	22	48	in	in	ADP
ejpam-6081	22	49	e	e	NOUN
ejpam-6081	22	50	,	,	PUNCT
ejpam-6081	22	51	given	give	VERB
ejpam-6081	22	52	by	by	ADP
ejpam-6081	22	53	υ	υ	PROPN
ejpam-6081	22	54	(	(	PUNCT
ejpam-6081	22	55	z	z	NOUN
ejpam-6081	22	56	)	)	PUNCT
ejpam-6081	22	57	=	=	NOUN
ejpam-6081	23	1	∞∑	∞∑	NUM
ejpam-6081	23	2	k=1	k=1	AUX
ejpam-6081	23	3	bkz	bkz	VERB
ejpam-6081	23	4	k	k	PROPN
ejpam-6081	23	5	,	,	PUNCT
ejpam-6081	23	6	z	z	PROPN
ejpam-6081	23	7	∈	∈	PROPN
ejpam-6081	23	8	e	e	X
ejpam-6081	23	9	and	and	CCONJ
ejpam-6081	23	10	satisfying	satisfy	VERB
ejpam-6081	23	11	υ	υ	PROPN
ejpam-6081	23	12	(	(	PUNCT
ejpam-6081	23	13	0	0	NUM
ejpam-6081	23	14	)	)	PUNCT
ejpam-6081	23	15	=	=	SYM
ejpam-6081	23	16	0	0	NUM
ejpam-6081	23	17	and	and	CCONJ
ejpam-6081	23	18	|υ	|υ	NOUN
ejpam-6081	23	19	(	(	PUNCT
ejpam-6081	23	20	z)|	z)|	X
ejpam-6081	23	21	<	<	X
ejpam-6081	23	22	1	1	NUM
ejpam-6081	23	23	.	.	PUNCT
ejpam-6081	24	1	if	if	SCONJ
ejpam-6081	24	2	p(z	p(z	NOUN
ejpam-6081	24	3	)	)	PUNCT
ejpam-6081	24	4	∈	∈	PROPN
ejpam-6081	24	5	p	p	NOUN
ejpam-6081	24	6	,	,	PUNCT
ejpam-6081	24	7	then	then	ADV
ejpam-6081	24	8	a	a	DET
ejpam-6081	24	9	schwarz	schwarz	PROPN
ejpam-6081	24	10	function	function	NOUN
ejpam-6081	24	11	υ(z	υ(z	NOUN
ejpam-6081	24	12	)	)	PUNCT
ejpam-6081	24	13	∈	∈	PROPN
ejpam-6081	24	14	h	h	NOUN
ejpam-6081	24	15	exists	exist	VERB
ejpam-6081	24	16	such	such	ADJ
ejpam-6081	24	17	that	that	SCONJ
ejpam-6081	24	18	p	p	X
ejpam-6081	24	19	(	(	PUNCT
ejpam-6081	24	20	z	z	NOUN
ejpam-6081	24	21	)	)	PUNCT
ejpam-6081	24	22	=	=	SYM
ejpam-6081	25	1	1	1	NUM
ejpam-6081	25	2	+	+	NUM
ejpam-6081	25	3	υ	υ	PROPN
ejpam-6081	25	4	(	(	PUNCT
ejpam-6081	25	5	z	z	NOUN
ejpam-6081	25	6	)	)	PUNCT
ejpam-6081	25	7	1−	1−	NUM
ejpam-6081	25	8	υ	υ	NOUN
ejpam-6081	25	9	(	(	PUNCT
ejpam-6081	25	10	z	z	NOUN
ejpam-6081	25	11	)	)	PUNCT
ejpam-6081	25	12	,	,	PUNCT
ejpam-6081	25	13	z	z	PROPN
ejpam-6081	25	14	∈	∈	PROPN
ejpam-6081	25	15	e.	e.	PROPN
ejpam-6081	25	16	(	(	PUNCT
ejpam-6081	25	17	7	7	X
ejpam-6081	25	18	)	)	PUNCT
ejpam-6081	25	19	let	let	VERB
ejpam-6081	25	20	g1	g1	PROPN
ejpam-6081	25	21	(	(	PUNCT
ejpam-6081	25	22	z	z	NOUN
ejpam-6081	25	23	)	)	PUNCT
ejpam-6081	25	24	and	and	CCONJ
ejpam-6081	25	25	g2	g2	PROPN
ejpam-6081	25	26	(	(	PUNCT
ejpam-6081	25	27	z	z	NOUN
ejpam-6081	25	28	)	)	PUNCT
ejpam-6081	25	29	be	be	AUX
ejpam-6081	25	30	two	two	NUM
ejpam-6081	25	31	analytic	analytic	ADJ
ejpam-6081	25	32	functions	function	NOUN
ejpam-6081	25	33	in	in	ADP
ejpam-6081	25	34	e	e	NOUN
ejpam-6081	25	35	,	,	PUNCT
ejpam-6081	25	36	with	with	ADP
ejpam-6081	25	37	the	the	DET
ejpam-6081	25	38	symbol	symbol	NOUN
ejpam-6081	25	39	≺	≺	NOUN
ejpam-6081	25	40	representing	represent	VERB
ejpam-6081	25	41	a	a	DET
ejpam-6081	25	42	subordination	subordination	NOUN
ejpam-6081	25	43	.	.	PUNCT
ejpam-6081	26	1	the	the	DET
ejpam-6081	26	2	function	function	NOUN
ejpam-6081	26	3	g1	g1	NOUN
ejpam-6081	26	4	(	(	PUNCT
ejpam-6081	26	5	z	z	NOUN
ejpam-6081	26	6	)	)	PUNCT
ejpam-6081	26	7	is	be	AUX
ejpam-6081	26	8	subordinate	subordinate	ADJ
ejpam-6081	26	9	to	to	PART
ejpam-6081	26	10	function	function	VERB
ejpam-6081	26	11	g2	g2	PROPN
ejpam-6081	26	12	(	(	PUNCT
ejpam-6081	26	13	z	z	NOUN
ejpam-6081	26	14	)	)	PUNCT
ejpam-6081	26	15	,	,	PUNCT
ejpam-6081	26	16	denoted	denote	VERB
ejpam-6081	26	17	g1	g1	PROPN
ejpam-6081	26	18	(	(	PUNCT
ejpam-6081	26	19	z	z	NOUN
ejpam-6081	26	20	)	)	PUNCT
ejpam-6081	26	21	≺	≺	NOUN
ejpam-6081	26	22	g2	g2	PROPN
ejpam-6081	26	23	(	(	PUNCT
ejpam-6081	26	24	z	z	NOUN
ejpam-6081	26	25	)	)	PUNCT
ejpam-6081	26	26	,	,	PUNCT
ejpam-6081	26	27	if	if	SCONJ
ejpam-6081	26	28	there	there	PRON
ejpam-6081	26	29	exists	exist	VERB
ejpam-6081	26	30	a	a	DET
ejpam-6081	26	31	schwarz	schwarz	PROPN
ejpam-6081	26	32	function	function	NOUN
ejpam-6081	26	33	υ	υ	PROPN
ejpam-6081	26	34	(	(	PUNCT
ejpam-6081	26	35	z	z	NOUN
ejpam-6081	26	36	)	)	PUNCT
ejpam-6081	26	37	∈	∈	PROPN
ejpam-6081	26	38	h	h	NOUN
ejpam-6081	27	1	such	such	ADJ
ejpam-6081	27	2	that	that	SCONJ
ejpam-6081	27	3	g1	g1	PROPN
ejpam-6081	27	4	(	(	PUNCT
ejpam-6081	27	5	z	z	NOUN
ejpam-6081	27	6	)	)	PUNCT
ejpam-6081	27	7	=	=	SYM
ejpam-6081	27	8	g2	g2	PROPN
ejpam-6081	27	9	(	(	PUNCT
ejpam-6081	27	10	υ	υ	X
ejpam-6081	27	11	(	(	PUNCT
ejpam-6081	27	12	z	z	NOUN
ejpam-6081	27	13	)	)	PUNCT
ejpam-6081	27	14	)	)	PUNCT
ejpam-6081	27	15	.	.	PUNCT
ejpam-6081	28	1	furthermore	furthermore	ADV
ejpam-6081	28	2	,	,	PUNCT
ejpam-6081	28	3	if	if	SCONJ
ejpam-6081	28	4	g1	g1	PROPN
ejpam-6081	28	5	(	(	PUNCT
ejpam-6081	28	6	z	z	NOUN
ejpam-6081	28	7	)	)	PUNCT
ejpam-6081	28	8	is	be	AUX
ejpam-6081	28	9	univalent	univalent	ADJ
ejpam-6081	28	10	in	in	ADP
ejpam-6081	28	11	e	e	NOUN
ejpam-6081	28	12	,	,	PUNCT
ejpam-6081	28	13	then	then	ADV
ejpam-6081	28	14	we	we	PRON
ejpam-6081	28	15	have	have	VERB
ejpam-6081	28	16	the	the	DET
ejpam-6081	28	17	following	follow	VERB
ejpam-6081	28	18	equivalence	equivalence	NOUN
ejpam-6081	28	19	g1	g1	NOUN
ejpam-6081	28	20	(	(	PUNCT
ejpam-6081	28	21	z	z	NOUN
ejpam-6081	28	22	)	)	PUNCT
ejpam-6081	28	23	≺	≺	NOUN
ejpam-6081	28	24	g2	g2	PROPN
ejpam-6081	28	25	(	(	PUNCT
ejpam-6081	28	26	z	z	NOUN
ejpam-6081	28	27	)	)	PUNCT
ejpam-6081	28	28	⇔	⇔	PROPN
ejpam-6081	28	29	g1	g1	PROPN
ejpam-6081	28	30	(	(	PUNCT
ejpam-6081	28	31	0	0	NUM
ejpam-6081	28	32	)	)	PUNCT
ejpam-6081	29	1	=	=	SYM
ejpam-6081	29	2	g2	g2	PROPN
ejpam-6081	29	3	(	(	PUNCT
ejpam-6081	29	4	0	0	NUM
ejpam-6081	29	5	)	)	PUNCT
ejpam-6081	29	6	and	and	CCONJ
ejpam-6081	29	7	g1	g1	PROPN
ejpam-6081	29	8	(	(	PUNCT
ejpam-6081	29	9	e	e	NOUN
ejpam-6081	29	10	)	)	PUNCT
ejpam-6081	29	11	=	=	SYM
ejpam-6081	29	12	g2	g2	PROPN
ejpam-6081	29	13	(	(	PUNCT
ejpam-6081	29	14	e	e	NOUN
ejpam-6081	29	15	)	)	PUNCT
ejpam-6081	29	16	.	.	PUNCT
ejpam-6081	30	1	milin	milin	PROPN
ejpam-6081	31	1	[	[	X
ejpam-6081	31	2	1–3	1–3	X
ejpam-6081	31	3	]	]	X
ejpam-6081	31	4	highlighted	highlight	VERB
ejpam-6081	31	5	the	the	DET
ejpam-6081	31	6	importance	importance	NOUN
ejpam-6081	31	7	of	of	ADP
ejpam-6081	31	8	logarithmic	logarithmic	ADJ
ejpam-6081	31	9	coefficients	coefficient	NOUN
ejpam-6081	31	10	in	in	ADP
ejpam-6081	31	11	estimating	estimate	VERB
ejpam-6081	31	12	taylor	taylor	PROPN
ejpam-6081	31	13	coefficients	coefficient	NOUN
ejpam-6081	31	14	of	of	ADP
ejpam-6081	31	15	univalent	univalent	ADJ
ejpam-6081	31	16	functions	function	NOUN
ejpam-6081	31	17	.	.	PUNCT
ejpam-6081	32	1	the	the	DET
ejpam-6081	32	2	inequalities	inequality	NOUN
ejpam-6081	32	3	conjectured	conjecture	VERB
ejpam-6081	32	4	by	by	ADP
ejpam-6081	32	5	milin	milin	PROPN
ejpam-6081	32	6	attracted	attract	VERB
ejpam-6081	32	7	much	much	ADJ
ejpam-6081	32	8	attention	attention	NOUN
ejpam-6081	32	9	,	,	PUNCT
ejpam-6081	32	10	which	which	PRON
ejpam-6081	32	11	led	lead	VERB
ejpam-6081	32	12	to	to	ADP
ejpam-6081	32	13	de	de	X
ejpam-6081	32	14	branges	brange	NOUN
ejpam-6081	32	15	[	[	X
ejpam-6081	32	16	4	4	X
ejpam-6081	32	17	]	]	PUNCT
ejpam-6081	32	18	establishing	establish	VERB
ejpam-6081	32	19	the	the	DET
ejpam-6081	32	20	bieberbach	bieberbach	NOUN
ejpam-6081	32	21	conjecture	conjecture	NOUN
ejpam-6081	32	22	.	.	PUNCT
ejpam-6081	33	1	logarithmic	logarithmic	ADJ
ejpam-6081	33	2	coefficients	coefficient	NOUN
ejpam-6081	33	3	also	also	ADV
ejpam-6081	33	4	play	play	VERB
ejpam-6081	33	5	a	a	DET
ejpam-6081	33	6	significant	significant	ADJ
ejpam-6081	33	7	role	role	NOUN
ejpam-6081	33	8	in	in	ADP
ejpam-6081	33	9	conformal	conformal	ADJ
ejpam-6081	33	10	mapping	mapping	NOUN
ejpam-6081	33	11	,	,	PUNCT
ejpam-6081	33	12	which	which	PRON
ejpam-6081	33	13	helped	help	VERB
ejpam-6081	33	14	kayumov	kayumov	ADJ
ejpam-6081	33	15	[	[	X
ejpam-6081	33	16	5	5	NUM
ejpam-6081	33	17	]	]	PUNCT
ejpam-6081	33	18	solve	solve	PROPN
ejpam-6081	33	19	brennan	brennan	PROPN
ejpam-6081	33	20	’s	’s	PART
ejpam-6081	33	21	conjecture	conjecture	NOUN
ejpam-6081	33	22	.	.	PUNCT
ejpam-6081	34	1	since	since	SCONJ
ejpam-6081	34	2	then	then	ADV
ejpam-6081	34	3	,	,	PUNCT
ejpam-6081	34	4	numerous	numerous	ADJ
ejpam-6081	34	5	studies	study	NOUN
ejpam-6081	34	6	on	on	ADP
ejpam-6081	34	7	logarithmic	logarithmic	ADJ
ejpam-6081	34	8	coefficients	coefficient	NOUN
ejpam-6081	34	9	,	,	PUNCT
ejpam-6081	34	10	which	which	PRON
ejpam-6081	34	11	play	play	VERB
ejpam-6081	34	12	a	a	DET
ejpam-6081	34	13	central	central	ADJ
ejpam-6081	34	14	role	role	NOUN
ejpam-6081	34	15	in	in	ADP
ejpam-6081	34	16	the	the	DET
ejpam-6081	34	17	theory	theory	NOUN
ejpam-6081	34	18	of	of	ADP
ejpam-6081	34	19	univalent	univalent	ADJ
ejpam-6081	34	20	functions	function	NOUN
ejpam-6081	34	21	,	,	PUNCT
ejpam-6081	34	22	have	have	AUX
ejpam-6081	34	23	continued	continue	VERB
ejpam-6081	34	24	,	,	PUNCT
ejpam-6081	34	25	with	with	ADP
ejpam-6081	34	26	examples	example	NOUN
ejpam-6081	34	27	found	find	VERB
ejpam-6081	34	28	in	in	ADP
ejpam-6081	34	29	[	[	X
ejpam-6081	34	30	6–9	6–9	NOUN
ejpam-6081	34	31	]	]	PUNCT
ejpam-6081	34	32	.	.	PUNCT
ejpam-6081	35	1	here	here	ADV
ejpam-6081	35	2	,	,	PUNCT
ejpam-6081	35	3	the	the	DET
ejpam-6081	35	4	logarithmic	logarithmic	ADJ
ejpam-6081	35	5	coefficients	coefficient	NOUN
ejpam-6081	35	6	γn	γn	ADP
ejpam-6081	35	7	,	,	PUNCT
ejpam-6081	35	8	n	n	CCONJ
ejpam-6081	35	9	⩾	⩾	PROPN
ejpam-6081	35	10	1	1	NUM
ejpam-6081	35	11	of	of	ADP
ejpam-6081	35	12	f	f	PROPN
ejpam-6081	35	13	(	(	PUNCT
ejpam-6081	35	14	z	z	NOUN
ejpam-6081	35	15	)	)	PUNCT
ejpam-6081	35	16	∈	∈	PROPN
ejpam-6081	35	17	s	s	NOUN
ejpam-6081	35	18	are	be	AUX
ejpam-6081	35	19	defined	define	VERB
ejpam-6081	35	20	by	by	ADP
ejpam-6081	35	21	log	log	PROPN
ejpam-6081	35	22	f	f	PROPN
ejpam-6081	35	23	(	(	PUNCT
ejpam-6081	35	24	z	z	NOUN
ejpam-6081	35	25	)	)	PUNCT
ejpam-6081	35	26	z	z	NOUN
ejpam-6081	35	27	=	=	SYM
ejpam-6081	35	28	2	2	NUM
ejpam-6081	35	29	∞∑	∞∑	NUM
ejpam-6081	35	30	n=1	n=1	NUM
ejpam-6081	35	31	γnz	γnz	VERB
ejpam-6081	35	32	n.	n.	NOUN
ejpam-6081	35	33	(	(	PUNCT
ejpam-6081	35	34	8)	8)	NUM
ejpam-6081	35	35	n.	n.	PROPN
ejpam-6081	35	36	h.	h.	PROPN
ejpam-6081	35	37	a.	a.	PROPN
ejpam-6081	35	38	a.	a.	PROPN
ejpam-6081	35	39	wahid	wahid	PROPN
ejpam-6081	35	40	,	,	PUNCT
ejpam-6081	35	41	s.	s.	PROPN
ejpam-6081	35	42	c.	c.	PROPN
ejpam-6081	35	43	soh	soh	PROPN
ejpam-6081	35	44	/	/	SYM
ejpam-6081	35	45	eur	eur	PROPN
ejpam-6081	35	46	.	.	PUNCT
ejpam-6081	36	1	j.	j.	PROPN
ejpam-6081	36	2	pure	pure	PROPN
ejpam-6081	36	3	appl	appl	PROPN
ejpam-6081	36	4	.	.	PROPN
ejpam-6081	36	5	math	math	PROPN
ejpam-6081	36	6	,	,	PUNCT
ejpam-6081	36	7	18	18	NUM
ejpam-6081	36	8	(	(	PUNCT
ejpam-6081	36	9	2	2	NUM
ejpam-6081	36	10	)	)	PUNCT
ejpam-6081	36	11	(	(	PUNCT
ejpam-6081	36	12	2025	2025	NUM
ejpam-6081	36	13	)	)	PUNCT
ejpam-6081	36	14	,	,	PUNCT
ejpam-6081	36	15	6081	6081	NUM
ejpam-6081	36	16	3	3	NUM
ejpam-6081	36	17	of	of	ADP
ejpam-6081	36	18	16	16	NUM
ejpam-6081	36	19	differentiating	differentiate	VERB
ejpam-6081	36	20	(	(	PUNCT
ejpam-6081	36	21	8)	8)	NUM
ejpam-6081	36	22	and	and	CCONJ
ejpam-6081	36	23	equating	equate	VERB
ejpam-6081	36	24	coefficients	coefficient	NOUN
ejpam-6081	36	25	of	of	ADP
ejpam-6081	36	26	zn	zn	PROPN
ejpam-6081	36	27	yield	yield	NOUN
ejpam-6081	36	28	expressions	expression	NOUN
ejpam-6081	36	29	for	for	ADP
ejpam-6081	36	30	the	the	DET
ejpam-6081	36	31	logarithmic	logarithmic	ADJ
ejpam-6081	36	32	coefficients	coefficient	NOUN
ejpam-6081	36	33	in	in	ADP
ejpam-6081	36	34	terms	term	NOUN
ejpam-6081	36	35	of	of	ADP
ejpam-6081	36	36	the	the	DET
ejpam-6081	36	37	taylor	taylor	PROPN
ejpam-6081	36	38	coefficients	coefficient	NOUN
ejpam-6081	36	39	for	for	ADP
ejpam-6081	36	40	f	f	PROPN
ejpam-6081	36	41	(	(	PUNCT
ejpam-6081	36	42	z	z	NOUN
ejpam-6081	36	43	)	)	PUNCT
ejpam-6081	36	44	∈	∈	PROPN
ejpam-6081	36	45	s	s	NOUN
ejpam-6081	36	46	,	,	PUNCT
ejpam-6081	36	47	specifically	specifically	ADV
ejpam-6081	36	48	for	for	ADP
ejpam-6081	36	49	n	n	NOUN
ejpam-6081	36	50	=	=	SYM
ejpam-6081	36	51	1	1	NUM
ejpam-6081	36	52	,	,	PUNCT
ejpam-6081	36	53	2	2	NUM
ejpam-6081	36	54	,	,	PUNCT
ejpam-6081	36	55	3	3	NUM
ejpam-6081	36	56	:	:	PUNCT
ejpam-6081	36	57	γ1	γ1	NOUN
ejpam-6081	36	58	=	=	NOUN
ejpam-6081	36	59	1	1	NUM
ejpam-6081	36	60	2	2	NUM
ejpam-6081	36	61	a2	a2	NOUN
ejpam-6081	36	62	,	,	PUNCT
ejpam-6081	36	63	(	(	PUNCT
ejpam-6081	36	64	9	9	X
ejpam-6081	36	65	)	)	PUNCT
ejpam-6081	36	66	γ2	γ2	NOUN
ejpam-6081	36	67	=	=	SYM
ejpam-6081	36	68	1	1	NUM
ejpam-6081	36	69	2	2	NUM
ejpam-6081	36	70	(	(	PUNCT
ejpam-6081	36	71	a3	a3	NOUN
ejpam-6081	36	72	−	−	NOUN
ejpam-6081	36	73	1	1	NUM
ejpam-6081	36	74	2	2	NUM
ejpam-6081	36	75	a2	a2	PROPN
ejpam-6081	36	76	2	2	NUM
ejpam-6081	36	77	)	)	PUNCT
ejpam-6081	36	78	,	,	PUNCT
ejpam-6081	36	79	(	(	PUNCT
ejpam-6081	36	80	10	10	NUM
ejpam-6081	36	81	)	)	PUNCT
ejpam-6081	36	82	and	and	CCONJ
ejpam-6081	36	83	γ3	γ3	NOUN
ejpam-6081	36	84	=	=	NOUN
ejpam-6081	36	85	1	1	NUM
ejpam-6081	36	86	2	2	NUM
ejpam-6081	36	87	(	(	PUNCT
ejpam-6081	36	88	a4	a4	NOUN
ejpam-6081	36	89	−	−	NOUN
ejpam-6081	37	1	a2a3	a2a3	NOUN
ejpam-6081	38	1	+	+	NUM
ejpam-6081	38	2	1	1	NUM
ejpam-6081	38	3	3	3	NUM
ejpam-6081	38	4	a2	a2	PROPN
ejpam-6081	38	5	3	3	NUM
ejpam-6081	38	6	)	)	PUNCT
ejpam-6081	38	7	.	.	PUNCT
ejpam-6081	39	1	(	(	PUNCT
ejpam-6081	39	2	11	11	NUM
ejpam-6081	39	3	)	)	PUNCT
ejpam-6081	39	4	the	the	DET
ejpam-6081	39	5	logarithmic	logarithmic	ADJ
ejpam-6081	39	6	coefficients	coefficient	NOUN
ejpam-6081	39	7	of	of	ADP
ejpam-6081	39	8	the	the	DET
ejpam-6081	39	9	inverse	inverse	NOUN
ejpam-6081	39	10	functions	function	NOUN
ejpam-6081	39	11	,	,	PUNCT
ejpam-6081	39	12	denoted	denote	VERB
ejpam-6081	39	13	γn	γn	NOUN
ejpam-6081	39	14	for	for	ADP
ejpam-6081	39	15	f	f	PROPN
ejpam-6081	39	16	(	(	PUNCT
ejpam-6081	39	17	z	z	NOUN
ejpam-6081	39	18	)	)	PUNCT
ejpam-6081	39	19	∈	∈	PROPN
ejpam-6081	39	20	s	s	VERB
ejpam-6081	39	21	were	be	AUX
ejpam-6081	39	22	introduced	introduce	VERB
ejpam-6081	39	23	by	by	ADP
ejpam-6081	39	24	ponnusamy	ponnusamy	NOUN
ejpam-6081	39	25	et	et	PROPN
ejpam-6081	39	26	al	al	PROPN
ejpam-6081	39	27	.	.	PUNCT
ejpam-6081	40	1	[	[	X
ejpam-6081	40	2	10	10	NUM
ejpam-6081	40	3	]	]	PUNCT
ejpam-6081	40	4	.	.	PUNCT
ejpam-6081	41	1	they	they	PRON
ejpam-6081	41	2	are	be	AUX
ejpam-6081	41	3	expressed	express	VERB
ejpam-6081	41	4	in	in	ADP
ejpam-6081	41	5	the	the	DET
ejpam-6081	41	6	series	series	NOUN
ejpam-6081	41	7	form	form	NOUN
ejpam-6081	41	8	as	as	ADP
ejpam-6081	41	9	log	log	NOUN
ejpam-6081	41	10	f−1	f−1	PROPN
ejpam-6081	41	11	(	(	PUNCT
ejpam-6081	41	12	w	w	NOUN
ejpam-6081	41	13	)	)	PUNCT
ejpam-6081	41	14	w	w	NOUN
ejpam-6081	41	15	=	=	SYM
ejpam-6081	41	16	2	2	NUM
ejpam-6081	41	17	∞∑	∞∑	NUM
ejpam-6081	41	18	n=1	n=1	PROPN
ejpam-6081	41	19	γnw	γnw	NOUN
ejpam-6081	41	20	n	n	CCONJ
ejpam-6081	41	21	,	,	PUNCT
ejpam-6081	41	22	|w|	|w|	VERB
ejpam-6081	41	23	<	<	X
ejpam-6081	41	24	1	1	NUM
ejpam-6081	41	25	4	4	NUM
ejpam-6081	41	26	,	,	PUNCT
ejpam-6081	41	27	where	where	SCONJ
ejpam-6081	41	28	,	,	PUNCT
ejpam-6081	41	29	in	in	ADP
ejpam-6081	41	30	particular	particular	ADJ
ejpam-6081	41	31	,	,	PUNCT
ejpam-6081	41	32	for	for	ADP
ejpam-6081	41	33	n	n	NOUN
ejpam-6081	41	34	=	=	SYM
ejpam-6081	41	35	1	1	NUM
ejpam-6081	41	36	,	,	PUNCT
ejpam-6081	41	37	2	2	NUM
ejpam-6081	41	38	,	,	PUNCT
ejpam-6081	41	39	3	3	NUM
ejpam-6081	41	40	:	:	PUNCT
ejpam-6081	41	41	γ1	γ1	NOUN
ejpam-6081	41	42	=	=	SYM
ejpam-6081	41	43	−1	−1	NOUN
ejpam-6081	41	44	2	2	NUM
ejpam-6081	41	45	a2	a2	PROPN
ejpam-6081	41	46	,	,	PUNCT
ejpam-6081	41	47	(	(	PUNCT
ejpam-6081	41	48	12	12	NUM
ejpam-6081	41	49	)	)	PUNCT
ejpam-6081	41	50	γ2	γ2	NOUN
ejpam-6081	41	51	=	=	SYM
ejpam-6081	41	52	−1	−1	NOUN
ejpam-6081	41	53	2	2	NUM
ejpam-6081	41	54	(	(	PUNCT
ejpam-6081	41	55	a3	a3	NOUN
ejpam-6081	41	56	−	−	PROPN
ejpam-6081	41	57	3	3	NUM
ejpam-6081	41	58	2	2	NUM
ejpam-6081	41	59	a2	a2	PROPN
ejpam-6081	41	60	2	2	NUM
ejpam-6081	41	61	)	)	PUNCT
ejpam-6081	41	62	,	,	PUNCT
ejpam-6081	41	63	(	(	PUNCT
ejpam-6081	41	64	13	13	NUM
ejpam-6081	41	65	)	)	PUNCT
ejpam-6081	41	66	and	and	CCONJ
ejpam-6081	42	1	γ3	γ3	NOUN
ejpam-6081	42	2	=	=	SYM
ejpam-6081	42	3	−1	−1	NOUN
ejpam-6081	42	4	2	2	NUM
ejpam-6081	42	5	(	(	PUNCT
ejpam-6081	42	6	a4	a4	NOUN
ejpam-6081	42	7	−	−	NOUN
ejpam-6081	42	8	4a2a3	4a2a3	NUM
ejpam-6081	43	1	+	+	CCONJ
ejpam-6081	43	2	10	10	NUM
ejpam-6081	43	3	3	3	NUM
ejpam-6081	43	4	a2	a2	PROPN
ejpam-6081	43	5	3	3	NUM
ejpam-6081	43	6	)	)	PUNCT
ejpam-6081	43	7	.	.	PUNCT
ejpam-6081	44	1	(	(	PUNCT
ejpam-6081	44	2	14	14	NUM
ejpam-6081	44	3	)	)	PUNCT
ejpam-6081	44	4	a	a	DET
ejpam-6081	44	5	typical	typical	ADJ
ejpam-6081	44	6	subject	subject	NOUN
ejpam-6081	44	7	in	in	ADP
ejpam-6081	44	8	geometric	geometric	ADJ
ejpam-6081	44	9	function	function	NOUN
ejpam-6081	44	10	theory	theory	NOUN
ejpam-6081	44	11	is	be	AUX
ejpam-6081	44	12	the	the	DET
ejpam-6081	44	13	study	study	NOUN
ejpam-6081	44	14	of	of	ADP
ejpam-6081	44	15	coefficient	coefficient	NOUN
ejpam-6081	44	16	functionals	functional	NOUN
ejpam-6081	44	17	,	,	PUNCT
ejpam-6081	44	18	which	which	PRON
ejpam-6081	44	19	are	be	AUX
ejpam-6081	44	20	equations	equation	NOUN
ejpam-6081	44	21	derived	derive	VERB
ejpam-6081	44	22	from	from	ADP
ejpam-6081	44	23	various	various	ADJ
ejpam-6081	44	24	combinations	combination	NOUN
ejpam-6081	44	25	of	of	ADP
ejpam-6081	44	26	taylor	taylor	PROPN
ejpam-6081	44	27	coefficients	coefficient	NOUN
ejpam-6081	44	28	for	for	ADP
ejpam-6081	44	29	subclasses	subclass	NOUN
ejpam-6081	44	30	in	in	ADP
ejpam-6081	44	31	s.	s.	PROPN
ejpam-6081	44	32	this	this	PRON
ejpam-6081	44	33	comprises	comprise	VERB
ejpam-6081	44	34	the	the	DET
ejpam-6081	44	35	taylor	taylor	PROPN
ejpam-6081	44	36	coefficients	coefficient	NOUN
ejpam-6081	44	37	of	of	ADP
ejpam-6081	44	38	inverse	inverse	NOUN
ejpam-6081	44	39	functions	function	NOUN
ejpam-6081	44	40	,	,	PUNCT
ejpam-6081	44	41	the	the	DET
ejpam-6081	44	42	logarithmic	logarithmic	ADJ
ejpam-6081	44	43	coefficients	coefficient	NOUN
ejpam-6081	44	44	of	of	ADP
ejpam-6081	44	45	functions	function	NOUN
ejpam-6081	44	46	and	and	CCONJ
ejpam-6081	44	47	inverse	inverse	NOUN
ejpam-6081	44	48	functions	function	NOUN
ejpam-6081	44	49	,	,	PUNCT
ejpam-6081	44	50	as	as	ADV
ejpam-6081	44	51	well	well	ADV
ejpam-6081	44	52	as	as	ADP
ejpam-6081	44	53	the	the	DET
ejpam-6081	44	54	vandermonde	vandermonde	NOUN
ejpam-6081	44	55	determinant	determinant	ADJ
ejpam-6081	44	56	.	.	PUNCT
ejpam-6081	45	1	the	the	DET
ejpam-6081	45	2	vandermonde	vandermonde	NOUN
ejpam-6081	45	3	determinant	determinant	ADJ
ejpam-6081	45	4	,	,	PUNCT
ejpam-6081	45	5	also	also	ADV
ejpam-6081	45	6	known	know	VERB
ejpam-6081	45	7	as	as	ADP
ejpam-6081	45	8	a	a	DET
ejpam-6081	45	9	discriminant	discriminant	NOUN
ejpam-6081	45	10	,	,	PUNCT
ejpam-6081	45	11	has	have	VERB
ejpam-6081	45	12	many	many	ADJ
ejpam-6081	45	13	applications	application	NOUN
ejpam-6081	45	14	in	in	ADP
ejpam-6081	45	15	a	a	DET
ejpam-6081	45	16	range	range	NOUN
ejpam-6081	45	17	of	of	ADP
ejpam-6081	45	18	domains	domain	NOUN
ejpam-6081	45	19	.	.	PUNCT
ejpam-6081	46	1	it	it	PRON
ejpam-6081	46	2	is	be	AUX
ejpam-6081	46	3	used	use	VERB
ejpam-6081	46	4	in	in	ADP
ejpam-6081	46	5	digital	digital	ADJ
ejpam-6081	46	6	signal	signal	NOUN
ejpam-6081	46	7	processing	processing	NOUN
ejpam-6081	46	8	to	to	PART
ejpam-6081	46	9	compute	compute	VERB
ejpam-6081	46	10	the	the	DET
ejpam-6081	46	11	discrete	discrete	ADJ
ejpam-6081	46	12	fourier	fourier	NOUN
ejpam-6081	46	13	transform	transform	NOUN
ejpam-6081	46	14	(	(	PUNCT
ejpam-6081	46	15	dft	dft	NOUN
ejpam-6081	46	16	)	)	PUNCT
ejpam-6081	46	17	and	and	CCONJ
ejpam-6081	46	18	the	the	DET
ejpam-6081	46	19	inverse	inverse	NOUN
ejpam-6081	46	20	discrete	discrete	NOUN
ejpam-6081	46	21	fourier	fourier	NOUN
ejpam-6081	46	22	transform	transform	NOUN
ejpam-6081	46	23	(	(	PUNCT
ejpam-6081	46	24	idft	idft	NOUN
ejpam-6081	46	25	)	)	PUNCT
ejpam-6081	46	26	,	,	PUNCT
ejpam-6081	46	27	as	as	ADV
ejpam-6081	46	28	well	well	ADV
ejpam-6081	46	29	as	as	ADP
ejpam-6081	46	30	in	in	ADP
ejpam-6081	46	31	approximation	approximation	NOUN
ejpam-6081	46	32	problems	problem	NOUN
ejpam-6081	46	33	[	[	X
ejpam-6081	46	34	11	11	NUM
ejpam-6081	46	35	]	]	PUNCT
ejpam-6081	46	36	.	.	PUNCT
ejpam-6081	47	1	it	it	PRON
ejpam-6081	47	2	is	be	AUX
ejpam-6081	47	3	also	also	ADV
ejpam-6081	47	4	an	an	DET
ejpam-6081	47	5	important	important	ADJ
ejpam-6081	47	6	tool	tool	NOUN
ejpam-6081	47	7	in	in	ADP
ejpam-6081	47	8	linear	linear	PROPN
ejpam-6081	47	9	algebra	algebra	NOUN
ejpam-6081	47	10	,	,	PUNCT
ejpam-6081	47	11	for	for	ADP
ejpam-6081	47	12	example	example	NOUN
ejpam-6081	47	13	,	,	PUNCT
ejpam-6081	47	14	in	in	ADP
ejpam-6081	47	15	determining	determine	VERB
ejpam-6081	47	16	the	the	DET
ejpam-6081	47	17	number	number	NOUN
ejpam-6081	47	18	of	of	ADP
ejpam-6081	47	19	roots	root	NOUN
ejpam-6081	47	20	of	of	ADP
ejpam-6081	47	21	polynomials	polynomial	NOUN
ejpam-6081	47	22	(	(	PUNCT
ejpam-6081	47	23	see	see	VERB
ejpam-6081	47	24	[	[	X
ejpam-6081	47	25	12	12	NUM
ejpam-6081	47	26	]	]	NUM
ejpam-6081	47	27	)	)	PUNCT
ejpam-6081	47	28	.	.	PUNCT
ejpam-6081	48	1	vijayalakshmi	vijayalakshmi	NOUN
ejpam-6081	48	2	et	et	PROPN
ejpam-6081	48	3	al	al	PROPN
ejpam-6081	48	4	.	.	PUNCT
ejpam-6081	49	1	[	[	X
ejpam-6081	49	2	11	11	NUM
ejpam-6081	49	3	]	]	PUNCT
ejpam-6081	49	4	studied	study	VERB
ejpam-6081	49	5	the	the	DET
ejpam-6081	49	6	vandermonde	vandermonde	ADJ
ejpam-6081	49	7	determinant	determinant	ADJ
ejpam-6081	49	8	vq	vq	NOUN
ejpam-6081	49	9	,	,	PUNCT
ejpam-6081	49	10	n	n	PROPN
ejpam-6081	49	11	(	(	PUNCT
ejpam-6081	49	12	f	f	X
ejpam-6081	49	13	)	)	PUNCT
ejpam-6081	49	14	,	,	PUNCT
ejpam-6081	49	15	where	where	SCONJ
ejpam-6081	49	16	n	n	CCONJ
ejpam-6081	49	17	,	,	PUNCT
ejpam-6081	49	18	q	q	X
ejpam-6081	49	19	≥	≥	NOUN
ejpam-6081	49	20	1	1	NUM
ejpam-6081	49	21	and	and	CCONJ
ejpam-6081	49	22	an	an	PRON
ejpam-6081	49	23	,	,	PUNCT
ejpam-6081	49	24	n	n	PRON
ejpam-6081	49	25	≥	≥	NOUN
ejpam-6081	49	26	2	2	NUM
ejpam-6081	49	27	are	be	AUX
ejpam-6081	49	28	the	the	DET
ejpam-6081	49	29	taylor	taylor	PROPN
ejpam-6081	49	30	series	series	PROPN
ejpam-6081	49	31	coefficients	coefficient	VERB
ejpam-6081	49	32	in	in	ADP
ejpam-6081	49	33	(	(	PUNCT
ejpam-6081	49	34	1	1	NUM
ejpam-6081	49	35	):	):	PUNCT
ejpam-6081	49	36	vq	vq	NOUN
ejpam-6081	49	37	,	,	PUNCT
ejpam-6081	49	38	n	n	PROPN
ejpam-6081	49	39	(	(	PUNCT
ejpam-6081	49	40	f	f	X
ejpam-6081	49	41	)	)	PUNCT
ejpam-6081	49	42	=	=	SYM
ejpam-6081	50	1	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	50	2	1	1	NUM
ejpam-6081	50	3	1	1	NUM
ejpam-6081	50	4	...	...	SYM
ejpam-6081	50	5	1	1	NUM
ejpam-6081	50	6	an	an	DET
ejpam-6081	50	7	an+1	an+1	NOUN
ejpam-6081	50	8	...	...	PUNCT
ejpam-6081	51	1	an+q−1	an+q−1	PRON
ejpam-6081	51	2	·	·	PUNCT
ejpam-6081	51	3	·	·	PUNCT
ejpam-6081	51	4	·	·	PUNCT
ejpam-6081	51	5	·	·	PUNCT
ejpam-6081	51	6	·	·	PUNCT
ejpam-6081	51	7	·	·	PUNCT
ejpam-6081	51	8	...	...	PUNCT
ejpam-6081	51	9	·	·	PUNCT
ejpam-6081	51	10	·	·	PUNCT
ejpam-6081	51	11	·	·	PUNCT
ejpam-6081	52	1	an	an	DET
ejpam-6081	52	2	q−1	q−1	PROPN
ejpam-6081	52	3	an+1	an+1	AUX
ejpam-6081	52	4	q−1	q−1	NOUN
ejpam-6081	52	5	...	...	PUNCT
ejpam-6081	53	1	an+q−1	an+q−1	PRON
ejpam-6081	53	2	q−1	q−1	PROPN
ejpam-6081	53	3	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	53	4	,	,	PUNCT
ejpam-6081	53	5	a1	a1	NOUN
ejpam-6081	53	6	=	=	SYM
ejpam-6081	53	7	1	1	X
ejpam-6081	53	8	.	.	PUNCT
ejpam-6081	53	9	(	(	PUNCT
ejpam-6081	53	10	15	15	NUM
ejpam-6081	53	11	)	)	PUNCT
ejpam-6081	53	12	n.	n.	NOUN
ejpam-6081	53	13	h.	h.	PROPN
ejpam-6081	53	14	a.	a.	PROPN
ejpam-6081	53	15	a.	a.	PROPN
ejpam-6081	53	16	wahid	wahid	PROPN
ejpam-6081	53	17	,	,	PUNCT
ejpam-6081	53	18	s.	s.	PROPN
ejpam-6081	53	19	c.	c.	PROPN
ejpam-6081	53	20	soh	soh	PROPN
ejpam-6081	53	21	/	/	SYM
ejpam-6081	53	22	eur	eur	PROPN
ejpam-6081	53	23	.	.	PUNCT
ejpam-6081	54	1	j.	j.	PROPN
ejpam-6081	54	2	pure	pure	PROPN
ejpam-6081	54	3	appl	appl	PROPN
ejpam-6081	54	4	.	.	PROPN
ejpam-6081	54	5	math	math	PROPN
ejpam-6081	54	6	,	,	PUNCT
ejpam-6081	54	7	18	18	NUM
ejpam-6081	54	8	(	(	PUNCT
ejpam-6081	54	9	2	2	NUM
ejpam-6081	54	10	)	)	PUNCT
ejpam-6081	54	11	(	(	PUNCT
ejpam-6081	54	12	2025	2025	NUM
ejpam-6081	54	13	)	)	PUNCT
ejpam-6081	54	14	,	,	PUNCT
ejpam-6081	54	15	6081	6081	NUM
ejpam-6081	54	16	4	4	NUM
ejpam-6081	54	17	of	of	ADP
ejpam-6081	54	18	16	16	NUM
ejpam-6081	54	19	it	it	PRON
ejpam-6081	54	20	is	be	AUX
ejpam-6081	54	21	noted	note	VERB
ejpam-6081	54	22	that	that	SCONJ
ejpam-6081	54	23	with	with	ADP
ejpam-6081	54	24	one	one	NUM
ejpam-6081	54	25	as	as	ADP
ejpam-6081	54	26	the	the	DET
ejpam-6081	54	27	first	first	ADJ
ejpam-6081	54	28	element	element	NOUN
ejpam-6081	54	29	,	,	PUNCT
ejpam-6081	54	30	this	this	PRON
ejpam-6081	54	31	determinant	determinant	ADJ
ejpam-6081	54	32	displays	display	VERB
ejpam-6081	54	33	a	a	DET
ejpam-6081	54	34	geometric	geometric	ADJ
ejpam-6081	54	35	sequence	sequence	NOUN
ejpam-6081	54	36	in	in	ADP
ejpam-6081	54	37	each	each	DET
ejpam-6081	54	38	row	row	NOUN
ejpam-6081	54	39	or	or	CCONJ
ejpam-6081	54	40	column	column	NOUN
ejpam-6081	54	41	.	.	PUNCT
ejpam-6081	55	1	abdul	abdul	PROPN
ejpam-6081	55	2	wahid	wahid	PROPN
ejpam-6081	55	3	et	et	PROPN
ejpam-6081	55	4	al	al	PROPN
ejpam-6081	55	5	.	.	PUNCT
ejpam-6081	56	1	[	[	X
ejpam-6081	56	2	13	13	NUM
ejpam-6081	56	3	]	]	PUNCT
ejpam-6081	56	4	introduced	introduce	VERB
ejpam-6081	56	5	the	the	DET
ejpam-6081	56	6	vandermonde	vandermonde	NOUN
ejpam-6081	56	7	determinant	determinant	ADJ
ejpam-6081	56	8	vq	vq	NOUN
ejpam-6081	56	9	,	,	PUNCT
ejpam-6081	56	10	n	n	CCONJ
ejpam-6081	56	11	(	(	PUNCT
ejpam-6081	56	12	γf	γf	PROPN
ejpam-6081	56	13	)	)	PUNCT
ejpam-6081	56	14	,	,	PUNCT
ejpam-6081	56	15	where	where	SCONJ
ejpam-6081	56	16	n	n	CCONJ
ejpam-6081	56	17	,	,	PUNCT
ejpam-6081	56	18	q	q	X
ejpam-6081	56	19	≥	≥	NOUN
ejpam-6081	56	20	1	1	NUM
ejpam-6081	56	21	by	by	ADP
ejpam-6081	56	22	looking	look	VERB
ejpam-6081	56	23	at	at	ADP
ejpam-6081	56	24	the	the	DET
ejpam-6081	56	25	logarithmic	logarithmic	ADJ
ejpam-6081	56	26	series	series	NOUN
ejpam-6081	56	27	coefficients	coefficient	VERB
ejpam-6081	56	28	γn	γn	NUM
ejpam-6081	56	29	,	,	PUNCT
ejpam-6081	56	30	n	n	PRON
ejpam-6081	56	31	≥	≥	NOUN
ejpam-6081	56	32	1	1	NUM
ejpam-6081	56	33	in	in	ADP
ejpam-6081	56	34	(	(	PUNCT
ejpam-6081	56	35	8)	8)	NUM
ejpam-6081	56	36	,	,	PUNCT
ejpam-6081	56	37	because	because	SCONJ
ejpam-6081	56	38	they	they	PRON
ejpam-6081	56	39	were	be	AUX
ejpam-6081	56	40	inspired	inspire	VERB
ejpam-6081	56	41	by	by	ADP
ejpam-6081	56	42	previous	previous	ADJ
ejpam-6081	56	43	studies	study	NOUN
ejpam-6081	56	44	on	on	ADP
ejpam-6081	56	45	hankel	hankel	NOUN
ejpam-6081	56	46	and	and	CCONJ
ejpam-6081	56	47	toeplitz	toeplitz	NOUN
ejpam-6081	56	48	determinants	determinant	NOUN
ejpam-6081	56	49	,	,	PUNCT
ejpam-6081	56	50	which	which	PRON
ejpam-6081	56	51	involved	involve	VERB
ejpam-6081	56	52	both	both	DET
ejpam-6081	56	53	taylor	taylor	PROPN
ejpam-6081	56	54	coefficients	coefficient	NOUN
ejpam-6081	56	55	and	and	CCONJ
ejpam-6081	56	56	logarithmic	logarithmic	ADJ
ejpam-6081	56	57	coefficients	coefficient	NOUN
ejpam-6081	56	58	.	.	PUNCT
ejpam-6081	57	1	this	this	DET
ejpam-6081	57	2	determinant	determinant	ADJ
ejpam-6081	57	3	is	be	AUX
ejpam-6081	57	4	given	give	VERB
ejpam-6081	57	5	by	by	ADP
ejpam-6081	57	6	[	[	PUNCT
ejpam-6081	57	7	13	13	NUM
ejpam-6081	57	8	]	]	SYM
ejpam-6081	57	9	vq	vq	NOUN
ejpam-6081	57	10	,	,	PUNCT
ejpam-6081	57	11	n	n	CCONJ
ejpam-6081	57	12	(	(	PUNCT
ejpam-6081	57	13	γf	γf	ADJ
