id	sid	tid	token	lemma	pos
ejpam-3429	1	1	european	european	PROPN
ejpam-3429	1	2	journal	journal	PROPN
ejpam-3429	1	3	of	of	ADP
ejpam-3429	1	4	pure	pure	ADJ
ejpam-3429	1	5	and	and	CCONJ
ejpam-3429	1	6	applied	apply	VERB
ejpam-3429	1	7	mathematics	mathematic	NOUN
ejpam-3429	1	8	vol	vol	NOUN
ejpam-3429	1	9	.	.	PROPN
ejpam-3429	2	1	12	12	NUM
ejpam-3429	2	2	,	,	PUNCT
ejpam-3429	2	3	no	no	INTJ
ejpam-3429	2	4	.	.	NOUN
ejpam-3429	2	5	3	3	NUM
ejpam-3429	2	6	,	,	PUNCT
ejpam-3429	2	7	2019	2019	NUM
ejpam-3429	2	8	,	,	PUNCT
ejpam-3429	2	9	846	846	NUM
ejpam-3429	2	10	-	-	SYM
ejpam-3429	2	11	856	856	NUM
ejpam-3429	2	12	issn	issn	PROPN
ejpam-3429	2	13	1307	1307	NUM
ejpam-3429	2	14	-	-	SYM
ejpam-3429	2	15	5543	5543	NUM
ejpam-3429	2	16	–	–	PUNCT
ejpam-3429	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3429	2	18	published	publish	VERB
ejpam-3429	2	19	by	by	ADP
ejpam-3429	2	20	new	new	PROPN
ejpam-3429	2	21	york	york	PROPN
ejpam-3429	2	22	business	business	PROPN
ejpam-3429	2	23	global	global	ADJ
ejpam-3429	2	24	inequalities	inequality	NOUN
ejpam-3429	2	25	for	for	ADP
ejpam-3429	2	26	the	the	DET
ejpam-3429	2	27	taylor	taylor	PROPN
ejpam-3429	2	28	coefficients	coefficient	NOUN
ejpam-3429	2	29	of	of	ADP
ejpam-3429	2	30	spiralike	spiralike	NOUN
ejpam-3429	2	31	functions	function	NOUN
ejpam-3429	2	32	involving	involve	VERB
ejpam-3429	2	33	q	q	ADJ
ejpam-3429	2	34	-	-	PUNCT
ejpam-3429	2	35	differential	differential	ADJ
ejpam-3429	2	36	operator	operator	NOUN
ejpam-3429	2	37	k.	k.	PROPN
ejpam-3429	2	38	amarender	amarender	PROPN
ejpam-3429	2	39	reddy1	reddy1	PROPN
ejpam-3429	2	40	,	,	PUNCT
ejpam-3429	2	41	k.	k.	PROPN
ejpam-3429	2	42	r.	r.	PROPN
ejpam-3429	2	43	karthikeyan1	karthikeyan1	PROPN
ejpam-3429	2	44	,	,	PUNCT
ejpam-3429	2	45	g.	g.	PROPN
ejpam-3429	2	46	murugusundaramoorthy2,∗	murugusundaramoorthy2,∗	PROPN
ejpam-3429	2	47	1	1	NUM
ejpam-3429	2	48	department	department	NOUN
ejpam-3429	2	49	of	of	ADP
ejpam-3429	2	50	mathematics	mathematic	NOUN
ejpam-3429	2	51	and	and	CCONJ
ejpam-3429	2	52	statistics	statistic	NOUN
ejpam-3429	2	53	,	,	PUNCT
ejpam-3429	2	54	college	college	NOUN
ejpam-3429	2	55	of	of	ADP
ejpam-3429	2	56	engineering	engineering	PROPN
ejpam-3429	2	57	,	,	PUNCT
ejpam-3429	2	58	national	national	ADJ
ejpam-3429	2	59	university	university	PROPN
ejpam-3429	2	60	of	of	ADP
ejpam-3429	2	61	science	science	NOUN
ejpam-3429	2	62	and	and	CCONJ
ejpam-3429	2	63	technology	technology	NOUN
ejpam-3429	2	64	,	,	PUNCT
ejpam-3429	2	65	muscat	muscat	PROPN
ejpam-3429	2	66	,	,	PUNCT
ejpam-3429	2	67	sultanate	sultanate	NOUN
ejpam-3429	2	68	of	of	ADP
ejpam-3429	2	69	oman	oman	PROPN
ejpam-3429	2	70	2	2	NUM
ejpam-3429	2	71	department	department	NOUN
ejpam-3429	2	72	of	of	ADP
ejpam-3429	2	73	mathematics	mathematic	NOUN
ejpam-3429	2	74	,	,	PUNCT
ejpam-3429	2	75	school	school	NOUN
ejpam-3429	2	76	of	of	ADP
ejpam-3429	2	77	advanced	advanced	ADJ
ejpam-3429	2	78	sciences	science	NOUN
ejpam-3429	2	79	,	,	PUNCT
ejpam-3429	2	80	vellore	vellore	PROPN
ejpam-3429	2	81	institute	institute	PROPN
ejpam-3429	2	82	of	of	ADP
ejpam-3429	2	83	technology	technology	PROPN
ejpam-3429	2	84	,	,	PUNCT
ejpam-3429	2	85	deemed	deem	VERB
ejpam-3429	2	86	to	to	PART
ejpam-3429	2	87	be	be	AUX
ejpam-3429	2	88	university	university	NOUN
ejpam-3429	2	89	,	,	PUNCT
ejpam-3429	2	90	vellore	vellore	NOUN
ejpam-3429	2	91	,	,	PUNCT
ejpam-3429	2	92	tamilnadu	tamilnadu	NOUN
ejpam-3429	2	93	,	,	PUNCT
ejpam-3429	2	94	india	india	PROPN
ejpam-3429	2	95	abstract	abstract	NOUN
ejpam-3429	2	96	.	.	PUNCT
ejpam-3429	3	1	making	make	VERB
ejpam-3429	3	2	use	use	NOUN
ejpam-3429	3	3	of	of	ADP
ejpam-3429	3	4	q	q	NOUN
ejpam-3429	3	5	-	-	PUNCT
ejpam-3429	3	6	analogue	analogue	NOUN
ejpam-3429	3	7	of	of	ADP
ejpam-3429	3	8	the	the	DET
ejpam-3429	3	9	well	well	ADV
ejpam-3429	3	10	-	-	PUNCT
ejpam-3429	3	11	known	know	VERB
ejpam-3429	3	12	differential	differential	NOUN
ejpam-3429	3	13	operator	operator	NOUN
ejpam-3429	3	14	,	,	PUNCT
ejpam-3429	3	15	we	we	PRON
ejpam-3429	3	16	provide	provide	VERB
ejpam-3429	3	17	a	a	DET
ejpam-3429	3	18	formal	formal	ADJ
ejpam-3429	3	19	extension	extension	NOUN
ejpam-3429	3	20	of	of	ADP
ejpam-3429	3	21	a	a	DET
ejpam-3429	3	22	bi	bi	ADJ
ejpam-3429	3	23	-	-	ADJ
ejpam-3429	3	24	univalent	univalent	ADJ
ejpam-3429	3	25	spiralike	spiralike	NOUN
ejpam-3429	3	26	and	and	CCONJ
ejpam-3429	3	27	bi	bi	ADJ
ejpam-3429	3	28	-	-	ADJ
ejpam-3429	3	29	univalent	univalent	ADJ
ejpam-3429	3	30	strongly	strongly	ADV
ejpam-3429	3	31	spiralike	spiralike	ADJ
ejpam-3429	3	32	functions	function	NOUN
ejpam-3429	3	33	.	.	PUNCT
ejpam-3429	4	1	we	we	PRON
ejpam-3429	4	2	obtain	obtain	VERB
ejpam-3429	4	3	the	the	DET
ejpam-3429	4	4	inequalities	inequality	NOUN
ejpam-3429	4	5	for	for	ADP
ejpam-3429	4	6	the	the	DET
ejpam-3429	4	7	maclaurin	maclaurin	NOUN
ejpam-3429	4	8	-	-	PUNCT
ejpam-3429	4	9	taylor	taylor	PROPN
ejpam-3429	4	10	coefficients	coefficient	NOUN
ejpam-3429	4	11	of	of	ADP
ejpam-3429	4	12	the	the	DET
ejpam-3429	4	13	functions	function	NOUN
ejpam-3429	4	14	belonging	belong	VERB
ejpam-3429	4	15	to	to	ADP
ejpam-3429	4	16	the	the	DET
ejpam-3429	4	17	defined	define	VERB
ejpam-3429	4	18	subclasses	subclass	NOUN
ejpam-3429	4	19	.	.	PUNCT
ejpam-3429	5	1	further	far	ADV
ejpam-3429	5	2	we	we	PRON
ejpam-3429	5	3	have	have	AUX
ejpam-3429	5	4	provided	provide	VERB
ejpam-3429	5	5	some	some	DET
ejpam-3429	5	6	applications	application	NOUN
ejpam-3429	5	7	of	of	ADP
ejpam-3429	5	8	our	our	PRON
ejpam-3429	5	9	main	main	ADJ
ejpam-3429	5	10	results	result	NOUN
ejpam-3429	5	11	.	.	PUNCT
ejpam-3429	6	1	2010	2010	NUM
ejpam-3429	6	2	mathematics	mathematic	NOUN
ejpam-3429	6	3	subject	subject	NOUN
ejpam-3429	6	4	classifications	classification	NOUN
ejpam-3429	6	5	:	:	PUNCT
ejpam-3429	6	6	30c45	30c45	NUM
ejpam-3429	6	7	key	key	ADJ
ejpam-3429	6	8	words	word	NOUN
ejpam-3429	6	9	and	and	CCONJ
ejpam-3429	6	10	phrases	phrase	NOUN
ejpam-3429	6	11	:	:	PUNCT
ejpam-3429	6	12	starlike	starlike	NOUN
ejpam-3429	6	13	functions	function	NOUN
ejpam-3429	6	14	,	,	PUNCT
ejpam-3429	6	15	spiralike	spiralike	NOUN
ejpam-3429	6	16	functions	function	NOUN
ejpam-3429	6	17	,	,	PUNCT
ejpam-3429	6	18	bi	bi	ADJ
ejpam-3429	6	19	-	-	ADJ
ejpam-3429	6	20	univalent	univalent	ADJ
ejpam-3429	6	21	functions	function	NOUN
ejpam-3429	6	22	,	,	PUNCT
ejpam-3429	6	23	coefficient	coefficient	NOUN
ejpam-3429	6	24	inequalities	inequality	NOUN
ejpam-3429	6	25	,	,	PUNCT
ejpam-3429	6	26	q	q	ADJ
ejpam-3429	6	27	-	-	PUNCT
ejpam-3429	6	28	calculus	calculus	NOUN
ejpam-3429	6	29	operator	operator	NOUN
ejpam-3429	6	30	1	1	NUM
ejpam-3429	6	31	.	.	PUNCT
ejpam-3429	7	1	introduction	introduction	NOUN
ejpam-3429	7	2	of	of	ADP
ejpam-3429	7	3	quantum	quantum	NOUN
ejpam-3429	7	4	calculus	calculus	NOUN
ejpam-3429	7	5	in	in	ADP
ejpam-3429	7	6	dual	dual	ADJ
ejpam-3429	7	7	with	with	ADP
ejpam-3429	7	8	univalent	univalent	ADJ
ejpam-3429	7	9	functions	function	NOUN
ejpam-3429	7	10	quantum	quantum	NOUN
ejpam-3429	7	11	calculus	calculus	NOUN
ejpam-3429	7	12	popularly	popularly	ADV
ejpam-3429	7	13	called	call	VERB
ejpam-3429	7	14	as	as	SCONJ
ejpam-3429	7	15	q	q	NOUN
ejpam-3429	7	16	-	-	PUNCT
ejpam-3429	7	17	calculus	calculus	NOUN
ejpam-3429	7	18	is	be	AUX
ejpam-3429	7	19	based	base	VERB
ejpam-3429	7	20	on	on	ADP
ejpam-3429	7	21	the	the	DET
ejpam-3429	7	22	idea	idea	NOUN
ejpam-3429	7	23	of	of	ADP
ejpam-3429	7	24	finite	finite	ADJ
ejpam-3429	7	25	difference	difference	NOUN
ejpam-3429	7	26	rescaling	rescaling	NOUN
ejpam-3429	7	27	.	.	PUNCT
ejpam-3429	8	1	the	the	DET
ejpam-3429	8	2	difference	difference	NOUN
ejpam-3429	8	3	of	of	ADP
ejpam-3429	8	4	quantum	quantum	ADJ
ejpam-3429	8	5	differentials	differential	NOUN
ejpam-3429	8	6	from	from	ADP
ejpam-3429	8	7	the	the	DET
ejpam-3429	8	8	ordinary	ordinary	ADJ
ejpam-3429	8	9	ones	one	NOUN
ejpam-3429	8	10	is	be	AUX
ejpam-3429	8	11	that	that	SCONJ
ejpam-3429	8	12	notion	notion	NOUN
ejpam-3429	8	13	of	of	ADP
ejpam-3429	8	14	limit	limit	NOUN
ejpam-3429	8	15	is	be	AUX
ejpam-3429	8	16	removed	remove	VERB
ejpam-3429	8	17	in	in	ADP
ejpam-3429	8	18	q	q	NOUN
ejpam-3429	8	19	-	-	NOUN
ejpam-3429	8	20	calculus	calculus	NOUN
ejpam-3429	8	21	,	,	PUNCT
ejpam-3429	8	22	that	that	PRON
ejpam-3429	8	23	is	be	AUX
ejpam-3429	8	24	q	q	ADJ
ejpam-3429	8	25	-	-	ADJ
ejpam-3429	8	26	derivative	derivative	ADJ
ejpam-3429	8	27	is	be	AUX
ejpam-3429	8	28	merely	merely	ADV
ejpam-3429	8	29	a	a	DET
ejpam-3429	8	30	ratio	ratio	NOUN
ejpam-3429	8	31	which	which	PRON
ejpam-3429	8	32	is	be	AUX
ejpam-3429	8	33	given	give	VERB
ejpam-3429	8	34	by	by	ADP
ejpam-3429	8	35	dqf(z	dqf(z	PROPN
ejpam-3429	8	36	)	)	PUNCT
ejpam-3429	8	37	=	=	SYM
ejpam-3429	8	38	f(qz)−	f(qz)−	PUNCT
ejpam-3429	8	39	f(z	f(z	PROPN
ejpam-3429	8	40	)	)	PUNCT
ejpam-3429	8	41	(	(	PUNCT
ejpam-3429	8	42	q	q	NOUN
ejpam-3429	8	43	−	−	PROPN
ejpam-3429	8	44	1)z	1)z	PROPN
ejpam-3429	8	45	.	.	PUNCT
ejpam-3429	9	1	notice	notice	VERB
ejpam-3429	9	2	that	that	SCONJ
ejpam-3429	9	3	as	as	SCONJ
ejpam-3429	9	4	limit	limit	VERB
ejpam-3429	9	5	q	q	X
ejpam-3429	9	6	→	→	SYM
ejpam-3429	9	7	1−	1−	NUM
ejpam-3429	9	8	,	,	PUNCT
ejpam-3429	9	9	dqf(z	dqf(z	X
ejpam-3429	9	10	)	)	PUNCT
ejpam-3429	9	11	=	=	SYM
ejpam-3429	9	12	f	f	PROPN
ejpam-3429	9	13	′(z	′(z	NOUN
ejpam-3429	9	14	)	)	PUNCT
ejpam-3429	9	15	.	.	PUNCT
ejpam-3429	10	1	q	q	X
ejpam-3429	10	2	-	-	PUNCT
ejpam-3429	10	3	calculus	calculus	NOUN
ejpam-3429	10	4	has	have	VERB
ejpam-3429	10	5	numerous	numerous	ADJ
ejpam-3429	10	6	applications	application	NOUN
ejpam-3429	10	7	in	in	ADP
ejpam-3429	10	8	variety	variety	NOUN
ejpam-3429	10	9	of	of	ADP
ejpam-3429	10	10	disciplines	discipline	NOUN
ejpam-3429	10	11	such	such	ADJ
ejpam-3429	10	12	as	as	ADP
ejpam-3429	10	13	theory	theory	NOUN
ejpam-3429	10	14	of	of	ADP
ejpam-3429	10	15	special	special	ADJ
ejpam-3429	10	16	functions	function	NOUN
ejpam-3429	10	17	,	,	PUNCT
ejpam-3429	10	18	operator	operator	NOUN
ejpam-3429	10	19	theory	theory	NOUN
ejpam-3429	10	20	,	,	PUNCT
ejpam-3429	10	21	quantummechanics	quantummechanic	NOUN
ejpam-3429	10	22	,	,	PUNCT
ejpam-3429	10	23	relativity	relativity	NOUN
ejpam-3429	10	24	etc	etc	X
ejpam-3429	10	25	.	.	X
ejpam-3429	10	26	notations	notation	NOUN
ejpam-3429	10	27	and	and	CCONJ
ejpam-3429	10	28	symbols	symbol	NOUN
ejpam-3429	10	29	play	play	VERB
ejpam-3429	10	30	an	an	DET
ejpam-3429	10	31	very	very	ADV
ejpam-3429	10	32	important	important	ADJ
ejpam-3429	10	33	role	role	NOUN
ejpam-3429	10	34	in	in	ADP
ejpam-3429	10	35	the	the	DET
ejpam-3429	10	36	study	study	NOUN
ejpam-3429	10	37	of	of	ADP
ejpam-3429	10	38	q	q	NOUN
ejpam-3429	10	39	-	-	NOUN
ejpam-3429	10	40	calculus	calculus	NOUN
ejpam-3429	10	41	.	.	PUNCT
ejpam-3429	11	1	throughout	throughout	ADP
ejpam-3429	11	2	this	this	DET
ejpam-3429	11	3	paper	paper	NOUN
ejpam-3429	11	4	,	,	PUNCT
ejpam-3429	11	5	we	we	PRON
ejpam-3429	11	6	let	let	VERB
ejpam-3429	11	7	[	[	PRON
ejpam-3429	11	8	n]q	n]q	X
ejpam-3429	11	9	=	=	PUNCT
ejpam-3429	11	10	n∑	n∑	NOUN
ejpam-3429	11	11	k=1	k=1	PUNCT
ejpam-3429	12	1	qk−1	qk−1	PROPN
ejpam-3429	12	2	,	,	PUNCT
ejpam-3429	12	3	[	[	X
ejpam-3429	12	4	0]q	0]q	NOUN
ejpam-3429	12	5	=	=	SYM
ejpam-3429	12	6	0	0	NUM
ejpam-3429	12	7	,	,	PUNCT
ejpam-3429	12	8	(	(	PUNCT
ejpam-3429	12	9	q	q	NOUN
ejpam-3429	12	10	∈	∈	PROPN
ejpam-3429	12	11	c	c	NOUN
ejpam-3429	12	12	)	)	PUNCT
ejpam-3429	12	13	∗corresponding	∗corresponde	VERB
ejpam-3429	12	14	author	author	NOUN
ejpam-3429	12	15	.	.	PUNCT
ejpam-3429	13	1	doi	doi	NOUN
ejpam-3429	13	2	:	:	PUNCT
ejpam-3429	13	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3429	https://doi.org/10.29020/nybg.ejpam.v12i3.3429	ADJ
ejpam-3429	13	4	email	email	NOUN
ejpam-3429	13	5	addresses	address	VERB
ejpam-3429	13	6	:	:	PUNCT
ejpam-3429	13	7	amarenderkommula@gmail.com	amarenderkommula@gmail.com	X
ejpam-3429	13	8	(	(	PUNCT
ejpam-3429	13	9	k.	k.	PROPN
ejpam-3429	13	10	a.	a.	PROPN
ejpam-3429	13	11	reddy	reddy	PROPN
ejpam-3429	13	12	)	)	PUNCT
ejpam-3429	13	13	,	,	PUNCT
ejpam-3429	13	14	kr	kr	PROPN
ejpam-3429	13	15	karthikeyan1979@yahoo.com	karthikeyan1979@yahoo.com	PROPN
ejpam-3429	13	16	(	(	PUNCT
ejpam-3429	13	17	k.	k.	PROPN
ejpam-3429	13	18	r.	r.	PROPN
ejpam-3429	13	19	karthikeyan	karthikeyan	PROPN
ejpam-3429	13	20	)	)	PUNCT
ejpam-3429	13	21	,	,	PUNCT
ejpam-3429	13	22	gmsmoorthy@yahoo.com	gmsmoorthy@yahoo.com	X
ejpam-3429	13	23	(	(	PUNCT
ejpam-3429	13	24	g.	g.	PROPN
ejpam-3429	13	25	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-3429	13	26	)	)	PUNCT
ejpam-3429	13	27	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3429	14	1	846	846	NUM
ejpam-3429	14	2	c	c	X
ejpam-3429	14	3	©	©	PROPN
ejpam-3429	14	4	2019	2019	NUM
ejpam-3429	14	5	ejpam	ejpam	NOUN
ejpam-3429	14	6	all	all	DET
ejpam-3429	14	7	rights	right	NOUN
ejpam-3429	14	8	reserved	reserve	VERB
ejpam-3429	14	9	.	.	PUNCT
ejpam-3429	15	1	k.	k.	PROPN
ejpam-3429	15	2	a.	a.	PROPN
ejpam-3429	15	3	reddy	reddy	PROPN
ejpam-3429	15	4	,	,	PUNCT
ejpam-3429	15	5	k.	k.	PROPN
ejpam-3429	15	6	r.	r.	PROPN
ejpam-3429	15	7	karthikeyan	karthikeyan	PROPN
ejpam-3429	15	8	,	,	PUNCT
ejpam-3429	15	9	g.	g.	PROPN
ejpam-3429	15	10	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	15	11	/	/	SYM
ejpam-3429	15	12	eur	eur	PROPN
ejpam-3429	15	13	.	.	PUNCT
ejpam-3429	16	1	j.	j.	PROPN
ejpam-3429	16	2	pure	pure	PROPN
ejpam-3429	16	3	appl	appl	PROPN
ejpam-3429	16	4	.	.	PROPN
ejpam-3429	16	5	math	math	PROPN
ejpam-3429	16	6	,	,	PUNCT
ejpam-3429	16	7	12	12	NUM
ejpam-3429	16	8	(	(	PUNCT
ejpam-3429	16	9	3	3	NUM
ejpam-3429	16	10	)	)	PUNCT
ejpam-3429	16	11	(	(	PUNCT
ejpam-3429	16	12	2019	2019	NUM
ejpam-3429	16	13	)	)	PUNCT
ejpam-3429	16	14	,	,	PUNCT
ejpam-3429	16	15	846	846	NUM
ejpam-3429	16	16	-	-	SYM
ejpam-3429	16	17	856	856	NUM
ejpam-3429	16	18	847	847	NUM
ejpam-3429	16	19	and	and	CCONJ
ejpam-3429	16	20	the	the	DET
ejpam-3429	16	21	q	q	ADJ
ejpam-3429	16	22	-	-	PUNCT
ejpam-3429	16	23	shifted	shift	VERB
ejpam-3429	16	24	factorial	factorial	NOUN
ejpam-3429	16	25	by	by	ADP
ejpam-3429	16	26	(	(	PUNCT
ejpam-3429	16	27	a	a	PRON
ejpam-3429	16	28	;	;	PUNCT
ejpam-3429	16	29	q)n	q)n	SYM
ejpam-3429	16	30	=	=	SYM
ejpam-3429	16	31	{	{	PUNCT
ejpam-3429	16	32	1	1	NUM
ejpam-3429	16	33	,	,	PUNCT
ejpam-3429	16	34	n	n	NOUN
ejpam-3429	16	35	=	=	SYM
ejpam-3429	16	36	0	0	NUM
ejpam-3429	17	1	(	(	PUNCT
ejpam-3429	17	2	1−	1−	NUM
ejpam-3429	17	3	a)(1−	a)(1−	PROPN
ejpam-3429	17	4	aq	aq	NOUN
ejpam-3429	17	5	)	)	PUNCT
ejpam-3429	17	6	.	.	PUNCT
ejpam-3429	17	7	.	.	PUNCT
ejpam-3429	18	1	.	.	PUNCT
ejpam-3429	19	1	(	(	PUNCT
ejpam-3429	19	2	1−	1−	NUM
ejpam-3429	19	3	aqn−1	aqn−1	PROPN
ejpam-3429	19	4	)	)	PUNCT
ejpam-3429	19	5	,	,	PUNCT
ejpam-3429	20	1	n	n	NOUN
ejpam-3429	20	2	=	=	SYM
ejpam-3429	20	3	1	1	NUM
ejpam-3429	20	4	,	,	PUNCT
ejpam-3429	20	5	2	2	NUM
ejpam-3429	20	6	,	,	PUNCT
ejpam-3429	20	7	.	.	PUNCT
ejpam-3429	20	8	.	.	PUNCT
ejpam-3429	20	9	.	.	PUNCT
ejpam-3429	20	10	.	.	PUNCT
ejpam-3429	21	1	the	the	DET
ejpam-3429	21	2	q	q	ADJ
ejpam-3429	21	3	-	-	PUNCT
ejpam-3429	21	4	hypergeometric	hypergeometric	ADJ
ejpam-3429	21	5	series	series	NOUN
ejpam-3429	21	6	was	be	AUX
ejpam-3429	21	7	developed	develop	VERB
ejpam-3429	21	8	by	by	ADP
ejpam-3429	21	9	heine	heine	PROPN
ejpam-3429	21	10	as	as	ADP
ejpam-3429	21	11	a	a	DET
ejpam-3429	21	12	generalization	generalization	NOUN
ejpam-3429	21	13	of	of	ADP
ejpam-3429	21	14	the	the	DET
ejpam-3429	21	15	hypergeometric	hypergeometric	ADJ
ejpam-3429	21	16	series	series	NOUN
ejpam-3429	21	17	2f1[a	2f1[a	PROPN
ejpam-3429	21	18	,	,	PUNCT
ejpam-3429	21	19	b	b	NOUN
ejpam-3429	21	20	;	;	PUNCT
ejpam-3429	21	21	c|q	c|q	PROPN
ejpam-3429	21	22	,	,	PUNCT
ejpam-3429	21	23	z	z	X
ejpam-3429	21	24	]	]	X
ejpam-3429	21	25	=	=	PUNCT
ejpam-3429	22	1	∞∑	∞∑	NUM
ejpam-3429	22	2	n=0	n=0	NUM
ejpam-3429	22	3	(	(	PUNCT
ejpam-3429	22	4	a	a	NOUN
ejpam-3429	22	5	;	;	PUNCT
ejpam-3429	22	6	q)n(b	q)n(b	ADJ
ejpam-3429	22	7	;	;	PUNCT
ejpam-3429	22	8	q)n	q)n	X
ejpam-3429	22	9	(	(	PUNCT
ejpam-3429	22	10	q	q	NOUN
ejpam-3429	22	11	;	;	PUNCT
ejpam-3429	22	12	q)n(c	q)n(c	PROPN
ejpam-3429	22	13	;	;	PUNCT
ejpam-3429	22	14	q)n	q)n	X
ejpam-3429	22	15	zn	zn	X
ejpam-3429	22	16	.	.	PUNCT
ejpam-3429	23	1	(	(	PUNCT
ejpam-3429	23	2	1	1	X
ejpam-3429	23	3	)	)	PUNCT
ejpam-3429	23	4	generalizing	generalize	VERB
ejpam-3429	23	5	the	the	DET
ejpam-3429	23	6	heine	heine	PROPN
ejpam-3429	23	7	’s	’s	PART
ejpam-3429	23	8	series	series	NOUN
ejpam-3429	23	9	,	,	PUNCT
ejpam-3429	23	10	we	we	PRON
ejpam-3429	23	11	define	define	VERB
ejpam-3429	23	12	rφs	rφ	NOUN
ejpam-3429	23	13	the	the	DET
ejpam-3429	23	14	basic	basic	ADJ
ejpam-3429	23	15	hypergeometric	hypergeometric	ADJ
ejpam-3429	23	16	series	series	NOUN
ejpam-3429	23	17	by	by	ADP
ejpam-3429	23	18	rφs	rφs	PROPN
ejpam-3429	23	19	(	(	PUNCT
ejpam-3429	23	20	a1	a1	NOUN
ejpam-3429	23	21	,	,	PUNCT
ejpam-3429	23	22	a2	a2	PROPN
ejpam-3429	23	23	,	,	PUNCT
ejpam-3429	23	24	.	.	PUNCT
ejpam-3429	23	25	.	.	PUNCT
ejpam-3429	24	1	.	.	PUNCT
ejpam-3429	25	1	,	,	PUNCT
ejpam-3429	25	2	ar	ar	PROPN
ejpam-3429	25	3	;	;	PUNCT
ejpam-3429	25	4	b1	b1	NOUN
ejpam-3429	25	5	,	,	PUNCT
ejpam-3429	25	6	b2	b2	NOUN
ejpam-3429	25	7	,	,	PUNCT
ejpam-3429	25	8	.	.	PUNCT
ejpam-3429	25	9	.	.	PUNCT
ejpam-3429	26	1	.	.	PUNCT
ejpam-3429	27	1	,	,	PUNCT
ejpam-3429	27	2	bs	bs	INTJ
ejpam-3429	27	3	;	;	PUNCT
ejpam-3429	27	4	q	q	ADJ
ejpam-3429	27	5	,	,	PUNCT
ejpam-3429	27	6	z	z	NOUN
ejpam-3429	27	7	)	)	PUNCT
ejpam-3429	27	8	=	=	PUNCT
ejpam-3429	28	1	∞∑	∞∑	NUM
ejpam-3429	28	2	n=0	n=0	NUM
ejpam-3429	28	3	(	(	PUNCT
ejpam-3429	28	4	a1	a1	NOUN
ejpam-3429	28	5	;	;	PUNCT
ejpam-3429	28	6	q)n(a2	q)n(a2	ADV
ejpam-3429	28	7	;	;	PUNCT
ejpam-3429	28	8	q)n	q)n	X
ejpam-3429	28	9	.	.	PUNCT
ejpam-3429	28	10	.	.	PUNCT
ejpam-3429	28	11	.	.	PUNCT
ejpam-3429	29	1	(	(	PUNCT
ejpam-3429	29	2	ar	ar	NOUN
ejpam-3429	29	3	;	;	PUNCT
ejpam-3429	29	4	q)n	q)n	X
ejpam-3429	29	5	(	(	PUNCT
ejpam-3429	29	6	q	q	NOUN
ejpam-3429	29	7	;	;	PUNCT
ejpam-3429	29	8	q)n(b1	q)n(b1	X
ejpam-3429	29	9	;	;	PUNCT
ejpam-3429	29	10	q)n	q)n	X
ejpam-3429	29	11	.	.	PUNCT
ejpam-3429	29	12	.	.	PUNCT
ejpam-3429	29	13	.	.	PUNCT
ejpam-3429	30	1	(	(	PUNCT
ejpam-3429	30	2	bs	bs	NOUN
ejpam-3429	30	3	;	;	PUNCT
ejpam-3429	30	4	q)n	q)n	X
ejpam-3429	30	5	[	[	PUNCT
ejpam-3429	30	6	(	(	PUNCT
ejpam-3429	30	7	−1)nq	−1)nq	PROPN
ejpam-3429	30	8	(	(	PUNCT
ejpam-3429	30	9	n	n	PROPN
ejpam-3429	30	10	2	2	NUM
ejpam-3429	30	11	)	)	PUNCT
ejpam-3429	30	12	]	]	PUNCT
ejpam-3429	30	13	1+s−r	1+s−r	NUM
ejpam-3429	30	14	zn	zn	PROPN
ejpam-3429	30	15	(	(	PUNCT
ejpam-3429	30	16	2	2	NUM
ejpam-3429	30	17	)	)	PUNCT
ejpam-3429	30	18	with	with	ADP
ejpam-3429	30	19	(	(	PUNCT
ejpam-3429	30	20	n	n	ADV
ejpam-3429	30	21	2	2	NUM
ejpam-3429	30	22	)	)	PUNCT
ejpam-3429	30	23	=	=	SYM
ejpam-3429	30	24	n(n−1	n(n−1	X
ejpam-3429	30	25	)	)	PUNCT
ejpam-3429	30	26	2	2	NUM
ejpam-3429	30	27	,	,	PUNCT
ejpam-3429	30	28	where	where	SCONJ
ejpam-3429	30	29	q	q	X
ejpam-3429	30	30	6=	6=	NUM
ejpam-3429	30	31	0	0	NUM
ejpam-3429	30	32	when	when	SCONJ
ejpam-3429	30	33	r	r	NOUN
ejpam-3429	30	34	>	>	X
ejpam-3429	30	35	s	s	X
ejpam-3429	31	1	+	+	NOUN
ejpam-3429	31	2	1	1	X
ejpam-3429	31	3	.	.	PUNCT
ejpam-3429	32	1	in	in	ADP
ejpam-3429	32	2	(	(	PUNCT
