id	sid	tid	token	lemma	pos
ejpam-739	1	1	19_739_sorin.dvi	19_739_sorin.dvi	NUM
ejpam-739	1	2	european	european	ADJ
ejpam-739	1	3	journal	journal	PROPN
ejpam-739	1	4	of	of	ADP
ejpam-739	1	5	pure	pure	ADJ
ejpam-739	1	6	and	and	CCONJ
ejpam-739	1	7	applied	apply	VERB
ejpam-739	1	8	mathematics	mathematic	NOUN
ejpam-739	1	9	vol	vol	NOUN
ejpam-739	1	10	.	.	PUNCT
ejpam-739	2	1	3	3	NUM
ejpam-739	2	2	,	,	PUNCT
ejpam-739	2	3	no	no	INTJ
ejpam-739	2	4	.	.	NOUN
ejpam-739	2	5	6	6	NUM
ejpam-739	2	6	,	,	PUNCT
ejpam-739	2	7	2010	2010	NUM
ejpam-739	2	8	,	,	PUNCT
ejpam-739	2	9	1150	1150	NUM
ejpam-739	2	10	-	-	SYM
ejpam-739	2	11	1164	1164	NUM
ejpam-739	2	12	issn	issn	PROPN
ejpam-739	2	13	1307	1307	NUM
ejpam-739	2	14	-	-	SYM
ejpam-739	2	15	5543	5543	NUM
ejpam-739	2	16	–	–	PUNCT
ejpam-739	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-739	2	18	special	special	ADJ
ejpam-739	2	19	issue	issue	NOUN
ejpam-739	2	20	on	on	ADP
ejpam-739	2	21	complex	complex	ADJ
ejpam-739	2	22	analysis	analysis	NOUN
ejpam-739	2	23	:	:	PUNCT
ejpam-739	2	24	theory	theory	NOUN
ejpam-739	2	25	and	and	CCONJ
ejpam-739	2	26	applications	application	NOUN
ejpam-739	2	27	dedicated	dedicate	VERB
ejpam-739	2	28	to	to	ADP
ejpam-739	2	29	professor	professor	PROPN
ejpam-739	2	30	hari	hari	PROPN
ejpam-739	2	31	m.	m.	PROPN
ejpam-739	2	32	srivastava	srivastava	PROPN
ejpam-739	2	33	,	,	PUNCT
ejpam-739	2	34	on	on	ADP
ejpam-739	2	35	the	the	DET
ejpam-739	2	36	occasion	occasion	NOUN
ejpam-739	2	37	of	of	ADP
ejpam-739	2	38	his	his	PRON
ejpam-739	2	39	70th	70th	ADJ
ejpam-739	2	40	birthday	birthday	NOUN
ejpam-739	2	41	approximation	approximation	NOUN
ejpam-739	2	42	by	by	ADP
ejpam-739	2	43	complex	complex	ADJ
ejpam-739	2	44	potentials	potential	NOUN
ejpam-739	2	45	generated	generate	VERB
ejpam-739	2	46	by	by	ADP
ejpam-739	2	47	the	the	DET
ejpam-739	2	48	euler	euler	NOUN
ejpam-739	2	49	’s	’s	PART
ejpam-739	2	50	beta	beta	PROPN
ejpam-739	2	51	function	function	NOUN
ejpam-739	2	52	sorin	sorin	NOUN
ejpam-739	2	53	g.	g.	PROPN
ejpam-739	2	54	gal	gal	PROPN
ejpam-739	2	55	department	department	PROPN
ejpam-739	2	56	of	of	ADP
ejpam-739	2	57	mathematics	mathematics	PROPN
ejpam-739	2	58	and	and	CCONJ
ejpam-739	2	59	computer	computer	NOUN
ejpam-739	2	60	science	science	NOUN
ejpam-739	2	61	,	,	PUNCT
ejpam-739	2	62	university	university	NOUN
ejpam-739	2	63	of	of	ADP
ejpam-739	2	64	oradea	oradea	PROPN
ejpam-739	2	65	,	,	PUNCT
ejpam-739	2	66	410087	410087	NUM
ejpam-739	2	67	oradea	oradea	NOUN
ejpam-739	2	68	,	,	PUNCT
ejpam-739	2	69	romania	romania	PROPN
ejpam-739	2	70	abstract	abstract	NOUN
ejpam-739	2	71	.	.	PUNCT
ejpam-739	3	1	in	in	ADP
ejpam-739	3	2	this	this	DET
ejpam-739	3	3	paper	paper	NOUN
ejpam-739	3	4	we	we	PRON
ejpam-739	3	5	find	find	VERB
ejpam-739	3	6	the	the	DET
ejpam-739	3	7	exact	exact	ADJ
ejpam-739	3	8	orders	order	NOUN
ejpam-739	3	9	of	of	ADP
ejpam-739	3	10	approximation	approximation	NOUN
ejpam-739	3	11	of	of	ADP
ejpam-739	3	12	analytic	analytic	ADJ
ejpam-739	3	13	functions	function	NOUN
ejpam-739	3	14	by	by	ADP
ejpam-739	3	15	the	the	DET
ejpam-739	3	16	complex	complex	ADJ
ejpam-739	3	17	versions	version	NOUN
ejpam-739	3	18	of	of	ADP
ejpam-739	3	19	several	several	ADJ
ejpam-739	3	20	potentials	potential	NOUN
ejpam-739	3	21	generated	generate	VERB
ejpam-739	3	22	by	by	ADP
ejpam-739	3	23	the	the	DET
ejpam-739	3	24	euler	euler	NOUN
ejpam-739	3	25	’s	’s	PART
ejpam-739	3	26	beta	beta	NOUN
ejpam-739	3	27	function	function	NOUN
ejpam-739	3	28	and	and	CCONJ
ejpam-739	3	29	by	by	ADP
ejpam-739	3	30	some	some	DET
ejpam-739	3	31	complex	complex	ADJ
ejpam-739	3	32	singular	singular	ADJ
ejpam-739	3	33	integrals	integral	NOUN
ejpam-739	3	34	.	.	PUNCT
ejpam-739	4	1	2000	2000	NUM
ejpam-739	4	2	mathematics	mathematic	NOUN
ejpam-739	4	3	subject	subject	NOUN
ejpam-739	4	4	classifications	classification	NOUN
ejpam-739	4	5	:	:	PUNCT
ejpam-739	4	6	30e10	30e10	NUM
ejpam-739	4	7	,	,	PUNCT
ejpam-739	4	8	41a35	41a35	NUM
ejpam-739	4	9	,	,	PUNCT
ejpam-739	4	10	41a25	41a25	NUM
ejpam-739	4	11	key	key	ADJ
ejpam-739	4	12	words	word	NOUN
ejpam-739	4	13	and	and	CCONJ
ejpam-739	4	14	phrases	phrase	NOUN
ejpam-739	4	15	:	:	PUNCT
ejpam-739	4	16	complex	complex	ADJ
ejpam-739	4	17	potentials	potential	NOUN
ejpam-739	4	18	,	,	PUNCT
ejpam-739	4	19	beta	beta	ADJ
ejpam-739	4	20	function	function	NOUN
ejpam-739	4	21	,	,	PUNCT
ejpam-739	4	22	complex	complex	ADJ
ejpam-739	4	23	singular	singular	ADJ
ejpam-739	4	24	integrals	integral	NOUN
ejpam-739	4	25	,	,	PUNCT
ejpam-739	4	26	exact	exact	ADJ
ejpam-739	4	27	order	order	NOUN
ejpam-739	4	28	of	of	ADP
ejpam-739	4	29	approximation	approximation	NOUN
ejpam-739	4	30	1	1	NUM
ejpam-739	4	31	.	.	PUNCT
ejpam-739	5	1	introduction	introduction	NOUN
ejpam-739	5	2	starting	start	VERB
ejpam-739	5	3	from	from	ADP
ejpam-739	5	4	the	the	DET
ejpam-739	5	5	flett	flett	ADJ
ejpam-739	5	6	real	real	ADJ
ejpam-739	5	7	potential	potential	NOUN
ejpam-739	5	8	defined	define	VERB
ejpam-739	5	9	for	for	ADP
ejpam-739	5	10	any	any	DET
ejpam-739	5	11	f	f	PROPN
ejpam-739	5	12	∈	∈	PROPN
ejpam-739	5	13	lp(r	lp(r	X
ejpam-739	5	14	)	)	PUNCT
ejpam-739	5	15	by	by	ADP
ejpam-739	5	16	[	[	PUNCT
ejpam-739	5	17	see	see	INTJ
ejpam-739	5	18	flett	flett	PROPN
ejpam-739	5	19	1	1	NUM
ejpam-739	5	20	]	]	SYM
ejpam-739	5	21	fα	fα	ADP
ejpam-739	5	22	(	(	PUNCT
ejpam-739	5	23	f	f	NOUN
ejpam-739	5	24	)	)	PUNCT
ejpam-739	5	25	(	(	PUNCT
ejpam-739	5	26	x	x	X
ejpam-739	5	27	)	)	PUNCT
ejpam-739	5	28	=	=	SYM
ejpam-739	5	29	1	1	NUM
ejpam-739	5	30	γ(α	γ(α	NOUN
ejpam-739	5	31	)	)	PUNCT
ejpam-739	5	32	∫	∫	PROPN
ejpam-739	6	1	∞	∞	PROPN
ejpam-739	6	2	0	0	NUM
ejpam-739	6	3	tα−1e−tq	tα−1e−tq	SYM
ejpam-739	6	4	t	t	PROPN
ejpam-739	6	5	(	(	PUNCT
ejpam-739	6	6	f	f	PROPN
ejpam-739	6	7	)	)	PUNCT
ejpam-739	6	8	(	(	PUNCT
ejpam-739	6	9	x)d	x)d	X
ejpam-739	6	10	t	t	PROPN
ejpam-739	6	11	,	,	PUNCT
ejpam-739	6	12	where	where	SCONJ
ejpam-739	6	13	q	q	PROPN
ejpam-739	6	14	t	t	PROPN
ejpam-739	6	15	(	(	PUNCT
ejpam-739	6	16	f	f	PROPN
ejpam-739	6	17	)	)	PUNCT
ejpam-739	6	18	(	(	PUNCT
ejpam-739	6	19	x	x	X
ejpam-739	6	20	)	)	PUNCT
ejpam-739	7	1	=	=	SYM
ejpam-739	7	2	t	t	PROPN
ejpam-739	7	3	π	π	PROPN
ejpam-739	7	4	∫∞	∫∞	NOUN
ejpam-739	7	5	−∞	−∞	ADP
ejpam-739	7	6	f	f	PROPN
ejpam-739	7	7	(	(	PUNCT
ejpam-739	7	8	x−u	x−u	PROPN
ejpam-739	7	9	)	)	PUNCT
ejpam-739	8	1	u2+t2	u2+t2	PRON
ejpam-739	8	2	du	du	NOUN
ejpam-739	8	3	is	be	AUX
ejpam-739	8	4	the	the	DET
ejpam-739	8	5	classical	classical	ADJ
ejpam-739	8	6	poisson	poisson	ADJ
ejpam-739	8	7	-	-	ADJ
ejpam-739	8	8	cauchy	cauchy	ADJ
ejpam-739	8	9	real	real	ADJ
ejpam-739	8	10	singular	singular	NOUN
ejpam-739	8	11	integral	integral	ADJ
ejpam-739	8	12	,	,	PUNCT
ejpam-739	8	13	in	in	ADP
ejpam-739	8	14	the	the	DET
ejpam-739	8	15	recent	recent	ADJ
ejpam-739	8	16	paper	paper	NOUN
ejpam-739	8	17	[	[	X
ejpam-739	8	18	3	3	X
ejpam-739	8	19	]	]	PUNCT
ejpam-739	8	20	we	we	PRON
ejpam-739	8	21	studied	study	VERB
ejpam-739	8	22	the	the	DET
ejpam-739	8	23	approximation	approximation	NOUN
ejpam-739	8	24	properties	property	NOUN
ejpam-739	8	25	for	for	ADP
ejpam-739	8	26	α	α	PROPN
ejpam-739	8	27	ց	ց	PROPN
ejpam-739	8	28	0	0	NUM
ejpam-739	8	29	,	,	PUNCT
ejpam-739	8	30	of	of	ADP
ejpam-739	8	31	its	its	PRON
ejpam-739	8	32	complex	complex	ADJ
ejpam-739	8	33	version	version	NOUN
ejpam-739	8	34	defined	define	VERB
ejpam-739	8	35	by	by	ADP
ejpam-739	8	36	fαu	fαu	NOUN
ejpam-739	8	37	(	(	PUNCT
ejpam-739	8	38	f	f	PROPN
ejpam-739	8	39	)	)	PUNCT
ejpam-739	8	40	(	(	PUNCT
ejpam-739	8	41	z	z	NOUN
ejpam-739	8	42	)	)	PUNCT
ejpam-739	8	43	=	=	SYM
ejpam-739	8	44	1	1	NUM
ejpam-739	8	45	γ(α	γ(α	NOUN
ejpam-739	8	46	)	)	PUNCT
ejpam-739	8	47	∫	∫	PROPN
ejpam-739	9	1	∞	∞	PROPN
ejpam-739	9	2	0	0	NUM
ejpam-739	9	3	tα−1e−tq	tα−1e−tq	SYM
ejpam-739	9	4	t	t	PROPN
ejpam-739	9	5	(	(	PUNCT
ejpam-739	9	6	f	f	PROPN
ejpam-739	9	7	)	)	PUNCT
ejpam-739	9	8	(	(	PUNCT
ejpam-739	9	9	z)d	z)d	NOUN
ejpam-739	9	10	t	t	PROPN
ejpam-739	9	11	,	,	PUNCT
ejpam-739	9	12	email	email	NOUN
ejpam-739	9	13	address	address	NOUN
ejpam-739	9	14	:	:	PUNCT
ejpam-739	9	15	galso�uoradea.ro	galso�uoradea.ro	NOUN
ejpam-739	9	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-739	9	17	1150	1150	NUM
ejpam-739	10	1	c	c	NOUN
ejpam-739	10	2	©	©	PROPN
ejpam-739	10	3	2010	2010	NUM
ejpam-739	10	4	ejpam	ejpam	NOUN
ejpam-739	10	5	all	all	DET
ejpam-739	10	6	rights	right	NOUN
ejpam-739	10	7	reserved	reserve	VERB
ejpam-739	10	8	.	.	PUNCT
ejpam-739	11	1	s.	s.	PROPN
ejpam-739	11	2	gal	gal	PROPN
ejpam-739	11	3	/	/	SYM
ejpam-739	11	4	eur	eur	PROPN
ejpam-739	11	5	.	.	PUNCT
ejpam-739	12	1	j.	j.	PROPN
ejpam-739	12	2	pure	pure	PROPN
ejpam-739	12	3	appl	appl	PROPN
ejpam-739	12	4	.	.	PROPN
ejpam-739	12	5	math	math	PROPN
ejpam-739	12	6	,	,	PUNCT
ejpam-739	12	7	3	3	NUM
ejpam-739	12	8	(	(	PUNCT
ejpam-739	12	9	2010	2010	NUM
ejpam-739	12	10	)	)	PUNCT
ejpam-739	12	11	,	,	PUNCT
ejpam-739	12	12	1150	1150	NUM
ejpam-739	12	13	-	-	SYM
ejpam-739	12	14	1164	1164	NUM
ejpam-739	12	15	1151	1151	NUM
ejpam-739	12	16	where	where	SCONJ
ejpam-739	12	17	q	q	PROPN
ejpam-739	12	18	t	t	PROPN
ejpam-739	12	19	(	(	PUNCT
ejpam-739	12	20	f	f	PROPN
ejpam-739	12	21	)	)	PUNCT
ejpam-739	12	22	(	(	PUNCT
ejpam-739	12	23	z	z	X
ejpam-739	12	24	)	)	PUNCT
ejpam-739	12	25	=	=	SYM
ejpam-739	13	1	t	t	PROPN
ejpam-739	13	2	π	π	PROPN
ejpam-739	13	3	∫∞	∫∞	NOUN
ejpam-739	13	4	−∞	−∞	ADP
ejpam-739	13	5	f	f	PROPN
ejpam-739	13	6	(	(	PUNCT
ejpam-739	13	7	ze−iu	ze−iu	NUM
ejpam-739	13	8	)	)	PUNCT
ejpam-739	13	9	u2+t2	u2+t2	NUM
ejpam-739	13	10	du	du	VERB
ejpam-739	13	11	.	.	PUNCT
ejpam-739	13	12	also	also	ADV
ejpam-739	13	13	,	,	PUNCT
ejpam-739	13	14	in	in	ADP
ejpam-739	13	15	the	the	DET
ejpam-739	13	16	same	same	ADJ
ejpam-739	13	17	paper	paper	NOUN
ejpam-739	13	18	[	[	X
ejpam-739	13	19	3	3	NUM
ejpam-739	13	20	]	]	PUNCT
ejpam-739	13	21	,	,	PUNCT
ejpam-739	13	22	the	the	DET
ejpam-739	13	23	approximation	approximation	NOUN
ejpam-739	13	24	properties	property	NOUN
ejpam-739	13	25	of	of	ADP
ejpam-739	13	26	following	follow	VERB
ejpam-739	13	27	types	type	NOUN
ejpam-739	13	28	of	of	ADP
ejpam-739	13	29	complex	complex	ADJ
ejpam-739	13	30	potentials	potential	NOUN
ejpam-739	13	31	generated	generate	VERB
ejpam-739	13	32	by	by	ADP
ejpam-739	13	33	the	the	DET
ejpam-739	13	34	gamma	gamma	NOUN
ejpam-739	13	35	function	function	NOUN
ejpam-739	13	36	and	and	CCONJ
ejpam-739	13	37	some	some	DET
ejpam-739	13	38	other	other	ADJ
ejpam-739	13	39	singular	singular	ADJ
ejpam-739	13	40	integrals	integral	NOUN
ejpam-739	13	41	were	be	AUX
ejpam-739	13	42	studied	study	VERB
ejpam-739	13	43	:	:	PUNCT
ejpam-739	13	44	fαu	fαu	NOUN
ejpam-739	13	45	(	(	PUNCT
ejpam-739	13	46	f	f	PROPN
ejpam-739	13	47	)	)	PUNCT
ejpam-739	13	48	(	(	PUNCT
ejpam-739	13	49	z	z	NOUN
ejpam-739	13	50	)	)	PUNCT
ejpam-739	13	51	=	=	SYM
ejpam-739	13	52	1	1	NUM
ejpam-739	13	53	γ(α	γ(α	NOUN
ejpam-739	13	54	)	)	PUNCT
ejpam-739	13	55	∫	∫	PROPN
ejpam-739	14	1	∞	∞	PROPN
ejpam-739	14	2	0	0	PROPN
ejpam-739	15	1	tα−1e−t	tα−1e−t	NOUN
ejpam-739	15	2	ut	ut	PROPN
ejpam-739	15	3	(	(	PUNCT
ejpam-739	15	4	f	f	PROPN
ejpam-739	15	5	)	)	PUNCT
ejpam-739	15	6	(	(	PUNCT
ejpam-739	15	7	z)d	z)d	NOUN
ejpam-739	15	8	t	t	PROPN
ejpam-739	15	9	,	,	PUNCT
ejpam-739	15	10	with	with	ADP
ejpam-739	15	11	ut	ut	PROPN
ejpam-739	15	12	(	(	PUNCT
ejpam-739	15	13	f	f	PROPN
ejpam-739	15	14	)	)	PUNCT
ejpam-739	15	15	(	(	PUNCT
ejpam-739	15	16	z	z	NOUN
ejpam-739	15	17	)	)	PUNCT
ejpam-739	15	18	=	=	SYM
ejpam-739	15	19	pt	pt	PROPN
ejpam-739	15	20	(	(	PUNCT
ejpam-739	15	21	f	f	PROPN
ejpam-739	15	22	)	)	PUNCT
ejpam-739	15	23	(	(	PUNCT
ejpam-739	15	24	z	z	NOUN
ejpam-739	15	25	)	)	PUNCT
ejpam-739	15	26	=	=	SYM
ejpam-739	15	27	1	1	NUM
ejpam-739	15	28	2	2	NUM
ejpam-739	15	29	t	t	NOUN
ejpam-739	15	30	∫	∫	NOUN
ejpam-739	16	1	+	+	X
ejpam-739	16	2	∞	∞	PROPN
ejpam-739	16	3	−∞	−∞	X
ejpam-739	16	4	f	f	PROPN
ejpam-739	16	5	(	(	PUNCT
ejpam-739	16	6	ze−iu)e−|u|/t	ze−iu)e−|u|/t	X
ejpam-739	16	7	du	du	PROPN
ejpam-739	16	8	,	,	PUNCT
ejpam-739	16	9	ut	ut	PROPN
ejpam-739	16	10	(	(	PUNCT
ejpam-739	16	11	f	f	PROPN
ejpam-739	16	12	)	)	PUNCT
ejpam-739	16	13	(	(	PUNCT
ejpam-739	16	14	z	z	NOUN
ejpam-739	16	15	)	)	PUNCT
ejpam-739	16	16	=	=	SYM
ejpam-739	16	17	r	r	NOUN
ejpam-739	16	18	t	t	PROPN
ejpam-739	16	19	(	(	PUNCT
ejpam-739	16	20	f	f	PROPN
ejpam-739	16	21	)	)	PUNCT
ejpam-739	16	22	(	(	PUNCT
ejpam-739	16	23	z	z	X
ejpam-739	16	24	)	)	PUNCT
ejpam-739	16	25	=	=	SYM
ejpam-739	16	26	2t3	2t3	NUM
ejpam-739	16	27	π	π	SYM
ejpam-739	16	28	∫	∫	PROPN
ejpam-739	17	1	+	+	ADJ
ejpam-739	17	2	∞	∞	PROPN
ejpam-739	17	3	−∞	−∞	X
ejpam-739	17	4	f	f	PROPN
ejpam-739	17	5	(	(	PUNCT
ejpam-739	17	6	ze−iu	ze−iu	NUM
ejpam-739	17	7	)	)	PUNCT
ejpam-739	17	8	(	(	PUNCT
ejpam-739	17	9	u2	u2	NOUN
ejpam-739	17	10	+	+	CCONJ
ejpam-739	17	11	t2)2	t2)2	X
ejpam-739	17	12	du	du	PROPN
ejpam-739	17	13	,	,	PUNCT
ejpam-739	17	14	ut	ut	PROPN
ejpam-739	17	15	(	(	PUNCT
ejpam-739	17	16	f	f	PROPN
ejpam-739	17	17	)	)	PUNCT
ejpam-739	17	18	(	(	PUNCT
ejpam-739	17	19	z	z	X
ejpam-739	17	20	)	)	PUNCT
ejpam-739	18	1	=	=	NOUN
ejpam-739	18	2	w	w	ADP
ejpam-739	18	3	∗t	∗t	PROPN
ejpam-739	18	4	(	(	PUNCT
ejpam-739	18	5	f	f	PROPN
ejpam-739	18	6	)	)	PUNCT
ejpam-739	18	7	(	(	PUNCT
ejpam-739	18	8	z	z	NOUN
ejpam-739	18	9	)	)	PUNCT
ejpam-739	18	10	=	=	SYM
ejpam-739	18	11	1p	1p	NUM
ejpam-739	18	12	πt	πt	ADP
ejpam-739	18	13	∫	∫	PROPN
ejpam-739	19	1	+	+	PROPN
ejpam-739	19	2	∞	∞	PROPN
ejpam-739	19	3	−∞	−∞	X
ejpam-739	19	4	f	f	PROPN
ejpam-739	19	5	(	(	PUNCT
ejpam-739	19	6	ze−iu)e−u2	ze−iu)e−u2	PROPN
ejpam-739	19	7	/	/	SYM
ejpam-739	19	8	t	t	PROPN
ejpam-739	19	9	du	du	PROPN
ejpam-739	19	10	,	,	PUNCT
ejpam-739	19	11	representing	represent	VERB
ejpam-739	19	12	the	the	DET
ejpam-739	19	13	complex	complex	ADJ
ejpam-739	19	14	versions	version	NOUN
ejpam-739	19	15	of	of	ADP
ejpam-739	19	16	the	the	DET
ejpam-739	19	17	picard	picard	NOUN
ejpam-739	19	18	,	,	PUNCT
ejpam-739	19	19	generalized	generalize	VERB
ejpam-739	19	20	poisson	poisson	NOUN
ejpam-739	19	21	-	-	ADJ
ejpam-739	19	22	cauchy	cauchy	ADJ
ejpam-739	19	23	and	and	CCONJ
ejpam-739	19	24	gaussweierstrass	gaussweierstrass	NOUN
ejpam-739	19	25	singular	singular	ADJ
ejpam-739	19	26	integrals	integral	NOUN
ejpam-739	19	27	,	,	PUNCT
ejpam-739	19	28	respectively	respectively	ADV
ejpam-739	19	29	.	.	PUNCT
ejpam-739	20	1	the	the	DET
ejpam-739	20	2	goal	goal	NOUN
ejpam-739	20	3	of	of	ADP
ejpam-739	20	4	the	the	DET
ejpam-739	20	5	present	present	ADJ
ejpam-739	20	6	paper	paper	NOUN
ejpam-739	20	7	is	be	AUX
ejpam-739	20	8	to	to	PART
ejpam-739	20	9	find	find	VERB
ejpam-739	20	10	the	the	DET
ejpam-739	20	11	exact	exact	ADJ
ejpam-739	20	12	orders	order	NOUN
ejpam-739	20	13	of	of	ADP
ejpam-739	20	14	approximation	approximation	NOUN
ejpam-739	20	15	by	by	ADP
ejpam-739	20	16	the	the	DET
ejpam-739	20	17	complex	complex	ADJ
ejpam-739	20	18	potentials	potential	NOUN
ejpam-739	20	19	generated	generate	VERB
ejpam-739	20	20	by	by	ADP
ejpam-739	20	21	the	the	DET
ejpam-739	20	22	euler	euler	NOUN
ejpam-739	20	23	’s	’s	PART
ejpam-739	20	24	beta	beta	NOUN
ejpam-739	20	25	function	function	NOUN
ejpam-739	20	26	,	,	PUNCT
ejpam-739	20	27	that	that	PRON
ejpam-739	20	28	is	be	AUX
ejpam-739	20	29	of	of	ADP
ejpam-739	20	30	the	the	DET
ejpam-739	20	31	form	form	NOUN
ejpam-739	20	32	g	g	PROPN
ejpam-739	20	33	α	α	PROPN
ejpam-739	20	34	,	,	PUNCT
ejpam-739	20	35	β	β	X
ejpam-739	20	36	u	u	NOUN
ejpam-739	20	37	(	(	PUNCT
ejpam-739	20	38	f	f	PROPN
ejpam-739	20	39	)	)	PUNCT
ejpam-739	20	40	(	(	PUNCT
ejpam-739	20	41	z	z	NOUN
ejpam-739	20	42	)	)	PUNCT
ejpam-739	20	43	=	=	SYM
ejpam-739	21	1	1	1	NUM
ejpam-739	21	2	beta(α	beta(α	NOUN
ejpam-739	21	3	,	,	PUNCT
ejpam-739	21	4	β	β	X
ejpam-739	21	5	)	)	PUNCT
ejpam-739	21	6	∫	∫	PROPN
ejpam-739	21	7	1	1	NUM
ejpam-739	21	8	0	0	NUM
ejpam-739	21	9	tα−1(1−	tα−1(1−	NOUN
ejpam-739	21	10	t)β−1ut	t)β−1ut	PROPN
ejpam-739	21	11	(	(	PUNCT
ejpam-739	21	12	f	f	NOUN
ejpam-739	21	13	)	)	PUNCT
ejpam-739	21	14	(	(	PUNCT
ejpam-739	21	15	z)d	z)d	NOUN
ejpam-739	21	16	t	t	PROPN
ejpam-739	21	17	,	,	PUNCT
ejpam-739	21	18	for	for	ADP
ejpam-739	21	19	q	q	PROPN
ejpam-739	21	20	t	t	PROPN
ejpam-739	21	21	(	(	PUNCT
ejpam-739	21	22	f	f	PROPN
ejpam-739	21	23	)	)	PUNCT
ejpam-739	21	24	(	(	PUNCT
ejpam-739	21	25	z	z	NOUN
ejpam-739	21	26	)	)	PUNCT
ejpam-739	21	27	and	and	CCONJ
ejpam-739	21	28	for	for	ADP
ejpam-739	21	29	all	all	DET
ejpam-739	21	30	the	the	DET
ejpam-739	21	31	ut	ut	PROPN
ejpam-739	21	32	(	(	PUNCT
ejpam-739	21	33	f	f	PROPN
ejpam-739	21	34	)	)	PUNCT
ejpam-739	21	35	(	(	PUNCT
ejpam-739	21	36	z	z	NOUN
ejpam-739	21	37	)	)	PUNCT
ejpam-739	21	38	defined	define	VERB
ejpam-739	21	39	above	above	ADV
ejpam-739	21	40	.	.	PUNCT
ejpam-739	22	1	2	2	X
ejpam-739	22	2	.	.	X
ejpam-739	22	3	main	main	ADJ
ejpam-739	22	4	result	result	NOUN
ejpam-739	22	5	for	for	ADP
ejpam-739	22	6	r	r	NOUN
ejpam-739	22	7	>	>	X
ejpam-739	22	8	0	0	PUNCT
ejpam-739	22	9	let	let	VERB
ejpam-739	22	10	us	we	PRON
ejpam-739	22	11	denote	denote	VERB
ejpam-739	22	12	dr	dr	PROPN
ejpam-739	22	13	=	=	PRON
ejpam-739	22	14	{	{	PUNCT
ejpam-739	22	15	z	z	NOUN
ejpam-739	22	16	∈	∈	PROPN
ejpam-739	22	17	c	c	NOUN
ejpam-739	22	18	;	;	PUNCT
ejpam-739	22	19	|z|	|z|	VERB
ejpam-739	22	20	<	<	X
ejpam-739	22	21	r	r	NOUN
ejpam-739	22	22	}	}	PUNCT
ejpam-739	22	23	.	.	PUNCT
ejpam-739	23	1	the	the	DET
ejpam-739	23	2	main	main	ADJ
ejpam-739	23	3	result	result	NOUN
ejpam-739	23	4	is	be	AUX
ejpam-739	23	5	the	the	DET
ejpam-739	23	6	following	following	NOUN
ejpam-739	23	7	.	.	PUNCT
ejpam-739	24	1	theorem	theorem	NOUN
ejpam-739	24	2	1	1	NUM
ejpam-739	24	3	.	.	PUNCT
ejpam-739	25	1	let	let	VERB
ejpam-739	25	2	us	we	PRON
ejpam-739	25	3	suppose	suppose	VERB
ejpam-739	25	4	that	that	SCONJ
ejpam-739	25	5	0	0	NUM
ejpam-739	25	6	<	<	X
ejpam-739	25	7	α≤	α≤	PROPN
ejpam-739	25	8	β	β	X
ejpam-739	25	9	≤	≤	NUM
ejpam-739	25	10	1	1	NUM
ejpam-739	25	11	,	,	PUNCT
ejpam-739	25	12	α+	α+	PUNCT
ejpam-739	25	13	β	β	X
ejpam-739	25	14	≥	≥	NOUN
ejpam-739	25	15	1	1	NUM
ejpam-739	25	16	and	and	CCONJ
ejpam-739	25	17	that	that	SCONJ
ejpam-739	25	18	f	f	X
ejpam-739	25	19	:	:	PUNCT
ejpam-739	25	20	dr→	dr→	NOUN
ejpam-739	25	21	c	c	NOUN
ejpam-739	25	22	,	,	PUNCT
ejpam-739	25	23	with	with	ADP
ejpam-739	25	24	r	r	NOUN
ejpam-739	25	25	>	>	SYM
ejpam-739	25	26	1	1	NUM
ejpam-739	25	27	,	,	PUNCT
ejpam-739	25	28	is	be	AUX
ejpam-739	25	29	analytic	analytic	ADJ
ejpam-739	25	30	in	in	ADP
ejpam-739	25	31	dr	dr	PROPN
ejpam-739	25	32	,	,	PUNCT
ejpam-739	25	33	that	that	PRON
ejpam-739	25	34	is	be	AUX
ejpam-739	25	35	f	f	PROPN
ejpam-739	25	36	(	(	PUNCT
ejpam-739	25	37	z	z	NOUN
ejpam-739	25	38	)	)	PUNCT
ejpam-739	25	39	=	=	NOUN
ejpam-739	25	40	∑∞	∑∞	NOUN
ejpam-739	25	41	k=0	k=0	PROPN
ejpam-739	25	42	akzk	akzk	PROPN
ejpam-739	25	43	,	,	PUNCT
ejpam-739	25	44	for	for	ADP
ejpam-739	25	45	all	all	DET
ejpam-739	25	46	z	z	PROPN
ejpam-739	25	47	∈	∈	PROPN
ejpam-739	25	48	dr	dr	PROPN
ejpam-739	25	49	.	.	PROPN
ejpam-739	25	50	(	(	PUNCT
ejpam-739	25	51	i	i	NOUN
ejpam-739	25	52	)	)	PUNCT
ejpam-739	25	53	for	for	ADP
ejpam-739	25	54	ut	ut	PROPN
ejpam-739	25	55	(	(	PUNCT
ejpam-739	25	56	f	f	PROPN
ejpam-739	25	57	)	)	PUNCT
ejpam-739	26	1	(	(	PUNCT
ejpam-739	26	2	z	z	X
ejpam-739	26	3	)	)	PUNCT
ejpam-739	26	4	=	=	SYM
ejpam-739	27	1	t	t	PROPN
ejpam-739	27	2	π	π	PROPN
ejpam-739	27	3	∫∞	∫∞	NOUN
ejpam-739	27	4	−∞	−∞	ADP
ejpam-739	27	5	f	f	PROPN
ejpam-739	27	6	(	(	PUNCT
ejpam-739	27	7	ze−iu	ze−iu	NUM
ejpam-739	27	8	)	)	PUNCT
ejpam-739	27	9	u2+t2	u2+t2	NUM
ejpam-739	27	10	du	du	NOUN
ejpam-739	27	11	we	we	PRON
ejpam-739	27	12	have	have	VERB
ejpam-739	27	13	that	that	PRON
ejpam-739	27	14	g	g	PROPN
ejpam-739	27	15	α	α	PROPN
ejpam-739	27	16	,	,	PUNCT
ejpam-739	27	17	β	β	X
ejpam-739	27	18	u	u	NOUN
ejpam-739	27	19	(	(	PUNCT
ejpam-739	27	20	f	f	PROPN
ejpam-739	27	21	)	)	PUNCT
ejpam-739	27	22	(	(	PUNCT
ejpam-739	27	23	z	z	NOUN
ejpam-739	27	24	)	)	PUNCT
ejpam-739	27	25	is	be	AUX
ejpam-739	27	26	analytic	analytic	ADJ
ejpam-739	27	27	in	in	ADP
ejpam-739	27	28	dr	dr	PROPN
ejpam-739	27	29	and	and	CCONJ
ejpam-739	27	30	we	we	PRON
ejpam-739	27	31	can	can	AUX
ejpam-739	27	32	write	write	VERB
ejpam-739	27	33	g	g	PROPN
ejpam-739	27	34	α	α	PROPN
ejpam-739	27	35	,	,	PUNCT
ejpam-739	27	36	β	β	X
ejpam-739	27	37	u	u	NOUN
ejpam-739	27	38	(	(	PUNCT
ejpam-739	27	39	f	f	PROPN
ejpam-739	27	40	)	)	PUNCT
ejpam-739	27	41	(	(	PUNCT
ejpam-739	27	42	z	z	NOUN
ejpam-739	27	43	)	)	PUNCT
ejpam-739	28	1	=	=	SYM
ejpam-739	29	1	∞	∞	NUM
ejpam-739	29	2	∑	∑	PROPN
ejpam-739	29	3	k=0	k=0	PROPN
ejpam-739	29	4	ak	ak	PROPN
ejpam-739	29	5	bk(α	bk(α	PROPN
ejpam-739	29	6	,	,	PUNCT
ejpam-739	29	7	β	β	X
ejpam-739	29	8	)	)	PUNCT
ejpam-739	29	9	·	·	PUNCT
ejpam-739	30	1	zk	zk	PROPN
ejpam-739	30	2	,	,	PUNCT
ejpam-739	30	3	z	z	PROPN
ejpam-739	30	4	∈	∈	PROPN
ejpam-739	30	5	dr	dr	PROPN
ejpam-739	30	6	,	,	PUNCT
ejpam-739	30	7	where	where	SCONJ
ejpam-739	30	8	bk(α	bk(α	X
ejpam-739	30	9	,	,	PUNCT
ejpam-739	30	10	β	β	X
ejpam-739	30	11	)	)	PUNCT
ejpam-739	30	12	=	=	SYM
ejpam-739	30	13	1	1	NUM
ejpam-739	30	14	beta(α	beta(α	NOUN
ejpam-739	30	15	,	,	PUNCT
ejpam-739	30	16	β	β	X
ejpam-739	30	17	)	)	PUNCT
ejpam-739	30	18	∫	∫	PROPN
ejpam-739	30	19	1	1	NUM
ejpam-739	30	20	0	0	NUM
ejpam-739	30	21	tα−1(1−	tα−1(1−	PROPN
ejpam-739	30	22	t)β−1e−kt	t)β−1e−kt	PROPN
ejpam-739	30	23	d	d	PROPN
ejpam-739	30	24	t.	t.	NOUN
ejpam-739	30	25	also	also	ADV
ejpam-739	30	26	,	,	PUNCT
ejpam-739	30	27	if	if	SCONJ
ejpam-739	30	28	f	f	PROPN
ejpam-739	30	29	is	be	AUX
ejpam-739	30	30	not	not	PART
ejpam-739	30	31	constant	constant	ADJ
ejpam-739	30	32	for	for	ADP
ejpam-739	30	33	q	q	NOUN
ejpam-739	30	34	=	=	SYM
ejpam-739	30	35	0	0	NUM
ejpam-739	30	36	,	,	PUNCT
ejpam-739	30	37	and	and	CCONJ
ejpam-739	30	38	not	not	PART
ejpam-739	30	39	a	a	DET
ejpam-739	30	40	polynomial	polynomial	NOUN
ejpam-739	30	41	of	of	ADP
ejpam-739	30	42	degree	degree	NOUN
ejpam-739	30	43	≤	≤	NUM
ejpam-739	30	44	q−	q−	PROPN
ejpam-739	30	45	1	1	NUM
ejpam-739	30	46	for	for	ADP
ejpam-739	30	47	q	q	PROPN
ejpam-739	30	48	∈	∈	PROPN
ejpam-739	30	49	n	n	CCONJ
ejpam-739	30	50	,	,	PUNCT
ejpam-739	30	51	then	then	ADV
ejpam-739	30	52	for	for	ADP
ejpam-739	30	53	all	all	DET
ejpam-739	30	54	1≤	1≤	NOUN
ejpam-739	30	55	r	r	NOUN
ejpam-739	30	56	<	<	X
ejpam-739	30	57	r1	r1	NOUN
ejpam-739	30	58	<	<	X
ejpam-739	30	59	r	r	NOUN
ejpam-739	30	60	,	,	PUNCT
ejpam-739	30	61	q	q	PROPN
ejpam-739	30	62	∈	∈	PROPN
ejpam-739	30	63	n∪	n∪	PROPN
ejpam-739	30	64	{	{	PUNCT
ejpam-739	30	65	0	0	NUM
ejpam-739	30	66	}	}	PUNCT
ejpam-739	30	67	,	,	PUNCT
ejpam-739	30	68	α	α	PROPN
ejpam-739	30	69	∈	∈	PROPN
ejpam-739	30	70	(	(	PUNCT
ejpam-739	30	71	0,β	0,β	PROPN
ejpam-739	30	72	]	]	X
ejpam-739	30	73	we	we	PRON
ejpam-739	30	74	have	have	VERB
ejpam-739	30	75	‖[gα	‖[gα	NOUN
ejpam-739	30	76	,	,	PUNCT
ejpam-739	30	77	β	β	X
ejpam-739	30	78	u	u	NOUN
ejpam-739	30	79	(	(	PUNCT
ejpam-739	30	80	f	f	PROPN
ejpam-739	30	81	)	)	PUNCT
ejpam-739	30	82	]	]	PUNCT
ejpam-739	30	83	(	(	PUNCT
ejpam-739	30	84	q)−	q)−	PROPN
ejpam-739	30	85	f	f	X
ejpam-739	30	86	(	(	PUNCT
ejpam-739	30	87	q)‖r	q)‖r	NOUN
ejpam-739	30	88	∼	∼	NOUN
ejpam-739	30	89	α	α	NOUN
ejpam-739	30	90	,	,	PUNCT
ejpam-739	30	91	s.	s.	PROPN
ejpam-739	30	92	gal	gal	PROPN
ejpam-739	30	93	/	/	SYM
ejpam-739	30	94	eur	eur	PROPN
ejpam-739	30	95	.	.	PUNCT
ejpam-739	31	1	j.	j.	PROPN
ejpam-739	31	2	pure	pure	PROPN
ejpam-739	31	3	appl	appl	PROPN
ejpam-739	31	4	.	.	PROPN
ejpam-739	31	5	math	math	PROPN
ejpam-739	31	6	,	,	PUNCT
ejpam-739	31	7	3	3	NUM
ejpam-739	31	8	(	(	PUNCT
ejpam-739	31	9	2010	2010	NUM
ejpam-739	31	10	)	)	PUNCT
ejpam-739	31	11	,	,	PUNCT
ejpam-739	31	12	1150	1150	NUM
ejpam-739	31	13	-	-	SYM
