id	sid	tid	token	lemma	pos
ejpam-670	1	1	10_xxx_xi.dvi	10_xxx_xi.dvi	NUM
ejpam-670	1	2	european	european	PROPN
ejpam-670	1	3	journal	journal	PROPN
ejpam-670	1	4	of	of	ADP
ejpam-670	1	5	pure	pure	ADJ
ejpam-670	1	6	and	and	CCONJ
ejpam-670	1	7	applied	apply	VERB
ejpam-670	1	8	mathematics	mathematic	NOUN
ejpam-670	1	9	vol	vol	NOUN
ejpam-670	1	10	.	.	PROPN
ejpam-670	1	11	4	4	NUM
ejpam-670	1	12	,	,	PUNCT
ejpam-670	1	13	no	no	INTJ
ejpam-670	1	14	.	.	NOUN
ejpam-670	1	15	1	1	NUM
ejpam-670	1	16	,	,	PUNCT
ejpam-670	1	17	2011	2011	NUM
ejpam-670	1	18	,	,	PUNCT
ejpam-670	1	19	83	83	NUM
ejpam-670	1	20	-	-	SYM
ejpam-670	1	21	88	88	NUM
ejpam-670	1	22	issn	issn	PROPN
ejpam-670	1	23	1307	1307	NUM
ejpam-670	1	24	-	-	SYM
ejpam-670	1	25	5543	5543	NUM
ejpam-670	1	26	–	–	PUNCT
ejpam-670	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-670	1	28	on	on	ADP
ejpam-670	1	29	a	a	DET
ejpam-670	1	30	strengthened	strengthen	VERB
ejpam-670	1	31	of	of	ADP
ejpam-670	1	32	the	the	DET
ejpam-670	1	33	more	more	ADV
ejpam-670	1	34	accurate	accurate	ADJ
ejpam-670	1	35	hilbert	hilbert	PROPN
ejpam-670	1	36	’s	’s	PART
ejpam-670	1	37	inequality	inequality	PROPN
ejpam-670	1	38	gaowen	gaowen	NOUN
ejpam-670	1	39	xi	xi	ADP
ejpam-670	1	40	college	college	PROPN
ejpam-670	1	41	of	of	ADP
ejpam-670	1	42	mathematics	mathematics	PROPN
ejpam-670	1	43	and	and	CCONJ
ejpam-670	1	44	physics	physics	PROPN
ejpam-670	1	45	,	,	PUNCT
ejpam-670	1	46	chongqing	chongqing	PROPN
ejpam-670	1	47	university	university	PROPN
ejpam-670	1	48	of	of	ADP
ejpam-670	1	49	science	science	NOUN
ejpam-670	1	50	and	and	CCONJ
ejpam-670	1	51	technology	technology	NOUN
ejpam-670	1	52	,	,	PUNCT
ejpam-670	1	53	chongqing	chongqing	NOUN
ejpam-670	1	54	,	,	PUNCT
ejpam-670	1	55	401331	401331	NUM
ejpam-670	1	56	,	,	PUNCT
ejpam-670	1	57	p.	p.	PROPN
ejpam-670	1	58	r.	r.	PROPN
ejpam-670	1	59	china	china	PROPN
ejpam-670	1	60	abstract	abstract	PROPN
ejpam-670	1	61	.	.	PUNCT
ejpam-670	2	1	by	by	ADP
ejpam-670	2	2	deducing	deduce	VERB
ejpam-670	2	3	the	the	DET
ejpam-670	2	4	inequality	inequality	NOUN
ejpam-670	2	5	of	of	ADP
ejpam-670	2	6	weight	weight	NOUN
ejpam-670	2	7	coefficient	coefficient	NOUN
ejpam-670	2	8	:	:	PUNCT
ejpam-670	2	9	ω(n	ω(n	NUM
ejpam-670	2	10	)	)	PUNCT
ejpam-670	2	11	=	=	SYM
ejpam-670	3	1	∞	∞	NUM
ejpam-670	3	2	∑	∑	PUNCT
ejpam-670	3	3	m=0	m=0	PROPN
ejpam-670	3	4	1	1	NUM
ejpam-670	3	5	m+	m+	NUM
ejpam-670	3	6	n+	n+	NUM
ejpam-670	3	7	1	1	NUM
ejpam-670	3	8	(	(	PUNCT
ejpam-670	3	9	2n+	2n+	NUM
ejpam-670	3	10	1	1	NUM
ejpam-670	3	11	2m+	2m+	NUM
ejpam-670	3	12	1	1	NUM
ejpam-670	3	13	)	)	PUNCT
ejpam-670	3	14	1	1	NUM
ejpam-670	3	15	2	2	NUM
ejpam-670	3	16	<	<	X
ejpam-670	3	17	π−	π−	PROPN
ejpam-670	3	18	5	5	NUM
ejpam-670	3	19	6	6	NUM
ejpam-670	3	20	(	(	PUNCT
ejpam-670	3	21	p	p	NOUN
ejpam-670	3	22	2n+	2n+	NUM
ejpam-670	3	23	1	1	NUM
ejpam-670	3	24	+	+	NUM
ejpam-670	3	25	3	3	NUM
ejpam-670	3	26	4	4	NUM
ejpam-670	3	27	p	p	NOUN
ejpam-670	3	28	(	(	PUNCT
ejpam-670	3	29	2n+	2n+	NUM
ejpam-670	3	30	1)−1	1)−1	NUM
ejpam-670	3	31	)	)	PUNCT
ejpam-670	3	32	,	,	PUNCT
ejpam-670	3	33	where	where	SCONJ
ejpam-670	3	34	n	n	X
ejpam-670	3	35	∈	∈	PROPN
ejpam-670	3	36	n	n	NOUN
ejpam-670	3	37	.	.	PUNCT
ejpam-670	4	1	we	we	PRON
ejpam-670	4	2	obtain	obtain	VERB
ejpam-670	4	3	on	on	ADP
ejpam-670	4	4	a	a	DET
ejpam-670	4	5	strengthened	strengthen	VERB
ejpam-670	4	6	of	of	ADP
ejpam-670	4	7	the	the	DET
ejpam-670	4	8	more	more	ADV
ejpam-670	4	9	accurate	accurate	ADJ
ejpam-670	4	10	hilbert	hilbert	NOUN
ejpam-670	4	11	’s	’s	PART
ejpam-670	4	12	inequality	inequality	NOUN
ejpam-670	4	13	.	.	PUNCT
ejpam-670	5	1	2000	2000	NUM
ejpam-670	5	2	mathematics	mathematic	NOUN
ejpam-670	5	3	subject	subject	NOUN
ejpam-670	5	4	classifications	classification	NOUN
ejpam-670	5	5	:	:	PUNCT
ejpam-670	5	6	26d15	26d15	NUM
ejpam-670	5	7	key	key	ADJ
ejpam-670	5	8	words	word	NOUN
ejpam-670	5	9	and	and	CCONJ
ejpam-670	5	10	phrases	phrase	NOUN
ejpam-670	5	11	:	:	PUNCT
ejpam-670	5	12	hilbert	hilbert	PROPN
ejpam-670	5	13	’s	’s	PART
ejpam-670	5	14	inequality	inequality	NOUN
ejpam-670	5	15	,	,	PUNCT
ejpam-670	5	16	weight	weight	NOUN
ejpam-670	5	17	coefficient	coefficient	NOUN
ejpam-670	5	18	,	,	PUNCT
ejpam-670	5	19	cauchy	cauchy	PROPN
ejpam-670	5	20	’s	’s	PART
ejpam-670	5	21	inequality	inequality	NOUN
ejpam-670	5	22	,	,	PUNCT
ejpam-670	5	23	strengthen	strengthen	VERB
ejpam-670	5	24	1	1	NUM
ejpam-670	5	25	.	.	PUNCT
ejpam-670	6	1	introduction	introduction	NOUN
ejpam-670	6	2	let	let	VERB
ejpam-670	6	3	p	p	PRON
ejpam-670	6	4	>	>	X
ejpam-670	6	5	1	1	NUM
ejpam-670	6	6	,	,	PUNCT
ejpam-670	6	7	1	1	NUM
ejpam-670	6	8	p	p	NOUN
ejpam-670	7	1	+	+	NOUN
ejpam-670	7	2	1	1	NUM
ejpam-670	7	3	q	q	NOUN
ejpam-670	7	4	=	=	SYM
ejpam-670	7	5	1	1	NUM
ejpam-670	7	6	,	,	PUNCT
ejpam-670	7	7	an	an	DET
ejpam-670	7	8	≥	≥	NOUN
ejpam-670	7	9	0	0	NUM
ejpam-670	7	10	,	,	PUNCT
ejpam-670	7	11	bn	bn	X
ejpam-670	7	12	≥	≥	NOUN
ejpam-670	7	13	0	0	NUM
ejpam-670	7	14	,	,	PUNCT
ejpam-670	7	15	and	and	CCONJ
ejpam-670	7	16	0	0	NUM
ejpam-670	7	17	<	<	X
ejpam-670	7	18	∞	∞	NUM
ejpam-670	7	19	∑	∑	PROPN
ejpam-670	7	20	n=1−λ	n=1−λ	PRON
ejpam-670	7	21	a	a	DET
ejpam-670	7	22	p	p	NOUN
ejpam-670	7	23	n	n	CCONJ
ejpam-670	7	24	<	<	X
ejpam-670	7	25	∞	∞	PROPN
ejpam-670	7	26	,	,	PUNCT
ejpam-670	7	27	0	0	NUM
ejpam-670	7	28	<	<	X
ejpam-670	7	29	∞	∞	NUM
ejpam-670	7	30	∑	∑	PROPN
ejpam-670	7	31	n=1−λ	n=1−λ	NUM
ejpam-670	7	32	b	b	PROPN
ejpam-670	7	33	q	q	X
ejpam-670	7	34	n	n	X
ejpam-670	7	35	<	<	X
ejpam-670	7	36	∞	∞	PROPN
ejpam-670	7	37	,	,	PUNCT
ejpam-670	7	38	(	(	PUNCT
ejpam-670	7	39	λ=	λ=	VERB
ejpam-670	7	40	0,1	0,1	NUM
ejpam-670	7	41	)	)	PUNCT
ejpam-670	7	42	,	,	PUNCT
ejpam-670	7	43	then	then	ADV
ejpam-670	7	44	∞	∞	NUM
ejpam-670	7	45	∑	∑	PROPN
ejpam-670	7	46	n=1−λ	n=1−λ	NUM
ejpam-670	7	47	∞	∞	NUM
ejpam-670	7	48	∑	∑	PUNCT
ejpam-670	7	49	m=1−λ	m=1−λ	NUM
ejpam-670	7	50	am	be	AUX
ejpam-670	7	51	bn	bn	NUM
ejpam-670	7	52	m+	m+	NOUN
ejpam-670	7	53	n+λ	n+λ	PROPN
ejpam-670	7	54	<	<	X
ejpam-670	7	55	π	π	PROPN
ejpam-670	7	56	{	{	PUNCT
ejpam-670	7	57	∞	∞	PROPN
ejpam-670	7	58	∑	∑	PROPN
ejpam-670	7	59	n=1−λ	n=1−λ	PROPN
ejpam-670	7	60	a2	a2	PROPN
ejpam-670	7	61	n	n	CCONJ
ejpam-670	7	62	∞	∞	NUM
ejpam-670	7	63	∑	∑	PROPN
ejpam-670	7	64	n=1−λ	n=1−λ	NUM
ejpam-670	7	65	b2	b2	NOUN
ejpam-670	7	66	n	n	CCONJ
ejpam-670	7	67	}	}	SYM
ejpam-670	7	68	1	1	NUM
ejpam-670	7	69	2	2	NUM
ejpam-670	7	70	,	,	PUNCT
ejpam-670	7	71	(	(	PUNCT
ejpam-670	7	72	1	1	X
ejpam-670	7	73	)	)	PUNCT
ejpam-670	7	74	∞	∞	NUM
ejpam-670	7	75	∑	∑	PUNCT
ejpam-670	7	76	n=1−λ	n=1−λ	NUM
ejpam-670	7	77	∞	∞	NUM
ejpam-670	7	78	∑	∑	PROPN
ejpam-670	7	79	m=1−λ	m=1−λ	ADP
ejpam-670	7	80	ambn	ambn	ADJ
ejpam-670	7	81	m+	m+	NUM
ejpam-670	7	82	n+λ	n+λ	PUNCT
ejpam-670	7	83	<	<	X
ejpam-670	7	84	π	π	PROPN
ejpam-670	7	85	sin(π	sin(π	PROPN
ejpam-670	7	86	p	p	NOUN
ejpam-670	7	87	)	)	PUNCT
ejpam-670	7	88	{	{	PUNCT
ejpam-670	8	1	∞	∞	NUM
ejpam-670	8	2	∑	∑	PROPN
ejpam-670	8	3	n=1−λ	n=1−λ	X
ejpam-670	8	4	ap	ap	PROPN
ejpam-670	8	5	n	n	CCONJ
ejpam-670	8	6	}	}	SYM
ejpam-670	8	7	1	1	NUM
ejpam-670	8	8	p	p	NOUN
ejpam-670	8	9	{	{	PUNCT
ejpam-670	8	10	∞	∞	PROPN
ejpam-670	8	11	∑	∑	PROPN
ejpam-670	8	12	n=1−λ	n=1−λ	X
ejpam-670	8	13	bq	bq	NOUN
ejpam-670	8	14	n	n	CCONJ
ejpam-670	8	15	}	}	SYM
ejpam-670	8	16	1	1	NUM
ejpam-670	8	17	q	q	NOUN
ejpam-670	8	18	,	,	PUNCT
ejpam-670	8	19	(	(	PUNCT
ejpam-670	8	20	2	2	NUM
ejpam-670	8	21	)	)	PUNCT
ejpam-670	8	22	where	where	SCONJ
ejpam-670	8	23	,	,	PUNCT
ejpam-670	8	24	constant	constant	ADJ
ejpam-670	8	25	π	π	NOUN
ejpam-670	8	26	and	and	CCONJ
ejpam-670	8	27	π	π	PROPN
ejpam-670	8	28	sin(π	sin(π	PROPN
ejpam-670	8	29	p	p	NOUN
ejpam-670	8	30	)	)	PUNCT
ejpam-670	8	31	is	be	AUX
ejpam-670	8	32	best	well	ADV
ejpam-670	8	33	possible	possible	ADJ
ejpam-670	8	34	.	.	PUNCT
ejpam-670	9	1	(	(	PUNCT
ejpam-670	9	2	1	1	X
ejpam-670	9	3	)	)	PUNCT
ejpam-670	9	4	is	be	AUX
ejpam-670	9	5	hilbert	hilbert	PROPN
ejpam-670	9	6	’s	’s	PART
ejpam-670	9	7	type	type	NOUN
ejpam-670	9	8	inequality	inequality	NOUN
ejpam-670	9	9	.	.	PUNCT
ejpam-670	10	1	for	for	ADP
ejpam-670	10	2	λ	λ	PROPN
ejpam-670	10	3	=	=	SYM
ejpam-670	10	4	1	1	NUM
ejpam-670	10	5	,	,	PUNCT
ejpam-670	10	6	we	we	PRON
ejpam-670	10	7	have	have	VERB
ejpam-670	10	8	∞	∞	PROPN
ejpam-670	10	9	∑	∑	PROPN
ejpam-670	10	10	n=0	n=0	PROPN