ejpam-3429	32	3	1	1	NUM
ejpam-3429	32	4	)	)	PUNCT
ejpam-3429	32	5	and	and	CCONJ
ejpam-3429	32	6	(	(	PUNCT
ejpam-3429	32	7	2	2	NUM
ejpam-3429	32	8	)	)	PUNCT
ejpam-3429	32	9	,	,	PUNCT
ejpam-3429	32	10	it	it	PRON
ejpam-3429	32	11	is	be	AUX
ejpam-3429	32	12	assumed	assume	VERB
ejpam-3429	32	13	that	that	SCONJ
ejpam-3429	32	14	the	the	DET
ejpam-3429	32	15	parameters	parameter	NOUN
ejpam-3429	32	16	b1	b1	VERB
ejpam-3429	32	17	,	,	PUNCT
ejpam-3429	32	18	b2	b2	NOUN
ejpam-3429	32	19	,	,	PUNCT
ejpam-3429	32	20	.	.	PUNCT
ejpam-3429	32	21	.	.	PUNCT
ejpam-3429	32	22	.	.	PUNCT
ejpam-3429	33	1	,	,	PUNCT
ejpam-3429	33	2	bs	b	NOUN
ejpam-3429	33	3	are	be	AUX
ejpam-3429	33	4	such	such	ADJ
ejpam-3429	33	5	that	that	SCONJ
ejpam-3429	33	6	the	the	DET
ejpam-3429	33	7	denominator	denominator	NOUN
ejpam-3429	33	8	factors	factor	NOUN
ejpam-3429	33	9	in	in	ADP
ejpam-3429	33	10	the	the	DET
ejpam-3429	33	11	terms	term	NOUN
ejpam-3429	33	12	of	of	ADP
ejpam-3429	33	13	the	the	DET
ejpam-3429	33	14	series	series	NOUN
ejpam-3429	33	15	are	be	AUX
ejpam-3429	33	16	never	never	ADV
ejpam-3429	33	17	zero	zero	NUM
ejpam-3429	33	18	.	.	PUNCT
ejpam-3429	34	1	let	let	VERB
ejpam-3429	34	2	a	a	DET
ejpam-3429	34	3	denote	denote	NOUN
ejpam-3429	34	4	the	the	DET
ejpam-3429	34	5	class	class	NOUN
ejpam-3429	34	6	of	of	ADP
ejpam-3429	34	7	all	all	DET
ejpam-3429	34	8	functions	function	NOUN
ejpam-3429	34	9	having	have	VERB
ejpam-3429	34	10	a	a	DET
ejpam-3429	34	11	taylor	taylor	PROPN
ejpam-3429	34	12	series	series	NOUN
ejpam-3429	34	13	expansion	expansion	NOUN
ejpam-3429	34	14	of	of	ADP
ejpam-3429	34	15	the	the	DET
ejpam-3429	34	16	form	form	NOUN
ejpam-3429	34	17	f(z	f(z	PROPN
ejpam-3429	34	18	)	)	PUNCT
ejpam-3429	35	1	=	=	SYM
ejpam-3429	35	2	z	z	NOUN
ejpam-3429	36	1	+	+	NOUN
ejpam-3429	36	2	∞∑	∞∑	NUM
ejpam-3429	36	3	n=2	n=2	PRON
ejpam-3429	36	4	knz	knz	NOUN
ejpam-3429	36	5	n	n	CCONJ
ejpam-3429	36	6	,	,	PUNCT
ejpam-3429	36	7	(	(	PUNCT
ejpam-3429	36	8	z	z	NOUN
ejpam-3429	36	9	∈	∈	PROPN
ejpam-3429	36	10	u	u	NOUN
ejpam-3429	36	11	)	)	PUNCT
ejpam-3429	36	12	.	.	PUNCT
ejpam-3429	37	1	(	(	PUNCT
ejpam-3429	37	2	3	3	X
ejpam-3429	37	3	)	)	PUNCT
ejpam-3429	37	4	for	for	ADP
ejpam-3429	37	5	complex	complex	ADJ
ejpam-3429	37	6	parameters	parameter	NOUN
ejpam-3429	37	7	a1	a1	VERB
ejpam-3429	37	8	,	,	PUNCT
ejpam-3429	37	9	.	.	PUNCT
ejpam-3429	37	10	.	.	PUNCT
ejpam-3429	37	11	.	.	PUNCT
ejpam-3429	38	1	,	,	PUNCT
ejpam-3429	38	2	ar	ar	PROPN
ejpam-3429	38	3	and	and	CCONJ
ejpam-3429	38	4	b1	b1	PROPN
ejpam-3429	38	5	,	,	PUNCT
ejpam-3429	38	6	.	.	PUNCT
ejpam-3429	38	7	.	.	PUNCT
ejpam-3429	39	1	.	.	PUNCT
ejpam-3429	40	1	,	,	PUNCT
ejpam-3429	40	2	bs	bs	INTJ
ejpam-3429	40	3	(	(	PUNCT
ejpam-3429	40	4	βj	βj	PART
ejpam-3429	40	5	∈	∈	PROPN
ejpam-3429	40	6	c\z−0	c\z−0	NOUN
ejpam-3429	40	7	;	;	PUNCT
ejpam-3429	41	1	z−0	z−0	PROPN
ejpam-3429	41	2	=	=	SYM
ejpam-3429	41	3	0,−1	0,−1	PROPN
ejpam-3429	41	4	,	,	PUNCT
ejpam-3429	41	5	−2	−2	NOUN
ejpam-3429	41	6	,	,	PUNCT
ejpam-3429	41	7	.	.	PUNCT
ejpam-3429	41	8	.	.	PUNCT
ejpam-3429	41	9	.	.	PUNCT
ejpam-3429	41	10	;	;	PUNCT
ejpam-3429	41	11	j	j	PROPN
ejpam-3429	41	12	=	=	SYM
ejpam-3429	41	13	1	1	NUM
ejpam-3429	41	14	,	,	PUNCT
ejpam-3429	41	15	.	.	PUNCT
ejpam-3429	41	16	.	.	PUNCT
ejpam-3429	41	17	.	.	PUNCT
ejpam-3429	41	18	,	,	PUNCT
ejpam-3429	41	19	s	s	X
ejpam-3429	41	20	)	)	PUNCT
ejpam-3429	41	21	,	,	PUNCT
ejpam-3429	41	22	we	we	PRON
ejpam-3429	41	23	define	define	VERB
ejpam-3429	41	24	the	the	DET
ejpam-3429	41	25	generalized	generalized	ADJ
ejpam-3429	41	26	q	q	ADJ
ejpam-3429	41	27	-	-	ADJ
ejpam-3429	41	28	hypergeometric	hypergeometric	ADJ
ejpam-3429	41	29	function	function	NOUN
ejpam-3429	41	30	rψs(a1	rψs(a1	PROPN
ejpam-3429	41	31	,	,	PUNCT
ejpam-3429	41	32	.	.	PUNCT
ejpam-3429	41	33	.	.	PUNCT
ejpam-3429	41	34	.	.	PUNCT
ejpam-3429	42	1	,	,	PUNCT
ejpam-3429	42	2	aq	aq	PROPN
ejpam-3429	42	3	;	;	PUNCT
ejpam-3429	42	4	b1	b1	NOUN
ejpam-3429	42	5	,	,	PUNCT
ejpam-3429	42	6	.	.	PUNCT
ejpam-3429	42	7	.	.	PUNCT
ejpam-3429	42	8	.	.	PUNCT
ejpam-3429	43	1	,	,	PUNCT
ejpam-3429	43	2	bs	bs	INTJ
ejpam-3429	43	3	;	;	PUNCT
ejpam-3429	43	4	q	q	ADJ
ejpam-3429	43	5	,	,	PUNCT
ejpam-3429	43	6	z	z	NOUN
ejpam-3429	43	7	)	)	PUNCT
ejpam-3429	43	8	by	by	ADP
ejpam-3429	43	9	rψs(a1	rψs(a1	PROPN
ejpam-3429	43	10	,	,	PUNCT
ejpam-3429	43	11	a2	a2	PROPN
ejpam-3429	43	12	,	,	PUNCT
ejpam-3429	43	13	.	.	PUNCT
ejpam-3429	43	14	.	.	PUNCT
ejpam-3429	43	15	.	.	PUNCT
ejpam-3429	44	1	,	,	PUNCT
ejpam-3429	44	2	aq	aq	PROPN
ejpam-3429	44	3	;	;	PUNCT
ejpam-3429	44	4	b1	b1	NOUN
ejpam-3429	44	5	,	,	PUNCT
ejpam-3429	44	6	b2	b2	NOUN
ejpam-3429	44	7	,	,	PUNCT
ejpam-3429	44	8	.	.	PUNCT
ejpam-3429	44	9	.	.	PUNCT
ejpam-3429	45	1	.	.	PUNCT
ejpam-3429	46	1	,	,	PUNCT
ejpam-3429	46	2	bs	bs	INTJ
ejpam-3429	46	3	;	;	PUNCT
ejpam-3429	46	4	q	q	ADJ
ejpam-3429	46	5	,	,	PUNCT
ejpam-3429	46	6	z	z	NOUN
ejpam-3429	46	7	)	)	PUNCT
ejpam-3429	46	8	=	=	PUNCT
ejpam-3429	47	1	∞∑	∞∑	NUM
ejpam-3429	47	2	n=0	n=0	NUM
ejpam-3429	47	3	(	(	PUNCT
ejpam-3429	47	4	a1	a1	NOUN
ejpam-3429	47	5	;	;	PUNCT
ejpam-3429	47	6	q)n(a2	q)n(a2	ADV
ejpam-3429	47	7	;	;	PUNCT
ejpam-3429	47	8	q)n	q)n	X
ejpam-3429	47	9	.	.	PUNCT
ejpam-3429	47	10	.	.	PUNCT
ejpam-3429	47	11	.	.	PUNCT
ejpam-3429	48	1	(	(	PUNCT
ejpam-3429	48	2	ar	ar	NOUN
ejpam-3429	48	3	;	;	PUNCT
ejpam-3429	48	4	q)n	q)n	X
ejpam-3429	48	5	(	(	PUNCT
ejpam-3429	48	6	q	q	NOUN
ejpam-3429	48	7	;	;	PUNCT
ejpam-3429	48	8	q)n(b1	q)n(b1	X
ejpam-3429	48	9	;	;	PUNCT
ejpam-3429	48	10	q)n	q)n	X
ejpam-3429	48	11	.	.	PUNCT
ejpam-3429	48	12	.	.	PUNCT
ejpam-3429	48	13	.	.	PUNCT
ejpam-3429	49	1	(	(	PUNCT
ejpam-3429	49	2	bs	bs	NOUN
ejpam-3429	49	3	;	;	PUNCT
ejpam-3429	49	4	q)n	q)n	X
ejpam-3429	49	5	zn	zn	X
ejpam-3429	49	6	(	(	PUNCT
ejpam-3429	49	7	4	4	NUM
ejpam-3429	49	8	)	)	PUNCT
ejpam-3429	49	9	(	(	PUNCT
ejpam-3429	49	10	r	r	NOUN
ejpam-3429	49	11	=	=	PUNCT
ejpam-3429	49	12	s+	s+	NUM
ejpam-3429	49	13	1	1	NUM
ejpam-3429	49	14	;	;	PUNCT
ejpam-3429	49	15	r	r	X
ejpam-3429	49	16	,	,	PUNCT
ejpam-3429	49	17	s	s	NOUN
ejpam-3429	49	18	∈	∈	PROPN
ejpam-3429	49	19	n0	n0	X
ejpam-3429	49	20	=	=	SYM
ejpam-3429	49	21	n	n	PRON
ejpam-3429	49	22	∪	∪	X
ejpam-3429	49	23	{	{	PUNCT
ejpam-3429	49	24	0	0	NUM
ejpam-3429	49	25	}	}	PUNCT
ejpam-3429	49	26	;	;	PUNCT
ejpam-3429	49	27	z	z	PROPN
ejpam-3429	49	28	∈	∈	PROPN
ejpam-3429	49	29	u	u	NOUN
ejpam-3429	49	30	)	)	PUNCT
ejpam-3429	49	31	,	,	PUNCT
ejpam-3429	49	32	where	where	SCONJ
ejpam-3429	49	33	n	n	PRON
ejpam-3429	49	34	denotes	denote	VERB
ejpam-3429	49	35	the	the	DET
ejpam-3429	49	36	set	set	NOUN
ejpam-3429	49	37	of	of	ADP
ejpam-3429	49	38	positive	positive	ADJ
ejpam-3429	49	39	integers	integer	NOUN
ejpam-3429	49	40	.	.	PUNCT
ejpam-3429	50	1	by	by	ADP
ejpam-3429	50	2	using	use	VERB
ejpam-3429	50	3	the	the	DET
ejpam-3429	50	4	ratio	ratio	NOUN
ejpam-3429	50	5	test	test	NOUN
ejpam-3429	50	6	,	,	PUNCT
ejpam-3429	50	7	we	we	PRON
ejpam-3429	50	8	should	should	AUX
ejpam-3429	50	9	note	note	VERB
ejpam-3429	50	10	that	that	SCONJ
ejpam-3429	50	11	,	,	PUNCT
ejpam-3429	50	12	if	if	SCONJ
ejpam-3429	50	13	|q|	|q|	VERB
ejpam-3429	50	14	<	<	X
ejpam-3429	50	15	1	1	NUM
ejpam-3429	50	16	,	,	PUNCT
ejpam-3429	50	17	the	the	DET
ejpam-3429	50	18	series	series	NOUN
ejpam-3429	50	19	(	(	PUNCT
ejpam-3429	50	20	4	4	X
ejpam-3429	50	21	)	)	PUNCT
ejpam-3429	50	22	converges	converge	VERB
ejpam-3429	50	23	absolutely	absolutely	ADV
ejpam-3429	50	24	for	for	ADP
ejpam-3429	50	25	|z|	|z|	NOUN
ejpam-3429	50	26	<	<	X
ejpam-3429	50	27	1	1	NUM
ejpam-3429	50	28	and	and	CCONJ
ejpam-3429	50	29	r	r	NOUN
ejpam-3429	50	30	=	=	SYM
ejpam-3429	50	31	s	s	X
ejpam-3429	50	32	+	+	NOUN
ejpam-3429	50	33	1	1	NUM
ejpam-3429	50	34	.	.	PUNCT
ejpam-3429	50	35	for	for	ADP
ejpam-3429	50	36	more	more	ADJ
ejpam-3429	50	37	mathematical	mathematical	ADJ
ejpam-3429	50	38	background	background	NOUN
ejpam-3429	50	39	of	of	ADP
ejpam-3429	50	40	these	these	DET
ejpam-3429	50	41	functions	function	NOUN
ejpam-3429	50	42	,	,	PUNCT
ejpam-3429	50	43	one	one	PRON
ejpam-3429	50	44	may	may	AUX
ejpam-3429	50	45	refer	refer	VERB
ejpam-3429	50	46	to	to	ADP
ejpam-3429	50	47	[	[	X
ejpam-3429	50	48	2	2	NUM
ejpam-3429	50	49	]	]	PUNCT
ejpam-3429	50	50	.	.	PUNCT
ejpam-3429	51	1	corresponding	correspond	VERB
ejpam-3429	51	2	to	to	ADP
ejpam-3429	51	3	a	a	DET
ejpam-3429	51	4	function	function	NOUN
ejpam-3429	51	5	gr	gr	PROPN
ejpam-3429	51	6	,	,	PUNCT
ejpam-3429	51	7	s(ai	s(ai	PROPN
ejpam-3429	51	8	,	,	PUNCT
ejpam-3429	51	9	bj	bj	AUX
ejpam-3429	51	10	;	;	PUNCT
ejpam-3429	51	11	q	q	X
ejpam-3429	51	12	,	,	PUNCT
ejpam-3429	51	13	z	z	NOUN
ejpam-3429	51	14	)	)	PUNCT
ejpam-3429	51	15	(	(	PUNCT
ejpam-3429	51	16	ai	ai	VERB
ejpam-3429	51	17	,	,	PUNCT
ejpam-3429	51	18	bj	bj	NOUN
ejpam-3429	51	19	are	be	AUX
ejpam-3429	51	20	real	real	ADJ
ejpam-3429	51	21	;	;	PUNCT
ejpam-3429	52	1	i	i	PRON
ejpam-3429	52	2	=	=	NOUN
ejpam-3429	52	3	1	1	NUM
ejpam-3429	52	4	,	,	PUNCT
ejpam-3429	52	5	2	2	NUM
ejpam-3429	52	6	,	,	PUNCT
ejpam-3429	52	7	.	.	PUNCT
ejpam-3429	52	8	.	.	PUNCT
ejpam-3429	52	9	.	.	PUNCT
ejpam-3429	53	1	,	,	PUNCT
ejpam-3429	53	2	r	r	NOUN
ejpam-3429	53	3	;	;	PUNCT
ejpam-3429	53	4	j	j	PROPN
ejpam-3429	53	5	=	=	SYM
ejpam-3429	53	6	1	1	NUM
ejpam-3429	53	7	,	,	PUNCT
ejpam-3429	53	8	2	2	NUM
ejpam-3429	53	9	,	,	PUNCT
ejpam-3429	53	10	.	.	PUNCT
ejpam-3429	53	11	.	.	PUNCT
ejpam-3429	53	12	.	.	PUNCT
ejpam-3429	54	1	,	,	PUNCT
ejpam-3429	54	2	s	s	X
ejpam-3429	54	3	)	)	PUNCT
ejpam-3429	54	4	defined	define	VERB
ejpam-3429	54	5	by	by	ADP
ejpam-3429	54	6	gr	gr	PROPN
ejpam-3429	54	7	,	,	PUNCT
ejpam-3429	54	8	s(ai	s(ai	PROPN
ejpam-3429	54	9	,	,	PUNCT
ejpam-3429	54	10	bj	bj	VERB
ejpam-3429	54	11	;	;	PUNCT
ejpam-3429	55	1	q	q	X
ejpam-3429	55	2	,	,	PUNCT
ejpam-3429	55	3	z	z	NOUN
ejpam-3429	55	4	)	)	PUNCT
ejpam-3429	55	5	:	:	PUNCT
ejpam-3429	56	1	=	=	PUNCT
ejpam-3429	56	2	z	z	X
ejpam-3429	56	3	qψs(a1	qψs(a1	PROPN
ejpam-3429	56	4	,	,	PUNCT
ejpam-3429	56	5	a2	a2	PROPN
ejpam-3429	56	6	,	,	PUNCT
ejpam-3429	56	7	.	.	PUNCT
ejpam-3429	56	8	.	.	PUNCT
ejpam-3429	56	9	.	.	PUNCT
ejpam-3429	57	1	,	,	PUNCT
ejpam-3429	57	2	ar	ar	PROPN
ejpam-3429	57	3	;	;	PUNCT
ejpam-3429	57	4	b1	b1	NOUN
ejpam-3429	57	5	,	,	PUNCT
ejpam-3429	57	6	b2	b2	NOUN
ejpam-3429	57	7	,	,	PUNCT
ejpam-3429	57	8	.	.	PUNCT
ejpam-3429	57	9	.	.	PUNCT
ejpam-3429	58	1	.	.	PUNCT
ejpam-3429	59	1	,	,	PUNCT
ejpam-3429	59	2	bs	bs	INTJ
ejpam-3429	59	3	;	;	PUNCT
ejpam-3429	59	4	q	q	ADJ
ejpam-3429	59	5	,	,	PUNCT
ejpam-3429	59	6	z	z	NOUN
ejpam-3429	59	7	)	)	PUNCT
ejpam-3429	59	8	.	.	PUNCT
ejpam-3429	60	1	(	(	PUNCT
ejpam-3429	60	2	5	5	X
ejpam-3429	60	3	)	)	PUNCT
ejpam-3429	60	4	we	we	PRON
ejpam-3429	60	5	now	now	ADV
ejpam-3429	60	6	define	define	VERB
ejpam-3429	60	7	the	the	DET
ejpam-3429	60	8	following	follow	VERB
ejpam-3429	60	9	operator	operator	NOUN
ejpam-3429	60	10	jmλ	jmλ	PROPN
ejpam-3429	60	11	(	(	PUNCT
ejpam-3429	60	12	a1	a1	PROPN
ejpam-3429	60	13	,	,	PUNCT
ejpam-3429	60	14	b1	b1	NOUN
ejpam-3429	60	15	;	;	PUNCT
ejpam-3429	60	16	q	q	ADJ
ejpam-3429	60	17	,	,	PUNCT
ejpam-3429	60	18	z)f	z)f	PUNCT
ejpam-3429	60	19	:	:	PUNCT
ejpam-3429	60	20	u	u	NOUN
ejpam-3429	60	21	−→	−→	NOUN
ejpam-3429	60	22	u	u	NOUN
ejpam-3429	60	23	by	by	ADP
ejpam-3429	60	24	j	j	PROPN
ejpam-3429	60	25	0	0	PROPN
ejpam-3429	61	1	λ	λ	PROPN
ejpam-3429	61	2	(	(	PUNCT
ejpam-3429	61	3	a1	a1	PROPN
ejpam-3429	61	4	,	,	PUNCT
ejpam-3429	61	5	b1	b1	NOUN
ejpam-3429	61	6	;	;	PUNCT
ejpam-3429	61	7	q	q	ADJ
ejpam-3429	61	8	,	,	PUNCT
ejpam-3429	61	9	z)f(z	z)f(z	NUM
ejpam-3429	61	10	)	)	PUNCT
ejpam-3429	61	11	=	=	SYM
ejpam-3429	61	12	f(z	f(z	PROPN
ejpam-3429	61	13	)	)	PUNCT
ejpam-3429	61	14	∗	∗	NOUN
ejpam-3429	61	15	gr	gr	PROPN
ejpam-3429	61	16	,	,	PUNCT
ejpam-3429	61	17	s(ai	s(ai	PROPN
ejpam-3429	61	18	,	,	PUNCT
ejpam-3429	61	19	bj	bj	VERB
ejpam-3429	61	20	;	;	PUNCT
ejpam-3429	61	21	q	q	X
ejpam-3429	61	22	,	,	PUNCT
ejpam-3429	61	23	z	z	NOUN
ejpam-3429	61	24	)	)	PUNCT
ejpam-3429	61	25	j	j	PROPN
ejpam-3429	61	26	1	1	NUM
ejpam-3429	61	27	λ	λ	PROPN
ejpam-3429	61	28	(	(	PUNCT
ejpam-3429	61	29	a1	a1	PROPN
ejpam-3429	61	30	,	,	PUNCT
ejpam-3429	61	31	b1	b1	NOUN
ejpam-3429	61	32	;	;	PUNCT
ejpam-3429	61	33	q	q	ADJ
ejpam-3429	61	34	,	,	PUNCT
ejpam-3429	61	35	z)f(z	z)f(z	NUM
ejpam-3429	61	36	)	)	PUNCT
ejpam-3429	61	37	=	=	SYM
ejpam-3429	61	38	(	(	PUNCT
ejpam-3429	61	39	1−λ)(f(z)∗gr	1−λ)(f(z)∗gr	NUM
ejpam-3429	61	40	,	,	PUNCT
ejpam-3429	61	41	s(ai	s(ai	PROPN
ejpam-3429	61	42	,	,	PUNCT
ejpam-3429	61	43	bj	bj	VERB
ejpam-3429	61	44	;	;	PUNCT
ejpam-3429	61	45	q	q	X
ejpam-3429	61	46	,	,	PUNCT
ejpam-3429	61	47	z))+λ	z))+λ	PROPN
ejpam-3429	61	48	zdq(f(z)∗gr	zdq(f(z)∗gr	PROPN
ejpam-3429	61	49	,	,	PUNCT
ejpam-3429	61	50	s(ai	s(ai	PROPN
ejpam-3429	61	51	,	,	PUNCT
ejpam-3429	61	52	bj	bj	VERB
ejpam-3429	61	53	;	;	PUNCT
ejpam-3429	61	54	q	q	X
ejpam-3429	61	55	,	,	PUNCT
ejpam-3429	61	56	z	z	NOUN
ejpam-3429	61	57	)	)	PUNCT
ejpam-3429	61	58	)	)	PUNCT
ejpam-3429	62	1	(	(	PUNCT
ejpam-3429	62	2	6	6	X
ejpam-3429	62	3	)	)	PUNCT
ejpam-3429	62	4	k.	k.	PROPN
ejpam-3429	62	5	a.	a.	PROPN
ejpam-3429	62	6	reddy	reddy	PROPN
ejpam-3429	62	7	,	,	PUNCT
ejpam-3429	62	8	k.	k.	PROPN
ejpam-3429	62	9	r.	r.	PROPN
ejpam-3429	62	10	karthikeyan	karthikeyan	PROPN
ejpam-3429	62	11	,	,	PUNCT
ejpam-3429	62	12	g.	g.	PROPN
ejpam-3429	62	13	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	62	14	/	/	SYM
ejpam-3429	62	15	eur	eur	PROPN
ejpam-3429	62	16	.	.	PUNCT
ejpam-3429	63	1	j.	j.	PROPN
ejpam-3429	63	2	pure	pure	PROPN
ejpam-3429	63	3	appl	appl	PROPN
ejpam-3429	63	4	.	.	PROPN
ejpam-3429	63	5	math	math	PROPN
ejpam-3429	63	6	,	,	PUNCT
ejpam-3429	63	7	12	12	NUM
ejpam-3429	63	8	(	(	PUNCT
ejpam-3429	63	9	3	3	NUM
ejpam-3429	63	10	)	)	PUNCT
ejpam-3429	63	11	(	(	PUNCT
ejpam-3429	63	12	2019	2019	NUM
ejpam-3429	63	13	)	)	PUNCT
ejpam-3429	63	14	,	,	PUNCT
ejpam-3429	63	15	846	846	NUM
ejpam-3429	63	16	-	-	SYM
ejpam-3429	63	17	856	856	NUM
ejpam-3429	63	18	848	848	NUM
ejpam-3429	63	19	jmλ	jmλ	PROPN
ejpam-3429	63	20	(	(	PUNCT
ejpam-3429	63	21	a1	a1	PROPN
ejpam-3429	63	22	,	,	PUNCT
ejpam-3429	63	23	b1	b1	NOUN
ejpam-3429	63	24	;	;	PUNCT
ejpam-3429	63	25	q	q	ADJ
ejpam-3429	63	26	,	,	PUNCT
ejpam-3429	63	27	z)f(z	z)f(z	NUM
ejpam-3429	63	28	)	)	PUNCT
ejpam-3429	63	29	=	=	SYM
ejpam-3429	64	1	j	j	PROPN
ejpam-3429	64	2	1	1	NUM
ejpam-3429	64	3	λ	λ	PROPN
ejpam-3429	64	4	(	(	PUNCT
ejpam-3429	64	5	jm−1λ	jm−1λ	X
ejpam-3429	64	6	(	(	PUNCT
ejpam-3429	64	7	a1	a1	PROPN
ejpam-3429	64	8	,	,	PUNCT
ejpam-3429	64	9	b1	b1	NOUN
ejpam-3429	64	10	;	;	PUNCT
ejpam-3429	64	11	q	q	ADJ
ejpam-3429	64	12	,	,	PUNCT
ejpam-3429	64	13	z)f(z	z)f(z	NUM
ejpam-3429	64	14	)	)	PUNCT
ejpam-3429	64	15	)	)	PUNCT
ejpam-3429	64	16	.	.	PUNCT
ejpam-3429	65	1	(	(	PUNCT
ejpam-3429	65	2	7	7	X
ejpam-3429	65	3	)	)	PUNCT
ejpam-3429	65	4	if	if	SCONJ
ejpam-3429	65	5	f	f	PROPN
ejpam-3429	65	6	∈	∈	PROPN
ejpam-3429	65	7	a	a	PROPN
ejpam-3429	65	8	,	,	PUNCT
ejpam-3429	65	9	then	then	ADV
ejpam-3429	65	10	from	from	ADP
ejpam-3429	65	11	(	(	PUNCT
ejpam-3429	65	12	6	6	NUM
ejpam-3429	65	13	)	)	PUNCT
ejpam-3429	65	14	and	and	CCONJ
ejpam-3429	65	15	(	(	PUNCT
ejpam-3429	65	16	7	7	X
ejpam-3429	65	17	)	)	PUNCT
ejpam-3429	65	18	we	we	PRON
ejpam-3429	65	19	may	may	AUX
ejpam-3429	65	20	easily	easily	ADV
ejpam-3429	65	21	deduce	deduce	VERB
ejpam-3429	65	22	that	that	SCONJ
ejpam-3429	65	23	jmλ	jmλ	PROPN
ejpam-3429	65	24	(	(	PUNCT
ejpam-3429	65	25	a1	a1	PROPN
ejpam-3429	65	26	,	,	PUNCT
ejpam-3429	65	27	b1	b1	NOUN
ejpam-3429	65	28	;	;	PUNCT
ejpam-3429	65	29	q	q	ADJ
ejpam-3429	65	30	,	,	PUNCT
ejpam-3429	65	31	z)f	z)f	X
ejpam-3429	65	32	=	=	PUNCT
ejpam-3429	66	1	z	z	NOUN
ejpam-3429	66	2	+	+	NOUN
ejpam-3429	66	3	∞∑	∞∑	NUM
ejpam-3429	66	4	n=2	n=2	PRON
ejpam-3429	67	1	[	[	X
ejpam-3429	67	2	1−	1−	NUM
ejpam-3429	67	3	λ+	λ+	PUNCT
ejpam-3429	67	4	[	[	X
ejpam-3429	67	5	n]qλ]m	n]qλ]m	INTJ
ejpam-3429	67	6	υnknz	υnknz	NOUN
ejpam-3429	67	7	n	n	CCONJ
ejpam-3429	67	8	,	,	PUNCT
ejpam-3429	67	9	(	(	PUNCT
ejpam-3429	67	10	8)	8)	NUM
ejpam-3429	67	11	(	(	PUNCT
ejpam-3429	67	12	m	m	PROPN
ejpam-3429	67	13	∈	∈	PROPN
ejpam-3429	67	14	n0	n0	X
ejpam-3429	67	15	=	=	SYM
ejpam-3429	67	16	n	n	PRON
ejpam-3429	67	17	∪	∪	X
ejpam-3429	67	18	{	{	PUNCT
ejpam-3429	67	19	0	0	NUM
ejpam-3429	67	20	}	}	PUNCT
ejpam-3429	67	21	and	and	CCONJ
ejpam-3429	67	22	λ	λ	X
ejpam-3429	67	23	≥	≥	NOUN
ejpam-3429	67	24	0	0	NUM
ejpam-3429	67	25	)	)	PUNCT
ejpam-3429	67	26	,	,	PUNCT
ejpam-3429	67	27	where	where	SCONJ
ejpam-3429	67	28	υn	υn	NOUN
ejpam-3429	67	29	=	=	SYM
ejpam-3429	67	30	(	(	PUNCT
ejpam-3429	67	31	a1	a1	NOUN
ejpam-3429	67	32	;	;	PUNCT
ejpam-3429	67	33	q)n−1(a2	q)n−1(a2	NUM
ejpam-3429	67	34	;	;	PUNCT
ejpam-3429	67	35	q)n−1	q)n−1	PROPN
ejpam-3429	67	36	.	.	PUNCT
ejpam-3429	67	37	.	.	PUNCT
ejpam-3429	68	1	.	.	PUNCT
ejpam-3429	69	1	(	(	PUNCT
ejpam-3429	69	2	ar	ar	PROPN
ejpam-3429	69	3	;	;	PUNCT
ejpam-3429	69	4	q)n−1	q)n−1	PROPN
ejpam-3429	69	5	(	(	PUNCT
ejpam-3429	69	6	q	q	NOUN
ejpam-3429	69	7	;	;	PUNCT
ejpam-3429	69	8	q)n−1(b1	q)n−1(b1	X
ejpam-3429	69	9	;	;	PUNCT
ejpam-3429	69	10	q)n−1	q)n−1	PROPN
ejpam-3429	69	11	.	.	PUNCT
ejpam-3429	69	12	.	.	PUNCT
ejpam-3429	69	13	.	.	PUNCT
ejpam-3429	70	1	(	(	PUNCT
ejpam-3429	70	2	bs	bs	NOUN
ejpam-3429	70	3	;	;	PUNCT
ejpam-3429	70	4	q)n−1	q)n−1	PROPN
ejpam-3429	70	5	,	,	PUNCT
ejpam-3429	70	6	(	(	PUNCT
ejpam-3429	70	7	|q|	|q|	VERB
ejpam-3429	70	8	<	<	X
ejpam-3429	70	9	1	1	NUM
ejpam-3429	70	10	)	)	PUNCT
ejpam-3429	70	11	.	.	PUNCT
ejpam-3429	71	1	remark	remark	NOUN
ejpam-3429	71	2	1	1	NUM
ejpam-3429	71	3	.	.	PUNCT
ejpam-3429	72	1	we	we	PRON
ejpam-3429	72	2	note	note	VERB
ejpam-3429	72	3	that	that	SCONJ
ejpam-3429	72	4	the	the	DET
ejpam-3429	72	5	linear	linear	ADJ
ejpam-3429	72	6	operator	operator	NOUN
ejpam-3429	72	7	(	(	PUNCT
ejpam-3429	72	8	8)	8)	NUM
ejpam-3429	72	9	is	be	AUX
ejpam-3429	72	10	q	q	NOUN
ejpam-3429	72	11	-	-	PUNCT
ejpam-3429	72	12	analogue	analogue	NOUN
ejpam-3429	72	13	of	of	ADP
ejpam-3429	72	14	the	the	DET
ejpam-3429	72	15	operator	operator	NOUN
ejpam-3429	72	16	defined	define	VERB
ejpam-3429	72	17	by	by	ADP
ejpam-3429	72	18	selvaraj	selvaraj	ADJ
ejpam-3429	72	19	and	and	CCONJ
ejpam-3429	72	20	karthikeyan	karthikeyan	ADJ
ejpam-3429	73	1	[	[	X
ejpam-3429	73	2	5	5	NUM
ejpam-3429	73	3	]	]	PUNCT
ejpam-3429	73	4	.	.	PUNCT
ejpam-3429	74	1	here	here	ADV
ejpam-3429	74	2	we	we	PRON
ejpam-3429	74	3	list	list	VERB
ejpam-3429	74	4	some	some	DET
ejpam-3429	74	5	special	special	ADJ
ejpam-3429	74	6	cases	case	NOUN
ejpam-3429	74	7	of	of	ADP
ejpam-3429	74	8	the	the	DET
ejpam-3429	74	9	operator	operator	NOUN
ejpam-3429	74	10	jmλ	jmλ	PROPN
ejpam-3429	74	11	(	(	PUNCT
ejpam-3429	74	12	a1	a1	PROPN
ejpam-3429	74	13	,	,	PUNCT
ejpam-3429	74	14	b1	b1	NOUN
ejpam-3429	74	15	;	;	PUNCT
ejpam-3429	74	16	q	q	ADJ
ejpam-3429	74	17	,	,	PUNCT
ejpam-3429	74	18	z)f	z)f	ADJ
ejpam-3429	74	19	.	.	PUNCT
ejpam-3429	75	1	1	1	X
ejpam-3429	75	2	.	.	X
ejpam-3429	75	3	for	for	ADP
ejpam-3429	75	4	a	a	DET
ejpam-3429	75	5	choice	choice	NOUN
ejpam-3429	75	6	of	of	ADP
ejpam-3429	75	7	the	the	DET
ejpam-3429	75	8	parameter	parameter	NOUN
ejpam-3429	75	9	m	m	NOUN
ejpam-3429	75	10	=	=	SYM
ejpam-3429	75	11	0	0	NUM
ejpam-3429	75	12	,	,	PUNCT
