id	sid	tid	token	lemma	pos
ap-1783	1	1	acta	acta	PROPN
ap-1783	1	2	polytechnica	polytechnica	PROPN
ap-1783	1	3	acta	acta	PROPN
ap-1783	1	4	polytechnica	polytechnica	PROPN
ap-1783	1	5	53(2):63–69	53(2):63–69	NUM
ap-1783	1	6	,	,	PUNCT
ap-1783	1	7	2013	2013	NUM
ap-1783	1	8	©	©	PROPN
ap-1783	1	9	czech	czech	PROPN
ap-1783	1	10	technical	technical	PROPN
ap-1783	1	11	university	university	PROPN
ap-1783	1	12	in	in	ADP
ap-1783	1	13	prague	prague	PROPN
ap-1783	1	14	,	,	PUNCT
ap-1783	1	15	2013	2013	NUM
ap-1783	1	16	available	available	ADJ
ap-1783	1	17	online	online	ADV
ap-1783	1	18	at	at	ADP
ap-1783	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1783	1	20	in	in	ADP
ap-1783	1	21	memory	memory	NOUN
ap-1783	1	22	of	of	ADP
ap-1783	1	23	alois	alois	PROPN
ap-1783	1	24	apfelbeck	apfelbeck	PROPN
ap-1783	1	25	:	:	PUNCT
ap-1783	1	26	an	an	DET
ap-1783	1	27	interconnection	interconnection	NOUN
ap-1783	1	28	between	between	ADP
ap-1783	1	29	cayley	cayley	ADJ
ap-1783	1	30	-	-	PUNCT
ap-1783	1	31	eisenstein	eisenstein	NOUN
ap-1783	1	32	-	-	PUNCT
ap-1783	1	33	pólya	pólya	NOUN
ap-1783	1	34	and	and	CCONJ
ap-1783	1	35	landau	landau	VERB
ap-1783	1	36	probability	probability	NOUN
ap-1783	1	37	distributions	distribution	NOUN
ap-1783	1	38	vladimír	vladimír	NOUN
ap-1783	1	39	vojta∗	vojta∗	PROPN
ap-1783	1	40	chotovická	chotovická	PROPN
ap-1783	1	41	12	12	NUM
ap-1783	1	42	,	,	PUNCT
ap-1783	1	43	182	182	NUM
ap-1783	1	44	00	00	NUM
ap-1783	1	45	praha	praha	PROPN
ap-1783	1	46	8	8	NUM
ap-1783	1	47	∗	∗	NOUN
ap-1783	1	48	corresponding	correspond	VERB
ap-1783	1	49	author	author	NOUN
ap-1783	1	50	:	:	PUNCT
ap-1783	1	51	vojta@karneval.cz	vojta@karneval.cz	NOUN
ap-1783	1	52	abstract	abstract	NOUN
ap-1783	1	53	.	.	PUNCT
ap-1783	2	1	the	the	DET
ap-1783	2	2	interconnection	interconnection	NOUN
ap-1783	2	3	between	between	ADP
ap-1783	2	4	the	the	DET
ap-1783	2	5	cayley	cayley	ADJ
ap-1783	2	6	-	-	PUNCT
ap-1783	2	7	eisenstein	eisenstein	NOUN
ap-1783	2	8	-	-	PUNCT
ap-1783	2	9	pólya	pólya	NOUN
ap-1783	2	10	distribution	distribution	NOUN
ap-1783	2	11	and	and	CCONJ
ap-1783	2	12	the	the	DET
ap-1783	2	13	landau	landau	NOUN
ap-1783	2	14	distribution	distribution	NOUN
ap-1783	2	15	is	be	AUX
ap-1783	2	16	studied	study	VERB
ap-1783	2	17	,	,	PUNCT
ap-1783	2	18	and	and	CCONJ
ap-1783	2	19	possibly	possibly	ADV
ap-1783	2	20	new	new	ADJ
ap-1783	2	21	transform	transform	NOUN
ap-1783	2	22	pairs	pair	NOUN
ap-1783	2	23	for	for	ADP
ap-1783	2	24	the	the	DET
ap-1783	2	25	laplace	laplace	NOUN
ap-1783	2	26	and	and	CCONJ
ap-1783	2	27	mellin	mellin	NOUN
ap-1783	2	28	transform	transform	VERB
ap-1783	2	29	and	and	CCONJ
ap-1783	2	30	integral	integral	ADJ
ap-1783	2	31	expressions	expression	NOUN
ap-1783	2	32	for	for	ADP
ap-1783	2	33	the	the	DET
ap-1783	2	34	lambert	lambert	PROPN
ap-1783	2	35	w	w	PROPN
ap-1783	2	36	function	function	PROPN
ap-1783	2	37	have	have	AUX
ap-1783	2	38	been	be	AUX
ap-1783	2	39	found	find	VERB
ap-1783	2	40	.	.	PUNCT
ap-1783	3	1	keywords	keyword	NOUN
ap-1783	3	2	:	:	PUNCT
ap-1783	3	3	cayley	cayley	ADJ
ap-1783	3	4	-	-	PUNCT
ap-1783	3	5	eisenstein	eisenstein	NOUN
ap-1783	3	6	-	-	PUNCT
ap-1783	3	7	pólya	pólya	NOUN
ap-1783	3	8	distribution	distribution	NOUN
ap-1783	3	9	,	,	PUNCT
ap-1783	3	10	landau	landau	VERB
ap-1783	3	11	distribution	distribution	NOUN
ap-1783	3	12	,	,	PUNCT
ap-1783	3	13	lambert	lambert	PROPN
ap-1783	3	14	function	function	PROPN
ap-1783	3	15	,	,	PUNCT
ap-1783	3	16	laplace	laplace	NOUN
ap-1783	3	17	transform	transform	NOUN
ap-1783	3	18	,	,	PUNCT
ap-1783	3	19	mellin	mellin	PROPN
ap-1783	3	20	transform	transform	NOUN
ap-1783	3	21	,	,	PUNCT
ap-1783	3	22	mellin	mellin	PROPN
ap-1783	3	23	multiplier	multipli	ADJ
ap-1783	3	24	,	,	PUNCT
ap-1783	3	25	hadamard	hadamard	ADJ
ap-1783	3	26	fractional	fractional	ADJ
ap-1783	3	27	integral	integral	ADJ
ap-1783	3	28	,	,	PUNCT
ap-1783	3	29	liouville	liouville	ADJ
ap-1783	3	30	fractional	fractional	ADJ
ap-1783	3	31	integral	integral	ADJ
ap-1783	3	32	.	.	PUNCT
ap-1783	4	1	ams	am	NOUN
ap-1783	4	2	mathematics	mathematics	PROPN
ap-1783	4	3	subject	subject	ADJ
ap-1783	4	4	classification	classification	NOUN
ap-1783	4	5	:	:	PUNCT
ap-1783	4	6	33e99	33e99	NUM
ap-1783	4	7	,	,	PUNCT
ap-1783	4	8	(	(	PUNCT
ap-1783	4	9	44a10	44a10	NUM
ap-1783	4	10	,	,	PUNCT
ap-1783	4	11	44a15	44a15	NUM
ap-1783	4	12	,	,	PUNCT
ap-1783	4	13	26a33	26a33	NUM
ap-1783	4	14	)	)	PUNCT
ap-1783	4	15	.	.	PUNCT
ap-1783	5	1	1	1	X
ap-1783	5	2	.	.	X
ap-1783	5	3	introduction	introduction	NOUN
ap-1783	5	4	in	in	ADP
ap-1783	5	5	their	their	PRON
ap-1783	5	6	seminal	seminal	ADJ
ap-1783	5	7	paper	paper	NOUN
ap-1783	5	8	on	on	ADP
ap-1783	5	9	queueing	queue	VERB
ap-1783	5	10	theory	theory	NOUN
ap-1783	5	11	[	[	X
ap-1783	5	12	1	1	NUM
ap-1783	5	13	]	]	PUNCT
ap-1783	5	14	abate	abate	NOUN
ap-1783	5	15	and	and	CCONJ
ap-1783	5	16	whitt	whitt	NOUN
ap-1783	5	17	studied	study	VERB
ap-1783	5	18	a	a	DET
ap-1783	5	19	cumulative	cumulative	ADJ
ap-1783	5	20	probability	probability	NOUN
ap-1783	5	21	distribution	distribution	NOUN
ap-1783	5	22	function	function	NOUN
ap-1783	5	23	(	(	PUNCT
ap-1783	5	24	c.d.f	c.d.f	NOUN
ap-1783	5	25	.	.	PUNCT
ap-1783	5	26	)	)	PUNCT
ap-1783	6	1	f	f	PROPN
ap-1783	6	2	(	(	PUNCT
ap-1783	6	3	x	x	X
ap-1783	6	4	)	)	PUNCT
ap-1783	6	5	with	with	ADP
ap-1783	6	6	a	a	DET
ap-1783	6	7	pertinent	pertinent	ADJ
ap-1783	6	8	probability	probability	NOUN
ap-1783	6	9	density	density	NOUN
ap-1783	6	10	function	function	NOUN
ap-1783	6	11	(	(	PUNCT
ap-1783	6	12	p.d.f	p.d.f	ADJ
ap-1783	6	13	.	.	PUNCT
ap-1783	6	14	)	)	PUNCT
ap-1783	7	1	f(x	f(x	PROPN
ap-1783	7	2	)	)	PUNCT
ap-1783	7	3	,	,	PUNCT
ap-1783	7	4	x	x	X
ap-1783	7	5	>	>	X
ap-1783	7	6	0	0	NUM
ap-1783	7	7	,	,	PUNCT
ap-1783	7	8	such	such	ADJ
ap-1783	7	9	that	that	SCONJ
ap-1783	7	10	its	its	PRON
ap-1783	7	11	moment	moment	NOUN
ap-1783	7	12	generating	generate	VERB
ap-1783	7	13	function	function	NOUN
ap-1783	7	14	g(s	g(s	NOUN
ap-1783	7	15	)	)	PUNCT
ap-1783	7	16	=	=	SYM
ap-1783	8	1	∫	∫	PROPN
ap-1783	9	1	∞	∞	PROPN
ap-1783	9	2	0	0	NUM
ap-1783	9	3	e−sx	e−sx	PROPN
ap-1783	9	4	df	df	NOUN
ap-1783	9	5	(	(	PUNCT
ap-1783	9	6	x	x	NOUN
ap-1783	9	7	)	)	PUNCT
ap-1783	9	8	=	=	SYM
ap-1783	9	9	∫	∫	PROPN
ap-1783	9	10	∞	∞	PROPN
ap-1783	9	11	0	0	PROPN
ap-1783	9	12	e−sxf(x	e−sxf(x	PROPN
ap-1783	9	13	)	)	PUNCT
ap-1783	9	14	dx	dx	PROPN
ap-1783	9	15	,	,	PUNCT
ap-1783	9	16	(	(	PUNCT
ap-1783	9	17	1.1	1.1	NUM
ap-1783	9	18	)	)	PUNCT
ap-1783	9	19	satisfies	satisfy	VERB
ap-1783	9	20	the	the	DET
ap-1783	9	21	functional	functional	ADJ
ap-1783	9	22	equation	equation	NOUN
ap-1783	9	23	g(s	g(s	NOUN
ap-1783	9	24	)	)	PUNCT
ap-1783	9	25	=	=	PUNCT
ap-1783	9	26	e−sg(s	e−sg(s	NOUN
ap-1783	9	27	)	)	PUNCT
ap-1783	9	28	.	.	PUNCT
ap-1783	10	1	(	(	PUNCT
ap-1783	10	2	1.2	1.2	NUM
ap-1783	10	3	)	)	PUNCT
ap-1783	10	4	it	it	PRON
ap-1783	10	5	was	be	AUX
ap-1783	10	6	shown	show	VERB
ap-1783	10	7	in	in	ADP
ap-1783	10	8	[	[	X
ap-1783	10	9	1	1	X
ap-1783	10	10	]	]	PUNCT
ap-1783	10	11	that	that	SCONJ
ap-1783	10	12	the	the	DET
ap-1783	10	13	moments	moment	NOUN
ap-1783	10	14	of	of	ADP
ap-1783	10	15	f	f	PROPN
ap-1783	10	16	(	(	PUNCT
ap-1783	10	17	x	x	X
ap-1783	10	18	)	)	PUNCT
ap-1783	10	19	are	be	AUX
ap-1783	10	20	mn	mn	PROPN
ap-1783	10	21	=	=	SYM
ap-1783	10	22	(	(	PUNCT
ap-1783	10	23	n+	n+	NUM
ap-1783	10	24	1)n−1	1)n−1	NUM
ap-1783	10	25	,	,	PUNCT
ap-1783	10	26	n	n	PRON
ap-1783	10	27	≥	≥	NOUN
ap-1783	10	28	0	0	NUM
ap-1783	10	29	.	.	PUNCT
ap-1783	11	1	(	(	PUNCT
ap-1783	11	2	1.3	1.3	NUM
ap-1783	11	3	)	)	PUNCT
ap-1783	11	4	the	the	DET
ap-1783	11	5	authors	author	NOUN
ap-1783	11	6	of	of	ADP
ap-1783	11	7	[	[	X
ap-1783	11	8	1	1	NUM
ap-1783	11	9	]	]	PUNCT
ap-1783	11	10	named	name	VERB
ap-1783	11	11	this	this	DET
ap-1783	11	12	probability	probability	NOUN
ap-1783	11	13	distribution	distribution	NOUN
ap-1783	11	14	the	the	DET
ap-1783	11	15	cayley	cayley	ADJ
ap-1783	11	16	-	-	PUNCT
ap-1783	11	17	eisenstein	eisenstein	NOUN
ap-1783	11	18	-	-	PUNCT
ap-1783	11	19	pólya	pólya	NOUN
ap-1783	11	20	(	(	PUNCT
ap-1783	11	21	c.e.p	c.e.p	PROPN
ap-1783	11	22	.	.	PUNCT
ap-1783	11	23	)	)	PUNCT
ap-1783	12	1	distribution	distribution	NOUN
ap-1783	12	2	.	.	PUNCT
ap-1783	13	1	the	the	DET
ap-1783	13	2	solution	solution	NOUN
ap-1783	13	3	of	of	ADP
ap-1783	13	4	the	the	DET
ap-1783	13	5	functional	functional	ADJ
ap-1783	13	6	equation	equation	NOUN
ap-1783	13	7	(	(	PUNCT
ap-1783	13	8	1.2	1.2	NUM
ap-1783	13	9	)	)	PUNCT
ap-1783	13	10	was	be	AUX
ap-1783	13	11	not	not	PART
ap-1783	13	12	carried	carry	VERB
ap-1783	13	13	out	out	ADP
ap-1783	13	14	in	in	ADP
ap-1783	13	15	[	[	X
ap-1783	13	16	1	1	NUM
ap-1783	13	17	]	]	PUNCT
ap-1783	13	18	.	.	PUNCT
ap-1783	14	1	the	the	DET
ap-1783	14	2	primary	primary	ADJ
ap-1783	14	3	effort	effort	NOUN
ap-1783	14	4	of	of	ADP
ap-1783	14	5	the	the	DET
ap-1783	14	6	author	author	NOUN
ap-1783	14	7	was	be	AUX
ap-1783	14	8	to	to	PART
ap-1783	14	9	solve	solve	VERB
ap-1783	14	10	this	this	DET
ap-1783	14	11	problem	problem	NOUN
ap-1783	14	12	with	with	ADP
ap-1783	14	13	the	the	DET
ap-1783	14	14	aim	aim	NOUN
ap-1783	14	15	to	to	PART
ap-1783	14	16	obtain	obtain	VERB
ap-1783	14	17	an	an	DET
ap-1783	14	18	explicit	explicit	ADJ
ap-1783	14	19	formula	formula	NOUN
ap-1783	14	20	for	for	ADP
ap-1783	14	21	the	the	DET
ap-1783	14	22	probability	probability	NOUN
ap-1783	14	23	density	density	NOUN
ap-1783	14	24	function	function	VERB
ap-1783	14	25	f(x	f(x	PROPN
ap-1783	14	26	)	)	PUNCT
ap-1783	14	27	.	.	PUNCT
ap-1783	15	1	during	during	ADP
ap-1783	15	2	the	the	DET
ap-1783	15	3	calculation	calculation	NOUN
ap-1783	15	4	of	of	ADP
ap-1783	15	5	f(x	f(x	PROPN
ap-1783	15	6	)	)	PUNCT
ap-1783	15	7	by	by	ADP
ap-1783	15	8	three	three	NUM
ap-1783	15	9	methods	method	NOUN
ap-1783	15	10	,	,	PUNCT
ap-1783	15	11	it	it	PRON
ap-1783	15	12	was	be	AUX
ap-1783	15	13	found	find	VERB
ap-1783	15	14	that	that	SCONJ
ap-1783	15	15	the	the	DET
ap-1783	15	16	c.e.p	c.e.p	PROPN
ap-1783	15	17	.	.	PUNCT
ap-1783	15	18	distribution	distribution	NOUN
ap-1783	15	19	is	be	AUX
ap-1783	15	20	in	in	ADP
ap-1783	15	21	relation	relation	NOUN
ap-1783	15	22	to	to	ADP
ap-1783	15	23	the	the	DET
ap-1783	15	24	landau	landau	NOUN
ap-1783	15	25	distribution	distribution	NOUN
ap-1783	15	26	function	function	NOUN
ap-1783	15	27	[	[	X
ap-1783	15	28	2	2	NUM
ap-1783	15	29	]	]	PUNCT
ap-1783	15	30	.	.	PUNCT
ap-1783	16	1	theorem	theorem	VERB
ap-1783	16	2	1.1	1.1	NUM
ap-1783	16	3	.	.	PUNCT
ap-1783	17	1	the	the	DET
ap-1783	17	2	solution	solution	NOUN
ap-1783	17	3	of	of	ADP
ap-1783	17	4	functional	functional	ADJ
ap-1783	17	5	equation	equation	NOUN
ap-1783	17	6	(	(	PUNCT
ap-1783	17	7	1.2	1.2	NUM
ap-1783	17	8	)	)	PUNCT
ap-1783	17	9	is	be	AUX
ap-1783	17	10	the	the	DET
ap-1783	17	11	function	function	NOUN
ap-1783	17	12	g(s	g(s	NOUN
ap-1783	17	13	)	)	PUNCT
ap-1783	18	1	=	=	SYM
ap-1783	18	2	w	w	PROPN
ap-1783	18	3	(	(	PUNCT
ap-1783	18	4	s)/s	s)/s	ADJ
ap-1783	18	5	=	=	PUNCT
ap-1783	18	6	e−w	e−w	NOUN
ap-1783	18	7	(	(	PUNCT
ap-1783	18	8	s	s	NOUN
ap-1783	18	9	)	)	PUNCT
ap-1783	18	10	,	,	PUNCT
ap-1783	18	11	s	s	VERB
ap-1783	18	12	∈	∈	PROPN
ap-1783	18	13	c	c	NOUN
ap-1783	18	14	,	,	PUNCT
ap-1783	18	15	where	where	SCONJ
ap-1783	18	16	w	w	PROPN
ap-1783	18	17	(	(	PUNCT
ap-1783	18	18	s	s	X
ap-1783	18	19	)	)	PUNCT
ap-1783	18	20	is	be	AUX
ap-1783	18	21	the	the	DET
ap-1783	18	22	lambert	lambert	PROPN
ap-1783	18	23	function	function	NOUN
ap-1783	18	24	[	[	X
ap-1783	18	25	3	3	X
ap-1783	18	26	]	]	PUNCT
ap-1783	18	27	and	and	CCONJ
ap-1783	18	28	c	c	PROPN
ap-1783	18	29	is	be	AUX
ap-1783	18	30	the	the	DET
ap-1783	18	31	set	set	NOUN
ap-1783	18	32	of	of	ADP
ap-1783	18	33	all	all	DET
ap-1783	18	34	complex	complex	ADJ
ap-1783	18	35	numbers	number	NOUN
ap-1783	18	36	.	.	PUNCT
ap-1783	19	1	proof	proof	NOUN
ap-1783	19	2	.	.	PUNCT
ap-1783	20	1	let	let	VERB
ap-1783	20	2	u(s	u(s	NUM
ap-1783	20	3	)	)	PUNCT
ap-1783	20	4	=	=	SYM
ap-1783	20	5	sg(s	sg(s	NUM
ap-1783	20	6	)	)	PUNCT
ap-1783	20	7	.	.	PUNCT
ap-1783	21	1	then	then	ADV
ap-1783	21	2	eq	eq	X
ap-1783	21	3	.	.	PUNCT
ap-1783	22	1	(	(	PUNCT
ap-1783	22	2	1.2	1.2	NUM
ap-1783	22	3	)	)	PUNCT
ap-1783	22	4	can	can	AUX
ap-1783	22	5	be	be	AUX
ap-1783	22	6	rewritten	rewrite	VERB
ap-1783	22	7	as	as	ADP
ap-1783	22	8	u(s)eu(s	u(s)eu(s	NOUN
ap-1783	22	9	)	)	PUNCT
ap-1783	22	10	=	=	PUNCT
ap-1783	23	1	s.	s.	PROPN
ap-1783	23	2	but	but	CCONJ
ap-1783	23	3	this	this	PRON
ap-1783	23	4	is	be	AUX
ap-1783	23	5	the	the	DET
ap-1783	23	6	definition	definition	NOUN
ap-1783	23	7	of	of	ADP
ap-1783	23	8	the	the	DET
ap-1783	23	9	lambert	lambert	PROPN
ap-1783	23	10	w	w	PROPN
ap-1783	23	11	function	function	NOUN
ap-1783	23	12	as	as	ADP
ap-1783	23	13	a	a	DET
ap-1783	23	14	solution	solution	NOUN
ap-1783	23	15	of	of	ADP
ap-1783	23	16	the	the	DET
ap-1783	23	17	functional	functional	ADJ
ap-1783	23	18	equation	equation	NOUN
ap-1783	23	19	w	w	PROPN
ap-1783	23	20	(	(	PUNCT
ap-1783	23	21	s)ew	s)ew	PROPN
ap-1783	23	22	(	(	PUNCT
ap-1783	23	23	s	s	X
ap-1783	23	24	)	)	PUNCT
ap-1783	23	25	=	=	VERB
ap-1783	23	26	s.	s.	PROPN
ap-1783	23	27	for	for	ADP
ap-1783	23	28	our	our	PRON
ap-1783	23	29	case	case	NOUN
ap-1783	23	30	,	,	PUNCT
ap-1783	23	31	we	we	PRON
ap-1783	23	32	select	select	VERB
ap-1783	23	33	the	the	DET
ap-1783	23	34	real	real	ADJ
ap-1783	23	35	branch	branch	NOUN
ap-1783	23	36	w0(s	w0(s	PROPN
ap-1783	23	37	)	)	PUNCT
ap-1783	23	38	of	of	ADP
ap-1783	23	39	w	w	PROPN
ap-1783	23	40	(	(	PUNCT
ap-1783	23	41	s	s	NOUN
ap-1783	23	42	)	)	PUNCT
ap-1783	23	43	,	,	PUNCT
ap-1783	23	44	which	which	PRON
ap-1783	23	45	is	be	AUX
ap-1783	23	46	a	a	DET
ap-1783	23	47	real	real	ADJ
ap-1783	23	48	function	function	NOUN
ap-1783	23	49	for	for	ADP
ap-1783	23	50	s	s	PRON
ap-1783	23	51	≥	≥	NOUN
ap-1783	23	52	−1	−1	PROPN
ap-1783	23	53	/	/	SYM
ap-1783	23	54	e.	e.	PROPN
ap-1783	24	1	the	the	DET
ap-1783	24	2	series	series	PROPN
ap-1783	24	3	expansion	expansion	NOUN
ap-1783	24	4	of	of	ADP
ap-1783	24	5	w0(s	w0(s	PROPN
ap-1783	24	6	)	)	PUNCT
ap-1783	24	7	at	at	ADP
ap-1783	24	8	s	s	NOUN
ap-1783	24	9	=	=	SYM
ap-1783	24	10	0	0	NUM
ap-1783	24	11	is	be	AUX
ap-1783	24	12	w0(s	w0(s	PROPN
ap-1783	24	13	)	)	PUNCT
ap-1783	24	14	=	=	NOUN
ap-1783	25	1	∞∑	∞∑	NUM
ap-1783	25	2	n=1	n=1	PUNCT
ap-1783	25	3	(	(	PUNCT
ap-1783	25	4	−n)n−1	−n)n−1	PROPN
ap-1783	25	5	s	s	PROPN
ap-1783	25	6	n	n	PRON
ap-1783	25	7	n	n	CCONJ
ap-1783	25	8	!	!	PUNCT
ap-1783	25	9	,	,	PUNCT
ap-1783	25	10	(	(	PUNCT
ap-1783	25	11	1.4	1.4	NUM
ap-1783	25	12	)	)	PUNCT
ap-1783	25	13	with	with	ADP
ap-1783	25	14	the	the	DET
ap-1783	25	15	radius	radius	NOUN
ap-1783	25	16	of	of	ADP
ap-1783	25	17	convergence	convergence	NOUN
ap-1783	25	18	equal	equal	ADJ
ap-1783	25	19	to	to	ADP
ap-1783	25	20	1	1	NUM
ap-1783	25	21	/	/	SYM
ap-1783	25	22	e	e	X
ap-1783	26	1	[	[	X
ap-1783	26	2	3	3	NUM
ap-1783	26	3	]	]	PUNCT
ap-1783	26	4	.	.	PUNCT
ap-1783	27	1	after	after	ADP
ap-1783	27	2	some	some	DET
ap-1783	27	3	algebraic	algebraic	ADJ
ap-1783	27	4	operations	operation	NOUN
ap-1783	27	5	,	,	PUNCT
ap-1783	27	6	we	we	PRON
ap-1783	27	7	obtain	obtain	VERB
ap-1783	27	8	the	the	DET
ap-1783	27	9	moment	moment	NOUN
ap-1783	27	10	generating	generate	VERB
ap-1783	27	11	function	function	NOUN
ap-1783	27	12	g(s	g(	NOUN
ap-1783	27	13	)	)	PUNCT
ap-1783	27	14	in	in	ADP
ap-1783	27	15	the	the	DET
ap-1783	27	16	form	form	NOUN
ap-1783	27	17	of	of	ADP
ap-1783	27	18	the	the	DET
ap-1783	27	19	series	series	NOUN
ap-1783	27	20	g(s	g(s	PROPN
ap-1783	27	21	)	)	PUNCT
ap-1783	27	22	=	=	SYM
ap-1783	27	23	w0(s	w0(s	PROPN
ap-1783	27	24	)	)	PUNCT
ap-1783	27	25	s	s	PART
ap-1783	27	26	=	=	VERB
ap-1783	28	1	∞∑	∞∑	NUM
ap-1783	28	2	n=0	n=0	NUM
ap-1783	28	3	(	(	PUNCT
ap-1783	28	4	n+	n+	NUM
ap-1783	28	5	1)n−1	1)n−1	NUM
ap-1783	28	6	(	(	PUNCT
ap-1783	28	7	−s)n	−s)n	NOUN
ap-1783	28	8	n	n	CCONJ
ap-1783	28	9	!	!	NOUN
ap-1783	28	10	,	,	PUNCT
ap-1783	28	11	g(0	g(0	PROPN
ap-1783	28	12	)	)	PUNCT
ap-1783	28	13	=	=	SYM
ap-1783	28	14	1	1	NUM
ap-1783	28	15	,	,	PUNCT
ap-1783	28	16	(	(	PUNCT
ap-1783	28	17	1.5	1.5	NUM
ap-1783	28	18	)	)	PUNCT
ap-1783	28	19	in	in	ADP
ap-1783	28	20	accordance	accordance	NOUN
ap-1783	28	21	with	with	ADP
ap-1783	28	22	(	(	PUNCT
ap-1783	28	23	1.3	1.3	NUM
ap-1783	28	24	)	)	PUNCT
ap-1783	28	25	.	.	PUNCT
ap-1783	29	1	the	the	DET
ap-1783	29	2	radius	radius	NOUN
ap-1783	29	3	of	of	ADP
ap-1783	29	4	convergence	convergence	NOUN
ap-1783	29	5	is	be	AUX
ap-1783	29	6	also	also	ADV
ap-1783	29	7	equal	equal	ADJ
ap-1783	29	8	to	to	ADP
ap-1783	29	9	1	1	NUM
ap-1783	29	10	/	/	SYM
ap-1783	29	11	e.	e.	PROPN
ap-1783	29	12	it	it	PRON
ap-1783	29	13	should	should	AUX
ap-1783	29	14	be	be	AUX
ap-1783	29	15	noted	note	VERB
ap-1783	29	16	that	that	SCONJ
ap-1783	29	17	the	the	DET
ap-1783	29	18	moment	moment	NOUN
ap-1783	29	19	generating	generate	VERB
ap-1783	29	20	function	function	NOUN
ap-1783	29	21	is	be	AUX
ap-1783	29	22	often	often	ADV
