id	sid	tid	token	lemma	pos
ejpam-816	1	1	6_816_paris.dvi	6_816_paris.dvi	NUM
ejpam-816	1	2	european	european	ADJ
ejpam-816	1	3	journal	journal	NOUN
ejpam-816	1	4	of	of	ADP
ejpam-816	1	5	pure	pure	ADJ
ejpam-816	1	6	and	and	CCONJ
ejpam-816	1	7	applied	apply	VERB
ejpam-816	1	8	mathematics	mathematic	NOUN
ejpam-816	1	9	vol	vol	NOUN
ejpam-816	1	10	.	.	PUNCT
ejpam-816	2	1	3	3	NUM
ejpam-816	2	2	,	,	PUNCT
ejpam-816	2	3	no	no	INTJ
ejpam-816	2	4	.	.	NOUN
ejpam-816	2	5	6	6	NUM
ejpam-816	2	6	,	,	PUNCT
ejpam-816	2	7	2010	2010	NUM
ejpam-816	2	8	,	,	PUNCT
ejpam-816	2	9	1006	1006	NUM
ejpam-816	2	10	-	-	SYM
ejpam-816	2	11	1031	1031	NUM
ejpam-816	2	12	issn	issn	PROPN
ejpam-816	2	13	1307	1307	NUM
ejpam-816	2	14	-	-	SYM
ejpam-816	2	15	5543	5543	NUM
ejpam-816	2	16	–	–	PUNCT
ejpam-816	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-816	2	18	special	special	ADJ
ejpam-816	2	19	issue	issue	NOUN
ejpam-816	2	20	on	on	ADP
ejpam-816	2	21	complex	complex	ADJ
ejpam-816	2	22	analysis	analysis	NOUN
ejpam-816	2	23	:	:	PUNCT
ejpam-816	2	24	theory	theory	NOUN
ejpam-816	2	25	and	and	CCONJ
ejpam-816	2	26	applications	application	NOUN
ejpam-816	2	27	dedicated	dedicate	VERB
ejpam-816	2	28	to	to	ADP
ejpam-816	2	29	professor	professor	PROPN
ejpam-816	2	30	hari	hari	PROPN
ejpam-816	2	31	m.	m.	PROPN
ejpam-816	2	32	srivastava	srivastava	PROPN
ejpam-816	2	33	,	,	PUNCT
ejpam-816	2	34	on	on	ADP
ejpam-816	2	35	the	the	DET
ejpam-816	2	36	occasion	occasion	NOUN
ejpam-816	2	37	of	of	ADP
ejpam-816	2	38	his	his	PRON
ejpam-816	2	39	70th	70th	ADJ
ejpam-816	2	40	birthday	birthday	NOUN
ejpam-816	2	41	asymptotic	asymptotic	ADJ
ejpam-816	2	42	expansion	expansion	NOUN
ejpam-816	2	43	of	of	ADP
ejpam-816	2	44	n	n	CCONJ
ejpam-816	2	45	-	-	PUNCT
ejpam-816	2	46	dimensional	dimensional	ADJ
ejpam-816	2	47	faxén	faxén	NOUN
ejpam-816	2	48	-	-	PUNCT
ejpam-816	2	49	type	type	NOUN
ejpam-816	2	50	integrals	integral	NOUN
ejpam-816	3	1	richard	richard	PROPN
ejpam-816	3	2	b.	b.	PROPN
ejpam-816	3	3	paris	paris	PROPN
ejpam-816	3	4	university	university	PROPN
ejpam-816	3	5	of	of	ADP
ejpam-816	3	6	abertay	abertay	PROPN
ejpam-816	3	7	dundee	dundee	PROPN
ejpam-816	3	8	,	,	PUNCT
ejpam-816	3	9	dundee	dundee	PROPN
ejpam-816	3	10	dd1	dd1	PROPN
ejpam-816	3	11	1hg	1hg	PROPN
ejpam-816	3	12	,	,	PUNCT
ejpam-816	3	13	uk	uk	PROPN
ejpam-816	3	14	abstract	abstract	NOUN
ejpam-816	3	15	.	.	PUNCT
ejpam-816	4	1	the	the	DET
ejpam-816	4	2	asymptotic	asymptotic	ADJ
ejpam-816	4	3	expansion	expansion	NOUN
ejpam-816	4	4	of	of	ADP
ejpam-816	4	5	n	n	CCONJ
ejpam-816	4	6	-	-	PUNCT
ejpam-816	4	7	dimensional	dimensional	ADJ
ejpam-816	4	8	extensions	extension	NOUN
ejpam-816	4	9	of	of	ADP
ejpam-816	4	10	faxén	faxén	NOUN
ejpam-816	4	11	’s	’s	PART
ejpam-816	4	12	integral	integral	ADJ
ejpam-816	4	13	in(z	in(z	NOUN
ejpam-816	4	14	)	)	PUNCT
ejpam-816	4	15	are	be	AUX
ejpam-816	4	16	derived	derive	VERB
ejpam-816	4	17	for	for	ADP
ejpam-816	4	18	large	large	ADJ
ejpam-816	4	19	complex	complex	ADJ
ejpam-816	4	20	values	value	NOUN
ejpam-816	4	21	of	of	ADP
ejpam-816	4	22	the	the	DET
ejpam-816	4	23	variable	variable	NOUN
ejpam-816	4	24	z.	z.	PROPN
ejpam-816	5	1	the	the	DET
ejpam-816	5	2	theory	theory	NOUN
ejpam-816	5	3	relies	rely	VERB
ejpam-816	5	4	on	on	ADP
ejpam-816	5	5	the	the	DET
ejpam-816	5	6	asymptotics	asymptotic	NOUN
ejpam-816	5	7	of	of	ADP
ejpam-816	5	8	the	the	DET
ejpam-816	5	9	generalised	generalise	VERB
ejpam-816	5	10	hypergeometric	hypergeometric	ADJ
ejpam-816	5	11	,	,	PUNCT
ejpam-816	5	12	or	or	CCONJ
ejpam-816	5	13	wright	wright	PROPN
ejpam-816	5	14	,	,	PUNCT
ejpam-816	5	15	function	function	NOUN
ejpam-816	5	16	.	.	PUNCT
ejpam-816	6	1	the	the	DET
ejpam-816	6	2	coefficients	coefficient	NOUN
ejpam-816	6	3	in	in	ADP
ejpam-816	6	4	the	the	DET
ejpam-816	6	5	exponential	exponential	ADJ
ejpam-816	6	6	expansion	expansion	NOUN
ejpam-816	6	7	are	be	AUX
ejpam-816	6	8	obtained	obtain	VERB
ejpam-816	6	9	by	by	ADP
ejpam-816	6	10	means	mean	NOUN
ejpam-816	6	11	of	of	ADP
ejpam-816	6	12	an	an	DET
ejpam-816	6	13	algorithm	algorithm	NOUN
ejpam-816	6	14	applicable	applicable	ADJ
ejpam-816	6	15	for	for	ADP
ejpam-816	6	16	arbitrary	arbitrary	ADJ
ejpam-816	6	17	n.	n.	PROPN
ejpam-816	6	18	numerical	numerical	ADJ
ejpam-816	6	19	examples	example	NOUN
ejpam-816	6	20	are	be	AUX
ejpam-816	6	21	given	give	VERB
ejpam-816	6	22	to	to	PART
ejpam-816	6	23	illustrate	illustrate	VERB
ejpam-816	6	24	the	the	DET
ejpam-816	6	25	accuracy	accuracy	NOUN
ejpam-816	6	26	of	of	ADP
ejpam-816	6	27	the	the	DET
ejpam-816	6	28	expansions	expansion	NOUN
ejpam-816	6	29	.	.	PUNCT
ejpam-816	7	1	2000	2000	NUM
ejpam-816	7	2	mathematics	mathematic	NOUN
ejpam-816	7	3	subject	subject	NOUN
ejpam-816	7	4	classifications	classification	NOUN
ejpam-816	7	5	:	:	PUNCT
ejpam-816	7	6	30e15	30e15	NUM
ejpam-816	7	7	,	,	PUNCT
ejpam-816	7	8	33c70	33c70	NUM
ejpam-816	7	9	,	,	PUNCT
ejpam-816	7	10	41a60	41a60	NUM
ejpam-816	7	11	,	,	PUNCT
ejpam-816	7	12	41a63	41a63	NUM
ejpam-816	7	13	key	key	ADJ
ejpam-816	7	14	words	word	NOUN
ejpam-816	7	15	and	and	CCONJ
ejpam-816	7	16	phrases	phrase	NOUN
ejpam-816	7	17	:	:	PUNCT
ejpam-816	7	18	faxén	faxén	PROPN
ejpam-816	7	19	’s	’s	PART
ejpam-816	7	20	integral	integral	ADJ
ejpam-816	7	21	,	,	PUNCT
ejpam-816	7	22	asymptotic	asymptotic	ADJ
ejpam-816	7	23	expansion	expansion	NOUN
ejpam-816	7	24	,	,	PUNCT
ejpam-816	7	25	wright	wright	PROPN
ejpam-816	7	26	function	function	PROPN
ejpam-816	7	27	,	,	PUNCT
ejpam-816	7	28	generalised	generalise	VERB
ejpam-816	7	29	hypergeometric	hypergeometric	ADJ
ejpam-816	7	30	functions	function	NOUN
ejpam-816	7	31	1	1	NUM
ejpam-816	7	32	.	.	PUNCT
ejpam-816	8	1	introduction	introduction	NOUN
ejpam-816	8	2	we	we	PRON
ejpam-816	8	3	consider	consider	VERB
ejpam-816	8	4	the	the	DET
ejpam-816	8	5	n	n	ADV
ejpam-816	8	6	-	-	PUNCT
ejpam-816	8	7	dimensional	dimensional	ADJ
ejpam-816	8	8	integral	integral	ADJ
ejpam-816	8	9	in(z	in(z	NOUN
ejpam-816	8	10	)	)	PUNCT
ejpam-816	9	1	=	=	SYM
ejpam-816	9	2	λn	λn	PROPN
ejpam-816	9	3	∫	∫	PROPN
ejpam-816	9	4	∞	∞	PROPN
ejpam-816	9	5	0	0	NUM
ejpam-816	9	6	.	.	PUNCT
ejpam-816	9	7	.	.	PUNCT
ejpam-816	9	8	.	.	PUNCT
ejpam-816	10	1	∫	∫	PROPN
ejpam-816	11	1	∞	∞	NUM
ejpam-816	11	2	0	0	NUM
ejpam-816	12	1	x	x	X
ejpam-816	12	2	ν1−1	ν1−1	ADV
ejpam-816	12	3	1	1	NUM
ejpam-816	12	4	.	.	PUNCT
ejpam-816	12	5	.	.	PUNCT
ejpam-816	12	6	.	.	PUNCT
ejpam-816	13	1	xνn−1	xνn−1	PROPN
ejpam-816	13	2	n	n	CCONJ
ejpam-816	13	3	e−	e−	PROPN
ejpam-816	13	4	f	f	PROPN
ejpam-816	13	5	(	(	PUNCT
ejpam-816	13	6	x1	x1	INTJ
ejpam-816	13	7	,	,	PUNCT
ejpam-816	13	8	...	...	PUNCT
ejpam-816	13	9	,	,	PUNCT
ejpam-816	13	10	xn;z	xn;z	NUM
ejpam-816	13	11	)	)	PUNCT
ejpam-816	14	1	d	d	X
ejpam-816	14	2	x1	x1	PROPN
ejpam-816	14	3	.	.	PUNCT
ejpam-816	14	4	.	.	PUNCT
ejpam-816	14	5	.	.	PUNCT
ejpam-816	15	1	d	d	X
ejpam-816	15	2	xn	xn	PUNCT
ejpam-816	15	3	,	,	PUNCT
ejpam-816	15	4	(	(	PUNCT
ejpam-816	15	5	1	1	X
ejpam-816	15	6	)	)	PUNCT
ejpam-816	16	1	where	where	SCONJ
ejpam-816	16	2	f	f	PROPN
ejpam-816	16	3	(	(	PUNCT
ejpam-816	16	4	x1	x1	PROPN
ejpam-816	16	5	,	,	PUNCT
ejpam-816	16	6	.	.	PUNCT
ejpam-816	16	7	.	.	PUNCT
ejpam-816	16	8	.	.	PUNCT
ejpam-816	17	1	,	,	PUNCT
ejpam-816	17	2	xn	xn	PROPN
ejpam-816	17	3	;	;	PUNCT
ejpam-816	17	4	z	z	X
ejpam-816	17	5	)	)	PUNCT
ejpam-816	17	6	=	=	SYM
ejpam-816	18	1	n	n	CCONJ
ejpam-816	18	2	∑	∑	ADV
ejpam-816	18	3	j=1	j=1	NOUN
ejpam-816	18	4	x	x	X
ejpam-816	18	5	µ	µ	X
ejpam-816	18	6	j	j	X
ejpam-816	18	7	j	j	PROPN
ejpam-816	18	8	−	−	PROPN
ejpam-816	18	9	zx	zx	NUM
ejpam-816	18	10	m1	m1	PROPN
ejpam-816	18	11	1	1	NUM
ejpam-816	18	12	.	.	PUNCT
ejpam-816	18	13	.	.	PUNCT
ejpam-816	18	14	.	.	PUNCT
ejpam-816	19	1	xmn	xmn	PROPN
ejpam-816	19	2	n	n	PROPN
ejpam-816	19	3	,	,	PUNCT
ejpam-816	19	4	λn	λn	PROPN
ejpam-816	19	5	=	=	SYM
ejpam-816	19	6	n	n	CCONJ
ejpam-816	19	7	∏	∏	PROPN
ejpam-816	19	8	j=1	j=1	PROPN
ejpam-816	19	9	µ	µ	PROPN
ejpam-816	19	10	j	j	PROPN
ejpam-816	19	11	,	,	PUNCT
ejpam-816	19	12	(	(	PUNCT
ejpam-816	19	13	2	2	NUM
ejpam-816	19	14	)	)	PUNCT
ejpam-816	19	15	and	and	CCONJ
ejpam-816	19	16	the	the	DET
ejpam-816	19	17	factor	factor	NOUN
ejpam-816	19	18	λn	λn	NOUN
ejpam-816	19	19	has	have	AUX
ejpam-816	19	20	been	be	AUX
ejpam-816	19	21	added	add	VERB
ejpam-816	19	22	for	for	ADP
ejpam-816	19	23	later	later	ADJ
ejpam-816	19	24	convenience	convenience	NOUN
ejpam-816	19	25	.	.	PUNCT
ejpam-816	20	1	we	we	PRON
ejpam-816	20	2	suppose	suppose	VERB
ejpam-816	20	3	that	that	SCONJ
ejpam-816	20	4	the	the	DET
ejpam-816	20	5	exponents	exponent	NOUN
ejpam-816	20	6	(	(	PUNCT
ejpam-816	20	7	not	not	PART
ejpam-816	20	8	necessarily	necessarily	ADV
ejpam-816	20	9	integers	integer	VERB
ejpam-816	20	10	)	)	PUNCT
ejpam-816	20	11	satisfy	satisfy	VERB
ejpam-816	20	12	µ	µ	PROPN
ejpam-816	20	13	j	j	X
ejpam-816	20	14	>	>	X
ejpam-816	20	15	m	m	PROPN
ejpam-816	20	16	j	j	X
ejpam-816	20	17	>	>	X
ejpam-816	20	18	0	0	PROPN
ejpam-816	20	19	,	,	PUNCT
ejpam-816	20	20	re	re	ADP
ejpam-816	20	21	(	(	PUNCT
ejpam-816	20	22	ν	ν	PROPN
ejpam-816	20	23	j	j	PROPN
ejpam-816	20	24	)	)	PUNCT
ejpam-816	20	25	>	>	X
ejpam-816	20	26	0	0	PUNCT
ejpam-816	21	1	(	(	PUNCT
ejpam-816	21	2	1≤	1≤	NUM
ejpam-816	21	3	j	j	PROPN
ejpam-816	21	4	≤	≤	PROPN
ejpam-816	21	5	n	n	CCONJ
ejpam-816	21	6	)	)	PUNCT
ejpam-816	21	7	and	and	CCONJ
ejpam-816	21	8	that	that	SCONJ
ejpam-816	21	9	z	z	NOUN
ejpam-816	21	10	denotes	denote	VERB
ejpam-816	21	11	a	a	DET
ejpam-816	21	12	complex	complex	ADJ
ejpam-816	21	13	email	email	NOUN
ejpam-816	21	14	address	address	NOUN
ejpam-816	21	15	:	:	PUNCT
ejpam-816	21	16	r.paris	r.paris	VERB
ejpam-816	21	17	�	�	PROPN
ejpam-816	21	18	abertay.a	abertay.a	PRON
ejpam-816	21	19	.uk	.uk	PUNCT
ejpam-816	22	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-816	22	2	1006	1006	NUM
ejpam-816	23	1	c	c	X
ejpam-816	23	2	©	©	PROPN
ejpam-816	23	3	2010	2010	NUM
ejpam-816	23	4	ejpam	ejpam	NOUN
ejpam-816	23	5	all	all	DET
ejpam-816	23	6	rights	right	NOUN
ejpam-816	23	7	reserved	reserve	VERB
ejpam-816	23	8	.	.	PUNCT
ejpam-816	24	1	r.	r.	PROPN
ejpam-816	24	2	paris	paris	PROPN
ejpam-816	24	3	/	/	SYM
ejpam-816	24	4	eur	eur	PROPN
ejpam-816	24	5	.	.	PUNCT
ejpam-816	25	1	j.	j.	PROPN
ejpam-816	25	2	pure	pure	PROPN
ejpam-816	25	3	appl	appl	PROPN
ejpam-816	25	4	.	.	PROPN
ejpam-816	25	5	math	math	PROPN
ejpam-816	25	6	,	,	PUNCT
ejpam-816	25	7	3	3	NUM
ejpam-816	25	8	(	(	PUNCT
ejpam-816	25	9	2010	2010	NUM
ejpam-816	25	10	)	)	PUNCT
ejpam-816	25	11	,	,	PUNCT
ejpam-816	25	12	1006	1006	NUM
ejpam-816	25	13	-	-	SYM
ejpam-816	25	14	1031	1031	NUM
ejpam-816	25	15	1007	1007	NUM
ejpam-816	25	16	variable	variable	NOUN
ejpam-816	25	17	.	.	PUNCT
ejpam-816	26	1	for	for	ADP
ejpam-816	26	2	convergence	convergence	NOUN
ejpam-816	26	3	of	of	ADP
ejpam-816	26	4	in(z	in(z	NOUN
ejpam-816	26	5	)	)	PUNCT
ejpam-816	26	6	we	we	PRON
ejpam-816	26	7	require	require	VERB
ejpam-816	26	8	that	that	SCONJ
ejpam-816	26	9	µ	µ	PROPN
ejpam-816	26	10	j	j	PROPN
ejpam-816	26	11	and	and	CCONJ
ejpam-816	26	12	m	m	PROPN
ejpam-816	26	13	j	j	NOUN
ejpam-816	26	14	be	be	AUX
ejpam-816	26	15	further	far	ADV
ejpam-816	26	16	restricted	restrict	VERB
ejpam-816	26	17	so	so	SCONJ
ejpam-816	26	18	that	that	SCONJ
ejpam-816	26	19	the	the	DET
ejpam-816	26	20	parameter	parameter	NOUN
ejpam-816	26	21	κ	κ	PROPN
ejpam-816	26	22	,	,	PUNCT
ejpam-816	26	23	defined	define	VERB
ejpam-816	26	24	by	by	ADP
ejpam-816	26	25	κ=	κ=	ADJ
ejpam-816	26	26	1−	1−	NUM
ejpam-816	27	1	n	n	NOUN
ejpam-816	27	2	∑	∑	PUNCT
ejpam-816	27	3	j=1	j=1	PROPN
ejpam-816	27	4	m	m	VERB
ejpam-816	27	5	j	j	PROPN
ejpam-816	27	6	µ	µ	X
ejpam-816	27	7	j	j	PROPN
ejpam-816	27	8	,	,	PUNCT
ejpam-816	27	9	(	(	PUNCT
ejpam-816	27	10	3	3	X
ejpam-816	27	11	)	)	PUNCT
ejpam-816	27	12	should	should	AUX
ejpam-816	27	13	satisfy	satisfy	VERB
ejpam-816	27	14	0	0	NUM
ejpam-816	27	15	<	<	X
ejpam-816	27	16	κ	κ	X
ejpam-816	27	17	<	<	X
ejpam-816	27	18	1	1	NUM
ejpam-816	27	19	.	.	PUNCT
ejpam-816	28	1	the	the	DET
ejpam-816	28	2	geometrical	geometrical	ADJ
ejpam-816	28	3	interpretation	interpretation	NOUN
ejpam-816	28	4	of	of	ADP
ejpam-816	28	5	this	this	DET
ejpam-816	28	6	condition	condition	NOUN
ejpam-816	28	7	results	result	VERB
ejpam-816	28	8	from	from	ADP
ejpam-816	28	9	consideration	consideration	NOUN
ejpam-816	28	10	of	of	ADP
ejpam-816	28	11	the	the	DET
ejpam-816	28	12	newton	newton	PROPN
ejpam-816	28	13	diagram	diagram	PROPN
ejpam-816	28	14	associated	associate	VERB
ejpam-816	28	15	with	with	ADP
ejpam-816	28	16	the	the	DET
ejpam-816	28	17	phase	phase	NOUN
ejpam-816	28	18	function	function	NOUN
ejpam-816	28	19	f	f	PROPN
ejpam-816	28	20	.	.	PUNCT
ejpam-816	29	1	in	in	ADP
ejpam-816	29	2	the	the	DET
ejpam-816	29	3	two	two	NUM
ejpam-816	29	4	-	-	PUNCT
ejpam-816	29	5	dimensional	dimensional	ADJ
ejpam-816	29	6	case	case	NOUN
ejpam-816	29	7	n	n	NOUN
ejpam-816	29	8	=	=	SYM
ejpam-816	29	9	2	2	NUM
ejpam-816	29	10	,	,	PUNCT
ejpam-816	29	11	the	the	DET
ejpam-816	29	12	newton	newton	PROPN
ejpam-816	29	13	diagram	diagram	NOUN
ejpam-816	29	14	is	be	AUX
ejpam-816	29	15	given	give	VERB
ejpam-816	29	16	by	by	ADP
ejpam-816	29	17	the	the	DET
ejpam-816	29	18	boundary	boundary	NOUN
ejpam-816	29	19	of	of	ADP
ejpam-816	29	20	the	the	DET
ejpam-816	29	21	convex	convex	PROPN
ejpam-816	29	22	hull	hull	NOUN
ejpam-816	29	23	formed	form	VERB
ejpam-816	29	24	by	by	ADP
ejpam-816	29	25	the	the	DET
ejpam-816	29	26	point	point	NOUN
ejpam-816	29	27	(	(	PUNCT
ejpam-816	29	28	m1	m1	NOUN
ejpam-816	29	29	,	,	PUNCT
ejpam-816	29	30	m2	m2	PROPN
ejpam-816	29	31	)	)	PUNCT
ejpam-816	29	32	and	and	CCONJ
ejpam-816	29	33	the	the	DET
ejpam-816	29	34	points	point	NOUN
ejpam-816	29	35	(	(	PUNCT
ejpam-816	29	36	µ1	µ1	PROPN
ejpam-816	29	37	,	,	PUNCT
ejpam-816	29	38	0	0	NUM
ejpam-816	29	39	)	)	PUNCT
ejpam-816	29	40	and	and	CCONJ
ejpam-816	29	41	(	(	PUNCT
ejpam-816	29	42	0,µ2	0,µ2	NOUN
ejpam-816	29	43	)	)	PUNCT
ejpam-816	29	44	situated	situate	VERB
ejpam-816	29	45	on	on	ADP
ejpam-816	29	46	the	the	DET
ejpam-816	29	47	coordinate	coordinate	NOUN
ejpam-816	29	48	axes	axis	NOUN
ejpam-816	29	49	,	,	PUNCT
ejpam-816	29	50	with	with	ADP
ejpam-816	29	51	the	the	DET
ejpam-816	29	52	line	line	NOUN
ejpam-816	29	53	joining	join	VERB
ejpam-816	29	54	these	these	DET
ejpam-816	29	55	last	last	ADJ
ejpam-816	29	56	two	two	NUM
ejpam-816	29	57	points	point	NOUN
ejpam-816	29	58	being	be	AUX
ejpam-816	29	59	termed	term	VERB
ejpam-816	29	60	the	the	DET
ejpam-816	29	61	back	back	ADJ
ejpam-816	29	62	face	face	NOUN
ejpam-816	29	63	.	.	PUNCT
ejpam-816	30	1	extension	extension	NOUN
ejpam-816	30	2	to	to	ADP
ejpam-816	30	3	n	n	PROPN
ejpam-816	30	4	≥	≥	NOUN
ejpam-816	30	5	3	3	NUM
ejpam-816	30	6	dimensions	dimension	NOUN
ejpam-816	30	7	is	be	AUX
ejpam-816	30	8	straightforward	straightforward	ADJ
ejpam-816	30	9	with	with	ADP
ejpam-816	30	10	the	the	DET
ejpam-816	30	11	back	back	ADJ
ejpam-816	30	12	face	face	NOUN
ejpam-816	30	13	being	be	AUX
ejpam-816	30	14	a	a	DET
ejpam-816	30	15	hyperplane	hyperplane	NOUN
ejpam-816	30	16	in	in	ADP
ejpam-816	30	17	n	n	ADP
ejpam-816	30	18	dimensions	dimension	NOUN
ejpam-816	30	19	passing	pass	VERB
ejpam-816	30	20	through	through	ADP
ejpam-816	30	21	the	the	DET
ejpam-816	30	22	points	point	NOUN
ejpam-816	30	23	µ	µ	PROPN
ejpam-816	30	24	j	j	X
ejpam-816	30	25	(	(	PUNCT
ejpam-816	30	26	1	1	NUM
ejpam-816	30	27	≤	≤	NUM
ejpam-816	30	28	j	j	PROPN
ejpam-816	30	29	≤	≤	NUM
ejpam-816	30	30	n	n	CCONJ
ejpam-816	30	31	)	)	PUNCT
ejpam-816	30	32	on	on	ADP
ejpam-816	30	33	the	the	DET
ejpam-816	30	34	coordinate	coordinate	NOUN
ejpam-816	30	35	axes	axis	NOUN
ejpam-816	30	36	.	.	PUNCT
ejpam-816	31	1	the	the	DET
ejpam-816	31	2	condition	condition	NOUN
ejpam-816	31	3	0	0	PUNCT
ejpam-816	31	4	<	<	X
ejpam-816	31	5	κ	κ	X
ejpam-816	31	6	<	<	X
ejpam-816	31	7	1	1	NUM
ejpam-816	31	8	then	then	ADV
ejpam-816	31	9	corresponds	correspond	VERB
ejpam-816	31	10	to	to	ADP
ejpam-816	31	11	the	the	DET
ejpam-816	31	12	internal	internal	ADJ
ejpam-816	31	13	point	point	NOUN
ejpam-816	31	14	(	(	PUNCT
ejpam-816	31	15	m1	m1	NOUN
ejpam-816	31	16	,	,	PUNCT
ejpam-816	31	17	.	.	PUNCT
ejpam-816	31	18	.	.	PUNCT
ejpam-816	32	1	.	.	PUNCT
ejpam-816	33	1	,	,	PUNCT
ejpam-816	33	2	mn	mn	PROPN
ejpam-816	33	3	)	)	PUNCT
ejpam-816	33	4	being	be	AUX
ejpam-816	33	5	situated	situate	VERB
ejpam-816	33	6	in	in	ADP
ejpam-816	33	7	front	front	NOUN
ejpam-816	33	8	of	of	ADP
ejpam-816	33	9	the	the	DET
ejpam-816	33	10	back	back	ADJ
ejpam-816	33	11	face	face	NOUN
ejpam-816	33	12	of	of	ADP
ejpam-816	33	13	the	the	DET
ejpam-816	33	14	newton	newton	PROPN
ejpam-816	33	15	diagram	diagram	PROPN
ejpam-816	33	16	.	.	PUNCT
ejpam-816	34	1	in	in	ADP
ejpam-816	34	2	the	the	DET
ejpam-816	34	3	case	case	NOUN
ejpam-816	34	4	n=	n=	ADJ
ejpam-816	34	5	1	1	NUM
ejpam-816	34	6	,	,	PUNCT
ejpam-816	34	7	we	we	PRON
ejpam-816	34	8	have	have	AUX
ejpam-816	34	9	(	(	PUNCT
ejpam-816	34	10	dropping	drop	VERB
ejpam-816	34	11	the	the	DET
ejpam-816	34	12	subscript	subscript	NOUN
ejpam-816	34	13	1	1	NUM
ejpam-816	34	14	on	on	ADP
ejpam-816	34	15	the	the	DET
ejpam-816	34	16	parameters	parameter	NOUN
ejpam-816	34	17	)	)	PUNCT
ejpam-816	34	18	i1(z	i1(z	PROPN
ejpam-816	34	19	)	)	PUNCT
ejpam-816	34	20	=	=	SYM
ejpam-816	34	21	µ	µ	X
ejpam-816	34	22	∫	∫	PROPN
ejpam-816	34	23	∞	∞	PROPN
ejpam-816	34	24	0	0	NUM
ejpam-816	35	1	xν−1e−xµ+zxm	xν−1e−xµ+zxm	PROPN
ejpam-816	36	1	d	d	NOUN
ejpam-816	36	2	x	x	X
ejpam-816	36	3	=	=	PUNCT
ejpam-816	36	4	∫	∫	PROPN
ejpam-816	36	5	∞	∞	PROPN
ejpam-816	36	6	0	0	NUM
ejpam-816	36	7	τ(ν/µ)−1e−τ+zτm/µ	τ(ν/µ)−1e−τ+zτm/µ	SYM
ejpam-816	36	8	dτ	dτ	NOUN
ejpam-816	36	9	,	,	PUNCT
ejpam-816	36	10	where	where	SCONJ
ejpam-816	36	11	κ=	κ=	ADJ
ejpam-816	36	12	1−(m/µ	1−(m/µ	NUM
ejpam-816	36	13	)	)	PUNCT
ejpam-816	36	14	<	<	X
ejpam-816	36	15	1	1	NUM
ejpam-816	36	16	.	.	PUNCT
ejpam-816	37	1	this	this	DET
ejpam-816	37	2	integral	integral	NOUN
ejpam-816	37	3	can	can	AUX
ejpam-816	37	4	be	be	AUX
ejpam-816	37	5	expressed	express	VERB
ejpam-816	37	6	as	as	ADP
ejpam-816	37	7	fi(m/µ,ν/µ	fi(m/µ,ν/µ	NOUN
ejpam-816	37	8	;	;	PUNCT
ejpam-816	37	9	z	z	X
ejpam-816	37	10	)	)	PUNCT
ejpam-816	37	11	,	,	PUNCT
ejpam-816	37	12	where	where	SCONJ
ejpam-816	37	13	fi	fi	NOUN
ejpam-816	37	14	denotes	denote	NOUN
ejpam-816	37	15	faxén	faxén	VERB
ejpam-816	37	16	’s	’s	PART
ejpam-816	38	1	integral	integral	ADJ
ejpam-816	38	2	defined	define	VERB
ejpam-816	38	3	by	by	ADP
ejpam-816	38	4	[	[	X
ejpam-816	38	5	9	9	NUM
ejpam-816	38	6	,	,	PUNCT
ejpam-816	38	7	p.	p.	NOUN
ejpam-816	38	8	332	332	NUM
ejpam-816	38	9	]	]	SYM
ejpam-816	38	10	fi(a	fi(a	X
ejpam-816	38	11	,	,	PUNCT
ejpam-816	38	12	b	b	NOUN
ejpam-816	38	13	;	;	PUNCT
ejpam-816	38	14	z	z	X
ejpam-816	38	15	)	)	PUNCT
ejpam-816	39	1	=	=	SYM
ejpam-816	39	2	∫	∫	PROPN
ejpam-816	40	1	∞	∞	NUM
ejpam-816	40	2	0	0	NUM
ejpam-816	40	3	τb−1e−τ+zτa	τb−1e−τ+zτa	SYM
ejpam-816	40	4	dτ	dτ	INTJ
ejpam-816	40	5	(	(	PUNCT
ejpam-816	40	6	0≤	0≤	NUM
ejpam-816	40	7	re(a	re(a	NOUN
ejpam-816	40	8	)	)	PUNCT
ejpam-816	40	9	<	<	X
ejpam-816	40	10	1	1	NUM
ejpam-816	40	11	,	,	PUNCT
ejpam-816	40	12	re(b	re(b	X
ejpam-816	40	13	)	)	PUNCT
ejpam-816	40	14	>	>	X
ejpam-816	40	15	0	0	NUM
ejpam-816	40	16	)	)	PUNCT
ejpam-816	40	17	.	.	PUNCT
ejpam-816	41	1	consequently	consequently	ADV
ejpam-816	41	2	,	,	PUNCT
ejpam-816	41	3	(	(	PUNCT
ejpam-816	41	4	1	1	X
ejpam-816	41	5	)	)	PUNCT
ejpam-816	41	6	can	can	AUX
ejpam-816	41	7	be	be	AUX
ejpam-816	41	8	considered	consider	VERB
ejpam-816	41	9	as	as	ADP
ejpam-816	41	10	an	an	DET
ejpam-816	41	11	n	n	ADV
ejpam-816	41	12	-	-	PUNCT
ejpam-816	41	13	dimensional	dimensional	ADJ
ejpam-816	41	14	extension	extension	NOUN
ejpam-816	41	15	of	of	ADP
ejpam-816	41	16	faxén	faxén	NOUN
ejpam-816	41	17	’s	’s	PART
ejpam-816	41	18	integral	integral	ADJ
ejpam-816	41	19	.	.	PUNCT
ejpam-816	42	1	a	a	DET
ejpam-816	42	2	different	different	ADJ
ejpam-816	42	3	extension	extension	NOUN
ejpam-816	42	4	of	of	ADP
ejpam-816	42	5	faxén	faxén	NOUN
ejpam-816	42	6	’s	’s	PART
ejpam-816	42	7	integral	integral	ADJ
ejpam-816	42	8	as	as	ADP
ejpam-816	42	9	a	a	DET
ejpam-816	42	10	one	one	NUM
ejpam-816	42	11	-	-	PUNCT
ejpam-816	42	12	dimensional	dimensional	ADJ
ejpam-816	42	13	integral	integral	ADJ
ejpam-816	42	14	with	with	ADP
ejpam-816	42	15	more	more	ADJ
ejpam-816	42	16	than	than	ADP
ejpam-816	42	17	one	one	NUM
ejpam-816	42	18	internal	internal	ADJ
ejpam-816	42	19	point	point	NOUN
ejpam-816	42	20	in	in	ADP
ejpam-816	42	21	the	the	DET
ejpam-816	42	22	phase	phase	NOUN
ejpam-816	42	23	function	function	NOUN
ejpam-816	42	24	f	f	PROPN
ejpam-816	42	25	has	have	AUX
ejpam-816	42	26	been	be	AUX
ejpam-816	42	27	considered	consider	VERB
ejpam-816	42	28	in	in	ADP
ejpam-816	42	29	[	[	X
ejpam-816	42	30	7	7	NUM
ejpam-816	42	31	]	]	PUNCT
ejpam-816	42	32	.	.	PUNCT
ejpam-816	43	1	another	another	DET
ejpam-816	43	2	integral	integral	ADJ
ejpam-816	43	3	that	that	PRON
ejpam-816	43	4	is	be	AUX
ejpam-816	43	5	related	relate	VERB
ejpam-816	43	6	to	to	ADP
ejpam-816	43	7	(	(	PUNCT
ejpam-816	43	8	1	1	NUM
ejpam-816	43	9	)	)	PUNCT
ejpam-816	43	10	,	,	PUNCT
ejpam-816	43	11	but	but	CCONJ
ejpam-816	43	12	with	with	ADP
ejpam-816	43	13	different	different	ADJ
ejpam-816	43	14	domains	domain	NOUN
ejpam-816	43	15	of	of	ADP
ejpam-816	43	16	integration	integration	NOUN
ejpam-816	43	17	,	,	PUNCT
ejpam-816	43	18	is	be	AUX
ejpam-816	43	19	jn(z	jn(z	NOUN
ejpam-816	43	20	)	)	PUNCT
ejpam-816	43	21	=	=	SYM
ejpam-816	44	1	λn	λn	PROPN
ejpam-816	44	2	∫	∫	PROPN
ejpam-816	44	3	∞	∞	PROPN
ejpam-816	44	4	−∞	−∞	PROPN
ejpam-816	44	5	.	.	PUNCT
ejpam-816	44	6	.	.	PUNCT
ejpam-816	44	7	.	.	PUNCT
ejpam-816	45	1	∫	∫	PROPN
ejpam-816	46	1	∞	∞	PROPN
ejpam-816	47	1	−∞	−∞	ADP
ejpam-816	47	2	x	x	X
ejpam-816	47	3	ν1−1	ν1−1	PRON
ejpam-816	47	4	1	1	NUM
ejpam-816	47	5	.	.	PUNCT
ejpam-816	47	6	.	.	PUNCT
ejpam-816	47	7	.	.	PUNCT
ejpam-816	48	1	xνn−1	xνn−1	PROPN
ejpam-816	48	2	n	n	CCONJ
ejpam-816	48	3	e−	e−	PROPN
ejpam-816	48	4	f	f	PROPN
ejpam-816	48	5	(	(	PUNCT
ejpam-816	48	6	x1,	x1,	NOUN
ejpam-816	48	7	...	...	PUNCT
ejpam-816	48	8	,xn;z	,xn;z	PUNCT
ejpam-816	48	9	)	)	PUNCT
ejpam-816	49	1	d	d	X
ejpam-816	49	2	x1	x1	PROPN
ejpam-816	49	3	.	.	PUNCT
ejpam-816	49	4	.	.	PUNCT
ejpam-816	49	5	.	.	PUNCT
ejpam-816	50	1	d	d	X
ejpam-816	50	2	xn	xn	PUNCT
ejpam-816	50	3	,	,	PUNCT
ejpam-816	50	4	(	(	PUNCT
ejpam-816	50	5	4	4	NUM
ejpam-816	50	6	)	)	PUNCT
ejpam-816	50	7	in	in	ADP
ejpam-816	50	8	which	which	PRON
ejpam-816	50	9	the	the	DET
ejpam-816	50	10	µ	µ	PROPN
ejpam-816	50	11	j	j	NOUN
ejpam-816	50	12	are	be	AUX
ejpam-816	50	13	now	now	ADV
ejpam-816	50	14	all	all	PRON
ejpam-816	50	15	restricted	restrict	VERB
ejpam-816	50	16	to	to	PART
ejpam-816	50	17	be	be	AUX
ejpam-816	50	18	positive	positive	ADJ
ejpam-816	50	19	even	even	ADV
ejpam-816	50	20	integers	integer	NOUN
ejpam-816	50	21	.	.	PUNCT
ejpam-816	51	1	when	when	SCONJ
ejpam-816	51	2	the	the	DET
ejpam-816	51	3	exponents	exponent	NOUN
ejpam-816	51	4	ν	ν	ADP
ejpam-816	51	5	j	j	PROPN
ejpam-816	51	6	are	be	AUX
ejpam-816	51	7	nonintegers	noninteger	NOUN
ejpam-816	51	8	,	,	PUNCT
ejpam-816	51	9	the	the	DET
ejpam-816	51	10	integral	integral	ADJ
ejpam-816	51	11	jn(z	jn(z	NOUN
ejpam-816	51	12	)	)	PUNCT
ejpam-816	51	13	is	be	AUX
ejpam-816	51	14	specified	specify	VERB
ejpam-816	51	15	by	by	ADP
ejpam-816	51	16	taking	take	VERB
ejpam-816	51	17	the	the	DET
ejpam-816	51	18	integration	integration	NOUN
ejpam-816	51	19	paths	path	NOUN
ejpam-816	51	20	along	along	ADP
ejpam-816	51	21	the	the	DET
ejpam-816	51	22	negative	negative	ADJ
ejpam-816	51	23	x	x	SYM
ejpam-816	51	24	j	j	NOUN
ejpam-816	51	25	-	-	PUNCT
ejpam-816	51	26	axes	axis	NOUN
ejpam-816	51	27	to	to	PART
ejpam-816	51	28	be	be	AUX
ejpam-816	51	29	along	along	ADP
ejpam-816	51	30	the	the	DET
ejpam-816	51	31	upper	upper	ADJ
ejpam-816	51	32	side	side	NOUN
ejpam-816	51	33	of	of	ADP
ejpam-816	51	34	the	the	DET
ejpam-816	51	35	branch	branch	NOUN
ejpam-816	51	36	cuts	cut	VERB
ejpam-816	51	37	on	on	ADP
ejpam-816	51	38	these	these	DET
ejpam-816	51	39	axes	axis	NOUN
ejpam-816	51	40	.	.	PUNCT
ejpam-816	52	1	variants	variant	NOUN
ejpam-816	52	2	of	of	ADP
ejpam-816	52	3	the	the	DET
ejpam-816	52	4	integral	integral	ADJ
ejpam-816	52	5	jn(z	jn(z	NOUN
ejpam-816	52	6	)	)	PUNCT
ejpam-816	52	7	can	can	AUX
ejpam-816	52	8	also	also	ADV
ejpam-816	52	9	be	be	AUX
ejpam-816	52	10	considered	consider	VERB
ejpam-816	52	11	in	in	ADP
ejpam-816	52	12	which	which	PRON
ejpam-816	52	13	p	p	X
ejpam-816	52	14	<	<	X
ejpam-816	52	15	n	n	X
ejpam-816	52	16	of	of	ADP
ejpam-816	52	17	the	the	DET
ejpam-816	52	18	integrals	integral	NOUN
ejpam-816	52	19	in	in	ADP
ejpam-816	52	20	(	(	PUNCT
ejpam-816	52	21	4	4	X
ejpam-816	52	22	)	)	PUNCT
ejpam-816	52	23	are	be	AUX
ejpam-816	52	24	evaluated	evaluate	VERB
ejpam-816	52	25	over	over	ADP
ejpam-816	52	26	the	the	DET
ejpam-816	52	27	interval	interval	NOUN
ejpam-816	52	28	(	(	PUNCT
ejpam-816	52	29	−∞,∞	−∞,∞	NOUN
ejpam-816	52	30	)	)	PUNCT
ejpam-816	52	31	,	,	PUNCT
ejpam-816	52	32	with	with	ADP
ejpam-816	52	33	the	the	DET
ejpam-816	52	34	remainder	remainder	NOUN
ejpam-816	52	35	over	over	ADP
ejpam-816	52	36	the	the	DET
ejpam-816	52	37	interval	interval	NOUN
ejpam-816	52	38	[	[	X
ejpam-816	52	39	0,∞	0,∞	NOUN
ejpam-816	52	40	)	)	PUNCT
ejpam-816	52	41	.	.	PUNCT
ejpam-816	53	1	special	special	ADJ
ejpam-816	53	2	cases	case	NOUN
ejpam-816	53	3	of	of	ADP
ejpam-816	53	4	the	the	DET
ejpam-816	53	5	integral	integral	ADJ
ejpam-816	53	6	in(z	in(z	NOUN
ejpam-816	53	7	)	)	PUNCT
ejpam-816	53	8	when	when	SCONJ
ejpam-816	53	9	n	n	X
ejpam-816	53	10	=	=	SYM
ejpam-816	53	11	1	1	NUM
ejpam-816	53	12	and	and	CCONJ
ejpam-816	53	13	ν	ν	X
ejpam-816	53	14	=	=	SYM
ejpam-816	53	15	1	1	NUM
ejpam-816	53	16	were	be	AUX
ejpam-816	53	17	first	first	ADV
ejpam-816	53	18	studied	study	VERB
ejpam-816	53	19	asymptotically	asymptotically	ADV
ejpam-816	53	20	in	in	ADP
ejpam-816	53	21	[	[	X
ejpam-816	53	22	4	4	NUM
ejpam-816	53	23	,	,	PUNCT
ejpam-816	53	24	5	5	NUM
ejpam-816	53	25	]	]	PUNCT
ejpam-816	53	26	,	,	PUNCT
ejpam-816	53	27	and	and	CCONJ
ejpam-816	53	28	more	more	ADV
ejpam-816	53	29	generally	generally	ADV
ejpam-816	53	30	in	in	ADP
ejpam-816	53	31	[	[	X
ejpam-816	53	32	1	1	NUM
ejpam-816	53	33	]	]	PUNCT
ejpam-816	53	34	,	,	PUNCT
ejpam-816	53	35	using	use	VERB
ejpam-816	53	36	the	the	DET
ejpam-816	53	37	method	method	NOUN
ejpam-816	53	38	of	of	ADP
ejpam-816	53	39	steepest	steep	ADJ
ejpam-816	53	40	descents	descent	NOUN
ejpam-816	53	41	.	.	PUNCT
ejpam-816	54	1	in	in	ADP
ejpam-816	54	2	[	[	X
ejpam-816	54	3	13	13	NUM
ejpam-816	54	4	]	]	PUNCT
ejpam-816	54	5	the	the	DET
ejpam-816	54	6	asymptotic	asymptotic	ADJ
ejpam-816	54	7	expansion	expansion	NOUN
ejpam-816	54	8	of	of	ADP
ejpam-816	54	9	in(z	in(z	NOUN
ejpam-816	54	10	)	)	PUNCT
ejpam-816	54	11	for	for	ADP
ejpam-816	54	12	large	large	ADJ
ejpam-816	54	13	complex	complex	ADJ
ejpam-816	54	14	z	z	NOUN
ejpam-816	54	15	was	be	AUX
ejpam-816	54	16	obtained	obtain	VERB
ejpam-816	54	17	by	by	ADP
ejpam-816	54	18	application	application	NOUN
ejpam-816	54	19	of	of	ADP
ejpam-816	54	20	the	the	DET
ejpam-816	54	21	asymptotic	asymptotic	ADJ
ejpam-816	54	22	theory	theory	NOUN
ejpam-816	54	23	of	of	ADP
ejpam-816	54	24	the	the	DET
ejpam-816	54	25	generalised	generalise	VERB
ejpam-816	54	26	hypergeometric	hypergeometric	ADJ
ejpam-816	54	27	,	,	PUNCT
ejpam-816	54	28	or	or	CCONJ
ejpam-816	54	29	wright	wright	PROPN
ejpam-816	54	30	,	,	PUNCT
ejpam-816	54	31	function	function	NOUN
ejpam-816	54	32	pψq(z	pψq(z	PROPN
ejpam-816	54	33	)	)	PUNCT
ejpam-816	54	34	defined	define	VERB
ejpam-816	54	35	in	in	ADP
ejpam-816	54	36	(	(	PUNCT
ejpam-816	54	37	5	5	NUM
ejpam-816	54	38	)	)	PUNCT
ejpam-816	54	39	.	.	PUNCT
ejpam-816	55	1	the	the	DET
ejpam-816	55	2	expansion	expansion	NOUN
ejpam-816	55	3	was	be	AUX
ejpam-816	55	4	found	find	VERB
ejpam-816	55	5	to	to	PART
ejpam-816	55	6	consist	consist	VERB
ejpam-816	55	7	of	of	ADP
ejpam-816	55	8	an	an	DET
ejpam-816	55	9	exponential	exponential	ADJ
ejpam-816	55	10	expansion	expansion	NOUN
ejpam-816	55	11	,	,	PUNCT
ejpam-816	55	12	which	which	PRON
ejpam-816	55	13	is	be	AUX
ejpam-816	55	14	dominant	dominant	ADJ
ejpam-816	55	15	in	in	ADP
ejpam-816	55	16	the	the	DET
ejpam-816	55	17	sector	sector	NOUN
ejpam-816	55	18	|arg	|arg	NOUN
ejpam-816	55	19	z|	z|	PROPN
ejpam-816	55	20	<	<	X
ejpam-816	55	21	1	1	NUM
ejpam-816	55	22	2	2	NUM
ejpam-816	55	23	πκ	πκ	NOUN
ejpam-816	55	24	,	,	PUNCT
ejpam-816	55	25	together	together	ADV
ejpam-816	55	26	with	with	ADP
ejpam-816	55	27	an	an	DET
ejpam-816	55	28	algebraic	algebraic	ADJ
ejpam-816	55	29	expansion	expansion	NOUN
ejpam-816	55	30	dominant	dominant	ADJ
ejpam-816	55	31	in	in	ADP
ejpam-816	55	32	the	the	DET
ejpam-816	55	33	rest	rest	NOUN
ejpam-816	55	34	of	of	ADP
ejpam-816	55	35	the	the	DET
ejpam-816	55	36	zplane	zplane	NOUN
ejpam-816	55	37	.	.	PUNCT
ejpam-816	56	1	an	an	DET
ejpam-816	56	2	application	application	NOUN
ejpam-816	56	3	of	of	ADP
ejpam-816	56	4	the	the	DET
ejpam-816	56	5	integral	integral	ADJ
ejpam-816	56	6	in(z	in(z	NOUN
ejpam-816	56	7	)	)	PUNCT
ejpam-816	56	8	in	in	ADP
ejpam-816	56	9	the	the	DET
ejpam-816	56	10	particular	particular	ADJ
ejpam-816	56	11	case	case	NOUN
ejpam-816	56	12	n=	n=	ADJ
ejpam-816	56	13	2	2	NUM
ejpam-816	56	14	has	have	AUX
ejpam-816	56	15	been	be	AUX
ejpam-816	56	16	given	give	VERB
ejpam-816	56	17	in	in	ADP
ejpam-816	56	18	[	[	NOUN
ejpam-816	56	19	8	8	NUM
ejpam-816	56	20	]	]	PUNCT
ejpam-816	56	21	in	in	ADP
ejpam-816	56	22	r.	r.	PROPN
ejpam-816	56	23	paris	paris	PROPN
ejpam-816	56	24	/	/	SYM
ejpam-816	56	25	eur	eur	PROPN
ejpam-816	56	26	.	.	PUNCT
ejpam-816	57	1	j.	j.	PROPN
ejpam-816	57	2	pure	pure	PROPN
ejpam-816	57	3	appl	appl	PROPN
ejpam-816	57	4	.	.	PROPN
ejpam-816	57	5	math	math	PROPN
ejpam-816	57	6	,	,	PUNCT
ejpam-816	57	7	3	3	NUM
ejpam-816	57	8	(	(	PUNCT
ejpam-816	57	9	2010	2010	NUM
ejpam-816	57	10	)	)	PUNCT
ejpam-816	57	11	,	,	PUNCT
ejpam-816	57	12	1006	1006	NUM
ejpam-816	57	13	-	-	SYM
ejpam-816	57	14	1031	1031	NUM
ejpam-816	57	15	1008	1008	NUM
ejpam-816	57	16	the	the	DET
ejpam-816	57	17	discussion	discussion	NOUN
ejpam-816	57	18	of	of	ADP
ejpam-816	57	19	two	two	NUM
ejpam-816	57	20	-	-	PUNCT
ejpam-816	57	21	dimensional	dimensional	ADJ
ejpam-816	57	22	laplace	laplace	NOUN
ejpam-816	57	23	integrals	integral	NOUN
ejpam-816	57	24	with	with	ADP
ejpam-816	57	25	more	more	ADJ
ejpam-816	57	26	general	general	ADJ
ejpam-816	57	27	phase	phase	NOUN
ejpam-816	57	28	and	and	CCONJ
ejpam-816	57	29	amplitude	amplitude	NOUN
ejpam-816	57	30	functions	function	NOUN
ejpam-816	57	31	.	.	PUNCT
ejpam-816	58	1	more	more	ADV
ejpam-816	58	2	recently	recently	ADV
ejpam-816	58	3	,	,	PUNCT
ejpam-816	58	4	breen	breen	NOUN
ejpam-816	58	5	and	and	CCONJ
ejpam-816	58	6	wood	wood	NOUN
ejpam-816	59	1	[	[	X
ejpam-816	59	2	3	3	X
ejpam-816	59	3	]	]	PUNCT
ejpam-816	59	4	have	have	AUX
ejpam-816	59	5	discussed	discuss	VERB
ejpam-816	59	6	an	an	DET
ejpam-816	59	7	application	application	NOUN
ejpam-816	59	8	of	of	ADP
ejpam-816	59	9	in(z	in(z	NOUN
ejpam-816	59	10	)	)	PUNCT
ejpam-816	59	11	as	as	ADP
ejpam-816	59	12	a	a	DET
ejpam-816	59	13	representation	representation	NOUN
ejpam-816	59	14	of	of	ADP
ejpam-816	59	15	the	the	DET
ejpam-816	59	16	solutions	solution	NOUN
ejpam-816	59	17	of	of	ADP
ejpam-816	59	18	certain	certain	ADJ
ejpam-816	59	19	high	high	ADJ
ejpam-816	59	20	-	-	PUNCT
ejpam-816	59	21	order	order	NOUN
ejpam-816	59	22	linear	linear	ADJ
ejpam-816	59	23	differential	differential	NOUN
ejpam-816	59	24	equations	equation	NOUN
ejpam-816	59	25	.	.	PUNCT
ejpam-816	60	1	one	one	NUM
ejpam-816	60	2	of	of	ADP
ejpam-816	60	3	these	these	DET
ejpam-816	60	4	equations	equation	NOUN
ejpam-816	60	5	has	have	VERB
ejpam-816	60	6	the	the	DET
ejpam-816	60	7	form	form	NOUN
ejpam-816	60	8	y(n)(z)−	y(n)(z)−	PROPN
ejpam-816	60	9	p	p	X
ejpam-816	60	10	∑	∑	PROPN
ejpam-816	60	11	r=0	r=0	PROPN
ejpam-816	60	12	αrzr	αrzr	NOUN
ejpam-816	60	13	y(r)(z	y(r)(z	NOUN
ejpam-816	60	14	)	)	PUNCT
ejpam-816	61	1	=	=	SYM
ejpam-816	61	2	0	0	PUNCT
ejpam-816	61	3	(	(	PUNCT
ejpam-816	61	4	n	n	CCONJ
ejpam-816	61	5	>	>	X
ejpam-816	61	6	p	p	X
ejpam-816	61	7	>	>	X
ejpam-816	61	8	0	0	NUM
ejpam-816	61	9	)	)	PUNCT
ejpam-816	61	10	,	,	PUNCT
ejpam-816	61	11	where	where	SCONJ
ejpam-816	61	12	the	the	DET
ejpam-816	61	13	αr	αr	NOUN
ejpam-816	61	14	are	be	AUX
ejpam-816	61	15	arbitrary	arbitrary	ADJ
ejpam-816	61	16	coefficients	coefficient	NOUN
ejpam-816	61	17	.	.	PUNCT
ejpam-816	62	1	this	this	DET
ejpam-816	62	2	equation	equation	NOUN
ejpam-816	62	3	has	have	VERB
ejpam-816	62	4	a	a	DET
ejpam-816	62	5	basis	basis	NOUN
ejpam-816	62	6	of	of	ADP
ejpam-816	62	7	solutions	solution	NOUN
ejpam-816	62	8	given	give	VERB
ejpam-816	62	9	by	by	ADP
ejpam-816	62	10	y(z	y(z	NOUN
ejpam-816	62	11	;	;	PUNCT
ejpam-816	62	12	s	s	X
ejpam-816	62	13	)	)	PUNCT
ejpam-816	62	14	=	=	SYM
ejpam-816	63	1	∫	∫	PROPN
ejpam-816	63	2	∞	∞	PROPN
ejpam-816	63	3	0	0	NUM
ejpam-816	63	4	.	.	PUNCT
ejpam-816	63	5	.	.	PUNCT
ejpam-816	64	1	.	.	PUNCT
ejpam-816	65	1	∫	∫	PROPN
ejpam-816	66	1	∞	∞	NUM
ejpam-816	66	2	0	0	NUM
ejpam-816	67	1	x	x	X
ejpam-816	67	2	ν1−1	ν1−1	ADV
ejpam-816	67	3	1	1	NUM
ejpam-816	67	4	.	.	PUNCT
ejpam-816	67	5	.	.	PUNCT
ejpam-816	67	6	.	.	PUNCT
ejpam-816	68	1	x	x	X
ejpam-816	68	2	νp−1	νp−1	ADJ
ejpam-816	68	3	p	p	NOUN
ejpam-816	68	4	exp{szx1	exp{szx1	NOUN
ejpam-816	68	5	.	.	PUNCT
ejpam-816	68	6	.	.	PUNCT
ejpam-816	68	7	.	.	PUNCT
ejpam-816	69	1	xp	xp	INTJ
ejpam-816	70	1	−	−	PROPN
ejpam-816	70	2	(	(	PUNCT
ejpam-816	70	3	x	x	SYM
ejpam-816	70	4	n	n	PRON
ejpam-816	70	5	1	1	NUM
ejpam-816	70	6	+	+	CCONJ
ejpam-816	70	7	.	.	PUNCT
ejpam-816	70	8	.	.	PUNCT
ejpam-816	71	1	.+	.+	NOUN
ejpam-816	71	2	xn	xn	PUNCT
ejpam-816	71	3	p)/n	p)/n	PROPN
ejpam-816	71	4	}	}	PUNCT
ejpam-816	71	5	d	d	PROPN
ejpam-816	71	6	x1	x1	PROPN
ejpam-816	71	7	.	.	PUNCT
ejpam-816	71	8	.	.	PUNCT
ejpam-816	71	9	.	.	PUNCT
ejpam-816	72	1	d	d	X
ejpam-816	72	2	xp	xp	PROPN
ejpam-816	72	3	,	,	PUNCT
ejpam-816	72	4	where	where	SCONJ
ejpam-816	72	5	sn	sn	PROPN
ejpam-816	72	6	=	=	PUNCT
ejpam-816	72	7	νp	νp	NOUN
ejpam-816	72	8	and	and	CCONJ
ejpam-816	72	9	the	the	DET
ejpam-816	72	10	exponents	exponent	NOUN
ejpam-816	72	11	νr	νr	ADP
ejpam-816	72	12	are	be	AUX
ejpam-816	72	13	related	relate	VERB
ejpam-816	72	14	to	to	ADP
ejpam-816	72	15	the	the	DET
ejpam-816	72	16	coefficients	coefficient	NOUN
ejpam-816	72	17	αr	αr	ADP
ejpam-816	72	18	in	in	ADP
ejpam-816	72	19	a	a	DET
ejpam-816	72	20	manner	manner	NOUN
ejpam-816	72	21	that	that	PRON
ejpam-816	72	22	we	we	PRON
ejpam-816	72	23	do	do	AUX
ejpam-816	72	24	not	not	PART
ejpam-816	72	25	specify	specify	VERB
ejpam-816	72	26	here	here	ADV
ejpam-816	72	27	.	.	PUNCT
ejpam-816	73	1	this	this	DET
ejpam-816	73	2	integral	integral	NOUN
ejpam-816	73	3	is	be	AUX
ejpam-816	73	4	clearly	clearly	ADV
ejpam-816	73	5	related	relate	VERB
ejpam-816	73	6	to	to	ADP
ejpam-816	73	7	ip(sz	ip(sz	NOUN
ejpam-816	73	8	)	)	PUNCT
ejpam-816	73	9	in	in	ADP
ejpam-816	73	10	(	(	PUNCT
ejpam-816	73	11	1	1	X
ejpam-816	73	12	)	)	PUNCT
ejpam-816	73	13	with	with	ADP
ejpam-816	73	14	the	the	DET
ejpam-816	73	15	parameters	parameter	NOUN
ejpam-816	73	16	µ	µ	X
ejpam-816	73	17	j	j	X
ejpam-816	73	18	=	=	SYM
ejpam-816	73	19	n	n	PROPN
ejpam-816	73	20	and	and	CCONJ
ejpam-816	73	21	m	m	PROPN
ejpam-816	73	22	j	j	NOUN
ejpam-816	73	23	=	=	SYM
ejpam-816	73	24	1	1	NUM
ejpam-816	73	25	(	(	PUNCT
ejpam-816	73	26	1≤	1≤	NUM
ejpam-816	73	27	j	j	PROPN
ejpam-816	73	28	≤	≤	PROPN
ejpam-816	73	29	p	p	X
ejpam-816	73	30	)	)	PUNCT
ejpam-816	73	31	.	.	PUNCT
ejpam-816	74	1	the	the	DET
ejpam-816	74	2	integral	integral	ADJ
ejpam-816	74	3	representation	representation	NOUN
ejpam-816	74	4	of	of	ADP
ejpam-816	74	5	solutions	solution	NOUN
ejpam-816	74	6	of	of	ADP
ejpam-816	74	7	the	the	DET
ejpam-816	74	8	above	above	ADJ
ejpam-816	74	9	differential	differential	ADJ
ejpam-816	74	10	equation	equation	NOUN
ejpam-816	74	11	when	when	SCONJ
ejpam-816	74	12	there	there	PRON
ejpam-816	74	13	are	be	VERB
ejpam-816	74	14	two	two	NUM
ejpam-816	74	15	lower	low	ADJ
ejpam-816	74	16	-	-	PUNCT
ejpam-816	74	17	order	order	NOUN
ejpam-816	74	18	derivatives	derivative	NOUN
ejpam-816	74	19	(	(	PUNCT
ejpam-816	74	20	p	p	NOUN
ejpam-816	74	21	=	=	NOUN
ejpam-816	74	22	2	2	NUM
ejpam-816	74	23	)	)	PUNCT
ejpam-816	74	24	was	be	AUX
ejpam-816	74	25	first	first	ADV
ejpam-816	74	26	given	give	VERB
ejpam-816	74	27	by	by	ADP
ejpam-816	74	28	spitzer	spitzer	NOUN
ejpam-816	74	29	[	[	X
ejpam-816	74	30	18	18	NUM
ejpam-816	74	31	]	]	PUNCT
ejpam-816	74	32	,	,	PUNCT
ejpam-816	74	33	with	with	ADP
ejpam-816	74	34	the	the	DET
ejpam-816	74	35	general	general	ADJ
ejpam-816	74	36	case	case	NOUN
ejpam-816	74	37	of	of	ADP
ejpam-816	74	38	p	p	X
ejpam-816	74	39	<	<	X
ejpam-816	74	40	n	n	CCONJ
ejpam-816	74	41	lower	low	ADJ
ejpam-816	74	42	-	-	PUNCT
ejpam-816	74	43	order	order	NOUN
ejpam-816	74	44	derivatives	derivative	NOUN
ejpam-816	74	45	being	be	AUX
ejpam-816	74	46	considered	consider	VERB
ejpam-816	74	47	in	in	ADP
ejpam-816	74	48	[	[	X
ejpam-816	74	49	16	16	NUM
ejpam-816	74	50	]	]	PUNCT
ejpam-816	74	51	.	.	PUNCT
ejpam-816	75	1	these	these	DET
ejpam-816	75	2	results	result	NOUN
ejpam-816	75	3	are	be	AUX
ejpam-816	75	4	described	describe	VERB
ejpam-816	75	5	in	in	ADP
ejpam-816	75	6	[	[	X
ejpam-816	75	7	14	14	NUM
ejpam-816	75	8	,	,	PUNCT
ejpam-816	75	9	pp	pp	ADJ
ejpam-816	75	10	.	.	PUNCT
ejpam-816	76	1	130–133	130–133	NUM
ejpam-816	76	2	]	]	PUNCT
ejpam-816	76	3	.	.	PUNCT
ejpam-816	77	1	in	in	ADP
ejpam-816	77	2	[	[	X
ejpam-816	77	3	3	3	X
ejpam-816	77	4	]	]	PUNCT
ejpam-816	77	5	the	the	DET
ejpam-816	77	6	asymptotics	asymptotic	NOUN
ejpam-816	77	7	of	of	ADP
ejpam-816	77	8	the	the	DET
ejpam-816	77	9	solutions	solution	NOUN
ejpam-816	77	10	y(z	y(z	NOUN
ejpam-816	77	11	;	;	PUNCT
ejpam-816	77	12	s	s	X
ejpam-816	77	13	)	)	PUNCT
ejpam-816	77	14	were	be	AUX
ejpam-816	77	15	obtained	obtain	VERB
ejpam-816	77	16	using	use	VERB
ejpam-816	77	17	the	the	DET
ejpam-816	77	18	theory	theory	NOUN
ejpam-816	77	19	developed	develop	VERB
ejpam-816	77	20	in	in	ADP
ejpam-816	77	21	[	[	X
ejpam-816	77	22	13	13	NUM
ejpam-816	77	23	]	]	PUNCT
ejpam-816	77	24	.	.	PUNCT
ejpam-816	78	1	in	in	ADP
ejpam-816	78	2	this	this	DET
ejpam-816	78	3	paper	paper	NOUN
ejpam-816	78	4	,	,	PUNCT
ejpam-816	78	5	we	we	PRON
ejpam-816	78	6	review	review	VERB
ejpam-816	78	7	the	the	DET
ejpam-816	78	8	asymptotic	asymptotic	ADJ
ejpam-816	78	9	expansion	expansion	NOUN
ejpam-816	78	10	of	of	ADP
ejpam-816	78	11	the	the	DET
ejpam-816	78	12	integral	integral	ADJ
ejpam-816	78	13	in(z	in(z	NOUN
ejpam-816	78	14	)	)	PUNCT
ejpam-816	78	15	in	in	ADP
ejpam-816	78	16	(	(	PUNCT
ejpam-816	78	17	1	1	X
ejpam-816	78	18	)	)	PUNCT
ejpam-816	78	19	using	use	VERB
ejpam-816	78	20	the	the	DET
ejpam-816	78	21	asymptotic	asymptotic	ADJ
ejpam-816	78	22	theory	theory	NOUN
ejpam-816	78	23	of	of	ADP
ejpam-816	78	24	the	the	DET
ejpam-816	78	25	wright	wright	PROPN
ejpam-816	78	26	function	function	PROPN
ejpam-816	78	27	.	.	PUNCT
ejpam-816	79	1	a	a	DET
ejpam-816	79	2	recent	recent	ADJ
ejpam-816	79	3	account	account	NOUN
ejpam-816	79	4	of	of	ADP
ejpam-816	79	5	the	the	DET
ejpam-816	79	6	asymptotic	asymptotic	ADJ
ejpam-816	79	7	theory	theory	NOUN
ejpam-816	79	8	of	of	ADP
ejpam-816	79	9	the	the	DET
ejpam-816	79	10	latter	latter	ADJ
ejpam-816	79	11	function	function	NOUN
ejpam-816	79	12	has	have	AUX
ejpam-816	79	13	been	be	AUX
ejpam-816	79	14	presented	present	VERB
ejpam-816	79	15	in	in	ADP
ejpam-816	79	16	[	[	X
ejpam-816	79	17	11	11	NUM
ejpam-816	79	18	]	]	PUNCT
ejpam-816	79	19	and	and	CCONJ
ejpam-816	79	20	a	a	DET
ejpam-816	79	21	discussion	discussion	NOUN
ejpam-816	79	22	of	of	ADP
ejpam-816	79	23	the	the	DET
ejpam-816	79	24	properties	property	NOUN
ejpam-816	79	25	of	of	ADP
ejpam-816	79	26	0ψ1(z	0ψ1(z	PROPN
ejpam-816	79	27	)	)	PUNCT
ejpam-816	79	28	(	(	PUNCT
ejpam-816	79	29	the	the	DET
ejpam-816	79	30	generalised	generalise	VERB
ejpam-816	79	31	bessel	bessel	ADJ
ejpam-816	79	32	function	function	NOUN
ejpam-816	79	33	)	)	PUNCT
ejpam-816	79	34	,	,	PUNCT
ejpam-816	79	35	together	together	ADV
ejpam-816	79	36	with	with	ADP
ejpam-816	79	37	its	its	PRON
ejpam-816	79	38	application	application	NOUN
ejpam-816	79	39	to	to	ADP
ejpam-816	79	40	the	the	DET
ejpam-816	79	41	solution	solution	NOUN
ejpam-816	79	42	of	of	ADP
ejpam-816	79	43	fractional	fractional	ADJ
ejpam-816	79	44	diffusionwave	diffusionwave	NOUN
ejpam-816	79	45	equations	equation	NOUN
ejpam-816	79	46	,	,	PUNCT
ejpam-816	79	47	can	can	AUX
