id	sid	tid	token	lemma	pos
ejpam-1314	1	1	european	european	PROPN
ejpam-1314	1	2	journal	journal	PROPN
ejpam-1314	1	3	of	of	ADP
ejpam-1314	1	4	pure	pure	ADJ
ejpam-1314	1	5	and	and	CCONJ
ejpam-1314	1	6	applied	apply	VERB
ejpam-1314	1	7	mathematics	mathematic	NOUN
ejpam-1314	1	8	vol	vol	NOUN
ejpam-1314	1	9	.	.	PROPN
ejpam-1314	2	1	6	6	NUM
ejpam-1314	2	2	,	,	PUNCT
ejpam-1314	2	3	no	no	INTJ
ejpam-1314	2	4	.	.	NOUN
ejpam-1314	2	5	4	4	NUM
ejpam-1314	2	6	,	,	PUNCT
ejpam-1314	2	7	2013	2013	NUM
ejpam-1314	2	8	,	,	PUNCT
ejpam-1314	2	9	451	451	NUM
ejpam-1314	2	10	-	-	SYM
ejpam-1314	2	11	459	459	NUM
ejpam-1314	2	12	issn	issn	PROPN
ejpam-1314	2	13	1307	1307	NUM
ejpam-1314	2	14	-	-	SYM
ejpam-1314	2	15	5543	5543	NUM
ejpam-1314	2	16	–	–	PUNCT
ejpam-1314	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1314	2	18	on	on	ADP
ejpam-1314	2	19	integrability	integrability	NOUN
ejpam-1314	2	20	of	of	ADP
ejpam-1314	2	21	trigonometric	trigonometric	ADJ
ejpam-1314	2	22	series	series	NOUN
ejpam-1314	2	23	with	with	ADP
ejpam-1314	2	24	special	special	ADJ
ejpam-1314	2	25	type	type	NOUN
ejpam-1314	2	26	of	of	ADP
ejpam-1314	2	27	coefficients	coefficient	NOUN
ejpam-1314	2	28	xhevat	xhevat	PROPN
ejpam-1314	2	29	z.	z.	PROPN
ejpam-1314	2	30	krasniqi	krasniqi	PROPN
ejpam-1314	2	31	department	department	PROPN
ejpam-1314	2	32	of	of	ADP
ejpam-1314	2	33	mathematics	mathematics	PROPN
ejpam-1314	2	34	and	and	CCONJ
ejpam-1314	2	35	informatics	informatic	NOUN
ejpam-1314	2	36	,	,	PUNCT
ejpam-1314	2	37	faculty	faculty	NOUN
ejpam-1314	2	38	of	of	ADP
ejpam-1314	2	39	education	education	NOUN
ejpam-1314	2	40	,	,	PUNCT
ejpam-1314	2	41	university	university	PROPN
ejpam-1314	2	42	of	of	ADP
ejpam-1314	2	43	prishtina	prishtina	PROPN
ejpam-1314	2	44	"	"	PUNCT
ejpam-1314	2	45	hasan	hasan	PROPN
ejpam-1314	2	46	prishtina	prishtina	PROPN
ejpam-1314	2	47	"	"	PUNCT
ejpam-1314	2	48	,	,	PUNCT
ejpam-1314	2	49	avenue	avenue	PROPN
ejpam-1314	2	50	"	"	PUNCT
ejpam-1314	2	51	mother	mother	NOUN
ejpam-1314	2	52	theresa	theresa	PROPN
ejpam-1314	2	53	"	"	PUNCT
ejpam-1314	2	54	5	5	NUM
ejpam-1314	2	55	,	,	PUNCT
ejpam-1314	2	56	10000	10000	NUM
ejpam-1314	2	57	prishtina	prishtina	PROPN
ejpam-1314	2	58	,	,	PUNCT
ejpam-1314	2	59	republic	republic	NOUN
ejpam-1314	2	60	of	of	ADP
ejpam-1314	2	61	kosovo	kosovo	PROPN
ejpam-1314	2	62	abstract	abstract	PROPN
ejpam-1314	2	63	.	.	PUNCT
ejpam-1314	3	1	in	in	ADP
ejpam-1314	3	2	this	this	DET
ejpam-1314	3	3	paper	paper	NOUN
ejpam-1314	3	4	some	some	DET
ejpam-1314	3	5	condition	condition	NOUN
ejpam-1314	3	6	on	on	ADP
ejpam-1314	3	7	integrability	integrability	NOUN
ejpam-1314	3	8	of	of	ADP
ejpam-1314	3	9	cosine	cosine	NOUN
ejpam-1314	3	10	and	and	CCONJ
ejpam-1314	3	11	sine	sine	ADJ
ejpam-1314	3	12	trigonometric	trigonometric	ADJ
ejpam-1314	3	13	series	series	NOUN
ejpam-1314	3	14	with	with	ADP
ejpam-1314	3	15	coefficients	coefficient	NOUN
ejpam-1314	3	16	that	that	PRON
ejpam-1314	3	17	keep	keep	VERB
ejpam-1314	3	18	their	their	PRON
ejpam-1314	3	19	signs	sign	NOUN
ejpam-1314	3	20	are	be	AUX
ejpam-1314	3	21	obtained	obtain	VERB
ejpam-1314	3	22	.	.	PUNCT
ejpam-1314	4	1	the	the	DET
ejpam-1314	4	2	results	result	NOUN
ejpam-1314	4	3	extend	extend	VERB
ejpam-1314	4	4	some	some	DET
ejpam-1314	4	5	previous	previous	ADJ
ejpam-1314	4	6	results	result	NOUN
ejpam-1314	4	7	of	of	ADP
ejpam-1314	4	8	telyakovskĭı	telyakovskĭı	PROPN
ejpam-1314	4	9	.	.	PUNCT
ejpam-1314	5	1	2010	2010	NUM
ejpam-1314	5	2	mathematics	mathematic	NOUN
ejpam-1314	5	3	subject	subject	NOUN
ejpam-1314	5	4	classifications	classification	NOUN
ejpam-1314	5	5	:	:	PUNCT
ejpam-1314	5	6	42a16	42a16	NUM
ejpam-1314	5	7	,	,	PUNCT
ejpam-1314	5	8	42a20	42a20	NUM
ejpam-1314	5	9	key	key	ADJ
ejpam-1314	5	10	words	word	NOUN
ejpam-1314	5	11	and	and	CCONJ
ejpam-1314	5	12	phrases	phrase	NOUN
ejpam-1314	5	13	:	:	PUNCT
ejpam-1314	5	14	trigonometric	trigonometric	ADJ
ejpam-1314	5	15	series	series	NOUN
ejpam-1314	5	16	,	,	PUNCT
ejpam-1314	5	17	quasi	quasi	ADJ
ejpam-1314	5	18	-	-	ADJ
ejpam-1314	5	19	convex	convex	ADJ
ejpam-1314	5	20	sequence	sequence	NOUN
ejpam-1314	5	21	,	,	PUNCT
ejpam-1314	5	22	bounded	bound	VERB
ejpam-1314	5	23	variation	variation	NOUN
ejpam-1314	5	24	sequence	sequence	NOUN
ejpam-1314	5	25	,	,	PUNCT
ejpam-1314	5	26	integrability	integrability	NOUN
ejpam-1314	5	27	1	1	NUM
ejpam-1314	5	28	.	.	PUNCT
ejpam-1314	6	1	introduction	introduction	NOUN
ejpam-1314	6	2	and	and	CCONJ
ejpam-1314	6	3	preliminaries	preliminary	NOUN
ejpam-1314	6	4	several	several	ADJ
ejpam-1314	6	5	mathematicians	mathematician	NOUN
ejpam-1314	6	6	have	have	AUX
ejpam-1314	6	7	studied	study	VERB
ejpam-1314	6	8	the	the	DET
ejpam-1314	6	9	integrability	integrability	NOUN
ejpam-1314	6	10	conditions	condition	NOUN
ejpam-1314	6	11	for	for	ADP
ejpam-1314	6	12	trigonometric	trigonometric	ADJ
ejpam-1314	6	13	series	series	NOUN
ejpam-1314	6	14	with	with	ADP
ejpam-1314	6	15	different	different	ADJ
ejpam-1314	6	16	types	type	NOUN
ejpam-1314	6	17	of	of	ADP
ejpam-1314	6	18	coefficients	coefficient	NOUN
ejpam-1314	6	19	.	.	PUNCT
ejpam-1314	7	1	the	the	DET
ejpam-1314	7	2	first	first	ADJ
ejpam-1314	7	3	results	result	NOUN
ejpam-1314	7	4	pertaining	pertain	VERB
ejpam-1314	7	5	to	to	ADP
ejpam-1314	7	6	the	the	DET
ejpam-1314	7	7	trigonometric	trigonometric	ADJ
ejpam-1314	7	8	series	series	NOUN
ejpam-1314	7	9	of	of	ADP
ejpam-1314	7	10	the	the	DET
ejpam-1314	7	11	form	form	NOUN
ejpam-1314	7	12	a0	a0	NOUN
ejpam-1314	7	13	2	2	NUM
ejpam-1314	7	14	+	+	CCONJ
ejpam-1314	7	15	∞	∞	NUM
ejpam-1314	7	16	∑	∑	PROPN
ejpam-1314	7	17	k=1	k=1	PROPN
ejpam-1314	7	18	ak	ak	PROPN
ejpam-1314	7	19	cos	cos	PROPN
ejpam-1314	7	20	kx	kx	PROPN
ejpam-1314	7	21	(	(	PUNCT
ejpam-1314	7	22	1	1	X
ejpam-1314	7	23	)	)	PUNCT
ejpam-1314	7	24	∞	∞	NUM
ejpam-1314	7	25	∑	∑	PUNCT
ejpam-1314	7	26	k=1	k=1	PROPN
ejpam-1314	7	27	ak	ak	PROPN
ejpam-1314	7	28	sin	sin	PROPN
ejpam-1314	7	29	kx	kx	PROPN
ejpam-1314	7	30	(	(	PUNCT
ejpam-1314	7	31	2	2	X
ejpam-1314	7	32	)	)	PUNCT
ejpam-1314	7	33	considered	consider	VERB
ejpam-1314	7	34	the	the	DET
ejpam-1314	7	35	case	case	NOUN
ejpam-1314	7	36	of	of	ADP
ejpam-1314	7	37	monotone	monotone	ADJ
ejpam-1314	7	38	coefficients	coefficient	NOUN
ejpam-1314	7	39	.	.	PUNCT
ejpam-1314	8	1	later	later	ADV
ejpam-1314	8	2	,	,	PUNCT
ejpam-1314	8	3	some	some	DET
ejpam-1314	8	4	authors	author	NOUN
ejpam-1314	8	5	investigated	investigate	VERB
ejpam-1314	8	6	the	the	DET
ejpam-1314	8	7	series	series	NOUN
ejpam-1314	8	8	(	(	PUNCT
ejpam-1314	8	9	1	1	NUM
ejpam-1314	8	10	)	)	PUNCT
ejpam-1314	8	11	with	with	ADP
ejpam-1314	8	12	quasi	quasi	ADJ
ejpam-1314	8	13	-	-	ADJ
ejpam-1314	8	14	monotone	monotone	ADJ
ejpam-1314	8	15	coefficients	coefficient	NOUN
ejpam-1314	8	16	(	(	PUNCT
ejpam-1314	8	17	an+1	an+1	NOUN
ejpam-1314	8	18	≤	≤	X
ejpam-1314	8	19	an(1+α	an(1+α	PROPN
ejpam-1314	8	20	/	/	SYM
ejpam-1314	8	21	n	n	CCONJ
ejpam-1314	8	22	)	)	PUNCT
ejpam-1314	8	23	,	,	PUNCT
ejpam-1314	8	24	n≥	n≥	PROPN
ejpam-1314	8	25	n0	n0	PROPN
ejpam-1314	8	26	,	,	PUNCT
ejpam-1314	8	27	α	α	PROPN
ejpam-1314	8	28	>	>	X
ejpam-1314	8	29	0	0	NUM
ejpam-1314	8	30	)	)	PUNCT
ejpam-1314	8	31	.	.	PUNCT
ejpam-1314	9	1	many	many	ADJ
ejpam-1314	9	2	papers	paper	NOUN
ejpam-1314	9	3	have	have	AUX
ejpam-1314	9	4	been	be	AUX
ejpam-1314	9	5	written	write	VERB
ejpam-1314	9	6	on	on	ADP
ejpam-1314	9	7	the	the	DET
ejpam-1314	9	8	series	series	NOUN
ejpam-1314	9	9	(	(	PUNCT
ejpam-1314	9	10	1	1	NUM
ejpam-1314	9	11	)	)	PUNCT
ejpam-1314	9	12	when	when	SCONJ
ejpam-1314	9	13	the	the	DET
ejpam-1314	9	14	sequence	sequence	NOUN
ejpam-1314	9	15	{	{	PUNCT
ejpam-1314	9	16	ak	ak	PROPN
ejpam-1314	9	17	}	}	PUNCT
ejpam-1314	9	18	is	be	AUX
ejpam-1314	9	19	a	a	DET
ejpam-1314	9	20	nullsequence	nullsequence	NOUN
ejpam-1314	9	21	and	and	CCONJ
ejpam-1314	9	22	convex	convex	NOUN
ejpam-1314	9	23	or	or	CCONJ
ejpam-1314	9	24	quasi	quasi	ADJ
ejpam-1314	9	25	-	-	NOUN
ejpam-1314	9	26	convex	convex	ADJ
ejpam-1314	9	27	,	,	PUNCT
ejpam-1314	9	28	i.e.	i.e.	X
ejpam-1314	9	29	42ak	42ak	ADJ
ejpam-1314	9	30	≥	≥	NOUN
ejpam-1314	9	31	0	0	NUM
ejpam-1314	9	32	or	or	CCONJ
ejpam-1314	9	33	∞	∞	NUM
ejpam-1314	9	34	∑	∑	PUNCT
ejpam-1314	9	35	k=1	k=1	PROPN
ejpam-1314	9	36	(	(	PUNCT
ejpam-1314	9	37	k+	k+	NOUN
ejpam-1314	9	38	1)|42ak|<∞	1)|42ak|<∞	NUM
ejpam-1314	9	39	,	,	PUNCT
ejpam-1314	9	40	(	(	PUNCT
ejpam-1314	9	41	3	3	X
ejpam-1314	9	42	)	)	PUNCT
ejpam-1314	9	43	where	where	SCONJ
ejpam-1314	9	44	42ak	42ak	ADJ
ejpam-1314	9	45	=	=	SYM
ejpam-1314	9	46	4	4	NUM
ejpam-1314	9	47	�	�	PROPN
ejpam-1314	9	48	4ak	4ak	ADJ
ejpam-1314	9	49	�	�	PROPN
ejpam-1314	9	50	,	,	PUNCT
ejpam-1314	9	51	4ak	4ak	ADJ
ejpam-1314	9	52	=	=	SYM
ejpam-1314	9	53	ak	ak	PROPN
ejpam-1314	9	54	−	−	PROPN
ejpam-1314	9	55	ak+1	ak+1	NOUN
ejpam-1314	9	56	.	.	PUNCT
ejpam-1314	9	57	email	email	NOUN
ejpam-1314	9	58	address	address	NOUN
ejpam-1314	9	59	:	:	PUNCT
ejpam-1314	9	60	xhevat.krasniqi@uni-pr.edu	xhevat.krasniqi@uni-pr.edu	PROPN
ejpam-1314	9	61	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1314	10	1	451	451	NUM
ejpam-1314	11	1	c	c	X
ejpam-1314	11	2	©	©	PROPN
ejpam-1314	11	3	2013	2013	NUM
ejpam-1314	11	4	ejpam	ejpam	NOUN
ejpam-1314	11	5	all	all	DET
ejpam-1314	11	6	rights	right	NOUN
ejpam-1314	11	7	reserved	reserve	VERB
ejpam-1314	11	8	.	.	PUNCT
ejpam-1314	12	1	xh	xh	PROPN
ejpam-1314	12	2	.	.	PUNCT
ejpam-1314	12	3	krasniqi	krasniqi	PROPN
ejpam-1314	12	4	/	/	SYM
ejpam-1314	12	5	eur	eur	PROPN
ejpam-1314	12	6	.	.	PUNCT
ejpam-1314	13	1	j.	j.	PROPN
ejpam-1314	13	2	pure	pure	PROPN
ejpam-1314	13	3	appl	appl	PROPN
ejpam-1314	13	4	.	.	PROPN
ejpam-1314	13	5	math	math	PROPN
ejpam-1314	13	6	,	,	PUNCT
ejpam-1314	13	7	6	6	NUM
ejpam-1314	13	8	(	(	PUNCT
ejpam-1314	13	9	2013	2013	NUM
ejpam-1314	13	10	)	)	PUNCT
ejpam-1314	13	11	,	,	PUNCT
ejpam-1314	13	12	451	451	NUM
ejpam-1314	13	13	-	-	SYM
ejpam-1314	13	14	459	459	NUM
ejpam-1314	13	15	452	452	NUM
ejpam-1314	13	16	furthermore	furthermore	ADV
ejpam-1314	13	17	,	,	PUNCT
ejpam-1314	13	18	when	when	SCONJ
ejpam-1314	13	19	{	{	PUNCT
ejpam-1314	13	20	ak	ak	PROPN
ejpam-1314	13	21	}	}	PUNCT
ejpam-1314	13	22	is	be	AUX
ejpam-1314	13	23	a	a	DET
ejpam-1314	13	24	null	null	ADJ
ejpam-1314	13	25	-	-	PUNCT
ejpam-1314	13	26	sequence	sequence	NOUN
ejpam-1314	13	27	of	of	ADP
ejpam-1314	13	28	bounded	bounded	ADJ
ejpam-1314	13	29	variation	variation	NOUN
ejpam-1314	13	30	,	,	PUNCT
ejpam-1314	13	31	i.e.	i.e.	X
ejpam-1314	13	32	∑∞	∑∞	X
ejpam-1314	13	33	k=1	k=1	X
ejpam-1314	13	34	|4ak|	|4ak|	PROPN
ejpam-1314	13	35	<	<	X
ejpam-1314	13	36	∞	∞	PROPN
ejpam-1314	13	37	,	,	PUNCT
ejpam-1314	13	38	is	be	AUX
ejpam-1314	13	39	also	also	ADV
ejpam-1314	13	40	considered	consider	VERB
ejpam-1314	13	41	.	.	PUNCT
ejpam-1314	14	1	we	we	PRON
ejpam-1314	14	2	shall	shall	AUX
ejpam-1314	14	3	consider	consider	VERB
ejpam-1314	14	4	the	the	DET
ejpam-1314	14	5	series	series	NOUN
ejpam-1314	14	6	(	(	PUNCT
ejpam-1314	14	7	1	1	NUM
ejpam-1314	14	8	)	)	PUNCT
ejpam-1314	14	9	and	and	CCONJ
ejpam-1314	14	10	(	(	PUNCT
ejpam-1314	14	11	2	2	X
ejpam-1314	14	12	)	)	PUNCT
ejpam-1314	14	13	whose	whose	DET
ejpam-1314	14	14	coefficients	coefficient	NOUN
ejpam-1314	14	15	tend	tend	VERB
ejpam-1314	14	16	to	to	ADP
ejpam-1314	14	17	zero	zero	NUM
ejpam-1314	14	18	and	and	CCONJ
ejpam-1314	14	19	satisfy	satisfy	VERB
ejpam-1314	14	20	any	any	DET
ejpam-1314	14	21	condition	condition	NOUN
ejpam-1314	14	22	that	that	PRON
ejpam-1314	14	23	provides	provide	VERB
ejpam-1314	14	24	their	their	PRON
ejpam-1314	14	25	convergence	convergence	NOUN
ejpam-1314	14	26	on	on	ADP
ejpam-1314	14	27	(	(	PUNCT
ejpam-1314	14	28	0,π	0,π	NOUN
ejpam-1314	14	29	]	]	PUNCT
ejpam-1314	14	30	.	.	PUNCT
ejpam-1314	15	1	let	let	VERB
ejpam-1314	15	2	us	we	PRON
ejpam-1314	15	3	denote	denote	VERB
ejpam-1314	15	4	their	their	PRON
ejpam-1314	15	5	sums	sum	NOUN
ejpam-1314	15	6	with	with	ADP
ejpam-1314	15	7	f	f	PROPN
ejpam-1314	15	8	(	(	PUNCT
ejpam-1314	15	9	x	x	NOUN
ejpam-1314	15	10	)	)	PUNCT
ejpam-1314	15	11	and	and	CCONJ
ejpam-1314	15	12	g(x	g(x	NOUN
ejpam-1314	15	13	)	)	PUNCT
ejpam-1314	15	14	respectively	respectively	ADV
ejpam-1314	15	15	.	.	PUNCT
ejpam-1314	16	1	if	if	SCONJ
ejpam-1314	16	2	the	the	DET
ejpam-1314	16	3	coefficients	coefficient	NOUN
ejpam-1314	16	4	ak	ak	PROPN
ejpam-1314	16	5	are	be	AUX
ejpam-1314	16	6	quasi	quasi	ADJ
ejpam-1314	16	7	-	-	NOUN
ejpam-1314	16	8	convex	convex	ADJ
ejpam-1314	16	9	,	,	PUNCT
ejpam-1314	16	10	it	it	PRON
ejpam-1314	16	11	is	be	AUX
ejpam-1314	16	12	well	well	ADV
ejpam-1314	16	13	-	-	PUNCT
ejpam-1314	16	14	known	know	VERB
ejpam-1314	16	15	that	that	SCONJ
ejpam-1314	16	16	f	f	PROPN
ejpam-1314	16	17	is	be	AUX
ejpam-1314	16	18	an	an	DET
ejpam-1314	16	19	integrable	integrable	ADJ
ejpam-1314	16	20	function	function	NOUN
ejpam-1314	16	21	on	on	ADP
ejpam-1314	16	22	[	[	X
ejpam-1314	16	23	0,π	0,π	X
ejpam-1314	16	24	]	]	X
ejpam-1314	16	25	(	(	PUNCT
ejpam-1314	16	26	see	see	VERB
ejpam-1314	16	27	[	[	X
ejpam-1314	16	28	1	1	NUM
ejpam-1314	16	29	]	]	NUM
ejpam-1314	16	30	)	)	PUNCT
ejpam-1314	16	31	,	,	PUNCT
ejpam-1314	16	32	and	and	CCONJ
ejpam-1314	16	33	the	the	DET
ejpam-1314	16	34	estimation	estimation	NOUN
ejpam-1314	16	35	∫	∫	PROPN
ejpam-1314	16	36	π	π	PROPN
ejpam-1314	16	37	0	0	PUNCT
ejpam-1314	17	1	|	|	ADV
ejpam-1314	17	2	f	f	X
ejpam-1314	17	3	(	(	PUNCT
ejpam-1314	17	4	x)|d	x)|d	PROPN
ejpam-1314	17	5	x	x	PUNCT
ejpam-1314	18	1	≤	≤	NUM
ejpam-1314	18	2	π	π	NOUN
ejpam-1314	18	3	∞	∞	PROPN
ejpam-1314	18	4	∑	∑	PUNCT
ejpam-1314	18	5	k=1	k=1	PROPN
ejpam-1314	18	6	(	(	PUNCT
ejpam-1314	18	7	k+	k+	PROPN
ejpam-1314	18	8	1)|42ak|	1)|42ak|	PROPN
ejpam-1314	18	9	is	be	AUX
ejpam-1314	18	10	valid	valid	ADJ
ejpam-1314	18	11	.	.	PUNCT
ejpam-1314	19	1	in	in	ADP
ejpam-1314	19	2	a	a	DET
ejpam-1314	19	3	similar	similar	ADJ
ejpam-1314	19	4	direction	direction	NOUN
ejpam-1314	19	5	,	,	PUNCT
ejpam-1314	19	6	among	among	ADP
ejpam-1314	19	7	others	other	NOUN
ejpam-1314	19	8	,	,	PUNCT
ejpam-1314	19	9	s.	s.	PROPN
ejpam-1314	19	10	a.	a.	PROPN
ejpam-1314	19	11	telyakovskĭı	telyakovskĭı	PROPN
ejpam-1314	20	1	[	[	X
ejpam-1314	20	2	6	6	NUM
ejpam-1314	20	3	]	]	PUNCT
ejpam-1314	20	4	obtained	obtain	VERB
ejpam-1314	20	5	some	some	DET
ejpam-1314	20	6	estimates	estimate	NOUN
ejpam-1314	20	7	of	of	ADP
ejpam-1314	20	8	the	the	DET
ejpam-1314	20	9	integrals	integral	NOUN
ejpam-1314	20	10	of	of	ADP
ejpam-1314	20	11	the	the	DET
ejpam-1314	20	12	following	follow	VERB
ejpam-1314	20	13	form	form	NOUN
ejpam-1314	20	14	∫	∫	PROPN
ejpam-1314	20	15	π/	π/	PROPN
ejpam-1314	20	16	`	`	PUNCT
ejpam-1314	20	17	π/(m+1	π/(m+1	PROPN
ejpam-1314	20	18	)	)	PUNCT
ejpam-1314	20	19	|φ(x)|d	|φ(x)|d	PROPN
ejpam-1314	20	20	x	x	SYM
ejpam-1314	20	21	,	,	PUNCT
