id	sid	tid	token	lemma	pos
ejpam-2677	1	1	european	european	PROPN
ejpam-2677	1	2	journal	journal	PROPN
ejpam-2677	1	3	of	of	ADP
ejpam-2677	1	4	pure	pure	ADJ
ejpam-2677	1	5	and	and	CCONJ
ejpam-2677	1	6	applied	apply	VERB
ejpam-2677	1	7	mathematics	mathematic	NOUN
ejpam-2677	1	8	vol	vol	NOUN
ejpam-2677	1	9	.	.	PROPN
ejpam-2677	2	1	10	10	NUM
ejpam-2677	2	2	,	,	PUNCT
ejpam-2677	2	3	no	no	INTJ
ejpam-2677	2	4	.	.	NOUN
ejpam-2677	2	5	5	5	NUM
ejpam-2677	2	6	,	,	PUNCT
ejpam-2677	2	7	2017	2017	NUM
ejpam-2677	2	8	,	,	PUNCT
ejpam-2677	2	9	1124	1124	NUM
ejpam-2677	2	10	-	-	SYM
ejpam-2677	2	11	1134	1134	NUM
ejpam-2677	2	12	issn	issn	PROPN
ejpam-2677	2	13	1307	1307	NUM
ejpam-2677	2	14	-	-	SYM
ejpam-2677	2	15	5543	5543	NUM
ejpam-2677	2	16	–	–	PUNCT
ejpam-2677	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2677	2	18	published	publish	VERB
ejpam-2677	2	19	by	by	ADP
ejpam-2677	2	20	new	new	PROPN
ejpam-2677	2	21	york	york	PROPN
ejpam-2677	2	22	business	business	PROPN
ejpam-2677	2	23	global	global	PROPN
ejpam-2677	2	24	on	on	ADP
ejpam-2677	2	25	trigonometric	trigonometric	ADJ
ejpam-2677	2	26	moments	moment	NOUN
ejpam-2677	2	27	of	of	ADP
ejpam-2677	2	28	the	the	DET
ejpam-2677	2	29	stereographic	stereographic	ADJ
ejpam-2677	2	30	semicircular	semicircular	ADJ
ejpam-2677	2	31	gamma	gamma	NOUN
ejpam-2677	2	32	distribution	distribution	NOUN
ejpam-2677	2	33	phani	phani	PROPN
ejpam-2677	2	34	yedlapalli1,∗	yedlapalli1,∗	PROPN
ejpam-2677	2	35	,	,	PUNCT
ejpam-2677	2	36	a.j.v.radhika2	a.j.v.radhika2	ADP
ejpam-2677	2	37	,	,	PUNCT
ejpam-2677	2	38	s.v.s.girija3	s.v.s.girija3	PROPN
ejpam-2677	2	39	,	,	PUNCT
ejpam-2677	3	1	a.v.dattatreya	a.v.dattatreya	PROPN
ejpam-2677	3	2	rao4	rao4	PROPN
ejpam-2677	3	3	1	1	NUM
ejpam-2677	3	4	department	department	NOUN
ejpam-2677	3	5	of	of	ADP
ejpam-2677	3	6	basic	basic	ADJ
ejpam-2677	3	7	science	science	NOUN
ejpam-2677	3	8	,	,	PUNCT
ejpam-2677	3	9	shri	shri	PROPN
ejpam-2677	3	10	vishnu	vishnu	PROPN
ejpam-2677	3	11	engineering	engineering	PROPN
ejpam-2677	3	12	college	college	NOUN
ejpam-2677	3	13	for	for	ADP
ejpam-2677	3	14	women	woman	NOUN
ejpam-2677	3	15	,	,	PUNCT
ejpam-2677	3	16	bhimavaram	bhimavaram	PROPN
ejpam-2677	3	17	,	,	PUNCT
ejpam-2677	3	18	a.p-534202	a.p-534202	PROPN
ejpam-2677	3	19	,	,	PUNCT
ejpam-2677	3	20	india	india	PROPN
ejpam-2677	3	21	2	2	NUM
ejpam-2677	3	22	department	department	NOUN
ejpam-2677	3	23	of	of	ADP
ejpam-2677	3	24	mathematics	mathematics	PROPN
ejpam-2677	3	25	,	,	PUNCT
ejpam-2677	3	26	university	university	NOUN
ejpam-2677	3	27	college	college	NOUN
ejpam-2677	3	28	of	of	ADP
ejpam-2677	3	29	engineering	engineering	PROPN
ejpam-2677	3	30	,	,	PUNCT
ejpam-2677	3	31	acharya	acharya	PROPN
ejpam-2677	3	32	nagarjuna	nagarjuna	PROPN
ejpam-2677	3	33	university	university	PROPN
ejpam-2677	3	34	,	,	PUNCT
ejpam-2677	3	35	guntur	guntur	PROPN
ejpam-2677	3	36	,	,	PUNCT
ejpam-2677	3	37	a.p	a.p	PROPN
ejpam-2677	3	38	,	,	PUNCT
ejpam-2677	3	39	india	india	PROPN
ejpam-2677	3	40	3	3	NUM
ejpam-2677	3	41	department	department	NOUN
ejpam-2677	3	42	of	of	ADP
ejpam-2677	3	43	mathematics	mathematic	NOUN
ejpam-2677	3	44	,	,	PUNCT
ejpam-2677	3	45	hindu	hindu	NOUN
ejpam-2677	3	46	college	college	NOUN
ejpam-2677	3	47	,	,	PUNCT
ejpam-2677	3	48	guntur	guntur	PROPN
ejpam-2677	3	49	,	,	PUNCT
ejpam-2677	3	50	a.p	a.p	PROPN
ejpam-2677	3	51	,	,	PUNCT
ejpam-2677	3	52	india	india	PROPN
ejpam-2677	3	53	4	4	NUM
ejpam-2677	3	54	department	department	NOUN
ejpam-2677	3	55	of	of	ADP
ejpam-2677	3	56	statistics	statistic	NOUN
ejpam-2677	3	57	,	,	PUNCT
ejpam-2677	3	58	acharya	acharya	PROPN
ejpam-2677	3	59	nagarjuna	nagarjuna	PROPN
ejpam-2677	3	60	university	university	PROPN
ejpam-2677	3	61	,	,	PUNCT
ejpam-2677	3	62	guntur	guntur	PROPN
ejpam-2677	3	63	,	,	PUNCT
ejpam-2677	3	64	a.p	a.p	PROPN
ejpam-2677	3	65	,	,	PUNCT
ejpam-2677	3	66	india	india	PROPN
ejpam-2677	3	67	.	.	PUNCT
ejpam-2677	4	1	abstract	abstract	PROPN
ejpam-2677	4	2	.	.	PUNCT
ejpam-2677	5	1	phani	phani	PROPN
ejpam-2677	5	2	(	(	PUNCT
ejpam-2677	5	3	2013	2013	NUM
ejpam-2677	5	4	)	)	PUNCT
ejpam-2677	5	5	constructed	construct	VERB
ejpam-2677	5	6	a	a	DET
ejpam-2677	5	7	good	good	ADJ
ejpam-2677	5	8	number	number	NOUN
ejpam-2677	5	9	of	of	ADP
ejpam-2677	5	10	circular	circular	ADJ
ejpam-2677	5	11	and	and	CCONJ
ejpam-2677	5	12	semicircular	semicircular	ADJ
ejpam-2677	5	13	models	model	NOUN
ejpam-2677	5	14	induced	induce	VERB
ejpam-2677	5	15	by	by	ADP
ejpam-2677	5	16	inverse	inverse	NOUN
ejpam-2677	5	17	stereographic	stereographic	ADJ
ejpam-2677	5	18	projection	projection	NOUN
ejpam-2677	5	19	.	.	PUNCT
ejpam-2677	6	1	minh	minh	NOUN
ejpam-2677	6	2	and	and	CCONJ
ejpam-2677	6	3	farnum	farnum	PROPN
ejpam-2677	6	4	(	(	PUNCT
ejpam-2677	6	5	2003	2003	NUM
ejpam-2677	6	6	)	)	PUNCT
ejpam-2677	6	7	and	and	CCONJ
ejpam-2677	6	8	toshihiro	toshihiro	NOUN
ejpam-2677	6	9	abe	abe	PROPN
ejpam-2677	6	10	et	et	PROPN
ejpam-2677	6	11	al	al	PROPN
ejpam-2677	6	12	(	(	PUNCT
ejpam-2677	6	13	2010	2010	NUM
ejpam-2677	6	14	)	)	PUNCT
ejpam-2677	6	15	proposed	propose	VERB
ejpam-2677	6	16	a	a	DET
ejpam-2677	6	17	new	new	ADJ
ejpam-2677	6	18	method	method	NOUN
ejpam-2677	6	19	to	to	PART
ejpam-2677	6	20	derive	derive	VERB
ejpam-2677	6	21	circular	circular	ADJ
ejpam-2677	6	22	distributions	distribution	NOUN
ejpam-2677	6	23	from	from	ADP
ejpam-2677	6	24	the	the	DET
ejpam-2677	6	25	existing	exist	VERB
ejpam-2677	6	26	linear	linear	NOUN
ejpam-2677	6	27	models	model	NOUN
ejpam-2677	6	28	.	.	PUNCT
ejpam-2677	7	1	in	in	ADP
ejpam-2677	7	2	this	this	DET
ejpam-2677	7	3	paper	paper	NOUN
ejpam-2677	7	4	,	,	PUNCT
ejpam-2677	7	5	a	a	DET
ejpam-2677	7	6	new	new	ADJ
ejpam-2677	7	7	semicircular	semicircular	ADJ
ejpam-2677	7	8	model	model	NOUN
ejpam-2677	7	9	,	,	PUNCT
ejpam-2677	7	10	which	which	PRON
ejpam-2677	7	11	is	be	AUX
ejpam-2677	7	12	coined	coin	VERB
ejpam-2677	7	13	as	as	SCONJ
ejpam-2677	7	14	stereographic	stereographic	ADJ
ejpam-2677	7	15	semicircular	semicircular	ADJ
ejpam-2677	7	16	gamma	gamma	NOUN
ejpam-2677	7	17	distribution	distribution	NOUN
ejpam-2677	7	18	is	be	AUX
ejpam-2677	7	19	derived	derive	VERB
ejpam-2677	7	20	by	by	ADP
ejpam-2677	7	21	inducing	induce	VERB
ejpam-2677	7	22	modified	modified	ADJ
ejpam-2677	7	23	inverse	inverse	NOUN
ejpam-2677	7	24	stereographic	stereographic	ADJ
ejpam-2677	7	25	projection	projection	NOUN
ejpam-2677	7	26	on	on	ADP
ejpam-2677	7	27	gamma	gamma	NOUN
ejpam-2677	7	28	distribution	distribution	NOUN
ejpam-2677	7	29	.	.	PUNCT
ejpam-2677	8	1	this	this	DET
ejpam-2677	8	2	distribution	distribution	NOUN
ejpam-2677	8	3	generalizes	generalize	VERB
ejpam-2677	8	4	stereographic	stereographic	ADJ
ejpam-2677	8	5	semicircular	semicircular	ADJ
ejpam-2677	8	6	exponential	exponential	ADJ
ejpam-2677	8	7	model	model	NOUN
ejpam-2677	8	8	(	(	PUNCT
ejpam-2677	8	9	phani	phani	PROPN
ejpam-2677	8	10	et	et	PROPN
ejpam-2677	8	11	al	al	PROPN
ejpam-2677	8	12	(	(	PUNCT
ejpam-2677	8	13	2013	2013	NUM
ejpam-2677	8	14	)	)	PUNCT
ejpam-2677	8	15	)	)	PUNCT
ejpam-2677	8	16	and	and	CCONJ
ejpam-2677	8	17	the	the	DET
ejpam-2677	8	18	density	density	NOUN
ejpam-2677	8	19	and	and	CCONJ
ejpam-2677	8	20	distribution	distribution	NOUN
ejpam-2677	8	21	functions	function	NOUN
ejpam-2677	8	22	of	of	ADP
ejpam-2677	8	23	proposed	propose	VERB
ejpam-2677	8	24	model	model	NOUN
ejpam-2677	8	25	admit	admit	VERB
ejpam-2677	8	26	closed	closed	ADJ
ejpam-2677	8	27	form	form	NOUN
ejpam-2677	8	28	.	.	PUNCT
ejpam-2677	9	1	explicit	explicit	ADJ
ejpam-2677	9	2	expressions	expression	NOUN
ejpam-2677	9	3	for	for	ADP
ejpam-2677	9	4	trigonometric	trigonometric	ADJ
ejpam-2677	9	5	moments	moment	NOUN
ejpam-2677	9	6	are	be	AUX
ejpam-2677	9	7	derived	derive	VERB
ejpam-2677	9	8	by	by	ADP
ejpam-2677	9	9	applying	apply	VERB
ejpam-2677	9	10	meijer	meijer	NOUN
ejpam-2677	9	11	’s	’s	PART
ejpam-2677	9	12	gfunction	gfunction	NOUN
ejpam-2677	9	13	and	and	CCONJ
ejpam-2677	9	14	the	the	DET
ejpam-2677	9	15	new	new	ADJ
ejpam-2677	9	16	semicircular	semicircular	ADJ
ejpam-2677	9	17	model	model	NOUN
ejpam-2677	9	18	is	be	AUX
ejpam-2677	9	19	extended	extend	VERB
ejpam-2677	9	20	to	to	PART
ejpam-2677	9	21	construct	construct	VERB
ejpam-2677	9	22	stereographic	stereographic	ADJ
ejpam-2677	9	23	laxial	laxial	ADJ
ejpam-2677	9	24	gamma	gamma	NOUN
ejpam-2677	9	25	distribution	distribution	NOUN
ejpam-2677	9	26	.	.	PUNCT
ejpam-2677	10	1	2010	2010	NUM
ejpam-2677	10	2	mathematics	mathematic	NOUN
ejpam-2677	10	3	subject	subject	NOUN
ejpam-2677	10	4	classifications	classification	NOUN
ejpam-2677	10	5	:	:	PUNCT
ejpam-2677	10	6	60e05	60e05	NUM
ejpam-2677	10	7	,	,	PUNCT
ejpam-2677	10	8	62h11	62h11	PRON
ejpam-2677	10	9	key	key	ADJ
ejpam-2677	10	10	words	word	NOUN
ejpam-2677	10	11	and	and	CCONJ
ejpam-2677	10	12	phrases	phrase	NOUN
ejpam-2677	10	13	:	:	PUNCT
ejpam-2677	10	14	circular	circular	ADJ
ejpam-2677	10	15	model	model	NOUN
ejpam-2677	10	16	,	,	PUNCT
ejpam-2677	10	17	directional	directional	ADJ
ejpam-2677	10	18	data	data	PROPN
ejpam-2677	10	19	,	,	PUNCT
ejpam-2677	10	20	meijer	meijer	NOUN
ejpam-2677	10	21	’s	’s	PART
ejpam-2677	10	22	g	g	NOUN
ejpam-2677	10	23	-	-	PUNCT
ejpam-2677	10	24	function	function	NOUN
ejpam-2677	10	25	,	,	PUNCT
ejpam-2677	10	26	stereographic	stereographic	ADJ
ejpam-2677	10	27	projection	projection	NOUN
ejpam-2677	10	28	,	,	PUNCT
ejpam-2677	10	29	trigonometric	trigonometric	ADJ
ejpam-2677	10	30	moments	moment	NOUN
ejpam-2677	10	31	.	.	PUNCT
ejpam-2677	11	1	1	1	X
ejpam-2677	11	2	.	.	X
ejpam-2677	11	3	introduction	introduction	NOUN
ejpam-2677	11	4	directions	direction	NOUN
ejpam-2677	11	5	in	in	ADP
ejpam-2677	11	6	two	two	NUM
ejpam-2677	11	7	dimensions	dimension	NOUN
ejpam-2677	11	8	can	can	AUX
ejpam-2677	11	9	be	be	AUX
ejpam-2677	11	10	represented	represent	VERB
ejpam-2677	11	11	as	as	ADP
ejpam-2677	11	12	points	point	NOUN
ejpam-2677	11	13	on	on	ADP
ejpam-2677	11	14	the	the	DET
ejpam-2677	11	15	circumference	circumference	NOUN
ejpam-2677	11	16	of	of	ADP
ejpam-2677	11	17	a	a	DET
ejpam-2677	11	18	unit	unit	NOUN
ejpam-2677	11	19	circle	circle	NOUN
ejpam-2677	11	20	and	and	CCONJ
ejpam-2677	11	21	models	model	NOUN
ejpam-2677	11	22	for	for	ADP
ejpam-2677	11	23	representing	represent	VERB
ejpam-2677	11	24	such	such	ADJ
ejpam-2677	11	25	data	datum	NOUN
ejpam-2677	11	26	are	be	AUX
ejpam-2677	11	27	called	call	VERB
ejpam-2677	11	28	circular	circular	ADJ
ejpam-2677	11	29	distributions	distribution	NOUN
ejpam-2677	11	30	.	.	PUNCT
ejpam-2677	12	1	quite	quite	DET
ejpam-2677	12	2	a	a	DET
ejpam-2677	12	3	lot	lot	NOUN
ejpam-2677	12	4	of	of	ADP
ejpam-2677	12	5	work	work	NOUN
ejpam-2677	12	6	was	be	AUX
ejpam-2677	12	7	done	do	VERB
ejpam-2677	12	8	on	on	ADP
ejpam-2677	12	9	circular	circular	ADJ
ejpam-2677	12	10	models	model	NOUN
ejpam-2677	12	11	defined	define	VERB
ejpam-2677	12	12	on	on	ADP
ejpam-2677	12	13	the	the	DET
ejpam-2677	12	14	unit	unit	NOUN
ejpam-2677	12	15	circle	circle	NOUN
ejpam-2677	12	16	(	(	PUNCT
ejpam-2677	12	17	fisher	fisher	PROPN
ejpam-2677	12	18	,	,	PUNCT
ejpam-2677	12	19	1993	1993	NUM
ejpam-2677	12	20	;	;	PUNCT
ejpam-2677	12	21	jammalamadaka	jammalamadaka	PROPN
ejpam-2677	12	22	and	and	CCONJ
ejpam-2677	12	23	sen	sen	PROPN
ejpam-2677	12	24	gupta	gupta	PROPN
ejpam-2677	12	25	(	(	PUNCT
ejpam-2677	12	26	2001	2001	NUM
ejpam-2677	12	27	)	)	PUNCT
ejpam-2677	12	28	;	;	PUNCT
ejpam-2677	12	29	mardia	mardia	NOUN
ejpam-2677	12	30	and	and	CCONJ
ejpam-2677	12	31	jupp	jupp	PROPN
ejpam-2677	12	32	,	,	PUNCT
ejpam-2677	12	33	(	(	PUNCT
ejpam-2677	12	34	2000	2000	NUM
ejpam-2677	12	35	)	)	PUNCT
ejpam-2677	12	36	)	)	PUNCT
ejpam-2677	13	1	and	and	CCONJ
ejpam-2677	13	2	recent	recent	ADJ
ejpam-2677	13	3	publications	publication	NOUN
ejpam-2677	13	4	(	(	PUNCT
ejpam-2677	13	5	dattatreya	dattatreya	PROPN
ejpam-2677	13	6	rao	rao	PROPN
ejpam-2677	13	7	et	et	PROPN
ejpam-2677	13	8	al	al	PROPN
ejpam-2677	13	9	(	(	PUNCT
ejpam-2677	13	10	2007	2007	NUM
ejpam-2677	13	11	)	)	PUNCT
ejpam-2677	13	12	,	,	PUNCT
ejpam-2677	13	13	girija	girija	X
ejpam-2677	13	14	(	(	PUNCT
ejpam-2677	13	15	2010	2010	NUM
ejpam-2677	13	16	)	)	PUNCT
ejpam-2677	13	17	,	,	PUNCT
ejpam-2677	13	18	phani	phani	PROPN
ejpam-2677	13	19	et	et	PROPN
ejpam-2677	13	20	al	al	PROPN
ejpam-2677	13	21	(	(	PUNCT
ejpam-2677	13	22	2012	2012	NUM
ejpam-2677	13	23	)	)	PUNCT
ejpam-2677	13	24	)	)	PUNCT
ejpam-2677	13	25	.	.	PUNCT
ejpam-2677	14	1	most	most	ADJ
ejpam-2677	14	2	of	of	ADP
ejpam-2677	14	3	these	these	DET
ejpam-2677	14	4	models	model	NOUN
ejpam-2677	14	5	are	be	AUX
ejpam-2677	14	6	applicable	applicable	ADJ
ejpam-2677	14	7	for	for	ADP
ejpam-2677	14	8	dealing	deal	VERB
ejpam-2677	14	9	circular	circular	ADJ
ejpam-2677	14	10	data	datum	NOUN
ejpam-2677	14	11	.	.	PUNCT
ejpam-2677	15	1	to	to	PART
ejpam-2677	15	2	fit	fit	VERB
ejpam-2677	15	3	/	/	SYM
ejpam-2677	15	4	model	model	NOUN
ejpam-2677	15	5	certain	certain	ADJ
ejpam-2677	15	6	practical	practical	ADJ
ejpam-2677	15	7	data	data	NOUN
ejpam-2677	15	8	sets	set	NOUN
ejpam-2677	15	9	,	,	PUNCT
ejpam-2677	15	10	it	it	PRON
ejpam-2677	15	11	is	be	AUX
ejpam-2677	15	12	not	not	PART
ejpam-2677	15	13	required	require	VERB
ejpam-2677	15	14	to	to	PART
ejpam-2677	15	15	go	go	VERB
ejpam-2677	15	16	for	for	ADP
ejpam-2677	15	17	full	full	ADJ
ejpam-2677	15	18	circular	circular	ADJ
ejpam-2677	15	19	models	model	NOUN
ejpam-2677	15	20	but	but	CCONJ
ejpam-2677	15	21	semicircular	semicircular	ADJ
ejpam-2677	15	22	/	/	SYM
ejpam-2677	15	23	arc	arc	NOUN
ejpam-2677	15	24	models	model	NOUN
ejpam-2677	15	25	are	be	AUX
ejpam-2677	15	26	adequate	adequate	ADJ
ejpam-2677	15	27	.	.	PUNCT
ejpam-2677	16	1	some	some	DET
ejpam-2677	16	2	recent	recent	ADJ
ejpam-2677	16	3	∗corresponding	∗corresponde	VERB
ejpam-2677	16	4	author	author	NOUN
ejpam-2677	16	5	.	.	PUNCT
ejpam-2677	17	1	email	email	NOUN
ejpam-2677	17	2	addresses	address	NOUN
ejpam-2677	17	3	:	:	PUNCT
ejpam-2677	18	1	phaniyedlapalli23@gmail.com	phaniyedlapalli23@gmail.com	X
ejpam-2677	18	2	(	(	PUNCT
ejpam-2677	18	3	p.	p.	NOUN
ejpam-2677	18	4	yedlapalli	yedlapalli	PROPN
ejpam-2677	18	5	)	)	PUNCT
ejpam-2677	18	6	ajv.radhika09@gmail.com	ajv.radhika09@gmail.com	PROPN
ejpam-2677	18	7	(	(	PUNCT
ejpam-2677	18	8	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	18	9	)	)	PUNCT
ejpam-2677	18	10	,	,	PUNCT
ejpam-2677	18	11	svs.girija@gmail.com	svs.girija@gmail.com	X
ejpam-2677	18	12	(	(	PUNCT
ejpam-2677	18	13	s.v.s.girija	s.v.s.girija	PROPN
ejpam-2677	18	14	)	)	PUNCT
ejpam-2677	18	15	avdrao@gmail.com	avdrao@gmail.com	X
ejpam-2677	18	16	(	(	PUNCT
ejpam-2677	18	17	a.v.dattatreya	a.v.dattatreya	PROPN
ejpam-2677	18	18	rao	rao	PROPN
ejpam-2677	18	19	)	)	PUNCT
ejpam-2677	18	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2677	18	21	1124	1124	NUM
ejpam-2677	19	1	c	c	X
ejpam-2677	19	2	©	©	PROPN
ejpam-2677	19	3	2017	2017	NUM
ejpam-2677	19	4	ejpam	ejpam	VERB
ejpam-2677	19	5	all	all	DET
ejpam-2677	19	6	rights	right	NOUN
ejpam-2677	19	7	reserved	reserve	VERB
ejpam-2677	19	8	.	.	PUNCT
ejpam-2677	20	1	p.	p.	NOUN
ejpam-2677	20	2	yedlapalli	yedlapalli	PROPN
ejpam-2677	20	3	,	,	PUNCT
ejpam-2677	20	4	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	20	5	,	,	PUNCT
ejpam-2677	20	6	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	20	7	,	,	PUNCT
ejpam-2677	20	8	a.v.d	a.v.d	NOUN
ejpam-2677	20	9	.	.	PUNCT
ejpam-2677	20	10	rao	rao	PROPN
ejpam-2677	20	11	/	/	SYM
ejpam-2677	20	12	eur	eur	PROPN
ejpam-2677	20	13	.	.	PUNCT
ejpam-2677	21	1	j.	j.	PROPN
ejpam-2677	21	2	pure	pure	PROPN
ejpam-2677	21	3	appl	appl	PROPN
ejpam-2677	21	4	.	.	PROPN
ejpam-2677	21	5	math	math	PROPN
ejpam-2677	21	6	,	,	PUNCT
ejpam-2677	21	7	10	10	NUM
ejpam-2677	21	8	(	(	PUNCT
ejpam-2677	21	9	5	5	NUM
ejpam-2677	21	10	)	)	PUNCT
ejpam-2677	21	11	(	(	PUNCT
ejpam-2677	21	12	2017	2017	NUM
ejpam-2677	21	13	)	)	PUNCT
ejpam-2677	21	14	,	,	PUNCT
ejpam-2677	21	15	1124	1124	NUM
ejpam-2677	21	16	-	-	SYM
ejpam-2677	21	17	1134	1134	NUM
ejpam-2677	21	18	1125	1125	NUM
ejpam-2677	21	19	papers	paper	NOUN
ejpam-2677	21	20	(	(	PUNCT
ejpam-2677	21	21	guardiola	guardiola	X
ejpam-2677	21	22	(	(	PUNCT
ejpam-2677	21	23	2004	2004	NUM
ejpam-2677	21	24	)	)	PUNCT
ejpam-2677	21	25	,	,	PUNCT
ejpam-2677	21	26	byoung	byoung	PROPN
ejpam-2677	21	27	et	et	PROPN
ejpam-2677	21	28	al	al	PROPN
ejpam-2677	21	29	(	(	PUNCT
ejpam-2677	21	30	2008	2008	NUM
ejpam-2677	21	31	)	)	PUNCT
ejpam-2677	21	32	and	and	CCONJ
ejpam-2677	21	33	phani	phani	PROPN
ejpam-2677	21	34	et	et	PROPN
ejpam-2677	21	35	al	al	PROPN
ejpam-2677	21	36	(	(	PUNCT
ejpam-2677	21	37	2013	2013	NUM
ejpam-2677	21	38	)	)	PUNCT
ejpam-2677	21	39	)	)	PUNCT
ejpam-2677	21	40	address	address	NOUN
ejpam-2677	21	41	this	this	DET
ejpam-2677	21	42	issue	issue	NOUN
ejpam-2677	21	43	and	and	CCONJ
ejpam-2677	21	44	provided	provide	VERB
ejpam-2677	21	45	some	some	DET
ejpam-2677	21	46	methodology	methodology	NOUN
ejpam-2677	21	47	for	for	ADP
ejpam-2677	21	48	constructing	construct	VERB
ejpam-2677	21	49	distributions	distribution	NOUN
ejpam-2677	21	50	suitable	suitable	ADJ
ejpam-2677	21	51	for	for	ADP
ejpam-2677	21	52	modeling	model	VERB
ejpam-2677	21	53	these	these	DET
ejpam-2677	21	54	types	type	NOUN
ejpam-2677	21	55	of	of	ADP
ejpam-2677	21	56	data	datum	NOUN
ejpam-2677	21	57	.	.	PUNCT
ejpam-2677	22	1	for	for	ADP
ejpam-2677	22	2	example	example	NOUN
ejpam-2677	22	3	,	,	PUNCT
ejpam-2677	22	4	when	when	SCONJ
ejpam-2677	22	5	sea	sea	NOUN
ejpam-2677	22	6	turtles	turtle	NOUN
ejpam-2677	22	7	emerge	emerge	VERB
ejpam-2677	22	8	from	from	ADP
ejpam-2677	22	9	the	the	DET
ejpam-2677	22	10	ocean	ocean	NOUN
ejpam-2677	22	11	in	in	ADP
ejpam-2677	22	12	search	search	NOUN
ejpam-2677	22	13	of	of	ADP
ejpam-2677	22	14	a	a	DET
ejpam-2677	22	15	nesting	nesting	ADJ
ejpam-2677	22	16	site	site	NOUN
ejpam-2677	22	17	on	on	ADP
ejpam-2677	22	18	dry	dry	ADJ
ejpam-2677	22	19	land	land	NOUN
ejpam-2677	22	20	,	,	PUNCT
ejpam-2677	22	21	a	a	DET
ejpam-2677	22	22	random	random	ADJ
ejpam-2677	22	23	variable	variable	NOUN
ejpam-2677	22	24	having	have	VERB
ejpam-2677	22	25	values	value	NOUN
ejpam-2677	22	26	on	on	ADP
ejpam-2677	22	27	a	a	DET
ejpam-2677	22	28	semicircle	semicircle	NOUN
ejpam-2677	22	29	is	be	AUX
ejpam-2677	22	30	very	very	ADV
ejpam-2677	22	31	much	much	ADV
ejpam-2677	22	32	sufficient	sufficient	ADJ
ejpam-2677	22	33	for	for	ADP
ejpam-2677	22	34	modeling	model	VERB
ejpam-2677	22	35	such	such	ADJ
ejpam-2677	22	36	data	datum	NOUN
ejpam-2677	22	37	.	.	PUNCT
ejpam-2677	23	1	given	give	VERB
ejpam-2677	23	2	the	the	DET
ejpam-2677	23	3	angles	angle	NOUN
ejpam-2677	23	4	of	of	ADP
ejpam-2677	23	5	initial	initial	ADJ
ejpam-2677	23	6	heading	heading	NOUN
ejpam-2677	23	7	and	and	CCONJ
