id	sid	tid	token	lemma	pos
ap-2224	1	1	acta	acta	PROPN
ap-2224	1	2	polytechnica	polytechnica	PROPN
ap-2224	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2224	1	4	/	/	SYM
ap-2224	1	5	ap.2014.54.0305	ap.2014.54.0305	PROPN
ap-2224	1	6	acta	acta	PROPN
ap-2224	1	7	polytechnica	polytechnica	PROPN
ap-2224	1	8	54(4):305–319	54(4):305–319	PROPN
ap-2224	1	9	,	,	PUNCT
ap-2224	1	10	2014	2014	NUM
ap-2224	1	11	©	©	PROPN
ap-2224	1	12	czech	czech	PROPN
ap-2224	1	13	technical	technical	PROPN
ap-2224	1	14	university	university	PROPN
ap-2224	1	15	in	in	ADP
ap-2224	1	16	prague	prague	PROPN
ap-2224	1	17	,	,	PUNCT
ap-2224	1	18	2014	2014	NUM
ap-2224	1	19	available	available	ADJ
ap-2224	1	20	online	online	ADV
ap-2224	1	21	at	at	ADP
ap-2224	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2224	1	23	fractional	fractional	ADJ
ap-2224	1	24	calculus	calculus	NOUN
ap-2224	1	25	and	and	CCONJ
ap-2224	1	26	lambert	lambert	PROPN
ap-2224	1	27	function	function	PROPN
ap-2224	1	28	i.	i.	PROPN
ap-2224	1	29	liouville	liouville	PROPN
ap-2224	1	30	–	–	PUNCT
ap-2224	1	31	weyl	weyl	VERB
ap-2224	1	32	fractional	fractional	ADJ
ap-2224	1	33	integral	integral	ADJ
ap-2224	1	34	vladimír	vladimír	NOUN
ap-2224	1	35	vojta	vojta	PROPN
ap-2224	1	36	chotovická	chotovická	PROPN
ap-2224	1	37	12	12	NUM
ap-2224	1	38	,	,	PUNCT
ap-2224	1	39	182	182	NUM
ap-2224	1	40	00	00	NUM
ap-2224	1	41	praha	praha	PROPN
ap-2224	1	42	8	8	NUM
ap-2224	1	43	correspondence	correspondence	NOUN
ap-2224	1	44	:	:	PUNCT
ap-2224	1	45	vojta@karneval.cz	vojta@karneval.cz	NOUN
ap-2224	1	46	abstract	abstract	NOUN
ap-2224	1	47	.	.	PUNCT
ap-2224	2	1	the	the	DET
ap-2224	2	2	interconnection	interconnection	NOUN
ap-2224	2	3	between	between	ADP
ap-2224	2	4	the	the	DET
ap-2224	2	5	liouville	liouville	NOUN
ap-2224	2	6	–	–	PUNCT
ap-2224	2	7	weyl	weyl	VERB
ap-2224	2	8	fractional	fractional	ADJ
ap-2224	2	9	integral	integral	ADJ
ap-2224	2	10	and	and	CCONJ
ap-2224	2	11	the	the	DET
ap-2224	2	12	lambert	lambert	PROPN
ap-2224	2	13	function	function	NOUN
ap-2224	2	14	is	be	AUX
ap-2224	2	15	studied	study	VERB
ap-2224	2	16	.	.	PUNCT
ap-2224	3	1	the	the	DET
ap-2224	3	2	class	class	NOUN
ap-2224	3	3	of	of	ADP
ap-2224	3	4	modified	modify	VERB
ap-2224	3	5	abel	abel	PROPN
ap-2224	3	6	equations	equation	NOUN
ap-2224	3	7	of	of	ADP
ap-2224	3	8	the	the	DET
ap-2224	3	9	first	first	ADJ
ap-2224	3	10	kind	kind	NOUN
ap-2224	3	11	is	be	AUX
ap-2224	3	12	solved	solve	VERB
ap-2224	3	13	.	.	PUNCT
ap-2224	4	1	a	a	DET
ap-2224	4	2	new	new	ADJ
ap-2224	4	3	integral	integral	ADJ
ap-2224	4	4	formula	formula	NOUN
ap-2224	4	5	for	for	ADP
ap-2224	4	6	the	the	DET
ap-2224	4	7	gamma	gamma	NOUN
ap-2224	4	8	function	function	NOUN
ap-2224	4	9	and	and	CCONJ
ap-2224	4	10	possibly	possibly	ADV
ap-2224	4	11	new	new	ADJ
ap-2224	4	12	transform	transform	NOUN
ap-2224	4	13	pairs	pair	NOUN
ap-2224	4	14	for	for	ADP
ap-2224	4	15	the	the	DET
ap-2224	4	16	laplace	laplace	NOUN
ap-2224	4	17	and	and	CCONJ
ap-2224	4	18	mellin	mellin	PROPN
ap-2224	4	19	transform	transform	NOUN
ap-2224	4	20	have	have	AUX
ap-2224	4	21	been	be	AUX
ap-2224	4	22	found	find	VERB
ap-2224	4	23	.	.	PUNCT
ap-2224	5	1	keywords	keyword	NOUN
ap-2224	5	2	:	:	PUNCT
ap-2224	5	3	variable	variable	ADJ
ap-2224	5	4	order	order	NOUN
ap-2224	5	5	fractional	fractional	ADJ
ap-2224	5	6	integral	integral	ADJ
ap-2224	5	7	,	,	PUNCT
ap-2224	5	8	liouville	liouville	ADJ
ap-2224	5	9	–	–	PUNCT
ap-2224	5	10	weyl	weyl	VERB
ap-2224	5	11	fractional	fractional	ADJ
ap-2224	5	12	integral	integral	ADJ
ap-2224	5	13	,	,	PUNCT
ap-2224	5	14	lambert	lambert	PROPN
ap-2224	5	15	function	function	PROPN
ap-2224	5	16	,	,	PUNCT
ap-2224	5	17	gamma	gamma	NOUN
ap-2224	5	18	function	function	PROPN
ap-2224	5	19	,	,	PUNCT
ap-2224	5	20	bickley	bickley	PROPN
ap-2224	5	21	function	function	PROPN
ap-2224	5	22	,	,	PUNCT
ap-2224	5	23	mcdonald	mcdonald	PROPN
ap-2224	5	24	function	function	PROPN
ap-2224	5	25	,	,	PUNCT
ap-2224	5	26	exponential	exponential	ADJ
ap-2224	5	27	integral	integral	ADJ
ap-2224	5	28	,	,	PUNCT
ap-2224	5	29	entire	entire	ADJ
ap-2224	5	30	functions	function	NOUN
ap-2224	5	31	,	,	PUNCT
ap-2224	5	32	completely	completely	ADV
ap-2224	5	33	monotone	monotone	ADJ
ap-2224	5	34	functions	function	NOUN
ap-2224	5	35	,	,	PUNCT
ap-2224	5	36	laplace	laplace	NOUN
ap-2224	5	37	transform	transform	NOUN
ap-2224	5	38	,	,	PUNCT
ap-2224	5	39	mellin	mellin	PROPN
ap-2224	5	40	transform	transform	NOUN
ap-2224	5	41	,	,	PUNCT
ap-2224	5	42	euler	euler	NOUN
ap-2224	5	43	integral	integral	ADJ
ap-2224	5	44	transform	transform	NOUN
ap-2224	5	45	,	,	PUNCT
ap-2224	5	46	volterra	volterra	NOUN
ap-2224	5	47	integral	integral	ADJ
ap-2224	5	48	equations	equation	NOUN
ap-2224	5	49	.	.	PUNCT
ap-2224	6	1	ams	am	NOUN
ap-2224	6	2	mathematics	mathematics	PROPN
ap-2224	6	3	subject	subject	ADJ
ap-2224	6	4	classification	classification	NOUN
ap-2224	6	5	:	:	PUNCT
ap-2224	6	6	26a33	26a33	NUM
ap-2224	6	7	,	,	PUNCT
ap-2224	6	8	(	(	PUNCT
ap-2224	6	9	33b15	33b15	NOUN
ap-2224	6	10	,	,	PUNCT
ap-2224	6	11	33e20	33e20	NUM
ap-2224	6	12	,	,	PUNCT
ap-2224	6	13	44a10	44a10	NUM
ap-2224	6	14	,	,	PUNCT
ap-2224	6	15	44a15	44a15	NUM
ap-2224	6	16	,	,	PUNCT
ap-2224	6	17	45d05	45d05	NUM
ap-2224	6	18	)	)	PUNCT
ap-2224	6	19	.	.	PUNCT
ap-2224	7	1	1	1	X
ap-2224	7	2	.	.	X
ap-2224	7	3	introduction	introduction	NOUN
ap-2224	7	4	for	for	ADP
ap-2224	7	5	a	a	DET
ap-2224	7	6	study	study	NOUN
ap-2224	7	7	of	of	ADP
ap-2224	7	8	the	the	DET
ap-2224	7	9	interconnection	interconnection	NOUN
ap-2224	7	10	between	between	ADP
ap-2224	7	11	fractional	fractional	ADJ
ap-2224	7	12	integrals	integral	NOUN
ap-2224	7	13	[	[	X
ap-2224	7	14	1	1	NUM
ap-2224	7	15	]	]	PUNCT
ap-2224	7	16	and	and	CCONJ
ap-2224	7	17	the	the	DET
ap-2224	7	18	lambert	lambert	PROPN
ap-2224	7	19	function	function	NOUN
ap-2224	8	1	[	[	X
ap-2224	8	2	2	2	NUM
ap-2224	8	3	]	]	PUNCT
ap-2224	8	4	,	,	PUNCT
ap-2224	8	5	we	we	PRON
ap-2224	8	6	start	start	VERB
ap-2224	8	7	with	with	ADP
ap-2224	8	8	the	the	DET
ap-2224	8	9	following	follow	VERB
ap-2224	8	10	variant	variant	NOUN
ap-2224	8	11	of	of	ADP
ap-2224	8	12	the	the	DET
ap-2224	8	13	fractional	fractional	ADJ
ap-2224	8	14	integral	integral	ADJ
ap-2224	8	15	,	,	PUNCT
ap-2224	8	16	known	know	VERB
ap-2224	8	17	as	as	ADP
ap-2224	8	18	the	the	DET
ap-2224	8	19	liouville	liouville	NOUN
ap-2224	8	20	,	,	PUNCT
ap-2224	8	21	liouville	liouville	ADJ
ap-2224	8	22	–	–	PUNCT
ap-2224	8	23	weyl	weyl	VERB
ap-2224	8	24	or	or	CCONJ
ap-2224	8	25	weyl	weyl	VERB
ap-2224	8	26	fractional	fractional	ADJ
ap-2224	8	27	integral	integral	ADJ
ap-2224	9	1	[	[	X
ap-2224	9	2	1	1	NUM
ap-2224	9	3	]	]	NUM
ap-2224	9	4	:	:	PUNCT
ap-2224	9	5	(	(	PUNCT
ap-2224	9	6	iν−f	iν−f	NOUN
ap-2224	9	7	)	)	PUNCT
ap-2224	9	8	(	(	PUNCT
ap-2224	9	9	y	y	NOUN
ap-2224	9	10	)	)	PUNCT
ap-2224	9	11	=	=	SYM
ap-2224	9	12	1	1	NUM
ap-2224	9	13	γ(ν	γ(ν	PROPN
ap-2224	9	14	)	)	PUNCT
ap-2224	9	15	∫	∫	PROPN
ap-2224	10	1	∞	∞	PROPN
ap-2224	10	2	y	y	PROPN
ap-2224	10	3	f	f	PROPN
ap-2224	10	4	(	(	PUNCT
ap-2224	10	5	x)(x−	x)(x−	PROPN
ap-2224	10	6	y)ν−1	y)ν−1	PROPN
ap-2224	10	7	dx	dx	PROPN
ap-2224	10	8	=	=	SYM
ap-2224	10	9	1	1	NUM
ap-2224	10	10	γ(ν	γ(ν	PROPN
ap-2224	10	11	)	)	PUNCT
ap-2224	10	12	∫	∫	PROPN
ap-2224	11	1	∞	∞	PROPN
ap-2224	11	2	0	0	NUM
ap-2224	11	3	f	f	PROPN
ap-2224	11	4	(	(	PUNCT
ap-2224	11	5	u+	u+	NUM
ap-2224	11	6	y)uν−1	y)uν−1	NOUN
ap-2224	11	7	du	du	NOUN
ap-2224	11	8	,	,	PUNCT
ap-2224	11	9	(	(	PUNCT
ap-2224	11	10	1.1	1.1	NUM
ap-2224	11	11	)	)	PUNCT
ap-2224	11	12	where	where	SCONJ
ap-2224	11	13	<	<	X
ap-2224	11	14	ν	ν	X
ap-2224	11	15	>	>	X
ap-2224	11	16	0	0	PUNCT
ap-2224	11	17	and	and	CCONJ
ap-2224	11	18	y	y	PROPN
ap-2224	11	19	>	>	X
ap-2224	11	20	−∞.	−∞.	PROPN
ap-2224	11	21	parameter	parameter	PROPN
ap-2224	11	22	ν	ν	PROPN
ap-2224	11	23	is	be	AUX
ap-2224	11	24	known	know	VERB
ap-2224	11	25	as	as	ADP
ap-2224	11	26	the	the	DET
ap-2224	11	27	order	order	NOUN
ap-2224	11	28	of	of	ADP
ap-2224	11	29	the	the	DET
ap-2224	11	30	fractional	fractional	ADJ
ap-2224	11	31	integral	integral	NOUN
ap-2224	11	32	.	.	PUNCT
ap-2224	12	1	the	the	DET
ap-2224	12	2	integral	integral	ADJ
ap-2224	12	3	on	on	ADP
ap-2224	12	4	the	the	DET
ap-2224	12	5	right	right	NOUN
ap-2224	12	6	of	of	ADP
ap-2224	12	7	(	(	PUNCT
ap-2224	12	8	1.1	1.1	NUM
ap-2224	12	9	)	)	PUNCT
ap-2224	12	10	is	be	AUX
ap-2224	12	11	the	the	DET
ap-2224	12	12	mellin	mellin	PROPN
ap-2224	12	13	transform	transform	NOUN
ap-2224	12	14	of	of	ADP
ap-2224	12	15	the	the	DET
ap-2224	12	16	shifted	shift	VERB
ap-2224	12	17	function	function	NOUN
ap-2224	12	18	f	f	PROPN
ap-2224	12	19	(	(	PUNCT
ap-2224	12	20	x	x	NOUN
ap-2224	12	21	)	)	PUNCT
ap-2224	12	22	.	.	PUNCT
ap-2224	13	1	this	this	PRON
ap-2224	13	2	means	mean	VERB
ap-2224	13	3	that	that	SCONJ
ap-2224	13	4	the	the	DET
ap-2224	13	5	mellin	mellin	PROPN
ap-2224	13	6	transform	transform	NOUN
ap-2224	13	7	of	of	ADP
ap-2224	13	8	function	function	NOUN
ap-2224	13	9	f	f	PROPN
ap-2224	13	10	(	(	PUNCT
ap-2224	13	11	·	·	PUNCT
ap-2224	13	12	)	)	PUNCT
ap-2224	13	13	is	be	AUX
ap-2224	13	14	its	its	PRON
ap-2224	13	15	liouville	liouville	NOUN
ap-2224	13	16	–	–	PUNCT
ap-2224	13	17	weyl	weyl	VERB
ap-2224	13	18	fractional	fractional	ADJ
ap-2224	13	19	integral	integral	ADJ
ap-2224	13	20	of	of	ADP
ap-2224	13	21	the	the	DET
ap-2224	13	22	order	order	NOUN
ap-2224	13	23	ν	ν	NOUN
ap-2224	13	24	at	at	ADP
ap-2224	13	25	y	y	PROPN
ap-2224	13	26	=	=	SYM
ap-2224	13	27	0	0	NUM
ap-2224	13	28	times	time	NOUN
ap-2224	13	29	the	the	DET
ap-2224	13	30	gamma	gamma	PROPN
ap-2224	13	31	function	function	NOUN
ap-2224	13	32	of	of	ADP
ap-2224	13	33	argument	argument	NOUN
ap-2224	13	34	ν	ν	X
ap-2224	13	35	.	.	PROPN
ap-2224	14	1	for	for	ADP
ap-2224	14	2	our	our	PRON
ap-2224	14	3	further	further	ADJ
ap-2224	14	4	investigation	investigation	NOUN
ap-2224	14	5	,	,	PUNCT
ap-2224	14	6	we	we	PRON
ap-2224	14	7	suppose	suppose	VERB
ap-2224	14	8	that	that	SCONJ
ap-2224	14	9	the	the	DET
ap-2224	14	10	integrals	integral	NOUN
ap-2224	14	11	in	in	ADP
ap-2224	14	12	(	(	PUNCT
ap-2224	14	13	1.1	1.1	NUM
ap-2224	14	14	)	)	PUNCT
ap-2224	14	15	converge	converge	VERB
ap-2224	14	16	absolutely	absolutely	ADV
ap-2224	14	17	and	and	CCONJ
ap-2224	14	18	that	that	DET
ap-2224	14	19	function	function	NOUN
ap-2224	14	20	f	f	X
ap-2224	14	21	(	(	PUNCT
ap-2224	14	22	x	x	X
ap-2224	14	23	)	)	PUNCT
ap-2224	14	24	is	be	AUX
ap-2224	14	25	an	an	DET
ap-2224	14	26	unilateral	unilateral	ADJ
ap-2224	14	27	laplace	laplace	NOUN
ap-2224	14	28	transform	transform	NOUN
ap-2224	14	29	(	(	PUNCT
ap-2224	14	30	picture	picture	NOUN
ap-2224	14	31	,	,	PUNCT
ap-2224	14	32	generating	generate	VERB
ap-2224	14	33	function	function	NOUN
ap-2224	14	34	)	)	PUNCT
ap-2224	14	35	of	of	ADP
ap-2224	14	36	the	the	DET
ap-2224	14	37	relevant	relevant	ADJ
ap-2224	14	38	original	original	ADJ
ap-2224	14	39	or	or	CCONJ
ap-2224	14	40	determining	determine	VERB
ap-2224	14	41	function	function	NOUN
ap-2224	14	42	f(t	f(t	NOUN
ap-2224	14	43	):	):	PUNCT
ap-2224	14	44	f	f	PROPN
ap-2224	14	45	(	(	PUNCT
ap-2224	14	46	x	x	X
ap-2224	14	47	)	)	PUNCT
ap-2224	14	48	=	=	SYM
ap-2224	15	1	∫	∫	PROPN
ap-2224	15	2	∞	∞	NUM
ap-2224	15	3	0	0	NUM
ap-2224	16	1	e−xtf(t	e−xtf(t	NUM
ap-2224	16	2	)	)	PUNCT
ap-2224	16	3	dt	dt	NOUN
ap-2224	16	4	,	,	PUNCT
ap-2224	16	5	(	(	PUNCT
ap-2224	16	6	1.2	1.2	NUM
ap-2224	16	7	)	)	PUNCT
ap-2224	16	8	where	where	SCONJ
ap-2224	16	9	f(t	f(t	NOUN
ap-2224	16	10	)	)	PUNCT
ap-2224	16	11	is	be	AUX
ap-2224	16	12	a	a	DET
ap-2224	16	13	locally	locally	ADV
ap-2224	16	14	integrable	integrable	ADJ
ap-2224	16	15	function	function	NOUN
ap-2224	16	16	on	on	ADP
ap-2224	16	17	the	the	DET
ap-2224	16	18	interval	interval	NOUN
ap-2224	16	19	[	[	X
ap-2224	16	20	0,∞	0,∞	NOUN
ap-2224	16	21	)	)	PUNCT
ap-2224	16	22	,	,	PUNCT
ap-2224	16	23	and	and	CCONJ
ap-2224	16	24	the	the	DET
ap-2224	16	25	integral	integral	ADJ
ap-2224	16	26	in	in	ADP
ap-2224	16	27	(	(	PUNCT
ap-2224	16	28	1.2	1.2	NUM
ap-2224	16	29	)	)	PUNCT
ap-2224	16	30	converges	converge	VERB
ap-2224	16	31	absolutely	absolutely	ADV
ap-2224	16	32	at	at	ADP
ap-2224	16	33	some	some	PRON
ap-2224	16	34	x	x	X
ap-2224	16	35	=	=	SYM
ap-2224	16	36	c.	c.	NOUN
ap-2224	16	37	then	then	ADV
ap-2224	16	38	the	the	DET
ap-2224	16	39	integral	integral	ADJ
ap-2224	16	40	in	in	ADP
ap-2224	16	41	(	(	PUNCT
ap-2224	16	42	1.2	1.2	NUM
ap-2224	16	43	)	)	PUNCT
ap-2224	16	44	converges	converge	VERB
ap-2224	16	45	absolutely	absolutely	ADV
ap-2224	16	46	and	and	CCONJ
ap-2224	16	47	uniformly	uniformly	ADV
ap-2224	16	48	in	in	ADP
ap-2224	16	49	the	the	DET
ap-2224	16	50	half	half	ADJ
ap-2224	16	51	-	-	PUNCT
ap-2224	16	52	plane	plane	NOUN
ap-2224	16	53	<	<	X
ap-2224	16	54	(	(	PUNCT
ap-2224	16	55	x	x	X
ap-2224	16	56	)	)	PUNCT
ap-2224	16	57	>	>	X
ap-2224	17	1	<	<	X
ap-2224	17	2	(	(	PUNCT
ap-2224	17	3	c	c	NOUN
ap-2224	17	4	)	)	PUNCT
ap-2224	18	1	[	[	X
ap-2224	18	2	3	3	NUM
ap-2224	18	3	]	]	PUNCT
ap-2224	18	4	.	.	PUNCT
ap-2224	19	1	if	if	SCONJ
ap-2224	19	2	f(t	f(t	NOUN
ap-2224	19	3	)	)	PUNCT
ap-2224	19	4	is	be	AUX
ap-2224	19	5	a	a	DET
ap-2224	19	6	function	function	NOUN
ap-2224	19	7	of	of	ADP
ap-2224	19	8	the	the	DET
ap-2224	19	9	exponential	exponential	ADJ
ap-2224	19	10	order	order	NOUN
ap-2224	19	11	α0	α0	ADJ
ap-2224	19	12	,	,	PUNCT
ap-2224	19	13	i.e.	i.e.	X
ap-2224	19	14	,	,	PUNCT
ap-2224	19	15	f(t	f(t	PROPN
ap-2224	19	16	)	)	PUNCT
ap-2224	19	17	=	=	SYM
ap-2224	19	18	o(expα0	o(expα0	PROPN
ap-2224	19	19	t	t	PROPN
ap-2224	19	20	)	)	PUNCT
ap-2224	19	21	for	for	ADP
ap-2224	19	22	t	t	NOUN
ap-2224	19	23	=	=	PUNCT
ap-2224	20	1	+	+	NUM
ap-2224	20	2	∞	∞	PROPN
ap-2224	20	3	(	(	PUNCT
ap-2224	20	4	see	see	VERB
ap-2224	20	5	[	[	X
ap-2224	20	6	21	21	NUM
ap-2224	20	7	,	,	PUNCT
ap-2224	20	8	chap	chap	NOUN
ap-2224	20	9	.	.	PUNCT
ap-2224	21	1	5	5	NUM
ap-2224	21	2	]	]	NUM
ap-2224	21	3	)	)	PUNCT
ap-2224	21	4	,	,	PUNCT
ap-2224	21	5	then	then	ADV
ap-2224	21	6	integral	integral	ADJ
ap-2224	21	7	(	(	PUNCT
ap-2224	21	8	1.2	1.2	NUM
ap-2224	21	9	)	)	PUNCT
ap-2224	21	10	converges	converge	VERB
ap-2224	21	11	absolutely	absolutely	ADV
ap-2224	21	12	at	at	ADP
ap-2224	21	13	least	least	ADJ
ap-2224	21	14	in	in	ADP
ap-2224	21	15	the	the	DET
ap-2224	21	16	region	region	NOUN
ap-2224	21	17	<	<	X
ap-2224	21	18	x	x	X
ap-2224	21	19	>	>	X
ap-2224	21	20	α0	α0	ADJ
ap-2224	21	21	and	and	CCONJ
ap-2224	21	22	uniformly	uniformly	ADV
ap-2224	21	23	for	for	ADP
ap-2224	21	24	<	<	X
ap-2224	21	25	x	x	X
ap-2224	21	26	>	>	X
ap-2224	21	27	α1	α1	PROPN
ap-2224	21	28	>	>	X
ap-2224	21	29	α0	α0	PROPN
ap-2224	21	30	.	.	PUNCT
ap-2224	22	1	function	function	PROPN
ap-2224	22	2	f	f	PROPN
ap-2224	22	3	(	(	PUNCT
ap-2224	22	4	x	x	X
ap-2224	22	5	)	)	PUNCT
ap-2224	22	6	is	be	AUX
ap-2224	22	7	holomorphic	holomorphic	ADJ
ap-2224	22	8	in	in	ADP
ap-2224	22	9	the	the	DET
ap-2224	22	10	region	region	NOUN
ap-2224	22	11	<	<	X
ap-2224	22	12	x	x	X
ap-2224	22	13	>	>	X
ap-2224	22	14	α0	α0	PROPN
ap-2224	22	15	.	.	PUNCT
ap-2224	23	1	it	it	PRON
ap-2224	23	2	can	can	AUX
ap-2224	23	3	easily	easily	ADV
ap-2224	23	4	be	be	AUX
ap-2224	23	5	shown	show	VERB
ap-2224	23	6	[	[	PUNCT
ap-2224	23	7	4	4	X
ap-2224	23	8	]	]	PUNCT
ap-2224	23	9	that	that	SCONJ
ap-2224	23	10	(	(	PUNCT
ap-2224	23	11	iν−f	iν−f	NOUN
ap-2224	23	12	)	)	PUNCT
ap-2224	23	13	(	(	PUNCT
ap-2224	23	14	y	y	NOUN
ap-2224	23	15	)	)	PUNCT
ap-2224	23	16	=	=	SYM
ap-2224	24	1	∫	∫	PROPN
ap-2224	24	2	∞	∞	PROPN
ap-2224	24	3	0	0	PROPN
ap-2224	24	4	e−yxx−νf(x	e−yxx−νf(x	PROPN
ap-2224	24	5	)	)	PUNCT
ap-2224	24	6	dx	dx	PROPN
ap-2224	24	7	,	,	PUNCT
ap-2224	24	8	<	<	X
ap-2224	24	9	ν	ν	X
ap-2224	24	10	≥	≥	NOUN
ap-2224	24	11	0	0	NUM
ap-2224	24	12	.	.	PUNCT
ap-2224	25	1	(	(	PUNCT
ap-2224	25	2	1.3	1.3	NUM
ap-2224	25	3	)	)	PUNCT
ap-2224	25	4	it	it	PRON
ap-2224	25	5	should	should	AUX
ap-2224	25	6	be	be	AUX
ap-2224	25	7	noted	note	VERB
ap-2224	25	8	that	that	SCONJ
ap-2224	25	9	(	(	PUNCT
ap-2224	25	10	1.3	1.3	NUM
ap-2224	25	11	)	)	PUNCT
ap-2224	25	12	is	be	AUX
ap-2224	25	13	defined	define	VERB
ap-2224	25	14	straightforwardly	straightforwardly	ADV
ap-2224	25	15	for	for	ADP
ap-2224	25	16	<	<	X
ap-2224	25	17	ν	ν	X
ap-2224	25	18	=	=	SYM
ap-2224	25	19	0	0	NUM
ap-2224	25	20	,	,	PUNCT
ap-2224	25	21	whereas	whereas	SCONJ
ap-2224	25	22	(	(	PUNCT
ap-2224	25	23	1.1	1.1	NUM
ap-2224	25	24	)	)	PUNCT
ap-2224	25	25	is	be	AUX
ap-2224	25	26	not	not	PART
ap-2224	25	27	.	.	PUNCT
ap-2224	26	1	the	the	DET
ap-2224	26	2	integral	integral	ADJ
ap-2224	26	3	in	in	ADP
ap-2224	26	4	(	(	PUNCT
ap-2224	26	5	1.3	1.3	NUM
ap-2224	26	6	)	)	PUNCT
ap-2224	26	7	can	can	AUX
ap-2224	26	8	be	be	AUX
ap-2224	26	9	regarded	regard	VERB
ap-2224	26	10	as	as	ADP
ap-2224	26	11	a	a	DET
ap-2224	26	12	laplace	laplace	NOUN
ap-2224	26	13	transform	transform	NOUN
ap-2224	26	14	for	for	ADP
ap-2224	26	15	variable	variable	ADJ
ap-2224	26	16	y	y	PROPN
ap-2224	26	17	,	,	PUNCT
ap-2224	26	18	or	or	CCONJ
ap-2224	26	19	as	as	ADP
ap-2224	26	20	a	a	DET
ap-2224	26	21	mellin	mellin	NOUN
ap-2224	26	22	transform	transform	NOUN
ap-2224	26	23	for	for	ADP
ap-2224	26	24	variable	variable	ADJ
ap-2224	26	25	−ν	−ν	NOUN
ap-2224	26	26	+	+	CCONJ
ap-2224	27	1	1	1	X
ap-2224	27	2	.	.	PUNCT
ap-2224	27	3	it	it	PRON
ap-2224	27	4	is	be	AUX
ap-2224	27	5	often	often	ADV
ap-2224	27	6	called	call	VERB
ap-2224	27	7	the	the	DET
ap-2224	27	8	laplace	laplace	NOUN
ap-2224	27	9	–	–	PUNCT
ap-2224	27	10	mellin	mellin	NOUN
ap-2224	27	11	transform	transform	NOUN
ap-2224	27	12	[	[	X
ap-2224	27	13	5	5	NUM
ap-2224	27	14	]	]	PUNCT
ap-2224	27	15	.	.	PUNCT
ap-2224	28	1	function	function	PROPN
ap-2224	28	2	f(x	f(x	PROPN
ap-2224	28	3	)	)	PUNCT
ap-2224	28	4	can	can	AUX
ap-2224	28	5	be	be	AUX
ap-2224	28	6	a	a	DET
ap-2224	28	7	generalized	generalized	ADJ
ap-2224	28	8	function	function	NOUN
ap-2224	28	9	,	,	PUNCT
ap-2224	28	10	namely	namely	ADV
ap-2224	28	11	a	a	DET
ap-2224	28	12	dirac	dirac	NOUN
ap-2224	28	13	delta	delta	NOUN
ap-2224	28	14	function	function	NOUN
ap-2224	28	15	,	,	PUNCT
ap-2224	28	16	see	see	VERB
ap-2224	28	17	[	[	X
ap-2224	28	18	3	3	NUM
ap-2224	28	19	]	]	PUNCT
ap-2224	28	20	.	.	PUNCT
ap-2224	29	1	these	these	DET
ap-2224	29	2	generalized	generalize	VERB
ap-2224	29	3	functions	function	NOUN
ap-2224	29	4	will	will	AUX
ap-2224	29	5	be	be	AUX
ap-2224	29	6	used	use	VERB
ap-2224	29	7	as	as	ADP
ap-2224	29	8	a	a	DET
ap-2224	29	9	tool	tool	NOUN
ap-2224	29	10	only	only	ADV
ap-2224	29	11	,	,	PUNCT
ap-2224	29	12	and	and	CCONJ
ap-2224	29	13	the	the	DET
ap-2224	29	14	results	result	NOUN
ap-2224	29	15	obtained	obtain	VERB
ap-2224	29	16	here	here	ADV
ap-2224	29	17	can	can	AUX
ap-2224	29	18	be	be	AUX
ap-2224	29	19	verified	verify	VERB
ap-2224	29	20	without	without	ADP
ap-2224	29	21	making	make	VERB
ap-2224	29	22	use	use	NOUN
ap-2224	29	23	of	of	ADP
ap-2224	29	24	them	they	PRON
ap-2224	29	25	.	.	PUNCT
ap-2224	30	1	definition	definition	NOUN
ap-2224	30	2	1.1	1.1	NUM
ap-2224	30	3	.	.	PUNCT
ap-2224	31	1	a	a	DET
ap-2224	31	2	completely	completely	ADV
ap-2224	31	3	monotone	monotone	ADJ
ap-2224	31	4	function	function	NOUN
ap-2224	31	5	is	be	AUX
ap-2224	31	6	defined	define	VERB
ap-2224	31	7	as	as	SCONJ
ap-2224	31	8	follows	follow	VERB
ap-2224	31	9	[	[	X
ap-2224	31	10	6	6	NUM
ap-2224	31	11	,	,	PUNCT
ap-2224	31	12	def	def	ADJ
ap-2224	31	13	.	.	PROPN
ap-2224	31	14	1.3	1.3	NUM
ap-2224	31	15	,	,	PUNCT
ap-2224	31	16	p.	p.	NOUN
ap-2224	31	17	2	2	NUM
ap-2224	31	18	]	]	X
ap-2224	31	19	:	:	PUNCT
ap-2224	31	20	a	a	DET
ap-2224	31	21	function	function	NOUN
ap-2224	31	22	f	f	NOUN
ap-2224	31	23	:	:	PUNCT
ap-2224	31	24	(	(	PUNCT
ap-2224	31	25	0,∞)→	0,∞)→	NOUN
ap-2224	31	26	r	r	NOUN
ap-2224	31	27	is	be	AUX
ap-2224	31	28	a	a	DET
ap-2224	31	29	completely	completely	ADV
ap-2224	31	30	monotone	monotone	ADJ
ap-2224	31	31	function	function	NOUN
ap-2224	31	32	if	if	SCONJ
ap-2224	31	33	f	f	X
ap-2224	31	34	(	(	PUNCT
ap-2224	31	35	·	·	PUNCT
ap-2224	31	36	)	)	PUNCT
ap-2224	31	37	is	be	AUX
ap-2224	31	38	a	a	DET
ap-2224	31	39	member	member	NOUN
ap-2224	31	40	of	of	ADP
ap-2224	31	41	the	the	DET
ap-2224	31	42	class	class	NOUN
ap-2224	31	43	c∞	c∞	PROPN
ap-2224	31	44	and	and	CCONJ
ap-2224	31	45	(	(	PUNCT
ap-2224	31	46	−1)nf	−1)nf	PROPN
ap-2224	31	47	(	(	PUNCT
ap-2224	31	48	n)(λ	n)(λ	PROPN
ap-2224	31	49	)	)	PUNCT
ap-2224	31	50	≥	≥	NOUN
ap-2224	31	51	0	0	NUM
ap-2224	31	52	,	,	PUNCT
ap-2224	31	53	n	n	PRON
ap-2224	31	54	∈	∈	PROPN
ap-2224	31	55	n	n	NOUN
ap-2224	31	56	∪	∪	X
ap-2224	31	57	{	{	PUNCT
ap-2224	31	58	0	0	NUM
ap-2224	31	59	}	}	PUNCT
ap-2224	31	60	,	,	PUNCT
ap-2224	31	61	λ	λ	X
ap-2224	31	62	>	>	X
ap-2224	31	63	0	0	NUM
ap-2224	31	64	.	.	PUNCT
ap-2224	32	1	(	(	PUNCT
ap-2224	32	2	1.4	1.4	NUM
ap-2224	32	3	)	)	PUNCT
ap-2224	32	4	equation	equation	NOUN
ap-2224	32	5	(	(	PUNCT
ap-2224	32	6	1.3	1.3	NUM
ap-2224	32	7	)	)	PUNCT
ap-2224	32	8	has	have	VERB
ap-2224	32	9	an	an	DET
ap-2224	32	10	interesting	interesting	ADJ
ap-2224	32	11	consequence	consequence	NOUN
ap-2224	32	12	based	base	VERB
ap-2224	32	13	on	on	ADP
ap-2224	32	14	the	the	DET
ap-2224	32	15	following	follow	VERB
ap-2224	32	16	theorems	theorem	NOUN
ap-2224	32	17	:	:	PUNCT
ap-2224	32	18	theorem	theorem	NOUN
ap-2224	32	19	1.2	1.2	NUM
ap-2224	32	20	.	.	PUNCT
ap-2224	33	1	the	the	DET
ap-2224	33	2	liouville	liouville	NOUN
ap-2224	33	3	–	–	PUNCT
ap-2224	33	4	weyl	weyl	VERB
ap-2224	33	5	fractional	fractional	ADJ
ap-2224	33	6	integral	integral	ADJ
ap-2224	33	7	of	of	ADP
ap-2224	33	8	a	a	DET
ap-2224	33	9	completely	completely	ADV
ap-2224	33	10	monotone	monotone	ADJ
ap-2224	33	11	function	function	NOUN
ap-2224	33	12	is	be	AUX
ap-2224	33	13	a	a	DET
ap-2224	33	14	completely	completely	ADV
ap-2224	33	15	monotone	monotone	ADJ
ap-2224	33	16	function	function	NOUN
ap-2224	33	17	.	.	PUNCT
ap-2224	34	1	305	305	NUM
ap-2224	34	2	http://dx.doi.org/10.14311/ap.2014.54.0305	http://dx.doi.org/10.14311/ap.2014.54.0305	PRON
ap-2224	34	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2224	34	4	vladimír	vladimír	NOUN
ap-2224	34	5	vojta	vojta	PROPN
ap-2224	34	6	acta	acta	PROPN
ap-2224	34	7	polytechnica	polytechnica	PROPN
ap-2224	34	8	proof	proof	NOUN
ap-2224	34	9	.	.	PUNCT
ap-2224	35	1	according	accord	VERB
ap-2224	35	2	to	to	ADP
ap-2224	35	3	the	the	DET
ap-2224	35	4	bernstein	bernstein	PROPN
ap-2224	35	5	theorem	theorem	PROPN
ap-2224	35	6	[	[	X
ap-2224	35	7	6	6	NUM
ap-2224	35	8	,	,	PUNCT
ap-2224	35	9	p.	p.	NOUN
ap-2224	35	10	3	3	NUM
ap-2224	35	11	]	]	PUNCT
ap-2224	35	12	,	,	PUNCT
ap-2224	35	13	the	the	DET
ap-2224	35	14	laplace	laplace	NOUN
ap-2224	35	15	transform	transform	NOUN
ap-2224	35	16	of	of	ADP
ap-2224	35	17	the	the	DET
ap-2224	35	18	nonnegative	nonnegative	ADJ
ap-2224	35	19	function	function	NOUN
ap-2224	35	20	is	be	AUX
ap-2224	35	21	completely	completely	ADV
ap-2224	35	22	monotone	monotone	ADJ
ap-2224	35	23	and	and	CCONJ
ap-2224	35	24	,	,	PUNCT
ap-2224	35	25	conversely	conversely	ADV
ap-2224	35	26	,	,	PUNCT
ap-2224	35	27	if	if	SCONJ
ap-2224	35	28	function	function	NOUN
ap-2224	35	29	f	f	X
ap-2224	35	30	(	(	PUNCT
ap-2224	35	31	x	x	X
ap-2224	35	32	)	)	PUNCT
ap-2224	35	33	,	,	PUNCT
ap-2224	35	34	defined	define	VERB
ap-2224	35	35	by	by	ADP
ap-2224	35	36	(	(	PUNCT
ap-2224	35	37	1.2	1.2	NUM
ap-2224	35	38	)	)	PUNCT
ap-2224	35	39	,	,	PUNCT
ap-2224	35	40	is	be	AUX
ap-2224	35	41	completely	completely	ADV
ap-2224	35	42	monotone	monotone	ADJ
ap-2224	35	43	,	,	PUNCT
ap-2224	35	44	then	then	ADV
ap-2224	35	45	function	function	VERB
ap-2224	35	46	f(t	f(t	PROPN
ap-2224	35	47	)	)	PUNCT
ap-2224	35	48	is	be	AUX
ap-2224	35	49	nonnegative	nonnegative	ADJ
ap-2224	35	50	for	for	ADP
ap-2224	35	51	t	t	PROPN
ap-2224	35	52	>	>	X
ap-2224	35	53	0	0	NUM
ap-2224	35	54	.	.	PUNCT
ap-2224	36	1	because	because	SCONJ
ap-2224	36	2	function	function	VERB
ap-2224	36	3	f(x	f(x	PROPN
ap-2224	36	4	)	)	PUNCT
ap-2224	36	5	is	be	AUX
ap-2224	36	6	nonnegative	nonnegative	ADJ
ap-2224	36	7	by	by	ADP
ap-2224	36	8	hypothesis	hypothesis	NOUN
ap-2224	36	9	,	,	PUNCT
ap-2224	36	10	the	the	DET
ap-2224	36	11	liouville	liouville	NOUN
ap-2224	36	12	–	–	PUNCT
ap-2224	36	13	weyl	weyl	VERB
ap-2224	36	14	fractional	fractional	ADJ
ap-2224	36	15	integral	integral	ADJ
ap-2224	36	16	defined	define	VERB
ap-2224	36	17	by	by	ADP
ap-2224	36	18	(	(	PUNCT
ap-2224	36	19	1.3	1.3	NUM
ap-2224	36	20	)	)	PUNCT
ap-2224	36	21	is	be	AUX
ap-2224	36	22	the	the	DET
ap-2224	36	23	laplace	laplace	NOUN
ap-2224	36	24	transform	transform	NOUN
ap-2224	36	25	of	of	ADP
ap-2224	36	26	a	a	DET
ap-2224	36	27	nonnegative	nonnegative	ADJ
ap-2224	36	28	function	function	NOUN
ap-2224	36	29	.	.	PUNCT
ap-2224	37	1	theorem	theorem	VERB
ap-2224	37	2	1.3	1.3	NUM
ap-2224	37	3	.	.	PUNCT
ap-2224	38	1	suppose	suppose	VERB
ap-2224	38	2	the	the	DET
ap-2224	38	3	following	follow	VERB
ap-2224	38	4	two	two	NUM
ap-2224	38	5	conditions	condition	NOUN
ap-2224	38	6	on	on	ADP
ap-2224	38	7	f	f	PROPN
ap-2224	38	8	(	(	PUNCT
ap-2224	38	9	·	·	PUNCT
ap-2224	38	10	)	)	PUNCT
ap-2224	38	11	are	be	AUX
ap-2224	38	12	satisfied	satisfied	ADJ
ap-2224	38	13	:	:	PUNCT
ap-2224	38	14	(	(	PUNCT
ap-2224	38	15	1	1	NUM
ap-2224	38	16	.	.	PUNCT
ap-2224	38	17	)	)	PUNCT
ap-2224	39	1	the	the	DET
ap-2224	39	2	liouville	liouville	NOUN
ap-2224	39	3	–	–	PUNCT
ap-2224	39	4	weyl	weyl	VERB
ap-2224	39	5	fractional	fractional	ADJ
ap-2224	39	6	integral	integral	ADJ
ap-2224	39	7	of	of	ADP
ap-2224	39	8	function	function	NOUN
ap-2224	39	9	f	f	PROPN
ap-2224	39	10	(	(	PUNCT
ap-2224	39	11	·	·	PUNCT
ap-2224	39	12	)	)	PUNCT
ap-2224	39	13	is	be	AUX
ap-2224	39	14	a	a	DET
ap-2224	39	15	completely	completely	ADV
ap-2224	39	16	monotone	monotone	ADJ
ap-2224	39	17	function	function	NOUN
ap-2224	39	18	;	;	PUNCT
ap-2224	39	19	(	(	PUNCT
ap-2224	39	20	2	2	NUM
ap-2224	39	21	.	.	PUNCT
ap-2224	39	22	)	)	PUNCT
ap-2224	39	23	function	function	NOUN
ap-2224	39	24	f	f	PROPN
ap-2224	39	25	(	(	PUNCT
ap-2224	39	26	·	·	PUNCT
ap-2224	39	27	)	)	PUNCT
ap-2224	39	28	is	be	AUX
ap-2224	39	29	a	a	DET
ap-2224	39	30	laplace	laplace	NOUN
ap-2224	39	31	transform	transform	NOUN
ap-2224	39	32	of	of	ADP
ap-2224	39	33	some	some	DET
ap-2224	39	34	function	function	NOUN
ap-2224	39	35	f	f	X
ap-2224	39	36	(	(	PUNCT
ap-2224	39	37	·	·	PUNCT
ap-2224	39	38	)	)	PUNCT
ap-2224	39	39	.	.	PUNCT
ap-2224	40	1	then	then	ADV
ap-2224	40	2	function	function	VERB
ap-2224	40	3	f	f	PROPN
ap-2224	40	4	(	(	PUNCT
ap-2224	40	5	·	·	PUNCT
ap-2224	40	6	)	)	PUNCT
ap-2224	40	7	is	be	AUX
ap-2224	40	8	completely	completely	ADV
ap-2224	40	9	monotone	monotone	ADJ
ap-2224	40	10	.	.	PUNCT
ap-2224	41	1	proof	proof	NOUN
ap-2224	41	2	.	.	PUNCT
ap-2224	42	1	in	in	ADP
ap-2224	42	2	consequence	consequence	NOUN
ap-2224	42	3	of	of	ADP
ap-2224	42	4	hypothesis	hypothesis	NOUN
ap-2224	42	5	2	2	NUM
ap-2224	42	6	.	.	NUM
ap-2224	42	7	,	,	PUNCT
ap-2224	42	8	the	the	DET
ap-2224	42	9	liouville	liouville	NOUN
ap-2224	42	10	–	–	PUNCT
ap-2224	42	11	weyl	weyl	VERB
ap-2224	42	12	fractional	fractional	ADJ
ap-2224	42	13	integral	integral	ADJ
ap-2224	42	14	is	be	AUX
ap-2224	42	15	represented	represent	VERB
ap-2224	42	16	by	by	ADP
ap-2224	42	17	(	(	PUNCT
ap-2224	42	18	1.3	1.3	NUM
ap-2224	42	19	)	)	PUNCT
ap-2224	42	20	.	.	PUNCT
ap-2224	43	1	according	accord	VERB
ap-2224	43	2	to	to	ADP
ap-2224	43	3	hypothesis	hypothesis	NOUN
ap-2224	43	4	1	1	NUM
ap-2224	43	5	.	.	PUNCT
ap-2224	44	1	and	and	CCONJ
ap-2224	44	2	the	the	DET
ap-2224	44	3	bernstein	bernstein	PROPN
ap-2224	44	4	theorem	theorem	PROPN
ap-2224	44	5	,	,	PUNCT
ap-2224	44	6	function	function	NOUN
ap-2224	44	7	x−nf(x	x−nf(x	PROPN
ap-2224	44	8	)	)	PUNCT
ap-2224	44	9	is	be	AUX
ap-2224	44	10	nonnegative	nonnegative	ADJ
ap-2224	44	11	for	for	ADP
ap-2224	44	12	<	<	X
ap-2224	44	13	x	x	X
ap-2224	44	14	>	>	X
ap-2224	44	15	0	0	PROPN
ap-2224	44	16	,	,	PUNCT
ap-2224	44	17	reν	reν	NOUN
ap-2224	44	18	>	>	X
ap-2224	44	19	0	0	X
ap-2224	44	20	.	.	PUNCT
ap-2224	45	1	this	this	PRON
ap-2224	45	2	implies	imply	VERB
ap-2224	45	3	that	that	PRON
ap-2224	45	4	function	function	VERB
ap-2224	45	5	f(t	f(t	NOUN
ap-2224	45	6	)	)	PUNCT
ap-2224	45	7	in	in	ADP
ap-2224	45	8	(	(	PUNCT
ap-2224	45	9	1.2	1.2	NUM
ap-2224	45	10	)	)	PUNCT
ap-2224	45	11	is	be	AUX
ap-2224	45	12	also	also	ADV
ap-2224	45	13	nonnegative	nonnegative	ADJ
ap-2224	45	14	.	.	PUNCT
ap-2224	46	1	this	this	PRON
ap-2224	46	2	means	mean	VERB
ap-2224	46	3	that	that	SCONJ
ap-2224	46	4	function	function	NOUN
ap-2224	46	5	f	f	X
ap-2224	46	6	(	(	PUNCT
ap-2224	46	7	·	·	PUNCT
ap-2224	46	8	)	)	PUNCT
ap-2224	46	9	is	be	AUX
ap-2224	46	10	completely	completely	ADV
ap-2224	46	11	monotone	monotone	ADJ
ap-2224	46	12	according	accord	VERB
ap-2224	46	13	to	to	ADP
ap-2224	46	14	the	the	DET
ap-2224	46	15	bernstein	bernstein	PROPN
ap-2224	46	16	theorem	theorem	PROPN
ap-2224	46	17	.	.	PUNCT
ap-2224	47	1	completely	completely	ADV
ap-2224	47	2	monotone	monotone	ADJ
ap-2224	47	3	functions	function	NOUN
ap-2224	47	4	play	play	VERB
ap-2224	47	5	a	a	DET
ap-2224	47	6	substantial	substantial	ADJ
ap-2224	47	7	role	role	NOUN
ap-2224	47	8	in	in	ADP
ap-2224	47	9	probability	probability	NOUN
ap-2224	47	10	theory	theory	NOUN
ap-2224	47	11	,	,	PUNCT
ap-2224	47	12	measure	measure	NOUN
ap-2224	47	13	theory	theory	NOUN
ap-2224	47	14	,	,	PUNCT
ap-2224	47	15	etc	etc	X
ap-2224	47	16	.	.	X
ap-2224	48	1	they	they	PRON
ap-2224	48	2	can	can	AUX
ap-2224	48	3	also	also	ADV
ap-2224	48	4	be	be	AUX
ap-2224	48	5	found	find	VERB
ap-2224	48	6	in	in	ADP
ap-2224	48	7	technological	technological	ADJ
ap-2224	48	8	practice	practice	NOUN
ap-2224	48	9	we	we	PRON
ap-2224	48	10	mention	mention	VERB
ap-2224	48	11	time	time	NOUN
ap-2224	48	12	-	-	PUNCT
ap-2224	48	13	dependent	dependent	ADJ
ap-2224	48	14	shear	shear	NOUN
ap-2224	48	15	,	,	PUNCT
ap-2224	48	16	bulk	bulk	NOUN
ap-2224	48	17	and	and	CCONJ
ap-2224	48	18	the	the	DET
ap-2224	48	19	young	young	ADJ
ap-2224	48	20	moduli	modulus	NOUN
ap-2224	48	21	of	of	ADP
ap-2224	48	22	linear	linear	ADJ
ap-2224	48	23	viscoelastic	viscoelastic	ADJ
ap-2224	48	24	materials	material	NOUN
ap-2224	48	25	,	,	PUNCT
ap-2224	48	26	because	because	SCONJ
ap-2224	48	27	they	they	PRON
ap-2224	48	28	are	be	AUX
ap-2224	48	29	laplace	laplace	NOUN
ap-2224	48	30	transforms	transform	NOUN
ap-2224	48	31	of	of	ADP
ap-2224	48	32	the	the	DET
ap-2224	48	33	relevant	relevant	ADJ
ap-2224	48	34	nonnegative	nonnegative	ADJ
ap-2224	48	35	relaxation	relaxation	NOUN
ap-2224	48	36	spectra	spectra	NOUN
ap-2224	49	1	[	[	X
ap-2224	49	2	7	7	NUM
ap-2224	49	3	]	]	PUNCT
ap-2224	49	4	.	.	PUNCT
ap-2224	50	1	2	2	X
ap-2224	50	2	.	.	X
ap-2224	50	3	diagonal	diagonal	ADJ
ap-2224	50	4	fractional	fractional	ADJ
ap-2224	50	5	integrals	integral	NOUN
ap-2224	50	6	in	in	ADP
ap-2224	50	7	the	the	DET
ap-2224	50	8	case	case	NOUN
ap-2224	50	9	that	that	SCONJ
ap-2224	50	10	order	order	NOUN
ap-2224	50	11	ν	ν	NOUN
ap-2224	50	12	of	of	ADP
ap-2224	50	13	the	the	DET
ap-2224	50	14	fractional	fractional	ADJ
ap-2224	50	15	integral	integral	ADJ
ap-2224	50	16	in	in	ADP
ap-2224	50	17	(	(	PUNCT
ap-2224	50	18	1.1	1.1	NUM
ap-2224	50	19	)	)	PUNCT
ap-2224	50	20	is	be	AUX
ap-2224	50	21	a	a	DET
ap-2224	50	22	function	function	NOUN
ap-2224	50	23	of	of	ADP
ap-2224	50	24	variable	variable	ADJ
ap-2224	50	25	y	y	PROPN
ap-2224	50	26	,	,	PUNCT
ap-2224	50	27	i.e.	i.e.	X
ap-2224	50	28	,	,	PUNCT
ap-2224	50	29	ν	ν	X
ap-2224	50	30	=	=	SYM
ap-2224	50	31	ν(y	ν(y	PROPN
ap-2224	50	32	)	)	PUNCT
ap-2224	50	33	,	,	PUNCT
ap-2224	50	34	the	the	DET
ap-2224	50	35	integral	integral	ADJ
ap-2224	50	36	in	in	ADP
ap-2224	50	37	(	(	PUNCT
ap-2224	50	38	1.1	1.1	NUM
ap-2224	50	39	)	)	PUNCT
ap-2224	50	40	is	be	AUX
ap-2224	50	41	called	call	VERB
ap-2224	50	42	a	a	DET
ap-2224	50	43	variable	variable	ADJ
ap-2224	50	44	order	order	NOUN
ap-2224	50	45	fractional	fractional	ADJ
ap-2224	50	46	integral	integral	ADJ
ap-2224	50	47	[	[	X
ap-2224	50	48	8	8	NUM
ap-2224	50	49	]	]	PUNCT
ap-2224	50	50	.	.	PUNCT
ap-2224	51	1	variable	variable	ADJ
ap-2224	51	2	order	order	NOUN
ap-2224	51	3	fractional	fractional	ADJ
ap-2224	51	4	integrals	integral	NOUN
ap-2224	51	5	and	and	CCONJ
ap-2224	51	6	derivatives	derivative	NOUN
ap-2224	51	7	have	have	AUX
ap-2224	51	8	been	be	AUX
ap-2224	51	9	studied	study	VERB
ap-2224	51	10	recently	recently	ADV
ap-2224	51	11	due	due	ADP
ap-2224	51	12	to	to	ADP
ap-2224	51	13	their	their	PRON
ap-2224	51	14	applications	application	NOUN
ap-2224	51	15	in	in	ADP
ap-2224	51	16	many	many	ADJ
ap-2224	51	17	branches	branch	NOUN
ap-2224	51	18	of	of	ADP
ap-2224	51	19	science	science	NOUN
ap-2224	51	20	where	where	SCONJ
ap-2224	51	21	the	the	DET
ap-2224	51	22	memory	memory	NOUN
ap-2224	51	23	effect	effect	NOUN
ap-2224	51	24	plays	play	VERB
ap-2224	51	25	an	an	DET
ap-2224	51	26	essential	essential	ADJ
ap-2224	51	27	role	role	NOUN
ap-2224	51	28	[	[	X
ap-2224	51	29	9	9	NUM
ap-2224	51	30	]	]	PUNCT
ap-2224	51	31	.	.	PUNCT
ap-2224	52	1	our	our	PRON
ap-2224	52	2	interest	interest	NOUN
ap-2224	52	3	will	will	AUX
ap-2224	52	4	be	be	AUX
ap-2224	52	5	concentrated	concentrate	VERB
ap-2224	52	6	on	on	ADP
ap-2224	52	7	the	the	DET
ap-2224	52	8	simplest	simple	ADJ
ap-2224	52	9	case	case	NOUN
ap-2224	52	10	ν(y	ν(y	PROPN
ap-2224	52	11	)	)	PUNCT
ap-2224	53	1	=	=	PUNCT
ap-2224	53	2	y.	y.	NOUN
ap-2224	53	3	definition	definition	NOUN
ap-2224	53	4	2.1	2.1	NUM
ap-2224	53	5	.	.	PUNCT
ap-2224	54	1	the	the	DET
ap-2224	54	2	fractional	fractional	ADJ
ap-2224	54	3	integral	integral	NOUN
ap-2224	54	4	of	of	ADP
ap-2224	54	5	variable	variable	ADJ
ap-2224	54	6	order	order	NOUN
ap-2224	54	7	(	(	PUNCT
ap-2224	54	8	iy−f	iy−f	NOUN
ap-2224	54	9	)	)	PUNCT
ap-2224	54	10	(	(	PUNCT
ap-2224	54	11	y	y	NOUN
ap-2224	54	12	)	)	PUNCT
ap-2224	54	13	=	=	SYM
ap-2224	54	14	1	1	NUM
ap-2224	54	15	γ(y	γ(y	PROPN
ap-2224	54	16	)	)	PUNCT
ap-2224	55	1	∫	∫	PROPN
ap-2224	56	1	∞	∞	PROPN
ap-2224	56	2	y	y	PROPN
ap-2224	56	3	f	f	PROPN
ap-2224	56	4	(	(	PUNCT
ap-2224	56	5	x)(x−	x)(x−	PROPN
ap-2224	56	6	y)y−1	y)y−1	NOUN
ap-2224	56	7	dx	dx	PROPN
ap-2224	56	8	=	=	SYM
ap-2224	56	9	∫	∫	PROPN
ap-2224	56	10	∞	∞	PROPN
ap-2224	56	11	0	0	NUM
ap-2224	56	12	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	56	13	)	)	PUNCT
ap-2224	56	14	dt	dt	PROPN
ap-2224	56	15	,	,	PUNCT
ap-2224	56	16	y	y	PROPN
ap-2224	56	17	>	>	X
ap-2224	56	18	0	0	NUM
ap-2224	56	19	,	,	PUNCT
ap-2224	56	20	(	(	PUNCT
ap-2224	56	21	2.1	2.1	NUM
ap-2224	56	22	)	)	PUNCT
ap-2224	56	23	will	will	AUX
ap-2224	56	24	be	be	AUX
ap-2224	56	25	called	call	VERB
ap-2224	56	26	the	the	DET
ap-2224	56	27	right	right	ADJ
ap-2224	56	28	liouville	liouville	NOUN
ap-2224	56	29	–	–	PUNCT
ap-2224	56	30	weyl	weyl	VERB
ap-2224	56	31	diagonal	diagonal	ADJ
ap-2224	56	32	fractional	fractional	ADJ
ap-2224	56	33	integral	integral	ADJ
ap-2224	56	34	or	or	CCONJ
ap-2224	56	35	simply	simply	ADV
ap-2224	56	36	the	the	DET
ap-2224	56	37	diagonal	diagonal	ADJ
ap-2224	56	38	integral	integral	NOUN
ap-2224	56	39	of	of	ADP
ap-2224	56	40	the	the	DET
ap-2224	56	41	function	function	NOUN
ap-2224	56	42	f	f	PROPN
ap-2224	56	43	(	(	PUNCT
ap-2224	56	44	x	x	NOUN
ap-2224	56	45	)	)	PUNCT
ap-2224	56	46	,	,	PUNCT
ap-2224	56	47	and	and	CCONJ
ap-2224	56	48	the	the	DET
ap-2224	56	49	integral	integral	ADJ
ap-2224	56	50	on	on	ADP
ap-2224	56	51	the	the	DET
ap-2224	56	52	right	right	ADJ
ap-2224	56	53	hand	hand	NOUN
ap-2224	56	54	side	side	NOUN
ap-2224	56	55	of	of	ADP
ap-2224	56	56	(	(	PUNCT
ap-2224	56	57	2.1	2.1	NUM
ap-2224	56	58	)	)	PUNCT
ap-2224	56	59	will	will	AUX
ap-2224	56	60	be	be	AUX
ap-2224	56	61	called	call	VERB
ap-2224	56	62	the	the	DET
ap-2224	56	63	anti	anti	ADJ
ap-2224	56	64	-	-	ADJ
ap-2224	56	65	diagonal	diagonal	ADJ
ap-2224	56	66	laplace	laplace	NOUN
ap-2224	56	67	–	–	PUNCT
ap-2224	56	68	mellin	mellin	NOUN
ap-2224	56	69	transform	transform	NOUN
ap-2224	56	70	of	of	ADP
ap-2224	56	71	function	function	NOUN
ap-2224	56	72	f(t	f(t	PROPN
ap-2224	56	73	)	)	PUNCT
ap-2224	56	74	.	.	PUNCT
ap-2224	57	1	the	the	DET
ap-2224	57	2	following	follow	VERB
ap-2224	57	3	two	two	NUM
ap-2224	57	4	theorems	theorem	NOUN
ap-2224	57	5	are	be	AUX
ap-2224	57	6	seminal	seminal	ADJ
ap-2224	57	7	for	for	ADP
ap-2224	57	8	this	this	DET
ap-2224	57	9	paper	paper	NOUN
ap-2224	57	10	.	.	PUNCT
ap-2224	58	1	theorem	theorem	VERB
ap-2224	58	2	2.2	2.2	NUM
ap-2224	58	3	.	.	PUNCT
ap-2224	59	1	the	the	DET
ap-2224	59	2	right	right	ADV
ap-2224	59	3	-	-	PUNCT
ap-2224	59	4	most	most	ADV
ap-2224	59	5	integral	integral	ADJ
ap-2224	59	6	in	in	ADP
ap-2224	59	7	(	(	PUNCT
ap-2224	59	8	2.1	2.1	NUM
ap-2224	59	9	)	)	PUNCT
ap-2224	59	10	can	can	AUX
ap-2224	59	11	be	be	AUX
ap-2224	59	12	written	write	VERB
ap-2224	59	13	as∫	as∫	PROPN
ap-2224	59	14	∞	∞	PROPN
ap-2224	59	15	0	0	NUM
ap-2224	59	16	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	59	17	)	)	PUNCT
ap-2224	59	18	dt	dt	NOUN
ap-2224	60	1	=	=	SYM
ap-2224	60	2	∫	∫	PROPN
ap-2224	60	3	∞	∞	PROPN
ap-2224	60	4	−∞	−∞	X
ap-2224	60	5	e−yuf	e−yuf	NOUN
ap-2224	60	6	(	(	PUNCT
ap-2224	60	7	w0(eu	w0(eu	PROPN
ap-2224	60	8	)	)	PUNCT
ap-2224	60	9	)	)	PUNCT
ap-2224	60	10	w0(eu	w0(eu	NOUN
ap-2224	60	11	)	)	PUNCT
ap-2224	60	12	1	1	NUM
ap-2224	61	1	+	+	NOUN
ap-2224	61	2	w0(eu	w0(eu	X
ap-2224	61	3	)	)	PUNCT
ap-2224	61	4	du	du	NOUN
ap-2224	61	5	,	,	PUNCT
ap-2224	61	6	(	(	PUNCT
ap-2224	61	7	2.2	2.2	NUM
ap-2224	61	8	)	)	PUNCT
ap-2224	61	9	where	where	SCONJ
ap-2224	61	10	function	function	NOUN
ap-2224	61	11	w0	w0	PROPN
ap-2224	61	12	(	(	PUNCT
ap-2224	61	13	·	·	PUNCT
ap-2224	61	14	)	)	PUNCT
ap-2224	61	15	is	be	AUX
ap-2224	61	16	the	the	DET
ap-2224	61	17	0th	0th	ADJ
ap-2224	61	18	branch	branch	NOUN
ap-2224	61	19	of	of	ADP
ap-2224	61	20	the	the	DET
ap-2224	61	21	lambert	lambert	PROPN
ap-2224	61	22	function	function	NOUN
ap-2224	61	23	[	[	X
ap-2224	61	24	2	2	NUM
