id	sid	tid	token	lemma	pos
ap-1368	1	1	wykresx.eps	wykresx.eps	X
ap-1368	1	2	acta	acta	PROPN
ap-1368	1	3	polytechnica	polytechnica	PROPN
ap-1368	1	4	vol	vol	NOUN
ap-1368	1	5	.	.	PUNCT
ap-1368	2	1	51	51	NUM
ap-1368	2	2	no	no	INTJ
ap-1368	2	3	.	.	PUNCT
ap-1368	3	1	1/2011	1/2011	NUM
ap-1368	3	2	some	some	DET
ap-1368	3	3	formulas	formula	NOUN
ap-1368	3	4	for	for	ADP
ap-1368	3	5	legendre	legendre	PROPN
ap-1368	3	6	functions	function	NOUN
ap-1368	3	7	induced	induce	VERB
ap-1368	3	8	by	by	ADP
ap-1368	3	9	the	the	DET
ap-1368	3	10	poisson	poisson	PROPN
ap-1368	3	11	transform	transform	VERB
ap-1368	3	12	i.	i.	PROPN
ap-1368	3	13	a.	a.	PROPN
ap-1368	3	14	shilin	shilin	PROPN
ap-1368	3	15	,	,	PUNCT
ap-1368	3	16	a.	a.	PROPN
ap-1368	3	17	i.	i.	PROPN
ap-1368	3	18	nizhnikov	nizhnikov	PROPN
ap-1368	3	19	abstract	abstract	PROPN
ap-1368	3	20	using	use	VERB
ap-1368	3	21	the	the	DET
ap-1368	3	22	poisson	poisson	NOUN
ap-1368	3	23	transform	transform	NOUN
ap-1368	3	24	,	,	PUNCT
ap-1368	3	25	which	which	PRON
ap-1368	3	26	maps	map	VERB
ap-1368	3	27	any	any	DET
ap-1368	3	28	homogeneous	homogeneous	ADJ
ap-1368	3	29	and	and	CCONJ
ap-1368	3	30	infinitely	infinitely	ADV
ap-1368	3	31	differentiable	differentiable	ADJ
ap-1368	3	32	function	function	NOUN
ap-1368	3	33	on	on	ADP
ap-1368	3	34	a	a	DET
ap-1368	3	35	cone	cone	NOUN
ap-1368	3	36	into	into	ADP
ap-1368	3	37	a	a	DET
ap-1368	3	38	corresponding	correspond	VERB
ap-1368	3	39	function	function	NOUN
ap-1368	3	40	on	on	ADP
ap-1368	3	41	a	a	DET
ap-1368	3	42	hyperboloid	hyperboloid	NOUN
ap-1368	3	43	,	,	PUNCT
ap-1368	3	44	we	we	PRON
ap-1368	3	45	derive	derive	VERB
ap-1368	3	46	some	some	DET
ap-1368	3	47	integral	integral	ADJ
ap-1368	3	48	representations	representation	NOUN
ap-1368	3	49	of	of	ADP
ap-1368	3	50	the	the	DET
ap-1368	3	51	legendre	legendre	PROPN
ap-1368	3	52	functions	function	NOUN
ap-1368	3	53	.	.	PUNCT
ap-1368	4	1	keywords	keyword	NOUN
ap-1368	4	2	:	:	PUNCT
ap-1368	4	3	legendre	legendre	NOUN
ap-1368	4	4	functions	function	NOUN
ap-1368	4	5	,	,	PUNCT
ap-1368	4	6	lorentz	lorentz	PROPN
ap-1368	4	7	group	group	NOUN
ap-1368	4	8	,	,	PUNCT
ap-1368	4	9	poisson	poisson	PROPN
ap-1368	4	10	transform	transform	NOUN
ap-1368	4	11	.	.	PUNCT
ap-1368	4	12	1	1	NUM
ap-1368	4	13	introduction	introduction	NOUN
ap-1368	4	14	let	let	VERB
ap-1368	4	15	us	we	PRON
ap-1368	4	16	assume	assume	VERB
ap-1368	4	17	that	that	SCONJ
ap-1368	4	18	the	the	DET
ap-1368	4	19	linear	linear	ADJ
ap-1368	4	20	space	space	NOUN
ap-1368	4	21	r	r	NOUN
ap-1368	4	22	n+1	n+1	PROPN
ap-1368	4	23	is	be	AUX
ap-1368	4	24	endowed	endow	VERB
ap-1368	4	25	with	with	ADP
ap-1368	4	26	the	the	DET
ap-1368	4	27	quadratic	quadratic	ADJ
ap-1368	4	28	form	form	NOUN
ap-1368	4	29	q(x	q(x	NOUN
ap-1368	4	30	)	)	PUNCT
ap-1368	4	31	:	:	PUNCT
ap-1368	5	1	=	=	SYM
ap-1368	5	2	x20	x20	NUM
ap-1368	5	3	−	−	PROPN
ap-1368	6	1	x21	x21	PROPN
ap-1368	6	2	−	−	PROPN
ap-1368	6	3	.	.	PUNCT
ap-1368	6	4	.	.	PUNCT
ap-1368	7	1	.−	.−	PUNCT
ap-1368	8	1	x2n	x2n	PROPN
ap-1368	8	2	.	.	PUNCT
ap-1368	9	1	we	we	PRON
ap-1368	9	2	denote	denote	VERB
ap-1368	9	3	the	the	DET
ap-1368	9	4	polar	polar	ADJ
ap-1368	9	5	bilinear	bilinear	NOUN
ap-1368	9	6	form	form	NOUN
ap-1368	9	7	for	for	ADP
ap-1368	9	8	q	q	PUNCT
ap-1368	9	9	by	by	ADP
ap-1368	9	10	q̂.	q̂.	NOUN
ap-1368	9	11	the	the	DET
ap-1368	9	12	lorentz	lorentz	PROPN
ap-1368	9	13	group	group	PROPN
ap-1368	9	14	so(n	so(n	PROPN
ap-1368	9	15	,	,	PUNCT
ap-1368	9	16	1	1	NUM
ap-1368	9	17	)	)	PUNCT
ap-1368	9	18	preserves	preserve	VERB
ap-1368	9	19	this	this	DET
ap-1368	9	20	form	form	NOUN
ap-1368	9	21	and	and	CCONJ
ap-1368	9	22	divides	divide	VERB
ap-1368	9	23	r	r	NOUN
ap-1368	9	24	n+1	n+1	PROPN
ap-1368	9	25	into	into	ADP
ap-1368	9	26	orbits	orbit	NOUN
ap-1368	9	27	.	.	PUNCT
ap-1368	10	1	we	we	PRON
ap-1368	10	2	will	will	AUX
ap-1368	10	3	deal	deal	VERB
ap-1368	10	4	with	with	ADP
ap-1368	10	5	two	two	NUM
ap-1368	10	6	kinds	kind	NOUN
ap-1368	10	7	of	of	ADP
ap-1368	10	8	these	these	DET
ap-1368	10	9	orbits	orbit	NOUN
ap-1368	10	10	.	.	PUNCT
ap-1368	11	1	one	one	NUM
ap-1368	11	2	of	of	ADP
ap-1368	11	3	them	they	PRON
ap-1368	11	4	is	be	AUX
ap-1368	11	5	c	c	NOUN
ap-1368	11	6	:	:	PUNCT
ap-1368	11	7	=	=	SYM
ap-1368	11	8	{	{	PUNCT
ap-1368	11	9	x	x	X
ap-1368	11	10	|	|	ADV
ap-1368	11	11	q(x	q(x	NOUN
ap-1368	11	12	)	)	PUNCT
ap-1368	11	13	=	=	PUNCT
ap-1368	11	14	0	0	NUM
ap-1368	11	15	}	}	PUNCT
ap-1368	11	16	;	;	PUNCT
ap-1368	11	17	it	it	PRON
ap-1368	11	18	is	be	AUX
ap-1368	11	19	a	a	DET
ap-1368	11	20	cone	cone	NOUN
ap-1368	11	21	.	.	PUNCT
ap-1368	12	1	the	the	DET
ap-1368	12	2	second	second	ADJ
ap-1368	12	3	kind	kind	NOUN
ap-1368	12	4	of	of	ADP
ap-1368	12	5	orbits	orbit	NOUN
ap-1368	12	6	consist	consist	VERB
ap-1368	12	7	of	of	ADP
ap-1368	12	8	two	two	NUM
ap-1368	12	9	-	-	PUNCT
ap-1368	12	10	sheet	sheet	NOUN
ap-1368	12	11	hyperboloids	hyperboloid	NOUN
ap-1368	12	12	h(r	h(r	NOUN
ap-1368	12	13	)	)	PUNCT
ap-1368	12	14	:	:	PUNCT
ap-1368	13	1	=	=	SYM
ap-1368	13	2	{	{	PUNCT
ap-1368	13	3	x	x	X
ap-1368	13	4	|	|	ADV
ap-1368	13	5	q(x	q(x	NOUN
ap-1368	13	6	)	)	PUNCT
ap-1368	13	7	=	=	PUNCT
ap-1368	13	8	r2	r2	PROPN
ap-1368	13	9	}	}	PUNCT
ap-1368	13	10	for	for	ADP
ap-1368	13	11	any	any	DET
ap-1368	13	12	r	r	NOUN
ap-1368	13	13	>	>	X
ap-1368	13	14	0	0	NUM
ap-1368	13	15	.	.	PUNCT
ap-1368	14	1	the	the	DET
ap-1368	14	2	group	group	PROPN
ap-1368	14	3	so(n	so(n	PROPN
ap-1368	14	4	,	,	PUNCT
ap-1368	14	5	1	1	NUM
ap-1368	14	6	)	)	PUNCT
ap-1368	14	7	has	have	VERB
ap-1368	14	8	2	2	NUM
ap-1368	14	9	connected	connected	ADJ
ap-1368	14	10	components	component	NOUN
ap-1368	14	11	.	.	PUNCT
ap-1368	15	1	one	one	NUM
ap-1368	15	2	of	of	ADP
ap-1368	15	3	them	they	PRON
ap-1368	15	4	contains	contain	VERB
ap-1368	15	5	the	the	DET
ap-1368	15	6	identity	identity	NOUN
ap-1368	15	7	and	and	CCONJ
ap-1368	15	8	will	will	AUX
ap-1368	15	9	be	be	AUX
ap-1368	15	10	under	under	ADP
ap-1368	15	11	our	our	PRON
ap-1368	15	12	consideration	consideration	NOUN
ap-1368	15	13	further	far	ADV
ap-1368	15	14	.	.	PUNCT
ap-1368	16	1	we	we	PRON
ap-1368	16	2	denote	denote	VERB
ap-1368	16	3	this	this	DET
ap-1368	16	4	subgroup	subgroup	NOUN
ap-1368	16	5	by	by	ADP
ap-1368	16	6	symbol	symbol	NOUN
ap-1368	16	7	g.	g.	NOUN
ap-1368	16	8	the	the	DET
ap-1368	16	9	action	action	NOUN
ap-1368	16	10	x	x	SYM
ap-1368	16	11	�	�	PROPN
ap-1368	16	12	−→	−→	ADJ
ap-1368	16	13	g−1x	g−1x	NOUN
ap-1368	16	14	of	of	ADP
ap-1368	16	15	the	the	DET
ap-1368	16	16	group	group	NOUN
ap-1368	16	17	g	g	PROPN
ap-1368	16	18	is	be	AUX
ap-1368	16	19	transitive	transitive	ADJ
ap-1368	16	20	on	on	ADP
ap-1368	16	21	c.	c.	PROPN
ap-1368	16	22	let	let	VERB
ap-1368	16	23	σ	σ	X
ap-1368	16	24	∈	∈	PROPN
ap-1368	16	25	c	c	PROPN
ap-1368	16	26	and	and	CCONJ
ap-1368	16	27	dσ	dσ	PROPN
ap-1368	16	28	be	be	AUX
ap-1368	16	29	a	a	DET
ap-1368	16	30	linear	linear	ADJ
ap-1368	16	31	subspace	subspace	NOUN
ap-1368	16	32	in	in	ADP
ap-1368	16	33	c∞(c	c∞(c	NOUN
ap-1368	16	34	)	)	PUNCT
ap-1368	16	35	consisting	consist	VERB
ap-1368	16	36	of	of	ADP
ap-1368	16	37	σ	σ	PROPN
ap-1368	16	38	-	-	PUNCT
ap-1368	16	39	homogeneous	homogeneous	ADJ
ap-1368	16	40	functions	function	NOUN
ap-1368	16	41	.	.	PUNCT
ap-1368	17	1	it	it	PRON
ap-1368	17	2	is	be	AUX
ap-1368	17	3	useful	useful	ADJ
ap-1368	17	4	to	to	PART
ap-1368	17	5	suppose	suppose	VERB
ap-1368	17	6	throughout	throughout	ADP
ap-1368	17	7	this	this	DET
ap-1368	17	8	paper	paper	NOUN
ap-1368	17	9	that	that	PRON
ap-1368	17	10	−n+	−n+	VERB
ap-1368	17	11	1	1	NUM
ap-1368	17	12	<	<	X
ap-1368	17	13	re	re	X
ap-1368	17	14	σ	σ	X
ap-1368	17	15	<	<	X
ap-1368	17	16	0	0	NUM
ap-1368	17	17	.	.	PUNCT
ap-1368	18	1	we	we	PRON
ap-1368	18	2	define	define	VERB
ap-1368	18	3	the	the	DET
ap-1368	18	4	representation	representation	NOUN
ap-1368	18	5	tσ	tσ	NOUN
ap-1368	18	6	in	in	ADP
ap-1368	18	7	dσ	dσ	PROPN
ap-1368	18	8	by	by	ADP
ap-1368	18	9	left	left	ADJ
ap-1368	18	10	shifts	shift	NOUN
ap-1368	18	11	:	:	PUNCT
ap-1368	18	12	tσ(g)[f(x	tσ(g)[f(x	NOUN
ap-1368	18	13	)	)	PUNCT
ap-1368	18	14	]	]	PUNCT
ap-1368	19	1	:	:	PUNCT
ap-1368	19	2	=	=	SYM
ap-1368	19	3	f(g−1x	f(g−1x	PROPN
ap-1368	19	4	)	)	PUNCT
ap-1368	19	5	.	.	PUNCT
ap-1368	20	1	suppose	suppose	VERB
ap-1368	20	2	that	that	SCONJ
ap-1368	20	3	γ	γ	PROPN
ap-1368	20	4	is	be	AUX
ap-1368	20	5	a	a	DET
ap-1368	20	6	contour	contour	NOUN
ap-1368	20	7	on	on	ADP
ap-1368	20	8	c	c	NOUN
ap-1368	20	9	intersecting	intersect	VERB
ap-1368	20	10	all	all	DET
ap-1368	20	11	generatrices	generatrix	NOUN
ap-1368	20	12	(	(	PUNCT
ap-1368	20	13	i.e.	i.e.	X
ap-1368	20	14	all	all	DET
ap-1368	20	15	lines	line	NOUN
ap-1368	20	16	containing	contain	VERB
ap-1368	20	17	the	the	DET
ap-1368	20	18	origin	origin	NOUN
ap-1368	20	19	)	)	PUNCT
ap-1368	20	20	.	.	PUNCT
ap-1368	21	1	every	every	DET
ap-1368	21	2	point	point	NOUN
ap-1368	21	3	x	x	X
ap-1368	21	4	∈	∈	NOUN
ap-1368	21	5	γ	γ	NOUN
ap-1368	21	6	depends	depend	VERB
ap-1368	21	7	on	on	ADP
ap-1368	21	8	n−1	n−1	PROPN
ap-1368	21	9	parameters	parameter	NOUN
ap-1368	21	10	,	,	PUNCT
ap-1368	21	11	so	so	ADV
ap-1368	21	12	every	every	DET
ap-1368	21	13	point	point	NOUN
ap-1368	21	14	x	x	X
ap-1368	21	15	∈	∈	NOUN
ap-1368	21	16	c	c	NOUN
ap-1368	21	17	can	can	AUX
ap-1368	21	18	be	be	AUX
ap-1368	21	19	represented	represent	VERB
ap-1368	21	20	as	as	ADP
ap-1368	21	21	xi	xi	X
ap-1368	21	22	=	=	PROPN
ap-1368	21	23	{	{	PUNCT
ap-1368	21	24	tfi(ξ1	tfi(ξ1	NOUN
ap-1368	21	25	,	,	PUNCT
ap-1368	21	26	.	.	PUNCT
ap-1368	21	27	.	.	PUNCT
ap-1368	22	1	.	.	PUNCT
ap-1368	23	1	,	,	PUNCT
ap-1368	23	2	ξn−1	ξn−1	PROPN