ejpam-6081	57	14	)	)	PUNCT
ejpam-6081	57	15	=	=	PUNCT
ejpam-6081	58	1	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	58	2	1	1	NUM
ejpam-6081	58	3	1	1	NUM
ejpam-6081	58	4	...	...	SYM
ejpam-6081	58	5	1	1	NUM
ejpam-6081	58	6	γn	γn	NOUN
ejpam-6081	58	7	γn+1	γn+1	NUM
ejpam-6081	58	8	...	...	PUNCT
ejpam-6081	59	1	γn+q−1	γn+q−1	PROPN
ejpam-6081	59	2	·	·	PUNCT
ejpam-6081	59	3	·	·	PUNCT
ejpam-6081	59	4	·	·	PUNCT
ejpam-6081	59	5	·	·	PUNCT
ejpam-6081	59	6	·	·	PUNCT
ejpam-6081	59	7	·	·	PUNCT
ejpam-6081	59	8	...	...	PUNCT
ejpam-6081	59	9	·	·	PUNCT
ejpam-6081	59	10	·	·	PUNCT
ejpam-6081	59	11	·	·	PUNCT
ejpam-6081	60	1	γn	γn	NUM
ejpam-6081	60	2	q−1	q−1	PROPN
ejpam-6081	60	3	γn+1	γn+1	NUM
ejpam-6081	60	4	q−1	q−1	PROPN
ejpam-6081	60	5	...	...	PUNCT
ejpam-6081	61	1	γn+q−1	γn+q−1	PROPN
ejpam-6081	61	2	q−1	q−1	PROPN
ejpam-6081	61	3	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	61	4	.	.	PUNCT
ejpam-6081	62	1	(	(	PUNCT
ejpam-6081	62	2	16	16	NUM
ejpam-6081	62	3	)	)	PUNCT
ejpam-6081	62	4	given	give	VERB
ejpam-6081	62	5	the	the	DET
ejpam-6081	62	6	importance	importance	NOUN
ejpam-6081	62	7	of	of	ADP
ejpam-6081	62	8	the	the	DET
ejpam-6081	62	9	vandermonde	vandermonde	NOUN
ejpam-6081	62	10	determinant	determinant	ADJ
ejpam-6081	62	11	and	and	CCONJ
ejpam-6081	62	12	inspired	inspire	VERB
ejpam-6081	62	13	by	by	ADP
ejpam-6081	62	14	the	the	DET
ejpam-6081	62	15	works	work	NOUN
ejpam-6081	62	16	of	of	ADP
ejpam-6081	62	17	abdul	abdul	PROPN
ejpam-6081	62	18	wahid	wahid	PROPN
ejpam-6081	62	19	et	et	PROPN
ejpam-6081	62	20	al	al	PROPN
ejpam-6081	62	21	.	.	PUNCT
ejpam-6081	63	1	[	[	X
ejpam-6081	63	2	14	14	NUM
ejpam-6081	63	3	]	]	X
ejpam-6081	63	4	,	,	PUNCT
ejpam-6081	63	5	shi	shi	PROPN
ejpam-6081	63	6	et	et	PROPN
ejpam-6081	63	7	al	al	PROPN
ejpam-6081	63	8	.	.	PUNCT
ejpam-6081	64	1	[	[	X
ejpam-6081	64	2	15	15	NUM
ejpam-6081	64	3	]	]	X
ejpam-6081	64	4	,	,	PUNCT
ejpam-6081	64	5	obradovi	obradovi	NOUN
ejpam-6081	64	6	and	and	CCONJ
ejpam-6081	64	7	tuneski	tuneski	ADJ
ejpam-6081	64	8	[	[	X
ejpam-6081	64	9	16	16	NUM
ejpam-6081	64	10	]	]	PUNCT
ejpam-6081	64	11	,	,	PUNCT
ejpam-6081	64	12	and	and	CCONJ
ejpam-6081	64	13	hadi	hadi	PROPN
ejpam-6081	64	14	et	et	PROPN
ejpam-6081	64	15	al	al	PROPN
ejpam-6081	64	16	.	.	PUNCT
ejpam-6081	65	1	[	[	X
ejpam-6081	65	2	17	17	NUM
ejpam-6081	65	3	]	]	PUNCT
ejpam-6081	65	4	,	,	PUNCT
ejpam-6081	65	5	which	which	PRON
ejpam-6081	65	6	deal	deal	VERB
ejpam-6081	65	7	with	with	ADP
ejpam-6081	65	8	solving	solve	VERB
ejpam-6081	65	9	determinant	determinant	ADJ
ejpam-6081	65	10	and	and	CCONJ
ejpam-6081	65	11	coefficient	coefficient	ADJ
ejpam-6081	65	12	functional	functional	ADJ
ejpam-6081	65	13	problems	problem	NOUN
ejpam-6081	65	14	for	for	ADP
ejpam-6081	65	15	the	the	DET
ejpam-6081	65	16	inverse	inverse	NOUN
ejpam-6081	65	17	of	of	ADP
ejpam-6081	65	18	analytic	analytic	ADJ
ejpam-6081	65	19	functions	function	NOUN
ejpam-6081	65	20	,	,	PUNCT
ejpam-6081	65	21	it	it	PRON
ejpam-6081	65	22	is	be	AUX
ejpam-6081	65	23	natural	natural	ADJ
ejpam-6081	65	24	to	to	PART
ejpam-6081	65	25	explore	explore	VERB
ejpam-6081	65	26	the	the	DET
ejpam-6081	65	27	vandermonde	vandermonde	NOUN
ejpam-6081	65	28	determinant	determinant	ADJ
ejpam-6081	65	29	with	with	ADP
ejpam-6081	65	30	an	an	PRON
ejpam-6081	65	31	and	and	CCONJ
ejpam-6081	65	32	γn	γn	NOUN
ejpam-6081	65	33	replacing	replace	VERB
ejpam-6081	65	34	an	an	PRON
ejpam-6081	65	35	and	and	CCONJ
ejpam-6081	65	36	γn	γn	NOUN
ejpam-6081	65	37	,	,	PUNCT
ejpam-6081	65	38	respectively	respectively	ADV
ejpam-6081	65	39	.	.	PUNCT
ejpam-6081	66	1	using	use	VERB
ejpam-6081	66	2	this	this	DET
ejpam-6081	66	3	idea	idea	NOUN
ejpam-6081	66	4	,	,	PUNCT
ejpam-6081	66	5	we	we	PRON
ejpam-6081	66	6	define	define	VERB
ejpam-6081	66	7	the	the	DET
ejpam-6081	66	8	vandermonde	vandermonde	ADJ
ejpam-6081	66	9	determinant	determinant	ADJ
ejpam-6081	66	10	of	of	ADP
ejpam-6081	66	11	taylor	taylor	PROPN
ejpam-6081	66	12	coefficients	coefficient	NOUN
ejpam-6081	66	13	and	and	CCONJ
ejpam-6081	66	14	logarithmic	logarithmic	ADJ
ejpam-6081	66	15	coefficients	coefficient	NOUN
ejpam-6081	66	16	of	of	ADP
ejpam-6081	66	17	inverse	inverse	NOUN
ejpam-6081	66	18	functions	function	NOUN
ejpam-6081	66	19	for	for	ADP
ejpam-6081	66	20	f	f	PROPN
ejpam-6081	66	21	(	(	PUNCT
ejpam-6081	66	22	z	z	NOUN
ejpam-6081	66	23	)	)	PUNCT
ejpam-6081	66	24	∈	∈	PROPN
ejpam-6081	66	25	s	s	NOUN
ejpam-6081	66	26	,	,	PUNCT
ejpam-6081	66	27	respectively	respectively	ADV
ejpam-6081	66	28	,	,	PUNCT
ejpam-6081	66	29	as	as	SCONJ
ejpam-6081	66	30	follows	follow	VERB
ejpam-6081	66	31	:	:	PUNCT
ejpam-6081	66	32	vq	vq	NOUN
ejpam-6081	66	33	,	,	PUNCT
ejpam-6081	66	34	n	n	PROPN
ejpam-6081	66	35	(	(	PUNCT
ejpam-6081	66	36	f−1	f−1	PROPN
ejpam-6081	66	37	)	)	PUNCT
ejpam-6081	67	1	=	=	PUNCT
ejpam-6081	67	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	67	3	1	1	NUM
ejpam-6081	67	4	1	1	NUM
ejpam-6081	67	5	...	...	SYM
ejpam-6081	67	6	1	1	NUM
ejpam-6081	67	7	an	an	DET
ejpam-6081	67	8	an+1	an+1	NOUN
ejpam-6081	67	9	...	...	PUNCT
ejpam-6081	68	1	an+q−1	an+q−1	PRON
ejpam-6081	68	2	·	·	PUNCT
ejpam-6081	68	3	·	·	PUNCT
ejpam-6081	68	4	·	·	PUNCT
ejpam-6081	68	5	·	·	PUNCT
ejpam-6081	68	6	·	·	PUNCT
ejpam-6081	68	7	·	·	PUNCT
ejpam-6081	68	8	...	...	PUNCT
ejpam-6081	68	9	·	·	PUNCT
ejpam-6081	68	10	·	·	PUNCT
ejpam-6081	68	11	·	·	PUNCT
ejpam-6081	69	1	an	an	DET
ejpam-6081	69	2	q−1	q−1	PROPN
ejpam-6081	69	3	an+1	an+1	AUX
ejpam-6081	69	4	q−1	q−1	NOUN
ejpam-6081	69	5	...	...	PUNCT
ejpam-6081	70	1	an+q−1	an+q−1	PRON
ejpam-6081	70	2	q−1	q−1	PROPN
ejpam-6081	70	3	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	70	4	(	(	PUNCT
ejpam-6081	70	5	17	17	NUM
ejpam-6081	70	6	)	)	PUNCT
ejpam-6081	70	7	and	and	CCONJ
ejpam-6081	70	8	vq	vq	PROPN
ejpam-6081	70	9	,	,	PUNCT
ejpam-6081	70	10	n	n	PROPN
ejpam-6081	70	11	(	(	PUNCT
ejpam-6081	70	12	γf−1	γf−1	PROPN
ejpam-6081	70	13	)	)	PUNCT
ejpam-6081	70	14	=	=	PUNCT
ejpam-6081	70	15	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	70	16	1	1	NUM
ejpam-6081	70	17	1	1	NUM
ejpam-6081	70	18	...	...	SYM
ejpam-6081	70	19	1	1	NUM
ejpam-6081	70	20	γn	γn	NOUN
ejpam-6081	70	21	γn+1	γn+1	NUM
ejpam-6081	70	22	...	...	PUNCT
ejpam-6081	70	23	γn+q−1	γn+q−1	PROPN
ejpam-6081	70	24	·	·	PUNCT
ejpam-6081	70	25	·	·	PUNCT
ejpam-6081	70	26	·	·	PUNCT
ejpam-6081	70	27	·	·	PUNCT
ejpam-6081	70	28	·	·	PUNCT
ejpam-6081	70	29	·	·	PUNCT
ejpam-6081	70	30	...	...	PUNCT
ejpam-6081	70	31	·	·	PUNCT
ejpam-6081	70	32	·	·	PUNCT
ejpam-6081	70	33	·	·	PUNCT
ejpam-6081	71	1	γn	γn	NUM
ejpam-6081	71	2	q−1	q−1	PROPN
ejpam-6081	71	3	γn+1	γn+1	NUM
ejpam-6081	71	4	q−1	q−1	PROPN
ejpam-6081	71	5	...	...	PUNCT
ejpam-6081	72	1	γn+q−1	γn+q−1	PROPN
ejpam-6081	72	2	q−1	q−1	PROPN
ejpam-6081	72	3	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-6081	72	4	.	.	PUNCT
ejpam-6081	73	1	(	(	PUNCT
ejpam-6081	73	2	18	18	NUM
ejpam-6081	73	3	)	)	PUNCT
ejpam-6081	73	4	recently	recently	ADV
ejpam-6081	73	5	,	,	PUNCT
ejpam-6081	73	6	kazımoğlu	kazımoğlu	PROPN
ejpam-6081	73	7	et	et	PROPN
ejpam-6081	73	8	al	al	PROPN
ejpam-6081	73	9	.	.	PUNCT
ejpam-6081	74	1	[	[	X
ejpam-6081	74	2	18	18	NUM
ejpam-6081	74	3	]	]	PUNCT
ejpam-6081	74	4	,	,	PUNCT
ejpam-6081	74	5	srivastava	srivastava	PROPN
ejpam-6081	74	6	et	et	PROPN
ejpam-6081	74	7	al	al	PROPN
ejpam-6081	74	8	.	.	PUNCT
ejpam-6081	75	1	[	[	X
ejpam-6081	75	2	19	19	NUM
ejpam-6081	75	3	]	]	PUNCT
ejpam-6081	75	4	,	,	PUNCT
ejpam-6081	75	5	tang	tang	X
ejpam-6081	75	6	et	et	PROPN
ejpam-6081	75	7	al	al	PROPN
ejpam-6081	75	8	.	.	PUNCT
ejpam-6081	76	1	[	[	X
ejpam-6081	76	2	20	20	NUM
ejpam-6081	76	3	]	]	PUNCT
ejpam-6081	76	4	,	,	PUNCT
ejpam-6081	76	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-6081	76	6	et	et	PROPN
ejpam-6081	76	7	al	al	PROPN
ejpam-6081	76	8	.	.	PUNCT
ejpam-6081	77	1	[	[	X
ejpam-6081	77	2	21	21	NUM
ejpam-6081	77	3	]	]	PUNCT
ejpam-6081	77	4	,	,	PUNCT
ejpam-6081	77	5	and	and	CCONJ
ejpam-6081	77	6	al	al	PROPN
ejpam-6081	77	7	-	-	PUNCT
ejpam-6081	77	8	hawarya	hawarya	PROPN
ejpam-6081	77	9	et	et	PROPN
ejpam-6081	77	10	al	al	PROPN
ejpam-6081	77	11	.	.	PUNCT
ejpam-6081	78	1	[	[	X
ejpam-6081	78	2	22	22	NUM
ejpam-6081	78	3	]	]	PUNCT
ejpam-6081	78	4	introduced	introduce	VERB
ejpam-6081	78	5	new	new	ADJ
ejpam-6081	78	6	classes	class	NOUN
ejpam-6081	78	7	of	of	ADP
ejpam-6081	78	8	univalent	univalent	ADJ
ejpam-6081	78	9	functions	function	NOUN
ejpam-6081	78	10	associated	associate	VERB
ejpam-6081	78	11	with	with	ADP
ejpam-6081	78	12	the	the	DET
ejpam-6081	78	13	generating	generate	VERB
ejpam-6081	78	14	function	function	NOUN
ejpam-6081	78	15	of	of	ADP
ejpam-6081	78	16	gregory	gregory	PROPN
ejpam-6081	78	17	coefficients	coefficient	NOUN
ejpam-6081	78	18	.	.	PUNCT
ejpam-6081	79	1	the	the	DET
ejpam-6081	79	2	gregory	gregory	PROPN
ejpam-6081	79	3	coefficients	coefficient	NOUN
ejpam-6081	79	4	,	,	PUNCT
ejpam-6081	79	5	also	also	ADV
ejpam-6081	79	6	known	know	VERB
ejpam-6081	79	7	as	as	ADP
ejpam-6081	79	8	reciprocal	reciprocal	ADJ
ejpam-6081	79	9	logarithmic	logarithmic	ADJ
ejpam-6081	79	10	numbers	number	NOUN
ejpam-6081	79	11	,	,	PUNCT
ejpam-6081	79	12	second	second	ADJ
ejpam-6081	79	13	-	-	PUNCT
ejpam-6081	79	14	kind	kind	NOUN
ejpam-6081	79	15	bernoulli	bernoulli	NOUN
ejpam-6081	79	16	numbers	number	NOUN
ejpam-6081	79	17	,	,	PUNCT
ejpam-6081	79	18	or	or	CCONJ
ejpam-6081	79	19	cauchy	cauchy	NOUN
ejpam-6081	79	20	numbers	number	NOUN
ejpam-6081	79	21	,	,	PUNCT
ejpam-6081	79	22	are	be	AUX
ejpam-6081	79	23	decreasing	decrease	VERB
ejpam-6081	79	24	rational	rational	ADJ
ejpam-6081	79	25	numbers	number	NOUN
ejpam-6081	79	26	that	that	PRON
ejpam-6081	79	27	serve	serve	VERB
ejpam-6081	79	28	a	a	DET
ejpam-6081	79	29	function	function	NOUN
ejpam-6081	79	30	similar	similar	ADJ
ejpam-6081	79	31	to	to	ADP
ejpam-6081	79	32	bernoulli	bernoulli	NOUN
ejpam-6081	79	33	numbers	number	NOUN
ejpam-6081	79	34	and	and	CCONJ
ejpam-6081	79	35	can	can	AUX
ejpam-6081	79	36	be	be	AUX
ejpam-6081	79	37	found	find	VERB
ejpam-6081	79	38	in	in	ADP
ejpam-6081	79	39	a	a	DET
ejpam-6081	79	40	wide	wide	ADJ
ejpam-6081	79	41	range	range	NOUN
ejpam-6081	79	42	of	of	ADP
ejpam-6081	79	43	problems	problem	NOUN
ejpam-6081	79	44	,	,	PUNCT
ejpam-6081	79	45	particularly	particularly	ADV
ejpam-6081	79	46	those	those	PRON
ejpam-6081	79	47	involving	involve	VERB
ejpam-6081	79	48	numerical	numerical	ADJ
ejpam-6081	79	49	analysis	analysis	NOUN
ejpam-6081	79	50	and	and	CCONJ
ejpam-6081	79	51	number	number	NOUN
ejpam-6081	79	52	theory	theory	NOUN
ejpam-6081	79	53	.	.	PUNCT
ejpam-6081	80	1	the	the	DET
ejpam-6081	80	2	generating	generate	VERB
ejpam-6081	80	3	function	function	NOUN
ejpam-6081	80	4	of	of	ADP
ejpam-6081	80	5	the	the	DET
ejpam-6081	80	6	gregory	gregory	PROPN
ejpam-6081	80	7	coefficients	coefficient	VERB
ejpam-6081	80	8	λn	λn	PROPN
ejpam-6081	80	9	,	,	PUNCT
ejpam-6081	80	10	for	for	ADP
ejpam-6081	80	11	n	n	PRON
ejpam-6081	80	12	≥	≥	NOUN
ejpam-6081	80	13	0	0	NUM
ejpam-6081	80	14	,	,	PUNCT
ejpam-6081	80	15	is	be	AUX
ejpam-6081	80	16	given	give	VERB
ejpam-6081	80	17	by	by	ADP
ejpam-6081	80	18	z	z	PROPN
ejpam-6081	80	19	ln	ln	NOUN
ejpam-6081	80	20	(	(	PUNCT
ejpam-6081	80	21	1	1	NUM
ejpam-6081	80	22	+	+	CCONJ
ejpam-6081	80	23	z	z	NOUN
ejpam-6081	80	24	)	)	PUNCT
ejpam-6081	80	25	=	=	PUNCT
ejpam-6081	81	1	∞∑	∞∑	NUM
ejpam-6081	81	2	n=0	n=0	NUM
ejpam-6081	81	3	λnz	λnz	NOUN
ejpam-6081	81	4	n	n	NOUN
ejpam-6081	81	5	=	=	SYM
ejpam-6081	81	6	1	1	NUM
ejpam-6081	81	7	+	+	CCONJ
ejpam-6081	81	8	1	1	NUM
ejpam-6081	81	9	2	2	NUM
ejpam-6081	81	10	z	z	NOUN
ejpam-6081	81	11	−	−	NOUN
ejpam-6081	81	12	1	1	NUM
ejpam-6081	81	13	12	12	NUM
ejpam-6081	81	14	z2	z2	NOUN
ejpam-6081	81	15	+	+	CCONJ
ejpam-6081	81	16	1	1	NUM
ejpam-6081	81	17	24	24	NUM
ejpam-6081	81	18	z3	z3	NOUN
ejpam-6081	81	19	−	−	PROPN
ejpam-6081	81	20	19	19	NUM
ejpam-6081	81	21	720	720	NUM
ejpam-6081	81	22	z4	z4	NOUN
ejpam-6081	81	23	+	+	CCONJ
ejpam-6081	81	24	3	3	NUM
ejpam-6081	81	25	160	160	NUM
ejpam-6081	81	26	z5	z5	NOUN
ejpam-6081	81	27	−	−	PROPN
ejpam-6081	81	28	.	.	PUNCT
ejpam-6081	81	29	.	.	PUNCT
ejpam-6081	81	30	.	.	PUNCT
ejpam-6081	81	31	.	.	PUNCT
ejpam-6081	82	1	(	(	PUNCT
ejpam-6081	82	2	19	19	NUM
ejpam-6081	82	3	)	)	PUNCT
ejpam-6081	82	4	in	in	ADP
ejpam-6081	82	5	connection	connection	NOUN
ejpam-6081	82	6	with	with	ADP
ejpam-6081	82	7	this	this	DET
ejpam-6081	82	8	function	function	NOUN
ejpam-6081	82	9	,	,	PUNCT
ejpam-6081	82	10	we	we	PRON
ejpam-6081	82	11	define	define	VERB
ejpam-6081	82	12	the	the	DET
ejpam-6081	82	13	following	follow	VERB
ejpam-6081	82	14	class	class	NOUN
ejpam-6081	82	15	:	:	PUNCT
ejpam-6081	82	16	n.	n.	PROPN
ejpam-6081	82	17	h.	h.	PROPN
ejpam-6081	82	18	a.	a.	PROPN
ejpam-6081	82	19	a.	a.	PROPN
ejpam-6081	82	20	wahid	wahid	PROPN
ejpam-6081	82	21	,	,	PUNCT
ejpam-6081	82	22	s.	s.	PROPN
ejpam-6081	82	23	c.	c.	PROPN
ejpam-6081	82	24	soh	soh	PROPN
ejpam-6081	82	25	/	/	SYM
ejpam-6081	82	26	eur	eur	PROPN
ejpam-6081	82	27	.	.	PUNCT
ejpam-6081	83	1	j.	j.	PROPN
ejpam-6081	83	2	pure	pure	PROPN
ejpam-6081	83	3	appl	appl	PROPN
ejpam-6081	83	4	.	.	PROPN
ejpam-6081	83	5	math	math	PROPN
ejpam-6081	83	6	,	,	PUNCT
ejpam-6081	83	7	18	18	NUM
ejpam-6081	83	8	(	(	PUNCT
ejpam-6081	83	9	2	2	NUM
ejpam-6081	83	10	)	)	PUNCT
ejpam-6081	83	11	(	(	PUNCT
ejpam-6081	83	12	2025	2025	NUM
ejpam-6081	83	13	)	)	PUNCT
ejpam-6081	83	14	,	,	PUNCT
ejpam-6081	83	15	6081	6081	NUM
ejpam-6081	83	16	5	5	NUM
ejpam-6081	83	17	of	of	ADP
ejpam-6081	83	18	16	16	NUM
ejpam-6081	83	19	definition	definition	NOUN
ejpam-6081	83	20	1	1	NUM
ejpam-6081	83	21	.	.	PUNCT
ejpam-6081	84	1	an	an	DET
ejpam-6081	84	2	analytic	analytic	ADJ
ejpam-6081	84	3	function	function	NOUN
ejpam-6081	84	4	f	f	PROPN
ejpam-6081	84	5	(	(	PUNCT
ejpam-6081	84	6	z	z	NOUN
ejpam-6081	84	7	)	)	PUNCT
ejpam-6081	84	8	of	of	ADP
ejpam-6081	84	9	the	the	DET
ejpam-6081	84	10	form	form	NOUN
ejpam-6081	84	11	(	(	PUNCT
ejpam-6081	84	12	1	1	X
ejpam-6081	84	13	)	)	PUNCT
ejpam-6081	84	14	is	be	AUX
ejpam-6081	84	15	said	say	VERB
ejpam-6081	84	16	to	to	PART
ejpam-6081	84	17	be	be	AUX
ejpam-6081	84	18	in	in	ADP
ejpam-6081	84	19	the	the	DET
ejpam-6081	84	20	class	class	NOUN
ejpam-6081	84	21	gg	gg	NOUN
ejpam-6081	84	22	(	(	PUNCT
ejpam-6081	84	23	α	α	PROPN
ejpam-6081	84	24	,	,	PUNCT
ejpam-6081	84	25	δ	δ	PROPN
ejpam-6081	84	26	)	)	PUNCT
ejpam-6081	84	27	if	if	SCONJ
ejpam-6081	84	28	the	the	DET
ejpam-6081	84	29	following	follow	VERB
ejpam-6081	84	30	condition	condition	NOUN
ejpam-6081	84	31	is	be	AUX
ejpam-6081	84	32	satisfied	satisfied	ADJ
ejpam-6081	84	33	:	:	PUNCT
ejpam-6081	84	34	eiαf	eiαf	NOUN
ejpam-6081	84	35	′	′	NUM
ejpam-6081	85	1	(	(	PUNCT
ejpam-6081	85	2	z)−	z)−	NOUN
ejpam-6081	85	3	i	i	PRON
ejpam-6081	85	4	sinα−	sinα−	VERB
ejpam-6081	85	5	δ	δ	PROPN
ejpam-6081	85	6	ταδ	ταδ	PROPN
ejpam-6081	85	7	≺	≺	NOUN
ejpam-6081	85	8	ψ(z	ψ(z	PROPN
ejpam-6081	85	9	)	)	PUNCT
ejpam-6081	85	10	,	,	PUNCT
ejpam-6081	85	11	z	z	NOUN
ejpam-6081	85	12	∈	∈	PROPN
ejpam-6081	85	13	e	e	NOUN
ejpam-6081	85	14	,	,	PUNCT
ejpam-6081	85	15	where	where	SCONJ
ejpam-6081	85	16	ψ(z	ψ(z	NOUN
ejpam-6081	85	17	)	)	PUNCT
ejpam-6081	85	18	=	=	SYM
ejpam-6081	85	19	z	z	NOUN
ejpam-6081	85	20	ln(1+z	ln(1+z	PROPN
ejpam-6081	85	21	)	)	PUNCT
ejpam-6081	85	22	,	,	PUNCT
ejpam-6081	85	23	ταδ	ταδ	PROPN
ejpam-6081	85	24	=	=	SYM
ejpam-6081	85	25	cosα−	cosα−	PROPN
ejpam-6081	85	26	δ	δ	PROPN
ejpam-6081	85	27	,	,	PUNCT
ejpam-6081	85	28	|α|	|α|	PROPN
ejpam-6081	85	29	<	<	X
ejpam-6081	85	30	π	π	PROPN
ejpam-6081	85	31	,	,	PUNCT
ejpam-6081	85	32	and	and	CCONJ
ejpam-6081	85	33	0	0	NUM
ejpam-6081	85	34	⩽	⩽	PROPN
ejpam-6081	85	35	δ	δ	PROPN
ejpam-6081	85	36	<	<	X
ejpam-6081	85	37	1	1	X
ejpam-6081	85	38	.	.	PUNCT
ejpam-6081	85	39	remark	remark	NOUN
ejpam-6081	85	40	1	1	NUM
ejpam-6081	85	41	.	.	PUNCT
ejpam-6081	85	42	selecting	select	VERB
ejpam-6081	85	43	specific	specific	ADJ
ejpam-6081	85	44	values	value	NOUN
ejpam-6081	85	45	for	for	ADP
ejpam-6081	85	46	the	the	DET
ejpam-6081	85	47	parameters	parameter	NOUN
ejpam-6081	85	48	α	α	PROPN
ejpam-6081	85	49	and	and	CCONJ
ejpam-6081	85	50	δ	δ	PROPN
ejpam-6081	85	51	in	in	ADP
ejpam-6081	85	52	the	the	DET
ejpam-6081	85	53	class	class	NOUN
ejpam-6081	85	54	gg	gg	NOUN
ejpam-6081	85	55	(	(	PUNCT
ejpam-6081	85	56	α	α	PROPN
ejpam-6081	85	57	,	,	PUNCT
ejpam-6081	85	58	δ	δ	PROPN
ejpam-6081	85	59	)	)	PUNCT
ejpam-6081	85	60	yields	yield	VERB
ejpam-6081	85	61	the	the	DET
ejpam-6081	85	62	following	follow	VERB
ejpam-6081	85	63	classes	class	NOUN
ejpam-6081	85	64	,	,	PUNCT
ejpam-6081	85	65	which	which	PRON
ejpam-6081	85	66	are	be	AUX
ejpam-6081	85	67	new	new	ADJ
ejpam-6081	85	68	and	and	CCONJ
ejpam-6081	85	69	have	have	AUX
ejpam-6081	85	70	not	not	PART
ejpam-6081	85	71	yet	yet	ADV
ejpam-6081	85	72	been	be	AUX
ejpam-6081	85	73	studied	study	VERB
ejpam-6081	85	74	by	by	ADP
ejpam-6081	85	75	others	other	NOUN
ejpam-6081	85	76	:	:	PUNCT
ejpam-6081	85	77	(	(	PUNCT
ejpam-6081	85	78	i	i	NOUN
ejpam-6081	85	79	)	)	PUNCT
ejpam-6081	85	80	gg	gg	PROPN
ejpam-6081	85	81	(	(	PUNCT
ejpam-6081	85	82	α	α	NOUN
ejpam-6081	85	83	,	,	PUNCT
ejpam-6081	85	84	0	0	NUM
ejpam-6081	85	85	)	)	PUNCT
ejpam-6081	85	86	≡	≡	PROPN
ejpam-6081	85	87	gg	gg	PROPN
ejpam-6081	85	88	(	(	PUNCT
ejpam-6081	85	89	α	α	NOUN
ejpam-6081	85	90	)	)	PUNCT
ejpam-6081	85	91	=	=	NOUN
ejpam-6081	86	1	{	{	PUNCT
ejpam-6081	86	2	f	f	PROPN
ejpam-6081	86	3	∈	∈	PROPN
ejpam-6081	86	4	s	s	PART
ejpam-6081	86	5	:	:	PUNCT
ejpam-6081	86	6	eiαf	eiαf	NOUN
ejpam-6081	86	7	′(z)−i	′(z)−i	PROPN
ejpam-6081	87	1	sinα	sinα	PROPN
ejpam-6081	88	1	cosα	cosα	PROPN
ejpam-6081	88	2	≺	≺	NOUN
ejpam-6081	88	3	ψ(z	ψ(z	PROPN
ejpam-6081	88	4	)	)	PUNCT
ejpam-6081	88	5	,	,	PUNCT
ejpam-6081	88	6	z	z	NOUN
ejpam-6081	88	7	∈	∈	PROPN
ejpam-6081	88	8	e	e	X
ejpam-6081	88	9	}	}	PUNCT
ejpam-6081	88	10	(	(	PUNCT
ejpam-6081	88	11	ii	ii	PROPN
ejpam-6081	88	12	)	)	PUNCT
ejpam-6081	88	13	gg	gg	NOUN
ejpam-6081	88	14	(	(	PUNCT
ejpam-6081	88	15	0	0	NUM
ejpam-6081	88	16	,	,	PUNCT
ejpam-6081	88	17	δ	δ	PROPN
ejpam-6081	88	18	)	)	PUNCT
ejpam-6081	88	19	≡	≡	PROPN
ejpam-6081	88	20	gg	gg	PROPN
ejpam-6081	88	21	(	(	PUNCT
ejpam-6081	88	22	δ	δ	PROPN
ejpam-6081	88	23	)	)	PUNCT
ejpam-6081	88	24	:	:	PUNCT
ejpam-6081	89	1	=	=	X
ejpam-6081	89	2	{	{	PUNCT
ejpam-6081	89	3	f	f	PROPN
ejpam-6081	89	4	∈	∈	PROPN
ejpam-6081	89	5	s	s	PART
ejpam-6081	89	6	:	:	PUNCT
ejpam-6081	89	7	f	f	PROPN
ejpam-6081	89	8	′(z)−δ	′(z)−δ	PROPN
ejpam-6081	89	9	1−δ	1−δ	NUM
ejpam-6081	89	10	≺	≺	NOUN
ejpam-6081	89	11	ψ(z	ψ(z	PROPN
ejpam-6081	89	12	)	)	PUNCT
ejpam-6081	89	13	,	,	PUNCT
ejpam-6081	89	14	z	z	NOUN
ejpam-6081	89	15	∈	∈	PROPN
ejpam-6081	89	16	e	e	X
ejpam-6081	89	17	}	}	PUNCT
ejpam-6081	89	18	(	(	PUNCT
ejpam-6081	89	19	iii	iii	X
ejpam-6081	89	20	)	)	PUNCT
ejpam-6081	89	21	gg	gg	NOUN
ejpam-6081	89	22	(	(	PUNCT
ejpam-6081	89	23	0	0	NUM
ejpam-6081	89	24	,	,	PUNCT
ejpam-6081	89	25	0	0	NUM
ejpam-6081	89	26	)	)	PUNCT
ejpam-6081	89	27	≡	≡	PROPN
ejpam-6081	89	28	gg	gg	PROPN
ejpam-6081	89	29	=	=	PRON
ejpam-6081	89	30	{	{	PUNCT
ejpam-6081	89	31	f	f	PROPN
ejpam-6081	89	32	∈	∈	PROPN
ejpam-6081	89	33	s	s	PART
ejpam-6081	89	34	:	:	PUNCT
ejpam-6081	89	35	f	f	NOUN
ejpam-6081	90	1	′	′	NUM
ejpam-6081	90	2	(	(	PUNCT
ejpam-6081	90	3	z	z	NOUN
ejpam-6081	90	4	)	)	PUNCT
ejpam-6081	90	5	≺	≺	NOUN
ejpam-6081	90	6	ψ(z	ψ(z	PROPN
ejpam-6081	90	7	)	)	PUNCT
ejpam-6081	90	8	,	,	PUNCT
ejpam-6081	90	9	z	z	NOUN
ejpam-6081	90	10	∈	∈	PROPN
ejpam-6081	90	11	e	e	X
ejpam-6081	90	12	}	}	PUNCT
ejpam-6081	90	13	the	the	DET
ejpam-6081	90	14	class	class	NOUN
ejpam-6081	90	15	gg	gg	NOUN
ejpam-6081	90	16	(	(	PUNCT
ejpam-6081	90	17	α	α	PROPN
ejpam-6081	90	18	,	,	PUNCT
ejpam-6081	90	19	δ	δ	PROPN
ejpam-6081	90	20	)	)	PUNCT
ejpam-6081	90	21	is	be	AUX
ejpam-6081	90	22	inspired	inspire	VERB
ejpam-6081	90	23	by	by	ADP
ejpam-6081	90	24	the	the	DET
ejpam-6081	90	25	generalized	generalized	ADJ
ejpam-6081	90	26	class	class	NOUN
ejpam-6081	90	27	of	of	ADP
ejpam-6081	90	28	bounded	bound	VERB
ejpam-6081	90	29	turning	turning	NOUN
ejpam-6081	90	30	functions	function	NOUN
ejpam-6081	90	31	g	g	NOUN
ejpam-6081	90	32	(	(	PUNCT
ejpam-6081	90	33	α	α	PROPN
ejpam-6081	90	34	,	,	PUNCT
ejpam-6081	90	35	δ	δ	PROPN
ejpam-6081	90	36	)	)	PUNCT
ejpam-6081	90	37	introduced	introduce	VERB
ejpam-6081	90	38	by	by	ADP
ejpam-6081	90	39	mohamad	mohamad	PROPN
ejpam-6081	91	1	[	[	X
ejpam-6081	91	2	23	23	NUM
ejpam-6081	91	3	]	]	PUNCT
ejpam-6081	91	4	,	,	PUNCT
ejpam-6081	91	5	which	which	PRON
ejpam-6081	91	6	satisfies	satisfy	VERB
ejpam-6081	91	7	{	{	PUNCT
ejpam-6081	91	8	f	f	PROPN
ejpam-6081	91	9	∈	∈	PROPN
ejpam-6081	91	10	s	s	PART
ejpam-6081	91	11	:	:	PUNCT
ejpam-6081	91	12	re	re	X
ejpam-6081	91	13	(	(	PUNCT
ejpam-6081	91	14	eiαf	eiαf	NOUN
ejpam-6081	91	15	′	′	NUM
ejpam-6081	92	1	(	(	PUNCT
ejpam-6081	92	2	z	z	NOUN
ejpam-6081	92	3	)	)	PUNCT
ejpam-6081	92	4	)	)	PUNCT
ejpam-6081	93	1	>	>	PUNCT
ejpam-6081	93	2	δ	δ	PROPN
ejpam-6081	93	3	,	,	PUNCT
ejpam-6081	93	4	z	z	NOUN
ejpam-6081	93	5	∈	∈	PROPN
ejpam-6081	93	6	e	e	X
ejpam-6081	93	7	}	}	PUNCT
ejpam-6081	93	8	.	.	PUNCT
ejpam-6081	94	1	then	then	ADV
ejpam-6081	94	2	there	there	PRON
ejpam-6081	94	3	exists	exist	VERB
ejpam-6081	94	4	a	a	DET
ejpam-6081	94	5	function	function	NOUN
ejpam-6081	94	6	p	p	X
ejpam-6081	94	7	(	(	PUNCT
ejpam-6081	94	8	z	z	NOUN
ejpam-6081	94	9	)	)	PUNCT
ejpam-6081	94	10	∈	∈	PROPN
ejpam-6081	94	11	p	p	NOUN
ejpam-6081	95	1	such	such	ADJ
ejpam-6081	95	2	that	that	SCONJ
ejpam-6081	95	3	[	[	X
ejpam-6081	95	4	23	23	NUM
ejpam-6081	95	5	]	]	PUNCT
ejpam-6081	95	6	eiαf	eiαf	NOUN
ejpam-6081	95	7	′	′	NUM
ejpam-6081	96	1	(	(	PUNCT
ejpam-6081	96	2	z)−	z)−	NOUN
ejpam-6081	96	3	i	i	PRON
ejpam-6081	96	4	sinα−	sinα−	VERB
ejpam-6081	96	5	δ	δ	X
ejpam-6081	96	6	ταδ	ταδ	PUNCT
ejpam-6081	97	1	=	=	SYM
ejpam-6081	97	2	p	p	X
ejpam-6081	97	3	(	(	PUNCT
ejpam-6081	97	4	z	z	NOUN
ejpam-6081	97	5	)	)	PUNCT
ejpam-6081	97	6	∈	∈	PROPN
ejpam-6081	97	7	p	p	X
ejpam-6081	97	8	,	,	PUNCT
ejpam-6081	97	9	where	where	SCONJ
ejpam-6081	97	10	ταδ	ταδ	ADV
ejpam-6081	97	11	=	=	SYM
ejpam-6081	97	12	cosα−	cosα−	PROPN
ejpam-6081	97	13	δ	δ	PROPN
ejpam-6081	97	14	,	,	PUNCT
ejpam-6081	97	15	|α|	|α|	PROPN
ejpam-6081	97	16	<	<	X
ejpam-6081	97	17	π	π	PROPN
ejpam-6081	97	18	,	,	PUNCT
ejpam-6081	97	19	0	0	NUM
ejpam-6081	97	20	⩽	⩽	PROPN
ejpam-6081	97	21	δ	δ	PROPN
ejpam-6081	97	22	<	<	X
ejpam-6081	97	23	1	1	NUM
ejpam-6081	97	24	,	,	PUNCT
ejpam-6081	97	25	and	and	CCONJ
ejpam-6081	97	26	cosα	cosα	NOUN
ejpam-6081	97	27	>	>	X
ejpam-6081	97	28	δ	δ	PROPN
ejpam-6081	97	29	.	.	PUNCT
ejpam-6081	97	30	remark	remark	PROPN
ejpam-6081	97	31	2	2	NUM
ejpam-6081	97	32	.	.	PUNCT
ejpam-6081	97	33	selecting	select	VERB
ejpam-6081	97	34	specific	specific	ADJ
ejpam-6081	97	35	values	value	NOUN
ejpam-6081	97	36	for	for	ADP
ejpam-6081	97	37	the	the	DET
ejpam-6081	97	38	parameters	parameter	NOUN
ejpam-6081	97	39	α	α	PROPN
ejpam-6081	97	40	and	and	CCONJ
ejpam-6081	97	41	δ	δ	PROPN
ejpam-6081	97	42	in	in	ADP
ejpam-6081	97	43	the	the	DET
ejpam-6081	97	44	class	class	NOUN
ejpam-6081	97	45	g	g	PROPN
ejpam-6081	97	46	(	(	PUNCT
ejpam-6081	97	47	α	α	PROPN
ejpam-6081	97	48	,	,	PUNCT
ejpam-6081	97	49	δ	δ	NOUN
ejpam-6081	97	50	)	)	PUNCT
ejpam-6081	97	51	results	result	NOUN
ejpam-6081	97	52	in	in	ADP
ejpam-6081	97	53	the	the	DET
ejpam-6081	97	54	following	follow	VERB
ejpam-6081	97	55	classes	class	NOUN
ejpam-6081	97	56	:	:	PUNCT
ejpam-6081	97	57	(	(	PUNCT
ejpam-6081	97	58	i	i	NOUN
ejpam-6081	97	59	)	)	PUNCT
ejpam-6081	97	60	g	g	PROPN
ejpam-6081	97	61	(	(	PUNCT
ejpam-6081	97	62	α	α	NOUN
ejpam-6081	97	63	,	,	PUNCT
ejpam-6081	97	64	0	0	NUM
ejpam-6081	97	65	)	)	PUNCT
ejpam-6081	97	66	≡	≡	PROPN
ejpam-6081	97	67	r	r	NOUN
ejpam-6081	97	68	(	(	PUNCT
ejpam-6081	97	69	α	α	NOUN
ejpam-6081	97	70	)	)	PUNCT
ejpam-6081	97	71	=	=	NOUN
ejpam-6081	97	72	{	{	PUNCT
ejpam-6081	97	73	f	f	PROPN
ejpam-6081	97	74	∈	∈	PROPN
ejpam-6081	97	75	s	s	PART
ejpam-6081	97	76	:	:	PUNCT
ejpam-6081	97	77	re	re	X
ejpam-6081	97	78	(	(	PUNCT
ejpam-6081	97	79	eiαf	eiαf	NOUN
ejpam-6081	97	80	′	′	NUM
ejpam-6081	98	1	(	(	PUNCT
ejpam-6081	98	2	z	z	NOUN
ejpam-6081	98	3	)	)	PUNCT
ejpam-6081	98	4	)	)	PUNCT
ejpam-6081	99	1	>	>	X
ejpam-6081	99	2	0	0	NUM
ejpam-6081	99	3	,	,	PUNCT
ejpam-6081	99	4	z	z	NOUN
ejpam-6081	99	5	∈	∈	PROPN
ejpam-6081	99	6	e	e	X
ejpam-6081	99	7	}	}	PUNCT
ejpam-6081	99	8	(	(	PUNCT
ejpam-6081	99	9	ii	ii	NOUN
ejpam-6081	99	10	)	)	PUNCT
ejpam-6081	99	11	g	g	NOUN
ejpam-6081	99	12	(	(	PUNCT
ejpam-6081	99	13	0	0	NUM
ejpam-6081	99	14	,	,	PUNCT
ejpam-6081	99	15	δ	δ	PROPN
ejpam-6081	99	16	)	)	PUNCT
ejpam-6081	99	17	≡	≡	PROPN
ejpam-6081	99	18	r	r	PROPN
ejpam-6081	99	19	(	(	PUNCT
ejpam-6081	99	20	δ	δ	NOUN
ejpam-6081	99	21	)	)	PUNCT
ejpam-6081	99	22	=	=	PRON
ejpam-6081	100	1	{	{	PUNCT
ejpam-6081	100	2	f	f	PROPN
ejpam-6081	100	3	∈	∈	PROPN
ejpam-6081	100	4	s	s	PART
ejpam-6081	100	5	:	:	PUNCT
ejpam-6081	100	6	re	re	X
ejpam-6081	100	7	(	(	PUNCT
ejpam-6081	100	8	f	f	NOUN
ejpam-6081	100	9	′	′	NUM
ejpam-6081	100	10	(	(	PUNCT
ejpam-6081	100	11	z	z	NOUN
ejpam-6081	100	12	)	)	PUNCT
ejpam-6081	100	13	)	)	PUNCT
ejpam-6081	100	14	>	>	PUNCT
ejpam-6081	101	1	δ	δ	PROPN
ejpam-6081	101	2	,	,	PUNCT
ejpam-6081	101	3	z	z	NOUN
ejpam-6081	101	4	∈	∈	PROPN
ejpam-6081	101	5	e	e	X
ejpam-6081	101	6	}	}	PUNCT
ejpam-6081	101	7	.	.	PUNCT
ejpam-6081	102	1	the	the	DET
ejpam-6081	102	2	class	class	NOUN
ejpam-6081	102	3	r	r	NOUN
ejpam-6081	102	4	(	(	PUNCT
ejpam-6081	102	5	δ	δ	NOUN
ejpam-6081	102	6	)	)	PUNCT
ejpam-6081	102	7	is	be	AUX
ejpam-6081	102	8	called	call	VERB
ejpam-6081	102	9	the	the	DET
ejpam-6081	102	10	class	class	NOUN
ejpam-6081	102	11	of	of	ADP
ejpam-6081	102	12	bounded	bounded	ADJ
ejpam-6081	102	13	turning	turning	NOUN
ejpam-6081	102	14	functions	function	NOUN
ejpam-6081	102	15	of	of	ADP
ejpam-6081	102	16	order	order	NOUN
ejpam-6081	102	17	δ	δ	PROPN
ejpam-6081	102	18	.	.	PUNCT
ejpam-6081	103	1	(	(	PUNCT
ejpam-6081	103	2	iii	iii	X
ejpam-6081	103	3	)	)	PUNCT
ejpam-6081	103	4	g	g	NOUN
ejpam-6081	103	5	(	(	PUNCT
ejpam-6081	103	6	0	0	NUM
ejpam-6081	103	7	,	,	PUNCT
ejpam-6081	103	8	0	0	NUM
ejpam-6081	103	9	)	)	PUNCT
ejpam-6081	103	10	≡	≡	PROPN
ejpam-6081	103	11	r	r	NOUN
ejpam-6081	103	12	=	=	PUNCT
ejpam-6081	103	13	{	{	PUNCT
ejpam-6081	103	14	f	f	PROPN
ejpam-6081	103	15	∈	∈	PROPN
ejpam-6081	103	16	s	s	PART
ejpam-6081	103	17	:	:	PUNCT
ejpam-6081	103	18	re	re	X
ejpam-6081	103	19	(	(	PUNCT
ejpam-6081	103	20	f	f	NOUN
ejpam-6081	103	21	′	′	NUM
ejpam-6081	103	22	(	(	PUNCT
ejpam-6081	103	23	z	z	NOUN
ejpam-6081	103	24	)	)	PUNCT
ejpam-6081	103	25	)	)	PUNCT
ejpam-6081	103	26	>	>	X
ejpam-6081	103	27	0	0	NUM
ejpam-6081	103	28	,	,	PUNCT
ejpam-6081	103	29	z	z	NOUN
ejpam-6081	103	30	∈	∈	PROPN
ejpam-6081	103	31	e	e	X
ejpam-6081	103	32	}	}	PUNCT
ejpam-6081	103	33	.	.	PUNCT
ejpam-6081	104	1	the	the	DET
ejpam-6081	104	2	class	class	NOUN
ejpam-6081	104	3	r	r	NOUN
ejpam-6081	104	4	is	be	AUX
ejpam-6081	104	5	called	call	VERB
ejpam-6081	104	6	the	the	DET
ejpam-6081	104	7	class	class	NOUN
ejpam-6081	104	8	of	of	ADP
ejpam-6081	104	9	bounded	bounded	ADJ
ejpam-6081	104	10	turning	turning	NOUN
ejpam-6081	104	11	functions	function	NOUN
ejpam-6081	104	12	.	.	PUNCT
ejpam-6081	105	1	pioneering	pioneer	VERB
ejpam-6081	105	2	researchers	researcher	NOUN
ejpam-6081	105	3	like	like	ADP
ejpam-6081	105	4	goel	goel	PROPN
ejpam-6081	105	5	and	and	CCONJ
ejpam-6081	105	6	mehrok	mehrok	ADJ
