id	sid	tid	token	lemma	pos
ejpam-3075	1	1	european	european	PROPN
ejpam-3075	1	2	journal	journal	PROPN
ejpam-3075	1	3	of	of	ADP
ejpam-3075	1	4	pure	pure	ADJ
ejpam-3075	1	5	and	and	CCONJ
ejpam-3075	1	6	applied	apply	VERB
ejpam-3075	1	7	mathematics	mathematic	NOUN
ejpam-3075	1	8	vol	vol	NOUN
ejpam-3075	1	9	.	.	PROPN
ejpam-3075	2	1	10	10	NUM
ejpam-3075	2	2	,	,	PUNCT
ejpam-3075	2	3	no	no	INTJ
ejpam-3075	2	4	.	.	NOUN
ejpam-3075	2	5	4	4	NUM
ejpam-3075	2	6	,	,	PUNCT
ejpam-3075	2	7	2017	2017	NUM
ejpam-3075	2	8	,	,	PUNCT
ejpam-3075	2	9	614	614	NUM
ejpam-3075	2	10	-	-	SYM
ejpam-3075	2	11	619	619	NUM
ejpam-3075	2	12	issn	issn	PROPN
ejpam-3075	2	13	1307	1307	NUM
ejpam-3075	2	14	-	-	SYM
ejpam-3075	2	15	5543	5543	NUM
ejpam-3075	2	16	–	–	PUNCT
ejpam-3075	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3075	2	18	published	publish	VERB
ejpam-3075	2	19	by	by	ADP
ejpam-3075	2	20	new	new	PROPN
ejpam-3075	2	21	york	york	PROPN
ejpam-3075	2	22	business	business	PROPN
ejpam-3075	2	23	global	global	PROPN
ejpam-3075	2	24	honorary	honorary	PROPN
ejpam-3075	2	25	invited	invite	VERB
ejpam-3075	2	26	paper	paper	NOUN
ejpam-3075	2	27	selberg	selberg	NOUN
ejpam-3075	2	28	-	-	PUNCT
ejpam-3075	2	29	type	type	NOUN
ejpam-3075	2	30	generalized	generalized	ADJ
ejpam-3075	2	31	quadratic	quadratic	ADJ
ejpam-3075	2	32	forms	form	NOUN
ejpam-3075	2	33	gamma	gamma	NOUN
ejpam-3075	2	34	and	and	CCONJ
ejpam-3075	2	35	beta	beta	NOUN
ejpam-3075	2	36	integrals	integral	NOUN
ejpam-3075	2	37	arjun	arjun	PROPN
ejpam-3075	2	38	k.	k.	PROPN
ejpam-3075	2	39	gupta1,∗	gupta1,∗	PROPN
ejpam-3075	2	40	,	,	PUNCT
ejpam-3075	3	1	d.	d.	PROPN
ejpam-3075	3	2	g.	g.	PROPN
ejpam-3075	3	3	kabe1,2	kabe1,2	PROPN
ejpam-3075	3	4	1	1	NUM
ejpam-3075	3	5	bowling	bowling	NOUN
ejpam-3075	3	6	green	green	ADJ
ejpam-3075	3	7	state	state	PROPN
ejpam-3075	3	8	university	university	PROPN
ejpam-3075	3	9	,	,	PUNCT
ejpam-3075	3	10	bowling	bowling	NOUN
ejpam-3075	3	11	green	green	NOUN
ejpam-3075	3	12	,	,	PUNCT
ejpam-3075	3	13	ohio	ohio	PROPN
ejpam-3075	3	14	,	,	PUNCT
ejpam-3075	3	15	usa	usa	PROPN
ejpam-3075	3	16	2	2	NUM
ejpam-3075	3	17	deceased	deceased	ADJ
ejpam-3075	3	18	abstract	abstract	NOUN
ejpam-3075	3	19	.	.	PUNCT
ejpam-3075	4	1	although	although	SCONJ
ejpam-3075	4	2	selberg	selberg	NOUN
ejpam-3075	4	3	-	-	PUNCT
ejpam-3075	4	4	type	type	NOUN
ejpam-3075	4	5	single	single	ADJ
ejpam-3075	4	6	positive	positive	ADJ
ejpam-3075	4	7	definite	definite	ADJ
ejpam-3075	4	8	symmetric	symmetric	ADJ
ejpam-3075	4	9	matrices	matrix	NOUN
ejpam-3075	4	10	gamma	gamma	NOUN
ejpam-3075	4	11	and	and	CCONJ
ejpam-3075	4	12	beta	beta	NOUN
ejpam-3075	4	13	integrals	integral	NOUN
ejpam-3075	4	14	have	have	AUX
ejpam-3075	4	15	been	be	AUX
ejpam-3075	4	16	evaluated	evaluate	VERB
ejpam-3075	4	17	by	by	ADP
ejpam-3075	4	18	several	several	ADJ
ejpam-3075	4	19	authors	author	NOUN
ejpam-3075	4	20	,	,	PUNCT
ejpam-3075	4	21	see	see	VERB
ejpam-3075	4	22	e.g.	e.g.	ADV
ejpam-3075	4	23	,	,	PUNCT
ejpam-3075	4	24	askey	askey	ADJ
ejpam-3075	4	25	and	and	CCONJ
ejpam-3075	4	26	richards	richard	NOUN
ejpam-3075	5	1	[	[	X
ejpam-3075	5	2	1	1	NUM
ejpam-3075	5	3	]	]	PUNCT
ejpam-3075	5	4	,	,	PUNCT
ejpam-3075	5	5	gupta	gupta	NOUN
ejpam-3075	5	6	and	and	CCONJ
ejpam-3075	5	7	kabe	kabe	NOUN
ejpam-3075	6	1	[	[	X
ejpam-3075	6	2	2	2	NUM
ejpam-3075	6	3	,	,	PUNCT
ejpam-3075	6	4	4	4	NUM
ejpam-3075	6	5	]	]	PUNCT
ejpam-3075	6	6	,	,	PUNCT
ejpam-3075	6	7	mathai	mathai	PROPN
ejpam-3075	7	1	[	[	X
ejpam-3075	7	2	8	8	NUM
ejpam-3075	7	3	]	]	PUNCT
ejpam-3075	7	4	,	,	PUNCT
ejpam-3075	7	5	and	and	CCONJ
ejpam-3075	7	6	elsewhere	elsewhere	ADV
ejpam-3075	7	7	in	in	ADP
ejpam-3075	7	8	the	the	DET
ejpam-3075	7	9	vast	vast	ADJ
ejpam-3075	7	10	multivariate	multivariate	NOUN
ejpam-3075	7	11	statistical	statistical	ADJ
ejpam-3075	7	12	analysis	analysis	NOUN
ejpam-3075	7	13	literature	literature	NOUN
ejpam-3075	7	14	.	.	PUNCT
ejpam-3075	8	1	however	however	ADV
ejpam-3075	8	2	,	,	PUNCT
ejpam-3075	8	3	several	several	ADJ
ejpam-3075	8	4	other	other	ADJ
ejpam-3075	8	5	types	type	NOUN
ejpam-3075	8	6	of	of	ADP
ejpam-3075	8	7	selberg	selberg	NOUN
ejpam-3075	8	8	-	-	PUNCT
ejpam-3075	8	9	type	type	NOUN
ejpam-3075	8	10	integrals	integral	NOUN
ejpam-3075	8	11	appear	appear	VERB
ejpam-3075	8	12	to	to	PART
ejpam-3075	8	13	have	have	AUX
ejpam-3075	8	14	been	be	AUX
ejpam-3075	8	15	neglected	neglect	VERB
ejpam-3075	8	16	in	in	ADP
ejpam-3075	8	17	the	the	DET
ejpam-3075	8	18	literature	literature	NOUN
ejpam-3075	8	19	.	.	PUNCT
ejpam-3075	9	1	thus	thus	ADV
ejpam-3075	9	2	e.g.	e.g.	ADV
ejpam-3075	9	3	,	,	PUNCT
ejpam-3075	9	4	selberg	selberg	NOUN
ejpam-3075	9	5	-	-	PUNCT
ejpam-3075	9	6	type	type	NOUN
ejpam-3075	9	7	integrals	integral	NOUN
ejpam-3075	9	8	associated	associate	VERB
ejpam-3075	9	9	with	with	ADP
ejpam-3075	9	10	inverse	inverse	ADJ
ejpam-3075	9	11	wishart	wishart	NOUN
ejpam-3075	9	12	densities	density	NOUN
ejpam-3075	9	13	,	,	PUNCT
ejpam-3075	9	14	inverse	inverse	NOUN
ejpam-3075	9	15	multivariate	multivariate	NOUN
ejpam-3075	9	16	beta	beta	ADJ
ejpam-3075	9	17	densities	density	NOUN
ejpam-3075	9	18	,	,	PUNCT
ejpam-3075	9	19	their	their	PRON
ejpam-3075	9	20	noncentral	noncentral	ADJ
ejpam-3075	9	21	counterparts	counterpart	NOUN
ejpam-3075	9	22	,	,	PUNCT
ejpam-3075	9	23	etc	etc	X
ejpam-3075	9	24	,	,	PUNCT
ejpam-3075	9	25	have	have	AUX
ejpam-3075	9	26	not	not	PART
ejpam-3075	9	27	been	be	AUX
ejpam-3075	9	28	explored	explore	VERB
ejpam-3075	9	29	as	as	ADP
ejpam-3075	9	30	yet	yet	ADV
ejpam-3075	9	31	.	.	PUNCT
ejpam-3075	10	1	the	the	DET
ejpam-3075	10	2	present	present	ADJ
ejpam-3075	10	3	paper	paper	NOUN
ejpam-3075	10	4	records	record	NOUN
ejpam-3075	10	5	selberg	selberg	NOUN
ejpam-3075	10	6	-	-	PUNCT
ejpam-3075	10	7	type	type	NOUN
ejpam-3075	10	8	generalized	generalized	ADJ
ejpam-3075	10	9	quadratic	quadratic	ADJ
ejpam-3075	10	10	forms	form	NOUN
ejpam-3075	10	11	gamma	gamma	NOUN
ejpam-3075	10	12	and	and	CCONJ
ejpam-3075	10	13	beta	beta	NOUN
ejpam-3075	10	14	integrals	integral	NOUN
ejpam-3075	10	15	.	.	PUNCT
ejpam-3075	11	1	our	our	PRON
ejpam-3075	11	2	methodology	methodology	NOUN
ejpam-3075	11	3	is	be	AUX
ejpam-3075	11	4	based	base	VERB
ejpam-3075	11	5	on	on	ADP
ejpam-3075	11	6	hypercomplex	hypercomplex	NOUN
ejpam-3075	11	7	(	(	PUNCT
ejpam-3075	11	8	hc	hc	NOUN
ejpam-3075	11	9	)	)	PUNCT
ejpam-3075	11	10	multivariate	multivariate	VERB
ejpam-3075	11	11	normal	normal	ADJ
ejpam-3075	11	12	distribution	distribution	NOUN
ejpam-3075	11	13	theory	theory	NOUN
ejpam-3075	11	14	,	,	PUNCT
ejpam-3075	11	15	kabe	kabe	ADJ
ejpam-3075	12	1	[	[	X
ejpam-3075	12	2	6	6	NUM
ejpam-3075	12	3	]	]	PUNCT
ejpam-3075	12	4	.	.	PUNCT
ejpam-3075	13	1	2010	2010	NUM
ejpam-3075	13	2	mathematics	mathematic	NOUN
ejpam-3075	13	3	subject	subject	NOUN
ejpam-3075	13	4	classifications	classification	NOUN
ejpam-3075	13	5	:	:	PUNCT
ejpam-3075	13	6	62h10	62h10	NUM
ejpam-3075	13	7	,	,	PUNCT
ejpam-3075	13	8	62h12	62h12	NUM
ejpam-3075	13	9	key	key	ADJ
ejpam-3075	13	10	words	word	NOUN
ejpam-3075	13	11	and	and	CCONJ
ejpam-3075	13	12	phrases	phrase	NOUN
ejpam-3075	13	13	:	:	PUNCT
ejpam-3075	13	14	selberg	selberg	NOUN
ejpam-3075	13	15	-	-	PUNCT
ejpam-3075	13	16	type	type	NOUN
ejpam-3075	13	17	integral	integral	ADJ
ejpam-3075	13	18	,	,	PUNCT
ejpam-3075	13	19	multivariate	multivariate	VERB
ejpam-3075	13	20	normal	normal	ADJ
ejpam-3075	13	21	distribution	distribution	NOUN
ejpam-3075	13	22	,	,	PUNCT
ejpam-3075	13	23	hermitian	hermitian	ADJ
ejpam-3075	13	24	matrix	matrix	NOUN
ejpam-3075	13	25	,	,	PUNCT
ejpam-3075	13	26	beta	beta	ADJ
ejpam-3075	13	27	density	density	NOUN
ejpam-3075	13	28	1	1	NUM
ejpam-3075	13	29	.	.	PUNCT
ejpam-3075	14	1	introduction	introduction	NOUN
ejpam-3075	14	2	the	the	DET
ejpam-3075	14	3	hc	hc	PROPN
ejpam-3075	14	4	multivariate	multivariate	NOUN
ejpam-3075	14	5	normal	normal	ADJ
ejpam-3075	14	6	distribution	distribution	NOUN
ejpam-3075	14	7	is	be	AUX
ejpam-3075	14	8	defined	define	VERB
ejpam-3075	14	9	as	as	SCONJ
ejpam-3075	14	10	follows	follow	VERB
ejpam-3075	14	11	.	.	PUNCT
ejpam-3075	15	1	let	let	VERB
ejpam-3075	15	2	x1	x1	NUM
ejpam-3075	15	3	,	,	PUNCT
ejpam-3075	15	4	x2	x2	INTJ
ejpam-3075	15	5	,	,	PUNCT
ejpam-3075	15	6	...	...	PUNCT
ejpam-3075	15	7	,	,	PUNCT
ejpam-3075	15	8	x4	x4	PROPN
ejpam-3075	15	9	t	t	PROPN
ejpam-3075	15	10	,	,	PUNCT
ejpam-3075	15	11	t	t	NOUN
ejpam-3075	15	12	=	=	SYM
ejpam-3075	15	13	1	1	NUM
ejpam-3075	15	14	4	4	NUM
ejpam-3075	15	15	,	,	PUNCT
ejpam-3075	15	16	1	1	NUM
ejpam-3075	15	17	2	2	NUM
ejpam-3075	15	18	,	,	PUNCT
ejpam-3075	15	19	1	1	NUM
ejpam-3075	15	20	,	,	PUNCT
ejpam-3075	15	21	2	2	NUM
ejpam-3075	15	22	be	be	VERB
ejpam-3075	15	23	4	4	NUM
ejpam-3075	15	24	t	t	NOUN
ejpam-3075	15	25	p×	p×	NOUN
ejpam-3075	15	26	n	n	PRON
ejpam-3075	15	27	real	real	ADJ
ejpam-3075	15	28	random	random	ADJ
ejpam-3075	15	29	matrices	matrix	NOUN
ejpam-3075	15	30	and	and	CCONJ
ejpam-3075	15	31	for	for	ADP
ejpam-3075	15	32	t	t	NOUN
ejpam-3075	15	33	=	=	SYM
ejpam-3075	15	34	2	2	NUM
ejpam-3075	15	35	,	,	PUNCT
ejpam-3075	15	36	i.e.	i.e.	X
ejpam-3075	15	37	,	,	PUNCT
ejpam-3075	15	38	the	the	DET
ejpam-3075	15	39	octonions	octonion	NOUN
ejpam-3075	15	40	case	case	NOUN
ejpam-3075	15	41	,	,	PUNCT
ejpam-3075	15	42	set	set	VERB
ejpam-3075	15	43	y	y	PROPN
ejpam-3075	15	44	=	=	PUNCT
ejpam-3075	15	45	x1	x1	PROPN
ejpam-3075	16	1	+	+	CCONJ
ejpam-3075	16	2	ix2,+jx3	ix2,+jx3	NOUN
ejpam-3075	16	3	+	+	X
ejpam-3075	16	4	kx4	kx4	NOUN
ejpam-3075	16	5	+	+	CCONJ
ejpam-3075	16	6	lx5	lx5	PROPN
ejpam-3075	16	7	+	+	PROPN
ejpam-3075	16	8	mx6	mx6	PROPN
ejpam-3075	16	9	+	+	CCONJ
ejpam-3075	16	10	nx7	nx7	PROPN
ejpam-3075	16	11	+	+	CCONJ
ejpam-3075	16	12	rx8	rx8	PROPN
ejpam-3075	16	13	,	,	PUNCT
ejpam-3075	16	14	(	(	PUNCT
ejpam-3075	16	15	1	1	X
ejpam-3075	16	16	)	)	PUNCT
ejpam-3075	16	17	where	where	SCONJ
ejpam-3075	16	18	the	the	DET
ejpam-3075	16	19	base	base	NOUN
ejpam-3075	16	20	octonions	octonions	PROPN
ejpam-3075	16	21	i	i	PROPN