ejpam-3429	75	13	the	the	DET
ejpam-3429	75	14	operator	operator	NOUN
ejpam-3429	75	15	j	j	PROPN
ejpam-3429	75	16	0	0	PUNCT
ejpam-3429	75	17	λ	λ	PROPN
ejpam-3429	75	18	(	(	PUNCT
ejpam-3429	75	19	α1	α1	PROPN
ejpam-3429	75	20	,	,	PUNCT
ejpam-3429	75	21	β1)f(z	β1)f(z	NOUN
ejpam-3429	75	22	)	)	PUNCT
ejpam-3429	75	23	reduces	reduce	VERB
ejpam-3429	75	24	to	to	ADP
ejpam-3429	75	25	the	the	DET
ejpam-3429	75	26	q	q	NOUN
ejpam-3429	75	27	-	-	PUNCT
ejpam-3429	75	28	analogue	analogue	NOUN
ejpam-3429	75	29	of	of	ADP
ejpam-3429	75	30	dzioksrivastava	dzioksrivastava	NOUN
ejpam-3429	75	31	operator	operator	NOUN
ejpam-3429	75	32	[	[	X
ejpam-3429	75	33	1	1	NUM
ejpam-3429	75	34	]	]	PUNCT
ejpam-3429	75	35	.	.	PUNCT
ejpam-3429	76	1	2	2	X
ejpam-3429	76	2	.	.	X
ejpam-3429	76	3	for	for	ADP
ejpam-3429	76	4	ai	ai	PROPN
ejpam-3429	76	5	=	=	VERB
ejpam-3429	76	6	qαi	qαi	NOUN
ejpam-3429	76	7	,	,	PUNCT
ejpam-3429	76	8	bj	bj	ADP
ejpam-3429	76	9	=	=	PUNCT
ejpam-3429	76	10	qβj	qβj	NOUN
ejpam-3429	76	11	,	,	PUNCT
ejpam-3429	76	12	αi	αi	PROPN
ejpam-3429	76	13	,	,	PUNCT
ejpam-3429	76	14	βj	βj	PROPN
ejpam-3429	76	15	∈	∈	PROPN
ejpam-3429	76	16	c	c	X
ejpam-3429	76	17	,	,	PUNCT
ejpam-3429	76	18	βj	βj	PROPN
ejpam-3429	76	19	6=	6=	ADP
ejpam-3429	76	20	0	0	NUM
ejpam-3429	76	21	,	,	PUNCT
ejpam-3429	76	22	,	,	PUNCT
ejpam-3429	76	23	(	(	PUNCT
ejpam-3429	76	24	i	i	NOUN
ejpam-3429	76	25	=	=	NOUN
ejpam-3429	76	26	1	1	NUM
ejpam-3429	76	27	,	,	PUNCT
ejpam-3429	76	28	.	.	PUNCT
ejpam-3429	76	29	.	.	PUNCT
ejpam-3429	76	30	.	.	PUNCT
ejpam-3429	77	1	,	,	PUNCT
ejpam-3429	77	2	r	r	X
ejpam-3429	77	3	,	,	PUNCT
ejpam-3429	77	4	j	j	NOUN
ejpam-3429	77	5	=	=	SYM
ejpam-3429	77	6	1	1	NUM
ejpam-3429	77	7	,	,	PUNCT
ejpam-3429	77	8	.	.	PUNCT
ejpam-3429	77	9	.	.	PUNCT
ejpam-3429	77	10	.	.	PUNCT
ejpam-3429	78	1	,	,	PUNCT
ejpam-3429	78	2	s	s	X
ejpam-3429	78	3	)	)	PUNCT
ejpam-3429	78	4	and	and	CCONJ
ejpam-3429	78	5	q	q	X
ejpam-3429	79	1	→	→	SYM
ejpam-3429	79	2	1−	1−	NUM
ejpam-3429	79	3	,	,	PUNCT
ejpam-3429	79	4	we	we	PRON
ejpam-3429	79	5	get	get	VERB
ejpam-3429	79	6	the	the	DET
ejpam-3429	79	7	operator	operator	NOUN
ejpam-3429	79	8	defined	define	VERB
ejpam-3429	79	9	by	by	ADP
ejpam-3429	79	10	selvaraj	selvaraj	ADJ
ejpam-3429	79	11	and	and	CCONJ
ejpam-3429	79	12	karthikeyan	karthikeyan	ADJ
ejpam-3429	80	1	[	[	X
ejpam-3429	80	2	5	5	NUM
ejpam-3429	80	3	]	]	PUNCT
ejpam-3429	80	4	.	.	PUNCT
ejpam-3429	81	1	3	3	X
ejpam-3429	81	2	.	.	X
ejpam-3429	81	3	for	for	ADP
ejpam-3429	81	4	r	r	NOUN
ejpam-3429	81	5	=	=	SYM
ejpam-3429	81	6	2	2	NUM
ejpam-3429	81	7	,	,	PUNCT
ejpam-3429	81	8	s	s	PART
ejpam-3429	81	9	=	=	SYM
ejpam-3429	81	10	1	1	NUM
ejpam-3429	81	11	;	;	PUNCT
ejpam-3429	81	12	a1	a1	NOUN
ejpam-3429	81	13	=	=	SYM
ejpam-3429	81	14	b1	b1	PROPN
ejpam-3429	81	15	,	,	PUNCT
ejpam-3429	81	16	a2	a2	PROPN
ejpam-3429	81	17	=	=	SYM
ejpam-3429	81	18	q	q	X
ejpam-3429	81	19	,	,	PUNCT
ejpam-3429	81	20	and	and	CCONJ
ejpam-3429	81	21	λ	λ	X
ejpam-3429	81	22	=	=	SYM
ejpam-3429	81	23	1	1	NUM
ejpam-3429	81	24	,	,	PUNCT
ejpam-3429	81	25	we	we	PRON
ejpam-3429	81	26	get	get	VERB
ejpam-3429	81	27	the	the	DET
ejpam-3429	81	28	qanalogue	qanalogue	NOUN
ejpam-3429	81	29	of	of	ADP
ejpam-3429	81	30	the	the	DET
ejpam-3429	81	31	well	well	ADV
ejpam-3429	81	32	known	know	VERB
ejpam-3429	81	33	sălăgean	sălăgean	ADJ
ejpam-3429	81	34	operator	operator	NOUN
ejpam-3429	81	35	(	(	PUNCT
ejpam-3429	81	36	see	see	VERB
ejpam-3429	81	37	[	[	X
ejpam-3429	81	38	4	4	NUM
ejpam-3429	81	39	]	]	NUM
ejpam-3429	81	40	)	)	PUNCT
ejpam-3429	81	41	.	.	PUNCT
ejpam-3429	82	1	also	also	ADV
ejpam-3429	82	2	many	many	ADJ
ejpam-3429	82	3	(	(	PUNCT
ejpam-3429	82	4	well	well	ADV
ejpam-3429	82	5	known	know	VERB
ejpam-3429	82	6	and	and	CCONJ
ejpam-3429	82	7	new	new	ADJ
ejpam-3429	82	8	)	)	PUNCT
ejpam-3429	82	9	integral	integral	ADJ
ejpam-3429	82	10	and	and	CCONJ
ejpam-3429	82	11	differential	differential	ADJ
ejpam-3429	82	12	operators	operator	NOUN
ejpam-3429	82	13	can	can	AUX
ejpam-3429	82	14	be	be	AUX
ejpam-3429	82	15	obtained	obtain	VERB
ejpam-3429	82	16	by	by	ADP
ejpam-3429	82	17	specializing	specialize	VERB
ejpam-3429	82	18	the	the	DET
ejpam-3429	82	19	parameters	parameter	NOUN
ejpam-3429	82	20	.	.	PUNCT
ejpam-3429	83	1	we	we	PRON
ejpam-3429	83	2	let	let	VERB
ejpam-3429	83	3	s∗	s∗	PROPN
ejpam-3429	83	4	,	,	PUNCT
ejpam-3429	83	5	c	c	PROPN
ejpam-3429	83	6	and	and	CCONJ
ejpam-3429	83	7	k	k	PROPN
ejpam-3429	83	8	to	to	PART
ejpam-3429	83	9	denote	denote	VERB
ejpam-3429	83	10	the	the	DET
ejpam-3429	83	11	well	well	ADV
ejpam-3429	83	12	known	know	VERB
ejpam-3429	83	13	classes	class	NOUN
ejpam-3429	83	14	of	of	ADP
ejpam-3429	83	15	starlike	starlike	NOUN
ejpam-3429	83	16	,	,	PUNCT
ejpam-3429	83	17	convex	convex	NOUN
ejpam-3429	83	18	and	and	CCONJ
ejpam-3429	83	19	close	close	ADJ
ejpam-3429	83	20	to	to	PART
ejpam-3429	83	21	convex	convex	VERB
ejpam-3429	83	22	function	function	NOUN
ejpam-3429	83	23	respectively	respectively	ADV
ejpam-3429	83	24	.	.	PUNCT
ejpam-3429	84	1	we	we	PRON
ejpam-3429	84	2	refer	refer	VERB
ejpam-3429	84	3	goodman[3	goodman[3	ADP
ejpam-3429	84	4	]	]	PUNCT
ejpam-3429	84	5	which	which	PRON
ejpam-3429	84	6	provides	provide	VERB
ejpam-3429	84	7	the	the	DET
ejpam-3429	84	8	study	study	NOUN
ejpam-3429	84	9	of	of	ADP
ejpam-3429	84	10	various	various	ADJ
ejpam-3429	84	11	subclasses	subclass	NOUN
ejpam-3429	84	12	of	of	ADP
ejpam-3429	84	13	univalent	univalent	ADJ
ejpam-3429	84	14	functions	function	NOUN
ejpam-3429	84	15	in	in	ADP
ejpam-3429	84	16	slow	slow	ADJ
ejpam-3429	84	17	motion	motion	NOUN
ejpam-3429	84	18	.	.	PUNCT
ejpam-3429	85	1	another	another	DET
ejpam-3429	85	2	very	very	ADV
ejpam-3429	85	3	important	important	ADJ
ejpam-3429	85	4	class	class	NOUN
ejpam-3429	85	5	in	in	ADP
ejpam-3429	85	6	the	the	DET
ejpam-3429	85	7	study	study	NOUN
ejpam-3429	85	8	of	of	ADP
ejpam-3429	85	9	various	various	ADJ
ejpam-3429	85	10	subclasses	subclass	NOUN
ejpam-3429	85	11	of	of	ADP
ejpam-3429	85	12	univalent	univalent	ADJ
ejpam-3429	85	13	functions	function	NOUN
ejpam-3429	85	14	is	be	AUX
ejpam-3429	85	15	the	the	DET
ejpam-3429	85	16	class	class	NOUN
ejpam-3429	85	17	of	of	ADP
ejpam-3429	85	18	functions	function	NOUN
ejpam-3429	85	19	with	with	ADP
ejpam-3429	85	20	positive	positive	ADJ
ejpam-3429	85	21	real	real	ADJ
ejpam-3429	85	22	part	part	NOUN
ejpam-3429	85	23	.	.	PUNCT
ejpam-3429	86	1	we	we	PRON
ejpam-3429	86	2	denote	denote	VERB
ejpam-3429	86	3	by	by	ADP
ejpam-3429	86	4	p	p	PROPN
ejpam-3429	86	5	(	(	PUNCT
ejpam-3429	86	6	ρ	ρ	PROPN
ejpam-3429	86	7	)	)	PUNCT
ejpam-3429	86	8	the	the	DET
ejpam-3429	86	9	class	class	NOUN
ejpam-3429	86	10	of	of	ADP
ejpam-3429	86	11	functions	function	NOUN
ejpam-3429	86	12	with	with	ADP
ejpam-3429	86	13	p(0	p(0	NOUN
ejpam-3429	86	14	)	)	PUNCT
ejpam-3429	86	15	=	=	SYM
ejpam-3429	86	16	1	1	NUM
ejpam-3429	86	17	which	which	PRON
ejpam-3429	86	18	satisfies	satisfie	NOUN
ejpam-3429	86	19	r{p(z	r{p(z	VERB
ejpam-3429	86	20	)	)	PUNCT
ejpam-3429	86	21	}	}	PUNCT
ejpam-3429	86	22	>	>	X
ejpam-3429	87	1	ρ	ρ	PROPN
ejpam-3429	87	2	.	.	PUNCT
ejpam-3429	88	1	it	it	PRON
ejpam-3429	88	2	is	be	AUX
ejpam-3429	88	3	well	well	ADV
ejpam-3429	88	4	known	know	VERB
ejpam-3429	88	5	that	that	SCONJ
ejpam-3429	88	6	p(z	p(z	NOUN
ejpam-3429	88	7	)	)	PUNCT
ejpam-3429	88	8	=	=	SYM
ejpam-3429	89	1	1+c1z+c2z	1+c1z+c2z	NUM
ejpam-3429	89	2	2	2	NUM
ejpam-3429	89	3	+	+	NOUN
ejpam-3429	89	4	·	·	PUNCT
ejpam-3429	89	5	·	·	PUNCT
ejpam-3429	89	6	·	·	PUNCT
ejpam-3429	90	1	∈	∈	PROPN
ejpam-3429	90	2	p	p	X
ejpam-3429	90	3	(	(	PUNCT
ejpam-3429	90	4	ρ	ρ	NOUN
ejpam-3429	90	5	)	)	PUNCT
ejpam-3429	90	6	implies	imply	VERB
ejpam-3429	90	7	|	|	ADV
ejpam-3429	90	8	pn	pn	VERB
ejpam-3429	90	9	|≤	|≤	PROPN
ejpam-3429	90	10	2(1−ρ	2(1−ρ	NOUN
ejpam-3429	90	11	)	)	PUNCT
ejpam-3429	90	12	for	for	ADP
ejpam-3429	90	13	all	all	DET
ejpam-3429	90	14	n	n	PRON
ejpam-3429	90	15	≥	≥	NOUN
ejpam-3429	90	16	1	1	NUM
ejpam-3429	90	17	.	.	PUNCT
ejpam-3429	91	1	the	the	DET
ejpam-3429	91	2	coefficients	coefficient	NOUN
ejpam-3429	91	3	for	for	ADP
ejpam-3429	91	4	the	the	DET
ejpam-3429	91	5	inverse	inverse	NOUN
ejpam-3429	91	6	of	of	ADP
ejpam-3429	91	7	a	a	DET
ejpam-3429	91	8	function	function	NOUN
ejpam-3429	91	9	f(z	f(z	PROPN
ejpam-3429	91	10	)	)	PUNCT
ejpam-3429	91	11	of	of	ADP
ejpam-3429	91	12	the	the	DET
ejpam-3429	91	13	form	form	NOUN
ejpam-3429	91	14	(	(	PUNCT
ejpam-3429	91	15	3	3	X
ejpam-3429	91	16	)	)	PUNCT
ejpam-3429	91	17	is	be	AUX
ejpam-3429	91	18	given	give	VERB
ejpam-3429	91	19	by	by	ADP
ejpam-3429	91	20	g(w	g(w	PROPN
ejpam-3429	91	21	)	)	PUNCT
ejpam-3429	91	22	=	=	SYM
ejpam-3429	91	23	f−1(z	f−1(z	PROPN
ejpam-3429	91	24	)	)	PUNCT
ejpam-3429	91	25	=	=	PUNCT
ejpam-3429	92	1	w	w	NOUN
ejpam-3429	92	2	−	−	PROPN
ejpam-3429	93	1	k2w2	k2w2	X
ejpam-3429	94	1	+	+	CCONJ
ejpam-3429	94	2	(	(	PUNCT
ejpam-3429	94	3	2k22	2k22	NOUN
ejpam-3429	94	4	−	−	NOUN
ejpam-3429	94	5	k3)w3	k3)w3	VERB
ejpam-3429	94	6	−	−	PROPN
ejpam-3429	94	7	(	(	PUNCT
ejpam-3429	94	8	5k32	5k32	NUM
ejpam-3429	94	9	−	−	NOUN
ejpam-3429	94	10	5k2k3	5k2k3	PROPN
ejpam-3429	94	11	+	+	CCONJ
ejpam-3429	94	12	k4)w	k4)w	PROPN
ejpam-3429	94	13	4	4	NUM
ejpam-3429	94	14	+	+	CCONJ
ejpam-3429	94	15	·	·	PUNCT
ejpam-3429	94	16	·	·	PUNCT
ejpam-3429	94	17	·	·	PUNCT
ejpam-3429	94	18	,	,	PUNCT
ejpam-3429	94	19	(	(	PUNCT
ejpam-3429	94	20	9	9	X
ejpam-3429	94	21	)	)	PUNCT
ejpam-3429	94	22	for	for	ADP
ejpam-3429	94	23	details	detail	NOUN
ejpam-3429	94	24	on	on	ADP
ejpam-3429	94	25	the	the	DET
ejpam-3429	94	26	coefficients	coefficient	NOUN
ejpam-3429	94	27	of	of	ADP
ejpam-3429	94	28	the	the	DET
ejpam-3429	94	29	inverse	inverse	NOUN
ejpam-3429	94	30	of	of	ADP
ejpam-3429	94	31	a	a	DET
ejpam-3429	94	32	function	function	NOUN
ejpam-3429	94	33	,	,	PUNCT
ejpam-3429	94	34	we	we	PRON
ejpam-3429	94	35	refer	refer	VERB
ejpam-3429	94	36	to	to	ADP
ejpam-3429	94	37	chapter	chapter	NOUN
ejpam-3429	94	38	5	5	NUM
ejpam-3429	94	39	in	in	ADP
ejpam-3429	94	40	[	[	X
ejpam-3429	94	41	3	3	NUM
ejpam-3429	94	42	]	]	PUNCT
ejpam-3429	94	43	.	.	PUNCT
ejpam-3429	95	1	the	the	DET
ejpam-3429	95	2	area	area	NOUN
ejpam-3429	95	3	of	of	ADP
ejpam-3429	95	4	a	a	DET
ejpam-3429	95	5	closed	closed	ADJ
ejpam-3429	95	6	disc	disc	NOUN
ejpam-3429	95	7	of	of	ADP
ejpam-3429	95	8	radius	radius	NOUN
ejpam-3429	95	9	r	r	NOUN
ejpam-3429	95	10	of	of	ADP
ejpam-3429	95	11	a	a	DET
ejpam-3429	95	12	function	function	NOUN
ejpam-3429	95	13	f	f	PROPN
ejpam-3429	95	14	∈	∈	PROPN
ejpam-3429	95	15	s	s	PROPN
ejpam-3429	95	16	,	,	PUNCT
ejpam-3429	95	17	provided	provide	VERB
ejpam-3429	95	18	us	we	PRON
ejpam-3429	95	19	with	with	ADP
ejpam-3429	95	20	an	an	DET
ejpam-3429	95	21	inequality	inequality	NOUN
ejpam-3429	95	22	which	which	PRON
ejpam-3429	95	23	in	in	ADP
ejpam-3429	95	24	turn	turn	NOUN
ejpam-3429	95	25	was	be	AUX
ejpam-3429	95	26	used	use	VERB
ejpam-3429	95	27	to	to	PART
ejpam-3429	95	28	prove	prove	VERB
ejpam-3429	95	29	several	several	ADJ
ejpam-3429	95	30	central	central	ADJ
ejpam-3429	95	31	theorems	theorem	NOUN
ejpam-3429	95	32	in	in	ADP
ejpam-3429	95	33	the	the	DET
ejpam-3429	95	34	field	field	NOUN
ejpam-3429	95	35	of	of	ADP
ejpam-3429	95	36	univalent	univalent	ADJ
ejpam-3429	95	37	functions	function	NOUN
ejpam-3429	95	38	.	.	PUNCT
ejpam-3429	96	1	in	in	ADP
ejpam-3429	96	2	the	the	DET
ejpam-3429	96	3	class	class	NOUN
ejpam-3429	96	4	s	s	PROPN
ejpam-3429	96	5	,	,	PUNCT
ejpam-3429	96	6	the	the	DET
ejpam-3429	96	7	upper	upper	ADJ
ejpam-3429	96	8	bound	bind	VERB
ejpam-3429	96	9	on	on	ADP
ejpam-3429	96	10	a2	a2	PROPN
ejpam-3429	96	11	was	be	AUX
ejpam-3429	96	12	very	very	ADV
ejpam-3429	96	13	useful	useful	ADJ
ejpam-3429	96	14	in	in	ADP
ejpam-3429	96	15	establishing	establish	VERB
ejpam-3429	96	16	the	the	DET
ejpam-3429	96	17	growth	growth	NOUN
ejpam-3429	96	18	,	,	PUNCT
ejpam-3429	96	19	distortion	distortion	NOUN
ejpam-3429	96	20	and	and	CCONJ
ejpam-3429	96	21	radius	radius	NOUN
ejpam-3429	96	22	problems	problem	NOUN
ejpam-3429	96	23	of	of	ADP
ejpam-3429	96	24	univalent	univalent	ADJ
ejpam-3429	96	25	functions	function	NOUN
ejpam-3429	96	26	.	.	PUNCT
ejpam-3429	97	1	so	so	ADV
ejpam-3429	97	2	finding	find	VERB
ejpam-3429	97	3	the	the	DET
ejpam-3429	97	4	initial	initial	ADJ
ejpam-3429	97	5	coefficients	coefficient	NOUN
ejpam-3429	97	6	of	of	ADP
ejpam-3429	97	7	various	various	ADJ
ejpam-3429	97	8	subclasses	subclass	NOUN
ejpam-3429	97	9	of	of	ADP
ejpam-3429	97	10	analytic	analytic	ADJ
ejpam-3429	97	11	functions	function	NOUN
ejpam-3429	97	12	has	have	AUX
ejpam-3429	97	13	always	always	ADV
ejpam-3429	97	14	been	be	AUX
ejpam-3429	97	15	a	a	DET
ejpam-3429	97	16	very	very	ADV
ejpam-3429	97	17	attractive	attractive	ADJ
ejpam-3429	97	18	topic	topic	NOUN
ejpam-3429	97	19	in	in	ADP
ejpam-3429	97	20	the	the	DET
ejpam-3429	97	21	study	study	NOUN
ejpam-3429	97	22	of	of	ADP
ejpam-3429	97	23	univalent	univalent	ADJ
ejpam-3429	97	24	function	function	NOUN
ejpam-3429	97	25	theory	theory	NOUN
ejpam-3429	97	26	.	.	PUNCT
ejpam-3429	98	1	the	the	DET
ejpam-3429	98	2	main	main	ADJ
ejpam-3429	98	3	purpose	purpose	NOUN
ejpam-3429	98	4	of	of	ADP
ejpam-3429	98	5	this	this	DET
ejpam-3429	98	6	paper	paper	NOUN
ejpam-3429	98	7	is	be	AUX
ejpam-3429	98	8	to	to	PART
ejpam-3429	98	9	obtain	obtain	VERB
ejpam-3429	98	10	the	the	DET
ejpam-3429	98	11	initial	initial	ADJ
ejpam-3429	98	12	coefficients	coefficient	NOUN
ejpam-3429	98	13	of	of	ADP
ejpam-3429	98	14	the	the	DET
ejpam-3429	98	15	two	two	NUM
ejpam-3429	98	16	classes	class	NOUN
ejpam-3429	98	17	of	of	ADP
ejpam-3429	98	18	spiralike	spiralike	NOUN
ejpam-3429	98	19	functions	function	NOUN
ejpam-3429	98	20	namely	namely	ADV
ejpam-3429	99	1	α	α	PRON
ejpam-3429	99	2	−	−	NOUN
ejpam-3429	99	3	sp∗(β	sp∗(β	NOUN
ejpam-3429	99	4	,	,	PUNCT
ejpam-3429	99	5	a	a	DET
ejpam-3429	99	6	,	,	PUNCT
ejpam-3429	99	7	b	b	NOUN
ejpam-3429	99	8	;	;	PUNCT
ejpam-3429	99	9	q	q	ADJ
ejpam-3429	99	10	,	,	PUNCT
ejpam-3429	99	11	z	z	NOUN
ejpam-3429	99	12	)	)	PUNCT
ejpam-3429	99	13	and	and	CCONJ
ejpam-3429	99	14	α−	α−	ADP
ejpam-3429	99	15	sp(ρ	sp(ρ	NOUN
ejpam-3429	99	16	,	,	PUNCT
ejpam-3429	99	17	a	a	DET
ejpam-3429	99	18	,	,	PUNCT
ejpam-3429	99	19	b	b	NOUN
ejpam-3429	99	20	;	;	PUNCT
ejpam-3429	99	21	q	q	ADJ
ejpam-3429	99	22	,	,	PUNCT
ejpam-3429	99	23	z	z	NOUN
ejpam-3429	99	24	)	)	PUNCT
ejpam-3429	99	25	.	.	PUNCT
ejpam-3429	100	1	k.	k.	PROPN
ejpam-3429	100	2	a.	a.	PROPN
ejpam-3429	100	3	reddy	reddy	PROPN
ejpam-3429	100	4	,	,	PUNCT
ejpam-3429	100	5	k.	k.	PROPN
ejpam-3429	100	6	r.	r.	PROPN
ejpam-3429	100	7	karthikeyan	karthikeyan	PROPN
ejpam-3429	100	8	,	,	PUNCT
ejpam-3429	100	9	g.	g.	PROPN
ejpam-3429	100	10	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	100	11	/	/	SYM
ejpam-3429	100	12	eur	eur	PROPN
ejpam-3429	100	13	.	.	PUNCT
ejpam-3429	101	1	j.	j.	PROPN
ejpam-3429	101	2	pure	pure	PROPN
ejpam-3429	101	3	appl	appl	PROPN
ejpam-3429	101	4	.	.	PROPN
ejpam-3429	101	5	math	math	PROPN
ejpam-3429	101	6	,	,	PUNCT
ejpam-3429	101	7	12	12	NUM
ejpam-3429	101	8	(	(	PUNCT
ejpam-3429	101	9	3	3	NUM
ejpam-3429	101	10	)	)	PUNCT
ejpam-3429	101	11	(	(	PUNCT
ejpam-3429	101	12	2019	2019	NUM
ejpam-3429	101	13	)	)	PUNCT
ejpam-3429	101	14	,	,	PUNCT
ejpam-3429	101	15	846	846	NUM
ejpam-3429	101	16	-	-	SYM
ejpam-3429	101	17	856	856	NUM
ejpam-3429	101	18	849	849	NUM
ejpam-3429	101	19	now	now	ADV
ejpam-3429	101	20	we	we	PRON
ejpam-3429	101	21	begin	begin	VERB
ejpam-3429	101	22	with	with	ADP
ejpam-3429	101	23	the	the	DET
ejpam-3429	101	24	following	follow	VERB
ejpam-3429	101	25	definitions	definition	NOUN
ejpam-3429	101	26	.	.	PUNCT
ejpam-3429	102	1	definition	definition	NOUN
ejpam-3429	102	2	1	1	NUM
ejpam-3429	102	3	.	.	PUNCT
ejpam-3429	103	1	the	the	DET
ejpam-3429	103	2	function	function	NOUN
ejpam-3429	103	3	f(z	f(z	PROPN
ejpam-3429	103	4	)	)	PUNCT
ejpam-3429	103	5	,	,	PUNCT
ejpam-3429	103	6	given	give	VERB
ejpam-3429	103	7	by	by	ADP
ejpam-3429	103	8	(	(	PUNCT
ejpam-3429	103	9	3	3	NUM
ejpam-3429	103	10	)	)	PUNCT
ejpam-3429	103	11	,	,	PUNCT
ejpam-3429	103	12	is	be	AUX
ejpam-3429	103	13	said	say	VERB
ejpam-3429	103	14	to	to	PART
ejpam-3429	103	15	be	be	AUX
ejpam-3429	103	16	a	a	DET
ejpam-3429	103	17	member	member	NOUN
ejpam-3429	103	18	of	of	ADP
ejpam-3429	103	19	α−sp∗(β	α−sp∗(β	PROPN
ejpam-3429	103	20	,	,	PUNCT
ejpam-3429	103	21	a	a	PRON
ejpam-3429	103	22	,	,	PUNCT
ejpam-3429	103	23	b	b	NOUN
ejpam-3429	103	24	;	;	PUNCT
ejpam-3429	103	25	q	q	ADJ
ejpam-3429	103	26	,	,	PUNCT
ejpam-3429	103	27	z	z	NOUN
ejpam-3429	103	28	)	)	PUNCT
ejpam-3429	103	29	,	,	PUNCT
ejpam-3429	103	30	if	if	SCONJ
ejpam-3429	103	31	each	each	PRON
ejpam-3429	103	32	of	of	ADP
ejpam-3429	103	33	the	the	DET
ejpam-3429	103	34	following	follow	VERB
ejpam-3429	103	35	conditions	condition	NOUN
ejpam-3429	103	36	are	be	AUX
ejpam-3429	103	37	satisfied	satisfied	ADJ
ejpam-3429	103	38	.	.	PUNCT
ejpam-3429	104	1	∣∣∣∣arg	∣∣∣∣arg	NOUN
ejpam-3429	104	2	(	(	PUNCT
ejpam-3429	104	3	eiα	eiα	NOUN
ejpam-3429	104	4	z	z	PROPN
ejpam-3429	105	1	[	[	X
ejpam-3429	105	2	dq(j	dq(j	NOUN
ejpam-3429	105	3	m	m	VERB
ejpam-3429	105	4	λ	λ	NOUN
ejpam-3429	105	5	(	(	PUNCT
ejpam-3429	105	6	a1	a1	PROPN
ejpam-3429	105	7	,	,	PUNCT
ejpam-3429	105	8	b1	b1	NOUN
ejpam-3429	105	9	;	;	PUNCT
ejpam-3429	105	10	q	q	ADJ
ejpam-3429	105	11	,	,	PUNCT
ejpam-3429	105	12	z)f	z)f	X
ejpam-3429	105	13	)	)	PUNCT
ejpam-3429	105	14	]	]	PUNCT
ejpam-3429	105	15	(	(	PUNCT
ejpam-3429	105	16	jmλ	jmλ	PROPN
ejpam-3429	105	17	(	(	PUNCT
ejpam-3429	105	18	a1	a1	PROPN
ejpam-3429	105	19	,	,	PUNCT
ejpam-3429	105	20	b1	b1	NOUN
ejpam-3429	105	21	;	;	PUNCT
ejpam-3429	105	22	q	q	ADJ
ejpam-3429	105	23	,	,	PUNCT
ejpam-3429	105	24	z)f	z)f	X
ejpam-3429	105	25	)	)	PUNCT
ejpam-3429	105	26	)	)	PUNCT
ejpam-3429	105	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3429	105	28	<	<	X
ejpam-3429	105	29	β	β	X
ejpam-3429	105	30	π	π	PROPN
ejpam-3429	105	31	2	2	NUM
ejpam-3429	105	32	,	,	PUNCT
ejpam-3429	105	33	(	(	PUNCT
ejpam-3429	105	34	z	z	NOUN
ejpam-3429	105	35	∈	∈	PROPN
ejpam-3429	105	36	u	u	NOUN
ejpam-3429	105	37	;	;	PUNCT
ejpam-3429	105	38	|	|	ADV
ejpam-3429	105	39	α	α	DET
ejpam-3429	105	40	|≤	|≤	PROPN
ejpam-3429	105	41	π/2	π/2	NUM
ejpam-3429	105	42	,	,	PUNCT
ejpam-3429	105	43	0	0	NUM
ejpam-3429	105	44	≤	≤	NUM
ejpam-3429	105	45	β	β	X
ejpam-3429	105	46	<	<	X
ejpam-3429	105	47	1	1	NUM
ejpam-3429	105	48	)	)	PUNCT
ejpam-3429	105	49	and	and	CCONJ
ejpam-3429	105	50	∣∣∣∣arg	∣∣∣∣arg	PROPN
ejpam-3429	105	51	(	(	PUNCT
ejpam-3429	105	52	eiα	eiα	NOUN
ejpam-3429	105	53	w	w	PROPN
ejpam-3429	106	1	[	[	X
ejpam-3429	106	2	dq(j	dq(j	NOUN
ejpam-3429	106	3	m	m	VERB
ejpam-3429	106	4	λ	λ	NOUN
ejpam-3429	106	5	(	(	PUNCT
ejpam-3429	106	6	a1	a1	PROPN
ejpam-3429	106	7	,	,	PUNCT
ejpam-3429	106	8	b1	b1	NOUN
ejpam-3429	106	9	;	;	PUNCT
ejpam-3429	106	10	q	q	NOUN
ejpam-3429	106	11	,	,	PUNCT
ejpam-3429	106	12	w)f	w)f	NOUN
ejpam-3429	106	13	)	)	PUNCT
ejpam-3429	106	14	]	]	PUNCT
ejpam-3429	106	15	(	(	PUNCT
ejpam-3429	106	16	jmλ	jmλ	PROPN
ejpam-3429	106	17	(	(	PUNCT
ejpam-3429	106	18	a1	a1	PROPN
ejpam-3429	106	19	,	,	PUNCT
ejpam-3429	106	20	b1	b1	NOUN
ejpam-3429	106	21	;	;	PUNCT
ejpam-3429	106	22	q	q	NOUN
ejpam-3429	106	23	,	,	PUNCT
ejpam-3429	106	24	w)f	w)f	ADJ