ap-1368	23	3	)	)	PUNCT
ap-1368	23	4	,	,	PUNCT
ap-1368	23	5	i	i	PRON
ap-1368	23	6	=	=	NOUN
ap-1368	23	7	1	1	NUM
ap-1368	23	8	,	,	PUNCT
ap-1368	23	9	.	.	PUNCT
ap-1368	23	10	.	.	PUNCT
ap-1368	23	11	.	.	PUNCT
ap-1368	24	1	,	,	PUNCT
ap-1368	24	2	n+	n+	PUNCT
ap-1368	24	3	1	1	X
ap-1368	24	4	.	.	X
ap-1368	25	1	denoting	denote	VERB
ap-1368	25	2	by	by	ADP
ap-1368	25	3	g̃	g̃	PROPN
ap-1368	25	4	the	the	DET
ap-1368	25	5	subgroup	subgroup	NOUN
ap-1368	25	6	of	of	ADP
ap-1368	25	7	g	g	PROPN
ap-1368	25	8	which	which	PRON
ap-1368	25	9	acts	act	VERB
ap-1368	25	10	transitively	transitively	PROPN
ap-1368	25	11	on	on	ADP
ap-1368	25	12	γ	γ	PROPN
ap-1368	25	13	,	,	PUNCT
ap-1368	25	14	we	we	PRON
ap-1368	25	15	have	have	VERB
ap-1368	25	16	dx	dx	PROPN
ap-1368	25	17	=	=	SYM
ap-1368	25	18	tn−3	tn−3	PROPN
ap-1368	25	19	dt	dt	X
ap-1368	25	20	dγ	dγ	ADP
ap-1368	25	21	,	,	PUNCT
ap-1368	25	22	(	(	PUNCT
ap-1368	25	23	1	1	X
ap-1368	25	24	)	)	PUNCT
ap-1368	25	25	where	where	SCONJ
ap-1368	25	26	dγ	dγ	NOUN
ap-1368	25	27	is	be	AUX
ap-1368	25	28	the	the	DET
ap-1368	25	29	g̃-invariant	g̃-invariant	ADJ
ap-1368	25	30	measure	measure	NOUN
ap-1368	25	31	on	on	ADP
ap-1368	25	32	γ	γ	PROPN
ap-1368	25	33	.	.	PROPN
ap-1368	25	34	for	for	ADP
ap-1368	25	35	any	any	DET
ap-1368	25	36	pair	pair	NOUN
ap-1368	25	37	(	(	PUNCT
ap-1368	25	38	dσ	dσ	PROPN
ap-1368	25	39	,	,	PUNCT
ap-1368	25	40	dσ̃	dσ̃	NOUN
ap-1368	25	41	)	)	PUNCT
ap-1368	25	42	,	,	PUNCT
ap-1368	25	43	we	we	PRON
ap-1368	25	44	define	define	VERB
ap-1368	25	45	the	the	DET
ap-1368	25	46	bilinear	bilinear	NOUN
ap-1368	25	47	functionals	functional	NOUN
ap-1368	25	48	fγ	fγ	ADV
ap-1368	25	49	:	:	PUNCT
ap-1368	25	50	(	(	PUNCT
ap-1368	25	51	dσ	dσ	VERB
ap-1368	25	52	,	,	PUNCT
ap-1368	25	53	dσ̃	dσ̃	NOUN
ap-1368	25	54	)	)	PUNCT
ap-1368	25	55	−→	−→	NOUN
ap-1368	25	56	c	c	NOUN
ap-1368	25	57	,	,	PUNCT
ap-1368	25	58	(	(	PUNCT
ap-1368	25	59	f1	f1	NOUN
ap-1368	25	60	,	,	PUNCT
ap-1368	25	61	f2	f2	PROPN
ap-1368	25	62	)	)	PUNCT
ap-1368	25	63	�	�	PROPN
ap-1368	25	64	−→	−→	ADJ
ap-1368	25	65	∫	∫	PROPN
ap-1368	25	66	γ	γ	PROPN
ap-1368	25	67	f1(x)f2(x	f1(x)f2(x	PROPN
ap-1368	25	68	)	)	PUNCT
ap-1368	25	69	dγ	dγ	PROPN
ap-1368	25	70	.	.	PUNCT
ap-1368	26	1	the	the	DET
ap-1368	26	2	functional	functional	ADJ
ap-1368	26	3	fγ	fγ	PROPN
ap-1368	26	4	does	do	AUX
ap-1368	26	5	not	not	PART
ap-1368	26	6	depend	depend	VERB
ap-1368	26	7	on	on	ADP
ap-1368	26	8	γ	γ	PROPN
ap-1368	26	9	if	if	SCONJ
ap-1368	26	10	σ̃	σ̃	PROPN
ap-1368	26	11	=	=	PUNCT
ap-1368	26	12	−σ	−σ	NOUN
ap-1368	26	13	−	−	PROPN
ap-1368	26	14	n+	n+	NOUN
ap-1368	26	15	1	1	NUM
ap-1368	26	16	,	,	PUNCT
ap-1368	26	17	because	because	SCONJ
ap-1368	26	18	,	,	PUNCT
ap-1368	26	19	first	first	ADV
ap-1368	26	20	,	,	PUNCT
ap-1368	26	21	we	we	PRON
ap-1368	26	22	have	have	VERB
ap-1368	26	23	formula	formula	NOUN
ap-1368	26	24	(	(	PUNCT
ap-1368	26	25	1	1	NUM
ap-1368	26	26	)	)	PUNCT
ap-1368	26	27	,	,	PUNCT
ap-1368	26	28	and	and	CCONJ
ap-1368	26	29	,	,	PUNCT
ap-1368	26	30	second	second	ADJ
ap-1368	26	31	,	,	PUNCT
ap-1368	26	32	f1	f1	NOUN
ap-1368	26	33	and	and	CCONJ
ap-1368	26	34	f2	f2	PROPN
ap-1368	26	35	are	be	AUX
ap-1368	26	36	both	both	DET
ap-1368	26	37	homogeneous	homogeneous	ADJ
ap-1368	26	38	functions	function	NOUN
ap-1368	26	39	,	,	PUNCT
ap-1368	26	40	and	and	CCONJ
ap-1368	26	41	,	,	PUNCT
ap-1368	26	42	third	third	ADJ
ap-1368	26	43	,	,	PUNCT
ap-1368	26	44	the	the	DET
ap-1368	26	45	g	g	NOUN
ap-1368	26	46	-	-	PUNCT
ap-1368	26	47	invariant	invariant	ADJ
ap-1368	26	48	measure	measure	NOUN
ap-1368	26	49	on	on	ADP
ap-1368	26	50	c	c	NOUN
ap-1368	26	51	can	can	AUX
ap-1368	26	52	be	be	AUX
ap-1368	26	53	represented	represent	VERB
ap-1368	26	54	in	in	ADP
ap-1368	26	55	the	the	DET
ap-1368	26	56	form	form	NOUN
ap-1368	26	57	dx	dx	PROPN
ap-1368	26	58	=	=	SYM
ap-1368	26	59	dxζ(1	dxζ(1	PROPN
ap-1368	26	60	)	)	PUNCT
ap-1368	26	61	.	.	PUNCT
ap-1368	26	62	.	.	PUNCT
ap-1368	26	63	.	.	PUNCT
ap-1368	27	1	dxζ(n	dxζ(n	PROPN
ap-1368	27	2	)	)	PUNCT
ap-1368	27	3	|xζ(n+1)|	|xζ(n+1)|	NOUN
ap-1368	27	4	,	,	PUNCT
ap-1368	27	5	(	(	PUNCT
ap-1368	27	6	2	2	X
ap-1368	27	7	)	)	PUNCT
ap-1368	27	8	where	where	SCONJ
ap-1368	27	9	ζ	ζ	PROPN
ap-1368	27	10	∈	∈	PROPN
ap-1368	27	11	s	s	PART
ap-1368	27	12	n	n	NOUN
ap-1368	27	13	and	and	CCONJ
ap-1368	27	14	s	s	PRON
ap-1368	27	15	n+1	n+1	PROPN
ap-1368	27	16	is	be	AUX
ap-1368	27	17	the	the	DET
ap-1368	27	18	permutation	permutation	NOUN
ap-1368	27	19	group	group	NOUN
ap-1368	27	20	of	of	ADP
ap-1368	27	21	the	the	DET
ap-1368	27	22	set	set	NOUN
ap-1368	27	23	{	{	PUNCT
ap-1368	27	24	1	1	NUM
ap-1368	27	25	,	,	PUNCT
ap-1368	27	26	.	.	PUNCT
ap-1368	27	27	.	.	PUNCT
ap-1368	27	28	.	.	PUNCT
ap-1368	28	1	,	,	PUNCT
ap-1368	28	2	n+	n+	ADP
ap-1368	28	3	1	1	NUM
ap-1368	28	4	}	}	PUNCT
ap-1368	28	5	.	.	PUNCT
ap-1368	29	1	let	let	VERB
ap-1368	29	2	f	f	PROPN
ap-1368	29	3	∈	∈	PROPN
ap-1368	29	4	dσ	dσ	PROPN
ap-1368	29	5	and	and	CCONJ
ap-1368	29	6	y	y	PROPN
ap-1368	29	7	∈	∈	PROPN
ap-1368	30	1	h(1	h(1	PROPN
ap-1368	30	2	)	)	PUNCT
ap-1368	30	3	.	.	PUNCT
ap-1368	31	1	we	we	PRON
ap-1368	31	2	refer	refer	VERB
ap-1368	31	3	to	to	ADP
ap-1368	31	4	the	the	DET
ap-1368	31	5	integral	integral	ADJ
ap-1368	31	6	transform	transform	NOUN
ap-1368	31	7	π(f)(y	π(f)(y	PROPN
ap-1368	31	8	)	)	PUNCT
ap-1368	31	9	:	:	PUNCT
ap-1368	32	1	=	=	PROPN
ap-1368	32	2	fγ(q̂	fγ(q̂	PROPN
ap-1368	32	3	−σ−n+1(y	−σ−n+1(y	PROPN
ap-1368	32	4	,	,	PUNCT
ap-1368	32	5	x	x	NOUN
ap-1368	32	6	)	)	PUNCT
ap-1368	32	7	,	,	PUNCT
ap-1368	32	8	f	f	X
ap-1368	32	9	)	)	PUNCT
ap-1368	32	10	as	as	SCONJ
ap-1368	32	11	the	the	DET
ap-1368	32	12	poisson	poisson	NOUN
ap-1368	32	13	transform	transform	VERB
ap-1368	32	14	[	[	X
ap-1368	32	15	1	1	NUM
ap-1368	32	16	]	]	PUNCT
ap-1368	32	17	.	.	PUNCT
ap-1368	32	18	2	2	NUM
ap-1368	32	19	formulas	formula	NOUN
ap-1368	32	20	related	relate	VERB
ap-1368	32	21	to	to	ADP
ap-1368	32	22	sphere	sphere	NOUN
ap-1368	32	23	and	and	CCONJ
ap-1368	32	24	paraboloid	paraboloid	ADJ
ap-1368	32	25	let	let	VERB
ap-1368	32	26	γ1	γ1	PROPN
ap-1368	32	27	be	be	AUX
ap-1368	32	28	the	the	DET
ap-1368	32	29	intersection	intersection	NOUN
ap-1368	32	30	of	of	ADP
ap-1368	32	31	the	the	DET
ap-1368	32	32	cone	cone	NOUN
ap-1368	32	33	c	c	NOUN
ap-1368	32	34	and	and	CCONJ
ap-1368	32	35	the	the	DET
ap-1368	32	36	plane	plane	NOUN
ap-1368	32	37	x0	x0	PROPN
ap-1368	32	38	=	=	PUNCT
ap-1368	33	1	1	1	X
ap-1368	33	2	.	.	PUNCT
ap-1368	33	3	each	each	DET
ap-1368	33	4	point	point	NOUN
ap-1368	33	5	x	x	X
ap-1368	33	6	∈	∈	PROPN
ap-1368	33	7	γ1	γ1	NOUN
ap-1368	33	8	depends	depend	VERB
ap-1368	33	9	on	on	ADP
ap-1368	33	10	spherical	spherical	ADJ
ap-1368	33	11	parameters	parameter	NOUN
ap-1368	33	12	φ1	φ1	PROPN
ap-1368	33	13	,	,	PUNCT
ap-1368	33	14	.	.	PUNCT
ap-1368	33	15	.	.	PUNCT
ap-1368	34	1	.	.	PUNCT
ap-1368	35	1	,	,	PUNCT
ap-1368	35	2	φn−1	φn−1	VERB
ap-1368	35	3	by	by	ADP
ap-1368	35	4	the	the	DET
ap-1368	35	5	formula	formula	NOUN
ap-1368	35	6	xs	xs	NOUN
ap-1368	36	1	=	=	PUNCT
ap-1368	36	2	n−s∏	n−s∏	PROPN
ap-1368	36	3	i=1	i=1	PROPN
ap-1368	36	4	sinφi	sinφi	VERB
ap-1368	36	5	·	·	PUNCT
ap-1368	36	6	cosφn−s+1	cosφn−s+1	VERB
ap-1368	36	7	,	,	PUNCT
ap-1368	36	8	s	s	NOUN
ap-1368	36	9	�	�	PROPN
ap-1368	36	10	=	=	SYM
ap-1368	36	11	0	0	PROPN
ap-1368	36	12	,	,	PUNCT
ap-1368	36	13	the	the	DET
ap-1368	36	14	research	research	NOUN
ap-1368	36	15	presented	present	VERB
ap-1368	36	16	in	in	ADP
ap-1368	36	17	this	this	DET
ap-1368	36	18	paper	paper	NOUN
ap-1368	36	19	was	be	AUX
ap-1368	36	20	supported	support	VERB
ap-1368	36	21	by	by	ADP
ap-1368	36	22	grant	grant	NOUN
ap-1368	36	23	nk	nk	PROPN
ap-1368	36	24	586p-30	586p-30	PROPN
ap-1368	36	25	from	from	ADP
ap-1368	36	26	the	the	DET
ap-1368	36	27	ministry	ministry	PROPN
ap-1368	36	28	of	of	ADP
ap-1368	36	29	education	education	PROPN
ap-1368	36	30	and	and	CCONJ
ap-1368	36	31	science	science	NOUN
ap-1368	36	32	of	of	ADP
ap-1368	36	33	the	the	DET
ap-1368	36	34	russian	russian	PROPN
ap-1368	36	35	federation	federation	PROPN
ap-1368	36	36	.	.	PUNCT
ap-1368	37	1	70	70	NUM
ap-1368	37	2	acta	acta	PROPN
ap-1368	37	3	polytechnica	polytechnica	PROPN
ap-1368	37	4	vol	vol	NOUN
ap-1368	37	5	.	.	PUNCT
ap-1368	38	1	51	51	NUM
ap-1368	38	2	no	no	INTJ
ap-1368	38	3	.	.	PUNCT
ap-1368	39	1	1/2011	1/2011	NUM
ap-1368	40	1	if	if	SCONJ
ap-1368	40	2	angle	angle	NOUN
ap-1368	40	3	φn−s+1	φn−s+1	ADJ
ap-1368	40	4	exists	exist	VERB
ap-1368	40	5	.	.	PUNCT
ap-1368	41	1	here	here	ADV
ap-1368	41	2	φn−1	φn−1	PROPN
ap-1368	41	3	∈	∈	PROPN
ap-1368	42	1	[	[	X
ap-1368	42	2	0	0	NUM
ap-1368	42	3	;	;	PUNCT
ap-1368	42	4	2π	2π	NOUN
ap-1368	42	5	)	)	PUNCT
ap-1368	42	6	and	and	CCONJ
ap-1368	42	7	φ1	φ1	PROPN
ap-1368	42	8	,	,	PUNCT
ap-1368	42	9	.	.	PUNCT
ap-1368	42	10	.	.	PUNCT
ap-1368	42	11	.	.	PUNCT
ap-1368	43	1	,	,	PUNCT
ap-1368	43	2	φn−2	φn−2	ADP
ap-1368	43	3	∈	∈	PROPN
ap-1368	44	1	[	[	X
ap-1368	44	2	0;π	0;π	NUM
ap-1368	44	3	)	)	PUNCT
ap-1368	44	4	.	.	PUNCT
ap-1368	45	1	the	the	DET
ap-1368	45	2	subgroup	subgroup	PROPN
ap-1368	45	3	h1	h1	PROPN
ap-1368	45	4	�	�	PROPN
ap-1368	45	5	so(n	so(n	PROPN
ap-1368	45	6	)	)	PUNCT
ap-1368	45	7	acts	act	VERB
ap-1368	45	8	transitively	transitively	PROPN
ap-1368	45	9	on	on	ADP
ap-1368	45	10	γ1	γ1	PROPN
ap-1368	45	11	,	,	PUNCT
ap-1368	45	12	and	and	CCONJ
ap-1368	45	13	any	any	DET
ap-1368	45	14	permutate	permutate	VERB
ap-1368	45	15	ζ	ζ	NOUN
ap-1368	45	16	∈	∈	NOUN
ap-1368	45	17	s	s	PART
ap-1368	45	18	n+1	n+1	NOUN
ap-1368	45	19	defines	define	VERB
ap-1368	45	20	the	the	DET
ap-1368	45	21	h1invariant	h1invariant	ADJ
ap-1368	45	22	measure	measure	NOUN