ejpam-816	79	48	be	be	AUX
ejpam-816	79	49	found	find	VERB
ejpam-816	79	50	in	in	ADP
ejpam-816	79	51	[	[	X
ejpam-816	79	52	6	6	NUM
ejpam-816	79	53	]	]	PUNCT
ejpam-816	79	54	.	.	PUNCT
ejpam-816	80	1	it	it	PRON
ejpam-816	80	2	is	be	AUX
ejpam-816	80	3	shown	show	VERB
ejpam-816	80	4	how	how	SCONJ
ejpam-816	80	5	the	the	DET
ejpam-816	80	6	expansion	expansion	NOUN
ejpam-816	80	7	of	of	ADP
ejpam-816	80	8	in(z)may	in(z)may	PROPN
ejpam-816	80	9	be	be	AUX
ejpam-816	80	10	employed	employ	VERB
ejpam-816	80	11	to	to	PART
ejpam-816	80	12	determine	determine	VERB
ejpam-816	80	13	the	the	DET
ejpam-816	80	14	asymptotic	asymptotic	ADJ
ejpam-816	80	15	structure	structure	NOUN
ejpam-816	80	16	of	of	ADP
ejpam-816	80	17	the	the	DET
ejpam-816	80	18	integral	integral	ADJ
ejpam-816	80	19	jn(z	jn(z	NOUN
ejpam-816	80	20	)	)	PUNCT
ejpam-816	80	21	and	and	CCONJ
ejpam-816	80	22	its	its	PRON
ejpam-816	80	23	variants	variant	NOUN
ejpam-816	80	24	when	when	SCONJ
ejpam-816	80	25	some	some	PRON
ejpam-816	80	26	of	of	ADP
ejpam-816	80	27	the	the	DET
ejpam-816	80	28	integrals	integral	NOUN
ejpam-816	80	29	in	in	ADP
ejpam-816	80	30	(	(	PUNCT
ejpam-816	80	31	4	4	X
ejpam-816	80	32	)	)	PUNCT
ejpam-816	80	33	are	be	AUX
ejpam-816	80	34	taken	take	VERB
ejpam-816	80	35	over	over	ADP
ejpam-816	80	36	[	[	X
ejpam-816	80	37	0,∞	0,∞	NOUN
ejpam-816	80	38	)	)	PUNCT
ejpam-816	80	39	.	.	PUNCT
ejpam-816	81	1	2	2	X
ejpam-816	81	2	.	.	X
ejpam-816	81	3	the	the	DET
ejpam-816	81	4	expansion	expansion	NOUN
ejpam-816	81	5	of	of	ADP
ejpam-816	81	6	the	the	DET
ejpam-816	81	7	wright	wright	PROPN
ejpam-816	81	8	function	function	PROPN
ejpam-816	81	9	pψq(z	pψq(z	PROPN
ejpam-816	81	10	)	)	PUNCT
ejpam-816	81	11	for	for	ADP
ejpam-816	81	12	|z|	|z|	NOUN
ejpam-816	81	13	→∞	→∞	PUNCT
ejpam-816	81	14	the	the	DET
ejpam-816	81	15	asymptotic	asymptotic	ADJ
ejpam-816	81	16	expansion	expansion	NOUN
ejpam-816	81	17	of	of	ADP
ejpam-816	81	18	the	the	DET
ejpam-816	81	19	integrals	integral	NOUN
ejpam-816	81	20	in(z	in(z	NOUN
ejpam-816	81	21	)	)	PUNCT
ejpam-816	81	22	and	and	CCONJ
ejpam-816	81	23	jn(z	jn(z	NOUN
ejpam-816	81	24	)	)	PUNCT
ejpam-816	81	25	will	will	AUX
ejpam-816	81	26	be	be	AUX
ejpam-816	81	27	obtained	obtain	VERB
ejpam-816	81	28	by	by	ADP
ejpam-816	81	29	utilising	utilise	VERB
ejpam-816	81	30	the	the	DET
ejpam-816	81	31	asymptotic	asymptotic	ADJ
ejpam-816	81	32	theory	theory	NOUN
ejpam-816	81	33	of	of	ADP
ejpam-816	81	34	the	the	DET
ejpam-816	81	35	wright	wright	PROPN
ejpam-816	81	36	(	(	PUNCT
ejpam-816	81	37	or	or	CCONJ
ejpam-816	81	38	generalised	generalise	VERB
ejpam-816	81	39	hypergeometric	hypergeometric	ADJ
ejpam-816	81	40	)	)	PUNCT
ejpam-816	81	41	function	function	NOUN
ejpam-816	81	42	which	which	PRON
ejpam-816	81	43	we	we	PRON
ejpam-816	81	44	present	present	VERB
ejpam-816	81	45	in	in	ADP
ejpam-816	81	46	this	this	DET
ejpam-816	81	47	section	section	NOUN
ejpam-816	81	48	.	.	PUNCT
ejpam-816	82	1	the	the	DET
ejpam-816	82	2	wright	wright	PROPN
ejpam-816	82	3	function	function	PROPN
ejpam-816	82	4	pψq(z	pψq(z	PROPN
ejpam-816	82	5	)	)	PUNCT
ejpam-816	82	6	is	be	AUX
ejpam-816	82	7	defined	define	VERB
ejpam-816	82	8	by	by	ADP
ejpam-816	82	9	pψq(z	pψq(z	PROPN
ejpam-816	82	10	)	)	PUNCT
ejpam-816	82	11	≡	≡	PROPN
ejpam-816	82	12	pψq	pψq	PROPN
ejpam-816	82	13	�	�	PROPN
ejpam-816	82	14	(	(	PUNCT
ejpam-816	82	15	α1	α1	PROPN
ejpam-816	82	16	,	,	PUNCT
ejpam-816	82	17	a1	a1	NOUN
ejpam-816	82	18	)	)	PUNCT
ejpam-816	82	19	,	,	PUNCT
ejpam-816	82	20	.	.	PUNCT
ejpam-816	82	21	.	.	PUNCT
ejpam-816	83	1	.	.	PUNCT
ejpam-816	84	1	,	,	PUNCT
ejpam-816	84	2	(	(	PUNCT
ejpam-816	84	3	αp	αp	NOUN
ejpam-816	84	4	,	,	PUNCT
ejpam-816	84	5	ap	ap	PROPN
ejpam-816	84	6	)	)	PUNCT
ejpam-816	84	7	(	(	PUNCT
ejpam-816	84	8	β1	β1	PROPN
ejpam-816	84	9	,	,	PUNCT
ejpam-816	84	10	b1	b1	NOUN
ejpam-816	84	11	)	)	PUNCT
ejpam-816	84	12	,	,	PUNCT
ejpam-816	84	13	.	.	PUNCT
ejpam-816	84	14	.	.	PUNCT
ejpam-816	84	15	.	.	PUNCT
ejpam-816	85	1	,	,	PUNCT
ejpam-816	85	2	(	(	PUNCT
ejpam-816	85	3	βq	βq	ADJ
ejpam-816	85	4	,	,	PUNCT
ejpam-816	85	5	bq	bq	INTJ
ejpam-816	85	6	)	)	PUNCT
ejpam-816	85	7	;	;	PUNCT
ejpam-816	85	8	z	z	NOUN
ejpam-816	85	9	�	�	PROPN
ejpam-816	85	10	=	=	SYM
ejpam-816	85	11	∞	∞	PROPN
ejpam-816	85	12	∑	∑	PUNCT
ejpam-816	85	13	k=0	k=0	PUNCT
ejpam-816	85	14	g(k	g(k	PROPN
ejpam-816	85	15	)	)	PUNCT
ejpam-816	85	16	zk	zk	PROPN
ejpam-816	86	1	k	k	PROPN
ejpam-816	86	2	!	!	PROPN
ejpam-816	86	3	,	,	PUNCT
ejpam-816	86	4	g(k	g(k	NOUN
ejpam-816	86	5	)	)	PUNCT
ejpam-816	86	6	:	:	PUNCT
ejpam-816	87	1	=	=	SYM
ejpam-816	87	2	∏p	∏p	NOUN
ejpam-816	87	3	r=1	r=1	NOUN
ejpam-816	87	4	γ(αr	γ(αr	PROPN
ejpam-816	87	5	k+	k+	X
ejpam-816	87	6	ar	ar	PROPN
ejpam-816	87	7	)	)	PUNCT
ejpam-816	87	8	∏q	∏q	PART
ejpam-816	88	1	r=1	r=1	NOUN
ejpam-816	88	2	γ(βr	γ(βr	X
ejpam-816	88	3	k+	k+	NOUN
ejpam-816	88	4	br	br	NOUN
ejpam-816	88	5	)	)	PUNCT
ejpam-816	88	6	,	,	PUNCT
ejpam-816	88	7	(	(	PUNCT
ejpam-816	88	8	5	5	X
ejpam-816	88	9	)	)	PUNCT
ejpam-816	88	10	where	where	SCONJ
ejpam-816	88	11	p	p	NOUN
ejpam-816	88	12	and	and	CCONJ
ejpam-816	88	13	q	q	NOUN
ejpam-816	88	14	are	be	AUX
ejpam-816	88	15	nonnegative	nonnegative	ADJ
ejpam-816	88	16	integers	integer	NOUN
ejpam-816	88	17	,	,	PUNCT
ejpam-816	88	18	the	the	DET
ejpam-816	88	19	parameters	parameter	NOUN
ejpam-816	88	20	αr	αr	VERB
ejpam-816	88	21	and	and	CCONJ
ejpam-816	88	22	βr	βr	PRON
ejpam-816	88	23	are	be	AUX
ejpam-816	88	24	real	real	ADJ
ejpam-816	88	25	and	and	CCONJ
ejpam-816	88	26	positive	positive	ADJ
ejpam-816	88	27	and	and	CCONJ
ejpam-816	88	28	ar	ar	NOUN
ejpam-816	88	29	and	and	CCONJ
ejpam-816	88	30	br	br	PROPN
ejpam-816	88	31	are	be	AUX
ejpam-816	88	32	arbitrary	arbitrary	ADJ
ejpam-816	88	33	complex	complex	ADJ
ejpam-816	88	34	numbers	number	NOUN
ejpam-816	88	35	.	.	PUNCT
ejpam-816	89	1	in	in	ADP
ejpam-816	89	2	addition	addition	NOUN
ejpam-816	89	3	,	,	PUNCT
ejpam-816	89	4	it	it	PRON
ejpam-816	89	5	is	be	AUX
ejpam-816	89	6	assumed	assume	VERB
ejpam-816	89	7	that	that	SCONJ
ejpam-816	89	8	the	the	DET
ejpam-816	89	9	αr	αr	PROPN
ejpam-816	89	10	and	and	CCONJ
ejpam-816	89	11	ar	ar	PROPN
ejpam-816	89	12	are	be	AUX
ejpam-816	89	13	subject	subject	ADJ
ejpam-816	89	14	to	to	ADP
ejpam-816	89	15	the	the	DET
ejpam-816	89	16	restriction	restriction	NOUN
ejpam-816	89	17	αr	αr	ADP
ejpam-816	89	18	k+	k+	PROPN
ejpam-816	89	19	ar	ar	PROPN
ejpam-816	89	20	6=	6=	PROPN
ejpam-816	89	21	0,−1,−2	0,−1,−2	NUM
ejpam-816	89	22	,	,	PUNCT
ejpam-816	89	23	.	.	PUNCT
ejpam-816	89	24	.	.	PUNCT
ejpam-816	89	25	.	.	PUNCT
ejpam-816	90	1	(	(	PUNCT
ejpam-816	90	2	k	k	X
ejpam-816	90	3	=	=	NOUN
ejpam-816	90	4	0,1,2	0,1,2	NUM
ejpam-816	90	5	,	,	PUNCT
ejpam-816	90	6	.	.	PUNCT
ejpam-816	90	7	.	.	PUNCT
ejpam-816	90	8	.	.	PUNCT
ejpam-816	91	1	;	;	PUNCT
ejpam-816	91	2	1≤	1≤	X
ejpam-816	91	3	r	r	NOUN
ejpam-816	91	4	≤	≤	PUNCT
ejpam-816	91	5	p	p	X
ejpam-816	91	6	)	)	PUNCT
ejpam-816	91	7	(	(	PUNCT
ejpam-816	91	8	6	6	NUM
ejpam-816	91	9	)	)	PUNCT
ejpam-816	91	10	so	so	SCONJ
ejpam-816	91	11	that	that	SCONJ
ejpam-816	91	12	no	no	DET
ejpam-816	91	13	gamma	gamma	NOUN
ejpam-816	91	14	function	function	NOUN
ejpam-816	91	15	in	in	ADP
ejpam-816	91	16	the	the	DET
ejpam-816	91	17	numerator	numerator	NOUN
ejpam-816	91	18	of	of	ADP
ejpam-816	91	19	(	(	PUNCT
ejpam-816	91	20	5	5	NUM
ejpam-816	91	21	)	)	PUNCT
ejpam-816	91	22	is	be	AUX
ejpam-816	91	23	singular	singular	ADJ
ejpam-816	91	24	.	.	PUNCT
ejpam-816	92	1	in	in	ADP
ejpam-816	92	2	the	the	DET
ejpam-816	92	3	special	special	ADJ
ejpam-816	92	4	case	case	NOUN
ejpam-816	92	5	αr	αr	ADP
ejpam-816	92	6	=	=	SYM
ejpam-816	92	7	βr	βr	NOUN
ejpam-816	92	8	=	=	NUM
ejpam-816	92	9	1	1	NUM
ejpam-816	92	10	,	,	PUNCT
ejpam-816	92	11	the	the	DET
ejpam-816	92	12	function	function	NOUN
ejpam-816	92	13	pψq(z	pψq(z	NOUN
ejpam-816	92	14	)	)	PUNCT
ejpam-816	92	15	reduces	reduce	VERB
ejpam-816	92	16	to	to	ADP
ejpam-816	92	17	a	a	DET
ejpam-816	92	18	multiple	multiple	NOUN
ejpam-816	92	19	of	of	ADP
ejpam-816	92	20	the	the	DET
ejpam-816	92	21	generalised	generalise	VERB
ejpam-816	92	22	hypergeometric	hypergeometric	ADJ
ejpam-816	92	23	function	function	NOUN
ejpam-816	92	24	pfq((ap	pfq((ap	PROPN
ejpam-816	92	25	)	)	PUNCT
ejpam-816	92	26	;	;	PUNCT
ejpam-816	92	27	(	(	PUNCT
ejpam-816	92	28	bq	bq	INTJ
ejpam-816	92	29	)	)	PUNCT
ejpam-816	92	30	;	;	PUNCT
ejpam-816	93	1	z	z	X
ejpam-816	93	2	)	)	PUNCT
ejpam-816	93	3	;	;	PUNCT
ejpam-816	93	4	see	see	VERB
ejpam-816	93	5	,	,	PUNCT
ejpam-816	93	6	for	for	ADP
ejpam-816	93	7	example	example	NOUN
ejpam-816	93	8	,	,	PUNCT
ejpam-816	93	9	[	[	X
ejpam-816	93	10	17	17	NUM
ejpam-816	93	11	,	,	PUNCT
ejpam-816	93	12	p.	p.	NOUN
ejpam-816	93	13	40	40	NUM
ejpam-816	93	14	]	]	PUNCT
ejpam-816	93	15	.	.	PUNCT
ejpam-816	94	1	r.	r.	PROPN
ejpam-816	94	2	paris	paris	PROPN
ejpam-816	94	3	/	/	SYM
ejpam-816	94	4	eur	eur	PROPN
ejpam-816	94	5	.	.	PUNCT
ejpam-816	95	1	j.	j.	PROPN
ejpam-816	95	2	pure	pure	PROPN
ejpam-816	95	3	appl	appl	PROPN
ejpam-816	95	4	.	.	PROPN
ejpam-816	95	5	math	math	PROPN
ejpam-816	95	6	,	,	PUNCT
ejpam-816	95	7	3	3	NUM
ejpam-816	95	8	(	(	PUNCT
ejpam-816	95	9	2010	2010	NUM
ejpam-816	95	10	)	)	PUNCT
ejpam-816	95	11	,	,	PUNCT
ejpam-816	95	12	1006	1006	NUM
ejpam-816	95	13	-	-	SYM
ejpam-816	95	14	1031	1031	NUM
ejpam-816	95	15	1009	1009	NUM
ejpam-816	95	16	we	we	PRON
ejpam-816	95	17	summarise	summarise	VERB
ejpam-816	95	18	the	the	DET
ejpam-816	95	19	asymptotic	asymptotic	ADJ
ejpam-816	95	20	expansion	expansion	NOUN
ejpam-816	95	21	of	of	ADP
ejpam-816	95	22	the	the	DET
ejpam-816	95	23	wright	wright	PROPN
ejpam-816	95	24	function	function	PROPN
ejpam-816	95	25	pψq(z	pψq(z	PROPN
ejpam-816	95	26	)	)	PUNCT
ejpam-816	95	27	for	for	ADP
ejpam-816	95	28	|z|	|z|	NOUN
ejpam-816	95	29	→∞	→∞	NOUN
ejpam-816	95	30	given	give	VERB
ejpam-816	95	31	in	in	ADP
ejpam-816	95	32	wright	wright	PROPN
ejpam-816	96	1	[	[	X
ejpam-816	96	2	20	20	NUM
ejpam-816	96	3	,	,	PUNCT
ejpam-816	96	4	21	21	NUM
ejpam-816	96	5	]	]	PUNCT
ejpam-816	97	1	and	and	CCONJ
ejpam-816	97	2	braaksma	braaksma	VERB
ejpam-816	98	1	[	[	X
ejpam-816	98	2	2	2	NUM
ejpam-816	98	3	]	]	PUNCT
ejpam-816	98	4	;	;	PUNCT
ejpam-816	98	5	for	for	ADP
ejpam-816	98	6	a	a	DET
ejpam-816	98	7	summary	summary	NOUN
ejpam-816	98	8	,	,	PUNCT
ejpam-816	98	9	see	see	VERB
ejpam-816	98	10	also	also	ADV
ejpam-816	98	11	[	[	X
ejpam-816	98	12	12	12	NUM
ejpam-816	98	13	,	,	PUNCT
ejpam-816	98	14	§	§	NOUN
ejpam-816	98	15	2.3	2.3	NUM
ejpam-816	98	16	]	]	PUNCT
ejpam-816	98	17	and	and	CCONJ
ejpam-816	99	1	[	[	X
ejpam-816	99	2	11	11	NUM
ejpam-816	99	3	]	]	PUNCT
ejpam-816	99	4	.	.	PUNCT
ejpam-816	100	1	we	we	PRON
ejpam-816	100	2	first	first	ADV
ejpam-816	100	3	introduce	introduce	VERB
ejpam-816	100	4	the	the	DET
ejpam-816	100	5	parameters	parameter	NOUN
ejpam-816	100	6	associated	associate	VERB
ejpam-816	100	7	with	with	ADP
ejpam-816	100	8	g(k	g(k	NOUN
ejpam-816	100	9	)	)	PUNCT
ejpam-816	100	10	given	give	VERB
ejpam-816	100	11	by	by	ADP
ejpam-816	100	12	κ=	κ=	VERB
ejpam-816	100	13	1	1	NUM
ejpam-816	100	14	+	+	NOUN
ejpam-816	100	15	q	q	ADJ
ejpam-816	100	16	∑	∑	PUNCT
ejpam-816	100	17	r=1	r=1	NOUN
ejpam-816	100	18	βr	βr	ADP
ejpam-816	100	19	−	−	PROPN
ejpam-816	100	20	p	p	NOUN
ejpam-816	100	21	∑	∑	PUNCT
ejpam-816	100	22	r=1	r=1	NOUN
ejpam-816	100	23	αr	αr	NUM
ejpam-816	100	24	,	,	PUNCT
ejpam-816	100	25	h=	h=	X
ejpam-816	100	26	p	p	PROPN
ejpam-816	100	27	∏	∏	PROPN
ejpam-816	100	28	r=1	r=1	NOUN
ejpam-816	100	29	ααr	ααr	NOUN
ejpam-816	100	30	r	r	PROPN
ejpam-816	100	31	q	q	X
ejpam-816	100	32	∏	∏	PROPN
ejpam-816	100	33	r=1	r=1	NOUN
ejpam-816	100	34	β−βr	β−βr	ADJ
ejpam-816	100	35	r	r	NOUN
ejpam-816	100	36	,	,	PUNCT
ejpam-816	100	37	ϑ	ϑ	X
ejpam-816	100	38	=	=	X
ejpam-816	100	39	p	p	ADJ
ejpam-816	100	40	∑	∑	PUNCT
ejpam-816	100	41	r=1	r=1	NOUN
ejpam-816	100	42	ar	ar	NOUN
ejpam-816	100	43	−	−	PROPN
ejpam-816	100	44	q	q	X
ejpam-816	100	45	∑	∑	PUNCT
ejpam-816	100	46	r=1	r=1	NOUN
ejpam-816	100	47	br	br	NOUN
ejpam-816	100	48	+	+	CCONJ
ejpam-816	100	49	1	1	NUM
ejpam-816	100	50	2	2	NUM
ejpam-816	100	51	(	(	PUNCT
ejpam-816	100	52	q−	q−	PROPN
ejpam-816	100	53	p	p	NOUN
ejpam-816	100	54	)	)	PUNCT
ejpam-816	100	55	,	,	PUNCT
ejpam-816	100	56	ϑ′	ϑ′	PUNCT
ejpam-816	100	57	=	=	SYM
ejpam-816	100	58	1−	1−	NUM
ejpam-816	100	59	ϑ	ϑ	X
ejpam-816	100	60	,	,	PUNCT
ejpam-816	100	61	(	(	PUNCT
ejpam-816	100	62	7	7	NUM
ejpam-816	100	63	)	)	PUNCT
ejpam-816	100	64	where	where	SCONJ
ejpam-816	100	65	,	,	PUNCT
ejpam-816	100	66	as	as	ADP
ejpam-816	100	67	usual	usual	ADJ
ejpam-816	100	68	,	,	PUNCT
ejpam-816	100	69	an	an	DET
ejpam-816	100	70	empty	empty	ADJ
ejpam-816	100	71	product	product	NOUN
ejpam-816	100	72	has	have	VERB
ejpam-816	100	73	unit	unit	NOUN
ejpam-816	100	74	value	value	NOUN
ejpam-816	100	75	.	.	PUNCT
ejpam-816	101	1	if	if	SCONJ
ejpam-816	101	2	it	it	PRON
ejpam-816	101	3	is	be	AUX
ejpam-816	101	4	supposed	suppose	VERB
ejpam-816	101	5	that	that	SCONJ
ejpam-816	101	6	αr	αr	PROPN
ejpam-816	101	7	and	and	CCONJ
ejpam-816	101	8	βr	βr	INTJ
ejpam-816	101	9	are	be	AUX
ejpam-816	101	10	such	such	ADJ
ejpam-816	101	11	that	that	SCONJ
ejpam-816	101	12	κ	κ	PROPN
ejpam-816	101	13	>	>	X
ejpam-816	101	14	0	0	PROPN
ejpam-816	101	15	,	,	PUNCT
ejpam-816	101	16	then	then	ADV
ejpam-816	101	17	pψq(z	pψq(z	PROPN
ejpam-816	101	18	)	)	PUNCT
ejpam-816	101	19	is	be	AUX
ejpam-816	101	20	uniformly	uniformly	ADJ
ejpam-816	101	21	and	and	CCONJ
ejpam-816	101	22	absolutely	absolutely	ADV
ejpam-816	101	23	convergent	convergent	ADJ
ejpam-816	101	24	for	for	ADP
ejpam-816	101	25	all	all	DET
ejpam-816	101	26	finite	finite	PROPN
ejpam-816	101	27	z.	z.	PROPN
ejpam-816	102	1	it	it	PRON
ejpam-816	102	2	is	be	AUX
ejpam-816	102	3	clear	clear	ADJ
ejpam-816	102	4	that	that	SCONJ
ejpam-816	102	5	pψq(z	pψq(z	PROPN
ejpam-816	102	6	)	)	PUNCT
ejpam-816	102	7	is	be	AUX
ejpam-816	102	8	an	an	DET
ejpam-816	102	9	entire	entire	ADJ
ejpam-816	102	10	function	function	NOUN
ejpam-816	102	11	of	of	ADP
ejpam-816	102	12	z	z	NOUN
ejpam-816	102	13	in	in	ADP
ejpam-816	102	14	this	this	DET
ejpam-816	102	15	case	case	NOUN
ejpam-816	102	16	.	.	PUNCT
ejpam-816	103	1	if	if	SCONJ
ejpam-816	103	2	κ	κ	X
ejpam-816	103	3	=	=	SYM
ejpam-816	103	4	0	0	PROPN
ejpam-816	103	5	,	,	PUNCT
ejpam-816	103	6	the	the	DET
ejpam-816	103	7	sum	sum	NOUN
ejpam-816	103	8	in	in	ADP
ejpam-816	103	9	(	(	PUNCT
ejpam-816	103	10	1	1	X
ejpam-816	103	11	)	)	PUNCT
ejpam-816	103	12	has	have	VERB
ejpam-816	103	13	a	a	DET
ejpam-816	103	14	finite	finite	ADJ
ejpam-816	103	15	radius	radius	NOUN
ejpam-816	103	16	of	of	ADP
ejpam-816	103	17	convergence	convergence	NOUN
ejpam-816	103	18	equal	equal	ADJ
ejpam-816	103	19	to	to	ADP
ejpam-816	103	20	h−1	h−1	PROPN
ejpam-816	103	21	,	,	PUNCT
ejpam-816	103	22	whereas	whereas	SCONJ
ejpam-816	103	23	for	for	ADP
ejpam-816	103	24	κ	κ	X
ejpam-816	103	25	<	<	X
ejpam-816	103	26	0	0	NUM
ejpam-816	104	1	the	the	DET
ejpam-816	104	2	sum	sum	NOUN
ejpam-816	104	3	is	be	AUX
ejpam-816	104	4	divergent	divergent	ADJ
ejpam-816	104	5	for	for	ADP
ejpam-816	104	6	all	all	DET
ejpam-816	104	7	nonzero	nonzero	ADJ
ejpam-816	104	8	values	value	NOUN
ejpam-816	104	9	of	of	ADP
ejpam-816	104	10	z.	z.	PROPN
ejpam-816	105	1	the	the	DET
ejpam-816	105	2	parameter	parameter	NOUN
ejpam-816	105	3	κ	κ	PROPN
ejpam-816	105	4	will	will	AUX
ejpam-816	105	5	be	be	AUX
ejpam-816	105	6	found	find	VERB
ejpam-816	105	7	to	to	PART
ejpam-816	105	8	play	play	VERB
ejpam-816	105	9	a	a	DET
ejpam-816	105	10	critical	critical	ADJ
ejpam-816	105	11	role	role	NOUN
ejpam-816	105	12	in	in	ADP
ejpam-816	105	13	the	the	DET
ejpam-816	105	14	asymptotic	asymptotic	ADJ
ejpam-816	105	15	theory	theory	NOUN
ejpam-816	105	16	of	of	ADP
ejpam-816	105	17	pψq(z	pψq(z	PROPN
ejpam-816	105	18	)	)	PUNCT
ejpam-816	105	19	by	by	ADP
ejpam-816	105	20	determining	determine	VERB
ejpam-816	105	21	the	the	DET
ejpam-816	105	22	sectors	sector	NOUN
ejpam-816	105	23	in	in	ADP
ejpam-816	105	24	the	the	DET
ejpam-816	105	25	z	z	NOUN
ejpam-816	105	26	-	-	NOUN
ejpam-816	105	27	plane	plane	NOUN
ejpam-816	105	28	in	in	ADP
ejpam-816	105	29	which	which	PRON
ejpam-816	105	30	its	its	PRON
ejpam-816	105	31	behaviour	behaviour	NOUN
ejpam-816	105	32	is	be	AUX
ejpam-816	105	33	either	either	ADV
ejpam-816	105	34	exponentially	exponentially	ADV
ejpam-816	105	35	large	large	ADJ
ejpam-816	105	36	,	,	PUNCT
ejpam-816	105	37	algebraic	algebraic	ADJ
ejpam-816	105	38	or	or	CCONJ
ejpam-816	105	39	exponentially	exponentially	ADV
ejpam-816	105	40	small	small	ADJ
ejpam-816	105	41	in	in	ADP
ejpam-816	105	42	character	character	NOUN
ejpam-816	105	43	as	as	ADP
ejpam-816	105	44	|z|	|z|	NOUN
ejpam-816	105	45	→∞.	→∞.	PUNCT
ejpam-816	105	46	the	the	DET
ejpam-816	105	47	exponential	exponential	ADJ
ejpam-816	105	48	expansion	expansion	NOUN
ejpam-816	105	49	ep	ep	PROPN
ejpam-816	105	50	,	,	PUNCT
ejpam-816	105	51	q(z	q(z	PROPN
ejpam-816	105	52	)	)	PUNCT
ejpam-816	105	53	is	be	AUX
ejpam-816	105	54	given	give	VERB
ejpam-816	105	55	by	by	ADP
ejpam-816	105	56	the	the	DET
ejpam-816	105	57	formal	formal	ADJ
ejpam-816	105	58	asymptotic	asymptotic	ADJ
ejpam-816	105	59	sum	sum	NOUN
ejpam-816	105	60	ep	ep	PROPN
ejpam-816	105	61	,	,	PUNCT
ejpam-816	105	62	q(z	q(z	PROPN
ejpam-816	105	63	)	)	PUNCT
ejpam-816	105	64	=	=	SYM
ejpam-816	105	65	zϑez	zϑez	NOUN
ejpam-816	105	66	∞	∞	PROPN
ejpam-816	105	67	∑	∑	PUNCT
ejpam-816	105	68	j=0	j=0	PROPN
ejpam-816	105	69	a	a	DET
ejpam-816	105	70	j	j	PROPN
ejpam-816	105	71	z	z	PROPN
ejpam-816	105	72	−	−	PROPN
ejpam-816	105	73	j	j	PROPN
ejpam-816	105	74	,	,	PUNCT
ejpam-816	105	75	z	z	NOUN
ejpam-816	105	76	=	=	SYM
ejpam-816	105	77	κ(hz)1	κ(hz)1	NOUN
ejpam-816	105	78	/	/	SYM
ejpam-816	105	79	κ	κ	NOUN
ejpam-816	105	80	,	,	PUNCT
ejpam-816	105	81	(	(	PUNCT
ejpam-816	105	82	8)	8)	NUM
ejpam-816	105	83	where	where	SCONJ
ejpam-816	105	84	the	the	DET
ejpam-816	105	85	coefficients	coefficient	NOUN
ejpam-816	105	86	a	a	DET
ejpam-816	105	87	j	j	PROPN
ejpam-816	105	88	are	be	AUX
ejpam-816	105	89	those	those	PRON
ejpam-816	105	90	appearing	appear	VERB
ejpam-816	105	91	in	in	ADP
ejpam-816	105	92	the	the	DET
ejpam-816	105	93	inverse	inverse	NOUN
ejpam-816	105	94	factorial	factorial	NOUN
ejpam-816	105	95	expansion	expansion	NOUN
ejpam-816	105	96	of	of	ADP
ejpam-816	105	97	g(s)/s	g(s)/s	PROPN
ejpam-816	105	98	!	!	PUNCT
ejpam-816	106	1	in	in	ADP
ejpam-816	106	2	the	the	DET
ejpam-816	106	3	form	form	NOUN
ejpam-816	106	4	g(s	g(s	NOUN
ejpam-816	106	5	)	)	PUNCT
ejpam-816	106	6	γ(s+	γ(s+	NOUN
ejpam-816	106	7	1	1	NUM
ejpam-816	106	8	)	)	PUNCT
ejpam-816	106	9	=	=	SYM
ejpam-816	106	10	κ(hκκ)s	κ(hκκ)	VERB
ejpam-816	106	11	�	�	NUM
ejpam-816	106	12	m−1	m−1	PROPN
ejpam-816	106	13	∑	∑	PUNCT
ejpam-816	106	14	j=0	j=0	X
ejpam-816	106	15	a	a	DET
ejpam-816	106	16	j	j	PROPN
ejpam-816	106	17	γ(κs+	γ(κs+	X
ejpam-816	106	18	ϑ′	ϑ′	X
ejpam-816	106	19	+	+	CCONJ
ejpam-816	106	20	j	j	NOUN
ejpam-816	106	21	)	)	PUNCT
ejpam-816	106	22	+	+	NUM
ejpam-816	106	23	o(1	o(1	NOUN
ejpam-816	106	24	)	)	PUNCT
ejpam-816	106	25	γ(κs+	γ(κs+	X
ejpam-816	106	26	ϑ′	ϑ′	X
ejpam-816	106	27	+	+	PROPN
ejpam-816	106	28	m	m	NOUN
ejpam-816	106	29	)	)	PUNCT
ejpam-816	106	30	�	�	PROPN
ejpam-816	106	31	(	(	PUNCT
ejpam-816	106	32	9	9	NUM
ejpam-816	106	33	)	)	PUNCT
ejpam-816	106	34	for	for	ADP
ejpam-816	106	35	|s|	|s|	PROPN
ejpam-816	106	36	→	→	SYM
ejpam-816	106	37	∞	∞	NUM
ejpam-816	106	38	uniformly	uniformly	ADV
ejpam-816	106	39	in	in	ADP
ejpam-816	106	40	|arg	|arg	NOUN
ejpam-816	106	41	s|	s|	VERB
ejpam-816	106	42	≤	≤	NUM
ejpam-816	106	43	π−	π−	PROPN
ejpam-816	106	44	ε	ε	PROPN
ejpam-816	106	45	,	,	PUNCT
ejpam-816	106	46	ε	ε	PROPN
ejpam-816	106	47	>	>	PUNCT
ejpam-816	106	48	0	0	PUNCT
ejpam-816	106	49	and	and	CCONJ
ejpam-816	106	50	arbitrary	arbitrary	ADJ
ejpam-816	106	51	positive	positive	ADJ
ejpam-816	106	52	integer	integer	NOUN
ejpam-816	106	53	m	m	NOUN
ejpam-816	106	54	.	.	PUNCT
ejpam-816	107	1	the	the	DET
ejpam-816	107	2	leading	lead	VERB
ejpam-816	107	3	coefficient	coefficient	NOUN
ejpam-816	107	4	a0	a0	NOUN
ejpam-816	107	5	is	be	AUX
ejpam-816	107	6	specified	specify	VERB
ejpam-816	107	7	by	by	ADP
ejpam-816	107	8	a0	a0	PROPN
ejpam-816	107	9	=	=	SYM
ejpam-816	107	10	(	(	PUNCT
ejpam-816	107	11	2π	2π	NOUN
ejpam-816	107	12	)	)	PUNCT
ejpam-816	107	13	1	1	NUM
ejpam-816	107	14	2	2	NUM
ejpam-816	107	15	(	(	PUNCT
ejpam-816	107	16	p−q)κ−	p−q)κ−	NOUN
ejpam-816	107	17	1	1	NUM
ejpam-816	107	18	2	2	NUM
ejpam-816	107	19	−ϑ	−ϑ	NOUN
ejpam-816	107	20	p	p	PROPN
ejpam-816	107	21	∏	∏	PROPN
ejpam-816	107	22	r=1	r=1	NOUN
ejpam-816	107	23	α	α	NOUN
ejpam-816	107	24	ar−	ar−	SYM
ejpam-816	107	25	1	1	NUM
ejpam-816	107	26	2	2	NUM
ejpam-816	107	27	r	r	NOUN
ejpam-816	107	28	q	q	X
ejpam-816	107	29	∏	∏	PROPN
ejpam-816	107	30	r=1	r=1	NOUN
ejpam-816	107	31	β	β	NOUN
ejpam-816	107	32	1	1	NUM
ejpam-816	107	33	2	2	NUM
ejpam-816	107	34	−br	−br	NOUN
ejpam-816	107	35	r	r	NOUN
ejpam-816	107	36	.	.	PUNCT
ejpam-816	108	1	(	(	PUNCT
ejpam-816	108	2	10	10	NUM
ejpam-816	108	3	)	)	PUNCT
ejpam-816	108	4	the	the	DET
ejpam-816	108	5	coefficients	coefficient	NOUN
ejpam-816	108	6	a	a	DET
ejpam-816	108	7	j	j	NOUN
ejpam-816	108	8	are	be	AUX
ejpam-816	108	9	independent	independent	ADJ
ejpam-816	108	10	of	of	ADP
ejpam-816	108	11	s	s	PRON
ejpam-816	108	12	and	and	CCONJ
ejpam-816	108	13	depend	depend	VERB
ejpam-816	108	14	only	only	ADV
ejpam-816	108	15	on	on	ADP
ejpam-816	108	16	the	the	DET
ejpam-816	108	17	parameters	parameter	NOUN
ejpam-816	108	18	p	p	X
ejpam-816	108	19	,	,	PUNCT
ejpam-816	108	20	q	q	X
ejpam-816	108	21	,	,	PUNCT
ejpam-816	108	22	αr	αr	INTJ
ejpam-816	108	23	,	,	PUNCT
ejpam-816	108	24	βr	βr	INTJ
ejpam-816	108	25	,	,	PUNCT
ejpam-816	108	26	ar	ar	PROPN
ejpam-816	108	27	and	and	CCONJ
ejpam-816	108	28	br	br	PROPN
ejpam-816	108	29	.	.	PUNCT
ejpam-816	109	1	an	an	DET
ejpam-816	109	2	algorithm	algorithm	NOUN
ejpam-816	109	3	for	for	ADP
ejpam-816	109	4	their	their	PRON
ejpam-816	109	5	evaluation	evaluation	NOUN
ejpam-816	109	6	in	in	ADP
ejpam-816	109	7	specific	specific	ADJ
ejpam-816	109	8	cases	case	NOUN
ejpam-816	109	9	when	when	SCONJ
ejpam-816	109	10	αr	αr	ADP
ejpam-816	109	11	>	>	X
ejpam-816	109	12	0	0	NUM
ejpam-816	109	13	,	,	PUNCT
ejpam-816	109	14	βr	βr	ADP
ejpam-816	109	15	>	>	X
ejpam-816	109	16	0	0	NUM
ejpam-816	109	17	is	be	AUX
ejpam-816	109	18	described	describe	VERB
ejpam-816	109	19	in	in	ADP
ejpam-816	109	20	appendix	appendix	ADJ
ejpam-816	109	21	a.	a.	NOUN
ejpam-816	109	22	the	the	DET
ejpam-816	109	23	algebraic	algebraic	ADJ
ejpam-816	109	24	expansion	expansion	NOUN
ejpam-816	109	25	hp	hp	PROPN
ejpam-816	109	26	,	,	PUNCT
ejpam-816	109	27	q(z	q(z	PROPN
ejpam-816	109	28	)	)	PUNCT
ejpam-816	109	29	follows	follow	VERB
ejpam-816	109	30	from	from	ADP
ejpam-816	109	31	the	the	DET
ejpam-816	109	32	mellin	mellin	NOUN
ejpam-816	109	33	-	-	PUNCT
ejpam-816	109	34	barnes	barnes	NOUN
ejpam-816	109	35	integral	integral	ADJ
ejpam-816	109	36	representation	representation	NOUN
ejpam-816	110	1	[	[	X
ejpam-816	110	2	12	12	NUM
ejpam-816	110	3	,	,	PUNCT
ejpam-816	110	4	§	§	NOUN
ejpam-816	110	5	2.3	2.3	NUM
ejpam-816	110	6	]	]	PUNCT
ejpam-816	110	7	pψq(z	pψq(z	PROPN
ejpam-816	110	8	)	)	PUNCT
ejpam-816	110	9	=	=	SYM
ejpam-816	110	10	1	1	NUM
ejpam-816	110	11	2πi	2πi	NOUN
ejpam-816	110	12	∫	∫	PROPN
ejpam-816	110	13	∞i	∞i	NUM
ejpam-816	111	1	−∞i	−∞i	PUNCT
ejpam-816	111	2	γ(s)g(−s)(ze∓πi)−sds	γ(s)g(−s)(ze∓πi)−sds	NOUN
ejpam-816	111	3	,	,	PUNCT
ejpam-816	111	4	|arg(−z)|	|arg(−z)|	PUNCT
ejpam-816	111	5	<	<	X
ejpam-816	111	6	1	1	NUM
ejpam-816	111	7	2	2	NUM
ejpam-816	111	8	π(2−	π(2−	PROPN
ejpam-816	111	9	κ	κ	NOUN
ejpam-816	111	10	)	)	PUNCT
ejpam-816	111	11	,	,	PUNCT
ejpam-816	111	12	(	(	PUNCT
ejpam-816	111	13	11	11	NUM
ejpam-816	111	14	)	)	PUNCT
ejpam-816	111	15	where	where	SCONJ
ejpam-816	111	16	the	the	DET
ejpam-816	111	17	upper	upper	ADJ
ejpam-816	111	18	or	or	CCONJ
ejpam-816	111	19	lower	low	ADJ
ejpam-816	111	20	sign	sign	NOUN
ejpam-816	111	21	is	be	AUX
ejpam-816	111	22	chosen	choose	VERB
ejpam-816	111	23	according	accord	VERB
ejpam-816	111	24	as	as	ADP
ejpam-816	111	25	arg	arg	NOUN
ejpam-816	111	26	z	z	NOUN
ejpam-816	111	27	>	>	X
ejpam-816	111	28	0	0	NUM
ejpam-816	111	29	or	or	CCONJ
ejpam-816	111	30	arg	arg	NOUN
ejpam-816	111	31	z	z	NOUN
ejpam-816	111	32	<	<	X
ejpam-816	111	33	0	0	NUM
ejpam-816	111	34	,	,	PUNCT
ejpam-816	111	35	respectively	respectively	ADV
ejpam-816	111	36	.	.	PUNCT
ejpam-816	112	1	the	the	DET
ejpam-816	112	2	path	path	NOUN
ejpam-816	112	3	of	of	ADP
ejpam-816	112	4	integration	integration	NOUN
ejpam-816	112	5	in	in	ADP
ejpam-816	112	6	(	(	PUNCT
ejpam-816	112	7	11	11	NUM
ejpam-816	112	8	)	)	PUNCT
ejpam-816	112	9	is	be	AUX
ejpam-816	112	10	indented	indent	VERB
ejpam-816	112	11	near	near	ADP
ejpam-816	112	12	s	s	NOUN
ejpam-816	112	13	=	=	NOUN
ejpam-816	112	14	0	0	NUM
ejpam-816	112	15	to	to	PART
ejpam-816	112	16	separate∗	separate∗	NOUN
ejpam-816	112	17	the	the	DET
ejpam-816	112	18	poles	pole	NOUN
ejpam-816	112	19	of	of	ADP
ejpam-816	112	20	γ(s	γ(	NOUN
ejpam-816	112	21	)	)	PUNCT
ejpam-816	112	22	situated	situate	VERB
ejpam-816	112	23	at	at	ADP
ejpam-816	112	24	∗this	∗this	PROPN
ejpam-816	112	25	is	be	AUX
ejpam-816	112	26	always	always	ADV
ejpam-816	112	27	possible	possible	ADJ
ejpam-816	112	28	when	when	SCONJ
ejpam-816	112	29	the	the	DET
ejpam-816	112	30	condition	condition	NOUN
ejpam-816	112	31	(	(	PUNCT
ejpam-816	112	32	6	6	NUM
ejpam-816	112	33	)	)	PUNCT
ejpam-816	112	34	is	be	AUX
ejpam-816	112	35	satisfied	satisfied	ADJ
ejpam-816	112	36	.	.	PUNCT
ejpam-816	113	1	r.	r.	PROPN
ejpam-816	113	2	paris	paris	PROPN
ejpam-816	113	3	/	/	SYM
ejpam-816	113	4	eur	eur	PROPN
ejpam-816	113	5	.	.	PUNCT
ejpam-816	114	1	j.	j.	PROPN
ejpam-816	114	2	pure	pure	PROPN
ejpam-816	114	3	appl	appl	PROPN
ejpam-816	114	4	.	.	PROPN
ejpam-816	114	5	math	math	PROPN
ejpam-816	114	6	,	,	PUNCT
ejpam-816	114	7	3	3	NUM
ejpam-816	114	8	(	(	PUNCT
ejpam-816	114	9	2010	2010	NUM
ejpam-816	114	10	)	)	PUNCT
ejpam-816	114	11	,	,	PUNCT
ejpam-816	114	12	1006	1006	NUM
ejpam-816	114	13	-	-	SYM
ejpam-816	114	14	1031	1031	NUM
ejpam-816	114	15	1010	1010	NUM
ejpam-816	114	16	s	s	NOUN
ejpam-816	114	17	=	=	NOUN
ejpam-816	114	18	0,−1,−2	0,−1,−2	NUM
ejpam-816	114	19	,	,	PUNCT
ejpam-816	114	20	.	.	PUNCT
ejpam-816	114	21	.	.	PUNCT
ejpam-816	114	22	.	.	PUNCT
ejpam-816	115	1	from	from	ADP
ejpam-816	115	2	those	those	PRON
ejpam-816	115	3	of	of	ADP
ejpam-816	115	4	g(−s	g(−	NOUN
ejpam-816	115	5	)	)	PUNCT
ejpam-816	115	6	at	at	ADP
ejpam-816	115	7	sk	sk	NOUN
ejpam-816	115	8	,	,	PUNCT
ejpam-816	115	9	r	r	NOUN
ejpam-816	115	10	=	=	PUNCT
ejpam-816	115	11	(	(	PUNCT
ejpam-816	115	12	ar	ar	PROPN
ejpam-816	115	13	+	+	CCONJ
ejpam-816	115	14	k)/αr	k)/αr	PROPN
ejpam-816	115	15	,	,	PUNCT
ejpam-816	115	16	k	k	PROPN
ejpam-816	115	17	=	=	NOUN
ejpam-816	115	18	0,1,2	0,1,2	NUM
ejpam-816	115	19	,	,	PUNCT
ejpam-816	115	20	.	.	PUNCT
ejpam-816	115	21	.	.	PUNCT
ejpam-816	115	22	.	.	PUNCT
ejpam-816	116	1	(	(	PUNCT
ejpam-816	116	2	1≤	1≤	X
ejpam-816	116	3	r	r	NOUN
ejpam-816	116	4	≤	≤	NOUN
ejpam-816	116	5	p	p	X
ejpam-816	116	6	)	)	PUNCT
ejpam-816	116	7	.	.	PUNCT
ejpam-816	117	1	(	(	PUNCT
ejpam-816	117	2	12	12	NUM
ejpam-816	117	3	)	)	PUNCT
ejpam-816	117	4	in	in	ADP
ejpam-816	117	5	general	general	ADJ
ejpam-816	117	6	there	there	PRON
ejpam-816	117	7	will	will	AUX
ejpam-816	117	8	be	be	AUX
ejpam-816	117	9	p	p	ADJ
ejpam-816	117	10	such	such	ADJ
ejpam-816	117	11	sequences	sequence	NOUN
ejpam-816	117	12	of	of	ADP
ejpam-816	117	13	simple	simple	ADJ
ejpam-816	117	14	poles	pole	NOUN
ejpam-816	117	15	though	though	ADV
ejpam-816	117	16	,	,	PUNCT
ejpam-816	117	17	depending	depend	VERB
ejpam-816	117	18	on	on	ADP
ejpam-816	117	19	the	the	DET
ejpam-816	117	20	values	value	NOUN
ejpam-816	117	21	of	of	ADP
ejpam-816	117	22	αr	αr	NUM
ejpam-816	117	23	and	and	CCONJ
ejpam-816	117	24	ar	ar	PROPN
ejpam-816	117	25	,	,	PUNCT
ejpam-816	117	26	some	some	PRON
ejpam-816	117	27	of	of	ADP
ejpam-816	117	28	these	these	DET
ejpam-816	117	29	poles	pole	NOUN
ejpam-816	117	30	could	could	AUX
ejpam-816	117	31	be	be	AUX
ejpam-816	117	32	multiple	multiple	ADJ
ejpam-816	117	33	poles	pole	NOUN
ejpam-816	117	34	or	or	CCONJ
ejpam-816	117	35	even	even	ADV
ejpam-816	117	36	ordinary	ordinary	ADJ
ejpam-816	117	37	points	point	NOUN
ejpam-816	117	38	if	if	SCONJ
ejpam-816	117	39	any	any	PRON
ejpam-816	117	40	of	of	ADP
ejpam-816	117	41	the	the	DET
ejpam-816	117	42	γ(βrs	γ(βrs	PROPN
ejpam-816	117	43	+	+	CCONJ
ejpam-816	117	44	br	br	NOUN
ejpam-816	117	45	)	)	PUNCT
ejpam-816	117	46	are	be	AUX
ejpam-816	117	47	singular	singular	ADJ
ejpam-816	117	48	there	there	ADV
ejpam-816	117	49	.	.	PUNCT
ejpam-816	118	1	displacement	displacement	NOUN
ejpam-816	118	2	of	of	ADP
ejpam-816	118	3	the	the	DET
ejpam-816	118	4	integration	integration	NOUN
ejpam-816	118	5	contour	contour	NOUN
ejpam-816	118	6	in	in	ADP
ejpam-816	118	7	(	(	PUNCT
ejpam-816	118	8	11	11	NUM
ejpam-816	118	9	)	)	PUNCT
ejpam-816	118	10	to	to	ADP
ejpam-816	118	11	the	the	DET
ejpam-816	118	12	right	right	NOUN
ejpam-816	118	13	over	over	ADP
ejpam-816	118	14	the	the	DET
ejpam-816	118	15	poles	pole	NOUN
ejpam-816	118	16	of	of	ADP
ejpam-816	118	17	g(−s	g(−	NOUN
ejpam-816	118	18	)	)	PUNCT
ejpam-816	118	19	followed	follow	VERB
ejpam-816	118	20	by	by	ADP
ejpam-816	118	21	evaluation	evaluation	NOUN
ejpam-816	118	22	of	of	ADP
ejpam-816	118	23	the	the	DET
ejpam-816	118	24	residues	residue	NOUN
ejpam-816	118	25	then	then	ADV
ejpam-816	118	26	generates	generate	VERB
ejpam-816	118	27	the	the	DET
ejpam-816	118	28	algebraic	algebraic	ADJ
ejpam-816	118	29	expansion	expansion	NOUN
ejpam-816	118	30	of	of	ADP
ejpam-816	118	31	pψq(z	pψq(z	PROPN
ejpam-816	118	32	)	)	PUNCT
ejpam-816	118	33	valid	valid	ADJ
ejpam-816	118	34	as	as	ADP
ejpam-816	118	35	|z|	|z|	NOUN
ejpam-816	118	36	→∞	→∞	NOUN
ejpam-816	118	37	in	in	ADP
ejpam-816	118	38	the	the	DET
ejpam-816	118	39	sector	sector	NOUN
ejpam-816	118	40	in	in	ADP
ejpam-816	118	41	(	(	PUNCT
ejpam-816	118	42	11	11	NUM
ejpam-816	118	43	)	)	PUNCT
ejpam-816	118	44	.	.	PUNCT
ejpam-816	119	1	if	if	SCONJ
ejpam-816	119	2	it	it	PRON
ejpam-816	119	3	is	be	AUX
ejpam-816	119	4	assumed	assume	VERB
ejpam-816	119	5	that	that	SCONJ
ejpam-816	119	6	the	the	DET
ejpam-816	119	7	parameters	parameter	NOUN
ejpam-816	119	8	are	be	AUX
ejpam-816	119	9	such	such	ADJ
ejpam-816	119	10	that	that	SCONJ
ejpam-816	119	11	the	the	DET
ejpam-816	119	12	poles	pole	NOUN
ejpam-816	119	13	in	in	ADP
ejpam-816	119	14	(	(	PUNCT
ejpam-816	119	15	12	12	NUM
ejpam-816	119	16	)	)	PUNCT
ejpam-816	119	17	are	be	AUX
ejpam-816	119	18	all	all	ADV
ejpam-816	119	19	simple	simple	ADJ
ejpam-816	119	20	,	,	PUNCT
ejpam-816	119	21	we	we	PRON
ejpam-816	119	22	obtain	obtain	VERB
ejpam-816	119	23	the	the	DET
ejpam-816	119	24	algebraic	algebraic	ADJ
ejpam-816	119	25	expansion	expansion	NOUN
ejpam-816	119	26	given	give	VERB
ejpam-816	119	27	by	by	ADP
ejpam-816	119	28	hp	hp	PROPN
ejpam-816	119	29	,	,	PUNCT
ejpam-816	119	30	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	119	31	)	)	PUNCT
ejpam-816	119	32	,	,	PUNCT
ejpam-816	119	33	where	where	SCONJ
ejpam-816	119	34	hp	hp	ADP
ejpam-816	119	35	,	,	PUNCT
ejpam-816	119	36	q(z	q(z	PROPN
ejpam-816	119	37	)	)	PUNCT
ejpam-816	119	38	=	=	PUNCT
ejpam-816	120	1	p	p	NOUN
ejpam-816	120	2	∑	∑	PUNCT
ejpam-816	120	3	j=1	j=1	PROPN
ejpam-816	120	4	α−1	α−1	PROPN
ejpam-816	120	5	j	j	PROPN
ejpam-816	120	6	z−a	z−a	PROPN
ejpam-816	120	7	j	j	PROPN
ejpam-816	120	8	/	/	SYM
ejpam-816	120	9	α	α	PROPN
ejpam-816	120	10	j	j	PROPN
ejpam-816	120	11	sp	sp	PROPN
ejpam-816	120	12	,	,	PUNCT
ejpam-816	120	13	q(z	q(z	PROPN
ejpam-816	120	14	;	;	PUNCT
ejpam-816	120	15	j	j	PROPN
ejpam-816	120	16	)	)	PUNCT
ejpam-816	120	17	(	(	PUNCT
ejpam-816	120	18	13	13	NUM
ejpam-816	120	19	)	)	PUNCT
ejpam-816	120	20	and	and	CCONJ
ejpam-816	120	21	sp	sp	ADP
ejpam-816	120	22	,	,	PUNCT
ejpam-816	120	23	q(z	q(z	PROPN
ejpam-816	120	24	;	;	PUNCT
ejpam-816	120	25	j	j	PROPN
ejpam-816	120	26	)	)	PUNCT
ejpam-816	120	27	denotes	denote	VERB
ejpam-816	120	28	the	the	DET
ejpam-816	120	29	formal	formal	ADJ
ejpam-816	120	30	asymptotic	asymptotic	ADJ
ejpam-816	120	31	sum	sum	NOUN
ejpam-816	120	32	sp	sp	NOUN
ejpam-816	120	33	,	,	PUNCT
ejpam-816	120	34	q(z	q(z	PROPN
ejpam-816	120	35	;	;	PUNCT
ejpam-816	120	36	j	j	NOUN
ejpam-816	120	37	)	)	PUNCT
ejpam-816	121	1	=	=	SYM
ejpam-816	122	1	∞	∞	PROPN
ejpam-816	122	2	∑	∑	PUNCT
ejpam-816	122	3	k=0	k=0	PROPN
ejpam-816	122	4	(	(	PUNCT
ejpam-816	122	5	−)k	−)k	PROPN
ejpam-816	122	6	k	k	PROPN
ejpam-816	122	7	!	!	PUNCT
ejpam-816	123	1	γ	γ	PROPN
ejpam-816	123	2	�	�	PROPN
ejpam-816	123	3	k+	k+	PUNCT
ejpam-816	123	4	a	a	DET
ejpam-816	123	5	j	j	PROPN
ejpam-816	123	6	α	α	PRON
ejpam-816	123	7	j	j	PROPN
ejpam-816	123	8	�	�	PROPN
ejpam-816	123	9	∏′	∏′	PROPN
ejpam-816	123	10	p	p	NOUN
ejpam-816	123	11	r=1	r=1	NOUN
ejpam-816	123	12	γ(ar	γ(ar	X
ejpam-816	123	13	−αrsk	−αrsk	PROPN
ejpam-816	123	14	,	,	PUNCT
ejpam-816	123	15	j	j	NOUN
ejpam-816	123	16	)	)	PUNCT
ejpam-816	123	17	∏q	∏q	VERB
ejpam-816	124	1	r=1	r=1	NOUN
ejpam-816	124	2	γ(br	γ(br	NOUN
ejpam-816	125	1	−	−	PROPN
ejpam-816	125	2	βrsk	βrsk	PROPN
ejpam-816	125	3	,	,	PUNCT
ejpam-816	125	4	j	j	NOUN
ejpam-816	125	5	)	)	PUNCT
ejpam-816	125	6	z−k	z−k	PROPN
ejpam-816	125	7	/	/	SYM
ejpam-816	125	8	α	α	PROPN
ejpam-816	125	9	j	j	PROPN
ejpam-816	125	10	,	,	PUNCT
ejpam-816	125	11	(	(	PUNCT
ejpam-816	125	12	14	14	NUM
ejpam-816	125	13	)	)	PUNCT
ejpam-816	125	14	with	with	ADP
ejpam-816	125	15	the	the	DET
ejpam-816	125	16	prime	prime	NOUN
ejpam-816	125	17	indicating	indicate	VERB
ejpam-816	125	18	the	the	DET
ejpam-816	125	19	omission	omission	NOUN
ejpam-816	125	20	of	of	ADP
ejpam-816	125	21	the	the	DET
ejpam-816	125	22	term	term	NOUN
ejpam-816	125	23	corresponding	correspond	VERB
ejpam-816	125	24	to	to	ADP
ejpam-816	125	25	r	r	NOUN
ejpam-816	125	26	=	=	SYM
ejpam-816	125	27	j	j	PROPN
ejpam-816	125	28	in	in	ADP
ejpam-816	125	29	the	the	DET
ejpam-816	125	30	product	product	NOUN
ejpam-816	125	31	.	.	PUNCT
ejpam-816	126	1	this	this	DET
ejpam-816	126	2	expression	expression	NOUN
ejpam-816	126	3	consists	consist	VERB
ejpam-816	126	4	of	of	ADP
ejpam-816	126	5	p	p	NOUN
ejpam-816	126	6	expansions	expansion	NOUN
ejpam-816	126	7	with	with	ADP
ejpam-816	126	8	the	the	DET
ejpam-816	126	9	leading	lead	VERB
ejpam-816	126	10	behaviour	behaviour	NOUN
ejpam-816	126	11	z−a	z−a	PROPN
ejpam-816	126	12	j	j	PROPN
ejpam-816	126	13	/	/	SYM
ejpam-816	126	14	α	α	PROPN
ejpam-816	126	15	j	j	PROPN
ejpam-816	126	16	(	(	PUNCT
ejpam-816	126	17	1≤	1≤	NUM
ejpam-816	126	18	j	j	PROPN
ejpam-816	126	19	≤	≤	PROPN
ejpam-816	126	20	p	p	X
ejpam-816	126	21	)	)	PUNCT
ejpam-816	126	22	.	.	PUNCT
ejpam-816	127	1	when	when	SCONJ
ejpam-816	127	2	the	the	DET
ejpam-816	127	3	parameters	parameter	NOUN
ejpam-816	127	4	αr	αr	VERB
ejpam-816	127	5	and	and	CCONJ
ejpam-816	127	6	ar	ar	PROPN
ejpam-816	127	7	are	be	AUX
ejpam-816	127	8	such	such	ADJ
ejpam-816	127	9	that	that	SCONJ
ejpam-816	127	10	some	some	PRON
ejpam-816	127	11	of	of	ADP
ejpam-816	127	12	the	the	DET
ejpam-816	127	13	poles	pole	NOUN
ejpam-816	127	14	are	be	AUX
ejpam-816	127	15	of	of	ADP
ejpam-816	127	16	higher	high	ADJ
ejpam-816	127	17	order	order	NOUN
ejpam-816	127	18	,	,	PUNCT
ejpam-816	127	19	the	the	DET
ejpam-816	127	20	expansion	expansion	NOUN
ejpam-816	127	21	(	(	PUNCT
ejpam-816	127	22	13	13	NUM
ejpam-816	127	23	)	)	PUNCT
ejpam-816	127	24	is	be	AUX
ejpam-816	127	25	invalid	invalid	ADJ
ejpam-816	127	26	and	and	CCONJ
ejpam-816	127	27	the	the	DET
ejpam-816	127	28	residues	residue	NOUN
ejpam-816	127	29	must	must	AUX
ejpam-816	127	30	then	then	ADV
ejpam-816	127	31	be	be	AUX
ejpam-816	127	32	evaluated	evaluate	VERB
ejpam-816	127	33	according	accord	VERB
ejpam-816	127	34	to	to	ADP
ejpam-816	127	35	the	the	DET
ejpam-816	127	36	multiplicity	multiplicity	NOUN
ejpam-816	127	37	of	of	ADP
ejpam-816	127	38	the	the	DET
ejpam-816	127	39	poles	pole	NOUN
ejpam-816	127	40	concerned	concern	VERB
ejpam-816	127	41	;	;	PUNCT
ejpam-816	127	42	this	this	PRON
ejpam-816	127	43	will	will	AUX
ejpam-816	127	44	lead	lead	VERB
ejpam-816	127	45	to	to	ADP
ejpam-816	127	46	terms	term	NOUN
ejpam-816	127	47	involving	involve	VERB
ejpam-816	127	48	log	log	PROPN
ejpam-816	127	49	z	z	NOUN
ejpam-816	127	50	in	in	ADP
ejpam-816	127	51	the	the	DET
ejpam-816	127	52	algebraic	algebraic	ADJ
ejpam-816	127	53	expansion	expansion	NOUN
ejpam-816	127	54	.	.	PUNCT
ejpam-816	128	1	we	we	PRON
ejpam-816	128	2	present	present	VERB
ejpam-816	128	3	the	the	DET
ejpam-816	128	4	asymptotic	asymptotic	ADJ
ejpam-816	128	5	expansion	expansion	NOUN
ejpam-816	128	6	of	of	ADP
ejpam-816	128	7	pψq(z	pψq(z	PROPN
ejpam-816	128	8	)	)	PUNCT
ejpam-816	128	9	for	for	ADP
ejpam-816	128	10	large	large	ADJ
ejpam-816	128	11	|z|	|z|	NOUN
ejpam-816	128	12	only	only	ADV
ejpam-816	128	13	in	in	ADP
ejpam-816	128	14	the	the	DET
ejpam-816	128	15	case	case	NOUN
ejpam-816	128	16	when	when	SCONJ
ejpam-816	128	17	0	0	NUM
ejpam-816	128	18	<	<	X
ejpam-816	128	19	κ	κ	X
ejpam-816	128	20	≤	≤	ADV
ejpam-816	128	21	2	2	NUM
ejpam-816	128	22	,	,	PUNCT
ejpam-816	128	23	since	since	SCONJ
ejpam-816	128	24	the	the	DET
ejpam-816	128	25	value	value	NOUN
ejpam-816	128	26	of	of	ADP
ejpam-816	128	27	this	this	DET
ejpam-816	128	28	parameter	parameter	NOUN
ejpam-816	128	29	associated	associate	VERB
ejpam-816	128	30	with	with	ADP
ejpam-816	128	31	the	the	DET
ejpam-816	128	32	integrals	integral	NOUN
ejpam-816	128	33	(	(	PUNCT
ejpam-816	128	34	1	1	NUM
ejpam-816	128	35	)	)	PUNCT
ejpam-816	128	36	and	and	CCONJ
ejpam-816	128	37	(	(	PUNCT
ejpam-816	128	38	4	4	X
ejpam-816	128	39	)	)	PUNCT
ejpam-816	128	40	must	must	AUX
ejpam-816	128	41	satisfy	satisfy	VERB
ejpam-816	128	42	0	0	NUM
ejpam-816	128	43	<	<	X
ejpam-816	128	44	κ	κ	X
ejpam-816	128	45	<	<	X
ejpam-816	128	46	1	1	NUM
ejpam-816	128	47	.	.	PUNCT
ejpam-816	129	1	a	a	DET
ejpam-816	129	2	fuller	full	ADJ
ejpam-816	129	3	list	list	NOUN
ejpam-816	129	4	of	of	ADP
ejpam-816	129	5	expansion	expansion	NOUN
ejpam-816	129	6	theorems	theorem	NOUN
ejpam-816	129	7	is	be	AUX
ejpam-816	129	8	given	give	VERB
ejpam-816	129	9	in	in	ADP
ejpam-816	129	10	[	[	X
ejpam-816	129	11	2	2	NUM
ejpam-816	129	12	,	,	PUNCT
ejpam-816	129	13	20	20	NUM
ejpam-816	129	14	,	,	PUNCT
ejpam-816	129	15	21	21	NUM
ejpam-816	129	16	]	]	PUNCT
ejpam-816	129	17	;	;	PUNCT
ejpam-816	129	18	see	see	VERB
ejpam-816	129	19	also	also	ADV
ejpam-816	129	20	[	[	X
ejpam-816	129	21	11	11	NUM
ejpam-816	129	22	]	]	PUNCT
ejpam-816	129	23	.	.	PUNCT
ejpam-816	130	1	we	we	PRON
ejpam-816	130	2	have	have	VERB
ejpam-816	130	3	the	the	DET
ejpam-816	130	4	following	follow	VERB
ejpam-816	130	5	theorems	theorem	NOUN
ejpam-816	130	6	,	,	PUNCT
ejpam-816	130	7	where	where	SCONJ
ejpam-816	130	8	throughout	throughout	ADP
ejpam-816	130	9	we	we	PRON
ejpam-816	130	10	let	let	VERB
ejpam-816	130	11	ε	ε	PROPN
ejpam-816	130	12	denote	denote	VERB
ejpam-816	130	13	an	an	DET
ejpam-816	130	14	arbitrarily	arbitrarily	ADV
ejpam-816	130	15	small	small	ADJ
ejpam-816	130	16	positive	positive	ADJ
ejpam-816	130	17	quantity	quantity	NOUN
ejpam-816	130	18	.	.	PUNCT
ejpam-816	131	1	theorem	theorem	NOUN
ejpam-816	131	2	1	1	NUM
ejpam-816	131	3	.	.	PUNCT
ejpam-816	132	1	if	if	SCONJ
ejpam-816	132	2	0	0	NUM
ejpam-816	132	3	<	<	X
ejpam-816	132	4	κ	κ	X
ejpam-816	132	5	<	<	X
ejpam-816	132	6	2	2	NUM
ejpam-816	132	7	,	,	PUNCT
ejpam-816	132	8	then	then	ADV
ejpam-816	132	9	pψq(z	pψq(z	PROPN
ejpam-816	132	10	)	)	PUNCT
ejpam-816	132	11	∼	∼	NOUN
ejpam-816	132	12	¨	¨	NOUN
ejpam-816	132	13	ep	ep	PROPN
ejpam-816	132	14	,	,	PUNCT
ejpam-816	132	15	q(z	q(z	PROPN
ejpam-816	132	16	)	)	PUNCT
ejpam-816	132	17	+	+	NOUN
ejpam-816	132	18	hp	hp	ADJ
ejpam-816	132	19	,	,	PUNCT
ejpam-816	132	20	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	132	21	)	)	PUNCT
ejpam-816	132	22	in	in	ADP
ejpam-816	132	23	|arg	|arg	VERB
ejpam-816	132	24	z|	z|	PRON
ejpam-816	132	25	≤	≤	NOUN
ejpam-816	132	26	1	1	NUM
ejpam-816	132	27	2	2	NUM
ejpam-816	132	28	πκ	πκ	NOUN
ejpam-816	132	29	hp	hp	PROPN
ejpam-816	132	30	,	,	PUNCT
ejpam-816	132	31	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	132	32	)	)	PUNCT
ejpam-816	132	33	in	in	ADP
ejpam-816	132	34	|arg(−z)|	|arg(−z)|	NOUN
ejpam-816	132	35	≤	≤	NUM
ejpam-816	132	36	1	1	NUM
ejpam-816	132	37	2	2	NUM
ejpam-816	132	38	π(2−	π(2−	PROPN
ejpam-816	132	39	κ)−	κ)−	PROPN
ejpam-816	132	40	ε	ε	PROPN
ejpam-816	132	41	(	(	PUNCT
ejpam-816	132	42	15	15	NUM
ejpam-816	132	43	)	)	PUNCT