ap-1783	29	23	taken	take	VERB
ap-1783	29	24	as	as	ADP
ap-1783	29	25	m(s	m(s	PROPN
ap-1783	29	26	)	)	PUNCT
ap-1783	30	1	=	=	PUNCT
ap-1783	30	2	g(−s	g(−	NOUN
ap-1783	30	3	)	)	PUNCT
ap-1783	30	4	,	,	PUNCT
ap-1783	30	5	because	because	SCONJ
ap-1783	30	6	in	in	ADP
ap-1783	30	7	this	this	DET
ap-1783	30	8	case	case	NOUN
ap-1783	30	9	the	the	DET
ap-1783	30	10	generating	generate	VERB
ap-1783	30	11	function	function	NOUN
ap-1783	30	12	has	have	VERB
ap-1783	30	13	the	the	DET
ap-1783	30	14	form	form	NOUN
ap-1783	30	15	of	of	ADP
ap-1783	30	16	an	an	DET
ap-1783	30	17	(	(	PUNCT
ap-1783	30	18	at	at	ADP
ap-1783	30	19	least	least	ADJ
ap-1783	30	20	formal	formal	ADJ
ap-1783	30	21	)	)	PUNCT
ap-1783	30	22	power	power	NOUN
ap-1783	30	23	series	series	NOUN
ap-1783	30	24	.	.	PUNCT
ap-1783	31	1	63	63	NUM
ap-1783	31	2	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1783	31	3	vladimír	vladimír	PROPN
ap-1783	31	4	vojta	vojta	PROPN
ap-1783	31	5	acta	acta	PROPN
ap-1783	31	6	polytechnica	polytechnica	PROPN
ap-1783	31	7	2	2	NUM
ap-1783	31	8	.	.	PUNCT
ap-1783	31	9	inversion	inversion	NOUN
ap-1783	31	10	of	of	ADP
ap-1783	31	11	the	the	DET
ap-1783	31	12	moment	moment	NOUN
ap-1783	31	13	generating	generate	VERB
ap-1783	31	14	function	function	NOUN
ap-1783	31	15	to	to	PART
ap-1783	31	16	obtain	obtain	VERB
ap-1783	31	17	p.d.f	p.d.f	ADJ
ap-1783	31	18	.	.	PUNCT
ap-1783	32	1	f(x	f(x	PROPN
ap-1783	32	2	)	)	PUNCT
ap-1783	32	3	,	,	PUNCT
ap-1783	32	4	we	we	PRON
ap-1783	32	5	had	have	VERB
ap-1783	32	6	to	to	PART
ap-1783	32	7	invert	invert	VERB
ap-1783	32	8	the	the	DET
ap-1783	32	9	laplace	laplace	NOUN
ap-1783	32	10	transform	transform	NOUN
ap-1783	32	11	(	(	PUNCT
ap-1783	32	12	1.1	1.1	NUM
ap-1783	32	13	)	)	PUNCT
ap-1783	32	14	.	.	PUNCT
ap-1783	33	1	three	three	NUM
ap-1783	33	2	procedures	procedure	NOUN
ap-1783	33	3	were	be	AUX
ap-1783	33	4	used	use	VERB
ap-1783	33	5	:	:	PUNCT
ap-1783	33	6	direct	direct	ADJ
ap-1783	33	7	,	,	PUNCT
ap-1783	33	8	mellin	mellin	PROPN
ap-1783	33	9	and	and	CCONJ
ap-1783	33	10	stieltjes	stieltjes	NOUN
ap-1783	33	11	.	.	PUNCT
ap-1783	34	1	2.1	2.1	NUM
ap-1783	34	2	.	.	PUNCT
ap-1783	34	3	direct	direct	ADJ
ap-1783	34	4	procedure	procedure	NOUN
ap-1783	34	5	theorem	theorem	VERB
ap-1783	34	6	2.1	2.1	NUM
ap-1783	34	7	.	.	PUNCT
ap-1783	35	1	the	the	DET
ap-1783	35	2	explicit	explicit	ADJ
ap-1783	35	3	form	form	NOUN
ap-1783	35	4	of	of	ADP
ap-1783	35	5	the	the	DET
ap-1783	35	6	cayley	cayley	ADJ
ap-1783	35	7	-	-	PUNCT
ap-1783	35	8	eisenstein	eisenstein	NOUN
ap-1783	35	9	-	-	PUNCT
ap-1783	35	10	pólya	pólya	NOUN
ap-1783	35	11	p.d.f	p.d.f	NOUN
ap-1783	35	12	.	.	PUNCT
ap-1783	35	13	is	be	AUX
ap-1783	35	14	:	:	PUNCT
ap-1783	35	15	f(x	f(x	PROPN
ap-1783	35	16	)	)	PUNCT
ap-1783	35	17	=	=	SYM
ap-1783	36	1	1	1	NUM
ap-1783	36	2	π	π	SYM
ap-1783	36	3	∫	∫	PROPN
ap-1783	36	4	π	π	X
ap-1783	36	5	0	0	PUNCT
ap-1783	37	1	(	(	PUNCT
ap-1783	37	2	y2	y2	PROPN
ap-1783	37	3	+	+	CCONJ
ap-1783	37	4	(	(	PUNCT
ap-1783	37	5	1−	1−	NUM
ap-1783	37	6	y	y	PROPN
ap-1783	37	7	cot	cot	NOUN
ap-1783	37	8	y)2)e−xy	y)2)e−xy	PROPN
ap-1783	37	9	csc	csc	PROPN
ap-1783	37	10	ye−y	ye−y	PROPN
ap-1783	37	11	cot	cot	NOUN
ap-1783	37	12	y	y	PROPN
ap-1783	37	13	dy	dy	NOUN
ap-1783	37	14	,	,	PUNCT
ap-1783	37	15	x	x	PROPN
ap-1783	37	16	>	>	X
ap-1783	37	17	0	0	NUM
ap-1783	37	18	,	,	PUNCT
ap-1783	37	19	(	(	PUNCT
ap-1783	37	20	2.1	2.1	NUM
ap-1783	37	21	)	)	PUNCT
ap-1783	37	22	proof	proof	NOUN
ap-1783	37	23	.	.	PUNCT
ap-1783	38	1	the	the	DET
ap-1783	38	2	proof	proof	NOUN
ap-1783	38	3	is	be	AUX
ap-1783	38	4	based	base	VERB
ap-1783	38	5	on	on	ADP
ap-1783	38	6	the	the	DET
ap-1783	38	7	relation	relation	NOUN
ap-1783	38	8	[	[	X
ap-1783	38	9	4	4	X
ap-1783	38	10	]	]	PUNCT
ap-1783	38	11	w0(s	w0(s	PROPN
ap-1783	38	12	)	)	PUNCT
ap-1783	38	13	s	s	PART
ap-1783	39	1	=	=	SYM
ap-1783	39	2	1	1	NUM
ap-1783	39	3	π	π	NOUN
ap-1783	39	4	∫	∫	PROPN
ap-1783	39	5	π	π	X
ap-1783	39	6	0	0	PUNCT
ap-1783	40	1	y2	y2	INTJ
ap-1783	40	2	+	+	CCONJ
ap-1783	40	3	(	(	PUNCT
ap-1783	40	4	1−	1−	NUM
ap-1783	40	5	y	y	PROPN
ap-1783	40	6	cot	cot	NOUN
ap-1783	40	7	y)2	y)2	NOUN
ap-1783	40	8	s+	s+	PUNCT
ap-1783	40	9	y	y	PROPN
ap-1783	40	10	csc	csc	PROPN
ap-1783	41	1	ye−y	ye−y	PROPN
ap-1783	41	2	cot	cot	NOUN
ap-1783	41	3	y	y	PROPN
ap-1783	41	4	dy	dy	X
ap-1783	41	5	,	,	PUNCT
ap-1783	41	6	s	s	PART
ap-1783	41	7	∈	∈	PROPN
ap-1783	41	8	c	c	NOUN
ap-1783	41	9	\	\	X
ap-1783	41	10	(	(	PUNCT
ap-1783	41	11	−∞,−1	−∞,−1	NOUN
ap-1783	41	12	/	/	SYM
ap-1783	41	13	e	e	NOUN
ap-1783	41	14	)	)	PUNCT
ap-1783	41	15	,	,	PUNCT
ap-1783	41	16	(	(	PUNCT
ap-1783	41	17	2.2	2.2	NUM
ap-1783	41	18	)	)	PUNCT
ap-1783	41	19	and	and	CCONJ
ap-1783	41	20	on	on	ADP
ap-1783	41	21	direct	direct	ADJ
ap-1783	41	22	application	application	NOUN
ap-1783	41	23	of	of	ADP
ap-1783	41	24	the	the	DET
ap-1783	41	25	bromwich	bromwich	NOUN
ap-1783	41	26	inversion	inversion	NOUN
ap-1783	41	27	formula	formula	NOUN
ap-1783	41	28	for	for	ADP
ap-1783	41	29	the	the	DET
ap-1783	41	30	laplace	laplace	NOUN
ap-1783	41	31	transform	transform	NOUN
ap-1783	41	32	and	and	CCONJ
ap-1783	41	33	of	of	ADP
ap-1783	41	34	the	the	DET
ap-1783	41	35	fubini	fubini	ADJ
ap-1783	41	36	theorem	theorem	NOUN
ap-1783	41	37	:	:	PUNCT
ap-1783	41	38	f(x	f(x	PROPN
ap-1783	41	39	)	)	PUNCT
ap-1783	41	40	=	=	SYM
ap-1783	42	1	1	1	NUM
ap-1783	42	2	2iπ	2iπ	NOUN
ap-1783	42	3	∫	∫	PROPN
ap-1783	42	4	c+i∞	c+i∞	PROPN
ap-1783	42	5	c−i∞	c−i∞	PROPN
ap-1783	42	6	exs	exs	PROPN
ap-1783	42	7	w0(s	w0(s	PROPN
ap-1783	42	8	)	)	PUNCT
ap-1783	42	9	s	s	PART
ap-1783	42	10	ds	ds	ADJ
ap-1783	42	11	=	=	SYM
ap-1783	42	12	1	1	NUM
ap-1783	43	1	π	π	NOUN
ap-1783	43	2	∫	∫	PROPN
ap-1783	43	3	π	π	X
ap-1783	43	4	0	0	PUNCT
ap-1783	44	1	(	(	PUNCT
ap-1783	44	2	y2	y2	PROPN
ap-1783	44	3	+	+	CCONJ
ap-1783	44	4	(	(	PUNCT
ap-1783	44	5	1−	1−	NUM
ap-1783	44	6	y	y	PROPN
ap-1783	44	7	cot	cot	NOUN
ap-1783	44	8	y)2	y)2	NOUN
ap-1783	44	9	)	)	PUNCT
ap-1783	44	10	1	1	NUM
ap-1783	44	11	2iπ	2iπ	NOUN
ap-1783	44	12	∫	∫	PROPN
ap-1783	44	13	c+i∞	c+i∞	PROPN
ap-1783	44	14	c−i∞	c−i∞	PROPN
ap-1783	44	15	exs	exs	PROPN
ap-1783	44	16	s+	s+	PUNCT
ap-1783	44	17	y	y	PROPN
ap-1783	44	18	csc	csc	PROPN
ap-1783	44	19	ye−y	ye−y	PROPN
ap-1783	44	20	cot	cot	NOUN
ap-1783	44	21	y	y	PROPN
ap-1783	44	22	ds	ds	PROPN
ap-1783	44	23	dy	dy	NOUN
ap-1783	44	24	,	,	PUNCT
ap-1783	44	25	c	c	X
ap-1783	44	26	>	>	X
ap-1783	44	27	−1	−1	PROPN
ap-1783	44	28	/	/	SYM
ap-1783	44	29	e	e	NOUN
ap-1783	44	30	,	,	PUNCT
ap-1783	44	31	x	x	X
ap-1783	44	32	>	>	X
ap-1783	44	33	0	0	NUM
ap-1783	44	34	.	.	PUNCT
ap-1783	45	1	(	(	PUNCT
ap-1783	45	2	2.3	2.3	NUM
ap-1783	45	3	)	)	PUNCT
ap-1783	45	4	the	the	DET
ap-1783	45	5	bromwich	bromwich	NOUN
ap-1783	45	6	integral	integral	ADJ
ap-1783	45	7	in	in	ADP
ap-1783	45	8	parentheses	parenthesis	NOUN
ap-1783	45	9	gives	give	VERB
ap-1783	45	10	e−xy	e−xy	PROPN
ap-1783	45	11	csc	csc	PROPN
ap-1783	45	12	ye−y	ye−y	PROPN
ap-1783	45	13	cot	cot	NOUN
ap-1783	45	14	y	y	PROPN
ap-1783	45	15	,	,	PUNCT
ap-1783	45	16	because	because	SCONJ
ap-1783	45	17	the	the	DET
ap-1783	45	18	inverse	inverse	NOUN
ap-1783	45	19	laplace	laplace	NOUN
ap-1783	45	20	transform	transform	NOUN
ap-1783	45	21	of	of	ADP
ap-1783	45	22	a	a	DET
ap-1783	45	23	function	function	NOUN
ap-1783	45	24	1/(s+	1/(s+	NUM
ap-1783	45	25	a	a	PRON
ap-1783	45	26	)	)	PUNCT
ap-1783	45	27	is	be	AUX
ap-1783	45	28	e−ax	e−ax	NOUN
ap-1783	45	29	,	,	PUNCT
ap-1783	45	30	and	and	CCONJ
ap-1783	45	31	we	we	PRON
ap-1783	45	32	have	have	VERB
ap-1783	45	33	finally	finally	ADV
ap-1783	45	34	eq	eq	ADJ
ap-1783	45	35	.	.	PUNCT
ap-1783	46	1	(	(	PUNCT
ap-1783	46	2	2.1	2.1	NUM
ap-1783	46	3	)	)	PUNCT
ap-1783	46	4	.	.	PUNCT
ap-1783	47	1	2.2	2.2	NUM
ap-1783	47	2	.	.	PUNCT
ap-1783	47	3	mellin	mellin	PROPN
ap-1783	47	4	procedure	procedure	NOUN
ap-1783	47	5	the	the	DET
ap-1783	47	6	mellin	mellin	ADJ
ap-1783	47	7	procedure	procedure	NOUN
ap-1783	47	8	is	be	AUX
ap-1783	47	9	based	base	VERB
ap-1783	47	10	on	on	ADP
ap-1783	47	11	the	the	DET
ap-1783	47	12	“	"	PUNCT
ap-1783	47	13	cannibalistic	cannibalistic	ADJ
ap-1783	47	14	”	"	PUNCT
ap-1783	47	15	feature	feature	NOUN
ap-1783	47	16	of	of	ADP
ap-1783	47	17	the	the	DET
ap-1783	47	18	mellin	mellin	PROPN
ap-1783	47	19	transform	transform	NOUN
ap-1783	47	20	:	:	PUNCT
ap-1783	47	21	the	the	DET
ap-1783	47	22	mellin	mellin	PROPN
ap-1783	47	23	transform	transform	NOUN
ap-1783	47	24	of	of	ADP
ap-1783	47	25	the	the	DET
ap-1783	47	26	laplace	laplace	NOUN
ap-1783	47	27	transform	transform	NOUN
ap-1783	47	28	(	(	PUNCT
ap-1783	47	29	and	and	CCONJ
ap-1783	47	30	of	of	ADP
ap-1783	47	31	many	many	ADJ
ap-1783	47	32	others	other	NOUN
ap-1783	47	33	as	as	ADV
ap-1783	47	34	well	well	ADV
ap-1783	47	35	)	)	PUNCT
ap-1783	47	36	of	of	ADP
ap-1783	47	37	some	some	DET
ap-1783	47	38	function	function	NOUN
ap-1783	47	39	is	be	AUX
ap-1783	47	40	given	give	VERB
ap-1783	47	41	by	by	ADP
ap-1783	47	42	the	the	DET
ap-1783	47	43	mellin	mellin	PROPN
ap-1783	47	44	transform	transform	NOUN
ap-1783	47	45	of	of	ADP
ap-1783	47	46	that	that	DET
ap-1783	47	47	function	function	NOUN
ap-1783	47	48	only	only	ADV
ap-1783	47	49	[	[	X
ap-1783	47	50	5	5	NUM
ap-1783	47	51	]	]	PUNCT
ap-1783	47	52	.	.	PUNCT
ap-1783	48	1	symbolically	symbolically	ADV
ap-1783	48	2	:	:	PUNCT
ap-1783	48	3	mt	mt	PROPN
ap-1783	48	4	[	[	PUNCT
ap-1783	48	5	lt	lt	X
ap-1783	48	6	[	[	PUNCT
ap-1783	48	7	h(t	h(t	PROPN
ap-1783	48	8	)	)	PUNCT
ap-1783	48	9	;	;	PUNCT
ap-1783	48	10	p	p	X
ap-1783	48	11	]	]	PUNCT
ap-1783	48	12	;	;	PUNCT
ap-1783	48	13	s	s	X
ap-1783	48	14	]	]	X
ap-1783	48	15	=	=	SYM
ap-1783	48	16	γ(s	γ(s	PROPN
ap-1783	48	17	)	)	PUNCT
ap-1783	48	18	mt	mt	PROPN
ap-1783	48	19	[	[	PUNCT
ap-1783	48	20	h(t	h(t	PROPN
ap-1783	48	21	)	)	PUNCT
ap-1783	48	22	;	;	PUNCT
ap-1783	48	23	1−	1−	NUM
ap-1783	48	24	s	s	X
ap-1783	48	25	]	]	PUNCT
ap-1783	48	26	,	,	PUNCT
ap-1783	48	27	mt	mt	PROPN
ap-1783	48	28	[	[	PUNCT
ap-1783	48	29	h(t	h(t	PROPN
ap-1783	48	30	)	)	PUNCT
ap-1783	48	31	;	;	PUNCT
ap-1783	48	32	s	s	X
ap-1783	48	33	]	]	X
ap-1783	48	34	=	=	PUNCT
ap-1783	48	35	mt	mt	PROPN
ap-1783	48	36	[	[	PUNCT
ap-1783	48	37	lt	lt	X
ap-1783	48	38	[	[	PUNCT
ap-1783	48	39	h(t	h(t	PROPN
ap-1783	48	40	)	)	PUNCT
ap-1783	48	41	;	;	PUNCT
ap-1783	48	42	p	p	X
ap-1783	48	43	]	]	X
ap-1783	48	44	;	;	PUNCT
ap-1783	48	45	1−	1−	NUM
ap-1783	48	46	s	s	X
ap-1783	48	47	]	]	PUNCT
ap-1783	48	48	/γ(1−	/γ(1−	PUNCT
ap-1783	48	49	s	s	X
ap-1783	48	50	)	)	PUNCT
ap-1783	48	51	,	,	PUNCT
ap-1783	48	52	(	(	PUNCT
ap-1783	48	53	2.4	2.4	NUM
ap-1783	48	54	)	)	PUNCT
ap-1783	48	55	where	where	SCONJ
ap-1783	48	56	mt	mt	PROPN
ap-1783	48	57	and	and	CCONJ
ap-1783	48	58	lt	lt	PROPN
ap-1783	48	59	represent	represent	VERB
ap-1783	48	60	the	the	DET
ap-1783	48	61	mellin	mellin	PROPN
ap-1783	48	62	transform	transform	NOUN
ap-1783	48	63	and	and	CCONJ
ap-1783	48	64	the	the	DET
ap-1783	48	65	laplace	laplace	NOUN
ap-1783	48	66	transform	transform	NOUN
ap-1783	48	67	,	,	PUNCT
ap-1783	48	68	and	and	CCONJ
ap-1783	48	69	γ(s	γ(	NOUN
ap-1783	48	70	)	)	PUNCT
ap-1783	48	71	is	be	AUX
ap-1783	48	72	the	the	DET
ap-1783	48	73	gamma	gamma	NOUN
ap-1783	48	74	function	function	NOUN
ap-1783	48	75	of	of	ADP
ap-1783	48	76	argument	argument	NOUN
ap-1783	48	77	s.	s.	PROPN
ap-1783	48	78	lemma	lemma	PROPN
ap-1783	48	79	2.2	2.2	NUM
ap-1783	48	80	.	.	PUNCT
ap-1783	49	1	the	the	DET
ap-1783	49	2	following	follow	VERB
ap-1783	49	3	mellin	mellin	PROPN
ap-1783	49	4	transform	transform	NOUN
ap-1783	49	5	pair	pair	NOUN
ap-1783	49	6	holds	hold	VERB
ap-1783	49	7	:	:	PUNCT
ap-1783	49	8	ss	ss	NOUN
ap-1783	49	9	=	=	PUNCT
ap-1783	49	10	∫	∫	PROPN
ap-1783	50	1	∞	∞	PROPN
ap-1783	50	2	0	0	NUM
ap-1783	50	3	xs−1f0(x	xs−1f0(x	PROPN
ap-1783	50	4	)	)	PUNCT
ap-1783	50	5	dx	dx	PROPN
ap-1783	50	6	,	,	PUNCT
ap-1783	50	7	s	s	PART
ap-1783	50	8	>	>	X
ap-1783	50	9	0	0	PROPN
ap-1783	50	10	,	,	PUNCT
ap-1783	50	11	where	where	SCONJ
ap-1783	50	12	f0(x	f0(x	NOUN
ap-1783	50	13	)	)	PUNCT
ap-1783	50	14	=	=	SYM
ap-1783	51	1	1	1	NUM
ap-1783	51	2	π	π	NOUN
ap-1783	51	3	∫	∫	PROPN
ap-1783	51	4	∞	∞	NUM
ap-1783	51	5	0	0	NUM
ap-1783	51	6	xyy−y	xyy−y	PROPN
ap-1783	51	7	sin	sin	NOUN
ap-1783	51	8	πy	πy	X
ap-1783	51	9	dy	dy	NOUN
ap-1783	51	10	,	,	PUNCT
ap-1783	51	11	x	x	X
ap-1783	51	12	>	>	X
ap-1783	51	13	0	0	NUM
ap-1783	51	14	.	.	PUNCT
ap-1783	52	1	(	(	PUNCT
ap-1783	52	2	2.5	2.5	NUM
ap-1783	52	3	)	)	PUNCT
ap-1783	52	4	proof	proof	NOUN
ap-1783	52	5	.	.	PUNCT
ap-1783	53	1	in	in	ADP
ap-1783	53	2	accordance	accordance	NOUN
ap-1783	53	3	with	with	ADP
ap-1783	53	4	the	the	DET
ap-1783	53	5	bromwich	bromwich	NOUN
ap-1783	53	6	inversion	inversion	NOUN
ap-1783	53	7	formula	formula	NOUN
ap-1783	53	8	for	for	ADP
ap-1783	53	9	the	the	DET
ap-1783	53	10	mellin	mellin	PROPN
ap-1783	53	11	transform	transform	NOUN
ap-1783	53	12	,	,	PUNCT
ap-1783	53	13	the	the	DET
ap-1783	53	14	function	function	NOUN
ap-1783	53	15	f0(x	f0(x	NOUN
ap-1783	53	16	)	)	PUNCT
ap-1783	53	17	can	can	AUX
ap-1783	53	18	be	be	AUX
ap-1783	53	19	recovered	recover	VERB
ap-1783	53	20	by	by	ADP
ap-1783	53	21	contour	contour	NOUN
ap-1783	53	22	integrals	integral	NOUN
ap-1783	53	23	f0(x	f0(x	NOUN
ap-1783	53	24	)	)	PUNCT
ap-1783	53	25	=	=	SYM
ap-1783	54	1	1	1	NUM
ap-1783	54	2	2iπ	2iπ	NOUN
ap-1783	54	3	∫	∫	PROPN
ap-1783	54	4	c+i∞	c+i∞	PROPN
ap-1783	54	5	c−i∞	c−i∞	PROPN
ap-1783	54	6	x−sss	x−sss	X
ap-1783	54	7	ds	ds	PROPN
ap-1783	54	8	=	=	NOUN
ap-1783	54	9	1	1	NUM
ap-1783	54	10	2iπ	2iπ	NOUN
ap-1783	54	11	∫	∫	PROPN
ap-1783	54	12	(	(	PUNCT
ap-1783	54	13	0	0	NUM
ap-1783	54	14	+	+	NOUN
ap-1783	54	15	)	)	PUNCT
ap-1783	54	16	−∞	−∞	X
ap-1783	54	17	x−sss	x−sss	X
ap-1783	54	18	ds	ds	PROPN
ap-1783	54	19	,	,	PUNCT
ap-1783	54	20	(	(	PUNCT
ap-1783	54	21	2.6	2.6	NUM
ap-1783	54	22	)	)	PUNCT
ap-1783	54	23	where	where	SCONJ
ap-1783	54	24	the	the	DET
ap-1783	54	25	first	first	ADJ
ap-1783	54	26	integral	integral	NOUN
ap-1783	54	27	is	be	AUX
ap-1783	54	28	along	along	ADP
ap-1783	54	29	the	the	DET
ap-1783	54	30	bromwich	bromwich	PROPN
ap-1783	54	31	contour	contour	NOUN
ap-1783	54	32	and	and	CCONJ
ap-1783	54	33	the	the	DET
ap-1783	54	34	second	second	ADJ
ap-1783	54	35	integral	integral	NOUN
ap-1783	54	36	is	be	AUX
ap-1783	54	37	along	along	ADP
ap-1783	54	38	the	the	DET
ap-1783	54	39	left	left	ADJ
ap-1783	54	40	anticlockwise	anticlockwise	NOUN
ap-1783	54	41	hankel	hankel	PROPN
ap-1783	54	42	contour	contour	NOUN
ap-1783	54	43	.	.	PUNCT
ap-1783	55	1	the	the	DET
ap-1783	55	2	equivalence	equivalence	NOUN
ap-1783	55	3	of	of	ADP
ap-1783	55	4	these	these	DET
ap-1783	55	5	two	two	NUM
ap-1783	55	6	integrals	integral	NOUN
ap-1783	55	7	is	be	AUX
ap-1783	55	8	based	base	VERB
ap-1783	55	9	on	on	ADP
ap-1783	55	10	the	the	DET
ap-1783	55	11	cauchy	cauchy	ADJ
ap-1783	55	12	integral	integral	ADJ
ap-1783	55	13	theorem	theorem	NOUN
ap-1783	55	14	,	,	PUNCT
ap-1783	55	15	and	and	CCONJ
ap-1783	55	16	on	on	ADP
ap-1783	55	17	the	the	DET
ap-1783	55	18	fact	fact	NOUN
ap-1783	55	19	that	that	SCONJ
ap-1783	55	20	the	the	DET
ap-1783	55	21	integrand	integrand	NOUN
ap-1783	55	22	has	have	AUX
ap-1783	55	23	two	two	NUM
ap-1783	55	24	branch	branch	NOUN
ap-1783	55	25	points	point	NOUN
ap-1783	55	26	s	s	PART
ap-1783	55	27	=	=	SYM
ap-1783	55	28	0	0	NUM
ap-1783	55	29	,	,	PUNCT
ap-1783	55	30	s	s	NOUN
ap-1783	55	31	=	=	PUNCT
ap-1783	55	32	−∞	−∞	NOUN
ap-1783	55	33	and	and	CCONJ
ap-1783	55	34	a	a	DET
ap-1783	55	35	branch	branch	NOUN
ap-1783	55	36	cut	cut	VERB
ap-1783	55	37	in	in	ADP
ap-1783	55	38	the	the	DET
ap-1783	55	39	s	s	NOUN
ap-1783	55	40	-	-	NOUN
ap-1783	55	41	plane	plane	NOUN
ap-1783	55	42	along	along	ADP
ap-1783	55	43	the	the	DET
ap-1783	55	44	interval	interval	NOUN
ap-1783	55	45	(	(	PUNCT
ap-1783	55	46	−∞	−∞	NOUN
ap-1783	55	47	,	,	PUNCT
ap-1783	55	48	0	0	NUM
ap-1783	55	49	)	)	PUNCT
ap-1783	55	50	,	,	PUNCT
ap-1783	55	51	and	and	CCONJ
ap-1783	55	52	no	no	DET
ap-1783	55	53	other	other	ADJ
ap-1783	55	54	singularity	singularity	NOUN
ap-1783	55	55	.	.	PUNCT
ap-1783	56	1	then	then	ADV
ap-1783	56	2	f0(x	f0(x	NOUN
ap-1783	56	3	)	)	PUNCT
ap-1783	56	4	=	=	SYM
ap-1783	57	1	1	1	NUM
ap-1783	57	2	2iπ	2iπ	NOUN
ap-1783	57	3	∫	∫	PROPN
ap-1783	57	4	(	(	PUNCT
ap-1783	57	5	0	0	NUM
ap-1783	57	6	+	+	NOUN
ap-1783	57	7	)	)	PUNCT
ap-1783	57	8	−∞	−∞	ADP
ap-1783	57	9	x−sss	x−sss	X
ap-1783	57	10	ds	ds	X
ap-1783	57	11	=	=	NOUN
ap-1783	57	12	1	1	NUM
ap-1783	57	13	2iπ	2iπ	NOUN
ap-1783	57	14	∫	∫	PROPN
ap-1783	57	15	∞	∞	NOUN
ap-1783	57	16	0	0	NUM
ap-1783	57	17	xye−y(ln	xye−y(ln	PROPN
ap-1783	57	18	y−iπ	y−iπ	PROPN
ap-1783	57	19	)	)	PUNCT
ap-1783	57	20	dy	dy	NOUN
ap-1783	57	21	−	−	NOUN
ap-1783	57	22	1	1	NUM
ap-1783	57	23	2iπ	2iπ	NOUN
ap-1783	57	24	∫	∫	PROPN
ap-1783	58	1	∞	∞	NOUN
ap-1783	58	2	0	0	NUM
ap-1783	58	3	xye−y(ln	xye−y(ln	PROPN
ap-1783	58	4	y+iπ	y+iπ	PROPN
ap-1783	58	5	)	)	PUNCT
ap-1783	58	6	dy	dy	NOUN
ap-1783	59	1	+	+	NOUN
ap-1783	60	1	1	1	NUM
ap-1783	60	2	2iπ	2iπ	NOUN