ap-1368	45	23	dγ1	dγ1	NOUN
ap-1368	45	24	=	=	SYM
ap-1368	45	25	dγζ(2	dγζ(2	NOUN
ap-1368	45	26	)	)	PUNCT
ap-1368	45	27	.	.	PUNCT
ap-1368	45	28	.	.	PUNCT
ap-1368	45	29	.	.	PUNCT
ap-1368	46	1	dγζ(n	dγζ(n	PROPN
ap-1368	46	2	)	)	PUNCT
ap-1368	46	3	|xζ(n+1)|	|xζ(n+1)|	NOUN
ap-1368	46	4	.	.	PUNCT
ap-1368	47	1	the	the	DET
ap-1368	47	2	invariant	invariant	ADJ
ap-1368	47	3	measure	measure	NOUN
ap-1368	47	4	in	in	ADP
ap-1368	47	5	spherical	spherical	ADJ
ap-1368	47	6	coordinates	coordinate	NOUN
ap-1368	47	7	is	be	AUX
ap-1368	47	8	given	give	VERB
ap-1368	47	9	by	by	ADP
ap-1368	47	10	9.1.1.(9	9.1.1.(9	NUM
ap-1368	47	11	)	)	PUNCT
ap-1368	48	1	[	[	X
ap-1368	48	2	2	2	X
ap-1368	48	3	]	]	PUNCT
ap-1368	48	4	let	let	VERB
ap-1368	48	5	γ2	γ2	PROPN
ap-1368	48	6	be	be	AUX
ap-1368	48	7	the	the	DET
ap-1368	48	8	intersection	intersection	NOUN
ap-1368	48	9	of	of	ADP
ap-1368	48	10	cone	cone	NOUN
ap-1368	48	11	c	c	PROPN
ap-1368	48	12	and	and	CCONJ
ap-1368	48	13	the	the	DET
ap-1368	48	14	hyperplane	hyperplane	NOUN
ap-1368	48	15	x0+xn	x0+xn	PUNCT
ap-1368	49	1	=	=	SYM
ap-1368	49	2	1	1	X
ap-1368	49	3	.	.	PUNCT
ap-1368	50	1	we	we	PRON
ap-1368	50	2	describe	describe	VERB
ap-1368	50	3	every	every	DET
ap-1368	50	4	point	point	NOUN
ap-1368	50	5	x	x	X
ap-1368	50	6	∈	∈	NOUN
ap-1368	50	7	γ2	γ2	NOUN
ap-1368	50	8	by	by	ADP
ap-1368	50	9	the	the	DET
ap-1368	50	10	coordinates	coordinate	NOUN
ap-1368	50	11	r	r	NOUN
ap-1368	50	12	,	,	PUNCT
ap-1368	50	13	φ1	φ1	PROPN
ap-1368	50	14	,	,	PUNCT
ap-1368	50	15	.	.	PUNCT
ap-1368	50	16	.	.	PUNCT
ap-1368	50	17	.	.	PUNCT
ap-1368	51	1	,	,	PUNCT
ap-1368	51	2	φn−2	φn−2	ADV
ap-1368	51	3	according	accord	VERB
ap-1368	51	4	to	to	ADP
ap-1368	51	5	the	the	DET
ap-1368	51	6	formulas	formula	NOUN
ap-1368	51	7	x0	x0	PROPN
ap-1368	52	1	=	=	PUNCT
ap-1368	52	2	1	1	NUM
ap-1368	53	1	+	+	NUM
ap-1368	53	2	r2	r2	PROPN
ap-1368	53	3	2	2	NUM
ap-1368	53	4	,	,	PUNCT
ap-1368	53	5	xn	xn	PROPN
ap-1368	53	6	=	=	SYM
ap-1368	53	7	1−	1−	NUM
ap-1368	53	8	r2	r2	PROPN
ap-1368	53	9	2	2	NUM
ap-1368	53	10	,	,	PUNCT
ap-1368	53	11	xs	xs	PROPN
ap-1368	54	1	=	=	SYM
ap-1368	54	2	r	r	NOUN
ap-1368	54	3	n−s−1∏	n−s−1∏	NOUN
ap-1368	54	4	i=1	i=1	PROPN
ap-1368	54	5	sinφi	sinφi	NOUN
ap-1368	54	6	cosφn−s	cosφn−s	PROPN
ap-1368	54	7	,	,	PUNCT
ap-1368	54	8	s	s	PART
ap-1368	54	9	/∈	/∈	PUNCT
ap-1368	54	10	{	{	PUNCT
ap-1368	54	11	0	0	NUM
ap-1368	54	12	,	,	PUNCT
ap-1368	54	13	n	n	CCONJ
ap-1368	54	14	}	}	PUNCT
ap-1368	54	15	(	(	PUNCT
ap-1368	54	16	if	if	SCONJ
ap-1368	54	17	angle	angle	NOUN
ap-1368	54	18	φn−s	φn−s	PROPN
ap-1368	54	19	exists	exist	VERB
ap-1368	54	20	)	)	PUNCT
ap-1368	54	21	,	,	PUNCT
ap-1368	54	22	where	where	SCONJ
ap-1368	54	23	r	r	NOUN
ap-1368	54	24	≥	≥	NOUN
ap-1368	54	25	0	0	NUM
ap-1368	54	26	,	,	PUNCT
ap-1368	54	27	φn−2	φn−2	ADP
ap-1368	54	28	∈	∈	PROPN
ap-1368	55	1	[	[	X
ap-1368	55	2	0	0	NUM
ap-1368	55	3	;	;	PUNCT
ap-1368	55	4	2π	2π	NOUN
ap-1368	55	5	)	)	PUNCT
ap-1368	55	6	and	and	CCONJ
ap-1368	55	7	φ1	φ1	PROPN
ap-1368	55	8	,	,	PUNCT
ap-1368	55	9	.	.	PUNCT
ap-1368	55	10	.	.	PUNCT
ap-1368	55	11	.	.	PUNCT
ap-1368	56	1	,	,	PUNCT
ap-1368	56	2	φn−3	φn−3	PROPN
ap-1368	56	3	∈	∈	PROPN
ap-1368	57	1	[	[	X
ap-1368	57	2	0;π	0;π	NUM
ap-1368	57	3	)	)	PUNCT
ap-1368	57	4	.	.	PUNCT
ap-1368	58	1	we	we	PRON
ap-1368	58	2	denote	denote	VERB
ap-1368	58	3	as	as	ADP
ap-1368	58	4	h2	h2	PROPN
ap-1368	58	5	the	the	DET
ap-1368	58	6	subgroup	subgroup	NOUN
ap-1368	58	7	of	of	ADP
ap-1368	58	8	g	g	PROPN
ap-1368	58	9	acting	act	VERB
ap-1368	58	10	transitively	transitively	PROPN
ap-1368	58	11	on	on	ADP
ap-1368	58	12	γ2	γ2	PROPN
ap-1368	58	13	.	.	PUNCT
ap-1368	59	1	h2	h2	PROPN
ap-1368	59	2	consists	consist	VERB
ap-1368	59	3	of	of	ADP
ap-1368	59	4	the	the	DET
ap-1368	59	5	matrices	matrix	NOUN
ap-1368	59	6	n(b	n(b	X
ap-1368	59	7	)	)	PUNCT
ap-1368	60	1	=	=	SYM
ap-1368	60	2	⎛⎜⎜⎜⎜⎝	⎛⎜⎜⎜⎜⎝	VERB
ap-1368	60	3	diag	diag	NOUN
ap-1368	60	4	(	(	PUNCT
ap-1368	60	5	1	1	NUM
ap-1368	60	6	,	,	PUNCT
ap-1368	60	7	.	.	PUNCT
ap-1368	60	8	.	.	PUNCT
ap-1368	61	1	.	.	PUNCT
ap-1368	62	1	,	,	PUNCT
ap-1368	62	2	1︸	1︸	NUM
ap-1368	62	3	︷︷	︷︷	NOUN
ap-1368	62	4	︸	︸	X
ap-1368	62	5	n−1	n−1	PROPN
ap-1368	62	6	)	)	PUNCT
ap-1368	62	7	bt	bt	VERB
ap-1368	62	8	bt	bt	NOUN
ap-1368	63	1	−b	−b	ADJ
ap-1368	63	2	1−	1−	NUM
ap-1368	64	1	b∗	b∗	ADJ
ap-1368	64	2	−b∗	−b∗	PROPN
ap-1368	64	3	b	b	NOUN
ap-1368	64	4	b∗	b∗	ADJ
ap-1368	64	5	b∗	b∗	PROPN
ap-1368	64	6	⎞⎟⎟⎟⎟⎠	⎞⎟⎟⎟⎟⎠	NOUN
ap-1368	64	7	,	,	PUNCT
ap-1368	64	8	where	where	SCONJ
ap-1368	64	9	b	b	X
ap-1368	64	10	=	=	SYM
ap-1368	64	11	(	(	PUNCT
ap-1368	64	12	b1	b1	PROPN
ap-1368	64	13	,	,	PUNCT
ap-1368	64	14	.	.	PUNCT
ap-1368	64	15	.	.	PUNCT
ap-1368	64	16	.	.	PUNCT
ap-1368	65	1	,	,	PUNCT
ap-1368	65	2	bn−1	bn−1	X
ap-1368	65	3	)	)	PUNCT
ap-1368	65	4	and	and	CCONJ
ap-1368	65	5	b∗	b∗	ADJ
ap-1368	65	6	=	=	SYM
ap-1368	65	7	1	1	NUM
ap-1368	65	8	2	2	NUM
ap-1368	65	9	(	(	PUNCT
ap-1368	65	10	b21	b21	PROPN
ap-1368	65	11	+	+	X
ap-1368	65	12	.	.	PUNCT
ap-1368	65	13	.	.	PUNCT
ap-1368	66	1	.+	.+	NOUN
ap-1368	66	2	b2n−1	b2n−1	ADJ
ap-1368	66	3	)	)	PUNCT
ap-1368	66	4	.	.	PUNCT
ap-1368	67	1	it	it	PRON
ap-1368	67	2	is	be	AUX
ap-1368	67	3	not	not	PART
ap-1368	67	4	too	too	ADV
ap-1368	67	5	hard	hard	ADJ
ap-1368	67	6	to	to	PART
ap-1368	67	7	derive	derive	VERB
ap-1368	67	8	the	the	DET
ap-1368	67	9	h2	h2	NOUN
ap-1368	67	10	-	-	PUNCT
ap-1368	67	11	invariant	invariant	ADJ
ap-1368	67	12	measure	measure	NOUN
ap-1368	67	13	dγ	dγ	ADP
ap-1368	67	14	=	=	PROPN
ap-1368	67	15	rn−2	rn−2	PROPN
ap-1368	67	16	dr	dr	PROPN
ap-1368	67	17	n−2∏	n−2∏	PROPN
ap-1368	67	18	i=1	i=1	PROPN
ap-1368	68	1	sinn−i−2	sinn−i−2	PROPN
ap-1368	68	2	φi	φi	ADP
ap-1368	68	3	dφi	dφi	NOUN
ap-1368	68	4	on	on	ADP
ap-1368	68	5	γ2	γ2	PROPN
ap-1368	68	6	.	.	PUNCT
ap-1368	69	1	let	let	VERB
ap-1368	69	2	λ	λ	PRON
ap-1368	69	3	>	>	X
ap-1368	69	4	0	0	PROPN
ap-1368	69	5	,	,	PUNCT
ap-1368	69	6	μ	μ	PROPN
ap-1368	69	7	∈	∈	PROPN
ap-1368	69	8	r	r	NOUN
ap-1368	69	9	,	,	PUNCT
ap-1368	69	10	k0	k0	PROPN
ap-1368	69	11	≥	≥	PROPN
ap-1368	69	12	k1	k1	PROPN
ap-1368	69	13	≥	≥	PROPN
ap-1368	69	14	.	.	PUNCT
ap-1368	69	15	.	.	PUNCT
ap-1368	70	1	.	.	PUNCT
ap-1368	71	1	≥	≥	PROPN
ap-1368	71	2	kn−2	kn−2	PROPN
ap-1368	71	3	≥	≥	NUM
ap-1368	71	4	0	0	NUM
ap-1368	71	5	,	,	PUNCT
ap-1368	71	6	l1	l1	PROPN
ap-1368	71	7	≥	≥	NUM
ap-1368	71	8	.	.	PUNCT
ap-1368	71	9	.	.	PUNCT
ap-1368	71	10	.	.	PUNCT
ap-1368	72	1	≥	≥	PROPN
ap-1368	72	2	ln−2	ln−2	PROPN
ap-1368	72	3	≥	≥	PROPN
ap-1368	72	4	0	0	NUM
ap-1368	72	5	,	,	PUNCT
ap-1368	72	6	m1	m1	PROPN
ap-1368	72	7	≥	≥	NUM
ap-1368	72	8	.	.	PUNCT
ap-1368	72	9	.	.	PUNCT
ap-1368	73	1	.	.	PUNCT
ap-1368	74	1	≥	≥	PROPN
ap-1368	75	1	mn−2	mn−2	PROPN
ap-1368	75	2	≥	≥	NOUN
ap-1368	75	3	0	0	NUM
ap-1368	75	4	,	,	PUNCT
ap-1368	75	5	k	k	X
ap-1368	75	6	=	=	PRON
ap-1368	75	7	(	(	PUNCT
ap-1368	75	8	k0	k0	PROPN
ap-1368	75	9	,	,	PUNCT
ap-1368	75	10	k1	k1	NOUN
ap-1368	75	11	,	,	PUNCT
ap-1368	75	12	.	.	PUNCT
ap-1368	75	13	.	.	PUNCT
ap-1368	75	14	.	.	PUNCT
ap-1368	76	1	,	,	PUNCT
ap-1368	76	2	kn−3,±kn−2	kn−3,±kn−2	PROPN
ap-1368	76	3	)	)	PUNCT
ap-1368	76	4	,	,	PUNCT
ap-1368	76	5	l	l	NOUN
ap-1368	77	1	=	=	SYM
ap-1368	77	2	(	(	PUNCT
ap-1368	77	3	l1	l1	PROPN
ap-1368	77	4	,	,	PUNCT
ap-1368	77	5	.	.	PUNCT
ap-1368	77	6	.	.	PUNCT
ap-1368	77	7	.	.	PUNCT
ap-1368	78	1	,	,	PUNCT
ap-1368	78	2	ln−3,±ln−2	ln−3,±ln−2	PROPN
ap-1368	78	3	)	)	PUNCT
ap-1368	78	4	,	,	PUNCT
ap-1368	78	5	m	m	VERB
ap-1368	78	6	=	=	SYM
ap-1368	78	7	(	(	PUNCT
ap-1368	78	8	m1	m1	PROPN
ap-1368	78	9	,	,	PUNCT
ap-1368	78	10	.	.	PUNCT
ap-1368	78	11	.	.	PUNCT
ap-1368	78	12	.	.	PUNCT
ap-1368	79	1	,	,	PUNCT
ap-1368	79	2	mn−3,±mn−2	mn−3,±mn−2	PROPN
ap-1368	79	3	)	)	PUNCT
ap-1368	79	4	.	.	PUNCT
ap-1368	80	1	we	we	PRON
ap-1368	80	2	will	will	AUX
ap-1368	80	3	now	now	ADV
ap-1368	80	4	deal	deal	VERB
ap-1368	80	5	with	with	ADP
ap-1368	80	6	two	two	NUM
ap-1368	80	7	bases	basis	NOUN
ap-1368	80	8	in	in	ADP
ap-1368	80	9	dσ	dσ	PROPN
ap-1368	80	10	.	.	PROPN
ap-1368	81	1	one	one	NUM
ap-1368	81	2	of	of	ADP
ap-1368	81	3	them	they	PRON
ap-1368	81	4	consists	consist	VERB
ap-1368	81	5	of	of	ADP
ap-1368	81	6	the	the	DET
ap-1368	81	7	functions	function	NOUN
ap-1368	81	8	fσ1	fσ1	PROPN
ap-1368	81	9	k	k	PROPN
ap-1368	81	10	(	(	PUNCT
ap-1368	81	11	x	x	X
ap-1368	81	12	)	)	PUNCT
ap-1368	81	13	=	=	SYM
ap-1368	81	14	xσ−k0	xσ−k0	PROPN
ap-1368	81	15	0	0	PROPN
ap-1368	81	16	ξn	ξn	PROPN
ap-1368	81	17	k(x	k(x	PROPN
ap-1368	81	18	)	)	PUNCT
ap-1368	81	19	,	,	PUNCT
ap-1368	81	20	where	where	SCONJ
ap-1368	81	21	k	k	PROPN
ap-1368	81	22	=	=	PRON
ap-1368	81	23	(	(	PUNCT
ap-1368	81	24	k0	k0	PROPN
ap-1368	81	25	,	,	PUNCT
ap-1368	81	26	k1	k1	NOUN
ap-1368	81	27	,	,	PUNCT
ap-1368	81	28	.	.	PUNCT
ap-1368	81	29	.	.	PUNCT
ap-1368	82	1	.	.	PUNCT
ap-1368	83	1	,	,	PUNCT
ap-1368	83	2	kn−3,±kn−2	kn−3,±kn−2	PROPN
ap-1368	83	3	)	)	PUNCT
ap-1368	83	4	∈	∈	PROPN
ap-1368	83	5	z	z	PROPN
ap-1368	83	6	n−1	n−1	PROPN
ap-1368	83	7	,	,	PUNCT
ap-1368	83	8	ki	ki	PROPN
ap-1368	83	9	≥	≥	NUM
ap-1368	83	10	ki+1	ki+1	PROPN
ap-1368	83	11	≥	≥	NOUN
ap-1368	83	12	0	0	NUM
ap-1368	83	13	and	and	CCONJ
ap-1368	83	14	ξn	ξn	PROPN
ap-1368	83	15	t	t	PROPN
ap-1368	83	16	(	(	PUNCT
ap-1368	83	17	x	x	NOUN
ap-1368	83	18	)	)	PUNCT
ap-1368	84	1	=	=	SYM
ap-1368	84	2	n−3∏	n−3∏	NOUN
ap-1368	84	3	i=1	i=1	NOUN
ap-1368	84	4	r	r	NOUN
ap-1368	84	5	ti−ti+1	ti−ti+1	NOUN
ap-1368	84	6	n−i	n−i	PROPN
ap-1368	84	7	·	·	PUNCT
ap-1368	84	8	c	c	NOUN
ap-1368	84	9	n−i	n−i	PROPN
ap-1368	84	10	2	2	NUM
ap-1368	84	11	−1	−1	NOUN
ap-1368	84	12	ti−ti+1	ti−ti+1	NOUN
ap-1368	84	13	(	(	PUNCT
ap-1368	84	14	xn−i	xn−i	NOUN