ejpam-3075	16	22	,	,	PUNCT
ejpam-3075	16	23	j	j	PROPN
ejpam-3075	16	24	,	,	PUNCT
ejpam-3075	16	25	k	k	PROPN
ejpam-3075	16	26	,	,	PUNCT
ejpam-3075	16	27	l	l	NOUN
ejpam-3075	16	28	,	,	PUNCT
ejpam-3075	16	29	m	m	PROPN
ejpam-3075	16	30	,	,	PUNCT
ejpam-3075	16	31	n	n	CCONJ
ejpam-3075	16	32	,	,	PUNCT
ejpam-3075	16	33	r	r	NOUN
ejpam-3075	16	34	satisfy	satisfy	VERB
ejpam-3075	16	35	the	the	DET
ejpam-3075	16	36	multiplication	multiplication	NOUN
ejpam-3075	16	37	rule	rule	NOUN
ejpam-3075	16	38	i2	i2	PROPN
ejpam-3075	16	39	=	=	SYM
ejpam-3075	16	40	j2	j2	PROPN
ejpam-3075	16	41	=	=	SYM
ejpam-3075	16	42	k2	k2	PROPN
ejpam-3075	16	43	=	=	PROPN
ejpam-3075	16	44	l2	l2	PROPN
ejpam-3075	16	45	=	=	SYM
ejpam-3075	16	46	m2	m2	PROPN
ejpam-3075	16	47	=	=	PROPN
ejpam-3075	16	48	n2	n2	PROPN
ejpam-3075	16	49	=	=	PROPN
ejpam-3075	16	50	r2	r2	PROPN
ejpam-3075	16	51	=	=	SYM
ejpam-3075	16	52	−1	−1	NOUN
ejpam-3075	16	53	=	=	SYM
ejpam-3075	16	54	ijk	ijk	PROPN
ejpam-3075	16	55	=	=	PROPN
ejpam-3075	16	56	ilm	ilm	NOUN
ejpam-3075	16	57	=	=	PROPN
ejpam-3075	16	58	irn	irn	PROPN
ejpam-3075	16	59	=	=	SYM
ejpam-3075	16	60	jmr	jmr	PROPN
ejpam-3075	16	61	=	=	SYM
ejpam-3075	16	62	kjr	kjr	PROPN
ejpam-3075	16	63	=	=	PUNCT
ejpam-3075	16	64	knm	knm	PROPN
ejpam-3075	16	65	.	.	PUNCT
ejpam-3075	17	1	(	(	PUNCT
ejpam-3075	17	2	2	2	X
ejpam-3075	17	3	)	)	PUNCT
ejpam-3075	17	4	∗corresponding	∗corresponde	VERB
ejpam-3075	17	5	author	author	NOUN
ejpam-3075	17	6	.	.	PUNCT
ejpam-3075	18	1	email	email	NOUN
ejpam-3075	18	2	addresses	address	NOUN
ejpam-3075	18	3	:	:	PUNCT
ejpam-3075	18	4	gupta@bgsu.edu	gupta@bgsu.edu	PROPN
ejpam-3075	18	5	(	(	PUNCT
ejpam-3075	18	6	a.	a.	PROPN
ejpam-3075	18	7	k.	k.	PROPN
ejpam-3075	18	8	gupta	gupta	PROPN
ejpam-3075	18	9	)	)	PUNCT
ejpam-3075	18	10	,	,	PUNCT
ejpam-3075	18	11	deceased	decease	VERB
ejpam-3075	18	12	(	(	PUNCT
ejpam-3075	18	13	d.	d.	PROPN
ejpam-3075	18	14	g.	g.	PROPN
ejpam-3075	18	15	kabe	kabe	PROPN
ejpam-3075	18	16	)	)	PUNCT
ejpam-3075	18	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3075	19	1	614	614	NUM
ejpam-3075	19	2	c	c	X
ejpam-3075	19	3	©	©	PROPN
ejpam-3075	19	4	2017	2017	NUM
ejpam-3075	19	5	ejpam	ejpam	VERB
ejpam-3075	19	6	all	all	DET
ejpam-3075	19	7	rights	right	NOUN
ejpam-3075	19	8	reserved	reserve	VERB
ejpam-3075	19	9	.	.	PUNCT
ejpam-3075	20	1	a.	a.	PROPN
ejpam-3075	20	2	k.	k.	PROPN
ejpam-3075	20	3	gupta	gupta	PROPN
ejpam-3075	20	4	,	,	PUNCT
ejpam-3075	20	5	d.	d.	PROPN
ejpam-3075	20	6	g.	g.	PROPN
ejpam-3075	20	7	kabe	kabe	PROPN
ejpam-3075	20	8	/	/	SYM
ejpam-3075	20	9	eur	eur	PROPN
ejpam-3075	20	10	.	.	PUNCT
ejpam-3075	21	1	j.	j.	PROPN
ejpam-3075	21	2	pure	pure	PROPN
ejpam-3075	21	3	appl	appl	PROPN
ejpam-3075	21	4	.	.	PROPN
ejpam-3075	21	5	math	math	PROPN
ejpam-3075	21	6	,	,	PUNCT
ejpam-3075	21	7	10	10	NUM
ejpam-3075	21	8	(	(	PUNCT
ejpam-3075	21	9	4	4	NUM
ejpam-3075	21	10	)	)	PUNCT
ejpam-3075	21	11	(	(	PUNCT
ejpam-3075	21	12	2017	2017	NUM
ejpam-3075	21	13	)	)	PUNCT
ejpam-3075	21	14	,	,	PUNCT
ejpam-3075	21	15	614	614	NUM
ejpam-3075	21	16	-	-	SYM
ejpam-3075	21	17	619	619	NUM
ejpam-3075	21	18	615	615	NUM
ejpam-3075	21	19	for	for	ADP
ejpam-3075	21	20	t	t	NOUN
ejpam-3075	21	21	=	=	SYM
ejpam-3075	21	22	1	1	NUM
ejpam-3075	21	23	,	,	PUNCT
ejpam-3075	21	24	t	t	NOUN
ejpam-3075	21	25	=	=	SYM
ejpam-3075	21	26	2	2	NUM
ejpam-3075	21	27	,	,	PUNCT
ejpam-3075	21	28	t	t	NOUN
ejpam-3075	21	29	=	=	SYM
ejpam-3075	21	30	4	4	NUM
ejpam-3075	21	31	,	,	PUNCT
ejpam-3075	21	32	t	t	NOUN
ejpam-3075	21	33	=	=	SYM
ejpam-3075	21	34	4i	4i	PROPN
ejpam-3075	21	35	is	be	AUX
ejpam-3075	21	36	the	the	DET
ejpam-3075	21	37	bioctonion	bioctonion	NOUN
ejpam-3075	21	38	case	case	NOUN
ejpam-3075	21	39	,	,	PUNCT
ejpam-3075	21	40	hypercomplex	hypercomplex	ADJ
ejpam-3075	21	41	variables	variable	NOUN
ejpam-3075	21	42	do	do	AUX
ejpam-3075	21	43	not	not	PART
ejpam-3075	21	44	form	form	VERB
ejpam-3075	21	45	a	a	DET
ejpam-3075	21	46	field	field	NOUN
ejpam-3075	21	47	,	,	PUNCT
ejpam-3075	21	48	they	they	PRON
ejpam-3075	21	49	are	be	AUX
ejpam-3075	21	50	known	know	VERB
ejpam-3075	21	51	to	to	PART
ejpam-3075	21	52	form	form	VERB
ejpam-3075	21	53	clifford	clifford	PROPN
ejpam-3075	21	54	algebras	algebras	PROPN
ejpam-3075	21	55	.	.	PUNCT
ejpam-3075	22	1	the	the	DET
ejpam-3075	22	2	octonions	octonion	NOUN
ejpam-3075	22	3	conjugate	conjugate	NOUN
ejpam-3075	22	4	of	of	ADP
ejpam-3075	22	5	y	y	PROPN
ejpam-3075	22	6	is	be	AUX
ejpam-3075	22	7	defined	define	VERB
ejpam-3075	22	8	by	by	ADP
ejpam-3075	22	9	ȳ	ȳ	PROPN
ejpam-3075	22	10	=	=	SYM
ejpam-3075	23	1	x1	x1	PROPN
ejpam-3075	23	2	−	−	PROPN
ejpam-3075	23	3	ix2	ix2	PROPN
ejpam-3075	23	4	−	−	PROPN
ejpam-3075	23	5	jx3	jx3	PROPN
ejpam-3075	23	6	−	−	PROPN
ejpam-3075	23	7	kx4	kx4	NOUN
ejpam-3075	23	8	−	−	PROPN
ejpam-3075	23	9	lx5	lx5	PROPN
ejpam-3075	23	10	−mx6	−mx6	PROPN
ejpam-3075	23	11	−	−	PROPN
ejpam-3075	23	12	nx7	nx7	NOUN
ejpam-3075	23	13	−	−	PROPN
ejpam-3075	23	14	rx8	rx8	PROPN
ejpam-3075	23	15	.	.	PROPN
ejpam-3075	24	1	(	(	PUNCT
ejpam-3075	24	2	3	3	X
ejpam-3075	24	3	)	)	PUNCT
ejpam-3075	24	4	note	note	NOUN
ejpam-3075	24	5	that	that	SCONJ
ejpam-3075	24	6	y	y	PROPN
ejpam-3075	24	7	ȳ	ȳ	PROPN
ejpam-3075	25	1	′	′	NUM
ejpam-3075	25	2	is	be	AUX
ejpam-3075	25	3	a	a	DET
ejpam-3075	25	4	positive	positive	ADJ
ejpam-3075	25	5	definite	definite	ADJ
ejpam-3075	25	6	hc	hc	X
ejpam-3075	25	7	hermitian	hermitian	ADJ
ejpam-3075	25	8	matrix	matrix	NOUN
ejpam-3075	25	9	(	(	PUNCT
ejpam-3075	25	10	hchm	hchm	NOUN
ejpam-3075	25	11	)	)	PUNCT
ejpam-3075	25	12	.	.	PUNCT
ejpam-3075	26	1	next	next	ADJ
ejpam-3075	26	2	set∑	set∑	PROPN
ejpam-3075	27	1	=	=	PUNCT
ejpam-3075	27	2	∑	∑	PUNCT
ejpam-3075	27	3	1	1	NUM
ejpam-3075	27	4	+	+	CCONJ
ejpam-3075	27	5	i	i	PRON
ejpam-3075	27	6	∑	∑	PUNCT
ejpam-3075	27	7	2	2	NUM
ejpam-3075	27	8	+	+	CCONJ
ejpam-3075	27	9	j	j	PROPN
ejpam-3075	27	10	∑	∑	PROPN
ejpam-3075	27	11	3	3	NUM
ejpam-3075	27	12	+	+	CCONJ
ejpam-3075	27	13	k	k	PROPN
ejpam-3075	27	14	∑	∑	PUNCT
ejpam-3075	27	15	4	4	NUM
ejpam-3075	27	16	+	+	SYM
ejpam-3075	27	17	l	l	NOUN
ejpam-3075	27	18	∑	∑	PUNCT
ejpam-3075	27	19	5	5	NUM
ejpam-3075	27	20	+	+	ADV
ejpam-3075	27	21	m	m	VERB
ejpam-3075	27	22	∑	∑	ADV
ejpam-3075	27	23	6	6	NUM
ejpam-3075	27	24	+	+	CCONJ
ejpam-3075	27	25	n	n	CCONJ
ejpam-3075	27	26	∑	∑	ADP
ejpam-3075	27	27	7	7	NUM
ejpam-3075	27	28	+	+	CCONJ
ejpam-3075	27	29	r	r	NOUN
ejpam-3075	27	30	∑	∑	PROPN
ejpam-3075	27	31	8	8	NUM
ejpam-3075	27	32	,	,	PUNCT
ejpam-3075	27	33	(	(	PUNCT
ejpam-3075	27	34	4	4	X
ejpam-3075	27	35	)	)	PUNCT
ejpam-3075	27	36	where	where	SCONJ
ejpam-3075	27	37	∑	∑	PROPN
ejpam-3075	27	38	1	1	NUM
ejpam-3075	27	39	is	be	AUX
ejpam-3075	27	40	a	a	DET
ejpam-3075	27	41	p×p	p×p	PROPN
ejpam-3075	27	42	positive	positive	ADJ
ejpam-3075	27	43	definite	definite	ADJ
ejpam-3075	27	44	symmetric	symmetric	ADJ
ejpam-3075	27	45	matrix	matrix	NOUN
ejpam-3075	27	46	,	,	PUNCT
ejpam-3075	27	47	and	and	CCONJ
ejpam-3075	27	48	∑	∑	PROPN
ejpam-3075	27	49	2	2	NUM
ejpam-3075	27	50	,	,	PUNCT
ejpam-3075	27	51	...	...	PUNCT
ejpam-3075	27	52	,	,	PUNCT
ejpam-3075	27	53	∑	∑	PROPN
ejpam-3075	27	54	8	8	NUM
ejpam-3075	27	55	are	be	AUX
ejpam-3075	27	56	real	real	ADJ
ejpam-3075	27	57	p×p	p×p	PROPN
ejpam-3075	27	58	skew	skew	NOUN
ejpam-3075	27	59	symmetric	symmetric	ADJ
ejpam-3075	27	60	matrices	matrix	NOUN
ejpam-3075	27	61	.	.	PUNCT
ejpam-3075	28	1	note	note	VERB
ejpam-3075	28	2	that	that	DET
ejpam-3075	28	3	∑−1	∑−1	NOUN
ejpam-3075	28	4	=	=	PUNCT
ejpam-3075	28	5	∑	∑	PUNCT
ejpam-3075	28	6	and	and	CCONJ
ejpam-3075	28	7	∑	∑	PROPN
ejpam-3075	28	8	is	be	AUX
ejpam-3075	28	9	hchm	hchm	NOUN
ejpam-3075	28	10	.	.	PUNCT
ejpam-3075	29	1	now	now	ADV
ejpam-3075	29	2	setting	set	VERB
ejpam-3075	29	3	dy	dy	NOUN
ejpam-3075	29	4	=	=	SYM
ejpam-3075	29	5	dx1	dx1	PROPN
ejpam-3075	29	6	...	...	PUNCT
ejpam-3075	29	7	dx8	dx8	PROPN
ejpam-3075	29	8	,	,	PUNCT
ejpam-3075	29	9	kabe	kabe	VERB
ejpam-3075	30	1	[	[	X
ejpam-3075	30	2	6	6	NUM
ejpam-3075	30	3	]	]	PUNCT
ejpam-3075	30	4	shows	show	VERB
ejpam-3075	30	5	that	that	SCONJ
ejpam-3075	30	6	the	the	DET
ejpam-3075	30	7	pn	pn	PROPN
ejpam-3075	30	8	variate	variate	NOUN
ejpam-3075	30	9	hc	hc	PROPN
ejpam-3075	30	10	multivariate	multivariate	NOUN
ejpam-3075	30	11	normal	normal	ADJ
ejpam-3075	30	12	density	density	NOUN
ejpam-3075	30	13	of	of	ADP
ejpam-3075	30	14	y	y	PROPN
ejpam-3075	30	15	can	can	AUX
ejpam-3075	30	16	be	be	AUX
ejpam-3075	30	17	written	write	VERB
ejpam-3075	30	18	as	as	ADP
ejpam-3075	30	19	f(y	f(y	NOUN
ejpam-3075	30	20	)	)	PUNCT
ejpam-3075	31	1	=	=	PUNCT
ejpam-3075	31	2	π−2pnt|	π−2pnt|	PROPN
ejpam-3075	31	3	∑	∑	PUNCT
ejpam-3075	31	4	|−2ntexp{−tr	|−2ntexp{−tr	X
ejpam-3075	31	5	∑	∑	SYM
ejpam-3075	31	6	−1y	−1y	PROPN
ejpam-3075	31	7	ȳ	ȳ	NOUN
ejpam-3075	31	8	}	}	PUNCT
ejpam-3075	31	9	,	,	PUNCT
ejpam-3075	31	10	(	(	PUNCT
ejpam-3075	31	11	5	5	NUM
ejpam-3075	31	12	)	)	PUNCT
ejpam-3075	31	13	and	and	CCONJ
ejpam-3075	31	14	hence	hence	ADV
ejpam-3075	31	15	the	the	DET
ejpam-3075	31	16	hc	hc	PROPN
ejpam-3075	31	17	wishart	wishart	PROPN
ejpam-3075	31	18	density	density	NOUN
ejpam-3075	31	19	of	of	ADP
ejpam-3075	31	20	the	the	DET
ejpam-3075	31	21	p×	p×	PROPN
ejpam-3075	31	22	p	p	NOUN
ejpam-3075	31	23	hchm	hchm	NOUN
ejpam-3075	31	24	g	g	PROPN
ejpam-3075	31	25	=	=	SYM
ejpam-3075	31	26	y	y	PROPN
ejpam-3075	31	27	ȳ	ȳ	NOUN
ejpam-3075	31	28	′	′	NOUN
ejpam-3075	31	29	is	be	AUX
ejpam-3075	31	30	f(g	f(g	NOUN
ejpam-3075	31	31	)	)	PUNCT
ejpam-3075	31	32	=	=	PRON
ejpam-3075	31	33	{	{	PUNCT
ejpam-3075	31	34	γp(2nt)}−1|	γp(2nt)}−1|	NOUN
ejpam-3075	31	35	∑	∑	ADV
ejpam-3075	31	36	|−2nt|g|−2t(n−p+1)−1exp{−tr	|−2nt|g|−2t(n−p+1)−1exp{−tr	PROPN
ejpam-3075	31	37	∑	∑	X
ejpam-3075	31	38	−1	−1	NOUN
ejpam-3075	31	39	g	g	NOUN
ejpam-3075	31	40	}	}	PUNCT
ejpam-3075	31	41	,	,	PUNCT
ejpam-3075	31	42	(	(	PUNCT
ejpam-3075	31	43	6	6	NUM
ejpam-3075	31	44	)	)	PUNCT
ejpam-3075	31	45	where	where	SCONJ
ejpam-3075	31	46	γp(a	γp(a	PUNCT
ejpam-3075	31	47	)	)	PUNCT