ejpam-739	31	14	1164	1164	NUM
ejpam-739	31	15	1152	1152	NUM
ejpam-739	31	16	where	where	SCONJ
ejpam-739	31	17	‖	‖	PROPN
ejpam-739	31	18	f	f	PROPN
ejpam-739	31	19	‖r	‖r	PROPN
ejpam-739	31	20	=	=	SYM
ejpam-739	31	21	sup{|	sup{|	PROPN
ejpam-739	31	22	f	f	PROPN
ejpam-739	31	23	(	(	PUNCT
ejpam-739	31	24	z)|	z)|	PROPN
ejpam-739	31	25	;	;	PUNCT
ejpam-739	31	26	|z|	|z|	VERB
ejpam-739	31	27	≤	≤	NUM
ejpam-739	31	28	r	r	NOUN
ejpam-739	31	29	}	}	PUNCT
ejpam-739	31	30	and	and	CCONJ
ejpam-739	31	31	the	the	DET
ejpam-739	31	32	constants	constant	NOUN
ejpam-739	31	33	in	in	ADP
ejpam-739	31	34	the	the	DET
ejpam-739	31	35	equivalence	equivalence	NOUN
ejpam-739	31	36	depend	depend	VERB
ejpam-739	31	37	only	only	ADV
ejpam-739	31	38	on	on	ADP
ejpam-739	31	39	f	f	PROPN
ejpam-739	31	40	,	,	PUNCT
ejpam-739	31	41	q	q	X
ejpam-739	31	42	,	,	PUNCT
ejpam-739	31	43	r	r	NOUN
ejpam-739	31	44	,	,	PUNCT
ejpam-739	31	45	r1	r1	NOUN
ejpam-739	31	46	,	,	PUNCT
ejpam-739	31	47	β	β	X
ejpam-739	31	48	.	.	PUNCT
ejpam-739	32	1	(	(	PUNCT
ejpam-739	32	2	ii	ii	NOUN
ejpam-739	32	3	)	)	PUNCT
ejpam-739	32	4	for	for	ADP
ejpam-739	32	5	ut	ut	PROPN
ejpam-739	32	6	(	(	PUNCT
ejpam-739	32	7	f	f	PROPN
ejpam-739	32	8	)	)	PUNCT
ejpam-739	32	9	(	(	PUNCT
ejpam-739	32	10	z	z	NOUN
ejpam-739	32	11	)	)	PUNCT
ejpam-739	32	12	=	=	SYM
ejpam-739	32	13	1	1	NUM
ejpam-739	32	14	2	2	NUM
ejpam-739	32	15	t	t	NOUN
ejpam-739	32	16	∫	∫	NOUN
ejpam-739	33	1	+	+	X
ejpam-739	33	2	∞	∞	PROPN
ejpam-739	33	3	−∞	−∞	X
ejpam-739	33	4	f	f	PROPN
ejpam-739	33	5	(	(	PUNCT
ejpam-739	33	6	ze−iu)e−|u|/t	ze−iu)e−|u|/t	AUX
ejpam-739	33	7	du	du	VERB
ejpam-739	33	8	we	we	PRON
ejpam-739	33	9	have	have	VERB
ejpam-739	33	10	that	that	PRON
ejpam-739	33	11	g	g	PROPN
ejpam-739	33	12	α	α	PROPN
ejpam-739	33	13	,	,	PUNCT
ejpam-739	33	14	β	β	X
ejpam-739	33	15	u	u	NOUN
ejpam-739	33	16	(	(	PUNCT
ejpam-739	33	17	f	f	PROPN
ejpam-739	33	18	)	)	PUNCT
ejpam-739	33	19	(	(	PUNCT
ejpam-739	33	20	z	z	NOUN
ejpam-739	33	21	)	)	PUNCT
ejpam-739	33	22	is	be	AUX
ejpam-739	33	23	analytic	analytic	ADJ
ejpam-739	33	24	in	in	ADP
ejpam-739	33	25	dr	dr	PROPN
ejpam-739	33	26	and	and	CCONJ
ejpam-739	33	27	we	we	PRON
ejpam-739	33	28	can	can	AUX
ejpam-739	33	29	write	write	VERB
ejpam-739	33	30	g	g	PROPN
ejpam-739	33	31	α	α	PROPN
ejpam-739	33	32	,	,	PUNCT
ejpam-739	33	33	β	β	X
ejpam-739	33	34	u	u	NOUN
ejpam-739	33	35	(	(	PUNCT
ejpam-739	33	36	f	f	PROPN
ejpam-739	33	37	)	)	PUNCT
ejpam-739	33	38	(	(	PUNCT
ejpam-739	33	39	z	z	NOUN
ejpam-739	33	40	)	)	PUNCT
ejpam-739	34	1	=	=	SYM
ejpam-739	35	1	∞	∞	NUM
ejpam-739	35	2	∑	∑	PROPN
ejpam-739	35	3	k=0	k=0	PROPN
ejpam-739	35	4	ak	ak	PROPN
ejpam-739	35	5	·	·	PUNCT
ejpam-739	35	6	bk(α	bk(α	PROPN
ejpam-739	35	7	,	,	PUNCT
ejpam-739	35	8	β	β	X
ejpam-739	35	9	)	)	PUNCT
ejpam-739	35	10	·	·	PUNCT
ejpam-739	36	1	zk	zk	PROPN
ejpam-739	36	2	,	,	PUNCT
ejpam-739	36	3	z	z	PROPN
ejpam-739	36	4	∈	∈	PROPN
ejpam-739	36	5	dr	dr	PROPN
ejpam-739	36	6	,	,	PUNCT
ejpam-739	36	7	where	where	SCONJ
ejpam-739	36	8	bk(α	bk(α	X
ejpam-739	36	9	,	,	PUNCT
ejpam-739	36	10	β	β	X
ejpam-739	36	11	)	)	PUNCT
ejpam-739	36	12	=	=	SYM
ejpam-739	36	13	1	1	NUM
ejpam-739	36	14	beta(α	beta(α	NOUN
ejpam-739	36	15	,	,	PUNCT
ejpam-739	36	16	β	β	X
ejpam-739	36	17	)	)	PUNCT
ejpam-739	36	18	∫	∫	PROPN
ejpam-739	36	19	1	1	NUM
ejpam-739	36	20	0	0	NUM
ejpam-739	36	21	tα−1(1−t)β−1	tα−1(1−t)β−1	NOUN
ejpam-739	36	22	1+t2k2	1+t2k2	NUM
ejpam-739	36	23	d	d	NOUN
ejpam-739	36	24	t.	t.	NOUN
ejpam-739	36	25	also	also	ADV
ejpam-739	36	26	,	,	PUNCT
ejpam-739	36	27	if	if	SCONJ
ejpam-739	36	28	f	f	PROPN
ejpam-739	36	29	is	be	AUX
ejpam-739	36	30	not	not	PART
ejpam-739	36	31	constant	constant	ADJ
ejpam-739	36	32	for	for	ADP
ejpam-739	36	33	q	q	NOUN
ejpam-739	36	34	=	=	SYM
ejpam-739	36	35	0	0	NUM
ejpam-739	36	36	,	,	PUNCT
ejpam-739	36	37	and	and	CCONJ
ejpam-739	36	38	not	not	PART
ejpam-739	36	39	a	a	DET
ejpam-739	36	40	polynomial	polynomial	NOUN
ejpam-739	36	41	of	of	ADP
ejpam-739	36	42	degree	degree	NOUN
ejpam-739	36	43	≤	≤	NUM
ejpam-739	36	44	q−	q−	PROPN
ejpam-739	36	45	1	1	NUM
ejpam-739	36	46	for	for	ADP
ejpam-739	36	47	q	q	PROPN
ejpam-739	36	48	∈	∈	PROPN
ejpam-739	36	49	n	n	CCONJ
ejpam-739	36	50	,	,	PUNCT
ejpam-739	36	51	then	then	ADV
ejpam-739	36	52	for	for	ADP
ejpam-739	36	53	all	all	DET
ejpam-739	36	54	1≤	1≤	NOUN
ejpam-739	36	55	r	r	NOUN
ejpam-739	36	56	<	<	X
ejpam-739	36	57	r1	r1	NOUN
ejpam-739	36	58	<	<	X
ejpam-739	36	59	r	r	NOUN
ejpam-739	36	60	,	,	PUNCT
ejpam-739	36	61	q	q	PROPN
ejpam-739	36	62	∈	∈	PROPN
ejpam-739	36	63	n∪	n∪	PROPN
ejpam-739	36	64	{	{	PUNCT
ejpam-739	36	65	0	0	NUM
ejpam-739	36	66	}	}	PUNCT
ejpam-739	36	67	,	,	PUNCT
ejpam-739	36	68	α	α	PROPN
ejpam-739	36	69	∈	∈	PROPN
ejpam-739	36	70	(	(	PUNCT
ejpam-739	36	71	0,β	0,β	PROPN
ejpam-739	36	72	]	]	X
ejpam-739	36	73	we	we	PRON
ejpam-739	36	74	have	have	VERB
ejpam-739	36	75	‖[gα	‖[gα	NOUN
ejpam-739	36	76	,	,	PUNCT
ejpam-739	36	77	β	β	X
ejpam-739	36	78	u	u	NOUN
ejpam-739	36	79	(	(	PUNCT
ejpam-739	36	80	f	f	PROPN
ejpam-739	36	81	)	)	PUNCT
ejpam-739	36	82	]	]	PUNCT
ejpam-739	36	83	(	(	PUNCT
ejpam-739	36	84	q)−	q)−	PROPN
ejpam-739	36	85	f	f	X
ejpam-739	36	86	(	(	PUNCT
ejpam-739	36	87	q)‖r	q)‖r	NOUN
ejpam-739	36	88	∼	∼	NOUN
ejpam-739	36	89	α	α	NOUN
ejpam-739	36	90	,	,	PUNCT
ejpam-739	36	91	where	where	SCONJ
ejpam-739	36	92	the	the	DET
ejpam-739	36	93	constants	constant	NOUN
ejpam-739	36	94	in	in	ADP
ejpam-739	36	95	the	the	DET
ejpam-739	36	96	equivalence	equivalence	NOUN
ejpam-739	36	97	depend	depend	VERB
ejpam-739	36	98	only	only	ADV
ejpam-739	36	99	on	on	ADP
ejpam-739	36	100	f	f	PROPN
ejpam-739	36	101	,	,	PUNCT
ejpam-739	36	102	q	q	X
ejpam-739	36	103	,	,	PUNCT
ejpam-739	36	104	r	r	NOUN
ejpam-739	36	105	,	,	PUNCT
ejpam-739	36	106	r1	r1	NOUN
ejpam-739	36	107	and	and	CCONJ
ejpam-739	36	108	β	β	X
ejpam-739	36	109	.	.	PUNCT
ejpam-739	37	1	(	(	PUNCT
ejpam-739	37	2	iii	iii	NOUN
ejpam-739	37	3	)	)	PUNCT
ejpam-739	37	4	for	for	ADP
ejpam-739	37	5	ut	ut	PROPN
ejpam-739	37	6	(	(	PUNCT
ejpam-739	37	7	f	f	PROPN
ejpam-739	37	8	)	)	PUNCT
ejpam-739	37	9	(	(	PUNCT
ejpam-739	37	10	z	z	X
ejpam-739	37	11	)	)	PUNCT
ejpam-739	37	12	=	=	SYM
ejpam-739	37	13	2t3	2t3	NUM
ejpam-739	37	14	π	π	SYM
ejpam-739	37	15	∫	∫	PROPN
ejpam-739	38	1	+	+	ADJ
ejpam-739	38	2	∞	∞	PROPN
ejpam-739	38	3	−∞	−∞	X
ejpam-739	38	4	f	f	PROPN
ejpam-739	38	5	(	(	PUNCT
ejpam-739	38	6	ze−iu	ze−iu	NUM
ejpam-739	38	7	)	)	PUNCT
ejpam-739	38	8	(	(	PUNCT
ejpam-739	38	9	u2+t2)2	u2+t2)2	NOUN
ejpam-739	38	10	du	du	NOUN
ejpam-739	38	11	we	we	PRON
ejpam-739	38	12	have	have	VERB
ejpam-739	38	13	that	that	PRON
ejpam-739	38	14	g	g	PROPN
ejpam-739	38	15	α	α	PROPN
ejpam-739	38	16	,	,	PUNCT
ejpam-739	38	17	β	β	X
ejpam-739	38	18	u	u	NOUN
ejpam-739	38	19	(	(	PUNCT
ejpam-739	38	20	f	f	PROPN
ejpam-739	38	21	)	)	PUNCT
ejpam-739	38	22	(	(	PUNCT
ejpam-739	38	23	z	z	NOUN
ejpam-739	38	24	)	)	PUNCT
ejpam-739	38	25	is	be	AUX
ejpam-739	38	26	analytic	analytic	ADJ
ejpam-739	38	27	in	in	ADP
ejpam-739	38	28	dr	dr	PROPN
ejpam-739	38	29	and	and	CCONJ
ejpam-739	38	30	we	we	PRON
ejpam-739	38	31	can	can	AUX
ejpam-739	38	32	write	write	VERB
ejpam-739	38	33	g	g	PROPN
ejpam-739	38	34	α	α	PROPN
ejpam-739	38	35	,	,	PUNCT
ejpam-739	38	36	β	β	X
ejpam-739	38	37	u	u	NOUN
ejpam-739	38	38	(	(	PUNCT
ejpam-739	38	39	f	f	PROPN
ejpam-739	38	40	)	)	PUNCT
ejpam-739	38	41	(	(	PUNCT
ejpam-739	38	42	z	z	NOUN
ejpam-739	38	43	)	)	PUNCT
ejpam-739	38	44	=	=	SYM
ejpam-739	39	1	∞	∞	NUM
ejpam-739	39	2	∑	∑	PROPN
ejpam-739	39	3	k=0	k=0	PROPN
ejpam-739	39	4	ak	ak	PROPN
ejpam-739	39	5	·	·	PUNCT
ejpam-739	39	6	bk(α	bk(α	PROPN
ejpam-739	39	7	,	,	PUNCT
ejpam-739	39	8	β	β	X
ejpam-739	39	9	)	)	PUNCT
ejpam-739	39	10	·	·	PUNCT
ejpam-739	40	1	zk	zk	PROPN
ejpam-739	40	2	,	,	PUNCT
ejpam-739	40	3	z	z	PROPN
ejpam-739	40	4	∈	∈	PROPN
ejpam-739	40	5	dr	dr	PROPN
ejpam-739	40	6	,	,	PUNCT
ejpam-739	40	7	where	where	SCONJ
ejpam-739	40	8	bk(α	bk(α	X
ejpam-739	40	9	,	,	PUNCT
ejpam-739	40	10	β	β	X
ejpam-739	40	11	)	)	PUNCT
ejpam-739	40	12	=	=	SYM
ejpam-739	40	13	1	1	NUM
ejpam-739	40	14	beta(α	beta(α	NOUN
ejpam-739	40	15	,	,	PUNCT
ejpam-739	40	16	β	β	X
ejpam-739	40	17	)	)	PUNCT
ejpam-739	40	18	∫	∫	PROPN
ejpam-739	40	19	1	1	NUM
ejpam-739	40	20	0	0	NUM
ejpam-739	40	21	tα−1(1−	tα−1(1−	NOUN
ejpam-739	40	22	t)β−1(1	t)β−1(1	X
ejpam-739	40	23	+	+	NUM
ejpam-739	40	24	kt)e−kt	kt)e−kt	NOUN
ejpam-739	40	25	d	d	NOUN
ejpam-739	40	26	t.	t.	PROPN
ejpam-739	40	27	also	also	ADV
ejpam-739	40	28	,	,	PUNCT
ejpam-739	40	29	if	if	SCONJ
ejpam-739	40	30	f	f	PROPN
ejpam-739	40	31	is	be	AUX
ejpam-739	40	32	not	not	PART
ejpam-739	40	33	constant	constant	ADJ
ejpam-739	40	34	for	for	ADP
ejpam-739	40	35	q	q	NOUN
ejpam-739	40	36	=	=	SYM
ejpam-739	40	37	0	0	NUM
ejpam-739	40	38	,	,	PUNCT
ejpam-739	40	39	and	and	CCONJ
ejpam-739	40	40	not	not	PART
ejpam-739	40	41	a	a	DET
ejpam-739	40	42	polynomial	polynomial	NOUN
ejpam-739	40	43	of	of	ADP
ejpam-739	40	44	degree	degree	NOUN
ejpam-739	40	45	≤	≤	NUM
ejpam-739	40	46	q−	q−	PROPN
ejpam-739	40	47	1	1	NUM
ejpam-739	40	48	for	for	ADP
ejpam-739	40	49	q	q	PROPN
ejpam-739	40	50	∈	∈	PROPN
ejpam-739	40	51	n	n	CCONJ
ejpam-739	40	52	,	,	PUNCT
ejpam-739	40	53	then	then	ADV
ejpam-739	40	54	for	for	ADP
ejpam-739	40	55	all	all	DET
ejpam-739	40	56	1≤	1≤	NOUN
ejpam-739	40	57	r	r	NOUN
ejpam-739	40	58	<	<	X
ejpam-739	40	59	r1	r1	NOUN
ejpam-739	40	60	<	<	X
ejpam-739	40	61	r	r	NOUN
ejpam-739	40	62	,	,	PUNCT
ejpam-739	40	63	q	q	PROPN
ejpam-739	40	64	∈	∈	PROPN
ejpam-739	40	65	n∪	n∪	PROPN
ejpam-739	40	66	{	{	PUNCT
ejpam-739	40	67	0	0	NUM
ejpam-739	40	68	}	}	PUNCT
ejpam-739	40	69	,	,	PUNCT
ejpam-739	40	70	α	α	PROPN
ejpam-739	40	71	∈	∈	PROPN
ejpam-739	40	72	(	(	PUNCT
ejpam-739	40	73	0,β	0,β	PROPN
ejpam-739	40	74	]	]	X
ejpam-739	40	75	we	we	PRON
ejpam-739	40	76	have	have	VERB
ejpam-739	40	77	‖[gα	‖[gα	NOUN
ejpam-739	40	78	,	,	PUNCT
ejpam-739	40	79	β	β	X
ejpam-739	40	80	u	u	NOUN
ejpam-739	40	81	(	(	PUNCT
ejpam-739	40	82	f	f	PROPN
ejpam-739	40	83	)	)	PUNCT
ejpam-739	40	84	]	]	PUNCT
ejpam-739	40	85	(	(	PUNCT
ejpam-739	40	86	q)−	q)−	PROPN
ejpam-739	40	87	f	f	X
ejpam-739	40	88	(	(	PUNCT
ejpam-739	40	89	q)‖r	q)‖r	NOUN
ejpam-739	40	90	∼	∼	NOUN
ejpam-739	40	91	α	α	NOUN
ejpam-739	40	92	,	,	PUNCT
ejpam-739	40	93	where	where	SCONJ
ejpam-739	40	94	the	the	DET
ejpam-739	40	95	constants	constant	NOUN
ejpam-739	40	96	in	in	ADP
ejpam-739	40	97	the	the	DET
ejpam-739	40	98	equivalence	equivalence	NOUN
ejpam-739	40	99	depend	depend	VERB
ejpam-739	40	100	only	only	ADV
ejpam-739	40	101	on	on	ADP
ejpam-739	40	102	f	f	PROPN
ejpam-739	40	103	,	,	PUNCT
ejpam-739	40	104	q	q	X
ejpam-739	40	105	,	,	PUNCT
ejpam-739	40	106	r	r	NOUN
ejpam-739	40	107	,	,	PUNCT
ejpam-739	40	108	r1	r1	NOUN
ejpam-739	40	109	and	and	CCONJ
ejpam-739	40	110	β	β	X
ejpam-739	40	111	.	.	PUNCT
ejpam-739	41	1	(	(	PUNCT
ejpam-739	41	2	iv	iv	X
ejpam-739	41	3	)	)	PUNCT
ejpam-739	41	4	for	for	ADP
ejpam-739	41	5	ut	ut	PROPN
ejpam-739	41	6	(	(	PUNCT
ejpam-739	41	7	f	f	PROPN
ejpam-739	41	8	)	)	PUNCT
ejpam-739	41	9	(	(	PUNCT
ejpam-739	41	10	z	z	NOUN
ejpam-739	41	11	)	)	PUNCT
ejpam-739	41	12	=	=	SYM
ejpam-739	41	13	1p	1p	NUM
ejpam-739	41	14	πt	πt	ADP
ejpam-739	41	15	∫+∞	∫+∞	ADV
ejpam-739	41	16	−∞	−∞	ADP
ejpam-739	41	17	f	f	PROPN
ejpam-739	41	18	(	(	PUNCT
ejpam-739	41	19	ze−iu)e−u2	ze−iu)e−u2	PROPN
ejpam-739	41	20	/	/	SYM
ejpam-739	41	21	t	t	NOUN
ejpam-739	41	22	du	du	NOUN
ejpam-739	41	23	we	we	PRON
ejpam-739	41	24	have	have	VERB
ejpam-739	41	25	that	that	PRON
ejpam-739	41	26	g	g	PROPN
ejpam-739	41	27	α	α	PROPN
ejpam-739	41	28	,	,	PUNCT
ejpam-739	41	29	β	β	X
ejpam-739	41	30	u	u	NOUN
ejpam-739	41	31	(	(	PUNCT
ejpam-739	41	32	f	f	PROPN
ejpam-739	41	33	)	)	PUNCT
ejpam-739	41	34	(	(	PUNCT
ejpam-739	41	35	z	z	NOUN
ejpam-739	41	36	)	)	PUNCT
ejpam-739	41	37	is	be	AUX
ejpam-739	41	38	analytic	analytic	ADJ
ejpam-739	41	39	in	in	ADP
ejpam-739	41	40	dr	dr	PROPN
ejpam-739	41	41	and	and	CCONJ
ejpam-739	41	42	we	we	PRON
ejpam-739	41	43	can	can	AUX
ejpam-739	41	44	write	write	VERB
ejpam-739	41	45	g	g	PROPN
ejpam-739	41	46	α	α	PROPN
ejpam-739	41	47	,	,	PUNCT
ejpam-739	41	48	β	β	X
ejpam-739	41	49	u	u	NOUN
ejpam-739	41	50	(	(	PUNCT
ejpam-739	41	51	f	f	PROPN
ejpam-739	41	52	)	)	PUNCT
ejpam-739	41	53	(	(	PUNCT
ejpam-739	41	54	z	z	NOUN
ejpam-739	41	55	)	)	PUNCT
ejpam-739	41	56	=	=	SYM
ejpam-739	42	1	∞	∞	NUM
ejpam-739	42	2	∑	∑	PROPN
ejpam-739	42	3	k=0	k=0	PROPN
ejpam-739	42	4	ak	ak	PROPN
ejpam-739	42	5	·	·	PUNCT
ejpam-739	42	6	bk(α	bk(α	PROPN
ejpam-739	42	7	,	,	PUNCT
ejpam-739	42	8	β)zk	β)zk	PROPN
ejpam-739	42	9	,	,	PUNCT
ejpam-739	42	10	z	z	PROPN
ejpam-739	42	11	∈	∈	PROPN
ejpam-739	42	12	dr	dr	PROPN
ejpam-739	42	13	,	,	PUNCT
ejpam-739	42	14	where	where	SCONJ
ejpam-739	42	15	bk(α	bk(α	X
ejpam-739	42	16	,	,	PUNCT
ejpam-739	42	17	β	β	X
ejpam-739	42	18	)	)	PUNCT
ejpam-739	42	19	=	=	SYM
ejpam-739	42	20	1	1	NUM
ejpam-739	42	21	beta(α	beta(α	NOUN
ejpam-739	42	22	,	,	PUNCT
ejpam-739	42	23	β	β	X
ejpam-739	42	24	)	)	PUNCT
ejpam-739	42	25	∫	∫	PROPN
ejpam-739	42	26	1	1	NUM
ejpam-739	42	27	0	0	NUM
ejpam-739	42	28	tα−1(1−	tα−1(1−	NOUN
ejpam-739	42	29	t)β−1e−(k	t)β−1e−(k	PROPN
ejpam-739	43	1	2/4)t	2/4)t	NUM
ejpam-739	44	1	d	d	NOUN
ejpam-739	44	2	t.	t.	PROPN
ejpam-739	44	3	also	also	ADV
ejpam-739	44	4	,	,	PUNCT
ejpam-739	44	5	if	if	SCONJ
ejpam-739	44	6	f	f	PROPN
ejpam-739	44	7	is	be	AUX
ejpam-739	44	8	not	not	PART
ejpam-739	44	9	constant	constant	ADJ
ejpam-739	44	10	for	for	ADP
ejpam-739	44	11	q	q	NOUN
ejpam-739	44	12	=	=	SYM
ejpam-739	44	13	0	0	NUM
ejpam-739	44	14	,	,	PUNCT
ejpam-739	44	15	and	and	CCONJ
ejpam-739	44	16	not	not	PART
ejpam-739	44	17	a	a	DET
ejpam-739	44	18	polynomial	polynomial	NOUN
ejpam-739	44	19	of	of	ADP
ejpam-739	44	20	degree	degree	NOUN
ejpam-739	44	21	≤	≤	NUM
ejpam-739	44	22	q−	q−	PROPN
ejpam-739	44	23	1	1	NUM
ejpam-739	44	24	for	for	ADP
ejpam-739	44	25	q	q	PROPN
ejpam-739	44	26	∈	∈	PROPN
ejpam-739	44	27	n	n	CCONJ
ejpam-739	44	28	,	,	PUNCT
ejpam-739	44	29	then	then	ADV
ejpam-739	44	30	for	for	ADP
ejpam-739	44	31	all	all	DET
ejpam-739	44	32	1≤	1≤	NOUN
ejpam-739	44	33	r	r	NOUN
ejpam-739	44	34	<	<	X
ejpam-739	44	35	r1	r1	NOUN
ejpam-739	44	36	<	<	X
ejpam-739	44	37	r	r	NOUN
ejpam-739	44	38	,	,	PUNCT
ejpam-739	44	39	q	q	PROPN
ejpam-739	44	40	∈	∈	PROPN
ejpam-739	44	41	n∪	n∪	PROPN
ejpam-739	44	42	{	{	PUNCT
ejpam-739	44	43	0	0	NUM
ejpam-739	44	44	}	}	PUNCT
ejpam-739	44	45	,	,	PUNCT
ejpam-739	44	46	α	α	PROPN
ejpam-739	44	47	∈	∈	PROPN
ejpam-739	44	48	(	(	PUNCT
ejpam-739	44	49	0,β	0,β	PROPN
ejpam-739	44	50	]	]	X
ejpam-739	44	51	we	we	PRON
ejpam-739	44	52	have	have	VERB
ejpam-739	44	53	‖[gα	‖[gα	NOUN
ejpam-739	44	54	,	,	PUNCT
ejpam-739	44	55	β	β	X
ejpam-739	44	56	u	u	NOUN
ejpam-739	44	57	(	(	PUNCT
ejpam-739	44	58	f	f	PROPN
ejpam-739	44	59	)	)	PUNCT
ejpam-739	44	60	]	]	PUNCT
ejpam-739	44	61	(	(	PUNCT
ejpam-739	44	62	q)−	q)−	PROPN
ejpam-739	44	63	f	f	X
ejpam-739	44	64	(	(	PUNCT
ejpam-739	44	65	q)‖r	q)‖r	NOUN
ejpam-739	44	66	∼	∼	NOUN
ejpam-739	44	67	α	α	NOUN
ejpam-739	44	68	,	,	PUNCT
ejpam-739	44	69	where	where	SCONJ
ejpam-739	44	70	the	the	DET
ejpam-739	44	71	constants	constant	NOUN
ejpam-739	44	72	in	in	ADP
ejpam-739	44	73	the	the	DET
ejpam-739	44	74	equivalence	equivalence	NOUN
ejpam-739	44	75	depend	depend	VERB
ejpam-739	44	76	only	only	ADV
ejpam-739	44	77	on	on	ADP
ejpam-739	44	78	f	f	PROPN
ejpam-739	44	79	,	,	PUNCT
ejpam-739	44	80	q	q	X
ejpam-739	44	81	,	,	PUNCT
ejpam-739	44	82	r	r	NOUN
ejpam-739	44	83	,	,	PUNCT
ejpam-739	44	84	r1	r1	NOUN
ejpam-739	44	85	and	and	CCONJ
ejpam-739	44	86	β	β	X
ejpam-739	44	87	.	.	PUNCT
ejpam-739	45	1	s.	s.	PROPN
ejpam-739	45	2	gal	gal	PROPN
ejpam-739	45	3	/	/	SYM
ejpam-739	45	4	eur	eur	PROPN
ejpam-739	45	5	.	.	PUNCT
ejpam-739	46	1	j.	j.	PROPN
ejpam-739	46	2	pure	pure	PROPN
ejpam-739	46	3	appl	appl	PROPN
ejpam-739	46	4	.	.	PROPN
ejpam-739	46	5	math	math	PROPN
ejpam-739	46	6	,	,	PUNCT
ejpam-739	46	7	3	3	NUM
ejpam-739	46	8	(	(	PUNCT
ejpam-739	46	9	2010	2010	NUM
ejpam-739	46	10	)	)	PUNCT
ejpam-739	46	11	,	,	PUNCT
ejpam-739	46	12	1150	1150	NUM
ejpam-739	46	13	-	-	SYM
ejpam-739	46	14	1164	1164	NUM
ejpam-739	46	15	1153	1153	NUM
ejpam-739	46	16	proof	proof	NOUN
ejpam-739	46	17	.	.	PUNCT
ejpam-739	47	1	(	(	PUNCT
ejpam-739	47	2	i	i	NOUN
ejpam-739	47	3	)	)	PUNCT
ejpam-739	47	4	by	by	ADP
ejpam-739	47	5	gal	gal	PROPN
ejpam-739	47	6	[	[	X
ejpam-739	47	7	2	2	NUM
ejpam-739	47	8	,	,	PUNCT
ejpam-739	47	9	p.	p.	NOUN
ejpam-739	47	10	213	213	NUM
ejpam-739	47	11	,	,	PUNCT
ejpam-739	47	12	theorem	theorem	VERB
ejpam-739	47	13	3.2.5	3.2.5	NUM
ejpam-739	47	14	,	,	PUNCT
ejpam-739	47	15	(	(	PUNCT
ejpam-739	47	16	i	i	NOUN
ejpam-739	47	17	)	)	PUNCT
ejpam-739	47	18	]	]	PUNCT
ejpam-739	47	19	,	,	PUNCT
ejpam-739	47	20	ut	ut	PROPN
ejpam-739	47	21	(	(	PUNCT
ejpam-739	47	22	f	f	PROPN
ejpam-739	47	23	)	)	PUNCT
ejpam-739	47	24	(	(	PUNCT
ejpam-739	47	25	z	z	NOUN
ejpam-739	47	26	)	)	PUNCT
ejpam-739	47	27	is	be	AUX
ejpam-739	47	28	analytic	analytic	ADJ
ejpam-739	47	29	(	(	PUNCT
ejpam-739	47	30	as	as	ADP
ejpam-739	47	31	function	function	NOUN
ejpam-739	47	32	of	of	ADP
ejpam-739	47	33	z	z	NOUN
ejpam-739	47	34	)	)	PUNCT
ejpam-739	47	35	in	in	ADP
ejpam-739	47	36	dr	dr	PROPN
ejpam-739	48	1	and	and	CCONJ
ejpam-739	48	2	we	we	PRON
ejpam-739	48	3	can	can	AUX
ejpam-739	48	4	write	write	VERB
ejpam-739	48	5	ut	ut	PROPN
ejpam-739	48	6	(	(	PUNCT
ejpam-739	48	7	f	f	PROPN
ejpam-739	48	8	)	)	PUNCT
ejpam-739	48	9	(	(	PUNCT
ejpam-739	48	10	z	z	NOUN
ejpam-739	48	11	)	)	PUNCT
ejpam-739	48	12	=	=	SYM
ejpam-739	49	1	∞	∞	NUM
ejpam-739	49	2	∑	∑	PUNCT
ejpam-739	49	3	k=0	k=0	PROPN
ejpam-739	49	4	ake−ktzk	ake−ktzk	NOUN
ejpam-739	49	5	,	,	PUNCT
ejpam-739	49	6	for	for	ADP
ejpam-739	49	7	all	all	DET
ejpam-739	49	8	|z|	|z|	NOUN
ejpam-739	49	9	<	<	X
ejpam-739	49	10	r	r	NOUN
ejpam-739	49	11	and	and	CCONJ
ejpam-739	49	12	t	t	PROPN
ejpam-739	49	13	≥	≥	NUM
ejpam-739	49	14	0	0	NUM
ejpam-739	49	15	.	.	PUNCT
ejpam-739	50	1	since	since	SCONJ
ejpam-739	50	2	|∑∞k=0	|∑∞k=0	PROPN
ejpam-739	50	3	ake−ktzk|	ake−ktzk|	PROPN
ejpam-739	50	4	≤∑∞k=0	≤∑∞k=0	NOUN
ejpam-739	50	5	|ak|·|z|k	|ak|·|z|k	NOUN
ejpam-739	50	6	<	<	X
ejpam-739	50	7	∞	∞	PROPN
ejpam-739	50	8	,	,	PUNCT
ejpam-739	50	9	this	this	PRON
ejpam-739	50	10	implies	imply	VERB
ejpam-739	50	11	that	that	SCONJ
ejpam-739	50	12	for	for	ADP
ejpam-739	50	13	fixed	fix	VERB
ejpam-739	50	14	|z|	|z|	NOUN
ejpam-739	50	15	<	<	X
ejpam-739	50	16	r	r	NOUN
ejpam-739	50	17	,	,	PUNCT
ejpam-739	50	18	the	the	DET
ejpam-739	50	19	series	series	NOUN
ejpam-739	50	20	in	in	ADP
ejpam-739	50	21	t	t	PROPN
ejpam-739	50	22	,	,	PUNCT
ejpam-739	50	23	∑∞	∑∞	PUNCT
ejpam-739	50	24	k=0	k=0	PROPN
ejpam-739	50	25	ake−ktzk	ake−ktzk	NOUN
ejpam-739	50	26	is	be	AUX
ejpam-739	50	27	uniformly	uniformly	ADV
ejpam-739	50	28	convergent	convergent	NOUN
ejpam-739	50	29	on	on	ADP
ejpam-739	50	30	[	[	X
ejpam-739	50	31	0,∞	0,∞	NOUN
ejpam-739	50	32	)	)	PUNCT
ejpam-739	50	33	,	,	PUNCT
ejpam-739	50	34	and	and	CCONJ
ejpam-739	50	35	therefore	therefore	ADV
ejpam-739	50	36	we	we	PRON
ejpam-739	50	37	immediately	immediately	ADV
ejpam-739	50	38	can	can	AUX
ejpam-739	50	39	write	write	VERB
ejpam-739	50	40	g	g	PROPN
ejpam-739	50	41	α	α	PROPN
ejpam-739	50	42	,	,	PUNCT
ejpam-739	50	43	β	β	X
ejpam-739	50	44	u	u	NOUN
ejpam-739	50	45	(	(	PUNCT
ejpam-739	50	46	f	f	PROPN
ejpam-739	50	47	)	)	PUNCT
ejpam-739	50	48	(	(	PUNCT
ejpam-739	50	49	z	z	NOUN
ejpam-739	50	50	)	)	PUNCT
ejpam-739	50	51	=	=	SYM
ejpam-739	51	1	∞	∞	NUM
ejpam-739	51	2	∑	∑	PROPN
ejpam-739	51	3	k=0	k=0	PROPN
ejpam-739	51	4	ak	ak	PROPN
ejpam-739	51	5	bk(α	bk(α	PROPN
ejpam-739	51	6	,	,	PUNCT
ejpam-739	51	7	β)zk	β)zk	PROPN
ejpam-739	51	8	,	,	PUNCT
ejpam-739	51	9	where	where	SCONJ
ejpam-739	51	10	bk(α	bk(α	NOUN
ejpam-739	51	11	,	,	PUNCT
ejpam-739	51	12	β	β	X
ejpam-739	51	13	)	)	PUNCT
ejpam-739	51	14	=	=	SYM
ejpam-739	51	15	1	1	NUM
ejpam-739	51	16	beta(α	beta(α	NOUN
ejpam-739	51	17	,	,	PUNCT
ejpam-739	51	18	β	β	X
ejpam-739	51	19	)	)	PUNCT
ejpam-739	51	20	∫	∫	PROPN
ejpam-739	51	21	1	1	NUM
ejpam-739	51	22	0	0	NUM
ejpam-739	51	23	tα−1(1−	tα−1(1−	PROPN
ejpam-739	51	24	t)β−1e−kt	t)β−1e−kt	PROPN
ejpam-739	51	25	d	d	NOUN
ejpam-739	51	26	t.	t.	NOUN
ejpam-739	51	27	in	in	ADP
ejpam-739	51	28	other	other	ADJ
ejpam-739	51	29	order	order	NOUN
ejpam-739	51	30	of	of	ADP
ejpam-739	51	31	ideas	idea	NOUN
ejpam-739	51	32	,	,	PUNCT
ejpam-739	51	33	we	we	PRON
ejpam-739	51	34	easily	easily	ADV
ejpam-739	51	35	can	can	AUX
ejpam-739	51	36	write	write	VERB
ejpam-739	51	37	g	g	PROPN
ejpam-739	51	38	α	α	PROPN
ejpam-739	51	39	,	,	PUNCT
ejpam-739	51	40	β	β	X
ejpam-739	51	41	u	u	NOUN
ejpam-739	51	42	(	(	PUNCT
ejpam-739	51	43	f	f	PROPN
ejpam-739	51	44	)	)	PUNCT
ejpam-739	51	45	(	(	PUNCT
ejpam-739	51	46	z)−	z)−	PROPN
ejpam-739	51	47	f	f	X
ejpam-739	51	48	(	(	PUNCT
ejpam-739	51	49	z	z	NOUN
ejpam-739	51	50	)	)	PUNCT
ejpam-739	51	51	=	=	SYM
ejpam-739	51	52	1	1	NUM
ejpam-739	51	53	beta(α	beta(α	NOUN
ejpam-739	51	54	,	,	PUNCT
ejpam-739	51	55	β	β	X
ejpam-739	51	56	)	)	PUNCT
ejpam-739	51	57	·	·	PUNCT
ejpam-739	52	1	∫	∫	PROPN
ejpam-739	52	2	1	1	NUM
ejpam-739	52	3	0	0	NUM
ejpam-739	52	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	52	5	t)β−1[ut	t)β−1[ut	PROPN
ejpam-739	52	6	(	(	PUNCT
ejpam-739	52	7	f	f	PROPN
ejpam-739	52	8	)	)	PUNCT
ejpam-739	52	9	(	(	PUNCT
ejpam-739	52	10	z)−	z)−	PROPN
ejpam-739	52	11	f	f	X
ejpam-739	52	12	(	(	PUNCT
ejpam-739	52	13	z)]d	z)]d	PROPN
ejpam-739	52	14	t	t	PROPN
ejpam-739	52	15	,	,	PUNCT
ejpam-739	52	16	which	which	PRON
ejpam-739	52	17	together	together	ADV
ejpam-739	52	18	with	with	ADP
ejpam-739	52	19	the	the	DET
ejpam-739	52	20	estimate	estimate	NOUN
ejpam-739	52	21	|ut	|ut	NOUN
ejpam-739	52	22	(	(	PUNCT
ejpam-739	52	23	f	f	PROPN
ejpam-739	52	24	)	)	PUNCT
ejpam-739	52	25	(	(	PUNCT
ejpam-739	52	26	z)−	z)−	PROPN
ejpam-739	52	27	f	f	X
ejpam-739	52	28	(	(	PUNCT
ejpam-739	52	29	z)|	z)|	NOUN
ejpam-739	52	30	≤	≤	PROPN
ejpam-739	52	31	cr	cr	PROPN
ejpam-739	53	1	(	(	PUNCT
ejpam-739	53	2	f	f	PROPN
ejpam-739	53	3	)	)	PUNCT
ejpam-739	53	4	t	t	PROPN
ejpam-739	53	5	in	in	ADP
ejpam-739	53	6	gal	gal	PROPN
ejpam-739	54	1	[	[	X
ejpam-739	54	2	2	2	NUM
ejpam-739	54	3	,	,	PUNCT
ejpam-739	54	4	p.	p.	NOUN
ejpam-739	54	5	213	213	NUM
ejpam-739	54	6	,	,	PUNCT
ejpam-739	54	7	theorem	theorem	VERB
ejpam-739	54	8	3.2.5	3.2.5	NUM
ejpam-739	54	9	,	,	PUNCT
ejpam-739	54	10	(	(	PUNCT
ejpam-739	54	11	iii	iii	NOUN
ejpam-739	54	12	)	)	PUNCT
ejpam-739	54	13	]	]	PUNCT
ejpam-739	54	14	,	,	PUNCT
ejpam-739	54	15	implies	imply	VERB
ejpam-739	54	16	|gα	|gα	PROPN
ejpam-739	54	17	,	,	PUNCT
ejpam-739	54	18	β	β	X
ejpam-739	54	19	u	u	NOUN
ejpam-739	54	20	(	(	PUNCT
ejpam-739	54	21	f	f	PROPN
ejpam-739	54	22	)	)	PUNCT
ejpam-739	54	23	(	(	PUNCT
ejpam-739	54	24	z)−	z)−	PROPN
ejpam-739	54	25	f	f	X
ejpam-739	54	26	(	(	PUNCT
ejpam-739	54	27	z)|	z)|	ADP
ejpam-739	54	28	≤	≤	ADV
ejpam-739	54	29	1	1	NUM
ejpam-739	54	30	beta(α	beta(α	NOUN
ejpam-739	54	31	,	,	PUNCT
ejpam-739	54	32	β	β	X
ejpam-739	54	33	)	)	PUNCT
ejpam-739	54	34	·	·	PUNCT
ejpam-739	55	1	∫	∫	PROPN
ejpam-739	55	2	1	1	NUM
ejpam-739	55	3	0	0	NUM
ejpam-739	55	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	55	5	t)β−1|ut	t)β−1|ut	NUM
ejpam-739	55	6	(	(	PUNCT
ejpam-739	55	7	f	f	NOUN
ejpam-739	55	8	)	)	PUNCT
ejpam-739	55	9	(	(	PUNCT
ejpam-739	55	10	z)−	z)−	PROPN
ejpam-739	55	11	f	f	PROPN
ejpam-739	55	12	(	(	PUNCT
ejpam-739	55	13	z)|d	z)|d	PROPN
ejpam-739	55	14	t	t	PROPN
ejpam-739	55	15	≤	≤	PROPN
ejpam-739	55	16	cr	cr	PROPN
ejpam-739	55	17	(	(	PUNCT
ejpam-739	55	18	f	f	PROPN
ejpam-739	55	19	)	)	PUNCT
ejpam-739	55	20	1	1	NUM
ejpam-739	55	21	beta(α	beta(α	NOUN
ejpam-739	55	22	,	,	PUNCT
ejpam-739	55	23	β	β	X
ejpam-739	55	24	)	)	PUNCT
ejpam-739	55	25	·	·	PUNCT