ejpam-3429	106	25	)	)	PUNCT
ejpam-3429	107	1	)	)	PUNCT
ejpam-3429	107	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3429	107	3	<	<	X
ejpam-3429	107	4	β	β	X
ejpam-3429	107	5	π	π	PROPN
ejpam-3429	107	6	2	2	NUM
ejpam-3429	107	7	,	,	PUNCT
ejpam-3429	107	8	(	(	PUNCT
ejpam-3429	107	9	w	w	PROPN
ejpam-3429	107	10	∈	∈	PROPN
ejpam-3429	107	11	u	u	NOUN
ejpam-3429	107	12	;	;	PUNCT
ejpam-3429	107	13	|	|	ADV
ejpam-3429	107	14	α	α	DET
ejpam-3429	107	15	|≤	|≤	PROPN
ejpam-3429	107	16	π/2	π/2	NUM
ejpam-3429	107	17	,	,	PUNCT
ejpam-3429	107	18	0	0	NUM
ejpam-3429	107	19	≤	≤	NUM
ejpam-3429	108	1	β	β	X
ejpam-3429	108	2	<	<	X
ejpam-3429	108	3	1	1	NUM
ejpam-3429	108	4	)	)	PUNCT
ejpam-3429	108	5	.	.	PUNCT
ejpam-3429	109	1	definition	definition	NOUN
ejpam-3429	109	2	2	2	NUM
ejpam-3429	109	3	.	.	PUNCT
ejpam-3429	110	1	the	the	DET
ejpam-3429	110	2	function	function	NOUN
ejpam-3429	110	3	f(z	f(z	PROPN
ejpam-3429	110	4	)	)	PUNCT
ejpam-3429	110	5	given	give	VERB
ejpam-3429	110	6	by	by	ADP
ejpam-3429	110	7	(	(	PUNCT
ejpam-3429	110	8	3	3	NUM
ejpam-3429	110	9	)	)	PUNCT
ejpam-3429	110	10	,	,	PUNCT
ejpam-3429	110	11	is	be	AUX
ejpam-3429	110	12	said	say	VERB
ejpam-3429	110	13	to	to	PART
ejpam-3429	110	14	be	be	AUX
ejpam-3429	110	15	a	a	DET
ejpam-3429	110	16	member	member	NOUN
ejpam-3429	110	17	of	of	ADP
ejpam-3429	110	18	α−sp(ρ	α−sp(ρ	PROPN
ejpam-3429	110	19	,	,	PUNCT
ejpam-3429	110	20	a	a	PRON
ejpam-3429	110	21	,	,	PUNCT
ejpam-3429	110	22	b	b	NOUN
ejpam-3429	110	23	;	;	PUNCT
ejpam-3429	110	24	q	q	ADJ
ejpam-3429	110	25	,	,	PUNCT
ejpam-3429	110	26	z	z	NOUN
ejpam-3429	110	27	)	)	PUNCT
ejpam-3429	110	28	,	,	PUNCT
ejpam-3429	110	29	if	if	SCONJ
ejpam-3429	110	30	each	each	PRON
ejpam-3429	110	31	of	of	ADP
ejpam-3429	110	32	the	the	DET
ejpam-3429	110	33	following	follow	VERB
ejpam-3429	110	34	conditions	condition	NOUN
ejpam-3429	110	35	are	be	AUX
ejpam-3429	110	36	satisfied	satisfied	ADJ
ejpam-3429	110	37	.	.	PUNCT
ejpam-3429	111	1	r	r	NOUN
ejpam-3429	111	2	(	(	PUNCT
ejpam-3429	111	3	eiα	eiα	NOUN
ejpam-3429	111	4	z	z	PROPN
ejpam-3429	112	1	[	[	X
ejpam-3429	112	2	dq(j	dq(j	NOUN
ejpam-3429	112	3	m	m	VERB
ejpam-3429	112	4	λ	λ	NOUN
ejpam-3429	112	5	(	(	PUNCT
ejpam-3429	112	6	a1	a1	PROPN
ejpam-3429	112	7	,	,	PUNCT
ejpam-3429	112	8	b1	b1	NOUN
ejpam-3429	112	9	;	;	PUNCT
ejpam-3429	112	10	q	q	ADJ
ejpam-3429	112	11	,	,	PUNCT
ejpam-3429	112	12	z)f	z)f	X
ejpam-3429	112	13	)	)	PUNCT
ejpam-3429	112	14	]	]	PUNCT
ejpam-3429	112	15	(	(	PUNCT
ejpam-3429	112	16	jmλ	jmλ	PROPN
ejpam-3429	112	17	(	(	PUNCT
ejpam-3429	112	18	a1	a1	PROPN
ejpam-3429	112	19	,	,	PUNCT
ejpam-3429	112	20	b1	b1	NOUN
ejpam-3429	112	21	;	;	PUNCT
ejpam-3429	112	22	q	q	ADJ
ejpam-3429	112	23	,	,	PUNCT
ejpam-3429	112	24	z)f	z)f	X
ejpam-3429	112	25	)	)	PUNCT
ejpam-3429	112	26	)	)	PUNCT
ejpam-3429	113	1	>	>	X
ejpam-3429	114	1	ρcos(α	ρcos(α	NUM
ejpam-3429	114	2	)	)	PUNCT
ejpam-3429	114	3	,	,	PUNCT
ejpam-3429	114	4	(	(	PUNCT
ejpam-3429	114	5	z	z	NOUN
ejpam-3429	114	6	∈	∈	PROPN
ejpam-3429	114	7	u	u	NOUN
ejpam-3429	114	8	;	;	PUNCT
ejpam-3429	114	9	|	|	ADV
ejpam-3429	114	10	α	α	DET
ejpam-3429	114	11	|≤	|≤	PROPN
ejpam-3429	114	12	π/2	π/2	NUM
ejpam-3429	114	13	,	,	PUNCT
ejpam-3429	114	14	0	0	NUM
ejpam-3429	114	15	≤	≤	NUM
ejpam-3429	114	16	ρ	ρ	NOUN
ejpam-3429	114	17	<	<	X
ejpam-3429	114	18	1	1	NUM
ejpam-3429	114	19	)	)	PUNCT
ejpam-3429	114	20	and	and	CCONJ
ejpam-3429	114	21	r	r	NOUN
ejpam-3429	114	22	(	(	PUNCT
ejpam-3429	114	23	eiα	eiα	NOUN
ejpam-3429	114	24	w	w	PROPN
ejpam-3429	115	1	[	[	X
ejpam-3429	115	2	dq(j	dq(j	NOUN
ejpam-3429	115	3	m	m	VERB
ejpam-3429	115	4	λ	λ	NOUN
ejpam-3429	115	5	(	(	PUNCT
ejpam-3429	115	6	a1	a1	PROPN
ejpam-3429	115	7	,	,	PUNCT
ejpam-3429	115	8	b1	b1	NOUN
ejpam-3429	115	9	;	;	PUNCT
ejpam-3429	115	10	q	q	NOUN
ejpam-3429	115	11	,	,	PUNCT
ejpam-3429	115	12	w)f	w)f	NOUN
ejpam-3429	115	13	)	)	PUNCT
ejpam-3429	115	14	]	]	PUNCT
ejpam-3429	115	15	(	(	PUNCT
ejpam-3429	115	16	jmλ	jmλ	PROPN
ejpam-3429	115	17	(	(	PUNCT
ejpam-3429	115	18	a1	a1	PROPN
ejpam-3429	115	19	,	,	PUNCT
ejpam-3429	115	20	b1	b1	NOUN
ejpam-3429	115	21	;	;	PUNCT
ejpam-3429	115	22	q	q	NOUN
ejpam-3429	115	23	,	,	PUNCT
ejpam-3429	115	24	w)f	w)f	NOUN
ejpam-3429	115	25	)	)	PUNCT
ejpam-3429	115	26	)	)	PUNCT
ejpam-3429	116	1	>	>	X
ejpam-3429	116	2	ρcos(α	ρcos(α	NUM
ejpam-3429	116	3	)	)	PUNCT
ejpam-3429	116	4	,	,	PUNCT
ejpam-3429	116	5	(	(	PUNCT
ejpam-3429	116	6	w	w	PROPN
ejpam-3429	116	7	∈	∈	PROPN
ejpam-3429	116	8	u	u	NOUN
ejpam-3429	116	9	;	;	PUNCT
ejpam-3429	116	10	|	|	ADV
ejpam-3429	116	11	α	α	DET
ejpam-3429	116	12	|≤	|≤	PROPN
ejpam-3429	116	13	π/2	π/2	NUM
ejpam-3429	116	14	,	,	PUNCT
ejpam-3429	116	15	0	0	NUM
ejpam-3429	116	16	≤	≤	NUM
ejpam-3429	116	17	ρ	ρ	NOUN
ejpam-3429	116	18	<	<	X
ejpam-3429	116	19	1	1	NUM
ejpam-3429	116	20	)	)	PUNCT
ejpam-3429	116	21	.	.	PUNCT
ejpam-3429	117	1	the	the	DET
ejpam-3429	117	2	classes	class	NOUN
ejpam-3429	117	3	of	of	ADP
ejpam-3429	117	4	α−sp∗(β	α−sp∗(β	PROPN
ejpam-3429	117	5	,	,	PUNCT
ejpam-3429	117	6	a	a	PRON
ejpam-3429	117	7	,	,	PUNCT
ejpam-3429	117	8	b	b	NOUN
ejpam-3429	117	9	;	;	PUNCT
ejpam-3429	117	10	q	q	ADJ
ejpam-3429	117	11	,	,	PUNCT
ejpam-3429	117	12	z	z	NOUN
ejpam-3429	117	13	)	)	PUNCT
ejpam-3429	117	14	and	and	CCONJ
ejpam-3429	117	15	α−sp(ρ	α−sp(ρ	PROPN
ejpam-3429	117	16	,	,	PUNCT
ejpam-3429	117	17	a	a	PRON
ejpam-3429	117	18	,	,	PUNCT
ejpam-3429	117	19	b	b	NOUN
ejpam-3429	117	20	;	;	PUNCT
ejpam-3429	117	21	q	q	ADJ
ejpam-3429	117	22	,	,	PUNCT
ejpam-3429	117	23	z	z	NOUN
ejpam-3429	117	24	)	)	PUNCT
ejpam-3429	117	25	were	be	AUX
ejpam-3429	117	26	motivated	motivate	VERB
ejpam-3429	117	27	by	by	ADP
ejpam-3429	117	28	[	[	X
ejpam-3429	117	29	6	6	NUM
ejpam-3429	117	30	]	]	PUNCT
ejpam-3429	117	31	.	.	PUNCT
ejpam-3429	118	1	if	if	SCONJ
ejpam-3429	118	2	we	we	PRON
ejpam-3429	118	3	let	let	VERB
ejpam-3429	118	4	m	m	VERB
ejpam-3429	118	5	=	=	NOUN
ejpam-3429	118	6	0	0	NUM
ejpam-3429	118	7	,	,	PUNCT
ejpam-3429	118	8	r	r	NOUN
ejpam-3429	118	9	=	=	SYM
ejpam-3429	118	10	2	2	NUM
ejpam-3429	118	11	,	,	PUNCT
ejpam-3429	118	12	s	s	PART
ejpam-3429	118	13	=	=	SYM
ejpam-3429	118	14	1	1	NUM
ejpam-3429	118	15	;	;	PUNCT
ejpam-3429	118	16	a1	a1	NOUN
ejpam-3429	118	17	=	=	SYM
ejpam-3429	118	18	b1	b1	PROPN
ejpam-3429	118	19	,	,	PUNCT
ejpam-3429	118	20	a2	a2	PROPN
ejpam-3429	118	21	=	=	PUNCT
ejpam-3429	118	22	q	q	X
ejpam-3429	118	23	and	and	CCONJ
ejpam-3429	118	24	by	by	ADP
ejpam-3429	118	25	taking	take	VERB
ejpam-3429	118	26	limit	limit	NOUN
ejpam-3429	118	27	q	q	X
ejpam-3429	118	28	→	→	SYM
ejpam-3429	118	29	1−	1−	NUM
ejpam-3429	118	30	in	in	ADP
ejpam-3429	118	31	α−sp∗(β	α−sp∗(β	PROPN
ejpam-3429	118	32	,	,	PUNCT
ejpam-3429	118	33	a	a	DET
ejpam-3429	118	34	,	,	PUNCT
ejpam-3429	118	35	b	b	NOUN
ejpam-3429	118	36	;	;	PUNCT
ejpam-3429	118	37	q	q	ADJ
ejpam-3429	118	38	,	,	PUNCT
ejpam-3429	118	39	z	z	NOUN
ejpam-3429	118	40	)	)	PUNCT
ejpam-3429	118	41	and	and	CCONJ
ejpam-3429	118	42	α	α	PRON
ejpam-3429	118	43	−	−	PROPN
ejpam-3429	118	44	sp(ρ	sp(ρ	NOUN
ejpam-3429	118	45	,	,	PUNCT
ejpam-3429	118	46	a	a	DET
ejpam-3429	118	47	,	,	PUNCT
ejpam-3429	118	48	b	b	NOUN
ejpam-3429	118	49	;	;	PUNCT
ejpam-3429	118	50	q	q	ADJ
ejpam-3429	118	51	,	,	PUNCT
ejpam-3429	118	52	z	z	NOUN
ejpam-3429	118	53	)	)	PUNCT
ejpam-3429	118	54	,	,	PUNCT
ejpam-3429	118	55	we	we	PRON
ejpam-3429	118	56	get	get	VERB
ejpam-3429	118	57	the	the	DET
ejpam-3429	118	58	classes	class	NOUN
ejpam-3429	118	59	introduced	introduce	VERB
ejpam-3429	118	60	by	by	ADP
ejpam-3429	118	61	m.	m.	NOUN
ejpam-3429	118	62	m.	m.	PROPN
ejpam-3429	118	63	soren	soren	PROPN
ejpam-3429	118	64	and	and	CCONJ
ejpam-3429	118	65	a.	a.	PROPN
ejpam-3429	118	66	k.	k.	PROPN
ejpam-3429	118	67	misra	misra	PROPN
ejpam-3429	119	1	[	[	X
ejpam-3429	119	2	6	6	NUM
ejpam-3429	119	3	]	]	PUNCT
ejpam-3429	119	4	.	.	PUNCT
ejpam-3429	120	1	2	2	X
ejpam-3429	120	2	.	.	X
ejpam-3429	120	3	main	main	ADJ
ejpam-3429	120	4	results	result	NOUN
ejpam-3429	120	5	theorem	theorem	VERB
ejpam-3429	120	6	1	1	NUM
ejpam-3429	120	7	.	.	PUNCT
ejpam-3429	121	1	let	let	VERB
ejpam-3429	121	2	f(z	f(z	NOUN
ejpam-3429	121	3	)	)	PUNCT
ejpam-3429	121	4	given	give	VERB
ejpam-3429	121	5	by	by	ADP
ejpam-3429	121	6	(	(	PUNCT
ejpam-3429	121	7	3	3	NUM
ejpam-3429	121	8	)	)	PUNCT
ejpam-3429	121	9	,	,	PUNCT
ejpam-3429	121	10	be	be	AUX
ejpam-3429	121	11	in	in	ADP
ejpam-3429	121	12	the	the	DET
ejpam-3429	121	13	class	class	NOUN
ejpam-3429	121	14	α−sp(ρ	α−sp(ρ	PROPN
ejpam-3429	121	15	,	,	PUNCT
ejpam-3429	121	16	a	a	PRON
ejpam-3429	121	17	,	,	PUNCT
ejpam-3429	121	18	b	b	NOUN
ejpam-3429	121	19	;	;	PUNCT
ejpam-3429	121	20	q	q	ADJ
ejpam-3429	121	21	,	,	PUNCT
ejpam-3429	121	22	z	z	NOUN
ejpam-3429	121	23	)	)	PUNCT
ejpam-3429	121	24	,	,	PUNCT
ejpam-3429	121	25	(	(	PUNCT
ejpam-3429	121	26	|	|	ADV
ejpam-3429	121	27	α	α	NOUN
ejpam-3429	121	28	|≤	|≤	PROPN
ejpam-3429	121	29	π	π	PROPN
ejpam-3429	121	30	2	2	NUM
ejpam-3429	121	31	,	,	PUNCT
ejpam-3429	121	32	0	0	NUM
ejpam-3429	121	33	≤	≤	NUM
ejpam-3429	121	34	ρ	ρ	NOUN
ejpam-3429	121	35	<	<	X
ejpam-3429	121	36	1	1	NUM
ejpam-3429	121	37	)	)	PUNCT
ejpam-3429	121	38	.	.	PUNCT
ejpam-3429	122	1	then	then	ADV
ejpam-3429	122	2	|	|	ADV
ejpam-3429	122	3	k2	k2	ADJ
ejpam-3429	122	4	|≤	|≤	PROPN
ejpam-3429	122	5	√	√	NUM
ejpam-3429	122	6	2	2	NUM
ejpam-3429	122	7	cosα(1−	cosα(1−	NOUN
ejpam-3429	122	8	ρ)√	ρ)√	NOUN
ejpam-3429	122	9	q	q	PUNCT
ejpam-3429	123	1	[	[	X
ejpam-3429	123	2	1−	1−	NUM
ejpam-3429	123	3	λ+	λ+	PUNCT
ejpam-3429	123	4	(	(	PUNCT
ejpam-3429	123	5	1	1	NUM
ejpam-3429	123	6	+	+	NUM
ejpam-3429	123	7	q)λ]2	q)λ]2	PROPN
ejpam-3429	123	8	m	m	VERB
ejpam-3429	123	9	γ22	γ22	NOUN
ejpam-3429	124	1	+	+	CCONJ
ejpam-3429	125	1	[	[	X
ejpam-3429	125	2	1−	1−	NUM
ejpam-3429	125	3	λ+	λ+	PUNCT
ejpam-3429	125	4	[	[	X
ejpam-3429	125	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	125	6	(	(	PUNCT
ejpam-3429	125	7	[	[	X
ejpam-3429	125	8	3]q	3]q	NUM
ejpam-3429	125	9	−	−	NOUN
ejpam-3429	125	10	1)γ3	1)γ3	NUM
ejpam-3429	125	11	,	,	PUNCT
ejpam-3429	125	12	|	|	ADV
ejpam-3429	125	13	k3	k3	VERB
ejpam-3429	125	14	|≤	|≤	PROPN
ejpam-3429	125	15	(	(	PUNCT
ejpam-3429	125	16	1−	1−	NUM
ejpam-3429	125	17	ρ	ρ	NOUN
ejpam-3429	125	18	)	)	PUNCT
ejpam-3429	125	19	cosα	cosα	NOUN
ejpam-3429	125	20	(	(	PUNCT
ejpam-3429	125	21	2	2	NUM
ejpam-3429	125	22	q	q	NOUN
ejpam-3429	126	1	[	[	X
ejpam-3429	126	2	1−	1−	NUM
ejpam-3429	126	3	λ+	λ+	PUNCT
ejpam-3429	126	4	(	(	PUNCT
ejpam-3429	126	5	1	1	NUM
ejpam-3429	126	6	+	+	NUM
ejpam-3429	126	7	q)λ]2	q)λ]2	PROPN
ejpam-3429	126	8	m	m	VERB
ejpam-3429	126	9	γ22	γ22	NOUN
ejpam-3429	127	1	+	+	CCONJ
ejpam-3429	128	1	[	[	X
ejpam-3429	128	2	1−	1−	NUM
ejpam-3429	128	3	λ+	λ+	PUNCT
ejpam-3429	128	4	[	[	X
ejpam-3429	128	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	128	6	(	(	PUNCT
ejpam-3429	128	7	[	[	X
ejpam-3429	128	8	3]q	3]q	NUM
ejpam-3429	128	9	−	−	PROPN
ejpam-3429	128	10	1)γ3	1)γ3	NUM
ejpam-3429	128	11	)	)	PUNCT
ejpam-3429	128	12	k.	k.	PROPN
ejpam-3429	128	13	a.	a.	PROPN
ejpam-3429	128	14	reddy	reddy	PROPN
ejpam-3429	128	15	,	,	PUNCT
ejpam-3429	128	16	k.	k.	PROPN
ejpam-3429	128	17	r.	r.	PROPN
ejpam-3429	128	18	karthikeyan	karthikeyan	PROPN
ejpam-3429	128	19	,	,	PUNCT
ejpam-3429	128	20	g.	g.	PROPN
ejpam-3429	128	21	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	128	22	/	/	SYM
ejpam-3429	128	23	eur	eur	PROPN
ejpam-3429	128	24	.	.	PUNCT
ejpam-3429	129	1	j.	j.	PROPN
ejpam-3429	129	2	pure	pure	PROPN
ejpam-3429	129	3	appl	appl	PROPN
ejpam-3429	129	4	.	.	PROPN
ejpam-3429	129	5	math	math	PROPN
ejpam-3429	129	6	,	,	PUNCT
ejpam-3429	129	7	12	12	NUM
ejpam-3429	129	8	(	(	PUNCT
ejpam-3429	129	9	3	3	NUM
ejpam-3429	129	10	)	)	PUNCT
ejpam-3429	129	11	(	(	PUNCT
ejpam-3429	129	12	2019	2019	NUM
ejpam-3429	129	13	)	)	PUNCT
ejpam-3429	129	14	,	,	PUNCT
ejpam-3429	129	15	846	846	NUM
ejpam-3429	129	16	-	-	SYM
ejpam-3429	129	17	856	856	NUM
ejpam-3429	129	18	850	850	NUM
ejpam-3429	129	19	and	and	CCONJ
ejpam-3429	129	20	|	|	ADV
ejpam-3429	129	21	k4	k4	VERB
ejpam-3429	129	22	|≤	|≤	PROPN
ejpam-3429	129	23	2(1−	2(1−	NUM
ejpam-3429	129	24	ρ	ρ	PROPN
ejpam-3429	129	25	)	)	PUNCT
ejpam-3429	129	26	cosα	cosα	NOUN
ejpam-3429	130	1	[	[	X
ejpam-3429	130	2	1−	1−	NUM
ejpam-3429	130	3	λ+	λ+	PUNCT
ejpam-3429	130	4	[	[	X
ejpam-3429	130	5	4]qλ]m	4]qλ]m	NUM
ejpam-3429	130	6	(	(	PUNCT
ejpam-3429	130	7	[	[	X
ejpam-3429	130	8	4]q	4]q	X
ejpam-3429	130	9	−	−	ADP
ejpam-3429	130	10	1)γ4	1)γ4	NUM
ejpam-3429	130	11	+	+	CCONJ
ejpam-3429	130	12	10	10	NUM
ejpam-3429	130	13	√	√	NUM
ejpam-3429	130	14	2[(1−	2[(1−	NUM
ejpam-3429	130	15	ρ	ρ	NOUN
ejpam-3429	130	16	)	)	PUNCT
ejpam-3429	130	17	cosα	cosα	NOUN
ejpam-3429	130	18	]	]	X
ejpam-3429	130	19	3	3	NUM
ejpam-3429	130	20	2	2	NUM
ejpam-3429	131	1	[	[	X
ejpam-3429	131	2	[	[	X
ejpam-3429	131	3	1−	1−	NUM
ejpam-3429	131	4	λ+	λ+	PUNCT
ejpam-3429	131	5	(	(	PUNCT
ejpam-3429	131	6	1	1	NUM
ejpam-3429	131	7	+	+	NUM
ejpam-3429	131	8	q)λ]2	q)λ]2	PROPN
ejpam-3429	131	9	m	m	VERB
ejpam-3429	131	10	(	(	PUNCT
ejpam-3429	131	11	q)γ22	q)γ22	X
ejpam-3429	131	12	+	+	PUNCT
ejpam-3429	132	1	[	[	X
ejpam-3429	132	2	1−	1−	NUM
ejpam-3429	132	3	λ+	λ+	PUNCT
ejpam-3429	132	4	[	[	X
ejpam-3429	132	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	132	6	(	(	PUNCT
ejpam-3429	132	7	[	[	X
ejpam-3429	132	8	3]q	3]q	NUM
ejpam-3429	132	9	−	−	ADP
ejpam-3429	132	10	1)γ3	1)γ3	NOUN
ejpam-3429	132	11	]	]	SYM
ejpam-3429	132	12	3	3	NUM
ejpam-3429	132	13	2	2	NUM
ejpam-3429	132	14	+	+	CCONJ
ejpam-3429	132	15	2	2	NUM
ejpam-3429	132	16	√	√	NUM
ejpam-3429	132	17	2[(1−	2[(1−	NUM
ejpam-3429	132	18	ρ	ρ	NOUN
ejpam-3429	132	19	)	)	PUNCT
ejpam-3429	132	20	cosα	cosα	NOUN
ejpam-3429	132	21	]	]	X
ejpam-3429	132	22	3	3	NUM
ejpam-3429	132	23	2	2	NUM
ejpam-3429	133	1	[	[	X
ejpam-3429	133	2	[	[	X
ejpam-3429	133	3	1−	1−	NUM
ejpam-3429	133	4	λ+	λ+	PUNCT
ejpam-3429	133	5	(	(	PUNCT
ejpam-3429	133	6	1	1	NUM
ejpam-3429	133	7	+	+	NUM
ejpam-3429	133	8	q)λ]2	q)λ]2	PROPN
ejpam-3429	133	9	m	m	VERB
ejpam-3429	133	10	(	(	PUNCT
ejpam-3429	133	11	q)γ22	q)γ22	X
ejpam-3429	133	12	+	+	PUNCT
ejpam-3429	134	1	[	[	X
ejpam-3429	134	2	1−	1−	NUM
ejpam-3429	134	3	λ+	λ+	PUNCT
ejpam-3429	134	4	[	[	X
ejpam-3429	134	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	134	6	(	(	PUNCT
ejpam-3429	134	7	[	[	X
ejpam-3429	134	8	3]q	3]q	NUM
ejpam-3429	134	9	−	−	ADP
ejpam-3429	134	10	1)γ3	1)γ3	NOUN
ejpam-3429	134	11	]	]	SYM
ejpam-3429	134	12	3	3	NUM
ejpam-3429	134	13	2	2	NUM
ejpam-3429	134	14	[	[	SYM
ejpam-3429	134	15	2	2	NUM
ejpam-3429	134	16	[	[	X
ejpam-3429	134	17	1−	1−	NUM
ejpam-3429	134	18	λ+	λ+	PUNCT
ejpam-3429	134	19	(	(	PUNCT
ejpam-3429	134	20	1	1	NUM
ejpam-3429	134	21	+	+	NUM
ejpam-3429	134	22	q)λ]m	q)λ]m	NOUN
ejpam-3429	135	1	[	[	X
ejpam-3429	135	2	1−	1−	NUM
ejpam-3429	135	3	λ+	λ+	PUNCT
ejpam-3429	135	4	[	[	X
ejpam-3429	135	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	135	6	γ2γ3(1	γ2γ3(1	VERB
ejpam-3429	135	7	+	+	NOUN
ejpam-3429	135	8	q	q	PUNCT
ejpam-3429	136	1	+	+	NUM
ejpam-3429	137	1	[	[	X
ejpam-3429	137	2	3]q	3]q	NUM
ejpam-3429	137	3	)	)	PUNCT
ejpam-3429	138	1	[	[	X
ejpam-3429	138	2	1−	1−	NUM
ejpam-3429	138	3	λ+	λ+	PUNCT
ejpam-3429	138	4	[	[	X
ejpam-3429	138	5	4]qλ]m	4]qλ]m	NUM
ejpam-3429	138	6	(	(	PUNCT
ejpam-3429	138	7	[	[	X
ejpam-3429	138	8	4]q	4]q	X
ejpam-3429	138	9	−	−	ADP
ejpam-3429	138	10	1)γ4	1)γ4	NUM
ejpam-3429	138	11	+	+	CCONJ
ejpam-3429	138	12	5	5	NUM
ejpam-3429	138	13	]	]	PUNCT
ejpam-3429	138	14	.	.	PUNCT
ejpam-3429	139	1	proof	proof	NOUN
ejpam-3429	139	2	.	.	PUNCT
ejpam-3429	140	1	let	let	VERB
ejpam-3429	140	2	f	f	PROPN
ejpam-3429	140	3	∈	∈	PROPN
ejpam-3429	140	4	α−	α−	ADP
ejpam-3429	140	5	sp(ρ	sp(ρ	NOUN
ejpam-3429	140	6	,	,	PUNCT
ejpam-3429	140	7	a	a	DET
ejpam-3429	140	8	,	,	PUNCT
ejpam-3429	140	9	b	b	NOUN
ejpam-3429	140	10	;	;	PUNCT
ejpam-3429	140	11	q	q	ADJ
ejpam-3429	140	12	,	,	PUNCT
ejpam-3429	140	13	z	z	NOUN
ejpam-3429	140	14	)	)	PUNCT
ejpam-3429	140	15	.	.	PUNCT
ejpam-3429	141	1	then	then	ADV
ejpam-3429	141	2	the	the	DET
ejpam-3429	141	3	inequalities	inequality	NOUN
ejpam-3429	141	4	in	in	ADP
ejpam-3429	141	5	definition	definition	NOUN
ejpam-3429	141	6	2	2	NUM
ejpam-3429	141	7	can	can	AUX
ejpam-3429	141	8	be	be	AUX
ejpam-3429	141	9	equivalently	equivalently	ADV
ejpam-3429	141	10	rewritten	rewrite	VERB
ejpam-3429	141	11	as	as	ADP
ejpam-3429	141	12	,	,	PUNCT
ejpam-3429	141	13	(	(	PUNCT
ejpam-3429	141	14	eiα	eiα	NOUN
ejpam-3429	141	15	z	z	PROPN
ejpam-3429	142	1	[	[	X
ejpam-3429	142	2	dq(j	dq(j	NOUN
ejpam-3429	142	3	m	m	VERB
ejpam-3429	142	4	λ	λ	NOUN
ejpam-3429	142	5	(	(	PUNCT
ejpam-3429	142	6	a1	a1	PROPN
ejpam-3429	142	7	,	,	PUNCT
ejpam-3429	142	8	b1	b1	NOUN
ejpam-3429	142	9	;	;	PUNCT
ejpam-3429	142	10	q	q	ADJ
ejpam-3429	142	11	,	,	PUNCT
ejpam-3429	142	12	z)f	z)f	X
ejpam-3429	142	13	)	)	PUNCT
ejpam-3429	142	14	]	]	PUNCT
ejpam-3429	142	15	(	(	PUNCT
ejpam-3429	142	16	jmλ	jmλ	PROPN
ejpam-3429	142	17	(	(	PUNCT
ejpam-3429	142	18	a1	a1	PROPN
ejpam-3429	142	19	,	,	PUNCT
ejpam-3429	142	20	b1	b1	NOUN
ejpam-3429	142	21	;	;	PUNCT
ejpam-3429	142	22	q	q	ADJ
ejpam-3429	142	23	,	,	PUNCT
ejpam-3429	142	24	z)f	z)f	X
ejpam-3429	142	25	)	)	PUNCT
ejpam-3429	142	26	)	)	PUNCT
ejpam-3429	143	1	=	=	PUNCT
ejpam-3429	143	2	p1(z	p1(z	PROPN
ejpam-3429	143	3	)	)	PUNCT
ejpam-3429	143	4	cosα+	cosα+	X
ejpam-3429	144	1	i	i	PRON
ejpam-3429	144	2	sinα	sinα	PROPN
ejpam-3429	144	3	(	(	PUNCT
ejpam-3429	144	4	10	10	NUM
ejpam-3429	144	5	)	)	PUNCT
ejpam-3429	144	6	and	and	CCONJ
ejpam-3429	144	7	(	(	PUNCT
ejpam-3429	144	8	eiα	eiα	NOUN
ejpam-3429	144	9	w	w	PROPN
ejpam-3429	145	1	[	[	X
ejpam-3429	145	2	dq(j	dq(j	NOUN
ejpam-3429	145	3	m	m	VERB
ejpam-3429	145	4	λ	λ	NOUN
ejpam-3429	145	5	(	(	PUNCT
ejpam-3429	145	6	a1	a1	PROPN
ejpam-3429	145	7	,	,	PUNCT
ejpam-3429	145	8	b1	b1	NOUN
ejpam-3429	145	9	;	;	PUNCT
ejpam-3429	145	10	q	q	NOUN
ejpam-3429	145	11	,	,	PUNCT
ejpam-3429	145	12	w)f	w)f	NOUN
ejpam-3429	145	13	)	)	PUNCT
ejpam-3429	145	14	]	]	PUNCT
ejpam-3429	145	15	(	(	PUNCT
ejpam-3429	145	16	jmλ	jmλ	PROPN
ejpam-3429	145	17	(	(	PUNCT
ejpam-3429	145	18	a1	a1	PROPN
ejpam-3429	145	19	,	,	PUNCT
ejpam-3429	145	20	b1	b1	NOUN
ejpam-3429	145	21	;	;	PUNCT
ejpam-3429	145	22	q	q	NOUN
ejpam-3429	145	23	,	,	PUNCT
ejpam-3429	145	24	w)f	w)f	NOUN
ejpam-3429	145	25	)	)	PUNCT
ejpam-3429	145	26	)	)	PUNCT
ejpam-3429	146	1	=	=	PUNCT
ejpam-3429	147	1	q1(w	q1(w	NOUN
ejpam-3429	147	2	)	)	PUNCT
ejpam-3429	147	3	cosα+	cosα+	X
ejpam-3429	148	1	i	i	PRON
ejpam-3429	148	2	sinα	sinα	PROPN
ejpam-3429	148	3	(	(	PUNCT
ejpam-3429	148	4	11	11	NUM
ejpam-3429	148	5	)	)	PUNCT
ejpam-3429	148	6	respectively	respectively	ADV
ejpam-3429	148	7	,	,	PUNCT
ejpam-3429	148	8	where	where	SCONJ
ejpam-3429	148	9	r(p1(z	r(p1(z	NOUN
ejpam-3429	148	10	)	)	PUNCT
ejpam-3429	148	11	)	)	PUNCT
ejpam-3429	148	12	>	>	X
ejpam-3429	148	13	ρ	ρ	PROPN
ejpam-3429	148	14	and	and	CCONJ
ejpam-3429	148	15	r(q1(z	r(q1(z	NOUN
ejpam-3429	148	16	)	)	PUNCT
ejpam-3429	148	17	)	)	PUNCT
ejpam-3429	148	18	>	>	X
ejpam-3429	149	1	ρ	ρ	PROPN
ejpam-3429	149	2	,	,	PUNCT
ejpam-3429	149	3	p1(z	p1(z	PROPN
ejpam-3429	149	4	)	)	PUNCT
ejpam-3429	149	5	=	=	SYM
ejpam-3429	149	6	1	1	NUM
ejpam-3429	150	1	+	+	CCONJ
ejpam-3429	150	2	c1z	c1z	PROPN