ejpam-3075	31	48	=	=	SYM
ejpam-3075	31	49	πtp(p−1)πp	πtp(p−1)πp	PROPN
ejpam-3075	31	50	i=1γ(a−	i=1γ(a−	ADP
ejpam-3075	31	51	2t(p−	2t(p−	NUM
ejpam-3075	31	52	i	i	NOUN
ejpam-3075	31	53	)	)	PUNCT
ejpam-3075	31	54	)	)	PUNCT
ejpam-3075	31	55	.	.	PUNCT
ejpam-3075	32	1	(	(	PUNCT
ejpam-3075	32	2	7	7	X
ejpam-3075	32	3	)	)	PUNCT
ejpam-3075	32	4	further	far	ADV
ejpam-3075	32	5	for	for	ADP
ejpam-3075	32	6	given	give	VERB
ejpam-3075	32	7	two	two	NUM
ejpam-3075	32	8	p×	p×	NOUN
ejpam-3075	32	9	p	p	NOUN
ejpam-3075	32	10	hchm	hchm	NOUN
ejpam-3075	32	11	matrices	matrice	VERB
ejpam-3075	32	12	a	a	PRON
ejpam-3075	32	13	and	and	CCONJ
ejpam-3075	32	14	b	b	NOUN
ejpam-3075	32	15	,	,	PUNCT
ejpam-3075	32	16	having	have	VERB
ejpam-3075	32	17	hc	hc	PRON
ejpam-3075	32	18	wishart	wishart	NOUN
ejpam-3075	32	19	densities	density	NOUN
ejpam-3075	32	20	with	with	ADP
ejpam-3075	32	21	n	n	NOUN
ejpam-3075	32	22	and	and	CCONJ
ejpam-3075	32	23	q	q	ADJ
ejpam-3075	32	24	degrees	degree	NOUN
ejpam-3075	32	25	of	of	ADP
ejpam-3075	32	26	freedom	freedom	NOUN
ejpam-3075	32	27	,	,	PUNCT
ejpam-3075	32	28	the	the	DET
ejpam-3075	32	29	density	density	NOUN
ejpam-3075	32	30	of	of	ADP
ejpam-3075	32	31	the	the	DET
ejpam-3075	32	32	p×	p×	PROPN
ejpam-3075	32	33	p	p	NOUN
ejpam-3075	32	34	hchm	hchm	NOUN
ejpam-3075	32	35	r	r	NOUN
ejpam-3075	32	36	defined	define	VERB
ejpam-3075	32	37	by	by	ADP
ejpam-3075	32	38	r	r	NOUN
ejpam-3075	32	39	=	=	SYM
ejpam-3075	32	40	g−	g−	ADJ
ejpam-3075	32	41	1	1	NUM
ejpam-3075	32	42	2ag−	2ag−	NUM
ejpam-3075	32	43	1	1	NUM
ejpam-3075	32	44	2	2	NUM
ejpam-3075	32	45	,	,	PUNCT
ejpam-3075	32	46	a+b	a+b	NUM
ejpam-3075	32	47	=	=	SYM
ejpam-3075	32	48	g	g	NOUN
ejpam-3075	32	49	,	,	PUNCT
ejpam-3075	32	50	(	(	PUNCT
ejpam-3075	32	51	8)	8)	NUM
ejpam-3075	32	52	is	be	AUX
ejpam-3075	32	53	given	give	VERB
ejpam-3075	32	54	by	by	ADP
ejpam-3075	32	55	the	the	DET
ejpam-3075	32	56	expression	expression	NOUN
ejpam-3075	32	57	f(r	f(r	NOUN
ejpam-3075	32	58	)	)	PUNCT
ejpam-3075	33	1	=	=	PRON
ejpam-3075	33	2	{	{	PUNCT
ejpam-3075	33	3	bp(2nt	bp(2nt	NOUN
ejpam-3075	33	4	,	,	PUNCT
ejpam-3075	33	5	2qt)}−1|i	2qt)}−1|i	NUM
ejpam-3075	33	6	−r|2t(n−p+1)−1|r|2t(q−p+1)−1	−r|2t(n−p+1)−1|r|2t(q−p+1)−1	NOUN
ejpam-3075	33	7	,	,	PUNCT
ejpam-3075	33	8	(	(	PUNCT
ejpam-3075	33	9	9	9	NUM
ejpam-3075	33	10	)	)	PUNCT
ejpam-3075	33	11	where	where	SCONJ
ejpam-3075	33	12	(	(	PUNCT
ejpam-3075	33	13	see	see	VERB
ejpam-3075	33	14	[	[	X
ejpam-3075	33	15	5	5	NUM
ejpam-3075	33	16	]	]	NUM
ejpam-3075	33	17	)	)	PUNCT
ejpam-3075	33	18	,	,	PUNCT
ejpam-3075	33	19	bp(a	bp(a	NUM
ejpam-3075	33	20	,	,	PUNCT
ejpam-3075	33	21	b	b	X
ejpam-3075	33	22	)	)	PUNCT
ejpam-3075	33	23	=	=	SYM
ejpam-3075	33	24	γp(a)γp(b	γp(a)γp(b	PROPN
ejpam-3075	33	25	)	)	PUNCT
ejpam-3075	33	26	γp(a+	γp(a+	PROPN
ejpam-3075	33	27	b	b	NOUN
ejpam-3075	33	28	)	)	PUNCT
ejpam-3075	33	29	.	.	PUNCT
ejpam-3075	34	1	(	(	PUNCT
ejpam-3075	34	2	10	10	NUM
ejpam-3075	34	3	)	)	PUNCT
ejpam-3075	34	4	if	if	SCONJ
ejpam-3075	34	5	now	now	ADV
ejpam-3075	34	6	∧	∧	PROPN
ejpam-3075	34	7	is	be	AUX
ejpam-3075	34	8	the	the	DET
ejpam-3075	34	9	p	p	X
ejpam-3075	34	10	×	×	NOUN
ejpam-3075	34	11	p	p	X
ejpam-3075	34	12	diagonal	diagonal	ADJ
ejpam-3075	34	13	matrix	matrix	NOUN
ejpam-3075	34	14	of	of	ADP
ejpam-3075	34	15	the	the	DET
ejpam-3075	34	16	roots	root	NOUN
ejpam-3075	34	17	of	of	ADP
ejpam-3075	34	18	r	r	NOUN
ejpam-3075	34	19	,	,	PUNCT
ejpam-3075	34	20	then	then	ADV
ejpam-3075	34	21	kabe	kabe	VERB
ejpam-3075	34	22	[	[	X
ejpam-3075	34	23	6	6	NUM
ejpam-3075	34	24	,	,	PUNCT
ejpam-3075	34	25	p.68	p.68	NOUN
ejpam-3075	34	26	,	,	PUNCT
ejpam-3075	34	27	equation	equation	NOUN
ejpam-3075	34	28	(	(	PUNCT
ejpam-3075	34	29	21	21	NUM
ejpam-3075	34	30	)	)	PUNCT
ejpam-3075	34	31	]	]	PUNCT
ejpam-3075	34	32	shows	show	VERB
ejpam-3075	34	33	that	that	SCONJ
ejpam-3075	34	34	the	the	DET
ejpam-3075	34	35	jacobian	jacobian	ADJ
ejpam-3075	34	36	j(r	j(r	PROPN
ejpam-3075	34	37	:	:	PUNCT
ejpam-3075	34	38	∧	∧	NOUN
ejpam-3075	34	39	)	)	PUNCT
ejpam-3075	34	40	=	=	NOUN
ejpam-3075	34	41	πp	πp	ADP
ejpam-3075	34	42	i	i	PRON
ejpam-3075	34	43	<	<	X
ejpam-3075	34	44	j(xi	j(xi	PROPN
ejpam-3075	34	45	−	−	PROPN
ejpam-3075	34	46	xj	xj	PROPN
ejpam-3075	34	47	)	)	PUNCT
ejpam-3075	35	1	4t,∧	4t,∧	PROPN
ejpam-3075	35	2	=	=	PUNCT
ejpam-3075	35	3	diag(λ1	diag(λ1	NOUN
ejpam-3075	35	4	,	,	PUNCT
ejpam-3075	35	5	...	...	PUNCT
ejpam-3075	35	6	,	,	PUNCT
ejpam-3075	35	7	λp	λp	PROPN
ejpam-3075	35	8	)	)	PUNCT
ejpam-3075	35	9	,	,	PUNCT
ejpam-3075	35	10	(	(	PUNCT
ejpam-3075	35	11	11	11	NUM
ejpam-3075	35	12	)	)	PUNCT
ejpam-3075	35	13	and	and	CCONJ
ejpam-3075	35	14	the	the	DET
ejpam-3075	35	15	hc	hc	PROPN
ejpam-3075	35	16	multivariate	multivariate	NOUN
ejpam-3075	35	17	beta	beta	NOUN
ejpam-3075	35	18	density	density	NOUN
ejpam-3075	35	19	of	of	ADP
ejpam-3075	35	20	∧	∧	PROPN
ejpam-3075	35	21	is	be	AUX
ejpam-3075	35	22	f(∧	f(∧	NUM
ejpam-3075	35	23	)	)	PUNCT
ejpam-3075	36	1	=	=	PRON
ejpam-3075	36	2	{	{	PUNCT
ejpam-3075	36	3	bp(2nt	bp(2nt	NOUN
ejpam-3075	36	4	,	,	PUNCT
ejpam-3075	36	5	2qt)−1|i	2qt)−1|i	NUM
ejpam-3075	36	6	−	−	PROPN
ejpam-3075	37	1	∧|2t(n−p+1)−1|	∧|2t(n−p+1)−1|	NUM
ejpam-3075	37	2	∧	∧	PROPN
ejpam-3075	37	3	|2t(q−p+1)−1πp	|2t(q−p+1)−1πp	NOUN
ejpam-3075	38	1	i	i	PRON
ejpam-3075	38	2	<	<	X
ejpam-3075	38	3	j(λi	j(λi	ADV
ejpam-3075	38	4	−	−	PROPN
ejpam-3075	38	5	λj	λj	PROPN
ejpam-3075	38	6	)	)	PUNCT
ejpam-3075	38	7	4	4	NUM
ejpam-3075	38	8	t	t	NOUN
ejpam-3075	38	9	,	,	PUNCT
ejpam-3075	38	10	(	(	PUNCT
ejpam-3075	38	11	12	12	NUM
ejpam-3075	38	12	)	)	PUNCT
ejpam-3075	38	13	with	with	ADP
ejpam-3075	38	14	a	a	DET
ejpam-3075	38	15	similar	similar	ADJ
ejpam-3075	38	16	result	result	NOUN
ejpam-3075	38	17	for	for	ADP
ejpam-3075	38	18	the	the	DET
ejpam-3075	38	19	density	density	NOUN
ejpam-3075	38	20	of	of	ADP
ejpam-3075	38	21	the	the	DET
ejpam-3075	38	22	roots	root	NOUN
ejpam-3075	38	23	matrix	matrix	NOUN
ejpam-3075	38	24	of	of	ADP
ejpam-3075	38	25	(	(	PUNCT
ejpam-3075	38	26	6	6	NUM
ejpam-3075	38	27	)	)	PUNCT
ejpam-3075	38	28	.	.	PUNCT
ejpam-3075	39	1	now	now	ADV
ejpam-3075	39	2	our	our	PRON
ejpam-3075	39	3	paper	paper	NOUN
ejpam-3075	39	4	proceeds	proceed	NOUN
ejpam-3075	39	5	as	as	SCONJ
ejpam-3075	39	6	follows	follow	VERB
ejpam-3075	39	7	.	.	PUNCT
ejpam-3075	40	1	the	the	DET
ejpam-3075	40	2	next	next	ADJ
ejpam-3075	40	3	section	section	NOUN
ejpam-3075	40	4	derives	derive	VERB
ejpam-3075	40	5	the	the	DET
ejpam-3075	40	6	real	real	ADV
ejpam-3075	40	7	generalized	generalized	ADJ
ejpam-3075	40	8	quadratic	quadratic	ADJ
ejpam-3075	40	9	forms	form	NOUN
ejpam-3075	40	10	wishart	wishart	NOUN
ejpam-3075	40	11	density	density	NOUN
ejpam-3075	40	12	(	(	PUNCT
ejpam-3075	40	13	gqfwd	gqfwd	ADJ
ejpam-3075	40	14	)	)	PUNCT
ejpam-3075	40	15	,	,	PUNCT
ejpam-3075	40	16	and	and	CCONJ
ejpam-3075	40	17	section	section	NOUN
ejpam-3075	40	18	3	3	NUM
ejpam-3075	40	19	develops	develop	VERB
ejpam-3075	40	20	the	the	DET
ejpam-3075	40	21	real	real	ADV
ejpam-3075	40	22	generalized	generalized	ADJ
ejpam-3075	40	23	quadratic	quadratic	ADJ
ejpam-3075	40	24	forms	form	NOUN
ejpam-3075	40	25	multivariate	multivariate	VERB
ejpam-3075	40	26	beta	beta	NOUN
ejpam-3075	40	27	density	density	NOUN
ejpam-3075	40	28	(	(	PUNCT
ejpam-3075	40	29	gqfmbd	gqfmbd	PROPN
ejpam-3075	40	30	)	)	PUNCT
ejpam-3075	40	31	.	.	PUNCT
ejpam-3075	41	1	section	section	NOUN
ejpam-3075	41	2	4	4	NUM
ejpam-3075	41	3	records	record	VERB
ejpam-3075	41	4	the	the	DET
ejpam-3075	41	5	gamma	gamma	NOUN
ejpam-3075	41	6	integrals	integral	NOUN
ejpam-3075	41	7	,	,	PUNCT
ejpam-3075	41	8	and	and	CCONJ
ejpam-3075	41	9	section	section	NOUN
ejpam-3075	41	10	5	5	NUM
ejpam-3075	41	11	records	record	VERB
ejpam-3075	41	12	the	the	DET
ejpam-3075	41	13	beta	beta	ADJ
ejpam-3075	41	14	integrals	integral	NOUN
ejpam-3075	41	15	of	of	ADP
ejpam-3075	41	16	the	the	DET
ejpam-3075	41	17	context	context	NOUN
ejpam-3075	41	18	.	.	PUNCT
ejpam-3075	42	1	a.	a.	PROPN
ejpam-3075	42	2	k.	k.	PROPN
ejpam-3075	42	3	gupta	gupta	PROPN
ejpam-3075	42	4	,	,	PUNCT
ejpam-3075	42	5	d.	d.	PROPN
ejpam-3075	42	6	g.	g.	PROPN
ejpam-3075	42	7	kabe	kabe	PROPN
ejpam-3075	42	8	/	/	SYM
ejpam-3075	42	9	eur	eur	PROPN
ejpam-3075	42	10	.	.	PUNCT
ejpam-3075	43	1	j.	j.	PROPN
ejpam-3075	43	2	pure	pure	PROPN
ejpam-3075	43	3	appl	appl	PROPN
ejpam-3075	43	4	.	.	PROPN
ejpam-3075	43	5	math	math	PROPN
ejpam-3075	43	6	,	,	PUNCT
ejpam-3075	43	7	10	10	NUM
ejpam-3075	43	8	(	(	PUNCT
ejpam-3075	43	9	4	4	NUM
ejpam-3075	43	10	)	)	PUNCT
ejpam-3075	43	11	(	(	PUNCT
ejpam-3075	43	12	2017	2017	NUM
ejpam-3075	43	13	)	)	PUNCT
ejpam-3075	43	14	,	,	PUNCT
ejpam-3075	43	15	614	614	NUM
ejpam-3075	43	16	-	-	SYM
ejpam-3075	43	17	619	619	NUM
ejpam-3075	43	18	616	616	NUM
ejpam-3075	43	19	2	2	NUM
ejpam-3075	43	20	.	.	X
ejpam-3075	43	21	gqfwd	gqfwd	PROPN
ejpam-3075	43	22	let	let	VERB
ejpam-3075	43	23	x	x	PRON
ejpam-3075	43	24	be	be	AUX
ejpam-3075	43	25	a	a	DET
ejpam-3075	43	26	p×n	p×n	PROPN
ejpam-3075	43	27	matrix	matrix	NOUN
ejpam-3075	43	28	of	of	ADP
ejpam-3075	43	29	rank	rank	NOUN
ejpam-3075	43	30	p	p	NOUN
ejpam-3075	43	31	≤	≤	NUM
ejpam-3075	43	32	n	n	CCONJ
ejpam-3075	43	33	,	,	PUNCT
ejpam-3075	43	34	and	and	CCONJ
ejpam-3075	43	35	∆	∆	PROPN
ejpam-3075	43	36	=	=	NOUN
ejpam-3075	43	37	diag(δ1	diag(δ1	NOUN
ejpam-3075	43	38	,	,	PUNCT
ejpam-3075	43	39	...	...	PUNCT
ejpam-3075	43	40	,	,	PUNCT
ejpam-3075	43	41	δn	δn	ADJ
ejpam-3075	43	42	)	)	PUNCT
ejpam-3075	43	43	n×n	n×n	PROPN
ejpam-3075	43	44	diagonal	diagonal	ADJ
ejpam-3075	43	45	matrix	matrix	NOUN
ejpam-3075	43	46	,	,	PUNCT
ejpam-3075	43	47	then	then	ADV
ejpam-3075	43	48	gqfwd	gqfwd	ADJ
ejpam-3075	43	49	of	of	ADP
ejpam-3075	43	50	p×	p×	PROPN
ejpam-3075	43	51	p	p	PROPN
ejpam-3075	43	52	t	t	PROPN
ejpam-3075	43	53	is	be	AUX
ejpam-3075	43	54	defined	define	VERB
ejpam-3075	43	55	by	by	ADP
ejpam-3075	43	56	the	the	DET
ejpam-3075	43	57	integral	integral	ADJ
ejpam-3075	43	58	f(t	f(t	NOUN
ejpam-3075	43	59	)	)	PUNCT