ejpam-739	56	1	∫	∫	PROPN
ejpam-739	57	1	1	1	NUM
ejpam-739	57	2	0	0	X
ejpam-739	58	1	tα(1−	tα(1−	NOUN
ejpam-739	58	2	t)β−1d	t)β−1d	PROPN
ejpam-739	58	3	t	t	NOUN
ejpam-739	58	4	=	=	SYM
ejpam-739	58	5	cr	cr	PROPN
ejpam-739	58	6	(	(	PUNCT
ejpam-739	58	7	f	f	PROPN
ejpam-739	58	8	)	)	PUNCT
ejpam-739	58	9	·	·	PUNCT
ejpam-739	58	10	beta(α+	beta(α+	NOUN
ejpam-739	58	11	1,β	1,β	NOUN
ejpam-739	58	12	)	)	PUNCT
ejpam-739	58	13	beta(α	beta(α	NOUN
ejpam-739	58	14	,	,	PUNCT
ejpam-739	58	15	β	β	NOUN
ejpam-739	58	16	)	)	PUNCT
ejpam-739	58	17	=	=	SYM
ejpam-739	59	1	cr	cr	PROPN
ejpam-739	59	2	(	(	PUNCT
ejpam-739	59	3	f	f	PROPN
ejpam-739	59	4	)	)	PUNCT
ejpam-739	59	5	·	·	PUNCT
ejpam-739	60	1	α	α	INTJ
ejpam-739	60	2	α+	α+	X
ejpam-739	60	3	β	β	NOUN
ejpam-739	60	4	≤	≤	NUM
ejpam-739	60	5	cr	cr	PROPN
ejpam-739	60	6	(	(	PUNCT
ejpam-739	60	7	f	f	PROPN
ejpam-739	60	8	)	)	PUNCT
ejpam-739	60	9	·	·	PUNCT
ejpam-739	60	10	α	α	NOUN
ejpam-739	60	11	,	,	PUNCT
ejpam-739	60	12	for	for	ADP
ejpam-739	60	13	all	all	DET
ejpam-739	60	14	|z|	|z|	NOUN
ejpam-739	60	15	≤	≤	NUM
ejpam-739	60	16	r	r	NOUN
ejpam-739	60	17	,	,	PUNCT
ejpam-739	60	18	where	where	SCONJ
ejpam-739	60	19	cr	cr	PROPN
ejpam-739	60	20	(	(	PUNCT
ejpam-739	60	21	f	f	PROPN
ejpam-739	60	22	)	)	PUNCT
ejpam-739	60	23	>	>	X
ejpam-739	60	24	0	0	PUNCT
ejpam-739	60	25	is	be	AUX
ejpam-739	60	26	independent	independent	ADJ
ejpam-739	60	27	of	of	ADP
ejpam-739	60	28	z	z	NOUN
ejpam-739	60	29	(	(	PUNCT
ejpam-739	60	30	and	and	CCONJ
ejpam-739	60	31	α	α	NOUN
ejpam-739	60	32	,	,	PUNCT
ejpam-739	60	33	β	β	NOUN
ejpam-739	60	34	)	)	PUNCT
ejpam-739	60	35	but	but	CCONJ
ejpam-739	60	36	depends	depend	VERB
ejpam-739	60	37	on	on	ADP
ejpam-739	60	38	f	f	PROPN
ejpam-739	60	39	and	and	CCONJ
ejpam-739	60	40	r.	r.	PROPN
ejpam-739	60	41	here	here	ADV
ejpam-739	60	42	we	we	PRON
ejpam-739	60	43	used	use	VERB
ejpam-739	60	44	the	the	DET
ejpam-739	60	45	well	well	ADV
ejpam-739	60	46	known	know	VERB
ejpam-739	60	47	formula	formula	NOUN
ejpam-739	60	48	beta(α+1,β	beta(α+1,β	NOUN
ejpam-739	60	49	)	)	PUNCT
ejpam-739	60	50	beta(α	beta(α	NOUN
ejpam-739	60	51	,	,	PUNCT
ejpam-739	60	52	β	β	X
ejpam-739	60	53	)	)	PUNCT
ejpam-739	61	1	=	=	SYM
ejpam-739	61	2	α	α	PROPN
ejpam-739	61	3	α+β	α+β	PROPN
ejpam-739	61	4	.	.	PUNCT
ejpam-739	62	1	now	now	ADV
ejpam-739	62	2	,	,	PUNCT
ejpam-739	62	3	let	let	VERB
ejpam-739	62	4	q	q	PROPN
ejpam-739	62	5	∈	∈	PROPN
ejpam-739	62	6	n	n	NOUN
ejpam-739	62	7	∪	∪	X
ejpam-739	62	8	{	{	PUNCT
ejpam-739	62	9	0	0	NUM
ejpam-739	62	10	}	}	PUNCT
ejpam-739	62	11	and	and	CCONJ
ejpam-739	62	12	1	1	NUM
ejpam-739	62	13	≤	≤	NOUN
ejpam-739	62	14	r	r	NOUN
ejpam-739	62	15	<	<	X
ejpam-739	62	16	r1	r1	PROPN
ejpam-739	62	17	<	<	X
ejpam-739	62	18	r.	r.	PROPN
ejpam-739	62	19	denoting	denote	VERB
ejpam-739	62	20	by	by	ADP
ejpam-739	62	21	γ	γ	PROPN
ejpam-739	62	22	the	the	DET
ejpam-739	62	23	circle	circle	NOUN
ejpam-739	62	24	of	of	ADP
ejpam-739	62	25	radius	radius	NOUN
ejpam-739	62	26	r1	r1	PROPN
ejpam-739	62	27	and	and	CCONJ
ejpam-739	62	28	center	center	NOUN
ejpam-739	62	29	0	0	NUM
ejpam-739	62	30	,	,	PUNCT
ejpam-739	62	31	since	since	SCONJ
ejpam-739	62	32	for	for	SCONJ
ejpam-739	62	33	any	any	DET
ejpam-739	62	34	|z|	|z|	NOUN
ejpam-739	62	35	≤	≤	NOUN
ejpam-739	62	36	r	r	NOUN
ejpam-739	62	37	and	and	CCONJ
ejpam-739	62	38	v	v	NOUN
ejpam-739	62	39	∈	∈	NOUN
ejpam-739	62	40	γ	γ	NOUN
ejpam-739	62	41	we	we	PRON
ejpam-739	62	42	have	have	VERB
ejpam-739	62	43	|v	|v	VERB
ejpam-739	62	44	−	−	PROPN
ejpam-739	62	45	z|	z|	PROPN
ejpam-739	62	46	≥	≥	NOUN
ejpam-739	62	47	r1	r1	VERB
ejpam-739	62	48	−	−	PROPN
ejpam-739	62	49	r	r	NOUN
ejpam-739	62	50	,	,	PUNCT
ejpam-739	62	51	by	by	ADP
ejpam-739	62	52	using	use	VERB
ejpam-739	62	53	the	the	DET
ejpam-739	62	54	cauchy	cauchy	NOUN
ejpam-739	62	55	’s	’s	PART
ejpam-739	62	56	formula	formula	NOUN
ejpam-739	62	57	,	,	PUNCT
ejpam-739	62	58	for	for	ADP
ejpam-739	62	59	all	all	DET
ejpam-739	62	60	|z|	|z|	NOUN
ejpam-739	62	61	≤	≤	NUM
ejpam-739	62	62	r	r	NOUN
ejpam-739	62	63	and	and	CCONJ
ejpam-739	62	64	0	0	NUM
ejpam-739	62	65	<	<	X
ejpam-739	62	66	α	α	PRON
ejpam-739	62	67	≤	≤	PUNCT
ejpam-739	62	68	β	β	X
ejpam-739	62	69	≤	≤	NUM
ejpam-739	62	70	1	1	NUM
ejpam-739	62	71	,	,	PUNCT
ejpam-739	62	72	α+	α+	PUNCT
ejpam-739	62	73	β	β	X
ejpam-739	62	74	≥	≥	NUM
ejpam-739	62	75	1	1	NUM
ejpam-739	62	76	,	,	PUNCT
ejpam-739	62	77	we	we	PRON
ejpam-739	62	78	get	get	VERB
ejpam-739	62	79	|[gα	|[gα	NOUN
ejpam-739	62	80	,	,	PUNCT
ejpam-739	62	81	β	β	X
ejpam-739	62	82	u	u	NOUN
ejpam-739	62	83	(	(	PUNCT
ejpam-739	62	84	f	f	PROPN
ejpam-739	62	85	)	)	PUNCT
ejpam-739	62	86	]	]	X
ejpam-739	62	87	(	(	PUNCT
ejpam-739	62	88	q)(z)−	q)(z)−	PROPN
ejpam-739	62	89	f	f	X
ejpam-739	62	90	(	(	PUNCT
ejpam-739	62	91	q)(z)|	q)(z)|	PROPN
ejpam-739	62	92	=	=	SYM
ejpam-739	62	93	q	q	NOUN
ejpam-739	62	94	!	!	PUNCT
ejpam-739	63	1	2π	2π	PROPN
ejpam-739	63	2	�	�	PROPN
ejpam-739	63	3	�	�	PROPN
ejpam-739	63	4	�	�	PROPN
ejpam-739	63	5	�	�	PROPN
ejpam-739	63	6	�	�	PROPN
ejpam-739	63	7	∫	∫	PROPN
ejpam-739	63	8	γ	γ	PROPN
ejpam-739	63	9	g	g	PROPN
ejpam-739	63	10	α	α	PROPN
ejpam-739	63	11	,	,	PUNCT
ejpam-739	63	12	β	β	X
ejpam-739	63	13	u	u	NOUN
ejpam-739	63	14	(	(	PUNCT
ejpam-739	63	15	f	f	PROPN
ejpam-739	63	16	)	)	PUNCT
ejpam-739	63	17	(	(	PUNCT
ejpam-739	63	18	z)−	z)−	PROPN
ejpam-739	63	19	f	f	X
ejpam-739	63	20	(	(	PUNCT
ejpam-739	63	21	z	z	NOUN
ejpam-739	63	22	)	)	PUNCT
ejpam-739	63	23	(	(	PUNCT
ejpam-739	63	24	v−	v−	PROPN
ejpam-739	63	25	z)q+1	z)q+1	PROPN
ejpam-739	63	26	dv	dv	PROPN
ejpam-739	63	27	�	�	PROPN
ejpam-739	63	28	�	�	PROPN
ejpam-739	63	29	�	�	PROPN
ejpam-739	63	30	�	�	PROPN
ejpam-739	63	31	�	�	PROPN
ejpam-739	63	32	≤	≤	PROPN
ejpam-739	63	33	cr1	cr1	PROPN
ejpam-739	63	34	(	(	PUNCT
ejpam-739	63	35	f	f	X
ejpam-739	63	36	)	)	PUNCT
ejpam-739	63	37	α	α	NOUN
ejpam-739	63	38	·	·	PUNCT
ejpam-739	64	1	q	q	NOUN
ejpam-739	64	2	2π	2π	NOUN
ejpam-739	64	3	·	·	PUNCT
ejpam-739	64	4	2πr1	2πr1	NUM
ejpam-739	64	5	(	(	PUNCT
ejpam-739	64	6	r1	r1	PROPN
ejpam-739	64	7	−	−	PROPN
ejpam-739	64	8	r)q+1	r)q+1	PROPN
ejpam-739	64	9	=	=	SYM
ejpam-739	64	10	c∗α	c∗α	PROPN
ejpam-739	64	11	,	,	PUNCT
ejpam-739	64	12	s.	s.	PROPN
ejpam-739	64	13	gal	gal	PROPN
ejpam-739	64	14	/	/	SYM
ejpam-739	64	15	eur	eur	PROPN
ejpam-739	64	16	.	.	PUNCT
ejpam-739	65	1	j.	j.	PROPN
ejpam-739	65	2	pure	pure	PROPN
ejpam-739	65	3	appl	appl	PROPN
ejpam-739	65	4	.	.	PROPN
ejpam-739	65	5	math	math	PROPN
ejpam-739	65	6	,	,	PUNCT
ejpam-739	65	7	3	3	NUM
ejpam-739	65	8	(	(	PUNCT
ejpam-739	65	9	2010	2010	NUM
ejpam-739	65	10	)	)	PUNCT
ejpam-739	65	11	,	,	PUNCT
ejpam-739	65	12	1150	1150	NUM
ejpam-739	65	13	-	-	SYM
ejpam-739	65	14	1164	1164	NUM
ejpam-739	65	15	1154	1154	NUM
ejpam-739	65	16	with	with	ADP
ejpam-739	65	17	c∗	c∗	NOUN
ejpam-739	65	18	depending	depend	VERB
ejpam-739	65	19	only	only	ADV
ejpam-739	65	20	on	on	ADP
ejpam-739	65	21	f	f	PROPN
ejpam-739	65	22	,	,	PUNCT
ejpam-739	65	23	q	q	X
ejpam-739	65	24	,	,	PUNCT
ejpam-739	65	25	r	r	NOUN
ejpam-739	65	26	and	and	CCONJ
ejpam-739	65	27	r1	r1	NOUN
ejpam-739	65	28	.	.	PUNCT
ejpam-739	66	1	it	it	PRON
ejpam-739	66	2	remains	remain	VERB
ejpam-739	66	3	to	to	PART
ejpam-739	66	4	prove	prove	VERB
ejpam-739	66	5	the	the	DET
ejpam-739	66	6	lower	low	ADJ
ejpam-739	66	7	estimate	estimate	NOUN
ejpam-739	66	8	.	.	PUNCT
ejpam-739	67	1	for	for	ADP
ejpam-739	67	2	this	this	DET
ejpam-739	67	3	purpose	purpose	NOUN
ejpam-739	67	4	,	,	PUNCT
ejpam-739	67	5	reasoning	reason	VERB
ejpam-739	67	6	exactly	exactly	ADV
ejpam-739	67	7	as	as	ADP
ejpam-739	67	8	in	in	ADP
ejpam-739	67	9	the	the	DET
ejpam-739	67	10	proof	proof	NOUN
ejpam-739	67	11	of	of	ADP
ejpam-739	67	12	theorem	theorem	ADJ
ejpam-739	67	13	3.2.5	3.2.5	NUM
ejpam-739	67	14	,	,	PUNCT
ejpam-739	67	15	at	at	ADP
ejpam-739	67	16	pages	page	NOUN
ejpam-739	67	17	218	218	NUM
ejpam-739	67	18	-	-	SYM
ejpam-739	67	19	219	219	NUM
ejpam-739	67	20	in	in	ADP
ejpam-739	67	21	the	the	DET
ejpam-739	67	22	book	book	NOUN
ejpam-739	67	23	gal	gal	NOUN
ejpam-739	68	1	[	[	X
ejpam-739	68	2	2	2	NUM
ejpam-739	68	3	]	]	PUNCT
ejpam-739	68	4	,	,	PUNCT
ejpam-739	68	5	for	for	ADP
ejpam-739	68	6	z	z	NOUN
ejpam-739	68	7	=	=	NOUN
ejpam-739	68	8	reiϕ	reiϕ	NOUN
ejpam-739	68	9	and	and	CCONJ
ejpam-739	68	10	p	p	PRON
ejpam-739	68	11	∈	∈	PROPN
ejpam-739	68	12	n∪	n∪	X
ejpam-739	68	13	{	{	PUNCT
ejpam-739	68	14	0	0	NUM
ejpam-739	68	15	}	}	PUNCT
ejpam-739	68	16	we	we	PRON
ejpam-739	68	17	get	get	VERB
ejpam-739	68	18	1	1	NUM
ejpam-739	68	19	2π	2π	NUM
ejpam-739	68	20	∫	∫	NOUN
ejpam-739	69	1	π	π	NOUN
ejpam-739	69	2	−π	−π	PROPN
ejpam-739	69	3	[	[	PUNCT
ejpam-739	69	4	f	f	X
ejpam-739	69	5	(	(	PUNCT
ejpam-739	69	6	q)(z)−	q)(z)−	X
ejpam-739	69	7	[	[	X
ejpam-739	69	8	ut	ut	PROPN
ejpam-739	69	9	(	(	PUNCT
ejpam-739	69	10	f	f	PROPN
ejpam-739	69	11	)	)	PUNCT
ejpam-739	69	12	]	]	PUNCT
ejpam-739	70	1	(	(	PUNCT
ejpam-739	70	2	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	PROPN
ejpam-739	70	3	=	=	SYM
ejpam-739	70	4	aq+p(q+	aq+p(q+	PROPN
ejpam-739	70	5	p)(q+	p)(q+	VERB
ejpam-739	70	6	p−	p−	NOUN
ejpam-739	70	7	1)	1)	NUM
ejpam-739	70	8	...	...	PUNCT
ejpam-739	70	9	(p+	(p+	PROPN
ejpam-739	70	10	1)r	1)r	NUM
ejpam-739	70	11	p[1−	p[1−	PROPN
ejpam-739	70	12	e−(q+p)t	e−(q+p)t	PROPN
ejpam-739	70	13	]	]	PUNCT
ejpam-739	70	14	.	.	PUNCT
ejpam-739	71	1	multiplying	multiply	VERB
ejpam-739	71	2	above	above	ADV
ejpam-739	71	3	with	with	ADP
ejpam-739	71	4	1	1	NUM
ejpam-739	71	5	beta(α	beta(α	NOUN
ejpam-739	71	6	,	,	PUNCT
ejpam-739	71	7	β	β	NOUN
ejpam-739	71	8	)	)	PUNCT
ejpam-739	71	9	tα−1(1−	tα−1(1−	NOUN
ejpam-739	71	10	t)β−1	t)β−1	ADP
ejpam-739	71	11	an	an	DET
ejpam-739	71	12	then	then	ADV
ejpam-739	71	13	integrating	integrate	VERB
ejpam-739	71	14	with	with	ADP
ejpam-739	71	15	respect	respect	NOUN
ejpam-739	71	16	to	to	ADP
ejpam-739	71	17	t	t	PROPN
ejpam-739	71	18	,	,	PUNCT
ejpam-739	71	19	it	it	PRON
ejpam-739	71	20	follows	follow	VERB
ejpam-739	71	21	i	i	PRON
ejpam-739	71	22	:	:	PUNCT
ejpam-739	71	23	=	=	SYM
ejpam-739	71	24	1	1	NUM
ejpam-739	71	25	beta(α	beta(α	NOUN
ejpam-739	71	26	,	,	PUNCT
ejpam-739	71	27	β	β	X
ejpam-739	71	28	)	)	PUNCT
ejpam-739	71	29	·	·	PUNCT
ejpam-739	72	1	∫	∫	PROPN
ejpam-739	72	2	1	1	NUM
ejpam-739	72	3	0	0	NUM
ejpam-739	72	4	¨	¨	NOUN
ejpam-739	72	5	1	1	NUM
ejpam-739	72	6	2π	2π	NUM
ejpam-739	72	7	∫	∫	PROPN
ejpam-739	73	1	π	π	NOUN
ejpam-739	73	2	−π	−π	PROPN
ejpam-739	73	3	[	[	PUNCT
ejpam-739	73	4	f	f	X
ejpam-739	73	5	(	(	PUNCT
ejpam-739	73	6	q)(z)−	q)(z)−	X
ejpam-739	73	7	[	[	X
ejpam-739	73	8	ut	ut	PROPN
ejpam-739	73	9	(	(	PUNCT
ejpam-739	73	10	f	f	PROPN
ejpam-739	73	11	)	)	PUNCT
ejpam-739	73	12	]	]	PUNCT
ejpam-739	74	1	(	(	PUNCT
ejpam-739	74	2	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	NOUN
ejpam-739	74	3	«	«	PUNCT
ejpam-739	74	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	74	5	t)β−1d	t)β−1d	NOUN
ejpam-739	74	6	t	t	NOUN
ejpam-739	74	7	=	=	SYM
ejpam-739	74	8	aq+p(q+	aq+p(q+	PROPN
ejpam-739	74	9	p)(q+	p)(q+	VERB
ejpam-739	74	10	p−	p−	NOUN
ejpam-739	74	11	1)	1)	NUM
ejpam-739	74	12	...	...	PUNCT
ejpam-739	74	13	(p+	(p+	X
ejpam-739	75	1	1)r	1)r	NUM
ejpam-739	75	2	p	p	NOUN
ejpam-739	75	3	1	1	NUM
ejpam-739	75	4	beta(α	beta(α	NOUN
ejpam-739	75	5	,	,	PUNCT
ejpam-739	75	6	β	β	X
ejpam-739	75	7	)	)	PUNCT
ejpam-739	75	8	∫	∫	PROPN
ejpam-739	75	9	1	1	NUM
ejpam-739	75	10	0	0	NUM
ejpam-739	75	11	tα−1(1−	tα−1(1−	PROPN
ejpam-739	75	12	t)β−1[1−	t)β−1[1−	PRON
ejpam-739	75	13	e−(q+p)t]d	e−(q+p)t]d	PRON
ejpam-739	75	14	t.	t.	NOUN
ejpam-739	75	15	applying	apply	VERB
ejpam-739	75	16	the	the	DET
ejpam-739	75	17	fubini	fubini	NOUN
ejpam-739	75	18	’s	’s	PART
ejpam-739	75	19	result	result	NOUN
ejpam-739	75	20	to	to	ADP
ejpam-739	75	21	the	the	DET
ejpam-739	75	22	double	double	ADJ
ejpam-739	75	23	integral	integral	ADJ
ejpam-739	75	24	i	i	PRON
ejpam-739	75	25	and	and	CCONJ
ejpam-739	75	26	then	then	ADV
ejpam-739	75	27	passing	pass	VERB
ejpam-739	75	28	to	to	ADP
ejpam-739	75	29	modulus	modulus	NOUN
ejpam-739	75	30	,	,	PUNCT
ejpam-739	75	31	we	we	PRON
ejpam-739	75	32	easily	easily	ADV
ejpam-739	75	33	obtain	obtain	VERB
ejpam-739	75	34	�	�	PROPN
ejpam-739	75	35	�	�	PROPN
ejpam-739	75	36	�	�	PROPN
ejpam-739	75	37	�	�	PROPN
ejpam-739	75	38	�	�	PROPN
ejpam-739	75	39	1	1	NUM
ejpam-739	75	40	2π	2π	PROPN
ejpam-739	75	41	∫	∫	PROPN
ejpam-739	76	1	π	π	PROPN
ejpam-739	76	2	−π	−π	PROPN
ejpam-739	76	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	76	4			PROPN
ejpam-739	76	5			NOUN
ejpam-739	76	6	1	1	NUM
ejpam-739	76	7	beta(α	beta(α	NOUN
ejpam-739	76	8	,	,	PUNCT
ejpam-739	76	9	β	β	X
ejpam-739	76	10	)	)	PUNCT
ejpam-739	76	11	∫	∫	PROPN
ejpam-739	77	1	1	1	NUM
ejpam-739	77	2	0	0	NUM
ejpam-739	78	1	[	[	PUNCT
ejpam-739	78	2	f	f	X
ejpam-739	78	3	(	(	PUNCT
ejpam-739	78	4	q)(z)−	q)(z)−	X
ejpam-739	78	5	[	[	X
ejpam-739	78	6	ut	ut	PROPN
ejpam-739	78	7	(	(	PUNCT
ejpam-739	78	8	f	f	PROPN
ejpam-739	78	9	)	)	PUNCT
ejpam-739	78	10	]	]	PUNCT
ejpam-739	78	11	(	(	PUNCT
ejpam-739	78	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	78	13	t)β−1d	t)β−1d	PROPN
ejpam-739	78	14	t	t	PROPN
ejpam-739	78	15			PROPN
ejpam-739	78	16			PROPN
ejpam-739	78	17	dϕ	dϕ	PRON
ejpam-739	78	18	�	�	PROPN
ejpam-739	78	19	�	�	PROPN
ejpam-739	78	20	�	�	PROPN
ejpam-739	78	21	�	�	PROPN
ejpam-739	78	22	�	�	PROPN
ejpam-739	78	23	=	=	SYM
ejpam-739	78	24	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	78	25	p)(q+	p)(q+	NOUN
ejpam-739	78	26	p−	p−	NOUN
ejpam-739	78	27	1)	1)	NUM
ejpam-739	78	28	...	...	PUNCT
ejpam-739	78	29	(p+	(p+	X
ejpam-739	79	1	1)r	1)r	PROPN
ejpam-739	79	2	p	p	X
ejpam-739	79	3	·	·	PUNCT
ejpam-739	79	4			PROPN
ejpam-739	79	5			NOUN
ejpam-739	79	6	1	1	NUM
ejpam-739	79	7	beta(α	beta(α	NOUN
ejpam-739	79	8	,	,	PUNCT
ejpam-739	79	9	β	β	X
ejpam-739	79	10	)	)	PUNCT
ejpam-739	79	11	∫	∫	PROPN
ejpam-739	79	12	1	1	NUM
ejpam-739	79	13	0	0	NUM
ejpam-739	79	14	tα−1(1−	tα−1(1−	PROPN
ejpam-739	79	15	t)β−1[1−	t)β−1[1−	PRON
ejpam-739	79	16	e−(q+p)t]d	e−(q+p)t]d	SYM
ejpam-739	79	17	t	t	PROPN
ejpam-739	79	18			PROPN
ejpam-739	79	19			PROPN
ejpam-739	79	20	.	.	PUNCT
ejpam-739	80	1	since	since	SCONJ
ejpam-739	80	2	1	1	NUM
ejpam-739	80	3	beta(α	beta(α	NOUN
ejpam-739	80	4	,	,	PUNCT
ejpam-739	80	5	β	β	X
ejpam-739	80	6	)	)	PUNCT
ejpam-739	80	7	∫	∫	PROPN
ejpam-739	80	8	1	1	NUM
ejpam-739	80	9	0	0	NUM
ejpam-739	81	1	[	[	PUNCT
ejpam-739	81	2	f	f	X
ejpam-739	81	3	(	(	PUNCT
ejpam-739	81	4	q)(z)−	q)(z)−	X
ejpam-739	81	5	[	[	X
ejpam-739	81	6	ut	ut	PROPN
ejpam-739	81	7	(	(	PUNCT
ejpam-739	81	8	f	f	PROPN
ejpam-739	81	9	)	)	PUNCT
ejpam-739	81	10	]	]	PUNCT
ejpam-739	81	11	(	(	PUNCT
ejpam-739	81	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	81	13	t)β−1d	t)β−1d	PROPN
ejpam-739	81	14	t	t	NOUN
ejpam-739	81	15	=	=	SYM
ejpam-739	81	16	f	f	PROPN
ejpam-739	81	17	(	(	PUNCT
ejpam-739	81	18	q)(z)−	q)(z)−	X
ejpam-739	81	19	[	[	X
ejpam-739	81	20	gα	gα	NOUN
ejpam-739	81	21	,	,	PUNCT
ejpam-739	81	22	β	β	X
ejpam-739	81	23	u	u	NOUN
ejpam-739	81	24	(	(	PUNCT
ejpam-739	81	25	f	f	PROPN
ejpam-739	81	26	)	)	PUNCT
ejpam-739	81	27	]	]	X
ejpam-739	81	28	(	(	PUNCT
ejpam-739	81	29	q)(z	q)(z	NOUN
ejpam-739	81	30	)	)	PUNCT
ejpam-739	81	31	,	,	PUNCT
ejpam-739	81	32	the	the	DET
ejpam-739	81	33	previous	previous	ADJ
ejpam-739	81	34	equality	equality	NOUN
ejpam-739	81	35	immediately	immediately	ADV
ejpam-739	81	36	implies	imply	VERB
ejpam-739	81	37	�	�	PROPN
ejpam-739	81	38	�	�	PROPN
ejpam-739	81	39	�	�	PROPN
ejpam-739	81	40	�	�	PROPN
ejpam-739	81	41	�	�	PROPN
ejpam-739	81	42	1	1	NUM
ejpam-739	81	43	2π	2π	PROPN
ejpam-739	81	44	∫	∫	PROPN
ejpam-739	82	1	π	π	NOUN
ejpam-739	82	2	−π	−π	PROPN
ejpam-739	82	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	83	1	h	h	PROPN
ejpam-739	83	2	f	f	PROPN
ejpam-739	83	3	(	(	PUNCT
ejpam-739	83	4	q)(z)−	q)(z)−	X
ejpam-739	83	5	(	(	PUNCT
ejpam-739	83	6	gα	gα	NOUN
ejpam-739	83	7	,	,	PUNCT
ejpam-739	83	8	β	β	X
ejpam-739	83	9	u	u	NOUN
ejpam-739	83	10	(	(	PUNCT
ejpam-739	83	11	f	f	PROPN
ejpam-739	83	12	)	)	PUNCT
ejpam-739	83	13	)	)	PUNCT
ejpam-739	83	14	(	(	PUNCT
ejpam-739	83	15	q)(z	q)(z	NOUN
ejpam-739	83	16	)	)	PUNCT
ejpam-739	83	17	i	i	PRON
ejpam-739	83	18	dϕ	dϕ	VERB
ejpam-739	84	1	�	�	PROPN
ejpam-739	84	2	�	�	PROPN
ejpam-739	84	3	�	�	PROPN
ejpam-739	84	4	�	�	PROPN
ejpam-739	84	5	�	�	PROPN
ejpam-739	84	6	=	=	SYM
ejpam-739	84	7	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	84	8	p)(q+	p)(q+	NOUN
ejpam-739	84	9	p−	p−	NOUN
ejpam-739	84	10	1)	1)	NUM
ejpam-739	84	11	...	...	PUNCT
ejpam-739	84	12	(p+	(p+	X
ejpam-739	84	13	1)r	1)r	PROPN
ejpam-739	84	14	p	p	X
ejpam-739	84	15	·	·	PUNCT
ejpam-739	84	16			PROPN
ejpam-739	84	17			NOUN
ejpam-739	84	18	1	1	NUM
ejpam-739	84	19	beta(α	beta(α	NOUN
ejpam-739	84	20	,	,	PUNCT
ejpam-739	84	21	β	β	X
ejpam-739	84	22	)	)	PUNCT
ejpam-739	84	23	∫	∫	PROPN
ejpam-739	85	1	1	1	NUM
ejpam-739	85	2	0	0	NUM
ejpam-739	85	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	85	4	t)β−1[1−	t)β−1[1−	PRON
ejpam-739	85	5	e−(q+p)t]d	e−(q+p)t]d	PUNCT
ejpam-739	85	6	t	t	PROPN
ejpam-739	85	7			PROPN
ejpam-739	85	8			PROPN
ejpam-739	85	9	s.	s.	PROPN
ejpam-739	85	10	gal	gal	PROPN
ejpam-739	85	11	/	/	SYM
ejpam-739	85	12	eur	eur	PROPN
ejpam-739	85	13	.	.	PUNCT
ejpam-739	86	1	j.	j.	PROPN
ejpam-739	86	2	pure	pure	PROPN
ejpam-739	86	3	appl	appl	PROPN
ejpam-739	86	4	.	.	PROPN
ejpam-739	86	5	math	math	PROPN
ejpam-739	86	6	,	,	PUNCT
ejpam-739	86	7	3	3	NUM
ejpam-739	86	8	(	(	PUNCT
ejpam-739	86	9	2010	2010	NUM
ejpam-739	86	10	)	)	PUNCT
ejpam-739	86	11	,	,	PUNCT
ejpam-739	86	12	1150	1150	NUM
ejpam-739	86	13	-	-	SYM
ejpam-739	86	14	1164	1164	NUM
ejpam-739	86	15	1155	1155	NUM
ejpam-739	86	16	and	and	CCONJ
ejpam-739	86	17	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	86	18	p)(q+	p)(q+	NOUN
ejpam-739	86	19	p−	p−	NOUN
ejpam-739	86	20	1)	1)	NUM
ejpam-739	86	21	...	...	PUNCT
ejpam-739	86	22	(p+	(p+	X
ejpam-739	86	23	1)r	1)r	PROPN
ejpam-739	86	24	p	p	X
ejpam-739	86	25	·	·	PUNCT
ejpam-739	86	26			PROPN
ejpam-739	86	27			NOUN
ejpam-739	86	28	1	1	NUM
ejpam-739	86	29	beta(α	beta(α	NOUN
ejpam-739	86	30	,	,	PUNCT
ejpam-739	86	31	β	β	X
ejpam-739	86	32	)	)	PUNCT
ejpam-739	86	33	∫	∫	PROPN
ejpam-739	86	34	1	1	NUM
ejpam-739	86	35	0	0	NUM
ejpam-739	86	36	tα−1(1−	tα−1(1−	PROPN
ejpam-739	86	37	t)β−1[1−	t)β−1[1−	PRON
ejpam-739	86	38	e−(q+p)t]d	e−(q+p)t]d	SYM
ejpam-739	86	39	t	t	PROPN
ejpam-739	86	40			PROPN
ejpam-739	86	41			PROPN
ejpam-739	86	42	≤	≤	NUM
ejpam-739	86	43	‖	‖	PROPN
ejpam-739	86	44	f	f	PROPN
ejpam-739	86	45	(	(	PUNCT
ejpam-739	86	46	q)−	q)−	PROPN
ejpam-739	86	47	(	(	PUNCT
ejpam-739	86	48	gα	gα	PROPN
ejpam-739	86	49	,	,	PUNCT
ejpam-739	86	50	β	β	X
ejpam-739	86	51	u	u	NOUN
ejpam-739	86	52	(	(	PUNCT
ejpam-739	86	53	f	f	PROPN
ejpam-739	86	54	)	)	PUNCT
ejpam-739	86	55	)	)	PUNCT
ejpam-739	86	56	(	(	PUNCT
ejpam-739	86	57	q)‖r	q)‖r	INTJ
ejpam-739	86	58	.	.	PUNCT
ejpam-739	87	1	first	first	ADV
ejpam-739	87	2	take	take	VERB
ejpam-739	87	3	q	q	NOUN
ejpam-739	87	4	=	=	NOUN
ejpam-739	87	5	0	0	X
ejpam-739	87	6	.	.	PUNCT
ejpam-739	88	1	in	in	ADP
ejpam-739	88	2	what	what	PRON
ejpam-739	88	3	follows	follow	VERB
ejpam-739	88	4	,	,	PUNCT
ejpam-739	88	5	denoting	denote	VERB
ejpam-739	88	6	vα	vα	ADP
ejpam-739	88	7	,	,	PUNCT
ejpam-739	88	8	β	β	X
ejpam-739	88	9	=	=	SYM
ejpam-739	88	10	inf	inf	NOUN
ejpam-739	88	11	p≥1	p≥1	NOUN
ejpam-739	88	12	1	1	NUM
ejpam-739	88	13	beta(α	beta(α	NOUN
ejpam-739	88	14	,	,	PUNCT
ejpam-739	88	15	β	β	X
ejpam-739	88	16	)	)	PUNCT
ejpam-739	88	17	∫	∫	PROPN
ejpam-739	89	1	1	1	NUM
ejpam-739	89	2	0	0	NUM
ejpam-739	89	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	89	4	t)β−1[1−	t)β−1[1−	PROPN
ejpam-739	89	5	e−pt]d	e−pt]d	PUNCT
ejpam-739	89	6	t	t	PROPN
ejpam-739	89	7	!	!	PUNCT
ejpam-739	90	1	,	,	PUNCT
ejpam-739	90	2	we	we	PRON
ejpam-739	90	3	clearly	clearly	ADV
ejpam-739	90	4	get	get	VERB
ejpam-739	90	5	vα	vα	ADP
ejpam-739	90	6	,	,	PUNCT
ejpam-739	90	7	β	β	X
ejpam-739	90	8	=	=	SYM
ejpam-739	90	9	1	1	NUM
ejpam-739	90	10	beta(α	beta(α	NOUN
ejpam-739	90	11	,	,	PUNCT
ejpam-739	90	12	β	β	X
ejpam-739	90	13	)	)	PUNCT
ejpam-739	90	14	∫	∫	PROPN
ejpam-739	90	15	1	1	NUM
ejpam-739	90	16	0	0	NUM
ejpam-739	90	17	tα−1(1−	tα−1(1−	PROPN
ejpam-739	90	18	t)β−1[1−	t)β−1[1−	PRON
ejpam-739	90	19	e−t]d	e−t]d	NOUN
ejpam-739	90	20	t.	t.	NOUN
ejpam-739	90	21	but	but	CCONJ
ejpam-739	90	22	denoting	denote	VERB
ejpam-739	90	23	g(t	g(t	PROPN
ejpam-739	90	24	)	)	PUNCT
ejpam-739	91	1	=	=	SYM
ejpam-739	91	2	e−t	e−t	NOUN
ejpam-739	91	3	,	,	PUNCT
ejpam-739	91	4	by	by	ADP
ejpam-739	91	5	the	the	DET
ejpam-739	91	6	mean	mean	ADJ
ejpam-739	91	7	value	value	NOUN
ejpam-739	91	8	theorem	theorem	VERB
ejpam-739	91	9	there	there	PRON
ejpam-739	91	10	exists	exist	VERB
ejpam-739	91	11	ξ	ξ	PROPN
ejpam-739	91	12	∈	∈	PROPN
ejpam-739	91	13	(	(	PUNCT
ejpam-739	91	14	0,1	0,1	NOUN
ejpam-739	91	15	)	)	PUNCT
ejpam-739	91	16	such	such	ADJ
ejpam-739	91	17	that	that	SCONJ
ejpam-739	91	18	1−	1−	NUM
ejpam-739	91	19	e−t	e−t	NOUN
ejpam-739	91	20	=	=	SYM
ejpam-739	91	21	g(0)−	g(0)−	NOUN
ejpam-739	91	22	g(t	g(t	PROPN
ejpam-739	91	23	)	)	PUNCT
ejpam-739	91	24	=	=	PUNCT
ejpam-739	92	1	te−ξ	te−ξ	NOUN
ejpam-739	92	2	≥	≥	NOUN
ejpam-739	92	3	t	t	X
ejpam-739	92	4	e	e	NOUN
ejpam-739	92	5	,	,	PUNCT
ejpam-739	92	6	which	which	PRON
ejpam-739	92	7	immediately	immediately	ADV
ejpam-739	92	8	implies	imply	VERB
ejpam-739	92	9	vα	vα	PROPN
ejpam-739	92	10	,	,	PUNCT
ejpam-739	92	11	β	β	X
ejpam-739	92	12	≥	≥	NUM
ejpam-739	92	13	1	1	NUM
ejpam-739	92	14	e	e	NOUN
ejpam-739	92	15	·	·	PUNCT
ejpam-739	92	16	beta(α	beta(α	ADP
ejpam-739	92	17	,	,	PUNCT
ejpam-739	92	18	β	β	NOUN
ejpam-739	92	19	)	)	PUNCT
ejpam-739	92	20	∫	∫	PROPN
ejpam-739	93	1	1	1	NUM
ejpam-739	93	2	0	0	X
ejpam-739	94	1	tα(1−	tα(1−	NOUN
ejpam-739	94	2	t)β−1d	t)β−1d	NOUN
ejpam-739	94	3	t	t	NOUN
ejpam-739	94	4	=	=	SYM
ejpam-739	94	5	beta(α+	beta(α+	X
ejpam-739	94	6	1,β	1,β	NUM
ejpam-739	94	7	)	)	PUNCT
ejpam-739	94	8	e	e	NOUN
ejpam-739	94	9	·	·	PUNCT
ejpam-739	94	10	beta(α	beta(α	ADP
ejpam-739	94	11	,	,	PUNCT
ejpam-739	94	12	β	β	X
ejpam-739	94	13	)	)	PUNCT
ejpam-739	94	14	=	=	SYM
ejpam-739	95	1	1	1	NUM
ejpam-739	95	2	e	e	X
ejpam-739	95	3	·	·	PUNCT
ejpam-739	95	4	α	α	NOUN
ejpam-739	95	5	α+	α+	X
ejpam-739	95	6	β	β	X
ejpam-739	95	7	≥	≥	NUM
ejpam-739	95	8	1	1	NUM
ejpam-739	95	9	e	e	X
ejpam-739	95	10	·	·	PUNCT
ejpam-739	95	11	α	α	PRON
ejpam-739	95	12	2β	2β	NOUN
ejpam-739	95	13	≥	≥	NOUN
ejpam-739	95	14	α	α	PRON
ejpam-739	95	15	2e	2e	PROPN
ejpam-739	95	16	.	.	PUNCT
ejpam-739	96	1	therefore	therefore	ADV
ejpam-739	96	2	,	,	PUNCT
ejpam-739	96	3	1	1	NUM
ejpam-739	96	4	2e	2e	NOUN
ejpam-739	96	5	·	·	PUNCT
ejpam-739	96	6	r	r	NOUN
ejpam-739	96	7	p	p	X
ejpam-739	96	8	·	·	PUNCT
ejpam-739	96	9	|ap|	|ap|	PROPN
ejpam-739	96	10	≤	≤	NUM
ejpam-739	96	11	‖	‖	PROPN
ejpam-739	96	12	f	f	NOUN
ejpam-739	96	13	−	−	PROPN
ejpam-739	96	14	g	g	PROPN
ejpam-739	96	15	α	α	PROPN
ejpam-739	96	16	,	,	PUNCT
ejpam-739	96	17	β	β	X
ejpam-739	96	18	u	u	NOUN
ejpam-739	96	19	(	(	PUNCT
ejpam-739	96	20	f	f	NOUN
ejpam-739	96	21	)	)	PUNCT
ejpam-739	96	22	‖r	‖r	PROPN
ejpam-739	96	23	α	α	PROPN
ejpam-739	96	24	,	,	PUNCT
ejpam-739	96	25	for	for	ADP
ejpam-739	96	26	all	all	DET
ejpam-739	96	27	p	p	PRON
ejpam-739	96	28	≥	≥	NUM
ejpam-739	96	29	1	1	NUM
ejpam-739	96	30	and	and	CCONJ
ejpam-739	96	31	0	0	NUM
ejpam-739	96	32	<	<	X
ejpam-739	96	33	α≤	α≤	NUM
ejpam-739	96	34	β	β	NOUN
ejpam-739	96	35	≤	≤	NOUN
ejpam-739	96	36	1,α+	1,α+	NUM
ejpam-739	97	1	β	β	NOUN
ejpam-739	97	2	≥	≥	NUM
ejpam-739	97	3	1	1	NUM
ejpam-739	97	4	.	.	PUNCT
ejpam-739	98	1	this	this	PRON
ejpam-739	98	2	implies	imply	VERB
ejpam-739	98	3	that	that	SCONJ
ejpam-739	98	4	if	if	SCONJ
ejpam-739	98	5	there	there	PRON