ejpam-3429	151	1	+	+	PUNCT
ejpam-3429	151	2	c2z	c2z	PROPN
ejpam-3429	151	3	2	2	NUM
ejpam-3429	151	4	+	+	CCONJ
ejpam-3429	151	5	·	·	PUNCT
ejpam-3429	151	6	·	·	PUNCT
ejpam-3429	151	7	·	·	PUNCT
ejpam-3429	152	1	(	(	PUNCT
ejpam-3429	152	2	z	z	NOUN
ejpam-3429	152	3	∈	∈	PROPN
ejpam-3429	152	4	u	u	NOUN
ejpam-3429	152	5	)	)	PUNCT
ejpam-3429	152	6	and	and	CCONJ
ejpam-3429	152	7	q1(w	q1(w	NOUN
ejpam-3429	152	8	)	)	PUNCT
ejpam-3429	152	9	=	=	SYM
ejpam-3429	152	10	1	1	NUM
ejpam-3429	152	11	+	+	CCONJ
ejpam-3429	152	12	l1w	l1w	NOUN
ejpam-3429	152	13	+	+	CCONJ
ejpam-3429	152	14	l2w	l2w	PROPN
ejpam-3429	152	15	2	2	NUM
ejpam-3429	152	16	+	+	CCONJ
ejpam-3429	152	17	·	·	PUNCT
ejpam-3429	152	18	·	·	PUNCT
ejpam-3429	152	19	·	·	PUNCT
ejpam-3429	153	1	(	(	PUNCT
ejpam-3429	153	2	w	w	PROPN
ejpam-3429	153	3	∈	∈	PROPN
ejpam-3429	153	4	u	u	NOUN
ejpam-3429	153	5	)	)	PUNCT
ejpam-3429	153	6	.	.	PUNCT
ejpam-3429	154	1	by	by	ADP
ejpam-3429	154	2	comparing	compare	VERB
ejpam-3429	154	3	the	the	DET
ejpam-3429	154	4	coefficients	coefficient	NOUN
ejpam-3429	154	5	in	in	ADP
ejpam-3429	154	6	(	(	PUNCT
ejpam-3429	154	7	10	10	NUM
ejpam-3429	154	8	)	)	PUNCT
ejpam-3429	154	9	,	,	PUNCT
ejpam-3429	154	10	we	we	PRON
ejpam-3429	154	11	have	have	VERB
ejpam-3429	154	12	eiα	eiα	NOUN
ejpam-3429	154	13	[	[	X
ejpam-3429	154	14	1−	1−	NUM
ejpam-3429	154	15	λ+	λ+	PUNCT
ejpam-3429	154	16	(	(	PUNCT
ejpam-3429	154	17	1	1	NUM
ejpam-3429	154	18	+	+	NUM
ejpam-3429	154	19	q)λ]m	q)λ]m	NUM
ejpam-3429	154	20	qγ2k2	qγ2k2	PROPN
ejpam-3429	154	21	=	=	SYM
ejpam-3429	154	22	c1	c1	PROPN
ejpam-3429	154	23	cosα	cosα	NOUN
ejpam-3429	154	24	(	(	PUNCT
ejpam-3429	154	25	12	12	NUM
ejpam-3429	154	26	)	)	PUNCT
ejpam-3429	154	27	eiα	eiα	NOUN
ejpam-3429	154	28	[	[	PUNCT
ejpam-3429	154	29	[	[	X
ejpam-3429	154	30	1−	1−	NUM
ejpam-3429	154	31	λ+	λ+	PUNCT
ejpam-3429	154	32	(	(	PUNCT
ejpam-3429	154	33	1	1	NUM
ejpam-3429	154	34	+	+	NUM
ejpam-3429	154	35	q)λ]2	q)λ]2	PROPN
ejpam-3429	154	36	m	m	NOUN
ejpam-3429	154	37	(	(	PUNCT
ejpam-3429	154	38	q)γ22k	q)γ22k	NOUN
ejpam-3429	154	39	2	2	NUM
ejpam-3429	154	40	2	2	NUM
ejpam-3429	154	41	+	+	CCONJ
ejpam-3429	155	1	[	[	X
ejpam-3429	155	2	1−	1−	NUM
ejpam-3429	155	3	λ+	λ+	PUNCT
ejpam-3429	155	4	[	[	X
ejpam-3429	155	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	155	6	(	(	PUNCT
ejpam-3429	155	7	[	[	X
ejpam-3429	155	8	3]q	3]q	NUM
ejpam-3429	155	9	−	−	NOUN
ejpam-3429	155	10	1	1	NUM
ejpam-3429	155	11	)	)	PUNCT
ejpam-3429	155	12	γ3k3	γ3k3	PRON
ejpam-3429	155	13	]	]	PUNCT
ejpam-3429	155	14	=	=	PUNCT
ejpam-3429	155	15	c2	c2	PROPN
ejpam-3429	155	16	cosα	cosα	NOUN
ejpam-3429	155	17	(	(	PUNCT
ejpam-3429	155	18	13	13	NUM
ejpam-3429	155	19	)	)	PUNCT
ejpam-3429	155	20	eiα	eiα	NOUN
ejpam-3429	155	21	[	[	PUNCT
ejpam-3429	155	22	[	[	X
ejpam-3429	155	23	1−	1−	NUM
ejpam-3429	155	24	λ+	λ+	PUNCT
ejpam-3429	155	25	[	[	X
ejpam-3429	155	26	4]qλ]m	4]qλ]m	NUM
ejpam-3429	155	27	(	(	PUNCT
ejpam-3429	155	28	[	[	X
ejpam-3429	155	29	4]q	4]q	X
ejpam-3429	155	30	−	−	NOUN
ejpam-3429	156	1	1)γ4k4	1)γ4k4	NUM
ejpam-3429	156	2	−	−	PROPN
ejpam-3429	156	3	(	(	PUNCT
ejpam-3429	156	4	1	1	NUM
ejpam-3429	156	5	+	+	CCONJ
ejpam-3429	156	6	q	q	NOUN
ejpam-3429	156	7	+	+	CCONJ
ejpam-3429	156	8	[	[	X
ejpam-3429	156	9	3]q	3]q	NUM
ejpam-3429	156	10	)	)	PUNCT
ejpam-3429	156	11	[	[	X
ejpam-3429	156	12	1−	1−	NUM
ejpam-3429	156	13	λ+	λ+	PUNCT
ejpam-3429	156	14	(	(	PUNCT
ejpam-3429	156	15	1	1	NUM
ejpam-3429	156	16	+	+	NUM
ejpam-3429	156	17	q)λ]m	q)λ]m	NOUN
ejpam-3429	157	1	[	[	X
ejpam-3429	157	2	1−	1−	NUM
ejpam-3429	157	3	λ+	λ+	PUNCT
ejpam-3429	157	4	[	[	X
ejpam-3429	157	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	157	6	γ2γ3k2k3	γ2γ3k2k3	NOUN
ejpam-3429	157	7	+	+	CCONJ
ejpam-3429	157	8	(	(	PUNCT
ejpam-3429	157	9	1	1	NUM
ejpam-3429	157	10	+	+	CCONJ
ejpam-3429	157	11	q	q	X
ejpam-3429	157	12	)	)	PUNCT
ejpam-3429	158	1	[	[	X
ejpam-3429	158	2	1−	1−	NUM
ejpam-3429	158	3	λ+	λ+	PUNCT
ejpam-3429	158	4	(	(	PUNCT
ejpam-3429	158	5	1	1	NUM
ejpam-3429	158	6	+	+	NUM
ejpam-3429	158	7	q)λ]2	q)λ]2	PROPN
ejpam-3429	158	8	m	m	VERB
ejpam-3429	158	9	γ22k	γ22k	NUM
ejpam-3429	158	10	2	2	NUM
ejpam-3429	158	11	2	2	NUM
ejpam-3429	158	12	]	]	PUNCT
ejpam-3429	158	13	=	=	SYM
ejpam-3429	158	14	c3	c3	PROPN
ejpam-3429	158	15	cosα	cosα	PROPN
ejpam-3429	158	16	.	.	PUNCT
ejpam-3429	159	1	(	(	PUNCT
ejpam-3429	159	2	14	14	NUM
ejpam-3429	159	3	)	)	PUNCT
ejpam-3429	159	4	similarly	similarly	ADV
ejpam-3429	159	5	by	by	ADP
ejpam-3429	159	6	equating	equate	VERB
ejpam-3429	159	7	the	the	DET
ejpam-3429	159	8	coefficients	coefficient	NOUN
ejpam-3429	159	9	in	in	ADP
ejpam-3429	159	10	(	(	PUNCT
ejpam-3429	159	11	11	11	NUM
ejpam-3429	159	12	)	)	PUNCT
ejpam-3429	159	13	,	,	PUNCT
ejpam-3429	159	14	we	we	PRON
ejpam-3429	159	15	get	get	VERB
ejpam-3429	159	16	−eiα	−eiα	PRON
ejpam-3429	160	1	[	[	X
ejpam-3429	160	2	1−	1−	NUM
ejpam-3429	160	3	λ+	λ+	PUNCT
ejpam-3429	160	4	(	(	PUNCT
ejpam-3429	160	5	1	1	NUM
ejpam-3429	160	6	+	+	NUM
ejpam-3429	160	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	160	8	(	(	PUNCT
ejpam-3429	160	9	q	q	NOUN
ejpam-3429	160	10	)	)	PUNCT
ejpam-3429	160	11	γ2k2	γ2k2	X
ejpam-3429	160	12	=	=	PROPN
ejpam-3429	160	13	l1	l1	PROPN
ejpam-3429	160	14	cosα	cosα	PROPN
ejpam-3429	160	15	(	(	PUNCT
ejpam-3429	160	16	15	15	NUM
ejpam-3429	160	17	)	)	PUNCT
ejpam-3429	160	18	eiα	eiα	NOUN
ejpam-3429	160	19	[	[	PUNCT
ejpam-3429	160	20	[	[	X
ejpam-3429	160	21	1−	1−	NUM
ejpam-3429	160	22	λ+	λ+	PUNCT
ejpam-3429	160	23	(	(	PUNCT
ejpam-3429	160	24	1	1	NUM
ejpam-3429	160	25	+	+	NUM
ejpam-3429	160	26	q)λ]2	q)λ]2	PROPN
ejpam-3429	160	27	m	m	NOUN
ejpam-3429	160	28	(	(	PUNCT
ejpam-3429	160	29	q)γ22k	q)γ22k	NOUN
ejpam-3429	160	30	2	2	NUM
ejpam-3429	160	31	2	2	NUM
ejpam-3429	160	32	+	+	CCONJ
ejpam-3429	160	33	[	[	X
ejpam-3429	160	34	1−	1−	NUM
ejpam-3429	160	35	λ+	λ+	PUNCT
ejpam-3429	160	36	[	[	X
ejpam-3429	160	37	3]qλ]m	3]qλ]m	NUM
ejpam-3429	160	38	(	(	PUNCT
ejpam-3429	160	39	[	[	X
ejpam-3429	160	40	3]q	3]q	NUM
ejpam-3429	160	41	−	−	NOUN
ejpam-3429	160	42	1	1	NUM
ejpam-3429	160	43	)	)	PUNCT
ejpam-3429	160	44	γ3(2k	γ3(2k	NOUN
ejpam-3429	160	45	2	2	NUM
ejpam-3429	160	46	2	2	NUM
ejpam-3429	160	47	−	−	NOUN
ejpam-3429	160	48	k3	k3	ADJ
ejpam-3429	160	49	)	)	PUNCT
ejpam-3429	160	50	]	]	PUNCT
ejpam-3429	161	1	=	=	PUNCT
ejpam-3429	161	2	l2	l2	PROPN
ejpam-3429	161	3	cosα	cosα	NOUN
ejpam-3429	161	4	.	.	PUNCT
ejpam-3429	162	1	(	(	PUNCT
ejpam-3429	162	2	16	16	NUM
ejpam-3429	162	3	)	)	PUNCT
ejpam-3429	162	4	k.	k.	PROPN
ejpam-3429	162	5	a.	a.	PROPN
ejpam-3429	162	6	reddy	reddy	PROPN
ejpam-3429	162	7	,	,	PUNCT
ejpam-3429	162	8	k.	k.	PROPN
ejpam-3429	162	9	r.	r.	PROPN
ejpam-3429	162	10	karthikeyan	karthikeyan	PROPN
ejpam-3429	162	11	,	,	PUNCT
ejpam-3429	162	12	g.	g.	PROPN
ejpam-3429	162	13	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	162	14	/	/	SYM
ejpam-3429	162	15	eur	eur	PROPN
ejpam-3429	162	16	.	.	PUNCT
ejpam-3429	163	1	j.	j.	PROPN
ejpam-3429	163	2	pure	pure	PROPN
ejpam-3429	163	3	appl	appl	PROPN
ejpam-3429	163	4	.	.	PROPN
ejpam-3429	163	5	math	math	PROPN
ejpam-3429	163	6	,	,	PUNCT
ejpam-3429	163	7	12	12	NUM
ejpam-3429	163	8	(	(	PUNCT
ejpam-3429	163	9	3	3	NUM
ejpam-3429	163	10	)	)	PUNCT
ejpam-3429	163	11	(	(	PUNCT
ejpam-3429	163	12	2019	2019	NUM
ejpam-3429	163	13	)	)	PUNCT
ejpam-3429	163	14	,	,	PUNCT
ejpam-3429	163	15	846	846	NUM
ejpam-3429	163	16	-	-	SYM
ejpam-3429	163	17	856	856	NUM
ejpam-3429	163	18	851	851	NUM
ejpam-3429	163	19	eiα	eiα	NOUN
ejpam-3429	163	20	[	[	PUNCT
ejpam-3429	163	21	[	[	X
ejpam-3429	163	22	1−	1−	NUM
ejpam-3429	163	23	λ+	λ+	PUNCT
ejpam-3429	163	24	[	[	X
ejpam-3429	163	25	4]qλ]m	4]qλ]m	NUM
ejpam-3429	163	26	(	(	PUNCT
ejpam-3429	163	27	[	[	X
ejpam-3429	163	28	4]q	4]q	NUM
ejpam-3429	163	29	−	−	NOUN
ejpam-3429	163	30	1)γ4(5k2k3	1)γ4(5k2k3	NOUN
ejpam-3429	163	31	−	−	PROPN
ejpam-3429	163	32	5k32	5k32	NOUN
ejpam-3429	163	33	−	−	NOUN
ejpam-3429	164	1	k4)−	k4)−	NOUN
ejpam-3429	164	2	(	(	PUNCT
ejpam-3429	164	3	1	1	NUM
ejpam-3429	164	4	+	+	CCONJ
ejpam-3429	164	5	q	q	NOUN
ejpam-3429	164	6	+	+	CCONJ
ejpam-3429	164	7	[	[	X
ejpam-3429	164	8	3]q	3]q	NUM
ejpam-3429	164	9	)	)	PUNCT
ejpam-3429	165	1	[	[	X
ejpam-3429	165	2	1−	1−	NUM
ejpam-3429	165	3	λ+	λ+	PUNCT
ejpam-3429	165	4	(	(	PUNCT
ejpam-3429	165	5	1	1	NUM
ejpam-3429	165	6	+	+	NUM
ejpam-3429	165	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	166	1	[	[	X
ejpam-3429	166	2	1−	1−	NUM
ejpam-3429	166	3	λ+	λ+	PUNCT
ejpam-3429	166	4	[	[	X
ejpam-3429	166	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	166	6	γ2γ3k2k3	γ2γ3k2k3	NUM
ejpam-3429	166	7	+	+	CCONJ
ejpam-3429	166	8	(	(	PUNCT
ejpam-3429	166	9	1	1	NUM
ejpam-3429	166	10	+	+	CCONJ
ejpam-3429	166	11	q	q	X
ejpam-3429	166	12	)	)	PUNCT
ejpam-3429	167	1	[	[	X
ejpam-3429	167	2	1−	1−	NUM
ejpam-3429	167	3	λ+	λ+	PUNCT
ejpam-3429	167	4	(	(	PUNCT
ejpam-3429	167	5	1	1	NUM
ejpam-3429	167	6	+	+	NUM
ejpam-3429	167	7	q)λ]2	q)λ]2	PROPN
ejpam-3429	167	8	m	m	VERB
ejpam-3429	167	9	γ22k	γ22k	NUM
ejpam-3429	167	10	2	2	NUM
ejpam-3429	167	11	2	2	NUM
ejpam-3429	167	12	]	]	PUNCT
ejpam-3429	167	13	=	=	SYM
ejpam-3429	167	14	l3	l3	PROPN
ejpam-3429	167	15	cosα	cosα	PROPN
ejpam-3429	167	16	.	.	PUNCT
ejpam-3429	168	1	(	(	PUNCT
ejpam-3429	168	2	17	17	NUM
ejpam-3429	168	3	)	)	PUNCT
ejpam-3429	168	4	from	from	ADP
ejpam-3429	168	5	(	(	PUNCT
ejpam-3429	168	6	12	12	NUM
ejpam-3429	168	7	)	)	PUNCT
ejpam-3429	168	8	and	and	CCONJ
ejpam-3429	168	9	(	(	PUNCT
ejpam-3429	168	10	15	15	NUM
ejpam-3429	168	11	)	)	PUNCT
ejpam-3429	168	12	,	,	PUNCT
ejpam-3429	168	13	we	we	PRON
ejpam-3429	168	14	get	get	VERB
ejpam-3429	168	15	l1	l1	PROPN
ejpam-3429	168	16	=	=	PROPN
ejpam-3429	168	17	−c1	−c1	PROPN
ejpam-3429	168	18	.	.	PUNCT
ejpam-3429	169	1	before	before	ADP
ejpam-3429	169	2	computing	compute	VERB
ejpam-3429	169	3	|	|	NOUN
ejpam-3429	169	4	a2	a2	PROPN
ejpam-3429	170	1	|	|	ADV
ejpam-3429	171	1	and	and	CCONJ
ejpam-3429	171	2	|	|	ADV
ejpam-3429	171	3	a3	a3	VERB
ejpam-3429	171	4	|	|	ADV
ejpam-3429	171	5	,	,	PUNCT
ejpam-3429	171	6	we	we	PRON
ejpam-3429	171	7	will	will	AUX
ejpam-3429	171	8	obtain	obtain	VERB
ejpam-3429	171	9	a	a	DET
ejpam-3429	171	10	refined	refined	ADJ
ejpam-3429	171	11	estimate	estimate	NOUN
ejpam-3429	171	12	of	of	ADP
ejpam-3429	171	13	|	|	ADV
ejpam-3429	171	14	c1	c1	PROPN
ejpam-3429	171	15	|	|	NOUN
ejpam-3429	171	16	.	.	PUNCT
ejpam-3429	172	1	for	for	ADP
ejpam-3429	172	2	this	this	DET
ejpam-3429	172	3	purpose	purpose	NOUN
ejpam-3429	172	4	,	,	PUNCT
ejpam-3429	172	5	we	we	PRON
ejpam-3429	172	6	first	first	ADV
ejpam-3429	172	7	add	add	VERB
ejpam-3429	172	8	(	(	PUNCT
ejpam-3429	172	9	13	13	NUM
ejpam-3429	172	10	)	)	PUNCT
ejpam-3429	172	11	and	and	CCONJ
ejpam-3429	172	12	(	(	PUNCT
ejpam-3429	172	13	16	16	NUM
ejpam-3429	172	14	)	)	PUNCT
ejpam-3429	172	15	2k22	2k22	NOUN
ejpam-3429	173	1	=	=	PUNCT
ejpam-3429	173	2	(	(	PUNCT
ejpam-3429	173	3	c2	c2	PROPN
ejpam-3429	173	4	+	+	CCONJ
ejpam-3429	173	5	l2	l2	NOUN
ejpam-3429	173	6	)	)	PUNCT
ejpam-3429	173	7	cosα	cosα	NOUN
ejpam-3429	173	8	eiα[[1−	eiα[[1−	PROPN
ejpam-3429	173	9	λ+	λ+	PUNCT
ejpam-3429	173	10	(	(	PUNCT
ejpam-3429	173	11	1	1	NUM
ejpam-3429	173	12	+	+	NUM
ejpam-3429	173	13	q)λ]2	q)λ]2	PROPN
ejpam-3429	173	14	m	m	VERB
ejpam-3429	173	15	(	(	PUNCT
ejpam-3429	173	16	q)γ22	q)γ22	X
ejpam-3429	173	17	+	+	PUNCT
ejpam-3429	174	1	[	[	X
ejpam-3429	174	2	1−	1−	NUM
ejpam-3429	174	3	λ+	λ+	PUNCT
ejpam-3429	174	4	[	[	X
ejpam-3429	174	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	174	6	(	(	PUNCT
ejpam-3429	174	7	1−	1−	NUM
ejpam-3429	174	8	[	[	X
ejpam-3429	174	9	3]q)γ3	3]q)γ3	X
ejpam-3429	174	10	]	]	PUNCT
ejpam-3429	174	11	.	.	PUNCT
ejpam-3429	175	1	using	use	VERB
ejpam-3429	175	2	(	(	PUNCT
ejpam-3429	175	3	12	12	NUM
ejpam-3429	175	4	)	)	PUNCT
ejpam-3429	175	5	in	in	ADP
ejpam-3429	175	6	the	the	DET
ejpam-3429	175	7	above	above	ADJ
ejpam-3429	175	8	equation	equation	NOUN
ejpam-3429	175	9	in	in	ADP
ejpam-3429	175	10	conjunction	conjunction	NOUN
ejpam-3429	175	11	with	with	ADP
ejpam-3429	175	12	the	the	DET
ejpam-3429	175	13	known	know	VERB
ejpam-3429	175	14	result	result	NOUN
ejpam-3429	175	15	that	that	SCONJ
ejpam-3429	175	16	|cn|	|cn|	ADJ
ejpam-3429	175	17	≤	≤	NOUN
ejpam-3429	175	18	2(1−	2(1−	NUM
ejpam-3429	175	19	ρ	ρ	NUM
ejpam-3429	175	20	)	)	PUNCT
ejpam-3429	175	21	and	and	CCONJ
ejpam-3429	175	22	|ln|	|ln|	VERB
ejpam-3429	175	23	≤	≤	NOUN
ejpam-3429	175	24	2(1−	2(1−	NUM
ejpam-3429	175	25	ρ	ρ	NUM
ejpam-3429	175	26	)	)	PUNCT
ejpam-3429	175	27	,	,	PUNCT
ejpam-3429	175	28	we	we	PRON
ejpam-3429	175	29	have	have	VERB
ejpam-3429	175	30	|	|	ADV
ejpam-3429	175	31	c21	c21	NOUN
ejpam-3429	176	1	|	|	ADV
ejpam-3429	176	2	=	=	SYM
ejpam-3429	176	3	∣∣∣∣∣(c2	∣∣∣∣∣(c2	ADP
ejpam-3429	176	4	+	+	NOUN
ejpam-3429	176	5	l2	l2	NOUN
ejpam-3429	176	6	)	)	PUNCT
ejpam-3429	176	7	eiα	eiα	NOUN
ejpam-3429	177	1	[	[	X
ejpam-3429	177	2	1−	1−	NUM
ejpam-3429	177	3	λ+	λ+	PUNCT
ejpam-3429	177	4	(	(	PUNCT
ejpam-3429	177	5	1	1	NUM
ejpam-3429	177	6	+	+	NUM
ejpam-3429	177	7	q)λ]2	q)λ]2	PROPN
ejpam-3429	177	8	m	m	VERB
ejpam-3429	177	9	(	(	PUNCT
ejpam-3429	177	10	q)2γ22	q)2γ22	PROPN
ejpam-3429	177	11	2	2	NUM
ejpam-3429	177	12	cosα[[1−	cosα[[1−	PROPN
ejpam-3429	177	13	λ+	λ+	PUNCT
ejpam-3429	177	14	(	(	PUNCT
ejpam-3429	177	15	1	1	NUM
ejpam-3429	177	16	+	+	NUM
ejpam-3429	177	17	q)λ]2	q)λ]2	PROPN
ejpam-3429	177	18	m	m	VERB
ejpam-3429	177	19	(	(	PUNCT
ejpam-3429	177	20	q)γ22	q)γ22	X
ejpam-3429	177	21	+	+	PUNCT
ejpam-3429	178	1	[	[	X
ejpam-3429	178	2	1−	1−	NUM
ejpam-3429	178	3	λ+	λ+	PUNCT
ejpam-3429	178	4	[	[	X
ejpam-3429	178	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	178	6	(	(	PUNCT
ejpam-3429	178	7	1−	1−	NUM
ejpam-3429	178	8	[	[	X
ejpam-3429	178	9	3]q)γ3	3]q)γ3	X
ejpam-3429	178	10	]	]	PUNCT
ejpam-3429	178	11	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3429	178	12	≤	≤	PROPN
ejpam-3429	178	13	|c2|+	|c2|+	X
ejpam-3429	178	14	|l2|	|l2|	NOUN
ejpam-3429	178	15	2	2	NUM
ejpam-3429	178	16	1	1	NUM
ejpam-3429	178	17	[	[	X
ejpam-3429	178	18	1−	1−	NUM
ejpam-3429	178	19	λ+	λ+	PUNCT
ejpam-3429	178	20	(	(	PUNCT
ejpam-3429	178	21	1	1	NUM
ejpam-3429	178	22	+	+	NUM
ejpam-3429	178	23	q)λ]2	q)λ]2	PROPN
ejpam-3429	178	24	m	m	VERB
ejpam-3429	178	25	(	(	PUNCT
ejpam-3429	178	26	q)2γ22	q)2γ22	PROPN
ejpam-3429	178	27	cosα[[1−	cosα[[1−	PROPN
ejpam-3429	178	28	λ+	λ+	PUNCT
ejpam-3429	178	29	(	(	PUNCT
ejpam-3429	178	30	1	1	NUM
ejpam-3429	178	31	+	+	NUM
ejpam-3429	178	32	q)λ]2	q)λ]2	PROPN
ejpam-3429	178	33	m	m	VERB
ejpam-3429	178	34	(	(	PUNCT
ejpam-3429	178	35	q)γ22	q)γ22	X
ejpam-3429	178	36	+	+	PUNCT
ejpam-3429	179	1	[	[	X
ejpam-3429	179	2	1−	1−	NUM
ejpam-3429	179	3	λ+	λ+	PUNCT
ejpam-3429	179	4	[	[	X
ejpam-3429	179	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	179	6	(	(	PUNCT
ejpam-3429	179	7	[	[	X
ejpam-3429	179	8	3]q	3]q	NUM
ejpam-3429	179	9	−	−	ADP
ejpam-3429	179	10	1)γ3	1)γ3	NOUN
ejpam-3429	179	11	]	]	PUNCT
ejpam-3429	179	12	≤	≤	NOUN
ejpam-3429	179	13	2(1−	2(1−	NUM
ejpam-3429	179	14	ρ	ρ	NUM
ejpam-3429	179	15	)	)	PUNCT
ejpam-3429	179	16	[	[	X
ejpam-3429	179	17	1−	1−	NUM
ejpam-3429	179	18	λ+	λ+	PUNCT
ejpam-3429	179	19	(	(	PUNCT
ejpam-3429	179	20	1	1	NUM
ejpam-3429	179	21	+	+	NUM
ejpam-3429	179	22	q)λ]2	q)λ]2	PROPN
ejpam-3429	179	23	m	m	VERB
ejpam-3429	179	24	(	(	PUNCT
ejpam-3429	179	25	q)2γ22	q)2γ22	PROPN
ejpam-3429	179	26	cosα[[1−	cosα[[1−	PROPN
ejpam-3429	179	27	λ+	λ+	PUNCT
ejpam-3429	179	28	(	(	PUNCT
ejpam-3429	179	29	1	1	NUM
ejpam-3429	179	30	+	+	NUM
ejpam-3429	179	31	q)λ]2	q)λ]2	PROPN
ejpam-3429	179	32	m	m	VERB
ejpam-3429	179	33	(	(	PUNCT
ejpam-3429	179	34	q)γ22	q)γ22	X
ejpam-3429	179	35	+	+	PUNCT
ejpam-3429	180	1	[	[	X
ejpam-3429	180	2	1−	1−	NUM
ejpam-3429	180	3	λ+	λ+	PUNCT
ejpam-3429	180	4	[	[	X
ejpam-3429	180	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	180	6	(	(	PUNCT
ejpam-3429	180	7	[	[	X
ejpam-3429	180	8	3]q	3]q	NUM
ejpam-3429	180	9	−	−	ADP
ejpam-3429	180	10	1)γ3	1)γ3	NOUN
ejpam-3429	180	11	]	]	PUNCT
ejpam-3429	180	12	|	|	ADV
ejpam-3429	180	13	c1	c1	PROPN
ejpam-3429	180	14	|≤	|≤	PROPN
ejpam-3429	180	15	√	√	NUM
ejpam-3429	180	16	2(1−	2(1−	NUM
ejpam-3429	180	17	ρ	ρ	NUM
ejpam-3429	180	18	)	)	PUNCT
ejpam-3429	181	1	[	[	X
ejpam-3429	181	2	1−	1−	NUM
ejpam-3429	181	3	λ+	λ+	PUNCT
ejpam-3429	181	4	(	(	PUNCT
ejpam-3429	181	5	1	1	NUM
ejpam-3429	181	6	+	+	NUM
ejpam-3429	181	7	q)λ]m	q)λ]m	PROPN
ejpam-3429	181	8	(	(	PUNCT
ejpam-3429	181	9	q)γ2√	q)γ2√	NOUN
ejpam-3429	181	10	cosα[[1−	cosα[[1−	PROPN
ejpam-3429	181	11	λ+	λ+	PUNCT
ejpam-3429	181	12	(	(	PUNCT
ejpam-3429	181	13	1	1	NUM
ejpam-3429	181	14	+	+	NUM
ejpam-3429	181	15	q)λ]2	q)λ]2	PROPN
ejpam-3429	181	16	m	m	VERB
ejpam-3429	181	17	(	(	PUNCT
ejpam-3429	181	18	q)γ22	q)γ22	X
ejpam-3429	181	19	+	+	PUNCT
ejpam-3429	182	1	[	[	X
ejpam-3429	182	2	1−	1−	NUM
ejpam-3429	182	3	λ+	λ+	PUNCT
ejpam-3429	182	4	[	[	X
ejpam-3429	182	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	182	6	(	(	PUNCT
ejpam-3429	182	7	[	[	X
ejpam-3429	182	8	3]q	3]q	NUM
ejpam-3429	182	9	−	−	ADP
ejpam-3429	182	10	1)γ3	1)γ3	NOUN
ejpam-3429	182	11	]	]	PUNCT
ejpam-3429	182	12	(	(	PUNCT
ejpam-3429	182	13	18	18	NUM
ejpam-3429	182	14	)	)	PUNCT
ejpam-3429	182	15	and	and	CCONJ
ejpam-3429	182	16	|	|	ADV
ejpam-3429	182	17	k2	k2	PROPN
ejpam-3429	182	18	|	|	ADV
ejpam-3429	182	19	≤	≤	PUNCT
ejpam-3429	182	20	|	|	ADV
ejpam-3429	182	21	c1	c1	PROPN
ejpam-3429	182	22	|	|	ADV
ejpam-3429	182	23	cosα	cosα	NOUN
ejpam-3429	183	1	[	[	X
ejpam-3429	183	2	1−	1−	NUM
ejpam-3429	183	3	λ+	λ+	PUNCT
ejpam-3429	183	4	(	(	PUNCT
ejpam-3429	183	5	1	1	NUM
ejpam-3429	183	6	+	+	NUM
ejpam-3429	183	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	183	8	(	(	PUNCT
ejpam-3429	183	9	[	[	X
ejpam-3429	183	10	2]q	2]q	NUM
ejpam-3429	183	11	−	−	ADP
ejpam-3429	183	12	1)γ2	1)γ2	NOUN
ejpam-3429	183	13	=	=	SYM
ejpam-3429	183	14	√	√	PROPN
ejpam-3429	183	15	2(1−	2(1−	NUM
ejpam-3429	183	16	ρ	ρ	NUM
ejpam-3429	183	17	)	)	PUNCT
ejpam-3429	183	18	cosα√	cosα√	NOUN
ejpam-3429	184	1	[	[	X
ejpam-3429	184	2	[	[	X
ejpam-3429	184	3	1−	1−	NUM
ejpam-3429	184	4	λ+	λ+	PUNCT
ejpam-3429	184	5	(	(	PUNCT
ejpam-3429	184	6	1	1	NUM
ejpam-3429	184	7	+	+	NUM
ejpam-3429	184	8	q)λ]2	q)λ]2	PROPN
ejpam-3429	184	9	m	m	VERB
ejpam-3429	184	10	(	(	PUNCT
ejpam-3429	184	11	q)γ22	q)γ22	X
ejpam-3429	185	1	+	+	PUNCT
ejpam-3429	186	1	[	[	X
ejpam-3429	186	2	1−	1−	NUM
ejpam-3429	186	3	λ+	λ+	PUNCT
ejpam-3429	186	4	[	[	X
ejpam-3429	186	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	186	6	(	(	PUNCT
ejpam-3429	186	7	[	[	X
ejpam-3429	186	8	3]q	3]q	NUM
ejpam-3429	186	9	−	−	ADP
ejpam-3429	186	10	1)γ3	1)γ3	NOUN
ejpam-3429	186	11	]	]	PUNCT
ejpam-3429	186	12	which	which	PRON
ejpam-3429	186	13	proves	prove	VERB
ejpam-3429	186	14	the	the	DET
ejpam-3429	186	15	assertion	assertion	NOUN
ejpam-3429	186	16	.	.	PUNCT
ejpam-3429	187	1	we	we	PRON
ejpam-3429	187	2	next	next	ADV
ejpam-3429	187	3	find	find	VERB
ejpam-3429	187	4	the	the	DET
ejpam-3429	187	5	upper	upper	ADJ
ejpam-3429	187	6	bound	bind	VERB
ejpam-3429	187	7	on	on	ADP
ejpam-3429	187	8	a3	a3	NOUN
ejpam-3429	187	9	.	.	PUNCT
ejpam-3429	188	1	for	for	ADP
ejpam-3429	188	2	this	this	PRON
ejpam-3429	188	3	we	we	PRON
ejpam-3429	188	4	subtract	subtract	VERB