ejpam-3075	44	1	=	=	SYM
ejpam-3075	44	2	k	k	PROPN
ejpam-3075	44	3	∫	∫	PROPN
ejpam-3075	44	4	xx′=t	xx′=t	PROPN
ejpam-3075	44	5	exp{−trx∆x	exp{−trx∆x	PROPN
ejpam-3075	44	6	′}dx	′}dx	PROPN
ejpam-3075	44	7	,	,	PUNCT
ejpam-3075	44	8	(	(	PUNCT
ejpam-3075	44	9	13	13	NUM
ejpam-3075	44	10	)	)	PUNCT
ejpam-3075	44	11	where	where	SCONJ
ejpam-3075	44	12	k	k	NOUN
ejpam-3075	44	13	,	,	PUNCT
ejpam-3075	44	14	as	as	ADP
ejpam-3075	44	15	a	a	DET
ejpam-3075	44	16	generic	generic	ADJ
ejpam-3075	44	17	letter	letter	NOUN
ejpam-3075	44	18	,	,	PUNCT
ejpam-3075	44	19	denotes	denote	VERB
ejpam-3075	44	20	the	the	DET
ejpam-3075	44	21	normalizing	normalizing	ADJ
ejpam-3075	44	22	constants	constant	NOUN
ejpam-3075	44	23	of	of	ADP
ejpam-3075	44	24	density	density	NOUN
ejpam-3075	44	25	functions	function	NOUN
ejpam-3075	44	26	in	in	ADP
ejpam-3075	44	27	this	this	DET
ejpam-3075	44	28	paper	paper	NOUN
ejpam-3075	44	29	.	.	PUNCT
ejpam-3075	45	1	the	the	DET
ejpam-3075	45	2	moment	moment	NOUN
ejpam-3075	45	3	generating	generate	VERB
ejpam-3075	45	4	function	function	NOUN
ejpam-3075	45	5	of	of	ADP
ejpam-3075	45	6	t	t	PROPN
ejpam-3075	45	7	is	be	AUX
ejpam-3075	45	8	φ(θ	φ(θ	PROPN
ejpam-3075	45	9	)	)	PUNCT
ejpam-3075	46	1	=	=	SYM
ejpam-3075	46	2	k	k	PROPN
ejpam-3075	46	3	∫	∫	PROPN
ejpam-3075	46	4	exp{−tr(x∆x	exp{−tr(x∆x	PROPN
ejpam-3075	47	1	′	′	NUM
ejpam-3075	47	2	−	−	PROPN
ejpam-3075	47	3	θxx	θxx	NOUN
ejpam-3075	47	4	′)}dx	′)}dx	NOUN
ejpam-3075	48	1	=	=	SYM
ejpam-3075	48	2	πn	πn	NUM
ejpam-3075	48	3	i=1	i=1	PROPN
ejpam-3075	48	4	|δii	|δii	PROPN
ejpam-3075	48	5	−	−	PROPN
ejpam-3075	48	6	θ|−	θ|−	VERB
ejpam-3075	48	7	1	1	NUM
ejpam-3075	48	8	2	2	NUM
ejpam-3075	48	9	,	,	PUNCT
ejpam-3075	48	10	(	(	PUNCT
ejpam-3075	48	11	14	14	NUM
ejpam-3075	48	12	)	)	PUNCT
ejpam-3075	48	13	where	where	SCONJ
ejpam-3075	48	14	θ	θ	NOUN
ejpam-3075	48	15	,	,	PUNCT
ejpam-3075	48	16	in	in	ADP
ejpam-3075	48	17	the	the	DET
ejpam-3075	48	18	usual	usual	ADJ
ejpam-3075	48	19	sense	sense	NOUN
ejpam-3075	48	20	,	,	PUNCT
ejpam-3075	48	21	is	be	AUX
ejpam-3075	48	22	p×	p×	NOUN
ejpam-3075	48	23	p	p	NOUN
ejpam-3075	48	24	positive	positive	ADJ
ejpam-3075	48	25	definite	definite	ADJ
ejpam-3075	48	26	symmetric	symmetric	ADJ
ejpam-3075	48	27	matrix	matrix	NOUN
ejpam-3075	48	28	.	.	PUNCT
ejpam-3075	49	1	indeed	indeed	ADV
ejpam-3075	49	2	,	,	PUNCT
ejpam-3075	49	3	mathai	mathai	PROPN
ejpam-3075	50	1	[	[	X
ejpam-3075	50	2	8	8	NUM
ejpam-3075	50	3	,	,	PUNCT
ejpam-3075	50	4	p.353	p.353	PROPN
ejpam-3075	50	5	]	]	PUNCT
ejpam-3075	50	6	,	,	PUNCT
ejpam-3075	50	7	derives	derive	VERB
ejpam-3075	50	8	the	the	DET
ejpam-3075	50	9	density	density	NOUN
ejpam-3075	50	10	(	(	PUNCT
ejpam-3075	50	11	13	13	NUM
ejpam-3075	50	12	)	)	PUNCT
ejpam-3075	50	13	;	;	PUNCT
ejpam-3075	50	14	however	however	ADV
ejpam-3075	50	15	,	,	PUNCT
ejpam-3075	50	16	his	his	PRON
ejpam-3075	50	17	density	density	NOUN
ejpam-3075	50	18	function	function	NOUN
ejpam-3075	50	19	is	be	AUX
ejpam-3075	50	20	not	not	PART
ejpam-3075	50	21	suitable	suitable	ADJ
ejpam-3075	50	22	in	in	ADP
ejpam-3075	50	23	our	our	PRON
ejpam-3075	50	24	context	context	NOUN
ejpam-3075	50	25	.	.	PUNCT
ejpam-3075	51	1	in	in	ADP
ejpam-3075	51	2	our	our	PRON
ejpam-3075	51	3	context	context	NOUN
ejpam-3075	51	4	inverting	inverting	NOUN
ejpam-3075	51	5	(	(	PUNCT
ejpam-3075	51	6	14	14	NUM
ejpam-3075	51	7	)	)	PUNCT
ejpam-3075	51	8	we	we	PRON
ejpam-3075	51	9	find	find	VERB
ejpam-3075	51	10	that	that	SCONJ
ejpam-3075	51	11	f(t	f(t	NOUN
ejpam-3075	51	12	)	)	PUNCT
ejpam-3075	52	1	=	=	SYM
ejpam-3075	52	2	|∆|−	|∆|−	VERB
ejpam-3075	52	3	1	1	NUM
ejpam-3075	52	4	2	2	NUM
ejpam-3075	52	5	p|δ1|−	p|δ1|−	NOUN
ejpam-3075	52	6	1	1	NUM
ejpam-3075	52	7	2	2	NUM
ejpam-3075	52	8	pnexp{−δ1trt}|t	pnexp{−δ1trt}|t	X
ejpam-3075	52	9	|	|	ADV
ejpam-3075	52	10	1	1	NUM
ejpam-3075	52	11	2	2	NUM
ejpam-3075	52	12	(	(	PUNCT
ejpam-3075	52	13	n−p−1){γp	n−p−1){γp	NOUN
ejpam-3075	52	14	(	(	PUNCT
ejpam-3075	52	15	1	1	NUM
ejpam-3075	52	16	2	2	NUM
ejpam-3075	52	17	n)}−1	n)}−1	PROPN
ejpam-3075	52	18	.1f1	.1f1	PROPN
ejpam-3075	52	19	(	(	PUNCT
ejpam-3075	52	20	1	1	NUM
ejpam-3075	52	21	2	2	NUM
ejpam-3075	52	22	(	(	PUNCT
ejpam-3075	52	23	n−	n−	NOUN
ejpam-3075	52	24	1	1	NUM
ejpam-3075	52	25	)	)	PUNCT
ejpam-3075	52	26	;	;	PUNCT
ejpam-3075	52	27	1	1	NUM
ejpam-3075	52	28	2	2	NUM
ejpam-3075	52	29	n	n	NUM
ejpam-3075	52	30	;	;	PUNCT
ejpam-3075	52	31	(	(	PUNCT
ejpam-3075	52	32	(	(	PUNCT
ejpam-3075	52	33	n−	n−	NOUN
ejpam-3075	52	34	1)δ1	1)δ1	NUM
ejpam-3075	52	35	−	−	NOUN
ejpam-3075	52	36	δ2	δ2	VERB
ejpam-3075	52	37	−	−	NOUN
ejpam-3075	52	38	...	...	PUNCT
ejpam-3075	52	39	−	−	PROPN
ejpam-3075	53	1	δn)t	δn)t	PROPN
ejpam-3075	53	2	)	)	PUNCT
ejpam-3075	53	3	(	(	PUNCT
ejpam-3075	53	4	15	15	NUM
ejpam-3075	53	5	)	)	PUNCT
ejpam-3075	53	6	where	where	SCONJ
ejpam-3075	53	7	δ1	δ1	NOUN
ejpam-3075	53	8	=	=	PUNCT
ejpam-3075	53	9	max(δ1	max(δ1	PROPN
ejpam-3075	53	10	,	,	PUNCT
ejpam-3075	53	11	...	...	PUNCT
ejpam-3075	53	12	,	,	PUNCT
ejpam-3075	53	13	δn	δn	ADJ
ejpam-3075	53	14	)	)	PUNCT
ejpam-3075	53	15	.	.	PUNCT
ejpam-3075	54	1	it	it	PRON
ejpam-3075	54	2	is	be	AUX
ejpam-3075	54	3	possible	possible	ADJ
ejpam-3075	54	4	to	to	PART
ejpam-3075	54	5	use	use	VERB
ejpam-3075	54	6	mathai	mathai	PROPN
ejpam-3075	54	7	’s	’s	PART
ejpam-3075	54	8	[	[	X
ejpam-3075	54	9	8	8	NUM
ejpam-3075	54	10	]	]	X
ejpam-3075	54	11	gqfwd	gqfwd	X
ejpam-3075	54	12	and	and	CCONJ
ejpam-3075	54	13	gqfmbd	gqfmbd	PROPN
ejpam-3075	54	14	results	result	NOUN
ejpam-3075	54	15	to	to	PART
ejpam-3075	54	16	derive	derive	VERB
ejpam-3075	54	17	selberg	selberg	NOUN
ejpam-3075	54	18	-	-	PUNCT
ejpam-3075	54	19	type	type	NOUN
ejpam-3075	54	20	gamma	gamma	NOUN
ejpam-3075	54	21	and	and	CCONJ
ejpam-3075	54	22	beta	beta	NOUN
ejpam-3075	54	23	integrals	integral	NOUN
ejpam-3075	54	24	of	of	ADP
ejpam-3075	54	25	our	our	PRON
ejpam-3075	54	26	context	context	NOUN
ejpam-3075	54	27	;	;	PUNCT
ejpam-3075	54	28	however	however	ADV
ejpam-3075	54	29	,	,	PUNCT
ejpam-3075	54	30	our	our	PRON
ejpam-3075	54	31	expressions	expression	NOUN
ejpam-3075	54	32	for	for	ADP
ejpam-3075	54	33	the	the	DET
ejpam-3075	54	34	gqfwd	gqfwd	PROPN
ejpam-3075	54	35	and	and	CCONJ
ejpam-3075	54	36	gqfmbd	gqfmbd	PROPN
ejpam-3075	54	37	appear	appear	VERB
ejpam-3075	54	38	to	to	PART
ejpam-3075	54	39	be	be	AUX
ejpam-3075	54	40	simpler	simple	ADJ
ejpam-3075	54	41	than	than	ADP
ejpam-3075	54	42	the	the	DET
ejpam-3075	54	43	ones	one	NOUN
ejpam-3075	54	44	given	give	VERB
ejpam-3075	54	45	by	by	ADP
ejpam-3075	54	46	mathai	mathai	PROPN
ejpam-3075	55	1	[	[	X
ejpam-3075	55	2	8	8	NUM
ejpam-3075	55	3	]	]	PUNCT
ejpam-3075	55	4	,	,	PUNCT
ejpam-3075	55	5	and	and	CCONJ
ejpam-3075	55	6	mathai	mathai	PROPN
ejpam-3075	55	7	,	,	PUNCT
ejpam-3075	55	8	provost	provost	NOUN
ejpam-3075	55	9	and	and	CCONJ
ejpam-3075	55	10	hayakawa	hayakawa	PROPN
ejpam-3075	55	11	[	[	X
ejpam-3075	55	12	7	7	NUM
ejpam-3075	55	13	,	,	PUNCT
ejpam-3075	55	14	chapter	chapter	NOUN
ejpam-3075	55	15	5	5	NUM
ejpam-3075	55	16	]	]	PUNCT
ejpam-3075	55	17	we	we	PRON
ejpam-3075	55	18	proceed	proceed	VERB
ejpam-3075	55	19	to	to	PART
ejpam-3075	55	20	prove	prove	VERB
ejpam-3075	55	21	(	(	PUNCT
ejpam-3075	55	22	15	15	NUM
ejpam-3075	55	23	)	)	PUNCT
ejpam-3075	55	24	.	.	PUNCT
ejpam-3075	56	1	given	give	VERB
ejpam-3075	56	2	the	the	DET
ejpam-3075	56	3	joint	joint	ADJ
ejpam-3075	56	4	density	density	NOUN
ejpam-3075	56	5	of	of	ADP
ejpam-3075	56	6	n	n	PRON
ejpam-3075	56	7	gamma	gamma	NOUN
ejpam-3075	56	8	variates	variate	NOUN
ejpam-3075	56	9	to	to	PART
ejpam-3075	56	10	be	be	AUX
ejpam-3075	56	11	f(y1	f(y1	NOUN
ejpam-3075	56	12	,	,	PUNCT
ejpam-3075	56	13	...	...	PUNCT
ejpam-3075	56	14	,	,	PUNCT
ejpam-3075	56	15	yn	yn	PROPN
ejpam-3075	56	16	)	)	PUNCT
ejpam-3075	56	17	=	=	SYM
ejpam-3075	56	18	kexp{−(α1y1	kexp{−(α1y1	PROPN
ejpam-3075	56	19	+	+	CCONJ
ejpam-3075	56	20	+	+	CCONJ
ejpam-3075	56	21	αnyn)}yg1−1	αnyn)}yg1−1	NOUN
ejpam-3075	56	22	1	1	NUM
ejpam-3075	56	23	...	...	PUNCT
ejpam-3075	56	24	ygn−1	ygn−1	PROPN
ejpam-3075	56	25	n	n	PROPN
ejpam-3075	56	26	,	,	PUNCT
ejpam-3075	56	27	(	(	PUNCT
ejpam-3075	56	28	16	16	NUM
ejpam-3075	56	29	)	)	PUNCT
ejpam-3075	56	30	the	the	DET
ejpam-3075	56	31	density	density	NOUN
ejpam-3075	56	32	of	of	ADP
ejpam-3075	56	33	t	t	NOUN
ejpam-3075	56	34	=	=	SYM
ejpam-3075	56	35	y1	y1	PROPN
ejpam-3075	56	36	+	+	CCONJ
ejpam-3075	56	37	...	...	PUNCT
ejpam-3075	57	1	+	+	CCONJ
ejpam-3075	57	2	yn	yn	PRON
ejpam-3075	57	3	is	be	AUX
ejpam-3075	57	4	desired	desire	VERB
ejpam-3075	57	5	,	,	PUNCT
ejpam-3075	57	6	where	where	SCONJ
ejpam-3075	57	7	α′s	α′s	NUM
ejpam-3075	57	8	are	be	AUX
ejpam-3075	57	9	distinct	distinct	ADJ
ejpam-3075	57	10	real	real	ADJ
ejpam-3075	57	11	positive	positive	ADJ
ejpam-3075	57	12	constants	constant	NOUN
ejpam-3075	57	13	.	.	PUNCT
ejpam-3075	58	1	the	the	DET
ejpam-3075	58	2	moment	moment	NOUN
ejpam-3075	58	3	generating	generate	VERB
ejpam-3075	58	4	function	function	NOUN
ejpam-3075	58	5	ψ(θ	ψ(θ	NOUN
ejpam-3075	58	6	)	)	PUNCT
ejpam-3075	58	7	of	of	ADP
ejpam-3075	58	8	t	t	PROPN
ejpam-3075	58	9	is	be	AUX
ejpam-3075	58	10	,	,	PUNCT
ejpam-3075	58	11	ψ(θ	ψ(θ	PROPN
ejpam-3075	58	12	)	)	PUNCT
ejpam-3075	58	13	=	=	SYM
ejpam-3075	58	14	(	(	PUNCT
ejpam-3075	58	15	α1	α1	PROPN
ejpam-3075	58	16	−	−	PROPN
ejpam-3075	58	17	θ)−g1	θ)−g1	PROPN
ejpam-3075	58	18	...	...	PUNCT
ejpam-3075	58	19	(	(	PUNCT
ejpam-3075	58	20	αn	αn	NOUN
ejpam-3075	58	21	−	−	NOUN
ejpam-3075	58	22	θ)−gn	θ)−gn	X
ejpam-3075	59	1	=	=	SYM
ejpam-3075	59	2	(	(	PUNCT
ejpam-3075	59	3	α1	α1	PROPN
ejpam-3075	59	4	−	−	NOUN
ejpam-3075	59	5	θ)−g1((α1	θ)−g1((α1	NOUN
ejpam-3075	59	6	−	−	PROPN
ejpam-3075	59	7	θ)−	θ)−	PROPN
ejpam-3075	59	8	(	(	PUNCT
ejpam-3075	59	9	α1	α1	PROPN
ejpam-3075	59	10	−	−	PROPN
ejpam-3075	59	11	α2))−g2	α2))−g2	NOUN
ejpam-3075	59	12	...	...	PUNCT
ejpam-3075	59	13	(	(	PUNCT
ejpam-3075	59	14	(	(	PUNCT
ejpam-3075	59	15	α1	α1	PROPN
ejpam-3075	59	16	−	−	PROPN
ejpam-3075	59	17	θ)−	θ)−	PROPN