ejpam-6081	106	1	[	[	X
ejpam-6081	106	2	24	24	NUM
ejpam-6081	106	3	]	]	PUNCT
ejpam-6081	106	4	,	,	PUNCT
ejpam-6081	106	5	macgregor	macgregor	PROPN
ejpam-6081	107	1	[	[	X
ejpam-6081	107	2	25	25	NUM
ejpam-6081	107	3	]	]	PUNCT
ejpam-6081	107	4	,	,	PUNCT
ejpam-6081	107	5	noshiro	noshiro	VERB
ejpam-6081	108	1	[	[	X
ejpam-6081	108	2	26	26	NUM
ejpam-6081	108	3	]	]	PUNCT
ejpam-6081	108	4	,	,	PUNCT
ejpam-6081	108	5	silverman	silverman	NOUN
ejpam-6081	108	6	and	and	CCONJ
ejpam-6081	108	7	silvia	silvia	PROPN
ejpam-6081	109	1	[	[	X
ejpam-6081	109	2	27	27	NUM
ejpam-6081	109	3	]	]	PUNCT
ejpam-6081	109	4	,	,	PUNCT
ejpam-6081	109	5	and	and	CCONJ
ejpam-6081	109	6	warschawski	warschawski	VERB
ejpam-6081	110	1	[	[	X
ejpam-6081	110	2	28	28	NUM
ejpam-6081	110	3	]	]	PUNCT
ejpam-6081	110	4	explored	explore	VERB
ejpam-6081	110	5	the	the	DET
ejpam-6081	110	6	classes	class	NOUN
ejpam-6081	110	7	r	r	NOUN
ejpam-6081	110	8	,	,	PUNCT
ejpam-6081	110	9	r	r	NOUN
ejpam-6081	110	10	(	(	PUNCT
ejpam-6081	110	11	δ	δ	PROPN
ejpam-6081	110	12	)	)	PUNCT
ejpam-6081	110	13	,	,	PUNCT
ejpam-6081	110	14	and	and	CCONJ
ejpam-6081	110	15	r	r	NOUN
ejpam-6081	110	16	(	(	PUNCT
ejpam-6081	110	17	α	α	NOUN
ejpam-6081	110	18	)	)	PUNCT
ejpam-6081	110	19	,	,	PUNCT
ejpam-6081	110	20	and	and	CCONJ
ejpam-6081	110	21	nonetheless	nonetheless	ADV
ejpam-6081	110	22	,	,	PUNCT
ejpam-6081	110	23	it	it	PRON
ejpam-6081	110	24	is	be	AUX
ejpam-6081	110	25	intriguing	intriguing	ADJ
ejpam-6081	110	26	to	to	PART
ejpam-6081	110	27	examine	examine	VERB
ejpam-6081	110	28	these	these	DET
ejpam-6081	110	29	classes	class	NOUN
ejpam-6081	110	30	in	in	ADP
ejpam-6081	110	31	light	light	NOUN
ejpam-6081	110	32	of	of	ADP
ejpam-6081	110	33	the	the	DET
ejpam-6081	110	34	generating	generating	NOUN
ejpam-6081	110	35	functions	function	NOUN
ejpam-6081	110	36	of	of	ADP
ejpam-6081	110	37	gregory	gregory	PROPN
ejpam-6081	110	38	coefficients	coefficient	NOUN
ejpam-6081	110	39	,	,	PUNCT
ejpam-6081	110	40	leading	lead	VERB
ejpam-6081	110	41	to	to	ADP
ejpam-6081	110	42	the	the	DET
ejpam-6081	110	43	geometric	geometric	ADJ
ejpam-6081	110	44	properties	property	NOUN
ejpam-6081	110	45	of	of	ADP
ejpam-6081	110	46	this	this	DET
ejpam-6081	110	47	class	class	NOUN
ejpam-6081	110	48	and	and	CCONJ
ejpam-6081	110	49	contributing	contribute	VERB
ejpam-6081	110	50	to	to	ADP
ejpam-6081	110	51	ongoing	ongoing	ADJ
ejpam-6081	110	52	developments	development	NOUN
ejpam-6081	110	53	in	in	ADP
ejpam-6081	110	54	geometry	geometry	NOUN
ejpam-6081	110	55	function	function	NOUN
ejpam-6081	110	56	theory	theory	NOUN
ejpam-6081	110	57	.	.	PUNCT
ejpam-6081	111	1	therefore	therefore	ADV
ejpam-6081	111	2	,	,	PUNCT
ejpam-6081	111	3	this	this	DET
ejpam-6081	111	4	paper	paper	NOUN
ejpam-6081	111	5	aims	aim	VERB
ejpam-6081	111	6	to	to	PART
ejpam-6081	111	7	estimate	estimate	VERB
ejpam-6081	111	8	the	the	DET
ejpam-6081	111	9	upper	upper	ADJ
ejpam-6081	111	10	bounds	bound	NOUN
ejpam-6081	111	11	of	of	ADP
ejpam-6081	111	12	the	the	DET
ejpam-6081	111	13	taylor	taylor	PROPN
ejpam-6081	111	14	coefficients	coefficient	NOUN
ejpam-6081	111	15	and	and	CCONJ
ejpam-6081	111	16	logarithmic	logarithmic	ADJ
ejpam-6081	111	17	coefficients	coefficient	NOUN
ejpam-6081	111	18	of	of	ADP
ejpam-6081	111	19	functions	function	NOUN
ejpam-6081	111	20	and	and	CCONJ
ejpam-6081	111	21	inverse	inverse	NOUN
ejpam-6081	111	22	functions	function	NOUN
ejpam-6081	111	23	belonging	belong	VERB
ejpam-6081	111	24	to	to	ADP
ejpam-6081	111	25	the	the	DET
ejpam-6081	111	26	classgg	classgg	NOUN
ejpam-6081	111	27	(	(	PUNCT
ejpam-6081	111	28	α	α	NOUN
ejpam-6081	111	29	,	,	PUNCT
ejpam-6081	111	30	δ	δ	PROPN
ejpam-6081	111	31	)	)	PUNCT
ejpam-6081	111	32	of	of	ADP
ejpam-6081	111	33	analytic	analytic	ADJ
ejpam-6081	111	34	functions	function	NOUN
ejpam-6081	111	35	,	,	PUNCT
ejpam-6081	111	36	which	which	PRON
ejpam-6081	111	37	is	be	AUX
ejpam-6081	111	38	associated	associate	VERB
ejpam-6081	111	39	with	with	ADP
ejpam-6081	111	40	generalized	generalized	ADJ
ejpam-6081	111	41	bounded	bounded	ADJ
ejpam-6081	111	42	turning	turning	NOUN
ejpam-6081	111	43	and	and	CCONJ
ejpam-6081	111	44	the	the	DET
ejpam-6081	111	45	generating	generating	NOUN
ejpam-6081	111	46	functions	function	NOUN
ejpam-6081	111	47	of	of	ADP
ejpam-6081	111	48	gregory	gregory	PROPN
ejpam-6081	111	49	coefficients	coefficient	NOUN
ejpam-6081	111	50	.	.	PUNCT
ejpam-6081	112	1	for	for	ADP
ejpam-6081	112	2	example	example	NOUN
ejpam-6081	112	3	,	,	PUNCT
ejpam-6081	112	4	|an|	|an|	PROPN
ejpam-6081	112	5	(	(	PUNCT
ejpam-6081	112	6	n	n	NOUN
ejpam-6081	112	7	=	=	SYM
ejpam-6081	112	8	2	2	NUM
ejpam-6081	112	9	,	,	PUNCT
ejpam-6081	112	10	3	3	NUM
ejpam-6081	112	11	,	,	PUNCT
ejpam-6081	112	12	4	4	NUM
ejpam-6081	112	13	,	,	PUNCT
ejpam-6081	112	14	5	5	NUM
ejpam-6081	112	15	)	)	PUNCT
ejpam-6081	112	16	,	,	PUNCT
ejpam-6081	112	17	|an|	|an|	NOUN
ejpam-6081	112	18	(	(	PUNCT
ejpam-6081	112	19	n	n	NOUN
ejpam-6081	112	20	=	=	SYM
ejpam-6081	112	21	2	2	NUM
ejpam-6081	112	22	,	,	PUNCT
ejpam-6081	112	23	3	3	NUM
ejpam-6081	112	24	,	,	PUNCT
ejpam-6081	112	25	4	4	NUM
ejpam-6081	112	26	,	,	PUNCT
ejpam-6081	112	27	5	5	NUM
ejpam-6081	112	28	)	)	PUNCT
ejpam-6081	112	29	,	,	PUNCT
ejpam-6081	112	30	|γn|	|γn|	PROPN
ejpam-6081	112	31	(	(	PUNCT
ejpam-6081	112	32	n	n	NOUN
ejpam-6081	112	33	=	=	SYM
ejpam-6081	112	34	1	1	NUM
ejpam-6081	112	35	,	,	PUNCT
ejpam-6081	112	36	2	2	NUM
ejpam-6081	112	37	,	,	PUNCT
ejpam-6081	112	38	3	3	NUM
ejpam-6081	112	39	)	)	PUNCT
ejpam-6081	112	40	,	,	PUNCT
ejpam-6081	112	41	and	and	CCONJ
ejpam-6081	112	42	|γn|	|γn|	PROPN
ejpam-6081	112	43	(	(	PUNCT
ejpam-6081	112	44	n	n	NOUN
ejpam-6081	112	45	=	=	SYM
ejpam-6081	112	46	1	1	NUM
ejpam-6081	112	47	,	,	PUNCT
ejpam-6081	112	48	2	2	NUM
ejpam-6081	112	49	,	,	PUNCT
ejpam-6081	112	50	3	3	NUM
ejpam-6081	112	51	)	)	PUNCT
ejpam-6081	112	52	.	.	PUNCT
ejpam-6081	113	1	as	as	ADP
ejpam-6081	113	2	a	a	DET
ejpam-6081	113	3	result	result	NOUN
ejpam-6081	113	4	,	,	PUNCT
ejpam-6081	113	5	we	we	PRON
ejpam-6081	113	6	focus	focus	VERB
ejpam-6081	113	7	on	on	ADP
ejpam-6081	113	8	estimating	estimate	VERB
ejpam-6081	113	9	the	the	DET
ejpam-6081	113	10	upper	upper	ADJ
ejpam-6081	113	11	bounds	bound	NOUN
ejpam-6081	113	12	of	of	ADP
ejpam-6081	113	13	the	the	DET
ejpam-6081	113	14	second	second	ADJ
ejpam-6081	113	15	-	-	PUNCT
ejpam-6081	113	16	order	order	NOUN
ejpam-6081	113	17	vandermonde	vandermonde	NOUN
ejpam-6081	113	18	determinant	determinant	ADJ
ejpam-6081	113	19	,	,	PUNCT
ejpam-6081	113	20	whose	whose	DET
ejpam-6081	113	21	entries	entry	NOUN
ejpam-6081	113	22	are	be	AUX
ejpam-6081	113	23	taylor	taylor	PROPN
ejpam-6081	113	24	coefficients	coefficient	NOUN
ejpam-6081	113	25	and	and	CCONJ
ejpam-6081	113	26	logarithmic	logarithmic	ADJ
ejpam-6081	113	27	coefficients	coefficient	NOUN
ejpam-6081	113	28	of	of	ADP
ejpam-6081	113	29	functions	function	NOUN
ejpam-6081	113	30	and	and	CCONJ
ejpam-6081	113	31	inverse	inverse	NOUN
ejpam-6081	113	32	functions	function	NOUN
ejpam-6081	113	33	in	in	ADP
ejpam-6081	113	34	gg	gg	PROPN
ejpam-6081	113	35	(	(	PUNCT
ejpam-6081	113	36	α	α	PROPN
ejpam-6081	113	37	,	,	PUNCT
ejpam-6081	113	38	δ	δ	PROPN
ejpam-6081	113	39	)	)	PUNCT
ejpam-6081	113	40	.	.	PUNCT
ejpam-6081	114	1	n.	n.	PROPN
ejpam-6081	114	2	h.	h.	PROPN
ejpam-6081	114	3	a.	a.	PROPN
ejpam-6081	114	4	a.	a.	PROPN
ejpam-6081	114	5	wahid	wahid	PROPN
ejpam-6081	114	6	,	,	PUNCT
ejpam-6081	114	7	s.	s.	PROPN
ejpam-6081	114	8	c.	c.	PROPN
ejpam-6081	114	9	soh	soh	PROPN
ejpam-6081	114	10	/	/	SYM
ejpam-6081	114	11	eur	eur	PROPN
ejpam-6081	114	12	.	.	PUNCT
ejpam-6081	115	1	j.	j.	PROPN
ejpam-6081	115	2	pure	pure	PROPN
ejpam-6081	115	3	appl	appl	PROPN
ejpam-6081	115	4	.	.	PROPN
ejpam-6081	115	5	math	math	PROPN
ejpam-6081	115	6	,	,	PUNCT
ejpam-6081	115	7	18	18	NUM
ejpam-6081	115	8	(	(	PUNCT
ejpam-6081	115	9	2	2	NUM
ejpam-6081	115	10	)	)	PUNCT
ejpam-6081	115	11	(	(	PUNCT
ejpam-6081	115	12	2025	2025	NUM
ejpam-6081	115	13	)	)	PUNCT
ejpam-6081	115	14	,	,	PUNCT
ejpam-6081	115	15	6081	6081	NUM
ejpam-6081	115	16	6	6	NUM
ejpam-6081	115	17	of	of	ADP
ejpam-6081	115	18	16	16	NUM
ejpam-6081	115	19	2	2	NUM
ejpam-6081	115	20	.	.	PUNCT
ejpam-6081	115	21	preliminary	preliminary	ADJ
ejpam-6081	115	22	results	result	NOUN
ejpam-6081	115	23	this	this	DET
ejpam-6081	115	24	section	section	NOUN
ejpam-6081	115	25	gives	give	VERB
ejpam-6081	115	26	a	a	DET
ejpam-6081	115	27	few	few	ADJ
ejpam-6081	115	28	sharp	sharp	ADJ
ejpam-6081	115	29	bounds	bound	NOUN
ejpam-6081	115	30	on	on	ADP
ejpam-6081	115	31	coefficient	coefficient	NOUN
ejpam-6081	115	32	functionals	functional	NOUN
ejpam-6081	115	33	for	for	ADP
ejpam-6081	115	34	functions	function	NOUN
ejpam-6081	115	35	with	with	ADP
ejpam-6081	115	36	a	a	DET
ejpam-6081	115	37	positive	positive	ADJ
ejpam-6081	115	38	real	real	ADJ
ejpam-6081	115	39	part	part	NOUN
ejpam-6081	115	40	,	,	PUNCT
ejpam-6081	115	41	in	in	ADP
ejpam-6081	115	42	the	the	DET
ejpam-6081	115	43	form	form	NOUN
ejpam-6081	115	44	of	of	ADP
ejpam-6081	115	45	the	the	DET
ejpam-6081	115	46	following	following	ADJ
ejpam-6081	115	47	lemmas	lemmas	NOUN
ejpam-6081	115	48	,	,	PUNCT
ejpam-6081	115	49	to	to	PART
ejpam-6081	115	50	verify	verify	VERB
ejpam-6081	115	51	our	our	PRON
ejpam-6081	115	52	main	main	ADJ
ejpam-6081	115	53	findings	finding	NOUN
ejpam-6081	115	54	:	:	PUNCT
ejpam-6081	115	55	lemma	lemma	PROPN
ejpam-6081	115	56	1	1	NUM
ejpam-6081	115	57	.	.	PUNCT
ejpam-6081	116	1	(	(	PUNCT
ejpam-6081	116	2	[	[	X
ejpam-6081	116	3	29	29	NUM
ejpam-6081	116	4	]	]	PUNCT
ejpam-6081	116	5	)	)	PUNCT
ejpam-6081	116	6	for	for	ADP
ejpam-6081	116	7	a	a	DET
ejpam-6081	116	8	function	function	NOUN
ejpam-6081	116	9	p	p	NOUN
ejpam-6081	116	10	(	(	PUNCT
ejpam-6081	116	11	z	z	NOUN
ejpam-6081	116	12	)	)	PUNCT
ejpam-6081	116	13	∈	∈	PROPN
ejpam-6081	116	14	p	p	NOUN
ejpam-6081	116	15	of	of	ADP
ejpam-6081	116	16	the	the	DET
ejpam-6081	116	17	form	form	NOUN
ejpam-6081	116	18	(	(	PUNCT
ejpam-6081	116	19	6	6	NUM
ejpam-6081	116	20	)	)	PUNCT
ejpam-6081	116	21	,	,	PUNCT
ejpam-6081	116	22	the	the	DET
ejpam-6081	116	23	sharp	sharp	ADJ
ejpam-6081	116	24	inequality	inequality	NOUN
ejpam-6081	116	25	|pn|	|pn|	ADJ
ejpam-6081	116	26	⩽	⩽	ADJ
ejpam-6081	116	27	2	2	NUM
ejpam-6081	116	28	holds	hold	VERB
ejpam-6081	116	29	for	for	ADP
ejpam-6081	116	30	each	each	DET
ejpam-6081	116	31	n	n	NOUN
ejpam-6081	116	32	⩾	⩾	NOUN
ejpam-6081	116	33	1	1	NUM
ejpam-6081	116	34	.	.	PUNCT
ejpam-6081	117	1	the	the	DET
ejpam-6081	117	2	equality	equality	NOUN
ejpam-6081	117	3	holds	hold	VERB
ejpam-6081	117	4	for	for	ADP
ejpam-6081	117	5	the	the	DET
ejpam-6081	117	6	function	function	NOUN
ejpam-6081	117	7	p	p	NOUN
ejpam-6081	117	8	(	(	PUNCT
ejpam-6081	117	9	z	z	NOUN
ejpam-6081	117	10	)	)	PUNCT
ejpam-6081	117	11	=	=	SYM
ejpam-6081	118	1	1+z	1+z	NUM
ejpam-6081	118	2	1−z	1−z	NUM
ejpam-6081	118	3	.	.	PUNCT
ejpam-6081	119	1	lemma	lemma	PROPN
ejpam-6081	119	2	2	2	NUM
ejpam-6081	119	3	.	.	PUNCT
ejpam-6081	120	1	(	(	PUNCT
ejpam-6081	120	2	[	[	X
ejpam-6081	120	3	30	30	NUM
ejpam-6081	120	4	]	]	PUNCT
ejpam-6081	120	5	)	)	PUNCT
ejpam-6081	120	6	let	let	VERB
ejpam-6081	120	7	p	p	NOUN
ejpam-6081	120	8	(	(	PUNCT
ejpam-6081	120	9	z	z	NOUN
ejpam-6081	120	10	)	)	PUNCT
ejpam-6081	120	11	∈	∈	PROPN
ejpam-6081	120	12	p	p	NOUN
ejpam-6081	120	13	be	be	AUX
ejpam-6081	120	14	a	a	DET
ejpam-6081	120	15	function	function	NOUN
ejpam-6081	120	16	of	of	ADP
ejpam-6081	120	17	the	the	DET
ejpam-6081	120	18	form	form	NOUN
ejpam-6081	120	19	(	(	PUNCT
ejpam-6081	120	20	6	6	NUM
ejpam-6081	120	21	)	)	PUNCT
ejpam-6081	120	22	and	and	CCONJ
ejpam-6081	120	23	µ∗	µ∗	VERB
ejpam-6081	120	24	∈	∈	PROPN
ejpam-6081	120	25	c.	c.	NOUN
ejpam-6081	121	1	then	then	ADV
ejpam-6081	121	2	|pn	|pn	X
ejpam-6081	121	3	−	−	PROPN
ejpam-6081	121	4	µ∗pkpn−k|	µ∗pkpn−k|	NOUN
ejpam-6081	121	5	⩽	⩽	PROPN
ejpam-6081	121	6	2max	2max	NUM
ejpam-6081	121	7	{	{	PUNCT
ejpam-6081	121	8	1	1	NUM
ejpam-6081	121	9	,	,	PUNCT
ejpam-6081	121	10	|2µ∗	|2µ∗	ADV
ejpam-6081	121	11	−	−	NOUN
ejpam-6081	121	12	1|	1|	NUM
ejpam-6081	121	13	}	}	PUNCT
ejpam-6081	121	14	,	,	PUNCT
ejpam-6081	121	15	1	1	NUM
ejpam-6081	121	16	⩽	⩽	NOUN
ejpam-6081	121	17	k	k	PROPN
ejpam-6081	121	18	⩽	⩽	ADJ
ejpam-6081	121	19	n−	n−	PROPN
ejpam-6081	121	20	1	1	NUM
ejpam-6081	121	21	.	.	PUNCT
ejpam-6081	122	1	if	if	SCONJ
ejpam-6081	122	2	|2µ∗	|2µ∗	ADV
ejpam-6081	122	3	−	−	PROPN
ejpam-6081	122	4	1|	1|	NUM
ejpam-6081	122	5	⩾	⩾	NOUN
ejpam-6081	122	6	1	1	NUM
ejpam-6081	122	7	,	,	PUNCT
ejpam-6081	122	8	then	then	ADV
ejpam-6081	122	9	the	the	DET
ejpam-6081	122	10	inequality	inequality	NOUN
ejpam-6081	122	11	is	be	AUX
ejpam-6081	122	12	sharp	sharp	ADJ
ejpam-6081	122	13	for	for	ADP
ejpam-6081	122	14	the	the	DET
ejpam-6081	122	15	function	function	NOUN
ejpam-6081	122	16	p	p	NOUN
ejpam-6081	122	17	(	(	PUNCT
ejpam-6081	122	18	z	z	NOUN
ejpam-6081	122	19	)	)	PUNCT
ejpam-6081	122	20	=	=	SYM
ejpam-6081	123	1	1+z	1+z	NUM
ejpam-6081	123	2	1−z	1−z	NUM
ejpam-6081	123	3	or	or	CCONJ
ejpam-6081	123	4	its	its	PRON
ejpam-6081	123	5	rotations	rotation	NOUN
ejpam-6081	123	6	.	.	PUNCT
ejpam-6081	124	1	if	if	SCONJ
ejpam-6081	124	2	|2µ∗	|2µ∗	ADV
ejpam-6081	124	3	−	−	PROPN
ejpam-6081	124	4	1|	1|	NUM
ejpam-6081	124	5	<	<	X
ejpam-6081	124	6	1	1	NUM
ejpam-6081	124	7	,	,	PUNCT
ejpam-6081	124	8	then	then	ADV
ejpam-6081	124	9	the	the	DET
ejpam-6081	124	10	inequality	inequality	NOUN
ejpam-6081	124	11	is	be	AUX
ejpam-6081	124	12	sharp	sharp	ADJ
ejpam-6081	124	13	for	for	ADP
ejpam-6081	124	14	the	the	DET
ejpam-6081	124	15	function	function	NOUN
ejpam-6081	124	16	p	p	NOUN
ejpam-6081	124	17	(	(	PUNCT
ejpam-6081	124	18	z	z	NOUN
ejpam-6081	124	19	)	)	PUNCT
ejpam-6081	124	20	=	=	PUNCT
ejpam-6081	125	1	1+zn	1+zn	NUM
ejpam-6081	125	2	1−zn	1−zn	NUM
ejpam-6081	125	3	or	or	CCONJ
ejpam-6081	125	4	its	its	PRON
ejpam-6081	125	5	rotations	rotation	NOUN
ejpam-6081	125	6	.	.	PUNCT
ejpam-6081	126	1	lemma	lemma	PROPN
ejpam-6081	126	2	3	3	NUM
ejpam-6081	126	3	.	.	PUNCT
ejpam-6081	127	1	(	(	PUNCT
ejpam-6081	127	2	[	[	X
ejpam-6081	127	3	31	31	NUM
ejpam-6081	127	4	]	]	PUNCT
ejpam-6081	127	5	)	)	PUNCT
ejpam-6081	127	6	let	let	VERB
ejpam-6081	127	7	p	p	NOUN
ejpam-6081	127	8	(	(	PUNCT
ejpam-6081	127	9	z	z	NOUN
ejpam-6081	127	10	)	)	PUNCT
ejpam-6081	127	11	∈	∈	PROPN
ejpam-6081	127	12	p	p	NOUN
ejpam-6081	127	13	be	be	AUX
ejpam-6081	127	14	a	a	DET
ejpam-6081	127	15	function	function	NOUN
ejpam-6081	127	16	of	of	ADP
ejpam-6081	127	17	the	the	DET
ejpam-6081	127	18	form	form	NOUN
ejpam-6081	127	19	(	(	PUNCT
ejpam-6081	127	20	6	6	NUM
ejpam-6081	127	21	)	)	PUNCT
ejpam-6081	127	22	and	and	CCONJ
ejpam-6081	127	23	α∗	α∗	NOUN
ejpam-6081	127	24	,	,	PUNCT
ejpam-6081	127	25	β∗	β∗	PROPN
ejpam-6081	127	26	,	,	PUNCT
ejpam-6081	127	27	γ∗	γ∗	PROPN
ejpam-6081	127	28	∈	∈	PROPN
ejpam-6081	127	29	ℜ.	ℜ.	PROPN
ejpam-6081	127	30	then∣∣α∗p1	then∣∣α∗p1	PROPN
ejpam-6081	127	31	3	3	NUM
ejpam-6081	127	32	−	−	NOUN
ejpam-6081	127	33	β∗p1p2	β∗p1p2	PROPN
ejpam-6081	128	1	+	+	CCONJ
ejpam-6081	128	2	γ∗p3	γ∗p3	NUM
ejpam-6081	128	3	∣∣	∣∣	NUM
ejpam-6081	128	4	⩽	⩽	ADJ
ejpam-6081	128	5	2	2	NUM
ejpam-6081	128	6	|α∗|+	|α∗|+	X
ejpam-6081	128	7	2	2	NUM
ejpam-6081	128	8	|β∗	|β∗	PROPN
ejpam-6081	128	9	−	−	PROPN
ejpam-6081	128	10	2α∗|+	2α∗|+	NOUN
ejpam-6081	128	11	2	2	NUM
ejpam-6081	128	12	|α∗	|α∗	PROPN
ejpam-6081	128	13	−	−	PROPN
ejpam-6081	128	14	β∗	β∗	NOUN
ejpam-6081	128	15	+	+	CCONJ
ejpam-6081	128	16	γ∗|	γ∗|	PROPN
ejpam-6081	128	17	.	.	PUNCT
ejpam-6081	129	1	lemma	lemma	PROPN
ejpam-6081	129	2	4	4	NUM
ejpam-6081	129	3	.	.	PUNCT
ejpam-6081	130	1	(	(	PUNCT
ejpam-6081	130	2	[	[	X
ejpam-6081	130	3	32	32	NUM
ejpam-6081	130	4	]	]	PUNCT
ejpam-6081	130	5	)	)	PUNCT
ejpam-6081	130	6	let	let	VERB
ejpam-6081	130	7	p	p	NOUN
ejpam-6081	130	8	(	(	PUNCT
ejpam-6081	130	9	z	z	NOUN
ejpam-6081	130	10	)	)	PUNCT
ejpam-6081	130	11	∈	∈	PROPN
ejpam-6081	130	12	p	p	NOUN
ejpam-6081	130	13	be	be	AUX
ejpam-6081	130	14	a	a	DET
ejpam-6081	130	15	function	function	NOUN
ejpam-6081	130	16	of	of	ADP
ejpam-6081	130	17	the	the	DET
ejpam-6081	130	18	form	form	NOUN
ejpam-6081	130	19	(	(	PUNCT
ejpam-6081	130	20	6	6	NUM
ejpam-6081	130	21	)	)	PUNCT
ejpam-6081	130	22	and	and	CCONJ
ejpam-6081	130	23	0	0	NUM
ejpam-6081	130	24	<	<	X
ejpam-6081	130	25	β	β	X
ejpam-6081	130	26	<	<	X
ejpam-6081	130	27	1	1	NUM
ejpam-6081	130	28	,	,	PUNCT
ejpam-6081	130	29	0	0	PUNCT
ejpam-6081	130	30	<	<	X
ejpam-6081	130	31	µ	µ	X
ejpam-6081	130	32	<	<	X
ejpam-6081	130	33	1	1	NUM
ejpam-6081	130	34	,	,	PUNCT
ejpam-6081	130	35	and	and	CCONJ
ejpam-6081	130	36	8β	8β	NUM
ejpam-6081	130	37	(	(	PUNCT
ejpam-6081	130	38	1−	1−	NUM
ejpam-6081	130	39	β	β	NOUN
ejpam-6081	130	40	)	)	PUNCT
ejpam-6081	130	41	[	[	PUNCT
ejpam-6081	130	42	(	(	PUNCT
ejpam-6081	130	43	µη	µη	ADP
ejpam-6081	130	44	−	−	NUM
ejpam-6081	130	45	2α)2	2α)2	NUM
ejpam-6081	130	46	+	+	CCONJ
ejpam-6081	130	47	(	(	PUNCT
ejpam-6081	130	48	µ	µ	X
ejpam-6081	130	49	(	(	PUNCT
ejpam-6081	130	50	β	β	X
ejpam-6081	130	51	+	+	PUNCT
ejpam-6081	130	52	µ)−	µ)−	VERB
ejpam-6081	130	53	η)2	η)2	NOUN
ejpam-6081	130	54	]	]	X
ejpam-6081	131	1	+	+	NUM
ejpam-6081	131	2	µ	µ	X
ejpam-6081	131	3	(	(	PUNCT
ejpam-6081	131	4	1−	1−	NUM
ejpam-6081	131	5	µ	µ	NUM
ejpam-6081	131	6	)	)	PUNCT
ejpam-6081	131	7	(	(	PUNCT
ejpam-6081	131	8	η	η	PROPN
ejpam-6081	131	9	−	−	PROPN
ejpam-6081	131	10	2βµ)2	2βµ)2	NUM
ejpam-6081	131	11	≤	≤	NOUN
ejpam-6081	131	12	4µ2β(1−	4µ2β(1−	ADJ
ejpam-6081	131	13	µ)2	µ)2	NOUN
ejpam-6081	131	14	(	(	PUNCT
ejpam-6081	131	15	1−	1−	NUM
ejpam-6081	131	16	β	β	NOUN
ejpam-6081	131	17	)	)	PUNCT
ejpam-6081	131	18	.	.	PUNCT
ejpam-6081	132	1	then	then	ADV
ejpam-6081	132	2	∣∣∣∣αp14	∣∣∣∣αp14	NOUN
ejpam-6081	132	3	+	+	CCONJ
ejpam-6081	132	4	βp2	βp2	NOUN
ejpam-6081	132	5	2	2	NUM
ejpam-6081	132	6	+	+	NOUN
ejpam-6081	132	7	2µp1p3	2µp1p3	NUM
ejpam-6081	132	8	−	−	NOUN
ejpam-6081	132	9	3	3	NUM
ejpam-6081	132	10	2	2	NUM
ejpam-6081	132	11	ηp1	ηp1	NOUN
ejpam-6081	132	12	2p2	2p2	NUM
ejpam-6081	132	13	−	−	DET
ejpam-6081	132	14	p4	p4	ADJ
ejpam-6081	132	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6081	132	16	≤	≤	NOUN
ejpam-6081	132	17	2	2	NUM
ejpam-6081	132	18	.	.	NOUN
ejpam-6081	132	19	3	3	NUM
ejpam-6081	132	20	.	.	X
ejpam-6081	132	21	main	main	ADJ
ejpam-6081	132	22	results	result	NOUN
ejpam-6081	132	23	this	this	DET
ejpam-6081	132	24	section	section	NOUN
ejpam-6081	132	25	presents	present	VERB
ejpam-6081	132	26	the	the	DET
ejpam-6081	132	27	proof	proof	NOUN
ejpam-6081	132	28	of	of	ADP
ejpam-6081	132	29	our	our	PRON
ejpam-6081	132	30	main	main	ADJ
ejpam-6081	132	31	findings	finding	NOUN
ejpam-6081	132	32	,	,	PUNCT
ejpam-6081	132	33	focusing	focus	VERB
ejpam-6081	132	34	primarily	primarily	ADV
ejpam-6081	132	35	on	on	ADP
ejpam-6081	132	36	the	the	DET
ejpam-6081	132	37	upper	upper	ADJ
ejpam-6081	132	38	bounds	bound	NOUN
ejpam-6081	132	39	of	of	ADP
ejpam-6081	132	40	taylor	taylor	PROPN
ejpam-6081	132	41	coefficients	coefficient	NOUN
ejpam-6081	132	42	,	,	PUNCT
ejpam-6081	132	43	logarithmic	logarithmic	ADJ
ejpam-6081	132	44	coefficients	coefficient	NOUN
ejpam-6081	132	45	,	,	PUNCT
ejpam-6081	132	46	and	and	CCONJ
ejpam-6081	132	47	vandermonde	vandermonde	VERB
ejpam-6081	132	48	determinant	determinant	ADJ
ejpam-6081	132	49	of	of	ADP
ejpam-6081	132	50	second	second	ADJ
ejpam-6081	132	51	-	-	PUNCT
ejpam-6081	132	52	order	order	NOUN
ejpam-6081	132	53	of	of	ADP
ejpam-6081	132	54	functions	function	NOUN
ejpam-6081	132	55	and	and	CCONJ
ejpam-6081	132	56	inverse	inverse	NOUN
ejpam-6081	132	57	functions	function	NOUN
ejpam-6081	132	58	belonging	belong	VERB
ejpam-6081	132	59	to	to	ADP
ejpam-6081	132	60	the	the	DET
ejpam-6081	132	61	class	class	NOUN
ejpam-6081	132	62	gg	gg	NOUN
ejpam-6081	132	63	(	(	PUNCT
ejpam-6081	132	64	α	α	PROPN
ejpam-6081	132	65	,	,	PUNCT
ejpam-6081	132	66	δ	δ	PROPN
ejpam-6081	132	67	)	)	PUNCT
ejpam-6081	132	68	.	.	PUNCT
ejpam-6081	133	1	3.1	3.1	NUM
ejpam-6081	133	2	.	.	PUNCT
ejpam-6081	134	1	taylor	taylor	PROPN
ejpam-6081	134	2	coefficients	coefficient	NOUN
ejpam-6081	134	3	we	we	PRON
ejpam-6081	134	4	now	now	ADV
ejpam-6081	134	5	estimate	estimate	VERB
ejpam-6081	134	6	the	the	DET
ejpam-6081	134	7	upper	upper	ADJ
ejpam-6081	134	8	bounds	bound	NOUN
ejpam-6081	134	9	of	of	ADP
ejpam-6081	134	10	the	the	DET
ejpam-6081	134	11	taylor	taylor	PROPN
ejpam-6081	134	12	coefficients	coefficient	NOUN
ejpam-6081	134	13	of	of	ADP
ejpam-6081	134	14	functions	function	NOUN
ejpam-6081	134	15	and	and	CCONJ
ejpam-6081	134	16	inverse	inverse	NOUN
ejpam-6081	134	17	functions	function	NOUN
ejpam-6081	134	18	in	in	ADP
ejpam-6081	134	19	gg	gg	PROPN
ejpam-6081	134	20	(	(	PUNCT
ejpam-6081	134	21	α	α	PROPN
ejpam-6081	134	22	,	,	PUNCT
ejpam-6081	134	23	δ	δ	PROPN
ejpam-6081	134	24	)	)	PUNCT
ejpam-6081	134	25	.	.	PUNCT
ejpam-6081	135	1	theorem	theorem	NOUN
ejpam-6081	135	2	1	1	NUM
ejpam-6081	135	3	.	.	PUNCT
ejpam-6081	136	1	let	let	VERB
ejpam-6081	136	2	f	f	PROPN
ejpam-6081	136	3	(	(	PUNCT
ejpam-6081	136	4	z	z	NOUN
ejpam-6081	136	5	)	)	PUNCT
ejpam-6081	136	6	∈	∈	PROPN
ejpam-6081	136	7	gg	gg	PROPN
ejpam-6081	136	8	(	(	PUNCT
ejpam-6081	136	9	α	α	PROPN
ejpam-6081	136	10	,	,	PUNCT
ejpam-6081	136	11	δ	δ	PROPN
ejpam-6081	136	12	)	)	PUNCT
ejpam-6081	136	13	.	.	PUNCT
ejpam-6081	137	1	then	then	ADV
ejpam-6081	137	2	|an|	|an|	VERB
ejpam-6081	137	3	≤	≤	NOUN
ejpam-6081	137	4	ταδ	ταδ	PROPN
ejpam-6081	137	5	2n	2n	NUM
ejpam-6081	137	6	,	,	PUNCT
ejpam-6081	137	7	n	n	NOUN
ejpam-6081	137	8	=	=	SYM
ejpam-6081	137	9	2	2	NUM
ejpam-6081	137	10	,	,	PUNCT
ejpam-6081	137	11	3	3	NUM
ejpam-6081	137	12	,	,	PUNCT
ejpam-6081	137	13	4	4	NUM
ejpam-6081	137	14	,	,	PUNCT
ejpam-6081	137	15	5	5	NUM
ejpam-6081	137	16	,	,	PUNCT
ejpam-6081	137	17	where	where	SCONJ
ejpam-6081	137	18	ταδ	ταδ	ADV
ejpam-6081	137	19	=	=	SYM
ejpam-6081	137	20	cosα−	cosα−	PROPN
ejpam-6081	137	21	δ	δ	PROPN
ejpam-6081	137	22	.	.	PUNCT
ejpam-6081	138	1	proof	proof	NOUN
ejpam-6081	138	2	.	.	PUNCT
ejpam-6081	139	1	let	let	VERB
ejpam-6081	139	2	a	a	DET
ejpam-6081	139	3	function	function	NOUN
ejpam-6081	139	4	f	f	X
ejpam-6081	139	5	(	(	PUNCT
ejpam-6081	139	6	z	z	NOUN
ejpam-6081	139	7	)	)	PUNCT
ejpam-6081	139	8	∈	∈	PROPN
ejpam-6081	139	9	gg	gg	PROPN
ejpam-6081	139	10	(	(	PUNCT
ejpam-6081	139	11	α	α	PROPN
ejpam-6081	139	12	,	,	PUNCT
ejpam-6081	139	13	δ	δ	PROPN
ejpam-6081	139	14	)	)	PUNCT
ejpam-6081	139	15	given	give	VERB
ejpam-6081	139	16	by	by	ADP
ejpam-6081	139	17	(	(	PUNCT
ejpam-6081	139	18	1	1	NUM
ejpam-6081	139	19	)	)	PUNCT
ejpam-6081	139	20	.	.	PUNCT
ejpam-6081	140	1	then	then	ADV
ejpam-6081	140	2	there	there	PRON
ejpam-6081	140	3	exists	exist	VERB
ejpam-6081	140	4	a	a	DET
ejpam-6081	140	5	schwarz	schwarz	PROPN
ejpam-6081	140	6	function	function	NOUN
ejpam-6081	140	7	υ	υ	PROPN
ejpam-6081	140	8	(	(	PUNCT
ejpam-6081	140	9	z	z	NOUN
ejpam-6081	140	10	)	)	PUNCT
ejpam-6081	140	11	with	with	ADP
ejpam-6081	140	12	υ	υ	PROPN
ejpam-6081	140	13	(	(	PUNCT
ejpam-6081	140	14	0	0	NUM
ejpam-6081	140	15	)	)	PUNCT
ejpam-6081	140	16	=	=	SYM
ejpam-6081	140	17	0	0	NUM
ejpam-6081	140	18	and	and	CCONJ
ejpam-6081	140	19	|υ	|υ	NOUN
ejpam-6081	140	20	(	(	PUNCT
ejpam-6081	140	21	z)|	z)|	X
ejpam-6081	140	22	<	<	X
ejpam-6081	140	23	1	1	NUM
ejpam-6081	140	24	in	in	ADP
ejpam-6081	140	25	e	e	PROPN
ejpam-6081	140	26	such	such	ADJ
ejpam-6081	140	27	that	that	SCONJ
ejpam-6081	140	28	eiαf	eiαf	NOUN
ejpam-6081	140	29	′	′	NUM
ejpam-6081	141	1	(	(	PUNCT
ejpam-6081	141	2	z)−	z)−	NOUN
ejpam-6081	141	3	i	i	PRON
ejpam-6081	141	4	sinα−	sinα−	VERB
ejpam-6081	141	5	δ	δ	X
ejpam-6081	141	6	ταδ	ταδ	PROPN
ejpam-6081	141	7	=	=	PUNCT
ejpam-6081	141	8	ψ(υ	ψ(υ	PROPN
ejpam-6081	141	9	(	(	PUNCT
ejpam-6081	141	10	z	z	NOUN
ejpam-6081	141	11	)	)	PUNCT
ejpam-6081	141	12	)	)	PUNCT
ejpam-6081	141	13	,	,	PUNCT
ejpam-6081	141	14	z	z	NOUN
ejpam-6081	141	15	∈	∈	PROPN
ejpam-6081	141	16	e	e	NOUN
ejpam-6081	141	17	,	,	PUNCT
ejpam-6081	141	18	(	(	PUNCT
ejpam-6081	141	19	20	20	X
ejpam-6081	141	20	)	)	PUNCT
ejpam-6081	141	21	n.	n.	NOUN
ejpam-6081	141	22	h.	h.	PROPN
ejpam-6081	141	23	a.	a.	PROPN
ejpam-6081	141	24	a.	a.	PROPN
ejpam-6081	141	25	wahid	wahid	PROPN
ejpam-6081	141	26	,	,	PUNCT
ejpam-6081	141	27	s.	s.	PROPN
ejpam-6081	141	28	c.	c.	PROPN
ejpam-6081	141	29	soh	soh	PROPN
ejpam-6081	141	30	/	/	SYM
ejpam-6081	141	31	eur	eur	PROPN
ejpam-6081	141	32	.	.	PUNCT
ejpam-6081	142	1	j.	j.	PROPN
ejpam-6081	142	2	pure	pure	PROPN
ejpam-6081	142	3	appl	appl	PROPN
ejpam-6081	142	4	.	.	PROPN
ejpam-6081	142	5	math	math	PROPN
ejpam-6081	142	6	,	,	PUNCT
ejpam-6081	142	7	18	18	NUM
ejpam-6081	142	8	(	(	PUNCT
ejpam-6081	142	9	2	2	NUM
ejpam-6081	142	10	)	)	PUNCT
ejpam-6081	142	11	(	(	PUNCT
ejpam-6081	142	12	2025	2025	NUM
ejpam-6081	142	13	)	)	PUNCT
ejpam-6081	142	14	,	,	PUNCT
ejpam-6081	142	15	6081	6081	NUM
ejpam-6081	142	16	7	7	NUM
ejpam-6081	142	17	of	of	ADP
ejpam-6081	142	18	16	16	NUM
ejpam-6081	142	19	where	where	SCONJ
ejpam-6081	142	20	ταδ	ταδ	ADV
ejpam-6081	142	21	=	=	SYM
ejpam-6081	142	22	cosα−	cosα−	PROPN
ejpam-6081	142	23	δ	δ	PROPN
ejpam-6081	142	24	.	.	PUNCT
ejpam-6081	143	1	define	define	VERB
ejpam-6081	143	2	the	the	DET
ejpam-6081	143	3	function	function	NOUN
ejpam-6081	143	4	p	p	NOUN
ejpam-6081	143	5	(	(	PUNCT
ejpam-6081	143	6	z	z	NOUN
ejpam-6081	143	7	)	)	PUNCT
ejpam-6081	143	8	by	by	ADP
ejpam-6081	143	9	p	p	PROPN
ejpam-6081	143	10	(	(	PUNCT
ejpam-6081	143	11	z	z	NOUN
ejpam-6081	143	12	)	)	PUNCT
ejpam-6081	143	13	=	=	SYM
ejpam-6081	144	1	1	1	NUM
ejpam-6081	144	2	+	+	NUM
ejpam-6081	144	3	υ	υ	PROPN
ejpam-6081	144	4	(	(	PUNCT
ejpam-6081	144	5	z	z	NOUN
ejpam-6081	144	6	)	)	PUNCT
ejpam-6081	144	7	1−	1−	NUM
ejpam-6081	144	8	υ	υ	NOUN
ejpam-6081	144	9	(	(	PUNCT
ejpam-6081	144	10	z	z	NOUN
ejpam-6081	144	11	)	)	PUNCT
ejpam-6081	144	12	,	,	PUNCT
ejpam-6081	144	13	z	z	NOUN
ejpam-6081	144	14	∈	∈	PROPN
ejpam-6081	144	15	e	e	NOUN
ejpam-6081	144	16	,	,	PUNCT
ejpam-6081	144	17	or	or	CCONJ
ejpam-6081	144	18	equivalently	equivalently	ADV
ejpam-6081	144	19	υ	υ	NOUN
ejpam-6081	144	20	(	(	PUNCT
ejpam-6081	144	21	z	z	NOUN
ejpam-6081	144	22	)	)	PUNCT
ejpam-6081	144	23	=	=	SYM
ejpam-6081	144	24	−1+p(z	−1+p(z	PROPN
ejpam-6081	144	25	)	)	PUNCT
ejpam-6081	144	26	1+p(z	1+p(z	NOUN
ejpam-6081	144	27	)	)	PUNCT
ejpam-6081	144	28	=	=	SYM
ejpam-6081	144	29	1	1	NUM
ejpam-6081	144	30	2p1z	2p1z	NOUN
ejpam-6081	145	1	+	+	CCONJ
ejpam-6081	145	2	1	1	NUM
ejpam-6081	145	3	2	2	NUM
ejpam-6081	145	4	(	(	PUNCT
ejpam-6081	145	5	p2	p2	PROPN
ejpam-6081	145	6	−	−	PROPN
ejpam-6081	145	7	1	1	NUM
ejpam-6081	145	8	2p1	2p1	NUM
ejpam-6081	145	9	2	2	NUM
ejpam-6081	145	10	)	)	PUNCT
ejpam-6081	145	11	z2	z2	NOUN
ejpam-6081	145	12	+	+	CCONJ
ejpam-6081	145	13	1	1	NUM
ejpam-6081	145	14	2	2	NUM
ejpam-6081	145	15	(	(	PUNCT
ejpam-6081	145	16	1	1	NUM
ejpam-6081	145	17	4p1	4p1	NUM
ejpam-6081	145	18	3	3	NUM
ejpam-6081	145	19	−	−	NOUN
ejpam-6081	146	1	p1p2	p1p2	PROPN
ejpam-6081	146	2	+	+	NUM
ejpam-6081	146	3	p3	p3	PROPN
ejpam-6081	146	4	)	)	PUNCT
ejpam-6081	147	1	z3	z3	PROPN
ejpam-6081	147	2	+1	+1	NOUN
ejpam-6081	147	3	2	2	NUM
ejpam-6081	147	4	(	(	PUNCT
ejpam-6081	147	5	−1	−1	NOUN
ejpam-6081	147	6	8p1	8p1	NUM
ejpam-6081	147	7	4	4	NUM
ejpam-6081	147	8	+	+	SYM
ejpam-6081	147	9	3	3	NUM
ejpam-6081	147	10	4p1	4p1	NUM
ejpam-6081	147	11	2p2	2p2	NUM
ejpam-6081	147	12	−	−	NOUN
ejpam-6081	148	1	p1p3	p1p3	ADP
ejpam-6081	148	2	−	−	PROPN
ejpam-6081	148	3	1	1	NUM