ejpam-816	132	44	as	as	ADP
ejpam-816	132	45	|z|	|z|	NOUN
ejpam-816	132	46	→	→	SYM
ejpam-816	132	47	∞.	∞.	PROPN
ejpam-816	132	48	the	the	DET
ejpam-816	132	49	upper	upper	ADJ
ejpam-816	132	50	or	or	CCONJ
ejpam-816	132	51	lower	low	ADJ
ejpam-816	132	52	sign	sign	NOUN
ejpam-816	132	53	in	in	ADP
ejpam-816	132	54	hp	hp	PROPN
ejpam-816	132	55	,	,	PUNCT
ejpam-816	132	56	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	132	57	)	)	PUNCT
ejpam-816	132	58	is	be	AUX
ejpam-816	132	59	chosen	choose	VERB
ejpam-816	132	60	according	accord	VERB
ejpam-816	132	61	as	as	SCONJ
ejpam-816	132	62	z	z	PROPN
ejpam-816	132	63	lies	lie	VERB
ejpam-816	132	64	in	in	ADP
ejpam-816	132	65	the	the	DET
ejpam-816	132	66	upper	upper	ADJ
ejpam-816	132	67	or	or	CCONJ
ejpam-816	132	68	lower	low	ADJ
ejpam-816	132	69	half	half	ADJ
ejpam-816	132	70	-	-	PUNCT
ejpam-816	132	71	plane	plane	NOUN
ejpam-816	132	72	,	,	PUNCT
ejpam-816	132	73	respectively	respectively	ADV
ejpam-816	132	74	.	.	PUNCT
ejpam-816	133	1	it	it	PRON
ejpam-816	133	2	is	be	AUX
ejpam-816	133	3	seen	see	VERB
ejpam-816	133	4	that	that	SCONJ
ejpam-816	133	5	the	the	DET
ejpam-816	133	6	z	z	NOUN
ejpam-816	133	7	-	-	PUNCT
ejpam-816	133	8	plane	plane	NOUN
ejpam-816	133	9	is	be	AUX
ejpam-816	133	10	divided	divide	VERB
ejpam-816	133	11	into	into	ADP
ejpam-816	133	12	two	two	NUM
ejpam-816	133	13	sectors	sector	NOUN
ejpam-816	133	14	,	,	PUNCT
ejpam-816	133	15	with	with	ADP
ejpam-816	133	16	a	a	DET
ejpam-816	133	17	common	common	ADJ
ejpam-816	133	18	vertex	vertex	NOUN
ejpam-816	133	19	at	at	ADP
ejpam-816	133	20	z	z	NOUN
ejpam-816	133	21	=	=	SYM
ejpam-816	133	22	0	0	NUM
ejpam-816	133	23	,	,	PUNCT
ejpam-816	133	24	by	by	ADP
ejpam-816	133	25	the	the	DET
ejpam-816	133	26	rays	ray	NOUN
ejpam-816	133	27	(	(	PUNCT
ejpam-816	133	28	the	the	DET
ejpam-816	133	29	anti	anti	ADJ
ejpam-816	133	30	-	-	ADJ
ejpam-816	133	31	stokes	stokes	ADJ
ejpam-816	133	32	lines	line	NOUN
ejpam-816	133	33	)	)	PUNCT
ejpam-816	134	1	arg	arg	NOUN
ejpam-816	134	2	z	z	NOUN
ejpam-816	134	3	=	=	PUNCT
ejpam-816	134	4	±1	±1	VERB
ejpam-816	134	5	2	2	NUM
ejpam-816	134	6	πκ	πκ	NOUN
ejpam-816	134	7	.	.	PUNCT
ejpam-816	135	1	in	in	ADP
ejpam-816	135	2	the	the	DET
ejpam-816	135	3	sector	sector	NOUN
ejpam-816	135	4	|arg	|arg	NOUN
ejpam-816	135	5	z|	z|	PROPN
ejpam-816	135	6	<	<	X
ejpam-816	135	7	1	1	NUM
ejpam-816	135	8	2	2	NUM
ejpam-816	135	9	πκ	πκ	NOUN
ejpam-816	135	10	,	,	PUNCT
ejpam-816	135	11	the	the	DET
ejpam-816	135	12	asymptotic	asymptotic	ADJ
ejpam-816	135	13	character	character	NOUN
ejpam-816	135	14	of	of	ADP
ejpam-816	135	15	pψq(z	pψq(z	PROPN
ejpam-816	135	16	)	)	PUNCT
ejpam-816	135	17	is	be	AUX
ejpam-816	135	18	exponentially	exponentially	ADV
ejpam-816	135	19	large	large	ADJ
ejpam-816	135	20	,	,	PUNCT
ejpam-816	135	21	whereas	whereas	SCONJ
ejpam-816	135	22	in	in	ADP
ejpam-816	135	23	the	the	DET
ejpam-816	135	24	complementary	complementary	ADJ
ejpam-816	135	25	sector	sector	NOUN
ejpam-816	135	26	|arg(−z)|	|arg(−z)|	PUNCT
ejpam-816	135	27	<	<	X
ejpam-816	135	28	1	1	NUM
ejpam-816	135	29	2	2	NUM
ejpam-816	135	30	π(2−	π(2−	PROPN
ejpam-816	135	31	κ	κ	NOUN
ejpam-816	135	32	)	)	PUNCT
ejpam-816	135	33	,	,	PUNCT
ejpam-816	135	34	pψq(z	pψq(z	PROPN
ejpam-816	135	35	)	)	PUNCT
ejpam-816	135	36	is	be	AUX
ejpam-816	135	37	algebraic	algebraic	ADJ
ejpam-816	135	38	in	in	ADP
ejpam-816	135	39	character	character	NOUN
ejpam-816	135	40	.	.	PUNCT
ejpam-816	136	1	the	the	DET
ejpam-816	136	2	choice	choice	NOUN
ejpam-816	136	3	of	of	ADP
ejpam-816	136	4	signs	sign	NOUN
ejpam-816	136	5	in	in	ADP
ejpam-816	136	6	hp	hp	PROPN
ejpam-816	136	7	,	,	PUNCT
ejpam-816	136	8	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	136	9	)	)	PUNCT
ejpam-816	136	10	results	result	NOUN
ejpam-816	136	11	from	from	ADP
ejpam-816	136	12	the	the	DET
ejpam-816	136	13	fact	fact	NOUN
ejpam-816	136	14	that	that	SCONJ
ejpam-816	136	15	the	the	DET
ejpam-816	136	16	positive	positive	ADJ
ejpam-816	136	17	real	real	ADJ
ejpam-816	136	18	axis	axis	NOUN
ejpam-816	136	19	arg	arg	NOUN
ejpam-816	136	20	z	z	NOUN
ejpam-816	136	21	=	=	SYM
ejpam-816	136	22	0	0	NUM
ejpam-816	136	23	is	be	AUX
ejpam-816	136	24	a	a	DET
ejpam-816	136	25	stokes	stoke	NOUN
ejpam-816	136	26	line	line	NOUN
ejpam-816	136	27	,	,	PUNCT
ejpam-816	136	28	where	where	SCONJ
ejpam-816	136	29	the	the	DET
ejpam-816	136	30	algebraic	algebraic	PROPN
ejpam-816	136	31	r.	r.	PROPN
ejpam-816	136	32	paris	paris	PROPN
ejpam-816	136	33	/	/	SYM
ejpam-816	136	34	eur	eur	PROPN
ejpam-816	136	35	.	.	PUNCT
ejpam-816	137	1	j.	j.	PROPN
ejpam-816	137	2	pure	pure	PROPN
ejpam-816	137	3	appl	appl	PROPN
ejpam-816	137	4	.	.	PROPN
ejpam-816	137	5	math	math	PROPN
ejpam-816	137	6	,	,	PUNCT
ejpam-816	137	7	3	3	NUM
ejpam-816	137	8	(	(	PUNCT
ejpam-816	137	9	2010	2010	NUM
ejpam-816	137	10	)	)	PUNCT
ejpam-816	137	11	,	,	PUNCT
ejpam-816	137	12	1006	1006	NUM
ejpam-816	137	13	-	-	SYM
ejpam-816	137	14	1031	1031	NUM
ejpam-816	137	15	1011	1011	NUM
ejpam-816	137	16	expansion	expansion	NOUN
ejpam-816	137	17	is	be	AUX
ejpam-816	137	18	maximally	maximally	ADV
ejpam-816	137	19	subdominant	subdominant	ADJ
ejpam-816	137	20	.	.	PUNCT
ejpam-816	138	1	since	since	SCONJ
ejpam-816	138	2	pψq(z	pψq(z	PROPN
ejpam-816	138	3	)	)	PUNCT
ejpam-816	138	4	is	be	AUX
ejpam-816	138	5	an	an	DET
ejpam-816	138	6	entire	entire	ADJ
ejpam-816	138	7	function	function	NOUN
ejpam-816	138	8	of	of	ADP
ejpam-816	138	9	z	z	PROPN
ejpam-816	138	10	,	,	PUNCT
ejpam-816	138	11	we	we	PRON
ejpam-816	138	12	may	may	AUX
ejpam-816	138	13	write	write	VERB
ejpam-816	138	14	pψq(z	pψq(z	PROPN
ejpam-816	138	15	)	)	PUNCT
ejpam-816	138	16	=	=	PUNCT
ejpam-816	138	17	pψq(ze−2πi	pψq(ze−2πi	PROPN
ejpam-816	138	18	)	)	PUNCT
ejpam-816	138	19	.	.	PUNCT
ejpam-816	139	1	then	then	ADV
ejpam-816	139	2	,	,	PUNCT
ejpam-816	139	3	when	when	SCONJ
ejpam-816	139	4	π≤	π≤	DET
ejpam-816	139	5	arg	arg	NOUN
ejpam-816	139	6	z	z	X
ejpam-816	139	7	<	<	X
ejpam-816	139	8	2π	2π	PROPN
ejpam-816	139	9	the	the	DET
ejpam-816	139	10	algebraic	algebraic	ADJ
ejpam-816	139	11	expansion	expansion	NOUN
ejpam-816	139	12	is	be	AUX
ejpam-816	139	13	(	(	PUNCT
ejpam-816	139	14	with	with	ADP
ejpam-816	139	15	the	the	DET
ejpam-816	139	16	lower	low	ADJ
ejpam-816	139	17	sign	sign	NOUN
ejpam-816	139	18	)	)	PUNCT
ejpam-816	139	19	hp	hp	PROPN
ejpam-816	139	20	,	,	PUNCT
ejpam-816	139	21	q(ze−2πi	q(ze−2πi	ADV
ejpam-816	139	22	eπi	eπi	PROPN
ejpam-816	139	23	)	)	PUNCT
ejpam-816	139	24	=	=	SYM
ejpam-816	139	25	hp	hp	PROPN
ejpam-816	139	26	,	,	PUNCT
ejpam-816	139	27	q(ze−πi	q(ze−πi	PROPN
ejpam-816	139	28	)	)	PUNCT
ejpam-816	139	29	,	,	PUNCT
ejpam-816	139	30	and	and	CCONJ
ejpam-816	139	31	so	so	ADV
ejpam-816	139	32	has	have	VERB
ejpam-816	139	33	the	the	DET
ejpam-816	139	34	same	same	ADJ
ejpam-816	139	35	form	form	NOUN
ejpam-816	139	36	as	as	ADP
ejpam-816	139	37	when	when	SCONJ
ejpam-816	139	38	0	0	NUM
ejpam-816	139	39	<	<	X
ejpam-816	139	40	arg	arg	NOUN
ejpam-816	139	41	z	z	NOUN
ejpam-816	139	42	≤	≤	NUM
ejpam-816	139	43	π	π	X
ejpam-816	139	44	.	.	PUNCT
ejpam-816	140	1	hence	hence	ADV
ejpam-816	140	2	the	the	DET
ejpam-816	140	3	algebraic	algebraic	ADJ
ejpam-816	140	4	expansion	expansion	NOUN
ejpam-816	140	5	associated	associate	VERB
ejpam-816	140	6	with	with	ADP
ejpam-816	140	7	pψq(z	pψq(z	PROPN
ejpam-816	140	8	)	)	PUNCT
ejpam-816	140	9	can	can	AUX
ejpam-816	140	10	be	be	AUX
ejpam-816	140	11	written	write	VERB
ejpam-816	140	12	alternatively	alternatively	ADV
ejpam-816	140	13	as	as	ADP
ejpam-816	140	14	hp	hp	PROPN
ejpam-816	140	15	,	,	PUNCT
ejpam-816	140	16	q(ze−πi	q(ze−πi	PROPN
ejpam-816	140	17	)	)	PUNCT
ejpam-816	140	18	in	in	ADP
ejpam-816	140	19	ε≤	ε≤	NOUN
ejpam-816	140	20	arg	arg	NOUN
ejpam-816	140	21	z	z	NOUN
ejpam-816	140	22	≤	≤	NOUN
ejpam-816	141	1	2π−	2π−	NUM
ejpam-816	141	2	ε	ε	PROPN
ejpam-816	141	3	.	.	PUNCT
ejpam-816	142	1	(	(	PUNCT
ejpam-816	142	2	16	16	NUM
ejpam-816	142	3	)	)	PUNCT
ejpam-816	142	4	the	the	DET
ejpam-816	142	5	above	above	ADJ
ejpam-816	142	6	theorem	theorem	NOUN
ejpam-816	142	7	does	do	AUX
ejpam-816	142	8	not	not	PART
ejpam-816	142	9	take	take	VERB
ejpam-816	142	10	into	into	ADP
ejpam-816	142	11	account	account	NOUN
ejpam-816	142	12	the	the	DET
ejpam-816	142	13	presence	presence	NOUN
ejpam-816	142	14	of	of	ADP
ejpam-816	142	15	an	an	DET
ejpam-816	142	16	exponentially	exponentially	ADV
ejpam-816	142	17	small	small	ADJ
ejpam-816	142	18	contribution	contribution	NOUN
ejpam-816	142	19	beyond	beyond	ADP
ejpam-816	142	20	the	the	DET
ejpam-816	142	21	sector	sector	NOUN
ejpam-816	142	22	|arg	|arg	VERB
ejpam-816	142	23	z|	z|	PROPN
ejpam-816	142	24	≤	≤	NOUN
ejpam-816	142	25	1	1	NUM
ejpam-816	142	26	2	2	NUM
ejpam-816	142	27	πκ	πκ	NOUN
ejpam-816	142	28	.	.	PUNCT
ejpam-816	143	1	this	this	PRON
ejpam-816	143	2	is	be	AUX
ejpam-816	143	3	covered	cover	VERB
ejpam-816	143	4	by	by	ADP
ejpam-816	143	5	the	the	DET
ejpam-816	143	6	more	more	ADV
ejpam-816	143	7	precise	precise	ADJ
ejpam-816	143	8	result	result	NOUN
ejpam-816	143	9	in	in	ADP
ejpam-816	143	10	the	the	DET
ejpam-816	143	11	following	following	NOUN
ejpam-816	143	12	theorem	theorem	NOUN
ejpam-816	143	13	[	[	X
ejpam-816	143	14	2	2	NUM
ejpam-816	143	15	,	,	PUNCT
ejpam-816	143	16	p.	p.	NOUN
ejpam-816	143	17	331	331	NUM
ejpam-816	143	18	]	]	PUNCT
ejpam-816	143	19	,	,	PUNCT
ejpam-816	143	20	[	[	X
ejpam-816	143	21	20	20	NUM
ejpam-816	143	22	,	,	PUNCT
ejpam-816	143	23	21	21	NUM
ejpam-816	143	24	]	]	PUNCT
ejpam-816	143	25	.	.	PUNCT
ejpam-816	144	1	theorem	theorem	NOUN
ejpam-816	144	2	2	2	NUM
ejpam-816	144	3	.	.	PUNCT
ejpam-816	145	1	if	if	SCONJ
ejpam-816	145	2	2	2	NUM
ejpam-816	145	3	3	3	NUM
ejpam-816	145	4	≤	≤	NOUN
ejpam-816	145	5	κ≤	κ≤	PRON
ejpam-816	145	6	2	2	NUM
ejpam-816	145	7	,	,	PUNCT
ejpam-816	145	8	then	then	ADV
ejpam-816	145	9	pψq(z)∼	pψq(z)∼	VERB
ejpam-816	145	10	ep	ep	PROPN
ejpam-816	145	11	,	,	PUNCT
ejpam-816	145	12	q(z	q(z	PROPN
ejpam-816	145	13	)	)	PUNCT
ejpam-816	145	14	+	+	CCONJ
ejpam-816	145	15	ep	ep	PROPN
ejpam-816	145	16	,	,	PUNCT
ejpam-816	145	17	q(ze∓2πi	q(ze∓2πi	PROPN
ejpam-816	145	18	)	)	PUNCT
ejpam-816	146	1	+	+	NOUN
ejpam-816	146	2	hp	hp	ADJ
ejpam-816	146	3	,	,	PUNCT
ejpam-816	146	4	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	146	5	)	)	PUNCT
ejpam-816	146	6	(	(	PUNCT
ejpam-816	146	7	|arg	|arg	VERB
ejpam-816	146	8	z|	z|	PRON
ejpam-816	146	9	≤	≤	NUM
ejpam-816	146	10	π	π	X
ejpam-816	146	11	)	)	PUNCT
ejpam-816	146	12	(	(	PUNCT
ejpam-816	146	13	17	17	NUM
ejpam-816	146	14	)	)	PUNCT
ejpam-816	146	15	as	as	ADP
ejpam-816	146	16	|z|	|z|	NOUN
ejpam-816	146	17	→∞.	→∞.	PUNCT
ejpam-816	146	18	when	when	SCONJ
ejpam-816	146	19	0	0	NUM
ejpam-816	146	20	<	<	X
ejpam-816	146	21	κ	κ	X
ejpam-816	146	22	<	<	X
ejpam-816	146	23	2	2	NUM
ejpam-816	146	24	3	3	NUM
ejpam-816	146	25	,	,	PUNCT
ejpam-816	146	26	we	we	PRON
ejpam-816	146	27	have	have	VERB
ejpam-816	146	28	pψq(z)∼	pψq(z)∼	VERB
ejpam-816	146	29	¨	¨	NOUN
ejpam-816	146	30	ep	ep	PROPN
ejpam-816	146	31	,	,	PUNCT
ejpam-816	146	32	q(z	q(z	PROPN
ejpam-816	146	33	)	)	PUNCT
ejpam-816	147	1	+	+	NOUN
ejpam-816	147	2	hp	hp	ADJ
ejpam-816	147	3	,	,	PUNCT
ejpam-816	147	4	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	147	5	)	)	PUNCT
ejpam-816	147	6	in	in	ADP
ejpam-816	147	7	|arg	|arg	VERB
ejpam-816	147	8	z|	z|	PROPN
ejpam-816	147	9	≤	≤	NOUN
ejpam-816	147	10	3	3	NUM
ejpam-816	147	11	2	2	NUM
ejpam-816	147	12	πκ−	πκ−	X
ejpam-816	147	13	ε	ε	PROPN
ejpam-816	147	14	hp	hp	PROPN
ejpam-816	147	15	,	,	PUNCT
ejpam-816	147	16	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	147	17	)	)	PUNCT
ejpam-816	147	18	in	in	ADP
ejpam-816	147	19	3	3	NUM
ejpam-816	147	20	2	2	NUM
ejpam-816	147	21	πκ+	πκ+	NOUN
ejpam-816	147	22	ε≤	ε≤	NOUN
ejpam-816	147	23	|arg	|arg	VERB
ejpam-816	147	24	z|	z|	PROPN
ejpam-816	147	25	≤	≤	NOUN
ejpam-816	147	26	π	π	X
ejpam-816	147	27	(	(	PUNCT
ejpam-816	147	28	18	18	NUM
ejpam-816	147	29	)	)	PUNCT
ejpam-816	147	30	as	as	ADP
ejpam-816	147	31	|z|	|z|	NOUN
ejpam-816	147	32	→∞.	→∞.	PUNCT
ejpam-816	147	33	the	the	DET
ejpam-816	147	34	upper	upper	ADJ
ejpam-816	147	35	or	or	CCONJ
ejpam-816	147	36	lower	low	ADJ
ejpam-816	147	37	signs	sign	NOUN
ejpam-816	147	38	are	be	AUX
ejpam-816	147	39	chosen	choose	VERB
ejpam-816	147	40	according	accord	VERB
ejpam-816	147	41	as	as	ADP
ejpam-816	147	42	arg	arg	NOUN
ejpam-816	147	43	z	z	NOUN
ejpam-816	147	44	>	>	X
ejpam-816	147	45	0	0	NUM
ejpam-816	147	46	or	or	CCONJ
ejpam-816	147	47	arg	arg	NOUN
ejpam-816	147	48	z	z	NOUN
ejpam-816	147	49	<	<	X
ejpam-816	147	50	0	0	NUM
ejpam-816	147	51	,	,	PUNCT
ejpam-816	147	52	respectively	respectively	ADV
ejpam-816	147	53	.	.	PUNCT
ejpam-816	148	1	since	since	SCONJ
ejpam-816	148	2	,	,	PUNCT
ejpam-816	148	3	when	when	SCONJ
ejpam-816	148	4	2	2	NUM
ejpam-816	148	5	3	3	NUM
ejpam-816	148	6	≤	≤	NOUN
ejpam-816	148	7	κ	κ	PROPN
ejpam-816	148	8	≤	≤	NOUN
ejpam-816	148	9	2	2	NUM
ejpam-816	148	10	,	,	PUNCT
ejpam-816	148	11	ep	ep	PROPN
ejpam-816	148	12	,	,	PUNCT
ejpam-816	148	13	q(z	q(z	PROPN
ejpam-816	148	14	)	)	PUNCT
ejpam-816	148	15	is	be	AUX
ejpam-816	148	16	exponentially	exponentially	ADV
ejpam-816	148	17	small	small	ADJ
ejpam-816	148	18	in	in	ADP
ejpam-816	148	19	1	1	NUM
ejpam-816	148	20	2	2	NUM
ejpam-816	148	21	πκ	πκ	NOUN
ejpam-816	148	22	<	<	X
ejpam-816	148	23	|arg	|arg	NOUN
ejpam-816	148	24	z|	z|	PRON
ejpam-816	148	25	≤	≤	NOUN
ejpam-816	148	26	π	π	PROPN
ejpam-816	148	27	then	then	ADV
ejpam-816	148	28	in	in	ADP
ejpam-816	148	29	the	the	DET
ejpam-816	148	30	sense	sense	NOUN
ejpam-816	148	31	of	of	ADP
ejpam-816	148	32	poincaré	poincaré	PROPN
ejpam-816	148	33	the	the	DET
ejpam-816	148	34	expansion	expansion	NOUN
ejpam-816	148	35	ep	ep	PROPN
ejpam-816	148	36	,	,	PUNCT
ejpam-816	148	37	q(z	q(z	PROPN
ejpam-816	148	38	)	)	PUNCT
ejpam-816	148	39	can	can	AUX
ejpam-816	148	40	be	be	AUX
ejpam-816	148	41	neglected	neglect	VERB
ejpam-816	148	42	.	.	PUNCT
ejpam-816	149	1	similarly	similarly	ADV
ejpam-816	149	2	,	,	PUNCT
ejpam-816	149	3	e(ze−2πi	e(ze−2πi	ADV
ejpam-816	149	4	)	)	PUNCT
ejpam-816	149	5	is	be	AUX
ejpam-816	149	6	exponentially	exponentially	ADV
ejpam-816	149	7	small	small	ADJ
ejpam-816	149	8	compared	compare	VERB
ejpam-816	149	9	to	to	ADP
ejpam-816	149	10	ep	ep	PROPN
ejpam-816	149	11	,	,	PUNCT
ejpam-816	149	12	q(z	q(z	PROPN
ejpam-816	149	13	)	)	PUNCT
ejpam-816	149	14	in	in	ADP
ejpam-816	149	15	0	0	NUM
ejpam-816	149	16	≤	≤	NUM
ejpam-816	149	17	arg	arg	NOUN
ejpam-816	149	18	z	z	X
ejpam-816	149	19	<	<	X
ejpam-816	149	20	π	π	X
ejpam-816	149	21	and	and	CCONJ
ejpam-816	149	22	consequently	consequently	ADV
ejpam-816	149	23	there	there	PRON
ejpam-816	149	24	is	be	VERB
ejpam-816	149	25	no	no	DET
ejpam-816	149	26	inconsistency	inconsistency	NOUN
ejpam-816	149	27	between	between	ADP
ejpam-816	149	28	(	(	PUNCT
ejpam-816	149	29	17	17	NUM
ejpam-816	149	30	)	)	PUNCT
ejpam-816	149	31	and	and	CCONJ
ejpam-816	149	32	the	the	DET
ejpam-816	149	33	second	second	ADJ
ejpam-816	149	34	expansion	expansion	NOUN
ejpam-816	149	35	in	in	ADP
ejpam-816	149	36	(	(	PUNCT
ejpam-816	149	37	15	15	NUM
ejpam-816	149	38	)	)	PUNCT
ejpam-816	149	39	.	.	PUNCT
ejpam-816	150	1	however	however	ADV
ejpam-816	150	2	,	,	PUNCT
ejpam-816	150	3	in	in	ADP
ejpam-816	150	4	the	the	DET
ejpam-816	150	5	neighbourhood	neighbourhood	NOUN
ejpam-816	150	6	of	of	ADP
ejpam-816	150	7	arg	arg	NOUN
ejpam-816	150	8	z	z	PROPN
ejpam-816	150	9	=	=	SYM
ejpam-816	150	10	π	π	PROPN
ejpam-816	150	11	,	,	PUNCT
ejpam-816	150	12	ep	ep	PROPN
ejpam-816	150	13	,	,	PUNCT
ejpam-816	150	14	q(z	q(z	PROPN
ejpam-816	150	15	)	)	PUNCT
ejpam-816	150	16	and	and	CCONJ
ejpam-816	150	17	ep	ep	PROPN
ejpam-816	150	18	,	,	PUNCT
ejpam-816	150	19	q(ze∓2πi	q(ze∓2πi	NOUN
ejpam-816	150	20	)	)	PUNCT
ejpam-816	150	21	are	be	AUX
ejpam-816	150	22	of	of	ADP
ejpam-816	150	23	comparable	comparable	ADJ
ejpam-816	150	24	magnitude	magnitude	NOUN
ejpam-816	150	25	and	and	CCONJ
ejpam-816	150	26	,	,	PUNCT
ejpam-816	150	27	for	for	ADP
ejpam-816	150	28	real	real	ADJ
ejpam-816	150	29	parameters	parameter	NOUN
ejpam-816	150	30	,	,	PUNCT
ejpam-816	150	31	they	they	PRON
ejpam-816	150	32	combine	combine	VERB
ejpam-816	150	33	to	to	PART
ejpam-816	150	34	generate	generate	VERB
ejpam-816	150	35	a	a	DET
ejpam-816	150	36	real	real	ADJ
ejpam-816	150	37	result	result	NOUN
ejpam-816	150	38	on	on	ADP
ejpam-816	150	39	arg	arg	NOUN
ejpam-816	151	1	z	z	NOUN
ejpam-816	151	2	=	=	SYM
ejpam-816	151	3	π	π	X
ejpam-816	151	4	.	.	PUNCT
ejpam-816	152	1	a	a	DET
ejpam-816	152	2	similar	similar	ADJ
ejpam-816	152	3	remark	remark	NOUN
ejpam-816	152	4	applies	apply	VERB
ejpam-816	152	5	to	to	ADP
ejpam-816	152	6	the	the	DET
ejpam-816	152	7	expansion	expansion	NOUN
ejpam-816	152	8	e(ze2πi	e(ze2πi	NOUN
ejpam-816	152	9	)	)	PUNCT
ejpam-816	152	10	in	in	ADP
ejpam-816	152	11	−π	−π	PROPN
ejpam-816	152	12	<	<	X
ejpam-816	152	13	arg	arg	X
ejpam-816	152	14	z	z	NOUN
ejpam-816	152	15	≤	≤	NUM
ejpam-816	152	16	0	0	NUM
ejpam-816	152	17	.	.	PUNCT
ejpam-816	153	1	when	when	SCONJ
ejpam-816	153	2	κ	κ	X
ejpam-816	153	3	<	<	X
ejpam-816	153	4	2	2	NUM
ejpam-816	153	5	3	3	NUM
ejpam-816	153	6	,	,	PUNCT
ejpam-816	153	7	ep	ep	PROPN
ejpam-816	153	8	,	,	PUNCT
ejpam-816	153	9	q(z	q(z	PROPN
ejpam-816	153	10	)	)	PUNCT
ejpam-816	153	11	is	be	AUX
ejpam-816	153	12	exponentially	exponentially	ADV
ejpam-816	153	13	small	small	ADJ
ejpam-816	153	14	in	in	ADP
ejpam-816	153	15	the	the	DET
ejpam-816	153	16	sectors	sector	NOUN
ejpam-816	153	17	1	1	NUM
ejpam-816	153	18	2	2	NUM
ejpam-816	153	19	πκ	πκ	NOUN
ejpam-816	153	20	<	<	X
ejpam-816	153	21	|arg	|arg	VERB
ejpam-816	153	22	z|	z|	PROPN
ejpam-816	153	23	<	<	X
ejpam-816	153	24	3	3	NUM
ejpam-816	153	25	2	2	NUM
ejpam-816	153	26	πκ	πκ	NOUN
ejpam-816	153	27	and	and	CCONJ
ejpam-816	153	28	the	the	DET
ejpam-816	153	29	behaviour	behaviour	NOUN
ejpam-816	153	30	of	of	ADP
ejpam-816	153	31	pψq(z	pψq(z	PROPN
ejpam-816	153	32	)	)	PUNCT
ejpam-816	153	33	in	in	ADP
ejpam-816	153	34	the	the	DET
ejpam-816	153	35	complementary	complementary	ADJ
ejpam-816	153	36	sector	sector	NOUN
ejpam-816	153	37	3	3	NUM
ejpam-816	153	38	2	2	NUM
ejpam-816	153	39	πκ	πκ	NOUN
ejpam-816	153	40	<	<	X
ejpam-816	153	41	|arg	|arg	NOUN
ejpam-816	153	42	z|	z|	PRON
ejpam-816	153	43	≤	≤	NOUN
ejpam-816	153	44	π	π	PROPN
ejpam-816	153	45	is	be	AUX
ejpam-816	153	46	then	then	ADV
ejpam-816	153	47	algebraic	algebraic	ADJ
ejpam-816	153	48	.	.	PUNCT
ejpam-816	154	1	an	an	DET
ejpam-816	154	2	even	even	ADV
ejpam-816	154	3	more	more	ADV
ejpam-816	154	4	precise	precise	ADJ
ejpam-816	154	5	result	result	NOUN
ejpam-816	154	6	can	can	AUX
ejpam-816	154	7	be	be	AUX
ejpam-816	154	8	given	give	VERB
ejpam-816	154	9	by	by	ADP
ejpam-816	154	10	recognising	recognise	VERB
ejpam-816	154	11	that	that	SCONJ
ejpam-816	154	12	the	the	DET
ejpam-816	154	13	rays	ray	NOUN
ejpam-816	154	14	arg	arg	VERB
ejpam-816	154	15	z	z	NOUN
ejpam-816	154	16	=	=	PUNCT
ejpam-816	154	17	±πκ	±πκ	NOUN
ejpam-816	154	18	are	be	AUX
ejpam-816	154	19	also	also	ADV
ejpam-816	154	20	stokes	stoke	NOUN
ejpam-816	154	21	lines	line	NOUN
ejpam-816	154	22	,	,	PUNCT
ejpam-816	154	23	where	where	SCONJ
ejpam-816	154	24	ep	ep	PROPN
ejpam-816	154	25	,	,	PUNCT
ejpam-816	154	26	q(z	q(z	PROPN
ejpam-816	154	27	)	)	PUNCT
ejpam-816	154	28	is	be	AUX
ejpam-816	154	29	maximally	maximally	ADV
ejpam-816	154	30	subdominant	subdominant	ADJ
ejpam-816	154	31	with	with	ADP
ejpam-816	154	32	respect	respect	NOUN
ejpam-816	154	33	to	to	ADP
ejpam-816	154	34	hp	hp	PROPN
ejpam-816	154	35	,	,	PUNCT
ejpam-816	154	36	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	154	37	)	)	PUNCT
ejpam-816	154	38	.	.	PUNCT
ejpam-816	155	1	this	this	PRON
ejpam-816	155	2	will	will	AUX
ejpam-816	155	3	result	result	VERB
ejpam-816	155	4	in	in	ADP
ejpam-816	155	5	the	the	DET
ejpam-816	155	6	expansion	expansion	NOUN
ejpam-816	155	7	ep	ep	PROPN
ejpam-816	155	8	,	,	PUNCT
ejpam-816	155	9	q(z	q(z	PROPN
ejpam-816	155	10	)	)	PUNCT
ejpam-816	155	11	switching	switch	VERB
ejpam-816	155	12	off	off	ADP
ejpam-816	155	13	(	(	PUNCT
ejpam-816	155	14	as	as	ADP
ejpam-816	155	15	|arg	|arg	VERB
ejpam-816	155	16	z|	z|	NOUN
ejpam-816	155	17	increases	increase	NOUN
ejpam-816	155	18	)	)	PUNCT
ejpam-816	155	19	across	across	ADP
ejpam-816	155	20	the	the	DET
ejpam-816	155	21	stokes	stokes	PROPN
ejpam-816	155	22	lines	lines	PROPN
ejpam-816	155	23	arg	arg	VERB
ejpam-816	155	24	z	z	NOUN
ejpam-816	155	25	=	=	PUNCT
ejpam-816	155	26	±πκ	±πκ	NOUN
ejpam-816	155	27	.	.	PUNCT
ejpam-816	156	1	thus	thus	ADV
ejpam-816	156	2	,	,	PUNCT
ejpam-816	156	3	when	when	SCONJ
ejpam-816	156	4	0	0	NUM
ejpam-816	156	5	<	<	X
ejpam-816	156	6	κ	κ	X
ejpam-816	156	7	<	<	X
ejpam-816	156	8	1	1	NUM
ejpam-816	156	9	,	,	PUNCT
ejpam-816	156	10	(	(	PUNCT
ejpam-816	156	11	17	17	NUM
ejpam-816	156	12	)	)	PUNCT
ejpam-816	156	13	and	and	CCONJ
ejpam-816	156	14	(	(	PUNCT
ejpam-816	156	15	18	18	NUM
ejpam-816	156	16	)	)	PUNCT
ejpam-816	156	17	can	can	AUX
ejpam-816	156	18	be	be	AUX
ejpam-816	156	19	replaced	replace	VERB
ejpam-816	156	20	by	by	ADP
ejpam-816	156	21	pψq(z	pψq(z	PROPN
ejpam-816	156	22	)	)	PUNCT
ejpam-816	156	23	∼	∼	NOUN
ejpam-816	156	24	¨	¨	NOUN
ejpam-816	156	25	ep	ep	PROPN
ejpam-816	156	26	,	,	PUNCT
ejpam-816	156	27	q(z	q(z	PROPN
ejpam-816	156	28	)	)	PUNCT
ejpam-816	157	1	+	+	NOUN
ejpam-816	157	2	hp	hp	ADJ
ejpam-816	157	3	,	,	PUNCT
ejpam-816	157	4	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	157	5	)	)	PUNCT
ejpam-816	157	6	in	in	ADP
ejpam-816	157	7	|arg	|arg	VERB
ejpam-816	157	8	z|	z|	PROPN
ejpam-816	157	9	≤	≤	X
ejpam-816	157	10	πκ−	πκ−	PUNCT
ejpam-816	157	11	ε	ε	PROPN
ejpam-816	157	12	hp	hp	PROPN
ejpam-816	157	13	,	,	PUNCT
ejpam-816	157	14	q(ze∓πi	q(ze∓πi	NOUN
ejpam-816	157	15	)	)	PUNCT
ejpam-816	157	16	in	in	ADP
ejpam-816	157	17	πκ+	πκ+	PROPN
ejpam-816	157	18	ε	ε	PROPN
ejpam-816	157	19	≤	≤	PROPN
ejpam-816	157	20	|arg	|arg	VERB
ejpam-816	157	21	z|	z|	ADJ
ejpam-816	157	22	≤	≤	NOUN
ejpam-816	157	23	π	π	X
ejpam-816	157	24	(	(	PUNCT
ejpam-816	157	25	19	19	NUM
ejpam-816	157	26	)	)	PUNCT
ejpam-816	157	27	as	as	ADP
ejpam-816	157	28	|z|	|z|	NOUN
ejpam-816	157	29	→	→	SYM
ejpam-816	157	30	∞.	∞.	PROPN
ejpam-816	157	31	in	in	ADP
ejpam-816	157	32	appendix	appendix	PROPN
ejpam-816	157	33	b	b	NOUN
ejpam-816	157	34	we	we	PRON
ejpam-816	157	35	present	present	VERB
ejpam-816	157	36	a	a	DET
ejpam-816	157	37	numerical	numerical	ADJ
ejpam-816	157	38	example	example	NOUN
ejpam-816	157	39	for	for	ADP
ejpam-816	157	40	2ψ0(z	2ψ0(z	NUM
ejpam-816	157	41	)	)	PUNCT
ejpam-816	157	42	which	which	PRON
ejpam-816	157	43	demonstrates	demonstrate	VERB
ejpam-816	157	44	the	the	DET
ejpam-816	157	45	truth	truth	NOUN
ejpam-816	157	46	of	of	ADP
ejpam-816	157	47	this	this	DET
ejpam-816	157	48	assertion	assertion	NOUN
ejpam-816	157	49	;	;	PUNCT
ejpam-816	157	50	a	a	DET
ejpam-816	157	51	fuller	full	ADJ
ejpam-816	157	52	discussion	discussion	NOUN
ejpam-816	157	53	is	be	AUX
ejpam-816	157	54	given	give	VERB
ejpam-816	157	55	in	in	ADP
ejpam-816	157	56	[	[	X
ejpam-816	157	57	10	10	NUM
ejpam-816	157	58	]	]	PUNCT
ejpam-816	157	59	.	.	PUNCT
ejpam-816	158	1	although	although	SCONJ
ejpam-816	158	2	the	the	DET
ejpam-816	158	3	expansions	expansion	NOUN
ejpam-816	158	4	in	in	ADP
ejpam-816	158	5	(	(	PUNCT
ejpam-816	158	6	15	15	NUM
ejpam-816	158	7	)	)	PUNCT
ejpam-816	158	8	and	and	CCONJ
ejpam-816	158	9	(	(	PUNCT
ejpam-816	158	10	18	18	NUM
ejpam-816	158	11	)	)	PUNCT
ejpam-816	158	12	are	be	AUX
ejpam-816	158	13	valid	valid	ADJ
ejpam-816	158	14	asymptotic	asymptotic	ADJ
ejpam-816	158	15	descriptions	description	NOUN
ejpam-816	158	16	,	,	PUNCT
ejpam-816	158	17	more	more	ADV
ejpam-816	158	18	accurate	accurate	ADJ
ejpam-816	158	19	evaluation	evaluation	NOUN
ejpam-816	158	20	will	will	AUX
ejpam-816	158	21	result	result	VERB
ejpam-816	158	22	from	from	ADP
ejpam-816	158	23	using	use	VERB
ejpam-816	158	24	(	(	PUNCT
ejpam-816	158	25	19	19	NUM
ejpam-816	158	26	)	)	PUNCT
ejpam-816	158	27	which	which	PRON
ejpam-816	158	28	takes	take	VERB
ejpam-816	158	29	into	into	ADP
ejpam-816	158	30	account	account	NOUN
ejpam-816	158	31	the	the	DET
ejpam-816	158	32	stokes	stoke	NOUN
ejpam-816	158	33	phenomenon.†	phenomenon.†	PROPN
ejpam-816	158	34	in	in	ADP
ejpam-816	158	35	the	the	DET
ejpam-816	158	36	application	application	NOUN
ejpam-816	158	37	to	to	ADP
ejpam-816	158	38	the	the	DET
ejpam-816	158	39	integrals	integral	NOUN
ejpam-816	158	40	in(z	in(z	NOUN
ejpam-816	158	41	)	)	PUNCT
ejpam-816	158	42	and	and	CCONJ
ejpam-816	158	43	jn(z	jn(z	NOUN
ejpam-816	158	44	)	)	PUNCT
ejpam-816	158	45	we	we	PRON
ejpam-816	158	46	shall	shall	AUX
ejpam-816	158	47	employ	employ	VERB
ejpam-816	158	48	the	the	DET
ejpam-816	158	49	expansion	expansion	NOUN
ejpam-816	158	50	of	of	ADP
ejpam-816	158	51	pψq(z	pψq(z	PROPN
ejpam-816	158	52	)	)	PUNCT
ejpam-816	158	53	in	in	ADP
ejpam-816	158	54	the	the	DET
ejpam-816	158	55	form	form	NOUN
ejpam-816	158	56	given	give	VERB
ejpam-816	158	57	in	in	ADP
ejpam-816	158	58	(	(	PUNCT
ejpam-816	158	59	19	19	NUM
ejpam-816	158	60	)	)	PUNCT
ejpam-816	158	61	.	.	PUNCT
ejpam-816	159	1	†the	†the	DET
ejpam-816	159	2	expansion	expansion	NOUN
ejpam-816	159	3	in	in	ADP
ejpam-816	159	4	the	the	DET
ejpam-816	159	5	neighbourhood	neighbourhood	NOUN
ejpam-816	159	6	of	of	ADP
ejpam-816	159	7	the	the	DET
ejpam-816	159	8	stokes	stokes	PROPN
ejpam-816	159	9	lines	lines	PROPN
ejpam-816	159	10	arg	arg	VERB
ejpam-816	159	11	z	z	NOUN
ejpam-816	159	12	=	=	SYM
ejpam-816	159	13	0	0	NUM
ejpam-816	159	14	and	and	CCONJ
ejpam-816	159	15	arg	arg	NOUN
ejpam-816	159	16	z	z	NOUN
ejpam-816	159	17	=	=	NOUN
ejpam-816	159	18	±πκ	±πκ	NOUN
ejpam-816	159	19	would	would	AUX
ejpam-816	159	20	necessitate	necessitate	VERB
ejpam-816	159	21	a	a	DET
ejpam-816	159	22	detailed	detailed	ADJ
ejpam-816	159	23	treatment	treatment	NOUN
ejpam-816	159	24	of	of	ADP
ejpam-816	159	25	the	the	DET
ejpam-816	159	26	stokes	stoke	NOUN
ejpam-816	159	27	phenomenon	phenomenon	NOUN
ejpam-816	159	28	that	that	SCONJ
ejpam-816	159	29	we	we	PRON
ejpam-816	159	30	do	do	AUX
ejpam-816	159	31	not	not	PART
ejpam-816	159	32	consider	consider	VERB
ejpam-816	159	33	here	here	ADV
ejpam-816	159	34	.	.	PUNCT
ejpam-816	160	1	r.	r.	PROPN
ejpam-816	160	2	paris	paris	PROPN
ejpam-816	160	3	/	/	SYM
ejpam-816	160	4	eur	eur	PROPN
ejpam-816	160	5	.	.	PUNCT
ejpam-816	161	1	j.	j.	PROPN
ejpam-816	161	2	pure	pure	PROPN
ejpam-816	161	3	appl	appl	PROPN
ejpam-816	161	4	.	.	PROPN
ejpam-816	161	5	math	math	PROPN
ejpam-816	161	6	,	,	PUNCT
ejpam-816	161	7	3	3	NUM
ejpam-816	161	8	(	(	PUNCT
ejpam-816	161	9	2010	2010	NUM
ejpam-816	161	10	)	)	PUNCT
ejpam-816	161	11	,	,	PUNCT
ejpam-816	161	12	1006	1006	NUM
ejpam-816	161	13	-	-	SYM
ejpam-816	161	14	1031	1031	NUM
ejpam-816	161	15	1012	1012	NUM
ejpam-816	161	16	3	3	NUM
ejpam-816	161	17	.	.	PUNCT
ejpam-816	162	1	the	the	DET
ejpam-816	162	2	expansion	expansion	NOUN
ejpam-816	162	3	of	of	ADP
ejpam-816	162	4	in(z	in(z	NOUN
ejpam-816	162	5	)	)	PUNCT
ejpam-816	162	6	for	for	ADP
ejpam-816	162	7	|z|	|z|	NOUN
ejpam-816	162	8	→∞	→∞	PROPN
ejpam-816	162	9	the	the	DET
ejpam-816	162	10	series	series	NOUN
ejpam-816	162	11	representation	representation	NOUN
ejpam-816	162	12	of	of	ADP
ejpam-816	162	13	the	the	DET
ejpam-816	162	14	integral	integral	ADJ
ejpam-816	162	15	in(z	in(z	NOUN
ejpam-816	162	16	)	)	PUNCT
ejpam-816	162	17	can	can	AUX
ejpam-816	162	18	be	be	AUX
ejpam-816	162	19	obtained	obtain	VERB
ejpam-816	162	20	by	by	ADP
ejpam-816	162	21	use	use	NOUN
ejpam-816	162	22	of	of	ADP
ejpam-816	162	23	the	the	DET
ejpam-816	162	24	maclaurin	maclaurin	NOUN
ejpam-816	162	25	expansion	expansion	NOUN
ejpam-816	162	26	of	of	ADP
ejpam-816	162	27	the	the	DET
ejpam-816	162	28	factor	factor	NOUN
ejpam-816	162	29	exp{zx	exp{zx	NOUN
ejpam-816	163	1	m1	m1	PROPN
ejpam-816	163	2	1	1	NUM
ejpam-816	163	3	.	.	PUNCT
ejpam-816	163	4	.	.	PUNCT
ejpam-816	163	5	.	.	PUNCT
ejpam-816	164	1	x	x	X
ejpam-816	164	2	mn	mn	PROPN
ejpam-816	164	3	n	n	PROPN
ejpam-816	164	4	}	}	PUNCT
ejpam-816	164	5	in	in	ADP
ejpam-816	164	6	(	(	PUNCT
ejpam-816	164	7	1	1	X
ejpam-816	164	8	)	)	PUNCT
ejpam-816	164	9	followed	follow	VERB
ejpam-816	164	10	by	by	ADP
ejpam-816	164	11	termwise	termwise	NOUN
ejpam-816	164	12	integration	integration	NOUN
ejpam-816	164	13	to	to	PART
ejpam-816	164	14	yield	yield	VERB
ejpam-816	164	15	in(z	in(z	NOUN
ejpam-816	164	16	)	)	PUNCT
ejpam-816	165	1	=	=	SYM
ejpam-816	165	2	λn	λn	PROPN
ejpam-816	165	3	∞	∞	NUM
ejpam-816	165	4	∑	∑	PROPN
ejpam-816	165	5	k=0	k=0	PROPN
ejpam-816	165	6	zk	zk	PROPN
ejpam-816	166	1	k	k	PROPN
ejpam-816	166	2	!	!	PUNCT
ejpam-816	166	3	n	n	CCONJ
ejpam-816	166	4	∏	∏	PROPN
ejpam-816	166	5	r=1	r=1	NOUN
ejpam-816	166	6	∫	∫	PROPN
ejpam-816	166	7	∞	∞	PROPN
ejpam-816	166	8	0	0	NUM
ejpam-816	167	1	xνr+mr	xνr+mr	PUNCT
ejpam-816	167	2	k−1	k−1	PROPN
ejpam-816	167	3	r	r	NOUN
ejpam-816	167	4	exp{−xµr	exp{−xµr	PROPN
ejpam-816	167	5	r	r	NOUN
ejpam-816	167	6	}	}	PUNCT
ejpam-816	168	1	d	d	NOUN
ejpam-816	168	2	xr	xr	PROPN
ejpam-816	168	3	=	=	SYM
ejpam-816	168	4	∞	∞	PROPN
ejpam-816	168	5	∑	∑	PUNCT
ejpam-816	168	6	k=0	k=0	PROPN
ejpam-816	168	7	n	n	CCONJ
ejpam-816	168	8	∏	∏	PROPN
ejpam-816	168	9	r=1	r=1	PROPN
ejpam-816	168	10	γ	γ	X
ejpam-816	168	11	�	�	PROPN
ejpam-816	168	12	νr	νr	ADP
ejpam-816	168	13	+	+	ADP
ejpam-816	168	14	mr	mr	PROPN
ejpam-816	168	15	k	k	PROPN
ejpam-816	168	16	µr	µr	ADP
ejpam-816	168	17	�	�	PROPN
ejpam-816	168	18	zk	zk	PROPN
ejpam-816	168	19	k	k	PROPN
ejpam-816	168	20	!	!	PUNCT
ejpam-816	168	21	.	.	PUNCT
ejpam-816	169	1	(	(	PUNCT
ejpam-816	169	2	20	20	X
ejpam-816	169	3	)	)	PUNCT
ejpam-816	169	4	comparison	comparison	NOUN
ejpam-816	169	5	with	with	ADP
ejpam-816	169	6	(	(	PUNCT
ejpam-816	169	7	5	5	NUM
ejpam-816	169	8	)	)	PUNCT
ejpam-816	169	9	shows	show	VERB
ejpam-816	169	10	that	that	SCONJ
ejpam-816	169	11	the	the	DET
ejpam-816	169	12	above	above	ADJ
ejpam-816	169	13	series	series	NOUN
ejpam-816	169	14	is	be	AUX
ejpam-816	169	15	a	a	DET
ejpam-816	169	16	particular	particular	ADJ
ejpam-816	169	17	case	case	NOUN
ejpam-816	169	18	of	of	ADP
ejpam-816	169	19	the	the	DET
ejpam-816	169	20	wright	wright	PROPN
ejpam-816	169	21	(	(	PUNCT
ejpam-816	169	22	or	or	CCONJ
ejpam-816	169	23	generalised	generalise	VERB
ejpam-816	169	24	hypergeometric	hypergeometric	ADJ
ejpam-816	169	25	)	)	PUNCT
ejpam-816	169	26	function	function	NOUN
ejpam-816	169	27	given	give	VERB
ejpam-816	169	28	by	by	ADP
ejpam-816	169	29	in(z	in(z	NOUN
ejpam-816	169	30	)	)	PUNCT
ejpam-816	169	31	=	=	SYM
ejpam-816	169	32	nψ0	nψ0	PROPN
ejpam-816	169	33	�	�	PROPN
ejpam-816	169	34	(	(	PUNCT
ejpam-816	169	35	α1	α1	PROPN
ejpam-816	169	36	,	,	PUNCT
ejpam-816	169	37	a1	a1	NOUN
ejpam-816	169	38	)	)	PUNCT
ejpam-816	169	39	,	,	PUNCT
ejpam-816	169	40	.	.	PUNCT
ejpam-816	169	41	.	.	PUNCT
ejpam-816	169	42	.	.	PUNCT
ejpam-816	170	1	,	,	PUNCT
ejpam-816	170	2	(	(	PUNCT
ejpam-816	170	3	αn	αn	NOUN
ejpam-816	170	4	,	,	PUNCT
ejpam-816	170	5	an	an	PRON
ejpam-816	170	6	)	)	PUNCT
ejpam-816	170	7	;	;	PUNCT
ejpam-816	170	8	z	z	PROPN
ejpam-816	170	9	�	�	PROPN
ejpam-816	170	10	≡	≡	PROPN
ejpam-816	170	11	nψ0(z	nψ0(z	PROPN
ejpam-816	170	12	)	)	PUNCT
ejpam-816	170	13	,	,	PUNCT
ejpam-816	170	14	(	(	PUNCT
ejpam-816	170	15	21	21	NUM
ejpam-816	170	16	)	)	PUNCT
ejpam-816	170	17	where	where	SCONJ
ejpam-816	170	18	the	the	DET
ejpam-816	170	19	parameters	parameter	NOUN
ejpam-816	170	20	αr	αr	ADP
ejpam-816	170	21	=	=	NOUN
ejpam-816	171	1	mr	mr	PROPN
ejpam-816	171	2	µr	µr	ADP
ejpam-816	171	3	,	,	PUNCT
ejpam-816	171	4	ar	ar	PROPN
ejpam-816	171	5	=	=	NOUN
ejpam-816	171	6	νr	νr	ADP
ejpam-816	171	7	µr	µr	ADP
ejpam-816	171	8	(	(	PUNCT
ejpam-816	171	9	1≤	1≤	NUM
ejpam-816	171	10	r	r	NOUN
ejpam-816	171	11	≤	≤	NUM
ejpam-816	171	12	n	n	CCONJ
ejpam-816	171	13	)	)	PUNCT
ejpam-816	171	14	(	(	PUNCT
ejpam-816	171	15	22	22	NUM
ejpam-816	171	16	)	)	PUNCT
ejpam-816	171	17	and	and	CCONJ
ejpam-816	171	18	the	the	DET
ejpam-816	171	19	dash	dash	NOUN
ejpam-816	171	20	denotes	denote	VERB
ejpam-816	171	21	the	the	DET
ejpam-816	171	22	omission	omission	NOUN
ejpam-816	171	23	of	of	ADP
ejpam-816	171	24	a	a	DET
ejpam-816	171	25	parameter	parameter	NOUN
ejpam-816	171	26	sequence	sequence	NOUN
ejpam-816	171	27	.	.	PUNCT
ejpam-816	172	1	the	the	DET
ejpam-816	172	2	asymptotic	asymptotic	ADJ
ejpam-816	172	3	expansion	expansion	NOUN
ejpam-816	172	4	of	of	ADP
ejpam-816	172	5	in(z	in(z	NOUN
ejpam-816	172	6	)	)	PUNCT
ejpam-816	172	7	for	for	ADP
ejpam-816	172	8	|z|	|z|	NOUN
ejpam-816	172	9	→	→	SYM
ejpam-816	172	10	∞	∞	NUM
ejpam-816	172	11	then	then	ADV
ejpam-816	172	12	follows	follow	VERB
ejpam-816	172	13	from	from	ADP
ejpam-816	172	14	(	(	PUNCT
ejpam-816	172	15	19	19	NUM
ejpam-816	172	16	)	)	PUNCT
ejpam-816	172	17	.	.	PUNCT
ejpam-816	173	1	with	with	ADP
ejpam-816	173	2	κ	κ	PROPN
ejpam-816	173	3	defined	define	VERB
ejpam-816	173	4	in	in	ADP
ejpam-816	173	5	(	(	PUNCT
ejpam-816	173	6	3	3	NUM
ejpam-816	173	7	)	)	PUNCT
ejpam-816	173	8	(	(	PUNCT
ejpam-816	173	9	which	which	PRON
ejpam-816	173	10	follows	follow	VERB
ejpam-816	173	11	from	from	ADP
ejpam-816	173	12	the	the	DET
ejpam-816	173	13	definition	definition	NOUN
ejpam-816	173	14	in	in	ADP
ejpam-816	173	15	(	(	PUNCT
ejpam-816	173	16	7	7	NUM
ejpam-816	173	17	)	)	PUNCT
ejpam-816	173	18	)	)	PUNCT
ejpam-816	173	19	we	we	PRON
ejpam-816	173	20	therefore	therefore	ADV
ejpam-816	173	21	have	have	VERB
ejpam-816	173	22	in(z)∼	in(z)∼	PROPN
ejpam-816	173	23	¨	¨	NOUN
ejpam-816	173	24	en,0(z	en,0(z	PROPN
ejpam-816	173	25	)	)	PUNCT
ejpam-816	174	1	+	+	SYM
ejpam-816	174	2	hn,0(ze∓πi	hn,0(ze∓πi	PROPN
ejpam-816	174	3	)	)	PUNCT
ejpam-816	174	4	in	in	ADP
ejpam-816	174	5	|arg	|arg	VERB
ejpam-816	174	6	z|	z|	PROPN
ejpam-816	174	7	≤	≤	X
ejpam-816	174	8	πκ−	πκ−	PUNCT
ejpam-816	174	9	ε	ε	PROPN
ejpam-816	174	10	hn,0(ze∓πi	hn,0(ze∓πi	PROPN
ejpam-816	174	11	)	)	PUNCT
ejpam-816	174	12	in	in	ADP
ejpam-816	174	13	πκ+	πκ+	PROPN
ejpam-816	174	14	ε≤	ε≤	PROPN
ejpam-816	174	15	|arg	|arg	VERB
ejpam-816	174	16	z|	z|	PROPN
ejpam-816	174	17	≤	≤	NOUN
ejpam-816	174	18	π	π	PROPN
ejpam-816	174	19	,	,	PUNCT
ejpam-816	174	20	(	(	PUNCT
ejpam-816	174	21	23	23	NUM
ejpam-816	174	22	)	)	PUNCT
ejpam-816	174	23	where	where	SCONJ
ejpam-816	174	24	the	the	DET
ejpam-816	174	25	exponential	exponential	ADJ
ejpam-816	174	26	expansion	expansion	NOUN
ejpam-816	174	27	en,0(z	en,0(z	PROPN
ejpam-816	174	28	)	)	PUNCT
ejpam-816	174	29	and	and	CCONJ
ejpam-816	174	30	the	the	DET
ejpam-816	174	31	algebraic	algebraic	ADJ
ejpam-816	174	32	expansion	expansion	NOUN
ejpam-816	174	33	hn,0(ze∓πi	hn,0(ze∓πi	PROPN
ejpam-816	174	34	)	)	PUNCT
ejpam-816	174	35	are	be	AUX
ejpam-816	174	36	obtained	obtain	VERB
ejpam-816	174	37	from	from	ADP
ejpam-816	174	38	(	(	PUNCT
ejpam-816	174	39	8)	8)	NUM
ejpam-816	174	40	,	,	PUNCT
ejpam-816	174	41	(	(	PUNCT
ejpam-816	174	42	13	13	NUM
ejpam-816	174	43	)	)	PUNCT
ejpam-816	174	44	and	and	CCONJ
ejpam-816	174	45	(	(	PUNCT
ejpam-816	174	46	14	14	NUM
ejpam-816	174	47	)	)	PUNCT
ejpam-816	174	48	with	with	ADP
ejpam-816	174	49	p	p	NOUN
ejpam-816	174	50	=	=	PUNCT
ejpam-816	174	51	n	n	CCONJ
ejpam-816	174	52	,	,	PUNCT
ejpam-816	174	53	q	q	X
ejpam-816	174	54	=	=	NOUN
ejpam-816	174	55	0	0	NUM
ejpam-816	174	56	,	,	PUNCT
ejpam-816	174	57	and	and	CCONJ
ejpam-816	174	58	the	the	DET
ejpam-816	174	59	upper	upper	ADJ
ejpam-816	174	60	or	or	CCONJ
ejpam-816	174	61	lower	low	ADJ
ejpam-816	174	62	signs	sign	NOUN
ejpam-816	174	63	are	be	AUX
ejpam-816	174	64	chosen	choose	VERB
ejpam-816	174	65	according	accord	VERB
ejpam-816	174	66	as	as	ADP
ejpam-816	174	67	arg	arg	NOUN
ejpam-816	174	68	z	z	NOUN
ejpam-816	174	69	>	>	X
ejpam-816	174	70	0	0	NUM
ejpam-816	174	71	or	or	CCONJ
ejpam-816	174	72	arg	arg	NOUN
ejpam-816	174	73	z	z	NOUN
ejpam-816	174	74	<	<	X
ejpam-816	174	75	0	0	NUM
ejpam-816	174	76	,	,	PUNCT
ejpam-816	174	77	respectively	respectively	ADV
ejpam-816	174	78	.	.	PUNCT
ejpam-816	175	1	the	the	DET
ejpam-816	175	2	leading	lead	VERB
ejpam-816	175	3	coefficient	coefficient	NOUN
ejpam-816	175	4	a0	a0	NOUN
ejpam-816	175	5	in	in	ADP
ejpam-816	175	6	en,0(z	en,0(z	PROPN
ejpam-816	175	7	)	)	PUNCT
ejpam-816	175	8	is	be	AUX
ejpam-816	175	9	,	,	PUNCT
ejpam-816	175	10	from	from	ADP
ejpam-816	175	11	(	(	PUNCT
ejpam-816	175	12	10	10	NUM
ejpam-816	175	13	)	)	PUNCT
ejpam-816	175	14	,	,	PUNCT
ejpam-816	175	15	given	give	VERB
ejpam-816	175	16	by	by	ADP
ejpam-816	175	17	a0	a0	PROPN
ejpam-816	175	18	=	=	SYM
ejpam-816	175	19	(	(	PUNCT
ejpam-816	175	20	2π	2π	NOUN
ejpam-816	175	21	)	)	PUNCT
ejpam-816	175	22	n/2κ−	n/2κ−	ADP
ejpam-816	175	23	1	1	NUM
ejpam-816	175	24	2	2	NUM
ejpam-816	175	25	−ϑ	−ϑ	NOUN
ejpam-816	175	26	n	n	CCONJ
ejpam-816	175	27	∏	∏	PROPN
ejpam-816	175	28	r=1	r=1	PROPN
ejpam-816	175	29	�	�	PROPN
ejpam-816	175	30	mr	mr	PROPN
ejpam-816	175	31	µr	µr	ADP
ejpam-816	175	32	�	�	PROPN
ejpam-816	175	33	(	(	PUNCT
ejpam-816	175	34	νr/µr	νr/µr	NUM
ejpam-816	175	35	)	)	PUNCT
ejpam-816	175	36	−	−	PROPN
ejpam-816	175	37	1	1	NUM
ejpam-816	175	38	2	2	NUM
ejpam-816	175	39	.	.	PUNCT
ejpam-816	176	1	(	(	PUNCT
ejpam-816	176	2	24	24	NUM
ejpam-816	176	3	)	)	PUNCT
ejpam-816	176	4	the	the	DET
ejpam-816	176	5	large	large	ADJ
ejpam-816	176	6	|z|	|z|	NOUN
ejpam-816	176	7	behaviour	behaviour	NOUN
ejpam-816	176	8	of	of	ADP
ejpam-816	176	9	in(z	in(z	NOUN
ejpam-816	176	10	)	)	PUNCT
ejpam-816	176	11	is	be	AUX
ejpam-816	176	12	consequently	consequently	ADV
ejpam-816	176	13	exponentially	exponentially	ADV
ejpam-816	176	14	large	large	ADJ
ejpam-816	176	15	in	in	ADP
ejpam-816	176	16	the	the	DET
ejpam-816	176	17	sector	sector	NOUN
ejpam-816	176	18	|arg	|arg	NOUN
ejpam-816	176	19	z|	z|	PROPN
ejpam-816	176	20	<	<	X
ejpam-816	176	21	1	1	NUM
ejpam-816	176	22	2	2	NUM
ejpam-816	176	23	πκ	πκ	NOUN
ejpam-816	176	24	.	.	NOUN
ejpam-816	176	25	outside	outside	ADP
ejpam-816	176	26	of	of	ADP
ejpam-816	176	27	this	this	DET
ejpam-816	176	28	sector	sector	NOUN
ejpam-816	176	29	the	the	DET
ejpam-816	176	30	behaviour	behaviour	NOUN
ejpam-816	176	31	is	be	AUX
ejpam-816	176	32	dominated	dominate	VERB
ejpam-816	176	33	by	by	ADP
ejpam-816	176	34	an	an	DET
ejpam-816	176	35	algebraic	algebraic	ADJ
ejpam-816	176	36	expansion	expansion	NOUN
ejpam-816	176	37	,	,	PUNCT
ejpam-816	176	38	with	with	ADP
ejpam-816	176	39	a	a	DET
ejpam-816	176	40	subdominant	subdominant	ADJ
ejpam-816	176	41	exponentially	exponentially	ADV
ejpam-816	176	42	small	small	ADJ
ejpam-816	176	43	contribution	contribution	NOUN
ejpam-816	176	44	being	be	AUX
ejpam-816	176	45	present	present	ADJ
ejpam-816	176	46	in	in	ADP
ejpam-816	176	47	the	the	DET
ejpam-816	176	48	sectors	sector	NOUN
ejpam-816	176	49	1	1	NUM
ejpam-816	176	50	2	2	NUM
ejpam-816	176	51	πκ	πκ	NOUN
ejpam-816	176	52	<	<	X
ejpam-816	176	53	|arg	|arg	NOUN
ejpam-816	177	1	z|	z|	PROPN
ejpam-816	177	2	<	<	X
ejpam-816	177	3	πκ	πκ	INTJ
ejpam-816	177	4	.	.	PUNCT
ejpam-816	177	5	we	we	PRON
ejpam-816	177	6	now	now	ADV
ejpam-816	177	7	give	give	VERB
ejpam-816	177	8	an	an	DET
ejpam-816	177	9	example	example	NOUN
ejpam-816	177	10	of	of	ADP
ejpam-816	177	11	the	the	DET
ejpam-816	177	12	expansion	expansion	NOUN
ejpam-816	177	13	of	of	ADP
ejpam-816	177	14	in(z	in(z	NOUN
ejpam-816	177	15	)	)	PUNCT
ejpam-816	177	16	when	when	SCONJ
ejpam-816	177	17	n=	n=	ADJ
ejpam-816	177	18	3	3	NUM
ejpam-816	177	19	;	;	PUNCT
ejpam-816	177	20	other	other	ADJ
ejpam-816	177	21	numerical	numerical	ADJ
ejpam-816	177	22	examples	example	NOUN
ejpam-816	177	23	can	can	AUX
ejpam-816	177	24	be	be	AUX
ejpam-816	177	25	found	find	VERB
ejpam-816	177	26	in	in	ADP
ejpam-816	177	27	[	[	X
ejpam-816	177	28	13	13	NUM
ejpam-816	177	29	]	]	PUNCT
ejpam-816	177	30	.	.	PUNCT
ejpam-816	178	1	consider	consider	VERB
ejpam-816	178	2	the	the	DET
ejpam-816	178	3	three	three	NUM
ejpam-816	178	4	-	-	PUNCT
ejpam-816	178	5	dimensional	dimensional	ADJ
ejpam-816	178	6	integral	integral	ADJ
ejpam-816	178	7	i3(z	i3(z	PROPN
ejpam-816	178	8	)	)	PUNCT
ejpam-816	178	9	=	=	PUNCT
ejpam-816	179	1	36	36	NUM
ejpam-816	179	2	∫	∫	NOUN
ejpam-816	179	3	∞	∞	NUM
ejpam-816	179	4	0	0	NUM
ejpam-816	180	1	∫	∫	PROPN
ejpam-816	181	1	∞	∞	PROPN
ejpam-816	181	2	0	0	NUM
ejpam-816	181	3	∫	∫	PROPN
ejpam-816	181	4	∞	∞	PROPN
ejpam-816	181	5	0	0	NUM
ejpam-816	181	6	(	(	PUNCT
ejpam-816	181	7	x3	x3	PROPN
ejpam-816	181	8	/	/	SYM
ejpam-816	181	9	x2	x2	ADJ
ejpam-816	181	10	)	)	PUNCT
ejpam-816	181	11	1	1	NUM
ejpam-816	181	12	2	2	NUM
ejpam-816	181	13	exp{−(x3	exp{−(x3	NOUN
ejpam-816	181	14	1	1	NUM
ejpam-816	182	1	+	+	CCONJ
ejpam-816	182	2	x3	x3	ADJ
ejpam-816	182	3	2	2	NUM
ejpam-816	182	4	+	+	CCONJ
