id	sid	tid	token	lemma	pos
ma-359	1	1	2025	2025	NUM
ma-359	1	2	ada	ada	PROPN
ma-359	1	3	academica	academica	PROPN
ma-359	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-359	1	5	.	.	PUNCT
ma-359	2	1	j.	j.	PROPN
ma-359	2	2	math	math	PROPN
ma-359	2	3	.	.	PUNCT
ma-359	3	1	anal	anal	ADJ
ma-359	3	2	.	.	PUNCT
ma-359	4	1	5	5	NUM
ma-359	4	2	(	(	PUNCT
ma-359	4	3	2025	2025	NUM
ma-359	4	4	)	)	PUNCT
ma-359	4	5	19doi	19doi	NOUN
ma-359	4	6	:	:	PUNCT
ma-359	4	7	10.28924	10.28924	NUM
ma-359	4	8	/	/	SYM
ma-359	4	9	ada	ada	PROPN
ma-359	4	10	/	/	SYM
ma-359	4	11	ma.5.19	ma.5.19	NOUN
ma-359	4	12	on	on	ADP
ma-359	4	13	the	the	DET
ma-359	4	14	cumulative	cumulative	ADJ
ma-359	4	15	distribution	distribution	NOUN
ma-359	4	16	function	function	NOUN
ma-359	4	17	of	of	ADP
ma-359	4	18	the	the	DET
ma-359	4	19	difference	difference	NOUN
ma-359	4	20	of	of	ADP
ma-359	4	21	two	two	NUM
ma-359	4	22	dependent	dependent	ADJ
ma-359	4	23	chi	chi	NOUN
ma-359	4	24	square	square	ADJ
ma-359	4	25	random	random	ADJ
ma-359	4	26	variables	variable	NOUN
ma-359	4	27	elias	elias	PROPN
ma-359	4	28	g.	g.	PROPN
ma-359	4	29	saleeby1,∗	saleeby1,∗	PROPN
ma-359	4	30	,	,	PUNCT
ma-359	4	31	anwar	anwar	PROPN
ma-359	4	32	h.	h.	PROPN
ma-359	4	33	joarder2	joarder2	PROPN
ma-359	4	34	,	,	PUNCT
ma-359	4	35	nima	nima	PROPN
ma-359	4	36	rabiei3	rabiei3	PROPN
ma-359	5	1	1dept	1dept	NUM
ma-359	5	2	.	.	NOUN
ma-359	5	3	of	of	ADP
ma-359	5	4	mathematics	mathematic	NOUN
ma-359	5	5	,	,	PUNCT
ma-359	5	6	al	al	PROPN
ma-359	5	7	akhawayn	akhawayn	PROPN
ma-359	5	8	university	university	PROPN
ma-359	5	9	(	(	PUNCT
ma-359	5	10	aui	aui	PROPN
ma-359	5	11	)	)	PUNCT
ma-359	5	12	,	,	PUNCT
ma-359	5	13	ifrane	ifrane	NOUN
ma-359	5	14	53000	53000	NUM
ma-359	5	15	,	,	PUNCT
ma-359	5	16	morocco	morocco	PROPN
ma-359	5	17	esaleeby@yahoo.com	esaleeby@yahoo.com	PROPN
ma-359	5	18	,	,	PUNCT
ma-359	5	19	e.saleeby@aui.ma	e.saleeby@aui.ma	PROPN
ma-359	5	20	2dept	2dept	NUM
ma-359	5	21	.	.	PUNCT
ma-359	5	22	of	of	ADP
ma-359	5	23	mathematics	mathematic	NOUN
ma-359	5	24	,	,	PUNCT
ma-359	5	25	al	al	PROPN
ma-359	5	26	akhawayn	akhawayn	PROPN
ma-359	5	27	university	university	PROPN
ma-359	5	28	(	(	PUNCT
ma-359	5	29	aui	aui	PROPN
ma-359	5	30	)	)	PUNCT
ma-359	5	31	,	,	PUNCT
ma-359	5	32	ifrane	ifrane	NOUN
ma-359	5	33	53000	53000	NUM
ma-359	5	34	,	,	PUNCT
ma-359	5	35	morocco	morocco	PROPN
ma-359	5	36	ajstat@gmail.com	ajstat@gmail.com	PUNCT
ma-359	6	1	3dept	3dept	NUM
ma-359	6	2	.	.	PROPN
ma-359	6	3	of	of	ADP
ma-359	6	4	engineering	engineering	NOUN
ma-359	6	5	and	and	CCONJ
ma-359	6	6	natural	natural	ADJ
ma-359	6	7	sciences	science	NOUN
ma-359	6	8	,	,	PUNCT
ma-359	6	9	international	international	ADJ
ma-359	6	10	university	university	PROPN
ma-359	6	11	of	of	ADP
ma-359	6	12	sarajevo	sarajevo	PROPN
ma-359	6	13	(	(	PUNCT
ma-359	6	14	ius	ius	NOUN
ma-359	6	15	)	)	PUNCT
ma-359	6	16	,	,	PUNCT
ma-359	6	17	sarajevo	sarajevo	PROPN
ma-359	6	18	,	,	PUNCT
ma-359	6	19	bih	bih	ADJ
ma-359	6	20	nrabiei@ius.edu.ba	nrabiei@ius.edu.ba	NOUN
ma-359	6	21	∗correspondence	∗correspondence	NOUN
ma-359	6	22	:	:	PUNCT
ma-359	6	23	esaleeby@yahoo.com	esaleeby@yahoo.com	PROPN
ma-359	6	24	,	,	PUNCT
ma-359	6	25	e.saleeby@aui.ma	e.saleeby@aui.ma	PROPN
ma-359	6	26	abstract	abstract	ADJ
ma-359	6	27	.	.	PUNCT
ma-359	7	1	in	in	ADP
ma-359	7	2	this	this	DET
ma-359	7	3	article	article	NOUN
ma-359	7	4	,	,	PUNCT
ma-359	7	5	we	we	PRON
ma-359	7	6	reexamine	reexamine	VERB
ma-359	7	7	the	the	DET
ma-359	7	8	derivation	derivation	NOUN
ma-359	7	9	of	of	ADP
ma-359	7	10	the	the	DET
ma-359	7	11	cumulative	cumulative	ADJ
ma-359	7	12	distribution	distribution	NOUN
ma-359	7	13	function	function	NOUN
ma-359	7	14	of	of	ADP
ma-359	7	15	thedifference	thedifference	NOUN
ma-359	7	16	of	of	ADP
ma-359	7	17	two	two	NUM
ma-359	7	18	dependent	dependent	ADJ
ma-359	7	19	chi	chi	ADJ
ma-359	7	20	-	-	PUNCT
ma-359	7	21	square	square	ADJ
ma-359	7	22	random	random	ADJ
ma-359	7	23	variables	variable	NOUN
ma-359	7	24	with	with	ADP
ma-359	7	25	the	the	DET
ma-359	7	26	same	same	ADJ
ma-359	7	27	degrees	degree	NOUN
ma-359	7	28	of	of	ADP
ma-359	7	29	freedom	freedom	NOUN
ma-359	7	30	.	.	PUNCT
ma-359	8	1	we	we	PRON
ma-359	8	2	derivethe	derivethe	VERB
ma-359	8	3	cdf	cdf	PROPN
ma-359	8	4	for	for	ADP
ma-359	8	5	this	this	DET
ma-359	8	6	difference	difference	NOUN
ma-359	8	7	for	for	ADP
ma-359	8	8	even	even	ADJ
ma-359	8	9	degrees	degree	NOUN
ma-359	8	10	of	of	ADP
ma-359	8	11	freedom	freedom	NOUN
ma-359	8	12	and	and	CCONJ
ma-359	8	13	discuss	discuss	VERB
ma-359	8	14	a	a	DET
ma-359	8	15	discrepancy	discrepancy	NOUN
ma-359	8	16	that	that	PRON
ma-359	8	17	we	we	PRON
ma-359	8	18	have	have	VERB
ma-359	8	19	foundwith	foundwith	NOUN
ma-359	8	20	a	a	DET
ma-359	8	21	reported	report	VERB
ma-359	8	22	cdf	cdf	PROPN
ma-359	8	23	of	of	ADP
ma-359	8	24	this	this	DET
ma-359	8	25	difference	difference	NOUN
ma-359	8	26	for	for	ADP
ma-359	8	27	even	even	ADJ
ma-359	8	28	degrees	degree	NOUN
ma-359	8	29	of	of	ADP
ma-359	8	30	freedom	freedom	NOUN
ma-359	8	31	in	in	ADP
ma-359	8	32	[	[	X
ma-359	8	33	6	6	NUM
ma-359	8	34	]	]	PUNCT
ma-359	8	35	.	.	PUNCT
ma-359	9	1	for	for	ADP
ma-359	9	2	odd	odd	ADJ
ma-359	9	3	degrees	degree	NOUN
ma-359	9	4	of	of	ADP
ma-359	9	5	freedom	freedom	NOUN
ma-359	9	6	,	,	PUNCT
ma-359	9	7	an	an	DET
ma-359	9	8	expression	expression	NOUN
ma-359	9	9	for	for	ADP
ma-359	9	10	the	the	DET
ma-359	9	11	cdf	cdf	PROPN
ma-359	9	12	seems	seem	VERB
ma-359	9	13	to	to	PART
ma-359	9	14	be	be	AUX
ma-359	9	15	unknown	unknown	ADJ
ma-359	9	16	.	.	PUNCT
ma-359	10	1	in	in	ADP
ma-359	10	2	this	this	DET
ma-359	10	3	case	case	NOUN
ma-359	10	4	,	,	PUNCT
ma-359	10	5	we	we	PRON
ma-359	10	6	derive	derive	VERB
ma-359	10	7	a	a	DET
ma-359	10	8	representation	representation	NOUN
ma-359	10	9	of	of	ADP
ma-359	10	10	the	the	DET
ma-359	10	11	cdfin	cdfin	NOUN
ma-359	10	12	terms	term	NOUN
ma-359	10	13	of	of	ADP
ma-359	10	14	the	the	DET
ma-359	10	15	meijer	meijer	NOUN
ma-359	10	16	g	g	NOUN
ma-359	10	17	-	-	PUNCT
ma-359	10	18	function	function	NOUN
ma-359	10	19	.	.	PUNCT
ma-359	11	1	these	these	DET
ma-359	11	2	representations	representation	NOUN
ma-359	11	3	allowed	allow	VERB
ma-359	11	4	us	we	PRON
ma-359	11	5	to	to	PART
ma-359	11	6	compute	compute	VERB
ma-359	11	7	percentiles	percentile	NOUN
ma-359	11	8	for	for	ADP
ma-359	11	9	evenand	evenand	NOUN
ma-359	11	10	odd	odd	ADJ
ma-359	11	11	degrees	degree	NOUN
ma-359	11	12	of	of	ADP
ma-359	11	13	freedom	freedom	NOUN
ma-359	11	14	.	.	PUNCT
ma-359	12	1	1	1	X
ma-359	12	2	.	.	X
ma-359	12	3	introduction	introduction	NOUN
ma-359	12	4	in	in	ADP
ma-359	12	5	the	the	DET
ma-359	12	6	algebra	algebra	NOUN
ma-359	12	7	of	of	ADP
ma-359	12	8	random	random	ADJ
ma-359	12	9	variables	variable	NOUN
ma-359	12	10	,	,	PUNCT
ma-359	12	11	finding	find	VERB
ma-359	12	12	the	the	DET
ma-359	12	13	probability	probability	NOUN
ma-359	12	14	density	density	NOUN
ma-359	12	15	function	function	NOUN
ma-359	12	16	(	(	PUNCT
ma-359	12	17	pdf	pdf	NOUN
ma-359	12	18	)	)	PUNCT
ma-359	12	19	and	and	CCONJ
ma-359	12	20	the	the	DET
ma-359	12	21	cumulativedistribution	cumulativedistribution	NOUN
ma-359	12	22	function	function	NOUN
ma-359	12	23	(	(	PUNCT
ma-359	12	24	cdf	cdf	PROPN
ma-359	12	25	)	)	PUNCT
ma-359	12	26	of	of	ADP
ma-359	12	27	the	the	DET
ma-359	12	28	difference	difference	NOUN
ma-359	12	29	and	and	CCONJ
ma-359	12	30	the	the	DET
ma-359	12	31	sum	sum	NOUN
ma-359	12	32	of	of	ADP
ma-359	12	33	two	two	NUM
ma-359	12	34	random	random	ADJ
ma-359	12	35	variables	variable	NOUN
ma-359	12	36	(	(	PUNCT
ma-359	12	37	rvs	rvs	NOUN
ma-359	12	38	)	)	PUNCT
ma-359	12	39	are	be	AUX
ma-359	12	40	standardproblems	standardproblem	NOUN
ma-359	12	41	.	.	PUNCT
ma-359	13	1	it	it	PRON
ma-359	13	2	is	be	AUX
ma-359	13	3	well	well	ADV
ma-359	13	4	known	know	VERB
ma-359	13	5	that	that	SCONJ
ma-359	13	6	such	such	ADJ
ma-359	13	7	combinations	combination	NOUN
ma-359	13	8	of	of	ADP
ma-359	13	9	rvs	rvs	NOUN
ma-359	13	10	appear	appear	VERB
ma-359	13	11	within	within	ADP
ma-359	13	12	the	the	DET
ma-359	13	13	theory	theory	NOUN
ma-359	13	14	of	of	ADP
ma-359	13	15	statisticsand	statisticsand	NOUN
ma-359	13	16	in	in	ADP
ma-359	13	17	its	its	PRON
ma-359	13	18	applications	application	NOUN
ma-359	13	19	.	.	PUNCT
ma-359	14	1	it	it	PRON
ma-359	14	2	is	be	AUX
ma-359	14	3	also	also	ADV
ma-359	14	4	clear	clear	ADJ
ma-359	14	5	that	that	SCONJ
ma-359	14	6	when	when	SCONJ
ma-359	14	7	the	the	DET
ma-359	14	8	two	two	NUM
ma-359	14	9	rvs	rvs	NOUN
ma-359	14	10	are	be	AUX
ma-359	14	11	dependent	dependent	ADJ
ma-359	14	12	,	,	PUNCT
ma-359	14	13	the	the	DET
ma-359	14	14	analysis	analysis	NOUN
ma-359	14	15	of	of	ADP
ma-359	14	16	theproblem	theproblem	NOUN
ma-359	14	17	is	be	AUX
ma-359	14	18	more	more	ADV
ma-359	14	19	technically	technically	ADV
ma-359	14	20	complicated	complicated	ADJ
ma-359	14	21	.	.	PUNCT
ma-359	15	1	in	in	ADP
ma-359	15	2	particular	particular	ADJ
ma-359	15	3	,	,	PUNCT
ma-359	15	4	in	in	ADP
ma-359	15	5	this	this	DET
ma-359	15	6	note	note	NOUN
ma-359	15	7	we	we	PRON
ma-359	15	8	focus	focus	VERB
ma-359	15	9	mainly	mainly	ADV
ma-359	15	10	on	on	ADP
ma-359	15	11	deriving	derive	VERB
ma-359	15	12	thecdf	thecdf	NOUN
ma-359	15	13	for	for	ADP
ma-359	15	14	the	the	DET
ma-359	15	15	difference	difference	NOUN
ma-359	15	16	of	of	ADP
ma-359	15	17	two	two	NUM
ma-359	15	18	dependent	dependent	ADJ
ma-359	15	19	central	central	ADJ
ma-359	15	20	chi	chi	ADJ
ma-359	15	21	-	-	PUNCT
ma-359	15	22	square	square	ADJ
ma-359	15	23	random	random	ADJ
ma-359	15	24	variables	variable	NOUN
ma-359	15	25	with	with	ADP
ma-359	15	26	the	the	DET
ma-359	15	27	same	same	ADJ
ma-359	15	28	numberof	numberof	NOUN
ma-359	15	29	degrees	degree	NOUN
ma-359	15	30	of	of	ADP
ma-359	15	31	freedom	freedom	NOUN
ma-359	15	32	.	.	PUNCT
ma-359	16	1	results	result	NOUN
ma-359	16	2	on	on	ADP
ma-359	16	3	this	this	DET
ma-359	16	4	problem	problem	NOUN
ma-359	16	5	seem	seem	VERB
ma-359	16	6	to	to	PART
ma-359	16	7	have	have	AUX
ma-359	16	8	been	be	AUX
ma-359	16	9	around	around	ADV
ma-359	16	10	for	for	ADP
ma-359	16	11	a	a	DET
ma-359	16	12	while	while	NOUN
ma-359	16	13	and	and	CCONJ
ma-359	16	14	arereported	arereporte	VERB
ma-359	16	15	in	in	ADP
ma-359	16	16	some	some	DET
ma-359	16	17	detail	detail	NOUN
ma-359	16	18	in	in	ADP
ma-359	16	19	[	[	X
ma-359	16	20	6	6	NUM
ma-359	16	21	]	]	PUNCT
ma-359	16	22	.	.	PUNCT
ma-359	17	1	not	not	PART
ma-359	17	2	aware	aware	ADJ
ma-359	17	3	initially	initially	ADV
ma-359	17	4	of	of	ADP
ma-359	17	5	the	the	DET
ma-359	17	6	results	result	NOUN
ma-359	17	7	in	in	ADP
ma-359	17	8	[	[	X
ma-359	17	9	6	6	NUM
ma-359	17	10	]	]	PUNCT
ma-359	17	11	,	,	PUNCT
ma-359	17	12	we	we	PRON
ma-359	17	13	have	have	AUX
ma-359	17	14	carried	carry	VERB
ma-359	17	15	out	out	ADP
ma-359	17	16	the	the	DET
ma-359	17	17	basicanalysis	basicanalysis	NOUN
ma-359	17	18	and	and	CCONJ
ma-359	17	19	derived	derive	VERB
ma-359	17	20	the	the	DET
ma-359	17	21	cdf	cdf	PROPN
ma-359	17	22	.	.	PUNCT
ma-359	18	1	the	the	DET
ma-359	18	2	cdf	cdf	PROPN
ma-359	18	3	expressions	expression	NOUN
ma-359	18	4	which	which	PRON
ma-359	18	5	we	we	PRON
ma-359	18	6	have	have	AUX
ma-359	18	7	obtained	obtain	VERB
ma-359	18	8	appear	appear	VERB
ma-359	18	9	in	in	ADP
ma-359	18	10	different	different	ADJ
ma-359	18	11	formsthan	formsthan	NOUN
ma-359	18	12	those	those	PRON
ma-359	18	13	reported	report	VERB
ma-359	18	14	in	in	ADP
ma-359	18	15	[	[	X
ma-359	18	16	6	6	NUM
ma-359	18	17	]	]	PUNCT
ma-359	18	18	.	.	PUNCT
ma-359	19	1	in	in	ADP
ma-359	19	2	an	an	DET
ma-359	19	3	attempt	attempt	NOUN
ma-359	19	4	to	to	PART
ma-359	19	5	see	see	VERB
ma-359	19	6	how	how	SCONJ
ma-359	19	7	these	these	DET
ma-359	19	8	different	different	ADJ
ma-359	19	9	representations	representation	NOUN
ma-359	19	10	correspond	correspond	VERB
ma-359	19	11	,	,	PUNCT
ma-359	19	12	we	we	PRON
ma-359	19	13	discovered	discover	VERB
ma-359	19	14	a	a	DET
ma-359	19	15	discrepancy	discrepancy	NOUN
ma-359	19	16	between	between	ADP
ma-359	19	17	the	the	DET
ma-359	19	18	two	two	NUM
ma-359	19	19	forms	form	NOUN
ma-359	19	20	of	of	ADP
ma-359	19	21	the	the	DET
ma-359	19	22	cdfs	cdfs	PROPN
ma-359	19	23	.	.	PUNCT
ma-359	20	1	in	in	ADP
ma-359	20	2	the	the	DET
ma-359	20	3	analysis	analysis	NOUN
ma-359	20	4	below	below	ADP
ma-359	20	5	we	we	PRON
ma-359	20	6	give	give	AUX
ma-359	20	7	received	receive	VERB
ma-359	20	8	:	:	PUNCT
ma-359	20	9	2	2	NUM
ma-359	20	10	apr	apr	NOUN
ma-359	20	11	2025	2025	NUM
ma-359	20	12	.	.	PUNCT
ma-359	21	1	key	key	ADJ
ma-359	21	2	words	word	NOUN
ma-359	21	3	and	and	CCONJ
ma-359	21	4	phrases	phrase	NOUN
ma-359	21	5	.	.	PUNCT
ma-359	22	1	cumulative	cumulative	ADJ
ma-359	22	2	distribution	distribution	NOUN
ma-359	22	3	;	;	PUNCT
ma-359	22	4	chi	chi	PROPN
ma-359	22	5	square	square	PROPN
ma-359	22	6	;	;	PUNCT
ma-359	22	7	difference	difference	NOUN
ma-359	22	8	of	of	ADP
ma-359	22	9	random	random	ADJ
ma-359	22	10	variables.1	variables.1	NOUN
ma-359	22	11	https://adac.ee	https://adac.ee	PROPN
ma-359	22	12	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	22	13	eur	eur	PROPN
ma-359	22	14	.	.	PUNCT
ma-359	23	1	j.	j.	PROPN
ma-359	23	2	math	math	PROPN
ma-359	23	3	.	.	PUNCT
ma-359	24	1	anal	anal	PROPN
ma-359	24	2	.	.	PUNCT
ma-359	25	1	10.28924	10.28924	NUM
ma-359	25	2	/	/	SYM
ma-359	25	3	ada	ada	PROPN
ma-359	25	4	/	/	SYM
ma-359	25	5	ma.5.19	ma.5.19	NOUN
ma-359	25	6	2a	2a	NUM
ma-359	25	7	modification	modification	NOUN
ma-359	25	8	to	to	ADP
ma-359	25	9	the	the	DET
ma-359	25	10	cdf	cdf	NOUN
ma-359	25	11	expression	expression	NOUN
ma-359	25	12	for	for	ADP
ma-359	25	13	even	even	ADJ
ma-359	25	14	degrees	degree	NOUN
ma-359	25	15	of	of	ADP
ma-359	25	16	freedom	freedom	NOUN
ma-359	25	17	reported	report	VERB
ma-359	25	18	in	in	ADP
ma-359	25	19	[	[	X
ma-359	25	20	6	6	NUM
ma-359	25	21	]	]	PUNCT
ma-359	25	22	.	.	PUNCT
ma-359	26	1	the	the	DET
ma-359	26	2	cdf	cdf	PROPN
ma-359	26	3	for	for	ADP
ma-359	26	4	thedifference	thedifference	NOUN
ma-359	26	5	of	of	ADP
ma-359	26	6	dependent	dependent	ADJ
ma-359	26	7	central	central	ADJ
ma-359	26	8	chi	chi	PROPN
ma-359	26	9	square	square	ADJ
ma-359	26	10	rvs	rvs	NOUN
ma-359	26	11	with	with	ADP
ma-359	26	12	odd	odd	ADJ
ma-359	26	13	degrees	degree	NOUN
ma-359	26	14	of	of	ADP
ma-359	26	15	freedom	freedom	NOUN
ma-359	26	16	seems	seem	VERB
ma-359	26	17	to	to	PART
ma-359	26	18	be	be	AUX
ma-359	26	19	unknown	unknown	ADJ
ma-359	26	20	,	,	PUNCT
ma-359	26	21	and	and	CCONJ
ma-359	26	22	it	it	PRON
ma-359	26	23	is	be	AUX
ma-359	26	24	not	not	PART
ma-359	26	25	reprted	reprte	VERB
ma-359	26	26	in	in	ADP
ma-359	26	27	[	[	X
ma-359	26	28	6	6	NUM
ma-359	26	29	]	]	PUNCT
ma-359	26	30	.	.	PUNCT
ma-359	27	1	a	a	DET
ma-359	27	2	representation	representation	NOUN
ma-359	27	3	of	of	ADP
ma-359	27	4	the	the	DET
ma-359	27	5	cdf	cdf	PROPN
ma-359	27	6	in	in	ADP
ma-359	27	7	terms	term	NOUN
ma-359	27	8	of	of	ADP
ma-359	27	9	a	a	DET
ma-359	27	10	meijer	meijer	NOUN
ma-359	27	11	g	g	NOUN
ma-359	27	12	-	-	PUNCT
ma-359	27	13	functions	function	NOUN
ma-359	27	14	seems	seem	VERB
ma-359	27	15	to	to	PART
ma-359	27	16	fillin	fillin	VERB
ma-359	27	17	this	this	DET
ma-359	27	18	gap	gap	NOUN
ma-359	27	19	.	.	PUNCT
ma-359	28	1	the	the	DET
ma-359	28	2	article	article	NOUN
ma-359	28	3	is	be	AUX
ma-359	28	4	organized	organize	VERB
ma-359	28	5	as	as	SCONJ
ma-359	28	6	follows	follow	VERB
ma-359	28	7	.	.	PUNCT
ma-359	29	1	we	we	PRON
ma-359	29	2	first	first	ADV
ma-359	29	3	discuss	discuss	VERB
ma-359	29	4	a	a	DET
ma-359	29	5	bivariate	bivariate	ADJ
ma-359	29	6	chi	chi	PROPN
ma-359	29	7	square	square	PROPN
ma-359	29	8	distributionof	distributionof	NOUN
ma-359	29	9	the	the	DET
ma-359	29	10	kibble	kibble	ADJ
ma-359	29	11	-	-	PUNCT
ma-359	29	12	type	type	NOUN
ma-359	29	13	on	on	ADP
ma-359	29	14	which	which	PRON
ma-359	29	15	the	the	DET
ma-359	29	16	rest	rest	NOUN
ma-359	29	17	of	of	ADP
ma-359	29	18	the	the	DET
ma-359	29	19	analysis	analysis	NOUN
ma-359	29	20	is	be	AUX
ma-359	29	21	based	base	VERB
ma-359	29	22	.	.	PUNCT
ma-359	30	1	then	then	ADV
ma-359	30	2	we	we	PRON
ma-359	30	3	present	present	VERB
ma-359	30	4	and	and	CCONJ
ma-359	30	5	discuss	discuss	VERB
ma-359	30	6	thepdf	thepdf	NOUN
ma-359	30	7	of	of	ADP
ma-359	30	8	the	the	DET
ma-359	30	9	difference	difference	NOUN
ma-359	30	10	of	of	ADP
ma-359	30	11	two	two	NUM
ma-359	30	12	dependent	dependent	ADJ
ma-359	30	13	chi	chi	NOUN
ma-359	30	14	square	square	PROPN
ma-359	30	15	rvs	rvs	NOUN
ma-359	30	16	,	,	PUNCT
ma-359	30	17	followed	follow	VERB
ma-359	30	18	by	by	ADP
ma-359	30	19	a	a	DET
ma-359	30	20	derivation	derivation	NOUN
ma-359	30	21	of	of	ADP
ma-359	30	22	the	the	DET
ma-359	30	23	cdf	cdf	PROPN
ma-359	30	24	of	of	ADP
ma-359	30	25	thisdifference	thisdifference	NOUN
ma-359	30	26	.	.	PUNCT
ma-359	31	1	we	we	PRON
ma-359	31	2	end	end	VERB
ma-359	31	3	the	the	DET
ma-359	31	4	article	article	NOUN
ma-359	31	5	by	by	ADP
ma-359	31	6	computing	compute	VERB
ma-359	31	7	a	a	DET
ma-359	31	8	sampling	sampling	NOUN
ma-359	31	9	of	of	ADP
ma-359	31	10	percentiles	percentile	NOUN
ma-359	31	11	from	from	ADP
ma-359	31	12	the	the	DET
ma-359	31	13	cdf	cdf	PROPN
ma-359	31	14	expressions	expression	NOUN
ma-359	31	15	forboth	forboth	NOUN
ma-359	31	16	even	even	ADV
ma-359	31	17	and	and	CCONJ
ma-359	31	18	odd	odd	ADJ
ma-359	31	19	degrees	degree	NOUN
ma-359	31	20	of	of	ADP
ma-359	31	21	freedom	freedom	NOUN
ma-359	31	22	.	.	PUNCT
ma-359	32	1	2	2	X
ma-359	32	2	.	.	X
ma-359	32	3	density	density	NOUN
ma-359	32	4	functions	function	NOUN