ejpam-670	10	11	∞	∞	PROPN
ejpam-670	10	12	∑	∑	PROPN
ejpam-670	10	13	m=0	m=0	PROPN
ejpam-670	10	14	am	be	AUX
ejpam-670	10	15	bn	bn	NUM
ejpam-670	10	16	m+	m+	NUM
ejpam-670	10	17	n+	n+	ADP
ejpam-670	10	18	1	1	NUM
ejpam-670	10	19	<	<	X
ejpam-670	10	20	π	π	PROPN
ejpam-670	10	21	{	{	PUNCT
ejpam-670	10	22	∞	∞	PROPN
ejpam-670	10	23	∑	∑	PROPN
ejpam-670	10	24	n=0	n=0	PROPN
ejpam-670	10	25	a2	a2	PROPN
ejpam-670	10	26	n	n	CCONJ
ejpam-670	10	27	∞	∞	NUM
ejpam-670	10	28	∑	∑	PROPN
ejpam-670	10	29	n=0	n=0	NUM
ejpam-670	10	30	b2	b2	NOUN
ejpam-670	10	31	n	n	CCONJ
ejpam-670	10	32	}	}	SYM
ejpam-670	10	33	1	1	NUM
ejpam-670	10	34	2	2	NUM
ejpam-670	10	35	.	.	PUNCT
ejpam-670	11	1	(	(	PUNCT
ejpam-670	11	2	3	3	X
ejpam-670	11	3	)	)	PUNCT
ejpam-670	11	4	email	email	NOUN
ejpam-670	11	5	address	address	NOUN
ejpam-670	11	6	:	:	PUNCT
ejpam-670	11	7	xigaowen	xigaowen	PROPN
ejpam-670	11	8	�	�	PROPN
ejpam-670	11	9	163	163	NUM
ejpam-670	11	10	.	.	PUNCT
ejpam-670	12	1	om	om	PROPN
ejpam-670	12	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-670	12	3	83	83	NUM
ejpam-670	13	1	c	c	X
ejpam-670	13	2	©	©	PROPN
ejpam-670	13	3	2010	2010	NUM
ejpam-670	13	4	ejpam	ejpam	NOUN
ejpam-670	13	5	all	all	DET
ejpam-670	13	6	rights	right	NOUN
ejpam-670	13	7	reserved	reserve	VERB
ejpam-670	13	8	.	.	PUNCT
ejpam-670	14	1	g.	g.	NOUN
ejpam-670	14	2	xi	xi	PROPN
ejpam-670	14	3	/	/	SYM
ejpam-670	14	4	eur	eur	PROPN
ejpam-670	14	5	.	.	PUNCT
ejpam-670	15	1	j.	j.	PROPN
ejpam-670	15	2	pure	pure	PROPN
ejpam-670	15	3	appl	appl	PROPN
ejpam-670	15	4	.	.	PROPN
ejpam-670	15	5	math	math	PROPN
ejpam-670	15	6	,	,	PUNCT
ejpam-670	15	7	4	4	NUM
ejpam-670	15	8	(	(	PUNCT
ejpam-670	15	9	2011	2011	NUM
ejpam-670	15	10	)	)	PUNCT
ejpam-670	15	11	,	,	PUNCT
ejpam-670	15	12	83	83	NUM
ejpam-670	15	13	-	-	SYM
ejpam-670	15	14	88	88	NUM
ejpam-670	15	15	84	84	NUM
ejpam-670	15	16	inequality	inequality	NOUN
ejpam-670	15	17	(	(	PUNCT
ejpam-670	15	18	3	3	NUM
ejpam-670	15	19	)	)	PUNCT
ejpam-670	15	20	is	be	AUX
ejpam-670	15	21	named	name	VERB
ejpam-670	15	22	of	of	ADP
ejpam-670	15	23	more	more	ADV
ejpam-670	15	24	accurate	accurate	ADJ
ejpam-670	15	25	hilbert	hilbert	NOUN
ejpam-670	15	26	’s	’s	PART
ejpam-670	15	27	inequality	inequality	NOUN
ejpam-670	15	28	.	.	PUNCT
ejpam-670	16	1	inequality	inequality	NOUN
ejpam-670	16	2	(	(	PUNCT
ejpam-670	16	3	2	2	NUM
ejpam-670	16	4	)	)	PUNCT
ejpam-670	16	5	is	be	AUX
ejpam-670	16	6	hardy	hardy	ADJ
ejpam-670	16	7	-	-	PUNCT
ejpam-670	16	8	hilbert	hilbert	NOUN
ejpam-670	16	9	’s	’s	NOUN
ejpam-670	16	10	.	.	PUNCT
ejpam-670	17	1	for	for	ADP
ejpam-670	17	2	λ=	λ=	ADJ
ejpam-670	17	3	1	1	NUM
ejpam-670	17	4	,	,	PUNCT
ejpam-670	17	5	inequality	inequality	NOUN
ejpam-670	17	6	(	(	PUNCT
ejpam-670	17	7	2	2	NUM
ejpam-670	17	8	)	)	PUNCT
ejpam-670	17	9	is	be	AUX
ejpam-670	17	10	named	name	VERB
ejpam-670	17	11	of	of	ADP
ejpam-670	17	12	more	more	ADV
ejpam-670	17	13	accurate	accurate	ADJ
ejpam-670	17	14	hardy	hardy	ADJ
ejpam-670	17	15	-	-	PUNCT
ejpam-670	17	16	hilbert	hilbert	NOUN
ejpam-670	17	17	’s	’s	PART
ejpam-670	17	18	inequality	inequality	NOUN
ejpam-670	17	19	[	[	X
ejpam-670	17	20	1	1	NUM
ejpam-670	17	21	]	]	PUNCT
ejpam-670	17	22	.	.	PUNCT
ejpam-670	18	1	in	in	ADP
ejpam-670	18	2	[	[	X
ejpam-670	18	3	2	2	NUM
ejpam-670	18	4	]	]	PUNCT
ejpam-670	18	5	,	,	PUNCT
ejpam-670	18	6	yang	yang	PROPN
ejpam-670	18	7	obtained	obtain	VERB
ejpam-670	18	8	a	a	DET
ejpam-670	18	9	strengthened	strengthen	VERB
ejpam-670	18	10	of	of	ADP
ejpam-670	18	11	inequality	inequality	NOUN
ejpam-670	18	12	(	(	PUNCT
ejpam-670	18	13	3	3	NUM
ejpam-670	18	14	):	):	PUNCT
ejpam-670	18	15	∞	∞	PROPN
ejpam-670	18	16	∑	∑	PROPN
ejpam-670	18	17	n=0	n=0	NUM
ejpam-670	18	18	∞	∞	PROPN
ejpam-670	18	19	∑	∑	PROPN
ejpam-670	18	20	m=0	m=0	PROPN
ejpam-670	18	21	ambn	ambn	PROPN
ejpam-670	18	22	m+	m+	NUM
ejpam-670	18	23	n+	n+	ADP
ejpam-670	18	24	1	1	NUM
ejpam-670	18	25	<	<	X
ejpam-670	18	26	{	{	PUNCT
ejpam-670	18	27	∞	∞	PROPN
ejpam-670	18	28	∑	∑	PUNCT
ejpam-670	18	29	n=0	n=0	PUNCT
ejpam-670	19	1	[	[	X
ejpam-670	19	2	π−	π−	NOUN
ejpam-670	19	3	θ	θ	PROPN
ejpam-670	19	4	(	(	PUNCT
ejpam-670	19	5	n+	n+	NOUN
ejpam-670	19	6	1	1	NUM
ejpam-670	19	7	)	)	PUNCT
ejpam-670	19	8	1	1	NUM
ejpam-670	19	9	2	2	NUM
ejpam-670	19	10	]	]	PUNCT
ejpam-670	19	11	a2	a2	PROPN
ejpam-670	19	12	n	n	CCONJ
ejpam-670	19	13	}	}	SYM
ejpam-670	19	14	1	1	NUM
ejpam-670	19	15	2	2	NUM
ejpam-670	19	16	·	·	PUNCT
ejpam-670	19	17	{	{	PUNCT
ejpam-670	19	18	∞	∞	PROPN
ejpam-670	19	19	∑	∑	PUNCT
ejpam-670	19	20	n=0	n=0	PUNCT
ejpam-670	20	1	[	[	X
ejpam-670	20	2	π−	π−	NOUN
ejpam-670	20	3	θ	θ	PROPN
ejpam-670	20	4	(	(	PUNCT
ejpam-670	20	5	n+	n+	NOUN
ejpam-670	20	6	1	1	NUM
ejpam-670	20	7	)	)	PUNCT
ejpam-670	20	8	1	1	NUM
ejpam-670	20	9	2	2	NUM
ejpam-670	20	10	]	]	PUNCT
ejpam-670	20	11	b2	b2	NOUN
ejpam-670	20	12	n	n	CCONJ
ejpam-670	20	13	}	}	SYM
ejpam-670	20	14	1	1	NUM
ejpam-670	20	15	2	2	NUM
ejpam-670	20	16	,	,	PUNCT
ejpam-670	20	17	(	(	PUNCT
ejpam-670	20	18	4	4	NUM
ejpam-670	20	19	)	)	PUNCT
ejpam-670	20	20	where	where	SCONJ
ejpam-670	20	21	,	,	PUNCT
ejpam-670	20	22	θ	θ	PROPN
ejpam-670	20	23	=	=	PUNCT
ejpam-670	20	24	π−	π−	NOUN
ejpam-670	20	25	∞	∞	PROPN
ejpam-670	20	26	∑	∑	PROPN
ejpam-670	20	27	m=0	m=0	PROPN
ejpam-670	20	28	1	1	NUM
ejpam-670	20	29	(	(	PUNCT
ejpam-670	20	30	m+1	m+1	NUM
ejpam-670	20	31	)	)	PUNCT
ejpam-670	20	32	3	3	NUM
ejpam-670	20	33	2	2	NUM
ejpam-670	20	34	=	=	SYM
ejpam-670	20	35	0.5292496	0.5292496	NUM
ejpam-670	20	36	+	+	NOUN
ejpam-670	20	37	.	.	PUNCT
ejpam-670	21	1	in	in	ADP
ejpam-670	21	2	[	[	X
ejpam-670	21	3	3	3	NUM
ejpam-670	21	4	]	]	PUNCT
ejpam-670	21	5	,	,	PUNCT
ejpam-670	21	6	by	by	ADP
ejpam-670	21	7	the	the	DET
ejpam-670	21	8	following	follow	VERB
ejpam-670	21	9	inequality	inequality	NOUN
ejpam-670	21	10	of	of	ADP
ejpam-670	21	11	weight	weight	NOUN
ejpam-670	21	12	coefficient	coefficient	NOUN
ejpam-670	21	13	:	:	PUNCT
ejpam-670	21	14	ω(n	ω(n	NUM
ejpam-670	21	15	,	,	PUNCT
ejpam-670	21	16	r	r	NOUN
ejpam-670	21	17	)	)	PUNCT
ejpam-670	21	18	=	=	SYM
ejpam-670	22	1	∞	∞	NUM
ejpam-670	22	2	∑	∑	PROPN
ejpam-670	22	3	m=0	m=0	PROPN
ejpam-670	22	4	1	1	NUM
ejpam-670	22	5	m+	m+	NUM
ejpam-670	22	6	n+	n+	NUM
ejpam-670	22	7	1	1	NUM
ejpam-670	22	8	(	(	PUNCT
ejpam-670	22	9	2n+	2n+	NUM
ejpam-670	22	10	1	1	NUM
ejpam-670	22	11	2m+	2m+	NUM
ejpam-670	22	12	1	1	NUM
ejpam-670	22	13	)	)	PUNCT
ejpam-670	22	14	1	1	NUM
ejpam-670	22	15	r	r	NOUN
ejpam-670	22	16	<	<	X
ejpam-670	22	17	π	π	X
ejpam-670	22	18	sin(π	sin(π	PROPN
ejpam-670	22	19	r	r	NOUN
ejpam-670	22	20	)	)	PUNCT
ejpam-670	22	21	−	−	PROPN
ejpam-670	22	22	θ	θ	PROPN
ejpam-670	22	23	(	(	PUNCT
ejpam-670	22	24	2n+	2n+	NUM
ejpam-670	22	25	1)2−	1)2−	NUM
ejpam-670	22	26	1	1	NUM
ejpam-670	22	27	r	r	NOUN
ejpam-670	22	28	,	,	PUNCT
ejpam-670	22	29	where	where	SCONJ
ejpam-670	22	30	r	r	NOUN
ejpam-670	22	31	>	>	X
ejpam-670	22	32	1	1	NUM
ejpam-670	22	33	,	,	PUNCT
ejpam-670	22	34	n	n	PRON
ejpam-670	22	35	∈	∈	NOUN
ejpam-670	22	36	n	n	NOUN
ejpam-670	22	37	,	,	PUNCT
ejpam-670	22	38	then	then	ADV
ejpam-670	22	39	∞	∞	NUM
ejpam-670	22	40	∑	∑	PROPN
ejpam-670	22	41	n=0	n=0	PROPN
ejpam-670	22	42	∞	∞	PROPN
ejpam-670	22	43	∑	∑	PROPN
ejpam-670	22	44	m=0	m=0	PROPN
ejpam-670	22	45	am	be	AUX
ejpam-670	22	46	bn	bn	NUM
ejpam-670	22	47	m+	m+	NUM
ejpam-670	22	48	n+	n+	ADP
ejpam-670	22	49	1	1	NUM
ejpam-670	22	50	<	<	X
ejpam-670	22	51	{	{	PUNCT
ejpam-670	22	52	∞	∞	PROPN
ejpam-670	22	53	∑	∑	PROPN
ejpam-670	22	54	n=0	n=0	PUNCT
ejpam-670	22	55	[	[	PUNCT
ejpam-670	22	56	π	π	X
ejpam-670	22	57	sin(π	sin(π	PROPN
ejpam-670	22	58	p	p	NOUN
ejpam-670	22	59	)	)	PUNCT
ejpam-670	23	1	−	−	PROPN
ejpam-670	24	1	ln	ln	ADJ
ejpam-670	24	2	2−	2−	NUM
ejpam-670	24	3	c	c	NOUN
ejpam-670	24	4	(	(	PUNCT
ejpam-670	24	5	2n+	2n+	NUM
ejpam-670	24	6	1	1	NUM
ejpam-670	24	7	)	)	PUNCT
ejpam-670	24	8	1	1	NUM
ejpam-670	24	9	+	+	SYM
ejpam-670	24	10	1	1	NUM
ejpam-670	24	11	p	p	NOUN
ejpam-670	24	12	]	]	X
ejpam-670	24	13	ap	ap	PROPN
ejpam-670	24	14	n	n	CCONJ
ejpam-670	24	15	}	}	SYM
ejpam-670	24	16	1	1	NUM
ejpam-670	24	17	p	p	NOUN
ejpam-670	24	18	·	·	PUNCT
ejpam-670	24	19	{	{	PUNCT
ejpam-670	24	20	∞	∞	PROPN
ejpam-670	24	21	∑	∑	PROPN
ejpam-670	24	22	n=0	n=0	PUNCT
ejpam-670	24	23	[	[	PUNCT
ejpam-670	24	24	π	π	X
ejpam-670	24	25	sin(π	sin(π	PROPN
ejpam-670	24	26	p	p	NOUN
ejpam-670	24	27	)	)	PUNCT
ejpam-670	24	28	−	−	PROPN