ejpam-816	182	5	x4	x4	PROPN
ejpam-816	182	6	3	3	NUM
ejpam-816	182	7	−	−	PROPN
ejpam-816	182	8	z(x1	z(x1	NOUN
ejpam-816	182	9	x2	x2	NOUN
ejpam-816	182	10	)	)	PUNCT
ejpam-816	182	11	1	1	NUM
ejpam-816	182	12	2	2	NUM
ejpam-816	182	13	x3	x3	ADJ
ejpam-816	182	14	)	)	PUNCT
ejpam-816	182	15	}	}	PUNCT
ejpam-816	183	1	d	d	PROPN
ejpam-816	183	2	x1d	x1d	PROPN
ejpam-816	183	3	x2d	x2d	PROPN
ejpam-816	183	4	x3	x3	PROPN
ejpam-816	183	5	,	,	PUNCT
ejpam-816	183	6	r.	r.	PROPN
ejpam-816	183	7	paris	paris	PROPN
ejpam-816	183	8	/	/	SYM
ejpam-816	183	9	eur	eur	PROPN
ejpam-816	183	10	.	.	PUNCT
ejpam-816	184	1	j.	j.	PROPN
ejpam-816	184	2	pure	pure	PROPN
ejpam-816	184	3	appl	appl	PROPN
ejpam-816	184	4	.	.	PROPN
ejpam-816	184	5	math	math	PROPN
ejpam-816	184	6	,	,	PUNCT
ejpam-816	184	7	3	3	NUM
ejpam-816	184	8	(	(	PUNCT
ejpam-816	184	9	2010	2010	NUM
ejpam-816	184	10	)	)	PUNCT
ejpam-816	184	11	,	,	PUNCT
ejpam-816	184	12	1006	1006	NUM
ejpam-816	184	13	-	-	SYM
ejpam-816	184	14	1031	1031	NUM
ejpam-816	184	15	1013	1013	NUM
ejpam-816	184	16	which	which	PRON
ejpam-816	184	17	is	be	AUX
ejpam-816	184	18	associated	associate	VERB
ejpam-816	184	19	with	with	ADP
ejpam-816	184	20	the	the	DET
ejpam-816	184	21	parameters	parameter	NOUN
ejpam-816	184	22	µ1	µ1	NOUN
ejpam-816	184	23	=	=	SYM
ejpam-816	184	24	µ2	µ2	PROPN
ejpam-816	184	25	=	=	SYM
ejpam-816	184	26	3	3	NUM
ejpam-816	184	27	,	,	PUNCT
ejpam-816	184	28	µ3	µ3	NOUN
ejpam-816	184	29	=	=	SYM
ejpam-816	184	30	4	4	NUM
ejpam-816	184	31	,	,	PUNCT
ejpam-816	184	32	m1	m1	PROPN
ejpam-816	184	33	=	=	SYM
ejpam-816	184	34	m2	m2	PROPN
ejpam-816	184	35	=	=	SYM
ejpam-816	184	36	1	1	NUM
ejpam-816	184	37	2	2	NUM
ejpam-816	184	38	,	,	PUNCT
ejpam-816	184	39	m3	m3	PROPN
ejpam-816	184	40	=	=	SYM
ejpam-816	184	41	1	1	NUM
ejpam-816	184	42	and	and	CCONJ
ejpam-816	184	43	ν1	ν1	NOUN
ejpam-816	184	44	=	=	SYM
ejpam-816	184	45	1	1	NUM
ejpam-816	184	46	,	,	PUNCT
ejpam-816	184	47	ν2	ν2	NOUN
ejpam-816	184	48	=	=	SYM
ejpam-816	184	49	1	1	NUM
ejpam-816	184	50	2	2	NUM
ejpam-816	184	51	,	,	PUNCT
ejpam-816	184	52	ν3	ν3	NOUN
ejpam-816	184	53	=	=	SYM
ejpam-816	184	54	3	3	NUM
ejpam-816	184	55	2	2	NUM
ejpam-816	184	56	.	.	PUNCT
ejpam-816	185	1	from	from	ADP
ejpam-816	185	2	(	(	PUNCT
ejpam-816	185	3	21	21	NUM
ejpam-816	185	4	)	)	PUNCT
ejpam-816	185	5	we	we	PRON
ejpam-816	185	6	therefore	therefore	ADV
ejpam-816	185	7	have	have	VERB
ejpam-816	185	8	i3(z	i3(z	X
ejpam-816	185	9	)	)	PUNCT
ejpam-816	185	10	=	=	SYM
ejpam-816	185	11	3ψ0	3ψ0	NUM
ejpam-816	185	12	�	�	PROPN
ejpam-816	185	13	(	(	PUNCT
ejpam-816	185	14	1	1	NUM
ejpam-816	185	15	6	6	NUM
ejpam-816	185	16	,	,	PUNCT
ejpam-816	185	17	1	1	NUM
ejpam-816	185	18	3	3	NUM
ejpam-816	185	19	)	)	PUNCT
ejpam-816	185	20	,	,	PUNCT
ejpam-816	185	21	(	(	PUNCT
ejpam-816	185	22	1	1	NUM
ejpam-816	185	23	6	6	NUM
ejpam-816	185	24	,	,	PUNCT
ejpam-816	185	25	1	1	NUM
ejpam-816	185	26	6	6	NUM
ejpam-816	185	27	)	)	PUNCT
ejpam-816	185	28	,	,	PUNCT
ejpam-816	185	29	(	(	PUNCT
ejpam-816	185	30	1	1	NUM
ejpam-816	185	31	4	4	NUM
ejpam-816	185	32	,	,	PUNCT
ejpam-816	185	33	3	3	NUM
ejpam-816	185	34	8	8	NUM
ejpam-816	185	35	)	)	PUNCT
ejpam-816	185	36	;	;	PUNCT
ejpam-816	185	37	z	z	PROPN
ejpam-816	185	38	�	�	PROPN
ejpam-816	185	39	≡	≡	PROPN
ejpam-816	185	40	3ψ0(z	3ψ0(z	NUM
ejpam-816	185	41	)	)	PUNCT
ejpam-816	185	42	.	.	PUNCT
ejpam-816	186	1	(	(	PUNCT
ejpam-816	186	2	25	25	NUM
ejpam-816	186	3	)	)	PUNCT
ejpam-816	186	4	from	from	ADP
ejpam-816	186	5	(	(	PUNCT
ejpam-816	186	6	3	3	NUM
ejpam-816	186	7	)	)	PUNCT
ejpam-816	186	8	,	,	PUNCT
ejpam-816	186	9	(	(	PUNCT
ejpam-816	186	10	7	7	X
ejpam-816	186	11	)	)	PUNCT
ejpam-816	186	12	and	and	CCONJ
ejpam-816	186	13	(	(	PUNCT
ejpam-816	186	14	24	24	NUM
ejpam-816	186	15	)	)	PUNCT
ejpam-816	186	16	we	we	PRON
ejpam-816	186	17	obtain	obtain	VERB
ejpam-816	186	18	the	the	DET
ejpam-816	186	19	parameters	parameter	NOUN
ejpam-816	186	20	κ	κ	X
ejpam-816	186	21	=	=	SYM
ejpam-816	186	22	5	5	NUM
ejpam-816	186	23	12	12	NUM
ejpam-816	186	24	,	,	PUNCT
ejpam-816	186	25	h=	h=	NOUN
ejpam-816	186	26	2−5/63−1/3	2−5/63−1/3	NUM
ejpam-816	186	27	,	,	PUNCT
ejpam-816	186	28	ϑ	ϑ	X
ejpam-816	186	29	=	=	X
ejpam-816	186	30	−5	−5	ADP
ejpam-816	186	31	8	8	NUM
ejpam-816	186	32	,	,	PUNCT
ejpam-816	187	1	a0	a0	NOUN
ejpam-816	187	2	=	=	SYM
ejpam-816	187	3	4π3/235/851/8	4π3/235/851/8	PROPN
ejpam-816	187	4	.	.	PUNCT
ejpam-816	188	1	then	then	ADV
ejpam-816	188	2	,	,	PUNCT
ejpam-816	188	3	from	from	ADP
ejpam-816	188	4	(	(	PUNCT
ejpam-816	188	5	8)	8)	NUM
ejpam-816	188	6	,	,	PUNCT
ejpam-816	188	7	e3,0(z	e3,0(z	PROPN
ejpam-816	188	8	)	)	PUNCT
ejpam-816	188	9	=	=	PUNCT
ejpam-816	189	1	z−5/8ez	z−5/8ez	PROPN
ejpam-816	189	2	∞	∞	NUM
ejpam-816	189	3	∑	∑	PUNCT
ejpam-816	189	4	j=0	j=0	X
ejpam-816	189	5	a	a	DET
ejpam-816	189	6	j	j	PROPN
ejpam-816	189	7	z	z	PROPN
ejpam-816	189	8	−	−	PROPN
ejpam-816	189	9	j	j	PROPN
ejpam-816	189	10	,	,	PUNCT
ejpam-816	189	11	z	z	PROPN
ejpam-816	189	12	=	=	SYM
ejpam-816	189	13	5	5	NUM
ejpam-816	189	14	48	48	NUM
ejpam-816	189	15	(	(	PUNCT
ejpam-816	189	16	1	1	NUM
ejpam-816	189	17	3	3	NUM
ejpam-816	189	18	z3)4/5	z3)4/5	ADV
ejpam-816	189	19	,	,	PUNCT
ejpam-816	189	20	(	(	PUNCT
ejpam-816	189	21	26	26	NUM
ejpam-816	189	22	)	)	PUNCT
ejpam-816	189	23	where	where	SCONJ
ejpam-816	189	24	,	,	PUNCT
ejpam-816	189	25	by	by	ADP
ejpam-816	189	26	use	use	NOUN
ejpam-816	189	27	of	of	ADP
ejpam-816	189	28	the	the	DET
ejpam-816	189	29	algorithm	algorithm	NOUN
ejpam-816	189	30	described	describe	VERB
ejpam-816	189	31	in	in	ADP
ejpam-816	189	32	appendix	appendix	PROPN
ejpam-816	189	33	a	a	PRON
ejpam-816	189	34	,	,	PUNCT
ejpam-816	189	35	the	the	DET
ejpam-816	189	36	first	first	ADJ
ejpam-816	189	37	few	few	ADJ
ejpam-816	189	38	normalised	normalise	VERB
ejpam-816	189	39	coefficients	coefficient	NOUN
ejpam-816	189	40	c	c	AUX
ejpam-816	189	41	j	j	PROPN
ejpam-816	189	42	≡	≡	PROPN
ejpam-816	189	43	a	a	DET
ejpam-816	189	44	j	j	PROPN
ejpam-816	189	45	/	/	SYM
ejpam-816	189	46	a0	a0	PROPN
ejpam-816	189	47	are	be	AUX
ejpam-816	189	48	found	find	VERB
ejpam-816	189	49	to	to	PART
ejpam-816	189	50	be	be	AUX
ejpam-816	189	51	c1	c1	PROPN
ejpam-816	189	52	=	=	PUNCT
ejpam-816	189	53	67	67	NUM
ejpam-816	189	54	144	144	NUM
ejpam-816	189	55	,	,	PUNCT
ejpam-816	189	56	c2	c2	PROPN
ejpam-816	189	57	=	=	SYM
ejpam-816	189	58	23785	23785	NUM
ejpam-816	189	59	41472	41472	NUM
ejpam-816	189	60	,	,	PUNCT
ejpam-816	189	61	c3	c3	PROPN
ejpam-816	189	62	=	=	PROPN
ejpam-816	189	63	106119923	106119923	NUM
ejpam-816	189	64	89579520	89579520	NUM
ejpam-816	189	65	,	,	PUNCT
ejpam-816	189	66	c4	c4	NOUN
ejpam-816	189	67	=	=	SYM
ejpam-816	189	68	181613304677	181613304677	NUM
ejpam-816	189	69	51597803520	51597803520	NUM
ejpam-816	189	70	,	,	PUNCT
ejpam-816	189	71	c5	c5	PROPN
ejpam-816	189	72	=	=	PROPN
ejpam-816	189	73	102937183723339	102937183723339	NUM
ejpam-816	189	74	7430083706880	7430083706880	NUM
ejpam-816	189	75	,	,	PUNCT
ejpam-816	189	76	.	.	PUNCT
ejpam-816	189	77	.	.	PUNCT
ejpam-816	189	78	.	.	PUNCT
ejpam-816	189	79	.	.	PUNCT
ejpam-816	190	1	the	the	DET
ejpam-816	190	2	poles	pole	NOUN
ejpam-816	190	3	in	in	ADP
ejpam-816	190	4	(	(	PUNCT
ejpam-816	190	5	12	12	NUM
ejpam-816	190	6	)	)	PUNCT
ejpam-816	190	7	are	be	AUX
ejpam-816	190	8	situated	situate	VERB
ejpam-816	190	9	at	at	ADP
ejpam-816	190	10	sk,1	sk,1	PROPN
ejpam-816	190	11	=	=	PROPN
ejpam-816	190	12	2	2	NUM
ejpam-816	190	13	+	+	NUM
ejpam-816	190	14	6k	6k	NOUN
ejpam-816	190	15	,	,	PUNCT
ejpam-816	190	16	sk,2	sk,2	PROPN
ejpam-816	190	17	=	=	SYM
ejpam-816	190	18	1	1	NUM
ejpam-816	190	19	+	+	NUM
ejpam-816	190	20	6k	6k	NOUN
ejpam-816	190	21	,	,	PUNCT
ejpam-816	190	22	sk,3	sk,3	X
ejpam-816	190	23	=	=	PUNCT
ejpam-816	190	24	3	3	NUM
ejpam-816	190	25	2	2	NUM
ejpam-816	190	26	+	+	NUM
ejpam-816	190	27	4k	4k	X
ejpam-816	190	28	(	(	PUNCT
ejpam-816	190	29	k	k	NOUN
ejpam-816	190	30	=	=	SYM
ejpam-816	190	31	0,1,2	0,1,2	NUM
ejpam-816	190	32	,	,	PUNCT
ejpam-816	190	33	.	.	PUNCT
ejpam-816	190	34	.	.	PUNCT
ejpam-816	190	35	.	.	PUNCT
ejpam-816	190	36	)	)	PUNCT
ejpam-816	191	1	and	and	CCONJ
ejpam-816	191	2	so	so	ADV
ejpam-816	191	3	are	be	AUX
ejpam-816	191	4	all	all	PRON
ejpam-816	191	5	simple	simple	ADJ
ejpam-816	191	6	poles	pole	NOUN
ejpam-816	191	7	.	.	PUNCT
ejpam-816	192	1	hence	hence	ADV
ejpam-816	192	2	,	,	PUNCT
ejpam-816	192	3	from	from	ADP
ejpam-816	192	4	(	(	PUNCT
ejpam-816	192	5	13	13	NUM
ejpam-816	192	6	)	)	PUNCT
ejpam-816	192	7	and	and	CCONJ
ejpam-816	192	8	(	(	PUNCT
ejpam-816	192	9	14	14	NUM
ejpam-816	192	10	)	)	PUNCT
ejpam-816	192	11	,	,	PUNCT
ejpam-816	192	12	we	we	PRON
ejpam-816	192	13	find	find	VERB
ejpam-816	192	14	the	the	DET
ejpam-816	192	15	algebraic	algebraic	ADJ
ejpam-816	192	16	expansion	expansion	NOUN
ejpam-816	192	17	given	give	VERB
ejpam-816	192	18	by	by	ADP
ejpam-816	192	19	h3,0(z	h3,0(z	PROPN
ejpam-816	192	20	)	)	PUNCT
ejpam-816	192	21	=	=	SYM
ejpam-816	193	1	3	3	NUM
ejpam-816	193	2	∑	∑	PROPN
ejpam-816	193	3	j=1	j=1	PROPN
ejpam-816	193	4	µ	µ	X
ejpam-816	193	5	j	j	PROPN
ejpam-816	193	6	m	m	PROPN
ejpam-816	193	7	j	j	PROPN
ejpam-816	193	8	z−ν	z−ν	PROPN
ejpam-816	193	9	j	j	PROPN
ejpam-816	193	10	/	/	PROPN
ejpam-816	193	11	m	m	PROPN
ejpam-816	193	12	j	j	PROPN
ejpam-816	193	13	s3,0(z	s3,0(z	PROPN
ejpam-816	193	14	;	;	PUNCT
ejpam-816	193	15	j	j	PROPN
ejpam-816	193	16	)	)	PUNCT
ejpam-816	193	17	,	,	PUNCT
ejpam-816	193	18	(	(	PUNCT
ejpam-816	193	19	27	27	NUM
ejpam-816	193	20	)	)	PUNCT
ejpam-816	193	21	where	where	SCONJ
ejpam-816	193	22	s3,0(z	s3,0(z	PROPN
ejpam-816	193	23	;	;	PUNCT
ejpam-816	193	24	j	j	X
ejpam-816	193	25	)	)	PUNCT
ejpam-816	193	26	=	=	SYM
ejpam-816	194	1	∞	∞	PROPN
ejpam-816	194	2	∑	∑	PUNCT
ejpam-816	194	3	k=0	k=0	PROPN
ejpam-816	194	4	(	(	PUNCT
ejpam-816	194	5	−)k	−)k	PROPN
ejpam-816	194	6	k	k	PROPN
ejpam-816	194	7	!	!	PUNCT
ejpam-816	195	1	γ	γ	PROPN
ejpam-816	195	2	�	�	PROPN
ejpam-816	195	3	µ	µ	PROPN
ejpam-816	195	4	jk+	jk+	PROPN
ejpam-816	195	5	ν	ν	X
ejpam-816	195	6	j	j	PROPN
ejpam-816	195	7	m	m	PROPN
ejpam-816	195	8	j	j	PROPN
ejpam-816	195	9	�	�	PROPN
ejpam-816	195	10	3	3	NUM
ejpam-816	195	11	∏	∏	PROPN
ejpam-816	195	12	r=1	r=1	NOUN
ejpam-816	195	13	′	′	NUM
ejpam-816	195	14	γ	γ	X
ejpam-816	195	15	�	�	PROPN
ejpam-816	195	16	νr	νr	ADP
ejpam-816	195	17	−mrsk	−mrsk	PROPN
ejpam-816	195	18	,	,	PUNCT
ejpam-816	195	19	j	j	PROPN
ejpam-816	195	20	µr	µr	ADP
ejpam-816	195	21	�	�	PROPN
ejpam-816	195	22	z−µ	z−µ	NUM
ejpam-816	195	23	j	j	PROPN
ejpam-816	196	1	k	k	X
ejpam-816	196	2	/	/	PROPN
ejpam-816	196	3	m	m	PROPN
ejpam-816	196	4	j	j	PROPN
ejpam-816	196	5	(	(	PUNCT
ejpam-816	196	6	28	28	NUM
ejpam-816	196	7	)	)	PUNCT
ejpam-816	196	8	with	with	ADP
ejpam-816	196	9	the	the	DET
ejpam-816	196	10	prime	prime	NOUN
ejpam-816	196	11	denoting	denote	VERB
ejpam-816	196	12	the	the	DET
ejpam-816	196	13	omission	omission	NOUN
ejpam-816	196	14	of	of	ADP
ejpam-816	196	15	the	the	DET
ejpam-816	196	16	gamma	gamma	NOUN
ejpam-816	196	17	function	function	NOUN
ejpam-816	196	18	factor	factor	NOUN
ejpam-816	196	19	corresponding	correspond	VERB
ejpam-816	196	20	to	to	ADP
ejpam-816	196	21	r	r	NOUN
ejpam-816	196	22	=	=	PUNCT
ejpam-816	196	23	j.	j.	PROPN
ejpam-816	196	24	then	then	ADV
ejpam-816	196	25	,	,	PUNCT
ejpam-816	196	26	from	from	ADP
ejpam-816	196	27	(	(	PUNCT
ejpam-816	196	28	23	23	NUM
ejpam-816	196	29	)	)	PUNCT
ejpam-816	196	30	we	we	PRON
ejpam-816	196	31	obtain	obtain	VERB
ejpam-816	196	32	the	the	DET
ejpam-816	196	33	expansion	expansion	NOUN
ejpam-816	196	34	i3(z	i3(z	NOUN
ejpam-816	196	35	)	)	PUNCT
ejpam-816	196	36	∼	∼	NOUN
ejpam-816	196	37	¨	¨	NOUN
ejpam-816	196	38	e3,0(z	e3,0(z	PROPN
ejpam-816	196	39	)	)	PUNCT
ejpam-816	197	1	+	+	ADJ
ejpam-816	197	2	h3,0(ze∓πi	h3,0(ze∓πi	NOUN
ejpam-816	197	3	)	)	PUNCT
ejpam-816	197	4	in	in	ADP
ejpam-816	197	5	|arg	|arg	VERB
ejpam-816	197	6	z|	z|	PROPN
ejpam-816	197	7	≤	≤	NOUN
ejpam-816	197	8	5	5	NUM
ejpam-816	197	9	12	12	NUM
ejpam-816	197	10	π−	π−	PROPN
ejpam-816	197	11	ε	ε	PROPN
ejpam-816	197	12	h3,0(ze∓πi	h3,0(ze∓πi	PROPN
ejpam-816	197	13	)	)	PUNCT
ejpam-816	197	14	in	in	ADP
ejpam-816	197	15	5	5	NUM
ejpam-816	197	16	12	12	NUM
ejpam-816	197	17	π+	π+	PUNCT
ejpam-816	197	18	ε≤	ε≤	PROPN
ejpam-816	197	19	|arg	|arg	VERB
ejpam-816	197	20	z|	z|	ADJ
ejpam-816	197	21	≤	≤	NOUN
ejpam-816	197	22	π	π	X
ejpam-816	197	23	(	(	PUNCT
ejpam-816	197	24	29	29	NUM
ejpam-816	197	25	)	)	PUNCT
ejpam-816	197	26	as	as	ADP
ejpam-816	197	27	|z|	|z|	NOUN
ejpam-816	197	28	→	→	PUNCT
ejpam-816	197	29	∞.	∞.	PROPN
ejpam-816	197	30	it	it	PRON
ejpam-816	197	31	follows	follow	VERB
ejpam-816	197	32	that	that	SCONJ
ejpam-816	197	33	i3(z	i3(z	PROPN
ejpam-816	197	34	)	)	PUNCT
ejpam-816	197	35	is	be	AUX
ejpam-816	197	36	exponentially	exponentially	ADV
ejpam-816	197	37	large	large	ADJ
ejpam-816	197	38	in	in	ADP
ejpam-816	197	39	the	the	DET
ejpam-816	197	40	sector	sector	NOUN
ejpam-816	197	41	|arg	|arg	NOUN
ejpam-816	197	42	z|	z|	PROPN
ejpam-816	197	43	<	<	X
ejpam-816	197	44	5	5	NUM
ejpam-816	197	45	24	24	NUM
ejpam-816	197	46	π	π	NOUN
ejpam-816	197	47	with	with	ADP
ejpam-816	197	48	the	the	DET
ejpam-816	197	49	dominant	dominant	ADJ
ejpam-816	197	50	expansion	expansion	NOUN
ejpam-816	197	51	being	be	AUX
ejpam-816	197	52	algebraic	algebraic	ADJ
ejpam-816	197	53	in	in	ADP
ejpam-816	197	54	the	the	DET
ejpam-816	197	55	rest	rest	NOUN
ejpam-816	197	56	of	of	ADP
ejpam-816	197	57	the	the	DET
ejpam-816	197	58	z	z	NOUN
ejpam-816	197	59	-	-	NOUN
ejpam-816	197	60	plane	plane	NOUN
ejpam-816	197	61	.	.	PUNCT
ejpam-816	198	1	in	in	ADP
ejpam-816	198	2	the	the	DET
ejpam-816	198	3	sectors	sector	NOUN
ejpam-816	198	4	5	5	NUM
ejpam-816	198	5	12	12	NUM
ejpam-816	198	6	π	π	NOUN
ejpam-816	198	7	<	<	X
ejpam-816	198	8	|arg	|arg	VERB
ejpam-816	198	9	z|	z|	PROPN
ejpam-816	198	10	<	<	X
ejpam-816	198	11	5	5	NUM
ejpam-816	198	12	24	24	NUM
ejpam-816	198	13	π	π	PROPN
ejpam-816	198	14	the	the	DET
ejpam-816	198	15	exponential	exponential	ADJ
ejpam-816	198	16	expansion	expansion	NOUN
ejpam-816	198	17	e3,0(z	e3,0(z	PROPN
ejpam-816	198	18	)	)	PUNCT
ejpam-816	198	19	is	be	AUX
ejpam-816	198	20	subdominant	subdominant	ADJ
ejpam-816	198	21	and	and	CCONJ
ejpam-816	198	22	switches	switch	VERB
ejpam-816	198	23	off	off	ADP
ejpam-816	198	24	(	(	PUNCT
ejpam-816	198	25	as	as	SCONJ
ejpam-816	198	26	|arg	|arg	VERB
ejpam-816	198	27	z|	z|	NOUN
ejpam-816	198	28	increases	increase	NOUN
ejpam-816	198	29	)	)	PUNCT
ejpam-816	198	30	across	across	ADP
ejpam-816	198	31	the	the	DET
ejpam-816	198	32	stokes	stokes	PROPN
ejpam-816	198	33	lines	lines	PROPN
ejpam-816	198	34	arg	arg	VERB
ejpam-816	198	35	z	z	NOUN
ejpam-816	198	36	=	=	SYM
ejpam-816	198	37	±	±	NUM
ejpam-816	198	38	5	5	NUM
ejpam-816	198	39	12	12	NUM
ejpam-816	198	40	π	π	NOUN
ejpam-816	198	41	.	.	PUNCT
ejpam-816	199	1	we	we	PRON
ejpam-816	199	2	show	show	VERB
ejpam-816	199	3	in	in	ADP
ejpam-816	199	4	table	table	NOUN
ejpam-816	199	5	1	1	NUM
ejpam-816	199	6	the	the	DET
ejpam-816	199	7	values	value	NOUN
ejpam-816	199	8	of	of	ADP
ejpam-816	199	9	the	the	DET
ejpam-816	199	10	absolute	absolute	ADJ
ejpam-816	199	11	relative	relative	ADJ
ejpam-816	199	12	error	error	NOUN
ejpam-816	199	13	in	in	ADP
ejpam-816	199	14	the	the	DET
ejpam-816	199	15	computation	computation	NOUN
ejpam-816	199	16	of	of	ADP
ejpam-816	199	17	i3(z	i3(z	PROPN
ejpam-816	199	18	)	)	PUNCT
ejpam-816	199	19	as	as	ADP
ejpam-816	199	20	a	a	DET
ejpam-816	199	21	function	function	NOUN
ejpam-816	199	22	of	of	ADP
ejpam-816	199	23	θ	θ	PROPN
ejpam-816	199	24	=	=	PUNCT
ejpam-816	199	25	arg	arg	NOUN
ejpam-816	199	26	z	z	NOUN
ejpam-816	199	27	when	when	SCONJ
ejpam-816	199	28	|z|	|z|	NOUN
ejpam-816	199	29	=	=	SYM
ejpam-816	199	30	15	15	NUM
ejpam-816	199	31	using	use	VERB
ejpam-816	199	32	the	the	DET
ejpam-816	199	33	optimally	optimally	ADV
ejpam-816	199	34	truncated	truncate	VERB
ejpam-816	199	35	asymptotic	asymptotic	ADJ
ejpam-816	199	36	expansions	expansion	NOUN
ejpam-816	199	37	(	(	PUNCT
ejpam-816	199	38	that	that	PRON
ejpam-816	199	39	is	is	ADV
ejpam-816	199	40	,	,	PUNCT
ejpam-816	199	41	truncated	truncate	VERB
ejpam-816	199	42	at	at	ADP
ejpam-816	199	43	or	or	CCONJ
ejpam-816	199	44	near	near	ADP
ejpam-816	199	45	the	the	DET
ejpam-816	199	46	least	least	ADJ
ejpam-816	199	47	term	term	NOUN
ejpam-816	199	48	in	in	ADP
ejpam-816	199	49	modulus	modulus	NOUN
ejpam-816	199	50	)	)	PUNCT
ejpam-816	199	51	in	in	ADP
ejpam-816	199	52	(	(	PUNCT
ejpam-816	199	53	29	29	NUM
ejpam-816	199	54	)	)	PUNCT
ejpam-816	199	55	.	.	PUNCT
ejpam-816	200	1	r.	r.	PROPN
ejpam-816	200	2	paris	paris	PROPN
ejpam-816	200	3	/	/	SYM
ejpam-816	200	4	eur	eur	PROPN
ejpam-816	200	5	.	.	PUNCT
ejpam-816	201	1	j.	j.	PROPN
ejpam-816	201	2	pure	pure	PROPN
ejpam-816	201	3	appl	appl	PROPN
ejpam-816	201	4	.	.	PROPN
ejpam-816	201	5	math	math	PROPN
ejpam-816	201	6	,	,	PUNCT
ejpam-816	201	7	3	3	NUM
ejpam-816	201	8	(	(	PUNCT
ejpam-816	201	9	2010	2010	NUM
ejpam-816	201	10	)	)	PUNCT
ejpam-816	201	11	,	,	PUNCT
ejpam-816	201	12	1006	1006	NUM
ejpam-816	201	13	-	-	SYM
ejpam-816	201	14	1031	1031	NUM
ejpam-816	201	15	1014	1014	NUM
ejpam-816	201	16	table	table	NOUN
ejpam-816	201	17	1	1	NUM
ejpam-816	201	18	:	:	PUNCT
ejpam-816	201	19	values	value	NOUN
ejpam-816	201	20	of	of	ADP
ejpam-816	201	21	the	the	DET
ejpam-816	201	22	absolute	absolute	ADJ
ejpam-816	201	23	relative	relative	ADJ
ejpam-816	201	24	error	error	NOUN
ejpam-816	201	25	in	in	ADP
ejpam-816	201	26	the	the	DET
ejpam-816	201	27	computation	computation	NOUN
ejpam-816	201	28	of	of	ADP
ejpam-816	201	29	i3(z	i3(z	PROPN
ejpam-816	201	30	)	)	PUNCT
ejpam-816	201	31	in	in	ADP
ejpam-816	201	32	(	(	PUNCT
ejpam-816	201	33	25	25	NUM
ejpam-816	201	34	)	)	PUNCT
ejpam-816	201	35	when	when	SCONJ
ejpam-816	201	36	|z|	|z|	NOUN
ejpam-816	201	37	=	=	SYM
ejpam-816	201	38	15	15	NUM
ejpam-816	201	39	as	as	ADP
ejpam-816	201	40	a	a	DET
ejpam-816	201	41	function	function	NOUN
ejpam-816	201	42	of	of	ADP
ejpam-816	201	43	θ	θ	PROPN
ejpam-816	201	44	=	=	PUNCT
ejpam-816	201	45	arg	arg	NOUN
ejpam-816	201	46	z	z	NOUN
ejpam-816	201	47	using	use	VERB
ejpam-816	201	48	an	an	DET
ejpam-816	201	49	optimal	optimal	ADJ
ejpam-816	201	50	truncation	truncation	NOUN
ejpam-816	201	51	of	of	ADP
ejpam-816	201	52	the	the	DET
ejpam-816	201	53	expansions	expansion	NOUN
ejpam-816	201	54	in	in	ADP
ejpam-816	201	55	(	(	PUNCT
ejpam-816	201	56	29	29	NUM
ejpam-816	201	57	)	)	PUNCT
ejpam-816	201	58	.	.	PUNCT
ejpam-816	202	1	θ	θ	X
ejpam-816	202	2	/	/	SYM
ejpam-816	202	3	π	π	PROPN
ejpam-816	202	4	|rel	|rel	NOUN
ejpam-816	202	5	.	.	PUNCT
ejpam-816	202	6	error|	error|	PROPN
ejpam-816	202	7	θ	θ	PROPN
ejpam-816	202	8	/	/	SYM
ejpam-816	202	9	π	π	PROPN
ejpam-816	202	10	|rel	|rel	NOUN
ejpam-816	202	11	.	.	PUNCT
ejpam-816	203	1	error|	error|	NOUN
ejpam-816	203	2	0	0	NUM
ejpam-816	204	1	5.816×	5.816×	NUM
ejpam-816	204	2	10−13	10−13	NUM
ejpam-816	204	3	0.625	0.625	NUM
ejpam-816	204	4	9.259×	9.259×	NUM
ejpam-816	205	1	10−14	10−14	NUM
ejpam-816	205	2	0.125	0.125	NUM
ejpam-816	205	3	9.262×	9.262×	NUM
ejpam-816	205	4	10−14	10−14	NUM
ejpam-816	205	5	0.750	0.750	NUM
ejpam-816	205	6	2.744×	2.744×	NUM
ejpam-816	205	7	10−13	10−13	NUM
ejpam-816	205	8	0.250	0.250	NUM
ejpam-816	205	9	1.612×	1.612×	NUM
ejpam-816	205	10	10−13	10−13	NUM
ejpam-816	205	11	0.875	0.875	NUM
ejpam-816	205	12	9.841×	9.841×	NUM
ejpam-816	206	1	10−14	10−14	NUM
ejpam-816	206	2	0.375	0.375	NUM
ejpam-816	206	3	3.534×	3.534×	PROPN
ejpam-816	206	4	10−14	10−14	NUM
ejpam-816	206	5	1.000	1.000	NUM
ejpam-816	206	6	1.727×	1.727×	NUM
ejpam-816	206	7	10−13	10−13	NUM
ejpam-816	206	8	0.500	0.500	NUM
ejpam-816	206	9	1.177×	1.177×	NUM
ejpam-816	206	10	10−13	10−13	NUM
ejpam-816	206	11	4	4	NUM
ejpam-816	206	12	.	.	PUNCT
ejpam-816	207	1	the	the	DET
ejpam-816	207	2	integral	integral	ADJ
ejpam-816	207	3	jn(z	jn(z	NOUN
ejpam-816	207	4	)	)	PUNCT
ejpam-816	207	5	we	we	PRON
ejpam-816	207	6	can	can	AUX
ejpam-816	207	7	apply	apply	VERB
ejpam-816	207	8	a	a	DET
ejpam-816	207	9	similar	similar	ADJ
ejpam-816	207	10	treatment	treatment	NOUN
ejpam-816	207	11	to	to	ADP
ejpam-816	207	12	the	the	DET
ejpam-816	207	13	integral	integral	ADJ
ejpam-816	207	14	jn(z	jn(z	NOUN
ejpam-816	207	15	)	)	PUNCT
ejpam-816	208	1	=	=	SYM
ejpam-816	208	2	λn	λn	PROPN
ejpam-816	208	3	∫	∫	PROPN
ejpam-816	208	4	∞	∞	PROPN
ejpam-816	208	5	−∞	−∞	PROPN
ejpam-816	208	6	.	.	PUNCT
ejpam-816	208	7	.	.	PUNCT
ejpam-816	208	8	.	.	PUNCT
ejpam-816	209	1	∫	∫	PROPN
ejpam-816	210	1	∞	∞	PROPN
ejpam-816	211	1	−∞	−∞	ADP
ejpam-816	211	2	x	x	X
ejpam-816	211	3	ν1−1	ν1−1	PRON
ejpam-816	211	4	1	1	NUM
ejpam-816	211	5	.	.	PUNCT
ejpam-816	211	6	.	.	PUNCT
ejpam-816	211	7	.	.	PUNCT
ejpam-816	212	1	xνn−1	xνn−1	PROPN
ejpam-816	212	2	n	n	CCONJ
ejpam-816	212	3	e−	e−	PROPN
ejpam-816	212	4	f	f	PROPN
ejpam-816	212	5	(	(	PUNCT
ejpam-816	212	6	x1,	x1,	NOUN
ejpam-816	212	7	...	...	PUNCT
ejpam-816	212	8	,xn;z	,xn;z	PUNCT
ejpam-816	212	9	)	)	PUNCT
ejpam-816	213	1	d	d	X
ejpam-816	213	2	x1	x1	PROPN
ejpam-816	213	3	.	.	PUNCT
ejpam-816	213	4	.	.	PUNCT
ejpam-816	213	5	.	.	PUNCT
ejpam-816	214	1	d	d	NOUN
ejpam-816	214	2	xn	xn	PUNCT
ejpam-816	215	1	=	=	NOUN
ejpam-816	215	2	λn	λn	PROPN
ejpam-816	215	3	∞	∞	NUM
ejpam-816	215	4	∑	∑	PROPN
ejpam-816	215	5	k=0	k=0	PROPN
ejpam-816	215	6	zk	zk	PROPN
ejpam-816	216	1	k	k	PROPN
ejpam-816	216	2	!	!	PUNCT
ejpam-816	216	3	n	n	CCONJ
ejpam-816	216	4	∏	∏	PROPN
ejpam-816	216	5	r=1	r=1	NOUN
ejpam-816	216	6	∫	∫	PROPN
ejpam-816	216	7	∞	∞	PROPN
ejpam-816	216	8	−∞	−∞	PROPN
ejpam-816	216	9	xνr+mr	xνr+mr	PUNCT
ejpam-816	216	10	k−1	k−1	PROPN
ejpam-816	216	11	r	r	NOUN
ejpam-816	216	12	exp{−xµr	exp{−xµr	PROPN
ejpam-816	216	13	r	r	NOUN
ejpam-816	216	14	}	}	PUNCT
ejpam-816	216	15	d	d	PROPN
ejpam-816	216	16	xr	xr	PROPN
ejpam-816	216	17	,	,	PUNCT
ejpam-816	216	18	where	where	SCONJ
ejpam-816	216	19	the	the	DET
ejpam-816	216	20	phase	phase	NOUN
ejpam-816	216	21	function	function	VERB
ejpam-816	216	22	f	f	PROPN
ejpam-816	216	23	and	and	CCONJ
ejpam-816	216	24	the	the	DET
ejpam-816	216	25	factor	factor	NOUN
ejpam-816	216	26	λn	λn	NOUN
ejpam-816	216	27	are	be	AUX
ejpam-816	216	28	defined	define	VERB
ejpam-816	216	29	in	in	ADP
ejpam-816	216	30	(	(	PUNCT
ejpam-816	216	31	2	2	NUM
ejpam-816	216	32	)	)	PUNCT
ejpam-816	216	33	and	and	CCONJ
ejpam-816	216	34	it	it	PRON
ejpam-816	216	35	is	be	AUX
ejpam-816	216	36	supposed	suppose	VERB
ejpam-816	216	37	that	that	SCONJ
ejpam-816	216	38	the	the	DET
ejpam-816	216	39	parameters	parameter	NOUN
ejpam-816	216	40	µ	µ	PROPN
ejpam-816	216	41	j	j	X
ejpam-816	216	42	(	(	PUNCT
ejpam-816	216	43	1	1	NUM
ejpam-816	216	44	≤	≤	NUM
ejpam-816	216	45	j	j	PROPN
ejpam-816	216	46	≤	≤	PROPN
ejpam-816	216	47	n	n	CCONJ
ejpam-816	216	48	)	)	PUNCT
ejpam-816	216	49	appearing	appear	VERB
ejpam-816	216	50	in	in	ADP
ejpam-816	216	51	f	f	PROPN
ejpam-816	216	52	are	be	AUX
ejpam-816	216	53	positive	positive	ADJ
ejpam-816	216	54	even	even	ADV
ejpam-816	216	55	integers	integer	NOUN
ejpam-816	216	56	.	.	PUNCT
ejpam-816	217	1	in	in	ADP
ejpam-816	217	2	the	the	DET
ejpam-816	217	3	evaluation	evaluation	NOUN
ejpam-816	217	4	of	of	ADP
ejpam-816	217	5	the	the	DET
ejpam-816	217	6	above	above	ADJ
ejpam-816	217	7	integrals	integral	NOUN
ejpam-816	217	8	when	when	SCONJ
ejpam-816	217	9	xr	xr	PROPN
ejpam-816	217	10	<	<	X
ejpam-816	217	11	0	0	PROPN
ejpam-816	217	12	,	,	PUNCT
ejpam-816	217	13	we	we	PRON
ejpam-816	217	14	shall	shall	AUX
ejpam-816	217	15	write	write	VERB
ejpam-816	217	16	xr	xr	PROPN
ejpam-816	217	17	=	=	PROPN
ejpam-816	217	18	|xr	|xr	PRON
ejpam-816	217	19	|e	|e	PROPN
ejpam-816	217	20	πi	πi	ADV
ejpam-816	217	21	.	.	PUNCT
ejpam-816	218	1	we	we	PRON
ejpam-816	218	2	now	now	ADV
ejpam-816	218	3	introduce	introduce	VERB
ejpam-816	218	4	the	the	DET
ejpam-816	218	5	notation	notation	NOUN
ejpam-816	218	6	e(x	e(x	NUM
ejpam-816	218	7	)	)	PUNCT
ejpam-816	218	8	for	for	ADP
ejpam-816	218	9	brevity	brevity	NOUN
ejpam-816	218	10	in	in	ADP
ejpam-816	218	11	this	this	DET
ejpam-816	218	12	section	section	NOUN
ejpam-816	218	13	and	and	CCONJ
ejpam-816	218	14	define	define	VERB
ejpam-816	218	15	the	the	DET
ejpam-816	218	16	quantities	quantity	NOUN
ejpam-816	218	17	br(k	br(k	NOUN
ejpam-816	218	18	)	)	PUNCT
ejpam-816	218	19	by	by	ADP
ejpam-816	218	20	e(x	e(x	NUM
ejpam-816	218	21	)	)	PUNCT
ejpam-816	218	22	:	:	PUNCT
ejpam-816	219	1	=	=	SYM
ejpam-816	219	2	eπi	eπi	PROPN
ejpam-816	219	3	x	x	X
ejpam-816	219	4	,	,	PUNCT
ejpam-816	219	5	br(k	br(k	NOUN
ejpam-816	219	6	)	)	PUNCT
ejpam-816	219	7	:	:	PUNCT
ejpam-816	219	8	=	=	SYM
ejpam-816	219	9	1−	1−	NUM
ejpam-816	219	10	e(νr	e(νr	X
ejpam-816	219	11	+	+	ADP
ejpam-816	219	12	mr	mr	PROPN
ejpam-816	219	13	k	k	PROPN
ejpam-816	219	14	)	)	PUNCT
ejpam-816	219	15	.	.	PUNCT
ejpam-816	220	1	(	(	PUNCT
ejpam-816	220	2	30	30	NUM
ejpam-816	220	3	)	)	PUNCT
ejpam-816	220	4	then	then	ADV
ejpam-816	220	5	we	we	PRON
ejpam-816	220	6	find	find	VERB
ejpam-816	220	7	µr	µr	ADP
ejpam-816	220	8	∫	∫	PROPN
ejpam-816	220	9	∞	∞	PROPN
ejpam-816	221	1	−∞	−∞	PROPN
ejpam-816	221	2	xνr+mr	xνr+mr	PUNCT
ejpam-816	221	3	k−1	k−1	PROPN
ejpam-816	221	4	r	r	NOUN
ejpam-816	221	5	exp{−xµr	exp{−xµr	PROPN
ejpam-816	221	6	r	r	NOUN
ejpam-816	221	7	}	}	PUNCT
ejpam-816	221	8	d	d	NOUN
ejpam-816	221	9	xr	xr	NOUN
ejpam-816	221	10	=	=	PUNCT
ejpam-816	221	11	µr	µr	ADP
ejpam-816	221	12	br(k	br(k	NOUN
ejpam-816	221	13	)	)	PUNCT
ejpam-816	221	14	∫	∫	PROPN
ejpam-816	222	1	∞	∞	NUM
ejpam-816	222	2	0	0	NUM
ejpam-816	223	1	xνr+mr	xνr+mr	PUNCT
ejpam-816	223	2	k−1	k−1	PROPN
ejpam-816	223	3	r	r	NOUN
ejpam-816	223	4	exp{−xµr	exp{−xµr	PROPN
ejpam-816	223	5	r	r	NOUN
ejpam-816	223	6	}	}	PUNCT
ejpam-816	223	7	d	d	NOUN
ejpam-816	223	8	xr	xr	PROPN
ejpam-816	223	9	=	=	SYM
ejpam-816	223	10	br(k)γ	br(k)γ	PROPN
ejpam-816	223	11	�	�	PROPN
ejpam-816	223	12	νr	νr	ADP
ejpam-816	224	1	+	+	NOUN
ejpam-816	224	2	mr	mr	PROPN
ejpam-816	224	3	k	k	PROPN
ejpam-816	224	4	µr	µr	ADP
ejpam-816	224	5	�	�	PROPN
ejpam-816	224	6	and	and	CCONJ
ejpam-816	224	7	hence	hence	ADV
ejpam-816	224	8	that	that	PRON
ejpam-816	224	9	jn(z	jn(z	VERB
ejpam-816	224	10	)	)	PUNCT
ejpam-816	225	1	=	=	SYM
ejpam-816	226	1	∞	∞	NUM
ejpam-816	226	2	∑	∑	PUNCT
ejpam-816	226	3	k=0	k=0	PROPN
ejpam-816	226	4	zk	zk	PROPN
ejpam-816	226	5	k	k	PROPN
ejpam-816	226	6	!	!	PUNCT
ejpam-816	227	1	n	n	CCONJ
ejpam-816	227	2	∏	∏	PROPN
ejpam-816	227	3	r=1	r=1	NOUN
ejpam-816	227	4	�	�	PROPN
ejpam-816	227	5	br(k)γ	br(k)γ	SYM
ejpam-816	227	6	�	�	PROPN
ejpam-816	227	7	νr	νr	ADP
ejpam-816	228	1	+	+	NOUN
ejpam-816	228	2	mr	mr	PROPN
ejpam-816	228	3	k	k	PROPN
ejpam-816	228	4	µr	µr	ADP
ejpam-816	228	5	�	�	PROPN
ejpam-816	228	6	�	�	PROPN
ejpam-816	228	7	.	.	PUNCT
ejpam-816	229	1	(	(	PUNCT
ejpam-816	229	2	31	31	NUM
ejpam-816	229	3	)	)	PUNCT
ejpam-816	229	4	4.1	4.1	NUM
ejpam-816	229	5	.	.	PUNCT
ejpam-816	230	1	the	the	DET
ejpam-816	230	2	representation	representation	NOUN
ejpam-816	230	3	of	of	ADP
ejpam-816	230	4	jn(z	jn(z	NOUN
ejpam-816	230	5	)	)	PUNCT
ejpam-816	230	6	in	in	ADP
ejpam-816	230	7	terms	term	NOUN
ejpam-816	230	8	of	of	ADP
ejpam-816	230	9	nψ0(z	nψ0(z	NOUN
ejpam-816	230	10	)	)	PUNCT
ejpam-816	230	11	functions	function	NOUN
ejpam-816	230	12	expansion	expansion	NOUN
ejpam-816	230	13	of	of	ADP
ejpam-816	230	14	the	the	DET
ejpam-816	230	15	product	product	NOUN
ejpam-816	230	16	of	of	ADP
ejpam-816	230	17	exponential	exponential	ADJ
ejpam-816	230	18	factors	factor	NOUN
ejpam-816	230	19	∏n	∏n	PART
ejpam-816	230	20	r=1	r=1	NOUN
ejpam-816	230	21	br(k	br(k	NOUN
ejpam-816	230	22	)	)	PUNCT
ejpam-816	230	23	in	in	ADP
ejpam-816	230	24	(	(	PUNCT
ejpam-816	230	25	31	31	NUM
ejpam-816	230	26	)	)	PUNCT
ejpam-816	230	27	can	can	AUX
ejpam-816	230	28	be	be	AUX
ejpam-816	230	29	achieved	achieve	VERB
ejpam-816	230	30	by	by	ADP
ejpam-816	230	31	making	make	VERB
ejpam-816	230	32	use	use	NOUN
ejpam-816	230	33	of	of	ADP
ejpam-816	230	34	the	the	DET
ejpam-816	230	35	standard	standard	ADJ
ejpam-816	230	36	expansion	expansion	NOUN
ejpam-816	230	37	(	(	PUNCT
ejpam-816	230	38	1−	1−	NUM
ejpam-816	230	39	z1)(1−	z1)(1−	PROPN
ejpam-816	230	40	z2	z2	PROPN
ejpam-816	230	41	)	)	PUNCT
ejpam-816	230	42	.	.	PUNCT
ejpam-816	230	43	.	.	PUNCT
ejpam-816	231	1	.	.	PUNCT
ejpam-816	232	1	(	(	PUNCT
ejpam-816	232	2	1−	1−	NUM
ejpam-816	232	3	zn	zn	NUM
ejpam-816	232	4	)	)	PUNCT
ejpam-816	232	5	=	=	SYM
ejpam-816	233	1	1−	1−	NUM
ejpam-816	233	2	n	n	CCONJ
ejpam-816	233	3	∑	∑	PUNCT
ejpam-816	233	4	i=1	i=1	PROPN
ejpam-816	233	5	zi	zi	NOUN
ejpam-816	233	6	+	+	CCONJ
ejpam-816	233	7	n−1	n−1	PROPN
ejpam-816	233	8	∑	∑	PUNCT
ejpam-816	233	9	i=1	i=1	PROPN
ejpam-816	233	10	n	n	PROPN
ejpam-816	233	11	∑	∑	PROPN
ejpam-816	233	12	j	j	X
ejpam-816	233	13	=	=	PROPN
ejpam-816	233	14	i+1	i+1	NOUN
ejpam-816	233	15	ziz	ziz	PROPN
ejpam-816	233	16	j	j	PROPN
ejpam-816	233	17	r.	r.	PROPN
ejpam-816	233	18	paris	paris	PROPN
ejpam-816	233	19	/	/	SYM
ejpam-816	233	20	eur	eur	PROPN
ejpam-816	233	21	.	.	PUNCT
ejpam-816	234	1	j.	j.	PROPN
ejpam-816	234	2	pure	pure	PROPN
ejpam-816	234	3	appl	appl	PROPN
ejpam-816	234	4	.	.	PROPN
ejpam-816	234	5	math	math	PROPN
ejpam-816	234	6	,	,	PUNCT
ejpam-816	234	7	3	3	NUM
ejpam-816	234	8	(	(	PUNCT
ejpam-816	234	9	2010	2010	NUM
ejpam-816	234	10	)	)	PUNCT
ejpam-816	234	11	,	,	PUNCT
ejpam-816	234	12	1006	1006	NUM
ejpam-816	234	13	-	-	SYM
ejpam-816	234	14	1031	1031	NUM
ejpam-816	234	15	1015	1015	NUM
ejpam-816	234	16	−	−	PROPN
ejpam-816	235	1	n−2	n−2	PROPN
ejpam-816	235	2	∑	∑	PROPN
ejpam-816	235	3	i=1	i=1	PROPN
ejpam-816	235	4	n−1	n−1	PROPN
ejpam-816	235	5	∑	∑	PUNCT
ejpam-816	235	6	j	j	X
ejpam-816	235	7	=	=	PROPN
ejpam-816	235	8	i+1	i+1	NOUN
ejpam-816	235	9	n	n	ADV
ejpam-816	235	10	∑	∑	PUNCT
ejpam-816	235	11	k=	k=	X
ejpam-816	236	1	j+1	j+1	PROPN
ejpam-816	236	2	ziz	ziz	PROPN
ejpam-816	236	3	jzk	jzk	NOUN
ejpam-816	237	1	+	+	X
ejpam-816	237	2	.	.	PUNCT
ejpam-816	237	3	.	.	PUNCT
ejpam-816	238	1	.+	.+	NOUN
ejpam-816	238	2	(	(	PUNCT
ejpam-816	238	3	−)nz1z2	−)nz1z2	PROPN
ejpam-816	238	4	.	.	PUNCT
ejpam-816	238	5	.	.	PUNCT
ejpam-816	238	6	.	.	PUNCT
ejpam-816	239	1	zn	zn	X
ejpam-816	239	2	.	.	PUNCT
ejpam-816	239	3	substitution	substitution	NOUN
ejpam-816	239	4	of	of	ADP
ejpam-816	239	5	this	this	DET
ejpam-816	239	6	expansion	expansion	NOUN
ejpam-816	239	7	into	into	ADP
ejpam-816	239	8	(	(	PUNCT
ejpam-816	239	9	31	31	NUM
ejpam-816	239	10	)	)	PUNCT
ejpam-816	239	11	with	with	ADP
ejpam-816	239	12	zr	zr	PROPN
ejpam-816	239	13	=	=	SYM
ejpam-816	239	14	e(νr	e(νr	X
ejpam-816	239	15	+	+	PROPN
ejpam-816	239	16	mr	mr	PROPN
ejpam-816	239	17	k	k	PROPN
ejpam-816	239	18	)	)	PUNCT
ejpam-816	239	19	then	then	ADV
ejpam-816	239	20	shows	show	VERB
ejpam-816	239	21	that	that	SCONJ
ejpam-816	239	22	jn(z	jn(z	VERB
ejpam-816	239	23	)	)	PUNCT
ejpam-816	239	24	may	may	AUX
ejpam-816	239	25	be	be	AUX
ejpam-816	239	26	expressed	express	VERB
ejpam-816	239	27	as	as	ADP
ejpam-816	239	28	a	a	DET
ejpam-816	239	29	linear	linear	ADJ
ejpam-816	239	30	combination	combination	NOUN
ejpam-816	239	31	of	of	ADP
ejpam-816	239	32	nψ0(z	nψ0(z	PROPN
ejpam-816	239	33	)	)	PUNCT
ejpam-816	239	34	with	with	ADP
ejpam-816	239	35	rotated	rotate	VERB
ejpam-816	239	36	argument	argument	NOUN
ejpam-816	239	37	in	in	ADP
ejpam-816	239	38	the	the	DET
ejpam-816	239	39	form	form	NOUN
ejpam-816	239	40	jn(z	jn(z	VERB
ejpam-816	239	41	)	)	PUNCT
ejpam-816	239	42	=	=	SYM
ejpam-816	239	43	nψ0(z)−	nψ0(z)−	VERB
ejpam-816	239	44	n	n	CCONJ
ejpam-816	239	45	∑	∑	PROPN
ejpam-816	239	46	i=1	i=1	PROPN
ejpam-816	239	47	e(νi	e(νi	PROPN
ejpam-816	239	48	)	)	PUNCT
ejpam-816	239	49	nψ0(ze(mi	nψ0(ze(mi	NOUN
ejpam-816	239	50	)	)	PUNCT
ejpam-816	239	51	)	)	PUNCT
ejpam-816	240	1	+	+	CCONJ
ejpam-816	241	1	n−1	n−1	PROPN
ejpam-816	241	2	∑	∑	PUNCT
ejpam-816	241	3	i=1	i=1	PROPN
ejpam-816	241	4	n	n	PROPN
ejpam-816	241	5	∑	∑	PROPN
ejpam-816	241	6	j	j	X
ejpam-816	241	7	=	=	PROPN
ejpam-816	241	8	i+1	i+1	ADP
ejpam-816	241	9	e(νi	e(νi	PROPN
ejpam-816	241	10	+	+	CCONJ
ejpam-816	241	11	ν	ν	PROPN
ejpam-816	241	12	j	j	NOUN
ejpam-816	241	13	)	)	PUNCT
ejpam-816	241	14	nψ0(ze(mi	nψ0(ze(mi	VERB
ejpam-816	242	1	+	+	PROPN
ejpam-816	242	2	m	m	PROPN
ejpam-816	242	3	j	j	NOUN
ejpam-816	242	4	)	)	PUNCT
ejpam-816	242	5	)	)	PUNCT
ejpam-816	243	1	−	−	PROPN
ejpam-816	244	1	n−2	n−2	PROPN
ejpam-816	244	2	∑	∑	PROPN
ejpam-816	244	3	i=1	i=1	PROPN
ejpam-816	244	4	n−1	n−1	PROPN
ejpam-816	244	5	∑	∑	PUNCT
ejpam-816	244	6	j	j	X
ejpam-816	244	7	=	=	PROPN
ejpam-816	244	8	i+1	i+1	NOUN
ejpam-816	244	9	n	n	ADV
ejpam-816	244	10	∑	∑	PUNCT
ejpam-816	244	11	k=	k=	NOUN
ejpam-816	245	1	j+1	j+1	PROPN
ejpam-816	245	2	e(νi	e(νi	PROPN
ejpam-816	245	3	+	+	CCONJ
ejpam-816	245	4	ν	ν	X
ejpam-816	245	5	j	j	NOUN
ejpam-816	245	6	+	+	CCONJ
ejpam-816	245	7	νk	νk	NOUN
ejpam-816	245	8	)	)	PUNCT
ejpam-816	245	9	nψ0(ze(mi	nψ0(ze(mi	NOUN
ejpam-816	246	1	+	+	NOUN
ejpam-816	246	2	m	m	NOUN
ejpam-816	246	3	j	j	NOUN
ejpam-816	247	1	+	+	NOUN
ejpam-816	248	1	mk))+	mk))+	PROPN
ejpam-816	248	2	.	.	PUNCT
ejpam-816	248	3	.	.	PUNCT
ejpam-816	249	1	.	.	PUNCT
ejpam-816	250	1	+	+	CCONJ
ejpam-816	250	2	(	(	PUNCT
ejpam-816	250	3	−)ne(n	−)ne(n	PROPN
ejpam-816	250	4	)	)	PUNCT
ejpam-816	250	5	nψ0(ze(m	nψ0(ze(m	NUM
ejpam-816	250	6	)	)	PUNCT
ejpam-816	250	7	)	)	PUNCT
ejpam-816	250	8	,	,	PUNCT
ejpam-816	250	9	(	(	PUNCT
ejpam-816	250	10	32	32	NUM
ejpam-816	250	11	)	)	PUNCT
ejpam-816	250	12	where	where	SCONJ
ejpam-816	250	13	we	we	PRON
ejpam-816	250	14	have	have	AUX
ejpam-816	250	15	defined	define	VERB
ejpam-816	250	16	n	n	NOUN
ejpam-816	250	17	:	:	PUNCT
ejpam-816	250	18	=	=	SYM
ejpam-816	250	19	ν1	ν1	NOUN
ejpam-816	250	20	+	+	X
ejpam-816	250	21	.	.	PUNCT
ejpam-816	250	22	.	.	PUNCT
ejpam-816	251	1	.+	.+	NOUN
ejpam-816	251	2	νn	νn	VERB
ejpam-816	251	3	,	,	PUNCT
ejpam-816	251	4	m	m	VERB
ejpam-816	251	5	:	:	PUNCT
ejpam-816	251	6	=	=	SYM
ejpam-816	251	7	m1	m1	PROPN
ejpam-816	251	8	+	+	CCONJ
ejpam-816	251	9	.	.	PUNCT
ejpam-816	251	10	.	.	PUNCT
ejpam-816	252	1	.+mn	.+mn	PROPN
ejpam-816	252	2	.	.	PUNCT
ejpam-816	253	1	(	(	PUNCT
ejpam-816	253	2	33	33	NUM
ejpam-816	253	3	)	)	PUNCT
ejpam-816	253	4	the	the	DET
ejpam-816	253	5	parameters	parameter	NOUN
ejpam-816	253	6	appearing	appear	VERB
ejpam-816	253	7	in	in	ADP
ejpam-816	253	8	each	each	DET
ejpam-816	253	9	nψ0	nψ0	NOUN
ejpam-816	253	10	function	function	NOUN
ejpam-816	253	11	are	be	AUX
ejpam-816	253	12	those	those	PRON
ejpam-816	253	13	given	give	VERB
ejpam-816	253	14	in	in	ADP
ejpam-816	253	15	(	(	PUNCT
ejpam-816	253	16	22	22	NUM
ejpam-816	253	17	)	)	PUNCT
ejpam-816	253	18	.	.	PUNCT
ejpam-816	254	1	the	the	DET
ejpam-816	254	2	asymptotic	asymptotic	ADJ
ejpam-816	254	3	expansion	expansion	NOUN
ejpam-816	254	4	(	(	PUNCT
ejpam-816	254	5	19	19	NUM
ejpam-816	254	6	)	)	PUNCT
ejpam-816	254	7	,	,	PUNCT
ejpam-816	254	8	or	or	CCONJ
ejpam-816	254	9	equivalently	equivalently	ADV
ejpam-816	254	10	(	(	PUNCT
ejpam-816	254	11	23	23	NUM
ejpam-816	254	12	)	)	PUNCT
ejpam-816	254	13	,	,	PUNCT
ejpam-816	254	14	can	can	AUX
ejpam-816	254	15	then	then	ADV
ejpam-816	254	16	be	be	AUX
ejpam-816	254	17	employed	employ	VERB
ejpam-816	254	18	to	to	PART
ejpam-816	254	19	deal	deal	VERB
ejpam-816	254	20	with	with	ADP
ejpam-816	254	21	each	each	DET
ejpam-816	254	22	nψ0(zeπiω	nψ0(zeπiω	NOUN
ejpam-816	254	23	)	)	PUNCT
ejpam-816	254	24	with	with	ADP
ejpam-816	254	25	argument	argument	NOUN
ejpam-816	254	26	rotated	rotate	VERB
ejpam-816	254	27	by	by	ADP
ejpam-816	254	28	ω	ω	PROPN
ejpam-816	254	29	,	,	PUNCT
ejpam-816	254	30	it	it	PRON
ejpam-816	254	31	being	be	AUX
ejpam-816	254	32	remembered	remember	VERB
ejpam-816	254	33	that	that	SCONJ
ejpam-816	254	34	nψ0(z	nψ0(z	PROPN
ejpam-816	254	35	)	)	PUNCT
ejpam-816	254	36	is	be	AUX
ejpam-816	254	37	an	an	DET
ejpam-816	254	38	integral	integral	ADJ
ejpam-816	254	39	function	function	NOUN
ejpam-816	254	40	of	of	ADP
ejpam-816	254	41	z	z	PROPN
ejpam-816	254	42	with	with	ADP
ejpam-816	254	43	arg	arg	NOUN
ejpam-816	255	1	z	z	NOUN
ejpam-816	255	2	evaluated	evaluate	VERB
ejpam-816	255	3	modulo	modulo	PROPN
ejpam-816	255	4	2π	2π	NOUN
ejpam-816	255	5	.	.	PUNCT
ejpam-816	256	1	rather	rather	ADV
ejpam-816	256	2	than	than	SCONJ
ejpam-816	256	3	attempt	attempt	VERB
ejpam-816	256	4	to	to	PART
ejpam-816	256	5	present	present	VERB
ejpam-816	256	6	a	a	DET
ejpam-816	256	7	complicated	complicated	ADJ
ejpam-816	256	8	general	general	ADJ
ejpam-816	256	9	result	result	NOUN
ejpam-816	256	10	,	,	PUNCT
ejpam-816	256	11	we	we	PRON
ejpam-816	256	12	indicate	indicate	VERB
ejpam-816	256	13	how	how	SCONJ
ejpam-816	256	14	to	to	PART
ejpam-816	256	15	proceed	proceed	VERB
ejpam-816	256	16	with	with	ADP
ejpam-816	256	17	the	the	DET
ejpam-816	256	18	asymptotic	asymptotic	ADJ
ejpam-816	256	19	expansion	expansion	NOUN
ejpam-816	256	20	of	of	ADP
ejpam-816	256	21	jn(z	jn(z	NOUN
ejpam-816	256	22	)	)	PUNCT
ejpam-816	256	23	as	as	ADP
ejpam-816	256	24	|z|	|z|	NOUN
ejpam-816	256	25	→∞	→∞	X
ejpam-816	256	26	in	in	ADP
ejpam-816	256	27	specific	specific	ADJ
ejpam-816	256	28	cases	case	NOUN
ejpam-816	256	29	in	in	ADP
ejpam-816	256	30	section	section	NOUN
ejpam-816	256	31	5	5	NUM
ejpam-816	256	32	.	.	PUNCT
ejpam-816	256	33	4.2	4.2	NUM
ejpam-816	256	34	.	.	PUNCT
ejpam-816	257	1	the	the	DET
ejpam-816	257	2	algebraic	algebraic	ADJ
ejpam-816	257	3	contribution	contribution	NOUN
ejpam-816	257	4	to	to	ADP
ejpam-816	257	5	the	the	DET
ejpam-816	257	6	expansion	expansion	NOUN
ejpam-816	257	7	of	of	ADP
ejpam-816	257	8	jn(z	jn(z	NOUN
ejpam-816	257	9	)	)	PUNCT
ejpam-816	257	10	we	we	PRON
ejpam-816	257	11	consider	consider	VERB
ejpam-816	257	12	the	the	DET
ejpam-816	257	13	contribution	contribution	NOUN
ejpam-816	257	14	to	to	ADP
ejpam-816	257	15	the	the	DET
ejpam-816	257	16	asymptotic	asymptotic	ADJ
ejpam-816	257	17	expansion	expansion	NOUN
ejpam-816	257	18	of	of	ADP
ejpam-816	257	19	the	the	DET
ejpam-816	257	20	integral	integral	ADJ
ejpam-816	257	21	jn(z	jn(z	NOUN
ejpam-816	257	22	)	)	PUNCT
ejpam-816	257	23	as	as	ADP
ejpam-816	257	24	|z|	|z|	NOUN
ejpam-816	257	25	→	→	SYM
ejpam-816	257	26	∞	∞	PROPN
ejpam-816	257	27	that	that	PRON
ejpam-816	257	28	results	result	VERB
ejpam-816	257	29	from	from	ADP
ejpam-816	257	30	the	the	DET
ejpam-816	257	31	algebraic	algebraic	ADJ
ejpam-816	257	32	expansions	expansion	NOUN
ejpam-816	257	33	associated	associate	VERB
ejpam-816	257	34	with	with	ADP
ejpam-816	257	35	each	each	DET
ejpam-816	257	36	nψ0	nψ0	NOUN
ejpam-816	257	37	function	function	NOUN
ejpam-816	257	38	of	of	ADP
ejpam-816	257	39	rotated	rotate	VERB
ejpam-816	257	40	argument	argument	NOUN
ejpam-816	257	41	in	in	ADP
ejpam-816	257	42	(	(	PUNCT
ejpam-816	257	43	32	32	NUM
ejpam-816	257	44	)	)	PUNCT
ejpam-816	257	45	.	.	PUNCT
ejpam-816	258	1	it	it	PRON
ejpam-816	258	2	will	will	AUX
ejpam-816	258	3	be	be	AUX
ejpam-816	258	4	shown	show	VERB
ejpam-816	258	5	that	that	SCONJ
ejpam-816	258	6	this	this	DET
ejpam-816	258	7	combination	combination	NOUN
ejpam-816	258	8	of	of	ADP
ejpam-816	258	9	algebraic	algebraic	ADJ
ejpam-816	258	10	expansions	expansion	NOUN
ejpam-816	258	11	cancels	cancel	VERB
ejpam-816	258	12	in	in	ADP
ejpam-816	258	13	the	the	DET
ejpam-816	258	14	sector	sector	NOUN
ejpam-816	258	15	ε≤	ε≤	NOUN
ejpam-816	258	16	arg	arg	NOUN
ejpam-816	258	17	z	z	NOUN
ejpam-816	258	18	≤	≤	NUM
ejpam-816	258	19	(	(	PUNCT
ejpam-816	258	20	2−m)π−	2−m)π−	NUM
ejpam-816	258	21	ε	ε	PROPN
ejpam-816	258	22	,	,	PUNCT
ejpam-816	258	23	(	(	PUNCT
ejpam-816	258	24	34	34	NUM
ejpam-816	258	25	)	)	PUNCT
ejpam-816	258	26	where	where	SCONJ
ejpam-816	258	27	m	m	NOUN
ejpam-816	258	28	is	be	AUX
ejpam-816	258	29	defined	define	VERB
ejpam-816	258	30	in	in	ADP
ejpam-816	258	31	(	(	PUNCT
ejpam-816	258	32	33	33	NUM
ejpam-816	258	33	)	)	PUNCT
ejpam-816	258	34	,	,	PUNCT
ejpam-816	258	35	and	and	CCONJ
ejpam-816	258	36	that	that	SCONJ
ejpam-816	258	37	consequently	consequently	ADV
ejpam-816	258	38	the	the	DET
ejpam-816	258	39	expansion	expansion	NOUN
ejpam-816	258	40	of	of	ADP
ejpam-816	258	41	jn(z	jn(z	NOUN
ejpam-816	258	42	)	)	PUNCT
ejpam-816	258	43	in	in	ADP
ejpam-816	258	44	this	this	DET
ejpam-816	258	45	sector	sector	NOUN
ejpam-816	258	46	is	be	AUX
ejpam-816	258	47	purely	purely	ADV
ejpam-816	258	48	exponential	exponential	ADJ
ejpam-816	258	49	in	in	ADP
ejpam-816	258	50	character	character	NOUN
ejpam-816	258	51	.	.	PUNCT
ejpam-816	259	1	we	we	PRON
ejpam-816	259	2	shall	shall	AUX
ejpam-816	259	3	suppose	suppose	VERB
ejpam-816	259	4	in	in	ADP
ejpam-816	259	5	this	this	DET
ejpam-816	259	6	section	section	NOUN
ejpam-816	259	7	that	that	PRON
ejpam-816	259	8	all	all	DET
ejpam-816	259	9	the	the	DET