ejpam-3075	59	18	(	(	PUNCT
ejpam-3075	59	19	α1	α1	PROPN
ejpam-3075	59	20	−	−	PROPN
ejpam-3075	59	21	αn))−gn	αn))−gn	NOUN
ejpam-3075	59	22	=	=	SYM
ejpam-3075	59	23	(	(	PUNCT
ejpam-3075	59	24	α1	α1	PROPN
ejpam-3075	59	25	−	−	PROPN
ejpam-3075	59	26	θ)−(g1+	θ)−(g1+	ADV
ejpam-3075	59	27	...	...	PUNCT
ejpam-3075	59	28	+gn+r2+	+gn+r2+	PROPN
ejpam-3075	59	29	...	...	PUNCT
ejpam-3075	59	30	rn	rn	NOUN
ejpam-3075	59	31	)	)	PUNCT
ejpam-3075	59	32	∑∞	∑∞	NOUN
ejpam-3075	59	33	r2=0	r2=0	PROPN
ejpam-3075	59	34	...	...	PUNCT
ejpam-3075	59	35	∑∞	∑∞	NOUN
ejpam-3075	59	36	rn=0	rn=0	NUM
ejpam-3075	59	37	(	(	PUNCT
ejpam-3075	59	38	g2+r2−1	g2+r2−1	PROPN
ejpam-3075	59	39	r2	r2	PROPN
ejpam-3075	59	40	)	)	PUNCT
ejpam-3075	59	41	...	...	PUNCT
ejpam-3075	60	1	(	(	PUNCT
ejpam-3075	60	2	gn+rn−1	gn+rn−1	PROPN
ejpam-3075	60	3	rn	rn	PROPN
ejpam-3075	60	4	)	)	PUNCT
ejpam-3075	60	5	(	(	PUNCT
ejpam-3075	60	6	α1	α1	PROPN
ejpam-3075	60	7	−	−	PROPN
ejpam-3075	61	1	α2)r2	α2)r2	PROPN
ejpam-3075	62	1	...	...	PUNCT
ejpam-3075	63	1	(	(	PUNCT
ejpam-3075	63	2	α1	α1	PROPN
ejpam-3075	63	3	−	−	PROPN
ejpam-3075	63	4	αn)rn	αn)rn	NUM
ejpam-3075	63	5	,	,	PUNCT
ejpam-3075	63	6	(	(	PUNCT
ejpam-3075	63	7	17	17	NUM
ejpam-3075	63	8	)	)	PUNCT
ejpam-3075	63	9	where	where	SCONJ
ejpam-3075	63	10	α1	α1	PROPN
ejpam-3075	63	11	=	=	SYM
ejpam-3075	63	12	max{α1	max{α1	NOUN
ejpam-3075	63	13	,	,	PUNCT
ejpam-3075	63	14	...	...	PUNCT
ejpam-3075	63	15	,	,	PUNCT
ejpam-3075	63	16	αn	αn	NOUN
ejpam-3075	63	17	}	}	PUNCT
ejpam-3075	63	18	.	.	PUNCT
ejpam-3075	64	1	and	and	CCONJ
ejpam-3075	64	2	now	now	ADV
ejpam-3075	64	3	inverting	invert	VERB
ejpam-3075	64	4	(	(	PUNCT
ejpam-3075	64	5	17	17	NUM
ejpam-3075	64	6	)	)	PUNCT
ejpam-3075	64	7	we	we	PRON
ejpam-3075	64	8	have	have	VERB
ejpam-3075	64	9	that	that	DET
ejpam-3075	64	10	f(t	f(t	NOUN
ejpam-3075	64	11	)	)	PUNCT
ejpam-3075	65	1	=	=	SYM
ejpam-3075	65	2	(	(	PUNCT
ejpam-3075	65	3	γ(g1	γ(g1	NOUN
ejpam-3075	65	4	+	+	CCONJ
ejpam-3075	65	5	+	+	NUM
ejpam-3075	65	6	gn))−1πn	gn))−1πn	NOUN
ejpam-3075	65	7	i=1α	i=1α	PROPN
ejpam-3075	65	8	gj	gj	PROPN
ejpam-3075	65	9	j	j	PROPN
ejpam-3075	65	10	(	(	PUNCT
ejpam-3075	65	11	α1)g1+	α1)g1+	ADV
ejpam-3075	65	12	...	...	PUNCT
ejpam-3075	66	1	+gnexp{−α1t}t(g1+	+gnexp{−α1t}t(g1+	ADJ
ejpam-3075	66	2	...	...	PUNCT
ejpam-3075	66	3	+gn−1	+gn−1	ADJ
ejpam-3075	66	4	)	)	PUNCT
ejpam-3075	66	5	a.	a.	PROPN
ejpam-3075	66	6	k.	k.	PROPN
ejpam-3075	66	7	gupta	gupta	PROPN
ejpam-3075	66	8	,	,	PUNCT
ejpam-3075	66	9	d.	d.	PROPN
ejpam-3075	66	10	g.	g.	PROPN
ejpam-3075	66	11	kabe	kabe	PROPN
ejpam-3075	66	12	/	/	SYM
ejpam-3075	66	13	eur	eur	PROPN
ejpam-3075	66	14	.	.	PUNCT
ejpam-3075	67	1	j.	j.	PROPN
ejpam-3075	67	2	pure	pure	PROPN
ejpam-3075	67	3	appl	appl	PROPN
ejpam-3075	67	4	.	.	PROPN
ejpam-3075	67	5	math	math	PROPN
ejpam-3075	67	6	,	,	PUNCT
ejpam-3075	67	7	10	10	NUM
ejpam-3075	67	8	(	(	PUNCT
ejpam-3075	67	9	4	4	NUM
ejpam-3075	67	10	)	)	PUNCT
ejpam-3075	67	11	(	(	PUNCT
ejpam-3075	67	12	2017	2017	NUM
ejpam-3075	67	13	)	)	PUNCT
ejpam-3075	67	14	,	,	PUNCT
ejpam-3075	67	15	614	614	NUM
ejpam-3075	67	16	-	-	SYM
ejpam-3075	67	17	619	619	NUM
ejpam-3075	67	18	617	617	NUM
ejpam-3075	67	19	ϕ(g2	ϕ(g2	ADJ
ejpam-3075	67	20	,	,	PUNCT
ejpam-3075	67	21	...	...	PUNCT
ejpam-3075	67	22	,	,	PUNCT
ejpam-3075	67	23	gn	gn	PROPN
ejpam-3075	67	24	;	;	PUNCT
ejpam-3075	67	25	g1	g1	PROPN
ejpam-3075	67	26	+	+	CCONJ
ejpam-3075	67	27	...	...	PUNCT
ejpam-3075	68	1	+	+	CCONJ
ejpam-3075	69	1	gn	gn	ADJ
ejpam-3075	69	2	;	;	PUNCT
ejpam-3075	69	3	(	(	PUNCT
ejpam-3075	69	4	α1	α1	PROPN
ejpam-3075	69	5	−	−	PROPN
ejpam-3075	69	6	α2)t	α2)t	PROPN
ejpam-3075	69	7	,	,	PUNCT
ejpam-3075	69	8	...	...	PUNCT
ejpam-3075	69	9	,	,	PUNCT
ejpam-3075	69	10	(	(	PUNCT
ejpam-3075	69	11	α1	α1	PROPN
ejpam-3075	69	12	−	−	PROPN
ejpam-3075	69	13	αn)t	αn)t	PROPN
ejpam-3075	69	14	)	)	PUNCT
ejpam-3075	69	15	.	.	PUNCT
ejpam-3075	70	1	(	(	PUNCT
ejpam-3075	70	2	18	18	NUM
ejpam-3075	70	3	)	)	PUNCT
ejpam-3075	70	4	here	here	ADV
ejpam-3075	70	5	,	,	PUNCT
ejpam-3075	70	6	ϕ	ϕ	NOUN
ejpam-3075	70	7	=	=	SYM
ejpam-3075	70	8	∑∞	∑∞	NOUN
ejpam-3075	70	9	r2=0	r2=0	PROPN
ejpam-3075	70	10	...	...	PUNCT
ejpam-3075	70	11	∑∞	∑∞	NOUN
ejpam-3075	71	1	rn=0	rn=0	NUM
ejpam-3075	71	2	γ(g2+r2)	γ(g2+r2)	NOUN
ejpam-3075	71	3	...	...	PUNCT
ejpam-3075	72	1	γ(gn+rn)(α1−α2)r2	γ(gn+rn)(α1−α2)r2	NOUN
ejpam-3075	72	2	(	(	PUNCT
ejpam-3075	72	3	α1−αn)rn	α1−αn)rn	NOUN
ejpam-3075	72	4	γ(g1+	γ(g1+	NOUN
ejpam-3075	72	5	...	...	PUNCT
ejpam-3075	72	6	+gn+r2+	+gn+r2+	NOUN
ejpam-3075	72	7	...	...	PUNCT
ejpam-3075	72	8	+rn)r2!	+rn)r2!	NOUN
ejpam-3075	72	9	...	...	PUNCT
ejpam-3075	72	10	rn	rn	X
ejpam-3075	72	11	!	!	PUNCT
ejpam-3075	73	1	=	=	SYM
ejpam-3075	73	2	1	1	NUM
ejpam-3075	73	3	f1(g2	f1(g2	NOUN
ejpam-3075	73	4	+	+	NOUN
ejpam-3075	73	5	...	...	PUNCT
ejpam-3075	74	1	+	+	CCONJ
ejpam-3075	74	2	gn	gn	ADJ
ejpam-3075	74	3	;	;	PUNCT
ejpam-3075	74	4	g1	g1	PROPN
ejpam-3075	74	5	+	+	CCONJ
ejpam-3075	74	6	...	...	PUNCT
ejpam-3075	75	1	+	+	CCONJ
ejpam-3075	75	2	gn	gn	ADJ
ejpam-3075	75	3	;	;	PUNCT
ejpam-3075	75	4	(	(	PUNCT
ejpam-3075	75	5	(	(	PUNCT
ejpam-3075	75	6	n−	n−	NOUN
ejpam-3075	75	7	1)α1	1)α1	NOUN
ejpam-3075	75	8	−	−	ADV
ejpam-3075	75	9	α2	α2	ADJ
ejpam-3075	75	10	−	−	PROPN
ejpam-3075	75	11	...	...	PUNCT
ejpam-3075	75	12	−	−	PROPN
ejpam-3075	75	13	αn)t	αn)t	PROPN
ejpam-3075	75	14	)	)	PUNCT
ejpam-3075	75	15	.	.	PUNCT
ejpam-3075	76	1	(	(	PUNCT
ejpam-3075	76	2	19	19	NUM
ejpam-3075	76	3	)	)	PUNCT
ejpam-3075	76	4	to	to	PART
ejpam-3075	76	5	prove	prove	VERB
ejpam-3075	76	6	(	(	PUNCT
ejpam-3075	76	7	19	19	NUM
ejpam-3075	76	8	)	)	PUNCT
ejpam-3075	76	9	we	we	PRON
ejpam-3075	76	10	proceed	proceed	VERB
ejpam-3075	76	11	as	as	SCONJ
ejpam-3075	76	12	follows	follow	VERB
ejpam-3075	76	13	.	.	PUNCT
ejpam-3075	77	1	the	the	DET
ejpam-3075	77	2	sum	sum	NOUN
ejpam-3075	77	3	of	of	ADP
ejpam-3075	77	4	the	the	DET
ejpam-3075	77	5	two	two	NUM
ejpam-3075	77	6	noncentral	noncentral	ADJ
ejpam-3075	77	7	p×p	p×p	PROPN
ejpam-3075	77	8	wishart	wishart	PROPN
ejpam-3075	77	9	matrices	matrice	VERB
ejpam-3075	77	10	a	a	PRON
ejpam-3075	77	11	and	and	CCONJ
ejpam-3075	77	12	b	b	NOUN
ejpam-3075	77	13	,	,	PUNCT
ejpam-3075	77	14	with	with	ADP
ejpam-3075	77	15	n	n	NOUN
ejpam-3075	77	16	and	and	CCONJ
ejpam-3075	77	17	q	q	ADJ
ejpam-3075	77	18	df	df	PROPN
ejpam-3075	77	19	,	,	PUNCT
ejpam-3075	77	20	and	and	CCONJ
ejpam-3075	77	21	noncentrality	noncentrality	NOUN
ejpam-3075	77	22	parameters	parameter	NOUN
ejpam-3075	77	23	∆	∆	PROPN
ejpam-3075	77	24	and	and	CCONJ
ejpam-3075	77	25	ω	ω	NUM
ejpam-3075	77	26	,	,	PUNCT
ejpam-3075	77	27	is	be	AUX
ejpam-3075	77	28	again	again	ADV
ejpam-3075	77	29	noncentral	noncentral	ADJ
ejpam-3075	77	30	wishart	wishart	NOUN
ejpam-3075	77	31	with	with	ADP
ejpam-3075	77	32	(	(	PUNCT
ejpam-3075	77	33	n+q)df	n+q)df	VERB
ejpam-3075	77	34	,	,	PUNCT
ejpam-3075	77	35	and	and	CCONJ
ejpam-3075	77	36	(	(	PUNCT
ejpam-3075	77	37	∆+ω	∆+ω	NUM
ejpam-3075	77	38	)	)	PUNCT
ejpam-3075	77	39	as	as	ADP
ejpam-3075	77	40	noncentrality	noncentrality	NOUN
ejpam-3075	77	41	parameter	parameter	NOUN
ejpam-3075	77	42	.	.	PUNCT
ejpam-3075	78	1	with	with	ADP
ejpam-3075	78	2	2g=(p+1	2g=(p+1	NUM
ejpam-3075	78	3	)	)	PUNCT
ejpam-3075	78	4	,	,	PUNCT
ejpam-3075	78	5	we	we	PRON
ejpam-3075	78	6	write	write	VERB
ejpam-3075	78	7	this	this	DET
ejpam-3075	78	8	result	result	NOUN
ejpam-3075	78	9	as	as	ADP
ejpam-3075	78	10	k	k	PROPN
ejpam-3075	78	11	∫	∫	PROPN
ejpam-3075	78	12	exp{−tr(a+b)}|a|n−g|b|q−g	exp{−tr(a+b)}|a|n−g|b|q−g	PROPN
ejpam-3075	78	13	0f1(n	0f1(n	PRON
ejpam-3075	78	14	;	;	PUNCT
ejpam-3075	78	15	∆a)0f1(q	∆a)0f1(q	NUM
ejpam-3075	78	16	;	;	PUNCT
ejpam-3075	78	17	ωb)da	ωb)da	NUM
ejpam-3075	78	18	db	db	X
ejpam-3075	78	19	=	=	SYM
ejpam-3075	78	20	exp{−trd}|d|n−g	exp{−trd}|d|n−g	PROPN
ejpam-3075	78	21	0f1(n+	0f1(n+	NOUN
ejpam-3075	78	22	q	q	X
ejpam-3075	78	23	;	;	PUNCT
ejpam-3075	78	24	(	(	PUNCT
ejpam-3075	78	25	∆	∆	X
ejpam-3075	78	26	+	+	CCONJ
ejpam-3075	78	27	ω)d	ω)d	NUM
ejpam-3075	78	28	)	)	PUNCT
ejpam-3075	78	29	,	,	PUNCT
ejpam-3075	78	30	(	(	PUNCT
ejpam-3075	78	31	20	20	NUM
ejpam-3075	78	32	)	)	PUNCT
ejpam-3075	78	33	0f1(n	0f1(n	PROPN
ejpam-3075	78	34	;	;	PUNCT
ejpam-3075	78	35	∆a)0f1(q	∆a)0f1(q	NUM
ejpam-3075	78	36	;	;	PUNCT
ejpam-3075	78	37	ωb	ωb	X
ejpam-3075	78	38	)	)	PUNCT
ejpam-3075	78	39	=	=	SYM
ejpam-3075	78	40	0	0	NUM
ejpam-3075	78	41	f1(n+	f1(n+	PROPN
ejpam-3075	78	42	q	q	PROPN
ejpam-3075	78	43	;	;	PUNCT
ejpam-3075	78	44	(	(	PUNCT
ejpam-3075	78	45	∆	∆	X
ejpam-3075	78	46	+	+	NUM
ejpam-3075	78	47	ω)(a+b	ω)(a+b	NUM
ejpam-3075	78	48	)	)	PUNCT
ejpam-3075	78	49	)	)	PUNCT
ejpam-3075	78	50	.	.	PUNCT
ejpam-3075	79	1	(	(	PUNCT
ejpam-3075	79	2	21	21	NUM
ejpam-3075	79	3	)	)	PUNCT
ejpam-3075	79	4	now	now	ADV
ejpam-3075	79	5	mathai	mathai	PROPN
ejpam-3075	80	1	[	[	X
ejpam-3075	80	2	8	8	NUM
ejpam-3075	80	3	,	,	PUNCT
ejpam-3075	80	4	p.	p.	NOUN
ejpam-3075	80	5	339	339	NUM
ejpam-3075	80	6	,	,	PUNCT
ejpam-3075	80	7	theorem	theorem	VERB
ejpam-3075	80	8	5.5	5.5	NUM
ejpam-3075	80	9	]	]	PUNCT
ejpam-3075	80	10	defines	define	NOUN
ejpam-3075	80	11	ϕ(b1	ϕ(b1	NOUN
ejpam-3075	80	12	,	,	PUNCT
ejpam-3075	80	13	b2	b2	NOUN
ejpam-3075	80	14	;	;	PUNCT
ejpam-3075	80	15	c;x1	c;x1	NOUN
ejpam-3075	80	16	,	,	PUNCT
ejpam-3075	80	17	x2	x2	PROPN
ejpam-3075	80	18	)	)	PUNCT
ejpam-3075	80	19	=	=	SYM
ejpam-3075	81	1	∫	∫	PROPN
ejpam-3075	81	2	|u1|d1−g|u2|d2−g|i	|u1|d1−g|u2|d2−g|i	NOUN
ejpam-3075	81	3	−	−	PROPN
ejpam-3075	81	4	u1	u1	NOUN
ejpam-3075	81	5	−	−	PROPN
ejpam-3075	81	6	u2|c−d1−d2−g	u2|c−d1−d2−g	PROPN
ejpam-3075	81	7	1f1(b1	1f1(b1	NOUN
ejpam-3075	81	8	;	;	PUNCT
ejpam-3075	81	9	d1;x1u1	d1;x1u1	NOUN
ejpam-3075	81	10	)	)	PUNCT
ejpam-3075	81	11	1f1(b2	1f1(b2	NUM
ejpam-3075	81	12	;	;	PUNCT
ejpam-3075	81	13	d2;x2u2)du1du2	d2;x2u2)du1du2	PROPN
ejpam-3075	81	14	=	=	SYM
ejpam-3075	81	15	∫	∫	PROPN
ejpam-3075	81	16	|u1|d1−g|u2|d2−g|i	|u1|d1−g|u2|d2−g|i	NOUN
ejpam-3075	81	17	−	−	NOUN
ejpam-3075	81	18	u1	u1	NOUN