ejpam-739	98	6	exists	exist	VERB
ejpam-739	98	7	a	a	DET
ejpam-739	98	8	subsequence	subsequence	NOUN
ejpam-739	98	9	(	(	PUNCT
ejpam-739	98	10	αk)k	αk)k	NUM
ejpam-739	98	11	in	in	ADP
ejpam-739	98	12	(	(	PUNCT
ejpam-739	98	13	0,β	0,β	NOUN
ejpam-739	98	14	]	]	X
ejpam-739	98	15	with	with	ADP
ejpam-739	98	16	limk→∞αk	limk→∞αk	NOUN
ejpam-739	98	17	=	=	SYM
ejpam-739	98	18	0	0	NUM
ejpam-739	98	19	and	and	CCONJ
ejpam-739	98	20	such	such	ADJ
ejpam-739	98	21	that	that	SCONJ
ejpam-739	98	22	limk→∞	limk→∞	PROPN
ejpam-739	98	23	‖gα	‖gα	NUM
ejpam-739	98	24	,	,	PUNCT
ejpam-739	98	25	β	β	X
ejpam-739	98	26	u	u	NOUN
ejpam-739	98	27	(	(	PUNCT
ejpam-739	98	28	f	f	PROPN
ejpam-739	98	29	)	)	PUNCT
ejpam-739	98	30	−	−	PROPN
ejpam-739	99	1	f	f	PROPN
ejpam-739	99	2	‖r	‖r	NOUN
ejpam-739	99	3	αk	αk	NOUN
ejpam-739	99	4	=	=	NOUN
ejpam-739	99	5	0	0	NUM
ejpam-739	99	6	,	,	PUNCT
ejpam-739	99	7	then	then	ADV
ejpam-739	99	8	ap	ap	PROPN
ejpam-739	100	1	=	=	NOUN
ejpam-739	100	2	0	0	PROPN
ejpam-739	100	3	for	for	ADP
ejpam-739	100	4	all	all	DET
ejpam-739	100	5	p	p	PRON
ejpam-739	100	6	≥	≥	NUM
ejpam-739	100	7	1	1	NUM
ejpam-739	100	8	,	,	PUNCT
ejpam-739	100	9	that	that	PRON
ejpam-739	100	10	is	is	ADV
ejpam-739	100	11	f	f	PROPN
ejpam-739	100	12	is	be	AUX
ejpam-739	100	13	constant	constant	ADJ
ejpam-739	100	14	on	on	ADP
ejpam-739	100	15	dr	dr	PROPN
ejpam-739	100	16	.	.	PUNCT
ejpam-739	101	1	therefore	therefore	ADV
ejpam-739	101	2	,	,	PUNCT
ejpam-739	101	3	if	if	SCONJ
ejpam-739	101	4	f	f	PROPN
ejpam-739	101	5	is	be	AUX
ejpam-739	101	6	not	not	PART
ejpam-739	101	7	a	a	DET
ejpam-739	101	8	constant	constant	ADJ
ejpam-739	101	9	function	function	NOUN
ejpam-739	101	10	,	,	PUNCT
ejpam-739	101	11	then	then	ADV
ejpam-739	101	12	infα∈(0,β	infα∈(0,β	PROPN
ejpam-739	101	13	]	]	SYM
ejpam-739	101	14	‖gα	‖gα	NUM
ejpam-739	101	15	,	,	PUNCT
ejpam-739	101	16	β	β	X
ejpam-739	101	17	u	u	NOUN
ejpam-739	101	18	(	(	PUNCT
ejpam-739	101	19	f	f	PROPN
ejpam-739	101	20	)	)	PUNCT
ejpam-739	101	21	−	−	PROPN
ejpam-739	102	1	f	f	PROPN
ejpam-739	102	2	‖r	‖r	PROPN
ejpam-739	102	3	α	α	PROPN
ejpam-739	102	4	>	>	X
ejpam-739	102	5	0	0	PROPN
ejpam-739	102	6	,	,	PUNCT
ejpam-739	102	7	which	which	PRON
ejpam-739	102	8	implies	imply	VERB
ejpam-739	102	9	that	that	SCONJ
ejpam-739	102	10	there	there	PRON
ejpam-739	102	11	exists	exist	VERB
ejpam-739	102	12	a	a	DET
ejpam-739	102	13	constant	constant	ADJ
ejpam-739	102	14	cr	cr	NOUN
ejpam-739	102	15	(	(	PUNCT
ejpam-739	102	16	f	f	PROPN
ejpam-739	102	17	)	)	PUNCT
ejpam-739	102	18	>	>	X
ejpam-739	102	19	0	0	PUNCT
ejpam-739	102	20	such	such	ADJ
ejpam-739	102	21	that	that	SCONJ
ejpam-739	102	22	‖gα	‖gα	NUM
ejpam-739	102	23	,	,	PUNCT
ejpam-739	102	24	β	β	X
ejpam-739	102	25	u	u	NOUN
ejpam-739	102	26	(	(	PUNCT
ejpam-739	102	27	f	f	PROPN
ejpam-739	102	28	)	)	PUNCT
ejpam-739	102	29	−	−	PROPN
ejpam-739	103	1	f	f	PROPN
ejpam-739	103	2	‖r	‖r	PROPN
ejpam-739	103	3	α	α	PROPN
ejpam-739	103	4	≥	≥	NOUN
ejpam-739	103	5	cr	cr	PROPN
ejpam-739	103	6	(	(	PUNCT
ejpam-739	103	7	f	f	PROPN
ejpam-739	103	8	)	)	PUNCT
ejpam-739	103	9	,	,	PUNCT
ejpam-739	103	10	that	that	PRON
ejpam-739	103	11	is	be	AUX
ejpam-739	103	12	‖gα	‖gα	NUM
ejpam-739	103	13	,	,	PUNCT
ejpam-739	103	14	β	β	X
ejpam-739	103	15	u	u	NOUN
ejpam-739	103	16	(	(	PUNCT
ejpam-739	103	17	f	f	PROPN
ejpam-739	103	18	)	)	PUNCT
ejpam-739	103	19	−	−	PROPN
ejpam-739	104	1	f	f	PROPN
ejpam-739	104	2	‖r	‖r	PROPN
ejpam-739	104	3	≥	≥	PROPN
ejpam-739	104	4	cr	cr	PROPN
ejpam-739	104	5	(	(	PUNCT
ejpam-739	104	6	f	f	PROPN
ejpam-739	104	7	)	)	PUNCT
ejpam-739	104	8	α	α	PROPN
ejpam-739	104	9	,	,	PUNCT
ejpam-739	104	10	for	for	ADP
ejpam-739	104	11	all	all	DET
ejpam-739	104	12	0	0	NUM
ejpam-739	104	13	<	<	X
ejpam-739	104	14	α	α	PRON
ejpam-739	104	15	≤	≤	VERB
ejpam-739	104	16	β	β	NOUN
ejpam-739	104	17	≤	≤	NOUN
ejpam-739	104	18	1,α+	1,α+	NUM
ejpam-739	104	19	β	β	NOUN
ejpam-739	104	20	≥	≥	NUM
ejpam-739	104	21	1	1	NUM
ejpam-739	104	22	.	.	PUNCT
ejpam-739	105	1	now	now	ADV
ejpam-739	105	2	,	,	PUNCT
ejpam-739	105	3	consider	consider	VERB
ejpam-739	105	4	q	q	NOUN
ejpam-739	105	5	≥	≥	NUM
ejpam-739	105	6	1	1	NUM
ejpam-739	105	7	and	and	CCONJ
ejpam-739	105	8	denote	denote	VERB
ejpam-739	105	9	vq	vq	PROPN
ejpam-739	105	10	,	,	PUNCT
ejpam-739	105	11	α	α	X
ejpam-739	105	12	,	,	PUNCT
ejpam-739	105	13	β	β	X
ejpam-739	105	14	=	=	SYM
ejpam-739	105	15	inf	inf	PROPN
ejpam-739	105	16	p≥0	p≥0	NOUN
ejpam-739	105	17	1	1	NUM
ejpam-739	105	18	beta(α	beta(α	NOUN
ejpam-739	105	19	,	,	PUNCT
ejpam-739	105	20	β	β	X
ejpam-739	105	21	)	)	PUNCT
ejpam-739	105	22	∫	∫	PROPN
ejpam-739	106	1	1	1	NUM
ejpam-739	106	2	0	0	NUM
ejpam-739	106	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	106	4	t)β−1[1−	t)β−1[1−	PRON
ejpam-739	106	5	e−(q+p)t]d	e−(q+p)t]d	X
ejpam-739	106	6	t	t	PROPN
ejpam-739	106	7	!	!	PUNCT
ejpam-739	106	8	.	.	PUNCT
ejpam-739	107	1	evidently	evidently	ADV
ejpam-739	107	2	that	that	SCONJ
ejpam-739	107	3	we	we	PRON
ejpam-739	107	4	have	have	VERB
ejpam-739	107	5	vq	vq	PROPN
ejpam-739	107	6	,	,	PUNCT
ejpam-739	107	7	α	α	X
ejpam-739	107	8	,	,	PUNCT
ejpam-739	107	9	β	β	X
ejpam-739	107	10	≥	≥	NOUN
ejpam-739	107	11	vα	vα	PROPN
ejpam-739	107	12	,	,	PUNCT
ejpam-739	107	13	β	β	X
ejpam-739	107	14	≥	≥	NOUN
ejpam-739	107	15	α	α	NOUN
ejpam-739	107	16	·	·	PUNCT
ejpam-739	107	17	1	1	NUM
ejpam-739	107	18	2e	2e	NOUN
ejpam-739	107	19	.	.	PUNCT
ejpam-739	108	1	s.	s.	PROPN
ejpam-739	108	2	gal	gal	PROPN
ejpam-739	108	3	/	/	SYM
ejpam-739	108	4	eur	eur	PROPN
ejpam-739	108	5	.	.	PUNCT
ejpam-739	109	1	j.	j.	PROPN
ejpam-739	109	2	pure	pure	PROPN
ejpam-739	109	3	appl	appl	PROPN
ejpam-739	109	4	.	.	PROPN
ejpam-739	109	5	math	math	PROPN
ejpam-739	109	6	,	,	PUNCT
ejpam-739	109	7	3	3	NUM
ejpam-739	109	8	(	(	PUNCT
ejpam-739	109	9	2010	2010	NUM
ejpam-739	109	10	)	)	PUNCT
ejpam-739	109	11	,	,	PUNCT
ejpam-739	109	12	1150	1150	NUM
ejpam-739	109	13	-	-	SYM
ejpam-739	109	14	1164	1164	NUM
ejpam-739	109	15	1156	1156	NUM
ejpam-739	109	16	reasoning	reasoning	NOUN
ejpam-739	109	17	as	as	ADP
ejpam-739	109	18	in	in	ADP
ejpam-739	109	19	the	the	DET
ejpam-739	109	20	case	case	NOUN
ejpam-739	109	21	of	of	ADP
ejpam-739	109	22	q	q	NOUN
ejpam-739	109	23	=	=	SYM
ejpam-739	109	24	0	0	NUM
ejpam-739	109	25	,	,	PUNCT
ejpam-739	109	26	we	we	PRON
ejpam-739	109	27	obtain	obtain	VERB
ejpam-739	109	28	‖[gα	‖[gα	NOUN
ejpam-739	109	29	,	,	PUNCT
ejpam-739	109	30	β	β	X
ejpam-739	109	31	u	u	NOUN
ejpam-739	109	32	(	(	PUNCT
ejpam-739	109	33	f	f	PROPN
ejpam-739	109	34	)	)	PUNCT
ejpam-739	109	35	]	]	PUNCT
ejpam-739	109	36	(	(	PUNCT
ejpam-739	109	37	q)−	q)−	PROPN
ejpam-739	109	38	f	f	X
ejpam-739	109	39	(	(	PUNCT
ejpam-739	109	40	q)‖r	q)‖r	NOUN
ejpam-739	109	41	α	α	NOUN
ejpam-739	109	42	≥	≥	NOUN
ejpam-739	109	43	|aq+p|	|aq+p|	VERB
ejpam-739	109	44	(	(	PUNCT
ejpam-739	109	45	q+	q+	NOUN
ejpam-739	109	46	p	p	NOUN
ejpam-739	109	47	)	)	PUNCT
ejpam-739	109	48	!	!	PUNCT
ejpam-739	110	1	p	p	X
ejpam-739	110	2	!	!	PUNCT
ejpam-739	110	3	·	·	PUNCT
ejpam-739	110	4	1	1	NUM
ejpam-739	110	5	2e	2e	NOUN
ejpam-739	110	6	·	·	PUNCT
ejpam-739	110	7	r	r	NOUN
ejpam-739	110	8	p	p	NOUN
ejpam-739	110	9	,	,	PUNCT
ejpam-739	110	10	for	for	ADP
ejpam-739	110	11	all	all	DET
ejpam-739	110	12	p	p	PRON
ejpam-739	110	13	≥	≥	NOUN
ejpam-739	110	14	0	0	NUM
ejpam-739	110	15	and	and	CCONJ
ejpam-739	110	16	0	0	NUM
ejpam-739	110	17	<	<	X
ejpam-739	110	18	α≤	α≤	NUM
ejpam-739	110	19	β	β	NOUN
ejpam-739	110	20	≤	≤	NOUN
ejpam-739	110	21	1,α+	1,α+	NUM
ejpam-739	111	1	β	β	NOUN
ejpam-739	111	2	≥	≥	NUM
ejpam-739	111	3	1	1	NUM
ejpam-739	111	4	.	.	PUNCT
ejpam-739	112	1	this	this	PRON
ejpam-739	112	2	implies	imply	VERB
ejpam-739	112	3	that	that	SCONJ
ejpam-739	112	4	if	if	SCONJ
ejpam-739	112	5	there	there	PRON
ejpam-739	112	6	exists	exist	VERB
ejpam-739	112	7	a	a	DET
ejpam-739	112	8	subsequence	subsequence	NOUN
ejpam-739	112	9	(	(	PUNCT
ejpam-739	112	10	αk)k	αk)k	NUM
ejpam-739	112	11	in	in	ADP
ejpam-739	112	12	(	(	PUNCT
ejpam-739	112	13	0,β	0,β	NOUN
ejpam-739	112	14	]	]	X
ejpam-739	112	15	with	with	ADP
ejpam-739	112	16	limk→∞αk	limk→∞αk	NOUN
ejpam-739	112	17	=	=	SYM
ejpam-739	112	18	0	0	NUM
ejpam-739	112	19	and	and	CCONJ
ejpam-739	112	20	such	such	ADJ
ejpam-739	112	21	that	that	SCONJ
ejpam-739	112	22	limk→∞	limk→∞	ADJ
ejpam-739	112	23	‖[gα	‖[gα	NOUN
ejpam-739	112	24	,	,	PUNCT
ejpam-739	112	25	β	β	X
ejpam-739	112	26	u	u	NOUN
ejpam-739	112	27	(	(	PUNCT
ejpam-739	112	28	f	f	PROPN
ejpam-739	112	29	)	)	PUNCT
ejpam-739	112	30	]	]	PUNCT
ejpam-739	112	31	(	(	PUNCT
ejpam-739	112	32	q)−	q)−	PROPN
ejpam-739	112	33	f	f	X
ejpam-739	112	34	(	(	PUNCT
ejpam-739	112	35	q)‖r	q)‖r	INTJ
ejpam-739	112	36	αk	αk	NOUN
ejpam-739	112	37	=	=	SYM
ejpam-739	112	38	0	0	NUM
ejpam-739	112	39	,	,	PUNCT
ejpam-739	112	40	then	then	ADV
ejpam-739	112	41	aq+p	aq+p	NOUN
ejpam-739	112	42	=	=	NOUN
ejpam-739	112	43	0	0	NUM
ejpam-739	112	44	for	for	ADP
ejpam-739	112	45	all	all	DET
ejpam-739	112	46	p	p	PRON
ejpam-739	112	47	≥	≥	NOUN
ejpam-739	112	48	0	0	NUM
ejpam-739	112	49	,	,	PUNCT
ejpam-739	112	50	that	that	PRON
ejpam-739	112	51	is	is	ADV
ejpam-739	112	52	f	f	PROPN
ejpam-739	112	53	is	be	AUX
ejpam-739	112	54	a	a	DET
ejpam-739	112	55	polynomial	polynomial	NOUN
ejpam-739	112	56	of	of	ADP
ejpam-739	112	57	degree	degree	NOUN
ejpam-739	112	58	≤	≤	NUM
ejpam-739	112	59	q−	q−	PROPN
ejpam-739	112	60	1	1	NUM
ejpam-739	112	61	on	on	ADP
ejpam-739	112	62	dr	dr	PROPN
ejpam-739	112	63	.	.	PUNCT
ejpam-739	113	1	therefore	therefore	ADV
ejpam-739	113	2	,	,	PUNCT
ejpam-739	113	3	because	because	SCONJ
ejpam-739	113	4	by	by	ADP
ejpam-739	113	5	hypothesis	hypothesis	NOUN
ejpam-739	113	6	f	f	NOUN
ejpam-739	113	7	is	be	AUX
ejpam-739	113	8	not	not	PART
ejpam-739	113	9	a	a	DET
ejpam-739	113	10	polynomial	polynomial	NOUN
ejpam-739	113	11	of	of	ADP
ejpam-739	113	12	degree	degree	NOUN
ejpam-739	113	13	≤	≤	NOUN
ejpam-739	113	14	q	q	NOUN
ejpam-739	113	15	−	−	NOUN
ejpam-739	113	16	1	1	NUM
ejpam-739	113	17	,	,	PUNCT
ejpam-739	113	18	we	we	PRON
ejpam-739	113	19	obtain	obtain	VERB
ejpam-739	113	20	infα∈(0,β	infα∈(0,β	PRON
ejpam-739	113	21	]	]	SYM
ejpam-739	113	22	‖[gα	‖[gα	NOUN
ejpam-739	113	23	,	,	PUNCT
ejpam-739	113	24	β	β	X
ejpam-739	113	25	u	u	NOUN
ejpam-739	113	26	(	(	PUNCT
ejpam-739	113	27	f	f	PROPN
ejpam-739	113	28	)	)	PUNCT
ejpam-739	113	29	]	]	PUNCT
ejpam-739	113	30	(	(	PUNCT
ejpam-739	113	31	q)−	q)−	PROPN
ejpam-739	113	32	f	f	X
ejpam-739	113	33	(	(	PUNCT
ejpam-739	113	34	q)‖r	q)‖r	INTJ
ejpam-739	113	35	α	α	X
ejpam-739	113	36	>	>	X
ejpam-739	113	37	0	0	PROPN
ejpam-739	113	38	,	,	PUNCT
ejpam-739	113	39	which	which	PRON
ejpam-739	113	40	implies	imply	VERB
ejpam-739	113	41	that	that	SCONJ
ejpam-739	113	42	there	there	PRON
ejpam-739	113	43	exists	exist	VERB
ejpam-739	113	44	a	a	DET
ejpam-739	113	45	constant	constant	ADJ
ejpam-739	113	46	cr	cr	NOUN
ejpam-739	113	47	,	,	PUNCT
ejpam-739	113	48	q	q	PROPN
ejpam-739	113	49	(	(	PUNCT
ejpam-739	113	50	f	f	PROPN
ejpam-739	113	51	)	)	PUNCT
ejpam-739	113	52	>	>	X
ejpam-739	113	53	0	0	PUNCT
ejpam-739	113	54	such	such	ADJ
ejpam-739	113	55	that	that	DET
ejpam-739	113	56	‖[gα	‖[gα	NOUN
ejpam-739	113	57	,	,	PUNCT
ejpam-739	113	58	β	β	X
ejpam-739	113	59	u	u	NOUN
ejpam-739	113	60	(	(	PUNCT
ejpam-739	113	61	f	f	PROPN
ejpam-739	113	62	)	)	PUNCT
ejpam-739	113	63	]	]	PUNCT
ejpam-739	113	64	(	(	PUNCT
ejpam-739	113	65	q)−	q)−	PROPN
ejpam-739	113	66	f	f	X
ejpam-739	113	67	(	(	PUNCT
ejpam-739	113	68	q)‖r	q)‖r	NOUN
ejpam-739	113	69	α	α	PROPN
ejpam-739	113	70	≥	≥	NOUN
ejpam-739	113	71	cr	cr	PROPN
ejpam-739	113	72	,	,	PUNCT
ejpam-739	113	73	q	q	PROPN
ejpam-739	113	74	(	(	PUNCT
ejpam-739	113	75	f	f	PROPN
ejpam-739	113	76	)	)	PUNCT
ejpam-739	113	77	,	,	PUNCT
ejpam-739	113	78	for	for	ADP
ejpam-739	113	79	all	all	DET
ejpam-739	113	80	α	α	DET
ejpam-739	113	81	∈	∈	PROPN
ejpam-739	113	82	(	(	PUNCT
ejpam-739	113	83	0,β	0,β	NUM
ejpam-739	113	84	]	]	X
ejpam-739	113	85	,	,	PUNCT
ejpam-739	113	86	that	that	PRON
ejpam-739	113	87	is	be	AUX
ejpam-739	113	88	‖[gα	‖[gα	NOUN
ejpam-739	113	89	,	,	PUNCT
ejpam-739	113	90	β	β	X
ejpam-739	113	91	u	u	NOUN
ejpam-739	113	92	(	(	PUNCT
ejpam-739	113	93	f	f	PROPN
ejpam-739	113	94	)	)	PUNCT
ejpam-739	113	95	]	]	PUNCT
ejpam-739	113	96	(	(	PUNCT
ejpam-739	113	97	q)−	q)−	PROPN
ejpam-739	113	98	f	f	X
ejpam-739	113	99	(	(	PUNCT
ejpam-739	113	100	q)‖r	q)‖r	NOUN
ejpam-739	113	101	≥	≥	X
ejpam-739	113	102	cr	cr	NOUN
ejpam-739	113	103	,	,	PUNCT
ejpam-739	113	104	q	q	PROPN
ejpam-739	113	105	(	(	PUNCT
ejpam-739	113	106	f	f	X
ejpam-739	113	107	)	)	PUNCT
ejpam-739	113	108	α	α	PROPN
ejpam-739	113	109	,	,	PUNCT
ejpam-739	113	110	for	for	ADP
ejpam-739	113	111	all	all	DET
ejpam-739	113	112	α	α	PRON
ejpam-739	113	113	∈	∈	PROPN
ejpam-739	113	114	(	(	PUNCT
ejpam-739	113	115	0,β	0,β	PROPN
ejpam-739	113	116	]	]	X
ejpam-739	113	117	.	.	PUNCT
ejpam-739	114	1	(	(	PUNCT
ejpam-739	114	2	ii	ii	NOUN
ejpam-739	114	3	)	)	PUNCT
ejpam-739	114	4	by	by	ADP
ejpam-739	114	5	gal	gal	PROPN
ejpam-739	115	1	[	[	X
ejpam-739	115	2	2	2	NUM
ejpam-739	115	3	,	,	PUNCT
ejpam-739	115	4	p.	p.	NOUN
ejpam-739	115	5	206	206	NUM
ejpam-739	115	6	,	,	PUNCT
ejpam-739	115	7	theorem	theorem	VERB
ejpam-739	115	8	3.2.1	3.2.1	NUM
ejpam-739	115	9	,	,	PUNCT
ejpam-739	115	10	(	(	PUNCT
ejpam-739	115	11	i	i	NOUN
ejpam-739	115	12	)	)	PUNCT
ejpam-739	115	13	]	]	PUNCT
ejpam-739	115	14	,	,	PUNCT
ejpam-739	115	15	ut	ut	PROPN
ejpam-739	115	16	(	(	PUNCT
ejpam-739	115	17	f	f	PROPN
ejpam-739	115	18	)	)	PUNCT
ejpam-739	115	19	(	(	PUNCT
ejpam-739	115	20	z	z	NOUN
ejpam-739	115	21	)	)	PUNCT
ejpam-739	115	22	is	be	AUX
ejpam-739	115	23	analytic	analytic	ADJ
ejpam-739	115	24	(	(	PUNCT
ejpam-739	115	25	as	as	ADP
ejpam-739	115	26	function	function	NOUN
ejpam-739	115	27	of	of	ADP
ejpam-739	115	28	z	z	NOUN
ejpam-739	115	29	)	)	PUNCT
ejpam-739	115	30	in	in	ADP
ejpam-739	115	31	dr	dr	PROPN
ejpam-739	116	1	and	and	CCONJ
ejpam-739	116	2	we	we	PRON
ejpam-739	116	3	can	can	AUX
ejpam-739	116	4	write	write	VERB
ejpam-739	116	5	ut	ut	PROPN
ejpam-739	116	6	(	(	PUNCT
ejpam-739	116	7	f	f	PROPN
ejpam-739	116	8	)	)	PUNCT
ejpam-739	116	9	(	(	PUNCT
ejpam-739	116	10	z	z	NOUN
ejpam-739	116	11	)	)	PUNCT
ejpam-739	116	12	=	=	SYM
ejpam-739	117	1	∞	∞	NUM
ejpam-739	117	2	∑	∑	PUNCT
ejpam-739	117	3	k=0	k=0	PROPN
ejpam-739	117	4	ak	ak	PROPN
ejpam-739	117	5	1	1	NUM
ejpam-739	117	6	+	+	CCONJ
ejpam-739	117	7	t2k2	t2k2	X
ejpam-739	117	8	zk	zk	PROPN
ejpam-739	117	9	,	,	PUNCT
ejpam-739	117	10	for	for	ADP
ejpam-739	117	11	all	all	DET
ejpam-739	117	12	|z|	|z|	NOUN
ejpam-739	117	13	<	<	X
ejpam-739	117	14	r	r	NOUN
ejpam-739	117	15	and	and	CCONJ
ejpam-739	117	16	t	t	PROPN
ejpam-739	117	17	≥	≥	NUM
ejpam-739	117	18	0	0	NUM
ejpam-739	117	19	.	.	PUNCT
ejpam-739	118	1	since	since	SCONJ
ejpam-739	118	2	|∑∞k=0	|∑∞k=0	PROPN
ejpam-739	118	3	ak	ak	PROPN
ejpam-739	118	4	1+t2k2	1+t2k2	PROPN
ejpam-739	118	5	zk|	zk|	PROPN
ejpam-739	118	6	≤∑∞k=0	≤∑∞k=0	NOUN
ejpam-739	118	7	|ak|·|z|k	|ak|·|z|k	NOUN
ejpam-739	118	8	<	<	X
ejpam-739	118	9	∞	∞	PROPN
ejpam-739	118	10	,	,	PUNCT
ejpam-739	118	11	this	this	PRON
ejpam-739	118	12	implies	imply	VERB
ejpam-739	118	13	that	that	SCONJ
ejpam-739	118	14	for	for	ADP
ejpam-739	118	15	fixed	fix	VERB
ejpam-739	118	16	|z|	|z|	NOUN
ejpam-739	118	17	<	<	X
ejpam-739	118	18	r	r	NOUN
ejpam-739	118	19	,	,	PUNCT
ejpam-739	118	20	the	the	DET
ejpam-739	118	21	series	series	NOUN
ejpam-739	118	22	in	in	ADP
ejpam-739	118	23	t	t	PROPN
ejpam-739	118	24	,	,	PUNCT
ejpam-739	118	25	∑∞	∑∞	PUNCT
ejpam-739	118	26	k=0	k=0	PROPN
ejpam-739	118	27	ak	ak	PROPN
ejpam-739	118	28	1+t2k2	1+t2k2	PROPN
ejpam-739	118	29	zk	zk	PROPN
ejpam-739	118	30	is	be	AUX
ejpam-739	118	31	uniformly	uniformly	ADV
ejpam-739	118	32	convergent	convergent	NOUN
ejpam-739	118	33	on	on	ADP
ejpam-739	118	34	[	[	X
ejpam-739	118	35	0,∞	0,∞	NOUN
ejpam-739	118	36	)	)	PUNCT
ejpam-739	118	37	,	,	PUNCT
ejpam-739	118	38	and	and	CCONJ
ejpam-739	118	39	therefore	therefore	ADV
ejpam-739	118	40	we	we	PRON
ejpam-739	118	41	immediately	immediately	ADV
ejpam-739	118	42	can	can	AUX
ejpam-739	118	43	write	write	VERB
ejpam-739	118	44	g	g	PROPN
ejpam-739	118	45	α	α	PROPN
ejpam-739	118	46	,	,	PUNCT
ejpam-739	118	47	β	β	X
ejpam-739	118	48	u	u	NOUN
ejpam-739	118	49	(	(	PUNCT
ejpam-739	118	50	f	f	PROPN
ejpam-739	118	51	)	)	PUNCT
ejpam-739	118	52	(	(	PUNCT
ejpam-739	118	53	z	z	NOUN
ejpam-739	118	54	)	)	PUNCT
ejpam-739	118	55	=	=	SYM
ejpam-739	118	56	∞	∞	NUM
ejpam-739	118	57	∑	∑	PUNCT
ejpam-739	118	58	k=0	k=0	PROPN
ejpam-739	118	59	akzk	akzk	NOUN
ejpam-739	118	60	1	1	NUM
ejpam-739	118	61	beta(α	beta(α	NOUN
ejpam-739	118	62	,	,	PUNCT
ejpam-739	118	63	β	β	X
ejpam-739	118	64	)	)	PUNCT
ejpam-739	118	65	∫	∫	PROPN
ejpam-739	118	66	1	1	NUM
ejpam-739	118	67	0	0	NUM
ejpam-739	118	68	tα−1(1−	tα−1(1−	NOUN
ejpam-739	118	69	t)β−1	t)β−1	ADP
ejpam-739	118	70	1	1	NUM
ejpam-739	118	71	+	+	NOUN
ejpam-739	118	72	t2k2	t2k2	NOUN
ejpam-739	118	73	d	d	X
ejpam-739	118	74	t.	t.	NOUN
ejpam-739	118	75	in	in	ADP
ejpam-739	118	76	other	other	ADJ
ejpam-739	118	77	order	order	NOUN
ejpam-739	118	78	of	of	ADP
ejpam-739	118	79	ideas	idea	NOUN
ejpam-739	118	80	,	,	PUNCT
ejpam-739	118	81	we	we	PRON
ejpam-739	118	82	easily	easily	ADV
ejpam-739	118	83	can	can	AUX
ejpam-739	118	84	write	write	VERB
ejpam-739	118	85	g	g	PROPN
ejpam-739	118	86	α	α	PROPN
ejpam-739	118	87	,	,	PUNCT
ejpam-739	118	88	β	β	X
ejpam-739	118	89	u	u	NOUN
ejpam-739	118	90	(	(	PUNCT
ejpam-739	118	91	f	f	PROPN
ejpam-739	118	92	)	)	PUNCT
ejpam-739	118	93	(	(	PUNCT
ejpam-739	118	94	z)−	z)−	PROPN
ejpam-739	118	95	f	f	X
ejpam-739	118	96	(	(	PUNCT
ejpam-739	118	97	z	z	NOUN
ejpam-739	118	98	)	)	PUNCT
ejpam-739	118	99	=	=	SYM
ejpam-739	118	100	1	1	NUM
ejpam-739	118	101	beta(α	beta(α	NOUN
ejpam-739	118	102	,	,	PUNCT
ejpam-739	118	103	β	β	X
ejpam-739	118	104	)	)	PUNCT
ejpam-739	118	105	·	·	PUNCT
ejpam-739	119	1	∫	∫	PROPN
ejpam-739	119	2	1	1	NUM
ejpam-739	119	3	0	0	NUM
ejpam-739	119	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	119	5	t)β−1[ut	t)β−1[ut	PROPN
ejpam-739	119	6	(	(	PUNCT
ejpam-739	119	7	f	f	PROPN
ejpam-739	119	8	)	)	PUNCT
ejpam-739	119	9	(	(	PUNCT
ejpam-739	119	10	z)−	z)−	PROPN
ejpam-739	119	11	f	f	X
ejpam-739	119	12	(	(	PUNCT
ejpam-739	119	13	z)]d	z)]d	PROPN
ejpam-739	119	14	t	t	PROPN
ejpam-739	119	15	,	,	PUNCT
ejpam-739	119	16	which	which	PRON
ejpam-739	119	17	together	together	ADV
ejpam-739	119	18	with	with	ADP
ejpam-739	119	19	the	the	DET
ejpam-739	119	20	estimate	estimate	NOUN
ejpam-739	119	21	|ut	|ut	NOUN
ejpam-739	119	22	(	(	PUNCT
ejpam-739	119	23	f	f	PROPN
ejpam-739	119	24	)	)	PUNCT
ejpam-739	119	25	(	(	PUNCT
ejpam-739	119	26	z)−	z)−	PROPN
ejpam-739	119	27	f	f	X
ejpam-739	119	28	(	(	PUNCT
ejpam-739	119	29	z)|	z)|	NOUN
ejpam-739	119	30	≤	≤	PROPN
ejpam-739	119	31	cr	cr	PROPN
ejpam-739	120	1	(	(	PUNCT
ejpam-739	120	2	f	f	PROPN
ejpam-739	120	3	)	)	PUNCT
ejpam-739	120	4	t	t	PROPN
ejpam-739	120	5	2	2	NUM
ejpam-739	120	6	in	in	ADP
ejpam-739	120	7	gal	gal	PROPN
ejpam-739	120	8	[	[	X
ejpam-739	120	9	2	2	NUM
ejpam-739	120	10	,	,	PUNCT
ejpam-739	120	11	p.	p.	NOUN
ejpam-739	120	12	207	207	NUM
ejpam-739	120	13	,	,	PUNCT
ejpam-739	120	14	theorem	theorem	VERB
ejpam-739	120	15	3.2.1	3.2.1	NUM
ejpam-739	120	16	,	,	PUNCT
ejpam-739	120	17	(	(	PUNCT
ejpam-739	120	18	iv	iv	X
ejpam-739	120	19	)	)	PUNCT
ejpam-739	120	20	]	]	PUNCT
ejpam-739	120	21	,	,	PUNCT
ejpam-739	120	22	implies	imply	VERB
ejpam-739	120	23	|gα	|gα	PROPN
ejpam-739	120	24	,	,	PUNCT
ejpam-739	120	25	β	β	X
ejpam-739	120	26	u	u	NOUN
ejpam-739	120	27	(	(	PUNCT
ejpam-739	120	28	f	f	PROPN
ejpam-739	120	29	)	)	PUNCT
ejpam-739	120	30	(	(	PUNCT
ejpam-739	120	31	z)−	z)−	PROPN
ejpam-739	120	32	f	f	X
ejpam-739	120	33	(	(	PUNCT
ejpam-739	120	34	z)|	z)|	ADP
ejpam-739	120	35	≤	≤	ADV
ejpam-739	120	36	1	1	NUM
ejpam-739	120	37	beta(α	beta(α	NOUN
ejpam-739	120	38	,	,	PUNCT
ejpam-739	120	39	β	β	X
ejpam-739	120	40	)	)	PUNCT
ejpam-739	120	41	·	·	PUNCT
ejpam-739	121	1	∫	∫	PROPN
ejpam-739	121	2	1	1	NUM
ejpam-739	121	3	0	0	NUM
ejpam-739	121	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	121	5	t)β−1|ut	t)β−1|ut	NUM
ejpam-739	121	6	(	(	PUNCT
ejpam-739	121	7	f	f	NOUN
ejpam-739	121	8	)	)	PUNCT
ejpam-739	121	9	(	(	PUNCT
ejpam-739	121	10	z)−	z)−	PROPN
ejpam-739	121	11	f	f	PROPN
ejpam-739	121	12	(	(	PUNCT
ejpam-739	121	13	z)|d	z)|d	PROPN
ejpam-739	121	14	t	t	PROPN
ejpam-739	121	15	≤	≤	PROPN
ejpam-739	121	16	cr	cr	PROPN
ejpam-739	121	17	(	(	PUNCT
ejpam-739	121	18	f	f	PROPN
ejpam-739	121	19	)	)	PUNCT
ejpam-739	121	20	1	1	NUM
ejpam-739	121	21	beta(α	beta(α	NOUN
ejpam-739	121	22	,	,	PUNCT
ejpam-739	121	23	β	β	X
ejpam-739	121	24	)	)	PUNCT
ejpam-739	121	25	·	·	PUNCT
ejpam-739	122	1	∫	∫	PROPN
ejpam-739	123	1	1	1	NUM
ejpam-739	123	2	0	0	NUM
ejpam-739	123	3	tα+1(1−	tα+1(1−	ADP
ejpam-739	123	4	t)β−1d	t)β−1d	PROPN
ejpam-739	123	5	t	t	PROPN
ejpam-739	123	6	=	=	SYM
ejpam-739	123	7	cr	cr	PROPN
ejpam-739	123	8	(	(	PUNCT
ejpam-739	123	9	f	f	PROPN
ejpam-739	123	10	)	)	PUNCT
ejpam-739	123	11	·	·	PUNCT
ejpam-739	123	12	beta(α+	beta(α+	NOUN
ejpam-739	123	13	2,β	2,β	ADV
ejpam-739	123	14	)	)	PUNCT
ejpam-739	123	15	beta(α	beta(α	NOUN
ejpam-739	123	16	,	,	PUNCT
ejpam-739	123	17	β	β	NOUN
ejpam-739	123	18	)	)	PUNCT
ejpam-739	123	19	=	=	SYM
ejpam-739	124	1	cr	cr	PROPN
ejpam-739	124	2	(	(	PUNCT
ejpam-739	124	3	f	f	PROPN
ejpam-739	124	4	)	)	PUNCT
ejpam-739	124	5	α+	α+	PRON
ejpam-739	124	6	1	1	NUM
ejpam-739	124	7	α+β	α+β	NUM
ejpam-739	124	8	+	+	CCONJ
ejpam-739	124	9	1	1	NUM
ejpam-739	124	10	·	·	SYM
ejpam-739	124	11	α	α	NOUN
ejpam-739	124	12	α+	α+	X
ejpam-739	124	13	β	β	NOUN
ejpam-739	124	14	≤	≤	NUM
ejpam-739	124	15	cr	cr	PROPN
ejpam-739	124	16	(	(	PUNCT
ejpam-739	124	17	f	f	PROPN
ejpam-739	124	18	)	)	PUNCT
ejpam-739	124	19	α(α+	α(α+	NUM
ejpam-739	124	20	1	1	NUM
ejpam-739	124	21	)	)	SYM
ejpam-739	124	22	2	2	NUM
ejpam-739	124	23	≤	≤	NUM
ejpam-739	124	24	cr	cr	ADP
ejpam-739	124	25	(	(	PUNCT
ejpam-739	124	26	f	f	PROPN
ejpam-739	124	27	)	)	PUNCT
ejpam-739	124	28	α	α	PROPN
ejpam-739	124	29	,	,	PUNCT
ejpam-739	124	30	s.	s.	PROPN
ejpam-739	124	31	gal	gal	PROPN
ejpam-739	124	32	/	/	SYM
ejpam-739	124	33	eur	eur	PROPN
ejpam-739	124	34	.	.	PUNCT
ejpam-739	125	1	j.	j.	PROPN
ejpam-739	125	2	pure	pure	PROPN
ejpam-739	125	3	appl	appl	PROPN
ejpam-739	125	4	.	.	PROPN
ejpam-739	125	5	math	math	PROPN
ejpam-739	125	6	,	,	PUNCT
ejpam-739	125	7	3	3	NUM
ejpam-739	125	8	(	(	PUNCT
ejpam-739	125	9	2010	2010	NUM
ejpam-739	125	10	)	)	PUNCT
ejpam-739	125	11	,	,	PUNCT
ejpam-739	125	12	1150	1150	NUM
ejpam-739	125	13	-	-	SYM
ejpam-739	125	14	1164	1164	NUM
ejpam-739	125	15	1157	1157	NUM
ejpam-739	125	16	for	for	ADP
ejpam-739	125	17	all	all	DET
ejpam-739	125	18	|z|	|z|	NOUN
ejpam-739	125	19	≤	≤	NUM
ejpam-739	125	20	r	r	NOUN
ejpam-739	125	21	,	,	PUNCT
ejpam-739	125	22	where	where	SCONJ
ejpam-739	125	23	cr	cr	PROPN
ejpam-739	125	24	(	(	PUNCT
ejpam-739	125	25	f	f	PROPN
ejpam-739	125	26	)	)	PUNCT
ejpam-739	125	27	>	>	X
ejpam-739	125	28	0	0	PUNCT
ejpam-739	125	29	is	be	AUX
ejpam-739	125	30	independent	independent	ADJ
ejpam-739	125	31	of	of	ADP
ejpam-739	125	32	z	z	NOUN
ejpam-739	125	33	(	(	PUNCT
ejpam-739	125	34	and	and	CCONJ
ejpam-739	125	35	α	α	NOUN
ejpam-739	125	36	,	,	PUNCT
ejpam-739	125	37	β	β	NOUN
ejpam-739	125	38	)	)	PUNCT
ejpam-739	126	1	but	but	CCONJ
ejpam-739	126	2	depends	depend	VERB
ejpam-739	126	3	on	on	ADP
ejpam-739	126	4	f	f	PROPN
ejpam-739	126	5	and	and	CCONJ
ejpam-739	126	6	r.	r.	PROPN
ejpam-739	126	7	now	now	ADV
ejpam-739	126	8	,	,	PUNCT
ejpam-739	126	9	let	let	VERB
ejpam-739	126	10	q	q	PROPN
ejpam-739	126	11	∈	∈	PROPN
ejpam-739	126	12	n∪	n∪	PROPN
ejpam-739	126	13	{	{	PUNCT
ejpam-739	126	14	0	0	NUM
ejpam-739	126	15	}	}	PUNCT
ejpam-739	126	16	and	and	CCONJ