ma-359	32	5	in	in	ADP
ma-359	32	6	this	this	DET
ma-359	32	7	section	section	NOUN
ma-359	32	8	,	,	PUNCT
ma-359	32	9	we	we	PRON
ma-359	32	10	examine	examine	VERB
ma-359	32	11	a	a	DET
ma-359	32	12	joint	joint	ADJ
ma-359	32	13	pdf	pdf	NOUN
ma-359	32	14	for	for	ADP
ma-359	32	15	correlated	correlate	VERB
ma-359	32	16	gamma	gamma	PROPN
ma-359	32	17	rvs	rvs	NOUN
ma-359	32	18	derived	derive	VERB
ma-359	32	19	by	by	ADP
ma-359	32	20	w.f	w.f	PROPN
ma-359	32	21	.	.	PROPN
ma-359	32	22	kibble	kibble	PROPN
ma-359	32	23	in	in	ADP
ma-359	32	24	[	[	X
ma-359	32	25	2	2	NUM
ma-359	32	26	]	]	PUNCT
ma-359	32	27	,	,	PUNCT
ma-359	32	28	obtainfrom	obtainfrom	VERB
ma-359	32	29	it	it	PRON
ma-359	32	30	the	the	DET
ma-359	32	31	joint	joint	ADJ
ma-359	32	32	pdf	pdf	NOUN
ma-359	32	33	of	of	ADP
ma-359	32	34	two	two	NUM
ma-359	32	35	dependent	dependent	ADJ
ma-359	32	36	central	central	ADJ
ma-359	32	37	chi	chi	PROPN
ma-359	32	38	square	square	ADJ
ma-359	32	39	rvs	rvs	NOUN
ma-359	32	40	,	,	PUNCT
ma-359	32	41	forms	form	VERB
ma-359	32	42	an	an	DET
ma-359	32	43	initial	initial	ADJ
ma-359	32	44	reference	reference	NOUN
ma-359	32	45	point	point	NOUN
ma-359	32	46	forfurther	forfurther	ADJ
ma-359	32	47	analysis	analysis	NOUN
ma-359	32	48	.	.	PUNCT
ma-359	33	1	this	this	DET
ma-359	33	2	joint	joint	ADJ
ma-359	33	3	pdf	pdf	NOUN
ma-359	33	4	turns	turn	VERB
ma-359	33	5	out	out	ADP
ma-359	33	6	to	to	PART
ma-359	33	7	be	be	AUX
ma-359	33	8	identical	identical	ADJ
ma-359	33	9	to	to	ADP
ma-359	33	10	the	the	DET
ma-359	33	11	joint	joint	ADJ
ma-359	33	12	pdf	pdf	NOUN
ma-359	33	13	reported	report	VERB
ma-359	33	14	in	in	ADP
ma-359	33	15	[	[	X
ma-359	33	16	6	6	NUM
ma-359	33	17	]	]	PUNCT
ma-359	33	18	.	.	PUNCT
ma-359	34	1	we	we	PRON
ma-359	34	2	thenobtain	thenobtain	VERB
ma-359	34	3	the	the	DET
ma-359	34	4	pdf	pdf	NOUN
ma-359	34	5	for	for	ADP
ma-359	34	6	the	the	DET
ma-359	34	7	difference	difference	NOUN
ma-359	34	8	of	of	ADP
ma-359	34	9	two	two	NUM
ma-359	34	10	dependent	dependent	ADJ
ma-359	34	11	central	central	ADJ
ma-359	34	12	chi	chi	NOUN
ma-359	34	13	square	square	ADJ
ma-359	34	14	random	random	ADJ
ma-359	34	15	variables	variable	NOUN
ma-359	34	16	and	and	CCONJ
ma-359	34	17	comparewith	comparewith	VERB
ma-359	34	18	the	the	DET
ma-359	34	19	piecewise	piecewise	NOUN
ma-359	34	20	given	give	VERB
ma-359	34	21	expressions	expression	NOUN
ma-359	34	22	of	of	ADP
ma-359	34	23	the	the	DET
ma-359	34	24	pdf	pdf	NOUN
ma-359	34	25	reported	report	VERB
ma-359	34	26	in	in	ADP
ma-359	34	27	[	[	X
ma-359	34	28	6].given	6].given	NUM
ma-359	34	29	a	a	DET
ma-359	34	30	vector	vector	NOUN
ma-359	34	31	(	(	PUNCT
ma-359	34	32	x1	x1	PROPN
ma-359	34	33	,	,	PUNCT
ma-359	34	34	·	·	PUNCT
ma-359	34	35	·	·	PUNCT
ma-359	34	36	·	·	PUNCT
ma-359	34	37	,	,	PUNCT
ma-359	34	38	xn	xn	PROPN
ma-359	34	39	)	)	PUNCT
ma-359	34	40	of	of	ADP
ma-359	34	41	gaussian	gaussian	PROPN
ma-359	34	42	rv	rv	PROPN
ma-359	34	43	’s	’s	NOUN
ma-359	34	44	with	with	ADP
ma-359	34	45	zero	zero	NUM
ma-359	34	46	mean	mean	NOUN
ma-359	34	47	,	,	PUNCT
ma-359	34	48	then	then	ADV
ma-359	34	49	for	for	ADP
ma-359	34	50	n	n	PROPN
ma-359	34	51	>	>	X
ma-359	34	52	1	1	NUM
ma-359	34	53	,	,	PUNCT
ma-359	34	54	y	y	PROPN
ma-359	34	55	=	=	PUNCT
ma-359	34	56	∑	∑	PUNCT
ma-359	34	57	limn	limn	PROPN
ma-359	34	58	i=1x	i=1x	VERB
ma-359	34	59	2	2	NUM
ma-359	34	60	iis	iis	NOUN
ma-359	34	61	a	a	DET
ma-359	34	62	central	central	ADJ
ma-359	34	63	chi	chi	PROPN
ma-359	34	64	square	square	PROPN
ma-359	34	65	rv	rv	PROPN
ma-359	34	66	with	with	ADP
ma-359	34	67	n	n	ADP
ma-359	34	68	degrees	degree	NOUN
ma-359	34	69	of	of	ADP
ma-359	34	70	freedom	freedom	NOUN
ma-359	34	71	.	.	PUNCT
ma-359	35	1	for	for	ADP
ma-359	35	2	simplicity	simplicity	NOUN
ma-359	35	3	,	,	PUNCT
ma-359	35	4	we	we	PRON
ma-359	35	5	assume	assume	VERB
ma-359	35	6	that	that	SCONJ
ma-359	35	7	the	the	DET
ma-359	35	8	rvs	rvs	NOUN
ma-359	35	9	xi	xi	ADP
ma-359	35	10	arestandard	arestandard	PROPN
ma-359	35	11	normal	normal	ADJ
ma-359	35	12	.	.	PUNCT
ma-359	36	1	take	take	VERB
ma-359	36	2	two	two	NUM
ma-359	36	3	such	such	ADJ
ma-359	36	4	vectors	vector	NOUN
ma-359	36	5	y1	y1	ADJ
ma-359	36	6	and	and	CCONJ
ma-359	36	7	y2	y2	NOUN
ma-359	36	8	.	.	PUNCT
ma-359	37	1	,	,	PUNCT
ma-359	37	2	their	their	PRON
ma-359	37	3	joint	joint	ADJ
ma-359	37	4	probability	probability	NOUN
ma-359	37	5	density	density	NOUN
ma-359	37	6	function	function	NOUN
ma-359	37	7	(	(	PUNCT
ma-359	37	8	pdf	pdf	NOUN
ma-359	37	9	)	)	PUNCT
ma-359	37	10	isgiven	isgiven	VERB
ma-359	37	11	by	by	ADP
ma-359	37	12	(	(	PUNCT
ma-359	37	13	e.g.	e.g.	ADV
ma-359	37	14	,	,	PUNCT
ma-359	37	15	see	see	VERB
ma-359	37	16	[	[	X
ma-359	37	17	6	6	NUM
ma-359	37	18	]	]	PUNCT
ma-359	37	19	,	,	PUNCT
ma-359	37	20	p.	p.	NOUN
ma-359	37	21	21	21	NUM
ma-359	37	22	)	)	PUNCT
ma-359	38	1	p	p	X
ma-359	38	2	y1,y2	y1,y2	PROPN
ma-359	38	3	(	(	PUNCT
ma-359	38	4	y1	y1	PROPN
ma-359	38	5	,	,	PUNCT
ma-359	38	6	y2	y2	NOUN
ma-359	38	7	)	)	PUNCT
ma-359	38	8	=	=	PRON
ma-359	38	9	(	(	PUNCT
ma-359	38	10	y1y2	y1y2	NOUN
ma-359	38	11	)	)	PUNCT
ma-359	38	12	1	1	NUM
ma-359	38	13	2	2	NUM
ma-359	38	14	(	(	PUNCT
ma-359	38	15	n2−1	n2−1	NOUN
ma-359	38	16	)	)	PUNCT
ma-359	38	17	4γ	4γ	NOUN
ma-359	38	18	(	(	PUNCT
ma-359	38	19	n	n	NOUN
ma-359	38	20	2	2	NUM
ma-359	38	21	)	)	PUNCT
ma-359	38	22	(	(	PUNCT
ma-359	38	23	1−	1−	NUM
ma-359	38	24	ρ2	ρ2	NOUN
ma-359	38	25	)	)	PUNCT
ma-359	38	26	(	(	PUNCT
ma-359	38	27	2	2	NUM
ma-359	38	28	|ρ|	|ρ|	NOUN
ma-359	38	29	)	)	PUNCT
ma-359	38	30	n	n	PRON
ma-359	38	31	2	2	NUM
ma-359	38	32	−1	−1	NOUN
ma-359	38	33	exp	exp	NOUN
ma-359	38	34	(	(	PUNCT
ma-359	38	35	−	−	PROPN
ma-359	38	36	y1	y1	NOUN
ma-359	39	1	+	+	CCONJ
ma-359	39	2	y2	y2	PROPN
ma-359	39	3	2	2	NUM
ma-359	39	4	√	√	NUM
ma-359	39	5	1−	1−	NUM
ma-359	39	6	ρ2	ρ2	NOUN
ma-359	39	7	)	)	PUNCT
ma-359	40	1	i	i	PRON
ma-359	40	2	n	n	ADV
ma-359	40	3	2	2	NUM
ma-359	40	4	−1	−1	NOUN
ma-359	40	5	(	(	PUNCT
ma-359	40	6	|ρ|	|ρ|	ADP
ma-359	40	7	√y1y2	√y1y2	PROPN
ma-359	40	8	1−	1−	NUM
ma-359	40	9	ρ2	ρ2	NOUN
ma-359	40	10	)	)	PUNCT
ma-359	40	11	,	,	PUNCT
ma-359	40	12	(	(	PUNCT
ma-359	40	13	1	1	X
ma-359	40	14	)	)	PUNCT
ma-359	40	15	where	where	SCONJ
ma-359	40	16	y1	y1	NOUN
ma-359	40	17	,	,	PUNCT
ma-359	40	18	y2	y2	PROPN
ma-359	40	19	≥	≥	NOUN
ma-359	40	20	0	0	NUM
ma-359	40	21	,	,	PUNCT
ma-359	40	22	−1	−1	NOUN
ma-359	40	23	<	<	X
ma-359	40	24	ρ	ρ	X
ma-359	40	25	<	<	X
ma-359	40	26	1	1	NUM
ma-359	40	27	,	,	PUNCT
ma-359	40	28	ρ	ρ	PROPN
ma-359	40	29	6=	6=	ADP
ma-359	40	30	0	0	NUM
ma-359	40	31	(	(	PUNCT
ma-359	40	32	if	if	SCONJ
ma-359	40	33	n	n	PROPN
ma-359	40	34	>	>	X
ma-359	40	35	2	2	NUM
ma-359	40	36	)	)	PUNCT
ma-359	40	37	,	,	PUNCT
ma-359	40	38	and	and	CCONJ
ma-359	40	39	iν	iν	NOUN
ma-359	40	40	is	be	AUX
ma-359	40	41	the	the	DET
ma-359	40	42	modified	modify	VERB
ma-359	40	43	bessel	bessel	NOUN
ma-359	40	44	function	function	NOUN
ma-359	40	45	of	of	ADP
ma-359	40	46	the	the	DET
ma-359	40	47	firstkind	firstkind	NOUN
ma-359	40	48	of	of	ADP
ma-359	40	49	order	order	NOUN
ma-359	40	50	ν	ν	NOUN
ma-359	40	51	.	.	PROPN
ma-359	41	1	as	as	SCONJ
ma-359	41	2	the	the	DET
ma-359	41	3	lim	lim	PROPN
ma-359	41	4	ρ→0	ρ→0	PUNCT
ma-359	41	5	i	i	PROPN
ma-359	41	6	n	n	PROPN
ma-359	41	7	2	2	NUM
ma-359	41	8	−1	−1	NOUN
ma-359	41	9	(	(	PUNCT
ma-359	41	10	|ρ|√y1y2	|ρ|√y1y2	PROPN
ma-359	41	11	1−ρ2	1−ρ2	NUM
ma-359	41	12	)	)	PUNCT
ma-359	41	13	|ρ|	|ρ|	NOUN
ma-359	41	14	n	n	PRON
ma-359	41	15	2	2	NUM
ma-359	41	16	−1	−1	NOUN
ma-359	41	17	=	=	SYM
ma-359	41	18	(	(	PUNCT
ma-359	41	19	y1y2	y1y2	NOUN
ma-359	41	20	)	)	PUNCT
ma-359	41	21	n−2	n−2	PROPN
ma-359	41	22	4	4	NUM
ma-359	41	23	2	2	NUM
ma-359	41	24	n	n	NUM
ma-359	41	25	2	2	NUM
ma-359	41	26	−1γ	−1γ	X
ma-359	41	27	(	(	PUNCT
ma-359	41	28	n	n	NOUN
ma-359	41	29	2	2	NUM
ma-359	41	30	)	)	PUNCT
ma-359	41	31	,	,	PUNCT
ma-359	41	32	the	the	DET
ma-359	41	33	joint	joint	ADJ
ma-359	41	34	pdf	pdf	NOUN
ma-359	41	35	reduces	reduce	VERB
ma-359	41	36	to	to	ADP
ma-359	41	37	the	the	DET
ma-359	41	38	product	product	NOUN
ma-359	41	39	of	of	ADP
ma-359	41	40	two	two	NUM
ma-359	41	41	univariate	univariate	ADJ
ma-359	41	42	chi	chi	ADJ
ma-359	41	43	square	square	ADJ
ma-359	41	44	pdfs	pdfs	PROPN
ma-359	41	45	.	.	PUNCT
ma-359	42	1	remark	remark	PROPN
ma-359	42	2	1	1	NUM
ma-359	42	3	.	.	PUNCT
ma-359	42	4	recall	recall	VERB
ma-359	42	5	that	that	SCONJ
ma-359	42	6	the	the	DET
ma-359	42	7	pdf	pdf	NOUN
ma-359	42	8	of	of	ADP
ma-359	42	9	the	the	DET
ma-359	42	10	unscaled	unscaled	ADJ
ma-359	42	11	univariate	univariate	ADJ
ma-359	42	12	gamma	gamma	NOUN
ma-359	42	13	distribution	distribution	NOUN
ma-359	42	14	is	be	AUX
ma-359	42	15	given	give	VERB
ma-359	42	16	by	by	ADP
ma-359	42	17	f	f	PROPN
ma-359	42	18	(	(	PUNCT
ma-359	42	19	x	x	PROPN
ma-359	42	20	;	;	PUNCT
ma-359	42	21	α	α	X
ma-359	42	22	,	,	PUNCT
ma-359	42	23	β	β	X
ma-359	42	24	)	)	PUNCT
ma-359	42	25	=	=	PUNCT
ma-359	43	1	xα−1e	xα−1e	NUM
ma-359	44	1	−	−	NOUN
ma-359	44	2	x	x	SYM
ma-359	44	3	β	β	X
ma-359	44	4	γ(α)βα	γ(α)βα	PROPN
ma-359	44	5	,	,	PUNCT
ma-359	44	6	where	where	SCONJ
ma-359	44	7	α	α	PROPN
ma-359	44	8	>	>	X
ma-359	44	9	0	0	PROPN
ma-359	44	10	,	,	PUNCT
ma-359	44	11	β	β	X
ma-359	44	12	>	>	X
ma-359	44	13	0	0	NUM
ma-359	44	14	,	,	PUNCT
ma-359	44	15	and	and	CCONJ
ma-359	44	16	x	x	X
ma-359	44	17	≥	≥	NOUN
ma-359	44	18	0	0	NUM
ma-359	44	19	.	.	PUNCT
ma-359	45	1	putting	put	VERB
ma-359	45	2	α	α	NOUN
ma-359	45	3	=	=	PUNCT
ma-359	45	4	n	n	PRON
ma-359	45	5	2	2	NUM
ma-359	45	6	,	,	PUNCT
ma-359	45	7	β	β	X
ma-359	45	8	=	=	SYM
ma-359	45	9	2	2	NUM
ma-359	45	10	,	,	PUNCT
ma-359	45	11	one	one	NOUN
ma-359	45	12	obtains	obtain	VERB
ma-359	45	13	the	the	DET
ma-359	45	14	univariate	univariate	ADJ
ma-359	45	15	chi	chi	ADJ
ma-359	45	16	square	square	ADJ
ma-359	45	17	distribution	distribution	NOUN
ma-359	45	18	as	as	ADP
ma-359	45	19	a	a	DET
ma-359	45	20	special	special	ADJ
ma-359	45	21	case	case	NOUN
ma-359	45	22	.	.	PUNCT
ma-359	46	1	it	it	PRON
ma-359	46	2	is	be	AUX
ma-359	46	3	well	well	ADV
ma-359	46	4	known	know	VERB
ma-359	46	5	that	that	SCONJ
ma-359	46	6	there	there	PRON
ma-359	46	7	are	be	VERB
ma-359	46	8	different	different	ADJ
ma-359	46	9	variants	variant	NOUN
ma-359	46	10	of	of	ADP
ma-359	46	11	the	the	DET
ma-359	46	12	bivariate	bivariate	ADJ
ma-359	46	13	gamma	gamma	PROPN
ma-359	46	14	pdf	pdf	PROPN
ma-359	46	15	’s	’s	X
ma-359	46	16	in	in	ADP
ma-359	46	17	the	the	DET
ma-359	46	18	literature	literature	NOUN
ma-359	46	19	(	(	PUNCT
ma-359	46	20	e.g.	e.g.	ADV
ma-359	46	21	,	,	PUNCT
ma-359	46	22	see	see	VERB
ma-359	46	23	[	[	X
ma-359	46	24	3	3	NUM
ma-359	46	25	]	]	PUNCT
ma-359	46	26	,	,	PUNCT
ma-359	46	27	ch	ch	NOUN
ma-359	46	28	.	.	PROPN
ma-359	46	29	48	48	NUM
ma-359	46	30	)	)	PUNCT
ma-359	46	31	.	.	PUNCT
ma-359	47	1	among	among	ADP
ma-359	47	2	the	the	DET
ma-359	47	3	earliest	early	ADJ
ma-359	47	4	bivariate	bivariate	ADJ
ma-359	47	5	pdfs	pdfs	NOUN
ma-359	47	6	for	for	ADP
ma-359	47	7	the	the	DET
ma-359	47	8	gamma	gamma	NOUN
ma-359	47	9	distribution	distribution	NOUN
ma-359	47	10	is	be	AUX
ma-359	47	11	that	that	PRON
ma-359	47	12	of	of	ADP
ma-359	47	13	kibble	kibble	ADJ
ma-359	47	14	[	[	X
ma-359	47	15	2	2	NUM
ma-359	47	16	]	]	PUNCT
ma-359	47	17	derived	derive	VERB
ma-359	47	18	for	for	ADP
ma-359	47	19	the	the	DET
ma-359	47	20	case	case	NOUN
ma-359	47	21	β	β	X
ma-359	47	22	=	=	SYM
ma-359	47	23	1	1	NUM
ma-359	47	24	(	(	PUNCT
ma-359	47	25	scaled	scale	VERB
ma-359	47	26	gamma	gamma	NOUN
ma-359	47	27	’s	’s	PART
ma-359	47	28	)	)	PUNCT
ma-359	47	29	.	.	PUNCT
ma-359	48	1	adjusting	adjust	VERB
ma-359	48	2	kibble	kibble	PROPN
ma-359	48	3	’s	’s	PART
ma-359	48	4	bivariate	bivariate	ADJ
ma-359	48	5	gamma	gamma	NOUN
ma-359	48	6	for	for	ADP
ma-359	48	7	the	the	DET
ma-359	48	8	scale	scale	NOUN
ma-359	48	9	parameter	parameter	NOUN
ma-359	48	10	β	β	X
ma-359	48	11	=	=	SYM
ma-359	48	12	2	2	NUM
ma-359	48	13	,	,	PUNCT
ma-359	48	14	with	with	ADP
ma-359	48	15	the	the	DET
ma-359	48	16	shape	shape	NOUN
ma-359	48	17	parameter	parameter	NOUN
ma-359	48	18	α	α	PROPN
ma-359	48	19	=	=	PROPN
ma-359	48	20	n	n	NUM
ma-359	48	21	2	2	NUM
ma-359	48	22	,	,	PUNCT
ma-359	48	23	one	one	NOUN
ma-359	48	24	obtains	obtain	VERB
ma-359	48	25	the	the	DET
ma-359	48	26	pdf	pdf	NOUN
ma-359	48	27	given	give	VERB
ma-359	48	28	in	in	ADP
ma-359	48	29	(	(	PUNCT
ma-359	48	30	1	1	NUM
ma-359	48	31	)	)	PUNCT
ma-359	48	32	which	which	PRON
ma-359	48	33	is	be	AUX
ma-359	48	34	a	a	DET
ma-359	48	35	kibble	kibble	ADJ
ma-359	48	36	type	type	NOUN
ma-359	48	37	bivariate	bivariate	ADJ
ma-359	48	38	chi	chi	PROPN
ma-359	48	39	square	square	PROPN
ma-359	48	40	pdf	pdf	PROPN
ma-359	48	41	.	.	PUNCT
ma-359	49	1	adjusting	adjust	VERB
ma-359	49	2	the	the	DET
ma-359	49	3	scale	scale	NOUN
ma-359	49	4	parameter	parameter	NOUN
ma-359	49	5	,	,	PUNCT
ma-359	49	6	one	one	PRON
ma-359	49	7	would	would	AUX
ma-359	49	8	obtain	obtain	VERB
ma-359	49	9	the	the	DET
ma-359	49	10	pdf	pdf	NOUN
ma-359	49	11	with	with	ADP
ma-359	49	12	σ2	σ2	PROPN
ma-359	49	13	1	1	NUM
ma-359	49	14	6=	6=	SYM
ma-359	49	15	1	1	NUM
ma-359	49	16	6=	6=	NUM
ma-359	49	17	σ2	σ2	PROPN
ma-359	49	18	2	2	NUM
ma-359	49	19	.	.	PUNCT
ma-359	50	1	consider	consider	VERB
ma-359	50	2	now	now	ADV
ma-359	50	3	the	the	DET
ma-359	50	4	difference	difference	NOUN
ma-359	50	5	w	w	NOUN
ma-359	50	6	of	of	ADP
ma-359	50	7	two	two	NUM
ma-359	50	8	dependent	dependent	ADJ
ma-359	50	9	central	central	ADJ
ma-359	50	10	chi	chi	PROPN
ma-359	50	11	square	square	ADJ
ma-359	50	12	rvs	rvs	NOUN
ma-359	50	13	,	,	PUNCT
ma-359	50	14	x	x	SYM
ma-359	50	15	,	,	PUNCT
ma-359	50	16	y	y	PROPN
ma-359	50	17	,	,	PUNCT
ma-359	50	18	each	each	PRON
ma-359	50	19	having	have	VERB
ma-359	50	20	a	a	DET
ma-359	50	21	n	n	NOUN
ma-359	50	22	=	=	SYM
ma-359	50	23	2	2	NUM
ma-359	50	24	m	m	NOUN
ma-359	50	25	,	,	PUNCT
ma-359	50	26	m	m	VERB
ma-359	50	27	>	>	X
ma-359	50	28	1	1	NUM
ma-359	50	29	,	,	PUNCT
ma-359	50	30	degrees	degree	NOUN
ma-359	50	31	of	of	ADP
ma-359	50	32	freedom	freedom	NOUN
ma-359	50	33	(	(	PUNCT
ma-359	50	34	using	use	VERB
ma-359	50	35	the	the	DET
ma-359	50	36	notation	notation	NOUN
ma-359	50	37	in	in	ADP
ma-359	50	38	[	[	X
ma-359	50	39	6	6	NUM
ma-359	50	40	]	]	PUNCT
ma-359	50	41	)	)	PUNCT
ma-359	50	42	.	.	PUNCT
ma-359	51	1	then	then	ADV
ma-359	51	2	it	it	PRON
ma-359	51	3	is	be	AUX
ma-359	51	4	reported	report	VERB
ma-359	51	5	in	in	ADP
ma-359	51	6	[	[	X
ma-359	51	7	6	6	NUM
ma-359	51	8	]	]	PUNCT
ma-359	51	9	that	that	SCONJ
ma-359	51	10	the	the	DET
ma-359	51	11	rvw	rvw	PROPN
ma-359	51	12	=	=	PROPN
ma-359	51	13	x−y	x−y	PROPN
ma-359	51	14	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	51	15	eur	eur	PROPN
ma-359	51	16	.	.	PUNCT
ma-359	52	1	j.	j.	PROPN
ma-359	52	2	math	math	PROPN
ma-359	52	3	.	.	PUNCT
ma-359	53	1	anal	anal	PROPN
ma-359	53	2	.	.	PUNCT
ma-359	54	1	10.28924	10.28924	NUM
ma-359	54	2	/	/	SYM
ma-359	54	3	ada	ada	PROPN
ma-359	54	4	/	/	SYM
ma-359	54	5	ma.5.19	ma.5.19	NOUN
ma-359	54	6	3has	3has	NUM
ma-359	55	1	the	the	DET
ma-359	55	2	following	follow	VERB
ma-359	55	3	piecewise	piecewise	NOUN
ma-359	55	4	defined	define	VERB
ma-359	55	5	pdf	pdf	NOUN
ma-359	55	6	pw	pw	X
ma-359	55	7	(	(	PUNCT
ma-359	55	8	w	w	NOUN
ma-359	55	9	)	)	PUNCT
ma-359	55	10	=	=	SYM
ma-359	55	11	|w	|w	ADJ
ma-359	55	12	|m−1	|m−1	PROPN
ma-359	55	13	(	(	PUNCT
ma-359	55	14	m	m	VERB
ma-359	55	15	−	−	PROPN
ma-359	55	16	1)!22	1)!22	NUM
ma-359	55	17	m	m	PROPN
ma-359	55	18	(	(	PUNCT
ma-359	55	19	1−	1−	NUM
ma-359	55	20	ρ2	ρ2	NOUN
ma-359	55	21	)	)	PUNCT
ma-359	55	22	m	m	PROPN
ma-359	55	23	2	2	NUM
ma-359	55	24	exp	exp	NOUN
ma-359	55	25	(	(	PUNCT
ma-359	55	26	w	w	PROPN
ma-359	55	27	2	2	NUM
ma-359	55	28	√	√	NUM
ma-359	55	29	1−	1−	NUM
ma-359	55	30	ρ2	ρ2	NOUN
ma-359	55	31	)	)	PUNCT
ma-359	55	32	m−1∑	m−1∑	PROPN
ma-359	55	33	i=0	i=0	PROPN
ma-359	55	34	(	(	PUNCT
ma-359	55	35	m	m	VERB
ma-359	55	36	+	+	ADJ
ma-359	55	37	i	i	PRON
ma-359	55	38	−	−	NOUN
ma-359	55	39	1	1	NUM
ma-359	55	40	)	)	PUNCT
ma-359	55	41	!	!	PUNCT
ma-359	56	1	i	i	PRON
ma-359	56	2	!	!	PUNCT
ma-359	57	1	(	(	PUNCT
ma-359	57	2	m	m	VERB
ma-359	57	3	−	−	NOUN
ma-359	58	1	i	i	PRON
ma-359	58	2	−	−	PROPN
ma-359	58	3	1	1	NUM
ma-359	58	4	)	)	PUNCT
ma-359	58	5	!	!	PUNCT
ma-359	59	1	(	(	PUNCT
ma-359	59	2	√	√	NUM
ma-359	59	3	1−	1−	NUM
ma-359	59	4	ρ2	ρ2	NOUN
ma-359	59	5	|w	|w	NOUN
ma-359	59	6	|	|	ADV
ma-359	59	7	)	)	PUNCT
ma-359	60	1	i	i	PRON
ma-359	60	2	,	,	PUNCT
ma-359	60	3	w	w	PROPN
ma-359	60	4	<	<	X
ma-359	60	5	0	0	NUM
ma-359	60	6	pw	pw	X
ma-359	60	7	(	(	PUNCT
ma-359	60	8	w	w	NOUN
ma-359	60	9	)	)	PUNCT
ma-359	60	10	=	=	SYM
ma-359	60	11	|w	|w	ADJ
ma-359	60	12	|m−1	|m−1	PROPN
ma-359	60	13	(	(	PUNCT
ma-359	60	14	m	m	VERB
ma-359	60	15	−	−	PROPN
ma-359	60	16	1)!22	1)!22	NUM
ma-359	60	17	m	m	PROPN
ma-359	60	18	(	(	PUNCT
ma-359	60	19	1−	1−	NUM
ma-359	60	20	ρ2	ρ2	NOUN
ma-359	60	21	)	)	PUNCT
ma-359	60	22	m	m	PROPN
ma-359	60	23	2	2	NUM
ma-359	60	24	exp	exp	NOUN
ma-359	60	25	(	(	PUNCT
ma-359	60	26	−	−	PROPN
ma-359	60	27	w	w	PROPN
ma-359	60	28	2	2	NUM
ma-359	60	29	√	√	NUM
ma-359	60	30	1−	1−	NUM
ma-359	60	31	ρ2	ρ2	NOUN
ma-359	60	32	)	)	PUNCT
ma-359	60	33	m−1∑	m−1∑	PROPN
ma-359	60	34	i=0	i=0	PROPN
ma-359	60	35	(	(	PUNCT
ma-359	60	36	m	m	VERB
ma-359	60	37	+	+	ADJ
ma-359	60	38	i	i	PRON
ma-359	60	39	−	−	NOUN
ma-359	60	40	1	1	NUM
ma-359	60	41	)	)	PUNCT
ma-359	60	42	!	!	PUNCT
ma-359	61	1	i	i	PRON
ma-359	61	2	!	!	PUNCT
ma-359	62	1	(	(	PUNCT
ma-359	62	2	m	m	VERB
ma-359	62	3	−	−	NOUN
ma-359	63	1	i	i	PRON
ma-359	63	2	−	−	PROPN
ma-359	63	3	1	1	NUM
ma-359	63	4	)	)	PUNCT