ejpam-1314	20	22	1≤	1≤	NUM
ejpam-1314	20	23	`	`	PUNCT
ejpam-1314	20	24	≤	≤	NUM
ejpam-1314	20	25	m	m	ADP
ejpam-1314	20	26	,	,	PUNCT
ejpam-1314	20	27	(	(	PUNCT
ejpam-1314	20	28	`	`	PUNCT
ejpam-1314	20	29	,	,	PUNCT
ejpam-1314	20	30	m	m	VERB
ejpam-1314	20	31	∈	∈	PROPN
ejpam-1314	20	32	n	n	CCONJ
ejpam-1314	20	33	)	)	PUNCT
ejpam-1314	20	34	,	,	PUNCT
ejpam-1314	20	35	(	(	PUNCT
ejpam-1314	20	36	4	4	X
ejpam-1314	20	37	)	)	PUNCT
ejpam-1314	20	38	expressed	express	VERB
ejpam-1314	20	39	in	in	ADP
ejpam-1314	20	40	terms	term	NOUN
ejpam-1314	20	41	of	of	ADP
ejpam-1314	20	42	the	the	DET
ejpam-1314	20	43	coefficients	coefficient	NOUN
ejpam-1314	20	44	ak	ak	PROPN
ejpam-1314	20	45	,	,	PUNCT
ejpam-1314	20	46	where	where	SCONJ
ejpam-1314	20	47	he	he	PRON
ejpam-1314	20	48	used	use	VERB
ejpam-1314	20	49	null	null	ADJ
ejpam-1314	20	50	-	-	PUNCT
ejpam-1314	20	51	sequences	sequence	NOUN
ejpam-1314	20	52	of	of	ADP
ejpam-1314	20	53	bounded	bounded	ADJ
ejpam-1314	20	54	variation	variation	NOUN
ejpam-1314	20	55	of	of	ADP
ejpam-1314	20	56	second	second	ADJ
ejpam-1314	20	57	order	order	NOUN
ejpam-1314	20	58	(	(	PUNCT
ejpam-1314	20	59	∑∞	∑∞	NOUN
ejpam-1314	20	60	k=1	k=1	X
ejpam-1314	20	61	|4	|4	X
ejpam-1314	20	62	2ak|	2ak|	NUM
ejpam-1314	20	63	<	<	X
ejpam-1314	20	64	∞	∞	PROPN
ejpam-1314	20	65	)	)	PUNCT
ejpam-1314	20	66	,	,	PUNCT
ejpam-1314	20	67	instead	instead	ADV
ejpam-1314	20	68	of	of	ADP
ejpam-1314	20	69	quasi	quasi	ADJ
ejpam-1314	20	70	-	-	ADJ
ejpam-1314	20	71	convex	convex	ADJ
ejpam-1314	20	72	null	null	ADJ
ejpam-1314	20	73	-	-	PUNCT
ejpam-1314	20	74	sequences	sequence	NOUN
ejpam-1314	20	75	.	.	PUNCT
ejpam-1314	21	1	here	here	ADV
ejpam-1314	21	2	φ(x	φ(x	PROPN
ejpam-1314	21	3	)	)	PUNCT
ejpam-1314	21	4	is	be	AUX
ejpam-1314	21	5	either	either	DET
ejpam-1314	21	6	f	f	PROPN
ejpam-1314	21	7	(	(	PUNCT
ejpam-1314	21	8	x	x	NOUN
ejpam-1314	21	9	)	)	PUNCT
ejpam-1314	21	10	or	or	CCONJ
ejpam-1314	21	11	g(x	g(x	NOUN
ejpam-1314	21	12	)	)	PUNCT
ejpam-1314	21	13	.	.	PUNCT
ejpam-1314	22	1	it	it	PRON
ejpam-1314	22	2	is	be	AUX
ejpam-1314	22	3	obvious	obvious	ADJ
ejpam-1314	22	4	that	that	SCONJ
ejpam-1314	22	5	the	the	DET
ejpam-1314	22	6	condition	condition	NOUN
ejpam-1314	22	7	∞	∞	PROPN
ejpam-1314	22	8	∑	∑	PUNCT
ejpam-1314	22	9	k=1	k=1	X
ejpam-1314	22	10	|42ak|<∞	|42ak|<∞	PUNCT
ejpam-1314	22	11	(	(	PUNCT
ejpam-1314	22	12	5	5	NUM
ejpam-1314	22	13	)	)	PUNCT
ejpam-1314	22	14	is	be	AUX
ejpam-1314	22	15	a	a	DET
ejpam-1314	22	16	weaker	weak	ADJ
ejpam-1314	22	17	condition	condition	NOUN
ejpam-1314	22	18	than	than	ADP
ejpam-1314	22	19	the	the	DET
ejpam-1314	22	20	condition	condition	NOUN
ejpam-1314	22	21	(	(	PUNCT
ejpam-1314	22	22	3	3	NUM
ejpam-1314	22	23	)	)	PUNCT
ejpam-1314	22	24	.	.	PUNCT
ejpam-1314	23	1	the	the	DET
ejpam-1314	23	2	following	follow	VERB
ejpam-1314	23	3	definition	definition	NOUN
ejpam-1314	23	4	is	be	AUX
ejpam-1314	23	5	introduced	introduce	VERB
ejpam-1314	23	6	in	in	ADP
ejpam-1314	23	7	[	[	X
ejpam-1314	23	8	4	4	NUM
ejpam-1314	23	9	]	]	PUNCT
ejpam-1314	23	10	:	:	PUNCT
ejpam-1314	23	11	a	a	DET
ejpam-1314	23	12	sequence	sequence	NOUN
ejpam-1314	23	13	{	{	PUNCT
ejpam-1314	23	14	ak	ak	PROPN
ejpam-1314	23	15	}	}	PUNCT
ejpam-1314	23	16	is	be	AUX
ejpam-1314	23	17	of	of	ADP
ejpam-1314	23	18	bounded	bounded	ADJ
ejpam-1314	23	19	variation	variation	NOUN
ejpam-1314	23	20	of	of	ADP
ejpam-1314	23	21	integer	integer	NOUN
ejpam-1314	23	22	order	order	NOUN
ejpam-1314	23	23	p	p	NOUN
ejpam-1314	23	24	≥	≥	NOUN
ejpam-1314	23	25	0	0	PUNCT
ejpam-1314	23	26	if	if	SCONJ
ejpam-1314	23	27	∞	∞	PROPN
ejpam-1314	23	28	∑	∑	PROPN
ejpam-1314	23	29	k=1	k=1	PROPN
ejpam-1314	23	30	|4pak|<∞	|4pak|<∞	PROPN
ejpam-1314	23	31	,	,	PUNCT
ejpam-1314	23	32	(	(	PUNCT
ejpam-1314	23	33	6	6	NUM
ejpam-1314	23	34	)	)	PUNCT
ejpam-1314	24	1	where	where	SCONJ
ejpam-1314	24	2	4pak	4pak	PROPN
ejpam-1314	24	3	=	=	NOUN
ejpam-1314	24	4	4	4	NUM
ejpam-1314	24	5	�	�	PROPN
ejpam-1314	24	6	4p−1ak	4p−1ak	PROPN
ejpam-1314	24	7	�	�	PROPN
ejpam-1314	24	8	=	=	SYM
ejpam-1314	24	9	4p−1ak	4p−1ak	PROPN
ejpam-1314	24	10	−4p−1ak+1	−4p−1ak+1	VERB
ejpam-1314	24	11	,	,	PUNCT
ejpam-1314	24	12	and	and	CCONJ
ejpam-1314	24	13	we	we	PRON
ejpam-1314	24	14	agree	agree	VERB
ejpam-1314	24	15	with	with	ADP
ejpam-1314	24	16	40ak	40ak	PROPN
ejpam-1314	24	17	=	=	SYM
ejpam-1314	24	18	ak	ak	PROPN
ejpam-1314	24	19	.	.	PROPN
ejpam-1314	24	20	in	in	ADP
ejpam-1314	24	21	[	[	X
ejpam-1314	24	22	4	4	X
ejpam-1314	24	23	]	]	X
ejpam-1314	24	24	an	an	DET
ejpam-1314	24	25	example	example	NOUN
ejpam-1314	24	26	is	be	AUX
ejpam-1314	24	27	given	give	VERB
ejpam-1314	24	28	to	to	PART
ejpam-1314	24	29	show	show	VERB
ejpam-1314	24	30	that	that	SCONJ
ejpam-1314	24	31	(	(	PUNCT
ejpam-1314	24	32	6	6	NUM
ejpam-1314	24	33	)	)	PUNCT
ejpam-1314	24	34	is	be	AUX
ejpam-1314	24	35	an	an	DET
ejpam-1314	24	36	effective	effective	ADJ
ejpam-1314	24	37	generalization	generalization	NOUN
ejpam-1314	24	38	of	of	ADP
ejpam-1314	24	39	the	the	DET
ejpam-1314	24	40	null	null	ADJ
ejpam-1314	24	41	sequences	sequence	NOUN
ejpam-1314	24	42	of	of	ADP
ejpam-1314	24	43	bounded	bounded	ADJ
ejpam-1314	24	44	variation	variation	NOUN
ejpam-1314	24	45	.	.	PUNCT
ejpam-1314	25	1	this	this	DET
ejpam-1314	25	2	fact	fact	NOUN
ejpam-1314	25	3	encouraged	encourage	VERB
ejpam-1314	25	4	the	the	DET
ejpam-1314	25	5	present	present	ADJ
ejpam-1314	25	6	author	author	NOUN
ejpam-1314	25	7	to	to	PART
ejpam-1314	25	8	consider	consider	VERB
ejpam-1314	25	9	the	the	DET
ejpam-1314	25	10	series	series	NOUN
ejpam-1314	25	11	(	(	PUNCT
ejpam-1314	25	12	1	1	NUM
ejpam-1314	25	13	)	)	PUNCT
ejpam-1314	25	14	with	with	ADP
ejpam-1314	25	15	coefficients	coefficient	NOUN
ejpam-1314	25	16	that	that	PRON
ejpam-1314	25	17	satisfy	satisfy	VERB
ejpam-1314	25	18	the	the	DET
ejpam-1314	25	19	condition	condition	NOUN
ejpam-1314	25	20	(	(	PUNCT
ejpam-1314	25	21	6	6	NUM
ejpam-1314	25	22	)	)	PUNCT
ejpam-1314	25	23	.	.	PUNCT
ejpam-1314	26	1	the	the	DET
ejpam-1314	26	2	results	result	NOUN
ejpam-1314	26	3	are	be	AUX
ejpam-1314	26	4	published	publish	VERB
ejpam-1314	26	5	in	in	ADP
ejpam-1314	26	6	[	[	X
ejpam-1314	26	7	2	2	NUM
ejpam-1314	26	8	]	]	PUNCT
ejpam-1314	26	9	.	.	PUNCT
ejpam-1314	27	1	also	also	ADV
ejpam-1314	27	2	similar	similar	ADJ
ejpam-1314	27	3	results	result	NOUN
ejpam-1314	27	4	the	the	DET
ejpam-1314	27	5	reader	reader	NOUN
ejpam-1314	27	6	can	can	AUX
ejpam-1314	27	7	find	find	VERB
ejpam-1314	27	8	in	in	ADP
ejpam-1314	27	9	[	[	X
ejpam-1314	27	10	3	3	NUM
ejpam-1314	27	11	,	,	PUNCT
ejpam-1314	27	12	4	4	NUM
ejpam-1314	27	13	]	]	PUNCT
ejpam-1314	27	14	.	.	PUNCT
ejpam-1314	28	1	for	for	ADP
ejpam-1314	28	2	an	an	DET
ejpam-1314	28	3	integer	integer	NOUN
ejpam-1314	28	4	non	non	ADJ
ejpam-1314	28	5	-	-	ADJ
ejpam-1314	28	6	negative	negative	ADJ
ejpam-1314	28	7	number	number	NOUN
ejpam-1314	28	8	r	r	NOUN
ejpam-1314	28	9	and	and	CCONJ
ejpam-1314	28	10	a	a	DET
ejpam-1314	28	11	sequence	sequence	NOUN
ejpam-1314	28	12	{	{	PUNCT
ejpam-1314	28	13	ak	ak	PROPN
ejpam-1314	28	14	}	}	PUNCT
ejpam-1314	28	15	we	we	PRON
ejpam-1314	28	16	write4r	write4r	VERB
ejpam-1314	28	17	ak	ak	PROPN
ejpam-1314	28	18	=	=	PUNCT
ejpam-1314	28	19	ak−ak+r	ak−ak+r	PROPN
ejpam-1314	28	20	and	and	CCONJ
ejpam-1314	28	21	42	42	NUM
ejpam-1314	28	22	r	r	NOUN
ejpam-1314	28	23	ak	ak	PROPN
ejpam-1314	28	24	=	=	NOUN
ejpam-1314	28	25	4r	4r	PROPN
ejpam-1314	28	26	�	�	PROPN
ejpam-1314	28	27	4r	4r	PROPN
ejpam-1314	28	28	ak	ak	PROPN
ejpam-1314	28	29	�	�	PROPN
ejpam-1314	28	30	=	=	PROPN
ejpam-1314	28	31	ak	ak	PROPN
ejpam-1314	29	1	−	−	PROPN
ejpam-1314	29	2	2ak+r	2ak+r	PROPN
ejpam-1314	29	3	+	+	NUM
ejpam-1314	29	4	ak+2r	ak+2r	NOUN
ejpam-1314	29	5	.	.	PUNCT
ejpam-1314	30	1	note	note	VERB
ejpam-1314	30	2	that	that	SCONJ
ejpam-1314	30	3	for	for	ADP
ejpam-1314	30	4	r	r	NOUN
ejpam-1314	30	5	=	=	SYM
ejpam-1314	30	6	1	1	NUM
ejpam-1314	30	7	we	we	PRON
ejpam-1314	30	8	obtain	obtain	VERB
ejpam-1314	30	9	ordinary	ordinary	ADJ
ejpam-1314	30	10	differences	difference	NOUN
ejpam-1314	30	11	4ak	4ak	NOUN
ejpam-1314	30	12	=	=	SYM
ejpam-1314	30	13	ak	ak	PROPN
ejpam-1314	30	14	−	−	PROPN
ejpam-1314	30	15	ak+1	ak+1	VERB
ejpam-1314	30	16	and	and	CCONJ
ejpam-1314	30	17	42ak	42ak	ADJ
ejpam-1314	30	18	=	=	SYM
ejpam-1314	30	19	4	4	NUM
ejpam-1314	30	20	�	�	PROPN
ejpam-1314	30	21	4ak	4ak	ADJ
ejpam-1314	30	22	�	�	PROPN
ejpam-1314	30	23	=	=	SYM
ejpam-1314	30	24	ak	ak	PROPN
ejpam-1314	30	25	−	−	PROPN
ejpam-1314	30	26	2ak+1	2ak+1	NUM
ejpam-1314	30	27	+	+	NUM
ejpam-1314	30	28	ak+2	ak+2	NUM
ejpam-1314	30	29	.	.	PUNCT
ejpam-1314	31	1	let	let	VERB
ejpam-1314	31	2	r	r	NOUN
ejpam-1314	31	3	∈	∈	PROPN
ejpam-1314	31	4	n	n	CCONJ
ejpam-1314	31	5	,	,	PUNCT
ejpam-1314	31	6	k	k	PROPN
ejpam-1314	31	7	=	=	SYM
ejpam-1314	31	8	1,2	1,2	NUM
ejpam-1314	31	9	,	,	PUNCT
ejpam-1314	31	10	.	.	PUNCT
ejpam-1314	31	11	.	.	PUNCT
ejpam-1314	32	1	.	.	PUNCT
ejpam-1314	33	1	,	,	PUNCT
ejpam-1314	33	2	r	r	NOUN
ejpam-1314	33	3	,	,	PUNCT
ejpam-1314	33	4	n=	n=	ADJ
ejpam-1314	33	5	0	0	NUM
ejpam-1314	33	6	,	,	PUNCT
ejpam-1314	33	7	1,2	1,2	NUM
ejpam-1314	33	8	,	,	PUNCT
ejpam-1314	33	9	.	.	PUNCT
ejpam-1314	33	10	.	.	PUNCT
ejpam-1314	33	11	.	.	PUNCT
ejpam-1314	34	1	,	,	PUNCT
ejpam-1314	34	2	b0	b0	VERB
ejpam-1314	34	3	0,r	0,r	NUM
ejpam-1314	34	4	,	,	PUNCT
ejpam-1314	34	5	k(x	k(x	PROPN
ejpam-1314	34	6	)	)	PUNCT
ejpam-1314	34	7	=	=	PRON
ejpam-1314	34	8	sin	sin	NOUN
ejpam-1314	34	9	(	(	PUNCT
ejpam-1314	34	10	(	(	PUNCT
ejpam-1314	34	11	2k−	2k−	PROPN
ejpam-1314	34	12	r)x/2	r)x/2	NOUN
ejpam-1314	34	13	)	)	PUNCT
ejpam-1314	34	14	2	2	NUM
ejpam-1314	34	15	sin(r	sin(r	PROPN
ejpam-1314	34	16	x/2	x/2	NUM
ejpam-1314	34	17	)	)	PUNCT
ejpam-1314	34	18	,	,	PUNCT
ejpam-1314	34	19	x	x	PUNCT
ejpam-1314	34	20	6=	6=	ADP
ejpam-1314	34	21	2mπ	2mπ	ADJ
ejpam-1314	34	22	/	/	SYM
ejpam-1314	34	23	r	r	NOUN
ejpam-1314	34	24	,	,	PUNCT
ejpam-1314	34	25	m	m	VERB
ejpam-1314	34	26	∈	∈	PROPN
ejpam-1314	34	27	z	z	PROPN
ejpam-1314	34	28	,	,	PUNCT
ejpam-1314	34	29	xh	xh	PROPN
ejpam-1314	34	30	.	.	PUNCT
ejpam-1314	35	1	krasniqi	krasniqi	PROPN
ejpam-1314	35	2	/	/	SYM
ejpam-1314	35	3	eur	eur	PROPN
ejpam-1314	35	4	.	.	PUNCT
ejpam-1314	36	1	j.	j.	PROPN
ejpam-1314	36	2	pure	pure	PROPN
ejpam-1314	36	3	appl	appl	PROPN
ejpam-1314	36	4	.	.	PROPN
ejpam-1314	36	5	math	math	PROPN
ejpam-1314	36	6	,	,	PUNCT
ejpam-1314	36	7	6	6	NUM
ejpam-1314	36	8	(	(	PUNCT
ejpam-1314	36	9	2013	2013	NUM
ejpam-1314	36	10	)	)	PUNCT
ejpam-1314	36	11	,	,	PUNCT
ejpam-1314	36	12	451	451	NUM
ejpam-1314	36	13	-	-	SYM
ejpam-1314	36	14	459	459	NUM
ejpam-1314	36	15	453	453	NUM
ejpam-1314	36	16	b0	b0	NOUN
ejpam-1314	36	17	n+1,r	n+1,r	PROPN
ejpam-1314	36	18	,	,	PUNCT
ejpam-1314	36	19	k(x	k(x	PROPN
ejpam-1314	36	20	)	)	PUNCT
ejpam-1314	36	21	=	=	SYM
ejpam-1314	37	1	cos(k+	cos(k+	PROPN
ejpam-1314	37	2	nr)x	nr)x	PROPN
ejpam-1314	37	3	,	,	PUNCT
ejpam-1314	37	4	bc1	bc1	PROPN
ejpam-1314	37	5	n	n	CCONJ
ejpam-1314	37	6	,	,	PUNCT
ejpam-1314	37	7	r,0(x	r,0(x	NOUN
ejpam-1314	37	8	)	)	PUNCT
ejpam-1314	37	9	=	=	PUNCT
ejpam-1314	37	10	sin	sin	PROPN
ejpam-1314	37	11	�	�	PROPN
ejpam-1314	37	12	(	(	PUNCT
ejpam-1314	37	13	2n+	2n+	NUM
ejpam-1314	37	14	1)r	1)r	NUM
ejpam-1314	37	15	x	x	SYM
ejpam-1314	37	16	2	2	NUM
ejpam-1314	37	17	�	�	PROPN
ejpam-1314	37	18	2sin	2sin	NUM
ejpam-1314	37	19	�	�	PROPN
ejpam-1314	37	20	r	r	NOUN
ejpam-1314	37	21	x	x	SYM
ejpam-1314	37	22	2	2	NUM
ejpam-1314	37	23	�	�	PROPN
ejpam-1314	37	24	b1	b1	PROPN
ejpam-1314	37	25	n	n	CCONJ
ejpam-1314	37	26	,	,	PUNCT
ejpam-1314	37	27	r	r	NOUN
ejpam-1314	37	28	,	,	PUNCT
ejpam-1314	37	29	k(x	k(x	PROPN
ejpam-1314	37	30	)	)	PUNCT
ejpam-1314	37	31	=	=	SYM
ejpam-1314	38	1	n	n	CCONJ
ejpam-1314	38	2	∑	∑	PUNCT
ejpam-1314	38	3	m=0	m=0	PROPN
ejpam-1314	38	4	b0	b0	PROPN
ejpam-1314	38	5	m	m	PROPN
ejpam-1314	38	6	,	,	PUNCT
ejpam-1314	38	7	r	r	NOUN
ejpam-1314	38	8	,	,	PUNCT
ejpam-1314	38	9	k(x	k(x	PROPN
ejpam-1314	38	10	)	)	PUNCT
ejpam-1314	38	11	,	,	PUNCT
ejpam-1314	38	12	b2	b2	NOUN
ejpam-1314	38	13	n	n	CCONJ
ejpam-1314	38	14	,	,	PUNCT
ejpam-1314	38	15	r	r	NOUN
ejpam-1314	38	16	,	,	PUNCT
ejpam-1314	38	17	k(x	k(x	PROPN
ejpam-1314	38	18	)	)	PUNCT
ejpam-1314	38	19	=	=	SYM
ejpam-1314	38	20	n	n	PRON
ejpam-1314	38	21	∑	∑	PUNCT
ejpam-1314	38	22	m=0	m=0	PROPN
ejpam-1314	38	23	b1	b1	PROPN
ejpam-1314	38	24	m	m	PROPN
ejpam-1314	38	25	,	,	PUNCT
ejpam-1314	38	26	r	r	NOUN
ejpam-1314	38	27	,	,	PUNCT
ejpam-1314	38	28	k(x	k(x	PROPN
ejpam-1314	38	29	)	)	PUNCT
ejpam-1314	38	30	,	,	PUNCT
ejpam-1314	38	31	bc1	bc1	NOUN
ejpam-1314	38	32	n	n	CCONJ
ejpam-1314	38	33	,	,	PUNCT
ejpam-1314	38	34	r	r	NOUN
ejpam-1314	38	35	,	,	PUNCT
ejpam-1314	38	36	k(x	k(x	PROPN
ejpam-1314	38	37	)	)	PUNCT
ejpam-1314	39	1	=	=	PUNCT
ejpam-1314	39	2	sin	sin	PROPN
ejpam-1314	39	3	�	�	PROPN
ejpam-1314	39	4	(	(	PUNCT
ejpam-1314	39	5	2k+	2k+	NUM
ejpam-1314	39	6	(	(	PUNCT
ejpam-1314	39	7	2n+	2n+	NUM
ejpam-1314	39	8	1)r	1)r	NUM
ejpam-1314	39	9	)	)	PUNCT
ejpam-1314	39	10	x	x	SYM
ejpam-1314	39	11	2	2	NUM
ejpam-1314	39	12	�	�	PROPN
ejpam-1314	39	13	−	−	PROPN
ejpam-1314	39	14	sin	sin	PROPN
ejpam-1314	39	15	�	�	PROPN
ejpam-1314	39	16	(	(	PUNCT
ejpam-1314	39	17	2k−	2k−	PROPN
ejpam-1314	39	18	r	r	NOUN
ejpam-1314	39	19	)	)	PUNCT
ejpam-1314	39	20	x	x	SYM
ejpam-1314	39	21	2	2	NUM
ejpam-1314	39	22	�	�	PROPN
ejpam-1314	39	23	2sin	2sin	NUM
ejpam-1314	39	24	�	�	PROPN
ejpam-1314	39	25	r	r	NOUN
ejpam-1314	39	26	x	x	SYM
ejpam-1314	39	27	2	2	NUM
ejpam-1314	39	28	�	�	PROPN
ejpam-1314	39	29	b	b	PROPN
ejpam-1314	39	30	1	1	NUM
ejpam-1314	39	31	n+1,r	n+1,r	PROPN
ejpam-1314	39	32	,	,	PUNCT
ejpam-1314	39	33	k(x	k(x	PROPN
ejpam-1314	39	34	)	)	PUNCT
ejpam-1314	39	35	=	=	SYM
ejpam-1314	39	36	n	n	CCONJ
ejpam-1314	39	37	∑	∑	PUNCT
ejpam-1314	39	38	m=0	m=0	PROPN
ejpam-1314	39	39	sin(k+mr)x	sin(k+mr)x	PROPN
ejpam-1314	39	40	=	=	SYM
ejpam-1314	39	41	cos	cos	PROPN
ejpam-1314	39	42	�	�	PROPN
ejpam-1314	39	43	(	(	PUNCT
ejpam-1314	39	44	2k−	2k−	PROPN
ejpam-1314	39	45	r	r	NOUN
ejpam-1314	39	46	)	)	PUNCT
ejpam-1314	39	47	x	x	SYM
ejpam-1314	39	48	2	2	NUM
ejpam-1314	39	49	�	�	PROPN
ejpam-1314	39	50	−	−	PROPN
ejpam-1314	39	51	cos	cos	PROPN
ejpam-1314	39	52	�	�	PROPN
ejpam-1314	39	53	(	(	PUNCT
ejpam-1314	39	54	2k+	2k+	NUM
ejpam-1314	39	55	(	(	PUNCT
ejpam-1314	39	56	2n+	2n+	NUM
ejpam-1314	39	57	1)r	1)r	NUM
ejpam-1314	39	58	)	)	PUNCT
ejpam-1314	39	59	x	x	SYM
ejpam-1314	39	60	2	2	NUM
ejpam-1314	39	61	�	�	SYM
ejpam-1314	39	62	2	2	NUM
ejpam-1314	39	63	sin	sin	NOUN
ejpam-1314	39	64	�	�	PROPN
ejpam-1314	39	65	r	r	NOUN
ejpam-1314	39	66	x	x	SYM
ejpam-1314	39	67	2	2	NUM
ejpam-1314	39	68	�	�	PROPN
ejpam-1314	39	69	.	.	PUNCT
ejpam-1314	40	1	the	the	DET
ejpam-1314	40	2	following	follow	VERB
ejpam-1314	40	3	definition	definition	NOUN