ap-1368	84	15	rn−i	rn−i	PROPN
ap-1368	84	16	)	)	PUNCT
ap-1368	85	1	(	(	PUNCT
ap-1368	85	2	x2	x2	PROPN
ap-1368	85	3	±	±	NOUN
ap-1368	85	4	ix1)tn−2	ix1)tn−2	PROPN
ap-1368	85	5	.	.	PUNCT
ap-1368	86	1	the	the	DET
ap-1368	86	2	second	second	ADJ
ap-1368	86	3	basis	basis	NOUN
ap-1368	86	4	consists	consist	VERB
ap-1368	86	5	of	of	ADP
ap-1368	86	6	the	the	DET
ap-1368	86	7	functions	function	NOUN
ap-1368	86	8	fσ2	fσ2	PROPN
ap-1368	86	9	(	(	PUNCT
ap-1368	86	10	l	l	NOUN
ap-1368	86	11	,	,	PUNCT
ap-1368	86	12	λ)(x	λ)(x	PROPN
ap-1368	86	13	)	)	PUNCT
ap-1368	86	14	=	=	PUNCT
ap-1368	87	1	(	(	PUNCT
ap-1368	87	2	x0	x0	PROPN
ap-1368	87	3	+	+	CCONJ
ap-1368	87	4	xn)σ+	xn)σ+	X
ap-1368	87	5	n−3	n−3	PROPN
ap-1368	87	6	2	2	NUM
ap-1368	87	7	·	·	PUNCT
ap-1368	87	8	(	(	PUNCT
ap-1368	87	9	λ	λ	X
ap-1368	87	10	2	2	NUM
ap-1368	87	11	)	)	PUNCT
ap-1368	87	12	l1	l1	PROPN
ap-1368	87	13	(	(	PUNCT
ap-1368	87	14	λrn−1	λrn−1	PROPN
ap-1368	87	15	2	2	NUM
ap-1368	87	16	)	)	PUNCT
ap-1368	87	17	3−n	3−n	NUM
ap-1368	87	18	2	2	NUM
ap-1368	87	19	−l1	−l1	PROPN
ap-1368	87	20	·	·	PUNCT
ap-1368	87	21	jl1	jl1	NOUN
ap-1368	87	22	+	+	CCONJ
ap-1368	87	23	n−3	n−3	PROPN
ap-1368	87	24	2	2	NUM
ap-1368	87	25	(	(	PUNCT
ap-1368	87	26	λrn−1	λrn−1	PROPN
ap-1368	87	27	x0	x0	PROPN
ap-1368	87	28	+	+	CCONJ
ap-1368	87	29	xn	xn	X
ap-1368	87	30	)	)	PUNCT
ap-1368	88	1	ξn−1	ξn−1	ADJ
ap-1368	88	2	l	l	NOUN
ap-1368	88	3	(	(	PUNCT
ap-1368	88	4	x	x	NOUN
ap-1368	88	5	)	)	PUNCT
ap-1368	88	6	,	,	PUNCT
ap-1368	88	7	where	where	SCONJ
ap-1368	88	8	r2j	r2j	PROPN
ap-1368	88	9	=	=	SYM
ap-1368	88	10	x21	x21	PROPN
ap-1368	88	11	+	+	CCONJ
ap-1368	88	12	.	.	PUNCT
ap-1368	88	13	.	.	PUNCT
ap-1368	89	1	.+	.+	NOUN
ap-1368	89	2	x2j	x2j	PUNCT
ap-1368	89	3	,	,	PUNCT
ap-1368	89	4	l	l	NOUN
ap-1368	89	5	=	=	SYM
ap-1368	89	6	(	(	PUNCT
ap-1368	89	7	l1	l1	PROPN
ap-1368	89	8	,	,	PUNCT
ap-1368	89	9	.	.	PUNCT
ap-1368	89	10	.	.	PUNCT
ap-1368	90	1	.	.	PUNCT
ap-1368	91	1	,	,	PUNCT
ap-1368	91	2	ln−3,±ln−2	ln−3,±ln−2	PROPN
ap-1368	91	3	)	)	PUNCT
ap-1368	91	4	∈	∈	PROPN
ap-1368	91	5	z	z	PROPN
ap-1368	91	6	n−2	n−2	PROPN
ap-1368	91	7	,	,	PUNCT
ap-1368	91	8	λ	λ	X
ap-1368	91	9	≥	≥	NOUN
ap-1368	91	10	0	0	NUM
ap-1368	91	11	and	and	CCONJ
ap-1368	91	12	li	li	PROPN
ap-1368	91	13	≥	≥	PROPN
ap-1368	91	14	li+1	li+1	PROPN
ap-1368	91	15	≥	≥	PROPN
ap-1368	91	16	0	0	NUM
ap-1368	91	17	.	.	PUNCT
ap-1368	92	1	suppose	suppose	VERB
ap-1368	92	2	,	,	PUNCT
ap-1368	92	3	in	in	ADP
ap-1368	92	4	addition	addition	NOUN
ap-1368	92	5	,	,	PUNCT
ap-1368	92	6	that	that	SCONJ
ap-1368	92	7	the	the	DET
ap-1368	92	8	functions	function	NOUN
ap-1368	92	9	of	of	ADP
ap-1368	92	10	the	the	DET
ap-1368	92	11	above	above	ADJ
ap-1368	92	12	bases	basis	NOUN
ap-1368	92	13	are	be	AUX
ap-1368	92	14	equipped	equip	VERB
ap-1368	92	15	with	with	ADP
ap-1368	92	16	the	the	DET
ap-1368	92	17	normalizing	normalizing	ADJ
ap-1368	92	18	factors	factor	NOUN
ap-1368	92	19	defined	define	VERB
ap-1368	92	20	by	by	ADP
ap-1368	92	21	formulas	formula	NOUN
ap-1368	92	22	[	[	X
ap-1368	92	23	2	2	NUM
ap-1368	92	24	,	,	PUNCT
ap-1368	92	25	9.4.1.7	9.4.1.7	NUM
ap-1368	92	26	,	,	PUNCT
ap-1368	92	27	10.3.4.9	10.3.4.9	NUM
ap-1368	92	28	]	]	PUNCT
ap-1368	92	29	.	.	PUNCT
ap-1368	93	1	let	let	VERB
ap-1368	93	2	us	we	PRON
ap-1368	93	3	consider	consider	VERB
ap-1368	93	4	the	the	DET
ap-1368	93	5	distribution	distribution	NOUN
ap-1368	94	1	fσ1	fσ1	PROPN
ap-1368	94	2	k	k	PROPN
ap-1368	94	3	(	(	PUNCT
ap-1368	94	4	x	x	X
ap-1368	94	5	)	)	PUNCT
ap-1368	94	6	=	=	SYM
ap-1368	94	7	∑	∑	PUNCT
ap-1368	94	8	l	l	NOUN
ap-1368	94	9	∫	∫	PROPN
ap-1368	95	1	+	+	NUM
ap-1368	95	2	∞	∞	NOUN
ap-1368	95	3	0	0	X
ap-1368	96	1	cσ12	cσ12	PROPN
ap-1368	96	2	k,(l	k,(l	PROPN
ap-1368	96	3	,	,	PUNCT
ap-1368	96	4	λ	λ	NOUN
ap-1368	96	5	)	)	PUNCT
ap-1368	96	6	f	f	PROPN
ap-1368	96	7	σ2	σ2	PROPN
ap-1368	96	8	(	(	PUNCT
ap-1368	96	9	l	l	NOUN
ap-1368	96	10	,	,	PUNCT
ap-1368	96	11	λ	λ	NOUN
ap-1368	96	12	)	)	PUNCT
ap-1368	96	13	dλ	dλ	NOUN
ap-1368	96	14	.	.	PUNCT
ap-1368	97	1	(	(	PUNCT
ap-1368	97	2	3	3	X
ap-1368	97	3	)	)	PUNCT
ap-1368	97	4	from	from	ADP
ap-1368	97	5	the	the	DET
ap-1368	97	6	orthogonality	orthogonality	NOUN
ap-1368	97	7	of	of	ADP
ap-1368	97	8	the	the	DET
ap-1368	97	9	functions	function	NOUN
ap-1368	97	10	ξn	ξn	PROPN
ap-1368	97	11	t	t	PROPN
ap-1368	97	12	,	,	PUNCT
ap-1368	97	13	we	we	PRON
ap-1368	97	14	obtain	obtain	VERB
ap-1368	97	15	the	the	DET
ap-1368	97	16	property	property	NOUN
ap-1368	97	17	fγ(fσ1	fγ(fσ1	PROPN
ap-1368	98	1	k	k	PROPN
ap-1368	98	2	,	,	PUNCT
ap-1368	98	3	f−σ−n−1,1	f−σ−n−1,1	VERB
ap-1368	98	4	−k̃	−k̃	NOUN
ap-1368	98	5	)	)	PUNCT
ap-1368	99	1	=	=	SYM
ap-1368	99	2	δkk̃	δkk̃	NOUN
ap-1368	99	3	.	.	PUNCT
ap-1368	100	1	from	from	ADP
ap-1368	100	2	this	this	DET
ap-1368	100	3	property	property	NOUN
ap-1368	100	4	,	,	PUNCT
ap-1368	100	5	it	it	PRON
ap-1368	100	6	immediately	immediately	ADV
ap-1368	100	7	follows	follow	VERB
ap-1368	100	8	that	that	SCONJ
ap-1368	100	9	cσ12	cσ12	PROPN
ap-1368	100	10	k,(l	k,(l	PROPN
ap-1368	100	11	,	,	PUNCT
ap-1368	100	12	λ	λ	NOUN
ap-1368	100	13	)	)	PUNCT
ap-1368	100	14	=	=	SYM
ap-1368	100	15	fγ(f	fγ(f	X
ap-1368	100	16	σ1	σ1	PROPN
ap-1368	100	17	k	k	PROPN
ap-1368	100	18	,	,	PUNCT
ap-1368	100	19	f−σ−n−1,2	f−σ−n−1,2	PROPN
ap-1368	100	20	(	(	PUNCT
ap-1368	100	21	l	l	NOUN
ap-1368	100	22	,	,	PUNCT
ap-1368	100	23	λ	λ	NOUN
ap-1368	100	24	)	)	PUNCT
ap-1368	100	25	)	)	PUNCT
ap-1368	100	26	.	.	PUNCT
ap-1368	101	1	let	let	VERB
ap-1368	101	2	γ	γ	PROPN
ap-1368	101	3	=	=	SYM
ap-1368	101	4	γ1	γ1	PROPN
ap-1368	101	5	.	.	PUNCT
ap-1368	102	1	then	then	ADV
ap-1368	102	2	from	from	ADP
ap-1368	102	3	the	the	DET
ap-1368	102	4	formula∫	formula∫	ADJ
ap-1368	102	5	1	1	NUM
ap-1368	102	6	−1	−1	NOUN
ap-1368	102	7	(	(	PUNCT
ap-1368	102	8	1−	1−	NUM
ap-1368	102	9	x2)ν−	x2)ν−	SYM
ap-1368	102	10	1	1	NUM
ap-1368	102	11	2	2	NUM
ap-1368	102	12	cν	cν	NOUN
ap-1368	102	13	m(x)c	m(x)c	PROPN
ap-1368	102	14	ν	ν	X
ap-1368	102	15	n(x	n(x	X
ap-1368	102	16	)	)	PUNCT
ap-1368	102	17	dx	dx	PROPN
ap-1368	102	18	=	=	SYM
ap-1368	102	19	0	0	PROPN
ap-1368	102	20	,	,	PUNCT
ap-1368	102	21	where	where	SCONJ
ap-1368	102	22	m	m	VERB
ap-1368	102	23	�	�	NOUN
ap-1368	102	24	=	=	SYM
ap-1368	102	25	n	n	CCONJ
ap-1368	102	26	,	,	PUNCT
ap-1368	102	27	re	re	ADP
ap-1368	102	28	ν	ν	X
ap-1368	102	29	>	>	X
ap-1368	102	30	−1	−1	NOUN
ap-1368	102	31	2	2	NUM
ap-1368	102	32	,	,	PUNCT
ap-1368	102	33	we	we	PRON
ap-1368	102	34	derive	derive	VERB
ap-1368	102	35	lemma	lemma	PROPN
ap-1368	102	36	1	1	NUM
ap-1368	102	37	.	.	PUNCT
ap-1368	103	1	if	if	SCONJ
ap-1368	103	2	n−2∑	n−2∑	PROPN
ap-1368	103	3	i=1	i=1	PROPN
ap-1368	103	4	(	(	PUNCT
ap-1368	103	5	ki	ki	PROPN
ap-1368	103	6	−	−	PROPN
ap-1368	103	7	li	li	PROPN
ap-1368	103	8	)	)	PUNCT
ap-1368	103	9	2	2	NUM
ap-1368	103	10	�	�	NOUN
ap-1368	103	11	=	=	SYM
ap-1368	103	12	0	0	NUM
ap-1368	103	13	,	,	PUNCT
ap-1368	103	14	then	then	ADV
ap-1368	103	15	cσ12	cσ12	PROPN
ap-1368	103	16	k,(l	k,(l	PROPN
ap-1368	103	17	,	,	PUNCT
ap-1368	103	18	λ	λ	X
ap-1368	103	19	)	)	PUNCT
ap-1368	103	20	=	=	SYM
ap-1368	103	21	0	0	X
ap-1368	103	22	.	.	PUNCT
ap-1368	104	1	let	let	VERB
ap-1368	104	2	us	we	PRON
ap-1368	104	3	assume	assume	VERB
ap-1368	104	4	another	another	DET
ap-1368	104	5	situation	situation	NOUN
ap-1368	104	6	.	.	PUNCT
ap-1368	105	1	lemma	lemma	PROPN
ap-1368	105	2	2	2	NUM
ap-1368	105	3	.	.	PUNCT
ap-1368	106	1	if	if	SCONJ
ap-1368	106	2	n−2∑	n−2∑	PROPN
ap-1368	106	3	i=1	i=1	PROPN
ap-1368	106	4	(	(	PUNCT
ap-1368	106	5	ki	ki	PROPN
ap-1368	106	6	−	−	PROPN
ap-1368	106	7	li	li	PROPN
ap-1368	106	8	)	)	PUNCT
ap-1368	106	9	2	2	NUM
ap-1368	106	10	=	=	SYM
ap-1368	106	11	0	0	NUM
ap-1368	106	12	,	,	PUNCT
ap-1368	106	13	then	then	ADV
ap-1368	106	14	cσ12	cσ12	PROPN
ap-1368	106	15	k,(l	k,(l	PROPN
ap-1368	106	16	,	,	PUNCT
ap-1368	106	17	λ	λ	NOUN
ap-1368	106	18	)	)	PUNCT
ap-1368	106	19	=	=	SYM
ap-1368	106	20	2	2	NUM
ap-1368	106	21	−σ+n+3k1−3	−σ+n+3k1−3	VERB
ap-1368	106	22	π−1	π−1	PROPN
ap-1368	106	23	ik1	ik1	ADJ
ap-1368	106	24	(	(	PUNCT
ap-1368	106	25	n+	n+	NUM
ap-1368	106	26	2k0	2k0	NUM
ap-1368	106	27	−	−	NOUN
ap-1368	106	28	2	2	NUM
ap-1368	106	29	)	)	PUNCT
ap-1368	106	30	1	1	NUM
ap-1368	106	31	2	2	NUM
ap-1368	106	32	·	·	PUNCT
ap-1368	106	33	√	√	NUM
ap-1368	106	34	(	(	PUNCT
ap-1368	106	35	k0	k0	PROPN
ap-1368	106	36	−	−	PROPN
ap-1368	106	37	k1)!λ	k1)!λ	PROPN
ap-1368	106	38	k1	k1	PROPN
ap-1368	106	39	γ	γ	X
ap-1368	106	40	(	(	PUNCT
ap-1368	106	41	n	n	CCONJ
ap-1368	106	42	−	−	PROPN
ap-1368	106	43	1	1	NUM
ap-1368	106	44	2	2	NUM
ap-1368	106	45	)	)	PUNCT
ap-1368	106	46	γ	γ	PROPN
ap-1368	106	47	(	(	PUNCT
ap-1368	106	48	n−	n−	NOUN
ap-1368	106	49	1	1	NUM
ap-1368	106	50	2	2	NUM
ap-1368	106	51	+	+	CCONJ
ap-1368	106	52	k1	k1	NOUN
ap-1368	106	53	)	)	PUNCT
ap-1368	106	54	·	·	PUNCT
ap-1368	106	55	γ	γ	X
ap-1368	106	56	(	(	PUNCT
ap-1368	106	57	n	n	CCONJ
ap-1368	106	58	2	2	NUM
ap-1368	106	59	+	+	NUM
ap-1368	106	60	k1	k1	NOUN
ap-1368	106	61	−	−	PROPN
ap-1368	106	62	1	1	NUM
ap-1368	106	63	)	)	PUNCT
ap-1368	106	64	γ	γ	NOUN
ap-1368	106	65	1	1	NUM
ap-1368	106	66	2	2	NUM
ap-1368	106	67	(	(	PUNCT
ap-1368	106	68	n−	n−	NOUN
ap-1368	106	69	1	1	NUM
ap-1368	106	70	2	2	NUM
ap-1368	106	71	)	)	PUNCT
ap-1368	106	72	γ−1(n+	γ−1(n+	NOUN
ap-1368	106	73	2k1	2k1	NUM
ap-1368	106	74	−	−	NOUN
ap-1368	106	75	2	2	NUM
ap-1368	106	76	)	)	PUNCT
ap-1368	106	77	·	·	PUNCT
ap-1368	106	78	γ−	γ−	VERB
ap-1368	106	79	1	1	NUM
ap-1368	106	80	2	2	NUM
ap-1368	106	81	(	(	PUNCT
ap-1368	106	82	n+	n+	NUM
ap-1368	106	83	k0	k0	PROPN
ap-1368	106	84	+	+	CCONJ
ap-1368	106	85	k1	k1	PROPN
ap-1368	106	86	−	−	PROPN