ejpam-6081	148	4	2p2	2p2	NUM
ejpam-6081	148	5	2	2	NUM
ejpam-6081	148	6	+	+	CCONJ
ejpam-6081	148	7	p4	p4	ADJ
ejpam-6081	148	8	)	)	PUNCT
ejpam-6081	148	9	z4	z4	PROPN
ejpam-6081	148	10	+	+	CCONJ
ejpam-6081	148	11	·	·	PUNCT
ejpam-6081	148	12	·	·	PUNCT
ejpam-6081	148	13	·	·	PUNCT
ejpam-6081	148	14	.	.	PUNCT
ejpam-6081	149	1	(	(	PUNCT
ejpam-6081	149	2	21	21	NUM
ejpam-6081	149	3	)	)	PUNCT
ejpam-6081	149	4	using	use	VERB
ejpam-6081	149	5	(	(	PUNCT
ejpam-6081	149	6	21	21	NUM
ejpam-6081	149	7	)	)	PUNCT
ejpam-6081	149	8	along	along	ADP
ejpam-6081	149	9	with	with	ADP
ejpam-6081	149	10	the	the	DET
ejpam-6081	149	11	expression	expression	NOUN
ejpam-6081	149	12	ψ	ψ	X
ejpam-6081	149	13	(	(	PUNCT
ejpam-6081	149	14	υ	υ	X
ejpam-6081	149	15	(	(	PUNCT
ejpam-6081	149	16	z	z	NOUN
ejpam-6081	149	17	)	)	PUNCT
ejpam-6081	149	18	)	)	PUNCT
ejpam-6081	150	1	=	=	SYM
ejpam-6081	150	2	υ(z	υ(z	ADJ
ejpam-6081	150	3	)	)	PUNCT
ejpam-6081	150	4	ln(1+υ(z	ln(1+υ(z	NOUN
ejpam-6081	150	5	)	)	PUNCT
ejpam-6081	150	6	)	)	PUNCT
ejpam-6081	150	7	,	,	PUNCT
ejpam-6081	150	8	we	we	PRON
ejpam-6081	150	9	obtain	obtain	VERB
ejpam-6081	150	10	ψ	ψ	X
ejpam-6081	150	11	(	(	PUNCT
ejpam-6081	150	12	υ	υ	X
ejpam-6081	150	13	(	(	PUNCT
ejpam-6081	150	14	z	z	NOUN
ejpam-6081	150	15	)	)	PUNCT
ejpam-6081	150	16	)	)	PUNCT
ejpam-6081	151	1	=	=	SYM
ejpam-6081	152	1	1	1	NUM
ejpam-6081	152	2	+	+	NUM
ejpam-6081	152	3	1	1	NUM
ejpam-6081	152	4	4p1z	4p1z	NUM
ejpam-6081	152	5	+	+	CCONJ
ejpam-6081	152	6	1	1	NUM
ejpam-6081	152	7	48	48	NUM
ejpam-6081	152	8	(	(	PUNCT
ejpam-6081	152	9	12p2	12p2	NUM
ejpam-6081	152	10	−	−	NOUN
ejpam-6081	152	11	7p1	7p1	NUM
ejpam-6081	152	12	2	2	NUM
ejpam-6081	152	13	)	)	PUNCT
ejpam-6081	152	14	z2	z2	NOUN
ejpam-6081	152	15	+	+	CCONJ
ejpam-6081	152	16	1	1	NUM
ejpam-6081	152	17	192	192	NUM
ejpam-6081	152	18	(	(	PUNCT
ejpam-6081	152	19	17p1	17p1	NUM
ejpam-6081	152	20	3	3	NUM
ejpam-6081	152	21	−	−	PROPN
ejpam-6081	152	22	56p1p2	56p1p2	ADJ
ejpam-6081	152	23	+	+	CCONJ
ejpam-6081	152	24	48p3	48p3	NUM
ejpam-6081	152	25	)	)	PUNCT
ejpam-6081	152	26	z3	z3	NOUN
ejpam-6081	153	1	+	+	CCONJ
ejpam-6081	153	2	1	1	NUM
ejpam-6081	153	3	11520	11520	NUM
ejpam-6081	153	4	(	(	PUNCT
ejpam-6081	153	5	−649p1	−649p1	PROPN
ejpam-6081	153	6	4	4	NUM
ejpam-6081	153	7	+	+	SYM
ejpam-6081	153	8	3060p1	3060p1	NUM
ejpam-6081	153	9	2p2	2p2	NUM
ejpam-6081	153	10	−	−	PROPN
ejpam-6081	153	11	3360p1p3	3360p1p3	NUM
ejpam-6081	153	12	−	−	NUM
ejpam-6081	153	13	1680p2	1680p2	NUM
ejpam-6081	153	14	2	2	NUM
ejpam-6081	153	15	+	+	CCONJ
ejpam-6081	153	16	2880p4	2880p4	NUM
ejpam-6081	153	17	)	)	PUNCT
ejpam-6081	153	18	z4	z4	PROPN
ejpam-6081	153	19	+	+	CCONJ
ejpam-6081	153	20	·	·	PUNCT
ejpam-6081	153	21	·	·	PUNCT
ejpam-6081	153	22	·	·	PUNCT
ejpam-6081	153	23	.	.	PUNCT
ejpam-6081	154	1	(	(	PUNCT
ejpam-6081	154	2	22	22	NUM
ejpam-6081	154	3	)	)	PUNCT
ejpam-6081	154	4	thus	thus	ADV
ejpam-6081	154	5	,	,	PUNCT
ejpam-6081	154	6	by	by	ADP
ejpam-6081	154	7	applying	apply	VERB
ejpam-6081	154	8	(	(	PUNCT
ejpam-6081	154	9	22	22	NUM
ejpam-6081	154	10	)	)	PUNCT
ejpam-6081	154	11	to	to	ADP
ejpam-6081	154	12	(	(	PUNCT
ejpam-6081	154	13	20	20	NUM
ejpam-6081	154	14	)	)	PUNCT
ejpam-6081	154	15	,	,	PUNCT
ejpam-6081	154	16	we	we	PRON
ejpam-6081	154	17	have	have	VERB
ejpam-6081	154	18	eiα	eiα	NOUN
ejpam-6081	155	1	[	[	X
ejpam-6081	155	2	(	(	PUNCT
ejpam-6081	155	3	1	1	NUM
ejpam-6081	155	4	+	+	CCONJ
ejpam-6081	155	5	2a2z	2a2z	NOUN
ejpam-6081	156	1	+	+	CCONJ
ejpam-6081	156	2	3a3z	3a3z	NOUN
ejpam-6081	156	3	2	2	NUM
ejpam-6081	157	1	+	+	CCONJ
ejpam-6081	157	2	4a4z	4a4z	ADJ
ejpam-6081	157	3	3	3	NUM
ejpam-6081	157	4	+	+	CCONJ
ejpam-6081	157	5	5a5z	5a5z	NUM
ejpam-6081	157	6	4	4	NUM
ejpam-6081	157	7	+	+	NUM
ejpam-6081	157	8	·	·	PUNCT
ejpam-6081	157	9	·	·	PUNCT
ejpam-6081	157	10	·	·	PUNCT
ejpam-6081	157	11	)	)	PUNCT
ejpam-6081	158	1	−	−	NOUN
ejpam-6081	158	2	1	1	NUM
ejpam-6081	158	3	]	]	PUNCT
ejpam-6081	158	4	=	=	PUNCT
ejpam-6081	158	5	ταδ	ταδ	PROPN
ejpam-6081	158	6	[	[	PUNCT
ejpam-6081	158	7	1	1	NUM
ejpam-6081	158	8	4p1z	4p1z	NUM
ejpam-6081	158	9	+	+	CCONJ
ejpam-6081	158	10	1	1	NUM
ejpam-6081	158	11	48	48	NUM
ejpam-6081	158	12	(	(	PUNCT
ejpam-6081	158	13	12p2	12p2	NUM
ejpam-6081	158	14	−	−	NOUN
ejpam-6081	158	15	7p1	7p1	NUM
ejpam-6081	158	16	2	2	NUM
ejpam-6081	158	17	)	)	PUNCT
ejpam-6081	158	18	z2	z2	NOUN
ejpam-6081	158	19	+	+	CCONJ
ejpam-6081	158	20	1	1	NUM
ejpam-6081	158	21	192	192	NUM
ejpam-6081	158	22	(	(	PUNCT
ejpam-6081	158	23	17p1	17p1	NUM
ejpam-6081	158	24	3	3	NUM
ejpam-6081	158	25	−	−	PROPN
ejpam-6081	158	26	56p1p2	56p1p2	ADJ
ejpam-6081	158	27	+	+	CCONJ
ejpam-6081	158	28	48p3	48p3	NUM
ejpam-6081	158	29	)	)	PUNCT
ejpam-6081	158	30	z3	z3	NOUN
ejpam-6081	159	1	+	+	CCONJ
ejpam-6081	159	2	1	1	NUM
ejpam-6081	159	3	11520	11520	NUM
ejpam-6081	159	4	(	(	PUNCT
ejpam-6081	159	5	−649p1	−649p1	PROPN
ejpam-6081	159	6	4	4	NUM
ejpam-6081	159	7	+	+	SYM
ejpam-6081	159	8	3060p1	3060p1	NUM
ejpam-6081	159	9	2p2	2p2	NUM
ejpam-6081	159	10	−	−	PROPN
ejpam-6081	159	11	3360p1p3	3360p1p3	NUM
ejpam-6081	159	12	−	−	NUM
ejpam-6081	159	13	1680p2	1680p2	NUM
ejpam-6081	159	14	2	2	NUM
ejpam-6081	159	15	+	+	CCONJ
ejpam-6081	159	16	2880p4	2880p4	NUM
ejpam-6081	159	17	)	)	PUNCT
ejpam-6081	159	18	z4	z4	PROPN
ejpam-6081	159	19	+	+	CCONJ
ejpam-6081	159	20	·	·	PUNCT
ejpam-6081	160	1	·	·	PUNCT
ejpam-6081	160	2	·	·	PUNCT
ejpam-6081	160	3	]	]	PUNCT
ejpam-6081	160	4	.	.	PUNCT
ejpam-6081	161	1	(	(	PUNCT
ejpam-6081	161	2	23	23	NUM
ejpam-6081	161	3	)	)	PUNCT
ejpam-6081	161	4	comparing	compare	VERB
ejpam-6081	161	5	the	the	DET
ejpam-6081	161	6	coefficients	coefficient	NOUN
ejpam-6081	161	7	of	of	ADP
ejpam-6081	161	8	zn	zn	PROPN
ejpam-6081	161	9	for	for	ADP
ejpam-6081	161	10	n	n	NOUN
ejpam-6081	161	11	=	=	SYM
ejpam-6081	161	12	1	1	NUM
ejpam-6081	161	13	,	,	PUNCT
ejpam-6081	161	14	2	2	NUM
ejpam-6081	161	15	,	,	PUNCT
ejpam-6081	161	16	3	3	NUM
ejpam-6081	161	17	,	,	PUNCT
ejpam-6081	161	18	4	4	NUM
ejpam-6081	161	19	on	on	ADP
ejpam-6081	161	20	both	both	DET
ejpam-6081	161	21	sides	side	NOUN
ejpam-6081	161	22	of	of	ADP
ejpam-6081	161	23	(	(	PUNCT
ejpam-6081	161	24	23	23	NUM
ejpam-6081	161	25	)	)	PUNCT
ejpam-6081	161	26	gives	give	VERB
ejpam-6081	161	27	a2	a2	PROPN
ejpam-6081	161	28	=	=	SYM
ejpam-6081	161	29	ταδe	ταδe	PROPN
ejpam-6081	161	30	−iα	−iα	PROPN
ejpam-6081	161	31	8	8	NUM
ejpam-6081	161	32	p1	p1	NOUN
ejpam-6081	161	33	,	,	PUNCT
ejpam-6081	161	34	a3	a3	NOUN
ejpam-6081	161	35	=	=	SYM
ejpam-6081	161	36	ταδe	ταδe	NOUN
ejpam-6081	161	37	−iα	−iα	VERB
ejpam-6081	161	38	144	144	NUM
ejpam-6081	162	1	(	(	PUNCT
ejpam-6081	162	2	12p2	12p2	NUM
ejpam-6081	162	3	−	−	NOUN
ejpam-6081	162	4	7p1	7p1	NUM
ejpam-6081	162	5	2	2	NUM
ejpam-6081	162	6	)	)	PUNCT
ejpam-6081	162	7	,	,	PUNCT
ejpam-6081	162	8	a4	a4	NOUN
ejpam-6081	162	9	=	=	SYM
ejpam-6081	162	10	ταδe	ταδe	NOUN
ejpam-6081	162	11	−iα	−iα	VERB
ejpam-6081	162	12	768	768	NUM
ejpam-6081	162	13	(	(	PUNCT
ejpam-6081	162	14	17p1	17p1	NUM
ejpam-6081	162	15	3	3	NUM
ejpam-6081	162	16	−	−	PROPN
ejpam-6081	162	17	56p1p2	56p1p2	ADJ
ejpam-6081	162	18	+	+	CCONJ
ejpam-6081	162	19	48p3	48p3	NUM
ejpam-6081	162	20	)	)	PUNCT
ejpam-6081	162	21	,	,	PUNCT
ejpam-6081	162	22	a5	a5	PROPN
ejpam-6081	162	23	=	=	PUNCT
ejpam-6081	162	24	ταδe	ταδe	NOUN
ejpam-6081	162	25	−iα	−iα	PROPN
ejpam-6081	162	26	57600	57600	NUM
ejpam-6081	162	27	(	(	PUNCT
ejpam-6081	162	28	−649p1	−649p1	PROPN
ejpam-6081	162	29	4	4	NUM
ejpam-6081	162	30	+	+	SYM
ejpam-6081	162	31	3060p1	3060p1	NUM
ejpam-6081	162	32	2p2	2p2	NUM
ejpam-6081	162	33	−	−	PROPN
ejpam-6081	162	34	3360p1p3	3360p1p3	NUM
ejpam-6081	162	35	−	−	NUM
ejpam-6081	162	36	1680p2	1680p2	NUM
ejpam-6081	162	37	2	2	NUM
ejpam-6081	162	38	+	+	CCONJ
ejpam-6081	162	39	2880p4	2880p4	NUM
ejpam-6081	162	40	)	)	PUNCT
ejpam-6081	162	41	.	.	PUNCT
ejpam-6081	163	1			PRON
ejpam-6081	163	2	(	(	PUNCT
ejpam-6081	163	3	24	24	NUM
ejpam-6081	163	4	)	)	PUNCT
ejpam-6081	163	5	based	base	VERB
ejpam-6081	163	6	on	on	ADP
ejpam-6081	163	7	lemmas	lemmas	PROPN
ejpam-6081	163	8	1	1	NUM
ejpam-6081	163	9	-	-	SYM
ejpam-6081	163	10	4	4	NUM
ejpam-6081	163	11	,	,	PUNCT
ejpam-6081	163	12	the	the	DET
ejpam-6081	163	13	equations	equation	NOUN
ejpam-6081	163	14	in	in	ADP
ejpam-6081	163	15	(	(	PUNCT
ejpam-6081	163	16	24	24	NUM
ejpam-6081	163	17	)	)	PUNCT
ejpam-6081	163	18	can	can	AUX
ejpam-6081	163	19	be	be	AUX
ejpam-6081	163	20	expressed	express	VERB
ejpam-6081	163	21	as	as	SCONJ
ejpam-6081	163	22	follows	follow	VERB
ejpam-6081	163	23	:	:	PUNCT
ejpam-6081	163	24	|a2|	|a2|	NOUN
ejpam-6081	163	25	=	=	SYM
ejpam-6081	163	26	∣∣∣∣ταδe−iα	∣∣∣∣ταδe−iα	ADJ
ejpam-6081	163	27	8	8	NUM
ejpam-6081	163	28	p1	p1	NOUN
ejpam-6081	163	29	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6081	163	30	,	,	PUNCT
ejpam-6081	163	31	(	(	PUNCT
ejpam-6081	163	32	25	25	NUM
ejpam-6081	163	33	)	)	PUNCT
ejpam-6081	163	34	|a3|	|a3|	NOUN
ejpam-6081	163	35	=	=	PUNCT
ejpam-6081	164	1	∣∣∣∣ταδe−iα	∣∣∣∣ταδe−iα	PROPN
ejpam-6081	164	2	144	144	NUM
ejpam-6081	164	3	[	[	PUNCT
ejpam-6081	164	4	12	12	NUM
ejpam-6081	164	5	(	(	PUNCT
ejpam-6081	164	6	p2	p2	PROPN
ejpam-6081	164	7	−	−	PROPN
ejpam-6081	164	8	7	7	NUM
ejpam-6081	164	9	12	12	NUM
ejpam-6081	164	10	p1	p1	NOUN
ejpam-6081	164	11	2	2	NUM
ejpam-6081	164	12	)	)	PUNCT
ejpam-6081	164	13	]	]	X
ejpam-6081	164	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6081	164	15	,	,	PUNCT
ejpam-6081	164	16	(	(	PUNCT
ejpam-6081	164	17	26	26	NUM
ejpam-6081	164	18	)	)	PUNCT
ejpam-6081	164	19	|a4|	|a4|	NOUN
ejpam-6081	164	20	=	=	SYM
ejpam-6081	164	21	∣∣∣∣ταδe−iα	∣∣∣∣ταδe−iα	PROPN
ejpam-6081	164	22	768	768	NUM
ejpam-6081	164	23	[	[	PUNCT
ejpam-6081	164	24	17p1	17p1	NUM
ejpam-6081	164	25	3	3	NUM
ejpam-6081	164	26	−	−	NOUN
ejpam-6081	164	27	56p1p2	56p1p2	ADJ
ejpam-6081	164	28	+	+	NUM
ejpam-6081	164	29	48p3	48p3	NUM
ejpam-6081	164	30	]	]	X
ejpam-6081	164	31	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6081	164	32	,	,	PUNCT
ejpam-6081	164	33	(	(	PUNCT
ejpam-6081	164	34	27	27	NUM
ejpam-6081	164	35	)	)	PUNCT
ejpam-6081	164	36	|a5|	|a5|	VERB
ejpam-6081	164	37	=	=	SYM
ejpam-6081	164	38	∣∣∣∣ταδe−iα	∣∣∣∣ταδe−iα	X
ejpam-6081	164	39	20	20	NUM
ejpam-6081	164	40	[	[	PUNCT
ejpam-6081	164	41	649	649	NUM
ejpam-6081	164	42	2880	2880	NUM
ejpam-6081	164	43	p1	p1	NOUN
ejpam-6081	164	44	4	4	NUM
ejpam-6081	164	45	+	+	CCONJ
ejpam-6081	164	46	1680	1680	NUM
ejpam-6081	164	47	2880	2880	NUM
ejpam-6081	164	48	p2	p2	X
ejpam-6081	164	49	2	2	NUM
ejpam-6081	165	1	+	+	NUM
ejpam-6081	165	2	2	2	NUM
ejpam-6081	165	3	(	(	PUNCT
ejpam-6081	165	4	1680	1680	NUM
ejpam-6081	165	5	2880	2880	NUM
ejpam-6081	165	6	)	)	PUNCT
ejpam-6081	166	1	p1p3	p1p3	ADP
ejpam-6081	166	2	−	−	PROPN
ejpam-6081	166	3	3	3	NUM
ejpam-6081	166	4	2	2	NUM
ejpam-6081	166	5	(	(	PUNCT
ejpam-6081	166	6	2040	2040	NUM
ejpam-6081	166	7	2880	2880	NUM
ejpam-6081	166	8	)	)	PUNCT
ejpam-6081	166	9	p1	p1	NOUN
ejpam-6081	166	10	2p2	2p2	NUM
ejpam-6081	167	1	−	−	PROPN
ejpam-6081	167	2	p4	p4	ADJ
ejpam-6081	167	3	]	]	X
ejpam-6081	167	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6081	167	5	.	.	PUNCT
ejpam-6081	168	1	(	(	PUNCT
ejpam-6081	168	2	28	28	NUM
ejpam-6081	168	3	)	)	PUNCT
ejpam-6081	168	4	n.	n.	PROPN
ejpam-6081	168	5	h.	h.	PROPN
ejpam-6081	168	6	a.	a.	PROPN
ejpam-6081	168	7	a.	a.	PROPN
ejpam-6081	168	8	wahid	wahid	PROPN
ejpam-6081	168	9	,	,	PUNCT
ejpam-6081	168	10	s.	s.	PROPN
ejpam-6081	168	11	c.	c.	PROPN
ejpam-6081	168	12	soh	soh	PROPN
ejpam-6081	168	13	/	/	SYM
ejpam-6081	168	14	eur	eur	PROPN
ejpam-6081	168	15	.	.	PUNCT
ejpam-6081	169	1	j.	j.	PROPN
ejpam-6081	169	2	pure	pure	PROPN
ejpam-6081	169	3	appl	appl	PROPN
ejpam-6081	169	4	.	.	PROPN
ejpam-6081	169	5	math	math	PROPN
ejpam-6081	169	6	,	,	PUNCT
ejpam-6081	169	7	18	18	NUM
ejpam-6081	169	8	(	(	PUNCT
ejpam-6081	169	9	2	2	NUM
ejpam-6081	169	10	)	)	PUNCT
ejpam-6081	169	11	(	(	PUNCT
ejpam-6081	169	12	2025	2025	NUM
ejpam-6081	169	13	)	)	PUNCT
ejpam-6081	169	14	,	,	PUNCT
ejpam-6081	169	15	6081	6081	NUM
ejpam-6081	169	16	8	8	NUM
ejpam-6081	169	17	of	of	ADP
ejpam-6081	169	18	16	16	NUM
ejpam-6081	169	19	it	it	PRON
ejpam-6081	169	20	is	be	AUX
ejpam-6081	169	21	observed	observe	VERB
ejpam-6081	169	22	that	that	SCONJ
ejpam-6081	169	23	|p1|	|p1|	ADJ
ejpam-6081	169	24	≤	≤	ADJ
ejpam-6081	169	25	2,∣∣p2	2,∣∣p2	NUM
ejpam-6081	170	1	−	−	NOUN
ejpam-6081	170	2	7	7	NUM
ejpam-6081	170	3	12p1	12p1	NUM
ejpam-6081	170	4	2	2	NUM
ejpam-6081	170	5	∣∣	∣∣	X
ejpam-6081	170	6	≤	≤	NOUN
ejpam-6081	170	7	2max	2max	NUM
ejpam-6081	170	8	{	{	PUNCT
ejpam-6081	170	9	1	1	NUM
ejpam-6081	170	10	,	,	PUNCT
ejpam-6081	170	11	∣∣2	∣∣2	NUM
ejpam-6081	170	12	(	(	PUNCT
ejpam-6081	170	13	7	7	NUM
ejpam-6081	170	14	12	12	NUM
ejpam-6081	170	15	)	)	PUNCT
ejpam-6081	170	16	−	−	NOUN
ejpam-6081	170	17	1	1	NUM
ejpam-6081	170	18	∣∣	∣∣	NOUN
ejpam-6081	170	19	}	}	PUNCT
ejpam-6081	170	20	=	=	SYM
ejpam-6081	170	21	2,∣∣17p13	2,∣∣17p13	NUM
ejpam-6081	170	22	−	−	NOUN
ejpam-6081	170	23	56p1p2	56p1p2	ADJ
ejpam-6081	170	24	+	+	CCONJ
ejpam-6081	170	25	48p3	48p3	NUM
ejpam-6081	170	26	∣∣	∣∣	NUM
ejpam-6081	170	27	≤	≤	ADV
ejpam-6081	170	28	2	2	NUM
ejpam-6081	170	29	|17|+	|17|+	NOUN
ejpam-6081	170	30	2	2	NUM
ejpam-6081	170	31	|56−	|56−	NOUN
ejpam-6081	170	32	2	2	NUM
ejpam-6081	170	33	(	(	PUNCT
ejpam-6081	170	34	17)|+	17)|+	PROPN
ejpam-6081	170	35	2	2	NUM
ejpam-6081	170	36	|17−	|17−	PROPN
ejpam-6081	170	37	56	56	NUM
ejpam-6081	170	38	+	+	NUM
ejpam-6081	170	39	48|	48|	NUM
ejpam-6081	170	40	=	=	SYM
ejpam-6081	171	1	96,∣∣	96,∣∣	NUM
ejpam-6081	171	2	649	649	NUM
ejpam-6081	171	3	2880p1	2880p1	NOUN
ejpam-6081	171	4	4	4	NUM
ejpam-6081	171	5	+	+	NUM
ejpam-6081	171	6	1680	1680	NUM
ejpam-6081	171	7	2880p2	2880p2	NUM
ejpam-6081	171	8	2	2	NUM
ejpam-6081	171	9	+	+	NUM
ejpam-6081	171	10	2	2	NUM
ejpam-6081	171	11	(	(	PUNCT
ejpam-6081	171	12	1680	1680	NUM
ejpam-6081	171	13	2880	2880	NUM
ejpam-6081	171	14	)	)	PUNCT
ejpam-6081	171	15	p1p3	p1p3	ADP
ejpam-6081	171	16	−	−	PROPN
ejpam-6081	171	17	3	3	NUM
ejpam-6081	171	18	2	2	NUM
ejpam-6081	171	19	(	(	PUNCT
ejpam-6081	171	20	2040	2040	NUM
ejpam-6081	171	21	2880	2880	NUM
ejpam-6081	171	22	)	)	PUNCT
ejpam-6081	171	23	p1	p1	NOUN
ejpam-6081	171	24	2p2	2p2	NUM
ejpam-6081	171	25	−	−	PROPN
ejpam-6081	171	26	p4	p4	ADJ
ejpam-6081	171	27	∣∣	∣∣	X
ejpam-6081	171	28	≤	≤	ADV
ejpam-6081	171	29	2	2	NUM
ejpam-6081	171	30	.	.	PUNCT
ejpam-6081	172	1	the	the	DET
ejpam-6081	172	2	upper	upper	ADJ
ejpam-6081	172	3	bounds	bound	NOUN
ejpam-6081	172	4	for	for	ADP
ejpam-6081	172	5	|a2|	|a2|	NOUN
ejpam-6081	172	6	,	,	PUNCT
ejpam-6081	172	7	|a3|	|a3|	NOUN
ejpam-6081	172	8	,	,	PUNCT
ejpam-6081	172	9	|a4|	|a4|	ADJ
ejpam-6081	172	10	,	,	PUNCT
ejpam-6081	172	11	and	and	CCONJ
ejpam-6081	172	12	|a5|	|a5|	VERB
ejpam-6081	172	13	result	result	NOUN
ejpam-6081	172	14	from	from	ADP
ejpam-6081	172	15	applying	apply	VERB
ejpam-6081	172	16	lemmas	lemmas	PROPN
ejpam-6081	172	17	1	1	NUM
ejpam-6081	172	18	-	-	SYM
ejpam-6081	172	19	4	4	NUM
ejpam-6081	172	20	,	,	PUNCT
ejpam-6081	172	21	respectively	respectively	ADV
ejpam-6081	172	22	:	:	PUNCT
ejpam-6081	172	23	|a2|	|a2|	NOUN
ejpam-6081	172	24	≤	≤	X
ejpam-6081	172	25	ταδ	ταδ	ADJ
ejpam-6081	172	26	8	8	NUM
ejpam-6081	172	27	(	(	PUNCT
ejpam-6081	172	28	2	2	NUM
ejpam-6081	172	29	)	)	PUNCT
ejpam-6081	172	30	=	=	VERB
ejpam-6081	172	31	ταδ	ταδ	ADJ
ejpam-6081	172	32	4	4	NUM
ejpam-6081	172	33	,	,	PUNCT
ejpam-6081	172	34	|a3|	|a3|	VERB
ejpam-6081	172	35	≤	≤	NUM
ejpam-6081	172	36	ταδ	ταδ	PROPN
ejpam-6081	172	37	12	12	NUM
ejpam-6081	172	38	(	(	PUNCT
ejpam-6081	172	39	2	2	NUM
ejpam-6081	172	40	)	)	PUNCT
ejpam-6081	172	41	=	=	PRON
ejpam-6081	172	42	ταδ	ταδ	ADJ
ejpam-6081	172	43	6	6	NUM
ejpam-6081	172	44	,	,	PUNCT
ejpam-6081	172	45	|a4|	|a4|	ADJ
ejpam-6081	172	46	≤	≤	NOUN
ejpam-6081	172	47	ταδ	ταδ	ADV
ejpam-6081	172	48	768	768	NUM
ejpam-6081	172	49	(	(	PUNCT
ejpam-6081	172	50	96	96	NUM
ejpam-6081	172	51	)	)	PUNCT
ejpam-6081	172	52	=	=	VERB
ejpam-6081	172	53	ταδ	ταδ	NUM
ejpam-6081	172	54	8	8	NUM
ejpam-6081	172	55	,	,	PUNCT
ejpam-6081	172	56	|a5|	|a5|	VERB
ejpam-6081	172	57	≤	≤	NUM
ejpam-6081	172	58	ταδ	ταδ	NUM
ejpam-6081	172	59	20	20	NUM
ejpam-6081	172	60	(	(	PUNCT
ejpam-6081	172	61	2	2	NUM
ejpam-6081	172	62	)	)	PUNCT
ejpam-6081	172	63	=	=	VERB
ejpam-6081	172	64	ταδ	ταδ	PROPN
ejpam-6081	172	65	10	10	NUM
ejpam-6081	172	66	.	.	PUNCT
ejpam-6081	173	1			NOUN
ejpam-6081	173	2	(	(	PUNCT
ejpam-6081	173	3	29	29	NUM
ejpam-6081	173	4	)	)	PUNCT
ejpam-6081	173	5	thus	thus	ADV
ejpam-6081	173	6	,	,	PUNCT
ejpam-6081	173	7	we	we	PRON
ejpam-6081	173	8	get	get	VERB
ejpam-6081	173	9	the	the	DET
ejpam-6081	173	10	desired	desire	VERB
ejpam-6081	173	11	bound	bind	VERB
ejpam-6081	173	12	.	.	PUNCT
ejpam-6081	174	1	this	this	PRON
ejpam-6081	174	2	completes	complete	VERB
ejpam-6081	174	3	the	the	DET
ejpam-6081	174	4	proof	proof	NOUN
ejpam-6081	174	5	of	of	ADP
ejpam-6081	174	6	theorem	theorem	ADJ
ejpam-6081	174	7	1	1	NUM
ejpam-6081	174	8	.	.	PUNCT
ejpam-6081	174	9	theorem	theorem	NOUN
ejpam-6081	174	10	2	2	NUM
ejpam-6081	174	11	.	.	PUNCT
ejpam-6081	175	1	let	let	VERB
ejpam-6081	175	2	f	f	PROPN
ejpam-6081	175	3	(	(	PUNCT
ejpam-6081	175	4	z	z	NOUN
ejpam-6081	175	5	)	)	PUNCT
ejpam-6081	175	6	∈	∈	PROPN
ejpam-6081	175	7	gg	gg	PROPN
ejpam-6081	175	8	(	(	PUNCT
ejpam-6081	175	9	α	α	PROPN
ejpam-6081	175	10	,	,	PUNCT
ejpam-6081	175	11	δ	δ	PROPN
ejpam-6081	175	12	)	)	PUNCT
ejpam-6081	175	13	.	.	PUNCT
ejpam-6081	176	1	then	then	ADV
ejpam-6081	176	2	|a2|	|a2|	VERB
ejpam-6081	176	3	≤	≤	NUM
ejpam-6081	176	4	ταδ	ταδ	ADJ
ejpam-6081	176	5	4	4	NUM
ejpam-6081	176	6	,	,	PUNCT
ejpam-6081	176	7	|a3|	|a3|	VERB
ejpam-6081	176	8	≤	≤	NUM
ejpam-6081	176	9	ταδ	ταδ	PROPN
ejpam-6081	176	10	6	6	NUM
ejpam-6081	176	11	,	,	PUNCT
ejpam-6081	176	12	|a4|	|a4|	ADJ
ejpam-6081	176	13	≤	≤	NUM
ejpam-6081	176	14	ταδ	ταδ	NUM
ejpam-6081	176	15	24	24	NUM
ejpam-6081	176	16	[	[	X
ejpam-6081	176	17	∣∣5ταδe−iα	∣∣5ταδe−iα	NOUN
ejpam-6081	176	18	+	+	CCONJ
ejpam-6081	176	19	7	7	NUM
ejpam-6081	176	20	∣∣+	∣∣+	NOUN
ejpam-6081	176	21	3	3	NUM
ejpam-6081	176	22	]	]	PUNCT
ejpam-6081	176	23	,	,	PUNCT
ejpam-6081	176	24	where	where	SCONJ
ejpam-6081	176	25	ταδ	ταδ	ADV
ejpam-6081	176	26	=	=	SYM
ejpam-6081	176	27	cosα−	cosα−	PROPN
ejpam-6081	176	28	δ	δ	PROPN
ejpam-6081	176	29	.	.	PUNCT
ejpam-6081	177	1	proof	proof	NOUN
ejpam-6081	177	2	.	.	PUNCT
ejpam-6081	178	1	by	by	ADP
ejpam-6081	178	2	substituting	substitute	VERB
ejpam-6081	178	3	(	(	PUNCT
ejpam-6081	178	4	24	24	NUM
ejpam-6081	178	5	)	)	PUNCT
ejpam-6081	178	6	into	into	ADP
ejpam-6081	178	7	(	(	PUNCT
ejpam-6081	178	8	3)-(5	3)-(5	NUM
ejpam-6081	178	9	)	)	PUNCT
ejpam-6081	178	10	,	,	PUNCT
ejpam-6081	178	11	we	we	PRON
ejpam-6081	178	12	get	get	VERB
ejpam-6081	178	13	a2	a2	PROPN
ejpam-6081	178	14	=	=	PUNCT
ejpam-6081	179	1	−	−	NOUN
ejpam-6081	179	2	ταδe	ταδe	NOUN
ejpam-6081	179	3	−iα	−iα	VERB
ejpam-6081	179	4	8	8	NUM
ejpam-6081	179	5	p1	p1	NOUN
ejpam-6081	179	6	,	,	PUNCT
ejpam-6081	179	7	a3	a3	NOUN
ejpam-6081	179	8	=	=	PUNCT
ejpam-6081	180	1	−	−	PROPN
ejpam-6081	180	2	ταδe	ταδe	NOUN
ejpam-6081	180	3	−iα	−iα	VERB
ejpam-6081	180	4	288	288	NUM
ejpam-6081	180	5	[	[	PUNCT
ejpam-6081	180	6	24p2	24p2	NUM
ejpam-6081	180	7	−	−	PROPN
ejpam-6081	180	8	(	(	PUNCT
ejpam-6081	180	9	14	14	NUM
ejpam-6081	180	10	+	+	CCONJ
ejpam-6081	180	11	9ταδe	9ταδe	NUM
ejpam-6081	180	12	−iα	−iα	NOUN
ejpam-6081	180	13	)	)	PUNCT
ejpam-6081	180	14	p1	p1	NOUN
ejpam-6081	180	15	2	2	NUM
ejpam-6081	180	16	]	]	PUNCT
ejpam-6081	180	17	,	,	PUNCT
ejpam-6081	180	18	a4	a4	NOUN
ejpam-6081	180	19	=	=	SYM
ejpam-6081	180	20	−	−	NOUN
ejpam-6081	181	1	ταδe	ταδe	NOUN
ejpam-6081	181	2	−iα	−iα	VERB
ejpam-6081	181	3	16	16	NUM
ejpam-6081	181	4	[	[	X
ejpam-6081	181	5	(	(	PUNCT
ejpam-6081	181	6	360ταδ	360ταδ	NUM
ejpam-6081	181	7	2e−2iα	2e−2iα	NUM
ejpam-6081	181	8	+	+	CCONJ
ejpam-6081	181	9	1120ταδe	1120ταδe	NUM
ejpam-6081	181	10	−iα	−iα	NOUN
ejpam-6081	181	11	+	+	NUM
ejpam-6081	181	12	816	816	NUM
ejpam-6081	181	13	)	)	PUNCT
ejpam-6081	181	14	p13	p13	NOUN
ejpam-6081	181	15	2304	2304	NUM
ejpam-6081	181	16	+	+	CCONJ
ejpam-6081	181	17	p3	p3	PROPN
ejpam-6081	181	18	−	−	PROPN
ejpam-6081	182	1	(	(	PUNCT
ejpam-6081	182	2	5ταδe	5ταδe	NUM
ejpam-6081	182	3	−iα+7	−iα+7	NUM
ejpam-6081	182	4	6	6	NUM
ejpam-6081	182	5	)	)	PUNCT
ejpam-6081	182	6	p1p2	p1p2	PROPN
ejpam-6081	182	7	]	]	PUNCT
ejpam-6081	182	8	.	.	PUNCT
ejpam-6081	183	1			PROPN
ejpam-6081	183	2	(	(	PUNCT
ejpam-6081	183	3	30	30	NUM
ejpam-6081	183	4	)	)	PUNCT
ejpam-6081	183	5	taking	take	VERB
ejpam-6081	183	6	the	the	DET
ejpam-6081	183	7	modulus	modulus	NOUN
ejpam-6081	183	8	on	on	ADP
ejpam-6081	183	9	both	both	DET
ejpam-6081	183	10	sides	side	NOUN
ejpam-6081	183	11	of	of	ADP
ejpam-6081	183	12	the	the	DET
ejpam-6081	183	13	equations	equation	NOUN
ejpam-6081	183	14	in	in	ADP
ejpam-6081	183	15	(	(	PUNCT
ejpam-6081	183	16	30	30	NUM
ejpam-6081	183	17	)	)	PUNCT
ejpam-6081	183	18	and	and	CCONJ
ejpam-6081	183	19	applying	apply	VERB
ejpam-6081	183	20	lemmas	lemmas	PROPN
ejpam-6081	183	21	1	1	NUM
ejpam-6081	183	22	-	-	SYM
ejpam-6081	183	23	3	3	NUM
ejpam-6081	183	24	,	,	PUNCT
ejpam-6081	183	25	we	we	PRON
ejpam-6081	183	26	can	can	AUX
ejpam-6081	183	27	express	express	VERB
ejpam-6081	183	28	the	the	DET
ejpam-6081	183	29	equations	equation	NOUN
ejpam-6081	183	30	in	in	ADP
ejpam-6081	183	31	(	(	PUNCT
ejpam-6081	183	32	30	30	NUM
ejpam-6081	183	33	)	)	PUNCT
ejpam-6081	183	34	as	as	SCONJ
ejpam-6081	183	35	follows	follow	VERB
ejpam-6081	183	36	:	:	PUNCT
ejpam-6081	183	37	|a2|	|a2|	NOUN
ejpam-6081	183	38	=	=	SYM
ejpam-6081	183	39	∣∣∣∣−ταδe	∣∣∣∣−ταδe	PROPN
ejpam-6081	183	40	−iα	−iα	PROPN
ejpam-6081	183	41	8	8	NUM
ejpam-6081	183	42	p1	p1	PROPN
ejpam-6081	183	43	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6081	183	44	,	,	PUNCT
ejpam-6081	183	45	(	(	PUNCT
ejpam-6081	183	46	31	31	NUM
ejpam-6081	183	47	)	)	PUNCT
ejpam-6081	183	48	|a3|	|a3|	NOUN
ejpam-6081	183	49	=	=	SYM
ejpam-6081	183	50	∣∣∣∣−ταδe	∣∣∣∣−ταδe	PROPN
ejpam-6081	183	51	−iα	−iα	PROPN
ejpam-6081	183	52	288	288	NUM
ejpam-6081	183	53	[	[	PUNCT
ejpam-6081	183	54	24	24	NUM
ejpam-6081	183	55	(	(	PUNCT
ejpam-6081	183	56	p2	p2	PROPN
ejpam-6081	183	57	−	−	PROPN
ejpam-6081	184	1	(	(	PUNCT
ejpam-6081	184	2	14	14	NUM
ejpam-6081	184	3	+	+	CCONJ
ejpam-6081	184	4	9ταδe	9ταδe	NUM
ejpam-6081	184	5	−iα	−iα	NOUN
ejpam-6081	184	6	24	24	NUM
ejpam-6081	184	7	)	)	PUNCT
ejpam-6081	184	8	p1	p1	NOUN
ejpam-6081	184	9	2	2	NUM
ejpam-6081	184	10	)	)	PUNCT
ejpam-6081	184	11	]	]	X
ejpam-6081	184	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6081	184	13	,	,	PUNCT
ejpam-6081	184	14	(	(	PUNCT
ejpam-6081	184	15	32	32	NUM
ejpam-6081	184	16	)	)	PUNCT
ejpam-6081	184	17	|a4|	|a4|	NOUN
ejpam-6081	184	18	=	=	SYM
ejpam-6081	184	19	∣∣∣∣ταδe−iα	∣∣∣∣ταδe−iα	PROPN
ejpam-6081	184	20	16	16	NUM
ejpam-6081	184	21	{	{	PUNCT
ejpam-6081	184	22	p1	p1	NOUN
ejpam-6081	184	23	(	(	PUNCT
ejpam-6081	184	24	5ταδe	5ταδe	NUM
ejpam-6081	184	25	−iα	−iα	NOUN
ejpam-6081	184	26	+	+	NUM
ejpam-6081	184	27	7	7	NUM
ejpam-6081	184	28	6	6	NUM
ejpam-6081	184	29	)	)	PUNCT
ejpam-6081	184	30	[	[	PUNCT
ejpam-6081	184	31	p2	p2	PROPN
ejpam-6081	184	32	−	−	PROPN
ejpam-6081	184	33	(	(	PUNCT
ejpam-6081	184	34	45ταδ	45ταδ	NOUN
ejpam-6081	184	35	2e−2iα	2e−2iα	PROPN
ejpam-6081	184	36	+	+	CCONJ
ejpam-6081	184	37	140ταδe	140ταδe	PROPN
ejpam-6081	184	38	−iα	−iα	NOUN
ejpam-6081	184	39	+	+	NUM
ejpam-6081	184	40	102	102	NUM
ejpam-6081	184	41	240ταδe−iα	240ταδe−iα	NUM
ejpam-6081	185	1	+	+	CCONJ
ejpam-6081	185	2	336	336	NUM
ejpam-6081	185	3	)	)	PUNCT
ejpam-6081	185	4	p1	p1	NOUN
ejpam-6081	185	5	2	2	NUM
ejpam-6081	185	6	]	]	PUNCT
ejpam-6081	185	7	−	−	PROPN
ejpam-6081	185	8	p3	p3	PROPN
ejpam-6081	185	9	}	}	PUNCT
ejpam-6081	185	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6081	185	11	.	.	PUNCT
ejpam-6081	186	1	(	(	PUNCT
ejpam-6081	186	2	33	33	NUM
ejpam-6081	186	3	)	)	PUNCT
ejpam-6081	186	4	n.	n.	PROPN
ejpam-6081	186	5	h.	h.	PROPN
ejpam-6081	186	6	a.	a.	PROPN
ejpam-6081	186	7	a.	a.	PROPN
ejpam-6081	186	8	wahid	wahid	PROPN
ejpam-6081	186	9	,	,	PUNCT
ejpam-6081	186	10	s.	s.	PROPN
ejpam-6081	186	11	c.	c.	PROPN
ejpam-6081	186	12	soh	soh	PROPN
ejpam-6081	186	13	/	/	SYM
ejpam-6081	186	14	eur	eur	PROPN
ejpam-6081	186	15	.	.	PUNCT
ejpam-6081	187	1	j.	j.	PROPN
ejpam-6081	187	2	pure	pure	PROPN
ejpam-6081	187	3	appl	appl	PROPN
ejpam-6081	187	4	.	.	PROPN
ejpam-6081	187	5	math	math	PROPN
ejpam-6081	187	6	,	,	PUNCT
ejpam-6081	187	7	18	18	NUM
ejpam-6081	187	8	(	(	PUNCT
ejpam-6081	187	9	2	2	NUM
ejpam-6081	187	10	)	)	PUNCT
ejpam-6081	187	11	(	(	PUNCT
ejpam-6081	187	12	2025	2025	NUM
ejpam-6081	187	13	)	)	PUNCT
ejpam-6081	187	14	,	,	PUNCT
ejpam-6081	187	15	6081	6081	NUM
ejpam-6081	187	16	9	9	NUM
ejpam-6081	187	17	of	of	ADP
ejpam-6081	187	18	16	16	NUM
ejpam-6081	187	19	it	it	PRON
ejpam-6081	187	20	is	be	AUX
ejpam-6081	187	21	observed	observe	VERB
ejpam-6081	187	22	that	that	SCONJ
ejpam-6081	187	23	|p1|	|p1|	ADV
ejpam-6081	187	24	≤	≤	ADJ
ejpam-6081	187	25	2	2	NUM
ejpam-6081	187	26	,	,	PUNCT
ejpam-6081	187	27	|p3|	|p3|	NOUN
ejpam-6081	187	28	≤	≤	ADV
ejpam-6081	187	29	2,∣∣∣p2	2,∣∣∣p2	NUM
ejpam-6081	187	30	−	−	PROPN
ejpam-6081	187	31	(	(	PUNCT
ejpam-6081	187	32	14	14	NUM
ejpam-6081	187	33	+	+	NOUN
ejpam-6081	187	34	9ταδe	9ταδe	NUM
ejpam-6081	187	35	−iα	−iα	NOUN
ejpam-6081	187	36	24	24	NUM
ejpam-6081	187	37	)	)	PUNCT
ejpam-6081	187	38	p1	p1	NOUN
ejpam-6081	187	39	2	2	NUM
ejpam-6081	187	40	∣∣∣	∣∣∣	NOUN
ejpam-6081	187	41	≤	≤	NOUN
ejpam-6081	187	42	2max	2max	NUM
ejpam-6081	187	43	{	{	PUNCT
ejpam-6081	187	44	1	1	NUM
ejpam-6081	187	45	,	,	PUNCT
ejpam-6081	187	46	∣∣∣2(14	∣∣∣2(14	PROPN
ejpam-6081	187	47	+	+	PROPN
ejpam-6081	187	48	9ταδe	9ταδe	NUM
ejpam-6081	187	49	−iα	−iα	NOUN
ejpam-6081	187	50	24	24	NUM
ejpam-6081	187	51	)	)	PUNCT
ejpam-6081	187	52	−	−	NOUN
ejpam-6081	187	53	1	1	NUM
ejpam-6081	187	54	∣∣∣	∣∣∣	ADJ
ejpam-6081	187	55	}	}	PUNCT
ejpam-6081	187	56	=	=	SYM
ejpam-6081	187	57	2,∣∣∣p2	2,∣∣∣p2	NUM
ejpam-6081	187	58	−	−	PROPN
ejpam-6081	187	59	(	(	PUNCT
ejpam-6081	187	60	45ταδ	45ταδ	NOUN
ejpam-6081	187	61	2e−2iα+140ταδe	2e−2iα+140ταδe	NUM
ejpam-6081	187	62	−iα+102	−iα+102	DET
ejpam-6081	187	63	240ταδe−iα+336	240ταδe−iα+336	NUM
ejpam-6081	187	64	)	)	PUNCT
ejpam-6081	187	65	p1	p1	NOUN
ejpam-6081	187	66	2	2	NUM
ejpam-6081	187	67	∣∣∣	∣∣∣	NOUN
ejpam-6081	187	68	≤	≤	NOUN
ejpam-6081	187	69	2max	2max	NUM
ejpam-6081	187	70	{	{	PUNCT
ejpam-6081	187	71	1	1	NUM
ejpam-6081	187	72	,	,	PUNCT
ejpam-6081	187	73	∣∣∣2(45ταδ	∣∣∣2(45ταδ	PROPN
ejpam-6081	187	74	2e−2iα+140ταδe	2e−2iα+140ταδe	NUM
ejpam-6081	187	75	−iα+102	−iα+102	ADP
ejpam-6081	187	76	240ταδe−iα+336	240ταδe−iα+336	NUM
ejpam-6081	187	77	)	)	PUNCT
ejpam-6081	188	1	−	−	ADP
ejpam-6081	188	2	1	1	NUM
ejpam-6081	188	3	∣∣∣	∣∣∣	ADJ
ejpam-6081	188	4	}	}	PUNCT
ejpam-6081	188	5	=	=	SYM
ejpam-6081	188	6	2	2	NUM
ejpam-6081	188	7	.	.	PUNCT
ejpam-6081	188	8	thus	thus	ADV
ejpam-6081	188	9	,	,	PUNCT
ejpam-6081	188	10	the	the	DET
ejpam-6081	188	11	upper	upper	ADJ
ejpam-6081	188	12	bounds	bound	NOUN
ejpam-6081	188	13	for	for	ADP
ejpam-6081	188	14	|a2|	|a2|	NOUN
ejpam-6081	188	15	and	and	CCONJ
ejpam-6081	188	16	|a3|	|a3|	NOUN
ejpam-6081	188	17	are	be	AUX
ejpam-6081	188	18	obtained	obtain	VERB
ejpam-6081	188	19	by	by	ADP
ejpam-6081	188	20	applying	apply	VERB
ejpam-6081	188	21	lemma	lemma	PROPN
ejpam-6081	188	22	1	1	NUM
ejpam-6081	188	23	and	and	CCONJ
ejpam-6081	188	24	lemma	lemma	PROPN