ma-359	63	5	!	!	PUNCT
ma-359	64	1	(	(	PUNCT
ma-359	64	2	√	√	NUM
ma-359	64	3	1−	1−	NUM
ma-359	64	4	ρ2	ρ2	NOUN
ma-359	64	5	|w	|w	NOUN
ma-359	64	6	|	|	ADV
ma-359	64	7	)	)	PUNCT
ma-359	65	1	i	i	PRON
ma-359	65	2	,	,	PUNCT
ma-359	65	3	w	w	PRON
ma-359	65	4	≥	≥	NOUN
ma-359	65	5	0	0	NUM
ma-359	65	6	using	use	VERB
ma-359	65	7	the	the	DET
ma-359	65	8	following	follow	VERB
ma-359	65	9	expansion	expansion	NOUN
ma-359	65	10	of	of	ADP
ma-359	65	11	the	the	DET
ma-359	65	12	macdonald	macdonald	PROPN
ma-359	65	13	function	function	NOUN
ma-359	65	14	[	[	X
ma-359	65	15	8	8	NUM
ma-359	65	16	]	]	PUNCT
ma-359	65	17	km−	km−	X
ma-359	65	18	1	1	NUM
ma-359	65	19	2	2	NUM
ma-359	65	20	(	(	PUNCT
ma-359	65	21	w	w	NOUN
ma-359	65	22	)	)	PUNCT
ma-359	65	23	=	=	SYM
ma-359	66	1	(	(	PUNCT
ma-359	66	2	π	π	PROPN
ma-359	66	3	2w	2w	NUM
ma-359	66	4	)	)	PUNCT
ma-359	66	5	1	1	NUM
ma-359	66	6	2	2	NUM
ma-359	66	7	e−w	e−w	NOUN
ma-359	66	8	m−1∑	m−1∑	PROPN
ma-359	66	9	i=0	i=0	X
ma-359	66	10	(	(	PUNCT
ma-359	66	11	m	m	VERB
ma-359	66	12	+	+	ADJ
ma-359	66	13	i	i	PRON
ma-359	66	14	−	−	NOUN
ma-359	66	15	1	1	NUM
ma-359	66	16	)	)	PUNCT
ma-359	66	17	!	!	PUNCT
ma-359	67	1	i	i	PRON
ma-359	67	2	!	!	PUNCT
ma-359	68	1	(	(	PUNCT
ma-359	68	2	m	m	VERB
ma-359	68	3	−	−	NOUN
ma-359	69	1	i	i	PRON
ma-359	69	2	−	−	PROPN
ma-359	69	3	1	1	NUM
ma-359	69	4	)	)	PUNCT
ma-359	69	5	!	!	PUNCT
ma-359	70	1	(	(	PUNCT
ma-359	70	2	2w)i	2w)i	NUM
ma-359	70	3	,	,	PUNCT
ma-359	70	4	and	and	CCONJ
ma-359	70	5	k−ν(w	k−ν(w	NOUN
ma-359	70	6	)	)	PUNCT
ma-359	70	7	=	=	SYM
ma-359	70	8	kν(w	kν(w	NOUN
ma-359	70	9	)	)	PUNCT
ma-359	70	10	,	,	PUNCT
ma-359	70	11	the	the	DET
ma-359	70	12	pdf	pdf	NOUN
ma-359	70	13	given	give	VERB
ma-359	70	14	in	in	ADP
ma-359	70	15	[	[	X
ma-359	70	16	6	6	NUM
ma-359	70	17	]	]	PUNCT
ma-359	70	18	for	for	ADP
ma-359	70	19	w	w	PROPN
ma-359	70	20	can	can	AUX
ma-359	70	21	be	be	AUX
ma-359	70	22	written	write	VERB
ma-359	70	23	as	as	ADP
ma-359	70	24	pw	pw	PROPN
ma-359	70	25	(	(	PUNCT
ma-359	70	26	w	w	NOUN
ma-359	70	27	)	)	PUNCT
ma-359	70	28	=	=	SYM
ma-359	71	1	|w	|w	ADJ
ma-359	71	2	|m−	|m−	PROPN
ma-359	71	3	1	1	NUM
ma-359	71	4	2	2	NUM
ma-359	71	5	22	22	NUM
ma-359	71	6	m	m	NOUN
ma-359	71	7	√	√	PROPN
ma-359	71	8	π	π	PROPN
ma-359	71	9	(	(	PUNCT
ma-359	71	10	1−	1−	NUM
ma-359	71	11	ρ2	ρ2	NOUN
ma-359	71	12	)	)	PUNCT
ma-359	71	13	2m+1	2m+1	NOUN
ma-359	71	14	4	4	NUM
ma-359	71	15	(	(	PUNCT
ma-359	71	16	m	m	NOUN
ma-359	71	17	−	−	NOUN
ma-359	71	18	1	1	NUM
ma-359	71	19	)	)	PUNCT
ma-359	71	20	!	!	PUNCT
ma-359	72	1	km−	km−	NOUN
ma-359	72	2	1	1	NUM
ma-359	72	3	2	2	NUM
ma-359	72	4	(	(	PUNCT
ma-359	72	5	|w	|w	NOUN
ma-359	72	6	|	|	ADV
ma-359	72	7	2	2	NUM
ma-359	72	8	√	√	NUM
ma-359	72	9	1−	1−	NUM
ma-359	72	10	ρ2	ρ2	NOUN
ma-359	72	11	)	)	PUNCT
ma-359	72	12	,	,	PUNCT
ma-359	72	13	w	w	PROPN
ma-359	72	14	6=	6=	PROPN
ma-359	72	15	0	0	NUM
ma-359	72	16	,	,	PUNCT
ma-359	72	17	and	and	CCONJ
ma-359	72	18	,	,	PUNCT
ma-359	72	19	pw	pw	X
ma-359	72	20	(	(	PUNCT
ma-359	72	21	0	0	NUM
ma-359	72	22	)	)	PUNCT
ma-359	72	23	:	:	PUNCT
ma-359	72	24	=	=	PUNCT
ma-359	72	25	limw→0	limw→0	VERB
ma-359	72	26	pw	pw	NOUN
ma-359	73	1	(	(	PUNCT
ma-359	73	2	w	w	NOUN
ma-359	73	3	)	)	PUNCT
ma-359	73	4	,	,	PUNCT
ma-359	73	5	which	which	PRON
ma-359	73	6	evaluates	evaluate	VERB
ma-359	73	7	to	to	ADP
ma-359	73	8	γ(m−	γ(m−	PROPN
ma-359	73	9	1	1	NUM
ma-359	73	10	2	2	NUM
ma-359	73	11	)	)	PUNCT
ma-359	73	12	4	4	NUM
ma-359	73	13	√	√	NUM
ma-359	73	14	π	π	NOUN
ma-359	73	15	√	√	NUM
ma-359	73	16	1−ρ2(m−1	1−ρ2(m−1	NUM
ma-359	73	17	)	)	PUNCT
ma-359	73	18	!	!	PUNCT
ma-359	73	19	.	.	PUNCT
ma-359	74	1	the	the	DET
ma-359	74	2	simplest	simple	ADJ
ma-359	74	3	definition	definition	NOUN
ma-359	74	4	of	of	ADP
ma-359	74	5	the	the	DET
ma-359	74	6	macdonald	macdonald	PROPN
ma-359	74	7	function	function	PROPN
ma-359	74	8	is	be	AUX
ma-359	74	9	k	k	PROPN
ma-359	74	10	m−	m−	PROPN
ma-359	74	11	1	1	NUM
ma-359	74	12	2	2	NUM
ma-359	74	13	(	(	PUNCT
ma-359	74	14	w	w	NOUN
ma-359	74	15	)	)	PUNCT
ma-359	74	16	:	:	PUNCT
ma-359	74	17	=	=	SYM
ma-359	74	18	π(−1)k−1	π(−1)k−1	X
ma-359	74	19	2	2	X
ma-359	74	20	(	(	PUNCT
ma-359	74	21	i−m+	i−m+	PROPN
ma-359	74	22	1	1	NUM
ma-359	74	23	2	2	NUM
ma-359	74	24	(	(	PUNCT
ma-359	74	25	w)−	w)−	PROPN
ma-359	74	26	im−	im−	PROPN
ma-359	74	27	1	1	NUM
ma-359	74	28	2	2	NUM
ma-359	74	29	(	(	PUNCT
ma-359	74	30	w	w	NOUN
ma-359	74	31	)	)	PUNCT
ma-359	74	32	)	)	PUNCT
ma-359	74	33	,	,	PUNCT
ma-359	74	34	m	m	NOUN
ma-359	74	35	integer	integer	NOUN
ma-359	74	36	,	,	PUNCT
ma-359	74	37	(	(	PUNCT
ma-359	74	38	amongother	amongother	ADJ
ma-359	74	39	names	name	NOUN
ma-359	74	40	of	of	ADP
ma-359	74	41	kν	kν	PROPN
ma-359	74	42	,	,	PUNCT
ma-359	74	43	it	it	PRON
ma-359	74	44	is	be	AUX
ma-359	74	45	often	often	ADV
ma-359	74	46	also	also	ADV
ma-359	74	47	called	call	VERB
ma-359	74	48	the	the	DET
ma-359	74	49	modified	modify	VERB
ma-359	74	50	bessel	bessel	NOUN
ma-359	74	51	function	function	NOUN
ma-359	74	52	of	of	ADP
ma-359	74	53	the	the	DET
ma-359	74	54	second	second	ADJ
ma-359	74	55	kind	kind	NOUN
ma-359	74	56	(	(	PUNCT
ma-359	74	57	like	like	INTJ
ma-359	74	58	inmathematica	inmathematica	NOUN
ma-359	74	59	)	)	PUNCT
ma-359	74	60	)	)	PUNCT
ma-359	74	61	.	.	PUNCT
ma-359	75	1	replacing	replace	VERB
ma-359	75	2	the	the	DET
ma-359	75	3	m	m	NOUN
ma-359	75	4	used	use	VERB
ma-359	75	5	in	in	ADP
ma-359	75	6	(	(	PUNCT
ma-359	75	7	[	[	X
ma-359	75	8	6	6	NUM
ma-359	75	9	]	]	PUNCT
ma-359	75	10	,	,	PUNCT
ma-359	75	11	p.	p.	NOUN
ma-359	75	12	29	29	NUM
ma-359	75	13	)	)	PUNCT
ma-359	75	14	by	by	ADP
ma-359	75	15	n	n	ADV
ma-359	75	16	2	2	NUM
ma-359	75	17	,	,	PUNCT
ma-359	75	18	where	where	SCONJ
ma-359	75	19	n	n	PRON
ma-359	75	20	now	now	ADV
ma-359	75	21	is	be	AUX
ma-359	75	22	the	the	DET
ma-359	75	23	number	number	NOUN
ma-359	75	24	of	of	ADP
ma-359	75	25	degreesof	degreesof	NOUN
ma-359	75	26	freedom	freedom	NOUN
ma-359	75	27	of	of	ADP
ma-359	75	28	the	the	DET
ma-359	75	29	rvs	rvs	NOUN
ma-359	75	30	x	x	X
ma-359	75	31	and	and	CCONJ
ma-359	75	32	y	y	PROPN
ma-359	75	33	,	,	PUNCT
ma-359	75	34	then	then	ADV
ma-359	75	35	followed	follow	VERB
ma-359	75	36	by	by	ADP
ma-359	75	37	replacing	replace	VERB
ma-359	75	38	n	n	PRON
ma-359	75	39	by	by	ADP
ma-359	75	40	m	m	PROPN
ma-359	75	41	,	,	PUNCT
ma-359	75	42	we	we	PRON
ma-359	75	43	obtain	obtain	VERB
ma-359	75	44	fw	fw	PROPN
ma-359	75	45	(	(	PUNCT
ma-359	75	46	w	w	NOUN
ma-359	75	47	)	)	PUNCT
ma-359	75	48	=	=	SYM
ma-359	76	1	|w	|w	NOUN
ma-359	77	1	|	|	ADV
ma-359	77	2	m−1	m−1	PROPN
ma-359	77	3	2	2	NUM
ma-359	77	4	2	2	NUM
ma-359	77	5	m	m	NOUN
ma-359	77	6	√	√	ADJ
ma-359	77	7	π	π	PROPN
ma-359	77	8	(	(	PUNCT
ma-359	77	9	1−	1−	NUM
ma-359	77	10	ρ2	ρ2	NOUN
ma-359	77	11	)	)	PUNCT
ma-359	77	12	m+1	m+1	NUM
ma-359	77	13	4	4	NUM
ma-359	77	14	γ	γ	X
ma-359	77	15	(	(	PUNCT
ma-359	77	16	m	m	PROPN
ma-359	77	17	2	2	NUM
ma-359	77	18	)	)	PUNCT
ma-359	77	19	km−1	km−1	NOUN
ma-359	77	20	2	2	NUM
ma-359	77	21	(	(	PUNCT
ma-359	77	22	|w	|w	NOUN
ma-359	77	23	|	|	ADV
ma-359	77	24	2	2	NUM
ma-359	77	25	√	√	NUM
ma-359	77	26	1−	1−	NUM
ma-359	77	27	ρ2	ρ2	NOUN
ma-359	77	28	)	)	PUNCT
ma-359	77	29	,	,	PUNCT
ma-359	77	30	w	w	PROPN
ma-359	77	31	∈	∈	PROPN
ma-359	77	32	r\{0	r\{0	PROPN
ma-359	77	33	}	}	PUNCT
ma-359	77	34	.	.	PUNCT
ma-359	78	1	(	(	PUNCT
ma-359	78	2	2	2	X
ma-359	78	3	)	)	PUNCT
ma-359	78	4	and	and	CCONJ
ma-359	78	5	fw	fw	ADJ
ma-359	78	6	(	(	PUNCT
ma-359	78	7	0	0	NUM
ma-359	78	8	)	)	PUNCT
ma-359	78	9	:	:	PUNCT
ma-359	79	1	=	=	SYM
ma-359	79	2	γ(m−1	γ(m−1	SYM
ma-359	79	3	2	2	X
ma-359	79	4	)	)	PUNCT
ma-359	79	5	4	4	NUM
ma-359	79	6	√	√	NUM
ma-359	79	7	π	π	NOUN
ma-359	79	8	√	√	PROPN
ma-359	79	9	1−ρ2γ(m2	1−ρ2γ(m2	NUM
ma-359	79	10	)	)	PUNCT
ma-359	79	11	.	.	PUNCT
ma-359	80	1	clearly	clearly	ADV
ma-359	80	2	fw	fw	PROPN
ma-359	80	3	(	(	PUNCT
ma-359	80	4	w	w	NOUN
ma-359	80	5	)	)	PUNCT
ma-359	80	6	=	=	SYM
ma-359	80	7	fw	fw	X
ma-359	80	8	(	(	PUNCT
ma-359	80	9	−w	−w	ADV
ma-359	80	10	)	)	PUNCT
ma-359	80	11	.	.	PUNCT
ma-359	81	1	for	for	ADP
ma-359	81	2	m	m	PROPN
ma-359	81	3	=	=	SYM
ma-359	81	4	1	1	NUM
ma-359	81	5	,	,	PUNCT
ma-359	81	6	fw	fw	X
ma-359	81	7	(	(	PUNCT
ma-359	81	8	w	w	NOUN
ma-359	81	9	)	)	PUNCT
ma-359	81	10	=	=	SYM
ma-359	81	11	1	1	NUM
ma-359	81	12	2π	2π	NUM
ma-359	81	13	√	√	ADV
ma-359	81	14	1−ρ2	1−ρ2	NUM
ma-359	81	15	k0	k0	PROPN
ma-359	81	16	(	(	PUNCT
ma-359	81	17	|w	|w	NOUN
ma-359	81	18	|	|	ADV
ma-359	81	19	2	2	NUM
ma-359	81	20	√	√	NUM
ma-359	81	21	1−ρ2	1−ρ2	NUM
ma-359	81	22	)	)	PUNCT
ma-359	81	23	.	.	PUNCT
ma-359	82	1	for	for	ADP
ma-359	82	2	m	m	PROPN
ma-359	82	3	=	=	SYM
ma-359	82	4	2	2	NUM
ma-359	82	5	,	,	PUNCT
ma-359	82	6	as	as	SCONJ
ma-359	82	7	k	k	PROPN
ma-359	82	8	1	1	NUM
ma-359	82	9	2	2	NUM
ma-359	82	10	(	(	PUNCT
ma-359	82	11	z	z	NOUN
ma-359	82	12	)	)	PUNCT
ma-359	82	13	=	=	PUNCT
ma-359	82	14	(	(	PUNCT
ma-359	82	15	π	π	PROPN
ma-359	82	16	2z	2z	NUM
ma-359	82	17	)	)	PUNCT
ma-359	82	18	1	1	NUM
ma-359	82	19	2	2	NUM
ma-359	82	20	e−z	e−z	NOUN
ma-359	82	21	,	,	PUNCT
ma-359	82	22	then	then	ADV
ma-359	82	23	fw	fw	PROPN
ma-359	82	24	(	(	PUNCT
ma-359	82	25	w	w	NOUN
ma-359	82	26	)	)	PUNCT
ma-359	82	27	=	=	SYM
ma-359	82	28	1	1	NUM
ma-359	82	29	4	4	NUM
ma-359	82	30	√	√	NUM
ma-359	82	31	1−ρ2	1−ρ2	NUM
ma-359	82	32	e	e	NOUN
ma-359	82	33	−	−	PROPN
ma-359	82	34	|w	|w	NOUN
ma-359	82	35	|	|	ADV
ma-359	82	36	2	2	NUM
ma-359	82	37	√	√	NUM
ma-359	82	38	1−ρ2	1−ρ2	NUM
ma-359	82	39	.these	.these	PUNCT
ma-359	82	40	cases	case	NOUN
ma-359	82	41	match	match	VERB
ma-359	82	42	with	with	ADP
ma-359	82	43	equations	equation	NOUN
ma-359	82	44	(	(	PUNCT
ma-359	82	45	4.20	4.20	NUM
ma-359	82	46	)	)	PUNCT
ma-359	82	47	and	and	CCONJ
ma-359	82	48	(	(	PUNCT
ma-359	82	49	4.23	4.23	NUM
ma-359	82	50	)	)	PUNCT
ma-359	82	51	given	give	VERB
ma-359	82	52	in	in	ADP
ma-359	82	53	(	(	PUNCT
ma-359	82	54	[	[	X
ma-359	82	55	6	6	NUM
ma-359	82	56	]	]	PUNCT
ma-359	82	57	,	,	PUNCT
ma-359	82	58	p.	p.	NOUN
ma-359	82	59	29	29	NUM
ma-359	82	60	)	)	PUNCT
ma-359	82	61	.	.	PUNCT
ma-359	83	1	for	for	ADP
ma-359	83	2	odd	odd	ADJ
ma-359	83	3	degrees	degree	NOUN
ma-359	83	4	offreedom	offreedom	ADJ
ma-359	83	5	,	,	PUNCT
ma-359	83	6	it	it	PRON
ma-359	83	7	is	be	AUX
ma-359	83	8	reported	report	VERB
ma-359	83	9	in	in	ADP
ma-359	83	10	(	(	PUNCT
ma-359	83	11	[	[	X
ma-359	83	12	6	6	NUM
ma-359	83	13	]	]	PUNCT
ma-359	83	14	,	,	PUNCT
ma-359	83	15	p.	p.	NOUN
ma-359	83	16	30	30	NUM
ma-359	83	17	)	)	PUNCT
ma-359	83	18	,	,	PUNCT
ma-359	83	19	using	use	VERB
ma-359	83	20	his	his	PRON
ma-359	83	21	notation	notation	NOUN
ma-359	83	22	for	for	ADP
ma-359	83	23	n	n	NOUN
ma-359	83	24	=	=	SYM
ma-359	83	25	n1	n1	NOUN
ma-359	83	26	=	=	SYM
ma-359	83	27	n2	n2	NOUN
ma-359	83	28	=	=	NOUN
ma-359	83	29	2	2	NUM
ma-359	83	30	m	m	NOUN
ma-359	83	31	+	+	NOUN
ma-359	83	32	1	1	NUM
ma-359	83	33	,	,	PUNCT
ma-359	83	34	and	and	CCONJ
ma-359	83	35	for	for	ADP
ma-359	83	36	σ1	σ1	PROPN
ma-359	83	37	=	=	SYM
ma-359	83	38	σ2	σ2	PROPN
ma-359	83	39	=	=	SYM
ma-359	83	40	1	1	NUM
ma-359	83	41	,	,	PUNCT
ma-359	83	42	that	that	SCONJ
ma-359	83	43	the	the	DET
ma-359	83	44	pdf	pdf	NOUN
ma-359	83	45	is	be	AUX
ma-359	83	46	given	give	VERB
ma-359	83	47	by	by	ADP
ma-359	83	48	pw	pw	PROPN
ma-359	83	49	(	(	PUNCT
ma-359	83	50	w	w	NOUN
ma-359	83	51	)	)	PUNCT
ma-359	83	52	=	=	SYM
ma-359	83	53	|w	|w	ADJ
ma-359	83	54	|m	|m	NOUN
ma-359	83	55	√	√	VERB
ma-359	83	56	πγ	πγ	PROPN
ma-359	83	57	(	(	PUNCT
ma-359	83	58	m	m	VERB
ma-359	83	59	+	+	X
ma-359	83	60	1	1	NUM
ma-359	83	61	2	2	NUM
ma-359	83	62	)	)	PUNCT
ma-359	83	63	(	(	PUNCT
ma-359	83	64	1−	1−	NUM
ma-359	83	65	ρ2	ρ2	NOUN
ma-359	83	66	)	)	PUNCT
ma-359	83	67	m+1	m+1	NUM
ma-359	83	68	2	2	NUM
ma-359	83	69	km	km	NOUN
ma-359	83	70	(	(	PUNCT
ma-359	83	71	|w	|w	NOUN
ma-359	83	72	|	|	ADV
ma-359	83	73	2	2	NUM
ma-359	83	74	√	√	NUM
ma-359	83	75	1−	1−	NUM
ma-359	83	76	ρ2	ρ2	NOUN
ma-359	83	77	)	)	PUNCT
ma-359	83	78	.	.	PUNCT
ma-359	84	1	(	(	PUNCT
ma-359	84	2	3	3	X
ma-359	84	3	)	)	PUNCT
ma-359	84	4	writing	write	VERB
ma-359	84	5	this	this	PRON
ma-359	84	6	in	in	ADP
ma-359	84	7	terms	term	NOUN
ma-359	84	8	of	of	ADP
ma-359	84	9	n	n	PRON
ma-359	84	10	and	and	CCONJ
ma-359	84	11	setting	set	VERB
ma-359	84	12	n	n	NOUN
ma-359	84	13	=	=	PRON
ma-359	84	14	m	m	VERB
ma-359	84	15	to	to	PART
ma-359	84	16	adjust	adjust	VERB
ma-359	84	17	back	back	ADV
ma-359	84	18	to	to	ADP
ma-359	84	19	our	our	PRON
ma-359	84	20	notation	notation	NOUN
ma-359	84	21	,	,	PUNCT
ma-359	84	22	we	we	PRON
ma-359	84	23	see	see	VERB
ma-359	84	24	that	that	SCONJ
ma-359	84	25	(	(	PUNCT
ma-359	84	26	3	3	X
ma-359	84	27	)	)	PUNCT
ma-359	84	28	matcheswith	matcheswith	NOUN
ma-359	84	29	(	(	PUNCT
ma-359	84	30	2	2	NUM
ma-359	84	31	)	)	PUNCT
ma-359	84	32	.	.	PUNCT
ma-359	85	1	figure	figure	NOUN
ma-359	85	2	1	1	NUM
ma-359	85	3	shows	show	VERB
ma-359	85	4	a	a	DET
ma-359	85	5	plot	plot	NOUN
ma-359	85	6	of	of	ADP
ma-359	85	7	fw	fw	PROPN
ma-359	85	8	(	(	PUNCT
ma-359	85	9	w	w	NOUN
ma-359	85	10	)	)	PUNCT
ma-359	85	11	.	.	PUNCT
ma-359	86	1	3	3	X
ma-359	86	2	.	.	NOUN
ma-359	86	3	cumulative	cumulative	ADJ
ma-359	86	4	distribution	distribution	NOUN
ma-359	86	5	functions	function	NOUN
ma-359	86	6	in	in	ADP
ma-359	86	7	this	this	DET
ma-359	86	8	section	section	NOUN
ma-359	86	9	,	,	PUNCT
ma-359	86	10	we	we	PRON
ma-359	86	11	derive	derive	VERB
ma-359	86	12	representations	representation	NOUN
ma-359	86	13	of	of	ADP
ma-359	86	14	the	the	DET
ma-359	86	15	cdf	cdf	PROPN
ma-359	86	16	of	of	ADP
ma-359	86	17	w	w	NOUN
ma-359	86	18	for	for	ADP
ma-359	86	19	even	even	ADV
ma-359	86	20	and	and	CCONJ
ma-359	86	21	odd	odd	ADJ
ma-359	86	22	degrees	degree	NOUN
ma-359	86	23	of	of	ADP
ma-359	86	24	freedom	freedom	NOUN
ma-359	86	25	.	.	PUNCT
ma-359	87	1	inthe	inthe	DET
ma-359	87	2	case	case	NOUN
ma-359	87	3	of	of	ADP
ma-359	87	4	even	even	ADJ
ma-359	87	5	degrees	degree	NOUN
ma-359	87	6	of	of	ADP
ma-359	87	7	freedom	freedom	NOUN
ma-359	87	8	,	,	PUNCT
ma-359	87	9	we	we	PRON
ma-359	87	10	compare	compare	VERB
ma-359	87	11	our	our	PRON
ma-359	87	12	result	result	NOUN
ma-359	87	13	with	with	ADP
ma-359	87	14	the	the	DET
ma-359	87	15	cdf	cdf	PROPN
ma-359	87	16	expression	expression	NOUN
ma-359	87	17	reported	report	VERB
ma-359	87	18	in	in	ADP
ma-359	87	19	[	[	PUNCT
ma-359	87	20	6].let	6].let	NUM
ma-359	87	21	c	c	NOUN
ma-359	87	22	=	=	SYM
ma-359	87	23	16	16	NUM
ma-359	87	24	(	(	PUNCT
ma-359	87	25	1−	1−	NUM
ma-359	87	26	ρ2	ρ2	NOUN
ma-359	87	27	)	)	PUNCT
ma-359	87	28	.	.	PUNCT
ma-359	88	1	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	89	1	eur	eur	PROPN
ma-359	89	2	.	.	PUNCT
ma-359	90	1	j.	j.	PROPN
ma-359	90	2	math	math	PROPN
ma-359	90	3	.	.	PUNCT
ma-359	91	1	anal	anal	PROPN
ma-359	91	2	.	.	PUNCT
ma-359	92	1	10.28924	10.28924	NUM
ma-359	92	2	/	/	SYM
ma-359	92	3	ada	ada	PROPN
ma-359	92	4	/	/	SYM
ma-359	92	5	ma.5.19	ma.5.19	NOUN
ma-359	92	6	4	4	NUM
ma-359	92	7	figure	figure	NOUN
ma-359	92	8	1	1	NUM
ma-359	92	9	.	.	PUNCT
ma-359	93	1	the	the	DET
ma-359	93	2	pdf	pdf	NOUN
ma-359	93	3	fw	fw	PROPN
ma-359	93	4	(	(	PUNCT
ma-359	93	5	w	w	NOUN
ma-359	93	6	)	)	PUNCT
ma-359	93	7	for	for	ADP
ma-359	93	8	m	m	PROPN
ma-359	93	9	=	=	NOUN
ma-359	93	10	10	10	NUM
ma-359	93	11	,	,	PUNCT
ma-359	93	12	15	15	NUM
ma-359	93	13	,	,	PUNCT
ma-359	93	14	20	20	NUM
ma-359	93	15	,	,	PUNCT
ma-359	93	16	and	and	CCONJ
ma-359	93	17	ρ	ρ	NUM
ma-359	93	18	=	=	SYM
ma-359	93	19	0.7	0.7	NUM
ma-359	93	20	.	.	PUNCT
ma-359	93	21	theorem	theorem	NOUN
ma-359	93	22	1	1	NUM
ma-359	93	23	.	.	PUNCT
ma-359	94	1	if	if	SCONJ
ma-359	94	2	the	the	DET
ma-359	94	3	symmetric	symmetric	ADJ
ma-359	94	4	pdf	pdf	NOUN
ma-359	94	5	of	of	ADP
ma-359	94	6	w	w	PROPN
ma-359	94	7	is	be	AUX
ma-359	94	8	given	give	VERB
ma-359	94	9	by	by	ADP
ma-359	94	10	(	(	PUNCT
ma-359	94	11	2	2	NUM
ma-359	94	12	)	)	PUNCT
ma-359	94	13	,	,	PUNCT
ma-359	94	14	then	then	ADV
ma-359	94	15	the	the	DET
ma-359	94	16	cdf	cdf	PROPN
ma-359	94	17	of	of	ADP
ma-359	94	18	w	w	PROPN
ma-359	94	19	for	for	ADP
ma-359	94	20	w	w	PROPN
ma-359	94	21	>	>	X
ma-359	94	22	0	0	NUM
ma-359	94	23	is	be	AUX
ma-359	94	24	given	give	VERB
ma-359	94	25	by	by	ADP
ma-359	94	26	fw	fw	PROPN
ma-359	94	27	(	(	PUNCT
ma-359	94	28	w	w	NOUN
ma-359	94	29	)	)	PUNCT
ma-359	94	30	=	=	SYM
ma-359	94	31	∫	∫	PROPN
ma-359	94	32	0	0	PUNCT
ma-359	95	1	−∞	−∞	X
ma-359	95	2	fw	fw	PROPN
ma-359	95	3	(	(	PUNCT
ma-359	95	4	w	w	NOUN
ma-359	95	5	)	)	PUNCT
ma-359	95	6	dw	dw	NOUN
ma-359	96	1	+	+	CCONJ
ma-359	97	1	∫	∫	PROPN
ma-359	97	2	w	w	PROPN
ma-359	97	3	0	0	NUM
ma-359	97	4	fw	fw	PROPN
ma-359	97	5	(	(	PUNCT
ma-359	97	6	s	s	NOUN
ma-359	97	7	)	)	PUNCT
ma-359	97	8	ds	ds	NOUN
ma-359	97	9	=	=	SYM
ma-359	97	10	1	1	NUM
ma-359	97	11	2	2	NUM
ma-359	97	12	+	+	CCONJ
ma-359	97	13	j.	j.	PROPN
ma-359	97	14	(	(	PUNCT
ma-359	97	15	4	4	NUM
ma-359	97	16	)	)	PUNCT
ma-359	97	17	for	for	ADP
ma-359	97	18	m	m	DET
ma-359	97	19	an	an	DET
ma-359	97	20	even	even	ADV
ma-359	97	21	positive	positive	ADJ
ma-359	97	22	integer	integer	NOUN
ma-359	97	23	>	>	X
ma-359	97	24	3	3	NUM
ma-359	97	25	,	,	PUNCT
ma-359	97	26	j	j	PROPN
ma-359	97	27	is	be	AUX
ma-359	97	28	given	give	VERB
ma-359	97	29	by	by	ADP
ma-359	97	30	j	j	PROPN
ma-359	97	31	=	=	SYM
ma-359	97	32	γ	γ	PROPN
ma-359	97	33	(	(	PUNCT
ma-359	97	34	m−1	m−1	PROPN
ma-359	97	35	2	2	NUM
ma-359	97	36	)	)	PUNCT
ma-359	97	37	w	w	NOUN
ma-359	97	38	4γ	4γ	NOUN
ma-359	97	39	(	(	PUNCT
ma-359	97	40	m	m	NOUN
ma-359	97	41	2	2	NUM
ma-359	97	42	)	)	PUNCT
ma-359	97	43	√	√	PROPN
ma-359	98	1	π	π	NOUN
ma-359	98	2	√	√	VERB
ma-359	98	3	1−	1−	NUM
ma-359	98	4	ρ2	ρ2	NOUN
ma-359	98	5	1f2	1f2	NUM
ma-359	98	6	(	(	PUNCT