ap-1368	106	87	2	2	NUM
ap-1368	106	88	)	)	PUNCT
ap-1368	106	89	k0−k1∑	k0−k1∑	PROPN
ap-1368	106	90	m=0	m=0	PROPN
ap-1368	107	1	(	(	PUNCT
ap-1368	107	2	−1)m	−1)m	PROPN
ap-1368	107	3	(	(	PUNCT
ap-1368	107	4	m!)−1	m!)−1	NOUN
ap-1368	107	5	·	·	PUNCT
ap-1368	107	6	γ(n+	γ(n+	NOUN
ap-1368	107	7	k0	k0	PROPN
ap-1368	107	8	+	+	CCONJ
ap-1368	107	9	k1	k1	PROPN
ap-1368	108	1	+	+	PROPN
ap-1368	108	2	m−	m−	PROPN
ap-1368	108	3	2	2	NUM
ap-1368	108	4	)	)	PUNCT
ap-1368	108	5	γ−1	γ−1	PROPN
ap-1368	108	6	(	(	PUNCT
ap-1368	108	7	n−	n−	NOUN
ap-1368	108	8	1	1	NUM
ap-1368	108	9	2	2	NUM
ap-1368	108	10	+	+	NUM
ap-1368	108	11	k1	k1	NOUN
ap-1368	108	12	+	+	NOUN
ap-1368	108	13	m	m	NOUN
ap-1368	108	14	)	)	PUNCT
ap-1368	109	1	·	·	PUNCT
ap-1368	109	2	γ−1(k0	γ−1(k0	NOUN
ap-1368	109	3	−	−	PROPN
ap-1368	109	4	k1	k1	NOUN
ap-1368	109	5	−m−	−m−	NOUN
ap-1368	109	6	1	1	NUM
ap-1368	109	7	)	)	PUNCT
ap-1368	109	8	γ−1(−σ	γ−1(−σ	PROPN
ap-1368	110	1	+	+	CCONJ
ap-1368	110	2	k1	k1	PROPN
ap-1368	110	3	+	+	PROPN
ap-1368	110	4	m	m	NOUN
ap-1368	110	5	)	)	PUNCT
ap-1368	110	6	·	·	PUNCT
ap-1368	110	7	g2113	g2113	PROPN
ap-1368	110	8	⎛⎝λ2	⎛⎝λ2	VERB
ap-1368	110	9	4	4	NUM
ap-1368	110	10	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ap-1368	110	11	−m	−m	ADJ
ap-1368	110	12	−σ	−σ	NOUN
ap-1368	110	13	+	+	CCONJ
ap-1368	110	14	k1	k1	NOUN
ap-1368	110	15	−	−	PROPN
ap-1368	110	16	1	1	NUM
ap-1368	110	17	,	,	PUNCT
ap-1368	110	18	n−	n−	NOUN
ap-1368	110	19	3	3	NUM
ap-1368	110	20	2	2	NUM
ap-1368	110	21	+	+	NUM
ap-1368	110	22	k1	k1	PROPN
ap-1368	110	23	⎞⎠	⎞⎠	PROPN
ap-1368	110	24	.	.	PUNCT
ap-1368	111	1	71	71	NUM
ap-1368	111	2	acta	acta	PROPN
ap-1368	111	3	polytechnica	polytechnica	PROPN
ap-1368	111	4	vol	vol	NOUN
ap-1368	111	5	.	.	PUNCT
ap-1368	112	1	51	51	NUM
ap-1368	112	2	no	no	NOUN
ap-1368	112	3	.	.	PUNCT
ap-1368	113	1	1/2011	1/2011	NUM
ap-1368	113	2	proof	proof	NOUN
ap-1368	113	3	.	.	PUNCT
ap-1368	114	1	suppose	suppose	VERB
ap-1368	114	2	γ	γ	X
ap-1368	114	3	=	=	SYM
ap-1368	114	4	γ2	γ2	PROPN
ap-1368	114	5	.	.	PUNCT
ap-1368	115	1	then	then	ADV
ap-1368	115	2	we	we	PRON
ap-1368	115	3	obtain	obtain	VERB
ap-1368	115	4	the	the	DET
ap-1368	115	5	integral	integral	ADJ
ap-1368	115	6	∫	∫	NOUN
ap-1368	116	1	+	+	NOUN
ap-1368	116	2	∞	∞	NOUN
ap-1368	116	3	0	0	NUM
ap-1368	116	4	r	r	NOUN
ap-1368	116	5	n−1	n−1	PROPN
ap-1368	116	6	2	2	NUM
ap-1368	116	7	+	+	NOUN
ap-1368	116	8	l1	l1	PROPN
ap-1368	116	9	(	(	PUNCT
ap-1368	116	10	r2	r2	PROPN
ap-1368	116	11	+	+	CCONJ
ap-1368	116	12	1)σ−k1	1)σ−k1	PROPN
ap-1368	116	13	·	·	PUNCT
ap-1368	116	14	c	c	PROPN
ap-1368	116	15	n	n	PRON
ap-1368	116	16	2−k1−1	2−k1−1	NUM
ap-1368	116	17	k0−k1	k0−k1	X
ap-1368	116	18	(	(	PUNCT
ap-1368	116	19	1−	1−	NUM
ap-1368	116	20	r2	r2	PROPN
ap-1368	116	21	1	1	NUM
ap-1368	116	22	+	+	CCONJ
ap-1368	116	23	r2	r2	PROPN
ap-1368	116	24	)	)	PUNCT
ap-1368	116	25	jn−3	jn−3	PROPN
ap-1368	116	26	2	2	NUM
ap-1368	117	1	+	+	PROPN
ap-1368	117	2	l1	l1	PROPN
ap-1368	117	3	(	(	PUNCT
ap-1368	117	4	λr	λr	PROPN
ap-1368	117	5	)	)	PUNCT
ap-1368	117	6	dr	dr	PROPN
ap-1368	117	7	,	,	PUNCT
ap-1368	117	8	which	which	PRON
ap-1368	117	9	can	can	AUX
ap-1368	117	10	be	be	AUX
ap-1368	117	11	solved	solve	VERB
ap-1368	117	12	explicitly	explicitly	ADV
ap-1368	117	13	after	after	ADP
ap-1368	117	14	replacing	replace	VERB
ap-1368	117	15	rk	rk	PRON
ap-1368	117	16	jk(λr	jk(λr	PROPN
ap-1368	117	17	)	)	PUNCT
ap-1368	118	1	=	=	PUNCT
ap-1368	118	2	2k	2k	NUM
ap-1368	118	3	λ−k	λ−k	PUNCT
ap-1368	118	4	g1002	g1002	NOUN
ap-1368	118	5	(	(	PUNCT
ap-1368	118	6	(	(	PUNCT
ap-1368	118	7	λr	λr	ADP
ap-1368	118	8	2	2	NUM
ap-1368	118	9	)	)	SYM
ap-1368	118	10	2	2	NUM
ap-1368	118	11	∣∣∣∣∣	∣∣∣∣∣	NOUN
ap-1368	118	12	0k	0k	NOUN
ap-1368	118	13	,	,	PUNCT
ap-1368	118	14	0	0	NUM
ap-1368	118	15	)	)	PUNCT
ap-1368	118	16	according	accord	VERB
ap-1368	118	17	to	to	ADP
ap-1368	118	18	formulas	formula	NOUN
ap-1368	118	19	[	[	X
ap-1368	118	20	3	3	NUM
ap-1368	118	21	,	,	PUNCT
ap-1368	118	22	8.932.1	8.932.1	NUM
ap-1368	118	23	,	,	PUNCT
ap-1368	118	24	8.932.2	8.932.2	NUM
ap-1368	118	25	]	]	PUNCT
ap-1368	118	26	and	and	CCONJ
ap-1368	118	27	[	[	X
ap-1368	118	28	4	4	NUM
ap-1368	118	29	,	,	PUNCT
ap-1368	118	30	20.5.4	20.5.4	NUM
ap-1368	118	31	]	]	PUNCT
ap-1368	118	32	.	.	PUNCT
ap-1368	119	1	�	�	PROPN
ap-1368	119	2	theorem	theorem	VERB
ap-1368	119	3	1	1	NUM
ap-1368	119	4	.	.	PUNCT
ap-1368	120	1	p	p	NOUN
ap-1368	120	2	−n	−n	ADJ
ap-1368	120	3	2	2	NUM
ap-1368	120	4	+	+	SYM
ap-1368	120	5	1	1	NUM
ap-1368	120	6	−σ−n	−σ−n	NOUN
ap-1368	120	7	2	2	NUM
ap-1368	120	8	(	(	PUNCT
ap-1368	120	9	coshα	coshα	PROPN
ap-1368	120	10	)	)	PUNCT
ap-1368	120	11	=	=	PUNCT
ap-1368	120	12	22n−	22n−	NUM
ap-1368	120	13	9	9	NUM
ap-1368	120	14	2	2	NUM
ap-1368	120	15	π−	π−	ADP
ap-1368	120	16	3	3	NUM
ap-1368	120	17	2	2	NUM
ap-1368	120	18	√	√	NUM
ap-1368	120	19	n−	n−	NOUN
ap-1368	120	20	1	1	NUM
ap-1368	120	21	·	·	PUNCT
ap-1368	120	22	sinh	sinh	NOUN
ap-1368	120	23	n	n	CCONJ
ap-1368	120	24	2−1	2−1	NUM
ap-1368	120	25	α	α	PRON
ap-1368	120	26	e(σ+n−1)α	e(σ+n−1)α	NOUN
ap-1368	120	27	γ	γ	X
ap-1368	120	28	(	(	PUNCT
ap-1368	120	29	n	n	PROPN
ap-1368	120	30	2	2	NUM
ap-1368	120	31	−	−	NOUN
ap-1368	120	32	1	1	NUM
ap-1368	120	33	)	)	PUNCT
ap-1368	120	34	γ	γ	PROPN
ap-1368	120	35	(	(	PUNCT
ap-1368	120	36	n+	n+	NUM
ap-1368	120	37	1	1	NUM
ap-1368	120	38	2	2	NUM
ap-1368	120	39	)	)	PUNCT
ap-1368	120	40	·	·	PUNCT
ap-1368	121	1	γ−1(−σ	γ−1(−σ	X
ap-1368	121	2	)	)	PUNCT
ap-1368	121	3	γ−	γ−	NOUN
ap-1368	121	4	1	1	NUM
ap-1368	121	5	2	2	NUM
ap-1368	121	6	(	(	PUNCT
ap-1368	121	7	n	n	CCONJ
ap-1368	121	8	−	−	PROPN
ap-1368	121	9	1	1	NUM
ap-1368	121	10	)	)	PUNCT
ap-1368	121	11	∫	∫	PROPN
ap-1368	122	1	+	+	PROPN
ap-1368	122	2	∞	∞	PROPN
ap-1368	122	3	0	0	NUM
ap-1368	122	4	λ−n+3	λ−n+3	PROPN
ap-1368	122	5	·	·	PUNCT
ap-1368	122	6	g2113	g2113	PROPN
ap-1368	122	7	⎛⎝λ2	⎛⎝λ2	VERB
ap-1368	122	8	4	4	NUM
ap-1368	122	9	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ap-1368	122	10	0	0	NUM
ap-1368	122	11	−σ	−σ	NOUN
ap-1368	122	12	−	−	PROPN
ap-1368	122	13	1	1	NUM
ap-1368	122	14	,	,	PUNCT
ap-1368	122	15	0	0	NUM
ap-1368	122	16	,	,	PUNCT
ap-1368	122	17	n−	n−	NOUN
ap-1368	122	18	3	3	NUM
ap-1368	122	19	2	2	NUM
ap-1368	122	20	⎞⎠	⎞⎠	NUM
ap-1368	122	21	·	·	PUNCT
ap-1368	122	22	g2113	g2113	PROPN
ap-1368	122	23	⎛⎝	⎛⎝	PROPN
ap-1368	122	24	(	(	PUNCT
ap-1368	122	25	λe−α)2	λe−α)2	NUM
ap-1368	122	26	4	4	NUM
ap-1368	122	27	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ap-1368	122	28	0	0	NUM
ap-1368	122	29	σ	σ	NOUN
ap-1368	122	30	−	−	PROPN
ap-1368	122	31	n−	n−	NOUN
ap-1368	122	32	1	1	NUM
ap-1368	122	33	2	2	NUM
ap-1368	122	34	,	,	PUNCT
ap-1368	122	35	0	0	NUM
ap-1368	122	36	,	,	PUNCT
ap-1368	122	37	n−	n−	NOUN
ap-1368	122	38	3	3	NUM
ap-1368	122	39	2	2	NUM
ap-1368	122	40	⎞⎠	⎞⎠	NUM
ap-1368	122	41	dλ	dλ	NOUN
ap-1368	122	42	.	.	PUNCT
ap-1368	123	1	proof	proof	NOUN
ap-1368	123	2	.	.	PUNCT
ap-1368	124	1	suppose	suppose	VERB
ap-1368	124	2	that	that	SCONJ
ap-1368	124	3	the	the	DET
ap-1368	124	4	condition	condition	NOUN
ap-1368	124	5	k1	k1	NOUN
ap-1368	124	6	=	=	SYM
ap-1368	124	7	l1	l1	PROPN
ap-1368	124	8	,	,	PUNCT
ap-1368	124	9	.	.	PUNCT
ap-1368	124	10	.	.	PUNCT
ap-1368	124	11	.	.	PUNCT
ap-1368	125	1	,	,	PUNCT
ap-1368	125	2	kn−2	kn−2	PROPN
ap-1368	125	3	=	=	SYM
ap-1368	125	4	ln−2	ln−2	PROPN
ap-1368	125	5	holds	hold	VERB
ap-1368	125	6	.	.	PUNCT
ap-1368	126	1	from	from	ADP
ap-1368	126	2	the	the	DET
ap-1368	126	3	distribution	distribution	NOUN
ap-1368	126	4	(	(	PUNCT
ap-1368	126	5	3	3	NUM
ap-1368	126	6	)	)	PUNCT
ap-1368	126	7	,	,	PUNCT
ap-1368	126	8	we	we	PRON
ap-1368	126	9	obtain	obtain	VERB
ap-1368	126	10	π(fσ1	π(fσ1	PROPN
ap-1368	126	11	k	k	NOUN
ap-1368	126	12	)	)	PUNCT
ap-1368	127	1	=	=	PUNCT
ap-1368	127	2	∫	∫	PROPN
ap-1368	128	1	+	+	ADJ
ap-1368	128	2	∞	∞	PROPN
ap-1368	128	3	0	0	X
ap-1368	129	1	cσ12	cσ12	PROPN
ap-1368	129	2	k,(l	k,(l	PROPN
ap-1368	129	3	,	,	PUNCT
ap-1368	129	4	λ)π(f	λ)π(f	PROPN
ap-1368	129	5	σ2	σ2	PROPN
ap-1368	129	6	(	(	PUNCT
ap-1368	129	7	l	l	PROPN
ap-1368	129	8	,	,	PUNCT
ap-1368	129	9	λ	λ	NOUN
ap-1368	129	10	)	)	PUNCT
ap-1368	129	11	)	)	PUNCT
ap-1368	129	12	dλ	dλ	NOUN
ap-1368	129	13	.	.	PUNCT
ap-1368	130	1	further	far	ADV
ap-1368	130	2	we	we	PRON
ap-1368	130	3	assume	assume	VERB
ap-1368	130	4	π(fσ1	π(fσ1	PROPN
ap-1368	130	5	k	k	NOUN
ap-1368	130	6	)	)	PUNCT
ap-1368	131	1	=	=	SYM
ap-1368	131	2	fγ1(q̂	fγ1(q̂	NOUN
ap-1368	131	3	−σ−n+1(y	−σ−n+1(y	PROPN
ap-1368	131	4	,	,	PUNCT
ap-1368	131	5	x	x	NOUN
ap-1368	131	6	)	)	PUNCT
ap-1368	131	7	,	,	PUNCT
ap-1368	131	8	fσ1	fσ1	PROPN
ap-1368	131	9	k	k	PROPN
ap-1368	131	10	)	)	PUNCT
ap-1368	131	11	and	and	CCONJ
ap-1368	131	12	π(fσ2	π(fσ2	NUM
ap-1368	131	13	(	(	PUNCT
ap-1368	131	14	l	l	NOUN
ap-1368	131	15	,	,	PUNCT
ap-1368	131	16	λ	λ	NOUN
ap-1368	131	17	)	)	PUNCT
ap-1368	131	18	)	)	PUNCT
ap-1368	132	1	=	=	PUNCT
ap-1368	132	2	fγ2(q̂	fγ2(q̂	PROPN
ap-1368	132	3	−σ−n+1(y	−σ−n+1(y	PROPN
ap-1368	132	4	,	,	PUNCT
ap-1368	132	5	x	x	NOUN
ap-1368	132	6	)	)	PUNCT
ap-1368	132	7	,	,	PUNCT
ap-1368	132	8	fσ2	fσ2	PROPN
ap-1368	132	9	(	(	PUNCT
ap-1368	132	10	l	l	NOUN
ap-1368	132	11	,	,	PUNCT
ap-1368	132	12	λ	λ	NOUN
ap-1368	132	13	)	)	PUNCT
ap-1368	132	14	)	)	PUNCT
ap-1368	132	15	,	,	PUNCT
ap-1368	132	16	then	then	ADV
ap-1368	132	17	for	for	ADP
ap-1368	132	18	the	the	DET
ap-1368	132	19	case	case	NOUN
ap-1368	132	20	y	y	PROPN
ap-1368	132	21	=	=	PRON
ap-1368	132	22	(	(	PUNCT
ap-1368	132	23	coshα	coshα	PROPN
ap-1368	132	24	,	,	PUNCT
ap-1368	132	25	0	0	NUM
ap-1368	132	26	,	,	PUNCT
ap-1368	132	27	.	.	PUNCT
ap-1368	132	28	.	.	PUNCT