ejpam-6081	188	25	2	2	NUM
ejpam-6081	188	26	,	,	PUNCT
ejpam-6081	188	27	respectively	respectively	ADV
ejpam-6081	188	28	.	.	PUNCT
ejpam-6081	189	1	meanwhile	meanwhile	ADV
ejpam-6081	189	2	,	,	PUNCT
ejpam-6081	189	3	the	the	DET
ejpam-6081	189	4	bound	bind	VERB
ejpam-6081	189	5	for	for	ADP
ejpam-6081	189	6	|a4|	|a4|	PRON
ejpam-6081	189	7	follows	follow	VERB
ejpam-6081	189	8	from	from	ADP
ejpam-6081	189	9	the	the	DET
ejpam-6081	189	10	combined	combine	VERB
ejpam-6081	189	11	application	application	NOUN
ejpam-6081	189	12	of	of	ADP
ejpam-6081	189	13	lemmas	lemmas	PROPN
ejpam-6081	189	14	1	1	NUM
ejpam-6081	189	15	and	and	CCONJ
ejpam-6081	189	16	2	2	NUM
ejpam-6081	189	17	,	,	PUNCT
ejpam-6081	189	18	along	along	ADP
ejpam-6081	189	19	with	with	ADP
ejpam-6081	189	20	the	the	DET
ejpam-6081	189	21	triangle	triangle	NOUN
ejpam-6081	189	22	inequality	inequality	NOUN
ejpam-6081	189	23	.	.	PUNCT
ejpam-6081	190	1	this	this	PRON
ejpam-6081	190	2	completes	complete	VERB
ejpam-6081	190	3	the	the	DET
ejpam-6081	190	4	proof	proof	NOUN
ejpam-6081	190	5	of	of	ADP
ejpam-6081	190	6	theorem	theorem	NOUN
ejpam-6081	190	7	2	2	NUM
ejpam-6081	190	8	.	.	NOUN
ejpam-6081	190	9	3.2	3.2	NUM
ejpam-6081	190	10	.	.	PUNCT
ejpam-6081	191	1	logarithmic	logarithmic	ADJ
ejpam-6081	191	2	coefficients	coefficient	NOUN
ejpam-6081	191	3	next	next	ADV
ejpam-6081	191	4	,	,	PUNCT
ejpam-6081	191	5	we	we	PRON
ejpam-6081	191	6	estimate	estimate	VERB
ejpam-6081	191	7	the	the	DET
ejpam-6081	191	8	upper	upper	ADJ
ejpam-6081	191	9	bounds	bound	NOUN
ejpam-6081	191	10	of	of	ADP
ejpam-6081	191	11	the	the	DET
ejpam-6081	191	12	logarithmic	logarithmic	ADJ
ejpam-6081	191	13	coefficients	coefficient	NOUN
ejpam-6081	191	14	for	for	ADP
ejpam-6081	191	15	functions	function	NOUN
ejpam-6081	191	16	and	and	CCONJ
ejpam-6081	191	17	their	their	PRON
ejpam-6081	191	18	inverse	inverse	NOUN
ejpam-6081	191	19	functions	function	NOUN
ejpam-6081	191	20	in	in	ADP
ejpam-6081	191	21	the	the	DET
ejpam-6081	191	22	class	class	NOUN
ejpam-6081	191	23	gg	gg	NOUN
ejpam-6081	191	24	(	(	PUNCT
ejpam-6081	191	25	α	α	PROPN
ejpam-6081	191	26	,	,	PUNCT
ejpam-6081	191	27	δ	δ	PROPN
ejpam-6081	191	28	)	)	PUNCT
ejpam-6081	191	29	.	.	PUNCT
ejpam-6081	192	1	theorem	theorem	NOUN
ejpam-6081	192	2	3	3	X
ejpam-6081	192	3	.	.	PUNCT
ejpam-6081	193	1	let	let	VERB
ejpam-6081	193	2	f	f	PROPN
ejpam-6081	193	3	(	(	PUNCT
ejpam-6081	193	4	z	z	NOUN
ejpam-6081	193	5	)	)	PUNCT
ejpam-6081	193	6	∈	∈	PROPN
ejpam-6081	193	7	gg	gg	PROPN
ejpam-6081	193	8	(	(	PUNCT
ejpam-6081	193	9	α	α	PROPN
ejpam-6081	193	10	,	,	PUNCT
ejpam-6081	193	11	δ	δ	PROPN
ejpam-6081	193	12	)	)	PUNCT
ejpam-6081	193	13	.	.	PUNCT
ejpam-6081	194	1	then	then	ADV
ejpam-6081	194	2	|γ1|	|γ1|	PROPN
ejpam-6081	194	3	≤	≤	PROPN
ejpam-6081	194	4	ταδ	ταδ	ADJ
ejpam-6081	194	5	8	8	NUM
ejpam-6081	194	6	,	,	PUNCT
ejpam-6081	194	7	|γ2|	|γ2|	VERB
ejpam-6081	194	8	≤	≤	NUM
ejpam-6081	194	9	ταδ	ταδ	NUM
ejpam-6081	194	10	12	12	NUM
ejpam-6081	194	11	,	,	PUNCT
ejpam-6081	194	12	and	and	CCONJ
ejpam-6081	194	13	|γ3|	|γ3|	PRON
ejpam-6081	194	14	≤	≤	NUM
ejpam-6081	194	15	ταδ	ταδ	ADV
ejpam-6081	194	16	48	48	NUM
ejpam-6081	194	17	[	[	PUNCT
ejpam-6081	194	18	3	3	NUM
ejpam-6081	194	19	+	+	NUM
ejpam-6081	194	20	∣∣ταδe−iα	∣∣ταδe−iα	NOUN
ejpam-6081	194	21	+	+	CCONJ
ejpam-6081	194	22	7	7	NUM
ejpam-6081	194	23	∣∣	∣∣	NOUN
ejpam-6081	194	24	]	]	PUNCT
ejpam-6081	194	25	,	,	PUNCT
ejpam-6081	194	26	where	where	SCONJ
ejpam-6081	194	27	ταδ	ταδ	ADV
ejpam-6081	194	28	=	=	SYM
ejpam-6081	194	29	cosα−	cosα−	PROPN
ejpam-6081	194	30	δ	δ	PROPN
ejpam-6081	194	31	.	.	PUNCT
ejpam-6081	195	1	proof	proof	NOUN
ejpam-6081	195	2	.	.	PUNCT
ejpam-6081	196	1	substituting	substitute	VERB
ejpam-6081	196	2	(	(	PUNCT
ejpam-6081	196	3	24	24	NUM
ejpam-6081	196	4	)	)	PUNCT
ejpam-6081	196	5	into	into	ADP
ejpam-6081	196	6	(	(	PUNCT
ejpam-6081	196	7	9)-(11	9)-(11	NUM
ejpam-6081	196	8	)	)	PUNCT
ejpam-6081	196	9	and	and	CCONJ
ejpam-6081	196	10	simplifying	simplify	VERB
ejpam-6081	196	11	,	,	PUNCT
ejpam-6081	196	12	we	we	PRON
ejpam-6081	196	13	obtain	obtain	VERB
ejpam-6081	196	14	γ1	γ1	NOUN
ejpam-6081	196	15	=	=	SYM
ejpam-6081	196	16	ταδe	ταδe	NOUN
ejpam-6081	196	17	−iα	−iα	PROPN
ejpam-6081	196	18	16	16	NUM
ejpam-6081	196	19	p1	p1	NOUN
ejpam-6081	196	20	,	,	PUNCT
ejpam-6081	196	21	(	(	PUNCT
ejpam-6081	196	22	34	34	NUM
ejpam-6081	196	23	)	)	PUNCT
ejpam-6081	196	24	γ2	γ2	NOUN
ejpam-6081	196	25	=	=	SYM
ejpam-6081	196	26	ταδe	ταδe	PROPN
ejpam-6081	196	27	−iα	−iα	PROPN
ejpam-6081	196	28	2304	2304	NUM
ejpam-6081	196	29	[	[	PUNCT
ejpam-6081	196	30	96p2	96p2	NUM
ejpam-6081	196	31	−	−	NOUN
ejpam-6081	196	32	(	(	PUNCT
ejpam-6081	196	33	57	57	NUM
ejpam-6081	197	1	+	+	SYM
ejpam-6081	197	2	9ταδe	9ταδe	NUM
ejpam-6081	197	3	−iα	−iα	NOUN
ejpam-6081	197	4	)	)	PUNCT
ejpam-6081	197	5	p1	p1	NOUN
ejpam-6081	197	6	2	2	NUM
ejpam-6081	197	7	]	]	PUNCT
ejpam-6081	197	8	,	,	PUNCT
ejpam-6081	197	9	(	(	PUNCT
ejpam-6081	197	10	35	35	NUM
ejpam-6081	197	11	)	)	PUNCT
ejpam-6081	197	12	γ3	γ3	NOUN
ejpam-6081	197	13	=	=	SYM
ejpam-6081	197	14	ταδe	ταδe	PROPN
ejpam-6081	197	15	−iα	−iα	NOUN
ejpam-6081	197	16	9216	9216	NUM
ejpam-6081	197	17	[	[	PUNCT
ejpam-6081	197	18	288p3	288p3	NUM
ejpam-6081	197	19	−	−	NOUN
ejpam-6081	197	20	(	(	PUNCT
ejpam-6081	197	21	48ταδe	48ταδe	NUM
ejpam-6081	197	22	−iα	−iα	NOUN
ejpam-6081	198	1	+	+	NUM
ejpam-6081	198	2	336	336	NUM
ejpam-6081	198	3	)	)	PUNCT
ejpam-6081	199	1	p1p2	p1p2	PROPN
ejpam-6081	199	2	+	+	CCONJ
ejpam-6081	199	3	(	(	PUNCT
ejpam-6081	199	4	3ταδ	3ταδ	PROPN
ejpam-6081	199	5	2e−2iα	2e−2iα	PROPN
ejpam-6081	199	6	+	+	CCONJ
ejpam-6081	200	1	28ταδe	28ταδe	NUM
ejpam-6081	200	2	−iα	−iα	VERB
ejpam-6081	200	3	+	+	NUM
ejpam-6081	200	4	102	102	X
ejpam-6081	200	5	)	)	PUNCT
ejpam-6081	200	6	p1	p1	NOUN
ejpam-6081	200	7	3	3	NUM
ejpam-6081	200	8	]	]	PUNCT
ejpam-6081	200	9	.	.	PUNCT
ejpam-6081	201	1	(	(	PUNCT
ejpam-6081	201	2	36	36	NUM
ejpam-6081	201	3	)	)	PUNCT
ejpam-6081	201	4	using	use	VERB
ejpam-6081	201	5	lemma	lemma	PROPN
ejpam-6081	201	6	1	1	NUM
ejpam-6081	201	7	on	on	ADP
ejpam-6081	201	8	(	(	PUNCT
ejpam-6081	201	9	34	34	NUM
ejpam-6081	201	10	)	)	PUNCT
ejpam-6081	201	11	yields	yield	NOUN
ejpam-6081	201	12	|γ1|	|γ1|	PROPN
ejpam-6081	201	13	≤	≤	NUM
ejpam-6081	201	14	ταδ	ταδ	ADV
ejpam-6081	201	15	16	16	NUM
ejpam-6081	201	16	(	(	PUNCT
ejpam-6081	201	17	2	2	NUM
ejpam-6081	201	18	)	)	PUNCT
ejpam-6081	201	19	=	=	VERB
ejpam-6081	201	20	ταδ	ταδ	NUM
ejpam-6081	201	21	8	8	NUM
ejpam-6081	201	22	.	.	PUNCT
ejpam-6081	202	1	applying	apply	VERB
ejpam-6081	202	2	lemma	lemma	PROPN
ejpam-6081	202	3	2	2	NUM
ejpam-6081	202	4	to	to	ADP
ejpam-6081	202	5	(	(	PUNCT
ejpam-6081	202	6	35	35	NUM
ejpam-6081	202	7	)	)	PUNCT
ejpam-6081	202	8	implies	imply	VERB
ejpam-6081	202	9	that	that	SCONJ
ejpam-6081	202	10	|γ2|	|γ2|	NOUN
ejpam-6081	202	11	=	=	SYM
ejpam-6081	202	12	ταδ	ταδ	PROPN
ejpam-6081	202	13	24	24	NUM
ejpam-6081	202	14	∣∣∣∣p2	∣∣∣∣p2	NOUN
ejpam-6081	203	1	−	−	PROPN
ejpam-6081	204	1	(	(	PUNCT
ejpam-6081	204	2	57	57	NUM
ejpam-6081	204	3	+	+	SYM
ejpam-6081	204	4	9ταδe	9ταδe	NUM
ejpam-6081	204	5	−iα	−iα	NOUN
ejpam-6081	204	6	96	96	NUM
ejpam-6081	204	7	)	)	PUNCT
ejpam-6081	204	8	p1	p1	NOUN
ejpam-6081	204	9	2	2	NUM
ejpam-6081	204	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6081	204	11	≤	≤	NOUN
ejpam-6081	204	12	ταδ	ταδ	NOUN
ejpam-6081	204	13	24	24	NUM
ejpam-6081	204	14	(	(	PUNCT
ejpam-6081	204	15	2	2	NUM
ejpam-6081	204	16	)	)	PUNCT
ejpam-6081	204	17	=	=	VERB
ejpam-6081	204	18	ταδ	ταδ	PROPN
ejpam-6081	204	19	12	12	NUM
ejpam-6081	204	20	.	.	PUNCT
ejpam-6081	205	1	n.	n.	PROPN
ejpam-6081	205	2	h.	h.	PROPN
ejpam-6081	205	3	a.	a.	PROPN
ejpam-6081	205	4	a.	a.	PROPN
ejpam-6081	205	5	wahid	wahid	PROPN
ejpam-6081	205	6	,	,	PUNCT
ejpam-6081	205	7	s.	s.	PROPN
ejpam-6081	205	8	c.	c.	PROPN
ejpam-6081	205	9	soh	soh	PROPN
ejpam-6081	205	10	/	/	SYM
ejpam-6081	205	11	eur	eur	PROPN
ejpam-6081	205	12	.	.	PUNCT
ejpam-6081	206	1	j.	j.	PROPN
ejpam-6081	206	2	pure	pure	PROPN
ejpam-6081	206	3	appl	appl	PROPN
ejpam-6081	206	4	.	.	PROPN
ejpam-6081	206	5	math	math	PROPN
ejpam-6081	206	6	,	,	PUNCT
ejpam-6081	206	7	18	18	NUM
ejpam-6081	206	8	(	(	PUNCT
ejpam-6081	206	9	2	2	NUM
ejpam-6081	206	10	)	)	PUNCT
ejpam-6081	206	11	(	(	PUNCT
ejpam-6081	206	12	2025	2025	NUM
ejpam-6081	206	13	)	)	PUNCT
ejpam-6081	206	14	,	,	PUNCT
ejpam-6081	206	15	6081	6081	NUM
ejpam-6081	206	16	10	10	NUM
ejpam-6081	206	17	of	of	ADP
ejpam-6081	206	18	16	16	NUM
ejpam-6081	206	19	now	now	ADV
ejpam-6081	206	20	,	,	PUNCT
ejpam-6081	206	21	by	by	ADP
ejpam-6081	206	22	rearranging	rearrange	VERB
ejpam-6081	206	23	the	the	DET
ejpam-6081	206	24	terms	term	NOUN
ejpam-6081	206	25	in	in	ADP
ejpam-6081	206	26	(	(	PUNCT
ejpam-6081	206	27	36	36	NUM
ejpam-6081	206	28	)	)	PUNCT
ejpam-6081	206	29	,	,	PUNCT
ejpam-6081	206	30	we	we	PRON
ejpam-6081	206	31	can	can	AUX
ejpam-6081	206	32	rewrite	rewrite	VERB
ejpam-6081	206	33	it	it	PRON
ejpam-6081	206	34	as	as	ADP
ejpam-6081	206	35	|γ3|	|γ3|	NOUN
ejpam-6081	206	36	=	=	SYM
ejpam-6081	206	37	∣∣∣∣ταδe−iα	∣∣∣∣ταδe−iα	ADJ
ejpam-6081	206	38	9216	9216	NUM
ejpam-6081	206	39	{	{	PUNCT
ejpam-6081	206	40	288p3	288p3	NUM
ejpam-6081	206	41	−	−	PROPN
ejpam-6081	206	42	(	(	PUNCT
ejpam-6081	206	43	48ταδe	48ταδe	NUM
ejpam-6081	206	44	−iα	−iα	NOUN
ejpam-6081	206	45	+	+	NUM
ejpam-6081	206	46	336	336	NUM
ejpam-6081	206	47	)	)	PUNCT
ejpam-6081	206	48	p1	p1	NOUN
ejpam-6081	206	49	[	[	PUNCT
ejpam-6081	206	50	p2	p2	PROPN
ejpam-6081	206	51	−	−	PROPN
ejpam-6081	207	1	(	(	PUNCT
ejpam-6081	207	2	3ταδ	3ταδ	PROPN
ejpam-6081	207	3	2e−2iα	2e−2iα	PROPN
ejpam-6081	207	4	+	+	CCONJ
ejpam-6081	208	1	28ταδe	28ταδe	NUM
ejpam-6081	208	2	−iα	−iα	VERB
ejpam-6081	208	3	+	+	NUM
ejpam-6081	208	4	102	102	NUM
ejpam-6081	208	5	48ταδe−iα	48ταδe−iα	NUM
ejpam-6081	209	1	+	+	CCONJ
ejpam-6081	209	2	336	336	NUM
ejpam-6081	209	3	)	)	PUNCT
ejpam-6081	209	4	p1	p1	NOUN
ejpam-6081	209	5	2	2	NUM
ejpam-6081	209	6	]	]	PUNCT
ejpam-6081	209	7	}	}	PUNCT
ejpam-6081	209	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6081	209	9	.	.	PUNCT
ejpam-6081	210	1	consequently	consequently	ADV
ejpam-6081	210	2	,	,	PUNCT
ejpam-6081	210	3	by	by	ADP
ejpam-6081	210	4	applying	apply	VERB
ejpam-6081	210	5	lemmas	lemmas	PROPN
ejpam-6081	210	6	1	1	NUM
ejpam-6081	210	7	and	and	CCONJ
ejpam-6081	210	8	2	2	NUM
ejpam-6081	210	9	,	,	PUNCT
ejpam-6081	210	10	along	along	ADP
ejpam-6081	210	11	with	with	ADP
ejpam-6081	210	12	the	the	DET
ejpam-6081	210	13	triangle	triangle	NOUN
ejpam-6081	210	14	inequality	inequality	NOUN
ejpam-6081	210	15	,	,	PUNCT
ejpam-6081	210	16	and	and	CCONJ
ejpam-6081	210	17	simplifying	simplifying	NOUN
ejpam-6081	210	18	,	,	PUNCT
ejpam-6081	210	19	we	we	PRON
ejpam-6081	210	20	obtain	obtain	VERB
ejpam-6081	210	21	|γ3|	|γ3|	NOUN
ejpam-6081	210	22	≤	≤	NUM
ejpam-6081	210	23	ταδ	ταδ	ADV
ejpam-6081	210	24	48	48	NUM
ejpam-6081	210	25	[	[	PUNCT
ejpam-6081	210	26	3	3	NUM
ejpam-6081	210	27	+	+	NUM
ejpam-6081	210	28	∣∣ταδe−iα	∣∣ταδe−iα	NOUN
ejpam-6081	210	29	+	+	CCONJ
ejpam-6081	210	30	7	7	NUM
ejpam-6081	210	31	∣∣	∣∣	NOUN
ejpam-6081	210	32	]	]	PUNCT
ejpam-6081	210	33	.	.	PUNCT
ejpam-6081	211	1	this	this	PRON
ejpam-6081	211	2	completes	complete	VERB
ejpam-6081	211	3	the	the	DET
ejpam-6081	211	4	proof	proof	NOUN
ejpam-6081	211	5	of	of	ADP
ejpam-6081	211	6	theorem	theorem	ADJ
ejpam-6081	211	7	3	3	NUM
ejpam-6081	211	8	.	.	PUNCT
ejpam-6081	211	9	theorem	theorem	NOUN
ejpam-6081	211	10	4	4	NUM
ejpam-6081	211	11	.	.	PUNCT
ejpam-6081	212	1	let	let	VERB
ejpam-6081	212	2	f	f	PROPN
ejpam-6081	212	3	(	(	PUNCT
ejpam-6081	212	4	z	z	NOUN
ejpam-6081	212	5	)	)	PUNCT
ejpam-6081	212	6	∈	∈	PROPN
ejpam-6081	212	7	gg	gg	PROPN
ejpam-6081	212	8	(	(	PUNCT
ejpam-6081	212	9	α	α	PROPN
ejpam-6081	212	10	,	,	PUNCT
ejpam-6081	212	11	δ	δ	PROPN
ejpam-6081	212	12	)	)	PUNCT
ejpam-6081	212	13	.	.	PUNCT
ejpam-6081	213	1	then	then	ADV
ejpam-6081	213	2	|γ1|	|γ1|	PROPN
ejpam-6081	213	3	≤	≤	PROPN
ejpam-6081	213	4	ταδ	ταδ	ADJ
ejpam-6081	213	5	8	8	NUM
ejpam-6081	213	6	,	,	PUNCT
ejpam-6081	213	7	|γ2|	|γ2|	VERB
ejpam-6081	213	8	≤	≤	NUM
ejpam-6081	213	9	ταδ	ταδ	NUM
ejpam-6081	213	10	12	12	NUM
ejpam-6081	213	11	,	,	PUNCT
ejpam-6081	213	12	and	and	CCONJ
ejpam-6081	213	13	|γ3|	|γ3|	PRON
ejpam-6081	213	14	≤	≤	NUM
ejpam-6081	213	15	ταδ	ταδ	ADV
ejpam-6081	213	16	48	48	NUM
ejpam-6081	213	17	[	[	PUNCT
ejpam-6081	213	18	3	3	NUM
ejpam-6081	213	19	+	+	CCONJ
ejpam-6081	213	20	∣∣4ταδe−iα	∣∣4ταδe−iα	ADJ
ejpam-6081	213	21	+	+	CCONJ
ejpam-6081	213	22	7	7	NUM
ejpam-6081	213	23	∣∣	∣∣	NOUN
ejpam-6081	213	24	]	]	PUNCT
ejpam-6081	213	25	,	,	PUNCT
ejpam-6081	213	26	where	where	SCONJ
ejpam-6081	213	27	ταδ	ταδ	ADV
ejpam-6081	213	28	=	=	SYM
ejpam-6081	213	29	cosα−	cosα−	PROPN
ejpam-6081	213	30	δ	δ	PROPN
ejpam-6081	213	31	.	.	PUNCT
ejpam-6081	214	1	proof	proof	NOUN
ejpam-6081	214	2	.	.	PUNCT
ejpam-6081	215	1	substituting	substitute	VERB
ejpam-6081	215	2	(	(	PUNCT
ejpam-6081	215	3	24	24	NUM
ejpam-6081	215	4	)	)	PUNCT
ejpam-6081	215	5	into	into	ADP
ejpam-6081	215	6	(	(	PUNCT
ejpam-6081	215	7	12)-(14	12)-(14	NUM
ejpam-6081	215	8	)	)	PUNCT
ejpam-6081	215	9	,	,	PUNCT
ejpam-6081	215	10	we	we	PRON
ejpam-6081	215	11	have	have	VERB
ejpam-6081	215	12	γ1	γ1	NOUN
ejpam-6081	215	13	=	=	SYM
ejpam-6081	215	14	−ταδe	−ταδe	PROPN
ejpam-6081	215	15	−iα	−iα	PROPN
ejpam-6081	215	16	16	16	NUM
ejpam-6081	215	17	p1	p1	NOUN
ejpam-6081	215	18	,	,	PUNCT
ejpam-6081	215	19	(	(	PUNCT
ejpam-6081	215	20	37	37	NUM
ejpam-6081	215	21	)	)	PUNCT
ejpam-6081	215	22	γ2	γ2	NOUN
ejpam-6081	215	23	=	=	PUNCT
ejpam-6081	216	1	−	−	NOUN
ejpam-6081	216	2	ταδe	ταδe	NOUN
ejpam-6081	216	3	−iα	−iα	PROPN
ejpam-6081	216	4	2304	2304	NUM
ejpam-6081	216	5	[	[	PUNCT
ejpam-6081	216	6	96p2	96p2	NUM
ejpam-6081	216	7	−	−	PROPN
ejpam-6081	216	8	(	(	PUNCT
ejpam-6081	216	9	27ταδe	27ταδe	NUM
ejpam-6081	216	10	−iα	−iα	NOUN
ejpam-6081	216	11	+	+	NUM
ejpam-6081	216	12	56	56	X
ejpam-6081	216	13	)	)	PUNCT
ejpam-6081	216	14	p1	p1	NOUN
ejpam-6081	216	15	2	2	NUM
ejpam-6081	216	16	]	]	PUNCT
ejpam-6081	216	17	=	=	PUNCT
ejpam-6081	217	1	−	−	NOUN
ejpam-6081	217	2	ταδe	ταδe	NOUN
ejpam-6081	217	3	−iα	−iα	NOUN
ejpam-6081	217	4	24	24	NUM
ejpam-6081	217	5	[	[	PUNCT
ejpam-6081	217	6	p2	p2	X
ejpam-6081	217	7	−	−	PROPN
ejpam-6081	217	8	(	(	PUNCT
ejpam-6081	217	9	27ταδe	27ταδe	NUM
ejpam-6081	217	10	−iα+56	−iα+56	PROPN
ejpam-6081	217	11	96	96	NUM
ejpam-6081	217	12	)	)	PUNCT
ejpam-6081	217	13	p1	p1	NOUN
ejpam-6081	217	14	2	2	NUM
ejpam-6081	217	15	]	]	PUNCT
ejpam-6081	217	16	,	,	PUNCT
ejpam-6081	217	17	(	(	PUNCT
ejpam-6081	217	18	38	38	NUM
ejpam-6081	217	19	)	)	PUNCT
ejpam-6081	217	20	γ3	γ3	NOUN
ejpam-6081	217	21	=	=	PUNCT
ejpam-6081	217	22	−	−	NOUN
ejpam-6081	218	1	ταδe	ταδe	NOUN
ejpam-6081	218	2	−iα	−iα	VERB
ejpam-6081	218	3	4608	4608	NUM
ejpam-6081	218	4	[	[	X
ejpam-6081	218	5	(	(	PUNCT
ejpam-6081	218	6	51	51	NUM
ejpam-6081	218	7	+	+	NUM
ejpam-6081	218	8	56ταδe	56ταδe	NUM
ejpam-6081	218	9	−iα	−iα	NOUN
ejpam-6081	218	10	+	+	NUM
ejpam-6081	218	11	15ταδ	15ταδ	PROPN
ejpam-6081	218	12	2e−2iα	2e−2iα	NUM
ejpam-6081	218	13	)	)	PUNCT
ejpam-6081	218	14	p1	p1	NOUN
ejpam-6081	218	15	3	3	NUM
ejpam-6081	218	16	−	−	NOUN
ejpam-6081	218	17	(	(	PUNCT
ejpam-6081	218	18	168	168	NUM
ejpam-6081	218	19	+	+	CCONJ
ejpam-6081	218	20	96ταδe	96ταδe	NUM
ejpam-6081	218	21	−iα	−iα	NOUN
ejpam-6081	218	22	)	)	PUNCT
ejpam-6081	219	1	p1p2	p1p2	PROPN
ejpam-6081	219	2	+	+	NOUN
ejpam-6081	219	3	144p3	144p3	NUM
ejpam-6081	219	4	]	]	PUNCT
ejpam-6081	220	1	=	=	PUNCT
ejpam-6081	220	2	−	−	NOUN
ejpam-6081	220	3	ταδe	ταδe	NOUN
ejpam-6081	220	4	−iα	−iα	PROPN
ejpam-6081	220	5	4608	4608	NUM
ejpam-6081	220	6	{	{	PUNCT
ejpam-6081	220	7	−p1	−p1	PROPN
ejpam-6081	220	8	(	(	PUNCT
ejpam-6081	220	9	168	168	NUM
ejpam-6081	220	10	+	+	CCONJ
ejpam-6081	220	11	96ταδe	96ταδe	NUM
ejpam-6081	220	12	−iα	−iα	NOUN
ejpam-6081	220	13	)	)	PUNCT
ejpam-6081	220	14	[	[	PUNCT
ejpam-6081	220	15	p2	p2	PROPN
ejpam-6081	220	16	−	−	PROPN
ejpam-6081	220	17	(	(	PUNCT
ejpam-6081	220	18	51	51	NUM
ejpam-6081	220	19	+	+	NUM
ejpam-6081	220	20	56ταδe	56ταδe	NUM
ejpam-6081	220	21	−iα+15ταδ	−iα+15ταδ	PROPN
ejpam-6081	220	22	2e−2iα	2e−2iα	PROPN
ejpam-6081	220	23	168	168	NUM
ejpam-6081	220	24	+	+	SYM
ejpam-6081	220	25	96ταδe−iα	96ταδe−iα	NUM
ejpam-6081	220	26	)	)	PUNCT
ejpam-6081	221	1	p1	p1	NOUN
ejpam-6081	221	2	2	2	NUM
ejpam-6081	221	3	]	]	PUNCT
ejpam-6081	221	4	+	+	CCONJ
ejpam-6081	221	5	144p3	144p3	NUM
ejpam-6081	221	6	}	}	PUNCT
ejpam-6081	221	7	.	.	PUNCT
ejpam-6081	222	1	(	(	PUNCT
ejpam-6081	222	2	39	39	NUM
ejpam-6081	222	3	)	)	PUNCT
ejpam-6081	222	4	the	the	DET
ejpam-6081	222	5	bounds	bound	NOUN
ejpam-6081	222	6	for	for	ADP
ejpam-6081	222	7	|γ1|	|γ1|	NOUN
ejpam-6081	222	8	and	and	CCONJ
ejpam-6081	222	9	|γ2|	|γ2|	NOUN
ejpam-6081	222	10	follow	follow	VERB
ejpam-6081	222	11	from	from	ADP
ejpam-6081	222	12	lemma	lemma	PROPN
ejpam-6081	222	13	1	1	NUM
ejpam-6081	222	14	and	and	CCONJ
ejpam-6081	222	15	lemma	lemma	PROPN
ejpam-6081	222	16	2	2	NUM
ejpam-6081	222	17	,	,	PUNCT
ejpam-6081	222	18	respectively	respectively	ADV
ejpam-6081	222	19	.	.	PUNCT
ejpam-6081	223	1	meanwhile	meanwhile	ADV
ejpam-6081	223	2	,	,	PUNCT
ejpam-6081	223	3	the	the	DET
ejpam-6081	223	4	bound	bind	VERB
ejpam-6081	223	5	for	for	ADP
ejpam-6081	223	6	|γ3|	|γ3|	NOUN
ejpam-6081	223	7	results	result	NOUN
ejpam-6081	223	8	from	from	ADP
ejpam-6081	223	9	applying	apply	VERB
ejpam-6081	223	10	both	both	CCONJ
ejpam-6081	223	11	lemmas	lemmas	PROPN
ejpam-6081	223	12	1	1	NUM
ejpam-6081	223	13	and	and	CCONJ
ejpam-6081	223	14	2	2	NUM
ejpam-6081	223	15	,	,	PUNCT
ejpam-6081	223	16	along	along	ADP
ejpam-6081	223	17	with	with	ADP
ejpam-6081	223	18	the	the	DET
ejpam-6081	223	19	triangle	triangle	NOUN
ejpam-6081	223	20	inequality	inequality	NOUN
ejpam-6081	223	21	.	.	PUNCT
ejpam-6081	224	1	this	this	PRON
ejpam-6081	224	2	completes	complete	VERB
ejpam-6081	224	3	the	the	DET
ejpam-6081	224	4	proof	proof	NOUN
ejpam-6081	224	5	of	of	ADP
ejpam-6081	224	6	theorem	theorem	ADJ
ejpam-6081	224	7	4	4	NUM
ejpam-6081	224	8	.	.	NOUN
ejpam-6081	224	9	3.3	3.3	NUM
ejpam-6081	224	10	.	.	PUNCT
ejpam-6081	225	1	vandermonde	vandermonde	VERB
ejpam-6081	225	2	determinant	determinant	ADJ
ejpam-6081	225	3	of	of	ADP
ejpam-6081	225	4	taylor	taylor	PROPN
ejpam-6081	225	5	coefficients	coefficient	NOUN
ejpam-6081	225	6	in	in	ADP
ejpam-6081	225	7	this	this	DET
ejpam-6081	225	8	subsection	subsection	NOUN
ejpam-6081	225	9	,	,	PUNCT
ejpam-6081	225	10	we	we	PRON
ejpam-6081	225	11	use	use	VERB
ejpam-6081	225	12	the	the	DET
ejpam-6081	225	13	results	result	NOUN
ejpam-6081	225	14	of	of	ADP
ejpam-6081	225	15	theorems	theorem	NOUN
ejpam-6081	225	16	1	1	NUM
ejpam-6081	225	17	and	and	CCONJ
ejpam-6081	225	18	2	2	NUM
ejpam-6081	225	19	to	to	PART
ejpam-6081	225	20	estimate	estimate	VERB
ejpam-6081	225	21	the	the	DET
ejpam-6081	225	22	upper	upper	ADJ
ejpam-6081	225	23	bounds	bound	NOUN
ejpam-6081	225	24	of	of	ADP
ejpam-6081	225	25	the	the	DET
ejpam-6081	225	26	vandermonde	vandermonde	NOUN
ejpam-6081	225	27	determinant	determinant	ADJ
ejpam-6081	225	28	of	of	ADP
ejpam-6081	225	29	second	second	ADJ
ejpam-6081	225	30	-	-	PUNCT
ejpam-6081	225	31	order	order	NOUN
ejpam-6081	225	32	,	,	PUNCT
ejpam-6081	225	33	where	where	SCONJ
ejpam-6081	225	34	the	the	DET
ejpam-6081	225	35	entries	entry	NOUN
ejpam-6081	225	36	are	be	AUX
ejpam-6081	225	37	taylor	taylor	PROPN
ejpam-6081	225	38	coefficients	coefficient	NOUN
ejpam-6081	225	39	of	of	ADP
ejpam-6081	225	40	functions	function	NOUN
ejpam-6081	225	41	and	and	CCONJ
ejpam-6081	225	42	inverse	inverse	NOUN
ejpam-6081	225	43	functions	function	NOUN
ejpam-6081	225	44	in	in	ADP
ejpam-6081	225	45	gg	gg	PROPN
ejpam-6081	225	46	(	(	PUNCT
ejpam-6081	225	47	α	α	PROPN
ejpam-6081	225	48	,	,	PUNCT
ejpam-6081	225	49	δ	δ	PROPN
ejpam-6081	225	50	)	)	PUNCT
ejpam-6081	225	51	,	,	PUNCT
ejpam-6081	225	52	that	that	ADV
ejpam-6081	225	53	is	is	ADV
ejpam-6081	225	54	,	,	PUNCT
ejpam-6081	225	55	|v2,2	|v2,2	PROPN
ejpam-6081	225	56	(	(	PUNCT
ejpam-6081	225	57	f)|	f)|	VERB
ejpam-6081	225	58	and	and	CCONJ
ejpam-6081	225	59	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	225	60	(	(	PUNCT
ejpam-6081	225	61	f−1	f−1	PROPN
ejpam-6081	225	62	)	)	PUNCT
ejpam-6081	225	63	∣∣.	∣∣.	PROPN
ejpam-6081	225	64	n.	n.	PROPN
ejpam-6081	225	65	h.	h.	PROPN
ejpam-6081	225	66	a.	a.	PROPN
ejpam-6081	225	67	a.	a.	PROPN
ejpam-6081	225	68	wahid	wahid	PROPN
ejpam-6081	225	69	,	,	PUNCT
ejpam-6081	225	70	s.	s.	PROPN
ejpam-6081	225	71	c.	c.	PROPN
ejpam-6081	225	72	soh	soh	PROPN
ejpam-6081	225	73	/	/	SYM
ejpam-6081	225	74	eur	eur	PROPN
ejpam-6081	225	75	.	.	PUNCT
ejpam-6081	226	1	j.	j.	PROPN
ejpam-6081	226	2	pure	pure	PROPN
ejpam-6081	226	3	appl	appl	PROPN
ejpam-6081	226	4	.	.	PROPN
ejpam-6081	226	5	math	math	PROPN
ejpam-6081	226	6	,	,	PUNCT
ejpam-6081	226	7	18	18	NUM
ejpam-6081	226	8	(	(	PUNCT
ejpam-6081	226	9	2	2	NUM
ejpam-6081	226	10	)	)	PUNCT
ejpam-6081	226	11	(	(	PUNCT
ejpam-6081	226	12	2025	2025	NUM
ejpam-6081	226	13	)	)	PUNCT
ejpam-6081	226	14	,	,	PUNCT
ejpam-6081	226	15	6081	6081	NUM
ejpam-6081	226	16	11	11	NUM
ejpam-6081	226	17	of	of	ADP
ejpam-6081	226	18	16	16	NUM
ejpam-6081	226	19	theorem	theorem	NOUN
ejpam-6081	226	20	5	5	NUM
ejpam-6081	226	21	.	.	PUNCT
ejpam-6081	227	1	let	let	VERB
ejpam-6081	227	2	f	f	PROPN
ejpam-6081	227	3	(	(	PUNCT
ejpam-6081	227	4	z	z	NOUN
ejpam-6081	227	5	)	)	PUNCT
ejpam-6081	227	6	∈	∈	PROPN
ejpam-6081	227	7	gg	gg	PROPN
ejpam-6081	227	8	(	(	PUNCT
ejpam-6081	227	9	α	α	PROPN
ejpam-6081	227	10	,	,	PUNCT
ejpam-6081	227	11	δ	δ	PROPN
ejpam-6081	227	12	)	)	PUNCT
ejpam-6081	227	13	.	.	PUNCT
ejpam-6081	228	1	then	then	ADV
ejpam-6081	228	2	|v2,2	|v2,2	PROPN
ejpam-6081	228	3	(	(	PUNCT
ejpam-6081	228	4	f)|	f)|	VERB
ejpam-6081	228	5	≤	≤	NUM
ejpam-6081	228	6	5ταδ	5ταδ	NUM
ejpam-6081	228	7	12	12	NUM
ejpam-6081	228	8	,	,	PUNCT
ejpam-6081	228	9	where	where	SCONJ
ejpam-6081	228	10	ταδ	ταδ	ADV
ejpam-6081	228	11	=	=	SYM
ejpam-6081	228	12	cosα−	cosα−	PROPN
ejpam-6081	228	13	δ	δ	PROPN
ejpam-6081	228	14	.	.	PUNCT
ejpam-6081	229	1	proof	proof	NOUN
ejpam-6081	229	2	.	.	PUNCT
ejpam-6081	230	1	in	in	ADP
ejpam-6081	230	2	view	view	NOUN
ejpam-6081	230	3	of	of	ADP
ejpam-6081	230	4	(	(	PUNCT
ejpam-6081	230	5	15	15	NUM
ejpam-6081	230	6	)	)	PUNCT
ejpam-6081	230	7	,	,	PUNCT
ejpam-6081	230	8	we	we	PRON
ejpam-6081	230	9	can	can	AUX
ejpam-6081	230	10	establish	establish	VERB
ejpam-6081	230	11	|v2,2	|v2,2	NOUN
ejpam-6081	230	12	(	(	PUNCT
ejpam-6081	230	13	f)|	f)|	VERB
ejpam-6081	230	14	=	=	PUNCT
ejpam-6081	230	15	|a3	|a3	NOUN
ejpam-6081	230	16	−	−	PROPN
ejpam-6081	230	17	a2|	a2|	PROPN
ejpam-6081	230	18	≤	≤	PROPN
ejpam-6081	230	19	|a3|+	|a3|+	PRON
ejpam-6081	230	20	|a2|	|a2|	NOUN
ejpam-6081	230	21	.	.	PUNCT
ejpam-6081	231	1	(	(	PUNCT
ejpam-6081	231	2	40	40	NUM
ejpam-6081	231	3	)	)	PUNCT
ejpam-6081	231	4	using	use	VERB
ejpam-6081	231	5	|a2|	|a2|	NOUN
ejpam-6081	231	6	≤	≤	NUM
ejpam-6081	231	7	ταδ	ταδ	ADV
ejpam-6081	231	8	4	4	NUM
ejpam-6081	231	9	and	and	CCONJ
ejpam-6081	231	10	|a3|	|a3|	VERB
ejpam-6081	231	11	≤	≤	NUM
ejpam-6081	231	12	ταδ	ταδ	PROPN
ejpam-6081	231	13	6	6	NUM
ejpam-6081	231	14	from	from	ADP
ejpam-6081	231	15	theorem	theorem	ADJ
ejpam-6081	231	16	1	1	NUM
ejpam-6081	231	17	,	,	PUNCT
ejpam-6081	231	18	we	we	PRON
ejpam-6081	231	19	obtain	obtain	VERB
ejpam-6081	231	20	|v2,2	|v2,2	NOUN
ejpam-6081	231	21	(	(	PUNCT
ejpam-6081	231	22	f)|	f)|	VERB
ejpam-6081	231	23	≤	≤	NUM
ejpam-6081	231	24	ταδ	ταδ	ADV
ejpam-6081	231	25	6	6	NUM
ejpam-6081	231	26	+	+	CCONJ
ejpam-6081	231	27	ταδ	ταδ	PROPN
ejpam-6081	231	28	4	4	NUM
ejpam-6081	231	29	=	=	SYM
ejpam-6081	231	30	5ταδ	5ταδ	NUM
ejpam-6081	231	31	12	12	NUM
ejpam-6081	231	32	.	.	PUNCT
ejpam-6081	232	1	(	(	PUNCT
ejpam-6081	232	2	41	41	NUM
ejpam-6081	232	3	)	)	PUNCT
ejpam-6081	232	4	thus	thus	ADV
ejpam-6081	232	5	,	,	PUNCT
ejpam-6081	232	6	we	we	PRON
ejpam-6081	232	7	get	get	VERB
ejpam-6081	232	8	the	the	DET
ejpam-6081	232	9	desired	desire	VERB
ejpam-6081	232	10	inequality	inequality	NOUN
ejpam-6081	232	11	,	,	PUNCT
ejpam-6081	232	12	thereby	thereby	ADV
ejpam-6081	232	13	completing	complete	VERB
ejpam-6081	232	14	the	the	DET
ejpam-6081	232	15	proof	proof	NOUN
ejpam-6081	232	16	of	of	ADP
ejpam-6081	232	17	theorem	theorem	ADJ
ejpam-6081	232	18	5	5	NUM
ejpam-6081	232	19	.	.	PUNCT
ejpam-6081	232	20	theorem	theorem	NOUN
ejpam-6081	232	21	6	6	NUM
ejpam-6081	232	22	.	.	PUNCT
ejpam-6081	233	1	let	let	VERB
ejpam-6081	233	2	f	f	PROPN
ejpam-6081	233	3	(	(	PUNCT
ejpam-6081	233	4	z	z	NOUN
ejpam-6081	233	5	)	)	PUNCT
ejpam-6081	233	6	∈	∈	PROPN
ejpam-6081	233	7	gg	gg	PROPN
ejpam-6081	233	8	(	(	PUNCT
ejpam-6081	233	9	α	α	PROPN
ejpam-6081	233	10	,	,	PUNCT
ejpam-6081	233	11	δ	δ	PROPN
ejpam-6081	233	12	)	)	PUNCT
ejpam-6081	233	13	.	.	PUNCT
ejpam-6081	234	1	then∣∣v2,2	then∣∣v2,2	NOUN
ejpam-6081	234	2	(	(	PUNCT
ejpam-6081	234	3	f−1	f−1	PROPN
ejpam-6081	234	4	)	)	PUNCT
ejpam-6081	234	5	∣∣	∣∣	X
ejpam-6081	234	6	≤	≤	NUM
ejpam-6081	235	1	5ταδ	5ταδ	NUM
ejpam-6081	235	2	12	12	NUM
ejpam-6081	235	3	,	,	PUNCT
ejpam-6081	235	4	where	where	SCONJ
ejpam-6081	235	5	ταδ	ταδ	ADV
ejpam-6081	235	6	=	=	SYM
ejpam-6081	235	7	cosα−	cosα−	PROPN
ejpam-6081	235	8	δ	δ	PROPN
ejpam-6081	235	9	.	.	PUNCT
ejpam-6081	236	1	proof	proof	NOUN
ejpam-6081	236	2	.	.	PUNCT
ejpam-6081	237	1	from	from	ADP
ejpam-6081	237	2	(	(	PUNCT
ejpam-6081	237	3	17	17	NUM
ejpam-6081	237	4	)	)	PUNCT
ejpam-6081	237	5	,	,	PUNCT
ejpam-6081	237	6	we	we	PRON
ejpam-6081	237	7	can	can	AUX
ejpam-6081	237	8	establish∣∣v2,2	establish∣∣v2,2	PROPN
ejpam-6081	237	9	(	(	PUNCT
ejpam-6081	237	10	f−1	f−1	PROPN
ejpam-6081	237	11	)	)	PUNCT
ejpam-6081	237	12	∣∣	∣∣	X
ejpam-6081	237	13	=	=	PUNCT
ejpam-6081	237	14	|a3	|a3	PROPN
ejpam-6081	237	15	−a2|	−a2|	PROPN
ejpam-6081	237	16	≤	≤	PROPN
ejpam-6081	237	17	|a3|+	|a3|+	PROPN
ejpam-6081	237	18	|a2|	|a2|	NOUN
ejpam-6081	237	19	.	.	PUNCT
ejpam-6081	238	1	(	(	PUNCT
ejpam-6081	238	2	42	42	X
ejpam-6081	238	3	)	)	PUNCT
ejpam-6081	238	4	making	make	VERB
ejpam-6081	238	5	use	use	NOUN
ejpam-6081	238	6	of	of	ADP
ejpam-6081	238	7	|a2|	|a2|	NOUN
ejpam-6081	238	8	≤	≤	NUM
ejpam-6081	238	9	ταδ	ταδ	ADV
ejpam-6081	238	10	4	4	NUM
ejpam-6081	238	11	and	and	CCONJ
ejpam-6081	238	12	|a3|	|a3|	VERB
ejpam-6081	238	13	≤	≤	NUM
ejpam-6081	238	14	ταδ	ταδ	PROPN
ejpam-6081	238	15	6	6	NUM
ejpam-6081	238	16	from	from	ADP
ejpam-6081	238	17	theorem	theorem	NOUN
ejpam-6081	238	18	2	2	NUM
ejpam-6081	238	19	,	,	PUNCT
ejpam-6081	238	20	we	we	PRON
ejpam-6081	238	21	get∣∣v2,2	get∣∣v2,2	PROPN
ejpam-6081	238	22	(	(	PUNCT
ejpam-6081	238	23	f−1	f−1	PROPN
ejpam-6081	238	24	)	)	PUNCT
ejpam-6081	238	25	∣∣	∣∣	PROPN
ejpam-6081	238	26	≤	≤	NUM
ejpam-6081	238	27	ταδ	ταδ	ADV
ejpam-6081	238	28	6	6	NUM
ejpam-6081	238	29	+	+	CCONJ
ejpam-6081	238	30	ταδ	ταδ	PROPN
ejpam-6081	238	31	4	4	NUM
ejpam-6081	238	32	=	=	SYM
ejpam-6081	238	33	5ταδ	5ταδ	NUM
ejpam-6081	238	34	12	12	NUM
ejpam-6081	238	35	,	,	PUNCT
ejpam-6081	238	36	(	(	PUNCT
ejpam-6081	238	37	43	43	NUM
ejpam-6081	238	38	)	)	PUNCT
ejpam-6081	238	39	thereby	thereby	ADV
ejpam-6081	238	40	concluding	conclude	VERB
ejpam-6081	238	41	the	the	DET
ejpam-6081	238	42	proof	proof	NOUN
ejpam-6081	238	43	of	of	ADP
ejpam-6081	238	44	theorem	theorem	ADJ
ejpam-6081	238	45	6	6	NUM
ejpam-6081	238	46	.	.	NOUN
ejpam-6081	238	47	3.4	3.4	NUM
ejpam-6081	238	48	.	.	PUNCT
ejpam-6081	239	1	vandermonde	vandermonde	VERB