ma-359	98	7	1	1	NUM
ma-359	98	8	2	2	NUM
ma-359	98	9	;	;	PUNCT
ma-359	98	10	3−m	3−m	NUM
ma-359	98	11	2	2	NUM
ma-359	98	12	,	,	PUNCT
ma-359	98	13	3	3	NUM
ma-359	98	14	2	2	NUM
ma-359	98	15	;	;	PUNCT
ma-359	98	16	w2	w2	NOUN
ma-359	98	17	c	c	PROPN
ma-359	98	18	)	)	PUNCT
ma-359	99	1	+	+	CCONJ
ma-359	99	2	γ	γ	X
ma-359	99	3	(	(	PUNCT
ma-359	99	4	1−m	1−m	NUM
ma-359	99	5	2	2	NUM
ma-359	99	6	)	)	PUNCT
ma-359	99	7	wm	wm	NOUN
ma-359	99	8	22mmγ	22mmγ	NOUN
ma-359	99	9	(	(	PUNCT
ma-359	99	10	m	m	PROPN
ma-359	99	11	2	2	NUM
ma-359	99	12	)	)	PUNCT
ma-359	99	13	√	√	PROPN
ma-359	99	14	π	π	PROPN
ma-359	99	15	(	(	PUNCT
ma-359	99	16	1−	1−	NUM
ma-359	99	17	ρ2	ρ2	NOUN
ma-359	99	18	)	)	PUNCT
ma-359	99	19	m	m	PROPN
ma-359	99	20	2	2	NUM
ma-359	99	21	1f2	1f2	NUM
ma-359	99	22	(	(	PUNCT
ma-359	99	23	m	m	PROPN
ma-359	99	24	2	2	NUM
ma-359	99	25	;	;	PUNCT
ma-359	99	26	m	m	VERB
ma-359	99	27	+	+	ADJ
ma-359	99	28	1	1	NUM
ma-359	99	29	2	2	NUM
ma-359	99	30	,	,	PUNCT
ma-359	99	31	m	m	VERB
ma-359	99	32	+	+	ADJ
ma-359	99	33	2	2	NUM
ma-359	99	34	2	2	NUM
ma-359	99	35	;	;	PUNCT
ma-359	99	36	w2	w2	NOUN
ma-359	99	37	c	c	PROPN
ma-359	99	38	)	)	PUNCT
ma-359	99	39	,	,	PUNCT
ma-359	99	40	where	where	SCONJ
ma-359	99	41	−1	−1	NOUN
ma-359	99	42	<	<	X
ma-359	99	43	ρ	ρ	X
ma-359	99	44	<	<	X
ma-359	99	45	1	1	NUM
ma-359	99	46	,	,	PUNCT
ma-359	99	47	1f2	1f2	NUM
ma-359	99	48	(	(	PUNCT
ma-359	99	49	w	w	NOUN
ma-359	99	50	)	)	PUNCT
ma-359	99	51	=	=	NOUN
ma-359	99	52	∑∞	∑∞	NOUN
ma-359	99	53	k=0	k=0	PROPN
ma-359	99	54	(	(	PUNCT
ma-359	99	55	a)k	a)k	X
ma-359	99	56	(	(	PUNCT
ma-359	99	57	b1)k(b2)k	b1)k(b2)k	NOUN
ma-359	99	58	wk	wk	X
ma-359	99	59	k	k	PROPN
ma-359	99	60	!	!	PROPN
ma-359	99	61	,	,	PUNCT
ma-359	99	62	and	and	CCONJ
ma-359	99	63	(	(	PUNCT
ma-359	99	64	γ)k	γ)k	X
ma-359	99	65	=	=	SYM
ma-359	99	66	γ(γ+k	γ(γ+k	NUM
ma-359	99	67	)	)	PUNCT
ma-359	99	68	γ(γ	γ(γ	NUM
ma-359	99	69	)	)	PUNCT
ma-359	99	70	,	,	PUNCT
ma-359	99	71	b1	b1	NOUN
ma-359	99	72	,	,	PUNCT
ma-359	99	73	b2	b2	PROPN
ma-359	99	74	6=	6=	NUM
ma-359	99	75	0,−1,−2	0,−1,−2	NUM
ma-359	99	76	,	,	PUNCT
ma-359	99	77	·	·	PUNCT
ma-359	99	78	·	·	PUNCT
ma-359	99	79	·	·	PUNCT
ma-359	99	80	.	.	PUNCT
ma-359	100	1	proof	proof	NOUN
ma-359	100	2	.	.	PUNCT
ma-359	101	1	first	first	ADV
ma-359	101	2	,	,	PUNCT
ma-359	101	3	observe	observe	VERB
ma-359	101	4	that	that	SCONJ
ma-359	101	5	by	by	ADP
ma-359	101	6	the	the	DET
ma-359	101	7	symmetry	symmetry	NOUN
ma-359	101	8	of	of	ADP
ma-359	101	9	the	the	DET
ma-359	101	10	pdf	pdf	NOUN
ma-359	101	11	in	in	ADP
ma-359	101	12	(	(	PUNCT
ma-359	101	13	2	2	NUM
ma-359	101	14	)	)	PUNCT
ma-359	101	15	,	,	PUNCT
ma-359	101	16	i	i	PRON
ma-359	101	17	=	=	NOUN
ma-359	101	18	1	1	NUM
ma-359	101	19	2	2	NUM
ma-359	101	20	.	.	PUNCT
ma-359	102	1	to	to	PART
ma-359	102	2	evaluate	evaluate	VERB
ma-359	102	3	j	j	PROPN
ma-359	102	4	,	,	PUNCT
ma-359	102	5	we	we	PRON
ma-359	102	6	use	use	VERB
ma-359	102	7	formula03.04.21.0014.01	formula03.04.21.0014.01	ADJ
ma-359	102	8	in	in	ADP
ma-359	102	9	[	[	X
ma-359	102	10	9	9	NUM
ma-359	102	11	]	]	PUNCT
ma-359	102	12	,	,	PUNCT
ma-359	102	13	namely,∫	namely,∫	NOUN
ma-359	102	14	zνkν	zνkν	NOUN
ma-359	102	15	(	(	PUNCT
ma-359	102	16	z	z	NOUN
ma-359	102	17	)	)	PUNCT
ma-359	102	18	dz	dz	PROPN
ma-359	102	19	=	=	PUNCT
ma-359	103	1	πz	πz	PROPN
ma-359	103	2	csc	csc	PROPN
ma-359	103	3	(	(	PUNCT
ma-359	103	4	νπ	νπ	NOUN
ma-359	103	5	)	)	PUNCT
ma-359	103	6	2ν+2	2ν+2	NUM
ma-359	103	7			NOUN
ma-359	103	8	4ν	4ν	NOUN
ma-359	104	1	√	√	NUM
ma-359	104	2	π	π	SYM
ma-359	104	3	1f̃2	1f̃2	PROPN
ma-359	104	4	(	(	PUNCT
ma-359	104	5	1	1	NUM
ma-359	104	6	2	2	NUM
ma-359	104	7	;	;	PUNCT
ma-359	104	8	1−	1−	NUM
ma-359	104	9	ν	ν	NOUN
ma-359	104	10	,	,	PUNCT
ma-359	104	11	3	3	NUM
ma-359	104	12	2	2	NUM
ma-359	104	13	;	;	PUNCT
ma-359	104	14	z	z	NOUN
ma-359	104	15	2	2	NUM
ma-359	104	16	4	4	NUM
ma-359	104	17	)	)	PUNCT
ma-359	104	18	−z2νγ	−z2νγ	NUM
ma-359	104	19	(	(	PUNCT
ma-359	104	20	ν	ν	X
ma-359	104	21	+	+	NOUN
ma-359	104	22	1	1	NUM
ma-359	104	23	2	2	NUM
ma-359	104	24	)	)	PUNCT
ma-359	104	25	1f̃2	1f̃2	PROPN
ma-359	104	26	(	(	PUNCT
ma-359	104	27	ν	ν	X
ma-359	104	28	+	+	NOUN
ma-359	104	29	1	1	NUM
ma-359	104	30	2	2	NUM
ma-359	104	31	;	;	PUNCT
ma-359	104	32	ν	ν	NOUN
ma-359	104	33	+	+	NOUN
ma-359	104	34	1	1	NUM
ma-359	104	35	,	,	PUNCT
ma-359	104	36	ν	ν	X
ma-359	104	37	+	+	NOUN
ma-359	104	38	3	3	NUM
ma-359	104	39	2	2	NUM
ma-359	104	40	;	;	PUNCT
ma-359	104	41	z	z	NOUN
ma-359	104	42	2	2	NUM
ma-359	104	43	4	4	NUM
ma-359	104	44	)	)	PUNCT
ma-359	104	45			PROPN
ma-359	104	46	,	,	PUNCT
ma-359	104	47	where	where	SCONJ
ma-359	104	48	1f̃2	1f̃2	PROPN
ma-359	104	49	(	(	PUNCT
ma-359	104	50	a	a	NOUN
ma-359	104	51	;	;	PUNCT
ma-359	104	52	b1	b1	NOUN
ma-359	104	53	,	,	PUNCT
ma-359	104	54	b2	b2	NOUN
ma-359	104	55	;	;	PUNCT
ma-359	104	56	z	z	X
ma-359	104	57	)	)	PUNCT
ma-359	104	58	:	:	PUNCT
ma-359	105	1	=	=	SYM
ma-359	105	2	1f2	1f2	NUM
ma-359	105	3	(	(	PUNCT
ma-359	105	4	a	a	NOUN
ma-359	105	5	;	;	PUNCT
ma-359	105	6	b1	b1	NOUN
ma-359	105	7	,	,	PUNCT
ma-359	105	8	b2	b2	NOUN
ma-359	105	9	;	;	PUNCT
ma-359	105	10	z	z	X
ma-359	105	11	)	)	PUNCT
ma-359	105	12	/	/	PUNCT
ma-359	105	13	(	(	PUNCT
ma-359	105	14	γ	γ	X
ma-359	105	15	(	(	PUNCT
ma-359	105	16	b1	b1	PROPN
ma-359	105	17	)	)	PUNCT
ma-359	105	18	γ	γ	PROPN
ma-359	105	19	(	(	PUNCT
ma-359	105	20	b2	b2	NOUN
ma-359	105	21	)	)	PUNCT
ma-359	105	22	)	)	PUNCT
ma-359	105	23	is	be	AUX
ma-359	105	24	the	the	DET
ma-359	105	25	regularized	regularize	VERB
ma-359	105	26	generalized	generalized	ADJ
ma-359	105	27	hyper	hyper	ADJ
ma-359	105	28	-	-	ADJ
ma-359	105	29	geometric	geometric	ADJ
ma-359	105	30	function	function	NOUN
ma-359	105	31	(	(	PUNCT
ma-359	105	32	rhgf	rhgf	NOUN
ma-359	105	33	)	)	PUNCT
ma-359	105	34	.	.	PUNCT
ma-359	106	1	then	then	ADV
ma-359	106	2	,	,	PUNCT
ma-359	106	3	it	it	PRON
ma-359	106	4	is	be	AUX
ma-359	106	5	straight	straight	ADV
ma-359	106	6	forward	forward	ADV
ma-359	106	7	to	to	PART
ma-359	106	8	show	show	VERB
ma-359	106	9	that	that	PRON
ma-359	106	10	j	j	PROPN
ma-359	106	11	=	=	SYM
ma-359	106	12	π	π	X
ma-359	106	13	csc	csc	PROPN
ma-359	106	14	(	(	PUNCT
ma-359	106	15	m−1	m−1	PROPN
ma-359	106	16	2	2	NUM
ma-359	106	17	π	π	NOUN
ma-359	106	18	)	)	PUNCT
ma-359	106	19	w	w	ADP
ma-359	106	20	23γ	23γ	NOUN
ma-359	106	21	(	(	PUNCT
ma-359	106	22	m	m	PROPN
ma-359	106	23	2	2	NUM
ma-359	106	24	)	)	PUNCT
ma-359	106	25	√	√	PROPN
ma-359	106	26	1−	1−	NUM
ma-359	106	27	ρ2	ρ2	PROPN
ma-359	106	28	1f̃2	1f̃2	PROPN
ma-359	106	29	(	(	PUNCT
ma-359	106	30	1	1	NUM
ma-359	106	31	2	2	NUM
ma-359	106	32	;	;	PUNCT
ma-359	106	33	3−m	3−m	NUM
ma-359	106	34	2	2	NUM
ma-359	106	35	,	,	PUNCT
ma-359	106	36	3	3	NUM
ma-359	106	37	2	2	NUM
ma-359	106	38	;	;	PUNCT
ma-359	106	39	w2	w2	NOUN
ma-359	106	40	c	c	PROPN
ma-359	106	41	)	)	PUNCT
ma-359	107	1	−	−	ADP
ma-359	108	1	√	√	NUM
ma-359	108	2	π	π	PROPN
ma-359	108	3	csc	csc	PROPN
ma-359	108	4	(	(	PUNCT
ma-359	108	5	m−1	m−1	PROPN
ma-359	108	6	2	2	NUM
ma-359	108	7	π	π	NOUN
ma-359	108	8	)	)	PUNCT
ma-359	108	9	wm	wm	PROPN
ma-359	108	10	22m+1	22m+1	PROPN
ma-359	108	11	(	(	PUNCT
ma-359	108	12	1−	1−	NUM
ma-359	108	13	ρ2	ρ2	NOUN
ma-359	108	14	)	)	PUNCT
ma-359	108	15	m	m	PROPN
ma-359	109	1	2	2	NUM
ma-359	109	2	1f̃2	1f̃2	NUM
ma-359	109	3	(	(	PUNCT
ma-359	109	4	m	m	PROPN
ma-359	109	5	2	2	NUM
ma-359	109	6	;	;	PUNCT
ma-359	109	7	m	m	VERB
ma-359	109	8	+	+	ADJ
ma-359	109	9	1	1	NUM
ma-359	109	10	2	2	NUM
ma-359	109	11	,	,	PUNCT
ma-359	109	12	m	m	VERB
ma-359	109	13	+	+	ADJ
ma-359	109	14	2	2	NUM
ma-359	109	15	2	2	NUM
ma-359	109	16	;	;	PUNCT
ma-359	109	17	w2	w2	NOUN
ma-359	109	18	c	c	PROPN
ma-359	109	19	)	)	PUNCT
ma-359	109	20	,	,	PUNCT
ma-359	109	21	where	where	SCONJ
ma-359	109	22	,	,	PUNCT
ma-359	109	23	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	109	24	eur	eur	PROPN
ma-359	109	25	.	.	PUNCT
ma-359	110	1	j.	j.	PROPN
ma-359	110	2	math	math	PROPN
ma-359	110	3	.	.	PUNCT
ma-359	111	1	anal	anal	PROPN
ma-359	111	2	.	.	PUNCT
ma-359	112	1	10.28924	10.28924	NUM
ma-359	112	2	/	/	SYM
ma-359	112	3	ada	ada	PROPN
ma-359	112	4	/	/	SYM
ma-359	112	5	ma.5.19	ma.5.19	NOUN
ma-359	112	6	5	5	NUM
ma-359	112	7	1f̃2	1f̃2	PROPN
ma-359	112	8	(	(	PUNCT
ma-359	112	9	1	1	NUM
ma-359	112	10	2	2	NUM
ma-359	112	11	;	;	PUNCT
ma-359	112	12	3−m	3−m	NUM
ma-359	112	13	2	2	NUM
ma-359	112	14	,	,	PUNCT
ma-359	112	15	3	3	NUM
ma-359	112	16	2	2	NUM
ma-359	112	17	;	;	PUNCT
ma-359	112	18	z	z	X
ma-359	112	19	)	)	PUNCT
ma-359	113	1	=	=	PUNCT
ma-359	114	1	∞∑	∞∑	NUM
ma-359	114	2	k=0	k=0	PROPN
ma-359	114	3	1	1	NUM
ma-359	114	4	√	√	PROPN
ma-359	114	5	π	π	PROPN
ma-359	114	6	(	(	PUNCT
ma-359	114	7	1	1	NUM
ma-359	114	8	2	2	NUM
ma-359	114	9	+	+	CCONJ
ma-359	114	10	k	k	NOUN
ma-359	114	11	)	)	PUNCT
ma-359	114	12	γ	γ	PROPN
ma-359	114	13	(	(	PUNCT
ma-359	114	14	3−m	3−m	NUM
ma-359	114	15	2	2	NUM
ma-359	114	16	+	+	NUM
ma-359	114	17	k	k	X
ma-359	114	18	)	)	PUNCT
ma-359	114	19	zk	zk	PROPN
ma-359	115	1	k	k	X
ma-359	115	2	!	!	PROPN
ma-359	115	3	,	,	PUNCT
ma-359	115	4	1f̃2	1f̃2	NUM
ma-359	115	5	(	(	PUNCT
ma-359	115	6	m	m	PROPN
ma-359	115	7	2	2	NUM
ma-359	115	8	;	;	PUNCT
ma-359	115	9	m	m	VERB
ma-359	115	10	+	+	ADJ
ma-359	115	11	1	1	NUM
ma-359	115	12	2	2	NUM
ma-359	115	13	,	,	PUNCT
ma-359	115	14	m	m	VERB
ma-359	115	15	+	+	ADJ
ma-359	115	16	2	2	NUM
ma-359	115	17	2	2	NUM
ma-359	115	18	;	;	PUNCT
ma-359	115	19	z	z	X
ma-359	115	20	)	)	PUNCT
ma-359	116	1	=	=	PUNCT
ma-359	117	1	∞∑	∞∑	NUM
ma-359	117	2	k=0	k=0	PROPN
ma-359	117	3	1	1	NUM
ma-359	117	4	(	(	PUNCT
ma-359	117	5	m	m	PROPN
ma-359	117	6	2	2	NUM
ma-359	117	7	+	+	CCONJ
ma-359	117	8	k	k	NOUN
ma-359	117	9	)	)	PUNCT
ma-359	117	10	γ	γ	PROPN
ma-359	117	11	(	(	PUNCT
ma-359	117	12	m	m	PROPN
ma-359	117	13	2	2	NUM
ma-359	117	14	)	)	PUNCT
ma-359	117	15	γ	γ	NOUN
ma-359	117	16	(	(	PUNCT
ma-359	117	17	m+1	m+1	NUM
ma-359	117	18	2	2	NUM
ma-359	117	19	+	+	CCONJ
ma-359	117	20	k	k	X
ma-359	117	21	)	)	PUNCT
ma-359	117	22	zk	zk	PROPN
ma-359	117	23	k	k	PROPN
ma-359	117	24	!	!	PUNCT
ma-359	117	25	;	;	PUNCT
ma-359	117	26	are	be	AUX
ma-359	117	27	the	the	DET
ma-359	117	28	rhgfs	rhgfs	NOUN
ma-359	117	29	defined	define	VERB
ma-359	117	30	for	for	ADP
ma-359	117	31	all	all	DET
ma-359	117	32	z	z	PROPN
ma-359	117	33	∈	∈	PROPN
ma-359	117	34	c.	c.	NOUN
ma-359	117	35	note	note	VERB
ma-359	117	36	that	that	SCONJ
ma-359	117	37	for	for	ADP
ma-359	117	38	m	m	VERB
ma-359	117	39	even	even	ADV
ma-359	117	40	,	,	PUNCT
ma-359	117	41	the	the	DET
ma-359	117	42	limz→0	limz→0	PROPN
ma-359	117	43	j	j	PROPN
ma-359	117	44	=	=	SYM
ma-359	117	45	0	0	PUNCT
ma-359	118	1	=	=	SYM
ma-359	118	2	j	j	PROPN
ma-359	118	3	(	(	PUNCT
ma-359	118	4	0	0	NUM
ma-359	118	5	)	)	PUNCT
ma-359	118	6	.using	.use	VERB
ma-359	118	7	euler	euler	PROPN
ma-359	118	8	’s	’s	PART
ma-359	118	9	reflection	reflection	NOUN
ma-359	118	10	formula	formula	NOUN
ma-359	118	11	(	(	PUNCT
ma-359	118	12	γ	γ	X
ma-359	118	13	(	(	PUNCT
ma-359	118	14	1−	1−	NUM
ma-359	118	15	z	z	NOUN
ma-359	118	16	)	)	PUNCT
ma-359	118	17	γ	γ	PROPN
ma-359	118	18	(	(	PUNCT
ma-359	118	19	z	z	NOUN
ma-359	118	20	)	)	PUNCT
ma-359	118	21	=	=	PUNCT
ma-359	119	1	π	π	X
ma-359	119	2	sinπz	sinπz	NOUN
ma-359	119	3	,	,	PUNCT
ma-359	119	4	z	z	PROPN
ma-359	119	5	=	=	SYM
ma-359	119	6	m−1	m−1	PROPN
ma-359	119	7	2	2	NUM
ma-359	119	8	,	,	PUNCT
ma-359	119	9	which	which	PRON
ma-359	119	10	is	be	AUX
ma-359	119	11	not	not	PART
ma-359	119	12	an	an	DET
ma-359	119	13	integer	integer	NOUN
ma-359	119	14	when	when	SCONJ
ma-359	119	15	m	m	PROPN
ma-359	119	16	is	be	AUX
ma-359	119	17	even	even	ADV
ma-359	119	18	)	)	PUNCT
ma-359	119	19	,	,	PUNCT
ma-359	119	20	we	we	PRON
ma-359	119	21	obtain	obtain	VERB
ma-359	119	22	j	j	PROPN
ma-359	119	23	=	=	SYM
ma-359	119	24	γ	γ	X
ma-359	119	25	(	(	PUNCT
ma-359	119	26	3−m	3−m	NUM
ma-359	119	27	2	2	NUM
ma-359	119	28	)	)	PUNCT
ma-359	119	29	γ	γ	NOUN
ma-359	119	30	(	(	PUNCT
ma-359	119	31	m−1	m−1	PROPN
ma-359	119	32	2	2	NUM
ma-359	119	33	)	)	PUNCT
ma-359	119	34	23γ	23γ	NUM
ma-359	119	35	(	(	PUNCT
ma-359	119	36	m	m	PROPN
ma-359	119	37	2	2	NUM
ma-359	119	38	)	)	PUNCT
ma-359	119	39	√	√	PROPN
ma-359	119	40	1−	1−	NUM
ma-359	119	41	ρ2	ρ2	PROPN
ma-359	119	42	w	w	PROPN
ma-359	119	43	1f̃2	1f̃2	PROPN
ma-359	119	44	(	(	PUNCT
ma-359	119	45	1	1	NUM
ma-359	119	46	2	2	NUM
ma-359	119	47	;	;	PUNCT
ma-359	119	48	3−m	3−m	NUM
ma-359	119	49	2	2	NUM
ma-359	119	50	,	,	PUNCT
ma-359	119	51	3	3	NUM
ma-359	119	52	2	2	NUM
ma-359	119	53	;	;	PUNCT
ma-359	119	54	w2	w2	PROPN
ma-359	119	55	c	c	PROPN
ma-359	119	56	)	)	PUNCT
ma-359	119	57	−	−	PROPN
ma-359	119	58	γ	γ	X
ma-359	119	59	(	(	PUNCT
ma-359	119	60	3−m	3−m	NUM
ma-359	119	61	2	2	NUM
ma-359	119	62	)	)	PUNCT
ma-359	119	63	γ	γ	NOUN
ma-359	119	64	(	(	PUNCT
ma-359	119	65	m−1	m−1	PROPN
ma-359	119	66	2	2	NUM
ma-359	119	67	)	)	PUNCT
ma-359	119	68	22m+1	22m+1	NUM
ma-359	119	69	√	√	NUM
ma-359	119	70	π	π	PROPN
ma-359	119	71	(	(	PUNCT
ma-359	119	72	1−	1−	NUM
ma-359	119	73	ρ2	ρ2	NOUN
ma-359	119	74	)	)	PUNCT
ma-359	119	75	m	m	PROPN
ma-359	119	76	2	2	NUM
ma-359	119	77	wm	wm	NUM
ma-359	119	78	1f̃2	1f̃2	PROPN
ma-359	119	79	(	(	PUNCT
ma-359	119	80	m	m	PROPN
ma-359	119	81	2	2	NUM
ma-359	119	82	;	;	PUNCT
ma-359	119	83	m	m	VERB
ma-359	119	84	+	+	ADJ
ma-359	119	85	1	1	NUM
ma-359	119	86	2	2	NUM
ma-359	119	87	,	,	PUNCT
ma-359	119	88	m	m	VERB
ma-359	119	89	+	+	ADJ
ma-359	119	90	2	2	NUM
ma-359	119	91	2	2	NUM
ma-359	119	92	;	;	PUNCT
ma-359	119	93	w2	w2	NOUN
ma-359	119	94	c	c	PROPN
ma-359	119	95	)	)	PUNCT
ma-359	119	96	.	.	PUNCT
ma-359	120	1	then	then	ADV
ma-359	120	2	using	use	VERB
ma-359	120	3	γ	γ	X
ma-359	120	4	(	(	PUNCT
ma-359	120	5	1	1	NUM
ma-359	120	6	+	+	CCONJ
ma-359	120	7	z	z	NOUN
ma-359	120	8	)	)	PUNCT
ma-359	120	9	=	=	SYM
ma-359	120	10	zγ	zγ	PROPN
ma-359	120	11	(	(	PUNCT
ma-359	120	12	z	z	NOUN
ma-359	120	13	)	)	PUNCT
ma-359	120	14	,	,	PUNCT
ma-359	120	15	the	the	DET
ma-359	120	16	j	j	PROPN
ma-359	120	17	given	give	VERB
ma-359	120	18	in	in	ADP
ma-359	120	19	the	the	DET
ma-359	120	20	theorem	theorem	NOUN
ma-359	120	21	follows	follow	VERB
ma-359	120	22	.	.	PUNCT
ma-359	121	1	�	�	PROPN
ma-359	121	2	note	note	VERB
ma-359	121	3	that	that	SCONJ
ma-359	121	4	the	the	DET
ma-359	121	5	integral	integral	ADJ
ma-359	121	6	i	i	NOUN
ma-359	121	7	=	=	PUNCT
ma-359	121	8	∫	∫	PROPN
ma-359	121	9	w	w	PROPN
ma-359	121	10	−∞	−∞	PROPN
ma-359	121	11	fw	fw	PROPN
ma-359	121	12	(	(	PUNCT
ma-359	121	13	w	w	NOUN
ma-359	121	14	)	)	PUNCT
ma-359	121	15	dw	dw	NOUN
ma-359	121	16	for	for	ADP
ma-359	121	17	re	re	PROPN
ma-359	121	18	(	(	PUNCT
ma-359	121	19	w	w	NOUN
ma-359	121	20	)	)	PUNCT
ma-359	121	21	<	<	X
ma-359	121	22	0	0	NUM
ma-359	121	23	,	,	PUNCT
ma-359	121	24	and	and	CCONJ
ma-359	121	25	even	even	ADV
ma-359	121	26	m	m	PROPN
ma-359	121	27	>	>	X
ma-359	121	28	0	0	NUM
ma-359	121	29	,	,	PUNCT
ma-359	121	30	evaluates	evaluate	VERB
ma-359	121	31	to	to	ADP
ma-359	121	32	i	i	PRON
ma-359	121	33	=	=	NOUN
ma-359	121	34	1	1	NUM
ma-359	121	35	2	2	NUM
ma-359	121	36	+	+	CCONJ
ma-359	121	37	γ	γ	X
ma-359	121	38	(	(	PUNCT
ma-359	121	39	m−1	m−1	PROPN
ma-359	121	40	2	2	NUM
ma-359	121	41	)	)	PUNCT
ma-359	121	42	w	w	NOUN
ma-359	121	43	4γ	4γ	NOUN
ma-359	121	44	(	(	PUNCT
ma-359	121	45	m	m	NOUN
ma-359	121	46	2	2	NUM
ma-359	121	47	)	)	PUNCT
ma-359	121	48	√	√	PROPN
ma-359	122	1	π	π	NOUN
ma-359	122	2	√	√	VERB
ma-359	122	3	1−	1−	NUM
ma-359	122	4	ρ2	ρ2	NOUN
ma-359	122	5	1f2	1f2	NUM
ma-359	122	6	(	(	PUNCT
ma-359	122	7	1	1	NUM
ma-359	122	8	2	2	NUM
ma-359	122	9	;	;	PUNCT
ma-359	122	10	3−m	3−m	NUM
ma-359	122	11	2	2	NUM
ma-359	122	12	,	,	PUNCT
ma-359	122	13	3	3	NUM
ma-359	122	14	2	2	NUM
ma-359	122	15	;	;	PUNCT
ma-359	122	16	w2	w2	PROPN
ma-359	122	17	c	c	PROPN
ma-359	122	18	)	)	PUNCT
ma-359	123	1	−	−	PROPN
ma-359	123	2	γ	γ	X
ma-359	123	3	(	(	PUNCT
ma-359	123	4	1−m	1−m	NUM
ma-359	123	5	2	2	NUM
ma-359	123	6	)	)	PUNCT
ma-359	123	7	(	(	PUNCT
ma-359	123	8	−w)m	−w)m	NOUN
ma-359	123	9	22mmγ	22mmγ	NOUN
ma-359	123	10	(	(	PUNCT
ma-359	123	11	m	m	NOUN
ma-359	123	12	2	2	NUM
ma-359	123	13	)	)	PUNCT
ma-359	123	14	√	√	PROPN
ma-359	123	15	π	π	PROPN
ma-359	123	16	(	(	PUNCT
ma-359	123	17	1−	1−	NUM
ma-359	123	18	ρ2	ρ2	NOUN
ma-359	123	19	)	)	PUNCT
ma-359	123	20	m	m	PROPN
ma-359	123	21	2	2	NUM
ma-359	123	22	1f2	1f2	NUM
ma-359	123	23	(	(	PUNCT
ma-359	123	24	m	m	PROPN
ma-359	123	25	2	2	NUM
ma-359	123	26	;	;	PUNCT
ma-359	123	27	m	m	VERB
ma-359	123	28	+	+	ADJ
ma-359	123	29	1	1	NUM
ma-359	123	30	2	2	NUM
ma-359	123	31	,	,	PUNCT
ma-359	123	32	m	m	VERB
ma-359	123	33	+	+	ADJ
ma-359	123	34	2	2	NUM
ma-359	123	35	2	2	NUM
ma-359	123	36	;	;	PUNCT
ma-359	123	37	w2	w2	NOUN
ma-359	123	38	c	c	PROPN
ma-359	123	39	)	)	PUNCT
ma-359	123	40	.	.	PUNCT
ma-359	124	1	(	(	PUNCT
ma-359	124	2	5	5	X
ma-359	124	3	)	)	PUNCT
ma-359	124	4	figure	figure	NOUN
ma-359	124	5	2	2	NUM
ma-359	124	6	shows	show	VERB
ma-359	124	7	plots	plot	NOUN
ma-359	124	8	for	for	ADP
ma-359	124	9	the	the	DET
ma-359	124	10	cdf	cdf	PROPN
ma-359	124	11	fw	fw	PROPN
ma-359	124	12	(	(	PUNCT
ma-359	124	13	w	w	NOUN
ma-359	124	14	)	)	PUNCT
ma-359	124	15	by	by	ADP
ma-359	124	16	eq.(4	eq.(4	ADJ
ma-359	124	17	)	)	PUNCT
ma-359	124	18	.	.	PUNCT
ma-359	125	1	figure	figure	NOUN
ma-359	125	2	2	2	NUM
ma-359	125	3	.	.	PUNCT
ma-359	126	1	the	the	DET
ma-359	126	2	cdf	cdf	PROPN
ma-359	126	3	fw	fw	PROPN
ma-359	126	4	(	(	PUNCT
ma-359	126	5	w	w	NOUN
ma-359	126	6	)	)	PUNCT
ma-359	126	7	for	for	ADP
ma-359	126	8	m	m	PROPN
ma-359	126	9	=	=	SYM
ma-359	126	10	4	4	NUM
ma-359	126	11	,	,	PUNCT
ma-359	126	12	16	16	NUM
ma-359	126	13	,	,	PUNCT
ma-359	126	14	and	and	CCONJ
ma-359	126	15	ρ	ρ	NUM
ma-359	126	16	=	=	SYM