ejpam-2677	23	8	departure	departure	NOUN
ejpam-2677	23	9	,	,	PUNCT
ejpam-2677	23	10	to	to	PART
ejpam-2677	23	11	trace	trace	VERB
ejpam-2677	23	12	the	the	DET
ejpam-2677	23	13	debris	debris	NOUN
ejpam-2677	23	14	of	of	ADP
ejpam-2677	23	15	aircraft	aircraft	NOUN
ejpam-2677	23	16	lost	lose	VERB
ejpam-2677	23	17	problem	problem	NOUN
ejpam-2677	23	18	,	,	PUNCT
ejpam-2677	23	19	semicircular	semicircular	ADJ
ejpam-2677	23	20	models	model	NOUN
ejpam-2677	23	21	need	need	VERB
ejpam-2677	23	22	to	to	PART
ejpam-2677	23	23	be	be	AUX
ejpam-2677	23	24	used	use	VERB
ejpam-2677	23	25	.	.	PUNCT
ejpam-2677	24	1	a	a	DET
ejpam-2677	24	2	few	few	ADJ
ejpam-2677	24	3	more	more	ADJ
ejpam-2677	24	4	examples	example	NOUN
ejpam-2677	24	5	of	of	ADP
ejpam-2677	24	6	semicircular	semicircular	ADJ
ejpam-2677	24	7	data	datum	NOUN
ejpam-2677	24	8	is	be	AUX
ejpam-2677	24	9	available	available	ADJ
ejpam-2677	24	10	in	in	ADP
ejpam-2677	24	11	ugai	ugai	PROPN
ejpam-2677	24	12	et	et	PROPN
ejpam-2677	24	13	al	al	PROPN
ejpam-2677	24	14	(	(	PUNCT
ejpam-2677	24	15	1977	1977	NUM
ejpam-2677	24	16	)	)	PUNCT
ejpam-2677	24	17	.	.	PUNCT
ejpam-2677	25	1	a	a	DET
ejpam-2677	25	2	little	little	ADJ
ejpam-2677	25	3	attention	attention	NOUN
ejpam-2677	25	4	is	be	AUX
ejpam-2677	25	5	paid	pay	VERB
ejpam-2677	25	6	on	on	ADP
ejpam-2677	25	7	the	the	DET
ejpam-2677	25	8	study	study	NOUN
ejpam-2677	25	9	of	of	ADP
ejpam-2677	25	10	semicircular	semicircular	ADJ
ejpam-2677	25	11	distributions	distribution	NOUN
ejpam-2677	25	12	.	.	PUNCT
ejpam-2677	26	1	the	the	DET
ejpam-2677	26	2	aim	aim	NOUN
ejpam-2677	26	3	of	of	ADP
ejpam-2677	26	4	the	the	DET
ejpam-2677	26	5	present	present	ADJ
ejpam-2677	26	6	article	article	NOUN
ejpam-2677	26	7	is	be	AUX
ejpam-2677	26	8	to	to	PART
ejpam-2677	26	9	contribute	contribute	VERB
ejpam-2677	26	10	towards	towards	ADP
ejpam-2677	26	11	filling	fill	VERB
ejpam-2677	26	12	this	this	DET
ejpam-2677	26	13	gap	gap	NOUN
ejpam-2677	26	14	.	.	PUNCT
ejpam-2677	27	1	in	in	ADP
ejpam-2677	27	2	this	this	DET
ejpam-2677	27	3	paper	paper	NOUN
ejpam-2677	27	4	,	,	PUNCT
ejpam-2677	27	5	the	the	DET
ejpam-2677	27	6	modified	modify	VERB
ejpam-2677	27	7	inverse	inverse	NOUN
ejpam-2677	27	8	stereographic	stereographic	ADJ
ejpam-2677	27	9	projection	projection	NOUN
ejpam-2677	27	10	is	be	AUX
ejpam-2677	27	11	used	use	VERB
ejpam-2677	27	12	to	to	PART
ejpam-2677	27	13	define	define	VERB
ejpam-2677	27	14	a	a	DET
ejpam-2677	27	15	new	new	ADJ
ejpam-2677	27	16	semicircular	semicircular	ADJ
ejpam-2677	27	17	model	model	NOUN
ejpam-2677	27	18	,	,	PUNCT
ejpam-2677	27	19	coined	coin	VERB
ejpam-2677	27	20	as	as	ADP
ejpam-2677	27	21	the	the	DET
ejpam-2677	27	22	stereographic	stereographic	ADJ
ejpam-2677	27	23	semicircular	semicircular	ADJ
ejpam-2677	27	24	gamma	gamma	NOUN
ejpam-2677	27	25	distribution	distribution	NOUN
ejpam-2677	27	26	which	which	PRON
ejpam-2677	27	27	generalizes	generalize	VERB
ejpam-2677	27	28	the	the	DET
ejpam-2677	27	29	stereographic	stereographic	ADJ
ejpam-2677	27	30	semicircular	semicircular	ADJ
ejpam-2677	27	31	exponential	exponential	ADJ
ejpam-2677	27	32	model	model	NOUN
ejpam-2677	27	33	(	(	PUNCT
ejpam-2677	27	34	phani	phani	PROPN
ejpam-2677	27	35	et	et	PROPN
ejpam-2677	27	36	al	al	PROPN
ejpam-2677	27	37	(	(	PUNCT
ejpam-2677	27	38	2013	2013	NUM
ejpam-2677	27	39	)	)	PUNCT
ejpam-2677	27	40	)	)	PUNCT
ejpam-2677	27	41	.	.	PUNCT
ejpam-2677	28	1	explicit	explicit	ADJ
ejpam-2677	28	2	expressions	expression	NOUN
ejpam-2677	28	3	for	for	ADP
ejpam-2677	28	4	trigonometric	trigonometric	ADJ
ejpam-2677	28	5	moments	moment	NOUN
ejpam-2677	28	6	are	be	AUX
ejpam-2677	28	7	derived	derive	VERB
ejpam-2677	28	8	in	in	ADP
ejpam-2677	28	9	terms	term	NOUN
ejpam-2677	28	10	of	of	ADP
ejpam-2677	28	11	meijer	meijer	NOUN
ejpam-2677	28	12	’s	’s	PART
ejpam-2677	28	13	gfunction	gfunction	NOUN
ejpam-2677	28	14	and	and	CCONJ
ejpam-2677	28	15	it	it	PRON
ejpam-2677	28	16	is	be	AUX
ejpam-2677	28	17	extended	extend	VERB
ejpam-2677	28	18	to	to	ADP
ejpam-2677	28	19	the	the	DET
ejpam-2677	28	20	stereographic	stereographic	ADJ
ejpam-2677	28	21	l	l	PROPN
ejpam-2677	28	22	axial	axial	ADJ
ejpam-2677	28	23	gamma	gamma	NOUN
ejpam-2677	28	24	distribution	distribution	NOUN
ejpam-2677	28	25	for	for	ADP
ejpam-2677	28	26	modeling	model	VERB
ejpam-2677	28	27	axial	axial	ADJ
ejpam-2677	28	28	data	datum	NOUN
ejpam-2677	28	29	.	.	PUNCT
ejpam-2677	29	1	in	in	ADP
ejpam-2677	29	2	section	section	NOUN
ejpam-2677	29	3	2	2	NUM
ejpam-2677	29	4	,	,	PUNCT
ejpam-2677	29	5	methodology	methodology	NOUN
ejpam-2677	29	6	of	of	ADP
ejpam-2677	29	7	modified	modified	ADJ
ejpam-2677	29	8	inverse	inverse	NOUN
ejpam-2677	29	9	stereographic	stereographic	ADJ
ejpam-2677	29	10	projection	projection	NOUN
ejpam-2677	29	11	is	be	AUX
ejpam-2677	29	12	presented	present	VERB
ejpam-2677	29	13	.	.	PUNCT
ejpam-2677	30	1	section	section	NOUN
ejpam-2677	30	2	3	3	NUM
ejpam-2677	30	3	is	be	AUX
ejpam-2677	30	4	devoted	devote	VERB
ejpam-2677	30	5	to	to	PART
ejpam-2677	30	6	introduce	introduce	VERB
ejpam-2677	30	7	the	the	DET
ejpam-2677	30	8	proposed	propose	VERB
ejpam-2677	30	9	distribution	distribution	NOUN
ejpam-2677	30	10	and	and	CCONJ
ejpam-2677	30	11	to	to	PART
ejpam-2677	30	12	present	present	VERB
ejpam-2677	30	13	graphs	graph	NOUN
ejpam-2677	30	14	of	of	ADP
ejpam-2677	30	15	probability	probability	NOUN
ejpam-2677	30	16	density	density	NOUN
ejpam-2677	30	17	function	function	NOUN
ejpam-2677	30	18	for	for	ADP
ejpam-2677	30	19	various	various	ADJ
ejpam-2677	30	20	values	value	NOUN
ejpam-2677	30	21	of	of	ADP
ejpam-2677	30	22	parameters	parameter	NOUN
ejpam-2677	30	23	.	.	PUNCT
ejpam-2677	31	1	in	in	ADP
ejpam-2677	31	2	section	section	NOUN
ejpam-2677	31	3	4	4	NUM
ejpam-2677	31	4	,	,	PUNCT
ejpam-2677	31	5	the	the	DET
ejpam-2677	31	6	first	first	ADJ
ejpam-2677	31	7	four	four	NUM
ejpam-2677	31	8	trigonometric	trigonometric	ADJ
ejpam-2677	31	9	moments	moment	NOUN
ejpam-2677	31	10	in	in	ADP
ejpam-2677	31	11	terms	term	NOUN
ejpam-2677	31	12	of	of	ADP
ejpam-2677	31	13	meijer	meijer	NOUN
ejpam-2677	31	14	’s	’s	PART
ejpam-2677	31	15	gfunction	gfunction	NOUN
ejpam-2677	31	16	are	be	AUX
ejpam-2677	31	17	derived	derive	VERB
ejpam-2677	31	18	and	and	CCONJ
ejpam-2677	31	19	the	the	DET
ejpam-2677	31	20	proposed	propose	VERB
ejpam-2677	31	21	model	model	NOUN
ejpam-2677	31	22	is	be	AUX
ejpam-2677	31	23	extended	extend	VERB
ejpam-2677	31	24	to	to	ADP
ejpam-2677	31	25	laxial	laxial	ADJ
ejpam-2677	31	26	distributions	distribution	NOUN
ejpam-2677	31	27	for	for	ADP
ejpam-2677	31	28	modeling	model	VERB
ejpam-2677	31	29	axial	axial	ADJ
ejpam-2677	31	30	data	datum	NOUN
ejpam-2677	31	31	in	in	ADP
ejpam-2677	31	32	section	section	NOUN
ejpam-2677	31	33	5	5	NUM
ejpam-2677	31	34	.	.	SYM
ejpam-2677	32	1	2	2	NUM
ejpam-2677	32	2	.	.	X
ejpam-2677	32	3	methodology	methodology	NOUN
ejpam-2677	32	4	of	of	ADP
ejpam-2677	32	5	modified	modified	ADJ
ejpam-2677	32	6	inverse	inverse	NOUN
ejpam-2677	32	7	stereographic	stereographic	ADJ
ejpam-2677	32	8	projection	projection	NOUN
ejpam-2677	32	9	(	(	PUNCT
ejpam-2677	32	10	phani	phani	PROPN
ejpam-2677	32	11	et	et	PROPN
ejpam-2677	32	12	al	al	PROPN
ejpam-2677	32	13	(	(	PUNCT
ejpam-2677	32	14	2012	2012	NUM
ejpam-2677	32	15	)	)	PUNCT
ejpam-2677	32	16	)	)	PUNCT
ejpam-2677	33	1	modified	modify	VERB
ejpam-2677	33	2	inverse	inverse	NOUN
ejpam-2677	33	3	stereographic	stereographic	ADJ
ejpam-2677	33	4	projection	projection	NOUN
ejpam-2677	33	5	is	be	AUX
ejpam-2677	33	6	defined	define	VERB
ejpam-2677	33	7	by	by	ADP
ejpam-2677	33	8	a	a	DET
ejpam-2677	33	9	one	one	NOUN
ejpam-2677	33	10	to	to	ADP
ejpam-2677	33	11	one	one	NUM
ejpam-2677	33	12	mapping	mapping	NOUN
ejpam-2677	33	13	given	give	VERB
ejpam-2677	33	14	by	by	ADP
ejpam-2677	33	15	t	t	PROPN
ejpam-2677	33	16	(	(	PUNCT
ejpam-2677	33	17	θ	θ	NOUN
ejpam-2677	33	18	)	)	PUNCT
ejpam-2677	33	19	=	=	SYM
ejpam-2677	34	1	x	x	X
ejpam-2677	34	2	=	=	PUNCT
ejpam-2677	34	3	vtan	vtan	PROPN
ejpam-2677	34	4	(	(	PUNCT
ejpam-2677	34	5	θ	θ	PROPN
ejpam-2677	34	6	2	2	NUM
ejpam-2677	34	7	)	)	PUNCT
ejpam-2677	34	8	,	,	PUNCT
ejpam-2677	34	9	where	where	SCONJ
ejpam-2677	34	10	x	x	X
ejpam-2677	34	11	∈	∈	PROPN
ejpam-2677	34	12	(	(	PUNCT
ejpam-2677	34	13	−∞,∞	−∞,∞	NOUN
ejpam-2677	34	14	)	)	PUNCT
ejpam-2677	34	15	,	,	PUNCT
ejpam-2677	34	16	θ	θ	PROPN
ejpam-2677	34	17	∈	∈	PROPN
ejpam-2677	34	18	[	[	X
ejpam-2677	34	19	−π	−π	PROPN
ejpam-2677	34	20	,	,	PUNCT
ejpam-2677	34	21	π	π	PROPN
ejpam-2677	34	22	)	)	PUNCT
ejpam-2677	34	23	,	,	PUNCT
ejpam-2677	34	24	v	v	ADP
ejpam-2677	34	25	>	>	X
ejpam-2677	34	26	0	0	X
ejpam-2677	34	27	.	.	PUNCT
ejpam-2677	34	28	suppose	suppose	VERB
ejpam-2677	34	29	x	x	PRON
ejpam-2677	34	30	is	be	AUX
ejpam-2677	34	31	randomly	randomly	ADV
ejpam-2677	34	32	chosen	choose	VERB
ejpam-2677	34	33	on	on	ADP
ejpam-2677	34	34	the	the	DET
ejpam-2677	34	35	interval	interval	NOUN
ejpam-2677	34	36	(	(	PUNCT
ejpam-2677	34	37	−∞,∞	−∞,∞	NOUN
ejpam-2677	34	38	)	)	PUNCT
ejpam-2677	34	39	.	.	PUNCT
ejpam-2677	35	1	let	let	VERB
ejpam-2677	35	2	f	f	PROPN
ejpam-2677	35	3	(	(	PUNCT
ejpam-2677	35	4	x	x	NOUN
ejpam-2677	35	5	)	)	PUNCT
ejpam-2677	35	6	and	and	CCONJ
ejpam-2677	35	7	f	f	PROPN
ejpam-2677	35	8	(	(	PUNCT
ejpam-2677	35	9	x	x	X
ejpam-2677	35	10	)	)	PUNCT
ejpam-2677	35	11	denote	denote	VERB
ejpam-2677	35	12	the	the	DET
ejpam-2677	35	13	cumulative	cumulative	ADJ
ejpam-2677	35	14	distribution	distribution	NOUN
ejpam-2677	35	15	and	and	CCONJ
ejpam-2677	35	16	probability	probability	NOUN
ejpam-2677	35	17	density	density	NOUN
ejpam-2677	35	18	functions	function	NOUN
ejpam-2677	35	19	of	of	ADP
ejpam-2677	35	20	the	the	DET
ejpam-2677	35	21	random	random	ADJ
ejpam-2677	35	22	variable	variable	NOUN
ejpam-2677	35	23	x	x	X
ejpam-2677	35	24	respectively	respectively	ADV
ejpam-2677	35	25	.	.	PUNCT
ejpam-2677	36	1	then	then	ADV
ejpam-2677	36	2	t−1	t−1	PROPN
ejpam-2677	36	3	(	(	PUNCT
ejpam-2677	36	4	x	x	X
ejpam-2677	36	5	)	)	PUNCT
ejpam-2677	36	6	=	=	SYM
ejpam-2677	36	7	θ	θ	X
ejpam-2677	36	8	=	=	SYM
ejpam-2677	36	9	2tan−1	2tan−1	PROPN
ejpam-2677	36	10	(	(	PUNCT
ejpam-2677	36	11	x	x	NOUN
ejpam-2677	36	12	v	v	NOUN
ejpam-2677	36	13	)	)	PUNCT
ejpam-2677	36	14	by	by	ADP
ejpam-2677	36	15	toshihiro	toshihiro	PROPN
ejpam-2677	36	16	abe	abe	PROPN
ejpam-2677	36	17	et	et	PROPN
ejpam-2677	36	18	al	al	PROPN
ejpam-2677	36	19	(	(	PUNCT
ejpam-2677	36	20	2010	2010	NUM
ejpam-2677	36	21	)	)	PUNCT
ejpam-2677	36	22	is	be	AUX
ejpam-2677	36	23	a	a	DET
ejpam-2677	36	24	random	random	ADJ
ejpam-2677	36	25	point	point	NOUN
ejpam-2677	36	26	on	on	ADP
ejpam-2677	36	27	the	the	DET
ejpam-2677	36	28	unit	unit	NOUN
ejpam-2677	36	29	circle	circle	NOUN
ejpam-2677	36	30	.	.	PUNCT
ejpam-2677	37	1	let	let	VERB
ejpam-2677	37	2	g	g	PROPN
ejpam-2677	37	3	(	(	PUNCT
ejpam-2677	37	4	θ	θ	NOUN
ejpam-2677	37	5	)	)	PUNCT
ejpam-2677	37	6	and	and	CCONJ
ejpam-2677	37	7	g	g	PROPN
ejpam-2677	37	8	(	(	PUNCT
ejpam-2677	37	9	θ	θ	NOUN
ejpam-2677	37	10	)	)	PUNCT
ejpam-2677	37	11	denote	denote	VERB
ejpam-2677	37	12	the	the	DET
ejpam-2677	37	13	cumulative	cumulative	ADJ
ejpam-2677	37	14	distribution	distribution	NOUN
ejpam-2677	37	15	and	and	CCONJ
ejpam-2677	37	16	probability	probability	NOUN
ejpam-2677	37	17	density	density	NOUN
ejpam-2677	37	18	functions	function	NOUN
ejpam-2677	37	19	of	of	ADP
ejpam-2677	37	20	this	this	DET
ejpam-2677	37	21	random	random	ADJ
ejpam-2677	37	22	point	point	NOUN
ejpam-2677	37	23	θ	θ	PROPN
ejpam-2677	37	24	respectively	respectively	ADV
ejpam-2677	37	25	.	.	PUNCT
ejpam-2677	38	1	then	then	ADV
ejpam-2677	38	2	g	g	PROPN
ejpam-2677	38	3	(	(	PUNCT
ejpam-2677	38	4	θ	θ	NOUN
ejpam-2677	38	5	)	)	PUNCT
ejpam-2677	38	6	and	and	CCONJ
ejpam-2677	38	7	g	g	PROPN
ejpam-2677	38	8	(	(	PUNCT
ejpam-2677	38	9	θ	θ	NOUN
ejpam-2677	38	10	)	)	PUNCT
ejpam-2677	38	11	can	can	AUX
ejpam-2677	38	12	be	be	AUX
ejpam-2677	38	13	written	write	VERB
ejpam-2677	38	14	in	in	ADP
ejpam-2677	38	15	terms	term	NOUN
ejpam-2677	38	16	of	of	ADP
ejpam-2677	38	17	f	f	PROPN
ejpam-2677	38	18	(	(	PUNCT
ejpam-2677	38	19	x	x	NOUN
ejpam-2677	38	20	)	)	PUNCT
ejpam-2677	38	21	and	and	CCONJ
ejpam-2677	38	22	f	f	PROPN
ejpam-2677	38	23	(	(	PUNCT
ejpam-2677	38	24	x)using	x)use	VERB
ejpam-2677	38	25	the	the	DET
ejpam-2677	38	26	following	follow	VERB
ejpam-2677	38	27	theorem	theorem	PROPN
ejpam-2677	38	28	.	.	PUNCT
ejpam-2677	38	29	theorem	theorem	VERB
ejpam-2677	38	30	2.1	2.1	NUM
ejpam-2677	38	31	.	.	PUNCT
ejpam-2677	39	1	for	for	ADP
ejpam-2677	39	2	v	v	NOUN
ejpam-2677	39	3	>	>	SYM
ejpam-2677	39	4	0	0	NUM
ejpam-2677	39	5	,	,	PUNCT
ejpam-2677	39	6	i	i	NOUN
ejpam-2677	39	7	)	)	PUNCT
ejpam-2677	39	8	g	g	PROPN
ejpam-2677	39	9	(	(	PUNCT
ejpam-2677	39	10	θ	θ	NOUN
ejpam-2677	39	11	)	)	PUNCT
ejpam-2677	39	12	=	=	SYM
ejpam-2677	39	13	f	f	PROPN
ejpam-2677	39	14	(	(	PUNCT
ejpam-2677	39	15	vtan	vtan	PROPN
ejpam-2677	39	16	(	(	PUNCT
ejpam-2677	39	17	θ	θ	PROPN
ejpam-2677	39	18	2	2	NUM
ejpam-2677	39	19	)	)	PUNCT
ejpam-2677	39	20	)	)	PUNCT
ejpam-2677	39	21	ii	ii	PROPN
ejpam-2677	39	22	)	)	PUNCT
ejpam-2677	39	23	g	g	PROPN
ejpam-2677	39	24	(	(	PUNCT
ejpam-2677	39	25	θ	θ	NOUN
ejpam-2677	39	26	)	)	PUNCT
ejpam-2677	39	27	=	=	SYM
ejpam-2677	39	28	v	v	NOUN
ejpam-2677	39	29	(	(	PUNCT
ejpam-2677	39	30	sec2	sec2	PROPN
ejpam-2677	39	31	(	(	PUNCT
ejpam-2677	39	32	θ2	θ2	PROPN
ejpam-2677	39	33	)	)	PUNCT
ejpam-2677	39	34	2	2	NUM
ejpam-2677	39	35	)	)	PUNCT
ejpam-2677	39	36	f	f	PROPN
ejpam-2677	39	37	(	(	PUNCT
ejpam-2677	39	38	vtan	vtan	PROPN
ejpam-2677	39	39	(	(	PUNCT
ejpam-2677	39	40	θ	θ	PROPN
ejpam-2677	39	41	2	2	NUM
ejpam-2677	39	42	)	)	PUNCT
ejpam-2677	39	43	)	)	PUNCT
ejpam-2677	40	1	by	by	ADP
ejpam-2677	40	2	applying	apply	VERB
ejpam-2677	40	3	this	this	DET
ejpam-2677	40	4	modified	modify	VERB
ejpam-2677	40	5	inverse	inverse	NOUN
ejpam-2677	40	6	stereographic	stereographic	ADJ
ejpam-2677	40	7	projection	projection	NOUN
ejpam-2677	40	8	on	on	ADP
ejpam-2677	40	9	linear	linear	PROPN
ejpam-2677	40	10	models	model	NOUN
ejpam-2677	40	11	with	with	ADP
ejpam-2677	40	12	support	support	NOUN
ejpam-2677	40	13	on	on	ADP
ejpam-2677	40	14	r+	r+	NOUN
ejpam-2677	40	15	(	(	PUNCT
ejpam-2677	40	16	r	r	NOUN
ejpam-2677	40	17	)	)	PUNCT
ejpam-2677	40	18	,	,	PUNCT
ejpam-2677	40	19	new	new	ADJ
ejpam-2677	40	20	distributions	distribution	NOUN
ejpam-2677	40	21	mapped	map	VERB
ejpam-2677	40	22	onto	onto	ADP
ejpam-2677	40	23	[	[	X
ejpam-2677	40	24	0	0	NUM
ejpam-2677	40	25	,	,	PUNCT
ejpam-2677	40	26	π	π	NOUN
ejpam-2677	40	27	)	)	PUNCT
ejpam-2677	40	28	(	(	PUNCT
ejpam-2677	41	1	[	[	X
ejpam-2677	41	2	−π	−π	ADJ
ejpam-2677	41	3	,	,	PUNCT
ejpam-2677	41	4	π	π	NOUN
ejpam-2677	41	5	)	)	PUNCT
ejpam-2677	41	6	)	)	PUNCT
ejpam-2677	41	7	are	be	AUX
ejpam-2677	41	8	derived	derive	VERB
ejpam-2677	41	9	to	to	PART
ejpam-2677	41	10	study	study	VERB
ejpam-2677	41	11	semicircular	semicircular	ADJ
ejpam-2677	41	12	(	(	PUNCT
ejpam-2677	41	13	circular	circular	ADJ
ejpam-2677	41	14	)	)	PUNCT
ejpam-2677	41	15	data	datum	NOUN
ejpam-2677	41	16	.	.	PUNCT
ejpam-2677	42	1	p.	p.	NOUN
ejpam-2677	42	2	yedlapalli	yedlapalli	PROPN
ejpam-2677	42	3	,	,	PUNCT
ejpam-2677	42	4	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	42	5	,	,	PUNCT
ejpam-2677	42	6	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	42	7	,	,	PUNCT
ejpam-2677	42	8	a.v.d	a.v.d	NOUN
ejpam-2677	42	9	.	.	PUNCT
ejpam-2677	42	10	rao	rao	PROPN
ejpam-2677	42	11	/	/	SYM
ejpam-2677	42	12	eur	eur	PROPN
ejpam-2677	42	13	.	.	PUNCT
ejpam-2677	43	1	j.	j.	PROPN
ejpam-2677	43	2	pure	pure	PROPN
ejpam-2677	43	3	appl	appl	PROPN
ejpam-2677	43	4	.	.	PROPN
ejpam-2677	43	5	math	math	PROPN
ejpam-2677	43	6	,	,	PUNCT
ejpam-2677	43	7	10	10	NUM
ejpam-2677	43	8	(	(	PUNCT
ejpam-2677	43	9	5	5	NUM
ejpam-2677	43	10	)	)	PUNCT
ejpam-2677	43	11	(	(	PUNCT
ejpam-2677	43	12	2017	2017	NUM
ejpam-2677	43	13	)	)	PUNCT
ejpam-2677	43	14	,	,	PUNCT
ejpam-2677	43	15	1124	1124	NUM
ejpam-2677	43	16	-	-	SYM
ejpam-2677	43	17	1134	1134	NUM
ejpam-2677	43	18	1126	1126	NUM
ejpam-2677	43	19	3	3	NUM
ejpam-2677	43	20	.	.	PUNCT
ejpam-2677	43	21	stereographic	stereographic	ADJ
ejpam-2677	43	22	semicircular	semicircular	ADJ
ejpam-2677	43	23	gamma	gamma	NOUN
ejpam-2677	43	24	model	model	NOUN
ejpam-2677	43	25	gamma	gamma	NOUN
ejpam-2677	43	26	distribution	distribution	NOUN
ejpam-2677	43	27	plays	play	VERB
ejpam-2677	43	28	a	a	DET
ejpam-2677	43	29	prominent	prominent	ADJ
ejpam-2677	43	30	role	role	NOUN
ejpam-2677	43	31	in	in	ADP
ejpam-2677	43	32	actuarial	actuarial	ADJ
ejpam-2677	43	33	science	science	NOUN
ejpam-2677	43	34	.	.	PUNCT
ejpam-2677	44	1	here	here	ADV
ejpam-2677	44	2	an	an	DET
ejpam-2677	44	3	attempt	attempt	NOUN
ejpam-2677	44	4	is	be	AUX
ejpam-2677	44	5	made	make	VERB
ejpam-2677	44	6	to	to	PART
ejpam-2677	44	7	construct	construct	VERB
ejpam-2677	44	8	stereographic	stereographic	ADJ
ejpam-2677	44	9	version	version	NOUN
ejpam-2677	44	10	of	of	ADP
ejpam-2677	44	11	semicircular	semicircular	ADJ
ejpam-2677	44	12	gamma	gamma	NOUN
ejpam-2677	44	13	distribution	distribution	NOUN
ejpam-2677	44	14	by	by	ADP
ejpam-2677	44	15	inducing	induce	VERB
ejpam-2677	44	16	inverse	inverse	ADJ
ejpam-2677	44	17	stereographic	stereographic	ADJ
ejpam-2677	44	18	projection	projection	NOUN
ejpam-2677	44	19	.	.	PUNCT
ejpam-2677	45	1	a	a	DET
ejpam-2677	45	2	random	random	ADJ
ejpam-2677	45	3	variable	variable	NOUN
ejpam-2677	45	4	x	x	PUNCT
ejpam-2677	45	5	on	on	ADP
ejpam-2677	45	6	the	the	DET
ejpam-2677	45	7	real	real	ADJ
ejpam-2677	45	8	line	line	NOUN
ejpam-2677	45	9	is	be	AUX
ejpam-2677	45	10	said	say	VERB
ejpam-2677	45	11	to	to	PART
ejpam-2677	45	12	have	have	VERB
ejpam-2677	45	13	gamma	gamma	NOUN
ejpam-2677	45	14	distribution	distribution	NOUN
ejpam-2677	45	15	with	with	ADP
ejpam-2677	45	16	index	index	NOUN
ejpam-2677	45	17	parameterc	parameterc	NOUN
ejpam-2677	45	18	>	>	X
ejpam-2677	45	19	0	0	PROPN
ejpam-2677	45	20	,	,	PUNCT
ejpam-2677	45	21	scale	scale	NOUN
ejpam-2677	45	22	parameter	parameter	NOUN
ejpam-2677	45	23	λ	λ	PROPN
ejpam-2677	45	24	>	>	X
ejpam-2677	45	25	0	0	PUNCT
ejpam-2677	45	26	and	and	CCONJ
ejpam-2677	45	27	location	location	NOUN
ejpam-2677	45	28	parameter	parameter	NOUN
ejpam-2677	45	29	α	α	PROPN
ejpam-2677	46	1	if	if	SCONJ
ejpam-2677	46	2	the	the	DET
ejpam-2677	46	3	probability	probability	NOUN
ejpam-2677	46	4	density	density	NOUN
ejpam-2677	46	5	,	,	PUNCT
ejpam-2677	46	6	cumulative	cumulative	ADJ
ejpam-2677	46	7	distribution	distribution	NOUN
ejpam-2677	46	8	and	and	CCONJ
ejpam-2677	46	9	characteristic	characteristic	ADJ
ejpam-2677	46	10	functions	function	NOUN
ejpam-2677	46	11	of	of	ADP
ejpam-2677	46	12	x	x	PUNCT
