id	sid	tid	token	lemma	pos
ejpam-620	1	1	8_620_nigam.dvi	8_620_nigam.dvi	NUM
ejpam-620	1	2	european	european	ADJ
ejpam-620	1	3	journal	journal	NOUN
ejpam-620	1	4	of	of	ADP
ejpam-620	1	5	pure	pure	ADJ
ejpam-620	1	6	and	and	CCONJ
ejpam-620	1	7	applied	apply	VERB
ejpam-620	1	8	mathematics	mathematic	NOUN
ejpam-620	1	9	vol	vol	NOUN
ejpam-620	1	10	.	.	PROPN
ejpam-620	1	11	4	4	NUM
ejpam-620	1	12	,	,	PUNCT
ejpam-620	1	13	no	no	INTJ
ejpam-620	1	14	.	.	NOUN
ejpam-620	1	15	3	3	NUM
ejpam-620	1	16	,	,	PUNCT
ejpam-620	1	17	2011	2011	NUM
ejpam-620	1	18	,	,	PUNCT
ejpam-620	1	19	276	276	NUM
ejpam-620	1	20	-	-	SYM
ejpam-620	1	21	286	286	NUM
ejpam-620	1	22	issn	issn	PROPN
ejpam-620	1	23	1307	1307	NUM
ejpam-620	1	24	-	-	SYM
ejpam-620	1	25	5543	5543	NUM
ejpam-620	1	26	–	–	PUNCT
ejpam-620	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-620	1	28	approximation	approximation	NOUN
ejpam-620	1	29	of	of	ADP
ejpam-620	1	30	conjugate	conjugate	NOUN
ejpam-620	1	31	of	of	ADP
ejpam-620	1	32	functions	function	NOUN
ejpam-620	1	33	belonging	belong	VERB
ejpam-620	1	34	to	to	ADP
ejpam-620	1	35	lipα	lipα	ADJ
ejpam-620	1	36	class	class	NOUN
ejpam-620	1	37	and	and	CCONJ
ejpam-620	1	38	w	w	PROPN
ejpam-620	1	39	�	�	PROPN
ejpam-620	1	40	lr	lr	PROPN
ejpam-620	1	41	,	,	PUNCT
ejpam-620	1	42	ξ	ξ	PROPN
ejpam-620	1	43	(	(	PUNCT
ejpam-620	1	44	t	t	NOUN
ejpam-620	1	45	)	)	PUNCT
ejpam-620	1	46	�	�	PROPN
ejpam-620	1	47	class	class	NOUN
ejpam-620	1	48	by	by	ADP
ejpam-620	1	49	product	product	NOUN
ejpam-620	1	50	means	mean	NOUN
ejpam-620	1	51	of	of	ADP
ejpam-620	1	52	conjugate	conjugate	ADJ
ejpam-620	1	53	fourier	fourier	NOUN
ejpam-620	1	54	series	series	PROPN
ejpam-620	1	55	h.	h.	PROPN
ejpam-620	1	56	k.	k.	PROPN
ejpam-620	1	57	nigam∗	nigam∗	PROPN
ejpam-620	1	58	,	,	PUNCT
ejpam-620	1	59	kusum	kusum	PROPN
ejpam-620	1	60	sharma	sharma	PROPN
ejpam-620	1	61	department	department	PROPN
ejpam-620	1	62	of	of	ADP
ejpam-620	1	63	mathematics	mathematic	NOUN
ejpam-620	1	64	,	,	PUNCT
ejpam-620	1	65	faculty	faculty	NOUN
ejpam-620	1	66	of	of	ADP
ejpam-620	1	67	engineering	engineering	NOUN
ejpam-620	1	68	and	and	CCONJ
ejpam-620	1	69	technology	technology	NOUN
ejpam-620	1	70	,	,	PUNCT
ejpam-620	1	71	mody	mody	PROPN
ejpam-620	1	72	institute	institute	PROPN
ejpam-620	1	73	of	of	ADP
ejpam-620	1	74	technology	technology	PROPN
ejpam-620	1	75	and	and	CCONJ
ejpam-620	1	76	science	science	NOUN
ejpam-620	1	77	(	(	PUNCT
ejpam-620	1	78	deemed	deem	VERB
ejpam-620	1	79	university	university	NOUN
ejpam-620	1	80	)	)	PUNCT
ejpam-620	1	81	,	,	PUNCT
ejpam-620	1	82	laxmangarh-332311	laxmangarh-332311	NOUN
ejpam-620	1	83	,	,	PUNCT
ejpam-620	1	84	sikar	sikar	NOUN
ejpam-620	1	85	(	(	PUNCT
ejpam-620	1	86	rajasthan	rajasthan	PROPN
ejpam-620	1	87	)	)	PUNCT
ejpam-620	1	88	,	,	PUNCT
ejpam-620	1	89	india	india	PROPN
ejpam-620	1	90	abstract	abstract	NOUN
ejpam-620	1	91	.	.	PUNCT
ejpam-620	2	1	in	in	ADP
ejpam-620	2	2	this	this	DET
ejpam-620	2	3	paper	paper	NOUN
ejpam-620	2	4	,	,	PUNCT
ejpam-620	2	5	two	two	NUM
ejpam-620	2	6	quite	quite	ADV
ejpam-620	2	7	new	new	ADJ
ejpam-620	2	8	theorems	theorem	NOUN
ejpam-620	2	9	on	on	ADP
ejpam-620	2	10	degree	degree	NOUN
ejpam-620	2	11	of	of	ADP
ejpam-620	2	12	approximation	approximation	NOUN
ejpam-620	2	13	of	of	ADP
ejpam-620	2	14	conjugate	conjugate	NOUN
ejpam-620	2	15	of	of	ADP
ejpam-620	2	16	functions	function	NOUN
ejpam-620	2	17	f	f	PROPN
ejpam-620	2	18	∈	∈	PROPN
ejpam-620	2	19	lipα	lipα	PROPN
ejpam-620	2	20	class	class	NOUN
ejpam-620	2	21	and	and	CCONJ
ejpam-620	2	22	f	f	PROPN
ejpam-620	2	23	∈w	∈w	PROPN
ejpam-620	2	24	�	�	PROPN
ejpam-620	2	25	lr	lr	PROPN
ejpam-620	2	26	,	,	PUNCT
ejpam-620	2	27	ξ	ξ	PROPN
ejpam-620	2	28	(	(	PUNCT
ejpam-620	2	29	t	t	NOUN
ejpam-620	2	30	)	)	PUNCT
ejpam-620	2	31	�	�	PROPN
ejpam-620	2	32	class	class	NOUN
ejpam-620	2	33	using	use	VERB
ejpam-620	2	34	(	(	PUNCT
ejpam-620	2	35	e	e	NOUN
ejpam-620	2	36	,	,	PUNCT
ejpam-620	2	37	1	1	NUM
ejpam-620	2	38	)	)	PUNCT
ejpam-620	2	39	(	(	PUNCT
ejpam-620	2	40	c	c	NOUN
ejpam-620	2	41	,	,	PUNCT
ejpam-620	2	42	1	1	X
ejpam-620	2	43	)	)	PUNCT
ejpam-620	2	44	product	product	NOUN
ejpam-620	2	45	summability	summability	NOUN
ejpam-620	2	46	means	mean	VERB
ejpam-620	2	47	of	of	ADP
ejpam-620	2	48	conjugate	conjugate	ADJ
ejpam-620	2	49	fourier	fourier	NOUN
ejpam-620	2	50	series	series	NOUN
ejpam-620	2	51	have	have	AUX
ejpam-620	2	52	been	be	AUX
ejpam-620	2	53	established	establish	VERB
ejpam-620	2	54	.	.	PUNCT
ejpam-620	3	1	2000	2000	NUM
ejpam-620	3	2	mathematics	mathematic	NOUN
ejpam-620	3	3	subject	subject	NOUN
ejpam-620	3	4	classifications	classification	NOUN
ejpam-620	3	5	:	:	PUNCT
ejpam-620	3	6	42b05	42b05	NUM
ejpam-620	3	7	,	,	PUNCT
ejpam-620	3	8	42b08	42b08	NUM
ejpam-620	3	9	key	key	ADJ
ejpam-620	3	10	words	word	NOUN
ejpam-620	3	11	and	and	CCONJ
ejpam-620	3	12	phrases	phrase	NOUN
ejpam-620	3	13	:	:	PUNCT
ejpam-620	3	14	degree	degree	NOUN
ejpam-620	3	15	of	of	ADP
ejpam-620	3	16	approximation	approximation	NOUN
ejpam-620	3	17	,	,	PUNCT
ejpam-620	3	18	lipα	lipα	ADJ
ejpam-620	3	19	class	class	NOUN
ejpam-620	3	20	,	,	PUNCT
ejpam-620	3	21	w	w	PROPN
ejpam-620	3	22	(	(	PUNCT
ejpam-620	3	23	lr	lr	INTJ
ejpam-620	3	24	,	,	PUNCT
ejpam-620	3	25	ξ(t	ξ(t	NOUN
ejpam-620	3	26	)	)	PUNCT
ejpam-620	3	27	)	)	PUNCT
ejpam-620	3	28	class	class	NOUN
ejpam-620	3	29	of	of	ADP
ejpam-620	3	30	functions	function	NOUN
ejpam-620	3	31	,	,	PUNCT
ejpam-620	3	32	(	(	PUNCT
ejpam-620	3	33	e	e	NOUN
ejpam-620	3	34	,	,	PUNCT
ejpam-620	3	35	1	1	NUM
ejpam-620	3	36	)	)	PUNCT
ejpam-620	3	37	summability	summability	NOUN
ejpam-620	3	38	,	,	PUNCT
ejpam-620	3	39	(	(	PUNCT
ejpam-620	3	40	c	c	NOUN
ejpam-620	3	41	,	,	PUNCT
ejpam-620	3	42	1	1	X
ejpam-620	3	43	)	)	PUNCT
ejpam-620	3	44	summability	summability	NOUN
ejpam-620	3	45	,	,	PUNCT
ejpam-620	3	46	(	(	PUNCT
ejpam-620	3	47	e	e	NOUN
ejpam-620	3	48	,	,	PUNCT
ejpam-620	3	49	1	1	NUM
ejpam-620	3	50	)	)	PUNCT
ejpam-620	3	51	(	(	PUNCT
ejpam-620	3	52	c	c	NOUN
ejpam-620	3	53	,	,	PUNCT
ejpam-620	3	54	1	1	X
ejpam-620	3	55	)	)	PUNCT
ejpam-620	3	56	product	product	NOUN
ejpam-620	3	57	summability	summability	NOUN
ejpam-620	3	58	,	,	PUNCT
ejpam-620	3	59	fourier	fourier	NOUN
ejpam-620	3	60	series	series	NOUN
ejpam-620	3	61	,	,	PUNCT
ejpam-620	3	62	conjugate	conjugate	ADJ
ejpam-620	3	63	fourier	fouri	ADJ
ejpam-620	3	64	series	series	NOUN
ejpam-620	3	65	,	,	PUNCT
ejpam-620	3	66	lebesgue	lebesgue	NOUN
ejpam-620	3	67	integral	integral	ADJ
ejpam-620	3	68	.	.	PUNCT
ejpam-620	4	1	1	1	X
ejpam-620	4	2	.	.	X
ejpam-620	4	3	introduction	introduction	NOUN
ejpam-620	4	4	a	a	DET
ejpam-620	4	5	good	good	ADJ
ejpam-620	4	6	amount	amount	NOUN
ejpam-620	4	7	of	of	ADP
ejpam-620	4	8	work	work	NOUN
ejpam-620	4	9	to	to	PART
ejpam-620	4	10	determine	determine	VERB
ejpam-620	4	11	the	the	DET
ejpam-620	4	12	degree	degree	NOUN
ejpam-620	4	13	of	of	ADP
ejpam-620	4	14	approximation	approximation	NOUN
ejpam-620	4	15	of	of	ADP
ejpam-620	4	16	functions	function	NOUN
ejpam-620	4	17	belonging	belong	VERB
ejpam-620	4	18	to	to	ADP
ejpam-620	4	19	the	the	DET
ejpam-620	4	20	classes	class	NOUN
ejpam-620	4	21	lipα	lipα	ADJ
ejpam-620	4	22	,	,	PUNCT
ejpam-620	4	23	lip	lip	NOUN
ejpam-620	4	24	(	(	PUNCT
ejpam-620	4	25	α	α	NOUN
ejpam-620	4	26	,	,	PUNCT
ejpam-620	4	27	r	r	NOUN
ejpam-620	4	28	)	)	PUNCT
ejpam-620	4	29	,	,	PUNCT
ejpam-620	4	30	lip	lip	NOUN
ejpam-620	4	31	(	(	PUNCT
ejpam-620	4	32	ξ	ξ	PROPN
ejpam-620	4	33	(	(	PUNCT
ejpam-620	4	34	t	t	PROPN
ejpam-620	4	35	)	)	PUNCT
ejpam-620	4	36	,	,	PUNCT
ejpam-620	4	37	r	r	NOUN
ejpam-620	4	38	)	)	PUNCT
ejpam-620	4	39	and	and	CCONJ
ejpam-620	4	40	w	w	PROPN
ejpam-620	4	41	�	�	PROPN
ejpam-620	4	42	lr	lr	PROPN
ejpam-620	4	43	,	,	PUNCT
ejpam-620	4	44	ξ	ξ	PROPN
ejpam-620	4	45	(	(	PUNCT
ejpam-620	4	46	t	t	NOUN
ejpam-620	4	47	)	)	PUNCT
ejpam-620	4	48	�	�	PROPN
ejpam-620	4	49	using	use	VERB
ejpam-620	4	50	cesàro	cesàro	PROPN
ejpam-620	4	51	,	,	PUNCT
ejpam-620	4	52	nörlund	nörlund	NOUN
ejpam-620	4	53	and	and	CCONJ
ejpam-620	4	54	generalized	generalize	VERB
ejpam-620	4	55	nörlund	nörlund	ADJ
ejpam-620	4	56	single	single	ADJ
ejpam-620	4	57	summability	summability	NOUN
ejpam-620	4	58	methods	method	NOUN
ejpam-620	4	59	has	have	AUX
ejpam-620	4	60	been	be	AUX
ejpam-620	4	61	done	do	VERB
ejpam-620	4	62	by	by	ADP
ejpam-620	4	63	several	several	ADJ
ejpam-620	4	64	researchers	researcher	NOUN
ejpam-620	4	65	like	like	ADP
ejpam-620	4	66	alexits	alexit	NOUN
ejpam-620	4	67	[	[	X
ejpam-620	4	68	1	1	NUM
ejpam-620	4	69	]	]	PUNCT
ejpam-620	4	70	,	,	PUNCT
ejpam-620	4	71	sahney	sahney	NOUN
ejpam-620	4	72	and	and	CCONJ
ejpam-620	4	73	goel	goel	PROPN
ejpam-620	5	1	[	[	X
ejpam-620	5	2	12	12	NUM
ejpam-620	5	3	]	]	PUNCT
ejpam-620	5	4	,	,	PUNCT
ejpam-620	5	5	qureshi	qureshi	PROPN
ejpam-620	5	6	and	and	CCONJ
ejpam-620	5	7	neha	neha	NOUN
ejpam-620	6	1	[	[	X
ejpam-620	6	2	8	8	NUM
ejpam-620	6	3	]	]	PUNCT
ejpam-620	6	4	,	,	PUNCT
ejpam-620	6	5	qureshi	qureshi	PROPN
ejpam-620	7	1	[	[	X
ejpam-620	7	2	9	9	NUM
ejpam-620	7	3	,	,	PUNCT
ejpam-620	7	4	10	10	NUM
ejpam-620	7	5	]	]	PUNCT
ejpam-620	7	6	,	,	PUNCT
ejpam-620	7	7	chandra	chandra	PROPN
ejpam-620	8	1	[	[	X
ejpam-620	8	2	2	2	NUM
ejpam-620	8	3	]	]	PUNCT
ejpam-620	8	4	,	,	PUNCT
ejpam-620	8	5	khan	khan	PROPN
ejpam-620	9	1	[	[	X
ejpam-620	9	2	4	4	NUM
ejpam-620	9	3	]	]	PUNCT
ejpam-620	9	4	,	,	PUNCT
ejpam-620	9	5	leindler	leindler	NOUN
ejpam-620	10	1	[	[	X
ejpam-620	10	2	6	6	NUM
ejpam-620	10	3	]	]	PUNCT
ejpam-620	10	4	and	and	CCONJ
ejpam-620	10	5	rhoades	rhoade	NOUN
ejpam-620	10	6	[	[	X
ejpam-620	10	7	11	11	NUM
ejpam-620	10	8	]	]	PUNCT
ejpam-620	10	9	.	.	PUNCT
ejpam-620	11	1	but	but	CCONJ
ejpam-620	11	2	nothing	nothing	PRON
ejpam-620	11	3	seems	seem	VERB
ejpam-620	11	4	to	to	PART
ejpam-620	11	5	have	have	AUX
ejpam-620	11	6	been	be	AUX
ejpam-620	11	7	done	do	VERB
ejpam-620	11	8	so	so	ADV
ejpam-620	11	9	far	far	ADV
ejpam-620	11	10	to	to	PART
ejpam-620	11	11	obtain	obtain	VERB
ejpam-620	11	12	degree	degree	NOUN
ejpam-620	11	13	of	of	ADP
ejpam-620	11	14	approximation	approximation	NOUN
ejpam-620	11	15	using	use	VERB
ejpam-620	11	16	different	different	ADJ
ejpam-620	11	17	class	class	NOUN
ejpam-620	11	18	of	of	ADP
ejpam-620	11	19	functions	function	NOUN
ejpam-620	11	20	by	by	ADP
ejpam-620	11	21	product	product	NOUN
ejpam-620	11	22	summability	summability	NOUN
ejpam-620	11	23	method	method	NOUN
ejpam-620	11	24	.	.	PUNCT
ejpam-620	12	1	therefore	therefore	ADV
ejpam-620	12	2	,	,	PUNCT
ejpam-620	12	3	in	in	ADP
ejpam-620	12	4	present	present	ADJ
ejpam-620	12	5	work	work	NOUN
ejpam-620	12	6	,	,	PUNCT
ejpam-620	12	7	two	two	NUM
ejpam-620	12	8	theorems	theorem	NOUN
ejpam-620	12	9	on	on	ADP
ejpam-620	12	10	degree	degree	NOUN
ejpam-620	12	11	of	of	ADP
ejpam-620	12	12	approximation	approximation	NOUN
ejpam-620	12	13	of	of	ADP
ejpam-620	12	14	the	the	DET
ejpam-620	12	15	conjugate	conjugate	NOUN
ejpam-620	12	16	of	of	ADP
ejpam-620	12	17	functions	function	NOUN
ejpam-620	12	18	f	f	PROPN
ejpam-620	12	19	∈	∈	PROPN
ejpam-620	12	20	lipα	lipα	PROPN
ejpam-620	12	21	and	and	CCONJ
ejpam-620	12	22	f	f	PROPN
ejpam-620	12	23	∈	∈	PROPN
ejpam-620	12	24	w	w	PROPN
ejpam-620	12	25	�	�	PROPN
ejpam-620	12	26	lr	lr	PROPN
ejpam-620	12	27	,	,	PUNCT
ejpam-620	12	28	ξ	ξ	PROPN
ejpam-620	12	29	(	(	PUNCT
ejpam-620	12	30	t	t	PROPN
ejpam-620	12	31	)	)	PUNCT
ejpam-620	12	32	�	�	PROPN
ejpam-620	12	33	,	,	PUNCT
ejpam-620	12	34	(	(	PUNCT
ejpam-620	12	35	r	r	NOUN
ejpam-620	12	36	≥	≥	NOUN
ejpam-620	12	37	1	1	NUM
ejpam-620	12	38	)	)	PUNCT
ejpam-620	12	39	using	use	VERB
ejpam-620	12	40	(	(	PUNCT
ejpam-620	12	41	e	e	NOUN
ejpam-620	12	42	,	,	PUNCT
ejpam-620	12	43	1	1	NUM
ejpam-620	12	44	)	)	PUNCT
ejpam-620	12	45	(	(	PUNCT
ejpam-620	12	46	c	c	NOUN
ejpam-620	12	47	,	,	PUNCT
ejpam-620	12	48	1	1	X
ejpam-620	12	49	)	)	PUNCT
ejpam-620	12	50	summability	summability	NOUN
ejpam-620	12	51	means	mean	NOUN
ejpam-620	12	52	of	of	ADP
ejpam-620	12	53	conjugate	conjugate	ADJ
ejpam-620	12	54	fourier	fourier	NOUN
ejpam-620	12	55	series	series	NOUN
ejpam-620	12	56	have	have	AUX
ejpam-620	12	57	been	be	AUX
ejpam-620	12	58	proved	prove	VERB
ejpam-620	12	59	.	.	PUNCT
ejpam-620	13	1	let	let	VERB
ejpam-620	13	2	∑∞	∑∞	NOUN
ejpam-620	13	3	n=0	n=0	X
ejpam-620	13	4	un	un	AUX
ejpam-620	13	5	be	be	VERB
ejpam-620	13	6	a	a	DET
ejpam-620	13	7	given	give	VERB
ejpam-620	13	8	infinite	infinite	ADJ
ejpam-620	13	9	series	series	NOUN
ejpam-620	13	10	with	with	ADP
ejpam-620	13	11	sequence	sequence	NOUN
ejpam-620	13	12	of	of	ADP
ejpam-620	13	13	its	its	PRON
ejpam-620	13	14	nth	nth	NOUN
ejpam-620	13	15	partial	partial	ADJ
ejpam-620	13	16	sum	sum	NOUN
ejpam-620	13	17	�	�	PROPN
ejpam-620	13	18	sn	sn	PROPN
ejpam-620	13	19	.	.	PUNCT
ejpam-620	14	1	∗corresponding	∗corresponde	VERB
ejpam-620	14	2	author	author	NOUN
ejpam-620	14	3	.	.	PUNCT
ejpam-620	15	1	email	email	NOUN
ejpam-620	15	2	addresses	address	NOUN
ejpam-620	15	3	:	:	PUNCT
ejpam-620	15	4	harekrishnan	harekrishnan	PROPN
ejpam-620	15	5	�	�	PROPN
ejpam-620	15	6	yahoo	yahoo	PROPN
ejpam-620	15	7	.	.	PUNCT
ejpam-620	16	1	om	om	PROPN
ejpam-620	16	2	(	(	PUNCT
ejpam-620	16	3	h.	h.	PROPN
ejpam-620	16	4	nigam	nigam	PROPN
ejpam-620	16	5	)	)	PUNCT
ejpam-620	16	6	,	,	PUNCT
ejpam-620	16	7	kusum31sharma	kusum31sharma	PROPN
ejpam-620	16	8	�	�	NOUN
ejpam-620	16	9	rediffmail	rediffmail	NOUN
ejpam-620	16	10	.	.	PUNCT
ejpam-620	17	1	om	om	PROPN
ejpam-620	17	2	(	(	PUNCT
ejpam-620	17	3	k.	k.	PROPN
ejpam-620	17	4	sharma	sharma	PROPN
ejpam-620	17	5	)	)	PUNCT
ejpam-620	17	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-620	18	1	276	276	NUM
ejpam-620	18	2	c	c	X
ejpam-620	18	3	©	©	PROPN
ejpam-620	18	4	2011	2011	NUM
ejpam-620	18	5	ejpam	ejpam	VERB
ejpam-620	18	6	all	all	DET
ejpam-620	18	7	rights	right	NOUN
ejpam-620	18	8	reserved	reserve	VERB
ejpam-620	18	9	.	.	PUNCT
ejpam-620	19	1	h.	h.	PROPN
ejpam-620	19	2	nigam	nigam	PROPN
ejpam-620	19	3	,	,	PUNCT
ejpam-620	19	4	k.	k.	PROPN
ejpam-620	19	5	sharma	sharma	PROPN
ejpam-620	19	6	/	/	SYM
ejpam-620	19	7	eur	eur	PROPN
ejpam-620	19	8	.	.	PUNCT
ejpam-620	20	1	j.	j.	PROPN
ejpam-620	20	2	pure	pure	PROPN
ejpam-620	20	3	appl	appl	PROPN
ejpam-620	20	4	.	.	PROPN
ejpam-620	20	5	math	math	PROPN
ejpam-620	20	6	,	,	PUNCT
ejpam-620	20	7	4	4	NUM
ejpam-620	20	8	(	(	PUNCT
ejpam-620	20	9	2011	2011	NUM
ejpam-620	20	10	)	)	PUNCT
ejpam-620	20	11	,	,	PUNCT
ejpam-620	20	12	276	276	NUM
ejpam-620	20	13	-	-	SYM
ejpam-620	20	14	286	286	NUM
ejpam-620	20	15	277	277	NUM
ejpam-620	20	16	if	if	SCONJ
ejpam-620	20	17	(	(	PUNCT
ejpam-620	20	18	e	e	NOUN
ejpam-620	20	19	,	,	PUNCT
ejpam-620	20	20	1	1	X
ejpam-620	20	21	)	)	PUNCT
ejpam-620	20	22	transform	transform	NOUN
ejpam-620	20	23	is	be	AUX
ejpam-620	20	24	defined	define	VERB
ejpam-620	20	25	as	as	ADP
ejpam-620	20	26	the	the	DET
ejpam-620	20	27	nth	nth	NOUN
ejpam-620	20	28	partial	partial	ADJ
ejpam-620	20	29	sum	sum	NOUN
ejpam-620	20	30	of	of	ADP
ejpam-620	20	31	(	(	PUNCT
ejpam-620	20	32	e	e	NOUN
ejpam-620	20	33	,	,	PUNCT
ejpam-620	20	34	1	1	X
ejpam-620	20	35	)	)	PUNCT
ejpam-620	20	36	summability	summability	NOUN
ejpam-620	20	37	and	and	CCONJ
ejpam-620	20	38	it	it	PRON
ejpam-620	20	39	can	can	AUX
ejpam-620	20	40	be	be	AUX
ejpam-620	20	41	denoted	denote	VERB
ejpam-620	20	42	by	by	ADP
ejpam-620	20	43	e1	e1	NOUN
ejpam-620	20	44	n	n	PROPN
ejpam-620	20	45	,	,	PUNCT
ejpam-620	20	46	which	which	PRON
ejpam-620	20	47	is	be	AUX
ejpam-620	20	48	given	give	VERB
ejpam-620	20	49	by	by	ADP
ejpam-620	20	50	e1	e1	NOUN
ejpam-620	20	51	n	n	NOUN
ejpam-620	20	52	=	=	SYM
ejpam-620	20	53	1	1	NUM
ejpam-620	20	54	2n	2n	NUM