ap-1368	133	1	.	.	PUNCT
ap-1368	134	1	,	,	PUNCT
ap-1368	134	2	0	0	NUM
ap-1368	134	3	,	,	PUNCT
ap-1368	134	4	sinhα	sinhα	NUM
ap-1368	134	5	)	)	PUNCT
ap-1368	134	6	and	and	CCONJ
ap-1368	134	7	put	put	VERB
ap-1368	134	8	k	k	PROPN
ap-1368	134	9	=	=	PUNCT
ap-1368	134	10	(	(	PUNCT
ap-1368	134	11	0	0	NUM
ap-1368	134	12	,	,	PUNCT
ap-1368	134	13	.	.	PUNCT
ap-1368	134	14	.	.	PUNCT
ap-1368	135	1	.	.	PUNCT
ap-1368	136	1	,	,	PUNCT
ap-1368	136	2	0	0	NUM
ap-1368	136	3	)	)	PUNCT
ap-1368	136	4	.	.	PUNCT
ap-1368	137	1	�	�	PROPN
ap-1368	137	2	consider	consider	VERB
ap-1368	137	3	the	the	DET
ap-1368	137	4	case	case	NOUN
ap-1368	137	5	so(2	so(2	NOUN
ap-1368	137	6	,	,	PUNCT
ap-1368	137	7	1	1	NUM
ap-1368	137	8	)	)	PUNCT
ap-1368	137	9	of	of	ADP
ap-1368	137	10	the	the	DET
ap-1368	137	11	group	group	NOUN
ap-1368	137	12	so(n	so(n	PROPN
ap-1368	137	13	,	,	PUNCT
ap-1368	137	14	1	1	NUM
ap-1368	137	15	)	)	PUNCT
ap-1368	137	16	.	.	PUNCT
ap-1368	138	1	in	in	ADP
ap-1368	138	2	this	this	DET
ap-1368	138	3	case	case	NOUN
ap-1368	138	4	,	,	PUNCT
ap-1368	138	5	k	k	PROPN
ap-1368	138	6	≡	≡	PROPN
ap-1368	138	7	k	k	PROPN
ap-1368	138	8	and	and	CCONJ
ap-1368	138	9	(	(	PUNCT
ap-1368	138	10	l	l	NOUN
ap-1368	138	11	,	,	PUNCT
ap-1368	138	12	λ	λ	NOUN
ap-1368	138	13	)	)	PUNCT
ap-1368	138	14	≡	≡	PROPN
ap-1368	138	15	λ	λ	PROPN
ap-1368	138	16	.	.	PUNCT
ap-1368	139	1	the	the	DET
ap-1368	139	2	following	follow	VERB
ap-1368	139	3	theorem	theorem	NOUN
ap-1368	139	4	is	be	AUX
ap-1368	139	5	related	relate	VERB
ap-1368	139	6	to	to	ADP
ap-1368	139	7	this	this	DET
ap-1368	139	8	case	case	NOUN
ap-1368	139	9	.	.	PUNCT
ap-1368	140	1	theorem	theorem	NOUN
ap-1368	140	2	2	2	NUM
ap-1368	140	3	.	.	PUNCT
ap-1368	141	1	if	if	SCONJ
ap-1368	141	2	−1	−1	NOUN
ap-1368	141	3	<	<	X
ap-1368	141	4	re	re	X
ap-1368	141	5	σ	σ	X
ap-1368	141	6	<	<	X
ap-1368	141	7	0	0	PROPN
ap-1368	141	8	and	and	CCONJ
ap-1368	141	9	α	α	PRON
ap-1368	141	10	�	�	PROPN
ap-1368	141	11	=	=	SYM
ap-1368	141	12	0	0	PROPN
ap-1368	141	13	,	,	PUNCT
ap-1368	141	14	then	then	ADV
ap-1368	141	15	p	p	NOUN
ap-1368	141	16	−l+	−l+	NOUN
ap-1368	141	17	12	12	NUM
ap-1368	141	18	σ+	σ+	NUM
ap-1368	141	19	12	12	NUM
ap-1368	141	20	(	(	PUNCT
ap-1368	141	21	coshα	coshα	PROPN
ap-1368	141	22	)	)	PUNCT
ap-1368	141	23	=	=	PUNCT
ap-1368	141	24	(	(	PUNCT
ap-1368	141	25	−1)l−1	−1)l−1	NOUN
ap-1368	141	26	2−σ−	2−σ−	NUM
ap-1368	141	27	l	l	NOUN
ap-1368	141	28	2−	2−	NUM
ap-1368	141	29	9	9	NUM
ap-1368	141	30	4	4	NUM
ap-1368	141	31	π−	π−	ADV
ap-1368	141	32	1	1	NUM
ap-1368	141	33	2	2	NUM
ap-1368	141	34	×	×	NOUN
ap-1368	141	35	e−α	e−α	VERB
ap-1368	141	36	sin(−πσ	sin(−πσ	NOUN
ap-1368	141	37	)	)	PUNCT
ap-1368	141	38	sinhl+	sinhl+	VERB
ap-1368	141	39	12	12	NUM
ap-1368	141	40	α	α	NOUN
ap-1368	141	41	·	·	PUNCT
ap-1368	141	42	(	(	PUNCT
ap-1368	141	43	coshα+	coshα+	X
ap-1368	141	44	1	1	NUM
ap-1368	141	45	coshα	coshα	NOUN
ap-1368	141	46	−	−	PROPN
ap-1368	141	47	1	1	NUM
ap-1368	141	48	)	)	PUNCT
ap-1368	141	49	l	l	NOUN
ap-1368	141	50	2	2	NUM
ap-1368	141	51	+	+	SYM
ap-1368	141	52	1	1	NUM
ap-1368	141	53	4	4	NUM
ap-1368	141	54	γ(σ	γ(σ	ADJ
ap-1368	141	55	−	−	PROPN
ap-1368	141	56	l	l	NOUN
ap-1368	141	57	+	+	PROPN
ap-1368	141	58	1)γ	1)γ	PROPN
ap-1368	141	59	(	(	PUNCT
ap-1368	141	60	l	l	NOUN
ap-1368	141	61	−	−	NOUN
ap-1368	141	62	3	3	NUM
ap-1368	141	63	2	2	NUM
ap-1368	141	64	)	)	PUNCT
ap-1368	141	65	·	·	PUNCT
ap-1368	142	1	γ−1	γ−1	PROPN
ap-1368	142	2	(	(	PUNCT
ap-1368	142	3	l	l	NOUN
ap-1368	142	4	+	+	NOUN
ap-1368	142	5	1	1	NUM
ap-1368	142	6	2	2	NUM
ap-1368	142	7	)	)	PUNCT
ap-1368	142	8	∫	∫	PROPN
ap-1368	143	1	∞	∞	PROPN
ap-1368	143	2	0	0	NUM
ap-1368	143	3	ρ−σ−1kσ+1(ρe−α	ρ−σ−1kσ+1(ρe−α	NOUN
ap-1368	143	4	)	)	PUNCT
ap-1368	143	5	·	·	PUNCT
ap-1368	143	6	(	(	PUNCT
ap-1368	143	7	4	4	X
ap-1368	143	8	)	)	PUNCT
ap-1368	143	9	∞∑	∞∑	PROPN
ap-1368	143	10	s=0	s=0	PROPN
ap-1368	143	11	(	(	PUNCT
ap-1368	143	12	−1)n	−1)n	PROPN
ap-1368	143	13	γ−2(s+	γ−2(s+	NUM
ap-1368	143	14	1)γ−1(s−	1)γ−1(s−	PROPN
ap-1368	143	15	σ	σ	NOUN
ap-1368	143	16	)	)	PUNCT
ap-1368	143	17	·	·	PUNCT
ap-1368	143	18	g2113	g2113	NOUN
ap-1368	143	19	(	(	PUNCT
ap-1368	143	20	ρ2	ρ2	NOUN
ap-1368	143	21	4	4	NUM
ap-1368	143	22	∣∣∣∣∣	∣∣∣∣∣	NOUN
ap-1368	143	23	−s	−s	NOUN
ap-1368	143	24	−σ	−σ	NOUN
ap-1368	143	25	−	−	PROPN
ap-1368	143	26	1	1	NUM
ap-1368	143	27	,	,	PUNCT
ap-1368	143	28	0	0	NUM
ap-1368	143	29	)	)	PUNCT
ap-1368	144	1	dρ	dρ	ADJ
ap-1368	144	2	proof	proof	NOUN
ap-1368	144	3	.	.	PUNCT
ap-1368	145	1	after	after	ADP
ap-1368	145	2	repeating	repeat	VERB
ap-1368	145	3	the	the	DET
ap-1368	145	4	proof	proof	NOUN
ap-1368	145	5	of	of	ADP
ap-1368	145	6	the	the	DET
ap-1368	145	7	previous	previous	ADJ
ap-1368	145	8	theorem	theorem	NOUN
ap-1368	145	9	,	,	PUNCT
ap-1368	145	10	we	we	PRON
ap-1368	145	11	derive	derive	VERB
ap-1368	145	12	the	the	DET
ap-1368	145	13	following	follow	VERB
ap-1368	145	14	representation	representation	NOUN
ap-1368	145	15	of	of	ADP
ap-1368	145	16	the	the	DET
ap-1368	145	17	gauss	gauss	ADJ
ap-1368	145	18	hypergeometric	hypergeometric	ADJ
ap-1368	145	19	function	function	NOUN
ap-1368	145	20	:	:	PUNCT
ap-1368	145	21	2f1	2f1	NUM
ap-1368	145	22	(	(	PUNCT
ap-1368	145	23	−σ	−σ	NOUN
ap-1368	145	24	−	−	PROPN
ap-1368	145	25	1	1	NUM
ap-1368	145	26	2	2	NUM
ap-1368	145	27	,	,	PUNCT
ap-1368	145	28	σ	σ	PROPN
ap-1368	145	29	+	+	CCONJ
ap-1368	145	30	3	3	NUM
ap-1368	145	31	2	2	NUM
ap-1368	145	32	;	;	PUNCT
ap-1368	145	33	1	1	NUM
ap-1368	145	34	2	2	NUM
ap-1368	145	35	+	+	NUM
ap-1368	145	36	l	l	NOUN
ap-1368	145	37	;	;	PUNCT
ap-1368	145	38	1−	1−	NUM
ap-1368	145	39	coshα	coshα	NOUN
ap-1368	145	40	2	2	NUM
ap-1368	145	41	)	)	PUNCT
ap-1368	145	42	=	=	SYM
ap-1368	145	43	(	(	PUNCT
ap-1368	145	44	−1)l−1	−1)l−1	NOUN
ap-1368	145	45	2−σ−	2−σ−	NUM
ap-1368	145	46	5	5	NUM
ap-1368	145	47	2	2	NUM
ap-1368	145	48	π−	π−	NOUN
ap-1368	145	49	1	1	NUM
ap-1368	145	50	2	2	NUM
ap-1368	145	51	e−α	e−α	PUNCT
ap-1368	145	52	sinhα	sinhα	VERB
ap-1368	145	53	sin(−πσ	sin(−πσ	NOUN
ap-1368	145	54	)	)	PUNCT
ap-1368	145	55	·	·	PUNCT
ap-1368	145	56	(	(	PUNCT
ap-1368	145	57	coshα+	coshα+	X
ap-1368	145	58	1	1	NUM
ap-1368	145	59	coshα	coshα	NOUN
ap-1368	145	60	−	−	PROPN
ap-1368	145	61	1	1	NUM
ap-1368	145	62	)	)	PUNCT
ap-1368	145	63	l	l	NOUN
ap-1368	145	64	2	2	NUM
ap-1368	145	65	+	+	SYM
ap-1368	145	66	1	1	NUM
ap-1368	145	67	4	4	NUM
ap-1368	145	68	γ(σ	γ(σ	ADJ
ap-1368	145	69	+	+	X
ap-1368	145	70	1−	1−	NUM
ap-1368	145	71	l	l	NOUN
ap-1368	145	72	)	)	PUNCT
ap-1368	145	73	γ	γ	NOUN
ap-1368	145	74	(	(	PUNCT
ap-1368	145	75	l	l	NOUN
ap-1368	145	76	−	−	NOUN
ap-1368	145	77	3	3	NUM
ap-1368	145	78	2	2	NUM
ap-1368	145	79	)	)	PUNCT
ap-1368	145	80	·	·	PUNCT
ap-1368	145	81	∫	∫	PROPN
ap-1368	145	82	∞	∞	PROPN
ap-1368	145	83	0	0	NUM
ap-1368	145	84	λ−σ−1kσ+1(λe−α	λ−σ−1kσ+1(λe−α	VERB
ap-1368	145	85	)	)	PUNCT
ap-1368	145	86	∞∑	∞∑	PROPN
ap-1368	145	87	s=0	s=0	X
ap-1368	145	88	(	(	PUNCT
ap-1368	145	89	−1)n	−1)n	PROPN
ap-1368	145	90	γ−2(s+	γ−2(s+	NUM
ap-1368	145	91	1	1	NUM
ap-1368	145	92	)	)	PUNCT
ap-1368	145	93	·	·	PUNCT
ap-1368	146	1	γ−1(s	γ−1(	NOUN
ap-1368	146	2	−	−	PROPN
ap-1368	146	3	σ)g2113	σ)g2113	PROPN
ap-1368	146	4	(	(	PUNCT
ap-1368	146	5	λ2	λ2	NOUN
ap-1368	146	6	4	4	NUM
ap-1368	146	7	∣∣∣∣∣	∣∣∣∣∣	NOUN
ap-1368	146	8	−s	−s	NOUN
ap-1368	146	9	−σ	−σ	NOUN
ap-1368	146	10	−	−	PROPN
ap-1368	146	11	1	1	NUM
ap-1368	146	12	,	,	PUNCT
ap-1368	146	13	0	0	NUM
ap-1368	146	14	,	,	PUNCT
ap-1368	146	15	0	0	NUM
ap-1368	146	16	)	)	PUNCT
ap-1368	146	17	dλ	dλ	NOUN
ap-1368	146	18	.	.	PUNCT
ap-1368	147	1	now	now	ADV
ap-1368	147	2	we	we	PRON
ap-1368	147	3	use	use	VERB
ap-1368	147	4	the	the	DET
ap-1368	147	5	formula	formula	NOUN
ap-1368	147	6	[	[	X
ap-1368	147	7	5	5	NUM
ap-1368	147	8	,	,	PUNCT
ap-1368	147	9	7.3.1.88	7.3.1.88	NUM
ap-1368	147	10	]	]	PUNCT
ap-1368	147	11	for	for	ADP
ap-1368	147	12	l	l	NOUN
ap-1368	147	13	=	=	SYM
ap-1368	147	14	0	0	X
ap-1368	147	15	.	.	PUNCT
ap-1368	147	16	�	�	PROPN
ap-1368	147	17	3	3	NUM
ap-1368	147	18	formulas	formula	NOUN
ap-1368	147	19	related	relate	VERB
ap-1368	147	20	to	to	ADP
ap-1368	147	21	paraboloid	paraboloid	ADJ
ap-1368	147	22	and	and	CCONJ
ap-1368	147	23	hyperboloid	hyperboloid	ADJ
ap-1368	147	24	let	let	VERB
ap-1368	147	25	γ3	γ3	NOUN
ap-1368	147	26	+	+	CCONJ
ap-1368	147	27	be	be	AUX
ap-1368	147	28	the	the	DET
ap-1368	147	29	intersection	intersection	NOUN
ap-1368	147	30	of	of	ADP
ap-1368	147	31	cone	cone	NOUN
ap-1368	147	32	c	c	PROPN
ap-1368	147	33	and	and	CCONJ
ap-1368	147	34	the	the	DET
ap-1368	147	35	plane	plane	NOUN
ap-1368	147	36	xn	xn	PUNCT
ap-1368	148	1	=	=	SYM
ap-1368	148	2	1	1	X
ap-1368	148	3	.	.	X
ap-1368	149	1	we	we	PRON
ap-1368	149	2	denote	denote	VERB
ap-1368	149	3	as	as	ADP
ap-1368	149	4	γ3−	γ3−	PROPN
ap-1368	149	5	the	the	DET
ap-1368	149	6	intersection	intersection	NOUN
ap-1368	149	7	of	of	ADP
ap-1368	149	8	c	c	PROPN
ap-1368	149	9	and	and	CCONJ
ap-1368	149	10	the	the	DET
ap-1368	149	11	plane	plane	NOUN
ap-1368	149	12	xn	xn	PUNCT
ap-1368	150	1	=	=	PUNCT
ap-1368	150	2	−1	−1	NOUN
ap-1368	150	3	.	.	PUNCT
ap-1368	151	1	let	let	VERB
ap-1368	151	2	γ3	γ3	NOUN
ap-1368	151	3	:	:	PUNCT
ap-1368	151	4	=	=	PUNCT
ap-1368	151	5	γ3	γ3	NOUN
ap-1368	151	6	+	+	CCONJ
ap-1368	151	7	∪	∪	X
ap-1368	151	8	γ3−.	γ3−.	ADP
ap-1368	151	9	the	the	DET
ap-1368	151	10	contour	contour	NOUN
ap-1368	151	11	γ3	γ3	NOUN
ap-1368	151	12	is	be	AUX
ap-1368	151	13	a	a	DET
ap-1368	151	14	homogeneous	homogeneous	ADJ
ap-1368	151	15	space	space	NOUN
ap-1368	151	16	with	with	ADP
ap-1368	151	17	respect	respect	NOUN
ap-1368	151	18	to	to	ADP
ap-1368	151	19	the	the	DET