ejpam-6081	239	2	determinant	determinant	ADJ
ejpam-6081	239	3	of	of	ADP
ejpam-6081	239	4	logarithmic	logarithmic	ADJ
ejpam-6081	239	5	coefficients	coefficient	NOUN
ejpam-6081	239	6	in	in	ADP
ejpam-6081	239	7	this	this	DET
ejpam-6081	239	8	subsection	subsection	NOUN
ejpam-6081	239	9	,	,	PUNCT
ejpam-6081	239	10	we	we	PRON
ejpam-6081	239	11	use	use	VERB
ejpam-6081	239	12	the	the	DET
ejpam-6081	239	13	results	result	NOUN
ejpam-6081	239	14	of	of	ADP
ejpam-6081	239	15	theorems	theorem	NOUN
ejpam-6081	239	16	3	3	NUM
ejpam-6081	239	17	and	and	CCONJ
ejpam-6081	239	18	4	4	NUM
ejpam-6081	239	19	to	to	PART
ejpam-6081	239	20	estimate	estimate	VERB
ejpam-6081	239	21	the	the	DET
ejpam-6081	239	22	upper	upper	ADJ
ejpam-6081	239	23	bounds	bound	NOUN
ejpam-6081	239	24	of	of	ADP
ejpam-6081	239	25	the	the	DET
ejpam-6081	239	26	vandermonde	vandermonde	NOUN
ejpam-6081	239	27	determinant	determinant	ADJ
ejpam-6081	239	28	of	of	ADP
ejpam-6081	239	29	second	second	ADJ
ejpam-6081	239	30	-	-	PUNCT
ejpam-6081	239	31	order	order	NOUN
ejpam-6081	239	32	,	,	PUNCT
ejpam-6081	239	33	where	where	SCONJ
ejpam-6081	239	34	the	the	DET
ejpam-6081	239	35	entries	entry	NOUN
ejpam-6081	239	36	are	be	AUX
ejpam-6081	239	37	logarithmic	logarithmic	ADJ
ejpam-6081	239	38	coefficients	coefficient	NOUN
ejpam-6081	239	39	of	of	ADP
ejpam-6081	239	40	functions	function	NOUN
ejpam-6081	239	41	and	and	CCONJ
ejpam-6081	239	42	inverse	inverse	NOUN
ejpam-6081	239	43	functions	function	NOUN
ejpam-6081	239	44	ingg	ingg	NOUN
ejpam-6081	239	45	(	(	PUNCT
ejpam-6081	239	46	α	α	NOUN
ejpam-6081	239	47	,	,	PUNCT
ejpam-6081	239	48	δ	δ	PROPN
ejpam-6081	239	49	)	)	PUNCT
ejpam-6081	239	50	,	,	PUNCT
ejpam-6081	239	51	that	that	ADV
ejpam-6081	239	52	is	is	ADV
ejpam-6081	239	53	,	,	PUNCT
ejpam-6081	239	54	|v2,1	|v2,1	PROPN
ejpam-6081	239	55	(	(	PUNCT
ejpam-6081	239	56	γf	γf	ADJ
ejpam-6081	239	57	)	)	PUNCT
ejpam-6081	239	58	|	|	ADV
ejpam-6081	239	59	,	,	PUNCT
ejpam-6081	239	60	|v2,2	|v2,2	NOUN
ejpam-6081	239	61	(	(	PUNCT
ejpam-6081	239	62	γf	γf	PROPN
ejpam-6081	239	63	)	)	PUNCT
ejpam-6081	239	64	|	|	ADV
ejpam-6081	239	65	,	,	PUNCT
ejpam-6081	239	66	∣∣v2,1	∣∣v2,1	PROPN
ejpam-6081	239	67	(	(	PUNCT
ejpam-6081	239	68	γf−1	γf−1	PROPN
ejpam-6081	239	69	)	)	PUNCT
ejpam-6081	239	70	∣∣	∣∣	PROPN
ejpam-6081	239	71	,	,	PUNCT
ejpam-6081	239	72	and	and	CCONJ
ejpam-6081	239	73	∣∣v2,1	∣∣v2,1	PROPN
ejpam-6081	239	74	(	(	PUNCT
ejpam-6081	239	75	γf−1	γf−1	PROPN
ejpam-6081	239	76	)	)	PUNCT
ejpam-6081	239	77	∣∣	∣∣	PROPN
ejpam-6081	239	78	.	.	PUNCT
ejpam-6081	240	1	theorem	theorem	VERB
ejpam-6081	240	2	7	7	NUM
ejpam-6081	240	3	.	.	PUNCT
ejpam-6081	241	1	let	let	VERB
ejpam-6081	241	2	f	f	PROPN
ejpam-6081	241	3	(	(	PUNCT
ejpam-6081	241	4	z	z	NOUN
ejpam-6081	241	5	)	)	PUNCT
ejpam-6081	241	6	∈	∈	PROPN
ejpam-6081	241	7	gg	gg	PROPN
ejpam-6081	241	8	(	(	PUNCT
ejpam-6081	241	9	α	α	PROPN
ejpam-6081	241	10	,	,	PUNCT
ejpam-6081	241	11	δ	δ	PROPN
ejpam-6081	241	12	)	)	PUNCT
ejpam-6081	241	13	.	.	PUNCT
ejpam-6081	242	1	then	then	ADV
ejpam-6081	242	2	|v2,1(γf	|v2,1(γf	ADV
ejpam-6081	242	3	)	)	PUNCT
ejpam-6081	242	4	|	|	ADV
ejpam-6081	242	5	≤	≤	NUM
ejpam-6081	242	6	5ταδ	5ταδ	NUM
ejpam-6081	242	7	24	24	NUM
ejpam-6081	242	8	and	and	CCONJ
ejpam-6081	242	9	|v2,2(γf	|v2,2(γf	NOUN
ejpam-6081	242	10	)	)	PUNCT
ejpam-6081	242	11	|	|	ADV
ejpam-6081	242	12	≤	≤	NUM
ejpam-6081	242	13	ταδ	ταδ	ADV
ejpam-6081	242	14	48	48	NUM
ejpam-6081	242	15	[	[	PUNCT
ejpam-6081	242	16	7	7	NUM
ejpam-6081	242	17	+	+	NOUN
ejpam-6081	242	18	∣∣7	∣∣7	NOUN
ejpam-6081	242	19	+	+	NUM
ejpam-6081	242	20	ταδe	ταδe	NOUN
ejpam-6081	242	21	−iα	−iα	VERB
ejpam-6081	242	22	∣∣	∣∣	X
ejpam-6081	242	23	]	]	PUNCT
ejpam-6081	242	24	,	,	PUNCT
ejpam-6081	242	25	where	where	SCONJ
ejpam-6081	242	26	ταδ	ταδ	ADV
ejpam-6081	242	27	=	=	SYM
ejpam-6081	242	28	cosα−	cosα−	PROPN
ejpam-6081	242	29	δ	δ	PROPN
ejpam-6081	242	30	.	.	PUNCT
ejpam-6081	242	31	n.	n.	PROPN
ejpam-6081	242	32	h.	h.	PROPN
ejpam-6081	242	33	a.	a.	PROPN
ejpam-6081	242	34	a.	a.	PROPN
ejpam-6081	242	35	wahid	wahid	PROPN
ejpam-6081	242	36	,	,	PUNCT
ejpam-6081	242	37	s.	s.	PROPN
ejpam-6081	242	38	c.	c.	PROPN
ejpam-6081	242	39	soh	soh	PROPN
ejpam-6081	242	40	/	/	SYM
ejpam-6081	242	41	eur	eur	PROPN
ejpam-6081	242	42	.	.	PUNCT
ejpam-6081	243	1	j.	j.	PROPN
ejpam-6081	243	2	pure	pure	PROPN
ejpam-6081	243	3	appl	appl	PROPN
ejpam-6081	243	4	.	.	PROPN
ejpam-6081	243	5	math	math	PROPN
ejpam-6081	243	6	,	,	PUNCT
ejpam-6081	243	7	18	18	NUM
ejpam-6081	243	8	(	(	PUNCT
ejpam-6081	243	9	2	2	NUM
ejpam-6081	243	10	)	)	PUNCT
ejpam-6081	243	11	(	(	PUNCT
ejpam-6081	243	12	2025	2025	NUM
ejpam-6081	243	13	)	)	PUNCT
ejpam-6081	243	14	,	,	PUNCT
ejpam-6081	243	15	6081	6081	NUM
ejpam-6081	243	16	12	12	NUM
ejpam-6081	243	17	of	of	ADP
ejpam-6081	243	18	16	16	NUM
ejpam-6081	243	19	proof	proof	NOUN
ejpam-6081	243	20	.	.	PUNCT
ejpam-6081	244	1	from	from	ADP
ejpam-6081	244	2	(	(	PUNCT
ejpam-6081	244	3	16	16	NUM
ejpam-6081	244	4	)	)	PUNCT
ejpam-6081	244	5	,	,	PUNCT
ejpam-6081	244	6	we	we	PRON
ejpam-6081	244	7	have	have	VERB
ejpam-6081	244	8	|v2,1(γf	|v2,1(γf	NOUN
ejpam-6081	244	9	)	)	PUNCT
ejpam-6081	244	10	|	|	ADV
ejpam-6081	245	1	=	=	PUNCT
ejpam-6081	245	2	|γ2	|γ2	NOUN
ejpam-6081	245	3	−	−	NOUN
ejpam-6081	245	4	γ1|	γ1|	PROPN
ejpam-6081	245	5	≤	≤	PROPN
ejpam-6081	246	1	|γ2|+	|γ2|+	PROPN
ejpam-6081	246	2	|γ1|	|γ1|	NOUN
ejpam-6081	246	3	(	(	PUNCT
ejpam-6081	246	4	44	44	NUM
ejpam-6081	246	5	)	)	PUNCT
ejpam-6081	246	6	and	and	CCONJ
ejpam-6081	246	7	|v2,2(γf	|v2,2(γf	NOUN
ejpam-6081	246	8	)	)	PUNCT
ejpam-6081	246	9	|	|	ADV
ejpam-6081	246	10	=	=	PUNCT
ejpam-6081	246	11	|γ3	|γ3	NOUN
ejpam-6081	246	12	−	−	NOUN
ejpam-6081	246	13	γ2|	γ2|	NOUN
ejpam-6081	246	14	≤	≤	NUM
ejpam-6081	246	15	|γ3|+	|γ3|+	NOUN
ejpam-6081	246	16	|γ2|	|γ2|	NOUN
ejpam-6081	246	17	.	.	PUNCT
ejpam-6081	247	1	(	(	PUNCT
ejpam-6081	247	2	45	45	NUM
ejpam-6081	247	3	)	)	PUNCT
ejpam-6081	247	4	substituting	substitute	VERB
ejpam-6081	247	5	|γ1|	|γ1|	NOUN
ejpam-6081	247	6	≤	≤	NUM
ejpam-6081	247	7	ταδ	ταδ	ADJ
ejpam-6081	247	8	8	8	NUM
ejpam-6081	247	9	and	and	CCONJ
ejpam-6081	247	10	|γ2|	|γ2|	VERB
ejpam-6081	247	11	≤	≤	NUM
ejpam-6081	247	12	ταδ	ταδ	ADV
ejpam-6081	247	13	12	12	NUM
ejpam-6081	247	14	into	into	ADP
ejpam-6081	247	15	(	(	PUNCT
ejpam-6081	247	16	44	44	NUM
ejpam-6081	247	17	)	)	PUNCT
ejpam-6081	247	18	,	,	PUNCT
ejpam-6081	247	19	as	as	ADV
ejpam-6081	247	20	well	well	ADV
ejpam-6081	247	21	as	as	ADP
ejpam-6081	247	22	|γ2|	|γ2|	ADJ
ejpam-6081	247	23	≤	≤	NUM
ejpam-6081	247	24	ταδ	ταδ	ADV
ejpam-6081	247	25	12	12	NUM
ejpam-6081	247	26	and	and	CCONJ
ejpam-6081	247	27	|γ3|	|γ3|	PRON
ejpam-6081	247	28	≤	≤	NUM
ejpam-6081	247	29	ταδ	ταδ	ADV
ejpam-6081	247	30	48	48	NUM
ejpam-6081	247	31	[	[	PUNCT
ejpam-6081	247	32	3	3	NUM
ejpam-6081	247	33	+	+	NUM
ejpam-6081	247	34	∣∣ταδe−iα	∣∣ταδe−iα	NOUN
ejpam-6081	247	35	+	+	CCONJ
ejpam-6081	247	36	7	7	NUM
ejpam-6081	247	37	∣∣	∣∣	NOUN
ejpam-6081	247	38	]	]	PUNCT
ejpam-6081	247	39	into	into	ADP
ejpam-6081	247	40	(	(	PUNCT
ejpam-6081	247	41	45	45	NUM
ejpam-6081	247	42	)	)	PUNCT
ejpam-6081	247	43	,	,	PUNCT
ejpam-6081	247	44	respectively	respectively	ADV
ejpam-6081	247	45	,	,	PUNCT
ejpam-6081	247	46	yields	yield	NOUN
ejpam-6081	247	47	|v2,1(γf	|v2,1(γf	NOUN
ejpam-6081	247	48	)	)	PUNCT
ejpam-6081	247	49	|	|	ADV
ejpam-6081	247	50	≤	≤	NUM
ejpam-6081	247	51	ταδ	ταδ	ADV
ejpam-6081	247	52	12	12	NUM
ejpam-6081	247	53	+	+	CCONJ
ejpam-6081	247	54	ταδ	ταδ	PROPN
ejpam-6081	247	55	8	8	NUM
ejpam-6081	247	56	=	=	SYM
ejpam-6081	247	57	5ταδ	5ταδ	NUM
ejpam-6081	247	58	24	24	NUM
ejpam-6081	247	59	and	and	CCONJ
ejpam-6081	247	60	|v2,2(γf	|v2,2(γf	NOUN
ejpam-6081	247	61	)	)	PUNCT
ejpam-6081	247	62	|	|	ADV
ejpam-6081	247	63	≤	≤	NUM
ejpam-6081	247	64	ταδ	ταδ	ADV
ejpam-6081	247	65	48	48	NUM
ejpam-6081	247	66	[	[	PUNCT
ejpam-6081	247	67	3	3	NUM
ejpam-6081	247	68	+	+	NUM
ejpam-6081	247	69	∣∣ταδe−iα	∣∣ταδe−iα	NOUN
ejpam-6081	247	70	+	+	CCONJ
ejpam-6081	247	71	7	7	NUM
ejpam-6081	247	72	∣∣]+	∣∣]+	VERB
ejpam-6081	247	73	ταδ	ταδ	PROPN
ejpam-6081	248	1	12	12	NUM
ejpam-6081	248	2	=	=	NOUN
ejpam-6081	248	3	ταδ	ταδ	PROPN
ejpam-6081	248	4	48	48	NUM
ejpam-6081	248	5	[	[	PUNCT
ejpam-6081	248	6	7	7	NUM
ejpam-6081	248	7	+	+	NUM
ejpam-6081	248	8	∣∣ταδe−iα	∣∣ταδe−iα	NOUN
ejpam-6081	248	9	+	+	CCONJ
ejpam-6081	248	10	7	7	NUM
ejpam-6081	248	11	∣∣	∣∣	NOUN
ejpam-6081	248	12	]	]	PUNCT
ejpam-6081	248	13	.	.	PUNCT
ejpam-6081	249	1	this	this	PRON
ejpam-6081	249	2	concludes	conclude	VERB
ejpam-6081	249	3	the	the	DET
ejpam-6081	249	4	proof	proof	NOUN
ejpam-6081	249	5	of	of	ADP
ejpam-6081	249	6	theorem	theorem	ADJ
ejpam-6081	249	7	7	7	NUM
ejpam-6081	249	8	.	.	PUNCT
ejpam-6081	249	9	theorem	theorem	NOUN
ejpam-6081	249	10	8	8	NUM
ejpam-6081	249	11	.	.	PUNCT
ejpam-6081	250	1	let	let	VERB
ejpam-6081	250	2	f	f	PROPN
ejpam-6081	250	3	(	(	PUNCT
ejpam-6081	250	4	z	z	NOUN
ejpam-6081	250	5	)	)	PUNCT
ejpam-6081	250	6	∈	∈	PROPN
ejpam-6081	250	7	gg	gg	PROPN
ejpam-6081	250	8	(	(	PUNCT
ejpam-6081	250	9	α	α	PROPN
ejpam-6081	250	10	,	,	PUNCT
ejpam-6081	250	11	δ	δ	PROPN
ejpam-6081	250	12	)	)	PUNCT
ejpam-6081	250	13	.	.	PUNCT
ejpam-6081	251	1	then∣∣v2,1	then∣∣v2,1	NOUN
ejpam-6081	251	2	(	(	PUNCT
ejpam-6081	251	3	γf−1	γf−1	PROPN
ejpam-6081	251	4	)	)	PUNCT
ejpam-6081	251	5	∣∣	∣∣	X
ejpam-6081	251	6	≤	≤	NUM
ejpam-6081	251	7	5ταδ	5ταδ	NUM
ejpam-6081	251	8	24	24	NUM
ejpam-6081	251	9	and	and	CCONJ
ejpam-6081	251	10	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	251	11	(	(	PUNCT
ejpam-6081	251	12	γf−1	γf−1	PROPN
ejpam-6081	251	13	)	)	PUNCT
ejpam-6081	251	14	∣∣	∣∣	PROPN
ejpam-6081	251	15	≤	≤	NUM
ejpam-6081	251	16	ταδ	ταδ	ADV
ejpam-6081	251	17	48	48	NUM
ejpam-6081	251	18	[	[	PUNCT
ejpam-6081	251	19	7	7	NUM
ejpam-6081	251	20	+	+	NOUN
ejpam-6081	251	21	∣∣7	∣∣7	NOUN
ejpam-6081	251	22	+	+	CCONJ
ejpam-6081	251	23	4ταδe	4ταδe	NUM
ejpam-6081	251	24	−iα	−iα	X
ejpam-6081	251	25	∣∣	∣∣	X
ejpam-6081	251	26	]	]	PUNCT
ejpam-6081	251	27	where	where	SCONJ
ejpam-6081	251	28	tαδ	tαδ	NOUN
ejpam-6081	251	29	=	=	SYM
ejpam-6081	251	30	cosα−	cosα−	PROPN
ejpam-6081	251	31	δ	δ	PROPN
ejpam-6081	251	32	.	.	PUNCT
ejpam-6081	252	1	proof	proof	NOUN
ejpam-6081	252	2	.	.	PUNCT
ejpam-6081	253	1	using	use	VERB
ejpam-6081	253	2	(	(	PUNCT
ejpam-6081	253	3	18	18	NUM
ejpam-6081	253	4	)	)	PUNCT
ejpam-6081	253	5	,	,	PUNCT
ejpam-6081	253	6	we	we	PRON
ejpam-6081	253	7	can	can	AUX
ejpam-6081	253	8	establish∣∣v2,1	establish∣∣v2,1	VERB
ejpam-6081	253	9	(	(	PUNCT
ejpam-6081	253	10	γf−1	γf−1	PROPN
ejpam-6081	253	11	)	)	PUNCT
ejpam-6081	253	12	∣∣	∣∣	X
ejpam-6081	254	1	=	=	PUNCT
ejpam-6081	254	2	|γ2	|γ2	NOUN
ejpam-6081	254	3	−	−	PROPN
ejpam-6081	254	4	γ1|	γ1|	PROPN
ejpam-6081	254	5	≤	≤	PROPN
ejpam-6081	255	1	|γ2|+	|γ2|+	PROPN
ejpam-6081	255	2	|γ1|	|γ1|	NOUN
ejpam-6081	255	3	(	(	PUNCT
ejpam-6081	255	4	46	46	NUM
ejpam-6081	255	5	)	)	PUNCT
ejpam-6081	255	6	and	and	CCONJ
ejpam-6081	255	7	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	255	8	(	(	PUNCT
ejpam-6081	255	9	γf−1	γf−1	PROPN
ejpam-6081	255	10	)	)	PUNCT
ejpam-6081	255	11	∣∣	∣∣	X
ejpam-6081	255	12	=	=	PUNCT
ejpam-6081	255	13	|γ3	|γ3	NOUN
ejpam-6081	255	14	−	−	NOUN
ejpam-6081	255	15	γ2|	γ2|	NOUN
ejpam-6081	255	16	≤	≤	NUM
ejpam-6081	255	17	|γ3|+	|γ3|+	NOUN
ejpam-6081	255	18	|γ2|	|γ2|	NOUN
ejpam-6081	255	19	.	.	PUNCT
ejpam-6081	256	1	(	(	PUNCT
ejpam-6081	256	2	47	47	NUM
ejpam-6081	256	3	)	)	PUNCT
ejpam-6081	256	4	using	use	VERB
ejpam-6081	256	5	the	the	DET
ejpam-6081	256	6	result	result	NOUN
ejpam-6081	256	7	of	of	ADP
ejpam-6081	256	8	theorem	theorem	NOUN
ejpam-6081	256	9	4	4	NUM
ejpam-6081	256	10	,	,	PUNCT
ejpam-6081	256	11	we	we	PRON
ejpam-6081	256	12	obtain∣∣v2,1	obtain∣∣v2,1	VERB
ejpam-6081	256	13	(	(	PUNCT
ejpam-6081	256	14	γf−1	γf−1	PROPN
ejpam-6081	256	15	)	)	PUNCT
ejpam-6081	256	16	∣∣	∣∣	PROPN
ejpam-6081	256	17	≤	≤	NUM
ejpam-6081	256	18	ταδ	ταδ	NOUN
ejpam-6081	256	19	12	12	NUM
ejpam-6081	256	20	+	+	CCONJ
ejpam-6081	256	21	ταδ	ταδ	PROPN
ejpam-6081	256	22	8	8	NUM
ejpam-6081	256	23	=	=	SYM
ejpam-6081	256	24	5ταδ	5ταδ	NUM
ejpam-6081	256	25	24	24	NUM
ejpam-6081	256	26	and	and	CCONJ
ejpam-6081	256	27	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	256	28	(	(	PUNCT
ejpam-6081	256	29	γf−1	γf−1	PROPN
ejpam-6081	256	30	)	)	PUNCT
ejpam-6081	256	31	∣∣	∣∣	PROPN
ejpam-6081	256	32	≤	≤	NUM
ejpam-6081	256	33	ταδ	ταδ	ADV
ejpam-6081	256	34	48	48	NUM
ejpam-6081	256	35	[	[	PUNCT
ejpam-6081	256	36	3	3	NUM
ejpam-6081	256	37	+	+	CCONJ
ejpam-6081	256	38	∣∣4ταδe−iα	∣∣4ταδe−iα	ADJ
ejpam-6081	256	39	+	+	SYM
ejpam-6081	256	40	7	7	NUM
ejpam-6081	256	41	∣∣]+	∣∣]+	VERB
ejpam-6081	256	42	ταδ	ταδ	PROPN
ejpam-6081	256	43	12	12	NUM
ejpam-6081	256	44	=	=	NOUN
ejpam-6081	256	45	ταδ	ταδ	PROPN
ejpam-6081	256	46	48	48	NUM
ejpam-6081	256	47	[	[	PUNCT
ejpam-6081	256	48	7	7	NUM
ejpam-6081	256	49	+	+	NOUN
ejpam-6081	256	50	∣∣7	∣∣7	NOUN
ejpam-6081	256	51	+	+	CCONJ
ejpam-6081	256	52	4ταδe	4ταδe	NUM
ejpam-6081	256	53	−iα	−iα	NOUN
ejpam-6081	256	54	∣∣	∣∣	PUNCT
ejpam-6081	256	55	]	]	PUNCT
ejpam-6081	256	56	this	this	PRON
ejpam-6081	256	57	concludes	conclude	VERB
ejpam-6081	256	58	the	the	DET
ejpam-6081	256	59	proof	proof	NOUN
ejpam-6081	256	60	of	of	ADP
ejpam-6081	256	61	theorem	theorem	ADJ
ejpam-6081	256	62	8	8	NUM
ejpam-6081	256	63	.	.	PUNCT
ejpam-6081	256	64	n.	n.	PROPN
ejpam-6081	256	65	h.	h.	PROPN
ejpam-6081	256	66	a.	a.	PROPN
ejpam-6081	256	67	a.	a.	PROPN
ejpam-6081	256	68	wahid	wahid	PROPN
ejpam-6081	256	69	,	,	PUNCT
ejpam-6081	256	70	s.	s.	PROPN
ejpam-6081	256	71	c.	c.	PROPN
ejpam-6081	256	72	soh	soh	PROPN
ejpam-6081	256	73	/	/	SYM
ejpam-6081	256	74	eur	eur	PROPN
ejpam-6081	256	75	.	.	PUNCT
ejpam-6081	257	1	j.	j.	PROPN
ejpam-6081	257	2	pure	pure	PROPN
ejpam-6081	257	3	appl	appl	PROPN
ejpam-6081	257	4	.	.	PROPN
ejpam-6081	257	5	math	math	PROPN
ejpam-6081	257	6	,	,	PUNCT
ejpam-6081	257	7	18	18	NUM
ejpam-6081	257	8	(	(	PUNCT
ejpam-6081	257	9	2	2	NUM
ejpam-6081	257	10	)	)	PUNCT
ejpam-6081	257	11	(	(	PUNCT
ejpam-6081	257	12	2025	2025	NUM
ejpam-6081	257	13	)	)	PUNCT
ejpam-6081	257	14	,	,	PUNCT
ejpam-6081	257	15	6081	6081	NUM
ejpam-6081	257	16	13	13	NUM
ejpam-6081	257	17	of	of	ADP
ejpam-6081	257	18	16	16	NUM
ejpam-6081	257	19	4	4	NUM
ejpam-6081	257	20	.	.	PUNCT
ejpam-6081	257	21	consequences	consequence	NOUN
ejpam-6081	257	22	and	and	CCONJ
ejpam-6081	257	23	corollaries	corollary	NOUN
ejpam-6081	257	24	this	this	DET
ejpam-6081	257	25	section	section	NOUN
ejpam-6081	257	26	explores	explore	VERB
ejpam-6081	257	27	several	several	ADJ
ejpam-6081	257	28	new	new	ADJ
ejpam-6081	257	29	implications	implication	NOUN
ejpam-6081	257	30	of	of	ADP
ejpam-6081	257	31	theorems	theorem	NOUN
ejpam-6081	257	32	1	1	NUM
ejpam-6081	257	33	-	-	SYM
ejpam-6081	257	34	8	8	NUM
ejpam-6081	257	35	,	,	PUNCT
ejpam-6081	257	36	as	as	SCONJ
ejpam-6081	257	37	gg	gg	PROPN
ejpam-6081	257	38	(	(	PUNCT
ejpam-6081	257	39	α	α	PROPN
ejpam-6081	257	40	,	,	PUNCT
ejpam-6081	257	41	δ	δ	NOUN
ejpam-6081	257	42	)	)	PUNCT
ejpam-6081	257	43	generalizes	generalize	VERB
ejpam-6081	257	44	the	the	DET
ejpam-6081	257	45	classes	class	NOUN
ejpam-6081	257	46	gg	gg	NOUN
ejpam-6081	257	47	(	(	PUNCT
ejpam-6081	257	48	α	α	NOUN
ejpam-6081	257	49	)	)	PUNCT
ejpam-6081	257	50	,	,	PUNCT
ejpam-6081	257	51	gg	gg	PROPN
ejpam-6081	257	52	(	(	PUNCT
ejpam-6081	257	53	δ	δ	PROPN
ejpam-6081	257	54	)	)	PUNCT
ejpam-6081	257	55	,	,	PUNCT
ejpam-6081	257	56	and	and	CCONJ
ejpam-6081	257	57	gg	gg	PROPN
ejpam-6081	257	58	.	.	PUNCT
ejpam-6081	258	1	selecting	select	VERB
ejpam-6081	258	2	δ	δ	PROPN
ejpam-6081	258	3	=	=	PUNCT
ejpam-6081	258	4	0	0	NUM
ejpam-6081	258	5	from	from	ADP
ejpam-6081	258	6	theorems	theorem	NOUN
ejpam-6081	258	7	1	1	NUM
ejpam-6081	258	8	-	-	SYM
ejpam-6081	258	9	8	8	NUM
ejpam-6081	258	10	,	,	PUNCT
ejpam-6081	258	11	we	we	PRON
ejpam-6081	258	12	get	get	VERB
ejpam-6081	258	13	the	the	DET
ejpam-6081	258	14	following	follow	VERB
ejpam-6081	258	15	estimates	estimate	NOUN
ejpam-6081	258	16	bounds	bound	VERB
ejpam-6081	258	17	for	for	ADP
ejpam-6081	258	18	the	the	DET
ejpam-6081	258	19	class	class	NOUN
ejpam-6081	258	20	gg	gg	NOUN
ejpam-6081	258	21	(	(	PUNCT
ejpam-6081	258	22	α	α	NOUN
ejpam-6081	258	23	)	)	PUNCT
ejpam-6081	258	24	.	.	PUNCT
ejpam-6081	259	1	corollary	corollary	ADJ
ejpam-6081	259	2	1	1	NUM
ejpam-6081	259	3	.	.	PUNCT
ejpam-6081	260	1	let	let	VERB
ejpam-6081	260	2	f	f	PROPN
ejpam-6081	260	3	(	(	PUNCT
ejpam-6081	260	4	z	z	NOUN
ejpam-6081	260	5	)	)	PUNCT
ejpam-6081	260	6	=	=	SYM
ejpam-6081	261	1	z+	z+	NUM
ejpam-6081	261	2	∞∑	∞∑	NUM
ejpam-6081	261	3	n=2	n=2	PRON
ejpam-6081	261	4	anz	anz	NOUN
ejpam-6081	261	5	n	n	PROPN
ejpam-6081	261	6	and	and	CCONJ
ejpam-6081	261	7	f−1	f−1	PROPN
ejpam-6081	261	8	(	(	PUNCT
ejpam-6081	261	9	w	w	NOUN
ejpam-6081	261	10	)	)	PUNCT
ejpam-6081	261	11	=	=	NOUN
ejpam-6081	261	12	w+	w+	PUNCT
ejpam-6081	261	13	∞∑	∞∑	NUM
ejpam-6081	261	14	n=2	n=2	PRON
ejpam-6081	261	15	anw	anw	NOUN
ejpam-6081	261	16	n	n	ADV
ejpam-6081	261	17	be	be	VERB
ejpam-6081	261	18	in	in	ADP
ejpam-6081	261	19	the	the	DET
ejpam-6081	261	20	class	class	NOUN
ejpam-6081	261	21	gg	gg	NOUN
ejpam-6081	261	22	(	(	PUNCT
ejpam-6081	261	23	α	α	NOUN
ejpam-6081	261	24	)	)	PUNCT
ejpam-6081	261	25	.	.	PUNCT
ejpam-6081	262	1	then	then	ADV
ejpam-6081	262	2	(	(	PUNCT
ejpam-6081	262	3	i	i	NOUN
ejpam-6081	262	4	)	)	PUNCT
ejpam-6081	262	5	|an|	|an|	NOUN
ejpam-6081	262	6	≤	≤	ADJ
ejpam-6081	262	7	cosα	cosα	NOUN
ejpam-6081	262	8	2n	2n	NUM
ejpam-6081	262	9	,	,	PUNCT
ejpam-6081	262	10	n	n	NOUN
ejpam-6081	262	11	=	=	SYM
ejpam-6081	262	12	2	2	NUM
ejpam-6081	262	13	,	,	PUNCT
ejpam-6081	262	14	3	3	NUM
ejpam-6081	262	15	,	,	PUNCT
ejpam-6081	262	16	4	4	NUM
ejpam-6081	262	17	,	,	PUNCT
ejpam-6081	262	18	5	5	NUM
ejpam-6081	262	19	(	(	PUNCT
ejpam-6081	262	20	ii	ii	NOUN
ejpam-6081	262	21	)	)	PUNCT
ejpam-6081	262	22	|a2|	|a2|	NOUN
ejpam-6081	262	23	≤	≤	ADJ
ejpam-6081	262	24	cosα	cosα	NOUN
ejpam-6081	262	25	4	4	NUM
ejpam-6081	262	26	,	,	PUNCT
ejpam-6081	262	27	|a3|	|a3|	VERB
ejpam-6081	262	28	≤	≤	ADJ
ejpam-6081	262	29	cosα	cosα	NOUN
ejpam-6081	262	30	6	6	NUM
ejpam-6081	262	31	,	,	PUNCT
ejpam-6081	262	32	|a4|	|a4|	ADJ
ejpam-6081	262	33	≤	≤	ADJ
ejpam-6081	262	34	cosα	cosα	NOUN
ejpam-6081	263	1	24	24	NUM
ejpam-6081	263	2	[	[	X
ejpam-6081	263	3	∣∣5e−iα	∣∣5e−iα	X
ejpam-6081	263	4	cosα+	cosα+	X
ejpam-6081	263	5	7	7	NUM
ejpam-6081	263	6	∣∣+	∣∣+	PROPN
ejpam-6081	263	7	3	3	NUM
ejpam-6081	263	8	]	]	PUNCT
ejpam-6081	263	9	(	(	PUNCT
ejpam-6081	263	10	iii	iii	X
ejpam-6081	263	11	)	)	PUNCT
ejpam-6081	263	12	|γ1|	|γ1|	NOUN
ejpam-6081	263	13	≤	≤	NUM
ejpam-6081	263	14	cosα	cosα	NOUN
ejpam-6081	263	15	8	8	NUM
ejpam-6081	263	16	,	,	PUNCT
ejpam-6081	263	17	|γ2|	|γ2|	VERB
ejpam-6081	263	18	≤	≤	ADJ
ejpam-6081	263	19	cosα	cosα	NOUN
ejpam-6081	263	20	12	12	NUM
ejpam-6081	263	21	,	,	PUNCT
ejpam-6081	263	22	|γ3|	|γ3|	ADP
ejpam-6081	263	23	≤	≤	NUM
ejpam-6081	263	24	cosα	cosα	NOUN
ejpam-6081	263	25	48	48	NUM
ejpam-6081	263	26	[	[	PUNCT
ejpam-6081	263	27	3	3	NUM
ejpam-6081	263	28	+	+	CCONJ
ejpam-6081	263	29	∣∣e−iα	∣∣e−iα	PROPN
ejpam-6081	263	30	cosα+	cosα+	NOUN
ejpam-6081	263	31	7	7	NUM
ejpam-6081	263	32	∣∣	∣∣	X
ejpam-6081	263	33	]	]	PUNCT
ejpam-6081	263	34	(	(	PUNCT
ejpam-6081	263	35	iv	iv	X
ejpam-6081	263	36	)	)	PUNCT
ejpam-6081	263	37	|γ1|	|γ1|	NOUN
ejpam-6081	264	1	≤	≤	NUM
ejpam-6081	264	2	cosα	cosα	NOUN
ejpam-6081	264	3	8	8	NUM
ejpam-6081	264	4	,	,	PUNCT
ejpam-6081	264	5	|γ2|	|γ2|	VERB
ejpam-6081	264	6	≤	≤	ADJ
ejpam-6081	264	7	cosα	cosα	NOUN
ejpam-6081	264	8	12	12	NUM
ejpam-6081	264	9	,	,	PUNCT
ejpam-6081	264	10	|γ3|	|γ3|	ADP
ejpam-6081	264	11	≤	≤	NUM
ejpam-6081	264	12	cosα	cosα	NOUN
ejpam-6081	264	13	48	48	NUM
ejpam-6081	264	14	[	[	SYM
ejpam-6081	264	15	3	3	NUM
ejpam-6081	264	16	+	+	CCONJ
ejpam-6081	264	17	∣∣4e−iα	∣∣4e−iα	NOUN
ejpam-6081	264	18	cosα+	cosα+	X
ejpam-6081	264	19	7	7	NUM
ejpam-6081	264	20	∣∣	∣∣	X
ejpam-6081	264	21	]	]	PUNCT
ejpam-6081	264	22	(	(	PUNCT
ejpam-6081	264	23	v	v	NOUN
ejpam-6081	264	24	)	)	PUNCT
ejpam-6081	264	25	|v2,2	|v2,2	NOUN
ejpam-6081	264	26	(	(	PUNCT
ejpam-6081	264	27	f)|	f)|	VERB
ejpam-6081	264	28	≤	≤	ADJ
ejpam-6081	264	29	5	5	NUM
ejpam-6081	264	30	cosα	cosα	NOUN
ejpam-6081	264	31	12	12	NUM
ejpam-6081	264	32	(	(	PUNCT
ejpam-6081	264	33	vi	vi	NOUN
ejpam-6081	264	34	)	)	PUNCT
ejpam-6081	264	35	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	265	1	(	(	PUNCT
ejpam-6081	265	2	f−1	f−1	PROPN
ejpam-6081	265	3	)	)	PUNCT
ejpam-6081	265	4	∣∣	∣∣	X
ejpam-6081	265	5	≤	≤	NUM
ejpam-6081	265	6	5	5	NUM
ejpam-6081	265	7	cosα	cosα	NOUN
ejpam-6081	265	8	12	12	NUM
ejpam-6081	265	9	(	(	PUNCT
ejpam-6081	265	10	vii	vii	PROPN
ejpam-6081	265	11	)	)	PUNCT
ejpam-6081	265	12	|v2,1(γf	|v2,1(γf	NOUN
ejpam-6081	265	13	)	)	PUNCT
ejpam-6081	265	14	|	|	ADV
ejpam-6081	265	15	≤	≤	NUM
ejpam-6081	265	16	5	5	NUM
ejpam-6081	265	17	cosα	cosα	NOUN
ejpam-6081	265	18	24	24	NUM
ejpam-6081	265	19	,	,	PUNCT
ejpam-6081	265	20	|v2,2(γf	|v2,2(γf	NOUN
ejpam-6081	265	21	)	)	PUNCT
ejpam-6081	265	22	|	|	ADV
ejpam-6081	265	23	≤	≤	NUM
ejpam-6081	265	24	cosα	cosα	NOUN
ejpam-6081	265	25	48	48	NUM
ejpam-6081	265	26	[	[	PUNCT
ejpam-6081	265	27	7	7	NUM
ejpam-6081	265	28	+	+	NOUN
ejpam-6081	265	29	∣∣7	∣∣7	NOUN
ejpam-6081	265	30	+	+	NUM
ejpam-6081	265	31	e−iα	e−iα	NOUN
ejpam-6081	265	32	cosα	cosα	NOUN
ejpam-6081	265	33	∣∣	∣∣	AUX
ejpam-6081	265	34	]	]	PUNCT
ejpam-6081	265	35	(	(	PUNCT
ejpam-6081	265	36	viii	viii	PROPN
ejpam-6081	265	37	)	)	PUNCT
ejpam-6081	265	38	∣∣v2,1	∣∣v2,1	PROPN
ejpam-6081	266	1	(	(	PUNCT
ejpam-6081	266	2	γf−1	γf−1	PROPN
ejpam-6081	266	3	)	)	PUNCT
ejpam-6081	266	4	∣∣	∣∣	PROPN
ejpam-6081	266	5	≤	≤	NUM
ejpam-6081	266	6	5	5	NUM
ejpam-6081	266	7	cosα	cosα	NOUN
ejpam-6081	266	8	24	24	NUM
ejpam-6081	266	9	,	,	PUNCT
ejpam-6081	266	10	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	266	11	(	(	PUNCT
ejpam-6081	266	12	γf−1	γf−1	PROPN
ejpam-6081	266	13	)	)	PUNCT
ejpam-6081	266	14	∣∣	∣∣	PROPN
ejpam-6081	266	15	≤	≤	NUM
ejpam-6081	266	16	cosα	cosα	NOUN
ejpam-6081	266	17	48	48	NUM
ejpam-6081	266	18	[	[	PUNCT
ejpam-6081	266	19	7	7	NUM
ejpam-6081	266	20	+	+	NOUN
ejpam-6081	266	21	∣∣7	∣∣7	NOUN
ejpam-6081	266	22	+	+	CCONJ
ejpam-6081	266	23	4e−iα	4e−iα	NUM
ejpam-6081	266	24	cosα	cosα	NOUN
ejpam-6081	266	25	∣∣	∣∣	AUX
ejpam-6081	266	26	]	]	X
ejpam-6081	266	27	taking	take	VERB
ejpam-6081	266	28	into	into	ADP
ejpam-6081	266	29	account	account	NOUN
ejpam-6081	266	30	α	α	NOUN
ejpam-6081	266	31	=	=	NOUN
ejpam-6081	266	32	0	0	NUM
ejpam-6081	266	33	in	in	ADP
ejpam-6081	266	34	theorems	theorem	NOUN
ejpam-6081	266	35	1	1	NUM
ejpam-6081	266	36	-	-	SYM
ejpam-6081	266	37	8	8	NUM
ejpam-6081	266	38	,	,	PUNCT
ejpam-6081	266	39	we	we	PRON
ejpam-6081	266	40	obtain	obtain	VERB
ejpam-6081	266	41	the	the	DET
ejpam-6081	266	42	following	follow	VERB
ejpam-6081	266	43	estimates	estimate	NOUN
ejpam-6081	266	44	bounds	bound	VERB
ejpam-6081	266	45	for	for	ADP
ejpam-6081	266	46	the	the	DET
ejpam-6081	266	47	class	class	NOUN
ejpam-6081	266	48	gg	gg	NOUN
ejpam-6081	266	49	(	(	PUNCT
ejpam-6081	266	50	δ	δ	PROPN
ejpam-6081	266	51	)	)	PUNCT
ejpam-6081	266	52	.	.	PUNCT
ejpam-6081	267	1	corollary	corollary	ADJ
ejpam-6081	267	2	2	2	NUM
ejpam-6081	267	3	.	.	PUNCT
ejpam-6081	268	1	let	let	VERB
ejpam-6081	268	2	f	f	PROPN
ejpam-6081	268	3	(	(	PUNCT
ejpam-6081	268	4	z	z	NOUN
ejpam-6081	268	5	)	)	PUNCT
ejpam-6081	268	6	=	=	SYM
ejpam-6081	269	1	z+	z+	NUM
ejpam-6081	269	2	∞∑	∞∑	NUM
ejpam-6081	269	3	n=2	n=2	PRON
ejpam-6081	269	4	anz	anz	NOUN
ejpam-6081	269	5	n	n	PROPN
ejpam-6081	269	6	and	and	CCONJ
ejpam-6081	269	7	f−1	f−1	PROPN
ejpam-6081	269	8	(	(	PUNCT
ejpam-6081	269	9	w	w	NOUN
ejpam-6081	269	10	)	)	PUNCT
ejpam-6081	269	11	=	=	NOUN
ejpam-6081	269	12	w+	w+	PUNCT
ejpam-6081	269	13	∞∑	∞∑	NUM
ejpam-6081	269	14	n=2	n=2	PRON
ejpam-6081	269	15	anw	anw	NOUN
ejpam-6081	269	16	n	n	ADV
ejpam-6081	269	17	be	be	VERB
ejpam-6081	269	18	in	in	ADP
ejpam-6081	269	19	the	the	DET
ejpam-6081	269	20	class	class	NOUN
ejpam-6081	269	21	gg	gg	NOUN
ejpam-6081	269	22	(	(	PUNCT
ejpam-6081	269	23	δ	δ	PROPN
ejpam-6081	269	24	)	)	PUNCT
ejpam-6081	269	25	.	.	PUNCT
ejpam-6081	270	1	then	then	ADV
ejpam-6081	270	2	(	(	PUNCT
ejpam-6081	270	3	i	i	NOUN
ejpam-6081	270	4	)	)	PUNCT
ejpam-6081	270	5	|an|	|an|	NOUN
ejpam-6081	270	6	≤	≤	NUM
ejpam-6081	270	7	1−δ	1−δ	NUM
ejpam-6081	270	8	2n	2n	NUM
ejpam-6081	270	9	,	,	PUNCT
ejpam-6081	270	10	n	n	NOUN
ejpam-6081	270	11	=	=	SYM
ejpam-6081	270	12	2	2	NUM
ejpam-6081	270	13	,	,	PUNCT
ejpam-6081	270	14	3	3	NUM
ejpam-6081	270	15	,	,	PUNCT
ejpam-6081	270	16	4	4	NUM
ejpam-6081	270	17	,	,	PUNCT
ejpam-6081	270	18	5	5	NUM
ejpam-6081	270	19	(	(	PUNCT
ejpam-6081	270	20	ii	ii	NOUN
ejpam-6081	270	21	)	)	PUNCT
ejpam-6081	270	22	|a2|	|a2|	VERB
ejpam-6081	270	23	≤	≤	ADV
ejpam-6081	270	24	1−δ	1−δ	NUM
ejpam-6081	270	25	4	4	NUM
ejpam-6081	270	26	,	,	PUNCT
ejpam-6081	270	27	|a3|	|a3|	VERB
ejpam-6081	270	28	≤	≤	ADJ
ejpam-6081	270	29	1−δ	1−δ	NUM
ejpam-6081	270	30	6	6	NUM
ejpam-6081	270	31	,	,	PUNCT
ejpam-6081	270	32	|a4|	|a4|	ADJ
ejpam-6081	270	33	≤	≤	NOUN
ejpam-6081	270	34	5(1−δ)(3−δ	5(1−δ)(3−δ	NUM
ejpam-6081	270	35	)	)	PUNCT
ejpam-6081	270	36	24	24	NUM
ejpam-6081	270	37	(	(	PUNCT
ejpam-6081	270	38	iii	iii	NOUN
ejpam-6081	270	39	)	)	PUNCT
ejpam-6081	270	40	|γ1|	|γ1|	NOUN
ejpam-6081	271	1	≤	≤	NUM
ejpam-6081	272	1	1−δ	1−δ	NUM
ejpam-6081	272	2	8	8	NUM
ejpam-6081	272	3	,	,	PUNCT
ejpam-6081	272	4	|γ2|	|γ2|	VERB
ejpam-6081	272	5	≤	≤	ADJ
ejpam-6081	272	6	1−δ	1−δ	NUM
ejpam-6081	272	7	12	12	NUM
ejpam-6081	272	8	,	,	PUNCT
ejpam-6081	272	9	|γ3|	|γ3|	ADJ
ejpam-6081	272	10	≤	≤	NUM
ejpam-6081	272	11	(	(	PUNCT
ejpam-6081	272	12	1−δ)(11−δ	1−δ)(11−δ	NUM
ejpam-6081	272	13	)	)	PUNCT
ejpam-6081	272	14	48	48	NUM
ejpam-6081	272	15	(	(	PUNCT
ejpam-6081	272	16	iv	iv	X
ejpam-6081	272	17	)	)	PUNCT
ejpam-6081	272	18	|γ1|	|γ1|	NOUN
ejpam-6081	273	1	≤	≤	NUM
ejpam-6081	273	2	1−δ	1−δ	NUM
ejpam-6081	273	3	8	8	NUM
ejpam-6081	273	4	,	,	PUNCT
ejpam-6081	273	5	|γ2|	|γ2|	VERB
ejpam-6081	273	6	≤	≤	ADJ
ejpam-6081	273	7	1−δ	1−δ	NUM
ejpam-6081	273	8	12	12	NUM
ejpam-6081	273	9	,	,	PUNCT
ejpam-6081	273	10	|γ3|	|γ3|	ADJ
ejpam-6081	273	11	≤	≤	NOUN
ejpam-6081	273	12	(	(	PUNCT
ejpam-6081	273	13	1−δ)(7−2δ	1−δ)(7−2δ	NUM
ejpam-6081	273	14	)	)	PUNCT
ejpam-6081	273	15	24	24	NUM
ejpam-6081	273	16	(	(	PUNCT
ejpam-6081	273	17	v	v	NOUN
ejpam-6081	273	18	)	)	PUNCT
ejpam-6081	273	19	|v2,2	|v2,2	NOUN
ejpam-6081	273	20	(	(	PUNCT
ejpam-6081	273	21	f)|	f)|	VERB
ejpam-6081	273	22	≤	≤	NUM
ejpam-6081	273	23	5(1−δ	5(1−δ	NUM
ejpam-6081	273	24	)	)	PUNCT
ejpam-6081	273	25	12	12	NUM
ejpam-6081	273	26	(	(	PUNCT
ejpam-6081	273	27	vi	vi	NOUN
ejpam-6081	273	28	)	)	PUNCT
ejpam-6081	273	29	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	274	1	(	(	PUNCT
ejpam-6081	274	2	f−1	f−1	PROPN
ejpam-6081	274	3	)	)	PUNCT
ejpam-6081	274	4	∣∣	∣∣	PROPN
ejpam-6081	274	5	≤	≤	NUM
ejpam-6081	274	6	5(1−δ	5(1−δ	NUM
ejpam-6081	274	7	)	)	PUNCT
ejpam-6081	274	8	12	12	NUM
ejpam-6081	274	9	(	(	PUNCT
ejpam-6081	274	10	vii	vii	PROPN
ejpam-6081	274	11	)	)	PUNCT
ejpam-6081	274	12	|v2,1(γf	|v2,1(γf	NOUN
ejpam-6081	274	13	)	)	PUNCT
ejpam-6081	274	14	|	|	ADV
ejpam-6081	274	15	≤	≤	NUM
ejpam-6081	274	16	5(1−δ	5(1−δ	NUM
ejpam-6081	274	17	)	)	PUNCT
ejpam-6081	274	18	24	24	NUM
ejpam-6081	274	19	,	,	PUNCT
ejpam-6081	274	20	|v2,2(γf	|v2,2(γf	NOUN
ejpam-6081	274	21	)	)	PUNCT
ejpam-6081	274	22	|	|	ADV