ejpam-670	25	1	ln2−	ln2−	PROPN
ejpam-670	26	1	c	c	NOUN
ejpam-670	26	2	(	(	PUNCT
ejpam-670	26	3	2n+	2n+	NUM
ejpam-670	26	4	1	1	NUM
ejpam-670	26	5	)	)	PUNCT
ejpam-670	26	6	1	1	NUM
ejpam-670	26	7	+	+	SYM
ejpam-670	26	8	1	1	NUM
ejpam-670	26	9	q	q	NOUN
ejpam-670	26	10	]	]	X
ejpam-670	26	11	bq	bq	NOUN
ejpam-670	26	12	n	n	CCONJ
ejpam-670	26	13	}	}	SYM
ejpam-670	26	14	1	1	NUM
ejpam-670	26	15	q	q	NOUN
ejpam-670	26	16	,	,	PUNCT
ejpam-670	26	17	where	where	SCONJ
ejpam-670	26	18	c	c	PROPN
ejpam-670	26	19	is	be	AUX
ejpam-670	26	20	euler	euler	NOUN
ejpam-670	26	21	constant	constant	ADJ
ejpam-670	26	22	.	.	PUNCT
ejpam-670	27	1	in	in	ADP
ejpam-670	27	2	particular	particular	ADJ
ejpam-670	27	3	,	,	PUNCT
ejpam-670	27	4	for	for	ADP
ejpam-670	27	5	p	p	NOUN
ejpam-670	27	6	=	=	NOUN
ejpam-670	27	7	q	q	NOUN
ejpam-670	27	8	=	=	SYM
ejpam-670	27	9	2	2	NUM
ejpam-670	27	10	,	,	PUNCT
ejpam-670	27	11	yang	yang	PROPN
ejpam-670	27	12	obtained	obtain	VERB
ejpam-670	27	13	again	again	ADV
ejpam-670	27	14	a	a	DET
ejpam-670	27	15	strengthened	strengthened	NOUN
ejpam-670	27	16	of	of	ADP
ejpam-670	27	17	inequality	inequality	NOUN
ejpam-670	27	18	(	(	PUNCT
ejpam-670	27	19	3	3	NUM
ejpam-670	27	20	):	):	PUNCT
ejpam-670	27	21	∞	∞	PROPN
ejpam-670	27	22	∑	∑	PROPN
ejpam-670	27	23	n=0	n=0	NUM
ejpam-670	28	1	∞	∞	PROPN
ejpam-670	28	2	∑	∑	PROPN
ejpam-670	28	3	m=0	m=0	PROPN
ejpam-670	28	4	am	be	AUX
ejpam-670	28	5	bn	bn	NUM
ejpam-670	28	6	m+	m+	NUM
ejpam-670	28	7	n+	n+	ADP
ejpam-670	28	8	1	1	NUM
ejpam-670	28	9	<	<	X
ejpam-670	28	10	{	{	PUNCT
ejpam-670	28	11	∞	∞	PROPN
ejpam-670	28	12	∑	∑	PUNCT
ejpam-670	28	13	n=0	n=0	PUNCT
ejpam-670	29	1	[	[	X
ejpam-670	29	2	π−	π−	ADV
ejpam-670	29	3	ln2−	ln2−	PROPN
ejpam-670	29	4	c	c	NOUN
ejpam-670	29	5	(	(	PUNCT
ejpam-670	29	6	2n+	2n+	NUM
ejpam-670	29	7	1	1	NUM
ejpam-670	29	8	)	)	PUNCT
ejpam-670	29	9	3	3	NUM
ejpam-670	29	10	2	2	NUM
ejpam-670	29	11	]	]	SYM
ejpam-670	29	12	a2	a2	PROPN
ejpam-670	29	13	n	n	CCONJ
ejpam-670	29	14	}	}	SYM
ejpam-670	29	15	1	1	NUM
ejpam-670	29	16	2	2	NUM
ejpam-670	29	17	·	·	PUNCT
ejpam-670	29	18	{	{	PUNCT
ejpam-670	29	19	∞	∞	PROPN
ejpam-670	29	20	∑	∑	PUNCT
ejpam-670	29	21	n=0	n=0	PUNCT
ejpam-670	30	1	[	[	X
ejpam-670	30	2	π−	π−	ADV
ejpam-670	30	3	ln2−	ln2−	PROPN
ejpam-670	30	4	c	c	NOUN
ejpam-670	30	5	(	(	PUNCT
ejpam-670	30	6	2n+	2n+	NUM
ejpam-670	30	7	1	1	NUM
ejpam-670	30	8	)	)	PUNCT
ejpam-670	30	9	3	3	NUM
ejpam-670	30	10	2	2	NUM
ejpam-670	30	11	]	]	PUNCT
ejpam-670	30	12	b2	b2	NOUN
ejpam-670	30	13	n	n	CCONJ
ejpam-670	30	14	}	}	SYM
ejpam-670	30	15	1	1	NUM
ejpam-670	30	16	2	2	NUM
ejpam-670	30	17	.	.	PUNCT
ejpam-670	31	1	(	(	PUNCT
ejpam-670	31	2	5	5	NUM
ejpam-670	31	3	)	)	PUNCT
ejpam-670	31	4	in	in	ADP
ejpam-670	31	5	this	this	DET
ejpam-670	31	6	paper	paper	NOUN
ejpam-670	31	7	,	,	PUNCT
ejpam-670	31	8	by	by	ADP
ejpam-670	31	9	establishing	establish	VERB
ejpam-670	31	10	the	the	DET
ejpam-670	31	11	inequality	inequality	NOUN
ejpam-670	31	12	of	of	ADP
ejpam-670	31	13	the	the	DET
ejpam-670	31	14	weight	weight	NOUN
ejpam-670	31	15	coefficient	coefficient	NOUN
ejpam-670	31	16	,	,	PUNCT
ejpam-670	31	17	we	we	PRON
ejpam-670	31	18	will	will	AUX
ejpam-670	31	19	obtain	obtain	VERB
ejpam-670	31	20	a	a	DET
ejpam-670	31	21	strengthened	strengthen	VERB
ejpam-670	31	22	of	of	ADP
ejpam-670	31	23	inequalities	inequality	NOUN
ejpam-670	31	24	(	(	PUNCT
ejpam-670	31	25	3	3	NUM
ejpam-670	31	26	)	)	PUNCT
ejpam-670	31	27	,	,	PUNCT
ejpam-670	31	28	(	(	PUNCT
ejpam-670	31	29	4	4	NUM
ejpam-670	31	30	)	)	PUNCT
ejpam-670	31	31	and	and	CCONJ
ejpam-670	31	32	(	(	PUNCT
ejpam-670	31	33	5	5	NUM
ejpam-670	31	34	)	)	PUNCT
ejpam-670	31	35	.	.	PUNCT
ejpam-670	32	1	2	2	X
ejpam-670	32	2	.	.	X
ejpam-670	32	3	some	some	DET
ejpam-670	32	4	lemmas	lemmas	ADJ
ejpam-670	32	5	first	first	ADV
ejpam-670	32	6	of	of	ADP
ejpam-670	32	7	all	all	PRON
ejpam-670	32	8	,	,	PUNCT
ejpam-670	32	9	we	we	PRON
ejpam-670	32	10	give	give	VERB
ejpam-670	32	11	several	several	ADJ
ejpam-670	32	12	lemmas	lemma	NOUN
ejpam-670	32	13	which	which	PRON
ejpam-670	32	14	are	be	AUX
ejpam-670	32	15	to	to	PART
ejpam-670	32	16	be	be	AUX
ejpam-670	32	17	used	use	VERB
ejpam-670	32	18	later	later	ADV
ejpam-670	32	19	.	.	PUNCT
ejpam-670	33	1	lemma	lemma	PROPN
ejpam-670	33	2	1	1	X
ejpam-670	33	3	.	.	PUNCT
ejpam-670	34	1	let	let	VERB
ejpam-670	34	2	f	f	PROPN
ejpam-670	34	3	(	(	PUNCT
ejpam-670	34	4	2r)(x	2r)(x	NUM
ejpam-670	34	5	)	)	PUNCT
ejpam-670	34	6	>	>	X
ejpam-670	34	7	0	0	NUM
ejpam-670	34	8	,	,	PUNCT
ejpam-670	34	9	f	f	X
ejpam-670	34	10	(	(	PUNCT
ejpam-670	34	11	2r+1)(x	2r+1)(x	NUM
ejpam-670	34	12	)	)	PUNCT
ejpam-670	34	13	<	<	X
ejpam-670	34	14	0	0	NUM
ejpam-670	34	15	,	,	PUNCT
ejpam-670	34	16	x	x	SYM
ejpam-670	34	17	∈	∈	PROPN
ejpam-670	35	1	[	[	X
ejpam-670	35	2	0	0	NUM
ejpam-670	35	3	,	,	PUNCT
ejpam-670	35	4	∞	∞	PROPN
ejpam-670	35	5	)	)	PUNCT
ejpam-670	35	6	,	,	PUNCT
ejpam-670	35	7	f	f	PROPN
ejpam-670	35	8	(	(	PUNCT
ejpam-670	35	9	r)(∞	r)(∞	NOUN
ejpam-670	35	10	)	)	PUNCT
ejpam-670	35	11	=	=	SYM
ejpam-670	35	12	0	0	PUNCT
ejpam-670	36	1	(	(	PUNCT
ejpam-670	36	2	r	r	NOUN
ejpam-670	36	3	=	=	SYM
ejpam-670	36	4	0	0	NUM
ejpam-670	36	5	,	,	PUNCT
ejpam-670	36	6	1	1	NUM
ejpam-670	36	7	,	,	PUNCT
ejpam-670	36	8	2	2	NUM
ejpam-670	36	9	,	,	PUNCT
ejpam-670	36	10	3	3	NUM
ejpam-670	36	11	)	)	PUNCT
ejpam-670	36	12	,	,	PUNCT
ejpam-670	36	13	∫∞	∫∞	NOUN
ejpam-670	36	14	0	0	PUNCT
ejpam-670	36	15	f	f	PROPN
ejpam-670	36	16	(	(	PUNCT
ejpam-670	36	17	x)d	x)d	PUNCT
ejpam-670	36	18	x	x	PUNCT
ejpam-670	37	1	<	<	X
ejpam-670	37	2	∞.	∞.	PROPN
ejpam-670	37	3	then	then	ADV
ejpam-670	37	4	∞	∞	NUM
ejpam-670	37	5	∑	∑	PROPN
ejpam-670	37	6	m=0	m=0	PROPN
ejpam-670	37	7	f	f	PROPN
ejpam-670	37	8	(	(	PUNCT
ejpam-670	37	9	m	m	PROPN
ejpam-670	37	10	)	)	PUNCT
ejpam-670	37	11	<	<	X
ejpam-670	37	12	∫	∫	PROPN
ejpam-670	37	13	∞	∞	NUM
ejpam-670	37	14	0	0	NUM
ejpam-670	37	15	f	f	PROPN
ejpam-670	37	16	(	(	PUNCT
ejpam-670	37	17	x)d	x)d	PUNCT
ejpam-670	37	18	x	x	PUNCT
ejpam-670	37	19	+	+	PUNCT
ejpam-670	37	20	1	1	NUM
ejpam-670	37	21	2	2	NUM
ejpam-670	37	22	f	f	NOUN
ejpam-670	37	23	(	(	PUNCT
ejpam-670	37	24	0)−	0)−	NOUN
ejpam-670	37	25	1	1	NUM
ejpam-670	37	26	12	12	NUM
ejpam-670	37	27	f	f	PROPN
ejpam-670	37	28	′(0	′(0	NOUN
ejpam-670	37	29	)	)	PUNCT
ejpam-670	37	30	.	.	PUNCT
ejpam-670	38	1	(	(	PUNCT
ejpam-670	38	2	6	6	X
ejpam-670	38	3	)	)	PUNCT
ejpam-670	38	4	proof	proof	NOUN
ejpam-670	38	5	.	.	PUNCT
ejpam-670	39	1	see	see	VERB
ejpam-670	39	2	[	[	X
ejpam-670	39	3	4	4	X
ejpam-670	39	4	]	]	PUNCT
ejpam-670	39	5	or	or	CCONJ
ejpam-670	39	6	[	[	X
ejpam-670	39	7	5	5	NUM
ejpam-670	39	8	]	]	PUNCT
ejpam-670	39	9	.	.	PUNCT
ejpam-670	40	1	g.	g.	NOUN
ejpam-670	40	2	xi	xi	PROPN
ejpam-670	40	3	/	/	SYM
ejpam-670	40	4	eur	eur	PROPN
ejpam-670	40	5	.	.	PUNCT
ejpam-670	41	1	j.	j.	PROPN
ejpam-670	41	2	pure	pure	PROPN
ejpam-670	41	3	appl	appl	PROPN
ejpam-670	41	4	.	.	PROPN
ejpam-670	41	5	math	math	PROPN
ejpam-670	41	6	,	,	PUNCT
ejpam-670	41	7	4	4	NUM
ejpam-670	41	8	(	(	PUNCT
ejpam-670	41	9	2011	2011	NUM
ejpam-670	41	10	)	)	PUNCT
ejpam-670	41	11	,	,	PUNCT
ejpam-670	41	12	83	83	NUM
ejpam-670	41	13	-	-	SYM
ejpam-670	41	14	88	88	NUM
ejpam-670	41	15	85	85	NUM
ejpam-670	41	16	lemma	lemma	PROPN
ejpam-670	41	17	2	2	NUM
ejpam-670	41	18	.	.	X
ejpam-670	42	1	we	we	PRON
ejpam-670	42	2	have	have	VERB
ejpam-670	42	3	ω(n	ω(n	NUM
ejpam-670	42	4	)	)	PUNCT
ejpam-670	42	5	=	=	SYM
ejpam-670	43	1	∞	∞	NUM
ejpam-670	43	2	∑	∑	PUNCT
ejpam-670	43	3	m=0	m=0	PROPN
ejpam-670	43	4	1	1	NUM
ejpam-670	43	5	m+	m+	NUM
ejpam-670	43	6	n+	n+	NUM
ejpam-670	43	7	1	1	NUM
ejpam-670	43	8	(	(	PUNCT
ejpam-670	43	9	2n+	2n+	NUM
ejpam-670	43	10	1	1	NUM
ejpam-670	43	11	2m+	2m+	NUM
ejpam-670	43	12	1	1	NUM
ejpam-670	43	13	)	)	PUNCT
ejpam-670	43	14	1	1	NUM
ejpam-670	43	15	2	2	NUM
ejpam-670	43	16	<	<	X
ejpam-670	43	17	π−	π−	PROPN
ejpam-670	43	18	1p	1p	NUM
ejpam-670	43	19	2n+	2n+	NUM
ejpam-670	43	20	1	1	NUM
ejpam-670	43	21	[	[	PUNCT
ejpam-670	43	22	5	5	NUM
ejpam-670	43	23	6	6	NUM
ejpam-670	43	24	+	+	CCONJ
ejpam-670	43	25	1	1	NUM
ejpam-670	43	26	6(2n+	6(2n+	NUM
ejpam-670	43	27	1	1	NUM
ejpam-670	43	28	)	)	PUNCT
ejpam-670	43	29	−	−	PROPN
ejpam-670	43	30	2	2	NUM
ejpam-670	43	31	(	(	PUNCT
ejpam-670	43	32	2n+	2n+	NUM
ejpam-670	43	33	1)2	1)2	NUM
ejpam-670	43	34	]	]	PUNCT
ejpam-670	43	35	,	,	PUNCT