ejpam-2677	46	13	are	be	AUX
ejpam-2677	46	14	respectively	respectively	ADV
ejpam-2677	46	15	given	give	VERB
ejpam-2677	46	16	by	by	ADP
ejpam-2677	46	17	(	(	PUNCT
ejpam-2677	46	18	1	1	NUM
ejpam-2677	46	19	)	)	PUNCT
ejpam-2677	46	20	f(x	f(x	PROPN
ejpam-2677	46	21	)	)	PUNCT
ejpam-2677	47	1	=	=	PUNCT
ejpam-2677	48	1	(	(	PUNCT
ejpam-2677	48	2	x−α)c−1	x−α)c−1	PROPN
ejpam-2677	48	3	λcγ(c	λcγ(c	PROPN
ejpam-2677	48	4	)	)	PUNCT
ejpam-2677	48	5	exp	exp	NOUN
ejpam-2677	48	6	(	(	PUNCT
ejpam-2677	48	7	−(x−α	−(x−α	NOUN
ejpam-2677	48	8	)	)	PUNCT
ejpam-2677	48	9	λ	λ	NOUN
ejpam-2677	48	10	)	)	PUNCT
ejpam-2677	48	11	for	for	ADP
ejpam-2677	48	12	λ	λ	PROPN
ejpam-2677	48	13	,	,	PUNCT
ejpam-2677	48	14	c	c	X
ejpam-2677	48	15	>	>	X
ejpam-2677	48	16	0	0	PROPN
ejpam-2677	48	17	,	,	PUNCT
ejpam-2677	48	18	x	x	X
ejpam-2677	48	19	>	>	X
ejpam-2677	48	20	0	0	PUNCT
ejpam-2677	48	21	and	and	CCONJ
ejpam-2677	48	22	α	α	X
ejpam-2677	48	23	>	>	X
ejpam-2677	48	24	0	0	PUNCT
ejpam-2677	48	25	(	(	PUNCT
ejpam-2677	48	26	2)f	2)f	NUM
ejpam-2677	48	27	(	(	PUNCT
ejpam-2677	48	28	x	x	NOUN
ejpam-2677	48	29	)	)	PUNCT
ejpam-2677	48	30	=	=	SYM
ejpam-2677	48	31	γ	γ	X
ejpam-2677	48	32	(	(	PUNCT
ejpam-2677	48	33	xλ)(c	xλ)(c	PROPN
ejpam-2677	48	34	)	)	PUNCT
ejpam-2677	48	35	γ(c	γ(c	NUM
ejpam-2677	48	36	)	)	PUNCT
ejpam-2677	48	37	forλ	forλ	NOUN
ejpam-2677	48	38	,	,	PUNCT
ejpam-2677	48	39	c	c	NOUN
ejpam-2677	48	40	>	>	X
ejpam-2677	48	41	0	0	PROPN
ejpam-2677	48	42	,	,	PUNCT
ejpam-2677	48	43	x	x	X
ejpam-2677	48	44	>	>	X
ejpam-2677	48	45	0	0	PUNCT
ejpam-2677	48	46	(	(	PUNCT
ejpam-2677	48	47	3	3	NUM
ejpam-2677	48	48	)	)	PUNCT
ejpam-2677	48	49	φx(t	φx(t	NOUN
ejpam-2677	48	50	)	)	PUNCT
ejpam-2677	48	51	=	=	SYM
ejpam-2677	48	52	1	1	NUM
ejpam-2677	48	53	(	(	PUNCT
ejpam-2677	48	54	1−iλt)c	1−iλt)c	NUM
ejpam-2677	48	55	where	where	SCONJ
ejpam-2677	48	56	t	t	PROPN
ejpam-2677	48	57	∈	∈	PROPN
ejpam-2677	48	58	r	r	NOUN
ejpam-2677	48	59	by	by	ADP
ejpam-2677	48	60	applying	apply	VERB
ejpam-2677	48	61	inverse	inverse	NOUN
ejpam-2677	48	62	stereographic	stereographic	ADJ
ejpam-2677	48	63	projection	projection	NOUN
ejpam-2677	48	64	defined	define	VERB
ejpam-2677	48	65	by	by	ADP
ejpam-2677	48	66	a	a	DET
ejpam-2677	48	67	one	one	NOUN
ejpam-2677	48	68	to	to	ADP
ejpam-2677	48	69	one	one	NUM
ejpam-2677	48	70	mapping	mapping	NOUN
ejpam-2677	48	71	x	x	PUNCT
ejpam-2677	48	72	=	=	SYM
ejpam-2677	48	73	v	v	NUM
ejpam-2677	48	74	tan	tan	PROPN
ejpam-2677	48	75	(	(	PUNCT
ejpam-2677	48	76	θ	θ	PROPN
ejpam-2677	48	77	2	2	NUM
ejpam-2677	48	78	)	)	PUNCT
ejpam-2677	48	79	,	,	PUNCT
ejpam-2677	48	80	v	v	ADP
ejpam-2677	48	81	>	>	X
ejpam-2677	48	82	0	0	NUM
ejpam-2677	48	83	,	,	PUNCT
ejpam-2677	48	84	0	0	NUM
ejpam-2677	48	85	≤	≤	NUM
ejpam-2677	49	1	θ	θ	X
ejpam-2677	49	2	<	<	X
ejpam-2677	49	3	π	π	X
ejpam-2677	49	4	a	a	DET
ejpam-2677	49	5	stereographic	stereographic	ADJ
ejpam-2677	49	6	semicircular	semicircular	ADJ
ejpam-2677	49	7	gamma	gamma	NOUN
ejpam-2677	49	8	distribution	distribution	NOUN
ejpam-2677	49	9	is	be	AUX
ejpam-2677	49	10	obtained	obtain	VERB
ejpam-2677	49	11	a	a	DET
ejpam-2677	49	12	semicircular	semicircular	ADJ
ejpam-2677	49	13	random	random	ADJ
ejpam-2677	49	14	variable	variable	NOUN
ejpam-2677	49	15	θ	θ	PROPN
ejpam-2677	49	16	is	be	AUX
ejpam-2677	49	17	said	say	VERB
ejpam-2677	49	18	to	to	PART
ejpam-2677	49	19	follow	follow	VERB
ejpam-2677	49	20	stereographic	stereographic	ADJ
ejpam-2677	49	21	semicircular	semicircular	ADJ
ejpam-2677	49	22	gamma	gamma	NOUN
ejpam-2677	49	23	distribution	distribution	NOUN
ejpam-2677	49	24	with	with	ADP
ejpam-2677	49	25	index	index	NOUN
ejpam-2677	49	26	parameter	parameter	NOUN
ejpam-2677	50	1	c	c	PROPN
ejpam-2677	50	2	>	>	X
ejpam-2677	50	3	0	0	PROPN
ejpam-2677	50	4	,	,	PUNCT
ejpam-2677	50	5	location	location	NOUN
ejpam-2677	50	6	parameter	parameter	NOUN
ejpam-2677	50	7	µ	µ	NOUN
ejpam-2677	50	8	and	and	CCONJ
ejpam-2677	50	9	scale	scale	NOUN
ejpam-2677	50	10	parameter	parameter	NOUN
ejpam-2677	50	11	σ	σ	PROPN
ejpam-2677	50	12	>	>	X
ejpam-2677	50	13	0	0	NUM
ejpam-2677	50	14	denoted	denote	VERB
ejpam-2677	50	15	by	by	ADP
ejpam-2677	50	16	sscg	sscg	PROPN
ejpam-2677	50	17	(	(	PUNCT
ejpam-2677	50	18	µ	µ	X
ejpam-2677	50	19	,	,	PUNCT
ejpam-2677	50	20	σ	σ	PROPN
ejpam-2677	50	21	,	,	PUNCT
ejpam-2677	50	22	c	c	NOUN
ejpam-2677	50	23	)	)	PUNCT
ejpam-2677	50	24	if	if	SCONJ
ejpam-2677	50	25	the	the	DET
ejpam-2677	50	26	probability	probability	NOUN
ejpam-2677	50	27	density	density	NOUN
ejpam-2677	50	28	and	and	CCONJ
ejpam-2677	50	29	cumulative	cumulative	ADJ
ejpam-2677	50	30	distribution	distribution	NOUN
ejpam-2677	50	31	functions	function	NOUN
ejpam-2677	50	32	are	be	AUX
ejpam-2677	50	33	respectively	respectively	ADV
ejpam-2677	50	34	given	give	VERB
ejpam-2677	50	35	by	by	ADP
ejpam-2677	50	36	g(θ	g(θ	NOUN
ejpam-2677	50	37	)	)	PUNCT
ejpam-2677	50	38	=	=	SYM
ejpam-2677	50	39	1	1	NUM
ejpam-2677	50	40	2σcγ(c	2σcγ(c	NUM
ejpam-2677	50	41	)	)	PUNCT
ejpam-2677	50	42	sec2	sec2	NOUN
ejpam-2677	50	43	(	(	PUNCT
ejpam-2677	50	44	θ	θ	NOUN
ejpam-2677	50	45	2	2	NUM
ejpam-2677	50	46	)	)	PUNCT
ejpam-2677	50	47	(	(	PUNCT
ejpam-2677	50	48	tan	tan	PROPN
ejpam-2677	50	49	(	(	PUNCT
ejpam-2677	50	50	θ	θ	PROPN
ejpam-2677	50	51	2	2	NUM
ejpam-2677	50	52	)	)	PUNCT
ejpam-2677	50	53	−	−	PROPN
ejpam-2677	50	54	µ	µ	X
ejpam-2677	50	55	)	)	PUNCT
ejpam-2677	50	56	c−1	c−1	PROPN
ejpam-2677	50	57	exp	exp	NOUN
ejpam-2677	50	58	(	(	PUNCT
ejpam-2677	50	59	−	−	PROPN
ejpam-2677	50	60	1	1	NUM
ejpam-2677	50	61	σ	σ	PROPN
ejpam-2677	50	62	(	(	PUNCT
ejpam-2677	50	63	tan	tan	PROPN
ejpam-2677	50	64	(	(	PUNCT
ejpam-2677	50	65	θ	θ	PROPN
ejpam-2677	50	66	2	2	NUM
ejpam-2677	50	67	)	)	PUNCT
ejpam-2677	50	68	−	−	PROPN
ejpam-2677	50	69	µ	µ	NOUN
ejpam-2677	50	70	)	)	PUNCT
ejpam-2677	50	71	)	)	PUNCT
ejpam-2677	51	1	where	where	SCONJ
ejpam-2677	51	2	0	0	NUM
ejpam-2677	51	3	≤	≤	NUM
ejpam-2677	51	4	θ	θ	X
ejpam-2677	51	5	<	<	X
ejpam-2677	51	6	π	π	PROPN
ejpam-2677	51	7	,	,	PUNCT
ejpam-2677	51	8	c	c	X
ejpam-2677	51	9	>	>	X
ejpam-2677	51	10	0	0	PROPN
ejpam-2677	51	11	,	,	PUNCT
ejpam-2677	51	12	σ	σ	NOUN
ejpam-2677	51	13	=	=	PUNCT
ejpam-2677	51	14	λ	λ	X
ejpam-2677	51	15	v	v	NOUN
ejpam-2677	51	16	>	>	SYM
ejpam-2677	51	17	0	0	NUM
ejpam-2677	51	18	and	and	CCONJ
ejpam-2677	51	19	µ	µ	X
ejpam-2677	51	20	=	=	SYM
ejpam-2677	51	21	α	α	PRON
ejpam-2677	51	22	v	v	NOUN
ejpam-2677	51	23	(	(	PUNCT
ejpam-2677	51	24	3.1	3.1	NUM
ejpam-2677	51	25	)	)	PUNCT
ejpam-2677	51	26	g(θ	g(θ	PROPN
ejpam-2677	51	27	)	)	PUNCT
ejpam-2677	51	28	=	=	SYM
ejpam-2677	51	29	γt(c	γt(c	NUM
ejpam-2677	51	30	)	)	PUNCT
ejpam-2677	51	31	γ(c	γ(c	NUM
ejpam-2677	51	32	)	)	PUNCT
ejpam-2677	51	33	where	where	SCONJ
ejpam-2677	51	34	t	t	NOUN
ejpam-2677	51	35	=	=	SYM
ejpam-2677	51	36	1	1	NUM
ejpam-2677	51	37	σ	σ	PROPN
ejpam-2677	51	38	tan	tan	PROPN
ejpam-2677	51	39	(	(	PUNCT
ejpam-2677	51	40	θ	θ	PROPN
ejpam-2677	51	41	2	2	NUM
ejpam-2677	51	42	)	)	PUNCT
ejpam-2677	51	43	,	,	PUNCT
ejpam-2677	51	44	θ	θ	PROPN
ejpam-2677	51	45	∈	∈	PROPN
ejpam-2677	52	1	[	[	X
ejpam-2677	52	2	0	0	NUM
ejpam-2677	52	3	,	,	PUNCT
ejpam-2677	52	4	π	π	NOUN
ejpam-2677	52	5	)	)	PUNCT
ejpam-2677	52	6	(	(	PUNCT
ejpam-2677	52	7	3.2	3.2	NUM
ejpam-2677	52	8	)	)	PUNCT
ejpam-2677	52	9	special	special	ADJ
ejpam-2677	52	10	case	case	NOUN
ejpam-2677	52	11	:	:	PUNCT
ejpam-2677	52	12	if	if	SCONJ
ejpam-2677	52	13	c	c	NOUN
ejpam-2677	52	14	=	=	SYM
ejpam-2677	52	15	1	1	NUM
ejpam-2677	52	16	in	in	ADP
ejpam-2677	52	17	(	(	PUNCT
ejpam-2677	52	18	3.1	3.1	NUM
ejpam-2677	52	19	)	)	PUNCT
ejpam-2677	52	20	reduces	reduce	VERB
ejpam-2677	52	21	to	to	ADP
ejpam-2677	52	22	the	the	DET
ejpam-2677	52	23	density	density	NOUN
ejpam-2677	52	24	function	function	NOUN
ejpam-2677	52	25	of	of	ADP
ejpam-2677	52	26	stereographic	stereographic	ADJ
ejpam-2677	52	27	semicircular	semicircular	ADJ
ejpam-2677	52	28	exponential	exponential	ADJ
ejpam-2677	52	29	distribution	distribution	NOUN
ejpam-2677	52	30	(	(	PUNCT
ejpam-2677	52	31	phani	phani	PROPN
ejpam-2677	52	32	et	et	PROPN
ejpam-2677	52	33	al	al	PROPN
ejpam-2677	52	34	(	(	PUNCT
ejpam-2677	52	35	2013	2013	NUM
ejpam-2677	52	36	)	)	PUNCT
ejpam-2677	52	37	)	)	PUNCT
ejpam-2677	52	38	.	.	PUNCT
ejpam-2677	53	1	4	4	X
ejpam-2677	53	2	.	.	X
ejpam-2677	53	3	trigonometric	trigonometric	ADJ
ejpam-2677	53	4	moments	moment	NOUN
ejpam-2677	53	5	of	of	ADP
ejpam-2677	53	6	stereographic	stereographic	ADJ
ejpam-2677	53	7	semicircular	semicircular	ADJ
ejpam-2677	53	8	gamma	gamma	NOUN
ejpam-2677	53	9	distribution	distribution	NOUN
ejpam-2677	53	10	the	the	DET
ejpam-2677	53	11	characteristic	characteristic	ADJ
ejpam-2677	53	12	function	function	NOUN
ejpam-2677	53	13	of	of	ADP
ejpam-2677	53	14	the	the	DET
ejpam-2677	53	15	stereographic	stereographic	ADJ
ejpam-2677	53	16	semicircular	semicircular	ADJ
ejpam-2677	53	17	gamma	gamma	NOUN
ejpam-2677	53	18	model	model	NOUN
ejpam-2677	53	19	is	be	AUX
ejpam-2677	53	20	φθ(p	φθ(p	NUM
ejpam-2677	53	21	)	)	PUNCT
ejpam-2677	53	22	=	=	PUNCT
ejpam-2677	54	1	π∫	π∫	X
ejpam-2677	54	2	0	0	NUM
ejpam-2677	54	3	eipθg(θ)dθ	eipθg(θ)dθ	NOUN
ejpam-2677	54	4	=	=	PUNCT
ejpam-2677	54	5	π∫	π∫	X
ejpam-2677	54	6	0	0	NUM
ejpam-2677	54	7	eipθ	eipθ	NOUN
ejpam-2677	54	8	1	1	NUM
ejpam-2677	54	9	2σcγ(c	2σcγ(c	NUM
ejpam-2677	54	10	)	)	PUNCT
ejpam-2677	54	11	sec2	sec2	NOUN
ejpam-2677	54	12	(	(	PUNCT
ejpam-2677	54	13	θ	θ	NOUN
ejpam-2677	54	14	2	2	NUM
ejpam-2677	54	15	)	)	PUNCT
ejpam-2677	54	16	(	(	PUNCT
ejpam-2677	54	17	tan	tan	PROPN
ejpam-2677	54	18	(	(	PUNCT
ejpam-2677	54	19	θ	θ	PROPN
ejpam-2677	54	20	2	2	NUM
ejpam-2677	54	21	)	)	PUNCT
ejpam-2677	54	22	−	−	PROPN
ejpam-2677	54	23	µ	µ	X
ejpam-2677	54	24	)	)	PUNCT
ejpam-2677	54	25	c−1	c−1	PROPN
ejpam-2677	54	26	exp	exp	NOUN
ejpam-2677	54	27	(	(	PUNCT
ejpam-2677	54	28	−	−	PROPN
ejpam-2677	54	29	1	1	NUM
ejpam-2677	54	30	σ	σ	PROPN
ejpam-2677	54	31	(	(	PUNCT
ejpam-2677	54	32	tan	tan	PROPN
ejpam-2677	54	33	(	(	PUNCT
ejpam-2677	54	34	θ	θ	PROPN
ejpam-2677	54	35	2	2	NUM
ejpam-2677	54	36	)	)	PUNCT
ejpam-2677	54	37	−	−	PROPN
ejpam-2677	54	38	µ	µ	NOUN
ejpam-2677	54	39	)	)	PUNCT
ejpam-2677	54	40	)	)	PUNCT
ejpam-2677	55	1	dθ	dθ	NOUN
ejpam-2677	55	2	the	the	DET
ejpam-2677	55	3	integration	integration	NOUN
ejpam-2677	55	4	is	be	AUX
ejpam-2677	55	5	not	not	PART
ejpam-2677	55	6	tractable	tractable	ADJ
ejpam-2677	55	7	.	.	PUNCT
ejpam-2677	56	1	but	but	CCONJ
ejpam-2677	56	2	trigonometric	trigonometric	ADJ
ejpam-2677	56	3	moments	moment	NOUN
ejpam-2677	56	4	can	can	AUX
ejpam-2677	56	5	be	be	AUX
ejpam-2677	56	6	derived	derive	VERB
ejpam-2677	56	7	by	by	ADP
ejpam-2677	56	8	applying	apply	VERB
ejpam-2677	56	9	the	the	DET
ejpam-2677	56	10	meijer	meijer	NOUN
ejpam-2677	56	11	g	g	PROPN
ejpam-2677	56	12	function	function	NOUN
ejpam-2677	56	13	[	[	X
ejpam-2677	56	14	gradshteyn	gradshteyn	NOUN
ejpam-2677	56	15	and	and	CCONJ
ejpam-2677	56	16	ryzhik	ryzhik	ADJ
ejpam-2677	56	17	(	(	PUNCT
ejpam-2677	56	18	2007	2007	NUM
ejpam-2677	56	19	)	)	PUNCT
ejpam-2677	56	20	]	]	PUNCT
ejpam-2677	56	21	.	.	PUNCT
ejpam-2677	57	1	the	the	DET
ejpam-2677	57	2	trigonometric	trigonometric	ADJ
ejpam-2677	57	3	moments	moment	NOUN
ejpam-2677	57	4	of	of	ADP
ejpam-2677	57	5	the	the	DET
ejpam-2677	57	6	distribution	distribution	NOUN
ejpam-2677	57	7	are	be	AUX
ejpam-2677	57	8	given	give	VERB
ejpam-2677	57	9	by	by	ADP
ejpam-2677	57	10	{	{	PUNCT
ejpam-2677	57	11	ϕp	ϕp	INTJ
ejpam-2677	57	12	:	:	PUNCT
ejpam-2677	57	13	±1,±2,±3	±1,±2,±3	ADJ
ejpam-2677	57	14	,	,	PUNCT
ejpam-2677	57	15	.	.	PUNCT
ejpam-2677	57	16	.	.	PUNCT
ejpam-2677	57	17	.	.	PUNCT
ejpam-2677	58	1	}	}	PUNCT
ejpam-2677	58	2	where	where	SCONJ
ejpam-2677	58	3	ϕp	ϕp	ADV
ejpam-2677	58	4	=	=	VERB
ejpam-2677	58	5	αp	αp	NOUN
ejpam-2677	59	1	+	+	CCONJ
ejpam-2677	59	2	i	i	PRON
ejpam-2677	59	3	βp	βp	VERB
ejpam-2677	59	4	with	with	ADP
ejpam-2677	59	5	p.	p.	PROPN
ejpam-2677	59	6	yedlapalli	yedlapalli	PROPN
ejpam-2677	59	7	,	,	PUNCT
ejpam-2677	59	8	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	59	9	,	,	PUNCT
ejpam-2677	59	10	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	59	11	,	,	PUNCT
ejpam-2677	59	12	a.v.d	a.v.d	NOUN
ejpam-2677	59	13	.	.	PUNCT
ejpam-2677	59	14	rao	rao	PROPN
ejpam-2677	59	15	/	/	SYM
ejpam-2677	59	16	eur	eur	PROPN
ejpam-2677	59	17	.	.	PUNCT
ejpam-2677	60	1	j.	j.	PROPN
ejpam-2677	60	2	pure	pure	PROPN
ejpam-2677	60	3	appl	appl	PROPN
ejpam-2677	60	4	.	.	PROPN
ejpam-2677	60	5	math	math	PROPN
ejpam-2677	60	6	,	,	PUNCT
ejpam-2677	60	7	10	10	NUM
ejpam-2677	60	8	(	(	PUNCT
ejpam-2677	60	9	5	5	NUM
ejpam-2677	60	10	)	)	PUNCT
ejpam-2677	60	11	(	(	PUNCT
ejpam-2677	60	12	2017	2017	NUM
ejpam-2677	60	13	)	)	PUNCT
ejpam-2677	60	14	,	,	PUNCT
ejpam-2677	60	15	1124	1124	NUM
ejpam-2677	60	16	-	-	SYM
ejpam-2677	60	17	1134	1134	NUM
ejpam-2677	60	18	1127	1127	NUM
ejpam-2677	60	19	figure	figure	NOUN
ejpam-2677	60	20	1	1	NUM
ejpam-2677	60	21	:	:	PUNCT
ejpam-2677	60	22	graphs	graph	NOUN
ejpam-2677	60	23	of	of	ADP
ejpam-2677	60	24	probability	probability	NOUN
ejpam-2677	60	25	density	density	NOUN
ejpam-2677	60	26	function	function	NOUN
ejpam-2677	60	27	of	of	ADP
ejpam-2677	60	28	stereographic	stereographic	ADJ
ejpam-2677	60	29	semicircular	semicircular	ADJ
ejpam-2677	60	30	gamma	gamma	NOUN
ejpam-2677	60	31	distribution	distribution	NOUN
ejpam-2677	60	32	for	for	ADP
ejpam-2677	60	33	various	various	ADJ
ejpam-2677	60	34	values	value	NOUN
ejpam-2677	60	35	of	of	ADP
ejpam-2677	60	36	σ	σ	PROPN
ejpam-2677	60	37	and	and	CCONJ
ejpam-2677	60	38	c	c	NOUN
ejpam-2677	60	39	=	=	SYM
ejpam-2677	60	40	1.5	1.5	NUM
ejpam-2677	60	41	αp	αp	NOUN
ejpam-2677	60	42	=	=	SYM
ejpam-2677	60	43	e(cos	e(co	NOUN
ejpam-2677	60	44	pθ	pθ	VERB
ejpam-2677	60	45	)	)	PUNCT
ejpam-2677	60	46	and	and	CCONJ
ejpam-2677	60	47	βp	βp	X
ejpam-2677	61	1	=	=	PROPN
ejpam-2677	61	2	e(sin	e(sin	PROPN
ejpam-2677	61	3	pθ	pθ	PROPN
ejpam-2677	61	4	)	)	PUNCT
ejpam-2677	61	5	being	be	AUX
ejpam-2677	61	6	the	the	DET
ejpam-2677	61	7	pth	pth	NOUN
ejpam-2677	61	8	order	order	NOUN
ejpam-2677	61	9	cosine	cosine	NOUN
ejpam-2677	61	10	and	and	CCONJ
ejpam-2677	61	11	sine	sine	ADJ
ejpam-2677	61	12	moments	moment	NOUN
ejpam-2677	61	13	of	of	ADP
ejpam-2677	61	14	the	the	DET
ejpam-2677	61	15	random	random	ADJ
ejpam-2677	61	16	angle	angle	NOUN
ejpam-2677	61	17	θ	θ	NOUN
ejpam-2677	61	18	,	,	PUNCT
ejpam-2677	61	19	respectively	respectively	ADV
ejpam-2677	61	20	and	and	CCONJ
ejpam-2677	61	21	are	be	AUX
ejpam-2677	61	22	required	require	VERB
ejpam-2677	61	23	to	to	PART
ejpam-2677	61	24	study	study	VERB
ejpam-2677	61	25	the	the	DET
ejpam-2677	61	26	population	population	NOUN
ejpam-2677	61	27	characteristics	characteristic	NOUN
ejpam-2677	61	28	.	.	PUNCT
ejpam-2677	62	1	theorem	theorem	VERB
ejpam-2677	62	2	4.1	4.1	NUM
ejpam-2677	62	3	:	:	PUNCT
ejpam-2677	62	4	the	the	DET
ejpam-2677	62	5	trigonometric	trigonometric	ADJ
ejpam-2677	62	6	moments	moment	NOUN
ejpam-2677	62	7	αp	αp	NOUN
ejpam-2677	63	1	=	=	SYM
ejpam-2677	63	2	e(cos	e(co	NOUN
ejpam-2677	63	3	pθ	pθ	VERB
ejpam-2677	63	4	)	)	PUNCT
ejpam-2677	63	5	and	and	CCONJ
ejpam-2677	63	6	βp	βp	X
ejpam-2677	63	7	=	=	PROPN
ejpam-2677	63	8	e(sin	e(sin	PROPN
ejpam-2677	63	9	pθ	pθ	PROPN
ejpam-2677	63	10	)	)	PUNCT
ejpam-2677	63	11	,	,	PUNCT
ejpam-2677	63	12	for	for	ADP
ejpam-2677	63	13	p	p	NOUN
ejpam-2677	63	14	=	=	SYM
ejpam-2677	63	15	1	1	NUM
ejpam-2677	63	16	,	,	PUNCT
ejpam-2677	63	17	2	2	NUM
ejpam-2677	63	18	,	,	PUNCT
ejpam-2677	63	19	3	3	NUM
ejpam-2677	63	20	,	,	PUNCT
ejpam-2677	63	21	4	4	NUM
ejpam-2677	63	22	of	of	ADP
ejpam-2677	63	23	the	the	DET
ejpam-2677	63	24	stereographic	stereographic	ADJ
ejpam-2677	63	25	semicircular	semicircular	ADJ
ejpam-2677	63	26	gamma	gamma	NOUN
ejpam-2677	63	27	distribution	distribution	NOUN
ejpam-2677	63	28	with	with	ADP
ejpam-2677	63	29	µ	µ	NOUN
ejpam-2677	63	30	=	=	SYM
ejpam-2677	63	31	0	0	NUM
ejpam-2677	63	32	,	,	PUNCT
ejpam-2677	63	33	are	be	AUX
ejpam-2677	63	34	given	give	VERB
ejpam-2677	63	35	as	as	SCONJ
ejpam-2677	63	36	follows	follow	VERB
ejpam-2677	63	37	α1	α1	PROPN
ejpam-2677	63	38	=	=	SYM
ejpam-2677	63	39	1−	1−	NUM
ejpam-2677	63	40	1	1	NUM
ejpam-2677	63	41	σc	σc	PROPN
ejpam-2677	63	42	√	√	NUM
ejpam-2677	63	43	π	π	PROPN
ejpam-2677	63	44	γ	γ	X
ejpam-2677	63	45	(	(	PUNCT
ejpam-2677	63	46	c	c	NOUN
ejpam-2677	63	47	)	)	PUNCT
ejpam-2677	63	48	g31	g31	NOUN
ejpam-2677	63	49	13	13	NUM
ejpam-2677	63	50	(	(	PUNCT
ejpam-2677	63	51	1	1	NUM
ejpam-2677	63	52	4σ2	4σ2	NUM
ejpam-2677	63	53	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	64	1	−	−	NOUN
ejpam-2677	64	2	c	c	NOUN
ejpam-2677	64	3	2	2	NUM
ejpam-2677	64	4	−	−	NOUN
ejpam-2677	64	5	c	c	NOUN
ejpam-2677	64	6	2	2	NUM
ejpam-2677	64	7	,	,	PUNCT
ejpam-2677	64	8	0	0	NUM
ejpam-2677	64	9	,	,	PUNCT
ejpam-2677	64	10	1	1	NUM
ejpam-2677	64	11	2	2	X
ejpam-2677	64	12	)	)	PUNCT
ejpam-2677	64	13	β1	β1	NOUN
ejpam-2677	64	14	=	=	NOUN
ejpam-2677	64	15	1	1	NUM
ejpam-2677	64	16	σc	σc	PROPN
ejpam-2677	64	17	√	√	NUM
ejpam-2677	64	18	π	π	PROPN
ejpam-2677	64	19	γ	γ	X
ejpam-2677	64	20	(	(	PUNCT
ejpam-2677	64	21	c	c	NOUN
ejpam-2677	64	22	)	)	PUNCT
ejpam-2677	64	23	g31	g31	NOUN
ejpam-2677	64	24	13	13	NUM
ejpam-2677	64	25	(	(	PUNCT
ejpam-2677	64	26	1	1	NUM
ejpam-2677	64	27	4σ2	4σ2	NUM
ejpam-2677	64	28	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	64	29	1−c	1−c	NUM
ejpam-2677	64	30	2	2	NUM
ejpam-2677	64	31	1−c	1−c	NUM
ejpam-2677	64	32	2	2	NUM
ejpam-2677	64	33	,	,	PUNCT
ejpam-2677	64	34	0	0	NUM
ejpam-2677	64	35	,	,	PUNCT
ejpam-2677	64	36	1	1	NUM
ejpam-2677	64	37	2	2	NUM
ejpam-2677	64	38	)	)	PUNCT
ejpam-2677	64	39	α2	α2	NOUN
ejpam-2677	64	40	=	=	SYM
ejpam-2677	64	41	1	1	NUM
ejpam-2677	64	42	+	+	NUM
ejpam-2677	64	43	4	4	NUM
ejpam-2677	64	44	σc	σc	NOUN
ejpam-2677	64	45	√	√	NUM
ejpam-2677	64	46	π	π	PROPN
ejpam-2677	64	47	γ	γ	X
ejpam-2677	64	48	(	(	PUNCT
ejpam-2677	64	49	c	c	NOUN
ejpam-2677	64	50	)	)	PUNCT
ejpam-2677	64	51	g31	g31	NOUN
ejpam-2677	64	52	13	13	NUM
ejpam-2677	64	53	(	(	PUNCT
ejpam-2677	64	54	1	1	NUM
ejpam-2677	64	55	4σ2	4σ2	NUM
ejpam-2677	64	56	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	65	1	−	−	NOUN
ejpam-2677	65	2	c	c	NOUN
ejpam-2677	65	3	2	2	NUM
ejpam-2677	65	4	−	−	NOUN
ejpam-2677	65	5	1	1	NUM
ejpam-2677	65	6	−	−	PROPN
ejpam-2677	65	7	c	c	NOUN
ejpam-2677	65	8	2	2	NUM
ejpam-2677	65	9	,	,	PUNCT
ejpam-2677	65	10	0	0	NUM
ejpam-2677	65	11	,	,	PUNCT
ejpam-2677	65	12	1	1	NUM
ejpam-2677	65	13	2	2	NUM
ejpam-2677	65	14	)	)	PUNCT
ejpam-2677	65	15	−	−	PROPN
ejpam-2677	65	16	4	4	NUM
ejpam-2677	65	17	σc	σc	PROPN
ejpam-2677	65	18	√	√	NUM
ejpam-2677	65	19	π	π	PROPN
ejpam-2677	65	20	γ	γ	X
ejpam-2677	65	21	(	(	PUNCT
ejpam-2677	65	22	c	c	NOUN
ejpam-2677	65	23	)	)	PUNCT