ejpam-3075	81	19	−	−	PROPN
ejpam-3075	81	20	u2|c−d1−d2−gexp{−tr(z1	u2|c−d1−d2−gexp{−tr(z1	PROPN
ejpam-3075	81	21	+	+	CCONJ
ejpam-3075	81	22	z2	z2	NOUN
ejpam-3075	81	23	)	)	PUNCT
ejpam-3075	81	24	}	}	PUNCT
ejpam-3075	81	25	|z1|b1−g|z2|b2−g	|z1|b1−g|z2|b2−g	VERB
ejpam-3075	81	26	0f1(d1;x1u1z1)0f1(d2;x2u2z2)dz1dz2du1du2	0f1(d1;x1u1z1)0f1(d2;x2u2z2)dz1dz2du1du2	ADJ
ejpam-3075	81	27	=	=	SYM
ejpam-3075	81	28	∫	∫	PROPN
ejpam-3075	81	29	|u1|d1−g|u2|d2−g|i	|u1|d1−g|u2|d2−g|i	NOUN
ejpam-3075	81	30	−	−	NOUN
ejpam-3075	81	31	u1	u1	NOUN
ejpam-3075	81	32	−	−	PROPN
ejpam-3075	81	33	u2|c−d1−d2−gexp{−tr(z1	u2|c−d1−d2−gexp{−tr(z1	PROPN
ejpam-3075	81	34	+	+	CCONJ
ejpam-3075	81	35	z2	z2	NOUN
ejpam-3075	81	36	)	)	PUNCT
ejpam-3075	81	37	}	}	PUNCT
ejpam-3075	81	38	|z1|b1−g|z2|b2−g	|z1|b1−g|z2|b2−g	VERB
ejpam-3075	81	39	0f1(d1	0f1(d1	NOUN
ejpam-3075	82	1	+	+	CCONJ
ejpam-3075	82	2	d2	d2	PROPN
ejpam-3075	82	3	;	;	PUNCT
ejpam-3075	82	4	(	(	PUNCT
ejpam-3075	82	5	x1	x1	PROPN
ejpam-3075	82	6	+	+	NOUN
ejpam-3075	82	7	x2)(u1	x2)(u1	X
ejpam-3075	82	8	+	+	CCONJ
ejpam-3075	82	9	u2)(z1	u2)(z1	NOUN
ejpam-3075	82	10	+	+	X
ejpam-3075	82	11	z2))dz1dz2du1du2	z2))dz1dz2du1du2	PUNCT
ejpam-3075	82	12	=	=	SYM
ejpam-3075	82	13	∫	∫	PROPN
ejpam-3075	82	14	|u1|d1−g|u2|d2−g|i	|u1|d1−g|u2|d2−g|i	NOUN
ejpam-3075	82	15	−	−	PROPN
ejpam-3075	82	16	u1	u1	NOUN
ejpam-3075	82	17	−	−	PROPN
ejpam-3075	82	18	u2|c−d1−d2−g	u2|c−d1−d2−g	NOUN
ejpam-3075	82	19	1f1(b1	1f1(b1	NUM
ejpam-3075	82	20	+	+	CCONJ
ejpam-3075	82	21	b2	b2	NOUN
ejpam-3075	82	22	;	;	PUNCT
ejpam-3075	82	23	d1	d1	PROPN
ejpam-3075	82	24	+	+	CCONJ
ejpam-3075	82	25	d2	d2	PROPN
ejpam-3075	82	26	;	;	PUNCT
ejpam-3075	82	27	(	(	PUNCT
ejpam-3075	82	28	x1	x1	PROPN
ejpam-3075	82	29	+	+	NOUN
ejpam-3075	82	30	x2)(u1	x2)(u1	X
ejpam-3075	82	31	+	+	CCONJ
ejpam-3075	82	32	u2))du1du2	u2))du1du2	NOUN
ejpam-3075	82	33	=	=	SYM
ejpam-3075	82	34	k2f2(d1	k2f2(d1	X
ejpam-3075	83	1	+	+	CCONJ
ejpam-3075	83	2	d2	d2	NOUN
ejpam-3075	83	3	;	;	PUNCT
ejpam-3075	83	4	b1	b1	NOUN
ejpam-3075	83	5	+	+	CCONJ
ejpam-3075	83	6	b2	b2	NOUN
ejpam-3075	83	7	;	;	PUNCT
ejpam-3075	83	8	d1	d1	PROPN
ejpam-3075	83	9	+	+	CCONJ
ejpam-3075	83	10	d2	d2	PROPN
ejpam-3075	83	11	;	;	PUNCT
ejpam-3075	83	12	c;x1	c;x1	PROPN
ejpam-3075	83	13	+	+	PROPN
ejpam-3075	83	14	x2	x2	ADJ
ejpam-3075	83	15	)	)	PUNCT
ejpam-3075	83	16	=	=	SYM
ejpam-3075	83	17	k1	k1	PROPN
ejpam-3075	83	18	1f1(b1	1f1(b1	NUM
ejpam-3075	83	19	+	+	CCONJ
ejpam-3075	83	20	b2	b2	NOUN
ejpam-3075	83	21	;	;	PUNCT
ejpam-3075	83	22	c;x1	c;x1	PROPN
ejpam-3075	83	23	+	+	PROPN
ejpam-3075	83	24	x2	x2	PROPN
ejpam-3075	83	25	)	)	PUNCT
ejpam-3075	83	26	,	,	PUNCT
ejpam-3075	83	27	(	(	PUNCT
ejpam-3075	83	28	22	22	NUM
ejpam-3075	83	29	)	)	PUNCT
ejpam-3075	83	30	and	and	CCONJ
ejpam-3075	83	31	hence	hence	ADV
ejpam-3075	83	32	(	(	PUNCT
ejpam-3075	83	33	15	15	NUM
ejpam-3075	83	34	)	)	PUNCT
ejpam-3075	83	35	and	and	CCONJ
ejpam-3075	83	36	(	(	PUNCT
ejpam-3075	83	37	19	19	NUM
ejpam-3075	83	38	)	)	PUNCT
ejpam-3075	83	39	follow	follow	NOUN
ejpam-3075	83	40	.	.	PUNCT
ejpam-3075	84	1	all	all	DET
ejpam-3075	84	2	matrices	matrix	NOUN
ejpam-3075	84	3	in	in	ADP
ejpam-3075	84	4	(	(	PUNCT
ejpam-3075	84	5	22	22	NUM
ejpam-3075	84	6	)	)	PUNCT
ejpam-3075	84	7	are	be	AUX
ejpam-3075	84	8	p×	p×	NOUN
ejpam-3075	84	9	p	p	X
ejpam-3075	84	10	positive	positive	ADJ
ejpam-3075	84	11	definite	definite	ADJ
ejpam-3075	84	12	matrices	matrix	NOUN
ejpam-3075	84	13	.	.	PUNCT
ejpam-3075	85	1	3	3	X
ejpam-3075	85	2	.	.	X
ejpam-3075	85	3	gqfmbd	gqfmbd	VERB
ejpam-3075	85	4	the	the	DET
ejpam-3075	85	5	gqfmbd	gqfmbd	NOUN
ejpam-3075	85	6	of	of	ADP
ejpam-3075	85	7	the	the	DET
ejpam-3075	85	8	p×	p×	PROPN
ejpam-3075	85	9	p	p	NOUN
ejpam-3075	85	10	matrix	matrix	NOUN
ejpam-3075	85	11	m	m	AUX
ejpam-3075	85	12	defined	define	VERB
ejpam-3075	85	13	by	by	ADP
ejpam-3075	85	14	the	the	DET
ejpam-3075	85	15	integral	integral	ADJ
ejpam-3075	85	16	f(m	f(m	PROPN
ejpam-3075	85	17	)	)	PUNCT
ejpam-3075	85	18	=	=	SYM
ejpam-3075	86	1	∫	∫	PROPN
ejpam-3075	86	2	r	r	NOUN
ejpam-3075	86	3	g(t1)g(t2)dt1dt2	g(t1)g(t2)dt1dt2	PROPN
ejpam-3075	86	4	,	,	PUNCT
ejpam-3075	86	5	(	(	PUNCT
ejpam-3075	86	6	23	23	NUM
ejpam-3075	86	7	)	)	PUNCT
ejpam-3075	86	8	a.	a.	NOUN
ejpam-3075	86	9	k.	k.	PROPN
ejpam-3075	86	10	gupta	gupta	PROPN
ejpam-3075	86	11	,	,	PUNCT
ejpam-3075	86	12	d.	d.	PROPN
ejpam-3075	86	13	g.	g.	PROPN
ejpam-3075	86	14	kabe	kabe	PROPN
ejpam-3075	86	15	/	/	SYM
ejpam-3075	86	16	eur	eur	PROPN
ejpam-3075	86	17	.	.	PUNCT
ejpam-3075	87	1	j.	j.	PROPN
ejpam-3075	87	2	pure	pure	PROPN
ejpam-3075	87	3	appl	appl	PROPN
ejpam-3075	87	4	.	.	PROPN
ejpam-3075	87	5	math	math	PROPN
ejpam-3075	87	6	,	,	PUNCT
ejpam-3075	87	7	10	10	NUM
ejpam-3075	87	8	(	(	PUNCT
ejpam-3075	87	9	4	4	NUM
ejpam-3075	87	10	)	)	PUNCT
ejpam-3075	87	11	(	(	PUNCT
ejpam-3075	87	12	2017	2017	NUM
ejpam-3075	87	13	)	)	PUNCT
ejpam-3075	87	14	,	,	PUNCT
ejpam-3075	87	15	614	614	NUM
ejpam-3075	87	16	-	-	SYM
ejpam-3075	87	17	619	619	NUM
ejpam-3075	87	18	618	618	NUM
ejpam-3075	87	19	wherer	wherer	NOUN
ejpam-3075	87	20	=	=	SYM
ejpam-3075	87	21	(	(	PUNCT
ejpam-3075	87	22	t1	t1	NOUN
ejpam-3075	87	23	+	+	NUM
ejpam-3075	87	24	t2	t2	NOUN
ejpam-3075	87	25	)	)	PUNCT
ejpam-3075	87	26	1	1	NUM
ejpam-3075	87	27	2m(t1	2m(t1	NUM
ejpam-3075	87	28	+	+	CCONJ
ejpam-3075	87	29	t2	t2	NOUN
ejpam-3075	87	30	)	)	PUNCT
ejpam-3075	87	31	1	1	NUM
ejpam-3075	87	32	2	2	NUM
ejpam-3075	87	33	=	=	SYM
ejpam-3075	87	34	t1	t1	NOUN
ejpam-3075	87	35	.	.	PUNCT
ejpam-3075	88	1	the	the	DET
ejpam-3075	88	2	joint	joint	ADJ
ejpam-3075	88	3	density	density	NOUN
ejpam-3075	88	4	of	of	ADP
ejpam-3075	88	5	p×	p×	PROPN
ejpam-3075	88	6	p	p	NOUN
ejpam-3075	88	7	t1	t1	NOUN
ejpam-3075	88	8	and	and	CCONJ
ejpam-3075	88	9	t2	t2	NOUN
ejpam-3075	88	10	is	be	AUX
ejpam-3075	88	11	f(t1	f(t1	NOUN
ejpam-3075	88	12	,	,	PUNCT
ejpam-3075	88	13	t2	t2	NOUN
ejpam-3075	88	14	)	)	PUNCT
ejpam-3075	88	15	=	=	SYM
ejpam-3075	89	1	|∆|p(δ1)pnexp{−δ1tr(t1	|∆|p(δ1)pnexp{−δ1tr(t1	NOUN
ejpam-3075	90	1	+	+	CCONJ
ejpam-3075	90	2	t2)}|t1|	t2)}|t1|	NOUN
ejpam-3075	90	3	1	1	NUM
ejpam-3075	90	4	2	2	NUM
ejpam-3075	90	5	(	(	PUNCT
ejpam-3075	90	6	n−p−1)|t2|	n−p−1)|t2|	NOUN
ejpam-3075	90	7	1	1	NUM
ejpam-3075	90	8	2	2	NUM
ejpam-3075	90	9	(	(	PUNCT
ejpam-3075	90	10	q−p−1	q−p−1	NOUN
ejpam-3075	90	11	)	)	PUNCT
ejpam-3075	90	12	1f1	1f1	NUM
ejpam-3075	90	13	(	(	PUNCT
ejpam-3075	90	14	1	1	NUM
ejpam-3075	90	15	2	2	NUM
ejpam-3075	90	16	(	(	PUNCT
ejpam-3075	90	17	n−	n−	NOUN
ejpam-3075	90	18	1	1	NUM
ejpam-3075	90	19	)	)	PUNCT
ejpam-3075	90	20	;	;	PUNCT
ejpam-3075	90	21	1	1	NUM
ejpam-3075	90	22	2	2	NUM
ejpam-3075	90	23	n	n	NUM
ejpam-3075	90	24	;	;	PUNCT
ejpam-3075	90	25	δt1)1f1	δt1)1f1	X
ejpam-3075	90	26	(	(	PUNCT
ejpam-3075	90	27	1	1	NUM
ejpam-3075	90	28	2	2	NUM
ejpam-3075	90	29	(	(	PUNCT
ejpam-3075	90	30	q	q	NOUN
ejpam-3075	90	31	−	−	PROPN
ejpam-3075	90	32	1	1	NUM
ejpam-3075	90	33	)	)	PUNCT
ejpam-3075	90	34	;	;	PUNCT
ejpam-3075	90	35	1	1	NUM
ejpam-3075	90	36	2	2	NUM
ejpam-3075	90	37	q	q	NOUN
ejpam-3075	90	38	;	;	PUNCT
ejpam-3075	90	39	δt2	δt2	PROPN
ejpam-3075	90	40	)	)	PUNCT
ejpam-3075	90	41	.	.	PUNCT
ejpam-3075	91	1	(	(	PUNCT
ejpam-3075	91	2	24	24	NUM
ejpam-3075	91	3	)	)	PUNCT
ejpam-3075	91	4	note	note	NOUN
ejpam-3075	91	5	that	that	SCONJ
ejpam-3075	91	6	the	the	DET
ejpam-3075	91	7	matrix	matrix	NOUN
ejpam-3075	91	8	m	m	AUX
ejpam-3075	91	9	has	have	VERB
ejpam-3075	91	10	a	a	DET
ejpam-3075	91	11	doubly	doubly	ADV
ejpam-3075	91	12	noncentral	noncentral	ADJ
ejpam-3075	91	13	multivariate	multivariate	NOUN
ejpam-3075	91	14	beta	beta	NOUN
ejpam-3075	91	15	density	density	NOUN
ejpam-3075	91	16	derived	derive	VERB
ejpam-3075	91	17	by	by	ADP
ejpam-3075	91	18	gupta	gupta	NOUN
ejpam-3075	91	19	and	and	CCONJ
ejpam-3075	91	20	kabe	kabe	NOUN
ejpam-3075	92	1	[	[	X
ejpam-3075	92	2	3	3	X
ejpam-3075	92	3	]	]	PUNCT
ejpam-3075	92	4	as	as	SCONJ
ejpam-3075	92	5	follows	follow	VERB
ejpam-3075	92	6	.	.	PUNCT
ejpam-3075	93	1	f(t1	f(t1	NOUN
ejpam-3075	93	2	,	,	PUNCT
ejpam-3075	93	3	t2	t2	NOUN
ejpam-3075	93	4	)	)	PUNCT
ejpam-3075	93	5	=	=	PUNCT
ejpam-3075	94	1	k	k	X
ejpam-3075	95	1	exp{−δ1tr(t1	exp{−δ1tr(t1	INTJ
ejpam-3075	96	1	+	+	CCONJ
ejpam-3075	96	2	t2)}|t1|	t2)}|t1|	NOUN
ejpam-3075	96	3	1	1	NUM
ejpam-3075	96	4	2	2	NUM
ejpam-3075	96	5	(	(	PUNCT
ejpam-3075	96	6	n−p−1)|t2|	n−p−1)|t2|	NOUN
ejpam-3075	96	7	1	1	NUM
ejpam-3075	96	8	2	2	NUM
ejpam-3075	96	9	(	(	PUNCT
ejpam-3075	96	10	q−p−1)∫	q−p−1)∫	NOUN
ejpam-3075	96	11	exp{−tr(z1	exp{−tr(z1	NOUN
ejpam-3075	96	12	+	+	CCONJ
ejpam-3075	96	13	z2)}|z1|	z2)}|z1|	X
ejpam-3075	96	14	1	1	NUM
ejpam-3075	96	15	2	2	NUM
ejpam-3075	96	16	(	(	PUNCT
ejpam-3075	96	17	n−1)−g|z2|	n−1)−g|z2|	PROPN
ejpam-3075	96	18	1	1	NUM
ejpam-3075	96	19	2	2	NUM
ejpam-3075	96	20	(	(	PUNCT
ejpam-3075	96	21	q−1)−g	q−1)−g	NOUN
ejpam-3075	96	22	0f1	0f1	NUM
ejpam-3075	96	23	(	(	PUNCT
ejpam-3075	96	24	1	1	NUM
ejpam-3075	96	25	2	2	NUM
ejpam-3075	96	26	n	n	NUM
ejpam-3075	96	27	;	;	PUNCT
ejpam-3075	96	28	δt1	δt1	NOUN
ejpam-3075	96	29	,	,	PUNCT
ejpam-3075	96	30	z1	z1	NOUN
ejpam-3075	96	31	)	)	PUNCT
ejpam-3075	96	32	0f1	0f1	NUM
ejpam-3075	96	33	(	(	PUNCT
ejpam-3075	96	34	1	1	NUM
ejpam-3075	96	35	2	2	NUM
ejpam-3075	96	36	q	q	NOUN
ejpam-3075	96	37	;	;	PUNCT
ejpam-3075	96	38	δt2)dz1dz2	δt2)dz1dz2	ADJ
ejpam-3075	96	39	,	,	PUNCT
ejpam-3075	96	40	(	(	PUNCT
ejpam-3075	96	41	25	25	NUM
ejpam-3075	96	42	)	)	PUNCT
ejpam-3075	96	43	and	and	CCONJ
ejpam-3075	96	44	hence	hence	ADV
ejpam-3075	96	45	the	the	DET
ejpam-3075	96	46	doubly	doubly	ADV
ejpam-3075	96	47	noncentral	noncentral	ADJ
ejpam-3075	96	48	multivariate	multivariate	NOUN
ejpam-3075	96	49	beta	beta	NOUN
ejpam-3075	96	50	density	density	NOUN
ejpam-3075	96	51	of	of	ADP
ejpam-3075	96	52	m	m	PROPN
ejpam-3075	96	53	is	be	AUX
ejpam-3075	96	54	f(m	f(m	PROPN
ejpam-3075	96	55	)	)	PUNCT
ejpam-3075	97	1	=	=	PUNCT
ejpam-3075	98	1	k	k	X
ejpam-3075	98	2	exp{−tr(t1	exp{−tr(t1	PROPN
ejpam-3075	98	3	+	+	CCONJ