ejpam-6081	274	23	≤	≤	NUM
ejpam-6081	274	24	(	(	PUNCT
ejpam-6081	274	25	1−δ)(15−δ	1−δ)(15−δ	NUM
ejpam-6081	274	26	)	)	PUNCT
ejpam-6081	274	27	48	48	NUM
ejpam-6081	274	28	n.	n.	PROPN
ejpam-6081	274	29	h.	h.	PROPN
ejpam-6081	274	30	a.	a.	PROPN
ejpam-6081	274	31	a.	a.	PROPN
ejpam-6081	274	32	wahid	wahid	PROPN
ejpam-6081	274	33	,	,	PUNCT
ejpam-6081	275	1	s.	s.	PROPN
ejpam-6081	275	2	c.	c.	PROPN
ejpam-6081	275	3	soh	soh	PROPN
ejpam-6081	275	4	/	/	SYM
ejpam-6081	275	5	eur	eur	PROPN
ejpam-6081	275	6	.	.	PUNCT
ejpam-6081	276	1	j.	j.	PROPN
ejpam-6081	276	2	pure	pure	PROPN
ejpam-6081	276	3	appl	appl	PROPN
ejpam-6081	276	4	.	.	PROPN
ejpam-6081	276	5	math	math	PROPN
ejpam-6081	276	6	,	,	PUNCT
ejpam-6081	276	7	18	18	NUM
ejpam-6081	276	8	(	(	PUNCT
ejpam-6081	276	9	2	2	NUM
ejpam-6081	276	10	)	)	PUNCT
ejpam-6081	276	11	(	(	PUNCT
ejpam-6081	276	12	2025	2025	NUM
ejpam-6081	276	13	)	)	PUNCT
ejpam-6081	276	14	,	,	PUNCT
ejpam-6081	276	15	6081	6081	NUM
ejpam-6081	276	16	14	14	NUM
ejpam-6081	276	17	of	of	ADP
ejpam-6081	276	18	16	16	NUM
ejpam-6081	276	19	(	(	PUNCT
ejpam-6081	276	20	viii	viii	PROPN
ejpam-6081	276	21	)	)	PUNCT
ejpam-6081	276	22	∣∣v2,1	∣∣v2,1	PROPN
ejpam-6081	276	23	(	(	PUNCT
ejpam-6081	276	24	γf−1	γf−1	PROPN
ejpam-6081	276	25	)	)	PUNCT
ejpam-6081	276	26	∣∣	∣∣	PROPN
ejpam-6081	277	1	≤	≤	NUM
ejpam-6081	277	2	5(1−δ	5(1−δ	NUM
ejpam-6081	277	3	)	)	PUNCT
ejpam-6081	277	4	24	24	NUM
ejpam-6081	277	5	,	,	PUNCT
ejpam-6081	277	6	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	277	7	(	(	PUNCT
ejpam-6081	277	8	γf−1	γf−1	PROPN
ejpam-6081	277	9	)	)	PUNCT
ejpam-6081	277	10	∣∣	∣∣	PROPN
ejpam-6081	277	11	≤	≤	NUM
ejpam-6081	277	12	(	(	PUNCT
ejpam-6081	277	13	1−δ)(9−2δ	1−δ)(9−2δ	NUM
ejpam-6081	277	14	)	)	PUNCT
ejpam-6081	277	15	24	24	NUM
ejpam-6081	277	16	putting	put	VERB
ejpam-6081	277	17	α	α	NOUN
ejpam-6081	277	18	=	=	SYM
ejpam-6081	277	19	0	0	NUM
ejpam-6081	277	20	and	and	CCONJ
ejpam-6081	277	21	δ	δ	PROPN
ejpam-6081	277	22	=	=	NOUN
ejpam-6081	277	23	0	0	NUM
ejpam-6081	277	24	in	in	ADP
ejpam-6081	277	25	theorems	theorem	NOUN
ejpam-6081	277	26	1	1	NUM
ejpam-6081	277	27	-	-	SYM
ejpam-6081	277	28	8	8	NUM
ejpam-6081	277	29	,	,	PUNCT
ejpam-6081	277	30	we	we	PRON
ejpam-6081	277	31	have	have	VERB
ejpam-6081	277	32	the	the	DET
ejpam-6081	277	33	following	follow	VERB
ejpam-6081	277	34	results	result	NOUN
ejpam-6081	277	35	for	for	ADP
ejpam-6081	277	36	the	the	DET
ejpam-6081	277	37	class	class	NOUN
ejpam-6081	277	38	gg	gg	PROPN
ejpam-6081	277	39	.	.	PUNCT
ejpam-6081	278	1	corollary	corollary	ADJ
ejpam-6081	278	2	3	3	X
ejpam-6081	278	3	.	.	PUNCT
ejpam-6081	279	1	let	let	VERB
ejpam-6081	279	2	f	f	PROPN
ejpam-6081	279	3	(	(	PUNCT
ejpam-6081	279	4	z	z	NOUN
ejpam-6081	279	5	)	)	PUNCT
ejpam-6081	279	6	=	=	SYM
ejpam-6081	280	1	z	z	NOUN
ejpam-6081	281	1	+	+	NOUN
ejpam-6081	281	2	∞∑	∞∑	NUM
ejpam-6081	281	3	n=2	n=2	VERB
ejpam-6081	281	4	anz	anz	NOUN
ejpam-6081	281	5	n	n	PROPN
ejpam-6081	281	6	and	and	CCONJ
ejpam-6081	281	7	f−1	f−1	PROPN
ejpam-6081	281	8	(	(	PUNCT
ejpam-6081	281	9	w	w	NOUN
ejpam-6081	281	10	)	)	PUNCT
ejpam-6081	281	11	=	=	SYM
ejpam-6081	282	1	w	w	PROPN
ejpam-6081	283	1	+	+	PUNCT
ejpam-6081	283	2	∞∑	∞∑	NUM
ejpam-6081	283	3	n=2	n=2	PRON
ejpam-6081	283	4	anw	anw	NOUN
ejpam-6081	284	1	n	n	ADV
ejpam-6081	284	2	be	be	VERB
ejpam-6081	284	3	in	in	ADP
ejpam-6081	284	4	the	the	DET
ejpam-6081	284	5	class	class	NOUN
ejpam-6081	284	6	gg	gg	NOUN
ejpam-6081	284	7	.	.	PUNCT
ejpam-6081	285	1	then	then	ADV
ejpam-6081	285	2	(	(	PUNCT
ejpam-6081	285	3	i	i	NOUN
ejpam-6081	285	4	)	)	PUNCT
ejpam-6081	285	5	|an|	|an|	NOUN
ejpam-6081	285	6	≤	≤	NUM
ejpam-6081	285	7	1	1	NUM
ejpam-6081	285	8	2n	2n	NUM
ejpam-6081	285	9	,	,	PUNCT
ejpam-6081	285	10	n	n	NOUN
ejpam-6081	285	11	=	=	SYM
ejpam-6081	285	12	2	2	NUM
ejpam-6081	285	13	,	,	PUNCT
ejpam-6081	285	14	3	3	NUM
ejpam-6081	285	15	,	,	PUNCT
ejpam-6081	285	16	4	4	NUM
ejpam-6081	285	17	,	,	PUNCT
ejpam-6081	285	18	5	5	NUM
ejpam-6081	285	19	(	(	PUNCT
ejpam-6081	285	20	ii	ii	NOUN
ejpam-6081	285	21	)	)	PUNCT
ejpam-6081	285	22	|a2|	|a2|	VERB
ejpam-6081	285	23	≤	≤	NUM
ejpam-6081	285	24	1	1	NUM
ejpam-6081	285	25	4	4	NUM
ejpam-6081	285	26	,	,	PUNCT
ejpam-6081	285	27	|a3|	|a3|	VERB
ejpam-6081	285	28	≤	≤	ADV
ejpam-6081	285	29	1	1	NUM
ejpam-6081	285	30	6	6	NUM
ejpam-6081	285	31	,	,	PUNCT
ejpam-6081	285	32	|a4|	|a4|	ADJ
ejpam-6081	285	33	≤	≤	NUM
ejpam-6081	285	34	5	5	NUM
ejpam-6081	285	35	8	8	NUM
ejpam-6081	285	36	(	(	PUNCT
ejpam-6081	285	37	iii	iii	NOUN
ejpam-6081	285	38	)	)	PUNCT
ejpam-6081	285	39	|γ1|	|γ1|	NOUN
ejpam-6081	285	40	≤	≤	NUM
ejpam-6081	285	41	1	1	NUM
ejpam-6081	285	42	8	8	NUM
ejpam-6081	285	43	,	,	PUNCT
ejpam-6081	285	44	|γ2|	|γ2|	VERB
ejpam-6081	285	45	≤	≤	NUM
ejpam-6081	285	46	1	1	NUM
ejpam-6081	285	47	12	12	NUM
ejpam-6081	285	48	,	,	PUNCT
ejpam-6081	285	49	|γ3|	|γ3|	ADJ
ejpam-6081	285	50	≤	≤	NUM
ejpam-6081	285	51	11	11	NUM
ejpam-6081	285	52	48	48	NUM
ejpam-6081	285	53	(	(	PUNCT
ejpam-6081	285	54	iv	iv	X
ejpam-6081	285	55	)	)	PUNCT
ejpam-6081	285	56	|γ1|	|γ1|	NOUN
ejpam-6081	286	1	≤	≤	NUM
ejpam-6081	286	2	1	1	NUM
ejpam-6081	286	3	8	8	NUM
ejpam-6081	286	4	,	,	PUNCT
ejpam-6081	286	5	|γ2|	|γ2|	VERB
ejpam-6081	286	6	≤	≤	NUM
ejpam-6081	286	7	1	1	NUM
ejpam-6081	286	8	12	12	NUM
ejpam-6081	286	9	,	,	PUNCT
ejpam-6081	286	10	|γ3|	|γ3|	ADJ
ejpam-6081	286	11	≤	≤	NUM
ejpam-6081	286	12	7	7	NUM
ejpam-6081	286	13	24	24	NUM
ejpam-6081	286	14	(	(	PUNCT
ejpam-6081	286	15	v	v	NOUN
ejpam-6081	286	16	)	)	PUNCT
ejpam-6081	286	17	|v2,2	|v2,2	NOUN
ejpam-6081	286	18	(	(	PUNCT
ejpam-6081	286	19	f)|	f)|	VERB
ejpam-6081	286	20	≤	≤	NUM
ejpam-6081	286	21	5	5	NUM
ejpam-6081	286	22	12	12	NUM
ejpam-6081	286	23	(	(	PUNCT
ejpam-6081	286	24	vi	vi	NOUN
ejpam-6081	286	25	)	)	PUNCT
ejpam-6081	286	26	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	287	1	(	(	PUNCT
ejpam-6081	287	2	f−1	f−1	PROPN
ejpam-6081	287	3	)	)	PUNCT
ejpam-6081	287	4	∣∣	∣∣	X
ejpam-6081	287	5	≤	≤	NUM
ejpam-6081	287	6	5	5	NUM
ejpam-6081	287	7	12	12	NUM
ejpam-6081	287	8	(	(	PUNCT
ejpam-6081	287	9	vii	vii	PROPN
ejpam-6081	287	10	)	)	PUNCT
ejpam-6081	287	11	|v2,1(γf	|v2,1(γf	NOUN
ejpam-6081	287	12	)	)	PUNCT
ejpam-6081	287	13	|	|	ADV
ejpam-6081	287	14	≤	≤	NUM
ejpam-6081	287	15	5	5	NUM
ejpam-6081	287	16	24	24	NUM
ejpam-6081	287	17	,	,	PUNCT
ejpam-6081	287	18	|v2,2(γf	|v2,2(γf	NOUN
ejpam-6081	287	19	)	)	PUNCT
ejpam-6081	287	20	|	|	ADV
ejpam-6081	287	21	≤	≤	NUM
ejpam-6081	287	22	5	5	NUM
ejpam-6081	287	23	16	16	NUM
ejpam-6081	287	24	(	(	PUNCT
ejpam-6081	287	25	viii	viii	PROPN
ejpam-6081	287	26	)	)	PUNCT
ejpam-6081	287	27	∣∣v2,1	∣∣v2,1	PROPN
ejpam-6081	287	28	(	(	PUNCT
ejpam-6081	287	29	γf−1	γf−1	PROPN
ejpam-6081	287	30	)	)	PUNCT
ejpam-6081	287	31	∣∣	∣∣	PROPN
ejpam-6081	287	32	≤	≤	NUM
ejpam-6081	287	33	5	5	NUM
ejpam-6081	287	34	24	24	NUM
ejpam-6081	287	35	,	,	PUNCT
ejpam-6081	287	36	∣∣v2,2	∣∣v2,2	PROPN
ejpam-6081	287	37	(	(	PUNCT
ejpam-6081	287	38	γf−1	γf−1	PROPN
ejpam-6081	287	39	)	)	PUNCT
ejpam-6081	287	40	∣∣	∣∣	X
ejpam-6081	287	41	≤	≤	NUM
ejpam-6081	287	42	3	3	NUM
ejpam-6081	287	43	8	8	NUM
ejpam-6081	287	44	5	5	NUM
ejpam-6081	287	45	.	.	PUNCT
ejpam-6081	288	1	conclusion	conclusion	NOUN
ejpam-6081	288	2	recent	recent	ADJ
ejpam-6081	288	3	research	research	NOUN
ejpam-6081	288	4	has	have	AUX
ejpam-6081	288	5	sparked	spark	VERB
ejpam-6081	288	6	considerable	considerable	ADJ
ejpam-6081	288	7	interest	interest	NOUN
ejpam-6081	288	8	in	in	ADP
ejpam-6081	288	9	vandermonde	vandermonde	ADJ
ejpam-6081	288	10	determinants	determinant	NOUN
ejpam-6081	288	11	.	.	PUNCT
ejpam-6081	289	1	this	this	PRON
ejpam-6081	289	2	has	have	AUX
ejpam-6081	289	3	inspired	inspire	VERB
ejpam-6081	289	4	us	we	PRON
ejpam-6081	289	5	to	to	PART
ejpam-6081	289	6	study	study	VERB
ejpam-6081	289	7	the	the	DET
ejpam-6081	289	8	vandermonde	vandermonde	NOUN
ejpam-6081	289	9	determinant	determinant	ADJ
ejpam-6081	289	10	of	of	ADP
ejpam-6081	289	11	functions	function	NOUN
ejpam-6081	289	12	and	and	CCONJ
ejpam-6081	289	13	inverse	inverse	NOUN
ejpam-6081	289	14	functions	function	NOUN
ejpam-6081	289	15	belonging	belong	VERB
ejpam-6081	289	16	to	to	ADP
ejpam-6081	289	17	the	the	DET
ejpam-6081	289	18	class	class	NOUN
ejpam-6081	289	19	gg	gg	NOUN
ejpam-6081	289	20	(	(	PUNCT
ejpam-6081	289	21	α	α	PROPN
ejpam-6081	289	22	,	,	PUNCT
ejpam-6081	289	23	δ	δ	PROPN
ejpam-6081	289	24	)	)	PUNCT
ejpam-6081	289	25	of	of	ADP
ejpam-6081	289	26	analytic	analytic	ADJ
ejpam-6081	289	27	functions	function	NOUN
ejpam-6081	289	28	,	,	PUNCT
ejpam-6081	289	29	which	which	PRON
ejpam-6081	289	30	is	be	AUX
ejpam-6081	289	31	associated	associate	VERB
ejpam-6081	289	32	with	with	ADP
ejpam-6081	289	33	generalized	generalized	ADJ
ejpam-6081	289	34	bounded	bounded	ADJ
ejpam-6081	289	35	turning	turning	NOUN
ejpam-6081	289	36	and	and	CCONJ
ejpam-6081	289	37	the	the	DET
ejpam-6081	289	38	generating	generating	NOUN
ejpam-6081	289	39	functions	function	NOUN
ejpam-6081	289	40	of	of	ADP
ejpam-6081	289	41	gregory	gregory	PROPN
ejpam-6081	289	42	coefficients	coefficient	NOUN
ejpam-6081	289	43	.	.	PUNCT
ejpam-6081	290	1	furthermore	furthermore	ADV
ejpam-6081	290	2	,	,	PUNCT
ejpam-6081	290	3	we	we	PRON
ejpam-6081	290	4	have	have	AUX
ejpam-6081	290	5	defined	define	VERB
ejpam-6081	290	6	vandermonde	vandermonde	ADJ
ejpam-6081	290	7	determinants	determinant	NOUN
ejpam-6081	290	8	whose	whose	DET
ejpam-6081	290	9	entries	entry	NOUN
ejpam-6081	290	10	are	be	AUX
ejpam-6081	290	11	logarithmic	logarithmic	ADJ
ejpam-6081	290	12	coefficients	coefficient	NOUN
ejpam-6081	290	13	of	of	ADP
ejpam-6081	290	14	functions	function	NOUN
ejpam-6081	290	15	and	and	CCONJ
ejpam-6081	290	16	inverse	inverse	NOUN
ejpam-6081	290	17	functions	function	NOUN
ejpam-6081	290	18	in	in	ADP
ejpam-6081	290	19	s.	s.	PROPN
ejpam-6081	290	20	thus	thus	ADV
ejpam-6081	290	21	,	,	PUNCT
ejpam-6081	290	22	in	in	ADP
ejpam-6081	290	23	this	this	DET
ejpam-6081	290	24	paper	paper	NOUN
ejpam-6081	290	25	,	,	PUNCT
ejpam-6081	290	26	we	we	PRON
ejpam-6081	290	27	have	have	AUX
ejpam-6081	290	28	obtained	obtain	VERB
ejpam-6081	290	29	estimates	estimate	NOUN
ejpam-6081	290	30	for	for	ADP
ejpam-6081	290	31	taylor	taylor	PROPN
ejpam-6081	290	32	coefficients	coefficient	NOUN
ejpam-6081	290	33	,	,	PUNCT
ejpam-6081	290	34	logarithmic	logarithmic	ADJ
ejpam-6081	290	35	coefficients	coefficient	NOUN
ejpam-6081	290	36	,	,	PUNCT
ejpam-6081	290	37	and	and	CCONJ
ejpam-6081	290	38	the	the	DET
ejpam-6081	290	39	second	second	ADJ
ejpam-6081	290	40	-	-	PUNCT
ejpam-6081	290	41	order	order	NOUN
ejpam-6081	290	42	vandermonde	vandermonde	NOUN
ejpam-6081	290	43	determinant	determinant	INTJ
ejpam-6081	290	44	whose	whose	DET
ejpam-6081	290	45	entries	entry	NOUN
ejpam-6081	290	46	are	be	AUX
ejpam-6081	290	47	taylor	taylor	PROPN
ejpam-6081	290	48	coefficients	coefficient	NOUN
ejpam-6081	290	49	and	and	CCONJ
ejpam-6081	290	50	logarithmic	logarithmic	ADJ
ejpam-6081	290	51	coefficients	coefficient	NOUN
ejpam-6081	290	52	of	of	ADP
ejpam-6081	290	53	functions	function	NOUN
ejpam-6081	290	54	and	and	CCONJ
ejpam-6081	290	55	inverse	inverse	NOUN
ejpam-6081	290	56	functions	function	NOUN
ejpam-6081	290	57	belonging	belong	VERB
ejpam-6081	290	58	to	to	ADP
ejpam-6081	290	59	the	the	DET
ejpam-6081	290	60	class	class	NOUN
ejpam-6081	290	61	gg	gg	NOUN
ejpam-6081	290	62	(	(	PUNCT
ejpam-6081	290	63	α	α	PROPN
ejpam-6081	290	64	,	,	PUNCT
ejpam-6081	290	65	δ	δ	PROPN
ejpam-6081	290	66	)	)	PUNCT
ejpam-6081	290	67	.	.	PUNCT
ejpam-6081	291	1	this	this	PRON
ejpam-6081	291	2	extends	extend	VERB
ejpam-6081	291	3	not	not	PART
ejpam-6081	291	4	only	only	ADV
ejpam-6081	291	5	the	the	DET
ejpam-6081	291	6	properties	property	NOUN
ejpam-6081	291	7	of	of	ADP
ejpam-6081	291	8	the	the	DET
ejpam-6081	291	9	class	class	NOUN
ejpam-6081	291	10	gg	gg	NOUN
ejpam-6081	291	11	(	(	PUNCT
ejpam-6081	291	12	α	α	PROPN
ejpam-6081	291	13	,	,	PUNCT
ejpam-6081	291	14	δ	δ	PROPN
ejpam-6081	291	15	)	)	PUNCT
ejpam-6081	291	16	but	but	CCONJ
ejpam-6081	291	17	also	also	ADV
ejpam-6081	291	18	those	those	PRON
ejpam-6081	291	19	of	of	ADP
ejpam-6081	291	20	gg	gg	PROPN
ejpam-6081	291	21	(	(	PUNCT
ejpam-6081	291	22	α	α	NOUN
ejpam-6081	291	23	)	)	PUNCT
ejpam-6081	291	24	,	,	PUNCT
ejpam-6081	291	25	gg	gg	PROPN
ejpam-6081	291	26	(	(	PUNCT
ejpam-6081	291	27	δ	δ	PROPN
ejpam-6081	291	28	)	)	PUNCT
ejpam-6081	291	29	,	,	PUNCT
ejpam-6081	291	30	and	and	CCONJ
ejpam-6081	291	31	gg	gg	PROPN
ejpam-6081	291	32	as	as	SCONJ
ejpam-6081	291	33	shown	show	VERB
ejpam-6081	291	34	in	in	ADP
ejpam-6081	291	35	corollaries	corollary	NOUN
ejpam-6081	291	36	1	1	NUM
ejpam-6081	291	37	-	-	SYM
ejpam-6081	291	38	3	3	NUM
ejpam-6081	291	39	.	.	PUNCT
ejpam-6081	292	1	the	the	DET
ejpam-6081	292	2	lemmas	lemma	NOUN
ejpam-6081	292	3	in	in	ADP
ejpam-6081	292	4	the	the	DET
ejpam-6081	292	5	preliminary	preliminary	ADJ
ejpam-6081	292	6	section	section	NOUN
ejpam-6081	292	7	have	have	AUX
ejpam-6081	292	8	proven	prove	VERB
ejpam-6081	292	9	invaluable	invaluable	ADJ
ejpam-6081	292	10	in	in	ADP
ejpam-6081	292	11	establishing	establish	VERB
ejpam-6081	292	12	upper	upper	ADJ
ejpam-6081	292	13	bounds	bound	NOUN
ejpam-6081	292	14	for	for	ADP
ejpam-6081	292	15	coefficient	coefficient	NOUN
ejpam-6081	292	16	functionals	functional	NOUN
ejpam-6081	292	17	in	in	ADP
ejpam-6081	292	18	theorems	theorem	NOUN
ejpam-6081	292	19	1	1	NUM
ejpam-6081	292	20	-	-	SYM
ejpam-6081	292	21	8	8	NUM
ejpam-6081	292	22	.	.	PUNCT
ejpam-6081	293	1	the	the	DET
ejpam-6081	293	2	findings	finding	NOUN
ejpam-6081	293	3	of	of	ADP
ejpam-6081	293	4	this	this	DET
ejpam-6081	293	5	work	work	NOUN
ejpam-6081	293	6	could	could	AUX
ejpam-6081	293	7	be	be	AUX
ejpam-6081	293	8	used	use	VERB
ejpam-6081	293	9	to	to	PART
ejpam-6081	293	10	further	far	ADV
ejpam-6081	293	11	investigate	investigate	VERB
ejpam-6081	293	12	the	the	DET
ejpam-6081	293	13	upper	upper	ADJ
ejpam-6081	293	14	bounds	bound	NOUN
ejpam-6081	293	15	for	for	ADP
ejpam-6081	293	16	the	the	DET
ejpam-6081	293	17	second	second	ADJ
ejpam-6081	293	18	-	-	PUNCT
ejpam-6081	293	19	order	order	NOUN
ejpam-6081	293	20	hankel	hankel	NOUN
ejpam-6081	293	21	,	,	PUNCT
ejpam-6081	293	22	toeplitz	toeplitz	NOUN
ejpam-6081	293	23	,	,	PUNCT
ejpam-6081	293	24	and	and	CCONJ
ejpam-6081	293	25	higher	high	ADJ
ejpam-6081	293	26	-	-	PUNCT
ejpam-6081	293	27	order	order	NOUN
ejpam-6081	293	28	vandermonde	vandermonde	ADJ
ejpam-6081	293	29	determinants	determinant	NOUN
ejpam-6081	293	30	,	,	PUNCT
ejpam-6081	293	31	specifically	specifically	ADV
ejpam-6081	293	32	within	within	ADP
ejpam-6081	293	33	bounded	bounded	ADJ
ejpam-6081	293	34	turning	turning	NOUN
ejpam-6081	293	35	functions	function	NOUN
ejpam-6081	293	36	connected	connect	VERB
ejpam-6081	293	37	to	to	ADP
ejpam-6081	293	38	gregory	gregory	PROPN
ejpam-6081	293	39	coefficients	coefficients	PROPN
ejpam-6081	293	40	.	.	PUNCT
ejpam-6081	294	1	n.	n.	PROPN
ejpam-6081	294	2	h.	h.	PROPN
ejpam-6081	294	3	a.	a.	PROPN
ejpam-6081	294	4	a.	a.	PROPN
ejpam-6081	294	5	wahid	wahid	PROPN
ejpam-6081	294	6	,	,	PUNCT
ejpam-6081	294	7	s.	s.	PROPN
ejpam-6081	294	8	c.	c.	PROPN
ejpam-6081	294	9	soh	soh	PROPN
ejpam-6081	294	10	/	/	SYM
ejpam-6081	294	11	eur	eur	PROPN
ejpam-6081	294	12	.	.	PUNCT
ejpam-6081	295	1	j.	j.	PROPN
ejpam-6081	295	2	pure	pure	PROPN
ejpam-6081	295	3	appl	appl	PROPN
ejpam-6081	295	4	.	.	PROPN
ejpam-6081	295	5	math	math	PROPN
ejpam-6081	295	6	,	,	PUNCT
ejpam-6081	295	7	18	18	NUM
ejpam-6081	295	8	(	(	PUNCT
ejpam-6081	295	9	2	2	NUM
ejpam-6081	295	10	)	)	PUNCT
ejpam-6081	295	11	(	(	PUNCT
ejpam-6081	295	12	2025	2025	NUM
ejpam-6081	295	13	)	)	PUNCT
ejpam-6081	295	14	,	,	PUNCT
ejpam-6081	295	15	6081	6081	NUM
ejpam-6081	295	16	15	15	NUM
ejpam-6081	295	17	of	of	ADP
ejpam-6081	295	18	16	16	NUM
ejpam-6081	295	19	acknowledgements	acknowledgement	NOUN
ejpam-6081	295	20	the	the	DET
ejpam-6081	295	21	authors	author	NOUN
ejpam-6081	295	22	gratefully	gratefully	ADV
ejpam-6081	295	23	appreciate	appreciate	VERB
ejpam-6081	295	24	the	the	DET
ejpam-6081	295	25	referees	referee	NOUN
ejpam-6081	295	26	’	’	PART
ejpam-6081	295	27	insightful	insightful	ADJ
ejpam-6081	295	28	remarks	remark	NOUN
ejpam-6081	295	29	and	and	CCONJ
ejpam-6081	295	30	express	express	VERB
ejpam-6081	295	31	their	their	PRON
ejpam-6081	295	32	deepest	deep	ADJ
ejpam-6081	295	33	gratitude	gratitude	NOUN
ejpam-6081	295	34	to	to	ADP
ejpam-6081	295	35	kementerian	kementerian	PROPN
ejpam-6081	295	36	pendidikan	pendidikan	PROPN
ejpam-6081	295	37	tinggi	tinggi	PROPN
ejpam-6081	295	38	(	(	PUNCT
ejpam-6081	295	39	kpt	kpt	PROPN
ejpam-6081	295	40	)	)	PUNCT
ejpam-6081	295	41	for	for	ADP
ejpam-6081	295	42	giving	give	VERB
ejpam-6081	295	43	the	the	DET
ejpam-6081	295	44	funding	funding	NOUN
ejpam-6081	295	45	(	(	PUNCT
ejpam-6081	295	46	reference	reference	NOUN
ejpam-6081	295	47	no	no	PROPN
ejpam-6081	295	48	.	.	PUNCT
ejpam-6081	296	1	frgs	frgs	PROPN
ejpam-6081	296	2	-	-	PUNCT
ejpam-6081	296	3	ec/1/2024	ec/1/2024	PROPN
ejpam-6081	296	4	/	/	SYM
ejpam-6081	296	5	stg06	stg06	NOUN
ejpam-6081	296	6	/	/	SYM
ejpam-6081	296	7	uitm/02/28	uitm/02/28	PROPN
ejpam-6081	296	8	)	)	PUNCT
ejpam-6081	296	9	that	that	PRON
ejpam-6081	296	10	supported	support	VERB
ejpam-6081	296	11	this	this	DET
ejpam-6081	296	12	research	research	NOUN
ejpam-6081	296	13	.	.	PUNCT
ejpam-6081	297	1	the	the	DET
ejpam-6081	297	2	authors	author	NOUN
ejpam-6081	297	3	also	also	ADV
ejpam-6081	297	4	thank	thank	VERB
ejpam-6081	297	5	the	the	DET
ejpam-6081	297	6	universiti	universiti	PROPN
ejpam-6081	297	7	teknologi	teknologi	PROPN
ejpam-6081	297	8	mara	mara	PROPN
ejpam-6081	297	9	for	for	ADP
ejpam-6081	297	10	their	their	PRON
ejpam-6081	297	11	support	support	NOUN
ejpam-6081	297	12	in	in	ADP
ejpam-6081	297	13	publishing	publish	VERB
ejpam-6081	297	14	this	this	DET
ejpam-6081	297	15	paper	paper	NOUN
ejpam-6081	297	16	.	.	PUNCT
ejpam-6081	298	1	references	reference	NOUN
ejpam-6081	298	2	[	[	X
ejpam-6081	298	3	1	1	NUM
ejpam-6081	298	4	]	]	PUNCT
ejpam-6081	298	5	i.	i.	PROPN
ejpam-6081	298	6	m.	m.	PROPN
ejpam-6081	298	7	milin	milin	PROPN
ejpam-6081	298	8	.	.	PUNCT
ejpam-6081	299	1	univalent	univalent	ADJ
ejpam-6081	299	2	functions	function	NOUN
ejpam-6081	299	3	and	and	CCONJ
ejpam-6081	299	4	orthonormal	orthonormal	ADJ
ejpam-6081	299	5	systems	system	NOUN
ejpam-6081	299	6	,	,	PUNCT
ejpam-6081	299	7	volume	volume	NOUN
ejpam-6081	299	8	49	49	NUM
ejpam-6081	299	9	of	of	ADP
ejpam-6081	299	10	translations	translation	NOUN
ejpam-6081	299	11	of	of	ADP
ejpam-6081	299	12	mathematical	mathematical	ADJ
ejpam-6081	299	13	monographs	monograph	NOUN
ejpam-6081	299	14	.	.	PUNCT
ejpam-6081	300	1	american	american	PROPN
ejpam-6081	300	2	mathematical	mathematical	PROPN
ejpam-6081	300	3	society	society	NOUN
ejpam-6081	300	4	,	,	PUNCT
ejpam-6081	300	5	providence	providence	NOUN
ejpam-6081	300	6	,	,	PUNCT
ejpam-6081	300	7	ri	ri	NOUN
ejpam-6081	300	8	,	,	PUNCT
ejpam-6081	300	9	1977	1977	NUM
ejpam-6081	300	10	.	.	PUNCT
ejpam-6081	301	1	[	[	X
ejpam-6081	301	2	2	2	NUM
ejpam-6081	301	3	]	]	PUNCT
ejpam-6081	301	4	i.	i.	PROPN
ejpam-6081	301	5	m.	m.	PROPN
ejpam-6081	301	6	milin	milin	PROPN
ejpam-6081	301	7	.	.	PUNCT
ejpam-6081	302	1	on	on	ADP
ejpam-6081	302	2	a	a	DET
ejpam-6081	302	3	property	property	NOUN
ejpam-6081	302	4	of	of	ADP
ejpam-6081	302	5	the	the	DET
ejpam-6081	302	6	logarithmic	logarithmic	ADJ
ejpam-6081	302	7	coefficients	coefficient	NOUN
ejpam-6081	302	8	of	of	ADP
ejpam-6081	302	9	univalent	univalent	ADJ
ejpam-6081	302	10	functions	function	NOUN
ejpam-6081	302	11	.	.	PUNCT
ejpam-6081	303	1	metric	metric	ADJ
ejpam-6081	303	2	questions	question	NOUN
ejpam-6081	303	3	in	in	ADP
ejpam-6081	303	4	the	the	DET
ejpam-6081	303	5	theory	theory	NOUN
ejpam-6081	303	6	of	of	ADP
ejpam-6081	303	7	functions	function	NOUN
ejpam-6081	303	8	,	,	PUNCT
ejpam-6081	303	9	pages	page	NOUN
ejpam-6081	303	10	86–90	86–90	NUM
ejpam-6081	303	11	,	,	PUNCT
ejpam-6081	303	12	1980	1980	NUM
ejpam-6081	303	13	.	.	PUNCT
ejpam-6081	304	1	[	[	X
ejpam-6081	304	2	3	3	NUM
ejpam-6081	304	3	]	]	X
ejpam-6081	304	4	i.	i.	PROPN
ejpam-6081	304	5	m.	m.	PROPN
ejpam-6081	304	6	milin	milin	PROPN
ejpam-6081	304	7	.	.	PUNCT
ejpam-6081	305	1	on	on	ADP
ejpam-6081	305	2	one	one	NUM
ejpam-6081	305	3	conjecture	conjecture	NOUN
ejpam-6081	305	4	for	for	ADP
ejpam-6081	305	5	the	the	DET
ejpam-6081	305	6	logarithmic	logarithmic	ADJ
ejpam-6081	305	7	coefficients	coefficient	NOUN
ejpam-6081	305	8	of	of	ADP
ejpam-6081	305	9	univalent	univalent	ADJ
ejpam-6081	305	10	functions	function	NOUN
ejpam-6081	305	11	.	.	PUNCT
ejpam-6081	306	1	zapiski	zapiski	PROPN
ejpam-6081	306	2	nauchnykh	nauchnykh	PROPN
ejpam-6081	306	3	seminarov	seminarov	PROPN
ejpam-6081	306	4	pomi	pomi	NOUN
ejpam-6081	306	5	,	,	PUNCT
ejpam-6081	306	6	125:135–143	125:135–143	NUM
ejpam-6081	306	7	,	,	PUNCT
ejpam-6081	306	8	1983	1983	NUM
ejpam-6081	306	9	.	.	PUNCT
ejpam-6081	307	1	[	[	X
ejpam-6081	307	2	4	4	X
ejpam-6081	307	3	]	]	SYM
ejpam-6081	307	4	louis	louis	ADJ
ejpam-6081	307	5	de	de	X
ejpam-6081	307	6	branges	brange	NOUN
ejpam-6081	307	7	.	.	PUNCT
ejpam-6081	308	1	a	a	DET
ejpam-6081	308	2	proof	proof	NOUN
ejpam-6081	308	3	of	of	ADP
ejpam-6081	308	4	the	the	DET
ejpam-6081	308	5	bieberbach	bieberbach	NOUN
ejpam-6081	308	6	conjecture	conjecture	NOUN
ejpam-6081	308	7	.	.	PUNCT
ejpam-6081	309	1	acta	acta	PROPN
ejpam-6081	309	2	mathematica	mathematica	PROPN
ejpam-6081	309	3	,	,	PUNCT
ejpam-6081	309	4	154(12):137–152	154(12):137–152	PROPN
ejpam-6081	309	5	,	,	PUNCT
ejpam-6081	309	6	1985	1985	NUM
ejpam-6081	309	7	.	.	PUNCT
ejpam-6081	310	1	[	[	X
ejpam-6081	310	2	5	5	NUM
ejpam-6081	310	3	]	]	X
ejpam-6081	310	4	i.	i.	PROPN
ejpam-6081	310	5	r.	r.	PROPN
ejpam-6081	310	6	kayumov	kayumov	PROPN
ejpam-6081	310	7	.	.	PUNCT
ejpam-6081	311	1	on	on	ADP
ejpam-6081	311	2	brennan	brennan	PROPN
ejpam-6081	311	3	’s	’s	PART
ejpam-6081	311	4	conjecture	conjecture	NOUN
ejpam-6081	311	5	for	for	ADP
ejpam-6081	311	6	a	a	DET
ejpam-6081	311	7	special	special	ADJ
ejpam-6081	311	8	class	class	NOUN
ejpam-6081	311	9	of	of	ADP
ejpam-6081	311	10	functions	function	NOUN
ejpam-6081	311	11	.	.	PUNCT
ejpam-6081	312	1	mathematical	mathematical	ADJ
ejpam-6081	312	2	notes	note	NOUN
ejpam-6081	312	3	,	,	PUNCT
ejpam-6081	312	4	78(3	78(3	PROPN
ejpam-6081	312	5	-	-	PUNCT
ejpam-6081	312	6	4):498–502	4):498–502	NUM
ejpam-6081	312	7	,	,	PUNCT
ejpam-6081	312	8	2005	2005	NUM
ejpam-6081	312	9	.	.	PUNCT
ejpam-6081	313	1	[	[	X
ejpam-6081	313	2	6	6	NUM
ejpam-6081	313	3	]	]	PUNCT
ejpam-6081	313	4	v.	v.	CCONJ
ejpam-6081	313	5	v.	v.	ADP
ejpam-6081	313	6	andreev	andreev	PROPN
ejpam-6081	313	7	and	and	CCONJ
ejpam-6081	314	1	p.	p.	NOUN
ejpam-6081	314	2	l.	l.	PROPN
ejpam-6081	314	3	duren	duren	PROPN
ejpam-6081	314	4	.	.	PROPN
ejpam-6081	315	1	inequalities	inequality	NOUN
ejpam-6081	315	2	for	for	ADP
ejpam-6081	315	3	logarithmic	logarithmic	ADJ
ejpam-6081	315	4	coefficients	coefficient	NOUN
ejpam-6081	315	5	of	of	ADP
ejpam-6081	315	6	univalent	univalent	ADJ
ejpam-6081	315	7	functions	function	NOUN
ejpam-6081	315	8	and	and	CCONJ
ejpam-6081	315	9	their	their	PRON
ejpam-6081	315	10	derivatives	derivative	NOUN
ejpam-6081	315	11	.	.	PUNCT
ejpam-6081	316	1	indiana	indiana	PROPN
ejpam-6081	316	2	university	university	PROPN
ejpam-6081	316	3	mathematics	mathematics	PROPN
ejpam-6081	316	4	journal	journal	NOUN
ejpam-6081	316	5	,	,	PUNCT
ejpam-6081	316	6	37(4):721	37(4):721	NUM
ejpam-6081	316	7	–	–	PUNCT
ejpam-6081	316	8	733	733	NUM
ejpam-6081	316	9	,	,	PUNCT
ejpam-6081	316	10	1988	1988	NUM
ejpam-6081	316	11	.	.	PUNCT
ejpam-6081	317	1	[	[	X
ejpam-6081	317	2	7	7	X
ejpam-6081	317	3	]	]	X
ejpam-6081	317	4	m.	m.	NOUN
ejpam-6081	317	5	m.	m.	PROPN
ejpam-6081	317	6	elhosh	elhosh	PROPN
ejpam-6081	317	7	.	.	PUNCT
ejpam-6081	318	1	on	on	ADP
ejpam-6081	318	2	the	the	DET
ejpam-6081	318	3	logarithmic	logarithmic	ADJ
ejpam-6081	318	4	coefficients	coefficient	NOUN
ejpam-6081	318	5	of	of	ADP
ejpam-6081	318	6	close	close	NOUN
ejpam-6081	318	7	-	-	PUNCT
ejpam-6081	318	8	to	to	ADP
ejpam-6081	318	9	-	-	PUNCT
ejpam-6081	318	10	convex	convex	NOUN
ejpam-6081	318	11	functions	function	NOUN
ejpam-6081	318	12	.	.	PUNCT
ejpam-6081	319	1	journal	journal	NOUN
ejpam-6081	319	2	of	of	ADP
ejpam-6081	319	3	the	the	DET
ejpam-6081	319	4	australian	australian	ADJ
ejpam-6081	319	5	mathematical	mathematical	ADJ
ejpam-6081	319	6	society	society	NOUN
ejpam-6081	319	7	,	,	PUNCT
ejpam-6081	319	8	60(1):1–6	60(1):1–6	NOUN
ejpam-6081	319	9	,	,	PUNCT
ejpam-6081	319	10	1996	1996	NUM
ejpam-6081	319	11	.	.	PUNCT
ejpam-6081	320	1	[	[	X
ejpam-6081	320	2	8	8	NUM
ejpam-6081	320	3	]	]	X
ejpam-6081	320	4	d.	d.	PROPN
ejpam-6081	320	5	girela	girela	PROPN
ejpam-6081	320	6	.	.	PUNCT
ejpam-6081	321	1	logarithmic	logarithmic	ADJ
ejpam-6081	321	2	coefficients	coefficient	NOUN
ejpam-6081	321	3	of	of	ADP
ejpam-6081	321	4	univalent	univalent	ADJ
ejpam-6081	321	5	functions	function	NOUN
ejpam-6081	321	6	.	.	PUNCT
ejpam-6081	322	1	annales	annale	NOUN
ejpam-6081	322	2	academiae	academiae	PROPN
ejpam-6081	322	3	scientiarum	scientiarum	PROPN
ejpam-6081	322	4	fennicae	fennicae	PROPN
ejpam-6081	322	5	mathematica	mathematica	PROPN
ejpam-6081	322	6	,	,	PUNCT
ejpam-6081	322	7	25(2):337–350	25(2):337–350	PROPN
ejpam-6081	322	8	,	,	PUNCT
ejpam-6081	322	9	2000	2000	NUM
ejpam-6081	322	10	.	.	PUNCT
ejpam-6081	323	1	[	[	X
ejpam-6081	323	2	9	9	NUM
ejpam-6081	323	3	]	]	X
ejpam-6081	323	4	o.	o.	PROPN
ejpam-6081	323	5	roth	roth	PROPN
ejpam-6081	323	6	.	.	PUNCT
ejpam-6081	324	1	a	a	DET
ejpam-6081	324	2	sharp	sharp	ADJ
ejpam-6081	324	3	inequality	inequality	NOUN
ejpam-6081	324	4	for	for	ADP
ejpam-6081	324	5	the	the	DET
ejpam-6081	324	6	logarithmic	logarithmic	ADJ
ejpam-6081	324	7	coefficients	coefficient	NOUN
ejpam-6081	324	8	of	of	ADP
ejpam-6081	324	9	univalent	univalent	ADJ
ejpam-6081	324	10	functions	function	NOUN
ejpam-6081	324	11	.	.	PUNCT
ejpam-6081	325	1	proceedings	proceeding	NOUN
ejpam-6081	325	2	of	of	ADP
ejpam-6081	325	3	the	the	DET
ejpam-6081	325	4	american	american	PROPN
ejpam-6081	325	5	mathematical	mathematical	PROPN
ejpam-6081	325	6	society	society	NOUN
ejpam-6081	325	7	,	,	PUNCT
ejpam-6081	325	8	135(7):2051–2054	135(7):2051–2054	NUM
ejpam-6081	325	9	,	,	PUNCT
ejpam-6081	325	10	2007	2007	NUM
ejpam-6081	325	11	.	.	PUNCT
ejpam-6081	326	1	[	[	X
ejpam-6081	326	2	10	10	NUM
ejpam-6081	326	3	]	]	X
ejpam-6081	326	4	s.	s.	PROPN
ejpam-6081	326	5	ponnusamy	ponnusamy	PROPN
ejpam-6081	326	6	,	,	PUNCT
ejpam-6081	326	7	n.	n.	PROPN
ejpam-6081	326	8	l.	l.	PROPN
ejpam-6081	326	9	sharma	sharma	PROPN
ejpam-6081	326	10	,	,	PUNCT
ejpam-6081	326	11	and	and	CCONJ
ejpam-6081	326	12	k.	k.	PROPN
ejpam-6081	326	13	j.	j.	PROPN
ejpam-6081	326	14	wirths	wirths	PROPN
ejpam-6081	326	15	.	.	PUNCT
ejpam-6081	327	1	logarithmic	logarithmic	ADJ
ejpam-6081	327	2	coefficients	coefficient	NOUN
ejpam-6081	327	3	of	of	ADP
ejpam-6081	327	4	the	the	DET
ejpam-6081	327	5	inverse	inverse	NOUN
ejpam-6081	327	6	of	of	ADP
ejpam-6081	327	7	univalent	univalent	ADJ
ejpam-6081	327	8	functions	function	NOUN
ejpam-6081	327	9	.	.	PUNCT
ejpam-6081	328	1	results	result	NOUN
ejpam-6081	328	2	in	in	ADP
ejpam-6081	328	3	mathematics	mathematic	NOUN
ejpam-6081	328	4	,	,	PUNCT
ejpam-6081	328	5	73(4):160	73(4):160	PROPN
ejpam-6081	328	6	,	,	PUNCT
ejpam-6081	328	7	2018	2018	NUM
ejpam-6081	328	8	.	.	PUNCT