ejpam-2677	65	24	g31	g31	NOUN
ejpam-2677	65	25	13	13	NUM
ejpam-2677	65	26	(	(	PUNCT
ejpam-2677	65	27	1	1	NUM
ejpam-2677	65	28	4σ2	4σ2	NUM
ejpam-2677	65	29	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	66	1	−	−	NOUN
ejpam-2677	66	2	c	c	NOUN
ejpam-2677	66	3	2	2	NUM
ejpam-2677	66	4	−	−	NOUN
ejpam-2677	66	5	c	c	NOUN
ejpam-2677	66	6	2	2	NUM
ejpam-2677	66	7	,	,	PUNCT
ejpam-2677	66	8	0	0	NUM
ejpam-2677	66	9	,	,	PUNCT
ejpam-2677	66	10	1	1	NUM
ejpam-2677	66	11	2	2	NUM
ejpam-2677	66	12	)	)	PUNCT
ejpam-2677	66	13	p.	p.	NOUN
ejpam-2677	66	14	yedlapalli	yedlapalli	PROPN
ejpam-2677	66	15	,	,	PUNCT
ejpam-2677	66	16	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	66	17	,	,	PUNCT
ejpam-2677	66	18	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	66	19	,	,	PUNCT
ejpam-2677	66	20	a.v.d	a.v.d	NOUN
ejpam-2677	66	21	.	.	PUNCT
ejpam-2677	66	22	rao	rao	PROPN
ejpam-2677	66	23	/	/	SYM
ejpam-2677	66	24	eur	eur	PROPN
ejpam-2677	66	25	.	.	PUNCT
ejpam-2677	67	1	j.	j.	PROPN
ejpam-2677	67	2	pure	pure	PROPN
ejpam-2677	67	3	appl	appl	PROPN
ejpam-2677	67	4	.	.	PROPN
ejpam-2677	67	5	math	math	PROPN
ejpam-2677	67	6	,	,	PUNCT
ejpam-2677	67	7	10	10	NUM
ejpam-2677	67	8	(	(	PUNCT
ejpam-2677	67	9	5	5	NUM
ejpam-2677	67	10	)	)	PUNCT
ejpam-2677	67	11	(	(	PUNCT
ejpam-2677	67	12	2017	2017	NUM
ejpam-2677	67	13	)	)	PUNCT
ejpam-2677	67	14	,	,	PUNCT
ejpam-2677	67	15	1124	1124	NUM
ejpam-2677	67	16	-	-	SYM
ejpam-2677	67	17	1134	1134	NUM
ejpam-2677	67	18	1128	1128	NUM
ejpam-2677	67	19	β2	β2	NOUN
ejpam-2677	67	20	=	=	NOUN
ejpam-2677	67	21	2	2	NUM
ejpam-2677	67	22	σc	σc	NOUN
ejpam-2677	67	23	√	√	NUM
ejpam-2677	67	24	π	π	PROPN
ejpam-2677	67	25	γ	γ	X
ejpam-2677	67	26	(	(	PUNCT
ejpam-2677	67	27	c	c	NOUN
ejpam-2677	67	28	)	)	PUNCT
ejpam-2677	67	29	g31	g31	NOUN
ejpam-2677	67	30	13	13	NUM
ejpam-2677	68	1	(	(	PUNCT
ejpam-2677	68	2	1	1	NUM
ejpam-2677	68	3	4σ2	4σ2	NUM
ejpam-2677	68	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	68	5	−	−	NOUN
ejpam-2677	68	6	c	c	NOUN
ejpam-2677	68	7	2	2	NUM
ejpam-2677	68	8	−	−	NOUN
ejpam-2677	68	9	c	c	NOUN
ejpam-2677	68	10	2	2	NUM
ejpam-2677	68	11	,	,	PUNCT
ejpam-2677	68	12	0	0	NUM
ejpam-2677	68	13	,	,	PUNCT
ejpam-2677	68	14	1	1	NUM
ejpam-2677	68	15	2	2	NUM
ejpam-2677	68	16	)	)	PUNCT
ejpam-2677	68	17	−	−	PROPN
ejpam-2677	68	18	4	4	NUM
ejpam-2677	68	19	σc	σc	PROPN
ejpam-2677	68	20	√	√	NUM
ejpam-2677	68	21	π	π	PROPN
ejpam-2677	68	22	γ	γ	X
ejpam-2677	68	23	(	(	PUNCT
ejpam-2677	68	24	c	c	NOUN
ejpam-2677	68	25	)	)	PUNCT
ejpam-2677	68	26	g31	g31	NOUN
ejpam-2677	68	27	13	13	NUM
ejpam-2677	68	28	(	(	PUNCT
ejpam-2677	68	29	1	1	NUM
ejpam-2677	68	30	4σ2	4σ2	NUM
ejpam-2677	68	31	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-2677	69	1	−	−	PROPN
ejpam-2677	70	1	(	(	PUNCT
ejpam-2677	70	2	c+1	c+1	NOUN
ejpam-2677	70	3	)	)	PUNCT
ejpam-2677	70	4	2	2	NUM
ejpam-2677	70	5	−	−	PROPN
ejpam-2677	70	6	(	(	PUNCT
ejpam-2677	70	7	1−c	1−c	NUM
ejpam-2677	70	8	)	)	PUNCT
ejpam-2677	70	9	2	2	NUM
ejpam-2677	70	10	,	,	PUNCT
ejpam-2677	70	11	0	0	NUM
ejpam-2677	70	12	,	,	PUNCT
ejpam-2677	70	13	1	1	NUM
ejpam-2677	70	14	2	2	NUM
ejpam-2677	70	15	)	)	PUNCT
ejpam-2677	70	16	α3	α3	NOUN
ejpam-2677	70	17	=	=	SYM
ejpam-2677	70	18	1−	1−	NUM
ejpam-2677	70	19	16	16	NUM
ejpam-2677	70	20	3σc	3σc	NOUN
ejpam-2677	70	21	√	√	PROPN
ejpam-2677	70	22	π	π	PROPN
ejpam-2677	70	23	γ(c	γ(c	PROPN
ejpam-2677	70	24	)	)	PUNCT
ejpam-2677	70	25	g31	g31	PROPN
ejpam-2677	70	26	13	13	NUM
ejpam-2677	70	27	(	(	PUNCT
ejpam-2677	70	28	1	1	NUM
ejpam-2677	70	29	4σ2	4σ2	NUM
ejpam-2677	70	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	71	1	−	−	NOUN
ejpam-2677	71	2	c	c	NOUN
ejpam-2677	71	3	2	2	NUM
ejpam-2677	71	4	−	−	NOUN
ejpam-2677	71	5	2	2	NUM
ejpam-2677	71	6	−	−	NOUN
ejpam-2677	71	7	c	c	NOUN
ejpam-2677	71	8	2	2	NUM
ejpam-2677	71	9	,	,	PUNCT
ejpam-2677	71	10	0	0	NUM
ejpam-2677	71	11	,	,	PUNCT
ejpam-2677	71	12	1	1	NUM
ejpam-2677	71	13	2	2	NUM
ejpam-2677	71	14	)	)	PUNCT
ejpam-2677	71	15	−	−	PROPN
ejpam-2677	71	16	24	24	NUM
ejpam-2677	71	17	σc	σc	PROPN
ejpam-2677	71	18	√	√	PROPN
ejpam-2677	71	19	π	π	PROPN
ejpam-2677	71	20	γ(c	γ(c	PROPN
ejpam-2677	71	21	)	)	PUNCT
ejpam-2677	71	22	g31	g31	PROPN
ejpam-2677	71	23	13	13	NUM
ejpam-2677	71	24	(	(	PUNCT
ejpam-2677	71	25	1	1	NUM
ejpam-2677	71	26	4σ2	4σ2	NUM
ejpam-2677	71	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	72	1	−	−	NOUN
ejpam-2677	72	2	c	c	NOUN
ejpam-2677	72	3	2	2	NUM
ejpam-2677	72	4	−	−	NOUN
ejpam-2677	72	5	1	1	NUM
ejpam-2677	72	6	−	−	PROPN
ejpam-2677	72	7	c	c	NOUN
ejpam-2677	72	8	2	2	NUM
ejpam-2677	72	9	,	,	PUNCT
ejpam-2677	72	10	0	0	NUM
ejpam-2677	72	11	,	,	PUNCT
ejpam-2677	72	12	1	1	NUM
ejpam-2677	72	13	2	2	NUM
ejpam-2677	72	14	)	)	PUNCT
ejpam-2677	72	15	−	−	PROPN
ejpam-2677	72	16	9	9	NUM
ejpam-2677	72	17	σc	σc	PROPN
ejpam-2677	72	18	√	√	PROPN
ejpam-2677	72	19	π	π	PROPN
ejpam-2677	72	20	γ(c	γ(c	PROPN
ejpam-2677	72	21	)	)	PUNCT
ejpam-2677	72	22	g31	g31	PROPN
ejpam-2677	72	23	13	13	NUM
ejpam-2677	72	24	(	(	PUNCT
ejpam-2677	72	25	1	1	NUM
ejpam-2677	72	26	4σ2	4σ2	NUM
ejpam-2677	72	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	73	1	−	−	NOUN
ejpam-2677	73	2	c	c	NOUN
ejpam-2677	73	3	2	2	NUM
ejpam-2677	73	4	−	−	NOUN
ejpam-2677	73	5	c	c	NOUN
ejpam-2677	73	6	2	2	NUM
ejpam-2677	73	7	,	,	PUNCT
ejpam-2677	73	8	0	0	NUM
ejpam-2677	73	9	,	,	PUNCT
ejpam-2677	73	10	1	1	NUM
ejpam-2677	73	11	2	2	NUM
ejpam-2677	73	12	)	)	PUNCT
ejpam-2677	73	13	β3	β3	NOUN
ejpam-2677	73	14	=	=	SYM
ejpam-2677	73	15	3	3	NUM
ejpam-2677	73	16	σc	σc	NOUN
ejpam-2677	73	17	√	√	NUM
ejpam-2677	73	18	π	π	PROPN
ejpam-2677	73	19	γ	γ	X
ejpam-2677	73	20	(	(	PUNCT
ejpam-2677	73	21	c	c	NOUN
ejpam-2677	73	22	)	)	PUNCT
ejpam-2677	73	23	g31	g31	NOUN
ejpam-2677	73	24	13	13	NUM
ejpam-2677	73	25	(	(	PUNCT
ejpam-2677	73	26	1	1	NUM
ejpam-2677	73	27	4σ2	4σ2	NUM
ejpam-2677	73	28	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	73	29	1−c	1−c	NUM
ejpam-2677	73	30	2	2	NUM
ejpam-2677	73	31	1−c	1−c	NUM
ejpam-2677	73	32	2	2	NUM
ejpam-2677	73	33	,	,	PUNCT
ejpam-2677	73	34	0	0	NUM
ejpam-2677	73	35	,	,	PUNCT
ejpam-2677	73	36	1	1	NUM
ejpam-2677	73	37	2	2	NUM
ejpam-2677	73	38	)	)	PUNCT
ejpam-2677	73	39	−	−	PROPN
ejpam-2677	73	40	8	8	NUM
ejpam-2677	73	41	σc	σc	PROPN
ejpam-2677	73	42	√	√	NUM
ejpam-2677	73	43	π	π	PROPN
ejpam-2677	73	44	γ	γ	X
ejpam-2677	73	45	(	(	PUNCT
ejpam-2677	73	46	c	c	NOUN
ejpam-2677	73	47	)	)	PUNCT
ejpam-2677	73	48	g31	g31	NOUN
ejpam-2677	73	49	13	13	NUM
ejpam-2677	73	50	(	(	PUNCT
ejpam-2677	73	51	1	1	NUM
ejpam-2677	73	52	4σ2	4σ2	NUM
ejpam-2677	73	53	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-2677	73	54	−	−	PROPN
ejpam-2677	73	55	(	(	PUNCT
ejpam-2677	73	56	c+1	c+1	NOUN
ejpam-2677	73	57	)	)	PUNCT
ejpam-2677	73	58	2	2	NUM
ejpam-2677	73	59	−	−	PROPN
ejpam-2677	73	60	(	(	PUNCT
ejpam-2677	73	61	1−c	1−c	NUM
ejpam-2677	73	62	)	)	PUNCT
ejpam-2677	73	63	2	2	NUM
ejpam-2677	73	64	,	,	PUNCT
ejpam-2677	73	65	0	0	NUM
ejpam-2677	73	66	,	,	PUNCT
ejpam-2677	73	67	1	1	NUM
ejpam-2677	73	68	2	2	NUM
ejpam-2677	73	69	)	)	PUNCT
ejpam-2677	73	70	α4	α4	NOUN
ejpam-2677	73	71	=	=	SYM
ejpam-2677	73	72	1	1	NUM
ejpam-2677	73	73	+	+	NUM
ejpam-2677	73	74	32	32	NUM
ejpam-2677	73	75	3σc	3σc	NOUN
ejpam-2677	73	76	√	√	PROPN
ejpam-2677	73	77	π	π	PROPN
ejpam-2677	73	78	γ(c	γ(c	PROPN
ejpam-2677	73	79	)	)	PUNCT
ejpam-2677	73	80	g31	g31	PROPN
ejpam-2677	73	81	13	13	NUM
ejpam-2677	73	82	(	(	PUNCT
ejpam-2677	73	83	1	1	NUM
ejpam-2677	73	84	4σ2	4σ2	NUM
ejpam-2677	73	85	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	74	1	−	−	NOUN
ejpam-2677	74	2	c	c	NOUN
ejpam-2677	74	3	2	2	NUM
ejpam-2677	74	4	−	−	NOUN
ejpam-2677	74	5	3	3	NUM
ejpam-2677	74	6	−	−	PROPN
ejpam-2677	74	7	c	c	NOUN
ejpam-2677	74	8	2	2	NUM
ejpam-2677	74	9	,	,	PUNCT
ejpam-2677	74	10	0	0	NUM
ejpam-2677	74	11	,	,	PUNCT
ejpam-2677	74	12	1	1	NUM
ejpam-2677	74	13	2	2	NUM
ejpam-2677	74	14	)	)	PUNCT
ejpam-2677	74	15	+	+	CCONJ
ejpam-2677	74	16	80	80	NUM
ejpam-2677	74	17	σc	σc	NOUN
ejpam-2677	74	18	√	√	NUM
ejpam-2677	74	19	π	π	PROPN
ejpam-2677	74	20	γ(c	γ(c	PROPN
ejpam-2677	74	21	)	)	PUNCT
ejpam-2677	74	22	g31	g31	PROPN
ejpam-2677	74	23	13	13	NUM
ejpam-2677	74	24	(	(	PUNCT
ejpam-2677	74	25	1	1	NUM
ejpam-2677	74	26	4σ2	4σ2	NUM
ejpam-2677	74	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	74	28	−	−	NOUN
ejpam-2677	74	29	c	c	NOUN
ejpam-2677	74	30	2	2	NUM
ejpam-2677	74	31	−	−	NOUN
ejpam-2677	74	32	1	1	NUM
ejpam-2677	74	33	−	−	PROPN
ejpam-2677	74	34	c	c	NOUN
ejpam-2677	74	35	2	2	NUM
ejpam-2677	74	36	,	,	PUNCT
ejpam-2677	74	37	0	0	NUM
ejpam-2677	74	38	,	,	PUNCT
ejpam-2677	74	39	1	1	NUM
ejpam-2677	74	40	2	2	NUM
ejpam-2677	74	41	)	)	PUNCT
ejpam-2677	74	42	−	−	PROPN
ejpam-2677	74	43	64	64	NUM
ejpam-2677	74	44	σc	σc	PROPN
ejpam-2677	74	45	√	√	NUM
ejpam-2677	74	46	π	π	PROPN
ejpam-2677	74	47	γ(c	γ(c	PROPN
ejpam-2677	74	48	)	)	PUNCT
ejpam-2677	74	49	g31	g31	PROPN
ejpam-2677	74	50	13	13	NUM
ejpam-2677	74	51	(	(	PUNCT
ejpam-2677	74	52	1	1	NUM
ejpam-2677	74	53	4σ2	4σ2	NUM
ejpam-2677	74	54	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	75	1	−	−	NOUN
ejpam-2677	75	2	c	c	NOUN
ejpam-2677	75	3	2	2	NUM
ejpam-2677	75	4	−	−	NOUN
ejpam-2677	75	5	2	2	NUM
ejpam-2677	75	6	−	−	NOUN
ejpam-2677	75	7	c	c	NOUN
ejpam-2677	75	8	2	2	NUM
ejpam-2677	75	9	,	,	PUNCT
ejpam-2677	75	10	0	0	NUM
ejpam-2677	75	11	,	,	PUNCT
ejpam-2677	75	12	1	1	NUM
ejpam-2677	75	13	2	2	NUM
ejpam-2677	75	14	)	)	PUNCT
ejpam-2677	75	15	−	−	PROPN
ejpam-2677	75	16	16	16	NUM
ejpam-2677	75	17	σc	σc	PROPN
ejpam-2677	75	18	√	√	PROPN
ejpam-2677	75	19	π	π	PROPN
ejpam-2677	75	20	γ(c	γ(c	PROPN
ejpam-2677	75	21	)	)	PUNCT
ejpam-2677	75	22	g31	g31	PROPN
ejpam-2677	75	23	13	13	NUM
ejpam-2677	75	24	(	(	PUNCT
ejpam-2677	75	25	1	1	NUM
ejpam-2677	75	26	4σ2	4σ2	NUM
ejpam-2677	75	27	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	76	1	−	−	NOUN
ejpam-2677	76	2	c	c	NOUN
ejpam-2677	76	3	2	2	NUM
ejpam-2677	76	4	−	−	NOUN
ejpam-2677	76	5	c	c	NOUN
ejpam-2677	76	6	2	2	NUM
ejpam-2677	76	7	,	,	PUNCT
ejpam-2677	76	8	0	0	NUM
ejpam-2677	76	9	,	,	PUNCT
ejpam-2677	76	10	1	1	NUM
ejpam-2677	76	11	2	2	NUM
ejpam-2677	76	12	)	)	PUNCT
ejpam-2677	76	13	β4	β4	PROPN
ejpam-2677	76	14	=	=	PUNCT
ejpam-2677	76	15	4	4	NUM
ejpam-2677	76	16	σc	σc	NOUN
ejpam-2677	76	17	√	√	NUM
ejpam-2677	76	18	π	π	PROPN
ejpam-2677	76	19	γ(c	γ(c	PROPN
ejpam-2677	76	20	)	)	PUNCT
ejpam-2677	76	21	g31	g31	PROPN
ejpam-2677	76	22	13	13	NUM
ejpam-2677	76	23	(	(	PUNCT
ejpam-2677	76	24	1	1	NUM
ejpam-2677	76	25	4σ2	4σ2	NUM
ejpam-2677	76	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	76	27	1−c	1−c	NUM
ejpam-2677	76	28	2	2	NUM
ejpam-2677	76	29	1−c	1−c	NUM
ejpam-2677	76	30	2	2	NUM
ejpam-2677	76	31	,	,	PUNCT
ejpam-2677	76	32	0	0	NUM
ejpam-2677	76	33	,	,	PUNCT
ejpam-2677	76	34	1	1	NUM
ejpam-2677	76	35	2	2	NUM
ejpam-2677	76	36	)	)	PUNCT
ejpam-2677	76	37	−	−	PROPN
ejpam-2677	76	38	8	8	NUM
ejpam-2677	76	39	σc	σc	PROPN
ejpam-2677	76	40	√	√	NUM
ejpam-2677	76	41	π	π	PROPN
ejpam-2677	76	42	γ(c	γ(c	PROPN
ejpam-2677	76	43	)	)	PUNCT
ejpam-2677	76	44	g31	g31	PROPN
ejpam-2677	76	45	13	13	NUM
ejpam-2677	76	46	(	(	PUNCT
ejpam-2677	76	47	1	1	NUM
ejpam-2677	76	48	4σ2	4σ2	NUM
ejpam-2677	77	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	77	2	−	−	NOUN
ejpam-2677	77	3	c+1	c+1	NUM
ejpam-2677	77	4	2	2	NUM
ejpam-2677	77	5	1−c	1−c	NUM
ejpam-2677	77	6	2	2	NUM
ejpam-2677	77	7	,	,	PUNCT
ejpam-2677	77	8	0	0	NUM
ejpam-2677	77	9	,	,	PUNCT
ejpam-2677	77	10	1	1	NUM
ejpam-2677	77	11	2	2	NUM
ejpam-2677	77	12	)	)	PUNCT
ejpam-2677	77	13	−	−	PROPN
ejpam-2677	77	14	16	16	NUM
ejpam-2677	77	15	σc	σc	PROPN
ejpam-2677	77	16	√	√	PROPN
ejpam-2677	77	17	π	π	PROPN
ejpam-2677	77	18	γ(c	γ(c	PROPN
ejpam-2677	77	19	)	)	PUNCT
ejpam-2677	77	20	g31	g31	PROPN
ejpam-2677	77	21	13	13	NUM
ejpam-2677	77	22	(	(	PUNCT
ejpam-2677	77	23	1	1	NUM
ejpam-2677	77	24	4σ2	4σ2	NUM
ejpam-2677	77	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	78	1	−	−	NOUN
ejpam-2677	78	2	c+1	c+1	NUM
ejpam-2677	78	3	2	2	NUM
ejpam-2677	78	4	3−c	3−c	NUM
ejpam-2677	78	5	2	2	NUM
ejpam-2677	78	6	,	,	PUNCT
ejpam-2677	78	7	0	0	NUM
ejpam-2677	78	8	,	,	PUNCT
ejpam-2677	78	9	1	1	NUM
ejpam-2677	78	10	2	2	NUM
ejpam-2677	78	11	)	)	PUNCT
ejpam-2677	78	12	−	−	PROPN
ejpam-2677	78	13	32	32	NUM
ejpam-2677	78	14	3σc	3σc	NOUN
ejpam-2677	78	15	√	√	PROPN
ejpam-2677	78	16	π	π	PROPN
ejpam-2677	78	17	γ(c	γ(c	PROPN
ejpam-2677	78	18	)	)	PUNCT
ejpam-2677	78	19	g31	g31	PROPN
ejpam-2677	78	20	13	13	NUM
ejpam-2677	79	1	(	(	PUNCT
ejpam-2677	79	2	1	1	NUM
ejpam-2677	79	3	4σ2	4σ2	NUM
ejpam-2677	79	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	79	5	−	−	NOUN
ejpam-2677	79	6	c+3	c+3	NOUN
ejpam-2677	79	7	2	2	NUM
ejpam-2677	79	8	3−c	3−c	NUM
ejpam-2677	79	9	2	2	NUM
ejpam-2677	79	10	,	,	PUNCT
ejpam-2677	79	11	0	0	NUM
ejpam-2677	79	12	,	,	PUNCT
ejpam-2677	79	13	1	1	NUM
ejpam-2677	79	14	2	2	NUM
ejpam-2677	79	15	)	)	PUNCT
ejpam-2677	79	16	where	where	SCONJ
ejpam-2677	79	17	∞∫	∞∫	PROPN
ejpam-2677	79	18	0	0	NUM
ejpam-2677	79	19	x2v−1	x2v−1	PROPN
ejpam-2677	79	20	(	(	PUNCT
ejpam-2677	79	21	u2	u2	PROPN
ejpam-2677	79	22	+	+	CCONJ
ejpam-2677	79	23	x2	x2	PROPN
ejpam-2677	79	24	)	)	PUNCT
ejpam-2677	79	25	q−1	q−1	PROPN
ejpam-2677	79	26	e−µxdx	e−µxdx	PROPN
ejpam-2677	80	1	=	=	SYM
ejpam-2677	80	2	u2v+2q−2	u2v+2q−2	PROPN
ejpam-2677	80	3	2	2	NUM
ejpam-2677	80	4	√	√	PROPN
ejpam-2677	80	5	πγ	πγ	PROPN
ejpam-2677	80	6	(	(	PUNCT
ejpam-2677	80	7	1−q	1−q	NUM
ejpam-2677	80	8	)	)	PUNCT
ejpam-2677	80	9	g31	g31	NOUN
ejpam-2677	80	10	13	13	NUM
ejpam-2677	80	11	(	(	PUNCT
ejpam-2677	80	12	µ2u2	µ2u2	PROPN
ejpam-2677	80	13	4	4	NUM
ejpam-2677	80	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	80	15	1−	1−	NUM
ejpam-2677	80	16	v	v	NOUN
ejpam-2677	80	17	1−q−	1−q−	NUM
ejpam-2677	80	18	v	v	NOUN
ejpam-2677	80	19	,	,	PUNCT
ejpam-2677	80	20	0	0	NUM
ejpam-2677	80	21	,	,	PUNCT
ejpam-2677	80	22	1	1	NUM
ejpam-2677	80	23	2	2	NUM
ejpam-2677	80	24	)	)	PUNCT
ejpam-2677	80	25	(	(	PUNCT
ejpam-2677	80	26	4.1	4.1	NUM
ejpam-2677	80	27	)	)	PUNCT
ejpam-2677	80	28	for	for	ADP
ejpam-2677	80	29	|	|	ADV
ejpam-2677	80	30	arg	arg	NOUN
ejpam-2677	80	31	uπ|	uπ|	ADV
ejpam-2677	80	32	<	<	X
ejpam-2677	80	33	π	π	PROPN
ejpam-2677	80	34	2	2	NUM
ejpam-2677	80	35	,	,	PUNCT
ejpam-2677	80	36	reµ	reµ	PROPN
ejpam-2677	80	37	>	>	X
ejpam-2677	80	38	0	0	PUNCT
ejpam-2677	80	39	and	and	CCONJ
ejpam-2677	80	40	rev	rev	VERB
ejpam-2677	80	41	>	>	X
ejpam-2677	80	42	0	0	PUNCT
ejpam-2677	80	43	and	and	CCONJ
ejpam-2677	80	44	g31	g31	PROPN
ejpam-2677	80	45	13	13	NUM
ejpam-2677	80	46	(	(	PUNCT
ejpam-2677	80	47	µ2u2	µ2u2	PROPN
ejpam-2677	80	48	4	4	NUM
ejpam-2677	80	49	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	80	50	1−	1−	NUM
ejpam-2677	80	51	v	v	NOUN
ejpam-2677	80	52	1−q−	1−q−	NUM
ejpam-2677	80	53	v	v	NOUN
ejpam-2677	80	54	,	,	PUNCT
ejpam-2677	80	55	0	0	NUM
ejpam-2677	80	56	,	,	PUNCT
ejpam-2677	80	57	1	1	NUM
ejpam-2677	80	58	2	2	NUM
ejpam-2677	80	59	)	)	PUNCT
ejpam-2677	80	60	is	be	AUX
ejpam-2677	80	61	called	call	VERB
ejpam-2677	80	62	the	the	DET
ejpam-2677	80	63	meijer	meijer	NOUN
ejpam-2677	80	64	’s	’s	PART
ejpam-2677	80	65	g	g	NOUN
ejpam-2677	80	66	-	-	PUNCT
ejpam-2677	80	67	function	function	NOUN
ejpam-2677	80	68	(	(	PUNCT
ejpam-2677	80	69	gradshteyn	gradshteyn	ADJ
ejpam-2677	80	70	and	and	CCONJ
ejpam-2677	80	71	ryzhik	ryzhik	ADJ
ejpam-2677	80	72	,	,	PUNCT
ejpam-2677	80	73	2007	2007	NUM
ejpam-2677	80	74	,	,	PUNCT
ejpam-2677	80	75	formula	formula	NOUN
ejpam-2677	80	76	no	no	NOUN
ejpam-2677	80	77	.	.	PUNCT
ejpam-2677	81	1	3.389.2	3.389.2	NUM
ejpam-2677	81	2	)	)	PUNCT
ejpam-2677	81	3	.	.	PUNCT
ejpam-2677	82	1	proof	proof	NOUN
ejpam-2677	82	2	.	.	PUNCT
ejpam-2677	83	1	ϕp	ϕp	X
ejpam-2677	84	1	=	=	PUNCT
ejpam-2677	84	2	π∫	π∫	NOUN
ejpam-2677	84	3	0	0	NUM
ejpam-2677	85	1	cos(pθ)dθ	cos(pθ)dθ	NOUN
ejpam-2677	86	1	+	+	NUM
ejpam-2677	87	1	i	i	PROPN
ejpam-2677	87	2	∞∫	∞∫	NOUN
ejpam-2677	87	3	0	0	PUNCT
ejpam-2677	88	1	sin(pθ)g(θ)dθ	sin(pθ)g(θ)dθ	ADJ
ejpam-2677	88	2	=	=	NOUN
ejpam-2677	88	3	αp	αp	NOUN
ejpam-2677	89	1	+	+	X
ejpam-2677	89	2	iβp	iβp	PROPN
ejpam-2677	89	3	where	where	SCONJ
ejpam-2677	89	4	αp	αp	NOUN
ejpam-2677	89	5	=	=	NOUN
ejpam-2677	89	6	1	1	NUM
ejpam-2677	89	7	2σcγ(c	2σcγ(c	NUM
ejpam-2677	89	8	)	)	PUNCT
ejpam-2677	89	9	π∫	π∫	NOUN
ejpam-2677	89	10	0	0	NUM
ejpam-2677	89	11	cos(pθ	cos(pθ	NOUN
ejpam-2677	89	12	)	)	PUNCT
ejpam-2677	89	13	sec2	sec2	NOUN
ejpam-2677	89	14	(	(	PUNCT
ejpam-2677	89	15	θ	θ	NOUN
ejpam-2677	89	16	2	2	NUM
ejpam-2677	89	17	)	)	PUNCT
ejpam-2677	89	18	(	(	PUNCT
ejpam-2677	89	19	tan	tan	PROPN
ejpam-2677	89	20	(	(	PUNCT
ejpam-2677	89	21	θ	θ	PROPN
ejpam-2677	89	22	2	2	NUM
ejpam-2677	89	23	)	)	PUNCT
ejpam-2677	89	24	)	)	PUNCT
ejpam-2677	90	1	c−1	c−1	PROPN
ejpam-2677	90	2	e−	e−	PROPN
ejpam-2677	90	3	1	1	NUM
ejpam-2677	90	4	σ	σ	PROPN
ejpam-2677	90	5	tan	tan	PROPN
ejpam-2677	90	6	(	(	PUNCT
ejpam-2677	90	7	θ2)dθ	θ2)dθ	PROPN
ejpam-2677	90	8	p.	p.	PROPN
ejpam-2677	90	9	yedlapalli	yedlapalli	PROPN
ejpam-2677	90	10	,	,	PUNCT
ejpam-2677	90	11	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	90	12	,	,	PUNCT
ejpam-2677	90	13	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	90	14	,	,	PUNCT
ejpam-2677	90	15	a.v.d	a.v.d	NOUN
ejpam-2677	90	16	.	.	PUNCT
ejpam-2677	90	17	rao	rao	PROPN
ejpam-2677	90	18	/	/	SYM
ejpam-2677	90	19	eur	eur	PROPN
ejpam-2677	90	20	.	.	PUNCT
ejpam-2677	91	1	j.	j.	PROPN
ejpam-2677	91	2	pure	pure	PROPN
ejpam-2677	91	3	appl	appl	PROPN
ejpam-2677	91	4	.	.	PROPN
ejpam-2677	91	5	math	math	PROPN
ejpam-2677	91	6	,	,	PUNCT
ejpam-2677	91	7	10	10	NUM
ejpam-2677	91	8	(	(	PUNCT
ejpam-2677	91	9	5	5	NUM
ejpam-2677	91	10	)	)	PUNCT
ejpam-2677	91	11	(	(	PUNCT
ejpam-2677	91	12	2017	2017	NUM
ejpam-2677	91	13	)	)	PUNCT
ejpam-2677	91	14	,	,	PUNCT
ejpam-2677	91	15	1124	1124	NUM
ejpam-2677	91	16	-	-	SYM
ejpam-2677	91	17	1134	1134	NUM
ejpam-2677	91	18	1129	1129	NUM
ejpam-2677	91	19	βp	βp	PUNCT
ejpam-2677	92	1	=	=	NOUN
ejpam-2677	92	2	1	1	NUM
ejpam-2677	92	3	2σcγ(c	2σcγ(c	NUM
ejpam-2677	92	4	)	)	PUNCT
ejpam-2677	92	5	π∫	π∫	X
ejpam-2677	92	6	0	0	NUM
ejpam-2677	92	7	sin(pθ	sin(pθ	X
ejpam-2677	92	8	)	)	PUNCT
ejpam-2677	92	9	sec2	sec2	NOUN
ejpam-2677	92	10	(	(	PUNCT
ejpam-2677	92	11	θ	θ	NOUN
ejpam-2677	92	12	2	2	NUM
ejpam-2677	92	13	)	)	PUNCT
ejpam-2677	92	14	(	(	PUNCT
ejpam-2677	92	15	tan	tan	PROPN
ejpam-2677	92	16	(	(	PUNCT
ejpam-2677	92	17	θ	θ	PROPN
ejpam-2677	92	18	2	2	NUM
ejpam-2677	92	19	)	)	PUNCT
ejpam-2677	92	20	)	)	PUNCT
ejpam-2677	93	1	c−1	c−1	PROPN
ejpam-2677	93	2	e−	e−	PROPN
ejpam-2677	93	3	1	1	NUM
ejpam-2677	93	4	σ	σ	PROPN
ejpam-2677	93	5	tan	tan	PROPN
ejpam-2677	93	6	(	(	PUNCT
ejpam-2677	93	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	93	8	to	to	PART