ap-1783	60	3	lim	lim	PROPN
ap-1783	60	4	r→0	r→0	VERB
ap-1783	60	5	∫	∫	PROPN
ap-1783	60	6	cr	cr	AUX
ap-1783	60	7	x−sss	x−sss	PROPN
ap-1783	60	8	ds	ds	PROPN
ap-1783	60	9	=	=	NOUN
ap-1783	60	10	1	1	NUM
ap-1783	60	11	2iπ	2iπ	NOUN
ap-1783	60	12	∫	∫	PROPN
ap-1783	60	13	∞	∞	NOUN
ap-1783	60	14	0	0	NUM
ap-1783	61	1	xye−y	xye−y	PROPN
ap-1783	61	2	ln	ln	ADJ
ap-1783	61	3	y(eiπy	y(eiπy	PROPN
ap-1783	61	4	−	−	PROPN
ap-1783	61	5	e−iπy	e−iπy	X
ap-1783	61	6	)	)	PUNCT
ap-1783	61	7	dy	dy	NOUN
ap-1783	62	1	+	+	NOUN
ap-1783	62	2	0	0	NUM
ap-1783	62	3	=	=	SYM
ap-1783	62	4	1	1	NUM
ap-1783	62	5	π	π	NOUN
ap-1783	62	6	∫	∫	PROPN
ap-1783	63	1	∞	∞	NUM
ap-1783	63	2	0	0	NUM
ap-1783	63	3	xyy−y	xyy−y	PROPN
ap-1783	63	4	sin	sin	NOUN
ap-1783	63	5	πy	πy	X
ap-1783	63	6	dy	dy	NOUN
ap-1783	63	7	,	,	PUNCT
ap-1783	63	8	x	x	X
ap-1783	63	9	>	>	X
ap-1783	63	10	0	0	NUM
ap-1783	63	11	,	,	PUNCT
ap-1783	63	12	(	(	PUNCT
ap-1783	63	13	2.7	2.7	NUM
ap-1783	63	14	)	)	PUNCT
ap-1783	63	15	where	where	SCONJ
ap-1783	63	16	cr	cr	PROPN
ap-1783	63	17	is	be	AUX
ap-1783	63	18	a	a	DET
ap-1783	63	19	small	small	ADJ
ap-1783	63	20	circle	circle	NOUN
ap-1783	63	21	with	with	ADP
ap-1783	63	22	radius	radius	NOUN
ap-1783	63	23	r	r	NOUN
ap-1783	63	24	around	around	ADP
ap-1783	63	25	the	the	DET
ap-1783	63	26	origin	origin	NOUN
ap-1783	63	27	.	.	PUNCT
ap-1783	64	1	theorem	theorem	VERB
ap-1783	64	2	2.3	2.3	NUM
ap-1783	64	3	.	.	PUNCT
ap-1783	65	1	the	the	DET
ap-1783	65	2	cayley	cayley	ADJ
ap-1783	65	3	-	-	PUNCT
ap-1783	65	4	eisenstein	eisenstein	NOUN
ap-1783	65	5	-	-	PUNCT
ap-1783	65	6	pólya	pólya	NOUN
ap-1783	65	7	p.d.f	p.d.f	NOUN
ap-1783	65	8	.	.	PUNCT
ap-1783	66	1	f(x	f(x	PROPN
ap-1783	66	2	)	)	PUNCT
ap-1783	66	3	is	be	AUX
ap-1783	66	4	represented	represent	VERB
ap-1783	66	5	by	by	ADP
ap-1783	66	6	the	the	DET
ap-1783	66	7	integral	integral	ADJ
ap-1783	66	8	f(x	f(x	PROPN
ap-1783	66	9	)	)	PUNCT
ap-1783	67	1	=	=	SYM
ap-1783	68	1	∫	∫	PROPN
ap-1783	69	1	∞	∞	NUM
ap-1783	69	2	x	x	PROPN
ap-1783	69	3	ln	ln	NOUN
ap-1783	69	4	z	z	NOUN
ap-1783	69	5	x	x	SYM
ap-1783	69	6	f0(z	f0(z	NUM
ap-1783	69	7	)	)	PUNCT
ap-1783	69	8	z	z	NOUN
ap-1783	69	9	dz	dz	PROPN
ap-1783	69	10	,	,	PUNCT
ap-1783	69	11	x	x	SYM
ap-1783	69	12	>	>	X
ap-1783	69	13	0	0	NUM
ap-1783	69	14	,	,	PUNCT
ap-1783	69	15	(	(	PUNCT
ap-1783	69	16	2.8	2.8	NUM
ap-1783	69	17	)	)	PUNCT
ap-1783	69	18	where	where	SCONJ
ap-1783	69	19	function	function	NOUN
ap-1783	69	20	f0(x	f0(x	NOUN
ap-1783	69	21	)	)	PUNCT
ap-1783	69	22	is	be	AUX
ap-1783	69	23	given	give	VERB
ap-1783	69	24	by	by	ADP
ap-1783	69	25	eq	eq	PROPN
ap-1783	69	26	.	.	PUNCT
ap-1783	70	1	(	(	PUNCT
ap-1783	70	2	2.7	2.7	NUM
ap-1783	70	3	)	)	PUNCT
ap-1783	70	4	.	.	PUNCT
ap-1783	71	1	64	64	NUM
ap-1783	71	2	vol	vol	NOUN
ap-1783	71	3	.	.	PUNCT
ap-1783	72	1	53	53	NUM
ap-1783	72	2	no	no	NOUN
ap-1783	72	3	.	.	PUNCT
ap-1783	73	1	2/2013	2/2013	NUM
ap-1783	73	2	cayley	cayley	ADJ
ap-1783	73	3	-	-	PUNCT
ap-1783	73	4	eisenstein	eisenstein	NOUN
ap-1783	73	5	-	-	PUNCT
ap-1783	73	6	pólya	pólya	NOUN
ap-1783	74	1	and	and	CCONJ
ap-1783	74	2	landau	landau	VERB
ap-1783	74	3	probability	probability	NOUN
ap-1783	74	4	distributions	distribution	NOUN
ap-1783	74	5	proof	proof	NOUN
ap-1783	74	6	.	.	PUNCT
ap-1783	75	1	we	we	PRON
ap-1783	75	2	start	start	VERB
ap-1783	75	3	the	the	DET
ap-1783	75	4	proof	proof	NOUN
ap-1783	75	5	from	from	ADP
ap-1783	75	6	the	the	DET
ap-1783	75	7	known	know	VERB
ap-1783	75	8	relationship	relationship	NOUN
ap-1783	75	9	[	[	X
ap-1783	75	10	3]∫	3]∫	NUM
ap-1783	75	11	∞	∞	NUM
ap-1783	75	12	0	0	PUNCT
ap-1783	76	1	us−1w0(u	us−1w0(u	NUM
ap-1783	76	2	)	)	PUNCT
ap-1783	76	3	du	du	NOUN
ap-1783	76	4	=	=	SYM
ap-1783	76	5	(	(	PUNCT
ap-1783	76	6	−s)−sγ(s	−s)−sγ(s	PROPN
ap-1783	76	7	)	)	PUNCT
ap-1783	76	8	s	s	PART
ap-1783	76	9	,	,	PUNCT
ap-1783	76	10	<	<	X
ap-1783	76	11	s	s	X
ap-1783	76	12	∈	∈	PROPN
ap-1783	76	13	(	(	PUNCT
ap-1783	76	14	−1	−1	NOUN
ap-1783	76	15	,	,	PUNCT
ap-1783	76	16	0	0	NUM
ap-1783	76	17	)	)	PUNCT
ap-1783	76	18	,	,	PUNCT
ap-1783	76	19	(	(	PUNCT
ap-1783	76	20	2.9	2.9	NUM
ap-1783	76	21	)	)	PUNCT
ap-1783	76	22	from	from	ADP
ap-1783	76	23	which	which	PRON
ap-1783	76	24	immediately	immediately	ADV
ap-1783	76	25	follows	follow	VERB
ap-1783	76	26	[	[	X
ap-1783	76	27	5	5	NUM
ap-1783	76	28	,	,	PUNCT
ap-1783	76	29	entry	entry	NOUN
ap-1783	76	30	1.3	1.3	NUM
ap-1783	76	31	,	,	PUNCT
ap-1783	76	32	p.	p.	NOUN
ap-1783	76	33	11]∫	11]∫	NUM
ap-1783	77	1	∞	∞	NOUN
ap-1783	77	2	0	0	NUM
ap-1783	78	1	us−1w0(u	us−1w0(u	NUM
ap-1783	78	2	)	)	PUNCT
ap-1783	79	1	u	u	NOUN
ap-1783	79	2	du	du	NOUN
ap-1783	79	3	=	=	X
ap-1783	79	4	(	(	PUNCT
ap-1783	79	5	1−	1−	NUM
ap-1783	79	6	s)1−sγ(s−	s)1−sγ(s−	NOUN
ap-1783	79	7	1	1	NUM
ap-1783	79	8	)	)	PUNCT
ap-1783	79	9	s−	s−	PROPN
ap-1783	79	10	1	1	NUM
ap-1783	79	11	,	,	PUNCT
ap-1783	79	12	<	<	X
ap-1783	79	13	s	s	X
ap-1783	79	14	∈	∈	PROPN
ap-1783	79	15	(	(	PUNCT
ap-1783	79	16	0	0	NUM
ap-1783	79	17	,	,	PUNCT
ap-1783	79	18	1	1	NUM
ap-1783	79	19	)	)	PUNCT
ap-1783	79	20	,	,	PUNCT
ap-1783	79	21	(	(	PUNCT
ap-1783	79	22	2.10	2.10	NUM
ap-1783	79	23	)	)	PUNCT
ap-1783	79	24	and	and	CCONJ
ap-1783	79	25	according	accord	VERB
ap-1783	79	26	to	to	ADP
ap-1783	79	27	eq	eq	PROPN
ap-1783	79	28	.	.	PUNCT
ap-1783	80	1	(	(	PUNCT
ap-1783	80	2	2.4	2.4	NUM
ap-1783	80	3	)	)	PUNCT
ap-1783	80	4	we	we	PRON
ap-1783	80	5	obtain	obtain	VERB
ap-1783	80	6	the	the	DET
ap-1783	80	7	mellin	mellin	ADJ
ap-1783	80	8	transform	transform	NOUN
ap-1783	80	9	of	of	ADP
ap-1783	80	10	the	the	DET
ap-1783	80	11	cayley	cayley	ADJ
ap-1783	80	12	-	-	PUNCT
ap-1783	80	13	eisenstein	eisenstein	NOUN
ap-1783	80	14	-	-	PUNCT
ap-1783	80	15	pólya	pólya	NOUN
ap-1783	80	16	p.d.f.:∫	p.d.f.:∫	PROPN
ap-1783	80	17	∞	∞	PROPN
ap-1783	80	18	0	0	NUM
ap-1783	80	19	xs−1f(x	xs−1f(x	PROPN
ap-1783	80	20	)	)	PUNCT
ap-1783	80	21	dx	dx	PROPN
ap-1783	81	1	=	=	SYM
ap-1783	81	2	ss	ss	PROPN
ap-1783	81	3	s2	s2	PROPN
ap-1783	81	4	,	,	PUNCT
ap-1783	81	5	<	<	X
ap-1783	81	6	s	s	X
ap-1783	81	7	>	>	X
ap-1783	81	8	0	0	NUM
ap-1783	81	9	.	.	PUNCT
ap-1783	82	1	(	(	PUNCT
ap-1783	82	2	2.11	2.11	NUM
ap-1783	82	3	)	)	PUNCT
ap-1783	82	4	inversion	inversion	NOUN
ap-1783	82	5	of	of	ADP
ap-1783	82	6	the	the	DET
ap-1783	82	7	mellin	mellin	PROPN
ap-1783	82	8	transform	transform	NOUN
ap-1783	82	9	(	(	PUNCT
ap-1783	82	10	2.11	2.11	NUM
ap-1783	82	11	)	)	PUNCT
ap-1783	82	12	can	can	AUX
ap-1783	82	13	be	be	AUX
ap-1783	82	14	divided	divide	VERB
ap-1783	82	15	into	into	ADP
ap-1783	82	16	two	two	NUM
ap-1783	82	17	steps	step	NOUN
ap-1783	82	18	.	.	PUNCT
ap-1783	83	1	the	the	DET
ap-1783	83	2	first	first	ADJ
ap-1783	83	3	step	step	NOUN
ap-1783	83	4	is	be	AUX
ap-1783	83	5	the	the	DET
ap-1783	83	6	inversion	inversion	NOUN
ap-1783	83	7	of	of	ADP
ap-1783	83	8	ss	ss	NOUN
ap-1783	83	9	,	,	PUNCT
ap-1783	83	10	giving	give	VERB
ap-1783	83	11	auxiliary	auxiliary	ADJ
ap-1783	83	12	function	function	NOUN
ap-1783	83	13	f0(x	f0(x	NOUN
ap-1783	83	14	)	)	PUNCT
ap-1783	83	15	according	accord	VERB
ap-1783	83	16	to	to	ADP
ap-1783	83	17	lemma	lemma	PROPN
ap-1783	83	18	2.1	2.1	NUM
ap-1783	83	19	,	,	PUNCT
ap-1783	83	20	eq	eq	NOUN
ap-1783	83	21	.	.	PUNCT
ap-1783	84	1	(	(	PUNCT
ap-1783	84	2	2.7	2.7	NUM
ap-1783	84	3	)	)	PUNCT
ap-1783	84	4	.	.	PUNCT
ap-1783	85	1	the	the	DET
ap-1783	85	2	second	second	ADJ
ap-1783	85	3	step	step	NOUN
ap-1783	85	4	,	,	PUNCT
ap-1783	85	5	according	accord	VERB
ap-1783	85	6	to	to	ADP
ap-1783	85	7	[	[	X
ap-1783	85	8	5	5	NUM
ap-1783	85	9	,	,	PUNCT
ap-1783	85	10	entry	entry	NOUN
ap-1783	85	11	1.17	1.17	NUM
ap-1783	85	12	,	,	PUNCT
ap-1783	85	13	p.	p.	NOUN
ap-1783	85	14	12	12	NUM
ap-1783	85	15	]	]	PUNCT
ap-1783	85	16	combined	combine	VERB
ap-1783	85	17	with	with	ADP
ap-1783	85	18	[	[	X
ap-1783	85	19	5	5	NUM
ap-1783	85	20	,	,	PUNCT
ap-1783	85	21	entry	entry	NOUN
ap-1783	85	22	1.3	1.3	NUM
ap-1783	85	23	,	,	PUNCT
ap-1783	85	24	p.	p.	NOUN
ap-1783	85	25	11	11	NUM
ap-1783	85	26	]	]	PUNCT
ap-1783	85	27	,	,	PUNCT
ap-1783	85	28	gives	give	VERB
ap-1783	85	29	the	the	DET
ap-1783	85	30	inversion	inversion	NOUN
ap-1783	85	31	f1(x	f1(x	NOUN
ap-1783	85	32	)	)	PUNCT
ap-1783	85	33	of	of	ADP
ap-1783	85	34	ss	ss	PROPN
ap-1783	85	35	/	/	SYM
ap-1783	85	36	s	s	NOUN
ap-1783	85	37	as	as	ADP
ap-1783	85	38	f1(x	f1(x	NOUN
ap-1783	85	39	)	)	PUNCT
ap-1783	85	40	=	=	SYM
ap-1783	86	1	∫	∫	PROPN
ap-1783	86	2	∞	∞	PROPN
ap-1783	86	3	x	x	SYM
ap-1783	86	4	f0(z	f0(z	PROPN
ap-1783	86	5	)	)	PUNCT
ap-1783	86	6	z	z	NOUN
ap-1783	86	7	dz	dz	PROPN
ap-1783	86	8	,	,	PUNCT
ap-1783	86	9	x	x	SYM
ap-1783	86	10	>	>	X
ap-1783	86	11	0	0	NUM
ap-1783	86	12	,	,	PUNCT
ap-1783	86	13	(	(	PUNCT
ap-1783	86	14	2.12	2.12	NUM
ap-1783	86	15	)	)	PUNCT
ap-1783	86	16	and	and	CCONJ
ap-1783	86	17	,	,	PUNCT
ap-1783	86	18	repeating	repeat	VERB
ap-1783	86	19	this	this	DET
ap-1783	86	20	procedure	procedure	NOUN
ap-1783	86	21	once	once	ADV
ap-1783	86	22	more	more	ADV
ap-1783	86	23	,	,	PUNCT
ap-1783	86	24	we	we	PRON
ap-1783	86	25	obtain	obtain	VERB
ap-1783	86	26	p.d.f	p.d.f	ADJ
ap-1783	86	27	.	.	PUNCT
ap-1783	87	1	f(x	f(x	PROPN
ap-1783	87	2	)	)	PUNCT
ap-1783	87	3	as	as	ADP
ap-1783	87	4	f(x	f(x	PROPN
ap-1783	87	5	)	)	PUNCT
ap-1783	87	6	=	=	SYM
ap-1783	88	1	∫	∫	PROPN
ap-1783	88	2	∞	∞	NUM
ap-1783	88	3	x	x	SYM
ap-1783	88	4	f1(z	f1(z	PROPN
ap-1783	88	5	)	)	PUNCT
ap-1783	88	6	z	z	NOUN
ap-1783	88	7	dz	dz	PROPN
ap-1783	88	8	,	,	PUNCT
ap-1783	88	9	x	x	X
ap-1783	88	10	>	>	X
ap-1783	88	11	0	0	NUM
ap-1783	88	12	.	.	PUNCT
ap-1783	89	1	(	(	PUNCT
ap-1783	89	2	2.13	2.13	NUM
ap-1783	89	3	)	)	PUNCT
ap-1783	89	4	two	two	NUM
ap-1783	89	5	consecutive	consecutive	ADJ
ap-1783	89	6	integrations	integration	NOUN
ap-1783	89	7	eq	eq	ADJ
ap-1783	89	8	.	.	PUNCT
ap-1783	90	1	(	(	PUNCT
ap-1783	90	2	2.12	2.12	NUM
ap-1783	90	3	)	)	PUNCT
ap-1783	90	4	and	and	CCONJ
ap-1783	90	5	eq	eq	NOUN
ap-1783	90	6	.	.	PUNCT
ap-1783	91	1	(	(	PUNCT
ap-1783	91	2	2.13	2.13	NUM
ap-1783	91	3	)	)	PUNCT
ap-1783	91	4	can	can	AUX
ap-1783	91	5	be	be	AUX
ap-1783	91	6	replaced	replace	VERB
ap-1783	91	7	by	by	ADP
ap-1783	91	8	one	one	NUM
ap-1783	91	9	integration	integration	NOUN
ap-1783	91	10	eq	eq	ADP
ap-1783	91	11	.	.	PUNCT
ap-1783	92	1	(	(	PUNCT
ap-1783	92	2	2.8	2.8	NUM
ap-1783	92	3	)	)	PUNCT
ap-1783	92	4	.	.	PUNCT
ap-1783	93	1	2.3	2.3	NUM
ap-1783	93	2	.	.	PUNCT
ap-1783	94	1	stieltjes	stieltjes	PROPN
ap-1783	94	2	procedure	procedure	NOUN
ap-1783	94	3	this	this	DET
ap-1783	94	4	procedure	procedure	NOUN
ap-1783	94	5	is	be	AUX
ap-1783	94	6	based	base	VERB
ap-1783	94	7	on	on	ADP
ap-1783	94	8	the	the	DET
ap-1783	94	9	fact	fact	NOUN
ap-1783	94	10	that	that	SCONJ
ap-1783	94	11	the	the	DET
ap-1783	94	12	function	function	NOUN
ap-1783	94	13	w0(s)/s	w0(s)/s	PROPN
ap-1783	94	14	is	be	AUX
ap-1783	94	15	a	a	DET
ap-1783	94	16	stieltjes	stieltjes	NOUN
ap-1783	94	17	function	function	NOUN
ap-1783	94	18	,	,	PUNCT
ap-1783	94	19	and	and	CCONJ
ap-1783	94	20	can	can	AUX
ap-1783	94	21	be	be	AUX
ap-1783	94	22	represented	represent	VERB
ap-1783	94	23	as	as	SCONJ
ap-1783	94	24	the	the	DET
ap-1783	94	25	stieltjes	stieltjes	NOUN
ap-1783	94	26	transform	transform	VERB
ap-1783	94	27	[	[	X
ap-1783	94	28	4	4	NUM
ap-1783	94	29	]	]	SYM
ap-1783	94	30	:	:	PUNCT
ap-1783	94	31	w0(s	w0(s	X
ap-1783	94	32	)	)	PUNCT
ap-1783	94	33	s	s	PART
ap-1783	94	34	=	=	SYM
ap-1783	95	1	1	1	NUM
ap-1783	95	2	π	π	NOUN
ap-1783	95	3	∫	∫	PROPN
ap-1783	95	4	∞	∞	NUM
ap-1783	95	5	1	1	NUM
ap-1783	95	6	/	/	SYM
ap-1783	95	7	e	e	NOUN
ap-1783	95	8	=	=	NOUN
ap-1783	95	9	w0(−u	w0(−u	X
ap-1783	95	10	)	)	PUNCT
ap-1783	95	11	u	u	NOUN
ap-1783	95	12	1	1	NUM
ap-1783	95	13	s+	s+	PUNCT
ap-1783	95	14	u	u	PROPN
ap-1783	95	15	du	du	PROPN
ap-1783	95	16	,	,	PUNCT
ap-1783	95	17	s	s	PART
ap-1783	95	18	∈	∈	PROPN
ap-1783	95	19	c	c	NOUN
ap-1783	95	20	\	\	X
ap-1783	95	21	(	(	PUNCT
ap-1783	95	22	−∞,−1	−∞,−1	NOUN
ap-1783	95	23	/	/	SYM
ap-1783	95	24	e	e	NOUN
ap-1783	95	25	)	)	PUNCT
ap-1783	95	26	,	,	PUNCT
ap-1783	95	27	(	(	PUNCT
ap-1783	95	28	2.14	2.14	NUM
ap-1783	95	29	)	)	PUNCT
ap-1783	95	30	where	where	SCONJ
ap-1783	95	31	w0(−u	w0(−u	ADP
ap-1783	95	32	)	)	PUNCT
ap-1783	96	1	=	=	SYM
ap-1783	96	2	limθ→0	limθ→0	PROPN
ap-1783	96	3	+	+	NUM
ap-1783	96	4	w0(−u+	w0(−u+	NOUN
ap-1783	96	5	iθ	iθ	NOUN
ap-1783	96	6	)	)	PUNCT
ap-1783	96	7	for	for	ADP
ap-1783	96	8	u	u	PROPN
ap-1783	96	9	>	>	X
ap-1783	96	10	−1	−1	PROPN
ap-1783	96	11	/	/	SYM
ap-1783	96	12	e	e	NOUN
ap-1783	96	13	and	and	CCONJ
ap-1783	96	14	=(	=(	NOUN
ap-1783	96	15	·	·	PUNCT
ap-1783	96	16	)	)	PUNCT
ap-1783	96	17	means	mean	VERB
ap-1783	96	18	the	the	DET
ap-1783	96	19	imaginary	imaginary	ADJ
ap-1783	96	20	part	part	NOUN
ap-1783	96	21	of	of	ADP
ap-1783	96	22	the	the	DET
ap-1783	96	23	argument	argument	NOUN
ap-1783	96	24	.	.	PUNCT
ap-1783	97	1	theorem	theorem	VERB
ap-1783	97	2	2.4	2.4	NUM
ap-1783	97	3	.	.	PUNCT
ap-1783	98	1	cayley	cayley	ADJ
ap-1783	98	2	-	-	PUNCT
ap-1783	98	3	eisenstein	eisenstein	NOUN
ap-1783	98	4	-	-	PUNCT
ap-1783	98	5	pólya	pólya	NOUN
ap-1783	98	6	p.d.f	p.d.f	NOUN
ap-1783	98	7	.	.	PUNCT
ap-1783	99	1	f(x	f(x	PROPN
ap-1783	99	2	)	)	PUNCT
ap-1783	99	3	is	be	AUX
ap-1783	99	4	represented	represent	VERB
ap-1783	99	5	by	by	ADP
ap-1783	99	6	the	the	DET
ap-1783	99	7	integral	integral	ADJ
ap-1783	99	8	f(x	f(x	PROPN
ap-1783	99	9	)	)	PUNCT
ap-1783	99	10	=	=	SYM
ap-1783	100	1	1	1	NUM
ap-1783	100	2	π	π	NOUN
ap-1783	100	3	∫	∫	PROPN
ap-1783	100	4	∞	∞	NUM
ap-1783	100	5	1	1	NUM
ap-1783	100	6	/	/	SYM
ap-1783	100	7	e	e	X
ap-1783	100	8	e−xu	e−xu	ADJ
ap-1783	100	9	=	=	SYM
ap-1783	100	10	w0(−u	w0(−u	NOUN
ap-1783	100	11	)	)	PUNCT
ap-1783	100	12	u	u	PROPN
ap-1783	100	13	du	du	X
ap-1783	100	14	,	,	PUNCT
ap-1783	100	15	x	x	X
ap-1783	100	16	>	>	X
ap-1783	100	17	0	0	NUM
ap-1783	100	18	.	.	PUNCT
ap-1783	101	1	(	(	PUNCT
ap-1783	101	2	2.15	2.15	NUM
ap-1783	101	3	)	)	PUNCT
ap-1783	101	4	proof	proof	NOUN
ap-1783	101	5	.	.	PUNCT
ap-1783	102	1	the	the	DET
ap-1783	102	2	proof	proof	NOUN
ap-1783	102	3	is	be	AUX
ap-1783	102	4	straightforward	straightforward	ADJ
ap-1783	102	5	,	,	PUNCT
ap-1783	102	6	because	because	SCONJ
ap-1783	102	7	the	the	DET
ap-1783	102	8	stieltjes	stieltjes	NOUN
ap-1783	102	9	transform	transform	VERB
ap-1783	102	10	is	be	AUX
ap-1783	102	11	equivalent	equivalent	ADJ
ap-1783	102	12	to	to	ADP
ap-1783	102	13	the	the	DET
ap-1783	102	14	iterated	iterated	ADJ
ap-1783	102	15	laplace	laplace	NOUN
ap-1783	102	16	transform	transform	NOUN
ap-1783	102	17	.	.	PUNCT
ap-1783	103	1	conversely	conversely	ADV
ap-1783	103	2	,	,	PUNCT
ap-1783	103	3	by	by	ADP
ap-1783	103	4	applying	apply	VERB
ap-1783	103	5	the	the	DET
ap-1783	103	6	euler	euler	NOUN
ap-1783	103	7	differential	differential	NOUN
ap-1783	103	8	operator	operator	NOUN
ap-1783	103	9	−xd	−xd	PROPN
ap-1783	103	10	/	/	SYM
ap-1783	103	11	dx	dx	PROPN
ap-1783	103	12	to	to	ADP
ap-1783	103	13	p.d.f	p.d.f	PROPN
ap-1783	103	14	.	.	PUNCT
ap-1783	103	15	f(x	f(x	PROPN
ap-1783	103	16	)	)	PUNCT
ap-1783	103	17	from	from	ADP
ap-1783	103	18	eq	eq	ADP
ap-1783	103	19	.	.	PUNCT
ap-1783	104	1	(	(	PUNCT
ap-1783	104	2	2.1	2.1	NUM
ap-1783	104	3	)	)	PUNCT
ap-1783	104	4	or	or	CCONJ
ap-1783	104	5	eq	eq	NOUN
ap-1783	104	6	.	.	PUNCT
ap-1783	105	1	(	(	PUNCT
ap-1783	105	2	2.15	2.15	NUM
ap-1783	105	3	)	)	PUNCT
ap-1783	105	4	,	,	PUNCT
ap-1783	105	5	respectively	respectively	ADV
ap-1783	105	6	,	,	PUNCT
ap-1783	105	7	we	we	PRON
ap-1783	105	8	obtain	obtain	VERB
ap-1783	105	9	the	the	DET
ap-1783	105	10	function	function	NOUN
ap-1783	105	11	f1(x	f1(x	NOUN
ap-1783	105	12	):	):	PUNCT
ap-1783	105	13	theorem	theorem	ADJ
ap-1783	105	14	2.5	2.5	NUM
ap-1783	105	15	.	.	PUNCT
ap-1783	106	1	function	function	NOUN
ap-1783	106	2	f1(x	f1(x	PROPN
ap-1783	106	3	)	)	PUNCT
ap-1783	106	4	is	be	AUX
ap-1783	106	5	represented	represent	VERB
ap-1783	106	6	by	by	ADP
ap-1783	106	7	the	the	DET
ap-1783	106	8	integrals	integral	NOUN
ap-1783	106	9	f1(x	f1(x	NUM
ap-1783	106	10	)	)	PUNCT
ap-1783	106	11	=	=	PUNCT
ap-1783	107	1	−x	−x	NOUN
ap-1783	107	2	d	d	NOUN
ap-1783	107	3	dx	dx	PROPN
ap-1783	107	4	f(x	f(x	PROPN
ap-1783	107	5	)	)	PUNCT
ap-1783	107	6	=	=	SYM
ap-1783	108	1	1	1	NUM
ap-1783	108	2	π	π	SYM
ap-1783	108	3	∫	∫	PROPN
ap-1783	108	4	π	π	X
ap-1783	108	5	0	0	PUNCT
ap-1783	109	1	(	(	PUNCT
ap-1783	109	2	y2	y2	PROPN
ap-1783	109	3	+	+	CCONJ
ap-1783	109	4	(	(	PUNCT
ap-1783	109	5	1−	1−	NUM
ap-1783	109	6	y	y	PROPN
ap-1783	109	7	cot	cot	NOUN
ap-1783	109	8	y)2)xy	y)2)xy	PROPN
ap-1783	109	9	csc	csc	PROPN
ap-1783	109	10	ye−xy	ye−xy	PROPN
ap-1783	109	11	csc	csc	PROPN
ap-1783	109	12	ye−y	ye−y	PROPN
ap-1783	109	13	cot	cot	NOUN
ap-1783	109	14	y−y	y−y	NOUN
ap-1783	109	15	cot	cot	VERB
ap-1783	109	16	y	y	NOUN
ap-1783	109	17	dy	dy	X
ap-1783	109	18	=	=	SYM
ap-1783	109	19	1	1	NUM
ap-1783	109	20	π	π	X
ap-1783	109	21	(	(	PUNCT
ap-1783	109	22	−x	−x	NOUN
ap-1783	109	23	d	d	NOUN
ap-1783	109	24	dx	dx	PROPN
ap-1783	109	25	)	)	PUNCT
ap-1783	109	26	∫	∫	PROPN
ap-1783	110	1	∞	∞	PROPN
ap-1783	110	2	1	1	NUM