ejpam-816	259	10	poles	pole	NOUN
ejpam-816	259	11	sk	sk	VERB
ejpam-816	259	12	,	,	PUNCT
ejpam-816	259	13	j	j	PROPN
ejpam-816	259	14	in	in	ADP
ejpam-816	259	15	(	(	PUNCT
ejpam-816	259	16	12	12	NUM
ejpam-816	259	17	)	)	PUNCT
ejpam-816	259	18	are	be	AUX
ejpam-816	259	19	simple	simple	ADJ
ejpam-816	259	20	;	;	PUNCT
ejpam-816	259	21	a	a	DET
ejpam-816	259	22	case	case	NOUN
ejpam-816	259	23	when	when	SCONJ
ejpam-816	259	24	there	there	PRON
ejpam-816	259	25	are	be	VERB
ejpam-816	259	26	multiple	multiple	ADJ
ejpam-816	259	27	poles	pole	NOUN
ejpam-816	259	28	present	present	ADJ
ejpam-816	259	29	is	be	AUX
ejpam-816	259	30	discussed	discuss	VERB
ejpam-816	259	31	in	in	ADP
ejpam-816	259	32	appendix	appendix	ADJ
ejpam-816	259	33	c.	c.	NOUN
ejpam-816	259	34	then	then	ADV
ejpam-816	259	35	,	,	PUNCT
ejpam-816	259	36	the	the	DET
ejpam-816	259	37	algebraic	algebraic	ADJ
ejpam-816	259	38	expansion	expansion	NOUN
ejpam-816	259	39	of	of	ADP
ejpam-816	259	40	nψ0(z	nψ0(z	PROPN
ejpam-816	259	41	)	)	PUNCT
ejpam-816	259	42	associated	associate	VERB
ejpam-816	259	43	with	with	ADP
ejpam-816	259	44	the	the	DET
ejpam-816	259	45	parameters	parameter	NOUN
ejpam-816	259	46	in	in	ADP
ejpam-816	259	47	(	(	PUNCT
ejpam-816	259	48	22	22	NUM
ejpam-816	259	49	)	)	PUNCT
ejpam-816	259	50	is	be	AUX
ejpam-816	259	51	,	,	PUNCT
ejpam-816	259	52	from	from	ADP
ejpam-816	259	53	(	(	PUNCT
ejpam-816	259	54	13	13	NUM
ejpam-816	259	55	)	)	PUNCT
ejpam-816	259	56	,	,	PUNCT
ejpam-816	259	57	(	(	PUNCT
ejpam-816	259	58	14	14	NUM
ejpam-816	259	59	)	)	PUNCT
ejpam-816	259	60	and	and	CCONJ
ejpam-816	259	61	(	(	PUNCT
ejpam-816	259	62	16	16	NUM
ejpam-816	259	63	)	)	PUNCT
ejpam-816	259	64	,	,	PUNCT
ejpam-816	259	65	given	give	VERB
ejpam-816	259	66	by	by	ADP
ejpam-816	259	67	hn,0(ze−πi	hn,0(ze−πi	ADJ
ejpam-816	259	68	)	)	PUNCT
ejpam-816	259	69	=	=	SYM
ejpam-816	260	1	n	n	CCONJ
ejpam-816	260	2	∑	∑	PROPN
ejpam-816	260	3	j=1	j=1	PROPN
ejpam-816	260	4	µ	µ	X
ejpam-816	260	5	j	j	PROPN
ejpam-816	260	6	m	m	PROPN
ejpam-816	260	7	j	j	PROPN
ejpam-816	260	8	h	h	NOUN
ejpam-816	260	9	j(z	j(z	PROPN
ejpam-816	260	10	)	)	PUNCT
ejpam-816	260	11	valid	valid	ADJ
ejpam-816	260	12	as	as	ADP
ejpam-816	260	13	|z|	|z|	NOUN
ejpam-816	260	14	→∞	→∞	NOUN
ejpam-816	260	15	in	in	ADP
ejpam-816	260	16	the	the	DET
ejpam-816	260	17	sector	sector	NOUN
ejpam-816	260	18	ε	ε	PROPN
ejpam-816	260	19	≤	≤	PROPN
ejpam-816	260	20	arg	arg	NOUN
ejpam-816	260	21	z	z	NOUN
ejpam-816	260	22	≤	≤	NOUN
ejpam-816	260	23	2π−	2π−	NUM
ejpam-816	260	24	ε	ε	PROPN
ejpam-816	260	25	,	,	PUNCT
ejpam-816	260	26	where	where	SCONJ
ejpam-816	260	27	h	h	NOUN
ejpam-816	260	28	j(z	j(z	PROPN
ejpam-816	260	29	)	)	PUNCT
ejpam-816	260	30	:	:	PUNCT
ejpam-816	260	31	=	=	SYM
ejpam-816	260	32	(	(	PUNCT
ejpam-816	260	33	ze−πi)−ν	ze−πi)−ν	PROPN
ejpam-816	260	34	j	j	PROPN
ejpam-816	260	35	/	/	PROPN
ejpam-816	260	36	m	m	PROPN
ejpam-816	260	37	j	j	PROPN
ejpam-816	260	38	sn,0(ze−πi	sn,0(ze−πi	PROPN
ejpam-816	260	39	;	;	PUNCT
ejpam-816	260	40	j	j	PROPN
ejpam-816	260	41	)	)	PUNCT
ejpam-816	260	42	(	(	PUNCT
ejpam-816	260	43	1≤	1≤	NUM
ejpam-816	260	44	j	j	PROPN
ejpam-816	260	45	≤	≤	PROPN
ejpam-816	260	46	n	n	CCONJ
ejpam-816	260	47	)	)	PUNCT
ejpam-816	260	48	(	(	PUNCT
ejpam-816	260	49	35	35	NUM
ejpam-816	260	50	)	)	PUNCT
ejpam-816	260	51	r.	r.	PROPN
ejpam-816	260	52	paris	paris	PROPN
ejpam-816	260	53	/	/	SYM
ejpam-816	260	54	eur	eur	PROPN
ejpam-816	260	55	.	.	PUNCT
ejpam-816	261	1	j.	j.	PROPN
ejpam-816	261	2	pure	pure	PROPN
ejpam-816	261	3	appl	appl	PROPN
ejpam-816	261	4	.	.	PROPN
ejpam-816	261	5	math	math	PROPN
ejpam-816	261	6	,	,	PUNCT
ejpam-816	261	7	3	3	NUM
ejpam-816	261	8	(	(	PUNCT
ejpam-816	261	9	2010	2010	NUM
ejpam-816	261	10	)	)	PUNCT
ejpam-816	261	11	,	,	PUNCT
ejpam-816	261	12	1006	1006	NUM
ejpam-816	261	13	-	-	SYM
ejpam-816	261	14	1031	1031	NUM
ejpam-816	261	15	1016	1016	NUM
ejpam-816	261	16	and	and	CCONJ
ejpam-816	261	17	sn,0(ze−πi	sn,0(ze−πi	NOUN
ejpam-816	261	18	;	;	PUNCT
ejpam-816	261	19	j	j	X
ejpam-816	261	20	)	)	PUNCT
ejpam-816	262	1	=	=	SYM
ejpam-816	262	2	∞	∞	PROPN
ejpam-816	262	3	∑	∑	PUNCT
ejpam-816	262	4	k=0	k=0	PROPN
ejpam-816	262	5	(	(	PUNCT
ejpam-816	262	6	−)k	−)k	PROPN
ejpam-816	262	7	k	k	PROPN
ejpam-816	262	8	!	!	PUNCT
ejpam-816	263	1	γ	γ	PROPN
ejpam-816	263	2	�	�	PROPN
ejpam-816	263	3	µ	µ	PROPN
ejpam-816	263	4	jk+	jk+	PROPN
ejpam-816	263	5	ν	ν	X
ejpam-816	263	6	j	j	PROPN
ejpam-816	263	7	m	m	PROPN
ejpam-816	263	8	j	j	PROPN
ejpam-816	263	9	�	�	PROPN
ejpam-816	263	10	n	n	CCONJ
ejpam-816	263	11	∏	∏	PROPN
ejpam-816	263	12	r=1	r=1	NOUN
ejpam-816	263	13	′	′	NUM
ejpam-816	263	14	γ	γ	X
ejpam-816	263	15	�	�	PROPN
ejpam-816	263	16	νr	νr	ADP
ejpam-816	263	17	−mrsk	−mrsk	PROPN
ejpam-816	263	18	,	,	PUNCT
ejpam-816	263	19	j	j	PROPN
ejpam-816	263	20	µr	µr	ADP
ejpam-816	263	21	�	�	PROPN
ejpam-816	263	22	(	(	PUNCT
ejpam-816	263	23	ze−πi)−µ	ze−πi)−µ	PROPN
ejpam-816	263	24	j	j	PROPN
ejpam-816	263	25	k	k	PROPN
ejpam-816	263	26	/	/	PROPN
ejpam-816	263	27	m	m	PROPN
ejpam-816	263	28	j	j	PROPN
ejpam-816	263	29	.	.	PUNCT
ejpam-816	264	1	from	from	ADP
ejpam-816	264	2	the	the	DET
ejpam-816	264	3	representation	representation	NOUN
ejpam-816	264	4	of	of	ADP
ejpam-816	264	5	jn(z	jn(z	NOUN
ejpam-816	264	6	)	)	PUNCT
ejpam-816	264	7	in	in	ADP
ejpam-816	264	8	(	(	PUNCT
ejpam-816	264	9	32	32	NUM
ejpam-816	264	10	)	)	PUNCT
ejpam-816	264	11	as	as	ADP
ejpam-816	264	12	a	a	DET
ejpam-816	264	13	finite	finite	ADJ
ejpam-816	264	14	sum	sum	NOUN
ejpam-816	264	15	of	of	ADP
ejpam-816	264	16	nψ0	nψ0	NOUN
ejpam-816	264	17	functions	function	NOUN
ejpam-816	264	18	of	of	ADP
ejpam-816	264	19	rotated	rotate	VERB
ejpam-816	264	20	argument	argument	NOUN
ejpam-816	264	21	,	,	PUNCT
ejpam-816	264	22	the	the	DET
ejpam-816	264	23	contribution	contribution	NOUN
ejpam-816	264	24	from	from	ADP
ejpam-816	264	25	the	the	DET
ejpam-816	264	26	different	different	ADJ
ejpam-816	264	27	algebraic	algebraic	ADJ
ejpam-816	264	28	expansions	expansion	NOUN
ejpam-816	264	29	when	when	SCONJ
ejpam-816	264	30	arg	arg	NOUN
ejpam-816	264	31	z	z	PROPN
ejpam-816	264	32	lies	lie	VERB
ejpam-816	264	33	in	in	ADP
ejpam-816	264	34	the	the	DET
ejpam-816	264	35	common	common	ADJ
ejpam-816	264	36	sector	sector	NOUN
ejpam-816	264	37	(	(	PUNCT
ejpam-816	264	38	34	34	NUM
ejpam-816	264	39	)	)	PUNCT
ejpam-816	264	40	can	can	AUX
ejpam-816	264	41	then	then	ADV
ejpam-816	264	42	be	be	AUX
ejpam-816	264	43	written	write	VERB
ejpam-816	264	44	in	in	ADP
ejpam-816	264	45	the	the	DET
ejpam-816	264	46	form	form	NOUN
ejpam-816	264	47	n	n	CCONJ
ejpam-816	264	48	∑	∑	PROPN
ejpam-816	264	49	j=1	j=1	PROPN
ejpam-816	264	50	µ	µ	X
ejpam-816	264	51	j	j	X
ejpam-816	264	52	m	m	PROPN
ejpam-816	264	53	j	j	PROPN
ejpam-816	264	54	n	n	PROPN
ejpam-816	264	55	∑	∑	ADV
ejpam-816	264	56	k=0	k=0	X
ejpam-816	264	57	(	(	PUNCT
ejpam-816	264	58	−)ktk	−)ktk	NOUN
ejpam-816	264	59	,	,	PUNCT
ejpam-816	264	60	j(z	j(z	PROPN
ejpam-816	264	61	)	)	PUNCT
ejpam-816	264	62	,	,	PUNCT
ejpam-816	264	63	(	(	PUNCT
ejpam-816	264	64	36	36	NUM
ejpam-816	264	65	)	)	PUNCT
ejpam-816	264	66	where	where	SCONJ
ejpam-816	264	67	t0	t0	NOUN
ejpam-816	264	68	,	,	PUNCT
ejpam-816	264	69	j(z	j(z	PROPN
ejpam-816	264	70	)	)	PUNCT
ejpam-816	264	71	=	=	SYM
ejpam-816	265	1	h	h	NOUN
ejpam-816	265	2	j(z	j(z	PROPN
ejpam-816	265	3	)	)	PUNCT
ejpam-816	265	4	,	,	PUNCT
ejpam-816	265	5	t1	t1	NOUN
ejpam-816	265	6	,	,	PUNCT
ejpam-816	265	7	j(z	j(z	PROPN
ejpam-816	265	8	)	)	PUNCT
ejpam-816	265	9	=	=	SYM
ejpam-816	266	1	n	n	PROPN
ejpam-816	266	2	∑	∑	PROPN
ejpam-816	266	3	j1=1	j1=1	PROPN
ejpam-816	266	4	e(ν	e(ν	PROPN
ejpam-816	266	5	j1	j1	PROPN
ejpam-816	266	6	)	)	PUNCT
ejpam-816	267	1	h	h	NOUN
ejpam-816	267	2	j(ze(m	j(ze(m	PROPN
ejpam-816	267	3	j1	j1	PROPN
ejpam-816	267	4	)	)	PUNCT
ejpam-816	267	5	)	)	PUNCT
ejpam-816	267	6	,	,	PUNCT
ejpam-816	267	7	t2	t2	NOUN
ejpam-816	267	8	,	,	PUNCT
ejpam-816	267	9	j(z	j(z	PROPN
ejpam-816	267	10	)	)	PUNCT
ejpam-816	267	11	=	=	SYM
ejpam-816	268	1	n−1	n−1	PROPN
ejpam-816	268	2	∑	∑	PUNCT
ejpam-816	268	3	j1=1	j1=1	PROPN
ejpam-816	268	4	n	n	CCONJ
ejpam-816	268	5	∑	∑	PROPN
ejpam-816	268	6	j2=	j2=	PROPN
ejpam-816	268	7	j1	j1	PROPN
ejpam-816	268	8	+	+	PROPN
ejpam-816	268	9	1	1	PROPN
ejpam-816	268	10	e(ν	e(ν	PROPN
ejpam-816	268	11	j1	j1	PROPN
ejpam-816	268	12	+	+	CCONJ
ejpam-816	268	13	ν	ν	PROPN
ejpam-816	268	14	j2	j2	NOUN
ejpam-816	268	15	)	)	PUNCT
ejpam-816	268	16	h	h	NOUN
ejpam-816	269	1	j(ze(m	j(ze(m	PROPN
ejpam-816	269	2	j1	j1	PROPN
ejpam-816	269	3	+	+	PROPN
ejpam-816	269	4	m	m	PROPN
ejpam-816	269	5	j2	j2	NOUN
ejpam-816	269	6	)	)	PUNCT
ejpam-816	269	7	)	)	PUNCT
ejpam-816	269	8	,	,	PUNCT
ejpam-816	269	9	t3	t3	NOUN
ejpam-816	269	10	,	,	PUNCT
ejpam-816	269	11	j(z	j(z	PROPN
ejpam-816	269	12	)	)	PUNCT
ejpam-816	269	13	=	=	SYM
ejpam-816	270	1	n−2	n−2	PROPN
ejpam-816	270	2	∑	∑	PUNCT
ejpam-816	270	3	j1=1	j1=1	PROPN
ejpam-816	270	4	n−1	n−1	PROPN
ejpam-816	270	5	∑	∑	PROPN
ejpam-816	270	6	j2=	j2=	PROPN
ejpam-816	270	7	j1	j1	PROPN
ejpam-816	270	8	+	+	PROPN
ejpam-816	270	9	1	1	NUM
ejpam-816	270	10	n	n	PRON
ejpam-816	270	11	∑	∑	PROPN
ejpam-816	270	12	j3=	j3=	PROPN
ejpam-816	270	13	j2	j2	PROPN
ejpam-816	270	14	+	+	PROPN
ejpam-816	270	15	1	1	PROPN
ejpam-816	270	16	e(ν	e(ν	PROPN
ejpam-816	270	17	j1	j1	PROPN
ejpam-816	270	18	+	+	CCONJ
ejpam-816	270	19	ν	ν	X
ejpam-816	270	20	j2	j2	NOUN
ejpam-816	270	21	+	+	CCONJ
ejpam-816	270	22	ν	ν	PROPN
ejpam-816	270	23	j3	j3	PROPN
ejpam-816	270	24	)	)	PUNCT
ejpam-816	270	25	h	h	NOUN
ejpam-816	271	1	j(ze(m	j(ze(m	PROPN
ejpam-816	271	2	j1	j1	PROPN
ejpam-816	271	3	+	+	PROPN
ejpam-816	271	4	m	m	PROPN
ejpam-816	271	5	j2	j2	NOUN
ejpam-816	271	6	+	+	PROPN
ejpam-816	271	7	m	m	PROPN
ejpam-816	271	8	j3	j3	PROPN
ejpam-816	271	9	)	)	PUNCT
ejpam-816	271	10	)	)	PUNCT
ejpam-816	271	11	,	,	PUNCT
ejpam-816	271	12	.	.	PUNCT
ejpam-816	271	13	.	.	PUNCT
ejpam-816	272	1	.	.	PUNCT
ejpam-816	273	1	and	and	CCONJ
ejpam-816	273	2	in	in	ADP
ejpam-816	273	3	general	general	ADJ
ejpam-816	273	4	,	,	PUNCT
ejpam-816	273	5	for	for	ADP
ejpam-816	273	6	1≤	1≤	NUM
ejpam-816	273	7	k	k	PROPN
ejpam-816	273	8	≤	≤	PROPN
ejpam-816	273	9	n−	n−	PROPN
ejpam-816	273	10	1	1	NUM
ejpam-816	273	11	,	,	PUNCT
ejpam-816	273	12	tk	tk	PROPN
ejpam-816	273	13	,	,	PUNCT
ejpam-816	273	14	j(z	j(z	PROPN
ejpam-816	273	15	)	)	PUNCT
ejpam-816	273	16	=	=	PUNCT
ejpam-816	273	17	n−k+1	n−k+1	VERB
ejpam-816	273	18	∑	∑	ADP
ejpam-816	273	19	j1=1	j1=1	PROPN
ejpam-816	273	20	n−k+2	n−k+2	PROPN
ejpam-816	273	21	∑	∑	PROPN
ejpam-816	273	22	j2=	j2=	PROPN
ejpam-816	273	23	j1	j1	PROPN
ejpam-816	273	24	+	+	PROPN
ejpam-816	273	25	1	1	NUM
ejpam-816	273	26	.	.	PUNCT
ejpam-816	273	27	.	.	PUNCT
ejpam-816	273	28	.	.	PUNCT
ejpam-816	274	1	n	n	X
ejpam-816	274	2	∑	∑	PROPN
ejpam-816	274	3	jk=	jk=	PROPN
ejpam-816	274	4	jk−1	jk−1	PROPN
ejpam-816	274	5	+	+	PROPN
ejpam-816	274	6	1	1	PROPN
ejpam-816	274	7	e(ν	e(ν	PROPN
ejpam-816	274	8	j1	j1	PROPN
ejpam-816	274	9	+	+	X
ejpam-816	274	10	.	.	PUNCT
ejpam-816	274	11	.	.	PUNCT
ejpam-816	275	1	.+	.+	NOUN
ejpam-816	275	2	ν	ν	X
ejpam-816	275	3	jk	jk	PROPN
ejpam-816	275	4	)	)	PUNCT
ejpam-816	275	5	h	h	PROPN
ejpam-816	275	6	j(ze(m	j(ze(m	PROPN
ejpam-816	275	7	j1	j1	PROPN
ejpam-816	275	8	+	+	X
ejpam-816	275	9	.	.	PUNCT
ejpam-816	275	10	.	.	PUNCT
ejpam-816	276	1	.+m	.+m	PROPN
ejpam-816	276	2	jk	jk	PROPN
ejpam-816	276	3	)	)	PUNCT
ejpam-816	276	4	)	)	PUNCT
ejpam-816	277	1	with	with	ADP
ejpam-816	277	2	tn	tn	PROPN
ejpam-816	277	3	,	,	PUNCT
ejpam-816	277	4	j(z	j(z	PROPN
ejpam-816	277	5	)	)	PUNCT
ejpam-816	277	6	=	=	SYM
ejpam-816	277	7	e(n)h	e(n)h	NOUN
ejpam-816	277	8	j(ze(m	j(ze(m	PROPN
ejpam-816	277	9	)	)	PUNCT
ejpam-816	277	10	)	)	PUNCT
ejpam-816	277	11	.	.	PUNCT
ejpam-816	278	1	(	(	PUNCT
ejpam-816	278	2	37	37	NUM
ejpam-816	278	3	)	)	PUNCT
ejpam-816	278	4	it	it	PRON
ejpam-816	278	5	will	will	AUX
ejpam-816	278	6	be	be	AUX
ejpam-816	278	7	sufficient	sufficient	ADJ
ejpam-816	278	8	to	to	PART
ejpam-816	278	9	consider	consider	VERB
ejpam-816	278	10	just	just	ADV
ejpam-816	278	11	one	one	NUM
ejpam-816	278	12	value	value	NOUN
ejpam-816	278	13	of	of	ADP
ejpam-816	278	14	j	j	PROPN
ejpam-816	278	15	and	and	CCONJ
ejpam-816	278	16	accordingly	accordingly	ADV
ejpam-816	278	17	we	we	PRON
ejpam-816	278	18	choose	choose	VERB
ejpam-816	278	19	j	j	PROPN
ejpam-816	278	20	=	=	NOUN
ejpam-816	278	21	1	1	X
ejpam-816	278	22	.	.	PUNCT
ejpam-816	279	1	since	since	SCONJ
ejpam-816	279	2	the	the	DET
ejpam-816	279	3	µ	µ	X
ejpam-816	279	4	j	j	X
ejpam-816	279	5	(	(	PUNCT
ejpam-816	279	6	1≤	1≤	NUM
ejpam-816	279	7	j	j	PROPN
ejpam-816	279	8	≤	≤	PROPN
ejpam-816	279	9	n	n	CCONJ
ejpam-816	279	10	)	)	PUNCT
ejpam-816	279	11	are	be	AUX
ejpam-816	279	12	even	even	ADV
ejpam-816	279	13	integers	integer	NOUN
ejpam-816	279	14	it	it	PRON
ejpam-816	279	15	follows	follow	VERB
ejpam-816	279	16	from	from	ADP
ejpam-816	279	17	(	(	PUNCT
ejpam-816	279	18	35	35	NUM
ejpam-816	279	19	)	)	PUNCT
ejpam-816	279	20	that	that	PRON
ejpam-816	279	21	e(ν	e(ν	PROPN
ejpam-816	279	22	j)h	j)h	VERB
ejpam-816	280	1	j(ze(m	j(ze(m	PROPN
ejpam-816	280	2	j	j	NOUN
ejpam-816	280	3	)	)	PUNCT
ejpam-816	280	4	)	)	PUNCT
ejpam-816	281	1	=	=	SYM
ejpam-816	282	1	h	h	NOUN
ejpam-816	282	2	j(z	j(z	PROPN
ejpam-816	282	3	)	)	PUNCT
ejpam-816	282	4	.	.	PUNCT
ejpam-816	283	1	(	(	PUNCT
ejpam-816	283	2	38	38	NUM
ejpam-816	283	3	)	)	PUNCT
ejpam-816	283	4	we	we	PRON
ejpam-816	283	5	now	now	ADV
ejpam-816	283	6	separate	separate	VERB
ejpam-816	283	7	off	off	ADP
ejpam-816	283	8	the	the	DET
ejpam-816	283	9	term	term	NOUN
ejpam-816	283	10	corresponding	correspond	VERB
ejpam-816	283	11	to	to	ADP
ejpam-816	283	12	j1	j1	PROPN
ejpam-816	283	13	=	=	NOUN
ejpam-816	283	14	1	1	NUM
ejpam-816	283	15	in	in	ADP
ejpam-816	283	16	the	the	DET
ejpam-816	283	17	sums	sum	NOUN
ejpam-816	283	18	tk	tk	PROPN
ejpam-816	283	19	,	,	PUNCT
ejpam-816	283	20	j(z	j(z	PROPN
ejpam-816	283	21	)	)	PUNCT
ejpam-816	283	22	and	and	CCONJ
ejpam-816	283	23	make	make	VERB
ejpam-816	283	24	repeated	repeated	ADJ
ejpam-816	283	25	use	use	NOUN
ejpam-816	283	26	of	of	ADP
ejpam-816	283	27	(	(	PUNCT
ejpam-816	283	28	38	38	NUM
ejpam-816	283	29	)	)	PUNCT
ejpam-816	283	30	to	to	PART
ejpam-816	283	31	find	find	VERB
ejpam-816	283	32	t1,1(z	t1,1(z	NOUN
ejpam-816	283	33	)	)	PUNCT
ejpam-816	283	34	=	=	SYM
ejpam-816	284	1	h1(z	h1(z	NOUN
ejpam-816	284	2	)	)	PUNCT
ejpam-816	284	3	+	+	CCONJ
ejpam-816	284	4	n	n	CCONJ
ejpam-816	284	5	∑	∑	PROPN
ejpam-816	284	6	j1=2	j1=2	PROPN
ejpam-816	284	7	e(ν	e(ν	PROPN
ejpam-816	284	8	j1	j1	PROPN
ejpam-816	284	9	)	)	PUNCT
ejpam-816	284	10	h1(ze(m	h1(ze(m	PROPN
ejpam-816	284	11	j1	j1	PROPN
ejpam-816	284	12	)	)	PUNCT
ejpam-816	284	13	)	)	PUNCT
ejpam-816	284	14	,	,	PUNCT
ejpam-816	284	15	t2,1(z	t2,1(z	NOUN
ejpam-816	284	16	)	)	PUNCT
ejpam-816	284	17	=	=	SYM
ejpam-816	284	18	n	n	PROPN
ejpam-816	284	19	∑	∑	PROPN
ejpam-816	284	20	j2=2	j2=2	PROPN
ejpam-816	284	21	e(ν	e(ν	PROPN
ejpam-816	284	22	j2	j2	PROPN
ejpam-816	284	23	)	)	PUNCT
ejpam-816	284	24	h1(ze(m	h1(ze(m	PROPN
ejpam-816	284	25	j2	j2	PROPN
ejpam-816	284	26	)	)	PUNCT
ejpam-816	284	27	)	)	PUNCT
ejpam-816	285	1	+	+	CCONJ
ejpam-816	285	2	n−1	n−1	PROPN
ejpam-816	285	3	∑	∑	PROPN
ejpam-816	285	4	j1=2	j1=2	PROPN
ejpam-816	285	5	n	n	CCONJ
ejpam-816	285	6	∑	∑	PROPN
ejpam-816	285	7	j2=	j2=	PROPN
ejpam-816	285	8	j1	j1	PROPN
ejpam-816	285	9	+	+	PROPN
ejpam-816	285	10	1	1	PROPN
ejpam-816	285	11	e(ν	e(ν	PROPN
ejpam-816	285	12	j1	j1	PROPN
ejpam-816	285	13	+	+	CCONJ
ejpam-816	285	14	ν	ν	PROPN
ejpam-816	285	15	j2	j2	NOUN
ejpam-816	285	16	)	)	PUNCT
ejpam-816	285	17	h1(ze(m	h1(ze(m	PROPN
ejpam-816	285	18	j1	j1	PROPN
ejpam-816	286	1	+	+	PROPN
ejpam-816	286	2	m	m	PROPN
ejpam-816	286	3	j2	j2	NOUN
ejpam-816	286	4	)	)	PUNCT
ejpam-816	286	5	)	)	PUNCT
ejpam-816	286	6	,	,	PUNCT
ejpam-816	286	7	t3,1(z	t3,1(z	PROPN
ejpam-816	286	8	)	)	PUNCT
ejpam-816	286	9	=	=	SYM
ejpam-816	287	1	n−1	n−1	PROPN
ejpam-816	287	2	∑	∑	PROPN
ejpam-816	287	3	j2=2	j2=2	PROPN
ejpam-816	287	4	n	n	PROPN
ejpam-816	287	5	∑	∑	PROPN
ejpam-816	287	6	j3=	j3=	PROPN
ejpam-816	287	7	j2	j2	PROPN
ejpam-816	287	8	+	+	PROPN
ejpam-816	287	9	1	1	PROPN
ejpam-816	287	10	e(ν	e(ν	PROPN
ejpam-816	287	11	j2	j2	PROPN
ejpam-816	287	12	+	+	CCONJ
ejpam-816	287	13	ν	ν	PROPN
ejpam-816	287	14	j3	j3	PROPN
ejpam-816	287	15	)	)	PUNCT
ejpam-816	287	16	h1(ze(m	h1(ze(m	PROPN
ejpam-816	287	17	j2	j2	PROPN
ejpam-816	287	18	+	+	PROPN
ejpam-816	287	19	m	m	PROPN
ejpam-816	287	20	j3	j3	PROPN
ejpam-816	287	21	)	)	PUNCT
ejpam-816	287	22	)	)	PUNCT
ejpam-816	288	1	r.	r.	PROPN
ejpam-816	288	2	paris	paris	PROPN
ejpam-816	288	3	/	/	SYM
ejpam-816	288	4	eur	eur	PROPN
ejpam-816	288	5	.	.	PUNCT
ejpam-816	289	1	j.	j.	PROPN
ejpam-816	289	2	pure	pure	PROPN
ejpam-816	289	3	appl	appl	PROPN
ejpam-816	289	4	.	.	PROPN
ejpam-816	289	5	math	math	PROPN
ejpam-816	289	6	,	,	PUNCT
ejpam-816	289	7	3	3	NUM
ejpam-816	289	8	(	(	PUNCT
ejpam-816	289	9	2010	2010	NUM
ejpam-816	289	10	)	)	PUNCT
ejpam-816	289	11	,	,	PUNCT
ejpam-816	289	12	1006	1006	NUM
ejpam-816	289	13	-	-	SYM
ejpam-816	289	14	1031	1031	NUM
ejpam-816	289	15	1017	1017	NUM
ejpam-816	289	16	+	+	CCONJ
ejpam-816	289	17	n−2	n−2	PROPN
ejpam-816	289	18	∑	∑	PROPN
ejpam-816	289	19	j1=2	j1=2	PROPN
ejpam-816	289	20	n−1	n−1	PROPN
ejpam-816	289	21	∑	∑	PROPN
ejpam-816	289	22	j2=	j2=	PROPN
ejpam-816	289	23	j1	j1	PROPN
ejpam-816	289	24	+	+	PROPN
ejpam-816	289	25	1	1	NUM
ejpam-816	289	26	n	n	PRON
ejpam-816	289	27	∑	∑	PROPN
ejpam-816	289	28	j3=	j3=	PROPN
ejpam-816	289	29	j2	j2	PROPN
ejpam-816	289	30	+	+	PROPN
ejpam-816	289	31	1	1	PROPN
ejpam-816	289	32	e(ν	e(ν	PROPN
ejpam-816	289	33	j1	j1	PROPN
ejpam-816	289	34	+	+	CCONJ
ejpam-816	289	35	ν	ν	X
ejpam-816	289	36	j2	j2	NOUN
ejpam-816	289	37	+	+	CCONJ
ejpam-816	289	38	ν	ν	PROPN
ejpam-816	289	39	j3	j3	PROPN
ejpam-816	289	40	)	)	PUNCT
ejpam-816	290	1	h1(ze(m	h1(ze(m	PROPN
ejpam-816	290	2	j1	j1	PROPN
ejpam-816	291	1	+	+	PROPN
ejpam-816	291	2	m	m	PROPN
ejpam-816	291	3	j2	j2	NOUN
ejpam-816	291	4	+	+	PROPN
ejpam-816	291	5	m	m	PROPN
ejpam-816	291	6	j3	j3	PROPN
ejpam-816	291	7	)	)	PUNCT
ejpam-816	291	8	)	)	PUNCT
ejpam-816	292	1	and	and	CCONJ
ejpam-816	292	2	so	so	ADV
ejpam-816	292	3	on	on	ADV
ejpam-816	292	4	.	.	PUNCT
ejpam-816	293	1	an	an	DET
ejpam-816	293	2	obvious	obvious	ADJ
ejpam-816	293	3	relabelling	relabelling	NOUN
ejpam-816	293	4	of	of	ADP
ejpam-816	293	5	the	the	DET
ejpam-816	293	6	summation	summation	NOUN
ejpam-816	293	7	indices	index	NOUN
ejpam-816	293	8	then	then	ADV
ejpam-816	293	9	shows	show	VERB
ejpam-816	293	10	that	that	SCONJ
ejpam-816	293	11	in	in	ADP
ejpam-816	293	12	the	the	DET
ejpam-816	293	13	inner	inner	ADJ
ejpam-816	293	14	sum	sum	NOUN
ejpam-816	293	15	in	in	ADP
ejpam-816	293	16	(	(	PUNCT
ejpam-816	293	17	36	36	NUM
ejpam-816	293	18	)	)	PUNCT
ejpam-816	293	19	,	,	PUNCT
ejpam-816	293	20	taken	take	VERB
ejpam-816	293	21	over	over	ADP
ejpam-816	293	22	0≤	0≤	ADJ
ejpam-816	293	23	k	k	NOUN
ejpam-816	293	24	≤	≤	ADJ
ejpam-816	293	25	n−	n−	NOUN
ejpam-816	293	26	1	1	NUM
ejpam-816	293	27	,	,	PUNCT
ejpam-816	293	28	all	all	DET
ejpam-816	293	29	the	the	DET
ejpam-816	293	30	terms	term	NOUN
ejpam-816	293	31	cancel	cancel	VERB
ejpam-816	293	32	except	except	SCONJ
ejpam-816	293	33	the	the	DET
ejpam-816	293	34	last	last	ADJ
ejpam-816	293	35	to	to	PART
ejpam-816	293	36	yield	yield	VERB
ejpam-816	293	37	n−1	n−1	PROPN
ejpam-816	293	38	∑	∑	ADP
ejpam-816	293	39	k=0	k=0	X
ejpam-816	293	40	(	(	PUNCT
ejpam-816	293	41	−)ktk,1(z	−)ktk,1(z	NOUN
ejpam-816	293	42	)	)	PUNCT
ejpam-816	293	43	=	=	SYM
ejpam-816	293	44	(	(	PUNCT
ejpam-816	293	45	−	−	NOUN
ejpam-816	293	46	)	)	PUNCT
ejpam-816	293	47	n−1	n−1	PROPN
ejpam-816	293	48	2	2	NUM
ejpam-816	293	49	∑	∑	PROPN
ejpam-816	293	50	j1=2	j1=2	PROPN
ejpam-816	293	51	3	3	NUM
ejpam-816	293	52	∑	∑	PROPN
ejpam-816	293	53	j2=	j2=	PROPN
ejpam-816	293	54	j1	j1	PROPN
ejpam-816	293	55	+	+	PROPN
ejpam-816	293	56	1	1	NUM
ejpam-816	293	57	.	.	PUNCT
ejpam-816	293	58	.	.	PUNCT
ejpam-816	293	59	.	.	PUNCT
ejpam-816	294	1	n	n	X
ejpam-816	294	2	∑	∑	PROPN
ejpam-816	294	3	jn=	jn=	PROPN
ejpam-816	294	4	jn−1	jn−1	PROPN
ejpam-816	294	5	+	+	PROPN
ejpam-816	294	6	1	1	PROPN
ejpam-816	294	7	e(ν	e(ν	PROPN
ejpam-816	294	8	j1	j1	PROPN
ejpam-816	294	9	+	+	X
ejpam-816	294	10	.	.	PUNCT
ejpam-816	294	11	.	.	PUNCT
ejpam-816	295	1	.+	.+	NOUN
ejpam-816	296	1	ν	ν	PROPN
ejpam-816	296	2	jn	jn	PROPN
ejpam-816	296	3	)	)	PUNCT
ejpam-816	296	4	h1(ze(m	h1(ze(m	PROPN
ejpam-816	296	5	j1	j1	PROPN
ejpam-816	296	6	+	+	X
ejpam-816	296	7	.	.	PUNCT
ejpam-816	296	8	.	.	PUNCT
ejpam-816	297	1	.+m	.+m	PROPN
ejpam-816	297	2	jn	jn	PROPN
ejpam-816	297	3	)	)	PUNCT
ejpam-816	297	4	)	)	PUNCT
ejpam-816	298	1	=	=	PRON
ejpam-816	298	2	(	(	PUNCT
ejpam-816	298	3	−)n−1e(ν2	−)n−1e(ν2	NOUN
ejpam-816	298	4	+	+	X
ejpam-816	298	5	.	.	PUNCT
ejpam-816	298	6	.	.	PUNCT
ejpam-816	299	1	.+	.+	NOUN
ejpam-816	299	2	νn)h1(ze(m2	νn)h1(ze(m2	PROPN
ejpam-816	299	3	+	+	X
ejpam-816	299	4	.	.	PUNCT
ejpam-816	299	5	.	.	PUNCT
ejpam-816	300	1	.+mn	.+mn	X
ejpam-816	300	2	)	)	PUNCT
ejpam-816	300	3	)	)	PUNCT
ejpam-816	300	4	.	.	PUNCT
ejpam-816	301	1	=	=	PUNCT
ejpam-816	301	2	(	(	PUNCT
ejpam-816	301	3	−)n−1e(n)h1(ze(m	−)n−1e(n)h1(ze(m	PROPN
ejpam-816	301	4	)	)	PUNCT
ejpam-816	301	5	)	)	PUNCT
ejpam-816	302	1	=	=	PRON
ejpam-816	302	2	(	(	PUNCT
ejpam-816	302	3	−)n−1tn,1(z	−)n−1tn,1(z	NUM
ejpam-816	302	4	)	)	PUNCT
ejpam-816	302	5	upon	upon	SCONJ
ejpam-816	302	6	application	application	NOUN
ejpam-816	302	7	of	of	ADP
ejpam-816	302	8	(	(	PUNCT
ejpam-816	302	9	38	38	NUM
ejpam-816	302	10	)	)	PUNCT
ejpam-816	302	11	.	.	PUNCT
ejpam-816	303	1	it	it	PRON
ejpam-816	303	2	therefore	therefore	ADV
ejpam-816	303	3	follows	follow	VERB
ejpam-816	303	4	that	that	SCONJ
ejpam-816	303	5	∑n	∑n	PROPN
ejpam-816	303	6	k=1(−	k=1(−	PROPN
ejpam-816	303	7	)	)	PUNCT
ejpam-816	303	8	ktk,1(z	ktk,1(z	PROPN
ejpam-816	303	9	)	)	PUNCT
ejpam-816	303	10	≡	≡	PROPN
ejpam-816	303	11	0	0	NUM
ejpam-816	303	12	.	.	PUNCT
ejpam-816	304	1	an	an	DET
ejpam-816	304	2	analogous	analogous	ADJ
ejpam-816	304	3	procedure	procedure	NOUN
ejpam-816	304	4	applies	apply	VERB
ejpam-816	304	5	to	to	ADP
ejpam-816	304	6	other	other	ADJ
ejpam-816	304	7	values	value	NOUN
ejpam-816	304	8	of	of	ADP
ejpam-816	304	9	j	j	PROPN
ejpam-816	304	10	≤	≤	PROPN
ejpam-816	304	11	n	n	CCONJ
ejpam-816	305	1	and	and	CCONJ
ejpam-816	305	2	so	so	ADV
ejpam-816	305	3	we	we	PRON
ejpam-816	305	4	obtain	obtain	VERB
ejpam-816	305	5	in	in	ADP
ejpam-816	305	6	the	the	DET
ejpam-816	305	7	simple	simple	ADJ
ejpam-816	305	8	-	-	PUNCT
ejpam-816	305	9	pole	pole	NOUN
ejpam-816	305	10	case	case	NOUN
ejpam-816	305	11	n	n	ADP
ejpam-816	305	12	∑	∑	ADV
ejpam-816	305	13	k=0	k=0	X
ejpam-816	305	14	(	(	PUNCT
ejpam-816	305	15	−)ktk	−)ktk	NOUN
ejpam-816	305	16	,	,	PUNCT
ejpam-816	305	17	j(z)≡	j(z)≡	PROPN
ejpam-816	305	18	0	0	NUM
ejpam-816	306	1	(	(	PUNCT
ejpam-816	306	2	1≤	1≤	NUM
ejpam-816	306	3	j	j	PROPN
ejpam-816	306	4	≤	≤	PROPN
ejpam-816	306	5	n	n	CCONJ
ejpam-816	306	6	)	)	PUNCT
ejpam-816	306	7	(	(	PUNCT
ejpam-816	306	8	39	39	NUM
ejpam-816	306	9	)	)	PUNCT
ejpam-816	306	10	in	in	ADP
ejpam-816	306	11	the	the	DET
ejpam-816	306	12	sector	sector	NOUN
ejpam-816	306	13	(	(	PUNCT
ejpam-816	306	14	34	34	NUM
ejpam-816	306	15	)	)	PUNCT
ejpam-816	306	16	.	.	PUNCT
ejpam-816	307	1	the	the	DET
ejpam-816	307	2	asymptotic	asymptotic	ADJ
ejpam-816	307	3	expansion	expansion	NOUN
ejpam-816	307	4	of	of	ADP
ejpam-816	307	5	jn(z	jn(z	NOUN
ejpam-816	307	6	)	)	PUNCT
ejpam-816	307	7	in	in	ADP
ejpam-816	307	8	this	this	DET
ejpam-816	307	9	sector	sector	NOUN
ejpam-816	307	10	is	be	AUX
ejpam-816	307	11	therefore	therefore	ADV
ejpam-816	307	12	purely	purely	ADV
ejpam-816	307	13	exponential	exponential	ADJ
ejpam-816	307	14	in	in	ADP
ejpam-816	307	15	character	character	NOUN
ejpam-816	307	16	.	.	PUNCT
ejpam-816	308	1	4.3	4.3	NUM
ejpam-816	308	2	.	.	PUNCT
ejpam-816	309	1	the	the	DET
ejpam-816	309	2	integral	integral	ADJ
ejpam-816	309	3	kn	kn	PROPN
ejpam-816	309	4	,	,	PUNCT
ejpam-816	309	5	p(z	p(z	PROPN
ejpam-816	309	6	)	)	PUNCT
ejpam-816	309	7	the	the	DET
ejpam-816	309	8	procedure	procedure	NOUN
ejpam-816	309	9	described	describe	VERB
ejpam-816	309	10	above	above	ADV
ejpam-816	309	11	can	can	AUX
ejpam-816	309	12	be	be	AUX
ejpam-816	309	13	applied	apply	VERB
ejpam-816	309	14	to	to	ADP
ejpam-816	309	15	the	the	DET
ejpam-816	309	16	variant	variant	NOUN
ejpam-816	309	17	of	of	ADP
ejpam-816	309	18	the	the	DET
ejpam-816	309	19	integral	integral	ADJ
ejpam-816	309	20	jn(z	jn(z	NOUN
ejpam-816	309	21	)	)	PUNCT
ejpam-816	309	22	obtained	obtain	VERB
ejpam-816	309	23	by	by	ADP
ejpam-816	309	24	taking	take	VERB
ejpam-816	309	25	p	p	PRON
ejpam-816	309	26	<	<	X
ejpam-816	309	27	n	n	PRON
ejpam-816	309	28	integrals	integral	NOUN
ejpam-816	309	29	evaluated	evaluate	VERB
ejpam-816	309	30	over	over	ADP
ejpam-816	309	31	(	(	PUNCT
ejpam-816	309	32	−∞,∞	−∞,∞	NOUN
ejpam-816	309	33	)	)	PUNCT
ejpam-816	309	34	with	with	ADP
ejpam-816	309	35	the	the	DET
ejpam-816	309	36	rest	rest	NOUN
ejpam-816	309	37	being	be	AUX
ejpam-816	309	38	evaluated	evaluate	VERB
ejpam-816	309	39	over	over	ADP
ejpam-816	309	40	[	[	X
ejpam-816	309	41	0,∞	0,∞	NOUN
ejpam-816	309	42	)	)	PUNCT
ejpam-816	309	43	.	.	PUNCT
ejpam-816	310	1	thus	thus	ADV
ejpam-816	310	2	,	,	PUNCT
ejpam-816	310	3	if	if	SCONJ
ejpam-816	310	4	we	we	PRON
ejpam-816	310	5	define	define	VERB
ejpam-816	310	6	kn	kn	PROPN
ejpam-816	310	7	,	,	PUNCT
ejpam-816	310	8	p(z	p(z	PROPN
ejpam-816	310	9	)	)	PUNCT
ejpam-816	311	1	=	=	SYM
ejpam-816	311	2	λn	λn	NOUN
ejpam-816	311	3	∫	∫	PROPN
ejpam-816	311	4	∞	∞	PROPN
ejpam-816	311	5	0	0	NUM
ejpam-816	311	6	.	.	PUNCT
ejpam-816	311	7	.	.	PUNCT
ejpam-816	311	8	.	.	PUNCT
ejpam-816	312	1	∫	∫	PROPN
ejpam-816	313	1	∞	∞	PROPN
ejpam-816	313	2	0	0	NUM
ejpam-816	313	3	�	�	PROPN
ejpam-816	313	4	∫	∫	PROPN
ejpam-816	313	5	∞	∞	PROPN
ejpam-816	313	6	−∞	−∞	PROPN
ejpam-816	313	7	.	.	PUNCT
ejpam-816	313	8	.	.	PUNCT
ejpam-816	313	9	.	.	PUNCT
ejpam-816	314	1	∫	∫	PROPN
ejpam-816	315	1	∞	∞	PROPN
ejpam-816	316	1	−∞	−∞	ADP
ejpam-816	316	2	x	x	X
ejpam-816	316	3	ν1−1	ν1−1	PRON
ejpam-816	316	4	1	1	NUM
ejpam-816	316	5	.	.	PUNCT
ejpam-816	316	6	.	.	PUNCT
ejpam-816	316	7	.	.	PUNCT
ejpam-816	317	1	xνn−1	xνn−1	PROPN
ejpam-816	317	2	n	n	CCONJ
ejpam-816	317	3	e−	e−	PROPN
ejpam-816	317	4	f	f	PROPN
ejpam-816	317	5	(	(	PUNCT
ejpam-816	317	6	x1,	x1,	NOUN
ejpam-816	317	7	...	...	PUNCT
ejpam-816	317	8	,xn;z	,xn;z	PUNCT
ejpam-816	317	9	)	)	PUNCT
ejpam-816	318	1	d	d	X
ejpam-816	318	2	x1	x1	PROPN
ejpam-816	318	3	.	.	PUNCT
ejpam-816	318	4	.	.	PUNCT
ejpam-816	318	5	.	.	PUNCT
ejpam-816	319	1	d	d	X
ejpam-816	319	2	xp	xp	X
ejpam-816	319	3	�	�	PROPN
ejpam-816	319	4	d	d	PROPN
ejpam-816	319	5	xp+1	xp+1	PROPN
ejpam-816	319	6	.	.	PUNCT
ejpam-816	319	7	.	.	PUNCT
ejpam-816	319	8	.	.	PUNCT
ejpam-816	320	1	d	d	X
ejpam-816	320	2	xn	xn	PUNCT
ejpam-816	320	3	,	,	PUNCT
ejpam-816	320	4	(	(	PUNCT
ejpam-816	320	5	40	40	NUM
ejpam-816	320	6	)	)	PUNCT
ejpam-816	320	7	where	where	SCONJ
ejpam-816	320	8	it	it	PRON
ejpam-816	320	9	is	be	AUX
ejpam-816	320	10	now	now	ADV
ejpam-816	320	11	supposed	suppose	VERB
ejpam-816	320	12	that	that	SCONJ
ejpam-816	320	13	µr	µr	ADP
ejpam-816	320	14	(	(	PUNCT
ejpam-816	320	15	1	1	NUM
ejpam-816	320	16	≤	≤	NUM
ejpam-816	320	17	r	r	NOUN
ejpam-816	320	18	≤	≤	NOUN
ejpam-816	320	19	p	p	X
ejpam-816	320	20	)	)	PUNCT
ejpam-816	320	21	are	be	AUX
ejpam-816	320	22	even	even	ADV
ejpam-816	320	23	integers	integer	NOUN
ejpam-816	320	24	and	and	CCONJ
ejpam-816	320	25	µr	µr	ADP
ejpam-816	320	26	>	>	X
ejpam-816	320	27	0	0	PUNCT
ejpam-816	321	1	(	(	PUNCT
ejpam-816	321	2	p	p	NOUN
ejpam-816	321	3	+	+	NOUN
ejpam-816	321	4	1	1	NUM
ejpam-816	321	5	≤	≤	NUM
ejpam-816	321	6	r	r	NOUN
ejpam-816	321	7	≤	≤	NOUN
ejpam-816	321	8	n	n	CCONJ
ejpam-816	321	9	)	)	PUNCT
ejpam-816	321	10	,	,	PUNCT
ejpam-816	321	11	then	then	ADV
ejpam-816	321	12	we	we	PRON
ejpam-816	321	13	obtain	obtain	VERB
ejpam-816	321	14	following	follow	VERB
ejpam-816	321	15	the	the	DET
ejpam-816	321	16	procedure	procedure	NOUN
ejpam-816	321	17	described	describe	VERB
ejpam-816	321	18	in	in	ADP
ejpam-816	321	19	section	section	NOUN
ejpam-816	321	20	4	4	NUM
ejpam-816	321	21	the	the	DET
ejpam-816	321	22	series	series	PROPN
ejpam-816	321	23	expansion	expansion	PROPN
ejpam-816	321	24	kn	kn	PROPN
ejpam-816	321	25	,	,	PUNCT
ejpam-816	321	26	p(z	p(z	PROPN
ejpam-816	321	27	)	)	PUNCT
ejpam-816	321	28	=	=	SYM
ejpam-816	322	1	∞	∞	NUM
ejpam-816	322	2	∑	∑	PUNCT
ejpam-816	322	3	k=0	k=0	PROPN
ejpam-816	322	4	zk	zk	PROPN
ejpam-816	323	1	k	k	PROPN
ejpam-816	323	2	!	!	PUNCT
ejpam-816	324	1	n	n	CCONJ
ejpam-816	324	2	∏	∏	PROPN
ejpam-816	324	3	r=1	r=1	PROPN
ejpam-816	324	4	γ	γ	X
ejpam-816	324	5	�	�	PROPN
ejpam-816	324	6	νr	νr	ADP
ejpam-816	324	7	+	+	ADP
ejpam-816	324	8	mr	mr	PROPN
ejpam-816	324	9	k	k	PROPN
ejpam-816	324	10	µr	µr	ADP
ejpam-816	324	11	�	�	PROPN
ejpam-816	324	12	p	p	X
ejpam-816	324	13	∏	∏	PROPN
ejpam-816	324	14	r=1	r=1	NOUN
ejpam-816	324	15	br(k	br(k	NOUN
ejpam-816	324	16	)	)	PUNCT
ejpam-816	324	17	.	.	PUNCT
ejpam-816	325	1	(	(	PUNCT
ejpam-816	325	2	41	41	NUM
ejpam-816	325	3	)	)	PUNCT
ejpam-816	325	4	in	in	ADP
ejpam-816	325	5	the	the	DET
ejpam-816	325	6	evaluation	evaluation	NOUN
ejpam-816	325	7	of	of	ADP
ejpam-816	325	8	the	the	DET
ejpam-816	325	9	integrals	integral	NOUN
ejpam-816	325	10	when	when	SCONJ
ejpam-816	325	11	xr	xr	PROPN
ejpam-816	325	12	<	<	X
ejpam-816	325	13	0	0	PUNCT
ejpam-816	326	1	(	(	PUNCT
ejpam-816	326	2	1≤	1≤	NUM
ejpam-816	326	3	r	r	NOUN
ejpam-816	326	4	≤	≤	NOUN
ejpam-816	326	5	p	p	X
ejpam-816	326	6	)	)	PUNCT
ejpam-816	326	7	we	we	PRON
ejpam-816	326	8	have	have	AUX
ejpam-816	326	9	again	again	ADV
ejpam-816	326	10	taken	take	VERB
ejpam-816	326	11	xr	xr	X
ejpam-816	326	12	=	=	PROPN
ejpam-816	326	13	|xr	|xr	PRON
ejpam-816	326	14	|e	|e	PROPN
ejpam-816	326	15	πi	πi	ADV
ejpam-816	326	16	.	.	PUNCT
ejpam-816	327	1	the	the	DET
ejpam-816	327	2	product	product	NOUN
ejpam-816	327	3	∏p	∏p	PART
ejpam-816	327	4	r=1	r=1	NOUN
ejpam-816	327	5	br(k	br(k	NOUN
ejpam-816	327	6	)	)	PUNCT
ejpam-816	327	7	may	may	AUX
ejpam-816	327	8	be	be	AUX
ejpam-816	327	9	expanded	expand	VERB
ejpam-816	327	10	as	as	ADP
ejpam-816	327	11	a	a	DET
ejpam-816	327	12	sum	sum	NOUN
ejpam-816	327	13	of	of	ADP
ejpam-816	327	14	exponentials	exponential	NOUN
ejpam-816	327	15	so	so	SCONJ
ejpam-816	327	16	that	that	SCONJ
ejpam-816	327	17	kn	kn	PROPN
ejpam-816	327	18	,	,	PUNCT
ejpam-816	327	19	p(z	p(z	PROPN
ejpam-816	327	20	)	)	PUNCT
ejpam-816	327	21	can	can	AUX
ejpam-816	327	22	be	be	AUX
ejpam-816	327	23	written	write	VERB
ejpam-816	327	24	as	as	ADP
ejpam-816	327	25	a	a	DET
ejpam-816	327	26	finite	finite	ADJ
ejpam-816	327	27	sum	sum	NOUN
ejpam-816	327	28	of	of	ADP
ejpam-816	327	29	nψ0(z	nψ0(z	PROPN
ejpam-816	327	30	)	)	PUNCT
ejpam-816	327	31	functions	function	NOUN
ejpam-816	327	32	of	of	ADP
ejpam-816	327	33	rotated	rotate	VERB
ejpam-816	327	34	argument	argument	NOUN
ejpam-816	327	35	and	and	CCONJ
ejpam-816	327	36	parameters	parameter	NOUN
ejpam-816	327	37	given	give	VERB
ejpam-816	327	38	in	in	ADP
ejpam-816	327	39	(	(	PUNCT
ejpam-816	327	40	22	22	NUM
ejpam-816	327	41	)	)	PUNCT
ejpam-816	327	42	in	in	ADP
ejpam-816	327	43	an	an	DET
ejpam-816	327	44	analogous	analogous	ADJ
ejpam-816	327	45	manner	manner	NOUN
ejpam-816	327	46	to	to	ADP
ejpam-816	327	47	that	that	PRON
ejpam-816	327	48	in	in	ADP
ejpam-816	327	49	(	(	PUNCT
ejpam-816	327	50	32	32	NUM
ejpam-816	327	51	)	)	PUNCT
ejpam-816	327	52	.	.	PUNCT
ejpam-816	328	1	the	the	DET
ejpam-816	328	2	asymptotic	asymptotic	ADJ
ejpam-816	328	3	expansion	expansion	NOUN
ejpam-816	328	4	of	of	ADP
ejpam-816	328	5	nψ0(z	nψ0(z	PROPN
ejpam-816	328	6	)	)	PUNCT
ejpam-816	328	7	in	in	ADP
ejpam-816	328	8	(	(	PUNCT
ejpam-816	328	9	19	19	NUM
ejpam-816	328	10	)	)	PUNCT
ejpam-816	328	11	can	can	AUX
ejpam-816	328	12	then	then	ADV
ejpam-816	328	13	be	be	AUX
ejpam-816	328	14	employed	employ	VERB
ejpam-816	328	15	to	to	PART
ejpam-816	328	16	obtain	obtain	VERB
ejpam-816	328	17	the	the	DET
ejpam-816	328	18	expansion	expansion	NOUN
ejpam-816	328	19	of	of	ADP
ejpam-816	328	20	kn	kn	PROPN
ejpam-816	328	21	,	,	PUNCT
ejpam-816	328	22	p(z	p(z	PROPN
ejpam-816	328	23	)	)	PUNCT
ejpam-816	328	24	as	as	ADP
ejpam-816	328	25	|z|	|z|	NOUN
ejpam-816	328	26	→	→	SYM
ejpam-816	328	27	∞.	∞.	PROPN
ejpam-816	328	28	we	we	PRON
ejpam-816	328	29	give	give	VERB
ejpam-816	328	30	an	an	DET
ejpam-816	328	31	example	example	NOUN
ejpam-816	328	32	of	of	ADP
ejpam-816	328	33	the	the	DET
ejpam-816	328	34	asymptotic	asymptotic	ADJ
ejpam-816	328	35	structure	structure	NOUN
ejpam-816	328	36	of	of	ADP
ejpam-816	328	37	kn	kn	PROPN
ejpam-816	328	38	,	,	PUNCT
ejpam-816	328	39	p(z	p(z	PROPN
ejpam-816	328	40	)	)	PUNCT
ejpam-816	328	41	in	in	ADP
ejpam-816	328	42	section	section	NOUN
ejpam-816	328	43	5	5	NUM
ejpam-816	328	44	.	.	PUNCT
ejpam-816	328	45	r.	r.	PROPN
ejpam-816	328	46	paris	paris	PROPN
ejpam-816	328	47	/	/	SYM
ejpam-816	328	48	eur	eur	PROPN
ejpam-816	328	49	.	.	PUNCT
ejpam-816	329	1	j.	j.	PROPN
ejpam-816	329	2	pure	pure	PROPN
ejpam-816	329	3	appl	appl	PROPN
ejpam-816	329	4	.	.	PROPN
ejpam-816	329	5	math	math	PROPN
ejpam-816	329	6	,	,	PUNCT
ejpam-816	329	7	3	3	NUM
ejpam-816	329	8	(	(	PUNCT
ejpam-816	329	9	2010	2010	NUM
ejpam-816	329	10	)	)	PUNCT
ejpam-816	329	11	,	,	PUNCT
ejpam-816	329	12	1006	1006	NUM
ejpam-816	329	13	-	-	SYM
ejpam-816	329	14	1031	1031	NUM
ejpam-816	329	15	1018	1018	NUM
ejpam-816	329	16	5	5	NUM
ejpam-816	329	17	.	.	PUNCT
ejpam-816	329	18	numerical	numerical	ADJ
ejpam-816	329	19	examples	example	NOUN
ejpam-816	329	20	in	in	ADP
ejpam-816	329	21	this	this	DET
ejpam-816	329	22	section	section	NOUN
ejpam-816	329	23	we	we	PRON
ejpam-816	329	24	give	give	VERB
ejpam-816	329	25	some	some	DET
ejpam-816	329	26	numerical	numerical	ADJ
ejpam-816	329	27	examples	example	NOUN
ejpam-816	329	28	to	to	PART
ejpam-816	329	29	illustrate	illustrate	VERB
ejpam-816	329	30	the	the	DET
ejpam-816	329	31	application	application	NOUN
ejpam-816	329	32	of	of	ADP
ejpam-816	329	33	the	the	DET
ejpam-816	329	34	expansion	expansion	NOUN
ejpam-816	329	35	(	(	PUNCT
ejpam-816	329	36	19	19	NUM
ejpam-816	329	37	)	)	PUNCT
ejpam-816	329	38	to	to	ADP
ejpam-816	329	39	the	the	DET
ejpam-816	329	40	construction	construction	NOUN
ejpam-816	329	41	of	of	ADP
ejpam-816	329	42	the	the	DET
ejpam-816	329	43	asymptotic	asymptotic	ADJ
ejpam-816	329	44	structure	structure	NOUN
ejpam-816	329	45	of	of	ADP
ejpam-816	329	46	the	the	DET
ejpam-816	329	47	integrals	integral	NOUN
ejpam-816	329	48	jn(z	jn(z	VERB
ejpam-816	329	49	)	)	PUNCT
ejpam-816	329	50	and	and	CCONJ
ejpam-816	329	51	kn	kn	PROPN
ejpam-816	329	52	,	,	PUNCT
ejpam-816	329	53	p(z	p(z	PROPN
ejpam-816	329	54	)	)	PUNCT
ejpam-816	329	55	defined	define	VERB
ejpam-816	329	56	in	in	ADP
ejpam-816	329	57	(	(	PUNCT
ejpam-816	329	58	4	4	NUM
ejpam-816	329	59	)	)	PUNCT
ejpam-816	329	60	and	and	CCONJ
ejpam-816	329	61	(	(	PUNCT
ejpam-816	329	62	40	40	NUM
ejpam-816	329	63	)	)	PUNCT
ejpam-816	329	64	.	.	PUNCT
ejpam-816	330	1	5.1	5.1	NUM
ejpam-816	330	2	.	.	PUNCT
ejpam-816	330	3	example	example	NOUN
ejpam-816	330	4	1	1	NUM
ejpam-816	330	5	let	let	VERB
ejpam-816	330	6	us	we	PRON
ejpam-816	330	7	consider	consider	VERB
ejpam-816	330	8	the	the	DET
ejpam-816	330	9	two	two	NUM
ejpam-816	330	10	-	-	PUNCT
ejpam-816	330	11	dimensional	dimensional	ADJ
ejpam-816	330	12	integral	integral	ADJ
ejpam-816	330	13	j2(z	j2(z	NOUN
ejpam-816	330	14	)	)	PUNCT
ejpam-816	330	15	=	=	PUNCT
ejpam-816	331	1	µ1µ2	µ1µ2	PUNCT
ejpam-816	331	2	∫	∫	PROPN
ejpam-816	331	3	∞	∞	PROPN
ejpam-816	331	4	−∞	−∞	ADP
ejpam-816	331	5	∫	∫	PROPN
ejpam-816	331	6	∞	∞	PROPN
ejpam-816	332	1	−∞	−∞	ADP
ejpam-816	332	2	x	x	X
ejpam-816	332	3	ν1−1	ν1−1	PRON
ejpam-816	332	4	1	1	NUM
ejpam-816	332	5	x	x	SYM
ejpam-816	332	6	ν2−1	ν2−1	ADP
ejpam-816	332	7	2	2	NUM
ejpam-816	332	8	exp{−x	exp{−x	SYM
ejpam-816	332	9	µ1	µ1	PROPN
ejpam-816	332	10	1	1	NUM
ejpam-816	332	11	−	−	NOUN
ejpam-816	333	1	x	x	PUNCT
ejpam-816	334	1	µ2	µ2	NOUN
ejpam-816	334	2	2	2	NUM
ejpam-816	334	3	+	+	CCONJ
ejpam-816	334	4	zx	zx	PROPN
ejpam-816	334	5	m1	m1	NOUN
ejpam-816	334	6	1	1	NUM
ejpam-816	334	7	x	x	SYM
ejpam-816	334	8	m2	m2	PROPN
ejpam-816	334	9	2	2	NUM
ejpam-816	334	10	}	}	PUNCT
ejpam-816	334	11	d	d	PROPN
ejpam-816	334	12	x1d	x1d	NUM
ejpam-816	334	13	x2	x2	PROPN
ejpam-816	334	14	,	,	PUNCT
ejpam-816	334	15	(	(	PUNCT
ejpam-816	334	16	42	42	NUM
ejpam-816	334	17	)	)	PUNCT
ejpam-816	334	18	where	where	SCONJ
ejpam-816	334	19	ν1	ν1	NOUN
ejpam-816	334	20	,	,	PUNCT
ejpam-816	334	21	ν2	ν2	ADV
ejpam-816	334	22	>	>	X
ejpam-816	334	23	0	0	NUM
ejpam-816	334	24	and	and	CCONJ
ejpam-816	334	25	µ1	µ1	PROPN
ejpam-816	334	26	,	,	PUNCT
ejpam-816	334	27	µ2	µ2	PROPN
ejpam-816	334	28	are	be	AUX
ejpam-816	334	29	positive	positive	ADJ
ejpam-816	334	30	even	even	ADV
ejpam-816	334	31	integers	integer	NOUN
ejpam-816	334	32	.	.	PUNCT
ejpam-816	335	1	from	from	ADP
ejpam-816	335	2	(	(	PUNCT
ejpam-816	335	3	32	32	NUM
ejpam-816	335	4	)	)	PUNCT
ejpam-816	335	5	and	and	CCONJ
ejpam-816	335	6	(	(	PUNCT
ejpam-816	335	7	21	21	NUM
ejpam-816	335	8	)	)	PUNCT
ejpam-816	335	9	,	,	PUNCT
ejpam-816	335	10	this	this	DET
ejpam-816	335	11	integral	integral	NOUN
ejpam-816	335	12	can	can	AUX
ejpam-816	335	13	be	be	AUX
ejpam-816	335	14	expressed	express	VERB
ejpam-816	335	15	in	in	ADP
ejpam-816	335	16	terms	term	NOUN
ejpam-816	335	17	of	of	ADP
ejpam-816	335	18	the	the	DET
ejpam-816	335	19	wright	wright	PROPN
ejpam-816	335	20	function	function	PROPN
ejpam-816	335	21	2ψ0(z	2ψ0(z	NUM
ejpam-816	335	22	)	)	PUNCT
ejpam-816	335	23	of	of	ADP
ejpam-816	335	24	rotated	rotate	VERB
ejpam-816	335	25	argument	argument	NOUN
ejpam-816	335	26	,	,	PUNCT
ejpam-816	335	27	where	where	SCONJ
ejpam-816	335	28	2ψ0(z)≡	2ψ0(z)≡	NUM
ejpam-816	335	29	2ψ0	2ψ0	NUM
ejpam-816	335	30	�	�	PROPN
ejpam-816	335	31	(	(	PUNCT
ejpam-816	335	32	m1	m1	PROPN
ejpam-816	335	33	µ1	µ1	PROPN
ejpam-816	335	34	,	,	PUNCT
ejpam-816	335	35	ν1	ν1	NOUN
ejpam-816	335	36	µ1	µ1	PROPN
ejpam-816	335	37	)	)	PUNCT
ejpam-816	335	38	,	,	PUNCT
ejpam-816	335	39	(	(	PUNCT
ejpam-816	335	40	m2	m2	PROPN
ejpam-816	335	41	µ2	µ2	PROPN
ejpam-816	335	42	,	,	PUNCT
ejpam-816	335	43	ν2	ν2	PROPN
ejpam-816	335	44	µ2	µ2	PROPN
ejpam-816	335	45	)	)	PUNCT
ejpam-816	335	46	;	;	PUNCT
ejpam-816	335	47	z	z	PROPN
ejpam-816	335	48	�	�	PROPN
ejpam-816	335	49	.	.	PUNCT
ejpam-816	336	1	for	for	ADP
ejpam-816	336	2	simplicity	simplicity	NOUN
ejpam-816	336	3	in	in	ADP
ejpam-816	336	4	presentation	presentation	NOUN
ejpam-816	336	5	we	we	PRON
ejpam-816	336	6	only	only	ADV
ejpam-816	336	7	consider	consider	VERB
ejpam-816	336	8	the	the	DET
ejpam-816	336	9	case	case	NOUN
ejpam-816	336	10	when	when	SCONJ
ejpam-816	336	11	m1	m1	PROPN
ejpam-816	336	12	=	=	PROPN
ejpam-816	336	13	m2	m2	PROPN
ejpam-816	336	14	=	=	PROPN
ejpam-816	336	15	m.	m.	NOUN
ejpam-816	336	16	then	then	ADV
ejpam-816	336	17	we	we	PRON
ejpam-816	336	18	find	find	VERB
ejpam-816	336	19	from	from	ADP
ejpam-816	336	20	(	(	PUNCT
ejpam-816	336	21	32	32	NUM
ejpam-816	336	22	)	)	PUNCT
ejpam-816	336	23	j2(z	j2(z	PROPN
ejpam-816	336	24	)	)	PUNCT
ejpam-816	336	25	=	=	SYM
ejpam-816	336	26	2ψ0(z)−	2ψ0(z)−	NUM
ejpam-816	336	27	b1	b1	NOUN
ejpam-816	336	28	2ψ0(zeπim	2ψ0(zeπim	NUM
ejpam-816	336	29	)	)	PUNCT
ejpam-816	336	30	+	+	NUM
ejpam-816	336	31	b2	b2	NOUN
ejpam-816	336	32	2ψ0(ze2πim	2ψ0(ze2πim	NUM
ejpam-816	336	33	)	)	PUNCT
ejpam-816	336	34	,	,	PUNCT
ejpam-816	336	35	(	(	PUNCT
ejpam-816	336	36	43	43	NUM
ejpam-816	336	37	)	)	PUNCT
ejpam-816	336	38	where	where	SCONJ
ejpam-816	336	39	b1	b1	NOUN
ejpam-816	336	40	=	=	SYM
ejpam-816	336	41	(	(	PUNCT
ejpam-816	336	42	e	e	NOUN
ejpam-816	336	43	πiν1	πiν1	NOUN
ejpam-816	336	44	+	+	CCONJ
ejpam-816	336	45	eπiν2	eπiν2	PROPN
ejpam-816	336	46	)	)	PUNCT
ejpam-816	336	47	,	,	PUNCT
ejpam-816	336	48	b2	b2	NOUN
ejpam-816	336	49	=	=	SYM
ejpam-816	336	50	eπi(ν1+ν2	eπi(ν1+ν2	NOUN
ejpam-816	336	51	)	)	PUNCT
ejpam-816	336	52	.	.	PUNCT
ejpam-816	337	1	(	(	PUNCT
ejpam-816	337	2	44	44	NUM
ejpam-816	337	3	)	)	PUNCT
ejpam-816	337	4	provided	provide	VERB
ejpam-816	337	5	ν1	ν1	NOUN
ejpam-816	337	6	and	and	CCONJ
ejpam-816	337	7	ν2	ν2	NOUN
ejpam-816	337	8	are	be	AUX
ejpam-816	337	9	real	real	ADJ
ejpam-816	337	10	,	,	PUNCT
ejpam-816	337	11	it	it	PRON
ejpam-816	337	12	is	be	AUX
ejpam-816	337	13	readily	readily	ADV
ejpam-816	337	14	shown	show	VERB
ejpam-816	337	15	that	that	SCONJ
ejpam-816	337	16	j2(z	j2(z	PROPN
ejpam-816	337	17	)	)	PUNCT