ap-2224	61	25	]	]	PUNCT
ap-2224	61	26	.	.	PUNCT
ap-2224	62	1	proof	proof	NOUN
ap-2224	62	2	.	.	PUNCT
ap-2224	63	1	we	we	PRON
ap-2224	63	2	compute∫	compute∫	VERB
ap-2224	63	3	∞	∞	PROPN
ap-2224	63	4	0	0	NUM
ap-2224	63	5	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	63	6	)	)	PUNCT
ap-2224	63	7	dt	dt	NOUN
ap-2224	64	1	=	=	SYM
ap-2224	64	2	∫	∫	PROPN
ap-2224	64	3	∞	∞	PROPN
ap-2224	64	4	0	0	NUM
ap-2224	64	5	e−y(t+ln	e−y(t+ln	NOUN
ap-2224	64	6	t)f(t	t)f(t	VERB
ap-2224	64	7	)	)	PUNCT
ap-2224	64	8	dt	dt	PUNCT
ap-2224	65	1	=	=	SYM
ap-2224	65	2	∫	∫	PROPN
ap-2224	65	3	∞	∞	PROPN
ap-2224	65	4	−∞	−∞	X
ap-2224	65	5	e−yuf	e−yuf	NOUN
ap-2224	65	6	(	(	PUNCT
ap-2224	65	7	w0(eu	w0(eu	PROPN
ap-2224	65	8	)	)	PUNCT
ap-2224	65	9	)	)	PUNCT
ap-2224	65	10	w0(eu	w0(eu	NOUN
ap-2224	65	11	)	)	PUNCT
ap-2224	65	12	1	1	NUM
ap-2224	66	1	+	+	NOUN
ap-2224	66	2	w0(eu	w0(eu	X
ap-2224	66	3	)	)	PUNCT
ap-2224	66	4	du	du	NOUN
ap-2224	66	5	,	,	PUNCT
ap-2224	66	6	where	where	SCONJ
ap-2224	66	7	the	the	DET
ap-2224	66	8	substitution	substitution	NOUN
ap-2224	66	9	t+	t+	PUNCT
ap-2224	66	10	ln	ln	PROPN
ap-2224	66	11	t	t	PROPN
ap-2224	66	12	=	=	SYM
ap-2224	66	13	u	u	PROPN
ap-2224	66	14	,	,	PUNCT
ap-2224	66	15	i.e.	i.e.	X
ap-2224	66	16	,	,	PUNCT
ap-2224	66	17	t	t	NOUN
ap-2224	66	18	=	=	SYM
ap-2224	66	19	w0(eu	w0(eu	PROPN
ap-2224	66	20	)	)	PUNCT
ap-2224	66	21	and	and	CCONJ
ap-2224	66	22	dt	dt	X
ap-2224	66	23	=	=	SYM
ap-2224	66	24	w0(eu)/(1	w0(eu)/(1	PROPN
ap-2224	66	25	+	+	NOUN
ap-2224	66	26	w0(eu	w0(eu	NOUN
ap-2224	66	27	)	)	PUNCT
ap-2224	66	28	)	)	PUNCT
ap-2224	66	29	,	,	PUNCT
ap-2224	66	30	was	be	AUX
ap-2224	66	31	performed	perform	VERB
ap-2224	66	32	.	.	PUNCT
ap-2224	67	1	the	the	DET
ap-2224	67	2	lambert	lambert	PROPN
ap-2224	67	3	function	function	NOUN
ap-2224	67	4	is	be	AUX
ap-2224	67	5	defined	define	VERB
ap-2224	67	6	as	as	ADP
ap-2224	67	7	a	a	DET
ap-2224	67	8	solution	solution	NOUN
ap-2224	67	9	of	of	ADP
ap-2224	67	10	the	the	DET
ap-2224	67	11	functional	functional	ADJ
ap-2224	67	12	equation	equation	NOUN
ap-2224	67	13	z	z	NOUN
ap-2224	68	1	=	=	SYM
ap-2224	68	2	w	w	X
ap-2224	68	3	(	(	PUNCT
ap-2224	68	4	z)ew	z)ew	PROPN
ap-2224	68	5	(	(	PUNCT
ap-2224	68	6	z	z	NOUN
ap-2224	68	7	)	)	PUNCT
ap-2224	68	8	for	for	ADP
ap-2224	68	9	any	any	DET
ap-2224	68	10	complex	complex	ADJ
ap-2224	68	11	z	z	NOUN
ap-2224	69	1	[	[	X
ap-2224	69	2	2	2	NUM
ap-2224	69	3	]	]	PUNCT
ap-2224	69	4	.	.	PUNCT
ap-2224	70	1	theorem	theorem	VERB
ap-2224	70	2	2.2	2.2	NUM
ap-2224	70	3	means	mean	VERB
ap-2224	70	4	that	that	SCONJ
ap-2224	70	5	the	the	DET
ap-2224	70	6	liouville	liouville	NOUN
ap-2224	70	7	–	–	PUNCT
ap-2224	70	8	weyl	weyl	VERB
ap-2224	70	9	diagonal	diagonal	ADJ
ap-2224	70	10	fractional	fractional	ADJ
ap-2224	70	11	integral	integral	NOUN
ap-2224	70	12	of	of	ADP
ap-2224	70	13	the	the	DET
ap-2224	70	14	unilateral	unilateral	ADJ
ap-2224	70	15	laplace	laplace	NOUN
ap-2224	70	16	transform	transform	NOUN
ap-2224	70	17	can	can	AUX
ap-2224	70	18	be	be	AUX
ap-2224	70	19	interpreted	interpret	VERB
ap-2224	70	20	as	as	ADP
ap-2224	70	21	a	a	DET
ap-2224	70	22	two	two	NUM
ap-2224	70	23	-	-	PUNCT
ap-2224	70	24	sided	sided	ADJ
ap-2224	70	25	laplace	laplace	NOUN
ap-2224	70	26	transform	transform	NOUN
ap-2224	70	27	with	with	ADP
ap-2224	70	28	the	the	DET
ap-2224	70	29	region	region	NOUN
ap-2224	70	30	of	of	ADP
ap-2224	70	31	convergence	convergence	NOUN
ap-2224	70	32	β0	β0	NOUN
ap-2224	70	33	<	<	X
ap-2224	70	34	y	y	PROPN
ap-2224	70	35	<	<	X
ap-2224	70	36	β1	β1	PROPN
ap-2224	70	37	.	.	PUNCT
ap-2224	71	1	alternatively	alternatively	ADV
ap-2224	71	2	,	,	PUNCT
ap-2224	71	3	we	we	PRON
ap-2224	71	4	can	can	AUX
ap-2224	71	5	express	express	VERB
ap-2224	71	6	the	the	DET
ap-2224	71	7	anti	anti	ADJ
ap-2224	71	8	-	-	ADJ
ap-2224	71	9	diagonal	diagonal	ADJ
ap-2224	71	10	laplace	laplace	NOUN
ap-2224	71	11	–	–	PUNCT
ap-2224	71	12	mellin	mellin	NOUN
ap-2224	71	13	transform	transform	NOUN
ap-2224	71	14	as	as	ADP
ap-2224	71	15	the	the	DET
ap-2224	71	16	mellin	mellin	PROPN
ap-2224	71	17	transform	transform	NOUN
ap-2224	71	18	.	.	PUNCT
ap-2224	72	1	theorem	theorem	VERB
ap-2224	72	2	2.3	2.3	NUM
ap-2224	72	3	.	.	PUNCT
ap-2224	73	1	the	the	DET
ap-2224	73	2	rightmost	rightmost	NOUN
ap-2224	73	3	integral	integral	ADJ
ap-2224	73	4	in	in	ADP
ap-2224	73	5	(	(	PUNCT
ap-2224	73	6	2.1	2.1	NUM
ap-2224	73	7	)	)	PUNCT
ap-2224	73	8	can	can	AUX
ap-2224	73	9	be	be	AUX
ap-2224	73	10	written	write	VERB
ap-2224	73	11	as∫	as∫	PROPN
ap-2224	73	12	∞	∞	PROPN
ap-2224	73	13	0	0	NUM
ap-2224	73	14	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	73	15	)	)	PUNCT
ap-2224	73	16	dt	dt	NOUN
ap-2224	74	1	=	=	SYM
ap-2224	74	2	∫	∫	PROPN
ap-2224	74	3	∞	∞	NUM
ap-2224	74	4	0	0	NUM
ap-2224	74	5	u−y−1f	u−y−1f	PROPN
ap-2224	74	6	(	(	PUNCT
ap-2224	74	7	w0(u	w0(u	NOUN
ap-2224	74	8	)	)	PUNCT
ap-2224	74	9	)	)	PUNCT
ap-2224	75	1	w0(u	w0(u	X
ap-2224	75	2	)	)	PUNCT
ap-2224	75	3	1	1	NUM
ap-2224	76	1	+	+	PUNCT
ap-2224	76	2	w0(u	w0(u	X
ap-2224	76	3	)	)	PUNCT
ap-2224	76	4	du	du	NOUN
ap-2224	76	5	.	.	PUNCT
ap-2224	77	1	(	(	PUNCT
ap-2224	77	2	2.3	2.3	NUM
ap-2224	77	3	)	)	PUNCT
ap-2224	77	4	proof	proof	NOUN
ap-2224	77	5	.	.	PUNCT
ap-2224	78	1	we	we	PRON
ap-2224	78	2	compute∫	compute∫	VERB
ap-2224	78	3	∞	∞	PROPN
ap-2224	78	4	0	0	NUM
ap-2224	78	5	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	78	6	)	)	PUNCT
ap-2224	78	7	dt	dt	NOUN
ap-2224	79	1	=	=	SYM
ap-2224	79	2	∫	∫	PROPN
ap-2224	79	3	∞	∞	PROPN
ap-2224	79	4	0	0	NUM
ap-2224	79	5	(	(	PUNCT
ap-2224	79	6	ett)−yf(t	ett)−yf(t	X
ap-2224	79	7	)	)	PUNCT
ap-2224	79	8	dt	dt	NOUN
ap-2224	80	1	=	=	SYM
ap-2224	80	2	∫	∫	PROPN
ap-2224	80	3	∞	∞	NUM
ap-2224	80	4	0	0	NUM
ap-2224	80	5	u−y−1f	u−y−1f	PROPN
ap-2224	80	6	(	(	PUNCT
ap-2224	80	7	w0(u	w0(u	NOUN
ap-2224	80	8	)	)	PUNCT
ap-2224	80	9	)	)	PUNCT
ap-2224	81	1	w0(u	w0(u	X
ap-2224	81	2	)	)	PUNCT
ap-2224	81	3	1	1	NUM
ap-2224	82	1	+	+	PUNCT
ap-2224	82	2	w0(u	w0(u	X
ap-2224	82	3	)	)	PUNCT
ap-2224	82	4	du	du	NOUN
ap-2224	82	5	where	where	SCONJ
ap-2224	82	6	the	the	DET
ap-2224	82	7	substitution	substitution	NOUN
ap-2224	82	8	ett	ett	PROPN
ap-2224	82	9	=	=	SYM
ap-2224	82	10	u	u	PROPN
ap-2224	82	11	,	,	PUNCT
ap-2224	82	12	i.e.	i.e.	X
ap-2224	82	13	,	,	PUNCT
ap-2224	82	14	t	t	PROPN
ap-2224	82	15	=	=	SYM
ap-2224	82	16	w0(u	w0(u	PROPN
ap-2224	82	17	)	)	PUNCT
ap-2224	82	18	and	and	CCONJ
ap-2224	82	19	dt	dt	X
ap-2224	82	20	=	=	SYM
ap-2224	82	21	w0(u	w0(u	PROPN
ap-2224	82	22	)	)	PUNCT
ap-2224	82	23	u(1+w0(u	u(1+w0(u	PROPN
ap-2224	82	24	)	)	PUNCT
ap-2224	82	25	)	)	PUNCT
ap-2224	82	26	du	du	PROPN
ap-2224	82	27	,	,	PUNCT
ap-2224	82	28	was	be	AUX
ap-2224	82	29	performed	perform	VERB
ap-2224	82	30	.	.	PUNCT
ap-2224	83	1	306	306	NUM
ap-2224	83	2	vol	vol	NOUN
ap-2224	83	3	.	.	PUNCT
ap-2224	84	1	54	54	NUM
ap-2224	84	2	no	no	NOUN
ap-2224	84	3	.	.	PUNCT
ap-2224	85	1	4/2014	4/2014	NUM
ap-2224	85	2	fractional	fractional	ADJ
ap-2224	85	3	calculus	calculus	NOUN
ap-2224	85	4	and	and	CCONJ
ap-2224	85	5	lambert	lambert	PROPN
ap-2224	85	6	function	function	NOUN
ap-2224	85	7	i	i	PRON
ap-2224	85	8	the	the	DET
ap-2224	85	9	integral	integral	ADJ
ap-2224	85	10	on	on	ADP
ap-2224	85	11	the	the	DET
ap-2224	85	12	right	right	NOUN
ap-2224	85	13	of	of	ADP
ap-2224	85	14	(	(	PUNCT
ap-2224	85	15	2.3	2.3	NUM
ap-2224	85	16	)	)	PUNCT
ap-2224	85	17	is	be	AUX
ap-2224	85	18	a	a	DET
ap-2224	85	19	mellin	mellin	ADJ
ap-2224	85	20	transform	transform	NOUN
ap-2224	85	21	in	in	ADP
ap-2224	85	22	variable	variable	NOUN
ap-2224	85	23	−y	−y	NOUN
ap-2224	85	24	.	.	PUNCT
ap-2224	86	1	in	in	ADP
ap-2224	86	2	this	this	DET
ap-2224	86	3	paper	paper	NOUN
ap-2224	86	4	,	,	PUNCT
ap-2224	86	5	we	we	PRON
ap-2224	86	6	will	will	AUX
ap-2224	86	7	omit	omit	VERB
ap-2224	86	8	the	the	DET
ap-2224	86	9	words	word	NOUN
ap-2224	86	10	“	"	PUNCT
ap-2224	86	11	in	in	ADP
ap-2224	86	12	variable	variable	NOUN
ap-2224	86	13	.	.	PUNCT
ap-2224	86	14	.	.	PUNCT
ap-2224	86	15	.	.	PUNCT
ap-2224	86	16	”	"	PUNCT
ap-2224	87	1	for	for	ADP
ap-2224	87	2	the	the	DET
ap-2224	87	3	sake	sake	NOUN
ap-2224	87	4	of	of	ADP
ap-2224	87	5	brevity	brevity	NOUN
ap-2224	87	6	.	.	PUNCT
ap-2224	88	1	in	in	ADP
ap-2224	88	2	the	the	DET
ap-2224	88	3	case	case	NOUN
ap-2224	88	4	of	of	ADP
ap-2224	88	5	the	the	DET
ap-2224	88	6	mellin	mellin	PROPN
ap-2224	88	7	transform	transform	NOUN
ap-2224	88	8	in	in	ADP
ap-2224	88	9	variable	variable	ADJ
ap-2224	88	10	y	y	NOUN
ap-2224	88	11	we	we	PRON
ap-2224	88	12	emphasize	emphasize	VERB
ap-2224	88	13	this	this	DET
ap-2224	88	14	circumstance	circumstance	NOUN
ap-2224	88	15	as	as	ADP
ap-2224	88	16	the	the	DET
ap-2224	88	17	“	"	PUNCT
ap-2224	88	18	mellin	mellin	NOUN
ap-2224	88	19	transform	transform	NOUN
ap-2224	88	20	in	in	ADP
ap-2224	88	21	standard	standard	ADJ
ap-2224	88	22	notation	notation	NOUN
ap-2224	88	23	”	"	PUNCT
ap-2224	88	24	if	if	SCONJ
ap-2224	88	25	necessary	necessary	ADJ
ap-2224	88	26	to	to	PART
ap-2224	88	27	avoid	avoid	VERB
ap-2224	88	28	confusion	confusion	NOUN
ap-2224	88	29	.	.	PUNCT
ap-2224	89	1	this	this	PRON
ap-2224	89	2	means	mean	VERB
ap-2224	89	3	that	that	SCONJ
ap-2224	89	4	the	the	DET
ap-2224	89	5	liouville	liouville	NOUN
ap-2224	89	6	–	–	PUNCT
ap-2224	89	7	weyl	weyl	VERB
ap-2224	89	8	diagonal	diagonal	ADJ
ap-2224	89	9	fractional	fractional	ADJ
ap-2224	89	10	integral	integral	NOUN
ap-2224	89	11	can	can	AUX
ap-2224	89	12	be	be	AUX
ap-2224	89	13	represented	represent	VERB
ap-2224	89	14	as	as	ADP
ap-2224	89	15	a	a	DET
ap-2224	89	16	mellin	mellin	NOUN
ap-2224	89	17	transform	transform	NOUN
ap-2224	89	18	with	with	ADP
ap-2224	89	19	the	the	DET
ap-2224	89	20	region	region	NOUN
ap-2224	89	21	of	of	ADP
ap-2224	89	22	convergence	convergence	NOUN
ap-2224	89	23	−β1	−β1	NOUN
ap-2224	89	24	<	<	X
ap-2224	89	25	−y	−y	X
ap-2224	89	26	<	<	X
ap-2224	89	27	−β0	−β0	PROPN
ap-2224	89	28	or	or	CCONJ
ap-2224	89	29	β0	β0	NOUN
ap-2224	89	30	<	<	X
ap-2224	89	31	y	y	PROPN
ap-2224	89	32	<	<	X
ap-2224	89	33	β1	β1	PROPN
ap-2224	89	34	.	.	PUNCT
ap-2224	90	1	the	the	DET
ap-2224	90	2	following	follow	VERB
ap-2224	90	3	corollaries	corollary	NOUN
ap-2224	90	4	easily	easily	ADV
ap-2224	90	5	follow	follow	VERB
ap-2224	90	6	from	from	ADP
ap-2224	90	7	theorems	theorem	NOUN
ap-2224	90	8	2.2	2.2	NUM
ap-2224	90	9	and	and	CCONJ
ap-2224	90	10	2.3	2.3	NUM
ap-2224	90	11	:	:	PUNCT
ap-2224	90	12	corollary	corollary	ADJ
ap-2224	90	13	2.4	2.4	NUM
ap-2224	90	14	.	.	PUNCT
ap-2224	91	1	let	let	VERB
ap-2224	91	2	the	the	DET
ap-2224	91	3	laplace	laplace	NOUN
ap-2224	91	4	transform	transform	NOUN
ap-2224	91	5	of	of	ADP
ap-2224	91	6	function	function	NOUN
ap-2224	91	7	h(t	h(t	PROPN
ap-2224	91	8	)	)	PUNCT
ap-2224	91	9	exist	exist	VERB
ap-2224	91	10	for	for	ADP
ap-2224	91	11	0	0	NUM
ap-2224	91	12	≤	≤	NOUN
ap-2224	91	13	a	a	DET
ap-2224	91	14	≤	≤	NUM
ap-2224	91	15	t	t	NOUN
ap-2224	91	16	<	<	X
ap-2224	91	17	b	b	X
ap-2224	91	18	≤	≤	NUM
ap-2224	91	19	∞	∞	PROPN
ap-2224	91	20	,	,	PUNCT
ap-2224	91	21	where	where	SCONJ
ap-2224	91	22	a	a	DET
ap-2224	91	23	=	=	SYM
ap-2224	91	24	w0(ea	w0(ea	NOUN
ap-2224	91	25	)	)	PUNCT
ap-2224	91	26	and	and	CCONJ
ap-2224	91	27	b	b	X
ap-2224	91	28	=	=	SYM
ap-2224	91	29	w0(eb	w0(eb	PROPN
ap-2224	91	30	)	)	PUNCT
ap-2224	91	31	,	,	PUNCT
ap-2224	91	32	i.e.	i.e.	X
ap-2224	91	33	,	,	PUNCT
ap-2224	91	34	a	a	PRON
ap-2224	91	35	=	=	X
ap-2224	91	36	a+	a+	PUNCT
ap-2224	91	37	ln	ln	NOUN
ap-2224	91	38	a	a	PROPN
ap-2224	91	39	and	and	CCONJ
ap-2224	91	40	b	b	X
ap-2224	91	41	=	=	X
ap-2224	91	42	b+	b+	X
ap-2224	91	43	ln	ln	PROPN
ap-2224	91	44	b.	b.	PROPN
ap-2224	91	45	then	then	ADV
ap-2224	91	46	for	for	ADP
ap-2224	91	47	the	the	DET
ap-2224	91	48	laplace	laplace	NOUN
ap-2224	91	49	transform	transform	NOUN
ap-2224	91	50	of	of	ADP
ap-2224	91	51	the	the	DET
ap-2224	91	52	compound	compound	NOUN
ap-2224	91	53	function	function	NOUN
ap-2224	91	54	h	h	NOUN
ap-2224	91	55	(	(	PUNCT
ap-2224	91	56	w0(eu	w0(eu	PROPN
ap-2224	91	57	)	)	PUNCT
ap-2224	91	58	)	)	PUNCT
ap-2224	92	1	it	it	PRON
ap-2224	92	2	holds	hold	VERB
ap-2224	92	3	∫	∫	PROPN
ap-2224	92	4	b	b	PROPN
ap-2224	92	5	a	a	DET
ap-2224	92	6	e−yuh	e−yuh	NOUN
ap-2224	92	7	(	(	PUNCT
ap-2224	92	8	w0(eu	w0(eu	NOUN
ap-2224	92	9	)	)	PUNCT
ap-2224	92	10	)	)	PUNCT
ap-2224	92	11	du	du	PROPN
ap-2224	92	12	=	=	SYM
ap-2224	92	13	∫	∫	PROPN
ap-2224	92	14	b	b	PROPN
ap-2224	92	15	a	a	DET
ap-2224	92	16	e−ytt−y(1	e−ytt−y(1	PROPN
ap-2224	92	17	+	+	CCONJ
ap-2224	92	18	t)h(t)/tdt	t)h(t)/tdt	PROPN
ap-2224	92	19	(	(	PUNCT
ap-2224	92	20	2.4	2.4	NUM
ap-2224	92	21	)	)	PUNCT
ap-2224	92	22	whenever	whenever	SCONJ
ap-2224	92	23	both	both	DET
ap-2224	92	24	integrals	integral	NOUN
ap-2224	92	25	exist	exist	VERB
ap-2224	92	26	.	.	PUNCT
ap-2224	93	1	if	if	SCONJ
ap-2224	93	2	−∞	−∞	ADP
ap-2224	93	3	<	<	X
ap-2224	93	4	a	a	DET
ap-2224	93	5	<	<	X
ap-2224	93	6	b	b	X
ap-2224	93	7	<	<	X
ap-2224	93	8	+	+	NOUN
ap-2224	93	9	∞	∞	PROPN
ap-2224	93	10	,	,	PUNCT
ap-2224	93	11	the	the	DET
ap-2224	93	12	laplace	laplace	NOUN
ap-2224	93	13	transform	transform	NOUN
ap-2224	93	14	on	on	ADP
ap-2224	93	15	the	the	DET
ap-2224	93	16	left	left	ADJ
ap-2224	93	17	side	side	NOUN
ap-2224	93	18	represents	represent	VERB
ap-2224	93	19	the	the	DET
ap-2224	93	20	entire	entire	ADJ
ap-2224	93	21	function	function	NOUN
ap-2224	93	22	.	.	PUNCT
ap-2224	94	1	in	in	ADP
ap-2224	94	2	that	that	DET
ap-2224	94	3	case	case	NOUN
ap-2224	94	4	,	,	PUNCT
ap-2224	94	5	we	we	PRON
ap-2224	94	6	can	can	AUX
ap-2224	94	7	substitute	substitute	VERB
ap-2224	94	8	the	the	DET
ap-2224	94	9	value	value	NOUN
ap-2224	94	10	y	y	PROPN
ap-2224	94	11	=	=	SYM
ap-2224	94	12	0	0	PUNCT
ap-2224	94	13	(	(	PUNCT
ap-2224	94	14	and	and	CCONJ
ap-2224	94	15	others	other	NOUN
ap-2224	94	16	of	of	ADP
ap-2224	94	17	course	course	NOUN
ap-2224	94	18	)	)	PUNCT
ap-2224	94	19	,	,	PUNCT
ap-2224	94	20	whenever	whenever	SCONJ
ap-2224	94	21	we	we	PRON
ap-2224	94	22	need	need	VERB
ap-2224	94	23	it	it	PRON
ap-2224	94	24	.	.	PUNCT
ap-2224	95	1	corollary	corollary	ADJ
ap-2224	95	2	2.5	2.5	NUM
ap-2224	95	3	.	.	PUNCT
ap-2224	96	1	let	let	VERB
ap-2224	96	2	the	the	DET
ap-2224	96	3	mellin	mellin	NOUN
ap-2224	96	4	transform	transform	NOUN
ap-2224	96	5	of	of	ADP
ap-2224	96	6	function	function	NOUN
ap-2224	96	7	h(t	h(t	PROPN
ap-2224	96	8	)	)	PUNCT
ap-2224	96	9	exist	exist	VERB
ap-2224	96	10	for	for	ADP
ap-2224	96	11	0	0	NUM
ap-2224	96	12	≤	≤	NOUN
ap-2224	96	13	a	a	DET
ap-2224	96	14	<	<	X
ap-2224	96	15	t	t	X
ap-2224	96	16	<	<	X
ap-2224	96	17	b	b	X
ap-2224	96	18	≤	≤	NUM
ap-2224	96	19	∞	∞	PROPN
ap-2224	96	20	,	,	PUNCT
ap-2224	96	21	a	a	DET
ap-2224	96	22	=	=	SYM
ap-2224	96	23	w0(a	w0(a	PROPN
ap-2224	96	24	)	)	PUNCT
ap-2224	96	25	and	and	CCONJ
ap-2224	96	26	b	b	X
ap-2224	96	27	=	=	SYM
ap-2224	96	28	w0(b	w0(b	PROPN
ap-2224	96	29	)	)	PUNCT
ap-2224	96	30	,	,	PUNCT
ap-2224	97	1	i.e.	i.e.	X
ap-2224	97	2	,	,	PUNCT
ap-2224	97	3	a	a	DET
ap-2224	97	4	=	=	X
ap-2224	97	5	aea	aea	PROPN
ap-2224	97	6	and	and	CCONJ
ap-2224	97	7	b	b	PROPN
ap-2224	97	8	=	=	PROPN
ap-2224	97	9	beb	beb	PROPN
ap-2224	97	10	.	.	PUNCT
ap-2224	98	1	then	then	ADV
ap-2224	98	2	for	for	ADP
ap-2224	98	3	the	the	DET
ap-2224	98	4	mellin	mellin	PROPN
ap-2224	98	5	transform	transform	NOUN
ap-2224	98	6	in	in	ADP
ap-2224	98	7	the	the	DET
ap-2224	98	8	standard	standard	ADJ
ap-2224	98	9	form	form	NOUN
ap-2224	98	10	of	of	ADP
ap-2224	98	11	the	the	DET
ap-2224	98	12	compound	compound	NOUN
ap-2224	98	13	function	function	NOUN
ap-2224	98	14	h	h	NOUN
ap-2224	98	15	(	(	PUNCT
ap-2224	98	16	w0(u	w0(u	PROPN
ap-2224	98	17	)	)	PUNCT
ap-2224	98	18	)	)	PUNCT
ap-2224	99	1	it	it	PRON
ap-2224	99	2	holds	hold	VERB
ap-2224	99	3	∫	∫	PROPN
ap-2224	99	4	b	b	PROPN
ap-2224	99	5	a	a	DET
ap-2224	99	6	uy−1h	uy−1h	PROPN
ap-2224	99	7	(	(	PUNCT
ap-2224	99	8	w0(u	w0(u	NOUN
ap-2224	99	9	)	)	PUNCT
ap-2224	99	10	)	)	PUNCT
ap-2224	100	1	du	du	PROPN
ap-2224	100	2	=	=	SYM
ap-2224	100	3	∫	∫	PROPN
ap-2224	100	4	b	b	PROPN
ap-2224	101	1	a	a	DET
ap-2224	101	2	ty−1eyt(1	ty−1eyt(1	PROPN
ap-2224	101	3	+	+	SYM
ap-2224	101	4	t)h(t	t)h(t	NOUN
ap-2224	101	5	)	)	PUNCT
ap-2224	101	6	dt	dt	X
ap-2224	101	7	(	(	PUNCT
ap-2224	101	8	2.5	2.5	NUM
ap-2224	101	9	)	)	PUNCT
ap-2224	101	10	whenever	whenever	SCONJ
ap-2224	101	11	both	both	DET
ap-2224	101	12	integrals	integral	NOUN
ap-2224	101	13	exist	exist	VERB
ap-2224	101	14	.	.	PUNCT
ap-2224	102	1	proof	proof	NOUN
ap-2224	102	2	.	.	PUNCT
ap-2224	103	1	instead	instead	ADV
ap-2224	103	2	of	of	ADP
ap-2224	103	3	f(t	f(t	NOUN
ap-2224	103	4	)	)	PUNCT
ap-2224	103	5	,	,	PUNCT
ap-2224	103	6	write	write	VERB
ap-2224	103	7	(	(	PUNCT
ap-2224	103	8	1	1	NUM
ap-2224	103	9	+	+	CCONJ
ap-2224	103	10	t)h(t)/t	t)h(t)/t	AUX
ap-2224	103	11	in	in	ADP
ap-2224	103	12	(	(	PUNCT
ap-2224	103	13	2.2)–(2.3	2.2)–(2.3	NUM
ap-2224	103	14	)	)	PUNCT
ap-2224	103	15	.	.	PUNCT
ap-2224	104	1	in	in	ADP
ap-2224	104	2	(	(	PUNCT
ap-2224	104	3	2.3	2.3	NUM
ap-2224	104	4	)	)	PUNCT
ap-2224	104	5	change	change	NOUN
ap-2224	104	6	−y	−y	VERB
ap-2224	104	7	to	to	ADP
ap-2224	104	8	y.	y.	VERB
ap-2224	104	9	in	in	ADP
ap-2224	104	10	both	both	DET
ap-2224	104	11	equations	equation	NOUN
ap-2224	104	12	recount	recount	VERB
ap-2224	104	13	the	the	DET
ap-2224	104	14	limits	limit	NOUN
ap-2224	104	15	of	of	ADP
ap-2224	104	16	integration	integration	NOUN
ap-2224	104	17	.	.	PUNCT
ap-2224	105	1	the	the	DET
ap-2224	105	2	integrals	integral	NOUN
ap-2224	105	3	on	on	ADP
ap-2224	105	4	the	the	DET
ap-2224	105	5	right	right	ADJ
ap-2224	105	6	sides	side	NOUN
ap-2224	105	7	of	of	ADP
ap-2224	105	8	(	(	PUNCT
ap-2224	105	9	2.4)–(2.5	2.4)–(2.5	NUM
ap-2224	105	10	)	)	PUNCT
ap-2224	105	11	can	can	AUX
ap-2224	105	12	often	often	ADV
ap-2224	105	13	be	be	AUX
ap-2224	105	14	calculated	calculate	VERB
ap-2224	105	15	more	more	ADV
ap-2224	105	16	easily	easily	ADV
ap-2224	105	17	than	than	ADP
ap-2224	105	18	the	the	DET
ap-2224	105	19	integrals	integral	NOUN
ap-2224	105	20	on	on	ADP
ap-2224	105	21	the	the	DET
ap-2224	105	22	left	left	ADJ
ap-2224	105	23	side	side	NOUN
ap-2224	105	24	.	.	PUNCT
ap-2224	106	1	example	example	NOUN
ap-2224	106	2	2.6	2.6	NUM
ap-2224	106	3	.	.	PUNCT
ap-2224	107	1	we	we	PRON
ap-2224	107	2	have∫	have∫	VERB
ap-2224	107	3	e	e	NOUN
ap-2224	107	4	0	0	NUM
ap-2224	107	5	sinw0(u	sinw0(u	CCONJ
ap-2224	107	6	)	)	PUNCT
ap-2224	107	7	du	du	PROPN
ap-2224	108	1	=	=	SYM
ap-2224	108	2	∫	∫	PROPN
ap-2224	108	3	1	1	NUM
ap-2224	108	4	0	0	NUM
ap-2224	108	5	et(1	et(1	PROPN
ap-2224	108	6	+	+	PROPN
ap-2224	108	7	t	t	PROPN
ap-2224	108	8	)	)	PUNCT
ap-2224	108	9	sin	sin	NOUN
ap-2224	108	10	tdt	tdt	PROPN
ap-2224	108	11	=	=	SYM
ap-2224	108	12	e	e	PROPN
ap-2224	108	13	2(2	2(2	NUM
ap-2224	108	14	sin	sin	NOUN
ap-2224	108	15	1−	1−	NUM
ap-2224	108	16	cos	cos	NOUN
ap-2224	108	17	1	1	NUM
ap-2224	108	18	)	)	PUNCT
ap-2224	108	19	≈	≈	PROPN
ap-2224	108	20	1.55301	1.55301	NUM
ap-2224	108	21	.	.	PUNCT
ap-2224	109	1	3	3	X
ap-2224	109	2	.	.	X
ap-2224	109	3	inversion	inversion	NOUN
ap-2224	109	4	of	of	ADP
ap-2224	109	5	the	the	DET
ap-2224	109	6	diagonal	diagonal	ADJ
ap-2224	109	7	fractional	fractional	ADJ
ap-2224	109	8	integral	integral	ADJ
ap-2224	109	9	a	a	DET
ap-2224	109	10	natural	natural	ADJ
ap-2224	109	11	question	question	NOUN
ap-2224	109	12	is	be	AUX
ap-2224	109	13	to	to	PART
ap-2224	109	14	find	find	VERB
ap-2224	109	15	function	function	NOUN
ap-2224	109	16	f	f	PROPN
ap-2224	109	17	(	(	PUNCT
ap-2224	109	18	x	x	X
ap-2224	109	19	)	)	PUNCT
ap-2224	109	20	knowing	know	VERB
ap-2224	109	21	its	its	PRON
ap-2224	109	22	diagonal	diagonal	ADJ
ap-2224	109	23	fractional	fractional	ADJ
ap-2224	109	24	integral	integral	ADJ
ap-2224	109	25	g(y	g(y	NOUN
ap-2224	109	26	):	):	PUNCT
ap-2224	109	27	1	1	NUM
ap-2224	109	28	γ(y	γ(y	PROPN
ap-2224	109	29	)	)	PUNCT
ap-2224	110	1	∫	∫	PROPN
ap-2224	111	1	∞	∞	PROPN
ap-2224	111	2	y	y	PROPN
ap-2224	111	3	f	f	PROPN
ap-2224	111	4	(	(	PUNCT
ap-2224	111	5	x)(x−	x)(x−	PROPN
ap-2224	111	6	y)y−1	y)y−1	NOUN
ap-2224	111	7	dx	dx	PROPN
ap-2224	111	8	=	=	SYM
ap-2224	111	9	g(y	g(y	PROPN
ap-2224	111	10	)	)	PUNCT
ap-2224	111	11	.	.	PUNCT
ap-2224	112	1	(	(	PUNCT
ap-2224	112	2	3.1	3.1	NUM
ap-2224	112	3	)	)	PUNCT
ap-2224	112	4	this	this	DET
ap-2224	112	5	equation	equation	NOUN
ap-2224	112	6	is	be	AUX
ap-2224	112	7	a	a	DET
ap-2224	112	8	volterra	volterra	NOUN
ap-2224	112	9	integral	integral	ADJ
ap-2224	112	10	equation	equation	NOUN
ap-2224	112	11	of	of	ADP
ap-2224	112	12	the	the	DET
ap-2224	112	13	first	first	ADJ
ap-2224	112	14	kind	kind	NOUN
ap-2224	112	15	and	and	CCONJ
ap-2224	112	16	of	of	ADP
ap-2224	112	17	the	the	DET
ap-2224	112	18	abel	abel	PROPN
ap-2224	112	19	type	type	NOUN
ap-2224	112	20	,	,	PUNCT
ap-2224	112	21	but	but	CCONJ
ap-2224	112	22	in	in	ADP
ap-2224	112	23	contrast	contrast	NOUN
ap-2224	112	24	to	to	ADP
ap-2224	112	25	(	(	PUNCT
ap-2224	112	26	1.1	1.1	NUM
ap-2224	112	27	)	)	PUNCT
ap-2224	112	28	,	,	PUNCT
ap-2224	112	29	equation	equation	NOUN
ap-2224	112	30	(	(	PUNCT
ap-2224	112	31	3.1	3.1	NUM
ap-2224	112	32	)	)	PUNCT
ap-2224	112	33	is	be	AUX
ap-2224	112	34	not	not	PART
ap-2224	112	35	a	a	DET
ap-2224	112	36	convolution	convolution	NOUN
ap-2224	112	37	.	.	PUNCT
ap-2224	113	1	if	if	SCONJ
ap-2224	113	2	f	f	PROPN
ap-2224	113	3	(	(	PUNCT
ap-2224	113	4	x	x	X
ap-2224	113	5	)	)	PUNCT
ap-2224	113	6	is	be	AUX
ap-2224	113	7	a	a	DET
ap-2224	113	8	unilateral	unilateral	ADJ
ap-2224	113	9	laplace	laplace	NOUN
ap-2224	113	10	transform	transform	NOUN
ap-2224	113	11	of	of	ADP
ap-2224	113	12	function	function	NOUN
ap-2224	113	13	f(t	f(t	PROPN
ap-2224	113	14	)	)	PUNCT
ap-2224	113	15	,	,	PUNCT
ap-2224	113	16	see	see	VERB
ap-2224	113	17	(	(	PUNCT
ap-2224	113	18	1.2	1.2	NUM
ap-2224	113	19	)	)	PUNCT
ap-2224	113	20	,	,	PUNCT
ap-2224	113	21	equation	equation	NOUN
ap-2224	113	22	(	(	PUNCT
ap-2224	113	23	3.1	3.1	NUM
ap-2224	113	24	)	)	PUNCT
ap-2224	113	25	can	can	AUX
ap-2224	113	26	easily	easily	ADV
ap-2224	113	27	be	be	AUX
ap-2224	113	28	solved	solve	VERB
ap-2224	113	29	for	for	ADP
ap-2224	113	30	f	f	PROPN
ap-2224	113	31	(	(	PUNCT
ap-2224	113	32	x	x	X
ap-2224	113	33	)	)	PUNCT
ap-2224	113	34	via	via	ADP
ap-2224	113	35	its	its	PRON
ap-2224	113	36	original	original	ADJ
ap-2224	113	37	function	function	NOUN
ap-2224	113	38	f(t	f(t	NOUN
ap-2224	113	39	)	)	PUNCT
ap-2224	113	40	.	.	PUNCT
ap-2224	114	1	because	because	SCONJ
ap-2224	114	2	g(y	g(y	NOUN
ap-2224	114	3	)	)	PUNCT
ap-2224	114	4	=	=	SYM
ap-2224	114	5	∫	∫	PROPN
ap-2224	114	6	∞	∞	PROPN
ap-2224	114	7	−∞	−∞	ADP
ap-2224	114	8	e−yug(u)du	e−yug(u)du	PROPN
ap-2224	114	9	=	=	SYM
ap-2224	114	10	(	(	PUNCT
ap-2224	114	11	iy−f	iy−f	NOUN
ap-2224	114	12	)	)	PUNCT
ap-2224	114	13	(	(	PUNCT
ap-2224	114	14	y	y	NOUN
ap-2224	114	15	)	)	PUNCT
ap-2224	114	16	=	=	SYM
ap-2224	114	17	∫	∫	PROPN
ap-2224	115	1	∞	∞	PROPN
ap-2224	115	2	−∞	−∞	X
ap-2224	115	3	e−yuf	e−yuf	NOUN
ap-2224	115	4	(	(	PUNCT
ap-2224	115	5	w0(eu	w0(eu	PROPN
ap-2224	115	6	)	)	PUNCT
ap-2224	115	7	)	)	PUNCT
ap-2224	115	8	w0(eu	w0(eu	NOUN
ap-2224	115	9	)	)	PUNCT
ap-2224	115	10	1	1	NUM
ap-2224	116	1	+	+	NOUN
ap-2224	116	2	w0(eu	w0(eu	X
ap-2224	116	3	)	)	PUNCT
ap-2224	116	4	du	du	NOUN
ap-2224	116	5	,	,	PUNCT
ap-2224	116	6	(	(	PUNCT
ap-2224	116	7	3.2	3.2	NUM
ap-2224	116	8	)	)	PUNCT
ap-2224	116	9	the	the	DET
ap-2224	116	10	following	follow	VERB
ap-2224	116	11	theorem	theorem	ADJ
ap-2224	116	12	holds	hold	NOUN
ap-2224	116	13	:	:	PUNCT
ap-2224	116	14	theorem	theorem	NOUN
ap-2224	116	15	3.1	3.1	NUM
ap-2224	116	16	.	.	PUNCT
ap-2224	117	1	the	the	DET
ap-2224	117	2	solution	solution	NOUN
ap-2224	117	3	of	of	ADP
ap-2224	117	4	(	(	PUNCT
ap-2224	117	5	3.2	3.2	NUM
ap-2224	117	6	)	)	PUNCT
ap-2224	117	7	is	be	AUX
ap-2224	117	8	given	give	VERB
ap-2224	117	9	by	by	ADP
ap-2224	117	10	the	the	DET
ap-2224	117	11	relation	relation	NOUN
ap-2224	117	12	f(t	f(t	NOUN
ap-2224	117	13	)	)	PUNCT
ap-2224	117	14	=	=	SYM
ap-2224	117	15	(	(	PUNCT
ap-2224	117	16	1	1	NUM
ap-2224	117	17	+	+	CCONJ
ap-2224	117	18	t)g(t+	t)g(t+	ADJ
ap-2224	117	19	ln	ln	ADJ
ap-2224	117	20	t)/t	t)/t	PROPN
ap-2224	117	21	,	,	PUNCT
ap-2224	117	22	t	t	PROPN
ap-2224	117	23	∈	∈	PROPN
ap-2224	117	24	(	(	PUNCT
ap-2224	117	25	0,∞	0,∞	NOUN
ap-2224	117	26	)	)	PUNCT
ap-2224	117	27	.	.	PUNCT
ap-2224	118	1	(	(	PUNCT
ap-2224	118	2	3.3	3.3	NUM
ap-2224	118	3	)	)	PUNCT
ap-2224	118	4	proof	proof	NOUN
ap-2224	118	5	.	.	PUNCT
ap-2224	119	1	both	both	DET
ap-2224	119	2	integrands	integrand	NOUN
ap-2224	119	3	must	must	AUX
ap-2224	119	4	be	be	AUX
ap-2224	119	5	identical	identical	ADJ
ap-2224	119	6	with	with	ADP
ap-2224	119	7	an	an	DET
ap-2224	119	8	identical	identical	ADJ
ap-2224	119	9	strip	strip	NOUN
ap-2224	119	10	of	of	ADP
ap-2224	119	11	convergence	convergence	NOUN
ap-2224	119	12	[	[	X
ap-2224	119	13	10	10	NUM
ap-2224	119	14	]	]	PUNCT
ap-2224	119	15	.	.	PUNCT
ap-2224	120	1	after	after	ADP
ap-2224	120	2	substituting	substitute	VERB
ap-2224	120	3	w0(eu	w0(eu	NOUN
ap-2224	120	4	)	)	PUNCT
ap-2224	120	5	=	=	SYM
ap-2224	120	6	t	t	PROPN
ap-2224	120	7	,	,	PUNCT
ap-2224	120	8	i.e.	i.e.	X
ap-2224	120	9	,	,	PUNCT
ap-2224	120	10	u	u	NOUN
ap-2224	120	11	=	=	PUNCT
ap-2224	120	12	t+	t+	PUNCT
ap-2224	120	13	ln	ln	PROPN
ap-2224	120	14	t	t	NOUN
ap-2224	120	15	into	into	ADP
ap-2224	120	16	(	(	PUNCT
ap-2224	120	17	3.2	3.2	NUM
ap-2224	120	18	)	)	PUNCT
ap-2224	120	19	we	we	PRON
ap-2224	120	20	obtain	obtain	VERB
ap-2224	120	21	(	(	PUNCT
ap-2224	120	22	3.3	3.3	NUM
ap-2224	120	23	)	)	PUNCT
ap-2224	120	24	.	.	PUNCT
ap-2224	121	1	a	a	DET
ap-2224	121	2	similar	similar	ADJ
ap-2224	121	3	argument	argument	NOUN
ap-2224	121	4	holds	hold	VERB
ap-2224	121	5	for	for	ADP
ap-2224	121	6	the	the	DET
ap-2224	121	7	“	"	PUNCT
ap-2224	121	8	mellin	mellin	ADJ
ap-2224	121	9	variant	variant	NOUN
ap-2224	121	10	”	"	PUNCT
ap-2224	121	11	(	(	PUNCT
ap-2224	121	12	2.5	2.5	NUM
ap-2224	121	13	)	)	PUNCT
ap-2224	121	14	.	.	PUNCT
ap-2224	122	1	in	in	ADP
ap-2224	122	2	this	this	DET
ap-2224	122	3	case	case	NOUN
ap-2224	122	4	g(y	g(y	NOUN
ap-2224	122	5	)	)	PUNCT
ap-2224	122	6	=	=	SYM
ap-2224	122	7	∫	∫	PROPN
ap-2224	122	8	∞	∞	PROPN
ap-2224	122	9	0	0	NUM
ap-2224	122	10	u−y−1g(u	u−y−1g(u	X
ap-2224	122	11	)	)	PUNCT
ap-2224	122	12	du	du	PROPN
ap-2224	122	13	=	=	SYM
ap-2224	122	14	(	(	PUNCT
ap-2224	122	15	iy−f	iy−f	NOUN
ap-2224	122	16	)	)	PUNCT
ap-2224	122	17	(	(	PUNCT
ap-2224	122	18	y	y	NOUN
ap-2224	122	19	)	)	PUNCT
ap-2224	122	20	=	=	SYM
ap-2224	122	21	∫	∫	PROPN
ap-2224	122	22	∞	∞	NUM
ap-2224	122	23	0	0	NUM
ap-2224	122	24	u−y−1f	u−y−1f	PROPN
ap-2224	122	25	(	(	PUNCT
ap-2224	122	26	w0(u	w0(u	NOUN
ap-2224	122	27	)	)	PUNCT
ap-2224	122	28	)	)	PUNCT
ap-2224	123	1	w0(u	w0(u	X
ap-2224	123	2	)	)	PUNCT
ap-2224	123	3	1	1	NUM
ap-2224	124	1	+	+	PUNCT
ap-2224	124	2	w0(u	w0(u	X
ap-2224	124	3	)	)	PUNCT
ap-2224	124	4	du	du	NOUN
ap-2224	124	5	.	.	PUNCT
ap-2224	125	1	(	(	PUNCT
ap-2224	125	2	3.4	3.4	NUM
ap-2224	125	3	)	)	PUNCT
ap-2224	125	4	theorem	theorem	VERB
ap-2224	125	5	3.2	3.2	NUM
ap-2224	125	6	.	.	PUNCT
ap-2224	126	1	the	the	DET
ap-2224	126	2	solution	solution	NOUN
ap-2224	126	3	of	of	ADP
ap-2224	126	4	(	(	PUNCT
ap-2224	126	5	3.4	3.4	NUM
ap-2224	126	6	)	)	PUNCT
ap-2224	126	7	is	be	AUX
ap-2224	126	8	given	give	VERB
ap-2224	126	9	by	by	ADP
ap-2224	126	10	the	the	DET
ap-2224	126	11	relation	relation	NOUN
ap-2224	126	12	f(t	f(t	PROPN
ap-2224	126	13	)	)	PUNCT
ap-2224	126	14	=	=	PUNCT
ap-2224	127	1	g(tet)1	g(tet)1	PROPN
ap-2224	128	1	+	+	CCONJ
ap-2224	128	2	t	t	PROPN
ap-2224	128	3	t	t	PROPN
ap-2224	128	4	,	,	PUNCT
ap-2224	128	5	t	t	PROPN
ap-2224	128	6	∈	∈	PROPN
ap-2224	128	7	(	(	PUNCT
ap-2224	128	8	0,∞	0,∞	NOUN
ap-2224	128	9	)	)	PUNCT
ap-2224	128	10	.	.	PUNCT
ap-2224	129	1	(	(	PUNCT
ap-2224	129	2	3.5	3.5	NUM
ap-2224	129	3	)	)	PUNCT
ap-2224	129	4	proof	proof	NOUN
ap-2224	129	5	.	.	PUNCT
ap-2224	130	1	as	as	ADP
ap-2224	130	2	in	in	ADP
ap-2224	130	3	the	the	DET
ap-2224	130	4	case	case	NOUN
ap-2224	130	5	of	of	ADP
ap-2224	130	6	theorem	theorem	NOUN
ap-2224	130	7	3.1	3.1	NUM
ap-2224	130	8	,	,	PUNCT
ap-2224	130	9	the	the	DET
ap-2224	130	10	two	two	NUM
ap-2224	130	11	integrands	integrand	NOUN
ap-2224	130	12	must	must	AUX
ap-2224	130	13	be	be	AUX
ap-2224	130	14	identical	identical	ADJ
ap-2224	130	15	with	with	ADP
ap-2224	130	16	an	an	DET
ap-2224	130	17	identical	identical	ADJ
ap-2224	130	18	strip	strip	NOUN
ap-2224	130	19	of	of	ADP
ap-2224	130	20	convergence	convergence	NOUN
ap-2224	130	21	.	.	PUNCT
ap-2224	131	1	after	after	ADP
ap-2224	131	2	substituting	substitute	VERB
ap-2224	131	3	w0(u	w0(u	NUM
ap-2224	131	4	)	)	PUNCT
ap-2224	131	5	=	=	SYM
ap-2224	131	6	t	t	PROPN
ap-2224	131	7	,	,	PUNCT
ap-2224	131	8	i.e.	i.e.	X
ap-2224	131	9	,	,	PUNCT
ap-2224	131	10	u	u	PROPN
ap-2224	131	11	=	=	PROPN
ap-2224	131	12	tet	tet	NOUN
ap-2224	131	13	in	in	ADP
ap-2224	131	14	(	(	PUNCT
ap-2224	131	15	3.4	3.4	NUM
ap-2224	131	16	)	)	PUNCT
ap-2224	131	17	we	we	PRON
ap-2224	131	18	obtain	obtain	VERB
ap-2224	131	19	(	(	PUNCT
ap-2224	131	20	3.5	3.5	NUM
ap-2224	131	21	)	)	PUNCT
ap-2224	131	22	.	.	PUNCT
ap-2224	132	1	307	307	NUM
ap-2224	132	2	vladimír	vladimír	PROPN
ap-2224	132	3	vojta	vojta	PROPN
ap-2224	132	4	acta	acta	PROPN
ap-2224	132	5	polytechnica	polytechnica	PROPN
ap-2224	132	6	3.1	3.1	NUM
ap-2224	132	7	.	.	PUNCT
ap-2224	133	1	examples	example	NOUN
ap-2224	133	2	3.1.1	3.1.1	NUM
ap-2224	133	3	.	.	PUNCT
ap-2224	134	1	example	example	NOUN
ap-2224	134	2	of	of	ADP
ap-2224	134	3	the	the	DET
ap-2224	134	4	laplace	laplace	NOUN
ap-2224	134	5	variant	variant	NOUN
ap-2224	134	6	(	(	PUNCT
ap-2224	134	7	cf	cf	NOUN
ap-2224	134	8	.	.	PUNCT
ap-2224	135	1	(	(	PUNCT
ap-2224	135	2	3.2)–(3.3	3.2)–(3.3	NUM
ap-2224	135	3	)	)	PUNCT
ap-2224	135	4	)	)	PUNCT
ap-2224	135	5	let	let	VERB
ap-2224	135	6	g(y	g(y	PRON
ap-2224	135	7	)	)	PUNCT
ap-2224	135	8	=	=	PUNCT
ap-2224	136	1	1/(y	1/(y	NUM
ap-2224	136	2	−	−	NOUN
ap-2224	136	3	1	1	NUM
ap-2224	136	4	)	)	PUNCT
ap-2224	136	5	,	,	PUNCT
ap-2224	136	6	y	y	PROPN
ap-2224	136	7	>	>	X
ap-2224	136	8	1	1	NUM
ap-2224	136	9	,	,	PUNCT
ap-2224	136	10	i.e.	i.e.	X
ap-2224	136	11	,	,	PUNCT
ap-2224	136	12	g(u	g(u	PROPN
ap-2224	136	13	)	)	PUNCT
ap-2224	136	14	=	=	SYM
ap-2224	136	15	eu	eu	PROPN
ap-2224	136	16	for	for	ADP
ap-2224	136	17	u	u	PROPN
ap-2224	136	18	≥	≥	NUM
ap-2224	136	19	0	0	NUM
ap-2224	136	20	and	and	CCONJ
ap-2224	136	21	g(u	g(u	PROPN
ap-2224	136	22	)	)	PUNCT
ap-2224	136	23	=	=	SYM
ap-2224	136	24	0	0	NUM
ap-2224	136	25	for	for	ADP
ap-2224	136	26	u	u	NOUN
ap-2224	136	27	<	<	X
ap-2224	136	28	0	0	NUM
ap-2224	136	29	.	.	PUNCT
ap-2224	137	1	then	then	ADV
ap-2224	137	2	f(t	f(t	NOUN
ap-2224	137	3	)	)	PUNCT
ap-2224	138	1	=	=	PRON
ap-2224	138	2	{	{	PUNCT
ap-2224	138	3	et(t+	et(t+	NOUN
ap-2224	138	4	1	1	NUM
ap-2224	138	5	)	)	PUNCT
ap-2224	138	6	for	for	ADP
ap-2224	138	7	t	t	NOUN
ap-2224	138	8	≥w0(1	≥w0(1	PROPN
ap-2224	138	9	)	)	PUNCT
ap-2224	138	10	,	,	PUNCT
ap-2224	138	11	0	0	NUM
ap-2224	139	1	for	for	ADP
ap-2224	139	2	t	t	PROPN
ap-2224	139	3	<	<	X
ap-2224	139	4	w0(1	w0(1	PROPN
ap-2224	139	5	)	)	PUNCT
ap-2224	139	6	,	,	PUNCT
ap-2224	139	7	f	f	PROPN
ap-2224	139	8	(	(	PUNCT
ap-2224	139	9	x	x	X
ap-2224	139	10	)	)	PUNCT
ap-2224	139	11	=	=	SYM
ap-2224	139	12	∫	∫	PROPN
ap-2224	139	13	∞	∞	PROPN
ap-2224	139	14	w0(1	w0(1	PROPN
ap-2224	139	15	)	)	PUNCT
ap-2224	139	16	e−xtf(t	e−xtf(t	NUM
ap-2224	139	17	)	)	PUNCT
ap-2224	139	18	dt	dt	NOUN
ap-2224	140	1	=	=	SYM
ap-2224	140	2	w0(1)x−1xw0(1	w0(1)x−1xw0(1	NOUN
ap-2224	140	3	)	)	PUNCT
ap-2224	141	1	+	+	CCONJ
ap-2224	141	2	x−w0(1	x−w0(1	NUM
ap-2224	141	3	)	)	PUNCT
ap-2224	142	1	(	(	PUNCT
ap-2224	142	2	x−	x−	PROPN
ap-2224	142	3	1)2	1)2	NUM
ap-2224	142	4	,	,	PUNCT
ap-2224	142	5	x	x	X
ap-2224	142	6	>	>	X
ap-2224	142	7	1	1	NUM
ap-2224	142	8	,	,	PUNCT
ap-2224	142	9	and	and	CCONJ
ap-2224	142	10	(	(	PUNCT
ap-2224	142	11	iy−f	iy−f	NOUN
ap-2224	142	12	)	)	PUNCT
ap-2224	142	13	(	(	PUNCT
ap-2224	142	14	y	y	NOUN
ap-2224	142	15	)	)	PUNCT
ap-2224	142	16	=	=	SYM
ap-2224	142	17	1	1	NUM
ap-2224	142	18	γ(y	γ(y	PROPN
ap-2224	142	19	)	)	PUNCT
ap-2224	142	20	∫	∫	PROPN
ap-2224	143	1	∞	∞	PROPN
ap-2224	143	2	y	y	PROPN
ap-2224	143	3	f	f	PROPN
ap-2224	143	4	(	(	PUNCT
ap-2224	143	5	x)(x−	x)(x−	PROPN
ap-2224	143	6	y)y−1	y)y−1	NOUN
ap-2224	143	7	dx	dx	PROPN
ap-2224	143	8	=	=	SYM
ap-2224	143	9	∫	∫	PROPN
ap-2224	143	10	∞	∞	PROPN
ap-2224	143	11	w0(1	w0(1	PROPN
ap-2224	143	12	)	)	PUNCT
ap-2224	143	13	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	143	14	)	)	PUNCT
ap-2224	143	15	dt	dt	NOUN
ap-2224	144	1	=	=	SYM
ap-2224	144	2	1	1	NUM
ap-2224	144	3	y	y	NOUN
ap-2224	144	4	−	−	PROPN
ap-2224	144	5	1	1	NUM
ap-2224	144	6	,	,	PUNCT
ap-2224	144	7	y	y	PROPN
ap-2224	144	8	>	>	X
ap-2224	144	9	1	1	NUM
ap-2224	144	10	.	.	X
ap-2224	145	1	3.1.2	3.1.2	NUM
ap-2224	145	2	.	.	NOUN
ap-2224	145	3	example	example	NOUN
ap-2224	145	4	of	of	ADP
ap-2224	145	5	the	the	DET
ap-2224	145	6	mellin	mellin	ADJ
ap-2224	145	7	variant	variant	NOUN
ap-2224	145	8	(	(	PUNCT
ap-2224	145	9	cf	cf	NOUN
ap-2224	145	10	.	.	PUNCT
ap-2224	146	1	(	(	PUNCT
ap-2224	146	2	3.4)–(3.5	3.4)–(3.5	NUM
ap-2224	146	3	)	)	PUNCT
ap-2224	146	4	)	)	PUNCT
ap-2224	147	1	let	let	VERB
ap-2224	147	2	g(y	g(y	PRON
ap-2224	147	3	)	)	PUNCT
ap-2224	147	4	=	=	SYM
ap-2224	148	1	−γ(−y)yy−1	−γ(−y)yy−1	PROPN
ap-2224	148	2	,	,	PUNCT
ap-2224	148	3	y	y	PROPN
ap-2224	148	4	∈	∈	PROPN
ap-2224	148	5	(	(	PUNCT
ap-2224	148	6	0	0	NUM
ap-2224	148	7	,	,	PUNCT
ap-2224	148	8	1	1	NUM
ap-2224	148	9	)	)	PUNCT
ap-2224	148	10	,	,	PUNCT
ap-2224	148	11	i.e.	i.e.	X
ap-2224	148	12	,	,	PUNCT
ap-2224	148	13	g(u	g(u	PROPN
ap-2224	148	14	)	)	PUNCT
ap-2224	148	15	=	=	SYM
ap-2224	148	16	w0(u	w0(u	PROPN
ap-2224	148	17	)	)	PUNCT
ap-2224	148	18	for	for	ADP
ap-2224	148	19	u	u	PROPN
ap-2224	148	20	≥	≥	NUM
ap-2224	148	21	0	0	NUM
ap-2224	148	22	and	and	CCONJ
ap-2224	148	23	g(u	g(u	PROPN
ap-2224	148	24	)	)	PUNCT
ap-2224	148	25	=	=	SYM
ap-2224	148	26	0	0	NUM
ap-2224	148	27	for	for	ADP
ap-2224	148	28	u	u	NOUN
ap-2224	148	29	<	<	X
ap-2224	148	30	0	0	NUM
ap-2224	148	31	.	.	PUNCT
ap-2224	149	1	then	then	ADV
ap-2224	149	2	f(t	f(t	NOUN
ap-2224	149	3	)	)	PUNCT
ap-2224	150	1	=	=	PRON
ap-2224	150	2	{	{	PUNCT
ap-2224	150	3	(	(	PUNCT
ap-2224	150	4	1	1	NUM
ap-2224	150	5	+	+	NUM
ap-2224	150	6	t)g(tet)/t	t)g(tet)/t	NOUN
ap-2224	150	7	=	=	SYM
ap-2224	150	8	1	1	NUM
ap-2224	150	9	+	+	NUM
ap-2224	150	10	t	t	PROPN
ap-2224	150	11	for	for	ADP
ap-2224	150	12	t	t	PROPN
ap-2224	150	13	≥	≥	NUM
ap-2224	150	14	0	0	NUM
ap-2224	150	15	,	,	PUNCT
ap-2224	150	16	0	0	NUM
ap-2224	150	17	for	for	ADP
ap-2224	150	18	t	t	PROPN
ap-2224	150	19	<	<	X
ap-2224	150	20	0	0	PROPN
ap-2224	150	21	,	,	PUNCT
ap-2224	150	22	beceause	beceause	NOUN
ap-2224	150	23	w0(tet	w0(tet	NOUN
ap-2224	150	24	)	)	PUNCT
ap-2224	150	25	=	=	PUNCT
ap-2224	151	1	t.	t.	NOUN
ap-2224	151	2	the	the	DET
ap-2224	151	3	laplace	laplace	NOUN
ap-2224	151	4	transform	transform	NOUN
ap-2224	151	5	of	of	ADP
ap-2224	151	6	f(t	f(t	PROPN
ap-2224	151	7	)	)	PUNCT
ap-2224	151	8	is	be	AUX
ap-2224	151	9	f	f	PROPN
ap-2224	151	10	(	(	PUNCT
ap-2224	151	11	x	x	X
ap-2224	151	12	)	)	PUNCT
ap-2224	151	13	=	=	SYM
ap-2224	152	1	∫	∫	PROPN
ap-2224	152	2	∞	∞	NUM
ap-2224	152	3	0	0	NUM
ap-2224	153	1	e−xtf(t	e−xtf(t	NUM
ap-2224	153	2	)	)	PUNCT
ap-2224	153	3	dt	dt	NOUN
ap-2224	153	4	=	=	NOUN
ap-2224	154	1	1	1	NUM
ap-2224	154	2	+	+	CCONJ
ap-2224	154	3	x	x	SYM
ap-2224	154	4	x2	x2	PROPN
ap-2224	154	5	.	.	PUNCT
ap-2224	155	1	finally	finally	ADV
ap-2224	155	2	we	we	PRON
ap-2224	155	3	obtain	obtain	VERB
ap-2224	155	4	(	(	PUNCT
ap-2224	155	5	iy−f	iy−f	NOUN
ap-2224	155	6	)	)	PUNCT
ap-2224	155	7	(	(	PUNCT
ap-2224	155	8	y	y	NOUN
ap-2224	155	9	)	)	PUNCT
ap-2224	155	10	=	=	SYM
ap-2224	155	11	1	1	NUM
ap-2224	155	12	γ(y	γ(y	PROPN
ap-2224	155	13	)	)	PUNCT
ap-2224	155	14	∫	∫	PROPN
ap-2224	156	1	∞	∞	PROPN
ap-2224	156	2	y	y	PROPN
ap-2224	156	3	f	f	PROPN
ap-2224	156	4	(	(	PUNCT
ap-2224	156	5	x)(x−	x)(x−	PROPN
ap-2224	156	6	y)y−1	y)y−1	NOUN
ap-2224	156	7	dx	dx	PROPN
ap-2224	156	8	=	=	SYM
ap-2224	156	9	∫	∫	PROPN
ap-2224	156	10	∞	∞	PROPN
ap-2224	156	11	0	0	NUM
ap-2224	156	12	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	156	13	)	)	PUNCT
ap-2224	156	14	dt	dt	NOUN
ap-2224	157	1	=	=	PUNCT
ap-2224	157	2	πyy−2	πyy−2	PROPN
ap-2224	157	3	cscπy	cscπy	VERB
ap-2224	157	4	γ(y	γ(y	PROPN
ap-2224	157	5	)	)	PUNCT
ap-2224	157	6	,	,	PUNCT
ap-2224	157	7	y	y	PROPN
ap-2224	157	8	∈	∈	PROPN
ap-2224	157	9	(	(	PUNCT
ap-2224	157	10	0	0	NUM
ap-2224	157	11	,	,	PUNCT
ap-2224	157	12	1	1	NUM
ap-2224	157	13	)	)	PUNCT
ap-2224	157	14	,	,	PUNCT
ap-2224	157	15	see	see	VERB
ap-2224	157	16	[	[	X
ap-2224	157	17	12	12	NUM
ap-2224	157	18	,	,	PUNCT
ap-2224	157	19	entry	entry	NOUN
ap-2224	157	20	8	8	NUM
ap-2224	157	21	,	,	PUNCT
ap-2224	157	22	p.	p.	NOUN
ap-2224	157	23	201	201	NUM
ap-2224	157	24	]	]	PUNCT
ap-2224	157	25	,	,	PUNCT
ap-2224	157	26	where	where	SCONJ
ap-2224	157	27	cscπy	cscπy	NOUN
ap-2224	157	28	=	=	SYM
ap-2224	157	29	1/	1/	NUM
ap-2224	157	30	sin	sin	NOUN
ap-2224	157	31	πy	πy	NOUN
ap-2224	157	32	.	.	PUNCT
ap-2224	158	1	this	this	PRON
ap-2224	158	2	means	mean	VERB
ap-2224	158	3	that	that	SCONJ
ap-2224	158	4	g(y	g(y	NOUN
ap-2224	158	5	)	)	PUNCT
ap-2224	158	6	=	=	SYM
ap-2224	159	1	∫	∫	PROPN
ap-2224	159	2	∞	∞	PROPN
ap-2224	159	3	0	0	NUM
ap-2224	159	4	u−y−1w0(u	u−y−1w0(u	NUM
ap-2224	159	5	)	)	PUNCT
ap-2224	160	1	du	du	NOUN
ap-2224	160	2	=	=	PUNCT
ap-2224	160	3	πyy−2	πyy−2	PROPN
ap-2224	160	4	cscπy	cscπy	VERB
ap-2224	160	5	γ(y	γ(y	PROPN
ap-2224	160	6	)	)	PUNCT
ap-2224	160	7	,	,	PUNCT
ap-2224	160	8	y	y	PROPN
ap-2224	160	9	∈	∈	PROPN
ap-2224	160	10	(	(	PUNCT
ap-2224	160	11	0	0	NUM
ap-2224	160	12	,	,	PUNCT
ap-2224	160	13	1	1	NUM
ap-2224	160	14	)	)	PUNCT
ap-2224	160	15	.	.	PUNCT
ap-2224	161	1	in	in	ADP