ap-1368	151	20	subgroup	subgroup	NOUN
ap-1368	151	21	h3	h3	PROPN
ap-1368	151	22	�	�	PROPN
ap-1368	151	23	so(n−1	so(n−1	PROPN
ap-1368	151	24	,	,	PUNCT
ap-1368	151	25	1	1	NUM
ap-1368	151	26	)	)	PUNCT
ap-1368	151	27	.	.	PUNCT
ap-1368	152	1	if	if	SCONJ
ap-1368	152	2	x	x	PRON
ap-1368	152	3	belongs	belong	VERB
ap-1368	152	4	to	to	ADP
ap-1368	152	5	γ3	γ3	NOUN
ap-1368	152	6	,	,	PUNCT
ap-1368	152	7	then	then	ADV
ap-1368	152	8	xn	xn	PROPN
ap-1368	152	9	=	=	SYM
ap-1368	152	10	±1	±1	VERB
ap-1368	152	11	,	,	PUNCT
ap-1368	152	12	x0	x0	PROPN
ap-1368	152	13	=	=	PUNCT
ap-1368	152	14	cosh	cosh	PROPN
ap-1368	152	15	t	t	PROPN
ap-1368	152	16	,	,	PUNCT
ap-1368	152	17	xs	xs	PROPN
ap-1368	152	18	=	=	PUNCT
ap-1368	152	19	sinh	sinh	PROPN
ap-1368	152	20	t	t	PROPN
ap-1368	152	21	n−s−1∏	n−s−1∏	PROPN
ap-1368	153	1	i=1	i=1	PROPN
ap-1368	153	2	sinφi	sinφi	NOUN
ap-1368	153	3	·	·	PUNCT
ap-1368	153	4	cosφn−s	cosφn−	VERB
ap-1368	153	5	,	,	PUNCT
ap-1368	153	6	s	s	PART
ap-1368	153	7	/∈	/∈	PUNCT
ap-1368	153	8	{	{	PUNCT
ap-1368	153	9	0	0	NUM
ap-1368	153	10	,	,	PUNCT
ap-1368	153	11	n	n	CCONJ
ap-1368	153	12	}	}	PUNCT
ap-1368	153	13	(	(	PUNCT
ap-1368	153	14	if	if	SCONJ
ap-1368	153	15	angle	angle	NOUN
ap-1368	153	16	φn−s	φn−s	PROPN
ap-1368	153	17	exists	exist	VERB
ap-1368	153	18	)	)	PUNCT
ap-1368	153	19	,	,	PUNCT
ap-1368	153	20	where	where	SCONJ
ap-1368	153	21	t	t	PROPN
ap-1368	153	22	∈	∈	PROPN
ap-1368	153	23	r	r	X
ap-1368	153	24	,	,	PUNCT
ap-1368	153	25	φn−2	φn−2	PROPN
ap-1368	153	26	∈	∈	NOUN
ap-1368	154	1	[	[	X
ap-1368	154	2	0	0	NUM
ap-1368	154	3	;	;	PUNCT
ap-1368	154	4	2π	2π	NOUN
ap-1368	154	5	)	)	PUNCT
ap-1368	154	6	and	and	CCONJ
ap-1368	154	7	φ1	φ1	PROPN
ap-1368	154	8	,	,	PUNCT
ap-1368	154	9	.	.	PUNCT
ap-1368	154	10	.	.	PUNCT
ap-1368	154	11	.	.	PUNCT
ap-1368	155	1	,	,	PUNCT
ap-1368	155	2	φn−3	φn−3	PROPN
ap-1368	155	3	∈	∈	PROPN
ap-1368	156	1	[	[	X
ap-1368	156	2	0;π	0;π	NUM
ap-1368	156	3	)	)	PUNCT
ap-1368	156	4	.	.	PUNCT
ap-1368	157	1	any	any	DET
ap-1368	157	2	permutation	permutation	NOUN
ap-1368	157	3	ζ	ζ	NOUN
ap-1368	157	4	∈	∈	NOUN
ap-1368	157	5	s	s	PART
ap-1368	157	6	n	n	NOUN
ap-1368	157	7	determines	determine	VERB
ap-1368	157	8	the	the	DET
ap-1368	157	9	h3invariant	h3invariant	ADJ
ap-1368	157	10	measure	measure	NOUN
ap-1368	157	11	dγ4	dγ4	PROPN
ap-1368	157	12	=	=	SYM
ap-1368	157	13	dxζ(1	dxζ(1	X
ap-1368	157	14	)	)	PUNCT
ap-1368	157	15	.	.	PUNCT
ap-1368	157	16	.	.	PUNCT
ap-1368	158	1	.	.	PUNCT
ap-1368	159	1	dxζ(n−1	dxζ(n−1	X
ap-1368	159	2	)	)	PUNCT
ap-1368	159	3	|xζ(n)|	|xζ(n)|	PROPN
ap-1368	159	4	on	on	ADP
ap-1368	159	5	γ3	γ3	NOUN
ap-1368	159	6	,	,	PUNCT
ap-1368	159	7	so	so	ADV
ap-1368	159	8	dγ3	dγ3	PROPN
ap-1368	159	9	=	=	PUNCT
ap-1368	160	1	cosh	cosh	PROPN
ap-1368	160	2	n−2	n−2	PROPN
ap-1368	160	3	t	t	PROPN
ap-1368	161	1	dt	dt	X
ap-1368	161	2	n−2∏	n−2∏	INTJ
ap-1368	161	3	i=1	i=1	PROPN
ap-1368	162	1	sinn−i−2	sinn−i−2	PROPN
ap-1368	162	2	φi	φi	ADP
ap-1368	162	3	dφi	dφi	NOUN
ap-1368	162	4	.	.	PUNCT
ap-1368	163	1	let	let	VERB
ap-1368	163	2	us	we	PRON
ap-1368	163	3	now	now	ADV
ap-1368	163	4	consider	consider	VERB
ap-1368	163	5	the	the	DET
ap-1368	163	6	basis	basis	NOUN
ap-1368	163	7	consisting	consist	VERB
ap-1368	163	8	of	of	ADP
ap-1368	163	9	the	the	DET
ap-1368	163	10	functions	function	NOUN
ap-1368	164	1	fσ2	fσ2	PROPN
ap-1368	164	2	(	(	PUNCT
ap-1368	164	3	m	m	PROPN
ap-1368	164	4	,	,	PUNCT
ap-1368	164	5	μ,±)(x	μ,±)(x	PROPN
ap-1368	164	6	)	)	PUNCT
ap-1368	164	7	=	=	SYM
ap-1368	164	8	(	(	PUNCT
ap-1368	164	9	xn	xn	X
ap-1368	164	10	)	)	PUNCT
ap-1368	164	11	σ+	σ+	X
ap-1368	164	12	n−3	n−3	PROPN
ap-1368	164	13	2	2	NUM
ap-1368	164	14	±	±	NOUN
ap-1368	164	15	r	r	NOUN
ap-1368	164	16	3−n	3−n	NUM
ap-1368	164	17	2	2	NUM
ap-1368	164	18	−m1	−m1	PROPN
ap-1368	164	19	n−1	n−1	PROPN
ap-1368	164	20	·	·	PUNCT
ap-1368	165	1	p	p	X
ap-1368	166	1	3−n	3−n	NUM
ap-1368	166	2	2	2	NUM
ap-1368	166	3	−m1	−m1	NOUN
ap-1368	166	4	−	−	NOUN
ap-1368	166	5	1	1	NUM
ap-1368	166	6	2+iμ	2+iμ	NUM
ap-1368	166	7	(	(	PUNCT
ap-1368	166	8	x0	x0	PROPN
ap-1368	166	9	xn	xn	PROPN
ap-1368	166	10	)	)	PUNCT
ap-1368	167	1	ξn−1	ξn−1	ADV
ap-1368	167	2	m	m	VERB
ap-1368	167	3	(	(	PUNCT
ap-1368	167	4	x	x	X
ap-1368	167	5	)	)	PUNCT
ap-1368	167	6	,	,	PUNCT
ap-1368	167	7	72	72	NUM
ap-1368	167	8	acta	acta	PROPN
ap-1368	167	9	polytechnica	polytechnica	PROPN
ap-1368	167	10	vol	vol	NOUN
ap-1368	167	11	.	.	PUNCT
ap-1368	168	1	51	51	NUM
ap-1368	168	2	no	no	NOUN
ap-1368	168	3	.	.	PUNCT
ap-1368	169	1	1/2011	1/2011	NUM
ap-1368	169	2	where	where	SCONJ
ap-1368	169	3	(	(	PUNCT
ap-1368	169	4	xn	xn	X
ap-1368	169	5	)	)	PUNCT
ap-1368	169	6	σ+	σ+	X
ap-1368	169	7	n−3	n−3	PROPN
ap-1368	169	8	2	2	NUM
ap-1368	169	9	±	±	NOUN
ap-1368	169	10	is	be	AUX
ap-1368	169	11	the	the	DET
ap-1368	169	12	generalized	generalize	VERB
ap-1368	169	13	function	function	NOUN
ap-1368	169	14	defined	define	VERB
ap-1368	169	15	as	as	ADP
ap-1368	169	16	(	(	PUNCT
ap-1368	169	17	xn	xn	NUM
ap-1368	169	18	)	)	PUNCT
ap-1368	169	19	σ+	σ+	X
ap-1368	169	20	n−3	n−3	PROPN
ap-1368	169	21	2	2	NUM
ap-1368	169	22	±	±	NUM
ap-1368	169	23	=	=	PUNCT
ap-1368	169	24	{	{	PUNCT
ap-1368	169	25	|xn|σ+	|xn|σ+	NOUN
ap-1368	169	26	n−3	n−3	PROPN
ap-1368	169	27	2	2	NUM
ap-1368	169	28	,	,	PUNCT
ap-1368	169	29	if	if	SCONJ
ap-1368	169	30	sign	sign	VERB
ap-1368	169	31	xn	xn	PUNCT
ap-1368	170	1	=	=	SYM
ap-1368	170	2	±1	±1	VERB
ap-1368	170	3	,	,	PUNCT
ap-1368	170	4	0	0	NUM
ap-1368	170	5	,	,	PUNCT
ap-1368	170	6	if	if	SCONJ
ap-1368	170	7	sign	sign	VERB
ap-1368	170	8	x	x	SYM
ap-1368	170	9	�	�	PROPN
ap-1368	170	10	=	=	SYM
ap-1368	170	11	±1	±1	NOUN
ap-1368	170	12	,	,	PUNCT
ap-1368	170	13	m	m	VERB
ap-1368	170	14	=	=	SYM
ap-1368	170	15	(	(	PUNCT
ap-1368	170	16	m1	m1	PROPN
ap-1368	170	17	,	,	PUNCT
ap-1368	170	18	.	.	PUNCT
ap-1368	170	19	.	.	PUNCT
ap-1368	171	1	.	.	PUNCT
ap-1368	172	1	,	,	PUNCT
ap-1368	172	2	mn−3,±mn−2	mn−3,±mn−2	PROPN
ap-1368	172	3	)	)	PUNCT
ap-1368	172	4	∈	∈	PROPN
ap-1368	172	5	z	z	PROPN
ap-1368	172	6	n−2	n−2	PROPN
ap-1368	172	7	,	,	PUNCT
ap-1368	172	8	mi	mi	PROPN
ap-1368	172	9	≥	≥	NOUN
ap-1368	172	10	mi+1	mi+1	DET
ap-1368	172	11	≥	≥	NOUN
ap-1368	172	12	0	0	NUM
ap-1368	172	13	and	and	CCONJ
ap-1368	172	14	μ	μ	PROPN
ap-1368	172	15	∈	∈	PROPN
ap-1368	172	16	r.	r.	NOUN
ap-1368	172	17	by	by	ADP
ap-1368	172	18	analogy	analogy	NOUN
ap-1368	172	19	with	with	ADP
ap-1368	172	20	the	the	DET
ap-1368	172	21	previous	previous	ADJ
ap-1368	172	22	case	case	NOUN
ap-1368	172	23	,	,	PUNCT
ap-1368	172	24	we	we	PRON
ap-1368	172	25	can	can	AUX
ap-1368	172	26	obtain	obtain	VERB
ap-1368	172	27	the	the	DET
ap-1368	172	28	coefficients	coefficient	NOUN
ap-1368	172	29	ck,(m	ck,(m	NOUN
ap-1368	172	30	,	,	PUNCT
ap-1368	172	31	μ,+	μ,+	NUM
ap-1368	172	32	)	)	PUNCT
ap-1368	172	33	.	.	PUNCT
ap-1368	173	1	let	let	VERB
ap-1368	173	2	us	we	PRON
ap-1368	173	3	suppose	suppose	VERB
ap-1368	173	4	that	that	SCONJ
ap-1368	173	5	n	n	PROPN
ap-1368	173	6	=	=	SYM
ap-1368	173	7	3	3	NUM
ap-1368	173	8	and	and	CCONJ
ap-1368	173	9	k	k	NOUN
ap-1368	173	10	=	=	SYM
ap-1368	173	11	(	(	PUNCT
ap-1368	173	12	l	l	NOUN
ap-1368	173	13	,	,	PUNCT
ap-1368	173	14	s	s	PART
ap-1368	173	15	)	)	PUNCT
ap-1368	173	16	,	,	PUNCT
ap-1368	173	17	m	m	PROPN
ap-1368	173	18	≡	≡	PROPN
ap-1368	173	19	m.	m.	NOUN
ap-1368	173	20	from	from	ADP
ap-1368	173	21	the	the	DET
ap-1368	173	22	distribution	distribution	NOUN
ap-1368	173	23	fσ3	fσ3	ADP
ap-1368	173	24	m	m	PROPN
ap-1368	173	25	,	,	PUNCT
ap-1368	173	26	μ,+(x	μ,+(x	NUM
ap-1368	173	27	)	)	PUNCT
ap-1368	173	28	=	=	PUNCT
ap-1368	174	1	∞∑	∞∑	NUM
ap-1368	174	2	l=0	l=0	PROPN
ap-1368	174	3	|l|∑	|l|∑	NOUN
ap-1368	174	4	s=−|l|	s=−|l|	PROPN
ap-1368	174	5	cl	cl	PROPN
ap-1368	174	6	,	,	PUNCT
ap-1368	174	7	s	s	X
ap-1368	174	8	,	,	PUNCT
ap-1368	174	9	m	m	PROPN
ap-1368	174	10	,	,	PUNCT
ap-1368	174	11	μ,+	μ,+	NUM
ap-1368	174	12	fσ1	fσ1	PROPN
ap-1368	174	13	l	l	PROPN
ap-1368	174	14	,	,	PUNCT
ap-1368	174	15	s	s	PART
ap-1368	174	16	(	(	PUNCT
ap-1368	174	17	x	x	NOUN
ap-1368	174	18	)	)	PUNCT
ap-1368	174	19	,	,	PUNCT
ap-1368	174	20	we	we	PRON
ap-1368	174	21	have	have	VERB
ap-1368	174	22	fσ3	fσ3	ADJ
ap-1368	174	23	−s	−s	NOUN
ap-1368	174	24	,	,	PUNCT
ap-1368	174	25	μ,+(x	μ,+(x	NUM
ap-1368	174	26	)	)	PUNCT
ap-1368	174	27	=	=	SYM
ap-1368	175	1	∞∑	∞∑	NUM
ap-1368	175	2	l=0	l=0	PROPN
ap-1368	175	3	cl	cl	NOUN
ap-1368	175	4	,	,	PUNCT
ap-1368	175	5	s,−s	s,−s	NOUN
ap-1368	175	6	,	,	PUNCT
ap-1368	175	7	μ,+	μ,+	NUM
ap-1368	175	8	fσ1	fσ1	PROPN
ap-1368	175	9	l	l	PROPN
ap-1368	175	10	,	,	PUNCT
ap-1368	175	11	s	s	PART
ap-1368	175	12	(	(	PUNCT
ap-1368	175	13	x	x	NOUN
ap-1368	175	14	)	)	PUNCT
ap-1368	175	15	and	and	CCONJ
ap-1368	175	16	,	,	PUNCT
ap-1368	175	17	therefore	therefore	ADV
ap-1368	175	18	,	,	PUNCT
ap-1368	175	19	π(fσ3	π(fσ3	NOUN
ap-1368	175	20	−s	−s	NOUN
ap-1368	175	21	,	,	PUNCT
ap-1368	175	22	μ,+	μ,+	NUM
ap-1368	175	23	)	)	PUNCT
ap-1368	175	24	=	=	NOUN
ap-1368	176	1	∞∑	∞∑	NUM
ap-1368	176	2	l=0	l=0	PROPN
ap-1368	176	3	|l|∑	|l|∑	NOUN
ap-1368	176	4	s=−|l|	s=−|l|	PROPN
ap-1368	176	5	cl	cl	NOUN
ap-1368	176	6	,	,	PUNCT
ap-1368	176	7	s,−s	s,−s	NOUN
ap-1368	176	8	,	,	PUNCT
ap-1368	176	9	μ,+π(fσ1	μ,+π(fσ1	PROPN
ap-1368	176	10	l	l	PROPN
ap-1368	176	11	,	,	PUNCT
ap-1368	176	12	s	s	PART
ap-1368	176	13	)	)	PUNCT
ap-1368	176	14	.	.	PUNCT
ap-1368	177	1	(	(	PUNCT
ap-1368	177	2	5	5	X
ap-1368	177	3	)	)	PUNCT
ap-1368	177	4	we	we	PRON
ap-1368	177	5	choose	choose	VERB
ap-1368	177	6	γ3	γ3	NOUN
ap-1368	177	7	(	(	PUNCT
ap-1368	177	8	in	in	ADP
ap-1368	177	9	fact	fact	NOUN
ap-1368	177	10	,	,	PUNCT
ap-1368	177	11	γ3	γ3	NOUN
ap-1368	177	12	+	+	NOUN