ejpam-739	126	17	1	1	NUM
ejpam-739	126	18	≤	≤	NOUN
ejpam-739	126	19	r	r	NOUN
ejpam-739	126	20	<	<	X
ejpam-739	126	21	r1	r1	PROPN
ejpam-739	126	22	<	<	X
ejpam-739	126	23	r.	r.	PROPN
ejpam-739	126	24	by	by	ADP
ejpam-739	126	25	using	use	VERB
ejpam-739	126	26	the	the	DET
ejpam-739	126	27	cauchy	cauchy	NOUN
ejpam-739	126	28	’s	’s	PART
ejpam-739	126	29	formula	formula	NOUN
ejpam-739	126	30	and	and	CCONJ
ejpam-739	126	31	reasoning	reasoning	NOUN
ejpam-739	126	32	as	as	ADP
ejpam-739	126	33	in	in	ADP
ejpam-739	126	34	the	the	DET
ejpam-739	126	35	proof	proof	NOUN
ejpam-739	126	36	of	of	ADP
ejpam-739	126	37	the	the	DET
ejpam-739	126	38	above	above	ADJ
ejpam-739	126	39	point	point	NOUN
ejpam-739	126	40	(	(	PUNCT
ejpam-739	126	41	i	i	NOUN
ejpam-739	126	42	)	)	PUNCT
ejpam-739	126	43	,	,	PUNCT
ejpam-739	126	44	we	we	PRON
ejpam-739	126	45	get	get	VERB
ejpam-739	126	46	the	the	DET
ejpam-739	126	47	upper	upper	ADJ
ejpam-739	126	48	estimate	estimate	NOUN
ejpam-739	126	49	‖[gα	‖[gα	NOUN
ejpam-739	126	50	,	,	PUNCT
ejpam-739	126	51	β	β	X
ejpam-739	126	52	u	u	NOUN
ejpam-739	126	53	(	(	PUNCT
ejpam-739	126	54	f	f	PROPN
ejpam-739	126	55	)	)	PUNCT
ejpam-739	126	56	]	]	PUNCT
ejpam-739	126	57	(	(	PUNCT
ejpam-739	126	58	q)−	q)−	PROPN
ejpam-739	126	59	f	f	X
ejpam-739	126	60	(	(	PUNCT
ejpam-739	126	61	q)‖r	q)‖r	NOUN
ejpam-739	126	62	≤	≤	NOUN
ejpam-739	126	63	c∗α	c∗α	NOUN
ejpam-739	126	64	,	,	PUNCT
ejpam-739	126	65	with	with	ADP
ejpam-739	126	66	c∗	c∗	NOUN
ejpam-739	126	67	depending	depend	VERB
ejpam-739	126	68	only	only	ADV
ejpam-739	126	69	on	on	ADP
ejpam-739	126	70	f	f	PROPN
ejpam-739	126	71	,	,	PUNCT
ejpam-739	126	72	q	q	X
ejpam-739	126	73	,	,	PUNCT
ejpam-739	126	74	r	r	NOUN
ejpam-739	126	75	and	and	CCONJ
ejpam-739	126	76	r1	r1	NOUN
ejpam-739	126	77	.	.	PUNCT
ejpam-739	127	1	it	it	PRON
ejpam-739	127	2	remains	remain	VERB
ejpam-739	127	3	to	to	PART
ejpam-739	127	4	prove	prove	VERB
ejpam-739	127	5	the	the	DET
ejpam-739	127	6	lower	low	ADJ
ejpam-739	127	7	estimate	estimate	NOUN
ejpam-739	127	8	.	.	PUNCT
ejpam-739	128	1	for	for	ADP
ejpam-739	128	2	this	this	DET
ejpam-739	128	3	purpose	purpose	NOUN
ejpam-739	128	4	,	,	PUNCT
ejpam-739	128	5	reasoning	reason	VERB
ejpam-739	128	6	exactly	exactly	ADV
ejpam-739	128	7	as	as	ADP
ejpam-739	128	8	in	in	ADP
ejpam-739	128	9	the	the	DET
ejpam-739	128	10	proof	proof	NOUN
ejpam-739	128	11	of	of	ADP
ejpam-739	128	12	theorem	theorem	ADJ
ejpam-739	128	13	3.2.1	3.2.1	NUM
ejpam-739	128	14	,	,	PUNCT
ejpam-739	128	15	at	at	ADP
ejpam-739	128	16	pages	page	NOUN
ejpam-739	128	17	209	209	NUM
ejpam-739	128	18	-	-	SYM
ejpam-739	128	19	210	210	NUM
ejpam-739	128	20	in	in	ADP
ejpam-739	128	21	the	the	DET
ejpam-739	128	22	book	book	NOUN
ejpam-739	128	23	gal	gal	NOUN
ejpam-739	129	1	[	[	X
ejpam-739	129	2	2	2	NUM
ejpam-739	129	3	]	]	PUNCT
ejpam-739	129	4	,	,	PUNCT
ejpam-739	129	5	for	for	ADP
ejpam-739	129	6	z	z	NOUN
ejpam-739	129	7	=	=	NOUN
ejpam-739	129	8	reiϕ	reiϕ	NOUN
ejpam-739	129	9	and	and	CCONJ
ejpam-739	129	10	p	p	PRON
ejpam-739	129	11	∈	∈	PROPN
ejpam-739	129	12	n∪	n∪	X
ejpam-739	129	13	{	{	PUNCT
ejpam-739	129	14	0	0	NUM
ejpam-739	129	15	}	}	PUNCT
ejpam-739	129	16	we	we	PRON
ejpam-739	129	17	get	get	VERB
ejpam-739	129	18	1	1	NUM
ejpam-739	129	19	2π	2π	NUM
ejpam-739	129	20	∫	∫	NOUN
ejpam-739	130	1	π	π	NOUN
ejpam-739	130	2	−π	−π	PROPN
ejpam-739	130	3	[	[	PUNCT
ejpam-739	130	4	f	f	X
ejpam-739	130	5	(	(	PUNCT
ejpam-739	130	6	q)(z)−	q)(z)−	X
ejpam-739	130	7	[	[	X
ejpam-739	130	8	ut	ut	PROPN
ejpam-739	130	9	(	(	PUNCT
ejpam-739	130	10	f	f	PROPN
ejpam-739	130	11	)	)	PUNCT
ejpam-739	130	12	]	]	PUNCT
ejpam-739	131	1	(	(	PUNCT
ejpam-739	131	2	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	PROPN
ejpam-739	131	3	=	=	SYM
ejpam-739	131	4	aq+p(q+	aq+p(q+	PROPN
ejpam-739	131	5	p)(q+	p)(q+	VERB
ejpam-739	131	6	p−	p−	NOUN
ejpam-739	131	7	1)	1)	NUM
ejpam-739	131	8	...	...	PUNCT
ejpam-739	131	9	(p+	(p+	X
ejpam-739	131	10	1)r	1)r	PROPN
ejpam-739	131	11	p	p	X
ejpam-739	131	12	·	·	PUNCT
ejpam-739	132	1	t2(q+	t2(q+	NUM
ejpam-739	132	2	p)2	p)2	NOUN
ejpam-739	132	3	1	1	NUM
ejpam-739	132	4	+	+	SYM
ejpam-739	132	5	t2(q+	t2(q+	PROPN
ejpam-739	132	6	p)2	p)2	NOUN
ejpam-739	132	7	.	.	PUNCT
ejpam-739	133	1	multiplying	multiply	VERB
ejpam-739	133	2	above	above	ADV
ejpam-739	133	3	with	with	ADP
ejpam-739	133	4	1	1	NUM
ejpam-739	133	5	beta(α	beta(α	NOUN
ejpam-739	133	6	,	,	PUNCT
ejpam-739	133	7	β	β	NOUN
ejpam-739	133	8	)	)	PUNCT
ejpam-739	133	9	tα−1(1−	tα−1(1−	NOUN
ejpam-739	133	10	t)β−1	t)β−1	ADP
ejpam-739	133	11	an	an	DET
ejpam-739	133	12	then	then	ADV
ejpam-739	133	13	integrating	integrate	VERB
ejpam-739	133	14	with	with	ADP
ejpam-739	133	15	respect	respect	NOUN
ejpam-739	133	16	to	to	ADP
ejpam-739	133	17	t	t	PROPN
ejpam-739	133	18	,	,	PUNCT
ejpam-739	133	19	it	it	PRON
ejpam-739	133	20	follows	follow	VERB
ejpam-739	133	21	i	i	PRON
ejpam-739	133	22	:	:	PUNCT
ejpam-739	133	23	=	=	SYM
ejpam-739	133	24	1	1	NUM
ejpam-739	133	25	beta(α	beta(α	NOUN
ejpam-739	133	26	,	,	PUNCT
ejpam-739	133	27	β	β	X
ejpam-739	133	28	)	)	PUNCT
ejpam-739	133	29	·	·	PUNCT
ejpam-739	134	1	∫	∫	PROPN
ejpam-739	134	2	1	1	NUM
ejpam-739	134	3	0	0	NUM
ejpam-739	134	4	¨	¨	NOUN
ejpam-739	134	5	1	1	NUM
ejpam-739	134	6	2π	2π	NUM
ejpam-739	134	7	∫	∫	PROPN
ejpam-739	135	1	π	π	NOUN
ejpam-739	135	2	−π	−π	PROPN
ejpam-739	135	3	[	[	PUNCT
ejpam-739	135	4	f	f	X
ejpam-739	135	5	(	(	PUNCT
ejpam-739	135	6	q)(z)−	q)(z)−	X
ejpam-739	135	7	[	[	X
ejpam-739	135	8	ut	ut	PROPN
ejpam-739	135	9	(	(	PUNCT
ejpam-739	135	10	f	f	PROPN
ejpam-739	135	11	)	)	PUNCT
ejpam-739	135	12	]	]	PUNCT
ejpam-739	136	1	(	(	PUNCT
ejpam-739	136	2	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	NOUN
ejpam-739	136	3	«	«	PUNCT
ejpam-739	136	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	136	5	t)β−1d	t)β−1d	NOUN
ejpam-739	136	6	t	t	NOUN
ejpam-739	136	7	=	=	SYM
ejpam-739	136	8	aq+p(q+	aq+p(q+	PROPN
ejpam-739	136	9	p)(q+	p)(q+	VERB
ejpam-739	136	10	p−	p−	NOUN
ejpam-739	136	11	1)	1)	NUM
ejpam-739	136	12	...	...	PUNCT
ejpam-739	136	13	(p+	(p+	X
ejpam-739	137	1	1)r	1)r	PROPN
ejpam-739	137	2	p	p	X
ejpam-739	137	3	·	·	PUNCT
ejpam-739	137	4	1	1	NUM
ejpam-739	137	5	beta(α	beta(α	NOUN
ejpam-739	137	6	,	,	PUNCT
ejpam-739	137	7	β	β	X
ejpam-739	137	8	)	)	PUNCT
ejpam-739	137	9	∫	∫	PROPN
ejpam-739	138	1	1	1	NUM
ejpam-739	138	2	0	0	NUM
ejpam-739	138	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	138	4	t)β−1	t)β−1	PUNCT
ejpam-739	138	5	�	�	PROPN
ejpam-739	139	1	t2(q+	t2(q+	PROPN
ejpam-739	139	2	p)2	p)2	NOUN
ejpam-739	139	3	1	1	NUM
ejpam-739	139	4	+	+	CCONJ
ejpam-739	139	5	t2(q+	t2(q+	PROPN
ejpam-739	139	6	p)2	p)2	NOUN
ejpam-739	139	7	�	�	PROPN
ejpam-739	139	8	d	d	ADP
ejpam-739	139	9	t.	t.	NOUN
ejpam-739	139	10	applying	apply	VERB
ejpam-739	139	11	the	the	DET
ejpam-739	139	12	fubini	fubini	NOUN
ejpam-739	139	13	’s	’s	PART
ejpam-739	139	14	result	result	NOUN
ejpam-739	139	15	to	to	ADP
ejpam-739	139	16	the	the	DET
ejpam-739	139	17	double	double	ADJ
ejpam-739	139	18	integral	integral	ADJ
ejpam-739	139	19	i	i	PRON
ejpam-739	139	20	and	and	CCONJ
ejpam-739	139	21	then	then	ADV
ejpam-739	139	22	passing	pass	VERB
ejpam-739	139	23	to	to	ADP
ejpam-739	139	24	modulus	modulus	NOUN
ejpam-739	139	25	,	,	PUNCT
ejpam-739	139	26	we	we	PRON
ejpam-739	139	27	easily	easily	ADV
ejpam-739	139	28	obtain	obtain	VERB
ejpam-739	139	29	�	�	PROPN
ejpam-739	139	30	�	�	PROPN
ejpam-739	139	31	�	�	PROPN
ejpam-739	139	32	�	�	PROPN
ejpam-739	139	33	�	�	PROPN
ejpam-739	139	34	1	1	NUM
ejpam-739	139	35	2π	2π	PROPN
ejpam-739	139	36	∫	∫	PROPN
ejpam-739	140	1	π	π	PROPN
ejpam-739	140	2	−π	−π	PROPN
ejpam-739	140	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	140	4			PROPN
ejpam-739	140	5			NOUN
ejpam-739	140	6	1	1	NUM
ejpam-739	140	7	beta(α	beta(α	NOUN
ejpam-739	140	8	,	,	PUNCT
ejpam-739	140	9	β	β	X
ejpam-739	140	10	)	)	PUNCT
ejpam-739	140	11	∫	∫	PROPN
ejpam-739	141	1	1	1	NUM
ejpam-739	141	2	0	0	NUM
ejpam-739	142	1	[	[	PUNCT
ejpam-739	142	2	f	f	X
ejpam-739	142	3	(	(	PUNCT
ejpam-739	142	4	q)(z)−	q)(z)−	X
ejpam-739	142	5	[	[	X
ejpam-739	142	6	ut	ut	PROPN
ejpam-739	142	7	(	(	PUNCT
ejpam-739	142	8	f	f	PROPN
ejpam-739	142	9	)	)	PUNCT
ejpam-739	142	10	]	]	PUNCT
ejpam-739	142	11	(	(	PUNCT
ejpam-739	142	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	142	13	t)β−1d	t)β−1d	PROPN
ejpam-739	142	14	t	t	PROPN
ejpam-739	142	15			PROPN
ejpam-739	142	16			PROPN
ejpam-739	142	17	dϕ	dϕ	PRON
ejpam-739	142	18	�	�	PROPN
ejpam-739	142	19	�	�	PROPN
ejpam-739	142	20	�	�	PROPN
ejpam-739	142	21	�	�	PROPN
ejpam-739	142	22	�	�	PROPN
ejpam-739	142	23	=	=	SYM
ejpam-739	142	24	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	142	25	p)(q+	p)(q+	NOUN
ejpam-739	142	26	p−	p−	NOUN
ejpam-739	142	27	1)	1)	NUM
ejpam-739	142	28	...	...	PUNCT
ejpam-739	142	29	(p+	(p+	X
ejpam-739	143	1	1)r	1)r	PROPN
ejpam-739	143	2	p	p	X
ejpam-739	143	3	·	·	PUNCT
ejpam-739	143	4			PROPN
ejpam-739	143	5			NOUN
ejpam-739	143	6	1	1	NUM
ejpam-739	143	7	beta(α	beta(α	NOUN
ejpam-739	143	8	,	,	PUNCT
ejpam-739	143	9	β	β	X
ejpam-739	143	10	)	)	PUNCT
ejpam-739	143	11	∫	∫	PROPN
ejpam-739	144	1	1	1	NUM
ejpam-739	144	2	0	0	NUM
ejpam-739	144	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	144	4	t)β−1	t)β−1	PUNCT
ejpam-739	144	5	�	�	PROPN
ejpam-739	145	1	t2(q+	t2(q+	PROPN
ejpam-739	145	2	p)2	p)2	NOUN
ejpam-739	145	3	1	1	NUM
ejpam-739	145	4	+	+	CCONJ
ejpam-739	145	5	t2(q+	t2(q+	PROPN
ejpam-739	145	6	p)2	p)2	NOUN
ejpam-739	145	7	�	�	PROPN
ejpam-739	145	8	d	d	PROPN
ejpam-739	145	9	t	t	PROPN
ejpam-739	145	10			PROPN
ejpam-739	145	11			PROPN
ejpam-739	145	12	.	.	PUNCT
ejpam-739	146	1	since	since	SCONJ
ejpam-739	146	2	1	1	NUM
ejpam-739	146	3	beta(α	beta(α	NOUN
ejpam-739	146	4	,	,	PUNCT
ejpam-739	146	5	β	β	X
ejpam-739	146	6	)	)	PUNCT
ejpam-739	146	7	∫	∫	PROPN
ejpam-739	146	8	1	1	NUM
ejpam-739	146	9	0	0	NUM
ejpam-739	147	1	[	[	PUNCT
ejpam-739	147	2	f	f	X
ejpam-739	147	3	(	(	PUNCT
ejpam-739	147	4	q)(z)−	q)(z)−	X
ejpam-739	147	5	[	[	X
ejpam-739	147	6	ut	ut	PROPN
ejpam-739	147	7	(	(	PUNCT
ejpam-739	147	8	f	f	PROPN
ejpam-739	147	9	)	)	PUNCT
ejpam-739	147	10	]	]	PUNCT
ejpam-739	147	11	(	(	PUNCT
ejpam-739	147	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	147	13	t)β−1d	t)β−1d	PROPN
ejpam-739	147	14	t	t	NOUN
ejpam-739	147	15	=	=	SYM
ejpam-739	147	16	f	f	PROPN
ejpam-739	147	17	(	(	PUNCT
ejpam-739	147	18	q)(z)−	q)(z)−	X
ejpam-739	147	19	[	[	X
ejpam-739	147	20	gα	gα	NOUN
ejpam-739	147	21	,	,	PUNCT
ejpam-739	147	22	β	β	X
ejpam-739	147	23	u	u	NOUN
ejpam-739	147	24	(	(	PUNCT
ejpam-739	147	25	f	f	PROPN
ejpam-739	147	26	)	)	PUNCT
ejpam-739	147	27	]	]	X
ejpam-739	147	28	(	(	PUNCT
ejpam-739	147	29	q)(z	q)(z	NOUN
ejpam-739	147	30	)	)	PUNCT
ejpam-739	147	31	,	,	PUNCT
ejpam-739	147	32	s.	s.	PROPN
ejpam-739	147	33	gal	gal	PROPN
ejpam-739	147	34	/	/	SYM
ejpam-739	147	35	eur	eur	PROPN
ejpam-739	147	36	.	.	PUNCT
ejpam-739	148	1	j.	j.	PROPN
ejpam-739	148	2	pure	pure	PROPN
ejpam-739	148	3	appl	appl	PROPN
ejpam-739	148	4	.	.	PROPN
ejpam-739	148	5	math	math	PROPN
ejpam-739	148	6	,	,	PUNCT
ejpam-739	148	7	3	3	NUM
ejpam-739	148	8	(	(	PUNCT
ejpam-739	148	9	2010	2010	NUM
ejpam-739	148	10	)	)	PUNCT
ejpam-739	148	11	,	,	PUNCT
ejpam-739	148	12	1150	1150	NUM
ejpam-739	148	13	-	-	SYM
ejpam-739	148	14	1164	1164	NUM
ejpam-739	148	15	1158	1158	NUM
ejpam-739	148	16	the	the	DET
ejpam-739	148	17	previous	previous	ADJ
ejpam-739	148	18	equality	equality	NOUN
ejpam-739	148	19	immediately	immediately	ADV
ejpam-739	148	20	implies	imply	VERB
ejpam-739	148	21	�	�	PROPN
ejpam-739	148	22	�	�	PROPN
ejpam-739	148	23	�	�	PROPN
ejpam-739	148	24	�	�	PROPN
ejpam-739	148	25	�	�	PROPN
ejpam-739	148	26	1	1	NUM
ejpam-739	148	27	2π	2π	PROPN
ejpam-739	148	28	∫	∫	PROPN
ejpam-739	149	1	π	π	NOUN
ejpam-739	149	2	−π	−π	PROPN
ejpam-739	149	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	150	1	h	h	PROPN
ejpam-739	150	2	f	f	PROPN
ejpam-739	150	3	(	(	PUNCT
ejpam-739	150	4	q)(z)−	q)(z)−	X
ejpam-739	150	5	(	(	PUNCT
ejpam-739	150	6	gα	gα	NOUN
ejpam-739	150	7	,	,	PUNCT
ejpam-739	150	8	β	β	X
ejpam-739	150	9	u	u	NOUN
ejpam-739	150	10	(	(	PUNCT
ejpam-739	150	11	f	f	PROPN
ejpam-739	150	12	)	)	PUNCT
ejpam-739	150	13	)	)	PUNCT
ejpam-739	150	14	(	(	PUNCT
ejpam-739	150	15	q)(z	q)(z	NOUN
ejpam-739	150	16	)	)	PUNCT
ejpam-739	150	17	i	i	PRON
ejpam-739	150	18	dϕ	dϕ	VERB
ejpam-739	151	1	�	�	PROPN
ejpam-739	151	2	�	�	PROPN
ejpam-739	151	3	�	�	PROPN
ejpam-739	151	4	�	�	PROPN
ejpam-739	151	5	�	�	PROPN
ejpam-739	151	6	=	=	SYM
ejpam-739	151	7	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	151	8	p)(q+	p)(q+	NOUN
ejpam-739	151	9	p−	p−	NOUN
ejpam-739	151	10	1)	1)	NUM
ejpam-739	151	11	...	...	PUNCT
ejpam-739	151	12	(p+	(p+	X
ejpam-739	151	13	1)r	1)r	PROPN
ejpam-739	151	14	p	p	X
ejpam-739	151	15	·	·	PUNCT
ejpam-739	151	16			PROPN
ejpam-739	151	17			NOUN
ejpam-739	151	18	1	1	NUM
ejpam-739	151	19	beta(α	beta(α	NOUN
ejpam-739	151	20	,	,	PUNCT
ejpam-739	151	21	β	β	X
ejpam-739	151	22	)	)	PUNCT
ejpam-739	151	23	∫	∫	PROPN
ejpam-739	152	1	1	1	NUM
ejpam-739	152	2	0	0	NUM
ejpam-739	152	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	152	4	t)β−1	t)β−1	PUNCT
ejpam-739	152	5	�	�	PROPN
ejpam-739	153	1	t2(q+	t2(q+	PROPN
ejpam-739	153	2	p)2	p)2	NOUN
ejpam-739	153	3	1	1	NUM
ejpam-739	153	4	+	+	CCONJ
ejpam-739	153	5	t2(q+	t2(q+	PROPN
ejpam-739	153	6	p)2	p)2	NOUN
ejpam-739	153	7	�	�	PROPN
ejpam-739	153	8	d	d	ADP
ejpam-739	153	9	t	t	PROPN
ejpam-739	153	10			PROPN
ejpam-739	153	11			PROPN
ejpam-739	153	12	and	and	CCONJ
ejpam-739	153	13	|aq+p|(q+	|aq+p|(q+	NOUN
ejpam-739	153	14	p)(q+	p)(q+	NOUN
ejpam-739	153	15	p−	p−	NOUN
ejpam-739	153	16	1)	1)	NUM
ejpam-739	153	17	...	...	PUNCT
ejpam-739	153	18	(p+	(p+	X
ejpam-739	153	19	1)r	1)r	PROPN
ejpam-739	153	20	p	p	X
ejpam-739	153	21	·	·	PUNCT
ejpam-739	153	22			PROPN
ejpam-739	153	23			NOUN
ejpam-739	153	24	1	1	NUM
ejpam-739	153	25	beta(α	beta(α	NOUN
ejpam-739	153	26	,	,	PUNCT
ejpam-739	153	27	β	β	X
ejpam-739	153	28	)	)	PUNCT
ejpam-739	153	29	∫	∫	PROPN
ejpam-739	154	1	1	1	NUM
ejpam-739	154	2	0	0	NUM
ejpam-739	154	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	154	4	t)β−1	t)β−1	PUNCT
ejpam-739	154	5	�	�	PROPN
ejpam-739	155	1	t2(q+	t2(q+	PROPN
ejpam-739	155	2	p)2	p)2	NOUN
ejpam-739	155	3	1	1	NUM
ejpam-739	155	4	+	+	CCONJ
ejpam-739	155	5	t2(q+	t2(q+	PROPN
ejpam-739	155	6	p)2	p)2	NOUN
ejpam-739	155	7	�	�	PROPN
ejpam-739	155	8	d	d	PROPN
ejpam-739	155	9	t	t	PROPN
ejpam-739	155	10			PROPN
ejpam-739	155	11	≤	≤	NOUN
ejpam-739	155	12	‖	‖	PROPN
ejpam-739	155	13	f	f	PROPN
ejpam-739	155	14	(	(	PUNCT
ejpam-739	155	15	q)−	q)−	PROPN
ejpam-739	155	16	(	(	PUNCT
ejpam-739	155	17	gα	gα	PROPN
ejpam-739	155	18	,	,	PUNCT
ejpam-739	155	19	β	β	X
ejpam-739	155	20	u	u	NOUN
ejpam-739	155	21	(	(	PUNCT
ejpam-739	155	22	f	f	PROPN
ejpam-739	155	23	)	)	PUNCT
ejpam-739	155	24	)	)	PUNCT
ejpam-739	155	25	(	(	PUNCT
ejpam-739	155	26	q)‖r	q)‖r	INTJ
ejpam-739	155	27	.	.	PUNCT
ejpam-739	156	1	first	first	ADV
ejpam-739	156	2	take	take	VERB
ejpam-739	156	3	q	q	NOUN
ejpam-739	156	4	=	=	PUNCT
ejpam-739	156	5	0	0	NUM
ejpam-739	156	6	.	.	PUNCT
ejpam-739	157	1	from	from	ADP
ejpam-739	157	2	the	the	DET
ejpam-739	157	3	previous	previous	ADJ
ejpam-739	157	4	inequality	inequality	NOUN
ejpam-739	157	5	we	we	PRON
ejpam-739	157	6	immediately	immediately	ADV
ejpam-739	157	7	obtain	obtain	VERB
ejpam-739	157	8	|ap|r	|ap|r	ADP
ejpam-739	157	9	p	p	NOUN
ejpam-739	157	10	1	1	NUM
ejpam-739	157	11	beta(α	beta(α	NOUN
ejpam-739	157	12	,	,	PUNCT
ejpam-739	157	13	β	β	X
ejpam-739	157	14	)	)	PUNCT
ejpam-739	157	15	∫	∫	PROPN
ejpam-739	158	1	1	1	NUM
ejpam-739	158	2	0	0	NUM
ejpam-739	158	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	158	4	t)β−1	t)β−1	PUNCT
ejpam-739	158	5	�	�	PROPN
ejpam-739	158	6	t2p2	t2p2	PROPN
ejpam-739	158	7	1	1	NUM
ejpam-739	158	8	+	+	NUM
ejpam-739	158	9	t2p2	t2p2	PROPN
ejpam-739	158	10	�	�	PROPN
ejpam-739	158	11	d	d	PROPN
ejpam-739	158	12	t	t	PROPN
ejpam-739	158	13	!	!	PUNCT
ejpam-739	159	1	≤	≤	NUM
ejpam-739	160	1	‖	‖	PROPN
ejpam-739	160	2	f	f	X
ejpam-739	160	3	−	−	PROPN
ejpam-739	160	4	g	g	PROPN
ejpam-739	160	5	α	α	PROPN
ejpam-739	160	6	,	,	PUNCT
ejpam-739	160	7	β	β	X
ejpam-739	160	8	u	u	NOUN
ejpam-739	160	9	(	(	PUNCT
ejpam-739	160	10	f	f	PROPN
ejpam-739	160	11	)	)	PUNCT
ejpam-739	160	12	‖r	‖r	NOUN
ejpam-739	160	13	.	.	PUNCT
ejpam-739	161	1	in	in	ADP
ejpam-739	161	2	what	what	PRON
ejpam-739	161	3	follows	follow	VERB
ejpam-739	161	4	,	,	PUNCT
ejpam-739	161	5	denoting	denote	VERB
ejpam-739	161	6	vα	vα	ADP
ejpam-739	161	7	,	,	PUNCT
ejpam-739	161	8	β	β	X
ejpam-739	161	9	=	=	SYM
ejpam-739	161	10	inf	inf	NOUN
ejpam-739	161	11	p≥1	p≥1	NOUN
ejpam-739	161	12	1	1	NUM
ejpam-739	161	13	beta(α	beta(α	NOUN
ejpam-739	161	14	,	,	PUNCT
ejpam-739	161	15	β	β	X
ejpam-739	161	16	)	)	PUNCT
ejpam-739	161	17	∫	∫	PROPN
ejpam-739	162	1	1	1	NUM
ejpam-739	162	2	0	0	NUM
ejpam-739	162	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	162	4	t)β−1	t)β−1	PUNCT
ejpam-739	162	5	�	�	PROPN
ejpam-739	162	6	t2p2	t2p2	PROPN
ejpam-739	162	7	1	1	NUM
ejpam-739	162	8	+	+	NUM
ejpam-739	162	9	t2p2	t2p2	PROPN
ejpam-739	162	10	�	�	PROPN
ejpam-739	162	11	d	d	PROPN
ejpam-739	162	12	t	t	PROPN
ejpam-739	162	13	!	!	PUNCT
ejpam-739	163	1	,	,	PUNCT
ejpam-739	163	2	we	we	PRON
ejpam-739	163	3	clearly	clearly	ADV
ejpam-739	163	4	get	get	VERB
ejpam-739	163	5	vα	vα	ADP
ejpam-739	163	6	,	,	PUNCT
ejpam-739	163	7	β	β	X
ejpam-739	163	8	=	=	SYM
ejpam-739	163	9	1	1	NUM
ejpam-739	163	10	beta(α	beta(α	NOUN
ejpam-739	163	11	,	,	PUNCT
ejpam-739	163	12	β	β	X
ejpam-739	163	13	)	)	PUNCT
ejpam-739	163	14	∫	∫	PROPN
ejpam-739	164	1	1	1	NUM
ejpam-739	164	2	0	0	NUM
ejpam-739	164	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	164	4	t)β−1	t)β−1	PUNCT
ejpam-739	164	5	�	�	PROPN
ejpam-739	164	6	t2	t2	PROPN
ejpam-739	164	7	1	1	NUM
ejpam-739	164	8	+	+	NUM
ejpam-739	164	9	t2	t2	PROPN
ejpam-739	164	10	�	�	PROPN
ejpam-739	164	11	d	d	NOUN
ejpam-739	164	12	t	t	PROPN
ejpam-739	164	13	=	=	SYM
ejpam-739	164	14	1	1	NUM
ejpam-739	164	15	beta(α	beta(α	NOUN
ejpam-739	164	16	,	,	PUNCT
ejpam-739	164	17	β	β	X
ejpam-739	164	18	)	)	PUNCT
ejpam-739	164	19	∫	∫	PROPN
ejpam-739	164	20	1	1	NUM
ejpam-739	164	21	0	0	NUM
ejpam-739	164	22	tα−1(1−	tα−1(1−	PROPN
ejpam-739	164	23	t)β−1	t)β−1	PUNCT
ejpam-739	164	24	�	�	PROPN
ejpam-739	164	25	1−	1−	NUM
ejpam-739	164	26	1	1	NUM
ejpam-739	164	27	1	1	NUM
ejpam-739	164	28	+	+	NUM
ejpam-739	164	29	t2	t2	PROPN
ejpam-739	164	30	�	�	PROPN
ejpam-739	164	31	d	d	NOUN
ejpam-739	164	32	t.	t.	NOUN
ejpam-739	165	1	but	but	CCONJ
ejpam-739	165	2	we	we	PRON
ejpam-739	165	3	have	have	VERB
ejpam-739	165	4	1−	1−	NUM
ejpam-739	165	5	1	1	NUM
ejpam-739	165	6	1+t2	1+t2	NUM
ejpam-739	165	7	≥	≥	NOUN
ejpam-739	165	8	t2	t2	PROPN
ejpam-739	165	9	4	4	NUM
ejpam-739	165	10	,	,	PUNCT
ejpam-739	165	11	for	for	ADP
ejpam-739	165	12	all	all	DET
ejpam-739	165	13	t	t	NOUN
ejpam-739	165	14	∈	∈	PROPN
ejpam-739	166	1	[	[	X
ejpam-739	166	2	0,1	0,1	NUM
ejpam-739	166	3	]	]	PUNCT
ejpam-739	166	4	.	.	PUNCT
ejpam-739	167	1	indeed	indeed	ADV
ejpam-739	167	2	,	,	PUNCT
ejpam-739	167	3	denoting	denote	VERB
ejpam-739	167	4	g(t	g(t	PROPN
ejpam-739	167	5	)	)	PUNCT
ejpam-739	168	1	=	=	SYM
ejpam-739	168	2	1−	1−	NUM
ejpam-739	168	3	1	1	NUM
ejpam-739	168	4	1+t2	1+t2	NUM
ejpam-739	168	5	−	−	PROPN
ejpam-739	168	6	t2	t2	PROPN
ejpam-739	168	7	4	4	NUM
ejpam-739	168	8	,	,	PUNCT
ejpam-739	168	9	we	we	PRON
ejpam-739	168	10	get	get	VERB
ejpam-739	168	11	g(0	g(0	NOUN
ejpam-739	168	12	)	)	PUNCT
ejpam-739	168	13	=	=	SYM
ejpam-739	168	14	0	0	NUM
ejpam-739	168	15	and	and	CCONJ
ejpam-739	168	16	g′(t	g′(t	PROPN
ejpam-739	168	17	)	)	PUNCT
ejpam-739	169	1	=	=	SYM
ejpam-739	169	2	2	2	NUM
ejpam-739	169	3	t	t	NOUN
ejpam-739	169	4	(	(	PUNCT
ejpam-739	169	5	1+t2)2	1+t2)2	NUM
ejpam-739	169	6	−	−	ADP
ejpam-739	169	7	2	2	NUM
ejpam-739	169	8	t	t	NOUN
ejpam-739	169	9	4	4	NUM
ejpam-739	169	10	=	=	SYM
ejpam-739	169	11	2	2	NUM
ejpam-739	169	12	t	t	NOUN
ejpam-739	169	13	�	�	NOUN
ejpam-739	169	14	1	1	NUM
ejpam-739	169	15	(	(	PUNCT
ejpam-739	169	16	1+t2)2	1+t2)2	NUM
ejpam-739	169	17	−	−	NOUN
ejpam-739	169	18	1	1	NUM
ejpam-739	169	19	4	4	NUM
ejpam-739	169	20	�	�	PROPN
ejpam-739	169	21	≥	≥	NUM
ejpam-739	169	22	0	0	NUM
ejpam-739	169	23	,	,	PUNCT
ejpam-739	169	24	for	for	ADP
ejpam-739	169	25	all	all	DET
ejpam-739	169	26	t	t	NOUN
ejpam-739	169	27	∈	∈	PROPN
ejpam-739	170	1	[	[	X
ejpam-739	170	2	0,1	0,1	NUM
ejpam-739	170	3	]	]	PUNCT
ejpam-739	170	4	.	.	PUNCT
ejpam-739	171	1	it	it	PRON
ejpam-739	171	2	follows	follow	VERB
ejpam-739	171	3	that	that	SCONJ
ejpam-739	171	4	g(t	g(t	PROPN
ejpam-739	171	5	)	)	PUNCT
ejpam-739	171	6	is	be	AUX
ejpam-739	171	7	nondecreasing	nondecrease	VERB
ejpam-739	171	8	on	on	ADP
ejpam-739	171	9	[	[	X
ejpam-739	171	10	0,1	0,1	NUM
ejpam-739	171	11	]	]	PUNCT
ejpam-739	171	12	and	and	CCONJ
ejpam-739	171	13	therefore	therefore	ADV
ejpam-739	171	14	g(t	g(t	PROPN
ejpam-739	171	15	)	)	PUNCT
ejpam-739	171	16	≥	≥	NOUN
ejpam-739	171	17	0	0	NUM
ejpam-739	171	18	for	for	ADP
ejpam-739	171	19	all	all	DET
ejpam-739	171	20	t	t	NOUN
ejpam-739	171	21	∈	∈	PROPN
ejpam-739	172	1	[	[	X
ejpam-739	172	2	0,1	0,1	NUM
ejpam-739	172	3	]	]	PUNCT
ejpam-739	172	4	.	.	PUNCT
ejpam-739	173	1	in	in	ADP
ejpam-739	173	2	conclusion	conclusion	NOUN
ejpam-739	173	3	,	,	PUNCT
ejpam-739	173	4	vα	vα	INTJ
ejpam-739	173	5	,	,	PUNCT
ejpam-739	173	6	β	β	X
ejpam-739	173	7	≥	≥	NUM
ejpam-739	173	8	1	1	NUM
ejpam-739	173	9	beta(α	beta(α	NOUN
ejpam-739	173	10	,	,	PUNCT
ejpam-739	173	11	β	β	X
ejpam-739	173	12	)	)	PUNCT
ejpam-739	173	13	∫	∫	PROPN
ejpam-739	173	14	1	1	NUM
ejpam-739	173	15	0	0	NUM
ejpam-739	173	16	tα−1(1−	tα−1(1−	NOUN
ejpam-739	173	17	t)β−1	t)β−1	NOUN
ejpam-739	173	18	t2	t2	NOUN
ejpam-739	173	19	4	4	NUM
ejpam-739	173	20	d	d	NOUN
ejpam-739	173	21	t	t	NOUN
ejpam-739	173	22	=	=	SYM
ejpam-739	173	23	1	1	NUM
ejpam-739	173	24	4	4	NUM
ejpam-739	173	25	·	·	PUNCT
ejpam-739	173	26	beta(α+	beta(α+	NOUN
ejpam-739	173	27	2,β	2,β	ADV
ejpam-739	173	28	)	)	PUNCT
ejpam-739	173	29	beta(α	beta(α	NOUN
ejpam-739	173	30	,	,	PUNCT
ejpam-739	173	31	β	β	X
ejpam-739	173	32	)	)	PUNCT
ejpam-739	173	33	=	=	SYM
ejpam-739	174	1	1	1	NUM
ejpam-739	174	2	4	4	NUM
ejpam-739	174	3	·	·	PUNCT
ejpam-739	174	4	α+	α+	PUNCT
ejpam-739	174	5	1	1	NUM
ejpam-739	174	6	α+	α+	X
ejpam-739	174	7	β	β	NOUN
ejpam-739	174	8	+	+	CCONJ
ejpam-739	174	9	1	1	NUM
ejpam-739	174	10	·	·	PUNCT
ejpam-739	174	11	α	α	NOUN
ejpam-739	174	12	α+	α+	X
ejpam-739	174	13	β	β	X
ejpam-739	174	14	s.	s.	PROPN
ejpam-739	174	15	gal	gal	PROPN
ejpam-739	174	16	/	/	SYM
ejpam-739	174	17	eur	eur	PROPN
ejpam-739	174	18	.	.	PUNCT
ejpam-739	175	1	j.	j.	PROPN
ejpam-739	175	2	pure	pure	PROPN
ejpam-739	175	3	appl	appl	PROPN
ejpam-739	175	4	.	.	PROPN
ejpam-739	175	5	math	math	PROPN
ejpam-739	175	6	,	,	PUNCT
ejpam-739	175	7	3	3	NUM
ejpam-739	175	8	(	(	PUNCT
ejpam-739	175	9	2010	2010	NUM
ejpam-739	175	10	)	)	PUNCT
ejpam-739	175	11	,	,	PUNCT
ejpam-739	175	12	1150	1150	NUM
ejpam-739	175	13	-	-	SYM
ejpam-739	175	14	1164	1164	NUM
ejpam-739	175	15	1159	1159	NUM
ejpam-739	175	16	≥	≥	NOUN
ejpam-739	175	17	1	1	NUM
ejpam-739	175	18	4	4	NUM
ejpam-739	175	19	·	·	PUNCT
ejpam-739	175	20	α(α+	α(α+	NUM
ejpam-739	175	21	1	1	NUM
ejpam-739	175	22	)	)	PUNCT
ejpam-739	175	23	2	2	NUM
ejpam-739	175	24	≥	≥	NOUN
ejpam-739	175	25	α	α	NOUN
ejpam-739	175	26	8	8	NUM
ejpam-739	175	27	.	.	PUNCT
ejpam-739	176	1	now	now	ADV
ejpam-739	176	2	,	,	PUNCT
ejpam-739	176	3	by	by	ADP
ejpam-739	176	4	following	follow	VERB
ejpam-739	176	5	for	for	ADP
ejpam-739	176	6	q	q	PROPN
ejpam-739	176	7	≥	≥	NOUN
ejpam-739	176	8	0	0	NUM
ejpam-739	176	9	similar	similar	ADJ