ejpam-620	20	55	n	n	ADP
ejpam-620	20	56	∑	∑	ADP
ejpam-620	20	57	k=0	k=0	PROPN
ejpam-620	20	58	�	�	PROPN
ejpam-620	20	59	n	n	CCONJ
ejpam-620	20	60	k	k	PROPN
ejpam-620	20	61	�	�	PROPN
ejpam-620	20	62	sk→	sk→	PROPN
ejpam-620	20	63	s	s	PROPN
ejpam-620	20	64	as	as	ADP
ejpam-620	20	65	n→∞	n→∞	X
ejpam-620	20	66	(	(	PUNCT
ejpam-620	20	67	1	1	NUM
ejpam-620	20	68	)	)	PUNCT
ejpam-620	20	69	then	then	ADV
ejpam-620	20	70	the	the	DET
ejpam-620	20	71	infinite	infinite	ADJ
ejpam-620	20	72	series	series	NOUN
ejpam-620	20	73	∑∞	∑∞	PROPN
ejpam-620	20	74	n=0	n=0	NUM
ejpam-620	20	75	un	un	PROPN
ejpam-620	20	76	is	be	AUX
ejpam-620	20	77	summable	summable	ADJ
ejpam-620	20	78	(	(	PUNCT
ejpam-620	20	79	e	e	NOUN
ejpam-620	20	80	,	,	PUNCT
ejpam-620	20	81	1	1	NUM
ejpam-620	20	82	)	)	PUNCT
ejpam-620	20	83	to	to	ADP
ejpam-620	20	84	a	a	DET
ejpam-620	20	85	definite	definite	ADJ
ejpam-620	20	86	number	number	NOUN
ejpam-620	20	87	s	s	PART
ejpam-620	20	88	(	(	PUNCT
ejpam-620	20	89	hardy	hardy	ADJ
ejpam-620	20	90	[	[	X
ejpam-620	20	91	3	3	NUM
ejpam-620	20	92	]	]	NUM
ejpam-620	20	93	)	)	PUNCT
ejpam-620	20	94	.	.	PUNCT
ejpam-620	21	1	if	if	SCONJ
ejpam-620	21	2	tn	tn	NOUN
ejpam-620	21	3	=	=	SYM
ejpam-620	21	4	s0	s0	PROPN
ejpam-620	21	5	+	+	CCONJ
ejpam-620	21	6	s1	s1	PROPN
ejpam-620	21	7	+	+	CCONJ
ejpam-620	21	8	s2	s2	NOUN
ejpam-620	21	9	+	+	X
ejpam-620	21	10	.	.	PUNCT
ejpam-620	21	11	.	.	PUNCT
ejpam-620	22	1	.+	.+	NOUN
ejpam-620	22	2	sn	sn	PROPN
ejpam-620	22	3	n+	n+	PUNCT
ejpam-620	22	4	1	1	NUM
ejpam-620	22	5	=	=	SYM
ejpam-620	22	6	1	1	NUM
ejpam-620	22	7	n+	n+	SYM
ejpam-620	22	8	1	1	NUM
ejpam-620	22	9	n	n	NOUN
ejpam-620	22	10	∑	∑	ADP
ejpam-620	22	11	k=0	k=0	PROPN
ejpam-620	22	12	sn→	sn→	PROPN
ejpam-620	22	13	s	s	NOUN
ejpam-620	22	14	as	as	ADP
ejpam-620	22	15	n→∞	n→∞	X
ejpam-620	22	16	(	(	PUNCT
ejpam-620	22	17	2	2	NUM
ejpam-620	22	18	)	)	PUNCT
ejpam-620	22	19	then	then	ADV
ejpam-620	22	20	the	the	DET
ejpam-620	22	21	infinite	infinite	ADJ
ejpam-620	22	22	series	series	NOUN
ejpam-620	22	23	∑∞	∑∞	PROPN
ejpam-620	22	24	n=0	n=0	NUM
ejpam-620	22	25	un	un	PROPN
ejpam-620	22	26	is	be	AUX
ejpam-620	22	27	summable	summable	ADJ
ejpam-620	22	28	to	to	ADP
ejpam-620	22	29	the	the	DET
ejpam-620	22	30	definite	definite	ADJ
ejpam-620	22	31	number	number	NOUN
ejpam-620	22	32	s	s	VERB
ejpam-620	22	33	by	by	X
ejpam-620	22	34	(	(	PUNCT
ejpam-620	22	35	c	c	NOUN
ejpam-620	22	36	,	,	PUNCT
ejpam-620	22	37	1	1	X
ejpam-620	22	38	)	)	PUNCT
ejpam-620	22	39	method	method	NOUN
ejpam-620	22	40	.	.	PUNCT
ejpam-620	23	1	the	the	DET
ejpam-620	23	2	(	(	PUNCT
ejpam-620	23	3	e	e	NOUN
ejpam-620	23	4	,	,	PUNCT
ejpam-620	23	5	1	1	X
ejpam-620	23	6	)	)	PUNCT
ejpam-620	23	7	transform	transform	NOUN
ejpam-620	23	8	of	of	ADP
ejpam-620	23	9	(	(	PUNCT
ejpam-620	23	10	c	c	NOUN
ejpam-620	23	11	,	,	PUNCT
ejpam-620	23	12	1	1	X
ejpam-620	23	13	)	)	PUNCT
ejpam-620	23	14	transform	transform	VERB
ejpam-620	23	15	defines	define	NOUN
ejpam-620	23	16	(	(	PUNCT
ejpam-620	23	17	e	e	NOUN
ejpam-620	23	18	,	,	PUNCT
ejpam-620	23	19	1)(c	1)(c	NUM
ejpam-620	23	20	,	,	PUNCT
ejpam-620	23	21	1	1	X
ejpam-620	23	22	)	)	PUNCT
ejpam-620	23	23	product	product	NOUN
ejpam-620	23	24	transform	transform	NOUN
ejpam-620	23	25	and	and	CCONJ
ejpam-620	23	26	we	we	PRON
ejpam-620	23	27	denote	denote	VERB
ejpam-620	23	28	it	it	PRON
ejpam-620	23	29	by	by	ADP
ejpam-620	23	30	(	(	PUNCT
ejpam-620	23	31	ec)1n	ec)1n	INTJ
ejpam-620	23	32	.	.	PUNCT
ejpam-620	24	1	thus	thus	ADV
ejpam-620	24	2	if	if	SCONJ
ejpam-620	24	3	(	(	PUNCT
ejpam-620	24	4	ec)1n	ec)1n	NOUN
ejpam-620	24	5	=	=	SYM
ejpam-620	24	6	1	1	NUM
ejpam-620	24	7	2n	2n	NUM
ejpam-620	24	8	n	n	ADP
ejpam-620	24	9	∑	∑	ADP
ejpam-620	24	10	k=0	k=0	PROPN
ejpam-620	24	11	�	�	PROPN
ejpam-620	24	12	n	n	CCONJ
ejpam-620	24	13	k	k	PROPN
ejpam-620	24	14	�	�	PROPN
ejpam-620	24	15	c1	c1	PROPN
ejpam-620	24	16	k	k	PROPN
ejpam-620	24	17	→	→	SYM
ejpam-620	24	18	s	s	PROPN
ejpam-620	24	19	as	as	ADP
ejpam-620	24	20	n→∞	n→∞	X
ejpam-620	24	21	(	(	PUNCT
ejpam-620	24	22	3	3	NUM
ejpam-620	24	23	)	)	PUNCT
ejpam-620	24	24	then	then	ADV
ejpam-620	24	25	the	the	DET
ejpam-620	24	26	infinite	infinite	ADJ
ejpam-620	24	27	series	series	NOUN
ejpam-620	24	28	∑∞	∑∞	PROPN
ejpam-620	24	29	n=0	n=0	NUM
ejpam-620	24	30	un	un	PROPN
ejpam-620	24	31	is	be	AUX
ejpam-620	24	32	said	say	VERB
ejpam-620	24	33	to	to	PART
ejpam-620	24	34	be	be	AUX
ejpam-620	24	35	summable	summable	ADJ
ejpam-620	24	36	by	by	ADP
ejpam-620	24	37	(	(	PUNCT
ejpam-620	24	38	e	e	NOUN
ejpam-620	24	39	,	,	PUNCT
ejpam-620	24	40	1	1	NUM
ejpam-620	24	41	)	)	PUNCT
ejpam-620	24	42	(	(	PUNCT
ejpam-620	24	43	c	c	NOUN
ejpam-620	24	44	,	,	PUNCT
ejpam-620	24	45	1	1	X
ejpam-620	24	46	)	)	PUNCT
ejpam-620	24	47	method	method	NOUN
ejpam-620	24	48	or	or	CCONJ
ejpam-620	24	49	summable	summable	ADJ
ejpam-620	24	50	(	(	PUNCT
ejpam-620	24	51	e	e	NOUN
ejpam-620	24	52	,	,	PUNCT
ejpam-620	24	53	1	1	NUM
ejpam-620	24	54	)	)	PUNCT
ejpam-620	24	55	(	(	PUNCT
ejpam-620	24	56	c	c	NOUN
ejpam-620	24	57	,	,	PUNCT
ejpam-620	24	58	1	1	NUM
ejpam-620	24	59	)	)	PUNCT
ejpam-620	24	60	to	to	ADP
ejpam-620	24	61	a	a	DET
ejpam-620	24	62	definite	definite	ADJ
ejpam-620	24	63	number	number	NOUN
ejpam-620	24	64	s.	s.	PROPN
ejpam-620	24	65	let	let	VERB
ejpam-620	24	66	f	f	PROPN
ejpam-620	24	67	(	(	PUNCT
ejpam-620	24	68	x	x	X
ejpam-620	24	69	)	)	PUNCT
ejpam-620	24	70	be	be	AUX
ejpam-620	24	71	a	a	DET
ejpam-620	24	72	2π	2π	NOUN
ejpam-620	24	73	-	-	ADJ
ejpam-620	24	74	periodic	periodic	ADJ
ejpam-620	24	75	function	function	NOUN
ejpam-620	24	76	and	and	CCONJ
ejpam-620	24	77	lebesgue	lebesgue	NOUN
ejpam-620	24	78	integrable	integrable	ADJ
ejpam-620	24	79	.	.	PUNCT
ejpam-620	25	1	the	the	DET
ejpam-620	25	2	fourier	fourier	PROPN
ejpam-620	25	3	series	series	NOUN
ejpam-620	25	4	of	of	ADP
ejpam-620	25	5	f	f	PROPN
ejpam-620	25	6	(	(	PUNCT
ejpam-620	25	7	x	x	X
ejpam-620	25	8	)	)	PUNCT
ejpam-620	25	9	is	be	AUX
ejpam-620	25	10	given	give	VERB
ejpam-620	25	11	by	by	ADP
ejpam-620	25	12	f	f	PROPN
ejpam-620	25	13	(	(	PUNCT
ejpam-620	25	14	x)∼	x)∼	PROPN
ejpam-620	25	15	a0	a0	PROPN
ejpam-620	25	16	2	2	NUM
ejpam-620	25	17	+	+	CCONJ
ejpam-620	25	18	∞	∞	NUM
ejpam-620	25	19	∑	∑	PUNCT
ejpam-620	25	20	n=1	n=1	PROPN
ejpam-620	25	21	�	�	PROPN
ejpam-620	25	22	an	an	DET
ejpam-620	25	23	cos	cos	PROPN
ejpam-620	25	24	nx	nx	PROPN
ejpam-620	25	25	+	+	CCONJ
ejpam-620	25	26	bn	bn	PROPN
ejpam-620	25	27	sin	sin	NOUN
ejpam-620	25	28	nx	nx	PROPN
ejpam-620	25	29	�	�	PROPN
ejpam-620	25	30	(	(	PUNCT
ejpam-620	25	31	4	4	NUM
ejpam-620	25	32	)	)	PUNCT
ejpam-620	25	33	with	with	ADP
ejpam-620	25	34	nth	nth	PROPN
ejpam-620	25	35	partial	partial	ADJ
ejpam-620	25	36	sum	sum	NOUN
ejpam-620	25	37	sn	sn	PROPN
ejpam-620	25	38	�	�	PROPN
ejpam-620	25	39	f	f	PROPN
ejpam-620	25	40	;	;	PUNCT
ejpam-620	25	41	x	x	X
ejpam-620	25	42	�	�	PROPN
ejpam-620	25	43	.	.	PUNCT
ejpam-620	26	1	the	the	DET
ejpam-620	26	2	conjugate	conjugate	ADJ
ejpam-620	26	3	series	series	NOUN
ejpam-620	26	4	of	of	ADP
ejpam-620	26	5	fourier	fourier	PROPN
ejpam-620	26	6	series	series	NOUN
ejpam-620	26	7	(	(	PUNCT
ejpam-620	26	8	4	4	NUM
ejpam-620	26	9	)	)	PUNCT
ejpam-620	26	10	is	be	AUX
ejpam-620	26	11	given	give	VERB
ejpam-620	26	12	by	by	ADP
ejpam-620	26	13	∞	∞	PROPN
ejpam-620	26	14	∑	∑	PROPN
ejpam-620	26	15	n=1	n=1	PROPN
ejpam-620	26	16	�	�	PROPN
ejpam-620	26	17	an	an	PRON
ejpam-620	26	18	cos	cos	PROPN
ejpam-620	26	19	nx	nx	PROPN
ejpam-620	26	20	−	−	PROPN
ejpam-620	26	21	bn	bn	NOUN
ejpam-620	26	22	sin	sin	PROPN
ejpam-620	26	23	nx	nx	PROPN
ejpam-620	26	24	�	�	PROPN
ejpam-620	26	25	,	,	PUNCT
ejpam-620	26	26	(	(	PUNCT
ejpam-620	26	27	5	5	NUM
ejpam-620	26	28	)	)	PUNCT
ejpam-620	26	29	and	and	CCONJ
ejpam-620	26	30	we	we	PRON
ejpam-620	26	31	shall	shall	AUX
ejpam-620	26	32	call	call	VERB
ejpam-620	26	33	it	it	PRON
ejpam-620	26	34	as	as	ADP
ejpam-620	26	35	conjugate	conjugate	ADJ
ejpam-620	26	36	fourier	fouri	ADJ
ejpam-620	26	37	series	series	NOUN
ejpam-620	26	38	.	.	PUNCT
ejpam-620	27	1	a	a	DET
ejpam-620	27	2	function	function	NOUN
ejpam-620	27	3	f	f	PROPN
ejpam-620	27	4	∈	∈	PROPN
ejpam-620	27	5	lipα	lipα	NOUN
ejpam-620	27	6	if	if	SCONJ
ejpam-620	27	7	f	f	PROPN
ejpam-620	27	8	(	(	PUNCT
ejpam-620	27	9	x	x	PROPN
ejpam-620	27	10	+	+	PUNCT
ejpam-620	27	11	t)−	t)−	PROPN
ejpam-620	27	12	f	f	X
ejpam-620	27	13	(	(	PUNCT
ejpam-620	27	14	x	x	X
ejpam-620	27	15	)	)	PUNCT
ejpam-620	28	1	=	=	SYM
ejpam-620	28	2	o	o	PROPN
ejpam-620	28	3	�	�	PROPN
ejpam-620	28	4	|t|α	|t|α	PROPN
ejpam-620	28	5	�	�	PROPN
ejpam-620	28	6	for	for	ADP
ejpam-620	28	7	0	0	NUM
ejpam-620	28	8	<	<	X
ejpam-620	28	9	α≤	α≤	PROPN
ejpam-620	28	10	1	1	NUM
ejpam-620	28	11	.	.	PUNCT
ejpam-620	29	1	(	(	PUNCT
ejpam-620	29	2	6	6	NUM
ejpam-620	29	3	)	)	PUNCT
ejpam-620	29	4	h.	h.	PROPN
ejpam-620	29	5	nigam	nigam	PROPN
ejpam-620	29	6	,	,	PUNCT
ejpam-620	29	7	k.	k.	PROPN
ejpam-620	29	8	sharma	sharma	PROPN
ejpam-620	29	9	/	/	SYM
ejpam-620	29	10	eur	eur	PROPN
ejpam-620	29	11	.	.	PUNCT
ejpam-620	30	1	j.	j.	PROPN
ejpam-620	30	2	pure	pure	PROPN
ejpam-620	30	3	appl	appl	PROPN
ejpam-620	30	4	.	.	PROPN
ejpam-620	30	5	math	math	PROPN
ejpam-620	30	6	,	,	PUNCT
ejpam-620	30	7	4	4	NUM
ejpam-620	30	8	(	(	PUNCT
ejpam-620	30	9	2011	2011	NUM
ejpam-620	30	10	)	)	PUNCT
ejpam-620	30	11	,	,	PUNCT
ejpam-620	30	12	276	276	NUM
ejpam-620	30	13	-	-	SYM
ejpam-620	30	14	286	286	NUM
ejpam-620	30	15	278	278	NUM
ejpam-620	30	16	f	f	NOUN
ejpam-620	30	17	∈	∈	PROPN
ejpam-620	30	18	lip	lip	NOUN
ejpam-620	30	19	(	(	PUNCT
ejpam-620	30	20	α	α	NOUN
ejpam-620	30	21	,	,	PUNCT
ejpam-620	30	22	r	r	NOUN
ejpam-620	30	23	)	)	PUNCT
ejpam-620	30	24	for	for	ADP
ejpam-620	30	25	0≤	0≤	NUM
ejpam-620	30	26	x	x	SYM
ejpam-620	30	27	≤	≤	ADJ
ejpam-620	30	28	2π	2π	NOUN
ejpam-620	30	29	,	,	PUNCT
ejpam-620	30	30	if	if	SCONJ
ejpam-620	30	31	[	[	X
ejpam-620	30	32	definition	definition	NOUN
ejpam-620	30	33	5.38	5.38	NUM
ejpam-620	30	34	of	of	ADP
ejpam-620	30	35	mcfadden	mcfadden	PROPN
ejpam-620	30	36	,	,	PUNCT
ejpam-620	30	37	7	7	NUM
ejpam-620	30	38	]	]	PUNCT
ejpam-620	30	39	∫	∫	PROPN
ejpam-620	30	40	2π	2π	PROPN
ejpam-620	30	41	0	0	NUM
ejpam-620	30	42	�	�	PROPN
ejpam-620	30	43	�	�	PROPN
ejpam-620	30	44	f	f	PROPN
ejpam-620	30	45	(	(	PUNCT
ejpam-620	30	46	x	x	PROPN
ejpam-620	30	47	+	+	PUNCT
ejpam-620	30	48	t)−	t)−	PROPN
ejpam-620	30	49	f	f	X
ejpam-620	30	50	(	(	PUNCT
ejpam-620	30	51	x	x	X
ejpam-620	30	52	)	)	PUNCT
ejpam-620	30	53	�	�	PROPN
ejpam-620	30	54	�	�	PROPN
ejpam-620	30	55	r	r	NOUN
ejpam-620	30	56	d	d	PROPN
ejpam-620	30	57	x	x	X
ejpam-620	30	58	!	!	PUNCT
ejpam-620	31	1	1	1	NUM
ejpam-620	31	2	r	r	NOUN
ejpam-620	31	3	=	=	SYM
ejpam-620	31	4	o	o	X
ejpam-620	31	5	�	�	PROPN
ejpam-620	31	6	|t|α	|t|α	PROPN
ejpam-620	31	7	�	�	PROPN
ejpam-620	31	8	,	,	PUNCT
ejpam-620	31	9	0	0	NUM
ejpam-620	31	10	<	<	X
ejpam-620	31	11	α≤	α≤	PROPN
ejpam-620	31	12	1	1	NUM
ejpam-620	31	13	,	,	PUNCT
ejpam-620	31	14	r	r	NOUN
ejpam-620	31	15	≥	≥	NOUN
ejpam-620	31	16	1	1	NUM
ejpam-620	31	17	.	.	PUNCT
ejpam-620	32	1	(	(	PUNCT
ejpam-620	32	2	7	7	X
ejpam-620	32	3	)	)	PUNCT
ejpam-620	32	4	given	give	VERB
ejpam-620	32	5	a	a	DET
ejpam-620	32	6	positive	positive	ADJ
ejpam-620	32	7	increasing	increase	VERB
ejpam-620	32	8	function	function	NOUN
ejpam-620	32	9	ξ	ξ	PROPN
ejpam-620	32	10	(	(	PUNCT
ejpam-620	32	11	t	t	PROPN
ejpam-620	32	12	)	)	PUNCT
ejpam-620	32	13	and	and	CCONJ
ejpam-620	32	14	an	an	DET
ejpam-620	32	15	integer	integer	NOUN
ejpam-620	32	16	r	r	NOUN
ejpam-620	32	17	≥	≥	NUM
ejpam-620	32	18	1	1	NUM
ejpam-620	32	19	,	,	PUNCT
ejpam-620	32	20	f	f	PROPN
ejpam-620	32	21	∈	∈	PROPN
ejpam-620	32	22	lip	lip	NOUN
ejpam-620	32	23	(	(	PUNCT
ejpam-620	32	24	ξ	ξ	PROPN
ejpam-620	32	25	(	(	PUNCT
ejpam-620	32	26	t	t	PROPN
ejpam-620	32	27	)	)	PUNCT
ejpam-620	32	28	,	,	PUNCT
ejpam-620	32	29	r	r	X
ejpam-620	32	30	)	)	PUNCT
ejpam-620	32	31	if	if	SCONJ
ejpam-620	32	32	∫	∫	PROPN
ejpam-620	32	33	2π	2π	PROPN
ejpam-620	32	34	0	0	NUM
ejpam-620	32	35	�	�	PROPN
ejpam-620	32	36	�	�	PROPN
ejpam-620	32	37	f	f	PROPN
ejpam-620	32	38	(	(	PUNCT
ejpam-620	32	39	x	x	PROPN
ejpam-620	32	40	+	+	PUNCT
ejpam-620	32	41	t)−	t)−	PROPN
ejpam-620	32	42	f	f	X
ejpam-620	32	43	(	(	PUNCT
ejpam-620	32	44	x	x	X
ejpam-620	32	45	)	)	PUNCT
ejpam-620	32	46	�	�	PROPN
ejpam-620	32	47	�	�	PROPN
ejpam-620	32	48	r	r	NOUN
ejpam-620	32	49	d	d	PROPN
ejpam-620	32	50	x	x	X
ejpam-620	32	51	!	!	PUNCT
ejpam-620	33	1	1	1	NUM
ejpam-620	33	2	r	r	NOUN
ejpam-620	33	3	=	=	SYM
ejpam-620	33	4	o	o	X
ejpam-620	33	5	(	(	PUNCT
ejpam-620	33	6	ξ	ξ	PROPN
ejpam-620	33	7	(	(	PUNCT
ejpam-620	33	8	t	t	PROPN
ejpam-620	33	9	)	)	PUNCT
ejpam-620	33	10	)	)	PUNCT
ejpam-620	33	11	(	(	PUNCT
ejpam-620	33	12	8)	8)	NUM
ejpam-620	33	13	and	and	CCONJ
ejpam-620	33	14	that	that	SCONJ
ejpam-620	33	15	f	f	PROPN
ejpam-620	33	16	∈w	∈w	VERB
ejpam-620	33	17	�	�	PROPN
ejpam-620	33	18	lr	lr	PROPN
ejpam-620	33	19	,	,	PUNCT
ejpam-620	33	20	ξ	ξ	PROPN
ejpam-620	33	21	(	(	PUNCT
ejpam-620	33	22	t	t	NOUN
ejpam-620	33	23	)	)	PUNCT
ejpam-620	33	24	�	�	PROPN
ejpam-620	34	1	if	if	SCONJ
ejpam-620	34	2	∫	∫	PROPN
ejpam-620	34	3	2π	2π	PROPN
ejpam-620	34	4	0	0	NUM
ejpam-620	34	5	�	�	PROPN
ejpam-620	34	6	�	�	PROPN
ejpam-620	34	7	�	�	PROPN
ejpam-620	34	8	f	f	PROPN
ejpam-620	34	9	(	(	PUNCT
ejpam-620	34	10	x	x	PROPN
ejpam-620	34	11	+	+	PUNCT
ejpam-620	34	12	t)−	t)−	PROPN
ejpam-620	34	13	f	f	X
ejpam-620	34	14	(	(	PUNCT
ejpam-620	34	15	x	x	NOUN
ejpam-620	34	16	)	)	PUNCT
ejpam-620	34	17	sinβ	sinβ	NOUN
ejpam-620	34	18	x	x	SYM
ejpam-620	34	19	�	�	PROPN
ejpam-620	34	20	�	�	PROPN
ejpam-620	34	21	r	r	NOUN
ejpam-620	34	22	d	d	PROPN
ejpam-620	34	23	x	x	X
ejpam-620	34	24	!	!	PUNCT
ejpam-620	34	25	1	1	NUM
ejpam-620	34	26	r	r	NOUN
ejpam-620	34	27	=	=	SYM
ejpam-620	34	28	o	o	X
ejpam-620	34	29	(	(	PUNCT
ejpam-620	34	30	ξ	ξ	PROPN
ejpam-620	34	31	(	(	PUNCT
ejpam-620	34	32	t	t	PROPN
ejpam-620	34	33	)	)	PUNCT
ejpam-620	34	34	)	)	PUNCT
ejpam-620	34	35	,	,	PUNCT
ejpam-620	34	36	β	β	X
ejpam-620	34	37	≥	≥	NOUN
ejpam-620	34	38	0	0	NUM
ejpam-620	34	39	.	.	PUNCT
ejpam-620	35	1	(	(	PUNCT
ejpam-620	35	2	9	9	NUM
ejpam-620	35	3	)	)	PUNCT
ejpam-620	35	4	where	where	SCONJ
ejpam-620	35	5	ξ(t	ξ(t	NOUN
ejpam-620	35	6	)	)	PUNCT
ejpam-620	35	7	is	be	AUX
ejpam-620	35	8	a	a	DET
ejpam-620	35	9	positive	positive	ADJ
ejpam-620	35	10	increasing	increase	VERB
ejpam-620	35	11	function	function	NOUN
ejpam-620	35	12	of	of	ADP
ejpam-620	35	13	t.	t.	PROPN
ejpam-620	35	14	if	if	SCONJ
ejpam-620	35	15	β	β	PROPN
ejpam-620	36	1	=	=	NOUN
ejpam-620	36	2	0	0	PUNCT
ejpam-620	37	1	then	then	ADV
ejpam-620	37	2	w	w	PROPN
ejpam-620	37	3	�	�	PROPN
ejpam-620	37	4	lr	lr	PROPN
ejpam-620	37	5	,	,	PUNCT
ejpam-620	37	6	ξ	ξ	PROPN
ejpam-620	37	7	(	(	PUNCT
ejpam-620	37	8	t	t	NOUN
ejpam-620	37	9	)	)	PUNCT
ejpam-620	37	10	�	�	PROPN
ejpam-620	37	11	reduces	reduce	VERB
ejpam-620	37	12	to	to	ADP
ejpam-620	37	13	the	the	DET
ejpam-620	37	14	class	class	NOUN
ejpam-620	37	15	lip	lip	NOUN
ejpam-620	37	16	(	(	PUNCT
ejpam-620	37	17	ξ	ξ	PROPN
ejpam-620	37	18	(	(	PUNCT
ejpam-620	37	19	t	t	PROPN
ejpam-620	37	20	)	)	PUNCT
ejpam-620	37	21	,	,	PUNCT
ejpam-620	37	22	r	r	NOUN
ejpam-620	37	23	)	)	PUNCT
ejpam-620	37	24	and	and	CCONJ
ejpam-620	37	25	if	if	SCONJ
ejpam-620	37	26	ξ(t	ξ(t	NOUN
ejpam-620	37	27	)	)	PUNCT
ejpam-620	37	28	=	=	SYM
ejpam-620	38	1	tα	tα	PROPN
ejpam-620	38	2	then	then	ADV
ejpam-620	38	3	lip(ξ(t	lip(ξ(t	PROPN
ejpam-620	38	4	)	)	PUNCT
ejpam-620	38	5	,	,	PUNCT
ejpam-620	38	6	r	r	NOUN
ejpam-620	38	7	)	)	PUNCT
ejpam-620	38	8	class	class	NOUN
ejpam-620	38	9	coincides	coincide	VERB
ejpam-620	38	10	with	with	ADP
ejpam-620	38	11	the	the	DET