ap-1783	110	3	/	/	SYM
ap-1783	110	4	e	e	X
ap-1783	110	5	e−xu	e−xu	ADJ
ap-1783	110	6	=	=	SYM
ap-1783	110	7	w0(−u	w0(−u	NOUN
ap-1783	110	8	)	)	PUNCT
ap-1783	110	9	u	u	NOUN
ap-1783	110	10	du	du	NOUN
ap-1783	110	11	=	=	PUNCT
ap-1783	110	12	x	x	SYM
ap-1783	111	1	π	π	NOUN
ap-1783	111	2	∫	∫	PROPN
ap-1783	111	3	∞	∞	PROPN
ap-1783	111	4	1	1	NUM
ap-1783	111	5	/	/	SYM
ap-1783	111	6	e	e	X
ap-1783	111	7	e−xu	e−xu	NOUN
ap-1783	111	8	=	=	SYM
ap-1783	111	9	w0(−u	w0(−u	NOUN
ap-1783	111	10	)	)	PUNCT
ap-1783	111	11	du	du	PROPN
ap-1783	111	12	,	,	PUNCT
ap-1783	111	13	x	x	X
ap-1783	111	14	>	>	X
ap-1783	111	15	0	0	NUM
ap-1783	111	16	.	.	PUNCT
ap-1783	112	1	(	(	PUNCT
ap-1783	112	2	2.16	2.16	NUM
ap-1783	112	3	)	)	PUNCT
ap-1783	112	4	proof	proof	NOUN
ap-1783	112	5	.	.	PUNCT
ap-1783	113	1	by	by	ADP
ap-1783	113	2	applying	apply	VERB
ap-1783	113	3	the	the	DET
ap-1783	113	4	differential	differential	ADJ
ap-1783	113	5	operator	operator	NOUN
ap-1783	113	6	−xd	−xd	PROPN
ap-1783	113	7	/	/	SYM
ap-1783	113	8	dx	dx	PROPN
ap-1783	113	9	to	to	ADP
ap-1783	113	10	p.d.f	p.d.f	PROPN
ap-1783	113	11	.	.	PUNCT
ap-1783	114	1	f(x	f(x	PROPN
ap-1783	114	2	)	)	PUNCT
ap-1783	114	3	from	from	ADP
ap-1783	114	4	eq	eq	ADP
ap-1783	114	5	.	.	PUNCT
ap-1783	115	1	(	(	PUNCT
ap-1783	115	2	2.1	2.1	NUM
ap-1783	115	3	)	)	PUNCT
ap-1783	115	4	and	and	CCONJ
ap-1783	115	5	eq	eq	NOUN
ap-1783	115	6	.	.	PUNCT
ap-1783	116	1	(	(	PUNCT
ap-1783	116	2	2.15	2.15	NUM
ap-1783	116	3	)	)	PUNCT
ap-1783	116	4	we	we	PRON
ap-1783	116	5	obtain	obtain	VERB
ap-1783	116	6	the	the	DET
ap-1783	116	7	function	function	NOUN
ap-1783	116	8	f1(x	f1(x	NUM
ap-1783	116	9	)	)	PUNCT
ap-1783	116	10	.	.	PUNCT
ap-1783	117	1	in	in	ADP
ap-1783	117	2	both	both	DET
ap-1783	117	3	cases	case	NOUN
ap-1783	117	4	,	,	PUNCT
ap-1783	117	5	the	the	DET
ap-1783	117	6	conditions	condition	NOUN
ap-1783	117	7	for	for	ADP
ap-1783	117	8	the	the	DET
ap-1783	117	9	interchange	interchange	NOUN
ap-1783	117	10	of	of	ADP
ap-1783	117	11	the	the	DET
ap-1783	117	12	derivation	derivation	NOUN
ap-1783	117	13	and	and	CCONJ
ap-1783	117	14	integration	integration	NOUN
ap-1783	117	15	are	be	AUX
ap-1783	117	16	fulfilled	fulfil	VERB
ap-1783	117	17	.	.	PUNCT
ap-1783	118	1	by	by	ADP
ap-1783	118	2	two	two	NUM
ap-1783	118	3	successive	successive	ADJ
ap-1783	118	4	applications	application	NOUN
ap-1783	118	5	of	of	ADP
ap-1783	118	6	the	the	DET
ap-1783	118	7	differential	differential	ADJ
ap-1783	118	8	operator	operator	NOUN
ap-1783	118	9	−xd	−xd	NOUN
ap-1783	118	10	/	/	SYM
ap-1783	118	11	dx	dx	PROPN
ap-1783	118	12	,	,	PUNCT
ap-1783	118	13	i.e.	i.e.	X
ap-1783	118	14	by	by	ADP
ap-1783	118	15	applying	apply	VERB
ap-1783	118	16	the	the	DET
ap-1783	118	17	euler	euler	NOUN
ap-1783	118	18	differential	differential	NOUN
ap-1783	118	19	operator	operator	NOUN
ap-1783	118	20	xd	xd	NOUN
ap-1783	118	21	/	/	SYM
ap-1783	118	22	dx+	dx+	NOUN
ap-1783	118	23	x2d2	x2d2	NOUN
ap-1783	118	24	/	/	SYM
ap-1783	118	25	dx2	dx2	PROPN
ap-1783	118	26	to	to	PART
ap-1783	118	27	p.d.f	p.d.f	VERB
ap-1783	118	28	.	.	PUNCT
ap-1783	119	1	f(x	f(x	PROPN
ap-1783	119	2	)	)	PUNCT
ap-1783	119	3	from	from	ADP
ap-1783	119	4	eq	eq	ADP
ap-1783	119	5	.	.	PUNCT
ap-1783	120	1	(	(	PUNCT
ap-1783	120	2	2.1	2.1	NUM
ap-1783	120	3	)	)	PUNCT
ap-1783	120	4	we	we	PRON
ap-1783	120	5	obtain	obtain	VERB
ap-1783	120	6	the	the	DET
ap-1783	120	7	function	function	NOUN
ap-1783	120	8	f0(x	f0(x	NOUN
ap-1783	120	9	):	):	PUNCT
ap-1783	120	10	65	65	NUM
ap-1783	120	11	vladimír	vladimír	PROPN
ap-1783	120	12	vojta	vojta	PROPN
ap-1783	120	13	acta	acta	PROPN
ap-1783	120	14	polytechnica	polytechnica	PROPN
ap-1783	120	15	theorem	theorem	VERB
ap-1783	120	16	2.6	2.6	NUM
ap-1783	120	17	.	.	PUNCT
ap-1783	121	1	function	function	PROPN
ap-1783	121	2	f0(x	f0(x	NOUN
ap-1783	121	3	)	)	PUNCT
ap-1783	121	4	is	be	AUX
ap-1783	121	5	represented	represent	VERB
ap-1783	121	6	by	by	ADP
ap-1783	121	7	the	the	DET
ap-1783	121	8	integrals	integral	NOUN
ap-1783	121	9	f0(x	f0(x	NOUN
ap-1783	121	10	)	)	PUNCT
ap-1783	121	11	=	=	PRON
ap-1783	122	1	(	(	PUNCT
ap-1783	122	2	x	x	PUNCT
ap-1783	122	3	d	d	X
ap-1783	122	4	dx	dx	PROPN
ap-1783	123	1	+	+	CCONJ
ap-1783	123	2	x2	x2	PROPN
ap-1783	123	3	d	d	PROPN
ap-1783	123	4	2	2	NUM
ap-1783	123	5	dx2	dx2	PROPN
ap-1783	123	6	)	)	PUNCT
ap-1783	123	7	f(x	f(x	PROPN
ap-1783	123	8	)	)	PUNCT
ap-1783	123	9	=	=	SYM
ap-1783	124	1	1	1	NUM
ap-1783	124	2	π	π	SYM
ap-1783	124	3	∫	∫	PROPN
ap-1783	124	4	π	π	X
ap-1783	124	5	0	0	PUNCT
ap-1783	125	1	(	(	PUNCT
ap-1783	125	2	y2	y2	PROPN
ap-1783	125	3	+	+	CCONJ
ap-1783	125	4	(	(	PUNCT
ap-1783	125	5	1−	1−	NUM
ap-1783	125	6	y	y	PROPN
ap-1783	125	7	cot	cot	PROPN
ap-1783	125	8	y)2)m(x	y)2)m(x	PROPN
ap-1783	125	9	,	,	PUNCT
ap-1783	125	10	y	y	PROPN
ap-1783	125	11	)	)	PUNCT
ap-1783	125	12	dy	dy	NOUN
ap-1783	125	13	,	,	PUNCT
ap-1783	125	14	x	x	X
ap-1783	125	15	≥	≥	NOUN
ap-1783	125	16	0	0	NUM
ap-1783	125	17	,	,	PUNCT
ap-1783	125	18	(	(	PUNCT
ap-1783	125	19	2.17	2.17	NUM
ap-1783	125	20	)	)	PUNCT
ap-1783	126	1	where	where	SCONJ
ap-1783	126	2	m(x	m(x	PROPN
ap-1783	126	3	,	,	PUNCT
ap-1783	126	4	y	y	NOUN
ap-1783	126	5	)	)	PUNCT
ap-1783	126	6	=	=	PUNCT
ap-1783	126	7	xy	xy	PROPN
ap-1783	126	8	csc	csc	PROPN
ap-1783	126	9	ye−xy	ye−xy	PROPN
ap-1783	126	10	csc	csc	PROPN
ap-1783	126	11	ye−y	ye−y	PROPN
ap-1783	126	12	cot	cot	NOUN
ap-1783	126	13	y−2y	y−2y	PROPN
ap-1783	126	14	cot	cot	VERB
ap-1783	126	15	y(xy	y(xy	PROPN
ap-1783	126	16	csc	csc	PROPN
ap-1783	126	17	y	y	PROPN
ap-1783	126	18	−	−	PROPN
ap-1783	126	19	ey	ey	PRON
ap-1783	126	20	cot	cot	NOUN
ap-1783	126	21	y	y	PROPN
ap-1783	126	22	)	)	PUNCT
ap-1783	126	23	,	,	PUNCT
ap-1783	126	24	(	(	PUNCT
ap-1783	126	25	2.18	2.18	NUM
ap-1783	126	26	)	)	PUNCT
ap-1783	126	27	and	and	CCONJ
ap-1783	126	28	f0(x	f0(x	NOUN
ap-1783	126	29	)	)	PUNCT
ap-1783	127	1	=	=	SYM
ap-1783	127	2	1	1	NUM
ap-1783	127	3	π	π	X
ap-1783	127	4	(	(	PUNCT
ap-1783	127	5	x	x	PUNCT
ap-1783	127	6	d	d	X
ap-1783	127	7	dx	dx	PROPN
ap-1783	128	1	+	+	CCONJ
ap-1783	128	2	x2	x2	PROPN
ap-1783	128	3	d	d	PROPN
ap-1783	128	4	2	2	NUM
ap-1783	128	5	dx2	dx2	PROPN
ap-1783	128	6	)	)	PUNCT
ap-1783	128	7	∫	∫	PROPN
ap-1783	129	1	∞	∞	PROPN
ap-1783	129	2	1	1	NUM
ap-1783	129	3	/	/	SYM
ap-1783	129	4	e	e	X
ap-1783	129	5	e−xu	e−xu	ADJ
ap-1783	129	6	=	=	SYM
ap-1783	129	7	w0(−u	w0(−u	NOUN
ap-1783	129	8	)	)	PUNCT
ap-1783	129	9	u	u	NOUN
ap-1783	129	10	du	du	NOUN
ap-1783	129	11	=	=	PUNCT
ap-1783	129	12	x	x	SYM
ap-1783	130	1	π	π	NOUN
ap-1783	130	2	∫	∫	PROPN
ap-1783	130	3	∞	∞	PROPN
ap-1783	130	4	1	1	NUM
ap-1783	130	5	/	/	SYM
ap-1783	130	6	e	e	X
ap-1783	130	7	e−xu	e−xu	NOUN
ap-1783	130	8	=	=	SYM
ap-1783	130	9	w0(−u	w0(−u	NOUN
ap-1783	130	10	)	)	PUNCT
ap-1783	130	11	(	(	PUNCT
ap-1783	130	12	xu−	xu−	PROPN
ap-1783	130	13	1	1	X
ap-1783	130	14	)	)	PUNCT
ap-1783	130	15	du	du	PROPN
ap-1783	130	16	,	,	PUNCT
ap-1783	130	17	x	x	X
ap-1783	130	18	>	>	X
ap-1783	130	19	0	0	NUM
ap-1783	130	20	.	.	PUNCT
ap-1783	131	1	(	(	PUNCT
ap-1783	131	2	2.19	2.19	NUM
ap-1783	131	3	)	)	PUNCT
ap-1783	131	4	proof	proof	NOUN
ap-1783	131	5	.	.	PUNCT
ap-1783	132	1	by	by	ADP
ap-1783	132	2	two	two	NUM
ap-1783	132	3	successive	successive	ADJ
ap-1783	132	4	applications	application	NOUN
ap-1783	132	5	of	of	ADP
ap-1783	132	6	the	the	DET
ap-1783	132	7	differential	differential	ADJ
ap-1783	132	8	operator	operator	NOUN
ap-1783	132	9	−xd	−xd	NOUN
ap-1783	132	10	/	/	SYM
ap-1783	132	11	dx	dx	PROPN
ap-1783	132	12	,	,	PUNCT
ap-1783	132	13	i.e.	i.e.	X
ap-1783	132	14	by	by	ADP
ap-1783	132	15	applying	apply	VERB
ap-1783	132	16	the	the	DET
ap-1783	132	17	euler	euler	NOUN
ap-1783	132	18	differential	differential	NOUN
ap-1783	132	19	operator	operator	NOUN
ap-1783	132	20	xd	xd	NOUN
ap-1783	132	21	/	/	SYM
ap-1783	132	22	dx+	dx+	NOUN
ap-1783	132	23	x2d2	x2d2	NOUN
ap-1783	132	24	/	/	SYM
ap-1783	132	25	dx2	dx2	PROPN
ap-1783	132	26	to	to	PART
ap-1783	132	27	p.d.f	p.d.f	VERB
ap-1783	132	28	.	.	PUNCT
ap-1783	133	1	f(x	f(x	PROPN
ap-1783	133	2	)	)	PUNCT
ap-1783	133	3	from	from	ADP
ap-1783	133	4	eq	eq	ADP
ap-1783	133	5	.	.	PUNCT
ap-1783	134	1	(	(	PUNCT
ap-1783	134	2	2.1	2.1	NUM
ap-1783	134	3	)	)	PUNCT
ap-1783	134	4	and	and	CCONJ
ap-1783	134	5	eq	eq	NOUN
ap-1783	134	6	.	.	PUNCT
ap-1783	135	1	(	(	PUNCT
ap-1783	135	2	2.15	2.15	NUM
ap-1783	135	3	)	)	PUNCT
ap-1783	135	4	,	,	PUNCT
ap-1783	135	5	we	we	PRON
ap-1783	135	6	obtain	obtain	VERB
ap-1783	135	7	function	function	NOUN
ap-1783	135	8	f0(x	f0(x	NOUN
ap-1783	135	9	)	)	PUNCT
ap-1783	135	10	.	.	PUNCT
ap-1783	136	1	after	after	ADP
ap-1783	136	2	the	the	DET
ap-1783	136	3	substitution	substitution	NOUN
ap-1783	136	4	x	x	PUNCT
ap-1783	136	5	=	=	PUNCT
ap-1783	136	6	e−λ	e−λ	NOUN
ap-1783	136	7	,	,	PUNCT
ap-1783	136	8	the	the	DET
ap-1783	136	9	resulting	result	VERB
ap-1783	136	10	integral	integral	NOUN
ap-1783	136	11	on	on	ADP
ap-1783	136	12	the	the	DET
ap-1783	136	13	right	right	ADJ
ap-1783	136	14	hand	hand	NOUN
ap-1783	136	15	side	side	NOUN
ap-1783	136	16	of	of	ADP
ap-1783	136	17	eq	eq	PROPN
ap-1783	136	18	.	.	PUNCT
ap-1783	137	1	(	(	PUNCT
ap-1783	137	2	2.7	2.7	NUM
ap-1783	137	3	)	)	PUNCT
ap-1783	137	4	gives	give	VERB
ap-1783	137	5	the	the	DET
ap-1783	137	6	well	well	ADV
ap-1783	137	7	-	-	PUNCT
ap-1783	137	8	known	know	VERB
ap-1783	137	9	landau	landau	NOUN
ap-1783	137	10	p.d.f	p.d.f	NOUN
ap-1783	137	11	.	.	PUNCT
ap-1783	138	1	[	[	X
ap-1783	138	2	2	2	NUM
ap-1783	138	3	]	]	PUNCT
ap-1783	138	4	(	(	PUNCT
ap-1783	138	5	more	more	ADV
ap-1783	138	6	precisely	precisely	ADV
ap-1783	138	7	its	its	PRON
ap-1783	138	8	universal	universal	ADJ
ap-1783	138	9	part	part	NOUN
ap-1783	138	10	)	)	PUNCT
ap-1783	138	11	,	,	PUNCT
ap-1783	138	12	which	which	PRON
ap-1783	138	13	describes	describe	VERB
ap-1783	138	14	the	the	DET
ap-1783	138	15	energy	energy	NOUN
ap-1783	138	16	loss	loss	NOUN
ap-1783	138	17	of	of	ADP
ap-1783	138	18	a	a	DET
ap-1783	138	19	fast	fast	ADJ
ap-1783	138	20	charged	charge	VERB
ap-1783	138	21	particle	particle	NOUN
ap-1783	138	22	by	by	ADP
ap-1783	138	23	ionization	ionization	NOUN
ap-1783	138	24	as	as	SCONJ
ap-1783	138	25	it	it	PRON
ap-1783	138	26	passes	pass	VERB
ap-1783	138	27	through	through	ADP
ap-1783	138	28	a	a	DET
ap-1783	138	29	thin	thin	ADJ
ap-1783	138	30	layer	layer	NOUN
ap-1783	138	31	of	of	ADP
ap-1783	138	32	matter	matter	NOUN
ap-1783	138	33	:	:	PUNCT
ap-1783	138	34	φ(λ	φ(λ	PROPN
ap-1783	138	35	)	)	PUNCT
ap-1783	138	36	=	=	SYM
ap-1783	139	1	1	1	NUM
ap-1783	139	2	π	π	NOUN
ap-1783	139	3	∫	∫	PROPN
ap-1783	139	4	∞	∞	NUM
ap-1783	139	5	0	0	NUM
ap-1783	139	6	e−λyy−y	e−λyy−y	NOUN
ap-1783	139	7	sin	sin	NOUN
ap-1783	139	8	πy	πy	X
ap-1783	139	9	dy	dy	NOUN
ap-1783	139	10	,	,	PUNCT
ap-1783	139	11	λ	λ	X
ap-1783	139	12	>	>	X
ap-1783	139	13	−∞.	−∞.	PROPN
ap-1783	139	14	(	(	PUNCT
ap-1783	139	15	2.20	2.20	NUM
ap-1783	139	16	)	)	PUNCT
ap-1783	139	17	from	from	ADP
ap-1783	139	18	eq	eq	ADP
ap-1783	139	19	.	.	PUNCT
ap-1783	140	1	(	(	PUNCT
ap-1783	140	2	2.17	2.17	NUM
ap-1783	140	3	)	)	PUNCT
ap-1783	140	4	and	and	CCONJ
ap-1783	140	5	eq	eq	NOUN
ap-1783	140	6	.	.	PUNCT
ap-1783	141	1	(	(	PUNCT
ap-1783	141	2	2.20	2.20	NUM
ap-1783	141	3	)	)	PUNCT
ap-1783	141	4	,	,	PUNCT
ap-1783	141	5	it	it	PRON
ap-1783	141	6	follows	follow	VERB
ap-1783	141	7	that	that	SCONJ
ap-1783	141	8	the	the	DET
ap-1783	141	9	landau	landau	NOUN
ap-1783	141	10	p.d.f	p.d.f	NOUN
ap-1783	141	11	.	.	PROPN
ap-1783	141	12	has	have	VERB
ap-1783	141	13	an	an	DET
ap-1783	141	14	alternative	alternative	ADJ
ap-1783	141	15	integral	integral	ADJ
ap-1783	141	16	representation	representation	NOUN
ap-1783	141	17	φ(λ	φ(λ	PROPN
ap-1783	141	18	)	)	PUNCT
ap-1783	141	19	=	=	SYM
ap-1783	142	1	1	1	NUM
ap-1783	142	2	π	π	SYM
ap-1783	142	3	∫	∫	PROPN
ap-1783	142	4	π	π	X
ap-1783	142	5	0	0	PUNCT
ap-1783	143	1	(	(	PUNCT
ap-1783	143	2	y2	y2	PROPN
ap-1783	143	3	+	+	CCONJ
ap-1783	143	4	(	(	PUNCT
ap-1783	143	5	1−	1−	NUM
ap-1783	143	6	y	y	PROPN
ap-1783	143	7	cot	cot	NOUN
ap-1783	143	8	y)2)m(e−λ	y)2)m(e−λ	NOUN
ap-1783	143	9	,	,	PUNCT
ap-1783	143	10	y	y	NOUN
ap-1783	143	11	)	)	PUNCT
ap-1783	143	12	dy	dy	NOUN
ap-1783	143	13	.	.	PUNCT
ap-1783	144	1	(	(	PUNCT
ap-1783	145	1	2.21	2.21	NUM
ap-1783	145	2	)	)	PUNCT
ap-1783	145	3	theorem	theorem	VERB
ap-1783	145	4	2.7	2.7	NUM
ap-1783	145	5	.	.	PUNCT
ap-1783	146	1	the	the	DET
ap-1783	146	2	interconnection	interconnection	NOUN
ap-1783	146	3	between	between	ADP
ap-1783	146	4	the	the	DET
ap-1783	146	5	cayley	cayley	ADJ
ap-1783	146	6	-	-	PUNCT
ap-1783	146	7	eisenstein	eisenstein	NOUN
ap-1783	146	8	-	-	PUNCT
ap-1783	146	9	pólya	pólya	NOUN
ap-1783	146	10	p.d.f	p.d.f	NOUN
ap-1783	146	11	.	.	PUNCT
ap-1783	146	12	and	and	CCONJ
ap-1783	146	13	the	the	DET
ap-1783	146	14	landau	landau	NOUN
ap-1783	146	15	p.d.f	p.d.f	NOUN
ap-1783	146	16	.	.	PROPN
ap-1783	146	17	is	be	AUX
ap-1783	146	18	given	give	VERB
ap-1783	146	19	by	by	ADP
ap-1783	146	20	f(x	f(x	PROPN
ap-1783	146	21	)	)	PUNCT
ap-1783	147	1	=	=	PUNCT
ap-1783	148	1	−	−	PROPN
ap-1783	148	2	∫	∫	NOUN
ap-1783	148	3	−	−	PROPN
ap-1783	149	1	ln	ln	NOUN
ap-1783	149	2	x	x	X
ap-1783	149	3	−∞	−∞	X
ap-1783	149	4	(	(	PUNCT
ap-1783	149	5	u+	u+	NUM
ap-1783	149	6	ln	ln	ADJ
ap-1783	149	7	x)φ(u	x)φ(u	PROPN
ap-1783	149	8	)	)	PUNCT
ap-1783	149	9	du	du	PROPN
ap-1783	149	10	,	,	PUNCT
ap-1783	149	11	x	x	X
ap-1783	149	12	>	>	X
ap-1783	149	13	0	0	NUM
ap-1783	149	14	.	.	PUNCT
ap-1783	150	1	(	(	PUNCT
ap-1783	150	2	2.22	2.22	NUM
ap-1783	150	3	)	)	PUNCT
ap-1783	150	4	proof	proof	NOUN
ap-1783	150	5	.	.	PUNCT
ap-1783	151	1	the	the	DET
ap-1783	151	2	differential	differential	ADJ
ap-1783	151	3	equation	equation	NOUN
ap-1783	151	4	in	in	ADP
ap-1783	151	5	(	(	PUNCT
ap-1783	151	6	2.17	2.17	NUM
ap-1783	151	7	)	)	PUNCT
ap-1783	151	8	is	be	AUX
ap-1783	151	9	the	the	DET
ap-1783	151	10	euler	euler	NOUN
ap-1783	151	11	nonhomogeneous	nonhomogeneous	ADJ
ap-1783	151	12	differential	differential	NOUN
ap-1783	151	13	equation	equation	NOUN
ap-1783	151	14	for	for	ADP
ap-1783	151	15	the	the	DET
ap-1783	151	16	unknown	unknown	ADJ
ap-1783	151	17	function	function	NOUN
ap-1783	151	18	f(x	f(x	PROPN
ap-1783	151	19	)	)	PUNCT
ap-1783	151	20	and	and	CCONJ
ap-1783	151	21	given	give	VERB
ap-1783	151	22	f0(x	f0(x	NOUN
ap-1783	151	23	)	)	PUNCT
ap-1783	151	24	with	with	ADP
ap-1783	151	25	a	a	DET
ap-1783	151	26	particular	particular	ADJ
ap-1783	151	27	integral	integral	ADJ
ap-1783	151	28	(	(	PUNCT
ap-1783	151	29	2.8	2.8	NUM
ap-1783	151	30	)	)	PUNCT
ap-1783	151	31	.	.	PUNCT
ap-1783	152	1	after	after	SCONJ
ap-1783	152	2	substituting	substitute	VERB
ap-1783	152	3	x	x	X
ap-1783	152	4	=	=	PRON
ap-1783	152	5	e−λ	e−λ	NOUN
ap-1783	152	6	to	to	ADP
ap-1783	152	7	this	this	DET
ap-1783	152	8	equation	equation	NOUN
ap-1783	152	9	we	we	PRON
ap-1783	152	10	obtain	obtain	VERB
ap-1783	152	11	the	the	DET
ap-1783	152	12	following	follow	VERB
ap-1783	152	13	simple	simple	ADJ
ap-1783	152	14	differential	differential	ADJ
ap-1783	152	15	equation	equation	NOUN
ap-1783	152	16	:	:	PUNCT
ap-1783	152	17	d2	d2	VERB
ap-1783	152	18	dλ2φ2(λ	dλ2φ2(λ	NOUN
ap-1783	152	19	)	)	PUNCT
ap-1783	152	20	=	=	SYM
ap-1783	152	21	d2	d2	PROPN
ap-1783	152	22	dλ2	dλ2	PROPN
ap-1783	152	23	f(e−λ	f(e−λ	PROPN
ap-1783	152	24	)	)	PUNCT
ap-1783	152	25	=	=	SYM
ap-1783	152	26	f0(e−λ	f0(e−λ	PROPN
ap-1783	152	27	)	)	PUNCT
ap-1783	152	28	=	=	SYM
ap-1783	152	29	φ(λ	φ(λ	PROPN
ap-1783	152	30	)	)	PUNCT
ap-1783	152	31	,	,	PUNCT
ap-1783	153	1	λ	λ	X
ap-1783	153	2	>	>	X
ap-1783	153	3	−∞	−∞	PROPN
ap-1783	153	4	,	,	PUNCT
ap-1783	153	5	(	(	PUNCT
ap-1783	153	6	2.23	2.23	NUM
ap-1783	153	7	)	)	PUNCT
ap-1783	153	8	where	where	SCONJ
ap-1783	153	9	φ2(λ	φ2(λ	X
ap-1783	153	10	)	)	PUNCT
ap-1783	153	11	=	=	SYM
ap-1783	153	12	f(e−λ	f(e−λ	PROPN
ap-1783	153	13	)	)	PUNCT
ap-1783	153	14	.	.	PUNCT
ap-1783	154	1	the	the	DET
ap-1783	154	2	particular	particular	ADJ
ap-1783	154	3	solution	solution	NOUN
ap-1783	154	4	of	of	ADP
ap-1783	154	5	eq	eq	PROPN
ap-1783	154	6	.	.	PUNCT
ap-1783	155	1	(	(	PUNCT
ap-1783	155	2	2.23	2.23	NUM
ap-1783	155	3	)	)	PUNCT
ap-1783	155	4	is	be	AUX
ap-1783	155	5	φ2(λ	φ2(λ	PROPN
ap-1783	155	6	)	)	PUNCT
ap-1783	155	7	=	=	SYM
ap-1783	155	8	∫	∫	PROPN
ap-1783	155	9	λ	λ	X
ap-1783	155	10	−∞	−∞	ADP
ap-1783	155	11	φ(u)(λ−	φ(u)(λ−	NUM
ap-1783	155	12	u	u	NOUN
ap-1783	155	13	)	)	PUNCT
ap-1783	155	14	du	du	PROPN
ap-1783	155	15	,	,	PUNCT
ap-1783	155	16	(	(	PUNCT
ap-1783	155	17	2.24	2.24	NUM
ap-1783	155	18	)	)	PUNCT
ap-1783	155	19	conformable	conformable	NOUN
ap-1783	155	20	to	to	ADP
ap-1783	155	21	eq	eq	PROPN
ap-1783	155	22	.	.	PUNCT
ap-1783	156	1	(	(	PUNCT
ap-1783	156	2	2.8	2.8	NUM
ap-1783	156	3	)	)	PUNCT
ap-1783	156	4	.	.	PUNCT
ap-1783	157	1	after	after	ADP
ap-1783	157	2	substituting	substitute	VERB
ap-1783	157	3	λ	λ	X
ap-1783	157	4	=	=	PUNCT
ap-1783	157	5	−	−	PROPN
ap-1783	157	6	ln	ln	NOUN
ap-1783	157	7	x	x	X
ap-1783	157	8	into	into	ADP
ap-1783	157	9	eq	eq	NOUN