ejpam-816	337	18	possesses	possess	VERB
ejpam-816	337	19	a	a	DET
ejpam-816	337	20	basic	basic	ADJ
ejpam-816	337	21	symmetry	symmetry	NOUN
ejpam-816	337	22	about	about	ADP
ejpam-816	337	23	the	the	DET
ejpam-816	337	24	half	half	ADJ
ejpam-816	337	25	-	-	PUNCT
ejpam-816	337	26	rays	ray	NOUN
ejpam-816	337	27	arg	arg	NOUN
ejpam-816	337	28	z	z	PROPN
ejpam-816	337	29	=	=	SYM
ejpam-816	337	30	ω	ω	PROPN
ejpam-816	337	31	and	and	CCONJ
ejpam-816	337	32	arg	arg	NOUN
ejpam-816	337	33	z	z	NOUN
ejpam-816	337	34	=	=	SYM
ejpam-816	337	35	ω−π	ω−π	NOUN
ejpam-816	337	36	,	,	PUNCT
ejpam-816	337	37	where	where	SCONJ
ejpam-816	337	38	ω	ω	NOUN
ejpam-816	337	39	=	=	SYM
ejpam-816	337	40	π(1−m	π(1−m	PROPN
ejpam-816	337	41	)	)	PUNCT
ejpam-816	337	42	.	.	PUNCT
ejpam-816	338	1	for	for	ADP
ejpam-816	338	2	,	,	PUNCT
ejpam-816	338	3	upon	upon	SCONJ
ejpam-816	338	4	recalling	recall	VERB
ejpam-816	338	5	that	that	SCONJ
ejpam-816	338	6	the	the	DET
ejpam-816	338	7	argument	argument	NOUN
ejpam-816	338	8	of	of	ADP
ejpam-816	338	9	pψq(z	pψq(z	PROPN
ejpam-816	338	10	)	)	PUNCT
ejpam-816	338	11	can	can	AUX
ejpam-816	338	12	be	be	AUX
ejpam-816	338	13	written	write	VERB
ejpam-816	338	14	modulo	modulo	PROPN
ejpam-816	338	15	2π	2π	NOUN
ejpam-816	338	16	,	,	PUNCT
ejpam-816	338	17	we	we	PRON
ejpam-816	338	18	find‡	find‡	VERB
ejpam-816	338	19	from	from	ADP
ejpam-816	338	20	(	(	PUNCT
ejpam-816	338	21	43	43	NUM
ejpam-816	338	22	)	)	PUNCT
ejpam-816	338	23	with	with	ADP
ejpam-816	338	24	the	the	DET
ejpam-816	338	25	above	above	ADJ
ejpam-816	338	26	definition	definition	NOUN
ejpam-816	338	27	of	of	ADP
ejpam-816	338	28	ω	ω	NUM
ejpam-816	338	29	that	that	PRON
ejpam-816	338	30	j2(zeiω	j2(zeiω	NOUN
ejpam-816	338	31	)	)	PUNCT
ejpam-816	339	1	=	=	SYM
ejpam-816	339	2	eπi(ν1+ν2	eπi(ν1+ν2	X
ejpam-816	339	3	)	)	PUNCT
ejpam-816	339	4	¦	¦	PROPN
ejpam-816	339	5	2ψ0(zeiω+2πim)−	2ψ0(zeiω+2πim)−	NUM
ejpam-816	339	6	(	(	PUNCT
ejpam-816	339	7	e−πiν1	e−πiν1	NOUN
ejpam-816	339	8	+	+	CCONJ
ejpam-816	339	9	e−πiν2	e−πiν2	ADJ
ejpam-816	339	10	)	)	PUNCT
ejpam-816	339	11	2ψ0(zeiω+πim	2ψ0(zeiω+πim	X
ejpam-816	339	12	)	)	PUNCT
ejpam-816	340	1	+	+	ADJ
ejpam-816	340	2	e−πi(ν1+ν2	e−πi(ν1+ν2	NOUN
ejpam-816	340	3	)	)	PUNCT
ejpam-816	340	4	2ψ0(zeiω	2ψ0(zeiω	NOUN
ejpam-816	340	5	)	)	PUNCT
ejpam-816	341	1	©	©	NOUN
ejpam-816	341	2	=	=	SYM
ejpam-816	341	3	eπi(ν1+ν2	eπi(ν1+ν2	NOUN
ejpam-816	341	4	)	)	PUNCT
ejpam-816	341	5	¦	¦	NOUN
ejpam-816	341	6	2ψ0(ze−iω)−	2ψ0(ze−iω)−	NUM
ejpam-816	341	7	(	(	PUNCT
ejpam-816	341	8	e−πiν1	e−πiν1	NOUN
ejpam-816	341	9	+	+	CCONJ
ejpam-816	341	10	e−πiν2	e−πiν2	ADJ
ejpam-816	341	11	)	)	PUNCT
ejpam-816	341	12	2ψ0(ze−πi	2ψ0(ze−πi	NUM
ejpam-816	341	13	)	)	PUNCT
ejpam-816	342	1	+	+	ADJ
ejpam-816	342	2	e−πi(ν1+ν2	e−πi(ν1+ν2	NOUN
ejpam-816	342	3	)	)	PUNCT
ejpam-816	342	4	2ψ0(zeiω−2πi	2ψ0(zeiω−2πi	NOUN
ejpam-816	342	5	)	)	PUNCT
ejpam-816	343	1	©	©	PROPN
ejpam-816	343	2	=	=	SYM
ejpam-816	343	3	eπi(ν1+ν2)j2(zeiω	eπi(ν1+ν2)j2(zeiω	PROPN
ejpam-816	343	4	)	)	PUNCT
ejpam-816	343	5	,	,	PUNCT
ejpam-816	343	6	(	(	PUNCT
ejpam-816	343	7	45	45	NUM
ejpam-816	343	8	)	)	PUNCT
ejpam-816	343	9	where	where	SCONJ
ejpam-816	343	10	the	the	DET
ejpam-816	343	11	bar	bar	NOUN
ejpam-816	343	12	denotes	denote	VERB
ejpam-816	343	13	the	the	DET
ejpam-816	343	14	complex	complex	ADJ
ejpam-816	343	15	conjugate	conjugate	NOUN
ejpam-816	343	16	.	.	PUNCT
ejpam-816	344	1	hence	hence	ADV
ejpam-816	344	2	it	it	PRON
ejpam-816	344	3	is	be	AUX
ejpam-816	344	4	sufficient	sufficient	ADJ
ejpam-816	344	5	in	in	ADP
ejpam-816	344	6	this	this	DET
ejpam-816	344	7	case	case	NOUN
ejpam-816	344	8	to	to	PART
ejpam-816	344	9	restrict	restrict	VERB
ejpam-816	344	10	our	our	PRON
ejpam-816	344	11	attention	attention	NOUN
ejpam-816	344	12	to	to	ADP
ejpam-816	344	13	an	an	DET
ejpam-816	344	14	appropriate	appropriate	ADJ
ejpam-816	344	15	half	half	ADJ
ejpam-816	344	16	-	-	PUNCT
ejpam-816	344	17	plane	plane	NOUN
ejpam-816	344	18	.	.	PUNCT
ejpam-816	345	1	we	we	PRON
ejpam-816	345	2	display	display	VERB
ejpam-816	345	3	in	in	ADP
ejpam-816	345	4	fig	fig	NOUN
ejpam-816	345	5	.	.	PUNCT
ejpam-816	346	1	1	1	NUM
ejpam-816	347	1	the	the	DET
ejpam-816	347	2	large-|z|	large-|z|	NOUN
ejpam-816	347	3	sectorial	sectorial	ADJ
ejpam-816	347	4	behaviour	behaviour	NOUN
ejpam-816	347	5	of	of	ADP
ejpam-816	347	6	j2(z	j2(z	NOUN
ejpam-816	347	7	)	)	PUNCT
ejpam-816	347	8	in	in	ADP
ejpam-816	347	9	the	the	DET
ejpam-816	347	10	case	case	NOUN
ejpam-816	347	11	µ1	µ1	NOUN
ejpam-816	347	12	=	=	SYM
ejpam-816	347	13	µ2	µ2	NOUN
ejpam-816	347	14	=	=	NOUN
ejpam-816	347	15	4	4	NUM
ejpam-816	347	16	for	for	ADP
ejpam-816	347	17	different	different	ADJ
ejpam-816	347	18	values	value	NOUN
ejpam-816	347	19	of	of	ADP
ejpam-816	347	20	m	m	PROPN
ejpam-816	347	21	,	,	PUNCT
ejpam-816	347	22	where	where	SCONJ
ejpam-816	347	23	we	we	PRON
ejpam-816	347	24	suppose	suppose	VERB
ejpam-816	347	25	that	that	SCONJ
ejpam-816	347	26	b1	b1	VERB
ejpam-816	347	27	6=	6=	PRON
ejpam-816	347	28	0	0	NUM
ejpam-816	347	29	.	.	PUNCT
ejpam-816	348	1	in	in	ADP
ejpam-816	348	2	fig	fig	NOUN
ejpam-816	348	3	.	.	PUNCT
ejpam-816	349	1	1(a	1(a	NUM
ejpam-816	349	2	)	)	PUNCT
ejpam-816	349	3	,	,	PUNCT
ejpam-816	349	4	m	m	VERB
ejpam-816	349	5	=	=	NOUN
ejpam-816	349	6	1	1	NUM
ejpam-816	349	7	4	4	NUM
ejpam-816	349	8	(	(	PUNCT
ejpam-816	349	9	κ	κ	X
ejpam-816	349	10	=	=	SYM
ejpam-816	349	11	7	7	NUM
ejpam-816	349	12	8	8	NUM
ejpam-816	349	13	)	)	PUNCT
ejpam-816	349	14	so	so	SCONJ
ejpam-816	349	15	that	that	SCONJ
ejpam-816	349	16	the	the	DET
ejpam-816	349	17	symmetry	symmetry	NOUN
ejpam-816	349	18	line	line	NOUN
ejpam-816	349	19	is	be	AUX
ejpam-816	349	20	arg	arg	NOUN
ejpam-816	349	21	z	z	NOUN
ejpam-816	349	22	=	=	SYM
ejpam-816	349	23	3	3	NUM
ejpam-816	349	24	4	4	NUM
ejpam-816	349	25	π	π	NOUN
ejpam-816	349	26	,	,	PUNCT
ejpam-816	349	27	−1	−1	NOUN
ejpam-816	349	28	4	4	NUM
ejpam-816	349	29	π	π	NOUN
ejpam-816	349	30	and	and	CCONJ
ejpam-816	349	31	,	,	PUNCT
ejpam-816	349	32	from	from	ADP
ejpam-816	349	33	(	(	PUNCT
ejpam-816	349	34	34	34	NUM
ejpam-816	349	35	)	)	PUNCT
ejpam-816	349	36	,	,	PUNCT
ejpam-816	349	37	the	the	DET
ejpam-816	349	38	algebraic	algebraic	ADJ
ejpam-816	349	39	expansions	expansion	NOUN
ejpam-816	349	40	cancel	cancel	VERB
ejpam-816	349	41	in	in	ADP
ejpam-816	349	42	the	the	DET
ejpam-816	349	43	‡when	‡when	PROPN
ejpam-816	349	44	m1	m1	PROPN
ejpam-816	349	45	6=	6=	NUM
ejpam-816	350	1	m2	m2	PROPN
ejpam-816	350	2	,	,	PUNCT
ejpam-816	350	3	it	it	PRON
ejpam-816	350	4	can	can	AUX
ejpam-816	350	5	be	be	AUX
ejpam-816	350	6	shown	show	VERB
ejpam-816	350	7	that	that	SCONJ
ejpam-816	350	8	the	the	DET
ejpam-816	350	9	symmetry	symmetry	NOUN
ejpam-816	350	10	relation	relation	NOUN
ejpam-816	350	11	(	(	PUNCT
ejpam-816	350	12	45	45	NUM
ejpam-816	350	13	)	)	PUNCT
ejpam-816	350	14	still	still	ADV
ejpam-816	350	15	holds	hold	VERB
ejpam-816	350	16	with	with	ADP
ejpam-816	350	17	ω	ω	PROPN
ejpam-816	350	18	=	=	SYM
ejpam-816	351	1	π−	π−	NOUN
ejpam-816	351	2	1	1	NUM
ejpam-816	351	3	2	2	NUM
ejpam-816	351	4	π(m1	π(m1	NOUN
ejpam-816	351	5	+	+	ADJ
ejpam-816	351	6	m2	m2	PROPN
ejpam-816	351	7	)	)	PUNCT
ejpam-816	351	8	.	.	PUNCT
ejpam-816	352	1	r.	r.	PROPN
ejpam-816	352	2	paris	paris	PROPN
ejpam-816	352	3	/	/	SYM
ejpam-816	352	4	eur	eur	PROPN
ejpam-816	352	5	.	.	PUNCT
ejpam-816	353	1	j.	j.	PROPN
ejpam-816	353	2	pure	pure	PROPN
ejpam-816	353	3	appl	appl	PROPN
ejpam-816	353	4	.	.	PROPN
ejpam-816	353	5	math	math	PROPN
ejpam-816	353	6	,	,	PUNCT
ejpam-816	353	7	3	3	NUM
ejpam-816	353	8	(	(	PUNCT
ejpam-816	353	9	2010	2010	NUM
ejpam-816	353	10	)	)	PUNCT
ejpam-816	353	11	,	,	PUNCT
ejpam-816	353	12	1006	1006	NUM
ejpam-816	353	13	-	-	SYM
ejpam-816	353	14	1031	1031	NUM
ejpam-816	353	15	1019	1019	NUM
ejpam-816	353	16	sector	sector	NOUN
ejpam-816	353	17	(	(	PUNCT
ejpam-816	353	18	0	0	NUM
ejpam-816	353	19	,	,	PUNCT
ejpam-816	353	20	3	3	NUM
ejpam-816	353	21	2	2	NUM
ejpam-816	353	22	π	π	NOUN
ejpam-816	353	23	)	)	PUNCT
ejpam-816	353	24	.	.	PUNCT
ejpam-816	354	1	there	there	PRON
ejpam-816	354	2	are	be	VERB
ejpam-816	354	3	three	three	NUM
ejpam-816	354	4	overlapping	overlap	VERB
ejpam-816	354	5	exponentially	exponentially	ADV
ejpam-816	354	6	large	large	ADJ
ejpam-816	354	7	sectors	sector	NOUN
ejpam-816	354	8	|arg(zeπir/4)|	|arg(zeπir/4)|	VERB
ejpam-816	354	9	<	<	X
ejpam-816	354	10	7	7	NUM
ejpam-816	354	11	16	16	NUM
ejpam-816	354	12	π	π	NOUN
ejpam-816	354	13	(	(	PUNCT
ejpam-816	354	14	r	r	NOUN
ejpam-816	354	15	=	=	SYM
ejpam-816	354	16	0,1,2	0,1,2	NUM
ejpam-816	354	17	)	)	PUNCT
ejpam-816	354	18	,	,	PUNCT
ejpam-816	354	19	with	with	ADP
ejpam-816	354	20	the	the	DET
ejpam-816	354	21	expansion	expansion	NOUN
ejpam-816	354	22	in	in	ADP
ejpam-816	354	23	the	the	DET
ejpam-816	354	24	sector	sector	NOUN
ejpam-816	354	25	(	(	PUNCT
ejpam-816	354	26	7	7	NUM
ejpam-816	354	27	16	16	NUM
ejpam-816	354	28	π	π	NOUN
ejpam-816	354	29	,	,	PUNCT
ejpam-816	354	30	17	17	NUM
ejpam-816	354	31	16	16	NUM
ejpam-816	354	32	π	π	NOUN
ejpam-816	354	33	)	)	PUNCT
ejpam-816	354	34	being	be	AUX
ejpam-816	354	35	exponentially	exponentially	ADV
ejpam-816	354	36	small	small	ADJ
ejpam-816	354	37	.	.	PUNCT
ejpam-816	355	1	it	it	PRON
ejpam-816	355	2	can	can	AUX
ejpam-816	355	3	be	be	AUX
ejpam-816	355	4	seen	see	VERB
ejpam-816	355	5	that	that	SCONJ
ejpam-816	355	6	there	there	PRON
ejpam-816	355	7	are	be	VERB
ejpam-816	355	8	sectors	sector	NOUN
ejpam-816	355	9	in	in	ADP
ejpam-816	355	10	which	which	PRON
ejpam-816	355	11	j2(z	j2(z	NUM
ejpam-816	355	12	)	)	PUNCT
ejpam-816	355	13	consists	consist	VERB
ejpam-816	355	14	of	of	ADP
ejpam-816	355	15	either	either	DET
ejpam-816	355	16	one	one	NUM
ejpam-816	355	17	,	,	PUNCT
ejpam-816	355	18	two	two	NUM
ejpam-816	355	19	or	or	CCONJ
ejpam-816	355	20	three	three	NUM
ejpam-816	356	1	exponentially	exponentially	ADV
ejpam-816	356	2	large	large	ADJ
ejpam-816	356	3	expansions	expansion	NOUN
ejpam-816	356	4	.	.	PUNCT
ejpam-816	357	1	in	in	ADP
ejpam-816	357	2	fig	fig	NOUN
ejpam-816	357	3	.	.	PUNCT
ejpam-816	358	1	1(b	1(b	NUM
ejpam-816	358	2	)	)	PUNCT
ejpam-816	358	3	,	,	PUNCT
ejpam-816	358	4	m	m	VERB
ejpam-816	358	5	=	=	NOUN
ejpam-816	358	6	1	1	NUM
ejpam-816	358	7	2	2	NUM
ejpam-816	358	8	(	(	PUNCT
ejpam-816	358	9	κ	κ	X
ejpam-816	358	10	=	=	SYM
ejpam-816	358	11	3	3	NUM
ejpam-816	358	12	4	4	NUM
ejpam-816	358	13	)	)	PUNCT
ejpam-816	358	14	so	so	SCONJ
ejpam-816	358	15	that	that	SCONJ
ejpam-816	358	16	the	the	DET
ejpam-816	358	17	symmetry	symmetry	NOUN
ejpam-816	358	18	line	line	NOUN
ejpam-816	358	19	is	be	AUX
ejpam-816	358	20	the	the	DET
ejpam-816	358	21	imaginary	imaginary	ADJ
ejpam-816	358	22	z	z	NOUN
ejpam-816	358	23	-	-	PUNCT
ejpam-816	358	24	axis	axis	NOUN
ejpam-816	358	25	and	and	CCONJ
ejpam-816	358	26	the	the	DET
ejpam-816	358	27	algebraic	algebraic	ADJ
ejpam-816	358	28	expansions	expansion	NOUN
ejpam-816	358	29	cancel	cancel	VERB
ejpam-816	358	30	in	in	ADP
ejpam-816	358	31	the	the	DET
ejpam-816	358	32	upper	upper	ADJ
ejpam-816	358	33	half	half	ADJ
ejpam-816	358	34	-	-	PUNCT
ejpam-816	358	35	plane	plane	NOUN
ejpam-816	358	36	.	.	PUNCT
ejpam-816	359	1	there	there	PRON
ejpam-816	359	2	are	be	VERB
ejpam-816	359	3	again	again	ADV
ejpam-816	359	4	three	three	NUM
ejpam-816	359	5	exponentially	exponentially	ADV
ejpam-816	359	6	large	large	ADJ
ejpam-816	359	7	sectors	sector	NOUN
ejpam-816	359	8	|arg(zeπir/2)|	|arg(zeπir/2)|	X
ejpam-816	359	9	<	<	X
ejpam-816	359	10	3	3	NUM
ejpam-816	359	11	8	8	NUM
ejpam-816	359	12	π	π	NOUN
ejpam-816	359	13	(	(	PUNCT
ejpam-816	359	14	r	r	NOUN
ejpam-816	359	15	=	=	SYM
ejpam-816	359	16	0,1,2	0,1,2	NUM
ejpam-816	359	17	)	)	PUNCT
ejpam-816	359	18	,	,	PUNCT
ejpam-816	359	19	which	which	PRON
ejpam-816	359	20	overlap	overlap	VERB
ejpam-816	359	21	to	to	PART
ejpam-816	359	22	produce	produce	VERB
ejpam-816	359	23	sectors	sector	NOUN
ejpam-816	359	24	containing	contain	VERB
ejpam-816	359	25	either	either	CCONJ
ejpam-816	359	26	one	one	NUM
ejpam-816	359	27	or	or	CCONJ
ejpam-816	359	28	two	two	NUM
ejpam-816	359	29	exponentially	exponentially	ADV
ejpam-816	359	30	large	large	ADJ
ejpam-816	359	31	expansions	expansion	NOUN
ejpam-816	359	32	,	,	PUNCT
ejpam-816	359	33	with	with	ADP
ejpam-816	359	34	the	the	DET
ejpam-816	359	35	exponentially	exponentially	ADV
ejpam-816	359	36	small	small	ADJ
ejpam-816	359	37	sector	sector	NOUN
ejpam-816	359	38	now	now	ADV
ejpam-816	359	39	being	be	AUX
ejpam-816	359	40	(	(	PUNCT
ejpam-816	359	41	3	3	NUM
ejpam-816	359	42	8	8	NUM
ejpam-816	359	43	π	π	NOUN
ejpam-816	359	44	,	,	PUNCT
ejpam-816	359	45	5	5	NUM
ejpam-816	359	46	8	8	NUM
ejpam-816	359	47	π	π	NOUN
ejpam-816	359	48	)	)	PUNCT
ejpam-816	359	49	.	.	PUNCT
ejpam-816	360	1	in	in	ADP
ejpam-816	360	2	fig	fig	NOUN
ejpam-816	360	3	.	.	PUNCT
ejpam-816	361	1	1(c	1(c	NUM
ejpam-816	361	2	)	)	PUNCT
ejpam-816	361	3	,	,	PUNCT
ejpam-816	361	4	m	m	VERB
ejpam-816	361	5	=	=	NOUN
ejpam-816	361	6	3	3	NUM
ejpam-816	361	7	4	4	NUM
ejpam-816	361	8	(	(	PUNCT
ejpam-816	361	9	κ	κ	NOUN
ejpam-816	361	10	=	=	SYM
ejpam-816	361	11	5	5	NUM
ejpam-816	361	12	8	8	NUM
ejpam-816	361	13	)	)	PUNCT
ejpam-816	361	14	so	so	SCONJ
ejpam-816	361	15	that	that	SCONJ
ejpam-816	361	16	the	the	DET
ejpam-816	361	17	symmetry	symmetry	NOUN
ejpam-816	361	18	line	line	NOUN
ejpam-816	361	19	is	be	AUX
ejpam-816	361	20	arg	arg	NOUN
ejpam-816	361	21	z	z	NOUN
ejpam-816	361	22	=	=	SYM
ejpam-816	361	23	1	1	NUM
ejpam-816	361	24	4	4	NUM
ejpam-816	361	25	π	π	NOUN
ejpam-816	361	26	,	,	PUNCT
ejpam-816	361	27	−3	−3	PROPN
ejpam-816	361	28	4	4	NUM
ejpam-816	361	29	π	π	NOUN
ejpam-816	361	30	and	and	CCONJ
ejpam-816	361	31	the	the	DET
ejpam-816	361	32	algebraic	algebraic	ADJ
ejpam-816	361	33	expansions	expansion	NOUN
ejpam-816	361	34	cancel	cancel	VERB
ejpam-816	361	35	in	in	ADP
ejpam-816	361	36	the	the	DET
ejpam-816	361	37	sector	sector	NOUN
ejpam-816	361	38	(	(	PUNCT
ejpam-816	361	39	0	0	NUM
ejpam-816	361	40	,	,	PUNCT
ejpam-816	361	41	1	1	NUM
ejpam-816	361	42	2	2	NUM
ejpam-816	361	43	π	π	NOUN
ejpam-816	361	44	)	)	PUNCT
ejpam-816	361	45	.	.	PUNCT
ejpam-816	362	1	the	the	DET
ejpam-816	362	2	exponentially	exponentially	ADV
ejpam-816	362	3	large	large	ADJ
ejpam-816	362	4	sectors	sector	NOUN
ejpam-816	362	5	|arg(ze3πir/4)|	|arg(ze3πir/4)|	X
ejpam-816	362	6	<	<	X
ejpam-816	362	7	5	5	NUM
ejpam-816	362	8	16	16	NUM
ejpam-816	362	9	π	π	NOUN
ejpam-816	362	10	(	(	PUNCT
ejpam-816	362	11	r	r	NOUN
ejpam-816	362	12	=	=	SYM
ejpam-816	362	13	0,1,2	0,1,2	NUM
ejpam-816	362	14	)	)	PUNCT
ejpam-816	362	15	only	only	ADV
ejpam-816	362	16	overlap	overlap	NOUN
ejpam-816	362	17	in	in	ADP
ejpam-816	362	18	the	the	DET
ejpam-816	362	19	sector	sector	NOUN
ejpam-816	362	20	(	(	PUNCT
ejpam-816	362	21	3	3	NUM
ejpam-816	362	22	16	16	NUM
ejpam-816	362	23	π	π	NOUN
ejpam-816	362	24	,	,	PUNCT
ejpam-816	362	25	5	5	NUM
ejpam-816	362	26	16	16	NUM
ejpam-816	362	27	π	π	NOUN
ejpam-816	362	28	)	)	PUNCT
ejpam-816	362	29	,	,	PUNCT
ejpam-816	362	30	with	with	ADP
ejpam-816	362	31	the	the	DET
ejpam-816	362	32	behaviour	behaviour	NOUN
ejpam-816	362	33	in	in	ADP
ejpam-816	362	34	the	the	DET
ejpam-816	362	35	sectors	sector	NOUN
ejpam-816	362	36	(	(	PUNCT
ejpam-816	362	37	13	13	NUM
ejpam-816	362	38	16	16	NUM
ejpam-816	362	39	π	π	NOUN
ejpam-816	362	40	,	,	PUNCT
ejpam-816	362	41	15	15	NUM
ejpam-816	362	42	16	16	NUM
ejpam-816	362	43	π	π	NOUN
ejpam-816	362	44	)	)	PUNCT
ejpam-816	362	45	and	and	CCONJ
ejpam-816	362	46	(	(	PUNCT
ejpam-816	362	47	−	−	PROPN
ejpam-816	362	48	7	7	NUM
ejpam-816	362	49	16	16	NUM
ejpam-816	362	50	π,−	π,−	NOUN
ejpam-816	362	51	5	5	NUM
ejpam-816	362	52	16	16	NUM
ejpam-816	362	53	π	π	NOUN
ejpam-816	362	54	)	)	PUNCT
ejpam-816	362	55	consisting	consist	VERB
ejpam-816	362	56	of	of	ADP
ejpam-816	362	57	algebraic	algebraic	ADJ
ejpam-816	362	58	and	and	CCONJ
ejpam-816	362	59	exponentially	exponentially	ADV
ejpam-816	362	60	small	small	ADJ
ejpam-816	362	61	expansions	expansion	NOUN
ejpam-816	362	62	.	.	PUNCT
ejpam-816	363	1	finally	finally	ADV
ejpam-816	363	2	in	in	ADP
ejpam-816	363	3	fig	fig	NOUN
ejpam-816	363	4	.	.	PUNCT
ejpam-816	364	1	1(d	1(d	NUM
ejpam-816	364	2	)	)	PUNCT
ejpam-816	364	3	,	,	PUNCT
ejpam-816	364	4	m	m	VERB
ejpam-816	364	5	=	=	SYM
ejpam-816	364	6	1	1	NUM
ejpam-816	364	7	(	(	PUNCT
ejpam-816	364	8	κ	κ	NOUN
ejpam-816	364	9	=	=	SYM
ejpam-816	364	10	1	1	NUM
ejpam-816	364	11	2	2	NUM
ejpam-816	364	12	)	)	PUNCT
ejpam-816	364	13	so	so	SCONJ
ejpam-816	364	14	that	that	SCONJ
ejpam-816	364	15	the	the	DET
ejpam-816	364	16	symmetry	symmetry	NOUN
ejpam-816	364	17	line	line	NOUN
ejpam-816	364	18	is	be	AUX
ejpam-816	364	19	the	the	DET
ejpam-816	364	20	real	real	ADJ
ejpam-816	364	21	z	z	NOUN
ejpam-816	364	22	-	-	PUNCT
ejpam-816	364	23	axis	axis	NOUN
ejpam-816	364	24	and	and	CCONJ
ejpam-816	364	25	,	,	PUNCT
ejpam-816	364	26	by	by	ADP
ejpam-816	364	27	(	(	PUNCT
ejpam-816	364	28	34	34	NUM
ejpam-816	364	29	)	)	PUNCT
ejpam-816	364	30	,	,	PUNCT
ejpam-816	364	31	there	there	PRON
ejpam-816	364	32	is	be	VERB
ejpam-816	364	33	no	no	PRON
ejpam-816	364	34	longer	long	ADV
ejpam-816	364	35	a	a	DET
ejpam-816	364	36	sector	sector	NOUN
ejpam-816	364	37	in	in	ADP
ejpam-816	364	38	which	which	PRON
ejpam-816	364	39	the	the	DET
ejpam-816	364	40	algebraic	algebraic	ADJ
ejpam-816	364	41	expansions	expansion	NOUN
ejpam-816	364	42	cancel	cancel	VERB
ejpam-816	364	43	.	.	PUNCT
ejpam-816	365	1	in	in	ADP
ejpam-816	365	2	this	this	DET
ejpam-816	365	3	case	case	NOUN
ejpam-816	365	4	,	,	PUNCT
ejpam-816	365	5	there	there	PRON
ejpam-816	365	6	are	be	VERB
ejpam-816	365	7	two	two	NUM
ejpam-816	365	8	non	non	ADJ
ejpam-816	365	9	-	-	ADJ
ejpam-816	365	10	overlapping	overlapping	ADJ
ejpam-816	365	11	exponentially	exponentially	ADV
ejpam-816	365	12	large	large	ADJ
ejpam-816	365	13	sectors	sector	NOUN
ejpam-816	365	14	given	give	VERB
ejpam-816	365	15	by	by	ADP
ejpam-816	365	16	|arg(zeπir	|arg(zeπir	PROPN
ejpam-816	365	17	)	)	PUNCT
ejpam-816	366	1	|	|	CCONJ
ejpam-816	366	2	<	<	X
ejpam-816	366	3	1	1	NUM
ejpam-816	366	4	4	4	NUM
ejpam-816	366	5	π	π	NOUN
ejpam-816	366	6	(	(	PUNCT
ejpam-816	366	7	r	r	NOUN
ejpam-816	366	8	=	=	SYM
ejpam-816	366	9	0,1	0,1	NUM
ejpam-816	366	10	)	)	PUNCT
ejpam-816	366	11	,	,	PUNCT
ejpam-816	366	12	with	with	ADP
ejpam-816	366	13	the	the	DET
ejpam-816	366	14	behaviour	behaviour	NOUN
ejpam-816	366	15	of	of	ADP
ejpam-816	366	16	j2(z	j2(z	NOUN
ejpam-816	366	17	)	)	PUNCT
ejpam-816	366	18	in	in	ADP
ejpam-816	366	19	the	the	DET
ejpam-816	366	20	sectors	sector	NOUN
ejpam-816	366	21	(	(	PUNCT
ejpam-816	366	22	1	1	NUM
ejpam-816	366	23	4	4	NUM
ejpam-816	366	24	π	π	NOUN
ejpam-816	366	25	,	,	PUNCT
ejpam-816	366	26	3	3	NUM
ejpam-816	366	27	4	4	NUM
ejpam-816	366	28	π	π	NOUN
ejpam-816	366	29	)	)	PUNCT
ejpam-816	366	30	and	and	CCONJ
ejpam-816	366	31	(	(	PUNCT
ejpam-816	366	32	−3	−3	NOUN
ejpam-816	366	33	4	4	NUM
ejpam-816	366	34	π,−1	π,−1	NOUN
ejpam-816	366	35	4	4	NUM
ejpam-816	366	36	π	π	NOUN
ejpam-816	366	37	)	)	PUNCT
ejpam-816	366	38	consisting	consist	VERB
ejpam-816	366	39	of	of	ADP
ejpam-816	366	40	algebraic	algebraic	ADJ
ejpam-816	366	41	and	and	CCONJ
ejpam-816	366	42	exponentially	exponentially	ADV
ejpam-816	366	43	small	small	ADJ
ejpam-816	366	44	expansions	expansion	NOUN
ejpam-816	366	45	.	.	PUNCT
ejpam-816	367	1	if	if	SCONJ
ejpam-816	367	2	the	the	DET
ejpam-816	367	3	parameters	parameter	NOUN
ejpam-816	367	4	ν1	ν1	NOUN
ejpam-816	367	5	and	and	CCONJ
ejpam-816	367	6	ν2	ν2	NOUN
ejpam-816	367	7	are	be	AUX
ejpam-816	367	8	such	such	ADJ
ejpam-816	367	9	that	that	DET
ejpam-816	367	10	b1	b1	NOUN
ejpam-816	367	11	=	=	SYM
ejpam-816	367	12	0	0	NUM
ejpam-816	367	13	,	,	PUNCT
ejpam-816	367	14	then	then	ADV
ejpam-816	367	15	the	the	DET
ejpam-816	367	16	number	number	NOUN
ejpam-816	367	17	of	of	ADP
ejpam-816	367	18	exponentially	exponentially	ADV
ejpam-816	367	19	large	large	ADJ
ejpam-816	367	20	sectors	sector	NOUN
ejpam-816	367	21	decreases	decrease	VERB
ejpam-816	367	22	by	by	ADP
ejpam-816	367	23	one	one	NUM
ejpam-816	367	24	.	.	PUNCT
ejpam-816	368	1	we	we	PRON
ejpam-816	368	2	now	now	ADV
ejpam-816	368	3	consider	consider	VERB
ejpam-816	368	4	the	the	DET
ejpam-816	368	5	asymptotic	asymptotic	ADJ
ejpam-816	368	6	expansion	expansion	NOUN
ejpam-816	368	7	of	of	ADP
ejpam-816	368	8	j2(z	j2(z	NOUN
ejpam-816	368	9	)	)	PUNCT
ejpam-816	368	10	in	in	ADP
ejpam-816	368	11	(	(	PUNCT
ejpam-816	368	12	42	42	NUM
ejpam-816	368	13	)	)	PUNCT
ejpam-816	368	14	when	when	SCONJ
ejpam-816	368	15	µ1	µ1	PROPN
ejpam-816	368	16	=	=	SYM
ejpam-816	368	17	µ2	µ2	NOUN
ejpam-816	368	18	=	=	NOUN
ejpam-816	368	19	4	4	NUM
ejpam-816	368	20	in	in	ADP
ejpam-816	368	21	some	some	DET
ejpam-816	368	22	specific	specific	ADJ
ejpam-816	368	23	cases	case	NOUN
ejpam-816	368	24	in	in	ADP
ejpam-816	368	25	more	more	ADJ
ejpam-816	368	26	detail	detail	NOUN
ejpam-816	368	27	.	.	PUNCT
ejpam-816	369	1	we	we	PRON
ejpam-816	369	2	first	first	ADV
ejpam-816	369	3	take	take	VERB
ejpam-816	369	4	m=	m=	PUNCT
ejpam-816	369	5	1	1	NUM
ejpam-816	369	6	2	2	NUM
ejpam-816	369	7	(	(	PUNCT
ejpam-816	369	8	κ	κ	X
ejpam-816	369	9	=	=	SYM
ejpam-816	369	10	3	3	NUM
ejpam-816	369	11	4	4	NUM
ejpam-816	369	12	)	)	PUNCT
ejpam-816	369	13	so	so	SCONJ
ejpam-816	369	14	that	that	SCONJ
ejpam-816	369	15	from	from	ADP
ejpam-816	369	16	(	(	PUNCT
ejpam-816	369	17	43	43	NUM
ejpam-816	369	18	)	)	PUNCT
ejpam-816	369	19	j2(z	j2(z	PROPN
ejpam-816	369	20	)	)	PUNCT
ejpam-816	369	21	=	=	SYM
ejpam-816	369	22	2ψ0(z)−	2ψ0(z)−	NUM
ejpam-816	369	23	b1	b1	NOUN
ejpam-816	369	24	2ψ0(ze	2ψ0(ze	NUM
ejpam-816	369	25	1	1	NUM
ejpam-816	369	26	2	2	NUM
ejpam-816	369	27	πi	πi	CCONJ
ejpam-816	369	28	)	)	PUNCT
ejpam-816	369	29	+	+	NUM
ejpam-816	369	30	b2	b2	NOUN
ejpam-816	369	31	2ψ0(ze∓πi	2ψ0(ze∓πi	NUM
ejpam-816	369	32	)	)	PUNCT
ejpam-816	369	33	,	,	PUNCT
ejpam-816	369	34	(	(	PUNCT
ejpam-816	369	35	46	46	NUM
ejpam-816	369	36	)	)	PUNCT
ejpam-816	369	37	where	where	SCONJ
ejpam-816	369	38	we	we	PRON
ejpam-816	369	39	choose	choose	VERB
ejpam-816	369	40	the	the	DET
ejpam-816	369	41	upper	upper	ADJ
ejpam-816	369	42	or	or	CCONJ
ejpam-816	369	43	lower	low	ADJ
ejpam-816	369	44	sign	sign	NOUN
ejpam-816	369	45	according	accord	VERB
ejpam-816	369	46	as	as	ADP
ejpam-816	369	47	arg	arg	NOUN
ejpam-816	369	48	z	z	NOUN
ejpam-816	369	49	>	>	X
ejpam-816	369	50	0	0	NUM
ejpam-816	369	51	or	or	CCONJ
ejpam-816	369	52	arg	arg	NOUN
ejpam-816	369	53	z	z	NOUN
ejpam-816	369	54	<	<	X
ejpam-816	369	55	0	0	NUM
ejpam-816	369	56	,	,	PUNCT
ejpam-816	369	57	respectively	respectively	ADV
ejpam-816	369	58	.	.	PUNCT
ejpam-816	370	1	recalling	recall	VERB
ejpam-816	370	2	from	from	ADP
ejpam-816	370	3	(	(	PUNCT
ejpam-816	370	4	19	19	NUM
ejpam-816	370	5	)	)	PUNCT
ejpam-816	370	6	that	that	PRON
ejpam-816	370	7	the	the	DET
ejpam-816	370	8	stokes	stokes	PROPN
ejpam-816	370	9	lines	line	NOUN
ejpam-816	370	10	for	for	ADP
ejpam-816	370	11	the	the	DET
ejpam-816	370	12	exponential	exponential	ADJ
ejpam-816	370	13	expansion	expansion	NOUN
ejpam-816	370	14	ep	ep	PROPN
ejpam-816	370	15	,	,	PUNCT
ejpam-816	370	16	q(z	q(z	PROPN
ejpam-816	370	17	)	)	PUNCT
ejpam-816	370	18	are	be	AUX
ejpam-816	370	19	given	give	VERB
ejpam-816	370	20	by	by	ADP
ejpam-816	370	21	arg	arg	NOUN
ejpam-816	370	22	z	z	NOUN
ejpam-816	370	23	=	=	PUNCT
ejpam-816	370	24	±πκ	±πκ	NOUN
ejpam-816	370	25	,	,	PUNCT
ejpam-816	370	26	we	we	PRON
ejpam-816	370	27	see	see	VERB
ejpam-816	370	28	that	that	SCONJ
ejpam-816	370	29	the	the	DET
ejpam-816	370	30	stokes	stokes	PROPN
ejpam-816	370	31	lines	line	NOUN
ejpam-816	370	32	associated	associate	VERB
ejpam-816	370	33	with	with	ADP
ejpam-816	370	34	e2,0(ze	e2,0(ze	NUM
ejpam-816	370	35	1	1	NUM
ejpam-816	370	36	2	2	NUM
ejpam-816	370	37	πir	πir	NOUN
ejpam-816	370	38	)	)	PUNCT
ejpam-816	370	39	(	(	PUNCT
ejpam-816	370	40	r	r	NOUN
ejpam-816	370	41	=	=	SYM
ejpam-816	370	42	0,1,2	0,1,2	X
ejpam-816	370	43	)	)	PUNCT
ejpam-816	370	44	are	be	AUX
ejpam-816	370	45	the	the	DET
ejpam-816	370	46	rays	ray	NOUN
ejpam-816	370	47	arg	arg	VERB
ejpam-816	370	48	z	z	NOUN
ejpam-816	370	49	=	=	SYM
ejpam-816	370	50	±3	±3	ADJ
ejpam-816	370	51	4	4	NUM
ejpam-816	370	52	π	π	NOUN
ejpam-816	370	53	,	,	PUNCT
ejpam-816	370	54	±1	±1	VERB
ejpam-816	370	55	4	4	NUM
ejpam-816	370	56	π	π	NOUN
ejpam-816	370	57	;	;	PUNCT
ejpam-816	370	58	see	see	VERB
ejpam-816	370	59	fig	fig	NOUN
ejpam-816	370	60	.	.	PUNCT
ejpam-816	371	1	1(b	1(b	NUM
ejpam-816	371	2	)	)	PUNCT
ejpam-816	371	3	.	.	PUNCT
ejpam-816	372	1	taking	take	VERB
ejpam-816	372	2	into	into	ADP
ejpam-816	372	3	account	account	NOUN
ejpam-816	372	4	these	these	DET
ejpam-816	372	5	stokes	stoke	NOUN
ejpam-816	372	6	lines	line	NOUN
ejpam-816	372	7	and	and	CCONJ
ejpam-816	372	8	the	the	DET
ejpam-816	372	9	fact	fact	NOUN
ejpam-816	372	10	that	that	SCONJ
ejpam-816	372	11	the	the	DET
ejpam-816	372	12	algebraic	algebraic	ADJ
ejpam-816	372	13	expansions	expansion	NOUN
ejpam-816	372	14	all	all	PRON
ejpam-816	372	15	cancel	cancel	VERB
ejpam-816	372	16	in	in	ADP
ejpam-816	372	17	the	the	DET
ejpam-816	372	18	upper	upper	ADJ
ejpam-816	372	19	half	half	ADJ
ejpam-816	372	20	-	-	PUNCT
ejpam-816	372	21	plane	plane	NOUN
ejpam-816	372	22	by	by	ADP
ejpam-816	372	23	(	(	PUNCT
ejpam-816	372	24	34	34	NUM
ejpam-816	372	25	)	)	PUNCT
ejpam-816	372	26	,	,	PUNCT
ejpam-816	372	27	we	we	PRON
ejpam-816	372	28	find	find	VERB
ejpam-816	372	29	that	that	SCONJ
ejpam-816	372	30	the	the	DET
ejpam-816	372	31	exponential	exponential	ADJ
ejpam-816	372	32	expansion	expansion	NOUN
ejpam-816	372	33	of	of	ADP
ejpam-816	372	34	j2(z	j2(z	NOUN
ejpam-816	372	35	)	)	PUNCT
ejpam-816	372	36	in	in	ADP
ejpam-816	372	37	(	(	PUNCT
ejpam-816	372	38	46	46	NUM
ejpam-816	372	39	)	)	PUNCT
ejpam-816	372	40	is	be	AUX
ejpam-816	372	41	then	then	ADV
ejpam-816	372	42	given	give	VERB
ejpam-816	372	43	by	by	ADP
ejpam-816	372	44	e2,0(z	e2,0(z	PROPN
ejpam-816	372	45	)	)	PUNCT
ejpam-816	373	1	+	+	NUM
ejpam-816	373	2	b2	b2	PROPN
ejpam-816	373	3	e2,0(ze−πi	e2,0(ze−πi	NOUN
ejpam-816	373	4	)	)	PUNCT
ejpam-816	373	5	in	in	ADP
ejpam-816	373	6	(	(	PUNCT
ejpam-816	373	7	1	1	NUM
ejpam-816	373	8	4	4	NUM
ejpam-816	373	9	π	π	NOUN
ejpam-816	373	10	,	,	PUNCT
ejpam-816	373	11	1	1	NUM
ejpam-816	373	12	2	2	NUM
ejpam-816	373	13	π	π	NOUN
ejpam-816	373	14	]	]	X
ejpam-816	373	15	e2,0(z)−	e2,0(z)−	PROPN
ejpam-816	373	16	b1	b1	NOUN
ejpam-816	373	17	e2,0(ze	e2,0(ze	NUM
ejpam-816	373	18	1	1	NUM
ejpam-816	373	19	2	2	NUM
ejpam-816	373	20	πi	πi	CCONJ
ejpam-816	373	21	)	)	PUNCT
ejpam-816	373	22	in	in	ADP
ejpam-816	373	23	(	(	PUNCT
ejpam-816	373	24	−1	−1	NOUN
ejpam-816	373	25	4	4	NUM
ejpam-816	373	26	π	π	NOUN
ejpam-816	373	27	,	,	PUNCT
ejpam-816	373	28	1	1	NUM
ejpam-816	373	29	4	4	NUM
ejpam-816	373	30	π	π	NOUN
ejpam-816	373	31	)	)	PUNCT
ejpam-816	373	32	e2,0(z)−	e2,0(z)−	PROPN
ejpam-816	373	33	b1	b1	NOUN
ejpam-816	373	34	e2,0(ze	e2,0(ze	NUM
ejpam-816	373	35	1	1	NUM
ejpam-816	373	36	2	2	NUM
ejpam-816	373	37	πi	πi	CCONJ
ejpam-816	373	38	)	)	PUNCT
ejpam-816	373	39	+	+	NUM
ejpam-816	373	40	b2	b2	NOUN
ejpam-816	373	41	e2,0(zeπi	e2,0(zeπi	VERB
ejpam-816	373	42	)	)	PUNCT
ejpam-816	373	43	in	in	ADP
ejpam-816	373	44	[	[	X
ejpam-816	373	45	−1	−1	NOUN
ejpam-816	373	46	2	2	NUM
ejpam-816	373	47	π,−1	π,−1	PROPN
ejpam-816	373	48	4	4	NUM
ejpam-816	373	49	π	π	NOUN
ejpam-816	373	50	)	)	PUNCT
ejpam-816	373	51	,	,	PUNCT
ejpam-816	373	52	as	as	ADP
ejpam-816	373	53	|z|	|z|	NOUN
ejpam-816	373	54	→	→	SYM
ejpam-816	373	55	∞	∞	NUM
ejpam-816	373	56	in	in	ADP
ejpam-816	373	57	the	the	DET
ejpam-816	373	58	right	right	ADJ
ejpam-816	373	59	-	-	PUNCT
ejpam-816	373	60	half	half	NOUN
ejpam-816	373	61	plane	plane	NOUN
ejpam-816	373	62	.	.	PUNCT
ejpam-816	374	1	the	the	DET
ejpam-816	374	2	expansion	expansion	NOUN
ejpam-816	374	3	e2,0(z	e2,0(z	PROPN
ejpam-816	374	4	)	)	PUNCT
ejpam-816	374	5	is	be	AUX
ejpam-816	374	6	obtained	obtain	VERB
ejpam-816	374	7	from	from	ADP
ejpam-816	374	8	(	(	PUNCT
ejpam-816	374	9	8)	8)	NUM
ejpam-816	374	10	with	with	ADP
ejpam-816	374	11	z	z	NOUN
ejpam-816	374	12	=	=	SYM
ejpam-816	374	13	3	3	NUM
ejpam-816	374	14	8	8	NUM
ejpam-816	374	15	z4/3	z4/3	NUM
ejpam-816	374	16	and	and	CCONJ
ejpam-816	374	17	ϑ	ϑ	X
ejpam-816	374	18	=	=	SYM
ejpam-816	374	19	1	1	NUM
ejpam-816	374	20	4	4	NUM
ejpam-816	374	21	(	(	PUNCT
ejpam-816	374	22	ν1	ν1	NOUN
ejpam-816	374	23	+	+	CCONJ
ejpam-816	374	24	ν2)−	ν2)−	PROPN
ejpam-816	374	25	1	1	NUM
ejpam-816	374	26	.	.	PUNCT
ejpam-816	375	1	the	the	DET
ejpam-816	375	2	coefficient	coefficient	NOUN
ejpam-816	375	3	a0	a0	PROPN
ejpam-816	375	4	is	be	AUX
ejpam-816	375	5	specified	specify	VERB
ejpam-816	375	6	by	by	ADP
ejpam-816	375	7	(	(	PUNCT
ejpam-816	375	8	24	24	NUM
ejpam-816	375	9	)	)	PUNCT
ejpam-816	375	10	with	with	ADP
ejpam-816	375	11	the	the	DET
ejpam-816	375	12	coefficients	coefficient	NOUN
ejpam-816	375	13	a	a	DET
ejpam-816	375	14	j	j	PROPN
ejpam-816	375	15	(	(	PUNCT
ejpam-816	375	16	j	j	PROPN
ejpam-816	375	17	≥	≥	NUM
ejpam-816	375	18	1	1	NUM
ejpam-816	375	19	)	)	PUNCT
ejpam-816	375	20	being	be	AUX
ejpam-816	375	21	determined	determine	VERB
ejpam-816	375	22	in	in	ADP
ejpam-816	375	23	specific	specific	ADJ
ejpam-816	375	24	cases	case	NOUN
ejpam-816	375	25	by	by	ADP
ejpam-816	375	26	the	the	DET
ejpam-816	375	27	algorithm	algorithm	NOUN
ejpam-816	375	28	described	describe	VERB
ejpam-816	375	29	in	in	ADP
ejpam-816	375	30	appendix	appendix	PROPN
ejpam-816	375	31	a.	a.	NOUN
ejpam-816	375	32	the	the	DET
ejpam-816	375	33	expansion	expansion	NOUN
ejpam-816	375	34	of	of	ADP
ejpam-816	375	35	j2(z	j2(z	NOUN
ejpam-816	375	36	)	)	PUNCT
ejpam-816	375	37	is	be	AUX
ejpam-816	375	38	exponentially	exponentially	ADV
ejpam-816	375	39	small	small	ADJ
ejpam-816	375	40	in	in	ADP
ejpam-816	375	41	the	the	DET
ejpam-816	375	42	sector	sector	NOUN
ejpam-816	375	43	(	(	PUNCT
ejpam-816	375	44	3	3	NUM
ejpam-816	375	45	8	8	NUM
ejpam-816	375	46	π	π	NOUN
ejpam-816	375	47	,	,	PUNCT
ejpam-816	375	48	5	5	NUM
ejpam-816	375	49	8	8	NUM
ejpam-816	375	50	π	π	NOUN
ejpam-816	375	51	)	)	PUNCT
ejpam-816	375	52	.	.	PUNCT
ejpam-816	376	1	although	although	SCONJ
ejpam-816	376	2	there	there	PRON
ejpam-816	376	3	is	be	VERB
ejpam-816	376	4	an	an	DET
ejpam-816	376	5	algebraic	algebraic	ADJ
ejpam-816	376	6	expansion	expansion	NOUN
ejpam-816	376	7	present	present	ADJ
ejpam-816	376	8	in	in	ADP
ejpam-816	376	9	the	the	DET
ejpam-816	376	10	lower	low	ADJ
ejpam-816	376	11	half	half	ADJ
ejpam-816	376	12	-	-	PUNCT
ejpam-816	376	13	plane	plane	NOUN
ejpam-816	376	14	,	,	PUNCT
ejpam-816	376	15	we	we	PRON
ejpam-816	376	16	do	do	AUX
ejpam-816	376	17	not	not	PART
ejpam-816	376	18	consider	consider	VERB
ejpam-816	376	19	its	its	PRON
ejpam-816	376	20	contribution	contribution	NOUN
ejpam-816	376	21	here	here	ADV
ejpam-816	376	22	as	as	SCONJ
ejpam-816	376	23	it	it	PRON
ejpam-816	376	24	is	be	AUX
ejpam-816	376	25	subdominant	subdominant	ADJ
ejpam-816	376	26	throughout	throughout	ADP
ejpam-816	376	27	this	this	DET
ejpam-816	376	28	domain	domain	NOUN
ejpam-816	376	29	.	.	PUNCT
ejpam-816	377	1	the	the	DET
ejpam-816	377	2	exponential	exponential	ADJ
ejpam-816	377	3	expansion	expansion	NOUN
ejpam-816	377	4	in	in	ADP
ejpam-816	377	5	the	the	DET
ejpam-816	377	6	left	left	ADJ
ejpam-816	377	7	-	-	PUNCT
ejpam-816	377	8	hand	hand	NOUN
ejpam-816	377	9	half	half	ADJ
ejpam-816	377	10	-	-	PUNCT
ejpam-816	377	11	plane	plane	NOUN
ejpam-816	377	12	can	can	AUX
ejpam-816	377	13	be	be	AUX
ejpam-816	377	14	obtained	obtain	VERB
ejpam-816	377	15	via	via	ADP
ejpam-816	377	16	(	(	PUNCT
ejpam-816	377	17	45	45	NUM
ejpam-816	377	18	)	)	PUNCT
ejpam-816	377	19	.	.	PUNCT
ejpam-816	378	1	for	for	ADP
ejpam-816	378	2	our	our	PRON
ejpam-816	378	3	second	second	ADJ
ejpam-816	378	4	case	case	NOUN
ejpam-816	378	5	,	,	PUNCT
ejpam-816	378	6	we	we	PRON
ejpam-816	378	7	take	take	VERB
ejpam-816	378	8	m	m	VERB
ejpam-816	378	9	=	=	NOUN
ejpam-816	378	10	3	3	NUM
ejpam-816	378	11	4	4	NUM
ejpam-816	378	12	(	(	PUNCT
ejpam-816	378	13	κ	κ	NOUN
ejpam-816	378	14	=	=	SYM
ejpam-816	378	15	5	5	NUM
ejpam-816	378	16	8	8	NUM
ejpam-816	378	17	)	)	PUNCT
ejpam-816	378	18	and	and	CCONJ
ejpam-816	378	19	ν1	ν1	NOUN
ejpam-816	378	20	=	=	SYM
ejpam-816	378	21	1	1	NUM
ejpam-816	378	22	2	2	NUM
ejpam-816	378	23	,	,	PUNCT
ejpam-816	378	24	ν2	ν2	NOUN
ejpam-816	378	25	=	=	SYM
ejpam-816	378	26	3	3	NUM
ejpam-816	378	27	2	2	NUM
ejpam-816	378	28	,	,	PUNCT
ejpam-816	378	29	so	so	SCONJ
ejpam-816	378	30	that	that	SCONJ
ejpam-816	378	31	from	from	ADP
ejpam-816	378	32	(	(	PUNCT
ejpam-816	378	33	44	44	NUM
ejpam-816	378	34	)	)	PUNCT
ejpam-816	378	35	we	we	PRON
ejpam-816	378	36	r.	r.	PROPN
ejpam-816	378	37	paris	paris	PROPN
ejpam-816	378	38	/	/	SYM
ejpam-816	378	39	eur	eur	PROPN
ejpam-816	378	40	.	.	PUNCT
ejpam-816	379	1	j.	j.	PROPN
ejpam-816	379	2	pure	pure	PROPN
ejpam-816	379	3	appl	appl	PROPN
ejpam-816	379	4	.	.	PROPN
ejpam-816	379	5	math	math	PROPN
ejpam-816	379	6	,	,	PUNCT
ejpam-816	379	7	3	3	NUM
ejpam-816	379	8	(	(	PUNCT
ejpam-816	379	9	2010	2010	NUM
ejpam-816	379	10	)	)	PUNCT
ejpam-816	379	11	,	,	PUNCT
ejpam-816	379	12	1006	1006	NUM
ejpam-816	379	13	-	-	SYM
ejpam-816	379	14	1031	1031	NUM
ejpam-816	379	15	1020	1020	NUM
ejpam-816	380	1	7π/16	7π/16	NUM
ejpam-816	380	2	3π/16	3π/16	NUM
ejpam-816	380	3	−π/16	−π/16	NOUN
ejpam-816	380	4	−7π/16−11π/16	−7π/16−11π/16	NOUN
ejpam-816	380	5	−15π/16	−15π/16	NOUN
ejpam-816	380	6	(	(	PUNCT
ejpam-816	380	7	a	a	X
ejpam-816	380	8	)	)	PUNCT
ejpam-816	380	9	3π/8	3π/8	NUM
ejpam-816	380	10	π/4	π/4	PUNCT
ejpam-816	380	11	−π/8	−π/8	PROPN
ejpam-816	380	12	−π/4	−π/4	PROPN
ejpam-816	380	13	−3π/8−5π/8−3π/4	−3π/8−5π/8−3π/4	PROPN
ejpam-816	380	14	−7π/8	−7π/8	NUM
ejpam-816	380	15	5π/8	5π/8	NUM
ejpam-816	380	16	3π/4	3π/4	NUM
ejpam-816	380	17	(	(	PUNCT
ejpam-816	380	18	b	b	X
ejpam-816	380	19	)	)	PUNCT
ejpam-816	381	1	5π/16	5π/16	NUM
ejpam-816	381	2	3π/16	3π/16	NUM
ejpam-816	381	3	−π/8	−π/8	NOUN
ejpam-816	381	4	−5π/16−5π/8	−5π/16−5π/8	NOUN
ejpam-816	381	5	9π/8	9π/8	NUM
ejpam-816	381	6	5π/8	5π/8	NUM
ejpam-816	381	7	13π/16	13π/16	NUM
ejpam-816	381	8	15π/16	15π/16	NUM
ejpam-816	381	9	−7π/16	−7π/16	NOUN
ejpam-816	381	10	(	(	PUNCT
ejpam-816	381	11	c	c	NOUN
ejpam-816	381	12	)	)	PUNCT
ejpam-816	381	13	π/4	π/4	PUNCT
ejpam-816	381	14	−π/4−3π/4	−π/4−3π/4	ADV
ejpam-816	381	15	3π/4	3π/4	NUM
ejpam-816	381	16	(	(	PUNCT
ejpam-816	381	17	d	d	NOUN
ejpam-816	381	18	)	)	PUNCT
ejpam-816	381	19	figure	figure	NOUN
ejpam-816	381	20	1	1	NUM
ejpam-816	381	21	:	:	PUNCT
ejpam-816	381	22	the	the	DET
ejpam-816	381	23	sectorial	sectorial	ADJ
ejpam-816	381	24	behaviour	behaviour	NOUN
ejpam-816	381	25	of	of	ADP
ejpam-816	381	26	j2(z	j2(z	PROPN
ejpam-816	381	27	)	)	PUNCT
ejpam-816	381	28	for	for	ADP
ejpam-816	381	29	µ1	µ1	NOUN
ejpam-816	381	30	=	=	SYM
ejpam-816	381	31	µ2	µ2	NOUN
ejpam-816	381	32	=	=	PROPN
ejpam-816	381	33	4	4	NUM
ejpam-816	381	34	and	and	CCONJ
ejpam-816	381	35	m1	m1	PROPN
ejpam-816	381	36	=	=	SYM
ejpam-816	381	37	m2	m2	PROPN
ejpam-816	381	38	=	=	PUNCT
ejpam-816	381	39	m	m	VERB
ejpam-816	381	40	when	when	SCONJ
ejpam-816	381	41	it	it	PRON
ejpam-816	381	42	is	be	AUX
ejpam-816	381	43	supposed	suppose	VERB
ejpam-816	381	44	that	that	PRON
ejpam-816	381	45	b1	b1	VERB
ejpam-816	381	46	6=	6=	PRON
ejpam-816	381	47	0	0	NUM
ejpam-816	381	48	:	:	PUNCT
ejpam-816	381	49	(	(	PUNCT
ejpam-816	381	50	a	a	X
ejpam-816	381	51	)	)	PUNCT
ejpam-816	381	52	m	m	VERB
ejpam-816	381	53	=	=	SYM
ejpam-816	381	54	1	1	NUM
ejpam-816	381	55	4	4	NUM
ejpam-816	381	56	,	,	PUNCT
ejpam-816	381	57	(	(	PUNCT
ejpam-816	381	58	b	b	X
ejpam-816	381	59	)	)	PUNCT
ejpam-816	381	60	m	m	VERB
ejpam-816	381	61	=	=	SYM
ejpam-816	381	62	1	1	NUM
ejpam-816	381	63	2	2	NUM
ejpam-816	381	64	,	,	PUNCT
ejpam-816	381	65	(	(	PUNCT
ejpam-816	381	66	c	c	X
ejpam-816	381	67	)	)	PUNCT
ejpam-816	381	68	m	m	VERB
ejpam-816	381	69	=	=	NOUN
ejpam-816	381	70	3	3	NUM
ejpam-816	381	71	4	4	NUM
ejpam-816	381	72	and	and	CCONJ
ejpam-816	381	73	(	(	PUNCT
ejpam-816	381	74	d	d	X
ejpam-816	381	75	)	)	PUNCT
ejpam-816	381	76	m	m	VERB
ejpam-816	381	77	=	=	NOUN
ejpam-816	381	78	1	1	X
ejpam-816	381	79	.	.	PUNCT
ejpam-816	382	1	the	the	DET
ejpam-816	382	2	sectors	sector	NOUN
ejpam-816	382	3	marked	mark	VERB
ejpam-816	382	4	with	with	ADP
ejpam-816	382	5	a	a	DET
ejpam-816	382	6	circular	circular	ADJ
ejpam-816	382	7	arc	arc	NOUN
ejpam-816	382	8	with	with	ADP
ejpam-816	382	9	arrows	arrow	NOUN
ejpam-816	382	10	denote	denote	VERB
ejpam-816	382	11	exponentially	exponentially	ADV
ejpam-816	382	12	large	large	ADJ
ejpam-816	382	13	sectors	sector	NOUN
ejpam-816	382	14	.	.	PUNCT
ejpam-816	383	1	the	the	DET
ejpam-816	383	2	hatched	hatch	VERB
ejpam-816	383	3	regions	region	NOUN
ejpam-816	383	4	denote	denote	VERB
ejpam-816	383	5	exponentially	exponentially	ADV
ejpam-816	383	6	small	small	ADJ
ejpam-816	383	7	behaviour	behaviour	NOUN
ejpam-816	383	8	and	and	CCONJ
ejpam-816	383	9	the	the	DET
ejpam-816	383	10	shaded	shade	VERB
ejpam-816	383	11	regions	region	NOUN
ejpam-816	383	12	denote	denote	VERB
ejpam-816	383	13	mixed	mixed	ADJ
ejpam-816	383	14	algebraic	algebraic	ADJ
ejpam-816	383	15	and	and	CCONJ
ejpam-816	383	16	exponentially	exponentially	ADV
ejpam-816	383	17	small	small	ADJ
ejpam-816	383	18	behaviour	behaviour	NOUN
ejpam-816	383	19	.	.	PUNCT
ejpam-816	384	1	the	the	DET
ejpam-816	384	2	dashed	dash	VERB
ejpam-816	384	3	lines	line	NOUN
ejpam-816	384	4	are	be	AUX
ejpam-816	384	5	stokes	stoke	NOUN
ejpam-816	384	6	lines	line	NOUN
ejpam-816	384	7	and	and	CCONJ
ejpam-816	384	8	the	the	DET
ejpam-816	384	9	dash	dash	NOUN
ejpam-816	384	10	-	-	PUNCT
ejpam-816	384	11	dot	dot	NOUN
ejpam-816	384	12	line	line	NOUN
ejpam-816	384	13	is	be	AUX
ejpam-816	384	14	the	the	DET
ejpam-816	384	15	axis	axis	NOUN
ejpam-816	384	16	of	of	ADP
ejpam-816	384	17	basic	basic	ADJ
ejpam-816	384	18	symmetry	symmetry	NOUN
ejpam-816	384	19	.	.	PUNCT
ejpam-816	385	1	have	have	VERB
ejpam-816	385	2	b1	b1	NOUN
ejpam-816	385	3	=	=	SYM
ejpam-816	385	4	0	0	NUM
ejpam-816	385	5	,	,	PUNCT
ejpam-816	385	6	b2	b2	NOUN
ejpam-816	385	7	=	=	SYM
ejpam-816	385	8	1	1	NUM
ejpam-816	385	9	and	and	CCONJ
ejpam-816	385	10	j2(z	j2(z	NUM
ejpam-816	385	11	)	)	PUNCT
ejpam-816	385	12	=	=	SYM
ejpam-816	385	13	2ψ0(z	2ψ0(z	NUM
ejpam-816	385	14	)	)	PUNCT
ejpam-816	386	1	+	+	CCONJ
ejpam-816	386	2	2ψ0(ze	2ψ0(ze	NUM
ejpam-816	386	3	3	3	NUM
ejpam-816	386	4	2	2	NUM
ejpam-816	386	5	πi	πi	NOUN
ejpam-816	386	6	)	)	PUNCT
ejpam-816	386	7	=	=	SYM
ejpam-816	387	1	2ψ0(z	2ψ0(z	NUM
ejpam-816	387	2	)	)	PUNCT
ejpam-816	388	1	+	+	CCONJ
ejpam-816	388	2	2ψ0(ze−	2ψ0(ze−	NUM
ejpam-816	388	3	1	1	NUM
ejpam-816	388	4	2	2	NUM
ejpam-816	388	5	πi	πi	NUM
ejpam-816	388	6	)	)	PUNCT
ejpam-816	388	7	.	.	PUNCT
ejpam-816	389	1	(	(	PUNCT
ejpam-816	389	2	47	47	NUM
ejpam-816	389	3	)	)	PUNCT
ejpam-816	389	4	the	the	DET
ejpam-816	389	5	sector	sector	NOUN
ejpam-816	389	6	in	in	ADP
ejpam-816	389	7	which	which	PRON
ejpam-816	389	8	the	the	DET
ejpam-816	389	9	algebraic	algebraic	ADJ
ejpam-816	389	10	expansions	expansion	NOUN
ejpam-816	389	11	associated	associate	VERB
ejpam-816	389	12	with	with	ADP
ejpam-816	389	13	j2(z	j2(z	NOUN
ejpam-816	389	14	)	)	PUNCT
ejpam-816	389	15	cancel	cancel	NOUN
ejpam-816	389	16	is	be	AUX
ejpam-816	389	17	(	(	PUNCT
ejpam-816	389	18	0	0	NUM
ejpam-816	389	19	,	,	PUNCT
ejpam-816	389	20	1	1	NUM
ejpam-816	389	21	2	2	NUM
ejpam-816	389	22	π	π	NOUN
ejpam-816	389	23	)	)	PUNCT
ejpam-816	389	24	.	.	PUNCT
ejpam-816	390	1	referring	refer	VERB
ejpam-816	390	2	to	to	ADP
ejpam-816	390	3	fig	fig	NOUN
ejpam-816	390	4	.	.	PUNCT
ejpam-816	391	1	2(a	2(a	NUM
ejpam-816	391	2	)	)	PUNCT
ejpam-816	391	3	,	,	PUNCT
ejpam-816	391	4	we	we	PRON
ejpam-816	391	5	see	see	VERB
ejpam-816	391	6	that	that	SCONJ
ejpam-816	391	7	the	the	DET
ejpam-816	391	8	expansion	expansion	NOUN
ejpam-816	391	9	of	of	ADP
ejpam-816	391	10	j2(z	j2(z	NOUN
ejpam-816	391	11	)	)	PUNCT
ejpam-816	391	12	as	as	ADP
ejpam-816	391	13	|z|	|z|	NOUN
ejpam-816	391	14	→	→	SYM
ejpam-816	391	15	∞	∞	PROPN
ejpam-816	391	16	is	be	AUX
ejpam-816	391	17	exponentially	exponentially	ADV
ejpam-816	391	18	large	large	ADJ
ejpam-816	391	19	in	in	ADP
ejpam-816	391	20	the	the	DET
ejpam-816	391	21	sector	sector	NOUN
ejpam-816	391	22	(	(	PUNCT
ejpam-816	391	23	−	−	PROPN
ejpam-816	391	24	5	5	NUM
ejpam-816	391	25	16	16	NUM
ejpam-816	391	26	π	π	NOUN
ejpam-816	391	27	,	,	PUNCT
ejpam-816	391	28	13	13	NUM
ejpam-816	391	29	16	16	NUM
ejpam-816	391	30	π	π	NOUN
ejpam-816	391	31	)	)	PUNCT
ejpam-816	391	32	,	,	PUNCT
ejpam-816	391	33	where	where	SCONJ
ejpam-816	391	34	e2,0(z	e2,0(z	NOUN
ejpam-816	391	35	)	)	PUNCT