ejpam-3075	98	4	t2)}|z1|	t2)}|z1|	NOUN
ejpam-3075	98	5	1	1	NUM
ejpam-3075	98	6	2	2	NUM
ejpam-3075	98	7	(	(	PUNCT
ejpam-3075	98	8	n−1)−g|z2|	n−1)−g|z2|	PROPN
ejpam-3075	98	9	1	1	NUM
ejpam-3075	98	10	2	2	NUM
ejpam-3075	98	11	(	(	PUNCT
ejpam-3075	98	12	q−1)−g|m	q−1)−g|m	NOUN
ejpam-3075	98	13	|	|	ADV
ejpam-3075	98	14	1	1	NUM
ejpam-3075	98	15	2	2	NUM
ejpam-3075	98	16	(	(	PUNCT
ejpam-3075	98	17	n−p−1	n−p−1	NOUN
ejpam-3075	98	18	)	)	PUNCT
ejpam-3075	98	19	|i	|i	VERB
ejpam-3075	98	20	−m	−m	NOUN
ejpam-3075	98	21	|	|	CCONJ
ejpam-3075	98	22	1	1	NUM
ejpam-3075	98	23	2	2	NUM
ejpam-3075	98	24	(	(	PUNCT
ejpam-3075	98	25	q−p−1	q−p−1	NOUN
ejpam-3075	98	26	)	)	PUNCT
ejpam-3075	98	27	1f1(1	1f1(1	NUM
ejpam-3075	98	28	2(n+	2(n+	NOUN
ejpam-3075	98	29	q	q	NOUN
ejpam-3075	98	30	)	)	PUNCT
ejpam-3075	98	31	;	;	PUNCT
ejpam-3075	98	32	1	1	NUM
ejpam-3075	98	33	2n	2n	NUM
ejpam-3075	98	34	;	;	PUNCT
ejpam-3075	98	35	δm(z1	δm(z1	X
ejpam-3075	98	36	+	+	CCONJ
ejpam-3075	98	37	z2)dz1dz2	z2)dz1dz2	NOUN
ejpam-3075	98	38	=	=	SYM
ejpam-3075	98	39	|∆|p(δ1	|∆|p(δ1	PROPN
ejpam-3075	98	40	)	)	PUNCT
ejpam-3075	98	41	1	1	NUM
ejpam-3075	98	42	2	2	NUM
ejpam-3075	98	43	(	(	PUNCT
ejpam-3075	98	44	n+q−2)|m	n+q−2)|m	PROPN
ejpam-3075	98	45	|	|	ADV
ejpam-3075	98	46	1	1	NUM
ejpam-3075	98	47	2	2	NUM
ejpam-3075	98	48	(	(	PUNCT
ejpam-3075	98	49	n−p−1)|i	n−p−1)|i	NOUN
ejpam-3075	98	50	−m	−m	NOUN
ejpam-3075	98	51	|	|	CCONJ
ejpam-3075	98	52	1	1	NUM
ejpam-3075	98	53	2	2	NUM
ejpam-3075	98	54	(	(	PUNCT
ejpam-3075	98	55	q−p−1){bp(1	q−p−1){bp(1	NUM
ejpam-3075	98	56	2n	2n	NUM
ejpam-3075	98	57	;	;	PUNCT
ejpam-3075	98	58	1	1	NUM
ejpam-3075	98	59	2q	2q	NUM
ejpam-3075	98	60	)	)	PUNCT
ejpam-3075	98	61	}	}	PUNCT
ejpam-3075	98	62	−1	−1	NOUN
ejpam-3075	98	63	2f1	2f1	NUM
ejpam-3075	98	64	(	(	PUNCT
ejpam-3075	98	65	1	1	NUM
ejpam-3075	98	66	2	2	NUM
ejpam-3075	98	67	(	(	PUNCT
ejpam-3075	98	68	n+	n+	ADP
ejpam-3075	98	69	q	q	NOUN
ejpam-3075	98	70	−	−	PROPN
ejpam-3075	98	71	2	2	NUM
ejpam-3075	98	72	)	)	PUNCT
ejpam-3075	98	73	;	;	PUNCT
ejpam-3075	98	74	1	1	NUM
ejpam-3075	98	75	2	2	NUM
ejpam-3075	98	76	(	(	PUNCT
ejpam-3075	98	77	n+	n+	NOUN
ejpam-3075	98	78	q	q	NOUN
ejpam-3075	98	79	)	)	PUNCT
ejpam-3075	98	80	;	;	PUNCT
ejpam-3075	98	81	1	1	NUM
ejpam-3075	98	82	2	2	NUM
ejpam-3075	98	83	n	n	NUM
ejpam-3075	98	84	;	;	PUNCT
ejpam-3075	98	85	δδ−p1	δδ−p1	ADJ
ejpam-3075	98	86	m	m	PROPN
ejpam-3075	98	87	)	)	PUNCT
ejpam-3075	98	88	.	.	PUNCT
ejpam-3075	99	1	(	(	PUNCT
ejpam-3075	99	2	26	26	NUM
ejpam-3075	99	3	)	)	PUNCT
ejpam-3075	99	4	we	we	PRON
ejpam-3075	99	5	now	now	ADV
ejpam-3075	99	6	proceed	proceed	VERB
ejpam-3075	99	7	to	to	PART
ejpam-3075	99	8	write	write	VERB
ejpam-3075	99	9	the	the	DET
ejpam-3075	99	10	hc	hc	PROPN
ejpam-3075	99	11	counterparts	counterpart	NOUN
ejpam-3075	99	12	of	of	ADP
ejpam-3075	99	13	(	(	PUNCT
ejpam-3075	99	14	15	15	NUM
ejpam-3075	99	15	)	)	PUNCT
ejpam-3075	99	16	and	and	CCONJ
ejpam-3075	99	17	(	(	PUNCT
ejpam-3075	99	18	25	25	NUM
ejpam-3075	99	19	)	)	PUNCT
ejpam-3075	99	20	,	,	PUNCT
ejpam-3075	99	21	with	with	ADP
ejpam-3075	99	22	δ	δ	PROPN
ejpam-3075	99	23	=	=	SYM
ejpam-3075	99	24	(	(	PUNCT
ejpam-3075	99	25	(	(	PUNCT
ejpam-3075	99	26	n−	n−	NOUN
ejpam-3075	99	27	1)δ1−	1)δ1−	NOUN
ejpam-3075	99	28	δ2−	δ2−	NOUN
ejpam-3075	99	29	−	−	NOUN
ejpam-3075	99	30	δn	δn	NOUN
ejpam-3075	99	31	)	)	PUNCT
ejpam-3075	99	32	.	.	PUNCT
ejpam-3075	100	1	4	4	X
ejpam-3075	100	2	.	.	X
ejpam-3075	100	3	hcgfwd	hcgfwd	ADP
ejpam-3075	100	4	the	the	DET
ejpam-3075	100	5	hcgfwd	hcgfwd	PROPN
ejpam-3075	100	6	of	of	ADP
ejpam-3075	100	7	(	(	PUNCT
ejpam-3075	100	8	15	15	NUM
ejpam-3075	100	9	)	)	PUNCT
ejpam-3075	100	10	is	be	AUX
ejpam-3075	100	11	f(t	f(t	NOUN
ejpam-3075	100	12	)	)	PUNCT
ejpam-3075	101	1	=	=	SYM
ejpam-3075	101	2	|∆|2ptexp{−δ1trt}|t	|∆|2ptexp{−δ1trt}|t	NOUN
ejpam-3075	101	3	|2t(n−p+1)−1{γp(2nt)}−1(δ1)2ptn	|2t(n−p+1)−1{γp(2nt)}−1(δ1)2ptn	X
ejpam-3075	101	4	1f1(2t(n−1	1f1(2t(n−1	NUM
ejpam-3075	101	5	)	)	PUNCT
ejpam-3075	101	6	;	;	PUNCT
ejpam-3075	101	7	2tn	2tn	NOUN
ejpam-3075	101	8	;	;	PUNCT
ejpam-3075	101	9	δt	δt	NOUN
ejpam-3075	101	10	)	)	PUNCT
ejpam-3075	101	11	,	,	PUNCT
ejpam-3075	101	12	(	(	PUNCT
ejpam-3075	101	13	27	27	NUM
ejpam-3075	101	14	)	)	PUNCT
ejpam-3075	101	15	and	and	CCONJ
ejpam-3075	101	16	hence	hence	ADV
ejpam-3075	101	17	the	the	DET
ejpam-3075	101	18	density	density	NOUN
ejpam-3075	101	19	of	of	ADP
ejpam-3075	101	20	the	the	DET
ejpam-3075	101	21	roots	root	NOUN
ejpam-3075	101	22	matrix	matrix	NOUN
ejpam-3075	101	23	p×	p×	PROPN
ejpam-3075	101	24	p	p	PROPN
ejpam-3075	101	25	∧	∧	PROPN
ejpam-3075	101	26	is	be	AUX
ejpam-3075	101	27	f(∧	f(∧	NUM
ejpam-3075	101	28	)	)	PUNCT
ejpam-3075	102	1	=	=	NOUN
ejpam-3075	102	2	|∆‖2ptexp{−δ1trt}|t	|∆‖2ptexp{−δ1trt}|t	NUM
ejpam-3075	102	3	|2t(n−p+1)−1{γp(2nt)}−1(δ1)2ptn	|2t(n−p+1)−1{γp(2nt)}−1(δ1)2ptn	NOUN
ejpam-3075	102	4	1f1(2t(n−	1f1(2t(n−	NUM
ejpam-3075	102	5	1	1	NUM
ejpam-3075	102	6	)	)	PUNCT
ejpam-3075	102	7	;	;	PUNCT
ejpam-3075	103	1	2tn	2tn	NOUN
ejpam-3075	103	2	;	;	PUNCT
ejpam-3075	103	3	δt	δt	NOUN
ejpam-3075	103	4	)	)	PUNCT
ejpam-3075	103	5	πp	πp	ADP
ejpam-3075	103	6	i	i	PRON
ejpam-3075	103	7	<	<	X
ejpam-3075	103	8	j(λi	j(λi	ADV
ejpam-3075	103	9	−	−	PROPN
ejpam-3075	103	10	λj	λj	PROPN
ejpam-3075	103	11	)	)	PUNCT
ejpam-3075	103	12	4	4	NUM
ejpam-3075	103	13	t	t	NOUN
ejpam-3075	103	14	(	(	PUNCT
ejpam-3075	103	15	28	28	NUM
ejpam-3075	103	16	)	)	PUNCT
ejpam-3075	103	17	and	and	CCONJ
ejpam-3075	103	18	setting	set	VERB
ejpam-3075	103	19	(	(	PUNCT
ejpam-3075	103	20	2	2	NUM
ejpam-3075	103	21	t	t	NOUN
ejpam-3075	103	22	=	=	SYM
ejpam-3075	103	23	h	h	NOUN
ejpam-3075	103	24	)	)	PUNCT
ejpam-3075	103	25	we	we	PRON
ejpam-3075	103	26	find	find	VERB
ejpam-3075	103	27	that∫	that∫	NOUN
ejpam-3075	103	28	exp{−δ1tr∧}|	exp{−δ1tr∧}|	PROPN
ejpam-3075	103	29	∧	∧	PROPN
ejpam-3075	103	30	|g−1	|g−1	VERB
ejpam-3075	103	31	1f1((n−	1f1((n−	NUM
ejpam-3075	103	32	1)h;nh	1)h;nh	NUM
ejpam-3075	103	33	;	;	PUNCT
ejpam-3075	103	34	δ∧)πp	δ∧)πp	VERB
ejpam-3075	103	35	i	i	PRON
ejpam-3075	103	36	<	<	X
ejpam-3075	103	37	j(λi	j(λi	ADV
ejpam-3075	103	38	−	−	PROPN
ejpam-3075	103	39	λj)2hd∧	λj)2hd∧	PROPN
ejpam-3075	103	40	=	=	SYM
ejpam-3075	103	41	|∆|−ph(δ1)pnh	|∆|−ph(δ1)pnh	CCONJ
ejpam-3075	103	42	γp(g	γp(g	PUNCT
ejpam-3075	104	1	+	+	CCONJ
ejpam-3075	104	2	hp−	hp−	DET
ejpam-3075	104	3	h	h	NOUN
ejpam-3075	104	4	)	)	PUNCT
ejpam-3075	104	5	γ(p+	γ(p+	PROPN
ejpam-3075	104	6	1	1	NUM
ejpam-3075	104	7	)	)	PUNCT
ejpam-3075	104	8	(	(	PUNCT
ejpam-3075	104	9	29	29	NUM
ejpam-3075	104	10	)	)	PUNCT
ejpam-3075	104	11	note	note	VERB
ejpam-3075	104	12	that	that	SCONJ
ejpam-3075	104	13	in	in	SCONJ
ejpam-3075	104	14	(	(	PUNCT
ejpam-3075	104	15	28	28	NUM
ejpam-3075	104	16	)	)	PUNCT
ejpam-3075	104	17	the	the	DET
ejpam-3075	104	18	roots	root	NOUN
ejpam-3075	104	19	are	be	AUX
ejpam-3075	104	20	ordered	order	VERB
ejpam-3075	104	21	,	,	PUNCT
ejpam-3075	104	22	but	but	CCONJ
ejpam-3075	104	23	in	in	ADP
ejpam-3075	104	24	selberg	selberg	NOUN
ejpam-3075	104	25	-	-	PUNCT
ejpam-3075	104	26	type	type	NOUN
ejpam-3075	104	27	they	they	PRON
ejpam-3075	104	28	are	be	AUX
ejpam-3075	104	29	unordered	unordered	ADJ
ejpam-3075	104	30	hence	hence	ADV
ejpam-3075	104	31	the	the	DET
ejpam-3075	104	32	factor	factor	NOUN
ejpam-3075	104	33	γ(p+	γ(p+	PROPN
ejpam-3075	104	34	1	1	X
ejpam-3075	104	35	)	)	PUNCT
ejpam-3075	104	36	in	in	ADP
ejpam-3075	104	37	(	(	PUNCT
ejpam-3075	104	38	29	29	NUM
ejpam-3075	104	39	)	)	PUNCT
ejpam-3075	104	40	.	.	PUNCT
ejpam-3075	105	1	references	reference	NOUN
ejpam-3075	105	2	619	619	NUM
ejpam-3075	105	3	5	5	NUM
ejpam-3075	105	4	.	.	PUNCT
ejpam-3075	106	1	hcgqfmbd	hcgqfmbd	PROPN
ejpam-3075	106	2	the	the	DET
ejpam-3075	106	3	hcgqfmbd	hcgqfmbd	PROPN
ejpam-3075	106	4	of	of	ADP
ejpam-3075	106	5	p×	p×	PROPN
ejpam-3075	106	6	p	p	NOUN
ejpam-3075	106	7	m	m	NOUN
ejpam-3075	106	8	is	be	AUX
ejpam-3075	106	9	f(m	f(m	PROPN
ejpam-3075	106	10	)	)	PUNCT
ejpam-3075	107	1	=	=	SYM
ejpam-3075	107	2	|∆|4pt(δ1)2pt(n−q+2){bp(2nt	|∆|4pt(δ1)2pt(n−q+2){bp(2nt	NOUN
ejpam-3075	107	3	;	;	PUNCT
ejpam-3075	107	4	2qt)}−1|m	2qt)}−1|m	NUM
ejpam-3075	107	5	|2t(n−p+1)−1|i	|2t(n−p+1)−1|i	NUM
ejpam-3075	107	6	−m	−m	PROPN
ejpam-3075	107	7	|2t(q−p+1)−1	|2t(q−p+1)−1	NOUN
ejpam-3075	107	8	2f1(2t(n+	2f1(2t(n+	NUM
ejpam-3075	107	9	q	q	NOUN
ejpam-3075	107	10	−	−	PROPN
ejpam-3075	107	11	2	2	NUM
ejpam-3075	107	12	)	)	PUNCT
ejpam-3075	107	13	;	;	PUNCT
ejpam-3075	107	14	2t(n+	2t(n+	PROPN
ejpam-3075	107	15	q	q	X
ejpam-3075	107	16	)	)	PUNCT
ejpam-3075	107	17	;	;	PUNCT
ejpam-3075	107	18	2tn	2tn	NOUN
ejpam-3075	107	19	;	;	PUNCT
ejpam-3075	107	20	δ−4pt	δ−4pt	VERB
ejpam-3075	107	21	1	1	NUM
ejpam-3075	107	22	δm	δm	NOUN
ejpam-3075	107	23	)	)	PUNCT
ejpam-3075	107	24	,	,	PUNCT
ejpam-3075	107	25	f(∧	f(∧	NUM
ejpam-3075	107	26	)	)	PUNCT
ejpam-3075	108	1	=	=	PRON
ejpam-3075	108	2	{	{	PUNCT
ejpam-3075	108	3	bp(2nt	bp(2nt	NOUN
ejpam-3075	108	4	;	;	PUNCT
ejpam-3075	108	5	2qt)}−1|∆|4pt(δ1)2pt(n−q+2)|	2qt)}−1|∆|4pt(δ1)2pt(n−q+2)|	NUM
ejpam-3075	108	6	∧	∧	PROPN
ejpam-3075	108	7	|2t(n−p+1)−1|i	|2t(n−p+1)−1|i	PROPN
ejpam-3075	108	8	−	−	PROPN
ejpam-3075	108	9	∧|2t(q−p+1)−1	∧|2t(q−p+1)−1	NOUN
ejpam-3075	108	10	2f1(2t(n+	2f1(2t(n+	NUM
ejpam-3075	108	11	q	q	NOUN
ejpam-3075	108	12	−	−	NOUN
ejpam-3075	108	13	2	2	NUM
ejpam-3075	108	14	)	)	PUNCT
ejpam-3075	108	15	;	;	PUNCT
ejpam-3075	108	16	2t(n+	2t(n+	PROPN
ejpam-3075	108	17	q	q	X
ejpam-3075	108	18	)	)	PUNCT
ejpam-3075	108	19	;	;	PUNCT
ejpam-3075	108	20	2tn	2tn	NOUN
ejpam-3075	108	21	;	;	PUNCT
ejpam-3075	108	22	δ−4pt	δ−4pt	VERB
ejpam-3075	108	23	1	1	NUM
ejpam-3075	108	24	δ∧)πp	δ∧)πp	VERB
ejpam-3075	108	25	i	i	PRON
ejpam-3075	108	26	<	<	X
ejpam-3075	108	27	j(λi	j(λi	ADV
ejpam-3075	108	28	−	−	PROPN
ejpam-3075	108	29	λj)4	λj)4	PROPN
ejpam-3075	108	30	t	t	PROPN
ejpam-3075	108	31	and	and	CCONJ
ejpam-3075	108	32	hence	hence	ADV
ejpam-3075	108	33	setting	set	VERB
ejpam-3075	108	34	2	2	NUM
ejpam-3075	108	35	t	t	NOUN
ejpam-3075	108	36	=	=	SYM