ap-2224	161	2	standard	standard	ADJ
ap-2224	161	3	notation	notation	NOUN
ap-2224	161	4	of	of	ADP
ap-2224	161	5	the	the	DET
ap-2224	161	6	mellin	mellin	PROPN
ap-2224	161	7	transform	transform	NOUN
ap-2224	161	8	we	we	PRON
ap-2224	161	9	have	have	VERB
ap-2224	161	10	the	the	DET
ap-2224	161	11	known	know	VERB
ap-2224	161	12	transform	transform	NOUN
ap-2224	161	13	pair	pair	NOUN
ap-2224	162	1	[	[	X
ap-2224	162	2	2]∫	2]∫	NOUN
ap-2224	162	3	∞	∞	NOUN
ap-2224	162	4	0	0	X
ap-2224	163	1	uy−1w0(u	uy−1w0(u	NUM
ap-2224	163	2	)	)	PUNCT
ap-2224	163	3	du	du	PROPN
ap-2224	163	4	=	=	PUNCT
ap-2224	163	5	π(−y)−y−2	π(−y)−y−2	PROPN
ap-2224	163	6	csc(−πy	csc(−πy	NOUN
ap-2224	163	7	)	)	PUNCT
ap-2224	163	8	γ(−y	γ(−y	NOUN
ap-2224	163	9	)	)	PUNCT
ap-2224	163	10	=	=	SYM
ap-2224	164	1	(	(	PUNCT
ap-2224	164	2	−y)−y	−y)−y	PROPN
ap-2224	164	3	γ(y	γ(y	PROPN
ap-2224	164	4	)	)	PUNCT
ap-2224	164	5	y	y	PROPN
ap-2224	164	6	,	,	PUNCT
ap-2224	164	7	y	y	PROPN
ap-2224	164	8	∈	∈	PROPN
ap-2224	164	9	(	(	PUNCT
ap-2224	164	10	−1	−1	NOUN
ap-2224	164	11	,	,	PUNCT
ap-2224	164	12	0	0	NUM
ap-2224	164	13	)	)	PUNCT
ap-2224	164	14	.	.	PUNCT
ap-2224	165	1	4	4	X
ap-2224	165	2	.	.	X
ap-2224	165	3	fixed	fix	VERB
ap-2224	165	4	point	point	NOUN
ap-2224	165	5	the	the	DET
ap-2224	165	6	following	follow	VERB
ap-2224	165	7	theorems	theorem	NOUN
ap-2224	165	8	assert	assert	VERB
ap-2224	165	9	that	that	SCONJ
ap-2224	165	10	the	the	DET
ap-2224	165	11	unilateral	unilateral	ADJ
ap-2224	165	12	laplace	laplace	NOUN
ap-2224	165	13	transform	transform	NOUN
ap-2224	165	14	can	can	AUX
ap-2224	165	15	be	be	AUX
ap-2224	165	16	represented	represent	VERB
ap-2224	165	17	by	by	ADP
ap-2224	165	18	the	the	DET
ap-2224	165	19	liouville	liouville	NOUN
ap-2224	165	20	–	–	PUNCT
ap-2224	165	21	weyl	weyl	VERB
ap-2224	165	22	diagonal	diagonal	ADJ
ap-2224	165	23	fractional	fractional	ADJ
ap-2224	165	24	integral	integral	NOUN
ap-2224	165	25	of	of	ADP
ap-2224	165	26	another	another	DET
ap-2224	165	27	laplace	laplace	NOUN
ap-2224	165	28	transform	transform	NOUN
ap-2224	165	29	.	.	PUNCT
ap-2224	166	1	theorem	theorem	VERB
ap-2224	166	2	4.1	4.1	NUM
ap-2224	166	3	.	.	PUNCT
ap-2224	167	1	every	every	DET
ap-2224	167	2	unilateral	unilateral	ADJ
ap-2224	167	3	laplace	laplace	NOUN
ap-2224	167	4	transform	transform	NOUN
ap-2224	167	5	f0(y	f0(y	PRON
ap-2224	167	6	)	)	PUNCT
ap-2224	167	7	=	=	SYM
ap-2224	168	1	∫	∫	PROPN
ap-2224	168	2	∞	∞	PROPN
ap-2224	169	1	a	a	DET
ap-2224	169	2	e−ytf(t	e−ytf(t	NUM
ap-2224	169	3	)	)	PUNCT
ap-2224	169	4	dt	dt	NOUN
ap-2224	169	5	,	,	PUNCT
ap-2224	169	6	a	a	DET
ap-2224	169	7	∈	∈	NOUN
ap-2224	170	1	[	[	X
ap-2224	170	2	0,∞	0,∞	NOUN
ap-2224	170	3	)	)	PUNCT
ap-2224	170	4	of	of	ADP
ap-2224	170	5	some	some	DET
ap-2224	170	6	function	function	NOUN
ap-2224	170	7	f(t	f(t	NOUN
ap-2224	170	8	)	)	PUNCT
ap-2224	170	9	of	of	ADP
ap-2224	170	10	exponential	exponential	ADJ
ap-2224	170	11	order	order	NOUN
ap-2224	170	12	α0	α0	ADJ
ap-2224	170	13	,	,	PUNCT
ap-2224	170	14	i.e.	i.e.	X
ap-2224	170	15	,	,	PUNCT
ap-2224	170	16	f(t	f(t	PROPN
ap-2224	170	17	)	)	PUNCT
ap-2224	170	18	=	=	SYM
ap-2224	170	19	o(expα0	o(expα0	PROPN
ap-2224	170	20	t	t	PROPN
ap-2224	170	21	)	)	PUNCT
ap-2224	170	22	for	for	ADP
ap-2224	170	23	t	t	PROPN
ap-2224	170	24	→	→	SYM
ap-2224	170	25	+	+	PROPN
ap-2224	170	26	∞	∞	PROPN
ap-2224	170	27	,	,	PUNCT
ap-2224	170	28	is	be	AUX
ap-2224	170	29	equivalent	equivalent	ADJ
ap-2224	170	30	to	to	ADP
ap-2224	170	31	the	the	DET
ap-2224	170	32	liouville	liouville	NOUN
ap-2224	170	33	–	–	PUNCT
ap-2224	170	34	weyl	weyl	VERB
ap-2224	170	35	diagonal	diagonal	ADJ
ap-2224	170	36	fractional	fractional	ADJ
ap-2224	170	37	integral	integral	NOUN
ap-2224	170	38	of	of	ADP
ap-2224	170	39	the	the	DET
ap-2224	170	40	function	function	NOUN
ap-2224	170	41	f1(x	f1(x	NOUN
ap-2224	170	42	)	)	PUNCT
ap-2224	170	43	=	=	SYM
ap-2224	171	1	∫	∫	PROPN
ap-2224	171	2	∞	∞	NUM
ap-2224	171	3	a1	a1	NOUN
ap-2224	171	4	e−xtf(t+	e−xtf(t+	PROPN
ap-2224	171	5	ln	ln	NOUN
ap-2224	171	6	t)1	t)1	PROPN
ap-2224	172	1	+	+	CCONJ
ap-2224	172	2	t	t	PROPN
ap-2224	172	3	t	t	X
ap-2224	172	4	dt	dt	X
ap-2224	172	5	,	,	PUNCT
ap-2224	172	6	x	x	PRON
ap-2224	172	7	≥	≥	NOUN
ap-2224	172	8	α0	α0	ADJ
ap-2224	172	9	,	,	PUNCT
ap-2224	172	10	(	(	PUNCT
ap-2224	172	11	4.1	4.1	NUM
ap-2224	172	12	)	)	PUNCT
ap-2224	172	13	where	where	SCONJ
ap-2224	172	14	a1	a1	NOUN
ap-2224	172	15	=	=	PUNCT
ap-2224	172	16	a(a	a(a	PROPN
ap-2224	172	17	)	)	PUNCT
ap-2224	173	1	=	=	SYM
ap-2224	173	2	w0(ea	w0(ea	PROPN
ap-2224	173	3	)	)	PUNCT
ap-2224	173	4	.	.	PUNCT
ap-2224	174	1	proof	proof	NOUN
ap-2224	174	2	.	.	PUNCT
ap-2224	175	1	we	we	PRON
ap-2224	175	2	rewrite	rewrite	VERB
ap-2224	175	3	the	the	DET
ap-2224	175	4	laplace	laplace	NOUN
ap-2224	175	5	transform	transform	NOUN
ap-2224	175	6	from	from	ADP
ap-2224	175	7	the	the	DET
ap-2224	175	8	hypothesis	hypothesis	NOUN
ap-2224	175	9	in	in	ADP
ap-2224	175	10	the	the	DET
ap-2224	175	11	form∫	form∫	ADJ
ap-2224	175	12	∞	∞	PROPN
ap-2224	175	13	a	a	DET
ap-2224	175	14	e−ytf(t	e−ytf(t	NUM
ap-2224	175	15	)	)	PUNCT
ap-2224	175	16	dt	dt	NOUN
ap-2224	176	1	=	=	SYM
ap-2224	176	2	∫	∫	PROPN
ap-2224	176	3	∞	∞	PROPN
ap-2224	176	4	a	a	DET
ap-2224	176	5	e−yth1	e−yth1	NOUN
ap-2224	176	6	(	(	PUNCT
ap-2224	176	7	w0(et	w0(et	PROPN
ap-2224	176	8	)	)	PUNCT
ap-2224	176	9	)	)	PUNCT
ap-2224	176	10	w0(et	w0(et	PROPN
ap-2224	176	11	)	)	PUNCT
ap-2224	176	12	1	1	NUM
ap-2224	177	1	+	+	NOUN
ap-2224	177	2	w0(et	w0(et	NOUN
ap-2224	177	3	)	)	PUNCT
ap-2224	177	4	dt	dt	NOUN
ap-2224	177	5	.	.	PUNCT
ap-2224	178	1	308	308	NUM
ap-2224	178	2	vol	vol	NOUN
ap-2224	178	3	.	.	PUNCT
ap-2224	179	1	54	54	NUM
ap-2224	179	2	no	no	NOUN
ap-2224	179	3	.	.	PUNCT
ap-2224	180	1	4/2014	4/2014	NUM
ap-2224	180	2	fractional	fractional	ADJ
ap-2224	180	3	calculus	calculus	NOUN
ap-2224	180	4	and	and	CCONJ
ap-2224	180	5	lambert	lambert	PROPN
ap-2224	180	6	function	function	NOUN
ap-2224	180	7	i	i	PRON
ap-2224	180	8	then	then	ADV
ap-2224	180	9	h1(w0(et	h1(w0(et	NOUN
ap-2224	180	10	)	)	PUNCT
ap-2224	180	11	)	)	PUNCT
ap-2224	181	1	=	=	SYM
ap-2224	181	2	f(t)(1+w0(et))/w0(et	f(t)(1+w0(et))/w0(et	NOUN
ap-2224	181	3	)	)	PUNCT
ap-2224	181	4	,	,	PUNCT
ap-2224	181	5	t	t	X
ap-2224	181	6	>	>	X
ap-2224	181	7	0	0	NUM
ap-2224	181	8	,	,	PUNCT
ap-2224	181	9	according	accord	VERB
ap-2224	181	10	to	to	ADP
ap-2224	181	11	the	the	DET
ap-2224	181	12	uniqueness	uniqueness	NOUN
ap-2224	181	13	(	(	PUNCT
ap-2224	181	14	lerch	lerch	PROPN
ap-2224	181	15	)	)	PUNCT
ap-2224	181	16	theorem	theorem	NOUN
ap-2224	181	17	for	for	ADP
ap-2224	181	18	the	the	DET
ap-2224	181	19	unilateral	unilateral	ADJ
ap-2224	181	20	laplace	laplace	NOUN
ap-2224	181	21	transform	transform	NOUN
ap-2224	181	22	[	[	X
ap-2224	181	23	3	3	NUM
ap-2224	181	24	,	,	PUNCT
ap-2224	181	25	p.	p.	NOUN
ap-2224	181	26	120	120	NUM
ap-2224	181	27	]	]	PUNCT
ap-2224	181	28	.	.	PUNCT
ap-2224	182	1	after	after	ADP
ap-2224	182	2	substituting	substitute	VERB
ap-2224	182	3	w0(et	w0(et	NOUN
ap-2224	182	4	)	)	PUNCT
ap-2224	182	5	=	=	SYM
ap-2224	182	6	u	u	NOUN
ap-2224	182	7	,	,	PUNCT
ap-2224	182	8	i.e.	i.e.	X
ap-2224	182	9	,	,	PUNCT
ap-2224	182	10	t	t	NOUN
ap-2224	182	11	=	=	SYM
ap-2224	182	12	u+	u+	NOUN
ap-2224	182	13	ln	ln	PROPN
ap-2224	182	14	u	u	NOUN
ap-2224	182	15	,	,	PUNCT
ap-2224	182	16	u	u	NOUN
ap-2224	182	17	≥w0(ea	≥w0(ea	PROPN
ap-2224	182	18	)	)	PUNCT
ap-2224	182	19	=	=	SYM
ap-2224	182	20	a(a	a(a	PROPN
ap-2224	182	21	)	)	PUNCT
ap-2224	182	22	≡	≡	PROPN
ap-2224	182	23	a1	a1	PROPN
ap-2224	182	24	>	>	X
ap-2224	182	25	0	0	NUM
ap-2224	182	26	,	,	PUNCT
ap-2224	182	27	we	we	PRON
ap-2224	182	28	obtain	obtain	VERB
ap-2224	182	29	∫	∫	PROPN
ap-2224	182	30	∞	∞	PROPN
ap-2224	182	31	a	a	DET
ap-2224	182	32	e−ytf(t)dt	e−ytf(t)dt	PROPN
ap-2224	182	33	=	=	SYM
ap-2224	182	34	∫	∫	PROPN
ap-2224	182	35	∞	∞	PROPN
ap-2224	182	36	a1	a1	PROPN
ap-2224	182	37	e−y(u+lnu)h1(u	e−y(u+lnu)h1(u	PROPN
ap-2224	182	38	)	)	PUNCT
ap-2224	182	39	du	du	PROPN
ap-2224	182	40	=	=	SYM
ap-2224	182	41	∫	∫	PROPN
ap-2224	182	42	∞	∞	PROPN
ap-2224	182	43	a1	a1	PROPN
ap-2224	182	44	e−yuu−yh1(u	e−yuu−yh1(u	NOUN
ap-2224	182	45	)	)	PUNCT
ap-2224	182	46	du	du	NOUN
ap-2224	182	47	.	.	PUNCT
ap-2224	183	1	(	(	PUNCT
ap-2224	183	2	4.2	4.2	NUM
ap-2224	183	3	)	)	PUNCT
ap-2224	183	4	the	the	DET
ap-2224	183	5	function	function	NOUN
ap-2224	183	6	h1(u	h1(u	PROPN
ap-2224	183	7	)	)	PUNCT
ap-2224	183	8	=	=	SYM
ap-2224	183	9	f(u+	f(u+	NOUN
ap-2224	183	10	ln	ln	X
ap-2224	183	11	u	u	NOUN
ap-2224	183	12	)	)	PUNCT
ap-2224	183	13	+	+	NUM
ap-2224	183	14	f(u+	f(u+	PROPN
ap-2224	183	15	ln	ln	X
ap-2224	183	16	u)/u	u)/u	PROPN
ap-2224	183	17	,	,	PUNCT
ap-2224	183	18	u	u	NOUN
ap-2224	183	19	≥w0(ea	≥w0(ea	PROPN
ap-2224	183	20	)	)	PUNCT
ap-2224	183	21	is	be	AUX
ap-2224	183	22	also	also	ADV
ap-2224	183	23	of	of	ADP
ap-2224	183	24	exponential	exponential	ADJ
ap-2224	183	25	order	order	NOUN
ap-2224	183	26	α0	α0	VERB
ap-2224	183	27	,	,	PUNCT
ap-2224	183	28	because	because	SCONJ
ap-2224	183	29	f(u+	f(u+	PROPN
ap-2224	183	30	ln	ln	X
ap-2224	183	31	u	u	NOUN
ap-2224	183	32	)	)	PUNCT
ap-2224	183	33	is	be	AUX
ap-2224	183	34	of	of	ADP
ap-2224	183	35	exponential	exponential	ADJ
ap-2224	183	36	order	order	NOUN
ap-2224	183	37	α0	α0	ADJ
ap-2224	183	38	and	and	CCONJ
ap-2224	183	39	the	the	DET
ap-2224	183	40	function	function	NOUN
ap-2224	183	41	f(u+	f(u+	NOUN
ap-2224	183	42	ln	ln	DET
ap-2224	183	43	u)/u	u)/u	PROPN
ap-2224	183	44	is	be	AUX
ap-2224	183	45	of	of	ADP
ap-2224	183	46	the	the	DET
ap-2224	183	47	order	order	NOUN
ap-2224	183	48	α	α	NOUN
ap-2224	183	49	<	<	X
ap-2224	183	50	α0	α0	PROPN
ap-2224	183	51	.	.	PUNCT
ap-2224	184	1	this	this	PRON
ap-2224	184	2	means	mean	VERB
ap-2224	184	3	that	that	SCONJ
ap-2224	184	4	the	the	DET
ap-2224	184	5	laplace	laplace	NOUN
ap-2224	184	6	transform	transform	VERB
ap-2224	184	7	f1(x	f1(x	NOUN
ap-2224	184	8	)	)	PUNCT
ap-2224	184	9	=	=	SYM
ap-2224	185	1	∫	∫	PROPN
ap-2224	185	2	∞	∞	NUM
ap-2224	185	3	a1	a1	NOUN
ap-2224	185	4	e−xth1(t	e−xth1(t	PROPN
ap-2224	185	5	)	)	PUNCT
ap-2224	185	6	dt	dt	PUNCT
ap-2224	186	1	=	=	SYM
ap-2224	186	2	∫	∫	PROPN
ap-2224	186	3	∞	∞	NUM
ap-2224	186	4	a1	a1	NOUN
ap-2224	186	5	e−xtf(t+	e−xtf(t+	PROPN
ap-2224	186	6	ln	ln	NOUN
ap-2224	186	7	t)1	t)1	PROPN
ap-2224	187	1	+	+	CCONJ
ap-2224	187	2	t	t	PROPN
ap-2224	187	3	t	t	NOUN
ap-2224	187	4	dt	dt	NOUN
ap-2224	188	1	=	=	SYM
ap-2224	188	2	∫	∫	PROPN
ap-2224	188	3	∞	∞	NUM
ap-2224	188	4	x	x	SYM
ap-2224	188	5	φ(u	φ(u	X
ap-2224	188	6	)	)	PUNCT
ap-2224	188	7	du+φ(x	du+φ(x	PROPN
ap-2224	188	8	)	)	PUNCT
ap-2224	188	9	,	,	PUNCT
ap-2224	188	10	x	x	X
ap-2224	188	11	≥	≥	NOUN
ap-2224	188	12	α0	α0	ADJ
ap-2224	188	13	,	,	PUNCT
ap-2224	188	14	where	where	SCONJ
ap-2224	188	15	φ(x	φ(x	NOUN
ap-2224	188	16	)	)	PUNCT
ap-2224	188	17	=	=	SYM
ap-2224	189	1	∫	∫	PROPN
ap-2224	189	2	∞	∞	NUM
ap-2224	189	3	a1	a1	PROPN
ap-2224	189	4	e−xtf(t+	e−xtf(t+	PROPN
ap-2224	189	5	ln	ln	PROPN
ap-2224	189	6	t	t	PROPN
ap-2224	189	7	)	)	PUNCT
ap-2224	189	8	dt	dt	NOUN
ap-2224	189	9	,	,	PUNCT
ap-2224	189	10	x	x	X
ap-2224	189	11	≥	≥	NUM
ap-2224	189	12	α0	α0	ADJ
ap-2224	189	13	exists	exist	VERB
ap-2224	189	14	,	,	PUNCT
ap-2224	189	15	and	and	CCONJ
ap-2224	189	16	that	that	SCONJ
ap-2224	189	17	the	the	DET
ap-2224	189	18	liouville	liouville	NOUN
ap-2224	189	19	–	–	PUNCT
ap-2224	189	20	weyl	weyl	VERB
ap-2224	189	21	diagonal	diagonal	ADJ
ap-2224	189	22	fractional	fractional	ADJ
ap-2224	189	23	integral	integral	ADJ
ap-2224	189	24	(	(	PUNCT
ap-2224	189	25	iy−f1)(y	iy−f1)(y	NOUN
ap-2224	189	26	)	)	PUNCT
ap-2224	189	27	=	=	SYM
ap-2224	189	28	1	1	NUM
ap-2224	189	29	γ(y	γ(y	PROPN
ap-2224	189	30	)	)	PUNCT
ap-2224	189	31	∫	∫	PROPN
ap-2224	190	1	∞	∞	PROPN
ap-2224	190	2	y	y	PROPN
ap-2224	190	3	f1(x)(x−	f1(x)(x−	PROPN
ap-2224	191	1	y)y−1	y)y−1	NOUN
ap-2224	191	2	dx	dx	PROPN
ap-2224	191	3	=	=	SYM
ap-2224	191	4	∫	∫	PROPN
ap-2224	192	1	∞	∞	PROPN
ap-2224	192	2	a1	a1	PROPN
ap-2224	192	3	e−yuu−yh1(u	e−yuu−yh1(u	NOUN
ap-2224	192	4	)	)	PUNCT
ap-2224	192	5	du	du	PROPN
ap-2224	192	6	=	=	SYM
ap-2224	192	7	∫	∫	PROPN
ap-2224	192	8	∞	∞	PROPN
ap-2224	192	9	a	a	DET
ap-2224	192	10	e−ytf(t	e−ytf(t	NUM
ap-2224	193	1	)	)	PUNCT
ap-2224	193	2	dt	dt	NOUN
ap-2224	193	3	=	=	SYM
ap-2224	193	4	f0(y	f0(y	PROPN
ap-2224	193	5	)	)	PUNCT
ap-2224	194	1	,	,	PUNCT
ap-2224	194	2	y	y	PROPN
ap-2224	194	3	>	>	X
ap-2224	194	4	α0	α0	PROPN
ap-2224	194	5	also	also	ADV
ap-2224	194	6	exists	exist	VERB
ap-2224	194	7	.	.	PUNCT
ap-2224	195	1	the	the	DET
ap-2224	195	2	same	same	ADJ
ap-2224	195	3	procedure	procedure	NOUN
ap-2224	195	4	as	as	ADP
ap-2224	195	5	above	above	ADV
ap-2224	195	6	can	can	AUX
ap-2224	195	7	be	be	AUX
ap-2224	195	8	applied	apply	VERB
ap-2224	195	9	to	to	PART
ap-2224	195	10	function	function	VERB
ap-2224	195	11	f1(y	f1(y	NUM
ap-2224	195	12	)	)	PUNCT
ap-2224	195	13	,	,	PUNCT
ap-2224	195	14	and	and	CCONJ
ap-2224	195	15	we	we	PRON
ap-2224	195	16	obtain	obtain	VERB
ap-2224	195	17	f2(x	f2(x	NOUN
ap-2224	195	18	)	)	PUNCT
ap-2224	196	1	=	=	SYM
ap-2224	196	2	∫	∫	PROPN
ap-2224	196	3	∞	∞	PROPN
ap-2224	196	4	a2	a2	PROPN
ap-2224	196	5	e−yth2(t	e−yth2(t	PROPN
ap-2224	196	6	)	)	PUNCT
ap-2224	196	7	dt	dt	PUNCT
ap-2224	197	1	=	=	SYM
ap-2224	197	2	∫	∫	PROPN
ap-2224	198	1	∞	∞	PROPN
ap-2224	198	2	a2	a2	PROPN
ap-2224	198	3	e−yth1(t+	e−yth1(t+	PROPN
ap-2224	198	4	ln	ln	PROPN
ap-2224	198	5	t)1	t)1	PROPN
ap-2224	199	1	+	+	CCONJ
ap-2224	199	2	t	t	PROPN
ap-2224	199	3	t	t	X
ap-2224	199	4	dt	dt	PROPN
ap-2224	199	5	,	,	PUNCT
ap-2224	199	6	(	(	PUNCT
ap-2224	199	7	iy−f2)(y	iy−f2)(y	NOUN
ap-2224	199	8	)	)	PUNCT
ap-2224	199	9	=	=	SYM
ap-2224	199	10	1	1	NUM
ap-2224	199	11	γ(y	γ(y	PROPN
ap-2224	199	12	)	)	PUNCT
ap-2224	199	13	∫	∫	PROPN
ap-2224	200	1	∞	∞	PROPN
ap-2224	200	2	y	y	PROPN
ap-2224	200	3	f2(x)(x−	f2(x)(x−	PROPN
ap-2224	200	4	y)y−1	y)y−1	NOUN
ap-2224	200	5	dx	dx	PROPN
ap-2224	200	6	=	=	SYM
ap-2224	200	7	∫	∫	PROPN
ap-2224	200	8	∞	∞	PROPN
ap-2224	200	9	a2	a2	PROPN
ap-2224	200	10	e−yuu−yh2(u	e−yuu−yh2(u	NOUN
ap-2224	200	11	)	)	PUNCT
ap-2224	200	12	du	du	PROPN
ap-2224	200	13	=	=	SYM
ap-2224	200	14	∫	∫	PROPN
ap-2224	200	15	∞	∞	PROPN
ap-2224	200	16	a1	a1	PROPN
ap-2224	200	17	e−yth1(t	e−yth1(t	NOUN
ap-2224	200	18	)	)	PUNCT
ap-2224	200	19	dt	dt	X
ap-2224	201	1	=	=	SYM
ap-2224	201	2	f1(y	f1(y	PROPN
ap-2224	201	3	)	)	PUNCT
ap-2224	202	1	,	,	PUNCT
ap-2224	202	2	y	y	PROPN
ap-2224	202	3	>	>	X
ap-2224	202	4	α0	α0	PROPN
ap-2224	202	5	,	,	PUNCT
ap-2224	202	6	where	where	SCONJ
ap-2224	202	7	a2	a2	PROPN
ap-2224	202	8	=	=	SYM
ap-2224	202	9	a(a(a	a(a(a	PROPN
ap-2224	202	10	)	)	PUNCT
ap-2224	202	11	)	)	PUNCT
ap-2224	203	1	=	=	SYM
ap-2224	203	2	w0(exp(w0(ea	w0(exp(w0(ea	PROPN
ap-2224	203	3	)	)	PUNCT
ap-2224	203	4	)	)	PUNCT
ap-2224	203	5	is	be	AUX
ap-2224	203	6	a	a	DET
ap-2224	203	7	second	second	ADJ
ap-2224	203	8	iterate	iterate	NOUN
ap-2224	203	9	of	of	ADP
ap-2224	203	10	the	the	DET
ap-2224	203	11	function	function	NOUN
ap-2224	203	12	a(a	a(a	PROPN
ap-2224	203	13	)	)	PUNCT
ap-2224	203	14	,	,	PUNCT
ap-2224	203	15	and	and	CCONJ
ap-2224	203	16	h2(u	h2(u	X
ap-2224	203	17	)	)	PUNCT
ap-2224	203	18	=	=	SYM
ap-2224	204	1	h1(u+	h1(u+	PROPN
ap-2224	204	2	ln	ln	ADJ
ap-2224	204	3	u)1	u)1	NOUN
ap-2224	204	4	+	+	CCONJ
ap-2224	204	5	u	u	NOUN
ap-2224	204	6	u	u	NOUN
ap-2224	204	7	=	=	PROPN
ap-2224	204	8	f	f	X
ap-2224	204	9	(	(	PUNCT
ap-2224	204	10	u+	u+	NUM
ap-2224	204	11	ln	ln	ADJ
ap-2224	204	12	u+	u+	NOUN
ap-2224	204	13	ln(u+	ln(u+	PROPN
ap-2224	204	14	ln	ln	ADP
ap-2224	204	15	u	u	NOUN
ap-2224	204	16	)	)	PUNCT
ap-2224	204	17	)	)	PUNCT
ap-2224	204	18	1	1	NUM
ap-2224	205	1	+	+	NUM
ap-2224	205	2	u+	u+	PRON
ap-2224	205	3	ln	ln	ADJ
ap-2224	205	4	u	u	NOUN
ap-2224	205	5	u+	u+	NOUN
ap-2224	205	6	ln	ln	NUM
ap-2224	205	7	u	u	NOUN
ap-2224	205	8	1	1	NUM
ap-2224	205	9	+	+	NUM
ap-2224	205	10	u	u	NOUN
ap-2224	205	11	u	u	NOUN
ap-2224	205	12	,	,	PUNCT
ap-2224	205	13	u	u	PROPN
ap-2224	205	14	≥	≥	NOUN
ap-2224	205	15	a2	a2	PROPN
ap-2224	205	16	.	.	PUNCT
ap-2224	206	1	this	this	DET
ap-2224	206	2	procedure	procedure	NOUN
ap-2224	206	3	can	can	AUX
ap-2224	206	4	be	be	AUX
ap-2224	206	5	repeated	repeat	VERB
ap-2224	206	6	without	without	ADP
ap-2224	206	7	restraint	restraint	NOUN
ap-2224	206	8	.	.	PUNCT
ap-2224	207	1	to	to	PART
ap-2224	207	2	understand	understand	VERB
ap-2224	207	3	its	its	PRON
ap-2224	207	4	behaviour	behaviour	NOUN
ap-2224	207	5	,	,	PUNCT
ap-2224	207	6	we	we	PRON
ap-2224	207	7	first	first	ADV
ap-2224	207	8	observe	observe	VERB
ap-2224	207	9	that	that	DET
ap-2224	207	10	point	point	NOUN
ap-2224	207	11	a	a	DET
ap-2224	207	12	=	=	SYM
ap-2224	207	13	1	1	NUM
ap-2224	207	14	is	be	AUX
ap-2224	207	15	a	a	DET
ap-2224	207	16	fixed	fix	VERB
ap-2224	207	17	point	point	NOUN
ap-2224	207	18	of	of	ADP
ap-2224	207	19	the	the	DET
ap-2224	207	20	function	function	NOUN
ap-2224	207	21	a(a	a(a	PROPN
ap-2224	207	22	)	)	PUNCT
ap-2224	208	1	=	=	SYM
ap-2224	208	2	w0(ea	w0(ea	PROPN
ap-2224	208	3	)	)	PUNCT
ap-2224	208	4	,	,	PUNCT
ap-2224	208	5	because	because	SCONJ
ap-2224	208	6	a(a	a(a	PROPN
ap-2224	208	7	)	)	PUNCT
ap-2224	208	8	is	be	AUX
ap-2224	208	9	a	a	DET
ap-2224	208	10	continuous	continuous	ADJ
ap-2224	208	11	function	function	NOUN
ap-2224	208	12	,	,	PUNCT
ap-2224	208	13	a(a	a(a	PROPN
ap-2224	208	14	)	)	PUNCT
ap-2224	208	15	>	>	X
ap-2224	209	1	a	a	PRON
ap-2224	209	2	for	for	ADP
ap-2224	209	3	a	a	DET
ap-2224	209	4	<	<	X
ap-2224	209	5	1	1	NUM
ap-2224	209	6	,	,	PUNCT
ap-2224	209	7	a(a	a(a	PROPN
ap-2224	209	8	)	)	PUNCT
ap-2224	210	1	<	<	X
ap-2224	210	2	a	a	PRON
ap-2224	210	3	for	for	ADP
ap-2224	210	4	a	a	DET
ap-2224	210	5	>	>	SYM
ap-2224	210	6	1	1	NUM
ap-2224	210	7	and	and	CCONJ
ap-2224	210	8	a(1	a(1	ADJ
ap-2224	210	9	)	)	PUNCT
ap-2224	210	10	=	=	SYM
ap-2224	211	1	1	1	X
ap-2224	211	2	.	.	PUNCT
ap-2224	212	1	this	this	DET
ap-2224	212	2	fixed	fix	VERB
ap-2224	212	3	point	point	NOUN
ap-2224	212	4	is	be	AUX
ap-2224	212	5	attractive	attractive	ADJ
ap-2224	212	6	because	because	SCONJ
ap-2224	212	7	of	of	ADP
ap-2224	212	8	a′(1	a′(1	PROPN
ap-2224	212	9	)	)	PUNCT
ap-2224	212	10	=	=	NOUN
ap-2224	212	11	1/2	1/2	NUM
ap-2224	212	12	<	<	X
ap-2224	212	13	1	1	NUM
ap-2224	212	14	.	.	PUNCT
ap-2224	213	1	for	for	ADP
ap-2224	213	2	this	this	DET
ap-2224	213	3	reason	reason	NOUN
ap-2224	213	4	,	,	PUNCT
ap-2224	213	5	limn→∞an(a	limn→∞an(a	PROPN
ap-2224	213	6	)	)	PUNCT
ap-2224	213	7	=	=	SYM
ap-2224	213	8	1	1	NUM
ap-2224	213	9	for	for	ADP
ap-2224	213	10	every	every	DET
ap-2224	213	11	a	a	DET
ap-2224	213	12	∈	∈	NOUN
ap-2224	214	1	[	[	X
ap-2224	214	2	0,∞	0,∞	NOUN
ap-2224	214	3	)	)	PUNCT
ap-2224	214	4	,	,	PUNCT
ap-2224	214	5	where	where	SCONJ
ap-2224	214	6	an(a	an(a	NOUN
ap-2224	214	7	)	)	PUNCT
ap-2224	214	8	means	mean	VERB
ap-2224	214	9	the	the	DET
ap-2224	214	10	nth	nth	PROPN
ap-2224	214	11	iterate	iterate	NOUN
ap-2224	214	12	of	of	ADP
ap-2224	214	13	function	function	NOUN
ap-2224	214	14	a(a	a(a	PROPN
ap-2224	214	15	)	)	PUNCT
ap-2224	214	16	.	.	PUNCT
ap-2224	215	1	the	the	DET
ap-2224	215	2	interval	interval	NOUN
ap-2224	215	3	[	[	X
ap-2224	215	4	0,∞	0,∞	NOUN
ap-2224	215	5	)	)	PUNCT
ap-2224	215	6	is	be	AUX
ap-2224	215	7	the	the	DET
ap-2224	215	8	domain	domain	NOUN
ap-2224	215	9	of	of	ADP
ap-2224	215	10	attraction	attraction	NOUN
ap-2224	215	11	of	of	ADP
ap-2224	215	12	this	this	DET
ap-2224	215	13	fixed	fix	VERB
ap-2224	215	14	point	point	NOUN
ap-2224	215	15	.	.	PUNCT
ap-2224	216	1	for	for	ADP
ap-2224	216	2	fn(x	fn(x	NOUN
ap-2224	216	3	)	)	PUNCT
ap-2224	216	4	,	,	PUNCT
ap-2224	216	5	we	we	PRON
ap-2224	216	6	obtain	obtain	VERB
ap-2224	216	7	fn(x	fn(x	PUNCT
ap-2224	216	8	)	)	PUNCT
ap-2224	217	1	=	=	SYM
ap-2224	218	1	∫	∫	PROPN
ap-2224	218	2	∞	∞	PROPN
ap-2224	219	1	an	an	DET
ap-2224	219	2	e−ythn(t	e−ythn(t	PROPN
ap-2224	219	3	)	)	PUNCT
ap-2224	219	4	dt	dt	PROPN
ap-2224	219	5	,	,	PUNCT
ap-2224	219	6	where	where	SCONJ
ap-2224	219	7	an	an	DET
ap-2224	219	8	=	=	NOUN
ap-2224	219	9	an(a	an(a	NOUN
ap-2224	219	10	)	)	PUNCT
ap-2224	219	11	,	,	PUNCT
ap-2224	219	12	hn(t	hn(t	NUM
ap-2224	219	13	)	)	PUNCT
ap-2224	220	1	=	=	SYM
ap-2224	220	2	f	f	X
ap-2224	220	3	(	(	PUNCT
ap-2224	220	4	(	(	PUNCT
ap-2224	220	5	t+	t+	NOUN
ap-2224	220	6	ln	ln	ADJ
ap-2224	220	7	t)n	t)n	NOUN
ap-2224	220	8	)	)	PUNCT
ap-2224	221	1	n−1∏	n−1∏	PROPN
ap-2224	221	2	k=0	k=0	PROPN
ap-2224	221	3	1	1	NUM
ap-2224	221	4	+	+	CCONJ
ap-2224	221	5	(	(	PUNCT
ap-2224	221	6	t+	t+	NOUN
ap-2224	221	7	ln	ln	ADJ
ap-2224	221	8	t)k	t)k	X
ap-2224	221	9	(	(	PUNCT
ap-2224	221	10	t+	t+	NOUN
ap-2224	221	11	ln	ln	ADJ
ap-2224	221	12	t)k	t)k	ADJ
ap-2224	221	13	,	,	PUNCT
ap-2224	221	14	t	t	PROPN
ap-2224	221	15	≥	≥	X
ap-2224	221	16	an	an	PRON
ap-2224	221	17	,	,	PUNCT
ap-2224	221	18	n	n	X
ap-2224	221	19	>	>	X
ap-2224	221	20	0	0	NUM
ap-2224	221	21	,	,	PUNCT
ap-2224	221	22	and	and	CCONJ
ap-2224	221	23	an(a	an(a	NUM
ap-2224	221	24	)	)	PUNCT
ap-2224	221	25	and	and	CCONJ
ap-2224	221	26	(	(	PUNCT
ap-2224	221	27	t+ln	t+ln	NOUN
ap-2224	221	28	t)n	t)n	NOUN
ap-2224	221	29	are	be	AUX
ap-2224	221	30	the	the	DET
ap-2224	221	31	nth	nth	PROPN
ap-2224	221	32	iterate	iterate	NOUN
ap-2224	221	33	(	(	PUNCT
ap-2224	221	34	not	not	PART
ap-2224	221	35	power	power	NOUN
ap-2224	221	36	)	)	PUNCT
ap-2224	221	37	of	of	ADP
ap-2224	221	38	the	the	DET
ap-2224	221	39	function	function	NOUN
ap-2224	221	40	a(a	a(a	PROPN
ap-2224	221	41	)	)	PUNCT
ap-2224	221	42	and	and	CCONJ
ap-2224	221	43	t+ln	t+ln	NOUN
ap-2224	221	44	t	t	PROPN
ap-2224	221	45	,	,	PUNCT
ap-2224	221	46	respectively	respectively	ADV
ap-2224	221	47	,	,	PUNCT
ap-2224	221	48	a0(a	a0(a	PROPN
ap-2224	221	49	)	)	PUNCT
ap-2224	221	50	=	=	SYM
ap-2224	221	51	a	a	PRON
ap-2224	221	52	,	,	PUNCT
ap-2224	221	53	(	(	PUNCT
ap-2224	221	54	t+	t+	NOUN
ap-2224	221	55	ln	ln	ADJ
ap-2224	221	56	t)0	t)0	NOUN
ap-2224	221	57	=	=	PUNCT
ap-2224	221	58	t.	t.	NOUN
ap-2224	221	59	the	the	DET
ap-2224	221	60	procedure	procedure	NOUN
ap-2224	221	61	just	just	ADV
ap-2224	221	62	described	describe	VERB
ap-2224	221	63	can	can	AUX
ap-2224	221	64	be	be	AUX
ap-2224	221	65	reversed	reverse	VERB
ap-2224	221	66	:	:	PUNCT
ap-2224	221	67	theorem	theorem	VERB
ap-2224	221	68	4.2	4.2	NUM
ap-2224	221	69	.	.	PUNCT
ap-2224	222	1	let	let	VERB
ap-2224	222	2	h(y	h(y	NOUN
ap-2224	222	3	)	)	PUNCT
ap-2224	222	4	=	=	SYM
ap-2224	222	5	∫∞	∫∞	PROPN
ap-2224	222	6	b	b	PROPN
ap-2224	222	7	e−ytg(t	e−ytg(t	PROPN
ap-2224	222	8	)	)	PUNCT
ap-2224	222	9	dt	dt	PROPN
ap-2224	222	10	,	,	PUNCT
ap-2224	222	11	0	0	NUM
ap-2224	222	12	≤	≤	NUM
ap-2224	222	13	b	b	NOUN
ap-2224	222	14	<	<	X
ap-2224	222	15	∞	∞	PROPN
ap-2224	222	16	,	,	PUNCT
ap-2224	222	17	be	be	AUX
ap-2224	222	18	a	a	DET
ap-2224	222	19	unilateral	unilateral	ADJ
ap-2224	222	20	laplace	laplace	NOUN
ap-2224	222	21	transform	transform	NOUN
ap-2224	222	22	,	,	PUNCT
ap-2224	222	23	where	where	SCONJ
ap-2224	222	24	g(t	g(t	PROPN
ap-2224	222	25	)	)	PUNCT
ap-2224	222	26	is	be	AUX
ap-2224	222	27	a	a	DET
ap-2224	222	28	locally	locally	ADV
ap-2224	222	29	integrable	integrable	ADJ
ap-2224	222	30	function	function	NOUN
ap-2224	222	31	on	on	ADP
ap-2224	222	32	the	the	DET
ap-2224	222	33	interval	interval	NOUN
ap-2224	222	34	[	[	X
ap-2224	222	35	b,∞	b,∞	NOUN
ap-2224	222	36	)	)	PUNCT
ap-2224	222	37	and	and	CCONJ
ap-2224	222	38	of	of	ADP
ap-2224	222	39	exponential	exponential	ADJ
ap-2224	222	40	order	order	NOUN
ap-2224	222	41	α0	α0	ADJ
ap-2224	222	42	.	.	PUNCT
ap-2224	223	1	then	then	ADV
ap-2224	223	2	the	the	DET
ap-2224	223	3	function	function	NOUN
ap-2224	223	4	h1(y	h1(y	PROPN
ap-2224	223	5	)	)	PUNCT
ap-2224	223	6	=	=	SYM
ap-2224	224	1	∫	∫	PROPN
ap-2224	224	2	∞	∞	PROPN
ap-2224	224	3	b	b	PROPN
ap-2224	224	4	e−yuf(u	e−yuf(u	NUM
ap-2224	224	5	)	)	PUNCT
ap-2224	224	6	du	du	PROPN
ap-2224	224	7	=	=	SYM
ap-2224	224	8	∫	∫	PROPN
ap-2224	224	9	∞	∞	PROPN
ap-2224	224	10	b	b	PROPN
ap-2224	224	11	e−yug	e−yug	NOUN
ap-2224	224	12	(	(	PUNCT
ap-2224	224	13	w0(eu	w0(eu	PROPN
ap-2224	224	14	)	)	PUNCT
ap-2224	224	15	)	)	PUNCT
ap-2224	224	16	w0(eu	w0(eu	NOUN
ap-2224	224	17	)	)	PUNCT
ap-2224	224	18	1	1	NUM
ap-2224	225	1	+	+	NOUN
ap-2224	225	2	w0(eu	w0(eu	X
ap-2224	225	3	)	)	PUNCT
ap-2224	225	4	du	du	NOUN
ap-2224	225	5	,	,	PUNCT
ap-2224	225	6	(	(	PUNCT
ap-2224	225	7	4.3	4.3	NUM
ap-2224	225	8	)	)	PUNCT
ap-2224	225	9	where	where	SCONJ
ap-2224	225	10	b	b	X
ap-2224	225	11	=	=	SYM
ap-2224	225	12	b(b	b(b	PROPN
ap-2224	225	13	)	)	PUNCT
ap-2224	225	14	=	=	PUNCT
ap-2224	225	15	b+	b+	X
ap-2224	225	16	ln	ln	PROPN
ap-2224	225	17	b	b	NOUN
ap-2224	225	18	,	,	PUNCT
ap-2224	225	19	is	be	AUX
ap-2224	225	20	a	a	DET
ap-2224	225	21	liouville	liouville	NOUN
ap-2224	225	22	–	–	PUNCT
ap-2224	225	23	weyl	weyl	VERB
ap-2224	225	24	diagonal	diagonal	ADJ
ap-2224	225	25	fractional	fractional	ADJ
ap-2224	225	26	integral	integral	NOUN
ap-2224	225	27	of	of	ADP
ap-2224	225	28	h(y	h(y	NOUN
ap-2224	225	29	)	)	PUNCT
ap-2224	225	30	.	.	PUNCT
ap-2224	226	1	proof	proof	NOUN
ap-2224	226	2	.	.	PUNCT
ap-2224	227	1	the	the	DET
ap-2224	227	2	proof	proof	NOUN
ap-2224	227	3	is	be	AUX
ap-2224	227	4	a	a	DET
ap-2224	227	5	direct	direct	ADJ
ap-2224	227	6	consequence	consequence	NOUN
ap-2224	227	7	of	of	ADP
ap-2224	227	8	theorem	theorem	NOUN
ap-2224	227	9	2.2	2.2	NUM
ap-2224	227	10	.	.	PUNCT
ap-2224	228	1	this	this	DET
ap-2224	228	2	procedure	procedure	NOUN
ap-2224	228	3	can	can	AUX
ap-2224	228	4	also	also	ADV
ap-2224	228	5	be	be	AUX
ap-2224	228	6	repeated	repeat	VERB
ap-2224	228	7	.	.	PUNCT
ap-2224	229	1	the	the	DET
ap-2224	229	2	point	point	NOUN
ap-2224	229	3	b	b	NOUN
ap-2224	229	4	=	=	SYM
ap-2224	229	5	1	1	NUM
ap-2224	229	6	is	be	AUX
ap-2224	229	7	a	a	DET
ap-2224	229	8	fixed	fix	VERB
ap-2224	229	9	point	point	NOUN
ap-2224	229	10	of	of	ADP
ap-2224	229	11	the	the	DET
ap-2224	229	12	function	function	NOUN
ap-2224	229	13	b(b	b(b	PROPN
ap-2224	229	14	)	)	PUNCT
ap-2224	230	1	=	=	PUNCT
ap-2224	230	2	b+	b+	X
ap-2224	230	3	ln	ln	PROPN
ap-2224	230	4	b	b	NOUN
ap-2224	230	5	,	,	PUNCT
ap-2224	230	6	because	because	SCONJ
ap-2224	230	7	b(b	b(b	PROPN
ap-2224	230	8	)	)	PUNCT
ap-2224	230	9	is	be	AUX
ap-2224	230	10	a	a	DET
ap-2224	230	11	continuous	continuous	ADJ
ap-2224	230	12	function	function	NOUN
ap-2224	230	13	,	,	PUNCT
ap-2224	230	14	b(b	b(b	PROPN
ap-2224	230	15	)	)	PUNCT
ap-2224	231	1	<	<	X
ap-2224	231	2	b	b	PROPN
ap-2224	231	3	for	for	ADP
ap-2224	231	4	b	b	NOUN
ap-2224	231	5	<	<	X
ap-2224	231	6	1	1	NUM
ap-2224	231	7	,	,	PUNCT
ap-2224	231	8	b(b	b(b	PROPN
ap-2224	231	9	)	)	PUNCT
ap-2224	231	10	>	>	X
ap-2224	232	1	b	b	PROPN
ap-2224	232	2	for	for	ADP
ap-2224	232	3	b	b	PROPN
ap-2224	232	4	>	>	SYM
ap-2224	232	5	1	1	NUM
ap-2224	232	6	and	and	CCONJ
ap-2224	232	7	b(1	b(1	PROPN
ap-2224	232	8	)	)	PUNCT
ap-2224	232	9	=	=	NOUN
ap-2224	233	1	1	1	X
ap-2224	233	2	.	.	PUNCT
ap-2224	234	1	this	this	DET
ap-2224	234	2	fixed	fix	VERB
ap-2224	234	3	point	point	NOUN
ap-2224	234	4	is	be	AUX
ap-2224	234	5	repulsive	repulsive	ADJ
ap-2224	234	6	because	because	SCONJ
ap-2224	234	7	of	of	ADP
ap-2224	234	8	b′(1	b′(1	PROPN
ap-2224	234	9	)	)	PUNCT
ap-2224	234	10	=	=	SYM
ap-2224	234	11	2	2	NUM
ap-2224	234	12	>	>	SYM
ap-2224	234	13	1	1	NUM
ap-2224	234	14	,	,	PUNCT
ap-2224	234	15	so	so	ADV
ap-2224	234	16	limn→∞bn(b	limn→∞bn(b	PROPN
ap-2224	234	17	)	)	PUNCT
ap-2224	234	18	=	=	PUNCT
ap-2224	235	1	+	+	PUNCT
ap-2224	235	2	∞	∞	NUM
ap-2224	235	3	for	for	ADP
ap-2224	235	4	b	b	PROPN
ap-2224	235	5	>	>	SYM
ap-2224	235	6	1	1	NUM
ap-2224	235	7	,	,	PUNCT
ap-2224	235	8	limn→∞bn(b	limn→∞bn(b	PROPN
ap-2224	235	9	)	)	PUNCT
ap-2224	235	10	=	=	SYM
ap-2224	235	11	1	1	NUM
ap-2224	235	12	for	for	ADP
ap-2224	235	13	b	b	NOUN
ap-2224	235	14	=	=	SYM
ap-2224	235	15	1	1	NUM
ap-2224	235	16	and	and	CCONJ
ap-2224	235	17	for	for	ADP
ap-2224	235	18	b	b	PROPN
ap-2224	235	19	<	<	X
ap-2224	235	20	1	1	NUM
ap-2224	235	21	the	the	DET
ap-2224	235	22	process	process	NOUN
ap-2224	235	23	ended	end	VERB
ap-2224	235	24	at	at	ADP
ap-2224	235	25	n	n	PROPN
ap-2224	235	26	for	for	ADP
ap-2224	235	27	which	which	PRON
ap-2224	235	28	bn+1(b	bn+1(b	ADP
ap-2224	235	29	)	)	PUNCT
ap-2224	235	30	<	<	X
ap-2224	235	31	0	0	X
ap-2224	235	32	.	.	X
ap-2224	235	33	309	309	NUM
ap-2224	235	34	vladimír	vladimír	PROPN
ap-2224	235	35	vojta	vojta	PROPN
ap-2224	235	36	acta	acta	PROPN
ap-2224	235	37	polytechnica	polytechnica	PROPN
ap-2224	235	38	5	5	NUM
ap-2224	235	39	.	.	PUNCT
ap-2224	235	40	complex	complex	ADJ
ap-2224	235	41	domain	domain	NOUN
ap-2224	235	42	as	as	SCONJ
ap-2224	235	43	yet	yet	CCONJ
ap-2224	235	44	there	there	PRON
ap-2224	235	45	has	have	AUX
ap-2224	235	46	been	be	AUX
ap-2224	235	47	no	no	DET
ap-2224	235	48	need	need	NOUN
ap-2224	235	49	to	to	PART
ap-2224	235	50	reason	reason	VERB
ap-2224	235	51	about	about	ADP
ap-2224	235	52	complex	complex	ADJ
ap-2224	235	53	values	value	NOUN
ap-2224	235	54	of	of	ADP
ap-2224	235	55	variable	variable	ADJ
ap-2224	235	56	y	y	PROPN
ap-2224	235	57	in	in	ADP
ap-2224	235	58	the	the	DET
ap-2224	235	59	definition	definition	NOUN
ap-2224	235	60	of	of	ADP
ap-2224	235	61	the	the	DET
ap-2224	235	62	diagonal	diagonal	ADJ
ap-2224	235	63	integral	integral	ADJ
ap-2224	235	64	and	and	CCONJ
ap-2224	235	65	in	in	ADP
ap-2224	235	66	the	the	DET
ap-2224	235	67	anti	anti	ADJ
ap-2224	235	68	-	-	ADJ
ap-2224	235	69	diagonal	diagonal	ADJ
ap-2224	235	70	laplace	laplace	NOUN
ap-2224	235	71	–	–	PUNCT
ap-2224	235	72	mellin	mellin	NOUN
ap-2224	235	73	transform	transform	NOUN
ap-2224	235	74	in	in	ADP
ap-2224	235	75	(	(	PUNCT
ap-2224	235	76	2.1	2.1	NUM
ap-2224	235	77	)	)	PUNCT
ap-2224	235	78	,	,	PUNCT
ap-2224	235	79	because	because	SCONJ
ap-2224	235	80	this	this	DET
ap-2224	235	81	paper	paper	NOUN
ap-2224	235	82	(	(	PUNCT
ap-2224	235	83	with	with	ADP
ap-2224	235	84	minimum	minimum	ADJ
ap-2224	235	85	exceptions	exception	NOUN
ap-2224	235	86	—	—	PUNCT
ap-2224	235	87	the	the	DET
ap-2224	235	88	gamma	gamma	NOUN
ap-2224	235	89	function	function	NOUN
ap-2224	235	90	and	and	CCONJ
ap-2224	235	91	examples	example	NOUN
ap-2224	235	92	6.12	6.12	NUM
ap-2224	235	93	and	and	CCONJ
ap-2224	235	94	6.13	6.13	NUM
ap-2224	235	95	)	)	PUNCT
ap-2224	235	96	deals	deal	NOUN
ap-2224	235	97	with	with	ADP
ap-2224	235	98	fractional	fractional	ADJ
ap-2224	235	99	integrals	integral	NOUN
ap-2224	235	100	of	of	ADP
ap-2224	235	101	generally	generally	ADV
ap-2224	235	102	complex	complex	ADJ
ap-2224	235	103	order	order	NOUN
ap-2224	235	104	but	but	CCONJ
ap-2224	235	105	on	on	ADP
ap-2224	235	106	the	the	DET
ap-2224	235	107	real	real	ADJ
ap-2224	235	108	axis	axis	NOUN
ap-2224	235	109	.	.	PUNCT
ap-2224	236	1	now	now	ADV
ap-2224	236	2	we	we	PRON
ap-2224	236	3	intend	intend	VERB
ap-2224	236	4	to	to	PART
ap-2224	236	5	infer	infer	VERB
ap-2224	236	6	an	an	DET
ap-2224	236	7	analog	analog	NOUN
ap-2224	236	8	of	of	ADP
ap-2224	236	9	the	the	DET
ap-2224	236	10	standard	standard	ADJ
ap-2224	236	11	bromwich	bromwich	PROPN
ap-2224	236	12	inversion	inversion	NOUN
ap-2224	236	13	formula	formula	NOUN
ap-2224	236	14	of	of	ADP
ap-2224	236	15	the	the	DET
ap-2224	236	16	laplace	laplace	NOUN
ap-2224	236	17	transform	transform	NOUN
ap-2224	236	18	for	for	ADP
ap-2224	236	19	the	the	DET
ap-2224	236	20	anti	anti	ADJ
ap-2224	236	21	-	-	ADJ
ap-2224	236	22	diagonal	diagonal	ADJ
ap-2224	236	23	laplace	laplace	NOUN
ap-2224	236	24	–	–	PUNCT
ap-2224	236	25	mellin	mellin	NOUN
ap-2224	236	26	transform	transform	NOUN
ap-2224	236	27	,	,	PUNCT
ap-2224	236	28	and	and	CCONJ
ap-2224	236	29	make	make	VERB
ap-2224	236	30	a	a	DET
ap-2224	236	31	mention	mention	NOUN
ap-2224	236	32	of	of	ADP
ap-2224	236	33	the	the	DET
ap-2224	236	34	entire	entire	ADJ
ap-2224	236	35	functions	function	NOUN
ap-2224	236	36	.	.	PUNCT
ap-2224	237	1	theorem	theorem	VERB
ap-2224	237	2	5.1	5.1	NUM
ap-2224	237	3	.	.	PUNCT
ap-2224	238	1	if	if	SCONJ
ap-2224	238	2	the	the	DET
ap-2224	238	3	integral	integral	ADJ
ap-2224	238	4	in	in	ADP
ap-2224	238	5	(	(	PUNCT
ap-2224	238	6	3.2	3.2	NUM
ap-2224	238	7	)	)	PUNCT
ap-2224	238	8	converges	converge	VERB
ap-2224	238	9	absolutely	absolutely	ADV
ap-2224	238	10	for	for	ADP
ap-2224	238	11	function	function	NOUN
ap-2224	238	12	g(u	g(u	PROPN
ap-2224	238	13	)	)	PUNCT
ap-2224	238	14	in	in	ADP
ap-2224	238	15	the	the	DET
ap-2224	238	16	region	region	NOUN
ap-2224	238	17	of	of	ADP
ap-2224	238	18	convergence	convergence	NOUN
ap-2224	238	19	−∞	−∞	ADP
ap-2224	238	20	≤	≤	PROPN
ap-2224	238	21	β0	β0	NOUN
ap-2224	238	22	<	<	X
ap-2224	238	23	<	<	X
ap-2224	238	24	y	y	X
ap-2224	238	25	<	<	X
ap-2224	238	26	β1	β1	PROPN
ap-2224	238	27	≤	≤	NOUN
ap-2224	238	28	+	+	PROPN
ap-2224	238	29	∞	∞	PROPN
ap-2224	238	30	,	,	PUNCT
ap-2224	238	31	giving	give	VERB
ap-2224	238	32	the	the	DET
ap-2224	238	33	holomorphic	holomorphic	ADJ
ap-2224	238	34	function	function	NOUN
ap-2224	238	35	g(y	g(y	NOUN
ap-2224	238	36	)	)	PUNCT
ap-2224	238	37	there	there	ADV
ap-2224	238	38	,	,	PUNCT
ap-2224	238	39	the	the	DET
ap-2224	238	40	following	follow	VERB
ap-2224	238	41	holds	hold	NOUN
ap-2224	238	42	:	:	PUNCT
ap-2224	238	43	f(t	f(t	NOUN
ap-2224	238	44	)	)	PUNCT
ap-2224	238	45	=	=	SYM
ap-2224	239	1	1	1	NUM
ap-2224	239	2	+	+	NUM
ap-2224	239	3	t	t	PROPN
ap-2224	239	4	2iπt	2iπt	NUM
ap-2224	239	5	∫	∫	NOUN
ap-2224	239	6	c+i∞	c+i∞	PROPN
ap-2224	239	7	c−i∞	c−i∞	PROPN
ap-2224	239	8	etytyg(y	etytyg(y	X
ap-2224	239	9	)	)	PUNCT
ap-2224	239	10	dy	dy	PROPN
ap-2224	239	11	,	,	PUNCT
ap-2224	239	12	t	t	X
ap-2224	239	13	>	>	X
ap-2224	239	14	0	0	PROPN
ap-2224	239	15	,	,	PUNCT
ap-2224	239	16	f(0	f(0	NOUN
ap-2224	239	17	)	)	PUNCT
ap-2224	239	18	=	=	PROPN
ap-2224	240	1	lim	lim	PROPN
ap-2224	240	2	t→0	t→0	PROPN
ap-2224	240	3	+	+	CCONJ
ap-2224	240	4	f(t	f(t	NOUN
ap-2224	240	5	)	)	PUNCT
ap-2224	240	6	,	,	PUNCT
ap-2224	240	7	(	(	PUNCT
ap-2224	240	8	5.1	5.1	NUM
ap-2224	240	9	)	)	PUNCT
ap-2224	240	10	where	where	SCONJ
ap-2224	240	11	β0	β0	NOUN
ap-2224	240	12	<	<	X
ap-2224	240	13	c	c	X
ap-2224	240	14	<	<	X
ap-2224	240	15	β1	β1	PROPN
ap-2224	240	16	and	and	CCONJ
ap-2224	240	17	the	the	DET
ap-2224	240	18	integral	integral	ADJ
ap-2224	240	19	in	in	ADP
ap-2224	240	20	(	(	PUNCT
ap-2224	240	21	5.1	5.1	NUM
ap-2224	240	22	)	)	PUNCT
ap-2224	240	23	is	be	AUX
ap-2224	240	24	taken	take	VERB
ap-2224	240	25	as	as	ADP
ap-2224	240	26	the	the	DET
ap-2224	240	27	cauchy	cauchy	ADJ
ap-2224	240	28	principal	principal	NOUN
ap-2224	240	29	value	value	NOUN
ap-2224	240	30	(	(	PUNCT
ap-2224	240	31	see	see	VERB
ap-2224	240	32	[	[	X
ap-2224	240	33	3	3	NUM
ap-2224	240	34	,	,	PUNCT
ap-2224	240	35	§	§	PROPN
ap-2224	240	36	5.8	5.8	NUM
ap-2224	240	37	]	]	PUNCT
ap-2224	240	38	)	)	PUNCT
ap-2224	240	39	.	.	PUNCT
ap-2224	241	1	moreover	moreover	ADV
ap-2224	241	2	,	,	PUNCT
ap-2224	241	3	(	(	PUNCT
ap-2224	241	4	5.1	5.1	NUM
ap-2224	241	5	)	)	PUNCT
ap-2224	241	6	is	be	AUX
ap-2224	241	7	also	also	ADV
ap-2224	241	8	true	true	ADJ
ap-2224	241	9	if	if	SCONJ
ap-2224	241	10	“	"	PUNCT
ap-2224	241	11	equation	equation	NOUN
ap-2224	241	12	(	(	PUNCT
ap-2224	241	13	3.2	3.2	NUM
ap-2224	241	14	)	)	PUNCT
ap-2224	241	15	”	"	PUNCT
ap-2224	241	16	in	in	ADP
ap-2224	241	17	the	the	DET
ap-2224	241	18	hypothesis	hypothesis	NOUN
ap-2224	241	19	is	be	AUX
ap-2224	241	20	changed	change	VERB
ap-2224	241	21	to	to	ADP
ap-2224	241	22	“	"	PUNCT
ap-2224	241	23	equation	equation	NOUN
ap-2224	241	24	(	(	PUNCT
ap-2224	241	25	3.4	3.4	NUM
ap-2224	241	26	)	)	PUNCT
ap-2224	241	27	”	"	PUNCT
ap-2224	241	28	.	.	PUNCT
ap-2224	242	1	proof	proof	NOUN
ap-2224	242	2	.	.	PUNCT
ap-2224	243	1	we	we	PRON
ap-2224	243	2	start	start	VERB
ap-2224	243	3	with	with	ADP
ap-2224	243	4	the	the	DET
ap-2224	243	5	standard	standard	ADJ
ap-2224	243	6	bromwich	bromwich	NOUN
ap-2224	243	7	inversion	inversion	NOUN
ap-2224	243	8	for	for	ADP
ap-2224	243	9	the	the	DET
ap-2224	243	10	bilateral	bilateral	ADJ
ap-2224	243	11	laplace	laplace	NOUN
ap-2224	243	12	transform	transform	NOUN
ap-2224	243	13	in	in	ADP
ap-2224	243	14	(	(	PUNCT
ap-2224	243	15	3.2	3.2	NUM
ap-2224	243	16	)	)	PUNCT
ap-2224	243	17	and	and	CCONJ
ap-2224	243	18	perform	perform	VERB
ap-2224	243	19	the	the	DET
ap-2224	243	20	substitution	substitution	NOUN
ap-2224	243	21	u	u	NOUN
ap-2224	243	22	=	=	PUNCT
ap-2224	243	23	t+	t+	PUNCT
ap-2224	243	24	ln	ln	ADJ
ap-2224	243	25	t.	t.	NOUN
ap-2224	243	26	we	we	PRON
ap-2224	243	27	obtain	obtain	VERB
ap-2224	243	28	g(t+	g(t+	PROPN
ap-2224	243	29	ln	ln	PROPN
ap-2224	243	30	t	t	PROPN
ap-2224	243	31	)	)	PUNCT
ap-2224	243	32	=	=	SYM
ap-2224	244	1	1	1	NUM
ap-2224	244	2	2iπ	2iπ	NOUN
ap-2224	244	3	∫	∫	PROPN
ap-2224	244	4	c+i∞	c+i∞	PROPN
ap-2224	244	5	c−i∞	c−i∞	PROPN
ap-2224	244	6	etytyg(y	etytyg(y	X
ap-2224	244	7	)	)	PUNCT
ap-2224	244	8	dy	dy	PROPN
ap-2224	244	9	,	,	PUNCT
ap-2224	244	10	t	t	X
ap-2224	244	11	>	>	X
ap-2224	244	12	0	0	PUNCT
ap-2224	244	13	(	(	PUNCT
ap-2224	244	14	5.2	5.2	NUM
ap-2224	244	15	)	)	PUNCT
ap-2224	244	16	and	and	CCONJ
ap-2224	244	17	according	accord	VERB
ap-2224	244	18	to	to	ADP
ap-2224	244	19	(	(	PUNCT
ap-2224	244	20	3.3	3.3	NUM
ap-2224	244	21	)	)	PUNCT
ap-2224	244	22	we	we	PRON
ap-2224	244	23	obtain	obtain	VERB
ap-2224	244	24	(	(	PUNCT
ap-2224	244	25	5.1	5.1	NUM
ap-2224	244	26	)	)	PUNCT
ap-2224	244	27	.	.	PUNCT
ap-2224	245	1	if	if	SCONJ
ap-2224	245	2	we	we	PRON
ap-2224	245	3	apply	apply	VERB
ap-2224	245	4	the	the	DET
ap-2224	245	5	bromwich	bromwich	NOUN
ap-2224	245	6	inversion	inversion	NOUN
ap-2224	245	7	to	to	ADP
ap-2224	245	8	the	the	DET
ap-2224	245	9	mellin	mellin	PROPN
ap-2224	245	10	transform	transform	NOUN
ap-2224	245	11	in	in	ADP
ap-2224	245	12	(	(	PUNCT
ap-2224	245	13	3.4	3.4	NUM
ap-2224	245	14	)	)	PUNCT
ap-2224	245	15	and	and	CCONJ
ap-2224	245	16	perform	perform	VERB
ap-2224	245	17	the	the	DET
ap-2224	245	18	substitution	substitution	NOUN
ap-2224	245	19	u	u	NOUN
ap-2224	245	20	=	=	NOUN