ejpam-816	391	36	is	be	AUX
ejpam-816	391	37	given	give	VERB
ejpam-816	391	38	by	by	ADP
ejpam-816	391	39	(	(	PUNCT
ejpam-816	391	40	8)	8)	NUM
ejpam-816	391	41	with	with	ADP
ejpam-816	391	42	z	z	NOUN
ejpam-816	391	43	=	=	SYM
ejpam-816	391	44	5	5	NUM
ejpam-816	391	45	64	64	NUM
ejpam-816	391	46	(	(	PUNCT
ejpam-816	391	47	63/5z8/5	63/5z8/5	NUM
ejpam-816	391	48	)	)	PUNCT
ejpam-816	391	49	and	and	CCONJ
ejpam-816	391	50	ϑ	ϑ	X
ejpam-816	391	51	=	=	X
ejpam-816	391	52	−1	−1	NOUN
ejpam-816	391	53	2	2	NUM
ejpam-816	391	54	.	.	PUNCT
ejpam-816	392	1	in	in	ADP
ejpam-816	392	2	the	the	DET
ejpam-816	392	3	sectors	sector	NOUN
ejpam-816	392	4	(	(	PUNCT
ejpam-816	392	5	13	13	NUM
ejpam-816	392	6	16	16	NUM
ejpam-816	392	7	π	π	NOUN
ejpam-816	392	8	,	,	PUNCT
ejpam-816	392	9	9	9	NUM
ejpam-816	392	10	8	8	NUM
ejpam-816	392	11	π	π	NOUN
ejpam-816	392	12	)	)	PUNCT
ejpam-816	392	13	and	and	CCONJ
ejpam-816	392	14	(	(	PUNCT
ejpam-816	392	15	−5	−5	ADP
ejpam-816	392	16	8	8	NUM
ejpam-816	392	17	π,−	π,−	NOUN
ejpam-816	392	18	5	5	NUM
ejpam-816	392	19	16	16	NUM
ejpam-816	392	20	π	π	NOUN
ejpam-816	392	21	)	)	PUNCT
ejpam-816	392	22	the	the	DET
ejpam-816	392	23	expansion	expansion	NOUN
ejpam-816	392	24	of	of	ADP
ejpam-816	392	25	j2(z	j2(z	NOUN
ejpam-816	392	26	)	)	PUNCT
ejpam-816	392	27	is	be	AUX
ejpam-816	392	28	mixed	mix	VERB
ejpam-816	392	29	algebraic	algebraic	ADJ
ejpam-816	392	30	and	and	CCONJ
ejpam-816	392	31	exponentially	exponentially	ADV
ejpam-816	392	32	small	small	ADJ
ejpam-816	392	33	,	,	PUNCT
ejpam-816	392	34	whereas	whereas	SCONJ
ejpam-816	392	35	due	due	ADP
ejpam-816	392	36	to	to	ADP
ejpam-816	392	37	the	the	DET
ejpam-816	392	38	presence	presence	NOUN
ejpam-816	392	39	of	of	ADP
ejpam-816	392	40	the	the	DET
ejpam-816	392	41	stokes	stoke	NOUN
ejpam-816	392	42	lines	line	NOUN
ejpam-816	392	43	associated	associate	VERB
ejpam-816	392	44	with	with	ADP
ejpam-816	392	45	the	the	DET
ejpam-816	392	46	exponential	exponential	ADJ
ejpam-816	392	47	expansions	expansion	NOUN
ejpam-816	392	48	on	on	ADP
ejpam-816	392	49	arg	arg	NOUN
ejpam-816	392	50	z	z	NOUN
ejpam-816	392	51	=	=	PUNCT
ejpam-816	393	1	−5	−5	NOUN
ejpam-816	393	2	8	8	NUM
ejpam-816	393	3	π	π	NOUN
ejpam-816	393	4	and	and	CCONJ
ejpam-816	393	5	arg	arg	NOUN
ejpam-816	393	6	z	z	NOUN
ejpam-816	393	7	=	=	SYM
ejpam-816	393	8	9	9	NUM
ejpam-816	393	9	8	8	NUM
ejpam-816	393	10	π	π	NOUN
ejpam-816	393	11	the	the	DET
ejpam-816	393	12	expansion	expansion	NOUN
ejpam-816	393	13	in	in	ADP
ejpam-816	393	14	the	the	DET
ejpam-816	393	15	sector	sector	NOUN
ejpam-816	393	16	|arg(ze−3πi/4)|	|arg(ze−3πi/4)|	VERB
ejpam-816	393	17	<	<	X
ejpam-816	393	18	1	1	NUM
ejpam-816	393	19	8	8	NUM
ejpam-816	393	20	π	π	NOUN
ejpam-816	393	21	is	be	AUX
ejpam-816	393	22	purely	purely	ADV
ejpam-816	393	23	algebraic	algebraic	ADJ
ejpam-816	393	24	.	.	PUNCT
ejpam-816	394	1	r.	r.	PROPN
ejpam-816	394	2	paris	paris	PROPN
ejpam-816	394	3	/	/	SYM
ejpam-816	394	4	eur	eur	PROPN
ejpam-816	394	5	.	.	PUNCT
ejpam-816	395	1	j.	j.	PROPN
ejpam-816	395	2	pure	pure	PROPN
ejpam-816	395	3	appl	appl	PROPN
ejpam-816	395	4	.	.	PROPN
ejpam-816	395	5	math	math	PROPN
ejpam-816	395	6	,	,	PUNCT
ejpam-816	395	7	3	3	NUM
ejpam-816	395	8	(	(	PUNCT
ejpam-816	395	9	2010	2010	NUM
ejpam-816	395	10	)	)	PUNCT
ejpam-816	395	11	,	,	PUNCT
ejpam-816	395	12	1006	1006	NUM
ejpam-816	395	13	-	-	SYM
ejpam-816	395	14	1031	1031	NUM
ejpam-816	395	15	1021	1021	NUM
ejpam-816	395	16	from	from	ADP
ejpam-816	395	17	(	(	PUNCT
ejpam-816	395	18	12	12	NUM
ejpam-816	395	19	)	)	PUNCT
ejpam-816	395	20	and	and	CCONJ
ejpam-816	395	21	(	(	PUNCT
ejpam-816	395	22	13	13	NUM
ejpam-816	395	23	)	)	PUNCT
ejpam-816	395	24	,	,	PUNCT
ejpam-816	395	25	the	the	DET
ejpam-816	395	26	algebraic	algebraic	ADJ
ejpam-816	395	27	expansion	expansion	NOUN
ejpam-816	395	28	h2,0(z	h2,0(z	PROPN
ejpam-816	395	29	)	)	PUNCT
ejpam-816	395	30	is	be	AUX
ejpam-816	395	31	controlled	control	VERB
ejpam-816	395	32	by	by	ADP
ejpam-816	395	33	the	the	DET
ejpam-816	395	34	poles	pole	NOUN
ejpam-816	395	35	situated	situate	VERB
ejpam-816	395	36	at	at	ADP
ejpam-816	395	37	sk,1	sk,1	PROPN
ejpam-816	395	38	=	=	SYM
ejpam-816	395	39	2	2	NUM
ejpam-816	395	40	3	3	NUM
ejpam-816	395	41	+	+	CCONJ
ejpam-816	395	42	16	16	NUM
ejpam-816	395	43	3	3	NUM
ejpam-816	395	44	k	k	NOUN
ejpam-816	395	45	,	,	PUNCT
ejpam-816	395	46	sk,2	sk,2	PROPN
ejpam-816	395	47	=	=	SYM
ejpam-816	395	48	2	2	NUM
ejpam-816	395	49	+	+	NUM
ejpam-816	395	50	16	16	NUM
ejpam-816	395	51	3	3	NUM
ejpam-816	395	52	k	k	NOUN
ejpam-816	395	53	(	(	PUNCT
ejpam-816	395	54	k	k	NOUN
ejpam-816	395	55	=	=	SYM
ejpam-816	395	56	0,1,2	0,1,2	NUM
ejpam-816	395	57	,	,	PUNCT
ejpam-816	395	58	.	.	PUNCT
ejpam-816	395	59	.	.	PUNCT
ejpam-816	396	1	.	.	PUNCT
ejpam-816	396	2	)	)	PUNCT
ejpam-816	397	1	which	which	PRON
ejpam-816	397	2	are	be	AUX
ejpam-816	397	3	all	all	ADV
ejpam-816	397	4	simple	simple	ADJ
ejpam-816	397	5	,	,	PUNCT
ejpam-816	397	6	and	and	CCONJ
ejpam-816	397	7	consequently	consequently	ADV
ejpam-816	397	8	h2,0(z	h2,0(z	ADJ
ejpam-816	397	9	)	)	PUNCT
ejpam-816	398	1	=	=	SYM
ejpam-816	398	2	16	16	NUM
ejpam-816	398	3	3	3	NUM
ejpam-816	398	4	2	2	NUM
ejpam-816	398	5	∑	∑	PUNCT
ejpam-816	398	6	j=1	j=1	NOUN
ejpam-816	398	7	∞	∞	PROPN
ejpam-816	398	8	∑	∑	PROPN
ejpam-816	398	9	k=0	k=0	PROPN
ejpam-816	398	10	(	(	PUNCT
ejpam-816	398	11	−)k	−)k	PROPN
ejpam-816	398	12	k	k	X
ejpam-816	398	13	!	!	PUNCT
ejpam-816	399	1	γ(sk	γ(sk	NUM
ejpam-816	399	2	,	,	PUNCT
ejpam-816	399	3	j)γ(γ	j)γ(γ	ADP
ejpam-816	399	4	j	j	PROPN
ejpam-816	399	5	−	−	PROPN
ejpam-816	399	6	3	3	NUM
ejpam-816	399	7	16	16	NUM
ejpam-816	399	8	sk	sk	NOUN
ejpam-816	399	9	,	,	PUNCT
ejpam-816	399	10	j)z	j)z	NOUN
ejpam-816	399	11	−sk	−sk	PROPN
ejpam-816	399	12	,	,	PUNCT
ejpam-816	399	13	j	j	PROPN
ejpam-816	399	14	with	with	ADP
ejpam-816	399	15	γ1	γ1	PROPN
ejpam-816	399	16	=	=	NOUN
ejpam-816	399	17	3	3	NUM
ejpam-816	399	18	8	8	NUM
ejpam-816	399	19	and	and	CCONJ
ejpam-816	399	20	γ2	γ2	NOUN
ejpam-816	399	21	=	=	SYM
ejpam-816	399	22	1	1	NUM
ejpam-816	399	23	8	8	NUM
ejpam-816	399	24	.	.	PUNCT
ejpam-816	400	1	taking	take	VERB
ejpam-816	400	2	into	into	ADP
ejpam-816	400	3	account	account	NOUN
ejpam-816	400	4	the	the	DET
ejpam-816	400	5	stokes	stokes	PROPN
ejpam-816	400	6	lines	line	NOUN
ejpam-816	400	7	on	on	ADP
ejpam-816	400	8	arg	arg	NOUN
ejpam-816	400	9	z	z	PROPN
ejpam-816	400	10	=	=	SYM
ejpam-816	400	11	0	0	NUM
ejpam-816	400	12	and	and	CCONJ
ejpam-816	400	13	arg	arg	NOUN
ejpam-816	400	14	z	z	NOUN
ejpam-816	400	15	=	=	SYM
ejpam-816	400	16	1	1	NUM
ejpam-816	400	17	2	2	NUM
ejpam-816	400	18	π	π	NOUN
ejpam-816	400	19	for	for	ADP
ejpam-816	400	20	the	the	DET
ejpam-816	400	21	algebraic	algebraic	ADJ
ejpam-816	400	22	expansions	expansion	NOUN
ejpam-816	400	23	associated	associate	VERB
ejpam-816	400	24	with	with	ADP
ejpam-816	400	25	2ψ0(z	2ψ0(z	NUM
ejpam-816	400	26	)	)	PUNCT
ejpam-816	400	27	and	and	CCONJ
ejpam-816	400	28	2ψ0(ze−πi/2	2ψ0(ze−πi/2	NUM
ejpam-816	400	29	)	)	PUNCT
ejpam-816	400	30	,	,	PUNCT
ejpam-816	400	31	respectively	respectively	ADV
ejpam-816	400	32	,	,	PUNCT
ejpam-816	400	33	we	we	PRON
ejpam-816	400	34	see	see	VERB
ejpam-816	400	35	from	from	ADP
ejpam-816	400	36	(	(	PUNCT
ejpam-816	400	37	15	15	NUM
ejpam-816	400	38	)	)	PUNCT
ejpam-816	400	39	and	and	CCONJ
ejpam-816	400	40	(	(	PUNCT
ejpam-816	400	41	16	16	NUM
ejpam-816	400	42	)	)	PUNCT
ejpam-816	400	43	that	that	SCONJ
ejpam-816	400	44	the	the	DET
ejpam-816	400	45	algebraic	algebraic	ADJ
ejpam-816	400	46	expansion	expansion	NOUN
ejpam-816	400	47	h(z	h(z	NOUN
ejpam-816	400	48	)	)	PUNCT
ejpam-816	400	49	of	of	ADP
ejpam-816	400	50	j2(z	j2(z	NUM
ejpam-816	400	51	)	)	PUNCT
ejpam-816	400	52	is	be	AUX
ejpam-816	400	53	given	give	VERB
ejpam-816	400	54	by	by	ADP
ejpam-816	400	55	h(z	h(z	NOUN
ejpam-816	400	56	)	)	PUNCT
ejpam-816	400	57	=	=	PRON
ejpam-816	400	58	(	(	PUNCT
ejpam-816	400	59	h2,0(ze−πi	h2,0(ze−πi	NOUN
ejpam-816	400	60	)	)	PUNCT
ejpam-816	401	1	+	+	NOUN
ejpam-816	401	2	h2,0(ze	h2,0(ze	ADJ
ejpam-816	401	3	1	1	NUM
ejpam-816	401	4	2	2	NUM
ejpam-816	401	5	πi)≡	πi)≡	NOUN
ejpam-816	401	6	0	0	NUM
ejpam-816	401	7	in	in	ADP
ejpam-816	401	8	(	(	PUNCT
ejpam-816	401	9	0	0	NUM
ejpam-816	401	10	,	,	PUNCT
ejpam-816	401	11	1	1	NUM
ejpam-816	401	12	2	2	NUM
ejpam-816	401	13	π	π	NOUN
ejpam-816	401	14	)	)	PUNCT
ejpam-816	401	15	h2,0(ze−πi	h2,0(ze−πi	PROPN
ejpam-816	401	16	)	)	PUNCT
ejpam-816	401	17	+	+	NOUN
ejpam-816	401	18	h2,0(ze−	h2,0(ze−	NOUN
ejpam-816	401	19	3	3	NUM
ejpam-816	401	20	2	2	NUM
ejpam-816	401	21	πi	πi	CCONJ
ejpam-816	401	22	)	)	PUNCT
ejpam-816	401	23	in	in	ADP
ejpam-816	401	24	(	(	PUNCT
ejpam-816	401	25	1	1	NUM
ejpam-816	401	26	2	2	NUM
ejpam-816	401	27	π	π	NOUN
ejpam-816	401	28	,	,	PUNCT
ejpam-816	401	29	2π	2π	NOUN
ejpam-816	401	30	)	)	PUNCT
ejpam-816	401	31	it	it	PRON
ejpam-816	401	32	is	be	AUX
ejpam-816	401	33	easily	easily	ADV
ejpam-816	401	34	verified	verify	VERB
ejpam-816	401	35	with	with	ADP
ejpam-816	401	36	the	the	DET
ejpam-816	401	37	above	above	ADJ
ejpam-816	401	38	form	form	NOUN
ejpam-816	401	39	of	of	ADP
ejpam-816	401	40	h2,0(z	h2,0(z	NOUN
ejpam-816	401	41	)	)	PUNCT
ejpam-816	401	42	that	that	SCONJ
ejpam-816	401	43	h(z	h(z	NOUN
ejpam-816	401	44	)	)	PUNCT
ejpam-816	401	45	≡	≡	PROPN
ejpam-816	401	46	0	0	NUM
ejpam-816	401	47	in	in	ADP
ejpam-816	401	48	the	the	DET
ejpam-816	401	49	sector	sector	NOUN
ejpam-816	401	50	(	(	PUNCT
ejpam-816	401	51	0	0	NUM
ejpam-816	401	52	,	,	PUNCT
ejpam-816	401	53	1	1	NUM
ejpam-816	401	54	2	2	NUM
ejpam-816	401	55	π	π	NOUN
ejpam-816	401	56	)	)	PUNCT
ejpam-816	401	57	,	,	PUNCT
ejpam-816	401	58	in	in	ADP
ejpam-816	401	59	accordance	accordance	NOUN
ejpam-816	401	60	with	with	ADP
ejpam-816	401	61	(	(	PUNCT
ejpam-816	401	62	34	34	NUM
ejpam-816	401	63	)	)	PUNCT
ejpam-816	401	64	.	.	PUNCT
ejpam-816	402	1	then	then	ADV
ejpam-816	402	2	the	the	DET
ejpam-816	402	3	asymptotic	asymptotic	ADJ
ejpam-816	402	4	expansion	expansion	NOUN
ejpam-816	402	5	of	of	ADP
ejpam-816	402	6	j2(z	j2(z	NOUN
ejpam-816	402	7	)	)	PUNCT
ejpam-816	402	8	in	in	ADP
ejpam-816	402	9	(	(	PUNCT
ejpam-816	402	10	47	47	NUM
ejpam-816	402	11	)	)	PUNCT
ejpam-816	402	12	has	have	VERB
ejpam-816	402	13	the	the	DET
ejpam-816	402	14	form	form	NOUN
ejpam-816	402	15	j2(z)∼	j2(z)∼	PROPN
ejpam-816	402	16			PRON
ejpam-816	402	17			NOUN
ejpam-816	402	18			PROPN
ejpam-816	402	19			NOUN
ejpam-816	402	20			PROPN
ejpam-816	402	21			PROPN
ejpam-816	402	22			PROPN
ejpam-816	402	23	e2,0(z	e2,0(z	PROPN
ejpam-816	402	24	)	)	PUNCT
ejpam-816	403	1	+	+	CCONJ
ejpam-816	403	2	e2,0(ze−	e2,0(ze−	PROPN
ejpam-816	403	3	1	1	NUM
ejpam-816	403	4	2	2	NUM
ejpam-816	403	5	πi	πi	CCONJ
ejpam-816	403	6	)	)	PUNCT
ejpam-816	403	7	in	in	ADP
ejpam-816	403	8	(	(	PUNCT
ejpam-816	403	9	0	0	NUM
ejpam-816	403	10	,	,	PUNCT
ejpam-816	403	11	1	1	NUM
ejpam-816	403	12	2	2	NUM
ejpam-816	403	13	π	π	NOUN
ejpam-816	403	14	)	)	PUNCT
ejpam-816	403	15	e2,0(z	e2,0(z	PROPN
ejpam-816	403	16	)	)	PUNCT
ejpam-816	404	1	+	+	CCONJ
ejpam-816	404	2	e2,0(ze−	e2,0(ze−	PROPN
ejpam-816	404	3	1	1	NUM
ejpam-816	404	4	2	2	NUM
ejpam-816	404	5	πi	πi	CCONJ
ejpam-816	404	6	)	)	PUNCT
ejpam-816	404	7	+	+	NOUN
ejpam-816	404	8	h(z	h(z	NOUN
ejpam-816	404	9	)	)	PUNCT
ejpam-816	404	10	in	in	ADP
ejpam-816	404	11	(	(	PUNCT
ejpam-816	404	12	1	1	NUM
ejpam-816	404	13	2	2	NUM
ejpam-816	404	14	π	π	NOUN
ejpam-816	404	15	,	,	PUNCT
ejpam-816	404	16	5	5	NUM
ejpam-816	404	17	8	8	NUM
ejpam-816	404	18	π	π	NOUN
ejpam-816	404	19	)	)	PUNCT
ejpam-816	404	20	e2,0(ze−	e2,0(ze−	PROPN
ejpam-816	404	21	1	1	NUM
ejpam-816	404	22	2	2	NUM
ejpam-816	404	23	πi	πi	CCONJ
ejpam-816	404	24	)	)	PUNCT
ejpam-816	404	25	+	+	NOUN
ejpam-816	404	26	h(z	h(z	NOUN
ejpam-816	404	27	)	)	PUNCT
ejpam-816	404	28	in	in	ADP
ejpam-816	404	29	(	(	PUNCT
ejpam-816	404	30	5	5	NUM
ejpam-816	404	31	8	8	NUM
ejpam-816	404	32	π	π	NOUN
ejpam-816	404	33	,	,	PUNCT
ejpam-816	404	34	9	9	NUM
ejpam-816	404	35	8	8	NUM
ejpam-816	404	36	π	π	NOUN
ejpam-816	404	37	)	)	PUNCT
ejpam-816	404	38	h(z	h(z	NOUN
ejpam-816	404	39	)	)	PUNCT
ejpam-816	404	40	in	in	ADP
ejpam-816	404	41	(	(	PUNCT
ejpam-816	404	42	9	9	NUM
ejpam-816	404	43	8	8	NUM
ejpam-816	404	44	π	π	NOUN
ejpam-816	404	45	,	,	PUNCT
ejpam-816	404	46	5	5	NUM
ejpam-816	404	47	4	4	NUM
ejpam-816	404	48	π	π	NOUN
ejpam-816	404	49	]	]	PUNCT
ejpam-816	404	50	as	as	ADP
ejpam-816	404	51	|z|	|z|	NOUN
ejpam-816	404	52	→∞	→∞	NOUN
ejpam-816	404	53	,	,	PUNCT
ejpam-816	404	54	with	with	ADP
ejpam-816	404	55	that	that	PRON
ejpam-816	404	56	in	in	ADP
ejpam-816	404	57	the	the	DET
ejpam-816	404	58	remainder	remainder	NOUN
ejpam-816	404	59	of	of	ADP
ejpam-816	404	60	the	the	DET
ejpam-816	404	61	plane	plane	NOUN
ejpam-816	404	62	being	be	AUX
ejpam-816	404	63	determined	determine	VERB
ejpam-816	404	64	by	by	ADP
ejpam-816	404	65	the	the	DET
ejpam-816	404	66	symmetry	symmetry	NOUN
ejpam-816	404	67	relation	relation	NOUN
ejpam-816	404	68	(	(	PUNCT
ejpam-816	404	69	45	45	NUM
ejpam-816	404	70	)	)	PUNCT
ejpam-816	404	71	.	.	PUNCT
ejpam-816	405	1	5π/16	5π/16	NUM
ejpam-816	406	1	3π/16	3π/16	NUM
ejpam-816	406	2	−π/8	−π/8	NOUN
ejpam-816	406	3	−5π/16−5π/8	−5π/16−5π/8	NOUN
ejpam-816	406	4	9π/8	9π/8	NUM
ejpam-816	406	5	5π/8	5π/8	NUM
ejpam-816	406	6	13π/16	13π/16	NOUN
ejpam-816	406	7	(	(	PUNCT
ejpam-816	406	8	a	a	NOUN
ejpam-816	406	9	)	)	PUNCT
ejpam-816	406	10	5π/12	5π/12	NUM
ejpam-816	406	11	5π/24	5π/24	NUM
ejpam-816	406	12	−5π/24	−5π/24	NUM
ejpam-816	406	13	−5π/12−7π/12	−5π/12−7π/12	PROPN
ejpam-816	406	14	−19π/24	−19π/24	NOUN
ejpam-816	406	15	7π/12	7π/12	PROPN
ejpam-816	406	16	19π/24	19π/24	NUM
ejpam-816	406	17	(	(	PUNCT
ejpam-816	406	18	b	b	NOUN
ejpam-816	406	19	)	)	PUNCT
ejpam-816	406	20	figure	figure	NOUN
ejpam-816	406	21	2	2	NUM
ejpam-816	406	22	:	:	PUNCT
ejpam-816	406	23	the	the	DET
ejpam-816	406	24	sectorial	sectorial	ADJ
ejpam-816	406	25	behaviour	behaviour	NOUN
ejpam-816	406	26	of	of	ADP
ejpam-816	406	27	(	(	PUNCT
ejpam-816	406	28	a	a	X
ejpam-816	406	29	)	)	PUNCT
ejpam-816	406	30	j2(z	j2(z	PROPN
ejpam-816	406	31	)	)	PUNCT
ejpam-816	406	32	for	for	ADP
ejpam-816	406	33	µ1	µ1	NOUN
ejpam-816	406	34	=	=	SYM
ejpam-816	406	35	µ2	µ2	NOUN
ejpam-816	406	36	=	=	PROPN
ejpam-816	406	37	4	4	NUM
ejpam-816	406	38	and	and	CCONJ
ejpam-816	406	39	m1	m1	PROPN
ejpam-816	406	40	=	=	SYM
ejpam-816	406	41	m2	m2	PROPN
ejpam-816	406	42	=	=	SYM
ejpam-816	406	43	3	3	NUM
ejpam-816	406	44	4	4	NUM
ejpam-816	406	45	when	when	SCONJ
ejpam-816	406	46	it	it	PRON
ejpam-816	406	47	is	be	AUX
ejpam-816	406	48	supposed	suppose	VERB
ejpam-816	406	49	that	that	SCONJ
ejpam-816	406	50	b1	b1	NOUN
ejpam-816	406	51	=	=	SYM
ejpam-816	406	52	0	0	PUNCT
ejpam-816	407	1	and	and	CCONJ
ejpam-816	407	2	(	(	PUNCT
ejpam-816	407	3	b	b	NOUN
ejpam-816	407	4	)	)	PUNCT
ejpam-816	407	5	of	of	ADP
ejpam-816	407	6	k3,1(z	k3,1(z	PROPN
ejpam-816	407	7	)	)	PUNCT
ejpam-816	407	8	for	for	ADP
ejpam-816	407	9	µ1	µ1	NOUN
ejpam-816	407	10	=	=	SYM
ejpam-816	407	11	µ2	µ2	PROPN
ejpam-816	407	12	=	=	SYM
ejpam-816	407	13	3	3	NUM
ejpam-816	407	14	,	,	PUNCT
ejpam-816	407	15	µ3	µ3	NOUN
ejpam-816	407	16	=	=	SYM
ejpam-816	407	17	4	4	NUM
ejpam-816	407	18	and	and	CCONJ
ejpam-816	407	19	m1	m1	PROPN
ejpam-816	407	20	=	=	SYM
ejpam-816	407	21	m2	m2	PROPN
ejpam-816	407	22	=	=	SYM
ejpam-816	407	23	1	1	NUM
ejpam-816	407	24	2	2	NUM
ejpam-816	407	25	,	,	PUNCT
ejpam-816	407	26	m3	m3	PROPN
ejpam-816	407	27	=	=	SYM
ejpam-816	407	28	1	1	X
ejpam-816	407	29	.	.	PUNCT
ejpam-816	408	1	the	the	DET
ejpam-816	408	2	sectors	sector	NOUN
ejpam-816	408	3	marked	mark	VERB
ejpam-816	408	4	with	with	ADP
ejpam-816	408	5	a	a	DET
ejpam-816	408	6	circular	circular	ADJ
ejpam-816	408	7	arc	arc	NOUN
ejpam-816	408	8	with	with	ADP
ejpam-816	408	9	arrows	arrow	NOUN
ejpam-816	408	10	denote	denote	VERB
ejpam-816	408	11	exponentially	exponentially	ADV
ejpam-816	408	12	large	large	ADJ
ejpam-816	408	13	sectors	sector	NOUN
ejpam-816	408	14	.	.	PUNCT
ejpam-816	409	1	the	the	DET
ejpam-816	409	2	shaded	shade	VERB
ejpam-816	409	3	regions	region	NOUN
ejpam-816	409	4	denote	denote	VERB
ejpam-816	409	5	mixed	mixed	ADJ
ejpam-816	409	6	algebraic	algebraic	ADJ
ejpam-816	409	7	and	and	CCONJ
ejpam-816	409	8	exponentially	exponentially	ADV
ejpam-816	409	9	small	small	ADJ
ejpam-816	409	10	behaviour	behaviour	NOUN
ejpam-816	409	11	.	.	PUNCT
ejpam-816	410	1	the	the	DET
ejpam-816	410	2	dashed	dash	VERB
ejpam-816	410	3	lines	line	NOUN
ejpam-816	410	4	are	be	AUX
ejpam-816	410	5	stokes	stoke	NOUN
ejpam-816	410	6	lines	line	NOUN
ejpam-816	410	7	and	and	CCONJ
ejpam-816	410	8	the	the	DET
ejpam-816	410	9	dash	dash	NOUN
ejpam-816	410	10	-	-	PUNCT
ejpam-816	410	11	dot	dot	NOUN
ejpam-816	410	12	line	line	NOUN
ejpam-816	410	13	is	be	AUX
ejpam-816	410	14	the	the	DET
ejpam-816	410	15	axis	axis	NOUN
ejpam-816	410	16	of	of	ADP
ejpam-816	410	17	basic	basic	ADJ
ejpam-816	410	18	symmetry	symmetry	NOUN
ejpam-816	410	19	.	.	PUNCT
ejpam-816	411	1	r.	r.	PROPN
ejpam-816	411	2	paris	paris	PROPN
ejpam-816	411	3	/	/	SYM
ejpam-816	411	4	eur	eur	PROPN
ejpam-816	411	5	.	.	PUNCT
ejpam-816	412	1	j.	j.	PROPN
ejpam-816	412	2	pure	pure	PROPN
ejpam-816	412	3	appl	appl	PROPN
ejpam-816	412	4	.	.	PROPN
ejpam-816	412	5	math	math	PROPN
ejpam-816	412	6	,	,	PUNCT
ejpam-816	412	7	3	3	NUM
ejpam-816	412	8	(	(	PUNCT
ejpam-816	412	9	2010	2010	NUM
ejpam-816	412	10	)	)	PUNCT
ejpam-816	412	11	,	,	PUNCT
ejpam-816	412	12	1006	1006	NUM
ejpam-816	412	13	-	-	SYM
ejpam-816	412	14	1031	1031	NUM
ejpam-816	412	15	1022	1022	NUM
ejpam-816	412	16	finally	finally	ADV
ejpam-816	412	17	,	,	PUNCT
ejpam-816	412	18	we	we	PRON
ejpam-816	412	19	consider	consider	VERB
ejpam-816	412	20	m=	m=	X
ejpam-816	412	21	1	1	NUM
ejpam-816	412	22	(	(	PUNCT
ejpam-816	412	23	κ	κ	NOUN
ejpam-816	412	24	=	=	SYM
ejpam-816	412	25	1	1	NUM
ejpam-816	412	26	2	2	NUM
ejpam-816	412	27	)	)	PUNCT
ejpam-816	412	28	and	and	CCONJ
ejpam-816	412	29	ν1	ν1	NOUN
ejpam-816	412	30	=	=	SYM
ejpam-816	412	31	ν2	ν2	NOUN
ejpam-816	412	32	=	=	SYM
ejpam-816	412	33	1	1	NUM
ejpam-816	412	34	4	4	NUM
ejpam-816	412	35	,	,	PUNCT
ejpam-816	412	36	so	so	SCONJ
ejpam-816	412	37	that	that	SCONJ
ejpam-816	412	38	b1	b1	NOUN
ejpam-816	412	39	=	=	SYM
ejpam-816	412	40	2eπi/4	2eπi/4	NUM
ejpam-816	412	41	and	and	CCONJ
ejpam-816	412	42	b2	b2	NOUN
ejpam-816	412	43	=	=	SYM
ejpam-816	412	44	i	i	PROPN
ejpam-816	412	45	and	and	CCONJ
ejpam-816	412	46	j2(z	j2(z	PROPN
ejpam-816	412	47	)	)	PUNCT
ejpam-816	412	48	=	=	SYM
ejpam-816	412	49	(	(	PUNCT
ejpam-816	412	50	1	1	NUM
ejpam-816	412	51	+	+	NUM
ejpam-816	412	52	i	i	NOUN
ejpam-816	412	53	)	)	PUNCT
ejpam-816	412	54	2ψ0(z)−	2ψ0(z)−	NUM
ejpam-816	412	55	2e	2e	NOUN
ejpam-816	412	56	1	1	NUM
ejpam-816	412	57	4	4	NUM
ejpam-816	412	58	πi	πi	ADP
ejpam-816	412	59	2ψ0(ze−πi	2ψ0(ze−πi	NUM
ejpam-816	412	60	)	)	PUNCT
ejpam-816	412	61	,	,	PUNCT
ejpam-816	412	62	(	(	PUNCT
ejpam-816	412	63	48	48	NUM
ejpam-816	412	64	)	)	PUNCT
ejpam-816	412	65	where	where	SCONJ
ejpam-816	412	66	we	we	PRON
ejpam-816	412	67	have	have	AUX
ejpam-816	412	68	replaced	replace	VERB
ejpam-816	412	69	the	the	DET
ejpam-816	412	70	argument	argument	NOUN
ejpam-816	412	71	of	of	ADP
ejpam-816	412	72	the	the	DET
ejpam-816	412	73	second	second	ADJ
ejpam-816	412	74	wright	wright	PROPN
ejpam-816	412	75	function	function	NOUN
ejpam-816	412	76	by	by	ADP
ejpam-816	412	77	ze−πi	ze−πi	PROPN
ejpam-816	412	78	.	.	PUNCT
ejpam-816	413	1	from	from	ADP
ejpam-816	413	2	fig	fig	NOUN
ejpam-816	413	3	.	.	PUNCT
ejpam-816	413	4	1(d	1(d	NUM
ejpam-816	413	5	)	)	PUNCT
ejpam-816	413	6	,	,	PUNCT
ejpam-816	413	7	the	the	DET
ejpam-816	413	8	stokes	stokes	PROPN
ejpam-816	413	9	lines	line	NOUN
ejpam-816	413	10	coincide	coincide	VERB
ejpam-816	413	11	with	with	ADP
ejpam-816	413	12	the	the	DET
ejpam-816	413	13	imaginary	imaginary	ADJ
ejpam-816	413	14	axis	axis	NOUN
ejpam-816	413	15	and	and	CCONJ
ejpam-816	413	16	the	the	DET
ejpam-816	413	17	symmetry	symmetry	NOUN
ejpam-816	413	18	axis	axis	NOUN
ejpam-816	413	19	is	be	AUX
ejpam-816	413	20	the	the	DET
ejpam-816	413	21	real	real	ADJ
ejpam-816	413	22	axis	axis	NOUN
ejpam-816	413	23	.	.	PUNCT
ejpam-816	414	1	the	the	DET
ejpam-816	414	2	exponential	exponential	ADJ
ejpam-816	414	3	expansion	expansion	NOUN
ejpam-816	414	4	e2,0(z	e2,0(z	PROPN
ejpam-816	414	5	)	)	PUNCT
ejpam-816	414	6	in	in	ADP
ejpam-816	414	7	(	(	PUNCT
ejpam-816	414	8	8)	8)	NUM
ejpam-816	414	9	has	have	AUX
ejpam-816	414	10	z	z	NOUN
ejpam-816	414	11	=	=	SYM
ejpam-816	414	12	1	1	NUM
ejpam-816	414	13	8	8	NUM
ejpam-816	414	14	z2	z2	NUM
ejpam-816	414	15	and	and	CCONJ
ejpam-816	414	16	ϑ	ϑ	X
ejpam-816	414	17	=	=	X
ejpam-816	414	18	−7	−7	ADP
ejpam-816	414	19	8	8	NUM
ejpam-816	414	20	.	.	PUNCT
ejpam-816	415	1	the	the	DET
ejpam-816	415	2	poles	poles	PROPN
ejpam-816	415	3	in	in	ADP
ejpam-816	415	4	(	(	PUNCT
ejpam-816	415	5	12	12	NUM
ejpam-816	415	6	)	)	PUNCT
ejpam-816	415	7	are	be	AUX
ejpam-816	415	8	all	all	PRON
ejpam-816	415	9	double	double	ADV
ejpam-816	415	10	situated	situate	VERB
ejpam-816	415	11	at	at	ADP
ejpam-816	415	12	sk	sk	NOUN
ejpam-816	415	13	=	=	NOUN
ejpam-816	415	14	4k+	4k+	NUM
ejpam-816	415	15	1	1	NUM
ejpam-816	415	16	4	4	NUM
ejpam-816	415	17	(	(	PUNCT
ejpam-816	415	18	k	k	NOUN
ejpam-816	415	19	=	=	SYM
ejpam-816	415	20	0,1,2	0,1,2	NUM
ejpam-816	415	21	,	,	PUNCT
ejpam-816	415	22	.	.	PUNCT
ejpam-816	415	23	.	.	PUNCT
ejpam-816	415	24	.	.	PUNCT
ejpam-816	415	25	)	)	PUNCT
ejpam-816	416	1	and	and	CCONJ
ejpam-816	416	2	,	,	PUNCT
ejpam-816	416	3	from	from	ADP
ejpam-816	416	4	(	(	PUNCT
ejpam-816	416	5	60	60	NUM
ejpam-816	416	6	)	)	PUNCT
ejpam-816	416	7	,	,	PUNCT
ejpam-816	416	8	we	we	PRON
ejpam-816	416	9	obtain	obtain	VERB
ejpam-816	416	10	the	the	DET
ejpam-816	416	11	algebraic	algebraic	ADJ
ejpam-816	416	12	expansion	expansion	NOUN
ejpam-816	416	13	in	in	ADP
ejpam-816	416	14	this	this	DET
ejpam-816	416	15	case	case	NOUN
ejpam-816	416	16	given	give	VERB
ejpam-816	416	17	by	by	ADP
ejpam-816	416	18	h2,0(z	h2,0(z	PROPN
ejpam-816	416	19	)	)	PUNCT
ejpam-816	416	20	=	=	SYM
ejpam-816	417	1	−16	−16	NUM
ejpam-816	417	2	∞	∞	NUM
ejpam-816	417	3	∑	∑	PROPN
ejpam-816	417	4	k=0	k=0	PROPN
ejpam-816	417	5	γ(4k+	γ(4k+	PROPN
ejpam-816	417	6	1	1	NUM
ejpam-816	417	7	4	4	NUM
ejpam-816	417	8	)	)	PUNCT
ejpam-816	417	9	(	(	PUNCT
ejpam-816	417	10	k!)2	k!)2	PROPN
ejpam-816	417	11	{	{	PUNCT
ejpam-816	417	12	ψ(4k+	ψ(4k+	NOUN
ejpam-816	417	13	1	1	NUM
ejpam-816	417	14	4	4	NUM
ejpam-816	417	15	)	)	PUNCT
ejpam-816	417	16	−	−	PROPN
ejpam-816	417	17	1	1	NUM
ejpam-816	417	18	2	2	NUM
ejpam-816	417	19	ψ(k+	ψ(k+	PUNCT
ejpam-816	417	20	1)−	1)−	PROPN
ejpam-816	417	21	log	log	NOUN
ejpam-816	417	22	z}z−4k−	z}z−4k−	NUM
ejpam-816	417	23	1	1	NUM
ejpam-816	417	24	4	4	NUM
ejpam-816	417	25	.	.	PUNCT
ejpam-816	418	1	since	since	ADV
ejpam-816	418	2	,	,	PUNCT
ejpam-816	418	3	by	by	ADP
ejpam-816	418	4	(	(	PUNCT
ejpam-816	418	5	34	34	NUM
ejpam-816	418	6	)	)	PUNCT
ejpam-816	418	7	,	,	PUNCT
ejpam-816	418	8	there	there	PRON
ejpam-816	418	9	is	be	VERB
ejpam-816	418	10	no	no	DET
ejpam-816	418	11	sector	sector	NOUN
ejpam-816	418	12	in	in	ADP
ejpam-816	418	13	which	which	PRON
ejpam-816	418	14	the	the	DET
ejpam-816	418	15	algebraic	algebraic	ADJ
ejpam-816	418	16	expansions	expansion	NOUN
ejpam-816	418	17	cancel	cancel	VERB
ejpam-816	418	18	when	when	SCONJ
ejpam-816	418	19	m	m	VERB
ejpam-816	418	20	=	=	SYM
ejpam-816	418	21	1	1	NUM
ejpam-816	418	22	,	,	PUNCT
ejpam-816	418	23	we	we	PRON
ejpam-816	418	24	obtain	obtain	VERB
ejpam-816	418	25	the	the	DET
ejpam-816	418	26	expansion	expansion	NOUN
ejpam-816	418	27	of	of	ADP
ejpam-816	418	28	j2(z	j2(z	NOUN
ejpam-816	418	29	)	)	PUNCT
ejpam-816	418	30	in	in	ADP
ejpam-816	418	31	(	(	PUNCT
ejpam-816	418	32	48	48	NUM
ejpam-816	418	33	)	)	PUNCT
ejpam-816	418	34	given	give	VERB
ejpam-816	418	35	by	by	ADP
ejpam-816	418	36	j2(z	j2(z	NOUN
ejpam-816	418	37	)	)	PUNCT
ejpam-816	418	38	∼	∼	NOUN
ejpam-816	418	39			NOUN
ejpam-816	418	40			PROPN
ejpam-816	418	41			NOUN
ejpam-816	418	42	(	(	PUNCT
ejpam-816	418	43	1	1	NUM
ejpam-816	418	44	+	+	SYM
ejpam-816	418	45	i){e2,0(z	i){e2,0(z	PROPN
ejpam-816	418	46	)	)	PUNCT
ejpam-816	419	1	+	+	PROPN
ejpam-816	419	2	h2,0(ze−πi)}−	h2,0(ze−πi)}−	PROPN
ejpam-816	419	3	2e	2e	NOUN
ejpam-816	419	4	1	1	NUM
ejpam-816	419	5	4	4	NUM
ejpam-816	419	6	πih2,0(z	πih2,0(z	NUM
ejpam-816	419	7	)	)	PUNCT
ejpam-816	419	8	in	in	ADP
ejpam-816	419	9	[	[	X
ejpam-816	419	10	0	0	NUM
ejpam-816	419	11	,	,	PUNCT
ejpam-816	419	12	1	1	NUM
ejpam-816	419	13	2	2	NUM
ejpam-816	419	14	π	π	NOUN
ejpam-816	419	15	)	)	PUNCT
ejpam-816	419	16	(	(	PUNCT
ejpam-816	419	17	1	1	NUM
ejpam-816	419	18	+	+	NUM
ejpam-816	419	19	i)h2,0(ze−πi)−	i)h2,0(ze−πi)−	NOUN
ejpam-816	419	20	2e	2e	NOUN
ejpam-816	419	21	1	1	NUM
ejpam-816	419	22	4	4	NUM
ejpam-816	419	23	πi{e(ze−πi	πi{e(ze−πi	NOUN
ejpam-816	419	24	)	)	PUNCT
ejpam-816	420	1	+	+	NOUN
ejpam-816	420	2	h2,0(z	h2,0(z	NOUN
ejpam-816	420	3	)	)	PUNCT
ejpam-816	420	4	}	}	PUNCT
ejpam-816	420	5	in	in	SCONJ
ejpam-816	420	6	(	(	PUNCT
ejpam-816	420	7	1	1	NUM
ejpam-816	420	8	2	2	NUM
ejpam-816	420	9	π	π	NOUN
ejpam-816	420	10	,	,	PUNCT
ejpam-816	420	11	π	π	X
ejpam-816	420	12	]	]	PUNCT
ejpam-816	420	13	as	as	ADP
ejpam-816	420	14	|z|	|z|	NOUN
ejpam-816	420	15	→∞.	→∞.	PUNCT
ejpam-816	420	16	the	the	DET
ejpam-816	420	17	expansion	expansion	NOUN
ejpam-816	420	18	in	in	ADP
ejpam-816	420	19	the	the	DET
ejpam-816	420	20	lower	low	ADJ
ejpam-816	420	21	half	half	ADJ
ejpam-816	420	22	-	-	PUNCT
ejpam-816	420	23	plane	plane	NOUN
ejpam-816	420	24	can	can	AUX
ejpam-816	420	25	be	be	AUX
ejpam-816	420	26	obtained	obtain	VERB
ejpam-816	420	27	by	by	ADP
ejpam-816	420	28	(	(	PUNCT
ejpam-816	420	29	45	45	NUM
ejpam-816	420	30	)	)	PUNCT
ejpam-816	420	31	.	.	PUNCT
ejpam-816	421	1	the	the	DET
ejpam-816	421	2	rays	ray	NOUN
ejpam-816	421	3	arg	arg	VERB
ejpam-816	421	4	z	z	NOUN
ejpam-816	421	5	=	=	SYM
ejpam-816	421	6	0	0	NUM
ejpam-816	421	7	,	,	PUNCT
ejpam-816	421	8	π	π	NOUN
ejpam-816	421	9	are	be	AUX
ejpam-816	421	10	stokes	stoke	NOUN
ejpam-816	421	11	lines	line	NOUN
ejpam-816	421	12	for	for	ADP
ejpam-816	421	13	the	the	DET
ejpam-816	421	14	algebraic	algebraic	ADJ
ejpam-816	421	15	expansions	expansion	NOUN
ejpam-816	421	16	h2,0(ze−πi	h2,0(ze−πi	NOUN
ejpam-816	421	17	)	)	PUNCT
ejpam-816	421	18	and	and	CCONJ
ejpam-816	421	19	h2,0(z	h2,0(z	PROPN
ejpam-816	421	20	)	)	PUNCT
ejpam-816	421	21	,	,	PUNCT
ejpam-816	421	22	respectively	respectively	ADV
ejpam-816	421	23	and	and	CCONJ
ejpam-816	421	24	the	the	DET
ejpam-816	421	25	rays	ray	NOUN
ejpam-816	421	26	arg	arg	VERB
ejpam-816	421	27	z	z	NOUN
ejpam-816	421	28	=	=	PRON
ejpam-816	421	29	±1	±1	VERB
ejpam-816	421	30	2	2	NUM
ejpam-816	421	31	π	π	NOUN
ejpam-816	421	32	are	be	AUX
ejpam-816	421	33	stokes	stoke	NOUN
ejpam-816	421	34	lines	line	NOUN
ejpam-816	421	35	for	for	ADP
ejpam-816	421	36	the	the	DET
ejpam-816	421	37	exponential	exponential	ADJ
ejpam-816	421	38	expansions	expansion	NOUN
ejpam-816	421	39	.	.	PUNCT
ejpam-816	422	1	in	in	ADP
ejpam-816	422	2	table	table	NOUN
ejpam-816	422	3	1	1	NUM
ejpam-816	422	4	we	we	PRON
ejpam-816	422	5	present	present	VERB
ejpam-816	422	6	the	the	DET
ejpam-816	422	7	absolute	absolute	ADJ
ejpam-816	422	8	relative	relative	ADJ
ejpam-816	422	9	errors	error	NOUN
ejpam-816	422	10	in	in	ADP
ejpam-816	422	11	the	the	DET
ejpam-816	422	12	asymptotic	asymptotic	ADJ
ejpam-816	422	13	expansion	expansion	NOUN
ejpam-816	422	14	of	of	ADP
ejpam-816	422	15	j2(z	j2(z	NOUN
ejpam-816	422	16	)	)	PUNCT
ejpam-816	422	17	in	in	ADP
ejpam-816	422	18	(	(	PUNCT
ejpam-816	422	19	46	46	NUM
ejpam-816	422	20	)	)	PUNCT
ejpam-816	422	21	,	,	PUNCT
ejpam-816	422	22	(	(	PUNCT
ejpam-816	422	23	47	47	NUM
ejpam-816	422	24	)	)	PUNCT
ejpam-816	422	25	and	and	CCONJ
ejpam-816	422	26	(	(	PUNCT
ejpam-816	422	27	48	48	NUM
ejpam-816	422	28	)	)	PUNCT
ejpam-816	422	29	for	for	ADP
ejpam-816	422	30	a	a	DET
ejpam-816	422	31	given	give	VERB
ejpam-816	422	32	value	value	NOUN
ejpam-816	422	33	of	of	ADP
ejpam-816	422	34	|z|	|z|	NOUN
ejpam-816	422	35	and	and	CCONJ
ejpam-816	422	36	varying	vary	VERB
ejpam-816	422	37	θ	θ	PROPN
ejpam-816	422	38	=	=	PUNCT
ejpam-816	422	39	arg	arg	PROPN
ejpam-816	422	40	z.	z.	PROPN
ejpam-816	422	41	in	in	ADP
ejpam-816	422	42	each	each	DET
ejpam-816	422	43	case	case	NOUN
ejpam-816	422	44	the	the	DET
ejpam-816	422	45	exponential	exponential	ADJ
ejpam-816	422	46	and	and	CCONJ
ejpam-816	422	47	algebraic	algebraic	ADJ
ejpam-816	422	48	expansions	expansion	NOUN
ejpam-816	422	49	have	have	AUX
ejpam-816	422	50	been	be	AUX
ejpam-816	422	51	optimally	optimally	ADV
ejpam-816	422	52	truncated	truncate	VERB
ejpam-816	422	53	,	,	PUNCT
ejpam-816	422	54	with	with	ADP
ejpam-816	422	55	the	the	DET
ejpam-816	422	56	exact	exact	ADJ
ejpam-816	422	57	value	value	NOUN
ejpam-816	422	58	of	of	ADP
ejpam-816	422	59	j2(z	j2(z	NOUN
ejpam-816	422	60	)	)	PUNCT
ejpam-816	422	61	being	be	AUX
ejpam-816	422	62	computed	compute	VERB
ejpam-816	422	63	both	both	PRON
ejpam-816	422	64	by	by	ADP
ejpam-816	422	65	evaluation	evaluation	NOUN
ejpam-816	422	66	of	of	ADP
ejpam-816	422	67	the	the	DET
ejpam-816	422	68	wright	wright	PROPN
ejpam-816	422	69	functions	function	NOUN
ejpam-816	422	70	and	and	CCONJ
ejpam-816	422	71	also	also	ADV
ejpam-816	422	72	high	high	ADJ
ejpam-816	422	73	-	-	PUNCT
ejpam-816	422	74	precision	precision	NOUN
ejpam-816	422	75	numerical	numerical	ADJ
ejpam-816	422	76	quadrature	quadrature	NOUN
ejpam-816	422	77	of	of	ADP
ejpam-816	422	78	the	the	DET
ejpam-816	422	79	integral	integral	ADJ
ejpam-816	422	80	in	in	ADP
ejpam-816	422	81	(	(	PUNCT
ejpam-816	422	82	42	42	NUM
ejpam-816	422	83	)	)	PUNCT
ejpam-816	422	84	.	.	PUNCT
ejpam-816	423	1	we	we	PRON
ejpam-816	423	2	remark	remark	VERB
ejpam-816	423	3	that	that	SCONJ
ejpam-816	423	4	in	in	ADP
ejpam-816	423	5	the	the	DET
ejpam-816	423	6	three	three	NUM
ejpam-816	423	7	cases	case	NOUN
ejpam-816	423	8	considered	consider	VERB
ejpam-816	423	9	,	,	PUNCT
ejpam-816	423	10	an	an	DET
ejpam-816	423	11	accurate	accurate	ADJ
ejpam-816	423	12	determination	determination	NOUN
ejpam-816	423	13	of	of	ADP
ejpam-816	423	14	the	the	DET
ejpam-816	423	15	subdominant	subdominant	ADJ
ejpam-816	423	16	expansions	expansion	NOUN
ejpam-816	423	17	on	on	ADP
ejpam-816	423	18	the	the	DET
ejpam-816	423	19	stokes	stoke	NOUN
ejpam-816	423	20	lines	line	NOUN
ejpam-816	423	21	would	would	AUX
ejpam-816	423	22	require	require	VERB
ejpam-816	423	23	a	a	DET
ejpam-816	423	24	detailed	detailed	ADJ
ejpam-816	423	25	treatment	treatment	NOUN
ejpam-816	423	26	of	of	ADP
ejpam-816	423	27	the	the	DET
ejpam-816	423	28	stokes	stoke	NOUN
ejpam-816	423	29	phenomenon	phenomenon	NOUN
ejpam-816	423	30	.	.	PUNCT
ejpam-816	424	1	5.2	5.2	NUM
ejpam-816	424	2	.	.	PUNCT
ejpam-816	424	3	example	example	NOUN
ejpam-816	424	4	2	2	NUM
ejpam-816	424	5	we	we	PRON
ejpam-816	424	6	consider	consider	VERB
ejpam-816	424	7	an	an	DET
ejpam-816	424	8	example	example	NOUN
ejpam-816	424	9	of	of	ADP
ejpam-816	424	10	the	the	DET
ejpam-816	424	11	integral	integral	ADJ
ejpam-816	424	12	kn	kn	PROPN
ejpam-816	424	13	,	,	PUNCT
ejpam-816	424	14	p(z	p(z	PROPN
ejpam-816	424	15	)	)	PUNCT
ejpam-816	424	16	defined	define	VERB
ejpam-816	424	17	in	in	ADP
ejpam-816	424	18	(	(	PUNCT
ejpam-816	424	19	40	40	NUM
ejpam-816	424	20	)	)	PUNCT
ejpam-816	424	21	with	with	ADP
ejpam-816	424	22	n=	n=	ADJ
ejpam-816	424	23	3	3	NUM
ejpam-816	424	24	,	,	PUNCT
ejpam-816	424	25	p	p	NOUN
ejpam-816	424	26	=	=	NOUN
ejpam-816	424	27	1	1	NUM
ejpam-816	424	28	,	,	PUNCT
ejpam-816	424	29	namely	namely	ADV
ejpam-816	424	30	k3,1(z	k3,1(z	PROPN
ejpam-816	424	31	)	)	PUNCT
ejpam-816	424	32	=	=	SYM
ejpam-816	424	33	36	36	NUM
ejpam-816	424	34	∫	∫	NOUN
ejpam-816	424	35	∞	∞	PROPN
ejpam-816	424	36	−∞	−∞	ADP
ejpam-816	424	37	�	�	PROPN
ejpam-816	424	38	∫	∫	PROPN
ejpam-816	424	39	∞	∞	PROPN
ejpam-816	424	40	0	0	NUM
ejpam-816	424	41	∫	∫	PROPN
ejpam-816	425	1	∞	∞	PROPN
ejpam-816	425	2	0	0	NUM
ejpam-816	425	3	(	(	PUNCT
ejpam-816	425	4	x3	x3	PROPN
ejpam-816	425	5	/	/	SYM
ejpam-816	425	6	x2	x2	ADJ
ejpam-816	425	7	)	)	PUNCT
ejpam-816	425	8	1	1	NUM
ejpam-816	425	9	2	2	NUM
ejpam-816	425	10	exp{−(x3	exp{−(x3	NOUN
ejpam-816	425	11	1	1	NUM
ejpam-816	426	1	+	+	CCONJ
ejpam-816	426	2	x3	x3	ADJ
ejpam-816	426	3	2	2	NUM
ejpam-816	426	4	+	+	CCONJ
ejpam-816	426	5	x4	x4	PROPN
ejpam-816	426	6	3	3	NUM
ejpam-816	426	7	−	−	PROPN
ejpam-816	426	8	z(x1	z(x1	NOUN
ejpam-816	426	9	x2	x2	NOUN
ejpam-816	426	10	)	)	PUNCT
ejpam-816	426	11	1	1	NUM
ejpam-816	426	12	2	2	NUM
ejpam-816	426	13	x3	x3	ADJ
ejpam-816	426	14	}	}	PUNCT
ejpam-816	427	1	d	d	PROPN
ejpam-816	427	2	x1d	x1d	SYM
ejpam-816	427	3	x2	x2	PROPN
ejpam-816	427	4	�	�	PROPN
ejpam-816	427	5	d	d	NOUN
ejpam-816	427	6	x3	x3	PROPN
ejpam-816	427	7	,	,	PUNCT
ejpam-816	427	8	which	which	PRON
ejpam-816	427	9	is	be	AUX
ejpam-816	427	10	associated	associate	VERB
ejpam-816	427	11	with	with	ADP
ejpam-816	427	12	the	the	DET
ejpam-816	427	13	parameters	parameter	NOUN
ejpam-816	427	14	µ1	µ1	NOUN
ejpam-816	427	15	=	=	SYM
ejpam-816	427	16	µ2	µ2	PROPN
ejpam-816	427	17	=	=	SYM
ejpam-816	427	18	3	3	NUM
ejpam-816	427	19	,	,	PUNCT
ejpam-816	427	20	µ3	µ3	NOUN
ejpam-816	427	21	=	=	SYM
ejpam-816	427	22	4	4	NUM
ejpam-816	427	23	,	,	PUNCT
ejpam-816	427	24	m1	m1	PROPN
ejpam-816	427	25	=	=	SYM
ejpam-816	427	26	m2	m2	PROPN
ejpam-816	427	27	=	=	SYM
ejpam-816	427	28	1	1	NUM
ejpam-816	427	29	2	2	NUM
ejpam-816	427	30	,	,	PUNCT
ejpam-816	427	31	m3	m3	PROPN
ejpam-816	427	32	=	=	SYM
ejpam-816	427	33	1	1	NUM
ejpam-816	427	34	and	and	CCONJ
ejpam-816	427	35	ν1	ν1	NOUN
ejpam-816	427	36	=	=	SYM
ejpam-816	427	37	1	1	NUM
ejpam-816	427	38	,	,	PUNCT
ejpam-816	427	39	ν2	ν2	NOUN
ejpam-816	427	40	=	=	SYM
ejpam-816	427	41	1	1	NUM
ejpam-816	427	42	2	2	NUM
ejpam-816	427	43	,	,	PUNCT
ejpam-816	427	44	ν3	ν3	NOUN
ejpam-816	427	45	=	=	SYM
ejpam-816	427	46	3	3	NUM
ejpam-816	427	47	2	2	NUM
ejpam-816	427	48	.	.	PUNCT
ejpam-816	428	1	from	from	ADP
ejpam-816	428	2	(	(	PUNCT
ejpam-816	428	3	41	41	NUM
ejpam-816	428	4	)	)	PUNCT
ejpam-816	428	5	,	,	PUNCT
ejpam-816	428	6	we	we	PRON
ejpam-816	428	7	therefore	therefore	ADV
ejpam-816	428	8	find	find	VERB
ejpam-816	428	9	k3,1(z	k3,1(z	NOUN
ejpam-816	428	10	)	)	PUNCT
ejpam-816	428	11	=	=	SYM
ejpam-816	429	1	∞	∞	NUM
ejpam-816	429	2	∑	∑	PUNCT
ejpam-816	429	3	k=0	k=0	PROPN
ejpam-816	429	4	zk	zk	PROPN
ejpam-816	430	1	k	k	PROPN
ejpam-816	430	2	!	!	PROPN
ejpam-816	430	3	3	3	NUM
ejpam-816	430	4	∏	∏	PROPN
ejpam-816	430	5	r=1	r=1	PROPN
ejpam-816	430	6	γ	γ	X
ejpam-816	430	7	�	�	PROPN
ejpam-816	430	8	νr	νr	ADP
ejpam-816	431	1	+	+	ADP
ejpam-816	431	2	mr	mr	PROPN
ejpam-816	431	3	k	k	PROPN
ejpam-816	431	4	µr	µr	ADP
ejpam-816	431	5	�	�	PROPN
ejpam-816	431	6	(	(	PUNCT
ejpam-816	431	7	1−	1−	NUM
ejpam-816	431	8	e(ν3	e(ν3	NOUN
ejpam-816	431	9	+	+	PROPN
ejpam-816	431	10	m3k	m3k	NOUN
ejpam-816	431	11	)	)	PUNCT
ejpam-816	431	12	)	)	PUNCT
ejpam-816	432	1	r.	r.	PROPN
ejpam-816	432	2	paris	paris	PROPN
ejpam-816	432	3	/	/	SYM
ejpam-816	432	4	eur	eur	PROPN
ejpam-816	432	5	.	.	PUNCT
ejpam-816	433	1	j.	j.	PROPN
ejpam-816	433	2	pure	pure	PROPN
ejpam-816	433	3	appl	appl	PROPN
ejpam-816	433	4	.	.	PROPN
ejpam-816	433	5	math	math	PROPN
ejpam-816	433	6	,	,	PUNCT
ejpam-816	433	7	3	3	NUM
ejpam-816	433	8	(	(	PUNCT
ejpam-816	433	9	2010	2010	NUM
ejpam-816	433	10	)	)	PUNCT
ejpam-816	433	11	,	,	PUNCT
ejpam-816	433	12	1006	1006	NUM
ejpam-816	433	13	-	-	SYM
ejpam-816	433	14	1031	1031	NUM
ejpam-816	433	15	1023	1023	NUM
ejpam-816	433	16	table	table	NOUN
ejpam-816	433	17	2	2	NUM
ejpam-816	433	18	:	:	PUNCT
ejpam-816	433	19	values	value	NOUN
ejpam-816	433	20	of	of	ADP
ejpam-816	433	21	the	the	DET
ejpam-816	433	22	absolute	absolute	ADJ
ejpam-816	433	23	relative	relative	ADJ
ejpam-816	433	24	error	error	NOUN
ejpam-816	433	25	in	in	ADP
ejpam-816	433	26	the	the	DET
ejpam-816	433	27	computation	computation	NOUN
ejpam-816	433	28	of	of	ADP
ejpam-816	433	29	j2(z	j2(z	NOUN
ejpam-816	433	30	)	)	PUNCT
ejpam-816	433	31	when	when	SCONJ
ejpam-816	433	32	µ1	µ1	PROPN
ejpam-816	433	33	=	=	SYM
ejpam-816	433	34	µ2	µ2	NOUN
ejpam-816	433	35	=	=	PROPN
ejpam-816	433	36	4	4	NUM
ejpam-816	433	37	and	and	CCONJ
ejpam-816	433	38	m1	m1	PROPN
ejpam-816	433	39	=	=	SYM
ejpam-816	433	40	m2	m2	PROPN
ejpam-816	433	41	=	=	PROPN
ejpam-816	433	42	m	m	PROPN
ejpam-816	433	43	as	as	ADP
ejpam-816	433	44	a	a	DET
ejpam-816	433	45	function	function	NOUN
ejpam-816	433	46	of	of	ADP
ejpam-816	433	47	θ	θ	PROPN
ejpam-816	433	48	=	=	PUNCT
ejpam-816	433	49	arg	arg	PROPN
ejpam-816	433	50	z.	z.	PROPN
ejpam-816	434	1	m=	m=	VERB
ejpam-816	434	2	1	1	NUM
ejpam-816	434	3	2	2	NUM
ejpam-816	434	4	,	,	PUNCT
ejpam-816	434	5	ν1	ν1	NOUN
ejpam-816	434	6	=	=	SYM
ejpam-816	434	7	1	1	NUM
ejpam-816	434	8	2	2	NUM
ejpam-816	434	9	,	,	PUNCT
ejpam-816	434	10	ν2	ν2	NOUN
ejpam-816	434	11	=	=	SYM
ejpam-816	434	12	1	1	NUM
ejpam-816	434	13	m=	m=	SYM
ejpam-816	434	14	3	3	NUM
ejpam-816	434	15	4	4	NUM
ejpam-816	434	16	,	,	PUNCT
ejpam-816	434	17	ν1	ν1	NOUN
ejpam-816	434	18	=	=	SYM
ejpam-816	434	19	1	1	NUM
ejpam-816	434	20	2	2	NUM
ejpam-816	434	21	,	,	PUNCT
ejpam-816	434	22	ν2	ν2	NOUN
ejpam-816	434	23	=	=	SYM
ejpam-816	434	24	3	3	NUM
ejpam-816	434	25	2	2	NUM
ejpam-816	434	26	m	m	NOUN
ejpam-816	434	27	=	=	SYM
ejpam-816	434	28	1	1	NUM
ejpam-816	434	29	,	,	PUNCT
ejpam-816	434	30	ν1	ν1	NOUN
ejpam-816	434	31	=	=	SYM
ejpam-816	434	32	ν2	ν2	NOUN
ejpam-816	434	33	=	=	SYM
ejpam-816	434	34	1	1	NUM
ejpam-816	434	35	4	4	NUM
ejpam-816	434	36	|z|	|z|	NOUN
ejpam-816	434	37	=	=	SYM
ejpam-816	434	38	20	20	NUM
ejpam-816	434	39	|z|	|z|	NOUN
ejpam-816	434	40	=	=	SYM
ejpam-816	434	41	20	20	NUM
ejpam-816	434	42	|z|	|z|	NOUN
ejpam-816	434	43	=	=	SYM
ejpam-816	434	44	15	15	NUM
ejpam-816	434	45	θ	θ	NOUN
ejpam-816	434	46	/	/	SYM
ejpam-816	434	47	π	π	PROPN
ejpam-816	434	48	|rel	|rel	NOUN
ejpam-816	434	49	.	.	PUNCT
ejpam-816	434	50	error|	error|	PROPN
ejpam-816	434	51	θ	θ	PROPN
ejpam-816	434	52	/	/	SYM
ejpam-816	434	53	π	π	PROPN
ejpam-816	434	54	|rel	|rel	NOUN
ejpam-816	434	55	.	.	PUNCT
ejpam-816	434	56	error|	error|	PROPN
ejpam-816	434	57	θ	θ	PROPN
ejpam-816	434	58	/	/	SYM
ejpam-816	434	59	π	π	PROPN
ejpam-816	434	60	|rel	|rel	NOUN
ejpam-816	434	61	.	.	PUNCT
ejpam-816	434	62	error|	error|	NOUN
ejpam-816	434	63	0	0	NUM
ejpam-816	435	1	2.172×	2.172×	NUM
ejpam-816	435	2	10−10	10−10	NUM
ejpam-816	435	3	0.250	0.250	NUM
ejpam-816	435	4	8.081×	8.081×	NUM
ejpam-816	436	1	10−14	10−14	NUM
ejpam-816	436	2	0	0	NUM
ejpam-816	437	1	4.869×	4.869×	NUM
ejpam-816	437	2	10−11	10−11	NUM
ejpam-816	437	3	0.125	0.125	NUM
ejpam-816	437	4	3.326×	3.326×	NUM
ejpam-816	437	5	10−10	10−10	NUM
ejpam-816	437	6	0.375	0.375	NUM
ejpam-816	437	7	2.528×	2.528×	NUM
ejpam-816	438	1	10−13	10−13	NUM
ejpam-816	438	2	0.125	0.125	NUM
ejpam-816	438	3	9.220×	9.220×	NUM
ejpam-816	438	4	10−12	10−12	NOUN
ejpam-816	438	5	0.250	0.250	NUM
ejpam-816	438	6	1.228×	1.228×	PROPN
ejpam-816	438	7	10−9	10−9	NUM
ejpam-816	438	8	0.500	0.500	NUM
ejpam-816	438	9	1.104×	1.104×	PROPN
ejpam-816	438	10	10−12	10−12	NOUN
ejpam-816	438	11	0.250	0.250	NUM
ejpam-816	438	12	4.427×	4.427×	PROPN
ejpam-816	439	1	10−14	10−14	NUM
ejpam-816	439	2	0.375	0.375	NUM
ejpam-816	439	3	3.939×	3.939×	NUM
ejpam-816	439	4	10−8	10−8	NUM
ejpam-816	439	5	0.625	0.625	NUM
ejpam-816	439	6	2.528×	2.528×	NUM
ejpam-816	440	1	10−13	10−13	NUM
ejpam-816	440	2	0.375	0.375	NUM
ejpam-816	440	3	1.025×	1.025×	NUM
ejpam-816	440	4	10−15	10−15	NOUN
ejpam-816	440	5	0.500	0.500	NUM
ejpam-816	440	6	1.756×	1.756×	PROPN
ejpam-816	440	7	10−4	10−4	NUM
ejpam-816	440	8	0.750	0.750	NUM
ejpam-816	440	9	1.414×	1.414×	PROPN
ejpam-816	440	10	10−13	10−13	NUM
ejpam-816	440	11	0.500	0.500	NUM
ejpam-816	440	12	5.061×	5.061×	PROPN
ejpam-816	440	13	10−15	10−15	NOUN
ejpam-816	440	14	−0.125	−0.125	NOUN
ejpam-816	441	1	3.326×	3.326×	NUM
ejpam-816	441	2	10−10	10−10	NUM
ejpam-816	441	3	0.875	0.875	NUM
ejpam-816	441	4	7.550×	7.550×	NUM
ejpam-816	441	5	10−14	10−14	NUM
ejpam-816	441	6	0.625	0.625	NUM
ejpam-816	441	7	1.046×	1.046×	NUM
ejpam-816	441	8	10−15	10−15	NOUN
ejpam-816	441	9	−0.250	−0.250	PROPN
ejpam-816	441	10	3.684×	3.684×	NUM
ejpam-816	441	11	10−10	10−10	NUM
ejpam-816	441	12	1.000	1.000	NUM
ejpam-816	441	13	7.014×	7.014×	NUM
ejpam-816	441	14	10−14	10−14	NUM
ejpam-816	441	15	0.750	0.750	NUM
ejpam-816	441	16	5.306×	5.306×	NUM
ejpam-816	441	17	10−14	10−14	NUM
ejpam-816	441	18	−0.375	−0.375	PROPN
ejpam-816	441	19	3.326×	3.326×	NUM
ejpam-816	441	20	10−10	10−10	NUM
ejpam-816	441	21	1.125	1.125	NUM
ejpam-816	441	22	2.584×	2.584×	NUM
ejpam-816	441	23	10−13	10−13	NUM