ejpam-739	176	10	reasonings	reasoning	NOUN
ejpam-739	176	11	with	with	ADP
ejpam-739	176	12	those	those	PRON
ejpam-739	176	13	in	in	ADP
ejpam-739	176	14	the	the	DET
ejpam-739	176	15	above	above	ADJ
ejpam-739	176	16	point	point	NOUN
ejpam-739	176	17	(	(	PUNCT
ejpam-739	176	18	i	i	NOUN
ejpam-739	176	19	)	)	PUNCT
ejpam-739	176	20	,	,	PUNCT
ejpam-739	176	21	we	we	PRON
ejpam-739	176	22	get	get	VERB
ejpam-739	176	23	the	the	DET
ejpam-739	176	24	desired	desire	VERB
ejpam-739	176	25	equivalence	equivalence	NOUN
ejpam-739	176	26	in	in	ADP
ejpam-739	176	27	the	the	DET
ejpam-739	176	28	statement	statement	NOUN
ejpam-739	176	29	.	.	PUNCT
ejpam-739	177	1	(	(	PUNCT
ejpam-739	177	2	iii	iii	NOUN
ejpam-739	177	3	)	)	PUNCT
ejpam-739	177	4	by	by	ADP
ejpam-739	177	5	gal	gal	PROPN
ejpam-739	178	1	[	[	X
ejpam-739	178	2	2	2	NUM
ejpam-739	178	3	,	,	PUNCT
ejpam-739	178	4	p.	p.	NOUN
ejpam-739	178	5	213	213	NUM
ejpam-739	178	6	,	,	PUNCT
ejpam-739	178	7	theorem	theorem	VERB
ejpam-739	178	8	3.2.5	3.2.5	NUM
ejpam-739	178	9	,	,	PUNCT
ejpam-739	178	10	(	(	PUNCT
ejpam-739	178	11	i	i	NOUN
ejpam-739	178	12	)	)	PUNCT
ejpam-739	178	13	]	]	PUNCT
ejpam-739	178	14	,	,	PUNCT
ejpam-739	178	15	ut	ut	PROPN
ejpam-739	178	16	(	(	PUNCT
ejpam-739	178	17	f	f	PROPN
ejpam-739	178	18	)	)	PUNCT
ejpam-739	178	19	(	(	PUNCT
ejpam-739	178	20	z	z	NOUN
ejpam-739	178	21	)	)	PUNCT
ejpam-739	178	22	is	be	AUX
ejpam-739	178	23	analytic	analytic	ADJ
ejpam-739	178	24	(	(	PUNCT
ejpam-739	178	25	as	as	ADP
ejpam-739	178	26	function	function	NOUN
ejpam-739	178	27	of	of	ADP
ejpam-739	178	28	z	z	NOUN
ejpam-739	178	29	)	)	PUNCT
ejpam-739	178	30	in	in	ADP
ejpam-739	178	31	dr	dr	PROPN
ejpam-739	179	1	and	and	CCONJ
ejpam-739	179	2	we	we	PRON
ejpam-739	179	3	can	can	AUX
ejpam-739	179	4	write	write	VERB
ejpam-739	179	5	ut	ut	PROPN
ejpam-739	179	6	(	(	PUNCT
ejpam-739	179	7	f	f	PROPN
ejpam-739	179	8	)	)	PUNCT
ejpam-739	179	9	(	(	PUNCT
ejpam-739	179	10	z	z	NOUN
ejpam-739	179	11	)	)	PUNCT
ejpam-739	179	12	=	=	SYM
ejpam-739	180	1	∞	∞	NUM
ejpam-739	180	2	∑	∑	PUNCT
ejpam-739	180	3	k=0	k=0	PROPN
ejpam-739	180	4	ak(1	ak(1	PROPN
ejpam-739	180	5	+	+	PROPN
ejpam-739	180	6	kt)e−ktzk	kt)e−ktzk	NOUN
ejpam-739	180	7	,	,	PUNCT
ejpam-739	180	8	for	for	ADP
ejpam-739	180	9	all	all	DET
ejpam-739	180	10	|z|	|z|	NOUN
ejpam-739	180	11	<	<	X
ejpam-739	180	12	r	r	NOUN
ejpam-739	180	13	and	and	CCONJ
ejpam-739	180	14	t	t	PROPN
ejpam-739	180	15	≥	≥	NUM
ejpam-739	180	16	0	0	NUM
ejpam-739	180	17	.	.	PUNCT
ejpam-739	181	1	since	since	SCONJ
ejpam-739	181	2	|∑∞k=0	|∑∞k=0	NOUN
ejpam-739	181	3	ake−kt(1+kt)zk|	ake−kt(1+kt)zk|	VERB
ejpam-739	181	4	≤	≤	ADJ
ejpam-739	181	5	2	2	NUM
ejpam-739	181	6	∑∞	∑∞	NOUN
ejpam-739	181	7	k=0	k=0	PROPN
ejpam-739	181	8	|ak|·|z|k	|ak|·|z|k	NOUN
ejpam-739	181	9	<	<	X
ejpam-739	181	10	∞	∞	PROPN
ejpam-739	181	11	,	,	PUNCT
ejpam-739	181	12	this	this	PRON
ejpam-739	181	13	implies	imply	VERB
ejpam-739	181	14	that	that	SCONJ
ejpam-739	181	15	for	for	ADP
ejpam-739	181	16	fixed	fix	VERB
ejpam-739	181	17	|z|	|z|	NOUN
ejpam-739	181	18	<	<	X
ejpam-739	181	19	r	r	NOUN
ejpam-739	181	20	,	,	PUNCT
ejpam-739	181	21	the	the	DET
ejpam-739	181	22	series	series	NOUN
ejpam-739	181	23	in	in	ADP
ejpam-739	181	24	t	t	PROPN
ejpam-739	181	25	,	,	PUNCT
ejpam-739	181	26	∑∞	∑∞	PUNCT
ejpam-739	181	27	k=0	k=0	PROPN
ejpam-739	181	28	ak(1	ak(1	PROPN
ejpam-739	181	29	+	+	PROPN
ejpam-739	181	30	kt)e−ktzk	kt)e−ktzk	NOUN
ejpam-739	181	31	is	be	AUX
ejpam-739	181	32	uniformly	uniformly	ADV
ejpam-739	181	33	convergent	convergent	NOUN
ejpam-739	181	34	on	on	ADP
ejpam-739	181	35	[	[	X
ejpam-739	181	36	0,∞	0,∞	NOUN
ejpam-739	181	37	)	)	PUNCT
ejpam-739	181	38	,	,	PUNCT
ejpam-739	181	39	and	and	CCONJ
ejpam-739	181	40	therefore	therefore	ADV
ejpam-739	181	41	we	we	PRON
ejpam-739	181	42	immediately	immediately	ADV
ejpam-739	181	43	can	can	AUX
ejpam-739	181	44	write	write	VERB
ejpam-739	181	45	g	g	PROPN
ejpam-739	181	46	α	α	PROPN
ejpam-739	181	47	,	,	PUNCT
ejpam-739	181	48	β	β	X
ejpam-739	181	49	u	u	NOUN
ejpam-739	181	50	(	(	PUNCT
ejpam-739	181	51	f	f	PROPN
ejpam-739	181	52	)	)	PUNCT
ejpam-739	181	53	(	(	PUNCT
ejpam-739	181	54	z	z	NOUN
ejpam-739	181	55	)	)	PUNCT
ejpam-739	181	56	=	=	SYM
ejpam-739	182	1	∞	∞	NUM
ejpam-739	182	2	∑	∑	PUNCT
ejpam-739	182	3	k=0	k=0	PROPN
ejpam-739	182	4	akzk	akzk	NOUN
ejpam-739	182	5	1	1	NUM
ejpam-739	182	6	beta(α	beta(α	NOUN
ejpam-739	182	7	,	,	PUNCT
ejpam-739	182	8	β	β	X
ejpam-739	182	9	)	)	PUNCT
ejpam-739	182	10	∫	∫	PROPN
ejpam-739	182	11	1	1	NUM
ejpam-739	182	12	0	0	NUM
ejpam-739	182	13	tα−1(1−	tα−1(1−	NOUN
ejpam-739	182	14	t)β−1(1	t)β−1(1	X
ejpam-739	182	15	+	+	NUM
ejpam-739	182	16	kt)e−kt	kt)e−kt	NOUN
ejpam-739	182	17	d	d	PROPN
ejpam-739	182	18	t	t	PROPN
ejpam-739	182	19	,	,	PUNCT
ejpam-739	182	20	where	where	SCONJ
ejpam-739	182	21	denoting	denote	VERB
ejpam-739	182	22	bk(α	bk(α	PROPN
ejpam-739	182	23	,	,	PUNCT
ejpam-739	182	24	β	β	X
ejpam-739	182	25	)	)	PUNCT
ejpam-739	182	26	=	=	SYM
ejpam-739	182	27	1	1	NUM
ejpam-739	182	28	beta(α	beta(α	NOUN
ejpam-739	182	29	,	,	PUNCT
ejpam-739	182	30	β	β	X
ejpam-739	182	31	)	)	PUNCT
ejpam-739	182	32	∫	∫	PROPN
ejpam-739	182	33	1	1	NUM
ejpam-739	182	34	0	0	NUM
ejpam-739	182	35	tα−1(1−	tα−1(1−	NOUN
ejpam-739	182	36	t)β−1(1	t)β−1(1	X
ejpam-739	182	37	+	+	NUM
ejpam-739	182	38	kt)e−kt	kt)e−kt	NOUN
ejpam-739	182	39	d	d	PROPN
ejpam-739	182	40	t	t	PROPN
ejpam-739	182	41	,	,	PUNCT
ejpam-739	182	42	we	we	PRON
ejpam-739	182	43	obtain	obtain	VERB
ejpam-739	182	44	g	g	PROPN
ejpam-739	182	45	α	α	NOUN
ejpam-739	182	46	,	,	PUNCT
ejpam-739	182	47	α	α	PROPN
ejpam-739	182	48	u	u	NOUN
ejpam-739	182	49	(	(	PUNCT
ejpam-739	182	50	f	f	PROPN
ejpam-739	182	51	)	)	PUNCT
ejpam-739	182	52	(	(	PUNCT
ejpam-739	182	53	z	z	NOUN
ejpam-739	182	54	)	)	PUNCT
ejpam-739	182	55	=	=	SYM
ejpam-739	183	1	∞	∞	NUM
ejpam-739	183	2	∑	∑	PROPN
ejpam-739	183	3	k=0	k=0	PROPN
ejpam-739	183	4	ak	ak	PROPN
ejpam-739	183	5	·	·	PUNCT
ejpam-739	183	6	bk(α	bk(α	PROPN
ejpam-739	183	7	,	,	PUNCT
ejpam-739	183	8	β	β	X
ejpam-739	183	9	)	)	PUNCT
ejpam-739	183	10	·	·	PUNCT
ejpam-739	184	1	zk	zk	X
ejpam-739	184	2	.	.	PROPN
ejpam-739	185	1	in	in	ADP
ejpam-739	185	2	other	other	ADJ
ejpam-739	185	3	order	order	NOUN
ejpam-739	185	4	of	of	ADP
ejpam-739	185	5	ideas	idea	NOUN
ejpam-739	185	6	,	,	PUNCT
ejpam-739	185	7	we	we	PRON
ejpam-739	185	8	easily	easily	ADV
ejpam-739	185	9	can	can	AUX
ejpam-739	185	10	write	write	VERB
ejpam-739	185	11	g	g	PROPN
ejpam-739	185	12	α	α	PROPN
ejpam-739	185	13	,	,	PUNCT
ejpam-739	185	14	β	β	X
ejpam-739	185	15	u	u	NOUN
ejpam-739	185	16	(	(	PUNCT
ejpam-739	185	17	f	f	PROPN
ejpam-739	185	18	)	)	PUNCT
ejpam-739	185	19	(	(	PUNCT
ejpam-739	185	20	z)−	z)−	PROPN
ejpam-739	185	21	f	f	X
ejpam-739	185	22	(	(	PUNCT
ejpam-739	185	23	z	z	NOUN
ejpam-739	185	24	)	)	PUNCT
ejpam-739	185	25	=	=	SYM
ejpam-739	185	26	1	1	NUM
ejpam-739	185	27	beta(α	beta(α	NOUN
ejpam-739	185	28	,	,	PUNCT
ejpam-739	185	29	β	β	X
ejpam-739	185	30	)	)	PUNCT
ejpam-739	185	31	·	·	PUNCT
ejpam-739	186	1	∫	∫	PROPN
ejpam-739	186	2	1	1	NUM
ejpam-739	186	3	0	0	NUM
ejpam-739	186	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	186	5	t)β−1[ut	t)β−1[ut	PROPN
ejpam-739	186	6	(	(	PUNCT
ejpam-739	186	7	f	f	PROPN
ejpam-739	186	8	)	)	PUNCT
ejpam-739	186	9	(	(	PUNCT
ejpam-739	186	10	z)−	z)−	PROPN
ejpam-739	186	11	f	f	X
ejpam-739	186	12	(	(	PUNCT
ejpam-739	186	13	z)]d	z)]d	PROPN
ejpam-739	186	14	t	t	PROPN
ejpam-739	186	15	,	,	PUNCT
ejpam-739	186	16	which	which	PRON
ejpam-739	186	17	together	together	ADV
ejpam-739	186	18	with	with	ADP
ejpam-739	186	19	the	the	DET
ejpam-739	186	20	estimate	estimate	NOUN
ejpam-739	186	21	|ut	|ut	NOUN
ejpam-739	186	22	(	(	PUNCT
ejpam-739	186	23	f	f	PROPN
ejpam-739	186	24	)	)	PUNCT
ejpam-739	186	25	(	(	PUNCT
ejpam-739	186	26	z)−	z)−	PROPN
ejpam-739	186	27	f	f	X
ejpam-739	186	28	(	(	PUNCT
ejpam-739	186	29	z)|	z)|	NOUN
ejpam-739	186	30	≤	≤	PROPN
ejpam-739	186	31	cr	cr	PROPN
ejpam-739	187	1	(	(	PUNCT
ejpam-739	187	2	f	f	PROPN
ejpam-739	187	3	)	)	PUNCT
ejpam-739	187	4	t	t	PROPN
ejpam-739	187	5	2	2	NUM
ejpam-739	187	6	in	in	ADP
ejpam-739	187	7	gal	gal	PROPN
ejpam-739	187	8	[	[	X
ejpam-739	187	9	2	2	NUM
ejpam-739	187	10	,	,	PUNCT
ejpam-739	187	11	p.	p.	NOUN
ejpam-739	187	12	213	213	NUM
ejpam-739	187	13	-	-	SYM
ejpam-739	187	14	214	214	NUM
ejpam-739	187	15	,	,	PUNCT
ejpam-739	187	16	theorem	theorem	VERB
ejpam-739	187	17	3.2.5	3.2.5	NUM
ejpam-739	187	18	,	,	PUNCT
ejpam-739	187	19	(	(	PUNCT
ejpam-739	187	20	iv	iv	X
ejpam-739	187	21	)	)	PUNCT
ejpam-739	187	22	]	]	PUNCT
ejpam-739	187	23	,	,	PUNCT
ejpam-739	187	24	implies	imply	VERB
ejpam-739	187	25	|gα	|gα	PROPN
ejpam-739	187	26	,	,	PUNCT
ejpam-739	187	27	β	β	X
ejpam-739	187	28	u	u	NOUN
ejpam-739	187	29	(	(	PUNCT
ejpam-739	187	30	f	f	PROPN
ejpam-739	187	31	)	)	PUNCT
ejpam-739	187	32	(	(	PUNCT
ejpam-739	187	33	z)−	z)−	PROPN
ejpam-739	187	34	f	f	X
ejpam-739	187	35	(	(	PUNCT
ejpam-739	187	36	z)|	z)|	ADP
ejpam-739	187	37	≤	≤	ADV
ejpam-739	187	38	1	1	NUM
ejpam-739	187	39	beta(α	beta(α	NOUN
ejpam-739	187	40	,	,	PUNCT
ejpam-739	187	41	β	β	X
ejpam-739	187	42	)	)	PUNCT
ejpam-739	187	43	·	·	PUNCT
ejpam-739	188	1	∫	∫	PROPN
ejpam-739	188	2	1	1	NUM
ejpam-739	188	3	0	0	NUM
ejpam-739	188	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	188	5	t)β−1|ut	t)β−1|ut	NUM
ejpam-739	188	6	(	(	PUNCT
ejpam-739	188	7	f	f	NOUN
ejpam-739	188	8	)	)	PUNCT
ejpam-739	188	9	(	(	PUNCT
ejpam-739	188	10	z)−	z)−	PROPN
ejpam-739	188	11	f	f	PROPN
ejpam-739	188	12	(	(	PUNCT
ejpam-739	188	13	z)|d	z)|d	PROPN
ejpam-739	188	14	t	t	PROPN
ejpam-739	188	15	≤	≤	PROPN
ejpam-739	188	16	cr	cr	PROPN
ejpam-739	188	17	(	(	PUNCT
ejpam-739	188	18	f	f	PROPN
ejpam-739	188	19	)	)	PUNCT
ejpam-739	188	20	1	1	NUM
ejpam-739	188	21	beta(α	beta(α	NOUN
ejpam-739	188	22	,	,	PUNCT
ejpam-739	188	23	β	β	X
ejpam-739	188	24	)	)	PUNCT
ejpam-739	188	25	·	·	PUNCT
ejpam-739	189	1	∫	∫	PROPN
ejpam-739	190	1	1	1	NUM
ejpam-739	190	2	0	0	NUM
ejpam-739	190	3	tα+1(1−	tα+1(1−	ADP
ejpam-739	190	4	t)β−1d	t)β−1d	PROPN
ejpam-739	190	5	t	t	PROPN
ejpam-739	190	6	=	=	SYM
ejpam-739	190	7	cr	cr	PROPN
ejpam-739	190	8	(	(	PUNCT
ejpam-739	190	9	f	f	PROPN
ejpam-739	190	10	)	)	PUNCT
ejpam-739	190	11	·	·	PUNCT
ejpam-739	191	1	beta(α+	beta(α+	NOUN
ejpam-739	191	2	2,β	2,β	ADV
ejpam-739	191	3	)	)	PUNCT
ejpam-739	191	4	beta(α	beta(α	NOUN
ejpam-739	191	5	,	,	PUNCT
ejpam-739	191	6	β	β	NOUN
ejpam-739	191	7	)	)	PUNCT
ejpam-739	191	8	≤	≤	NOUN
ejpam-739	191	9	cr	cr	ADP
ejpam-739	191	10	(	(	PUNCT
ejpam-739	191	11	f	f	PROPN
ejpam-739	191	12	)	)	PUNCT
ejpam-739	191	13	α	α	PROPN
ejpam-739	191	14	,	,	PUNCT
ejpam-739	191	15	for	for	ADP
ejpam-739	191	16	all	all	DET
ejpam-739	191	17	|z|	|z|	NOUN
ejpam-739	191	18	≤	≤	NUM
ejpam-739	191	19	r	r	NOUN
ejpam-739	191	20	,	,	PUNCT
ejpam-739	191	21	where	where	SCONJ
ejpam-739	191	22	cr	cr	PROPN
ejpam-739	191	23	(	(	PUNCT
ejpam-739	191	24	f	f	PROPN
ejpam-739	191	25	)	)	PUNCT
ejpam-739	191	26	>	>	X
ejpam-739	191	27	0	0	PUNCT
ejpam-739	191	28	is	be	AUX
ejpam-739	191	29	independent	independent	ADJ
ejpam-739	191	30	of	of	ADP
ejpam-739	191	31	z	z	NOUN
ejpam-739	191	32	(	(	PUNCT
ejpam-739	191	33	and	and	CCONJ
ejpam-739	191	34	α	α	X
ejpam-739	191	35	)	)	PUNCT
ejpam-739	192	1	but	but	CCONJ
ejpam-739	192	2	depends	depend	VERB
ejpam-739	192	3	on	on	ADP
ejpam-739	192	4	f	f	PROPN
ejpam-739	192	5	and	and	CCONJ
ejpam-739	192	6	r.	r.	PROPN
ejpam-739	192	7	we	we	PRON
ejpam-739	192	8	used	use	VERB
ejpam-739	192	9	here	here	ADV
ejpam-739	192	10	the	the	DET
ejpam-739	192	11	estimate	estimate	NOUN
ejpam-739	192	12	from	from	ADP
ejpam-739	192	13	the	the	DET
ejpam-739	192	14	above	above	ADJ
ejpam-739	192	15	point	point	NOUN
ejpam-739	192	16	(	(	PUNCT
ejpam-739	192	17	ii	ii	NOUN
ejpam-739	192	18	)	)	PUNCT
ejpam-739	192	19	.	.	PUNCT
ejpam-739	193	1	now	now	ADV
ejpam-739	193	2	,	,	PUNCT
ejpam-739	193	3	let	let	VERB
ejpam-739	193	4	q	q	PROPN
ejpam-739	193	5	∈	∈	PROPN
ejpam-739	193	6	n∪	n∪	PROPN
ejpam-739	193	7	{	{	PUNCT
ejpam-739	193	8	0	0	NUM
ejpam-739	193	9	}	}	PUNCT
ejpam-739	193	10	and	and	CCONJ
ejpam-739	193	11	1	1	NUM
ejpam-739	193	12	≤	≤	NOUN
ejpam-739	193	13	r	r	NOUN
ejpam-739	193	14	<	<	X
ejpam-739	193	15	r1	r1	PROPN
ejpam-739	193	16	<	<	X
ejpam-739	193	17	r.	r.	PROPN
ejpam-739	193	18	by	by	ADP
ejpam-739	193	19	using	use	VERB
ejpam-739	193	20	the	the	DET
ejpam-739	193	21	cauchy	cauchy	NOUN
ejpam-739	193	22	’s	’s	PART
ejpam-739	193	23	formula	formula	NOUN
ejpam-739	193	24	and	and	CCONJ
ejpam-739	193	25	reasoning	reasoning	NOUN
ejpam-739	193	26	as	as	ADP
ejpam-739	193	27	in	in	ADP
ejpam-739	193	28	the	the	DET
ejpam-739	193	29	proof	proof	NOUN
ejpam-739	193	30	of	of	ADP
ejpam-739	193	31	the	the	DET
ejpam-739	193	32	above	above	ADJ
ejpam-739	193	33	point	point	NOUN
ejpam-739	193	34	(	(	PUNCT
ejpam-739	193	35	i	i	NOUN
ejpam-739	193	36	)	)	PUNCT
ejpam-739	193	37	,	,	PUNCT
ejpam-739	193	38	we	we	PRON
ejpam-739	193	39	get	get	VERB
ejpam-739	193	40	the	the	DET
ejpam-739	193	41	upper	upper	ADJ
ejpam-739	193	42	estimate	estimate	NOUN
ejpam-739	193	43	‖[gα	‖[gα	NOUN
ejpam-739	193	44	,	,	PUNCT
ejpam-739	193	45	β	β	X
ejpam-739	193	46	u	u	NOUN
ejpam-739	193	47	(	(	PUNCT
ejpam-739	193	48	f	f	PROPN
ejpam-739	193	49	)	)	PUNCT
ejpam-739	193	50	]	]	PUNCT
ejpam-739	193	51	(	(	PUNCT
ejpam-739	193	52	q)−	q)−	PROPN
ejpam-739	193	53	f	f	X
ejpam-739	193	54	(	(	PUNCT
ejpam-739	193	55	q)‖r	q)‖r	NOUN
ejpam-739	193	56	≤	≤	NOUN
ejpam-739	193	57	c∗α	c∗α	NOUN
ejpam-739	193	58	,	,	PUNCT
ejpam-739	193	59	s.	s.	PROPN
ejpam-739	193	60	gal	gal	PROPN
ejpam-739	193	61	/	/	SYM
ejpam-739	193	62	eur	eur	PROPN
ejpam-739	193	63	.	.	PUNCT
ejpam-739	194	1	j.	j.	PROPN
ejpam-739	194	2	pure	pure	PROPN
ejpam-739	194	3	appl	appl	PROPN
ejpam-739	194	4	.	.	PROPN
ejpam-739	194	5	math	math	PROPN
ejpam-739	194	6	,	,	PUNCT
ejpam-739	194	7	3	3	NUM
ejpam-739	194	8	(	(	PUNCT
ejpam-739	194	9	2010	2010	NUM
ejpam-739	194	10	)	)	PUNCT
ejpam-739	194	11	,	,	PUNCT
ejpam-739	194	12	1150	1150	NUM
ejpam-739	194	13	-	-	SYM
ejpam-739	194	14	1164	1164	NUM
ejpam-739	194	15	1160	1160	NUM
ejpam-739	194	16	with	with	ADP
ejpam-739	194	17	c∗	c∗	NOUN
ejpam-739	194	18	depending	depend	VERB
ejpam-739	194	19	only	only	ADV
ejpam-739	194	20	on	on	ADP
ejpam-739	194	21	f	f	PROPN
ejpam-739	194	22	,	,	PUNCT
ejpam-739	194	23	q	q	X
ejpam-739	194	24	,	,	PUNCT
ejpam-739	194	25	r	r	NOUN
ejpam-739	194	26	and	and	CCONJ
ejpam-739	194	27	r1	r1	NOUN
ejpam-739	194	28	.	.	PUNCT
ejpam-739	195	1	it	it	PRON
ejpam-739	195	2	remains	remain	VERB
ejpam-739	195	3	to	to	PART
ejpam-739	195	4	prove	prove	VERB
ejpam-739	195	5	the	the	DET
ejpam-739	195	6	lower	low	ADJ
ejpam-739	195	7	estimate	estimate	NOUN
ejpam-739	195	8	.	.	PUNCT
ejpam-739	196	1	for	for	ADP
ejpam-739	196	2	this	this	DET
ejpam-739	196	3	purpose	purpose	NOUN
ejpam-739	196	4	,	,	PUNCT
ejpam-739	196	5	reasoning	reason	VERB
ejpam-739	196	6	exactly	exactly	ADV
ejpam-739	196	7	as	as	ADP
ejpam-739	196	8	in	in	ADP
ejpam-739	196	9	the	the	DET
ejpam-739	196	10	proof	proof	NOUN
ejpam-739	196	11	of	of	ADP
ejpam-739	196	12	theorem	theorem	ADJ
ejpam-739	196	13	3.2.5	3.2.5	NUM
ejpam-739	196	14	,	,	PUNCT
ejpam-739	196	15	at	at	ADP
ejpam-739	196	16	pages	page	NOUN
ejpam-739	196	17	219	219	NUM
ejpam-739	196	18	-	-	SYM
ejpam-739	196	19	220	220	NUM
ejpam-739	196	20	in	in	ADP
ejpam-739	196	21	the	the	DET
ejpam-739	196	22	book	book	NOUN
ejpam-739	196	23	gal	gal	NOUN
ejpam-739	197	1	[	[	X
ejpam-739	197	2	2	2	NUM
ejpam-739	197	3	]	]	PUNCT
ejpam-739	197	4	,	,	PUNCT
ejpam-739	197	5	for	for	ADP
ejpam-739	197	6	z	z	NOUN
ejpam-739	197	7	=	=	NOUN
ejpam-739	197	8	reiϕ	reiϕ	NOUN
ejpam-739	197	9	and	and	CCONJ
ejpam-739	197	10	p	p	PRON
ejpam-739	197	11	∈	∈	PROPN
ejpam-739	197	12	n∪	n∪	X
ejpam-739	197	13	{	{	PUNCT
ejpam-739	197	14	0	0	NUM
ejpam-739	197	15	}	}	PUNCT
ejpam-739	197	16	we	we	PRON
ejpam-739	197	17	get	get	VERB
ejpam-739	197	18	1	1	NUM
ejpam-739	197	19	2π	2π	NUM
ejpam-739	197	20	∫	∫	NOUN
ejpam-739	198	1	π	π	NOUN
ejpam-739	198	2	−π	−π	PROPN
ejpam-739	198	3	[	[	PUNCT
ejpam-739	198	4	f	f	X
ejpam-739	198	5	(	(	PUNCT
ejpam-739	198	6	q)(z)−	q)(z)−	X
ejpam-739	198	7	[	[	X
ejpam-739	198	8	ut	ut	PROPN
ejpam-739	198	9	(	(	PUNCT
ejpam-739	198	10	f	f	PROPN
ejpam-739	198	11	)	)	PUNCT
ejpam-739	198	12	]	]	PUNCT
ejpam-739	199	1	(	(	PUNCT
ejpam-739	199	2	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	PROPN
ejpam-739	199	3	=	=	SYM
ejpam-739	199	4	aq+p(q+	aq+p(q+	PROPN
ejpam-739	199	5	p)(q+	p)(q+	VERB
ejpam-739	199	6	p−	p−	NOUN
ejpam-739	199	7	1)	1)	NUM
ejpam-739	199	8	...	...	PUNCT
ejpam-739	199	9	(p+	(p+	PROPN
ejpam-739	199	10	1)r	1)r	NUM
ejpam-739	199	11	p[1−	p[1−	PROPN
ejpam-739	199	12	(	(	PUNCT
ejpam-739	199	13	1	1	NUM
ejpam-739	199	14	+	+	CCONJ
ejpam-739	199	15	(	(	PUNCT
ejpam-739	199	16	q+	q+	ADV
ejpam-739	199	17	p)t)e−(q+p)t	p)t)e−(q+p)t	PROPN
ejpam-739	199	18	]	]	X
ejpam-739	199	19	.	.	PUNCT
ejpam-739	200	1	multiplying	multiply	VERB
ejpam-739	200	2	above	above	ADV
ejpam-739	200	3	with	with	ADP
ejpam-739	200	4	1	1	NUM
ejpam-739	200	5	beta(α	beta(α	NOUN
ejpam-739	200	6	,	,	PUNCT
ejpam-739	200	7	β	β	NOUN
ejpam-739	200	8	)	)	PUNCT
ejpam-739	200	9	tα−1(1−	tα−1(1−	NOUN
ejpam-739	200	10	t)β−1	t)β−1	ADP
ejpam-739	200	11	an	an	DET
ejpam-739	200	12	then	then	ADV
ejpam-739	200	13	integrating	integrate	VERB
ejpam-739	200	14	with	with	ADP
ejpam-739	200	15	respect	respect	NOUN
ejpam-739	200	16	to	to	ADP
ejpam-739	200	17	t	t	PROPN
ejpam-739	200	18	,	,	PUNCT
ejpam-739	200	19	it	it	PRON
ejpam-739	200	20	follows	follow	VERB
ejpam-739	200	21	i	i	PRON
ejpam-739	200	22	:	:	PUNCT
ejpam-739	200	23	=	=	SYM
ejpam-739	200	24	1	1	NUM
ejpam-739	200	25	beta(α	beta(α	NOUN
ejpam-739	200	26	,	,	PUNCT
ejpam-739	200	27	β	β	X
ejpam-739	200	28	)	)	PUNCT
ejpam-739	200	29	·	·	PUNCT
ejpam-739	201	1	∫	∫	PROPN
ejpam-739	201	2	1	1	NUM
ejpam-739	201	3	0	0	NUM
ejpam-739	201	4	¨	¨	NOUN
ejpam-739	201	5	1	1	NUM
ejpam-739	201	6	2π	2π	NUM
ejpam-739	201	7	∫	∫	PROPN
ejpam-739	202	1	π	π	NOUN
ejpam-739	202	2	−π	−π	PROPN
ejpam-739	202	3	[	[	PUNCT
ejpam-739	202	4	f	f	X
ejpam-739	202	5	(	(	PUNCT
ejpam-739	202	6	q)(z)−	q)(z)−	X
ejpam-739	202	7	[	[	X
ejpam-739	202	8	ut	ut	PROPN
ejpam-739	202	9	(	(	PUNCT
ejpam-739	202	10	f	f	PROPN
ejpam-739	202	11	)	)	PUNCT
ejpam-739	202	12	]	]	PUNCT
ejpam-739	203	1	(	(	PUNCT
ejpam-739	203	2	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	NOUN
ejpam-739	203	3	«	«	PUNCT
ejpam-739	203	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	203	5	t)β−1d	t)β−1d	NOUN
ejpam-739	203	6	t	t	NOUN
ejpam-739	203	7	=	=	SYM
ejpam-739	203	8	aq+p(q+	aq+p(q+	PROPN
ejpam-739	203	9	p)(q+	p)(q+	VERB
ejpam-739	203	10	p−	p−	NOUN
ejpam-739	203	11	1)	1)	NUM
ejpam-739	203	12	...	...	PUNCT
ejpam-739	203	13	(p+	(p+	X
ejpam-739	204	1	1)r	1)r	PROPN
ejpam-739	204	2	p	p	X
ejpam-739	204	3	·	·	PUNCT
ejpam-739	204	4	1	1	NUM
ejpam-739	204	5	beta(α	beta(α	NOUN
ejpam-739	204	6	,	,	PUNCT
ejpam-739	204	7	β	β	X
ejpam-739	204	8	)	)	PUNCT
ejpam-739	204	9	∫	∫	PROPN
ejpam-739	205	1	1	1	NUM
ejpam-739	205	2	0	0	NUM
ejpam-739	205	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	205	4	t)β−1	t)β−1	ADP
ejpam-739	205	5	�	�	PROPN
ejpam-739	205	6	1−	1−	NUM
ejpam-739	205	7	(	(	PUNCT
ejpam-739	205	8	1	1	NUM
ejpam-739	205	9	+	+	CCONJ
ejpam-739	205	10	(	(	PUNCT
ejpam-739	205	11	q+	q+	ADV
ejpam-739	205	12	p)t)e−(q+p)t	p)t)e−(q+p)t	PROPN
ejpam-739	205	13	�	�	PROPN
ejpam-739	205	14	d	d	ADP
ejpam-739	205	15	t.	t.	NOUN
ejpam-739	205	16	applying	apply	VERB
ejpam-739	205	17	the	the	DET
ejpam-739	205	18	fubini	fubini	NOUN
ejpam-739	205	19	’s	’s	PART
ejpam-739	205	20	result	result	NOUN
ejpam-739	205	21	to	to	ADP
ejpam-739	205	22	the	the	DET
ejpam-739	205	23	double	double	ADJ
ejpam-739	205	24	integral	integral	ADJ
ejpam-739	205	25	i	i	PRON
ejpam-739	205	26	and	and	CCONJ
ejpam-739	205	27	then	then	ADV
ejpam-739	205	28	passing	pass	VERB
ejpam-739	205	29	to	to	ADP
ejpam-739	205	30	modulus	modulus	NOUN
ejpam-739	205	31	,	,	PUNCT
ejpam-739	205	32	we	we	PRON
ejpam-739	205	33	easily	easily	ADV
ejpam-739	205	34	obtain	obtain	VERB
ejpam-739	205	35	�	�	PROPN
ejpam-739	205	36	�	�	PROPN
ejpam-739	205	37	�	�	PROPN
ejpam-739	205	38	�	�	PROPN
ejpam-739	205	39	�	�	PROPN
ejpam-739	205	40	1	1	NUM
ejpam-739	205	41	2π	2π	PROPN
ejpam-739	205	42	∫	∫	PROPN
ejpam-739	206	1	π	π	PROPN
ejpam-739	206	2	−π	−π	PROPN
ejpam-739	206	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	206	4			PROPN
ejpam-739	206	5			NOUN
ejpam-739	206	6	1	1	NUM
ejpam-739	206	7	beta(α	beta(α	NOUN
ejpam-739	206	8	,	,	PUNCT
ejpam-739	206	9	β	β	X
ejpam-739	206	10	)	)	PUNCT
ejpam-739	206	11	∫	∫	PROPN
ejpam-739	207	1	1	1	NUM
ejpam-739	207	2	0	0	NUM
ejpam-739	208	1	[	[	PUNCT
ejpam-739	208	2	f	f	X
ejpam-739	208	3	(	(	PUNCT
ejpam-739	208	4	q)(z)−	q)(z)−	X
ejpam-739	208	5	[	[	X
ejpam-739	208	6	ut	ut	PROPN
ejpam-739	208	7	(	(	PUNCT
ejpam-739	208	8	f	f	PROPN
ejpam-739	208	9	)	)	PUNCT
ejpam-739	208	10	]	]	PUNCT
ejpam-739	208	11	(	(	PUNCT
ejpam-739	208	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	208	13	t)β−1d	t)β−1d	PROPN
ejpam-739	208	14	t	t	PROPN
ejpam-739	208	15			PROPN
ejpam-739	208	16			PROPN
ejpam-739	208	17	dϕ	dϕ	PRON
ejpam-739	208	18	�	�	PROPN
ejpam-739	208	19	�	�	PROPN
ejpam-739	208	20	�	�	PROPN
ejpam-739	208	21	�	�	PROPN
ejpam-739	208	22	�	�	PROPN
ejpam-739	208	23	=	=	SYM
ejpam-739	208	24	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	208	25	p)(q+	p)(q+	NOUN
ejpam-739	208	26	p−	p−	NOUN
ejpam-739	208	27	1)	1)	NUM
ejpam-739	208	28	...	...	PUNCT
ejpam-739	208	29	(p+	(p+	X
ejpam-739	209	1	1)r	1)r	PROPN
ejpam-739	209	2	p	p	X
ejpam-739	209	3	·	·	PUNCT
ejpam-739	209	4			PROPN
ejpam-739	209	5			NOUN
ejpam-739	209	6	1	1	NUM
ejpam-739	209	7	beta(α	beta(α	NOUN
ejpam-739	209	8	,	,	PUNCT
ejpam-739	209	9	β	β	X
ejpam-739	209	10	)	)	PUNCT
ejpam-739	209	11	∫	∫	PROPN
ejpam-739	210	1	1	1	NUM
ejpam-739	210	2	0	0	NUM
ejpam-739	210	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	210	4	t)β−1	t)β−1	ADP
ejpam-739	210	5	�	�	PROPN
ejpam-739	210	6	1−	1−	NUM
ejpam-739	210	7	(	(	PUNCT
ejpam-739	210	8	1	1	NUM
ejpam-739	210	9	+	+	CCONJ
ejpam-739	210	10	(	(	PUNCT
ejpam-739	210	11	q+	q+	ADV
ejpam-739	210	12	p)t)e−(q+p)t	p)t)e−(q+p)t	PROPN
ejpam-739	210	13	�	�	PROPN
ejpam-739	210	14	d	d	PROPN
ejpam-739	210	15	t	t	PROPN
ejpam-739	210	16			PROPN
ejpam-739	210	17			PROPN
ejpam-739	210	18	.	.	PUNCT
ejpam-739	211	1	since	since	SCONJ
ejpam-739	211	2	1	1	NUM
ejpam-739	211	3	beta(α	beta(α	NOUN
ejpam-739	211	4	,	,	PUNCT
ejpam-739	211	5	β	β	X
ejpam-739	211	6	)	)	PUNCT
ejpam-739	211	7	∫	∫	PROPN
ejpam-739	211	8	1	1	NUM
ejpam-739	211	9	0	0	NUM
ejpam-739	212	1	[	[	PUNCT
ejpam-739	212	2	f	f	X
ejpam-739	212	3	(	(	PUNCT
ejpam-739	212	4	q)(z)−	q)(z)−	X
ejpam-739	212	5	[	[	X
ejpam-739	212	6	ut	ut	PROPN
ejpam-739	212	7	(	(	PUNCT
ejpam-739	212	8	f	f	PROPN
ejpam-739	212	9	)	)	PUNCT
ejpam-739	212	10	]	]	PUNCT
ejpam-739	212	11	(	(	PUNCT
ejpam-739	212	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	212	13	t)β−1d	t)β−1d	PROPN
ejpam-739	212	14	t	t	NOUN
ejpam-739	212	15	=	=	SYM
ejpam-739	212	16	f	f	PROPN
ejpam-739	212	17	(	(	PUNCT
ejpam-739	212	18	q)(z)−	q)(z)−	X
ejpam-739	212	19	[	[	X
ejpam-739	212	20	gα	gα	NOUN
ejpam-739	212	21	,	,	PUNCT
ejpam-739	212	22	β	β	X
ejpam-739	212	23	u	u	NOUN
ejpam-739	212	24	(	(	PUNCT
ejpam-739	212	25	f	f	PROPN
ejpam-739	212	26	)	)	PUNCT
ejpam-739	212	27	]	]	X
ejpam-739	212	28	(	(	PUNCT
ejpam-739	212	29	q)(z	q)(z	NOUN
ejpam-739	212	30	)	)	PUNCT
ejpam-739	212	31	,	,	PUNCT
ejpam-739	212	32	the	the	DET
ejpam-739	212	33	previous	previous	ADJ
ejpam-739	212	34	equality	equality	NOUN
ejpam-739	212	35	immediately	immediately	ADV
ejpam-739	212	36	implies	imply	VERB
ejpam-739	212	37	�	�	PROPN