ap-2224	245	21	tet	tet	NOUN
ap-2224	245	22	we	we	PRON
ap-2224	245	23	obtain	obtain	VERB
ap-2224	245	24	g(tet	g(tet	NOUN
ap-2224	245	25	)	)	PUNCT
ap-2224	245	26	=	=	PUNCT
ap-2224	245	27	1	1	NUM
ap-2224	245	28	2iπ	2iπ	NOUN
ap-2224	245	29	∫	∫	PROPN
ap-2224	245	30	c+i∞	c+i∞	PROPN
ap-2224	245	31	c−i∞	c−i∞	PROPN
ap-2224	245	32	etytyg(y	etytyg(y	X
ap-2224	245	33	)	)	PUNCT
ap-2224	245	34	dy	dy	PROPN
ap-2224	245	35	,	,	PUNCT
ap-2224	245	36	t	t	X
ap-2224	245	37	>	>	X
ap-2224	245	38	0	0	PUNCT
ap-2224	246	1	(	(	PUNCT
ap-2224	246	2	5.3	5.3	NUM
ap-2224	246	3	)	)	PUNCT
ap-2224	246	4	and	and	CCONJ
ap-2224	246	5	according	accord	VERB
ap-2224	246	6	to	to	ADP
ap-2224	246	7	(	(	PUNCT
ap-2224	246	8	3.5	3.5	NUM
ap-2224	246	9	)	)	PUNCT
ap-2224	246	10	we	we	PRON
ap-2224	246	11	also	also	ADV
ap-2224	246	12	obtain	obtain	VERB
ap-2224	246	13	(	(	PUNCT
ap-2224	246	14	5.1	5.1	NUM
ap-2224	246	15	)	)	PUNCT
ap-2224	246	16	.	.	PUNCT
ap-2224	247	1	if	if	SCONJ
ap-2224	247	2	g	g	PROPN
ap-2224	247	3	(	(	PUNCT
ap-2224	247	4	·	·	PUNCT
ap-2224	247	5	)	)	PUNCT
ap-2224	247	6	is	be	AUX
ap-2224	247	7	the	the	DET
ap-2224	247	8	mellin	mellin	PROPN
ap-2224	247	9	transform	transform	NOUN
ap-2224	247	10	of	of	ADP
ap-2224	247	11	function	function	NOUN
ap-2224	247	12	g	g	PROPN
ap-2224	247	13	(	(	PUNCT
ap-2224	247	14	·	·	PUNCT
ap-2224	247	15	)	)	PUNCT
ap-2224	247	16	in	in	ADP
ap-2224	247	17	standard	standard	ADJ
ap-2224	247	18	notation	notation	NOUN
ap-2224	247	19	,	,	PUNCT
ap-2224	247	20	formula	formula	NOUN
ap-2224	247	21	(	(	PUNCT
ap-2224	247	22	5.3	5.3	NUM
ap-2224	247	23	)	)	PUNCT
ap-2224	247	24	obtains	obtain	VERB
ap-2224	247	25	the	the	DET
ap-2224	247	26	form	form	NOUN
ap-2224	247	27	g(tet	g(tet	NOUN
ap-2224	247	28	)	)	PUNCT
ap-2224	247	29	=	=	PUNCT
ap-2224	248	1	1	1	NUM
ap-2224	248	2	2iπ	2iπ	NOUN
ap-2224	248	3	∫	∫	PROPN
ap-2224	248	4	c+i∞	c+i∞	PROPN
ap-2224	248	5	c−i∞	c−i∞	PROPN
ap-2224	248	6	e−tyt−yg(y	e−tyt−yg(y	X
ap-2224	248	7	)	)	PUNCT
ap-2224	248	8	dy	dy	PROPN
ap-2224	248	9	,	,	PUNCT
ap-2224	248	10	t	t	X
ap-2224	248	11	>	>	X
ap-2224	248	12	0	0	PROPN
ap-2224	248	13	.	.	PUNCT
ap-2224	249	1	(	(	PUNCT
ap-2224	249	2	5.4	5.4	NUM
ap-2224	249	3	)	)	PUNCT
ap-2224	249	4	corollary	corollary	NOUN
ap-2224	249	5	5.2	5.2	NUM
ap-2224	249	6	.	.	PUNCT
ap-2224	250	1	let	let	VERB
ap-2224	250	2	function	function	PROPN
ap-2224	250	3	g(t	g(t	PROPN
ap-2224	250	4	)	)	PUNCT
ap-2224	251	1	have	have	AUX
ap-2224	251	2	the	the	DET
ap-2224	251	3	(	(	PUNCT
ap-2224	251	4	generally	generally	ADV
ap-2224	251	5	bilateral	bilateral	ADJ
ap-2224	251	6	)	)	PUNCT
ap-2224	251	7	laplace	laplace	NOUN
ap-2224	251	8	transform	transform	VERB
ap-2224	251	9	g(x	g(x	NOUN
ap-2224	251	10	)	)	PUNCT
ap-2224	251	11	,	,	PUNCT
ap-2224	251	12	then∫	then∫	NOUN
ap-2224	251	13	∞	∞	NOUN
ap-2224	251	14	0	0	NUM
ap-2224	252	1	e−xtg(t+	e−xtg(t+	PROPN
ap-2224	252	2	ln	ln	PROPN
ap-2224	252	3	t	t	PROPN
ap-2224	252	4	)	)	PUNCT
ap-2224	252	5	dt	dt	NOUN
ap-2224	253	1	=	=	NOUN
ap-2224	254	1	1	1	NUM
ap-2224	254	2	2iπ	2iπ	NOUN
ap-2224	254	3	∫	∫	PROPN
ap-2224	254	4	c+i∞	c+i∞	PROPN
ap-2224	254	5	c−i∞	c−i∞	PROPN
ap-2224	254	6	(	(	PUNCT
ap-2224	254	7	x−	x−	PROPN
ap-2224	254	8	y)−y−1γ(1	y)−y−1γ(1	PROPN
ap-2224	254	9	+	+	CCONJ
ap-2224	254	10	y)g(y	y)g(y	NOUN
ap-2224	254	11	)	)	PUNCT
ap-2224	254	12	dy	dy	NOUN
ap-2224	254	13	,	,	PUNCT
ap-2224	254	14	<	<	X
ap-2224	254	15	x	x	X
ap-2224	254	16	>	>	X
ap-2224	254	17	c	c	X
ap-2224	254	18	>	>	X
ap-2224	254	19	−1	−1	NOUN
ap-2224	254	20	,	,	PUNCT
ap-2224	254	21	<	<	X
ap-2224	254	22	x	x	X
ap-2224	254	23	≥	≥	PROPN
ap-2224	254	24	α1	α1	PROPN
ap-2224	254	25	>	>	X
ap-2224	254	26	α0	α0	PROPN
ap-2224	254	27	,	,	PUNCT
ap-2224	254	28	(	(	PUNCT
ap-2224	254	29	5.5	5.5	NUM
ap-2224	254	30	)	)	PUNCT
ap-2224	254	31	where	where	SCONJ
ap-2224	254	32	x	x	PRON
ap-2224	254	33	lies	lie	VERB
ap-2224	254	34	in	in	ADP
ap-2224	254	35	the	the	DET
ap-2224	254	36	interior	interior	NOUN
ap-2224	254	37	of	of	ADP
ap-2224	254	38	the	the	DET
ap-2224	254	39	region	region	NOUN
ap-2224	254	40	of	of	ADP
ap-2224	254	41	holomorphy	holomorphy	NOUN
ap-2224	254	42	of	of	ADP
ap-2224	254	43	the	the	DET
ap-2224	254	44	laplace	laplace	NOUN
ap-2224	254	45	integral	integral	ADJ
ap-2224	254	46	on	on	ADP
ap-2224	254	47	the	the	DET
ap-2224	254	48	left	left	ADJ
ap-2224	254	49	side	side	NOUN
ap-2224	254	50	of	of	ADP
ap-2224	254	51	(	(	PUNCT
ap-2224	254	52	5.5	5.5	NUM
ap-2224	254	53	)	)	PUNCT
ap-2224	254	54	.	.	PUNCT
ap-2224	255	1	proof	proof	NOUN
ap-2224	255	2	.	.	PUNCT
ap-2224	256	1	application	application	NOUN
ap-2224	256	2	of	of	ADP
ap-2224	256	3	the	the	DET
ap-2224	256	4	laplace	laplace	NOUN
ap-2224	256	5	transform	transform	NOUN
ap-2224	256	6	to	to	ADP
ap-2224	256	7	both	both	DET
ap-2224	256	8	sides	side	NOUN
ap-2224	256	9	of	of	ADP
ap-2224	256	10	(	(	PUNCT
ap-2224	256	11	5.2	5.2	NUM
ap-2224	256	12	)	)	PUNCT
ap-2224	256	13	with	with	ADP
ap-2224	256	14	respect	respect	NOUN
ap-2224	256	15	to	to	ADP
ap-2224	256	16	the	the	DET
ap-2224	256	17	fubini	fubini	ADJ
ap-2224	256	18	theorem	theorem	NOUN
ap-2224	256	19	gives	give	VERB
ap-2224	256	20	(	(	PUNCT
ap-2224	256	21	5.5	5.5	NUM
ap-2224	256	22	)	)	PUNCT
ap-2224	256	23	.	.	PUNCT
ap-2224	257	1	the	the	DET
ap-2224	257	2	formula	formula	NOUN
ap-2224	257	3	for	for	ADP
ap-2224	257	4	solving	solve	VERB
ap-2224	257	5	the	the	DET
ap-2224	257	6	integral	integral	ADJ
ap-2224	257	7	equation	equation	NOUN
ap-2224	257	8	(	(	PUNCT
ap-2224	257	9	3.1	3.1	NUM
ap-2224	257	10	)	)	PUNCT
ap-2224	257	11	in	in	ADP
ap-2224	257	12	the	the	DET
ap-2224	257	13	case	case	NOUN
ap-2224	257	14	that	that	PRON
ap-2224	257	15	function	function	VERB
ap-2224	257	16	g(y	g(y	PROPN
ap-2224	257	17	)	)	PUNCT
ap-2224	257	18	is	be	AUX
ap-2224	257	19	a	a	DET
ap-2224	257	20	laplace	laplace	NOUN
ap-2224	257	21	or	or	CCONJ
ap-2224	257	22	mellin	mellin	ADJ
ap-2224	257	23	transform	transform	NOUN
ap-2224	257	24	of	of	ADP
ap-2224	257	25	the	the	DET
ap-2224	257	26	pertinent	pertinent	NOUN
ap-2224	257	27	determining	determine	VERB
ap-2224	257	28	functions	function	NOUN
ap-2224	257	29	g(t	g(t	PROPN
ap-2224	257	30	)	)	PUNCT
ap-2224	257	31	is	be	AUX
ap-2224	257	32	given	give	VERB
ap-2224	257	33	by	by	ADP
ap-2224	257	34	the	the	DET
ap-2224	257	35	laplace	laplace	NOUN
ap-2224	257	36	transform	transform	NOUN
ap-2224	257	37	of	of	ADP
ap-2224	257	38	(	(	PUNCT
ap-2224	257	39	5.1	5.1	NUM
ap-2224	257	40	):	):	PUNCT
ap-2224	257	41	theorem	theorem	VERB
ap-2224	257	42	5.3	5.3	NUM
ap-2224	257	43	.	.	PUNCT
ap-2224	258	1	let	let	VERB
ap-2224	258	2	function	function	VERB
ap-2224	258	3	g(y	g(y	NOUN
ap-2224	258	4	)	)	PUNCT
ap-2224	258	5	on	on	ADP
ap-2224	258	6	the	the	DET
ap-2224	258	7	right	right	ADJ
ap-2224	258	8	hand	hand	NOUN
ap-2224	258	9	side	side	NOUN
ap-2224	258	10	of	of	ADP
ap-2224	258	11	(	(	PUNCT
ap-2224	258	12	3.1	3.1	NUM
ap-2224	258	13	)	)	PUNCT
ap-2224	258	14	be	be	AUX
ap-2224	258	15	a	a	DET
ap-2224	258	16	laplace	laplace	NOUN
ap-2224	258	17	or	or	CCONJ
ap-2224	258	18	mellin	mellin	NOUN
ap-2224	258	19	transform	transform	NOUN
ap-2224	258	20	.	.	PUNCT
ap-2224	259	1	then	then	ADV
ap-2224	259	2	solution	solution	NOUN
ap-2224	259	3	f	f	PROPN
ap-2224	259	4	(	(	PUNCT
ap-2224	259	5	x	x	NOUN
ap-2224	259	6	)	)	PUNCT
ap-2224	259	7	of	of	ADP
ap-2224	259	8	integral	integral	ADJ
ap-2224	259	9	equation	equation	NOUN
ap-2224	259	10	(	(	PUNCT
ap-2224	259	11	3.1	3.1	NUM
ap-2224	259	12	)	)	PUNCT
ap-2224	259	13	is	be	AUX
ap-2224	259	14	f	f	PROPN
ap-2224	259	15	(	(	PUNCT
ap-2224	259	16	x	x	X
ap-2224	259	17	)	)	PUNCT
ap-2224	259	18	=	=	SYM
ap-2224	260	1	∫	∫	PROPN
ap-2224	260	2	∞	∞	NUM
ap-2224	260	3	0	0	NUM
ap-2224	261	1	e−xtf(t	e−xtf(t	NUM
ap-2224	261	2	)	)	PUNCT
ap-2224	262	1	dt	dt	NOUN
ap-2224	263	1	=	=	NOUN
ap-2224	264	1	1	1	NUM
ap-2224	264	2	2iπ	2iπ	NOUN
ap-2224	264	3	∫	∫	PROPN
ap-2224	264	4	c+i∞	c+i∞	ADJ
ap-2224	264	5	c−i∞	c−i∞	PROPN
ap-2224	264	6	g(y	g(y	PROPN
ap-2224	264	7	)	)	PUNCT
ap-2224	264	8	∫	∫	PROPN
ap-2224	264	9	∞	∞	PROPN
ap-2224	264	10	0	0	NUM
ap-2224	264	11	(	(	PUNCT
ap-2224	264	12	1	1	NUM
ap-2224	264	13	+	+	CCONJ
ap-2224	264	14	teytty)e−xt	teytty)e−xt	PROPN
ap-2224	264	15	t	t	PROPN
ap-2224	264	16	dtdy	dtdy	NOUN
ap-2224	264	17	=	=	PUNCT
ap-2224	264	18	x	x	SYM
ap-2224	264	19	2iπ	2iπ	ADJ
ap-2224	264	20	∫	∫	PROPN
ap-2224	264	21	c+i∞	c+i∞	PROPN
ap-2224	264	22	c−i∞	c−i∞	PROPN
ap-2224	264	23	(	(	PUNCT
ap-2224	264	24	x−	x−	PROPN
ap-2224	264	25	y)−y−1γ(y)g(y	y)−y−1γ(y)g(y	PROPN
ap-2224	264	26	)	)	PUNCT
ap-2224	264	27	dy	dy	PROPN
ap-2224	264	28	,	,	PUNCT
ap-2224	264	29	<	<	X
ap-2224	264	30	x	x	X
ap-2224	264	31	>	>	X
ap-2224	264	32	c	c	X
ap-2224	264	33	,	,	PUNCT
ap-2224	264	34	<	<	X
ap-2224	264	35	c	c	X
ap-2224	264	36	≥	≥	PROPN
ap-2224	264	37	α1	α1	PROPN
ap-2224	264	38	>	>	X
ap-2224	264	39	α0	α0	PROPN
ap-2224	264	40	,	,	PUNCT
ap-2224	264	41	(	(	PUNCT
ap-2224	264	42	5.6	5.6	NUM
ap-2224	264	43	)	)	PUNCT
ap-2224	264	44	where	where	SCONJ
ap-2224	264	45	the	the	DET
ap-2224	264	46	real	real	ADJ
ap-2224	264	47	constant	constant	ADJ
ap-2224	264	48	c	c	NOUN
ap-2224	264	49	determines	determine	VERB
ap-2224	264	50	the	the	DET
ap-2224	264	51	bromwich	bromwich	NOUN
ap-2224	264	52	contour	contour	NOUN
ap-2224	264	53	inside	inside	ADP
ap-2224	264	54	the	the	DET
ap-2224	264	55	region	region	NOUN
ap-2224	264	56	of	of	ADP
ap-2224	264	57	holomorphy	holomorphy	NOUN
ap-2224	264	58	of	of	ADP
ap-2224	264	59	function	function	NOUN
ap-2224	264	60	g(y	g(y	PROPN
ap-2224	264	61	)	)	PUNCT
ap-2224	264	62	,	,	PUNCT
ap-2224	264	63	providing	provide	VERB
ap-2224	264	64	f(t	f(t	NOUN
ap-2224	264	65	)	)	PUNCT
ap-2224	264	66	is	be	AUX
ap-2224	264	67	of	of	ADP
ap-2224	264	68	exponential	exponential	ADJ
ap-2224	264	69	order	order	NOUN
ap-2224	264	70	α0	α0	ADJ
ap-2224	264	71	,	,	PUNCT
ap-2224	264	72	i.e.	i.e.	X
ap-2224	264	73	,	,	PUNCT
ap-2224	264	74	f(t	f(t	PROPN
ap-2224	264	75	)	)	PUNCT
ap-2224	264	76	=	=	SYM
ap-2224	264	77	o(expα0	o(expα0	PROPN
ap-2224	264	78	t	t	PROPN
ap-2224	264	79	)	)	PUNCT
ap-2224	264	80	as	as	ADP
ap-2224	264	81	t→	t→	DET
ap-2224	264	82	+	+	ADJ
ap-2224	264	83	∞.	∞.	PROPN
ap-2224	264	84	proof	proof	NOUN
ap-2224	264	85	.	.	PUNCT
ap-2224	265	1	we	we	PRON
ap-2224	265	2	perform	perform	VERB
ap-2224	265	3	the	the	DET
ap-2224	265	4	laplace	laplace	NOUN
ap-2224	265	5	transform	transform	NOUN
ap-2224	265	6	of	of	ADP
ap-2224	265	7	(	(	PUNCT
ap-2224	265	8	5.1	5.1	NUM
ap-2224	265	9	)	)	PUNCT
ap-2224	265	10	and	and	CCONJ
ap-2224	265	11	change	change	VERB
ap-2224	265	12	the	the	DET
ap-2224	265	13	order	order	NOUN
ap-2224	265	14	of	of	ADP
ap-2224	265	15	the	the	DET
ap-2224	265	16	integration	integration	NOUN
ap-2224	265	17	according	accord	VERB
ap-2224	265	18	to	to	ADP
ap-2224	265	19	the	the	DET
ap-2224	265	20	fubini	fubini	NOUN
ap-2224	265	21	theorem	theorem	NOUN
ap-2224	265	22	.	.	PROPN
ap-2224	265	23	310	310	NUM
ap-2224	265	24	vol	vol	NOUN
ap-2224	265	25	.	.	PUNCT
ap-2224	266	1	54	54	NUM
ap-2224	266	2	no	no	NOUN
ap-2224	266	3	.	.	PUNCT
ap-2224	267	1	4/2014	4/2014	NUM
ap-2224	267	2	fractional	fractional	ADJ
ap-2224	267	3	calculus	calculus	NOUN
ap-2224	267	4	and	and	CCONJ
ap-2224	267	5	lambert	lambert	PROPN
ap-2224	267	6	function	function	NOUN
ap-2224	267	7	i	i	PRON
ap-2224	267	8	the	the	DET
ap-2224	267	9	importance	importance	NOUN
ap-2224	267	10	of	of	ADP
ap-2224	267	11	theorem	theorem	ADJ
ap-2224	267	12	5.3	5.3	NUM
ap-2224	267	13	in	in	ADP
ap-2224	267	14	comparison	comparison	NOUN
ap-2224	267	15	with	with	ADP
ap-2224	267	16	theorem	theorem	ADJ
ap-2224	267	17	3.1	3.1	NUM
ap-2224	267	18	is	be	AUX
ap-2224	267	19	embodied	embody	VERB
ap-2224	267	20	in	in	ADP
ap-2224	267	21	the	the	DET
ap-2224	267	22	fact	fact	NOUN
ap-2224	267	23	that	that	SCONJ
ap-2224	267	24	there	there	PRON
ap-2224	267	25	is	be	VERB
ap-2224	267	26	no	no	DET
ap-2224	267	27	need	need	NOUN
ap-2224	267	28	to	to	PART
ap-2224	267	29	know	know	VERB
ap-2224	267	30	the	the	DET
ap-2224	267	31	laplace	laplace	NOUN
ap-2224	267	32	inverse	inverse	NOUN
ap-2224	267	33	of	of	ADP
ap-2224	267	34	function	function	NOUN
ap-2224	267	35	g(y	g(y	PROPN
ap-2224	267	36	)	)	PUNCT
ap-2224	267	37	and	and	CCONJ
ap-2224	267	38	that	that	DET
ap-2224	267	39	solution	solution	NOUN
ap-2224	267	40	f	f	X
ap-2224	267	41	(	(	PUNCT
ap-2224	267	42	x	x	X
ap-2224	267	43	)	)	PUNCT
ap-2224	267	44	is	be	AUX
ap-2224	267	45	obtained	obtain	VERB
ap-2224	267	46	directly	directly	ADV
ap-2224	267	47	.	.	PUNCT
ap-2224	268	1	moreover	moreover	ADV
ap-2224	268	2	numerical	numerical	ADJ
ap-2224	268	3	experiments	experiment	NOUN
ap-2224	268	4	indicate	indicate	VERB
ap-2224	268	5	that	that	SCONJ
ap-2224	268	6	(	(	PUNCT
ap-2224	268	7	5.6	5.6	NUM
ap-2224	268	8	)	)	PUNCT
ap-2224	268	9	also	also	ADV
ap-2224	268	10	holds	hold	VERB
ap-2224	268	11	for	for	ADP
ap-2224	268	12	functions	function	NOUN
ap-2224	268	13	g(y	g(y	NOUN
ap-2224	268	14	)	)	PUNCT
ap-2224	268	15	that	that	PRON
ap-2224	268	16	are	be	AUX
ap-2224	268	17	either	either	CCONJ
ap-2224	268	18	laplace	laplace	NOUN
ap-2224	268	19	or	or	CCONJ
ap-2224	268	20	mellin	mellin	PROPN
ap-2224	268	21	transforms	transform	VERB
ap-2224	268	22	of	of	ADP
ap-2224	268	23	generalized	generalized	ADJ
ap-2224	268	24	functions	function	NOUN
ap-2224	268	25	(	(	PUNCT
ap-2224	268	26	const	const	PROPN
ap-2224	268	27	.	.	PROPN
ap-2224	268	28	,	,	PUNCT
ap-2224	268	29	yn	yn	PROPN
ap-2224	268	30	,	,	PUNCT
ap-2224	268	31	e−ay	e−ay	PROPN
ap-2224	268	32	,	,	PUNCT
ap-2224	268	33	ζ(1−	ζ(1−	PROPN
ap-2224	268	34	y	y	PROPN
ap-2224	268	35	)	)	PUNCT
ap-2224	268	36	,	,	PUNCT
ap-2224	268	37	yn	yn	PROPN
ap-2224	268	38	e−ay	e−ay	PROPN
ap-2224	268	39	,	,	PUNCT
ap-2224	268	40	tanh	tanh	PROPN
ap-2224	268	41	y	y	PROPN
ap-2224	268	42	)	)	PUNCT
ap-2224	268	43	,	,	PUNCT
ap-2224	268	44	or	or	CCONJ
ap-2224	268	45	it	it	PRON
ap-2224	268	46	is	be	AUX
ap-2224	268	47	not	not	PART
ap-2224	268	48	known	know	VERB
ap-2224	268	49	to	to	ADP
ap-2224	268	50	the	the	DET
ap-2224	268	51	author	author	NOUN
ap-2224	268	52	if	if	SCONJ
ap-2224	268	53	they	they	PRON
ap-2224	268	54	are	be	AUX
ap-2224	268	55	transforms	transform	VERB
ap-2224	268	56	at	at	ADV
ap-2224	268	57	all	all	ADV
ap-2224	268	58	(	(	PUNCT
ap-2224	268	59	sin	sin	NOUN
ap-2224	268	60	y	y	PROPN
ap-2224	268	61	,	,	PUNCT
ap-2224	268	62	ln	ln	PROPN
ap-2224	268	63	y	y	PROPN
ap-2224	268	64	,	,	PUNCT
ap-2224	268	65	1	1	NUM
ap-2224	268	66	/	/	SYM
ap-2224	268	67	γ(y	γ(y	PROPN
ap-2224	268	68	)	)	PUNCT
ap-2224	268	69	,	,	PUNCT
ap-2224	268	70	tan	tan	PROPN
ap-2224	268	71	y	y	PROPN
ap-2224	268	72	)	)	PUNCT
ap-2224	268	73	.	.	PUNCT
ap-2224	269	1	on	on	ADP
ap-2224	269	2	the	the	DET
ap-2224	269	3	other	other	ADJ
ap-2224	269	4	hand	hand	NOUN
ap-2224	269	5	,	,	PUNCT
ap-2224	269	6	it	it	PRON
ap-2224	269	7	should	should	AUX
ap-2224	269	8	be	be	AUX
ap-2224	269	9	emphasized	emphasize	VERB
ap-2224	269	10	that	that	SCONJ
ap-2224	269	11	bare	bare	ADJ
ap-2224	269	12	convergence	convergence	NOUN
ap-2224	269	13	of	of	ADP
ap-2224	269	14	the	the	DET
ap-2224	269	15	integral	integral	ADJ
ap-2224	269	16	in	in	ADP
ap-2224	269	17	(	(	PUNCT
ap-2224	269	18	5.6	5.6	NUM
ap-2224	269	19	)	)	PUNCT
ap-2224	269	20	does	do	AUX
ap-2224	269	21	not	not	PART
ap-2224	269	22	guarantee	guarantee	VERB
ap-2224	269	23	the	the	DET
ap-2224	269	24	correct	correct	ADJ
ap-2224	269	25	solution	solution	NOUN
ap-2224	269	26	.	.	PUNCT
ap-2224	270	1	an	an	DET
ap-2224	270	2	example	example	NOUN
ap-2224	270	3	is	be	AUX
ap-2224	270	4	g(y	g(y	NOUN
ap-2224	270	5	)	)	PUNCT
ap-2224	270	6	=	=	SYM
ap-2224	270	7	exp	exp	NOUN
ap-2224	270	8	y2	y2	NOUN
ap-2224	270	9	,	,	PUNCT
ap-2224	270	10	which	which	PRON
ap-2224	270	11	is	be	AUX
ap-2224	270	12	neither	neither	CCONJ
ap-2224	270	13	a	a	DET
ap-2224	270	14	laplace	laplace	NOUN
ap-2224	270	15	nor	nor	CCONJ
ap-2224	270	16	a	a	DET
ap-2224	270	17	mellin	mellin	ADJ
ap-2224	270	18	transform	transform	NOUN
ap-2224	270	19	of	of	ADP
ap-2224	270	20	any	any	DET
ap-2224	270	21	function	function	NOUN
ap-2224	270	22	.	.	PUNCT
ap-2224	271	1	the	the	DET
ap-2224	271	2	resulting	result	VERB
ap-2224	271	3	function	function	NOUN
ap-2224	271	4	f	f	PROPN
ap-2224	271	5	(	(	PUNCT
ap-2224	271	6	x	x	X
ap-2224	271	7	)	)	PUNCT
ap-2224	271	8	is	be	AUX
ap-2224	271	9	not	not	PART
ap-2224	271	10	a	a	DET
ap-2224	271	11	solution	solution	NOUN
ap-2224	271	12	of	of	ADP
ap-2224	271	13	(	(	PUNCT
ap-2224	271	14	3.1	3.1	NUM
ap-2224	271	15	)	)	PUNCT
ap-2224	271	16	.	.	PUNCT
ap-2224	272	1	testing	test	VERB
ap-2224	272	2	the	the	DET
ap-2224	272	3	solution	solution	NOUN
ap-2224	272	4	is	be	AUX
ap-2224	272	5	recommended	recommend	VERB
ap-2224	272	6	.	.	PUNCT
ap-2224	273	1	lemma	lemma	PROPN
ap-2224	273	2	5.4	5.4	NUM
ap-2224	273	3	.	.	PUNCT
ap-2224	274	1	if	if	SCONJ
ap-2224	274	2	f	f	PROPN
ap-2224	274	3	(	(	PUNCT
ap-2224	274	4	x	x	X
ap-2224	274	5	)	)	PUNCT
ap-2224	274	6	is	be	AUX
ap-2224	274	7	a	a	DET
ap-2224	274	8	finite	finite	ADJ
ap-2224	274	9	laplace	laplace	NOUN
ap-2224	274	10	transform	transform	NOUN
ap-2224	274	11	of	of	ADP
ap-2224	274	12	the	the	DET
ap-2224	274	13	original	original	ADJ
ap-2224	274	14	f(t	f(t	NOUN
ap-2224	274	15	)	)	PUNCT
ap-2224	274	16	,	,	PUNCT
ap-2224	274	17	i.e.	i.e.	X
ap-2224	274	18	,	,	PUNCT
ap-2224	274	19	f	f	PROPN
ap-2224	274	20	(	(	PUNCT
ap-2224	274	21	x	x	X
ap-2224	274	22	)	)	PUNCT
ap-2224	274	23	=	=	SYM
ap-2224	275	1	∫	∫	PROPN
ap-2224	275	2	b	b	PROPN
ap-2224	275	3	a	a	DET
ap-2224	275	4	e−xtf(t	e−xtf(t	NUM
ap-2224	275	5	)	)	PUNCT
ap-2224	275	6	dt	dt	NOUN
ap-2224	275	7	,	,	PUNCT
ap-2224	275	8	0	0	NUM
ap-2224	275	9	≤	≤	NOUN
ap-2224	275	10	a	a	DET
ap-2224	275	11	<	<	X
ap-2224	275	12	b	b	X
ap-2224	275	13	<	<	X
ap-2224	275	14	∞	∞	PROPN
ap-2224	275	15	,	,	PUNCT
ap-2224	275	16	(	(	PUNCT
ap-2224	275	17	5.7	5.7	NUM
ap-2224	275	18	)	)	PUNCT
ap-2224	275	19	then	then	ADV
ap-2224	275	20	(	(	PUNCT
ap-2224	275	21	iy−f	iy−f	NOUN
ap-2224	275	22	)	)	PUNCT
ap-2224	275	23	(	(	PUNCT
ap-2224	275	24	y	y	NOUN
ap-2224	275	25	)	)	PUNCT
ap-2224	275	26	=	=	SYM
ap-2224	276	1	∫	∫	PROPN
ap-2224	276	2	b	b	PROPN
ap-2224	276	3	a	a	DET
ap-2224	276	4	e−xtt−yf(t	e−xtt−yf(t	NOUN
ap-2224	276	5	)	)	PUNCT
ap-2224	276	6	dt	dt	PUNCT
ap-2224	277	1	=	=	SYM
ap-2224	277	2	∫	∫	PROPN
ap-2224	277	3	b+ln	b+ln	PROPN
ap-2224	277	4	b	b	PROPN
ap-2224	277	5	a+ln	a+ln	NOUN
ap-2224	277	6	a	a	DET
ap-2224	277	7	e−yuf	e−yuf	NOUN
ap-2224	277	8	(	(	PUNCT
ap-2224	277	9	w0(eu	w0(eu	PROPN
ap-2224	277	10	)	)	PUNCT
ap-2224	277	11	)	)	PUNCT
ap-2224	277	12	w0(eu	w0(eu	NOUN
ap-2224	277	13	)	)	PUNCT
ap-2224	277	14	1	1	NUM
ap-2224	278	1	+	+	NOUN
ap-2224	278	2	w0(eu	w0(eu	X
ap-2224	278	3	)	)	PUNCT
ap-2224	278	4	du	du	NOUN
ap-2224	278	5	(	(	PUNCT
ap-2224	278	6	5.8	5.8	NUM
ap-2224	278	7	)	)	PUNCT
ap-2224	278	8	and	and	CCONJ
ap-2224	278	9	(	(	PUNCT
ap-2224	278	10	iy−f	iy−f	NOUN
ap-2224	278	11	)	)	PUNCT
ap-2224	278	12	(	(	PUNCT
ap-2224	278	13	y	y	NOUN
ap-2224	278	14	)	)	PUNCT
ap-2224	278	15	=	=	SYM
ap-2224	279	1	∫	∫	PROPN
ap-2224	279	2	b	b	PROPN
ap-2224	279	3	a	a	DET
ap-2224	279	4	e−xtt−yf(t	e−xtt−yf(t	NOUN
ap-2224	279	5	)	)	PUNCT
ap-2224	279	6	dt	dt	PUNCT
ap-2224	280	1	=	=	SYM
ap-2224	280	2	∫	∫	PROPN
ap-2224	280	3	b	b	PROPN
ap-2224	280	4	exp	exp	PROPN
ap-2224	280	5	b	b	PROPN
ap-2224	280	6	a	a	DET
ap-2224	280	7	exp	exp	NOUN
ap-2224	280	8	a	a	DET
ap-2224	280	9	u−y−1f	u−y−1f	ADJ
ap-2224	280	10	(	(	PUNCT
ap-2224	280	11	w0(u	w0(u	NOUN
ap-2224	280	12	)	)	PUNCT
ap-2224	280	13	)	)	PUNCT
ap-2224	281	1	w0(u	w0(u	X
ap-2224	281	2	)	)	PUNCT
ap-2224	281	3	1	1	NUM
ap-2224	282	1	+	+	PUNCT
ap-2224	282	2	w0(u	w0(u	X
ap-2224	282	3	)	)	PUNCT
ap-2224	282	4	du	du	NOUN
ap-2224	282	5	.	.	PUNCT
ap-2224	283	1	(	(	PUNCT
ap-2224	283	2	5.9	5.9	NUM
ap-2224	283	3	)	)	PUNCT
ap-2224	283	4	proof	proof	NOUN
ap-2224	283	5	.	.	PUNCT
ap-2224	284	1	substituting	substitute	VERB
ap-2224	284	2	w0(eu	w0(eu	NOUN
ap-2224	284	3	)	)	PUNCT
ap-2224	284	4	=	=	SYM
ap-2224	284	5	t	t	PROPN
ap-2224	284	6	,	,	PUNCT
ap-2224	284	7	i.e.	i.e.	X
ap-2224	284	8	,	,	PUNCT
ap-2224	284	9	u	u	NOUN
ap-2224	284	10	=	=	PUNCT
ap-2224	284	11	t+	t+	PUNCT
ap-2224	284	12	ln	ln	PROPN
ap-2224	284	13	t	t	PROPN
ap-2224	284	14	in	in	ADP
ap-2224	284	15	(	(	PUNCT
ap-2224	284	16	5.6	5.6	NUM
ap-2224	284	17	)	)	PUNCT
ap-2224	284	18	and	and	CCONJ
ap-2224	284	19	substituting	substitute	VERB
ap-2224	284	20	w0(u	w0(u	NUM
ap-2224	284	21	)	)	PUNCT
ap-2224	284	22	=	=	SYM
ap-2224	284	23	t	t	PROPN
ap-2224	284	24	,	,	PUNCT
ap-2224	284	25	i.e.	i.e.	X
ap-2224	284	26	,	,	PUNCT
ap-2224	284	27	u	u	PROPN
ap-2224	284	28	=	=	NOUN
ap-2224	284	29	tet	tet	NOUN
ap-2224	284	30	in	in	ADP
ap-2224	284	31	left	left	ADJ
ap-2224	284	32	integral	integral	ADJ
ap-2224	284	33	of	of	ADP
ap-2224	284	34	(	(	PUNCT
ap-2224	284	35	5.7	5.7	NUM
ap-2224	284	36	)	)	PUNCT
ap-2224	284	37	,	,	PUNCT
ap-2224	284	38	as	as	ADP
ap-2224	284	39	in	in	ADP
ap-2224	284	40	theorems	theorem	NOUN
ap-2224	284	41	3.1	3.1	NUM
ap-2224	284	42	and	and	CCONJ
ap-2224	284	43	3.2	3.2	NUM
ap-2224	284	44	,	,	PUNCT
ap-2224	284	45	respectively	respectively	ADV
ap-2224	284	46	.	.	PUNCT
ap-2224	284	47	theorem	theorem	VERB
ap-2224	284	48	5.5	5.5	NUM
ap-2224	284	49	.	.	PUNCT
ap-2224	285	1	if	if	SCONJ
ap-2224	285	2	f	f	PROPN
ap-2224	285	3	(	(	PUNCT
ap-2224	285	4	x	x	X
ap-2224	285	5	)	)	PUNCT
ap-2224	285	6	is	be	AUX
ap-2224	285	7	a	a	DET
ap-2224	285	8	finite	finite	ADJ
ap-2224	285	9	laplace	laplace	NOUN
ap-2224	285	10	transform	transform	NOUN
ap-2224	285	11	of	of	ADP
ap-2224	285	12	the	the	DET
ap-2224	285	13	piecewise	piecewise	NOUN
ap-2224	285	14	continuous	continuous	ADJ
ap-2224	285	15	original	original	ADJ
ap-2224	285	16	f(t	f(t	NOUN
ap-2224	285	17	)	)	PUNCT
ap-2224	285	18	,	,	PUNCT
ap-2224	285	19	i.e.	i.e.	X
ap-2224	285	20	,	,	PUNCT
ap-2224	285	21	f	f	PROPN
ap-2224	285	22	(	(	PUNCT
ap-2224	285	23	x	x	X
ap-2224	285	24	)	)	PUNCT
ap-2224	285	25	=	=	SYM
ap-2224	286	1	∫	∫	PROPN
ap-2224	286	2	b	b	PROPN
ap-2224	286	3	a	a	DET
ap-2224	286	4	e−xtf(t	e−xtf(t	NUM
ap-2224	286	5	)	)	PUNCT
ap-2224	286	6	dt	dt	NOUN
ap-2224	286	7	,	,	PUNCT
ap-2224	286	8	0	0	PUNCT
ap-2224	286	9	<	<	X
ap-2224	286	10	a	a	DET
ap-2224	286	11	<	<	X
ap-2224	286	12	b	b	X
ap-2224	286	13	<	<	X
ap-2224	286	14	∞	∞	PROPN
ap-2224	286	15	,	,	PUNCT
ap-2224	286	16	(	(	PUNCT
ap-2224	286	17	5.10	5.10	NUM
ap-2224	286	18	)	)	PUNCT
ap-2224	286	19	then	then	ADV
ap-2224	286	20	the	the	DET
ap-2224	286	21	liouville	liouville	NOUN
ap-2224	286	22	–	–	PUNCT
ap-2224	286	23	weyl	weyl	VERB
ap-2224	286	24	diagonal	diagonal	ADJ
ap-2224	286	25	fractional	fractional	ADJ
ap-2224	286	26	integral	integral	ADJ
ap-2224	286	27	(	(	PUNCT
ap-2224	286	28	iy−f	iy−f	NOUN
ap-2224	286	29	)	)	PUNCT
ap-2224	286	30	(	(	PUNCT
ap-2224	286	31	y	y	NOUN
ap-2224	286	32	)	)	PUNCT
ap-2224	286	33	=	=	SYM
ap-2224	287	1	∫	∫	PROPN
ap-2224	287	2	b	b	PROPN
ap-2224	287	3	a	a	DET
ap-2224	287	4	e−xtt−yf(t	e−xtt−yf(t	NOUN
ap-2224	287	5	)	)	PUNCT
ap-2224	287	6	dt	dt	PROPN
ap-2224	287	7	,	,	PUNCT
ap-2224	287	8	y	y	PROPN
ap-2224	287	9	∈	∈	PROPN
ap-2224	287	10	c	c	PROPN
ap-2224	287	11	(	(	PUNCT
ap-2224	287	12	5.11	5.11	NUM
ap-2224	287	13	)	)	PUNCT
ap-2224	287	14	is	be	AUX
ap-2224	287	15	an	an	DET
ap-2224	287	16	entire	entire	ADJ
ap-2224	287	17	function	function	NOUN
ap-2224	287	18	.	.	PUNCT
ap-2224	288	1	proof	proof	NOUN
ap-2224	288	2	.	.	PUNCT
ap-2224	289	1	it	it	PRON
ap-2224	289	2	is	be	AUX
ap-2224	289	3	known	know	VERB
ap-2224	289	4	that	that	SCONJ
ap-2224	289	5	the	the	DET
ap-2224	289	6	finite	finite	ADJ
ap-2224	289	7	laplace	laplace	NOUN
ap-2224	289	8	transform	transform	NOUN
ap-2224	289	9	of	of	ADP
ap-2224	289	10	an	an	DET
ap-2224	289	11	almost	almost	ADV
ap-2224	289	12	piecewise	piecewise	NOUN
ap-2224	289	13	continuous	continuous	ADJ
ap-2224	289	14	function	function	NOUN
ap-2224	289	15	is	be	AUX
ap-2224	289	16	an	an	DET
ap-2224	289	17	entire	entire	ADJ
ap-2224	289	18	function	function	NOUN
ap-2224	289	19	[	[	X
ap-2224	289	20	10	10	NUM
ap-2224	289	21	]	]	PUNCT
ap-2224	289	22	.	.	PUNCT
ap-2224	290	1	if	if	SCONJ
ap-2224	290	2	0	0	NUM
ap-2224	290	3	<	<	X
ap-2224	290	4	a	a	DET
ap-2224	290	5	<	<	X
ap-2224	290	6	b	b	X
ap-2224	290	7	<	<	X
ap-2224	290	8	∞	∞	PROPN
ap-2224	290	9	,	,	PUNCT
ap-2224	290	10	then	then	ADV
ap-2224	290	11	the	the	DET
ap-2224	290	12	integral	integral	ADJ
ap-2224	290	13	on	on	ADP
ap-2224	290	14	the	the	DET
ap-2224	290	15	right	right	NOUN
ap-2224	290	16	of	of	ADP
ap-2224	290	17	(	(	PUNCT
ap-2224	290	18	5.8	5.8	NUM
ap-2224	290	19	)	)	PUNCT
ap-2224	290	20	is	be	AUX
ap-2224	290	21	a	a	DET
ap-2224	290	22	finite	finite	ADJ
ap-2224	290	23	laplace	laplace	NOUN
ap-2224	290	24	transform	transform	NOUN
ap-2224	290	25	of	of	ADP
ap-2224	290	26	the	the	DET
ap-2224	290	27	almost	almost	ADV
ap-2224	290	28	piecewise	piecewise	NOUN
ap-2224	290	29	continuous	continuous	ADJ
ap-2224	290	30	function	function	NOUN
ap-2224	290	31	,	,	PUNCT
ap-2224	290	32	i.e.	i.e.	X
ap-2224	290	33	,	,	PUNCT
ap-2224	290	34	(	(	PUNCT
ap-2224	290	35	iy−f	iy−f	NOUN
ap-2224	290	36	)	)	PUNCT
ap-2224	290	37	(	(	PUNCT
ap-2224	290	38	y	y	NOUN
ap-2224	290	39	)	)	PUNCT
ap-2224	290	40	,	,	PUNCT
ap-2224	291	1	y	y	PROPN
ap-2224	291	2	∈	∈	PROPN
ap-2224	291	3	c	c	AUX
ap-2224	291	4	,	,	PUNCT
ap-2224	291	5	is	be	AUX
ap-2224	291	6	an	an	DET
ap-2224	291	7	entire	entire	ADJ
ap-2224	291	8	function	function	NOUN
ap-2224	291	9	.	.	PUNCT
ap-2224	292	1	remark	remark	VERB
ap-2224	292	2	5.6	5.6	NUM
ap-2224	292	3	.	.	PUNCT
ap-2224	293	1	the	the	DET
ap-2224	293	2	sharp	sharp	ADJ
ap-2224	293	3	inequality	inequality	NOUN
ap-2224	293	4	0	0	PUNCT
ap-2224	293	5	<	<	X
ap-2224	293	6	a	a	PRON
ap-2224	293	7	in	in	ADP
ap-2224	293	8	the	the	DET
ap-2224	293	9	hypothesis	hypothesis	NOUN
ap-2224	293	10	of	of	ADP
ap-2224	293	11	theorem	theorem	ADJ
ap-2224	293	12	5.5	5.5	NUM
ap-2224	293	13	is	be	AUX
ap-2224	293	14	essential	essential	ADJ
ap-2224	293	15	.	.	PUNCT
ap-2224	294	1	if	if	SCONJ
ap-2224	294	2	a	a	DET
ap-2224	294	3	=	=	SYM
ap-2224	294	4	0	0	NUM
ap-2224	294	5	,	,	PUNCT
ap-2224	294	6	function	function	NOUN
ap-2224	294	7	f	f	PROPN
ap-2224	294	8	(	(	PUNCT
ap-2224	294	9	x	x	X
ap-2224	294	10	)	)	PUNCT
ap-2224	294	11	is	be	AUX
ap-2224	294	12	entire	entire	ADJ
ap-2224	294	13	,	,	PUNCT
ap-2224	294	14	but	but	CCONJ
ap-2224	294	15	its	its	PRON
ap-2224	294	16	diagonal	diagonal	ADJ
ap-2224	294	17	fractional	fractional	ADJ
ap-2224	294	18	integral	integral	ADJ
ap-2224	294	19	need	need	NOUN
ap-2224	294	20	not	not	PART
ap-2224	294	21	be	be	AUX
ap-2224	294	22	entire	entire	ADJ
ap-2224	294	23	,	,	PUNCT
ap-2224	294	24	because	because	SCONJ
ap-2224	294	25	(	(	PUNCT
ap-2224	294	26	5.8	5.8	NUM
ap-2224	294	27	)	)	PUNCT
ap-2224	294	28	is	be	AUX
ap-2224	294	29	not	not	PART
ap-2224	294	30	a	a	DET
ap-2224	294	31	finite	finite	ADJ
ap-2224	294	32	laplace	laplace	NOUN
ap-2224	294	33	transform	transform	NOUN
ap-2224	294	34	in	in	ADP
ap-2224	294	35	that	that	DET
ap-2224	294	36	case	case	NOUN
ap-2224	294	37	.	.	PUNCT
ap-2224	295	1	remark	remark	VERB
ap-2224	295	2	5.7	5.7	NUM
ap-2224	295	3	.	.	PUNCT
ap-2224	296	1	from	from	ADP
ap-2224	296	2	(	(	PUNCT
ap-2224	296	3	5.11	5.11	NUM
ap-2224	296	4	)	)	PUNCT
ap-2224	296	5	it	it	PRON
ap-2224	296	6	results	result	VERB
ap-2224	296	7	that	that	SCONJ
ap-2224	296	8	the	the	DET
ap-2224	296	9	question	question	NOUN
ap-2224	296	10	of	of	ADP
ap-2224	296	11	the	the	DET
ap-2224	296	12	path	path	NOUN
ap-2224	296	13	of	of	ADP
ap-2224	296	14	integration	integration	NOUN
ap-2224	296	15	in	in	ADP
ap-2224	296	16	the	the	DET
ap-2224	296	17	complex	complex	ADJ
ap-2224	296	18	domain	domain	NOUN
ap-2224	296	19	,	,	PUNCT
ap-2224	296	20	not	not	PART
ap-2224	296	21	only	only	ADV
ap-2224	296	22	for	for	ADP
ap-2224	296	23	the	the	DET
ap-2224	296	24	diagonal	diagonal	ADJ
ap-2224	296	25	integral	integral	ADJ
ap-2224	296	26	but	but	CCONJ
ap-2224	296	27	also	also	ADV
ap-2224	296	28	for	for	ADP
ap-2224	296	29	the	the	DET
ap-2224	296	30	general	general	ADJ
ap-2224	296	31	liouville	liouville	PROPN
ap-2224	296	32	–	–	PUNCT
ap-2224	296	33	weyl	weyl	VERB
ap-2224	296	34	fractional	fractional	ADJ
ap-2224	296	35	integral	integral	ADJ
ap-2224	296	36	(	(	PUNCT
ap-2224	296	37	iν−f	iν−f	NOUN
ap-2224	296	38	)	)	PUNCT
ap-2224	296	39	(	(	PUNCT
ap-2224	296	40	y	y	NOUN
ap-2224	296	41	)	)	PUNCT
ap-2224	296	42	,	,	PUNCT
ap-2224	296	43	ν	ν	X
ap-2224	296	44	,	,	PUNCT
ap-2224	296	45	y	y	PROPN
ap-2224	296	46	∈	∈	PROPN
ap-2224	296	47	c	c	AUX
ap-2224	296	48	,	,	PUNCT
ap-2224	296	49	is	be	AUX
ap-2224	296	50	irrelevant	irrelevant	ADJ
ap-2224	296	51	in	in	ADP
ap-2224	296	52	the	the	DET
ap-2224	296	53	case	case	NOUN
ap-2224	296	54	that	that	PRON
ap-2224	296	55	function	function	VERB
ap-2224	296	56	f	f	X
ap-2224	296	57	(	(	PUNCT
ap-2224	296	58	·	·	PUNCT
ap-2224	296	59	)	)	PUNCT
ap-2224	296	60	is	be	AUX
ap-2224	296	61	a	a	DET
ap-2224	296	62	laplace	laplace	NOUN
ap-2224	296	63	transform	transform	NOUN
ap-2224	296	64	.	.	PUNCT
ap-2224	297	1	however	however	ADV
ap-2224	297	2	,	,	PUNCT
ap-2224	297	3	the	the	DET
ap-2224	297	4	specific	specific	ADJ
ap-2224	297	5	path	path	NOUN
ap-2224	297	6	of	of	ADP
ap-2224	297	7	integration	integration	NOUN
ap-2224	297	8	often	often	ADV
ap-2224	297	9	helps	help	VERB
ap-2224	297	10	in	in	ADP
ap-2224	297	11	the	the	DET
ap-2224	297	12	case	case	NOUN
ap-2224	297	13	when	when	SCONJ
ap-2224	297	14	γ(ν)(iν−f	γ(ν)(iν−f	NOUN
ap-2224	297	15	)	)	PUNCT
ap-2224	297	16	(	(	PUNCT
ap-2224	297	17	y	y	NOUN
ap-2224	297	18	)	)	PUNCT
ap-2224	297	19	,	,	PUNCT
ap-2224	297	20	ν	ν	PROPN
ap-2224	297	21	,	,	PUNCT
ap-2224	297	22	y	y	PROPN
ap-2224	297	23	∈	∈	PROPN
ap-2224	297	24	c	c	NOUN
ap-2224	297	25	is	be	AUX
ap-2224	297	26	used	use	VERB
ap-2224	297	27	as	as	ADP
ap-2224	297	28	the	the	DET
ap-2224	297	29	euler	euler	NOUN
ap-2224	297	30	transform	transform	NOUN
ap-2224	297	31	for	for	ADP
ap-2224	297	32	solving	solve	VERB
ap-2224	297	33	differential	differential	ADJ
ap-2224	297	34	equations	equation	NOUN
ap-2224	297	35	[	[	X
ap-2224	297	36	17	17	NUM
ap-2224	297	37	]	]	SYM
ap-2224	297	38	.	.	PUNCT
ap-2224	298	1	6	6	X
ap-2224	298	2	.	.	X
ap-2224	298	3	applications	application	NOUN
ap-2224	298	4	many	many	ADJ
ap-2224	298	5	special	special	ADJ
ap-2224	298	6	functions	function	NOUN
ap-2224	298	7	have	have	VERB
ap-2224	298	8	a	a	DET
ap-2224	298	9	connection	connection	NOUN
ap-2224	298	10	with	with	ADP
ap-2224	298	11	the	the	DET
ap-2224	298	12	liouville	liouville	NOUN
ap-2224	298	13	–	–	PUNCT
ap-2224	298	14	weyl	weyl	VERB
ap-2224	298	15	fractional	fractional	ADJ
ap-2224	298	16	integral	integral	ADJ
ap-2224	298	17	according	accord	VERB
ap-2224	298	18	to	to	ADP
ap-2224	298	19	(	(	PUNCT
ap-2224	298	20	1.1)–(1.3	1.1)–(1.3	NUM
ap-2224	298	21	)	)	PUNCT
ap-2224	298	22	.	.	PUNCT
ap-2224	299	1	we	we	PRON
ap-2224	299	2	will	will	AUX
ap-2224	299	3	concentrate	concentrate	VERB
ap-2224	299	4	on	on	ADP
ap-2224	299	5	the	the	DET
ap-2224	299	6	diagonal	diagonal	ADJ
ap-2224	299	7	restriction	restriction	NOUN
ap-2224	299	8	ν	ν	X
ap-2224	299	9	=	=	PUNCT
ap-2224	299	10	y.	y.	PROPN
ap-2224	299	11	6.1	6.1	NUM
ap-2224	299	12	.	.	PUNCT
ap-2224	300	1	gamma	gamma	PROPN
ap-2224	300	2	function	function	PROPN
ap-2224	300	3	it	it	PRON
ap-2224	300	4	is	be	AUX
ap-2224	300	5	known	know	VERB
ap-2224	300	6	[	[	X
ap-2224	300	7	15	15	NUM
ap-2224	300	8	]	]	PUNCT
ap-2224	300	9	that	that	SCONJ
ap-2224	300	10	there	there	PRON
ap-2224	300	11	does	do	AUX
ap-2224	300	12	not	not	PART
ap-2224	300	13	exist	exist	VERB
ap-2224	300	14	a	a	DET
ap-2224	300	15	pair	pair	NOUN
ap-2224	300	16	(	(	PUNCT
ap-2224	300	17	f	f	X
ap-2224	300	18	(	(	PUNCT
ap-2224	300	19	x	x	NOUN
ap-2224	300	20	)	)	PUNCT
ap-2224	300	21	,	,	PUNCT
ap-2224	300	22	ν	ν	NOUN
ap-2224	300	23	)	)	PUNCT
ap-2224	300	24	such	such	ADJ
ap-2224	301	1	that	that	SCONJ
ap-2224	301	2	the	the	DET
ap-2224	301	3	fractional	fractional	ADJ
ap-2224	301	4	integral	integral	ADJ
ap-2224	301	5	(	(	PUNCT
ap-2224	301	6	1.1	1.1	NUM
ap-2224	301	7	)	)	PUNCT
ap-2224	301	8	is	be	AUX
ap-2224	301	9	equal	equal	ADJ
ap-2224	301	10	to	to	ADP
ap-2224	301	11	a	a	DET
ap-2224	301	12	constant	constant	ADJ
ap-2224	301	13	.	.	PUNCT
ap-2224	302	1	but	but	CCONJ
ap-2224	302	2	there	there	PRON
ap-2224	302	3	exists	exist	VERB
ap-2224	302	4	a	a	DET
ap-2224	302	5	function	function	NOUN
ap-2224	302	6	f	f	X
ap-2224	302	7	(	(	PUNCT
ap-2224	302	8	x	x	X
ap-2224	302	9	)	)	PUNCT
ap-2224	302	10	the	the	DET
ap-2224	302	11	diagonal	diagonal	ADJ
ap-2224	302	12	integral	integral	NOUN
ap-2224	302	13	of	of	ADP
ap-2224	302	14	which	which	PRON
ap-2224	302	15	is	be	AUX
ap-2224	302	16	equal	equal	ADJ
ap-2224	302	17	to	to	ADP
ap-2224	302	18	1	1	NUM
ap-2224	302	19	.	.	PUNCT
ap-2224	303	1	lemma	lemma	PROPN
ap-2224	303	2	6.1	6.1	NUM
ap-2224	303	3	.	.	PUNCT
ap-2224	304	1	let	let	VERB
ap-2224	304	2	g(y	g(y	NOUN
ap-2224	304	3	)	)	PUNCT
ap-2224	304	4	=	=	SYM
ap-2224	304	5	1	1	NUM
ap-2224	304	6	,	,	PUNCT
ap-2224	304	7	g(u	g(u	PROPN
ap-2224	304	8	)	)	PUNCT
ap-2224	305	1	=	=	SYM
ap-2224	305	2	δ(u	δ(u	PROPN
ap-2224	305	3	)	)	PUNCT
ap-2224	305	4	,	,	PUNCT
ap-2224	305	5	u	u	PROPN
ap-2224	305	6	∈	∈	PROPN
ap-2224	305	7	(	(	PUNCT
ap-2224	305	8	−∞,∞	−∞,∞	NOUN
ap-2224	305	9	)	)	PUNCT
ap-2224	305	10	,	,	PUNCT
ap-2224	305	11	where	where	SCONJ
ap-2224	305	12	δ(u	δ(u	NUM
ap-2224	305	13	)	)	PUNCT
ap-2224	305	14	is	be	AUX
ap-2224	305	15	the	the	DET
ap-2224	305	16	dirac	dirac	PROPN
ap-2224	305	17	delta	delta	NOUN
ap-2224	305	18	function	function	NOUN
ap-2224	305	19	.	.	PUNCT
ap-2224	306	1	then	then	ADV
ap-2224	306	2	f(t	f(t	NOUN
ap-2224	306	3	)	)	PUNCT
ap-2224	306	4	=	=	SYM
ap-2224	306	5	(	(	PUNCT
ap-2224	306	6	t+	t+	NOUN
ap-2224	306	7	1)δ(t+	1)δ(t+	NUM
ap-2224	306	8	ln	ln	ADJ
ap-2224	306	9	t)/t	t)/t	NOUN
ap-2224	306	10	=	=	SYM
ap-2224	306	11	δ	δ	PROPN
ap-2224	306	12	(	(	PUNCT
ap-2224	306	13	t−w0(1	t−w0(1	PROPN
ap-2224	306	14	)	)	PUNCT
ap-2224	306	15	)	)	PUNCT
ap-2224	306	16	,	,	PUNCT
ap-2224	306	17	t	t	X
ap-2224	306	18	>	>	X
ap-2224	306	19	0	0	NUM
ap-2224	306	20	,	,	PUNCT
ap-2224	306	21	and	and	CCONJ
ap-2224	306	22	for	for	ADP
ap-2224	306	23	the	the	DET
ap-2224	306	24	laplace	laplace	NOUN
ap-2224	306	25	transform	transform	NOUN
ap-2224	306	26	we	we	PRON
ap-2224	306	27	have	have	VERB
ap-2224	306	28	f	f	PROPN
ap-2224	306	29	(	(	PUNCT
ap-2224	306	30	x	x	NOUN
ap-2224	306	31	)	)	PUNCT
ap-2224	306	32	=	=	SYM
ap-2224	307	1	∫	∫	PROPN
ap-2224	307	2	∞	∞	NUM
ap-2224	307	3	0	0	NUM
ap-2224	308	1	e−xtf(t	e−xtf(t	NUM
ap-2224	308	2	)	)	PUNCT
ap-2224	309	1	dt	dt	NOUN
ap-2224	309	2	=	=	SYM
ap-2224	309	3	w0(1)x	w0(1)x	PROPN
ap-2224	309	4	,	,	PUNCT
ap-2224	309	5	x	x	PROPN
ap-2224	309	6	∈	∈	PROPN
ap-2224	309	7	r.	r.	PROPN
ap-2224	309	8	311	311	NUM
ap-2224	309	9	vladimír	vladimír	PROPN
ap-2224	309	10	vojta	vojta	PROPN
ap-2224	309	11	acta	acta	PROPN
ap-2224	309	12	polytechnica	polytechnica	PROPN
ap-2224	309	13	proof	proof	NOUN
ap-2224	309	14	.	.	PUNCT
ap-2224	310	1	we	we	PRON
ap-2224	310	2	start	start	VERB
ap-2224	310	3	with	with	ADP
ap-2224	310	4	the	the	DET
ap-2224	310	5	relation	relation	NOUN
ap-2224	310	6	δ(t	δ(t	PROPN
ap-2224	310	7	+	+	CCONJ
ap-2224	310	8	ln	ln	PROPN
ap-2224	310	9	t	t	PROPN
ap-2224	310	10	)	)	PUNCT
ap-2224	310	11	=	=	SYM
ap-2224	310	12	δ(t−w0(1	δ(t−w0(1	NOUN
ap-2224	310	13	)	)	PUNCT
ap-2224	310	14	)	)	PUNCT
ap-2224	310	15	1	1	NUM
ap-2224	311	1	+	+	SYM
ap-2224	311	2	1	1	NUM
ap-2224	311	3	/	/	SYM
ap-2224	311	4	w0(1	w0(1	NOUN
ap-2224	311	5	)	)	PUNCT
ap-2224	311	6	because	because	SCONJ
ap-2224	311	7	the	the	DET
ap-2224	311	8	root	root	NOUN
ap-2224	311	9	of	of	ADP
ap-2224	311	10	the	the	DET
ap-2224	311	11	equation	equation	NOUN
ap-2224	311	12	t	t	NOUN
ap-2224	311	13	+	+	CCONJ
ap-2224	311	14	ln	ln	PROPN
ap-2224	311	15	t	t	NOUN
ap-2224	311	16	=	=	SYM
ap-2224	311	17	0	0	NUM
ap-2224	311	18	is	be	AUX
ap-2224	311	19	equal	equal	ADJ
ap-2224	311	20	to	to	ADP
ap-2224	311	21	w0(1	w0(1	PROPN
ap-2224	311	22	)	)	PUNCT
ap-2224	311	23	.	.	PUNCT
ap-2224	312	1	then	then	ADV
ap-2224	312	2	the	the	DET
ap-2224	312	3	laplace	laplace	NOUN
ap-2224	312	4	transform	transform	NOUN
ap-2224	312	5	of	of	ADP
ap-2224	312	6	the	the	DET
ap-2224	312	7	function	function	NOUN
ap-2224	312	8	f(t	f(t	NOUN
ap-2224	312	9	)	)	PUNCT
ap-2224	312	10	is	be	AUX
ap-2224	312	11	equal	equal	ADJ
ap-2224	312	12	to	to	ADP
ap-2224	312	13	exp(−xw0(1	exp(−xw0(1	ADJ
ap-2224	312	14	)	)	PUNCT
ap-2224	312	15	)	)	PUNCT
ap-2224	313	1	=	=	PUNCT
ap-2224	313	2	w0(1)x	w0(1)x	NOUN
ap-2224	313	3	because	because	SCONJ
ap-2224	313	4	w0(1	w0(1	ADJ
ap-2224	313	5	)	)	PUNCT
ap-2224	314	1	expw0(1	expw0(1	ADJ
ap-2224	314	2	)	)	PUNCT
ap-2224	314	3	=	=	SYM
ap-2224	315	1	1	1	X
ap-2224	315	2	.	.	X
ap-2224	315	3	lemma	lemma	PROPN
ap-2224	315	4	6.2	6.2	NUM
ap-2224	315	5	.	.	PUNCT
ap-2224	316	1	we	we	PRON
ap-2224	316	2	have	have	VERB
ap-2224	316	3	γ(y	γ(y	PROPN
ap-2224	316	4	)	)	PUNCT
ap-2224	317	1	=	=	SYM
ap-2224	318	1	∫	∫	PROPN
ap-2224	319	1	∞	∞	PROPN
ap-2224	319	2	y	y	PROPN
ap-2224	319	3	w0(1)x(x−	w0(1)x(x−	ADP
ap-2224	319	4	y)y−1	y)y−1	PROPN
ap-2224	319	5	dx	dx	PROPN
ap-2224	319	6	,	,	PUNCT
ap-2224	319	7	y	y	PROPN
ap-2224	319	8	>	>	X
ap-2224	319	9	0	0	PROPN
ap-2224	319	10	.	.	PUNCT
ap-2224	320	1	(	(	PUNCT
ap-2224	320	2	6.1	6.1	NUM
ap-2224	320	3	)	)	PUNCT
ap-2224	320	4	proof	proof	NOUN
ap-2224	320	5	.	.	PUNCT
ap-2224	321	1	we	we	PRON
ap-2224	321	2	have	have	VERB
ap-2224	321	3	(	(	PUNCT
ap-2224	321	4	iy−f	iy−f	NOUN
ap-2224	321	5	)	)	PUNCT
ap-2224	321	6	(	(	PUNCT
ap-2224	321	7	y	y	NOUN
ap-2224	321	8	)	)	PUNCT
ap-2224	321	9	=	=	SYM
ap-2224	321	10	1	1	NUM
ap-2224	321	11	γ(y	γ(y	PROPN
ap-2224	321	12	)	)	PUNCT
ap-2224	321	13	∫	∫	PROPN
ap-2224	322	1	∞	∞	PROPN
ap-2224	322	2	y	y	PROPN