ma-359	126	17	0.7	0.7	NUM
ma-359	126	18	,	,	PUNCT
ma-359	126	19	0.9	0.9	NUM
ma-359	126	20	.	.	PUNCT
ma-359	127	1	the	the	DET
ma-359	127	2	cdf	cdf	PROPN
ma-359	127	3	for	for	ADP
ma-359	127	4	the	the	DET
ma-359	127	5	difference	difference	NOUN
ma-359	127	6	w	w	NOUN
ma-359	127	7	of	of	ADP
ma-359	127	8	two	two	NUM
ma-359	127	9	dependent	dependent	ADJ
ma-359	127	10	central	central	ADJ
ma-359	127	11	chi	chi	NOUN
ma-359	127	12	square	square	ADJ
ma-359	127	13	random	random	ADJ
ma-359	127	14	variables	variable	NOUN
ma-359	127	15	with	with	ADP
ma-359	127	16	2	2	NUM
ma-359	127	17	m	m	NOUN
ma-359	127	18	degreesof	degreesof	NOUN
ma-359	127	19	freedom	freedom	NOUN
ma-359	127	20	is	be	AUX
ma-359	127	21	reported	report	VERB
ma-359	127	22	in	in	ADP
ma-359	127	23	(	(	PUNCT
ma-359	127	24	[	[	X
ma-359	127	25	6	6	NUM
ma-359	127	26	]	]	PUNCT
ma-359	127	27	,	,	PUNCT
ma-359	127	28	p.	p.	NOUN
ma-359	127	29	30	30	NUM
ma-359	127	30	)	)	PUNCT
ma-359	127	31	(	(	PUNCT
ma-359	127	32	for	for	ADP
ma-359	127	33	σ2	σ2	PROPN
ma-359	127	34	1	1	NUM
ma-359	127	35	=	=	SYM
ma-359	127	36	σ2	σ2	PROPN
ma-359	127	37	2	2	NUM
ma-359	127	38	=	=	SYM
ma-359	127	39	1	1	NUM
ma-359	127	40	)	)	PUNCT
ma-359	127	41	as	as	ADP
ma-359	127	42	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	127	43	eur	eur	PROPN
ma-359	127	44	.	.	PUNCT
ma-359	128	1	j.	j.	PROPN
ma-359	128	2	math	math	PROPN
ma-359	128	3	.	.	PUNCT
ma-359	129	1	anal	anal	PROPN
ma-359	129	2	.	.	PUNCT
ma-359	130	1	10.28924	10.28924	NUM
ma-359	130	2	/	/	SYM
ma-359	130	3	ada	ada	PROPN
ma-359	130	4	/	/	SYM
ma-359	130	5	ma.5.19	ma.5.19	NOUN
ma-359	130	6	6	6	NUM
ma-359	130	7	pw	pw	NOUN
ma-359	130	8	(	(	PUNCT
ma-359	130	9	w	w	NOUN
ma-359	130	10	)	)	PUNCT
ma-359	130	11	=	=	SYM
ma-359	130	12			X
ma-359	130	13	(	(	PUNCT
ma-359	130	14	1−ρ2	1−ρ2	NUM
ma-359	130	15	)	)	PUNCT
ma-359	130	16	m	m	VERB
ma-359	130	17	2	2	NUM
ma-359	130	18	22m(m−1	22m(m−1	NUM
ma-359	130	19	)	)	PUNCT
ma-359	130	20	!	!	PUNCT
ma-359	131	1	exp	exp	NOUN
ma-359	131	2	(	(	PUNCT
ma-359	131	3	w	w	PROPN
ma-359	131	4	2	2	NUM
ma-359	131	5	√	√	NUM
ma-359	131	6	1−ρ2	1−ρ2	NUM
ma-359	131	7	)	)	PUNCT
ma-359	131	8	∑m−1	∑m−1	NOUN
ma-359	131	9	i=0	i=0	PROPN
ma-359	131	10	∑m−i−1	∑m−i−1	PROPN
ma-359	131	11	l=0	l=0	PROPN
ma-359	131	12	(	(	PUNCT
ma-359	131	13	m+i−1)!(1−ρ2	m+i−1)!(1−ρ2	NOUN
ma-359	131	14	)	)	PUNCT
ma-359	131	15	i+l+1	i+l+1	PROPN
ma-359	131	16	2l+1	2l+1	PROPN
ma-359	131	17	i!(m−i−l−1)!l	i!(m−i−l−1)!l	PROPN
ma-359	131	18	!	!	PUNCT
ma-359	132	1	(	(	PUNCT
ma-359	132	2	−w)m−i−l−1	−w)m−i−l−1	PROPN
ma-359	132	3	,	,	PUNCT
ma-359	132	4	w	w	ADP
ma-359	132	5	<	<	X
ma-359	132	6	0	0	NUM
ma-359	132	7	1−	1−	NUM
ma-359	132	8	(	(	PUNCT
ma-359	132	9	1−ρ2	1−ρ2	NUM
ma-359	132	10	)	)	PUNCT
ma-359	132	11	m	m	VERB
ma-359	132	12	2	2	NUM
ma-359	132	13	22m(m−1	22m(m−1	NUM
ma-359	132	14	)	)	PUNCT
ma-359	132	15	!	!	PUNCT
ma-359	133	1	exp	exp	NOUN
ma-359	133	2	(	(	PUNCT
ma-359	133	3	−	−	PROPN
ma-359	133	4	w	w	PROPN
ma-359	133	5	2	2	NUM
ma-359	133	6	√	√	NUM
ma-359	133	7	1−ρ2	1−ρ2	NUM
ma-359	133	8	)	)	PUNCT
ma-359	133	9	∑m−1	∑m−1	NOUN
ma-359	133	10	i=0	i=0	PROPN
ma-359	133	11	∑m−i−1	∑m−i−1	PROPN
ma-359	133	12	l=0	l=0	PROPN
ma-359	133	13	(	(	PUNCT
ma-359	133	14	m+i−1)!(1−ρ2	m+i−1)!(1−ρ2	NOUN
ma-359	133	15	)	)	PUNCT
ma-359	133	16	i+l+1	i+l+1	PROPN
ma-359	133	17	2l+1	2l+1	PROPN
ma-359	133	18	i!(m−i−l−1)!l	i!(m−i−l−1)!l	PROPN
ma-359	133	19	!	!	PUNCT
ma-359	134	1	(	(	PUNCT
ma-359	134	2	w)m−i−l−1	w)m−i−l−1	X
ma-359	134	3	,	,	PUNCT
ma-359	134	4	w	w	PROPN
ma-359	134	5	≥	≥	NOUN
ma-359	134	6	0	0	NUM
ma-359	135	1			PROPN
ma-359	135	2	comparing	compare	VERB
ma-359	135	3	this	this	DET
ma-359	135	4	cdf	cdf	NOUN
ma-359	135	5	with	with	ADP
ma-359	135	6	the	the	DET
ma-359	135	7	cdf	cdf	PROPN
ma-359	135	8	in	in	ADP
ma-359	135	9	(	(	PUNCT
ma-359	135	10	4	4	NUM
ma-359	135	11	)	)	PUNCT
ma-359	135	12	,	,	PUNCT
ma-359	135	13	we	we	PRON
ma-359	135	14	have	have	AUX
ma-359	135	15	noticed	notice	VERB
ma-359	135	16	that	that	SCONJ
ma-359	135	17	there	there	PRON
ma-359	135	18	were	be	VERB
ma-359	135	19	discrepancies	discrepancy	NOUN
ma-359	135	20	between	between	ADP
ma-359	135	21	thetwo	thetwo	NUM
ma-359	135	22	cdfs	cdfs	PROPN
ma-359	135	23	.	.	PUNCT
ma-359	136	1	for	for	ADP
ma-359	136	2	example	example	NOUN
ma-359	136	3	,	,	PUNCT
ma-359	136	4	in	in	ADP
ma-359	136	5	figure	figure	NOUN
ma-359	136	6	3	3	NUM
ma-359	136	7	the	the	DET
ma-359	136	8	plots	plot	NOUN
ma-359	136	9	of	of	ADP
ma-359	136	10	the	the	DET
ma-359	136	11	cdf	cdf	PROPN
ma-359	136	12	fw	fw	PROPN
ma-359	136	13	(	(	PUNCT
ma-359	136	14	w	w	NOUN
ma-359	136	15	)	)	PUNCT
ma-359	136	16	and	and	CCONJ
ma-359	136	17	the	the	DET
ma-359	136	18	cdf	cdf	PROPN
ma-359	136	19	pw	pw	PROPN
ma-359	136	20	(	(	PUNCT
ma-359	136	21	w	w	NOUN
ma-359	136	22	)	)	PUNCT
ma-359	136	23	are	be	AUX
ma-359	136	24	displayedfor	displayedfor	ADP
ma-359	136	25	ρ	ρ	PROPN
ma-359	136	26	=	=	SYM
ma-359	136	27	0.7	0.7	NUM
ma-359	136	28	,	,	PUNCT
ma-359	136	29	where	where	SCONJ
ma-359	136	30	m	m	VERB
ma-359	136	31	=	=	SYM
ma-359	136	32	2	2	NUM
ma-359	136	33	is	be	AUX
ma-359	136	34	used	use	VERB
ma-359	136	35	in	in	ADP
ma-359	136	36	pw	pw	PROPN
ma-359	136	37	(	(	PUNCT
ma-359	136	38	w	w	NOUN
ma-359	136	39	)	)	PUNCT
ma-359	136	40	,	,	PUNCT
ma-359	136	41	and	and	CCONJ
ma-359	136	42	m	m	VERB
ma-359	136	43	=	=	NOUN
ma-359	136	44	4	4	NUM
ma-359	136	45	is	be	AUX
ma-359	136	46	used	use	VERB
ma-359	136	47	in	in	ADP
ma-359	136	48	fw	fw	PROPN
ma-359	136	49	(	(	PUNCT
ma-359	136	50	w	w	NOUN
ma-359	136	51	)	)	PUNCT
ma-359	136	52	(	(	PUNCT
ma-359	136	53	that	that	ADV
ma-359	136	54	is	is	ADV
ma-359	136	55	,	,	PUNCT
ma-359	136	56	the	the	DET
ma-359	136	57	degreesof	degreesof	NOUN
ma-359	136	58	freedom	freedom	NOUN
ma-359	136	59	equal	equal	ADJ
ma-359	136	60	4	4	NUM
ma-359	136	61	)	)	PUNCT
ma-359	136	62	.	.	PUNCT
ma-359	137	1	figure	figure	VERB
ma-359	137	2	3	3	NUM
ma-359	137	3	.	.	NOUN
ma-359	137	4	comparison	comparison	NOUN
ma-359	137	5	of	of	ADP
ma-359	137	6	the	the	DET
ma-359	137	7	cdfs	cdfs	PROPN
ma-359	137	8	pw	pw	PROPN
ma-359	137	9	(	(	PUNCT
ma-359	137	10	w	w	NOUN
ma-359	137	11	)	)	PUNCT
ma-359	137	12	and	and	CCONJ
ma-359	137	13	fw	fw	PROPN
ma-359	137	14	(	(	PUNCT
ma-359	137	15	w	w	NOUN
ma-359	137	16	)	)	PUNCT
ma-359	137	17	for	for	ADP
ma-359	137	18	ρ	ρ	PROPN
ma-359	137	19	=	=	SYM
ma-359	137	20	0.7	0.7	NUM
ma-359	137	21	and	and	CCONJ
ma-359	137	22	degrees	degree	NOUN
ma-359	137	23	offreedom	offreedom	ADJ
ma-359	137	24	4	4	NUM
ma-359	137	25	.	.	PUNCT
ma-359	138	1	in	in	ADP
ma-359	138	2	order	order	NOUN
ma-359	138	3	to	to	PART
ma-359	138	4	determine	determine	VERB
ma-359	138	5	the	the	DET
ma-359	138	6	source	source	NOUN
ma-359	138	7	of	of	ADP
ma-359	138	8	this	this	DET
ma-359	138	9	discrepancy	discrepancy	NOUN
ma-359	138	10	,	,	PUNCT
ma-359	138	11	we	we	PRON
ma-359	138	12	examine	examine	VERB
ma-359	138	13	the	the	DET
ma-359	138	14	derivation	derivation	NOUN
ma-359	138	15	of	of	ADP
ma-359	138	16	pw	pw	PROPN
ma-359	138	17	(	(	PUNCT
ma-359	138	18	w	w	NOUN
ma-359	138	19	)	)	PUNCT
ma-359	138	20	for	for	ADP
ma-359	138	21	w	w	NOUN
ma-359	138	22	<	<	X
ma-359	138	23	0.this	0.this	X
ma-359	138	24	is	be	AUX
ma-359	138	25	enough	enough	ADJ
ma-359	138	26	,	,	PUNCT
ma-359	138	27	as	as	ADP
ma-359	138	28	for	for	ADP
ma-359	138	29	a	a	DET
ma-359	138	30	symmetric	symmetric	ADJ
ma-359	138	31	density	density	NOUN
ma-359	138	32	function	function	NOUN
ma-359	138	33	about	about	ADP
ma-359	138	34	the	the	DET
ma-359	138	35	y	y	NOUN
ma-359	138	36	-	-	PUNCT
ma-359	138	37	axis	axis	NOUN
ma-359	138	38	one	one	NOUN
ma-359	138	39	has	have	VERB
ma-359	138	40	f	f	PROPN
ma-359	138	41	(	(	PUNCT
ma-359	138	42	x	x	NOUN
ma-359	138	43	)	)	PUNCT
ma-359	138	44	=	=	SYM
ma-359	139	1	1	1	NUM
ma-359	139	2	−	−	PROPN
ma-359	139	3	f	f	X
ma-359	139	4	(	(	PUNCT
ma-359	139	5	−x).this	−x).this	DET
ma-359	139	6	formula	formula	NOUN
ma-359	139	7	was	be	AUX
ma-359	139	8	employed	employ	VERB
ma-359	139	9	in	in	ADP
ma-359	139	10	[	[	X
ma-359	139	11	6	6	NUM
ma-359	139	12	]	]	PUNCT
ma-359	139	13	for	for	ADP
ma-359	139	14	his	his	PRON
ma-359	139	15	piecewise	piecewise	NOUN
ma-359	139	16	presentation	presentation	NOUN
ma-359	139	17	of	of	ADP
ma-359	139	18	pw	pw	PROPN
ma-359	139	19	(	(	PUNCT
ma-359	139	20	w	w	NOUN
ma-359	139	21	)	)	PUNCT
ma-359	139	22	.	.	PUNCT
ma-359	140	1	to	to	PART
ma-359	140	2	start	start	VERB
ma-359	140	3	with	with	ADP
ma-359	140	4	,	,	PUNCT
ma-359	140	5	consider	consider	VERB
ma-359	140	6	the	the	DET
ma-359	140	7	following	follow	VERB
ma-359	140	8	integral∫	integral∫	NOUN
ma-359	140	9	w	w	NOUN
ma-359	140	10	−∞	−∞	PROPN
ma-359	140	11	(	(	PUNCT
ma-359	140	12	−y)m−i−1	−y)m−i−1	PROPN
ma-359	140	13	e	e	PROPN
ma-359	140	14	y	y	PROPN
ma-359	140	15	a	a	DET
ma-359	140	16	dy	dy	X
ma-359	140	17	=	=	SYM
ma-359	140	18	am−iγ(m	am−iγ(m	PROPN
ma-359	141	1	−	−	NOUN
ma-359	142	1	i	i	PRON
ma-359	142	2	,	,	PUNCT
ma-359	142	3	−	−	PROPN
ma-359	142	4	w	w	NOUN
ma-359	142	5	a	a	PRON
ma-359	142	6	)	)	PUNCT
ma-359	142	7	,	,	PUNCT
ma-359	142	8	re	re	X
ma-359	142	9	(	(	PUNCT
ma-359	142	10	w	w	NOUN
ma-359	142	11	)	)	PUNCT
ma-359	142	12	<	<	X
ma-359	142	13	0	0	NUM
ma-359	142	14	,	,	PUNCT
ma-359	142	15	where	where	SCONJ
ma-359	142	16	a	a	DET
ma-359	142	17	=	=	SYM
ma-359	142	18	2	2	NUM
ma-359	142	19	√	√	NUM
ma-359	142	20	1−	1−	NUM
ma-359	142	21	ρ2	ρ2	NOUN
ma-359	142	22	,	,	PUNCT
ma-359	142	23	and	and	CCONJ
ma-359	142	24	γ[n	γ[n	NUM
ma-359	142	25	,	,	PUNCT
ma-359	142	26	x	x	X
ma-359	142	27	]	]	X
ma-359	142	28	is	be	AUX
ma-359	142	29	the	the	DET
ma-359	142	30	upper	upper	ADJ
ma-359	142	31	(	(	PUNCT
ma-359	142	32	or	or	CCONJ
ma-359	142	33	complementary	complementary	ADJ
ma-359	142	34	)	)	PUNCT
ma-359	142	35	incomplete	incomplete	ADJ
ma-359	142	36	gamma	gamma	NOUN
ma-359	142	37	function	function	PROPN
ma-359	142	38	.	.	PUNCT
ma-359	143	1	foran	foran	PROPN
ma-359	143	2	integer	integer	PROPN
ma-359	143	3	n	n	CCONJ
ma-359	143	4	,	,	PUNCT
ma-359	143	5	the	the	DET
ma-359	143	6	expansion	expansion	NOUN
ma-359	143	7	γ(n	γ(n	NOUN
ma-359	143	8	,	,	PUNCT
ma-359	143	9	x	x	X
ma-359	143	10	)	)	PUNCT
ma-359	143	11	=	=	SYM
ma-359	143	12	(	(	PUNCT
ma-359	143	13	n	n	CCONJ
ma-359	143	14	−	−	PROPN
ma-359	143	15	1)!e−x	1)!e−x	NUM
ma-359	143	16	∑n−1	∑n−1	ADP
ma-359	143	17	k=0	k=0	PROPN
ma-359	143	18	xk	xk	PROPN
ma-359	144	1	k	k	PROPN
ma-359	144	2	!	!	PROPN
ma-359	144	3	is	be	AUX
ma-359	144	4	given	give	VERB
ma-359	144	5	in	in	ADP
ma-359	144	6	[	[	X
ma-359	144	7	7	7	NUM
ma-359	144	8	]	]	PUNCT
ma-359	144	9	.	.	PUNCT
ma-359	145	1	therefore	therefore	ADV
ma-359	145	2	,	,	PUNCT
ma-359	145	3	the	the	PRON
ma-359	145	4	correctionof	correctionof	NOUN
ma-359	145	5	the	the	DET
ma-359	145	6	cdf	cdf	PROPN
ma-359	145	7	in	in	ADP
ma-359	145	8	the	the	DET
ma-359	145	9	notation	notation	NOUN
ma-359	145	10	given	give	VERB
ma-359	145	11	in	in	ADP
ma-359	145	12	[	[	X
ma-359	145	13	6	6	NUM
ma-359	145	14	]	]	PUNCT
ma-359	145	15	,	,	PUNCT
ma-359	145	16	for	for	ADP
ma-359	145	17	w	w	PROPN
ma-359	145	18	<	<	X
ma-359	145	19	0	0	NUM
ma-359	145	20	,	,	PUNCT
ma-359	145	21	can	can	AUX
ma-359	145	22	be	be	AUX
ma-359	145	23	written	write	VERB
ma-359	145	24	as	as	ADP
ma-359	145	25	pw	pw	PROPN
ma-359	145	26	(	(	PUNCT
ma-359	145	27	w	w	NOUN
ma-359	145	28	)	)	PUNCT
ma-359	145	29	=	=	SYM
ma-359	145	30	1	1	NUM
ma-359	145	31	2	2	NUM
ma-359	145	32	m	m	VERB
ma-359	145	33	(	(	PUNCT
ma-359	145	34	m	m	NOUN
ma-359	145	35	−	−	NOUN
ma-359	145	36	1	1	NUM
ma-359	145	37	)	)	PUNCT
ma-359	145	38	!	!	PUNCT
ma-359	146	1	exp	exp	NOUN
ma-359	146	2	(	(	PUNCT
ma-359	146	3	w	w	PROPN
ma-359	146	4	2	2	NUM
ma-359	146	5	√	√	NUM
ma-359	146	6	1−	1−	NUM
ma-359	146	7	ρ2	ρ2	NOUN
ma-359	146	8	)	)	PUNCT
ma-359	146	9	m−1∑	m−1∑	PROPN
ma-359	146	10	i=0	i=0	PROPN
ma-359	146	11	m−i−1∑	m−i−1∑	PROPN
ma-359	146	12	l=0	l=0	PROPN
ma-359	146	13	(	(	PUNCT
ma-359	146	14	m	m	VERB
ma-359	146	15	+	+	ADJ
ma-359	146	16	i	i	PRON
ma-359	146	17	−	−	NOUN
ma-359	146	18	1	1	NUM
ma-359	146	19	)	)	PUNCT
ma-359	146	20	!	!	PUNCT
ma-359	147	1	2i	2i	NOUN
ma-359	147	2	i	i	PRON
ma-359	147	3	!	!	PUNCT
ma-359	148	1	l	l	X
ma-359	148	2	!	!	PUNCT
ma-359	149	1	(	(	PUNCT
ma-359	149	2	−w	−w	ADV
ma-359	149	3	2	2	NUM
ma-359	149	4	√	√	PROPN
ma-359	149	5	1−	1−	NUM
ma-359	149	6	ρ2	ρ2	NOUN
ma-359	149	7	)	)	PUNCT
ma-359	149	8	l	l	NOUN
ma-359	149	9	.	.	PUNCT
ma-359	150	1	the	the	DET
ma-359	150	2	results	result	NOUN
ma-359	150	3	from	from	ADP
ma-359	150	4	this	this	DET
ma-359	150	5	formula	formula	NOUN
ma-359	150	6	matches	match	VERB
ma-359	150	7	those	those	PRON
ma-359	150	8	obtained	obtain	VERB
ma-359	150	9	from	from	ADP
ma-359	150	10	our	our	PRON
ma-359	150	11	cdf	cdf	PROPN
ma-359	150	12	(	(	PUNCT
ma-359	150	13	5	5	NUM
ma-359	150	14	)	)	PUNCT
ma-359	150	15	.	.	PUNCT
ma-359	151	1	furthermore	furthermore	ADV
ma-359	151	2	,	,	PUNCT
ma-359	151	3	it	it	PRON
ma-359	151	4	is	be	AUX
ma-359	151	5	worthnoting	worthnote	VERB
ma-359	151	6	that	that	SCONJ
ma-359	151	7	the	the	DET
ma-359	151	8	pdf	pdf	NOUN
ma-359	151	9	and	and	CCONJ
ma-359	151	10	the	the	DET
ma-359	151	11	cdf	cdf	NOUN
ma-359	151	12	of	of	ADP
ma-359	151	13	a	a	DET
ma-359	151	14	sum	sum	NOUN
ma-359	151	15	of	of	ADP
ma-359	151	16	dependent	dependent	ADJ
ma-359	151	17	rvs	rvs	NOUN
ma-359	151	18	x	x	X
ma-359	151	19	and	and	CCONJ
ma-359	151	20	y	y	PROPN
ma-359	151	21	,	,	PUNCT
ma-359	151	22	say	say	VERB
ma-359	151	23	v	v	ADP
ma-359	151	24	=	=	SYM
ma-359	151	25	x	x	SYM
ma-359	152	1	+	+	NUM
ma-359	152	2	y	y	NOUN
ma-359	152	3	,	,	PUNCT
ma-359	152	4	is	be	AUX
ma-359	152	5	sometimes	sometimes	ADV
ma-359	152	6	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	152	7	eur	eur	PROPN
ma-359	152	8	.	.	PUNCT
ma-359	153	1	j.	j.	PROPN
ma-359	153	2	math	math	PROPN
ma-359	153	3	.	.	PUNCT
ma-359	154	1	anal	anal	PROPN
ma-359	154	2	.	.	PUNCT
ma-359	155	1	10.28924	10.28924	NUM
ma-359	155	2	/	/	SYM
ma-359	155	3	ada	ada	PROPN
ma-359	155	4	/	/	SYM
ma-359	155	5	ma.5.19	ma.5.19	NOUN
ma-359	156	1	7derived	7derived	NUM
ma-359	156	2	indirectly	indirectly	ADV
ma-359	156	3	from	from	ADP
ma-359	156	4	w	w	PROPN
ma-359	156	5	=	=	PUNCT
ma-359	156	6	x	x	SYM
ma-359	157	1	−	−	PROPN
ma-359	157	2	z	z	NOUN
ma-359	157	3	by	by	ADP
ma-359	157	4	setting	set	VERB
ma-359	157	5	y	y	PROPN
ma-359	157	6	=	=	PUNCT
ma-359	157	7	−z	−z	PROPN
ma-359	157	8	(	(	PUNCT
ma-359	157	9	e.g.	e.g.	ADV
ma-359	157	10	,	,	PUNCT
ma-359	157	11	see	see	VERB
ma-359	157	12	[	[	X
ma-359	157	13	6	6	NUM
ma-359	157	14	]	]	PUNCT
ma-359	157	15	,	,	PUNCT
ma-359	157	16	ch	ch	NOUN
ma-359	157	17	.	.	PROPN
ma-359	157	18	5	5	NUM
ma-359	157	19	)	)	PUNCT
ma-359	157	20	.	.	PUNCT
ma-359	158	1	for	for	ADP
ma-359	158	2	m	m	PRON
ma-359	158	3	odd	odd	ADJ
ma-359	158	4	,	,	PUNCT
ma-359	158	5	we	we	PRON
ma-359	158	6	note	note	VERB
ma-359	158	7	that	that	SCONJ
ma-359	158	8	no	no	DET
ma-359	158	9	expression	expression	NOUN
ma-359	158	10	for	for	ADP
ma-359	158	11	the	the	DET
ma-359	158	12	cdf	cdf	PROPN
ma-359	158	13	is	be	AUX
ma-359	158	14	given	give	VERB
ma-359	158	15	in	in	ADP
ma-359	158	16	[	[	X
ma-359	158	17	6	6	NUM
ma-359	158	18	]	]	PUNCT
ma-359	158	19	,	,	PUNCT
ma-359	158	20	and	and	CCONJ
ma-359	158	21	to	to	ADP
ma-359	158	22	our	our	PRON
ma-359	158	23	knowelege	knowelege	NOUN
ma-359	158	24	it	it	PRON
ma-359	158	25	is	be	AUX
ma-359	158	26	unknown.in	unknown.in	PRON
ma-359	158	27	our	our	PRON
ma-359	158	28	representation	representation	NOUN
ma-359	158	29	of	of	ADP
ma-359	158	30	the	the	DET
ma-359	158	31	cdf	cdf	PROPN
ma-359	158	32	in	in	ADP
ma-359	158	33	(	(	PUNCT
ma-359	158	34	4	4	NUM
ma-359	158	35	)	)	PUNCT
ma-359	158	36	,	,	PUNCT
ma-359	158	37	or	or	CCONJ
ma-359	158	38	in	in	ADP
ma-359	158	39	its	its	PRON
ma-359	158	40	regularized	regularize	VERB
ma-359	158	41	version	version	NOUN
ma-359	158	42	,	,	PUNCT
ma-359	158	43	we	we	PRON
ma-359	158	44	encouter	encouter	VERB
ma-359	158	45	the	the	DET
ma-359	158	46	evaluation	evaluation	NOUN
ma-359	158	47	of	of	ADP
ma-359	158	48	thegamma	thegamma	PROPN
ma-359	158	49	function	function	NOUN
ma-359	158	50	at	at	ADP
ma-359	158	51	negative	negative	ADJ
ma-359	158	52	integers	integer	NOUN
ma-359	158	53	(	(	PUNCT
ma-359	158	54	poles	pole	NOUN
ma-359	158	55	)	)	PUNCT
ma-359	158	56	where	where	SCONJ
ma-359	158	57	it	it	PRON
ma-359	158	58	is	be	AUX
ma-359	158	59	not	not	PART
ma-359	158	60	defined	define	VERB
ma-359	158	61	.	.	PUNCT
ma-359	159	1	it	it	PRON
ma-359	159	2	turns	turn	VERB
ma-359	159	3	out	out	ADP
ma-359	159	4	that	that	SCONJ
ma-359	159	5	for	for	ADP
ma-359	159	6	odd	odd	ADJ
ma-359	159	7	m	m	PROPN
ma-359	159	8	theintegral	theintegral	ADJ
ma-359	159	9	j	j	PROPN
ma-359	159	10	can	can	AUX
ma-359	159	11	be	be	AUX
ma-359	159	12	expressed	express	VERB
ma-359	159	13	in	in	ADP
ma-359	159	14	terms	term	NOUN
ma-359	159	15	of	of	ADP
ma-359	159	16	the	the	DET
ma-359	159	17	meijer	meijer	NOUN
ma-359	159	18	g	g	NOUN
ma-359	159	19	-	-	PUNCT
ma-359	159	20	function	function	NOUN
ma-359	159	21	.	.	PUNCT
ma-359	160	1	recall	recall	NOUN
ma-359	160	2	,	,	PUNCT
ma-359	160	3	that	that	SCONJ
ma-359	160	4	the	the	DET
ma-359	160	5	meijer	meijer	NOUN
ma-359	160	6	g	g	NOUN
ma-359	160	7	-	-	PUNCT
ma-359	160	8	functionis	functionis	NOUN
ma-359	160	9	defined	define	VERB
ma-359	160	10	as	as	ADP
ma-359	160	11	a	a	DET
ma-359	160	12	mellin	mellin	NOUN
ma-359	160	13	-	-	PUNCT
ma-359	160	14	barnes	barnes	NOUN
ma-359	160	15	integral	integral	ADJ
ma-359	160	16	(	(	PUNCT
ma-359	160	17	an	an	DET
ma-359	160	18	inverse	inverse	NOUN