ap-1783	157	10	.	.	PUNCT
ap-1783	157	11	(	(	PUNCT
ap-1783	157	12	2.24	2.24	NUM
ap-1783	157	13	)	)	PUNCT
ap-1783	157	14	,	,	PUNCT
ap-1783	157	15	we	we	PRON
ap-1783	157	16	obtain	obtain	VERB
ap-1783	157	17	eq	eq	ADP
ap-1783	157	18	.	.	PUNCT
ap-1783	158	1	(	(	PUNCT
ap-1783	158	2	2.22	2.22	NUM
ap-1783	158	3	)	)	PUNCT
ap-1783	158	4	.	.	PUNCT
ap-1783	159	1	3	3	X
ap-1783	159	2	.	.	NOUN
ap-1783	159	3	integrals	integral	NOUN
ap-1783	159	4	and	and	CCONJ
ap-1783	159	5	integral	integral	ADJ
ap-1783	159	6	transforms	transform	VERB
ap-1783	159	7	the	the	DET
ap-1783	159	8	integral	integral	ADJ
ap-1783	159	9	operator	operator	NOUN
ap-1783	159	10	t	t	PROPN
ap-1783	159	11	defined	define	VERB
ap-1783	159	12	by	by	ADP
ap-1783	159	13	eq	eq	PROPN
ap-1783	159	14	.	.	PUNCT
ap-1783	160	1	(	(	PUNCT
ap-1783	160	2	2.12	2.12	NUM
ap-1783	160	3	):	):	PUNCT
ap-1783	160	4	t	t	PROPN
ap-1783	160	5	(	(	PUNCT
ap-1783	160	6	f0)(x	f0)(x	PROPN
ap-1783	160	7	)	)	PUNCT
ap-1783	160	8	=	=	SYM
ap-1783	160	9	∫∞	∫∞	NOUN
ap-1783	160	10	x	x	X
ap-1783	160	11	f0(z	f0(z	X
ap-1783	160	12	)	)	PUNCT
ap-1783	160	13	z	z	NOUN
ap-1783	160	14	dz	dz	PROPN
ap-1783	160	15	,	,	PUNCT
ap-1783	160	16	x	x	SYM
ap-1783	160	17	>	>	X
ap-1783	160	18	0	0	NUM
ap-1783	160	19	,	,	PUNCT
ap-1783	160	20	is	be	AUX
ap-1783	160	21	an	an	DET
ap-1783	160	22	example	example	NOUN
ap-1783	160	23	of	of	ADP
ap-1783	160	24	a	a	DET
ap-1783	160	25	mellin	mellin	NOUN
ap-1783	160	26	multiplier	multipli	ADJ
ap-1783	160	27	operator	operator	NOUN
ap-1783	160	28	with	with	ADP
ap-1783	160	29	multiplier	multipli	ADJ
ap-1783	160	30	1	1	NUM
ap-1783	160	31	/	/	SYM
ap-1783	160	32	s	s	PART
ap-1783	160	33	[	[	X
ap-1783	160	34	6	6	NUM
ap-1783	160	35	]	]	PUNCT
ap-1783	160	36	.	.	PUNCT
ap-1783	161	1	this	this	PRON
ap-1783	161	2	means	mean	VERB
ap-1783	161	3	that	that	SCONJ
ap-1783	161	4	the	the	DET
ap-1783	161	5	fractional	fractional	ADJ
ap-1783	161	6	powers	power	NOUN
ap-1783	161	7	of	of	ADP
ap-1783	161	8	the	the	DET
ap-1783	161	9	operator	operator	NOUN
ap-1783	161	10	t	t	NOUN
ap-1783	161	11	are	be	AUX
ap-1783	161	12	[	[	X
ap-1783	161	13	6	6	NUM
ap-1783	161	14	]	]	PUNCT
ap-1783	161	15	:	:	PUNCT
ap-1783	161	16	tα(f0)(x	tα(f0)(x	X
ap-1783	161	17	)	)	PUNCT
ap-1783	161	18	=	=	SYM
ap-1783	161	19	1	1	NUM
ap-1783	161	20	γ(α	γ(α	NOUN
ap-1783	161	21	)	)	PUNCT
ap-1783	161	22	∫	∫	PROPN
ap-1783	162	1	∞	∞	NUM
ap-1783	162	2	x	x	PUNCT
ap-1783	163	1	lnα−1	lnα−1	NOUN
ap-1783	163	2	z	z	NOUN
ap-1783	163	3	x	x	SYM
ap-1783	163	4	f0(z	f0(z	NUM
ap-1783	163	5	)	)	PUNCT
ap-1783	163	6	z	z	NOUN
ap-1783	163	7	dz	dz	PROPN
ap-1783	163	8	,	,	PUNCT
ap-1783	163	9	x	x	SYM
ap-1783	163	10	>	>	X
ap-1783	163	11	0	0	PROPN
ap-1783	163	12	,	,	PUNCT
ap-1783	163	13	α	α	NOUN
ap-1783	163	14	>	>	X
ap-1783	163	15	0	0	PROPN
ap-1783	163	16	,	,	PUNCT
ap-1783	163	17	t	t	NOUN
ap-1783	163	18	0	0	NUM
ap-1783	164	1	=	=	SYM
ap-1783	164	2	i	i	PROPN
ap-1783	164	3	,	,	PUNCT
ap-1783	164	4	(	(	PUNCT
ap-1783	164	5	3.1	3.1	NUM
ap-1783	164	6	)	)	PUNCT
ap-1783	164	7	where	where	SCONJ
ap-1783	164	8	i	i	PRON
ap-1783	164	9	is	be	AUX
ap-1783	164	10	the	the	DET
ap-1783	164	11	identity	identity	NOUN
ap-1783	164	12	operator	operator	NOUN
ap-1783	164	13	,	,	PUNCT
ap-1783	164	14	and	and	CCONJ
ap-1783	164	15	that	that	SCONJ
ap-1783	164	16	it	it	PRON
ap-1783	164	17	holds	hold	VERB
ap-1783	164	18	for	for	ADP
ap-1783	164	19	the	the	DET
ap-1783	164	20	mellin	mellin	PROPN
ap-1783	164	21	transform	transform	NOUN
ap-1783	164	22	of	of	ADP
ap-1783	164	23	eq	eq	NOUN
ap-1783	164	24	.	.	PUNCT
ap-1783	165	1	(	(	PUNCT
ap-1783	165	2	3.1	3.1	NUM
ap-1783	165	3	):	):	PUNCT
ap-1783	165	4	mt	mt	PROPN
ap-1783	165	5	[	[	PUNCT
ap-1783	165	6	tα(f0)(x	tα(f0)(x	PROPN
ap-1783	165	7	)	)	PUNCT
ap-1783	165	8	;	;	PUNCT
ap-1783	165	9	s	s	X
ap-1783	165	10	]	]	X
ap-1783	165	11	=	=	SYM
ap-1783	165	12	s−α	s−α	PROPN
ap-1783	165	13	mt	mt	PROPN
ap-1783	165	14	[	[	PUNCT
ap-1783	165	15	f0(x	f0(x	NOUN
ap-1783	165	16	)	)	PUNCT
ap-1783	165	17	;	;	PUNCT
ap-1783	165	18	s	s	X
ap-1783	165	19	]	]	PUNCT
ap-1783	165	20	.	.	PUNCT
ap-1783	166	1	(	(	PUNCT
ap-1783	166	2	3.2	3.2	NUM
ap-1783	166	3	)	)	PUNCT
ap-1783	166	4	we	we	PRON
ap-1783	166	5	thus	thus	ADV
ap-1783	166	6	have	have	VERB
ap-1783	166	7	a	a	DET
ap-1783	166	8	one	one	NUM
ap-1783	166	9	-	-	PUNCT
ap-1783	166	10	parameter	parameter	NOUN
ap-1783	166	11	family	family	NOUN
ap-1783	166	12	of	of	ADP
ap-1783	166	13	the	the	DET
ap-1783	166	14	functions	function	NOUN
ap-1783	166	15	fα(x	fα(x	NOUN
ap-1783	166	16	)	)	PUNCT
ap-1783	166	17	,	,	PUNCT
ap-1783	166	18	0	0	NUM
ap-1783	166	19	≤	≤	NUM
ap-1783	166	20	α	α	NOUN
ap-1783	166	21	≤	≤	NUM
ap-1783	166	22	2	2	NUM
ap-1783	166	23	,	,	PUNCT
ap-1783	166	24	f2(x	f2(x	NUM
ap-1783	166	25	)	)	PUNCT
ap-1783	166	26	≡	≡	PROPN
ap-1783	166	27	f(x	f(x	PROPN
ap-1783	166	28	)	)	PUNCT
ap-1783	166	29	,	,	PUNCT
ap-1783	166	30	given	give	VERB
ap-1783	166	31	by	by	ADP
ap-1783	166	32	fα(x	fα(x	NOUN
ap-1783	166	33	)	)	PUNCT
ap-1783	167	1	=	=	SYM
ap-1783	167	2	tα(f0)(x	tα(f0)(x	PROPN
ap-1783	167	3	)	)	PUNCT
ap-1783	167	4	,	,	PUNCT
ap-1783	167	5	x	x	X
ap-1783	167	6	>	>	X
ap-1783	167	7	0	0	NUM
ap-1783	167	8	.	.	PUNCT
ap-1783	168	1	(	(	PUNCT
ap-1783	168	2	3.3	3.3	NUM
ap-1783	168	3	)	)	PUNCT
ap-1783	168	4	moreover	moreover	ADV
ap-1783	168	5	,	,	PUNCT
ap-1783	168	6	the	the	DET
ap-1783	168	7	integral	integral	ADJ
ap-1783	168	8	operator	operator	NOUN
ap-1783	168	9	tα(f0)(x	tα(f0)(x	PROPN
ap-1783	168	10	)	)	PUNCT
ap-1783	168	11	in	in	ADP
ap-1783	168	12	eq	eq	ADP
ap-1783	168	13	.	.	PUNCT
ap-1783	169	1	(	(	PUNCT
ap-1783	169	2	3.1	3.1	NUM
ap-1783	169	3	)	)	PUNCT
ap-1783	169	4	is	be	AUX
ap-1783	169	5	the	the	DET
ap-1783	169	6	hadamard	hadamard	ADJ
ap-1783	169	7	right	right	ADV
ap-1783	169	8	-	-	PUNCT
ap-1783	169	9	sided	sided	ADJ
ap-1783	169	10	fractional	fractional	ADJ
ap-1783	169	11	integral	integral	ADJ
ap-1783	169	12	of	of	ADP
ap-1783	169	13	the	the	DET
ap-1783	169	14	order	order	NOUN
ap-1783	169	15	α	α	NOUN
ap-1783	169	16	of	of	ADP
ap-1783	169	17	the	the	DET
ap-1783	169	18	function	function	NOUN
ap-1783	169	19	f0(x	f0(x	NOUN
ap-1783	169	20	)	)	PUNCT
ap-1783	170	1	[	[	X
ap-1783	170	2	7	7	NUM
ap-1783	170	3	]	]	PUNCT
ap-1783	170	4	.	.	PUNCT
ap-1783	171	1	by	by	ADP
ap-1783	171	2	analogy	analogy	NOUN
ap-1783	171	3	,	,	PUNCT
ap-1783	171	4	there	there	PRON
ap-1783	171	5	exists	exist	VERB
ap-1783	171	6	a	a	DET
ap-1783	171	7	one	one	NUM
ap-1783	171	8	-	-	PUNCT
ap-1783	171	9	parameter	parameter	NOUN
ap-1783	171	10	family	family	NOUN
ap-1783	171	11	of	of	ADP
ap-1783	171	12	the	the	DET
ap-1783	171	13	functions	function	NOUN
ap-1783	171	14	φα(x	φα(x	PUNCT
ap-1783	171	15	)	)	PUNCT
ap-1783	171	16	,	,	PUNCT
ap-1783	171	17	0	0	NUM
ap-1783	171	18	≤	≤	NUM
ap-1783	171	19	α	α	NOUN
ap-1783	171	20	≤	≤	NUM
ap-1783	171	21	2	2	NUM
ap-1783	171	22	,	,	PUNCT
ap-1783	171	23	φ0(x	φ0(x	NOUN
ap-1783	171	24	)	)	PUNCT
ap-1783	171	25	≡	≡	PROPN
ap-1783	171	26	φ(x	φ(x	PROPN
ap-1783	171	27	)	)	PUNCT
ap-1783	171	28	,	,	PUNCT
ap-1783	171	29	given	give	VERB
ap-1783	171	30	by	by	ADP
ap-1783	171	31	φα(x	φα(x	PUNCT
ap-1783	171	32	)	)	PUNCT
ap-1783	171	33	=	=	SYM
ap-1783	171	34	uα(φ0)(x	uα(φ0)(x	PROPN
ap-1783	171	35	)	)	PUNCT
ap-1783	171	36	,	,	PUNCT
ap-1783	171	37	x	x	X
ap-1783	171	38	>	>	X
ap-1783	171	39	−∞	−∞	NOUN
ap-1783	171	40	,	,	PUNCT
ap-1783	171	41	(	(	PUNCT
ap-1783	171	42	3.4	3.4	NUM
ap-1783	171	43	)	)	PUNCT
ap-1783	171	44	66	66	NUM
ap-1783	171	45	vol	vol	NOUN
ap-1783	171	46	.	.	PUNCT
ap-1783	172	1	53	53	NUM
ap-1783	172	2	no	no	NOUN
ap-1783	172	3	.	.	PUNCT
ap-1783	173	1	2/2013	2/2013	NUM
ap-1783	173	2	cayley	cayley	ADJ
ap-1783	173	3	-	-	PUNCT
ap-1783	173	4	eisenstein	eisenstein	NOUN
ap-1783	173	5	-	-	PUNCT
ap-1783	173	6	pólya	pólya	NOUN
ap-1783	174	1	and	and	CCONJ
ap-1783	174	2	landau	landau	VERB
ap-1783	174	3	probability	probability	NOUN
ap-1783	174	4	distributions	distribution	NOUN
ap-1783	174	5	where	where	SCONJ
ap-1783	174	6	uα(φ0)(x	uα(φ0)(x	VERB
ap-1783	174	7	)	)	PUNCT
ap-1783	174	8	=	=	SYM
ap-1783	174	9	1	1	NUM
ap-1783	174	10	γ(α	γ(α	NOUN
ap-1783	174	11	)	)	PUNCT
ap-1783	174	12	∫	∫	PROPN
ap-1783	175	1	x	x	PROPN
ap-1783	175	2	−∞	−∞	PROPN
ap-1783	175	3	(	(	PUNCT
ap-1783	175	4	x−	x−	PROPN
ap-1783	175	5	z)α−1φ0(z	z)α−1φ0(z	NUM
ap-1783	175	6	)	)	PUNCT
ap-1783	175	7	dz	dz	NOUN
ap-1783	175	8	,	,	PUNCT
ap-1783	175	9	x	x	X
ap-1783	175	10	>	>	X
ap-1783	175	11	−∞	−∞	PROPN
ap-1783	175	12	,	,	PUNCT
ap-1783	175	13	α	α	PROPN
ap-1783	175	14	>	>	X
ap-1783	175	15	0	0	PROPN
ap-1783	175	16	,	,	PUNCT
ap-1783	175	17	u0	u0	NOUN
ap-1783	175	18	=	=	ADJ
ap-1783	175	19	i	i	PROPN
ap-1783	175	20	,	,	PUNCT
ap-1783	175	21	(	(	PUNCT
ap-1783	175	22	3.5	3.5	NUM
ap-1783	175	23	)	)	PUNCT
ap-1783	175	24	is	be	AUX
ap-1783	175	25	the	the	DET
ap-1783	175	26	liouville	liouville	NOUN
ap-1783	176	1	left	left	ADJ
ap-1783	176	2	-	-	PUNCT
ap-1783	176	3	sided	sided	ADJ
ap-1783	176	4	fractional	fractional	ADJ
ap-1783	176	5	integral	integral	ADJ
ap-1783	176	6	[	[	X
ap-1783	176	7	7	7	NUM
ap-1783	176	8	]	]	PUNCT
ap-1783	176	9	of	of	ADP
ap-1783	176	10	the	the	DET
ap-1783	176	11	order	order	NOUN
ap-1783	176	12	α	α	NOUN
ap-1783	176	13	of	of	ADP
ap-1783	176	14	the	the	DET
ap-1783	176	15	landau	landau	NOUN
ap-1783	176	16	p.d.f	p.d.f	PROPN
ap-1783	176	17	.	.	PUNCT
ap-1783	176	18	equation	equation	NOUN
ap-1783	176	19	(	(	PUNCT
ap-1783	176	20	2.24	2.24	NUM
ap-1783	176	21	)	)	PUNCT
ap-1783	176	22	is	be	AUX
ap-1783	176	23	a	a	DET
ap-1783	176	24	special	special	ADJ
ap-1783	176	25	case	case	NOUN
ap-1783	176	26	for	for	ADP
ap-1783	176	27	α	α	NOUN
ap-1783	176	28	=	=	SYM
ap-1783	176	29	2	2	NUM
ap-1783	176	30	.	.	PUNCT
ap-1783	176	31	because	because	SCONJ
ap-1783	176	32	w0(s)/s	w0(s)/s	PROPN
ap-1783	176	33	is	be	AUX
ap-1783	176	34	a	a	DET
ap-1783	176	35	laplace	laplace	NOUN
ap-1783	176	36	transform	transform	NOUN
ap-1783	176	37	of	of	ADP
ap-1783	176	38	the	the	DET
ap-1783	176	39	p.d.f	p.d.f	NOUN
ap-1783	176	40	.	.	PUNCT
ap-1783	177	1	f(x	f(x	PROPN
ap-1783	177	2	)	)	PUNCT
ap-1783	177	3	,	,	PUNCT
ap-1783	177	4	it	it	PRON
ap-1783	177	5	is	be	AUX
ap-1783	177	6	natural	natural	ADJ
ap-1783	177	7	to	to	PART
ap-1783	177	8	ask	ask	VERB
ap-1783	177	9	what	what	PRON
ap-1783	177	10	the	the	DET
ap-1783	177	11	laplace	laplace	NOUN
ap-1783	177	12	transform	transform	NOUN
ap-1783	177	13	of	of	ADP
ap-1783	177	14	the	the	DET
ap-1783	177	15	functions	function	NOUN
ap-1783	177	16	f0(x	f0(x	NOUN
ap-1783	177	17	)	)	PUNCT
ap-1783	177	18	and	and	CCONJ
ap-1783	177	19	f1(x	f1(x	NUM
ap-1783	177	20	)	)	PUNCT
ap-1783	177	21	is	be	AUX
ap-1783	177	22	.	.	PUNCT
ap-1783	178	1	theorem	theorem	VERB
ap-1783	178	2	3.1	3.1	NUM
ap-1783	178	3	.	.	PUNCT
ap-1783	179	1	we	we	PRON
ap-1783	179	2	have∫	have∫	VERB
ap-1783	179	3	∞	∞	PROPN
ap-1783	179	4	0	0	NUM
ap-1783	179	5	e−sxf1(x	e−sxf1(x	NOUN
ap-1783	179	6	)	)	PUNCT
ap-1783	179	7	dx	dx	PROPN
ap-1783	180	1	=	=	SYM
ap-1783	180	2	d	d	X
ap-1783	180	3	ds	ds	X
ap-1783	180	4	w0(s	w0(s	PROPN
ap-1783	180	5	)	)	PUNCT
ap-1783	180	6	=	=	SYM
ap-1783	180	7	w0(s	w0(s	PROPN
ap-1783	180	8	)	)	PUNCT
ap-1783	180	9	s(1	s(1	PROPN
ap-1783	180	10	+	+	PROPN
ap-1783	180	11	w0(s	w0(s	PROPN
ap-1783	180	12	)	)	PUNCT
ap-1783	180	13	)	)	PUNCT
ap-1783	181	1	=	=	SYM
ap-1783	181	2	e−w0(s	e−w0(s	X
ap-1783	181	3	)	)	PUNCT
ap-1783	181	4	1	1	NUM
ap-1783	182	1	+	+	NOUN
ap-1783	182	2	w0(s	w0(s	X
ap-1783	182	3	)	)	PUNCT
ap-1783	182	4	,	,	PUNCT
ap-1783	182	5	<	<	X
ap-1783	182	6	s	s	X
ap-1783	182	7	>	>	X
ap-1783	182	8	−1	−1	PROPN
ap-1783	182	9	/	/	SYM
ap-1783	182	10	e	e	NOUN
ap-1783	182	11	,	,	PUNCT
ap-1783	182	12	(	(	PUNCT
ap-1783	182	13	3.6	3.6	NUM
ap-1783	182	14	)	)	PUNCT
ap-1783	182	15	∫	∫	PROPN
ap-1783	183	1	∞	∞	PROPN
ap-1783	183	2	0	0	NUM
ap-1783	183	3	e−sxf0(x	e−sxf0(x	PROPN
ap-1783	183	4	)	)	PUNCT
ap-1783	183	5	dx	dx	PROPN
ap-1783	184	1	=	=	PUNCT
ap-1783	185	1	−	−	PROPN
ap-1783	185	2	d	d	X
ap-1783	185	3	ds	ds	ADJ
ap-1783	185	4	w0(s	w0(s	PROPN
ap-1783	185	5	)	)	PUNCT
ap-1783	185	6	+	+	CCONJ
ap-1783	185	7	d2	d2	PROPN
ap-1783	185	8	ds2	ds2	PROPN
ap-1783	185	9	(	(	PUNCT
ap-1783	185	10	sw0(s	sw0(s	PROPN
ap-1783	185	11	)	)	PUNCT
ap-1783	185	12	)	)	PUNCT
ap-1783	185	13	=	=	SYM
ap-1783	186	1	w0(s	w0(s	PROPN
ap-1783	186	2	)	)	PUNCT
ap-1783	186	3	s(1	s(1	PROPN
ap-1783	187	1	+	+	PROPN
ap-1783	187	2	w0(s))3	w0(s))3	PROPN
ap-1783	187	3	,	,	PUNCT
ap-1783	187	4	<	<	X
ap-1783	187	5	s	s	X
ap-1783	187	6	>	>	X
ap-1783	187	7	−1	−1	PROPN
ap-1783	187	8	/	/	SYM
ap-1783	187	9	e.	e.	PROPN
ap-1783	187	10	(	(	PUNCT
ap-1783	187	11	3.7	3.7	NUM
ap-1783	187	12	)	)	PUNCT
ap-1783	187	13	proof	proof	NOUN
ap-1783	187	14	.	.	PUNCT
ap-1783	188	1	with	with	ADP
ap-1783	188	2	the	the	DET
ap-1783	188	3	aid	aid	NOUN
ap-1783	188	4	of	of	ADP
ap-1783	188	5	the	the	DET
ap-1783	188	6	standard	standard	ADJ
ap-1783	188	7	rules	rule	NOUN
ap-1783	188	8	for	for	ADP
ap-1783	188	9	the	the	DET
ap-1783	188	10	laplace	laplace	NOUN
ap-1783	188	11	transform	transform	NOUN
ap-1783	188	12	,	,	PUNCT
ap-1783	188	13	e.g.	e.g.	ADV
ap-1783	188	14	[	[	X
ap-1783	188	15	8	8	NUM
ap-1783	188	16	,	,	PUNCT
ap-1783	188	17	entry	entry	NOUN
ap-1783	188	18	1.24	1.24	NUM
ap-1783	188	19	,	,	PUNCT
ap-1783	188	20	p.6	p.6	ADP
ap-1783	188	21	]	]	PUNCT
ap-1783	188	22	,	,	PUNCT
ap-1783	188	23	applied	apply	VERB
ap-1783	188	24	to	to	ADP
ap-1783	188	25	eq	eq	PROPN
ap-1783	188	26	.	.	PUNCT
ap-1783	189	1	(	(	PUNCT
ap-1783	189	2	2.16	2.16	NUM
ap-1783	189	3	)	)	PUNCT
ap-1783	189	4	and	and	CCONJ
ap-1783	189	5	eq	eq	NOUN
ap-1783	189	6	.	.	PUNCT
ap-1783	190	1	(	(	PUNCT
ap-1783	190	2	2.17	2.17	NUM
ap-1783	190	3	)	)	PUNCT
ap-1783	190	4	,	,	PUNCT
ap-1783	190	5	respectively	respectively	ADV
ap-1783	190	6	,	,	PUNCT
ap-1783	190	7	we	we	PRON
ap-1783	190	8	obtain	obtain	VERB
ap-1783	190	9	the	the	DET
ap-1783	190	10	results	result	NOUN
ap-1783	190	11	.	.	PUNCT
ap-1783	191	1	corollary	corollary	ADJ
ap-1783	191	2	3.2	3.2	NUM
ap-1783	191	3	.	.	PUNCT
ap-1783	192	1	the	the	DET
ap-1783	192	2	following	follow	VERB
ap-1783	192	3	mellin	mellin	PROPN
ap-1783	192	4	transform	transform	VERB
ap-1783	192	5	pairs	pair	NOUN
ap-1783	192	6	hold:∫	hold:∫	INTJ
ap-1783	192	7	∞	∞	NOUN
ap-1783	192	8	0	0	X
ap-1783	193	1	us−1	us−1	PROPN
ap-1783	193	2	w0(u	w0(u	NUM
ap-1783	193	3	)	)	PUNCT
ap-1783	194	1	u(1	u(1	PROPN
ap-1783	194	2	+	+	PROPN
ap-1783	194	3	w0(u	w0(u	NOUN
ap-1783	194	4	)	)	PUNCT
ap-1783	194	5	)	)	PUNCT
ap-1783	195	1	du	du	PROPN
ap-1783	195	2	=	=	PUNCT
ap-1783	195	3	γ(s)(1−	γ(s)(1−	X
ap-1783	195	4	s)−s	s)−s	PROPN
ap-1783	195	5	,	,	PUNCT
ap-1783	195	6	<	<	X
ap-1783	195	7	s	s	X
ap-1783	195	8	∈	∈	NOUN
ap-1783	195	9	(	(	PUNCT
ap-1783	195	10	0	0	NUM
ap-1783	195	11	,	,	PUNCT
ap-1783	195	12	1	1	NUM
ap-1783	195	13	)	)	PUNCT
ap-1783	195	14	,	,	PUNCT
ap-1783	195	15	(	(	PUNCT
ap-1783	195	16	3.8	3.8	NUM
ap-1783	195	17	)	)	PUNCT
ap-1783	195	18	∫	∫	PROPN
ap-1783	196	1	∞	∞	NOUN
ap-1783	196	2	0	0	X
ap-1783	197	1	us−1	us−1	PROPN
ap-1783	197	2	w0(u	w0(u	NUM
ap-1783	197	3	)	)	PUNCT
ap-1783	198	1	u(1	u(1	PROPN
ap-1783	199	1	+	+	PROPN
ap-1783	199	2	w0(u))3	w0(u))3	PROPN
ap-1783	199	3	du	du	X
ap-1783	199	4	=	=	PROPN
ap-1783	199	5	γ(s)(1−	γ(s)(1−	NUM
ap-1783	199	6	s)1−s	s)1−s	NOUN
ap-1783	199	7	,	,	PUNCT
ap-1783	199	8	<	<	X
ap-1783	199	9	s	s	X
ap-1783	199	10	∈	∈	NOUN
ap-1783	199	11	(	(	PUNCT
ap-1783	199	12	0	0	NUM
ap-1783	199	13	,	,	PUNCT
ap-1783	199	14	1	1	NUM
ap-1783	199	15	)	)	PUNCT
ap-1783	199	16	.	.	PUNCT
ap-1783	200	1	(	(	PUNCT
ap-1783	200	2	3.9	3.9	NUM
ap-1783	200	3	)	)	PUNCT
ap-1783	200	4	proof	proof	NOUN
ap-1783	200	5	.	.	PUNCT
ap-1783	201	1	because	because	SCONJ
ap-1783	201	2	eq	eq	ADJ
ap-1783	201	3	.	.	PUNCT
ap-1783	201	4	(	(	PUNCT
ap-1783	201	5	3.6	3.6	NUM
ap-1783	201	6	)	)	PUNCT
ap-1783	201	7	holds	hold	NOUN
ap-1783	201	8	and	and	CCONJ
ap-1783	201	9	mt	mt	PROPN
ap-1783	201	10	[	[	PUNCT
ap-1783	201	11	f1(x	f1(x	PROPN
ap-1783	201	12	)	)	PUNCT
ap-1783	201	13	;	;	PUNCT
ap-1783	201	14	s	s	X
ap-1783	201	15	]	]	X
ap-1783	201	16	=	=	PUNCT
ap-1783	201	17	ss	ss	PROPN
ap-1783	201	18	/	/	SYM
ap-1783	201	19	s	s	PROPN
ap-1783	201	20	,	,	PUNCT
ap-1783	201	21	we	we	PRON
ap-1783	201	22	apply	apply	VERB
ap-1783	201	23	the	the	DET
ap-1783	201	24	relation	relation	NOUN
ap-1783	201	25	(	(	PUNCT
ap-1783	201	26	2.4	2.4	NUM
ap-1783	201	27	)	)	PUNCT
ap-1783	201	28	and	and	CCONJ
ap-1783	201	29	obtain	obtain	VERB
ap-1783	201	30	eq	eq	NOUN
ap-1783	201	31	.	.	PUNCT
ap-1783	202	1	(	(	PUNCT
ap-1783	202	2	3.8	3.8	NUM
ap-1783	202	3	)	)	PUNCT
ap-1783	202	4	.	.	PUNCT
ap-1783	203	1	an	an	DET
ap-1783	203	2	analogous	analogous	ADJ
ap-1783	203	3	procedure	procedure	NOUN
ap-1783	203	4	with	with	ADP
ap-1783	203	5	eq	eq	NOUN
ap-1783	203	6	.	.	PUNCT
ap-1783	203	7	(	(	PUNCT
ap-1783	203	8	3.7	3.7	NUM
ap-1783	203	9	)	)	PUNCT
ap-1783	203	10	,	,	PUNCT
ap-1783	203	11	and	and	CCONJ
ap-1783	203	12	the	the	DET
ap-1783	203	13	fact	fact	NOUN