ejpam-670	43	36	(	(	PUNCT
ejpam-670	43	37	7	7	X
ejpam-670	43	38	)	)	PUNCT
ejpam-670	43	39	where	where	SCONJ
ejpam-670	43	40	n	n	NUM
ejpam-670	43	41	∈	∈	PROPN
ejpam-670	43	42	n.	n.	NOUN
ejpam-670	43	43	proof	proof	NOUN
ejpam-670	43	44	.	.	PUNCT
ejpam-670	44	1	let	let	VERB
ejpam-670	44	2	fn(x	fn(x	PRON
ejpam-670	44	3	)	)	PUNCT
ejpam-670	44	4	=	=	SYM
ejpam-670	44	5	1	1	NUM
ejpam-670	44	6	(	(	PUNCT
ejpam-670	44	7	x+n+1	x+n+1	PROPN
ejpam-670	44	8	)	)	PUNCT
ejpam-670	44	9	(	(	PUNCT
ejpam-670	44	10	2n+1	2n+1	PROPN
ejpam-670	44	11	2x+1	2x+1	PROPN
ejpam-670	44	12	)	)	PUNCT
ejpam-670	44	13	1	1	NUM
ejpam-670	44	14	2	2	NUM
ejpam-670	44	15	,	,	PUNCT
ejpam-670	44	16	x	x	PUNCT
ejpam-670	44	17	∈	∈	PROPN
ejpam-670	45	1	[	[	X
ejpam-670	45	2	0,∞	0,∞	NOUN
ejpam-670	45	3	)	)	PUNCT
ejpam-670	45	4	,	,	PUNCT
ejpam-670	45	5	then	then	ADV
ejpam-670	45	6	fn(0	fn(0	NOUN
ejpam-670	45	7	)	)	PUNCT
ejpam-670	45	8	=	=	PUNCT
ejpam-670	46	1	p	p	NOUN
ejpam-670	46	2	2n+	2n+	NUM
ejpam-670	46	3	1	1	NUM
ejpam-670	46	4	n+	n+	ADP
ejpam-670	46	5	1	1	NUM
ejpam-670	46	6	.	.	PUNCT
ejpam-670	47	1	f	f	PROPN
ejpam-670	47	2	′n(x	′n(x	PROPN
ejpam-670	47	3	)	)	PUNCT
ejpam-670	47	4	=	=	SYM
ejpam-670	48	1	p	p	NOUN
ejpam-670	48	2	2n+	2n+	NUM
ejpam-670	48	3	1[−	1[−	NOUN
ejpam-670	48	4	1	1	NUM
ejpam-670	48	5	(	(	PUNCT
ejpam-670	48	6	x	x	SYM
ejpam-670	48	7	+	+	X
ejpam-670	48	8	n+	n+	NUM
ejpam-670	48	9	1	1	NUM
ejpam-670	48	10	)	)	PUNCT
ejpam-670	48	11	·	·	PUNCT
ejpam-670	48	12	(	(	PUNCT
ejpam-670	48	13	2x	2x	NUM
ejpam-670	48	14	+	+	CCONJ
ejpam-670	48	15	1	1	X
ejpam-670	48	16	)	)	PUNCT
ejpam-670	48	17	3	3	NUM
ejpam-670	48	18	2	2	NUM
ejpam-670	48	19	−	−	NOUN
ejpam-670	48	20	1	1	NUM
ejpam-670	48	21	(	(	PUNCT
ejpam-670	48	22	x	x	PROPN
ejpam-670	48	23	+	+	X
ejpam-670	48	24	n+	n+	NUM
ejpam-670	48	25	1)2	1)2	NUM
ejpam-670	48	26	·	·	PUNCT
ejpam-670	48	27	(	(	PUNCT
ejpam-670	48	28	2x	2x	NUM
ejpam-670	48	29	+	+	CCONJ
ejpam-670	48	30	1	1	X
ejpam-670	48	31	)	)	PUNCT
ejpam-670	48	32	1	1	NUM
ejpam-670	48	33	2	2	NUM
ejpam-670	48	34	]	]	PUNCT
ejpam-670	48	35	.	.	PUNCT
ejpam-670	49	1	f	f	PROPN
ejpam-670	49	2	′n(0	′n(0	PROPN
ejpam-670	49	3	)	)	PUNCT
ejpam-670	49	4	=	=	PUNCT
ejpam-670	50	1	p	p	NOUN
ejpam-670	50	2	2n+	2n+	NUM
ejpam-670	50	3	1[−	1[−	NOUN
ejpam-670	50	4	1	1	NUM
ejpam-670	50	5	n+	n+	ADP
ejpam-670	50	6	1	1	NUM
ejpam-670	50	7	−	−	NOUN
ejpam-670	50	8	1	1	NUM
ejpam-670	50	9	(	(	PUNCT
ejpam-670	50	10	n+	n+	NUM
ejpam-670	50	11	1)2	1)2	NUM
ejpam-670	50	12	]	]	PUNCT
ejpam-670	50	13	.	.	PUNCT
ejpam-670	51	1	∫	∫	PROPN
ejpam-670	52	1	∞	∞	PROPN
ejpam-670	52	2	0	0	PUNCT
ejpam-670	53	1	fn(x)d	fn(x)d	PROPN
ejpam-670	53	2	x	x	SYM
ejpam-670	53	3	=	=	SYM
ejpam-670	53	4	∫	∫	PROPN
ejpam-670	53	5	∞	∞	NUM
ejpam-670	53	6	1	1	NUM
ejpam-670	53	7	2n+1	2n+1	PROPN
ejpam-670	53	8	1	1	NUM
ejpam-670	53	9	(	(	PUNCT
ejpam-670	53	10	y	y	PROPN
ejpam-670	53	11	+	+	NUM
ejpam-670	53	12	1)y	1)y	NUM
ejpam-670	53	13	1	1	NUM
ejpam-670	53	14	2	2	NUM
ejpam-670	53	15	d	d	SYM
ejpam-670	53	16	y	y	PROPN
ejpam-670	53	17	=	=	SYM
ejpam-670	53	18	∫	∫	PROPN
ejpam-670	53	19	∞	∞	NUM
ejpam-670	53	20	0	0	NUM
ejpam-670	53	21	1	1	NUM
ejpam-670	53	22	(	(	PUNCT
ejpam-670	53	23	y	y	PROPN
ejpam-670	53	24	+	+	NUM
ejpam-670	53	25	1)y	1)y	NUM
ejpam-670	53	26	1	1	NUM
ejpam-670	53	27	2	2	NUM
ejpam-670	53	28	d	d	SYM
ejpam-670	53	29	y	y	PROPN
ejpam-670	53	30	−	−	PROPN
ejpam-670	53	31	∫	∫	PROPN
ejpam-670	53	32	1	1	NUM
ejpam-670	53	33	2n+1	2n+1	PROPN
ejpam-670	53	34	0	0	NUM
ejpam-670	53	35	1	1	NUM
ejpam-670	53	36	(	(	PUNCT
ejpam-670	53	37	y	y	PROPN
ejpam-670	53	38	+	+	NUM
ejpam-670	53	39	1)y	1)y	NUM
ejpam-670	53	40	1	1	NUM
ejpam-670	53	41	2	2	NUM
ejpam-670	53	42	d	d	SYM
ejpam-670	53	43	y	y	NOUN
ejpam-670	53	44	=	=	SYM
ejpam-670	54	1	π−	π−	NOUN
ejpam-670	54	2	2	2	NUM
ejpam-670	54	3	∫	∫	NOUN
ejpam-670	54	4	1	1	NUM
ejpam-670	54	5	2n+1	2n+1	PROPN
ejpam-670	54	6	0	0	NUM
ejpam-670	54	7	1	1	NUM
ejpam-670	54	8	y	y	NOUN
ejpam-670	54	9	+	+	CCONJ
ejpam-670	54	10	1	1	NUM
ejpam-670	54	11	d	d	SYM
ejpam-670	54	12	y	y	PROPN
ejpam-670	54	13	1	1	NUM
ejpam-670	54	14	2	2	NUM
ejpam-670	54	15	=	=	SYM
ejpam-670	54	16	π−	π−	NOUN
ejpam-670	54	17	2	2	NUM
ejpam-670	54	18	[	[	PUNCT
ejpam-670	54	19	p	p	NOUN
ejpam-670	54	20	2n+	2n+	NUM
ejpam-670	54	21	1	1	NUM
ejpam-670	54	22	2(n+	2(n+	NOUN
ejpam-670	54	23	1	1	NUM
ejpam-670	54	24	)	)	PUNCT
ejpam-670	54	25	+	+	CCONJ
ejpam-670	54	26	2	2	NUM
ejpam-670	54	27	3	3	NUM
ejpam-670	54	28	∫	∫	PROPN
ejpam-670	54	29	1	1	NUM
ejpam-670	54	30	2n+1	2n+1	PROPN
ejpam-670	54	31	0	0	NUM
ejpam-670	54	32	1	1	NUM
ejpam-670	54	33	(	(	PUNCT
ejpam-670	54	34	y	y	PROPN
ejpam-670	54	35	+	+	PROPN
ejpam-670	55	1	1)2	1)2	NUM
ejpam-670	55	2	d	d	SYM
ejpam-670	55	3	y	y	PROPN
ejpam-670	55	4	3	3	NUM
ejpam-670	55	5	2	2	NUM
ejpam-670	55	6	]	]	PUNCT
ejpam-670	56	1	=	=	PUNCT
ejpam-670	56	2	π−	π−	NOUN
ejpam-670	56	3	2	2	NUM
ejpam-670	56	4	[	[	PUNCT
ejpam-670	56	5	p	p	NOUN
ejpam-670	56	6	2n+	2n+	NUM
ejpam-670	56	7	1	1	NUM
ejpam-670	56	8	2(n+	2(n+	NOUN
ejpam-670	56	9	1	1	NUM
ejpam-670	56	10	)	)	PUNCT
ejpam-670	56	11	+	+	CCONJ
ejpam-670	56	12	p	p	NOUN
ejpam-670	56	13	2n+	2n+	NUM
ejpam-670	56	14	1	1	NUM
ejpam-670	56	15	6(n+	6(n+	X
ejpam-670	56	16	1)2	1)2	NUM
ejpam-670	56	17	+	+	CCONJ
ejpam-670	56	18	4	4	NUM
ejpam-670	56	19	3	3	NUM
ejpam-670	56	20	∫	∫	PROPN
ejpam-670	56	21	1	1	NUM
ejpam-670	56	22	2n+1	2n+1	PROPN
ejpam-670	56	23	0	0	NUM
ejpam-670	56	24	1	1	NUM
ejpam-670	56	25	(	(	PUNCT
ejpam-670	56	26	y	y	PROPN
ejpam-670	56	27	+	+	PROPN
ejpam-670	56	28	1)3	1)3	PROPN
ejpam-670	56	29	d	d	SYM
ejpam-670	56	30	y	y	PROPN
ejpam-670	56	31	3	3	NUM
ejpam-670	56	32	2	2	NUM
ejpam-670	56	33	]	]	PUNCT
ejpam-670	56	34	<	<	X
ejpam-670	56	35	π−	π−	PROPN
ejpam-670	57	1	[	[	PUNCT
ejpam-670	57	2	p	p	NOUN
ejpam-670	57	3	2n+	2n+	NUM
ejpam-670	57	4	1	1	NUM
ejpam-670	57	5	(	(	PUNCT
ejpam-670	57	6	n+	n+	NOUN
ejpam-670	57	7	1	1	NUM
ejpam-670	57	8	)	)	PUNCT
ejpam-670	57	9	+	+	CCONJ
ejpam-670	57	10	p	p	NOUN
ejpam-670	57	11	2n+	2n+	NUM
ejpam-670	57	12	1	1	NUM
ejpam-670	57	13	3(n+	3(n+	NUM
ejpam-670	57	14	1)2	1)2	NUM
ejpam-670	57	15	]	]	PUNCT
ejpam-670	57	16	.	.	PUNCT
ejpam-670	58	1	if	if	SCONJ
ejpam-670	58	2	ω(n	ω(n	NUM
ejpam-670	58	3	)	)	PUNCT
ejpam-670	59	1	=	=	SYM
ejpam-670	60	1	∞	∞	NUM
ejpam-670	60	2	∑	∑	PUNCT
ejpam-670	60	3	m=0	m=0	PROPN
ejpam-670	60	4	1	1	NUM
ejpam-670	60	5	m+n+1	m+n+1	NOUN
ejpam-670	60	6	(	(	PUNCT
ejpam-670	60	7	2n+1	2n+1	PROPN
ejpam-670	60	8	2m+1	2m+1	PROPN
ejpam-670	60	9	)	)	PUNCT
ejpam-670	60	10	1	1	NUM
ejpam-670	60	11	2	2	NUM
ejpam-670	60	12	,	,	PUNCT
ejpam-670	60	13	so	so	ADV
ejpam-670	60	14	ω(n	ω(n	NUM
ejpam-670	60	15	)	)	PUNCT
ejpam-670	60	16	=	=	SYM
ejpam-670	61	1	∞	∞	NUM
ejpam-670	61	2	∑	∑	PROPN
ejpam-670	61	3	m=0	m=0	PROPN
ejpam-670	61	4	fn(m	fn(m	PROPN
ejpam-670	61	5	)	)	PUNCT
ejpam-670	61	6	.	.	PUNCT
ejpam-670	62	1	by	by	ADP
ejpam-670	62	2	lemma	lemma	PROPN
ejpam-670	62	3	1	1	NUM
ejpam-670	62	4	,	,	PUNCT
ejpam-670	62	5	we	we	PRON
ejpam-670	62	6	have	have	VERB
ejpam-670	62	7	ω(n	ω(n	NUM
ejpam-670	62	8	)	)	PUNCT
ejpam-670	62	9	=	=	SYM
ejpam-670	63	1	∞	∞	NUM
ejpam-670	63	2	∑	∑	PROPN
ejpam-670	63	3	m=0	m=0	PROPN
ejpam-670	63	4	fn(m	fn(m	PROPN
ejpam-670	63	5	)	)	PUNCT
ejpam-670	63	6	<	<	X
ejpam-670	63	7	∫	∫	PROPN
ejpam-670	63	8	∞	∞	NOUN
ejpam-670	63	9	0	0	PUNCT
ejpam-670	64	1	fn(x)d	fn(x)d	PROPN
ejpam-670	64	2	x	x	PUNCT
ejpam-670	65	1	+	+	NOUN
ejpam-670	65	2	1	1	NUM
ejpam-670	65	3	2	2	NUM
ejpam-670	65	4	fn(0)−	fn(0)−	NOUN
ejpam-670	65	5	1	1	NUM
ejpam-670	65	6	12	12	NUM
ejpam-670	65	7	f	f	PROPN
ejpam-670	65	8	′n(0	′n(0	PROPN
ejpam-670	65	9	)	)	PUNCT
ejpam-670	65	10	g.	g.	PROPN
ejpam-670	65	11	xi	xi	INTJ
ejpam-670	65	12	/	/	SYM
ejpam-670	65	13	eur	eur	PROPN
ejpam-670	65	14	.	.	PUNCT
ejpam-670	66	1	j.	j.	PROPN
ejpam-670	66	2	pure	pure	PROPN
ejpam-670	66	3	appl	appl	PROPN
ejpam-670	66	4	.	.	PROPN
ejpam-670	66	5	math	math	PROPN
ejpam-670	66	6	,	,	PUNCT
ejpam-670	66	7	4	4	NUM
ejpam-670	66	8	(	(	PUNCT
ejpam-670	66	9	2011	2011	NUM
ejpam-670	66	10	)	)	PUNCT
ejpam-670	66	11	,	,	PUNCT
ejpam-670	66	12	83	83	NUM
ejpam-670	66	13	-	-	SYM
ejpam-670	66	14	88	88	NUM
ejpam-670	66	15	86	86	NUM
ejpam-670	66	16	<	<	X
ejpam-670	66	17	π−	π−	PROPN
ejpam-670	66	18	[	[	PUNCT
ejpam-670	66	19	p	p	NOUN
ejpam-670	66	20	2n+	2n+	NUM
ejpam-670	66	21	1	1	NUM