ma-359	160	19	mellin	mellin	NOUN
ma-359	160	20	transform	transform	NOUN
ma-359	160	21	)	)	PUNCT
ma-359	160	22	(	(	PUNCT
ma-359	160	23	see	see	VERB
ma-359	160	24	[	[	X
ma-359	160	25	1	1	NUM
ma-359	160	26	]	]	SYM
ma-359	160	27	)	)	PUNCT
ma-359	160	28	gm	gm	PROPN
ma-359	160	29	,	,	PUNCT
ma-359	160	30	np	np	INTJ
ma-359	160	31	,	,	PUNCT
ma-359	160	32	q	q	PROPN
ma-359	161	1	(	(	PUNCT
ma-359	161	2	ap	ap	PROPN
ma-359	161	3	bq	bq	PROPN
ma-359	161	4	|z	|z	PROPN
ma-359	161	5	,	,	PUNCT
ma-359	161	6	r	r	NOUN
ma-359	161	7	)	)	PUNCT
ma-359	161	8	:	:	PUNCT
ma-359	162	1	=	=	SYM
ma-359	162	2	r	r	NOUN
ma-359	162	3	2πi	2πi	NOUN
ma-359	162	4	∫	∫	PROPN
ma-359	162	5	l	l	X
ma-359	162	6	∏m	∏m	NUM
ma-359	162	7	j=1	j=1	PROPN
ma-359	162	8	γ	γ	X
ma-359	162	9	(	(	PUNCT
ma-359	162	10	bj	bj	ADP
ma-359	162	11	−	−	NOUN
ma-359	162	12	r	r	NOUN
ma-359	162	13	s	s	NOUN
ma-359	162	14	)	)	PUNCT
ma-359	162	15	∏n	∏n	ADJ
ma-359	162	16	j=1	j=1	ADJ
ma-359	162	17	γ	γ	X
ma-359	162	18	(	(	PUNCT
ma-359	162	19	1−	1−	NUM
ma-359	162	20	aj	aj	PROPN
ma-359	162	21	−	−	PROPN
ma-359	162	22	r	r	NOUN
ma-359	162	23	s	s	PROPN
ma-359	162	24	)	)	PUNCT
ma-359	162	25	∏q	∏q	PROPN
ma-359	163	1	j	j	X
ma-359	163	2	=	=	NOUN
ma-359	163	3	m+1	m+1	NUM
ma-359	163	4	γ	γ	X
ma-359	163	5	(	(	PUNCT
ma-359	163	6	1−	1−	NUM
ma-359	163	7	bj	bj	VERB
ma-359	163	8	+	+	CCONJ
ma-359	163	9	r	r	NOUN
ma-359	163	10	s	s	PART
ma-359	163	11	)	)	PUNCT
ma-359	163	12	∏p	∏p	NOUN
ma-359	163	13	j=1	j=1	PROPN
ma-359	163	14	γ	γ	PROPN
ma-359	163	15	(	(	PUNCT
ma-359	163	16	aj	aj	PROPN
ma-359	163	17	−	−	PROPN
ma-359	163	18	r	r	PROPN
ma-359	163	19	s	s	PROPN
ma-359	163	20	)	)	PUNCT
ma-359	163	21	z	z	PROPN
ma-359	163	22	sds	sds	PROPN
ma-359	163	23	,	,	PUNCT
ma-359	163	24	where	where	SCONJ
ma-359	163	25	ap	ap	PROPN
ma-359	163	26	=	=	PUNCT
ma-359	163	27	(	(	PUNCT
ma-359	163	28	a1	a1	PROPN
ma-359	163	29	,	,	PUNCT
ma-359	163	30	·	·	PUNCT
ma-359	163	31	·	·	PUNCT
ma-359	163	32	·	·	PUNCT
ma-359	163	33	,	,	PUNCT
ma-359	163	34	ap	ap	PROPN
ma-359	163	35	)	)	PUNCT
ma-359	163	36	and	and	CCONJ
ma-359	163	37	bq	bq	NOUN
ma-359	163	38	=	=	SYM
ma-359	163	39	(	(	PUNCT
ma-359	163	40	b1	b1	PROPN
ma-359	163	41	,	,	PUNCT
ma-359	163	42	·	·	PUNCT
ma-359	163	43	·	·	PUNCT
ma-359	163	44	·	·	PUNCT
ma-359	163	45	,	,	PUNCT
ma-359	163	46	bq	bq	INTJ
ma-359	163	47	)	)	PUNCT
ma-359	163	48	,	,	PUNCT
ma-359	163	49	and	and	CCONJ
ma-359	163	50	l	l	NOUN
ma-359	163	51	is	be	AUX
ma-359	163	52	a	a	DET
ma-359	163	53	contour	contour	NOUN
ma-359	163	54	in	in	ADP
ma-359	163	55	the	the	DET
ma-359	163	56	complex	complex	ADJ
ma-359	163	57	s	s	NOUN
ma-359	163	58	-	-	PUNCT
ma-359	163	59	plane	plane	NOUN
ma-359	163	60	withcertain	withcertain	NOUN
ma-359	163	61	properties	property	NOUN
ma-359	163	62	(	(	PUNCT
ma-359	163	63	e.g.	e.g.	ADV
ma-359	163	64	,	,	PUNCT
ma-359	163	65	see	see	VERB
ma-359	163	66	[	[	X
ma-359	163	67	11	11	NUM
ma-359	163	68	]	]	PUNCT
ma-359	163	69	for	for	ADP
ma-359	163	70	further	further	ADJ
ma-359	163	71	conditions	condition	NOUN
ma-359	163	72	for	for	ADP
ma-359	163	73	which	which	PRON
ma-359	163	74	the	the	DET
ma-359	163	75	definition	definition	NOUN
ma-359	163	76	holds	hold	VERB
ma-359	163	77	)	)	PUNCT
ma-359	163	78	.	.	PUNCT
ma-359	164	1	for	for	ADP
ma-359	164	2	brevity	brevity	NOUN
ma-359	164	3	,	,	PUNCT
ma-359	164	4	we	we	PRON
ma-359	164	5	describe	describe	VERB
ma-359	164	6	this	this	DET
ma-359	164	7	integral	integral	ADJ
ma-359	164	8	in	in	ADP
ma-359	164	9	the	the	DET
ma-359	164	10	following	follow	VERB
ma-359	164	11	remark	remark	NOUN
ma-359	164	12	in	in	ADP
ma-359	164	13	a	a	DET
ma-359	164	14	bit	bit	NOUN
ma-359	164	15	more	more	ADJ
ma-359	164	16	details	detail	NOUN
ma-359	164	17	in	in	ADP
ma-359	164	18	our	our	PRON
ma-359	164	19	specific	specific	ADJ
ma-359	164	20	case	case	NOUN
ma-359	164	21	.	.	PUNCT
ma-359	165	1	remark	remark	NOUN
ma-359	165	2	2	2	NUM
ma-359	165	3	.	.	PUNCT
ma-359	165	4	returning	return	VERB
ma-359	165	5	to	to	ADP
ma-359	165	6	the	the	DET
ma-359	165	7	contour	contour	ADJ
ma-359	165	8	integral	integral	ADJ
ma-359	165	9	representation	representation	NOUN
ma-359	165	10	of	of	ADP
ma-359	165	11	meijer	meijer	NOUN
ma-359	165	12	g	g	NOUN
ma-359	165	13	,	,	PUNCT
ma-359	165	14	but	but	CCONJ
ma-359	165	15	now	now	ADV
ma-359	165	16	as	as	SCONJ
ma-359	165	17	given	give	VERB
ma-359	165	18	in	in	ADP
ma-359	165	19	[	[	X
ma-359	165	20	10	10	NUM
ma-359	165	21	]	]	PUNCT
ma-359	165	22	,	,	PUNCT
ma-359	165	23	we	we	PRON
ma-359	165	24	see	see	VERB
ma-359	165	25	in	in	ADP
ma-359	165	26	our	our	PRON
ma-359	165	27	specific	specific	ADJ
ma-359	165	28	case	case	NOUN
ma-359	165	29	that	that	SCONJ
ma-359	165	30	g2,1	g2,1	PROPN
ma-359	165	31	1,3	1,3	NUM
ma-359	165	32	(	(	PUNCT
ma-359	165	33	1	1	NUM
ma-359	165	34	1	1	NUM
ma-359	165	35	2	2	NUM
ma-359	165	36	m	m	NUM
ma-359	165	37	2	2	NUM
ma-359	165	38	0	0	NUM
ma-359	165	39	|z	|z	PROPN
ma-359	165	40	)	)	PUNCT
ma-359	166	1	=	=	SYM
ma-359	166	2	1	1	NUM
ma-359	166	3	2πi	2πi	ADJ
ma-359	166	4	∫	∫	PROPN
ma-359	166	5	l	l	X
ma-359	166	6	γ	γ	X
ma-359	166	7	(	(	PUNCT
ma-359	166	8	1	1	NUM
ma-359	166	9	2	2	NUM
ma-359	166	10	+	+	NOUN
ma-359	166	11	s)γ(m2	s)γ(m2	X
ma-359	167	1	+	+	ADJ
ma-359	167	2	s)γ(−s	s)γ(−	NOUN
ma-359	167	3	)	)	PUNCT
ma-359	167	4	γ(1+s	γ(1+s	PROPN
ma-359	167	5	)	)	PUNCT
ma-359	167	6	z−sds	z−sds	NOUN
ma-359	167	7	,	,	PUNCT
ma-359	167	8	where	where	SCONJ
ma-359	167	9	l	l	NOUN
ma-359	167	10	is	be	AUX
ma-359	167	11	a	a	DET
ma-359	167	12	contour	contour	NOUN
ma-359	167	13	in	in	ADP
ma-359	167	14	the	the	DET
ma-359	167	15	complex	complex	ADJ
ma-359	167	16	s	s	NOUN
ma-359	167	17	-	-	NOUN
ma-359	167	18	plane	plane	NOUN
ma-359	167	19	,	,	PUNCT
ma-359	167	20	which	which	PRON
ma-359	167	21	exists	exist	VERB
ma-359	167	22	as	as	ADP
ma-359	167	23	a1	a1	NOUN
ma-359	167	24	−	−	PROPN
ma-359	167	25	bi	bi	NOUN
ma-359	167	26	−	−	PROPN
ma-359	167	27	1	1	NUM
ma-359	167	28	/∈	/∈	SYM
ma-359	167	29	n	n	CCONJ
ma-359	167	30	(	(	PUNCT
ma-359	167	31	see	see	VERB
ma-359	167	32	[	[	X
ma-359	167	33	11	11	NUM
ma-359	167	34	]	]	NUM
ma-359	167	35	)	)	PUNCT
ma-359	167	36	.	.	PUNCT
ma-359	168	1	in	in	ADP
ma-359	168	2	[	[	X
ma-359	168	3	10	10	NUM
ma-359	168	4	]	]	PUNCT
ma-359	168	5	,	,	PUNCT
ma-359	168	6	s	s	VERB
ma-359	168	7	is	be	AUX
ma-359	168	8	replaced	replace	VERB
ma-359	168	9	with	with	ADP
ma-359	168	10	−s	−s	NOUN
ma-359	168	11	,	,	PUNCT
ma-359	168	12	and	and	CCONJ
ma-359	168	13	hence	hence	ADV
ma-359	168	14	the	the	DET
ma-359	168	15	poles	pole	NOUN
ma-359	168	16	and	and	CCONJ
ma-359	168	17	l	l	NOUN
ma-359	168	18	undergo	undergo	VERB
ma-359	168	19	a	a	DET
ma-359	168	20	reflection	reflection	NOUN
ma-359	168	21	.	.	PUNCT
ma-359	169	1	more	more	ADV
ma-359	169	2	specifically	specifically	ADV
ma-359	169	3	,	,	PUNCT
ma-359	169	4	a	a	DET
ma-359	169	5	contour	contour	NOUN
ma-359	169	6	l	l	NOUN
ma-359	169	7	is	be	AUX
ma-359	169	8	chosen	choose	VERB
ma-359	169	9	to	to	PART
ma-359	169	10	separate	separate	VERB
ma-359	169	11	the	the	DET
ma-359	169	12	poles	pole	NOUN
ma-359	169	13	of	of	ADP
ma-359	169	14	γ	γ	X
ma-359	169	15	(	(	PUNCT
ma-359	169	16	1	1	NUM
ma-359	169	17	2	2	NUM
ma-359	169	18	+	+	SYM
ma-359	169	19	s	s	PART
ma-359	169	20	)	)	PUNCT
ma-359	169	21	and	and	CCONJ
ma-359	169	22	γ	γ	PROPN
ma-359	169	23	(	(	PUNCT
ma-359	169	24	m	m	PROPN
ma-359	169	25	2	2	NUM
ma-359	169	26	+	+	SYM
ma-359	169	27	s	s	PART
ma-359	169	28	)	)	PUNCT
ma-359	169	29	from	from	ADP
ma-359	169	30	those	those	PRON
ma-359	169	31	of	of	ADP
ma-359	169	32	γ	γ	PROPN
ma-359	169	33	(	(	PUNCT
ma-359	169	34	−s	−s	NOUN
ma-359	169	35	)	)	PUNCT
ma-359	169	36	.	.	PUNCT
ma-359	170	1	the	the	DET
ma-359	170	2	contour	contour	NOUN
ma-359	170	3	in	in	ADP
ma-359	170	4	our	our	PRON
ma-359	170	5	case	case	NOUN
ma-359	170	6	starts	start	VERB
ma-359	170	7	at	at	ADP
ma-359	170	8	−∞	−∞	X
ma-359	170	9	encircling	encircle	VERB
ma-359	170	10	the	the	DET
ma-359	170	11	poles	pole	NOUN
ma-359	170	12	of	of	ADP
ma-359	170	13	γ	γ	X
ma-359	170	14	(	(	PUNCT
ma-359	170	15	1	1	NUM
ma-359	170	16	2	2	NUM
ma-359	170	17	+	+	SYM
ma-359	170	18	s	s	NOUN
ma-359	170	19	)	)	PUNCT
ma-359	170	20	(	(	PUNCT
ma-359	170	21	at	at	ADP
ma-359	170	22	s	s	NOUN
ma-359	170	23	=	=	NOUN
ma-359	170	24	−1	−1	NOUN
ma-359	170	25	2	2	NUM
ma-359	170	26	−	−	NOUN
ma-359	170	27	n	n	CCONJ
ma-359	170	28	,	,	PUNCT
ma-359	170	29	n	n	NOUN
ma-359	170	30	=	=	SYM
ma-359	170	31	0	0	NUM
ma-359	170	32	,	,	PUNCT
ma-359	170	33	1	1	NUM
ma-359	170	34	,	,	PUNCT
ma-359	170	35	2	2	NUM
ma-359	170	36	,	,	PUNCT
ma-359	170	37	·	·	PUNCT
ma-359	170	38	·	·	PUNCT
ma-359	170	39	·	·	PUNCT
ma-359	170	40	)	)	PUNCT
ma-359	170	41	and	and	CCONJ
ma-359	170	42	those	those	PRON
ma-359	170	43	of	of	ADP
ma-359	170	44	γ	γ	X
ma-359	170	45	(	(	PUNCT
ma-359	170	46	m	m	PROPN
ma-359	170	47	2	2	NUM
ma-359	170	48	+	+	SYM
ma-359	170	49	s	s	NOUN
ma-359	170	50	)	)	PUNCT
ma-359	170	51	(	(	PUNCT
ma-359	170	52	at	at	ADP
ma-359	170	53	s	s	NOUN
ma-359	170	54	=	=	PUNCT
ma-359	170	55	−m2	−m2	NOUN
ma-359	170	56	−	−	NUM
ma-359	170	57	n	n	CCONJ
ma-359	170	58	,	,	PUNCT
ma-359	170	59	n	n	PROPN
ma-359	170	60	=	=	SYM
ma-359	170	61	0	0	NUM
ma-359	170	62	,	,	PUNCT
ma-359	170	63	1	1	NUM
ma-359	170	64	,	,	PUNCT
ma-359	170	65	2	2	NUM
ma-359	170	66	,	,	PUNCT
ma-359	170	67	·	·	PUNCT
ma-359	170	68	·	·	PUNCT
ma-359	170	69	·	·	PUNCT
ma-359	170	70	)	)	PUNCT
ma-359	170	71	but	but	CCONJ
ma-359	170	72	not	not	PART
ma-359	170	73	those	those	PRON
ma-359	170	74	of	of	ADP
ma-359	170	75	γ	γ	X
ma-359	170	76	(	(	PUNCT
ma-359	170	77	−s	−s	NOUN
ma-359	170	78	)	)	PUNCT
ma-359	170	79	(	(	PUNCT
ma-359	170	80	at	at	ADP
ma-359	170	81	n	n	NOUN
ma-359	170	82	=	=	SYM
ma-359	170	83	0	0	NUM
ma-359	170	84	,	,	PUNCT
ma-359	170	85	1	1	NUM
ma-359	170	86	,	,	PUNCT
ma-359	170	87	2	2	NUM
ma-359	170	88	,	,	PUNCT
ma-359	170	89	·	·	PUNCT
ma-359	170	90	·	·	PUNCT
ma-359	170	91	·	·	PUNCT
ma-359	170	92	)	)	PUNCT
ma-359	170	93	and	and	CCONJ
ma-359	170	94	returning	return	VERB
ma-359	170	95	to	to	ADP
ma-359	170	96	−∞.	−∞.	NOUN
ma-359	170	97	since	since	SCONJ
ma-359	170	98	in	in	ADP
ma-359	170	99	our	our	PRON
ma-359	170	100	case	case	NOUN
ma-359	170	101	it	it	PRON
ma-359	170	102	holds	hold	VERB
ma-359	170	103	that	that	SCONJ
ma-359	170	104	0	0	NUM
ma-359	170	105	≤	≤	NUM
ma-359	171	1	m	m	VERB
ma-359	171	2	<	<	X
ma-359	171	3	q	q	X
ma-359	171	4	and	and	CCONJ
ma-359	171	5	0	0	NUM
ma-359	171	6	≤	≤	NOUN
ma-359	172	1	p	p	X
ma-359	172	2	<	<	X
ma-359	172	3	q	q	X
ma-359	172	4	;	;	PUNCT
ma-359	172	5	and	and	CCONJ
ma-359	172	6	that	that	SCONJ
ma-359	172	7	1	1	NUM
ma-359	172	8	+	+	SYM
ma-359	172	9	1	1	NUM
ma-359	172	10	2	2	NUM
ma-359	172	11	,	,	PUNCT
ma-359	172	12	1	1	NUM
ma-359	172	13	+	+	CCONJ
ma-359	172	14	m	m	VERB
ma-359	172	15	2	2	NUM
ma-359	172	16	are	be	AUX
ma-359	172	17	not	not	PART
ma-359	172	18	integers	integer	NOUN
ma-359	172	19	whenever	whenever	SCONJ
ma-359	172	20	m	m	VERB
ma-359	172	21	is	be	AUX
ma-359	172	22	odd	odd	ADJ
ma-359	172	23	,	,	PUNCT
ma-359	172	24	the	the	DET
ma-359	172	25	integral	integral	ADJ
ma-359	172	26	converges	converge	NOUN
ma-359	172	27	for	for	ADP
ma-359	172	28	all	all	DET
ma-359	172	29	z	z	NOUN
ma-359	172	30	6=	6=	ADP
ma-359	172	31	0	0	NUM
ma-359	172	32	;	;	PUNCT
ma-359	172	33	and	and	CCONJ
ma-359	172	34	the	the	DET
ma-359	172	35	meijer	meijer	NOUN
ma-359	172	36	function	function	NOUN
ma-359	172	37	is	be	AUX
ma-359	172	38	an	an	DET
ma-359	172	39	analytic	analytic	ADJ
ma-359	172	40	function	function	NOUN
ma-359	172	41	except	except	SCONJ
ma-359	172	42	for	for	ADP
ma-359	172	43	z	z	NOUN
ma-359	172	44	=	=	SYM
ma-359	172	45	0	0	NUM
ma-359	172	46	(	(	PUNCT
ma-359	172	47	e.g.	e.g.	ADV
ma-359	172	48	,	,	PUNCT
ma-359	172	49	see	see	VERB
ma-359	172	50	[	[	X
ma-359	172	51	11	11	NUM
ma-359	172	52	]	]	NUM
ma-359	172	53	)	)	PUNCT
ma-359	172	54	.	.	PUNCT
ma-359	173	1	theorem	theorem	NOUN
ma-359	173	2	2	2	NUM
ma-359	173	3	.	.	X
ma-359	173	4	for	for	ADP
ma-359	173	5	odd	odd	ADJ
ma-359	173	6	m	m	PROPN
ma-359	173	7	>	>	X
ma-359	173	8	0	0	PROPN
ma-359	173	9	,	,	PUNCT
ma-359	173	10	the	the	DET
ma-359	173	11	j	j	PROPN
ma-359	173	12	in	in	ADP
ma-359	173	13	(	(	PUNCT
ma-359	173	14	4	4	NUM
ma-359	173	15	)	)	PUNCT
ma-359	173	16	is	be	AUX
ma-359	173	17	given	give	VERB
ma-359	173	18	in	in	ADP
ma-359	173	19	trems	trem	NOUN
ma-359	173	20	of	of	ADP
ma-359	173	21	the	the	DET
ma-359	173	22	meijer	meijer	NOUN
ma-359	173	23	g	g	NOUN
ma-359	173	24	-	-	PUNCT
ma-359	173	25	function	function	NOUN
ma-359	173	26	,	,	PUNCT
ma-359	173	27	and	and	CCONJ
ma-359	173	28	hence	hence	ADV
ma-359	173	29	,	,	PUNCT
ma-359	173	30	the	the	DET
ma-359	173	31	cdf	cdf	PROPN
ma-359	173	32	can	can	AUX
ma-359	173	33	be	be	AUX
ma-359	173	34	expressed	express	VERB
ma-359	173	35	as	as	ADP
ma-359	173	36	fw	fw	PROPN
ma-359	173	37	(	(	PUNCT
ma-359	173	38	w	w	NOUN
ma-359	173	39	)	)	PUNCT
ma-359	173	40	=	=	SYM
ma-359	174	1	1	1	NUM
ma-359	174	2	2	2	NUM
ma-359	174	3	+	+	CCONJ
ma-359	174	4	1	1	NUM
ma-359	174	5	2	2	NUM
ma-359	174	6	√	√	NUM
ma-359	174	7	πγ	πγ	PROPN
ma-359	174	8	(	(	PUNCT
ma-359	174	9	m	m	PROPN
ma-359	174	10	2	2	NUM
ma-359	174	11	)	)	PUNCT
ma-359	174	12	g2,1	g2,1	PROPN
ma-359	174	13	1,3	1,3	NUM
ma-359	174	14	(	(	PUNCT
ma-359	174	15	1	1	NUM
ma-359	174	16	1	1	NUM
ma-359	174	17	2	2	NUM
ma-359	174	18	m	m	NUM
ma-359	174	19	2	2	NUM
ma-359	174	20	0	0	NUM
ma-359	174	21	|	|	NOUN
ma-359	174	22	w2	w2	PROPN
ma-359	174	23	c	c	PROPN
ma-359	174	24	)	)	PUNCT
ma-359	174	25	,	,	PUNCT
ma-359	174	26	w	w	ADP
ma-359	174	27	>	>	X
ma-359	174	28	0	0	X
ma-359	174	29	.	.	PUNCT
ma-359	175	1	(	(	PUNCT
ma-359	175	2	6	6	X
ma-359	175	3	)	)	PUNCT
ma-359	175	4	proof	proof	NOUN
ma-359	175	5	.	.	PUNCT
ma-359	176	1	the	the	DET
ma-359	176	2	entry	entry	NOUN
ma-359	176	3	07.34.03.0605.01	07.34.03.0605.01	NUM
ma-359	176	4	in	in	ADP
ma-359	176	5	[	[	X
ma-359	176	6	10	10	NUM
ma-359	176	7	]	]	PUNCT
ma-359	176	8	gives	give	VERB
ma-359	176	9	a	a	DET
ma-359	176	10	representation	representation	NOUN
ma-359	176	11	of	of	ADP
ma-359	176	12	the	the	DET
ma-359	176	13	bessel	bessel	NOUN
ma-359	176	14	k	k	PROPN
ma-359	176	15	function	function	NOUN
ma-359	176	16	as	as	ADP
ma-359	176	17	g2,0	g2,0	PROPN
ma-359	176	18	0,2	0,2	NUM
ma-359	176	19	(	(	PUNCT
ma-359	176	20	−	−	PROPN
ma-359	176	21	b1	b1	NOUN
ma-359	176	22	,	,	PUNCT
ma-359	176	23	b2	b2	NOUN
ma-359	176	24	|z	|z	PROPN
ma-359	176	25	)	)	PUNCT
ma-359	177	1	=	=	X
ma-359	178	1	2z	2z	NUM
ma-359	178	2	b1+b2	b1+b2	PROPN
ma-359	178	3	2	2	NUM
ma-359	178	4	kb1−b2	kb1−b2	NOUN
ma-359	178	5	(	(	PUNCT
ma-359	178	6	2	2	NUM
ma-359	178	7	√	√	PROPN
ma-359	178	8	z	z	NOUN
ma-359	178	9	)	)	PUNCT
ma-359	178	10	.	.	PUNCT
ma-359	179	1	however	however	ADV
ma-359	179	2	,	,	PUNCT
ma-359	179	3	the	the	DET
ma-359	179	4	meijerreduce	meijerreduce	NOUN
ma-359	179	5	command	command	NOUN
ma-359	179	6	in	in	ADP
ma-359	179	7	[	[	X
ma-359	179	8	5	5	NUM
ma-359	179	9	]	]	PUNCT
ma-359	179	10	gave	give	VERB
ma-359	179	11	us	we	PRON
ma-359	179	12	g2,0	g2,0	PROPN
ma-359	179	13	0,2	0,2	NUM
ma-359	179	14	(	(	PUNCT
ma-359	179	15	−	−	PROPN
ma-359	179	16	b1	b1	NOUN
ma-359	179	17	,	,	PUNCT
ma-359	179	18	b2	b2	PROPN
ma-359	179	19	|z	|z	PROPN
ma-359	179	20	,	,	PUNCT
ma-359	179	21	1	1	NUM
ma-359	179	22	2	2	NUM
ma-359	179	23	)	)	PUNCT
ma-359	179	24	=	=	NOUN
ma-359	180	1	2z	2z	NUM
ma-359	180	2	b1+b2	b1+b2	PROPN
ma-359	180	3	2	2	NUM
ma-359	180	4	kb1−b2	kb1−b2	NOUN
ma-359	180	5	(	(	PUNCT
ma-359	180	6	2	2	NUM
ma-359	180	7	√	√	PROPN
ma-359	180	8	z	z	NOUN
ma-359	180	9	)	)	PUNCT
ma-359	180	10	,	,	PUNCT
ma-359	180	11	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	180	12	eur	eur	PROPN
ma-359	180	13	.	.	PUNCT
ma-359	181	1	j.	j.	PROPN
ma-359	181	2	math	math	PROPN
ma-359	181	3	.	.	PUNCT
ma-359	182	1	anal	anal	PROPN
ma-359	182	2	.	.	PUNCT
ma-359	183	1	10.28924	10.28924	NUM
ma-359	183	2	/	/	SYM
ma-359	183	3	ada	ada	PROPN
ma-359	183	4	/	/	SYM
ma-359	183	5	ma.5.19	ma.5.19	NOUN
ma-359	183	6	8where	8where	NUM
ma-359	183	7	the	the	DET
ma-359	183	8	1	1	NUM
ma-359	183	9	2	2	NUM
ma-359	183	10	equals	equal	VERB
ma-359	183	11	the	the	DET
ma-359	183	12	r	r	NOUN
ma-359	183	13	in	in	ADP
ma-359	183	14	the	the	DET
ma-359	183	15	contour	contour	NOUN
ma-359	183	16	integral	integral	NOUN
ma-359	183	17	in	in	ADP
ma-359	183	18	the	the	DET
ma-359	183	19	definition	definition	NOUN
ma-359	183	20	of	of	ADP
ma-359	183	21	the	the	DET
ma-359	183	22	meijer	meijer	NOUN
ma-359	183	23	g	g	NOUN
ma-359	183	24	-	-	PUNCT
ma-359	183	25	function	function	NOUN
ma-359	183	26	givenabove	givenabove	NOUN
ma-359	183	27	.	.	PUNCT
ma-359	184	1	consequently	consequently	ADV
ma-359	184	2	,	,	PUNCT
ma-359	184	3	the	the	DET
ma-359	184	4	integral	integral	ADJ
ma-359	184	5	in	in	ADP
ma-359	184	6	terms	term	NOUN
ma-359	184	7	of	of	ADP
ma-359	184	8	the	the	DET
ma-359	184	9	meijer	meijer	NOUN
ma-359	184	10	g	g	NOUN
ma-359	184	11	-	-	PUNCT
ma-359	184	12	function	function	NOUN
ma-359	184	13	becomes∫	becomes∫	NOUN
ma-359	185	1	w	w	NOUN
ma-359	185	2	0	0	NUM
ma-359	185	3	x	x	SYM
ma-359	185	4	m−1	m−1	PROPN
ma-359	185	5	2	2	NUM
ma-359	185	6	km−1	km−1	NOUN
ma-359	185	7	2	2	NUM
ma-359	185	8	(	(	PUNCT
ma-359	185	9	x	x	SYM
ma-359	185	10	2	2	NUM
ma-359	185	11	√	√	NUM
ma-359	185	12	1−	1−	NUM
ma-359	185	13	ρ2	ρ2	NOUN
ma-359	185	14	)	)	PUNCT
ma-359	185	15	dx	dx	PROPN
ma-359	186	1	=	=	SYM
ma-359	186	2	∫	∫	PROPN
ma-359	187	1	w	w	NOUN
ma-359	187	2	0	0	NUM
ma-359	187	3	1	1	NUM
ma-359	187	4	2	2	NUM
ma-359	187	5	x	x	SYM
ma-359	187	6	m−1	m−1	PROPN
ma-359	187	7	2	2	NUM
ma-359	187	8	g2,0	g2,0	PROPN