ejpam-739	212	38	�	�	PROPN
ejpam-739	212	39	�	�	PROPN
ejpam-739	212	40	�	�	PROPN
ejpam-739	212	41	�	�	PROPN
ejpam-739	212	42	1	1	NUM
ejpam-739	212	43	2π	2π	PROPN
ejpam-739	212	44	∫	∫	PROPN
ejpam-739	213	1	π	π	NOUN
ejpam-739	213	2	−π	−π	PROPN
ejpam-739	213	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	214	1	h	h	PROPN
ejpam-739	214	2	f	f	PROPN
ejpam-739	214	3	(	(	PUNCT
ejpam-739	214	4	q)(z)−	q)(z)−	X
ejpam-739	214	5	(	(	PUNCT
ejpam-739	214	6	gα	gα	NOUN
ejpam-739	214	7	,	,	PUNCT
ejpam-739	214	8	β	β	X
ejpam-739	214	9	u	u	NOUN
ejpam-739	214	10	(	(	PUNCT
ejpam-739	214	11	f	f	PROPN
ejpam-739	214	12	)	)	PUNCT
ejpam-739	214	13	)	)	PUNCT
ejpam-739	214	14	(	(	PUNCT
ejpam-739	214	15	q)(z	q)(z	NOUN
ejpam-739	214	16	)	)	PUNCT
ejpam-739	214	17	i	i	PRON
ejpam-739	214	18	dϕ	dϕ	VERB
ejpam-739	215	1	�	�	PROPN
ejpam-739	215	2	�	�	PROPN
ejpam-739	215	3	�	�	PROPN
ejpam-739	215	4	�	�	PROPN
ejpam-739	215	5	�	�	PROPN
ejpam-739	215	6	=	=	SYM
ejpam-739	215	7	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	215	8	p)(q+	p)(q+	NOUN
ejpam-739	215	9	p−	p−	NOUN
ejpam-739	215	10	1)	1)	NUM
ejpam-739	215	11	...	...	PUNCT
ejpam-739	215	12	(p+	(p+	X
ejpam-739	215	13	1)r	1)r	PROPN
ejpam-739	215	14	p	p	X
ejpam-739	215	15	s.	s.	PROPN
ejpam-739	215	16	gal	gal	PROPN
ejpam-739	215	17	/	/	SYM
ejpam-739	215	18	eur	eur	PROPN
ejpam-739	215	19	.	.	PUNCT
ejpam-739	216	1	j.	j.	PROPN
ejpam-739	216	2	pure	pure	PROPN
ejpam-739	216	3	appl	appl	PROPN
ejpam-739	216	4	.	.	PROPN
ejpam-739	216	5	math	math	PROPN
ejpam-739	216	6	,	,	PUNCT
ejpam-739	216	7	3	3	NUM
ejpam-739	216	8	(	(	PUNCT
ejpam-739	216	9	2010	2010	NUM
ejpam-739	216	10	)	)	PUNCT
ejpam-739	216	11	,	,	PUNCT
ejpam-739	216	12	1150	1150	NUM
ejpam-739	216	13	-	-	SYM
ejpam-739	216	14	1164	1164	NUM
ejpam-739	216	15	1161	1161	NUM
ejpam-739	216	16	·	·	PUNCT
ejpam-739	216	17			NOUN
ejpam-739	216	18			NOUN
ejpam-739	216	19	1	1	NUM
ejpam-739	216	20	beta(α	beta(α	NOUN
ejpam-739	216	21	,	,	PUNCT
ejpam-739	216	22	β	β	X
ejpam-739	216	23	)	)	PUNCT
ejpam-739	216	24	∫	∫	PROPN
ejpam-739	217	1	1	1	NUM
ejpam-739	217	2	0	0	NUM
ejpam-739	217	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	217	4	t)β−1	t)β−1	ADP
ejpam-739	217	5	�	�	PROPN
ejpam-739	217	6	1−	1−	NUM
ejpam-739	217	7	(	(	PUNCT
ejpam-739	217	8	1	1	NUM
ejpam-739	217	9	+	+	CCONJ
ejpam-739	217	10	(	(	PUNCT
ejpam-739	217	11	q+	q+	ADV
ejpam-739	217	12	p)t)e−(q+p)t	p)t)e−(q+p)t	PROPN
ejpam-739	217	13	�	�	PROPN
ejpam-739	217	14	d	d	PROPN
ejpam-739	217	15	t	t	PROPN
ejpam-739	217	16			PROPN
ejpam-739	217	17			PROPN
ejpam-739	217	18	and	and	CCONJ
ejpam-739	217	19	|aq+p|(q+	|aq+p|(q+	NOUN
ejpam-739	217	20	p)(q+	p)(q+	NOUN
ejpam-739	217	21	p−	p−	NOUN
ejpam-739	217	22	1)	1)	NUM
ejpam-739	217	23	...	...	PUNCT
ejpam-739	217	24	(p+	(p+	X
ejpam-739	217	25	1)r	1)r	PROPN
ejpam-739	217	26	p	p	X
ejpam-739	217	27	·	·	PUNCT
ejpam-739	217	28			PROPN
ejpam-739	217	29			NOUN
ejpam-739	217	30	1	1	NUM
ejpam-739	217	31	beta(α	beta(α	NOUN
ejpam-739	217	32	,	,	PUNCT
ejpam-739	217	33	β	β	X
ejpam-739	217	34	)	)	PUNCT
ejpam-739	217	35	∫	∫	PROPN
ejpam-739	218	1	1	1	NUM
ejpam-739	218	2	0	0	NUM
ejpam-739	218	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	218	4	t)β−1	t)β−1	ADP
ejpam-739	218	5	�	�	PROPN
ejpam-739	218	6	1−	1−	NUM
ejpam-739	218	7	(	(	PUNCT
ejpam-739	218	8	1	1	NUM
ejpam-739	218	9	+	+	CCONJ
ejpam-739	218	10	(	(	PUNCT
ejpam-739	218	11	q+	q+	ADV
ejpam-739	218	12	p)t)e−(q+p)t	p)t)e−(q+p)t	PROPN
ejpam-739	218	13	�	�	PROPN
ejpam-739	218	14	d	d	PROPN
ejpam-739	218	15	t	t	PROPN
ejpam-739	218	16			PROPN
ejpam-739	218	17			PROPN
ejpam-739	218	18	≤	≤	NUM
ejpam-739	218	19	‖	‖	PROPN
ejpam-739	218	20	f	f	PROPN
ejpam-739	218	21	(	(	PUNCT
ejpam-739	218	22	q)−	q)−	PROPN
ejpam-739	218	23	(	(	PUNCT
ejpam-739	218	24	gα	gα	PROPN
ejpam-739	218	25	,	,	PUNCT
ejpam-739	218	26	β	β	X
ejpam-739	218	27	u	u	NOUN
ejpam-739	218	28	(	(	PUNCT
ejpam-739	218	29	f	f	PROPN
ejpam-739	218	30	)	)	PUNCT
ejpam-739	218	31	)	)	PUNCT
ejpam-739	218	32	(	(	PUNCT
ejpam-739	218	33	q)‖r	q)‖r	INTJ
ejpam-739	218	34	.	.	PUNCT
ejpam-739	219	1	first	first	ADV
ejpam-739	219	2	take	take	VERB
ejpam-739	219	3	q	q	NOUN
ejpam-739	219	4	=	=	PUNCT
ejpam-739	219	5	0	0	NUM
ejpam-739	219	6	.	.	PUNCT
ejpam-739	220	1	from	from	ADP
ejpam-739	220	2	the	the	DET
ejpam-739	220	3	previous	previous	ADJ
ejpam-739	220	4	inequality	inequality	NOUN
ejpam-739	220	5	we	we	PRON
ejpam-739	220	6	immediately	immediately	ADV
ejpam-739	220	7	obtain	obtain	VERB
ejpam-739	220	8	|ap|r	|ap|r	ADP
ejpam-739	220	9	p	p	NOUN
ejpam-739	220	10	1	1	NUM
ejpam-739	220	11	beta(α	beta(α	NOUN
ejpam-739	220	12	,	,	PUNCT
ejpam-739	220	13	β	β	X
ejpam-739	220	14	)	)	PUNCT
ejpam-739	220	15	∫	∫	PROPN
ejpam-739	221	1	1	1	NUM
ejpam-739	221	2	0	0	NUM
ejpam-739	221	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	221	4	t)β−1	t)β−1	ADP
ejpam-739	221	5	�	�	PROPN
ejpam-739	221	6	1−	1−	NUM
ejpam-739	221	7	(	(	PUNCT
ejpam-739	221	8	1	1	NUM
ejpam-739	221	9	+	+	NUM
ejpam-739	221	10	pt)e−pt	pt)e−pt	NOUN
ejpam-739	221	11	�	�	PROPN
ejpam-739	221	12	d	d	NOUN
ejpam-739	221	13	t	t	PROPN
ejpam-739	221	14	!	!	PUNCT
ejpam-739	222	1	≤	≤	NUM
ejpam-739	223	1	‖	‖	PROPN
ejpam-739	223	2	f	f	X
ejpam-739	223	3	−	−	PROPN
ejpam-739	223	4	g	g	PROPN
ejpam-739	223	5	α	α	PROPN
ejpam-739	223	6	,	,	PUNCT
ejpam-739	223	7	β	β	X
ejpam-739	223	8	u	u	NOUN
ejpam-739	223	9	(	(	PUNCT
ejpam-739	223	10	f	f	PROPN
ejpam-739	223	11	)	)	PUNCT
ejpam-739	223	12	‖r	‖r	NOUN
ejpam-739	223	13	.	.	PUNCT
ejpam-739	224	1	in	in	ADP
ejpam-739	224	2	what	what	PRON
ejpam-739	224	3	follows	follow	VERB
ejpam-739	224	4	,	,	PUNCT
ejpam-739	224	5	denoting	denote	VERB
ejpam-739	224	6	vα	vα	ADP
ejpam-739	224	7	,	,	PUNCT
ejpam-739	224	8	β	β	X
ejpam-739	224	9	=	=	SYM
ejpam-739	224	10	inf	inf	NOUN
ejpam-739	224	11	p≥1	p≥1	NOUN
ejpam-739	224	12	1	1	NUM
ejpam-739	224	13	beta(α	beta(α	NOUN
ejpam-739	224	14	,	,	PUNCT
ejpam-739	224	15	β	β	X
ejpam-739	224	16	)	)	PUNCT
ejpam-739	224	17	∫	∫	PROPN
ejpam-739	225	1	1	1	NUM
ejpam-739	225	2	0	0	NUM
ejpam-739	225	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	225	4	t)β−1	t)β−1	ADP
ejpam-739	225	5	�	�	PROPN
ejpam-739	225	6	1−	1−	NUM
ejpam-739	225	7	(	(	PUNCT
ejpam-739	225	8	1	1	NUM
ejpam-739	225	9	+	+	NUM
ejpam-739	225	10	pt)e−pt	pt)e−pt	NOUN
ejpam-739	225	11	�	�	PROPN
ejpam-739	225	12	d	d	NOUN
ejpam-739	225	13	t	t	PROPN
ejpam-739	225	14	!	!	PUNCT
ejpam-739	226	1	,	,	PUNCT
ejpam-739	226	2	we	we	PRON
ejpam-739	226	3	immediately	immediately	ADV
ejpam-739	226	4	get	get	VERB
ejpam-739	226	5	vα	vα	ADP
ejpam-739	226	6	,	,	PUNCT
ejpam-739	226	7	β	β	X
ejpam-739	226	8	=	=	SYM
ejpam-739	226	9	1	1	NUM
ejpam-739	226	10	beta(α	beta(α	NOUN
ejpam-739	226	11	,	,	PUNCT
ejpam-739	226	12	β	β	X
ejpam-739	226	13	)	)	PUNCT
ejpam-739	226	14	∫	∫	PROPN
ejpam-739	227	1	1	1	NUM
ejpam-739	227	2	0	0	NUM
ejpam-739	227	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	227	4	t)β−1	t)β−1	ADP
ejpam-739	227	5	�	�	PROPN
ejpam-739	227	6	1−	1−	NUM
ejpam-739	227	7	(	(	PUNCT
ejpam-739	227	8	1	1	NUM
ejpam-739	227	9	+	+	NUM
ejpam-739	227	10	t)e−t	t)e−t	NOUN
ejpam-739	227	11	�	�	PROPN
ejpam-739	227	12	d	d	NOUN
ejpam-739	227	13	t.	t.	NOUN
ejpam-739	228	1	but	but	CCONJ
ejpam-739	228	2	we	we	PRON
ejpam-739	228	3	have	have	VERB
ejpam-739	228	4	1−	1−	NUM
ejpam-739	228	5	(	(	PUNCT
ejpam-739	228	6	1	1	NUM
ejpam-739	228	7	+	+	NUM
ejpam-739	228	8	t)e−t	t)e−t	NOUN
ejpam-739	228	9	≥	≥	NOUN
ejpam-739	228	10	t2	t2	PROPN
ejpam-739	228	11	e	e	NOUN
ejpam-739	228	12	,	,	PUNCT
ejpam-739	228	13	for	for	ADP
ejpam-739	228	14	all	all	DET
ejpam-739	228	15	t	t	NOUN
ejpam-739	228	16	∈	∈	PROPN
ejpam-739	229	1	[	[	X
ejpam-739	229	2	0,1	0,1	NUM
ejpam-739	229	3	]	]	PUNCT
ejpam-739	229	4	.	.	PUNCT
ejpam-739	230	1	indeed	indeed	ADV
ejpam-739	230	2	,	,	PUNCT
ejpam-739	230	3	denoting	denote	VERB
ejpam-739	230	4	g(t	g(t	PROPN
ejpam-739	230	5	)	)	PUNCT
ejpam-739	231	1	=	=	SYM
ejpam-739	231	2	1−	1−	NUM
ejpam-739	231	3	(	(	PUNCT
ejpam-739	231	4	1	1	NUM
ejpam-739	231	5	+	+	NUM
ejpam-739	231	6	t)e−t	t)e−t	NOUN
ejpam-739	231	7	−	−	PROPN
ejpam-739	231	8	t2	t2	PROPN
ejpam-739	231	9	e	e	NOUN
ejpam-739	231	10	,	,	PUNCT
ejpam-739	231	11	we	we	PRON
ejpam-739	231	12	have	have	VERB
ejpam-739	231	13	g(0	g(0	NOUN
ejpam-739	231	14	)	)	PUNCT
ejpam-739	231	15	=	=	SYM
ejpam-739	231	16	0	0	NUM
ejpam-739	231	17	and	and	CCONJ
ejpam-739	231	18	g′(t	g′(t	PROPN
ejpam-739	231	19	)	)	PUNCT
ejpam-739	231	20	=	=	SYM
ejpam-739	231	21	te−t	te−t	NOUN
ejpam-739	231	22	−	−	NOUN
ejpam-739	231	23	t	t	NOUN
ejpam-739	231	24	e	e	PROPN
ejpam-739	231	25	=	=	PROPN
ejpam-739	231	26	t	t	PROPN
ejpam-739	231	27	�	�	PROPN
ejpam-739	231	28	1	1	NUM
ejpam-739	232	1	e	e	NOUN
ejpam-739	232	2	t	t	NOUN
ejpam-739	232	3	−	−	PROPN
ejpam-739	232	4	1	1	NUM
ejpam-739	232	5	e	e	PROPN
ejpam-739	232	6	�	�	PROPN
ejpam-739	232	7	≥	≥	X
ejpam-739	232	8	0	0	NUM
ejpam-739	232	9	for	for	ADP
ejpam-739	232	10	all	all	DET
ejpam-739	232	11	t	t	NOUN
ejpam-739	232	12	∈	∈	PROPN
ejpam-739	233	1	[	[	X
ejpam-739	233	2	0,1	0,1	NUM
ejpam-739	233	3	]	]	PUNCT
ejpam-739	233	4	.	.	PUNCT
ejpam-739	234	1	this	this	PRON
ejpam-739	234	2	implies	imply	VERB
ejpam-739	234	3	that	that	SCONJ
ejpam-739	234	4	g(t	g(t	PROPN
ejpam-739	234	5	)	)	PUNCT
ejpam-739	234	6	is	be	AUX
ejpam-739	234	7	nondecreasing	nondecrease	VERB
ejpam-739	234	8	on	on	ADP
ejpam-739	234	9	[	[	X
ejpam-739	234	10	0,1	0,1	NUM
ejpam-739	234	11	]	]	PUNCT
ejpam-739	234	12	and	and	CCONJ
ejpam-739	234	13	therefore	therefore	ADV
ejpam-739	234	14	g(t	g(t	PROPN
ejpam-739	234	15	)	)	PUNCT
ejpam-739	234	16	≥	≥	NOUN
ejpam-739	234	17	0	0	NUM
ejpam-739	234	18	for	for	ADP
ejpam-739	234	19	all	all	DET
ejpam-739	234	20	t	t	NOUN
ejpam-739	234	21	∈	∈	PROPN
ejpam-739	235	1	[	[	X
ejpam-739	235	2	0,1	0,1	NUM
ejpam-739	235	3	]	]	PUNCT
ejpam-739	235	4	.	.	PUNCT
ejpam-739	236	1	therefore	therefore	ADV
ejpam-739	236	2	,	,	PUNCT
ejpam-739	236	3	vα	vα	INTJ
ejpam-739	236	4	,	,	PUNCT
ejpam-739	236	5	β	β	X
ejpam-739	236	6	≥	≥	NUM
ejpam-739	236	7	1	1	NUM
ejpam-739	236	8	beta(α	beta(α	NOUN
ejpam-739	236	9	,	,	PUNCT
ejpam-739	236	10	β	β	X
ejpam-739	236	11	)	)	PUNCT
ejpam-739	236	12	∫	∫	PROPN
ejpam-739	236	13	1	1	NUM
ejpam-739	236	14	0	0	NUM
ejpam-739	236	15	tα−1(1−	tα−1(1−	PROPN
ejpam-739	237	1	t)β−1	t)β−1	NOUN
ejpam-739	237	2	t2	t2	NOUN
ejpam-739	237	3	2e	2e	PROPN
ejpam-739	237	4	d	d	X
ejpam-739	237	5	t	t	NOUN
ejpam-739	237	6	=	=	PUNCT
ejpam-739	237	7	beta(α+	beta(α+	X
ejpam-739	237	8	2,β	2,β	NUM
ejpam-739	237	9	)	)	PUNCT
ejpam-739	237	10	2e	2e	PROPN
ejpam-739	237	11	·	·	PUNCT
ejpam-739	237	12	b(α	b(α	PROPN
ejpam-739	237	13	,	,	PUNCT
ejpam-739	237	14	β	β	X
ejpam-739	237	15	)	)	PUNCT
ejpam-739	237	16	=	=	SYM
ejpam-739	237	17	1	1	NUM
ejpam-739	237	18	2e	2e	NOUN
ejpam-739	237	19	·	·	PUNCT
ejpam-739	237	20	α+	α+	PUNCT
ejpam-739	237	21	1	1	NUM
ejpam-739	237	22	α+	α+	X
ejpam-739	237	23	β	β	NOUN
ejpam-739	237	24	+	+	CCONJ
ejpam-739	237	25	1	1	NUM
ejpam-739	237	26	·	·	PUNCT
ejpam-739	237	27	α	α	NOUN
ejpam-739	237	28	α+	α+	X
ejpam-739	237	29	β	β	X
ejpam-739	237	30	≥	≥	NUM
ejpam-739	237	31	1	1	NUM
ejpam-739	237	32	2e	2e	NOUN
ejpam-739	237	33	·	·	PUNCT
ejpam-739	237	34	α(α+	α(α+	NUM
ejpam-739	237	35	1	1	NUM
ejpam-739	237	36	)	)	PUNCT
ejpam-739	237	37	2	2	NUM
ejpam-739	237	38	≥	≥	NOUN
ejpam-739	237	39	α	α	NOUN
ejpam-739	237	40	4e	4e	PROPN
ejpam-739	237	41	.	.	PUNCT
ejpam-739	238	1	now	now	ADV
ejpam-739	238	2	,	,	PUNCT
ejpam-739	238	3	by	by	ADP
ejpam-739	238	4	following	follow	VERB
ejpam-739	238	5	for	for	ADP
ejpam-739	238	6	q	q	PROPN
ejpam-739	238	7	≥	≥	NOUN
ejpam-739	238	8	0	0	NUM
ejpam-739	238	9	similar	similar	ADJ
ejpam-739	238	10	reasonings	reasoning	NOUN
ejpam-739	238	11	with	with	ADP
ejpam-739	238	12	those	those	PRON
ejpam-739	238	13	in	in	ADP
ejpam-739	238	14	the	the	DET
ejpam-739	238	15	above	above	ADJ
ejpam-739	238	16	point	point	NOUN
ejpam-739	238	17	(	(	PUNCT
ejpam-739	238	18	i	i	NOUN
ejpam-739	238	19	)	)	PUNCT
ejpam-739	238	20	,	,	PUNCT
ejpam-739	238	21	we	we	PRON
ejpam-739	238	22	get	get	VERB
ejpam-739	238	23	the	the	DET
ejpam-739	238	24	desired	desire	VERB
ejpam-739	238	25	equivalence	equivalence	NOUN
ejpam-739	238	26	in	in	ADP
ejpam-739	238	27	the	the	DET
ejpam-739	238	28	statement	statement	NOUN
ejpam-739	238	29	.	.	PUNCT
ejpam-739	239	1	s.	s.	PROPN
ejpam-739	239	2	gal	gal	PROPN
ejpam-739	239	3	/	/	SYM
ejpam-739	239	4	eur	eur	PROPN
ejpam-739	239	5	.	.	PUNCT
ejpam-739	240	1	j.	j.	PROPN
ejpam-739	240	2	pure	pure	PROPN
ejpam-739	240	3	appl	appl	PROPN
ejpam-739	240	4	.	.	PROPN
ejpam-739	240	5	math	math	PROPN
ejpam-739	240	6	,	,	PUNCT
ejpam-739	240	7	3	3	NUM
ejpam-739	240	8	(	(	PUNCT
ejpam-739	240	9	2010	2010	NUM
ejpam-739	240	10	)	)	PUNCT
ejpam-739	240	11	,	,	PUNCT
ejpam-739	240	12	1150	1150	NUM
ejpam-739	240	13	-	-	SYM
ejpam-739	240	14	1164	1164	NUM
ejpam-739	240	15	1162	1162	NUM
ejpam-739	240	16	(	(	PUNCT
ejpam-739	240	17	iv	iv	X
ejpam-739	240	18	)	)	PUNCT
ejpam-739	240	19	by	by	ADP
ejpam-739	240	20	gal	gal	PROPN
ejpam-739	241	1	[	[	X
ejpam-739	241	2	2	2	NUM
ejpam-739	241	3	,	,	PUNCT
ejpam-739	241	4	p.	p.	NOUN
ejpam-739	241	5	223	223	NUM
ejpam-739	241	6	,	,	PUNCT
ejpam-739	241	7	theorem	theorem	VERB
ejpam-739	241	8	3.2.8	3.2.8	NUM
ejpam-739	241	9	,	,	PUNCT
ejpam-739	241	10	(	(	PUNCT
ejpam-739	241	11	i	i	NOUN
ejpam-739	241	12	)	)	PUNCT
ejpam-739	241	13	]	]	PUNCT
ejpam-739	241	14	,	,	PUNCT
ejpam-739	241	15	ut	ut	PROPN
ejpam-739	241	16	(	(	PUNCT
ejpam-739	241	17	f	f	PROPN
ejpam-739	241	18	)	)	PUNCT
ejpam-739	241	19	(	(	PUNCT
ejpam-739	241	20	z	z	NOUN
ejpam-739	241	21	)	)	PUNCT
ejpam-739	241	22	is	be	AUX
ejpam-739	241	23	analytic	analytic	ADJ
ejpam-739	241	24	(	(	PUNCT
ejpam-739	241	25	as	as	ADP
ejpam-739	241	26	function	function	NOUN
ejpam-739	241	27	of	of	ADP
ejpam-739	241	28	z	z	NOUN
ejpam-739	241	29	)	)	PUNCT
ejpam-739	241	30	in	in	ADP
ejpam-739	241	31	dr	dr	PROPN
ejpam-739	242	1	and	and	CCONJ
ejpam-739	242	2	we	we	PRON
ejpam-739	242	3	can	can	AUX
ejpam-739	242	4	write	write	VERB
ejpam-739	242	5	ut	ut	PROPN
ejpam-739	242	6	(	(	PUNCT
ejpam-739	242	7	f	f	PROPN
ejpam-739	242	8	)	)	PUNCT
ejpam-739	242	9	(	(	PUNCT
ejpam-739	242	10	z	z	NOUN
ejpam-739	242	11	)	)	PUNCT
ejpam-739	242	12	=	=	SYM
ejpam-739	243	1	∞	∞	NUM
ejpam-739	243	2	∑	∑	PUNCT
ejpam-739	243	3	k=0	k=0	PROPN
ejpam-739	243	4	ake−k2	ake−k2	PART
ejpam-739	244	1	t/4zk	t/4zk	NOUN
ejpam-739	244	2	,	,	PUNCT
ejpam-739	244	3	for	for	ADP
ejpam-739	244	4	all	all	DET
ejpam-739	244	5	|z|	|z|	NOUN
ejpam-739	244	6	<	<	X
ejpam-739	244	7	r	r	NOUN
ejpam-739	244	8	and	and	CCONJ
ejpam-739	244	9	t	t	PROPN
ejpam-739	244	10	≥	≥	NUM
ejpam-739	244	11	0	0	NUM
ejpam-739	244	12	.	.	PUNCT
ejpam-739	245	1	since	since	SCONJ
ejpam-739	245	2	|∑∞k=0	|∑∞k=0	NOUN
ejpam-739	245	3	ake−k2	ake−k2	X
ejpam-739	245	4	t/4zk|	t/4zk|	PROPN
ejpam-739	245	5	≤	≤	NUM
ejpam-739	245	6	∑∞k=0	∑∞k=0	X
ejpam-739	245	7	|ak|	|ak|	X
ejpam-739	245	8	·	·	PUNCT
ejpam-739	246	1	|z|k	|z|k	NOUN
ejpam-739	246	2	<	<	X
ejpam-739	246	3	∞	∞	PROPN
ejpam-739	246	4	,	,	PUNCT
ejpam-739	246	5	this	this	PRON
ejpam-739	246	6	implies	imply	VERB
ejpam-739	246	7	that	that	SCONJ
ejpam-739	246	8	for	for	ADP
ejpam-739	246	9	fixed	fix	VERB
ejpam-739	246	10	|z|	|z|	NOUN
ejpam-739	246	11	<	<	X
ejpam-739	246	12	r	r	NOUN
ejpam-739	246	13	,	,	PUNCT
ejpam-739	246	14	the	the	DET
ejpam-739	246	15	series	series	NOUN
ejpam-739	246	16	in	in	ADP
ejpam-739	246	17	t	t	PROPN
ejpam-739	246	18	,	,	PUNCT
ejpam-739	246	19	∑∞	∑∞	PUNCT
ejpam-739	246	20	k=0	k=0	PROPN
ejpam-739	246	21	ake−k2	ake−k2	PUNCT
ejpam-739	247	1	t/4zk	t/4zk	PRON
ejpam-739	247	2	is	be	AUX
ejpam-739	247	3	uniformly	uniformly	ADV
ejpam-739	247	4	convergent	convergent	NOUN
ejpam-739	247	5	on	on	ADP
ejpam-739	247	6	[	[	X
ejpam-739	247	7	0,∞	0,∞	NOUN
ejpam-739	247	8	)	)	PUNCT
ejpam-739	247	9	,	,	PUNCT
ejpam-739	247	10	and	and	CCONJ
ejpam-739	247	11	therefore	therefore	ADV
ejpam-739	247	12	we	we	PRON
ejpam-739	247	13	immediately	immediately	ADV
ejpam-739	247	14	can	can	AUX
ejpam-739	247	15	write	write	VERB
ejpam-739	247	16	g	g	PROPN
ejpam-739	247	17	α	α	PROPN
ejpam-739	247	18	,	,	PUNCT
ejpam-739	247	19	β	β	X
ejpam-739	247	20	u	u	NOUN
ejpam-739	247	21	(	(	PUNCT
ejpam-739	247	22	f	f	PROPN
ejpam-739	247	23	)	)	PUNCT
ejpam-739	247	24	(	(	PUNCT
ejpam-739	247	25	z	z	NOUN
ejpam-739	247	26	)	)	PUNCT
ejpam-739	247	27	=	=	SYM
ejpam-739	248	1	∞	∞	NUM
ejpam-739	248	2	∑	∑	PUNCT
ejpam-739	248	3	k=0	k=0	PROPN
ejpam-739	248	4	akzk	akzk	NOUN
ejpam-739	248	5	1	1	NUM
ejpam-739	248	6	beta(α	beta(α	NOUN
ejpam-739	248	7	,	,	PUNCT
ejpam-739	248	8	β	β	X
ejpam-739	248	9	)	)	PUNCT
ejpam-739	248	10	∫	∫	PROPN
ejpam-739	248	11	1	1	NUM
ejpam-739	248	12	0	0	NUM
ejpam-739	248	13	tα−1(1−	tα−1(1−	NOUN
ejpam-739	248	14	t)β−1e−(k	t)β−1e−(k	PROPN
ejpam-739	248	15	2/4)t	2/4)t	NUM
ejpam-739	248	16	d	d	PROPN
ejpam-739	248	17	t	t	PROPN
ejpam-739	248	18	,	,	PUNCT
ejpam-739	248	19	where	where	SCONJ
ejpam-739	248	20	denoting	denote	VERB
ejpam-739	248	21	bk(α	bk(α	PROPN
ejpam-739	248	22	,	,	PUNCT
ejpam-739	248	23	β	β	X
ejpam-739	248	24	)	)	PUNCT
ejpam-739	248	25	=	=	SYM
ejpam-739	248	26	1	1	NUM
ejpam-739	248	27	beta(α	beta(α	NOUN
ejpam-739	248	28	,	,	PUNCT
ejpam-739	248	29	β	β	X
ejpam-739	248	30	)	)	PUNCT
ejpam-739	248	31	∫	∫	PROPN
ejpam-739	248	32	1	1	NUM
ejpam-739	248	33	0	0	NUM
ejpam-739	248	34	tα−1(1−	tα−1(1−	NOUN
ejpam-739	248	35	t)β−1e−(k	t)β−1e−(k	PROPN
ejpam-739	249	1	2/4)t	2/4)t	NUM
ejpam-739	249	2	d	d	NOUN
ejpam-739	249	3	t	t	X
ejpam-739	249	4	we	we	PRON
ejpam-739	249	5	can	can	AUX
ejpam-739	249	6	write	write	VERB
ejpam-739	249	7	g	g	PROPN
ejpam-739	249	8	α	α	PROPN
ejpam-739	249	9	,	,	PUNCT
ejpam-739	249	10	β	β	X
ejpam-739	249	11	u	u	NOUN
ejpam-739	249	12	(	(	PUNCT
ejpam-739	249	13	f	f	PROPN
ejpam-739	249	14	)	)	PUNCT
ejpam-739	249	15	(	(	PUNCT
ejpam-739	249	16	z	z	NOUN
ejpam-739	249	17	)	)	PUNCT
ejpam-739	249	18	=	=	SYM
ejpam-739	250	1	∞	∞	NUM
ejpam-739	250	2	∑	∑	PROPN
ejpam-739	250	3	k=0	k=0	PROPN
ejpam-739	250	4	ak	ak	PROPN
ejpam-739	250	5	·	·	PUNCT
ejpam-739	250	6	bk(α	bk(α	PROPN
ejpam-739	250	7	,	,	PUNCT
ejpam-739	250	8	β	β	X
ejpam-739	250	9	)	)	PUNCT
ejpam-739	250	10	·	·	PUNCT
ejpam-739	251	1	zk	zk	X
ejpam-739	251	2	.	.	PROPN
ejpam-739	252	1	in	in	ADP
ejpam-739	252	2	other	other	ADJ
ejpam-739	252	3	order	order	NOUN
ejpam-739	252	4	of	of	ADP
ejpam-739	252	5	ideas	idea	NOUN
ejpam-739	252	6	,	,	PUNCT
ejpam-739	252	7	we	we	PRON
ejpam-739	252	8	easily	easily	ADV
ejpam-739	252	9	can	can	AUX
ejpam-739	252	10	write	write	VERB
ejpam-739	252	11	g	g	PROPN
ejpam-739	252	12	α	α	PROPN
ejpam-739	252	13	,	,	PUNCT
ejpam-739	252	14	β	β	X
ejpam-739	252	15	u	u	NOUN
ejpam-739	252	16	(	(	PUNCT
ejpam-739	252	17	f	f	PROPN
ejpam-739	252	18	)	)	PUNCT
ejpam-739	252	19	(	(	PUNCT
ejpam-739	252	20	z)−	z)−	PROPN
ejpam-739	252	21	f	f	X
ejpam-739	252	22	(	(	PUNCT
ejpam-739	252	23	z	z	NOUN
ejpam-739	252	24	)	)	PUNCT
ejpam-739	252	25	=	=	SYM
ejpam-739	252	26	1	1	NUM
ejpam-739	252	27	beta(α	beta(α	NOUN
ejpam-739	252	28	,	,	PUNCT
ejpam-739	252	29	β	β	X
ejpam-739	252	30	)	)	PUNCT
ejpam-739	252	31	·	·	PUNCT
ejpam-739	253	1	∫	∫	PROPN
ejpam-739	253	2	1	1	NUM
ejpam-739	253	3	0	0	NUM
ejpam-739	253	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	253	5	t)β−1[ut	t)β−1[ut	PROPN
ejpam-739	253	6	(	(	PUNCT
ejpam-739	253	7	f	f	PROPN
ejpam-739	253	8	)	)	PUNCT
ejpam-739	253	9	(	(	PUNCT
ejpam-739	253	10	z)−	z)−	PROPN
ejpam-739	253	11	f	f	X
ejpam-739	253	12	(	(	PUNCT
ejpam-739	253	13	z)]d	z)]d	PROPN
ejpam-739	253	14	t	t	PROPN
ejpam-739	253	15	,	,	PUNCT
ejpam-739	253	16	which	which	PRON
ejpam-739	253	17	together	together	ADV
ejpam-739	253	18	with	with	ADP
ejpam-739	253	19	the	the	DET
ejpam-739	253	20	estimate	estimate	NOUN
ejpam-739	253	21	|ut	|ut	NOUN
ejpam-739	253	22	(	(	PUNCT
ejpam-739	253	23	f	f	PROPN
ejpam-739	253	24	)	)	PUNCT
ejpam-739	253	25	(	(	PUNCT
ejpam-739	253	26	z)−	z)−	PROPN
ejpam-739	253	27	f	f	X
ejpam-739	253	28	(	(	PUNCT
ejpam-739	253	29	z)|	z)|	NOUN
ejpam-739	253	30	≤	≤	PROPN
ejpam-739	253	31	cr	cr	PROPN
ejpam-739	254	1	(	(	PUNCT
ejpam-739	254	2	f	f	PROPN
ejpam-739	254	3	)	)	PUNCT
ejpam-739	254	4	t	t	PROPN
ejpam-739	254	5	in	in	ADP
ejpam-739	254	6	gal	gal	PROPN
ejpam-739	255	1	[	[	X
ejpam-739	255	2	2	2	NUM
ejpam-739	255	3	,	,	PUNCT
ejpam-739	255	4	p.	p.	NOUN
ejpam-739	255	5	224	224	NUM
ejpam-739	255	6	,	,	PUNCT
ejpam-739	255	7	theorem	theorem	VERB
ejpam-739	255	8	3.2.8	3.2.8	NUM
ejpam-739	255	9	,	,	PUNCT
ejpam-739	255	10	(	(	PUNCT
ejpam-739	255	11	iv	iv	X
ejpam-739	255	12	)	)	PUNCT
ejpam-739	255	13	]	]	PUNCT
ejpam-739	255	14	,	,	PUNCT
ejpam-739	255	15	implies	imply	VERB
ejpam-739	255	16	|gα	|gα	PROPN
ejpam-739	255	17	,	,	PUNCT
ejpam-739	255	18	β	β	X
ejpam-739	255	19	u	u	NOUN
ejpam-739	255	20	(	(	PUNCT
ejpam-739	255	21	f	f	PROPN
ejpam-739	255	22	)	)	PUNCT
ejpam-739	255	23	(	(	PUNCT
ejpam-739	255	24	z)−	z)−	PROPN
ejpam-739	255	25	f	f	X
ejpam-739	255	26	(	(	PUNCT
ejpam-739	255	27	z)|	z)|	ADP
ejpam-739	255	28	≤	≤	ADV
ejpam-739	255	29	1	1	NUM
ejpam-739	255	30	beta(α	beta(α	NOUN
ejpam-739	255	31	,	,	PUNCT
ejpam-739	255	32	β	β	X
ejpam-739	255	33	)	)	PUNCT
ejpam-739	255	34	·	·	PUNCT
ejpam-739	256	1	∫	∫	PROPN
ejpam-739	256	2	1	1	NUM
ejpam-739	256	3	0	0	NUM
ejpam-739	256	4	tα−1(1−	tα−1(1−	PROPN
ejpam-739	256	5	t)β−1|ut	t)β−1|ut	NUM
ejpam-739	256	6	(	(	PUNCT
ejpam-739	256	7	f	f	NOUN
ejpam-739	256	8	)	)	PUNCT
ejpam-739	256	9	(	(	PUNCT
ejpam-739	256	10	z)−	z)−	PROPN
ejpam-739	256	11	f	f	PROPN
ejpam-739	256	12	(	(	PUNCT
ejpam-739	256	13	z)|d	z)|d	PROPN
ejpam-739	256	14	t	t	PROPN
ejpam-739	256	15	≤	≤	PROPN
ejpam-739	256	16	cr	cr	PROPN
ejpam-739	256	17	(	(	PUNCT
ejpam-739	256	18	f	f	PROPN
ejpam-739	256	19	)	)	PUNCT
ejpam-739	256	20	1	1	NUM
ejpam-739	256	21	beta(α	beta(α	NOUN
ejpam-739	256	22	,	,	PUNCT
ejpam-739	256	23	β	β	X
ejpam-739	256	24	)	)	PUNCT
ejpam-739	256	25	·	·	PUNCT
ejpam-739	257	1	∫	∫	PROPN
ejpam-739	258	1	1	1	NUM
ejpam-739	258	2	0	0	X
ejpam-739	259	1	tα(1−	tα(1−	NOUN
ejpam-739	259	2	t)β−1d	t)β−1d	PROPN
ejpam-739	259	3	t	t	NOUN
ejpam-739	259	4	=	=	SYM
ejpam-739	259	5	cr	cr	PROPN
ejpam-739	259	6	(	(	PUNCT
ejpam-739	259	7	f	f	PROPN
ejpam-739	259	8	)	)	PUNCT
ejpam-739	259	9	·	·	PUNCT
ejpam-739	259	10	beta(α+	beta(α+	NOUN
ejpam-739	259	11	1,β	1,β	NOUN
ejpam-739	259	12	)	)	PUNCT
ejpam-739	259	13	beta(α	beta(α	NOUN
ejpam-739	259	14	,	,	PUNCT
ejpam-739	259	15	β	β	NOUN
ejpam-739	259	16	)	)	PUNCT
ejpam-739	259	17	≤	≤	NOUN
ejpam-739	259	18	cr	cr	ADP
ejpam-739	259	19	(	(	PUNCT
ejpam-739	259	20	f	f	PROPN
ejpam-739	259	21	)	)	PUNCT
ejpam-739	259	22	α	α	PROPN
ejpam-739	259	23	,	,	PUNCT
ejpam-739	259	24	for	for	ADP
ejpam-739	259	25	all	all	DET
ejpam-739	259	26	|z|	|z|	NOUN
ejpam-739	259	27	≤	≤	NUM
ejpam-739	259	28	r	r	NOUN
ejpam-739	259	29	,	,	PUNCT
ejpam-739	259	30	where	where	SCONJ
ejpam-739	259	31	cr	cr	PROPN
ejpam-739	259	32	(	(	PUNCT
ejpam-739	259	33	f	f	PROPN
ejpam-739	259	34	)	)	PUNCT
ejpam-739	259	35	>	>	X
ejpam-739	259	36	0	0	PUNCT
ejpam-739	259	37	is	be	AUX
ejpam-739	259	38	independent	independent	ADJ
ejpam-739	259	39	of	of	ADP
ejpam-739	259	40	z	z	NOUN
ejpam-739	259	41	(	(	PUNCT
ejpam-739	259	42	and	and	CCONJ
ejpam-739	259	43	α	α	X
ejpam-739	259	44	)	)	PUNCT
ejpam-739	260	1	but	but	CCONJ
ejpam-739	260	2	depends	depend	VERB
ejpam-739	260	3	on	on	ADP
ejpam-739	260	4	f	f	PROPN
ejpam-739	260	5	and	and	CCONJ
ejpam-739	260	6	r.	r.	PROPN
ejpam-739	260	7	now	now	ADV
ejpam-739	260	8	,	,	PUNCT
ejpam-739	260	9	let	let	VERB
ejpam-739	260	10	q	q	PROPN
ejpam-739	260	11	∈	∈	PROPN
ejpam-739	260	12	n∪	n∪	PROPN
ejpam-739	260	13	{	{	PUNCT
ejpam-739	260	14	0	0	NUM
ejpam-739	260	15	}	}	PUNCT
ejpam-739	260	16	and	and	CCONJ
ejpam-739	260	17	1	1	NUM