ejpam-620	38	12	class	class	NOUN
ejpam-620	38	13	lip(α	lip(α	PROPN
ejpam-620	38	14	,	,	PUNCT
ejpam-620	38	15	r	r	NOUN
ejpam-620	38	16	)	)	PUNCT
ejpam-620	38	17	and	and	CCONJ
ejpam-620	38	18	if	if	SCONJ
ejpam-620	38	19	r	r	NOUN
ejpam-620	38	20	→	→	SYM
ejpam-620	38	21	∞	∞	PROPN
ejpam-620	38	22	then	then	ADV
ejpam-620	38	23	lip(α	lip(α	PROPN
ejpam-620	38	24	,	,	PUNCT
ejpam-620	38	25	r	r	NOUN
ejpam-620	38	26	)	)	PUNCT
ejpam-620	38	27	class	class	NOUN
ejpam-620	38	28	reduces	reduce	VERB
ejpam-620	38	29	to	to	ADP
ejpam-620	38	30	the	the	DET
ejpam-620	38	31	class	class	NOUN
ejpam-620	38	32	lipα	lipα	PROPN
ejpam-620	38	33	.	.	PUNCT
ejpam-620	39	1	l∞-norm	l∞-norm	NOUN
ejpam-620	39	2	of	of	ADP
ejpam-620	39	3	a	a	DET
ejpam-620	39	4	function	function	NOUN
ejpam-620	39	5	f	f	NOUN
ejpam-620	39	6	:	:	PUNCT
ejpam-620	39	7	r→	r→	PROPN
ejpam-620	39	8	r	r	NOUN
ejpam-620	39	9	is	be	AUX
ejpam-620	39	10	defined	define	VERB
ejpam-620	39	11	by	by	ADP
ejpam-620	39	12	f	f	PROPN
ejpam-620	39	13	∞	∞	PROPN
ejpam-620	39	14	=	=	SYM
ejpam-620	39	15	sup	sup	PROPN
ejpam-620	39	16	¦	¦	PROPN
ejpam-620	39	17	�	�	PROPN
ejpam-620	39	18	�	�	PROPN
ejpam-620	39	19	f	f	PROPN
ejpam-620	39	20	(	(	PUNCT
ejpam-620	39	21	x	x	X
ejpam-620	39	22	)	)	PUNCT
ejpam-620	39	23	�	�	PROPN
ejpam-620	39	24	�	�	PROPN
ejpam-620	39	25	:	:	PUNCT
ejpam-620	39	26	x	x	PUNCT
ejpam-620	39	27	∈	∈	NOUN
ejpam-620	39	28	r	r	NOUN
ejpam-620	39	29	©	©	NOUN
ejpam-620	39	30	(	(	PUNCT
ejpam-620	39	31	10	10	NUM
ejpam-620	39	32	)	)	PUNCT
ejpam-620	39	33	lr	lr	NOUN
ejpam-620	39	34	-norm	-norm	PROPN
ejpam-620	39	35	is	be	AUX
ejpam-620	39	36	defined	define	VERB
ejpam-620	39	37	by	by	ADP
ejpam-620	39	38	f	f	PROPN
ejpam-620	39	39	r	r	NOUN
ejpam-620	39	40	=	=	SYM
ejpam-620	39	41	∫	∫	PROPN
ejpam-620	39	42	2π	2π	PROPN
ejpam-620	39	43	0	0	NUM
ejpam-620	40	1	�	�	PROPN
ejpam-620	40	2	�	�	PROPN
ejpam-620	40	3	f	f	PROPN
ejpam-620	40	4	(	(	PUNCT
ejpam-620	40	5	x	x	X
ejpam-620	40	6	)	)	PUNCT
ejpam-620	40	7	�	�	PROPN
ejpam-620	40	8	�	�	PROPN
ejpam-620	40	9	r	r	NOUN
ejpam-620	40	10	d	d	PROPN
ejpam-620	40	11	x	x	X
ejpam-620	40	12	!	!	PUNCT
ejpam-620	41	1	1	1	NUM
ejpam-620	41	2	r	r	NOUN
ejpam-620	41	3	,	,	PUNCT
ejpam-620	41	4	r	r	NOUN
ejpam-620	41	5	≥	≥	NOUN
ejpam-620	41	6	1	1	NUM
ejpam-620	41	7	.	.	PUNCT
ejpam-620	42	1	(	(	PUNCT
ejpam-620	42	2	11	11	NUM
ejpam-620	42	3	)	)	PUNCT
ejpam-620	42	4	the	the	DET
ejpam-620	42	5	degree	degree	NOUN
ejpam-620	42	6	of	of	ADP
ejpam-620	42	7	approximation	approximation	NOUN
ejpam-620	42	8	of	of	ADP
ejpam-620	42	9	a	a	DET
ejpam-620	42	10	function	function	NOUN
ejpam-620	42	11	f	f	NOUN
ejpam-620	42	12	:	:	PUNCT
ejpam-620	42	13	r→	r→	VERB
ejpam-620	42	14	r	r	NOUN
ejpam-620	42	15	by	by	ADP
ejpam-620	42	16	a	a	DET
ejpam-620	42	17	trigonometric	trigonometric	ADJ
ejpam-620	42	18	polynomial	polynomial	ADJ
ejpam-620	42	19	tn	tn	PROPN
ejpam-620	42	20	of	of	ADP
ejpam-620	42	21	degree	degree	NOUN
ejpam-620	42	22	n	n	CCONJ
ejpam-620	42	23	under	under	ADP
ejpam-620	42	24	sup	sup	NOUN
ejpam-620	42	25	norm	norm	NOUN
ejpam-620	42	26	‖·‖∞	‖·‖∞	VERB
ejpam-620	42	27	is	be	AUX
ejpam-620	42	28	defined	define	VERB
ejpam-620	42	29	as	as	ADP
ejpam-620	42	30	[	[	X
ejpam-620	42	31	zygmund	zygmund	NOUN
ejpam-620	42	32	,	,	PUNCT
ejpam-620	42	33	13	13	NUM
ejpam-620	42	34	]	]	PUNCT
ejpam-620	42	35	tn	tn	NOUN
ejpam-620	43	1	−	−	PROPN
ejpam-620	43	2	f	f	NOUN
ejpam-620	44	1	∞	∞	NUM
ejpam-620	44	2	=	=	SYM
ejpam-620	44	3	sup	sup	PROPN
ejpam-620	44	4	¦	¦	PROPN
ejpam-620	44	5	�	�	PROPN
ejpam-620	44	6	�	�	PROPN
ejpam-620	44	7	tn	tn	PROPN
ejpam-620	44	8	(	(	PUNCT
ejpam-620	44	9	x)−	x)−	PROPN
ejpam-620	44	10	f	f	PROPN
ejpam-620	44	11	(	(	PUNCT
ejpam-620	44	12	x	x	X
ejpam-620	44	13	)	)	PUNCT
ejpam-620	44	14	�	�	PROPN
ejpam-620	44	15	�	�	PROPN
ejpam-620	44	16	:	:	PUNCT
ejpam-620	44	17	x	x	PUNCT
ejpam-620	44	18	∈	∈	NOUN
ejpam-620	44	19	r	r	NOUN
ejpam-620	44	20	©	©	NOUN
ejpam-620	44	21	(	(	PUNCT
ejpam-620	44	22	12	12	NUM
ejpam-620	44	23	)	)	PUNCT
ejpam-620	44	24	and	and	CCONJ
ejpam-620	44	25	en	en	ADP
ejpam-620	44	26	�	�	PROPN
ejpam-620	44	27	f	f	PROPN
ejpam-620	44	28	�	�	PROPN
ejpam-620	44	29	of	of	ADP
ejpam-620	44	30	a	a	DET
ejpam-620	44	31	function	function	NOUN
ejpam-620	44	32	f	f	PROPN
ejpam-620	44	33	∈	∈	PROPN
ejpam-620	44	34	lr	lr	NOUN
ejpam-620	44	35	is	be	AUX
ejpam-620	44	36	given	give	VERB
ejpam-620	44	37	by	by	ADP
ejpam-620	44	38	en	en	PROPN
ejpam-620	44	39	�	�	PROPN
ejpam-620	44	40	f	f	PROPN
ejpam-620	44	41	�	�	PROPN
ejpam-620	44	42	=	=	SYM
ejpam-620	44	43	min	min	PROPN
ejpam-620	44	44	tn	tn	PROPN
ejpam-620	44	45	tn	tn	PROPN
ejpam-620	45	1	−	−	PROPN
ejpam-620	45	2	f	f	NOUN
ejpam-620	45	3	r	r	NOUN
ejpam-620	45	4	(	(	PUNCT
ejpam-620	45	5	13	13	NUM
ejpam-620	45	6	)	)	PUNCT
ejpam-620	45	7	we	we	PRON
ejpam-620	45	8	use	use	VERB
ejpam-620	45	9	the	the	DET
ejpam-620	45	10	following	follow	VERB
ejpam-620	45	11	notations	notation	NOUN
ejpam-620	45	12	throughout	throughout	ADP
ejpam-620	45	13	this	this	DET
ejpam-620	45	14	paper	paper	NOUN
ejpam-620	45	15	:	:	PUNCT
ejpam-620	45	16	ψ	ψ	X
ejpam-620	45	17	(	(	PUNCT
ejpam-620	45	18	t	t	PROPN
ejpam-620	45	19	)	)	PUNCT
ejpam-620	45	20	=	=	SYM
ejpam-620	46	1	f	f	PROPN
ejpam-620	46	2	(	(	PUNCT
ejpam-620	46	3	x	x	PROPN
ejpam-620	46	4	+	+	NUM
ejpam-620	46	5	t	t	NOUN
ejpam-620	46	6	)	)	PUNCT
ejpam-620	47	1	+	+	NUM
ejpam-620	47	2	f	f	X
ejpam-620	47	3	(	(	PUNCT
ejpam-620	47	4	x	x	PROPN
ejpam-620	47	5	−	−	PROPN
ejpam-620	47	6	t	t	PROPN
ejpam-620	47	7	)	)	PUNCT
ejpam-620	47	8	k̄n	k̄n	PROPN
ejpam-620	47	9	(	(	PUNCT
ejpam-620	47	10	t	t	NOUN
ejpam-620	47	11	)	)	PUNCT
ejpam-620	47	12	=	=	SYM
ejpam-620	47	13	1	1	NUM
ejpam-620	47	14	π	π	SYM
ejpam-620	47	15	2n+1	2n+1	PROPN
ejpam-620	47	16	n	n	PROPN
ejpam-620	47	17	∑	∑	ADP
ejpam-620	47	18	k=0	k=0	PROPN
ejpam-620	47	19	(	(	PUNCT
ejpam-620	47	20	�	�	PROPN
ejpam-620	47	21	n	n	CCONJ
ejpam-620	47	22	k	k	PROPN
ejpam-620	47	23	�	�	PROPN
ejpam-620	47	24	1	1	NUM
ejpam-620	47	25	(	(	PUNCT
ejpam-620	47	26	1	1	NUM
ejpam-620	47	27	+	+	NUM
ejpam-620	47	28	k	k	NOUN
ejpam-620	47	29	)	)	PUNCT
ejpam-620	48	1	k	k	NOUN
ejpam-620	48	2	∑	∑	PUNCT
ejpam-620	48	3	ν=0	ν=0	PROPN
ejpam-620	48	4	cos	cos	PROPN
ejpam-620	48	5	�	�	PROPN
ejpam-620	48	6	ν	ν	PROPN
ejpam-620	48	7	+	+	CCONJ
ejpam-620	48	8	1	1	NUM
ejpam-620	48	9	2	2	NUM
ejpam-620	48	10	�	�	PROPN
ejpam-620	48	11	t	t	PROPN
ejpam-620	48	12	sin	sin	NOUN
ejpam-620	48	13	t	t	PROPN
ejpam-620	48	14	2	2	NUM
ejpam-620	48	15	)	)	PUNCT
ejpam-620	48	16	τ	τ	PROPN
ejpam-620	48	17	=	=	SYM
ejpam-620	48	18	�	�	PROPN
ejpam-620	48	19	1	1	NUM
ejpam-620	48	20	t	t	PROPN
ejpam-620	48	21	�	�	PROPN
ejpam-620	48	22	,	,	PUNCT
ejpam-620	48	23	where	where	SCONJ
ejpam-620	48	24	τ	τ	PROPN
ejpam-620	48	25	denotes	denote	VERB
ejpam-620	48	26	the	the	DET
ejpam-620	48	27	greatest	great	ADJ
ejpam-620	48	28	integer	integer	NOUN
ejpam-620	48	29	not	not	PART
ejpam-620	48	30	greater	great	ADJ
ejpam-620	48	31	than	than	ADP
ejpam-620	48	32	1	1	NUM
ejpam-620	48	33	t	t	NOUN
ejpam-620	48	34	.	.	PUNCT
ejpam-620	49	1	h.	h.	PROPN
ejpam-620	49	2	nigam	nigam	PROPN
ejpam-620	49	3	,	,	PUNCT
ejpam-620	49	4	k.	k.	PROPN
ejpam-620	49	5	sharma	sharma	PROPN
ejpam-620	49	6	/	/	SYM
ejpam-620	49	7	eur	eur	PROPN
ejpam-620	49	8	.	.	PUNCT
ejpam-620	50	1	j.	j.	PROPN
ejpam-620	50	2	pure	pure	PROPN
ejpam-620	50	3	appl	appl	PROPN
ejpam-620	50	4	.	.	PROPN
ejpam-620	50	5	math	math	PROPN
ejpam-620	50	6	,	,	PUNCT
ejpam-620	50	7	4	4	NUM
ejpam-620	50	8	(	(	PUNCT
ejpam-620	50	9	2011	2011	NUM
ejpam-620	50	10	)	)	PUNCT
ejpam-620	50	11	,	,	PUNCT
ejpam-620	50	12	276	276	NUM
ejpam-620	50	13	-	-	SYM
ejpam-620	50	14	286	286	NUM
ejpam-620	50	15	279	279	NUM
ejpam-620	50	16	2	2	NUM
ejpam-620	50	17	.	.	PUNCT
ejpam-620	50	18	main	main	ADJ
ejpam-620	50	19	theorems	theorem	NOUN
ejpam-620	50	20	we	we	PRON
ejpam-620	50	21	prove	prove	VERB
ejpam-620	50	22	the	the	DET
ejpam-620	50	23	following	follow	VERB
ejpam-620	50	24	theorems	theorem	NOUN
ejpam-620	50	25	:	:	PUNCT
ejpam-620	50	26	theorem	theorem	NOUN
ejpam-620	50	27	1	1	NUM
ejpam-620	50	28	.	.	PUNCT
ejpam-620	51	1	if	if	SCONJ
ejpam-620	51	2	a	a	DET
ejpam-620	51	3	function	function	NOUN
ejpam-620	51	4	f	f	X
ejpam-620	51	5	,	,	PUNCT
ejpam-620	51	6	conjugate	conjugate	VERB
ejpam-620	51	7	to	to	ADP
ejpam-620	51	8	a	a	DET
ejpam-620	51	9	2π	2π	NOUN
ejpam-620	51	10	-	-	ADJ
ejpam-620	51	11	periodic	periodic	ADJ
ejpam-620	51	12	function	function	NOUN
ejpam-620	51	13	f	f	PROPN
ejpam-620	51	14	,	,	PUNCT
ejpam-620	51	15	belongs	belong	VERB
ejpam-620	51	16	to	to	ADP
ejpam-620	51	17	lipα	lipα	PROPN
ejpam-620	51	18	class	class	NOUN
ejpam-620	51	19	,	,	PUNCT
ejpam-620	51	20	then	then	ADV
ejpam-620	51	21	its	its	PRON
ejpam-620	51	22	degree	degree	NOUN
ejpam-620	51	23	of	of	ADP
ejpam-620	51	24	approximation	approximation	NOUN
ejpam-620	51	25	by	by	ADP
ejpam-620	51	26	(	(	PUNCT
ejpam-620	51	27	e	e	NOUN
ejpam-620	51	28	,	,	PUNCT
ejpam-620	51	29	1	1	NUM
ejpam-620	51	30	)	)	PUNCT
ejpam-620	51	31	(	(	PUNCT
ejpam-620	51	32	c	c	NOUN
ejpam-620	51	33	,	,	PUNCT
ejpam-620	51	34	1	1	X
ejpam-620	51	35	)	)	PUNCT
ejpam-620	51	36	means	mean	NOUN
ejpam-620	51	37	of	of	ADP
ejpam-620	51	38	conjugate	conjugate	ADJ
ejpam-620	51	39	fourier	fourier	NOUN
ejpam-620	51	40	series	series	NOUN
ejpam-620	51	41	is	be	AUX
ejpam-620	51	42	given	give	VERB
ejpam-620	51	43	by	by	ADP
ejpam-620	51	44	sup	sup	PROPN
ejpam-620	51	45	0	0	NUM
ejpam-620	51	46	<	<	NOUN
ejpam-620	51	47	x<2π	x<2π	PROPN
ejpam-620	51	48	�	�	PROPN
ejpam-620	51	49	�	�	PROPN
ejpam-620	51	50	�	�	PROPN
ejpam-620	51	51	(	(	PUNCT
ejpam-620	51	52	ec)1n	ec)1n	X
ejpam-620	51	53	(	(	PUNCT
ejpam-620	51	54	x)−	x)−	PROPN
ejpam-620	51	55	f	f	PROPN
ejpam-620	51	56	�	�	PROPN
ejpam-620	51	57	�	�	PROPN
ejpam-620	51	58	�	�	PROPN
ejpam-620	51	59	=	=	PRON
ejpam-620	51	60	(	(	PUNCT
ejpam-620	51	61	ec)1n	ec)1n	NOUN
ejpam-620	51	62	−	−	PROPN
ejpam-620	51	63	f	f	NOUN
ejpam-620	51	64	∞	∞	PROPN
ejpam-620	51	65	=	=	SYM
ejpam-620	51	66	o	o	X
ejpam-620	51	67	�	�	PROPN
ejpam-620	51	68	1	1	NUM
ejpam-620	51	69	(	(	PUNCT
ejpam-620	51	70	n+	n+	NUM
ejpam-620	51	71	1)α	1)α	NUM
ejpam-620	51	72	�	�	PROPN
ejpam-620	51	73	,	,	PUNCT
ejpam-620	51	74	0	0	PUNCT
ejpam-620	51	75	<	<	X
ejpam-620	51	76	α	α	X
ejpam-620	51	77	<	<	X
ejpam-620	51	78	1	1	NUM
ejpam-620	51	79	(	(	PUNCT
ejpam-620	51	80	14	14	NUM
ejpam-620	51	81	)	)	PUNCT
ejpam-620	51	82	where	where	SCONJ
ejpam-620	51	83	(	(	PUNCT
ejpam-620	51	84	ec)1n	ec)1n	PROPN
ejpam-620	51	85	denotes	denote	VERB
ejpam-620	51	86	the	the	DET
ejpam-620	51	87	(	(	PUNCT
ejpam-620	51	88	e	e	NOUN
ejpam-620	51	89	,	,	PUNCT
ejpam-620	51	90	1	1	NUM
ejpam-620	51	91	)	)	PUNCT
ejpam-620	51	92	(	(	PUNCT
ejpam-620	51	93	c	c	NOUN
ejpam-620	51	94	,	,	PUNCT
ejpam-620	51	95	1	1	X
ejpam-620	51	96	)	)	PUNCT
ejpam-620	51	97	transform	transform	NOUN
ejpam-620	51	98	as	as	ADV
ejpam-620	51	99	defined	define	VERB
ejpam-620	51	100	in	in	ADP
ejpam-620	51	101	(	(	PUNCT
ejpam-620	51	102	3	3	NUM
ejpam-620	51	103	)	)	PUNCT
ejpam-620	51	104	.	.	PUNCT
ejpam-620	52	1	theorem	theorem	NOUN
ejpam-620	52	2	2	2	NUM
ejpam-620	52	3	.	.	PUNCT
ejpam-620	53	1	if	if	SCONJ
ejpam-620	53	2	f	f	PROPN
ejpam-620	53	3	,	,	PUNCT
ejpam-620	53	4	conjugate	conjugate	VERB
ejpam-620	53	5	to	to	ADP
ejpam-620	53	6	a	a	DET
ejpam-620	53	7	2π	2π	NOUN
ejpam-620	53	8	-	-	ADJ
ejpam-620	53	9	periodic	periodic	ADJ
ejpam-620	53	10	function	function	NOUN
ejpam-620	53	11	f	f	PROPN
ejpam-620	53	12	,	,	PUNCT
ejpam-620	53	13	belongs	belong	VERB
ejpam-620	53	14	to	to	ADP
ejpam-620	53	15	w	w	PROPN
ejpam-620	53	16	�	�	PROPN
ejpam-620	53	17	lr	lr	PROPN
ejpam-620	53	18	,	,	PUNCT
ejpam-620	53	19	ξ(t	ξ(t	NOUN
ejpam-620	53	20	)	)	PUNCT
ejpam-620	53	21	�	�	PROPN
ejpam-620	53	22	class	class	NOUN
ejpam-620	53	23	,	,	PUNCT
ejpam-620	53	24	then	then	ADV
ejpam-620	53	25	its	its	PRON
ejpam-620	53	26	degree	degree	NOUN
ejpam-620	53	27	of	of	ADP
ejpam-620	53	28	approximation	approximation	NOUN
ejpam-620	53	29	by	by	ADP
ejpam-620	53	30	(	(	PUNCT
ejpam-620	53	31	e	e	NOUN
ejpam-620	53	32	,	,	PUNCT
ejpam-620	53	33	1	1	NUM
ejpam-620	53	34	)	)	PUNCT
ejpam-620	53	35	(	(	PUNCT
ejpam-620	53	36	c	c	NOUN
ejpam-620	53	37	,	,	PUNCT
ejpam-620	53	38	1	1	X
ejpam-620	53	39	)	)	PUNCT
ejpam-620	53	40	means	mean	NOUN
ejpam-620	53	41	of	of	ADP
ejpam-620	53	42	conjugate	conjugate	ADJ
ejpam-620	53	43	fourier	fourier	NOUN
ejpam-620	53	44	series	series	NOUN
ejpam-620	53	45	is	be	AUX
ejpam-620	53	46	given	give	VERB
ejpam-620	53	47	by	by	ADP
ejpam-620	53	48	(	(	PUNCT
ejpam-620	53	49	ec)1n	ec)1n	NOUN
ejpam-620	53	50	−	−	PROPN
ejpam-620	53	51	f	f	NOUN
ejpam-620	53	52	r	r	NOUN
ejpam-620	53	53	=	=	PUNCT
ejpam-620	53	54	o	o	X
ejpam-620	53	55	�	�	PROPN
ejpam-620	53	56	(	(	PUNCT
ejpam-620	53	57	n+	n+	NUM
ejpam-620	53	58	1)β+	1)β+	NUM
ejpam-620	53	59	1	1	NUM
ejpam-620	53	60	r	r	NOUN
ejpam-620	53	61	ξ	ξ	X
ejpam-620	53	62	�	�	PROPN
ejpam-620	53	63	1	1	NUM
ejpam-620	53	64	n+	n+	SYM
ejpam-620	53	65	1	1	NUM
ejpam-620	53	66	�	�	PROPN
ejpam-620	53	67	�	�	PROPN
ejpam-620	53	68	(	(	PUNCT
ejpam-620	53	69	15	15	NUM
ejpam-620	53	70	)	)	PUNCT
ejpam-620	53	71	provided	provide	VERB
ejpam-620	53	72	ξ	ξ	PROPN
ejpam-620	53	73	(	(	PUNCT
ejpam-620	53	74	t	t	NOUN
ejpam-620	53	75	)	)	PUNCT
ejpam-620	53	76	satisfies	satisfy	VERB
ejpam-620	53	77	the	the	DET
ejpam-620	53	78	following	follow	VERB
ejpam-620	53	79	conditions	condition	NOUN
ejpam-620	53	80	:	:	PUNCT
ejpam-620	53	81	�	�	PROPN
ejpam-620	53	82	ξ	ξ	PROPN
ejpam-620	53	83	(	(	PUNCT
ejpam-620	53	84	t	t	PROPN
ejpam-620	53	85	)	)	PUNCT
ejpam-620	53	86	t	t	PROPN
ejpam-620	53	87	�	�	PROPN
ejpam-620	53	88	be	be	AUX
ejpam-620	53	89	a	a	DET
ejpam-620	53	90	decreasing	decrease	VERB
ejpam-620	53	91	sequence	sequence	NOUN
ejpam-620	53	92	,	,	PUNCT
ejpam-620	53	93	(	(	PUNCT
ejpam-620	53	94	16	16	NUM
ejpam-620	53	95	)	)	PUNCT
ejpam-620	53	96			PROPN
ejpam-620	53	97			PRON
ejpam-620	53	98			ADJ
ejpam-620	53	99	∫	∫	PROPN
ejpam-620	53	100	1	1	NUM
ejpam-620	53	101	n+1	n+1	PROPN
ejpam-620	53	102	0	0	NUM
ejpam-620	53	103	t	t	PROPN
ejpam-620	53	104	�	�	PROPN
ejpam-620	53	105	�	�	PROPN
ejpam-620	53	106	ψ	ψ	PROPN
ejpam-620	53	107	(	(	PUNCT
ejpam-620	53	108	t	t	PROPN
ejpam-620	53	109	)	)	PUNCT
ejpam-620	53	110	�	�	PROPN
ejpam-620	53	111	�	�	PROPN
ejpam-620	53	112	ξ	ξ	PROPN
ejpam-620	53	113	(	(	PUNCT
ejpam-620	53	114	t	t	PROPN
ejpam-620	53	115	)	)	PUNCT
ejpam-620	53	116	!	!	PUNCT
ejpam-620	54	1	r	r	NOUN
ejpam-620	54	2	sinβ	sinβ	NOUN
ejpam-620	54	3	r	r	NOUN
ejpam-620	54	4	t	t	PROPN
ejpam-620	54	5	d	d	X
ejpam-620	54	6	t	t	PROPN
ejpam-620	55	1			PROPN
ejpam-620	55	2			PROPN
ejpam-620	55	3			NOUN
ejpam-620	55	4	1	1	NUM
ejpam-620	55	5	r	r	NOUN
ejpam-620	55	6	=	=	SYM
ejpam-620	55	7	o	o	X
ejpam-620	55	8	�	�	PROPN
ejpam-620	55	9	1	1	NUM
ejpam-620	55	10	n+	n+	SYM
ejpam-620	55	11	1	1	NUM
ejpam-620	55	12	�	�	PROPN
ejpam-620	55	13	(	(	PUNCT
ejpam-620	55	14	17	17	NUM
ejpam-620	55	15	)	)	PUNCT
ejpam-620	55	16	and	and	CCONJ
ejpam-620	55	17			PROPN
ejpam-620	55	18			PRON
ejpam-620	55	19			ADJ
ejpam-620	55	20	∫	∫	PROPN
ejpam-620	56	1	π	π	PROPN
ejpam-620	56	2	1	1	X
ejpam-620	56	3	n+1	n+1	PROPN
ejpam-620	56	4	t−δ	t−δ	PROPN
ejpam-620	56	5	�	�	PROPN
ejpam-620	56	6	�	�	PROPN
ejpam-620	56	7	ψ	ψ	PROPN
ejpam-620	56	8	(	(	PUNCT
ejpam-620	56	9	t	t	PROPN
ejpam-620	56	10	)	)	PUNCT
ejpam-620	56	11	�	�	PROPN
ejpam-620	56	12	�	�	PROPN
ejpam-620	56	13	ξ	ξ	PROPN
ejpam-620	56	14	(	(	PUNCT
ejpam-620	56	15	t	t	PROPN
ejpam-620	56	16	)	)	PUNCT
ejpam-620	56	17	!	!	PUNCT
ejpam-620	57	1	r	r	NOUN
ejpam-620	57	2	d	d	NOUN
ejpam-620	57	3	t	t	NOUN
ejpam-620	57	4			PROPN
ejpam-620	57	5			PROPN