ap-1783	203	14	that	that	SCONJ
ap-1783	203	15	mt	mt	PROPN
ap-1783	203	16	[	[	PUNCT
ap-1783	203	17	f0(x	f0(x	NOUN
ap-1783	203	18	)	)	PUNCT
ap-1783	203	19	;	;	PUNCT
ap-1783	203	20	s	s	X
ap-1783	203	21	]	]	X
ap-1783	203	22	=	=	PUNCT
ap-1783	203	23	ss	ss	NOUN
ap-1783	203	24	gives	give	VERB
ap-1783	203	25	eq	eq	NOUN
ap-1783	203	26	.	.	PUNCT
ap-1783	204	1	(	(	PUNCT
ap-1783	204	2	3.9	3.9	NUM
ap-1783	204	3	)	)	PUNCT
ap-1783	204	4	.	.	PUNCT
ap-1783	205	1	corollary	corollary	ADJ
ap-1783	205	2	3.3	3.3	NUM
ap-1783	205	3	.	.	PUNCT
ap-1783	206	1	the	the	DET
ap-1783	206	2	following	follow	VERB
ap-1783	206	3	laplace	laplace	NOUN
ap-1783	206	4	transform	transform	NOUN
ap-1783	206	5	pairs	pair	NOUN
ap-1783	206	6	hold	hold	VERB
ap-1783	206	7	:	:	PUNCT
ap-1783	206	8	f1(x	f1(x	NUM
ap-1783	206	9	)	)	PUNCT
ap-1783	206	10	=	=	SYM
ap-1783	207	1	1	1	NUM
ap-1783	207	2	π	π	NOUN
ap-1783	207	3	∫	∫	PROPN
ap-1783	207	4	∞	∞	NUM
ap-1783	207	5	1	1	NUM
ap-1783	207	6	/	/	SYM
ap-1783	207	7	e	e	NOUN
ap-1783	207	8	e−xu=	e−xu=	NOUN
ap-1783	207	9	(	(	PUNCT
ap-1783	207	10	w0(−u	w0(−u	ADJ
ap-1783	207	11	)	)	PUNCT
ap-1783	207	12	u	u	NOUN
ap-1783	207	13	(	(	PUNCT
ap-1783	207	14	1	1	NUM
ap-1783	207	15	+	+	ADJ
ap-1783	207	16	w0(−u	w0(−u	NOUN
ap-1783	207	17	)	)	PUNCT
ap-1783	207	18	)	)	PUNCT
ap-1783	207	19	)	)	PUNCT
ap-1783	207	20	du	du	PROPN
ap-1783	207	21	,	,	PUNCT
ap-1783	207	22	x	x	X
ap-1783	207	23	≥	≥	NOUN
ap-1783	207	24	0	0	NUM
ap-1783	207	25	,	,	PUNCT
ap-1783	207	26	(	(	PUNCT
ap-1783	207	27	3.10	3.10	NUM
ap-1783	207	28	)	)	PUNCT
ap-1783	207	29	f0(x	f0(x	NOUN
ap-1783	207	30	)	)	PUNCT
ap-1783	207	31	=	=	PUNCT
ap-1783	208	1	x	x	PUNCT
ap-1783	208	2	π	π	NOUN
ap-1783	208	3	∫	∫	PROPN
ap-1783	208	4	∞	∞	PROPN
ap-1783	208	5	1	1	NUM
ap-1783	208	6	/	/	SYM
ap-1783	208	7	e	e	NOUN
ap-1783	208	8	e−xu=	e−xu=	NOUN
ap-1783	208	9	(	(	PUNCT
ap-1783	208	10	w0(−u	w0(−u	PROPN
ap-1783	208	11	)	)	PUNCT
ap-1783	208	12	1	1	NUM
ap-1783	209	1	+	+	ADJ
ap-1783	209	2	w0(−u	w0(−u	X
ap-1783	209	3	)	)	PUNCT
ap-1783	209	4	)	)	PUNCT
ap-1783	209	5	du	du	PROPN
ap-1783	209	6	,	,	PUNCT
ap-1783	209	7	x	x	X
ap-1783	209	8	>	>	X
ap-1783	209	9	0	0	NUM
ap-1783	209	10	.	.	PUNCT
ap-1783	210	1	(	(	PUNCT
ap-1783	210	2	3.11	3.11	NUM
ap-1783	210	3	)	)	PUNCT
ap-1783	210	4	proof	proof	NOUN
ap-1783	210	5	.	.	PUNCT
ap-1783	211	1	function	function	VERB
ap-1783	211	2	w0(s	w0(s	PRON
ap-1783	211	3	)	)	PUNCT
ap-1783	211	4	s(1+w0(s	s(1+w0(s	PROPN
ap-1783	211	5	)	)	PUNCT
ap-1783	211	6	)	)	PUNCT
ap-1783	211	7	is	be	AUX
ap-1783	211	8	a	a	DET
ap-1783	211	9	stieltjes	stieltjes	NOUN
ap-1783	211	10	function	function	NOUN
ap-1783	211	11	[	[	X
ap-1783	211	12	4	4	NUM
ap-1783	211	13	]	]	PUNCT
ap-1783	211	14	.	.	PUNCT
ap-1783	212	1	from	from	ADP
ap-1783	212	2	the	the	DET
ap-1783	212	3	definition	definition	NOUN
ap-1783	212	4	of	of	ADP
ap-1783	212	5	the	the	DET
ap-1783	212	6	stieltjes	stieltjes	NOUN
ap-1783	212	7	transform	transform	VERB
ap-1783	212	8	and	and	CCONJ
ap-1783	212	9	from	from	ADP
ap-1783	212	10	eq	eq	ADP
ap-1783	212	11	.	.	PUNCT
ap-1783	213	1	(	(	PUNCT
ap-1783	213	2	3.6	3.6	NUM
ap-1783	213	3	)	)	PUNCT
ap-1783	213	4	,	,	PUNCT
ap-1783	213	5	it	it	PRON
ap-1783	213	6	follows	follow	VERB
ap-1783	213	7	that∫	that∫	NOUN
ap-1783	213	8	∞	∞	PROPN
ap-1783	213	9	0	0	NUM
ap-1783	214	1	e−szf1(x	e−szf1(x	PROPN
ap-1783	214	2	)	)	PUNCT
ap-1783	214	3	dx	dx	PROPN
ap-1783	215	1	=	=	SYM
ap-1783	215	2	1	1	NUM
ap-1783	215	3	π	π	NOUN
ap-1783	215	4	∫	∫	PROPN
ap-1783	215	5	∞	∞	NUM
ap-1783	215	6	1	1	NUM
ap-1783	215	7	/	/	SYM
ap-1783	215	8	e	e	NOUN
ap-1783	215	9	=	=	SYM
ap-1783	215	10	(	(	PUNCT
ap-1783	215	11	w0(−u	w0(−u	X
ap-1783	215	12	)	)	PUNCT
ap-1783	215	13	u	u	NOUN
ap-1783	215	14	(	(	PUNCT
ap-1783	215	15	1	1	NUM
ap-1783	215	16	+	+	ADJ
ap-1783	215	17	w0(−u	w0(−u	NOUN
ap-1783	215	18	)	)	PUNCT
ap-1783	215	19	)	)	PUNCT
ap-1783	215	20	)	)	PUNCT
ap-1783	215	21	1	1	NUM
ap-1783	215	22	s+	s+	PUNCT
ap-1783	215	23	u	u	PROPN
ap-1783	215	24	du	du	PROPN
ap-1783	215	25	,	,	PUNCT
ap-1783	215	26	<	<	X
ap-1783	215	27	s	s	X
ap-1783	215	28	>	>	X
ap-1783	215	29	−1	−1	PROPN
ap-1783	215	30	/	/	SYM
ap-1783	215	31	e	e	NOUN
ap-1783	215	32	,	,	PUNCT
ap-1783	215	33	(	(	PUNCT
ap-1783	215	34	3.12	3.12	NUM
ap-1783	215	35	)	)	PUNCT
ap-1783	215	36	and	and	CCONJ
ap-1783	215	37	after	after	ADP
ap-1783	215	38	inversion	inversion	NOUN
ap-1783	215	39	of	of	ADP
ap-1783	215	40	the	the	DET
ap-1783	215	41	laplace	laplace	NOUN
ap-1783	215	42	transform	transform	NOUN
ap-1783	215	43	we	we	PRON
ap-1783	215	44	obtain	obtain	VERB
ap-1783	215	45	eq	eq	ADP
ap-1783	215	46	.	.	PUNCT
ap-1783	216	1	(	(	PUNCT
ap-1783	216	2	3.10	3.10	NUM
ap-1783	216	3	)	)	PUNCT
ap-1783	216	4	.	.	PUNCT
ap-1783	217	1	equation	equation	NOUN
ap-1783	217	2	(	(	PUNCT
ap-1783	217	3	3.11	3.11	NUM
ap-1783	217	4	)	)	PUNCT
ap-1783	217	5	is	be	AUX
ap-1783	217	6	a	a	DET
ap-1783	217	7	consequence	consequence	NOUN
ap-1783	217	8	of	of	ADP
ap-1783	217	9	the	the	DET
ap-1783	217	10	relation	relation	NOUN
ap-1783	217	11	f0(x	f0(x	NOUN
ap-1783	217	12	)	)	PUNCT
ap-1783	217	13	=	=	SYM
ap-1783	217	14	−xd	−xd	NOUN
ap-1783	217	15	/	/	SYM
ap-1783	217	16	dxf1(x	dxf1(x	NOUN
ap-1783	217	17	)	)	PUNCT
ap-1783	217	18	..	..	PUNCT
ap-1783	218	1	the	the	DET
ap-1783	218	2	integral	integral	NOUN
ap-1783	218	3	in	in	ADP
ap-1783	218	4	eq	eq	PROPN
ap-1783	218	5	.	.	PUNCT
ap-1783	219	1	(	(	PUNCT
ap-1783	219	2	3.10	3.10	NUM
ap-1783	219	3	)	)	PUNCT
ap-1783	219	4	also	also	ADV
ap-1783	219	5	converges	converge	VERB
ap-1783	219	6	for	for	ADP
ap-1783	219	7	x	x	SYM
ap-1783	219	8	=	=	SYM
ap-1783	219	9	0	0	PROPN
ap-1783	219	10	.	.	PUNCT
ap-1783	219	11	theorem	theorem	VERB
ap-1783	219	12	3.4	3.4	NUM
ap-1783	219	13	.	.	PUNCT
ap-1783	220	1	we	we	PRON
ap-1783	220	2	have	have	VERB
ap-1783	220	3	∫	∫	PROPN
ap-1783	220	4	∞	∞	PROPN
ap-1783	220	5	0	0	NUM
ap-1783	220	6	e−sx	e−sx	PROPN
ap-1783	220	7	f0(x	f0(x	NOUN
ap-1783	220	8	)	)	PUNCT
ap-1783	220	9	x	x	SYM
ap-1783	220	10	dx	dx	PROPN
ap-1783	220	11	=	=	SYM
ap-1783	220	12	1	1	NUM
ap-1783	220	13	1	1	NUM
ap-1783	220	14	+	+	NOUN
ap-1783	220	15	w0(s	w0(s	PROPN
ap-1783	220	16	)	)	PUNCT
ap-1783	220	17	,	,	PUNCT
ap-1783	220	18	<	<	X
ap-1783	220	19	s	s	X
ap-1783	220	20	>	>	X
ap-1783	220	21	−1	−1	PROPN
ap-1783	220	22	/	/	SYM
ap-1783	220	23	e.	e.	PROPN
ap-1783	220	24	(	(	PUNCT
ap-1783	220	25	3.13	3.13	NUM
ap-1783	220	26	)	)	PUNCT
ap-1783	220	27	proof	proof	NOUN
ap-1783	220	28	.	.	PUNCT
ap-1783	221	1	because	because	SCONJ
ap-1783	221	2	d	d	NOUN
ap-1783	221	3	ds	ds	ADJ
ap-1783	221	4	∫	∫	PROPN
ap-1783	221	5	∞	∞	PROPN
ap-1783	221	6	0	0	NUM
ap-1783	221	7	e−sx	e−sx	PROPN
ap-1783	221	8	f0(x	f0(x	NOUN
ap-1783	221	9	)	)	PUNCT
ap-1783	221	10	x	x	SYM
ap-1783	221	11	dx	dx	PROPN
ap-1783	222	1	=	=	PUNCT
ap-1783	222	2	−	−	PROPN
ap-1783	222	3	∫	∫	PROPN
ap-1783	222	4	∞	∞	PROPN
ap-1783	222	5	0	0	NUM
ap-1783	222	6	e−sxf0(x	e−sxf0(x	NOUN
ap-1783	222	7	)	)	PUNCT
ap-1783	222	8	dx	dx	PROPN
ap-1783	223	1	=	=	PUNCT
ap-1783	224	1	−	−	PROPN
ap-1783	224	2	w0(s	w0(s	PROPN
ap-1783	224	3	)	)	PUNCT
ap-1783	224	4	s	s	PART
ap-1783	224	5	(	(	PUNCT
ap-1783	224	6	1	1	NUM
ap-1783	224	7	+	+	NOUN
ap-1783	224	8	w0(s	w0(s	PROPN
ap-1783	224	9	)	)	PUNCT
ap-1783	224	10	)	)	PUNCT
ap-1783	224	11	3	3	NUM
ap-1783	224	12	,	,	PUNCT
ap-1783	224	13	<	<	X
ap-1783	224	14	s	s	X
ap-1783	224	15	>	>	X
ap-1783	224	16	−1	−1	PROPN
ap-1783	224	17	/	/	SYM
ap-1783	224	18	e	e	NOUN
ap-1783	224	19	(	(	PUNCT
ap-1783	224	20	3.14	3.14	NUM
ap-1783	224	21	)	)	PUNCT
ap-1783	224	22	and	and	CCONJ
ap-1783	224	23	d	d	NOUN
ap-1783	224	24	ds	ds	ADJ
ap-1783	224	25	1	1	NUM
ap-1783	224	26	1	1	NUM
ap-1783	224	27	+	+	NOUN
ap-1783	224	28	w0(s	w0(s	X
ap-1783	224	29	)	)	PUNCT
ap-1783	224	30	=	=	PUNCT
ap-1783	225	1	−	−	PROPN
ap-1783	225	2	w0(s	w0(s	PROPN
ap-1783	225	3	)	)	PUNCT
ap-1783	225	4	s	s	PART
ap-1783	225	5	(	(	PUNCT
ap-1783	225	6	1	1	NUM
ap-1783	225	7	+	+	NOUN
ap-1783	225	8	w0(s	w0(s	PROPN
ap-1783	225	9	)	)	PUNCT
ap-1783	225	10	)	)	PUNCT
ap-1783	225	11	3	3	NUM
ap-1783	225	12	,	,	PUNCT
ap-1783	225	13	(	(	PUNCT
ap-1783	225	14	3.15	3.15	NUM
ap-1783	225	15	)	)	PUNCT
ap-1783	225	16	we	we	PRON
ap-1783	225	17	obtain	obtain	VERB
ap-1783	225	18	eq	eq	ADP
ap-1783	225	19	.	.	PUNCT
ap-1783	226	1	(	(	PUNCT
ap-1783	226	2	3.13	3.13	NUM
ap-1783	226	3	)	)	PUNCT
ap-1783	226	4	.	.	PUNCT
ap-1783	227	1	67	67	NUM
ap-1783	227	2	vladimír	vladimír	PROPN
ap-1783	227	3	vojta	vojta	PROPN
ap-1783	227	4	acta	acta	PROPN
ap-1783	227	5	polytechnica	polytechnica	PROPN
ap-1783	227	6	corollary	corollary	ADJ
ap-1783	227	7	3.5	3.5	NUM
ap-1783	227	8	.	.	PUNCT
ap-1783	228	1	we	we	PRON
ap-1783	228	2	have	have	VERB
ap-1783	228	3	1	1	NUM
ap-1783	228	4	π	π	NOUN
ap-1783	228	5	∫	∫	PROPN
ap-1783	228	6	∞	∞	NUM
ap-1783	228	7	0	0	NUM
ap-1783	228	8	s−yy−y	s−yy−y	NOUN
ap-1783	228	9	sin	sin	VERB
ap-1783	228	10	πy	πy	ADP
ap-1783	229	1	γ(1	γ(1	PROPN
ap-1783	229	2	+	+	CCONJ
ap-1783	229	3	y	y	NOUN
ap-1783	229	4	)	)	PUNCT
ap-1783	229	5	dy	dy	NOUN
ap-1783	229	6	=	=	PUNCT
ap-1783	229	7	w0(s	w0(s	PROPN
ap-1783	229	8	)	)	PUNCT
ap-1783	229	9	(	(	PUNCT
ap-1783	229	10	1	1	NUM
ap-1783	229	11	+	+	NOUN
ap-1783	229	12	w0(s	w0(s	PROPN
ap-1783	229	13	)	)	PUNCT
ap-1783	229	14	)	)	PUNCT
ap-1783	229	15	3	3	NUM
ap-1783	229	16	,	,	PUNCT
ap-1783	229	17	s	s	PART
ap-1783	229	18	∈	∈	PROPN
ap-1783	229	19	c	c	NOUN
ap-1783	229	20	\d1	\d1	AUX
ap-1783	229	21	/	/	SYM
ap-1783	229	22	e	e	NOUN
ap-1783	229	23	,	,	PUNCT
ap-1783	229	24	(	(	PUNCT
ap-1783	229	25	3.16	3.16	NUM
ap-1783	229	26	)	)	PUNCT
ap-1783	229	27	1	1	NUM
ap-1783	229	28	π	π	NOUN
ap-1783	229	29	∫	∫	PROPN
ap-1783	229	30	∞	∞	NUM
ap-1783	229	31	0	0	NUM
ap-1783	229	32	s−yy−y	s−yy−y	NOUN
ap-1783	229	33	sin	sin	VERB
ap-1783	229	34	πy	πy	ADP
ap-1783	229	35	γ(y	γ(y	PROPN
ap-1783	229	36	)	)	PUNCT
ap-1783	229	37	dy	dy	NOUN
ap-1783	229	38	=	=	NOUN
ap-1783	229	39	1	1	NUM
ap-1783	229	40	1	1	NUM
ap-1783	229	41	+	+	NOUN
ap-1783	229	42	w0(s	w0(s	PROPN
ap-1783	229	43	)	)	PUNCT
ap-1783	229	44	,	,	PUNCT
ap-1783	229	45	s	s	VERB
ap-1783	229	46	∈	∈	PROPN
ap-1783	229	47	c	c	NOUN
ap-1783	229	48	\d1	\d1	AUX
ap-1783	229	49	/	/	SYM
ap-1783	229	50	e	e	NOUN
ap-1783	229	51	,	,	PUNCT
ap-1783	229	52	(	(	PUNCT
ap-1783	229	53	3.17	3.17	NUM
ap-1783	229	54	)	)	PUNCT
ap-1783	229	55	where	where	SCONJ
ap-1783	229	56	d1	d1	NOUN
ap-1783	229	57	/	/	SYM
ap-1783	229	58	e	e	NOUN
ap-1783	229	59	is	be	AUX
ap-1783	229	60	an	an	DET
ap-1783	229	61	open	open	ADJ
ap-1783	229	62	disc	disc	NOUN
ap-1783	229	63	of	of	ADP
ap-1783	229	64	complex	complex	ADJ
ap-1783	229	65	numbers	number	NOUN
ap-1783	229	66	with	with	ADP
ap-1783	229	67	absolute	absolute	ADJ
ap-1783	229	68	value	value	NOUN
ap-1783	229	69	r	r	NOUN
ap-1783	229	70	<	<	X
ap-1783	229	71	1	1	NUM
ap-1783	229	72	/	/	SYM
ap-1783	229	73	e.	e.	PROPN
ap-1783	229	74	proof	proof	PROPN
ap-1783	229	75	.	.	PUNCT
ap-1783	230	1	substitution	substitution	NOUN
ap-1783	230	2	of	of	ADP
ap-1783	230	3	f0(x	f0(x	NOUN
ap-1783	230	4	)	)	PUNCT
ap-1783	230	5	from	from	ADP
ap-1783	230	6	eq	eq	ADP
ap-1783	230	7	.	.	PUNCT
ap-1783	231	1	(	(	PUNCT
ap-1783	231	2	2.7	2.7	NUM
ap-1783	231	3	)	)	PUNCT
ap-1783	231	4	to	to	ADP
ap-1783	231	5	eq	eq	NOUN
ap-1783	231	6	.	.	PUNCT
ap-1783	232	1	(	(	PUNCT
ap-1783	232	2	3.7	3.7	NUM
ap-1783	232	3	)	)	PUNCT
ap-1783	232	4	and	and	CCONJ
ap-1783	232	5	eq	eq	NOUN
ap-1783	232	6	.	.	PUNCT
ap-1783	233	1	(	(	PUNCT
ap-1783	233	2	3.13	3.13	NUM
ap-1783	233	3	)	)	PUNCT
ap-1783	233	4	gives	give	VERB
ap-1783	233	5	eq	eq	NOUN
ap-1783	233	6	.	.	PUNCT
ap-1783	234	1	(	(	PUNCT
ap-1783	234	2	3.16	3.16	NUM
ap-1783	234	3	)	)	PUNCT
ap-1783	234	4	and	and	CCONJ
ap-1783	234	5	eq	eq	NOUN
ap-1783	234	6	.	.	PUNCT
ap-1783	235	1	(	(	PUNCT
ap-1783	235	2	3.17	3.17	NUM
ap-1783	235	3	)	)	PUNCT
ap-1783	235	4	,	,	PUNCT
ap-1783	235	5	respectively	respectively	ADV
ap-1783	235	6	.	.	PUNCT
ap-1783	236	1	after	after	ADP
ap-1783	236	2	substituting	substitute	VERB
ap-1783	236	3	s	s	PART
ap-1783	236	4	=	=	SYM
ap-1783	236	5	ep	ep	PROPN
ap-1783	236	6	into	into	ADP
ap-1783	236	7	eq	eq	PROPN
ap-1783	236	8	.	.	PUNCT
ap-1783	237	1	(	(	PUNCT
ap-1783	237	2	3.16	3.16	NUM
ap-1783	237	3	)	)	PUNCT
ap-1783	237	4	and	and	CCONJ
ap-1783	237	5	eq	eq	NOUN
ap-1783	237	6	.	.	PUNCT
ap-1783	238	1	(	(	PUNCT
ap-1783	238	2	3.17	3.17	NUM
ap-1783	238	3	)	)	PUNCT
ap-1783	238	4	we	we	PRON
ap-1783	238	5	obtain	obtain	VERB
ap-1783	238	6	the	the	DET
ap-1783	238	7	laplace	laplace	NOUN
ap-1783	238	8	transform	transform	NOUN
ap-1783	238	9	pairs∫	pairs∫	NOUN
ap-1783	238	10	∞	∞	PROPN
ap-1783	238	11	0	0	NUM
ap-1783	239	1	e−pyy−y	e−pyy−y	NOUN
ap-1783	239	2	sin	sin	NOUN
ap-1783	239	3	πy	πy	ADP
ap-1783	240	1	γ(1	γ(1	PROPN
ap-1783	240	2	+	+	CCONJ
ap-1783	240	3	y	y	NOUN
ap-1783	240	4	)	)	PUNCT
ap-1783	240	5	dy	dy	NOUN
ap-1783	240	6	=	=	SYM
ap-1783	240	7	πw0(ep	πw0(ep	X
ap-1783	240	8	)	)	PUNCT
ap-1783	240	9	(	(	PUNCT
ap-1783	240	10	1	1	NUM
ap-1783	240	11	+	+	NOUN
ap-1783	240	12	w0(ep	w0(ep	X
ap-1783	240	13	)	)	PUNCT
ap-1783	240	14	)	)	PUNCT
ap-1783	240	15	3	3	NUM
ap-1783	240	16	,	,	PUNCT
ap-1783	240	17	<	<	X
ap-1783	240	18	p	p	X
ap-1783	240	19	>	>	X
ap-1783	240	20	−1	−1	NOUN
ap-1783	240	21	,	,	PUNCT
ap-1783	240	22	−π	−π	ADV
ap-1783	240	23	<	<	X
ap-1783	241	1	=	=	X
ap-1783	241	2	p	p	X
ap-1783	241	3	≤	≤	NUM
ap-1783	241	4	π	π	PROPN
ap-1783	241	5	,	,	PUNCT
ap-1783	241	6	(	(	PUNCT
ap-1783	241	7	3.18	3.18	NUM
ap-1783	241	8	)	)	PUNCT
ap-1783	241	9	∫	∫	PROPN
ap-1783	241	10	∞	∞	PROPN
ap-1783	241	11	0	0	NUM
ap-1783	242	1	e−pyy−y	e−pyy−y	NOUN
ap-1783	242	2	sin	sin	NOUN
ap-1783	242	3	πy	πy	ADP
ap-1783	242	4	γ(y	γ(y	PROPN
ap-1783	242	5	)	)	PUNCT
ap-1783	242	6	dy	dy	NOUN
ap-1783	242	7	=	=	PUNCT
ap-1783	242	8	π	π	PROPN
ap-1783	242	9	1	1	NUM
ap-1783	242	10	+	+	NOUN
ap-1783	242	11	w0(ep	w0(ep	X
ap-1783	242	12	)	)	PUNCT
ap-1783	242	13	,	,	PUNCT
ap-1783	242	14	<	<	X
ap-1783	242	15	p	p	X
ap-1783	242	16	>	>	X
ap-1783	242	17	−1	−1	NOUN
ap-1783	242	18	,	,	PUNCT
ap-1783	242	19	−π	−π	ADV
ap-1783	242	20	<	<	X
ap-1783	243	1	=	=	X
ap-1783	243	2	p	p	X
ap-1783	243	3	≤	≤	NUM
ap-1783	243	4	π	π	NOUN
ap-1783	243	5	.	.	PUNCT
ap-1783	244	1	(	(	PUNCT
ap-1783	244	2	3.19	3.19	NUM
ap-1783	244	3	)	)	PUNCT
ap-1783	244	4	the	the	DET
ap-1783	244	5	fact	fact	NOUN
ap-1783	244	6	that	that	SCONJ
ap-1783	244	7	the	the	DET
ap-1783	244	8	abscissa	abscissa	NOUN
ap-1783	244	9	of	of	ADP
ap-1783	244	10	convergence	convergence	NOUN
ap-1783	244	11	of	of	ADP
ap-1783	244	12	the	the	DET
ap-1783	244	13	two	two	NUM
ap-1783	244	14	previous	previous	ADJ
ap-1783	244	15	laplace	laplace	NOUN
ap-1783	244	16	integrals	integral	NOUN
ap-1783	244	17	is	be	AUX
ap-1783	244	18	equal	equal	ADJ
ap-1783	244	19	to	to	PART
ap-1783	244	20	−1	−1	NOUN
ap-1783	244	21	can	can	AUX
ap-1783	244	22	be	be	AUX
ap-1783	244	23	verified	verify	VERB
ap-1783	244	24	by	by	ADP
ap-1783	244	25	the	the	DET
ap-1783	244	26	stirling	stirling	NOUN
ap-1783	244	27	formula	formula	NOUN
ap-1783	244	28	.	.	PUNCT
ap-1783	245	1	it	it	PRON
ap-1783	245	2	should	should	AUX
ap-1783	245	3	be	be	AUX
ap-1783	245	4	emphasized	emphasize	VERB
ap-1783	245	5	,	,	PUNCT
ap-1783	245	6	however	however	ADV
ap-1783	245	7	,	,	PUNCT
ap-1783	245	8	that	that	SCONJ
ap-1783	245	9	the	the	DET
ap-1783	245	10	right	right	ADJ
ap-1783	245	11	hand	hand	NOUN
ap-1783	245	12	sides	side	NOUN
ap-1783	245	13	of	of	ADP
ap-1783	245	14	eq	eq	PROPN
ap-1783	245	15	.	.	PUNCT
ap-1783	246	1	(	(	PUNCT
ap-1783	246	2	3.18	3.18	NUM
ap-1783	246	3	)	)	PUNCT
ap-1783	246	4	and	and	CCONJ
ap-1783	246	5	eq	eq	NOUN
ap-1783	246	6	.	.	PUNCT
ap-1783	247	1	(	(	PUNCT
ap-1783	247	2	3.19	3.19	NUM
ap-1783	247	3	)	)	PUNCT
ap-1783	247	4	are	be	AUX
ap-1783	247	5	not	not	PART
ap-1783	247	6	holomorphic	holomorphic	ADJ
ap-1783	247	7	functions	function	NOUN
ap-1783	247	8	in	in	ADP
ap-1783	247	9	the	the	DET
ap-1783	247	10	half	half	ADJ
ap-1783	247	11	-	-	PUNCT
ap-1783	247	12	plane	plane	NOUN
ap-1783	247	13	<	<	X
ap-1783	247	14	p	p	X
ap-1783	247	15	≥	≥	NOUN
ap-1783	247	16	a	a	DET
ap-1783	247	17	>	>	X
ap-1783	247	18	−1	−1	NOUN
ap-1783	247	19	,	,	PUNCT
ap-1783	247	20	a	a	DET
ap-1783	247	21	otherwise	otherwise	ADV
ap-1783	247	22	arbitrary	arbitrary	ADJ
ap-1783	247	23	.	.	PUNCT
ap-1783	248	1	this	this	PRON
ap-1783	248	2	means	mean	VERB
ap-1783	248	3	that	that	SCONJ
ap-1783	248	4	there	there	PRON
ap-1783	248	5	exist	exist	VERB
ap-1783	248	6	functions	function	NOUN
ap-1783	248	7	holomorphic	holomorphic	ADJ
ap-1783	248	8	in	in	ADP
ap-1783	248	9	the	the	DET
ap-1783	248	10	half	half	ADJ
ap-1783	248	11	-	-	PUNCT
ap-1783	248	12	plane	plane	NOUN
ap-1783	248	13	<	<	X
ap-1783	248	14	p	p	X
ap-1783	248	15	>	>	X
ap-1783	248	16	−1	−1	NOUN
ap-1783	248	17	,	,	PUNCT
ap-1783	248	18	defined	define	VERB
ap-1783	248	19	by	by	ADP
ap-1783	248	20	the	the	DET
ap-1783	248	21	integrals	integral	NOUN
ap-1783	248	22	on	on	ADP
ap-1783	248	23	the	the	DET
ap-1783	248	24	left	left	ADJ