ejpam-3429	188	5	(	(	PUNCT
ejpam-3429	188	6	13	13	NUM
ejpam-3429	188	7	)	)	PUNCT
ejpam-3429	188	8	and	and	CCONJ
ejpam-3429	188	9	(	(	PUNCT
ejpam-3429	188	10	16	16	NUM
ejpam-3429	188	11	)	)	PUNCT
ejpam-3429	188	12	and	and	CCONJ
ejpam-3429	188	13	using	use	VERB
ejpam-3429	188	14	c1	c1	PROPN
ejpam-3429	188	15	=	=	SYM
ejpam-3429	188	16	−l1	−l1	PROPN
ejpam-3429	188	17	,	,	PUNCT
ejpam-3429	188	18	we	we	PRON
ejpam-3429	188	19	get	get	VERB
ejpam-3429	188	20	k3	k3	ADJ
ejpam-3429	188	21	=	=	PUNCT
ejpam-3429	188	22	(	(	PUNCT
ejpam-3429	188	23	c2	c2	PROPN
ejpam-3429	188	24	−	−	PROPN
ejpam-3429	188	25	l2	l2	PROPN
ejpam-3429	188	26	)	)	PUNCT
ejpam-3429	189	1	cosα	cosα	NOUN
ejpam-3429	189	2	2eiα	2eiα	NUM
ejpam-3429	189	3	[	[	X
ejpam-3429	189	4	1−	1−	NUM
ejpam-3429	189	5	λ+	λ+	PUNCT
ejpam-3429	189	6	[	[	X
ejpam-3429	189	7	3]qλ]m	3]qλ]m	NUM
ejpam-3429	189	8	(	(	PUNCT
ejpam-3429	189	9	[	[	X
ejpam-3429	189	10	3]q	3]q	NUM
ejpam-3429	189	11	−	−	ADP
ejpam-3429	189	12	1)γ3	1)γ3	NUM
ejpam-3429	189	13	+	+	NUM
ejpam-3429	189	14	k22	k22	NOUN
ejpam-3429	189	15	.	.	PUNCT
ejpam-3429	190	1	(	(	PUNCT
ejpam-3429	190	2	19	19	NUM
ejpam-3429	190	3	)	)	PUNCT
ejpam-3429	190	4	on	on	ADP
ejpam-3429	190	5	simplification	simplification	NOUN
ejpam-3429	190	6	,	,	PUNCT
ejpam-3429	190	7	we	we	PRON
ejpam-3429	190	8	get	get	VERB
ejpam-3429	190	9	k.	k.	PROPN
ejpam-3429	190	10	a.	a.	PROPN
ejpam-3429	190	11	reddy	reddy	PROPN
ejpam-3429	190	12	,	,	PUNCT
ejpam-3429	190	13	k.	k.	PROPN
ejpam-3429	190	14	r.	r.	PROPN
ejpam-3429	190	15	karthikeyan	karthikeyan	PROPN
ejpam-3429	190	16	,	,	PUNCT
ejpam-3429	190	17	g.	g.	PROPN
ejpam-3429	190	18	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	190	19	/	/	SYM
ejpam-3429	190	20	eur	eur	PROPN
ejpam-3429	190	21	.	.	PUNCT
ejpam-3429	191	1	j.	j.	PROPN
ejpam-3429	191	2	pure	pure	PROPN
ejpam-3429	191	3	appl	appl	PROPN
ejpam-3429	191	4	.	.	PROPN
ejpam-3429	191	5	math	math	PROPN
ejpam-3429	191	6	,	,	PUNCT
ejpam-3429	191	7	12	12	NUM
ejpam-3429	191	8	(	(	PUNCT
ejpam-3429	191	9	3	3	NUM
ejpam-3429	191	10	)	)	PUNCT
ejpam-3429	191	11	(	(	PUNCT
ejpam-3429	191	12	2019	2019	NUM
ejpam-3429	191	13	)	)	PUNCT
ejpam-3429	191	14	,	,	PUNCT
ejpam-3429	191	15	846	846	NUM
ejpam-3429	191	16	-	-	SYM
ejpam-3429	191	17	856	856	NUM
ejpam-3429	191	18	852	852	NUM
ejpam-3429	191	19	k3	k3	NOUN
ejpam-3429	191	20	=	=	SYM
ejpam-3429	191	21	(	(	PUNCT
ejpam-3429	191	22	c2	c2	PROPN
ejpam-3429	191	23	−	−	PROPN
ejpam-3429	191	24	l2	l2	PROPN
ejpam-3429	191	25	)	)	PUNCT
ejpam-3429	191	26	cosα	cosα	NOUN
ejpam-3429	191	27	2eiα	2eiα	NUM
ejpam-3429	192	1	[	[	X
ejpam-3429	192	2	1−	1−	NUM
ejpam-3429	192	3	λ+	λ+	PUNCT
ejpam-3429	192	4	[	[	X
ejpam-3429	192	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	192	6	(	(	PUNCT
ejpam-3429	192	7	[	[	X
ejpam-3429	192	8	3]q	3]q	NUM
ejpam-3429	192	9	−	−	NOUN
ejpam-3429	192	10	1)γ3	1)γ3	NUM
ejpam-3429	192	11	+	+	NUM
ejpam-3429	192	12	c21	c21	NOUN
ejpam-3429	192	13	cos2	cos2	PROPN
ejpam-3429	192	14	α	α	PROPN
ejpam-3429	192	15	e2iα	e2iα	VERB
ejpam-3429	192	16	[	[	X
ejpam-3429	192	17	1−	1−	NUM
ejpam-3429	192	18	λ+	λ+	PUNCT
ejpam-3429	192	19	(	(	PUNCT
ejpam-3429	192	20	1	1	NUM
ejpam-3429	192	21	+	+	NUM
ejpam-3429	192	22	q)λ]2	q)λ]2	PROPN
ejpam-3429	192	23	m	m	VERB
ejpam-3429	192	24	(	(	PUNCT
ejpam-3429	192	25	q)2	q)2	PROPN
ejpam-3429	192	26	=	=	SYM
ejpam-3429	192	27	(	(	PUNCT
ejpam-3429	192	28	c2	c2	PROPN
ejpam-3429	192	29	−	−	PROPN
ejpam-3429	192	30	l2	l2	PROPN
ejpam-3429	192	31	)	)	PUNCT
ejpam-3429	192	32	cosα	cosα	NOUN
ejpam-3429	192	33	2eiα	2eiα	NUM
ejpam-3429	193	1	[	[	X
ejpam-3429	193	2	1−	1−	NUM
ejpam-3429	193	3	λ+	λ+	PUNCT
ejpam-3429	193	4	[	[	X
ejpam-3429	193	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	193	6	(	(	PUNCT
ejpam-3429	193	7	[	[	X
ejpam-3429	193	8	3]q	3]q	NUM
ejpam-3429	193	9	−	−	ADP
ejpam-3429	193	10	1)γ3	1)γ3	NUM
ejpam-3429	193	11	+	+	CCONJ
ejpam-3429	193	12	(	(	PUNCT
ejpam-3429	193	13	c2	c2	PROPN
ejpam-3429	193	14	+	+	CCONJ
ejpam-3429	193	15	l2	l2	NOUN
ejpam-3429	193	16	)	)	PUNCT
ejpam-3429	193	17	cosα	cosα	NOUN
ejpam-3429	193	18	2eiα[[1−	2eiα[[1−	NUM
ejpam-3429	193	19	λ+	λ+	PUNCT
ejpam-3429	193	20	(	(	PUNCT
ejpam-3429	193	21	1	1	NUM
ejpam-3429	193	22	+	+	NUM
ejpam-3429	193	23	q)λ]2	q)λ]2	PROPN
ejpam-3429	193	24	m	m	VERB
ejpam-3429	193	25	(	(	PUNCT
ejpam-3429	193	26	q)γ22	q)γ22	X
ejpam-3429	193	27	+	+	PUNCT
ejpam-3429	194	1	[	[	X
ejpam-3429	194	2	1−	1−	NUM
ejpam-3429	194	3	λ+	λ+	PUNCT
ejpam-3429	194	4	[	[	X
ejpam-3429	194	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	194	6	(	(	PUNCT
ejpam-3429	194	7	[	[	X
ejpam-3429	194	8	3]q	3]q	NUM
ejpam-3429	194	9	−	−	ADP
ejpam-3429	194	10	1)γ3	1)γ3	NOUN
ejpam-3429	194	11	]	]	X
ejpam-3429	194	12	=	=	PUNCT
ejpam-3429	194	13	cosα	cosα	NOUN
ejpam-3429	194	14	2eiα	2eiα	PROPN
ejpam-3429	194	15	[	[	PUNCT
ejpam-3429	194	16	c2	c2	PROPN
ejpam-3429	194	17	[	[	X
ejpam-3429	194	18	1−	1−	NUM
ejpam-3429	194	19	λ+	λ+	PUNCT
ejpam-3429	194	20	[	[	X
ejpam-3429	194	21	3]qλ]m	3]qλ]m	NUM
ejpam-3429	194	22	(	(	PUNCT
ejpam-3429	194	23	[	[	X
ejpam-3429	194	24	3]q	3]q	NUM
ejpam-3429	194	25	−	−	ADP
ejpam-3429	194	26	1)γ3	1)γ3	NUM
ejpam-3429	194	27	+	+	NUM
ejpam-3429	194	28	c2	c2	PROPN
ejpam-3429	194	29	[	[	X
ejpam-3429	194	30	1−	1−	NUM
ejpam-3429	194	31	λ+	λ+	PUNCT
ejpam-3429	194	32	(	(	PUNCT
ejpam-3429	194	33	1	1	NUM
ejpam-3429	194	34	+	+	NUM
ejpam-3429	194	35	q)λ]2	q)λ]2	PROPN
ejpam-3429	194	36	m	m	VERB
ejpam-3429	194	37	(	(	PUNCT
ejpam-3429	194	38	q)γ2	q)γ2	PROPN
ejpam-3429	194	39	+	+	CCONJ
ejpam-3429	195	1	[	[	X
ejpam-3429	195	2	1−	1−	NUM
ejpam-3429	195	3	λ+	λ+	PUNCT
ejpam-3429	195	4	[	[	X
ejpam-3429	195	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	195	6	(	(	PUNCT
ejpam-3429	195	7	[	[	X
ejpam-3429	195	8	3]q	3]q	NUM
ejpam-3429	195	9	−	−	ADP
ejpam-3429	195	10	1)γ3	1)γ3	NUM
ejpam-3429	195	11	]	]	PUNCT
ejpam-3429	196	1	+	+	CCONJ
ejpam-3429	196	2	cosα	cosα	NOUN
ejpam-3429	196	3	2eiα	2eiα	NOUN
ejpam-3429	196	4	[	[	PUNCT
ejpam-3429	196	5	l2	l2	NOUN
ejpam-3429	196	6	[	[	X
ejpam-3429	196	7	1−	1−	NUM
ejpam-3429	196	8	λ+	λ+	PUNCT
ejpam-3429	196	9	(	(	PUNCT
ejpam-3429	196	10	1	1	NUM
ejpam-3429	196	11	+	+	NUM
ejpam-3429	196	12	q)λ]2	q)λ]2	PROPN
ejpam-3429	196	13	m	m	VERB
ejpam-3429	196	14	(	(	PUNCT
ejpam-3429	196	15	q)γ2	q)γ2	PROPN
ejpam-3429	196	16	+	+	CCONJ
ejpam-3429	197	1	[	[	X
ejpam-3429	197	2	1−	1−	NUM
ejpam-3429	197	3	λ+	λ+	PUNCT
ejpam-3429	197	4	[	[	X
ejpam-3429	197	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	197	6	(	(	PUNCT
ejpam-3429	197	7	[	[	X
ejpam-3429	197	8	3]q	3]q	NUM
ejpam-3429	197	9	−	−	NOUN
ejpam-3429	197	10	1)γ3	1)γ3	NUM
ejpam-3429	197	11	−	−	NOUN
ejpam-3429	197	12	l2	l2	NOUN
ejpam-3429	197	13	[	[	X
ejpam-3429	197	14	1−	1−	NUM
ejpam-3429	197	15	λ+	λ+	PUNCT
ejpam-3429	197	16	[	[	X
ejpam-3429	197	17	3]qλ]m	3]qλ]m	NUM
ejpam-3429	197	18	(	(	PUNCT
ejpam-3429	197	19	1−	1−	NUM
ejpam-3429	198	1	[	[	X
ejpam-3429	198	2	3]q)γ3	3]q)γ3	X
ejpam-3429	198	3	]	]	PUNCT
ejpam-3429	198	4	.	.	PUNCT
ejpam-3429	199	1	on	on	ADP
ejpam-3429	199	2	taking	take	VERB
ejpam-3429	199	3	the	the	DET
ejpam-3429	199	4	modulus	modulus	NOUN
ejpam-3429	199	5	,	,	PUNCT
ejpam-3429	199	6	we	we	PRON
ejpam-3429	199	7	have	have	AUX
ejpam-3429	199	8	|	|	ADV
ejpam-3429	199	9	k3	k3	VERB
ejpam-3429	199	10	|≤	|≤	PROPN
ejpam-3429	199	11	(	(	PUNCT
ejpam-3429	199	12	1−	1−	NUM
ejpam-3429	199	13	ρ	ρ	NOUN
ejpam-3429	199	14	)	)	PUNCT
ejpam-3429	199	15	cosα	cosα	NOUN
ejpam-3429	199	16	[	[	PUNCT
ejpam-3429	199	17	2	2	NUM
ejpam-3429	199	18	[	[	X
ejpam-3429	199	19	1−	1−	NUM
ejpam-3429	199	20	λ+	λ+	PUNCT
ejpam-3429	199	21	(	(	PUNCT
ejpam-3429	199	22	1	1	NUM
ejpam-3429	199	23	+	+	NUM
ejpam-3429	199	24	q)λ]2	q)λ]2	PROPN
ejpam-3429	199	25	m	m	VERB
ejpam-3429	199	26	(	(	PUNCT
ejpam-3429	199	27	q)γ22	q)γ22	X
ejpam-3429	199	28	+	+	PUNCT
ejpam-3429	200	1	[	[	X
ejpam-3429	200	2	1−	1−	NUM
ejpam-3429	200	3	λ+	λ+	PUNCT
ejpam-3429	200	4	[	[	X
ejpam-3429	200	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	200	6	(	(	PUNCT
ejpam-3429	200	7	[	[	X
ejpam-3429	200	8	3]q	3]q	NUM
ejpam-3429	200	9	−	−	ADP
ejpam-3429	200	10	1)γ3	1)γ3	NUM
ejpam-3429	200	11	]	]	PUNCT
ejpam-3429	200	12	.	.	PUNCT
ejpam-3429	201	1	(	(	PUNCT
ejpam-3429	201	2	20	20	NUM
ejpam-3429	201	3	)	)	PUNCT
ejpam-3429	201	4	hence	hence	ADV
ejpam-3429	201	5	the	the	DET
ejpam-3429	201	6	upper	upper	ADJ
ejpam-3429	201	7	bound	bound	NOUN
ejpam-3429	201	8	of	of	ADP
ejpam-3429	201	9	k3	k3	PROPN
ejpam-3429	201	10	.	.	PUNCT
ejpam-3429	202	1	now	now	ADV
ejpam-3429	202	2	we	we	PRON
ejpam-3429	202	3	shall	shall	AUX
ejpam-3429	202	4	we	we	PRON
ejpam-3429	202	5	move	move	VERB
ejpam-3429	202	6	onto	onto	PART
ejpam-3429	202	7	find	find	VERB
ejpam-3429	202	8	the	the	DET
ejpam-3429	202	9	estimate	estimate	NOUN
ejpam-3429	202	10	on	on	ADP
ejpam-3429	202	11	|	|	ADV
ejpam-3429	202	12	k4	k4	ADJ
ejpam-3429	202	13	|	|	ADV
ejpam-3429	202	14	.	.	PUNCT
ejpam-3429	203	1	by	by	ADP
ejpam-3429	203	2	subtracting	subtract	VERB
ejpam-3429	203	3	the	the	DET
ejpam-3429	203	4	equations	equation	NOUN
ejpam-3429	203	5	(	(	PUNCT
ejpam-3429	203	6	14	14	NUM
ejpam-3429	203	7	)	)	PUNCT
ejpam-3429	203	8	and	and	CCONJ
ejpam-3429	203	9	(	(	PUNCT
ejpam-3429	203	10	17	17	NUM
ejpam-3429	203	11	)	)	PUNCT
ejpam-3429	203	12	,	,	PUNCT
ejpam-3429	203	13	we	we	PRON
ejpam-3429	203	14	get	get	VERB
ejpam-3429	203	15	2k4	2k4	NUM
ejpam-3429	203	16	=	=	SYM
ejpam-3429	203	17	e−iα	e−iα	NOUN
ejpam-3429	203	18	cosα(c3	cosα(c3	ADJ
ejpam-3429	203	19	−	−	PROPN
ejpam-3429	203	20	l3	l3	NOUN
ejpam-3429	203	21	)	)	PUNCT
ejpam-3429	204	1	[	[	X
ejpam-3429	204	2	1−	1−	NUM
ejpam-3429	204	3	λ+	λ+	PUNCT
ejpam-3429	204	4	[	[	X
ejpam-3429	204	5	4]qλ]m	4]qλ]m	NUM
ejpam-3429	204	6	(	(	PUNCT
ejpam-3429	204	7	[	[	X
ejpam-3429	204	8	4]q	4]q	X
ejpam-3429	204	9	−	−	ADP
ejpam-3429	204	10	1)γ4	1)γ4	NUM
ejpam-3429	204	11	+	+	SYM
ejpam-3429	204	12	5c1	5c1	NOUN
ejpam-3429	204	13	cosαk3	cosαk3	NOUN
ejpam-3429	204	14	eiα	eiα	NOUN
ejpam-3429	205	1	[	[	X
ejpam-3429	205	2	1−	1−	NUM
ejpam-3429	205	3	λ+	λ+	PUNCT
ejpam-3429	205	4	(	(	PUNCT
ejpam-3429	205	5	1	1	NUM
ejpam-3429	205	6	+	+	NUM
ejpam-3429	205	7	q)λ]m	q)λ]m	PROPN
ejpam-3429	205	8	(	(	PUNCT
ejpam-3429	205	9	q)γ2	q)γ2	PROPN
ejpam-3429	205	10	−	−	PROPN
ejpam-3429	205	11	c31	c31	PROPN
ejpam-3429	205	12	cos3	cos3	PROPN
ejpam-3429	205	13	α	α	PROPN
ejpam-3429	205	14	e3iα	e3iα	PUNCT
ejpam-3429	206	1	[	[	X
ejpam-3429	206	2	1−	1−	NUM
ejpam-3429	206	3	λ+	λ+	PUNCT
ejpam-3429	206	4	(	(	PUNCT
ejpam-3429	206	5	1	1	NUM
ejpam-3429	206	6	+	+	NUM
ejpam-3429	206	7	q)λ]3	q)λ]3	ADJ
ejpam-3429	206	8	m	m	VERB
ejpam-3429	206	9	(	(	PUNCT
ejpam-3429	206	10	q)3γ32	q)3γ32	PROPN
ejpam-3429	206	11	[	[	PUNCT
ejpam-3429	206	12	2	2	NUM
ejpam-3429	206	13	[	[	X
ejpam-3429	206	14	1−	1−	NUM
ejpam-3429	206	15	λ+	λ+	PUNCT
ejpam-3429	206	16	(	(	PUNCT
ejpam-3429	206	17	1	1	NUM
ejpam-3429	206	18	+	+	NUM
ejpam-3429	206	19	q)λ]m	q)λ]m	NOUN
ejpam-3429	207	1	[	[	X
ejpam-3429	207	2	1−	1−	NUM
ejpam-3429	207	3	λ+	λ+	PUNCT
ejpam-3429	207	4	[	[	X
ejpam-3429	207	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	207	6	γ2γ3((1	γ2γ3((1	NUM
ejpam-3429	207	7	+	+	CCONJ
ejpam-3429	207	8	q	q	X
ejpam-3429	207	9	)	)	PUNCT
ejpam-3429	207	10	+	+	CCONJ
ejpam-3429	208	1	[	[	X
ejpam-3429	208	2	3]q	3]q	NUM
ejpam-3429	208	3	)	)	PUNCT
ejpam-3429	209	1	[	[	X
ejpam-3429	209	2	1−	1−	NUM
ejpam-3429	209	3	λ+	λ+	PUNCT
ejpam-3429	209	4	[	[	X
ejpam-3429	209	5	4]qλ]m	4]qλ]m	NUM
ejpam-3429	209	6	(	(	PUNCT
ejpam-3429	209	7	[	[	X
ejpam-3429	209	8	4]q	4]q	X
ejpam-3429	209	9	−	−	ADP
ejpam-3429	209	10	1)γ4	1)γ4	NUM
ejpam-3429	209	11	+	+	CCONJ
ejpam-3429	209	12	5	5	NUM
ejpam-3429	209	13	]	]	PUNCT
ejpam-3429	209	14	.	.	PUNCT
ejpam-3429	210	1	|	|	ADV
ejpam-3429	210	2	k4	k4	VERB
ejpam-3429	210	3	|≤	|≤	PROPN
ejpam-3429	210	4	2(1−	2(1−	NUM
ejpam-3429	210	5	ρ	ρ	PROPN
ejpam-3429	210	6	)	)	PUNCT
ejpam-3429	210	7	cosα	cosα	NOUN
ejpam-3429	211	1	[	[	X
ejpam-3429	211	2	1−	1−	NUM
ejpam-3429	211	3	λ+	λ+	PUNCT
ejpam-3429	211	4	[	[	X
ejpam-3429	211	5	4]qλ]m	4]qλ]m	NUM
ejpam-3429	211	6	(	(	PUNCT
ejpam-3429	211	7	[	[	X
ejpam-3429	211	8	4]q	4]q	X
ejpam-3429	211	9	−	−	ADP
ejpam-3429	211	10	1)γ4	1)γ4	NUM
ejpam-3429	211	11	+	+	CCONJ
ejpam-3429	211	12	10	10	NUM
ejpam-3429	211	13	√	√	NUM
ejpam-3429	211	14	2[(1−	2[(1−	NUM
ejpam-3429	211	15	ρ	ρ	NOUN
ejpam-3429	211	16	)	)	PUNCT
ejpam-3429	211	17	cosα	cosα	NOUN
ejpam-3429	211	18	]	]	X
ejpam-3429	211	19	3	3	NUM
ejpam-3429	211	20	2	2	NUM
ejpam-3429	212	1	[	[	X
ejpam-3429	212	2	[	[	X
ejpam-3429	212	3	1−	1−	NUM
ejpam-3429	212	4	λ+	λ+	PUNCT
ejpam-3429	212	5	(	(	PUNCT
ejpam-3429	212	6	1	1	NUM
ejpam-3429	212	7	+	+	NUM
ejpam-3429	212	8	q)λ]2	q)λ]2	PROPN
ejpam-3429	212	9	m	m	VERB
ejpam-3429	212	10	(	(	PUNCT
ejpam-3429	212	11	q)γ22	q)γ22	X
ejpam-3429	212	12	+	+	PUNCT
ejpam-3429	213	1	[	[	X
ejpam-3429	213	2	1−	1−	NUM
ejpam-3429	213	3	λ+	λ+	PUNCT
ejpam-3429	213	4	[	[	X
ejpam-3429	213	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	213	6	(	(	PUNCT
ejpam-3429	213	7	[	[	X
ejpam-3429	213	8	3]q	3]q	NUM
ejpam-3429	213	9	−	−	ADP
ejpam-3429	213	10	1)γ3	1)γ3	NOUN
ejpam-3429	213	11	]	]	SYM
ejpam-3429	213	12	3	3	NUM
ejpam-3429	213	13	2	2	NUM
ejpam-3429	213	14	+	+	CCONJ
ejpam-3429	213	15	2	2	NUM
ejpam-3429	213	16	√	√	NUM
ejpam-3429	213	17	2[(1−	2[(1−	NUM
ejpam-3429	213	18	ρ	ρ	NOUN
ejpam-3429	213	19	)	)	PUNCT
ejpam-3429	213	20	cosα	cosα	NOUN
ejpam-3429	213	21	]	]	X
ejpam-3429	213	22	3	3	NUM
ejpam-3429	213	23	2	2	NUM
ejpam-3429	214	1	[	[	X
ejpam-3429	214	2	[	[	X
ejpam-3429	214	3	1−	1−	NUM
ejpam-3429	214	4	λ+	λ+	PUNCT
ejpam-3429	214	5	(	(	PUNCT
ejpam-3429	214	6	1	1	NUM
ejpam-3429	214	7	+	+	NUM
ejpam-3429	214	8	q)λ]2	q)λ]2	PROPN
ejpam-3429	214	9	m	m	VERB
ejpam-3429	214	10	(	(	PUNCT
ejpam-3429	214	11	q)γ22	q)γ22	X
ejpam-3429	214	12	+	+	PUNCT
ejpam-3429	215	1	[	[	X
ejpam-3429	215	2	1−	1−	NUM
ejpam-3429	215	3	λ+	λ+	PUNCT
ejpam-3429	215	4	[	[	X
ejpam-3429	215	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	215	6	(	(	PUNCT
ejpam-3429	215	7	[	[	X
ejpam-3429	215	8	3]q	3]q	NUM
ejpam-3429	215	9	−	−	ADP
ejpam-3429	215	10	1)γ3	1)γ3	NOUN
ejpam-3429	215	11	]	]	SYM
ejpam-3429	215	12	3	3	NUM
ejpam-3429	215	13	2	2	NUM
ejpam-3429	215	14	[	[	SYM
ejpam-3429	215	15	2	2	NUM
ejpam-3429	215	16	[	[	X
ejpam-3429	215	17	1−	1−	NUM
ejpam-3429	215	18	λ+	λ+	PUNCT
ejpam-3429	215	19	(	(	PUNCT
ejpam-3429	215	20	1	1	NUM
ejpam-3429	215	21	+	+	NUM
ejpam-3429	215	22	q)λ]m	q)λ]m	NOUN
ejpam-3429	216	1	[	[	X
ejpam-3429	216	2	1−	1−	NUM
ejpam-3429	216	3	λ+	λ+	PUNCT
ejpam-3429	216	4	[	[	X
ejpam-3429	216	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	216	6	γ2γ3(1	γ2γ3(1	VERB
ejpam-3429	216	7	+	+	NOUN
ejpam-3429	216	8	q	q	PUNCT
ejpam-3429	217	1	+	+	NUM
ejpam-3429	218	1	[	[	X
ejpam-3429	218	2	3]q	3]q	NUM
ejpam-3429	218	3	)	)	PUNCT
ejpam-3429	219	1	[	[	X
ejpam-3429	219	2	1−	1−	NUM
ejpam-3429	219	3	λ+	λ+	PUNCT
ejpam-3429	219	4	[	[	X
ejpam-3429	219	5	4]qλ]m	4]qλ]m	NUM
ejpam-3429	219	6	(	(	PUNCT
ejpam-3429	219	7	[	[	X
ejpam-3429	219	8	4]q	4]q	X
ejpam-3429	219	9	−	−	ADP
ejpam-3429	219	10	1)γ4	1)γ4	NUM
ejpam-3429	219	11	+	+	CCONJ
ejpam-3429	219	12	5	5	NUM
ejpam-3429	219	13	]	]	PUNCT
ejpam-3429	219	14	.	.	PUNCT
ejpam-3429	220	1	this	this	PRON
ejpam-3429	220	2	completes	complete	VERB
ejpam-3429	220	3	the	the	DET
ejpam-3429	220	4	proof	proof	NOUN
ejpam-3429	220	5	of	of	ADP
ejpam-3429	220	6	the	the	DET
ejpam-3429	220	7	theorem	theorem	NOUN
ejpam-3429	220	8	1	1	NUM
ejpam-3429	220	9	.	.	PUNCT
ejpam-3429	220	10	k.	k.	PROPN
ejpam-3429	220	11	a.	a.	PROPN
ejpam-3429	220	12	reddy	reddy	PROPN
ejpam-3429	220	13	,	,	PUNCT
ejpam-3429	220	14	k.	k.	PROPN
ejpam-3429	220	15	r.	r.	PROPN
ejpam-3429	220	16	karthikeyan	karthikeyan	PROPN
ejpam-3429	220	17	,	,	PUNCT
ejpam-3429	220	18	g.	g.	PROPN
ejpam-3429	220	19	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	220	20	/	/	SYM
ejpam-3429	220	21	eur	eur	PROPN
ejpam-3429	220	22	.	.	PUNCT
ejpam-3429	221	1	j.	j.	PROPN
ejpam-3429	221	2	pure	pure	PROPN
ejpam-3429	221	3	appl	appl	PROPN
ejpam-3429	221	4	.	.	PROPN
ejpam-3429	221	5	math	math	PROPN
ejpam-3429	221	6	,	,	PUNCT
ejpam-3429	221	7	12	12	NUM
ejpam-3429	221	8	(	(	PUNCT
ejpam-3429	221	9	3	3	NUM
ejpam-3429	221	10	)	)	PUNCT
ejpam-3429	221	11	(	(	PUNCT
ejpam-3429	221	12	2019	2019	NUM
ejpam-3429	221	13	)	)	PUNCT
ejpam-3429	221	14	,	,	PUNCT
ejpam-3429	221	15	846	846	NUM
ejpam-3429	221	16	-	-	SYM
ejpam-3429	221	17	856	856	NUM
ejpam-3429	221	18	853	853	NUM
ejpam-3429	221	19	theorem	theorem	NOUN
ejpam-3429	221	20	2	2	NUM
ejpam-3429	221	21	.	.	PUNCT
ejpam-3429	222	1	let	let	VERB
ejpam-3429	222	2	f(z	f(z	NOUN
ejpam-3429	222	3	)	)	PUNCT
ejpam-3429	222	4	,	,	PUNCT
ejpam-3429	222	5	given	give	VERB
ejpam-3429	222	6	by	by	ADP
ejpam-3429	222	7	(	(	PUNCT
ejpam-3429	222	8	3	3	NUM
ejpam-3429	222	9	)	)	PUNCT
ejpam-3429	222	10	,	,	PUNCT
ejpam-3429	222	11	be	be	AUX
ejpam-3429	222	12	in	in	ADP
ejpam-3429	222	13	the	the	DET
ejpam-3429	222	14	class	class	NOUN
ejpam-3429	223	1	α	α	NOUN
ejpam-3429	223	2	−	−	PROPN
ejpam-3429	223	3	sp∗(β	sp∗(β	NOUN
ejpam-3429	223	4	,	,	PUNCT
ejpam-3429	223	5	a	a	DET
ejpam-3429	223	6	,	,	PUNCT
ejpam-3429	223	7	b	b	NOUN
ejpam-3429	223	8	;	;	PUNCT
ejpam-3429	223	9	q	q	ADJ
ejpam-3429	223	10	,	,	PUNCT
ejpam-3429	223	11	z	z	NOUN
ejpam-3429	223	12	)	)	PUNCT
ejpam-3429	223	13	(	(	PUNCT
ejpam-3429	223	14	|	|	ADV
ejpam-3429	223	15	α	α	PRON
ejpam-3429	223	16	|≤	|≤	PROPN
ejpam-3429	223	17	π	π	PROPN
ejpam-3429	223	18	2	2	NUM
ejpam-3429	223	19	,	,	PUNCT
ejpam-3429	223	20	0	0	NUM
ejpam-3429	223	21	≤	≤	NUM
ejpam-3429	224	1	β	β	X
ejpam-3429	224	2	<	<	X
ejpam-3429	224	3	1	1	NUM
ejpam-3429	224	4	)	)	PUNCT
ejpam-3429	224	5	.	.	PUNCT
ejpam-3429	225	1	then	then	ADV
ejpam-3429	225	2	|	|	ADV
ejpam-3429	225	3	k2	k2	ADJ
ejpam-3429	225	4	|≤	|≤	PROPN
ejpam-3429	225	5	β	β	SYM
ejpam-3429	225	6	√	√	NUM
ejpam-3429	225	7	2	2	NUM
ejpam-3429	225	8	cos(αβ	cos(αβ	NOUN
ejpam-3429	225	9	)	)	PUNCT
ejpam-3429	225	10	q	q	PUNCT
ejpam-3429	226	1	[	[	X
ejpam-3429	226	2	1−	1−	NUM
ejpam-3429	226	3	λ+	λ+	PUNCT
ejpam-3429	226	4	(	(	PUNCT
ejpam-3429	226	5	1	1	NUM
ejpam-3429	226	6	+	+	NUM
ejpam-3429	226	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	226	8	|	|	ADV
ejpam-3429	226	9	γ2	γ2	NOUN
ejpam-3429	226	10	|	|	ADV
ejpam-3429	226	11	√	√	PROPN
ejpam-3429	227	1	[	[	X
ejpam-3429	227	2	1−	1−	NUM
ejpam-3429	227	3	λ+	λ+	PUNCT
ejpam-3429	227	4	[	[	X
ejpam-3429	227	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	227	6	(	(	PUNCT
ejpam-3429	227	7	[	[	X
ejpam-3429	227	8	3]q	3]q	NUM
ejpam-3429	227	9	−	−	NOUN
ejpam-3429	227	10	1)γ3	1)γ3	NUM
ejpam-3429	227	11	cos(αβ	cos(αβ	NOUN
ejpam-3429	227	12	)	)	PUNCT
ejpam-3429	227	13	δ	δ	NOUN
ejpam-3429	227	14	and	and	CCONJ
ejpam-3429	227	15	|	|	ADV
ejpam-3429	227	16	k3	k3	VERB
ejpam-3429	227	17	|≤	|≤	ADJ
ejpam-3429	227	18	2β	2β	NOUN
ejpam-3429	227	19	cos(αβ	cos(αβ	NOUN
ejpam-3429	227	20	)	)	PUNCT
ejpam-3429	228	1	[	[	X
ejpam-3429	228	2	1−	1−	NUM
ejpam-3429	228	3	λ+	λ+	PUNCT
ejpam-3429	228	4	[	[	X
ejpam-3429	228	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	228	6	(	(	PUNCT
ejpam-3429	228	7	[	[	X
ejpam-3429	228	8	3]q	3]q	NUM
ejpam-3429	228	9	−	−	NOUN
ejpam-3429	228	10	1)γ3	1)γ3	NUM