ejpam-620	57	6			NOUN
ejpam-620	57	7	1	1	NUM
ejpam-620	57	8	r	r	NOUN
ejpam-620	57	9	=	=	SYM
ejpam-620	57	10	o	o	X
ejpam-620	57	11	¦	¦	PROPN
ejpam-620	57	12	(	(	PUNCT
ejpam-620	57	13	n+	n+	NUM
ejpam-620	57	14	1)δ	1)δ	NUM
ejpam-620	57	15	©	©	PROPN
ejpam-620	57	16	(	(	PUNCT
ejpam-620	57	17	18	18	NUM
ejpam-620	57	18	)	)	PUNCT
ejpam-620	57	19	where	where	SCONJ
ejpam-620	57	20	δ	δ	PROPN
ejpam-620	57	21	is	be	AUX
ejpam-620	57	22	an	an	DET
ejpam-620	57	23	arbitrary	arbitrary	ADJ
ejpam-620	57	24	number	number	NOUN
ejpam-620	57	25	such	such	ADJ
ejpam-620	57	26	that	that	PRON
ejpam-620	57	27	s	s	X
ejpam-620	57	28	(	(	PUNCT
ejpam-620	57	29	1−δ)−1	1−δ)−1	PROPN
ejpam-620	57	30	>	>	X
ejpam-620	57	31	0	0	NUM
ejpam-620	57	32	,	,	PUNCT
ejpam-620	57	33	1	1	NUM
ejpam-620	57	34	r	r	NOUN
ejpam-620	57	35	+	+	NOUN
ejpam-620	57	36	1	1	NUM
ejpam-620	57	37	s	s	NOUN
ejpam-620	57	38	=	=	SYM
ejpam-620	57	39	1	1	NUM
ejpam-620	57	40	,	,	PUNCT
ejpam-620	57	41	conditions	condition	NOUN
ejpam-620	57	42	(	(	PUNCT
ejpam-620	57	43	17	17	NUM
ejpam-620	57	44	)	)	PUNCT
ejpam-620	57	45	and	and	CCONJ
ejpam-620	57	46	(	(	PUNCT
ejpam-620	57	47	18	18	NUM
ejpam-620	57	48	)	)	PUNCT
ejpam-620	57	49	hold	hold	VERB
ejpam-620	57	50	uniformly	uniformly	ADV
ejpam-620	57	51	in	in	ADP
ejpam-620	57	52	x	x	PUNCT
ejpam-620	57	53	and	and	CCONJ
ejpam-620	57	54	(	(	PUNCT
ejpam-620	57	55	ec)1n	ec)1n	INTJ
ejpam-620	57	56	,	,	PUNCT
ejpam-620	57	57	as	as	SCONJ
ejpam-620	57	58	defined	define	VERB
ejpam-620	57	59	in	in	ADP
ejpam-620	57	60	(	(	PUNCT
ejpam-620	57	61	3	3	NUM
ejpam-620	57	62	)	)	PUNCT
ejpam-620	57	63	,	,	PUNCT
ejpam-620	57	64	is	be	AUX
ejpam-620	57	65	(	(	PUNCT
ejpam-620	57	66	e	e	NOUN
ejpam-620	57	67	,	,	PUNCT
ejpam-620	57	68	1	1	NUM
ejpam-620	57	69	)	)	PUNCT
ejpam-620	57	70	(	(	PUNCT
ejpam-620	57	71	c	c	NOUN
ejpam-620	57	72	,	,	PUNCT
ejpam-620	57	73	1	1	X
ejpam-620	57	74	)	)	PUNCT
ejpam-620	57	75	means	mean	NOUN
ejpam-620	57	76	of	of	ADP
ejpam-620	57	77	the	the	DET
ejpam-620	57	78	series	series	NOUN
ejpam-620	57	79	(	(	PUNCT
ejpam-620	57	80	5	5	NUM
ejpam-620	57	81	)	)	PUNCT
ejpam-620	57	82	and	and	CCONJ
ejpam-620	57	83	f	f	PROPN
ejpam-620	57	84	(	(	PUNCT
ejpam-620	57	85	x	x	X
ejpam-620	57	86	)	)	PUNCT
ejpam-620	58	1	=	=	SYM
ejpam-620	58	2	−	−	PROPN
ejpam-620	58	3	1	1	NUM
ejpam-620	58	4	2π	2π	NUM
ejpam-620	58	5	∫	∫	PROPN
ejpam-620	58	6	2π	2π	PROPN
ejpam-620	58	7	0	0	NUM
ejpam-620	59	1	ψ	ψ	X
ejpam-620	59	2	(	(	PUNCT
ejpam-620	59	3	t	t	NOUN
ejpam-620	59	4	)	)	PUNCT
ejpam-620	59	5	cot	cot	NOUN
ejpam-620	59	6	�	�	PROPN
ejpam-620	59	7	t	t	PROPN
ejpam-620	59	8	2	2	NUM
ejpam-620	59	9	�	�	PROPN
ejpam-620	59	10	d	d	PROPN
ejpam-620	59	11	t	t	PROPN
ejpam-620	59	12	(	(	PUNCT
ejpam-620	59	13	19	19	NUM
ejpam-620	59	14	)	)	PUNCT
ejpam-620	59	15	3	3	NUM
ejpam-620	59	16	.	.	PUNCT
ejpam-620	59	17	lemmas	lemmas	PROPN
ejpam-620	59	18	for	for	ADP
ejpam-620	59	19	the	the	DET
ejpam-620	59	20	proof	proof	NOUN
ejpam-620	59	21	of	of	ADP
ejpam-620	59	22	our	our	PRON
ejpam-620	59	23	theorems	theorem	NOUN
ejpam-620	59	24	,	,	PUNCT
ejpam-620	59	25	following	follow	VERB
ejpam-620	59	26	lemmas	lemma	NOUN
ejpam-620	59	27	are	be	AUX
ejpam-620	59	28	required	require	VERB
ejpam-620	59	29	:	:	PUNCT
ejpam-620	59	30	lemma	lemma	PROPN
ejpam-620	59	31	1	1	X
ejpam-620	59	32	.	.	PUNCT
ejpam-620	59	33	�	�	PROPN
ejpam-620	59	34	�	�	PROPN
ejpam-620	59	35	gn	gn	PROPN
ejpam-620	59	36	(	(	PUNCT
ejpam-620	59	37	t	t	PROPN
ejpam-620	59	38	)	)	PUNCT
ejpam-620	59	39	�	�	PROPN
ejpam-620	59	40	�	�	PROPN
ejpam-620	59	41	=	=	PUNCT
ejpam-620	59	42	o	o	PROPN
ejpam-620	59	43	�	�	PROPN
ejpam-620	59	44	1	1	NUM
ejpam-620	59	45	t	t	PROPN
ejpam-620	59	46	�	�	PROPN
ejpam-620	59	47	,	,	PUNCT
ejpam-620	59	48	for	for	ADP
ejpam-620	59	49	0≤	0≤	NUM
ejpam-620	59	50	t	t	NOUN
ejpam-620	59	51	≤	≤	NOUN
ejpam-620	59	52	1	1	NUM
ejpam-620	59	53	n+	n+	SYM
ejpam-620	59	54	1	1	NUM
ejpam-620	59	55	h.	h.	PROPN
ejpam-620	59	56	nigam	nigam	PROPN
ejpam-620	59	57	,	,	PUNCT
ejpam-620	59	58	k.	k.	PROPN
ejpam-620	59	59	sharma	sharma	PROPN
ejpam-620	59	60	/	/	SYM
ejpam-620	59	61	eur	eur	PROPN
ejpam-620	59	62	.	.	PUNCT
ejpam-620	60	1	j.	j.	PROPN
ejpam-620	60	2	pure	pure	PROPN
ejpam-620	60	3	appl	appl	PROPN
ejpam-620	60	4	.	.	PROPN
ejpam-620	60	5	math	math	PROPN
ejpam-620	60	6	,	,	PUNCT
ejpam-620	60	7	4	4	NUM
ejpam-620	60	8	(	(	PUNCT
ejpam-620	60	9	2011	2011	NUM
ejpam-620	60	10	)	)	PUNCT
ejpam-620	60	11	,	,	PUNCT
ejpam-620	60	12	276	276	NUM
ejpam-620	60	13	-	-	SYM
ejpam-620	60	14	286	286	NUM
ejpam-620	60	15	280	280	NUM
ejpam-620	60	16	proof	proof	NOUN
ejpam-620	60	17	.	.	PUNCT
ejpam-620	61	1	for	for	ADP
ejpam-620	61	2	0≤	0≤	NUM
ejpam-620	61	3	t	t	PROPN
ejpam-620	61	4	≤	≤	NUM
ejpam-620	61	5	1	1	NUM
ejpam-620	61	6	n+1	n+1	NUM
ejpam-620	61	7	,	,	PUNCT
ejpam-620	61	8	sin	sin	PROPN
ejpam-620	61	9	�	�	PROPN
ejpam-620	61	10	t	t	PROPN
ejpam-620	61	11	2	2	NUM
ejpam-620	61	12	�	�	PROPN
ejpam-620	61	13	≥	≥	PROPN
ejpam-620	61	14	t	t	PROPN
ejpam-620	61	15	π	π	PROPN
ejpam-620	61	16	and	and	CCONJ
ejpam-620	61	17	|cos	|cos	PROPN
ejpam-620	61	18	nt|	nt|	PROPN
ejpam-620	61	19	≤	≤	NOUN
ejpam-620	61	20	1	1	NUM
ejpam-620	61	21	�	�	PROPN
ejpam-620	61	22	�	�	PROPN
ejpam-620	61	23	gn	gn	PROPN
ejpam-620	61	24	(	(	PUNCT
ejpam-620	61	25	t	t	PROPN
ejpam-620	61	26	)	)	PUNCT
ejpam-620	61	27	�	�	PROPN
ejpam-620	61	28	�	�	PROPN
ejpam-620	61	29	≤	≤	NOUN
ejpam-620	61	30	1	1	NUM
ejpam-620	61	31	π	π	PROPN
ejpam-620	61	32	2n+1	2n+1	PROPN
ejpam-620	61	33	�	�	PROPN
ejpam-620	61	34	�	�	PROPN
ejpam-620	61	35	�	�	PROPN
ejpam-620	61	36	�	�	PROPN
ejpam-620	61	37	�	�	PROPN
ejpam-620	61	38	n	n	CCONJ
ejpam-620	61	39	∑	∑	ADP
ejpam-620	61	40	k=0	k=0	PROPN
ejpam-620	61	41	(	(	PUNCT
ejpam-620	61	42	�	�	PROPN
ejpam-620	61	43	n	n	CCONJ
ejpam-620	61	44	k	k	PROPN
ejpam-620	61	45	�	�	PROPN
ejpam-620	61	46	1	1	NUM
ejpam-620	61	47	(	(	PUNCT
ejpam-620	61	48	1	1	NUM
ejpam-620	61	49	+	+	NUM
ejpam-620	61	50	k	k	NOUN
ejpam-620	61	51	)	)	PUNCT
ejpam-620	62	1	k	k	NOUN
ejpam-620	62	2	∑	∑	PUNCT
ejpam-620	62	3	ν=0	ν=0	PROPN
ejpam-620	62	4	cos	cos	PROPN
ejpam-620	62	5	�	�	PROPN
ejpam-620	62	6	ν	ν	PROPN
ejpam-620	62	7	+	+	CCONJ
ejpam-620	62	8	1	1	NUM
ejpam-620	62	9	2	2	NUM
ejpam-620	62	10	�	�	PROPN
ejpam-620	62	11	t	t	PROPN
ejpam-620	62	12	sin	sin	NOUN
ejpam-620	62	13	t	t	PROPN
ejpam-620	62	14	2	2	NUM
ejpam-620	62	15	)	)	PUNCT
ejpam-620	62	16	�	�	PROPN
ejpam-620	62	17	�	�	PROPN
ejpam-620	62	18	�	�	PROPN
ejpam-620	62	19	�	�	PROPN
ejpam-620	62	20	�	�	PROPN
ejpam-620	62	21	≤	≤	NOUN
ejpam-620	62	22	1	1	NUM
ejpam-620	62	23	π	π	PROPN
ejpam-620	62	24	2n+1	2n+1	PROPN
ejpam-620	62	25	n	n	CCONJ
ejpam-620	62	26	∑	∑	ADP
ejpam-620	62	27	k=0	k=0	PROPN
ejpam-620	62	28			VERB
ejpam-620	62	29			ADP
ejpam-620	62	30			ADJ
ejpam-620	62	31	�	�	PROPN
ejpam-620	62	32	n	n	CCONJ
ejpam-620	62	33	k	k	PROPN
ejpam-620	62	34	�	�	PROPN
ejpam-620	62	35	1	1	NUM
ejpam-620	62	36	(	(	PUNCT
ejpam-620	62	37	1	1	NUM
ejpam-620	62	38	+	+	NUM
ejpam-620	62	39	k	k	NOUN
ejpam-620	62	40	)	)	PUNCT
ejpam-620	62	41	k	k	NOUN
ejpam-620	62	42	∑	∑	PUNCT
ejpam-620	62	43	ν=0	ν=0	PROPN
ejpam-620	62	44	�	�	PROPN
ejpam-620	62	45	�	�	PROPN
ejpam-620	62	46	�	�	PROPN
ejpam-620	62	47	cos	cos	PROPN
ejpam-620	62	48	�	�	PROPN
ejpam-620	62	49	ν	ν	PROPN
ejpam-620	62	50	+	+	CCONJ
ejpam-620	62	51	1	1	NUM
ejpam-620	62	52	2	2	NUM
ejpam-620	62	53	�	�	PROPN
ejpam-620	62	54	t	t	PROPN
ejpam-620	62	55	�	�	PROPN
ejpam-620	62	56	�	�	PROPN
ejpam-620	62	57	�	�	PROPN
ejpam-620	62	58	�	�	PROPN
ejpam-620	62	59	�	�	PROPN
ejpam-620	62	60	�	�	PROPN
ejpam-620	62	61	sin	sin	PROPN
ejpam-620	62	62	t	t	PROPN
ejpam-620	62	63	2	2	NUM
ejpam-620	62	64	�	�	PROPN
ejpam-620	62	65	�	�	PROPN
ejpam-620	62	66	�	�	PROPN
ejpam-620	62	67			PROPN
ejpam-620	62	68			PROPN
ejpam-620	62	69			NOUN
ejpam-620	62	70	=	=	SYM
ejpam-620	62	71	1	1	NUM
ejpam-620	62	72	t	t	NOUN
ejpam-620	62	73	2n+1	2n+1	PROPN
ejpam-620	62	74	n	n	CCONJ
ejpam-620	62	75	∑	∑	ADP
ejpam-620	62	76	k=0	k=0	PROPN
ejpam-620	62	77	(	(	PUNCT
ejpam-620	62	78	�	�	PROPN
ejpam-620	62	79	n	n	CCONJ
ejpam-620	62	80	k	k	PROPN
ejpam-620	62	81	�	�	PROPN
ejpam-620	62	82	�	�	PROPN
ejpam-620	62	83	1	1	NUM
ejpam-620	62	84	1	1	NUM
ejpam-620	62	85	+	+	NUM
ejpam-620	62	86	k	k	PROPN
ejpam-620	62	87	�	�	PROPN
ejpam-620	62	88	k	k	PROPN
ejpam-620	62	89	∑	∑	PUNCT
ejpam-620	62	90	ν=0	ν=0	PROPN
ejpam-620	62	91	1	1	NUM
ejpam-620	62	92	)	)	PUNCT
ejpam-620	62	93	=	=	SYM
ejpam-620	62	94	1	1	NUM
ejpam-620	62	95	t	t	NOUN
ejpam-620	62	96	2n+1	2n+1	PROPN
ejpam-620	62	97	n	n	CCONJ
ejpam-620	62	98	∑	∑	ADP
ejpam-620	62	99	k=0	k=0	PROPN
ejpam-620	62	100	¨	¨	ADJ
ejpam-620	62	101	�	�	PROPN
ejpam-620	62	102	n	n	CCONJ
ejpam-620	62	103	k	k	PROPN
ejpam-620	62	104	�	�	PROPN
ejpam-620	62	105	«	«	PUNCT
ejpam-620	62	106	=	=	SYM
ejpam-620	62	107	1	1	NUM
ejpam-620	62	108	t	t	NOUN
ejpam-620	62	109	2n+1	2n+1	PROPN
ejpam-620	62	110	2n	2n	NUM
ejpam-620	63	1	=	=	PUNCT
ejpam-620	63	2	o	o	X
ejpam-620	63	3	�	�	PROPN
ejpam-620	63	4	1	1	NUM
ejpam-620	63	5	t	t	PROPN
ejpam-620	63	6	�	�	PROPN
ejpam-620	63	7	since	since	SCONJ
ejpam-620	63	8	n	n	PROPN
ejpam-620	63	9	∑	∑	ADV
ejpam-620	63	10	k=0	k=0	PROPN
ejpam-620	63	11	�	�	PROPN
ejpam-620	63	12	n	n	CCONJ
ejpam-620	63	13	k	k	PROPN
ejpam-620	63	14	�	�	PROPN
ejpam-620	63	15	=	=	SYM
ejpam-620	63	16	2n	2n	NUM
ejpam-620	63	17	lemma	lemma	PROPN
ejpam-620	63	18	2	2	NUM
ejpam-620	63	19	.	.	PUNCT
ejpam-620	64	1	for	for	ADP
ejpam-620	64	2	0≤	0≤	DET
ejpam-620	64	3	a	a	DET
ejpam-620	64	4	≤	≤	NUM
ejpam-620	64	5	b	b	X
ejpam-620	64	6	≤∞	≤∞	PROPN
ejpam-620	64	7	,	,	PUNCT
ejpam-620	64	8	0≤	0≤	NUM
ejpam-620	64	9	t	t	NOUN
ejpam-620	64	10	≤	≤	NOUN
ejpam-620	64	11	π	π	PROPN
ejpam-620	64	12	and	and	CCONJ
ejpam-620	64	13	any	any	DET
ejpam-620	64	14	n	n	CCONJ
ejpam-620	64	15	,	,	PUNCT
ejpam-620	64	16	we	we	PRON
ejpam-620	64	17	have	have	VERB
ejpam-620	64	18	�	�	PROPN
ejpam-620	64	19	�	�	PROPN
ejpam-620	64	20	gn	gn	PROPN
ejpam-620	64	21	(	(	PUNCT
ejpam-620	64	22	t	t	PROPN
ejpam-620	64	23	)	)	PUNCT
ejpam-620	64	24	�	�	PROPN
ejpam-620	64	25	�	�	PROPN
ejpam-620	64	26	=	=	SYM
ejpam-620	64	27	o	o	NOUN
ejpam-620	64	28	�	�	PROPN
ejpam-620	64	29	1	1	NUM
ejpam-620	64	30	t	t	NOUN
ejpam-620	64	31	�	�	PROPN
ejpam-620	64	32	proof	proof	NOUN
ejpam-620	64	33	.	.	PUNCT
ejpam-620	65	1	for	for	ADP
ejpam-620	65	2	0≤	0≤	NUM
ejpam-620	65	3	1	1	NUM
ejpam-620	65	4	n+1	n+1	PROPN
ejpam-620	65	5	≤	≤	PUNCT
ejpam-620	65	6	t	t	PROPN
ejpam-620	65	7	≤	≤	PROPN
ejpam-620	65	8	π	π	PROPN
ejpam-620	65	9	,	,	PUNCT
ejpam-620	65	10	sin	sin	PROPN
ejpam-620	65	11	�	�	PROPN
ejpam-620	65	12	t	t	PROPN
ejpam-620	65	13	2	2	NUM
ejpam-620	65	14	�	�	PROPN
ejpam-620	65	15	≥	≥	PROPN
ejpam-620	65	16	t	t	PROPN
ejpam-620	65	17	π	π	PROPN
ejpam-620	65	18	.	.	PUNCT
ejpam-620	65	19	�	�	PROPN
ejpam-620	65	20	�	�	PROPN
ejpam-620	65	21	gn	gn	PROPN
ejpam-620	65	22	(	(	PUNCT
ejpam-620	65	23	t	t	PROPN
ejpam-620	65	24	)	)	PUNCT
ejpam-620	65	25	�	�	PROPN
ejpam-620	65	26	�	�	PROPN
ejpam-620	65	27	≤	≤	NOUN
ejpam-620	65	28	1	1	NUM
ejpam-620	65	29	π	π	PROPN
ejpam-620	65	30	2n+1	2n+1	PROPN
ejpam-620	65	31	�	�	PROPN
ejpam-620	65	32	�	�	PROPN
ejpam-620	65	33	�	�	PROPN
ejpam-620	65	34	�	�	PROPN
ejpam-620	65	35	�	�	PROPN
ejpam-620	65	36	n	n	CCONJ
ejpam-620	65	37	∑	∑	ADP
ejpam-620	65	38	k=0	k=0	PROPN
ejpam-620	65	39	(	(	PUNCT
ejpam-620	65	40	�	�	PROPN
ejpam-620	65	41	n	n	CCONJ
ejpam-620	65	42	k	k	PROPN
ejpam-620	65	43	�	�	PROPN
ejpam-620	65	44	1	1	NUM
ejpam-620	65	45	(	(	PUNCT
ejpam-620	65	46	1	1	NUM
ejpam-620	65	47	+	+	NUM
ejpam-620	65	48	k	k	NOUN
ejpam-620	65	49	)	)	PUNCT
ejpam-620	66	1	k	k	NOUN
ejpam-620	66	2	∑	∑	PUNCT
ejpam-620	66	3	ν=0	ν=0	PROPN
ejpam-620	66	4	cos	cos	PROPN
ejpam-620	66	5	�	�	PROPN
ejpam-620	66	6	ν	ν	PROPN
ejpam-620	66	7	+	+	CCONJ
ejpam-620	66	8	1	1	NUM
ejpam-620	66	9	2	2	NUM
ejpam-620	66	10	�	�	PROPN
ejpam-620	66	11	t	t	PROPN
ejpam-620	66	12	sin	sin	NOUN
ejpam-620	66	13	t	t	PROPN
ejpam-620	66	14	2	2	NUM
ejpam-620	66	15	)	)	PUNCT
ejpam-620	66	16	�	�	PROPN
ejpam-620	66	17	�	�	PROPN
ejpam-620	66	18	�	�	PROPN
ejpam-620	66	19	�	�	PROPN
ejpam-620	66	20	�	�	PROPN
ejpam-620	66	21	≤	≤	PROPN
ejpam-620	66	22	1	1	NUM
ejpam-620	66	23	2n+1	2n+1	PROPN
ejpam-620	66	24	t	t	PROPN
ejpam-620	66	25	�	�	PROPN
ejpam-620	66	26	�	�	PROPN
ejpam-620	66	27	�	�	PROPN
ejpam-620	66	28	�	�	PROPN
ejpam-620	66	29	�	�	PROPN
ejpam-620	66	30	n	n	CCONJ
ejpam-620	66	31	∑	∑	ADP
ejpam-620	66	32	k=0	k=0	PROPN
ejpam-620	66	33			PROPN
ejpam-620	66	34			NUM
ejpam-620	66	35	�	�	PROPN
ejpam-620	66	36	n	n	CCONJ
ejpam-620	66	37	k	k	PROPN
ejpam-620	66	38	�	�	PROPN
ejpam-620	66	39	1	1	NUM
ejpam-620	66	40	(	(	PUNCT
ejpam-620	66	41	1	1	NUM
ejpam-620	66	42	+	+	NUM
ejpam-620	66	43	k	k	NOUN
ejpam-620	66	44	)	)	PUNCT
ejpam-620	66	45	re	re	VERB
ejpam-620	66	46	(	(	PUNCT
ejpam-620	66	47	k	k	X
ejpam-620	66	48	∑	∑	PUNCT
ejpam-620	66	49	ν=0	ν=0	PROPN
ejpam-620	66	50	ei	ei	X
ejpam-620	66	51	�	�	PROPN
ejpam-620	66	52	ν+	ν+	PROPN
ejpam-620	66	53	1	1	NUM
ejpam-620	66	54	2	2	NUM
ejpam-620	66	55	�	�	PROPN
ejpam-620	66	56	t	t	PROPN
ejpam-620	66	57	)	)	PUNCT
ejpam-620	66	58			PROPN
ejpam-620	66	59			PROPN
ejpam-620	66	60	�	�	PROPN
ejpam-620	66	61	�	�	PROPN
ejpam-620	66	62	�	�	PROPN
ejpam-620	66	63	�	�	PROPN
ejpam-620	66	64	�	�	PROPN
ejpam-620	66	65	≤	≤	PROPN
ejpam-620	66	66	1	1	NUM
ejpam-620	66	67	2n+1	2n+1	PROPN
ejpam-620	66	68	t	t	PROPN
ejpam-620	66	69	�	�	PROPN
ejpam-620	66	70	�	�	PROPN
ejpam-620	66	71	�	�	PROPN
ejpam-620	66	72	�	�	PROPN
ejpam-620	66	73	�	�	PROPN
ejpam-620	66	74	n	n	CCONJ
ejpam-620	66	75	∑	∑	ADP
ejpam-620	66	76	k=0	k=0	PROPN
ejpam-620	66	77			PROPN
ejpam-620	66	78			NUM
ejpam-620	66	79	�	�	PROPN
ejpam-620	66	80	n	n	CCONJ
ejpam-620	66	81	k	k	PROPN
ejpam-620	66	82	�	�	PROPN
ejpam-620	66	83	1	1	NUM
ejpam-620	66	84	(	(	PUNCT
ejpam-620	66	85	1	1	NUM
ejpam-620	66	86	+	+	NUM
ejpam-620	66	87	k	k	NOUN
ejpam-620	66	88	)	)	PUNCT
ejpam-620	66	89	re	re	VERB
ejpam-620	66	90	(	(	PUNCT
ejpam-620	66	91	k	k	NOUN
ejpam-620	66	92	∑	∑	PUNCT
ejpam-620	66	93	ν=0	ν=0	PRON
ejpam-620	66	94	eiν	eiν	PROPN
ejpam-620	66	95	t	t	NOUN
ejpam-620	66	96	)	)	PUNCT
ejpam-620	66	97			PROPN
ejpam-620	66	98			PROPN
ejpam-620	66	99	�	�	PROPN
ejpam-620	66	100	�	�	PROPN
ejpam-620	66	101	�	�	PROPN
ejpam-620	66	102	�	�	PROPN
ejpam-620	66	103	�	�	PROPN
ejpam-620	66	104	�	�	PROPN
ejpam-620	66	105	�	�	PROPN
ejpam-620	66	106	�	�	PROPN
ejpam-620	66	107	e	e	PROPN
ejpam-620	66	108	i	i	PRON
ejpam-620	66	109	t	t	PROPN
ejpam-620	66	110	2	2	NUM
ejpam-620	66	111	�	�	PROPN
ejpam-620	66	112	�	�	PROPN
ejpam-620	66	113	�	�	PROPN
ejpam-620	66	114	≤	≤	PROPN
ejpam-620	66	115	1	1	NUM
ejpam-620	66	116	2n+1	2n+1	PROPN
ejpam-620	66	117	t	t	PROPN
ejpam-620	66	118	�	�	PROPN
ejpam-620	66	119	�	�	PROPN
ejpam-620	66	120	�	�	PROPN
ejpam-620	66	121	�	�	PROPN
ejpam-620	66	122	�	�	PROPN
ejpam-620	66	123	n	n	CCONJ
ejpam-620	66	124	∑	∑	ADP
ejpam-620	66	125	k=0	k=0	PROPN
ejpam-620	66	126			PROPN
ejpam-620	66	127			NUM
ejpam-620	66	128	�	�	PROPN
ejpam-620	66	129	n	n	CCONJ
ejpam-620	66	130	k	k	PROPN
ejpam-620	66	131	�	�	PROPN
ejpam-620	66	132	1	1	NUM
ejpam-620	66	133	(	(	PUNCT
ejpam-620	66	134	1	1	NUM
ejpam-620	66	135	+	+	NUM
ejpam-620	66	136	k	k	NOUN
ejpam-620	66	137	)	)	PUNCT
ejpam-620	66	138	re	re	VERB
ejpam-620	66	139	(	(	PUNCT
ejpam-620	66	140	k	k	NOUN
ejpam-620	66	141	∑	∑	PUNCT
ejpam-620	66	142	ν=0	ν=0	PRON
ejpam-620	66	143	eiν	eiν	PROPN
ejpam-620	66	144	t	t	NOUN
ejpam-620	66	145	)	)	PUNCT
ejpam-620	66	146			PROPN
ejpam-620	66	147			PROPN
ejpam-620	66	148	�	�	PROPN
ejpam-620	66	149	�	�	PROPN
ejpam-620	66	150	�	�	PROPN
ejpam-620	66	151	�	�	PROPN
ejpam-620	66	152	�	�	PROPN