ejpam-1314	40	4	is	be	AUX
ejpam-1314	40	5	introduced	introduce	VERB
ejpam-1314	40	6	in	in	ADP
ejpam-1314	40	7	[	[	X
ejpam-1314	40	8	5	5	NUM
ejpam-1314	40	9	]	]	PUNCT
ejpam-1314	40	10	:	:	PUNCT
ejpam-1314	40	11	a	a	DET
ejpam-1314	40	12	sequence	sequence	NOUN
ejpam-1314	40	13	{	{	PUNCT
ejpam-1314	40	14	an	an	PRON
ejpam-1314	40	15	}	}	PUNCT
ejpam-1314	40	16	keeps	keep	VERB
ejpam-1314	40	17	its	its	PRON
ejpam-1314	40	18	sign	sign	NOUN
ejpam-1314	40	19	if	if	SCONJ
ejpam-1314	40	20	either	either	CCONJ
ejpam-1314	40	21	an	an	DET
ejpam-1314	40	22	≥	≥	NOUN
ejpam-1314	40	23	0	0	NUM
ejpam-1314	40	24	for	for	ADP
ejpam-1314	40	25	all	all	DET
ejpam-1314	40	26	n	n	CCONJ
ejpam-1314	40	27	,	,	PUNCT
ejpam-1314	40	28	or	or	CCONJ
ejpam-1314	40	29	an	an	DET
ejpam-1314	40	30	≤	≤	NUM
ejpam-1314	40	31	0	0	NUM
ejpam-1314	40	32	for	for	ADP
ejpam-1314	40	33	all	all	DET
ejpam-1314	40	34	n.	n.	NOUN
ejpam-1314	40	35	also	also	ADV
ejpam-1314	40	36	in	in	ADP
ejpam-1314	40	37	the	the	DET
ejpam-1314	40	38	same	same	ADJ
ejpam-1314	40	39	paper	paper	NOUN
ejpam-1314	40	40	are	be	AUX
ejpam-1314	40	41	proved	prove	VERB
ejpam-1314	40	42	some	some	DET
ejpam-1314	40	43	lemmas	lemma	NOUN
ejpam-1314	40	44	formulated	formulate	VERB
ejpam-1314	40	45	below	below	ADV
ejpam-1314	40	46	.	.	PUNCT
ejpam-1314	41	1	lemma	lemma	PROPN
ejpam-1314	41	2	1	1	X
ejpam-1314	41	3	.	.	PUNCT
ejpam-1314	42	1	let	let	VERB
ejpam-1314	42	2	r	r	NOUN
ejpam-1314	42	3	∈	∈	PROPN
ejpam-1314	42	4	n	n	CCONJ
ejpam-1314	42	5	,	,	PUNCT
ejpam-1314	42	6	k	k	PROPN
ejpam-1314	42	7	=	=	SYM
ejpam-1314	42	8	1,2	1,2	NUM
ejpam-1314	42	9	,	,	PUNCT
ejpam-1314	42	10	.	.	PUNCT
ejpam-1314	42	11	.	.	PUNCT
ejpam-1314	43	1	.	.	PUNCT
ejpam-1314	44	1	,	,	PUNCT
ejpam-1314	44	2	r	r	NOUN
ejpam-1314	44	3	,	,	PUNCT
ejpam-1314	44	4	n=	n=	ADJ
ejpam-1314	44	5	0,1	0,1	NUM
ejpam-1314	44	6	,	,	PUNCT
ejpam-1314	44	7	2	2	NUM
ejpam-1314	44	8	,	,	PUNCT
ejpam-1314	44	9	.	.	PUNCT
ejpam-1314	44	10	.	.	PUNCT
ejpam-1314	44	11	.	.	PUNCT
ejpam-1314	44	12	.	.	PUNCT
ejpam-1314	45	1	(	(	PUNCT
ejpam-1314	45	2	a	a	X
ejpam-1314	45	3	)	)	PUNCT
ejpam-1314	45	4	if	if	SCONJ
ejpam-1314	45	5	the	the	DET
ejpam-1314	45	6	sequence	sequence	NOUN
ejpam-1314	45	7	{	{	PUNCT
ejpam-1314	45	8	4r	4r	NOUN
ejpam-1314	45	9	ak+nr	ak+nr	ADJ
ejpam-1314	45	10	}	}	PUNCT
ejpam-1314	45	11	keeps	keep	VERB
ejpam-1314	45	12	its	its	PRON
ejpam-1314	45	13	sign	sign	NOUN
ejpam-1314	45	14	separately	separately	ADV
ejpam-1314	45	15	for	for	ADP
ejpam-1314	45	16	each	each	DET
ejpam-1314	45	17	k	k	NOUN
ejpam-1314	45	18	,	,	PUNCT
ejpam-1314	45	19	then	then	ADV
ejpam-1314	45	20	the	the	DET
ejpam-1314	45	21	series	series	NOUN
ejpam-1314	45	22	(	(	PUNCT
ejpam-1314	45	23	1	1	NUM
ejpam-1314	45	24	)	)	PUNCT
ejpam-1314	45	25	and	and	CCONJ
ejpam-1314	45	26	(	(	PUNCT
ejpam-1314	45	27	2	2	X
ejpam-1314	45	28	)	)	PUNCT
ejpam-1314	45	29	converge	converge	VERB
ejpam-1314	45	30	for	for	ADP
ejpam-1314	45	31	almost	almost	ADV
ejpam-1314	45	32	all	all	PRON
ejpam-1314	45	33	x.	x.	NOUN
ejpam-1314	46	1	the	the	DET
ejpam-1314	46	2	function	function	NOUN
ejpam-1314	46	3	g(x	g(x	PROPN
ejpam-1314	46	4	+	+	NOUN
ejpam-1314	46	5	m2π	m2π	NOUN
ejpam-1314	46	6	r	r	NOUN
ejpam-1314	46	7	)	)	PUNCT
ejpam-1314	46	8	is	be	AUX
ejpam-1314	46	9	almost	almost	ADV
ejpam-1314	46	10	everywhere	everywhere	ADV
ejpam-1314	46	11	representable	representable	ADJ
ejpam-1314	46	12	in	in	ADP
ejpam-1314	46	13	the	the	DET
ejpam-1314	46	14	form	form	NOUN
ejpam-1314	46	15	g(x	g(x	PROPN
ejpam-1314	47	1	+	+	NOUN
ejpam-1314	47	2	m	m	PROPN
ejpam-1314	47	3	2π	2π	PROPN
ejpam-1314	47	4	r	r	NOUN
ejpam-1314	47	5	)	)	PUNCT
ejpam-1314	48	1	=	=	PUNCT
ejpam-1314	48	2	r	r	NOUN
ejpam-1314	48	3	∑	∑	PUNCT
ejpam-1314	48	4	k=1	k=1	PROPN
ejpam-1314	48	5	cos	cos	PROPN
ejpam-1314	48	6	�	�	PROPN
ejpam-1314	48	7	km	km	PROPN
ejpam-1314	48	8	2π	2π	PROPN
ejpam-1314	48	9	r	r	NOUN
ejpam-1314	48	10	�	�	NOUN
ejpam-1314	48	11	∞	∞	PROPN
ejpam-1314	48	12	∑	∑	PROPN
ejpam-1314	48	13	n=0	n=0	PROPN
ejpam-1314	48	14	4r	4r	NOUN
ejpam-1314	48	15	ak+nr	ak+nr	PROPN
ejpam-1314	48	16	b	b	SYM
ejpam-1314	48	17	1	1	NUM
ejpam-1314	48	18	n+1,r	n+1,r	NOUN
ejpam-1314	48	19	,	,	PUNCT
ejpam-1314	48	20	k(x	k(x	PROPN
ejpam-1314	48	21	)	)	PUNCT
ejpam-1314	49	1	+	+	CCONJ
ejpam-1314	49	2	r−1	r−1	PROPN
ejpam-1314	49	3	∑	∑	PUNCT
ejpam-1314	49	4	k=1	k=1	PROPN
ejpam-1314	49	5	sin	sin	PROPN
ejpam-1314	49	6	�	�	PROPN
ejpam-1314	49	7	km	km	PROPN
ejpam-1314	49	8	2π	2π	PROPN
ejpam-1314	49	9	r	r	NOUN
ejpam-1314	49	10	�	�	NOUN
ejpam-1314	49	11	∞	∞	PROPN
ejpam-1314	49	12	∑	∑	PROPN
ejpam-1314	49	13	n=0	n=0	PROPN
ejpam-1314	49	14	4r	4r	NUM
ejpam-1314	49	15	ak+nr	ak+nr	NOUN
ejpam-1314	49	16	bc1	bc1	PROPN
ejpam-1314	49	17	n	n	CCONJ
ejpam-1314	49	18	,	,	PUNCT
ejpam-1314	49	19	r	r	NOUN
ejpam-1314	49	20	,	,	PUNCT
ejpam-1314	49	21	k(x	k(x	PROPN
ejpam-1314	49	22	)	)	PUNCT
ejpam-1314	49	23	.	.	PUNCT
ejpam-1314	50	1	(	(	PUNCT
ejpam-1314	50	2	b	b	X
ejpam-1314	50	3	)	)	PUNCT
ejpam-1314	50	4	if	if	SCONJ
ejpam-1314	50	5	the	the	DET
ejpam-1314	50	6	sequence	sequence	NOUN
ejpam-1314	50	7	{	{	PUNCT
ejpam-1314	50	8	42	42	NUM
ejpam-1314	50	9	r	r	NOUN
ejpam-1314	50	10	ak+nr	ak+nr	ADV
ejpam-1314	50	11	}	}	PUNCT
ejpam-1314	50	12	keeps	keep	VERB
ejpam-1314	50	13	its	its	PRON
ejpam-1314	50	14	sign	sign	NOUN
ejpam-1314	50	15	separately	separately	ADV
ejpam-1314	50	16	for	for	ADP
ejpam-1314	50	17	each	each	DET
ejpam-1314	50	18	k	k	NOUN
ejpam-1314	50	19	,	,	PUNCT
ejpam-1314	50	20	then	then	ADV
ejpam-1314	50	21	f	f	X
ejpam-1314	50	22	(	(	PUNCT
ejpam-1314	50	23	x	x	X
ejpam-1314	50	24	)	)	PUNCT
ejpam-1314	50	25	is	be	AUX
ejpam-1314	50	26	almost	almost	ADV
ejpam-1314	50	27	everywhere	everywhere	ADV
ejpam-1314	50	28	representable	representable	ADJ
ejpam-1314	50	29	in	in	ADP
ejpam-1314	50	30	the	the	DET
ejpam-1314	50	31	form	form	NOUN
ejpam-1314	50	32	f	f	X
ejpam-1314	50	33	(	(	PUNCT
ejpam-1314	50	34	x	x	NOUN
ejpam-1314	50	35	)	)	PUNCT
ejpam-1314	50	36	=	=	SYM
ejpam-1314	51	1	r	r	NOUN
ejpam-1314	51	2	∑	∑	PUNCT
ejpam-1314	51	3	k=1	k=1	PROPN
ejpam-1314	51	4	∞	∞	NUM
ejpam-1314	51	5	∑	∑	PROPN
ejpam-1314	51	6	n=0	n=0	NUM
ejpam-1314	51	7	42	42	NUM
ejpam-1314	51	8	r	r	NOUN
ejpam-1314	51	9	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	51	10	b2	b2	NOUN
ejpam-1314	51	11	n	n	CCONJ
ejpam-1314	51	12	,	,	PUNCT
ejpam-1314	51	13	r	r	NOUN
ejpam-1314	51	14	,	,	PUNCT
ejpam-1314	51	15	k(x	k(x	PROPN
ejpam-1314	51	16	)	)	PUNCT
ejpam-1314	51	17	.	.	PUNCT
ejpam-1314	52	1	lemma	lemma	PROPN
ejpam-1314	52	2	2	2	X
ejpam-1314	52	3	.	.	PUNCT
ejpam-1314	53	1	let	let	VERB
ejpam-1314	53	2	r	r	NOUN
ejpam-1314	53	3	∈	∈	PROPN
ejpam-1314	53	4	n	n	CCONJ
ejpam-1314	53	5	,	,	PUNCT
ejpam-1314	53	6	an→	an→	NOUN
ejpam-1314	53	7	0	0	NUM
ejpam-1314	53	8	for	for	ADP
ejpam-1314	53	9	n→∞	n→∞	NUM
ejpam-1314	53	10	and	and	CCONJ
ejpam-1314	53	11	42,r	42,r	NUM
ejpam-1314	53	12	an	an	DET
ejpam-1314	53	13	≥	≥	NOUN
ejpam-1314	53	14	0	0	NUM
ejpam-1314	53	15	for	for	ADP
ejpam-1314	53	16	all	all	DET
ejpam-1314	53	17	n.	n.	NOUN
ejpam-1314	53	18	then	then	ADV
ejpam-1314	53	19	4r	4r	NUM
ejpam-1314	53	20	an	an	DET
ejpam-1314	53	21	≥	≥	NOUN
ejpam-1314	53	22	0	0	NUM
ejpam-1314	53	23	and	and	CCONJ
ejpam-1314	53	24	an	an	DET
ejpam-1314	53	25	≥	≥	NOUN
ejpam-1314	53	26	0	0	NUM
ejpam-1314	53	27	for	for	ADP
ejpam-1314	53	28	all	all	DET
ejpam-1314	53	29	n.	n.	NOUN
ejpam-1314	53	30	the	the	DET
ejpam-1314	53	31	aim	aim	NOUN
ejpam-1314	53	32	of	of	ADP
ejpam-1314	53	33	this	this	DET
ejpam-1314	53	34	paper	paper	NOUN
ejpam-1314	53	35	is	be	AUX
ejpam-1314	53	36	to	to	PART
ejpam-1314	53	37	achieve	achieve	VERB
ejpam-1314	53	38	some	some	DET
ejpam-1314	53	39	results	result	NOUN
ejpam-1314	53	40	,	,	PUNCT
ejpam-1314	53	41	similar	similar	ADJ
ejpam-1314	53	42	to	to	ADP
ejpam-1314	53	43	those	those	PRON
ejpam-1314	53	44	of	of	ADP
ejpam-1314	53	45	telyakovskĭı	telyakovskĭı	PROPN
ejpam-1314	54	1	[	[	X
ejpam-1314	54	2	6	6	NUM
ejpam-1314	54	3	]	]	PUNCT
ejpam-1314	54	4	,	,	PUNCT
ejpam-1314	54	5	for	for	ADP
ejpam-1314	54	6	the	the	DET
ejpam-1314	54	7	series	series	NOUN
ejpam-1314	54	8	(	(	PUNCT
ejpam-1314	54	9	1	1	NUM
ejpam-1314	54	10	)	)	PUNCT
ejpam-1314	54	11	and	and	CCONJ
ejpam-1314	54	12	(	(	PUNCT
ejpam-1314	54	13	2	2	X
ejpam-1314	54	14	)	)	PUNCT
ejpam-1314	54	15	with	with	ADP
ejpam-1314	54	16	coefficients	coefficient	NOUN
ejpam-1314	54	17	that	that	PRON
ejpam-1314	54	18	satisfy	satisfy	VERB
ejpam-1314	54	19	the	the	DET
ejpam-1314	54	20	conditions	condition	NOUN
ejpam-1314	54	21	:	:	PUNCT
ejpam-1314	54	22	the	the	DET
ejpam-1314	54	23	sequences	sequence	NOUN
ejpam-1314	54	24	{	{	PUNCT
ejpam-1314	54	25	4r	4r	NUM
ejpam-1314	54	26	ak+nr	ak+nr	ADJ
ejpam-1314	54	27	}	}	PUNCT
ejpam-1314	54	28	and	and	CCONJ
ejpam-1314	54	29	{	{	PUNCT
ejpam-1314	54	30	42	42	NUM
ejpam-1314	54	31	r	r	NOUN
ejpam-1314	54	32	ak+nr	ak+nr	NOUN
ejpam-1314	54	33	}	}	PUNCT
ejpam-1314	54	34	keep	keep	VERB
ejpam-1314	54	35	their	their	PRON
ejpam-1314	54	36	sign	sign	NOUN
ejpam-1314	54	37	separately	separately	ADV
ejpam-1314	54	38	for	for	ADP
ejpam-1314	54	39	each	each	DET
ejpam-1314	54	40	k.	k.	NOUN
ejpam-1314	55	1	we	we	PRON
ejpam-1314	55	2	write	write	VERB
ejpam-1314	55	3	g(u	g(u	PROPN
ejpam-1314	55	4	)	)	PUNCT
ejpam-1314	56	1	=	=	SYM
ejpam-1314	56	2	or	or	CCONJ
ejpam-1314	56	3	(	(	PUNCT
ejpam-1314	56	4	h(u	h(u	PROPN
ejpam-1314	56	5	)	)	PUNCT
ejpam-1314	56	6	)	)	PUNCT
ejpam-1314	57	1	,	,	PUNCT
ejpam-1314	57	2	u→	u→	PROPN
ejpam-1314	57	3	0	0	NUM
ejpam-1314	57	4	,	,	PUNCT
ejpam-1314	57	5	if	if	SCONJ
ejpam-1314	57	6	there	there	PRON
ejpam-1314	57	7	exists	exist	VERB
ejpam-1314	57	8	a	a	DET
ejpam-1314	57	9	positive	positive	ADJ
ejpam-1314	57	10	constant	constant	ADJ
ejpam-1314	57	11	ar	ar	NOUN
ejpam-1314	57	12	,	,	PUNCT
ejpam-1314	57	13	that	that	PRON
ejpam-1314	57	14	depends	depend	VERB
ejpam-1314	57	15	only	only	ADV
ejpam-1314	57	16	on	on	ADP
ejpam-1314	57	17	r	r	NOUN
ejpam-1314	57	18	,	,	PUNCT
ejpam-1314	57	19	such	such	ADJ
ejpam-1314	57	20	that	that	SCONJ
ejpam-1314	57	21	g(u)≤	g(u)≤	NOUN
ejpam-1314	57	22	arh(u	arh(u	NOUN
ejpam-1314	57	23	)	)	PUNCT
ejpam-1314	57	24	in	in	ADP
ejpam-1314	57	25	a	a	DET
ejpam-1314	57	26	neighborhood	neighborhood	NOUN
ejpam-1314	57	27	of	of	ADP
ejpam-1314	57	28	the	the	DET
ejpam-1314	57	29	point	point	NOUN
ejpam-1314	57	30	u=	u=	ADV
ejpam-1314	57	31	0	0	NUM
ejpam-1314	57	32	.	.	PUNCT
ejpam-1314	58	1	the	the	DET
ejpam-1314	58	2	constants	constant	NOUN
ejpam-1314	58	3	ar	ar	PROPN
ejpam-1314	58	4	may	may	AUX
ejpam-1314	58	5	be	be	AUX
ejpam-1314	58	6	,	,	PUNCT
ejpam-1314	58	7	in	in	ADP
ejpam-1314	58	8	general	general	ADJ
ejpam-1314	58	9	,	,	PUNCT
ejpam-1314	58	10	different	different	ADJ
ejpam-1314	58	11	in	in	ADP
ejpam-1314	58	12	different	different	ADJ
ejpam-1314	58	13	estimates	estimate	NOUN
ejpam-1314	58	14	.	.	PUNCT
ejpam-1314	59	1	xh	xh	PROPN
ejpam-1314	59	2	.	.	PUNCT
ejpam-1314	59	3	krasniqi	krasniqi	PROPN
ejpam-1314	59	4	/	/	SYM
ejpam-1314	59	5	eur	eur	PROPN
ejpam-1314	59	6	.	.	PUNCT
ejpam-1314	60	1	j.	j.	PROPN
ejpam-1314	60	2	pure	pure	PROPN
ejpam-1314	60	3	appl	appl	PROPN
ejpam-1314	60	4	.	.	PROPN
ejpam-1314	60	5	math	math	PROPN
ejpam-1314	60	6	,	,	PUNCT
ejpam-1314	60	7	6	6	NUM
ejpam-1314	60	8	(	(	PUNCT
ejpam-1314	60	9	2013	2013	NUM
ejpam-1314	60	10	)	)	PUNCT
ejpam-1314	60	11	,	,	PUNCT
ejpam-1314	60	12	451	451	NUM
ejpam-1314	60	13	-	-	SYM
ejpam-1314	60	14	459	459	NUM
ejpam-1314	60	15	454	454	NUM
ejpam-1314	60	16	2	2	NUM
ejpam-1314	60	17	.	.	PUNCT
ejpam-1314	60	18	main	main	ADJ
ejpam-1314	60	19	results	result	NOUN
ejpam-1314	60	20	we	we	PRON
ejpam-1314	60	21	begin	begin	VERB
ejpam-1314	60	22	with	with	ADP
ejpam-1314	60	23	the	the	DET
ejpam-1314	60	24	following	following	ADJ
ejpam-1314	60	25	result	result	NOUN
ejpam-1314	60	26	regarding	regard	VERB
ejpam-1314	60	27	to	to	ADP
ejpam-1314	60	28	the	the	DET
ejpam-1314	60	29	cosine	cosine	NOUN
ejpam-1314	60	30	series	series	NOUN
ejpam-1314	60	31	.	.	PUNCT
ejpam-1314	61	1	theorem	theorem	NOUN
ejpam-1314	61	2	1	1	NUM
ejpam-1314	61	3	.	.	PUNCT
ejpam-1314	62	1	let	let	VERB
ejpam-1314	62	2	r	r	NOUN
ejpam-1314	62	3	∈	∈	PROPN
ejpam-1314	62	4	n	n	CCONJ
ejpam-1314	62	5	,	,	PUNCT
ejpam-1314	62	6	k	k	PROPN
ejpam-1314	62	7	=	=	SYM
ejpam-1314	62	8	1	1	NUM
ejpam-1314	62	9	,	,	PUNCT
ejpam-1314	62	10	2	2	NUM
ejpam-1314	62	11	,	,	PUNCT
ejpam-1314	62	12	.	.	PUNCT
ejpam-1314	62	13	.	.	PUNCT
ejpam-1314	63	1	.	.	PUNCT
ejpam-1314	64	1	,	,	PUNCT
ejpam-1314	64	2	r.	r.	PROPN
ejpam-1314	64	3	if	if	SCONJ
ejpam-1314	64	4	an	an	DET
ejpam-1314	64	5	→	→	SYM
ejpam-1314	64	6	0	0	NUM
ejpam-1314	64	7	as	as	ADP
ejpam-1314	64	8	n→∞	n→∞	NUM
ejpam-1314	64	9	and	and	CCONJ
ejpam-1314	64	10	the	the	DET
ejpam-1314	64	11	sequence	sequence	NOUN
ejpam-1314	64	12	{	{	PUNCT
ejpam-1314	64	13	42	42	NUM
ejpam-1314	64	14	r	r	NOUN
ejpam-1314	64	15	ak+nr	ak+nr	ADV
ejpam-1314	64	16	}	}	PUNCT
ejpam-1314	64	17	keeps	keep	VERB
ejpam-1314	64	18	its	its	PRON
ejpam-1314	64	19	sign	sign	NOUN
ejpam-1314	64	20	separately	separately	ADV
ejpam-1314	64	21	for	for	ADP
ejpam-1314	64	22	each	each	DET
ejpam-1314	64	23	k	k	NOUN
ejpam-1314	64	24	,	,	PUNCT
ejpam-1314	64	25	then	then	ADV
ejpam-1314	64	26	the	the	DET
ejpam-1314	64	27	series	series	NOUN
ejpam-1314	64	28	(	(	PUNCT
ejpam-1314	64	29	1	1	X
ejpam-1314	64	30	)	)	PUNCT
ejpam-1314	64	31	converges	converge	VERB
ejpam-1314	64	32	for	for	ADP
ejpam-1314	64	33	almost	almost	ADV
ejpam-1314	64	34	all	all	PRON
ejpam-1314	64	35	x	x	NOUN
ejpam-1314	64	36	,	,	PUNCT
ejpam-1314	64	37	and	and	CCONJ
ejpam-1314	64	38	for	for	ADP
ejpam-1314	64	39	1	1	NUM
ejpam-1314	64	40	≤	≤	NUM
ejpam-1314	64	41	`	`	PUNCT
ejpam-1314	64	42	≤	≤	NUM
ejpam-1314	64	43	m	m	PROPN
ejpam-1314	64	44	,	,	PUNCT
ejpam-1314	64	45	the	the	DET
ejpam-1314	64	46	sum	sum	NOUN
ejpam-1314	64	47	function	function	NOUN
ejpam-1314	64	48	f	f	PROPN
ejpam-1314	64	49	(	(	PUNCT
ejpam-1314	64	50	x	x	X
ejpam-1314	64	51	)	)	PUNCT
ejpam-1314	64	52	satisfies	satisfie	NOUN
ejpam-1314	64	53	∫	∫	PROPN
ejpam-1314	64	54	π/	π/	PROPN
ejpam-1314	64	55	`	`	PUNCT
ejpam-1314	64	56	π/(m+1	π/(m+1	PROPN
ejpam-1314	64	57	)	)	PUNCT
ejpam-1314	65	1	|	|	ADV
ejpam-1314	65	2	f	f	PROPN
ejpam-1314	65	3	(	(	PUNCT
ejpam-1314	65	4	x)|d	x)|d	NOUN
ejpam-1314	65	5	x	x	PUNCT
ejpam-1314	66	1	=	=	PUNCT
ejpam-1314	66	2	o	o	X
ejpam-1314	66	3	m+	m+	NUM
ejpam-1314	66	4	1−	1−	NUM
ejpam-1314	66	5	`	`	PUNCT
ejpam-1314	66	6	m	m	VERB
ejpam-1314	66	7	r	r	NOUN
ejpam-1314	66	8	∑	∑	PUNCT
ejpam-1314	66	9	k=1	k=1	X
ejpam-1314	66	10	`	`	PUNCT
ejpam-1314	66	11	−1	−1	NOUN
ejpam-1314	66	12	∑	∑	ADP
ejpam-1314	66	13	n=0	n=0	X
ejpam-1314	66	14	n+	n+	PUNCT
ejpam-1314	66	15	1	1	NUM