ejpam-670	66	22	(	(	PUNCT
ejpam-670	66	23	n+	n+	NOUN
ejpam-670	66	24	1	1	NUM
ejpam-670	66	25	)	)	PUNCT
ejpam-670	66	26	+	+	CCONJ
ejpam-670	67	1	p	p	NOUN
ejpam-670	67	2	2n+	2n+	NUM
ejpam-670	67	3	1	1	NUM
ejpam-670	67	4	3(n+	3(n+	NUM
ejpam-670	67	5	1)2	1)2	NUM
ejpam-670	67	6	]	]	PUNCT
ejpam-670	68	1	+	+	CCONJ
ejpam-670	68	2	p	p	X
ejpam-670	68	3	2n+	2n+	NUM
ejpam-670	68	4	1	1	NUM
ejpam-670	68	5	2(n+	2(n+	NOUN
ejpam-670	68	6	1	1	NUM
ejpam-670	68	7	)	)	PUNCT
ejpam-670	68	8	+	+	CCONJ
ejpam-670	68	9	p	p	NOUN
ejpam-670	68	10	2n+	2n+	NUM
ejpam-670	68	11	1	1	NUM
ejpam-670	68	12	12	12	NUM
ejpam-670	68	13	[	[	PUNCT
ejpam-670	68	14	1	1	NUM
ejpam-670	68	15	n+	n+	SYM
ejpam-670	68	16	1	1	NUM
ejpam-670	68	17	+	+	NUM
ejpam-670	68	18	1	1	NUM
ejpam-670	68	19	(	(	PUNCT
ejpam-670	68	20	n+	n+	NUM
ejpam-670	68	21	1)2	1)2	NUM
ejpam-670	68	22	]	]	PUNCT
ejpam-670	69	1	<	<	X
ejpam-670	69	2	π−	π−	PROPN
ejpam-670	69	3	p	p	X
ejpam-670	69	4	2n+	2n+	NUM
ejpam-670	69	5	1	1	NUM
ejpam-670	69	6	[	[	PUNCT
ejpam-670	69	7	5	5	NUM
ejpam-670	69	8	12(n+	12(n+	NUM
ejpam-670	69	9	1	1	NUM
ejpam-670	69	10	)	)	PUNCT
ejpam-670	69	11	+	+	CCONJ
ejpam-670	69	12	1	1	NUM
ejpam-670	69	13	4(n+	4(n+	NUM
ejpam-670	69	14	1)2	1)2	NUM
ejpam-670	69	15	]	]	PUNCT
ejpam-670	70	1	<	<	X
ejpam-670	70	2	π−	π−	PROPN
ejpam-670	70	3	1p	1p	NUM
ejpam-670	70	4	2n+	2n+	NUM
ejpam-670	70	5	1	1	NUM
ejpam-670	70	6	[	[	PUNCT
ejpam-670	70	7	5(2n+	5(2n+	NUM
ejpam-670	70	8	1	1	NUM
ejpam-670	70	9	)	)	PUNCT
ejpam-670	70	10	12(n+	12(n+	NUM
ejpam-670	70	11	1	1	NUM
ejpam-670	70	12	)	)	PUNCT
ejpam-670	70	13	+	+	CCONJ
ejpam-670	71	1	2n+	2n+	NUM
ejpam-670	71	2	1	1	NUM
ejpam-670	71	3	4(n+	4(n+	PROPN
ejpam-670	71	4	1)2	1)2	NUM
ejpam-670	71	5	]	]	PUNCT
ejpam-670	71	6	.	.	PUNCT
ejpam-670	72	1	for	for	ADP
ejpam-670	72	2	n	n	PRON
ejpam-670	72	3	∈	∈	PROPN
ejpam-670	72	4	n	n	NOUN
ejpam-670	72	5	,	,	PUNCT
ejpam-670	72	6	we	we	PRON
ejpam-670	72	7	have	have	VERB
ejpam-670	72	8	5(2n+	5(2n+	NUM
ejpam-670	72	9	1	1	NUM
ejpam-670	72	10	)	)	PUNCT
ejpam-670	72	11	12(n+	12(n+	NUM
ejpam-670	72	12	1	1	NUM
ejpam-670	72	13	)	)	PUNCT
ejpam-670	73	1	+	+	CCONJ
ejpam-670	73	2	2n+	2n+	NUM
ejpam-670	73	3	1	1	NUM
ejpam-670	73	4	4(n+	4(n+	NUM
ejpam-670	73	5	1)2	1)2	NUM
ejpam-670	73	6	=	=	SYM
ejpam-670	73	7	5	5	NUM
ejpam-670	73	8	6	6	NUM
ejpam-670	73	9	(	(	PUNCT
ejpam-670	73	10	1	1	NUM
ejpam-670	73	11	+	+	NUM
ejpam-670	73	12	1	1	NUM
ejpam-670	73	13	2n+	2n+	NUM
ejpam-670	73	14	1	1	NUM
ejpam-670	73	15	)	)	PUNCT
ejpam-670	73	16	−1	−1	NOUN
ejpam-670	73	17	+	+	SYM
ejpam-670	73	18	1	1	NUM
ejpam-670	73	19	2n+	2n+	NUM
ejpam-670	73	20	1	1	NUM
ejpam-670	73	21	(	(	PUNCT
ejpam-670	73	22	1	1	NUM
ejpam-670	73	23	+	+	NUM
ejpam-670	73	24	1	1	NUM
ejpam-670	73	25	2n+	2n+	NUM
ejpam-670	73	26	1	1	NUM
ejpam-670	73	27	)	)	PUNCT
ejpam-670	73	28	−2	−2	NOUN
ejpam-670	73	29	>	>	X
ejpam-670	73	30	5	5	NUM
ejpam-670	73	31	6	6	NUM
ejpam-670	73	32	(	(	PUNCT
ejpam-670	73	33	1−	1−	NUM
ejpam-670	73	34	1	1	NUM
ejpam-670	73	35	2n+	2n+	NUM
ejpam-670	73	36	1	1	NUM
ejpam-670	73	37	)	)	PUNCT
ejpam-670	73	38	+	+	CCONJ
ejpam-670	73	39	1	1	NUM
ejpam-670	73	40	2n+	2n+	NUM
ejpam-670	73	41	1	1	NUM
ejpam-670	73	42	(	(	PUNCT
ejpam-670	73	43	1−	1−	NUM
ejpam-670	73	44	2	2	NUM
ejpam-670	73	45	2n+	2n+	NUM
ejpam-670	73	46	1	1	NUM
ejpam-670	73	47	)	)	PUNCT
ejpam-670	73	48	>	>	X
ejpam-670	73	49	5	5	NUM
ejpam-670	73	50	6	6	NUM
ejpam-670	73	51	+	+	CCONJ
ejpam-670	73	52	1	1	NUM
ejpam-670	73	53	6(2n+	6(2n+	NUM
ejpam-670	73	54	1	1	NUM
ejpam-670	73	55	)	)	PUNCT
ejpam-670	73	56	−	−	PROPN
ejpam-670	73	57	2	2	NUM
ejpam-670	73	58	(	(	PUNCT
ejpam-670	73	59	2n+	2n+	NUM
ejpam-670	73	60	1)2	1)2	NUM
ejpam-670	73	61	.	.	PUNCT
ejpam-670	74	1	the	the	DET
ejpam-670	74	2	proof	proof	NOUN
ejpam-670	74	3	of	of	ADP
ejpam-670	74	4	the	the	DET
ejpam-670	74	5	lemma	lemma	PROPN
ejpam-670	74	6	is	be	AUX
ejpam-670	74	7	completed	complete	VERB
ejpam-670	74	8	.	.	PUNCT
ejpam-670	75	1	lemma	lemma	PROPN
ejpam-670	75	2	3	3	X
ejpam-670	75	3	.	.	X
ejpam-670	76	1	we	we	PRON
ejpam-670	76	2	have	have	VERB
ejpam-670	76	3	ω(n	ω(n	NUM
ejpam-670	76	4	)	)	PUNCT
ejpam-670	76	5	=	=	SYM
ejpam-670	77	1	∞	∞	NUM
ejpam-670	77	2	∑	∑	PUNCT
ejpam-670	77	3	m=0	m=0	PROPN
ejpam-670	77	4	1	1	NUM
ejpam-670	77	5	m+	m+	NUM
ejpam-670	77	6	n+	n+	NUM
ejpam-670	77	7	1	1	NUM
ejpam-670	77	8	(	(	PUNCT
ejpam-670	77	9	2n+	2n+	NUM
ejpam-670	77	10	1	1	NUM
ejpam-670	77	11	2m+	2m+	NUM
ejpam-670	77	12	1	1	NUM
ejpam-670	77	13	)	)	PUNCT
ejpam-670	77	14	1	1	NUM
ejpam-670	77	15	2	2	NUM
ejpam-670	77	16	<	<	X
ejpam-670	77	17	π−	π−	PROPN
ejpam-670	77	18	5	5	NUM
ejpam-670	77	19	6	6	NUM
ejpam-670	77	20	(	(	PUNCT
ejpam-670	77	21	p	p	NOUN
ejpam-670	77	22	2n+	2n+	NUM
ejpam-670	77	23	1	1	NUM
ejpam-670	77	24	+	+	NUM
ejpam-670	77	25	3	3	NUM
ejpam-670	77	26	4	4	NUM
ejpam-670	77	27	p	p	NOUN
ejpam-670	77	28	(	(	PUNCT
ejpam-670	77	29	2n+	2n+	NUM
ejpam-670	77	30	1)−1	1)−1	NUM
ejpam-670	77	31	)	)	PUNCT
ejpam-670	77	32	,	,	PUNCT
ejpam-670	77	33	(	(	PUNCT
ejpam-670	77	34	8)	8)	NUM
ejpam-670	77	35	where	where	SCONJ
ejpam-670	77	36	n	n	PRON
ejpam-670	77	37	∈	∈	PROPN
ejpam-670	77	38	n.	n.	NOUN
ejpam-670	77	39	proof	proof	NOUN
ejpam-670	77	40	.	.	PUNCT
ejpam-670	78	1	since	since	SCONJ
ejpam-670	78	2	[	[	PUNCT
ejpam-670	78	3	5	5	NUM
ejpam-670	78	4	6	6	NUM
ejpam-670	78	5	+	+	CCONJ
ejpam-670	78	6	1	1	NUM
ejpam-670	78	7	6(2n+	6(2n+	NUM
ejpam-670	78	8	1	1	NUM
ejpam-670	78	9	)	)	PUNCT
ejpam-670	78	10	−	−	PROPN
ejpam-670	78	11	2	2	NUM
ejpam-670	78	12	(	(	PUNCT
ejpam-670	78	13	2n+	2n+	NUM
ejpam-670	78	14	1)2	1)2	NUM
ejpam-670	78	15	]	]	PUNCT
ejpam-670	78	16	(	(	PUNCT
ejpam-670	78	17	1	1	NUM
ejpam-670	78	18	+	+	NUM
ejpam-670	78	19	a	a	DET
ejpam-670	78	20	2n+	2n+	NUM
ejpam-670	78	21	1	1	NUM
ejpam-670	78	22	)	)	PUNCT
ejpam-670	78	23	=	=	SYM
ejpam-670	78	24	5	5	NUM
ejpam-670	78	25	6	6	NUM
ejpam-670	78	26	+	+	SYM
ejpam-670	78	27	1	1	NUM
ejpam-670	78	28	2n+	2n+	NUM
ejpam-670	78	29	1	1	NUM
ejpam-670	78	30	[	[	PUNCT
ejpam-670	78	31	5a+	5a+	NUM
ejpam-670	78	32	1	1	NUM
ejpam-670	78	33	6	6	NUM
ejpam-670	78	34	−	−	NOUN
ejpam-670	78	35	12−	12−	PRON
ejpam-670	78	36	a	a	DET
ejpam-670	78	37	6(2n+	6(2n+	NUM
ejpam-670	78	38	1	1	NUM
ejpam-670	78	39	)	)	PUNCT
ejpam-670	78	40	−	−	PROPN
ejpam-670	78	41	2a	2a	NUM
ejpam-670	78	42	(	(	PUNCT
ejpam-670	78	43	2n+	2n+	NUM
ejpam-670	78	44	1)2	1)2	NUM
ejpam-670	78	45	]	]	PUNCT
ejpam-670	78	46	=	=	SYM
ejpam-670	78	47	5	5	NUM
ejpam-670	78	48	6	6	NUM
ejpam-670	78	49	+	+	SYM
ejpam-670	78	50	1	1	NUM
ejpam-670	78	51	2n+	2n+	NUM
ejpam-670	78	52	1	1	NUM
ejpam-670	78	53	·	·	PUNCT
ejpam-670	78	54	(	(	PUNCT
ejpam-670	78	55	5a+	5a+	NUM
ejpam-670	78	56	1)(2n+	1)(2n+	NUM
ejpam-670	78	57	1)2−	1)2−	NUM
ejpam-670	78	58	(	(	PUNCT
ejpam-670	78	59	12−	12−	NUM
ejpam-670	78	60	a)(2n+	a)(2n+	PROPN
ejpam-670	78	61	1)−	1)−	PROPN
ejpam-670	78	62	12a	12a	NOUN
ejpam-670	78	63	6(2n+	6(2n+	NUM
ejpam-670	78	64	1)2	1)2	NUM
ejpam-670	78	65	.	.	PUNCT
ejpam-670	79	1	for	for	ADP
ejpam-670	79	2	n=	n=	ADJ
ejpam-670	79	3	1	1	NUM
ejpam-670	79	4	,	,	PUNCT
ejpam-670	79	5	a	a	DET
ejpam-670	79	6	≥	≥	NOUN
ejpam-670	79	7	3	3	NUM
ejpam-670	79	8	4	4	NUM
ejpam-670	79	9	,	,	PUNCT
ejpam-670	79	10	we	we	PRON
ejpam-670	79	11	have	have	VERB
ejpam-670	79	12	(	(	PUNCT
ejpam-670	79	13	5a+	5a+	NUM
ejpam-670	79	14	1)(2n+	1)(2n+	NUM
ejpam-670	80	1	1)2−	1)2−	NOUN
ejpam-670	80	2	(	(	PUNCT
ejpam-670	80	3	12−	12−	NUM
ejpam-670	80	4	a)(2n+	a)(2n+	PROPN
ejpam-670	80	5	1)−	1)−	PROPN
ejpam-670	80	6	12a	12a	NOUN
ejpam-670	80	7	6(2n+	6(2n+	NUM
ejpam-670	80	8	1)2	1)2	NUM
ejpam-670	80	9	=	=	SYM
ejpam-670	80	10	45a+	45a+	NUM
ejpam-670	80	11	9−	9−	NUM
ejpam-670	80	12	36	36	NUM
ejpam-670	80	13	+	+	SYM
ejpam-670	80	14	3a−	3a−	PROPN
ejpam-670	80	15	12a	12a	NOUN
ejpam-670	80	16	54	54	NUM
ejpam-670	80	17	=	=	SYM
ejpam-670	80	18	36a−	36a−	NUM
ejpam-670	80	19	27	27	NUM
ejpam-670	80	20	150	150	NUM
ejpam-670	80	21	≥	≥	NOUN
ejpam-670	80	22	0	0	NUM
ejpam-670	80	23	.	.	PUNCT
ejpam-670	81	1	then	then	ADV
ejpam-670	81	2	for	for	ADP
ejpam-670	81	3	n≥	n≥	PROPN
ejpam-670	81	4	1	1	NUM
ejpam-670	81	5	,	,	PUNCT
ejpam-670	81	6	n	n	PRON
ejpam-670	81	7	∈	∈	PROPN
ejpam-670	81	8	n	n	NOUN
ejpam-670	81	9	and	and	CCONJ
ejpam-670	81	10	a	a	DET
ejpam-670	81	11	≥	≥	NOUN
ejpam-670	81	12	3	3	NUM
ejpam-670	81	13	4	4	NUM
ejpam-670	81	14	,	,	PUNCT
ejpam-670	81	15	[	[	PUNCT