ejpam-620	66	153	≤	≤	PROPN
ejpam-620	66	154	1	1	NUM
ejpam-620	66	155	2n+1	2n+1	PROPN
ejpam-620	66	156	t	t	PROPN
ejpam-620	66	157	�	�	PROPN
ejpam-620	66	158	�	�	PROPN
ejpam-620	66	159	�	�	PROPN
ejpam-620	66	160	�	�	PROPN
ejpam-620	66	161	�	�	PROPN
ejpam-620	66	162	τ−1	τ−1	PROPN
ejpam-620	66	163	∑	∑	PROPN
ejpam-620	66	164	k=0	k=0	PROPN
ejpam-620	66	165			PROPN
ejpam-620	66	166			NUM
ejpam-620	66	167	�	�	PROPN
ejpam-620	66	168	n	n	CCONJ
ejpam-620	66	169	k	k	PROPN
ejpam-620	66	170	�	�	PROPN
ejpam-620	66	171	1	1	NUM
ejpam-620	66	172	(	(	PUNCT
ejpam-620	66	173	1	1	NUM
ejpam-620	66	174	+	+	NUM
ejpam-620	66	175	k	k	NOUN
ejpam-620	66	176	)	)	PUNCT
ejpam-620	66	177	re	re	VERB
ejpam-620	66	178	(	(	PUNCT
ejpam-620	66	179	k	k	NOUN
ejpam-620	66	180	∑	∑	PUNCT
ejpam-620	66	181	ν=0	ν=0	PRON
ejpam-620	66	182	eiν	eiν	PROPN
ejpam-620	66	183	t	t	NOUN
ejpam-620	66	184	)	)	PUNCT
ejpam-620	66	185			PROPN
ejpam-620	66	186			PROPN
ejpam-620	66	187	�	�	PROPN
ejpam-620	66	188	�	�	PROPN
ejpam-620	66	189	�	�	PROPN
ejpam-620	66	190	�	�	PROPN
ejpam-620	66	191	�	�	PROPN
ejpam-620	66	192	+	+	CCONJ
ejpam-620	66	193	1	1	NUM
ejpam-620	66	194	2n+1	2n+1	PROPN
ejpam-620	66	195	t	t	PROPN
ejpam-620	66	196	�	�	PROPN
ejpam-620	66	197	�	�	PROPN
ejpam-620	66	198	�	�	PROPN
ejpam-620	66	199	�	�	PROPN
ejpam-620	66	200	�	�	PROPN
ejpam-620	66	201	n	n	CCONJ
ejpam-620	66	202	∑	∑	PROPN
ejpam-620	66	203	k	k	X
ejpam-620	66	204	=	=	PROPN
ejpam-620	66	205	τ	τ	PROPN
ejpam-620	66	206			PROPN
ejpam-620	66	207			X
ejpam-620	66	208	�	�	PROPN
ejpam-620	66	209	n	n	CCONJ
ejpam-620	66	210	k	k	PROPN
ejpam-620	66	211	�	�	PROPN
ejpam-620	66	212	1	1	NUM
ejpam-620	66	213	(	(	PUNCT
ejpam-620	66	214	1	1	NUM
ejpam-620	66	215	+	+	NUM
ejpam-620	66	216	k	k	NOUN
ejpam-620	66	217	)	)	PUNCT
ejpam-620	66	218	re	re	VERB
ejpam-620	66	219	(	(	PUNCT
ejpam-620	66	220	k	k	NOUN
ejpam-620	66	221	∑	∑	PUNCT
ejpam-620	66	222	ν=0	ν=0	PRON
ejpam-620	66	223	eiν	eiν	PROPN
ejpam-620	66	224	t	t	NOUN
ejpam-620	66	225	)	)	PUNCT
ejpam-620	66	226			PROPN
ejpam-620	66	227			PROPN
ejpam-620	66	228	�	�	PROPN
ejpam-620	66	229	�	�	PROPN
ejpam-620	66	230	�	�	PROPN
ejpam-620	66	231	�	�	PROPN
ejpam-620	66	232	�	�	PROPN
ejpam-620	66	233	(	(	PUNCT
ejpam-620	66	234	20	20	NUM
ejpam-620	66	235	)	)	PUNCT
ejpam-620	66	236	h.	h.	PROPN
ejpam-620	66	237	nigam	nigam	PROPN
ejpam-620	66	238	,	,	PUNCT
ejpam-620	66	239	k.	k.	PROPN
ejpam-620	66	240	sharma	sharma	PROPN
ejpam-620	66	241	/	/	SYM
ejpam-620	66	242	eur	eur	PROPN
ejpam-620	66	243	.	.	PUNCT
ejpam-620	67	1	j.	j.	PROPN
ejpam-620	67	2	pure	pure	PROPN
ejpam-620	67	3	appl	appl	PROPN
ejpam-620	67	4	.	.	PROPN
ejpam-620	67	5	math	math	PROPN
ejpam-620	67	6	,	,	PUNCT
ejpam-620	67	7	4	4	NUM
ejpam-620	67	8	(	(	PUNCT
ejpam-620	67	9	2011	2011	NUM
ejpam-620	67	10	)	)	PUNCT
ejpam-620	67	11	,	,	PUNCT
ejpam-620	67	12	276	276	NUM
ejpam-620	67	13	-	-	SYM
ejpam-620	67	14	286	286	NUM
ejpam-620	67	15	281	281	NUM
ejpam-620	67	16	now	now	ADV
ejpam-620	67	17	considering	consider	VERB
ejpam-620	67	18	the	the	DET
ejpam-620	67	19	first	first	ADJ
ejpam-620	67	20	term	term	NOUN
ejpam-620	67	21	of	of	ADP
ejpam-620	67	22	(	(	PUNCT
ejpam-620	67	23	20	20	NUM
ejpam-620	67	24	)	)	PUNCT
ejpam-620	67	25	,	,	PUNCT
ejpam-620	68	1	1	1	NUM
ejpam-620	68	2	2n+1	2n+1	PROPN
ejpam-620	68	3	t	t	PROPN
ejpam-620	68	4	�	�	PROPN
ejpam-620	68	5	�	�	PROPN
ejpam-620	68	6	�	�	PROPN
ejpam-620	68	7	�	�	PROPN
ejpam-620	68	8	�	�	PROPN
ejpam-620	68	9	τ−1	τ−1	PROPN
ejpam-620	68	10	∑	∑	PROPN
ejpam-620	68	11	k=0	k=0	PROPN
ejpam-620	68	12			PROPN
ejpam-620	68	13			NUM
ejpam-620	68	14	�	�	PROPN
ejpam-620	68	15	n	n	CCONJ
ejpam-620	68	16	k	k	PROPN
ejpam-620	68	17	�	�	PROPN
ejpam-620	68	18	1	1	NUM
ejpam-620	68	19	(	(	PUNCT
ejpam-620	68	20	1	1	NUM
ejpam-620	68	21	+	+	NUM
ejpam-620	68	22	k	k	NOUN
ejpam-620	68	23	)	)	PUNCT
ejpam-620	69	1	re	re	VERB
ejpam-620	69	2	(	(	PUNCT
ejpam-620	69	3	k	k	NOUN
ejpam-620	69	4	∑	∑	PUNCT
ejpam-620	69	5	ν=0	ν=0	PRON
ejpam-620	69	6	eiν	eiν	PROPN
ejpam-620	69	7	t	t	NOUN
ejpam-620	69	8	)	)	PUNCT
ejpam-620	69	9			PROPN
ejpam-620	69	10			PROPN
ejpam-620	69	11	�	�	PROPN
ejpam-620	69	12	�	�	PROPN
ejpam-620	69	13	�	�	PROPN
ejpam-620	69	14	�	�	PROPN
ejpam-620	69	15	�	�	PROPN
ejpam-620	69	16	≤	≤	PROPN
ejpam-620	69	17	1	1	NUM
ejpam-620	69	18	2n+1	2n+1	PROPN
ejpam-620	69	19	t	t	PROPN
ejpam-620	69	20	�	�	PROPN
ejpam-620	69	21	�	�	PROPN
ejpam-620	69	22	�	�	PROPN
ejpam-620	69	23	�	�	PROPN
ejpam-620	69	24	�	�	PROPN
ejpam-620	69	25	τ−1	τ−1	PROPN
ejpam-620	69	26	∑	∑	PROPN
ejpam-620	69	27	k=0	k=0	PROPN
ejpam-620	69	28			PROPN
ejpam-620	69	29			NUM
ejpam-620	69	30	�	�	PROPN
ejpam-620	69	31	n	n	CCONJ
ejpam-620	69	32	k	k	PROPN
ejpam-620	69	33	�	�	PROPN
ejpam-620	69	34	1	1	NUM
ejpam-620	69	35	(	(	PUNCT
ejpam-620	69	36	1	1	NUM
ejpam-620	69	37	+	+	NUM
ejpam-620	69	38	k	k	NOUN
ejpam-620	69	39	)	)	PUNCT
ejpam-620	69	40	(	(	PUNCT
ejpam-620	69	41	k	k	NOUN
ejpam-620	69	42	∑	∑	PUNCT
ejpam-620	69	43	ν=0	ν=0	PROPN
ejpam-620	69	44	1	1	NUM
ejpam-620	69	45	)	)	PUNCT
ejpam-620	69	46			PROPN
ejpam-620	69	47			PROPN
ejpam-620	69	48	�	�	PROPN
ejpam-620	69	49	�	�	PROPN
ejpam-620	69	50	�	�	PROPN
ejpam-620	69	51	�	�	PROPN
ejpam-620	69	52	�	�	PROPN
ejpam-620	69	53	�	�	PROPN
ejpam-620	69	54	�	�	PROPN
ejpam-620	69	55	eiν	eiν	PROPN
ejpam-620	69	56	t	t	PROPN
ejpam-620	69	57	�	�	PROPN
ejpam-620	69	58	�	�	PROPN
ejpam-620	69	59	≤	≤	PROPN
ejpam-620	69	60	1	1	NUM
ejpam-620	69	61	2n+1	2n+1	PROPN
ejpam-620	69	62	t	t	PROPN
ejpam-620	69	63	�	�	PROPN
ejpam-620	69	64	�	�	PROPN
ejpam-620	69	65	�	�	PROPN
ejpam-620	69	66	�	�	PROPN
ejpam-620	69	67	�	�	PROPN
ejpam-620	69	68	τ−1	τ−1	PROPN
ejpam-620	69	69	∑	∑	PROPN
ejpam-620	69	70	k=0	k=0	PROPN
ejpam-620	69	71	�	�	PROPN
ejpam-620	69	72	�	�	PROPN
ejpam-620	69	73	n	n	CCONJ
ejpam-620	69	74	k	k	PROPN
ejpam-620	69	75	�	�	PROPN
ejpam-620	69	76	�	�	PROPN
ejpam-620	69	77	�	�	PROPN
ejpam-620	69	78	�	�	PROPN
ejpam-620	69	79	�	�	PROPN
ejpam-620	69	80	�	�	PROPN
ejpam-620	69	81	�	�	PROPN
ejpam-620	69	82	(	(	PUNCT
ejpam-620	69	83	21	21	NUM
ejpam-620	69	84	)	)	PUNCT
ejpam-620	69	85	now	now	ADV
ejpam-620	69	86	considering	consider	VERB
ejpam-620	69	87	the	the	DET
ejpam-620	69	88	second	second	ADJ
ejpam-620	69	89	term	term	NOUN
ejpam-620	69	90	of	of	ADP
ejpam-620	69	91	(	(	PUNCT
ejpam-620	69	92	20	20	NUM
ejpam-620	69	93	)	)	PUNCT
ejpam-620	69	94	and	and	CCONJ
ejpam-620	69	95	using	use	VERB
ejpam-620	69	96	abel	abel	PROPN
ejpam-620	69	97	’s	’s	PART
ejpam-620	69	98	lemma	lemma	PROPN
ejpam-620	69	99	1	1	NUM
ejpam-620	69	100	2n+1	2n+1	PROPN
ejpam-620	69	101	t	t	PROPN
ejpam-620	69	102	�	�	PROPN
ejpam-620	69	103	�	�	PROPN
ejpam-620	69	104	�	�	PROPN
ejpam-620	69	105	�	�	PROPN
ejpam-620	69	106	�	�	PROPN
ejpam-620	69	107	n	n	CCONJ
ejpam-620	69	108	∑	∑	PROPN
ejpam-620	69	109	k	k	X
ejpam-620	69	110	=	=	PROPN
ejpam-620	69	111	τ	τ	PROPN
ejpam-620	69	112			PROPN
ejpam-620	69	113			X
ejpam-620	69	114	�	�	PROPN
ejpam-620	69	115	n	n	CCONJ
ejpam-620	69	116	k	k	PROPN
ejpam-620	69	117	�	�	PROPN
ejpam-620	69	118	1	1	NUM
ejpam-620	69	119	(	(	PUNCT
ejpam-620	69	120	1	1	NUM
ejpam-620	69	121	+	+	NUM
ejpam-620	69	122	k	k	NOUN
ejpam-620	69	123	)	)	PUNCT
ejpam-620	69	124	re	re	VERB
ejpam-620	69	125	(	(	PUNCT
ejpam-620	69	126	k	k	NOUN
ejpam-620	69	127	∑	∑	PUNCT
ejpam-620	69	128	ν=0	ν=0	PRON
ejpam-620	69	129	eiν	eiν	PROPN
ejpam-620	69	130	t	t	NOUN
ejpam-620	69	131	)	)	PUNCT
ejpam-620	69	132			PROPN
ejpam-620	69	133			PROPN
ejpam-620	69	134	�	�	PROPN
ejpam-620	69	135	�	�	PROPN
ejpam-620	69	136	�	�	PROPN
ejpam-620	69	137	�	�	PROPN
ejpam-620	69	138	�	�	PROPN
ejpam-620	69	139	≤	≤	PROPN
ejpam-620	69	140	1	1	NUM
ejpam-620	69	141	2n+1	2n+1	PROPN
ejpam-620	69	142	t	t	PROPN
ejpam-620	69	143	n	n	NOUN
ejpam-620	69	144	∑	∑	PROPN
ejpam-620	69	145	k	k	X
ejpam-620	69	146	=	=	PROPN
ejpam-620	69	147	τ	τ	X
ejpam-620	69	148	�	�	PROPN
ejpam-620	69	149	n	n	CCONJ
ejpam-620	69	150	k	k	PROPN
ejpam-620	69	151	�	�	PROPN
ejpam-620	69	152	1	1	NUM
ejpam-620	69	153	(	(	PUNCT
ejpam-620	69	154	1	1	NUM
ejpam-620	69	155	+	+	NUM
ejpam-620	69	156	k	k	NOUN
ejpam-620	69	157	)	)	PUNCT
ejpam-620	69	158	max	max	PROPN
ejpam-620	69	159	0≤	0≤	NUM
ejpam-620	69	160	m≤	m≤	PROPN
ejpam-620	69	161	k	k	PROPN
ejpam-620	69	162	�	�	PROPN
ejpam-620	69	163	�	�	PROPN
ejpam-620	69	164	�	�	PROPN
ejpam-620	69	165	�	�	PROPN
ejpam-620	69	166	�	�	PROPN
ejpam-620	69	167	m	m	VERB
ejpam-620	69	168	∑	∑	PROPN
ejpam-620	69	169	ν=0	ν=0	DET
ejpam-620	69	170	eiν	eiν	PROPN
ejpam-620	69	171	t	t	PROPN
ejpam-620	69	172	�	�	PROPN
ejpam-620	69	173	�	�	PROPN
ejpam-620	69	174	�	�	PROPN
ejpam-620	69	175	�	�	PROPN
ejpam-620	69	176	�	�	PROPN
ejpam-620	69	177	≤	≤	PROPN
ejpam-620	69	178	1	1	NUM
ejpam-620	69	179	2n+1	2n+1	PROPN
ejpam-620	69	180	t	t	PROPN
ejpam-620	69	181	n	n	NOUN
ejpam-620	69	182	∑	∑	PROPN
ejpam-620	69	183	k	k	X
ejpam-620	69	184	=	=	PROPN
ejpam-620	69	185	τ	τ	X
ejpam-620	69	186	�	�	PROPN
ejpam-620	69	187	n	n	CCONJ
ejpam-620	69	188	k	k	PROPN
ejpam-620	69	189	�	�	PROPN
ejpam-620	69	190	1	1	NUM
ejpam-620	69	191	(	(	PUNCT
ejpam-620	69	192	1	1	NUM
ejpam-620	69	193	+	+	NUM
ejpam-620	69	194	k	k	NOUN
ejpam-620	69	195	)	)	PUNCT
ejpam-620	69	196	(	(	PUNCT
ejpam-620	69	197	1	1	NUM
ejpam-620	69	198	+	+	NUM
ejpam-620	69	199	k	k	NOUN
ejpam-620	69	200	)	)	PUNCT
ejpam-620	69	201	=	=	SYM
ejpam-620	69	202	1	1	NUM
ejpam-620	69	203	2n+1	2n+1	PROPN
ejpam-620	69	204	t	t	PROPN
ejpam-620	69	205	n	n	NOUN
ejpam-620	69	206	∑	∑	PROPN
ejpam-620	69	207	k	k	X
ejpam-620	69	208	=	=	PROPN
ejpam-620	69	209	τ	τ	X
ejpam-620	69	210	�	�	PROPN
ejpam-620	69	211	n	n	CCONJ
ejpam-620	69	212	k	k	PROPN
ejpam-620	69	213	�	�	PROPN
ejpam-620	69	214	(	(	PUNCT
ejpam-620	69	215	22	22	NUM
ejpam-620	69	216	)	)	PUNCT
ejpam-620	69	217	combining	combine	VERB
ejpam-620	69	218	(	(	PUNCT
ejpam-620	69	219	20	20	NUM
ejpam-620	69	220	)	)	PUNCT
ejpam-620	69	221	,	,	PUNCT
ejpam-620	69	222	(	(	PUNCT
ejpam-620	69	223	21	21	NUM
ejpam-620	69	224	)	)	PUNCT
ejpam-620	69	225	and	and	CCONJ
ejpam-620	69	226	(	(	PUNCT
ejpam-620	69	227	22	22	NUM
ejpam-620	69	228	)	)	PUNCT
ejpam-620	69	229	,	,	PUNCT
ejpam-620	69	230	we	we	PRON
ejpam-620	69	231	get	get	VERB
ejpam-620	69	232	�	�	PROPN
ejpam-620	69	233	�	�	PROPN
ejpam-620	69	234	gn	gn	PROPN
ejpam-620	69	235	(	(	PUNCT
ejpam-620	69	236	t	t	PROPN
ejpam-620	69	237	)	)	PUNCT
ejpam-620	69	238	�	�	PROPN
ejpam-620	69	239	�	�	PROPN
ejpam-620	69	240	≤	≤	PROPN
ejpam-620	69	241	1	1	NUM
ejpam-620	69	242	2n+1	2n+1	PROPN
ejpam-620	69	243	t	t	NOUN
ejpam-620	69	244	τ−1	τ−1	PROPN
ejpam-620	69	245	∑	∑	PROPN
ejpam-620	69	246	k=0	k=0	PROPN
ejpam-620	69	247	�	�	PROPN
ejpam-620	69	248	n	n	CCONJ
ejpam-620	69	249	k	k	PROPN
ejpam-620	69	250	�	�	PROPN
ejpam-620	69	251	+	+	CCONJ
ejpam-620	69	252	1	1	NUM
ejpam-620	69	253	2n+1	2n+1	PROPN
ejpam-620	69	254	t	t	PROPN
ejpam-620	69	255	n	n	NOUN
ejpam-620	69	256	∑	∑	PROPN
ejpam-620	69	257	k	k	X
ejpam-620	69	258	=	=	PROPN
ejpam-620	69	259	τ	τ	X
ejpam-620	69	260	�	�	PROPN
ejpam-620	69	261	n	n	CCONJ
ejpam-620	69	262	k	k	PROPN
ejpam-620	69	263	�	�	PROPN
ejpam-620	69	264	=	=	PUNCT
ejpam-620	69	265	o	o	PROPN
ejpam-620	69	266	�	�	PROPN
ejpam-620	69	267	1	1	NUM
ejpam-620	69	268	t	t	PROPN
ejpam-620	69	269	�	�	PROPN
ejpam-620	69	270	4	4	NUM
ejpam-620	69	271	.	.	PUNCT
ejpam-620	69	272	proof	proof	NOUN
ejpam-620	69	273	of	of	ADP
ejpam-620	69	274	theorems	theorem	NOUN
ejpam-620	69	275	4.1	4.1	NUM
ejpam-620	69	276	.	.	PUNCT
ejpam-620	70	1	proof	proof	NOUN
ejpam-620	70	2	of	of	ADP
ejpam-620	70	3	theorem	theorem	ADJ
ejpam-620	70	4	1	1	NUM
ejpam-620	70	5	let	let	VERB
ejpam-620	70	6	sn	sn	PROPN
ejpam-620	70	7	�	�	PROPN
ejpam-620	70	8	f	f	PROPN
ejpam-620	70	9	;	;	PUNCT
ejpam-620	70	10	x	x	PART
ejpam-620	70	11	�	�	PROPN
ejpam-620	70	12	denote	denote	VERB
ejpam-620	70	13	the	the	DET
ejpam-620	70	14	partial	partial	ADJ
ejpam-620	70	15	sum	sum	NOUN
ejpam-620	70	16	of	of	ADP
ejpam-620	70	17	series	series	NOUN
ejpam-620	70	18	(	(	PUNCT
ejpam-620	70	19	5	5	NUM
ejpam-620	70	20	)	)	PUNCT
ejpam-620	70	21	.	.	PUNCT
ejpam-620	71	1	then	then	ADV
ejpam-620	71	2	following	follow	VERB
ejpam-620	71	3	lal	lal	PROPN
ejpam-620	71	4	[	[	X
ejpam-620	71	5	5	5	NUM
ejpam-620	71	6	]	]	PUNCT
ejpam-620	71	7	,	,	PUNCT
ejpam-620	71	8	we	we	PRON
ejpam-620	71	9	have	have	VERB
ejpam-620	71	10	sn	sn	PROPN
ejpam-620	71	11	(	(	PUNCT
ejpam-620	71	12	x)−	x)−	PROPN
ejpam-620	71	13	f	f	PROPN
ejpam-620	71	14	(	(	PUNCT
ejpam-620	71	15	x	x	X
ejpam-620	71	16	)	)	PUNCT
ejpam-620	71	17	=	=	SYM
ejpam-620	71	18	1	1	NUM
ejpam-620	71	19	2π	2π	NUM
ejpam-620	71	20	∫	∫	PROPN
ejpam-620	72	1	π	π	X
ejpam-620	72	2	0	0	PUNCT
ejpam-620	72	3	ψ	ψ	X
ejpam-620	72	4	(	(	PUNCT
ejpam-620	72	5	t	t	NOUN
ejpam-620	72	6	)	)	PUNCT
ejpam-620	72	7	cos	cos	PROPN
ejpam-620	72	8	�	�	PROPN
ejpam-620	72	9	n+	n+	PUNCT
ejpam-620	72	10	1	1	NUM
ejpam-620	72	11	2	2	NUM
ejpam-620	72	12	�	�	PROPN
ejpam-620	72	13	t	t	PROPN
ejpam-620	72	14	sin	sin	NOUN
ejpam-620	72	15	�	�	PROPN
ejpam-620	72	16	t	t	PROPN
ejpam-620	72	17	2	2	NUM
ejpam-620	72	18	�	�	PROPN
ejpam-620	72	19	d	d	PROPN
ejpam-620	72	20	t	t	PROPN
ejpam-620	72	21	using	use	VERB
ejpam-620	72	22	(	(	PUNCT
ejpam-620	72	23	5	5	NUM
ejpam-620	72	24	)	)	PUNCT
ejpam-620	72	25	the	the	DET
ejpam-620	72	26	(	(	PUNCT
ejpam-620	72	27	c	c	NOUN
ejpam-620	72	28	,	,	PUNCT
ejpam-620	72	29	1	1	X
ejpam-620	72	30	)	)	PUNCT
ejpam-620	72	31	transform	transform	VERB
ejpam-620	72	32	c1	c1	PROPN
ejpam-620	72	33	n	n	PROPN
ejpam-620	72	34	of	of	ADP
ejpam-620	72	35	sn	sn	PROPN
ejpam-620	72	36	�	�	PROPN
ejpam-620	72	37	f	f	PROPN
ejpam-620	72	38	;	;	PUNCT
ejpam-620	72	39	x	x	X
ejpam-620	72	40	�	�	PROPN
ejpam-620	72	41	is	be	AUX
ejpam-620	72	42	given	give	VERB
ejpam-620	72	43	by	by	ADP
ejpam-620	72	44	c1	c1	PROPN
ejpam-620	72	45	n	n	CCONJ
ejpam-620	72	46	−	−	PROPN
ejpam-620	72	47	f	f	PROPN
ejpam-620	72	48	(	(	PUNCT
ejpam-620	72	49	x	x	X
ejpam-620	72	50	)	)	PUNCT
ejpam-620	72	51	=	=	SYM
ejpam-620	72	52	1	1	NUM
ejpam-620	72	53	2π	2π	NOUN
ejpam-620	72	54	(	(	PUNCT
ejpam-620	72	55	n+	n+	NOUN
ejpam-620	72	56	1	1	NUM
ejpam-620	72	57	)	)	PUNCT
ejpam-620	72	58	∫	∫	PROPN
ejpam-620	73	1	π	π	PROPN
ejpam-620	73	2	0	0	PUNCT
ejpam-620	73	3	ψ	ψ	X
ejpam-620	73	4	(	(	PUNCT
ejpam-620	73	5	t	t	PROPN
ejpam-620	73	6	)	)	PUNCT
ejpam-620	73	7	n	n	NOUN
ejpam-620	73	8	∑	∑	ADP
ejpam-620	73	9	k=0	k=0	PROPN
ejpam-620	73	10	cos	cos	PROPN
ejpam-620	73	11	�	�	PROPN
ejpam-620	73	12	k+	k+	AUX
ejpam-620	73	13	1	1	NUM
ejpam-620	73	14	2	2	NUM
ejpam-620	73	15	�	�	PROPN
ejpam-620	73	16	t	t	PROPN
ejpam-620	73	17	sin	sin	NOUN
ejpam-620	73	18	t	t	PROPN
ejpam-620	73	19	2	2	NUM
ejpam-620	73	20	d	d	NOUN
ejpam-620	73	21	t	t	PROPN
ejpam-620	73	22	(	(	PUNCT
ejpam-620	73	23	23	23	NUM
ejpam-620	73	24	)	)	PUNCT
ejpam-620	73	25	h.	h.	PROPN
ejpam-620	73	26	nigam	nigam	PROPN
ejpam-620	73	27	,	,	PUNCT
ejpam-620	73	28	k.	k.	PROPN
ejpam-620	73	29	sharma	sharma	PROPN
ejpam-620	73	30	/	/	SYM
ejpam-620	73	31	eur	eur	PROPN
ejpam-620	73	32	.	.	PUNCT
ejpam-620	74	1	j.	j.	PROPN
ejpam-620	74	2	pure	pure	PROPN
ejpam-620	74	3	appl	appl	PROPN
ejpam-620	74	4	.	.	PROPN
ejpam-620	74	5	math	math	PROPN
ejpam-620	74	6	,	,	PUNCT
ejpam-620	74	7	4	4	NUM
ejpam-620	74	8	(	(	PUNCT
ejpam-620	74	9	2011	2011	NUM
ejpam-620	74	10	)	)	PUNCT
ejpam-620	74	11	,	,	PUNCT
ejpam-620	74	12	276	276	NUM
ejpam-620	74	13	-	-	SYM
ejpam-620	74	14	286	286	NUM
ejpam-620	74	15	282	282	NUM
ejpam-620	74	16	now	now	ADV
ejpam-620	74	17	denoting	denote	VERB
ejpam-620	74	18	(	(	PUNCT
ejpam-620	74	19	e	e	NOUN
ejpam-620	74	20	,	,	PUNCT
ejpam-620	74	21	1	1	NUM
ejpam-620	74	22	)	)	PUNCT
ejpam-620	74	23	(	(	PUNCT
ejpam-620	74	24	c	c	NOUN