ejpam-3429	228	11	[	[	PUNCT
ejpam-3429	228	12	β	β	X
ejpam-3429	228	13	q2	q2	NOUN
ejpam-3429	229	1	[	[	X
ejpam-3429	229	2	1−	1−	NUM
ejpam-3429	229	3	λ+	λ+	PUNCT
ejpam-3429	229	4	(	(	PUNCT
ejpam-3429	229	5	1	1	NUM
ejpam-3429	229	6	+	+	NUM
ejpam-3429	229	7	q)λ]2	q)λ]2	ADV
ejpam-3429	229	8	m	m	AUX
ejpam-3429	229	9	γ22δ	γ22δ	VERB
ejpam-3429	229	10	−	−	PROPN
ejpam-3429	229	11	1	1	NUM
ejpam-3429	229	12	]	]	PUNCT
ejpam-3429	229	13	where	where	SCONJ
ejpam-3429	229	14	δ	δ	X
ejpam-3429	229	15	=	=	PUNCT
ejpam-3429	229	16	β	β	X
ejpam-3429	229	17	q2	q2	NOUN
ejpam-3429	229	18	[	[	X
ejpam-3429	229	19	1−	1−	NUM
ejpam-3429	229	20	λ+	λ+	PUNCT
ejpam-3429	229	21	(	(	PUNCT
ejpam-3429	229	22	1	1	NUM
ejpam-3429	229	23	+	+	NUM
ejpam-3429	229	24	q)λ]2	q)λ]2	PROPN
ejpam-3429	229	25	m	m	VERB
ejpam-3429	229	26	γ22	γ22	NOUN
ejpam-3429	230	1	−	−	PROPN
ejpam-3429	230	2	[	[	PUNCT
ejpam-3429	230	3	1	1	NUM
ejpam-3429	230	4	+	+	CCONJ
ejpam-3429	230	5	β−1	β−1	SYM
ejpam-3429	230	6	2	2	NUM
ejpam-3429	230	7	(	(	PUNCT
ejpam-3429	230	8	q	q	NOUN
ejpam-3429	230	9	+	+	NUM
ejpam-3429	230	10	2	2	NUM
ejpam-3429	230	11	)	)	PUNCT
ejpam-3429	230	12	]	]	PUNCT
ejpam-3429	230	13	q	q	X
ejpam-3429	231	1	[	[	X
ejpam-3429	231	2	1−	1−	NUM
ejpam-3429	231	3	λ+	λ+	PUNCT
ejpam-3429	231	4	[	[	X
ejpam-3429	231	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	231	6	(	(	PUNCT
ejpam-3429	231	7	[	[	X
ejpam-3429	231	8	3]q	3]q	NUM
ejpam-3429	231	9	−	−	PROPN
ejpam-3429	231	10	1)γ3	1)γ3	NUM
ejpam-3429	231	11	.	.	PUNCT
ejpam-3429	232	1	proof	proof	NOUN
ejpam-3429	232	2	.	.	PUNCT
ejpam-3429	233	1	from	from	ADP
ejpam-3429	233	2	definition	definition	NOUN
ejpam-3429	233	3	1	1	NUM
ejpam-3429	233	4	,	,	PUNCT
ejpam-3429	233	5	we	we	PRON
ejpam-3429	233	6	have	have	VERB
ejpam-3429	233	7	dq(j	dq(j	NOUN
ejpam-3429	233	8	m	m	VERB
ejpam-3429	233	9	λ	λ	NOUN
ejpam-3429	233	10	(	(	PUNCT
ejpam-3429	233	11	a1	a1	PROPN
ejpam-3429	233	12	,	,	PUNCT
ejpam-3429	233	13	b1	b1	NOUN
ejpam-3429	233	14	;	;	PUNCT
ejpam-3429	233	15	q	q	ADJ
ejpam-3429	233	16	,	,	PUNCT
ejpam-3429	233	17	z)f	z)f	X
ejpam-3429	233	18	)	)	PUNCT
ejpam-3429	234	1	=	=	SYM
ejpam-3429	234	2	jmλ	jmλ	PROPN
ejpam-3429	234	3	(	(	PUNCT
ejpam-3429	234	4	a1	a1	PROPN
ejpam-3429	234	5	,	,	PUNCT
ejpam-3429	234	6	b1	b1	NOUN
ejpam-3429	234	7	;	;	PUNCT
ejpam-3429	234	8	q	q	ADJ
ejpam-3429	234	9	,	,	PUNCT
ejpam-3429	234	10	z)f	z)f	X
ejpam-3429	234	11	z	z	NOUN
ejpam-3429	234	12	e−iαh(z	e−iαh(z	NUM
ejpam-3429	234	13	)	)	PUNCT
ejpam-3429	234	14	(	(	PUNCT
ejpam-3429	234	15	21	21	NUM
ejpam-3429	234	16	)	)	PUNCT
ejpam-3429	234	17	where	where	SCONJ
ejpam-3429	234	18	h(z	h(z	NOUN
ejpam-3429	234	19	)	)	PUNCT
ejpam-3429	234	20	is	be	AUX
ejpam-3429	234	21	analytic	analytic	ADJ
ejpam-3429	234	22	in	in	ADP
ejpam-3429	234	23	u	u	NOUN
ejpam-3429	234	24	and	and	CCONJ
ejpam-3429	234	25	satisfies	satisfy	VERB
ejpam-3429	234	26	h(0	h(0	PROPN
ejpam-3429	234	27	)	)	PUNCT
ejpam-3429	234	28	=	=	SYM
ejpam-3429	234	29	eiα	eiα	NOUN
ejpam-3429	234	30	and	and	CCONJ
ejpam-3429	234	31	|	|	ADV
ejpam-3429	234	32	arg	arg	VERB
ejpam-3429	234	33	h(z	h(z	NOUN
ejpam-3429	234	34	)	)	PUNCT
ejpam-3429	234	35	|	|	ADV
ejpam-3429	234	36	<	<	X
ejpam-3429	234	37	βπ/2	βπ/2	X
ejpam-3429	234	38	(	(	PUNCT
ejpam-3429	234	39	z	z	NOUN
ejpam-3429	234	40	∈	∈	PROPN
ejpam-3429	234	41	u	u	NOUN
ejpam-3429	234	42	)	)	PUNCT
ejpam-3429	234	43	.	.	PUNCT
ejpam-3429	235	1	it	it	PRON
ejpam-3429	235	2	can	can	AUX
ejpam-3429	235	3	be	be	AUX
ejpam-3429	235	4	checked	check	VERB
ejpam-3429	235	5	that	that	SCONJ
ejpam-3429	235	6	the	the	DET
ejpam-3429	235	7	function	function	NOUN
ejpam-3429	235	8	q(z	q(z	PROPN
ejpam-3429	235	9	)	)	PUNCT
ejpam-3429	235	10	defined	define	VERB
ejpam-3429	235	11	by	by	ADP
ejpam-3429	235	12	h(z	h(z	NOUN
ejpam-3429	235	13	)	)	PUNCT
ejpam-3429	235	14	1	1	NUM
ejpam-3429	235	15	β	β	X
ejpam-3429	235	16	=	=	PUNCT
ejpam-3429	235	17	cos	cos	PROPN
ejpam-3429	235	18	(	(	PUNCT
ejpam-3429	235	19	α	α	X
ejpam-3429	235	20	β	β	NOUN
ejpam-3429	235	21	)	)	PUNCT
ejpam-3429	235	22	q(z	q(z	PROPN
ejpam-3429	235	23	)	)	PUNCT
ejpam-3429	235	24	+	+	CCONJ
ejpam-3429	235	25	i	i	PRON
ejpam-3429	235	26	sin	sin	VERB
ejpam-3429	235	27	(	(	PUNCT
ejpam-3429	235	28	α	α	NOUN
ejpam-3429	235	29	β	β	NOUN
ejpam-3429	235	30	)	)	PUNCT
ejpam-3429	235	31	(	(	PUNCT
ejpam-3429	235	32	z	z	NOUN
ejpam-3429	235	33	∈	∈	PROPN
ejpam-3429	235	34	u	u	NOUN
ejpam-3429	235	35	)	)	PUNCT
ejpam-3429	235	36	is	be	AUX
ejpam-3429	235	37	a	a	DET
ejpam-3429	235	38	member	member	NOUN
ejpam-3429	235	39	of	of	ADP
ejpam-3429	235	40	the	the	DET
ejpam-3429	235	41	class	class	NOUN
ejpam-3429	235	42	p.	p.	NOUN
ejpam-3429	235	43	suppose	suppose	VERB
ejpam-3429	235	44	that	that	SCONJ
ejpam-3429	235	45	q(z	q(z	PROPN
ejpam-3429	235	46	)	)	PUNCT
ejpam-3429	235	47	=	=	SYM
ejpam-3429	236	1	1	1	NUM
ejpam-3429	236	2	+	+	CCONJ
ejpam-3429	237	1	c1z	c1z	PROPN
ejpam-3429	238	1	+	+	PUNCT
ejpam-3429	238	2	c2z	c2z	PROPN
ejpam-3429	238	3	2	2	NUM
ejpam-3429	238	4	+	+	CCONJ
ejpam-3429	238	5	.	.	PUNCT
ejpam-3429	238	6	.	.	PUNCT
ejpam-3429	238	7	.	.	PUNCT
ejpam-3429	239	1	.	.	PUNCT
ejpam-3429	240	1	(	(	PUNCT
ejpam-3429	240	2	z	z	NOUN
ejpam-3429	240	3	∈	∈	PROPN
ejpam-3429	240	4	u	u	NOUN
ejpam-3429	240	5	)	)	PUNCT
ejpam-3429	240	6	.	.	PUNCT
ejpam-3429	241	1	by	by	ADP
ejpam-3429	241	2	comparing	compare	VERB
ejpam-3429	241	3	coefficients	coefficient	NOUN
ejpam-3429	241	4	in	in	ADP
ejpam-3429	241	5	(	(	PUNCT
ejpam-3429	241	6	21	21	NUM
ejpam-3429	241	7	)	)	PUNCT
ejpam-3429	241	8	,	,	PUNCT
ejpam-3429	241	9	we	we	PRON
ejpam-3429	241	10	have	have	VERB
ejpam-3429	241	11	k2	k2	ADJ
ejpam-3429	241	12	=	=	SYM
ejpam-3429	241	13	βc1e	βc1e	PROPN
ejpam-3429	241	14	−i(α	−i(α	PROPN
ejpam-3429	241	15	β	β	X
ejpam-3429	241	16	)	)	PUNCT
ejpam-3429	241	17	cos(αβ	cos(αβ	NOUN
ejpam-3429	241	18	)	)	PUNCT
ejpam-3429	241	19	q	q	PUNCT
ejpam-3429	242	1	[	[	X
ejpam-3429	242	2	1−	1−	NUM
ejpam-3429	242	3	λ+	λ+	PUNCT
ejpam-3429	242	4	(	(	PUNCT
ejpam-3429	242	5	1	1	NUM
ejpam-3429	242	6	+	+	NUM
ejpam-3429	242	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	242	8	γ2	γ2	NOUN
ejpam-3429	242	9	(	(	PUNCT
ejpam-3429	242	10	22	22	NUM
ejpam-3429	242	11	)	)	PUNCT
ejpam-3429	242	12	and	and	CCONJ
ejpam-3429	242	13	k3	k3	X
ejpam-3429	242	14	=	=	PUNCT
ejpam-3429	242	15	βc2e	βc2e	PROPN
ejpam-3429	242	16	−i(α	−i(α	PROPN
ejpam-3429	242	17	β	β	X
ejpam-3429	242	18	)	)	PUNCT
ejpam-3429	242	19	cos(αβ	cos(αβ	NOUN
ejpam-3429	242	20	)	)	PUNCT
ejpam-3429	243	1	+	+	CCONJ
ejpam-3429	243	2	β	β	X
ejpam-3429	243	3	q	q	X
ejpam-3429	243	4	c	c	NOUN
ejpam-3429	243	5	2	2	NUM
ejpam-3429	243	6	1e	1e	NOUN
ejpam-3429	243	7	−2i(α	−2i(α	PROPN
ejpam-3429	243	8	β	β	X
ejpam-3429	243	9	)	)	PUNCT
ejpam-3429	243	10	cos2(αβ	cos2(αβ	NOUN
ejpam-3429	243	11	)	)	PUNCT
ejpam-3429	244	1	[	[	PUNCT
ejpam-3429	244	2	1	1	NUM
ejpam-3429	244	3	+	+	CCONJ
ejpam-3429	244	4	β−1	β−1	SYM
ejpam-3429	244	5	2	2	NUM
ejpam-3429	244	6	(	(	PUNCT
ejpam-3429	244	7	q	q	NOUN
ejpam-3429	244	8	+	+	NUM
ejpam-3429	244	9	2	2	NUM
ejpam-3429	244	10	)	)	PUNCT
ejpam-3429	244	11	]	]	PUNCT
ejpam-3429	245	1	[	[	X
ejpam-3429	245	2	1−	1−	NUM
ejpam-3429	245	3	λ+	λ+	PUNCT
ejpam-3429	245	4	[	[	X
ejpam-3429	245	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	245	6	(	(	PUNCT
ejpam-3429	245	7	[	[	X
ejpam-3429	245	8	3]q	3]q	NUM
ejpam-3429	245	9	−	−	PROPN
ejpam-3429	245	10	1)γ3	1)γ3	NUM
ejpam-3429	245	11	.	.	PUNCT
ejpam-3429	246	1	(	(	PUNCT
ejpam-3429	246	2	23	23	NUM
ejpam-3429	246	3	)	)	PUNCT
ejpam-3429	246	4	similarly	similarly	ADV
ejpam-3429	246	5	,	,	PUNCT
ejpam-3429	246	6	we	we	PRON
ejpam-3429	246	7	take	take	VERB
ejpam-3429	246	8	dq(j	dq(j	NOUN
ejpam-3429	246	9	m	m	VERB
ejpam-3429	246	10	λ	λ	NOUN
ejpam-3429	246	11	(	(	PUNCT
ejpam-3429	246	12	a1	a1	PROPN
ejpam-3429	246	13	,	,	PUNCT
ejpam-3429	246	14	b1	b1	NOUN
ejpam-3429	246	15	;	;	PUNCT
ejpam-3429	246	16	q	q	NOUN
ejpam-3429	246	17	,	,	PUNCT
ejpam-3429	246	18	w)f	w)f	ADJ
ejpam-3429	246	19	)	)	PUNCT
ejpam-3429	246	20	=	=	SYM
ejpam-3429	246	21	jmλ	jmλ	PROPN
ejpam-3429	246	22	(	(	PUNCT
ejpam-3429	246	23	a1	a1	PROPN
ejpam-3429	246	24	,	,	PUNCT
ejpam-3429	246	25	b1	b1	NOUN
ejpam-3429	246	26	;	;	PUNCT
ejpam-3429	246	27	q	q	X
ejpam-3429	246	28	,	,	PUNCT
ejpam-3429	246	29	w)f	w)f	X
ejpam-3429	246	30	w	w	ADP
ejpam-3429	246	31	e−iαh(w	e−iαh(w	NUM
ejpam-3429	246	32	)	)	PUNCT
ejpam-3429	246	33	,	,	PUNCT
ejpam-3429	246	34	(	(	PUNCT
ejpam-3429	246	35	24	24	NUM
ejpam-3429	246	36	)	)	PUNCT
ejpam-3429	246	37	k.	k.	PROPN
ejpam-3429	246	38	a.	a.	PROPN
ejpam-3429	246	39	reddy	reddy	PROPN
ejpam-3429	246	40	,	,	PUNCT
ejpam-3429	246	41	k.	k.	PROPN
ejpam-3429	246	42	r.	r.	PROPN
ejpam-3429	246	43	karthikeyan	karthikeyan	PROPN
ejpam-3429	246	44	,	,	PUNCT
ejpam-3429	246	45	g.	g.	PROPN
ejpam-3429	246	46	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-3429	246	47	/	/	SYM
ejpam-3429	246	48	eur	eur	PROPN
ejpam-3429	246	49	.	.	PUNCT
ejpam-3429	247	1	j.	j.	PROPN
ejpam-3429	247	2	pure	pure	PROPN
ejpam-3429	247	3	appl	appl	PROPN
ejpam-3429	247	4	.	.	PROPN
ejpam-3429	247	5	math	math	PROPN
ejpam-3429	247	6	,	,	PUNCT
ejpam-3429	247	7	12	12	NUM
ejpam-3429	247	8	(	(	PUNCT
ejpam-3429	247	9	3	3	NUM
ejpam-3429	247	10	)	)	PUNCT
ejpam-3429	247	11	(	(	PUNCT
ejpam-3429	247	12	2019	2019	NUM
ejpam-3429	247	13	)	)	PUNCT
ejpam-3429	247	14	,	,	PUNCT
ejpam-3429	247	15	846	846	NUM
ejpam-3429	247	16	-	-	SYM
ejpam-3429	247	17	856	856	NUM
ejpam-3429	247	18	854	854	NUM
ejpam-3429	247	19	where	where	SCONJ
ejpam-3429	247	20	h(w	h(w	PROPN
ejpam-3429	247	21	)	)	PUNCT
ejpam-3429	247	22	is	be	AUX
ejpam-3429	247	23	analytic	analytic	ADJ
ejpam-3429	247	24	in	in	ADP
ejpam-3429	247	25	u	u	NOUN
ejpam-3429	247	26	and	and	CCONJ
ejpam-3429	247	27	satisfies	satisfy	VERB
ejpam-3429	247	28	h(0	h(0	PROPN
ejpam-3429	247	29	)	)	PUNCT
ejpam-3429	247	30	=	=	SYM
ejpam-3429	247	31	eiα	eiα	NOUN
ejpam-3429	247	32	and	and	CCONJ
ejpam-3429	247	33	|	|	ADV
ejpam-3429	247	34	arg	arg	NOUN
ejpam-3429	247	35	h(w	h(w	NOUN
ejpam-3429	247	36	)	)	PUNCT
ejpam-3429	247	37	|	|	ADV
ejpam-3429	247	38	<	<	X
ejpam-3429	247	39	βπ/2	βπ/2	X
ejpam-3429	247	40	(	(	PUNCT
ejpam-3429	247	41	w	w	PROPN
ejpam-3429	247	42	∈	∈	PROPN
ejpam-3429	247	43	u	u	NOUN
ejpam-3429	247	44	)	)	PUNCT
ejpam-3429	247	45	.	.	PUNCT
ejpam-3429	248	1	it	it	PRON
ejpam-3429	248	2	can	can	AUX
ejpam-3429	248	3	be	be	AUX
ejpam-3429	248	4	checked	check	VERB
ejpam-3429	248	5	that	that	SCONJ
ejpam-3429	248	6	the	the	DET
ejpam-3429	248	7	function	function	NOUN
ejpam-3429	248	8	p(w	p(w	PROPN
ejpam-3429	248	9	)	)	PUNCT
ejpam-3429	248	10	defined	define	VERB
ejpam-3429	248	11	by	by	ADP
ejpam-3429	248	12	:	:	PUNCT
ejpam-3429	248	13	h(w	h(w	PROPN
ejpam-3429	248	14	)	)	PUNCT
ejpam-3429	248	15	1	1	NUM
ejpam-3429	248	16	β	β	X
ejpam-3429	248	17	=	=	PUNCT
ejpam-3429	248	18	cos	cos	PROPN
ejpam-3429	248	19	(	(	PUNCT
ejpam-3429	248	20	α	α	NOUN
ejpam-3429	248	21	β	β	NOUN
ejpam-3429	248	22	)	)	PUNCT
ejpam-3429	248	23	p(w	p(w	PROPN
ejpam-3429	248	24	)	)	PUNCT
ejpam-3429	249	1	+	+	CCONJ
ejpam-3429	249	2	i	i	PRON
ejpam-3429	249	3	sin	sin	VERB
ejpam-3429	249	4	(	(	PUNCT
ejpam-3429	249	5	α	α	NOUN
ejpam-3429	249	6	β	β	NOUN
ejpam-3429	249	7	)	)	PUNCT
ejpam-3429	249	8	(	(	PUNCT
ejpam-3429	249	9	w	w	PROPN
ejpam-3429	249	10	∈	∈	PROPN
ejpam-3429	249	11	u	u	NOUN
ejpam-3429	249	12	)	)	PUNCT
ejpam-3429	249	13	is	be	AUX
ejpam-3429	249	14	a	a	DET
ejpam-3429	249	15	member	member	NOUN
ejpam-3429	249	16	of	of	ADP
ejpam-3429	249	17	the	the	DET
ejpam-3429	249	18	class	class	NOUN
ejpam-3429	249	19	p.	p.	NOUN
ejpam-3429	249	20	if	if	SCONJ
ejpam-3429	249	21	p(w	p(w	NOUN
ejpam-3429	249	22	)	)	PUNCT
ejpam-3429	249	23	=	=	PUNCT
ejpam-3429	250	1	1	1	NUM
ejpam-3429	250	2	+	+	CCONJ
ejpam-3429	250	3	l1w	l1w	NOUN
ejpam-3429	250	4	+	+	CCONJ
ejpam-3429	250	5	l2w	l2w	PROPN
ejpam-3429	250	6	2	2	NUM
ejpam-3429	250	7	+	+	CCONJ
ejpam-3429	250	8	.	.	PUNCT
ejpam-3429	250	9	.	.	PUNCT
ejpam-3429	250	10	.	.	PUNCT
ejpam-3429	251	1	(	(	PUNCT
ejpam-3429	251	2	w	w	PROPN
ejpam-3429	251	3	∈	∈	PROPN
ejpam-3429	251	4	u	u	NOUN
ejpam-3429	251	5	)	)	PUNCT
ejpam-3429	251	6	,	,	PUNCT
ejpam-3429	251	7	then	then	ADV
ejpam-3429	251	8	again	again	ADV
ejpam-3429	251	9	by	by	ADP
ejpam-3429	251	10	comparing	compare	VERB
ejpam-3429	251	11	the	the	DET
ejpam-3429	251	12	coefficients	coefficient	NOUN
ejpam-3429	251	13	in	in	ADP
ejpam-3429	251	14	(	(	PUNCT
ejpam-3429	251	15	24	24	NUM
ejpam-3429	251	16	)	)	PUNCT
ejpam-3429	251	17	,	,	PUNCT
ejpam-3429	251	18	we	we	PRON
ejpam-3429	251	19	have	have	VERB
ejpam-3429	251	20	the	the	DET
ejpam-3429	251	21	following	follow	VERB
ejpam-3429	251	22	−k2	−k2	PROPN
ejpam-3429	251	23	=	=	SYM
ejpam-3429	251	24	βl1e	βl1e	PROPN
ejpam-3429	251	25	−i(α	−i(α	NOUN
ejpam-3429	251	26	β	β	NOUN
ejpam-3429	251	27	)	)	PUNCT
ejpam-3429	251	28	cos(αβ	cos(αβ	NOUN
ejpam-3429	251	29	)	)	PUNCT
ejpam-3429	251	30	q	q	PUNCT
ejpam-3429	252	1	[	[	X
ejpam-3429	252	2	1−	1−	NUM
ejpam-3429	252	3	λ+	λ+	PUNCT
ejpam-3429	252	4	(	(	PUNCT
ejpam-3429	252	5	1	1	NUM
ejpam-3429	252	6	+	+	NUM
ejpam-3429	252	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	252	8	γ2	γ2	NOUN
ejpam-3429	252	9	(	(	PUNCT
ejpam-3429	252	10	25	25	NUM
ejpam-3429	252	11	)	)	PUNCT
ejpam-3429	252	12	and	and	CCONJ
ejpam-3429	252	13	2k22	2k22	NUM
ejpam-3429	252	14	−	−	NOUN
ejpam-3429	252	15	k3	k3	X
ejpam-3429	252	16	=	=	PUNCT
ejpam-3429	252	17	βl2e	βl2e	PROPN
ejpam-3429	252	18	−i(α	−i(α	PROPN
ejpam-3429	252	19	β	β	SYM
ejpam-3429	252	20	)	)	PUNCT
ejpam-3429	252	21	cos(αβ	cos(αβ	NOUN
ejpam-3429	252	22	)	)	PUNCT
ejpam-3429	253	1	+	+	CCONJ
ejpam-3429	253	2	β	β	X
ejpam-3429	253	3	q	q	X
ejpam-3429	253	4	l	l	NOUN
ejpam-3429	253	5	2	2	NUM
ejpam-3429	253	6	1e	1e	NOUN
ejpam-3429	253	7	−2i(α	−2i(α	PROPN
ejpam-3429	253	8	β	β	X
ejpam-3429	253	9	)	)	PUNCT
ejpam-3429	253	10	cos2(αβ	cos2(αβ	NOUN
ejpam-3429	253	11	)	)	PUNCT
ejpam-3429	253	12	[	[	PUNCT
ejpam-3429	253	13	1	1	NUM
ejpam-3429	253	14	+	+	CCONJ
ejpam-3429	253	15	β−1	β−1	SYM
ejpam-3429	253	16	2	2	NUM
ejpam-3429	253	17	(	(	PUNCT
ejpam-3429	253	18	q	q	NOUN
ejpam-3429	253	19	+	+	NUM
ejpam-3429	253	20	2	2	NUM
ejpam-3429	253	21	)	)	PUNCT
ejpam-3429	253	22	]	]	PUNCT
ejpam-3429	254	1	[	[	X
ejpam-3429	254	2	1−	1−	NUM
ejpam-3429	254	3	λ+	λ+	PUNCT
ejpam-3429	254	4	[	[	X
ejpam-3429	254	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	254	6	(	(	PUNCT
ejpam-3429	254	7	[	[	X
ejpam-3429	254	8	3]q	3]q	NUM
ejpam-3429	254	9	−	−	PROPN
ejpam-3429	254	10	1)γ3	1)γ3	NUM
ejpam-3429	254	11	.	.	PUNCT
ejpam-3429	255	1	(	(	PUNCT
ejpam-3429	255	2	26	26	NUM
ejpam-3429	255	3	)	)	PUNCT
ejpam-3429	255	4	it	it	PRON
ejpam-3429	255	5	is	be	AUX
ejpam-3429	255	6	obvious	obvious	ADJ
ejpam-3429	255	7	from	from	ADP
ejpam-3429	255	8	(	(	PUNCT
ejpam-3429	255	9	22	22	NUM
ejpam-3429	255	10	)	)	PUNCT
ejpam-3429	255	11	and	and	CCONJ
ejpam-3429	255	12	(	(	PUNCT
ejpam-3429	255	13	25	25	NUM
ejpam-3429	255	14	)	)	PUNCT
ejpam-3429	255	15	that	that	DET
ejpam-3429	255	16	l1	l1	PROPN
ejpam-3429	255	17	=	=	PROPN
ejpam-3429	255	18	−c1	−c1	PROPN
ejpam-3429	255	19	.	.	PUNCT
ejpam-3429	256	1	from	from	ADP
ejpam-3429	256	2	(	(	PUNCT
ejpam-3429	256	3	23	23	NUM
ejpam-3429	256	4	)	)	PUNCT
ejpam-3429	256	5	and	and	CCONJ
ejpam-3429	256	6	(	(	PUNCT
ejpam-3429	256	7	26	26	NUM
ejpam-3429	256	8	)	)	PUNCT
ejpam-3429	256	9	,	,	PUNCT
ejpam-3429	256	10	we	we	PRON
ejpam-3429	256	11	get	get	VERB
ejpam-3429	256	12	c21	c21	NOUN
ejpam-3429	257	1	=	=	SYM
ejpam-3429	257	2	(	(	PUNCT
ejpam-3429	257	3	c2	c2	PROPN
ejpam-3429	257	4	+	+	CCONJ
ejpam-3429	257	5	l2	l2	NOUN
ejpam-3429	257	6	)	)	PUNCT
ejpam-3429	257	7	2	2	NUM
ejpam-3429	258	1	[	[	X
ejpam-3429	258	2	1−	1−	NUM
ejpam-3429	258	3	λ+	λ+	PUNCT
ejpam-3429	258	4	[	[	X
ejpam-3429	258	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	258	6	(	(	PUNCT
ejpam-3429	258	7	[	[	X
ejpam-3429	258	8	3]q	3]q	NUM
ejpam-3429	258	9	−	−	NOUN
ejpam-3429	258	10	1)γ3e	1)γ3e	NOUN
ejpam-3429	258	11	−i(α	−i(α	PROPN
ejpam-3429	258	12	β	β	SYM
ejpam-3429	258	13	)	)	PUNCT
ejpam-3429	258	14	cos(αβ	cos(αβ	NOUN
ejpam-3429	258	15	)	)	PUNCT
ejpam-3429	258	16	δ	δ	PROPN
ejpam-3429	258	17	(	(	PUNCT
ejpam-3429	258	18	27	27	NUM
ejpam-3429	258	19	)	)	PUNCT
ejpam-3429	258	20	where	where	SCONJ
ejpam-3429	258	21	δ	δ	X
ejpam-3429	258	22	=	=	PUNCT
ejpam-3429	258	23	β	β	X
ejpam-3429	258	24	q2	q2	NOUN
ejpam-3429	259	1	[	[	X
ejpam-3429	259	2	1−	1−	NUM
ejpam-3429	259	3	λ+	λ+	PUNCT
ejpam-3429	259	4	(	(	PUNCT
ejpam-3429	259	5	1	1	NUM
ejpam-3429	259	6	+	+	NUM
ejpam-3429	259	7	q)λ]2	q)λ]2	PROPN
ejpam-3429	259	8	m	m	VERB
ejpam-3429	259	9	γ22	γ22	NOUN
ejpam-3429	259	10	−	−	PROPN
ejpam-3429	260	1	[	[	PUNCT
ejpam-3429	260	2	1	1	NUM
ejpam-3429	260	3	+	+	CCONJ
ejpam-3429	260	4	β−1	β−1	SYM
ejpam-3429	260	5	2	2	NUM
ejpam-3429	260	6	(	(	PUNCT
ejpam-3429	260	7	q	q	NOUN
ejpam-3429	260	8	+	+	NUM
ejpam-3429	260	9	2	2	NUM
ejpam-3429	260	10	)	)	PUNCT
ejpam-3429	260	11	]	]	PUNCT
ejpam-3429	260	12	q	q	X
ejpam-3429	261	1	[	[	X
ejpam-3429	261	2	1−	1−	NUM
ejpam-3429	261	3	λ+	λ+	PUNCT
ejpam-3429	261	4	[	[	X
ejpam-3429	261	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	261	6	(	(	PUNCT
ejpam-3429	261	7	[	[	X
ejpam-3429	261	8	3]q	3]q	NUM
ejpam-3429	261	9	−	−	PROPN
ejpam-3429	261	10	1)γ3	1)γ3	NUM
ejpam-3429	261	11	.	.	PUNCT
ejpam-3429	262	1	by	by	ADP
ejpam-3429	262	2	applying	apply	VERB
ejpam-3429	262	3	the	the	DET
ejpam-3429	262	4	familiar	familiar	ADJ
ejpam-3429	262	5	inequalities	inequality	NOUN
ejpam-3429	262	6	|	|	ADV
ejpam-3429	262	7	c2	c2	VERB
ejpam-3429	262	8	|≤	|≤	PROPN
ejpam-3429	262	9	2	2	NUM
ejpam-3429	262	10	and	and	CCONJ
ejpam-3429	262	11	|	|	ADV
ejpam-3429	262	12	l2	l2	VERB
ejpam-3429	262	13	|≤	|≤	ADJ
ejpam-3429	262	14	2	2	NUM
ejpam-3429	262	15	,	,	PUNCT
ejpam-3429	262	16	we	we	PRON
ejpam-3429	262	17	get	get	VERB
ejpam-3429	262	18	|	|	ADV
ejpam-3429	262	19	c1	c1	PROPN
ejpam-3429	262	20	|≤	|≤	PROPN
ejpam-3429	262	21	√	√	PROPN
ejpam-3429	262	22	2√	2√	PUNCT
ejpam-3429	263	1	[	[	X
ejpam-3429	263	2	1−	1−	NUM
ejpam-3429	263	3	λ+	λ+	PUNCT
ejpam-3429	263	4	[	[	X
ejpam-3429	263	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	263	6	(	(	PUNCT
ejpam-3429	263	7	[	[	X
ejpam-3429	263	8	3]q	3]q	NUM
ejpam-3429	263	9	−	−	NOUN
ejpam-3429	263	10	1)γ3	1)γ3	NUM
ejpam-3429	263	11	cos(αβ	cos(αβ	NOUN
ejpam-3429	263	12	)	)	PUNCT
ejpam-3429	263	13	δ	δ	PROPN
ejpam-3429	263	14	(	(	PUNCT
ejpam-3429	263	15	28	28	NUM
ejpam-3429	263	16	)	)	PUNCT
ejpam-3429	263	17	and	and	CCONJ
ejpam-3429	263	18	|	|	ADV
ejpam-3429	263	19	k2	k2	PROPN
ejpam-3429	263	20	|	|	ADV
ejpam-3429	263	21	=	=	SYM
ejpam-3429	263	22	β	β	PROPN
ejpam-3429	263	23	|	|	ADV
ejpam-3429	263	24	c1	c1	PROPN
ejpam-3429	263	25	|	|	ADV
ejpam-3429	263	26	cos(αβ	cos(αβ	NOUN
ejpam-3429	263	27	)	)	PUNCT
ejpam-3429	263	28	q	q	PUNCT
ejpam-3429	264	1	[	[	X
ejpam-3429	264	2	1−	1−	NUM
ejpam-3429	264	3	λ+	λ+	PUNCT
ejpam-3429	264	4	(	(	PUNCT
ejpam-3429	264	5	1	1	NUM
ejpam-3429	264	6	+	+	NUM
ejpam-3429	264	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	264	8	|	|	ADV
ejpam-3429	264	9	γ2	γ2	NOUN
ejpam-3429	264	10	|	|	ADV
ejpam-3429	264	11	(	(	PUNCT
ejpam-3429	264	12	29	29	NUM
ejpam-3429	264	13	)	)	PUNCT
ejpam-3429	264	14	≤	≤	NOUN