ejpam-3075	108	37	h	h	NOUN
ejpam-3075	108	38	,	,	PUNCT
ejpam-3075	108	39	we	we	PRON
ejpam-3075	108	40	have	have	VERB
ejpam-3075	108	41	that∫	that∫	NOUN
ejpam-3075	109	1	|	|	ADV
ejpam-3075	109	2	∧	∧	PROPN
ejpam-3075	109	3	|g−1|i	|g−1|i	PROPN
ejpam-3075	109	4	−	−	PROPN
ejpam-3075	109	5	∧|t−1	∧|t−1	PROPN
ejpam-3075	109	6	2f1(h(n+	2f1(h(n+	NUM
ejpam-3075	109	7	q	q	NOUN
ejpam-3075	110	1	−	−	PROPN
ejpam-3075	110	2	2);h(n+	2);h(n+	NUM
ejpam-3075	110	3	q);hn	q);hn	NOUN
ejpam-3075	110	4	;	;	PUNCT
ejpam-3075	111	1	δ(δ1)−2hp∧)πp	δ(δ1)−2hp∧)πp	PROPN
ejpam-3075	111	2	i	i	PRON
ejpam-3075	111	3	<	<	X
ejpam-3075	111	4	j(λi	j(λi	ADV
ejpam-3075	111	5	−	−	PROPN
ejpam-3075	112	1	λj)4td∧	λj)4td∧	X
ejpam-3075	112	2	=	=	X
ejpam-3075	112	3	bp(g	bp(g	PUNCT
ejpam-3075	112	4	+	+	CCONJ
ejpam-3075	112	5	hp−	hp−	PRON
ejpam-3075	112	6	h	h	NOUN
ejpam-3075	112	7	;	;	PUNCT
ejpam-3075	112	8	t+	t+	ADP
ejpam-3075	112	9	hp−	hp−	PRON
ejpam-3075	112	10	h)|∆|−2hp(δ1)−hp(n−q+2	h)|∆|−2hp(δ1)−hp(n−q+2	NOUN
ejpam-3075	112	11	)	)	PUNCT
ejpam-3075	112	12	γ(p+	γ(p+	VERB
ejpam-3075	112	13	1	1	NUM
ejpam-3075	112	14	)	)	PUNCT
ejpam-3075	112	15	(	(	PUNCT
ejpam-3075	112	16	30	30	NUM
ejpam-3075	112	17	)	)	PUNCT
ejpam-3075	112	18	thus	thus	ADV
ejpam-3075	112	19	(	(	PUNCT
ejpam-3075	112	20	29	29	NUM
ejpam-3075	112	21	)	)	PUNCT
ejpam-3075	112	22	and	and	CCONJ
ejpam-3075	112	23	(	(	PUNCT
ejpam-3075	112	24	30	30	NUM
ejpam-3075	112	25	)	)	PUNCT
ejpam-3075	112	26	are	be	AUX
ejpam-3075	112	27	the	the	DET
ejpam-3075	112	28	selberg	selberg	NOUN
ejpam-3075	112	29	-	-	PUNCT
ejpam-3075	112	30	type	type	NOUN
ejpam-3075	112	31	integrals	integral	NOUN
ejpam-3075	112	32	of	of	ADP
ejpam-3075	112	33	our	our	PRON
ejpam-3075	112	34	context	context	NOUN
ejpam-3075	112	35	.	.	PUNCT
ejpam-3075	113	1	references	reference	NOUN
ejpam-3075	113	2	[	[	X
ejpam-3075	113	3	1	1	NUM
ejpam-3075	113	4	]	]	X
ejpam-3075	113	5	askey	askey	NOUN
ejpam-3075	113	6	,	,	PUNCT
ejpam-3075	113	7	richard	richard	PROPN
ejpam-3075	113	8	and	and	CCONJ
ejpam-3075	113	9	richards	richards	PROPN
ejpam-3075	113	10	,	,	PUNCT
ejpam-3075	113	11	donald	donald	PROPN
ejpam-3075	113	12	.	.	PUNCT
ejpam-3075	114	1	(	(	PUNCT
ejpam-3075	114	2	1989	1989	NUM
ejpam-3075	114	3	)	)	PUNCT
ejpam-3075	114	4	selbergs	selberg	NOUN
ejpam-3075	114	5	second	second	ADJ
ejpam-3075	114	6	beta	beta	NOUN
ejpam-3075	114	7	integral	integral	ADJ
ejpam-3075	114	8	and	and	CCONJ
ejpam-3075	114	9	an	an	DET
ejpam-3075	114	10	integral	integral	ADJ
ejpam-3075	114	11	of	of	ADP
ejpam-3075	114	12	mehta	mehta	PROPN
ejpam-3075	114	13	,	,	PUNCT
ejpam-3075	114	14	probability	probability	NOUN
ejpam-3075	114	15	,	,	PUNCT
ejpam-3075	114	16	statistics	statistic	NOUN
ejpam-3075	114	17	,	,	PUNCT
ejpam-3075	114	18	and	and	CCONJ
ejpam-3075	114	19	mathematics	mathematic	NOUN
ejpam-3075	114	20	.	.	PUNCT
ejpam-3075	115	1	academic	academic	ADJ
ejpam-3075	115	2	press	press	NOUN
ejpam-3075	115	3	,	,	PUNCT
ejpam-3075	115	4	(	(	PUNCT
ejpam-3075	115	5	karlin	karlin	PROPN
ejpam-3075	115	6	volume	volume	NOUN
ejpam-3075	115	7	)	)	PUNCT
ejpam-3075	115	8	,	,	PUNCT
ejpam-3075	115	9	new	new	PROPN
ejpam-3075	115	10	york	york	PROPN
ejpam-3075	115	11	.	.	PUNCT
ejpam-3075	116	1	[	[	X
ejpam-3075	116	2	2	2	NUM
ejpam-3075	116	3	]	]	X
ejpam-3075	116	4	gupta	gupta	PROPN
ejpam-3075	116	5	,	,	PUNCT
ejpam-3075	116	6	a.k	a.k	PROPN
ejpam-3075	116	7	.	.	PROPN
ejpam-3075	116	8	and	and	CCONJ
ejpam-3075	116	9	kabe	kabe	ADJ
ejpam-3075	116	10	,	,	PUNCT
ejpam-3075	116	11	d.g	d.g	PROPN
ejpam-3075	116	12	.	.	PROPN
ejpam-3075	116	13	(	(	PUNCT
ejpam-3075	116	14	2005	2005	NUM
ejpam-3075	116	15	)	)	PUNCT
ejpam-3075	116	16	.	.	PUNCT
ejpam-3075	117	1	on	on	ADP
ejpam-3075	117	2	selberg	selberg	X
ejpam-3075	117	3	beta	beta	NOUN
ejpam-3075	117	4	integrals	integral	NOUN
ejpam-3075	117	5	random	random	ADJ
ejpam-3075	117	6	obr	obr	NOUN
ejpam-3075	117	7	.	.	PUNCT
ejpam-3075	118	1	and	and	CCONJ
ejpam-3075	118	2	stocastic	stocastic	ADJ
ejpam-3075	118	3	eqn	eqn	PROPN
ejpam-3075	118	4	13	13	NUM
ejpam-3075	118	5	,	,	PUNCT
ejpam-3075	118	6	11	11	NUM
ejpam-3075	118	7	-	-	SYM
ejpam-3075	118	8	16	16	NUM
ejpam-3075	118	9	.	.	PUNCT
ejpam-3075	119	1	[	[	X
ejpam-3075	119	2	3	3	NUM
ejpam-3075	119	3	]	]	X
ejpam-3075	119	4	gupta	gupta	PROPN
ejpam-3075	119	5	,	,	PUNCT
ejpam-3075	119	6	a.k	a.k	PROPN
ejpam-3075	119	7	.	.	PROPN
ejpam-3075	119	8	and	and	CCONJ
ejpam-3075	119	9	kabe	kabe	ADJ
ejpam-3075	119	10	,	,	PUNCT
ejpam-3075	119	11	d.g	d.g	PROPN
ejpam-3075	119	12	.	.	PROPN
ejpam-3075	119	13	(	(	PUNCT
ejpam-3075	119	14	2007	2007	NUM
ejpam-3075	119	15	)	)	PUNCT
ejpam-3075	119	16	.	.	PUNCT
ejpam-3075	120	1	the	the	DET
ejpam-3075	120	2	doubly	doubly	ADV
ejpam-3075	120	3	noncentral	noncentral	ADJ
ejpam-3075	120	4	multivariate	multivariate	NOUN
ejpam-3075	120	5	beta	beta	ADJ
ejpam-3075	120	6	distribution	distribution	NOUN
ejpam-3075	120	7	.	.	PUNCT
ejpam-3075	121	1	j.	j.	PROPN
ejpam-3075	121	2	appli	appli	PROPN
ejpam-3075	121	3	.	.	PUNCT
ejpam-3075	122	1	stat	stat	PROPN
ejpam-3075	122	2	.	.	PUNCT
ejpam-3075	123	1	sc	sc	PROPN
ejpam-3075	123	2	.	.	PUNCT
ejpam-3075	123	3	1,21	1,21	PROPN
ejpam-3075	123	4	-	-	PUNCT
ejpam-3075	123	5	25	25	NUM
ejpam-3075	123	6	.	.	PUNCT
ejpam-3075	124	1	[	[	X
ejpam-3075	124	2	4	4	NUM
ejpam-3075	124	3	]	]	X
ejpam-3075	124	4	gupta	gupta	PROPN
ejpam-3075	124	5	,	,	PUNCT
ejpam-3075	124	6	a.k	a.k	PROPN
ejpam-3075	124	7	.	.	PROPN
ejpam-3075	124	8	and	and	CCONJ
ejpam-3075	124	9	kabe	kabe	ADJ
ejpam-3075	124	10	,	,	PUNCT
ejpam-3075	124	11	d.g	d.g	PROPN
ejpam-3075	124	12	.	.	PROPN
ejpam-3075	124	13	(	(	PUNCT
ejpam-3075	124	14	2008	2008	NUM
ejpam-3075	124	15	)	)	PUNCT
ejpam-3075	124	16	.	.	PUNCT
ejpam-3075	124	17	selberg	selberg	NOUN
ejpam-3075	124	18	-	-	PUNCT
ejpam-3075	124	19	type	type	NOUN
ejpam-3075	124	20	squared	square	VERB
ejpam-3075	124	21	matrices	matrix	NOUN
ejpam-3075	124	22	gamma	gamma	NOUN
ejpam-3075	124	23	and	and	CCONJ
ejpam-3075	124	24	beta	beta	NOUN
ejpam-3075	124	25	integrals	integral	NOUN
ejpam-3075	124	26	.	.	PUNCT
ejpam-3075	125	1	eu	eu	PROPN
ejpam-3075	125	2	.	.	PUNCT
ejpam-3075	125	3	j.	j.	PROPN
ejpam-3075	125	4	pure	pure	PROPN
ejpam-3075	125	5	and	and	CCONJ
ejpam-3075	125	6	appli	appli	PROPN
ejpam-3075	125	7	.	.	PUNCT
ejpam-3075	125	8	math	math	PROPN
ejpam-3075	125	9	.	.	PUNCT
ejpam-3075	126	1	1,197	1,197	NUM
ejpam-3075	126	2	-	-	SYM
ejpam-3075	126	3	201	201	NUM
ejpam-3075	126	4	.	.	PUNCT
ejpam-3075	127	1	[	[	X
ejpam-3075	127	2	5	5	NUM
ejpam-3075	127	3	]	]	X
ejpam-3075	127	4	gupta	gupta	PROPN
ejpam-3075	127	5	,	,	PUNCT
ejpam-3075	127	6	a.k	a.k	PROPN
ejpam-3075	127	7	.	.	PROPN
ejpam-3075	127	8	and	and	CCONJ
ejpam-3075	127	9	nagar	nagar	PROPN
ejpam-3075	127	10	,	,	PUNCT
ejpam-3075	127	11	d.k	d.k	PROPN
ejpam-3075	127	12	.	.	PROPN
ejpam-3075	127	13	(	(	PUNCT
ejpam-3075	127	14	2007	2007	NUM
ejpam-3075	127	15	)	)	PUNCT
ejpam-3075	127	16	.	.	PUNCT
ejpam-3075	127	17	matrix	matrix	NOUN
ejpam-3075	127	18	variate	variate	NOUN
ejpam-3075	127	19	distributions	distribution	NOUN
ejpam-3075	127	20	[	[	X
ejpam-3075	127	21	6	6	NUM
ejpam-3075	127	22	]	]	X
ejpam-3075	127	23	kabe	kabe	NOUN
ejpam-3075	127	24	,	,	PUNCT
ejpam-3075	127	25	d.g	d.g	PROPN
ejpam-3075	127	26	.	.	PROPN
ejpam-3075	127	27	(	(	PUNCT
ejpam-3075	127	28	1984	1984	NUM
ejpam-3075	127	29	)	)	PUNCT
ejpam-3075	127	30	.	.	PUNCT
ejpam-3075	128	1	classical	classical	ADJ
ejpam-3075	128	2	statistical	statistical	ADJ
ejpam-3075	128	3	analysis	analysis	NOUN
ejpam-3075	128	4	based	base	VERB
ejpam-3075	128	5	on	on	ADP
ejpam-3075	128	6	a	a	DET
ejpam-3075	128	7	certain	certain	ADJ
ejpam-3075	128	8	hypercomplex	hypercomplex	NOUN
ejpam-3075	128	9	multivariate	multivariate	NOUN
ejpam-3075	128	10	normal	normal	ADJ
ejpam-3075	128	11	distribution	distribution	NOUN
ejpam-3075	128	12	.	.	PUNCT
ejpam-3075	129	1	metrika	metrika	NOUN
ejpam-3075	129	2	.	.	PUNCT
ejpam-3075	130	1	31	31	NUM
ejpam-3075	130	2	,	,	PUNCT
ejpam-3075	130	3	63	63	NUM
ejpam-3075	130	4	-	-	SYM
ejpam-3075	130	5	76	76	NUM
ejpam-3075	130	6	.	.	PUNCT
ejpam-3075	131	1	[	[	X
ejpam-3075	131	2	7	7	X
ejpam-3075	131	3	]	]	X
ejpam-3075	131	4	mathai	mathai	PROPN
ejpam-3075	131	5	,	,	PUNCT
ejpam-3075	131	6	a.m.	a.m.	ADV
ejpam-3075	131	7	,	,	PUNCT
ejpam-3075	131	8	hayakawa	hayakawa	PROPN
ejpam-3075	131	9	,	,	PUNCT
ejpam-3075	131	10	t.	t.	PROPN
ejpam-3075	131	11	,	,	PUNCT
ejpam-3075	131	12	provost	provost	NOUN
ejpam-3075	131	13	,	,	PUNCT
ejpam-3075	131	14	s.b	s.b	PROPN
ejpam-3075	131	15	.	.	PROPN
ejpam-3075	131	16	(	(	PUNCT
ejpam-3075	131	17	1995	1995	NUM
ejpam-3075	131	18	)	)	PUNCT
ejpam-3075	131	19	.	.	PUNCT
ejpam-3075	132	1	bilinear	bilinear	NOUN
ejpam-3075	132	2	forms	form	NOUN
ejpam-3075	132	3	and	and	CCONJ
ejpam-3075	132	4	zonal	zonal	ADJ
ejpam-3075	132	5	polynomials	polynomial	NOUN
ejpam-3075	132	6	.	.	PUNCT
ejpam-3075	133	1	springer	springer	NOUN
ejpam-3075	133	2	-	-	PUNCT
ejpam-3075	133	3	verlag	verlag	PROPN
ejpam-3075	133	4	,	,	PUNCT
ejpam-3075	133	5	new	new	PROPN
ejpam-3075	133	6	york	york	PROPN
ejpam-3075	133	7	.	.	PUNCT
ejpam-3075	134	1	[	[	X
ejpam-3075	134	2	8	8	X
ejpam-3075	134	3	]	]	X
ejpam-3075	134	4	mathai	mathai	PROPN
ejpam-3075	134	5	,	,	PUNCT
ejpam-3075	134	6	a.m.	a.m.	PROPN
ejpam-3075	134	7	(	(	PUNCT
ejpam-3075	134	8	1997	1997	NUM
ejpam-3075	134	9	)	)	PUNCT
ejpam-3075	134	10	.	.	PUNCT
ejpam-3075	135	1	jacobians	jacobian	NOUN
ejpam-3075	135	2	of	of	ADP
ejpam-3075	135	3	matrix	matrix	NOUN
ejpam-3075	135	4	transformations	transformation	NOUN
ejpam-3075	135	5	and	and	CCONJ
ejpam-3075	135	6	functions	function	NOUN
ejpam-3075	135	7	of	of	ADP
ejpam-3075	135	8	matrix	matrix	NOUN
ejpam-3075	135	9	arguments	argument	NOUN
ejpam-3075	135	10	.	.	PUNCT
ejpam-3075	136	1	world	world	NOUN
ejpam-3075	136	2	scientific	scientific	PROPN
ejpam-3075	136	3	,	,	PUNCT
ejpam-3075	136	4	london	london	PROPN
ejpam-3075	136	5	,	,	PUNCT
ejpam-3075	136	6	england	england	PROPN
ejpam-3075	136	7	.	.	PUNCT