ap-2224	322	3	w0(1)x(x−	w0(1)x(x−	ADP
ap-2224	322	4	y)y−1	y)y−1	PROPN
ap-2224	322	5	dx	dx	PROPN
ap-2224	322	6	=	=	SYM
ap-2224	322	7	∫	∫	PROPN
ap-2224	322	8	∞	∞	PROPN
ap-2224	322	9	0	0	PUNCT
ap-2224	323	1	e−ytt−yδ	e−ytt−yδ	PROPN
ap-2224	323	2	(	(	PUNCT
ap-2224	323	3	t−w0(1	t−w0(1	NOUN
ap-2224	323	4	)	)	PUNCT
ap-2224	323	5	)	)	PUNCT
ap-2224	324	1	dt	dt	PUNCT
ap-2224	325	1	=	=	SYM
ap-2224	325	2	1	1	NUM
ap-2224	325	3	,	,	PUNCT
ap-2224	325	4	because	because	SCONJ
ap-2224	325	5	w0(1	w0(1	ADJ
ap-2224	325	6	)	)	PUNCT
ap-2224	326	1	expw0(1	expw0(1	ADJ
ap-2224	326	2	)	)	PUNCT
ap-2224	326	3	=	=	SYM
ap-2224	327	1	1	1	X
ap-2224	327	2	.	.	PUNCT
ap-2224	328	1	finally	finally	ADV
ap-2224	328	2	we	we	PRON
ap-2224	328	3	get	get	VERB
ap-2224	328	4	(	(	PUNCT
ap-2224	328	5	6.1	6.1	NUM
ap-2224	328	6	)	)	PUNCT
ap-2224	328	7	.	.	PUNCT
ap-2224	329	1	after	after	ADP
ap-2224	329	2	substituting	substitute	VERB
ap-2224	329	3	u	u	NOUN
ap-2224	329	4	=	=	PROPN
ap-2224	329	5	x−	x−	PROPN
ap-2224	329	6	y	y	PROPN
ap-2224	329	7	in	in	ADP
ap-2224	329	8	(	(	PUNCT
ap-2224	329	9	6.1	6.1	NUM
ap-2224	329	10	)	)	PUNCT
ap-2224	329	11	we	we	PRON
ap-2224	329	12	obtain	obtain	VERB
ap-2224	329	13	its	its	PRON
ap-2224	329	14	mellin	mellin	NOUN
ap-2224	329	15	transform	transform	NOUN
ap-2224	329	16	form	form	NOUN
ap-2224	329	17	γ(y	γ(y	PROPN
ap-2224	329	18	)	)	PUNCT
ap-2224	330	1	=	=	PRON
ap-2224	330	2	w0(1)y	w0(1)y	VERB
ap-2224	330	3	∫	∫	PROPN
ap-2224	330	4	∞	∞	PROPN
ap-2224	330	5	0	0	NUM
ap-2224	331	1	w0(1)uuy−1	w0(1)uuy−1	PROPN
ap-2224	331	2	du	du	X
ap-2224	331	3	,	,	PUNCT
ap-2224	331	4	(	(	PUNCT
ap-2224	331	5	6.2	6.2	NUM
ap-2224	331	6	)	)	PUNCT
ap-2224	331	7	which	which	PRON
ap-2224	331	8	holds	hold	VERB
ap-2224	331	9	not	not	PART
ap-2224	331	10	only	only	ADV
ap-2224	331	11	for	for	ADP
ap-2224	331	12	y	y	PROPN
ap-2224	331	13	>	>	X
ap-2224	331	14	0	0	PUNCT
ap-2224	332	1	but	but	CCONJ
ap-2224	332	2	also	also	ADV
ap-2224	332	3	for	for	ADP
ap-2224	332	4	<	<	X
ap-2224	332	5	y	y	PROPN
ap-2224	332	6	>	>	X
ap-2224	332	7	0	0	PROPN
ap-2224	332	8	,	,	PUNCT
ap-2224	332	9	see	see	VERB
ap-2224	332	10	[	[	X
ap-2224	332	11	16	16	NUM
ap-2224	332	12	,	,	PUNCT
ap-2224	332	13	entry	entry	NOUN
ap-2224	332	14	3.1	3.1	NUM
ap-2224	332	15	,	,	PUNCT
ap-2224	332	16	p.	p.	NOUN
ap-2224	332	17	25	25	NUM
ap-2224	332	18	]	]	PUNCT
ap-2224	332	19	.	.	PUNCT
ap-2224	333	1	the	the	DET
ap-2224	333	2	usual	usual	ADJ
ap-2224	333	3	mellin	mellin	NOUN
ap-2224	333	4	transform	transform	NOUN
ap-2224	333	5	formula	formula	NOUN
ap-2224	333	6	for	for	ADP
ap-2224	333	7	the	the	DET
ap-2224	333	8	gamma	gamma	NOUN
ap-2224	333	9	function	function	NOUN
ap-2224	333	10	can	can	AUX
ap-2224	333	11	be	be	AUX
ap-2224	333	12	obtained	obtain	VERB
ap-2224	333	13	from	from	ADP
ap-2224	333	14	(	(	PUNCT
ap-2224	333	15	6.1	6.1	NUM
ap-2224	333	16	):	):	PUNCT
ap-2224	333	17	γ(y	γ(y	PROPN
ap-2224	333	18	)	)	PUNCT
ap-2224	334	1	=	=	SYM
ap-2224	335	1	∫	∫	PROPN
ap-2224	336	1	∞	∞	NUM
ap-2224	336	2	y	y	PROPN
ap-2224	336	3	w0(1)(x−	w0(1)(x−	PROPN
ap-2224	336	4	y)y−1	y)y−1	PROPN
ap-2224	336	5	dx	dx	PROPN
ap-2224	337	1	=	=	SYM
ap-2224	337	2	∫	∫	PROPN
ap-2224	338	1	∞	∞	PROPN
ap-2224	338	2	0	0	NUM
ap-2224	338	3	w0(1)u	w0(1)u	PROPN
ap-2224	338	4	/	/	SYM
ap-2224	338	5	w0(1)uy−1	w0(1)uy−1	NOUN
ap-2224	338	6	du	du	X
ap-2224	338	7	=	=	SYM
ap-2224	338	8	∫	∫	PROPN
ap-2224	338	9	∞	∞	PROPN
ap-2224	338	10	0	0	NUM
ap-2224	339	1	e−uuy−1	e−uuy−1	PROPN
ap-2224	339	2	du	du	PROPN
ap-2224	339	3	,	,	PUNCT
ap-2224	339	4	using	use	VERB
ap-2224	339	5	the	the	DET
ap-2224	339	6	linear	linear	ADJ
ap-2224	339	7	substitution	substitution	NOUN
ap-2224	339	8	x	x	PUNCT
ap-2224	339	9	=	=	PUNCT
ap-2224	339	10	y	y	PROPN
ap-2224	339	11	+	+	NUM
ap-2224	339	12	u	u	NOUN
ap-2224	339	13	/	/	SYM
ap-2224	339	14	w0(1	w0(1	ADJ
ap-2224	339	15	)	)	PUNCT
ap-2224	339	16	and	and	CCONJ
ap-2224	339	17	the	the	DET
ap-2224	339	18	relation	relation	NOUN
ap-2224	339	19	ln(w0(1))/w0(1	ln(w0(1))/w0(1	PROPN
ap-2224	339	20	)	)	PUNCT
ap-2224	339	21	=	=	SYM
ap-2224	339	22	−1	−1	NOUN
ap-2224	339	23	.	.	PUNCT
ap-2224	340	1	this	this	DET
ap-2224	340	2	proof	proof	NOUN
ap-2224	340	3	of	of	ADP
ap-2224	340	4	(	(	PUNCT
ap-2224	340	5	6.1	6.1	NUM
ap-2224	340	6	)	)	PUNCT
ap-2224	340	7	is	be	AUX
ap-2224	340	8	independent	independent	ADJ
ap-2224	340	9	from	from	ADP
ap-2224	340	10	generalized	generalized	ADJ
ap-2224	340	11	functions	function	NOUN
ap-2224	340	12	[	[	X
ap-2224	340	13	18	18	NUM
ap-2224	340	14	]	]	PUNCT
ap-2224	340	15	.	.	PUNCT
ap-2224	341	1	equation	equation	NOUN
ap-2224	341	2	(	(	PUNCT
ap-2224	341	3	6.1	6.1	NUM
ap-2224	341	4	)	)	PUNCT
ap-2224	341	5	can	can	AUX
ap-2224	341	6	be	be	AUX
ap-2224	341	7	generalized	generalize	VERB
ap-2224	341	8	for	for	ADP
ap-2224	341	9	a	a	DET
ap-2224	341	10	complex	complex	ADJ
ap-2224	341	11	argument	argument	NOUN
ap-2224	341	12	:	:	PUNCT
ap-2224	341	13	theorem	theorem	VERB
ap-2224	341	14	6.3	6.3	NUM
ap-2224	341	15	.	.	PUNCT
ap-2224	342	1	the	the	DET
ap-2224	342	2	function	function	NOUN
ap-2224	342	3	γ(z	γ(z	PROPN
ap-2224	342	4	)	)	PUNCT
ap-2224	342	5	,	,	PUNCT
ap-2224	342	6	<	<	X
ap-2224	342	7	z	z	X
ap-2224	342	8	>	>	X
ap-2224	342	9	0	0	PUNCT
ap-2224	342	10	is	be	AUX
ap-2224	342	11	an	an	DET
ap-2224	342	12	euler	euler	NOUN
ap-2224	342	13	integral	integral	ADJ
ap-2224	342	14	transform	transform	NOUN
ap-2224	342	15	[	[	X
ap-2224	342	16	17	17	NUM
ap-2224	342	17	,	,	PUNCT
ap-2224	342	18	p.	p.	NOUN
ap-2224	342	19	258	258	NUM
ap-2224	342	20	]	]	PUNCT
ap-2224	342	21	with	with	ADP
ap-2224	342	22	parameter	parameter	PROPN
ap-2224	342	23	z	z	PROPN
ap-2224	342	24	of	of	ADP
ap-2224	342	25	the	the	DET
ap-2224	342	26	function	function	NOUN
ap-2224	342	27	w0(1)u	w0(1)u	NOUN
ap-2224	342	28	along	along	ADP
ap-2224	342	29	path	path	PROPN
ap-2224	342	30	l	l	PROPN
ap-2224	342	31	,	,	PUNCT
ap-2224	342	32	which	which	PRON
ap-2224	342	33	is	be	AUX
ap-2224	342	34	a	a	DET
ap-2224	342	35	half	half	ADJ
ap-2224	342	36	straight	straight	ADJ
ap-2224	342	37	line	line	NOUN
ap-2224	342	38	starting	start	VERB
ap-2224	342	39	at	at	ADP
ap-2224	342	40	the	the	DET
ap-2224	342	41	point	point	NOUN
ap-2224	342	42	z	z	NOUN
ap-2224	342	43	=	=	SYM
ap-2224	342	44	a+	a+	PUNCT
ap-2224	342	45	ic	ic	PROPN
ap-2224	342	46	and	and	CCONJ
ap-2224	342	47	is	be	AUX
ap-2224	342	48	parallel	parallel	ADJ
ap-2224	342	49	to	to	ADP
ap-2224	342	50	the	the	DET
ap-2224	342	51	x	x	ADJ
ap-2224	342	52	axis	axis	NOUN
ap-2224	342	53	:	:	PUNCT
ap-2224	342	54	γ(z	γ(z	ADJ
ap-2224	342	55	)	)	PUNCT
ap-2224	342	56	=	=	SYM
ap-2224	343	1	∫	∫	PROPN
ap-2224	343	2	l	l	NOUN
ap-2224	343	3	w0(1)u(u−	w0(1)u(u−	PROPN
ap-2224	343	4	z)z−1	z)z−1	PROPN
ap-2224	343	5	du	du	PROPN
ap-2224	343	6	,	,	PUNCT
ap-2224	343	7	<	<	X
ap-2224	343	8	z	z	X
ap-2224	343	9	>	>	X
ap-2224	343	10	0	0	NUM
ap-2224	343	11	.	.	PUNCT
ap-2224	344	1	(	(	PUNCT
ap-2224	344	2	6.3	6.3	NUM
ap-2224	344	3	)	)	PUNCT
ap-2224	344	4	proof	proof	NOUN
ap-2224	344	5	.	.	PUNCT
ap-2224	345	1	let	let	VERB
ap-2224	345	2	u	u	PRON
ap-2224	345	3	=	=	NOUN
ap-2224	345	4	x+	x+	PROPN
ap-2224	345	5	ic	ic	PROPN
ap-2224	345	6	,	,	PUNCT
ap-2224	345	7	c	c	PROPN
ap-2224	345	8	∈	∈	PROPN
ap-2224	345	9	(	(	PUNCT
ap-2224	345	10	−∞,∞	−∞,∞	NOUN
ap-2224	345	11	)	)	PUNCT
ap-2224	345	12	.	.	PUNCT
ap-2224	346	1	then∫	then∫	NUM
ap-2224	346	2	l	l	PROPN
ap-2224	346	3	w0(1)u(u−	w0(1)u(u−	PROPN
ap-2224	347	1	z)z−1	z)z−1	PROPN
ap-2224	347	2	du	du	X
ap-2224	347	3	=	=	SYM
ap-2224	347	4	∫	∫	PROPN
ap-2224	347	5	∞	∞	PROPN
ap-2224	347	6	a	a	DET
ap-2224	347	7	w0(1)x+ic(x−	w0(1)x+ic(x−	PROPN
ap-2224	347	8	a)a+ic−1	a)a+ic−1	PROPN
ap-2224	348	1	dx	dx	PROPN
ap-2224	348	2	=	=	SYM
ap-2224	348	3	∫	∫	PROPN
ap-2224	348	4	∞	∞	PROPN
ap-2224	348	5	0	0	NUM
ap-2224	348	6	w0(1)y+a+icya+ic−1	w0(1)y+a+icya+ic−1	PROPN
ap-2224	349	1	dy	dy	NOUN
ap-2224	349	2	=	=	PROPN
ap-2224	349	3	w0(1)a+ic	w0(1)a+ic	PROPN
ap-2224	349	4	∫	∫	PROPN
ap-2224	349	5	∞	∞	NOUN
ap-2224	349	6	0	0	X
ap-2224	350	1	w0(1)yya+ic−1	w0(1)yya+ic−1	ADJ
ap-2224	350	2	dy	dy	NOUN
ap-2224	350	3	=	=	SYM
ap-2224	350	4	γ(a+	γ(a+	NOUN
ap-2224	350	5	ic	ic	NUM
ap-2224	350	6	)	)	PUNCT
ap-2224	350	7	=	=	SYM
ap-2224	350	8	γ(z	γ(z	PROPN
ap-2224	350	9	)	)	PUNCT
ap-2224	350	10	,	,	PUNCT
ap-2224	350	11	(	(	PUNCT
ap-2224	350	12	6.4	6.4	NUM
ap-2224	350	13	)	)	PUNCT
ap-2224	350	14	compare	compare	NOUN
ap-2224	350	15	(	(	PUNCT
ap-2224	350	16	6.2	6.2	NUM
ap-2224	350	17	)	)	PUNCT
ap-2224	350	18	or	or	CCONJ
ap-2224	350	19	[	[	X
ap-2224	350	20	19	19	NUM
ap-2224	350	21	,	,	PUNCT
ap-2224	350	22	entry	entry	NOUN
ap-2224	350	23	3.3	3.3	NUM
ap-2224	350	24	,	,	PUNCT
ap-2224	350	25	p.	p.	NOUN
ap-2224	350	26	21	21	NUM
ap-2224	350	27	]	]	PUNCT
ap-2224	350	28	.	.	PUNCT
ap-2224	351	1	remark	remark	PROPN
ap-2224	351	2	6.4	6.4	NUM
ap-2224	351	3	.	.	PUNCT
ap-2224	352	1	constant	constant	ADJ
ap-2224	352	2	w0(1	w0(1	NOUN
ap-2224	352	3	)	)	PUNCT
ap-2224	353	1	=	=	PUNCT
ap-2224	353	2	0.56714	0.56714	NUM
ap-2224	353	3	·	·	PUNCT
ap-2224	353	4	·	·	PUNCT
ap-2224	353	5	·	·	PUNCT
ap-2224	353	6	is	be	AUX
ap-2224	353	7	known	know	VERB
ap-2224	353	8	as	as	ADP
ap-2224	353	9	the	the	DET
ap-2224	353	10	omega	omega	NOUN
ap-2224	353	11	constant	constant	ADJ
ap-2224	353	12	,	,	PUNCT
ap-2224	353	13	see	see	VERB
ap-2224	353	14	http://oeis.org/a030178	http://oeis.org/a030178	NOUN
ap-2224	353	15	.	.	PUNCT
ap-2224	354	1	6.2	6.2	NUM
ap-2224	354	2	.	.	PUNCT
ap-2224	355	1	diagonal	diagonal	ADJ
ap-2224	355	2	restriction	restriction	NOUN
ap-2224	355	3	of	of	ADP
ap-2224	355	4	some	some	DET
ap-2224	355	5	special	special	ADJ
ap-2224	355	6	functions	function	NOUN
ap-2224	355	7	many	many	ADJ
ap-2224	355	8	standard	standard	ADJ
ap-2224	355	9	special	special	ADJ
ap-2224	355	10	functions	function	NOUN
ap-2224	355	11	may	may	AUX
ap-2224	355	12	be	be	AUX
ap-2224	355	13	represented	represent	VERB
ap-2224	355	14	as	as	ADP
ap-2224	355	15	the	the	DET
ap-2224	355	16	laplace	laplace	NOUN
ap-2224	355	17	–	–	PUNCT
ap-2224	355	18	mellin	mellin	NOUN
ap-2224	355	19	transform	transform	NOUN
ap-2224	355	20	in	in	ADP
ap-2224	355	21	(	(	PUNCT
ap-2224	355	22	1.3	1.3	NUM
ap-2224	355	23	)	)	PUNCT
ap-2224	355	24	.	.	PUNCT
ap-2224	356	1	as	as	ADP
ap-2224	356	2	examples	example	NOUN
ap-2224	356	3	,	,	PUNCT
ap-2224	356	4	we	we	PRON
ap-2224	356	5	mention	mention	VERB
ap-2224	356	6	the	the	DET
ap-2224	356	7	incomplete	incomplete	ADJ
ap-2224	356	8	gamma	gamma	NOUN
ap-2224	356	9	function	function	NOUN
ap-2224	356	10	,	,	PUNCT
ap-2224	356	11	the	the	DET
ap-2224	356	12	exponential	exponential	ADJ
ap-2224	356	13	integral	integral	ADJ
ap-2224	356	14	and	and	CCONJ
ap-2224	356	15	the	the	DET
ap-2224	356	16	macdonald	macdonald	PROPN
ap-2224	356	17	function	function	PROPN
ap-2224	356	18	.	.	PUNCT
ap-2224	357	1	the	the	DET
ap-2224	357	2	same	same	ADJ
ap-2224	357	3	representation	representation	NOUN
ap-2224	357	4	occurs	occur	VERB
ap-2224	357	5	for	for	ADP
ap-2224	357	6	a	a	DET
ap-2224	357	7	function	function	NOUN
ap-2224	357	8	specific	specific	ADJ
ap-2224	357	9	for	for	ADP
ap-2224	357	10	certain	certain	ADJ
ap-2224	357	11	fields	field	NOUN
ap-2224	357	12	of	of	ADP
ap-2224	357	13	physics	physics	NOUN
ap-2224	357	14	.	.	PUNCT
ap-2224	358	1	we	we	PRON
ap-2224	358	2	mention	mention	VERB
ap-2224	358	3	here	here	ADV
ap-2224	358	4	only	only	ADV
ap-2224	358	5	the	the	DET
ap-2224	358	6	bickley	bickley	PROPN
ap-2224	358	7	function	function	NOUN
ap-2224	358	8	,	,	PUNCT
ap-2224	358	9	known	know	VERB
ap-2224	358	10	in	in	ADP
ap-2224	358	11	neutron	neutron	NOUN
ap-2224	358	12	physics	physics	NOUN
ap-2224	359	1	[	[	X
ap-2224	359	2	11	11	NUM
ap-2224	359	3	]	]	PUNCT
ap-2224	359	4	.	.	PUNCT
ap-2224	360	1	other	other	ADJ
ap-2224	360	2	applications	application	NOUN
ap-2224	360	3	,	,	PUNCT
ap-2224	360	4	e.g.	e.g.	ADV
ap-2224	360	5	,	,	PUNCT
ap-2224	360	6	as	as	ADP
ap-2224	360	7	thermonuclear	thermonuclear	ADJ
ap-2224	360	8	reaction	reaction	NOUN
ap-2224	360	9	rate	rate	NOUN
ap-2224	360	10	integrals	integral	NOUN
ap-2224	360	11	[	[	X
ap-2224	360	12	20	20	NUM
ap-2224	360	13	,	,	PUNCT
ap-2224	360	14	p.	p.	NOUN
ap-2224	360	15	371	371	NUM
ap-2224	360	16	]	]	PUNCT
ap-2224	360	17	are	be	AUX
ap-2224	360	18	left	leave	VERB
ap-2224	360	19	for	for	SCONJ
ap-2224	360	20	the	the	DET
ap-2224	360	21	reader	reader	NOUN
ap-2224	360	22	to	to	PART
ap-2224	360	23	investigate	investigate	VERB
ap-2224	360	24	.	.	PUNCT
ap-2224	361	1	6.2.1	6.2.1	X
ap-2224	361	2	.	.	PUNCT
ap-2224	361	3	incomplete	incomplete	ADJ
ap-2224	361	4	gamma	gamma	PROPN
ap-2224	361	5	function	function	NOUN
ap-2224	361	6	we	we	PRON
ap-2224	361	7	start	start	VERB
ap-2224	361	8	with	with	ADP
ap-2224	361	9	the	the	DET
ap-2224	361	10	formula	formula	NOUN
ap-2224	361	11	γ(ν	γ(ν	PROPN
ap-2224	361	12	,	,	PUNCT
ap-2224	361	13	y	y	PROPN
ap-2224	361	14	)	)	PUNCT
ap-2224	361	15	=	=	SYM
ap-2224	361	16	e−y	e−y	PROPN
ap-2224	361	17	γ(1−	γ(1−	NOUN
ap-2224	361	18	ν	ν	PROPN
ap-2224	361	19	)	)	PUNCT
ap-2224	361	20	∫	∫	PROPN
ap-2224	361	21	∞	∞	PROPN
ap-2224	361	22	0	0	PROPN
ap-2224	361	23	eyt	eyt	PROPN
ap-2224	361	24	t	t	PROPN
ap-2224	361	25	−ν	−ν	NOUN
ap-2224	361	26	t+	t+	PUNCT
ap-2224	361	27	1	1	NUM
ap-2224	361	28	dt	dt	NOUN
ap-2224	361	29	=	=	PROPN
ap-2224	361	30	e−y	e−y	PROPN
ap-2224	361	31	γ(1−	γ(1−	PROPN
ap-2224	361	32	ν)γ(ν	ν)γ(ν	X
ap-2224	361	33	)	)	PUNCT
ap-2224	361	34	∫	∫	PROPN
ap-2224	361	35	∞	∞	PROPN
ap-2224	361	36	y	y	PROPN
ap-2224	361	37	exγ(0	exγ(0	PROPN
ap-2224	361	38	,	,	PUNCT
ap-2224	361	39	x)(x−	x)(x−	PROPN
ap-2224	361	40	y)ν−1	y)ν−1	PROPN
ap-2224	361	41	dt	dt	PROPN
ap-2224	361	42	,	,	PUNCT
ap-2224	361	43	y	y	PROPN
ap-2224	361	44	>	>	X
ap-2224	361	45	0	0	PROPN
ap-2224	361	46	,	,	PUNCT
ap-2224	361	47	ν	ν	X
ap-2224	361	48	<	<	X
ap-2224	361	49	1	1	NUM
ap-2224	361	50	,	,	PUNCT
ap-2224	361	51	(	(	PUNCT
ap-2224	361	52	6.5	6.5	NUM
ap-2224	361	53	)	)	PUNCT
ap-2224	361	54	see	see	VERB
ap-2224	361	55	[	[	X
ap-2224	361	56	13	13	NUM
ap-2224	361	57	,	,	PUNCT
ap-2224	361	58	p.	p.	NOUN
ap-2224	361	59	87	87	NUM
ap-2224	361	60	]	]	PUNCT
ap-2224	361	61	.	.	PUNCT
ap-2224	362	1	its	its	PRON
ap-2224	362	2	diagonal	diagonal	ADJ
ap-2224	362	3	restriction	restriction	NOUN
ap-2224	362	4	ν	ν	NOUN
ap-2224	362	5	=	=	SYM
ap-2224	362	6	y	y	PROPN
ap-2224	362	7	gives	give	VERB
ap-2224	362	8	γ(y	γ(y	PROPN
ap-2224	362	9	,	,	PUNCT
ap-2224	362	10	y	y	PROPN
ap-2224	362	11	)	)	PUNCT
ap-2224	362	12	=	=	SYM
ap-2224	363	1	e−y	e−y	PROPN
ap-2224	363	2	γ(1−	γ(1−	PROPN
ap-2224	363	3	y	y	PROPN
ap-2224	363	4	)	)	PUNCT
ap-2224	363	5	∫	∫	PROPN
ap-2224	364	1	∞	∞	PROPN
ap-2224	364	2	0	0	NUM
ap-2224	365	1	e−yt	e−yt	PROPN
ap-2224	365	2	t	t	PROPN
ap-2224	365	3	−y	−y	VERB
ap-2224	365	4	t+	t+	PUNCT
ap-2224	365	5	1	1	NUM
ap-2224	365	6	dt	dt	NOUN
ap-2224	365	7	=	=	PROPN
ap-2224	365	8	e−y	e−y	ADP
ap-2224	365	9	γ(y	γ(y	PROPN
ap-2224	365	10	−	−	PROPN
ap-2224	365	11	1	1	NUM
ap-2224	365	12	)	)	PUNCT
ap-2224	365	13	∫	∫	PROPN
ap-2224	365	14	∞	∞	PROPN
ap-2224	365	15	−∞	−∞	ADP
ap-2224	365	16	eyu	eyu	PROPN
ap-2224	365	17	w0(eu	w0(eu	PROPN
ap-2224	365	18	)	)	PUNCT
ap-2224	365	19	(	(	PUNCT
ap-2224	365	20	1	1	NUM
ap-2224	365	21	+	+	NOUN
ap-2224	365	22	w0(eu))2	w0(eu))2	X
ap-2224	365	23	du	du	X
ap-2224	365	24	=	=	PUNCT
ap-2224	365	25	e−y	e−y	PROPN
ap-2224	365	26	sin	sin	NOUN
ap-2224	366	1	πy	πy	X
ap-2224	366	2	π	π	NOUN
ap-2224	366	3	∫	∫	PROPN
ap-2224	366	4	∞	∞	PROPN
ap-2224	366	5	y	y	PROPN
ap-2224	366	6	exγ(0	exγ(0	PROPN
ap-2224	366	7	,	,	PUNCT
ap-2224	366	8	x)(x−	x)(x−	PROPN
ap-2224	366	9	y)y−1	y)y−1	PROPN
ap-2224	366	10	dx	dx	PROPN
ap-2224	366	11	,	,	PUNCT
ap-2224	366	12	y	y	PROPN
ap-2224	366	13	∈	∈	PROPN
ap-2224	366	14	(	(	PUNCT
ap-2224	366	15	0	0	NUM
ap-2224	366	16	,	,	PUNCT
ap-2224	366	17	1	1	NUM
ap-2224	366	18	)	)	PUNCT
ap-2224	366	19	.	.	PUNCT
ap-2224	367	1	(	(	PUNCT
ap-2224	367	2	6.6	6.6	NUM
ap-2224	367	3	)	)	PUNCT
ap-2224	367	4	312	312	NUM
ap-2224	367	5	http://oeis.org/a030178	http://oeis.org/a030178	NOUN
ap-2224	367	6	vol	vol	NOUN
ap-2224	367	7	.	.	PUNCT
ap-2224	368	1	54	54	NUM
ap-2224	368	2	no	no	NOUN
ap-2224	368	3	.	.	PUNCT
ap-2224	369	1	4/2014	4/2014	NUM
ap-2224	369	2	fractional	fractional	ADJ
ap-2224	369	3	calculus	calculus	NOUN
ap-2224	369	4	and	and	CCONJ
ap-2224	369	5	lambert	lambert	PROPN
ap-2224	369	6	function	function	NOUN
ap-2224	369	7	i	i	PRON
ap-2224	369	8	on	on	ADP
ap-2224	369	9	the	the	DET
ap-2224	369	10	other	other	ADJ
ap-2224	369	11	side	side	NOUN
ap-2224	369	12	,	,	PUNCT
ap-2224	369	13	integral	integral	ADJ
ap-2224	369	14	(	(	PUNCT
ap-2224	369	15	6.1	6.1	NUM
ap-2224	369	16	)	)	PUNCT
ap-2224	369	17	can	can	AUX
ap-2224	369	18	be	be	AUX
ap-2224	369	19	split	split	VERB
ap-2224	369	20	into	into	ADP
ap-2224	369	21	two	two	NUM
ap-2224	369	22	parts	part	NOUN
ap-2224	369	23	γ(y	γ(y	PROPN
ap-2224	369	24	)	)	PUNCT
ap-2224	370	1	=	=	SYM
ap-2224	371	1	∫	∫	PROPN
ap-2224	371	2	y(1	y(1	PROPN
ap-2224	372	1	+	+	PROPN
ap-2224	372	2	1	1	NUM
ap-2224	372	3	/	/	SYM
ap-2224	372	4	w0(1	w0(1	NOUN
ap-2224	372	5	)	)	PUNCT
ap-2224	372	6	)	)	PUNCT
ap-2224	373	1	y	y	PROPN
ap-2224	373	2	w0(1)x(x−	w0(1)x(x−	ADP
ap-2224	373	3	y)y−1	y)y−1	PROPN
ap-2224	373	4	dx+	dx+	PROPN
ap-2224	373	5	∫	∫	PROPN
ap-2224	373	6	∞	∞	PROPN
ap-2224	373	7	y(1	y(1	PROPN
ap-2224	374	1	+	+	PROPN
ap-2224	374	2	1	1	NUM
ap-2224	374	3	/	/	SYM
ap-2224	374	4	w0(1	w0(1	NOUN
ap-2224	374	5	)	)	PUNCT
ap-2224	374	6	)	)	PUNCT
ap-2224	374	7	w0(1)x(x−	w0(1)x(x−	ADP
ap-2224	374	8	y)y−1	y)y−1	PROPN
ap-2224	374	9	dx	dx	PROPN
ap-2224	374	10	=	=	PROPN
ap-2224	374	11	γ(y	γ(y	PROPN
ap-2224	374	12	,	,	PUNCT
ap-2224	374	13	y	y	PROPN
ap-2224	374	14	)	)	PUNCT
ap-2224	374	15	+	+	CCONJ
ap-2224	374	16	γ(y	γ(y	PROPN
ap-2224	374	17	,	,	PUNCT
ap-2224	374	18	y	y	PROPN
ap-2224	374	19	)	)	PUNCT
ap-2224	374	20	,	,	PUNCT
ap-2224	374	21	y	y	PROPN
ap-2224	374	22	>	>	X
ap-2224	374	23	0	0	NUM
ap-2224	374	24	,	,	PUNCT
ap-2224	374	25	(	(	PUNCT
ap-2224	374	26	6.7	6.7	NUM
ap-2224	374	27	)	)	PUNCT
ap-2224	374	28	see	see	VERB
ap-2224	374	29	[	[	X
ap-2224	374	30	16	16	NUM
ap-2224	374	31	,	,	PUNCT
ap-2224	374	32	entries	entry	NOUN
ap-2224	374	33	3.2	3.2	NUM
ap-2224	374	34	and	and	CCONJ
ap-2224	374	35	3.3	3.3	NUM
ap-2224	374	36	,	,	PUNCT
ap-2224	374	37	p.	p.	NOUN
ap-2224	374	38	25	25	NUM
ap-2224	374	39	]	]	PUNCT
ap-2224	374	40	and	and	CCONJ
ap-2224	374	41	(	(	PUNCT
ap-2224	374	42	1.3	1.3	NUM
ap-2224	374	43	)	)	PUNCT
ap-2224	374	44	,	,	PUNCT
ap-2224	374	45	i.e.	i.e.	X
ap-2224	374	46	,	,	PUNCT
ap-2224	374	47	another	another	DET
ap-2224	374	48	representation	representation	NOUN
ap-2224	374	49	of	of	ADP
ap-2224	374	50	the	the	DET
ap-2224	374	51	diagonal	diagonal	ADJ
ap-2224	374	52	restriction	restriction	NOUN
ap-2224	374	53	of	of	ADP
ap-2224	374	54	both	both	DET
ap-2224	374	55	incomplete	incomplete	ADJ
ap-2224	374	56	gamma	gamma	NOUN
ap-2224	374	57	functions	function	NOUN
ap-2224	374	58	.	.	PUNCT
ap-2224	375	1	the	the	DET
ap-2224	375	2	second	second	ADJ
ap-2224	375	3	integral	integral	ADJ
ap-2224	375	4	means	mean	NOUN
ap-2224	375	5	that	that	SCONJ
ap-2224	375	6	γ(y	γ(y	PROPN
ap-2224	375	7	,	,	PUNCT
ap-2224	375	8	y	y	NOUN
ap-2224	375	9	)	)	PUNCT
ap-2224	375	10	is	be	AUX
ap-2224	375	11	equal	equal	ADJ
ap-2224	375	12	to	to	ADP
ap-2224	375	13	the	the	DET
ap-2224	375	14	γ(y	γ(y	PROPN
ap-2224	375	15	)	)	PUNCT
ap-2224	375	16	times	time	NOUN
ap-2224	375	17	liouville	liouville	ADJ
ap-2224	375	18	–	–	PUNCT
ap-2224	375	19	weyl	weyl	VERB
ap-2224	375	20	fractional	fractional	ADJ
ap-2224	375	21	integral	integral	ADJ
ap-2224	375	22	of	of	ADP
ap-2224	375	23	the	the	DET
ap-2224	375	24	order	order	NOUN
ap-2224	375	25	y	y	NOUN
ap-2224	375	26	at	at	ADP
ap-2224	375	27	the	the	DET
ap-2224	375	28	point	point	NOUN
ap-2224	375	29	y(1	y(1	PROPN
ap-2224	376	1	+	+	CCONJ
ap-2224	376	2	1	1	NUM
ap-2224	376	3	/	/	SYM
ap-2224	376	4	w0(1	w0(1	NOUN
ap-2224	376	5	)	)	PUNCT
ap-2224	376	6	)	)	PUNCT
ap-2224	376	7	of	of	ADP
ap-2224	376	8	the	the	DET
ap-2224	376	9	function	function	NOUN
ap-2224	376	10	w0(1)x	w0(1)x	NOUN
ap-2224	376	11	.	.	PUNCT
ap-2224	377	1	6.2.2	6.2.2	X
ap-2224	377	2	.	.	PUNCT
ap-2224	378	1	exponential	exponential	PROPN
ap-2224	378	2	integral	integral	ADJ
ap-2224	378	3	the	the	DET
ap-2224	378	4	general	general	ADJ
ap-2224	378	5	exponential	exponential	ADJ
ap-2224	378	6	integral	integral	ADJ
ap-2224	378	7	function	function	NOUN
ap-2224	378	8	is	be	AUX
ap-2224	378	9	defined	define	VERB
ap-2224	378	10	as	as	ADP
ap-2224	378	11	[	[	X
ap-2224	378	12	13	13	NUM
ap-2224	378	13	,	,	PUNCT
ap-2224	378	14	p.	p.	NOUN
ap-2224	378	15	132	132	NUM
ap-2224	378	16	]	]	X
ap-2224	378	17	:	:	PUNCT
ap-2224	378	18	eν(y	eν(y	NUM
ap-2224	378	19	)	)	PUNCT
ap-2224	379	1	=	=	SYM
ap-2224	379	2	∫	∫	PROPN
ap-2224	380	1	∞	∞	NUM
ap-2224	380	2	1	1	NUM
ap-2224	380	3	e−ytt−ν	e−ytt−ν	NOUN
ap-2224	380	4	dt	dt	X
ap-2224	380	5	=	=	SYM
ap-2224	380	6	yν−1γ(1−	yν−1γ(1−	PROPN
ap-2224	380	7	ν	ν	PROPN
ap-2224	380	8	,	,	PUNCT
ap-2224	380	9	y	y	PROPN
ap-2224	380	10	)	)	PUNCT
ap-2224	380	11	,	,	PUNCT
ap-2224	380	12	<	<	X
ap-2224	380	13	y	y	X
ap-2224	380	14	>	>	X
ap-2224	380	15	0	0	PROPN
ap-2224	380	16	,	,	PUNCT
ap-2224	380	17	ν	ν	PROPN
ap-2224	380	18	∈	∈	PROPN
ap-2224	380	19	c.	c.	NOUN
ap-2224	380	20	(	(	PUNCT
ap-2224	380	21	6.8	6.8	NUM
ap-2224	380	22	)	)	PUNCT
ap-2224	380	23	this	this	DET
ap-2224	380	24	formula	formula	NOUN
ap-2224	380	25	can	can	AUX
ap-2224	380	26	be	be	AUX
ap-2224	380	27	written	write	VERB
ap-2224	380	28	in	in	ADP
ap-2224	380	29	the	the	DET
ap-2224	380	30	form	form	NOUN
ap-2224	380	31	of	of	ADP
ap-2224	380	32	the	the	DET
ap-2224	380	33	liouville	liouville	NOUN
ap-2224	380	34	–	–	PUNCT
ap-2224	380	35	weyl	weyl	VERB
ap-2224	380	36	fractional	fractional	ADJ
ap-2224	380	37	integral	integral	ADJ
ap-2224	380	38	eν(y	eν(y	NOUN
ap-2224	380	39	)	)	PUNCT
ap-2224	380	40	=	=	SYM
ap-2224	381	1	∫	∫	PROPN
ap-2224	381	2	∞	∞	NUM
ap-2224	381	3	0	0	NUM
ap-2224	382	1	e−ytt−νh(t−	e−ytt−νh(t−	NOUN
ap-2224	382	2	1	1	X
ap-2224	382	3	)	)	PUNCT
ap-2224	382	4	dt	dt	NOUN
ap-2224	382	5	=	=	SYM
ap-2224	382	6	1	1	NUM
ap-2224	382	7	γ(ν	γ(ν	PROPN
ap-2224	382	8	)	)	PUNCT
ap-2224	382	9	∫	∫	PROPN
ap-2224	383	1	∞	∞	PROPN
ap-2224	383	2	y	y	PROPN
ap-2224	383	3	e−x	e−x	PROPN
ap-2224	383	4	x	x	SYM
ap-2224	383	5	(	(	PUNCT
ap-2224	383	6	x−	x−	PROPN
ap-2224	383	7	y)ν−1	y)ν−1	PROPN
ap-2224	383	8	dx	dx	PROPN
ap-2224	383	9	,	,	PUNCT
ap-2224	383	10	y	y	PROPN
ap-2224	383	11	>	>	X
ap-2224	383	12	0	0	PROPN
ap-2224	383	13	,	,	PUNCT
ap-2224	383	14	ν	ν	X
ap-2224	383	15	>	>	X
ap-2224	383	16	0	0	NUM
ap-2224	383	17	.	.	PUNCT
ap-2224	384	1	the	the	DET
ap-2224	384	2	integral	integral	ADJ
ap-2224	384	3	on	on	ADP
ap-2224	384	4	the	the	DET
ap-2224	384	5	right	right	NOUN
ap-2224	384	6	is	be	AUX
ap-2224	384	7	the	the	DET
ap-2224	384	8	liouville	liouville	NOUN
ap-2224	384	9	–	–	PUNCT
ap-2224	384	10	weyl	weyl	VERB
ap-2224	384	11	fractional	fractional	ADJ
ap-2224	384	12	integral	integral	ADJ
ap-2224	384	13	of	of	ADP
ap-2224	384	14	the	the	DET
ap-2224	384	15	laplace	laplace	NOUN
ap-2224	384	16	transform	transform	NOUN
ap-2224	384	17	of	of	ADP
ap-2224	384	18	the	the	DET
ap-2224	384	19	shifted	shift	VERB
ap-2224	384	20	heaviside	heaviside	ADJ
ap-2224	384	21	function	function	NOUN
ap-2224	384	22	h(t−	h(t−	PROPN
ap-2224	384	23	1	1	NUM
ap-2224	384	24	)	)	PUNCT
ap-2224	384	25	.	.	PUNCT
ap-2224	385	1	theorem	theorem	VERB
ap-2224	385	2	6.5	6.5	NUM
ap-2224	385	3	.	.	PUNCT
ap-2224	386	1	the	the	DET
ap-2224	386	2	general	general	ADJ
ap-2224	386	3	exponential	exponential	ADJ
ap-2224	386	4	integral	integral	ADJ
ap-2224	386	5	eν(y	eν(y	NOUN
ap-2224	386	6	)	)	PUNCT
ap-2224	386	7	is	be	AUX
ap-2224	386	8	a	a	DET
ap-2224	386	9	completely	completely	ADV
ap-2224	386	10	monotone	monotone	ADJ
ap-2224	386	11	function	function	NOUN
ap-2224	386	12	in	in	ADP
ap-2224	386	13	variable	variable	ADJ
ap-2224	386	14	y	y	PROPN
ap-2224	386	15	∈	∈	PROPN
ap-2224	386	16	r+	r+	NOUN
ap-2224	386	17	for	for	ADP
ap-2224	386	18	fixed	fix	VERB
ap-2224	386	19	ν	ν	NOUN
ap-2224	386	20	and	and	CCONJ
ap-2224	386	21	a	a	DET
ap-2224	386	22	completely	completely	ADV
ap-2224	386	23	monotone	monotone	ADJ
ap-2224	386	24	function	function	NOUN
ap-2224	386	25	in	in	ADP
ap-2224	386	26	parameter	parameter	NOUN
ap-2224	386	27	ν	ν	PRON
ap-2224	386	28	∈	∈	PROPN
ap-2224	386	29	r+	r+	NOUN
ap-2224	386	30	for	for	ADP
ap-2224	386	31	fixed	fix	VERB
ap-2224	386	32	y	y	PROPN
ap-2224	386	33	∈	∈	PROPN
ap-2224	386	34	r+	r+	X
ap-2224	386	35	.	.	PUNCT
ap-2224	387	1	proof	proof	NOUN
ap-2224	387	2	.	.	PUNCT
ap-2224	388	1	the	the	DET
ap-2224	388	2	integral	integral	ADJ
ap-2224	388	3	on	on	ADP
ap-2224	388	4	the	the	DET
ap-2224	388	5	left	left	NOUN
ap-2224	388	6	of	of	ADP
ap-2224	388	7	(	(	PUNCT
ap-2224	388	8	6.8	6.8	NUM
ap-2224	388	9	)	)	PUNCT
ap-2224	388	10	is	be	AUX
ap-2224	388	11	the	the	DET
ap-2224	388	12	laplace	laplace	NOUN
ap-2224	388	13	transform	transform	NOUN
ap-2224	388	14	of	of	ADP
ap-2224	388	15	the	the	DET
ap-2224	388	16	non	non	ADJ
ap-2224	388	17	-	-	ADJ
ap-2224	388	18	negative	negative	ADJ
ap-2224	388	19	function	function	NOUN
ap-2224	388	20	in	in	ADP
ap-2224	388	21	the	the	DET
ap-2224	388	22	interval	interval	NOUN
ap-2224	388	23	t	t	PROPN
ap-2224	388	24	∈	∈	PROPN
ap-2224	389	1	[	[	X
ap-2224	389	2	0,∞	0,∞	NUM
ap-2224	389	3	)	)	PUNCT
ap-2224	389	4	and	and	CCONJ
ap-2224	389	5	ν	ν	X
ap-2224	389	6	>	>	X
ap-2224	389	7	0	0	NUM
ap-2224	389	8	.	.	PUNCT
ap-2224	390	1	this	this	PRON
ap-2224	390	2	means	mean	VERB
ap-2224	390	3	,	,	PUNCT
ap-2224	390	4	according	accord	VERB
ap-2224	390	5	to	to	ADP
ap-2224	390	6	theorem	theorem	NOUN
ap-2224	390	7	1.3	1.3	NUM
ap-2224	390	8	,	,	PUNCT
ap-2224	390	9	that	that	DET
ap-2224	390	10	eν(y	eν(y	NUM
ap-2224	390	11	)	)	PUNCT
ap-2224	390	12	is	be	AUX
ap-2224	390	13	a	a	DET
ap-2224	390	14	completely	completely	ADV
ap-2224	390	15	monotone	monotone	ADJ
ap-2224	390	16	function	function	NOUN
ap-2224	390	17	in	in	ADP
ap-2224	390	18	variable	variable	ADJ
ap-2224	390	19	y.	y.	NOUN
ap-2224	390	20	after	after	ADP
ap-2224	390	21	substituting	substitute	VERB
ap-2224	390	22	t	t	NOUN
ap-2224	390	23	=	=	SYM
ap-2224	390	24	ex	ex	NOUN
ap-2224	390	25	into	into	ADP
ap-2224	390	26	the	the	DET
ap-2224	390	27	integral	integral	ADJ
ap-2224	390	28	in	in	ADP
ap-2224	390	29	(	(	PUNCT
ap-2224	390	30	6.8	6.8	NUM
ap-2224	390	31	)	)	PUNCT
ap-2224	390	32	,	,	PUNCT
ap-2224	390	33	we	we	PRON
ap-2224	390	34	obtain	obtain	VERB
ap-2224	390	35	eν(y	eν(y	PUNCT
ap-2224	390	36	)	)	PUNCT
ap-2224	390	37	=	=	SYM
ap-2224	391	1	∫	∫	PROPN
ap-2224	392	1	∞	∞	NOUN
ap-2224	392	2	0	0	PUNCT
ap-2224	393	1	ex−yex	ex−yex	X
ap-2224	393	2	e−νx	e−νx	PROPN
ap-2224	393	3	dx	dx	PROPN
ap-2224	393	4	.	.	PUNCT
ap-2224	394	1	this	this	DET
ap-2224	394	2	integral	integral	ADJ
ap-2224	394	3	is	be	AUX
ap-2224	394	4	the	the	DET
ap-2224	394	5	laplace	laplace	NOUN
ap-2224	394	6	transform	transform	NOUN
ap-2224	394	7	of	of	ADP
ap-2224	394	8	a	a	DET
ap-2224	394	9	positive	positive	ADJ
ap-2224	394	10	function	function	NOUN
ap-2224	394	11	,	,	PUNCT
ap-2224	394	12	and	and	CCONJ
ap-2224	394	13	according	accord	VERB
ap-2224	394	14	to	to	ADP
ap-2224	394	15	theorem	theorem	VERB
ap-2224	394	16	1.3	1.3	NUM
ap-2224	394	17	eν(y	eν(y	NUM
ap-2224	394	18	)	)	PUNCT
ap-2224	395	1	is	be	AUX
ap-2224	395	2	a	a	DET
ap-2224	395	3	completely	completely	ADV
ap-2224	395	4	monotone	monotone	ADJ
ap-2224	395	5	function	function	NOUN
ap-2224	395	6	in	in	ADP
ap-2224	395	7	parameter	parameter	NOUN
ap-2224	395	8	ν	ν	PROPN
ap-2224	395	9	.	.	PUNCT
ap-2224	396	1	the	the	DET
ap-2224	396	2	diagonal	diagonal	ADJ
ap-2224	396	3	restriction	restriction	NOUN
ap-2224	396	4	of	of	ADP
ap-2224	396	5	eν(y	eν(y	NOUN
ap-2224	396	6	)	)	PUNCT
ap-2224	396	7	is	be	AUX
ap-2224	396	8	ey(y	ey(y	NOUN
ap-2224	396	9	)	)	PUNCT
ap-2224	397	1	=	=	SYM
ap-2224	397	2	∫	∫	PROPN
ap-2224	398	1	∞	∞	NUM
ap-2224	398	2	1	1	NUM
ap-2224	398	3	e−ytt−y	e−ytt−y	NOUN
ap-2224	398	4	dt	dt	NOUN
ap-2224	398	5	=	=	SYM
ap-2224	398	6	∫	∫	PROPN
ap-2224	398	7	∞	∞	NUM
ap-2224	398	8	1	1	NUM
ap-2224	398	9	e−yu	e−yu	X
ap-2224	398	10	w0(eu	w0(eu	NOUN
ap-2224	398	11	)	)	PUNCT
ap-2224	398	12	1	1	NUM
ap-2224	398	13	+	+	NOUN
ap-2224	398	14	w0(eu	w0(eu	X
ap-2224	398	15	)	)	PUNCT
ap-2224	398	16	du	du	PROPN
ap-2224	398	17	=	=	PROPN
ap-2224	398	18	yy−1γ(1−	yy−1γ(1−	PROPN
ap-2224	398	19	y	y	PROPN
ap-2224	398	20	,	,	PUNCT
ap-2224	398	21	y	y	PROPN
ap-2224	398	22	)	)	PUNCT
ap-2224	398	23	.	.	PUNCT
ap-2224	399	1	(	(	PUNCT
ap-2224	399	2	6.9	6.9	NUM
ap-2224	399	3	)	)	PUNCT
ap-2224	399	4	it	it	PRON
ap-2224	399	5	is	be	AUX
ap-2224	399	6	evident	evident	ADJ
ap-2224	399	7	that	that	SCONJ
ap-2224	399	8	ey(y	ey(y	NOUN
ap-2224	399	9	)	)	PUNCT
ap-2224	399	10	is	be	AUX
ap-2224	399	11	a	a	DET
ap-2224	399	12	completely	completely	ADV
ap-2224	399	13	monotone	monotone	ADJ
ap-2224	399	14	function	function	NOUN
ap-2224	399	15	for	for	ADP
ap-2224	399	16	y	y	PROPN
ap-2224	399	17	∈	∈	PROPN
ap-2224	399	18	r+	r+	NOUN
ap-2224	399	19	,	,	PUNCT
ap-2224	399	20	because	because	SCONJ
ap-2224	399	21	it	it	PRON
ap-2224	399	22	is	be	AUX
ap-2224	399	23	the	the	DET
ap-2224	399	24	laplace	laplace	NOUN
ap-2224	399	25	transform	transform	NOUN
ap-2224	399	26	of	of	ADP
ap-2224	399	27	the	the	DET
ap-2224	399	28	nonnegative	nonnegative	ADJ
ap-2224	399	29	function	function	NOUN
ap-2224	400	1	w0(eu)/(1	w0(eu)/(1	PROPN
ap-2224	400	2	+	+	PROPN
ap-2224	400	3	w0(eu	w0(eu	NOUN
ap-2224	400	4	)	)	PUNCT
ap-2224	400	5	)	)	PUNCT
ap-2224	400	6	.	.	PUNCT
ap-2224	401	1	6.2.3	6.2.3	X
ap-2224	401	2	.	.	PUNCT
ap-2224	401	3	modified	modify	VERB
ap-2224	401	4	bessel	bessel	ADJ
ap-2224	401	5	function	function	NOUN
ap-2224	401	6	of	of	ADP
ap-2224	401	7	the	the	DET
ap-2224	401	8	second	second	ADJ
ap-2224	401	9	kind	kind	NOUN
ap-2224	401	10	(	(	PUNCT
ap-2224	401	11	macdonald	macdonald	PROPN
ap-2224	401	12	function	function	PROPN
ap-2224	401	13	)	)	PUNCT
ap-2224	401	14	kν(x	kν(x	PROPN
ap-2224	401	15	)	)	PUNCT
ap-2224	402	1	we	we	PRON
ap-2224	402	2	start	start	VERB
ap-2224	402	3	with	with	ADP
ap-2224	402	4	the	the	DET
ap-2224	402	5	relation	relation	NOUN
ap-2224	402	6	∫	∫	PROPN
ap-2224	402	7	∞	∞	PROPN
ap-2224	402	8	0	0	NUM
ap-2224	402	9	e−ytt−ν−1e−1	e−ytt−ν−1e−1	PROPN
ap-2224	402	10	/	/	SYM
ap-2224	402	11	t	t	NOUN
ap-2224	402	12	dt	dt	NOUN
ap-2224	402	13	=	=	SYM
ap-2224	402	14	2yν/2kν(2√y	2yν/2kν(2√y	NUM
ap-2224	402	15	)	)	PUNCT
ap-2224	402	16	,	,	PUNCT
ap-2224	402	17	y	y	PROPN
ap-2224	402	18	>	>	X
ap-2224	402	19	0	0	PROPN
ap-2224	402	20	,	,	PUNCT
ap-2224	402	21	ν	ν	X
ap-2224	402	22	≥	≥	NOUN
ap-2224	402	23	0	0	NUM
ap-2224	402	24	.	.	PUNCT
ap-2224	403	1	(	(	PUNCT
ap-2224	403	2	6.10	6.10	NUM
ap-2224	403	3	)	)	PUNCT
ap-2224	403	4	according	accord	VERB
ap-2224	403	5	to	to	ADP
ap-2224	403	6	(	(	PUNCT
ap-2224	403	7	2.2	2.2	NUM
ap-2224	403	8	)	)	PUNCT
ap-2224	403	9	we	we	PRON
ap-2224	403	10	have	have	VERB
ap-2224	403	11	for	for	ADP
ap-2224	403	12	ν	ν	NOUN
ap-2224	403	13	=	=	PUNCT
ap-2224	403	14	y	y	PROPN
ap-2224	403	15	2yy/2ky(2√y	2yy/2ky(2√y	NUM
ap-2224	403	16	)	)	PUNCT
ap-2224	404	1	=	=	SYM
ap-2224	404	2	∫	∫	PROPN
ap-2224	405	1	∞	∞	PROPN
ap-2224	405	2	−∞	−∞	ADP
ap-2224	405	3	e−yu	e−yu	PROPN
ap-2224	405	4	exp(−1	exp(−1	PROPN
ap-2224	405	5	/	/	SYM
ap-2224	405	6	w0(eu	w0(eu	PROPN
ap-2224	405	7	)	)	PUNCT
ap-2224	405	8	)	)	PUNCT
ap-2224	405	9	1	1	NUM
ap-2224	406	1	+	+	X
ap-2224	406	2	w0(eu	w0(eu	X
ap-2224	406	3	)	)	PUNCT
ap-2224	406	4	du	du	PROPN
ap-2224	406	5	,	,	PUNCT
ap-2224	406	6	y	y	PROPN
ap-2224	406	7	>	>	X
ap-2224	406	8	0	0	NUM
ap-2224	406	9	,	,	PUNCT
ap-2224	406	10	(	(	PUNCT
ap-2224	406	11	6.11	6.11	NUM
ap-2224	406	12	)	)	PUNCT
ap-2224	406	13	or	or	CCONJ
ap-2224	406	14	equivalently	equivalently	ADV
ap-2224	406	15	ky(2√y	ky(2√y	NOUN
ap-2224	406	16	)	)	PUNCT
ap-2224	406	17	=	=	SYM
ap-2224	406	18	y−y/2	y−y/2	PROPN
ap-2224	406	19	γ(y	γ(y	PROPN
ap-2224	406	20	)	)	PUNCT
ap-2224	406	21	∫	∫	PROPN
ap-2224	407	1	∞	∞	PROPN
ap-2224	407	2	y	y	PROPN
ap-2224	407	3	k0(2	k0(2	PROPN
ap-2224	407	4	√	√	ADP
ap-2224	407	5	x)(x−	x)(x−	PROPN
ap-2224	408	1	y)y−1	y)y−1	PROPN
ap-2224	408	2	dx	dx	PROPN
ap-2224	408	3	,	,	PUNCT
ap-2224	408	4	y	y	PROPN
ap-2224	408	5	>	>	X
ap-2224	408	6	0	0	NUM
ap-2224	408	7	,	,	PUNCT
ap-2224	408	8	(	(	PUNCT
ap-2224	408	9	6.12	6.12	NUM
ap-2224	408	10	)	)	PUNCT
ap-2224	408	11	because	because	SCONJ
ap-2224	408	12	∫	∫	PROPN
ap-2224	408	13	∞	∞	PROPN
ap-2224	408	14	0	0	NUM
ap-2224	409	1	e−yt	e−yt	PROPN
ap-2224	409	2	e	e	PROPN
ap-2224	409	3	−1	−1	NOUN
ap-2224	409	4	/	/	SYM
ap-2224	409	5	t	t	NOUN
ap-2224	409	6	t	t	NOUN
ap-2224	409	7	dt	dt	NOUN
ap-2224	409	8	=	=	SYM
ap-2224	409	9	2k0(2√y	2k0(2√y	X
ap-2224	409	10	)	)	PUNCT
ap-2224	409	11	,	,	PUNCT
ap-2224	409	12	y	y	PROPN
ap-2224	409	13	>	>	X
ap-2224	409	14	0	0	X
ap-2224	409	15	.	.	PUNCT
ap-2224	410	1	in	in	ADP
ap-2224	410	2	classical	classical	ADJ
ap-2224	410	3	fractional	fractional	ADJ
ap-2224	410	4	calculus	calculus	NOUN
ap-2224	410	5	,	,	PUNCT
ap-2224	410	6	we	we	PRON
ap-2224	410	7	have	have	VERB
ap-2224	410	8	from	from	ADP
ap-2224	410	9	(	(	PUNCT
ap-2224	410	10	6.10	6.10	NUM
ap-2224	410	11	)	)	PUNCT
ap-2224	410	12	the	the	DET
ap-2224	410	13	relation	relation	NOUN
ap-2224	410	14	kν(2√y	kν(2√y	NOUN
ap-2224	410	15	)	)	PUNCT
ap-2224	410	16	=	=	SYM
ap-2224	410	17	y−ν/2	y−ν/2	PROPN
ap-2224	410	18	γ(ν	γ(ν	PROPN
ap-2224	410	19	)	)	PUNCT
ap-2224	411	1	∫	∫	PROPN
ap-2224	412	1	∞	∞	PROPN
ap-2224	412	2	y	y	PROPN
ap-2224	412	3	k0(2	k0(2	PROPN
ap-2224	412	4	√	√	ADP
ap-2224	412	5	x)(x−	x)(x−	PROPN
ap-2224	412	6	y)ν−1	y)ν−1	PROPN
ap-2224	412	7	dx	dx	PROPN
ap-2224	412	8	,	,	PUNCT
ap-2224	412	9	y	y	PROPN
ap-2224	412	10	>	>	X
ap-2224	412	11	0	0	PROPN
ap-2224	412	12	,	,	PUNCT
ap-2224	412	13	ν	ν	X
ap-2224	412	14	>	>	X
ap-2224	412	15	0	0	NUM
ap-2224	412	16	,	,	PUNCT
ap-2224	412	17	(	(	PUNCT
ap-2224	412	18	6.13	6.13	NUM
ap-2224	412	19	)	)	PUNCT
ap-2224	412	20	313	313	NUM
ap-2224	412	21	vladimír	vladimír	PROPN
ap-2224	412	22	vojta	vojta	PROPN
ap-2224	412	23	acta	acta	PROPN
ap-2224	412	24	polytechnica	polytechnica	PROPN
ap-2224	412	25	i.e.	i.e.	ADV
ap-2224	412	26	,	,	PUNCT
ap-2224	412	27	the	the	DET
ap-2224	412	28	modified	modify	VERB
ap-2224	412	29	bessel	bessel	NOUN
ap-2224	412	30	function	function	NOUN
ap-2224	412	31	of	of	ADP
ap-2224	412	32	the	the	DET
ap-2224	412	33	second	second	ADJ
ap-2224	412	34	kind	kind	NOUN
ap-2224	412	35	with	with	ADP
ap-2224	412	36	index	index	NOUN
ap-2224	412	37	ν	ν	NOUN
ap-2224	412	38	is	be	AUX
ap-2224	412	39	given	give	VERB
ap-2224	412	40	by	by	ADP
ap-2224	412	41	the	the	DET
ap-2224	412	42	liouville	liouville	NOUN
ap-2224	412	43	–	–	PUNCT
ap-2224	412	44	weyl	weyl	VERB
ap-2224	412	45	fractional	fractional	ADJ
ap-2224	412	46	integral	integral	ADJ
ap-2224	412	47	of	of	ADP
ap-2224	412	48	order	order	NOUN
ap-2224	412	49	ν	ν	NOUN
ap-2224	412	50	of	of	ADP
ap-2224	412	51	the	the	DET
ap-2224	412	52	modified	modify	VERB
ap-2224	412	53	bessel	bessel	NOUN
ap-2224	412	54	function	function	NOUN
ap-2224	412	55	of	of	ADP
ap-2224	412	56	the	the	DET
ap-2224	412	57	second	second	ADJ
ap-2224	412	58	kind	kind	NOUN
ap-2224	412	59	with	with	ADP
ap-2224	412	60	zero	zero	NUM
ap-2224	412	61	index	index	NOUN
ap-2224	412	62	.	.	PUNCT
ap-2224	413	1	particularly	particularly	ADV
ap-2224	413	2	if	if	SCONJ
ap-2224	413	3	ν	ν	NOUN
ap-2224	413	4	=	=	SYM
ap-2224	413	5	1	1	NUM
ap-2224	413	6	we	we	PRON
ap-2224	413	7	obtain	obtain	VERB
ap-2224	413	8	k1(2√y	k1(2√y	PRON
ap-2224	413	9	)	)	PUNCT
ap-2224	414	1	=	=	SYM
ap-2224	414	2	y−1/2	y−1/2	PROPN
ap-2224	415	1	∫	∫	PROPN
ap-2224	416	1	∞	∞	PROPN
ap-2224	416	2	y	y	PROPN
ap-2224	416	3	k0(2	k0(2	PROPN
ap-2224	416	4	√	√	NUM
ap-2224	416	5	x	x	SYM
ap-2224	416	6	)	)	PUNCT
ap-2224	416	7	dx	dx	PROPN
ap-2224	416	8	,	,	PUNCT
ap-2224	416	9	y	y	PROPN
ap-2224	416	10	>	>	X
ap-2224	416	11	0	0	X
ap-2224	416	12	.	.	PUNCT
ap-2224	417	1	due	due	ADP
ap-2224	417	2	to	to	ADP
ap-2224	417	3	the	the	DET
ap-2224	417	4	semigroup	semigroup	ADJ
ap-2224	417	5	property	property	NOUN
ap-2224	417	6	of	of	ADP
ap-2224	417	7	the	the	DET
ap-2224	417	8	fractional	fractional	ADJ
ap-2224	417	9	integrals	integral	NOUN
ap-2224	417	10	(	(	PUNCT
ap-2224	417	11	additive	additive	ADJ
ap-2224	417	12	index	index	NOUN
ap-2224	417	13	law	law	NOUN
ap-2224	417	14	)	)	PUNCT
ap-2224	418	1	[	[	X
ap-2224	418	2	1	1	X
ap-2224	418	3	]	]	PUNCT
ap-2224	418	4	(	(	PUNCT
ap-2224	418	5	iν+µ	iν+µ	NOUN
ap-2224	418	6	−	−	PROPN
ap-2224	418	7	f	f	NOUN
ap-2224	418	8	)	)	PUNCT
ap-2224	418	9	(	(	PUNCT
ap-2224	418	10	y	y	NOUN
ap-2224	418	11	)	)	PUNCT
ap-2224	418	12	=	=	SYM
ap-2224	418	13	(	(	PUNCT
ap-2224	418	14	iν−(iµ−f	iν−(iµ−f	NOUN
ap-2224	418	15	)	)	PUNCT
ap-2224	418	16	)	)	PUNCT
ap-2224	419	1	(	(	PUNCT
ap-2224	419	2	y	y	NOUN
ap-2224	419	3	)	)	PUNCT
ap-2224	419	4	,	,	PUNCT
ap-2224	419	5	ν	ν	X
ap-2224	419	6	>	>	X
ap-2224	419	7	0	0	NUM
ap-2224	419	8	,	,	PUNCT
ap-2224	419	9	µ	µ	X
ap-2224	419	10	>	>	X
ap-2224	419	11	0	0	NUM
ap-2224	419	12	,	,	PUNCT
ap-2224	419	13	providing	provide	VERB
ap-2224	419	14	that	that	SCONJ
ap-2224	419	15	f	f	PROPN
ap-2224	419	16	(	(	PUNCT
ap-2224	419	17	x	x	X
ap-2224	419	18	)	)	PUNCT
ap-2224	419	19	∈	∈	PROPN
ap-2224	419	20	l1	l1	PROPN
ap-2224	419	21	loc(0,∞	loc(0,∞	PROPN
ap-2224	419	22	)	)	PUNCT
ap-2224	419	23	(	(	PUNCT
ap-2224	419	24	space	space	NOUN
ap-2224	419	25	of	of	ADP
ap-2224	419	26	locally	locally	ADV
ap-2224	419	27	integrable	integrable	ADJ
ap-2224	419	28	functions	function	NOUN
ap-2224	419	29	)	)	PUNCT
ap-2224	419	30	,	,	PUNCT
ap-2224	419	31	we	we	PRON
ap-2224	419	32	can	can	AUX
ap-2224	419	33	rewrite	rewrite	VERB
ap-2224	419	34	(	(	PUNCT
ap-2224	419	35	6.13	6.13	NUM
ap-2224	419	36	)	)	PUNCT