ap-1783	248	25	hand	hand	NOUN
ap-1783	248	26	sides	side	NOUN
ap-1783	248	27	of	of	ADP
ap-1783	248	28	equations	equation	NOUN
ap-1783	248	29	(	(	PUNCT
ap-1783	248	30	3.18	3.18	NUM
ap-1783	248	31	)	)	PUNCT
ap-1783	248	32	and	and	CCONJ
ap-1783	248	33	(	(	PUNCT
ap-1783	248	34	3.19	3.19	NUM
ap-1783	248	35	)	)	PUNCT
ap-1783	248	36	,	,	PUNCT
ap-1783	248	37	and	and	CCONJ
ap-1783	248	38	equivalent	equivalent	ADJ
ap-1783	248	39	to	to	ADP
ap-1783	248	40	the	the	DET
ap-1783	248	41	functions	function	NOUN
ap-1783	248	42	on	on	ADP
ap-1783	248	43	the	the	DET
ap-1783	248	44	right	right	ADJ
ap-1783	248	45	hand	hand	NOUN
ap-1783	248	46	sides	side	NOUN
ap-1783	248	47	in	in	ADP
ap-1783	248	48	the	the	DET
ap-1783	248	49	region	region	NOUN
ap-1783	248	50	defined	define	VERB
ap-1783	248	51	in	in	ADP
ap-1783	248	52	eq	eq	ADP
ap-1783	248	53	.	.	PUNCT
ap-1783	249	1	(	(	PUNCT
ap-1783	249	2	3.18	3.18	NUM
ap-1783	249	3	)	)	PUNCT
ap-1783	249	4	and	and	CCONJ
ap-1783	249	5	eq	eq	NOUN
ap-1783	249	6	.	.	PUNCT
ap-1783	250	1	(	(	PUNCT
ap-1783	250	2	3.19	3.19	NUM
ap-1783	250	3	)	)	PUNCT
ap-1783	250	4	.	.	PUNCT
ap-1783	251	1	regarding	regard	VERB
ap-1783	251	2	eq	eq	ADP
ap-1783	251	3	.	.	PUNCT
ap-1783	251	4	(	(	PUNCT
ap-1783	251	5	3.18	3.18	NUM
ap-1783	251	6	)	)	PUNCT
ap-1783	251	7	or	or	CCONJ
ap-1783	251	8	eq	eq	NOUN
ap-1783	251	9	.	.	PUNCT
ap-1783	252	1	(	(	PUNCT
ap-1783	252	2	3.19	3.19	NUM
ap-1783	252	3	)	)	PUNCT
ap-1783	252	4	as	as	SCONJ
ap-1783	252	5	inverse	inverse	NOUN
ap-1783	252	6	problem	problem	NOUN
ap-1783	252	7	needs	need	VERB
ap-1783	252	8	to	to	PART
ap-1783	252	9	apply	apply	VERB
ap-1783	252	10	the	the	DET
ap-1783	252	11	real	real	ADJ
ap-1783	252	12	methods	method	NOUN
ap-1783	252	13	for	for	ADP
ap-1783	252	14	the	the	DET
ap-1783	252	15	laplace	laplace	NOUN
ap-1783	252	16	transform	transform	NOUN
ap-1783	252	17	inversion	inversion	NOUN
ap-1783	252	18	.	.	PUNCT
ap-1783	253	1	theorem	theorem	VERB
ap-1783	253	2	3.6	3.6	NUM
ap-1783	253	3	.	.	PUNCT
ap-1783	254	1	we	we	PRON
ap-1783	254	2	have	have	VERB
ap-1783	254	3	γ(s	γ(	NOUN
ap-1783	254	4	)	)	PUNCT
ap-1783	255	1	π	π	X
ap-1783	255	2	∫	∫	PROPN
ap-1783	255	3	∞	∞	NUM
ap-1783	255	4	0	0	PROPN
ap-1783	255	5	y−sy−y	y−sy−y	PROPN
ap-1783	255	6	sin	sin	NOUN
ap-1783	255	7	πyγ(y	πyγ(y	NOUN
ap-1783	255	8	)	)	PUNCT
ap-1783	255	9	dy	dy	NOUN
ap-1783	255	10	=	=	SYM
ap-1783	255	11	∫	∫	PROPN
ap-1783	255	12	∞	∞	NOUN
ap-1783	255	13	0	0	NUM
ap-1783	256	1	ys−1	ys−1	NOUN
ap-1783	256	2	1	1	NUM
ap-1783	256	3	+	+	ADJ
ap-1783	256	4	w0(ey	w0(ey	X
ap-1783	256	5	)	)	PUNCT
ap-1783	256	6	dy	dy	NOUN
ap-1783	256	7	,	,	PUNCT
ap-1783	256	8	0	0	PUNCT
ap-1783	256	9	<	<	X
ap-1783	256	10	<	<	X
ap-1783	256	11	s	s	X
ap-1783	256	12	<	<	X
ap-1783	256	13	1	1	NUM
ap-1783	256	14	.	.	PUNCT
ap-1783	256	15	(	(	PUNCT
ap-1783	256	16	3.20	3.20	NUM
ap-1783	256	17	)	)	PUNCT
ap-1783	256	18	proof	proof	NOUN
ap-1783	256	19	.	.	PUNCT
ap-1783	257	1	application	application	NOUN
ap-1783	257	2	of	of	ADP
ap-1783	257	3	the	the	DET
ap-1783	257	4	mellin	mellin	PROPN
ap-1783	257	5	transform	transform	NOUN
ap-1783	257	6	to	to	ADP
ap-1783	257	7	both	both	DET
ap-1783	257	8	sides	side	NOUN
ap-1783	257	9	of	of	ADP
ap-1783	257	10	eq	eq	PROPN
ap-1783	257	11	.	.	PUNCT
ap-1783	258	1	(	(	PUNCT
ap-1783	258	2	3.19	3.19	NUM
ap-1783	258	3	)	)	PUNCT
ap-1783	258	4	,	,	PUNCT
ap-1783	258	5	and	and	CCONJ
ap-1783	258	6	taking	take	VERB
ap-1783	258	7	eq	eq	NOUN
ap-1783	258	8	.	.	PUNCT
ap-1783	259	1	(	(	PUNCT
ap-1783	259	2	2.4	2.4	NUM
ap-1783	259	3	)	)	PUNCT
ap-1783	259	4	into	into	ADP
ap-1783	259	5	account	account	NOUN
ap-1783	259	6	,	,	PUNCT
ap-1783	259	7	gives	give	VERB
ap-1783	259	8	the	the	DET
ap-1783	259	9	result	result	NOUN
ap-1783	259	10	.	.	PUNCT
ap-1783	260	1	note	note	VERB
ap-1783	260	2	that	that	SCONJ
ap-1783	260	3	both	both	DET
ap-1783	260	4	integrals	integral	NOUN
ap-1783	260	5	in	in	ADP
ap-1783	260	6	eq	eq	ADP
ap-1783	260	7	.	.	PUNCT
ap-1783	261	1	(	(	PUNCT
ap-1783	261	2	3.20	3.20	NUM
ap-1783	261	3	)	)	PUNCT
ap-1783	261	4	are	be	AUX
ap-1783	261	5	mellin	mellin	NOUN
ap-1783	261	6	transforms	transform	NOUN
ap-1783	261	7	.	.	PUNCT
ap-1783	262	1	theorem	theorem	VERB
ap-1783	262	2	3.7	3.7	NUM
ap-1783	262	3	.	.	PUNCT
ap-1783	263	1	we	we	PRON
ap-1783	263	2	have	have	VERB
ap-1783	263	3	γ(s	γ(	NOUN
ap-1783	263	4	)	)	PUNCT
ap-1783	264	1	π	π	X
ap-1783	264	2	∫	∫	PROPN
ap-1783	264	3	∞	∞	NUM
ap-1783	264	4	1	1	NUM
ap-1783	264	5	/	/	SYM
ap-1783	264	6	e	e	NOUN
ap-1783	264	7	u−s−1	u−s−1	NOUN
ap-1783	264	8	=	=	SYM
ap-1783	264	9	w0(−u	w0(−u	NOUN
ap-1783	264	10	)	)	PUNCT
ap-1783	264	11	du	du	NOUN
ap-1783	264	12	=	=	SYM
ap-1783	264	13	ss	ss	PROPN
ap-1783	264	14	s2	s2	PROPN
ap-1783	264	15	,	,	PUNCT
ap-1783	264	16	<	<	X
ap-1783	264	17	s	s	X
ap-1783	264	18	>	>	X
ap-1783	264	19	0	0	NUM
ap-1783	264	20	.	.	PUNCT
ap-1783	265	1	(	(	PUNCT
ap-1783	265	2	3.21	3.21	NUM
ap-1783	265	3	)	)	PUNCT
ap-1783	265	4	proof	proof	NOUN
ap-1783	265	5	.	.	PUNCT
ap-1783	266	1	from	from	ADP
ap-1783	266	2	the	the	DET
ap-1783	266	3	mellin	mellin	PROPN
ap-1783	266	4	transform	transform	NOUN
ap-1783	266	5	of	of	ADP
ap-1783	266	6	eq	eq	NOUN
ap-1783	266	7	.	.	PUNCT
ap-1783	267	1	(	(	PUNCT
ap-1783	267	2	2.15	2.15	NUM
ap-1783	267	3	)	)	PUNCT
ap-1783	267	4	,	,	PUNCT
ap-1783	267	5	taking	take	VERB
ap-1783	267	6	eq	eq	NOUN
ap-1783	267	7	.	.	PUNCT
ap-1783	268	1	(	(	PUNCT
ap-1783	268	2	2.11	2.11	NUM
ap-1783	268	3	)	)	PUNCT
ap-1783	268	4	and	and	CCONJ
ap-1783	268	5	eq	eq	NOUN
ap-1783	268	6	.	.	PUNCT
ap-1783	269	1	(	(	PUNCT
ap-1783	269	2	2.4	2.4	NUM
ap-1783	269	3	)	)	PUNCT
ap-1783	269	4	into	into	ADP
ap-1783	269	5	account	account	NOUN
ap-1783	269	6	,	,	PUNCT
ap-1783	269	7	it	it	PRON
ap-1783	269	8	follows	follow	VERB
ap-1783	269	9	that	that	SCONJ
ap-1783	269	10	ss	ss	PROPN
ap-1783	269	11	s2	s2	PROPN
ap-1783	269	12	=	=	PROPN
ap-1783	269	13	mt	mt	PROPN
ap-1783	269	14	[	[	PUNCT
ap-1783	269	15	1	1	NUM
ap-1783	269	16	π	π	PROPN
ap-1783	269	17	∫	∫	PROPN
ap-1783	269	18	∞	∞	NUM
ap-1783	269	19	1	1	NUM
ap-1783	269	20	/	/	SYM
ap-1783	269	21	e	e	X
ap-1783	269	22	e−xu	e−xu	ADJ
ap-1783	269	23	=	=	SYM
ap-1783	269	24	w0(−u	w0(−u	NOUN
ap-1783	269	25	)	)	PUNCT
ap-1783	269	26	u	u	PROPN
ap-1783	269	27	du	du	X
ap-1783	269	28	;	;	PUNCT
ap-1783	269	29	s	s	X
ap-1783	269	30	]	]	X
ap-1783	269	31	=	=	SYM
ap-1783	269	32	γ(s	γ(	NOUN
ap-1783	269	33	)	)	PUNCT
ap-1783	270	1	π	π	X
ap-1783	270	2	∫	∫	PROPN
ap-1783	270	3	∞	∞	NUM
ap-1783	270	4	1	1	NUM
ap-1783	270	5	/	/	SYM
ap-1783	270	6	e	e	NOUN
ap-1783	270	7	u−s	u−s	NOUN
ap-1783	270	8	=	=	SYM
ap-1783	270	9	w0(−u	w0(−u	X
ap-1783	270	10	)	)	PUNCT
ap-1783	270	11	u	u	PROPN
ap-1783	270	12	du	du	NOUN
ap-1783	270	13	,	,	PUNCT
ap-1783	270	14	<	<	X
ap-1783	270	15	s	s	X
ap-1783	270	16	>	>	X
ap-1783	270	17	0	0	NUM
ap-1783	270	18	.	.	PUNCT
ap-1783	271	1	(	(	PUNCT
ap-1783	271	2	3.22	3.22	NUM
ap-1783	271	3	)	)	PUNCT
ap-1783	271	4	theorem	theorem	VERB
ap-1783	271	5	3.8	3.8	NUM
ap-1783	271	6	.	.	PUNCT
ap-1783	272	1	we	we	PRON
ap-1783	272	2	have	have	VERB
ap-1783	272	3	f1(x	f1(x	NUM
ap-1783	272	4	)	)	PUNCT
ap-1783	272	5	=	=	SYM
ap-1783	273	1	1−	1−	NUM
ap-1783	273	2	1	1	NUM
ap-1783	273	3	π	π	SYM
ap-1783	273	4	∫	∫	PROPN
ap-1783	273	5	∞	∞	NUM
ap-1783	273	6	0	0	NUM
ap-1783	273	7	xyy−y−1	xyy−y−1	PROPN
ap-1783	273	8	sin	sin	NOUN
ap-1783	273	9	πy	πy	X
ap-1783	273	10	dy	dy	NOUN
ap-1783	273	11	,	,	PUNCT
ap-1783	273	12	x	x	X
ap-1783	273	13	≥	≥	NOUN
ap-1783	273	14	0	0	NUM
ap-1783	273	15	.	.	PUNCT
ap-1783	274	1	(	(	PUNCT
ap-1783	274	2	3.23	3.23	NUM
ap-1783	274	3	)	)	PUNCT
ap-1783	274	4	proof	proof	NOUN
ap-1783	274	5	.	.	PUNCT
ap-1783	275	1	from	from	ADP
ap-1783	275	2	eq	eq	ADP
ap-1783	275	3	.	.	PUNCT
ap-1783	276	1	(	(	PUNCT
ap-1783	276	2	3.13	3.13	NUM
ap-1783	276	3	)	)	PUNCT
ap-1783	276	4	it	it	PRON
ap-1783	276	5	follows	follow	VERB
ap-1783	276	6	that	that	SCONJ
ap-1783	276	7	∫	∫	PROPN
ap-1783	276	8	∞	∞	NOUN
ap-1783	276	9	0	0	NUM
ap-1783	276	10	f1(x	f1(x	NUM
ap-1783	276	11	)	)	PUNCT
ap-1783	277	1	x	x	SYM
ap-1783	277	2	dx	dx	PROPN
ap-1783	277	3	=	=	SYM
ap-1783	277	4	1	1	NUM
ap-1783	277	5	1	1	NUM
ap-1783	277	6	+	+	NOUN
ap-1783	277	7	w0(0	w0(0	PROPN
ap-1783	277	8	)	)	PUNCT
ap-1783	277	9	=	=	SYM
ap-1783	278	1	1	1	X
ap-1783	278	2	.	.	PUNCT
ap-1783	278	3	(	(	PUNCT
ap-1783	278	4	3.24	3.24	NUM
ap-1783	278	5	)	)	PUNCT
ap-1783	278	6	eq	eq	NOUN
ap-1783	278	7	.	.	PUNCT
ap-1783	279	1	(	(	PUNCT
ap-1783	279	2	2.12	2.12	NUM
ap-1783	279	3	)	)	PUNCT
ap-1783	279	4	thus	thus	ADV
ap-1783	279	5	can	can	AUX
ap-1783	279	6	be	be	AUX
ap-1783	279	7	rewritten	rewrite	VERB
ap-1783	279	8	in	in	ADP
ap-1783	279	9	the	the	DET
ap-1783	279	10	form	form	NOUN
ap-1783	279	11	f1(x	f1(x	NOUN
ap-1783	279	12	)	)	PUNCT
ap-1783	279	13	=	=	SYM
ap-1783	280	1	1−	1−	NUM
ap-1783	280	2	∫	∫	NOUN
ap-1783	280	3	x	x	SYM
ap-1783	280	4	0	0	NUM
ap-1783	280	5	f0(z	f0(z	NUM
ap-1783	280	6	)	)	PUNCT
ap-1783	280	7	z	z	NOUN
ap-1783	280	8	dz	dz	NOUN
ap-1783	280	9	=	=	SYM
ap-1783	281	1	1−	1−	NUM
ap-1783	281	2	1	1	NUM
ap-1783	281	3	π	π	SYM
ap-1783	281	4	∫	∫	PROPN
ap-1783	281	5	∞	∞	NUM
ap-1783	281	6	0	0	NUM
ap-1783	281	7	y−y	y−y	NOUN
ap-1783	281	8	sin	sin	VERB
ap-1783	281	9	πy	πy	ADP
ap-1783	281	10	∫	∫	PROPN
ap-1783	281	11	x	x	SYM
ap-1783	281	12	0	0	PUNCT
ap-1783	281	13	zy−1	zy−1	PROPN
ap-1783	281	14	dz	dz	X
ap-1783	281	15	dy	dy	PROPN
ap-1783	281	16	,	,	PUNCT
ap-1783	281	17	(	(	PUNCT
ap-1783	281	18	3.25	3.25	NUM
ap-1783	281	19	)	)	PUNCT
ap-1783	281	20	where	where	SCONJ
ap-1783	281	21	we	we	PRON
ap-1783	281	22	substituted	substitute	VERB
ap-1783	281	23	f0(z	f0(z	PROPN
ap-1783	281	24	)	)	PUNCT
ap-1783	281	25	from	from	ADP
ap-1783	281	26	eq	eq	ADP
ap-1783	281	27	.	.	PUNCT
ap-1783	282	1	(	(	PUNCT
ap-1783	282	2	2.7	2.7	NUM
ap-1783	282	3	)	)	PUNCT
ap-1783	282	4	.	.	PUNCT
ap-1783	283	1	because	because	SCONJ
ap-1783	283	2	∫	∫	PROPN
ap-1783	283	3	x	x	SYM
ap-1783	283	4	0	0	PROPN
ap-1783	283	5	zy−1	zy−1	PROPN
ap-1783	283	6	dz	dz	NOUN
ap-1783	283	7	=	=	PUNCT
ap-1783	283	8	xy	xy	PROPN
ap-1783	283	9	/	/	SYM
ap-1783	283	10	y	y	PROPN
ap-1783	283	11	,	,	PUNCT
ap-1783	283	12	y	y	PROPN
ap-1783	283	13	>	>	X
ap-1783	283	14	0	0	PROPN
ap-1783	283	15	,	,	PUNCT
ap-1783	283	16	we	we	PRON
ap-1783	283	17	obtain	obtain	VERB
ap-1783	283	18	eq	eq	ADP
ap-1783	283	19	.	.	PUNCT
ap-1783	284	1	(	(	PUNCT
ap-1783	284	2	3.23	3.23	NUM
ap-1783	284	3	)	)	PUNCT
ap-1783	284	4	.	.	PUNCT
ap-1783	285	1	68	68	NUM
ap-1783	285	2	vol	vol	NOUN
ap-1783	285	3	.	.	PUNCT
ap-1783	286	1	53	53	NUM
ap-1783	286	2	no	no	NOUN
ap-1783	286	3	.	.	PUNCT
ap-1783	287	1	2/2013	2/2013	NUM
ap-1783	287	2	cayley	cayley	ADJ
ap-1783	287	3	-	-	PUNCT
ap-1783	287	4	eisenstein	eisenstein	NOUN
ap-1783	287	5	-	-	PUNCT
ap-1783	287	6	pólya	pólya	NOUN
ap-1783	288	1	and	and	CCONJ
ap-1783	288	2	landau	landau	VERB
ap-1783	288	3	probability	probability	NOUN
ap-1783	288	4	distributions	distribution	NOUN
ap-1783	288	5	corollary	corollary	ADJ
ap-1783	288	6	3.9	3.9	NUM
ap-1783	288	7	.	.	PUNCT
ap-1783	289	1	we	we	PRON
ap-1783	289	2	have	have	VERB
ap-1783	289	3	f1(x	f1(x	NUM
ap-1783	289	4	)	)	PUNCT
ap-1783	289	5	=	=	SYM
ap-1783	290	1	1−	1−	NUM
ap-1783	290	2	∫	∫	NOUN
ap-1783	290	3	∞	∞	NUM
ap-1783	291	1	−	−	PROPN
ap-1783	291	2	ln	ln	ADJ
ap-1783	291	3	x	x	SYM
ap-1783	291	4	φ(u	φ(u	X
ap-1783	291	5	)	)	PUNCT
ap-1783	291	6	du	du	PROPN
ap-1783	291	7	=	=	SYM
ap-1783	291	8	∫	∫	PROPN
ap-1783	292	1	−	−	PROPN
ap-1783	292	2	ln	ln	NOUN
ap-1783	292	3	x	x	X
ap-1783	292	4	−∞	−∞	ADP
ap-1783	292	5	φ(u	φ(u	NOUN
ap-1783	292	6	)	)	PUNCT
ap-1783	292	7	du	du	NOUN
ap-1783	292	8	,	,	PUNCT
ap-1783	292	9	x	x	X
ap-1783	292	10	≥	≥	NOUN
ap-1783	292	11	0	0	NUM
ap-1783	292	12	,	,	PUNCT
ap-1783	292	13	(	(	PUNCT
ap-1783	292	14	3.26	3.26	NUM
ap-1783	292	15	)	)	PUNCT
ap-1783	292	16	where	where	SCONJ
ap-1783	292	17	φ(u	φ(u	NOUN
ap-1783	292	18	)	)	PUNCT
ap-1783	292	19	is	be	AUX
ap-1783	292	20	landau	landau	NOUN
ap-1783	292	21	p.d.f	p.d.f	ADJ
ap-1783	292	22	.	.	PUNCT
ap-1783	293	1	(	(	PUNCT
ap-1783	293	2	2.20	2.20	NUM
ap-1783	293	3	)	)	PUNCT
ap-1783	293	4	.	.	PUNCT
ap-1783	294	1	proof	proof	NOUN
ap-1783	294	2	.	.	PUNCT
ap-1783	295	1	equation	equation	NOUN
ap-1783	295	2	(	(	PUNCT
ap-1783	295	3	2.12	2.12	NUM
ap-1783	295	4	)	)	PUNCT
ap-1783	295	5	can	can	AUX
ap-1783	295	6	also	also	ADV
ap-1783	295	7	be	be	AUX
ap-1783	295	8	rewritten	rewrite	VERB
ap-1783	295	9	in	in	ADP
ap-1783	295	10	the	the	DET
ap-1783	295	11	form	form	NOUN
ap-1783	295	12	f1(x	f1(x	NOUN
ap-1783	295	13	)	)	PUNCT
ap-1783	295	14	=	=	SYM
ap-1783	296	1	1−	1−	NUM
ap-1783	296	2	∫	∫	NOUN
ap-1783	296	3	x	x	SYM
ap-1783	296	4	0	0	NUM
ap-1783	296	5	f0(z	f0(z	NUM
ap-1783	296	6	)	)	PUNCT
ap-1783	296	7	z	z	NOUN
ap-1783	296	8	dz	dz	NOUN
ap-1783	296	9	=	=	SYM
ap-1783	296	10	1−	1−	NUM
ap-1783	296	11	∫	∫	NOUN
ap-1783	296	12	∞	∞	NUM
ap-1783	297	1	−	−	PROPN
ap-1783	297	2	ln	ln	ADJ
ap-1783	297	3	x	x	SYM
ap-1783	297	4	φ(u	φ(u	X
ap-1783	297	5	)	)	PUNCT
ap-1783	297	6	du	du	NOUN
ap-1783	297	7	,	,	PUNCT
ap-1783	297	8	(	(	PUNCT
ap-1783	297	9	3.27	3.27	NUM
ap-1783	297	10	)	)	PUNCT
ap-1783	297	11	where	where	SCONJ
ap-1783	297	12	the	the	DET
ap-1783	297	13	substitution	substitution	NOUN
ap-1783	297	14	z	z	NOUN
ap-1783	297	15	=	=	SYM
ap-1783	297	16	e−u	e−u	PROPN
ap-1783	297	17	is	be	AUX
ap-1783	297	18	used	use	VERB
ap-1783	297	19	.	.	PUNCT
ap-1783	298	1	the	the	DET
ap-1783	298	2	integral	integral	ADJ
ap-1783	298	3	on	on	ADP
ap-1783	298	4	the	the	DET
ap-1783	298	5	right	right	NOUN
ap-1783	298	6	of	of	ADP
ap-1783	298	7	eq	eq	PROPN
ap-1783	298	8	.	.	PUNCT
ap-1783	299	1	(	(	PUNCT
ap-1783	299	2	3.26	3.26	NUM
ap-1783	299	3	)	)	PUNCT
ap-1783	299	4	is	be	AUX
ap-1783	299	5	a	a	DET
ap-1783	299	6	direct	direct	ADJ
ap-1783	299	7	consequence	consequence	NOUN
ap-1783	299	8	of	of	ADP
ap-1783	299	9	the	the	DET
ap-1783	299	10	same	same	ADJ
ap-1783	299	11	substitution	substitution	NOUN
ap-1783	299	12	into	into	ADP
ap-1783	299	13	eq	eq	NOUN
ap-1783	299	14	.	.	PUNCT
ap-1783	300	1	(	(	PUNCT
ap-1783	300	2	2.12	2.12	NUM
ap-1783	300	3	)	)	PUNCT
ap-1783	300	4	.	.	PUNCT
ap-1783	301	1	corollary	corollary	ADJ
ap-1783	301	2	3.10	3.10	NUM
ap-1783	301	3	.	.	PUNCT
ap-1783	302	1	we	we	PRON
ap-1783	302	2	have	have	VERB
ap-1783	302	3	f(x	f(x	PROPN
ap-1783	302	4	)	)	PUNCT
ap-1783	303	1	=	=	PUNCT
ap-1783	304	1	−	−	PROPN
ap-1783	304	2	ln	ln	INTJ
ap-1783	305	1	xf1(x)−	xf1(x)−	PROPN
ap-1783	305	2	∫	∫	PROPN
ap-1783	306	1	−	−	PROPN
ap-1783	306	2	ln	ln	NOUN
ap-1783	306	3	x	x	X
ap-1783	306	4	−∞	−∞	ADP
ap-1783	306	5	uφ(u	uφ(u	NOUN
ap-1783	306	6	)	)	PUNCT
ap-1783	306	7	du	du	PROPN
ap-1783	306	8	,	,	PUNCT
ap-1783	306	9	x	x	X
ap-1783	306	10	>	>	X
ap-1783	306	11	0	0	NUM
ap-1783	306	12	.	.	PUNCT
ap-1783	307	1	(	(	PUNCT
ap-1783	307	2	3.28	3.28	NUM
ap-1783	307	3	)	)	PUNCT
ap-1783	307	4	proof	proof	NOUN
ap-1783	307	5	.	.	PUNCT
ap-1783	308	1	equation	equation	NOUN
ap-1783	308	2	(	(	PUNCT
ap-1783	308	3	3.28	3.28	NUM
ap-1783	308	4	)	)	PUNCT
ap-1783	308	5	is	be	AUX
ap-1783	308	6	a	a	DET
ap-1783	308	7	consequence	consequence	NOUN
ap-1783	308	8	of	of	ADP
ap-1783	308	9	eq	eq	PROPN
ap-1783	308	10	.	.	PUNCT
ap-1783	309	1	(	(	PUNCT
ap-1783	309	2	2.22	2.22	NUM
ap-1783	309	3	)	)	PUNCT
ap-1783	309	4	and	and	CCONJ
ap-1783	309	5	of	of	ADP
ap-1783	309	6	eq	eq	PROPN
ap-1783	309	7	.	.	PUNCT
ap-1783	310	1	(	(	PUNCT
ap-1783	310	2	3.26	3.26	NUM
ap-1783	310	3	)	)	PUNCT
ap-1783	310	4	.	.	PUNCT
ap-1783	311	1	theorem	theorem	NOUN
ap-1783	311	2	3.11	3.11	NUM
ap-1783	311	3	.	.	PUNCT
ap-1783	312	1	we	we	PRON
ap-1783	312	2	have	have	VERB
ap-1783	312	3	f1(x	f1(x	NUM
ap-1783	312	4	)	)	PUNCT
ap-1783	312	5	=	=	SYM
ap-1783	313	1	∫	∫	PUNCT
ap-1783	313	2	x	x	SYM
ap-1783	313	3	0	0	NUM
ap-1783	313	4	f(x−	f(x−	PROPN
ap-1783	313	5	u)f0(u	u)f0(u	PROPN
ap-1783	313	6	)	)	PUNCT
ap-1783	313	7	u	u	PROPN
ap-1783	313	8	du	du	X
ap-1783	313	9	,	,	PUNCT
ap-1783	313	10	x	x	X
ap-1783	313	11	>	>	X
ap-1783	313	12	0	0	NUM
ap-1783	313	13	.	.	PUNCT
ap-1783	314	1	(	(	PUNCT
ap-1783	314	2	3.29	3.29	NUM
ap-1783	314	3	)	)	PUNCT
ap-1783	314	4	proof	proof	NOUN
ap-1783	314	5	.	.	PUNCT
ap-1783	315	1	w0(s)/s	w0(s)/s	PROPN
ap-1783	315	2	is	be	AUX
ap-1783	315	3	a	a	DET
ap-1783	315	4	laplace	laplace	NOUN
ap-1783	315	5	transform	transform	NOUN
ap-1783	315	6	of	of	ADP
ap-1783	315	7	the	the	DET
ap-1783	315	8	p.d.f	p.d.f	NOUN
ap-1783	315	9	.	.	PUNCT
ap-1783	316	1	f(x	f(x	PROPN
ap-1783	316	2	)	)	PUNCT
ap-1783	316	3	.	.	PUNCT
ap-1783	317	1	from	from	ADP
ap-1783	317	2	equations	equation	NOUN
ap-1783	317	3	(	(	PUNCT
ap-1783	317	4	3.6	3.6	NUM
ap-1783	317	5	)	)	PUNCT
ap-1783	317	6	and	and	CCONJ
ap-1783	317	7	(	(	PUNCT
ap-1783	317	8	3.13	3.13	NUM
ap-1783	317	9	)	)	PUNCT
ap-1783	317	10	,	,	PUNCT
ap-1783	317	11	it	it	PRON
ap-1783	317	12	immediately	immediately	ADV
ap-1783	317	13	follows	follow	VERB
ap-1783	317	14	that	that	SCONJ
ap-1783	317	15	function	function	NOUN
ap-1783	317	16	f1(x	f1(x	NOUN