ejpam-1314	66	16	`	`	PUNCT
ejpam-1314	66	17	|4r	|4r	X
ejpam-1314	66	18	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	66	19	|	|	ADV
ejpam-1314	66	20	!	!	PUNCT
ejpam-1314	67	1	+	+	NOUN
ejpam-1314	67	2	o	o	X
ejpam-1314	67	3	r	r	NOUN
ejpam-1314	67	4	∑	∑	PUNCT
ejpam-1314	67	5	k=1	k=1	X
ejpam-1314	67	6	∞	∞	PROPN
ejpam-1314	67	7	∑	∑	SYM
ejpam-1314	67	8	n=	n=	ADV
ejpam-1314	67	9	`	`	PUNCT
ejpam-1314	67	10	min(n+	min(n+	PROPN
ejpam-1314	67	11	1−	1−	NUM
ejpam-1314	67	12	`	`	PUNCT
ejpam-1314	67	13	,	,	PUNCT
ejpam-1314	67	14	m+	m+	NUM
ejpam-1314	67	15	1−	1−	NUM
ejpam-1314	67	16	`	`	PUNCT
ejpam-1314	67	17	)	)	PUNCT
ejpam-1314	67	18	|42	|42	NOUN
ejpam-1314	67	19	r	r	NOUN
ejpam-1314	67	20	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	67	21	|	|	ADV
ejpam-1314	67	22	!	!	PUNCT
ejpam-1314	67	23	.	.	PUNCT
ejpam-1314	68	1	proof	proof	NOUN
ejpam-1314	68	2	.	.	PUNCT
ejpam-1314	69	1	the	the	DET
ejpam-1314	69	2	convergence	convergence	NOUN
ejpam-1314	69	3	for	for	ADP
ejpam-1314	69	4	almost	almost	ADV
ejpam-1314	69	5	all	all	PRON
ejpam-1314	69	6	x	x	NOUN
ejpam-1314	69	7	of	of	ADP
ejpam-1314	69	8	the	the	DET
ejpam-1314	69	9	series	series	NOUN
ejpam-1314	69	10	(	(	PUNCT
ejpam-1314	69	11	1	1	X
ejpam-1314	69	12	)	)	PUNCT
ejpam-1314	69	13	has	have	AUX
ejpam-1314	69	14	been	be	AUX
ejpam-1314	69	15	proved	prove	VERB
ejpam-1314	69	16	in	in	ADP
ejpam-1314	69	17	lemma	lemma	PROPN
ejpam-1314	69	18	1(a	1(a	NUM
ejpam-1314	69	19	)	)	PUNCT
ejpam-1314	69	20	.	.	PUNCT
ejpam-1314	70	1	moreover	moreover	ADV
ejpam-1314	70	2	,	,	PUNCT
ejpam-1314	70	3	from	from	ADP
ejpam-1314	70	4	lemma	lemma	PROPN
ejpam-1314	70	5	1(b	1(b	NUM
ejpam-1314	70	6	)	)	PUNCT
ejpam-1314	70	7	the	the	DET
ejpam-1314	70	8	sum	sum	NOUN
ejpam-1314	70	9	function	function	NOUN
ejpam-1314	70	10	f	f	PROPN
ejpam-1314	70	11	(	(	PUNCT
ejpam-1314	70	12	x	x	X
ejpam-1314	70	13	)	)	PUNCT
ejpam-1314	70	14	is	be	AUX
ejpam-1314	70	15	almost	almost	ADV
ejpam-1314	70	16	everywhere	everywhere	ADV
ejpam-1314	70	17	representable	representable	ADJ
ejpam-1314	70	18	in	in	ADP
ejpam-1314	70	19	the	the	DET
ejpam-1314	70	20	form	form	NOUN
ejpam-1314	70	21	f	f	X
ejpam-1314	70	22	(	(	PUNCT
ejpam-1314	70	23	x	x	NOUN
ejpam-1314	70	24	)	)	PUNCT
ejpam-1314	70	25	=	=	SYM
ejpam-1314	71	1	r	r	NOUN
ejpam-1314	71	2	∑	∑	PUNCT
ejpam-1314	71	3	k=1	k=1	PROPN
ejpam-1314	71	4	∞	∞	NUM
ejpam-1314	71	5	∑	∑	PROPN
ejpam-1314	71	6	n=0	n=0	NUM
ejpam-1314	71	7	42	42	NUM
ejpam-1314	71	8	r	r	NOUN
ejpam-1314	71	9	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	71	10	b2	b2	NOUN
ejpam-1314	71	11	n	n	CCONJ
ejpam-1314	71	12	,	,	PUNCT
ejpam-1314	71	13	r	r	NOUN
ejpam-1314	71	14	,	,	PUNCT
ejpam-1314	71	15	k(x	k(x	PROPN
ejpam-1314	71	16	)	)	PUNCT
ejpam-1314	71	17	.	.	PUNCT
ejpam-1314	72	1	(	(	PUNCT
ejpam-1314	72	2	7	7	X
ejpam-1314	72	3	)	)	PUNCT
ejpam-1314	72	4	let	let	VERB
ejpam-1314	72	5	i	i	PRON
ejpam-1314	72	6	be	be	AUX
ejpam-1314	72	7	a	a	DET
ejpam-1314	72	8	positive	positive	ADJ
ejpam-1314	72	9	integer	integer	NOUN
ejpam-1314	72	10	and	and	CCONJ
ejpam-1314	73	1	x	x	PART
ejpam-1314	73	2	∈	∈	PROPN
ejpam-1314	73	3	�	�	PROPN
ejpam-1314	73	4	π	π	PROPN
ejpam-1314	73	5	i+1	i+1	NUM
ejpam-1314	73	6	,	,	PUNCT
ejpam-1314	74	1	π	π	PROPN
ejpam-1314	74	2	i	i	PROPN
ejpam-1314	74	3	�	�	PROPN
ejpam-1314	74	4	.	.	PUNCT
ejpam-1314	75	1	with	with	ADP
ejpam-1314	75	2	agreement	agreement	NOUN
ejpam-1314	75	3	that	that	PRON
ejpam-1314	75	4	b2	b2	NOUN
ejpam-1314	75	5	−1,r	−1,r	PROPN
ejpam-1314	75	6	,	,	PUNCT
ejpam-1314	75	7	k(x)≡	k(x)≡	PROPN
ejpam-1314	75	8	0	0	NUM
ejpam-1314	75	9	and	and	CCONJ
ejpam-1314	75	10	using	use	VERB
ejpam-1314	75	11	the	the	DET
ejpam-1314	75	12	equality	equality	NOUN
ejpam-1314	75	13	r	r	NOUN
ejpam-1314	75	14	∑	∑	NOUN
ejpam-1314	75	15	k=1	k=1	PROPN
ejpam-1314	75	16	i−1	i−1	PROPN
ejpam-1314	75	17	∑	∑	PROPN
ejpam-1314	75	18	n=0	n=0	PROPN
ejpam-1314	75	19	42	42	NUM
ejpam-1314	75	20	r	r	NOUN
ejpam-1314	75	21	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	75	22	b2	b2	NOUN
ejpam-1314	75	23	n	n	CCONJ
ejpam-1314	75	24	,	,	PUNCT
ejpam-1314	75	25	r	r	NOUN
ejpam-1314	75	26	,	,	PUNCT
ejpam-1314	75	27	k(x	k(x	PROPN
ejpam-1314	75	28	)	)	PUNCT
ejpam-1314	75	29	=	=	PUNCT
ejpam-1314	76	1	=	=	PUNCT
ejpam-1314	76	2	r	r	X
ejpam-1314	76	3	∑	∑	PUNCT
ejpam-1314	76	4	k=1	k=1	PROPN
ejpam-1314	76	5	i−1	i−1	PROPN
ejpam-1314	76	6	∑	∑	PUNCT
ejpam-1314	76	7	n=0	n=0	PROPN
ejpam-1314	76	8	�	�	PROPN
ejpam-1314	76	9	4r	4r	NOUN
ejpam-1314	76	10	ak+(n−1)r	ak+(n−1)r	PROPN
ejpam-1314	76	11	−4r	−4r	PROPN
ejpam-1314	76	12	ak+nr	ak+nr	PROPN
ejpam-1314	76	13	�	�	PROPN
ejpam-1314	76	14	b2	b2	PROPN
ejpam-1314	76	15	n	n	CCONJ
ejpam-1314	76	16	,	,	PUNCT
ejpam-1314	76	17	r	r	NOUN
ejpam-1314	76	18	,	,	PUNCT
ejpam-1314	76	19	k(x	k(x	PROPN
ejpam-1314	76	20	)	)	PUNCT
ejpam-1314	76	21	=	=	PUNCT
ejpam-1314	77	1	r	r	NOUN
ejpam-1314	77	2	∑	∑	PUNCT
ejpam-1314	77	3	k=1	k=1	PROPN
ejpam-1314	77	4	i−1	i−1	PROPN
ejpam-1314	77	5	∑	∑	PUNCT
ejpam-1314	77	6	n=0	n=0	PROPN
ejpam-1314	77	7	4r	4r	NOUN
ejpam-1314	77	8	ak+(n−1)r	ak+(n−1)r	PROPN
ejpam-1314	77	9	�	�	PROPN
ejpam-1314	77	10	b2	b2	PROPN
ejpam-1314	77	11	n	n	CCONJ
ejpam-1314	77	12	,	,	PUNCT
ejpam-1314	77	13	r	r	NOUN
ejpam-1314	77	14	,	,	PUNCT
ejpam-1314	77	15	k(x)−	k(x)−	PROPN
ejpam-1314	77	16	b2	b2	PROPN
ejpam-1314	77	17	n−1,r	n−1,r	PROPN
ejpam-1314	77	18	,	,	PUNCT
ejpam-1314	77	19	k(x	k(x	PROPN
ejpam-1314	77	20	)	)	PUNCT
ejpam-1314	77	21	�	�	PROPN
ejpam-1314	77	22	−4r	−4r	PROPN
ejpam-1314	77	23	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	77	24	b2	b2	NOUN
ejpam-1314	77	25	i−1,r	i−1,r	NOUN
ejpam-1314	77	26	,	,	PUNCT
ejpam-1314	77	27	k(x	k(x	PROPN
ejpam-1314	77	28	)	)	PUNCT
ejpam-1314	77	29	!	!	PUNCT
ejpam-1314	78	1	=	=	PUNCT
ejpam-1314	78	2	r	r	X
ejpam-1314	78	3	∑	∑	PUNCT
ejpam-1314	78	4	k=1	k=1	PROPN
ejpam-1314	78	5	i−1	i−1	PROPN
ejpam-1314	78	6	∑	∑	PUNCT
ejpam-1314	78	7	n=0	n=0	PROPN
ejpam-1314	78	8	4r	4r	NOUN
ejpam-1314	78	9	ak+(n−1)r	ak+(n−1)r	PROPN
ejpam-1314	78	10	b1	b1	PROPN
ejpam-1314	78	11	n	n	CCONJ
ejpam-1314	78	12	,	,	PUNCT
ejpam-1314	78	13	r	r	NOUN
ejpam-1314	78	14	,	,	PUNCT
ejpam-1314	78	15	k(x)−4r	k(x)−4r	PROPN
ejpam-1314	78	16	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	78	17	b2	b2	NOUN
ejpam-1314	78	18	i−1,r	i−1,r	NOUN
ejpam-1314	78	19	,	,	PUNCT
ejpam-1314	78	20	k(x	k(x	PROPN
ejpam-1314	78	21	)	)	PUNCT
ejpam-1314	78	22	!	!	PUNCT
ejpam-1314	79	1	,	,	PUNCT
ejpam-1314	79	2	from	from	ADP
ejpam-1314	79	3	(	(	PUNCT
ejpam-1314	79	4	7	7	X
ejpam-1314	79	5	)	)	PUNCT
ejpam-1314	79	6	we	we	PRON
ejpam-1314	79	7	have	have	VERB
ejpam-1314	79	8	f	f	PROPN
ejpam-1314	79	9	(	(	PUNCT
ejpam-1314	79	10	x	x	NOUN
ejpam-1314	79	11	)	)	PUNCT
ejpam-1314	80	1	=	=	SYM
ejpam-1314	80	2	r	r	NOUN
ejpam-1314	80	3	∑	∑	PUNCT
ejpam-1314	80	4	k=1	k=1	PROPN
ejpam-1314	80	5	i−1	i−1	PROPN
ejpam-1314	80	6	∑	∑	PUNCT
ejpam-1314	80	7	n=0	n=0	PROPN
ejpam-1314	80	8	4r	4r	NOUN
ejpam-1314	80	9	ak+(n−1)r	ak+(n−1)r	PROPN
ejpam-1314	80	10	b1	b1	PROPN
ejpam-1314	80	11	n	n	CCONJ
ejpam-1314	80	12	,	,	PUNCT
ejpam-1314	80	13	r	r	NOUN
ejpam-1314	80	14	,	,	PUNCT
ejpam-1314	80	15	k(x	k(x	PROPN
ejpam-1314	80	16	)	)	PUNCT
ejpam-1314	81	1	+	+	CCONJ
ejpam-1314	81	2	∞	∞	NUM
ejpam-1314	81	3	∑	∑	PUNCT
ejpam-1314	81	4	n	n	X
ejpam-1314	81	5	=	=	NOUN
ejpam-1314	81	6	i	i	NOUN
ejpam-1314	81	7	42	42	NUM
ejpam-1314	81	8	r	r	NOUN
ejpam-1314	81	9	ak+(n−1)r	ak+(n−1)r	PROPN
ejpam-1314	81	10	�	�	PROPN
ejpam-1314	81	11	b2	b2	PROPN
ejpam-1314	81	12	n	n	CCONJ
ejpam-1314	81	13	,	,	PUNCT
ejpam-1314	81	14	r	r	NOUN
ejpam-1314	81	15	,	,	PUNCT
ejpam-1314	81	16	k(x)−	k(x)−	PROPN
ejpam-1314	81	17	b2	b2	NOUN
ejpam-1314	81	18	i−1,r	i−1,r	NOUN
ejpam-1314	81	19	,	,	PUNCT
ejpam-1314	81	20	k(x	k(x	PROPN
ejpam-1314	81	21	)	)	PUNCT
ejpam-1314	81	22	�	�	PROPN
ejpam-1314	81	23	!	!	PUNCT
ejpam-1314	81	24	.	.	PUNCT
ejpam-1314	82	1	it	it	PRON
ejpam-1314	82	2	is	be	AUX
ejpam-1314	82	3	obvious	obvious	ADJ
ejpam-1314	82	4	that	that	SCONJ
ejpam-1314	82	5	|b1	|b1	PROPN
ejpam-1314	82	6	n	n	CCONJ
ejpam-1314	82	7	,	,	PUNCT
ejpam-1314	82	8	r	r	NOUN
ejpam-1314	82	9	,	,	PUNCT
ejpam-1314	82	10	k(x)|	k(x)|	X
ejpam-1314	82	11	≤	≤	NUM
ejpam-1314	82	12	n+	n+	PUNCT
ejpam-1314	82	13	1	1	NUM
ejpam-1314	82	14	,	,	PUNCT
ejpam-1314	82	15	and	and	CCONJ
ejpam-1314	82	16	since	since	SCONJ
ejpam-1314	82	17	from	from	ADP
ejpam-1314	82	18	(	(	PUNCT
ejpam-1314	82	19	see	see	VERB
ejpam-1314	82	20	[	[	X
ejpam-1314	82	21	5	5	NUM
ejpam-1314	82	22	,	,	PUNCT
ejpam-1314	82	23	page	page	NOUN
ejpam-1314	82	24	65	65	NUM
ejpam-1314	82	25	]	]	PUNCT
ejpam-1314	82	26	)	)	PUNCT
ejpam-1314	82	27	b2	b2	NOUN
ejpam-1314	82	28	n	n	CCONJ
ejpam-1314	82	29	,	,	PUNCT
ejpam-1314	82	30	r	r	NOUN
ejpam-1314	82	31	,	,	PUNCT
ejpam-1314	82	32	k(x	k(x	PROPN
ejpam-1314	82	33	)	)	PUNCT
ejpam-1314	83	1	=	=	SYM
ejpam-1314	83	2	sin2	sin2	PROPN
ejpam-1314	83	3	�	�	PROPN
ejpam-1314	83	4	(	(	PUNCT
ejpam-1314	83	5	k+	k+	PROPN
ejpam-1314	83	6	nr	nr	PROPN
ejpam-1314	83	7	)	)	PUNCT
ejpam-1314	83	8	x	x	SYM
ejpam-1314	83	9	2	2	NUM
ejpam-1314	83	10	�	�	PROPN
ejpam-1314	83	11	−	−	PROPN
ejpam-1314	83	12	sin2	sin2	PROPN
ejpam-1314	83	13	�	�	PROPN
ejpam-1314	83	14	(	(	PUNCT
ejpam-1314	83	15	k−	k−	NOUN
ejpam-1314	83	16	r	r	NOUN
ejpam-1314	83	17	)	)	PUNCT
ejpam-1314	83	18	x	x	SYM
ejpam-1314	83	19	2	2	NUM
ejpam-1314	83	20	�	�	PROPN
ejpam-1314	83	21	2sin2	2sin2	NUM
ejpam-1314	83	22	�	�	NOUN
ejpam-1314	83	23	r	r	NOUN
ejpam-1314	83	24	x	x	SYM
ejpam-1314	83	25	2	2	NUM
ejpam-1314	83	26	�	�	PROPN
ejpam-1314	83	27	xh	xh	PROPN
ejpam-1314	83	28	.	.	PUNCT
ejpam-1314	84	1	krasniqi	krasniqi	PROPN
ejpam-1314	84	2	/	/	SYM
ejpam-1314	84	3	eur	eur	PROPN
ejpam-1314	84	4	.	.	PUNCT
ejpam-1314	85	1	j.	j.	PROPN
ejpam-1314	85	2	pure	pure	PROPN
ejpam-1314	85	3	appl	appl	PROPN
ejpam-1314	85	4	.	.	PROPN
ejpam-1314	85	5	math	math	PROPN
ejpam-1314	85	6	,	,	PUNCT
ejpam-1314	85	7	6	6	NUM
ejpam-1314	85	8	(	(	PUNCT
ejpam-1314	85	9	2013	2013	NUM
ejpam-1314	85	10	)	)	PUNCT
ejpam-1314	85	11	,	,	PUNCT
ejpam-1314	85	12	451	451	NUM
ejpam-1314	85	13	-	-	SYM
ejpam-1314	85	14	459	459	NUM
ejpam-1314	85	15	455	455	NUM
ejpam-1314	85	16	follows	follow	VERB
ejpam-1314	85	17	|b2	|b2	NOUN
ejpam-1314	85	18	n	n	CCONJ
ejpam-1314	85	19	,	,	PUNCT
ejpam-1314	85	20	r	r	NOUN
ejpam-1314	85	21	,	,	PUNCT
ejpam-1314	85	22	k(x)−	k(x)−	PROPN
ejpam-1314	85	23	b2	b2	NOUN
ejpam-1314	85	24	i−1,r	i−1,r	NOUN
ejpam-1314	85	25	,	,	PUNCT
ejpam-1314	85	26	k(x)|	k(x)|	VERB
ejpam-1314	85	27	≤	≤	ADJ
ejpam-1314	85	28	2	2	NUM
ejpam-1314	85	29	sin2	sin2	NOUN
ejpam-1314	85	30	�	�	PROPN
ejpam-1314	85	31	r	r	NOUN
ejpam-1314	85	32	x	x	SYM
ejpam-1314	85	33	2	2	NUM
ejpam-1314	85	34	�	�	PROPN
ejpam-1314	85	35	,	,	PUNCT
ejpam-1314	85	36	we	we	PRON
ejpam-1314	85	37	have	have	VERB
ejpam-1314	85	38	∫	∫	PROPN
ejpam-1314	85	39	π	π	PROPN
ejpam-1314	85	40	/	/	SYM
ejpam-1314	85	41	i	i	PRON
ejpam-1314	85	42	π/(i+1	π/(i+1	ADJ
ejpam-1314	85	43	)	)	PUNCT
ejpam-1314	86	1	|	|	ADV
ejpam-1314	86	2	f	f	X
ejpam-1314	86	3	(	(	PUNCT
ejpam-1314	86	4	x)|d	x)|d	NOUN
ejpam-1314	86	5	x	x	PUNCT
ejpam-1314	87	1	=	=	PUNCT
ejpam-1314	87	2	o	o	X
ejpam-1314	87	3	(	(	PUNCT
ejpam-1314	87	4	r	r	NOUN
ejpam-1314	87	5	∑	∑	PUNCT
ejpam-1314	87	6	k=1	k=1	PROPN
ejpam-1314	87	7	i−1	i−1	PROPN
ejpam-1314	87	8	∑	∑	PUNCT
ejpam-1314	87	9	n=0	n=0	X
ejpam-1314	87	10	|4r	|4r	ADJ
ejpam-1314	87	11	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	87	12	|	|	ADV
ejpam-1314	87	13	k+	k+	NOUN
ejpam-1314	87	14	1	1	NUM
ejpam-1314	87	15	i(i+	i(i+	ADP
ejpam-1314	87	16	1	1	NUM
ejpam-1314	87	17	)	)	PUNCT
ejpam-1314	87	18	+	+	CCONJ
ejpam-1314	87	19	∞	∞	NUM
ejpam-1314	87	20	∑	∑	PUNCT
ejpam-1314	87	21	n	n	PROPN
ejpam-1314	87	22	=	=	NOUN
ejpam-1314	87	23	i	i	NOUN
ejpam-1314	87	24	|42	|42	NOUN
ejpam-1314	87	25	r	r	NOUN
ejpam-1314	87	26	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	87	27	|	|	ADV
ejpam-1314	87	28	!	!	PUNCT
ejpam-1314	87	29	)	)	PUNCT
ejpam-1314	87	30	.	.	PUNCT
ejpam-1314	88	1	now	now	ADV
ejpam-1314	88	2	if	if	SCONJ
ejpam-1314	88	3	we	we	PRON
ejpam-1314	88	4	take	take	VERB
ejpam-1314	88	5	the	the	DET
ejpam-1314	88	6	summation	summation	NOUN
ejpam-1314	88	7	,	,	PUNCT
ejpam-1314	88	8	when	when	SCONJ
ejpam-1314	88	9	i	i	PRON
ejpam-1314	88	10	goes	go	VERB
ejpam-1314	88	11	from	from	ADP
ejpam-1314	88	12	`	`	PUNCT
ejpam-1314	88	13	to	to	ADP
ejpam-1314	88	14	m	m	PROPN
ejpam-1314	88	15	,	,	PUNCT
ejpam-1314	88	16	to	to	ADP
ejpam-1314	88	17	the	the	DET
ejpam-1314	88	18	both	both	DET
ejpam-1314	88	19	sides	side	NOUN
ejpam-1314	88	20	of	of	ADP
ejpam-1314	88	21	the	the	DET
ejpam-1314	88	22	above	above	ADJ
ejpam-1314	88	23	equality	equality	NOUN
ejpam-1314	88	24	we	we	PRON
ejpam-1314	88	25	get	get	VERB
ejpam-1314	88	26	∫	∫	PROPN
ejpam-1314	88	27	π/	π/	PROPN
ejpam-1314	88	28	`	`	PUNCT
ejpam-1314	88	29	π/(m+1	π/(m+1	PROPN
ejpam-1314	88	30	)	)	PUNCT
ejpam-1314	89	1	|	|	ADV
ejpam-1314	89	2	f	f	PROPN
ejpam-1314	89	3	(	(	PUNCT
ejpam-1314	89	4	x)|d	x)|d	NOUN
ejpam-1314	89	5	x	x	PUNCT
ejpam-1314	90	1	=	=	PUNCT
ejpam-1314	90	2	o	o	X
ejpam-1314	90	3	(	(	PUNCT
ejpam-1314	90	4	r	r	NOUN
ejpam-1314	90	5	∑	∑	PUNCT
ejpam-1314	90	6	k=1	k=1	ADJ
ejpam-1314	90	7	m	m	VERB
ejpam-1314	90	8	∑	∑	PUNCT
ejpam-1314	90	9	i=	i=	PROPN
ejpam-1314	90	10	`	`	PUNCT
ejpam-1314	90	11	i−1	i−1	PROPN
ejpam-1314	90	12	∑	∑	PUNCT
ejpam-1314	90	13	n=0	n=0	X
ejpam-1314	90	14	|4r	|4r	ADJ
ejpam-1314	90	15	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	90	16	|	|	ADV
ejpam-1314	90	17	n+	n+	ADP
ejpam-1314	90	18	1	1	NUM
ejpam-1314	90	19	i(i+	i(i+	ADP
ejpam-1314	90	20	1	1	NUM
ejpam-1314	90	21	)	)	PUNCT
ejpam-1314	90	22	+	+	NUM
ejpam-1314	90	23	m	m	VERB
ejpam-1314	90	24	∑	∑	PUNCT
ejpam-1314	90	25	i=	i=	PROPN
ejpam-1314	90	26	`	`	PUNCT
ejpam-1314	90	27	∞	∞	PROPN
ejpam-1314	90	28	∑	∑	PUNCT
ejpam-1314	90	29	n	n	PROPN
ejpam-1314	90	30	=	=	NOUN
ejpam-1314	90	31	i	i	NOUN
ejpam-1314	90	32	|42	|42	NOUN
ejpam-1314	90	33	r	r	NOUN
ejpam-1314	90	34	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	90	35	|	|	ADV
ejpam-1314	90	36	!	!	PUNCT
ejpam-1314	90	37	)	)	PUNCT
ejpam-1314	90	38	.	.	PUNCT
ejpam-1314	91	1	(	(	PUNCT
ejpam-1314	91	2	8)	8)	NUM
ejpam-1314	91	3	for	for	ADP
ejpam-1314	91	4	the	the	DET
ejpam-1314	91	5	first	first	ADJ
ejpam-1314	91	6	term	term	NOUN
ejpam-1314	91	7	in	in	ADP
ejpam-1314	91	8	the	the	DET
ejpam-1314	91	9	parentheses	parenthesis	NOUN
ejpam-1314	91	10	of	of	ADP
ejpam-1314	91	11	the	the	DET
ejpam-1314	91	12	right	right	ADJ
ejpam-1314	91	13	-	-	PUNCT
ejpam-1314	91	14	hand	hand	NOUN
ejpam-1314	91	15	side	side	NOUN
ejpam-1314	91	16	of	of	ADP
ejpam-1314	91	17	(	(	PUNCT
ejpam-1314	91	18	8)	8)	NUM
ejpam-1314	91	19	we	we	PRON
ejpam-1314	91	20	have	have	AUX