ap-2224	419	37	easily	easily	ADV
ap-2224	419	38	in	in	ADP
ap-2224	419	39	the	the	DET
ap-2224	419	40	form	form	NOUN
ap-2224	419	41	kν+µ(2√y	kν+µ(2√y	PRON
ap-2224	419	42	)	)	PUNCT
ap-2224	420	1	=	=	PUNCT
ap-2224	420	2	y−(ν+µ)/2	y−(ν+µ)/2	PROPN
ap-2224	420	3	γ(ν	γ(ν	PROPN
ap-2224	420	4	)	)	PUNCT
ap-2224	420	5	∫	∫	PROPN
ap-2224	421	1	∞	∞	PROPN
ap-2224	421	2	y	y	PROPN
ap-2224	421	3	xµ/2kµ(2	xµ/2kµ(2	PROPN
ap-2224	421	4	√	√	PROPN
ap-2224	421	5	x)(x−	x)(x−	PROPN
ap-2224	421	6	y)ν−1	y)ν−1	PROPN
ap-2224	421	7	dx	dx	PROPN
ap-2224	421	8	=	=	PROPN
ap-2224	421	9	y−(ν+µ)/2	y−(ν+µ)/2	PROPN
ap-2224	421	10	γ(µ	γ(µ	PROPN
ap-2224	421	11	)	)	PUNCT
ap-2224	421	12	∫	∫	PROPN
ap-2224	422	1	∞	∞	PROPN
ap-2224	422	2	y	y	PROPN
ap-2224	422	3	xν/2kν(2	xν/2kν(2	PROPN
ap-2224	422	4	√	√	PROPN
ap-2224	422	5	x)(x−	x)(x−	PROPN
ap-2224	422	6	y)µ−1	y)µ−1	PROPN
ap-2224	422	7	dx	dx	PROPN
ap-2224	422	8	,	,	PUNCT
ap-2224	422	9	y	y	PROPN
ap-2224	422	10	>	>	X
ap-2224	422	11	0	0	PROPN
ap-2224	422	12	,	,	PUNCT
ap-2224	422	13	ν	ν	X
ap-2224	422	14	>	>	X
ap-2224	422	15	0	0	NUM
ap-2224	422	16	.	.	PUNCT
ap-2224	422	17	(	(	PUNCT
ap-2224	422	18	6.14	6.14	NUM
ap-2224	422	19	)	)	PUNCT
ap-2224	422	20	6.2.4	6.2.4	NUM
ap-2224	422	21	.	.	PUNCT
ap-2224	423	1	bickley	bickley	PROPN
ap-2224	423	2	function	function	VERB
ap-2224	423	3	the	the	DET
ap-2224	423	4	bickley	bickley	PROPN
ap-2224	423	5	function	function	NOUN
ap-2224	423	6	of	of	ADP
ap-2224	423	7	order	order	NOUN
ap-2224	423	8	ν	ν	NOUN
ap-2224	423	9	is	be	AUX
ap-2224	423	10	defined	define	VERB
ap-2224	423	11	by	by	ADP
ap-2224	423	12	the	the	DET
ap-2224	423	13	fractional	fractional	ADJ
ap-2224	423	14	integral	integral	ADJ
ap-2224	423	15	[	[	PUNCT
ap-2224	423	16	11	11	NUM
ap-2224	423	17	,	,	PUNCT
ap-2224	423	18	entry	entry	NOUN
ap-2224	423	19	10.43.11	10.43.11	NUM
ap-2224	423	20	,	,	PUNCT
ap-2224	423	21	p.	p.	NOUN
ap-2224	423	22	259	259	NUM
ap-2224	423	23	]	]	X
ap-2224	423	24	kiν(y	kiν(y	PROPN
ap-2224	423	25	)	)	PUNCT
ap-2224	424	1	=	=	PROPN
ap-2224	424	2	1	1	NUM
ap-2224	424	3	γ(ν	γ(ν	PROPN
ap-2224	424	4	)	)	PUNCT
ap-2224	424	5	∫	∫	PROPN
ap-2224	425	1	∞	∞	PROPN
ap-2224	425	2	y	y	PROPN
ap-2224	425	3	ki0(x)(x−	ki0(x)(x−	PROPN
ap-2224	425	4	y)ν−1	y)ν−1	PROPN
ap-2224	425	5	dx	dx	PROPN
ap-2224	425	6	,	,	PUNCT
ap-2224	425	7	y	y	PROPN
ap-2224	425	8	>	>	X
ap-2224	425	9	0	0	PROPN
ap-2224	425	10	,	,	PUNCT
ap-2224	425	11	ν	ν	X
ap-2224	425	12	>	>	X
ap-2224	425	13	0	0	NUM
ap-2224	425	14	,	,	PUNCT
ap-2224	425	15	(	(	PUNCT
ap-2224	425	16	6.15	6.15	NUM
ap-2224	425	17	)	)	PUNCT
ap-2224	425	18	where	where	SCONJ
ap-2224	425	19	ki0(x	ki0(x	NOUN
ap-2224	425	20	)	)	PUNCT
ap-2224	425	21	=	=	SYM
ap-2224	425	22	k0(x	k0(x	NOUN
ap-2224	425	23	)	)	PUNCT
ap-2224	425	24	.	.	PUNCT
ap-2224	426	1	because	because	SCONJ
ap-2224	426	2	k0(y	k0(y	X
ap-2224	426	3	)	)	PUNCT
ap-2224	426	4	=	=	SYM
ap-2224	426	5	∫	∫	PROPN
ap-2224	426	6	∞	∞	NUM
ap-2224	426	7	1	1	NUM
ap-2224	426	8	e−yu√	e−yu√	NOUN
ap-2224	426	9	u2	u2	NOUN
ap-2224	426	10	−	−	PROPN
ap-2224	426	11	1	1	NUM
ap-2224	426	12	du	du	NOUN
ap-2224	426	13	,	,	PUNCT
ap-2224	426	14	<	<	X
ap-2224	426	15	y	y	X
ap-2224	426	16	>	>	X
ap-2224	426	17	0	0	PROPN
ap-2224	426	18	,	,	PUNCT
ap-2224	426	19	it	it	PRON
ap-2224	426	20	holds	hold	VERB
ap-2224	426	21	that	that	SCONJ
ap-2224	426	22	the	the	DET
ap-2224	426	23	bickley	bickley	NOUN
ap-2224	426	24	function	function	NOUN
ap-2224	426	25	is	be	AUX
ap-2224	426	26	given	give	VERB
ap-2224	426	27	by	by	ADP
ap-2224	426	28	the	the	DET
ap-2224	426	29	laplace	laplace	NOUN
ap-2224	426	30	–	–	PUNCT
ap-2224	426	31	mellin	mellin	NOUN
ap-2224	426	32	transform	transform	NOUN
ap-2224	426	33	kiν(y	kiν(y	PROPN
ap-2224	426	34	)	)	PUNCT
ap-2224	427	1	=	=	SYM
ap-2224	427	2	∫	∫	PROPN
ap-2224	428	1	∞	∞	NUM
ap-2224	428	2	1	1	NUM
ap-2224	428	3	e−yuu−ν√	e−yuu−ν√	PROPN
ap-2224	428	4	u2	u2	NOUN
ap-2224	428	5	−	−	PROPN
ap-2224	428	6	1	1	NUM
ap-2224	428	7	du	du	NOUN
ap-2224	428	8	,	,	PUNCT
ap-2224	428	9	<	<	X
ap-2224	428	10	y	y	X
ap-2224	428	11	>	>	X
ap-2224	428	12	0	0	PROPN
ap-2224	428	13	,	,	PUNCT
ap-2224	428	14	ν	ν	X
ap-2224	428	15	>	>	X
ap-2224	428	16	0	0	NUM
ap-2224	428	17	.	.	PUNCT
ap-2224	428	18	(	(	PUNCT
ap-2224	428	19	6.16	6.16	NUM
ap-2224	428	20	)	)	PUNCT
ap-2224	428	21	from	from	ADP
ap-2224	428	22	(	(	PUNCT
ap-2224	428	23	6.16	6.16	NUM
ap-2224	428	24	)	)	PUNCT
ap-2224	428	25	,	,	PUNCT
ap-2224	428	26	it	it	PRON
ap-2224	428	27	is	be	AUX
ap-2224	428	28	evident	evident	ADJ
ap-2224	428	29	that	that	SCONJ
ap-2224	428	30	the	the	DET
ap-2224	428	31	bickley	bickley	PROPN
ap-2224	428	32	function	function	NOUN
ap-2224	428	33	is	be	AUX
ap-2224	428	34	completely	completely	ADV
ap-2224	428	35	monotone	monotone	ADJ
ap-2224	428	36	in	in	ADP
ap-2224	428	37	y	y	PROPN
ap-2224	428	38	for	for	ADP
ap-2224	428	39	fixed	fix	VERB
ap-2224	428	40	ν	ν	NOUN
ap-2224	428	41	and	and	CCONJ
ap-2224	428	42	completely	completely	ADV
ap-2224	428	43	monotone	monotone	ADJ
ap-2224	428	44	in	in	ADP
ap-2224	428	45	ν	ν	NOUN
ap-2224	428	46	for	for	ADP
ap-2224	428	47	fixed	fix	VERB
ap-2224	428	48	y.	y.	PROPN
ap-2224	428	49	diagonal	diagonal	ADJ
ap-2224	428	50	restriction	restriction	NOUN
ap-2224	428	51	of	of	ADP
ap-2224	428	52	(	(	PUNCT
ap-2224	428	53	6.16	6.16	NUM
ap-2224	428	54	)	)	PUNCT
ap-2224	428	55	in	in	ADP
ap-2224	428	56	the	the	DET
ap-2224	428	57	form	form	NOUN
ap-2224	428	58	of	of	ADP
ap-2224	428	59	the	the	DET
ap-2224	428	60	pure	pure	ADJ
ap-2224	428	61	laplace	laplace	NOUN
ap-2224	428	62	or	or	CCONJ
ap-2224	428	63	mellin	mellin	NOUN
ap-2224	428	64	transform	transform	NOUN
ap-2224	428	65	can	can	AUX
ap-2224	428	66	be	be	AUX
ap-2224	428	67	obtained	obtain	VERB
ap-2224	428	68	very	very	ADV
ap-2224	428	69	simply	simply	ADV
ap-2224	428	70	,	,	PUNCT
ap-2224	428	71	and	and	CCONJ
ap-2224	428	72	is	be	AUX
ap-2224	428	73	not	not	PART
ap-2224	428	74	introduced	introduce	VERB
ap-2224	428	75	here	here	ADV
ap-2224	428	76	.	.	PUNCT
ap-2224	429	1	instead	instead	ADV
ap-2224	429	2	the	the	DET
ap-2224	429	3	mellin	mellin	PROPN
ap-2224	429	4	transform	transform	NOUN
ap-2224	429	5	pair	pair	NOUN
ap-2224	429	6	in	in	ADP
ap-2224	429	7	standard	standard	ADJ
ap-2224	429	8	notation	notation	NOUN
ap-2224	429	9	for	for	ADP
ap-2224	429	10	the	the	DET
ap-2224	429	11	bickley	bickley	PROPN
ap-2224	429	12	function	function	NOUN
ap-2224	429	13	is	be	AUX
ap-2224	429	14	elicited	elicit	VERB
ap-2224	429	15	.	.	PUNCT
ap-2224	430	1	theorem	theorem	VERB
ap-2224	430	2	6.6	6.6	NUM
ap-2224	430	3	.	.	PUNCT
ap-2224	431	1	the	the	DET
ap-2224	431	2	mellin	mellin	PROPN
ap-2224	431	3	transform	transform	NOUN
ap-2224	431	4	of	of	ADP
ap-2224	431	5	the	the	DET
ap-2224	431	6	bickley	bickley	PROPN
ap-2224	431	7	function	function	NOUN
ap-2224	431	8	is	be	AUX
ap-2224	431	9	given	give	VERB
ap-2224	431	10	by	by	ADP
ap-2224	431	11	the	the	DET
ap-2224	431	12	formula∫	formula∫	ADJ
ap-2224	431	13	∞	∞	PROPN
ap-2224	431	14	0	0	NUM
ap-2224	431	15	yp−1kiν(y	yp−1kiν(y	NOUN
ap-2224	431	16	)	)	PUNCT
ap-2224	431	17	dy	dy	NOUN
ap-2224	431	18	=	=	PUNCT
ap-2224	431	19	√	√	PROPN
ap-2224	431	20	π	π	PROPN
ap-2224	431	21	4	4	NUM
ap-2224	431	22	γ(p)γ(p2	γ(p)γ(p2	PRON
ap-2224	431	23	+	+	CCONJ
ap-2224	431	24	ν	ν	NOUN
ap-2224	431	25	2	2	NUM
ap-2224	431	26	)	)	PUNCT
ap-2224	431	27	γ(p2	γ(p2	VERB
ap-2224	432	1	+	+	CCONJ
ap-2224	432	2	ν	ν	NOUN
ap-2224	432	3	2	2	NUM
ap-2224	432	4	+	+	CCONJ
ap-2224	432	5	1	1	NUM
ap-2224	432	6	2	2	NUM
ap-2224	432	7	)	)	PUNCT
ap-2224	432	8	,	,	PUNCT
ap-2224	432	9	<	<	X
ap-2224	432	10	p	p	X
ap-2224	432	11	>	>	X
ap-2224	432	12	0	0	PROPN
ap-2224	432	13	,	,	PUNCT
ap-2224	432	14	ν	ν	X
ap-2224	432	15	>	>	X
ap-2224	432	16	0	0	NUM
ap-2224	432	17	.	.	PUNCT
ap-2224	432	18	(	(	PUNCT
ap-2224	432	19	6.17	6.17	NUM
ap-2224	432	20	)	)	PUNCT
ap-2224	432	21	proof	proof	NOUN
ap-2224	432	22	.	.	PUNCT
ap-2224	433	1	we	we	PRON
ap-2224	433	2	have∫	have∫	VERB
ap-2224	433	3	∞	∞	PROPN
ap-2224	433	4	0	0	NUM
ap-2224	433	5	yp−1kiν(y	yp−1kiν(y	PROPN
ap-2224	433	6	)	)	PUNCT
ap-2224	433	7	dy	dy	NOUN
ap-2224	434	1	=	=	SYM
ap-2224	434	2	∫	∫	PROPN
ap-2224	434	3	∞	∞	NUM
ap-2224	434	4	1	1	NUM
ap-2224	434	5	u−ν√	u−ν√	NOUN
ap-2224	434	6	u2	u2	PROPN
ap-2224	434	7	−	−	PROPN
ap-2224	434	8	1	1	NUM
ap-2224	434	9	∫	∫	NOUN
ap-2224	434	10	∞	∞	NOUN
ap-2224	434	11	0	0	NUM
ap-2224	435	1	yp−1e−yu	yp−1e−yu	PROPN
ap-2224	435	2	dy	dy	X
ap-2224	435	3	du	du	PROPN
ap-2224	435	4	=	=	SYM
ap-2224	435	5	γ(p	γ(p	PROPN
ap-2224	435	6	)	)	PUNCT
ap-2224	435	7	∫	∫	PROPN
ap-2224	436	1	∞	∞	NUM
ap-2224	436	2	1	1	NUM
ap-2224	436	3	u−ν−p√	u−ν−p√	PROPN
ap-2224	436	4	u2	u2	NOUN
ap-2224	436	5	−	−	PROPN
ap-2224	436	6	1	1	NUM
ap-2224	436	7	du	du	NOUN
ap-2224	436	8	=	=	NOUN
ap-2224	436	9	√	√	PROPN
ap-2224	436	10	π	π	PROPN
ap-2224	436	11	4	4	NUM
ap-2224	436	12	γ(p)γ(p2	γ(p)γ(p2	PRON
ap-2224	436	13	+	+	CCONJ
ap-2224	436	14	ν	ν	NOUN
ap-2224	436	15	2	2	NUM
ap-2224	436	16	)	)	PUNCT
ap-2224	436	17	γ(p2	γ(p2	VERB
ap-2224	436	18	+	+	CCONJ
ap-2224	436	19	ν	ν	NOUN
ap-2224	436	20	2	2	NUM
ap-2224	436	21	+	+	CCONJ
ap-2224	436	22	1	1	NUM
ap-2224	436	23	2	2	NUM
ap-2224	436	24	)	)	PUNCT
ap-2224	436	25	,	,	PUNCT
ap-2224	437	1	<	<	X
ap-2224	437	2	p	p	X
ap-2224	437	3	>	>	X
ap-2224	437	4	0	0	PROPN
ap-2224	437	5	,	,	PUNCT
ap-2224	437	6	ν	ν	X
ap-2224	437	7	>	>	X
ap-2224	437	8	0	0	NUM
ap-2224	437	9	,	,	PUNCT
ap-2224	437	10	where	where	SCONJ
ap-2224	437	11	(	(	PUNCT
ap-2224	437	12	6.16	6.16	NUM
ap-2224	437	13	)	)	PUNCT
ap-2224	437	14	and	and	CCONJ
ap-2224	437	15	the	the	DET
ap-2224	437	16	fubini	fubini	ADJ
ap-2224	437	17	theorem	theorem	NOUN
ap-2224	437	18	have	have	AUX
ap-2224	437	19	been	be	AUX
ap-2224	437	20	applied	apply	VERB
ap-2224	437	21	.	.	PUNCT
ap-2224	438	1	the	the	DET
ap-2224	438	2	fact	fact	NOUN
ap-2224	438	3	that	that	SCONJ
ap-2224	438	4	the	the	DET
ap-2224	438	5	region	region	NOUN
ap-2224	438	6	of	of	ADP
ap-2224	438	7	holomorphy	holomorphy	NOUN
ap-2224	438	8	of	of	ADP
ap-2224	438	9	the	the	DET
ap-2224	438	10	mellin	mellin	PROPN
ap-2224	438	11	transform	transform	NOUN
ap-2224	438	12	(	(	PUNCT
ap-2224	438	13	6.17	6.17	NUM
ap-2224	438	14	)	)	PUNCT
ap-2224	438	15	is	be	AUX
ap-2224	438	16	unbounded	unbounde	VERB
ap-2224	438	17	from	from	ADP
ap-2224	438	18	above	above	ADJ
ap-2224	438	19	unveils	unveil	VERB
ap-2224	438	20	that	that	DET
ap-2224	438	21	mn	mn	PROPN
ap-2224	439	1	=	=	SYM
ap-2224	439	2	∫	∫	PROPN
ap-2224	440	1	∞	∞	PROPN
ap-2224	440	2	0	0	NUM
ap-2224	440	3	ynkiν(y	ynkiν(y	PROPN
ap-2224	440	4	)	)	PUNCT
ap-2224	440	5	dy	dy	NOUN
ap-2224	440	6	=	=	PUNCT
ap-2224	440	7	√	√	PROPN
ap-2224	440	8	π	π	PROPN
ap-2224	440	9	4	4	NUM
ap-2224	440	10	γ(n+	γ(n+	NUM
ap-2224	440	11	1)γ(n2	1)γ(n2	NUM
ap-2224	440	12	+	+	CCONJ
ap-2224	440	13	ν	ν	NOUN
ap-2224	440	14	2	2	NUM
ap-2224	440	15	+	+	CCONJ
ap-2224	440	16	1	1	NUM
ap-2224	440	17	2	2	NUM
ap-2224	440	18	)	)	PUNCT
ap-2224	440	19	γ(n2	γ(n2	NOUN
ap-2224	441	1	+	+	CCONJ
ap-2224	441	2	ν	ν	NOUN
ap-2224	441	3	2	2	NUM
ap-2224	441	4	+	+	CCONJ
ap-2224	441	5	1	1	NUM
ap-2224	441	6	)	)	PUNCT
ap-2224	441	7	,	,	PUNCT
ap-2224	441	8	ν	ν	X
ap-2224	441	9	>	>	X
ap-2224	441	10	0	0	NUM
ap-2224	441	11	,	,	PUNCT
ap-2224	441	12	n	n	NOUN
ap-2224	441	13	=	=	SYM
ap-2224	441	14	0	0	NUM
ap-2224	441	15	,	,	PUNCT
ap-2224	441	16	1	1	NUM
ap-2224	441	17	,	,	PUNCT
ap-2224	441	18	2	2	NUM
ap-2224	441	19	,	,	PUNCT
ap-2224	441	20	.	.	PUNCT
ap-2224	441	21	.	.	PUNCT
ap-2224	441	22	.	.	PUNCT
ap-2224	442	1	is	be	AUX
ap-2224	442	2	the	the	DET
ap-2224	442	3	n	n	CCONJ
ap-2224	442	4	-	-	PUNCT
ap-2224	442	5	th	th	VERB
ap-2224	442	6	stieltjes	stieltjes	NOUN
ap-2224	442	7	moment	moment	NOUN
ap-2224	442	8	of	of	ADP
ap-2224	442	9	the	the	DET
ap-2224	442	10	bickley	bickley	PROPN
ap-2224	442	11	function	function	NOUN
ap-2224	442	12	kiν(y	kiν(y	PROPN
ap-2224	442	13	)	)	PUNCT
ap-2224	442	14	.	.	PUNCT
ap-2224	443	1	314	314	NUM
ap-2224	443	2	vol	vol	NOUN
ap-2224	443	3	.	.	PUNCT
ap-2224	444	1	54	54	NUM
ap-2224	444	2	no	no	NOUN
ap-2224	444	3	.	.	PUNCT
ap-2224	445	1	4/2014	4/2014	NUM
ap-2224	445	2	fractional	fractional	ADJ
ap-2224	445	3	calculus	calculus	NOUN
ap-2224	445	4	and	and	CCONJ
ap-2224	445	5	lambert	lambert	PROPN
ap-2224	445	6	function	function	NOUN
ap-2224	445	7	i	i	PRON
ap-2224	445	8	6.3	6.3	NUM
ap-2224	445	9	.	.	PUNCT
ap-2224	446	1	integral	integral	ADJ
ap-2224	446	2	transform	transform	NOUN
ap-2224	446	3	pairs	pair	NOUN
ap-2224	446	4	containing	contain	VERB
ap-2224	446	5	the	the	DET
ap-2224	446	6	lambert	lambert	PROPN
ap-2224	446	7	function	function	NOUN
ap-2224	446	8	we	we	PRON
ap-2224	446	9	use	use	VERB
ap-2224	446	10	(	(	PUNCT
ap-2224	446	11	2.4	2.4	NUM
ap-2224	446	12	)	)	PUNCT
ap-2224	446	13	from	from	ADP
ap-2224	446	14	corollary	corollary	ADJ
ap-2224	446	15	2.4	2.4	NUM
ap-2224	446	16	and	and	CCONJ
ap-2224	446	17	(	(	PUNCT
ap-2224	446	18	2.5	2.5	NUM
ap-2224	446	19	)	)	PUNCT
ap-2224	446	20	from	from	ADP
ap-2224	446	21	corollary	corollary	ADJ
ap-2224	446	22	2.5	2.5	NUM
ap-2224	446	23	.	.	PUNCT
ap-2224	446	24	example	example	NOUN
ap-2224	446	25	6.7	6.7	NUM
ap-2224	446	26	.	.	PUNCT
ap-2224	447	1	let	let	VERB
ap-2224	447	2	h(t	h(t	PRON
ap-2224	447	3	)	)	PUNCT
ap-2224	448	1	=	=	SYM
ap-2224	449	1	t.	t.	NOUN
ap-2224	449	2	then∫	then∫	NOUN
ap-2224	449	3	∞	∞	NUM
ap-2224	449	4	1	1	NUM
ap-2224	449	5	e−yuw0(eu	e−yuw0(eu	NOUN
ap-2224	449	6	)	)	PUNCT
ap-2224	449	7	du	du	PROPN
ap-2224	449	8	=	=	SYM
ap-2224	449	9	∫	∫	PROPN
ap-2224	449	10	∞	∞	PROPN
ap-2224	449	11	e	e	X
ap-2224	449	12	u−y−1w0(u	u−y−1w0(u	NUM
ap-2224	449	13	)	)	PUNCT
ap-2224	449	14	du	du	PROPN
ap-2224	449	15	=	=	SYM
ap-2224	449	16	∫	∫	PROPN
ap-2224	449	17	∞	∞	NUM
ap-2224	449	18	1	1	NUM
ap-2224	449	19	e−ytt−y(1	e−ytt−y(1	NOUN
ap-2224	449	20	+	+	NUM
ap-2224	449	21	t	t	NOUN
ap-2224	449	22	)	)	PUNCT
ap-2224	449	23	dt	dt	NOUN
ap-2224	449	24	=	=	PUNCT
ap-2224	449	25	ey(y	ey(y	X
ap-2224	449	26	)	)	PUNCT
ap-2224	450	1	+	+	CCONJ
ap-2224	450	2	e−y	e−y	ADP
ap-2224	450	3	y	y	PROPN
ap-2224	450	4	,	,	PUNCT
ap-2224	450	5	<	<	X
ap-2224	450	6	y	y	X
ap-2224	450	7	>	>	X
ap-2224	450	8	0	0	NUM
ap-2224	450	9	,	,	PUNCT
ap-2224	450	10	(	(	PUNCT
ap-2224	450	11	6.18)∫	6.18)∫	NOUN
ap-2224	450	12	∞	∞	NOUN
ap-2224	450	13	0	0	NUM
ap-2224	450	14	e−yuw0(eu	e−yuw0(eu	NOUN
ap-2224	450	15	)	)	PUNCT
ap-2224	450	16	du	du	PROPN
ap-2224	450	17	=	=	SYM
ap-2224	450	18	∫	∫	PROPN
ap-2224	450	19	∞	∞	PROPN
ap-2224	450	20	1	1	NUM
ap-2224	450	21	u−y−1w0(u	u−y−1w0(u	NUM
ap-2224	450	22	)	)	PUNCT
ap-2224	450	23	du	du	PROPN
ap-2224	450	24	=	=	SYM
ap-2224	450	25	∫	∫	PROPN
ap-2224	450	26	∞	∞	PROPN
ap-2224	450	27	w0(1	w0(1	PROPN
ap-2224	450	28	)	)	PUNCT
ap-2224	450	29	e−ytt−y(1	e−ytt−y(1	PROPN
ap-2224	451	1	+	+	CCONJ
ap-2224	451	2	t	t	NOUN
ap-2224	451	3	)	)	PUNCT
ap-2224	451	4	dt	dt	NOUN
ap-2224	451	5	=	=	SYM
ap-2224	451	6	w0(1)w0(1)−yey(yw0(1	w0(1)w0(1)−yey(yw0(1	PROPN
ap-2224	451	7	)	)	PUNCT
ap-2224	451	8	)	)	PUNCT
ap-2224	452	1	+	+	CCONJ
ap-2224	452	2	1	1	NUM
ap-2224	452	3	y	y	NOUN
ap-2224	452	4	,	,	PUNCT
ap-2224	452	5	<	<	X
ap-2224	452	6	y	y	X
ap-2224	452	7	>	>	X
ap-2224	452	8	0,∫	0,∫	X
ap-2224	452	9	∞	∞	PROPN
ap-2224	452	10	−∞	−∞	ADP
ap-2224	452	11	e−yuw0(eu	e−yuw0(eu	NOUN
ap-2224	452	12	)	)	PUNCT
ap-2224	452	13	du	du	PROPN
ap-2224	452	14	=	=	SYM
ap-2224	452	15	∫	∫	PROPN
ap-2224	452	16	∞	∞	PROPN
ap-2224	452	17	0	0	NUM
ap-2224	452	18	u−y−1w0(u	u−y−1w0(u	NUM
ap-2224	452	19	)	)	PUNCT
ap-2224	452	20	du	du	PROPN
ap-2224	453	1	=	=	SYM
ap-2224	453	2	∫	∫	PROPN
ap-2224	453	3	∞	∞	PROPN
ap-2224	453	4	0	0	NUM
ap-2224	454	1	e−ytt−y(1	e−ytt−y(1	PROPN
ap-2224	455	1	+	+	NUM
ap-2224	455	2	t	t	NOUN
ap-2224	455	3	)	)	PUNCT
ap-2224	455	4	dt	dt	PUNCT
ap-2224	456	1	=	=	SYM
ap-2224	456	2	yy−2γ(1−	yy−2γ(1−	PROPN
ap-2224	456	3	y	y	PROPN
ap-2224	456	4	)	)	PUNCT
ap-2224	456	5	,	,	PUNCT
ap-2224	456	6	0	0	PUNCT
ap-2224	456	7	<	<	X
ap-2224	456	8	<	<	X
ap-2224	456	9	y	y	X
ap-2224	456	10	<	<	X
ap-2224	456	11	1	1	NUM
ap-2224	456	12	.	.	PUNCT
ap-2224	456	13	(	(	PUNCT
ap-2224	456	14	6.19	6.19	NUM
ap-2224	456	15	)	)	PUNCT
ap-2224	456	16	inversion	inversion	NOUN
ap-2224	456	17	of	of	ADP
ap-2224	456	18	the	the	DET
ap-2224	456	19	mellin	mellin	PROPN
ap-2224	456	20	transform	transform	NOUN
ap-2224	456	21	in	in	ADP
ap-2224	456	22	(	(	PUNCT
ap-2224	456	23	6.18	6.18	NUM
ap-2224	456	24	)	)	PUNCT
ap-2224	456	25	gives	give	VERB
ap-2224	456	26	w0(u	w0(u	PRON
ap-2224	456	27	)	)	PUNCT
ap-2224	456	28	=	=	SYM
ap-2224	457	1	1	1	NUM
ap-2224	457	2	2iπ	2iπ	NOUN
ap-2224	457	3	∫	∫	PROPN
ap-2224	457	4	c+i∞	c+i∞	PROPN
ap-2224	457	5	c−i∞	c−i∞	PROPN
ap-2224	457	6	uy	uy	PROPN
ap-2224	457	7	ey(y	ey(y	PROPN
ap-2224	457	8	)	)	PUNCT
ap-2224	458	1	+	+	CCONJ
ap-2224	458	2	e−y	e−y	PROPN
ap-2224	458	3	y	y	PROPN
ap-2224	458	4	dy	dy	PROPN
ap-2224	458	5	,	,	PUNCT
ap-2224	458	6	c	c	X
ap-2224	458	7	>	>	X
ap-2224	458	8	0	0	PROPN
ap-2224	458	9	,	,	PUNCT
ap-2224	458	10	u	u	NOUN
ap-2224	458	11	>	>	X
ap-2224	458	12	e	e	X
ap-2224	458	13	(	(	PUNCT
ap-2224	458	14	6.20	6.20	NUM
ap-2224	458	15	)	)	PUNCT
ap-2224	458	16	and	and	CCONJ
ap-2224	458	17	inversion	inversion	NOUN
ap-2224	458	18	in	in	ADP
ap-2224	458	19	(	(	PUNCT
ap-2224	458	20	6.19	6.19	NUM
ap-2224	458	21	)	)	PUNCT
ap-2224	458	22	gives	give	VERB
ap-2224	458	23	w0(u	w0(u	PRON
ap-2224	458	24	)	)	PUNCT
ap-2224	458	25	=	=	SYM
ap-2224	459	1	1	1	NUM
ap-2224	459	2	2iπ	2iπ	NOUN
ap-2224	459	3	∫	∫	PROPN
ap-2224	459	4	c+i∞	c+i∞	PROPN
ap-2224	459	5	c−i∞	c−i∞	PROPN
ap-2224	459	6	uyyy−2γ(1−	uyyy−2γ(1−	PROPN
ap-2224	459	7	y	y	PROPN
ap-2224	459	8	)	)	PUNCT
ap-2224	459	9	dy	dy	NOUN
ap-2224	459	10	,	,	PUNCT
ap-2224	459	11	c	c	PROPN
ap-2224	459	12	∈	∈	PROPN
ap-2224	459	13	(	(	PUNCT
ap-2224	459	14	0	0	NUM
ap-2224	459	15	,	,	PUNCT
ap-2224	459	16	1	1	NUM
ap-2224	459	17	)	)	PUNCT
ap-2224	459	18	,	,	PUNCT
ap-2224	459	19	u	u	NOUN
ap-2224	459	20	≥	≥	NOUN
ap-2224	459	21	0	0	NUM
ap-2224	459	22	.	.	PUNCT
ap-2224	460	1	(	(	PUNCT
ap-2224	460	2	6.21	6.21	NUM
ap-2224	460	3	)	)	PUNCT
ap-2224	460	4	this	this	PRON
ap-2224	460	5	is	be	AUX
ap-2224	460	6	a	a	DET
ap-2224	460	7	representation	representation	NOUN
ap-2224	460	8	of	of	ADP
ap-2224	460	9	w0(u	w0(u	NOUN
ap-2224	460	10	)	)	PUNCT
ap-2224	460	11	in	in	ADP
ap-2224	460	12	the	the	DET
ap-2224	460	13	form	form	NOUN
ap-2224	460	14	of	of	ADP
ap-2224	460	15	complex	complex	ADJ
ap-2224	460	16	integrals	integral	NOUN
ap-2224	460	17	.	.	PUNCT
ap-2224	461	1	it	it	PRON
ap-2224	461	2	should	should	AUX
ap-2224	461	3	be	be	AUX
ap-2224	461	4	noted	note	VERB
ap-2224	461	5	,	,	PUNCT
ap-2224	461	6	however	however	ADV
ap-2224	461	7	,	,	PUNCT
ap-2224	461	8	that	that	SCONJ
ap-2224	461	9	the	the	DET
ap-2224	461	10	integral	integral	ADJ
ap-2224	461	11	in	in	ADP
ap-2224	461	12	(	(	PUNCT
ap-2224	461	13	6.20	6.20	NUM
ap-2224	461	14	)	)	PUNCT
ap-2224	461	15	defines	define	VERB
ap-2224	461	16	a	a	DET
ap-2224	461	17	function	function	NOUN
ap-2224	461	18	different	different	ADJ
ap-2224	461	19	from	from	ADP
ap-2224	461	20	the	the	DET
ap-2224	461	21	function	function	NOUN
ap-2224	461	22	defined	define	VERB
ap-2224	461	23	by	by	ADP
ap-2224	461	24	the	the	DET
ap-2224	461	25	integral	integral	ADJ
ap-2224	461	26	in	in	ADP
ap-2224	461	27	(	(	PUNCT
ap-2224	461	28	6.21	6.21	NUM
ap-2224	461	29	)	)	PUNCT
ap-2224	461	30	.	.	PUNCT
ap-2224	462	1	the	the	DET
ap-2224	462	2	two	two	NUM
ap-2224	462	3	functions	function	NOUN
ap-2224	462	4	are	be	AUX
ap-2224	462	5	equivalent	equivalent	ADJ
ap-2224	462	6	for	for	ADP
ap-2224	462	7	u	u	PROPN
ap-2224	462	8	>	>	X
ap-2224	462	9	e.	e.	PROPN
ap-2224	463	1	but	but	CCONJ
ap-2224	463	2	(	(	PUNCT
ap-2224	463	3	6.21	6.21	NUM
ap-2224	463	4	)	)	PUNCT
ap-2224	463	5	is	be	AUX
ap-2224	463	6	equal	equal	ADJ
ap-2224	463	7	to	to	ADP
ap-2224	463	8	w0(u	w0(u	NUM
ap-2224	463	9	)	)	PUNCT
ap-2224	463	10	also	also	ADV
ap-2224	463	11	for	for	ADP
ap-2224	463	12	0	0	NUM
ap-2224	463	13	<	<	X
ap-2224	463	14	u	u	X
ap-2224	463	15	<	<	X
ap-2224	463	16	e	e	NOUN
ap-2224	463	17	,	,	PUNCT
ap-2224	463	18	whereas	whereas	SCONJ
ap-2224	463	19	(	(	PUNCT
ap-2224	463	20	6.20	6.20	NUM
ap-2224	463	21	)	)	PUNCT
ap-2224	463	22	is	be	AUX
ap-2224	463	23	equal	equal	ADJ
ap-2224	463	24	to	to	ADP
ap-2224	463	25	zero	zero	NUM
ap-2224	463	26	for	for	ADP
ap-2224	463	27	0	0	NUM
ap-2224	463	28	<	<	X
ap-2224	463	29	u	u	X
ap-2224	463	30	<	<	X
ap-2224	463	31	e	e	NOUN
ap-2224	463	32	and	and	CCONJ
ap-2224	463	33	to	to	AUX
ap-2224	463	34	w0(e)/2	w0(e)/2	VERB
ap-2224	463	35	for	for	ADP
ap-2224	463	36	u	u	NOUN
ap-2224	463	37	=	=	PROPN
ap-2224	463	38	e.	e.	PROPN
ap-2224	463	39	this	this	PRON
ap-2224	463	40	is	be	AUX
ap-2224	463	41	typical	typical	ADJ
ap-2224	463	42	for	for	ADP
ap-2224	463	43	integration	integration	NOUN
ap-2224	463	44	along	along	ADP
ap-2224	463	45	the	the	DET
ap-2224	463	46	bromwich	bromwich	PROPN
ap-2224	463	47	contour	contour	NOUN
ap-2224	463	48	.	.	PUNCT
ap-2224	464	1	equation	equation	NOUN
ap-2224	464	2	(	(	PUNCT
ap-2224	464	3	6.18	6.18	NUM
ap-2224	464	4	)	)	PUNCT
ap-2224	464	5	is	be	AUX
ap-2224	464	6	compelling	compelling	ADJ
ap-2224	464	7	also	also	ADV
ap-2224	464	8	for	for	ADP
ap-2224	464	9	another	another	DET
ap-2224	464	10	reason	reason	NOUN
ap-2224	464	11	given	give	VERB
ap-2224	464	12	by	by	ADP
ap-2224	464	13	the	the	DET
ap-2224	464	14	following	following	ADJ
ap-2224	464	15	conjecture	conjecture	NOUN
ap-2224	464	16	that	that	PRON
ap-2224	464	17	links	link	VERB
ap-2224	464	18	the	the	DET
ap-2224	464	19	lambert	lambert	PROPN
ap-2224	464	20	function	function	NOUN
ap-2224	464	21	and	and	CCONJ
ap-2224	464	22	the	the	DET
ap-2224	464	23	residue	residue	NOUN
ap-2224	464	24	of	of	ADP
ap-2224	464	25	another	another	DET
ap-2224	464	26	function	function	NOUN
ap-2224	464	27	:	:	PUNCT
ap-2224	464	28	conjecture	conjecture	VERB
ap-2224	464	29	6.8	6.8	NUM
ap-2224	464	30	.	.	PUNCT
ap-2224	465	1	function	function	NOUN
ap-2224	465	2	uy(ey(y	uy(ey(y	PROPN
ap-2224	465	3	)	)	PUNCT
ap-2224	466	1	+	+	CCONJ
ap-2224	466	2	e−y)/y	e−y)/y	PRON
ap-2224	466	3	of	of	ADP
ap-2224	466	4	complex	complex	ADJ
ap-2224	466	5	variable	variable	NOUN
ap-2224	466	6	y	y	PROPN
ap-2224	466	7	∈	∈	PROPN
ap-2224	466	8	c	c	PROPN
ap-2224	466	9	has	have	VERB
ap-2224	466	10	for	for	ADP
ap-2224	466	11	fixed	fix	VERB
ap-2224	466	12	u	u	NOUN
ap-2224	466	13	∈	∈	PROPN
ap-2224	466	14	c	c	NOUN
ap-2224	466	15	only	only	ADV
ap-2224	466	16	one	one	NUM
ap-2224	466	17	singular	singular	ADJ
ap-2224	466	18	point	point	NOUN
ap-2224	466	19	y	y	NOUN
ap-2224	466	20	=	=	PUNCT
ap-2224	466	21	0	0	NUM
ap-2224	466	22	in	in	ADP
ap-2224	466	23	which	which	PRON
ap-2224	466	24	this	this	DET
ap-2224	466	25	function	function	NOUN
ap-2224	466	26	has	have	VERB
ap-2224	466	27	non	non	ADJ
ap-2224	466	28	-	-	ADJ
ap-2224	466	29	removable	removable	ADJ
ap-2224	466	30	point	point	NOUN
ap-2224	466	31	singularity	singularity	NOUN
ap-2224	466	32	.	.	PUNCT
ap-2224	467	1	if	if	SCONJ
ap-2224	467	2	this	this	PRON
ap-2224	467	3	is	be	AUX
ap-2224	467	4	true	true	ADJ
ap-2224	467	5	,	,	PUNCT
ap-2224	467	6	then	then	ADV
ap-2224	467	7	w0(u	w0(u	NUM
ap-2224	467	8	)	)	PUNCT
ap-2224	468	1	=	=	NOUN
ap-2224	468	2	res	re	NOUN
ap-2224	468	3	(	(	PUNCT
ap-2224	468	4	uy	uy	NOUN
ap-2224	468	5	ey(y	ey(y	PROPN
ap-2224	468	6	)	)	PUNCT
ap-2224	469	1	+	+	CCONJ
ap-2224	469	2	e−y	e−y	ADP
ap-2224	469	3	y	y	PROPN
ap-2224	469	4	,	,	PUNCT
ap-2224	469	5	y	y	PROPN
ap-2224	469	6	=	=	NOUN
ap-2224	469	7	0	0	NUM
ap-2224	469	8	)	)	PUNCT
ap-2224	469	9	,	,	PUNCT
ap-2224	469	10	u	u	PROPN
ap-2224	469	11	≥	≥	PROPN
ap-2224	469	12	e.	e.	PROPN
ap-2224	469	13	(	(	PUNCT
ap-2224	469	14	6.22	6.22	NUM
ap-2224	469	15	)	)	PUNCT
ap-2224	469	16	this	this	DET
ap-2224	469	17	formula	formula	NOUN
ap-2224	469	18	is	be	AUX
ap-2224	469	19	a	a	DET
ap-2224	469	20	consequence	consequence	NOUN
ap-2224	469	21	of	of	ADP
ap-2224	469	22	the	the	DET
ap-2224	469	23	cauchy	cauchy	ADJ
ap-2224	469	24	residue	residue	NOUN
ap-2224	469	25	theorem	theorem	NOUN
ap-2224	469	26	and	and	CCONJ
ap-2224	469	27	the	the	DET
ap-2224	469	28	jordan	jordan	PROPN
ap-2224	469	29	lemma	lemma	PROPN
ap-2224	469	30	because	because	SCONJ
ap-2224	469	31	the	the	DET
ap-2224	469	32	bromwich	bromwich	PROPN
ap-2224	469	33	contour	contour	NOUN
ap-2224	469	34	in	in	ADP
ap-2224	469	35	(	(	PUNCT
ap-2224	469	36	6.20	6.20	NUM
ap-2224	469	37	)	)	PUNCT
ap-2224	469	38	can	can	AUX
ap-2224	469	39	be	be	AUX
ap-2224	469	40	closed	close	VERB
ap-2224	469	41	to	to	ADP
ap-2224	469	42	the	the	DET
ap-2224	469	43	left	left	NOUN
ap-2224	469	44	for	for	ADP
ap-2224	469	45	u	u	PROPN
ap-2224	469	46	>	>	X
ap-2224	469	47	e	e	PROPN
ap-2224	469	48	and	and	CCONJ
ap-2224	469	49	c	c	X
ap-2224	469	50	>	>	X
ap-2224	469	51	0	0	X
ap-2224	469	52	.	.	PUNCT
ap-2224	470	1	indeed	indeed	ADV
ap-2224	470	2	,	,	PUNCT
ap-2224	470	3	because	because	SCONJ
ap-2224	470	4	eν(y	eν(y	NUM
ap-2224	470	5	)	)	PUNCT
ap-2224	470	6	∝	∝	PROPN
ap-2224	470	7	e−y	e−y	PROPN
ap-2224	470	8	/	/	SYM
ap-2224	470	9	y	y	PROPN
ap-2224	470	10	,	,	PUNCT
ap-2224	470	11	y	y	PROPN
ap-2224	470	12	→	→	SYM
ap-2224	470	13	∞	∞	NUM
ap-2224	470	14	independently	independently	ADV
ap-2224	470	15	on	on	ADP
ap-2224	470	16	ν	ν	NOUN
ap-2224	470	17	,	,	PUNCT
ap-2224	470	18	it	it	PRON
ap-2224	470	19	holds	hold	VERB
ap-2224	470	20	that	that	SCONJ
ap-2224	470	21	uy(ey(y	uy(ey(y	NOUN
ap-2224	470	22	)	)	PUNCT
ap-2224	471	1	+	+	CCONJ
ap-2224	471	2	e−y)/y	e−y)/y	VERB
ap-2224	471	3	∝	∝	PROPN
ap-2224	471	4	e−y	e−y	PROPN
ap-2224	471	5	/	/	SYM
ap-2224	471	6	y	y	PROPN
ap-2224	471	7	,	,	PUNCT
ap-2224	471	8	y	y	PROPN
ap-2224	471	9	→∞	→∞	PROPN
ap-2224	471	10	and	and	CCONJ
ap-2224	471	11	|uy(ey(y	|uy(ey(y	NUM
ap-2224	471	12	)	)	PUNCT
ap-2224	472	1	+	+	CCONJ
ap-2224	472	2	e−y)/y|	e−y)/y|	PROPN
ap-2224	472	3	→	→	SYM
ap-2224	472	4	0	0	NUM
ap-2224	472	5	for	for	ADP
ap-2224	472	6	|y|	|y|	PROPN
ap-2224	472	7	→	→	SYM
ap-2224	472	8	∞	∞	PROPN
ap-2224	472	9	,	,	PUNCT
ap-2224	472	10	u	u	NOUN
ap-2224	472	11	>	>	X
ap-2224	472	12	e	e	NOUN
ap-2224	472	13	,	,	PUNCT
ap-2224	472	14	<	<	X
ap-2224	472	15	y	y	X
ap-2224	472	16	<	<	X
ap-2224	472	17	c.	c.	PROPN
ap-2224	472	18	this	this	DET
ap-2224	472	19	conjecture	conjecture	NOUN
ap-2224	472	20	is	be	AUX
ap-2224	472	21	supported	support	VERB
ap-2224	472	22	by	by	ADP
ap-2224	472	23	numerical	numerical	ADJ
ap-2224	472	24	experiments	experiment	NOUN
ap-2224	472	25	in	in	ADP
ap-2224	472	26	mathematica	mathematica	PROPN
ap-2224	472	27	®	®	PROPN
ap-2224	472	28	.	.	PROPN
ap-2224	473	1	numerical	numerical	ADJ
ap-2224	473	2	calculation	calculation	NOUN
ap-2224	473	3	of	of	ADP
ap-2224	473	4	the	the	DET
ap-2224	473	5	residue	residue	NOUN
ap-2224	473	6	by	by	ADP
ap-2224	473	7	closed	close	VERB
ap-2224	473	8	contour	contour	NOUN
ap-2224	473	9	integration	integration	NOUN
ap-2224	473	10	in	in	ADP
ap-2224	473	11	the	the	DET
ap-2224	473	12	complex	complex	ADJ
ap-2224	473	13	plane	plane	NOUN
ap-2224	473	14	by	by	ADP
ap-2224	473	15	the	the	DET
ap-2224	473	16	built	build	VERB
ap-2224	473	17	-	-	PUNCT
ap-2224	473	18	in	in	ADP
ap-2224	473	19	nintegrate	nintegrate	ADJ
ap-2224	473	20	function	function	NOUN
ap-2224	473	21	gave	give	VERB
ap-2224	473	22	excellent	excellent	ADJ
ap-2224	473	23	results	result	NOUN
ap-2224	473	24	.	.	PUNCT
ap-2224	474	1	the	the	DET
ap-2224	474	2	laplace	laplace	NOUN
ap-2224	474	3	transform	transform	NOUN
ap-2224	474	4	of	of	ADP
ap-2224	474	5	(	(	PUNCT
ap-2224	474	6	6.21	6.21	NUM
ap-2224	474	7	)	)	PUNCT
ap-2224	474	8	gives	give	VERB
ap-2224	474	9	the	the	DET
ap-2224	474	10	following	follow	VERB
ap-2224	474	11	transform	transform	VERB
ap-2224	474	12	pair	pair	NOUN
ap-2224	474	13	:	:	PUNCT
ap-2224	474	14	theorem	theorem	VERB
ap-2224	474	15	6.9	6.9	NUM
ap-2224	474	16	.	.	PUNCT
ap-2224	475	1	we	we	PRON
ap-2224	475	2	have∫	have∫	VERB
ap-2224	475	3	∞	∞	PROPN
ap-2224	475	4	0	0	NUM
ap-2224	475	5	e−puw0(u	e−puw0(u	PROPN
ap-2224	475	6	)	)	PUNCT
ap-2224	475	7	du	du	NOUN
ap-2224	475	8	=	=	NOUN
ap-2224	476	1	1	1	NUM
ap-2224	476	2	2iπ	2iπ	NOUN
ap-2224	476	3	∫	∫	PROPN
ap-2224	476	4	c+i∞	c+i∞	NOUN
ap-2224	476	5	c−i∞	c−i∞	PROPN
ap-2224	476	6	p−1−yyy−2γ(1−	p−1−yyy−2γ(1−	PROPN
ap-2224	476	7	y)γ(1	y)γ(1	PROPN
ap-2224	476	8	+	+	CCONJ
ap-2224	476	9	y	y	NOUN
ap-2224	476	10	)	)	PUNCT
ap-2224	476	11	dy	dy	NOUN
ap-2224	476	12	=	=	SYM
ap-2224	476	13	1	1	NUM
ap-2224	476	14	2i	2i	NUM
ap-2224	476	15	∫	∫	NOUN
ap-2224	476	16	c+i∞	c+i∞	PROPN
ap-2224	476	17	c−i∞	c−i∞	PROPN
ap-2224	476	18	p−1−y	p−1−y	NOUN
ap-2224	476	19	y	y	PROPN
ap-2224	476	20	y−1	y−1	PROPN
ap-2224	476	21	sin	sin	NOUN
ap-2224	476	22	πy	πy	ADP
ap-2224	476	23	dy	dy	NOUN
ap-2224	476	24	,	,	PUNCT
ap-2224	476	25	<	<	X
ap-2224	476	26	p	p	X
ap-2224	476	27	>	>	X
ap-2224	476	28	0	0	PROPN
ap-2224	476	29	,	,	PUNCT
ap-2224	476	30	c	c	PROPN
ap-2224	476	31	∈	∈	PROPN
ap-2224	476	32	(	(	PUNCT
ap-2224	476	33	0	0	NUM
ap-2224	476	34	,	,	PUNCT
ap-2224	476	35	1	1	NUM
ap-2224	476	36	)	)	PUNCT
ap-2224	476	37	.	.	PUNCT
ap-2224	477	1	(	(	PUNCT
ap-2224	477	2	6.23	6.23	NUM
ap-2224	477	3	)	)	PUNCT
ap-2224	477	4	proof	proof	NOUN
ap-2224	477	5	.	.	PUNCT
ap-2224	478	1	perform	perform	VERB
ap-2224	478	2	the	the	DET
ap-2224	478	3	laplace	laplace	NOUN
ap-2224	478	4	transform	transform	NOUN
ap-2224	478	5	of	of	ADP
ap-2224	478	6	(	(	PUNCT
ap-2224	478	7	6.21	6.21	NUM
ap-2224	478	8	)	)	PUNCT
ap-2224	478	9	and	and	CCONJ
ap-2224	478	10	change	change	VERB
ap-2224	478	11	the	the	DET
ap-2224	478	12	order	order	NOUN
ap-2224	478	13	of	of	ADP
ap-2224	478	14	integration	integration	NOUN
ap-2224	478	15	according	accord	VERB
ap-2224	478	16	to	to	ADP
ap-2224	478	17	the	the	DET
ap-2224	478	18	fubini	fubini	ADJ
ap-2224	478	19	theorem	theorem	NOUN
ap-2224	478	20	.	.	PUNCT
ap-2224	479	1	then	then	ADV
ap-2224	479	2	the	the	DET
ap-2224	479	3	laplace	laplace	NOUN
ap-2224	479	4	transform	transform	NOUN
ap-2224	479	5	of	of	ADP
ap-2224	479	6	the	the	DET
ap-2224	479	7	function	function	NOUN
ap-2224	479	8	φ(u	φ(u	NOUN
ap-2224	479	9	)	)	PUNCT
ap-2224	480	1	=	=	SYM
ap-2224	480	2	uy	uy	NOUN
ap-2224	480	3	is	be	AUX
ap-2224	480	4	p−1−yγ(1	p−1−yγ(1	PROPN
ap-2224	480	5	+	+	CCONJ
ap-2224	480	6	y	y	NOUN
ap-2224	480	7	)	)	PUNCT
ap-2224	480	8	.	.	PUNCT
ap-2224	481	1	the	the	DET
ap-2224	481	2	integrand	integrand	NOUN
ap-2224	481	3	in	in	ADP
ap-2224	481	4	the	the	DET
ap-2224	481	5	second	second	ADJ
ap-2224	481	6	integral	integral	NOUN
ap-2224	481	7	on	on	ADP
ap-2224	481	8	the	the	DET
ap-2224	481	9	right	right	ADJ
ap-2224	481	10	side	side	NOUN
ap-2224	481	11	is	be	AUX
ap-2224	481	12	given	give	VERB
ap-2224	481	13	by	by	ADP
ap-2224	481	14	the	the	DET
ap-2224	481	15	reflection	reflection	NOUN
ap-2224	481	16	formula	formula	NOUN
ap-2224	481	17	γ(1	γ(1	PROPN
ap-2224	482	1	+	+	PUNCT
ap-2224	482	2	y)γ(1−	y)γ(1−	PROPN
ap-2224	482	3	y	y	PROPN
ap-2224	482	4	)	)	PUNCT
ap-2224	482	5	=	=	SYM
ap-2224	482	6	πy/	πy/	NOUN
ap-2224	482	7	sin	sin	NOUN
ap-2224	482	8	πy	πy	NOUN
ap-2224	482	9	.	.	PUNCT
ap-2224	483	1	both	both	DET
ap-2224	483	2	complex	complex	ADJ
ap-2224	483	3	integrals	integral	NOUN
ap-2224	483	4	on	on	ADP
ap-2224	483	5	the	the	DET
ap-2224	483	6	right	right	ADJ
ap-2224	483	7	side	side	NOUN
ap-2224	483	8	of	of	ADP
ap-2224	483	9	(	(	PUNCT
ap-2224	483	10	6.23	6.23	NUM
ap-2224	483	11	)	)	PUNCT
ap-2224	483	12	are	be	AUX
ap-2224	483	13	de	de	X
ap-2224	483	14	facto	facto	X
ap-2224	483	15	bromwich	bromwich	NOUN
ap-2224	483	16	inversion	inversion	NOUN
ap-2224	483	17	integrals	integral	NOUN
ap-2224	483	18	of	of	ADP
ap-2224	483	19	the	the	DET
ap-2224	483	20	mellin	mellin	PROPN
ap-2224	483	21	transform	transform	NOUN
ap-2224	483	22	and	and	CCONJ
ap-2224	483	23	converge	converge	VERB
ap-2224	483	24	for	for	ADP
ap-2224	483	25	all	all	DET
ap-2224	483	26	complex	complex	ADJ
ap-2224	483	27	p	p	NOUN
ap-2224	483	28	except	except	SCONJ
ap-2224	483	29	p	p	PROPN
ap-2224	483	30	=	=	PROPN
ap-2224	483	31	0	0	NUM
ap-2224	483	32	,	,	PUNCT
ap-2224	483	33	while	while	SCONJ
ap-2224	483	34	the	the	DET
ap-2224	483	35	laplace	laplace	NOUN
ap-2224	483	36	integral	integral	ADJ
ap-2224	483	37	on	on	ADP
ap-2224	483	38	the	the	DET
ap-2224	483	39	left	left	ADJ
ap-2224	483	40	side	side	NOUN
ap-2224	483	41	converges	converge	NOUN
ap-2224	483	42	for	for	ADP
ap-2224	483	43	<	<	X
ap-2224	483	44	p	p	X
ap-2224	483	45	>	>	X
ap-2224	483	46	0	0	PUNCT
ap-2224	484	1	only	only	ADV
ap-2224	484	2	.	.	PUNCT
ap-2224	485	1	we	we	PRON
ap-2224	485	2	thus	thus	ADV
ap-2224	485	3	have	have	VERB
ap-2224	485	4	the	the	DET
ap-2224	485	5	analytic	analytic	ADJ
ap-2224	485	6	continuation	continuation	NOUN
ap-2224	485	7	of	of	ADP
ap-2224	485	8	the	the	DET
ap-2224	485	9	function	function	NOUN
ap-2224	485	10	defined	define	VERB
ap-2224	485	11	by	by	ADP
ap-2224	485	12	the	the	DET
ap-2224	485	13	laplace	laplace	NOUN
ap-2224	485	14	integral	integral	ADJ
ap-2224	485	15	on	on	ADP
ap-2224	485	16	the	the	DET
ap-2224	485	17	left	left	NOUN
ap-2224	485	18	to	to	ADP
ap-2224	485	19	the	the	DET
ap-2224	485	20	region	region	NOUN
ap-2224	485	21	c	c	PROPN
ap-2224	485	22	\	\	PROPN
ap-2224	485	23	{	{	PUNCT
ap-2224	485	24	0	0	NUM
ap-2224	485	25	}	}	PUNCT
ap-2224	485	26	.	.	PUNCT
ap-2224	486	1	315	315	NUM
ap-2224	486	2	vladimír	vladimír	PROPN
ap-2224	486	3	vojta	vojta	PROPN
ap-2224	486	4	acta	acta	PROPN
ap-2224	486	5	polytechnica	polytechnica	PROPN
ap-2224	486	6	example	example	NOUN
ap-2224	486	7	6.10	6.10	NUM
ap-2224	486	8	.	.	PUNCT
ap-2224	487	1	let	let	VERB
ap-2224	487	2	h(t	h(t	PRON
ap-2224	487	3	)	)	PUNCT
ap-2224	487	4	=	=	PUNCT
ap-2224	488	1	t/(1	t/(1	PROPN
ap-2224	488	2	+	+	PROPN
ap-2224	488	3	t	t	PROPN
ap-2224	488	4	)	)	PUNCT
ap-2224	488	5	.	.	PUNCT
ap-2224	489	1	then∫	then∫	NOUN
ap-2224	489	2	∞	∞	NUM
ap-2224	489	3	1	1	NUM
ap-2224	489	4	e−yu	e−yu	X
ap-2224	489	5	w0(eu	w0(eu	NOUN
ap-2224	489	6	)	)	PUNCT
ap-2224	489	7	1	1	NUM
ap-2224	490	1	+	+	NOUN
ap-2224	490	2	w0(eu	w0(eu	X
ap-2224	490	3	)	)	PUNCT
ap-2224	490	4	du	du	PROPN
ap-2224	490	5	=	=	SYM
ap-2224	490	6	∫	∫	PROPN
ap-2224	490	7	∞	∞	PROPN
ap-2224	490	8	e	e	X
ap-2224	490	9	u−y−1	u−y−1	PROPN
ap-2224	490	10	w0(u	w0(u	NUM
ap-2224	490	11	)	)	PUNCT
ap-2224	490	12	1	1	NUM
ap-2224	491	1	+	+	PUNCT
ap-2224	491	2	w0(u	w0(u	X
ap-2224	491	3	)	)	PUNCT
ap-2224	491	4	du	du	NOUN
ap-2224	491	5	=	=	SYM
ap-2224	491	6	∫	∫	PROPN
ap-2224	491	7	∞	∞	NUM
ap-2224	491	8	1	1	NUM
ap-2224	491	9	e−ytt−y	e−ytt−y	NOUN
ap-2224	491	10	dt	dt	NOUN
ap-2224	491	11	=	=	SYM
ap-2224	491	12	ey(y	ey(y	X
ap-2224	491	13	)	)	PUNCT
ap-2224	492	1	=	=	SYM
ap-2224	492	2	yy−1γ(1−	yy−1γ(1−	PROPN
ap-2224	492	3	y	y	PROPN
ap-2224	492	4	,	,	PUNCT
ap-2224	492	5	y	y	PROPN
ap-2224	492	6	)	)	PUNCT
ap-2224	492	7	,	,	PUNCT
ap-2224	492	8	<	<	X
ap-2224	492	9	y	y	X
ap-2224	492	10	>	>	X
ap-2224	492	11	0,∫	0,∫	PROPN
ap-2224	492	12	∞	∞	PROPN
ap-2224	492	13	0	0	NUM
ap-2224	492	14	e−yu	e−yu	PROPN
ap-2224	492	15	w0(eu	w0(eu	NOUN
ap-2224	492	16	)	)	PUNCT
ap-2224	492	17	1	1	NUM
ap-2224	493	1	+	+	NOUN
ap-2224	493	2	w0(eu	w0(eu	X
ap-2224	493	3	)	)	PUNCT
ap-2224	493	4	du	du	PROPN
ap-2224	493	5	=	=	SYM
ap-2224	493	6	∫	∫	PROPN
ap-2224	493	7	∞	∞	PROPN
ap-2224	493	8	1	1	NUM
ap-2224	493	9	u−y−1	u−y−1	PROPN
ap-2224	493	10	w0(u	w0(u	NUM
ap-2224	493	11	)	)	PUNCT
ap-2224	493	12	1	1	NUM
ap-2224	494	1	+	+	PUNCT
ap-2224	494	2	w0(u	w0(u	X
ap-2224	494	3	)	)	PUNCT
ap-2224	494	4	du	du	NOUN
ap-2224	494	5	=	=	SYM
ap-2224	494	6	∫	∫	PROPN
ap-2224	494	7	∞	∞	PROPN
ap-2224	494	8	w0(1	w0(1	PROPN
ap-2224	494	9	)	)	PUNCT
ap-2224	495	1	e−ytt−y	e−ytt−y	NOUN
ap-2224	495	2	dt	dt	NOUN
ap-2224	496	1	=	=	SYM
ap-2224	496	2	yy−1γ	yy−1γ	PROPN
ap-2224	496	3	(	(	PUNCT
ap-2224	496	4	1−	1−	NUM
ap-2224	496	5	y	y	PROPN
ap-2224	496	6	,	,	PUNCT
ap-2224	496	7	yw0(1	yw0(1	NUM
ap-2224	496	8	)	)	PUNCT
ap-2224	496	9	)	)	PUNCT
ap-2224	496	10	,	,	PUNCT
ap-2224	496	11	<	<	X
ap-2224	496	12	y	y	X
ap-2224	496	13	>	>	X
ap-2224	496	14	0,∫	0,∫	X
ap-2224	496	15	∞	∞	PROPN
ap-2224	497	1	−∞	−∞	ADP
ap-2224	497	2	e−yu	e−yu	PROPN
ap-2224	497	3	w0(eu	w0(eu	AUX
ap-2224	497	4	)	)	PUNCT
ap-2224	497	5	1	1	NUM
ap-2224	497	6	+	+	NOUN
ap-2224	497	7	w0(eu	w0(eu	X
ap-2224	497	8	)	)	PUNCT
ap-2224	497	9	du	du	PROPN
ap-2224	497	10	=	=	SYM
ap-2224	497	11	∫	∫	PROPN
ap-2224	497	12	∞	∞	PROPN
ap-2224	497	13	0	0	NUM
ap-2224	497	14	u−y−1	u−y−1	PROPN
ap-2224	497	15	w0(u	w0(u	NUM
ap-2224	497	16	)	)	PUNCT
ap-2224	497	17	1	1	NUM
ap-2224	498	1	+	+	PUNCT
ap-2224	498	2	w0(u	w0(u	X
ap-2224	498	3	)	)	PUNCT
ap-2224	498	4	du	du	NOUN
ap-2224	498	5	=	=	SYM
ap-2224	498	6	∫	∫	PROPN
ap-2224	498	7	∞	∞	NOUN
ap-2224	498	8	0	0	NUM
ap-2224	499	1	e−ytt−y	e−ytt−y	NOUN
ap-2224	499	2	dt	dt	X
ap-2224	499	3	=	=	SYM
ap-2224	499	4	−yyγ(−y	−yyγ(−y	PROPN
ap-2224	499	5	)	)	PUNCT
ap-2224	499	6	,	,	PUNCT
ap-2224	499	7	0	0	PUNCT
ap-2224	500	1	<	<	X
ap-2224	500	2	<	<	X
ap-2224	500	3	y	y	X
ap-2224	500	4	<	<	X
ap-2224	500	5	1	1	NUM
ap-2224	500	6	.	.	PUNCT
ap-2224	500	7	example	example	NOUN
ap-2224	500	8	6.11	6.11	NUM
ap-2224	500	9	.	.	PUNCT
ap-2224	501	1	let	let	VERB
ap-2224	501	2	h(t	h(t	PRON
ap-2224	501	3	)	)	PUNCT
ap-2224	502	1	=	=	PUNCT
ap-2224	503	1	1/(1	1/(1	NUM
ap-2224	503	2	+	+	NUM
ap-2224	503	3	t	t	PROPN
ap-2224	503	4	)	)	PUNCT
ap-2224	503	5	.	.	PUNCT
ap-2224	504	1	then∫	then∫	NOUN
ap-2224	504	2	∞	∞	NUM
ap-2224	504	3	1	1	NUM
ap-2224	504	4	e−yu	e−yu	PROPN
ap-2224	504	5	1	1	NUM
ap-2224	504	6	+	+	NOUN
ap-2224	504	7	w0(eu	w0(eu	X
ap-2224	504	8	)	)	PUNCT
ap-2224	504	9	du	du	PROPN
ap-2224	504	10	=	=	SYM
ap-2224	504	11	∫	∫	PROPN
ap-2224	505	1	∞	∞	PROPN
ap-2224	505	2	e	e	PROPN
ap-2224	505	3	u−y−1	u−y−1	PROPN
ap-2224	505	4	1	1	NUM
ap-2224	505	5	+	+	ADJ
ap-2224	505	6	w0(u	w0(u	X
ap-2224	505	7	)	)	PUNCT
ap-2224	505	8	du	du	NOUN
ap-2224	505	9	=	=	SYM
ap-2224	505	10	∫	∫	PROPN
ap-2224	505	11	∞	∞	PROPN
ap-2224	505	12	1	1	NUM
ap-2224	505	13	e−yt	e−yt	PROPN