ejpam-620	74	25	,	,	PUNCT
ejpam-620	74	26	1	1	X
ejpam-620	74	27	)	)	PUNCT
ejpam-620	74	28	transform	transform	NOUN
ejpam-620	74	29	of	of	ADP
ejpam-620	74	30	sn	sn	NOUN
ejpam-620	74	31	by	by	ADP
ejpam-620	74	32	(	(	PUNCT
ejpam-620	74	33	ec)1n	ec)1n	INTJ
ejpam-620	74	34	,	,	PUNCT
ejpam-620	74	35	we	we	PRON
ejpam-620	74	36	write	write	VERB
ejpam-620	74	37	(	(	PUNCT
ejpam-620	74	38	ec)1n	ec)1n	NOUN
ejpam-620	75	1	−	−	PROPN
ejpam-620	75	2	f	f	PROPN
ejpam-620	75	3	(	(	PUNCT
ejpam-620	75	4	x	x	X
ejpam-620	75	5	)	)	PUNCT
ejpam-620	75	6	=	=	SYM
ejpam-620	75	7	1	1	NUM
ejpam-620	75	8	2n+1	2n+1	PROPN
ejpam-620	75	9	π	π	PROPN
ejpam-620	75	10	n	n	CCONJ
ejpam-620	75	11	∑	∑	ADP
ejpam-620	75	12	k=0	k=0	PROPN
ejpam-620	75	13			PROPN
ejpam-620	75	14			NUM
ejpam-620	75	15	�	�	PROPN
ejpam-620	75	16	n	n	CCONJ
ejpam-620	75	17	k	k	PROPN
ejpam-620	75	18	�	�	PROPN
ejpam-620	75	19	∫	∫	PROPN
ejpam-620	75	20	π	π	PROPN
ejpam-620	75	21	0	0	PUNCT
ejpam-620	75	22	ψ	ψ	X
ejpam-620	75	23	(	(	PUNCT
ejpam-620	75	24	t	t	NOUN
ejpam-620	75	25	)	)	PUNCT
ejpam-620	75	26	sin	sin	NOUN
ejpam-620	75	27	t	t	PROPN
ejpam-620	75	28	2	2	NUM
ejpam-620	75	29	�	�	PROPN
ejpam-620	75	30	1	1	NUM
ejpam-620	75	31	k+	k+	NOUN
ejpam-620	75	32	1	1	NUM
ejpam-620	75	33	�	�	PROPN
ejpam-620	75	34	(	(	PUNCT
ejpam-620	75	35	k	k	NOUN
ejpam-620	75	36	∑	∑	PUNCT
ejpam-620	75	37	ν=0	ν=0	PROPN
ejpam-620	75	38	cos	cos	PROPN
ejpam-620	75	39	�	�	PROPN
ejpam-620	76	1	ν	ν	PROPN
ejpam-620	76	2	+	+	CCONJ
ejpam-620	76	3	1	1	NUM
ejpam-620	76	4	2	2	NUM
ejpam-620	76	5	�	�	PROPN
ejpam-620	76	6	t	t	PROPN
ejpam-620	76	7	)	)	PUNCT
ejpam-620	77	1	d	d	NOUN
ejpam-620	77	2	t	t	X
ejpam-620	77	3			PROPN
ejpam-620	77	4			PROPN
ejpam-620	77	5	=	=	SYM
ejpam-620	77	6	∫	∫	PROPN
ejpam-620	77	7	π	π	PROPN
ejpam-620	77	8	0	0	PUNCT
ejpam-620	77	9	ψ	ψ	X
ejpam-620	77	10	(	(	PUNCT
ejpam-620	77	11	t	t	PROPN
ejpam-620	77	12	)	)	PUNCT
ejpam-620	77	13	gn	gn	PROPN
ejpam-620	77	14	(	(	PUNCT
ejpam-620	77	15	t	t	PROPN
ejpam-620	77	16	)	)	PUNCT
ejpam-620	77	17	d	d	PROPN
ejpam-620	77	18	t	t	NOUN
ejpam-620	77	19	=	=	PUNCT
ejpam-620	77	20			PROPN
ejpam-620	77	21			NOUN
ejpam-620	77	22			NUM
ejpam-620	77	23	∫	∫	PROPN
ejpam-620	77	24	1	1	NUM
ejpam-620	77	25	n+1	n+1	PROPN
ejpam-620	77	26	0	0	NUM
ejpam-620	78	1	+	+	NUM
ejpam-620	78	2	∫	∫	PROPN
ejpam-620	78	3	π	π	PROPN
ejpam-620	78	4	1	1	NUM
ejpam-620	78	5	n+1	n+1	PROPN
ejpam-620	78	6			PROPN
ejpam-620	78	7			PROPN
ejpam-620	78	8	ψ	ψ	NOUN
ejpam-620	78	9	(	(	PUNCT
ejpam-620	78	10	t	t	PROPN
ejpam-620	78	11	)	)	PUNCT
ejpam-620	78	12	gn	gn	PROPN
ejpam-620	78	13	(	(	PUNCT
ejpam-620	78	14	t	t	PROPN
ejpam-620	78	15	)	)	PUNCT
ejpam-620	78	16	d	d	NOUN
ejpam-620	78	17	t	t	NOUN
ejpam-620	78	18	=	=	PUNCT
ejpam-620	78	19	i1.1	i1.1	NOUN
ejpam-620	78	20	+	+	X
ejpam-620	78	21	i1.2	i1.2	NOUN
ejpam-620	78	22	(	(	PUNCT
ejpam-620	78	23	say	say	INTJ
ejpam-620	78	24	)	)	PUNCT
ejpam-620	78	25	(	(	PUNCT
ejpam-620	78	26	24	24	NUM
ejpam-620	78	27	)	)	PUNCT
ejpam-620	78	28	now	now	ADV
ejpam-620	78	29	using	use	VERB
ejpam-620	78	30	lemma	lemma	PROPN
ejpam-620	78	31	1	1	NUM
ejpam-620	78	32	,	,	PUNCT
ejpam-620	78	33	we	we	PRON
ejpam-620	78	34	have	have	VERB
ejpam-620	78	35	�	�	PROPN
ejpam-620	78	36	�	�	PROPN
ejpam-620	78	37	i1.1	i1.1	PROPN
ejpam-620	78	38	�	�	PROPN
ejpam-620	78	39	�	�	PROPN
ejpam-620	78	40	≤	≤	PROPN
ejpam-620	78	41	∫	∫	PROPN
ejpam-620	78	42	1	1	NUM
ejpam-620	78	43	n+1	n+1	PROPN
ejpam-620	78	44	0	0	NUM
ejpam-620	78	45	�	�	PROPN
ejpam-620	78	46	�	�	PROPN
ejpam-620	78	47	ψ	ψ	PROPN
ejpam-620	78	48	(	(	PUNCT
ejpam-620	78	49	t	t	PROPN
ejpam-620	78	50	)	)	PUNCT
ejpam-620	78	51	�	�	PROPN
ejpam-620	78	52	�	�	PROPN
ejpam-620	78	53	�	�	PROPN
ejpam-620	78	54	�	�	PROPN
ejpam-620	78	55	gn	gn	PROPN
ejpam-620	78	56	(	(	PUNCT
ejpam-620	78	57	t	t	PROPN
ejpam-620	78	58	)	)	PUNCT
ejpam-620	78	59	�	�	PROPN
ejpam-620	78	60	�	�	PROPN
ejpam-620	79	1	d	d	PROPN
ejpam-620	79	2	t	t	NOUN
ejpam-620	79	3	=	=	SYM
ejpam-620	79	4	∫	∫	PROPN
ejpam-620	79	5	1	1	NUM
ejpam-620	79	6	n+1	n+1	PROPN
ejpam-620	79	7	0	0	NUM
ejpam-620	79	8	|tα|	|tα|	PROPN
ejpam-620	79	9	t	t	PROPN
ejpam-620	79	10	d	d	X
ejpam-620	79	11	t	t	PROPN
ejpam-620	79	12	=	=	SYM
ejpam-620	79	13	∫	∫	PROPN
ejpam-620	79	14	1	1	NUM
ejpam-620	79	15	n+1	n+1	PROPN
ejpam-620	79	16	0	0	NUM
ejpam-620	79	17	tα−1d	tα−1d	PROPN
ejpam-620	79	18	t	t	NOUN
ejpam-620	79	19	=	=	SYM
ejpam-620	79	20	�	�	PROPN
ejpam-620	79	21	tα	tα	PROPN
ejpam-620	80	1	α	α	PRON
ejpam-620	80	2	�	�	PROPN
ejpam-620	80	3	1	1	NUM
ejpam-620	80	4	n+1	n+1	PROPN
ejpam-620	80	5	0	0	NUM
ejpam-620	80	6	=	=	SYM
ejpam-620	80	7	o	o	X
ejpam-620	80	8	�	�	PROPN
ejpam-620	80	9	1	1	NUM
ejpam-620	80	10	(	(	PUNCT
ejpam-620	80	11	n+	n+	NUM
ejpam-620	80	12	1)α	1)α	NUM
ejpam-620	80	13	�	�	PROPN
ejpam-620	80	14	(	(	PUNCT
ejpam-620	80	15	25	25	NUM
ejpam-620	80	16	)	)	PUNCT
ejpam-620	80	17	using	use	VERB
ejpam-620	80	18	lemma	lemma	PROPN
ejpam-620	80	19	2	2	NUM
ejpam-620	80	20	,	,	PUNCT
ejpam-620	80	21	we	we	PRON
ejpam-620	80	22	have	have	AUX
ejpam-620	80	23	�	�	PROPN
ejpam-620	80	24	�	�	PROPN
ejpam-620	80	25	i1.2	i1.2	PROPN
ejpam-620	80	26	�	�	PROPN
ejpam-620	80	27	�	�	PROPN
ejpam-620	80	28	=	=	SYM
ejpam-620	80	29	∫	∫	PROPN
ejpam-620	81	1	π	π	PROPN
ejpam-620	81	2	1	1	NUM
ejpam-620	81	3	n+1	n+1	PROPN
ejpam-620	81	4	�	�	PROPN
ejpam-620	81	5	�	�	PROPN
ejpam-620	81	6	ψ	ψ	PROPN
ejpam-620	81	7	(	(	PUNCT
ejpam-620	81	8	t	t	PROPN
ejpam-620	81	9	)	)	PUNCT
ejpam-620	81	10	�	�	PROPN
ejpam-620	81	11	�	�	PROPN
ejpam-620	81	12	�	�	PROPN
ejpam-620	81	13	�	�	PROPN
ejpam-620	81	14	gn	gn	PROPN
ejpam-620	81	15	(	(	PUNCT
ejpam-620	81	16	t	t	PROPN
ejpam-620	81	17	)	)	PUNCT
ejpam-620	81	18	�	�	PROPN
ejpam-620	81	19	�	�	PROPN
ejpam-620	81	20	d	d	PROPN
ejpam-620	81	21	t	t	PROPN
ejpam-620	81	22	=	=	SYM
ejpam-620	81	23	∫	∫	PROPN
ejpam-620	81	24	π	π	PROPN
ejpam-620	81	25	1	1	NUM
ejpam-620	81	26	n+1	n+1	PROPN
ejpam-620	81	27	|tα|	|tα|	PROPN
ejpam-620	81	28	|t|	|t|	PROPN
ejpam-620	81	29	d	d	PROPN
ejpam-620	81	30	t	t	PROPN
ejpam-620	81	31	=	=	SYM
ejpam-620	81	32	∫	∫	PROPN
ejpam-620	81	33	π	π	PROPN
ejpam-620	81	34	1	1	NUM
ejpam-620	81	35	n+1	n+1	PROPN
ejpam-620	81	36	tα−1d	tα−1d	X
ejpam-620	81	37	t	t	NOUN
ejpam-620	81	38	=	=	SYM
ejpam-620	81	39	�	�	PROPN
ejpam-620	81	40	tα	tα	PROPN
ejpam-620	81	41	α	α	PROPN
ejpam-620	81	42	�	�	PROPN
ejpam-620	81	43	π	π	PROPN
ejpam-620	81	44	1	1	NUM
ejpam-620	81	45	n+1	n+1	PROPN
ejpam-620	81	46	=	=	SYM
ejpam-620	81	47	o	o	X
ejpam-620	81	48	�	�	PROPN
ejpam-620	81	49	1	1	NUM
ejpam-620	81	50	(	(	PUNCT
ejpam-620	81	51	n+	n+	NUM
ejpam-620	81	52	1)α	1)α	NUM
ejpam-620	81	53	�	�	PROPN
ejpam-620	81	54	(	(	PUNCT
ejpam-620	81	55	26	26	NUM
ejpam-620	81	56	)	)	PUNCT
ejpam-620	81	57	h.	h.	PROPN
ejpam-620	81	58	nigam	nigam	PROPN
ejpam-620	81	59	,	,	PUNCT
ejpam-620	81	60	k.	k.	PROPN
ejpam-620	81	61	sharma	sharma	PROPN
ejpam-620	81	62	/	/	SYM
ejpam-620	81	63	eur	eur	PROPN
ejpam-620	81	64	.	.	PUNCT
ejpam-620	82	1	j.	j.	PROPN
ejpam-620	82	2	pure	pure	PROPN
ejpam-620	82	3	appl	appl	PROPN
ejpam-620	82	4	.	.	PROPN
ejpam-620	82	5	math	math	PROPN
ejpam-620	82	6	,	,	PUNCT
ejpam-620	82	7	4	4	NUM
ejpam-620	82	8	(	(	PUNCT
ejpam-620	82	9	2011	2011	NUM
ejpam-620	82	10	)	)	PUNCT
ejpam-620	82	11	,	,	PUNCT
ejpam-620	82	12	276	276	NUM
ejpam-620	82	13	-	-	SYM
ejpam-620	82	14	286	286	NUM
ejpam-620	82	15	283	283	NUM
ejpam-620	82	16	combining	combine	VERB
ejpam-620	82	17	(	(	PUNCT
ejpam-620	82	18	24	24	NUM
ejpam-620	82	19	)	)	PUNCT
ejpam-620	82	20	,	,	PUNCT
ejpam-620	82	21	(	(	PUNCT
ejpam-620	82	22	25	25	NUM
ejpam-620	82	23	)	)	PUNCT
ejpam-620	82	24	and	and	CCONJ
ejpam-620	82	25	(	(	PUNCT
ejpam-620	82	26	26	26	NUM
ejpam-620	82	27	)	)	PUNCT
ejpam-620	82	28	,	,	PUNCT
ejpam-620	82	29	we	we	PRON
ejpam-620	82	30	get	get	VERB
ejpam-620	82	31	(	(	PUNCT
ejpam-620	82	32	ec)1n−	ec)1n−	X
ejpam-620	82	33	f	f	PROPN
ejpam-620	82	34	∞	∞	PROPN
ejpam-620	82	35	=	=	SYM
ejpam-620	82	36	§	§	PROPN
ejpam-620	82	37	�	�	PROPN
ejpam-620	82	38	�	�	PROPN
ejpam-620	82	39	�	�	PROPN
ejpam-620	82	40	(	(	PUNCT
ejpam-620	82	41	ec)1n	ec)1n	NOUN
ejpam-620	82	42	−	−	PROPN
ejpam-620	82	43	f	f	PROPN
ejpam-620	82	44	�	�	PROPN
ejpam-620	82	45	�	�	PROPN
ejpam-620	82	46	�	�	PROPN
ejpam-620	82	47	:	:	PUNCT
ejpam-620	82	48	x	x	PUNCT
ejpam-620	82	49	∈	∈	PROPN
ejpam-620	83	1	[	[	X
ejpam-620	83	2	0,2π	0,2π	NOUN
ejpam-620	83	3	]	]	X
ejpam-620	83	4	ª	ª	PROPN
ejpam-620	83	5	=	=	PUNCT
ejpam-620	83	6	o	o	X
ejpam-620	83	7	�	�	PROPN
ejpam-620	83	8	1	1	NUM
ejpam-620	83	9	(	(	PUNCT
ejpam-620	83	10	n+	n+	NUM
ejpam-620	83	11	1)α	1)α	NUM
ejpam-620	83	12	�	�	PROPN
ejpam-620	83	13	this	this	PRON
ejpam-620	83	14	completes	complete	VERB
ejpam-620	83	15	the	the	DET
ejpam-620	83	16	proof	proof	NOUN
ejpam-620	83	17	of	of	ADP
ejpam-620	83	18	theorem	theorem	NOUN
ejpam-620	83	19	1	1	NUM
ejpam-620	83	20	.	.	NOUN
ejpam-620	83	21	4.2	4.2	NUM
ejpam-620	83	22	.	.	PUNCT
ejpam-620	84	1	proof	proof	NOUN
ejpam-620	84	2	of	of	ADP
ejpam-620	84	3	theorem	theorem	ADJ
ejpam-620	84	4	2	2	NUM
ejpam-620	84	5	following	follow	VERB
ejpam-620	84	6	the	the	DET
ejpam-620	84	7	proof	proof	NOUN
ejpam-620	84	8	of	of	ADP
ejpam-620	84	9	theorem	theorem	NOUN
ejpam-620	84	10	1	1	NUM
ejpam-620	84	11	,	,	PUNCT
ejpam-620	84	12	(	(	PUNCT
ejpam-620	84	13	ec)1n−	ec)1n−	PROPN
ejpam-620	84	14	f	f	PROPN
ejpam-620	84	15	(	(	PUNCT
ejpam-620	84	16	x	x	X
ejpam-620	84	17	)	)	PUNCT
ejpam-620	84	18	=	=	NOUN
ejpam-620	85	1			PROPN
ejpam-620	85	2			NOUN
ejpam-620	85	3			NUM
ejpam-620	85	4	∫	∫	PROPN
ejpam-620	85	5	1	1	NUM
ejpam-620	85	6	n+1	n+1	PROPN
ejpam-620	85	7	0	0	NUM
ejpam-620	86	1	+	+	NUM
ejpam-620	86	2	∫	∫	PROPN
ejpam-620	86	3	π	π	PROPN
ejpam-620	86	4	1	1	NUM
ejpam-620	86	5	n+1	n+1	PROPN
ejpam-620	86	6			PROPN
ejpam-620	86	7			PROPN
ejpam-620	86	8	ψ	ψ	NOUN
ejpam-620	86	9	(	(	PUNCT
ejpam-620	86	10	t	t	PROPN
ejpam-620	86	11	)	)	PUNCT
ejpam-620	86	12	gn	gn	PROPN
ejpam-620	86	13	(	(	PUNCT
ejpam-620	86	14	t	t	PROPN
ejpam-620	86	15	)	)	PUNCT
ejpam-620	86	16	d	d	NOUN
ejpam-620	86	17	t	t	NOUN
ejpam-620	86	18	=	=	PUNCT
ejpam-620	86	19	i2.1	i2.1	X
ejpam-620	86	20	+	+	CCONJ
ejpam-620	86	21	i2.2	i2.2	PROPN
ejpam-620	86	22	(	(	PUNCT
ejpam-620	86	23	say	say	INTJ
ejpam-620	86	24	)	)	PUNCT
ejpam-620	86	25	(	(	PUNCT
ejpam-620	86	26	27	27	NUM
ejpam-620	86	27	)	)	PUNCT
ejpam-620	86	28	applying	apply	VERB
ejpam-620	86	29	hölder	hölder	NOUN
ejpam-620	86	30	’s	’s	PART
ejpam-620	86	31	inequality	inequality	NOUN
ejpam-620	86	32	and	and	CCONJ
ejpam-620	86	33	the	the	DET
ejpam-620	86	34	fact	fact	NOUN
ejpam-620	86	35	that	that	SCONJ
ejpam-620	86	36	ψ	ψ	X
ejpam-620	86	37	(	(	PUNCT
ejpam-620	86	38	t	t	NOUN
ejpam-620	86	39	)	)	PUNCT
ejpam-620	86	40	∈w	∈w	VERB
ejpam-620	86	41	�	�	PROPN
ejpam-620	86	42	lr	lr	PROPN
ejpam-620	86	43	,	,	PUNCT
ejpam-620	86	44	ξ	ξ	PROPN
ejpam-620	86	45	(	(	PUNCT
ejpam-620	86	46	t	t	PROPN
ejpam-620	86	47	)	)	PUNCT
ejpam-620	86	48	�	�	PROPN
ejpam-620	86	49	,	,	PUNCT
ejpam-620	86	50	condition	condition	NOUN
ejpam-620	86	51	(	(	PUNCT
ejpam-620	86	52	17	17	NUM
ejpam-620	86	53	)	)	PUNCT
ejpam-620	86	54	,	,	PUNCT
ejpam-620	86	55	lemma	lemma	PROPN
ejpam-620	86	56	1	1	NUM
ejpam-620	86	57	and	and	CCONJ
ejpam-620	86	58	second	second	ADJ
ejpam-620	86	59	mean	mean	NOUN
ejpam-620	86	60	value	value	NOUN
ejpam-620	86	61	theorem	theorem	NOUN
ejpam-620	86	62	for	for	ADP
ejpam-620	86	63	integrals	integral	NOUN
ejpam-620	86	64	,	,	PUNCT
ejpam-620	86	65	we	we	PRON
ejpam-620	86	66	have	have	VERB
ejpam-620	86	67	�	�	PROPN
ejpam-620	86	68	�	�	PROPN
ejpam-620	86	69	i2.1	i2.1	PROPN
ejpam-620	86	70	�	�	PROPN
ejpam-620	86	71	�	�	PROPN
ejpam-620	86	72	≤	≤	PROPN
ejpam-620	86	73			PROPN
ejpam-620	86	74			NOUN
ejpam-620	86	75			NUM
ejpam-620	86	76	∫	∫	PROPN
ejpam-620	86	77	1	1	NUM
ejpam-620	87	1	n+1	n+1	PROPN
ejpam-620	87	2	0	0	NUM
ejpam-620	88	1	(	(	PUNCT
ejpam-620	88	2	t	t	PROPN
ejpam-620	88	3	�	�	PROPN
ejpam-620	88	4	�	�	PROPN
ejpam-620	88	5	ψ	ψ	PROPN
ejpam-620	88	6	(	(	PUNCT
ejpam-620	88	7	t	t	PROPN
ejpam-620	88	8	)	)	PUNCT
ejpam-620	88	9	�	�	PROPN
ejpam-620	88	10	�	�	PROPN
ejpam-620	88	11	sinβ	sinβ	NOUN
ejpam-620	88	12	t	t	PROPN
ejpam-620	88	13	ξ	ξ	PROPN
ejpam-620	88	14	(	(	PUNCT
ejpam-620	88	15	t	t	PROPN
ejpam-620	88	16	)	)	PUNCT
ejpam-620	88	17	)	)	PUNCT
ejpam-620	89	1	r	r	NOUN
ejpam-620	89	2	d	d	NOUN
ejpam-620	89	3	t	t	NOUN
ejpam-620	89	4			PROPN
ejpam-620	89	5			PROPN
ejpam-620	89	6			PROPN
ejpam-620	89	7	1	1	NUM
ejpam-620	89	8	r	r	NOUN
ejpam-620	89	9			NOUN
ejpam-620	89	10			NOUN
ejpam-620	89	11			NUM
ejpam-620	89	12	∫	∫	PROPN
ejpam-620	89	13	1	1	NUM
ejpam-620	89	14	n+1	n+1	PROPN
ejpam-620	89	15	0	0	NUM
ejpam-620	89	16	(	(	PUNCT
ejpam-620	89	17	ξ	ξ	PROPN
ejpam-620	89	18	(	(	PUNCT
ejpam-620	89	19	t	t	PROPN
ejpam-620	89	20	)	)	PUNCT
ejpam-620	89	21	�	�	PROPN
ejpam-620	89	22	�	�	PROPN
ejpam-620	89	23	gn	gn	PROPN
ejpam-620	89	24	(	(	PUNCT
ejpam-620	89	25	t	t	PROPN
ejpam-620	89	26	)	)	PUNCT
ejpam-620	89	27	�	�	PROPN
ejpam-620	89	28	�	�	PROPN
ejpam-620	89	29	t	t	PROPN
ejpam-620	89	30	sinβ	sinβ	NOUN
ejpam-620	89	31	t	t	PROPN
ejpam-620	89	32	)	)	PUNCT
ejpam-620	89	33	s	s	PART
ejpam-620	89	34	d	d	X
ejpam-620	89	35	t	t	NOUN
ejpam-620	89	36			PROPN
ejpam-620	89	37			PROPN
ejpam-620	89	38			PROPN
ejpam-620	89	39	1	1	NUM
ejpam-620	89	40	s	s	NOUN
ejpam-620	89	41	=	=	NOUN
ejpam-620	89	42	o	o	X
ejpam-620	89	43	�	�	PROPN
ejpam-620	89	44	1	1	NUM
ejpam-620	89	45	n+	n+	SYM
ejpam-620	89	46	1	1	NUM
ejpam-620	89	47	�	�	PROPN
ejpam-620	89	48			PROPN
ejpam-620	89	49			PROPN
ejpam-620	89	50			NUM
ejpam-620	89	51	∫	∫	PROPN
ejpam-620	89	52	1	1	NUM
ejpam-620	89	53	n+1	n+1	PROPN
ejpam-620	89	54	0	0	NUM
ejpam-620	89	55	�	�	PROPN
ejpam-620	89	56	ξ	ξ	PROPN
ejpam-620	89	57	(	(	PUNCT
ejpam-620	89	58	t	t	NOUN
ejpam-620	89	59	)	)	PUNCT
ejpam-620	89	60	t2+β	t2+β	PROPN
ejpam-620	89	61	�	�	PROPN
ejpam-620	89	62	s	s	PART
ejpam-620	89	63	d	d	X
ejpam-620	89	64	t	t	NOUN
ejpam-620	89	65			PROPN
ejpam-620	89	66			PROPN
ejpam-620	89	67			PROPN
ejpam-620	89	68	1	1	NUM
ejpam-620	89	69	s	s	NOUN
ejpam-620	89	70	=	=	NOUN
ejpam-620	89	71	o	o	NOUN
ejpam-620	89	72	�	�	PROPN
ejpam-620	89	73	�	�	PROPN
ejpam-620	89	74	1	1	NUM
ejpam-620	89	75	n+	n+	SYM
ejpam-620	89	76	1	1	NUM
ejpam-620	89	77	�	�	PROPN
ejpam-620	89	78	ξ	ξ	PROPN
ejpam-620	89	79	�	�	PROPN
ejpam-620	89	80	1	1	NUM
ejpam-620	89	81	n+	n+	SYM
ejpam-620	89	82	1	1	NUM
ejpam-620	89	83	�	�	PROPN
ejpam-620	89	84	�	�	PROPN
ejpam-620	89	85			PROPN
ejpam-620	89	86			PROPN
ejpam-620	89	87			NUM
ejpam-620	89	88	∫	∫	PROPN
ejpam-620	89	89	1	1	NUM
ejpam-620	89	90	n+1	n+1	PROPN
ejpam-620	89	91	∈	∈	PROPN
ejpam-620	89	92	d	d	NOUN
ejpam-620	89	93	t	t	NOUN
ejpam-620	89	94	t(2+β)s	t(2+β)	NOUN
ejpam-620	89	95			NUM
ejpam-620	89	96			PROPN
ejpam-620	89	97			PROPN
ejpam-620	89	98	1	1	NUM
ejpam-620	89	99	s	s	NOUN
ejpam-620	89	100	for	for	ADP
ejpam-620	89	101	some	some	PRON
ejpam-620	89	102	0<∈	0<∈	NUM
ejpam-620	89	103	<	<	X
ejpam-620	89	104	1	1	NUM
ejpam-620	89	105	n+	n+	SYM
ejpam-620	89	106	1	1	NUM
ejpam-620	89	107	=	=	SYM
ejpam-620	89	108	o	o	NOUN
ejpam-620	89	109			PROPN
ejpam-620	89	110			NOUN
ejpam-620	89	111			NUM
ejpam-620	89	112	�	�	PROPN
ejpam-620	89	113	1	1	NUM
ejpam-620	89	114	n+	n+	SYM
ejpam-620	89	115	1	1	NUM
ejpam-620	89	116	�	�	PROPN
ejpam-620	89	117	ξ	ξ	PROPN
ejpam-620	89	118	�	�	PROPN
ejpam-620	89	119	1	1	NUM
ejpam-620	89	120	n+	n+	SYM
ejpam-620	89	121	1	1	NUM
ejpam-620	89	122	�	�	PROPN
ejpam-620	89	123	(	(	PUNCT
ejpam-620	89	124	t−(2+β)s+1	t−(2+β)s+1	ADP
ejpam-620	89	125	−	−	PROPN
ejpam-620	89	126	�	�	PROPN
ejpam-620	89	127	2	2	NUM
ejpam-620	89	128	+	+	CCONJ
ejpam-620	89	129	β	β	X