ejpam-3429	264	15	β	β	X
ejpam-3429	264	16	√	√	ADP
ejpam-3429	264	17	2	2	NUM
ejpam-3429	264	18	cos(αβ	cos(αβ	NOUN
ejpam-3429	264	19	)	)	PUNCT
ejpam-3429	264	20	q	q	PUNCT
ejpam-3429	265	1	[	[	X
ejpam-3429	265	2	1−	1−	NUM
ejpam-3429	265	3	λ+	λ+	PUNCT
ejpam-3429	265	4	(	(	PUNCT
ejpam-3429	265	5	1	1	NUM
ejpam-3429	265	6	+	+	NUM
ejpam-3429	265	7	q)λ]m	q)λ]m	NOUN
ejpam-3429	265	8	|	|	ADV
ejpam-3429	265	9	γ2	γ2	NOUN
ejpam-3429	265	10	|	|	ADV
ejpam-3429	265	11	√	√	PROPN
ejpam-3429	266	1	[	[	X
ejpam-3429	266	2	1−	1−	NUM
ejpam-3429	266	3	λ+	λ+	PUNCT
ejpam-3429	266	4	[	[	X
ejpam-3429	266	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	266	6	(	(	PUNCT
ejpam-3429	266	7	[	[	X
ejpam-3429	266	8	3]q	3]q	NUM
ejpam-3429	266	9	−	−	NOUN
ejpam-3429	266	10	1)γ3	1)γ3	NUM
ejpam-3429	266	11	cos(αβ	cos(αβ	NOUN
ejpam-3429	266	12	)	)	PUNCT
ejpam-3429	266	13	δ	δ	PROPN
ejpam-3429	266	14	.	.	PUNCT
ejpam-3429	267	1	(	(	PUNCT
ejpam-3429	267	2	30	30	NUM
ejpam-3429	267	3	)	)	PUNCT
ejpam-3429	267	4	we	we	PRON
ejpam-3429	267	5	next	next	ADV
ejpam-3429	267	6	find	find	VERB
ejpam-3429	267	7	a	a	DET
ejpam-3429	267	8	upper	upper	ADJ
ejpam-3429	267	9	bound	bind	VERB
ejpam-3429	267	10	on	on	ADP
ejpam-3429	267	11	|	|	ADV
ejpam-3429	267	12	a3	a3	VERB
ejpam-3429	267	13	|	|	ADV
ejpam-3429	267	14	.	.	PUNCT
ejpam-3429	268	1	for	for	ADP
ejpam-3429	268	2	this	this	PRON
ejpam-3429	268	3	we	we	PRON
ejpam-3429	268	4	subtract	subtract	VERB
ejpam-3429	268	5	(	(	PUNCT
ejpam-3429	268	6	26	26	NUM
ejpam-3429	268	7	)	)	PUNCT
ejpam-3429	268	8	from	from	ADP
ejpam-3429	268	9	(	(	PUNCT
ejpam-3429	268	10	23	23	NUM
ejpam-3429	268	11	)	)	PUNCT
ejpam-3429	268	12	and	and	CCONJ
ejpam-3429	268	13	get	get	VERB
ejpam-3429	268	14	2k3	2k3	NUM
ejpam-3429	268	15	=	=	SYM
ejpam-3429	268	16	2k22	2k22	NOUN
ejpam-3429	268	17	−	−	PROPN
ejpam-3429	269	1	βl2e	βl2e	PROPN
ejpam-3429	269	2	−i(α	−i(α	PROPN
ejpam-3429	269	3	β	β	SYM
ejpam-3429	269	4	)	)	PUNCT
ejpam-3429	269	5	cos(αβ	cos(αβ	NOUN
ejpam-3429	269	6	)	)	PUNCT
ejpam-3429	270	1	+	+	CCONJ
ejpam-3429	270	2	β	β	X
ejpam-3429	270	3	q	q	X
ejpam-3429	270	4	l	l	NOUN
ejpam-3429	270	5	2	2	NUM
ejpam-3429	270	6	1e	1e	NOUN
ejpam-3429	270	7	−2i(α	−2i(α	PROPN
ejpam-3429	270	8	β	β	X
ejpam-3429	270	9	)	)	PUNCT
ejpam-3429	270	10	cos2(αβ	cos2(αβ	NOUN
ejpam-3429	270	11	)	)	PUNCT
ejpam-3429	270	12	[	[	PUNCT
ejpam-3429	270	13	1	1	NUM
ejpam-3429	270	14	+	+	CCONJ
ejpam-3429	270	15	β−1	β−1	SYM
ejpam-3429	270	16	2	2	NUM
ejpam-3429	270	17	(	(	PUNCT
ejpam-3429	270	18	q	q	NOUN
ejpam-3429	270	19	+	+	NUM
ejpam-3429	270	20	2	2	NUM
ejpam-3429	270	21	)	)	PUNCT
ejpam-3429	270	22	]	]	PUNCT
ejpam-3429	271	1	[	[	X
ejpam-3429	271	2	1−	1−	NUM
ejpam-3429	271	3	λ+	λ+	PUNCT
ejpam-3429	271	4	[	[	X
ejpam-3429	271	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	271	6	(	(	PUNCT
ejpam-3429	271	7	[	[	X
ejpam-3429	271	8	3]q	3]q	NUM
ejpam-3429	271	9	−	−	NOUN
ejpam-3429	271	10	1)γ3	1)γ3	NUM
ejpam-3429	271	11	+	+	NUM
ejpam-3429	271	12	references	reference	NOUN
ejpam-3429	271	13	855	855	NUM
ejpam-3429	271	14	βc2e	βc2e	ADP
ejpam-3429	271	15	−i(α	−i(α	PROPN
ejpam-3429	271	16	β	β	X
ejpam-3429	271	17	)	)	PUNCT
ejpam-3429	271	18	cos(αβ	cos(αβ	NOUN
ejpam-3429	271	19	)	)	PUNCT
ejpam-3429	272	1	+	+	CCONJ
ejpam-3429	272	2	β	β	X
ejpam-3429	272	3	q	q	X
ejpam-3429	272	4	c	c	NOUN
ejpam-3429	272	5	2	2	NUM
ejpam-3429	272	6	1e	1e	NOUN
ejpam-3429	272	7	−2i(α	−2i(α	PROPN
ejpam-3429	272	8	β	β	X
ejpam-3429	272	9	)	)	PUNCT
ejpam-3429	272	10	cos2(αβ	cos2(αβ	NOUN
ejpam-3429	272	11	)	)	PUNCT
ejpam-3429	273	1	[	[	PUNCT
ejpam-3429	273	2	1	1	NUM
ejpam-3429	273	3	+	+	CCONJ
ejpam-3429	273	4	β−1	β−1	SYM
ejpam-3429	273	5	2	2	NUM
ejpam-3429	273	6	(	(	PUNCT
ejpam-3429	273	7	q	q	NOUN
ejpam-3429	273	8	+	+	NUM
ejpam-3429	273	9	2	2	NUM
ejpam-3429	273	10	)	)	PUNCT
ejpam-3429	273	11	]	]	PUNCT
ejpam-3429	274	1	[	[	X
ejpam-3429	274	2	1−	1−	NUM
ejpam-3429	274	3	λ+	λ+	PUNCT
ejpam-3429	274	4	[	[	X
ejpam-3429	274	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	274	6	(	(	PUNCT
ejpam-3429	274	7	[	[	X
ejpam-3429	274	8	3]q	3]q	NUM
ejpam-3429	274	9	−	−	PROPN
ejpam-3429	274	10	1)γ3	1)γ3	NUM
ejpam-3429	274	11	.	.	PUNCT
ejpam-3429	275	1	now	now	ADV
ejpam-3429	275	2	putting	put	VERB
ejpam-3429	275	3	that	that	DET
ejpam-3429	275	4	c21	c21	NOUN
ejpam-3429	275	5	=	=	SYM
ejpam-3429	275	6	l21	l21	NOUN
ejpam-3429	275	7	and	and	CCONJ
ejpam-3429	275	8	k2	k2	ADJ
ejpam-3429	275	9	values	value	NOUN
ejpam-3429	275	10	in	in	ADP
ejpam-3429	275	11	above	above	ADP
ejpam-3429	275	12	equation	equation	NOUN
ejpam-3429	275	13	,	,	PUNCT
ejpam-3429	275	14	we	we	PRON
ejpam-3429	275	15	obtain	obtain	VERB
ejpam-3429	275	16	2k3	2k3	NUM
ejpam-3429	275	17	=	=	SYM
ejpam-3429	275	18	βe	βe	PRON
ejpam-3429	275	19	−i(α	−i(α	PROPN
ejpam-3429	275	20	β	β	X
ejpam-3429	275	21	)	)	PUNCT
ejpam-3429	275	22	cos(αβ	cos(αβ	NOUN
ejpam-3429	275	23	)	)	PUNCT
ejpam-3429	276	1	[	[	X
ejpam-3429	276	2	1−	1−	NUM
ejpam-3429	276	3	λ+	λ+	PUNCT
ejpam-3429	276	4	[	[	X
ejpam-3429	276	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	276	6	(	(	PUNCT
ejpam-3429	276	7	[	[	X
ejpam-3429	276	8	3]q	3]q	NUM
ejpam-3429	276	9	−	−	NOUN
ejpam-3429	276	10	1)γ3	1)γ3	NOUN
ejpam-3429	276	11	[	[	PUNCT
ejpam-3429	276	12	β(c2	β(c2	PRON
ejpam-3429	276	13	+	+	CCONJ
ejpam-3429	276	14	l2	l2	NOUN
ejpam-3429	276	15	)	)	PUNCT
ejpam-3429	276	16	q2	q2	NOUN
ejpam-3429	277	1	[	[	X
ejpam-3429	277	2	1−	1−	NUM
ejpam-3429	277	3	λ+	λ+	PUNCT
ejpam-3429	277	4	(	(	PUNCT
ejpam-3429	277	5	1	1	NUM
ejpam-3429	277	6	+	+	NUM
ejpam-3429	277	7	q)λ]2	q)λ]2	ADV
ejpam-3429	277	8	m	m	AUX
ejpam-3429	277	9	γ22δ	γ22δ	VERB
ejpam-3429	277	10	−	−	PROPN
ejpam-3429	277	11	(	(	PUNCT
ejpam-3429	277	12	c2	c2	PROPN
ejpam-3429	277	13	−	−	PROPN
ejpam-3429	277	14	l2	l2	PROPN
ejpam-3429	277	15	)	)	PUNCT
ejpam-3429	277	16	]	]	PUNCT
ejpam-3429	277	17	.	.	PUNCT
ejpam-3429	278	1	(	(	PUNCT
ejpam-3429	278	2	31	31	NUM
ejpam-3429	278	3	)	)	PUNCT
ejpam-3429	278	4	by	by	ADP
ejpam-3429	278	5	applying	apply	VERB
ejpam-3429	278	6	the	the	DET
ejpam-3429	278	7	familiar	familiar	ADJ
ejpam-3429	278	8	inequalities	inequality	NOUN
ejpam-3429	278	9	|	|	ADV
ejpam-3429	278	10	c2	c2	VERB
ejpam-3429	278	11	|≤	|≤	PROPN
ejpam-3429	278	12	2	2	NUM
ejpam-3429	278	13	and	and	CCONJ
ejpam-3429	278	14	|	|	ADV
ejpam-3429	278	15	l2	l2	VERB
ejpam-3429	278	16	|≤	|≤	ADJ
ejpam-3429	278	17	2	2	NUM
ejpam-3429	278	18	we	we	PRON
ejpam-3429	278	19	get	get	AUX
ejpam-3429	278	20	|	|	ADV
ejpam-3429	278	21	k3	k3	VERB
ejpam-3429	278	22	|≤	|≤	ADJ
ejpam-3429	278	23	2β	2β	NOUN
ejpam-3429	278	24	cos(αβ	cos(αβ	NOUN
ejpam-3429	278	25	)	)	PUNCT
ejpam-3429	279	1	[	[	X
ejpam-3429	279	2	1−	1−	NUM
ejpam-3429	279	3	λ+	λ+	PUNCT
ejpam-3429	279	4	[	[	X
ejpam-3429	279	5	3]qλ]m	3]qλ]m	NUM
ejpam-3429	279	6	(	(	PUNCT
ejpam-3429	279	7	[	[	X
ejpam-3429	279	8	3]q	3]q	NUM
ejpam-3429	279	9	−	−	NOUN
ejpam-3429	279	10	1)γ3	1)γ3	NUM
ejpam-3429	279	11	[	[	PUNCT
ejpam-3429	279	12	β	β	X
ejpam-3429	279	13	q2	q2	NOUN
ejpam-3429	280	1	[	[	X
ejpam-3429	280	2	1−	1−	NUM
ejpam-3429	280	3	λ+	λ+	PUNCT
ejpam-3429	280	4	(	(	PUNCT
ejpam-3429	280	5	1	1	NUM
ejpam-3429	280	6	+	+	NUM
ejpam-3429	280	7	q)λ]2	q)λ]2	ADV
ejpam-3429	280	8	m	m	AUX
ejpam-3429	280	9	γ22δ	γ22δ	VERB
ejpam-3429	280	10	−	−	PROPN
ejpam-3429	280	11	1	1	NUM
ejpam-3429	280	12	]	]	PUNCT
ejpam-3429	280	13	.	.	PUNCT
ejpam-3429	281	1	(	(	PUNCT
ejpam-3429	281	2	32	32	NUM
ejpam-3429	281	3	)	)	PUNCT
ejpam-3429	281	4	the	the	DET
ejpam-3429	281	5	proof	proof	NOUN
ejpam-3429	281	6	of	of	ADP
ejpam-3429	281	7	theorem	theorem	ADJ
ejpam-3429	281	8	2	2	NUM
ejpam-3429	281	9	is	be	AUX
ejpam-3429	281	10	thus	thus	ADV
ejpam-3429	281	11	completed	complete	VERB
ejpam-3429	281	12	.	.	PUNCT
ejpam-3429	282	1	3	3	X
ejpam-3429	282	2	.	.	X
ejpam-3429	282	3	concluding	conclude	VERB
ejpam-3429	282	4	remarks	remark	NOUN
ejpam-3429	282	5	remark	remark	NOUN
ejpam-3429	282	6	2	2	NUM
ejpam-3429	282	7	.	.	X
ejpam-3429	283	1	for	for	ADP
ejpam-3429	283	2	the	the	DET
ejpam-3429	283	3	choice	choice	NOUN
ejpam-3429	283	4	of	of	ADP
ejpam-3429	283	5	the	the	DET
ejpam-3429	283	6	parameters	parameter	NOUN
ejpam-3429	283	7	,	,	PUNCT
ejpam-3429	283	8	m	m	VERB
ejpam-3429	283	9	=	=	NOUN
ejpam-3429	283	10	0	0	NUM
ejpam-3429	283	11	,	,	PUNCT
ejpam-3429	283	12	r	r	NOUN
ejpam-3429	283	13	=	=	SYM
ejpam-3429	283	14	2	2	NUM
ejpam-3429	283	15	,	,	PUNCT
ejpam-3429	283	16	s	s	PART
ejpam-3429	283	17	=	=	SYM
ejpam-3429	283	18	1	1	NUM
ejpam-3429	283	19	;	;	PUNCT
ejpam-3429	283	20	a1	a1	NOUN
ejpam-3429	283	21	=	=	SYM
ejpam-3429	283	22	b1	b1	PROPN
ejpam-3429	283	23	,	,	PUNCT
ejpam-3429	283	24	a2	a2	PROPN
ejpam-3429	283	25	=	=	SYM
ejpam-3429	283	26	q	q	X
ejpam-3429	283	27	,	,	PUNCT
ejpam-3429	283	28	and	and	CCONJ
ejpam-3429	283	29	by	by	ADP
ejpam-3429	283	30	taking	take	VERB
ejpam-3429	283	31	limit	limit	NOUN
ejpam-3429	283	32	q	q	X
ejpam-3429	283	33	→	→	SYM
ejpam-3429	283	34	1−	1−	NUM
ejpam-3429	283	35	in	in	ADP
ejpam-3429	283	36	theorem	theorem	ADJ
ejpam-3429	283	37	1	1	NUM
ejpam-3429	283	38	and	and	CCONJ
ejpam-3429	283	39	theorem	theorem	VERB
ejpam-3429	283	40	2	2	NUM
ejpam-3429	283	41	,	,	PUNCT
ejpam-3429	283	42	we	we	PRON
ejpam-3429	283	43	get	get	VERB
ejpam-3429	283	44	the	the	DET
ejpam-3429	283	45	results	result	NOUN
ejpam-3429	283	46	obtained	obtain	VERB
ejpam-3429	283	47	in	in	ADP
ejpam-3429	283	48	[	[	X
ejpam-3429	283	49	6	6	NUM
ejpam-3429	283	50	]	]	PUNCT
ejpam-3429	283	51	.	.	PUNCT
ejpam-3429	284	1	remark	remark	PROPN
ejpam-3429	284	2	3	3	NUM
ejpam-3429	284	3	.	.	PUNCT
ejpam-3429	285	1	for	for	ADP
ejpam-3429	285	2	appropriate	appropriate	ADJ
ejpam-3429	285	3	choice	choice	NOUN
ejpam-3429	285	4	of	of	ADP
ejpam-3429	285	5	the	the	DET
ejpam-3429	285	6	parameter	parameter	NOUN
ejpam-3429	285	7	in	in	ADP
ejpam-3429	285	8	theorem	theorem	NOUN
ejpam-3429	285	9	1	1	NUM
ejpam-3429	285	10	,	,	PUNCT
ejpam-3429	285	11	we	we	PRON
ejpam-3429	285	12	get	get	VERB
ejpam-3429	285	13	the	the	DET
ejpam-3429	285	14	following	follow	VERB
ejpam-3429	285	15	inequalities	inequality	NOUN
ejpam-3429	285	16	for	for	ADP
ejpam-3429	285	17	a	a	DET
ejpam-3429	285	18	class	class	NOUN
ejpam-3429	285	19	of	of	ADP
ejpam-3429	285	20	functions	function	NOUN
ejpam-3429	285	21	bi	bi	NOUN
ejpam-3429	285	22	-	-	NOUN
ejpam-3429	285	23	starlike	starlike	NOUN
ejpam-3429	285	24	of	of	ADP
ejpam-3429	285	25	order	order	NOUN
ejpam-3429	285	26	ρ	ρ	PROPN
ejpam-3429	285	27	(	(	PUNCT
ejpam-3429	285	28	0	0	NUM
ejpam-3429	285	29	≤	≤	NUM
ejpam-3429	285	30	ρ	ρ	NOUN
ejpam-3429	285	31	<	<	X
ejpam-3429	285	32	1	1	NUM
ejpam-3429	285	33	)	)	PUNCT
ejpam-3429	285	34	.	.	PUNCT
ejpam-3429	286	1	|k2|	|k2|	PROPN
ejpam-3429	286	2	≤	≤	NUM
ejpam-3429	286	3	√	√	NUM
ejpam-3429	286	4	2(1−	2(1−	NUM
ejpam-3429	286	5	ρ	ρ	NUM
ejpam-3429	286	6	)	)	PUNCT
ejpam-3429	286	7	and	and	CCONJ
ejpam-3429	286	8	|k3|	|k3|	ADJ
ejpam-3429	286	9	≤	≤	NUM
ejpam-3429	286	10	2(1−	2(1−	NUM
ejpam-3429	286	11	ρ	ρ	NUM
ejpam-3429	286	12	)	)	PUNCT
ejpam-3429	286	13	.	.	PUNCT
ejpam-3429	287	1	remark	remark	PROPN
ejpam-3429	287	2	4	4	NUM
ejpam-3429	287	3	.	.	PUNCT
ejpam-3429	287	4	similarly	similarly	ADV
ejpam-3429	287	5	for	for	ADP
ejpam-3429	287	6	the	the	DET
ejpam-3429	287	7	appropriate	appropriate	ADJ
ejpam-3429	287	8	choice	choice	NOUN
ejpam-3429	287	9	of	of	ADP
ejpam-3429	287	10	the	the	DET
ejpam-3429	287	11	parameter	parameter	NOUN
ejpam-3429	287	12	in	in	ADP
ejpam-3429	287	13	theorem	theorem	NOUN
ejpam-3429	287	14	1	1	NUM
ejpam-3429	287	15	,	,	PUNCT
ejpam-3429	287	16	we	we	PRON
ejpam-3429	287	17	get	get	VERB
ejpam-3429	287	18	the	the	DET
ejpam-3429	287	19	following	follow	VERB
ejpam-3429	287	20	inequalities	inequality	NOUN
ejpam-3429	287	21	for	for	ADP
ejpam-3429	287	22	a	a	DET
ejpam-3429	287	23	class	class	NOUN
ejpam-3429	287	24	of	of	ADP
ejpam-3429	287	25	functions	function	NOUN
ejpam-3429	287	26	which	which	PRON
ejpam-3429	287	27	are	be	AUX
ejpam-3429	287	28	bi	bi	ADJ
ejpam-3429	287	29	-	-	NOUN
ejpam-3429	287	30	convex	convex	NOUN
ejpam-3429	287	31	of	of	ADP
ejpam-3429	287	32	order	order	NOUN
ejpam-3429	287	33	ρ	ρ	X
ejpam-3429	287	34	(	(	PUNCT
ejpam-3429	287	35	0	0	NUM
ejpam-3429	287	36	≤	≤	NUM
ejpam-3429	287	37	ρ	ρ	NOUN
ejpam-3429	287	38	<	<	X
ejpam-3429	287	39	1	1	NUM
ejpam-3429	287	40	)	)	PUNCT
ejpam-3429	287	41	.	.	PUNCT
ejpam-3429	288	1	|k2|	|k2|	PROPN
ejpam-3429	289	1	≤	≤	NUM
ejpam-3429	289	2	√	√	NUM
ejpam-3429	289	3	(	(	PUNCT
ejpam-3429	289	4	1−	1−	NUM
ejpam-3429	289	5	ρ	ρ	NUM
ejpam-3429	289	6	)	)	PUNCT
ejpam-3429	289	7	and	and	CCONJ
ejpam-3429	289	8	|k3|	|k3|	ADJ
ejpam-3429	289	9	≤	≤	NUM
ejpam-3429	289	10	(	(	PUNCT
ejpam-3429	289	11	1−	1−	NUM
ejpam-3429	289	12	ρ	ρ	NUM
ejpam-3429	289	13	)	)	PUNCT
ejpam-3429	289	14	.	.	PUNCT
ejpam-3429	290	1	references	reference	NOUN
ejpam-3429	290	2	[	[	X
ejpam-3429	290	3	1	1	NUM
ejpam-3429	290	4	]	]	PUNCT
ejpam-3429	290	5	m.	m.	NOUN
ejpam-3429	290	6	darus	darus	NOUN
ejpam-3429	290	7	.	.	PUNCT
ejpam-3429	291	1	a	a	DET
ejpam-3429	291	2	new	new	ADJ
ejpam-3429	291	3	look	look	NOUN
ejpam-3429	291	4	at	at	ADP
ejpam-3429	291	5	q	q	ADJ
ejpam-3429	291	6	-	-	ADJ
ejpam-3429	291	7	hypergeometric	hypergeometric	ADJ
ejpam-3429	291	8	functions	function	NOUN
ejpam-3429	291	9	.	.	PUNCT
ejpam-3429	292	1	twms	twms	PROPN
ejpam-3429	292	2	j.	j.	PROPN
ejpam-3429	292	3	appl	appl	PROPN
ejpam-3429	292	4	.	.	PUNCT
ejpam-3429	293	1	eng	eng	PROPN
ejpam-3429	293	2	.	.	PROPN
ejpam-3429	293	3	math	math	PROPN
ejpam-3429	293	4	.	.	PUNCT
ejpam-3429	293	5	,	,	PUNCT
ejpam-3429	293	6	4(1):16–19	4(1):16–19	NUM
ejpam-3429	293	7	,	,	PUNCT
ejpam-3429	293	8	2014	2014	NUM
ejpam-3429	293	9	.	.	PUNCT
ejpam-3429	294	1	[	[	X
ejpam-3429	294	2	2	2	X
ejpam-3429	294	3	]	]	X
ejpam-3429	294	4	g.	g.	PROPN
ejpam-3429	294	5	gasper	gasper	PROPN
ejpam-3429	294	6	and	and	CCONJ
ejpam-3429	294	7	m.	m.	PROPN
ejpam-3429	294	8	rahman	rahman	PROPN
ejpam-3429	294	9	.	.	PUNCT
ejpam-3429	295	1	basic	basic	ADJ
ejpam-3429	295	2	hypergeometric	hypergeometric	ADJ
ejpam-3429	295	3	series	series	NOUN
ejpam-3429	295	4	,	,	PUNCT
ejpam-3429	295	5	volume	volume	NOUN
ejpam-3429	295	6	35	35	NUM
ejpam-3429	295	7	of	of	ADP
ejpam-3429	295	8	encyclopedia	encyclopedia	NOUN
ejpam-3429	295	9	of	of	ADP
ejpam-3429	295	10	mathematics	mathematic	NOUN
ejpam-3429	295	11	and	and	CCONJ
ejpam-3429	295	12	its	its	PRON
ejpam-3429	295	13	applications	application	NOUN
ejpam-3429	295	14	.	.	PUNCT
ejpam-3429	296	1	cambridge	cambridge	PROPN
ejpam-3429	296	2	university	university	PROPN
ejpam-3429	296	3	press	press	PROPN
ejpam-3429	296	4	,	,	PUNCT
ejpam-3429	296	5	cambridge	cambridge	PROPN
ejpam-3429	296	6	,	,	PUNCT
ejpam-3429	296	7	1990	1990	NUM
ejpam-3429	296	8	.	.	PUNCT
ejpam-3429	297	1	with	with	ADP
ejpam-3429	297	2	a	a	DET
ejpam-3429	297	3	foreword	foreword	NOUN
ejpam-3429	297	4	by	by	ADP
ejpam-3429	297	5	richard	richard	PROPN
ejpam-3429	297	6	askey	askey	PROPN
ejpam-3429	297	7	.	.	PUNCT
ejpam-3429	298	1	[	[	X
ejpam-3429	298	2	3	3	NUM
ejpam-3429	298	3	]	]	PUNCT
ejpam-3429	298	4	a.	a.	PROPN
ejpam-3429	298	5	w.	w.	PROPN
ejpam-3429	298	6	goodman	goodman	PROPN
ejpam-3429	298	7	.	.	PUNCT
ejpam-3429	299	1	univalent	univalent	ADJ
ejpam-3429	299	2	functions	function	NOUN
ejpam-3429	299	3	.	.	PUNCT
ejpam-3429	300	1	vol	vol	NOUN
ejpam-3429	300	2	.	.	PUNCT
ejpam-3429	300	3	ii	ii	PROPN
ejpam-3429	300	4	.	.	PUNCT
ejpam-3429	300	5	mariner	mariner	PROPN
ejpam-3429	300	6	publishing	publishing	PROPN
ejpam-3429	300	7	co.	co.	PROPN
ejpam-3429	300	8	,	,	PUNCT
ejpam-3429	300	9	inc	inc	PROPN
ejpam-3429	300	10	.	.	PROPN
ejpam-3429	300	11	,	,	PUNCT
ejpam-3429	300	12	tampa	tampa	PROPN
ejpam-3429	300	13	,	,	PUNCT
ejpam-3429	300	14	fl	fl	PROPN
ejpam-3429	300	15	,	,	PUNCT
ejpam-3429	300	16	1983	1983	NUM
ejpam-3429	300	17	.	.	PUNCT
ejpam-3429	301	1	[	[	X
ejpam-3429	301	2	4	4	X
ejpam-3429	301	3	]	]	PUNCT
ejpam-3429	301	4	k.	k.	PROPN
ejpam-3429	301	5	r.	r.	PROPN
ejpam-3429	301	6	karthikeyan	karthikeyan	PROPN
ejpam-3429	301	7	,	,	PUNCT
ejpam-3429	301	8	m.	m.	NOUN
ejpam-3429	301	9	ibrahim	ibrahim	PROPN
ejpam-3429	301	10	,	,	PUNCT
ejpam-3429	301	11	and	and	CCONJ
ejpam-3429	301	12	s.	s.	PROPN
ejpam-3429	301	13	srinivasan	srinivasan	PROPN
ejpam-3429	301	14	.	.	PUNCT
ejpam-3429	302	1	fractional	fractional	ADJ
ejpam-3429	302	2	class	class	NOUN
ejpam-3429	302	3	of	of	ADP
ejpam-3429	302	4	analytic	analytic	ADJ
ejpam-3429	302	5	functions	function	NOUN
ejpam-3429	302	6	defined	define	VERB
ejpam-3429	302	7	using	use	VERB
ejpam-3429	302	8	q	q	ADJ
ejpam-3429	302	9	-	-	PUNCT
ejpam-3429	302	10	differential	differential	ADJ
ejpam-3429	302	11	operator	operator	NOUN
ejpam-3429	302	12	.	.	PUNCT
ejpam-3429	303	1	aust	aust	PROPN
ejpam-3429	303	2	.	.	PUNCT
ejpam-3429	304	1	j.	j.	PROPN
ejpam-3429	304	2	math	math	PROPN
ejpam-3429	304	3	.	.	PUNCT
ejpam-3429	305	1	anal	anal	PROPN
ejpam-3429	305	2	.	.	PUNCT
ejpam-3429	306	1	appl	appl	PROPN
ejpam-3429	306	2	.	.	PROPN
ejpam-3429	306	3	,	,	PUNCT
ejpam-3429	306	4	15(1):art	15(1):art	NUM
ejpam-3429	306	5	.	.	PUNCT
ejpam-3429	307	1	9	9	NUM
ejpam-3429	307	2	,	,	PUNCT
ejpam-3429	307	3	15	15	NUM
ejpam-3429	307	4	,	,	PUNCT
ejpam-3429	307	5	2018	2018	NUM
ejpam-3429	307	6	.	.	PUNCT
ejpam-3429	308	1	references	reference	NOUN
ejpam-3429	308	2	856	856	NUM
ejpam-3429	308	3	[	[	X
ejpam-3429	308	4	5	5	NUM
ejpam-3429	308	5	]	]	X
ejpam-3429	308	6	c.	c.	PROPN
ejpam-3429	308	7	selvaraj	selvaraj	PROPN
ejpam-3429	308	8	and	and	CCONJ
ejpam-3429	308	9	k.	k.	PROPN
ejpam-3429	308	10	r.	r.	PROPN
ejpam-3429	308	11	karthikeyan	karthikeyan	PROPN
ejpam-3429	308	12	.	.	PUNCT
ejpam-3429	309	1	differential	differential	ADJ
ejpam-3429	309	2	sandwich	sandwich	NOUN
ejpam-3429	309	3	theorems	theorem	NOUN
ejpam-3429	309	4	for	for	ADP
ejpam-3429	309	5	certain	certain	ADJ
ejpam-3429	309	6	subclasses	subclass	NOUN
ejpam-3429	309	7	of	of	ADP
ejpam-3429	309	8	analytic	analytic	ADJ
ejpam-3429	309	9	functions	function	NOUN
ejpam-3429	309	10	.	.	PUNCT
ejpam-3429	310	1	math	math	NOUN
ejpam-3429	310	2	.	.	PUNCT
ejpam-3429	311	1	commun	commun	PROPN
ejpam-3429	311	2	.	.	PROPN
ejpam-3429	311	3	,	,	PUNCT
ejpam-3429	311	4	13(2):311–319	13(2):311–319	PROPN
ejpam-3429	311	5	,	,	PUNCT
ejpam-3429	311	6	2008	2008	NUM
ejpam-3429	311	7	.	.	PUNCT
ejpam-3429	312	1	[	[	X
ejpam-3429	312	2	6	6	NUM
ejpam-3429	312	3	]	]	PUNCT
ejpam-3429	312	4	m.	m.	NOUN
ejpam-3429	312	5	mohan	mohan	PROPN
ejpam-3429	312	6	soren	soren	PROPN
ejpam-3429	312	7	and	and	CCONJ
ejpam-3429	312	8	akshaya	akshaya	PROPN
ejpam-3429	312	9	kumar	kumar	PROPN
ejpam-3429	312	10	mishra	mishra	PROPN
ejpam-3429	312	11	.	.	PROPN
ejpam-3429	312	12	coefficient	coefficient	PROPN
ejpam-3429	312	13	bounds	bound	VERB
ejpam-3429	312	14	for	for	ADP
ejpam-3429	312	15	bi	bi	ADJ
ejpam-3429	312	16	-	-	ADJ
ejpam-3429	312	17	spirallike	spirallike	ADJ
ejpam-3429	312	18	analytic	analytic	ADJ
ejpam-3429	312	19	functions	function	NOUN
ejpam-3429	312	20	.	.	PUNCT
ejpam-3429	313	1	kyungpook	kyungpook	PROPN
ejpam-3429	313	2	math	math	PROPN
ejpam-3429	313	3	.	.	PUNCT
ejpam-3429	314	1	j.	j.	PROPN
ejpam-3429	314	2	,	,	PUNCT
ejpam-3429	314	3	58(4):697–709	58(4):697–709	PROPN
ejpam-3429	314	4	,	,	PUNCT
ejpam-3429	314	5	2018	2018	NUM
ejpam-3429	314	6	.	.	PUNCT