ejpam-1314	91	21	m	m	PROPN
ejpam-1314	91	22	∑	∑	PUNCT
ejpam-1314	91	23	i=	i=	PROPN
ejpam-1314	91	24	`	`	PUNCT
ejpam-1314	91	25	i−1	i−1	PROPN
ejpam-1314	91	26	∑	∑	PUNCT
ejpam-1314	91	27	n=0	n=0	X
ejpam-1314	91	28	|4r	|4r	ADJ
ejpam-1314	91	29	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	91	30	|	|	ADV
ejpam-1314	91	31	n+	n+	ADP
ejpam-1314	91	32	1	1	NUM
ejpam-1314	91	33	i(i+	i(i+	ADP
ejpam-1314	91	34	1	1	NUM
ejpam-1314	91	35	)	)	PUNCT
ejpam-1314	91	36	=	=	PUNCT
ejpam-1314	92	1	=	=	PUNCT
ejpam-1314	92	2	m	m	VERB
ejpam-1314	92	3	∑	∑	PUNCT
ejpam-1314	92	4	i=	i=	PROPN
ejpam-1314	92	5	`	`	PUNCT
ejpam-1314	92	6	`	`	PUNCT
ejpam-1314	92	7	−1	−1	NOUN
ejpam-1314	92	8	∑	∑	PUNCT
ejpam-1314	92	9	n=0	n=0	NUM
ejpam-1314	92	10	|4r	|4r	ADJ
ejpam-1314	92	11	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	92	12	|	|	ADV
ejpam-1314	92	13	n+	n+	ADP
ejpam-1314	92	14	1	1	NUM
ejpam-1314	92	15	i(i+	i(i+	ADP
ejpam-1314	92	16	1	1	NUM
ejpam-1314	92	17	)	)	PUNCT
ejpam-1314	92	18	+	+	NUM
ejpam-1314	92	19	m	m	VERB
ejpam-1314	92	20	∑	∑	PUNCT
ejpam-1314	92	21	i=`+1	i=`+1	PUNCT
ejpam-1314	92	22	i−1	i−1	PROPN
ejpam-1314	92	23	∑	∑	PUNCT
ejpam-1314	92	24	n=	n=	ADV
ejpam-1314	92	25	`	`	PUNCT
ejpam-1314	92	26	|4r	|4r	X
ejpam-1314	92	27	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	92	28	|	|	ADV
ejpam-1314	92	29	n+	n+	ADP
ejpam-1314	92	30	1	1	NUM
ejpam-1314	92	31	i(i+	i(i+	ADP
ejpam-1314	92	32	1	1	NUM
ejpam-1314	92	33	)	)	PUNCT
ejpam-1314	92	34	=	=	PRON
ejpam-1314	92	35	`	`	PUNCT
ejpam-1314	92	36	−1	−1	NOUN
ejpam-1314	92	37	∑	∑	ADP
ejpam-1314	92	38	n=0	n=0	NUM
ejpam-1314	92	39	(	(	PUNCT
ejpam-1314	92	40	n+	n+	NUM
ejpam-1314	92	41	1)|4r	1)|4r	NUM
ejpam-1314	93	1	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	93	2	|	|	CCONJ
ejpam-1314	93	3	�	�	PROPN
ejpam-1314	93	4	1	1	NUM
ejpam-1314	93	5	`	`	PUNCT
ejpam-1314	93	6	−	−	PROPN
ejpam-1314	93	7	1	1	NUM
ejpam-1314	93	8	m+	m+	NUM
ejpam-1314	93	9	1	1	NUM
ejpam-1314	93	10	�	�	PROPN
ejpam-1314	93	11	+	+	CCONJ
ejpam-1314	93	12	m−1	m−1	PROPN
ejpam-1314	93	13	∑	∑	PUNCT
ejpam-1314	93	14	n=	n=	ADV
ejpam-1314	93	15	`	`	PUNCT
ejpam-1314	93	16	(	(	PUNCT
ejpam-1314	93	17	n+	n+	NUM
ejpam-1314	93	18	1)|4r	1)|4r	NUM
ejpam-1314	93	19	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	93	20	|	|	CCONJ
ejpam-1314	93	21	�	�	PROPN
ejpam-1314	93	22	1	1	NUM
ejpam-1314	93	23	n+	n+	ADP
ejpam-1314	93	24	1	1	NUM
ejpam-1314	93	25	−	−	NUM
ejpam-1314	93	26	1	1	NUM
ejpam-1314	93	27	m+	m+	NUM
ejpam-1314	93	28	1	1	NUM
ejpam-1314	93	29	�	�	PROPN
ejpam-1314	93	30	≤	≤	NUM
ejpam-1314	93	31	m+	m+	NUM
ejpam-1314	93	32	1−	1−	NUM
ejpam-1314	93	33	`	`	PUNCT
ejpam-1314	93	34	m	m	VERB
ejpam-1314	93	35	`	`	PUNCT
ejpam-1314	93	36	−1	−1	NOUN
ejpam-1314	93	37	∑	∑	ADP
ejpam-1314	93	38	n=0	n=0	X
ejpam-1314	93	39	n+	n+	PUNCT
ejpam-1314	93	40	1	1	NUM
ejpam-1314	93	41	`	`	PUNCT
ejpam-1314	93	42	|4r	|4r	PUNCT
ejpam-1314	93	43	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	93	44	|+	|+	NOUN
ejpam-1314	93	45	m	m	VERB
ejpam-1314	93	46	∑	∑	INTJ
ejpam-1314	93	47	n=	n=	ADJ
ejpam-1314	93	48	`	`	PUNCT
ejpam-1314	93	49	∞	∞	PROPN
ejpam-1314	93	50	∑	∑	PROPN
ejpam-1314	93	51	j	j	PROPN
ejpam-1314	93	52	=	=	PROPN
ejpam-1314	93	53	n	n	ADP
ejpam-1314	93	54	|42	|42	NOUN
ejpam-1314	93	55	r	r	NOUN
ejpam-1314	93	56	ak+	ak+	PROPN
ejpam-1314	93	57	(	(	PUNCT
ejpam-1314	93	58	j−1)r	j−1)r	PROPN
ejpam-1314	93	59	|	|	INTJ
ejpam-1314	93	60	.	.	PUNCT
ejpam-1314	94	1	(	(	PUNCT
ejpam-1314	94	2	9	9	NUM
ejpam-1314	94	3	)	)	PUNCT
ejpam-1314	94	4	but	but	CCONJ
ejpam-1314	94	5	the	the	DET
ejpam-1314	94	6	second	second	ADJ
ejpam-1314	94	7	term	term	NOUN
ejpam-1314	94	8	in	in	ADP
ejpam-1314	94	9	(	(	PUNCT
ejpam-1314	94	10	9	9	NUM
ejpam-1314	94	11	)	)	PUNCT
ejpam-1314	94	12	can	can	AUX
ejpam-1314	94	13	be	be	AUX
ejpam-1314	94	14	written	write	VERB
ejpam-1314	94	15	as	as	ADP
ejpam-1314	94	16	m	m	PROPN
ejpam-1314	94	17	∑	∑	PUNCT
ejpam-1314	94	18	i=	i=	PROPN
ejpam-1314	94	19	`	`	PUNCT
ejpam-1314	94	20	∞	∞	PROPN
ejpam-1314	94	21	∑	∑	PUNCT
ejpam-1314	94	22	n	n	PROPN
ejpam-1314	94	23	=	=	NOUN
ejpam-1314	94	24	i	i	NOUN
ejpam-1314	94	25	|42	|42	NOUN
ejpam-1314	94	26	r	r	NOUN
ejpam-1314	94	27	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	94	28	|=	|=	PUNCT
ejpam-1314	94	29	m	m	VERB
ejpam-1314	94	30	∑	∑	PUNCT
ejpam-1314	94	31	i=	i=	PROPN
ejpam-1314	94	32	`	`	PUNCT
ejpam-1314	94	33	m	m	PROPN
ejpam-1314	94	34	∑	∑	PROPN
ejpam-1314	94	35	n	n	X
ejpam-1314	94	36	=	=	NOUN
ejpam-1314	94	37	i	i	NOUN
ejpam-1314	94	38	|42	|42	NOUN
ejpam-1314	94	39	r	r	NOUN
ejpam-1314	94	40	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	94	41	|+	|+	NOUN
ejpam-1314	94	42	m	m	VERB
ejpam-1314	94	43	∑	∑	PUNCT
ejpam-1314	94	44	i=	i=	PROPN
ejpam-1314	94	45	`	`	PUNCT
ejpam-1314	94	46	∞	∞	PROPN
ejpam-1314	94	47	∑	∑	PUNCT
ejpam-1314	94	48	n	n	PROPN
ejpam-1314	94	49	=	=	NOUN
ejpam-1314	94	50	i	i	NOUN
ejpam-1314	94	51	|42	|42	NOUN
ejpam-1314	94	52	r	r	NOUN
ejpam-1314	94	53	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	94	54	|	|	NOUN
ejpam-1314	94	55	=	=	SYM
ejpam-1314	94	56	m	m	PROPN
ejpam-1314	94	57	∑	∑	INTJ
ejpam-1314	94	58	n=	n=	ADV
ejpam-1314	94	59	`	`	PUNCT
ejpam-1314	94	60	(	(	PUNCT
ejpam-1314	94	61	n+	n+	NUM
ejpam-1314	94	62	1−	1−	NUM
ejpam-1314	94	63	`	`	PUNCT
ejpam-1314	94	64	)	)	PUNCT
ejpam-1314	94	65	|42	|42	NOUN
ejpam-1314	94	66	r	r	NOUN
ejpam-1314	94	67	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	95	1	|	|	NOUN
ejpam-1314	95	2	+	+	CCONJ
ejpam-1314	95	3	(	(	PUNCT
ejpam-1314	95	4	m+	m+	NUM
ejpam-1314	95	5	1−	1−	NUM
ejpam-1314	95	6	`	`	PUNCT
ejpam-1314	95	7	)	)	PUNCT
ejpam-1314	95	8	∞	∞	PROPN
ejpam-1314	95	9	∑	∑	PUNCT
ejpam-1314	95	10	n	n	CCONJ
ejpam-1314	95	11	=	=	NOUN
ejpam-1314	95	12	m+1	m+1	X
ejpam-1314	95	13	|42	|42	NOUN
ejpam-1314	95	14	r	r	NOUN
ejpam-1314	95	15	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	95	16	|	|	NOUN
ejpam-1314	95	17	.	.	PUNCT
ejpam-1314	96	1	(	(	PUNCT
ejpam-1314	96	2	10	10	NUM
ejpam-1314	96	3	)	)	PUNCT
ejpam-1314	96	4	the	the	DET
ejpam-1314	96	5	proof	proof	NOUN
ejpam-1314	96	6	of	of	ADP
ejpam-1314	96	7	theorem	theorem	NOUN
ejpam-1314	96	8	follows	follow	VERB
ejpam-1314	96	9	from	from	ADP
ejpam-1314	96	10	(	(	PUNCT
ejpam-1314	96	11	8)	8)	NUM
ejpam-1314	96	12	,	,	PUNCT
ejpam-1314	96	13	(	(	PUNCT
ejpam-1314	96	14	9	9	NUM
ejpam-1314	96	15	)	)	PUNCT
ejpam-1314	96	16	and	and	CCONJ
ejpam-1314	96	17	(	(	PUNCT
ejpam-1314	96	18	10	10	NUM
ejpam-1314	96	19	)	)	PUNCT
ejpam-1314	96	20	.	.	PUNCT
ejpam-1314	97	1	now	now	ADV
ejpam-1314	97	2	we	we	PRON
ejpam-1314	97	3	shall	shall	AUX
ejpam-1314	97	4	prove	prove	VERB
ejpam-1314	97	5	an	an	DET
ejpam-1314	97	6	estimation	estimation	NOUN
ejpam-1314	97	7	of	of	ADP
ejpam-1314	97	8	the	the	DET
ejpam-1314	97	9	integral	integral	ADJ
ejpam-1314	97	10	in	in	ADP
ejpam-1314	97	11	theorem	theorem	NOUN
ejpam-1314	97	12	1	1	NUM
ejpam-1314	97	13	only	only	ADV
ejpam-1314	97	14	in	in	ADP
ejpam-1314	97	15	terms	term	NOUN
ejpam-1314	97	16	of	of	ADP
ejpam-1314	97	17	second	second	ADJ
ejpam-1314	97	18	order	order	NOUN
ejpam-1314	97	19	difference	difference	NOUN
ejpam-1314	97	20	of	of	ADP
ejpam-1314	97	21	the	the	DET
ejpam-1314	97	22	sequence	sequence	NOUN
ejpam-1314	97	23	{	{	PUNCT
ejpam-1314	97	24	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	97	25	}	}	PUNCT
ejpam-1314	97	26	.	.	PUNCT
ejpam-1314	98	1	xh	xh	PROPN
ejpam-1314	98	2	.	.	PUNCT
ejpam-1314	98	3	krasniqi	krasniqi	PROPN
ejpam-1314	98	4	/	/	SYM
ejpam-1314	98	5	eur	eur	PROPN
ejpam-1314	98	6	.	.	PUNCT
ejpam-1314	99	1	j.	j.	PROPN
ejpam-1314	99	2	pure	pure	PROPN
ejpam-1314	99	3	appl	appl	PROPN
ejpam-1314	99	4	.	.	PROPN
ejpam-1314	99	5	math	math	PROPN
ejpam-1314	99	6	,	,	PUNCT
ejpam-1314	99	7	6	6	NUM
ejpam-1314	99	8	(	(	PUNCT
ejpam-1314	99	9	2013	2013	NUM
ejpam-1314	99	10	)	)	PUNCT
ejpam-1314	99	11	,	,	PUNCT
ejpam-1314	99	12	451	451	NUM
ejpam-1314	99	13	-	-	SYM
ejpam-1314	99	14	459	459	NUM
ejpam-1314	99	15	456	456	NUM
ejpam-1314	99	16	corollary	corollary	ADJ
ejpam-1314	99	17	1	1	NUM
ejpam-1314	99	18	.	.	PUNCT
ejpam-1314	100	1	if	if	SCONJ
ejpam-1314	100	2	the	the	DET
ejpam-1314	100	3	coefficients	coefficient	NOUN
ejpam-1314	100	4	of	of	ADP
ejpam-1314	100	5	the	the	DET
ejpam-1314	100	6	series	series	NOUN
ejpam-1314	100	7	(	(	PUNCT
ejpam-1314	100	8	1	1	X
ejpam-1314	100	9	)	)	PUNCT
ejpam-1314	100	10	satisfy	satisfy	NOUN
ejpam-1314	100	11	conditions	condition	NOUN
ejpam-1314	100	12	of	of	ADP
ejpam-1314	100	13	the	the	DET
ejpam-1314	100	14	theorem	theorem	NOUN
ejpam-1314	100	15	1	1	NUM
ejpam-1314	100	16	,	,	PUNCT
ejpam-1314	100	17	then	then	ADV
ejpam-1314	100	18	∫	∫	PROPN
ejpam-1314	100	19	π/	π/	PROPN
ejpam-1314	100	20	`	`	PUNCT
ejpam-1314	100	21	π/(m+1	π/(m+1	PROPN
ejpam-1314	100	22	)	)	PUNCT
ejpam-1314	101	1	|	|	ADV
ejpam-1314	101	2	f	f	PROPN
ejpam-1314	101	3	(	(	PUNCT
ejpam-1314	101	4	x)|d	x)|d	NOUN
ejpam-1314	101	5	x	x	PUNCT
ejpam-1314	102	1	=	=	PUNCT
ejpam-1314	102	2	o	o	X
ejpam-1314	102	3	m+	m+	NUM
ejpam-1314	102	4	1−	1−	NUM
ejpam-1314	103	1	`	`	PUNCT
ejpam-1314	103	2	m	m	VERB
ejpam-1314	103	3	r	r	NOUN
ejpam-1314	103	4	∑	∑	PUNCT
ejpam-1314	103	5	k=1	k=1	X
ejpam-1314	103	6	∞	∞	NUM
ejpam-1314	103	7	∑	∑	PROPN
ejpam-1314	103	8	n=0	n=0	NUM
ejpam-1314	103	9	min	min	NOUN
ejpam-1314	103	10	�	�	PROPN
ejpam-1314	103	11	(	(	PUNCT
ejpam-1314	103	12	n+	n+	NUM
ejpam-1314	103	13	1)2	1)2	NUM
ejpam-1314	103	14	`	`	PUNCT
ejpam-1314	103	15	,	,	PUNCT
ejpam-1314	103	16	n+	n+	ADP
ejpam-1314	103	17	1	1	NUM
ejpam-1314	103	18	,	,	PUNCT
ejpam-1314	103	19	m	m	VERB
ejpam-1314	103	20	�	�	NOUN
ejpam-1314	103	21	|42	|42	NOUN
ejpam-1314	103	22	r	r	NOUN
ejpam-1314	103	23	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	103	24	|	|	ADV
ejpam-1314	103	25	!	!	PUNCT
ejpam-1314	103	26	.	.	PUNCT
ejpam-1314	104	1	proof	proof	NOUN
ejpam-1314	104	2	.	.	PUNCT
ejpam-1314	105	1	to	to	PART
ejpam-1314	105	2	deduce	deduce	VERB
ejpam-1314	105	3	the	the	DET
ejpam-1314	105	4	required	require	VERB
ejpam-1314	105	5	estimation	estimation	NOUN
ejpam-1314	105	6	we	we	PRON
ejpam-1314	105	7	use	use	VERB
ejpam-1314	105	8	the	the	DET
ejpam-1314	105	9	identity	identity	NOUN
ejpam-1314	105	10	4r	4r	NOUN
ejpam-1314	105	11	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	105	12	=	=	SYM
ejpam-1314	106	1	∞	∞	PROPN
ejpam-1314	106	2	∑	∑	PROPN
ejpam-1314	106	3	i	i	PROPN
ejpam-1314	106	4	=	=	PROPN
ejpam-1314	106	5	n	n	X
ejpam-1314	106	6	�	�	NOUN
ejpam-1314	106	7	42	42	NUM
ejpam-1314	106	8	r	r	NOUN
ejpam-1314	106	9	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	106	10	�	�	PROPN
ejpam-1314	106	11	.	.	PUNCT
ejpam-1314	107	1	we	we	PRON
ejpam-1314	107	2	have	have	VERB
ejpam-1314	107	3	`	`	PUNCT
ejpam-1314	107	4	−1	−1	VERB
ejpam-1314	107	5	∑	∑	ADP
ejpam-1314	107	6	n=0	n=0	X
ejpam-1314	107	7	n+	n+	PUNCT
ejpam-1314	107	8	1	1	NUM
ejpam-1314	107	9	`	`	PUNCT
ejpam-1314	107	10	|4r	|4r	PUNCT
ejpam-1314	107	11	ak+(n−1)r	ak+(n−1)r	NOUN
ejpam-1314	107	12	|	|	ADV
ejpam-1314	107	13	≤	≤	NUM
ejpam-1314	107	14	`	`	PUNCT
ejpam-1314	107	15	−1	−1	NOUN
ejpam-1314	107	16	∑	∑	ADP
ejpam-1314	107	17	n=0	n=0	X
ejpam-1314	107	18	n+	n+	PUNCT
ejpam-1314	107	19	1	1	NUM
ejpam-1314	107	20	`	`	PUNCT
ejpam-1314	107	21	∞	∞	PROPN
ejpam-1314	107	22	∑	∑	PROPN
ejpam-1314	107	23	i	i	PROPN
ejpam-1314	107	24	=	=	NOUN
ejpam-1314	107	25	n	n	NOUN
ejpam-1314	107	26	|42	|42	NOUN
ejpam-1314	107	27	r	r	NOUN
ejpam-1314	107	28	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	107	29	|	|	NOUN
ejpam-1314	107	30	=	=	SYM
ejpam-1314	107	31	`	`	PUNCT
ejpam-1314	107	32	−1	−1	NOUN
ejpam-1314	107	33	∑	∑	PUNCT
ejpam-1314	107	34	i=0	i=0	PROPN
ejpam-1314	107	35	i	i	PRON
ejpam-1314	107	36	∑	∑	ADP
ejpam-1314	107	37	n=0	n=0	X
ejpam-1314	107	38	n+	n+	PUNCT
ejpam-1314	107	39	1	1	NUM
ejpam-1314	107	40	`	`	PUNCT
ejpam-1314	107	41	|42	|42	NOUN
ejpam-1314	107	42	r	r	NOUN
ejpam-1314	107	43	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	107	44	|+	|+	NOUN
ejpam-1314	107	45	∞	∞	PROPN
ejpam-1314	107	46	∑	∑	PROPN
ejpam-1314	107	47	i=	i=	PROPN
ejpam-1314	107	48	`	`	PUNCT
ejpam-1314	107	49	`	`	PUNCT
ejpam-1314	107	50	−1	−1	NOUN
ejpam-1314	107	51	∑	∑	ADP
ejpam-1314	107	52	n=0	n=0	NUM
ejpam-1314	107	53	n+	n+	ADP
ejpam-1314	107	54	1	1	NUM
ejpam-1314	107	55	`	`	PUNCT
ejpam-1314	107	56	|42	|42	NOUN
ejpam-1314	107	57	r	r	NOUN
ejpam-1314	107	58	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	107	59	|	|	ADV
ejpam-1314	107	60	≤	≤	NUM
ejpam-1314	107	61	`	`	PUNCT
ejpam-1314	107	62	−1	−1	NOUN
ejpam-1314	107	63	∑	∑	PUNCT
ejpam-1314	107	64	i=0	i=0	PROPN
ejpam-1314	107	65	(	(	PUNCT
ejpam-1314	107	66	i+	i+	NUM
ejpam-1314	107	67	1)2	1)2	NUM
ejpam-1314	107	68	`	`	PUNCT
ejpam-1314	107	69	|42	|42	NOUN
ejpam-1314	107	70	r	r	NOUN
ejpam-1314	107	71	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	107	72	|+	|+	NOUN
ejpam-1314	107	73	`	`	PUNCT
ejpam-1314	107	74	∞	∞	PROPN
ejpam-1314	107	75	∑	∑	PUNCT
ejpam-1314	107	76	i=	i=	PROPN
ejpam-1314	107	77	`	`	PUNCT
ejpam-1314	107	78	|42	|42	SYM
ejpam-1314	107	79	r	r	NOUN
ejpam-1314	107	80	ak+(i−1)r	ak+(i−1)r	NOUN
ejpam-1314	107	81	|	|	NOUN
ejpam-1314	107	82	.	.	PUNCT
ejpam-1314	108	1	(	(	PUNCT
ejpam-1314	108	2	11	11	NUM
ejpam-1314	108	3	)	)	PUNCT
ejpam-1314	108	4	if	if	SCONJ
ejpam-1314	108	5	k	k	PROPN
ejpam-1314	108	6	<	<	X
ejpam-1314	108	7	m	m	PROPN
ejpam-1314	108	8	,	,	PUNCT
ejpam-1314	108	9	then	then	ADV
ejpam-1314	108	10	we	we	PRON
ejpam-1314	108	11	can	can	AUX
ejpam-1314	108	12	estimate	estimate	VERB
ejpam-1314	108	13	the	the	DET
ejpam-1314	108	14	second	second	ADJ
ejpam-1314	108	15	term	term	NOUN
ejpam-1314	108	16	in	in	ADP
ejpam-1314	108	17	the	the	DET
ejpam-1314	108	18	estimation	estimation	NOUN
ejpam-1314	108	19	of	of	ADP
ejpam-1314	108	20	the	the	DET
ejpam-1314	108	21	theorem	theorem	NOUN
ejpam-1314	108	22	1	1	NUM
ejpam-1314	108	23	by	by	ADP
ejpam-1314	108	24	means	mean	NOUN
ejpam-1314	108	25	of	of	ADP
ejpam-1314	108	26	the	the	DET
ejpam-1314	108	27	fact	fact	NOUN
ejpam-1314	108	28	that	that	SCONJ
ejpam-1314	108	29	n+	n+	ADP
ejpam-1314	108	30	1−	1−	NUM
ejpam-1314	108	31	`	`	PUNCT
ejpam-1314	108	32	≤	≤	NUM
ejpam-1314	108	33	n+	n+	NUM
ejpam-1314	108	34	1−	1−	NUM
ejpam-1314	108	35	`	`	PUNCT
ejpam-1314	108	36	n+	n+	NUM
ejpam-1314	108	37	1	1	NUM
ejpam-1314	108	38	m	m	NOUN
ejpam-1314	108	39	=	=	VERB
ejpam-1314	108	40	m−	m−	PROPN
ejpam-1314	109	1	`	`	PUNCT
ejpam-1314	109	2	m	m	PROPN
ejpam-1314	109	3	(	(	PUNCT
ejpam-1314	109	4	n+	n+	NOUN
ejpam-1314	109	5	1	1	NUM
ejpam-1314	109	6	)	)	PUNCT
ejpam-1314	109	7	.	.	PUNCT
ejpam-1314	110	1	finally	finally	ADV
ejpam-1314	110	2	,	,	PUNCT
ejpam-1314	110	3	from	from	ADP
ejpam-1314	110	4	the	the	DET
ejpam-1314	110	5	above	above	ADJ