ejpam-620	89	130	�	�	PROPN
ejpam-620	89	131	s+	s+	PUNCT
ejpam-620	89	132	1	1	NUM
ejpam-620	89	133	)	)	SYM
ejpam-620	89	134	1	1	NUM
ejpam-620	89	135	n+1	n+1	PROPN
ejpam-620	89	136	∈	∈	PROPN
ejpam-620	89	137			PROPN
ejpam-620	89	138			PROPN
ejpam-620	89	139			PROPN
ejpam-620	89	140	1	1	NUM
ejpam-620	89	141	s	s	NOUN
ejpam-620	89	142	=	=	NOUN
ejpam-620	89	143	o	o	NOUN
ejpam-620	89	144	�	�	PROPN
ejpam-620	89	145	�	�	PROPN
ejpam-620	89	146	1	1	NUM
ejpam-620	89	147	n+	n+	SYM
ejpam-620	89	148	1	1	NUM
ejpam-620	89	149	�	�	PROPN
ejpam-620	89	150	ξ	ξ	PROPN
ejpam-620	89	151	�	�	PROPN
ejpam-620	89	152	1	1	NUM
ejpam-620	89	153	n+	n+	SYM
ejpam-620	89	154	1	1	NUM
ejpam-620	89	155	�	�	PROPN
ejpam-620	89	156	(	(	PUNCT
ejpam-620	89	157	n+	n+	NUM
ejpam-620	89	158	1)2+β−	1)2+β−	NUM
ejpam-620	89	159	1	1	NUM
ejpam-620	89	160	s	s	NOUN
ejpam-620	89	161	�	�	PROPN
ejpam-620	89	162	=	=	SYM
ejpam-620	89	163	o	o	PROPN
ejpam-620	89	164	�	�	PROPN
ejpam-620	89	165	(	(	PUNCT
ejpam-620	89	166	n+	n+	NUM
ejpam-620	89	167	1)β+1−	1)β+1−	NUM
ejpam-620	89	168	1	1	NUM
ejpam-620	89	169	s	s	PROPN
ejpam-620	89	170	ξ	ξ	PROPN
ejpam-620	89	171	�	�	PROPN
ejpam-620	89	172	1	1	NUM
ejpam-620	89	173	n+	n+	SYM
ejpam-620	89	174	1	1	NUM
ejpam-620	89	175	�	�	PROPN
ejpam-620	89	176	�	�	PROPN
ejpam-620	89	177	=	=	SYM
ejpam-620	89	178	o	o	PROPN
ejpam-620	89	179	�	�	PROPN
ejpam-620	89	180	(	(	PUNCT
ejpam-620	89	181	n+	n+	NUM
ejpam-620	89	182	1)β+	1)β+	NUM
ejpam-620	89	183	1	1	NUM
ejpam-620	89	184	r	r	NOUN
ejpam-620	89	185	ξ	ξ	X
ejpam-620	89	186	�	�	PROPN
ejpam-620	89	187	1	1	NUM
ejpam-620	89	188	n+	n+	SYM
ejpam-620	89	189	1	1	NUM
ejpam-620	89	190	�	�	PROPN
ejpam-620	89	191	�	�	PROPN
ejpam-620	89	192	since	since	SCONJ
ejpam-620	89	193	1	1	NUM
ejpam-620	89	194	r	r	NOUN
ejpam-620	89	195	+	+	NUM
ejpam-620	89	196	1	1	NUM
ejpam-620	89	197	s	s	NOUN
ejpam-620	89	198	=	=	NOUN
ejpam-620	89	199	1,1≤	1,1≤	NUM
ejpam-620	89	200	r	r	NOUN
ejpam-620	89	201	≤∞.	≤∞.	NOUN
ejpam-620	89	202	(	(	PUNCT
ejpam-620	89	203	28	28	NUM
ejpam-620	89	204	)	)	PUNCT
ejpam-620	89	205	now	now	ADV
ejpam-620	89	206	using	use	VERB
ejpam-620	89	207	hölder	hölder	PROPN
ejpam-620	89	208	’s	’s	PART
ejpam-620	89	209	inequality	inequality	NOUN
ejpam-620	89	210	,	,	PUNCT
ejpam-620	89	211	|sin	|sin	VERB
ejpam-620	89	212	t|	t|	PROPN
ejpam-620	89	213	<	<	X
ejpam-620	89	214	1	1	NUM
ejpam-620	89	215	,	,	PUNCT
ejpam-620	89	216	sin	sin	PROPN
ejpam-620	89	217	t	t	PROPN
ejpam-620	89	218	≥	≥	PROPN
ejpam-620	89	219	�	�	PROPN
ejpam-620	89	220	2	2	NUM
ejpam-620	89	221	t	t	PROPN
ejpam-620	89	222	π	π	PROPN
ejpam-620	89	223	�	�	PROPN
ejpam-620	89	224	,	,	PUNCT
ejpam-620	89	225	conditions	condition	NOUN
ejpam-620	89	226	(	(	PUNCT
ejpam-620	89	227	16	16	NUM
ejpam-620	89	228	)	)	PUNCT
ejpam-620	89	229	and	and	CCONJ
ejpam-620	89	230	(	(	PUNCT
ejpam-620	89	231	18	18	NUM
ejpam-620	89	232	)	)	PUNCT
ejpam-620	89	233	,	,	PUNCT
ejpam-620	89	234	lemma	lemma	PROPN
ejpam-620	89	235	2	2	NUM
ejpam-620	89	236	and	and	CCONJ
ejpam-620	89	237	second	second	ADJ
ejpam-620	89	238	mean	mean	NOUN
ejpam-620	89	239	value	value	NOUN
ejpam-620	89	240	theorem	theorem	NOUN
ejpam-620	89	241	for	for	ADP
ejpam-620	89	242	integrals	integral	NOUN
ejpam-620	89	243	,	,	PUNCT
ejpam-620	89	244	we	we	PRON
ejpam-620	89	245	have	have	VERB
ejpam-620	89	246	�	�	PROPN
ejpam-620	89	247	�	�	PROPN
ejpam-620	89	248	i2.2	i2.2	PROPN
ejpam-620	89	249	�	�	PROPN
ejpam-620	89	250	�	�	PROPN
ejpam-620	89	251	≤	≤	PROPN
ejpam-620	89	252			NOUN
ejpam-620	89	253			PROPN
ejpam-620	89	254			NUM
ejpam-620	89	255	∫	∫	PROPN
ejpam-620	90	1	π	π	NOUN
ejpam-620	90	2	1	1	X
ejpam-620	90	3	n+1	n+1	PROPN
ejpam-620	90	4	(	(	PUNCT
ejpam-620	90	5	t−δ	t−δ	NUM
ejpam-620	90	6	�	�	PROPN
ejpam-620	90	7	�	�	PROPN
ejpam-620	90	8	ψ	ψ	PROPN
ejpam-620	90	9	(	(	PUNCT
ejpam-620	90	10	t	t	PROPN
ejpam-620	90	11	)	)	PUNCT
ejpam-620	90	12	�	�	PROPN
ejpam-620	90	13	�	�	PROPN
ejpam-620	90	14	sinβ	sinβ	NOUN
ejpam-620	90	15	t	t	PROPN
ejpam-620	90	16	ξ	ξ	PROPN
ejpam-620	90	17	(	(	PUNCT
ejpam-620	90	18	t	t	PROPN
ejpam-620	90	19	)	)	PUNCT
ejpam-620	90	20	)	)	PUNCT
ejpam-620	91	1	r	r	NOUN
ejpam-620	91	2	d	d	NOUN
ejpam-620	91	3	t	t	NOUN
ejpam-620	91	4			PROPN
ejpam-620	91	5			PROPN
ejpam-620	91	6			PROPN
ejpam-620	91	7	1	1	NUM
ejpam-620	91	8	r	r	NOUN
ejpam-620	91	9			NOUN
ejpam-620	91	10			NOUN
ejpam-620	91	11			NUM
ejpam-620	91	12	∫	∫	PROPN
ejpam-620	92	1	π	π	NOUN
ejpam-620	92	2	1	1	X
ejpam-620	92	3	n+1	n+1	PROPN
ejpam-620	92	4	(	(	PUNCT
ejpam-620	92	5	ξ	ξ	PROPN
ejpam-620	92	6	(	(	PUNCT
ejpam-620	92	7	t	t	PROPN
ejpam-620	92	8	)	)	PUNCT
ejpam-620	92	9	�	�	PROPN
ejpam-620	92	10	�	�	PROPN
ejpam-620	92	11	gn	gn	PROPN
ejpam-620	92	12	(	(	PUNCT
ejpam-620	92	13	t	t	PROPN
ejpam-620	92	14	)	)	PUNCT
ejpam-620	92	15	�	�	PROPN
ejpam-620	92	16	�	�	PROPN
ejpam-620	92	17	t−δ	t−δ	NUM
ejpam-620	92	18	sinβ	sinβ	NOUN
ejpam-620	92	19	t	t	PROPN
ejpam-620	92	20	)	)	PUNCT
ejpam-620	92	21	s	s	PART
ejpam-620	92	22	d	d	X
ejpam-620	92	23	t	t	NOUN
ejpam-620	92	24			PROPN
ejpam-620	92	25			PROPN
ejpam-620	92	26			PROPN
ejpam-620	92	27	1	1	NUM
ejpam-620	92	28	s	s	PART
ejpam-620	92	29	h.	h.	PROPN
ejpam-620	92	30	nigam	nigam	PROPN
ejpam-620	92	31	,	,	PUNCT
ejpam-620	92	32	k.	k.	PROPN
ejpam-620	92	33	sharma	sharma	PROPN
ejpam-620	92	34	/	/	SYM
ejpam-620	92	35	eur	eur	PROPN
ejpam-620	92	36	.	.	PUNCT
ejpam-620	93	1	j.	j.	PROPN
ejpam-620	93	2	pure	pure	PROPN
ejpam-620	93	3	appl	appl	PROPN
ejpam-620	93	4	.	.	PROPN
ejpam-620	93	5	math	math	PROPN
ejpam-620	93	6	,	,	PUNCT
ejpam-620	93	7	4	4	NUM
ejpam-620	93	8	(	(	PUNCT
ejpam-620	93	9	2011	2011	NUM
ejpam-620	93	10	)	)	PUNCT
ejpam-620	93	11	,	,	PUNCT
ejpam-620	93	12	276	276	NUM
ejpam-620	93	13	-	-	SYM
ejpam-620	93	14	286	286	NUM
ejpam-620	93	15	284	284	NUM
ejpam-620	93	16	=	=	SYM
ejpam-620	93	17	o	o	X
ejpam-620	93	18	¦	¦	PROPN
ejpam-620	93	19	(	(	PUNCT
ejpam-620	93	20	n+	n+	NUM
ejpam-620	93	21	1)δ	1)δ	NUM
ejpam-620	93	22	©	©	PROPN
ejpam-620	93	23			NOUN
ejpam-620	93	24			NOUN
ejpam-620	93	25			NUM
ejpam-620	93	26	∫	∫	PROPN
ejpam-620	94	1	π	π	PROPN
ejpam-620	94	2	1	1	NUM
ejpam-620	94	3	n+1	n+1	PROPN
ejpam-620	94	4	�	�	PROPN
ejpam-620	94	5	ξ	ξ	PROPN
ejpam-620	94	6	(	(	PUNCT
ejpam-620	94	7	t	t	NOUN
ejpam-620	94	8	)	)	PUNCT
ejpam-620	94	9	t1−δ+β	t1−δ+β	PROPN
ejpam-620	94	10	�	�	PROPN
ejpam-620	94	11	s	s	PROPN
ejpam-620	94	12	d	d	X
ejpam-620	94	13	t	t	NOUN
ejpam-620	94	14			PROPN
ejpam-620	94	15			PROPN
ejpam-620	94	16			PROPN
ejpam-620	94	17	1	1	NUM
ejpam-620	94	18	s	s	NOUN
ejpam-620	94	19	=	=	NOUN
ejpam-620	94	20	o	o	X
ejpam-620	94	21	¦	¦	PROPN
ejpam-620	94	22	(	(	PUNCT
ejpam-620	94	23	n+	n+	NUM
ejpam-620	94	24	1)δ	1)δ	NUM
ejpam-620	94	25	©	©	PROPN
ejpam-620	94	26			NOUN
ejpam-620	94	27			ADJ
ejpam-620	94	28			ADJ
ejpam-620	94	29			ADJ
ejpam-620	94	30			NUM
ejpam-620	94	31	∫	∫	PROPN
ejpam-620	94	32	n+1	n+1	NUM
ejpam-620	94	33	1	1	NUM
ejpam-620	94	34	π	π	NOUN
ejpam-620	94	35			PROPN
ejpam-620	94	36			ADP
ejpam-620	94	37			NOUN
ejpam-620	94	38	ξ	ξ	PROPN
ejpam-620	94	39	�	�	PROPN
ejpam-620	94	40	1	1	NUM
ejpam-620	94	41	y	y	PROPN
ejpam-620	94	42	�	�	PROPN
ejpam-620	94	43	yδ−1−β	yδ−1−β	PROPN
ejpam-620	94	44			PROPN
ejpam-620	94	45			PROPN
ejpam-620	94	46			NOUN
ejpam-620	94	47	s	s	PART
ejpam-620	94	48	d	d	X
ejpam-620	94	49	y	y	ADJ
ejpam-620	94	50	y2	y2	PROPN
ejpam-620	94	51			PROPN
ejpam-620	94	52			PROPN
ejpam-620	94	53			PROPN
ejpam-620	94	54			PROPN
ejpam-620	94	55			PROPN
ejpam-620	94	56	1	1	NUM
ejpam-620	94	57	s	s	NOUN
ejpam-620	94	58	=	=	NOUN
ejpam-620	94	59	o	o	X
ejpam-620	94	60	�	�	PROPN
ejpam-620	94	61	(	(	PUNCT
ejpam-620	94	62	n+	n+	NUM
ejpam-620	94	63	1)δ	1)δ	NUM
ejpam-620	94	64	ξ	ξ	PROPN
ejpam-620	94	65	�	�	PROPN
ejpam-620	94	66	1	1	NUM
ejpam-620	94	67	n+	n+	SYM
ejpam-620	94	68	1	1	NUM
ejpam-620	94	69	�	�	PROPN
ejpam-620	94	70	�	�	PROPN
ejpam-620	94	71			PROPN
ejpam-620	94	72			X
ejpam-620	94	73	∫	∫	PROPN
ejpam-620	95	1	n+1	n+1	PROPN
ejpam-620	95	2	1	1	NUM
ejpam-620	95	3	π	π	NOUN
ejpam-620	95	4	d	d	X
ejpam-620	95	5	y	y	PROPN
ejpam-620	95	6	ys(δ−1−β)+2	ys(δ−1−β)+2	PROPN
ejpam-620	95	7			PROPN
ejpam-620	95	8			PROPN
ejpam-620	95	9	1	1	NUM
ejpam-620	95	10	s	s	NOUN
ejpam-620	95	11	=	=	NOUN
ejpam-620	95	12	o	o	X
ejpam-620	95	13	�	�	PROPN
ejpam-620	95	14	(	(	PUNCT
ejpam-620	95	15	n+	n+	NUM
ejpam-620	95	16	1)δ	1)δ	NUM
ejpam-620	95	17	ξ	ξ	PROPN
ejpam-620	95	18	�	�	PROPN
ejpam-620	95	19	1	1	NUM
ejpam-620	95	20	n+	n+	SYM
ejpam-620	95	21	1	1	NUM
ejpam-620	95	22	�	�	PROPN
ejpam-620	95	23	�	�	PROPN
ejpam-620	95	24			PROPN
ejpam-620	95	25			NUM
ejpam-620	95	26	(	(	PUNCT
ejpam-620	95	27	n+	n+	NUM
ejpam-620	95	28	1)s(1+β−δ)−1	1)s(1+β−δ)−1	NUM
ejpam-620	95	29	−πs(δ−1−β)+1	−πs(δ−1−β)+1	NOUN
ejpam-620	95	30	s	s	PART
ejpam-620	95	31	�	�	PROPN
ejpam-620	95	32	1	1	NUM
ejpam-620	95	33	+	+	NUM
ejpam-620	95	34	β	β	PROPN
ejpam-620	95	35	−	−	PROPN
ejpam-620	95	36	δ	δ	PROPN
ejpam-620	95	37	�	�	PROPN
ejpam-620	95	38	−	−	PROPN
ejpam-620	95	39	1	1	NUM
ejpam-620	95	40			PROPN
ejpam-620	95	41			NUM
ejpam-620	95	42	1	1	NUM
ejpam-620	95	43	s	s	NOUN
ejpam-620	95	44	=	=	NOUN
ejpam-620	95	45	o	o	X
ejpam-620	95	46	�	�	PROPN
ejpam-620	95	47	(	(	PUNCT
ejpam-620	95	48	n+	n+	NUM
ejpam-620	95	49	1)δ	1)δ	NUM
ejpam-620	95	50	ξ	ξ	PROPN
ejpam-620	95	51	�	�	PROPN
ejpam-620	95	52	1	1	NUM
ejpam-620	95	53	n+	n+	SYM
ejpam-620	95	54	1	1	NUM
ejpam-620	95	55	�	�	PROPN
ejpam-620	95	56	�	�	PROPN
ejpam-620	95	57	h	h	PROPN
ejpam-620	95	58	(	(	PUNCT
ejpam-620	95	59	n+	n+	NUM
ejpam-620	95	60	1)(1+β−δ)−	1)(1+β−δ)−	NUM
ejpam-620	95	61	1	1	NUM
ejpam-620	95	62	s	s	NOUN
ejpam-620	95	63	i	i	NOUN
ejpam-620	95	64	=	=	NOUN
ejpam-620	95	65	o	o	X
ejpam-620	95	66	�	�	PROPN
ejpam-620	95	67	(	(	PUNCT
ejpam-620	95	68	n+	n+	NUM
ejpam-620	95	69	1)β+1−	1)β+1−	NUM
ejpam-620	95	70	1	1	NUM
ejpam-620	95	71	s	s	PROPN
ejpam-620	95	72	ξ	ξ	PROPN
ejpam-620	95	73	�	�	PROPN
ejpam-620	95	74	1	1	NUM
ejpam-620	95	75	n+	n+	SYM
ejpam-620	95	76	1	1	NUM
ejpam-620	95	77	�	�	PROPN
ejpam-620	95	78	�	�	PROPN
ejpam-620	95	79	=	=	SYM
ejpam-620	95	80	o	o	PROPN
ejpam-620	95	81	�	�	PROPN
ejpam-620	95	82	(	(	PUNCT
ejpam-620	95	83	n+	n+	NUM
ejpam-620	95	84	1)β+	1)β+	NUM
ejpam-620	95	85	1	1	NUM
ejpam-620	95	86	r	r	NOUN
ejpam-620	95	87	ξ	ξ	X
ejpam-620	95	88	�	�	PROPN
ejpam-620	95	89	1	1	NUM
ejpam-620	95	90	n+	n+	SYM
ejpam-620	95	91	1	1	NUM
ejpam-620	95	92	�	�	PROPN
ejpam-620	95	93	�	�	PROPN
ejpam-620	95	94	since	since	SCONJ
ejpam-620	95	95	1	1	NUM
ejpam-620	95	96	r	r	NOUN
ejpam-620	95	97	+	+	NOUN
ejpam-620	95	98	1	1	NUM
ejpam-620	95	99	s	s	NOUN
ejpam-620	95	100	=	=	SYM
ejpam-620	95	101	1	1	NUM
ejpam-620	95	102	(	(	PUNCT
ejpam-620	95	103	29	29	NUM
ejpam-620	95	104	)	)	PUNCT
ejpam-620	95	105	now	now	ADV
ejpam-620	95	106	combining	combine	VERB
ejpam-620	95	107	(	(	PUNCT
ejpam-620	95	108	27	27	NUM
ejpam-620	95	109	)	)	PUNCT
ejpam-620	95	110	to	to	ADP
ejpam-620	95	111	(	(	PUNCT
ejpam-620	95	112	29	29	NUM
ejpam-620	95	113	)	)	PUNCT
ejpam-620	95	114	,	,	PUNCT
ejpam-620	95	115	we	we	PRON
ejpam-620	95	116	get	get	VERB
ejpam-620	95	117	�	�	PROPN
ejpam-620	95	118	�	�	PROPN
ejpam-620	95	119	�	�	PROPN
ejpam-620	95	120	(	(	PUNCT
ejpam-620	95	121	ec)1n−	ec)1n−	PROPN
ejpam-620	95	122	f	f	PROPN
ejpam-620	95	123	�	�	PROPN
ejpam-620	95	124	�	�	PROPN
ejpam-620	95	125	�	�	PROPN
ejpam-620	95	126	=	=	SYM
ejpam-620	95	127	o	o	PROPN
ejpam-620	95	128	�	�	PROPN
ejpam-620	95	129	(	(	PUNCT
ejpam-620	95	130	n+	n+	NUM
ejpam-620	95	131	1)β+	1)β+	NUM
ejpam-620	95	132	1	1	NUM
ejpam-620	95	133	r	r	NOUN
ejpam-620	95	134	ξ	ξ	X
ejpam-620	95	135	�	�	PROPN
ejpam-620	95	136	1	1	NUM
ejpam-620	95	137	n+	n+	SYM
ejpam-620	95	138	1	1	NUM
ejpam-620	95	139	�	�	PROPN
ejpam-620	95	140	�	�	PROPN
ejpam-620	95	141	(	(	PUNCT
ejpam-620	95	142	ec)1n	ec)1n	NOUN
ejpam-620	96	1	−	−	PROPN
ejpam-620	96	2	f	f	NOUN
ejpam-620	96	3	r	r	NOUN
ejpam-620	96	4	=	=	PUNCT
ejpam-620	96	5	(	(	PUNCT
ejpam-620	96	6	∫	∫	PROPN
ejpam-620	96	7	2π	2π	PROPN
ejpam-620	96	8	0	0	NUM
ejpam-620	96	9	�	�	PROPN
ejpam-620	96	10	�	�	PROPN
ejpam-620	96	11	�	�	PROPN
ejpam-620	96	12	(	(	PUNCT
ejpam-620	96	13	ec)1n−	ec)1n−	PROPN
ejpam-620	96	14	f	f	PROPN
ejpam-620	96	15	�	�	PROPN
ejpam-620	96	16	�	�	PROPN
ejpam-620	96	17	�	�	PROPN
ejpam-620	96	18	r	r	NOUN
ejpam-620	96	19	d	d	PROPN
ejpam-620	96	20	x	x	X
ejpam-620	96	21	)	)	PUNCT
ejpam-620	96	22	1	1	NUM
ejpam-620	96	23	r	r	NOUN
ejpam-620	96	24	=	=	PUNCT
ejpam-620	96	25	(	(	PUNCT
ejpam-620	96	26	∫	∫	PROPN
ejpam-620	96	27	2π	2π	PROPN
ejpam-620	96	28	0	0	NUM
ejpam-620	96	29	�	�	PROPN
ejpam-620	96	30	(	(	PUNCT
ejpam-620	96	31	n+	n+	NUM
ejpam-620	96	32	1)β+	1)β+	NUM
ejpam-620	96	33	1	1	NUM
ejpam-620	96	34	r	r	NOUN
ejpam-620	96	35	ξ	ξ	X
ejpam-620	96	36	�	�	PROPN
ejpam-620	96	37	1	1	NUM
ejpam-620	96	38	n+	n+	SYM
ejpam-620	96	39	1	1	NUM
ejpam-620	96	40	�	�	PROPN
ejpam-620	96	41	�	�	NOUN
ejpam-620	96	42	r	r	NOUN
ejpam-620	96	43	d	d	NOUN
ejpam-620	96	44	x	x	X
ejpam-620	96	45	)	)	PUNCT
ejpam-620	96	46	1	1	NUM
ejpam-620	96	47	r	r	NOUN
ejpam-620	96	48	=	=	SYM
ejpam-620	96	49	o	o	X
ejpam-620	96	50	�	�	PROPN
ejpam-620	96	51	(	(	PUNCT
ejpam-620	96	52	n+	n+	NUM
ejpam-620	96	53	1)β+	1)β+	NUM
ejpam-620	96	54	1	1	NUM
ejpam-620	96	55	r	r	NOUN
ejpam-620	96	56	ξ	ξ	X
ejpam-620	96	57	�	�	PROPN
ejpam-620	96	58	1	1	NUM
ejpam-620	96	59	n+	n+	SYM
ejpam-620	96	60	1	1	NUM
ejpam-620	96	61	�	�	PROPN
ejpam-620	96	62	�	�	PROPN
ejpam-620	96	63			PROPN
ejpam-620	96	64			NOUN
ejpam-620	96	65			NOUN
ejpam-620	96	66	(	(	PUNCT
ejpam-620	96	67	∫	∫	PROPN
ejpam-620	96	68	2π	2π	PROPN
ejpam-620	96	69	0	0	PUNCT
ejpam-620	97	1	d	d	NOUN
ejpam-620	97	2	x	x	X
ejpam-620	97	3	)	)	PUNCT
ejpam-620	97	4	1	1	NUM
ejpam-620	97	5	r	r	NOUN
ejpam-620	97	6			PROPN
ejpam-620	97	7			PROPN
ejpam-620	97	8			PROPN
ejpam-620	97	9	=	=	SYM
ejpam-620	97	10	�	�	PROPN
ejpam-620	97	11	(	(	PUNCT
ejpam-620	97	12	n+	n+	NUM
ejpam-620	97	13	1)β+	1)β+	NUM
ejpam-620	97	14	1	1	NUM
ejpam-620	97	15	r	r	NOUN
ejpam-620	97	16	ξ	ξ	X
ejpam-620	97	17	�	�	PROPN
ejpam-620	97	18	1	1	NUM
ejpam-620	97	19	n+	n+	SYM
ejpam-620	97	20	1	1	NUM
ejpam-620	97	21	�	�	PROPN
ejpam-620	97	22	�	�	PROPN
ejpam-620	97	23	this	this	PRON
ejpam-620	97	24	completes	complete	VERB
ejpam-620	97	25	the	the	DET
ejpam-620	97	26	proof	proof	NOUN
ejpam-620	97	27	of	of	ADP
ejpam-620	97	28	the	the	DET
ejpam-620	97	29	theorem	theorem	NOUN
ejpam-620	97	30	2	2	NUM
ejpam-620	97	31	.	.	NOUN
ejpam-620	97	32	5	5	NUM
ejpam-620	97	33	.	.	PUNCT
ejpam-620	97	34	applications	application	NOUN
ejpam-620	97	35	following	follow	VERB
ejpam-620	97	36	corollaries	corollary	NOUN
ejpam-620	97	37	can	can	AUX
ejpam-620	97	38	be	be	AUX
ejpam-620	97	39	derived	derive	VERB
ejpam-620	97	40	from	from	ADP
ejpam-620	97	41	our	our	PRON
ejpam-620	97	42	main	main	ADJ
ejpam-620	97	43	theorem	theorem	NOUN
ejpam-620	97	44	:	:	PUNCT
ejpam-620	97	45	references	reference	NOUN
ejpam-620	97	46	285	285	NUM
ejpam-620	97	47	corollary	corollary	ADJ
ejpam-620	97	48	1	1	NUM
ejpam-620	97	49	.	.	PUNCT
ejpam-620	98	1	if	if	SCONJ
ejpam-620	98	2	β	β	X
ejpam-620	98	3	=	=	SYM
ejpam-620	98	4	0	0	NUM
ejpam-620	98	5	and	and	CCONJ
ejpam-620	98	6	ξ	ξ	PROPN
ejpam-620	98	7	(	(	PUNCT
ejpam-620	98	8	t	t	PROPN
ejpam-620	98	9	)	)	PUNCT
ejpam-620	98	10	=	=	SYM
ejpam-620	98	11	tα	tα	PROPN
ejpam-620	98	12	,	,	PUNCT
ejpam-620	98	13	then	then	ADV
ejpam-620	98	14	the	the	DET
ejpam-620	98	15	degree	degree	NOUN
ejpam-620	98	16	of	of	ADP
ejpam-620	98	17	approximation	approximation	NOUN
ejpam-620	98	18	of	of	ADP
ejpam-620	98	19	a	a	DET
ejpam-620	98	20	function	function	NOUN
ejpam-620	98	21	f	f	NOUN
ejpam-620	98	22	,	,	PUNCT
ejpam-620	98	23	conjugate	conjugate	ADJ