ejpam-2677	93	9	derive	derive	VERB
ejpam-2677	93	10	the	the	DET
ejpam-2677	93	11	first	first	ADJ
ejpam-2677	93	12	order	order	NOUN
ejpam-2677	93	13	cosine	cosine	NOUN
ejpam-2677	93	14	and	and	CCONJ
ejpam-2677	93	15	sine	sine	ADJ
ejpam-2677	93	16	moments	moment	NOUN
ejpam-2677	93	17	α1	α1	PROPN
ejpam-2677	93	18	=	=	SYM
ejpam-2677	93	19	1	1	NUM
ejpam-2677	93	20	2σcγ(c	2σcγ(c	NUM
ejpam-2677	93	21	)	)	PUNCT
ejpam-2677	93	22	π∫	π∫	NOUN
ejpam-2677	93	23	0	0	NUM
ejpam-2677	93	24	cos(θ	cos(θ	NOUN
ejpam-2677	93	25	)	)	PUNCT
ejpam-2677	93	26	sec2	sec2	NOUN
ejpam-2677	93	27	(	(	PUNCT
ejpam-2677	93	28	θ	θ	NOUN
ejpam-2677	93	29	2	2	NUM
ejpam-2677	93	30	)	)	PUNCT
ejpam-2677	93	31	(	(	PUNCT
ejpam-2677	93	32	tan	tan	PROPN
ejpam-2677	93	33	(	(	PUNCT
ejpam-2677	93	34	θ	θ	PROPN
ejpam-2677	93	35	2	2	NUM
ejpam-2677	93	36	)	)	PUNCT
ejpam-2677	93	37	)	)	PUNCT
ejpam-2677	94	1	c−1	c−1	PROPN
ejpam-2677	94	2	e−	e−	PROPN
ejpam-2677	94	3	1	1	NUM
ejpam-2677	94	4	σ	σ	PROPN
ejpam-2677	94	5	tan	tan	PROPN
ejpam-2677	94	6	(	(	PUNCT
ejpam-2677	94	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	94	8	consider	consider	VERB
ejpam-2677	94	9	the	the	DET
ejpam-2677	94	10	transformation	transformation	NOUN
ejpam-2677	94	11	x	x	PUNCT
ejpam-2677	94	12	=	=	NOUN
ejpam-2677	94	13	tan	tan	PROPN
ejpam-2677	94	14	(	(	PUNCT
ejpam-2677	94	15	θ	θ	PROPN
ejpam-2677	94	16	2	2	NUM
ejpam-2677	94	17	)	)	PUNCT
ejpam-2677	94	18	,	,	PUNCT
ejpam-2677	94	19	cos	cos	PROPN
ejpam-2677	94	20	θ	θ	PROPN
ejpam-2677	94	21	=	=	SYM
ejpam-2677	94	22	1−	1−	NUM
ejpam-2677	94	23	2x2	2x2	NUM
ejpam-2677	94	24	1+x2	1+x2	NUM
ejpam-2677	94	25	and	and	CCONJ
ejpam-2677	94	26	formula	formula	NOUN
ejpam-2677	94	27	(	(	PUNCT
ejpam-2677	94	28	4.1	4.1	NUM
ejpam-2677	94	29	)	)	PUNCT
ejpam-2677	94	30	α1	α1	NOUN
ejpam-2677	94	31	=	=	SYM
ejpam-2677	94	32	1	1	NUM
ejpam-2677	94	33	σcγ(c	σcγ(c	PROPN
ejpam-2677	94	34	)	)	PUNCT
ejpam-2677	94	35	π∫	π∫	NOUN
ejpam-2677	94	36	0	0	NUM
ejpam-2677	95	1	[	[	PUNCT
ejpam-2677	96	1	1−	1−	NUM
ejpam-2677	96	2	2x2	2x2	NUM
ejpam-2677	96	3	1+x2	1+x2	NUM
ejpam-2677	96	4	]	]	PUNCT
ejpam-2677	97	1	xc−1e	xc−1e	PROPN
ejpam-2677	97	2	1	1	NUM
ejpam-2677	97	3	σ	σ	PROPN
ejpam-2677	97	4	xdx	xdx	PROPN
ejpam-2677	97	5	=	=	SYM
ejpam-2677	97	6	1−	1−	NUM
ejpam-2677	97	7	2	2	NUM
ejpam-2677	97	8	σcγ(c	σcγ(c	NOUN
ejpam-2677	97	9	)	)	PUNCT
ejpam-2677	97	10	π∫	π∫	NOUN
ejpam-2677	97	11	0	0	NUM
ejpam-2677	97	12	xc+1	xc+1	NOUN
ejpam-2677	97	13	(	(	PUNCT
ejpam-2677	97	14	1	1	NUM
ejpam-2677	97	15	+	+	NUM
ejpam-2677	97	16	x2	x2	NOUN
ejpam-2677	97	17	)	)	PUNCT
ejpam-2677	97	18	−1	−1	NOUN
ejpam-2677	97	19	e	e	NOUN
ejpam-2677	97	20	1	1	NUM
ejpam-2677	97	21	σ	σ	PROPN
ejpam-2677	97	22	xdx	xdx	PROPN
ejpam-2677	97	23	α1	α1	PROPN
ejpam-2677	97	24	=	=	SYM
ejpam-2677	97	25	1−	1−	NUM
ejpam-2677	97	26	1	1	NUM
ejpam-2677	97	27	σc	σc	PROPN
ejpam-2677	97	28	√	√	NUM
ejpam-2677	97	29	π	π	PROPN
ejpam-2677	97	30	γ	γ	X
ejpam-2677	97	31	(	(	PUNCT
ejpam-2677	97	32	c	c	NOUN
ejpam-2677	97	33	)	)	PUNCT
ejpam-2677	97	34	g31	g31	NOUN
ejpam-2677	97	35	13	13	NUM
ejpam-2677	97	36	(	(	PUNCT
ejpam-2677	97	37	1	1	NUM
ejpam-2677	97	38	4σ2	4σ2	NUM
ejpam-2677	97	39	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	98	1	−	−	NOUN
ejpam-2677	98	2	c	c	NOUN
ejpam-2677	98	3	2	2	NUM
ejpam-2677	98	4	−	−	NOUN
ejpam-2677	98	5	c	c	NOUN
ejpam-2677	98	6	2	2	NUM
ejpam-2677	98	7	,	,	PUNCT
ejpam-2677	98	8	0	0	NUM
ejpam-2677	98	9	,	,	PUNCT
ejpam-2677	98	10	1	1	NUM
ejpam-2677	98	11	2	2	X
ejpam-2677	98	12	)	)	PUNCT
ejpam-2677	98	13	β1	β1	NOUN
ejpam-2677	98	14	=	=	PUNCT
ejpam-2677	98	15	1	1	NUM
ejpam-2677	98	16	2σcγ(c	2σcγ(c	NUM
ejpam-2677	98	17	)	)	PUNCT
ejpam-2677	98	18	π∫	π∫	NOUN
ejpam-2677	98	19	0	0	NUM
ejpam-2677	98	20	sin(θ	sin(θ	ADJ
ejpam-2677	98	21	)	)	PUNCT
ejpam-2677	98	22	sec2	sec2	NOUN
ejpam-2677	98	23	(	(	PUNCT
ejpam-2677	98	24	θ	θ	NOUN
ejpam-2677	98	25	2	2	NUM
ejpam-2677	98	26	)	)	PUNCT
ejpam-2677	98	27	(	(	PUNCT
ejpam-2677	98	28	tan	tan	PROPN
ejpam-2677	98	29	(	(	PUNCT
ejpam-2677	98	30	θ	θ	PROPN
ejpam-2677	98	31	2	2	NUM
ejpam-2677	98	32	)	)	PUNCT
ejpam-2677	98	33	)	)	PUNCT
ejpam-2677	99	1	c−1	c−1	PROPN
ejpam-2677	99	2	e−	e−	PROPN
ejpam-2677	99	3	1	1	NUM
ejpam-2677	99	4	σ	σ	PROPN
ejpam-2677	99	5	tan	tan	PROPN
ejpam-2677	99	6	(	(	PUNCT
ejpam-2677	99	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	99	8	consider	consider	VERB
ejpam-2677	99	9	the	the	DET
ejpam-2677	99	10	transformation	transformation	NOUN
ejpam-2677	99	11	x	x	PUNCT
ejpam-2677	99	12	=	=	NOUN
ejpam-2677	99	13	tan	tan	PROPN
ejpam-2677	99	14	(	(	PUNCT
ejpam-2677	99	15	θ	θ	PROPN
ejpam-2677	99	16	2	2	NUM
ejpam-2677	99	17	)	)	PUNCT
ejpam-2677	99	18	,	,	PUNCT
ejpam-2677	99	19	sin	sin	VERB
ejpam-2677	99	20	θ	θ	NOUN
ejpam-2677	99	21	=	=	PUNCT
ejpam-2677	99	22	2x	2x	NUM
ejpam-2677	99	23	1+x2	1+x2	NUM
ejpam-2677	99	24	and	and	CCONJ
ejpam-2677	99	25	formula	formula	NOUN
ejpam-2677	99	26	(	(	PUNCT
ejpam-2677	99	27	4.1	4.1	NUM
ejpam-2677	99	28	)	)	PUNCT
ejpam-2677	99	29	β1	β1	NOUN
ejpam-2677	99	30	=	=	NOUN
ejpam-2677	99	31	1	1	NUM
ejpam-2677	99	32	σcγ(c	σcγ(c	PROPN
ejpam-2677	99	33	)	)	PUNCT
ejpam-2677	99	34	π∫	π∫	NOUN
ejpam-2677	99	35	0	0	NUM
ejpam-2677	99	36	[	[	PUNCT
ejpam-2677	99	37	2x	2x	NUM
ejpam-2677	99	38	1+x2	1+x2	NUM
ejpam-2677	99	39	]	]	PUNCT
ejpam-2677	100	1	xc−1e	xc−1e	PROPN
ejpam-2677	100	2	1	1	NUM
ejpam-2677	100	3	σ	σ	PROPN
ejpam-2677	100	4	xdx	xdx	PROPN
ejpam-2677	100	5	=	=	SYM
ejpam-2677	100	6	2	2	NUM
ejpam-2677	100	7	σcγ(c	σcγ(c	PROPN
ejpam-2677	100	8	)	)	PUNCT
ejpam-2677	100	9	π∫	π∫	NOUN
ejpam-2677	100	10	0	0	NUM
ejpam-2677	100	11	xc	xc	PROPN
ejpam-2677	100	12	(	(	PUNCT
ejpam-2677	100	13	1	1	NUM
ejpam-2677	100	14	+	+	NUM
ejpam-2677	100	15	x2	x2	NOUN
ejpam-2677	100	16	)	)	PUNCT
ejpam-2677	100	17	−1	−1	NOUN
ejpam-2677	100	18	e	e	NOUN
ejpam-2677	100	19	1	1	NUM
ejpam-2677	100	20	σ	σ	PROPN
ejpam-2677	100	21	xdx	xdx	PROPN
ejpam-2677	100	22	β1	β1	PROPN
ejpam-2677	100	23	=	=	PUNCT
ejpam-2677	100	24	1	1	NUM
ejpam-2677	100	25	σc	σc	PROPN
ejpam-2677	100	26	√	√	NUM
ejpam-2677	100	27	π	π	PROPN
ejpam-2677	100	28	γ	γ	X
ejpam-2677	100	29	(	(	PUNCT
ejpam-2677	100	30	c	c	NOUN
ejpam-2677	100	31	)	)	PUNCT
ejpam-2677	100	32	g31	g31	NOUN
ejpam-2677	100	33	13	13	NUM
ejpam-2677	100	34	(	(	PUNCT
ejpam-2677	100	35	1	1	NUM
ejpam-2677	100	36	4σ2	4σ2	NUM
ejpam-2677	100	37	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	100	38	1−c	1−c	NUM
ejpam-2677	100	39	2	2	NUM
ejpam-2677	100	40	1−c	1−c	NUM
ejpam-2677	100	41	2	2	NUM
ejpam-2677	100	42	,	,	PUNCT
ejpam-2677	100	43	0	0	NUM
ejpam-2677	100	44	,	,	PUNCT
ejpam-2677	100	45	1	1	NUM
ejpam-2677	100	46	2	2	NUM
ejpam-2677	100	47	)	)	PUNCT
ejpam-2677	100	48	to	to	PART
ejpam-2677	100	49	derive	derive	VERB
ejpam-2677	100	50	the	the	DET
ejpam-2677	100	51	second	second	ADJ
ejpam-2677	100	52	order	order	NOUN
ejpam-2677	100	53	cosine	cosine	NOUN
ejpam-2677	100	54	and	and	CCONJ
ejpam-2677	100	55	sine	sine	ADJ
ejpam-2677	100	56	moments	moment	NOUN
ejpam-2677	100	57	α2	α2	PROPN
ejpam-2677	100	58	=	=	SYM
ejpam-2677	100	59	1	1	NUM
ejpam-2677	100	60	2σcγ(c	2σcγ(c	NUM
ejpam-2677	100	61	)	)	PUNCT
ejpam-2677	100	62	π∫	π∫	NOUN
ejpam-2677	100	63	0	0	NUM
ejpam-2677	100	64	cos(2θ	cos(2θ	NOUN
ejpam-2677	100	65	)	)	PUNCT
ejpam-2677	100	66	sec2	sec2	NOUN
ejpam-2677	100	67	(	(	PUNCT
ejpam-2677	100	68	θ	θ	NOUN
ejpam-2677	100	69	2	2	NUM
ejpam-2677	100	70	)	)	PUNCT
ejpam-2677	100	71	(	(	PUNCT
ejpam-2677	100	72	tan	tan	PROPN
ejpam-2677	100	73	(	(	PUNCT
ejpam-2677	100	74	θ	θ	PROPN
ejpam-2677	100	75	2	2	NUM
ejpam-2677	100	76	)	)	PUNCT
ejpam-2677	100	77	)	)	PUNCT
ejpam-2677	101	1	c−1	c−1	PROPN
ejpam-2677	101	2	e−	e−	PROPN
ejpam-2677	101	3	1	1	NUM
ejpam-2677	101	4	σ	σ	PROPN
ejpam-2677	101	5	tan	tan	PROPN
ejpam-2677	101	6	(	(	PUNCT
ejpam-2677	101	7	θ2)dθ	θ2)dθ	PROPN
ejpam-2677	101	8	p.	p.	PROPN
ejpam-2677	101	9	yedlapalli	yedlapalli	PROPN
ejpam-2677	101	10	,	,	PUNCT
ejpam-2677	101	11	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	101	12	,	,	PUNCT
ejpam-2677	101	13	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	101	14	,	,	PUNCT
ejpam-2677	101	15	a.v.d	a.v.d	NOUN
ejpam-2677	101	16	.	.	PUNCT
ejpam-2677	101	17	rao	rao	PROPN
ejpam-2677	101	18	/	/	SYM
ejpam-2677	101	19	eur	eur	PROPN
ejpam-2677	101	20	.	.	PUNCT
ejpam-2677	102	1	j.	j.	PROPN
ejpam-2677	102	2	pure	pure	PROPN
ejpam-2677	102	3	appl	appl	PROPN
ejpam-2677	102	4	.	.	PROPN
ejpam-2677	102	5	math	math	PROPN
ejpam-2677	102	6	,	,	PUNCT
ejpam-2677	102	7	10	10	NUM
ejpam-2677	102	8	(	(	PUNCT
ejpam-2677	102	9	5	5	NUM
ejpam-2677	102	10	)	)	PUNCT
ejpam-2677	102	11	(	(	PUNCT
ejpam-2677	102	12	2017	2017	NUM
ejpam-2677	102	13	)	)	PUNCT
ejpam-2677	102	14	,	,	PUNCT
ejpam-2677	102	15	1124	1124	NUM
ejpam-2677	102	16	-	-	SYM
ejpam-2677	102	17	1134	1134	NUM
ejpam-2677	102	18	1130	1130	NUM
ejpam-2677	102	19	consider	consider	VERB
ejpam-2677	102	20	the	the	DET
ejpam-2677	102	21	transformation	transformation	NOUN
ejpam-2677	102	22	x	x	PUNCT
ejpam-2677	103	1	=	=	NOUN
ejpam-2677	103	2	tan	tan	PROPN
ejpam-2677	103	3	(	(	PUNCT
ejpam-2677	103	4	θ	θ	PROPN
ejpam-2677	103	5	2	2	NUM
ejpam-2677	103	6	)	)	PUNCT
ejpam-2677	103	7	,	,	PUNCT
ejpam-2677	103	8	cos	cos	ADP
ejpam-2677	103	9	2θ	2θ	NUM
ejpam-2677	103	10	=	=	SYM
ejpam-2677	103	11	1	1	NUM
ejpam-2677	103	12	+	+	NUM
ejpam-2677	103	13	8x4	8x4	NUM
ejpam-2677	103	14	(	(	PUNCT
ejpam-2677	103	15	1+x2)2	1+x2)2	NUM
ejpam-2677	103	16	−	−	PROPN
ejpam-2677	103	17	8x2	8x2	NUM
ejpam-2677	103	18	(	(	PUNCT
ejpam-2677	103	19	1+x2	1+x2	NUM
ejpam-2677	103	20	)	)	PUNCT
ejpam-2677	103	21	and	and	CCONJ
ejpam-2677	103	22	formula	formula	NOUN
ejpam-2677	103	23	(	(	PUNCT
ejpam-2677	103	24	4.1	4.1	NUM
ejpam-2677	103	25	)	)	PUNCT
ejpam-2677	103	26	α2	α2	NOUN
ejpam-2677	103	27	=	=	SYM
ejpam-2677	103	28	1	1	NUM
ejpam-2677	103	29	σcγ(c	σcγ(c	PROPN
ejpam-2677	103	30	)	)	PUNCT
ejpam-2677	103	31	∞∫	∞∫	NOUN
ejpam-2677	103	32	0	0	PUNCT
ejpam-2677	104	1	[	[	PUNCT
ejpam-2677	104	2	1	1	NUM
ejpam-2677	104	3	+	+	NUM
ejpam-2677	104	4	8x4	8x4	NUM
ejpam-2677	104	5	(	(	PUNCT
ejpam-2677	104	6	1+x2)2	1+x2)2	NUM
ejpam-2677	104	7	−	−	PROPN
ejpam-2677	104	8	8x2	8x2	NUM
ejpam-2677	104	9	(	(	PUNCT
ejpam-2677	104	10	1+x2	1+x2	NUM
ejpam-2677	104	11	)	)	PUNCT
ejpam-2677	104	12	]	]	PUNCT
ejpam-2677	105	1	xc−1e−	xc−1e−	PROPN
ejpam-2677	105	2	1	1	NUM
ejpam-2677	105	3	σ	σ	PROPN
ejpam-2677	105	4	xdx	xdx	X
ejpam-2677	105	5	=	=	NOUN
ejpam-2677	105	6	1	1	NUM
ejpam-2677	105	7	σcγ(c	σcγ(c	PROPN
ejpam-2677	105	8	)	)	PUNCT
ejpam-2677	105	9	∞∫	∞∫	NOUN
ejpam-2677	105	10	0	0	PUNCT
ejpam-2677	106	1	xc−1e−	xc−1e−	PROPN
ejpam-2677	106	2	1	1	NUM
ejpam-2677	106	3	σ	σ	NOUN
ejpam-2677	106	4	xdx+	xdx+	PROPN
ejpam-2677	106	5	8	8	NUM
ejpam-2677	106	6	σcγ(c	σcγ(c	PROPN
ejpam-2677	106	7	)	)	PUNCT
ejpam-2677	106	8	∞∫	∞∫	NOUN
ejpam-2677	106	9	0	0	NUM
ejpam-2677	106	10	xc+3	xc+3	PROPN
ejpam-2677	107	1	(	(	PUNCT
ejpam-2677	107	2	1+x2)2	1+x2)2	NUM
ejpam-2677	107	3	e−	e−	PROPN
ejpam-2677	107	4	1	1	NUM
ejpam-2677	107	5	σ	σ	NUM
ejpam-2677	107	6	xdx−	xdx−	PROPN
ejpam-2677	107	7	8	8	NUM
ejpam-2677	107	8	σcγ(c	σcγ(c	PROPN
ejpam-2677	107	9	)	)	PUNCT
ejpam-2677	107	10	∞∫	∞∫	NOUN
ejpam-2677	107	11	0	0	NUM
ejpam-2677	108	1	xc+1	xc+1	PROPN
ejpam-2677	108	2	(	(	PUNCT
ejpam-2677	108	3	1+x2	1+x2	NUM
ejpam-2677	108	4	)	)	PUNCT
ejpam-2677	108	5	e−	e−	PROPN
ejpam-2677	108	6	1	1	NUM
ejpam-2677	108	7	σ	σ	PROPN
ejpam-2677	108	8	xdx	xdx	PROPN
ejpam-2677	108	9	α2	α2	PROPN
ejpam-2677	108	10	=	=	PROPN
ejpam-2677	108	11	1	1	NUM
ejpam-2677	108	12	+	+	NUM
ejpam-2677	108	13	4	4	NUM
ejpam-2677	108	14	σc	σc	NOUN
ejpam-2677	108	15	√	√	NUM
ejpam-2677	108	16	πγ(c	πγ(c	NUM
ejpam-2677	108	17	)	)	PUNCT
ejpam-2677	108	18	g31	g31	PROPN
ejpam-2677	108	19	13	13	NUM
ejpam-2677	108	20	(	(	PUNCT
ejpam-2677	108	21	1	1	NUM
ejpam-2677	108	22	4σ2	4σ2	NUM
ejpam-2677	108	23	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	108	24	−	−	NOUN
ejpam-2677	108	25	c	c	NOUN
ejpam-2677	108	26	2	2	NUM
ejpam-2677	108	27	−	−	NOUN
ejpam-2677	108	28	1	1	NUM
ejpam-2677	108	29	−	−	PROPN
ejpam-2677	108	30	c	c	NOUN
ejpam-2677	108	31	2	2	NUM
ejpam-2677	108	32	,	,	PUNCT
ejpam-2677	108	33	0	0	NUM
ejpam-2677	108	34	,	,	PUNCT
ejpam-2677	108	35	1	1	NUM
ejpam-2677	108	36	2	2	NUM
ejpam-2677	108	37	)	)	PUNCT
ejpam-2677	108	38	−	−	PROPN
ejpam-2677	108	39	4	4	NUM
ejpam-2677	108	40	σc	σc	NOUN
ejpam-2677	108	41	√	√	NUM
ejpam-2677	108	42	πγ(c	πγ(c	NOUN
ejpam-2677	108	43	)	)	PUNCT
ejpam-2677	108	44	g31	g31	PROPN
ejpam-2677	108	45	13	13	NUM
ejpam-2677	108	46	(	(	PUNCT
ejpam-2677	108	47	1	1	NUM
ejpam-2677	108	48	4σ2	4σ2	NUM
ejpam-2677	108	49	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	108	50	−	−	NOUN
ejpam-2677	108	51	c	c	NOUN
ejpam-2677	108	52	2	2	NUM
ejpam-2677	108	53	−	−	NOUN
ejpam-2677	108	54	c	c	NOUN
ejpam-2677	108	55	2	2	NUM
ejpam-2677	108	56	,	,	PUNCT
ejpam-2677	108	57	0	0	NUM
ejpam-2677	108	58	,	,	PUNCT
ejpam-2677	108	59	1	1	NUM
ejpam-2677	108	60	2	2	NUM
ejpam-2677	108	61	)	)	PUNCT
ejpam-2677	108	62	β2	β2	NOUN
ejpam-2677	108	63	=	=	NOUN
ejpam-2677	108	64	1	1	NUM
ejpam-2677	108	65	2σcγ(c	2σcγ(c	NUM
ejpam-2677	108	66	)	)	PUNCT
ejpam-2677	108	67	π∫	π∫	NOUN
ejpam-2677	108	68	0	0	NUM
ejpam-2677	108	69	sin	sin	NOUN
ejpam-2677	108	70	2θ	2θ	NUM
ejpam-2677	108	71	sec2	sec2	NOUN
ejpam-2677	108	72	(	(	PUNCT
ejpam-2677	108	73	θ	θ	NOUN
ejpam-2677	108	74	2	2	NUM
ejpam-2677	108	75	)	)	PUNCT
ejpam-2677	108	76	(	(	PUNCT
ejpam-2677	108	77	tan	tan	PROPN
ejpam-2677	108	78	(	(	PUNCT
ejpam-2677	108	79	θ	θ	PROPN
ejpam-2677	108	80	2	2	NUM
ejpam-2677	108	81	)	)	PUNCT
ejpam-2677	108	82	)	)	PUNCT
ejpam-2677	109	1	c−1	c−1	PROPN
ejpam-2677	109	2	e−	e−	PROPN
ejpam-2677	109	3	1	1	NUM
ejpam-2677	109	4	σ	σ	PROPN
ejpam-2677	109	5	tan	tan	PROPN
ejpam-2677	109	6	(	(	PUNCT
ejpam-2677	109	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	109	8	consider	consider	VERB
ejpam-2677	109	9	the	the	DET
ejpam-2677	109	10	transformation	transformation	NOUN
ejpam-2677	109	11	x	x	PUNCT
ejpam-2677	109	12	=	=	NOUN
ejpam-2677	109	13	tan	tan	PROPN
ejpam-2677	109	14	(	(	PUNCT
ejpam-2677	109	15	θ	θ	PROPN
ejpam-2677	109	16	2	2	NUM
ejpam-2677	109	17	)	)	PUNCT
ejpam-2677	109	18	,	,	PUNCT
ejpam-2677	109	19	sin	sin	VERB
ejpam-2677	109	20	2θ	2θ	NUM
ejpam-2677	109	21	=	=	SYM
ejpam-2677	109	22	4x	4x	NOUN
ejpam-2677	109	23	(	(	PUNCT
ejpam-2677	109	24	1+x2	1+x2	NUM
ejpam-2677	109	25	)	)	PUNCT
ejpam-2677	109	26	−	−	PROPN
ejpam-2677	109	27	8x3	8x3	NOUN
ejpam-2677	109	28	(	(	PUNCT
ejpam-2677	109	29	1+x2)2	1+x2)2	NUM
ejpam-2677	109	30	and	and	CCONJ
ejpam-2677	109	31	by	by	ADP
ejpam-2677	109	32	formula	formula	NOUN
ejpam-2677	109	33	(	(	PUNCT
ejpam-2677	109	34	4.1	4.1	NUM
ejpam-2677	109	35	)	)	PUNCT
ejpam-2677	109	36	β2	β2	NOUN
ejpam-2677	109	37	=	=	NOUN
ejpam-2677	109	38	1	1	NUM
ejpam-2677	109	39	σcγ(c	σcγ(c	PROPN
ejpam-2677	109	40	)	)	PUNCT
ejpam-2677	109	41	∞∫	∞∫	NOUN
ejpam-2677	109	42	0	0	PUNCT
ejpam-2677	110	1	[	[	PUNCT
ejpam-2677	110	2	4x	4x	NUM
ejpam-2677	110	3	(	(	PUNCT
ejpam-2677	110	4	1+x2	1+x2	NUM
ejpam-2677	110	5	)	)	PUNCT
ejpam-2677	110	6	−	−	PROPN
ejpam-2677	110	7	8x3	8x3	NOUN
ejpam-2677	110	8	(	(	PUNCT
ejpam-2677	110	9	1+x2)2	1+x2)2	X
ejpam-2677	110	10	]	]	PUNCT
ejpam-2677	110	11	xc−1e−	xc−1e−	PROPN
ejpam-2677	110	12	1	1	NUM
ejpam-2677	110	13	σ	σ	PROPN
ejpam-2677	110	14	xdx	xdx	X
ejpam-2677	110	15	=	=	NOUN
ejpam-2677	110	16	4	4	NUM
ejpam-2677	110	17	σcγ(c	σcγ(c	PROPN
ejpam-2677	110	18	)	)	PUNCT
ejpam-2677	110	19	∞∫	∞∫	PROPN
ejpam-2677	110	20	0	0	NUM
ejpam-2677	111	1	xc	xc	PROPN
ejpam-2677	111	2	(	(	PUNCT
ejpam-2677	111	3	1+x2	1+x2	NUM
ejpam-2677	111	4	)	)	PUNCT
ejpam-2677	111	5	e−	e−	PROPN
ejpam-2677	111	6	1	1	NUM
ejpam-2677	111	7	σ	σ	NUM
ejpam-2677	111	8	xdx−	xdx−	PROPN
ejpam-2677	111	9	8	8	NUM
ejpam-2677	111	10	σcγ(c	σcγ(c	PROPN
ejpam-2677	111	11	)	)	PUNCT
ejpam-2677	111	12	∞∫	∞∫	NOUN
ejpam-2677	111	13	0	0	NUM
ejpam-2677	112	1	xc+2	xc+2	PROPN
ejpam-2677	112	2	(	(	PUNCT
ejpam-2677	112	3	1+x2)2	1+x2)2	NUM
ejpam-2677	112	4	e−	e−	PROPN
ejpam-2677	112	5	1	1	NUM
ejpam-2677	112	6	σ	σ	PROPN
ejpam-2677	112	7	xdx	xdx	PROPN
ejpam-2677	112	8	β2	β2	NOUN
ejpam-2677	112	9	=	=	NOUN
ejpam-2677	112	10	2	2	NUM
ejpam-2677	112	11	σc	σc	PROPN
ejpam-2677	112	12	√	√	NUM
ejpam-2677	112	13	πγ(c	πγ(c	NOUN
ejpam-2677	112	14	)	)	PUNCT
ejpam-2677	112	15	g31	g31	PROPN
ejpam-2677	112	16	13	13	NUM
ejpam-2677	112	17	(	(	PUNCT
ejpam-2677	112	18	1	1	NUM
ejpam-2677	112	19	4σ2	4σ2	NUM
ejpam-2677	112	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	112	21	1−c	1−c	NUM
ejpam-2677	112	22	2	2	NUM
ejpam-2677	112	23	1−c	1−c	NUM
ejpam-2677	112	24	2	2	NUM
ejpam-2677	112	25	,	,	PUNCT
ejpam-2677	112	26	0	0	NUM
ejpam-2677	112	27	,	,	PUNCT
ejpam-2677	112	28	1	1	NUM
ejpam-2677	112	29	2	2	NUM
ejpam-2677	112	30	)	)	PUNCT
ejpam-2677	112	31	−	−	PROPN
ejpam-2677	112	32	4	4	NUM
ejpam-2677	112	33	σc	σc	NOUN
ejpam-2677	112	34	√	√	NUM
ejpam-2677	112	35	πγ(c	πγ(c	NOUN
ejpam-2677	112	36	)	)	PUNCT
ejpam-2677	112	37	g31	g31	PROPN
ejpam-2677	112	38	13	13	NUM
ejpam-2677	112	39	(	(	PUNCT
ejpam-2677	112	40	1	1	NUM
ejpam-2677	112	41	4σ2	4σ2	NUM
ejpam-2677	112	42	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-2677	112	43	−	−	PROPN
ejpam-2677	112	44	(	(	PUNCT
ejpam-2677	112	45	c+1	c+1	NOUN
ejpam-2677	112	46	)	)	PUNCT
ejpam-2677	112	47	2	2	NUM
ejpam-2677	112	48	(	(	PUNCT
ejpam-2677	112	49	1−c	1−c	NUM
ejpam-2677	112	50	)	)	PUNCT
ejpam-2677	112	51	2	2	NUM
ejpam-2677	112	52	,	,	PUNCT
ejpam-2677	112	53	0	0	NUM
ejpam-2677	112	54	,	,	PUNCT
ejpam-2677	112	55	1	1	NUM
ejpam-2677	112	56	2	2	NUM
ejpam-2677	112	57	)	)	PUNCT
ejpam-2677	112	58	to	to	PART
ejpam-2677	112	59	derive	derive	VERB
ejpam-2677	112	60	the	the	DET
ejpam-2677	112	61	third	third	ADJ
ejpam-2677	112	62	cosine	cosine	NOUN
ejpam-2677	112	63	and	and	CCONJ
ejpam-2677	112	64	sine	sine	ADJ
ejpam-2677	112	65	moments	moment	NOUN
ejpam-2677	112	66	α3	α3	PROPN
ejpam-2677	113	1	=	=	NOUN
ejpam-2677	113	2	1	1	NUM
ejpam-2677	113	3	σc2γ(c	σc2γ(c	NOUN
ejpam-2677	113	4	)	)	PUNCT
ejpam-2677	113	5	π∫	π∫	NOUN
ejpam-2677	113	6	0	0	NUM
ejpam-2677	113	7	cos	cos	PROPN
ejpam-2677	113	8	3θ	3θ	PROPN
ejpam-2677	113	9	sec2	sec2	NOUN
ejpam-2677	113	10	(	(	PUNCT
ejpam-2677	113	11	θ	θ	NOUN
ejpam-2677	113	12	2	2	NUM
ejpam-2677	113	13	)	)	PUNCT
ejpam-2677	113	14	(	(	PUNCT
ejpam-2677	113	15	tan	tan	PROPN
ejpam-2677	113	16	(	(	PUNCT
ejpam-2677	113	17	θ	θ	PROPN
ejpam-2677	113	18	2	2	NUM
ejpam-2677	113	19	)	)	PUNCT
ejpam-2677	113	20	)	)	PUNCT
ejpam-2677	114	1	c−1	c−1	PROPN
ejpam-2677	114	2	e−	e−	PROPN
ejpam-2677	114	3	1	1	NUM
ejpam-2677	114	4	σ	σ	PROPN
ejpam-2677	114	5	tan	tan	PROPN
ejpam-2677	114	6	(	(	PUNCT