ejpam-670	81	16	5	5	NUM
ejpam-670	81	17	6	6	NUM
ejpam-670	81	18	+	+	CCONJ
ejpam-670	81	19	1	1	NUM
ejpam-670	81	20	6(2n+	6(2n+	NUM
ejpam-670	81	21	1	1	NUM
ejpam-670	81	22	)	)	PUNCT
ejpam-670	81	23	−	−	PROPN
ejpam-670	81	24	2	2	NUM
ejpam-670	81	25	(	(	PUNCT
ejpam-670	81	26	2n+	2n+	NUM
ejpam-670	81	27	1)2	1)2	NUM
ejpam-670	81	28	]	]	PUNCT
ejpam-670	81	29	(	(	PUNCT
ejpam-670	81	30	1	1	NUM
ejpam-670	81	31	+	+	NUM
ejpam-670	81	32	a	a	DET
ejpam-670	81	33	2n+	2n+	NUM
ejpam-670	81	34	1	1	NUM
ejpam-670	81	35	)	)	PUNCT
ejpam-670	81	36	>	>	X
ejpam-670	81	37	5	5	NUM
ejpam-670	81	38	6	6	NUM
ejpam-670	81	39	.	.	PUNCT
ejpam-670	82	1	g.	g.	NOUN
ejpam-670	82	2	xi	xi	PROPN
ejpam-670	82	3	/	/	SYM
ejpam-670	82	4	eur	eur	PROPN
ejpam-670	82	5	.	.	PUNCT
ejpam-670	83	1	j.	j.	PROPN
ejpam-670	83	2	pure	pure	PROPN
ejpam-670	83	3	appl	appl	PROPN
ejpam-670	83	4	.	.	PROPN
ejpam-670	83	5	math	math	PROPN
ejpam-670	83	6	,	,	PUNCT
ejpam-670	83	7	4	4	NUM
ejpam-670	83	8	(	(	PUNCT
ejpam-670	83	9	2011	2011	NUM
ejpam-670	83	10	)	)	PUNCT
ejpam-670	83	11	,	,	PUNCT
ejpam-670	83	12	83	83	NUM
ejpam-670	83	13	-	-	SYM
ejpam-670	83	14	88	88	NUM
ejpam-670	83	15	87	87	NUM
ejpam-670	83	16	for	for	ADP
ejpam-670	83	17	a	a	DET
ejpam-670	83	18	=	=	SYM
ejpam-670	83	19	3	3	NUM
ejpam-670	83	20	4	4	NUM
ejpam-670	83	21	,	,	PUNCT
ejpam-670	83	22	n=	n=	ADJ
ejpam-670	83	23	0	0	NUM
ejpam-670	83	24	,	,	PUNCT
ejpam-670	83	25	θ	θ	X
ejpam-670	84	1	=	=	PUNCT
ejpam-670	84	2	π−	π−	NOUN
ejpam-670	84	3	∞	∞	PROPN
ejpam-670	84	4	∑	∑	PROPN
ejpam-670	84	5	m=0	m=0	PROPN
ejpam-670	84	6	1	1	NUM
ejpam-670	84	7	(	(	PUNCT
ejpam-670	84	8	m+1	m+1	NUM
ejpam-670	84	9	)	)	PUNCT
ejpam-670	84	10	3	3	NUM
ejpam-670	84	11	2	2	NUM
ejpam-670	84	12	=	=	SYM
ejpam-670	84	13	0.5292496	0.5292496	NUM
ejpam-670	84	14	+	+	NOUN
ejpam-670	84	15	,	,	PUNCT
ejpam-670	84	16	we	we	PRON
ejpam-670	84	17	have	have	VERB
ejpam-670	84	18	θ	θ	PROPN
ejpam-670	84	19	(	(	PUNCT
ejpam-670	84	20	n+	n+	NOUN
ejpam-670	84	21	1	1	NUM
ejpam-670	84	22	)	)	PUNCT
ejpam-670	84	23	1	1	NUM
ejpam-670	84	24	2	2	NUM
ejpam-670	84	25	>	>	SYM
ejpam-670	84	26	5	5	NUM
ejpam-670	84	27	6	6	NUM
ejpam-670	84	28	(	(	PUNCT
ejpam-670	84	29	p	p	NOUN
ejpam-670	84	30	2n+	2n+	NUM
ejpam-670	84	31	1	1	NUM
ejpam-670	84	32	+	+	NUM
ejpam-670	84	33	3	3	NUM
ejpam-670	84	34	4	4	NUM
ejpam-670	84	35	p	p	NOUN
ejpam-670	84	36	(	(	PUNCT
ejpam-670	84	37	2n+	2n+	NUM
ejpam-670	84	38	1)−1	1)−1	NUM
ejpam-670	84	39	)	)	PUNCT
ejpam-670	84	40	,	,	PUNCT
ejpam-670	84	41	and	and	CCONJ
ejpam-670	84	42	π−	π−	PROPN
ejpam-670	84	43	θ	θ	PROPN
ejpam-670	84	44	(	(	PUNCT
ejpam-670	84	45	n+	n+	NOUN
ejpam-670	84	46	1	1	NUM
ejpam-670	84	47	)	)	PUNCT
ejpam-670	84	48	1	1	NUM
ejpam-670	84	49	2	2	NUM
ejpam-670	84	50	<	<	X
ejpam-670	84	51	π−	π−	PROPN
ejpam-670	84	52	5	5	NUM
ejpam-670	84	53	6	6	NUM
ejpam-670	84	54	(	(	PUNCT
ejpam-670	84	55	p	p	NOUN
ejpam-670	84	56	2n+	2n+	NUM
ejpam-670	84	57	1	1	NUM
ejpam-670	84	58	+	+	NUM
ejpam-670	84	59	3	3	NUM
ejpam-670	84	60	4	4	NUM
ejpam-670	84	61	p	p	NOUN
ejpam-670	84	62	(	(	PUNCT
ejpam-670	84	63	2n+	2n+	NUM
ejpam-670	84	64	1)−1	1)−1	NUM
ejpam-670	84	65	)	)	PUNCT
ejpam-670	84	66	.	.	PUNCT
ejpam-670	85	1	the	the	DET
ejpam-670	85	2	proof	proof	NOUN
ejpam-670	85	3	of	of	ADP
ejpam-670	85	4	the	the	DET
ejpam-670	85	5	lemma	lemma	PROPN
ejpam-670	85	6	is	be	AUX
ejpam-670	85	7	completed	complete	VERB
ejpam-670	85	8	.	.	PUNCT
ejpam-670	86	1	3	3	X
ejpam-670	86	2	.	.	X
ejpam-670	86	3	main	main	ADJ
ejpam-670	86	4	results	result	NOUN
ejpam-670	86	5	theorem	theorem	VERB
ejpam-670	86	6	1	1	X
ejpam-670	86	7	.	.	PUNCT
ejpam-670	87	1	let	let	VERB
ejpam-670	87	2	an	an	DET
ejpam-670	87	3	≥	≥	NOUN
ejpam-670	87	4	0	0	NUM
ejpam-670	87	5	,	,	PUNCT
ejpam-670	87	6	bn	bn	X
ejpam-670	87	7	≥	≥	NOUN
ejpam-670	87	8	0	0	NUM
ejpam-670	87	9	,	,	PUNCT
ejpam-670	87	10	and	and	CCONJ
ejpam-670	87	11	0	0	NUM
ejpam-670	87	12	<	<	X
ejpam-670	87	13	∞	∞	NUM
ejpam-670	87	14	∑	∑	PROPN
ejpam-670	87	15	n=1	n=1	PROPN
ejpam-670	87	16	a2	a2	PROPN
ejpam-670	87	17	n	n	CCONJ
ejpam-670	87	18	<	<	X
ejpam-670	87	19	∞	∞	PROPN
ejpam-670	87	20	,	,	PUNCT
ejpam-670	87	21	0	0	NUM
ejpam-670	87	22	<	<	X
ejpam-670	87	23	∞	∞	NUM
ejpam-670	87	24	∑	∑	PUNCT
ejpam-670	87	25	n=1	n=1	PROPN
ejpam-670	87	26	b2	b2	NOUN
ejpam-670	87	27	n	n	CCONJ
ejpam-670	87	28	<	<	X
ejpam-670	87	29	∞	∞	PROPN
ejpam-670	87	30	,	,	PUNCT
ejpam-670	87	31	then	then	ADV
ejpam-670	87	32	∞	∞	NUM
ejpam-670	87	33	∑	∑	PROPN
ejpam-670	87	34	n=0	n=0	PROPN
ejpam-670	87	35	∞	∞	PROPN
ejpam-670	87	36	∑	∑	PROPN
ejpam-670	88	1	m=0	m=0	PROPN
ejpam-670	88	2	ambn	ambn	PROPN
ejpam-670	88	3	m+	m+	NUM
ejpam-670	88	4	n+	n+	ADP
ejpam-670	88	5	1	1	NUM
ejpam-670	88	6	<	<	X
ejpam-670	88	7	{	{	PUNCT
ejpam-670	88	8	∞	∞	PROPN
ejpam-670	88	9	∑	∑	PUNCT
ejpam-670	88	10	n=0	n=0	PUNCT
ejpam-670	89	1	[	[	X
ejpam-670	89	2	π−	π−	NOUN
ejpam-670	89	3	5	5	NUM
ejpam-670	89	4	6	6	NUM
ejpam-670	89	5	(	(	PUNCT
ejpam-670	89	6	p	p	NOUN
ejpam-670	89	7	2n+	2n+	NUM
ejpam-670	89	8	1	1	NUM
ejpam-670	89	9	+	+	NUM
ejpam-670	89	10	3	3	NUM
ejpam-670	89	11	4	4	NUM
ejpam-670	89	12	p	p	NOUN
ejpam-670	89	13	(	(	PUNCT
ejpam-670	89	14	2n+	2n+	NUM
ejpam-670	89	15	1)−1	1)−1	NUM
ejpam-670	89	16	)	)	PUNCT
ejpam-670	89	17	]	]	PUNCT
ejpam-670	89	18	a2	a2	PROPN
ejpam-670	89	19	n	n	X
ejpam-670	89	20	·	·	PUNCT
ejpam-670	89	21	∞	∞	NUM
ejpam-670	89	22	∑	∑	PUNCT
ejpam-670	89	23	n=0	n=0	PUNCT
ejpam-670	90	1	[	[	X
ejpam-670	90	2	π−	π−	NOUN
ejpam-670	90	3	5	5	NUM
ejpam-670	90	4	6	6	NUM
ejpam-670	90	5	(	(	PUNCT
ejpam-670	90	6	p	p	NOUN
ejpam-670	90	7	2n+	2n+	NUM
ejpam-670	90	8	1	1	NUM
ejpam-670	90	9	+	+	NUM
ejpam-670	90	10	3	3	NUM
ejpam-670	90	11	4	4	NUM
ejpam-670	90	12	p	p	NOUN
ejpam-670	90	13	(	(	PUNCT
ejpam-670	90	14	2n+	2n+	NUM
ejpam-670	90	15	1)−1	1)−1	NUM
ejpam-670	90	16	)	)	PUNCT
ejpam-670	90	17	]	]	PUNCT
ejpam-670	90	18	b2	b2	NOUN
ejpam-670	90	19	n	n	CCONJ
ejpam-670	90	20	}	}	SYM
ejpam-670	90	21	1	1	NUM
ejpam-670	90	22	2	2	NUM
ejpam-670	90	23	,	,	PUNCT
ejpam-670	90	24	(	(	PUNCT
ejpam-670	90	25	9	9	NUM
ejpam-670	90	26	)	)	PUNCT
ejpam-670	90	27	and	and	CCONJ
ejpam-670	90	28	∞	∞	NUM
ejpam-670	90	29	∑	∑	PROPN
ejpam-670	90	30	n=0	n=0	NUM
ejpam-670	90	31	(	(	PUNCT
ejpam-670	90	32	∞	∞	PROPN
ejpam-670	90	33	∑	∑	PROPN
ejpam-670	90	34	m=0	m=0	PROPN
ejpam-670	90	35	am	be	AUX
ejpam-670	90	36	m+	m+	NUM
ejpam-670	90	37	n+	n+	ADP
ejpam-670	90	38	1	1	NUM
ejpam-670	90	39	)	)	SYM
ejpam-670	90	40	2	2	NUM
ejpam-670	90	41	<	<	X
ejpam-670	90	42	π	π	PROPN
ejpam-670	90	43	{	{	PUNCT
ejpam-670	90	44	∞	∞	PROPN
ejpam-670	90	45	∑	∑	PROPN
ejpam-670	90	46	n=0	n=0	PUNCT
ejpam-670	91	1	[	[	X
ejpam-670	91	2	π−	π−	NOUN
ejpam-670	91	3	5	5	NUM
ejpam-670	91	4	6	6	NUM
ejpam-670	91	5	(	(	PUNCT
ejpam-670	91	6	p	p	NOUN
ejpam-670	91	7	2n+	2n+	NUM
ejpam-670	91	8	1	1	NUM
ejpam-670	91	9	+	+	NUM
ejpam-670	91	10	3	3	NUM
ejpam-670	91	11	4	4	NUM
ejpam-670	91	12	p	p	NOUN
ejpam-670	91	13	(	(	PUNCT
ejpam-670	91	14	2n+	2n+	NUM
ejpam-670	91	15	1)−1	1)−1	NUM
ejpam-670	91	16	)	)	PUNCT
ejpam-670	91	17	]	]	PUNCT
ejpam-670	91	18	a2	a2	PROPN
ejpam-670	91	19	n.	n.	NOUN
ejpam-670	91	20	(	(	PUNCT
ejpam-670	91	21	10	10	NUM
ejpam-670	91	22	)	)	PUNCT
ejpam-670	91	23	proof	proof	NOUN
ejpam-670	91	24	.	.	PUNCT
ejpam-670	92	1	by	by	ADP
ejpam-670	92	2	cauchy	cauchy	PROPN
ejpam-670	92	3	’s	’s	PART
ejpam-670	92	4	inequality	inequality	NOUN
ejpam-670	92	5	,	,	PUNCT
ejpam-670	92	6	we	we	PRON
ejpam-670	92	7	have	have	VERB
ejpam-670	92	8	∞	∞	PROPN
ejpam-670	92	9	∑	∑	PROPN
ejpam-670	92	10	n=0	n=0	PROPN
ejpam-670	92	11	∞	∞	PROPN
ejpam-670	92	12	∑	∑	PROPN
ejpam-670	92	13	m=0	m=0	PROPN
ejpam-670	92	14	ambn	ambn	PROPN
ejpam-670	93	1	m+	m+	NUM
ejpam-670	93	2	n+	n+	NOUN
ejpam-670	93	3	1	1	NUM
ejpam-670	93	4	=	=	SYM
ejpam-670	93	5	∞	∞	NUM
ejpam-670	93	6	∑	∑	PUNCT
ejpam-670	93	7	n=0	n=0	NUM
ejpam-670	93	8	∞	∞	PROPN
ejpam-670	93	9	∑	∑	PROPN
ejpam-670	93	10	m=0	m=0	PROPN
ejpam-670	93	11	[	[	PUNCT
ejpam-670	93	12	am	be	AUX
ejpam-670	93	13	(	(	PUNCT
ejpam-670	93	14	m+	m+	NUM
ejpam-670	93	15	n+	n+	NOUN
ejpam-670	93	16	1	1	NUM
ejpam-670	93	17	)	)	PUNCT
ejpam-670	93	18	1	1	NUM
ejpam-670	93	19	2	2	NUM
ejpam-670	93	20	(	(	PUNCT
ejpam-670	93	21	2m+	2m+	NUM
ejpam-670	93	22	1	1	NUM
ejpam-670	93	23	2n+	2n+	NUM
ejpam-670	93	24	1	1	NUM
ejpam-670	93	25	)	)	PUNCT
ejpam-670	93	26	1	1	NUM