ejpam-6081	329	1	[	[	X
ejpam-6081	329	2	11	11	NUM
ejpam-6081	329	3	]	]	PUNCT
ejpam-6081	329	4	s.	s.	PROPN
ejpam-6081	329	5	p.	p.	PROPN
ejpam-6081	329	6	vijayalakshmi	vijayalakshmi	PROPN
ejpam-6081	329	7	,	,	PUNCT
ejpam-6081	329	8	s.	s.	PROPN
ejpam-6081	329	9	bulut	bulut	PROPN
ejpam-6081	329	10	,	,	PUNCT
ejpam-6081	329	11	and	and	CCONJ
ejpam-6081	329	12	t.	t.	PROPN
ejpam-6081	329	13	v.	v.	PROPN
ejpam-6081	329	14	sudharsan	sudharsan	PROPN
ejpam-6081	329	15	.	.	PUNCT
ejpam-6081	330	1	vandermonde	vandermonde	VERB
ejpam-6081	330	2	determinant	determinant	ADJ
ejpam-6081	330	3	for	for	ADP
ejpam-6081	330	4	a	a	DET
ejpam-6081	330	5	certain	certain	ADJ
ejpam-6081	330	6	sakaguchi	sakaguchi	ADJ
ejpam-6081	330	7	type	type	NOUN
ejpam-6081	330	8	function	function	NOUN
ejpam-6081	330	9	in	in	ADP
ejpam-6081	330	10	limaçon	limaçon	NOUN
ejpam-6081	330	11	domain	domain	NOUN
ejpam-6081	330	12	.	.	PUNCT
ejpam-6081	331	1	asian	asian	ADJ
ejpam-6081	331	2	-	-	PUNCT
ejpam-6081	331	3	european	european	ADJ
ejpam-6081	331	4	journal	journal	NOUN
ejpam-6081	331	5	of	of	ADP
ejpam-6081	331	6	mathematics	mathematic	NOUN
ejpam-6081	331	7	,	,	PUNCT
ejpam-6081	331	8	15(12):2250212	15(12):2250212	NUM
ejpam-6081	331	9	,	,	PUNCT
ejpam-6081	331	10	2022	2022	NUM
ejpam-6081	331	11	.	.	PUNCT
ejpam-6081	332	1	[	[	X
ejpam-6081	332	2	12	12	NUM
ejpam-6081	332	3	]	]	X
ejpam-6081	332	4	y.	y.	PROPN
ejpam-6081	332	5	li	li	PROPN
ejpam-6081	332	6	and	and	CCONJ
ejpam-6081	332	7	x.	x.	NOUN
ejpam-6081	332	8	ding	ding	PROPN
ejpam-6081	332	9	.	.	PUNCT
ejpam-6081	333	1	vandermonde	vandermonde	ADJ
ejpam-6081	333	2	determinant	determinant	ADJ
ejpam-6081	333	3	and	and	CCONJ
ejpam-6081	333	4	its	its	PRON
ejpam-6081	333	5	applications	application	NOUN
ejpam-6081	333	6	.	.	PUNCT
ejpam-6081	334	1	journal	journal	NOUN
ejpam-6081	334	2	of	of	ADP
ejpam-6081	334	3	education	education	NOUN
ejpam-6081	334	4	and	and	CCONJ
ejpam-6081	334	5	culture	culture	NOUN
ejpam-6081	334	6	studies	study	NOUN
ejpam-6081	334	7	,	,	PUNCT
ejpam-6081	334	8	7(4):16–24	7(4):16–24	NUM
ejpam-6081	334	9	,	,	PUNCT
ejpam-6081	334	10	2023	2023	NUM
ejpam-6081	334	11	.	.	PUNCT
ejpam-6081	335	1	[	[	X
ejpam-6081	335	2	13	13	NUM
ejpam-6081	335	3	]	]	X
ejpam-6081	335	4	n.	n.	PROPN
ejpam-6081	335	5	h.	h.	PROPN
ejpam-6081	335	6	a.	a.	PROPN
ejpam-6081	335	7	a.	a.	PROPN
ejpam-6081	335	8	wahid	wahid	PROPN
ejpam-6081	335	9	,	,	PUNCT
ejpam-6081	335	10	i.	i.	PROPN
ejpam-6081	335	11	q.	q.	PROPN
ejpam-6081	335	12	amirnuddin	amirnuddin	PROPN
ejpam-6081	335	13	,	,	PUNCT
ejpam-6081	335	14	and	and	CCONJ
ejpam-6081	335	15	n.	n.	PROPN
ejpam-6081	335	16	i.	i.	PROPN
ejpam-6081	335	17	m.	m.	PROPN
ejpam-6081	335	18	azmi	azmi	PROPN
ejpam-6081	335	19	.	.	PUNCT
ejpam-6081	336	1	bounds	bound	VERB
ejpam-6081	336	2	for	for	ADP
ejpam-6081	336	3	certain	certain	ADJ
ejpam-6081	336	4	determinants	determinant	NOUN
ejpam-6081	336	5	of	of	ADP
ejpam-6081	336	6	logarithmic	logarithmic	ADJ
ejpam-6081	336	7	coefficients	coefficient	NOUN
ejpam-6081	336	8	for	for	ADP
ejpam-6081	336	9	the	the	DET
ejpam-6081	336	10	class	class	NOUN
ejpam-6081	336	11	of	of	ADP
ejpam-6081	336	12	functions	function	NOUN
ejpam-6081	336	13	with	with	ADP
ejpam-6081	336	14	bounded	bounded	ADJ
ejpam-6081	336	15	turning	turning	NOUN
ejpam-6081	336	16	.	.	PUNCT
ejpam-6081	337	1	european	european	PROPN
ejpam-6081	337	2	journal	journal	PROPN
ejpam-6081	337	3	of	of	ADP
ejpam-6081	337	4	pure	pure	ADJ
ejpam-6081	337	5	and	and	CCONJ
ejpam-6081	337	6	applied	applied	ADJ
ejpam-6081	337	7	mathematics	mathematic	NOUN
ejpam-6081	337	8	,	,	PUNCT
ejpam-6081	337	9	17(4):2738–2752	17(4):2738–2752	NUM
ejpam-6081	337	10	,	,	PUNCT
ejpam-6081	337	11	2024	2024	NUM
ejpam-6081	337	12	.	.	PUNCT
ejpam-6081	338	1	[	[	X
ejpam-6081	338	2	14	14	NUM
ejpam-6081	338	3	]	]	X
ejpam-6081	338	4	n.	n.	PROPN
ejpam-6081	338	5	h.	h.	PROPN
ejpam-6081	338	6	a.	a.	PROPN
ejpam-6081	338	7	a.	a.	PROPN
ejpam-6081	338	8	wahid	wahid	PROPN
ejpam-6081	338	9	,	,	PUNCT
ejpam-6081	338	10	a.	a.	NOUN
ejpam-6081	338	11	tumiran	tumiran	NOUN
ejpam-6081	338	12	,	,	PUNCT
ejpam-6081	338	13	and	and	CCONJ
ejpam-6081	338	14	t.	t.	PROPN
ejpam-6081	338	15	g.	g.	PROPN
ejpam-6081	338	16	shaba	shaba	PROPN
ejpam-6081	338	17	.	.	PUNCT
ejpam-6081	339	1	hankel	hankel	NOUN
ejpam-6081	339	2	and	and	CCONJ
ejpam-6081	339	3	toeplitz	toeplitz	NOUN
ejpam-6081	339	4	determinants	determinant	NOUN
ejpam-6081	339	5	of	of	ADP
ejpam-6081	339	6	logarithmic	logarithmic	ADJ
ejpam-6081	339	7	coefficients	coefficient	NOUN
ejpam-6081	339	8	of	of	ADP
ejpam-6081	339	9	inverse	inverse	NOUN
ejpam-6081	339	10	functions	function	NOUN
ejpam-6081	339	11	for	for	ADP
ejpam-6081	339	12	the	the	DET
ejpam-6081	339	13	subclass	subclass	NOUN
ejpam-6081	339	14	of	of	ADP
ejpam-6081	339	15	starlike	starlike	NOUN
ejpam-6081	339	16	functions	function	NOUN
ejpam-6081	339	17	with	with	ADP
ejpam-6081	339	18	respect	respect	NOUN
ejpam-6081	339	19	to	to	ADP
ejpam-6081	339	20	symmetric	symmetric	ADJ
ejpam-6081	339	21	conjugate	conjugate	ADJ
ejpam-6081	339	22	points	point	NOUN
ejpam-6081	339	23	.	.	PUNCT
ejpam-6081	340	1	european	european	ADJ
ejpam-6081	340	2	journal	journal	PROPN
ejpam-6081	340	3	of	of	ADP
ejpam-6081	340	4	pure	pure	ADJ
ejpam-6081	340	5	and	and	CCONJ
ejpam-6081	340	6	applied	applied	ADJ
ejpam-6081	340	7	mathematics	mathematic	NOUN
ejpam-6081	340	8	,	,	PUNCT
ejpam-6081	340	9	17(3):1818–1830	17(3):1818–1830	NUM
ejpam-6081	340	10	,	,	PUNCT
ejpam-6081	340	11	2024	2024	NUM
ejpam-6081	340	12	.	.	PUNCT
ejpam-6081	341	1	[	[	X
ejpam-6081	341	2	15	15	NUM
ejpam-6081	341	3	]	]	X
ejpam-6081	341	4	l.	l.	PROPN
ejpam-6081	341	5	shi	shi	PROPN
ejpam-6081	341	6	,	,	PUNCT
ejpam-6081	341	7	m.	m.	NOUN
ejpam-6081	341	8	abbas	abbas	PROPN
ejpam-6081	341	9	,	,	PUNCT
ejpam-6081	341	10	m.	m.	NOUN
ejpam-6081	341	11	raza	raza	PROPN
ejpam-6081	341	12	,	,	PUNCT
ejpam-6081	341	13	m.	m.	PROPN
ejpam-6081	341	14	arif	arif	PROPN
ejpam-6081	341	15	,	,	PUNCT
ejpam-6081	341	16	and	and	CCONJ
ejpam-6081	341	17	p.	p.	PROPN
ejpam-6081	341	18	kumam	kumam	PROPN
ejpam-6081	341	19	.	.	PUNCT
ejpam-6081	342	1	inverse	inverse	PROPN
ejpam-6081	342	2	logarithmic	logarithmic	ADJ
ejpam-6081	342	3	coefficient	coefficient	NOUN
ejpam-6081	342	4	n.	n.	PROPN
ejpam-6081	342	5	h.	h.	PROPN
ejpam-6081	342	6	a.	a.	PROPN
ejpam-6081	342	7	a.	a.	PROPN
ejpam-6081	342	8	wahid	wahid	PROPN
ejpam-6081	342	9	,	,	PUNCT
ejpam-6081	342	10	s.	s.	PROPN
ejpam-6081	342	11	c.	c.	PROPN
ejpam-6081	342	12	soh	soh	PROPN
ejpam-6081	342	13	/	/	SYM
ejpam-6081	342	14	eur	eur	PROPN
ejpam-6081	342	15	.	.	PUNCT
ejpam-6081	343	1	j.	j.	PROPN
ejpam-6081	343	2	pure	pure	PROPN
ejpam-6081	343	3	appl	appl	PROPN
ejpam-6081	343	4	.	.	PROPN
ejpam-6081	343	5	math	math	PROPN
ejpam-6081	343	6	,	,	PUNCT
ejpam-6081	343	7	18	18	NUM
ejpam-6081	343	8	(	(	PUNCT
ejpam-6081	343	9	2	2	NUM
ejpam-6081	343	10	)	)	PUNCT
ejpam-6081	343	11	(	(	PUNCT
ejpam-6081	343	12	2025	2025	NUM
ejpam-6081	343	13	)	)	PUNCT
ejpam-6081	343	14	,	,	PUNCT
ejpam-6081	343	15	6081	6081	NUM
ejpam-6081	343	16	16	16	NUM
ejpam-6081	343	17	of	of	ADP
ejpam-6081	343	18	16	16	NUM
ejpam-6081	343	19	bounds	bound	NOUN
ejpam-6081	343	20	for	for	ADP
ejpam-6081	343	21	starlike	starlike	NOUN
ejpam-6081	343	22	functions	function	NOUN
ejpam-6081	343	23	subordinated	subordinate	VERB
ejpam-6081	343	24	to	to	ADP
ejpam-6081	343	25	the	the	DET
ejpam-6081	343	26	exponential	exponential	ADJ
ejpam-6081	343	27	functions	function	NOUN
ejpam-6081	343	28	.	.	PUNCT
ejpam-6081	344	1	journal	journal	NOUN
ejpam-6081	344	2	of	of	ADP
ejpam-6081	344	3	inequalities	inequality	NOUN
ejpam-6081	344	4	and	and	CCONJ
ejpam-6081	344	5	applications	application	NOUN
ejpam-6081	344	6	,	,	PUNCT
ejpam-6081	344	7	2024(1):17	2024(1):17	NUM
ejpam-6081	344	8	,	,	PUNCT
ejpam-6081	344	9	2024	2024	NUM
ejpam-6081	344	10	.	.	PUNCT
ejpam-6081	345	1	[	[	X
ejpam-6081	345	2	16	16	NUM
ejpam-6081	345	3	]	]	PUNCT
ejpam-6081	345	4	m.	m.	NOUN
ejpam-6081	345	5	obradović	obradović	NOUN
ejpam-6081	345	6	and	and	CCONJ
ejpam-6081	345	7	n.	n.	PROPN
ejpam-6081	345	8	tuneski	tuneski	PROPN
ejpam-6081	345	9	.	.	PUNCT
ejpam-6081	346	1	hankel	hankel	NOUN
ejpam-6081	346	2	determinant	determinant	ADJ
ejpam-6081	346	3	of	of	ADP
ejpam-6081	346	4	second	second	ADJ
ejpam-6081	346	5	order	order	NOUN
ejpam-6081	346	6	for	for	ADP
ejpam-6081	346	7	inverse	inverse	NOUN
ejpam-6081	346	8	functions	function	NOUN
ejpam-6081	346	9	of	of	ADP
ejpam-6081	346	10	certain	certain	ADJ
ejpam-6081	346	11	classes	class	NOUN
ejpam-6081	346	12	of	of	ADP
ejpam-6081	346	13	univalent	univalent	ADJ
ejpam-6081	346	14	functions	function	NOUN
ejpam-6081	346	15	.	.	PUNCT
ejpam-6081	347	1	advances	advance	NOUN
ejpam-6081	347	2	in	in	ADP
ejpam-6081	347	3	mathematics	mathematic	NOUN
ejpam-6081	347	4	:	:	PUNCT
ejpam-6081	347	5	scientific	scientific	ADJ
ejpam-6081	347	6	journal	journal	NOUN
ejpam-6081	347	7	,	,	PUNCT
ejpam-6081	347	8	12(4):519–528	12(4):519–528	NUM
ejpam-6081	347	9	,	,	PUNCT
ejpam-6081	347	10	2023	2023	NUM
ejpam-6081	347	11	.	.	PUNCT
ejpam-6081	348	1	[	[	X
ejpam-6081	348	2	17	17	NUM
ejpam-6081	348	3	]	]	PUNCT
ejpam-6081	348	4	s.	s.	PROPN
ejpam-6081	348	5	h.	h.	PROPN
ejpam-6081	348	6	hadi	hadi	PROPN
ejpam-6081	348	7	,	,	PUNCT
ejpam-6081	348	8	y.	y.	PROPN
ejpam-6081	348	9	h.	h.	PROPN
ejpam-6081	348	10	saleem	saleem	PROPN
ejpam-6081	348	11	,	,	PUNCT
ejpam-6081	348	12	a.	a.	NOUN
ejpam-6081	348	13	a.	a.	NOUN
ejpam-6081	348	14	lupaş	lupaş	PROPN
ejpam-6081	348	15	,	,	PUNCT
ejpam-6081	348	16	k.	k.	PROPN
ejpam-6081	348	17	m.	m.	PROPN
ejpam-6081	348	18	alshammari	alshammari	PROPN
ejpam-6081	348	19	,	,	PUNCT
ejpam-6081	348	20	and	and	CCONJ
ejpam-6081	348	21	a.	a.	PROPN
ejpam-6081	348	22	alatawi	alatawi	PROPN
ejpam-6081	348	23	.	.	PUNCT
ejpam-6081	349	1	toeplitz	toeplitz	NOUN
ejpam-6081	349	2	determinants	determinant	NOUN
ejpam-6081	349	3	for	for	ADP
ejpam-6081	349	4	inverse	inverse	NOUN
ejpam-6081	349	5	of	of	ADP
ejpam-6081	349	6	analytic	analytic	ADJ
ejpam-6081	349	7	functions	function	NOUN
ejpam-6081	349	8	.	.	PUNCT
ejpam-6081	350	1	mathematics	mathematic	NOUN
ejpam-6081	350	2	,	,	PUNCT
ejpam-6081	350	3	13(4):676	13(4):676	NUM
ejpam-6081	350	4	,	,	PUNCT
ejpam-6081	350	5	2025	2025	NUM
ejpam-6081	350	6	.	.	PUNCT
ejpam-6081	351	1	[	[	X
ejpam-6081	351	2	18	18	NUM
ejpam-6081	351	3	]	]	X
ejpam-6081	351	4	s.	s.	PROPN
ejpam-6081	351	5	kazımoğlu	kazımoğlu	PROPN
ejpam-6081	351	6	,	,	PUNCT
ejpam-6081	351	7	e.	e.	PROPN
ejpam-6081	351	8	deniz	deniz	PROPN
ejpam-6081	351	9	,	,	PUNCT
ejpam-6081	351	10	and	and	CCONJ
ejpam-6081	351	11	h.	h.	PROPN
ejpam-6081	351	12	m.	m.	PROPN
ejpam-6081	351	13	srivastava	srivastava	PROPN
ejpam-6081	351	14	.	.	PUNCT
ejpam-6081	352	1	sharp	sharp	ADJ
ejpam-6081	352	2	coefficients	coefficient	NOUN
ejpam-6081	352	3	bounds	bound	VERB
ejpam-6081	352	4	for	for	ADP
ejpam-6081	352	5	starlike	starlike	NOUN
ejpam-6081	352	6	functions	function	NOUN
ejpam-6081	352	7	associated	associate	VERB
ejpam-6081	352	8	with	with	ADP
ejpam-6081	352	9	gregory	gregory	PROPN
ejpam-6081	352	10	coefficients	coefficient	NOUN
ejpam-6081	352	11	.	.	PUNCT
ejpam-6081	353	1	complex	complex	ADJ
ejpam-6081	353	2	analysis	analysis	NOUN
ejpam-6081	353	3	and	and	CCONJ
ejpam-6081	353	4	operator	operator	NOUN
ejpam-6081	353	5	theory	theory	NOUN
ejpam-6081	353	6	,	,	PUNCT
ejpam-6081	353	7	18(1):6	18(1):6	PROPN
ejpam-6081	353	8	,	,	PUNCT
ejpam-6081	353	9	2024	2024	NUM
ejpam-6081	353	10	.	.	PUNCT
ejpam-6081	354	1	[	[	X
ejpam-6081	354	2	19	19	NUM
ejpam-6081	354	3	]	]	X
ejpam-6081	354	4	h.	h.	PROPN
ejpam-6081	354	5	m.	m.	PROPN
ejpam-6081	354	6	srivastava	srivastava	PROPN
ejpam-6081	354	7	,	,	PUNCT
ejpam-6081	354	8	n.	n.	PROPN
ejpam-6081	354	9	e.	e.	PROPN
ejpam-6081	354	10	cho	cho	PROPN
ejpam-6081	354	11	,	,	PUNCT
ejpam-6081	354	12	a.	a.	NOUN
ejpam-6081	354	13	a.	a.	PROPN
ejpam-6081	354	14	alderremy	alderremy	PROPN
ejpam-6081	354	15	,	,	PUNCT
ejpam-6081	354	16	a.	a.	NOUN
ejpam-6081	354	17	a.	a.	NOUN
ejpam-6081	354	18	lupaş	lupaş	PROPN
ejpam-6081	354	19	,	,	PUNCT
ejpam-6081	354	20	e.	e.	PROPN
ejpam-6081	354	21	e.	e.	PROPN
ejpam-6081	354	22	mahmoud	mahmoud	PROPN
ejpam-6081	354	23	,	,	PUNCT
ejpam-6081	354	24	and	and	CCONJ
ejpam-6081	354	25	s.	s.	PROPN
ejpam-6081	354	26	khan	khan	PROPN
ejpam-6081	354	27	.	.	PUNCT
ejpam-6081	355	1	sharp	sharp	ADJ
ejpam-6081	355	2	inequalities	inequality	NOUN
ejpam-6081	355	3	for	for	ADP
ejpam-6081	355	4	a	a	DET
ejpam-6081	355	5	class	class	NOUN
ejpam-6081	355	6	of	of	ADP
ejpam-6081	355	7	novel	novel	ADJ
ejpam-6081	355	8	convex	convex	NOUN
ejpam-6081	355	9	functions	function	NOUN
ejpam-6081	355	10	associated	associate	VERB
ejpam-6081	355	11	with	with	ADP
ejpam-6081	355	12	gregory	gregory	PROPN
ejpam-6081	355	13	polynomials	polynomial	NOUN
ejpam-6081	355	14	.	.	PUNCT
ejpam-6081	356	1	journal	journal	PROPN
ejpam-6081	356	2	of	of	ADP
ejpam-6081	356	3	inequalities	inequality	NOUN
ejpam-6081	356	4	and	and	CCONJ
ejpam-6081	356	5	applications	application	NOUN
ejpam-6081	356	6	,	,	PUNCT
ejpam-6081	356	7	2024(1):140	2024(1):140	NUM
ejpam-6081	356	8	,	,	PUNCT
ejpam-6081	356	9	2024	2024	NUM
ejpam-6081	356	10	.	.	PUNCT
ejpam-6081	357	1	[	[	X
ejpam-6081	357	2	20	20	NUM
ejpam-6081	357	3	]	]	X
ejpam-6081	357	4	h.	h.	PROPN
ejpam-6081	357	5	tang	tang	PROPN
ejpam-6081	357	6	,	,	PUNCT
ejpam-6081	357	7	z.	z.	PROPN
ejpam-6081	357	8	mujahid	mujahid	PROPN
ejpam-6081	357	9	,	,	PUNCT
ejpam-6081	357	10	f.	f.	PROPN
ejpam-6081	357	11	tchier	tchier	PROPN
ejpam-6081	357	12	,	,	PUNCT
ejpam-6081	357	13	and	and	CCONJ
ejpam-6081	357	14	m.	m.	PROPN
ejpam-6081	357	15	g.	g.	PROPN
ejpam-6081	357	16	khan	khan	PROPN
ejpam-6081	357	17	.	.	PUNCT
ejpam-6081	358	1	generalized	generalize	VERB
ejpam-6081	358	2	bounded	bounded	ADJ
ejpam-6081	358	3	turning	turning	NOUN
ejpam-6081	358	4	functions	function	NOUN
ejpam-6081	358	5	connected	connect	VERB
ejpam-6081	358	6	with	with	ADP
ejpam-6081	358	7	gregory	gregory	PROPN
ejpam-6081	358	8	coefficients	coefficient	NOUN
ejpam-6081	358	9	.	.	PUNCT
ejpam-6081	359	1	axioms	axiom	NOUN
ejpam-6081	359	2	,	,	PUNCT
ejpam-6081	359	3	13(6):359	13(6):359	NUM
ejpam-6081	359	4	,	,	PUNCT
ejpam-6081	359	5	2024	2024	NUM
ejpam-6081	359	6	.	.	PUNCT
ejpam-6081	360	1	[	[	X
ejpam-6081	360	2	21	21	NUM
ejpam-6081	360	3	]	]	X
ejpam-6081	360	4	g.	g.	PROPN
ejpam-6081	360	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-6081	360	6	,	,	PUNCT
ejpam-6081	360	7	k.	k.	PROPN
ejpam-6081	360	8	vijaya	vijaya	PROPN
ejpam-6081	360	9	,	,	PUNCT
ejpam-6081	360	10	and	and	CCONJ
ejpam-6081	360	11	t.	t.	PROPN
ejpam-6081	360	12	bulboacă.	bulboacă.	PROPN
ejpam-6081	360	13	initial	initial	ADJ
ejpam-6081	360	14	coefficient	coefficient	NOUN
ejpam-6081	360	15	bounds	bound	VERB
ejpam-6081	360	16	for	for	ADP
ejpam-6081	360	17	bi	bi	ADJ
ejpam-6081	360	18	-	-	ADJ
ejpam-6081	360	19	univalent	univalent	ADJ
ejpam-6081	360	20	functions	function	NOUN
ejpam-6081	360	21	related	relate	VERB
ejpam-6081	360	22	to	to	ADP
ejpam-6081	360	23	gregory	gregory	PROPN
ejpam-6081	360	24	coefficients	coefficient	NOUN
ejpam-6081	360	25	.	.	PUNCT
ejpam-6081	361	1	mathematics	mathematic	NOUN
ejpam-6081	361	2	,	,	PUNCT
ejpam-6081	361	3	11(13):2857	11(13):2857	NUM
ejpam-6081	361	4	,	,	PUNCT
ejpam-6081	361	5	2023	2023	NUM
ejpam-6081	361	6	.	.	PUNCT
ejpam-6081	362	1	[	[	X
ejpam-6081	362	2	22	22	NUM
ejpam-6081	362	3	]	]	PUNCT
ejpam-6081	362	4	t.	t.	PROPN
ejpam-6081	362	5	al	al	PROPN
ejpam-6081	362	6	-	-	PUNCT
ejpam-6081	362	7	hawary	hawary	PROPN
ejpam-6081	362	8	,	,	PUNCT
ejpam-6081	362	9	a.	a.	PROPN
ejpam-6081	362	10	amourah	amourah	PROPN
ejpam-6081	362	11	,	,	PUNCT
ejpam-6081	362	12	j.	j.	PROPN
ejpam-6081	362	13	salah	salah	PROPN
ejpam-6081	362	14	,	,	PUNCT
ejpam-6081	362	15	m.	m.	PROPN
ejpam-6081	362	16	al	al	PROPN
ejpam-6081	362	17	-	-	PUNCT
ejpam-6081	362	18	khlyleh	khlyleh	PROPN
ejpam-6081	362	19	,	,	PUNCT
ejpam-6081	362	20	and	and	CCONJ
ejpam-6081	362	21	b.	b.	PROPN
ejpam-6081	362	22	a.	a.	PROPN
ejpam-6081	362	23	frasin	frasin	PROPN
ejpam-6081	362	24	.	.	PUNCT
ejpam-6081	363	1	new	new	ADJ
ejpam-6081	363	2	comprehensive	comprehensive	ADJ
ejpam-6081	363	3	two	two	NUM
ejpam-6081	363	4	subclasses	subclass	NOUN
ejpam-6081	363	5	related	relate	VERB
ejpam-6081	363	6	to	to	ADP
ejpam-6081	363	7	gregory	gregory	PROPN
ejpam-6081	363	8	numbers	number	NOUN
ejpam-6081	363	9	of	of	ADP
ejpam-6081	363	10	analytic	analytic	ADJ
ejpam-6081	363	11	bi	bi	ADJ
ejpam-6081	363	12	-	-	ADJ
ejpam-6081	363	13	univalent	univalent	ADJ
ejpam-6081	363	14	functions	function	NOUN
ejpam-6081	363	15	.	.	PUNCT
ejpam-6081	364	1	journal	journal	NOUN
ejpam-6081	364	2	of	of	ADP
ejpam-6081	364	3	mathematics	mathematic	NOUN
ejpam-6081	364	4	and	and	CCONJ
ejpam-6081	364	5	computer	computer	NOUN
ejpam-6081	364	6	science	science	NOUN
ejpam-6081	364	7	,	,	PUNCT
ejpam-6081	364	8	37(3):337–346	37(3):337–346	NUM
ejpam-6081	364	9	,	,	PUNCT
ejpam-6081	364	10	2025	2025	NUM
ejpam-6081	364	11	.	.	PUNCT
ejpam-6081	365	1	[	[	X
ejpam-6081	365	2	23	23	NUM
ejpam-6081	365	3	]	]	X
ejpam-6081	365	4	d.	d.	PROPN
ejpam-6081	365	5	mohamad	mohamad	PROPN
ejpam-6081	365	6	.	.	PUNCT
ejpam-6081	366	1	on	on	ADP
ejpam-6081	366	2	a	a	DET
ejpam-6081	366	3	class	class	NOUN
ejpam-6081	366	4	of	of	ADP
ejpam-6081	366	5	functions	function	NOUN
ejpam-6081	366	6	whose	whose	DET
ejpam-6081	366	7	derivatives	derivative	NOUN
ejpam-6081	366	8	map	map	VERB
ejpam-6081	366	9	the	the	DET
ejpam-6081	366	10	unit	unit	NOUN
ejpam-6081	366	11	disc	disc	VERB
ejpam-6081	366	12	into	into	ADP
ejpam-6081	366	13	a	a	DET
ejpam-6081	366	14	half	half	ADJ
ejpam-6081	366	15	plane	plane	NOUN
ejpam-6081	366	16	.	.	PUNCT
ejpam-6081	367	1	bulletin	bulletin	NOUN
ejpam-6081	367	2	of	of	ADP
ejpam-6081	367	3	the	the	DET
ejpam-6081	367	4	malaysian	malaysian	PROPN
ejpam-6081	367	5	mathematical	mathematical	PROPN
ejpam-6081	367	6	sciences	sciences	PROPN
ejpam-6081	367	7	society	society	NOUN
ejpam-6081	367	8	,	,	PUNCT
ejpam-6081	367	9	23(2):141–150	23(2):141–150	PROPN
ejpam-6081	367	10	,	,	PUNCT
ejpam-6081	367	11	2000	2000	NUM
ejpam-6081	367	12	.	.	PUNCT
ejpam-6081	368	1	[	[	X
ejpam-6081	368	2	24	24	NUM
ejpam-6081	368	3	]	]	X
ejpam-6081	368	4	r.	r.	PROPN
ejpam-6081	368	5	m.	m.	PROPN
ejpam-6081	368	6	goel	goel	PROPN
ejpam-6081	368	7	and	and	CCONJ
ejpam-6081	368	8	b.	b.	PROPN
ejpam-6081	368	9	s.	s.	PROPN
ejpam-6081	368	10	mehrok	mehrok	PROPN
ejpam-6081	368	11	.	.	PUNCT
ejpam-6081	369	1	a	a	DET
ejpam-6081	369	2	subclass	subclass	NOUN
ejpam-6081	369	3	of	of	ADP
ejpam-6081	369	4	univalent	univalent	ADJ
ejpam-6081	369	5	functions	function	NOUN
ejpam-6081	369	6	.	.	PUNCT
ejpam-6081	370	1	journal	journal	NOUN
ejpam-6081	370	2	of	of	ADP
ejpam-6081	370	3	the	the	DET
ejpam-6081	370	4	australian	australian	ADJ
ejpam-6081	370	5	mathematical	mathematical	ADJ
ejpam-6081	370	6	society	society	NOUN
ejpam-6081	370	7	,	,	PUNCT
ejpam-6081	370	8	35(1):1–17	35(1):1–17	NUM
ejpam-6081	370	9	,	,	PUNCT
ejpam-6081	370	10	1983	1983	NUM
ejpam-6081	370	11	.	.	PUNCT
ejpam-6081	371	1	[	[	X
ejpam-6081	371	2	25	25	NUM
ejpam-6081	371	3	]	]	PUNCT
ejpam-6081	371	4	t.	t.	PROPN
ejpam-6081	371	5	h.	h.	PROPN
ejpam-6081	371	6	macgregor	macgregor	PROPN
ejpam-6081	371	7	.	.	PUNCT
ejpam-6081	372	1	functions	function	NOUN
ejpam-6081	372	2	whose	whose	DET
ejpam-6081	372	3	derivative	derivative	NOUN
ejpam-6081	372	4	has	have	VERB
ejpam-6081	372	5	a	a	DET
ejpam-6081	372	6	positive	positive	ADJ
ejpam-6081	372	7	real	real	ADJ
ejpam-6081	372	8	part	part	NOUN
ejpam-6081	372	9	.	.	PUNCT
ejpam-6081	373	1	transactions	transaction	NOUN
ejpam-6081	373	2	of	of	ADP
ejpam-6081	373	3	the	the	DET
ejpam-6081	373	4	american	american	PROPN
ejpam-6081	373	5	mathematical	mathematical	PROPN
ejpam-6081	373	6	society	society	NOUN
ejpam-6081	373	7	,	,	PUNCT
ejpam-6081	373	8	104(3):532–537	104(3):532–537	NUM
ejpam-6081	373	9	,	,	PUNCT
ejpam-6081	373	10	1962	1962	NUM
ejpam-6081	373	11	.	.	PUNCT
ejpam-6081	374	1	[	[	X
ejpam-6081	374	2	26	26	NUM
ejpam-6081	374	3	]	]	PUNCT
ejpam-6081	374	4	k.	k.	PROPN
ejpam-6081	374	5	noshiro	noshiro	PROPN
ejpam-6081	374	6	.	.	PUNCT
ejpam-6081	375	1	on	on	ADP
ejpam-6081	375	2	the	the	DET
ejpam-6081	375	3	theory	theory	NOUN
ejpam-6081	375	4	of	of	ADP
ejpam-6081	375	5	schlicht	schlicht	NOUN
ejpam-6081	375	6	functions	function	NOUN
ejpam-6081	375	7	.	.	PUNCT
ejpam-6081	376	1	journal	journal	NOUN
ejpam-6081	376	2	of	of	ADP
ejpam-6081	376	3	the	the	DET
ejpam-6081	376	4	faculty	faculty	NOUN
ejpam-6081	376	5	of	of	ADP
ejpam-6081	376	6	science	science	NOUN
ejpam-6081	376	7	,	,	PUNCT
ejpam-6081	376	8	hokkaido	hokkaido	PROPN
ejpam-6081	376	9	imperial	imperial	PROPN
ejpam-6081	376	10	university	university	PROPN
ejpam-6081	376	11	.	.	PUNCT
ejpam-6081	377	1	series	series	PROPN
ejpam-6081	377	2	i.	i.	PROPN
ejpam-6081	377	3	mathematics	mathematics	PROPN
ejpam-6081	377	4	,	,	PUNCT
ejpam-6081	377	5	2(3	2(3	PROPN
ejpam-6081	377	6	-	-	SYM
ejpam-6081	377	7	4):129–155	4):129–155	NUM
ejpam-6081	377	8	,	,	PUNCT
ejpam-6081	377	9	1934	1934	NUM
ejpam-6081	377	10	.	.	PUNCT
ejpam-6081	378	1	[	[	X
ejpam-6081	378	2	27	27	NUM
ejpam-6081	378	3	]	]	X
ejpam-6081	378	4	h.	h.	PROPN
ejpam-6081	378	5	silverman	silverman	PROPN
ejpam-6081	378	6	and	and	CCONJ
ejpam-6081	378	7	e.	e.	PROPN
ejpam-6081	378	8	m.	m.	PROPN
ejpam-6081	378	9	silvia	silvia	PROPN
ejpam-6081	378	10	.	.	PUNCT
ejpam-6081	379	1	on	on	ADP
ejpam-6081	379	2	α	α	NOUN
ejpam-6081	379	3	-	-	PUNCT
ejpam-6081	379	4	close	close	VERB
ejpam-6081	379	5	-	-	PUNCT
ejpam-6081	379	6	to	to	ADP
ejpam-6081	379	7	-	-	PUNCT
ejpam-6081	379	8	convex	convex	NOUN
ejpam-6081	379	9	functions	function	NOUN
ejpam-6081	379	10	.	.	PUNCT
ejpam-6081	380	1	publicationes	publicatione	NOUN
ejpam-6081	380	2	mathematicae	mathematicae	PROPN
ejpam-6081	380	3	debrecen	debrecen	PROPN
ejpam-6081	380	4	,	,	PUNCT
ejpam-6081	380	5	49(3	49(3	PROPN
ejpam-6081	380	6	-	-	PUNCT
ejpam-6081	380	7	4):305–316	4):305–316	NUM
ejpam-6081	380	8	,	,	PUNCT
ejpam-6081	380	9	1996	1996	NUM
ejpam-6081	380	10	.	.	PUNCT
ejpam-6081	381	1	[	[	X
ejpam-6081	381	2	28	28	NUM
ejpam-6081	381	3	]	]	X
ejpam-6081	381	4	s.	s.	PROPN
ejpam-6081	381	5	e.	e.	PROPN
ejpam-6081	381	6	warschawski	warschawski	PROPN
ejpam-6081	381	7	.	.	PUNCT
ejpam-6081	382	1	on	on	ADP
ejpam-6081	382	2	the	the	DET
ejpam-6081	382	3	higher	high	ADJ
ejpam-6081	382	4	derivatives	derivative	NOUN
ejpam-6081	382	5	at	at	ADP
ejpam-6081	382	6	the	the	DET
ejpam-6081	382	7	boundary	boundary	NOUN
ejpam-6081	382	8	in	in	ADP
ejpam-6081	382	9	conformal	conformal	ADJ
ejpam-6081	382	10	mapping	mapping	NOUN
ejpam-6081	382	11	.	.	PUNCT
ejpam-6081	383	1	transactions	transaction	NOUN
ejpam-6081	383	2	of	of	ADP
ejpam-6081	383	3	the	the	DET
ejpam-6081	383	4	american	american	PROPN
ejpam-6081	383	5	mathematical	mathematical	PROPN
ejpam-6081	383	6	society	society	NOUN
ejpam-6081	383	7	,	,	PUNCT
ejpam-6081	383	8	38(2):310–340	38(2):310–340	PROPN
ejpam-6081	383	9	,	,	PUNCT
ejpam-6081	383	10	1935	1935	NUM
ejpam-6081	383	11	.	.	PUNCT
ejpam-6081	384	1	[	[	X
ejpam-6081	384	2	29	29	NUM
ejpam-6081	384	3	]	]	X
ejpam-6081	385	1	p.	p.	NOUN
ejpam-6081	385	2	l.	l.	PROPN
ejpam-6081	385	3	duren	duren	PROPN
ejpam-6081	385	4	.	.	PUNCT
ejpam-6081	386	1	univalent	univalent	ADJ
ejpam-6081	386	2	functions	function	NOUN
ejpam-6081	386	3	,	,	PUNCT
ejpam-6081	386	4	volume	volume	NOUN
ejpam-6081	386	5	259	259	NUM
ejpam-6081	386	6	of	of	ADP
ejpam-6081	386	7	grundlehren	grundlehren	PROPN
ejpam-6081	386	8	der	der	PROPN
ejpam-6081	386	9	mathematischen	mathematischen	PROPN
ejpam-6081	386	10	wissenschaften	wissenschaften	PROPN
ejpam-6081	386	11	.	.	PUNCT
ejpam-6081	387	1	springer	springer	NOUN
ejpam-6081	387	2	-	-	PUNCT
ejpam-6081	387	3	verlag	verlag	PROPN
ejpam-6081	387	4	,	,	PUNCT
ejpam-6081	387	5	new	new	PROPN
ejpam-6081	387	6	york	york	PROPN
ejpam-6081	387	7	,	,	PUNCT
ejpam-6081	387	8	1983	1983	NUM
ejpam-6081	387	9	.	.	PUNCT
ejpam-6081	388	1	[	[	X
ejpam-6081	388	2	30	30	NUM
ejpam-6081	388	3	]	]	X
ejpam-6081	388	4	i.	i.	NOUN
ejpam-6081	388	5	efraimidis	efraimidis	PROPN
ejpam-6081	388	6	.	.	PUNCT
ejpam-6081	389	1	a	a	DET
ejpam-6081	389	2	generalization	generalization	NOUN
ejpam-6081	389	3	of	of	ADP
ejpam-6081	389	4	livingston	livingston	PROPN
ejpam-6081	389	5	’s	’s	PART
ejpam-6081	389	6	coefficient	coefficient	NOUN
ejpam-6081	389	7	inequalities	inequality	NOUN
ejpam-6081	389	8	for	for	ADP
ejpam-6081	389	9	functions	function	NOUN
ejpam-6081	389	10	with	with	ADP
ejpam-6081	389	11	positive	positive	ADJ
ejpam-6081	389	12	real	real	ADJ
ejpam-6081	389	13	part	part	NOUN
ejpam-6081	389	14	.	.	PUNCT
ejpam-6081	390	1	journal	journal	PROPN
ejpam-6081	390	2	of	of	ADP
ejpam-6081	390	3	mathematical	mathematical	ADJ
ejpam-6081	390	4	analysis	analysis	NOUN
ejpam-6081	390	5	and	and	CCONJ
ejpam-6081	390	6	applications	application	NOUN
ejpam-6081	390	7	,	,	PUNCT
ejpam-6081	390	8	435(1):369–379	435(1):369–379	PROPN
ejpam-6081	390	9	,	,	PUNCT
ejpam-6081	390	10	2016	2016	NUM
ejpam-6081	390	11	.	.	PUNCT
ejpam-6081	391	1	[	[	X
ejpam-6081	391	2	31	31	NUM
ejpam-6081	391	3	]	]	PUNCT
ejpam-6081	391	4	m.	m.	PROPN
ejpam-6081	391	5	arif	arif	PROPN
ejpam-6081	391	6	,	,	PUNCT
ejpam-6081	391	7	m.	m.	NOUN
ejpam-6081	391	8	raza	raza	PROPN
ejpam-6081	391	9	,	,	PUNCT
ejpam-6081	391	10	h.	h.	PROPN
ejpam-6081	391	11	tang	tang	PROPN
ejpam-6081	391	12	,	,	PUNCT
ejpam-6081	391	13	s.	s.	PROPN
ejpam-6081	391	14	hussain	hussain	PROPN
ejpam-6081	391	15	,	,	PUNCT
ejpam-6081	391	16	and	and	CCONJ
ejpam-6081	391	17	h.	h.	PROPN
ejpam-6081	391	18	khan	khan	PROPN
ejpam-6081	391	19	.	.	PUNCT
ejpam-6081	392	1	hankel	hankel	NOUN
ejpam-6081	392	2	determinant	determinant	ADJ
ejpam-6081	392	3	of	of	ADP
ejpam-6081	392	4	order	order	NOUN
ejpam-6081	392	5	three	three	NUM
ejpam-6081	392	6	for	for	ADP
ejpam-6081	392	7	familiar	familiar	ADJ
ejpam-6081	392	8	subsets	subset	NOUN
ejpam-6081	392	9	of	of	ADP
ejpam-6081	392	10	analytic	analytic	ADJ
ejpam-6081	392	11	functions	function	NOUN
ejpam-6081	392	12	related	relate	VERB
ejpam-6081	392	13	with	with	ADP
ejpam-6081	392	14	sine	sine	ADJ
ejpam-6081	392	15	function	function	NOUN
ejpam-6081	392	16	.	.	PUNCT
ejpam-6081	393	1	open	open	ADJ
ejpam-6081	393	2	mathematics	mathematic	NOUN
ejpam-6081	393	3	,	,	PUNCT
ejpam-6081	393	4	17(1):1615–1630	17(1):1615–1630	PROPN
ejpam-6081	393	5	,	,	PUNCT
ejpam-6081	393	6	2019	2019	NUM
ejpam-6081	393	7	.	.	PUNCT
ejpam-6081	394	1	[	[	X
ejpam-6081	394	2	32	32	NUM
ejpam-6081	394	3	]	]	PUNCT
ejpam-6081	394	4	v.	v.	CCONJ
ejpam-6081	394	5	ravichandran	ravichandran	NOUN
ejpam-6081	394	6	and	and	CCONJ
ejpam-6081	394	7	s.	s.	PROPN
ejpam-6081	394	8	verma	verma	PROPN
ejpam-6081	394	9	.	.	PUNCT
ejpam-6081	395	1	bound	bind	VERB
ejpam-6081	395	2	for	for	ADP
ejpam-6081	395	3	the	the	DET
ejpam-6081	395	4	fifth	fifth	ADJ
ejpam-6081	395	5	coefficient	coefficient	NOUN
ejpam-6081	395	6	of	of	ADP
ejpam-6081	395	7	certain	certain	ADJ
ejpam-6081	395	8	starlike	starlike	NOUN
ejpam-6081	395	9	functions	function	NOUN
ejpam-6081	395	10	.	.	PUNCT
ejpam-6081	396	1	comptes	compte	VERB
ejpam-6081	396	2	rendus	rendus	PROPN
ejpam-6081	396	3	mathematique	mathematique	PROPN
ejpam-6081	396	4	,	,	PUNCT
ejpam-6081	396	5	353(6):505–510	353(6):505–510	NUM
ejpam-6081	396	6	,	,	PUNCT
ejpam-6081	396	7	2015	2015	NUM
ejpam-6081	396	8	.	.	PUNCT