ejpam-2677	114	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	114	8	consider	consider	VERB
ejpam-2677	114	9	the	the	DET
ejpam-2677	114	10	transformation	transformation	NOUN
ejpam-2677	114	11	x	x	PUNCT
ejpam-2677	114	12	=	=	NOUN
ejpam-2677	114	13	tan	tan	PROPN
ejpam-2677	114	14	(	(	PUNCT
ejpam-2677	114	15	θ	θ	PROPN
ejpam-2677	114	16	2	2	NUM
ejpam-2677	114	17	)	)	PUNCT
ejpam-2677	114	18	,	,	PUNCT
ejpam-2677	114	19	cos	cos	PROPN
ejpam-2677	114	20	3θ	3θ	PROPN
ejpam-2677	114	21	=	=	SYM
ejpam-2677	114	22	1−	1−	NUM
ejpam-2677	114	23	32x6	32x6	NUM
ejpam-2677	114	24	(	(	PUNCT
ejpam-2677	114	25	1+x2)3	1+x2)3	NUM
ejpam-2677	114	26	+	+	NUM
ejpam-2677	114	27	48x4	48x4	NUM
ejpam-2677	114	28	(	(	PUNCT
ejpam-2677	114	29	1+x2)2	1+x2)2	NUM
ejpam-2677	114	30	−	−	NUM
ejpam-2677	114	31	18x2	18x2	NUM
ejpam-2677	114	32	(	(	PUNCT
ejpam-2677	114	33	1+x2	1+x2	NOUN
ejpam-2677	114	34	)	)	PUNCT
ejpam-2677	114	35	α3	α3	NOUN
ejpam-2677	114	36	=	=	SYM
ejpam-2677	114	37	1	1	NUM
ejpam-2677	114	38	σcγ(c	σcγ(c	PROPN
ejpam-2677	114	39	)	)	PUNCT
ejpam-2677	114	40	∞∫	∞∫	NOUN
ejpam-2677	114	41	0	0	PUNCT
ejpam-2677	115	1	[	[	PUNCT
ejpam-2677	115	2	1−	1−	NUM
ejpam-2677	115	3	32x6	32x6	NUM
ejpam-2677	115	4	(	(	PUNCT
ejpam-2677	115	5	1+x2)3	1+x2)3	NUM
ejpam-2677	115	6	+	+	NUM
ejpam-2677	115	7	48x4	48x4	NUM
ejpam-2677	115	8	(	(	PUNCT
ejpam-2677	115	9	1+x2)2	1+x2)2	NUM
ejpam-2677	115	10	−	−	NUM
ejpam-2677	115	11	18x2	18x2	NUM
ejpam-2677	115	12	(	(	PUNCT
ejpam-2677	115	13	1+x2	1+x2	NUM
ejpam-2677	115	14	)	)	PUNCT
ejpam-2677	115	15	]	]	PUNCT
ejpam-2677	115	16	xc−1e−	xc−1e−	PROPN
ejpam-2677	115	17	1	1	NUM
ejpam-2677	115	18	σ	σ	PROPN
ejpam-2677	115	19	xdx	xdx	PROPN
ejpam-2677	115	20	=	=	SYM
ejpam-2677	115	21	1−	1−	NUM
ejpam-2677	115	22	32	32	NUM
ejpam-2677	115	23	σcγ(c	σcγ(c	PROPN
ejpam-2677	115	24	)	)	PUNCT
ejpam-2677	115	25	∞∫	∞∫	NOUN
ejpam-2677	115	26	0	0	NUM
ejpam-2677	115	27	xc+5(1	xc+5(1	PUNCT
ejpam-2677	116	1	+	+	CCONJ
ejpam-2677	116	2	x2)−3e−	x2)−3e−	PROPN
ejpam-2677	116	3	1	1	NUM
ejpam-2677	116	4	σ	σ	NOUN
ejpam-2677	116	5	xdx+	xdx+	PROPN
ejpam-2677	116	6	48	48	NUM
ejpam-2677	116	7	σcγ(c	σcγ(c	PROPN
ejpam-2677	116	8	)	)	PUNCT
ejpam-2677	116	9	∞∫	∞∫	NOUN
ejpam-2677	116	10	0	0	NUM
ejpam-2677	116	11	xc+3(1	xc+3(1	PUNCT
ejpam-2677	117	1	+	+	CCONJ
ejpam-2677	117	2	x2)−2e−	x2)−2e−	NOUN
ejpam-2677	117	3	1	1	NUM
ejpam-2677	117	4	σ	σ	PROPN
ejpam-2677	117	5	xdx	xdx	PROPN
ejpam-2677	117	6	−	−	PROPN
ejpam-2677	117	7	18	18	NUM
ejpam-2677	117	8	σcγ(c	σcγ(c	PROPN
ejpam-2677	117	9	)	)	PUNCT
ejpam-2677	117	10	∞∫	∞∫	NOUN
ejpam-2677	117	11	0	0	NUM
ejpam-2677	117	12	xc+1(1	xc+1(1	PUNCT
ejpam-2677	117	13	+	+	CCONJ
ejpam-2677	117	14	x2)−1e−	x2)−1e−	NUM
ejpam-2677	117	15	1	1	NUM
ejpam-2677	117	16	σ	σ	PROPN
ejpam-2677	117	17	xdx	xdx	PROPN
ejpam-2677	117	18	p.	p.	PROPN
ejpam-2677	117	19	yedlapalli	yedlapalli	PROPN
ejpam-2677	117	20	,	,	PUNCT
ejpam-2677	117	21	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	117	22	,	,	PUNCT
ejpam-2677	117	23	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	117	24	,	,	PUNCT
ejpam-2677	117	25	a.v.d	a.v.d	NOUN
ejpam-2677	117	26	.	.	PUNCT
ejpam-2677	117	27	rao	rao	PROPN
ejpam-2677	117	28	/	/	SYM
ejpam-2677	117	29	eur	eur	PROPN
ejpam-2677	117	30	.	.	PUNCT
ejpam-2677	118	1	j.	j.	PROPN
ejpam-2677	118	2	pure	pure	PROPN
ejpam-2677	118	3	appl	appl	PROPN
ejpam-2677	118	4	.	.	PROPN
ejpam-2677	118	5	math	math	PROPN
ejpam-2677	118	6	,	,	PUNCT
ejpam-2677	118	7	10	10	NUM
ejpam-2677	118	8	(	(	PUNCT
ejpam-2677	118	9	5	5	NUM
ejpam-2677	118	10	)	)	PUNCT
ejpam-2677	118	11	(	(	PUNCT
ejpam-2677	118	12	2017	2017	NUM
ejpam-2677	118	13	)	)	PUNCT
ejpam-2677	118	14	,	,	PUNCT
ejpam-2677	118	15	1124	1124	NUM
ejpam-2677	118	16	-	-	SYM
ejpam-2677	118	17	1134	1134	NUM
ejpam-2677	118	18	1131	1131	NUM
ejpam-2677	118	19	α3	α3	NOUN
ejpam-2677	118	20	=	=	SYM
ejpam-2677	118	21	1−	1−	NUM
ejpam-2677	118	22	16	16	NUM
ejpam-2677	118	23	3σc	3σc	NOUN
ejpam-2677	118	24	√	√	NUM
ejpam-2677	118	25	πγ(c	πγ(c	NOUN
ejpam-2677	118	26	)	)	PUNCT
ejpam-2677	118	27	g31	g31	PROPN
ejpam-2677	118	28	13	13	NUM
ejpam-2677	118	29	(	(	PUNCT
ejpam-2677	118	30	1	1	NUM
ejpam-2677	118	31	4σ2	4σ2	NUM
ejpam-2677	118	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	119	1	−	−	NOUN
ejpam-2677	119	2	c	c	NOUN
ejpam-2677	119	3	2	2	NUM
ejpam-2677	119	4	−	−	NOUN
ejpam-2677	119	5	2	2	NUM
ejpam-2677	119	6	−	−	NOUN
ejpam-2677	119	7	c	c	NOUN
ejpam-2677	119	8	2	2	NUM
ejpam-2677	119	9	,	,	PUNCT
ejpam-2677	119	10	0	0	NUM
ejpam-2677	119	11	,	,	PUNCT
ejpam-2677	119	12	1	1	NUM
ejpam-2677	119	13	2	2	NUM
ejpam-2677	119	14	)	)	PUNCT
ejpam-2677	119	15	+	+	CCONJ
ejpam-2677	119	16	24	24	NUM
ejpam-2677	119	17	σc	σc	PROPN
ejpam-2677	119	18	√	√	NUM
ejpam-2677	119	19	πγ(c	πγ(c	NUM
ejpam-2677	119	20	)	)	PUNCT
ejpam-2677	119	21	g31	g31	PROPN
ejpam-2677	119	22	13	13	NUM
ejpam-2677	119	23	(	(	PUNCT
ejpam-2677	119	24	1	1	NUM
ejpam-2677	119	25	4σ2	4σ2	NUM
ejpam-2677	119	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	120	1	−	−	NOUN
ejpam-2677	120	2	c	c	NOUN
ejpam-2677	120	3	2	2	NUM
ejpam-2677	120	4	−	−	NOUN
ejpam-2677	120	5	1	1	NUM
ejpam-2677	120	6	−	−	PROPN
ejpam-2677	120	7	c	c	NOUN
ejpam-2677	120	8	2	2	NUM
ejpam-2677	120	9	,	,	PUNCT
ejpam-2677	120	10	0	0	NUM
ejpam-2677	120	11	,	,	PUNCT
ejpam-2677	120	12	1	1	NUM
ejpam-2677	120	13	2	2	NUM
ejpam-2677	120	14	)	)	PUNCT
ejpam-2677	120	15	−	−	PROPN
ejpam-2677	120	16	9√	9√	PROPN
ejpam-2677	120	17	πσcγ(c	πσcγ(c	PROPN
ejpam-2677	120	18	)	)	PUNCT
ejpam-2677	120	19	g31	g31	NOUN
ejpam-2677	120	20	13	13	NUM
ejpam-2677	120	21	(	(	PUNCT
ejpam-2677	120	22	1	1	NUM
ejpam-2677	120	23	4σ2	4σ2	NUM
ejpam-2677	120	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	121	1	−	−	NOUN
ejpam-2677	121	2	c	c	NOUN
ejpam-2677	121	3	2	2	NUM
ejpam-2677	121	4	−	−	NOUN
ejpam-2677	121	5	c	c	NOUN
ejpam-2677	121	6	2	2	NUM
ejpam-2677	121	7	,	,	PUNCT
ejpam-2677	121	8	0	0	NUM
ejpam-2677	121	9	,	,	PUNCT
ejpam-2677	121	10	1	1	NUM
ejpam-2677	121	11	2	2	NUM
ejpam-2677	121	12	)	)	PUNCT
ejpam-2677	121	13	β3	β3	NOUN
ejpam-2677	121	14	=	=	SYM
ejpam-2677	121	15	1	1	NUM
ejpam-2677	121	16	2σcγ(c	2σcγ(c	NUM
ejpam-2677	121	17	)	)	PUNCT
ejpam-2677	121	18	π∫	π∫	NOUN
ejpam-2677	121	19	0	0	NUM
ejpam-2677	121	20	sin	sin	NOUN
ejpam-2677	121	21	3θ	3θ	NUM
ejpam-2677	121	22	sec2	sec2	NOUN
ejpam-2677	121	23	(	(	PUNCT
ejpam-2677	121	24	θ	θ	NOUN
ejpam-2677	121	25	2	2	NUM
ejpam-2677	121	26	)	)	PUNCT
ejpam-2677	121	27	(	(	PUNCT
ejpam-2677	121	28	tan	tan	PROPN
ejpam-2677	121	29	(	(	PUNCT
ejpam-2677	121	30	θ	θ	PROPN
ejpam-2677	121	31	2	2	NUM
ejpam-2677	121	32	)	)	PUNCT
ejpam-2677	121	33	)	)	PUNCT
ejpam-2677	122	1	c−1	c−1	PROPN
ejpam-2677	122	2	e−	e−	PROPN
ejpam-2677	122	3	1	1	NUM
ejpam-2677	122	4	σ	σ	PROPN
ejpam-2677	122	5	tan	tan	PROPN
ejpam-2677	122	6	(	(	PUNCT
ejpam-2677	122	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	122	8	consider	consider	VERB
ejpam-2677	122	9	the	the	DET
ejpam-2677	122	10	transformation	transformation	NOUN
ejpam-2677	122	11	x	x	PUNCT
ejpam-2677	122	12	=	=	NOUN
ejpam-2677	122	13	tan	tan	PROPN
ejpam-2677	122	14	(	(	PUNCT
ejpam-2677	122	15	θ	θ	PROPN
ejpam-2677	122	16	2	2	NUM
ejpam-2677	122	17	)	)	PUNCT
ejpam-2677	122	18	,	,	PUNCT
ejpam-2677	122	19	sin	sin	NOUN
ejpam-2677	122	20	3θ	3θ	NUM
ejpam-2677	122	21	=	=	SYM
ejpam-2677	122	22	6x	6x	NOUN
ejpam-2677	122	23	(	(	PUNCT
ejpam-2677	122	24	1+x2	1+x2	NUM
ejpam-2677	122	25	)	)	PUNCT
ejpam-2677	123	1	−	−	PROPN
ejpam-2677	123	2	32x3	32x3	NUM
ejpam-2677	123	3	(	(	PUNCT
ejpam-2677	123	4	1+x2)3	1+x2)3	NUM
ejpam-2677	123	5	β3	β3	ADJ
ejpam-2677	123	6	=	=	SYM
ejpam-2677	123	7	1	1	NUM
ejpam-2677	123	8	σcγ(c	σcγ(c	PROPN
ejpam-2677	123	9	)	)	PUNCT
ejpam-2677	123	10	∞∫	∞∫	NOUN
ejpam-2677	123	11	0	0	PUNCT
ejpam-2677	124	1	[	[	PUNCT
ejpam-2677	124	2	6x	6x	NUM
ejpam-2677	124	3	(	(	PUNCT
ejpam-2677	124	4	1+x2	1+x2	NUM
ejpam-2677	124	5	)	)	PUNCT
ejpam-2677	124	6	−	−	PROPN
ejpam-2677	124	7	32x3	32x3	NUM
ejpam-2677	124	8	(	(	PUNCT
ejpam-2677	124	9	1+x2)3	1+x2)3	NUM
ejpam-2677	124	10	]	]	X
ejpam-2677	124	11	xc−1e−	xc−1e−	PROPN
ejpam-2677	124	12	1	1	NUM
ejpam-2677	124	13	σ	σ	PROPN
ejpam-2677	124	14	xdx	xdx	PROPN
ejpam-2677	124	15	=	=	NOUN
ejpam-2677	124	16	6	6	NUM
ejpam-2677	124	17	σcγ(c	σcγ(c	PROPN
ejpam-2677	124	18	)	)	PUNCT
ejpam-2677	124	19	∞∫	∞∫	NOUN
ejpam-2677	124	20	0	0	NUM
ejpam-2677	125	1	xc(1	xc(1	PROPN
ejpam-2677	126	1	+	+	NUM
ejpam-2677	126	2	x2)−1e−σxdx−	x2)−1e−σxdx−	PROPN
ejpam-2677	126	3	32	32	NUM
ejpam-2677	126	4	σcγ(c	σcγ(c	PROPN
ejpam-2677	126	5	)	)	PUNCT
ejpam-2677	126	6	∞∫	∞∫	NOUN
ejpam-2677	126	7	0	0	NUM
ejpam-2677	126	8	xc+2(1	xc+2(1	PUNCT
ejpam-2677	127	1	+	+	CCONJ
ejpam-2677	127	2	x2)−3e−	x2)−3e−	PROPN
ejpam-2677	127	3	1	1	NUM
ejpam-2677	127	4	σ	σ	PROPN
ejpam-2677	127	5	xdx	xdx	PROPN
ejpam-2677	127	6	β3	β3	PROPN
ejpam-2677	127	7	=	=	SYM
ejpam-2677	127	8	3	3	NUM
ejpam-2677	127	9	σc	σc	PROPN
ejpam-2677	127	10	√	√	NUM
ejpam-2677	127	11	πγ(c	πγ(c	NOUN
ejpam-2677	127	12	)	)	PUNCT
ejpam-2677	127	13	g31	g31	PROPN
ejpam-2677	127	14	13	13	NUM
ejpam-2677	127	15	(	(	PUNCT
ejpam-2677	127	16	1	1	NUM
ejpam-2677	127	17	4σ2	4σ2	NUM
ejpam-2677	127	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	127	19	1−c	1−c	NUM
ejpam-2677	127	20	2	2	NUM
ejpam-2677	127	21	1−c	1−c	NUM
ejpam-2677	127	22	2	2	NUM
ejpam-2677	127	23	,	,	PUNCT
ejpam-2677	127	24	0	0	NUM
ejpam-2677	127	25	,	,	PUNCT
ejpam-2677	127	26	1	1	NUM
ejpam-2677	127	27	2	2	NUM
ejpam-2677	127	28	)	)	PUNCT
ejpam-2677	127	29	−	−	PROPN
ejpam-2677	127	30	8	8	NUM
ejpam-2677	127	31	σc	σc	PROPN
ejpam-2677	127	32	√	√	NUM
ejpam-2677	127	33	πγ(c	πγ(c	NUM
ejpam-2677	127	34	)	)	PUNCT
ejpam-2677	127	35	g31	g31	PROPN
ejpam-2677	127	36	13	13	NUM
ejpam-2677	127	37	(	(	PUNCT
ejpam-2677	127	38	1	1	NUM
ejpam-2677	127	39	4σ2	4σ2	NUM
ejpam-2677	127	40	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	127	41	−	−	PROPN
ejpam-2677	127	42	(	(	PUNCT
ejpam-2677	127	43	c+1	c+1	NOUN
ejpam-2677	127	44	)	)	PUNCT
ejpam-2677	127	45	2	2	NUM
ejpam-2677	127	46	1−c	1−c	NUM
ejpam-2677	127	47	2	2	NUM
ejpam-2677	127	48	,	,	PUNCT
ejpam-2677	127	49	0	0	NUM
ejpam-2677	127	50	,	,	PUNCT
ejpam-2677	127	51	1	1	NUM
ejpam-2677	127	52	2	2	NUM
ejpam-2677	127	53	)	)	PUNCT
ejpam-2677	127	54	to	to	PART
ejpam-2677	127	55	derive	derive	VERB
ejpam-2677	127	56	the	the	DET
ejpam-2677	127	57	fourth	fourth	ADJ
ejpam-2677	127	58	cosine	cosine	NOUN
ejpam-2677	127	59	and	and	CCONJ
ejpam-2677	127	60	sine	sine	ADJ
ejpam-2677	127	61	moments	moment	NOUN
ejpam-2677	127	62	α4	α4	PROPN
ejpam-2677	127	63	=	=	SYM
ejpam-2677	127	64	1	1	NUM
ejpam-2677	127	65	2σcγ(c	2σcγ(c	NUM
ejpam-2677	127	66	)	)	PUNCT
ejpam-2677	127	67	π∫	π∫	NOUN
ejpam-2677	127	68	0	0	NUM
ejpam-2677	127	69	cos	cos	ADP
ejpam-2677	127	70	4θ	4θ	PROPN
ejpam-2677	127	71	sec2	sec2	NOUN
ejpam-2677	127	72	(	(	PUNCT
ejpam-2677	127	73	θ	θ	NOUN
ejpam-2677	127	74	2	2	NUM
ejpam-2677	127	75	)	)	PUNCT
ejpam-2677	127	76	(	(	PUNCT
ejpam-2677	127	77	tan	tan	PROPN
ejpam-2677	127	78	(	(	PUNCT
ejpam-2677	127	79	θ	θ	PROPN
ejpam-2677	127	80	2	2	NUM
ejpam-2677	127	81	)	)	PUNCT
ejpam-2677	127	82	)	)	PUNCT
ejpam-2677	128	1	c−1	c−1	PROPN
ejpam-2677	128	2	e−	e−	PROPN
ejpam-2677	128	3	1	1	NUM
ejpam-2677	128	4	σ	σ	PROPN
ejpam-2677	128	5	tan	tan	PROPN
ejpam-2677	128	6	(	(	PUNCT
ejpam-2677	128	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	128	8	consider	consider	VERB
ejpam-2677	128	9	the	the	DET
ejpam-2677	128	10	transformation	transformation	NOUN
ejpam-2677	128	11	x	x	PUNCT
ejpam-2677	128	12	=	=	NOUN
ejpam-2677	128	13	tan	tan	PROPN
ejpam-2677	128	14	(	(	PUNCT
ejpam-2677	128	15	θ	θ	PROPN
ejpam-2677	128	16	2	2	NUM
ejpam-2677	128	17	)	)	PUNCT
ejpam-2677	128	18	,	,	PUNCT
ejpam-2677	128	19	cos	cos	ADP
ejpam-2677	128	20	4θ	4θ	NOUN
ejpam-2677	128	21	=	=	SYM
ejpam-2677	128	22	1	1	NUM
ejpam-2677	128	23	+	+	NUM
ejpam-2677	128	24	128x8	128x8	NUM
ejpam-2677	128	25	(	(	PUNCT
ejpam-2677	128	26	1+x2)4	1+x2)4	NUM
ejpam-2677	128	27	+	+	SYM
ejpam-2677	128	28	160x4	160x4	NUM
ejpam-2677	128	29	(	(	PUNCT
ejpam-2677	128	30	1+x2)2	1+x2)2	NUM
ejpam-2677	128	31	−	−	NUM
ejpam-2677	128	32	256x6	256x6	NUM
ejpam-2677	128	33	(	(	PUNCT
ejpam-2677	128	34	1+x2)3	1+x2)3	NUM
ejpam-2677	128	35	−	−	NUM
ejpam-2677	128	36	32x2	32x2	NUM
ejpam-2677	128	37	(	(	PUNCT
ejpam-2677	128	38	1+x2	1+x2	NUM
ejpam-2677	128	39	)	)	PUNCT
ejpam-2677	128	40	and	and	CCONJ
ejpam-2677	128	41	formula	formula	NOUN
ejpam-2677	128	42	(	(	PUNCT
ejpam-2677	128	43	4.1	4.1	NUM
ejpam-2677	128	44	)	)	PUNCT
ejpam-2677	128	45	α4	α4	NOUN
ejpam-2677	128	46	=	=	SYM
ejpam-2677	128	47	1	1	NUM
ejpam-2677	128	48	+	+	NUM
ejpam-2677	128	49	128	128	NUM
ejpam-2677	128	50	σcγ(c	σcγ(c	NOUN
ejpam-2677	128	51	)	)	PUNCT
ejpam-2677	128	52	∞∫	∞∫	NOUN
ejpam-2677	128	53	0	0	NUM
ejpam-2677	128	54	xc+7(1	xc+7(1	PUNCT
ejpam-2677	129	1	+	+	CCONJ
ejpam-2677	130	1	x2)−4e−	x2)−4e−	NOUN
ejpam-2677	130	2	1	1	NUM
ejpam-2677	130	3	σ	σ	NOUN
ejpam-2677	130	4	xdx+	xdx+	PROPN
ejpam-2677	130	5	160	160	NUM
ejpam-2677	130	6	σcγ(c	σcγ(c	PROPN
ejpam-2677	130	7	)	)	PUNCT
ejpam-2677	130	8	∞∫	∞∫	NOUN
ejpam-2677	130	9	0	0	NUM
ejpam-2677	130	10	xc+3(1	xc+3(1	PUNCT
ejpam-2677	131	1	+	+	CCONJ
ejpam-2677	132	1	x2)−2e−	x2)−2e−	NOUN
ejpam-2677	132	2	1	1	NUM
ejpam-2677	132	3	σ	σ	PROPN
ejpam-2677	132	4	xdx	xdx	PROPN
ejpam-2677	132	5	−	−	PROPN
ejpam-2677	132	6	256	256	NUM
ejpam-2677	132	7	σcγ(c	σcγ(c	PROPN
ejpam-2677	132	8	)	)	PUNCT
ejpam-2677	132	9	∞∫	∞∫	NOUN
ejpam-2677	132	10	0	0	NUM
ejpam-2677	132	11	xc+5(1	xc+5(1	PUNCT
ejpam-2677	133	1	+	+	CCONJ
ejpam-2677	133	2	x2)−3e−	x2)−3e−	PROPN
ejpam-2677	133	3	1	1	NUM
ejpam-2677	133	4	σ	σ	PROPN
ejpam-2677	133	5	xdx−	xdx−	PROPN
ejpam-2677	133	6	32	32	NUM
ejpam-2677	133	7	σcγ(c	σcγ(c	PROPN
ejpam-2677	133	8	)	)	PUNCT
ejpam-2677	133	9	∞∫	∞∫	NOUN
ejpam-2677	133	10	0	0	NUM
ejpam-2677	133	11	xc+1(1	xc+1(1	PUNCT
ejpam-2677	133	12	+	+	CCONJ
ejpam-2677	133	13	x2)−1e−	x2)−1e−	NUM
ejpam-2677	133	14	1	1	NUM
ejpam-2677	133	15	σ	σ	PROPN
ejpam-2677	133	16	xdx	xdx	X
ejpam-2677	134	1	=	=	PUNCT
ejpam-2677	134	2	1	1	NUM
ejpam-2677	134	3	+	+	CCONJ
ejpam-2677	134	4	128	128	NUM
ejpam-2677	134	5	σcγ(c	σcγ(c	NOUN
ejpam-2677	134	6	)	)	PUNCT
ejpam-2677	134	7	∞∫	∞∫	NOUN
ejpam-2677	134	8	0	0	NUM
ejpam-2677	135	1	x2	x2	PROPN
ejpam-2677	135	2	(	(	PUNCT
ejpam-2677	135	3	c2	c2	PROPN
ejpam-2677	135	4	+	+	PROPN
ejpam-2677	135	5	4)−1(1	4)−1(1	NUM
ejpam-2677	135	6	+	+	ADJ
ejpam-2677	135	7	x2)−3−1e−	x2)−3−1e−	PROPN
ejpam-2677	135	8	1	1	NUM
ejpam-2677	135	9	σ	σ	NOUN
ejpam-2677	135	10	xdx+	xdx+	PROPN
ejpam-2677	135	11	160	160	NUM
ejpam-2677	135	12	σcγ(c	σcγ(c	PROPN
ejpam-2677	135	13	)	)	PUNCT
ejpam-2677	135	14	∞∫	∞∫	NOUN
ejpam-2677	135	15	0	0	NUM
ejpam-2677	136	1	x2	x2	PROPN
ejpam-2677	136	2	(	(	PUNCT
ejpam-2677	136	3	c2	c2	PROPN
ejpam-2677	136	4	+	+	PROPN
ejpam-2677	136	5	2)−1(1	2)−1(1	NUM
ejpam-2677	136	6	+	+	CCONJ
ejpam-2677	136	7	x2)−1−1e−	x2)−1−1e−	PROPN
ejpam-2677	136	8	1	1	NUM
ejpam-2677	136	9	σ	σ	PROPN
ejpam-2677	136	10	xdx	xdx	PROPN
ejpam-2677	136	11	−	−	PROPN
ejpam-2677	136	12	256	256	NUM
ejpam-2677	136	13	σcγ(c	σcγ(c	PROPN
ejpam-2677	136	14	)	)	PUNCT
ejpam-2677	136	15	∞∫	∞∫	NOUN
ejpam-2677	136	16	0	0	NUM
ejpam-2677	137	1	x2	x2	PROPN
ejpam-2677	137	2	(	(	PUNCT
ejpam-2677	137	3	c2	c2	PROPN
ejpam-2677	137	4	+	+	PROPN
ejpam-2677	137	5	3)−1(1	3)−1(1	NUM
ejpam-2677	137	6	+	+	CCONJ
ejpam-2677	137	7	x2)−2−1e−	x2)−2−1e−	PROPN
ejpam-2677	137	8	1	1	NUM
ejpam-2677	137	9	σ	σ	PROPN
ejpam-2677	137	10	xdx−	xdx−	PROPN
ejpam-2677	137	11	32	32	NUM
ejpam-2677	137	12	σcγ(c	σcγ(c	PROPN
ejpam-2677	137	13	)	)	PUNCT
ejpam-2677	137	14	∞∫	∞∫	NOUN
ejpam-2677	137	15	0	0	NUM
ejpam-2677	138	1	x2	x2	PROPN
ejpam-2677	138	2	(	(	PUNCT
ejpam-2677	138	3	c2	c2	PROPN
ejpam-2677	138	4	+	+	PROPN
ejpam-2677	138	5	1)−1(1	1)−1(1	NUM
ejpam-2677	138	6	+	+	CCONJ
ejpam-2677	138	7	x2)0−1e−	x2)0−1e−	PROPN
ejpam-2677	138	8	1	1	NUM
ejpam-2677	138	9	σ	σ	PROPN
ejpam-2677	138	10	xdx	xdx	PROPN
ejpam-2677	138	11	p.	p.	PROPN
ejpam-2677	138	12	yedlapalli	yedlapalli	PROPN
ejpam-2677	138	13	,	,	PUNCT
ejpam-2677	138	14	a.j.v.radhika	a.j.v.radhika	PROPN
ejpam-2677	138	15	,	,	PUNCT
ejpam-2677	138	16	s.v.s.girija	s.v.s.girija	NOUN
ejpam-2677	138	17	,	,	PUNCT
ejpam-2677	138	18	a.v.d	a.v.d	NOUN
ejpam-2677	138	19	.	.	PUNCT
ejpam-2677	138	20	rao	rao	PROPN
ejpam-2677	138	21	/	/	SYM
ejpam-2677	138	22	eur	eur	PROPN
ejpam-2677	138	23	.	.	PUNCT
ejpam-2677	139	1	j.	j.	PROPN
ejpam-2677	139	2	pure	pure	PROPN
ejpam-2677	139	3	appl	appl	PROPN
ejpam-2677	139	4	.	.	PROPN
ejpam-2677	139	5	math	math	PROPN
ejpam-2677	139	6	,	,	PUNCT
ejpam-2677	139	7	10	10	NUM
ejpam-2677	139	8	(	(	PUNCT
ejpam-2677	139	9	5	5	NUM
ejpam-2677	139	10	)	)	PUNCT
ejpam-2677	139	11	(	(	PUNCT
ejpam-2677	139	12	2017	2017	NUM
ejpam-2677	139	13	)	)	PUNCT
ejpam-2677	139	14	,	,	PUNCT
ejpam-2677	139	15	1124	1124	NUM
ejpam-2677	139	16	-	-	SYM
ejpam-2677	139	17	1134	1134	NUM
ejpam-2677	139	18	1132	1132	NUM
ejpam-2677	139	19	α4	α4	NOUN
ejpam-2677	139	20	=	=	SYM
ejpam-2677	139	21	1	1	NUM
ejpam-2677	139	22	+	+	NUM
ejpam-2677	139	23	32	32	NUM
ejpam-2677	139	24	3σc	3σc	NOUN
ejpam-2677	139	25	√	√	NUM
ejpam-2677	139	26	πγ(c	πγ(c	NOUN
ejpam-2677	139	27	)	)	PUNCT
ejpam-2677	139	28	g31	g31	PROPN
ejpam-2677	139	29	13	13	NUM
ejpam-2677	139	30	(	(	PUNCT
ejpam-2677	139	31	1	1	NUM
ejpam-2677	139	32	4σ2	4σ2	NUM
ejpam-2677	139	33	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	140	1	−	−	NOUN
ejpam-2677	140	2	c	c	NOUN
ejpam-2677	140	3	2	2	NUM
ejpam-2677	140	4	−	−	NOUN
ejpam-2677	140	5	3	3	NUM
ejpam-2677	140	6	−	−	PROPN
ejpam-2677	140	7	c	c	NOUN
ejpam-2677	140	8	2	2	NUM
ejpam-2677	140	9	,	,	PUNCT
ejpam-2677	140	10	0	0	NUM
ejpam-2677	140	11	,	,	PUNCT
ejpam-2677	140	12	1	1	NUM
ejpam-2677	140	13	2	2	NUM
ejpam-2677	140	14	)	)	PUNCT
ejpam-2677	140	15	+	+	CCONJ
ejpam-2677	140	16	80	80	NUM
ejpam-2677	140	17	σc	σc	NOUN
ejpam-2677	140	18	√	√	NUM
ejpam-2677	140	19	πγ(c	πγ(c	NUM
ejpam-2677	140	20	)	)	PUNCT
ejpam-2677	140	21	g31	g31	PROPN
ejpam-2677	140	22	13	13	NUM
ejpam-2677	140	23	(	(	PUNCT
ejpam-2677	140	24	1	1	NUM
ejpam-2677	140	25	4σ2	4σ2	NUM
ejpam-2677	140	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	141	1	−	−	NOUN
ejpam-2677	141	2	c	c	NOUN
ejpam-2677	141	3	2	2	NUM
ejpam-2677	141	4	−	−	NOUN
ejpam-2677	141	5	1	1	NUM
ejpam-2677	141	6	−c	−c	NOUN
ejpam-2677	141	7	,	,	PUNCT
ejpam-2677	141	8	0	0	NUM
ejpam-2677	141	9	,	,	PUNCT
ejpam-2677	141	10	1	1	NUM
ejpam-2677	141	11	2	2	NUM
ejpam-2677	141	12	)	)	PUNCT
ejpam-2677	141	13	−	−	PROPN
ejpam-2677	141	14	64	64	NUM
ejpam-2677	141	15	σc	σc	NOUN
ejpam-2677	141	16	√	√	NUM
ejpam-2677	141	17	πγ(c	πγ(c	NUM
ejpam-2677	141	18	)	)	PUNCT
ejpam-2677	141	19	g31	g31	PROPN