ejpam-670	93	27	4	4	NUM
ejpam-670	93	28	]	]	PUNCT
ejpam-670	93	29	·	·	PUNCT
ejpam-670	93	30	[	[	PUNCT
ejpam-670	93	31	bn	bn	INTJ
ejpam-670	93	32	(	(	PUNCT
ejpam-670	93	33	m+	m+	NUM
ejpam-670	93	34	n+	n+	NOUN
ejpam-670	93	35	1	1	NUM
ejpam-670	93	36	)	)	PUNCT
ejpam-670	93	37	1	1	NUM
ejpam-670	93	38	2	2	NUM
ejpam-670	93	39	(	(	PUNCT
ejpam-670	93	40	2n+	2n+	NUM
ejpam-670	93	41	1	1	NUM
ejpam-670	93	42	2m+	2m+	NUM
ejpam-670	93	43	1	1	NUM
ejpam-670	93	44	)	)	PUNCT
ejpam-670	93	45	1	1	NUM
ejpam-670	93	46	4	4	NUM
ejpam-670	93	47	]	]	PUNCT
ejpam-670	93	48	≤	≤	X
ejpam-670	93	49	{	{	PUNCT
ejpam-670	93	50	∞	∞	PROPN
ejpam-670	93	51	∑	∑	PROPN
ejpam-670	93	52	n=0	n=0	NUM
ejpam-670	93	53	∞	∞	PROPN
ejpam-670	93	54	∑	∑	PROPN
ejpam-670	93	55	m=0	m=0	PROPN
ejpam-670	93	56	[	[	PUNCT
ejpam-670	93	57	a2	a2	PROPN
ejpam-670	93	58	m	m	PROPN
ejpam-670	93	59	m+	m+	NUM
ejpam-670	93	60	n+	n+	ADP
ejpam-670	93	61	1	1	NUM
ejpam-670	93	62	(	(	PUNCT
ejpam-670	93	63	2m+	2m+	NUM
ejpam-670	93	64	1	1	NUM
ejpam-670	93	65	2n+	2n+	NUM
ejpam-670	93	66	1	1	NUM
ejpam-670	93	67	)	)	PUNCT
ejpam-670	93	68	1	1	NUM
ejpam-670	93	69	2	2	NUM
ejpam-670	93	70	]	]	PUNCT
ejpam-670	93	71	·	·	PUNCT
ejpam-670	93	72	∞	∞	NUM
ejpam-670	93	73	∑	∑	PUNCT
ejpam-670	93	74	n=0	n=0	NUM
ejpam-670	93	75	∞	∞	PROPN
ejpam-670	93	76	∑	∑	PROPN
ejpam-670	93	77	m=0	m=0	PROPN
ejpam-670	93	78	[	[	PUNCT
ejpam-670	93	79	b2	b2	NOUN
ejpam-670	93	80	n	n	CCONJ
ejpam-670	93	81	m+	m+	NUM
ejpam-670	93	82	n+	n+	ADP
ejpam-670	93	83	1	1	NUM
ejpam-670	93	84	(	(	PUNCT
ejpam-670	93	85	2n+	2n+	NUM
ejpam-670	93	86	1	1	NUM
ejpam-670	93	87	2m+	2m+	NUM
ejpam-670	93	88	1	1	NUM
ejpam-670	93	89	)	)	PUNCT
ejpam-670	93	90	1	1	NUM
ejpam-670	93	91	2	2	NUM
ejpam-670	93	92	]	]	PUNCT
ejpam-670	93	93	}	}	PUNCT
ejpam-670	93	94	1	1	NUM
ejpam-670	93	95	2	2	NUM
ejpam-670	93	96	=	=	SYM
ejpam-670	93	97	{	{	PUNCT
ejpam-670	93	98	∞	∞	PROPN
ejpam-670	93	99	∑	∑	PROPN
ejpam-670	93	100	m=0	m=0	PROPN
ejpam-670	93	101	[	[	PUNCT
ejpam-670	93	102	∞	∞	PROPN
ejpam-670	93	103	∑	∑	PROPN
ejpam-670	93	104	n=0	n=0	PROPN
ejpam-670	93	105	1	1	NUM
ejpam-670	93	106	m+	m+	NUM
ejpam-670	93	107	n+	n+	ADP
ejpam-670	93	108	1	1	NUM
ejpam-670	93	109	(	(	PUNCT
ejpam-670	93	110	2m+	2m+	NUM
ejpam-670	93	111	1	1	NUM
ejpam-670	93	112	2n+	2n+	NUM
ejpam-670	93	113	1	1	NUM
ejpam-670	93	114	)	)	PUNCT
ejpam-670	93	115	1	1	NUM
ejpam-670	93	116	2	2	NUM
ejpam-670	93	117	]	]	PUNCT
ejpam-670	93	118	a2	a2	PROPN
ejpam-670	93	119	m	m	PROPN
ejpam-670	93	120	·	·	PUNCT
ejpam-670	93	121	∞	∞	NUM
ejpam-670	93	122	∑	∑	PUNCT
ejpam-670	93	123	n=0	n=0	PUNCT
ejpam-670	93	124	[	[	PUNCT
ejpam-670	93	125	∞	∞	NUM
ejpam-670	93	126	∑	∑	PROPN
ejpam-670	93	127	m=0	m=0	PROPN
ejpam-670	93	128	1	1	NUM
ejpam-670	93	129	m+	m+	NUM
ejpam-670	93	130	n+	n+	NUM
ejpam-670	93	131	1	1	NUM
ejpam-670	93	132	(	(	PUNCT
ejpam-670	93	133	2n+	2n+	NUM
ejpam-670	93	134	1	1	NUM
ejpam-670	93	135	2m+	2m+	NUM
ejpam-670	93	136	1	1	NUM
ejpam-670	93	137	)	)	PUNCT
ejpam-670	93	138	1	1	NUM
ejpam-670	93	139	2	2	NUM
ejpam-670	93	140	]	]	PUNCT
ejpam-670	93	141	b2	b2	NOUN
ejpam-670	93	142	n	n	CCONJ
ejpam-670	93	143	}	}	SYM
ejpam-670	93	144	1	1	NUM
ejpam-670	93	145	2	2	NUM
ejpam-670	93	146	=	=	SYM
ejpam-670	93	147	{	{	PUNCT
ejpam-670	93	148	∞	∞	PROPN
ejpam-670	93	149	∑	∑	PROPN
ejpam-670	93	150	m=0	m=0	PROPN
ejpam-670	93	151	ω(m)a2	ω(m)a2	VERB
ejpam-670	93	152	m	m	NOUN
ejpam-670	93	153	∞	∞	NUM
ejpam-670	93	154	∑	∑	PROPN
ejpam-670	93	155	n=0	n=0	X
ejpam-670	93	156	ω(n)b2	ω(n)b2	NOUN
ejpam-670	93	157	n	n	CCONJ
ejpam-670	93	158	}	}	SYM
ejpam-670	93	159	1	1	NUM
ejpam-670	93	160	2	2	NUM
ejpam-670	93	161	.	.	PUNCT
ejpam-670	94	1	by	by	ADP
ejpam-670	94	2	lemma	lemma	PROPN
ejpam-670	94	3	3	3	NUM
ejpam-670	94	4	,	,	PUNCT
ejpam-670	94	5	we	we	PRON
ejpam-670	94	6	have	have	VERB
ejpam-670	94	7	inequality	inequality	NOUN
ejpam-670	94	8	(	(	PUNCT
ejpam-670	94	9	9	9	NUM
ejpam-670	94	10	)	)	PUNCT
ejpam-670	94	11	.	.	PUNCT
ejpam-670	95	1	references	reference	NOUN
ejpam-670	95	2	88	88	NUM
ejpam-670	95	3	let	let	VERB
ejpam-670	95	4	bn	bn	NOUN
ejpam-670	95	5	=	=	SYM
ejpam-670	96	1	∞	∞	NUM
ejpam-670	96	2	∑	∑	PUNCT
ejpam-670	96	3	m=0	m=0	PROPN
ejpam-670	96	4	am	be	AUX
ejpam-670	96	5	m+n+1	m+n+1	NOUN
ejpam-670	96	6	,	,	PUNCT
ejpam-670	96	7	then	then	ADV
ejpam-670	96	8	0	0	NUM
ejpam-670	96	9	<	<	X
ejpam-670	96	10	∞	∞	NUM
ejpam-670	96	11	∑	∑	PROPN
ejpam-670	96	12	n=0	n=0	X
ejpam-670	96	13	b2	b2	NOUN
ejpam-670	96	14	n	n	NOUN
ejpam-670	96	15	=	=	SYM
ejpam-670	96	16	∞	∞	NUM
ejpam-670	96	17	∑	∑	PROPN
ejpam-670	96	18	n=0	n=0	NUM
ejpam-670	96	19	(	(	PUNCT
ejpam-670	96	20	∞	∞	PROPN
ejpam-670	96	21	∑	∑	PROPN
ejpam-670	96	22	m=0	m=0	PROPN
ejpam-670	96	23	am	be	AUX
ejpam-670	96	24	m+n+1	m+n+1	NOUN
ejpam-670	96	25	)	)	PUNCT
ejpam-670	96	26	2	2	NUM
ejpam-670	96	27	<	<	X
ejpam-670	96	28	∞	∞	PROPN
ejpam-670	96	29	,	,	PUNCT
ejpam-670	96	30	so	so	CCONJ
ejpam-670	96	31	(	(	PUNCT
ejpam-670	96	32	∞	∞	PROPN
ejpam-670	96	33	∑	∑	PROPN
ejpam-670	96	34	n=0	n=0	X
ejpam-670	96	35	b2	b2	NOUN
ejpam-670	96	36	n	n	CCONJ
ejpam-670	96	37	)	)	PUNCT
ejpam-670	96	38	2	2	NUM
ejpam-670	96	39	=	=	SYM
ejpam-670	96	40	[	[	PUNCT
ejpam-670	96	41	∞	∞	NUM
ejpam-670	96	42	∑	∑	PROPN
ejpam-670	96	43	n=0	n=0	NUM
ejpam-670	96	44	(	(	PUNCT
ejpam-670	96	45	∞	∞	PROPN
ejpam-670	96	46	∑	∑	PROPN
ejpam-670	96	47	m=0	m=0	PROPN
ejpam-670	96	48	am	be	AUX
ejpam-670	96	49	m+	m+	NUM
ejpam-670	96	50	n+	n+	ADP
ejpam-670	96	51	1	1	NUM
ejpam-670	96	52	)	)	PUNCT
ejpam-670	96	53	2]2	2]2	NUM
ejpam-670	97	1	=	=	PUNCT
ejpam-670	97	2	(	(	PUNCT
ejpam-670	97	3	∞	∞	PROPN
ejpam-670	97	4	∑	∑	PROPN
ejpam-670	97	5	n=0	n=0	PROPN
ejpam-670	97	6	∞	∞	PROPN
ejpam-670	97	7	∑	∑	PROPN
ejpam-670	97	8	m=0	m=0	PROPN
ejpam-670	97	9	ambn	ambn	PROPN
ejpam-670	97	10	m+	m+	NUM
ejpam-670	97	11	n+	n+	NOUN
ejpam-670	97	12	1	1	NUM
ejpam-670	97	13	)	)	SYM
ejpam-670	97	14	2	2	NUM
ejpam-670	97	15	<	<	X
ejpam-670	97	16	∞	∞	NUM
ejpam-670	97	17	∑	∑	PUNCT
ejpam-670	97	18	n=0	n=0	PUNCT
ejpam-670	98	1	[	[	X
ejpam-670	98	2	π−	π−	NOUN
ejpam-670	98	3	5	5	NUM
ejpam-670	98	4	6	6	NUM
ejpam-670	98	5	(	(	PUNCT
ejpam-670	98	6	p	p	NOUN
ejpam-670	98	7	2n+	2n+	NUM
ejpam-670	98	8	1	1	NUM
ejpam-670	98	9	+	+	NUM
ejpam-670	98	10	3	3	NUM
ejpam-670	98	11	4	4	NUM
ejpam-670	98	12	p	p	NOUN
ejpam-670	98	13	(	(	PUNCT
ejpam-670	98	14	2n+	2n+	NUM
ejpam-670	98	15	1)−1	1)−1	NUM
ejpam-670	98	16	)	)	PUNCT
ejpam-670	98	17	]	]	PUNCT
ejpam-670	98	18	a2	a2	PROPN
ejpam-670	98	19	n	n	X
ejpam-670	98	20	·	·	PUNCT
ejpam-670	98	21	∞	∞	NUM
ejpam-670	98	22	∑	∑	PUNCT
ejpam-670	98	23	n=0	n=0	PUNCT
ejpam-670	99	1	[	[	X
ejpam-670	99	2	π−	π−	NOUN
ejpam-670	99	3	5	5	NUM
ejpam-670	99	4	6	6	NUM
ejpam-670	99	5	(	(	PUNCT
ejpam-670	99	6	p	p	NOUN
ejpam-670	99	7	2n+	2n+	NUM
ejpam-670	99	8	1	1	NUM
ejpam-670	99	9	+	+	NUM
ejpam-670	99	10	3	3	NUM
ejpam-670	99	11	4	4	NUM
ejpam-670	99	12	p	p	NOUN
ejpam-670	99	13	(	(	PUNCT
ejpam-670	99	14	2n+	2n+	NUM
ejpam-670	99	15	1)−1	1)−1	NUM
ejpam-670	99	16	)	)	PUNCT
ejpam-670	99	17	]	]	PUNCT
ejpam-670	99	18	b2	b2	NOUN
ejpam-670	99	19	n	n	CCONJ
ejpam-670	99	20	<	<	X
ejpam-670	99	21	π	π	X
ejpam-670	99	22	∞	∞	PROPN
ejpam-670	99	23	∑	∑	PUNCT
ejpam-670	99	24	n=0	n=0	PUNCT
ejpam-670	100	1	[	[	X
ejpam-670	100	2	π−	π−	NOUN
ejpam-670	100	3	5	5	NUM
ejpam-670	100	4	6	6	NUM
ejpam-670	100	5	(	(	PUNCT
ejpam-670	100	6	p	p	NOUN
ejpam-670	100	7	2n+	2n+	NUM
ejpam-670	100	8	1	1	NUM
ejpam-670	100	9	+	+	NUM
ejpam-670	100	10	3	3	NUM
ejpam-670	100	11	4	4	NUM
ejpam-670	100	12	p	p	NOUN
ejpam-670	100	13	(	(	PUNCT
ejpam-670	100	14	2n+	2n+	NUM
ejpam-670	100	15	1)−1	1)−1	NUM
ejpam-670	100	16	)	)	PUNCT
ejpam-670	100	17	]	]	PUNCT
ejpam-670	100	18	a2	a2	PROPN
ejpam-670	100	19	n	n	X
ejpam-670	100	20	·	·	PUNCT
ejpam-670	100	21	∞	∞	NUM
ejpam-670	100	22	∑	∑	PUNCT
ejpam-670	100	23	n=0	n=0	NUM
ejpam-670	100	24	b2	b2	NOUN
ejpam-670	100	25	n.	n.	NOUN
ejpam-670	100	26	we	we	PRON
ejpam-670	100	27	have	have	VERB
ejpam-670	100	28	inequality	inequality	NOUN
ejpam-670	100	29	(	(	PUNCT
ejpam-670	100	30	10	10	NUM
ejpam-670	100	31	)	)	PUNCT
ejpam-670	100	32	.	.	PUNCT
ejpam-670	101	1	the	the	DET
ejpam-670	101	2	proof	proof	NOUN
ejpam-670	101	3	of	of	ADP
ejpam-670	101	4	the	the	DET
ejpam-670	101	5	theorem	theorem	NOUN
ejpam-670	101	6	is	be	AUX
ejpam-670	101	7	completed	complete	VERB
ejpam-670	101	8	.	.	PUNCT