ma-359	187	9	0,2	0,2	NUM
ma-359	187	10	(	(	PUNCT
ma-359	187	11	−	−	PROPN
ma-359	187	12	m−1	m−1	PROPN
ma-359	187	13	4	4	NUM
ma-359	187	14	,	,	PUNCT
ma-359	187	15	1−m	1−m	NUM
ma-359	187	16	4	4	NUM
ma-359	187	17	|	|	ADV
ma-359	187	18	x	x	SYM
ma-359	187	19	4	4	NUM
ma-359	187	20	√	√	NUM
ma-359	187	21	1−	1−	NUM
ma-359	187	22	ρ2	ρ2	NOUN
ma-359	187	23	,	,	PUNCT
ma-359	187	24	1	1	NUM
ma-359	187	25	2	2	NUM
ma-359	187	26	)	)	PUNCT
ma-359	187	27	dx	dx	PROPN
ma-359	187	28	.	.	PUNCT
ma-359	188	1	this	this	DET
ma-359	188	2	integral	integral	ADJ
ma-359	188	3	evaluates	evaluate	NOUN
ma-359	188	4	to	to	ADP
ma-359	188	5	a	a	DET
ma-359	188	6	meijer	meijer	NOUN
ma-359	188	7	g	g	NOUN
ma-359	188	8	-	-	PUNCT
ma-359	188	9	function	function	NOUN
ma-359	188	10	with	with	ADP
ma-359	188	11	r	r	NOUN
ma-359	188	12	=	=	SYM
ma-359	188	13	1	1	NUM
ma-359	188	14	when	when	SCONJ
ma-359	188	15	an	an	DET
ma-359	188	16	odd	odd	ADJ
ma-359	188	17	positive	positive	ADJ
ma-359	188	18	numerical	numerical	ADJ
ma-359	188	19	value	value	NOUN
ma-359	188	20	of	of	ADP
ma-359	188	21	m	m	PROPN
ma-359	188	22	is	be	AUX
ma-359	188	23	specified	specify	VERB
ma-359	188	24	.	.	PUNCT
ma-359	189	1	observing	observe	VERB
ma-359	189	2	the	the	DET
ma-359	189	3	pattern	pattern	NOUN
ma-359	189	4	,	,	PUNCT
ma-359	189	5	we	we	PRON
ma-359	189	6	arrive	arrive	VERB
ma-359	189	7	at	at	ADP
ma-359	189	8	the	the	DET
ma-359	189	9	expression	expression	NOUN
ma-359	189	10	in	in	ADP
ma-359	189	11	(	(	PUNCT
ma-359	189	12	6	6	NUM
ma-359	189	13	)	)	PUNCT
ma-359	189	14	.	.	PUNCT
ma-359	190	1	by	by	ADP
ma-359	190	2	remark	remark	NOUN
ma-359	190	3	2	2	NUM
ma-359	190	4	,	,	PUNCT
ma-359	190	5	z	z	NOUN
ma-359	190	6	6=	6=	NUM
ma-359	190	7	0	0	NUM
ma-359	190	8	,	,	PUNCT
ma-359	190	9	andas	andas	X
ma-359	190	10	the	the	DET
ma-359	190	11	limit	limit	NOUN
ma-359	190	12	of	of	ADP
ma-359	190	13	g2,1	g2,1	PROPN
ma-359	190	14	1,3	1,3	NUM
ma-359	190	15	(	(	PUNCT
ma-359	190	16	z	z	NOUN
ma-359	190	17	|	|	NOUN
ma-359	190	18	·	·	PUNCT
ma-359	190	19	)	)	PUNCT
ma-359	190	20	→	→	SYM
ma-359	190	21	0	0	PUNCT
ma-359	190	22	as	as	ADP
ma-359	190	23	z	z	PROPN
ma-359	190	24	→	→	SYM
ma-359	190	25	0	0	NUM
ma-359	190	26	,	,	PUNCT
ma-359	190	27	fw	fw	X
ma-359	190	28	(	(	PUNCT
ma-359	190	29	0	0	NUM
ma-359	190	30	)	)	PUNCT
ma-359	190	31	:	:	PUNCT
ma-359	191	1	=	=	SYM
ma-359	191	2	1	1	NUM
ma-359	191	3	2	2	NUM
ma-359	191	4	.	.	PUNCT
ma-359	192	1	moreover	moreover	ADV
ma-359	192	2	,	,	PUNCT
ma-359	192	3	limw→∞	limw→∞	PROPN
ma-359	192	4	fw	fw	PROPN
ma-359	192	5	(	(	PUNCT
ma-359	192	6	w	w	NOUN
ma-359	192	7	)	)	PUNCT
ma-359	192	8	=	=	SYM
ma-359	192	9	1	1	X
ma-359	192	10	.	.	X
ma-359	192	11	�	�	PROPN
ma-359	192	12	let	let	VERB
ma-359	192	13	b	b	NOUN
ma-359	192	14	=	=	SYM
ma-359	192	15	2	2	NUM
ma-359	192	16	√	√	NUM
ma-359	192	17	1−	1−	NUM
ma-359	192	18	ρ2	ρ2	NOUN
ma-359	192	19	,	,	PUNCT
ma-359	192	20	and	and	CCONJ
ma-359	192	21	hence	hence	ADV
ma-359	192	22	4b2	4b2	NUM
ma-359	192	23	=	=	NOUN
ma-359	193	1	c.the	c.the	DET
ma-359	193	2	integral	integral	ADJ
ma-359	193	3	i	i	NOUN
ma-359	193	4	=	=	PUNCT
ma-359	193	5	∫	∫	PROPN
ma-359	193	6	w	w	PROPN
ma-359	193	7	−∞	−∞	PROPN
ma-359	193	8	fw	fw	PROPN
ma-359	193	9	(	(	PUNCT
ma-359	193	10	w	w	NOUN
ma-359	193	11	)	)	PUNCT
ma-359	193	12	dw	dw	NOUN
ma-359	193	13	for	for	ADP
ma-359	193	14	re	re	PROPN
ma-359	193	15	(	(	PUNCT
ma-359	193	16	w	w	NOUN
ma-359	193	17	)	)	PUNCT
ma-359	193	18	<	<	X
ma-359	193	19	0	0	NUM
ma-359	193	20	,	,	PUNCT
ma-359	193	21	and	and	CCONJ
ma-359	193	22	odd	odd	ADJ
ma-359	193	23	m	m	PROPN
ma-359	193	24	>	>	X
ma-359	193	25	2	2	NUM
ma-359	193	26	,	,	PUNCT
ma-359	193	27	evaluates	evaluate	VERB
ma-359	193	28	to	to	ADP
ma-359	193	29	i	i	PROPN
ma-359	193	30	=	=	SYM
ma-359	193	31	b	b	PROPN
ma-359	193	32	m+1	m+1	NUM
ma-359	193	33	2	2	NUM
ma-359	193	34	[	[	PUNCT
ma-359	193	35	2π(m	2π(m	NUM
ma-359	193	36	−	−	PROPN
ma-359	193	37	2)!!−	2)!!−	NUM
ma-359	193	38	2	2	NUM
ma-359	193	39	m+1	m+1	NUM
ma-359	193	40	2	2	NUM
ma-359	193	41	g3,1	g3,1	NOUN
ma-359	193	42	1,2	1,2	NUM
ma-359	193	43	(	(	PUNCT
ma-359	193	44	1	1	NUM
ma-359	193	45	1	1	NUM
ma-359	193	46	2	2	NUM
ma-359	193	47	,	,	PUNCT
ma-359	193	48	m	m	VERB
ma-359	193	49	2	2	NUM
ma-359	193	50	,	,	PUNCT
ma-359	193	51	0	0	NUM
ma-359	193	52	|	|	ADV
ma-359	193	53	w2	w2	PROPN
ma-359	193	54	4b2	4b2	NUM
ma-359	193	55	)	)	PUNCT
ma-359	193	56	]	]	PUNCT
ma-359	194	1	2m+2	2m+2	NOUN
ma-359	194	2	√	√	NOUN
ma-359	194	3	π	π	PROPN
ma-359	194	4	(	(	PUNCT
ma-359	194	5	1−	1−	NUM
ma-359	194	6	ρ2	ρ2	NOUN
ma-359	194	7	)	)	PUNCT
ma-359	194	8	m+1	m+1	NUM
ma-359	194	9	4	4	NUM
ma-359	194	10	γ	γ	X
ma-359	194	11	(	(	PUNCT
ma-359	194	12	m	m	PROPN
ma-359	194	13	2	2	NUM
ma-359	194	14	)	)	PUNCT
ma-359	194	15	,	,	PUNCT
ma-359	194	16	m	m	VERB
ma-359	194	17	=	=	VERB
ma-359	194	18	4k	4k	NOUN
ma-359	194	19	−	−	NOUN
ma-359	194	20	1	1	NUM
ma-359	194	21	;	;	PUNCT
ma-359	194	22	i	i	PROPN
ma-359	194	23	=	=	SYM
ma-359	194	24	b	b	PROPN
ma-359	195	1	m+1	m+1	NUM
ma-359	195	2	2	2	NUM
ma-359	195	3	π	π	NOUN
ma-359	195	4	(	(	PUNCT
ma-359	195	5	m	m	NOUN
ma-359	195	6	−	−	NOUN
ma-359	195	7	2	2	NUM
ma-359	195	8	)	)	PUNCT
ma-359	195	9	!	!	PUNCT
ma-359	195	10	!	!	PUNCT
ma-359	196	1	+	+	CCONJ
ma-359	196	2	w	w	ADJ
ma-359	196	3	m+1	m+1	NUM
ma-359	196	4	2	2	NUM
ma-359	196	5	g3,1	g3,1	NOUN
ma-359	196	6	1,2	1,2	NUM
ma-359	196	7	(	(	PUNCT
ma-359	196	8	3−m	3−m	NUM
ma-359	196	9	4	4	NUM
ma-359	196	10	1−m	1−m	NUM
ma-359	196	11	4	4	NUM
ma-359	196	12	,	,	PUNCT
ma-359	196	13	m−1	m−1	PROPN
ma-359	196	14	4	4	NUM
ma-359	196	15	,	,	PUNCT
ma-359	196	16	−m+1	−m+1	PROPN
ma-359	196	17	4	4	NUM
ma-359	196	18	|	|	NOUN
ma-359	196	19	w2	w2	NOUN
ma-359	196	20	4b2	4b2	NUM
ma-359	196	21	)	)	PUNCT
ma-359	196	22	2m+2	2m+2	NOUN
ma-359	197	1	√	√	NOUN
ma-359	197	2	π	π	PROPN
ma-359	197	3	(	(	PUNCT
ma-359	197	4	1−	1−	NUM
ma-359	197	5	ρ2	ρ2	NOUN
ma-359	197	6	)	)	PUNCT
ma-359	197	7	m+1	m+1	NUM
ma-359	197	8	4	4	NUM
ma-359	197	9	γ	γ	X
ma-359	197	10	(	(	PUNCT
ma-359	197	11	m	m	PROPN
ma-359	197	12	2	2	NUM
ma-359	197	13	)	)	PUNCT
ma-359	197	14	,	,	PUNCT
ma-359	197	15	m	m	VERB
ma-359	197	16	=	=	SYM
ma-359	197	17	4k	4k	NOUN
ma-359	197	18	+	+	NOUN
ma-359	197	19	1	1	NUM
ma-359	197	20	,	,	PUNCT
ma-359	197	21	where	where	SCONJ
ma-359	197	22	k	k	PROPN
ma-359	197	23	=	=	SYM
ma-359	197	24	1	1	NUM
ma-359	197	25	,	,	PUNCT
ma-359	197	26	2	2	NUM
ma-359	197	27	,	,	PUNCT
ma-359	197	28	·	·	PUNCT
ma-359	197	29	·	·	PUNCT
ma-359	197	30	·	·	PUNCT
ma-359	197	31	;	;	PUNCT
ma-359	197	32	and	and	CCONJ
ma-359	197	33	n	n	CCONJ
ma-359	197	34	!	!	PUNCT
ma-359	197	35	!	!	PUNCT
ma-359	198	1	is	be	AUX
ma-359	198	2	the	the	DET
ma-359	198	3	double	double	ADJ
ma-359	198	4	factorial	factorial	NOUN
ma-359	198	5	,	,	PUNCT
ma-359	198	6	which	which	PRON
ma-359	198	7	is	be	AUX
ma-359	198	8	the	the	DET
ma-359	198	9	product	product	NOUN
ma-359	198	10	of	of	ADP
ma-359	198	11	all	all	DET
ma-359	198	12	positive	positive	ADJ
ma-359	198	13	odd	odd	ADJ
ma-359	198	14	integersup	integersup	NOUN
ma-359	198	15	to	to	ADP
ma-359	198	16	n.	n.	NOUN
ma-359	198	17	figure	figure	NOUN
ma-359	198	18	4	4	NUM
ma-359	198	19	.	.	PUNCT
ma-359	199	1	the	the	DET
ma-359	199	2	cdf	cdf	PROPN
ma-359	199	3	fw	fw	PROPN
ma-359	199	4	(	(	PUNCT
ma-359	199	5	w	w	NOUN
ma-359	199	6	)	)	PUNCT
ma-359	199	7	for	for	ADP
ma-359	199	8	m	m	PROPN
ma-359	199	9	=	=	NOUN
ma-359	199	10	11	11	NUM
ma-359	199	11	,	,	PUNCT
ma-359	199	12	18	18	NUM
ma-359	199	13	,	,	PUNCT
ma-359	199	14	25	25	NUM
ma-359	199	15	and	and	CCONJ
ma-359	199	16	ρ	ρ	NUM
ma-359	199	17	=	=	SYM
ma-359	199	18	0.7	0.7	NUM
ma-359	199	19	.	.	PUNCT
ma-359	199	20	figure	figure	NOUN
ma-359	199	21	4	4	NUM
ma-359	199	22	shows	show	VERB
ma-359	199	23	plots	plot	NOUN
ma-359	199	24	of	of	ADP
ma-359	199	25	the	the	DET
ma-359	199	26	cdf	cdf	PROPN
ma-359	199	27	generated	generate	VERB
ma-359	199	28	using	use	VERB
ma-359	199	29	the	the	DET
ma-359	199	30	meijer	meijer	NOUN
ma-359	199	31	function	function	NOUN
ma-359	199	32	representation	representation	NOUN
ma-359	199	33	of	of	ADP
ma-359	199	34	fw	fw	PROPN
ma-359	199	35	(	(	PUNCT
ma-359	199	36	w	w	NOUN
ma-359	199	37	)	)	PUNCT
ma-359	199	38	.	.	PUNCT
ma-359	200	1	4	4	X
ma-359	200	2	.	.	X
ma-359	200	3	percentiles	percentile	NOUN
ma-359	200	4	in	in	ADP
ma-359	200	5	this	this	DET
ma-359	200	6	section	section	NOUN
ma-359	200	7	,	,	PUNCT
ma-359	200	8	to	to	PART
ma-359	200	9	illustrate	illustrate	VERB
ma-359	200	10	the	the	DET
ma-359	200	11	use	use	NOUN
ma-359	200	12	of	of	ADP
ma-359	200	13	the	the	DET
ma-359	200	14	equation	equation	NOUN
ma-359	200	15	fw	fw	PROPN
ma-359	200	16	(	(	PUNCT
ma-359	200	17	w	w	NOUN
ma-359	200	18	)	)	PUNCT
ma-359	200	19	=	=	SYM
ma-359	201	1	1	1	NUM
ma-359	201	2	2	2	NUM
ma-359	201	3	+	+	NOUN
ma-359	201	4	j	j	NOUN
ma-359	201	5	,	,	PUNCT
ma-359	201	6	we	we	PRON
ma-359	201	7	compute	compute	VERB
ma-359	201	8	the	the	DET
ma-359	201	9	95th	95th	ADJ
ma-359	201	10	percentile	percentile	NOUN
ma-359	201	11	(	(	PUNCT
ma-359	201	12	α	α	NOUN
ma-359	201	13	=	=	NOUN
ma-359	201	14	0.05	0.05	NUM
ma-359	201	15	)	)	PUNCT
ma-359	201	16	,	,	PUNCT
ma-359	201	17	for	for	ADP
ma-359	201	18	ρ	ρ	PROPN
ma-359	201	19	=	=	SYM
ma-359	201	20	0.8	0.8	NUM
ma-359	201	21	,	,	PUNCT
ma-359	201	22	0.9	0.9	NUM
ma-359	201	23	,	,	PUNCT
ma-359	201	24	0.95	0.95	NUM
ma-359	201	25	,	,	PUNCT
ma-359	201	26	and	and	CCONJ
ma-359	201	27	for	for	ADP
ma-359	201	28	degrees	degree	NOUN
ma-359	201	29	of	of	ADP
ma-359	201	30	freedom	freedom	NOUN
ma-359	201	31	m	m	NOUN
ma-359	201	32	=	=	SYM
ma-359	201	33	3	3	NUM
ma-359	201	34	,	,	PUNCT
ma-359	201	35	·	·	PUNCT
ma-359	201	36	·	·	PUNCT
ma-359	201	37	·	·	PUNCT
ma-359	201	38	,	,	PUNCT
ma-359	201	39	30	30	NUM
ma-359	201	40	.	.	PUNCT
ma-359	202	1	for	for	ADP
ma-359	202	2	m	m	VERB
ma-359	202	3	even	even	ADV
ma-359	202	4	,	,	PUNCT
ma-359	202	5	using	use	VERB
ma-359	202	6	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	202	7	eur	eur	PROPN
ma-359	202	8	.	.	PUNCT
ma-359	203	1	j.	j.	PROPN
ma-359	203	2	math	math	PROPN
ma-359	203	3	.	.	PUNCT
ma-359	204	1	anal	anal	PROPN
ma-359	204	2	.	.	PUNCT
ma-359	205	1	10.28924	10.28924	NUM
ma-359	205	2	/	/	SYM
ma-359	205	3	ada	ada	PROPN
ma-359	205	4	/	/	SYM
ma-359	205	5	ma.5.19	ma.5.19	NOUN
ma-359	205	6	9either	9either	NUM
ma-359	205	7	(	(	PUNCT
ma-359	205	8	4	4	NUM
ma-359	205	9	)	)	PUNCT
ma-359	205	10	,	,	PUNCT
ma-359	205	11	or	or	CCONJ
ma-359	205	12	the	the	DET
ma-359	205	13	regularized	regularize	VERB
ma-359	205	14	generalized	generalized	ADJ
ma-359	205	15	hypergeometric	hypergeometric	ADJ
ma-359	205	16	function	function	NOUN
ma-359	205	17	representations	representation	NOUN
ma-359	205	18	of	of	ADP
ma-359	205	19	j	j	PROPN
ma-359	205	20	,	,	PUNCT
ma-359	205	21	one	one	NUM
ma-359	205	22	obtainsthe	obtainsthe	DET
ma-359	205	23	percentiles	percentile	NOUN
ma-359	205	24	reported	report	VERB
ma-359	205	25	in	in	ADP
ma-359	205	26	table	table	NOUN
ma-359	205	27	1	1	NUM
ma-359	205	28	.	.	PUNCT
ma-359	205	29	remark	remark	PROPN
ma-359	205	30	3	3	NUM
ma-359	205	31	.	.	PUNCT
ma-359	206	1	given	give	VERB
ma-359	206	2	that	that	SCONJ
ma-359	206	3	the	the	DET
ma-359	206	4	integral	integral	ADJ
ma-359	206	5	representig	representig	NOUN
ma-359	206	6	g2,1	g2,1	PROPN
ma-359	206	7	1,3	1,3	NUM
ma-359	206	8	converges	converge	NOUN
ma-359	206	9	,	,	PUNCT
ma-359	206	10	l.	l.	PROPN
ma-359	206	11	slater	slater	PROPN
ma-359	206	12	’s	’s	PROPN
ma-359	206	13	theorem	theorem	PROPN
ma-359	206	14	(	(	PUNCT
ma-359	206	15	e.g.	e.g.	ADV
ma-359	206	16	,	,	PUNCT
ma-359	206	17	see	see	VERB
ma-359	206	18	[	[	X
ma-359	206	19	11	11	NUM
ma-359	206	20	]	]	PUNCT
ma-359	206	21	for	for	ADP
ma-359	206	22	the	the	DET
ma-359	206	23	general	general	ADJ
ma-359	206	24	statement	statement	NOUN
ma-359	206	25	,	,	PUNCT
ma-359	206	26	[	[	X
ma-359	206	27	1,4,12	1,4,12	NUM
ma-359	206	28	]	]	PUNCT
ma-359	206	29	)	)	PUNCT
ma-359	206	30	which	which	PRON
ma-359	206	31	gives	give	VERB
ma-359	206	32	us	we	PRON
ma-359	206	33	an	an	DET
ma-359	206	34	expression	expression	NOUN
ma-359	206	35	of	of	ADP
ma-359	206	36	the	the	DET
ma-359	206	37	meijer	meijer	NOUN
ma-359	206	38	g	g	NOUN
ma-359	206	39	-	-	PUNCT
ma-359	206	40	function	function	NOUN
ma-359	206	41	in	in	ADP
ma-359	206	42	terms	term	NOUN
ma-359	206	43	of	of	ADP
ma-359	206	44	two	two	NUM
ma-359	206	45	generalized	generalized	ADJ
ma-359	206	46	hypergeometric	hypergeometric	ADJ
ma-359	206	47	functions	function	NOUN
ma-359	206	48	for	for	ADP
ma-359	206	49	bi	bi	NOUN
ma-359	206	50	−	−	PROPN
ma-359	206	51	bj	bj	NOUN
ma-359	206	52	/∈	/∈	PUNCT
ma-359	207	1	z	z	X
ma-359	207	2	,	,	PUNCT
ma-359	207	3	i	i	PROPN
ma-359	207	4	6=	6=	PROPN
ma-359	207	5	j	j	PROPN
ma-359	207	6	.	.	PUNCT
ma-359	208	1	in	in	ADP
ma-359	208	2	our	our	PRON
ma-359	208	3	specific	specific	ADJ
ma-359	208	4	case	case	NOUN
ma-359	208	5	,	,	PUNCT
ma-359	208	6	using	use	VERB
ma-359	208	7	this	this	DET
ma-359	208	8	theorem	theorem	NOUN
ma-359	208	9	gives	give	VERB
ma-359	208	10	us	we	PRON
ma-359	208	11	that	that	SCONJ
ma-359	208	12	g2,1	g2,1	PROPN
ma-359	208	13	1,3	1,3	NUM
ma-359	208	14	(	(	PUNCT
ma-359	208	15	a1	a1	NOUN
ma-359	208	16	b1	b1	NOUN
ma-359	208	17	b2	b2	NOUN
ma-359	208	18	b3	b3	PROPN
ma-359	208	19	|z	|z	PROPN
ma-359	208	20	)	)	PUNCT
ma-359	209	1	=	=	PRON
ma-359	209	2	∏2	∏2	NOUN
ma-359	209	3	j=1	j=1	PROPN
ma-359	209	4	γ	γ	X
ma-359	209	5	(	(	PUNCT
ma-359	209	6	bj	bj	ADP
ma-359	209	7	−	−	PROPN
ma-359	209	8	bh=1	bh=1	NOUN
ma-359	209	9	)	)	PUNCT
ma-359	210	1	∗∏1	∗∏1	NOUN
ma-359	210	2	j=1	j=1	NOUN
ma-359	210	3	γ	γ	X
ma-359	210	4	(	(	PUNCT
ma-359	210	5	1	1	NUM
ma-359	210	6	+	+	NUM
ma-359	210	7	b1	b1	PROPN
ma-359	210	8	−	−	PROPN
ma-359	210	9	aj	aj	PROPN
ma-359	210	10	)	)	PUNCT
ma-359	210	11	∏	∏	PROPN
ma-359	210	12	lim3	lim3	PROPN
ma-359	210	13	j=3	j=3	PROPN
ma-359	210	14	γ	γ	PROPN
ma-359	210	15	(	(	PUNCT
ma-359	210	16	1	1	NUM
ma-359	210	17	+	+	NUM
ma-359	210	18	b1	b1	NOUN
ma-359	210	19	−	−	NOUN
ma-359	210	20	bj	bj	NOUN
ma-359	210	21	)	)	PUNCT
ma-359	210	22	1f2	1f2	NUM
ma-359	210	23	(	(	PUNCT
ma-359	210	24	1	1	NUM
ma-359	210	25	+	+	NUM
ma-359	210	26	b1	b1	NOUN
ma-359	210	27	−	−	NOUN
ma-359	210	28	a1	a1	NOUN
ma-359	210	29	;	;	PUNCT
ma-359	210	30	1	1	NUM
ma-359	210	31	+	+	NUM
ma-359	210	32	b1	b1	NOUN
ma-359	210	33	−	−	PROPN
ma-359	210	34	b2	b2	NOUN
ma-359	210	35	,	,	PUNCT
ma-359	210	36	1	1	NUM
ma-359	210	37	+	+	NUM
ma-359	210	38	b1	b1	NOUN
ma-359	210	39	−	−	PROPN
ma-359	210	40	b3	b3	PROPN
ma-359	210	41	;	;	PUNCT
ma-359	210	42	z	z	X
ma-359	210	43	)	)	PUNCT
ma-359	211	1	+	+	NUM
ma-359	211	2	∏2	∏2	X
ma-359	211	3	j=1	j=1	PROPN
ma-359	211	4	γ	γ	X
ma-359	211	5	(	(	PUNCT
ma-359	211	6	bj	bj	ADP
ma-359	211	7	−	−	PROPN
ma-359	211	8	bh=2	bh=2	NOUN
ma-359	211	9	)	)	PUNCT
ma-359	211	10	∗∏1	∗∏1	NOUN
ma-359	211	11	j=1	j=1	NOUN
ma-359	211	12	γ	γ	X
ma-359	211	13	(	(	PUNCT
ma-359	211	14	1	1	NUM
ma-359	211	15	+	+	NUM
ma-359	211	16	b2	b2	NOUN
ma-359	211	17	−	−	PROPN
ma-359	211	18	aj	aj	PROPN
ma-359	211	19	)	)	PUNCT
ma-359	211	20	∏3	∏3	PROPN
ma-359	211	21	j=3	j=3	PROPN
ma-359	211	22	γ	γ	PROPN
ma-359	211	23	(	(	PUNCT
ma-359	211	24	1	1	NUM
ma-359	211	25	+	+	NUM
ma-359	211	26	b2	b2	NOUN
ma-359	211	27	−	−	NOUN
ma-359	211	28	bj	bj	NOUN
ma-359	211	29	)	)	PUNCT
ma-359	211	30	1f2	1f2	NUM
ma-359	211	31	(	(	PUNCT
ma-359	211	32	1	1	NUM
ma-359	211	33	+	+	NUM
ma-359	211	34	b2	b2	NOUN
ma-359	211	35	−	−	NOUN
ma-359	211	36	a1	a1	NOUN
ma-359	211	37	;	;	PUNCT
ma-359	211	38	1	1	NUM
ma-359	211	39	+	+	NUM
ma-359	211	40	b2	b2	NOUN
ma-359	211	41	−	−	NOUN
ma-359	211	42	b1	b1	NOUN
ma-359	211	43	,	,	PUNCT
ma-359	211	44	1	1	NUM
ma-359	211	45	+	+	NUM
ma-359	211	46	b2	b2	NOUN
ma-359	211	47	−	−	NOUN
ma-359	211	48	b3	b3	NOUN
ma-359	211	49	;	;	PUNCT
ma-359	211	50	z	z	X
ma-359	211	51	)	)	PUNCT
ma-359	211	52	,	,	PUNCT
ma-359	211	53	where	where	SCONJ
ma-359	211	54	the	the	DET
ma-359	211	55	*	*	PUNCT
ma-359	211	56	indicates	indicate	VERB
ma-359	211	57	that	that	SCONJ
ma-359	211	58	the	the	DET
ma-359	211	59	term	term	NOUN
ma-359	211	60	corresponding	correspond	VERB
ma-359	211	61	to	to	ADP
ma-359	211	62	j	j	PROPN
ma-359	211	63	=	=	NOUN
ma-359	211	64	h	h	NOUN
ma-359	211	65	is	be	AUX
ma-359	211	66	omitted	omit	VERB
ma-359	211	67	.	.	PUNCT
ma-359	212	1	this	this	DET
ma-359	212	2	equation	equation	NOUN
ma-359	212	3	reduces	reduce	VERB
ma-359	212	4	to	to	ADP
ma-359	212	5	the	the	DET
ma-359	212	6	expression	expression	NOUN
ma-359	212	7	1	1	NUM
ma-359	212	8	2	2	NUM
ma-359	212	9	√	√	NUM
ma-359	212	10	πγ(m2	πγ(m2	VERB
ma-359	212	11	)	)	PUNCT
ma-359	212	12	g2,1	g2,1	PROPN
ma-359	212	13	1,3	1,3	NUM
ma-359	212	14	(	(	PUNCT
ma-359	212	15	1	1	NUM
ma-359	212	16	1	1	NUM
ma-359	212	17	2	2	NUM
ma-359	212	18	m	m	NUM
ma-359	212	19	2	2	NUM
ma-359	212	20	0	0	NUM
ma-359	212	21	|	|	NOUN
ma-359	212	22	w2	w2	NOUN
ma-359	212	23	16(1−ρ2	16(1−ρ2	NUM
ma-359	212	24	)	)	PUNCT
ma-359	212	25	)	)	PUNCT
ma-359	213	1	=	=	PUNCT
ma-359	213	2	j	j	PROPN
ma-359	213	3	,	,	PUNCT
ma-359	213	4	where	where	SCONJ
ma-359	213	5	j	j	PROPN
ma-359	213	6	is	be	AUX
ma-359	213	7	as	as	ADP
ma-359	213	8	in	in	ADP
ma-359	213	9	theorem	theorem	NOUN
ma-359	213	10	1	1	NUM
ma-359	213	11	.	.	PUNCT
ma-359	214	1	a	a	DET
ma-359	214	2	similar	similar	ADJ
ma-359	214	3	conclusion	conclusion	NOUN
ma-359	214	4	can	can	AUX
ma-359	214	5	be	be	AUX
ma-359	214	6	obtained	obtain	VERB
ma-359	214	7	from	from	ADP
ma-359	214	8	formula	formula	NOUN
ma-359	214	9	07.34.03.0727.01	07.34.03.0727.01	NUM
ma-359	214	10	in	in	ADP
ma-359	214	11	[	[	X
ma-359	214	12	10	10	NUM