ejpam-1314	110	6	and	and	CCONJ
ejpam-1314	110	7	(	(	PUNCT
ejpam-1314	110	8	11	11	NUM
ejpam-1314	110	9	)	)	PUNCT
ejpam-1314	110	10	along	along	ADP
ejpam-1314	110	11	with	with	ADP
ejpam-1314	110	12	the	the	DET
ejpam-1314	110	13	estimate	estimate	NOUN
ejpam-1314	110	14	of	of	ADP
ejpam-1314	110	15	the	the	DET
ejpam-1314	110	16	theorem	theorem	NOUN
ejpam-1314	110	17	1	1	NUM
ejpam-1314	110	18	we	we	PRON
ejpam-1314	110	19	immediately	immediately	ADV
ejpam-1314	110	20	obtain	obtain	VERB
ejpam-1314	110	21	the	the	DET
ejpam-1314	110	22	required	required	ADJ
ejpam-1314	110	23	estimation	estimation	NOUN
ejpam-1314	110	24	.	.	PUNCT
ejpam-1314	111	1	in	in	ADP
ejpam-1314	111	2	the	the	DET
ejpam-1314	111	3	following	following	NOUN
ejpam-1314	111	4	we	we	PRON
ejpam-1314	111	5	shall	shall	AUX
ejpam-1314	111	6	deal	deal	VERB
ejpam-1314	111	7	with	with	ADP
ejpam-1314	111	8	trigonometric	trigonometric	ADJ
ejpam-1314	111	9	series	series	NOUN
ejpam-1314	111	10	of	of	ADP
ejpam-1314	111	11	the	the	DET
ejpam-1314	111	12	form	form	NOUN
ejpam-1314	111	13	(	(	PUNCT
ejpam-1314	111	14	2	2	NUM
ejpam-1314	111	15	)	)	PUNCT
ejpam-1314	111	16	.	.	PUNCT
ejpam-1314	112	1	theorem	theorem	NOUN
ejpam-1314	112	2	2	2	NUM
ejpam-1314	112	3	.	.	PUNCT
ejpam-1314	113	1	let	let	VERB
ejpam-1314	113	2	r	r	NOUN
ejpam-1314	113	3	∈	∈	PROPN
ejpam-1314	113	4	n	n	CCONJ
ejpam-1314	113	5	,	,	PUNCT
ejpam-1314	113	6	k	k	PROPN
ejpam-1314	113	7	=	=	SYM
ejpam-1314	113	8	1	1	NUM
ejpam-1314	113	9	,	,	PUNCT
ejpam-1314	113	10	2	2	NUM
ejpam-1314	113	11	,	,	PUNCT
ejpam-1314	113	12	.	.	PUNCT
ejpam-1314	113	13	.	.	PUNCT
ejpam-1314	114	1	.	.	PUNCT
ejpam-1314	115	1	,	,	PUNCT
ejpam-1314	115	2	r.	r.	PROPN
ejpam-1314	115	3	if	if	SCONJ
ejpam-1314	115	4	an	an	DET
ejpam-1314	115	5	→	→	SYM
ejpam-1314	115	6	0	0	NUM
ejpam-1314	115	7	as	as	ADP
ejpam-1314	115	8	n→∞	n→∞	NUM
ejpam-1314	115	9	and	and	CCONJ
ejpam-1314	115	10	the	the	DET
ejpam-1314	115	11	sequence	sequence	NOUN
ejpam-1314	115	12	{	{	PUNCT
ejpam-1314	115	13	4r	4r	NOUN
ejpam-1314	115	14	ak+nr	ak+nr	ADJ
ejpam-1314	115	15	}	}	PUNCT
ejpam-1314	115	16	keeps	keep	VERB
ejpam-1314	115	17	its	its	PRON
ejpam-1314	115	18	sign	sign	NOUN
ejpam-1314	115	19	separately	separately	ADV
ejpam-1314	115	20	for	for	ADP
ejpam-1314	115	21	each	each	DET
ejpam-1314	115	22	k	k	NOUN
ejpam-1314	115	23	,	,	PUNCT
ejpam-1314	115	24	then	then	ADV
ejpam-1314	115	25	the	the	DET
ejpam-1314	115	26	series	series	NOUN
ejpam-1314	115	27	(	(	PUNCT
ejpam-1314	115	28	2	2	X
ejpam-1314	115	29	)	)	PUNCT
ejpam-1314	115	30	converges	converge	NOUN
ejpam-1314	115	31	for	for	ADP
ejpam-1314	115	32	almost	almost	ADV
ejpam-1314	115	33	all	all	PRON
ejpam-1314	115	34	x	x	NOUN
ejpam-1314	115	35	,	,	PUNCT
ejpam-1314	115	36	and	and	CCONJ
ejpam-1314	115	37	for	for	ADP
ejpam-1314	115	38	1	1	NUM
ejpam-1314	115	39	≤	≤	NUM
ejpam-1314	115	40	`	`	PUNCT
ejpam-1314	115	41	≤	≤	NUM
ejpam-1314	115	42	m	m	PROPN
ejpam-1314	115	43	,	,	PUNCT
ejpam-1314	115	44	the	the	DET
ejpam-1314	115	45	sum	sum	NOUN
ejpam-1314	115	46	function	function	NOUN
ejpam-1314	115	47	g(x	g(x	NOUN
ejpam-1314	115	48	)	)	PUNCT
ejpam-1314	115	49	satisfies	satisfie	NOUN
ejpam-1314	115	50	∫	∫	PROPN
ejpam-1314	115	51	π/	π/	PROPN
ejpam-1314	115	52	`	`	PUNCT
ejpam-1314	115	53	π/(m+1	π/(m+1	PROPN
ejpam-1314	115	54	)	)	PUNCT
ejpam-1314	116	1	|	|	ADV
ejpam-1314	116	2	f	f	PROPN
ejpam-1314	116	3	(	(	PUNCT
ejpam-1314	116	4	x)|d	x)|d	NOUN
ejpam-1314	116	5	x	x	PUNCT
ejpam-1314	117	1	=	=	PUNCT
ejpam-1314	117	2	r	r	X
ejpam-1314	117	3	∑	∑	PUNCT
ejpam-1314	117	4	k=1	k=1	VERB
ejpam-1314	117	5	m	m	VERB
ejpam-1314	117	6	∑	∑	PUNCT
ejpam-1314	117	7	i=	i=	PROPN
ejpam-1314	117	8	`	`	PUNCT
ejpam-1314	117	9	di	di	PROPN
ejpam-1314	117	10	,	,	PUNCT
ejpam-1314	117	11	r	r	PROPN
ejpam-1314	117	12	,	,	PUNCT
ejpam-1314	117	13	k	k	PROPN
ejpam-1314	117	14	k	k	X
ejpam-1314	117	15	|ak+ir	|ak+ir	VERB
ejpam-1314	117	16	|	|	ADV
ejpam-1314	117	17	+	+	NOUN
ejpam-1314	117	18	or	or	CCONJ
ejpam-1314	117	19			NOUN
ejpam-1314	117	20			NOUN
ejpam-1314	117	21			NOUN
ejpam-1314	117	22	m+	m+	NUM
ejpam-1314	117	23	1−	1−	NUM
ejpam-1314	118	1	`	`	PUNCT
ejpam-1314	118	2	m	m	VERB
ejpam-1314	118	3	r	r	NOUN
ejpam-1314	118	4	∑	∑	PUNCT
ejpam-1314	118	5	k=1	k=1	X
ejpam-1314	118	6	`	`	PUNCT
ejpam-1314	118	7	−1	−1	NOUN
ejpam-1314	118	8	∑	∑	ADP
ejpam-1314	118	9	n=1	n=1	PROPN
ejpam-1314	118	10	n2	n2	NOUN
ejpam-1314	118	11	`	`	PUNCT
ejpam-1314	118	12	2	2	NUM
ejpam-1314	118	13	|4r	|4r	ADJ
ejpam-1314	118	14	ak+nr	ak+nr	PROPN
ejpam-1314	118	15	|+	|+	NOUN
ejpam-1314	118	16	r	r	NOUN
ejpam-1314	118	17	∑	∑	PUNCT
ejpam-1314	118	18	k=1	k=1	ADJ
ejpam-1314	118	19	m	m	VERB
ejpam-1314	118	20	∑	∑	INTJ
ejpam-1314	118	21	n=	n=	ADJ
ejpam-1314	118	22	`	`	PUNCT
ejpam-1314	118	23	∞	∞	PROPN
ejpam-1314	118	24	∑	∑	PROPN
ejpam-1314	118	25	j	j	PROPN
ejpam-1314	118	26	=	=	PROPN
ejpam-1314	118	27	n	n	ADP
ejpam-1314	118	28	|42	|42	NOUN
ejpam-1314	118	29	r	r	NOUN
ejpam-1314	118	30	ak+	ak+	PROPN
ejpam-1314	118	31	jr	jr	PROPN
ejpam-1314	119	1	|	|	ADV
ejpam-1314	119	2			PROPN
ejpam-1314	119	3			VERB
ejpam-1314	119	4			PUNCT
ejpam-1314	119	5	,	,	PUNCT
ejpam-1314	119	6	where	where	SCONJ
ejpam-1314	119	7	di	di	NOUN
ejpam-1314	119	8	,	,	PUNCT
ejpam-1314	119	9	r	r	PROPN
ejpam-1314	119	10	,	,	PUNCT
ejpam-1314	119	11	k	k	NOUN
ejpam-1314	119	12	:	:	PUNCT
ejpam-1314	119	13	=	=	SYM
ejpam-1314	119	14	ln	ln	ADJ
ejpam-1314	119	15	sin	sin	NOUN
ejpam-1314	119	16	rπ	rπ	NOUN
ejpam-1314	119	17	2i	2i	NUM
ejpam-1314	119	18	sin	sin	VERB
ejpam-1314	119	19	rπ	rπ	NOUN
ejpam-1314	119	20	2(i+1	2(i+1	NOUN
ejpam-1314	119	21	)	)	PUNCT
ejpam-1314	120	1	+	+	CCONJ
ejpam-1314	120	2	cos	cos	ADP
ejpam-1314	120	3	kπ	kπ	PROPN
ejpam-1314	120	4	2i(i+	2i(i+	PROPN
ejpam-1314	120	5	1	1	NUM
ejpam-1314	120	6	)	)	PUNCT
ejpam-1314	120	7	cos	cos	ADP
ejpam-1314	120	8	kπ(2i+	kπ(2i+	NOUN
ejpam-1314	120	9	1	1	NUM
ejpam-1314	120	10	)	)	PUNCT
ejpam-1314	120	11	2i(i+	2i(i+	NUM
ejpam-1314	120	12	1	1	NUM
ejpam-1314	120	13	)	)	PUNCT
ejpam-1314	120	14	.	.	PUNCT
ejpam-1314	121	1	xh	xh	PROPN
ejpam-1314	121	2	.	.	PUNCT
ejpam-1314	121	3	krasniqi	krasniqi	PROPN
ejpam-1314	121	4	/	/	SYM
ejpam-1314	121	5	eur	eur	PROPN
ejpam-1314	121	6	.	.	PUNCT
ejpam-1314	122	1	j.	j.	PROPN
ejpam-1314	122	2	pure	pure	PROPN
ejpam-1314	122	3	appl	appl	PROPN
ejpam-1314	122	4	.	.	PROPN
ejpam-1314	122	5	math	math	PROPN
ejpam-1314	122	6	,	,	PUNCT
ejpam-1314	122	7	6	6	NUM
ejpam-1314	122	8	(	(	PUNCT
ejpam-1314	122	9	2013	2013	NUM
ejpam-1314	122	10	)	)	PUNCT
ejpam-1314	122	11	,	,	PUNCT
ejpam-1314	122	12	451	451	NUM
ejpam-1314	122	13	-	-	SYM
ejpam-1314	122	14	459	459	NUM
ejpam-1314	122	15	457	457	NUM
ejpam-1314	122	16	proof	proof	NOUN
ejpam-1314	122	17	.	.	PUNCT
ejpam-1314	123	1	under	under	ADP
ejpam-1314	123	2	assumptions	assumption	NOUN
ejpam-1314	123	3	of	of	ADP
ejpam-1314	123	4	the	the	DET
ejpam-1314	123	5	theorem	theorem	NOUN
ejpam-1314	123	6	and	and	CCONJ
ejpam-1314	123	7	lemma	lemma	PROPN
ejpam-1314	123	8	1(a	1(a	NUM
ejpam-1314	123	9	)	)	PUNCT
ejpam-1314	123	10	the	the	DET
ejpam-1314	123	11	series	series	NOUN
ejpam-1314	123	12	(	(	PUNCT
ejpam-1314	123	13	2	2	X
ejpam-1314	123	14	)	)	PUNCT
ejpam-1314	123	15	converges	converge	NOUN
ejpam-1314	123	16	for	for	ADP
ejpam-1314	123	17	almost	almost	ADV
ejpam-1314	123	18	all	all	PRON
ejpam-1314	123	19	x	x	NOUN
ejpam-1314	123	20	and	and	CCONJ
ejpam-1314	123	21	for	for	ADP
ejpam-1314	123	22	m	m	PROPN
ejpam-1314	123	23	=	=	SYM
ejpam-1314	123	24	0	0	NUM
ejpam-1314	124	1	the	the	DET
ejpam-1314	124	2	sum	sum	NOUN
ejpam-1314	124	3	function	function	NOUN
ejpam-1314	124	4	g(x	g(x	NOUN
ejpam-1314	124	5	)	)	PUNCT
ejpam-1314	124	6	is	be	AUX
ejpam-1314	124	7	almost	almost	ADV
ejpam-1314	124	8	everywhere	everywhere	ADV
ejpam-1314	124	9	representable	representable	ADJ
ejpam-1314	124	10	in	in	ADP
ejpam-1314	124	11	the	the	DET
ejpam-1314	124	12	form	form	NOUN
ejpam-1314	124	13	g(x	g(x	NOUN
ejpam-1314	124	14	)	)	PUNCT
ejpam-1314	125	1	=	=	PUNCT
ejpam-1314	125	2	r	r	NOUN
ejpam-1314	125	3	∑	∑	PUNCT
ejpam-1314	125	4	k=1	k=1	X
ejpam-1314	125	5	∞	∞	NUM
ejpam-1314	125	6	∑	∑	ADP
ejpam-1314	125	7	n=0	n=0	PROPN
ejpam-1314	125	8	4r	4r	NOUN
ejpam-1314	125	9	ak+nr	ak+nr	PROPN
ejpam-1314	125	10	b	b	SYM
ejpam-1314	125	11	1	1	NUM
ejpam-1314	125	12	n+1,r	n+1,r	NOUN
ejpam-1314	125	13	,	,	PUNCT
ejpam-1314	125	14	k(x	k(x	PROPN
ejpam-1314	125	15	)	)	PUNCT
ejpam-1314	125	16	.	.	PUNCT
ejpam-1314	126	1	let	let	VERB
ejpam-1314	126	2	us	we	PRON
ejpam-1314	126	3	denote	denote	VERB
ejpam-1314	126	4	ϕn	ϕn	INTJ
ejpam-1314	126	5	,	,	PUNCT
ejpam-1314	126	6	r	r	NOUN
ejpam-1314	126	7	,	,	PUNCT
ejpam-1314	126	8	k(x	k(x	PROPN
ejpam-1314	126	9	)	)	PUNCT
ejpam-1314	126	10	:	:	PUNCT
ejpam-1314	127	1	=	=	SYM
ejpam-1314	127	2	−	−	PROPN
ejpam-1314	128	1	cos(2k+	cos(2k+	X
ejpam-1314	128	2	(	(	PUNCT
ejpam-1314	128	3	2n+	2n+	NUM
ejpam-1314	128	4	1)r	1)r	NUM
ejpam-1314	128	5	)	)	PUNCT
ejpam-1314	128	6	x	x	SYM
ejpam-1314	128	7	2	2	NUM
ejpam-1314	128	8	2sin	2sin	NUM
ejpam-1314	128	9	�	�	PROPN
ejpam-1314	128	10	r	r	NOUN
ejpam-1314	128	11	x	x	SYM
ejpam-1314	128	12	2	2	NUM
ejpam-1314	128	13	�	�	PROPN
ejpam-1314	128	14	,	,	PUNCT
ejpam-1314	128	15	ψn	ψn	INTJ
ejpam-1314	128	16	,	,	PUNCT
ejpam-1314	128	17	r	r	NOUN
ejpam-1314	128	18	,	,	PUNCT
ejpam-1314	128	19	k(x	k(x	PROPN
ejpam-1314	128	20	)	)	PUNCT
ejpam-1314	128	21	:	:	PUNCT
ejpam-1314	128	22	=	=	SYM
ejpam-1314	128	23	n	n	PART
ejpam-1314	128	24	∑	∑	PUNCT
ejpam-1314	128	25	s=0	s=0	PROPN
ejpam-1314	128	26	ϕs	ϕs	INTJ
ejpam-1314	128	27	,	,	PUNCT
ejpam-1314	128	28	r	r	NOUN
ejpam-1314	128	29	,	,	PUNCT
ejpam-1314	128	30	k(x	k(x	PROPN
ejpam-1314	128	31	)	)	PUNCT
ejpam-1314	128	32	=	=	SYM
ejpam-1314	129	1	sin(k+	sin(k+	PROPN
ejpam-1314	129	2	nr)x	nr)x	PROPN
ejpam-1314	129	3	+	+	CCONJ
ejpam-1314	129	4	sin	sin	NOUN
ejpam-1314	129	5	kx	kx	PROPN
ejpam-1314	129	6	4sin2	4sin2	NUM
ejpam-1314	129	7	�	�	NOUN
ejpam-1314	129	8	r	r	NOUN
ejpam-1314	129	9	x	x	SYM
ejpam-1314	129	10	2	2	NUM
ejpam-1314	129	11	�	�	PROPN
ejpam-1314	129	12	.	.	PUNCT
ejpam-1314	130	1	let	let	VERB
ejpam-1314	130	2	i	i	PRON
ejpam-1314	130	3	∈	∈	PROPN
ejpam-1314	130	4	n	n	AUX
ejpam-1314	130	5	be	be	VERB
ejpam-1314	130	6	such	such	ADJ
ejpam-1314	130	7	that	that	SCONJ
ejpam-1314	130	8	i	i	PRON
ejpam-1314	130	9	≥	≥	AUX
ejpam-1314	130	10	r.	r.	NOUN
ejpam-1314	130	11	from	from	ADP
ejpam-1314	130	12	definition	definition	NOUN
ejpam-1314	130	13	of	of	ADP
ejpam-1314	130	14	b	b	PROPN
ejpam-1314	130	15	1	1	NUM
ejpam-1314	130	16	n+1,r	n+1,r	PROPN
ejpam-1314	130	17	,	,	PUNCT
ejpam-1314	130	18	k(x	k(x	PROPN
ejpam-1314	130	19	)	)	PUNCT
ejpam-1314	130	20	we	we	PRON
ejpam-1314	130	21	can	can	AUX
ejpam-1314	130	22	write	write	VERB
ejpam-1314	130	23	g(x	g(x	NOUN
ejpam-1314	130	24	)	)	PUNCT
ejpam-1314	131	1	=	=	PUNCT
ejpam-1314	131	2	r	r	NOUN
ejpam-1314	131	3	∑	∑	PUNCT
ejpam-1314	131	4	k=1	k=1	PROPN
ejpam-1314	131	5	i−1	i−1	PROPN
ejpam-1314	131	6	∑	∑	PUNCT
ejpam-1314	131	7	n=0	n=0	PROPN
ejpam-1314	131	8	4r	4r	NUM
ejpam-1314	131	9	ak+nr	ak+nr	PROPN
ejpam-1314	131	10	b	b	SYM
ejpam-1314	131	11	1	1	NUM
ejpam-1314	131	12	n+1,r	n+1,r	NOUN
ejpam-1314	131	13	,	,	PUNCT
ejpam-1314	131	14	k(x	k(x	PROPN
ejpam-1314	131	15	)	)	PUNCT
ejpam-1314	132	1	+	+	CCONJ
ejpam-1314	132	2	r	r	NOUN
ejpam-1314	132	3	∑	∑	PUNCT
ejpam-1314	132	4	k=1	k=1	PROPN
ejpam-1314	132	5	∞	∞	NUM
ejpam-1314	132	6	∑	∑	PUNCT
ejpam-1314	132	7	n	n	CCONJ
ejpam-1314	132	8	=	=	NOUN
ejpam-1314	132	9	i	i	PROPN
ejpam-1314	132	10	4r	4r	NUM
ejpam-1314	132	11	ak+nr	ak+nr	PROPN
ejpam-1314	132	12	b	b	PROPN
ejpam-1314	132	13	1	1	NUM
ejpam-1314	132	14	n+1,r	n+1,r	NOUN
ejpam-1314	132	15	,	,	PUNCT
ejpam-1314	132	16	k(x	k(x	PROPN
ejpam-1314	132	17	)	)	PUNCT
ejpam-1314	133	1	=	=	PUNCT
ejpam-1314	133	2	r	r	NOUN
ejpam-1314	133	3	∑	∑	PUNCT
ejpam-1314	133	4	k=1	k=1	PROPN
ejpam-1314	133	5	i−1	i−1	PROPN
ejpam-1314	133	6	∑	∑	PUNCT
ejpam-1314	133	7	n=0	n=0	PROPN
ejpam-1314	133	8	4r	4r	NUM
ejpam-1314	133	9	ak+nr	ak+nr	PROPN
ejpam-1314	133	10	b	b	SYM
ejpam-1314	133	11	1	1	NUM
ejpam-1314	133	12	n+1,r	n+1,r	NOUN
ejpam-1314	133	13	,	,	PUNCT
ejpam-1314	133	14	k(x	k(x	PROPN
ejpam-1314	133	15	)	)	PUNCT
ejpam-1314	134	1	+	+	CCONJ
ejpam-1314	134	2	r	r	NOUN
ejpam-1314	134	3	∑	∑	PUNCT
ejpam-1314	134	4	k=1	k=1	PROPN
ejpam-1314	134	5	∞	∞	NUM
ejpam-1314	134	6	∑	∑	PUNCT
ejpam-1314	134	7	n	n	CCONJ
ejpam-1314	134	8	=	=	NOUN
ejpam-1314	134	9	i	i	PROPN
ejpam-1314	134	10	4r	4r	NOUN
ejpam-1314	134	11	ak+nr	ak+nr	NOUN
ejpam-1314	134	12	cos(2k−	cos(2k−	VERB
ejpam-1314	134	13	r	r	X
ejpam-1314	134	14	)	)	PUNCT
ejpam-1314	134	15	x	x	SYM
ejpam-1314	134	16	2	2	NUM
ejpam-1314	134	17	2	2	NUM
ejpam-1314	134	18	sin	sin	NOUN
ejpam-1314	134	19	�	�	PROPN
ejpam-1314	134	20	r	r	NOUN
ejpam-1314	134	21	x	x	SYM
ejpam-1314	134	22	2	2	NUM
ejpam-1314	134	23	�	�	NOUN
ejpam-1314	134	24	−	−	NOUN
ejpam-1314	135	1	r	r	NOUN
ejpam-1314	135	2	∑	∑	PUNCT
ejpam-1314	135	3	k=1	k=1	PROPN
ejpam-1314	135	4	∞	∞	NUM
ejpam-1314	135	5	∑	∑	PUNCT
ejpam-1314	135	6	n	n	CCONJ
ejpam-1314	135	7	=	=	NOUN
ejpam-1314	135	8	i	i	PROPN
ejpam-1314	135	9	4r	4r	NOUN
ejpam-1314	135	10	ak+nr	ak+nr	PROPN
ejpam-1314	136	1	cos(2k+	cos(2k+	PROPN
ejpam-1314	136	2	(	(	PUNCT
ejpam-1314	136	3	2n+	2n+	NUM
ejpam-1314	136	4	1)r	1)r	NUM
ejpam-1314	136	5	)	)	PUNCT
ejpam-1314	136	6	x	x	SYM
ejpam-1314	136	7	2	2	NUM
ejpam-1314	136	8	2	2	NUM
ejpam-1314	136	9	sin	sin	NOUN
ejpam-1314	136	10	�	�	PROPN
ejpam-1314	136	11	r	r	NOUN
ejpam-1314	136	12	x	x	SYM
ejpam-1314	136	13	2	2	NUM
ejpam-1314	136	14	�	�	NOUN
ejpam-1314	136	15	=	=	PUNCT
ejpam-1314	136	16	r	r	NOUN
ejpam-1314	136	17	∑	∑	PUNCT
ejpam-1314	136	18	k=1	k=1	VERB
ejpam-1314	136	19	ak+ir	ak+ir	X
ejpam-1314	136	20	cos(2k−	cos(2k−	NOUN
ejpam-1314	136	21	r	r	NOUN
ejpam-1314	136	22	)	)	PUNCT
ejpam-1314	136	23	x	x	SYM
ejpam-1314	136	24	2	2	NUM
ejpam-1314	136	25	2	2	NUM
ejpam-1314	136	26	sin	sin	NOUN
ejpam-1314	136	27	�	�	PROPN
ejpam-1314	136	28	r	r	NOUN
ejpam-1314	136	29	x	x	SYM
ejpam-1314	136	30	2	2	NUM
ejpam-1314	136	31	�	�	NOUN
ejpam-1314	136	32	+	+	CCONJ
ejpam-1314	136	33	r	r	NOUN
ejpam-1314	136	34	∑	∑	PUNCT
ejpam-1314	136	35	k=1	k=1	PROPN
ejpam-1314	136	36	i−1	i−1	PROPN
ejpam-1314	136	37	∑	∑	PUNCT
ejpam-1314	136	38	n=0	n=0	PROPN
ejpam-1314	136	39	4r	4r	NUM
ejpam-1314	136	40	ak+nr	ak+nr	PROPN
ejpam-1314	136	41	b	b	SYM
ejpam-1314	136	42	1	1	NUM
ejpam-1314	136	43	n+1,r	n+1,r	NOUN
ejpam-1314	136	44	,	,	PUNCT
ejpam-1314	136	45	k(x	k(x	PROPN
ejpam-1314	136	46	)	)	PUNCT
ejpam-1314	137	1	+	+	CCONJ
ejpam-1314	137	2	r	r	NOUN
ejpam-1314	137	3	∑	∑	PUNCT
ejpam-1314	137	4	k=1	k=1	PROPN
ejpam-1314	137	5	∞	∞	NUM
ejpam-1314	137	6	∑	∑	PUNCT
ejpam-1314	137	7	n	n	CCONJ
ejpam-1314	137	8	=	=	NOUN