ejpam-739	260	18	≤	≤	NOUN
ejpam-739	260	19	r	r	NOUN
ejpam-739	260	20	<	<	X
ejpam-739	260	21	r1	r1	PROPN
ejpam-739	260	22	<	<	X
ejpam-739	260	23	r.	r.	PROPN
ejpam-739	260	24	by	by	ADP
ejpam-739	260	25	using	use	VERB
ejpam-739	260	26	the	the	DET
ejpam-739	260	27	cauchy	cauchy	NOUN
ejpam-739	260	28	’s	’s	PART
ejpam-739	260	29	formula	formula	NOUN
ejpam-739	260	30	and	and	CCONJ
ejpam-739	260	31	reasoning	reasoning	NOUN
ejpam-739	260	32	as	as	ADP
ejpam-739	260	33	in	in	ADP
ejpam-739	260	34	the	the	DET
ejpam-739	260	35	proof	proof	NOUN
ejpam-739	260	36	of	of	ADP
ejpam-739	260	37	the	the	DET
ejpam-739	260	38	above	above	ADJ
ejpam-739	260	39	point	point	NOUN
ejpam-739	260	40	(	(	PUNCT
ejpam-739	260	41	i	i	NOUN
ejpam-739	260	42	)	)	PUNCT
ejpam-739	260	43	,	,	PUNCT
ejpam-739	260	44	we	we	PRON
ejpam-739	260	45	get	get	VERB
ejpam-739	260	46	the	the	DET
ejpam-739	260	47	upper	upper	ADJ
ejpam-739	260	48	estimate	estimate	NOUN
ejpam-739	260	49	‖[gα	‖[gα	NOUN
ejpam-739	260	50	,	,	PUNCT
ejpam-739	260	51	β	β	X
ejpam-739	260	52	u	u	NOUN
ejpam-739	260	53	(	(	PUNCT
ejpam-739	260	54	f	f	PROPN
ejpam-739	260	55	)	)	PUNCT
ejpam-739	260	56	]	]	PUNCT
ejpam-739	260	57	(	(	PUNCT
ejpam-739	260	58	q)−	q)−	PROPN
ejpam-739	260	59	f	f	X
ejpam-739	260	60	(	(	PUNCT
ejpam-739	260	61	q)‖r	q)‖r	NOUN
ejpam-739	260	62	≤	≤	NOUN
ejpam-739	260	63	c∗α	c∗α	NOUN
ejpam-739	260	64	,	,	PUNCT
ejpam-739	260	65	with	with	ADP
ejpam-739	260	66	c∗	c∗	NOUN
ejpam-739	260	67	depending	depend	VERB
ejpam-739	260	68	only	only	ADV
ejpam-739	260	69	on	on	ADP
ejpam-739	260	70	f	f	PROPN
ejpam-739	260	71	,	,	PUNCT
ejpam-739	260	72	q	q	X
ejpam-739	260	73	,	,	PUNCT
ejpam-739	260	74	r	r	NOUN
ejpam-739	260	75	and	and	CCONJ
ejpam-739	260	76	r1	r1	NOUN
ejpam-739	260	77	.	.	PUNCT
ejpam-739	261	1	it	it	PRON
ejpam-739	261	2	remains	remain	VERB
ejpam-739	261	3	to	to	PART
ejpam-739	261	4	prove	prove	VERB
ejpam-739	261	5	the	the	DET
ejpam-739	261	6	lower	low	ADJ
ejpam-739	261	7	estimate	estimate	NOUN
ejpam-739	261	8	.	.	PUNCT
ejpam-739	262	1	for	for	ADP
ejpam-739	262	2	this	this	DET
ejpam-739	262	3	purpose	purpose	NOUN
ejpam-739	262	4	,	,	PUNCT
ejpam-739	262	5	reasoning	reason	VERB
ejpam-739	262	6	exactly	exactly	ADV
ejpam-739	262	7	as	as	ADP
ejpam-739	262	8	in	in	ADP
ejpam-739	262	9	the	the	DET
ejpam-739	262	10	proof	proof	NOUN
ejpam-739	262	11	of	of	ADP
ejpam-739	262	12	theorem	theorem	NOUN
ejpam-739	262	13	3.2.8	3.2.8	NUM
ejpam-739	262	14	,	,	PUNCT
ejpam-739	262	15	at	at	ADP
ejpam-739	262	16	pages	page	NOUN
ejpam-739	262	17	227	227	NUM
ejpam-739	262	18	-	-	SYM
ejpam-739	262	19	228	228	NUM
ejpam-739	262	20	in	in	ADP
ejpam-739	262	21	the	the	DET
ejpam-739	262	22	book	book	NOUN
ejpam-739	262	23	gal	gal	NOUN
ejpam-739	263	1	[	[	X
ejpam-739	263	2	2	2	NUM
ejpam-739	263	3	]	]	PUNCT
ejpam-739	263	4	,	,	PUNCT
ejpam-739	263	5	for	for	ADP
ejpam-739	263	6	z	z	NOUN
ejpam-739	263	7	=	=	NOUN
ejpam-739	263	8	reiϕ	reiϕ	NOUN
ejpam-739	263	9	and	and	CCONJ
ejpam-739	263	10	p	p	PRON
ejpam-739	263	11	∈	∈	PROPN
ejpam-739	263	12	n∪	n∪	X
ejpam-739	263	13	{	{	PUNCT
ejpam-739	263	14	0	0	NUM
ejpam-739	263	15	}	}	PUNCT
ejpam-739	263	16	we	we	PRON
ejpam-739	263	17	get	get	VERB
ejpam-739	263	18	1	1	NUM
ejpam-739	263	19	2π	2π	NUM
ejpam-739	263	20	∫	∫	NOUN
ejpam-739	264	1	π	π	NOUN
ejpam-739	264	2	−π	−π	PROPN
ejpam-739	264	3	[	[	PUNCT
ejpam-739	264	4	f	f	X
ejpam-739	264	5	(	(	PUNCT
ejpam-739	264	6	q)(z)−	q)(z)−	X
ejpam-739	264	7	[	[	X
ejpam-739	264	8	ut	ut	PROPN
ejpam-739	264	9	(	(	PUNCT
ejpam-739	264	10	f	f	PROPN
ejpam-739	264	11	)	)	PUNCT
ejpam-739	264	12	]	]	PUNCT
ejpam-739	265	1	(	(	PUNCT
ejpam-739	265	2	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	PROPN
ejpam-739	265	3	s.	s.	PROPN
ejpam-739	265	4	gal	gal	PROPN
ejpam-739	265	5	/	/	SYM
ejpam-739	265	6	eur	eur	PROPN
ejpam-739	265	7	.	.	PUNCT
ejpam-739	266	1	j.	j.	PROPN
ejpam-739	266	2	pure	pure	PROPN
ejpam-739	266	3	appl	appl	PROPN
ejpam-739	266	4	.	.	PROPN
ejpam-739	266	5	math	math	PROPN
ejpam-739	266	6	,	,	PUNCT
ejpam-739	266	7	3	3	NUM
ejpam-739	266	8	(	(	PUNCT
ejpam-739	266	9	2010	2010	NUM
ejpam-739	266	10	)	)	PUNCT
ejpam-739	266	11	,	,	PUNCT
ejpam-739	266	12	1150	1150	NUM
ejpam-739	266	13	-	-	SYM
ejpam-739	266	14	1164	1164	NUM
ejpam-739	266	15	1163	1163	NUM
ejpam-739	266	16	=	=	SYM
ejpam-739	266	17	aq+p(q+	aq+p(q+	PROPN
ejpam-739	266	18	p)(q+	p)(q+	VERB
ejpam-739	266	19	p−	p−	NOUN
ejpam-739	266	20	1)	1)	NUM
ejpam-739	266	21	...	...	PUNCT
ejpam-739	267	1	(p+	(p+	X
ejpam-739	267	2	1)r	1)r	ADP
ejpam-739	267	3	p[1−	p[1−	PROPN
ejpam-739	267	4	e−(q+p)2	e−(q+p)2	PROPN
ejpam-739	267	5	t/4	t/4	X
ejpam-739	267	6	]	]	PUNCT
ejpam-739	267	7	.	.	PUNCT
ejpam-739	268	1	multiplying	multiply	VERB
ejpam-739	268	2	above	above	ADV
ejpam-739	268	3	with	with	ADP
ejpam-739	268	4	1	1	NUM
ejpam-739	268	5	beta(α	beta(α	NOUN
ejpam-739	268	6	,	,	PUNCT
ejpam-739	268	7	β	β	NOUN
ejpam-739	268	8	)	)	PUNCT
ejpam-739	268	9	tα−1(1−	tα−1(1−	NOUN
ejpam-739	268	10	t)β−1	t)β−1	ADP
ejpam-739	268	11	an	an	DET
ejpam-739	268	12	then	then	ADV
ejpam-739	268	13	integrating	integrate	VERB
ejpam-739	268	14	with	with	ADP
ejpam-739	268	15	respect	respect	NOUN
ejpam-739	268	16	to	to	ADP
ejpam-739	268	17	t	t	PROPN
ejpam-739	268	18	,	,	PUNCT
ejpam-739	268	19	it	it	PRON
ejpam-739	268	20	follows	follow	VERB
ejpam-739	268	21	i	i	PRON
ejpam-739	268	22	:	:	PUNCT
ejpam-739	268	23	=	=	SYM
ejpam-739	268	24	1	1	NUM
ejpam-739	268	25	beta(α	beta(α	NOUN
ejpam-739	268	26	,	,	PUNCT
ejpam-739	268	27	β	β	X
ejpam-739	268	28	)	)	PUNCT
ejpam-739	268	29	·	·	PUNCT
ejpam-739	269	1	∫	∫	PROPN
ejpam-739	269	2	1	1	NUM
ejpam-739	269	3	0	0	NUM
ejpam-739	269	4	¨	¨	NOUN
ejpam-739	269	5	1	1	NUM
ejpam-739	269	6	2π	2π	NUM
ejpam-739	269	7	∫	∫	PROPN
ejpam-739	270	1	π	π	NOUN
ejpam-739	270	2	−π	−π	PROPN
ejpam-739	270	3	[	[	PUNCT
ejpam-739	270	4	f	f	X
ejpam-739	270	5	(	(	PUNCT
ejpam-739	270	6	q)(z)−	q)(z)−	X
ejpam-739	270	7	[	[	X
ejpam-739	270	8	ut	ut	PROPN
ejpam-739	270	9	(	(	PUNCT
ejpam-739	270	10	f	f	PROPN
ejpam-739	270	11	)	)	PUNCT
ejpam-739	270	12	]	]	PUNCT
ejpam-739	270	13	(	(	PUNCT
ejpam-739	270	14	q)(z)]e−ipϕdϕ	q)(z)]e−ipϕdϕ	NOUN
ejpam-739	270	15	«	«	PUNCT
ejpam-739	270	16	tα−1)1−	tα−1)1−	NOUN
ejpam-739	270	17	t)β−1d	t)β−1d	PROPN
ejpam-739	270	18	t	t	NOUN
ejpam-739	270	19	=	=	SYM
ejpam-739	270	20	aq+p(q+	aq+p(q+	PROPN
ejpam-739	270	21	p)(q+	p)(q+	VERB
ejpam-739	270	22	p−	p−	NOUN
ejpam-739	270	23	1)	1)	NUM
ejpam-739	270	24	...	...	PUNCT
ejpam-739	270	25	(p+	(p+	X
ejpam-739	271	1	1)r	1)r	PROPN
ejpam-739	271	2	p	p	X
ejpam-739	271	3	·	·	PUNCT
ejpam-739	271	4	1	1	NUM
ejpam-739	271	5	beta(α	beta(α	NOUN
ejpam-739	271	6	,	,	PUNCT
ejpam-739	271	7	β	β	X
ejpam-739	271	8	)	)	PUNCT
ejpam-739	271	9	∫	∫	PROPN
ejpam-739	271	10	1	1	NUM
ejpam-739	271	11	0	0	NUM
ejpam-739	271	12	tα−1(1−	tα−1(1−	PROPN
ejpam-739	271	13	t)β−1	t)β−1	ADP
ejpam-739	271	14	h	h	NOUN
ejpam-739	271	15	1−	1−	NUM
ejpam-739	271	16	e−(q+p)2	e−(q+p)2	PROPN
ejpam-739	271	17	t/4	t/4	VERB
ejpam-739	272	1	i	i	PRON
ejpam-739	273	1	d	d	X
ejpam-739	273	2	t.	t.	NOUN
ejpam-739	273	3	applying	apply	VERB
ejpam-739	273	4	the	the	DET
ejpam-739	273	5	fubini	fubini	NOUN
ejpam-739	273	6	’s	’s	PART
ejpam-739	273	7	result	result	NOUN
ejpam-739	273	8	to	to	ADP
ejpam-739	273	9	the	the	DET
ejpam-739	273	10	double	double	ADJ
ejpam-739	273	11	integral	integral	ADJ
ejpam-739	273	12	i	i	PRON
ejpam-739	273	13	and	and	CCONJ
ejpam-739	273	14	then	then	ADV
ejpam-739	273	15	passing	pass	VERB
ejpam-739	273	16	to	to	ADP
ejpam-739	273	17	modulus	modulus	NOUN
ejpam-739	273	18	,	,	PUNCT
ejpam-739	273	19	we	we	PRON
ejpam-739	273	20	easily	easily	ADV
ejpam-739	273	21	obtain	obtain	VERB
ejpam-739	273	22	�	�	PROPN
ejpam-739	273	23	�	�	PROPN
ejpam-739	273	24	�	�	PROPN
ejpam-739	273	25	�	�	PROPN
ejpam-739	273	26	�	�	PROPN
ejpam-739	273	27	1	1	NUM
ejpam-739	273	28	2π	2π	PROPN
ejpam-739	273	29	∫	∫	PROPN
ejpam-739	274	1	π	π	PROPN
ejpam-739	274	2	−π	−π	PROPN
ejpam-739	274	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	274	4	�	�	PROPN
ejpam-739	274	5	1	1	NUM
ejpam-739	274	6	beta(α	beta(α	NOUN
ejpam-739	274	7	,	,	PUNCT
ejpam-739	274	8	β	β	NOUN
ejpam-739	274	9	)	)	PUNCT
ejpam-739	274	10	∫	∫	PROPN
ejpam-739	274	11	∞	∞	PROPN
ejpam-739	274	12	0	0	PUNCT
ejpam-739	275	1	[	[	PUNCT
ejpam-739	275	2	f	f	X
ejpam-739	275	3	(	(	PUNCT
ejpam-739	275	4	q)(z)−	q)(z)−	X
ejpam-739	275	5	[	[	X
ejpam-739	275	6	ut	ut	PROPN
ejpam-739	275	7	(	(	PUNCT
ejpam-739	275	8	f	f	PROPN
ejpam-739	275	9	)	)	PUNCT
ejpam-739	275	10	]	]	PUNCT
ejpam-739	275	11	(	(	PUNCT
ejpam-739	275	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	275	13	t)β−1d	t)β−1d	PROPN
ejpam-739	275	14	t	t	PROPN
ejpam-739	275	15	�	�	PROPN
ejpam-739	275	16	dϕ	dϕ	PROPN
ejpam-739	275	17	�	�	PROPN
ejpam-739	275	18	�	�	PROPN
ejpam-739	275	19	�	�	PROPN
ejpam-739	275	20	�	�	PROPN
ejpam-739	275	21	�	�	PROPN
ejpam-739	275	22	=	=	SYM
ejpam-739	275	23	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	275	24	p)(q+	p)(q+	NOUN
ejpam-739	275	25	p−	p−	NOUN
ejpam-739	275	26	1)	1)	NUM
ejpam-739	275	27	...	...	PUNCT
ejpam-739	275	28	(p+	(p+	X
ejpam-739	276	1	1)r	1)r	PROPN
ejpam-739	276	2	p	p	X
ejpam-739	276	3	·	·	PUNCT
ejpam-739	276	4			PROPN
ejpam-739	276	5			NOUN
ejpam-739	276	6	1	1	NUM
ejpam-739	276	7	beta(α	beta(α	NOUN
ejpam-739	276	8	,	,	PUNCT
ejpam-739	276	9	β	β	X
ejpam-739	276	10	)	)	PUNCT
ejpam-739	276	11	∫	∫	PROPN
ejpam-739	277	1	1	1	NUM
ejpam-739	277	2	0	0	NUM
ejpam-739	277	3	tα−1e−t	tα−1e−t	NOUN
ejpam-739	277	4	h	h	NOUN
ejpam-739	277	5	1−	1−	NUM
ejpam-739	277	6	e−(q+p)2	e−(q+p)2	PROPN
ejpam-739	277	7	t/4	t/4	VERB
ejpam-739	278	1	i	i	PRON
ejpam-739	278	2	d	d	X
ejpam-739	278	3	t	t	X
ejpam-739	278	4			PROPN
ejpam-739	278	5			PROPN
ejpam-739	278	6	.	.	PUNCT
ejpam-739	279	1	since	since	SCONJ
ejpam-739	279	2	1	1	NUM
ejpam-739	279	3	beta(α	beta(α	NOUN
ejpam-739	279	4	,	,	PUNCT
ejpam-739	279	5	β	β	X
ejpam-739	279	6	)	)	PUNCT
ejpam-739	279	7	∫	∫	PROPN
ejpam-739	279	8	1	1	NUM
ejpam-739	279	9	0	0	NUM
ejpam-739	280	1	[	[	PUNCT
ejpam-739	280	2	f	f	X
ejpam-739	280	3	(	(	PUNCT
ejpam-739	280	4	q)(z)−	q)(z)−	X
ejpam-739	280	5	[	[	X
ejpam-739	280	6	ut	ut	PROPN
ejpam-739	280	7	(	(	PUNCT
ejpam-739	280	8	f	f	PROPN
ejpam-739	280	9	)	)	PUNCT
ejpam-739	280	10	]	]	PUNCT
ejpam-739	280	11	(	(	PUNCT
ejpam-739	280	12	q)(z)]tα−1(1−	q)(z)]tα−1(1−	X
ejpam-739	280	13	t)β−1d	t)β−1d	PROPN
ejpam-739	280	14	t	t	NOUN
ejpam-739	280	15	=	=	SYM
ejpam-739	280	16	f	f	PROPN
ejpam-739	280	17	(	(	PUNCT
ejpam-739	280	18	q)(z)−	q)(z)−	X
ejpam-739	280	19	[	[	X
ejpam-739	280	20	gα	gα	NOUN
ejpam-739	280	21	,	,	PUNCT
ejpam-739	280	22	β	β	X
ejpam-739	280	23	u	u	NOUN
ejpam-739	280	24	(	(	PUNCT
ejpam-739	280	25	f	f	PROPN
ejpam-739	280	26	)	)	PUNCT
ejpam-739	280	27	]	]	X
ejpam-739	280	28	(	(	PUNCT
ejpam-739	280	29	q)(z	q)(z	NOUN
ejpam-739	280	30	)	)	PUNCT
ejpam-739	280	31	,	,	PUNCT
ejpam-739	280	32	the	the	DET
ejpam-739	280	33	previous	previous	ADJ
ejpam-739	280	34	equality	equality	NOUN
ejpam-739	280	35	immediately	immediately	ADV
ejpam-739	280	36	implies	imply	VERB
ejpam-739	280	37	�	�	PROPN
ejpam-739	280	38	�	�	PROPN
ejpam-739	280	39	�	�	PROPN
ejpam-739	280	40	�	�	PROPN
ejpam-739	280	41	�	�	PROPN
ejpam-739	280	42	1	1	NUM
ejpam-739	280	43	2π	2π	PROPN
ejpam-739	280	44	∫	∫	PROPN
ejpam-739	281	1	π	π	NOUN
ejpam-739	281	2	−π	−π	PROPN
ejpam-739	281	3	e−ipϕ	e−ipϕ	PROPN
ejpam-739	282	1	h	h	PROPN
ejpam-739	282	2	f	f	PROPN
ejpam-739	282	3	(	(	PUNCT
ejpam-739	282	4	q)(z)−	q)(z)−	X
ejpam-739	282	5	(	(	PUNCT
ejpam-739	282	6	gα	gα	NOUN
ejpam-739	282	7	,	,	PUNCT
ejpam-739	282	8	β	β	X
ejpam-739	282	9	u	u	NOUN
ejpam-739	282	10	(	(	PUNCT
ejpam-739	282	11	f	f	PROPN
ejpam-739	282	12	)	)	PUNCT
ejpam-739	282	13	)	)	PUNCT
ejpam-739	282	14	(	(	PUNCT
ejpam-739	282	15	q)(z	q)(z	NOUN
ejpam-739	282	16	)	)	PUNCT
ejpam-739	282	17	i	i	PRON
ejpam-739	282	18	dϕ	dϕ	VERB
ejpam-739	283	1	�	�	PROPN
ejpam-739	283	2	�	�	PROPN
ejpam-739	283	3	�	�	PROPN
ejpam-739	283	4	�	�	PROPN
ejpam-739	283	5	�	�	PROPN
ejpam-739	283	6	=	=	SYM
ejpam-739	283	7	|aq+p|(q+	|aq+p|(q+	PROPN
ejpam-739	283	8	p)(q+	p)(q+	NOUN
ejpam-739	283	9	p−	p−	NOUN
ejpam-739	283	10	1)	1)	NUM
ejpam-739	283	11	...	...	PUNCT
ejpam-739	283	12	(p+	(p+	X
ejpam-739	283	13	1)r	1)r	PROPN
ejpam-739	283	14	p	p	X
ejpam-739	283	15	·	·	PUNCT
ejpam-739	283	16			PROPN
ejpam-739	283	17			NOUN
ejpam-739	283	18	1	1	NUM
ejpam-739	283	19	beta(α	beta(α	NOUN
ejpam-739	283	20	,	,	PUNCT
ejpam-739	283	21	β	β	X
ejpam-739	283	22	)	)	PUNCT
ejpam-739	283	23	∫	∫	PROPN
ejpam-739	283	24	1	1	NUM
ejpam-739	283	25	0	0	NUM
ejpam-739	283	26	tα−1(1−	tα−1(1−	PROPN
ejpam-739	283	27	t)β−1	t)β−1	ADP
ejpam-739	283	28	h	h	NOUN
ejpam-739	283	29	1−	1−	NUM
ejpam-739	283	30	e−(q+p)2	e−(q+p)2	PROPN
ejpam-739	283	31	t/4	t/4	VERB
ejpam-739	284	1	i	i	PRON
ejpam-739	284	2	d	d	X
ejpam-739	284	3	t	t	X
ejpam-739	284	4			PROPN
ejpam-739	284	5			PROPN
ejpam-739	284	6	and	and	CCONJ
ejpam-739	284	7	|aq+p|(q+	|aq+p|(q+	NOUN
ejpam-739	284	8	p)(q+	p)(q+	NOUN
ejpam-739	284	9	p−	p−	NOUN
ejpam-739	284	10	1)	1)	NUM
ejpam-739	284	11	...	...	PUNCT
ejpam-739	284	12	(p+	(p+	X
ejpam-739	285	1	1)r	1)r	PROPN
ejpam-739	285	2	p	p	X
ejpam-739	285	3	·	·	PUNCT
ejpam-739	285	4			PROPN
ejpam-739	285	5			NOUN
ejpam-739	285	6	1	1	NUM
ejpam-739	285	7	beta(α	beta(α	NOUN
ejpam-739	285	8	,	,	PUNCT
ejpam-739	285	9	β	β	X
ejpam-739	285	10	)	)	PUNCT
ejpam-739	285	11	∫	∫	PROPN
ejpam-739	286	1	1	1	NUM
ejpam-739	286	2	0	0	NUM
ejpam-739	286	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	286	4	t)β−1	t)β−1	ADP
ejpam-739	286	5	h	h	NOUN
ejpam-739	286	6	1−	1−	NUM
ejpam-739	286	7	e−(q+p)2	e−(q+p)2	PROPN
ejpam-739	286	8	t/4	t/4	VERB
ejpam-739	287	1	i	i	PRON
ejpam-739	287	2	d	d	X
ejpam-739	287	3	t	t	X
ejpam-739	287	4			PROPN
ejpam-739	287	5			PROPN
ejpam-739	287	6	references	reference	NOUN
ejpam-739	287	7	1164	1164	NUM
ejpam-739	288	1	≤	≤	NUM
ejpam-739	288	2	‖	‖	PROPN
ejpam-739	288	3	f	f	PROPN
ejpam-739	288	4	(	(	PUNCT
ejpam-739	288	5	q)−	q)−	PROPN
ejpam-739	288	6	(	(	PUNCT
ejpam-739	288	7	gα	gα	PROPN
ejpam-739	288	8	,	,	PUNCT
ejpam-739	288	9	β	β	X
ejpam-739	288	10	u	u	NOUN
ejpam-739	288	11	(	(	PUNCT
ejpam-739	288	12	f	f	PROPN
ejpam-739	288	13	)	)	PUNCT
ejpam-739	288	14	)	)	PUNCT
ejpam-739	288	15	(	(	PUNCT
ejpam-739	288	16	q)‖r	q)‖r	INTJ
ejpam-739	288	17	.	.	PUNCT
ejpam-739	289	1	first	first	ADV
ejpam-739	289	2	take	take	VERB
ejpam-739	289	3	q	q	NOUN
ejpam-739	289	4	=	=	PUNCT
ejpam-739	289	5	0	0	NUM
ejpam-739	289	6	.	.	PUNCT
ejpam-739	290	1	from	from	ADP
ejpam-739	290	2	the	the	DET
ejpam-739	290	3	previous	previous	ADJ
ejpam-739	290	4	inequality	inequality	NOUN
ejpam-739	290	5	we	we	PRON
ejpam-739	290	6	immediately	immediately	ADV
ejpam-739	290	7	obtain	obtain	VERB
ejpam-739	290	8	|ap|r	|ap|r	ADP
ejpam-739	290	9	p	p	NOUN
ejpam-739	290	10	1	1	NUM
ejpam-739	290	11	beta(α	beta(α	NOUN
ejpam-739	290	12	,	,	PUNCT
ejpam-739	290	13	β	β	X
ejpam-739	290	14	)	)	PUNCT
ejpam-739	290	15	∫	∫	PROPN
ejpam-739	291	1	1	1	NUM
ejpam-739	291	2	0	0	NUM
ejpam-739	291	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	291	4	t)β−1	t)β−1	NOUN
ejpam-739	291	5	h	h	NOUN
ejpam-739	291	6	1−	1−	NUM
ejpam-739	291	7	e−p2	e−p2	NOUN
ejpam-739	291	8	t/4	t/4	PROPN
ejpam-739	292	1	i	i	PRON
ejpam-739	292	2	d	d	X
ejpam-739	292	3	t	t	NOUN
ejpam-739	292	4	!	!	PUNCT
ejpam-739	293	1	≤	≤	NUM
ejpam-739	294	1	‖	‖	PROPN
ejpam-739	294	2	f	f	X
ejpam-739	294	3	−	−	PROPN
ejpam-739	294	4	g	g	PROPN
ejpam-739	294	5	α	α	PROPN
ejpam-739	294	6	,	,	PUNCT
ejpam-739	294	7	β	β	X
ejpam-739	294	8	u	u	NOUN
ejpam-739	294	9	(	(	PUNCT
ejpam-739	294	10	f	f	PROPN
ejpam-739	294	11	)	)	PUNCT
ejpam-739	294	12	‖r	‖r	NOUN
ejpam-739	294	13	.	.	PUNCT
ejpam-739	295	1	in	in	ADP
ejpam-739	295	2	what	what	PRON
ejpam-739	295	3	follows	follow	VERB
ejpam-739	295	4	,	,	PUNCT
ejpam-739	295	5	denoting	denote	VERB
ejpam-739	295	6	vα	vα	ADP
ejpam-739	295	7	,	,	PUNCT
ejpam-739	295	8	β	β	X
ejpam-739	295	9	=	=	SYM
ejpam-739	295	10	inf	inf	NOUN
ejpam-739	295	11	p≥1	p≥1	NOUN
ejpam-739	295	12	1	1	NUM
ejpam-739	295	13	beta(α	beta(α	NOUN
ejpam-739	295	14	,	,	PUNCT
ejpam-739	295	15	β	β	X
ejpam-739	295	16	)	)	PUNCT
ejpam-739	295	17	∫	∫	PROPN
ejpam-739	296	1	1	1	NUM
ejpam-739	296	2	0	0	NUM
ejpam-739	296	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	296	4	t)β−1	t)β−1	NOUN
ejpam-739	296	5	h	h	NOUN
ejpam-739	296	6	1−	1−	NUM
ejpam-739	296	7	e−p2	e−p2	NOUN
ejpam-739	296	8	t/4	t/4	PROPN
ejpam-739	297	1	i	i	PRON
ejpam-739	297	2	d	d	X
ejpam-739	297	3	t	t	PROPN
ejpam-739	297	4	!	!	PUNCT
ejpam-739	298	1	,	,	PUNCT
ejpam-739	298	2	by	by	ADP
ejpam-739	298	3	simple	simple	ADJ
ejpam-739	298	4	calculation	calculation	NOUN
ejpam-739	298	5	we	we	PRON
ejpam-739	298	6	get	get	AUX
ejpam-739	298	7	vα	vα	ADP
ejpam-739	298	8	,	,	PUNCT
ejpam-739	298	9	β	β	X
ejpam-739	298	10	=	=	SYM
ejpam-739	298	11	1	1	NUM
ejpam-739	298	12	beta(α	beta(α	NOUN
ejpam-739	298	13	,	,	PUNCT
ejpam-739	298	14	β	β	X
ejpam-739	298	15	)	)	PUNCT
ejpam-739	298	16	∫	∫	PROPN
ejpam-739	299	1	1	1	NUM
ejpam-739	299	2	0	0	NUM
ejpam-739	299	3	tα−1(1−	tα−1(1−	PROPN
ejpam-739	299	4	t)β−1	t)β−1	PUNCT
ejpam-739	299	5	�	�	PROPN
ejpam-739	299	6	1−	1−	NUM
ejpam-739	299	7	e−t/4	e−t/4	PROPN
ejpam-739	299	8	�	�	PROPN
ejpam-739	299	9	d	d	NOUN
ejpam-739	299	10	t.	t.	PROPN
ejpam-739	299	11	but	but	CCONJ
ejpam-739	299	12	denoting	denote	VERB
ejpam-739	299	13	g(t	g(t	PROPN
ejpam-739	299	14	)	)	PUNCT
ejpam-739	299	15	=	=	SYM
ejpam-739	299	16	e−t/4	e−t/4	PROPN
ejpam-739	299	17	,	,	PUNCT
ejpam-739	299	18	by	by	ADP
ejpam-739	299	19	the	the	DET
ejpam-739	299	20	mean	mean	ADJ
ejpam-739	299	21	value	value	NOUN
ejpam-739	299	22	theorem	theorem	VERB
ejpam-739	299	23	there	there	PRON
ejpam-739	299	24	exists	exist	VERB
ejpam-739	299	25	ξ	ξ	PROPN
ejpam-739	299	26	∈	∈	PROPN
ejpam-739	299	27	(	(	PUNCT
ejpam-739	299	28	0,1	0,1	NOUN
ejpam-739	299	29	)	)	PUNCT
ejpam-739	299	30	such	such	ADJ
ejpam-739	299	31	that	that	SCONJ
ejpam-739	299	32	1−	1−	NUM
ejpam-739	299	33	e−t/4	e−t/4	PROPN
ejpam-739	299	34	=	=	PUNCT
ejpam-739	299	35	g(0)−	g(0)−	NOUN
ejpam-739	299	36	g(t	g(t	PROPN
ejpam-739	299	37	)	)	PUNCT
ejpam-739	300	1	=	=	SYM
ejpam-739	300	2	t	t	PROPN
ejpam-739	300	3	e−ξ/4	e−ξ/4	PROPN
ejpam-739	300	4	4	4	NUM
ejpam-739	300	5	≥	≥	NOUN
ejpam-739	300	6	t	t	PROPN
ejpam-739	300	7	4e1/4	4e1/4	PROPN
ejpam-739	300	8	,	,	PUNCT
ejpam-739	300	9	which	which	PRON
ejpam-739	300	10	immediately	immediately	ADV
ejpam-739	300	11	implies	imply	VERB
ejpam-739	300	12	vα	vα	PROPN
ejpam-739	300	13	,	,	PUNCT
ejpam-739	300	14	β	β	X
ejpam-739	300	15	≥	≥	NUM
ejpam-739	300	16	1	1	NUM
ejpam-739	300	17	4e1/4	4e1/4	NUM
ejpam-739	300	18	·	·	PUNCT
ejpam-739	300	19	beta(α	beta(α	ADP
ejpam-739	300	20	,	,	PUNCT
ejpam-739	300	21	β	β	NOUN
ejpam-739	300	22	)	)	PUNCT
ejpam-739	300	23	∫	∫	PROPN
ejpam-739	301	1	1	1	NUM
ejpam-739	301	2	0	0	X
ejpam-739	302	1	tα(1−	tα(1−	NOUN
ejpam-739	302	2	t)β−1d	t)β−1d	NOUN
ejpam-739	302	3	t	t	NOUN
ejpam-739	302	4	=	=	SYM
ejpam-739	302	5	beta(α+	beta(α+	X
ejpam-739	302	6	1,β	1,β	NUM
ejpam-739	302	7	)	)	PUNCT
ejpam-739	302	8	4e1/4	4e1/4	NOUN
ejpam-739	303	1	·	·	PUNCT
ejpam-739	303	2	beta(α	beta(α	ADP
ejpam-739	303	3	,	,	PUNCT
ejpam-739	303	4	β	β	X
ejpam-739	303	5	)	)	PUNCT
ejpam-739	303	6	=	=	SYM
ejpam-739	303	7	1	1	NUM
ejpam-739	303	8	4e1/4	4e1/4	NUM
ejpam-739	303	9	·	·	PUNCT
ejpam-739	304	1	α	α	INTJ
ejpam-739	304	2	α+	α+	X
ejpam-739	304	3	β	β	X
ejpam-739	304	4	≥	≥	NUM
ejpam-739	304	5	1	1	NUM
ejpam-739	304	6	4e1/4	4e1/4	NUM
ejpam-739	304	7	·	·	PUNCT
ejpam-739	305	1	α	α	PRON
ejpam-739	305	2	2β	2β	NOUN
ejpam-739	305	3	≥	≥	NOUN
ejpam-739	305	4	α	α	PROPN
ejpam-739	305	5	8e1/4	8e1/4	PROPN
ejpam-739	305	6	.	.	PUNCT
ejpam-739	306	1	now	now	ADV
ejpam-739	306	2	,	,	PUNCT
ejpam-739	306	3	by	by	ADP
ejpam-739	306	4	following	follow	VERB
ejpam-739	306	5	for	for	ADP
ejpam-739	306	6	q	q	PROPN
ejpam-739	306	7	≥	≥	NOUN
ejpam-739	306	8	0	0	NUM
ejpam-739	306	9	similar	similar	ADJ
ejpam-739	306	10	reasonings	reasoning	NOUN
ejpam-739	306	11	with	with	ADP
ejpam-739	306	12	those	those	PRON
ejpam-739	306	13	in	in	ADP
ejpam-739	306	14	the	the	DET
ejpam-739	306	15	above	above	ADJ
ejpam-739	306	16	point	point	NOUN
ejpam-739	306	17	(	(	PUNCT
ejpam-739	306	18	i	i	NOUN
ejpam-739	306	19	)	)	PUNCT
ejpam-739	306	20	,	,	PUNCT
ejpam-739	306	21	we	we	PRON
ejpam-739	306	22	get	get	VERB
ejpam-739	306	23	the	the	DET
ejpam-739	306	24	desired	desire	VERB
ejpam-739	306	25	equivalence	equivalence	NOUN
ejpam-739	306	26	in	in	ADP
ejpam-739	306	27	the	the	DET
ejpam-739	306	28	statement	statement	NOUN
ejpam-739	306	29	.	.	PUNCT
ejpam-739	307	1	references	reference	NOUN
ejpam-739	307	2	[	[	X
ejpam-739	307	3	1	1	NUM
ejpam-739	307	4	]	]	X
ejpam-739	307	5	t.m	t.m	PROPN
ejpam-739	307	6	.	.	PROPN
ejpam-739	307	7	flett	flett	PROPN
ejpam-739	307	8	.	.	PUNCT
ejpam-739	308	1	temperatures	temperature	NOUN
ejpam-739	308	2	,	,	PUNCT
ejpam-739	308	3	bessel	bessel	NOUN
ejpam-739	308	4	potentials	potential	NOUN
ejpam-739	308	5	and	and	CCONJ
ejpam-739	308	6	lipschitz	lipschitz	VERB
ejpam-739	308	7	space	space	NOUN
ejpam-739	308	8	.	.	PUNCT
ejpam-739	309	1	proceedings	proceeding	NOUN
ejpam-739	309	2	of	of	ADP
ejpam-739	309	3	the	the	DET
ejpam-739	309	4	london	london	PROPN
ejpam-739	309	5	mathematical	mathematical	ADJ
ejpam-739	309	6	society	society	NOUN
ejpam-739	309	7	,	,	PUNCT
ejpam-739	309	8	22(3):385–451	22(3):385–451	NOUN
ejpam-739	309	9	,	,	PUNCT
ejpam-739	309	10	1971	1971	NUM
ejpam-739	309	11	.	.	PUNCT
ejpam-739	310	1	[	[	X
ejpam-739	310	2	2	2	NUM
ejpam-739	310	3	]	]	X
ejpam-739	310	4	s.g	s.g	PROPN
ejpam-739	310	5	.	.	PROPN
ejpam-739	310	6	gal	gal	PROPN
ejpam-739	310	7	.	.	PUNCT
ejpam-739	310	8	approximation	approximation	NOUN
ejpam-739	310	9	by	by	ADP
ejpam-739	310	10	complex	complex	ADJ
ejpam-739	310	11	bernstein	bernstein	PROPN
ejpam-739	310	12	and	and	CCONJ
ejpam-739	310	13	convolution	convolution	NOUN
ejpam-739	310	14	type	type	NOUN
ejpam-739	310	15	operators	operator	NOUN
ejpam-739	310	16	.	.	PUNCT
ejpam-739	311	1	world	world	NOUN
ejpam-739	311	2	scientific	scientific	ADJ
ejpam-739	311	3	publishing	publishing	NOUN
ejpam-739	311	4	company	company	NOUN
ejpam-739	311	5	,	,	PUNCT
ejpam-739	311	6	new	new	PROPN
ejpam-739	311	7	jersey	jersey	PROPN
ejpam-739	311	8	,	,	PUNCT
ejpam-739	311	9	london	london	PROPN
ejpam-739	311	10	,	,	PUNCT
ejpam-739	311	11	singapore	singapore	PROPN
ejpam-739	311	12	,	,	PUNCT
ejpam-739	311	13	beijing	beijing	PROPN
ejpam-739	311	14	,	,	PUNCT
ejpam-739	311	15	shanghai	shanghai	PROPN
ejpam-739	311	16	,	,	PUNCT
ejpam-739	311	17	hong	hong	PROPN
ejpam-739	311	18	kong	kong	PROPN
ejpam-739	311	19	,	,	PUNCT
ejpam-739	311	20	taipei	taipei	PROPN
ejpam-739	311	21	,	,	PUNCT
ejpam-739	311	22	chennai	chennai	PROPN
ejpam-739	311	23	,	,	PUNCT
ejpam-739	311	24	2009	2009	NUM
ejpam-739	311	25	.	.	PUNCT
ejpam-739	312	1	[	[	X
ejpam-739	312	2	3	3	X
ejpam-739	312	3	]	]	X
ejpam-739	312	4	s.g	s.g	PROPN
ejpam-739	312	5	.	.	PROPN
ejpam-739	312	6	gal	gal	PROPN
ejpam-739	312	7	.	.	PUNCT
ejpam-739	312	8	approximation	approximation	NOUN
ejpam-739	312	9	by	by	ADP
ejpam-739	312	10	complex	complex	ADJ
ejpam-739	312	11	potentials	potential	NOUN
ejpam-739	312	12	generated	generate	VERB
ejpam-739	312	13	by	by	ADP
ejpam-739	312	14	the	the	DET
ejpam-739	312	15	gamma	gamma	PROPN
ejpam-739	312	16	function	function	NOUN
ejpam-739	312	17	.	.	PUNCT
ejpam-739	313	1	turkish	turkish	ADJ
ejpam-739	313	2	journal	journal	NOUN
ejpam-739	313	3	of	of	ADP
ejpam-739	313	4	mathematics	mathematic	NOUN
ejpam-739	313	5	,	,	PUNCT
ejpam-739	313	6	accepted	accept	VERB
ejpam-739	313	7	for	for	ADP
ejpam-739	313	8	publication	publication	NOUN
ejpam-739	313	9	.	.	PUNCT