ap-1368	177	13	)	)	PUNCT
ap-1368	177	14	on	on	ADP
ap-1368	177	15	the	the	DET
ap-1368	177	16	left	left	ADJ
ap-1368	177	17	side	side	NOUN
ap-1368	177	18	of	of	ADP
ap-1368	177	19	equality	equality	NOUN
ap-1368	177	20	(	(	PUNCT
ap-1368	177	21	5	5	NUM
ap-1368	177	22	)	)	PUNCT
ap-1368	177	23	and	and	CCONJ
ap-1368	177	24	γ1	γ1	NOUN
ap-1368	177	25	on	on	ADP
ap-1368	177	26	the	the	DET
ap-1368	177	27	opposite	opposite	ADJ
ap-1368	177	28	side	side	NOUN
ap-1368	177	29	.	.	PUNCT
ap-1368	178	1	in	in	ADP
ap-1368	178	2	accordance	accordance	NOUN
ap-1368	178	3	with	with	ADP
ap-1368	178	4	our	our	PRON
ap-1368	178	5	choice	choice	NOUN
ap-1368	178	6	,	,	PUNCT
ap-1368	178	7	we	we	PRON
ap-1368	178	8	use	use	VERB
ap-1368	178	9	two	two	NUM
ap-1368	178	10	parametrizations	parametrization	NOUN
ap-1368	178	11	of	of	ADP
ap-1368	178	12	a	a	DET
ap-1368	178	13	point	point	NOUN
ap-1368	178	14	y	y	PROPN
ap-1368	178	15	∈	∈	PROPN
ap-1368	179	1	h(1	h(1	NOUN
ap-1368	179	2	):	):	PUNCT
ap-1368	179	3	y(v	y(v	PROPN
ap-1368	179	4	)	)	PUNCT
ap-1368	179	5	=	=	PRON
ap-1368	180	1	(	(	PUNCT
ap-1368	180	2	v	v	X
ap-1368	180	3	+	+	CCONJ
ap-1368	181	1	v−1	v−1	PROPN
ap-1368	181	2	2	2	NUM
ap-1368	181	3	,	,	PUNCT
ap-1368	181	4	0	0	NUM
ap-1368	181	5	,	,	PUNCT
ap-1368	181	6	.	.	PUNCT
ap-1368	181	7	.	.	PUNCT
ap-1368	181	8	.	.	PUNCT
ap-1368	182	1	,	,	PUNCT
ap-1368	182	2	0	0	NUM
ap-1368	182	3	,	,	PUNCT
ap-1368	183	1	v−1	v−1	PROPN
ap-1368	183	2	−	−	NOUN
ap-1368	183	3	v	v	ADP
ap-1368	183	4	2	2	NUM
ap-1368	183	5	)	)	PUNCT
ap-1368	183	6	and	and	CCONJ
ap-1368	183	7	y(t	y(t	NUM
ap-1368	183	8	)	)	PUNCT
ap-1368	184	1	=	=	PRON
ap-1368	184	2	(	(	PUNCT
ap-1368	184	3	cosh	cosh	PROPN
ap-1368	184	4	t	t	PROPN
ap-1368	184	5	,	,	PUNCT
ap-1368	184	6	0	0	NUM
ap-1368	184	7	,	,	PUNCT
ap-1368	184	8	.	.	PUNCT
ap-1368	184	9	.	.	PUNCT
ap-1368	185	1	.	.	PUNCT
ap-1368	186	1	,	,	PUNCT
ap-1368	186	2	0	0	NUM
ap-1368	186	3	,	,	PUNCT
ap-1368	186	4	sinh	sinh	PROPN
ap-1368	186	5	t	t	PROPN
ap-1368	186	6	)	)	PUNCT
ap-1368	186	7	respectively	respectively	ADV
ap-1368	186	8	,	,	PUNCT
ap-1368	186	9	so	so	ADV
ap-1368	186	10	v	v	NOUN
ap-1368	186	11	=	=	NOUN
ap-1368	186	12	e−t	e−t	PROPN
ap-1368	186	13	.	.	PUNCT
ap-1368	187	1	after	after	ADP
ap-1368	187	2	integration	integration	NOUN
ap-1368	187	3	we	we	PRON
ap-1368	187	4	have	have	VERB
ap-1368	187	5	sin[π(σ	sin[π(σ	VERB
ap-1368	187	6	+	+	NOUN
ap-1368	187	7	1	1	NUM
ap-1368	187	8	)	)	PUNCT
ap-1368	187	9	]	]	PUNCT
ap-1368	188	1	cosh−1	cosh−1	X
ap-1368	188	2	tγ	tγ	NOUN
ap-1368	188	3	(	(	PUNCT
ap-1368	188	4	iμ−	iμ−	PROPN
ap-1368	188	5	σ	σ	NOUN
ap-1368	188	6	−	−	NUM
ap-1368	188	7	1	1	NUM
ap-1368	188	8	2	2	NUM
ap-1368	188	9	)	)	PUNCT
ap-1368	188	10	·	·	PUNCT
ap-1368	189	1	γ	γ	X
ap-1368	189	2	(	(	PUNCT
ap-1368	189	3	−3	−3	PROPN
ap-1368	189	4	2	2	NUM
ap-1368	189	5	−	−	PROPN
ap-1368	189	6	σ	σ	NOUN
ap-1368	189	7	−	−	PROPN
ap-1368	189	8	iμ	iμ	NOUN
ap-1368	189	9	)	)	PUNCT
ap-1368	189	10	p	p	X
ap-1368	190	1	σ+1	σ+1	X
ap-1368	190	2	−	−	PROPN
ap-1368	190	3	1	1	NUM
ap-1368	190	4	2+iμ	2+iμ	NUM
ap-1368	190	5	(	(	PUNCT
ap-1368	190	6	tanh	tanh	PROPN
ap-1368	190	7	t	t	PROPN
ap-1368	190	8	)	)	PUNCT
ap-1368	190	9	=	=	SYM
ap-1368	191	1	√	√	NUM
ap-1368	191	2	2	2	NUM
ap-1368	191	3	π	π	NOUN
ap-1368	191	4	3	3	NUM
ap-1368	191	5	2	2	NUM
ap-1368	191	6	∞∑	∞∑	NUM
ap-1368	191	7	l=0	l=0	PROPN
ap-1368	191	8	(	(	PUNCT
ap-1368	191	9	−1)l	−1)l	X
ap-1368	191	10	(	(	PUNCT
ap-1368	191	11	l!)−1al	l!)−1al	NOUN
ap-1368	191	12	sinh	sinh	NOUN
ap-1368	191	13	1	1	NUM
ap-1368	191	14	2	2	NUM
ap-1368	191	15	t	t	NOUN
ap-1368	191	16	·	·	PUNCT
ap-1368	192	1	γ(l	γ(l	NOUN
ap-1368	192	2	+	+	PUNCT
ap-1368	192	3	1)γ−1(σ	1)γ−1(σ	NUM
ap-1368	192	4	−	−	PROPN
ap-1368	192	5	l	l	NOUN
ap-1368	193	1	+	+	NOUN
ap-1368	194	1	1)p	1)p	NUM
ap-1368	194	2	−	−	NOUN
ap-1368	194	3	1	1	NUM
ap-1368	194	4	2−l	2−l	NUM
ap-1368	194	5	σ+	σ+	NUM
ap-1368	194	6	12	12	NUM
ap-1368	194	7	(	(	PUNCT
ap-1368	194	8	cosh	cosh	PROPN
ap-1368	194	9	t	t	PROPN
ap-1368	194	10	)	)	PUNCT
ap-1368	194	11	,	,	PUNCT
ap-1368	194	12	where	where	SCONJ
ap-1368	194	13	al	al	PROPN
ap-1368	194	14	is	be	AUX
ap-1368	194	15	the	the	DET
ap-1368	194	16	normalizing	normalizing	ADJ
ap-1368	194	17	factor	factor	NOUN
ap-1368	194	18	of	of	ADP
ap-1368	194	19	the	the	DET
ap-1368	194	20	function	function	NOUN
ap-1368	194	21	fσ1	fσ1	PROPN
ap-1368	194	22	l	l	PROPN
ap-1368	194	23	,	,	PUNCT
ap-1368	194	24	s	s	PART
ap-1368	194	25	(	(	PUNCT
ap-1368	194	26	x	x	NOUN
ap-1368	194	27	)	)	PUNCT
ap-1368	194	28	.	.	PUNCT
ap-1368	195	1	references	reference	NOUN
ap-1368	195	2	[	[	X
ap-1368	195	3	1	1	NUM
ap-1368	195	4	]	]	X
ap-1368	195	5	vilenkin	vilenkin	PROPN
ap-1368	195	6	,	,	PUNCT
ap-1368	195	7	n.	n.	PROPN
ap-1368	195	8	ja	ja	PROPN
ap-1368	195	9	.	.	PROPN
ap-1368	195	10	,	,	PUNCT
ap-1368	195	11	klimyk	klimyk	PROPN
ap-1368	195	12	,	,	PUNCT
ap-1368	195	13	a.	a.	NOUN
ap-1368	195	14	u.	u.	PROPN
ap-1368	195	15	:	:	PUNCT
ap-1368	195	16	representation	representation	NOUN
ap-1368	195	17	of	of	ADP
ap-1368	195	18	lie	lie	NOUN
ap-1368	195	19	groups	group	NOUN
ap-1368	195	20	and	and	CCONJ
ap-1368	195	21	special	special	ADJ
ap-1368	195	22	functions	function	NOUN
ap-1368	195	23	,	,	PUNCT
ap-1368	195	24	vol	vol	NOUN
ap-1368	195	25	.	.	PROPN
ap-1368	195	26	2	2	NUM
ap-1368	195	27	,	,	PUNCT
ap-1368	195	28	1993	1993	NUM
ap-1368	195	29	.	.	PUNCT
ap-1368	196	1	[	[	X
ap-1368	196	2	2	2	NUM
ap-1368	196	3	]	]	X
ap-1368	196	4	vilenkin	vilenkin	PROPN
ap-1368	196	5	,	,	PUNCT
ap-1368	196	6	n.	n.	PROPN
ap-1368	196	7	ja	ja	PROPN
ap-1368	196	8	.	.	PUNCT
ap-1368	196	9	:	:	PUNCT
ap-1368	196	10	special	special	ADJ
ap-1368	196	11	functions	function	NOUN
ap-1368	196	12	and	and	CCONJ
ap-1368	196	13	theory	theory	NOUN
ap-1368	196	14	of	of	ADP
ap-1368	196	15	group	group	NOUN
ap-1368	196	16	representations	representation	NOUN
ap-1368	196	17	,	,	PUNCT
ap-1368	196	18	1968	1968	NUM
ap-1368	196	19	.	.	PUNCT
ap-1368	197	1	[	[	X
ap-1368	197	2	3	3	NUM
ap-1368	197	3	]	]	SYM
ap-1368	197	4	erdelyi	erdelyi	NOUN
ap-1368	197	5	,	,	PUNCT
ap-1368	197	6	a.	a.	NOUN
ap-1368	197	7	:	:	PUNCT
ap-1368	197	8	tables	table	NOUN
ap-1368	197	9	of	of	ADP
ap-1368	197	10	integral	integral	ADJ
ap-1368	197	11	transforms	transform	NOUN
ap-1368	197	12	,	,	PUNCT
ap-1368	197	13	1954	1954	NUM
ap-1368	197	14	.	.	PUNCT
ap-1368	198	1	[	[	X
ap-1368	198	2	4	4	NUM
ap-1368	198	3	]	]	PUNCT
ap-1368	198	4	gradstein	gradstein	ADV
ap-1368	198	5	,	,	PUNCT
ap-1368	198	6	i.	i.	PROPN
ap-1368	198	7	s.	s.	PROPN
ap-1368	198	8	,	,	PUNCT
ap-1368	198	9	ryshik	ryshik	PROPN
ap-1368	198	10	,	,	PUNCT
ap-1368	198	11	i.	i.	NOUN
ap-1368	198	12	m.	m.	PROPN
ap-1368	198	13	:	:	PUNCT
ap-1368	198	14	tables	table	NOUN
ap-1368	198	15	of	of	ADP
ap-1368	198	16	series	series	NOUN
ap-1368	198	17	,	,	PUNCT
ap-1368	198	18	products	product	NOUN
ap-1368	198	19	and	and	CCONJ
ap-1368	198	20	integrals	integral	NOUN
ap-1368	198	21	,	,	PUNCT
ap-1368	198	22	1981	1981	NUM
ap-1368	198	23	.	.	PUNCT
ap-1368	199	1	[	[	X
ap-1368	199	2	5	5	NUM
ap-1368	199	3	]	]	X
ap-1368	199	4	prudnikov	prudnikov	NOUN
ap-1368	199	5	,	,	PUNCT
ap-1368	199	6	a.	a.	NOUN
ap-1368	199	7	p.	p.	PROPN
ap-1368	199	8	,	,	PUNCT
ap-1368	199	9	brychkov	brychkov	PROPN
ap-1368	199	10	,	,	PUNCT
ap-1368	199	11	yu	yu	PROPN
ap-1368	199	12	.	.	PUNCT
ap-1368	199	13	a.	a.	PROPN
ap-1368	199	14	,	,	PUNCT
ap-1368	199	15	marichev	marichev	ADV
ap-1368	199	16	,	,	PUNCT
ap-1368	199	17	o.	o.	PROPN
ap-1368	199	18	i.	i.	PROPN
ap-1368	199	19	:	:	PUNCT
ap-1368	199	20	integrals	integral	NOUN
ap-1368	199	21	and	and	CCONJ
ap-1368	199	22	series	series	NOUN
ap-1368	199	23	,	,	PUNCT
ap-1368	199	24	vol	vol	NOUN
ap-1368	199	25	.	.	PUNCT
ap-1368	200	1	3	3	NUM
ap-1368	200	2	:	:	PUNCT
ap-1368	200	3	more	more	ADJ
ap-1368	200	4	special	special	ADJ
ap-1368	200	5	functions	function	NOUN
ap-1368	200	6	,	,	PUNCT
ap-1368	200	7	1989	1989	NUM
ap-1368	200	8	.	.	PUNCT
ap-1368	201	1	ilya	ilya	PROPN
ap-1368	201	2	shilin	shilin	PROPN
ap-1368	201	3	dept	dept	PROPN
ap-1368	201	4	of	of	ADP
ap-1368	201	5	higher	high	ADJ
ap-1368	201	6	mathematics	mathematics	PROPN
ap-1368	201	7	m.	m.	NOUN
ap-1368	201	8	scholokhov	scholokhov	PROPN
ap-1368	201	9	moscow	moscow	PROPN
ap-1368	201	10	state	state	PROPN
ap-1368	201	11	university	university	PROPN
ap-1368	201	12	for	for	ADP
ap-1368	201	13	the	the	DET
ap-1368	201	14	humanities	humanity	NOUN
ap-1368	201	15	verhnya	verhnya	VERB
ap-1368	201	16	radishevskaya	radishevskaya	ADP
ap-1368	201	17	16–18	16–18	NUM
ap-1368	201	18	moscow	moscow	PROPN
ap-1368	201	19	109240	109240	NUM
ap-1368	201	20	,	,	PUNCT
ap-1368	201	21	russia	russia	PROPN
ap-1368	201	22	dept	dept	VERB
ap-1368	201	23	311	311	NUM
ap-1368	201	24	moscow	moscow	PROPN
ap-1368	201	25	aviation	aviation	PROPN
ap-1368	201	26	institute	institute	PROPN
ap-1368	201	27	volokolamskoe	volokolamskoe	ADV
ap-1368	201	28	shosse	shosse	PROPN
ap-1368	201	29	4	4	NUM
ap-1368	201	30	,	,	PUNCT
ap-1368	201	31	moscow	moscow	PROPN
ap-1368	201	32	125993	125993	NUM
ap-1368	201	33	,	,	PUNCT
ap-1368	201	34	russia	russia	PROPN
ap-1368	201	35	aleksandr	aleksandr	PROPN
ap-1368	201	36	nizhnikov	nizhnikov	PROPN
ap-1368	201	37	moscow	moscow	PROPN
ap-1368	201	38	pedagogical	pedagogical	ADJ
ap-1368	201	39	state	state	PROPN
ap-1368	201	40	university	university	PROPN
ap-1368	201	41	m.	m.	NOUN
ap-1368	201	42	pirogovskaya	pirogovskaya	NOUN
ap-1368	201	43	1	1	NUM
ap-1368	201	44	,	,	PUNCT
ap-1368	201	45	moscow	moscow	PROPN
ap-1368	201	46	119991	119991	NUM
ap-1368	201	47	,	,	PUNCT
ap-1368	201	48	russia	russia	PROPN
ap-1368	201	49	73	73	NUM