ejpam-620	98	24	to	to	ADP
ejpam-620	98	25	2π	2π	NOUN
ejpam-620	98	26	-	-	ADJ
ejpam-620	98	27	periodic	periodic	ADJ
ejpam-620	98	28	function	function	NOUN
ejpam-620	98	29	f	f	PROPN
ejpam-620	98	30	∈	∈	PROPN
ejpam-620	98	31	lip	lip	NOUN
ejpam-620	98	32	(	(	PUNCT
ejpam-620	98	33	α	α	NOUN
ejpam-620	98	34	,	,	PUNCT
ejpam-620	98	35	r	r	NOUN
ejpam-620	98	36	)	)	PUNCT
ejpam-620	98	37	,	,	PUNCT
ejpam-620	98	38	1	1	NUM
ejpam-620	98	39	r	r	NOUN
ejpam-620	98	40	≤	≤	PUNCT
ejpam-620	98	41	α	α	NOUN
ejpam-620	98	42	≤	≤	NUM
ejpam-620	98	43	1	1	NUM
ejpam-620	98	44	,	,	PUNCT
ejpam-620	98	45	is	be	AUX
ejpam-620	98	46	given	give	VERB
ejpam-620	98	47	by	by	ADP
ejpam-620	98	48	(	(	PUNCT
ejpam-620	98	49	ec)1n	ec)1n	NOUN
ejpam-620	98	50	−	−	PROPN
ejpam-620	98	51	f	f	NOUN
ejpam-620	98	52	r	r	NOUN
ejpam-620	98	53	=	=	PUNCT
ejpam-620	98	54	o	o	X
ejpam-620	99	1	(	(	PUNCT
ejpam-620	99	2	1	1	NUM
ejpam-620	99	3	(	(	PUNCT
ejpam-620	99	4	n+	n+	NUM
ejpam-620	99	5	1)α−	1)α−	NOUN
ejpam-620	99	6	1	1	NUM
ejpam-620	99	7	r	r	NOUN
ejpam-620	99	8	)	)	PUNCT
ejpam-620	99	9	corollary	corollary	NOUN
ejpam-620	99	10	2	2	NUM
ejpam-620	99	11	.	.	PUNCT
ejpam-620	100	1	if	if	SCONJ
ejpam-620	100	2	r	r	NOUN
ejpam-620	100	3	→	→	SYM
ejpam-620	100	4	∞	∞	NUM
ejpam-620	100	5	in	in	ADP
ejpam-620	100	6	corollary	corollary	ADJ
ejpam-620	100	7	1	1	NUM
ejpam-620	100	8	,	,	PUNCT
ejpam-620	100	9	then	then	ADV
ejpam-620	100	10	lip	lip	NOUN
ejpam-620	100	11	(	(	PUNCT
ejpam-620	100	12	α	α	NOUN
ejpam-620	100	13	,	,	PUNCT
ejpam-620	100	14	r	r	NOUN
ejpam-620	100	15	)	)	PUNCT
ejpam-620	100	16	reduces	reduce	VERB
ejpam-620	100	17	to	to	PART
ejpam-620	100	18	lipα	lipα	VERB
ejpam-620	100	19	for	for	ADP
ejpam-620	100	20	0	0	NUM
ejpam-620	100	21	<	<	X
ejpam-620	100	22	α	α	X
ejpam-620	100	23	<	<	X
ejpam-620	100	24	1	1	NUM
ejpam-620	100	25	,	,	PUNCT
ejpam-620	100	26	and	and	CCONJ
ejpam-620	100	27	we	we	PRON
ejpam-620	100	28	have	have	VERB
ejpam-620	100	29	(	(	PUNCT
ejpam-620	100	30	ec)1n−	ec)1n−	X
ejpam-620	100	31	f	f	PROPN
ejpam-620	100	32	r	r	NOUN
ejpam-620	100	33	=	=	PUNCT
ejpam-620	100	34	o	o	X
ejpam-620	100	35	�	�	PROPN
ejpam-620	100	36	1	1	NUM
ejpam-620	100	37	(	(	PUNCT
ejpam-620	100	38	n+	n+	NUM
ejpam-620	100	39	1)α	1)α	NUM
ejpam-620	100	40	�	�	PROPN
ejpam-620	100	41	remark	remark	NOUN
ejpam-620	100	42	1	1	NUM
ejpam-620	100	43	.	.	PUNCT
ejpam-620	101	1	an	an	DET
ejpam-620	101	2	independent	independent	ADJ
ejpam-620	101	3	proof	proof	NOUN
ejpam-620	101	4	of	of	ADP
ejpam-620	101	5	corollary	corollary	ADJ
ejpam-620	101	6	1	1	NUM
ejpam-620	101	7	can	can	AUX
ejpam-620	101	8	be	be	AUX
ejpam-620	101	9	obtained	obtain	VERB
ejpam-620	101	10	along	along	ADP
ejpam-620	101	11	the	the	DET
ejpam-620	101	12	same	same	ADJ
ejpam-620	101	13	lines	line	NOUN
ejpam-620	101	14	of	of	ADP
ejpam-620	101	15	our	our	PRON
ejpam-620	101	16	theorem	theorem	NOUN
ejpam-620	101	17	2	2	NUM
ejpam-620	101	18	.	.	PUNCT
ejpam-620	101	19	acknowledgements	acknowledgement	NOUN
ejpam-620	101	20	the	the	DET
ejpam-620	101	21	first	first	ADJ
ejpam-620	101	22	author	author	NOUN
ejpam-620	101	23	is	be	AUX
ejpam-620	101	24	thankful	thankful	ADJ
ejpam-620	101	25	to	to	ADP
ejpam-620	101	26	his	his	PRON
ejpam-620	101	27	parents	parent	NOUN
ejpam-620	101	28	for	for	ADP
ejpam-620	101	29	their	their	PRON
ejpam-620	101	30	encouragement	encouragement	NOUN
ejpam-620	101	31	and	and	CCONJ
ejpam-620	101	32	support	support	NOUN
ejpam-620	101	33	to	to	ADP
ejpam-620	101	34	this	this	DET
ejpam-620	101	35	work	work	NOUN
ejpam-620	101	36	.	.	PUNCT
ejpam-620	102	1	references	reference	NOUN
ejpam-620	102	2	[	[	X
ejpam-620	102	3	1	1	NUM
ejpam-620	102	4	]	]	X
ejpam-620	102	5	g	g	PROPN
ejpam-620	102	6	alexits	alexit	NOUN
ejpam-620	102	7	,	,	PUNCT
ejpam-620	102	8	convergence	convergence	NOUN
ejpam-620	102	9	problems	problem	NOUN
ejpam-620	102	10	of	of	ADP
ejpam-620	102	11	orthogonal	orthogonal	ADJ
ejpam-620	102	12	series	series	NOUN
ejpam-620	102	13	,	,	PUNCT
ejpam-620	102	14	pergamon	pergamon	PROPN
ejpam-620	102	15	press	press	PROPN
ejpam-620	102	16	,	,	PUNCT
ejpam-620	102	17	london	london	PROPN
ejpam-620	102	18	,	,	PUNCT
ejpam-620	102	19	1961	1961	NUM
ejpam-620	102	20	.	.	PUNCT
ejpam-620	103	1	[	[	X
ejpam-620	103	2	2	2	X
ejpam-620	103	3	]	]	X
ejpam-620	103	4	p	p	X
ejpam-620	103	5	chandra	chandra	PROPN
ejpam-620	103	6	,	,	PUNCT
ejpam-620	103	7	trigonometric	trigonometric	ADJ
ejpam-620	103	8	approximation	approximation	NOUN
ejpam-620	103	9	of	of	ADP
ejpam-620	103	10	functions	function	NOUN
ejpam-620	103	11	in	in	ADP
ejpam-620	103	12	lp	lp	PROPN
ejpam-620	103	13	norm	norm	NOUN
ejpam-620	103	14	,	,	PUNCT
ejpam-620	103	15	j.	j.	PROPN
ejpam-620	103	16	math	math	PROPN
ejpam-620	103	17	.	.	PUNCT
ejpam-620	104	1	anal	anal	PROPN
ejpam-620	104	2	.	.	PUNCT
ejpam-620	105	1	appl	appl	PROPN
ejpam-620	105	2	.	.	PUNCT
ejpam-620	106	1	275	275	NUM
ejpam-620	106	2	no	no	NOUN
ejpam-620	106	3	.	.	NOUN
ejpam-620	106	4	1	1	NUM
ejpam-620	106	5	,	,	PUNCT
ejpam-620	106	6	13	13	NUM
ejpam-620	106	7	-	-	SYM
ejpam-620	106	8	26	26	NUM
ejpam-620	106	9	.	.	PUNCT
ejpam-620	106	10	2002	2002	NUM
ejpam-620	106	11	.	.	PUNCT
ejpam-620	107	1	[	[	X
ejpam-620	107	2	3	3	X
ejpam-620	107	3	]	]	X
ejpam-620	107	4	g	g	NOUN
ejpam-620	107	5	hardy	hardy	ADJ
ejpam-620	107	6	,	,	PUNCT
ejpam-620	107	7	divergent	divergent	ADJ
ejpam-620	107	8	series	series	NOUN
ejpam-620	107	9	,	,	PUNCT
ejpam-620	107	10	first	first	ADJ
ejpam-620	107	11	edition	edition	NOUN
ejpam-620	107	12	,	,	PUNCT
ejpam-620	107	13	oxford	oxford	PROPN
ejpam-620	107	14	university	university	PROPN
ejpam-620	107	15	press	press	NOUN
ejpam-620	107	16	,	,	PUNCT
ejpam-620	107	17	70	70	NUM
ejpam-620	107	18	.	.	PUNCT
ejpam-620	107	19	1949	1949	NUM
ejpam-620	107	20	.	.	PUNCT
ejpam-620	108	1	[	[	X
ejpam-620	108	2	4	4	NUM
ejpam-620	108	3	]	]	X
ejpam-620	108	4	h	h	PROPN
ejpam-620	108	5	khan	khan	PROPN
ejpam-620	108	6	,	,	PUNCT
ejpam-620	108	7	on	on	ADP
ejpam-620	108	8	degree	degree	NOUN
ejpam-620	108	9	of	of	ADP
ejpam-620	108	10	approximation	approximation	NOUN
ejpam-620	108	11	of	of	ADP
ejpam-620	108	12	functions	function	NOUN
ejpam-620	108	13	belonging	belong	VERB
ejpam-620	108	14	to	to	ADP
ejpam-620	108	15	the	the	DET
ejpam-620	108	16	class	class	NOUN
ejpam-620	108	17	lip(α	lip(α	PROPN
ejpam-620	108	18	,	,	PUNCT
ejpam-620	108	19	p	p	NOUN
ejpam-620	108	20	)	)	PUNCT
ejpam-620	108	21	,	,	PUNCT
ejpam-620	108	22	indian	indian	PROPN
ejpam-620	108	23	j.	j.	PROPN
ejpam-620	108	24	pure	pure	PROPN
ejpam-620	108	25	appl	appl	PROPN
ejpam-620	108	26	.	.	PUNCT
ejpam-620	108	27	math	math	NOUN
ejpam-620	108	28	.	.	PUNCT
ejpam-620	109	1	5	5	NUM
ejpam-620	109	2	no	no	NOUN
ejpam-620	109	3	.	.	NOUN
ejpam-620	109	4	2	2	NUM
ejpam-620	109	5	,	,	PUNCT
ejpam-620	109	6	132	132	NUM
ejpam-620	109	7	-	-	SYM
ejpam-620	109	8	136	136	NUM
ejpam-620	109	9	.	.	PUNCT
ejpam-620	109	10	1974	1974	NUM
ejpam-620	109	11	.	.	PUNCT
ejpam-620	110	1	[	[	X
ejpam-620	110	2	5	5	NUM
ejpam-620	110	3	]	]	X
ejpam-620	110	4	s	s	PART
ejpam-620	110	5	lal	lal	PROPN
ejpam-620	110	6	,	,	PUNCT
ejpam-620	110	7	on	on	ADP
ejpam-620	110	8	kλ	kλ	DET
ejpam-620	110	9	summability	summability	NOUN
ejpam-620	110	10	of	of	ADP
ejpam-620	110	11	conjugate	conjugate	ADJ
ejpam-620	110	12	series	series	NOUN
ejpam-620	110	13	of	of	ADP
ejpam-620	110	14	fourier	fourier	PROPN
ejpam-620	110	15	series	series	NOUN
ejpam-620	110	16	,	,	PUNCT
ejpam-620	110	17	bulletin	bulletin	NOUN
ejpam-620	110	18	of	of	ADP
ejpam-620	110	19	calcutta	calcutta	PROPN
ejpam-620	110	20	math	math	NOUN
ejpam-620	110	21	.	.	PUNCT
ejpam-620	111	1	soc	soc	PROPN
ejpam-620	111	2	.	.	PUNCT
ejpam-620	111	3	,	,	PUNCT
ejpam-620	111	4	89	89	NUM
ejpam-620	111	5	,	,	PUNCT
ejpam-620	111	6	97	97	NUM
ejpam-620	111	7	-	-	SYM
ejpam-620	111	8	104	104	NUM
ejpam-620	111	9	.	.	PUNCT
ejpam-620	111	10	1997	1997	NUM
ejpam-620	111	11	.	.	PUNCT
ejpam-620	112	1	[	[	X
ejpam-620	112	2	6	6	NUM
ejpam-620	112	3	]	]	PUNCT
ejpam-620	112	4	l	l	NOUN
ejpam-620	112	5	leindler	leindler	NOUN
ejpam-620	112	6	,	,	PUNCT
ejpam-620	112	7	trigonometric	trigonometric	ADJ
ejpam-620	112	8	approximation	approximation	NOUN
ejpam-620	112	9	of	of	ADP
ejpam-620	112	10	functions	function	NOUN
ejpam-620	112	11	in	in	ADP
ejpam-620	112	12	lp	lp	PROPN
ejpam-620	112	13	norm	norm	NOUN
ejpam-620	112	14	,	,	PUNCT
ejpam-620	112	15	j.	j.	PROPN
ejpam-620	112	16	math	math	PROPN
ejpam-620	112	17	.	.	PUNCT
ejpam-620	113	1	anal	anal	PROPN
ejpam-620	113	2	.	.	PUNCT
ejpam-620	114	1	appl	appl	PROPN
ejpam-620	114	2	.	.	PROPN
ejpam-620	115	1	302	302	NUM
ejpam-620	115	2	.	.	PUNCT
ejpam-620	115	3	2005	2005	NUM
ejpam-620	115	4	.	.	PUNCT
ejpam-620	116	1	[	[	X
ejpam-620	116	2	7	7	X
ejpam-620	116	3	]	]	X
ejpam-620	116	4	l.	l.	PROPN
ejpam-620	116	5	mcfadden	mcfadden	PROPN
ejpam-620	116	6	,	,	PUNCT
ejpam-620	116	7	absolute	absolute	PROPN
ejpam-620	116	8	nörlund	nörlund	NOUN
ejpam-620	116	9	summability	summability	NOUN
ejpam-620	116	10	,	,	PUNCT
ejpam-620	116	11	duke	duke	PROPN
ejpam-620	116	12	math	math	PROPN
ejpam-620	116	13	.	.	PUNCT
ejpam-620	117	1	j.	j.	PROPN
ejpam-620	117	2	9	9	PROPN
ejpam-620	117	3	,	,	PUNCT
ejpam-620	117	4	168	168	NUM
ejpam-620	117	5	-	-	SYM
ejpam-620	117	6	207	207	NUM
ejpam-620	117	7	.	.	PUNCT
ejpam-620	117	8	1942	1942	NUM
ejpam-620	117	9	.	.	PUNCT
ejpam-620	118	1	[	[	X
ejpam-620	118	2	8	8	NUM
ejpam-620	118	3	]	]	X
ejpam-620	118	4	k	k	PROPN
ejpam-620	118	5	qureshi	qureshi	PROPN
ejpam-620	118	6	,	,	PUNCT
ejpam-620	118	7	h	h	NOUN
ejpam-620	118	8	neha	neha	NOUN
ejpam-620	118	9	,	,	PUNCT
ejpam-620	118	10	a	a	DET
ejpam-620	118	11	class	class	NOUN
ejpam-620	118	12	of	of	ADP
ejpam-620	118	13	functions	function	NOUN
ejpam-620	118	14	and	and	CCONJ
ejpam-620	118	15	their	their	PRON
ejpam-620	118	16	degree	degree	NOUN
ejpam-620	118	17	of	of	ADP
ejpam-620	118	18	approximation	approximation	NOUN
ejpam-620	118	19	,	,	PUNCT
ejpam-620	118	20	ganita	ganita	NOUN
ejpam-620	118	21	.	.	PUNCT
ejpam-620	119	1	41	41	NUM
ejpam-620	119	2	no	no	NOUN
ejpam-620	119	3	.	.	NOUN
ejpam-620	119	4	1	1	NUM
ejpam-620	119	5	,	,	PUNCT
ejpam-620	119	6	37	37	NUM
ejpam-620	119	7	-	-	SYM
ejpam-620	119	8	42	42	NUM
ejpam-620	119	9	.	.	PUNCT
ejpam-620	119	10	1990	1990	NUM
ejpam-620	119	11	.	.	PUNCT
ejpam-620	120	1	[	[	X
ejpam-620	120	2	9	9	NUM
ejpam-620	120	3	]	]	X
ejpam-620	120	4	k	k	PROPN
ejpam-620	120	5	qureshi	qureshi	PROPN
ejpam-620	120	6	,	,	PUNCT
ejpam-620	120	7	on	on	ADP
ejpam-620	120	8	the	the	DET
ejpam-620	120	9	degree	degree	NOUN
ejpam-620	120	10	of	of	ADP
ejpam-620	120	11	approximation	approximation	NOUN
ejpam-620	120	12	of	of	ADP
ejpam-620	120	13	a	a	DET
ejpam-620	120	14	periodic	periodic	ADJ
ejpam-620	120	15	function	function	NOUN
ejpam-620	120	16	f	f	NOUN
ejpam-620	120	17	by	by	ADP
ejpam-620	120	18	almost	almost	ADV
ejpam-620	120	19	nörlund	nörlund	NOUN
ejpam-620	120	20	means	mean	NOUN
ejpam-620	120	21	,	,	PUNCT
ejpam-620	120	22	tamkang	tamkang	PROPN
ejpam-620	120	23	j.	j.	PROPN
ejpam-620	120	24	math	math	PROPN
ejpam-620	120	25	.	.	PUNCT
ejpam-620	121	1	12	12	NUM
ejpam-620	121	2	no	no	NOUN
ejpam-620	121	3	.	.	NOUN
ejpam-620	121	4	1	1	NUM
ejpam-620	121	5	,	,	PUNCT
ejpam-620	121	6	35	35	NUM
ejpam-620	121	7	-	-	SYM
ejpam-620	121	8	38	38	NUM
ejpam-620	121	9	.	.	PUNCT
ejpam-620	121	10	1981	1981	NUM
ejpam-620	121	11	.	.	PUNCT
ejpam-620	122	1	[	[	X
ejpam-620	122	2	10	10	NUM
ejpam-620	122	3	]	]	X
ejpam-620	122	4	k	k	PROPN
ejpam-620	122	5	qureshi	qureshi	PROPN
ejpam-620	122	6	,	,	PUNCT
ejpam-620	122	7	on	on	ADP
ejpam-620	122	8	the	the	DET
ejpam-620	122	9	degree	degree	NOUN
ejpam-620	122	10	of	of	ADP
ejpam-620	122	11	approximation	approximation	NOUN
ejpam-620	122	12	of	of	ADP
ejpam-620	122	13	a	a	DET
ejpam-620	122	14	function	function	NOUN
ejpam-620	122	15	belonging	belong	VERB
ejpam-620	122	16	to	to	ADP
ejpam-620	122	17	the	the	DET
ejpam-620	122	18	class	class	NOUN
ejpam-620	122	19	lipα	lipα	PROPN
ejpam-620	122	20	,	,	PUNCT
ejpam-620	122	21	indian	indian	PROPN
ejpam-620	122	22	j.	j.	PROPN
ejpam-620	122	23	pure	pure	PROPN
ejpam-620	122	24	appl	appl	PROPN
ejpam-620	122	25	.	.	PUNCT
ejpam-620	122	26	math	math	NOUN
ejpam-620	122	27	.	.	PUNCT
ejpam-620	123	1	13	13	NUM
ejpam-620	123	2	no	no	NOUN
ejpam-620	123	3	.	.	NOUN
ejpam-620	123	4	8	8	NUM
ejpam-620	123	5	,	,	PUNCT
ejpam-620	123	6	560	560	NUM
ejpam-620	123	7	-	-	SYM
ejpam-620	123	8	563	563	NUM
ejpam-620	123	9	.	.	NOUN
ejpam-620	123	10	1982	1982	NUM
ejpam-620	123	11	.	.	PUNCT
ejpam-620	124	1	references	reference	NOUN
ejpam-620	124	2	286	286	NUM
ejpam-620	125	1	[	[	X
ejpam-620	125	2	11	11	NUM
ejpam-620	125	3	]	]	SYM
ejpam-620	125	4	b	b	NOUN
ejpam-620	125	5	rhaodes	rhaode	NOUN
ejpam-620	125	6	,	,	PUNCT
ejpam-620	125	7	on	on	ADP
ejpam-620	125	8	the	the	DET
ejpam-620	125	9	degree	degree	NOUN
ejpam-620	125	10	of	of	ADP
ejpam-620	125	11	approximation	approximation	NOUN
ejpam-620	125	12	of	of	ADP
ejpam-620	125	13	functions	function	NOUN
ejpam-620	125	14	belonging	belong	VERB
ejpam-620	125	15	to	to	ADP
ejpam-620	125	16	lipschitz	lipschitz	VERB
ejpam-620	125	17	class	class	NOUN
ejpam-620	125	18	by	by	ADP
ejpam-620	125	19	hausdorff	hausdorff	NOUN
ejpam-620	125	20	means	mean	NOUN
ejpam-620	125	21	of	of	ADP
ejpam-620	125	22	its	its	PRON
ejpam-620	125	23	fourier	fourier	NOUN
ejpam-620	125	24	series	series	NOUN
ejpam-620	125	25	,	,	PUNCT
ejpam-620	125	26	tamkang	tamkang	PROPN
ejpam-620	125	27	j.	j.	PROPN
ejpam-620	125	28	math	math	PROPN
ejpam-620	125	29	,	,	PUNCT
ejpam-620	125	30	34	34	NUM
ejpam-620	125	31	no	no	NOUN
ejpam-620	125	32	.	.	NOUN
ejpam-620	126	1	3	3	NUM
ejpam-620	126	2	,	,	PUNCT
ejpam-620	126	3	245	245	NUM
ejpam-620	126	4	-	-	SYM
ejpam-620	126	5	247	247	NUM
ejpam-620	126	6	.	.	PUNCT
ejpam-620	127	1	2003	2003	NUM
ejpam-620	127	2	.	.	PUNCT
ejpam-620	128	1	[	[	X
ejpam-620	128	2	12	12	NUM
ejpam-620	128	3	]	]	SYM
ejpam-620	128	4	b	b	X
ejpam-620	128	5	sahney	sahney	NOUN
ejpam-620	128	6	,	,	PUNCT
ejpam-620	128	7	d.	d.	PROPN
ejpam-620	128	8	s.	s.	PROPN
ejpam-620	128	9	goel	goel	PROPN
ejpam-620	128	10	,	,	PUNCT
ejpam-620	128	11	on	on	ADP
ejpam-620	128	12	the	the	DET
ejpam-620	128	13	degree	degree	NOUN
ejpam-620	128	14	of	of	ADP
ejpam-620	128	15	continuous	continuous	ADJ
ejpam-620	128	16	functions	function	NOUN
ejpam-620	128	17	,	,	PUNCT
ejpam-620	128	18	ranchi	ranchi	PROPN
ejpam-620	128	19	university	university	PROPN
ejpam-620	128	20	,	,	PUNCT
ejpam-620	128	21	math	math	NOUN
ejpam-620	128	22	.	.	PUNCT
ejpam-620	129	1	jour	jour	PROPN
ejpam-620	129	2	.	.	PROPN
ejpam-620	129	3	,	,	PUNCT
ejpam-620	129	4	4	4	NUM
ejpam-620	129	5	,	,	PUNCT
ejpam-620	129	6	50	50	NUM
ejpam-620	129	7	-	-	SYM
ejpam-620	129	8	53	53	NUM
ejpam-620	129	9	.	.	NUM
ejpam-620	129	10	1973	1973	NUM
ejpam-620	129	11	.	.	PUNCT
ejpam-620	130	1	[	[	X
ejpam-620	130	2	13	13	NUM
ejpam-620	130	3	]	]	X
ejpam-620	130	4	a	a	DET
ejpam-620	130	5	zygmund	zygmund	NOUN
ejpam-620	130	6	,	,	PUNCT
ejpam-620	130	7	trigonometric	trigonometric	ADJ
ejpam-620	130	8	series	series	NOUN
ejpam-620	130	9	,	,	PUNCT
ejpam-620	130	10	2nd	2nd	PROPN
ejpam-620	130	11	rev	rev	PROPN
ejpam-620	130	12	.	.	PUNCT
ejpam-620	131	1	ed	ed	NOUN
ejpam-620	131	2	.	.	PROPN
ejpam-620	131	3	,	,	PUNCT
ejpam-620	131	4	vol	vol	NOUN
ejpam-620	131	5	.	.	PROPN
ejpam-620	131	6	1	1	NUM
ejpam-620	131	7	,	,	PUNCT
ejpam-620	131	8	cambridge	cambridge	PROPN
ejpam-620	131	9	univ	univ	PROPN
ejpam-620	131	10	.	.	PUNCT
ejpam-620	132	1	press	press	PROPN
ejpam-620	132	2	,	,	PUNCT
ejpam-620	132	3	cambridge	cambridge	PROPN
ejpam-620	132	4	,	,	PUNCT
ejpam-620	132	5	1959	1959	NUM
ejpam-620	132	6	.	.	PUNCT