ejpam-1314	137	9	i	i	PROPN
ejpam-1314	137	10	4r	4r	NOUN
ejpam-1314	137	11	ak+nrϕn	ak+nrϕn	PUNCT
ejpam-1314	137	12	,	,	PUNCT
ejpam-1314	137	13	r	r	NOUN
ejpam-1314	137	14	,	,	PUNCT
ejpam-1314	137	15	k(x	k(x	PROPN
ejpam-1314	137	16	)	)	PUNCT
ejpam-1314	137	17	:	:	PUNCT
ejpam-1314	138	1	=	=	PUNCT
ejpam-1314	138	2	h0(x	h0(x	X
ejpam-1314	138	3	)	)	PUNCT
ejpam-1314	138	4	+	+	NOUN
ejpam-1314	138	5	h1(x	h1(x	X
ejpam-1314	138	6	)	)	PUNCT
ejpam-1314	138	7	+	+	NUM
ejpam-1314	138	8	h2(x	h2(x	NUM
ejpam-1314	138	9	)	)	PUNCT
ejpam-1314	138	10	.	.	PUNCT
ejpam-1314	139	1	(	(	PUNCT
ejpam-1314	139	2	12	12	NUM
ejpam-1314	139	3	)	)	PUNCT
ejpam-1314	139	4	for	for	ADP
ejpam-1314	139	5	x	x	PROPN
ejpam-1314	139	6	∈	∈	PROPN
ejpam-1314	139	7	�	�	PROPN
ejpam-1314	139	8	π	π	PROPN
ejpam-1314	139	9	i+1	i+1	NUM
ejpam-1314	139	10	,	,	PUNCT
ejpam-1314	139	11	π	π	VERB
ejpam-1314	139	12	i	i	PRON
ejpam-1314	139	13	�	�	PROPN
ejpam-1314	139	14	,	,	PUNCT
ejpam-1314	139	15	i	i	PRON
ejpam-1314	139	16	=	=	NOUN
ejpam-1314	139	17	1,2	1,2	NUM
ejpam-1314	139	18	,	,	PUNCT
ejpam-1314	139	19	.	.	PUNCT
ejpam-1314	139	20	.	.	PUNCT
ejpam-1314	140	1	.	.	PUNCT
ejpam-1314	141	1	,	,	PUNCT
ejpam-1314	141	2	we	we	PRON
ejpam-1314	141	3	have	have	VERB
ejpam-1314	141	4	∫	∫	PROPN
ejpam-1314	141	5	π/	π/	PROPN
ejpam-1314	141	6	`	`	PUNCT
ejpam-1314	141	7	π/(m+1	π/(m+1	PROPN
ejpam-1314	141	8	)	)	PUNCT
ejpam-1314	141	9	|h1(x)|d	|h1(x)|d	NOUN
ejpam-1314	141	10	x	x	PUNCT
ejpam-1314	142	1	≤	≤	NUM
ejpam-1314	142	2	m	m	VERB
ejpam-1314	142	3	∑	∑	PUNCT
ejpam-1314	142	4	i=	i=	PROPN
ejpam-1314	142	5	`	`	PUNCT
ejpam-1314	142	6	∫	∫	PROPN
ejpam-1314	142	7	π	π	X
ejpam-1314	142	8	/	/	SYM
ejpam-1314	142	9	i	i	PRON
ejpam-1314	142	10	π/(i+1	π/(i+1	ADJ
ejpam-1314	142	11	)	)	PUNCT
ejpam-1314	142	12	r	r	NOUN
ejpam-1314	142	13	∑	∑	PUNCT
ejpam-1314	142	14	k=1	k=1	PROPN
ejpam-1314	142	15	i−1	i−1	PROPN
ejpam-1314	142	16	∑	∑	PUNCT
ejpam-1314	142	17	n=0	n=0	X
ejpam-1314	142	18	|4r	|4r	PUNCT
ejpam-1314	142	19	ak+nr	ak+nr	PROPN
ejpam-1314	142	20	||b	||b	PROPN
ejpam-1314	142	21	1	1	NUM
ejpam-1314	142	22	n+1,r	n+1,r	NOUN
ejpam-1314	142	23	,	,	PUNCT
ejpam-1314	142	24	k(x)|d	k(x)|d	NOUN
ejpam-1314	142	25	x	x	PUNCT
ejpam-1314	143	1	=	=	PUNCT
ejpam-1314	143	2	r	r	NOUN
ejpam-1314	143	3	∑	∑	PUNCT
ejpam-1314	143	4	k=1	k=1	VERB
ejpam-1314	143	5	m	m	VERB
ejpam-1314	143	6	∑	∑	PUNCT
ejpam-1314	143	7	i=	i=	PROPN
ejpam-1314	143	8	`	`	PUNCT
ejpam-1314	143	9	`	`	PUNCT
ejpam-1314	143	10	−1	−1	NOUN
ejpam-1314	143	11	∑	∑	PUNCT
ejpam-1314	143	12	n=0	n=0	X
ejpam-1314	143	13	|4r	|4r	ADV
ejpam-1314	143	14	ak+nr	ak+nr	ADV
ejpam-1314	144	1	|	|	ADV
ejpam-1314	144	2	∫	∫	PROPN
ejpam-1314	144	3	π	π	X
ejpam-1314	144	4	/	/	SYM
ejpam-1314	144	5	i	i	PRON
ejpam-1314	144	6	π/(i+1	π/(i+1	PROPN
ejpam-1314	144	7	)	)	PUNCT
ejpam-1314	144	8	|b1	|b1	PROPN
ejpam-1314	144	9	n+1,r	n+1,r	PROPN
ejpam-1314	144	10	,	,	PUNCT
ejpam-1314	144	11	k(x)|d	k(x)|d	PROPN
ejpam-1314	144	12	x	x	PROPN
ejpam-1314	145	1	+	+	CCONJ
ejpam-1314	145	2	r	r	NOUN
ejpam-1314	145	3	∑	∑	PUNCT
ejpam-1314	145	4	k=1	k=1	VERB
ejpam-1314	145	5	m	m	VERB
ejpam-1314	145	6	∑	∑	VERB
ejpam-1314	145	7	i=`+1	i=`+1	PUNCT
ejpam-1314	145	8	i−1	i−1	PROPN
ejpam-1314	145	9	∑	∑	PUNCT
ejpam-1314	145	10	n=	n=	ADV
ejpam-1314	145	11	`	`	PUNCT
ejpam-1314	145	12	|4r	|4r	PRON
ejpam-1314	145	13	ak+nr	ak+nr	PROPN
ejpam-1314	145	14	|	|	ADV
ejpam-1314	145	15	∫	∫	PROPN
ejpam-1314	145	16	π	π	X
ejpam-1314	145	17	/	/	SYM
ejpam-1314	145	18	i	i	PRON
ejpam-1314	145	19	π/(i+1	π/(i+1	PROPN
ejpam-1314	145	20	)	)	PUNCT
ejpam-1314	145	21	|b1	|b1	PROPN
ejpam-1314	145	22	n+1,r	n+1,r	PROPN
ejpam-1314	145	23	,	,	PUNCT
ejpam-1314	145	24	k(x)|d	k(x)|d	PROPN
ejpam-1314	145	25	x	x	PUNCT
ejpam-1314	145	26	=	=	PUNCT
ejpam-1314	145	27	r	r	NOUN
ejpam-1314	145	28	∑	∑	PUNCT
ejpam-1314	145	29	k=1	k=1	X
ejpam-1314	145	30	`	`	PUNCT
ejpam-1314	145	31	−1	−1	NOUN
ejpam-1314	145	32	∑	∑	PUNCT
ejpam-1314	145	33	n=0	n=0	X
ejpam-1314	145	34	|4r	|4r	ADV
ejpam-1314	145	35	ak+nr	ak+nr	ADV
ejpam-1314	145	36	|	|	ADV
ejpam-1314	145	37	∫	∫	PROPN
ejpam-1314	145	38	π/	π/	PROPN
ejpam-1314	145	39	`	`	PUNCT
ejpam-1314	145	40	π/(m+1	π/(m+1	PROPN
ejpam-1314	145	41	)	)	PUNCT
ejpam-1314	145	42	|b1	|b1	NOUN
ejpam-1314	145	43	n+1,r	n+1,r	PROPN
ejpam-1314	145	44	,	,	PUNCT
ejpam-1314	145	45	k(x)|d	k(x)|d	PROPN
ejpam-1314	145	46	x	x	PROPN
ejpam-1314	145	47	xh	xh	PROPN
ejpam-1314	145	48	.	.	PUNCT
ejpam-1314	146	1	krasniqi	krasniqi	PROPN
ejpam-1314	146	2	/	/	SYM
ejpam-1314	146	3	eur	eur	PROPN
ejpam-1314	146	4	.	.	PUNCT
ejpam-1314	147	1	j.	j.	PROPN
ejpam-1314	147	2	pure	pure	PROPN
ejpam-1314	147	3	appl	appl	PROPN
ejpam-1314	147	4	.	.	PROPN
ejpam-1314	147	5	math	math	PROPN
ejpam-1314	147	6	,	,	PUNCT
ejpam-1314	147	7	6	6	NUM
ejpam-1314	147	8	(	(	PUNCT
ejpam-1314	147	9	2013	2013	NUM
ejpam-1314	147	10	)	)	PUNCT
ejpam-1314	147	11	,	,	PUNCT
ejpam-1314	147	12	451	451	NUM
ejpam-1314	147	13	-	-	SYM
ejpam-1314	147	14	459	459	NUM
ejpam-1314	147	15	458	458	NUM
ejpam-1314	148	1	+	+	CCONJ
ejpam-1314	148	2	r	r	NOUN
ejpam-1314	148	3	∑	∑	NOUN
ejpam-1314	148	4	k=1	k=1	PROPN
ejpam-1314	148	5	m−1	m−1	PROPN
ejpam-1314	148	6	∑	∑	PUNCT
ejpam-1314	148	7	n=	n=	ADV
ejpam-1314	148	8	`	`	PUNCT
ejpam-1314	148	9	|4r	|4r	PRON
ejpam-1314	148	10	ak+nr	ak+nr	PROPN
ejpam-1314	148	11	|	|	ADV
ejpam-1314	148	12	∫	∫	PROPN
ejpam-1314	148	13	π/(n+1	π/(n+1	PROPN
ejpam-1314	148	14	)	)	PUNCT
ejpam-1314	148	15	π/(m+1	π/(m+1	PROPN
ejpam-1314	148	16	)	)	PUNCT
ejpam-1314	148	17	|b1	|b1	NOUN
ejpam-1314	148	18	n+1,r	n+1,r	PROPN
ejpam-1314	148	19	,	,	PUNCT
ejpam-1314	148	20	k(x)|d	k(x)|d	PROPN
ejpam-1314	148	21	x	x	X
ejpam-1314	148	22	.	.	PUNCT
ejpam-1314	149	1	(	(	PUNCT
ejpam-1314	149	2	13	13	NUM
ejpam-1314	149	3	)	)	PUNCT
ejpam-1314	149	4	since	since	SCONJ
ejpam-1314	149	5	|b1	|b1	PROPN
ejpam-1314	149	6	n+1,r	n+1,r	PROPN
ejpam-1314	149	7	,	,	PUNCT
ejpam-1314	149	8	k(x)|	k(x)|	VERB
ejpam-1314	149	9	≤	≤	NUM
ejpam-1314	149	10	n	n	CCONJ
ejpam-1314	149	11	∑	∑	PROPN
ejpam-1314	149	12	m=0	m=0	PROPN
ejpam-1314	149	13	(	(	PUNCT
ejpam-1314	149	14	k+mr)x	k+mr)x	ADJ
ejpam-1314	149	15	≤	≤	NUM
ejpam-1314	149	16	4rn2	4rn2	NUM
ejpam-1314	150	1	x	x	NOUN
ejpam-1314	150	2	,	,	PUNCT
ejpam-1314	150	3	then	then	ADV
ejpam-1314	150	4	from	from	ADP
ejpam-1314	150	5	(	(	PUNCT
ejpam-1314	150	6	13	13	NUM
ejpam-1314	150	7	)	)	PUNCT
ejpam-1314	150	8	it	it	PRON
ejpam-1314	150	9	follows	follow	VERB
ejpam-1314	150	10	that	that	SCONJ
ejpam-1314	150	11	∫	∫	PROPN
ejpam-1314	150	12	π/	π/	PROPN
ejpam-1314	150	13	`	`	PUNCT
ejpam-1314	150	14	π/(m+1	π/(m+1	PROPN
ejpam-1314	150	15	)	)	PUNCT
ejpam-1314	150	16	|h1(x)|d	|h1(x)|d	NOUN
ejpam-1314	150	17	x	x	SYM
ejpam-1314	150	18	≤cr	≤cr	PROPN
ejpam-1314	150	19	r	r	NOUN
ejpam-1314	150	20	∑	∑	PUNCT
ejpam-1314	150	21	k=1	k=1	X
ejpam-1314	150	22	`	`	PUNCT
ejpam-1314	150	23	−1	−1	NOUN
ejpam-1314	150	24	∑	∑	PUNCT
ejpam-1314	150	25	n=1	n=1	PROPN
ejpam-1314	150	26	n2|4r	n2|4r	PUNCT
ejpam-1314	150	27	ak+nr	ak+nr	PROPN
ejpam-1314	150	28	|	|	ADV
ejpam-1314	150	29	�	�	PROPN
ejpam-1314	150	30	1	1	NUM
ejpam-1314	150	31	`	`	PUNCT
ejpam-1314	150	32	2	2	NUM
ejpam-1314	150	33	−	−	NOUN
ejpam-1314	150	34	1	1	NUM
ejpam-1314	150	35	(	(	PUNCT
ejpam-1314	150	36	m+	m+	NUM
ejpam-1314	150	37	1)2	1)2	NUM
ejpam-1314	150	38	�	�	PROPN
ejpam-1314	150	39	+	+	CCONJ
ejpam-1314	150	40	cr	cr	NOUN
ejpam-1314	150	41	r	r	NOUN
ejpam-1314	150	42	∑	∑	PROPN
ejpam-1314	150	43	k=1	k=1	PROPN
ejpam-1314	150	44	m−1	m−1	PROPN
ejpam-1314	150	45	∑	∑	PUNCT
ejpam-1314	150	46	n=	n=	ADV
ejpam-1314	150	47	`	`	NUM
ejpam-1314	150	48	n2|4r	n2|4r	VERB
ejpam-1314	150	49	ak+nr	ak+nr	PROPN
ejpam-1314	150	50	|	|	ADV
ejpam-1314	150	51	�	�	PROPN
ejpam-1314	150	52	1	1	NUM
ejpam-1314	150	53	(	(	PUNCT
ejpam-1314	150	54	n+	n+	NUM
ejpam-1314	150	55	1)2	1)2	NUM
ejpam-1314	150	56	−	−	NOUN
ejpam-1314	150	57	1	1	NUM
ejpam-1314	150	58	(	(	PUNCT
ejpam-1314	150	59	m+	m+	NUM
ejpam-1314	150	60	1)2	1)2	NUM
ejpam-1314	150	61	�	�	NOUN
ejpam-1314	150	62	≤cr	≤cr	PROPN
ejpam-1314	150	63	m+	m+	NUM
ejpam-1314	150	64	1−	1−	NUM
ejpam-1314	151	1	`	`	PUNCT
ejpam-1314	151	2	m	m	VERB
ejpam-1314	151	3	r	r	NOUN
ejpam-1314	151	4	∑	∑	PUNCT
ejpam-1314	151	5	k=1	k=1	X
ejpam-1314	151	6	`	`	PUNCT
ejpam-1314	151	7	−1	−1	NOUN
ejpam-1314	151	8	∑	∑	ADP
ejpam-1314	151	9	n=1	n=1	PROPN
ejpam-1314	151	10	n2	n2	NOUN
ejpam-1314	151	11	`	`	PUNCT
ejpam-1314	151	12	2	2	NUM
ejpam-1314	151	13	|4r	|4r	ADJ
ejpam-1314	151	14	ak+nr	ak+nr	PROPN
ejpam-1314	151	15	|+	|+	NOUN
ejpam-1314	151	16	cr	cr	ADP
ejpam-1314	151	17	r	r	NOUN
ejpam-1314	151	18	∑	∑	PUNCT
ejpam-1314	151	19	k=1	k=1	ADJ
ejpam-1314	151	20	m	m	VERB
ejpam-1314	151	21	∑	∑	INTJ
ejpam-1314	151	22	n=	n=	ADJ
ejpam-1314	151	23	`	`	PUNCT
ejpam-1314	151	24	∞	∞	PROPN
ejpam-1314	151	25	∑	∑	PROPN
ejpam-1314	151	26	j	j	PROPN
ejpam-1314	151	27	=	=	PROPN
ejpam-1314	151	28	n	n	ADP
ejpam-1314	151	29	|42	|42	NOUN
ejpam-1314	151	30	r	r	NOUN
ejpam-1314	151	31	ak+	ak+	PROPN
ejpam-1314	151	32	jr	jr	PROPN
ejpam-1314	152	1	|	|	INTJ
ejpam-1314	152	2	.	.	PUNCT
ejpam-1314	153	1	(	(	PUNCT
ejpam-1314	153	2	14	14	NUM
ejpam-1314	153	3	)	)	PUNCT
ejpam-1314	153	4	now	now	ADV
ejpam-1314	153	5	we	we	PRON
ejpam-1314	153	6	shall	shall	AUX
ejpam-1314	153	7	estimate	estimate	VERB
ejpam-1314	153	8	the	the	DET
ejpam-1314	153	9	integral	integral	NOUN
ejpam-1314	153	10	of	of	ADP
ejpam-1314	153	11	the	the	DET
ejpam-1314	153	12	function	function	NOUN
ejpam-1314	153	13	|h2(x)|	|h2(x)|	PUNCT
ejpam-1314	153	14	for	for	ADP
ejpam-1314	153	15	x	x	PROPN
ejpam-1314	153	16	∈	∈	PROPN
ejpam-1314	153	17	�	�	PROPN
ejpam-1314	153	18	π	π	PROPN
ejpam-1314	153	19	i+1	i+1	NUM
ejpam-1314	153	20	,	,	PUNCT
ejpam-1314	153	21	π	π	PROPN
ejpam-1314	153	22	i	i	PROPN
ejpam-1314	153	23	�	�	PROPN
ejpam-1314	153	24	.	.	PUNCT
ejpam-1314	154	1	indeed	indeed	ADV
ejpam-1314	154	2	,	,	PUNCT
ejpam-1314	154	3	the	the	DET
ejpam-1314	154	4	summation	summation	NOUN
ejpam-1314	154	5	by	by	ADP
ejpam-1314	154	6	parts	part	NOUN
ejpam-1314	154	7	gives	give	VERB
ejpam-1314	154	8	h2(x	h2(x	PRON
ejpam-1314	154	9	)	)	PUNCT
ejpam-1314	154	10	=	=	VERB
ejpam-1314	154	11	lim	lim	PROPN
ejpam-1314	154	12	p→∞	p→∞	ADJ
ejpam-1314	154	13	r	r	NOUN
ejpam-1314	154	14	∑	∑	PUNCT
ejpam-1314	154	15	k=1	k=1	PROPN
ejpam-1314	154	16	p	p	PROPN
ejpam-1314	154	17	∑	∑	PROPN
ejpam-1314	154	18	n	n	CCONJ
ejpam-1314	154	19	=	=	NOUN
ejpam-1314	154	20	i	i	PROPN
ejpam-1314	154	21	4r	4r	NOUN
ejpam-1314	154	22	ak+nrϕn	ak+nrϕn	PUNCT
ejpam-1314	154	23	,	,	PUNCT
ejpam-1314	154	24	r	r	NOUN
ejpam-1314	154	25	,	,	PUNCT
ejpam-1314	154	26	k(x	k(x	PROPN
ejpam-1314	154	27	)	)	PUNCT
ejpam-1314	155	1	=	=	PUNCT
ejpam-1314	155	2	r	r	NOUN
ejpam-1314	155	3	∑	∑	PUNCT
ejpam-1314	155	4	k=1	k=1	PROPN
ejpam-1314	155	5	lim	lim	PROPN
ejpam-1314	155	6	p→∞	p→∞	PROPN
ejpam-1314	155	7	�	�	PROPN
ejpam-1314	155	8	p−1	p−1	PROPN
ejpam-1314	155	9	∑	∑	PROPN
ejpam-1314	155	10	n	n	PROPN
ejpam-1314	155	11	=	=	NOUN
ejpam-1314	155	12	i	i	PROPN
ejpam-1314	155	13	42	42	NUM
ejpam-1314	155	14	r	r	NOUN
ejpam-1314	155	15	ak+nr	ak+nr	NOUN
ejpam-1314	155	16	n	n	PROPN
ejpam-1314	155	17	∑	∑	PUNCT
ejpam-1314	155	18	s=0	s=0	PROPN
ejpam-1314	155	19	ϕs	ϕs	INTJ
ejpam-1314	155	20	,	,	PUNCT
ejpam-1314	155	21	r	r	NOUN
ejpam-1314	155	22	,	,	PUNCT
ejpam-1314	155	23	k(x	k(x	PROPN
ejpam-1314	155	24	)	)	PUNCT
ejpam-1314	156	1	−4r	−4r	VERB
ejpam-1314	156	2	ak+ir	ak+ir	PROPN
ejpam-1314	156	3	i−1	i−1	PROPN
ejpam-1314	156	4	∑	∑	PUNCT
ejpam-1314	156	5	s=0	s=0	PROPN
ejpam-1314	156	6	ϕs	ϕs	INTJ
ejpam-1314	156	7	,	,	PUNCT
ejpam-1314	156	8	r	r	NOUN
ejpam-1314	156	9	,	,	PUNCT
ejpam-1314	156	10	k(x	k(x	PROPN
ejpam-1314	156	11	)	)	PUNCT
ejpam-1314	156	12	+4r	+4r	PROPN
ejpam-1314	157	1	ak+pr	ak+pr	PROPN
ejpam-1314	157	2	p	p	X
ejpam-1314	157	3	∑	∑	PROPN
ejpam-1314	157	4	s=0	s=0	PROPN
ejpam-1314	157	5	ϕs	ϕs	INTJ
ejpam-1314	157	6	,	,	PUNCT
ejpam-1314	157	7	r	r	NOUN
ejpam-1314	157	8	,	,	PUNCT
ejpam-1314	157	9	k(x	k(x	PROPN
ejpam-1314	157	10	)	)	PUNCT
ejpam-1314	157	11	�	�	PROPN
ejpam-1314	157	12	=	=	PUNCT
ejpam-1314	157	13	r	r	NOUN
ejpam-1314	157	14	∑	∑	PUNCT
ejpam-1314	157	15	k=1	k=1	PROPN
ejpam-1314	157	16	∞	∞	NUM
ejpam-1314	157	17	∑	∑	PUNCT
ejpam-1314	157	18	n	n	CCONJ
ejpam-1314	157	19	=	=	NOUN
ejpam-1314	157	20	i	i	NOUN
ejpam-1314	157	21	42	42	NUM
ejpam-1314	157	22	r	r	NOUN
ejpam-1314	157	23	ak+nrψn	ak+nrψn	PROPN
ejpam-1314	157	24	,	,	PUNCT
ejpam-1314	157	25	r	r	NOUN
ejpam-1314	157	26	,	,	PUNCT
ejpam-1314	157	27	k(x)−4r	k(x)−4r	PROPN
ejpam-1314	157	28	ak+irψi−1,r	ak+irψi−1,r	PROPN
ejpam-1314	157	29	,	,	PUNCT
ejpam-1314	157	30	k(x	k(x	PROPN
ejpam-1314	157	31	)	)	PUNCT
ejpam-1314	157	32	!	!	PUNCT
ejpam-1314	158	1	=	=	PUNCT
ejpam-1314	158	2	r	r	X
ejpam-1314	158	3	∑	∑	PUNCT
ejpam-1314	158	4	k=1	k=1	PROPN
ejpam-1314	158	5	∞	∞	NUM
ejpam-1314	158	6	∑	∑	PUNCT
ejpam-1314	158	7	n	n	CCONJ
ejpam-1314	158	8	=	=	NOUN
ejpam-1314	158	9	i	i	PROPN
ejpam-1314	158	10	42	42	NUM
ejpam-1314	158	11	r	r	NOUN
ejpam-1314	158	12	ak+nr	ak+nr	PROPN
ejpam-1314	158	13	�	�	PROPN
ejpam-1314	158	14	ψn	ψn	NOUN
ejpam-1314	158	15	,	,	PUNCT
ejpam-1314	158	16	r	r	PROPN
ejpam-1314	158	17	,	,	PUNCT
ejpam-1314	158	18	k(x)−ψi−1,r	k(x)−ψi−1,r	PROPN
ejpam-1314	158	19	,	,	PUNCT
ejpam-1314	158	20	k(x	k(x	PROPN
ejpam-1314	158	21	)	)	PUNCT
ejpam-1314	158	22	�	�	PROPN
ejpam-1314	158	23	,	,	PUNCT
ejpam-1314	158	24	where	where	SCONJ
ejpam-1314	158	25	ψn	ψn	X
ejpam-1314	158	26	,	,	PUNCT
ejpam-1314	158	27	r	r	NOUN
ejpam-1314	158	28	,	,	PUNCT
ejpam-1314	158	29	k(x	k(x	PROPN
ejpam-1314	158	30	)	)	PUNCT
ejpam-1314	158	31	are	be	AUX
ejpam-1314	158	32	defined	define	VERB
ejpam-1314	158	33	as	as	ADP
ejpam-1314	158	34	above	above	ADV
ejpam-1314	158	35	.	.	PUNCT
ejpam-1314	159	1	so	so	ADV
ejpam-1314	159	2	,	,	PUNCT
ejpam-1314	159	3	we	we	PRON
ejpam-1314	159	4	have	have	VERB
ejpam-1314	159	5	∫	∫	PROPN
ejpam-1314	159	6	π/	π/	PROPN
ejpam-1314	159	7	`	`	PUNCT
ejpam-1314	159	8	π/(m+1	π/(m+1	PROPN
ejpam-1314	159	9	)	)	PUNCT
ejpam-1314	159	10	|h2(x)|d	|h2(x)|d	NOUN
ejpam-1314	160	1	x	x	X
ejpam-1314	160	2	≤cr	≤cr	PROPN
ejpam-1314	160	3	r	r	NOUN
ejpam-1314	160	4	∑	∑	PUNCT
ejpam-1314	160	5	k=1	k=1	VERB
ejpam-1314	160	6	m	m	VERB
ejpam-1314	160	7	∑	∑	PUNCT
ejpam-1314	160	8	i=	i=	PROPN
ejpam-1314	160	9	`	`	PUNCT
ejpam-1314	160	10	∫	∫	PROPN
ejpam-1314	160	11	π	π	X
ejpam-1314	160	12	/	/	SYM
ejpam-1314	160	13	i	i	PRON
ejpam-1314	160	14	π/(i+1	π/(i+1	ADJ
ejpam-1314	160	15	)	)	PUNCT
ejpam-1314	160	16	∞	∞	PROPN
ejpam-1314	160	17	∑	∑	PUNCT
ejpam-1314	160	18	n	n	X
ejpam-1314	160	19	=	=	NOUN
ejpam-1314	160	20	i	i	NOUN
ejpam-1314	160	21	|42	|42	NOUN
ejpam-1314	160	22	r	r	NOUN
ejpam-1314	161	1	ak+nr	ak+nr	NOUN
ejpam-1314	162	1	|	|	ADV
ejpam-1314	163	1	d	d	NOUN