ap-2224	505	14	t	t	PROPN
ap-2224	505	15	−y	−y	VERB
ap-2224	505	16	t	t	PROPN
ap-2224	505	17	dt	dt	NOUN
ap-2224	506	1	=	=	SYM
ap-2224	506	2	e1+y(y	e1+y(y	X
ap-2224	506	3	)	)	PUNCT
ap-2224	507	1	=	=	SYM
ap-2224	507	2	yyγ(−y	yyγ(−y	PROPN
ap-2224	507	3	,	,	PUNCT
ap-2224	507	4	y	y	NOUN
ap-2224	507	5	)	)	PUNCT
ap-2224	507	6	,	,	PUNCT
ap-2224	507	7	<	<	X
ap-2224	507	8	y	y	X
ap-2224	507	9	>	>	X
ap-2224	507	10	0,∫	0,∫	PROPN
ap-2224	507	11	∞	∞	NUM
ap-2224	507	12	0	0	PUNCT
ap-2224	507	13	e−yu	e−yu	PROPN
ap-2224	507	14	1	1	NUM
ap-2224	507	15	+	+	NOUN
ap-2224	507	16	w0(eu	w0(eu	X
ap-2224	507	17	)	)	PUNCT
ap-2224	507	18	du	du	PROPN
ap-2224	507	19	=	=	SYM
ap-2224	507	20	∫	∫	PROPN
ap-2224	507	21	∞	∞	PROPN
ap-2224	507	22	1	1	NUM
ap-2224	507	23	u−y−1	u−y−1	PROPN
ap-2224	507	24	1	1	NUM
ap-2224	507	25	+	+	NOUN
ap-2224	507	26	w0(u	w0(u	X
ap-2224	507	27	)	)	PUNCT
ap-2224	507	28	du	du	NOUN
ap-2224	507	29	=	=	SYM
ap-2224	507	30	∫	∫	PROPN
ap-2224	508	1	∞	∞	PROPN
ap-2224	508	2	w0(1	w0(1	PROPN
ap-2224	508	3	)	)	PUNCT
ap-2224	509	1	e−yt	e−yt	PROPN
ap-2224	509	2	t	t	PROPN
ap-2224	509	3	−y	−y	VERB
ap-2224	509	4	t	t	PROPN
ap-2224	509	5	dt	dt	NOUN
ap-2224	510	1	=	=	PUNCT
ap-2224	510	2	yyγ	yyγ	PROPN
ap-2224	510	3	(	(	PUNCT
ap-2224	510	4	−y	−y	PROPN
ap-2224	510	5	,	,	PUNCT
ap-2224	510	6	yw0(1	yw0(1	NUM
ap-2224	510	7	)	)	PUNCT
ap-2224	510	8	)	)	PUNCT
ap-2224	510	9	,	,	PUNCT
ap-2224	510	10	<	<	X
ap-2224	510	11	y	y	X
ap-2224	510	12	>	>	X
ap-2224	510	13	0	0	X
ap-2224	510	14	.	.	PUNCT
ap-2224	511	1	moreover	moreover	ADV
ap-2224	511	2	function	function	VERB
ap-2224	511	3	1/(1	1/(1	PROPN
ap-2224	511	4	+	+	NOUN
ap-2224	511	5	w0(eu	w0(eu	NOUN
ap-2224	511	6	)	)	PUNCT
ap-2224	511	7	)	)	PUNCT
ap-2224	511	8	is	be	AUX
ap-2224	511	9	also	also	ADV
ap-2224	511	10	a	a	DET
ap-2224	511	11	laplace	laplace	NOUN
ap-2224	511	12	transform	transform	NOUN
ap-2224	511	13	[	[	X
ap-2224	511	14	14]:∫	14]:∫	NUM
ap-2224	511	15	∞	∞	NUM
ap-2224	511	16	0	0	PUNCT
ap-2224	511	17	e−uxx−x	e−uxx−x	VERB
ap-2224	511	18	sin	sin	NOUN
ap-2224	511	19	πxγ(x	πxγ(x	NOUN
ap-2224	511	20	)	)	PUNCT
ap-2224	511	21	dx	dx	PROPN
ap-2224	512	1	=	=	PUNCT
ap-2224	512	2	π	π	PROPN
ap-2224	512	3	1	1	NUM
ap-2224	512	4	+	+	NOUN
ap-2224	512	5	w0(eu	w0(eu	X
ap-2224	512	6	)	)	PUNCT
ap-2224	512	7	,	,	PUNCT
ap-2224	512	8	u	u	NOUN
ap-2224	512	9	>	>	X
ap-2224	512	10	−1	−1	NOUN
ap-2224	512	11	.	.	PUNCT
ap-2224	513	1	this	this	PRON
ap-2224	513	2	means	mean	VERB
ap-2224	513	3	that	that	SCONJ
ap-2224	513	4	the	the	DET
ap-2224	513	5	following	follow	VERB
ap-2224	513	6	stieltjes	stieltjes	NOUN
ap-2224	513	7	transform	transform	VERB
ap-2224	513	8	pair	pair	NOUN
ap-2224	513	9	holds:∫	holds:∫	NOUN
ap-2224	513	10	∞	∞	PROPN
ap-2224	513	11	0	0	PUNCT
ap-2224	514	1	x−xe−x	x−xe−x	PRON
ap-2224	514	2	sin	sin	PROPN
ap-2224	514	3	πxγ(x	πxγ(x	PROPN
ap-2224	514	4	)	)	PUNCT
ap-2224	514	5	y	y	PROPN
ap-2224	515	1	+	+	NUM
ap-2224	515	2	x	x	SYM
ap-2224	515	3	dx	dx	PROPN
ap-2224	515	4	=	=	SYM
ap-2224	515	5	πeyyyγ(−y	πeyyyγ(−y	PROPN
ap-2224	515	6	,	,	PUNCT
ap-2224	515	7	y	y	PROPN
ap-2224	515	8	)	)	PUNCT
ap-2224	515	9	,	,	PUNCT
ap-2224	515	10	y	y	PROPN
ap-2224	515	11	∈	∈	PROPN
ap-2224	515	12	c	c	X
ap-2224	515	13	\	\	X
ap-2224	515	14	(	(	PUNCT
ap-2224	515	15	−∞	−∞	NOUN
ap-2224	515	16	,	,	PUNCT
ap-2224	515	17	0	0	NUM
ap-2224	515	18	]	]	PUNCT
ap-2224	515	19	,	,	PUNCT
ap-2224	515	20	(	(	PUNCT
ap-2224	515	21	6.24)∫	6.24)∫	NUM
ap-2224	515	22	∞	∞	NUM
ap-2224	515	23	0	0	NUM
ap-2224	516	1	x−x	x−x	PROPN
ap-2224	516	2	sin	sin	VERB
ap-2224	516	3	πxγ(x	πxγ(x	PROPN
ap-2224	516	4	)	)	PUNCT
ap-2224	516	5	y	y	PROPN
ap-2224	517	1	+	+	NUM
ap-2224	517	2	x	x	PUNCT
ap-2224	517	3	dx	dx	PROPN
ap-2224	517	4	=	=	SYM
ap-2224	517	5	πyyγ(−y	πyyγ(−y	PROPN
ap-2224	517	6	,	,	PUNCT
ap-2224	517	7	yw0(1	yw0(1	NUM
ap-2224	517	8	)	)	PUNCT
ap-2224	517	9	)	)	PUNCT
ap-2224	517	10	,	,	PUNCT
ap-2224	517	11	y	y	PROPN
ap-2224	517	12	∈	∈	PROPN
ap-2224	517	13	c	c	X
ap-2224	517	14	\	\	X
ap-2224	517	15	(	(	PUNCT
ap-2224	517	16	−∞	−∞	NOUN
ap-2224	517	17	,	,	PUNCT
ap-2224	517	18	0	0	NUM
ap-2224	517	19	]	]	PUNCT
ap-2224	517	20	.	.	PUNCT
ap-2224	518	1	(	(	PUNCT
ap-2224	518	2	6.25	6.25	NUM
ap-2224	518	3	)	)	PUNCT
ap-2224	518	4	we	we	PRON
ap-2224	518	5	now	now	ADV
ap-2224	518	6	take	take	VERB
ap-2224	518	7	the	the	DET
ap-2224	518	8	finite	finite	ADJ
ap-2224	518	9	laplace	laplace	NOUN
ap-2224	518	10	transform	transform	NOUN
ap-2224	518	11	qx(y	qx(y	NOUN
ap-2224	518	12	)	)	PUNCT
ap-2224	518	13	=	=	SYM
ap-2224	519	1	∫	∫	PROPN
ap-2224	519	2	x+ln	x+ln	NOUN
ap-2224	519	3	x	x	SYM
ap-2224	519	4	1	1	NUM
ap-2224	519	5	e−yu	e−yu	NOUN
ap-2224	519	6	1	1	NUM
ap-2224	519	7	+	+	NOUN
ap-2224	519	8	w0(eu	w0(eu	X
ap-2224	519	9	)	)	PUNCT
ap-2224	519	10	=	=	SYM
ap-2224	520	1	∫	∫	PROPN
ap-2224	520	2	x	x	SYM
ap-2224	520	3	exp	exp	NOUN
ap-2224	520	4	x	x	SYM
ap-2224	520	5	e	e	NOUN
ap-2224	520	6	u−y−1	u−y−1	PROPN
ap-2224	520	7	1	1	NUM
ap-2224	521	1	+	+	ADJ
ap-2224	521	2	w0(u	w0(u	X
ap-2224	521	3	)	)	PUNCT
ap-2224	521	4	du	du	NOUN
ap-2224	521	5	=	=	SYM
ap-2224	521	6	∫	∫	PROPN
ap-2224	521	7	x	x	SYM
ap-2224	521	8	1	1	NUM
ap-2224	521	9	e−yt	e−yt	PROPN
ap-2224	521	10	t	t	PROPN
ap-2224	521	11	−y	−y	VERB
ap-2224	521	12	t	t	NOUN
ap-2224	521	13	dt	dt	NOUN
ap-2224	522	1	=	=	SYM
ap-2224	522	2	yy	yy	PROPN
ap-2224	522	3	(	(	PUNCT
ap-2224	522	4	γ(−y	γ(−y	NOUN
ap-2224	522	5	,	,	PUNCT
ap-2224	522	6	y)−	y)−	PROPN
ap-2224	522	7	γ(−y	γ(−y	NOUN
ap-2224	522	8	,	,	PUNCT
ap-2224	522	9	xy	xy	NOUN
ap-2224	522	10	)	)	PUNCT
ap-2224	522	11	)	)	PUNCT
ap-2224	522	12	,	,	PUNCT
ap-2224	522	13	x	x	X
ap-2224	522	14	>	>	X
ap-2224	522	15	0	0	NUM
ap-2224	522	16	.	.	PUNCT
ap-2224	523	1	because	because	SCONJ
ap-2224	523	2	the	the	DET
ap-2224	523	3	finite	finite	ADJ
ap-2224	523	4	laplace	laplace	NOUN
ap-2224	523	5	transform	transform	NOUN
ap-2224	523	6	is	be	AUX
ap-2224	523	7	an	an	DET
ap-2224	523	8	entire	entire	ADJ
ap-2224	523	9	function	function	NOUN
ap-2224	523	10	in	in	ADP
ap-2224	523	11	the	the	DET
ap-2224	523	12	transform	transform	NOUN
ap-2224	523	13	variable	variable	ADJ
ap-2224	523	14	y	y	PROPN
ap-2224	523	15	it	it	PRON
ap-2224	523	16	holds	hold	VERB
ap-2224	523	17	that	that	SCONJ
ap-2224	523	18	qx(0	qx(0	NOUN
ap-2224	523	19	)	)	PUNCT
ap-2224	524	1	=	=	NOUN
ap-2224	524	2	∫	∫	NOUN
ap-2224	524	3	x	x	SYM
ap-2224	524	4	1	1	NUM
ap-2224	524	5	1	1	NUM
ap-2224	524	6	t	t	NOUN
ap-2224	524	7	dt	dt	NOUN
ap-2224	524	8	=	=	SYM
ap-2224	524	9	ln	ln	PROPN
ap-2224	524	10	x	x	NOUN
ap-2224	524	11	,	,	PUNCT
ap-2224	524	12	which	which	PRON
ap-2224	524	13	means	mean	VERB
ap-2224	524	14	that	that	SCONJ
ap-2224	525	1	lim	lim	PROPN
ap-2224	525	2	y→0	y→0	PROPN
ap-2224	525	3	yy	yy	INTJ
ap-2224	525	4	(	(	PUNCT
ap-2224	525	5	γ(−y	γ(−y	NOUN
ap-2224	525	6	,	,	PUNCT
ap-2224	525	7	y)−	y)−	PROPN
ap-2224	525	8	γ(−y	γ(−y	NOUN
ap-2224	525	9	,	,	PUNCT
ap-2224	525	10	xy	xy	NOUN
ap-2224	525	11	)	)	PUNCT
ap-2224	525	12	)	)	PUNCT
ap-2224	526	1	=	=	PUNCT
ap-2224	527	1	ln	ln	ADJ
ap-2224	527	2	x	x	NOUN
ap-2224	527	3	,	,	PUNCT
ap-2224	527	4	x	x	X
ap-2224	527	5	>	>	X
ap-2224	527	6	0	0	NUM
ap-2224	527	7	,	,	PUNCT
ap-2224	527	8	(	(	PUNCT
ap-2224	527	9	6.26)∫	6.26)∫	NOUN
ap-2224	527	10	a	a	DET
ap-2224	527	11	1	1	NUM
ap-2224	527	12	1	1	NUM
ap-2224	527	13	1	1	NUM
ap-2224	527	14	+	+	NOUN
ap-2224	527	15	w0(eu	w0(eu	X
ap-2224	527	16	)	)	PUNCT
ap-2224	527	17	du	du	PROPN
ap-2224	527	18	=	=	SYM
ap-2224	527	19	lnw0(ea	lnw0(ea	PROPN
ap-2224	527	20	)	)	PUNCT
ap-2224	527	21	=	=	SYM
ap-2224	527	22	a−w0(ea	a−w0(ea	PROPN
ap-2224	527	23	)	)	PUNCT
ap-2224	527	24	.	.	PUNCT
ap-2224	528	1	(	(	PUNCT
ap-2224	528	2	6.27	6.27	NUM
ap-2224	528	3	)	)	PUNCT
ap-2224	528	4	example	example	NOUN
ap-2224	528	5	6.12	6.12	NUM
ap-2224	528	6	.	.	PUNCT
ap-2224	529	1	let	let	VERB
ap-2224	529	2	h(t	h(t	PRON
ap-2224	529	3	)	)	PUNCT
ap-2224	529	4	=	=	PUNCT
ap-2224	530	1	t/(1	t/(1	VERB
ap-2224	530	2	+	+	CCONJ
ap-2224	530	3	t)3	t)3	NOUN
ap-2224	530	4	.	.	PUNCT
ap-2224	531	1	then∫	then∫	NOUN
ap-2224	531	2	∞	∞	PROPN
ap-2224	532	1	−∞	−∞	PUNCT
ap-2224	532	2	e−yu	e−yu	PROPN
ap-2224	532	3	w0(eu	w0(eu	PROPN
ap-2224	532	4	)	)	PUNCT
ap-2224	532	5	(	(	PUNCT
ap-2224	532	6	1	1	NUM
ap-2224	532	7	+	+	ADJ
ap-2224	532	8	w0(eu))3	w0(eu))3	NUM
ap-2224	532	9	=	=	SYM
ap-2224	532	10	∫	∫	PROPN
ap-2224	532	11	∞	∞	PROPN
ap-2224	532	12	0	0	NUM
ap-2224	532	13	u−y−1	u−y−1	PROPN
ap-2224	532	14	w0(u	w0(u	NUM
ap-2224	532	15	)	)	PUNCT
ap-2224	532	16	(	(	PUNCT
ap-2224	532	17	1	1	NUM
ap-2224	532	18	+	+	ADJ
ap-2224	532	19	w0(u))3	w0(u))3	ADJ
ap-2224	532	20	du	du	X
ap-2224	532	21	=	=	SYM
ap-2224	532	22	∫	∫	PROPN
ap-2224	533	1	∞	∞	PROPN
ap-2224	533	2	0	0	NUM
ap-2224	534	1	e−yt	e−yt	PROPN
ap-2224	534	2	t−y	t−y	NOUN
ap-2224	534	3	(	(	PUNCT
ap-2224	534	4	1	1	NUM
ap-2224	534	5	+	+	NUM
ap-2224	534	6	t)2	t)2	NOUN
ap-2224	534	7	dt	dt	NOUN
ap-2224	534	8	=	=	PROPN
ap-2224	534	9	yyγ(1−	yyγ(1−	PROPN
ap-2224	534	10	y	y	PROPN
ap-2224	534	11	)	)	PUNCT
ap-2224	534	12	,	,	PUNCT
ap-2224	534	13	0	0	PUNCT
ap-2224	534	14	<	<	X
ap-2224	534	15	<	<	X
ap-2224	534	16	y	y	X
ap-2224	534	17	<	<	X
ap-2224	534	18	1	1	NUM
ap-2224	534	19	.	.	PUNCT
ap-2224	534	20	(	(	PUNCT
ap-2224	534	21	6.28	6.28	NUM
ap-2224	534	22	)	)	PUNCT
ap-2224	534	23	examples	example	NOUN
ap-2224	534	24	6.7	6.7	NUM
ap-2224	534	25	,	,	PUNCT
ap-2224	534	26	6.10–6.12	6.10–6.12	NUM
ap-2224	534	27	have	have	VERB
ap-2224	534	28	one	one	NUM
ap-2224	534	29	common	common	ADJ
ap-2224	534	30	feature	feature	NOUN
ap-2224	534	31	.	.	PUNCT
ap-2224	535	1	this	this	PRON
ap-2224	535	2	is	be	AUX
ap-2224	535	3	the	the	DET
ap-2224	535	4	function	function	NOUN
ap-2224	535	5	yy	yy	PROPN
ap-2224	535	6	,	,	PUNCT
ap-2224	535	7	first	first	ADV
ap-2224	535	8	studied	study	VERB
ap-2224	535	9	by	by	ADP
ap-2224	535	10	johann	johann	PROPN
ap-2224	535	11	bernoulli	bernoulli	PROPN
ap-2224	535	12	in	in	ADP
ap-2224	535	13	the	the	DET
ap-2224	535	14	17th	17th	ADJ
ap-2224	535	15	century	century	NOUN
ap-2224	535	16	.	.	PUNCT
ap-2224	536	1	it	it	PRON
ap-2224	536	2	is	be	AUX
ap-2224	536	3	known	know	VERB
ap-2224	536	4	that	that	SCONJ
ap-2224	536	5	this	this	DET
ap-2224	536	6	function	function	NOUN
ap-2224	536	7	is	be	AUX
ap-2224	536	8	a	a	DET
ap-2224	536	9	bilateral	bilateral	ADJ
ap-2224	536	10	laplace	laplace	NOUN
ap-2224	536	11	transform	transform	NOUN
ap-2224	536	12	of	of	ADP
ap-2224	536	13	the	the	DET
ap-2224	536	14	landau	landau	NOUN
ap-2224	536	15	probability	probability	NOUN
ap-2224	536	16	density	density	NOUN
ap-2224	536	17	function	function	NOUN
ap-2224	536	18	that	that	PRON
ap-2224	536	19	describes	describe	VERB
ap-2224	536	20	the	the	DET
ap-2224	536	21	energy	energy	NOUN
ap-2224	536	22	loss	loss	NOUN
ap-2224	536	23	of	of	ADP
ap-2224	536	24	a	a	DET
ap-2224	536	25	fast	fast	ADJ
ap-2224	536	26	charged	charge	VERB
ap-2224	536	27	particle	particle	NOUN
ap-2224	536	28	by	by	ADP
ap-2224	536	29	ionization	ionization	NOUN
ap-2224	536	30	while	while	SCONJ
ap-2224	536	31	passing	pass	VERB
ap-2224	536	32	through	through	ADP
ap-2224	536	33	a	a	DET
ap-2224	536	34	thin	thin	ADJ
ap-2224	536	35	layer	layer	NOUN
ap-2224	536	36	of	of	ADP
ap-2224	536	37	a	a	DET
ap-2224	536	38	matter	matter	NOUN
ap-2224	537	1	[	[	X
ap-2224	537	2	14	14	NUM
ap-2224	537	3	]	]	X
ap-2224	537	4	:	:	PUNCT
ap-2224	537	5	yy	yy	X
ap-2224	537	6	=	=	SYM
ap-2224	538	1	∫	∫	PROPN
ap-2224	538	2	∞	∞	PROPN
ap-2224	538	3	−∞	−∞	ADP
ap-2224	538	4	e−yul(u	e−yul(u	NUM
ap-2224	538	5	)	)	PUNCT
ap-2224	538	6	du	du	NOUN
ap-2224	538	7	,	,	PUNCT
ap-2224	538	8	<	<	X
ap-2224	538	9	y	y	X
ap-2224	538	10	>	>	X
ap-2224	538	11	0	0	PROPN
ap-2224	538	12	,	,	PUNCT
ap-2224	538	13	where	where	SCONJ
ap-2224	538	14	l(u	l(u	NOUN
ap-2224	538	15	)	)	PUNCT
ap-2224	539	1	=	=	SYM
ap-2224	540	1	1	1	NUM
ap-2224	540	2	π	π	NOUN
ap-2224	540	3	∫	∫	PROPN
ap-2224	540	4	∞	∞	NUM
ap-2224	540	5	0	0	NUM
ap-2224	540	6	e−uxx−x	e−uxx−x	PROPN
ap-2224	540	7	sin	sin	PROPN
ap-2224	540	8	πxdx	πxdx	PROPN
ap-2224	540	9	,	,	PUNCT
ap-2224	540	10	u	u	X
ap-2224	540	11	>	>	X
ap-2224	540	12	−∞	−∞	PUNCT
ap-2224	540	13	is	be	AUX
ap-2224	540	14	the	the	DET
ap-2224	540	15	landau	landau	NOUN
ap-2224	540	16	p.d.f	p.d.f	ADJ
ap-2224	540	17	.	.	PUNCT
ap-2224	541	1	for	for	ADP
ap-2224	541	2	example	example	NOUN
ap-2224	541	3	,	,	PUNCT
ap-2224	541	4	the	the	DET
ap-2224	541	5	left	left	ADJ
ap-2224	541	6	hand	hand	NOUN
ap-2224	541	7	side	side	NOUN
ap-2224	541	8	yyγ(1	yyγ(1	NOUN
ap-2224	541	9	−	−	PROPN
ap-2224	541	10	y	y	PROPN
ap-2224	541	11	)	)	PUNCT
ap-2224	541	12	,	,	PUNCT
ap-2224	541	13	0	0	PUNCT
ap-2224	541	14	<	<	X
ap-2224	541	15	<	<	X
ap-2224	541	16	y	y	X
ap-2224	541	17	<	<	X
ap-2224	541	18	1	1	NUM
ap-2224	541	19	,	,	PUNCT
ap-2224	541	20	of	of	ADP
ap-2224	541	21	(	(	PUNCT
ap-2224	541	22	6.28	6.28	NUM
ap-2224	541	23	)	)	PUNCT
ap-2224	541	24	is	be	AUX
ap-2224	541	25	a	a	DET
ap-2224	541	26	bilateral	bilateral	ADJ
ap-2224	541	27	laplace	laplace	NOUN
ap-2224	541	28	transform	transform	NOUN
ap-2224	541	29	of	of	ADP
ap-2224	541	30	the	the	DET
ap-2224	541	31	convolution	convolution	NOUN
ap-2224	541	32	∫	∫	PROPN
ap-2224	541	33	∞	∞	PROPN
ap-2224	541	34	−∞	−∞	X
ap-2224	541	35	exp(−ex−t)ex−tl(t	exp(−ex−t)ex−tl(t	PROPN
ap-2224	541	36	)	)	PUNCT
ap-2224	541	37	dt	dt	PROPN
ap-2224	541	38	,	,	PUNCT
ap-2224	541	39	316	316	NUM
ap-2224	541	40	vol	vol	NOUN
ap-2224	541	41	.	.	PUNCT
ap-2224	542	1	54	54	NUM
ap-2224	542	2	no	no	NOUN
ap-2224	542	3	.	.	PUNCT
ap-2224	543	1	4/2014	4/2014	NUM
ap-2224	543	2	fractional	fractional	ADJ
ap-2224	543	3	calculus	calculus	NOUN
ap-2224	543	4	and	and	CCONJ
ap-2224	543	5	lambert	lambert	PROPN
ap-2224	543	6	function	function	NOUN
ap-2224	543	7	i	i	PRON
ap-2224	543	8	and	and	CCONJ
ap-2224	543	9	from	from	ADP
ap-2224	543	10	this	this	PRON
ap-2224	543	11	and	and	CCONJ
ap-2224	543	12	from	from	ADP
ap-2224	543	13	(	(	PUNCT
ap-2224	543	14	6.28	6.28	NUM
ap-2224	543	15	)	)	PUNCT
ap-2224	543	16	it	it	PRON
ap-2224	543	17	follows	follow	VERB
ap-2224	543	18	that∫	that∫	NOUN
ap-2224	543	19	∞	∞	PROPN
ap-2224	543	20	−∞	−∞	X
ap-2224	543	21	exp(−ex−t)ex−tl(t	exp(−ex−t)ex−tl(t	PROPN
ap-2224	543	22	)	)	PUNCT
ap-2224	543	23	dt	dt	NOUN
ap-2224	543	24	=	=	SYM
ap-2224	543	25	w0(ex	w0(ex	NUM
ap-2224	543	26	)	)	PUNCT
ap-2224	543	27	(	(	PUNCT
ap-2224	543	28	1	1	NUM
ap-2224	544	1	+	+	NOUN
ap-2224	544	2	w0(ex))3	w0(ex))3	ADJ
ap-2224	544	3	,	,	PUNCT
ap-2224	544	4	x	x	PROPN
ap-2224	544	5	∈	∈	PROPN
ap-2224	544	6	r.	r.	PROPN
ap-2224	544	7	example	example	NOUN
ap-2224	544	8	6.13	6.13	NUM
ap-2224	544	9	.	.	PUNCT
ap-2224	545	1	let	let	VERB
ap-2224	545	2	h(t	h(t	PRON
ap-2224	545	3	)	)	PUNCT
ap-2224	546	1	=	=	PUNCT
ap-2224	547	1	t2et/(1	t2et/(1	PROPN
ap-2224	547	2	+	+	NUM
ap-2224	547	3	t	t	PROPN
ap-2224	547	4	)	)	PUNCT
ap-2224	547	5	,	,	PUNCT
ap-2224	547	6	t	t	X
ap-2224	547	7	>	>	X
ap-2224	547	8	ln	ln	ADJ
ap-2224	547	9	2	2	X
ap-2224	547	10	.	.	PUNCT
ap-2224	548	1	this	this	DET
ap-2224	548	2	example	example	NOUN
ap-2224	548	3	originates	originate	VERB
ap-2224	548	4	from	from	ADP
ap-2224	548	5	the	the	DET
ap-2224	548	6	theory	theory	NOUN
ap-2224	548	7	of	of	ADP
ap-2224	548	8	the	the	DET
ap-2224	548	9	distribution	distribution	NOUN
ap-2224	548	10	of	of	ADP
ap-2224	548	11	prime	prime	ADJ
ap-2224	548	12	numbers	number	NOUN
ap-2224	548	13	[	[	X
ap-2224	548	14	21	21	NUM
ap-2224	548	15	]	]	PUNCT
ap-2224	548	16	and	and	CCONJ
ap-2224	548	17	consists	consist	VERB
ap-2224	548	18	in	in	ADP
ap-2224	548	19	calculating	calculate	VERB
ap-2224	548	20	the	the	DET
ap-2224	548	21	integral∫	integral∫	NOUN
ap-2224	548	22	∞	∞	PROPN
ap-2224	548	23	ln	ln	PROPN
ap-2224	548	24	2	2	NUM
ap-2224	548	25	t−(y−1)e−(y−1)t	t−(y−1)e−(y−1)t	NOUN
ap-2224	548	26	dt	dt	NOUN
ap-2224	549	1	=	=	SYM
ap-2224	549	2	∫	∫	PROPN
ap-2224	549	3	∞	∞	NUM
ap-2224	549	4	2	2	NUM
ap-2224	549	5	ln	ln	PROPN
ap-2224	549	6	2	2	NUM
ap-2224	549	7	u−y−1	u−y−1	NOUN
ap-2224	549	8	expw0(u	expw0(u	NUM
ap-2224	549	9	)	)	PUNCT
ap-2224	549	10	(	(	PUNCT
ap-2224	549	11	w0(u	w0(u	NOUN
ap-2224	549	12	)	)	PUNCT
ap-2224	549	13	)	)	PUNCT
ap-2224	549	14	2	2	NUM
ap-2224	549	15	1	1	NUM
ap-2224	549	16	+	+	NOUN
ap-2224	549	17	w0(u	w0(u	NOUN
ap-2224	549	18	)	)	PUNCT
ap-2224	549	19	du	du	NOUN
ap-2224	549	20	=	=	SYM
ap-2224	549	21	(	(	PUNCT
ap-2224	549	22	y	y	PROPN
ap-2224	549	23	−	−	PROPN
ap-2224	549	24	1)y−2γ	1)y−2γ	NUM
ap-2224	549	25	(	(	PUNCT
ap-2224	549	26	2−	2−	NUM
ap-2224	549	27	y	y	NOUN
ap-2224	549	28	,	,	PUNCT
ap-2224	549	29	(	(	PUNCT
ap-2224	549	30	y	y	PROPN
ap-2224	549	31	−	−	PROPN
ap-2224	549	32	1	1	X
ap-2224	549	33	)	)	PUNCT
ap-2224	549	34	ln	ln	ADJ
ap-2224	549	35	2	2	NUM
ap-2224	549	36	)	)	PUNCT
ap-2224	549	37	,	,	PUNCT
ap-2224	549	38	<	<	X
ap-2224	549	39	y	y	X
ap-2224	549	40	>	>	X
ap-2224	549	41	1	1	NUM
ap-2224	549	42	.	.	PUNCT
ap-2224	550	1	(	(	PUNCT
ap-2224	550	2	6.29	6.29	NUM
ap-2224	550	3	)	)	PUNCT
ap-2224	550	4	example	example	NOUN
ap-2224	550	5	6.14	6.14	NUM
ap-2224	550	6	.	.	PUNCT
ap-2224	551	1	let	let	VERB
ap-2224	551	2	h(t	h(t	PRON
ap-2224	551	3	)	)	PUNCT
ap-2224	552	1	=	=	PRON
ap-2224	552	2	sin	sin	NOUN
ap-2224	552	3	t.	t.	PROPN
ap-2224	552	4	the	the	DET
ap-2224	552	5	task	task	NOUN
ap-2224	552	6	is	be	AUX
ap-2224	552	7	to	to	PART
ap-2224	552	8	calculate∫	calculate∫	VERB
ap-2224	552	9	∞	∞	PROPN
ap-2224	552	10	−∞	−∞	X
ap-2224	552	11	e−yu	e−yu	PROPN
ap-2224	552	12	sinw0(eu	sinw0(eu	NOUN
ap-2224	552	13	)	)	PUNCT
ap-2224	552	14	du	du	PROPN
ap-2224	552	15	=	=	SYM
ap-2224	552	16	∫	∫	PROPN
ap-2224	552	17	∞	∞	PROPN
ap-2224	552	18	0	0	PROPN
ap-2224	552	19	u−y−1	u−y−1	PROPN
ap-2224	552	20	sinw0(eu	sinw0(eu	NOUN
ap-2224	552	21	)	)	PUNCT
ap-2224	552	22	du	du	NOUN
ap-2224	552	23	.	.	PUNCT
ap-2224	553	1	according	accord	VERB
ap-2224	553	2	to	to	ADP
ap-2224	553	3	corollary	corollary	ADJ
ap-2224	553	4	2.4	2.4	NUM
ap-2224	553	5	,	,	PUNCT
ap-2224	553	6	these	these	DET
ap-2224	553	7	integrals	integral	NOUN
ap-2224	553	8	are	be	AUX
ap-2224	553	9	equal	equal	ADJ
ap-2224	553	10	to∫	to∫	NOUN
ap-2224	553	11	∞	∞	PROPN
ap-2224	553	12	0	0	PUNCT
ap-2224	554	1	e−ytt−y	e−ytt−y	NOUN
ap-2224	554	2	(	(	PUNCT
ap-2224	554	3	1	1	NUM
ap-2224	554	4	+	+	NUM
ap-2224	554	5	t	t	NOUN
ap-2224	554	6	)	)	PUNCT
ap-2224	554	7	sin	sin	NOUN
ap-2224	554	8	t	t	PROPN
ap-2224	554	9	t	t	NOUN
ap-2224	554	10	dt	dt	NOUN
ap-2224	555	1	=	=	SYM
ap-2224	555	2	−1	−1	NOUN
ap-2224	555	3	2	2	NUM
ap-2224	555	4	(	(	PUNCT
ap-2224	555	5	(	(	PUNCT
ap-2224	555	6	y	y	PROPN
ap-2224	555	7	−	−	PROPN
ap-2224	555	8	i)y−1	i)y−1	PROPN
ap-2224	555	9	+	+	CCONJ
ap-2224	555	10	(	(	PUNCT
ap-2224	555	11	y	y	PROPN
ap-2224	555	12	+	+	PROPN
ap-2224	555	13	i)y−1)γ(−y	i)y−1)γ(−y	PROPN
ap-2224	555	14	)	)	PUNCT
ap-2224	555	15	=	=	SYM
ap-2224	556	1	−(y2	−(y2	PRON
ap-2224	556	2	+	+	NUM
ap-2224	556	3	1)(y−1)/2γ(−y	1)(y−1)/2γ(−y	NUM
ap-2224	556	4	)	)	PUNCT
ap-2224	556	5	cos	co	NOUN
ap-2224	556	6	(	(	PUNCT
ap-2224	556	7	(	(	PUNCT
ap-2224	556	8	y	y	PROPN
ap-2224	556	9	−	−	PROPN
ap-2224	556	10	1	1	NUM
ap-2224	556	11	)	)	PUNCT
ap-2224	556	12	arctan	arctan	PROPN
ap-2224	556	13	1	1	NUM
ap-2224	556	14	y	y	PROPN
ap-2224	556	15	)	)	PUNCT
ap-2224	556	16	,	,	PUNCT
ap-2224	556	17	0	0	PUNCT
ap-2224	557	1	<	<	X
ap-2224	557	2	<	<	X
ap-2224	557	3	y	y	X
ap-2224	557	4	<	<	X
ap-2224	557	5	1	1	NUM
ap-2224	557	6	,	,	PUNCT
ap-2224	557	7	where	where	SCONJ
ap-2224	557	8	i	i	PRON
ap-2224	557	9	=	=	VERB
ap-2224	557	10	√	√	NUM
ap-2224	557	11	−1	−1	NOUN
ap-2224	557	12	.	.	PUNCT
ap-2224	558	1	7	7	X
ap-2224	558	2	.	.	X
ap-2224	558	3	eigenproblem	eigenproblem	NOUN
ap-2224	558	4	the	the	DET
ap-2224	558	5	next	next	ADJ
ap-2224	558	6	topic	topic	NOUN
ap-2224	558	7	in	in	ADP
ap-2224	558	8	this	this	DET
ap-2224	558	9	paper	paper	NOUN
ap-2224	558	10	is	be	AUX
ap-2224	558	11	the	the	DET
ap-2224	558	12	problem	problem	NOUN
ap-2224	558	13	of	of	ADP
ap-2224	558	14	real	real	ADJ
ap-2224	558	15	eigenvalues	eigenvalue	NOUN
ap-2224	558	16	and	and	CCONJ
ap-2224	558	17	eigenvectors	eigenvector	NOUN
ap-2224	558	18	in	in	ADP
ap-2224	558	19	either	either	DET
ap-2224	558	20	form	form	NOUN
ap-2224	558	21	:	:	PUNCT
ap-2224	558	22	1	1	NUM
ap-2224	558	23	γ(y	γ(y	PROPN
ap-2224	558	24	)	)	PUNCT
ap-2224	558	25	∫	∫	PROPN
ap-2224	559	1	∞	∞	PROPN
ap-2224	559	2	y	y	PROPN
ap-2224	559	3	f	f	PROPN
ap-2224	559	4	(	(	PUNCT
ap-2224	559	5	x)(x−	x)(x−	PROPN
ap-2224	559	6	y)y−1	y)y−1	NOUN
ap-2224	559	7	dx	dx	PROPN
ap-2224	560	1	=	=	SYM
ap-2224	560	2	λf	λf	PROPN
ap-2224	560	3	(	(	PUNCT
ap-2224	560	4	y	y	NOUN
ap-2224	560	5	)	)	PUNCT
ap-2224	560	6	,	,	PUNCT
ap-2224	560	7	(	(	PUNCT
ap-2224	560	8	7.1	7.1	NUM
ap-2224	560	9	)	)	PUNCT
ap-2224	560	10	µ	µ	PRON
ap-2224	560	11	γ(y	γ(y	PROPN
ap-2224	560	12	)	)	PUNCT
ap-2224	560	13	∫	∫	PROPN
ap-2224	561	1	∞	∞	PROPN
ap-2224	561	2	y	y	PROPN
ap-2224	561	3	f	f	PROPN
ap-2224	561	4	(	(	PUNCT
ap-2224	561	5	x)(x−	x)(x−	PROPN
ap-2224	561	6	y)y−1	y)y−1	NOUN
ap-2224	561	7	dx	dx	PROPN
ap-2224	562	1	=	=	SYM
ap-2224	562	2	f	f	PROPN
ap-2224	562	3	(	(	PUNCT
ap-2224	562	4	y	y	PROPN
ap-2224	562	5	)	)	PUNCT
ap-2224	562	6	.	.	PUNCT
ap-2224	563	1	(	(	PUNCT
ap-2224	563	2	7.2	7.2	NUM
ap-2224	563	3	)	)	PUNCT
ap-2224	563	4	it	it	PRON
ap-2224	563	5	can	can	AUX
ap-2224	563	6	easily	easily	ADV
ap-2224	563	7	be	be	AUX
ap-2224	563	8	shown	show	VERB
ap-2224	563	9	that	that	SCONJ
ap-2224	563	10	f	f	PROPN
ap-2224	563	11	(	(	PUNCT
ap-2224	563	12	y	y	NOUN
ap-2224	563	13	)	)	PUNCT
ap-2224	563	14	=	=	SYM
ap-2224	563	15	e−y	e−y	PROPN
ap-2224	563	16	is	be	AUX
ap-2224	563	17	an	an	DET
ap-2224	563	18	eigenfunction	eigenfunction	NOUN
ap-2224	563	19	of	of	ADP
ap-2224	563	20	the	the	DET
ap-2224	563	21	liouville	liouville	NOUN
ap-2224	563	22	–	–	PUNCT
ap-2224	563	23	weyl	weyl	VERB
ap-2224	563	24	diagonal	diagonal	ADJ
ap-2224	563	25	fractional	fractional	ADJ
ap-2224	563	26	integral	integral	ADJ
ap-2224	563	27	for	for	ADP
ap-2224	563	28	the	the	DET
ap-2224	563	29	eigenvalue	eigenvalue	PROPN
ap-2224	563	30	µ	µ	X
ap-2224	563	31	=	=	SYM
ap-2224	563	32	λ	λ	NOUN
ap-2224	563	33	=	=	NOUN
ap-2224	563	34	1	1	NUM
ap-2224	563	35	.	.	PUNCT
ap-2224	564	1	the	the	DET
ap-2224	564	2	determining	determine	VERB
ap-2224	564	3	function	function	NOUN
ap-2224	564	4	(	(	PUNCT
ap-2224	564	5	original	original	ADJ
ap-2224	564	6	)	)	PUNCT
ap-2224	564	7	f(t	f(t	PROPN
ap-2224	564	8	)	)	PUNCT
ap-2224	564	9	of	of	ADP
ap-2224	564	10	f	f	PROPN
ap-2224	564	11	(	(	PUNCT
ap-2224	564	12	y	y	NOUN
ap-2224	564	13	)	)	PUNCT
ap-2224	564	14	is	be	AUX
ap-2224	564	15	the	the	DET
ap-2224	564	16	dirac	dirac	PROPN
ap-2224	564	17	delta	delta	NOUN
ap-2224	564	18	-	-	PUNCT
ap-2224	564	19	function	function	NOUN
ap-2224	564	20	δ(t−	δ(t−	NOUN
ap-2224	564	21	1	1	NUM
ap-2224	564	22	)	)	PUNCT
ap-2224	564	23	.	.	PUNCT
ap-2224	565	1	there	there	PRON
ap-2224	565	2	exists	exist	VERB
ap-2224	565	3	at	at	ADP
ap-2224	565	4	least	least	ADV
ap-2224	565	5	one	one	NUM
ap-2224	565	6	other	other	ADJ
ap-2224	565	7	real	real	ADJ
ap-2224	565	8	eigenvalue	eigenvalue	NOUN
ap-2224	565	9	.	.	PUNCT
ap-2224	566	1	theorem	theorem	VERB
ap-2224	566	2	7.1	7.1	NUM
ap-2224	566	3	.	.	PUNCT
ap-2224	567	1	we	we	PRON
ap-2224	567	2	have	have	VERB
ap-2224	567	3	that	that	PRON
ap-2224	567	4	λ	λ	NOUN
ap-2224	567	5	=	=	SYM
ap-2224	567	6	1/2	1/2	NUM
ap-2224	567	7	is	be	AUX
ap-2224	567	8	the	the	DET
ap-2224	567	9	eigenvalue	eigenvalue	NOUN
ap-2224	567	10	of	of	ADP
ap-2224	567	11	(	(	PUNCT
ap-2224	567	12	7.1	7.1	NUM
ap-2224	567	13	)	)	PUNCT
ap-2224	567	14	.	.	PUNCT
ap-2224	568	1	proof	proof	NOUN
ap-2224	568	2	.	.	PUNCT
ap-2224	569	1	equation	equation	NOUN
ap-2224	569	2	(	(	PUNCT
ap-2224	569	3	7.1	7.1	NUM
ap-2224	569	4	)	)	PUNCT
ap-2224	569	5	is	be	AUX
ap-2224	569	6	equivalent	equivalent	ADJ
ap-2224	569	7	to∫	to∫	NOUN
ap-2224	569	8	∞	∞	PROPN
ap-2224	569	9	1	1	NUM
ap-2224	569	10	e−yuf	e−yuf	NOUN
ap-2224	569	11	(	(	PUNCT
ap-2224	569	12	w0(eu	w0(eu	PROPN
ap-2224	569	13	)	)	PUNCT
ap-2224	569	14	)	)	PUNCT
ap-2224	569	15	w0(eu	w0(eu	NOUN
ap-2224	569	16	)	)	PUNCT
ap-2224	569	17	1	1	NUM
ap-2224	570	1	+	+	NOUN
ap-2224	570	2	w0(eu	w0(eu	X
ap-2224	570	3	)	)	PUNCT
ap-2224	570	4	du	du	NOUN
ap-2224	570	5	=	=	SYM
ap-2224	570	6	λ	λ	PROPN
ap-2224	570	7	∫	∫	PROPN
ap-2224	570	8	∞	∞	PROPN
ap-2224	570	9	1	1	NUM
ap-2224	570	10	e−yuf(u	e−yuf(u	NUM
ap-2224	570	11	)	)	PUNCT
ap-2224	570	12	du	du	NOUN
ap-2224	570	13	,	,	PUNCT
ap-2224	570	14	(	(	PUNCT
ap-2224	570	15	7.3	7.3	NUM
ap-2224	570	16	)	)	PUNCT
ap-2224	570	17	where	where	SCONJ
ap-2224	570	18	the	the	DET
ap-2224	570	19	lower	low	ADJ
ap-2224	570	20	limit	limit	NOUN
ap-2224	570	21	of	of	ADP
ap-2224	570	22	the	the	DET
ap-2224	570	23	integrals	integral	NOUN
ap-2224	570	24	must	must	AUX
ap-2224	570	25	be	be	AUX
ap-2224	570	26	equal	equal	ADJ
ap-2224	570	27	to	to	ADP
ap-2224	570	28	1	1	NUM
ap-2224	570	29	because	because	SCONJ
ap-2224	570	30	this	this	DET
ap-2224	570	31	value	value	NOUN
ap-2224	570	32	satisfies	satisfy	VERB
ap-2224	570	33	the	the	DET
ap-2224	570	34	requirement	requirement	NOUN
ap-2224	570	35	x	x	X
ap-2224	570	36	=	=	PUNCT
ap-2224	570	37	x+	x+	PROPN
ap-2224	570	38	ln	ln	ADJ
ap-2224	570	39	x	x	NOUN
ap-2224	570	40	,	,	PUNCT
ap-2224	570	41	and	and	CCONJ
ap-2224	570	42	the	the	DET
ap-2224	570	43	laplace	laplace	NOUN
ap-2224	570	44	transform	transform	NOUN
ap-2224	570	45	on	on	ADP
ap-2224	570	46	the	the	DET
ap-2224	570	47	right	right	NOUN
ap-2224	570	48	must	must	AUX
ap-2224	570	49	be	be	AUX
ap-2224	570	50	unilateral	unilateral	ADJ
ap-2224	570	51	,	,	PUNCT
ap-2224	570	52	see	see	VERB
ap-2224	570	53	(	(	PUNCT
ap-2224	570	54	1.2	1.2	NUM
ap-2224	570	55	)	)	PUNCT
ap-2224	570	56	.	.	PUNCT
ap-2224	571	1	in	in	ADP
ap-2224	571	2	this	this	DET
ap-2224	571	3	case	case	NOUN
ap-2224	571	4	,	,	PUNCT
ap-2224	571	5	the	the	DET
ap-2224	571	6	uniqueness	uniqueness	NOUN
ap-2224	571	7	(	(	PUNCT
ap-2224	571	8	lerch	lerch	PROPN
ap-2224	571	9	)	)	PUNCT
ap-2224	571	10	theorem	theorem	VERB
ap-2224	571	11	[	[	X
ap-2224	571	12	10	10	NUM
ap-2224	571	13	]	]	PUNCT
ap-2224	571	14	can	can	AUX
ap-2224	571	15	be	be	AUX
ap-2224	571	16	applied	apply	VERB
ap-2224	571	17	and	and	CCONJ
ap-2224	571	18	the	the	DET
ap-2224	571	19	functional	functional	ADJ
ap-2224	571	20	equation	equation	NOUN
ap-2224	571	21	f	f	X
ap-2224	571	22	(	(	PUNCT
ap-2224	571	23	w0(eu	w0(eu	PROPN
ap-2224	571	24	)	)	PUNCT
ap-2224	571	25	)	)	PUNCT
ap-2224	572	1	=	=	PUNCT
ap-2224	572	2	λf(u)1	λf(u)1	VERB
ap-2224	572	3	+	+	NOUN
ap-2224	572	4	w0(eu	w0(eu	PROPN
ap-2224	572	5	)	)	PUNCT
ap-2224	572	6	w0(eu	w0(eu	PROPN
ap-2224	572	7	)	)	PUNCT
ap-2224	572	8	,	,	PUNCT
ap-2224	572	9	1	1	NUM
ap-2224	572	10	≤	≤	NUM
ap-2224	572	11	u	u	NOUN
ap-2224	572	12	<	<	X
ap-2224	572	13	∞	∞	PROPN
ap-2224	572	14	,	,	PUNCT
ap-2224	572	15	(	(	PUNCT
ap-2224	572	16	7.4	7.4	NUM
ap-2224	572	17	)	)	PUNCT
ap-2224	572	18	is	be	AUX
ap-2224	572	19	to	to	PART
ap-2224	572	20	be	be	AUX
ap-2224	572	21	solved	solve	VERB
ap-2224	572	22	.	.	PUNCT
ap-2224	573	1	according	accord	VERB
ap-2224	573	2	to	to	ADP
ap-2224	573	3	[	[	X
ap-2224	573	4	22	22	NUM
ap-2224	573	5	,	,	PUNCT
ap-2224	573	6	eqs	eqs	X
ap-2224	573	7	.	.	PUNCT
ap-2224	573	8	(	(	PUNCT
ap-2224	573	9	2.3.6)–(2.3.7	2.3.6)–(2.3.7	NOUN
ap-2224	573	10	)	)	PUNCT
ap-2224	573	11	,	,	PUNCT
ap-2224	573	12	p.	p.	NOUN
ap-2224	573	13	63	63	NUM
ap-2224	573	14	]	]	PUNCT
ap-2224	573	15	we	we	PRON
ap-2224	573	16	can	can	AUX
ap-2224	573	17	deduce	deduce	VERB
ap-2224	573	18	that	that	DET
ap-2224	573	19	λ	λ	NOUN
ap-2224	573	20	=	=	SYM
ap-2224	573	21	1/2	1/2	NUM
ap-2224	573	22	(	(	PUNCT
ap-2224	573	23	see	see	VERB
ap-2224	573	24	later	later	ADV
ap-2224	573	25	)	)	PUNCT
ap-2224	573	26	is	be	AUX
ap-2224	573	27	a	a	DET
ap-2224	573	28	necessary	necessary	ADJ
ap-2224	573	29	condition	condition	NOUN
ap-2224	573	30	for	for	ADP
ap-2224	573	31	f(u	f(u	PROPN
ap-2224	573	32	)	)	PUNCT
ap-2224	573	33	being	be	AUX
ap-2224	573	34	a	a	DET
ap-2224	573	35	monotonic	monotonic	ADJ
ap-2224	573	36	solution	solution	NOUN
ap-2224	573	37	of	of	ADP
ap-2224	573	38	(	(	PUNCT
ap-2224	573	39	7.3	7.3	NUM
ap-2224	573	40	):	):	PUNCT
ap-2224	573	41	f(u	f(u	PROPN
ap-2224	573	42	)	)	PUNCT
ap-2224	573	43	=	=	SYM
ap-2224	573	44	f(u0	f(u0	ADJ
ap-2224	573	45	)	)	PUNCT
ap-2224	573	46	∞∏	∞∏	NOUN
ap-2224	573	47	n=0	n=0	ADV
ap-2224	573	48	p(qn(u0	p(qn(u0	NOUN
ap-2224	573	49	)	)	PUNCT
ap-2224	573	50	)	)	PUNCT
ap-2224	573	51	p(qn(u	p(qn(u	NOUN
ap-2224	573	52	)	)	PUNCT
ap-2224	573	53	)	)	PUNCT
ap-2224	573	54	,	,	PUNCT
ap-2224	573	55	(	(	PUNCT
ap-2224	573	56	7.5	7.5	NUM
ap-2224	573	57	)	)	PUNCT
ap-2224	573	58	where	where	SCONJ
ap-2224	573	59	q(u	q(u	NOUN
ap-2224	573	60	)	)	PUNCT
ap-2224	573	61	=	=	SYM
ap-2224	573	62	w0(eu	w0(eu	NOUN
ap-2224	573	63	)	)	PUNCT
ap-2224	573	64	,	,	PUNCT
ap-2224	573	65	qn(u	qn(u	NOUN
ap-2224	573	66	)	)	PUNCT
ap-2224	573	67	is	be	AUX
ap-2224	573	68	the	the	DET
ap-2224	573	69	n	n	ADV
ap-2224	573	70	-	-	PUNCT
ap-2224	573	71	th	th	VERB
ap-2224	573	72	iterate	iterate	NOUN
ap-2224	573	73	(	(	PUNCT
ap-2224	573	74	not	not	PART
ap-2224	573	75	power	power	NOUN
ap-2224	573	76	)	)	PUNCT
ap-2224	573	77	of	of	ADP
ap-2224	573	78	the	the	DET
ap-2224	573	79	function	function	NOUN
ap-2224	573	80	q(u	q(u	PROPN
ap-2224	573	81	)	)	PUNCT
ap-2224	573	82	,	,	PUNCT
ap-2224	573	83	p(u	p(u	NOUN
ap-2224	573	84	)	)	PUNCT
ap-2224	573	85	=	=	PUNCT
ap-2224	574	1	λ(1	λ(1	PROPN
ap-2224	574	2	+	+	NUM
ap-2224	574	3	q(u))/q(u	q(u))/q(u	NUM
ap-2224	574	4	)	)	PUNCT
ap-2224	574	5	and	and	CCONJ
ap-2224	574	6	1	1	NUM
ap-2224	574	7	≤	≤	NOUN
ap-2224	574	8	u0	u0	ADJ
ap-2224	574	9	<	<	X
ap-2224	574	10	∞	∞	PROPN
ap-2224	574	11	is	be	AUX
ap-2224	574	12	fixed	fix	VERB
ap-2224	574	13	.	.	PUNCT
ap-2224	575	1	this	this	PRON
ap-2224	575	2	implies	imply	VERB
ap-2224	575	3	that	that	SCONJ
ap-2224	575	4	the	the	DET
ap-2224	575	5	eigenvalue	eigenvalue	PROPN
ap-2224	575	6	λ	λ	PROPN
ap-2224	575	7	=	=	SYM
ap-2224	575	8	1/2	1/2	NUM
ap-2224	575	9	is	be	AUX
ap-2224	575	10	degenerated	degenerated	ADJ
ap-2224	575	11	.	.	PUNCT
ap-2224	576	1	the	the	DET
ap-2224	576	2	fact	fact	NOUN
ap-2224	576	3	that	that	SCONJ
ap-2224	576	4	limn→∞	limn→∞	PROPN
ap-2224	576	5	qn(u	qn(u	NOUN
ap-2224	576	6	)	)	PUNCT
ap-2224	576	7	=	=	SYM
ap-2224	576	8	1	1	NUM
ap-2224	576	9	,	,	PUNCT
ap-2224	576	10	limn→∞	limn→∞	X
ap-2224	576	11	p(qn(u	p(qn(u	NOUN
ap-2224	576	12	)	)	PUNCT
ap-2224	576	13	)	)	PUNCT
ap-2224	577	1	=	=	SYM
ap-2224	577	2	2λ	2λ	NOUN
ap-2224	577	3	for	for	ADP
ap-2224	577	4	1	1	NUM
ap-2224	577	5	≤	≤	NUM
ap-2224	577	6	u	u	NOUN
ap-2224	577	7	<	<	X
ap-2224	577	8	∞	∞	PROPN
ap-2224	577	9	implies	imply	VERB
ap-2224	577	10	that	that	SCONJ
ap-2224	577	11	λ	λ	NOUN
ap-2224	577	12	must	must	AUX
ap-2224	577	13	be	be	AUX
ap-2224	577	14	equal	equal	ADJ
ap-2224	577	15	to	to	ADP
ap-2224	577	16	1/2	1/2	NUM
ap-2224	577	17	,	,	PUNCT
ap-2224	577	18	because	because	SCONJ
ap-2224	577	19	a	a	DET
ap-2224	577	20	necessary	necessary	ADJ
ap-2224	577	21	condition	condition	NOUN
ap-2224	577	22	for	for	ADP
ap-2224	577	23	(	(	PUNCT
ap-2224	577	24	7.5	7.5	NUM
ap-2224	577	25	)	)	PUNCT
ap-2224	577	26	is	be	AUX
ap-2224	577	27	limn→∞	limn→∞	PROPN
ap-2224	577	28	p(qn(u	p(qn(u	NOUN
ap-2224	577	29	)	)	PUNCT
ap-2224	577	30	)	)	PUNCT
ap-2224	578	1	=	=	SYM
ap-2224	578	2	2λ	2λ	NOUN
ap-2224	578	3	for	for	ADP
ap-2224	578	4	1	1	NUM
ap-2224	578	5	≤	≤	NUM
ap-2224	578	6	u	u	NOUN
ap-2224	578	7	<	<	X
ap-2224	578	8	∞	∞	PROPN
ap-2224	578	9	(	(	PUNCT
ap-2224	578	10	see	see	VERB
ap-2224	578	11	[	[	X
ap-2224	578	12	22	22	NUM
ap-2224	578	13	,	,	PUNCT
ap-2224	578	14	p.	p.	NOUN
ap-2224	578	15	63	63	NUM
ap-2224	578	16	]	]	PUNCT
ap-2224	578	17	)	)	PUNCT
ap-2224	578	18	.	.	PUNCT
ap-2224	579	1	function	function	PROPN
ap-2224	579	2	f(u	f(u	PROPN
ap-2224	579	3	)	)	PUNCT
ap-2224	580	1	in	in	ADP
ap-2224	580	2	(	(	PUNCT
ap-2224	580	3	7.5	7.5	NUM
ap-2224	580	4	)	)	PUNCT
ap-2224	580	5	was	be	AUX
ap-2224	580	6	calculated	calculate	VERB
ap-2224	580	7	numerically	numerically	ADV
ap-2224	580	8	with	with	ADP
ap-2224	580	9	the	the	DET
ap-2224	580	10	aid	aid	NOUN
ap-2224	580	11	of	of	ADP
ap-2224	580	12	the	the	DET
ap-2224	580	13	mathematica	mathematica	PROPN
ap-2224	580	14	function	function	PROPN
ap-2224	580	15	nest	nest	NOUN
ap-2224	580	16	for	for	ADP
ap-2224	580	17	calculating	calculate	VERB
ap-2224	580	18	the	the	DET
ap-2224	580	19	iterate	iterate	NOUN
ap-2224	580	20	of	of	ADP
ap-2224	580	21	the	the	DET
ap-2224	580	22	function	function	NOUN
ap-2224	580	23	.	.	PUNCT
ap-2224	581	1	317	317	NUM
ap-2224	581	2	vladimír	vladimír	PROPN
ap-2224	581	3	vojta	vojta	PROPN
ap-2224	581	4	acta	acta	PROPN
ap-2224	581	5	polytechnica	polytechnica	PROPN
ap-2224	581	6	8	8	NUM
ap-2224	581	7	.	.	PUNCT
ap-2224	582	1	generalization	generalization	NOUN
ap-2224	582	2	the	the	DET
ap-2224	582	3	diagonal	diagonal	ADJ
ap-2224	582	4	fractional	fractional	ADJ
ap-2224	582	5	integral	integral	ADJ
ap-2224	582	6	is	be	AUX
ap-2224	582	7	the	the	DET
ap-2224	582	8	simplest	simple	ADJ
ap-2224	582	9	form	form	NOUN
ap-2224	582	10	of	of	ADP
ap-2224	582	11	the	the	DET
ap-2224	582	12	variable	variable	ADJ
ap-2224	582	13	order	order	NOUN
ap-2224	582	14	fractional	fractional	ADJ
ap-2224	582	15	integral	integral	ADJ
ap-2224	582	16	g(y	g(y	NOUN
ap-2224	582	17	)	)	PUNCT
ap-2224	582	18	=	=	PUNCT
ap-2224	582	19	(	(	PUNCT
ap-2224	582	20	iν(y	iν(y	PROPN
ap-2224	582	21	)	)	PUNCT
ap-2224	583	1	−	−	PROPN
ap-2224	583	2	f	f	PROPN
ap-2224	583	3	)	)	PUNCT
ap-2224	583	4	(	(	PUNCT
ap-2224	583	5	y	y	NOUN
ap-2224	583	6	)	)	PUNCT
ap-2224	583	7	=	=	SYM
ap-2224	583	8	1	1	NUM
ap-2224	583	9	γ(ν(y	γ(ν(y	PROPN
ap-2224	583	10	)	)	PUNCT
ap-2224	583	11	)	)	PUNCT
ap-2224	584	1	∫	∫	PROPN
ap-2224	585	1	∞	∞	PROPN
ap-2224	585	2	y	y	PROPN
ap-2224	585	3	f	f	PROPN
ap-2224	585	4	(	(	PUNCT
ap-2224	585	5	x)(x−y)ν(y)−1	x)(x−y)ν(y)−1	PROPN
ap-2224	585	6	dx	dx	PROPN
ap-2224	585	7	=	=	SYM
ap-2224	585	8	1	1	NUM
ap-2224	585	9	γ(ν(y	γ(ν(y	PROPN
ap-2224	585	10	)	)	PUNCT
ap-2224	585	11	)	)	PUNCT
ap-2224	586	1	∫	∫	PROPN
ap-2224	587	1	∞	∞	PROPN
ap-2224	587	2	0	0	NUM
ap-2224	588	1	f	f	PROPN
ap-2224	588	2	(	(	PUNCT
ap-2224	588	3	u+y)yν(y)−1	u+y)yν(y)−1	NOUN
ap-2224	588	4	du	du	PROPN
ap-2224	588	5	,	,	PUNCT
ap-2224	588	6	<	<	X
ap-2224	588	7	ν(y	ν(y	PROPN
ap-2224	588	8	)	)	PUNCT
ap-2224	588	9	>	>	X
ap-2224	588	10	0	0	X
ap-2224	588	11	.	.	PUNCT
ap-2224	588	12	(	(	PUNCT
ap-2224	588	13	8.1	8.1	NUM
ap-2224	588	14	)	)	PUNCT
ap-2224	588	15	then	then	ADV
ap-2224	588	16	integral	integral	ADJ
ap-2224	588	17	(	(	PUNCT
ap-2224	588	18	8.1	8.1	NUM
ap-2224	588	19	)	)	PUNCT
ap-2224	588	20	is	be	AUX
ap-2224	588	21	equivalent	equivalent	ADJ
ap-2224	588	22	to	to	ADP
ap-2224	588	23	g(y	g(y	NOUN
ap-2224	588	24	)	)	PUNCT
ap-2224	588	25	=	=	SYM
ap-2224	589	1	∫	∫	PROPN
ap-2224	589	2	∞	∞	PROPN
ap-2224	589	3	0	0	NUM
ap-2224	589	4	e−ytt−ν(t)f(t	e−ytt−ν(t)f(t	NOUN
ap-2224	589	5	)	)	PUNCT
ap-2224	589	6	dt	dt	PROPN
ap-2224	589	7	,	,	PUNCT
ap-2224	589	8	(	(	PUNCT
ap-2224	589	9	8.2	8.2	NUM
ap-2224	589	10	)	)	PUNCT
ap-2224	590	1	providing	provide	VERB
ap-2224	590	2	that	that	SCONJ
ap-2224	590	3	f	f	PROPN
ap-2224	590	4	(	(	PUNCT
ap-2224	590	5	x	x	X
ap-2224	590	6	)	)	PUNCT
ap-2224	590	7	is	be	AUX
ap-2224	590	8	a	a	DET
ap-2224	590	9	unilateral	unilateral	ADJ
ap-2224	590	10	laplace	laplace	NOUN
ap-2224	590	11	transform	transform	NOUN
ap-2224	590	12	of	of	ADP
ap-2224	590	13	function	function	NOUN
ap-2224	590	14	f(t	f(t	PROPN
ap-2224	590	15	)	)	PUNCT
ap-2224	590	16	.	.	PUNCT
ap-2224	590	17	example	example	NOUN
ap-2224	591	1	8.1	8.1	NUM
ap-2224	591	2	.	.	PUNCT
ap-2224	592	1	let	let	VERB
ap-2224	592	2	ν(y	ν(y	PROPN
ap-2224	592	3	)	)	PUNCT
ap-2224	593	1	=	=	SYM
ap-2224	593	2	1	1	NUM
ap-2224	593	3	2	2	NUM
ap-2224	593	4	sin	sin	NOUN
ap-2224	593	5	y	y	NOUN
ap-2224	593	6	=	=	PUNCT
ap-2224	593	7	s(y	s(y	PROPN
ap-2224	593	8	)	)	PUNCT
ap-2224	593	9	and	and	CCONJ
ap-2224	593	10	f(t	f(t	NOUN
ap-2224	593	11	)	)	PUNCT
ap-2224	593	12	=	=	SYM
ap-2224	594	1	1	1	X
ap-2224	594	2	.	.	PUNCT
ap-2224	595	1	then	then	ADV
ap-2224	595	2	we	we	PRON
ap-2224	595	3	obtain∫	obtain∫	VERB
ap-2224	595	4	∞	∞	PROPN
ap-2224	595	5	0	0	NUM
ap-2224	595	6	e−ytt−s(y	e−ytt−s(y	NOUN
ap-2224	595	7	)	)	PUNCT
ap-2224	595	8	dt	dt	NOUN
ap-2224	596	1	=	=	SYM
ap-2224	596	2	ys(y)−1γ	ys(y)−1γ	PROPN
ap-2224	596	3	(	(	PUNCT
ap-2224	596	4	1−	1−	NUM
ap-2224	596	5	s(y	s(y	NOUN
ap-2224	596	6	)	)	PUNCT
ap-2224	596	7	)	)	PUNCT
ap-2224	596	8	,	,	PUNCT
ap-2224	596	9	y	y	PROPN
ap-2224	596	10	>	>	X
ap-2224	596	11	0	0	NUM
ap-2224	596	12	,	,	PUNCT
ap-2224	596	13	(	(	PUNCT
ap-2224	596	14	8.3	8.3	NUM
ap-2224	596	15	)	)	PUNCT
ap-2224	596	16	which	which	PRON
ap-2224	596	17	represents	represent	VERB
ap-2224	596	18	values	value	NOUN
ap-2224	596	19	of	of	ADP
ap-2224	596	20	the	the	DET
ap-2224	596	21	fractional	fractional	ADJ
ap-2224	596	22	integral	integral	ADJ
ap-2224	596	23	(	(	PUNCT
ap-2224	596	24	8.1	8.1	NUM
ap-2224	596	25	)	)	PUNCT
ap-2224	596	26	of	of	ADP
ap-2224	596	27	the	the	DET
ap-2224	596	28	function	function	NOUN
ap-2224	596	29	f	f	PROPN
ap-2224	596	30	(	(	PUNCT
ap-2224	596	31	x	x	X
ap-2224	596	32	)	)	PUNCT
ap-2224	596	33	=	=	SYM
ap-2224	596	34	1	1	NUM
ap-2224	596	35	/	/	SYM
ap-2224	596	36	x	x	X
ap-2224	596	37	(	(	PUNCT
ap-2224	596	38	i.e.	i.e.	X
ap-2224	596	39	,	,	PUNCT
ap-2224	596	40	f(t	f(t	NOUN
ap-2224	596	41	)	)	PUNCT
ap-2224	596	42	=	=	SYM
ap-2224	596	43	1	1	NUM
ap-2224	596	44	,	,	PUNCT
ap-2224	596	45	t	t	X
ap-2224	596	46	>	>	X
ap-2224	596	47	0	0	NUM
ap-2224	596	48	)	)	PUNCT
ap-2224	596	49	of	of	ADP
ap-2224	596	50	the	the	DET
ap-2224	596	51	order	order	NOUN
ap-2224	596	52	ν(y	ν(y	PROPN
ap-2224	596	53	)	)	PUNCT
ap-2224	596	54	=	=	SYM
ap-2224	596	55	1	1	NUM
ap-2224	596	56	2	2	NUM
ap-2224	596	57	sin	sin	NOUN
ap-2224	596	58	y	y	PROPN