ap-1783	317	17	)	)	PUNCT
ap-1783	317	18	is	be	AUX
ap-1783	317	19	a	a	DET
ap-1783	317	20	laplace	laplace	NOUN
ap-1783	317	21	convolution	convolution	NOUN
ap-1783	317	22	of	of	ADP
ap-1783	317	23	the	the	DET
ap-1783	317	24	functions	function	NOUN
ap-1783	317	25	f(x	f(x	PROPN
ap-1783	317	26	)	)	PUNCT
ap-1783	317	27	and	and	CCONJ
ap-1783	317	28	f0(x)/x	f0(x)/x	PROPN
ap-1783	317	29	.	.	PUNCT
ap-1783	318	1	theorem	theorem	VERB
ap-1783	318	2	3.12	3.12	NUM
ap-1783	318	3	.	.	PUNCT
ap-1783	319	1	we	we	PRON
ap-1783	319	2	have	have	VERB
ap-1783	319	3	∫	∫	PROPN
ap-1783	319	4	x	x	SYM
ap-1783	319	5	0	0	PUNCT
ap-1783	320	1	(	(	PUNCT
ap-1783	320	2	1	1	NUM
ap-1783	320	3	+	+	CCONJ
ap-1783	320	4	f(x−	f(x−	PROPN
ap-1783	320	5	u	u	NOUN
ap-1783	320	6	)	)	PUNCT
ap-1783	320	7	)	)	PUNCT
ap-1783	321	1	f0(u	f0(u	X
ap-1783	321	2	)	)	PUNCT
ap-1783	321	3	u	u	NOUN
ap-1783	321	4	du	du	X
ap-1783	321	5	=	=	SYM
ap-1783	321	6	1	1	NUM
ap-1783	321	7	,	,	PUNCT
ap-1783	321	8	x	x	X
ap-1783	321	9	>	>	X
ap-1783	321	10	0	0	NUM
ap-1783	321	11	.	.	PUNCT
ap-1783	322	1	(	(	PUNCT
ap-1783	322	2	3.30	3.30	NUM
ap-1783	322	3	)	)	PUNCT
ap-1783	322	4	proof	proof	NOUN
ap-1783	322	5	.	.	PUNCT
ap-1783	323	1	according	accord	VERB
ap-1783	323	2	to	to	ADP
ap-1783	323	3	eq	eq	PROPN
ap-1783	323	4	.	.	PUNCT
ap-1783	324	1	(	(	PUNCT
ap-1783	324	2	3.25	3.25	NUM
ap-1783	324	3	)	)	PUNCT
ap-1783	324	4	and	and	CCONJ
ap-1783	324	5	eq	eq	NOUN
ap-1783	324	6	.	.	PUNCT
ap-1783	325	1	(	(	PUNCT
ap-1783	325	2	3.29	3.29	NUM
ap-1783	325	3	)	)	PUNCT
ap-1783	325	4	,	,	PUNCT
ap-1783	325	5	we	we	PRON
ap-1783	325	6	find	find	VERB
ap-1783	325	7	that∫	that∫	NOUN
ap-1783	325	8	x	x	X
ap-1783	325	9	0	0	PUNCT
ap-1783	326	1	(	(	PUNCT
ap-1783	326	2	1	1	NUM
ap-1783	326	3	+	+	CCONJ
ap-1783	326	4	f(x−	f(x−	PROPN
ap-1783	326	5	u	u	NOUN
ap-1783	326	6	)	)	PUNCT
ap-1783	326	7	)	)	PUNCT
ap-1783	327	1	f0(u	f0(u	X
ap-1783	327	2	)	)	PUNCT
ap-1783	327	3	u	u	NOUN
ap-1783	327	4	du	du	X
ap-1783	327	5	=	=	SYM
ap-1783	327	6	∫	∫	PROPN
ap-1783	327	7	x	x	SYM
ap-1783	327	8	0	0	NUM
ap-1783	327	9	f0(u	f0(u	NUM
ap-1783	327	10	)	)	PUNCT
ap-1783	327	11	u	u	NOUN
ap-1783	327	12	du+	du+	NOUN
ap-1783	327	13	∫	∫	PROPN
ap-1783	327	14	x	x	SYM
ap-1783	327	15	0	0	NUM
ap-1783	327	16	f(x−	f(x−	PROPN
ap-1783	327	17	u)f0(u	u)f0(u	PROPN
ap-1783	327	18	)	)	PUNCT
ap-1783	327	19	u	u	NOUN
ap-1783	327	20	du	du	NOUN
ap-1783	327	21	=	=	X
ap-1783	327	22	(	(	PUNCT
ap-1783	327	23	1−	1−	NUM
ap-1783	327	24	f1(x	f1(x	NUM
ap-1783	327	25	)	)	PUNCT
ap-1783	327	26	)	)	PUNCT
ap-1783	328	1	+	+	CCONJ
ap-1783	328	2	f1(x	f1(x	X
ap-1783	328	3	)	)	PUNCT
ap-1783	328	4	=	=	SYM
ap-1783	328	5	1	1	X
ap-1783	328	6	.	.	PUNCT
ap-1783	328	7	(	(	PUNCT
ap-1783	328	8	3.31	3.31	NUM
ap-1783	328	9	)	)	PUNCT
ap-1783	328	10	4	4	NUM
ap-1783	328	11	.	.	PUNCT
ap-1783	328	12	conclusion	conclusion	NOUN
ap-1783	328	13	defining	define	VERB
ap-1783	328	14	the	the	DET
ap-1783	328	15	moment	moment	NOUN
ap-1783	328	16	generating	generate	VERB
ap-1783	328	17	function	function	NOUN
ap-1783	328	18	of	of	ADP
ap-1783	328	19	the	the	DET
ap-1783	328	20	probability	probability	NOUN
ap-1783	328	21	distributions	distribution	NOUN
ap-1783	328	22	by	by	ADP
ap-1783	328	23	means	mean	NOUN
ap-1783	328	24	of	of	ADP
ap-1783	328	25	the	the	DET
ap-1783	328	26	laplace	laplace	NOUN
ap-1783	328	27	or	or	CCONJ
ap-1783	328	28	laplacestieltjes	laplacestieltjes	PROPN
ap-1783	328	29	transform	transform	NOUN
ap-1783	328	30	proposed	propose	VERB
ap-1783	328	31	in	in	ADP
ap-1783	328	32	[	[	X
ap-1783	328	33	1	1	X
ap-1783	328	34	]	]	PUNCT
ap-1783	328	35	makes	make	VERB
ap-1783	328	36	it	it	PRON
ap-1783	328	37	possible	possible	ADJ
ap-1783	328	38	to	to	PART
ap-1783	328	39	obtain	obtain	VERB
ap-1783	328	40	the	the	DET
ap-1783	328	41	interconnection	interconnection	NOUN
ap-1783	328	42	between	between	ADP
ap-1783	328	43	the	the	DET
ap-1783	328	44	cayley	cayley	ADJ
ap-1783	328	45	-	-	PUNCT
ap-1783	328	46	eisensteinpólya	eisensteinpólya	NOUN
ap-1783	328	47	probability	probability	NOUN
ap-1783	328	48	distribution	distribution	NOUN
ap-1783	328	49	,	,	PUNCT
ap-1783	328	50	which	which	PRON
ap-1783	328	51	is	be	AUX
ap-1783	328	52	native	native	ADJ
ap-1783	328	53	in	in	ADP
ap-1783	328	54	queueing	queue	VERB
ap-1783	328	55	theory	theory	NOUN
ap-1783	328	56	with	with	ADP
ap-1783	328	57	the	the	DET
ap-1783	328	58	landau	landau	NOUN
ap-1783	328	59	distribution	distribution	NOUN
ap-1783	328	60	originating	originating	NOUN
ap-1783	328	61	in	in	ADP
ap-1783	328	62	atomic	atomic	ADJ
ap-1783	328	63	physics	physic	NOUN
ap-1783	328	64	.	.	PUNCT
ap-1783	329	1	this	this	DET
ap-1783	329	2	interrelation	interrelation	NOUN
ap-1783	329	3	is	be	AUX
ap-1783	329	4	given	give	VERB
ap-1783	329	5	by	by	ADP
ap-1783	329	6	an	an	DET
ap-1783	329	7	integral	integral	ADJ
ap-1783	329	8	relation	relation	NOUN
ap-1783	329	9	/	/	SYM
ap-1783	329	10	equation	equation	NOUN
ap-1783	329	11	of	of	ADP
ap-1783	329	12	the	the	DET
ap-1783	329	13	first	first	ADJ
ap-1783	329	14	kind	kind	NOUN
ap-1783	329	15	eq	eq	NOUN
ap-1783	329	16	.	.	PUNCT
ap-1783	330	1	(	(	PUNCT
ap-1783	330	2	2.22	2.22	NUM
ap-1783	330	3	)	)	PUNCT
ap-1783	330	4	and	and	CCONJ
ap-1783	330	5	in	in	ADP
ap-1783	330	6	principle	principle	NOUN
ap-1783	330	7	by	by	ADP
ap-1783	330	8	a	a	DET
ap-1783	330	9	euler	euler	PROPN
ap-1783	330	10	differential	differential	PROPN
ap-1783	330	11	relation	relation	NOUN
ap-1783	330	12	/	/	SYM
ap-1783	330	13	equation	equation	NOUN
ap-1783	330	14	in	in	ADP
ap-1783	330	15	eq	eq	ADP
ap-1783	330	16	.	.	PUNCT
ap-1783	331	1	(	(	PUNCT
ap-1783	331	2	2.17	2.17	NUM
ap-1783	331	3	)	)	PUNCT
ap-1783	331	4	,	,	PUNCT
ap-1783	331	5	differential	differential	NOUN
ap-1783	331	6	relation	relation	NOUN
ap-1783	331	7	eq	eq	ADJ
ap-1783	331	8	.	.	PUNCT
ap-1783	332	1	(	(	PUNCT
ap-1783	332	2	2.23	2.23	NUM
ap-1783	332	3	)	)	PUNCT
ap-1783	332	4	and	and	CCONJ
ap-1783	332	5	by	by	ADP
ap-1783	332	6	the	the	DET
ap-1783	332	7	laplace	laplace	NOUN
ap-1783	332	8	convolution	convolution	NOUN
ap-1783	332	9	eq	eq	ADP
ap-1783	332	10	.	.	PUNCT
ap-1783	333	1	(	(	PUNCT
ap-1783	333	2	3.30	3.30	NUM
ap-1783	333	3	)	)	PUNCT
ap-1783	333	4	.	.	PUNCT
ap-1783	334	1	from	from	ADP
ap-1783	334	2	the	the	DET
ap-1783	334	3	formal	formal	ADJ
ap-1783	334	4	point	point	NOUN
ap-1783	334	5	of	of	ADP
ap-1783	334	6	view	view	NOUN
ap-1783	334	7	,	,	PUNCT
ap-1783	334	8	the	the	DET
ap-1783	334	9	absolute	absolute	ADJ
ap-1783	334	10	convergence	convergence	NOUN
ap-1783	334	11	of	of	ADP
ap-1783	334	12	the	the	DET
ap-1783	334	13	laplace	laplace	NOUN
ap-1783	334	14	transform	transform	VERB
ap-1783	334	15	integral	integral	ADJ
ap-1783	334	16	and	and	CCONJ
ap-1783	334	17	moreover	moreover	ADV
ap-1783	334	18	its	its	PRON
ap-1783	334	19	uniform	uniform	ADJ
ap-1783	334	20	convergence	convergence	NOUN
ap-1783	334	21	generally	generally	ADV
ap-1783	334	22	constitute	constitute	VERB
ap-1783	334	23	an	an	DET
ap-1783	334	24	advantage	advantage	NOUN
ap-1783	334	25	in	in	ADP
ap-1783	334	26	the	the	DET
ap-1783	334	27	calculations	calculation	NOUN
ap-1783	334	28	and	and	CCONJ
ap-1783	334	29	in	in	ADP
ap-1783	334	30	the	the	DET
ap-1783	334	31	process	process	NOUN
ap-1783	334	32	of	of	ADP
ap-1783	334	33	inference	inference	NOUN
ap-1783	334	34	of	of	ADP
ap-1783	334	35	the	the	DET
ap-1783	334	36	formulae	formulae	NOUN
ap-1783	334	37	.	.	PUNCT
ap-1783	335	1	as	as	SCONJ
ap-1783	335	2	regards	regard	VERB
ap-1783	335	3	the	the	DET
ap-1783	335	4	integral	integral	ADJ
ap-1783	335	5	transform	transform	NOUN
ap-1783	335	6	pairs	pair	NOUN
ap-1783	335	7	that	that	PRON
ap-1783	335	8	are	be	AUX
ap-1783	335	9	a	a	DET
ap-1783	335	10	byproduct	byproduct	NOUN
ap-1783	335	11	of	of	ADP
ap-1783	335	12	this	this	DET
ap-1783	335	13	study	study	NOUN
ap-1783	335	14	,	,	PUNCT
ap-1783	335	15	the	the	DET
ap-1783	335	16	author	author	NOUN
ap-1783	335	17	can	can	AUX
ap-1783	335	18	not	not	PART
ap-1783	335	19	guarantee	guarantee	VERB
ap-1783	335	20	their	their	PRON
ap-1783	335	21	novelty	novelty	NOUN
ap-1783	335	22	.	.	PUNCT
ap-1783	336	1	however	however	ADV
ap-1783	336	2	,	,	PUNCT
ap-1783	336	3	but	but	CCONJ
ap-1783	336	4	he	he	PRON
ap-1783	336	5	has	have	AUX
ap-1783	336	6	not	not	PART
ap-1783	336	7	found	find	VERB
ap-1783	336	8	them	they	PRON
ap-1783	336	9	elsewhere	elsewhere	ADV
ap-1783	336	10	.	.	PUNCT
ap-1783	337	1	acknowledgements	acknowledgement	NOUN
ap-1783	337	2	many	many	ADJ
ap-1783	337	3	thanks	thank	NOUN
ap-1783	337	4	to	to	ADP
ap-1783	337	5	both	both	DET
ap-1783	337	6	referees	referee	NOUN
ap-1783	337	7	for	for	ADP
ap-1783	337	8	their	their	PRON
ap-1783	337	9	valuable	valuable	ADJ
ap-1783	337	10	comments	comment	NOUN
ap-1783	337	11	and	and	CCONJ
ap-1783	337	12	suggestions	suggestion	NOUN
ap-1783	337	13	.	.	PUNCT
ap-1783	338	1	references	reference	NOUN
ap-1783	339	1	[	[	X
ap-1783	339	2	1]abate	1]abate	NUM
ap-1783	339	3	j.	j.	PROPN
ap-1783	339	4	,	,	PUNCT
ap-1783	339	5	whitt	whitt	PROPN
ap-1783	339	6	w.	w.	PROPN
ap-1783	339	7	:	:	PUNCT
ap-1783	339	8	an	an	DET
ap-1783	339	9	operational	operational	ADJ
ap-1783	339	10	calculus	calculus	NOUN
ap-1783	339	11	for	for	ADP
ap-1783	339	12	probability	probability	NOUN
ap-1783	339	13	distributions	distribution	NOUN
ap-1783	339	14	via	via	ADP
ap-1783	339	15	laplace	laplace	NOUN
ap-1783	339	16	transforms	transform	VERB
ap-1783	339	17	,	,	PUNCT
ap-1783	339	18	adv	adv	PROPN
ap-1783	339	19	.	.	PUNCT
ap-1783	339	20	appl	appl	PROPN
ap-1783	339	21	.	.	PUNCT
ap-1783	340	1	probab	probab	PROPN
ap-1783	340	2	.	.	PUNCT
ap-1783	341	1	28	28	NUM
ap-1783	341	2	,	,	PUNCT
ap-1783	341	3	(	(	PUNCT
ap-1783	341	4	1	1	NUM
ap-1783	341	5	)	)	PUNCT
ap-1783	341	6	,	,	PUNCT
ap-1783	341	7	1996	1996	NUM
ap-1783	341	8	,	,	PUNCT
ap-1783	342	1	p.	p.	PROPN
ap-1783	342	2	75–113	75–113	PROPN
ap-1783	342	3	.	.	PUNCT
ap-1783	343	1	[	[	X
ap-1783	343	2	2]landau	2]landau	NUM
ap-1783	343	3	l.d	l.d	PROPN
ap-1783	343	4	.	.	PUNCT
ap-1783	343	5	:	:	PUNCT
ap-1783	343	6	on	on	ADP
ap-1783	343	7	the	the	DET
ap-1783	343	8	energy	energy	NOUN
ap-1783	343	9	loss	loss	NOUN
ap-1783	343	10	of	of	ADP
ap-1783	343	11	fast	fast	ADJ
ap-1783	343	12	particles	particle	NOUN
ap-1783	343	13	by	by	ADP
ap-1783	343	14	ionisation	ionisation	NOUN
ap-1783	343	15	,	,	PUNCT
ap-1783	343	16	j.phys	j.phy	NOUN
ap-1783	343	17	.	.	PUNCT
ap-1783	344	1	u.s.s.r	u.s.s.r	PROPN
ap-1783	344	2	.	.	NOUN
ap-1783	344	3	8	8	NUM
ap-1783	344	4	,	,	PUNCT
ap-1783	344	5	1944	1944	NUM
ap-1783	344	6	,	,	PUNCT
ap-1783	344	7	also	also	ADV
ap-1783	344	8	in	in	ADP
ap-1783	344	9	editor	editor	NOUN
ap-1783	344	10	:	:	PUNCT
ap-1783	344	11	d.	d.	PROPN
ap-1783	344	12	ter	ter	PROPN
ap-1783	344	13	haar	haar	PROPN
ap-1783	344	14	.	.	PUNCT
ap-1783	345	1	:	:	PUNCT
ap-1783	345	2	collected	collect	VERB
ap-1783	345	3	papers	paper	NOUN
ap-1783	345	4	of	of	ADP
ap-1783	345	5	l.d.landau	l.d.landau	NOUN
ap-1783	345	6	,	,	PUNCT
ap-1783	345	7	oxford	oxford	PROPN
ap-1783	345	8	:	:	PUNCT
ap-1783	345	9	pergamon	pergamon	PROPN
ap-1783	345	10	press	press	PROPN
ap-1783	345	11	,	,	PUNCT
ap-1783	345	12	1965	1965	NUM
ap-1783	345	13	,	,	PUNCT
ap-1783	345	14	p.417–424	p.417–424	VERB
ap-1783	345	15	.	.	PUNCT
ap-1783	346	1	[	[	X
ap-1783	346	2	3]corless	3]corless	NUM
ap-1783	346	3	r.	r.	PROPN
ap-1783	346	4	m.	m.	PROPN
ap-1783	346	5	et	et	PROPN
ap-1783	346	6	al	al	PROPN
ap-1783	346	7	:	:	PUNCT
ap-1783	346	8	on	on	ADP
ap-1783	346	9	the	the	DET
ap-1783	346	10	lambert	lambert	PROPN
ap-1783	346	11	w	w	PROPN
ap-1783	346	12	function	function	PROPN
ap-1783	346	13	,	,	PUNCT
ap-1783	346	14	adv	adv	PROPN
ap-1783	346	15	.	.	PUNCT
ap-1783	346	16	comput	comput	PROPN
ap-1783	346	17	.	.	PUNCT
ap-1783	347	1	math	math	NOUN
ap-1783	347	2	.	.	PUNCT
ap-1783	348	1	5	5	NUM
ap-1783	348	2	,	,	PUNCT
ap-1783	348	3	1996	1996	NUM
ap-1783	348	4	,	,	PUNCT
ap-1783	348	5	p.329–359	p.329–359	VERB
ap-1783	348	6	.	.	PUNCT
ap-1783	349	1	[	[	X
ap-1783	349	2	4]kalugin	4]kalugin	NUM
ap-1783	349	3	g.a	g.a	PROPN
ap-1783	349	4	.	.	PROPN
ap-1783	349	5	et	et	PROPN
ap-1783	349	6	al	al	PROPN
ap-1783	349	7	:	:	PUNCT
ap-1783	349	8	bernstein	bernstein	PROPN
ap-1783	349	9	,	,	PUNCT
ap-1783	349	10	pick	pick	VERB
ap-1783	349	11	,	,	PUNCT
ap-1783	349	12	poisson	poisson	NOUN
ap-1783	349	13	and	and	CCONJ
ap-1783	349	14	related	relate	VERB
ap-1783	349	15	integral	integral	ADJ
ap-1783	349	16	expressions	expression	NOUN
ap-1783	349	17	for	for	ADP
ap-1783	349	18	lambert	lambert	PROPN
ap-1783	349	19	w	w	PROPN
ap-1783	349	20	,	,	PUNCT
ap-1783	349	21	to	to	PART
ap-1783	349	22	apear	apear	VERB
ap-1783	349	23	in	in	ADP
ap-1783	349	24	integral	integral	ADJ
ap-1783	349	25	transforms	transform	NOUN
ap-1783	349	26	spec	spec	NOUN
ap-1783	349	27	.	.	PUNCT
ap-1783	350	1	funct	funct	ADJ
ap-1783	350	2	.	.	PUNCT
ap-1783	351	1	[	[	X
ap-1783	351	2	5]oberhettinger	5]oberhettinger	NUM
ap-1783	351	3	f.	f.	NOUN
ap-1783	351	4	:	:	PUNCT
ap-1783	351	5	tables	table	NOUN
ap-1783	351	6	of	of	ADP
ap-1783	351	7	mellin	mellin	PROPN
ap-1783	351	8	transforms	transform	VERB
ap-1783	351	9	,	,	PUNCT
ap-1783	351	10	new	new	PROPN
ap-1783	351	11	york	york	PROPN
ap-1783	351	12	:	:	PUNCT
ap-1783	351	13	springer	springer	NOUN
ap-1783	351	14	-	-	PUNCT
ap-1783	351	15	verlag	verlag	PROPN
ap-1783	351	16	,	,	PUNCT
ap-1783	351	17	1974	1974	NUM
ap-1783	351	18	.	.	PUNCT
ap-1783	352	1	[	[	X
ap-1783	352	2	6]rooney	6]rooney	X
ap-1783	352	3	p.g	p.g	PROPN
ap-1783	352	4	.	.	PROPN
ap-1783	352	5	:	:	PUNCT
ap-1783	353	1	a	a	DET
ap-1783	353	2	survey	survey	NOUN
ap-1783	353	3	of	of	ADP
ap-1783	353	4	mellin	mellin	PROPN
ap-1783	353	5	multipliers	multiplier	NOUN
ap-1783	353	6	,	,	PUNCT
ap-1783	353	7	in	in	ADP
ap-1783	353	8	:	:	PUNCT
ap-1783	353	9	“	"	PUNCT
ap-1783	353	10	fractional	fractional	ADJ
ap-1783	353	11	calculus	calculus	NOUN
ap-1783	353	12	”	"	PUNCT
ap-1783	353	13	(	(	PUNCT
ap-1783	353	14	editors	editor	NOUN
ap-1783	353	15	:	:	PUNCT
ap-1783	353	16	a.	a.	PROPN
ap-1783	353	17	c.	c.	PROPN
ap-1783	353	18	mcbride	mcbride	PROPN
ap-1783	353	19	,	,	PUNCT
ap-1783	353	20	g.f.roach	g.f.roach	NOUN
ap-1783	353	21	)	)	PUNCT
ap-1783	353	22	.	.	PUNCT
ap-1783	354	1	london	london	PROPN
ap-1783	354	2	:	:	PUNCT
ap-1783	354	3	pitman	pitman	NOUN
ap-1783	354	4	publishing	publishing	NOUN
ap-1783	354	5	,	,	PUNCT
ap-1783	354	6	1985	1985	NUM
ap-1783	354	7	,	,	PUNCT
ap-1783	354	8	p.	p.	NOUN
ap-1783	354	9	176–187	176–187	NUM
ap-1783	354	10	.	.	PUNCT
ap-1783	355	1	[	[	X
ap-1783	355	2	7]kilbas	7]kilbas	NUM
ap-1783	355	3	a.a	a.a	PROPN
ap-1783	355	4	.	.	PROPN
ap-1783	355	5	et	et	PROPN
ap-1783	355	6	al	al	PROPN
ap-1783	355	7	:	:	PUNCT
ap-1783	355	8	theory	theory	NOUN
ap-1783	355	9	and	and	CCONJ
ap-1783	355	10	applications	application	NOUN
ap-1783	355	11	of	of	ADP
ap-1783	355	12	fractional	fractional	ADJ
ap-1783	355	13	differential	differential	ADJ
ap-1783	355	14	equations	equation	NOUN
ap-1783	355	15	,	,	PUNCT
ap-1783	355	16	amsterdam	amsterdam	PROPN
ap-1783	355	17	:	:	PUNCT
ap-1783	355	18	elsevier	elsevier	NOUN
ap-1783	355	19	,	,	PUNCT
ap-1783	355	20	2006	2006	NUM
ap-1783	355	21	.	.	PUNCT
ap-1783	356	1	[	[	X
ap-1783	356	2	8]oberhettinger	8]oberhettinger	NUM
ap-1783	356	3	f.	f.	NOUN
ap-1783	356	4	,	,	PUNCT
ap-1783	356	5	badii	badii	PROPN
ap-1783	356	6	l.	l.	PROPN
ap-1783	356	7	:	:	PUNCT
ap-1783	356	8	tables	table	NOUN
ap-1783	356	9	of	of	ADP
ap-1783	356	10	laplace	laplace	NOUN
ap-1783	356	11	transforms	transform	VERB
ap-1783	356	12	,	,	PUNCT
ap-1783	356	13	new	new	PROPN
ap-1783	356	14	york	york	PROPN
ap-1783	356	15	:	:	PUNCT
ap-1783	356	16	springer	springer	NOUN
ap-1783	356	17	-	-	PUNCT
ap-1783	356	18	verlag	verlag	PROPN
ap-1783	356	19	,	,	PUNCT
ap-1783	356	20	1973	1973	NUM
ap-1783	356	21	.	.	PUNCT
ap-1783	357	1	69	69	NUM
ap-1783	357	2	acta	acta	PROPN
ap-1783	357	3	polytechnica	polytechnica	PROPN
ap-1783	357	4	53(2):63–69	53(2):63–69	NUM
ap-1783	357	5	,	,	PUNCT
ap-1783	357	6	2013	2013	NUM
ap-1783	357	7	1	1	NUM
ap-1783	357	8	introduction	introduction	NOUN
ap-1783	357	9	2	2	NUM
ap-1783	357	10	inversion	inversion	NOUN
ap-1783	357	11	of	of	ADP
ap-1783	357	12	the	the	DET
ap-1783	357	13	moment	moment	NOUN
ap-1783	357	14	generating	generate	VERB
ap-1783	357	15	function	function	NOUN
ap-1783	357	16	2.1	2.1	NUM
ap-1783	357	17	direct	direct	ADJ
ap-1783	357	18	procedure	procedure	NOUN
ap-1783	357	19	2.2	2.2	NUM
ap-1783	357	20	mellin	mellin	NOUN
ap-1783	357	21	procedure	procedure	NOUN
ap-1783	357	22	2.3	2.3	NUM
ap-1783	357	23	stieltjes	stieltjes	NOUN
ap-1783	357	24	procedure	procedure	NOUN
ap-1783	357	25	3	3	NUM
ap-1783	357	26	integrals	integral	NOUN
ap-1783	357	27	and	and	CCONJ
ap-1783	357	28	integral	integral	ADJ
ap-1783	357	29	transforms	transform	VERB
ap-1783	357	30	4	4	NUM
ap-1783	357	31	conclusion	conclusion	NOUN
ap-1783	357	32	acknowledgements	acknowledgement	NOUN
ap-1783	357	33	references	reference	NOUN