ma-359	214	13	]	]	X
ma-359	214	14	g2,1	g2,1	PROPN
ma-359	214	15	1,3	1,3	NUM
ma-359	214	16	(	(	PUNCT
ma-359	214	17	a1	a1	NOUN
ma-359	214	18	b1	b1	NOUN
ma-359	214	19	b2	b2	NOUN
ma-359	214	20	b3	b3	PROPN
ma-359	214	21	|z	|z	PROPN
ma-359	214	22	)	)	PUNCT
ma-359	215	1	=	=	PUNCT
ma-359	215	2	π	π	X
ma-359	215	3	csc	csc	PROPN
ma-359	215	4	(	(	PUNCT
ma-359	215	5	(	(	PUNCT
ma-359	215	6	b2	b2	NOUN
ma-359	215	7	−	−	NOUN
ma-359	215	8	b1)π	b1)π	NOUN
ma-359	215	9	)	)	PUNCT
ma-359	215	10	[	[	PUNCT
ma-359	215	11	γ	γ	X
ma-359	215	12	(	(	PUNCT
ma-359	215	13	1−	1−	NUM
ma-359	215	14	a1	a1	NOUN
ma-359	215	15	+	+	CCONJ
ma-359	215	16	b1	b1	NOUN
ma-359	215	17	)	)	PUNCT
ma-359	215	18	zb1	zb1	NOUN
ma-359	216	1	1f̃2	1f̃2	NUM
ma-359	216	2	(	(	PUNCT
ma-359	216	3	1−	1−	NUM
ma-359	216	4	a1	a1	NOUN
ma-359	216	5	+	+	CCONJ
ma-359	216	6	b1	b1	NOUN
ma-359	216	7	;	;	PUNCT
ma-359	216	8	b1	b1	NOUN
ma-359	216	9	−	−	PROPN
ma-359	216	10	b2	b2	NOUN
ma-359	216	11	+	+	CCONJ
ma-359	216	12	1	1	NUM
ma-359	216	13	,	,	PUNCT
ma-359	216	14	b1	b1	NOUN
ma-359	216	15	−	−	PROPN
ma-359	216	16	b3	b3	PROPN
ma-359	216	17	+	+	CCONJ
ma-359	216	18	1	1	NUM
ma-359	216	19	;	;	PUNCT
ma-359	216	20	z	z	X
ma-359	216	21	)	)	PUNCT
ma-359	216	22	−γ	−γ	NOUN
ma-359	216	23	(	(	PUNCT
ma-359	216	24	1−	1−	NUM
ma-359	216	25	a1	a1	NOUN
ma-359	216	26	+	+	CCONJ
ma-359	216	27	b2	b2	NOUN
ma-359	216	28	)	)	PUNCT
ma-359	216	29	zb2	zb2	NOUN
ma-359	217	1	1f̃2	1f̃2	NUM
ma-359	217	2	(	(	PUNCT
ma-359	217	3	1−	1−	NUM
ma-359	217	4	a1	a1	NOUN
ma-359	217	5	+	+	CCONJ
ma-359	217	6	b2	b2	NOUN
ma-359	217	7	;	;	PUNCT
ma-359	217	8	1−	1−	NUM
ma-359	217	9	b1	b1	NOUN
ma-359	217	10	+	+	CCONJ
ma-359	217	11	b2	b2	NOUN
ma-359	217	12	,	,	PUNCT
ma-359	217	13	b2	b2	NOUN
ma-359	217	14	−	−	PROPN
ma-359	217	15	b3	b3	PROPN
ma-359	217	16	+	+	CCONJ
ma-359	217	17	1	1	NUM
ma-359	217	18	;	;	PUNCT
ma-359	217	19	z	z	X
ma-359	217	20	)	)	PUNCT
ma-359	217	21	]	]	PUNCT
ma-359	217	22	,	,	PUNCT
ma-359	217	23	where	where	SCONJ
ma-359	217	24	b2	b2	NOUN
ma-359	217	25	−	−	PROPN
ma-359	217	26	b1	b1	NOUN
ma-359	217	27	/∈	/∈	PUNCT
ma-359	218	1	z.	z.	PROPN
ma-359	219	1	solving	solve	VERB
ma-359	219	2	the	the	DET
ma-359	219	3	linear	linear	ADJ
ma-359	219	4	system	system	NOUN
ma-359	219	5	1−	1−	NUM
ma-359	219	6	a1	a1	NOUN
ma-359	219	7	+	+	CCONJ
ma-359	219	8	b1	b1	NOUN
ma-359	219	9	=	=	SYM
ma-359	219	10	1	1	NUM
ma-359	219	11	2	2	NUM
ma-359	219	12	,	,	PUNCT
ma-359	219	13	b1	b1	NOUN
ma-359	219	14	−	−	PROPN
ma-359	219	15	b2	b2	NOUN
ma-359	219	16	+	+	CCONJ
ma-359	219	17	1	1	NUM
ma-359	219	18	=	=	SYM
ma-359	219	19	3−m	3−m	NUM
ma-359	219	20	2	2	NUM
ma-359	219	21	,	,	PUNCT
ma-359	219	22	b1	b1	NOUN
ma-359	219	23	−	−	PROPN
ma-359	219	24	b3	b3	PROPN
ma-359	219	25	+	+	CCONJ
ma-359	219	26	1	1	NUM
ma-359	219	27	=	=	SYM
ma-359	219	28	3	3	NUM
ma-359	219	29	2	2	NUM
ma-359	219	30	,	,	PUNCT
ma-359	219	31	1−	1−	NUM
ma-359	219	32	a1	a1	NOUN
ma-359	219	33	+	+	CCONJ
ma-359	219	34	b2	b2	NOUN
ma-359	219	35	=	=	SYM
ma-359	219	36	m	m	NOUN
ma-359	219	37	2	2	NUM
ma-359	219	38	,	,	PUNCT
ma-359	219	39	1−	1−	NUM
ma-359	219	40	b1	b1	NOUN
ma-359	219	41	+	+	CCONJ
ma-359	219	42	b2	b2	NOUN
ma-359	220	1	=	=	NOUN
ma-359	220	2	m	m	VERB
ma-359	220	3	+	+	NOUN
ma-359	220	4	1	1	NUM
ma-359	220	5	2	2	NUM
ma-359	220	6	,	,	PUNCT
ma-359	220	7	b2	b2	NOUN
ma-359	220	8	−	−	PROPN
ma-359	220	9	b3	b3	PROPN
ma-359	220	10	+	+	CCONJ
ma-359	220	11	1	1	NUM
ma-359	220	12	=	=	SYM
ma-359	220	13	m	m	VERB
ma-359	220	14	+	+	NOUN
ma-359	220	15	2	2	NUM
ma-359	220	16	2	2	NUM
ma-359	221	1	;	;	PUNCT
ma-359	221	2	we	we	PRON
ma-359	221	3	obtain	obtain	VERB
ma-359	221	4	that	that	DET
ma-359	221	5	a1	a1	NOUN
ma-359	221	6	=	=	SYM
ma-359	221	7	1	1	NUM
ma-359	221	8	+	+	NUM
ma-359	221	9	b3	b3	NOUN
ma-359	221	10	,	,	PUNCT
ma-359	221	11	b1	b1	NOUN
ma-359	221	12	=	=	SYM
ma-359	221	13	1	1	NUM
ma-359	221	14	2	2	NUM
ma-359	221	15	+	+	NUM
ma-359	221	16	b3	b3	NOUN
ma-359	221	17	,	,	PUNCT
ma-359	221	18	b2	b2	NOUN
ma-359	221	19	=	=	SYM
ma-359	221	20	m	m	VERB
ma-359	221	21	2	2	NUM
ma-359	221	22	+	+	NUM
ma-359	221	23	b3	b3	NOUN
ma-359	221	24	.	.	PUNCT
ma-359	222	1	for	for	ADP
ma-359	222	2	simplicity	simplicity	NOUN
ma-359	222	3	,	,	PUNCT
ma-359	222	4	take	take	VERB
ma-359	222	5	b3	b3	NOUN
ma-359	222	6	=	=	SYM
ma-359	222	7	0	0	NUM
ma-359	222	8	,	,	PUNCT
ma-359	222	9	and	and	CCONJ
ma-359	222	10	then	then	ADV
ma-359	222	11	we	we	PRON
ma-359	222	12	have	have	VERB
ma-359	222	13	g2,1	g2,1	PROPN
ma-359	222	14	1,3	1,3	NUM
ma-359	222	15	(	(	PUNCT
ma-359	222	16	1	1	NUM
ma-359	222	17	1	1	NUM
ma-359	222	18	2	2	NUM
ma-359	222	19	m	m	NUM
ma-359	222	20	2	2	NUM
ma-359	222	21	0	0	NUM
ma-359	222	22	|w2	|w2	NOUN
ma-359	222	23	c	c	NOUN
ma-359	222	24	)	)	PUNCT
ma-359	222	25	,	,	PUNCT
ma-359	222	26	with	with	ADP
ma-359	222	27	m−1	m−1	PROPN
ma-359	222	28	2	2	NUM
ma-359	222	29	/∈	/∈	NOUN
ma-359	223	1	z	z	NOUN
ma-359	223	2	,	,	PUNCT
ma-359	223	3	w	w	ADP
ma-359	223	4	>	>	X
ma-359	223	5	0	0	X
ma-359	223	6	.	.	PUNCT
ma-359	224	1	furthermore	furthermore	ADV
ma-359	224	2	,	,	PUNCT
ma-359	224	3	evaluating	evaluate	VERB
ma-359	224	4	the	the	DET
ma-359	224	5	contour	contour	NOUN
ma-359	224	6	integral	integral	ADJ
ma-359	224	7	described	describe	VERB
ma-359	224	8	in	in	ADP
ma-359	224	9	remark	remark	NOUN
ma-359	224	10	2	2	NUM
ma-359	224	11	,	,	PUNCT
ma-359	224	12	using	use	VERB
ma-359	224	13	formula	formula	NOUN
ma-359	224	14	07.34.06.0045.01	07.34.06.0045.01	NUM
ma-359	224	15	in	in	ADP
ma-359	224	16	[	[	X
ma-359	224	17	10	10	NUM
ma-359	224	18	]	]	PUNCT
ma-359	224	19	for	for	ADP
ma-359	224	20	the	the	DET
ma-359	224	21	residues	residue	NOUN
ma-359	224	22	series	series	NOUN
ma-359	224	23	,	,	PUNCT
ma-359	224	24	resulted	result	VERB
ma-359	224	25	in	in	ADP
ma-359	224	26	combination	combination	NOUN
ma-359	224	27	of	of	ADP
ma-359	224	28	four	four	NUM
ma-359	224	29	1f2	1f2	NUM
ma-359	224	30	generalized	generalized	ADJ
ma-359	224	31	hypergeometric	hypergeometric	ADJ
ma-359	224	32	functions	function	NOUN
ma-359	224	33	that	that	PRON
ma-359	224	34	also	also	ADV
ma-359	224	35	blow	blow	VERB
ma-359	224	36	up	up	ADP
ma-359	224	37	for	for	ADP
ma-359	224	38	odd	odd	ADJ
ma-359	224	39	m.	m.	NOUN
ma-359	224	40	therefore	therefore	ADV
ma-359	224	41	,	,	PUNCT
ma-359	224	42	it	it	PRON
ma-359	224	43	appears	appear	VERB
ma-359	224	44	that	that	SCONJ
ma-359	224	45	in	in	ADP
ma-359	224	46	the	the	DET
ma-359	224	47	hypergeometric	hypergeometric	ADJ
ma-359	224	48	representation	representation	NOUN
ma-359	224	49	of	of	ADP
ma-359	224	50	this	this	DET
ma-359	224	51	meijer	meijer	NOUN
ma-359	224	52	g	g	NOUN
ma-359	224	53	-	-	PUNCT
ma-359	224	54	function	function	NOUN
ma-359	224	55	,	,	PUNCT
ma-359	224	56	the	the	DET
ma-359	224	57	restriction	restriction	NOUN
ma-359	224	58	b2	b2	NOUN
ma-359	224	59	−	−	PROPN
ma-359	224	60	b1	b1	NOUN
ma-359	224	61	/∈	/∈	PUNCT
ma-359	224	62	z	z	NOUN
ma-359	224	63	for	for	ADP
ma-359	224	64	odd	odd	ADJ
ma-359	224	65	m	m	VERB
ma-359	224	66	can	can	AUX
ma-359	224	67	not	not	PART
ma-359	224	68	be	be	AUX
ma-359	224	69	removed	remove	VERB
ma-359	224	70	.	.	PUNCT
ma-359	225	1	clearly	clearly	ADV
ma-359	225	2	,	,	PUNCT
ma-359	225	3	the	the	DET
ma-359	225	4	representation	representation	NOUN
ma-359	225	5	in	in	ADP
ma-359	225	6	(	(	PUNCT
ma-359	225	7	6	6	NUM
ma-359	225	8	)	)	PUNCT
ma-359	225	9	holds	hold	VERB
ma-359	225	10	for	for	ADP
ma-359	225	11	even	even	ADV
ma-359	225	12	m	m	NOUN
ma-359	225	13	as	as	ADP
ma-359	225	14	the	the	DET
ma-359	225	15	condition	condition	NOUN
ma-359	225	16	m−1	m−1	PROPN
ma-359	225	17	2	2	NUM
ma-359	225	18	/∈	/∈	SYM
ma-359	225	19	z	z	NOUN
ma-359	225	20	holds	hold	VERB
ma-359	225	21	;	;	PUNCT
ma-359	225	22	and	and	CCONJ
ma-359	225	23	thecomputed	thecompute	VERB
ma-359	225	24	percentiles	percentile	NOUN
ma-359	225	25	from	from	ADP
ma-359	225	26	this	this	DET
ma-359	225	27	expression	expression	NOUN
ma-359	225	28	were	be	AUX
ma-359	225	29	identical	identical	ADJ
ma-359	225	30	to	to	ADP
ma-359	225	31	those	those	PRON
ma-359	225	32	reported	report	VERB
ma-359	225	33	in	in	ADP
ma-359	225	34	table	table	NOUN
ma-359	225	35	1	1	NUM
ma-359	225	36	.	.	PUNCT
ma-359	226	1	it	it	PRON
ma-359	226	2	turns	turn	VERB
ma-359	226	3	outthat	outthat	PROPN
ma-359	226	4	in	in	ADP
ma-359	226	5	mathematica	mathematica	PROPN
ma-359	227	1	[	[	X
ma-359	227	2	5	5	NUM
ma-359	227	3	]	]	PUNCT
ma-359	227	4	for	for	ADP
ma-359	227	5	the	the	DET
ma-359	227	6	case	case	NOUN
ma-359	227	7	where	where	SCONJ
ma-359	227	8	m	m	PROPN
ma-359	227	9	≥	≥	NUM
ma-359	227	10	1	1	NUM
ma-359	227	11	is	be	AUX
ma-359	227	12	odd	odd	ADJ
ma-359	227	13	,	,	PUNCT
ma-359	227	14	it	it	PRON
ma-359	227	15	is	be	AUX
ma-359	227	16	possible	possible	ADJ
ma-359	227	17	to	to	PART
ma-359	227	18	solve	solve	VERB
ma-359	227	19	for	for	ADP
ma-359	227	20	w	w	PROPN
ma-359	227	21	>	>	X
ma-359	227	22	0	0	PUNCT
ma-359	227	23	using	use	VERB
ma-359	227	24	https://doi.org/10.28924/ada/ma.5.19	https://doi.org/10.28924/ada/ma.5.19	PROPN
ma-359	227	25	eur	eur	PROPN
ma-359	227	26	.	.	PUNCT
ma-359	228	1	j.	j.	PROPN
ma-359	228	2	math	math	PROPN
ma-359	228	3	.	.	PUNCT
ma-359	229	1	anal	anal	PROPN
ma-359	229	2	.	.	PUNCT
ma-359	230	1	10.28924	10.28924	NUM
ma-359	230	2	/	/	SYM
ma-359	230	3	ada	ada	PROPN
ma-359	230	4	/	/	SYM
ma-359	230	5	ma.5.19	ma.5.19	PROPN
ma-359	230	6	10the	10the	PROPN
ma-359	230	7	findroot	findroot	PROPN
ma-359	230	8	command	command	NOUN
ma-359	230	9	,	,	PUNCT
ma-359	230	10	which	which	PRON
ma-359	230	11	solves	solve	VERB
ma-359	230	12	numerically	numerically	ADV
ma-359	230	13	for	for	ADP
ma-359	230	14	an	an	DET
ma-359	230	15	initial	initial	ADJ
ma-359	230	16	guess	guess	NOUN
ma-359	230	17	at	at	ADP
ma-359	230	18	the	the	DET
ma-359	230	19	root	root	NOUN
ma-359	230	20	.	.	PUNCT
ma-359	231	1	as	as	SCONJ
ma-359	231	2	it	it	PRON
ma-359	231	3	is	be	AUX
ma-359	231	4	not	not	PART
ma-359	231	5	clearenough	clearenough	ADJ
ma-359	231	6	how	how	SCONJ
ma-359	231	7	the	the	DET
ma-359	231	8	regularization	regularization	NOUN
ma-359	231	9	has	have	AUX
ma-359	231	10	occured	occur	VERB
ma-359	231	11	for	for	ADP
ma-359	231	12	odd	odd	ADJ
ma-359	231	13	m	m	PROPN
ma-359	231	14	,	,	PUNCT
ma-359	231	15	we	we	PRON
ma-359	231	16	implemented	implement	VERB
ma-359	231	17	newton	newton	PROPN
ma-359	231	18	’s	’s	PART
ma-359	231	19	method	method	NOUN
ma-359	231	20	to	to	ADP
ma-359	231	21	findthe	findthe	DET
ma-359	231	22	root	root	NOUN
ma-359	231	23	using	use	VERB
ma-359	231	24	formula	formula	NOUN
ma-359	231	25	07.34.20.0001.01	07.34.20.0001.01	NUM
ma-359	231	26	in	in	ADP
ma-359	231	27	[	[	X
ma-359	231	28	10	10	NUM
ma-359	231	29	]	]	PUNCT
ma-359	231	30	for	for	ADP
ma-359	231	31	the	the	DET
ma-359	231	32	derivative	derivative	NOUN
ma-359	231	33	of	of	ADP
ma-359	231	34	the	the	DET
ma-359	231	35	meijer	meijer	NOUN
ma-359	231	36	g	g	NOUN
ma-359	231	37	-	-	PUNCT
ma-359	231	38	function	function	NOUN
ma-359	232	1	f	f	NOUN
ma-359	233	1	′w	′w	NOUN
ma-359	234	1	(	(	PUNCT
ma-359	234	2	w	w	NOUN
ma-359	234	3	)	)	PUNCT
ma-359	234	4	=	=	SYM
ma-359	235	1	2w	2w	NUM
ma-359	235	2	2c	2c	NUM
ma-359	235	3	√	√	PUNCT
ma-359	235	4	wγ	wγ	NOUN
ma-359	235	5	(	(	PUNCT
ma-359	235	6	m	m	NOUN
ma-359	235	7	2	2	NUM
ma-359	235	8	)	)	PUNCT
ma-359	235	9	g2,2	g2,2	PROPN
ma-359	235	10	2,4	2,4	NUM
ma-359	235	11	(	(	PUNCT
ma-359	235	12	−1	−1	NOUN
ma-359	235	13	,	,	PUNCT
ma-359	235	14	0	0	NUM
ma-359	235	15	−1	−1	NOUN
ma-359	235	16	2	2	NUM
ma-359	235	17	,	,	PUNCT
ma-359	235	18	m	m	VERB
ma-359	235	19	2	2	NUM
ma-359	235	20	−	−	NUM
ma-359	235	21	1	1	NUM
ma-359	235	22	,	,	PUNCT
ma-359	235	23	0,−1	0,−1	PRON
ma-359	235	24	|	|	ADV
ma-359	235	25	w2	w2	NOUN
ma-359	235	26	c	c	PROPN
ma-359	235	27	)	)	PUNCT
ma-359	235	28	.	.	PUNCT
ma-359	236	1	solving	solve	VERB
ma-359	236	2	(	(	PUNCT
ma-359	236	3	6	6	NUM
ma-359	236	4	)	)	PUNCT
ma-359	236	5	by	by	ADP
ma-359	236	6	newton	newton	PROPN
ma-359	236	7	’s	’s	PART
ma-359	236	8	method	method	NOUN
ma-359	236	9	,	,	PUNCT
ma-359	236	10	using	use	VERB
ma-359	236	11	positive	positive	ADJ
ma-359	236	12	initial	initial	ADJ
ma-359	236	13	guesses	guess	NOUN
ma-359	236	14	,	,	PUNCT
ma-359	236	15	gave	give	VERB
ma-359	236	16	the	the	DET
ma-359	236	17	same	same	ADJ
ma-359	236	18	values	value	NOUN
ma-359	236	19	as	as	ADP
ma-359	236	20	those	those	PRON
ma-359	236	21	reported	report	VERB
ma-359	236	22	in	in	ADP
ma-359	236	23	table	table	NOUN
ma-359	236	24	1	1	NUM
ma-359	236	25	.	.	PUNCT
ma-359	236	26	newton	newton	PROPN
ma-359	236	27	’s	’s	PART
ma-359	236	28	method	method	NOUN
ma-359	236	29	worked	work	VERB
ma-359	236	30	as	as	ADP
ma-359	236	31	an	an	DET
ma-359	236	32	expansion	expansion	NOUN
ma-359	236	33	of	of	ADP
ma-359	236	34	g2,1	g2,1	PROPN
ma-359	236	35	1,3	1,3	NUM
ma-359	236	36	(	(	PUNCT
ma-359	236	37	1	1	NUM
ma-359	236	38	1	1	NUM
ma-359	236	39	2	2	NUM
ma-359	236	40	m	m	NUM
ma-359	236	41	2	2	NUM
ma-359	236	42	0	0	NUM
ma-359	236	43	|z	|z	PROPN
ma-359	236	44	)	)	PUNCT
ma-359	236	45	can	can	AUX
ma-359	236	46	be	be	AUX
ma-359	236	47	written	write	VERB
ma-359	236	48	as	as	ADP
ma-359	236	49	π	π	PROPN
ma-359	236	50	sec	sec	PROPN
ma-359	236	51	(	(	PUNCT
ma-359	236	52	mπ	mπ	NOUN
ma-359	236	53	2	2	NUM
ma-359	236	54	)	)	PUNCT
ma-359	236	55	(	(	PUNCT
ma-359	236	56	−	−	PROPN
ma-359	236	57	√	√	PROPN
ma-359	237	1	πz	πz	VERB
ma-359	237	2	1f̃2	1f̃2	NUM
ma-359	237	3	(	(	PUNCT
ma-359	237	4	1	1	NUM
ma-359	237	5	2	2	NUM
ma-359	237	6	;	;	PUNCT
ma-359	237	7	3−m	3−m	NUM
ma-359	237	8	2	2	NUM
ma-359	237	9	,	,	PUNCT
ma-359	237	10	3	3	NUM
ma-359	237	11	2	2	NUM
ma-359	237	12	;	;	PUNCT
ma-359	237	13	z	z	X
ma-359	237	14	)	)	PUNCT
ma-359	238	1	+	+	CCONJ
ma-359	238	2	z	z	NOUN
ma-359	238	3	m	m	VERB
ma-359	238	4	2	2	NUM
ma-359	238	5	γ	γ	X
ma-359	238	6	(	(	PUNCT
ma-359	238	7	m	m	PROPN
ma-359	238	8	2	2	NUM
ma-359	238	9	)	)	PUNCT
ma-359	238	10	1f̃2	1f̃2	PROPN
ma-359	238	11	(	(	PUNCT
ma-359	238	12	m	m	PROPN
ma-359	238	13	2	2	NUM
ma-359	238	14	;	;	PUNCT
ma-359	238	15	m	m	VERB
ma-359	238	16	+	+	ADJ
ma-359	238	17	1	1	NUM
ma-359	238	18	2	2	NUM
ma-359	238	19	,	,	PUNCT
ma-359	238	20	m	m	VERB
ma-359	238	21	+	+	ADJ
ma-359	238	22	2	2	NUM
ma-359	238	23	2	2	NUM
ma-359	238	24	;	;	PUNCT
ma-359	238	25	z	z	NOUN
ma-359	238	26	)	)	PUNCT
ma-359	238	27	)	)	PUNCT
ma-359	238	28	.	.	PUNCT
ma-359	239	1	then	then	ADV
ma-359	239	2	the	the	DET
ma-359	239	3	ratio	ratio	NOUN
ma-359	239	4	of	of	ADP
ma-359	239	5	this	this	DET
ma-359	239	6	g	g	NOUN
ma-359	239	7	-	-	PUNCT
ma-359	239	8	function	function	NOUN
ma-359	239	9	to	to	ADP
ma-359	239	10	its	its	PRON
ma-359	239	11	derivative	derivative	NOUN
ma-359	239	12	is	be	AUX
ma-359	239	13	clearly	clearly	ADV
ma-359	239	14	regular	regular	ADJ
ma-359	239	15	for	for	ADP
ma-359	239	16	odd	odd	ADJ
ma-359	239	17	m	m	PROPN
ma-359	239	18	and	and	CCONJ
ma-359	239	19	w	w	ADP
ma-359	239	20	>	>	X
ma-359	239	21	0	0	NUM
ma-359	239	22	,	,	PUNCT
ma-359	239	23	as	as	SCONJ
ma-359	239	24	thesecant	thesecant	ADJ
ma-359	239	25	function	function	NOUN
ma-359	239	26	cancels	cancel	VERB
ma-359	239	27	out	out	ADP
ma-359	239	28	.	.	PUNCT
ma-359	240	1	m\ρ	m\ρ	VERB
ma-359	240	2	0.8	0.8	NUM
ma-359	240	3	0.9	0.9	NUM
ma-359	240	4	0.95	0.95	NUM
ma-359	240	5	m\ρ	m\ρ	NOUN
ma-359	240	6	0.8	0.8	NUM
ma-359	240	7	0.9	0.9	NUM
ma-359	240	8	0.95	0.95	NUM
ma-359	240	9	4	4	NUM
ma-359	240	10	3.92617	3.92617	NUM
ma-359	240	11	2.85230	2.85230	NUM
ma-359	240	12	2.04325	2.04325	NUM
ma-359	240	13	3	3	NUM
ma-359	240	14	3.39639	3.39639	NUM
ma-359	240	15	2.46742	2.46742	NUM
ma-359	240	16	1.76754	1.76754	NUM
ma-359	240	17	6	6	NUM
ma-359	240	18	4.81249	4.81249	NUM
ma-359	240	19	3.49619	3.49619	NUM
ma-359	240	20	2.50450	2.50450	NUM
ma-359	240	21	5	5	NUM
ma-359	240	22	4.39180	4.39180	NUM
ma-359	240	23	3.19057	3.19057	NUM
ma-359	240	24	2.28557	2.28557	NUM
ma-359	240	25	8	8	NUM
ma-359	240	26	5.55949	5.55949	NUM
ma-359	240	27	4.03888	4.03888	NUM
ma-359	240	28	2.89325	2.89325	NUM
ma-359	240	29	7	7	NUM
ma-359	240	30	5.19934	5.19934	NUM
ma-359	240	31	3.77723	3.77723	NUM
ma-359	240	32	2.70582	2.70582	NUM
ma-359	240	33	10	10	NUM
ma-359	240	34	6.21796	6.21796	NUM
ma-359	240	35	4.51724	4.51724	NUM
ma-359	240	36	3.23593	3.23593	NUM
ma-359	240	37	9	9	NUM
ma-359	240	38	5.89785	5.89785	NUM
ma-359	240	39	4.28469	4.28469	NUM
ma-359	240	40	3.06934	3.06934	NUM
ma-359	240	41	12	12	NUM
ma-359	240	42	6.81358	6.81358	NUM
ma-359	240	43	4.94995	4.94995	NUM
ma-359	240	44	3.54590	3.54590	NUM
ma-359	240	45	11	11	NUM
ma-359	240	46	6.52251	6.52251	NUM
ma-359	240	47	4.73850	4.73850	NUM
ma-359	240	48	3.39442	3.39442	NUM
ma-359	240	49	14	14	NUM
ma-359	240	50	7.36152	7.36152	NUM
ma-359	240	51	5.34802	5.34802	NUM
ma-359	240	52	3.83106	3.83106	NUM
ma-359	240	53	13	13	NUM
ma-359	240	54	7.09280	7.09280	NUM
ma-359	240	55	5.15280	5.15280	NUM
ma-359	240	56	3.69121	3.69121	NUM
ma-359	240	57	16	16	NUM
ma-359	240	58	7.87168	7.87168	NUM
ma-359	240	59	5.71864	5.71864	NUM
ma-359	240	60	4.09655	4.09655	NUM
ma-359	240	61	15	15	NUM
ma-359	240	62	7.62084	7.62084	NUM
ma-359	240	63	5.53641	5.53641	NUM
ma-359	240	64	3.96601	3.96601	NUM
ma-359	240	65	18	18	NUM
ma-359	240	66	8.35093	8.35093	NUM
ma-359	240	67	6.06681	6.06681	NUM
ma-359	240	68	4.34596	4.34596	NUM
ma-359	240	69	17	17	NUM
ma-359	240	70	8.11482	8.11482	NUM
ma-359	240	71	5.89528	5.89528	NUM
ma-359	240	72	4.22309	4.22309	NUM
ma-359	240	73	20	20	NUM
ma-359	240	74	8.80428	8.80428	NUM
ma-359	240	75	6.39616	6.39616	NUM
ma-359	240	76	4.58189	4.58189	NUM
ma-359	240	77	19	19	NUM
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