ejpam-2677	141	20	13	13	NUM
ejpam-2677	141	21	(	(	PUNCT
ejpam-2677	141	22	1	1	NUM
ejpam-2677	141	23	4σ2	4σ2	NUM
ejpam-2677	141	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	142	1	−	−	NOUN
ejpam-2677	142	2	c	c	NOUN
ejpam-2677	142	3	2	2	NUM
ejpam-2677	142	4	−	−	NOUN
ejpam-2677	142	5	2	2	NUM
ejpam-2677	142	6	−	−	NOUN
ejpam-2677	142	7	c	c	NOUN
ejpam-2677	142	8	2	2	NUM
ejpam-2677	142	9	,	,	PUNCT
ejpam-2677	142	10	0	0	NUM
ejpam-2677	142	11	,	,	PUNCT
ejpam-2677	142	12	1	1	NUM
ejpam-2677	142	13	2	2	NUM
ejpam-2677	142	14	)	)	PUNCT
ejpam-2677	142	15	−	−	PROPN
ejpam-2677	142	16	16	16	NUM
ejpam-2677	142	17	σc	σc	PROPN
ejpam-2677	142	18	√	√	NUM
ejpam-2677	142	19	πγ(c	πγ(c	NUM
ejpam-2677	142	20	)	)	PUNCT
ejpam-2677	142	21	g31	g31	PROPN
ejpam-2677	142	22	13	13	NUM
ejpam-2677	142	23	(	(	PUNCT
ejpam-2677	142	24	1	1	NUM
ejpam-2677	142	25	4σ2	4σ2	NUM
ejpam-2677	142	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	143	1	−	−	NOUN
ejpam-2677	143	2	c	c	NOUN
ejpam-2677	143	3	2	2	NUM
ejpam-2677	143	4	−	−	NOUN
ejpam-2677	143	5	c	c	NOUN
ejpam-2677	143	6	2	2	NUM
ejpam-2677	143	7	,	,	PUNCT
ejpam-2677	143	8	0	0	NUM
ejpam-2677	143	9	,	,	PUNCT
ejpam-2677	143	10	1	1	NUM
ejpam-2677	143	11	2	2	NUM
ejpam-2677	143	12	)	)	PUNCT
ejpam-2677	143	13	β4	β4	PROPN
ejpam-2677	143	14	=	=	SYM
ejpam-2677	143	15	1	1	NUM
ejpam-2677	143	16	2σcγ(c	2σcγ(c	NUM
ejpam-2677	143	17	)	)	PUNCT
ejpam-2677	143	18	π∫	π∫	NOUN
ejpam-2677	143	19	0	0	NUM
ejpam-2677	143	20	sin	sin	NOUN
ejpam-2677	143	21	4θ	4θ	NOUN
ejpam-2677	143	22	sec2	sec2	NOUN
ejpam-2677	143	23	(	(	PUNCT
ejpam-2677	143	24	θ	θ	NOUN
ejpam-2677	143	25	2	2	NUM
ejpam-2677	143	26	)	)	PUNCT
ejpam-2677	143	27	(	(	PUNCT
ejpam-2677	143	28	tan	tan	PROPN
ejpam-2677	143	29	(	(	PUNCT
ejpam-2677	143	30	θ	θ	PROPN
ejpam-2677	143	31	2	2	NUM
ejpam-2677	143	32	)	)	PUNCT
ejpam-2677	143	33	)	)	PUNCT
ejpam-2677	144	1	c−1	c−1	PROPN
ejpam-2677	144	2	e−	e−	PROPN
ejpam-2677	144	3	1	1	NUM
ejpam-2677	144	4	σ	σ	PROPN
ejpam-2677	144	5	tan	tan	PROPN
ejpam-2677	144	6	(	(	PUNCT
ejpam-2677	144	7	θ2)dθ	θ2)dθ	NOUN
ejpam-2677	144	8	sin	sin	NOUN
ejpam-2677	144	9	4θ	4θ	NOUN
ejpam-2677	144	10	=	=	SYM
ejpam-2677	144	11	8x	8x	PROPN
ejpam-2677	144	12	(	(	PUNCT
ejpam-2677	144	13	1+x2	1+x2	NUM
ejpam-2677	144	14	)	)	PUNCT
ejpam-2677	144	15	−	−	PROPN
ejpam-2677	144	16	16x3	16x3	NUM
ejpam-2677	144	17	(	(	PUNCT
ejpam-2677	144	18	1+x2)2	1+x2)2	NUM
ejpam-2677	144	19	−	−	NUM
ejpam-2677	144	20	64x3	64x3	NUM
ejpam-2677	144	21	(	(	PUNCT
ejpam-2677	144	22	1+x2)3	1+x2)3	NUM
ejpam-2677	144	23	+	+	NUM
ejpam-2677	144	24	128x5	128x5	NUM
ejpam-2677	144	25	(	(	PUNCT
ejpam-2677	144	26	1+x2)4	1+x2)4	NUM
ejpam-2677	144	27	and	and	CCONJ
ejpam-2677	144	28	formula	formula	NOUN
ejpam-2677	144	29	(	(	PUNCT
ejpam-2677	144	30	4.1	4.1	NUM
ejpam-2677	144	31	)	)	PUNCT
ejpam-2677	144	32	β4	β4	PROPN
ejpam-2677	144	33	=	=	SYM
ejpam-2677	144	34	8	8	NUM
ejpam-2677	144	35	σcγ(c	σcγ(c	PROPN
ejpam-2677	144	36	)	)	PUNCT
ejpam-2677	144	37	∞∫	∞∫	NOUN
ejpam-2677	144	38	0	0	NUM
ejpam-2677	145	1	xc(1	xc(1	PROPN
ejpam-2677	145	2	+	+	CCONJ
ejpam-2677	145	3	x2)−1e−	x2)−1e−	PROPN
ejpam-2677	145	4	1	1	NUM
ejpam-2677	145	5	σ	σ	NOUN
ejpam-2677	145	6	xdx−	xdx−	PROPN
ejpam-2677	145	7	16	16	NUM
ejpam-2677	145	8	σλγ(c	σλγ(c	NOUN
ejpam-2677	145	9	)	)	PUNCT
ejpam-2677	145	10	∞∫	∞∫	NOUN
ejpam-2677	145	11	0	0	NUM
ejpam-2677	145	12	xc+2(1	xc+2(1	PUNCT
ejpam-2677	146	1	+	+	CCONJ
ejpam-2677	146	2	x2)−2e−	x2)−2e−	PROPN
ejpam-2677	146	3	1	1	NUM
ejpam-2677	146	4	σ	σ	PROPN
ejpam-2677	146	5	xdx	xdx	PROPN
ejpam-2677	146	6	−	−	PROPN
ejpam-2677	146	7	64	64	NUM
ejpam-2677	146	8	σcγ(c	σcγ(c	PROPN
ejpam-2677	146	9	)	)	PUNCT
ejpam-2677	146	10	∞∫	∞∫	NOUN
ejpam-2677	146	11	0	0	NUM
ejpam-2677	146	12	xc+2(1	xc+2(1	PUNCT
ejpam-2677	147	1	+	+	CCONJ
ejpam-2677	147	2	x2)−3e−	x2)−3e−	PROPN
ejpam-2677	147	3	1	1	NUM
ejpam-2677	147	4	σ	σ	NOUN
ejpam-2677	147	5	xdx+	xdx+	PROPN
ejpam-2677	147	6	128	128	NUM
ejpam-2677	147	7	σcγ(c	σcγ(c	PROPN
ejpam-2677	147	8	)	)	PUNCT
ejpam-2677	147	9	∞∫	∞∫	NOUN
ejpam-2677	147	10	0	0	NUM
ejpam-2677	147	11	xc+4(1	xc+4(1	X
ejpam-2677	148	1	+	+	CCONJ
ejpam-2677	148	2	x2)−4e−	x2)−4e−	SYM
ejpam-2677	148	3	1	1	NUM
ejpam-2677	148	4	σ	σ	PROPN
ejpam-2677	148	5	xdx	xdx	PROPN
ejpam-2677	148	6	=	=	NOUN
ejpam-2677	148	7	8	8	NUM
ejpam-2677	148	8	σcγ(c	σcγ(c	PROPN
ejpam-2677	148	9	)	)	PUNCT
ejpam-2677	148	10	∞∫	∞∫	NOUN
ejpam-2677	148	11	0	0	NUM
ejpam-2677	148	12	x2	x2	PROPN
ejpam-2677	148	13	(	(	PUNCT
ejpam-2677	148	14	c2	c2	PROPN
ejpam-2677	148	15	+	+	CCONJ
ejpam-2677	148	16	1	1	NUM
ejpam-2677	148	17	2)−1(1	2)−1(1	NUM
ejpam-2677	148	18	+	+	CCONJ
ejpam-2677	148	19	x2)0−1e−	x2)0−1e−	PROPN
ejpam-2677	148	20	1	1	NUM
ejpam-2677	148	21	σ	σ	NOUN
ejpam-2677	148	22	xdx−	xdx−	PROPN
ejpam-2677	148	23	16	16	NUM
ejpam-2677	148	24	σcγ(c	σcγ(c	PROPN
ejpam-2677	148	25	)	)	PUNCT
ejpam-2677	148	26	∞∫	∞∫	NOUN
ejpam-2677	148	27	0	0	NUM
ejpam-2677	149	1	x2	x2	PROPN
ejpam-2677	149	2	(	(	PUNCT
ejpam-2677	149	3	c2	c2	PROPN
ejpam-2677	149	4	+	+	CCONJ
ejpam-2677	149	5	3	3	NUM
ejpam-2677	149	6	2)−1(1	2)−1(1	NUM
ejpam-2677	149	7	+	+	CCONJ
ejpam-2677	149	8	x2)−1−1e−	x2)−1−1e−	PROPN
ejpam-2677	149	9	1	1	NUM
ejpam-2677	149	10	σ	σ	PROPN
ejpam-2677	149	11	xdx	xdx	PROPN
ejpam-2677	150	1	−	−	PROPN
ejpam-2677	150	2	64	64	NUM
ejpam-2677	150	3	σcγ(c	σcγ(c	PROPN
ejpam-2677	150	4	)	)	PUNCT
ejpam-2677	150	5	∞∫	∞∫	NOUN
ejpam-2677	150	6	0	0	NUM
ejpam-2677	151	1	x2	x2	PROPN
ejpam-2677	151	2	(	(	PUNCT
ejpam-2677	151	3	c2	c2	PROPN
ejpam-2677	151	4	+	+	CCONJ
ejpam-2677	151	5	3	3	NUM
ejpam-2677	151	6	2)−1(1	2)−1(1	NUM
ejpam-2677	151	7	+	+	CCONJ
ejpam-2677	151	8	x2)−2−1e−	x2)−2−1e−	PROPN
ejpam-2677	151	9	1	1	NUM
ejpam-2677	151	10	σ	σ	PROPN
ejpam-2677	151	11	xdx+	xdx+	PROPN
ejpam-2677	151	12	128	128	NUM
ejpam-2677	151	13	σcγ(c	σcγ(c	PROPN
ejpam-2677	151	14	)	)	PUNCT
ejpam-2677	151	15	∞∫	∞∫	NOUN
ejpam-2677	151	16	0	0	NUM
ejpam-2677	152	1	x2	x2	PROPN
ejpam-2677	152	2	(	(	PUNCT
ejpam-2677	152	3	c2	c2	PROPN
ejpam-2677	152	4	+	+	CCONJ
ejpam-2677	152	5	5	5	NUM
ejpam-2677	152	6	2)−1(1	2)−1(1	NUM
ejpam-2677	152	7	+	+	CCONJ
ejpam-2677	152	8	x2)−3−1e−	x2)−3−1e−	PROPN
ejpam-2677	152	9	1	1	NUM
ejpam-2677	152	10	σ	σ	PROPN
ejpam-2677	152	11	xdx	xdx	PROPN
ejpam-2677	152	12	β4	β4	PROPN
ejpam-2677	152	13	=	=	PUNCT
ejpam-2677	152	14	4	4	NUM
ejpam-2677	152	15	σc	σc	NOUN
ejpam-2677	152	16	√	√	NUM
ejpam-2677	152	17	πγ(c	πγ(c	NOUN
ejpam-2677	152	18	)	)	PUNCT
ejpam-2677	152	19	g31	g31	PROPN
ejpam-2677	152	20	13	13	NUM
ejpam-2677	152	21	(	(	PUNCT
ejpam-2677	152	22	1	1	NUM
ejpam-2677	152	23	4σ2	4σ2	NUM
ejpam-2677	152	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	152	25	1−c	1−c	NUM
ejpam-2677	152	26	2	2	NUM
ejpam-2677	152	27	1−c	1−c	NUM
ejpam-2677	152	28	2	2	NUM
ejpam-2677	152	29	,	,	PUNCT
ejpam-2677	152	30	0	0	NUM
ejpam-2677	152	31	,	,	PUNCT
ejpam-2677	152	32	1	1	NUM
ejpam-2677	152	33	2	2	NUM
ejpam-2677	152	34	)	)	PUNCT
ejpam-2677	152	35	−	−	PROPN
ejpam-2677	152	36	8	8	NUM
ejpam-2677	152	37	σc	σc	PROPN
ejpam-2677	152	38	√	√	NUM
ejpam-2677	152	39	πγ(c	πγ(c	NUM
ejpam-2677	152	40	)	)	PUNCT
ejpam-2677	152	41	g31	g31	PROPN
ejpam-2677	152	42	13	13	NUM
ejpam-2677	152	43	(	(	PUNCT
ejpam-2677	152	44	1	1	NUM
ejpam-2677	152	45	4σ2	4σ2	NUM
ejpam-2677	152	46	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	152	47	−	−	PROPN
ejpam-2677	152	48	(	(	PUNCT
ejpam-2677	152	49	c+1	c+1	NOUN
ejpam-2677	152	50	)	)	PUNCT
ejpam-2677	152	51	2	2	NUM
ejpam-2677	152	52	1−c	1−c	NUM
ejpam-2677	152	53	2	2	NUM
ejpam-2677	152	54	,	,	PUNCT
ejpam-2677	152	55	0	0	NUM
ejpam-2677	152	56	,	,	PUNCT
ejpam-2677	152	57	1	1	NUM
ejpam-2677	152	58	2	2	NUM
ejpam-2677	152	59	)	)	PUNCT
ejpam-2677	152	60	−	−	PROPN
ejpam-2677	152	61	16	16	NUM
ejpam-2677	152	62	σc	σc	PROPN
ejpam-2677	152	63	√	√	NUM
ejpam-2677	152	64	πγ(c	πγ(c	NUM
ejpam-2677	152	65	)	)	PUNCT
ejpam-2677	152	66	g31	g31	PROPN
ejpam-2677	152	67	13	13	NUM
ejpam-2677	152	68	(	(	PUNCT
ejpam-2677	152	69	1	1	NUM
ejpam-2677	152	70	4σ2	4σ2	NUM
ejpam-2677	152	71	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	152	72	−	−	PROPN
ejpam-2677	152	73	(	(	PUNCT
ejpam-2677	152	74	c+1	c+1	NOUN
ejpam-2677	152	75	)	)	PUNCT
ejpam-2677	152	76	2	2	NUM
ejpam-2677	152	77	3−c	3−c	NUM
ejpam-2677	152	78	2	2	NUM
ejpam-2677	152	79	,	,	PUNCT
ejpam-2677	152	80	0	0	NUM
ejpam-2677	152	81	,	,	PUNCT
ejpam-2677	152	82	1	1	NUM
ejpam-2677	152	83	2	2	NUM
ejpam-2677	152	84	)	)	PUNCT
ejpam-2677	152	85	−	−	PROPN
ejpam-2677	152	86	32	32	NUM
ejpam-2677	152	87	3σc	3σc	NOUN
ejpam-2677	152	88	√	√	NUM
ejpam-2677	152	89	πγ(c	πγ(c	NOUN
ejpam-2677	152	90	)	)	PUNCT
ejpam-2677	152	91	g31	g31	PROPN
ejpam-2677	152	92	13	13	NUM
ejpam-2677	152	93	(	(	PUNCT
ejpam-2677	152	94	1	1	NUM
ejpam-2677	152	95	4σ2	4σ2	NUM
ejpam-2677	152	96	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2677	152	97	−	−	PROPN
ejpam-2677	152	98	(	(	PUNCT
ejpam-2677	152	99	c+3	c+3	NOUN
ejpam-2677	152	100	)	)	PUNCT
ejpam-2677	152	101	2	2	NUM
ejpam-2677	152	102	3−c	3−c	NUM
ejpam-2677	152	103	2	2	NUM
ejpam-2677	152	104	,	,	PUNCT
ejpam-2677	152	105	0	0	NUM
ejpam-2677	152	106	,	,	PUNCT
ejpam-2677	152	107	1	1	NUM
ejpam-2677	152	108	2	2	NUM
ejpam-2677	152	109	)	)	PUNCT
ejpam-2677	152	110	on	on	ADP
ejpam-2677	152	111	the	the	DET
ejpam-2677	152	112	similar	similar	ADJ
ejpam-2677	152	113	lines	line	NOUN
ejpam-2677	152	114	the	the	DET
ejpam-2677	152	115	higher	high	ADJ
ejpam-2677	152	116	-	-	PUNCT
ejpam-2677	152	117	order	order	NOUN
ejpam-2677	152	118	moments	moment	NOUN
ejpam-2677	152	119	can	can	AUX
ejpam-2677	152	120	be	be	AUX
ejpam-2677	152	121	obtained	obtain	VERB
ejpam-2677	152	122	.	.	PUNCT
ejpam-2677	153	1	5	5	X
ejpam-2677	153	2	.	.	X
ejpam-2677	153	3	stereographic	stereographic	ADJ
ejpam-2677	153	4	-l	-l	NUM
ejpam-2677	153	5	-	-	PUNCT
ejpam-2677	153	6	axial	axial	ADJ
ejpam-2677	153	7	semicircular	semicircular	ADJ
ejpam-2677	153	8	gamma	gamma	NOUN
ejpam-2677	153	9	distribution	distribution	NOUN
ejpam-2677	153	10	the	the	DET
ejpam-2677	153	11	above	above	ADJ
ejpam-2677	153	12	proposed	propose	VERB
ejpam-2677	153	13	model	model	NOUN
ejpam-2677	153	14	is	be	AUX
ejpam-2677	153	15	extended	extend	VERB
ejpam-2677	153	16	to	to	ADP
ejpam-2677	153	17	the	the	DET
ejpam-2677	153	18	l	l	ADJ
ejpam-2677	153	19	-	-	ADJ
ejpam-2677	153	20	axial	axial	ADJ
ejpam-2677	153	21	distribution	distribution	NOUN
ejpam-2677	153	22	,	,	PUNCT
ejpam-2677	153	23	which	which	PRON
ejpam-2677	153	24	is	be	AUX
ejpam-2677	153	25	applicable	applicable	ADJ
ejpam-2677	153	26	to	to	ADP
ejpam-2677	153	27	any	any	DET
ejpam-2677	153	28	arc	arc	NOUN
ejpam-2677	153	29	of	of	ADP
ejpam-2677	153	30	arbitrary	arbitrary	ADJ
ejpam-2677	153	31	length	length	NOUN
ejpam-2677	153	32	say	say	VERB
ejpam-2677	153	33	2π	2π	PROPN
ejpam-2677	153	34	l	l	NOUN
ejpam-2677	153	35	for	for	ADP
ejpam-2677	153	36	l	l	PROPN
ejpam-2677	153	37	∈	∈	PROPN
ejpam-2677	153	38	n	n	CCONJ
ejpam-2677	153	39	,	,	PUNCT
ejpam-2677	153	40	.	.	PUNCT
ejpam-2677	154	1	it	it	PRON
ejpam-2677	154	2	is	be	AUX
ejpam-2677	154	3	possible	possible	ADJ
ejpam-2677	154	4	and	and	CCONJ
ejpam-2677	154	5	useful	useful	ADJ
ejpam-2677	154	6	to	to	PART
ejpam-2677	154	7	extend	extend	VERB
ejpam-2677	154	8	the	the	DET
ejpam-2677	154	9	stereographic	stereographic	ADJ
ejpam-2677	154	10	semicircular	semicircular	ADJ
ejpam-2677	154	11	gamma	gamma	NOUN
ejpam-2677	154	12	distribution	distribution	NOUN
ejpam-2677	154	13	to	to	PART
ejpam-2677	154	14	construct	construct	VERB
ejpam-2677	154	15	the	the	DET
ejpam-2677	154	16	stereographic	stereographic	ADJ
ejpam-2677	154	17	-	-	PUNCT
ejpam-2677	154	18	l	l	NOUN
ejpam-2677	154	19	-	-	ADJ
ejpam-2677	154	20	axial	axial	ADJ
ejpam-2677	154	21	gamma	gamma	NOUN
ejpam-2677	154	22	distribution	distribution	NOUN
ejpam-2677	154	23	.	.	PUNCT
ejpam-2677	155	1	the	the	DET
ejpam-2677	155	2	density	density	NOUN
ejpam-2677	155	3	function	function	NOUN
ejpam-2677	155	4	of	of	ADP
ejpam-2677	155	5	stereographic	stereographic	ADJ
ejpam-2677	155	6	semicircular	semicircular	ADJ
ejpam-2677	155	7	gamma	gamma	NOUN
ejpam-2677	155	8	distribution	distribution	NOUN
ejpam-2677	155	9	by	by	ADP
ejpam-2677	155	10	using	use	VERB
ejpam-2677	155	11	the	the	DET
ejpam-2677	155	12	transformation	transformation	NOUN
ejpam-2677	155	13	φ	φ	NOUN
ejpam-2677	155	14	=	=	SYM
ejpam-2677	155	15	2θ	2θ	NUM
ejpam-2677	155	16	l	l	NOUN
ejpam-2677	155	17	,	,	PUNCT
ejpam-2677	155	18	l	l	PROPN
ejpam-2677	155	19	∈	∈	PROPN
ejpam-2677	155	20	n.	n.	NOUN
ejpam-2677	155	21	on	on	ADP
ejpam-2677	155	22	the	the	DET
ejpam-2677	155	23	probability	probability	NOUN
ejpam-2677	155	24	density	density	NOUN
ejpam-2677	155	25	function	function	NOUN
ejpam-2677	155	26	of	of	ADP
ejpam-2677	155	27	φ	φ	PROPN
ejpam-2677	155	28	is	be	AUX
ejpam-2677	155	29	given	give	VERB
ejpam-2677	155	30	by	by	ADP
ejpam-2677	155	31	g(φ	g(φ	NOUN
ejpam-2677	155	32	)	)	PUNCT
ejpam-2677	155	33	=	=	SYM
ejpam-2677	155	34	1	1	NUM
ejpam-2677	155	35	2σcγ(c	2σcγ(c	NUM
ejpam-2677	155	36	)	)	PUNCT
ejpam-2677	155	37	sec2	sec2	NOUN
ejpam-2677	155	38	(	(	PUNCT
ejpam-2677	155	39	lφ	lφ	ADV
ejpam-2677	155	40	4	4	NUM
ejpam-2677	155	41	)	)	PUNCT
ejpam-2677	155	42	(	(	PUNCT
ejpam-2677	155	43	tan	tan	PROPN
ejpam-2677	155	44	(	(	PUNCT
ejpam-2677	155	45	lφ	lφ	ADV
ejpam-2677	155	46	4	4	NUM
ejpam-2677	155	47	)	)	PUNCT
ejpam-2677	155	48	)	)	PUNCT
ejpam-2677	156	1	c−1	c−1	PROPN
ejpam-2677	156	2	exp	exp	NOUN
ejpam-2677	156	3	(	(	PUNCT
ejpam-2677	156	4	−	−	PROPN
ejpam-2677	156	5	1	1	NUM
ejpam-2677	156	6	σ	σ	PROPN
ejpam-2677	156	7	(	(	PUNCT
ejpam-2677	156	8	tan	tan	PROPN
ejpam-2677	156	9	(	(	PUNCT
ejpam-2677	156	10	lφ	lφ	ADV
ejpam-2677	156	11	4	4	NUM
ejpam-2677	156	12	)	)	PUNCT
ejpam-2677	156	13	)	)	PUNCT
ejpam-2677	156	14	)	)	PUNCT
ejpam-2677	156	15	(	(	PUNCT
ejpam-2677	156	16	5.1	5.1	NUM
ejpam-2677	156	17	)	)	PUNCT
ejpam-2677	156	18	references	reference	NOUN
ejpam-2677	156	19	1133	1133	NUM
ejpam-2677	156	20	0	0	NUM
ejpam-2677	156	21	<	<	X
ejpam-2677	156	22	φ	φ	X
ejpam-2677	156	23	<	<	X
ejpam-2677	156	24	2π	2π	PROPN
ejpam-2677	156	25	l	l	NOUN
ejpam-2677	156	26	,	,	PUNCT
ejpam-2677	156	27	σ	σ	X
ejpam-2677	156	28	>	>	X
ejpam-2677	156	29	0	0	PROPN
ejpam-2677	156	30	,	,	PUNCT
ejpam-2677	156	31	c	c	NOUN
ejpam-2677	156	32	>	>	X
ejpam-2677	156	33	0	0	PUNCT
ejpam-2677	157	1	and	and	CCONJ
ejpam-2677	157	2	l	l	NOUN
ejpam-2677	157	3	=	=	SYM
ejpam-2677	157	4	1	1	NUM
ejpam-2677	157	5	,	,	PUNCT
ejpam-2677	157	6	2	2	NUM
ejpam-2677	157	7	,	,	PUNCT
ejpam-2677	157	8	.	.	PUNCT
ejpam-2677	157	9	.	.	PUNCT
ejpam-2677	158	1	.	.	PUNCT
ejpam-2677	159	1	it	it	PRON
ejpam-2677	159	2	is	be	AUX
ejpam-2677	159	3	coined	coin	VERB
ejpam-2677	159	4	as	as	ADP
ejpam-2677	159	5	stereographic	stereographic	ADJ
ejpam-2677	159	6	-l	-l	NUM
ejpam-2677	159	7	-	-	PUNCT
ejpam-2677	159	8	axial	axial	ADJ
ejpam-2677	159	9	gamma	gamma	NOUN
ejpam-2677	159	10	distribution	distribution	NOUN
ejpam-2677	159	11	case	case	NOUN
ejpam-2677	159	12	(	(	PUNCT
ejpam-2677	159	13	1	1	X
ejpam-2677	159	14	)	)	PUNCT
ejpam-2677	159	15	when	when	SCONJ
ejpam-2677	159	16	l	l	NOUN
ejpam-2677	159	17	=	=	SYM
ejpam-2677	159	18	1	1	NUM
ejpam-2677	159	19	,	,	PUNCT
ejpam-2677	159	20	in	in	ADP
ejpam-2677	159	21	the	the	DET
ejpam-2677	159	22	probability	probability	NOUN
ejpam-2677	159	23	density	density	NOUN
ejpam-2677	159	24	function	function	NOUN
ejpam-2677	159	25	(	(	PUNCT
ejpam-2677	159	26	5.1	5.1	NUM
ejpam-2677	159	27	)	)	PUNCT
ejpam-2677	159	28	,	,	PUNCT
ejpam-2677	159	29	we	we	PRON
ejpam-2677	159	30	get	get	VERB
ejpam-2677	159	31	the	the	DET
ejpam-2677	159	32	density	density	NOUN
ejpam-2677	159	33	function	function	NOUN
ejpam-2677	159	34	g(φ	g(φ	NOUN
ejpam-2677	159	35	)	)	PUNCT
ejpam-2677	159	36	=	=	SYM
ejpam-2677	159	37	1	1	NUM
ejpam-2677	159	38	2σcγ(c	2σcγ(c	NUM
ejpam-2677	159	39	)	)	PUNCT
ejpam-2677	159	40	sec2	sec2	NOUN
ejpam-2677	159	41	(	(	PUNCT
ejpam-2677	159	42	φ−	φ−	PROPN
ejpam-2677	159	43	µ	µ	PROPN
ejpam-2677	159	44	4	4	NUM
ejpam-2677	159	45	)	)	PUNCT
ejpam-2677	159	46	(	(	PUNCT
ejpam-2677	159	47	tan	tan	PROPN
ejpam-2677	159	48	(	(	PUNCT
ejpam-2677	159	49	φ−	φ−	PROPN
ejpam-2677	159	50	µ	µ	PROPN
ejpam-2677	159	51	4	4	NUM
ejpam-2677	159	52	)	)	PUNCT
ejpam-2677	159	53	)	)	PUNCT
ejpam-2677	160	1	c−1	c−1	PROPN
ejpam-2677	160	2	exp	exp	NOUN
ejpam-2677	160	3	(	(	PUNCT
ejpam-2677	160	4	−	−	PROPN
ejpam-2677	160	5	1	1	NUM
ejpam-2677	160	6	σ	σ	PROPN
ejpam-2677	160	7	(	(	PUNCT
ejpam-2677	160	8	tan	tan	PROPN
ejpam-2677	160	9	(	(	PUNCT
ejpam-2677	160	10	φ−	φ−	PROPN
ejpam-2677	160	11	µ	µ	PROPN
ejpam-2677	160	12	4	4	NUM
ejpam-2677	160	13	)	)	PUNCT
ejpam-2677	160	14	)	)	PUNCT
ejpam-2677	160	15	)	)	PUNCT
ejpam-2677	160	16	(	(	PUNCT
ejpam-2677	160	17	5.2	5.2	NUM
ejpam-2677	160	18	)	)	PUNCT
ejpam-2677	160	19	0	0	PUNCT
ejpam-2677	161	1	<	<	X
ejpam-2677	161	2	φ	φ	X
ejpam-2677	161	3	<	<	X
ejpam-2677	161	4	2π	2π	NOUN
ejpam-2677	161	5	,	,	PUNCT
ejpam-2677	161	6	σ	σ	PROPN
ejpam-2677	161	7	>	>	X
ejpam-2677	161	8	0	0	PUNCT
ejpam-2677	161	9	and	and	CCONJ
ejpam-2677	161	10	c	c	X
ejpam-2677	161	11	>	>	X
ejpam-2677	161	12	0	0	PUNCT
ejpam-2677	162	1	it	it	PRON
ejpam-2677	162	2	is	be	AUX
ejpam-2677	162	3	named	name	VERB
ejpam-2677	162	4	by	by	ADP
ejpam-2677	162	5	us	we	PRON
ejpam-2677	162	6	as	as	ADP
ejpam-2677	162	7	stereographic	stereographic	ADJ
ejpam-2677	162	8	circular	circular	ADJ
ejpam-2677	162	9	gamma	gamma	NOUN
ejpam-2677	162	10	distribution	distribution	NOUN
ejpam-2677	162	11	.	.	PUNCT
ejpam-2677	163	1	case	case	NOUN
ejpam-2677	163	2	(	(	PUNCT
ejpam-2677	163	3	2	2	NUM
ejpam-2677	163	4	)	)	PUNCT
ejpam-2677	163	5	when	when	SCONJ
ejpam-2677	163	6	l	l	NOUN
ejpam-2677	163	7	=	=	SYM
ejpam-2677	163	8	2	2	NUM
ejpam-2677	163	9	,	,	PUNCT
ejpam-2677	163	10	the	the	DET
ejpam-2677	163	11	probability	probability	NOUN
ejpam-2677	163	12	density	density	NOUN
ejpam-2677	163	13	function	function	NOUN
ejpam-2677	163	14	(	(	PUNCT
ejpam-2677	163	15	5.1	5.1	NUM
ejpam-2677	163	16	)	)	PUNCT
ejpam-2677	163	17	is	be	AUX
ejpam-2677	163	18	the	the	DET
ejpam-2677	163	19	same	same	ADJ
ejpam-2677	163	20	as	as	ADP
ejpam-2677	163	21	that	that	PRON
ejpam-2677	163	22	of	of	ADP
ejpam-2677	163	23	stereographic	stereographic	ADJ
ejpam-2677	163	24	semicircular	semicircular	ADJ
ejpam-2677	163	25	gamma	gamma	NOUN
ejpam-2677	163	26	distribution	distribution	NOUN
ejpam-2677	163	27	.	.	PUNCT
ejpam-2677	164	1	case	case	NOUN
ejpam-2677	164	2	(	(	PUNCT
ejpam-2677	164	3	3	3	NUM
ejpam-2677	164	4	)	)	PUNCT
ejpam-2677	164	5	when	when	SCONJ
ejpam-2677	164	6	l	l	NOUN
ejpam-2677	164	7	=	=	SYM
ejpam-2677	164	8	2	2	NUM
ejpam-2677	164	9	and	and	CCONJ
ejpam-2677	164	10	c	c	NOUN
ejpam-2677	164	11	=	=	SYM