ejpam-670	102	1	remark	remark	NOUN
ejpam-670	102	2	1	1	NUM
ejpam-670	102	3	.	.	PUNCT
ejpam-670	103	1	obviously	obviously	ADV
ejpam-670	103	2	,	,	PUNCT
ejpam-670	103	3	inequality	inequality	NOUN
ejpam-670	103	4	(	(	PUNCT
ejpam-670	103	5	9	9	NUM
ejpam-670	103	6	)	)	PUNCT
ejpam-670	103	7	is	be	AUX
ejpam-670	103	8	a	a	DET
ejpam-670	103	9	strengthened	strengthen	VERB
ejpam-670	103	10	of	of	ADP
ejpam-670	103	11	inequality	inequality	NOUN
ejpam-670	103	12	(	(	PUNCT
ejpam-670	103	13	3	3	NUM
ejpam-670	103	14	)	)	PUNCT
ejpam-670	103	15	.	.	PUNCT
ejpam-670	104	1	since	since	SCONJ
ejpam-670	104	2	,	,	PUNCT
ejpam-670	104	3	for	for	ADP
ejpam-670	104	4	n	n	PRON
ejpam-670	104	5	∈	∈	PROPN
ejpam-670	104	6	n	n	CCONJ
ejpam-670	104	7	,	,	PUNCT
ejpam-670	104	8	5	5	NUM
ejpam-670	104	9	6	6	NUM
ejpam-670	104	10	(	(	PUNCT
ejpam-670	104	11	p	p	NOUN
ejpam-670	104	12	2n+	2n+	NUM
ejpam-670	104	13	1	1	NUM
ejpam-670	104	14	+	+	NUM
ejpam-670	104	15	3	3	NUM
ejpam-670	104	16	4	4	NUM
ejpam-670	104	17	p	p	NOUN
ejpam-670	104	18	(	(	PUNCT
ejpam-670	104	19	2n+	2n+	NUM
ejpam-670	104	20	1)−1	1)−1	NUM
ejpam-670	104	21	)	)	PUNCT
ejpam-670	104	22	>	>	X
ejpam-670	104	23	θ	θ	PROPN
ejpam-670	104	24	(	(	PUNCT
ejpam-670	104	25	n+	n+	NOUN
ejpam-670	104	26	1	1	NUM
ejpam-670	104	27	)	)	PUNCT
ejpam-670	104	28	1	1	NUM
ejpam-670	104	29	2	2	NUM
ejpam-670	104	30	,	,	PUNCT
ejpam-670	104	31	and	and	CCONJ
ejpam-670	104	32	5	5	NUM
ejpam-670	104	33	6	6	NUM
ejpam-670	104	34	(	(	PUNCT
ejpam-670	104	35	p	p	NOUN
ejpam-670	104	36	2n+	2n+	NUM
ejpam-670	104	37	1	1	NUM
ejpam-670	104	38	+	+	NUM
ejpam-670	104	39	3	3	NUM
ejpam-670	104	40	4	4	NUM
ejpam-670	104	41	p	p	NOUN
ejpam-670	104	42	(	(	PUNCT
ejpam-670	104	43	2n+	2n+	NUM
ejpam-670	104	44	1)−1	1)−1	NUM
ejpam-670	104	45	)	)	PUNCT
ejpam-670	104	46	>	>	X
ejpam-670	105	1	ln	ln	ADJ
ejpam-670	105	2	2−	2−	NUM
ejpam-670	105	3	c	c	NOUN
ejpam-670	105	4	3	3	NUM
ejpam-670	105	5	p	p	NOUN
ejpam-670	105	6	(	(	PUNCT
ejpam-670	105	7	2n+	2n+	NUM
ejpam-670	105	8	1)2	1)2	NUM
ejpam-670	105	9	.	.	PUNCT
ejpam-670	106	1	then	then	ADV
ejpam-670	106	2	inequality	inequality	NOUN
ejpam-670	106	3	(	(	PUNCT
ejpam-670	106	4	9	9	NUM
ejpam-670	106	5	)	)	PUNCT
ejpam-670	106	6	is	be	AUX
ejpam-670	106	7	also	also	ADV
ejpam-670	106	8	a	a	DET
ejpam-670	106	9	strengthened	strengthen	VERB
ejpam-670	106	10	of	of	ADP
ejpam-670	106	11	inequality	inequality	NOUN
ejpam-670	106	12	(	(	PUNCT
ejpam-670	106	13	4	4	NUM
ejpam-670	106	14	)	)	PUNCT
ejpam-670	106	15	and	and	CCONJ
ejpam-670	106	16	(	(	PUNCT
ejpam-670	106	17	5	5	NUM
ejpam-670	106	18	)	)	PUNCT
ejpam-670	106	19	.	.	PUNCT
ejpam-670	107	1	acknowledgements	acknowledgement	NOUN
ejpam-670	107	2	this	this	DET
ejpam-670	107	3	research	research	NOUN
ejpam-670	107	4	is	be	AUX
ejpam-670	107	5	funded	fund	VERB
ejpam-670	107	6	by	by	ADP
ejpam-670	107	7	research	research	NOUN
ejpam-670	107	8	foundation	foundation	NOUN
ejpam-670	107	9	of	of	ADP
ejpam-670	107	10	chongqing	chongqing	PROPN
ejpam-670	107	11	university	university	PROPN
ejpam-670	107	12	of	of	ADP
ejpam-670	107	13	science	science	NOUN
ejpam-670	107	14	and	and	CCONJ
ejpam-670	107	15	technology	technology	NOUN
ejpam-670	107	16	,	,	PUNCT
ejpam-670	107	17	the	the	DET
ejpam-670	107	18	project	project	NOUN
ejpam-670	107	19	no	no	INTJ
ejpam-670	107	20	.	.	PUNCT
ejpam-670	107	21	is	be	AUX
ejpam-670	107	22	ck2010b03	ck2010b03	PROPN
ejpam-670	107	23	.	.	PUNCT
ejpam-670	108	1	references	reference	NOUN
ejpam-670	108	2	[	[	X
ejpam-670	108	3	1	1	NUM
ejpam-670	108	4	]	]	PUNCT
ejpam-670	108	5	g.	g.	PROPN
ejpam-670	108	6	h.	h.	PROPN
ejpam-670	108	7	hardy	hardy	PROPN
ejpam-670	108	8	,	,	PUNCT
ejpam-670	108	9	j.	j.	PROPN
ejpam-670	108	10	e.	e.	PROPN
ejpam-670	108	11	littlewood	littlewood	PROPN
ejpam-670	108	12	and	and	CCONJ
ejpam-670	108	13	g.	g.	PROPN
ejpam-670	108	14	polya	polya	PROPN
ejpam-670	108	15	,	,	PUNCT
ejpam-670	108	16	inequalities	inequality	NOUN
ejpam-670	108	17	,	,	PUNCT
ejpam-670	108	18	cambridge	cambridge	PROPN
ejpam-670	108	19	univ	univ	PROPN
ejpam-670	108	20	.	.	PUNCT
ejpam-670	109	1	press	press	PROPN
ejpam-670	109	2	,	,	PUNCT
ejpam-670	109	3	1952	1952	NUM
ejpam-670	109	4	.	.	PUNCT
ejpam-670	110	1	[	[	X
ejpam-670	110	2	2	2	NUM
ejpam-670	110	3	]	]	PUNCT
ejpam-670	110	4	b.	b.	PROPN
ejpam-670	110	5	yang	yang	PROPN
ejpam-670	110	6	,	,	PUNCT
ejpam-670	110	7	a	a	DET
ejpam-670	110	8	refinement	refinement	NOUN
ejpam-670	110	9	of	of	ADP
ejpam-670	110	10	hilbert	hilbert	PROPN
ejpam-670	110	11	’s	’s	PART
ejpam-670	110	12	inequality	inequality	NOUN
ejpam-670	110	13	,	,	PUNCT
ejpam-670	110	14	huanghuai	huanghuai	PROPN
ejpam-670	110	15	journal	journal	PROPN
ejpam-670	110	16	,	,	PUNCT
ejpam-670	110	17	13.2	13.2	NUM
ejpam-670	110	18	:	:	PUNCT
ejpam-670	110	19	47	47	NUM
ejpam-670	110	20	-	-	SYM
ejpam-670	110	21	51	51	NUM
ejpam-670	110	22	.	.	PUNCT
ejpam-670	110	23	1997	1997	NUM
ejpam-670	110	24	.	.	PUNCT
ejpam-670	111	1	[	[	X
ejpam-670	111	2	3	3	X
ejpam-670	111	3	]	]	X
ejpam-670	111	4	b.	b.	PROPN
ejpam-670	111	5	yang	yang	PROPN
ejpam-670	111	6	,	,	PUNCT
ejpam-670	111	7	on	on	ADP
ejpam-670	111	8	a	a	DET
ejpam-670	111	9	strengthened	strengthen	VERB
ejpam-670	111	10	version	version	NOUN
ejpam-670	111	11	of	of	ADP
ejpam-670	111	12	the	the	DET
ejpam-670	111	13	more	more	ADV
ejpam-670	111	14	accurate	accurate	ADJ
ejpam-670	111	15	hardy	hardy	ADJ
ejpam-670	111	16	-	-	PUNCT
ejpam-670	111	17	hilbert	hilbert	NOUN
ejpam-670	111	18	’s	’s	PART
ejpam-670	111	19	inequality	inequality	NOUN
ejpam-670	111	20	,	,	PUNCT
ejpam-670	111	21	acta	acta	PROPN
ejpam-670	111	22	mathematica	mathematica	PROPN
ejpam-670	111	23	sinica	sinica	PROPN
ejpam-670	111	24	,	,	PUNCT
ejpam-670	111	25	42.6	42.6	NUM
ejpam-670	111	26	:	:	SYM
ejpam-670	111	27	1103	1103	NUM
ejpam-670	111	28	-	-	SYM
ejpam-670	111	29	1110	1110	NUM
ejpam-670	111	30	.	.	PUNCT
ejpam-670	112	1	1999	1999	NUM
ejpam-670	112	2	.	.	PUNCT
ejpam-670	113	1	[	[	X
ejpam-670	113	2	4	4	X
ejpam-670	113	3	]	]	PUNCT
ejpam-670	113	4	b.	b.	PROPN
ejpam-670	113	5	yang	yang	PROPN
ejpam-670	113	6	and	and	CCONJ
ejpam-670	113	7	l.	l.	PROPN
ejpam-670	113	8	debnath	debnath	PROPN
ejpam-670	113	9	,	,	PUNCT
ejpam-670	113	10	on	on	ADP
ejpam-670	113	11	a	a	DET
ejpam-670	113	12	new	new	ADJ
ejpam-670	113	13	generalization	generalization	NOUN
ejpam-670	113	14	of	of	ADP
ejpam-670	113	15	hardy	hardy	ADJ
ejpam-670	113	16	-	-	PUNCT
ejpam-670	113	17	hilbert	hilbert	NOUN
ejpam-670	113	18	’s	’s	PART
ejpam-670	113	19	inequality	inequality	NOUN
ejpam-670	113	20	and	and	CCONJ
ejpam-670	113	21	its	its	PRON
ejpam-670	113	22	applications	application	NOUN
ejpam-670	113	23	,	,	PUNCT
ejpam-670	113	24	journal	journal	NOUN
ejpam-670	113	25	of	of	ADP
ejpam-670	113	26	mathematical	mathematical	ADJ
ejpam-670	113	27	analysis	analysis	NOUN
ejpam-670	113	28	and	and	CCONJ
ejpam-670	113	29	applications	application	NOUN
ejpam-670	113	30	,	,	PUNCT
ejpam-670	113	31	233	233	NUM
ejpam-670	113	32	,	,	PUNCT
ejpam-670	113	33	484	484	NUM
ejpam-670	113	34	-	-	SYM
ejpam-670	113	35	497	497	NUM
ejpam-670	113	36	.	.	PUNCT
ejpam-670	113	37	1999	1999	NUM
ejpam-670	113	38	.	.	PUNCT
ejpam-670	114	1	[	[	X
ejpam-670	114	2	5	5	X
ejpam-670	114	3	]	]	PUNCT
ejpam-670	114	4	j.	j.	PROPN
ejpam-670	114	5	c.	c.	PROPN
ejpam-670	114	6	kuang	kuang	PROPN
ejpam-670	114	7	and	and	CCONJ
ejpam-670	114	8	l.	l.	PROPN
ejpam-670	114	9	debnath	debnath	PROPN
ejpam-670	114	10	,	,	PUNCT
ejpam-670	114	11	on	on	ADP
ejpam-670	114	12	a	a	DET
ejpam-670	114	13	new	new	ADJ
ejpam-670	114	14	generalization	generalization	NOUN
ejpam-670	114	15	of	of	ADP
ejpam-670	114	16	hilbert	hilbert	PROPN
ejpam-670	114	17	’s	’s	PART
ejpam-670	114	18	inequality	inequality	NOUN
ejpam-670	114	19	and	and	CCONJ
ejpam-670	114	20	their	their	PRON
ejpam-670	114	21	applications	application	NOUN
ejpam-670	114	22	,	,	PUNCT
ejpam-670	114	23	j.	j.	PROPN
ejpam-670	114	24	math	math	PROPN
ejpam-670	114	25	.	.	PUNCT
ejpam-670	115	1	anal	anal	PROPN
ejpam-670	115	2	.	.	PUNCT
ejpam-670	115	3	appl	appl	PROPN
ejpam-670	115	4	.	.	PROPN
ejpam-670	115	5	,	,	PUNCT
ejpam-670	115	6	245	245	NUM
ejpam-670	115	7	:	:	PUNCT
ejpam-670	115	8	248	248	NUM
ejpam-670	115	9	-	-	SYM
ejpam-670	115	10	265	265	NUM
ejpam-670	115	11	.	.	PUNCT
ejpam-670	115	12	2000	2000	NUM
ejpam-670	115	13	.	.	PUNCT