ap-2224	596	59	in	in	ADP
ap-2224	596	60	regions	region	NOUN
ap-2224	596	61	where	where	SCONJ
ap-2224	596	62	the	the	DET
ap-2224	596	63	sinusoid	sinusoid	NOUN
ap-2224	596	64	has	have	VERB
ap-2224	596	65	non	non	ADJ
ap-2224	596	66	-	-	ADJ
ap-2224	596	67	negative	negative	ADJ
ap-2224	596	68	values	value	NOUN
ap-2224	596	69	and	and	CCONJ
ap-2224	596	70	the	the	DET
ap-2224	596	71	fractional	fractional	ADJ
ap-2224	596	72	derivative	derivative	NOUN
ap-2224	596	73	of	of	ADP
ap-2224	596	74	the	the	DET
ap-2224	596	75	same	same	ADJ
ap-2224	596	76	order	order	NOUN
ap-2224	596	77	of	of	ADP
ap-2224	596	78	the	the	DET
ap-2224	596	79	function	function	NOUN
ap-2224	596	80	f	f	PROPN
ap-2224	596	81	(	(	PUNCT
ap-2224	596	82	x	x	NOUN
ap-2224	596	83	)	)	PUNCT
ap-2224	596	84	,	,	PUNCT
ap-2224	596	85	otherwise	otherwise	ADV
ap-2224	596	86	[	[	X
ap-2224	596	87	23	23	NUM
ap-2224	596	88	]	]	PUNCT
ap-2224	596	89	.	.	PUNCT
ap-2224	597	1	the	the	DET
ap-2224	597	2	connection	connection	NOUN
ap-2224	597	3	to	to	ADP
ap-2224	597	4	the	the	DET
ap-2224	597	5	lambert	lambert	NOUN
ap-2224	597	6	function	function	NOUN
ap-2224	597	7	for	for	ADP
ap-2224	597	8	a	a	DET
ap-2224	597	9	general	general	ADJ
ap-2224	597	10	variable	variable	ADJ
ap-2224	597	11	order	order	NOUN
ap-2224	597	12	fractional	fractional	ADJ
ap-2224	597	13	integral	integral	ADJ
ap-2224	597	14	is	be	AUX
ap-2224	597	15	lost	lose	VERB
ap-2224	597	16	,	,	PUNCT
ap-2224	597	17	but	but	CCONJ
ap-2224	597	18	for	for	ADP
ap-2224	597	19	the	the	DET
ap-2224	597	20	linear	linear	ADJ
ap-2224	597	21	order	order	NOUN
ap-2224	597	22	ν(y	ν(y	NOUN
ap-2224	597	23	)	)	PUNCT
ap-2224	598	1	=	=	PUNCT
ap-2224	599	1	a	a	DET
ap-2224	599	2	+	+	X
ap-2224	599	3	by	by	ADP
ap-2224	599	4	≥	≥	NOUN
ap-2224	599	5	0	0	NUM
ap-2224	599	6	,	,	PUNCT
ap-2224	599	7	equation	equation	NOUN
ap-2224	599	8	(	(	PUNCT
ap-2224	599	9	8.2	8.2	NUM
ap-2224	599	10	)	)	PUNCT
ap-2224	599	11	has	have	VERB
ap-2224	599	12	the	the	DET
ap-2224	599	13	laplace	laplace	NOUN
ap-2224	599	14	transform	transform	VERB
ap-2224	599	15	form∫	form∫	ADJ
ap-2224	599	16	∞	∞	PROPN
ap-2224	599	17	0	0	NUM
ap-2224	600	1	e−ytt−1−byf(t	e−ytt−1−byf(t	NUM
ap-2224	600	2	)	)	PUNCT
ap-2224	600	3	dt	dt	PUNCT
ap-2224	601	1	=	=	SYM
ap-2224	601	2	∫	∫	PROPN
ap-2224	601	3	∞	∞	PROPN
ap-2224	601	4	0	0	NUM
ap-2224	601	5	e−y(t+b	e−y(t+b	PUNCT
ap-2224	601	6	ln	ln	ADJ
ap-2224	601	7	t)t−af(t	t)t−af(t	PROPN
ap-2224	601	8	)	)	PUNCT
ap-2224	601	9	dt	dt	NOUN
ap-2224	602	1	=	=	SYM
ap-2224	602	2	b−a	b−a	X
ap-2224	602	3	∫	∫	PROPN
ap-2224	602	4	∞	∞	PROPN
ap-2224	602	5	−∞	−∞	ADP
ap-2224	602	6	e−yuf	e−yuf	NOUN
ap-2224	602	7	(	(	PUNCT
ap-2224	602	8	bw0(eu	bw0(eu	PROPN
ap-2224	602	9	/	/	SYM
ap-2224	602	10	b	b	NOUN
ap-2224	602	11	/	/	SYM
ap-2224	602	12	b	b	NOUN
ap-2224	602	13	)	)	PUNCT
ap-2224	602	14	)	)	PUNCT
ap-2224	602	15	(	(	PUNCT
ap-2224	602	16	w0(eu	w0(eu	X
ap-2224	602	17	/	/	SYM
ap-2224	602	18	b	b	NOUN
ap-2224	602	19	/	/	SYM
ap-2224	602	20	b))1−a	b))1−a	NUM
ap-2224	602	21	1	1	NUM
ap-2224	602	22	+	+	NOUN
ap-2224	602	23	w0(eu	w0(eu	X
ap-2224	602	24	/	/	SYM
ap-2224	602	25	b	b	NOUN
ap-2224	602	26	/	/	SYM
ap-2224	602	27	b	b	NOUN
ap-2224	602	28	)	)	PUNCT
ap-2224	602	29	du	du	PROPN
ap-2224	602	30	,	,	PUNCT
ap-2224	602	31	y	y	PROPN
ap-2224	602	32	>	>	X
ap-2224	602	33	0	0	PROPN
ap-2224	602	34	.	.	PUNCT
ap-2224	603	1	(	(	PUNCT
ap-2224	603	2	8.4	8.4	NUM
ap-2224	603	3	)	)	PUNCT
ap-2224	603	4	in	in	ADP
ap-2224	603	5	the	the	DET
ap-2224	603	6	case	case	NOUN
ap-2224	603	7	that	that	SCONJ
ap-2224	603	8	a	a	DET
ap-2224	603	9	<	<	X
ap-2224	603	10	0	0	NUM
ap-2224	603	11	and	and	CCONJ
ap-2224	603	12	b	b	NOUN
ap-2224	603	13	>	>	X
ap-2224	603	14	0	0	PUNCT
ap-2224	603	15	there	there	PRON
ap-2224	603	16	exists	exist	VERB
ap-2224	603	17	a	a	DET
ap-2224	603	18	critical	critical	ADJ
ap-2224	603	19	point	point	NOUN
ap-2224	603	20	c	c	NOUN
ap-2224	604	1	=	=	SYM
ap-2224	605	1	−a	−a	PROPN
ap-2224	605	2	/	/	SYM
ap-2224	605	3	b	b	NOUN
ap-2224	605	4	such	such	ADJ
ap-2224	605	5	that	that	PRON
ap-2224	605	6	for	for	ADP
ap-2224	605	7	y	y	PROPN
ap-2224	605	8	>	>	X
ap-2224	605	9	c	c	X
ap-2224	605	10	,	,	PUNCT
ap-2224	605	11	equation	equation	NOUN
ap-2224	605	12	(	(	PUNCT
ap-2224	605	13	8.4	8.4	NUM
ap-2224	605	14	)	)	PUNCT
ap-2224	605	15	represents	represent	VERB
ap-2224	605	16	the	the	DET
ap-2224	605	17	liouville	liouville	NOUN
ap-2224	605	18	–	–	PUNCT
ap-2224	605	19	weyl	weyl	VERB
ap-2224	605	20	fractional	fractional	ADJ
ap-2224	605	21	integral	integral	ADJ
ap-2224	605	22	and	and	CCONJ
ap-2224	605	23	for	for	ADP
ap-2224	605	24	y	y	PROPN
ap-2224	605	25	<	<	X
ap-2224	605	26	c	c	X
ap-2224	605	27	the	the	DET
ap-2224	605	28	liouville	liouville	NOUN
ap-2224	605	29	–	–	PUNCT
ap-2224	605	30	weyl	weyl	VERB
ap-2224	605	31	fractional	fractional	ADJ
ap-2224	605	32	derivative	derivative	NOUN
ap-2224	606	1	[	[	X
ap-2224	606	2	23	23	NUM
ap-2224	606	3	]	]	PUNCT
ap-2224	606	4	.	.	PUNCT
ap-2224	607	1	the	the	DET
ap-2224	607	2	same	same	ADJ
ap-2224	607	3	critical	critical	ADJ
ap-2224	607	4	point	point	NOUN
ap-2224	607	5	c	c	NOUN
ap-2224	607	6	=	=	SYM
ap-2224	607	7	−a	−a	PROPN
ap-2224	607	8	/	/	SYM
ap-2224	607	9	b	b	NOUN
ap-2224	607	10	exists	exist	VERB
ap-2224	607	11	for	for	ADP
ap-2224	607	12	a	a	DET
ap-2224	607	13	>	>	X
ap-2224	607	14	0	0	NUM
ap-2224	607	15	and	and	CCONJ
ap-2224	607	16	b	b	X
ap-2224	607	17	<	<	X
ap-2224	607	18	0	0	NUM
ap-2224	607	19	.	.	PUNCT
ap-2224	608	1	in	in	ADP
ap-2224	608	2	that	that	DET
ap-2224	608	3	case	case	NOUN
ap-2224	608	4	(	(	PUNCT
ap-2224	608	5	8.4	8.4	NUM
ap-2224	608	6	)	)	PUNCT
ap-2224	608	7	represents	represent	VERB
ap-2224	608	8	fractional	fractional	ADJ
ap-2224	608	9	integral	integral	ADJ
ap-2224	608	10	for	for	ADP
ap-2224	608	11	y	y	PROPN
ap-2224	608	12	<	<	X
ap-2224	608	13	c	c	PROPN
ap-2224	608	14	and	and	CCONJ
ap-2224	608	15	fractional	fractional	ADJ
ap-2224	608	16	derivative	derivative	NOUN
ap-2224	608	17	for	for	ADP
ap-2224	608	18	y	y	PROPN
ap-2224	608	19	>	>	X
ap-2224	608	20	c.	c.	PROPN
ap-2224	608	21	example	example	NOUN
ap-2224	608	22	8.2	8.2	NUM
ap-2224	608	23	.	.	PUNCT
ap-2224	609	1	let	let	VERB
ap-2224	609	2	f(t	f(t	NOUN
ap-2224	609	3	)	)	PUNCT
ap-2224	610	1	=	=	PUNCT
ap-2224	610	2	sin	sin	PROPN
ap-2224	610	3	t	t	PROPN
ap-2224	610	4	,	,	PUNCT
ap-2224	610	5	a	a	DET
ap-2224	610	6	=	=	X
ap-2224	610	7	−3	−3	PROPN
ap-2224	610	8	,	,	PUNCT
ap-2224	610	9	b	b	X
ap-2224	610	10	=	=	SYM
ap-2224	610	11	1	1	X
ap-2224	610	12	.	.	PUNCT
ap-2224	611	1	then	then	ADV
ap-2224	611	2	f	f	X
ap-2224	611	3	(	(	PUNCT
ap-2224	611	4	x	x	X
ap-2224	611	5	)	)	PUNCT
ap-2224	611	6	=	=	SYM
ap-2224	612	1	1/(1	1/(1	NUM
ap-2224	612	2	+	+	CCONJ
ap-2224	612	3	x2	x2	ADJ
ap-2224	612	4	)	)	PUNCT
ap-2224	612	5	and	and	CCONJ
ap-2224	612	6	c	c	NOUN
ap-2224	612	7	=	=	SYM
ap-2224	612	8	3	3	X
ap-2224	612	9	.	.	PUNCT
ap-2224	612	10	then	then	ADV
ap-2224	612	11	integral	integral	ADJ
ap-2224	612	12	(	(	PUNCT
ap-2224	612	13	8.4	8.4	NUM
ap-2224	612	14	)	)	PUNCT
ap-2224	612	15	gives:∫	gives:∫	NOUN
ap-2224	612	16	∞	∞	PROPN
ap-2224	612	17	−∞	−∞	PUNCT
ap-2224	612	18	e−ytt3−y	e−ytt3−y	PROPN
ap-2224	612	19	sin	sin	PROPN
ap-2224	612	20	tdt	tdt	PROPN
ap-2224	612	21	=	=	SYM
ap-2224	612	22	−(y2	−(y2	PROPN
ap-2224	612	23	+	+	NUM
ap-2224	612	24	1)(y−4)/2γ(4−	1)(y−4)/2γ(4−	NUM
ap-2224	612	25	y	y	NOUN
ap-2224	612	26	)	)	PUNCT
ap-2224	612	27	sin	sin	NOUN
ap-2224	612	28	(	(	PUNCT
ap-2224	612	29	(	(	PUNCT
ap-2224	612	30	y	y	PROPN
ap-2224	612	31	−	−	PROPN
ap-2224	612	32	4	4	NUM
ap-2224	612	33	)	)	PUNCT
ap-2224	612	34	arctan	arctan	PROPN
ap-2224	612	35	1	1	NUM
ap-2224	612	36	y	y	PROPN
ap-2224	612	37	)	)	PUNCT
ap-2224	612	38	.	.	PUNCT
ap-2224	613	1	this	this	PRON
ap-2224	613	2	gives	give	VERB
ap-2224	613	3	for	for	ADP
ap-2224	613	4	y	y	PROPN
ap-2224	613	5	<	<	X
ap-2224	613	6	3	3	NUM
ap-2224	613	7	the	the	DET
ap-2224	613	8	liouville	liouville	NOUN
ap-2224	613	9	–	–	PUNCT
ap-2224	613	10	weyl	weyl	VERB
ap-2224	613	11	fractional	fractional	ADJ
ap-2224	613	12	derivative	derivative	NOUN
ap-2224	613	13	and	and	CCONJ
ap-2224	613	14	for	for	ADP
ap-2224	613	15	3	3	NUM
ap-2224	613	16	<	<	X
ap-2224	613	17	y	y	X
ap-2224	613	18	<	<	X
ap-2224	613	19	5	5	NUM
ap-2224	613	20	the	the	DET
ap-2224	613	21	fractional	fractional	ADJ
ap-2224	613	22	integral	integral	NOUN
ap-2224	613	23	of	of	ADP
ap-2224	613	24	the	the	DET
ap-2224	613	25	function	function	NOUN
ap-2224	613	26	1/(1	1/(1	PROPN
ap-2224	613	27	+	+	CCONJ
ap-2224	613	28	x2	x2	NOUN
ap-2224	613	29	)	)	PUNCT
ap-2224	613	30	both	both	PRON
ap-2224	613	31	of	of	ADP
ap-2224	613	32	the	the	DET
ap-2224	613	33	variable	variable	ADJ
ap-2224	613	34	order	order	NOUN
ap-2224	613	35	|−3	|−3	NOUN
ap-2224	614	1	+	+	CCONJ
ap-2224	614	2	y|	y|	NOUN
ap-2224	614	3	at	at	ADP
ap-2224	614	4	point	point	NOUN
ap-2224	614	5	y.	y.	NOUN
ap-2224	614	6	it	it	PRON
ap-2224	614	7	must	must	AUX
ap-2224	614	8	be	be	AUX
ap-2224	614	9	emphasized	emphasize	VERB
ap-2224	614	10	,	,	PUNCT
ap-2224	614	11	however	however	ADV
ap-2224	614	12	,	,	PUNCT
ap-2224	614	13	that	that	SCONJ
ap-2224	614	14	the	the	DET
ap-2224	614	15	case	case	NOUN
ap-2224	614	16	b	b	X
ap-2224	614	17	<	<	X
ap-2224	614	18	0	0	NUM
ap-2224	614	19	essentially	essentially	ADV
ap-2224	614	20	changes	change	VERB
ap-2224	614	21	the	the	DET
ap-2224	614	22	situation	situation	NOUN
ap-2224	614	23	.	.	PUNCT
ap-2224	615	1	this	this	PRON
ap-2224	615	2	is	be	AUX
ap-2224	615	3	the	the	DET
ap-2224	615	4	topic	topic	NOUN
ap-2224	615	5	of	of	ADP
ap-2224	615	6	[	[	X
ap-2224	615	7	23	23	NUM
ap-2224	615	8	]	]	PUNCT
ap-2224	615	9	.	.	PUNCT
ap-2224	616	1	remark	remark	PROPN
ap-2224	616	2	8.3	8.3	NUM
ap-2224	616	3	.	.	PUNCT
ap-2224	617	1	we	we	PRON
ap-2224	617	2	call	call	VERB
ap-2224	617	3	the	the	DET
ap-2224	617	4	transform	transform	NOUN
ap-2224	617	5	∫∞	∫∞	NOUN
ap-2224	617	6	0	0	NUM
ap-2224	617	7	e−ytt−yf(t	e−ytt−yf(t	NOUN
ap-2224	617	8	)	)	PUNCT
ap-2224	618	1	dt	dt	PROPN
ap-2224	618	2	,	,	PUNCT
ap-2224	618	3	y	y	PROPN
ap-2224	618	4	>	>	X
ap-2224	618	5	0	0	PROPN
ap-2224	618	6	,	,	PUNCT
ap-2224	618	7	the	the	DET
ap-2224	618	8	anti	anti	ADJ
ap-2224	618	9	-	-	ADJ
ap-2224	618	10	diagonal	diagonal	ADJ
ap-2224	618	11	laplace	laplace	NOUN
ap-2224	618	12	–	–	PUNCT
ap-2224	618	13	mellin	mellin	NOUN
ap-2224	618	14	transform	transform	NOUN
ap-2224	618	15	because	because	SCONJ
ap-2224	618	16	the	the	DET
ap-2224	618	17	term	term	NOUN
ap-2224	618	18	diagonal	diagonal	ADJ
ap-2224	618	19	laplace	laplace	NOUN
ap-2224	618	20	–	–	PUNCT
ap-2224	618	21	mellin	mellin	NOUN
ap-2224	618	22	transform	transform	NOUN
ap-2224	618	23	is	be	AUX
ap-2224	618	24	reserved	reserve	VERB
ap-2224	618	25	for	for	ADP
ap-2224	618	26	the	the	DET
ap-2224	618	27	transformation	transformation	NOUN
ap-2224	618	28	∫∞	∫∞	NOUN
ap-2224	618	29	0	0	NUM
ap-2224	619	1	e−yttyf(t	e−yttyf(t	PROPN
ap-2224	619	2	)	)	PUNCT
ap-2224	619	3	dt	dt	PROPN
ap-2224	619	4	,	,	PUNCT
ap-2224	619	5	y	y	PROPN
ap-2224	619	6	>	>	X
ap-2224	619	7	0	0	PROPN
ap-2224	619	8	,	,	PUNCT
ap-2224	619	9	which	which	PRON
ap-2224	619	10	is	be	AUX
ap-2224	619	11	closely	closely	ADV
ap-2224	619	12	related	relate	VERB
ap-2224	619	13	to	to	ADP
ap-2224	619	14	the	the	DET
ap-2224	619	15	fractional	fractional	ADJ
ap-2224	619	16	derivative	derivative	NOUN
ap-2224	620	1	[	[	X
ap-2224	620	2	23	23	NUM
ap-2224	620	3	]	]	PUNCT
ap-2224	620	4	.	.	PUNCT
ap-2224	621	1	9	9	X
ap-2224	621	2	.	.	X
ap-2224	621	3	conclusion	conclusion	NOUN
ap-2224	621	4	this	this	DET
ap-2224	621	5	paper	paper	NOUN
ap-2224	621	6	has	have	AUX
ap-2224	621	7	focused	focus	VERB
ap-2224	621	8	on	on	ADP
ap-2224	621	9	the	the	DET
ap-2224	621	10	simplest	simple	ADJ
ap-2224	621	11	form	form	NOUN
ap-2224	621	12	of	of	ADP
ap-2224	621	13	the	the	DET
ap-2224	621	14	variable	variable	ADJ
ap-2224	621	15	order	order	NOUN
ap-2224	621	16	liouville	liouville	X
ap-2224	621	17	–	–	PUNCT
ap-2224	621	18	weyl	weyl	VERB
ap-2224	621	19	fractional	fractional	ADJ
ap-2224	621	20	integral	integral	ADJ
ap-2224	621	21	,	,	PUNCT
ap-2224	621	22	where	where	SCONJ
ap-2224	621	23	the	the	DET
ap-2224	621	24	order	order	NOUN
ap-2224	621	25	ν(y	ν(y	PROPN
ap-2224	621	26	)	)	PUNCT
ap-2224	621	27	=	=	VERB
ap-2224	622	1	y.	y.	NOUN
ap-2224	622	2	the	the	DET
ap-2224	622	3	liouville	liouville	NOUN
ap-2224	622	4	–	–	PUNCT
ap-2224	622	5	weyl	weyl	VERB
ap-2224	622	6	fractional	fractional	ADJ
ap-2224	622	7	integral	integral	ADJ
ap-2224	622	8	is	be	AUX
ap-2224	622	9	not	not	PART
ap-2224	622	10	so	so	ADV
ap-2224	622	11	often	often	ADV
ap-2224	622	12	used	use	VERB
ap-2224	622	13	in	in	ADP
ap-2224	622	14	physical	physical	ADJ
ap-2224	622	15	and	and	CCONJ
ap-2224	622	16	technical	technical	ADJ
ap-2224	622	17	applications	application	NOUN
ap-2224	622	18	as	as	ADP
ap-2224	622	19	the	the	DET
ap-2224	622	20	riemann	riemann	PROPN
ap-2224	622	21	–	–	PUNCT
ap-2224	622	22	liouville	liouville	NOUN
ap-2224	622	23	integral	integral	ADJ
ap-2224	622	24	,	,	PUNCT
ap-2224	622	25	but	but	CCONJ
ap-2224	622	26	the	the	DET
ap-2224	622	27	liouville	liouville	NOUN
ap-2224	622	28	–	–	PUNCT
ap-2224	622	29	weyl	weyl	VERB
ap-2224	622	30	fractional	fractional	ADJ
ap-2224	622	31	integral	integral	ADJ
ap-2224	622	32	fulfills	fulfill	VERB
ap-2224	622	33	the	the	DET
ap-2224	622	34	relation	relation	NOUN
ap-2224	622	35	of	of	ADP
ap-2224	622	36	(	(	PUNCT
ap-2224	622	37	1.3	1.3	NUM
ap-2224	622	38	)	)	PUNCT
ap-2224	622	39	.	.	PUNCT
ap-2224	623	1	this	this	PRON
ap-2224	623	2	makes	make	VERB
ap-2224	623	3	it	it	PRON
ap-2224	623	4	possible	possible	ADJ
ap-2224	623	5	to	to	PART
ap-2224	623	6	take	take	VERB
ap-2224	623	7	advantage	advantage	NOUN
ap-2224	623	8	of	of	ADP
ap-2224	623	9	the	the	DET
ap-2224	623	10	laplace	laplace	NOUN
ap-2224	623	11	transform	transform	NOUN
ap-2224	623	12	or	or	CCONJ
ap-2224	623	13	the	the	DET
ap-2224	623	14	mellin	mellin	PROPN
ap-2224	623	15	transform	transform	NOUN
ap-2224	623	16	,	,	PUNCT
ap-2224	623	17	and	and	CCONJ
ap-2224	623	18	to	to	PART
ap-2224	623	19	find	find	VERB
ap-2224	623	20	a	a	DET
ap-2224	623	21	connection	connection	NOUN
ap-2224	623	22	to	to	ADP
ap-2224	623	23	the	the	DET
ap-2224	623	24	lambert	lambert	PROPN
ap-2224	623	25	function	function	PROPN
ap-2224	623	26	.	.	PUNCT
ap-2224	624	1	numerical	numerical	PROPN
ap-2224	624	2	calculations	calculation	NOUN
ap-2224	624	3	have	have	AUX
ap-2224	624	4	been	be	AUX
ap-2224	624	5	performed	perform	VERB
ap-2224	624	6	with	with	ADP
ap-2224	624	7	the	the	DET
ap-2224	624	8	aid	aid	NOUN
ap-2224	624	9	of	of	ADP
ap-2224	624	10	mathematica	mathematica	PROPN
ap-2224	624	11	®	®	PROPN
ap-2224	624	12	ver	ver	PROPN
ap-2224	624	13	.	.	PUNCT
ap-2224	625	1	8.0.1.0	8.0.1.0	NUM
ap-2224	625	2	.	.	PUNCT
ap-2224	626	1	analytical	analytical	ADJ
ap-2224	626	2	calculations	calculation	NOUN
ap-2224	626	3	were	be	AUX
ap-2224	626	4	checked	check	VERB
ap-2224	626	5	by	by	ADP
ap-2224	626	6	the	the	DET
ap-2224	626	7	same	same	ADJ
ap-2224	626	8	version	version	NOUN
ap-2224	626	9	of	of	ADP
ap-2224	626	10	mathematica	mathematica	PROPN
ap-2224	626	11	.	.	PUNCT
ap-2224	627	1	in	in	ADP
ap-2224	627	2	several	several	ADJ
ap-2224	627	3	cases	case	NOUN
ap-2224	627	4	,	,	PUNCT
ap-2224	627	5	the	the	DET
ap-2224	627	6	formulas	formula	NOUN
ap-2224	627	7	generated	generate	VERB
ap-2224	627	8	by	by	ADP
ap-2224	627	9	mathematica	mathematica	PROPN
ap-2224	627	10	have	have	AUX
ap-2224	627	11	been	be	AUX
ap-2224	627	12	used	use	VERB
ap-2224	627	13	instead	instead	ADV
ap-2224	627	14	of	of	ADP
ap-2224	627	15	the	the	DET
ap-2224	627	16	equivalent	equivalent	ADJ
ap-2224	627	17	formulas	formula	NOUN
ap-2224	627	18	presented	present	VERB
ap-2224	627	19	in	in	ADP
ap-2224	627	20	[	[	X
ap-2224	627	21	12	12	NUM
ap-2224	627	22	,	,	PUNCT
ap-2224	627	23	16	16	NUM
ap-2224	627	24	,	,	PUNCT
ap-2224	627	25	19	19	NUM
ap-2224	627	26	]	]	PUNCT
ap-2224	627	27	.	.	PUNCT
ap-2224	628	1	acknowledgements	acknowledgement	VERB
ap-2224	628	2	the	the	DET
ap-2224	628	3	author	author	NOUN
ap-2224	628	4	is	be	AUX
ap-2224	628	5	grateful	grateful	ADJ
ap-2224	628	6	to	to	ADP
ap-2224	628	7	both	both	DET
ap-2224	628	8	referees	referee	NOUN
ap-2224	628	9	for	for	ADP
ap-2224	628	10	their	their	PRON
ap-2224	628	11	valuable	valuable	ADJ
ap-2224	628	12	comments	comment	NOUN
ap-2224	628	13	and	and	CCONJ
ap-2224	628	14	suggestions	suggestion	NOUN
ap-2224	628	15	.	.	PUNCT
ap-2224	629	1	318	318	NUM
ap-2224	629	2	vol	vol	NOUN
ap-2224	629	3	.	.	PUNCT
ap-2224	630	1	54	54	NUM
ap-2224	630	2	no	no	NOUN
ap-2224	630	3	.	.	PUNCT
ap-2224	631	1	4/2014	4/2014	NUM
ap-2224	631	2	fractional	fractional	ADJ
ap-2224	631	3	calculus	calculus	NOUN
ap-2224	631	4	and	and	CCONJ
ap-2224	631	5	lambert	lambert	PROPN
ap-2224	631	6	function	function	NOUN
ap-2224	631	7	i	i	PRON
ap-2224	631	8	references	reference	VERB
ap-2224	631	9	[	[	X
ap-2224	631	10	1	1	NUM
ap-2224	631	11	]	]	PUNCT
ap-2224	631	12	kilbas	kilbas	PROPN
ap-2224	631	13	a.a	a.a	PROPN
ap-2224	631	14	.	.	PROPN
ap-2224	631	15	et	et	PROPN
ap-2224	631	16	al	al	PROPN
ap-2224	631	17	.	.	PROPN
ap-2224	631	18	theory	theory	NOUN
ap-2224	631	19	and	and	CCONJ
ap-2224	631	20	applications	application	NOUN
ap-2224	631	21	of	of	ADP
ap-2224	631	22	the	the	DET
ap-2224	631	23	fractional	fractional	ADJ
ap-2224	631	24	differential	differential	NOUN
ap-2224	631	25	equations	equation	NOUN
ap-2224	631	26	,	,	PUNCT
ap-2224	631	27	amsterdam	amsterdam	PROPN
ap-2224	631	28	:	:	PUNCT
ap-2224	631	29	elsevier	elsevier	NOUN
ap-2224	631	30	,	,	PUNCT
ap-2224	631	31	2006	2006	NUM
ap-2224	631	32	.	.	PUNCT
ap-2224	632	1	[	[	X
ap-2224	632	2	2	2	NUM
ap-2224	632	3	]	]	X
ap-2224	632	4	corless	corless	PROPN
ap-2224	632	5	r.m	r.m	PROPN
ap-2224	632	6	.	.	PROPN
ap-2224	632	7	et	et	PROPN
ap-2224	632	8	al	al	PROPN
ap-2224	632	9	.	.	PROPN
ap-2224	633	1	on	on	ADP
ap-2224	633	2	the	the	DET
ap-2224	633	3	lambert	lambert	PROPN
ap-2224	633	4	w	w	PROPN
ap-2224	633	5	function	function	PROPN
ap-2224	633	6	,	,	PUNCT
ap-2224	633	7	adv	adv	PROPN
ap-2224	633	8	.	.	PUNCT
ap-2224	633	9	comput	comput	PROPN
ap-2224	633	10	.	.	PUNCT
ap-2224	633	11	math	math	NOUN
ap-2224	633	12	.	.	PUNCT
ap-2224	634	1	5	5	NUM
ap-2224	634	2	,	,	PUNCT
ap-2224	634	3	1996	1996	NUM
ap-2224	634	4	,	,	PUNCT
ap-2224	634	5	p.	p.	NOUN
ap-2224	634	6	329–359	329–359	NUM
ap-2224	634	7	.	.	PUNCT
ap-2224	635	1	[	[	X
ap-2224	635	2	3	3	NUM
ap-2224	635	3	]	]	X
ap-2224	635	4	zayed	zayed	PROPN
ap-2224	635	5	a.i	a.i	PROPN
ap-2224	635	6	.	.	PROPN
ap-2224	635	7	handbook	handbook	NOUN
ap-2224	635	8	of	of	ADP
ap-2224	635	9	function	function	NOUN
ap-2224	635	10	and	and	CCONJ
ap-2224	635	11	generalized	generalized	ADJ
ap-2224	635	12	function	function	NOUN
ap-2224	635	13	transformations	transformation	NOUN
ap-2224	635	14	,	,	PUNCT
ap-2224	635	15	boca	boca	PROPN
ap-2224	635	16	raton	raton	PROPN
ap-2224	635	17	:	:	PUNCT
ap-2224	635	18	crc	crc	PROPN
ap-2224	635	19	press	press	PROPN
ap-2224	635	20	,	,	PUNCT
ap-2224	635	21	1996	1996	NUM
ap-2224	635	22	.	.	PUNCT
ap-2224	636	1	[	[	X
ap-2224	636	2	4	4	NUM
ap-2224	636	3	]	]	X
ap-2224	636	4	yuerekli	yuerekli	ADJ
ap-2224	636	5	o.	o.	PROPN
ap-2224	636	6	identities	identity	NOUN
ap-2224	636	7	on	on	ADP
ap-2224	636	8	fractional	fractional	ADJ
ap-2224	636	9	integrals	integral	NOUN
ap-2224	636	10	and	and	CCONJ
ap-2224	636	11	various	various	ADJ
ap-2224	636	12	integral	integral	ADJ
ap-2224	636	13	transforms	transform	NOUN
ap-2224	636	14	,	,	PUNCT
ap-2224	636	15	appl	appl	PROPN
ap-2224	636	16	.	.	PROPN
ap-2224	636	17	math	math	NOUN
ap-2224	636	18	.	.	PUNCT
ap-2224	637	1	comput	comput	NOUN
ap-2224	637	2	.	.	PUNCT
ap-2224	638	1	187	187	NUM
ap-2224	638	2	,	,	PUNCT
ap-2224	638	3	2007	2007	NUM
ap-2224	638	4	,	,	PUNCT
ap-2224	638	5	p.	p.	NOUN
ap-2224	638	6	559	559	NUM
ap-2224	638	7	566	566	NUM
ap-2224	638	8	.	.	PUNCT
ap-2224	639	1	[	[	X
ap-2224	639	2	5	5	X
ap-2224	639	3	]	]	X
ap-2224	639	4	jorgenson	jorgenson	PROPN
ap-2224	639	5	j.	j.	PROPN
ap-2224	639	6	,a	,a	PROPN
ap-2224	639	7	.	.	PROPN
ap-2224	639	8	,	,	PUNCT
ap-2224	639	9	lang	lang	PROPN
ap-2224	639	10	s.	s.	PROPN
ap-2224	639	11	basic	basic	ADJ
ap-2224	639	12	analysis	analysis	NOUN
ap-2224	639	13	of	of	ADP
ap-2224	639	14	regularized	regularize	VERB
ap-2224	639	15	series	series	NOUN
ap-2224	639	16	and	and	CCONJ
ap-2224	639	17	products	product	NOUN
ap-2224	639	18	,	,	PUNCT
ap-2224	639	19	berlin	berlin	PROPN
ap-2224	639	20	:	:	PUNCT
ap-2224	639	21	springer	springer	NOUN
ap-2224	639	22	-	-	PUNCT
ap-2224	639	23	verlag	verlag	PROPN
ap-2224	639	24	,	,	PUNCT
ap-2224	639	25	1993	1993	NUM
ap-2224	639	26	.	.	PUNCT
ap-2224	640	1	[	[	X
ap-2224	640	2	6	6	NUM
ap-2224	640	3	]	]	PUNCT
ap-2224	640	4	schilling	schille	VERB
ap-2224	640	5	r.l	r.l	PROPN
ap-2224	640	6	.	.	PROPN
ap-2224	640	7	et	et	PROPN
ap-2224	640	8	al	al	PROPN
ap-2224	640	9	.	.	PROPN
ap-2224	640	10	bernstein	bernstein	PROPN
ap-2224	640	11	functions	functions	PROPN
ap-2224	640	12	,	,	PUNCT
ap-2224	640	13	berlin	berlin	PROPN
ap-2224	640	14	:	:	PUNCT
ap-2224	640	15	de	de	ADJ
ap-2224	640	16	gruyter	gruyter	NOUN
ap-2224	640	17	,	,	PUNCT
ap-2224	640	18	2010	2010	NUM
ap-2224	640	19	.	.	PUNCT
ap-2224	641	1	[	[	X
ap-2224	641	2	7	7	X
ap-2224	641	3	]	]	X
ap-2224	641	4	christensen	christensen	PROPN
ap-2224	641	5	r.m	r.m	PROPN
ap-2224	641	6	.	.	PROPN
ap-2224	641	7	theory	theory	NOUN
ap-2224	641	8	of	of	ADP
ap-2224	641	9	viscoelasticity	viscoelasticity	NOUN
ap-2224	641	10	,	,	PUNCT
ap-2224	641	11	new	new	PROPN
ap-2224	641	12	york	york	PROPN
ap-2224	641	13	:	:	PUNCT
ap-2224	641	14	academic	academic	ADJ
ap-2224	641	15	press	press	NOUN
ap-2224	641	16	,	,	PUNCT
ap-2224	641	17	1982	1982	NUM
ap-2224	641	18	.	.	PUNCT
ap-2224	642	1	[	[	X
ap-2224	642	2	8	8	NUM
ap-2224	642	3	]	]	X
ap-2224	642	4	samko	samko	PROPN
ap-2224	642	5	s.	s.	PROPN
ap-2224	642	6	g.	g.	PROPN
ap-2224	642	7	,	,	PUNCT
ap-2224	642	8	ross	ross	PROPN
ap-2224	642	9	b.	b.	PROPN
ap-2224	642	10	integration	integration	NOUN
ap-2224	642	11	and	and	CCONJ
ap-2224	642	12	differentiation	differentiation	NOUN
ap-2224	642	13	to	to	ADP
ap-2224	642	14	a	a	DET
ap-2224	642	15	variable	variable	ADJ
ap-2224	642	16	fractional	fractional	ADJ
ap-2224	642	17	order	order	NOUN
ap-2224	642	18	,	,	PUNCT
ap-2224	642	19	integral	integral	ADJ
ap-2224	642	20	transforms	transform	VERB
ap-2224	642	21	spec	spec	NOUN
ap-2224	642	22	.	.	PUNCT
ap-2224	643	1	funct	funct	ADJ
ap-2224	643	2	.	.	PUNCT
ap-2224	644	1	1	1	NUM
ap-2224	644	2	,	,	PUNCT
ap-2224	644	3	1993	1993	NUM
ap-2224	644	4	,	,	PUNCT
ap-2224	644	5	p.	p.	NOUN
ap-2224	644	6	277–300	277–300	NUM
ap-2224	644	7	.	.	PUNCT
ap-2224	645	1	[	[	X
ap-2224	645	2	9	9	NUM
ap-2224	645	3	]	]	X
ap-2224	645	4	sun	sun	PROPN
ap-2224	645	5	h.g	h.g	PROPN
ap-2224	645	6	.	.	PROPN
ap-2224	645	7	et	et	PROPN
ap-2224	645	8	al	al	PROPN
ap-2224	645	9	.	.	PUNCT
ap-2224	646	1	a	a	DET
ap-2224	646	2	comparative	comparative	ADJ
ap-2224	646	3	study	study	NOUN
ap-2224	646	4	of	of	ADP
ap-2224	646	5	constant	constant	ADJ
ap-2224	646	6	-	-	PUNCT
ap-2224	646	7	order	order	NOUN
ap-2224	646	8	and	and	CCONJ
ap-2224	646	9	variable	variable	ADJ
ap-2224	646	10	-	-	PUNCT
ap-2224	646	11	order	order	NOUN
ap-2224	646	12	fractional	fractional	ADJ
ap-2224	646	13	models	model	NOUN
ap-2224	646	14	in	in	ADP
ap-2224	646	15	characterizing	characterize	VERB
ap-2224	646	16	memory	memory	NOUN
ap-2224	646	17	property	property	NOUN
ap-2224	646	18	of	of	ADP
ap-2224	646	19	systems	system	NOUN
ap-2224	646	20	,	,	PUNCT
ap-2224	646	21	eur	eur	PROPN
ap-2224	646	22	.	.	PUNCT
ap-2224	647	1	phys	phy	NOUN
ap-2224	647	2	.	.	PUNCT
ap-2224	648	1	j.	j.	PROPN
ap-2224	648	2	special	special	ADJ
ap-2224	648	3	topics	topic	NOUN
ap-2224	648	4	193	193	NUM
ap-2224	648	5	,	,	PUNCT
ap-2224	648	6	2011	2011	NUM
ap-2224	648	7	,	,	PUNCT
ap-2224	648	8	p.	p.	NOUN
ap-2224	648	9	185	185	NUM
ap-2224	648	10	-	-	SYM
ap-2224	648	11	192	192	NUM
ap-2224	648	12	.	.	PUNCT
ap-2224	649	1	[	[	X
ap-2224	649	2	10	10	NUM
ap-2224	649	3	]	]	X
ap-2224	649	4	lepage	lepage	PROPN
ap-2224	649	5	w.r	w.r	PROPN
ap-2224	649	6	.	.	PROPN
ap-2224	649	7	complex	complex	ADJ
ap-2224	649	8	variables	variable	NOUN
ap-2224	649	9	and	and	CCONJ
ap-2224	649	10	the	the	DET
ap-2224	649	11	laplace	laplace	NOUN
ap-2224	649	12	transform	transform	NOUN
ap-2224	649	13	for	for	ADP
ap-2224	649	14	engineers	engineer	NOUN
ap-2224	649	15	,	,	PUNCT
ap-2224	649	16	new	new	PROPN
ap-2224	649	17	york	york	PROPN
ap-2224	649	18	:	:	PUNCT
ap-2224	649	19	dover	dover	PROPN
ap-2224	649	20	,	,	PUNCT
ap-2224	649	21	1980	1980	NUM
ap-2224	649	22	;	;	PUNCT
ap-2224	649	23	van	van	PROPN
ap-2224	649	24	der	der	PROPN
ap-2224	649	25	pol	pol	PROPN
ap-2224	649	26	b.	b.	PROPN
ap-2224	649	27	,	,	PUNCT
ap-2224	649	28	bremmer	bremmer	PROPN
ap-2224	649	29	h.	h.	PROPN
ap-2224	649	30	:	:	PUNCT
ap-2224	649	31	operational	operational	ADJ
ap-2224	649	32	calculus	calculus	NOUN
ap-2224	649	33	based	base	VERB
ap-2224	649	34	on	on	ADP
ap-2224	649	35	two	two	NUM
ap-2224	649	36	-	-	PUNCT
ap-2224	649	37	sided	sided	ADJ
ap-2224	649	38	laplace	laplace	NOUN
ap-2224	649	39	integral	integral	ADJ
ap-2224	649	40	,	,	PUNCT
ap-2224	649	41	london	london	PROPN
ap-2224	649	42	:	:	PUNCT
ap-2224	649	43	cambridge	cambridge	PROPN
ap-2224	649	44	university	university	PROPN
ap-2224	649	45	press	press	NOUN
ap-2224	649	46	,	,	PUNCT
ap-2224	649	47	1964	1964	NUM
ap-2224	649	48	.	.	PUNCT
ap-2224	650	1	[	[	X
ap-2224	650	2	11	11	NUM
ap-2224	650	3	]	]	X
ap-2224	650	4	olver	olver	ADJ
ap-2224	650	5	f.w.j	f.w.j	NOUN
ap-2224	650	6	.	.	PUNCT
ap-2224	650	7	et	et	PROPN
ap-2224	651	1	al	al	PROPN
ap-2224	651	2	.	.	PROPN
ap-2224	651	3	nist	nist	PROPN
ap-2224	651	4	handbook	handbook	PROPN
ap-2224	651	5	of	of	ADP
ap-2224	651	6	mathematical	mathematical	ADJ
ap-2224	651	7	functions	function	NOUN
ap-2224	651	8	,	,	PUNCT
ap-2224	651	9	nist	nist	NOUN
ap-2224	651	10	and	and	CCONJ
ap-2224	651	11	cambridge	cambridge	PROPN
ap-2224	651	12	university	university	PROPN
ap-2224	651	13	press	press	NOUN
ap-2224	651	14	,	,	PUNCT
ap-2224	651	15	2010	2010	NUM
ap-2224	651	16	.	.	PUNCT
ap-2224	652	1	[	[	X
ap-2224	652	2	12	12	NUM
ap-2224	652	3	]	]	PUNCT
ap-2224	652	4	erdélyi	erdélyi	PROPN
ap-2224	652	5	a.	a.	PROPN
ap-2224	652	6	et	et	PROPN
ap-2224	652	7	al	al	PROPN
ap-2224	652	8	.	.	PUNCT
ap-2224	652	9	tables	table	NOUN
ap-2224	652	10	of	of	ADP
ap-2224	652	11	integral	integral	ADJ
ap-2224	652	12	transforms	transform	NOUN
ap-2224	652	13	,	,	PUNCT
ap-2224	652	14	vol	vol	NOUN
ap-2224	652	15	.	.	PUNCT
ap-2224	652	16	ii	ii	PROPN
ap-2224	652	17	,	,	PUNCT
ap-2224	652	18	new	new	PROPN
ap-2224	652	19	york	york	PROPN
ap-2224	652	20	:	:	PUNCT
ap-2224	652	21	mcgraw	mcgraw	PROPN
ap-2224	652	22	-	-	PUNCT
ap-2224	652	23	hill	hill	NOUN
ap-2224	652	24	,	,	PUNCT
ap-2224	652	25	1954	1954	NUM
ap-2224	652	26	.	.	PUNCT
ap-2224	653	1	[	[	X
ap-2224	653	2	13	13	NUM
ap-2224	653	3	]	]	PUNCT
ap-2224	653	4	chaudhry	chaudhry	PROPN
ap-2224	653	5	m.a	m.a	PROPN
ap-2224	653	6	.	.	PROPN
ap-2224	653	7	,	,	PUNCT
ap-2224	653	8	zubair	zubair	PROPN
ap-2224	653	9	s.m	s.m	PROPN
ap-2224	653	10	.	.	PROPN
ap-2224	654	1	on	on	ADP
ap-2224	654	2	a	a	DET
ap-2224	654	3	class	class	NOUN
ap-2224	654	4	of	of	ADP
ap-2224	654	5	incomplete	incomplete	ADJ
ap-2224	654	6	gamma	gamma	NOUN
ap-2224	654	7	functions	function	NOUN
ap-2224	654	8	with	with	ADP
ap-2224	654	9	applications	application	NOUN
ap-2224	654	10	,	,	PUNCT
ap-2224	654	11	boca	boca	PROPN
ap-2224	654	12	raton	raton	PROPN
ap-2224	654	13	:	:	PUNCT
ap-2224	654	14	chapman	chapman	PROPN
ap-2224	654	15	&	&	CCONJ
ap-2224	654	16	hall	hall	PROPN
ap-2224	654	17	/	/	SYM
ap-2224	654	18	crc	crc	PROPN
ap-2224	654	19	,	,	PUNCT
ap-2224	654	20	2002	2002	NUM
ap-2224	654	21	.	.	PUNCT
ap-2224	655	1	[	[	X
ap-2224	655	2	14	14	NUM
ap-2224	655	3	]	]	PUNCT
ap-2224	655	4	vojta	vojta	NOUN
ap-2224	655	5	v.	v.	ADP
ap-2224	655	6	in	in	ADP
ap-2224	655	7	memory	memory	NOUN
ap-2224	655	8	of	of	ADP
ap-2224	655	9	alois	alois	PROPN
ap-2224	655	10	apfelbeck	apfelbeck	PROPN
ap-2224	655	11	:	:	PUNCT
ap-2224	655	12	an	an	DET
ap-2224	655	13	interconnection	interconnection	NOUN
ap-2224	655	14	between	between	ADP
ap-2224	655	15	cayley	cayley	NOUN
ap-2224	655	16	–	–	PUNCT
ap-2224	655	17	eisenstein	eisenstein	NOUN
ap-2224	655	18	–	–	PUNCT
ap-2224	655	19	pólya	pólya	NOUN
ap-2224	655	20	and	and	CCONJ
ap-2224	655	21	landau	landau	VERB
ap-2224	655	22	probability	probability	NOUN
ap-2224	655	23	distributions	distribution	NOUN
ap-2224	655	24	,	,	PUNCT
ap-2224	655	25	acta	acta	PROPN
ap-2224	655	26	polytechnica	polytechnica	PROPN
ap-2224	655	27	53	53	NUM
ap-2224	655	28	,	,	PUNCT
ap-2224	655	29	(	(	PUNCT
ap-2224	655	30	2	2	NUM
ap-2224	655	31	)	)	PUNCT
ap-2224	655	32	,	,	PUNCT
ap-2224	655	33	2013	2013	NUM
ap-2224	655	34	,	,	PUNCT
ap-2224	655	35	p.	p.	NOUN
ap-2224	655	36	63–69	63–69	NUM
ap-2224	655	37	.	.	PUNCT
ap-2224	656	1	[	[	X
ap-2224	656	2	15	15	NUM
ap-2224	656	3	]	]	X
ap-2224	656	4	roberts	roberts	PROPN
ap-2224	656	5	k.l	k.l	PROPN
ap-2224	656	6	.	.	PROPN
ap-2224	657	1	on	on	ADP
ap-2224	657	2	fractional	fractional	ADJ
ap-2224	657	3	integrals	integral	NOUN
ap-2224	657	4	equivalent	equivalent	ADJ
ap-2224	657	5	to	to	ADP
ap-2224	657	6	a	a	DET
ap-2224	657	7	constant	constant	ADJ
ap-2224	657	8	,	,	PUNCT
ap-2224	657	9	can	can	AUX
ap-2224	657	10	.	.	PUNCT
ap-2224	658	1	math	math	NOUN
ap-2224	658	2	.	.	PUNCT
ap-2224	659	1	bull	bull	NOUN
ap-2224	659	2	.	.	PUNCT
ap-2224	660	1	25	25	NUM
ap-2224	660	2	,	,	PUNCT
ap-2224	660	3	1982	1982	NUM
ap-2224	660	4	,	,	PUNCT
ap-2224	660	5	p.	p.	NOUN
ap-2224	660	6	335–338	335–338	NUM
ap-2224	660	7	.	.	PUNCT
ap-2224	661	1	[	[	X
ap-2224	661	2	16	16	NUM
ap-2224	661	3	]	]	X
ap-2224	661	4	oberhettinger	oberhettinger	NOUN
ap-2224	661	5	f.	f.	PROPN
ap-2224	661	6	tables	table	NOUN
ap-2224	661	7	of	of	ADP
ap-2224	661	8	mellin	mellin	PROPN
ap-2224	661	9	transforms	transform	VERB
ap-2224	661	10	,	,	PUNCT
ap-2224	661	11	new	new	PROPN
ap-2224	661	12	york	york	PROPN
ap-2224	661	13	:	:	PUNCT
ap-2224	661	14	springer	springer	NOUN
ap-2224	661	15	-	-	PUNCT
ap-2224	661	16	verlag	verlag	PROPN
ap-2224	661	17	,	,	PUNCT
ap-2224	661	18	1974	1974	NUM
ap-2224	661	19	.	.	PUNCT
ap-2224	662	1	[	[	X
ap-2224	662	2	17	17	NUM
ap-2224	662	3	]	]	X
ap-2224	662	4	hille	hille	PROPN
ap-2224	662	5	e.	e.	PROPN
ap-2224	662	6	ordinary	ordinary	ADJ
ap-2224	662	7	differential	differential	ADJ
ap-2224	662	8	equations	equation	NOUN
ap-2224	662	9	in	in	ADP
ap-2224	662	10	the	the	DET
ap-2224	662	11	complex	complex	ADJ
ap-2224	662	12	domain	domain	NOUN
ap-2224	662	13	,	,	PUNCT
ap-2224	662	14	mineola	mineola	PROPN
ap-2224	662	15	,	,	PUNCT
ap-2224	662	16	new	new	PROPN
ap-2224	662	17	york	york	PROPN
ap-2224	662	18	:	:	PUNCT
ap-2224	662	19	dover	dover	PROPN
ap-2224	662	20	publications	publication	NOUN
ap-2224	662	21	,	,	PUNCT
ap-2224	662	22	1997	1997	NUM
ap-2224	662	23	.	.	PUNCT
ap-2224	663	1	[	[	X
ap-2224	663	2	18	18	NUM
ap-2224	663	3	]	]	X
ap-2224	663	4	semrád	semrád	PROPN
ap-2224	663	5	i.	i.	PROPN
ap-2224	663	6	private	private	ADJ
ap-2224	663	7	communication	communication	NOUN
ap-2224	663	8	.	.	PUNCT
ap-2224	664	1	[	[	X
ap-2224	664	2	19	19	NUM
ap-2224	664	3	]	]	X
ap-2224	664	4	oberhettinger	oberhettinger	NOUN
ap-2224	664	5	f.	f.	PROPN
ap-2224	664	6	,	,	PUNCT
ap-2224	664	7	badii	badii	PROPN
ap-2224	664	8	l.	l.	PROPN
ap-2224	664	9	tables	table	NOUN
ap-2224	664	10	of	of	ADP
ap-2224	664	11	laplace	laplace	NOUN
ap-2224	664	12	transforms	transform	VERB
ap-2224	664	13	,	,	PUNCT
ap-2224	664	14	new	new	PROPN
ap-2224	664	15	york	york	PROPN
ap-2224	664	16	:	:	PUNCT
ap-2224	664	17	springer	springer	NOUN
ap-2224	664	18	-	-	PUNCT
ap-2224	664	19	verlag	verlag	PROPN
ap-2224	664	20	,	,	PUNCT
ap-2224	664	21	1973	1973	NUM
ap-2224	664	22	.	.	PUNCT
ap-2224	665	1	[	[	X
ap-2224	665	2	20	20	NUM
ap-2224	665	3	]	]	X
ap-2224	665	4	mathai	mathai	PROPN
ap-2224	665	5	a.m.	a.m.	PROPN
ap-2224	665	6	,	,	PUNCT
ap-2224	665	7	haubold	haubold	PROPN
ap-2224	665	8	h.j	h.j	PROPN
ap-2224	665	9	.	.	PROPN
ap-2224	665	10	special	special	ADJ
ap-2224	665	11	functions	function	NOUN
ap-2224	665	12	for	for	ADP
ap-2224	665	13	applied	applied	ADJ
ap-2224	665	14	scientists	scientist	NOUN
ap-2224	665	15	,	,	PUNCT
ap-2224	665	16	new	new	PROPN
ap-2224	665	17	york	york	PROPN
ap-2224	665	18	:	:	PUNCT
ap-2224	665	19	springer	springer	NOUN
ap-2224	665	20	science	science	NOUN
ap-2224	665	21	,	,	PUNCT
ap-2224	665	22	2008	2008	NUM
ap-2224	665	23	.	.	PUNCT
ap-2224	666	1	[	[	X
ap-2224	666	2	21	21	NUM
ap-2224	666	3	]	]	X
ap-2224	666	4	chernoff	chernoff	PROPN
ap-2224	666	5	p.r	p.r	PROPN
ap-2224	666	6	.	.	PROPN
ap-2224	667	1	a	a	DET
ap-2224	667	2	pseudo	pseudo	NOUN
ap-2224	667	3	zeta	zeta	NOUN
ap-2224	667	4	function	function	NOUN
ap-2224	667	5	and	and	CCONJ
ap-2224	667	6	the	the	DET
ap-2224	667	7	distribution	distribution	NOUN
ap-2224	667	8	of	of	ADP
ap-2224	667	9	primes	prime	NOUN
ap-2224	667	10	,	,	PUNCT
ap-2224	667	11	proc	proc	NOUN
ap-2224	667	12	.	.	PUNCT
ap-2224	668	1	natl	natl	PROPN
ap-2224	668	2	.	.	PUNCT
ap-2224	669	1	acad	acad	PROPN
ap-2224	669	2	.	.	PUNCT
ap-2224	670	1	sci	sci	PROPN
ap-2224	670	2	.	.	PROPN
ap-2224	670	3	usa	usa	PROPN
ap-2224	670	4	97	97	NUM
ap-2224	670	5	,	,	PUNCT
ap-2224	670	6	(	(	PUNCT
ap-2224	670	7	14	14	NUM
ap-2224	670	8	)	)	PUNCT
ap-2224	670	9	,	,	PUNCT
ap-2224	670	10	2000	2000	NUM
ap-2224	670	11	,	,	PUNCT
ap-2224	670	12	p.	p.	NOUN
ap-2224	670	13	7697–7699	7697–7699	NUM
ap-2224	670	14	.	.	PUNCT
ap-2224	671	1	[	[	X
ap-2224	671	2	22	22	NUM
ap-2224	671	3	]	]	X
ap-2224	671	4	kuczma	kuczma	PROPN
ap-2224	671	5	m.	m.	PROPN
ap-2224	671	6	et	et	PROPN
ap-2224	671	7	al	al	PROPN
ap-2224	671	8	.	.	PROPN
ap-2224	671	9	iterative	iterative	ADJ
ap-2224	671	10	functional	functional	ADJ
ap-2224	671	11	equations	equation	NOUN
ap-2224	671	12	,	,	PUNCT
ap-2224	671	13	cambridge	cambridge	PROPN
ap-2224	671	14	:	:	PUNCT
ap-2224	671	15	cambridge	cambridge	PROPN
ap-2224	671	16	university	university	PROPN
ap-2224	671	17	press	press	NOUN
ap-2224	671	18	,	,	PUNCT
ap-2224	671	19	1990	1990	NUM
ap-2224	671	20	.	.	PUNCT
ap-2224	672	1	[	[	X
ap-2224	672	2	23	23	NUM
ap-2224	672	3	]	]	PUNCT
ap-2224	672	4	vojta	vojta	NOUN
ap-2224	672	5	v.	v.	ADP
ap-2224	672	6	fractional	fractional	ADJ
ap-2224	672	7	derivatives	derivative	NOUN
ap-2224	672	8	and	and	CCONJ
ap-2224	672	9	lambert	lambert	NOUN
ap-2224	672	10	function	function	NOUN
ap-2224	672	11	,	,	PUNCT
ap-2224	672	12	in	in	ADP
ap-2224	672	13	preparation	preparation	NOUN
ap-2224	672	14	.	.	PUNCT
ap-2224	673	1	319	319	NUM
ap-2224	673	2	acta	acta	PROPN
ap-2224	673	3	polytechnica	polytechnica	PROPN
ap-2224	673	4	54(4):305–319	54(4):305–319	PROPN
ap-2224	673	5	,	,	PUNCT
ap-2224	673	6	2014	2014	NUM
ap-2224	673	7	1	1	NUM
ap-2224	673	8	introduction	introduction	NOUN
ap-2224	673	9	2	2	NUM
ap-2224	673	10	diagonal	diagonal	ADJ
ap-2224	673	11	fractional	fractional	ADJ
ap-2224	673	12	integrals	integral	NOUN
ap-2224	673	13	3	3	NUM
ap-2224	673	14	inversion	inversion	NOUN
ap-2224	673	15	of	of	ADP
ap-2224	673	16	the	the	DET
ap-2224	673	17	diagonal	diagonal	ADJ
ap-2224	673	18	fractional	fractional	ADJ
ap-2224	673	19	integral	integral	ADJ
ap-2224	673	20	3.1	3.1	NUM
ap-2224	673	21	examples	example	NOUN
ap-2224	673	22	3.1.1	3.1.1	NUM
ap-2224	673	23	example	example	NOUN
ap-2224	673	24	of	of	ADP
ap-2224	673	25	the	the	DET
ap-2224	673	26	laplace	laplace	NOUN
ap-2224	673	27	variant	variant	NOUN
ap-2224	673	28	3.1.2	3.1.2	NUM
ap-2224	673	29	example	example	NOUN
ap-2224	673	30	of	of	ADP
ap-2224	673	31	the	the	DET
ap-2224	673	32	mellin	mellin	PROPN
ap-2224	673	33	variant	variant	NOUN
ap-2224	673	34	4	4	NUM
ap-2224	673	35	fixed	fix	VERB
ap-2224	673	36	point	point	NOUN
ap-2224	673	37	5	5	NUM
ap-2224	673	38	complex	complex	ADJ
ap-2224	673	39	domain	domain	NOUN
ap-2224	673	40	6	6	NUM
ap-2224	673	41	applications	application	NOUN
ap-2224	673	42	6.1	6.1	NUM
ap-2224	673	43	gamma	gamma	NOUN
ap-2224	673	44	function	function	VERB
ap-2224	673	45	6.2	6.2	NUM
ap-2224	673	46	diagonal	diagonal	ADJ
ap-2224	673	47	restriction	restriction	NOUN
ap-2224	673	48	of	of	ADP
ap-2224	673	49	some	some	DET
ap-2224	673	50	special	special	ADJ
ap-2224	673	51	functions	function	NOUN
ap-2224	673	52	6.2.1	6.2.1	NUM
ap-2224	673	53	incomplete	incomplete	ADJ
ap-2224	673	54	gamma	gamma	NOUN
ap-2224	673	55	function	function	VERB
ap-2224	673	56	6.2.2	6.2.2	NUM
ap-2224	673	57	exponential	exponential	ADJ
ap-2224	673	58	integral	integral	ADJ
ap-2224	673	59	6.2.3	6.2.3	NUM
ap-2224	673	60	modified	modify	VERB
ap-2224	673	61	bessel	bessel	NOUN
ap-2224	673	62	function	function	NOUN
ap-2224	673	63	of	of	ADP
ap-2224	673	64	the	the	DET
ap-2224	673	65	second	second	ADJ
ap-2224	673	66	kind	kind	NOUN
ap-2224	673	67	(	(	PUNCT
ap-2224	673	68	macdonald	macdonald	PROPN
ap-2224	673	69	function	function	PROPN
ap-2224	673	70	)	)	PUNCT
ap-2224	674	1	k	k	X
ap-2224	674	2	nu(x	nu(x	PROPN
ap-2224	674	3	)	)	PUNCT
ap-2224	674	4	6.2.4	6.2.4	NUM
ap-2224	674	5	bickley	bickley	NOUN
ap-2224	674	6	function	function	VERB
ap-2224	674	7	6.3	6.3	NUM
ap-2224	674	8	integral	integral	ADJ
ap-2224	674	9	transform	transform	NOUN
ap-2224	674	10	pairs	pair	NOUN
ap-2224	674	11	containing	contain	VERB
ap-2224	674	12	the	the	DET
ap-2224	674	13	lambert	lambert	PROPN
ap-2224	674	14	function	function	NOUN
ap-2224	674	15	7	7	NUM
ap-2224	674	16	eigenproblem	eigenproblem	NOUN
ap-2224	674	17	8	8	NUM
ap-2224	674	18	generalization	generalization	NOUN
ap-2224	674	19	9	9	NUM
ap-2224	674	20	conclusion	conclusion	NOUN
ap-2224	674	21	acknowledgements	acknowledgement	NOUN
ap-2224	674	22	references	reference	NOUN