ejpam-2677	164	12	1	1	NUM
ejpam-2677	164	13	,	,	PUNCT
ejpam-2677	164	14	in	in	ADP
ejpam-2677	164	15	the	the	DET
ejpam-2677	164	16	probability	probability	NOUN
ejpam-2677	164	17	density	density	NOUN
ejpam-2677	164	18	function	function	NOUN
ejpam-2677	164	19	(	(	PUNCT
ejpam-2677	164	20	5.1	5.1	NUM
ejpam-2677	164	21	)	)	PUNCT
ejpam-2677	164	22	we	we	PRON
ejpam-2677	164	23	get	get	VERB
ejpam-2677	164	24	the	the	DET
ejpam-2677	164	25	density	density	NOUN
ejpam-2677	164	26	function	function	NOUN
ejpam-2677	164	27	of	of	ADP
ejpam-2677	164	28	stereographic	stereographic	ADJ
ejpam-2677	164	29	semicircular	semicircular	ADJ
ejpam-2677	164	30	exponential	exponential	ADJ
ejpam-2677	164	31	distribution	distribution	NOUN
ejpam-2677	164	32	[	[	X
ejpam-2677	164	33	phani	phani	PROPN
ejpam-2677	164	34	et	et	PROPN
ejpam-2677	164	35	al	al	PROPN
ejpam-2677	164	36	(	(	PUNCT
ejpam-2677	164	37	2013	2013	NUM
ejpam-2677	164	38	)	)	PUNCT
ejpam-2677	164	39	]	]	PUNCT
ejpam-2677	164	40	.	.	PUNCT
ejpam-2677	165	1	6	6	X
ejpam-2677	165	2	.	.	X
ejpam-2677	165	3	conclusion	conclusion	NOUN
ejpam-2677	165	4	in	in	ADP
ejpam-2677	165	5	this	this	DET
ejpam-2677	165	6	paper	paper	NOUN
ejpam-2677	165	7	,	,	PUNCT
ejpam-2677	165	8	we	we	PRON
ejpam-2677	165	9	derived	derive	VERB
ejpam-2677	165	10	the	the	DET
ejpam-2677	165	11	semicircular	semicircular	ADJ
ejpam-2677	165	12	distribution	distribution	NOUN
ejpam-2677	165	13	induced	induce	VERB
ejpam-2677	165	14	by	by	ADP
ejpam-2677	165	15	modified	modified	ADJ
ejpam-2677	165	16	inverse	inverse	NOUN
ejpam-2677	165	17	stereographic	stereographic	ADJ
ejpam-2677	165	18	projection	projection	NOUN
ejpam-2677	165	19	on	on	ADP
ejpam-2677	165	20	gamma	gamma	NOUN
ejpam-2677	165	21	distribution	distribution	NOUN
ejpam-2677	165	22	is	be	AUX
ejpam-2677	165	23	discussed	discuss	VERB
ejpam-2677	165	24	and	and	CCONJ
ejpam-2677	165	25	named	name	VERB
ejpam-2677	165	26	it	it	PRON
ejpam-2677	165	27	by	by	ADP
ejpam-2677	165	28	us	we	PRON
ejpam-2677	165	29	as	as	ADP
ejpam-2677	165	30	stereographic	stereographic	ADJ
ejpam-2677	165	31	semicircular	semicircular	ADJ
ejpam-2677	165	32	gamma	gamma	NOUN
ejpam-2677	165	33	distribution	distribution	NOUN
ejpam-2677	165	34	.	.	PUNCT
ejpam-2677	166	1	the	the	DET
ejpam-2677	166	2	density	density	NOUN
ejpam-2677	166	3	and	and	CCONJ
ejpam-2677	166	4	distribution	distribution	NOUN
ejpam-2677	166	5	function	function	NOUN
ejpam-2677	166	6	of	of	ADP
ejpam-2677	166	7	stereographic	stereographic	ADJ
ejpam-2677	166	8	semicircular	semicircular	ADJ
ejpam-2677	166	9	gamma	gamma	NOUN
ejpam-2677	166	10	distribution	distribution	NOUN
ejpam-2677	166	11	admit	admit	VERB
ejpam-2677	166	12	explicit	explicit	ADJ
ejpam-2677	166	13	forms	form	NOUN
ejpam-2677	166	14	,	,	PUNCT
ejpam-2677	166	15	as	as	SCONJ
ejpam-2677	166	16	do	do	VERB
ejpam-2677	166	17	trigonometric	trigonometric	NOUN
ejpam-2677	166	18	moments	moment	NOUN
ejpam-2677	166	19	.	.	PUNCT
ejpam-2677	167	1	as	as	SCONJ
ejpam-2677	167	2	this	this	DET
ejpam-2677	167	3	distribution	distribution	NOUN
ejpam-2677	167	4	is	be	AUX
ejpam-2677	167	5	asymmetric	asymmetric	ADJ
ejpam-2677	167	6	,	,	PUNCT
ejpam-2677	167	7	it	it	PRON
ejpam-2677	167	8	is	be	AUX
ejpam-2677	167	9	suitable	suitable	ADJ
ejpam-2677	167	10	for	for	ADP
ejpam-2677	167	11	modeling	model	VERB
ejpam-2677	167	12	skewed	skewed	ADJ
ejpam-2677	167	13	directional	directional	ADJ
ejpam-2677	167	14	data	datum	NOUN
ejpam-2677	167	15	.	.	PUNCT
ejpam-2677	168	1	references	reference	NOUN
ejpam-2677	168	2	[	[	X
ejpam-2677	168	3	1	1	NUM
ejpam-2677	168	4	]	]	X
ejpam-2677	168	5	byoung	byoung	ADJ
ejpam-2677	168	6	,	,	PUNCT
ejpam-2677	168	7	j.a	j.a	PROPN
ejpam-2677	168	8	and	and	CCONJ
ejpam-2677	168	9	hyoung	hyoung	PROPN
ejpam-2677	168	10	m.k	m.k	PROPN
ejpam-2677	168	11	.	.	PROPN
ejpam-2677	168	12	,a	,a	PUNCT
ejpam-2677	168	13	new	new	ADJ
ejpam-2677	168	14	family	family	NOUN
ejpam-2677	168	15	of	of	ADP
ejpam-2677	168	16	semicircular	semicircular	ADJ
ejpam-2677	168	17	models	model	NOUN
ejpam-2677	168	18	:	:	PUNCT
ejpam-2677	168	19	the	the	DET
ejpam-2677	168	20	semicircular	semicircular	ADJ
ejpam-2677	168	21	laplace	laplace	NOUN
ejpam-2677	168	22	distributions	distribution	NOUN
ejpam-2677	168	23	,	,	PUNCT
ejpam-2677	168	24	communications	communication	NOUN
ejpam-2677	168	25	of	of	ADP
ejpam-2677	168	26	the	the	DET
ejpam-2677	168	27	korean	korean	ADJ
ejpam-2677	168	28	statistical	statistical	ADJ
ejpam-2677	168	29	society	society	NOUN
ejpam-2677	168	30	vol.15(2008	vol.15(2008	NOUN
ejpam-2677	168	31	)	)	PUNCT
ejpam-2677	168	32	,	,	PUNCT
ejpam-2677	168	33	775	775	NUM
ejpam-2677	168	34	-	-	SYM
ejpam-2677	168	35	781	781	NUM
ejpam-2677	168	36	.	.	PUNCT
ejpam-2677	169	1	[	[	X
ejpam-2677	169	2	2	2	NUM
ejpam-2677	169	3	]	]	PUNCT
ejpam-2677	169	4	dattatreya	dattatreya	PROPN
ejpam-2677	169	5	rao	rao	PROPN
ejpam-2677	169	6	,	,	PUNCT
ejpam-2677	169	7	a.v	a.v	PROPN
ejpam-2677	169	8	.	.	PROPN
ejpam-2677	169	9	,	,	PUNCT
ejpam-2677	169	10	ramabhadra	ramabhadra	PROPN
ejpam-2677	169	11	sarma	sarma	PROPN
ejpam-2677	169	12	,	,	PUNCT
ejpam-2677	169	13	i.	i.	NOUN
ejpam-2677	169	14	and	and	CCONJ
ejpam-2677	169	15	girija	girija	NOUN
ejpam-2677	169	16	,	,	PUNCT
ejpam-2677	169	17	s.v.s	s.v.s	ADJ
ejpam-2677	169	18	.	.	PROPN
ejpam-2677	169	19	,	,	PUNCT
ejpam-2677	169	20	on	on	ADP
ejpam-2677	169	21	wrapped	wrap	VERB
ejpam-2677	169	22	version	version	NOUN
ejpam-2677	169	23	of	of	ADP
ejpam-2677	169	24	some	some	DET
ejpam-2677	169	25	life	life	NOUN
ejpam-2677	169	26	testing	testing	NOUN
ejpam-2677	169	27	models	model	NOUN
ejpam-2677	169	28	,	,	PUNCT
ejpam-2677	169	29	comm	comm	NOUN
ejpam-2677	169	30	statist	statist	NOUN
ejpam-2677	169	31	,	,	PUNCT
ejpam-2677	169	32	theor.meth	theor.meth	PROPN
ejpam-2677	169	33	.	.	NOUN
ejpam-2677	169	34	,	,	PUNCT
ejpam-2677	169	35	vol.36(11)(2007	vol.36(11)(2007	PROPN
ejpam-2677	169	36	)	)	PUNCT
ejpam-2677	169	37	,	,	PUNCT
ejpam-2677	169	38	20272035	20272035	NUM
ejpam-2677	169	39	.	.	PUNCT
ejpam-2677	170	1	[	[	X
ejpam-2677	170	2	3	3	NUM
ejpam-2677	170	3	]	]	X
ejpam-2677	170	4	fisher	fisher	PROPN
ejpam-2677	170	5	,	,	PUNCT
ejpam-2677	170	6	n.	n.	PROPN
ejpam-2677	170	7	i.	i.	PROPN
ejpam-2677	170	8	,statistical	,statistical	PUNCT
ejpam-2677	170	9	analysis	analysis	NOUN
ejpam-2677	170	10	of	of	ADP
ejpam-2677	170	11	circular	circular	ADJ
ejpam-2677	170	12	data	datum	NOUN
ejpam-2677	170	13	.	.	PUNCT
ejpam-2677	171	1	cambridge	cambridge	PROPN
ejpam-2677	171	2	university	university	PROPN
ejpam-2677	171	3	press	press	PROPN
ejpam-2677	171	4	,	,	PUNCT
ejpam-2677	171	5	cambridge	cambridge	PROPN
ejpam-2677	171	6	(	(	PUNCT
ejpam-2677	171	7	1993	1993	NUM
ejpam-2677	171	8	)	)	PUNCT
ejpam-2677	171	9	.	.	PUNCT
ejpam-2677	172	1	[	[	X
ejpam-2677	172	2	4	4	NUM
ejpam-2677	172	3	]	]	X
ejpam-2677	172	4	girija	girija	NOUN
ejpam-2677	172	5	,	,	PUNCT
ejpam-2677	172	6	s.v.s	s.v.s	ADJ
ejpam-2677	172	7	.	.	PROPN
ejpam-2677	172	8	,	,	PUNCT
ejpam-2677	172	9	construction	construction	NOUN
ejpam-2677	172	10	of	of	ADP
ejpam-2677	172	11	new	new	ADJ
ejpam-2677	172	12	circular	circular	ADJ
ejpam-2677	172	13	models	model	NOUN
ejpam-2677	172	14	,	,	PUNCT
ejpam-2677	172	15	vdm	vdm	NOUN
ejpam-2677	172	16	verlag	verlag	PROPN
ejpam-2677	172	17	,	,	PUNCT
ejpam-2677	172	18	germany	germany	PROPN
ejpam-2677	172	19	.	.	PUNCT
ejpam-2677	173	1	isbn	isbn	PROPN
ejpam-2677	173	2	978	978	NUM
ejpam-2677	173	3	-	-	SYM
ejpam-2677	173	4	3	3	NUM
ejpam-2677	173	5	-	-	PUNCT
ejpam-2677	173	6	639	639	NUM
ejpam-2677	173	7	-	-	PUNCT
ejpam-2677	173	8	27939	27939	NUM
ejpam-2677	173	9	-	-	PUNCT
ejpam-2677	173	10	9,(2010	9,(2010	NOUN
ejpam-2677	173	11	)	)	PUNCT
ejpam-2677	173	12	.	.	PUNCT
ejpam-2677	174	1	[	[	X
ejpam-2677	174	2	5	5	NUM
ejpam-2677	174	3	]	]	X
ejpam-2677	174	4	gradshteyn	gradshteyn	ADJ
ejpam-2677	174	5	and	and	CCONJ
ejpam-2677	174	6	ryzhik	ryzhik	ADJ
ejpam-2677	174	7	table	table	NOUN
ejpam-2677	174	8	of	of	ADP
ejpam-2677	174	9	integrals	integral	NOUN
ejpam-2677	174	10	,	,	PUNCT
ejpam-2677	174	11	series	series	NOUN
ejpam-2677	174	12	and	and	CCONJ
ejpam-2677	174	13	products	product	NOUN
ejpam-2677	174	14	,	,	PUNCT
ejpam-2677	174	15	7th	7th	ADJ
ejpam-2677	174	16	edition	edition	NOUN
ejpam-2677	174	17	,	,	PUNCT
ejpam-2677	174	18	academic	academic	NOUN
ejpam-2677	174	19	press(2007	press(2007	ADJ
ejpam-2677	174	20	)	)	PUNCT
ejpam-2677	174	21	.	.	PUNCT
ejpam-2677	175	1	references	reference	NOUN
ejpam-2677	175	2	1134	1134	NUM
ejpam-2677	175	3	[	[	X
ejpam-2677	175	4	6	6	NUM
ejpam-2677	175	5	]	]	X
ejpam-2677	175	6	guardiola	guardiola	PROPN
ejpam-2677	175	7	,	,	PUNCT
ejpam-2677	175	8	j.h	j.h	PROPN
ejpam-2677	175	9	.	.	PROPN
ejpam-2677	175	10	,	,	PUNCT
ejpam-2677	175	11	the	the	DET
ejpam-2677	175	12	semicircular	semicircular	ADJ
ejpam-2677	175	13	normal	normal	ADJ
ejpam-2677	175	14	distribution	distribution	NOUN
ejpam-2677	175	15	,	,	PUNCT
ejpam-2677	175	16	ph.d	ph.d	PROPN
ejpam-2677	175	17	dissertation	dissertation	NOUN
ejpam-2677	175	18	,	,	PUNCT
ejpam-2677	175	19	baylor	baylor	PROPN
ejpam-2677	175	20	university	university	PROPN
ejpam-2677	175	21	,	,	PUNCT
ejpam-2677	175	22	institute	institute	NOUN
ejpam-2677	175	23	of	of	ADP
ejpam-2677	175	24	statistics(2004	statistics(2004	PROPN
ejpam-2677	175	25	)	)	PUNCT
ejpam-2677	175	26	.	.	PUNCT
ejpam-2677	176	1	[	[	X
ejpam-2677	176	2	7	7	X
ejpam-2677	176	3	]	]	X
ejpam-2677	176	4	jammalamadaka	jammalamadaka	PROPN
ejpam-2677	176	5	s.	s.	PROPN
ejpam-2677	176	6	rao	rao	PROPN
ejpam-2677	176	7	and	and	CCONJ
ejpam-2677	176	8	sen	sen	PROPN
ejpam-2677	176	9	gupta	gupta	PROPN
ejpam-2677	176	10	,	,	PUNCT
ejpam-2677	176	11	a.	a.	NOUN
ejpam-2677	176	12	,	,	PUNCT
ejpam-2677	176	13	topics	topic	NOUN
ejpam-2677	176	14	in	in	ADP
ejpam-2677	176	15	circular	circular	ADJ
ejpam-2677	176	16	statistics	statistic	NOUN
ejpam-2677	176	17	,	,	PUNCT
ejpam-2677	176	18	world	world	NOUN
ejpam-2677	176	19	scientific	scientific	ADJ
ejpam-2677	176	20	press	press	NOUN
ejpam-2677	176	21	,	,	PUNCT
ejpam-2677	176	22	singapore(2001	singapore(2001	PROPN
ejpam-2677	176	23	)	)	PUNCT
ejpam-2677	176	24	.	.	PUNCT
ejpam-2677	177	1	[	[	X
ejpam-2677	177	2	8	8	NUM
ejpam-2677	177	3	]	]	X
ejpam-2677	177	4	mardia	mardia	NOUN
ejpam-2677	177	5	,	,	PUNCT
ejpam-2677	177	6	k.v	k.v	PROPN
ejpam-2677	177	7	.	.	PROPN
ejpam-2677	177	8	and	and	CCONJ
ejpam-2677	177	9	jupp	jupp	PROPN
ejpam-2677	177	10	,	,	PUNCT
ejpam-2677	177	11	p.e	p.e	PROPN
ejpam-2677	177	12	.	.	PROPN
ejpam-2677	177	13	,	,	PUNCT
ejpam-2677	177	14	directional	directional	ADJ
ejpam-2677	177	15	statistics	statistic	NOUN
ejpam-2677	177	16	,	,	PUNCT
ejpam-2677	177	17	john	john	PROPN
ejpam-2677	177	18	wiley	wiley	PROPN
ejpam-2677	177	19	,	,	PUNCT
ejpam-2677	177	20	chichester(2000	chichester(2000	PROPN
ejpam-2677	177	21	)	)	PUNCT
ejpam-2677	177	22	.	.	PUNCT
ejpam-2677	178	1	[	[	X
ejpam-2677	178	2	9	9	NUM
ejpam-2677	178	3	]	]	SYM
ejpam-2677	178	4	minh	minh	NOUN
ejpam-2677	178	5	,	,	PUNCT
ejpam-2677	178	6	do	do	AUX
ejpam-2677	178	7	le	le	X
ejpam-2677	178	8	and	and	CCONJ
ejpam-2677	178	9	farnum	farnum	PROPN
ejpam-2677	178	10	,	,	PUNCT
ejpam-2677	178	11	nicholas	nicholas	PROPN
ejpam-2677	178	12	r.	r.	PROPN
ejpam-2677	178	13	,	,	PUNCT
ejpam-2677	178	14	using	use	VERB
ejpam-2677	178	15	bilinear	bilinear	NOUN
ejpam-2677	178	16	transformations	transformation	NOUN
ejpam-2677	178	17	to	to	PART
ejpam-2677	178	18	induce	induce	VERB
ejpam-2677	178	19	probability	probability	NOUN
ejpam-2677	178	20	distributions	distribution	NOUN
ejpam-2677	178	21	,	,	PUNCT
ejpam-2677	178	22	communication	communication	NOUN
ejpam-2677	178	23	in	in	ADP
ejpam-2677	178	24	statistics	statistic	NOUN
ejpam-2677	178	25	theory	theory	NOUN
ejpam-2677	178	26	and	and	CCONJ
ejpam-2677	178	27	methods	method	NOUN
ejpam-2677	178	28	,	,	PUNCT
ejpam-2677	178	29	vol.32	vol.32	ADJ
ejpam-2677	178	30	(	(	PUNCT
ejpam-2677	178	31	1)(2003	1)(2003	NUM
ejpam-2677	178	32	)	)	PUNCT
ejpam-2677	178	33	,	,	PUNCT
ejpam-2677	178	34	1	1	NUM
ejpam-2677	178	35	9	9	NUM
ejpam-2677	178	36	.	.	PUNCT
ejpam-2677	179	1	[	[	X
ejpam-2677	179	2	10	10	NUM
ejpam-2677	179	3	]	]	X
ejpam-2677	179	4	phani	phani	PROPN
ejpam-2677	179	5	,	,	PUNCT
ejpam-2677	179	6	y.	y.	PROPN
ejpam-2677	179	7	,	,	PUNCT
ejpam-2677	179	8	girija	girija	PROPN
ejpam-2677	179	9	s.v.s	s.v.s	NOUN
ejpam-2677	179	10	.	.	PUNCT
ejpam-2677	180	1	and	and	CCONJ
ejpam-2677	180	2	dattatreya	dattatreya	PROPN
ejpam-2677	180	3	rao	rao	PROPN
ejpam-2677	180	4	a.v	a.v	PROPN
ejpam-2677	180	5	.	.	PROPN
ejpam-2677	180	6	,	,	PUNCT
ejpam-2677	180	7	circular	circular	ADJ
ejpam-2677	180	8	model	model	NOUN
ejpam-2677	180	9	induced	induce	VERB
ejpam-2677	180	10	by	by	ADP
ejpam-2677	180	11	inverse	inverse	NOUN
ejpam-2677	180	12	stereographic	stereographic	ADJ
ejpam-2677	180	13	projection	projection	NOUN
ejpam-2677	180	14	on	on	ADP
ejpam-2677	180	15	extreme	extreme	ADJ
ejpam-2677	180	16	-	-	PUNCT
ejpam-2677	180	17	value	value	NOUN
ejpam-2677	180	18	distribution	distribution	NOUN
ejpam-2677	180	19	,	,	PUNCT
ejpam-2677	180	20	iracst	iracst	NOUN
ejpam-2677	180	21	engineering	engineering	NOUN
ejpam-2677	180	22	science	science	NOUN
ejpam-2677	180	23	and	and	CCONJ
ejpam-2677	180	24	technology	technology	NOUN
ejpam-2677	180	25	:	:	PUNCT
ejpam-2677	180	26	an	an	DET
ejpam-2677	180	27	international	international	ADJ
ejpam-2677	180	28	journal	journal	NOUN
ejpam-2677	180	29	(	(	PUNCT
ejpam-2677	180	30	estij	estij	PROPN
ejpam-2677	180	31	)	)	PUNCT
ejpam-2677	180	32	,	,	PUNCT
ejpam-2677	180	33	issn	issn	PROPN
ejpam-2677	180	34	:	:	PUNCT
ejpam-2677	180	35	2250	2250	NUM
ejpam-2677	180	36	-	-	SYM
ejpam-2677	180	37	3498	3498	NUM
ejpam-2677	180	38	,	,	PUNCT
ejpam-2677	180	39	vol.2(5)(2012),881	vol.2(5)(2012),881	PROPN
ejpam-2677	180	40	888	888	NUM
ejpam-2677	180	41	.	.	PUNCT
ejpam-2677	181	1	[	[	X
ejpam-2677	181	2	11	11	NUM
ejpam-2677	181	3	]	]	X
ejpam-2677	181	4	phani	phani	PROPN
ejpam-2677	181	5	,	,	PUNCT
ejpam-2677	181	6	y.	y.	PROPN
ejpam-2677	181	7	,	,	PUNCT
ejpam-2677	181	8	girija	girija	PROPN
ejpam-2677	181	9	s.v.s	s.v.s	NOUN
ejpam-2677	181	10	.	.	PUNCT
ejpam-2677	182	1	and	and	CCONJ
ejpam-2677	182	2	dattatreya	dattatreya	PROPN
ejpam-2677	182	3	rao	rao	PROPN
ejpam-2677	182	4	a.v	a.v	PROPN
ejpam-2677	182	5	.	.	PROPN
ejpam-2677	182	6	,on	,on	PUNCT
ejpam-2677	182	7	construction	construction	NOUN
ejpam-2677	182	8	of	of	ADP
ejpam-2677	182	9	stereographic	stereographic	ADJ
ejpam-2677	182	10	semicircular	semicircular	ADJ
ejpam-2677	182	11	models	model	NOUN
ejpam-2677	182	12	,	,	PUNCT
ejpam-2677	182	13	journal	journal	NOUN
ejpam-2677	182	14	of	of	ADP
ejpam-2677	182	15	applied	apply	VERB
ejpam-2677	182	16	probability	probability	NOUN
ejpam-2677	182	17	and	and	CCONJ
ejpam-2677	182	18	statistics	statistic	NOUN
ejpam-2677	182	19	,	,	PUNCT
ejpam-2677	182	20	vol	vol	NOUN
ejpam-2677	182	21	.	.	PROPN
ejpam-2677	182	22	8	8	NUM
ejpam-2677	182	23	(	(	PUNCT
ejpam-2677	182	24	1)(2013	1)(2013	NUM
ejpam-2677	182	25	)	)	PUNCT
ejpam-2677	182	26	,	,	PUNCT
ejpam-2677	182	27	pp	pp	ADP
ejpam-2677	182	28	.	.	PUNCT
ejpam-2677	183	1	75	75	NUM
ejpam-2677	183	2	-	-	SYM
ejpam-2677	183	3	90	90	NUM
ejpam-2677	183	4	.	.	PUNCT
ejpam-2677	184	1	[	[	X
ejpam-2677	184	2	12	12	NUM
ejpam-2677	184	3	]	]	X
ejpam-2677	184	4	phani	phani	PROPN
ejpam-2677	184	5	y.	y.	PROPN
ejpam-2677	184	6	,	,	PUNCT
ejpam-2677	184	7	on	on	ADP
ejpam-2677	184	8	stereographic	stereographic	ADJ
ejpam-2677	184	9	circular	circular	ADJ
ejpam-2677	184	10	and	and	CCONJ
ejpam-2677	184	11	semicircular	semicircular	ADJ
ejpam-2677	184	12	models	model	NOUN
ejpam-2677	184	13	,	,	PUNCT
ejpam-2677	184	14	thesis	thesis	NOUN
ejpam-2677	184	15	submitted	submit	VERB
ejpam-2677	184	16	to	to	ADP
ejpam-2677	184	17	acharya	acharya	PROPN
ejpam-2677	184	18	nagarjuna	nagarjuna	PROPN
ejpam-2677	184	19	university	university	PROPN
ejpam-2677	184	20	for	for	ADP
ejpam-2677	184	21	the	the	DET
ejpam-2677	184	22	award	award	NOUN
ejpam-2677	184	23	of	of	ADP
ejpam-2677	184	24	ph.d.(2013	ph.d.(2013	NOUN
ejpam-2677	184	25	)	)	PUNCT
ejpam-2677	184	26	.	.	PUNCT
ejpam-2677	185	1	[	[	X
ejpam-2677	185	2	13	13	NUM
ejpam-2677	185	3	]	]	SYM
ejpam-2677	185	4	ugai	ugai	NOUN
ejpam-2677	185	5	.	.	PUNCT
ejpam-2677	186	1	s.k	s.k	PROPN
ejpam-2677	186	2	.	.	PROPN
ejpam-2677	186	3	,	,	PUNCT
ejpam-2677	186	4	nishijima	nishijima	PROPN
ejpam-2677	186	5	,	,	PUNCT
ejpam-2677	186	6	m.	m.	NOUN
ejpam-2677	186	7	and	and	CCONJ
ejpam-2677	186	8	kan	kan	PROPN
ejpam-2677	186	9	,	,	PUNCT
ejpam-2677	186	10	t.	t.	PROPN
ejpam-2677	186	11	,	,	PUNCT
ejpam-2677	186	12	characteristics	characteristic	NOUN
ejpam-2677	186	13	of	of	ADP
ejpam-2677	186	14	raindrop	raindrop	NOUN
ejpam-2677	186	15	size	size	NOUN
ejpam-2677	186	16	and	and	CCONJ
ejpam-2677	186	17	raindrop	raindrop	PROPN
ejpam-2677	186	18	shape	shape	NOUN
ejpam-2677	186	19	,	,	PUNCT
ejpam-2677	186	20	open	open	ADJ
ejpam-2677	186	21	symposium	symposium	NOUN
ejpam-2677	186	22	ursi	ursi	ADJ
ejpam-2677	186	23	commission	commission	NOUN
ejpam-2677	186	24	f,(1977	f,(1977	PROPN
ejpam-2677	186	25	)	)	PUNCT
ejpam-2677	186	26	,	,	PUNCT
ejpam-2677	186	27	225	225	NUM
ejpam-2677	186	28	-	-	SYM
ejpam-2677	186	29	230	230	NUM
ejpam-2677	186	30	.	.	PUNCT
ejpam-2677	187	1	[	[	X
ejpam-2677	187	2	14	14	NUM
ejpam-2677	187	3	]	]	X
ejpam-2677	187	4	toshihiro	toshihiro	PROPN
ejpam-2677	187	5	abe	abe	PROPN
ejpam-2677	187	6	,	,	PUNCT
ejpam-2677	187	7	kunio	kunio	PROPN
ejpam-2677	187	8	shimizu	shimizu	PROPN
ejpam-2677	187	9	and	and	CCONJ
ejpam-2677	187	10	arthur	arthur	PROPN
ejpam-2677	187	11	pewsey	pewsey	PROPN
ejpam-2677	187	12	,	,	PUNCT
ejpam-2677	187	13	symmetric	symmetric	ADJ
ejpam-2677	187	14	unimodal	unimodal	ADJ
ejpam-2677	187	15	models	model	NOUN
ejpam-2677	187	16	for	for	ADP
ejpam-2677	187	17	directional	directional	ADJ
ejpam-2677	187	18	data	datum	NOUN
ejpam-2677	187	19	motivated	motivate	VERB
ejpam-2677	187	20	by	by	ADP
ejpam-2677	187	21	inverse	inverse	NOUN
ejpam-2677	187	22	stereographic	stereographic	ADJ
ejpam-2677	187	23	projection	projection	NOUN
ejpam-2677	187	24	,	,	PUNCT
ejpam-2677	187	25	j.	j.	PROPN
ejpam-2677	187	26	japan	japan	PROPN
ejpam-2677	187	27	statist	statist	PROPN
ejpam-2677	187	28	.	.	PUNCT
ejpam-2677	188	1	soc	soc	PROPN
ejpam-2677	188	2	.	.	PUNCT
ejpam-2677	189	1	,	,	PUNCT
ejpam-2677	189	2	vol	vol	NOUN
ejpam-2677	189	3	.	.	PROPN
ejpam-2677	190	1	40	40	NUM
ejpam-2677	190	2	(	(	PUNCT
ejpam-2677	190	3	1)(2010	1)(2010	NUM
ejpam-2677	190	4	)	)	PUNCT
ejpam-2677	190	5	,	,	PUNCT
ejpam-2677	190	6	45	45	NUM
ejpam-2677	190	7	-	-	SYM
ejpam-2677	190	8	61	61	NUM
ejpam-2677	190	9	.	.	PUNCT