ejpam-1314	163	2	x	x	SYM
ejpam-1314	164	1	x2	x2	INTJ
ejpam-1314	164	2	≤cr	≤cr	PROPN
ejpam-1314	164	3	r	r	NOUN
ejpam-1314	164	4	∑	∑	PUNCT
ejpam-1314	164	5	k=1	k=1	VERB
ejpam-1314	164	6	m	m	VERB
ejpam-1314	164	7	∑	∑	PUNCT
ejpam-1314	164	8	i=	i=	PROPN
ejpam-1314	164	9	`	`	PUNCT
ejpam-1314	164	10	∞	∞	PROPN
ejpam-1314	164	11	∑	∑	PUNCT
ejpam-1314	164	12	n	n	PROPN
ejpam-1314	164	13	=	=	NOUN
ejpam-1314	164	14	i	i	NOUN
ejpam-1314	164	15	|42	|42	NOUN
ejpam-1314	164	16	r	r	NOUN
ejpam-1314	164	17	ak+nr	ak+nr	NOUN
ejpam-1314	164	18	|	|	NOUN
ejpam-1314	164	19	.	.	PUNCT
ejpam-1314	165	1	(	(	PUNCT
ejpam-1314	165	2	15	15	NUM
ejpam-1314	165	3	)	)	PUNCT
ejpam-1314	165	4	references	reference	NOUN
ejpam-1314	165	5	459	459	NUM
ejpam-1314	166	1	it	it	PRON
ejpam-1314	166	2	is	be	AUX
ejpam-1314	166	3	clear	clear	ADJ
ejpam-1314	166	4	that	that	SCONJ
ejpam-1314	166	5	for	for	ADP
ejpam-1314	166	6	i	i	PRON
ejpam-1314	166	7	≥	≥	VERB
ejpam-1314	166	8	r	r	NOUN
ejpam-1314	166	9	∫	∫	PROPN
ejpam-1314	166	10	π	π	X
ejpam-1314	166	11	/	/	SYM
ejpam-1314	166	12	i	i	PRON
ejpam-1314	166	13	π/(i+1	π/(i+1	ADJ
ejpam-1314	166	14	)	)	PUNCT
ejpam-1314	166	15	�	�	PROPN
ejpam-1314	166	16	�	�	PROPN
ejpam-1314	166	17	�	�	PROPN
ejpam-1314	166	18	�	�	PROPN
ejpam-1314	166	19	cos(2k−	cos(2k−	PROPN
ejpam-1314	166	20	r	r	NOUN
ejpam-1314	166	21	)	)	PUNCT
ejpam-1314	166	22	x	x	SYM
ejpam-1314	166	23	2	2	NUM
ejpam-1314	166	24	2	2	NUM
ejpam-1314	166	25	sin	sin	NOUN
ejpam-1314	166	26	�	�	PROPN
ejpam-1314	166	27	r	r	NOUN
ejpam-1314	166	28	x	x	SYM
ejpam-1314	166	29	2	2	NUM
ejpam-1314	166	30	�	�	PROPN
ejpam-1314	166	31	�	�	PROPN
ejpam-1314	166	32	�	�	PROPN
ejpam-1314	166	33	�	�	PROPN
ejpam-1314	166	34	�	�	PROPN
ejpam-1314	166	35	d	d	NOUN
ejpam-1314	166	36	x	x	SYM
ejpam-1314	166	37	=	=	SYM
ejpam-1314	166	38	1	1	NUM
ejpam-1314	166	39	2	2	NUM
ejpam-1314	166	40	∫	∫	NOUN
ejpam-1314	166	41	π	π	X
ejpam-1314	166	42	/	/	SYM
ejpam-1314	166	43	i	i	PRON
ejpam-1314	166	44	π/(i+1	π/(i+1	ADJ
ejpam-1314	166	45	)	)	PUNCT
ejpam-1314	166	46	�	�	PROPN
ejpam-1314	166	47	�	�	PROPN
ejpam-1314	166	48	�	�	PROPN
ejpam-1314	166	49	�	�	PROPN
ejpam-1314	166	50	cos	cos	PROPN
ejpam-1314	166	51	kx	kx	PROPN
ejpam-1314	166	52	cot	cot	PROPN
ejpam-1314	166	53	�	�	PROPN
ejpam-1314	166	54	r	r	NOUN
ejpam-1314	166	55	x	x	SYM
ejpam-1314	166	56	2	2	NUM
ejpam-1314	166	57	�	�	PROPN
ejpam-1314	166	58	+	+	CCONJ
ejpam-1314	166	59	sin	sin	PROPN
ejpam-1314	167	1	kx	kx	PROPN
ejpam-1314	167	2	�	�	PROPN
ejpam-1314	167	3	�	�	PROPN
ejpam-1314	167	4	�	�	PROPN
ejpam-1314	167	5	�	�	PROPN
ejpam-1314	167	6	d	d	NOUN
ejpam-1314	167	7	x	x	SYM
ejpam-1314	167	8	≤	≤	NUM
ejpam-1314	167	9	1	1	NUM
ejpam-1314	167	10	2	2	NUM
ejpam-1314	167	11	∫	∫	NOUN
ejpam-1314	167	12	π	π	X
ejpam-1314	167	13	/	/	SYM
ejpam-1314	167	14	i	i	PRON
ejpam-1314	167	15	π/(i+1	π/(i+1	ADJ
ejpam-1314	167	16	)	)	PUNCT
ejpam-1314	167	17	cot	cot	NOUN
ejpam-1314	167	18	�	�	PROPN
ejpam-1314	167	19	r	r	NOUN
ejpam-1314	167	20	x	x	SYM
ejpam-1314	167	21	2	2	NUM
ejpam-1314	167	22	�	�	NOUN
ejpam-1314	167	23	d	d	NOUN
ejpam-1314	167	24	x	x	PROPN
ejpam-1314	167	25	+	+	NOUN
ejpam-1314	167	26	1	1	NUM
ejpam-1314	167	27	2	2	NUM
ejpam-1314	167	28	∫	∫	NOUN
ejpam-1314	167	29	π	π	X
ejpam-1314	167	30	/	/	SYM
ejpam-1314	167	31	i	i	PRON
ejpam-1314	167	32	π/(i+1	π/(i+1	ADJ
ejpam-1314	167	33	)	)	PUNCT
ejpam-1314	167	34	sin	sin	NOUN
ejpam-1314	167	35	kxd	kxd	NOUN
ejpam-1314	167	36	x	x	SYM
ejpam-1314	167	37	≤	≤	NUM
ejpam-1314	167	38	1	1	NUM
ejpam-1314	167	39	k	k	NOUN
ejpam-1314	167	40	ln	ln	ADJ
ejpam-1314	167	41	sin	sin	NOUN
ejpam-1314	167	42	rπ	rπ	NOUN
ejpam-1314	167	43	2i	2i	NUM
ejpam-1314	167	44	sin	sin	VERB
ejpam-1314	167	45	rπ	rπ	NOUN
ejpam-1314	167	46	2(i+1	2(i+1	NOUN
ejpam-1314	167	47	)	)	PUNCT
ejpam-1314	168	1	+	+	CCONJ
ejpam-1314	168	2	cos	cos	ADP
ejpam-1314	168	3	kπ	kπ	PROPN
ejpam-1314	168	4	2i(i+	2i(i+	PROPN
ejpam-1314	168	5	1	1	NUM
ejpam-1314	168	6	)	)	PUNCT
ejpam-1314	168	7	cos	cos	ADP
ejpam-1314	168	8	kπ(2i+	kπ(2i+	NOUN
ejpam-1314	168	9	1	1	NUM
ejpam-1314	168	10	)	)	PUNCT
ejpam-1314	168	11	2i(i+	2i(i+	NUM
ejpam-1314	168	12	1	1	NUM
ejpam-1314	168	13	)	)	PUNCT
ejpam-1314	168	14	!	!	PUNCT
ejpam-1314	169	1	=	=	PUNCT
ejpam-1314	169	2	di	di	PROPN
ejpam-1314	169	3	,	,	PUNCT
ejpam-1314	169	4	r	r	NOUN
ejpam-1314	169	5	,	,	PUNCT
ejpam-1314	169	6	k	k	PROPN
ejpam-1314	169	7	k	k	PROPN
ejpam-1314	169	8	.	.	PUNCT
ejpam-1314	170	1	(	(	PUNCT
ejpam-1314	170	2	16	16	NUM
ejpam-1314	170	3	)	)	PUNCT
ejpam-1314	170	4	therefore	therefore	ADV
ejpam-1314	170	5	from	from	ADP
ejpam-1314	170	6	(	(	PUNCT
ejpam-1314	170	7	16	16	NUM
ejpam-1314	170	8	)	)	PUNCT
ejpam-1314	170	9	we	we	PRON
ejpam-1314	170	10	have	have	VERB
ejpam-1314	170	11	∫	∫	PROPN
ejpam-1314	170	12	π/	π/	PROPN
ejpam-1314	170	13	`	`	PUNCT
ejpam-1314	170	14	π/(m+1	π/(m+1	PROPN
ejpam-1314	170	15	)	)	PUNCT
ejpam-1314	170	16	|h0(x)|d	|h0(x)|d	NOUN
ejpam-1314	170	17	x	x	PUNCT
ejpam-1314	170	18	≤	≤	NUM
ejpam-1314	170	19	r	r	NOUN
ejpam-1314	170	20	∑	∑	PUNCT
ejpam-1314	170	21	k=1	k=1	ADJ
ejpam-1314	170	22	m	m	VERB
ejpam-1314	170	23	∑	∑	PUNCT
ejpam-1314	170	24	i=	i=	PROPN
ejpam-1314	170	25	`	`	PUNCT
ejpam-1314	170	26	|ak+ir	|ak+ir	ADJ
ejpam-1314	171	1	|	|	ADV
ejpam-1314	171	2	∫	∫	PROPN
ejpam-1314	172	1	π	π	X
ejpam-1314	172	2	/	/	SYM
ejpam-1314	172	3	i	i	PRON
ejpam-1314	172	4	π/(i+1	π/(i+1	ADJ
ejpam-1314	172	5	)	)	PUNCT
ejpam-1314	172	6	�	�	PROPN
ejpam-1314	172	7	�	�	PROPN
ejpam-1314	172	8	�	�	PROPN
ejpam-1314	172	9	�	�	PROPN
ejpam-1314	172	10	cos(2k−	cos(2k−	PROPN
ejpam-1314	172	11	r	r	NOUN
ejpam-1314	172	12	)	)	PUNCT
ejpam-1314	172	13	x	x	SYM
ejpam-1314	172	14	2	2	NUM
ejpam-1314	172	15	2sin	2sin	NUM
ejpam-1314	172	16	�	�	PROPN
ejpam-1314	172	17	r	r	NOUN
ejpam-1314	172	18	x	x	SYM
ejpam-1314	172	19	2	2	NUM
ejpam-1314	172	20	�	�	PROPN
ejpam-1314	172	21	�	�	PROPN
ejpam-1314	172	22	�	�	PROPN
ejpam-1314	172	23	�	�	PROPN
ejpam-1314	172	24	�	�	PROPN
ejpam-1314	172	25	d	d	NOUN
ejpam-1314	172	26	x	x	SYM
ejpam-1314	172	27	≤	≤	NUM
ejpam-1314	172	28	r	r	NOUN
ejpam-1314	172	29	∑	∑	PUNCT
ejpam-1314	172	30	k=1	k=1	ADJ
ejpam-1314	172	31	m	m	VERB
ejpam-1314	172	32	∑	∑	PUNCT
ejpam-1314	172	33	i=	i=	PROPN
ejpam-1314	172	34	`	`	PUNCT
ejpam-1314	172	35	di	di	PROPN
ejpam-1314	172	36	,	,	PUNCT
ejpam-1314	172	37	r	r	PROPN
ejpam-1314	172	38	,	,	PUNCT
ejpam-1314	172	39	k	k	PROPN
ejpam-1314	172	40	k	k	X
ejpam-1314	172	41	|ak+ir	|ak+ir	VERB
ejpam-1314	172	42	|	|	ADV
ejpam-1314	172	43	.	.	PUNCT
ejpam-1314	173	1	(	(	PUNCT
ejpam-1314	173	2	17	17	NUM
ejpam-1314	173	3	)	)	PUNCT
ejpam-1314	173	4	finally	finally	ADV
ejpam-1314	173	5	,	,	PUNCT
ejpam-1314	173	6	the	the	DET
ejpam-1314	173	7	proof	proof	NOUN
ejpam-1314	173	8	of	of	ADP
ejpam-1314	173	9	the	the	DET
ejpam-1314	173	10	theorem	theorem	NOUN
ejpam-1314	173	11	is	be	AUX
ejpam-1314	173	12	an	an	DET
ejpam-1314	173	13	immediate	immediate	ADJ
ejpam-1314	173	14	result	result	NOUN
ejpam-1314	173	15	of	of	ADP
ejpam-1314	173	16	relations	relation	NOUN
ejpam-1314	173	17	(	(	PUNCT
ejpam-1314	173	18	12	12	NUM
ejpam-1314	173	19	)	)	PUNCT
ejpam-1314	173	20	,	,	PUNCT
ejpam-1314	173	21	(	(	PUNCT
ejpam-1314	173	22	14	14	NUM
ejpam-1314	173	23	)	)	PUNCT
ejpam-1314	173	24	,	,	PUNCT
ejpam-1314	173	25	(	(	PUNCT
ejpam-1314	173	26	15	15	NUM
ejpam-1314	173	27	)	)	PUNCT
ejpam-1314	173	28	and	and	CCONJ
ejpam-1314	173	29	(	(	PUNCT
ejpam-1314	173	30	17	17	NUM
ejpam-1314	173	31	)	)	PUNCT
ejpam-1314	173	32	.	.	PUNCT
ejpam-1314	174	1	references	reference	NOUN
ejpam-1314	174	2	[	[	X
ejpam-1314	174	3	1	1	NUM
ejpam-1314	174	4	]	]	PUNCT
ejpam-1314	174	5	a.	a.	NOUN
ejpam-1314	174	6	n.	n.	PROPN
ejpam-1314	174	7	kolmogorov	kolmogorov	PROPN
ejpam-1314	174	8	.	.	PUNCT
ejpam-1314	175	1	sur	sur	PROPN
ejpam-1314	175	2	l’ordre	l’ordre	PROPN
ejpam-1314	175	3	de	de	PROPN
ejpam-1314	175	4	grandeur	grandeur	PROPN
ejpam-1314	175	5	des	des	PROPN
ejpam-1314	175	6	coefficients	coefficients	PROPN
ejpam-1314	175	7	de	de	X
ejpam-1314	175	8	la	la	X
ejpam-1314	175	9	série	série	PROPN
ejpam-1314	175	10	de	de	PROPN
ejpam-1314	175	11	fourierlebesgue	fourierlebesgue	PROPN
ejpam-1314	175	12	.	.	PUNCT
ejpam-1314	176	1	bulletin	bulletin	PROPN
ejpam-1314	176	2	de	de	PROPN
ejpam-1314	176	3	l’academie	l’academie	VERB
ejpam-1314	176	4	polonaise	polonaise	NOUN
ejpam-1314	176	5	,	,	PUNCT
ejpam-1314	176	6	83–86	83–86	NUM
ejpam-1314	176	7	,	,	PUNCT
ejpam-1314	176	8	1923	1923	NUM
ejpam-1314	176	9	.	.	PUNCT
ejpam-1314	177	1	[	[	X
ejpam-1314	177	2	2	2	NUM
ejpam-1314	177	3	]	]	X
ejpam-1314	177	4	xh	xh	PROPN
ejpam-1314	177	5	.	.	PUNCT
ejpam-1314	178	1	z.	z.	PROPN
ejpam-1314	178	2	krasniqi	krasniqi	PROPN
ejpam-1314	178	3	.	.	PUNCT
ejpam-1314	179	1	integrability	integrability	NOUN
ejpam-1314	179	2	of	of	ADP
ejpam-1314	179	3	cosine	cosine	NOUN
ejpam-1314	179	4	trigonometric	trigonometric	PROPN
ejpam-1314	179	5	series	series	NOUN
ejpam-1314	179	6	with	with	ADP
ejpam-1314	179	7	coefficients	coefficient	NOUN
ejpam-1314	179	8	of	of	ADP
ejpam-1314	179	9	bounded	bounded	ADJ
ejpam-1314	179	10	variation	variation	NOUN
ejpam-1314	179	11	of	of	ADP
ejpam-1314	179	12	order	order	NOUN
ejpam-1314	179	13	p.	p.	NOUN
ejpam-1314	179	14	applied	apply	VERB
ejpam-1314	179	15	mathematics	mathematics	PROPN
ejpam-1314	179	16	e	e	NOUN
ejpam-1314	179	17	-	-	NOUN
ejpam-1314	179	18	notes	note	NOUN
ejpam-1314	179	19	,	,	PUNCT
ejpam-1314	179	20	11:61–66	11:61–66	NUM
ejpam-1314	179	21	,	,	PUNCT
ejpam-1314	179	22	2011	2011	NUM
ejpam-1314	179	23	.	.	PUNCT
ejpam-1314	180	1	[	[	X
ejpam-1314	180	2	3	3	X
ejpam-1314	180	3	]	]	X
ejpam-1314	180	4	xh	xh	PROPN
ejpam-1314	180	5	.	.	PUNCT
ejpam-1314	181	1	z.	z.	PROPN
ejpam-1314	181	2	krasniqi	krasniqi	PROPN
ejpam-1314	181	3	.	.	PUNCT
ejpam-1314	182	1	on	on	ADP
ejpam-1314	182	2	the	the	DET
ejpam-1314	182	3	first	first	ADJ
ejpam-1314	182	4	derivative	derivative	NOUN
ejpam-1314	182	5	of	of	ADP
ejpam-1314	182	6	the	the	DET
ejpam-1314	182	7	sums	sum	NOUN
ejpam-1314	182	8	of	of	ADP
ejpam-1314	182	9	trigonometric	trigonometric	ADJ
ejpam-1314	182	10	series	series	NOUN
ejpam-1314	182	11	with	with	ADP
ejpam-1314	182	12	quasiconvex	quasiconvex	NOUN
ejpam-1314	182	13	coefficients	coefficient	NOUN
ejpam-1314	182	14	of	of	ADP
ejpam-1314	182	15	higher	high	ADJ
ejpam-1314	182	16	order	order	NOUN
ejpam-1314	182	17	.	.	PUNCT
ejpam-1314	183	1	acta	acta	PROPN
ejpam-1314	183	2	et	et	PROPN
ejpam-1314	183	3	commentationes	commentatione	VERB
ejpam-1314	183	4	universitatis	universitatis	PROPN
ejpam-1314	183	5	tartuensis	tartuensis	PROPN
ejpam-1314	183	6	de	de	X
ejpam-1314	183	7	mathematica	mathematica	PROPN
ejpam-1314	183	8	,	,	PUNCT
ejpam-1314	183	9	14:53–63	14:53–63	NUM
ejpam-1314	183	10	,	,	PUNCT
ejpam-1314	183	11	2010	2010	NUM
ejpam-1314	183	12	.	.	PUNCT
ejpam-1314	184	1	[	[	X
ejpam-1314	184	2	4	4	X
ejpam-1314	184	3	]	]	X
ejpam-1314	184	4	xh	xh	PROPN
ejpam-1314	184	5	.	.	PUNCT
ejpam-1314	185	1	z.	z.	PROPN
ejpam-1314	185	2	krasniqi	krasniqi	PROPN
ejpam-1314	185	3	.	.	PUNCT
ejpam-1314	186	1	integrability	integrability	NOUN
ejpam-1314	186	2	of	of	ADP
ejpam-1314	186	3	double	double	ADJ
ejpam-1314	186	4	cosine	cosine	NOUN
ejpam-1314	186	5	trigonometric	trigonometric	NOUN
ejpam-1314	186	6	series	series	NOUN
ejpam-1314	186	7	with	with	ADP
ejpam-1314	186	8	coefficients	coefficient	NOUN
ejpam-1314	186	9	of	of	ADP
ejpam-1314	186	10	bounded	bounded	ADJ
ejpam-1314	186	11	variation	variation	NOUN
ejpam-1314	186	12	of	of	ADP
ejpam-1314	186	13	second	second	ADJ
ejpam-1314	186	14	order	order	NOUN
ejpam-1314	186	15	.	.	PUNCT
ejpam-1314	187	1	commentationes	commentatione	NOUN
ejpam-1314	187	2	mathematicae	mathematicae	PROPN
ejpam-1314	187	3	,	,	PUNCT
ejpam-1314	187	4	51:125	51:125	NUM
ejpam-1314	187	5	-	-	SYM
ejpam-1314	187	6	139	139	NUM
ejpam-1314	187	7	,	,	PUNCT
ejpam-1314	187	8	2011	2011	NUM
ejpam-1314	187	9	.	.	PUNCT
ejpam-1314	188	1	[	[	X
ejpam-1314	188	2	5	5	NUM
ejpam-1314	188	3	]	]	X
ejpam-1314	188	4	b.	b.	PROPN
ejpam-1314	188	5	v.	v.	ADP
ejpam-1314	188	6	simonov	simonov	PROPN
ejpam-1314	188	7	.	.	PUNCT
ejpam-1314	189	1	trigonometric	trigonometric	PROPN
ejpam-1314	189	2	series	series	NOUN
ejpam-1314	189	3	in	in	ADP
ejpam-1314	189	4	the	the	DET
ejpam-1314	189	5	orlicz	orlicz	NOUN
ejpam-1314	189	6	–	–	PUNCT
ejpam-1314	189	7	lorentz	lorentz	NOUN
ejpam-1314	189	8	spaces	space	NOUN
ejpam-1314	189	9	.	.	PUNCT
ejpam-1314	190	1	izvestiya	izvestiya	PROPN
ejpam-1314	190	2	vysshikh	vysshikh	PROPN
ejpam-1314	190	3	uchebnykh	uchebnykh	ADJ
ejpam-1314	190	4	zavedenii	zavedenii	NOUN
ejpam-1314	190	5	.	.	PUNCT
ejpam-1314	191	1	matematika	matematika	PROPN
ejpam-1314	191	2	,	,	PUNCT
ejpam-1314	191	3	51:61–74	51:61–74	NUM
ejpam-1314	191	4	,	,	PUNCT
ejpam-1314	191	5	2007	2007	NUM
ejpam-1314	191	6	.	.	PUNCT
ejpam-1314	192	1	[	[	X
ejpam-1314	192	2	6	6	X
ejpam-1314	192	3	]	]	PUNCT
ejpam-1314	192	4	s.	s.	PROPN
ejpam-1314	192	5	a.	a.	PROPN
ejpam-1314	192	6	telyakovskĭı	telyakovskĭı	PROPN
ejpam-1314	192	7	.	.	PUNCT
ejpam-1314	193	1	localizing	localize	VERB
ejpam-1314	193	2	the	the	DET
ejpam-1314	193	3	conditions	condition	NOUN
ejpam-1314	193	4	of	of	ADP
ejpam-1314	193	5	integrability	integrability	NOUN
ejpam-1314	193	6	of	of	ADP
ejpam-1314	193	7	trigonometric	trigonometric	ADJ
ejpam-1314	193	8	series	series	NOUN
ejpam-1314	193	9	(	(	PUNCT
ejpam-1314	193	10	russian	russian	PROPN
ejpam-1314	193	11	)	)	PUNCT
ejpam-1314	193	12	.	.	PUNCT
ejpam-1314	194	1	theory	theory	NOUN
ejpam-1314	194	2	of	of	ADP
ejpam-1314	194	3	functions	function	NOUN
ejpam-1314	194	4	and	and	CCONJ
ejpam-1314	194	5	differential	differential	ADJ
ejpam-1314	194	6	equations	equation	NOUN
ejpam-1314	194	7	,	,	PUNCT
ejpam-1314	194	8	collection	collection	NOUN
ejpam-1314	194	9	of	of	ADP
ejpam-1314	194	10	articles	article	NOUN
ejpam-1314	194	11	.	.	PUNCT
ejpam-1314	195	1	in	in	ADP
ejpam-1314	195	2	honor	honor	NOUN
ejpam-1314	195	3	of	of	ADP
ejpam-1314	195	4	the	the	DET
ejpam-1314	195	5	ninetieth	ninetieth	ADJ
ejpam-1314	195	6	birthday	birthday	NOUN
ejpam-1314	195	7	of	of	ADP
ejpam-1314	195	8	academician	academician	PROPN
ejpam-1314	195	9	s.	s.	PROPN
ejpam-1314	195	10	m.	m.	PROPN
ejpam-1314	195	11	nikolskii(russian	nikolskii(russian	PROPN
ejpam-1314	195	12	)	)	PUNCT
ejpam-1314	195	13	,	,	PUNCT
ejpam-1314	195	14	trudy	trudy	PROPN
ejpam-1314	195	15	matematicheskogo	matematicheskogo	PROPN
ejpam-1314	195	16	instituta	instituta	ADV
ejpam-1314	195	17	imeni	imeni	PROPN
ejpam-1314	195	18	v.	v.	ADP
ejpam-1314	195	19	a.	a.	PROPN
ejpam-1314	195	20	steklova	steklova	PROPN
ejpam-1314	195	21	,	,	PUNCT
ejpam-1314	195	22	210:264–273	210:264–273	NUM
ejpam-1314	195	23	,	,	PUNCT
ejpam-1314	195	24	1995	1995	NUM
ejpam-1314	195	25	.	.	PUNCT