ejpam-816	441	24	0.875	0.875	NUM
ejpam-816	441	25	9.220×	9.220×	NUM
ejpam-816	441	26	10−12	10−12	NOUN
ejpam-816	441	27	−0.500	−0.500	NOUN
ejpam-816	441	28	2.172×	2.172×	NUM
ejpam-816	441	29	10−10	10−10	NUM
ejpam-816	441	30	1.250	1.250	NUM
ejpam-816	441	31	1.058×	1.058×	PROPN
ejpam-816	441	32	10−13	10−13	NUM
ejpam-816	441	33	1.000	1.000	NUM
ejpam-816	441	34	4.869×	4.869×	NUM
ejpam-816	441	35	10−11	10−11	NUM
ejpam-816	441	36	=	=	SYM
ejpam-816	441	37	3ψ0(z	3ψ0(z	NUM
ejpam-816	441	38	)	)	PUNCT
ejpam-816	442	1	+	+	CCONJ
ejpam-816	442	2	i	i	PRON
ejpam-816	442	3	3ψ0(ze∓πi	3ψ0(ze∓πi	NUM
ejpam-816	442	4	)	)	PUNCT
ejpam-816	442	5	,	,	PUNCT
ejpam-816	442	6	where	where	SCONJ
ejpam-816	442	7	the	the	DET
ejpam-816	442	8	3ψ0(z	3ψ0(z	NUM
ejpam-816	442	9	)	)	PUNCT
ejpam-816	442	10	function	function	NOUN
ejpam-816	442	11	is	be	AUX
ejpam-816	442	12	that	that	SCONJ
ejpam-816	442	13	defined	define	VERB
ejpam-816	442	14	in	in	ADP
ejpam-816	442	15	(	(	PUNCT
ejpam-816	442	16	25	25	NUM
ejpam-816	442	17	)	)	PUNCT
ejpam-816	442	18	with	with	ADP
ejpam-816	442	19	the	the	DET
ejpam-816	442	20	same	same	ADJ
ejpam-816	442	21	parameter	parameter	NOUN
ejpam-816	442	22	values	value	NOUN
ejpam-816	442	23	.	.	PUNCT
ejpam-816	443	1	it	it	PRON
ejpam-816	443	2	is	be	AUX
ejpam-816	443	3	easily	easily	ADV
ejpam-816	443	4	shown	show	VERB
ejpam-816	443	5	that	that	SCONJ
ejpam-816	443	6	k3,1(ze±πi	k3,1(ze±πi	NOUN
ejpam-816	443	7	)	)	PUNCT
ejpam-816	443	8	=	=	SYM
ejpam-816	443	9	ik3,1(z	ik3,1(z	NOUN
ejpam-816	443	10	)	)	PUNCT
ejpam-816	443	11	,	,	PUNCT
ejpam-816	443	12	where	where	SCONJ
ejpam-816	443	13	the	the	DET
ejpam-816	443	14	bar	bar	NOUN
ejpam-816	443	15	denotes	denote	VERB
ejpam-816	443	16	the	the	DET
ejpam-816	443	17	complex	complex	ADJ
ejpam-816	443	18	conjugate	conjugate	NOUN
ejpam-816	443	19	,	,	PUNCT
ejpam-816	443	20	so	so	SCONJ
ejpam-816	443	21	that	that	SCONJ
ejpam-816	443	22	there	there	PRON
ejpam-816	443	23	is	be	VERB
ejpam-816	443	24	a	a	DET
ejpam-816	443	25	basic	basic	ADJ
ejpam-816	443	26	symmetry	symmetry	NOUN
ejpam-816	443	27	about	about	ADP
ejpam-816	443	28	the	the	DET
ejpam-816	443	29	imaginary	imaginary	ADJ
ejpam-816	443	30	axis	axis	NOUN
ejpam-816	443	31	.	.	PUNCT
ejpam-816	444	1	the	the	DET
ejpam-816	444	2	sectorial	sectorial	ADJ
ejpam-816	444	3	behaviour	behaviour	NOUN
ejpam-816	444	4	of	of	ADP
ejpam-816	444	5	k3,1(z	k3,1(z	PROPN
ejpam-816	444	6	)	)	PUNCT
ejpam-816	444	7	is	be	AUX
ejpam-816	444	8	shown	show	VERB
ejpam-816	444	9	in	in	ADP
ejpam-816	444	10	fig	fig	NOUN
ejpam-816	444	11	.	.	PUNCT
ejpam-816	445	1	2(b	2(b	NUM
ejpam-816	445	2	)	)	PUNCT
ejpam-816	445	3	with	with	ADP
ejpam-816	445	4	κ	κ	NOUN
ejpam-816	445	5	=	=	SYM
ejpam-816	445	6	5	5	NUM
ejpam-816	445	7	12	12	NUM
ejpam-816	445	8	.	.	PUNCT
ejpam-816	446	1	there	there	PRON
ejpam-816	446	2	are	be	VERB
ejpam-816	446	3	two	two	NUM
ejpam-816	446	4	exponentially	exponentially	ADV
ejpam-816	446	5	large	large	ADJ
ejpam-816	446	6	sectors	sector	NOUN
ejpam-816	446	7	,	,	PUNCT
ejpam-816	446	8	four	four	NUM
ejpam-816	446	9	sectors	sector	NOUN
ejpam-816	446	10	with	with	ADP
ejpam-816	446	11	mixed	mixed	ADJ
ejpam-816	446	12	algebraic	algebraic	ADJ
ejpam-816	446	13	and	and	CCONJ
ejpam-816	446	14	exponentially	exponentially	ADV
ejpam-816	446	15	small	small	ADJ
ejpam-816	446	16	behaviour	behaviour	NOUN
ejpam-816	446	17	and	and	CCONJ
ejpam-816	446	18	two	two	NUM
ejpam-816	446	19	sectors	sector	NOUN
ejpam-816	446	20	straddling	straddle	VERB
ejpam-816	446	21	the	the	DET
ejpam-816	446	22	imaginary	imaginary	ADJ
ejpam-816	446	23	axis	axis	NOUN
ejpam-816	446	24	of	of	ADP
ejpam-816	446	25	angular	angular	ADJ
ejpam-816	446	26	width	width	NOUN
ejpam-816	446	27	1	1	NUM
ejpam-816	446	28	6	6	NUM
ejpam-816	446	29	π	π	NOUN
ejpam-816	446	30	(	(	PUNCT
ejpam-816	446	31	bounded	bound	VERB
ejpam-816	446	32	by	by	ADP
ejpam-816	446	33	the	the	DET
ejpam-816	446	34	stokes	stokes	PROPN
ejpam-816	446	35	lines	line	NOUN
ejpam-816	446	36	)	)	PUNCT
ejpam-816	446	37	in	in	ADP
ejpam-816	446	38	which	which	PRON
ejpam-816	446	39	the	the	DET
ejpam-816	446	40	large-|z|	large-|z|	NOUN
ejpam-816	446	41	behaviour	behaviour	NOUN
ejpam-816	446	42	is	be	AUX
ejpam-816	446	43	algebraic	algebraic	ADJ
ejpam-816	446	44	.	.	PUNCT
ejpam-816	447	1	from	from	ADP
ejpam-816	447	2	the	the	DET
ejpam-816	447	3	asymptotic	asymptotic	ADJ
ejpam-816	447	4	expansion	expansion	NOUN
ejpam-816	447	5	of	of	ADP
ejpam-816	447	6	3ψ0(z	3ψ0(z	NUM
ejpam-816	447	7	)	)	PUNCT
ejpam-816	447	8	given	give	VERB
ejpam-816	447	9	in	in	ADP
ejpam-816	447	10	(	(	PUNCT
ejpam-816	447	11	29	29	NUM
ejpam-816	447	12	)	)	PUNCT
ejpam-816	447	13	we	we	PRON
ejpam-816	447	14	then	then	ADV
ejpam-816	447	15	obtain	obtain	VERB
ejpam-816	447	16	k3,1(z	k3,1(z	PROPN
ejpam-816	447	17	)	)	PUNCT
ejpam-816	447	18	∼	∼	NOUN
ejpam-816	447	19			PRON
ejpam-816	447	20			ADV
ejpam-816	447	21			PRON
ejpam-816	447	22			PROPN
ejpam-816	447	23			NOUN
ejpam-816	447	24	e3,0(z	e3,0(z	PROPN
ejpam-816	447	25	)	)	PUNCT
ejpam-816	448	1	+	+	NOUN
ejpam-816	448	2	h3,0(ze−πi	h3,0(ze−πi	NOUN
ejpam-816	448	3	)	)	PUNCT
ejpam-816	448	4	+	+	CCONJ
ejpam-816	448	5	ih3,0(z	ih3,0(z	PROPN
ejpam-816	448	6	)	)	PUNCT
ejpam-816	448	7	in	in	ADP
ejpam-816	448	8	(	(	PUNCT
ejpam-816	448	9	0	0	NUM
ejpam-816	448	10	,	,	PUNCT
ejpam-816	448	11	5	5	NUM
ejpam-816	448	12	12	12	NUM
ejpam-816	448	13	π	π	NOUN
ejpam-816	448	14	)	)	PUNCT
ejpam-816	448	15	h3,0(ze−πi	h3,0(ze−πi	NOUN
ejpam-816	448	16	)	)	PUNCT
ejpam-816	448	17	+	+	CCONJ
ejpam-816	448	18	ih3,0(z	ih3,0(z	PROPN
ejpam-816	448	19	)	)	PUNCT
ejpam-816	448	20	in	in	ADP
ejpam-816	448	21	(	(	PUNCT
ejpam-816	448	22	5	5	NUM
ejpam-816	448	23	12	12	NUM
ejpam-816	448	24	π	π	NOUN
ejpam-816	448	25	,	,	PUNCT
ejpam-816	448	26	1	1	NUM
ejpam-816	448	27	2	2	NUM
ejpam-816	448	28	π	π	NOUN
ejpam-816	448	29	]	]	X
ejpam-816	448	30	e3,0(z	e3,0(z	PROPN
ejpam-816	448	31	)	)	PUNCT
ejpam-816	448	32	+	+	NOUN
ejpam-816	448	33	h3,0(zeπi	h3,0(zeπi	X
ejpam-816	448	34	)	)	PUNCT
ejpam-816	448	35	+	+	CCONJ
ejpam-816	448	36	ih3,0(z	ih3,0(z	PROPN
ejpam-816	448	37	)	)	PUNCT
ejpam-816	448	38	in	in	ADP
ejpam-816	448	39	(	(	PUNCT
ejpam-816	448	40	−	−	PROPN
ejpam-816	448	41	5	5	NUM
ejpam-816	448	42	12	12	NUM
ejpam-816	448	43	π	π	PROPN
ejpam-816	448	44	,	,	PUNCT
ejpam-816	448	45	0	0	NUM
ejpam-816	448	46	)	)	PUNCT
ejpam-816	448	47	h3,0(zeπi	h3,0(zeπi	NOUN
ejpam-816	448	48	)	)	PUNCT
ejpam-816	448	49	+	+	CCONJ
ejpam-816	448	50	ih3,0(z	ih3,0(z	PROPN
ejpam-816	448	51	)	)	PUNCT
ejpam-816	448	52	in	in	ADP
ejpam-816	448	53	[	[	X
ejpam-816	448	54	−1	−1	NOUN
ejpam-816	448	55	2	2	NUM
ejpam-816	448	56	π,−	π,−	NOUN
ejpam-816	448	57	5	5	NUM
ejpam-816	448	58	12	12	NUM
ejpam-816	448	59	π	π	NOUN
ejpam-816	448	60	)	)	PUNCT
ejpam-816	448	61	as	as	ADP
ejpam-816	448	62	|z|	|z|	NOUN
ejpam-816	448	63	→	→	SYM
ejpam-816	448	64	∞	∞	PROPN
ejpam-816	448	65	,	,	PUNCT
ejpam-816	448	66	where	where	SCONJ
ejpam-816	448	67	the	the	DET
ejpam-816	448	68	expansions	expansion	NOUN
ejpam-816	448	69	e3,0(z	e3,0(z	NUM
ejpam-816	448	70	)	)	PUNCT
ejpam-816	448	71	and	and	CCONJ
ejpam-816	448	72	h3,0(z	h3,0(z	PROPN
ejpam-816	448	73	)	)	PUNCT
ejpam-816	448	74	are	be	AUX
ejpam-816	448	75	given	give	VERB
ejpam-816	448	76	in	in	ADP
ejpam-816	448	77	(	(	PUNCT
ejpam-816	448	78	26	26	NUM
ejpam-816	448	79	)	)	PUNCT
ejpam-816	448	80	,	,	PUNCT
ejpam-816	448	81	(	(	PUNCT
ejpam-816	448	82	27	27	NUM
ejpam-816	448	83	)	)	PUNCT
ejpam-816	448	84	and	and	CCONJ
ejpam-816	448	85	(	(	PUNCT
ejpam-816	448	86	28	28	NUM
ejpam-816	448	87	)	)	PUNCT
ejpam-816	448	88	.	.	PUNCT
ejpam-816	449	1	the	the	DET
ejpam-816	449	2	expansion	expansion	NOUN
ejpam-816	449	3	of	of	ADP
ejpam-816	449	4	k3,1(z	k3,1(z	PROPN
ejpam-816	449	5	)	)	PUNCT
ejpam-816	449	6	in	in	ADP
ejpam-816	449	7	the	the	DET
ejpam-816	449	8	left	left	ADJ
ejpam-816	449	9	-	-	PUNCT
ejpam-816	449	10	hand	hand	NOUN
ejpam-816	449	11	half	half	ADJ
ejpam-816	449	12	-	-	PUNCT
ejpam-816	449	13	plane	plane	NOUN
ejpam-816	449	14	is	be	AUX
ejpam-816	449	15	described	describe	VERB
ejpam-816	449	16	by	by	ADP
ejpam-816	449	17	the	the	DET
ejpam-816	449	18	above	above	PROPN
ejpam-816	449	19	symmetry	symmetry	NOUN
ejpam-816	449	20	relation	relation	NOUN
ejpam-816	449	21	.	.	PUNCT
ejpam-816	450	1	6	6	X
ejpam-816	450	2	.	.	X
ejpam-816	450	3	concluding	conclude	VERB
ejpam-816	450	4	remarks	remark	NOUN
ejpam-816	450	5	we	we	PRON
ejpam-816	450	6	have	have	AUX
ejpam-816	450	7	shown	show	VERB
ejpam-816	450	8	how	how	SCONJ
ejpam-816	450	9	the	the	DET
ejpam-816	450	10	n	n	CCONJ
ejpam-816	450	11	-	-	PUNCT
ejpam-816	450	12	dimensional	dimensional	ADJ
ejpam-816	450	13	analogues	analogue	NOUN
ejpam-816	450	14	of	of	ADP
ejpam-816	450	15	faxén	faxén	NOUN
ejpam-816	450	16	’s	’s	PART
ejpam-816	450	17	integral	integral	ADJ
ejpam-816	450	18	in	in	ADP
ejpam-816	450	19	(	(	PUNCT
ejpam-816	450	20	1	1	NUM
ejpam-816	450	21	)	)	PUNCT
ejpam-816	450	22	,	,	PUNCT
ejpam-816	450	23	(	(	PUNCT
ejpam-816	450	24	4	4	NUM
ejpam-816	450	25	)	)	PUNCT
ejpam-816	450	26	and	and	CCONJ
ejpam-816	450	27	(	(	PUNCT
ejpam-816	450	28	40	40	NUM
ejpam-816	450	29	)	)	PUNCT
ejpam-816	450	30	can	can	AUX
ejpam-816	450	31	be	be	AUX
ejpam-816	450	32	expressed	express	VERB
ejpam-816	450	33	in	in	ADP
ejpam-816	450	34	terms	term	NOUN
ejpam-816	450	35	of	of	ADP
ejpam-816	450	36	either	either	CCONJ
ejpam-816	450	37	a	a	DET
ejpam-816	450	38	single	single	ADJ
ejpam-816	450	39	wright	wright	PROPN
ejpam-816	450	40	function	function	PROPN
ejpam-816	450	41	nψ0(z	nψ0(z	PROPN
ejpam-816	450	42	)	)	PUNCT
ejpam-816	450	43	,	,	PUNCT
ejpam-816	450	44	or	or	CCONJ
ejpam-816	450	45	a	a	DET
ejpam-816	450	46	linear	linear	ADJ
ejpam-816	450	47	combination	combination	NOUN
ejpam-816	450	48	of	of	ADP
ejpam-816	450	49	such	such	ADJ
ejpam-816	450	50	functions	function	NOUN
ejpam-816	450	51	with	with	ADP
ejpam-816	450	52	rotated	rotate	VERB
ejpam-816	450	53	arguments	argument	NOUN
ejpam-816	450	54	.	.	PUNCT
ejpam-816	451	1	knowledge	knowledge	NOUN
ejpam-816	451	2	of	of	ADP
ejpam-816	451	3	the	the	DET
ejpam-816	451	4	asymptotic	asymptotic	ADJ
ejpam-816	451	5	expansion	expansion	NOUN
ejpam-816	451	6	of	of	ADP
ejpam-816	451	7	nψ0(z	nψ0(z	PROPN
ejpam-816	451	8	)	)	PUNCT
ejpam-816	451	9	for	for	ADP
ejpam-816	451	10	|z|	|z|	NOUN
ejpam-816	451	11	→	→	SYM
ejpam-816	451	12	∞	∞	NUM
ejpam-816	451	13	then	then	ADV
ejpam-816	451	14	enables	enable	VERB
ejpam-816	451	15	the	the	DET
ejpam-816	451	16	asymptotic	asymptotic	ADJ
ejpam-816	451	17	structure	structure	NOUN
ejpam-816	451	18	of	of	ADP
ejpam-816	451	19	these	these	DET
ejpam-816	451	20	integrals	integral	NOUN
ejpam-816	451	21	to	to	PART
ejpam-816	451	22	be	be	AUX
ejpam-816	451	23	determined	determine	VERB
ejpam-816	451	24	.	.	PUNCT
ejpam-816	452	1	not	not	PART
ejpam-816	452	2	surprisingly	surprisingly	ADV
ejpam-816	452	3	,	,	PUNCT
ejpam-816	452	4	this	this	DET
ejpam-816	452	5	asymptotic	asymptotic	ADJ
ejpam-816	452	6	structure	structure	NOUN
ejpam-816	452	7	becomes	become	VERB
ejpam-816	452	8	more	more	ADV
ejpam-816	452	9	complicated	complicated	ADJ
ejpam-816	452	10	the	the	PRON
ejpam-816	452	11	larger	large	ADJ
ejpam-816	452	12	the	the	DET
ejpam-816	452	13	value	value	NOUN
ejpam-816	452	14	of	of	ADP
ejpam-816	452	15	n.	n.	NOUN
ejpam-816	452	16	the	the	DET
ejpam-816	452	17	asymptotic	asymptotic	ADJ
ejpam-816	452	18	behaviour	behaviour	NOUN
ejpam-816	452	19	of	of	ADP
ejpam-816	452	20	nψ0(z	nψ0(z	PROPN
ejpam-816	452	21	)	)	PUNCT
ejpam-816	452	22	for	for	ADP
ejpam-816	452	23	large	large	ADJ
ejpam-816	452	24	|z|	|z|	NOUN
ejpam-816	452	25	consists	consist	VERB
ejpam-816	452	26	of	of	ADP
ejpam-816	452	27	an	an	DET
ejpam-816	452	28	exponential	exponential	ADJ
ejpam-816	452	29	expansion	expansion	NOUN
ejpam-816	452	30	and	and	CCONJ
ejpam-816	452	31	an	an	DET
ejpam-816	452	32	algebraic	algebraic	ADJ
ejpam-816	452	33	expansion	expansion	NOUN
ejpam-816	452	34	.	.	PUNCT
ejpam-816	453	1	the	the	DET
ejpam-816	453	2	formal	formal	ADJ
ejpam-816	453	3	sum	sum	NOUN
ejpam-816	453	4	en,0(z	en,0(z	PROPN
ejpam-816	453	5	)	)	PUNCT
ejpam-816	453	6	is	be	AUX
ejpam-816	453	7	a	a	DET
ejpam-816	453	8	compact	compact	ADJ
ejpam-816	453	9	representation	representation	NOUN
ejpam-816	453	10	of	of	ADP
ejpam-816	453	11	the	the	DET
ejpam-816	453	12	exponential	exponential	ADJ
ejpam-816	453	13	references	reference	NOUN
ejpam-816	453	14	1024	1024	NUM
ejpam-816	453	15	expansion	expansion	NOUN
ejpam-816	453	16	in	in	ADP
ejpam-816	453	17	the	the	DET
ejpam-816	453	18	n	n	ADV
ejpam-816	453	19	-	-	PUNCT
ejpam-816	453	20	dimensional	dimensional	ADJ
ejpam-816	453	21	case	case	NOUN
ejpam-816	453	22	.	.	PUNCT
ejpam-816	454	1	the	the	DET
ejpam-816	454	2	evaluation	evaluation	NOUN
ejpam-816	454	3	of	of	ADP
ejpam-816	454	4	the	the	DET
ejpam-816	454	5	coefficients	coefficient	NOUN
ejpam-816	454	6	in	in	ADP
ejpam-816	454	7	this	this	DET
ejpam-816	454	8	expansion	expansion	NOUN
ejpam-816	454	9	can	can	AUX
ejpam-816	454	10	be	be	AUX
ejpam-816	454	11	easily	easily	ADV
ejpam-816	454	12	carried	carry	VERB
ejpam-816	454	13	out	out	ADP
ejpam-816	454	14	in	in	ADP
ejpam-816	454	15	specific	specific	ADJ
ejpam-816	454	16	cases	case	NOUN
ejpam-816	454	17	for	for	ADP
ejpam-816	454	18	low	low	ADJ
ejpam-816	454	19	values	value	NOUN
ejpam-816	454	20	of	of	ADP
ejpam-816	454	21	n	n	CCONJ
ejpam-816	454	22	,	,	PUNCT
ejpam-816	454	23	although	although	SCONJ
ejpam-816	454	24	the	the	DET
ejpam-816	454	25	computational	computational	ADJ
ejpam-816	454	26	effort	effort	NOUN
ejpam-816	454	27	involved	involve	VERB
ejpam-816	454	28	in	in	ADP
ejpam-816	454	29	their	their	PRON
ejpam-816	454	30	calculation	calculation	NOUN
ejpam-816	454	31	rapidly	rapidly	ADV
ejpam-816	454	32	increases	increase	VERB
ejpam-816	454	33	with	with	ADP
ejpam-816	454	34	the	the	DET
ejpam-816	454	35	dimension	dimension	NOUN
ejpam-816	454	36	of	of	ADP
ejpam-816	454	37	the	the	DET
ejpam-816	454	38	integrals	integral	NOUN
ejpam-816	454	39	.	.	PUNCT
ejpam-816	455	1	the	the	DET
ejpam-816	455	2	algebraic	algebraic	ADJ
ejpam-816	455	3	expansion	expansion	NOUN
ejpam-816	455	4	hn,0(z	hn,0(z	PROPN
ejpam-816	455	5	)	)	PUNCT
ejpam-816	455	6	consists	consist	VERB
ejpam-816	455	7	,	,	PUNCT
ejpam-816	455	8	in	in	ADP
ejpam-816	455	9	general	general	ADJ
ejpam-816	455	10	,	,	PUNCT
ejpam-816	455	11	of	of	ADP
ejpam-816	455	12	n	n	CCONJ
ejpam-816	455	13	different	different	ADJ
ejpam-816	455	14	expansions	expansion	NOUN
ejpam-816	455	15	each	each	PRON
ejpam-816	455	16	with	with	ADP
ejpam-816	455	17	its	its	PRON
ejpam-816	455	18	own	own	ADJ
ejpam-816	455	19	asymptotic	asymptotic	ADJ
ejpam-816	455	20	scale	scale	NOUN
ejpam-816	455	21	.	.	PUNCT
ejpam-816	456	1	the	the	DET
ejpam-816	456	2	occurrence	occurrence	NOUN
ejpam-816	456	3	of	of	ADP
ejpam-816	456	4	terms	term	NOUN
ejpam-816	456	5	in	in	ADP
ejpam-816	456	6	log	log	PROPN
ejpam-816	456	7	z	z	NOUN
ejpam-816	456	8	(	(	PUNCT
ejpam-816	456	9	when	when	SCONJ
ejpam-816	456	10	n≥	n≥	PROPN
ejpam-816	456	11	2	2	NUM
ejpam-816	456	12	)	)	PUNCT
ejpam-816	456	13	depends	depend	VERB
ejpam-816	456	14	to	to	ADP
ejpam-816	456	15	a	a	DET
ejpam-816	456	16	considerable	considerable	ADJ
ejpam-816	456	17	degree	degree	NOUN
ejpam-816	456	18	on	on	ADP
ejpam-816	456	19	the	the	DET
ejpam-816	456	20	symmetry	symmetry	NOUN
ejpam-816	456	21	in	in	ADP
ejpam-816	456	22	the	the	DET
ejpam-816	456	23	associated	associated	PROPN
ejpam-816	456	24	newton	newton	PROPN
ejpam-816	456	25	diagram	diagram	NOUN
ejpam-816	456	26	of	of	ADP
ejpam-816	456	27	the	the	DET
ejpam-816	456	28	phase	phase	NOUN
ejpam-816	456	29	function	function	NOUN
ejpam-816	456	30	f	f	PROPN
ejpam-816	456	31	(	(	PUNCT
ejpam-816	456	32	x1	x1	PROPN
ejpam-816	456	33	,	,	PUNCT
ejpam-816	456	34	.	.	PUNCT
ejpam-816	456	35	.	.	PUNCT
ejpam-816	456	36	.	.	PUNCT
ejpam-816	457	1	,	,	PUNCT
ejpam-816	457	2	xn	xn	PROPN
ejpam-816	457	3	;	;	PUNCT
ejpam-816	457	4	z	z	X
ejpam-816	457	5	)	)	PUNCT
ejpam-816	457	6	defined	define	VERB
ejpam-816	457	7	in	in	ADP
ejpam-816	457	8	(	(	PUNCT
ejpam-816	457	9	2	2	NUM
ejpam-816	457	10	)	)	PUNCT
ejpam-816	457	11	.	.	PUNCT
ejpam-816	458	1	references	reference	NOUN
ejpam-816	458	2	[	[	X
ejpam-816	458	3	1	1	NUM
ejpam-816	458	4	]	]	PUNCT
ejpam-816	458	5	n	n	CCONJ
ejpam-816	458	6	g	g	PROPN
ejpam-816	458	7	bakhoom	bakhoom	NOUN
ejpam-816	458	8	,	,	PUNCT
ejpam-816	458	9	asymptotic	asymptotic	ADJ
ejpam-816	458	10	expansions	expansion	NOUN
ejpam-816	458	11	of	of	ADP
ejpam-816	458	12	the	the	DET
ejpam-816	458	13	function	function	NOUN
ejpam-816	458	14	fk(x	fk(x	NOUN
ejpam-816	458	15	)	)	PUNCT
ejpam-816	458	16	=	=	SYM
ejpam-816	458	17	∫∞	∫∞	NOUN
ejpam-816	458	18	0	0	NUM
ejpam-816	458	19	exp(xu−uk)du	exp(xu−uk)du	PROPN
ejpam-816	458	20	,	,	PUNCT
ejpam-816	458	21	proc	proc	NOUN
ejpam-816	458	22	.	.	PUNCT
ejpam-816	459	1	lond	lond	PROPN
ejpam-816	459	2	.	.	PUNCT
ejpam-816	460	1	math	math	NOUN
ejpam-816	460	2	.	.	PUNCT
ejpam-816	461	1	soc	soc	PROPN
ejpam-816	461	2	.	.	PUNCT
ejpam-816	462	1	35:83–100	35:83–100	NUM
ejpam-816	462	2	,	,	PUNCT
ejpam-816	462	3	1935	1935	NUM
ejpam-816	462	4	.	.	PUNCT
ejpam-816	463	1	[	[	X
ejpam-816	463	2	2	2	NUM
ejpam-816	463	3	]	]	SYM
ejpam-816	463	4	b	b	NOUN
ejpam-816	463	5	l	l	NOUN
ejpam-816	463	6	j	j	PROPN
ejpam-816	463	7	braaksma	braaksma	NOUN
ejpam-816	463	8	,	,	PUNCT
ejpam-816	463	9	asymptotic	asymptotic	ADJ
ejpam-816	463	10	expansions	expansion	NOUN
ejpam-816	463	11	and	and	CCONJ
ejpam-816	463	12	analytic	analytic	ADJ
ejpam-816	463	13	continuations	continuation	NOUN
ejpam-816	463	14	for	for	ADP
ejpam-816	463	15	a	a	DET
ejpam-816	463	16	class	class	NOUN
ejpam-816	463	17	of	of	ADP
ejpam-816	463	18	barnesintegrals	barnesintegral	NOUN
ejpam-816	463	19	,	,	PUNCT
ejpam-816	463	20	compos	compos	PROPN
ejpam-816	463	21	.	.	PUNCT
ejpam-816	464	1	math	math	NOUN
ejpam-816	464	2	.	.	PUNCT
ejpam-816	465	1	15:239–341	15:239–341	NUM
ejpam-816	465	2	,	,	PUNCT
ejpam-816	465	3	1963	1963	NUM
ejpam-816	465	4	[	[	X
ejpam-816	465	5	3	3	NUM
ejpam-816	465	6	]	]	X
ejpam-816	465	7	s	s	X
ejpam-816	465	8	breen	breen	NOUN
ejpam-816	465	9	and	and	CCONJ
ejpam-816	465	10	a	a	DET
ejpam-816	465	11	d	d	NOUN
ejpam-816	465	12	wood	wood	NOUN
ejpam-816	465	13	,	,	PUNCT
ejpam-816	465	14	on	on	ADP
ejpam-816	465	15	the	the	DET
ejpam-816	465	16	asymptotic	asymptotic	ADJ
ejpam-816	465	17	behaviour	behaviour	NOUN
ejpam-816	465	18	of	of	ADP
ejpam-816	465	19	laplace	laplace	NOUN
ejpam-816	465	20	-	-	PUNCT
ejpam-816	465	21	type	type	NOUN
ejpam-816	465	22	multiple	multiple	ADJ
ejpam-816	465	23	integral	integral	ADJ
ejpam-816	465	24	solutions	solution	NOUN
ejpam-816	465	25	of	of	ADP
ejpam-816	465	26	linear	linear	PROPN
ejpam-816	465	27	differential	differential	ADJ
ejpam-816	465	28	equations	equation	NOUN
ejpam-816	465	29	,	,	PUNCT
ejpam-816	465	30	j.	j.	PROPN
ejpam-816	465	31	comp	comp	PROPN
ejpam-816	465	32	.	.	PUNCT
ejpam-816	466	1	appl	appl	PROPN
ejpam-816	466	2	.	.	PROPN
ejpam-816	466	3	math	math	NOUN
ejpam-816	466	4	.	.	PUNCT
ejpam-816	467	1	171:103–112	171:103–112	NUM
ejpam-816	467	2	,	,	PUNCT
ejpam-816	467	3	2004	2004	NUM
ejpam-816	467	4	.	.	PUNCT
ejpam-816	468	1	[	[	X
ejpam-816	468	2	4	4	NUM
ejpam-816	468	3	]	]	X
ejpam-816	468	4	l	l	NOUN
ejpam-816	468	5	brillouin	brillouin	NOUN
ejpam-816	468	6	,	,	PUNCT
ejpam-816	468	7	sur	sur	PROPN
ejpam-816	468	8	une	une	PROPN
ejpam-816	468	9	méthode	méthode	PROPN
ejpam-816	468	10	de	de	PROPN
ejpam-816	468	11	calcul	calcul	PROPN
ejpam-816	468	12	approcheé	approcheé	PROPN
ejpam-816	468	13	de	de	PROPN
ejpam-816	468	14	certaines	certaines	PROPN
ejpam-816	468	15	intégrales	intégrale	NOUN
ejpam-816	468	16	,	,	PUNCT
ejpam-816	468	17	dite	dite	PROPN
ejpam-816	468	18	méthode	méthode	PROPN
ejpam-816	468	19	de	de	PROPN
ejpam-816	468	20	col	col	PROPN
ejpam-816	468	21	,	,	PUNCT
ejpam-816	468	22	ann	ann	PROPN
ejpam-816	468	23	.	.	PUNCT
ejpam-816	468	24	sci	sci	PROPN
ejpam-816	468	25	.	.	PROPN
ejpam-816	468	26	ecole	ecole	PROPN
ejpam-816	468	27	norm	norm	PROPN
ejpam-816	468	28	.	.	PUNCT
ejpam-816	469	1	sup	sup	NOUN
ejpam-816	469	2	.	.	PUNCT
ejpam-816	470	1	33:17–69	33:17–69	NUM
ejpam-816	470	2	,	,	PUNCT
ejpam-816	470	3	1916	1916	NUM
ejpam-816	470	4	.	.	PUNCT
ejpam-816	471	1	[	[	X
ejpam-816	471	2	5	5	NUM
ejpam-816	471	3	]	]	SYM
ejpam-816	471	4	w	w	NOUN
ejpam-816	471	5	r	r	NOUN
ejpam-816	471	6	burwell	burwell	PROPN
ejpam-816	471	7	,	,	PUNCT
ejpam-816	471	8	asymptotic	asymptotic	ADJ
ejpam-816	471	9	expansions	expansion	NOUN
ejpam-816	471	10	of	of	ADP
ejpam-816	471	11	generalised	generalise	VERB
ejpam-816	471	12	hypergeometric	hypergeometric	ADJ
ejpam-816	471	13	functions	function	NOUN
ejpam-816	471	14	,	,	PUNCT
ejpam-816	471	15	proc	proc	NOUN
ejpam-816	471	16	.	.	PUNCT
ejpam-816	472	1	lond	lond	PROPN
ejpam-816	472	2	.	.	PUNCT
ejpam-816	473	1	math	math	NOUN
ejpam-816	473	2	.	.	PUNCT
ejpam-816	474	1	soc	soc	NOUN
ejpam-816	474	2	.	.	PUNCT
ejpam-816	475	1	53:599–611	53:599–611	NUM
ejpam-816	475	2	,	,	PUNCT
ejpam-816	475	3	1924	1924	NUM
ejpam-816	475	4	.	.	PUNCT
ejpam-816	476	1	[	[	X
ejpam-816	476	2	6	6	NUM
ejpam-816	476	3	]	]	SYM
ejpam-816	476	4	r	r	NOUN
ejpam-816	476	5	gorenflo	gorenflo	NOUN
ejpam-816	476	6	,	,	PUNCT
ejpam-816	476	7	y	y	PROPN
ejpam-816	476	8	luchko	luchko	VERB
ejpam-816	476	9	and	and	CCONJ
ejpam-816	476	10	f	f	PROPN
ejpam-816	476	11	mainardi	mainardi	PROPN
ejpam-816	476	12	,	,	PUNCT
ejpam-816	476	13	analytical	analytical	ADJ
ejpam-816	476	14	properties	property	NOUN
ejpam-816	476	15	and	and	CCONJ
ejpam-816	476	16	applications	application	NOUN
ejpam-816	476	17	of	of	ADP
ejpam-816	476	18	the	the	DET
ejpam-816	476	19	wright	wright	PROPN
ejpam-816	476	20	function	function	PROPN
ejpam-816	476	21	,	,	PUNCT
ejpam-816	476	22	frac	frac	PROPN
ejpam-816	476	23	.	.	PUNCT
ejpam-816	477	1	calc	calc	PROPN
ejpam-816	477	2	.	.	PUNCT
ejpam-816	478	1	appl	appl	PROPN
ejpam-816	478	2	.	.	PUNCT
ejpam-816	479	1	anal	anal	PROPN
ejpam-816	479	2	.	.	PUNCT
ejpam-816	480	1	2:383–414	2:383–414	NUM
ejpam-816	480	2	,	,	PUNCT
ejpam-816	480	3	1998	1998	NUM
ejpam-816	480	4	.	.	PUNCT
ejpam-816	481	1	[	[	X
ejpam-816	481	2	7	7	X
ejpam-816	481	3	]	]	X
ejpam-816	481	4	d	d	X
ejpam-816	481	5	kaminski	kaminski	PROPN
ejpam-816	481	6	and	and	CCONJ
ejpam-816	481	7	r	r	PROPN
ejpam-816	481	8	b	b	PROPN
ejpam-816	481	9	paris	paris	PROPN
ejpam-816	481	10	,	,	PUNCT
ejpam-816	481	11	asymptotics	asymptotic	NOUN
ejpam-816	481	12	via	via	ADP
ejpam-816	481	13	iterated	iterated	ADJ
ejpam-816	481	14	mellin	mellin	PROPN
ejpam-816	481	15	-	-	PUNCT
ejpam-816	481	16	barnes	barnes	PROPN
ejpam-816	481	17	integrals	integral	NOUN
ejpam-816	481	18	:	:	PUNCT
ejpam-816	481	19	application	application	NOUN
ejpam-816	481	20	to	to	ADP
ejpam-816	481	21	the	the	DET
ejpam-816	481	22	generalised	generalise	VERB
ejpam-816	481	23	faxén	faxén	NOUN
ejpam-816	481	24	integral	integral	ADJ
ejpam-816	481	25	,	,	PUNCT
ejpam-816	481	26	methods	method	NOUN
ejpam-816	481	27	appl	appl	NOUN
ejpam-816	481	28	.	.	PUNCT
ejpam-816	482	1	anal	anal	PROPN
ejpam-816	482	2	.	.	PUNCT
ejpam-816	483	1	4:311–325	4:311–325	PROPN
ejpam-816	483	2	,	,	PUNCT
ejpam-816	483	3	1997	1997	NUM
ejpam-816	483	4	.	.	PUNCT
ejpam-816	484	1	[	[	X
ejpam-816	484	2	8	8	NUM
ejpam-816	484	3	]	]	X
ejpam-816	484	4	g	g	NOUN
ejpam-816	484	5	v	v	NOUN
ejpam-816	484	6	liakhovetski	liakhovetski	NOUN
ejpam-816	484	7	and	and	CCONJ
ejpam-816	484	8	r	r	PROPN
ejpam-816	484	9	b	b	PROPN
ejpam-816	484	10	paris	paris	PROPN
ejpam-816	484	11	,	,	PUNCT
ejpam-816	484	12	asymptotic	asymptotic	ADJ
ejpam-816	484	13	expansions	expansion	NOUN
ejpam-816	484	14	of	of	ADP
ejpam-816	484	15	laplace	laplace	NOUN
ejpam-816	484	16	-	-	PUNCT
ejpam-816	484	17	type	type	NOUN
ejpam-816	484	18	integrals	integral	NOUN
ejpam-816	484	19	iii	iii	PROPN
ejpam-816	484	20	,	,	PUNCT
ejpam-816	484	21	j.	j.	PROPN
ejpam-816	484	22	comp	comp	PROPN
ejpam-816	484	23	.	.	PUNCT
ejpam-816	485	1	appl	appl	PROPN
ejpam-816	485	2	.	.	PROPN
ejpam-816	485	3	math	math	PROPN
ejpam-816	485	4	.	.	PUNCT
ejpam-816	486	1	132:409–429	132:409–429	NUM
ejpam-816	486	2	,	,	PUNCT
ejpam-816	486	3	2001	2001	NUM
ejpam-816	486	4	.	.	PUNCT
ejpam-816	487	1	[	[	X
ejpam-816	487	2	9	9	NUM
ejpam-816	487	3	]	]	X
ejpam-816	487	4	f	f	PROPN
ejpam-816	487	5	w	w	PROPN
ejpam-816	487	6	j	j	PROPN
ejpam-816	487	7	olver	olver	ADV
ejpam-816	487	8	,	,	PUNCT
ejpam-816	487	9	asymptotics	asymptotic	NOUN
ejpam-816	487	10	and	and	CCONJ
ejpam-816	487	11	special	special	ADJ
ejpam-816	487	12	functions	function	NOUN
ejpam-816	487	13	,	,	PUNCT
ejpam-816	487	14	academic	academic	ADJ
ejpam-816	487	15	press	press	NOUN
ejpam-816	487	16	,	,	PUNCT
ejpam-816	487	17	new	new	PROPN
ejpam-816	487	18	york	york	PROPN
ejpam-816	487	19	,	,	PUNCT
ejpam-816	487	20	1974	1974	NUM
ejpam-816	487	21	.	.	PUNCT
ejpam-816	488	1	reprinted	reprint	VERB
ejpam-816	488	2	in	in	ADP
ejpam-816	488	3	a	a	DET
ejpam-816	488	4	k	k	PROPN
ejpam-816	488	5	peters	peters	PROPN
ejpam-816	488	6	,	,	PUNCT
ejpam-816	488	7	massachussets	massachusset	NOUN
ejpam-816	488	8	,	,	PUNCT
ejpam-816	488	9	1997	1997	NUM
ejpam-816	488	10	.	.	PUNCT
ejpam-816	489	1	[	[	X
ejpam-816	489	2	10	10	NUM
ejpam-816	489	3	]	]	X
ejpam-816	489	4	r	r	NOUN
ejpam-816	489	5	b	b	PROPN
ejpam-816	489	6	paris	paris	PROPN
ejpam-816	489	7	,	,	PUNCT
ejpam-816	489	8	smoothing	smooth	VERB
ejpam-816	489	9	of	of	ADP
ejpam-816	489	10	the	the	DET
ejpam-816	489	11	stokes	stoke	NOUN
ejpam-816	489	12	phenomenon	phenomenon	NOUN
ejpam-816	489	13	for	for	ADP
ejpam-816	489	14	high	high	ADJ
ejpam-816	489	15	-	-	PUNCT
ejpam-816	489	16	order	order	NOUN
ejpam-816	489	17	differential	differential	ADJ
ejpam-816	489	18	equations	equation	NOUN
ejpam-816	489	19	,	,	PUNCT
ejpam-816	489	20	proc	proc	NOUN
ejpam-816	489	21	.	.	PUNCT
ejpam-816	490	1	roy	roy	PROPN
ejpam-816	490	2	.	.	PROPN
ejpam-816	490	3	soc	soc	PROPN
ejpam-816	490	4	.	.	PUNCT
ejpam-816	491	1	london	london	PROPN
ejpam-816	491	2	a	a	DET
ejpam-816	491	3	436:165–186	436:165–186	NUM
ejpam-816	491	4	,	,	PUNCT
ejpam-816	491	5	1992	1992	NUM
ejpam-816	491	6	.	.	PUNCT
ejpam-816	492	1	[	[	X
ejpam-816	492	2	11	11	NUM
ejpam-816	492	3	]	]	X
ejpam-816	492	4	r	r	NOUN
ejpam-816	492	5	b	b	PROPN
ejpam-816	492	6	paris	paris	PROPN
ejpam-816	492	7	,	,	PUNCT
ejpam-816	492	8	exponentially	exponentially	ADV
ejpam-816	492	9	small	small	ADJ
ejpam-816	492	10	expansions	expansion	NOUN
ejpam-816	492	11	in	in	ADP
ejpam-816	492	12	the	the	DET
ejpam-816	492	13	asymptotics	asymptotic	NOUN
ejpam-816	492	14	of	of	ADP
ejpam-816	492	15	the	the	DET
ejpam-816	492	16	wright	wright	PROPN
ejpam-816	492	17	function	function	PROPN
ejpam-816	492	18	,	,	PUNCT
ejpam-816	492	19	j.	j.	PROPN
ejpam-816	492	20	comp	comp	PROPN
ejpam-816	492	21	.	.	PUNCT
ejpam-816	493	1	appl	appl	PROPN
ejpam-816	493	2	.	.	PROPN
ejpam-816	493	3	math	math	NOUN
ejpam-816	493	4	.	.	PUNCT
ejpam-816	494	1	234:488–504	234:488–504	NUM
ejpam-816	494	2	,	,	PUNCT
ejpam-816	494	3	2010	2010	NUM
ejpam-816	494	4	.	.	PUNCT
ejpam-816	495	1	[	[	X
ejpam-816	495	2	12	12	NUM
ejpam-816	495	3	]	]	X
ejpam-816	495	4	r	r	NOUN
ejpam-816	495	5	b	b	PROPN
ejpam-816	495	6	paris	paris	PROPN
ejpam-816	495	7	and	and	CCONJ
ejpam-816	495	8	d	d	PROPN
ejpam-816	495	9	kaminski	kaminski	PROPN
ejpam-816	495	10	,	,	PUNCT
ejpam-816	495	11	asymptotics	asymptotic	NOUN
ejpam-816	495	12	and	and	CCONJ
ejpam-816	495	13	mellin	mellin	PROPN
ejpam-816	495	14	-	-	PUNCT
ejpam-816	495	15	barnes	barnes	PROPN
ejpam-816	495	16	integrals	integral	NOUN
ejpam-816	495	17	,	,	PUNCT
ejpam-816	495	18	cambridge	cambridge	PROPN
ejpam-816	495	19	university	university	PROPN
ejpam-816	495	20	press	press	PROPN
ejpam-816	495	21	,	,	PUNCT
ejpam-816	495	22	cambridge	cambridge	PROPN
ejpam-816	495	23	,	,	PUNCT
ejpam-816	495	24	2001	2001	NUM
ejpam-816	495	25	.	.	PUNCT
ejpam-816	496	1	[	[	X
ejpam-816	496	2	13	13	NUM
ejpam-816	496	3	]	]	X
ejpam-816	496	4	r	r	NOUN
ejpam-816	496	5	b	b	PROPN
ejpam-816	496	6	paris	paris	PROPN
ejpam-816	496	7	and	and	CCONJ
ejpam-816	496	8	g	g	PROPN
ejpam-816	496	9	v	v	ADP
ejpam-816	496	10	liakhovetski	liakhovetski	ADJ
ejpam-816	496	11	,	,	PUNCT
ejpam-816	496	12	asymptotics	asymptotic	NOUN
ejpam-816	496	13	of	of	ADP
ejpam-816	496	14	the	the	DET
ejpam-816	496	15	multidimensional	multidimensional	ADJ
ejpam-816	496	16	faxén	faxén	NOUN
ejpam-816	496	17	integral	integral	ADJ
ejpam-816	496	18	,	,	PUNCT
ejpam-816	496	19	frac	frac	PROPN
ejpam-816	496	20	.	.	PUNCT
ejpam-816	496	21	calc	calc	PROPN
ejpam-816	496	22	.	.	PUNCT
ejpam-816	497	1	appl	appl	PROPN
ejpam-816	497	2	.	.	PUNCT
ejpam-816	498	1	anal	anal	PROPN
ejpam-816	498	2	.	.	PUNCT
ejpam-816	499	1	3:63–73	3:63–73	NUM
ejpam-816	499	2	,	,	PUNCT
ejpam-816	499	3	2000	2000	NUM
ejpam-816	499	4	.	.	PUNCT
ejpam-816	500	1	references	reference	NOUN
ejpam-816	500	2	1025	1025	NUM
ejpam-816	500	3	[	[	X
ejpam-816	500	4	14	14	NUM
ejpam-816	500	5	]	]	X
ejpam-816	500	6	r	r	NOUN
ejpam-816	500	7	b	b	PROPN
ejpam-816	500	8	paris	paris	PROPN
ejpam-816	500	9	and	and	CCONJ
ejpam-816	500	10	a	a	DET
ejpam-816	500	11	d	d	NOUN
ejpam-816	500	12	wood	wood	NOUN
ejpam-816	500	13	,	,	PUNCT
ejpam-816	500	14	asymptotics	asymptotic	NOUN
ejpam-816	500	15	of	of	ADP
ejpam-816	500	16	high	high	ADJ
ejpam-816	500	17	order	order	NOUN
ejpam-816	500	18	differential	differential	NOUN
ejpam-816	500	19	equations	equation	NOUN
ejpam-816	500	20	,	,	PUNCT
ejpam-816	500	21	pitman	pitman	NOUN
ejpam-816	500	22	research	research	NOUN
ejpam-816	500	23	notes	note	NOUN
ejpam-816	500	24	in	in	ADP
ejpam-816	500	25	mathematics	mathematic	NOUN
ejpam-816	500	26	,	,	PUNCT
ejpam-816	500	27	129	129	NUM
ejpam-816	500	28	,	,	PUNCT
ejpam-816	500	29	longman	longman	NOUN
ejpam-816	500	30	scientific	scientific	ADJ
ejpam-816	500	31	and	and	CCONJ
ejpam-816	500	32	technical	technical	ADJ
ejpam-816	500	33	,	,	PUNCT
ejpam-816	500	34	harlow	harlow	NOUN
ejpam-816	500	35	,	,	PUNCT
ejpam-816	500	36	1986	1986	NUM
ejpam-816	500	37	.	.	PUNCT
ejpam-816	501	1	[	[	X
ejpam-816	501	2	15	15	NUM
ejpam-816	501	3	]	]	X
ejpam-816	501	4	t	t	NOUN
ejpam-816	501	5	d	d	PROPN
ejpam-816	501	6	riney	riney	NOUN
ejpam-816	501	7	,	,	PUNCT
ejpam-816	501	8	on	on	ADP
ejpam-816	501	9	the	the	DET
ejpam-816	501	10	coefficients	coefficient	NOUN
ejpam-816	501	11	in	in	ADP
ejpam-816	501	12	asymptotic	asymptotic	ADJ
ejpam-816	501	13	factorial	factorial	ADJ
ejpam-816	501	14	expansions	expansion	NOUN
ejpam-816	501	15	,	,	PUNCT
ejpam-816	501	16	proc	proc	NOUN
ejpam-816	501	17	.	.	PUNCT
ejpam-816	502	1	amer	amer	PROPN
ejpam-816	502	2	.	.	PUNCT
ejpam-816	502	3	math	math	PROPN
ejpam-816	502	4	.	.	PUNCT
ejpam-816	503	1	soc	soc	PROPN
ejpam-816	503	2	.	.	PUNCT
ejpam-816	504	1	7:245–249	7:245–249	NUM
ejpam-816	504	2	,	,	PUNCT
ejpam-816	504	3	1956	1956	NUM
ejpam-816	504	4	.	.	PUNCT
ejpam-816	505	1	[	[	X
ejpam-816	505	2	16	16	NUM
ejpam-816	505	3	]	]	X
ejpam-816	505	4	r	r	NOUN
ejpam-816	505	5	saxton	saxton	NOUN
ejpam-816	505	6	,	,	PUNCT
ejpam-816	505	7	an	an	DET
ejpam-816	505	8	integral	integral	ADJ
ejpam-816	505	9	representation	representation	NOUN
ejpam-816	505	10	solution	solution	NOUN
ejpam-816	505	11	for	for	ADP
ejpam-816	505	12	a	a	DET
ejpam-816	505	13	class	class	NOUN
ejpam-816	505	14	of	of	ADP
ejpam-816	505	15	higher	high	ADJ
ejpam-816	505	16	order	order	NOUN
ejpam-816	505	17	linear	linear	VERB
ejpam-816	505	18	ordinary	ordinary	ADJ
ejpam-816	505	19	differential	differential	ADJ
ejpam-816	505	20	equations	equation	NOUN
ejpam-816	505	21	,	,	PUNCT
ejpam-816	505	22	msc	msc	PROPN
ejpam-816	505	23	dissertation	dissertation	PROPN
ejpam-816	505	24	,	,	PUNCT
ejpam-816	505	25	cranfield	cranfield	PROPN
ejpam-816	505	26	institute	institute	PROPN
ejpam-816	505	27	of	of	ADP
ejpam-816	505	28	technology	technology	PROPN
ejpam-816	505	29	,	,	PUNCT
ejpam-816	505	30	1978	1978	NUM
ejpam-816	505	31	.	.	PUNCT
ejpam-816	506	1	[	[	X
ejpam-816	506	2	17	17	NUM
ejpam-816	506	3	]	]	X
ejpam-816	506	4	l	l	PROPN
ejpam-816	506	5	j	j	PROPN
ejpam-816	506	6	slater	slater	PROPN
ejpam-816	506	7	,	,	PUNCT
ejpam-816	506	8	generalised	generalise	VERB
ejpam-816	506	9	hypergeometric	hypergeometric	ADJ
ejpam-816	506	10	functions	function	NOUN
ejpam-816	506	11	,	,	PUNCT
ejpam-816	506	12	cambridge	cambridge	PROPN
ejpam-816	506	13	university	university	PROPN
ejpam-816	506	14	press	press	PROPN
ejpam-816	506	15	,	,	PUNCT
ejpam-816	506	16	cambridge	cambridge	PROPN
ejpam-816	506	17	,	,	PUNCT
ejpam-816	506	18	1966	1966	NUM
ejpam-816	506	19	.	.	PUNCT
ejpam-816	507	1	[	[	X
ejpam-816	507	2	18	18	NUM
ejpam-816	507	3	]	]	SYM
ejpam-816	507	4	s	s	PART
ejpam-816	507	5	spitzer	spitzer	NOUN
ejpam-816	507	6	,	,	PUNCT
ejpam-816	507	7	integration	integration	NOUN
ejpam-816	507	8	der	der	NOUN
ejpam-816	507	9	linearen	linearen	PROPN
ejpam-816	507	10	differentialgleichung	differentialgleichung	VERB
ejpam-816	507	11	y(n	y(n	PRON
ejpam-816	507	12	)	)	PUNCT
ejpam-816	508	1	=	=	PUNCT
ejpam-816	508	2	ax2	ax2	NOUN
ejpam-816	508	3	y	y	PROPN
ejpam-816	508	4	′′	′′	PROPN
ejpam-816	508	5	+	+	CCONJ
ejpam-816	508	6	bx	bx	VERB
ejpam-816	508	7	y	y	NOUN
ejpam-816	508	8	′	′	NUM
ejpam-816	509	1	+	+	CCONJ
ejpam-816	510	1	c	c	NOUN
ejpam-816	510	2	y	y	NOUN
ejpam-816	510	3	,	,	PUNCT
ejpam-816	510	4	in	in	ADP
ejpam-816	510	5	welcher	welcher	NOUN
ejpam-816	510	6	n	n	PROPN
ejpam-816	510	7	eine	eine	PROPN
ejpam-816	510	8	ganze	ganze	PROPN
ejpam-816	510	9	positive	positive	PROPN
ejpam-816	510	10	zahl	zahl	PROPN
ejpam-816	510	11	und	und	VERB
ejpam-816	510	12	a	a	DET
ejpam-816	510	13	,	,	PUNCT
ejpam-816	510	14	b	b	NOUN
ejpam-816	510	15	,	,	PUNCT
ejpam-816	510	16	c	c	PROPN
ejpam-816	510	17	constante	constante	PROPN
ejpam-816	510	18	zahlen	zahlen	PROPN
ejpam-816	510	19	bezeichnen	bezeichnen	NOUN
ejpam-816	510	20	,	,	PUNCT
ejpam-816	510	21	mittelst	mittelst	NOUN
ejpam-816	510	22	bestimmter	bestimmter	VERB
ejpam-816	510	23	integrale	integrale	NOUN
ejpam-816	510	24	,	,	PUNCT
ejpam-816	510	25	math	math	NOUN
ejpam-816	510	26	.	.	PUNCT
ejpam-816	511	1	ann	ann	PROPN
ejpam-816	511	2	.	.	PUNCT
ejpam-816	512	1	3:453–455	3:453–455	NUM
ejpam-816	512	2	,	,	PUNCT
ejpam-816	512	3	1871	1871	NUM
ejpam-816	512	4	.	.	PUNCT
ejpam-816	513	1	[	[	X
ejpam-816	513	2	19	19	NUM
ejpam-816	513	3	]	]	SYM
ejpam-816	513	4	n	n	PRON
ejpam-816	513	5	m	m	PROPN
ejpam-816	513	6	temme	temme	NOUN
ejpam-816	513	7	,	,	PUNCT
ejpam-816	513	8	special	special	ADJ
ejpam-816	513	9	functions	function	NOUN
ejpam-816	513	10	:	:	PUNCT
ejpam-816	513	11	an	an	DET
ejpam-816	513	12	introduction	introduction	NOUN
ejpam-816	513	13	to	to	ADP
ejpam-816	513	14	the	the	DET
ejpam-816	513	15	classical	classical	ADJ
ejpam-816	513	16	functions	function	NOUN
ejpam-816	513	17	of	of	ADP
ejpam-816	513	18	mathematical	mathematical	ADJ
ejpam-816	513	19	physics	physics	NOUN
ejpam-816	513	20	,	,	PUNCT
ejpam-816	513	21	wiley	wiley	PROPN
ejpam-816	513	22	,	,	PUNCT
ejpam-816	513	23	new	new	PROPN
ejpam-816	513	24	york	york	PROPN
ejpam-816	513	25	,	,	PUNCT
ejpam-816	513	26	1996	1996	NUM
ejpam-816	513	27	.	.	PUNCT
ejpam-816	514	1	[	[	X
ejpam-816	514	2	20	20	NUM
ejpam-816	514	3	]	]	SYM
ejpam-816	514	4	e	e	PROPN
ejpam-816	514	5	m	m	PROPN
ejpam-816	514	6	wright	wright	PROPN
ejpam-816	514	7	,	,	PUNCT
ejpam-816	514	8	the	the	DET
ejpam-816	514	9	asymptotic	asymptotic	ADJ
ejpam-816	514	10	expansion	expansion	NOUN
ejpam-816	514	11	of	of	ADP
ejpam-816	514	12	the	the	DET
ejpam-816	514	13	generalized	generalized	ADJ
ejpam-816	514	14	hypergeometric	hypergeometric	ADJ
ejpam-816	514	15	function	function	NOUN
ejpam-816	514	16	,	,	PUNCT
ejpam-816	514	17	proc	proc	NOUN
ejpam-816	514	18	.	.	PUNCT
ejpam-816	515	1	lond	lond	PROPN
ejpam-816	515	2	.	.	PUNCT
ejpam-816	516	1	math	math	NOUN
ejpam-816	516	2	.	.	PUNCT
ejpam-816	517	1	soc	soc	PROPN
ejpam-816	517	2	.	.	PUNCT
ejpam-816	518	1	(	(	PUNCT
ejpam-816	518	2	ser	ser	NOUN
ejpam-816	518	3	.	.	PROPN
ejpam-816	518	4	2	2	NUM
ejpam-816	518	5	)	)	PUNCT
ejpam-816	518	6	10:286–293	10:286–293	NUM
ejpam-816	518	7	,	,	PUNCT
ejpam-816	518	8	1935	1935	NUM
ejpam-816	518	9	.	.	PUNCT
ejpam-816	519	1	[	[	X
ejpam-816	519	2	21	21	NUM
ejpam-816	519	3	]	]	X
ejpam-816	519	4	e	e	PROPN
ejpam-816	519	5	m	m	PROPN
ejpam-816	519	6	wright	wright	PROPN
ejpam-816	519	7	,	,	PUNCT
ejpam-816	519	8	the	the	DET
ejpam-816	519	9	asymptotic	asymptotic	ADJ
ejpam-816	519	10	expansion	expansion	NOUN
ejpam-816	519	11	of	of	ADP
ejpam-816	519	12	the	the	DET
ejpam-816	519	13	generalized	generalized	ADJ
ejpam-816	519	14	hypergeometric	hypergeometric	ADJ
ejpam-816	519	15	function	function	NOUN
ejpam-816	519	16	,	,	PUNCT
ejpam-816	519	17	proc	proc	NOUN
ejpam-816	519	18	.	.	PUNCT
ejpam-816	520	1	lond	lond	PROPN
ejpam-816	520	2	.	.	PUNCT
ejpam-816	521	1	math	math	NOUN
ejpam-816	521	2	.	.	PUNCT
ejpam-816	522	1	soc	soc	PROPN
ejpam-816	522	2	.	.	PUNCT
ejpam-816	523	1	(	(	PUNCT
ejpam-816	523	2	ser	ser	NOUN
ejpam-816	523	3	.	.	PROPN
ejpam-816	523	4	2	2	NUM
ejpam-816	523	5	)	)	PUNCT
ejpam-816	523	6	46:389–408	46:389–408	PROPN
ejpam-816	523	7	,	,	PUNCT
ejpam-816	523	8	1940	1940	NUM
ejpam-816	523	9	.	.	PUNCT
ejpam-816	524	1	[	[	X
ejpam-816	524	2	22	22	NUM
ejpam-816	524	3	]	]	X
ejpam-816	524	4	e	e	PROPN
ejpam-816	524	5	m	m	PROPN
ejpam-816	524	6	wright	wright	PROPN
ejpam-816	524	7	,	,	PUNCT
ejpam-816	524	8	a	a	DET
ejpam-816	524	9	recursion	recursion	NOUN
ejpam-816	524	10	formula	formula	NOUN
ejpam-816	524	11	for	for	ADP
ejpam-816	524	12	the	the	DET
ejpam-816	524	13	coefficients	coefficient	NOUN
ejpam-816	524	14	in	in	ADP
ejpam-816	524	15	an	an	DET
ejpam-816	524	16	asymptotic	asymptotic	ADJ
ejpam-816	524	17	expansion	expansion	NOUN
ejpam-816	524	18	,	,	PUNCT
ejpam-816	524	19	proc	proc	NOUN
ejpam-816	524	20	.	.	PUNCT
ejpam-816	525	1	glasgow	glasgow	PROPN
ejpam-816	525	2	math	math	PROPN
ejpam-816	525	3	.	.	PUNCT
ejpam-816	526	1	assoc	assoc	PROPN
ejpam-816	526	2	.	.	PUNCT
ejpam-816	527	1	4:38–41	4:38–41	NUM
ejpam-816	527	2	,	,	PUNCT
ejpam-816	527	3	1958	1958	NUM
ejpam-816	527	4	.	.	PUNCT
ejpam-816	528	1	appendix	appendix	VERB
ejpam-816	528	2	a.	a.	NOUN
ejpam-816	528	3	an	an	DET
ejpam-816	528	4	algorithm	algorithm	NOUN
ejpam-816	528	5	for	for	ADP
ejpam-816	528	6	the	the	DET
ejpam-816	528	7	computation	computation	NOUN
ejpam-816	528	8	of	of	ADP
ejpam-816	528	9	the	the	DET
ejpam-816	528	10	coefficients	coefficient	NOUN
ejpam-816	529	1	c	c	PROPN
ejpam-816	529	2	j	j	PROPN
ejpam-816	529	3	=	=	PUNCT
ejpam-816	529	4	a	a	DET
ejpam-816	529	5	j	j	PROPN
ejpam-816	529	6	/	/	SYM
ejpam-816	529	7	a0	a0	PROPN
ejpam-816	529	8	we	we	PRON
ejpam-816	529	9	describe	describe	VERB
ejpam-816	529	10	an	an	DET
ejpam-816	529	11	algorithm	algorithm	NOUN
ejpam-816	529	12	for	for	ADP
ejpam-816	529	13	the	the	DET
ejpam-816	529	14	computation	computation	NOUN
ejpam-816	529	15	of	of	ADP
ejpam-816	529	16	the	the	DET
ejpam-816	529	17	normalised	normalise	VERB
ejpam-816	529	18	coefficients	coefficient	NOUN
ejpam-816	529	19	a	a	DET
ejpam-816	529	20	j	j	PROPN
ejpam-816	529	21	/	/	SYM
ejpam-816	529	22	a0	a0	PROPN
ejpam-816	529	23	appearing	appear	VERB
ejpam-816	529	24	in	in	ADP
ejpam-816	529	25	the	the	DET
ejpam-816	529	26	exponential	exponential	ADJ
ejpam-816	529	27	expansion	expansion	NOUN
ejpam-816	529	28	ep	ep	PROPN
ejpam-816	529	29	,	,	PUNCT
ejpam-816	529	30	q(z	q(z	PROPN
ejpam-816	529	31	)	)	PUNCT
ejpam-816	529	32	in	in	ADP
ejpam-816	529	33	(	(	PUNCT
ejpam-816	529	34	8)	8)	NUM
ejpam-816	529	35	.	.	PUNCT
ejpam-816	529	36	methods	method	NOUN
ejpam-816	529	37	of	of	ADP
ejpam-816	529	38	computing	compute	VERB
ejpam-816	529	39	these	these	DET
ejpam-816	529	40	coefficients	coefficient	NOUN
ejpam-816	529	41	by	by	ADP
ejpam-816	529	42	recursion	recursion	NOUN
ejpam-816	529	43	in	in	ADP
ejpam-816	529	44	the	the	DET
ejpam-816	529	45	case	case	NOUN
ejpam-816	529	46	when	when	SCONJ
ejpam-816	529	47	αr	αr	PROPN
ejpam-816	529	48	=	=	SYM
ejpam-816	529	49	βr	βr	NOUN
ejpam-816	529	50	=	=	NOUN
ejpam-816	529	51	1	1	NUM
ejpam-816	529	52	have	have	AUX
ejpam-816	529	53	been	be	AUX
ejpam-816	529	54	given	give	VERB
ejpam-816	529	55	by	by	ADP
ejpam-816	529	56	riney	riney	NOUN
ejpam-816	529	57	[	[	X
ejpam-816	529	58	15	15	NUM
ejpam-816	529	59	]	]	PUNCT
ejpam-816	529	60	and	and	CCONJ
ejpam-816	529	61	wright	wright	PROPN
ejpam-816	530	1	[	[	X
ejpam-816	530	2	22	22	NUM
ejpam-816	530	3	]	]	PUNCT
ejpam-816	530	4	.	.	PUNCT
ejpam-816	531	1	here	here	ADV
ejpam-816	531	2	we	we	PRON
ejpam-816	531	3	describe	describe	VERB
ejpam-816	531	4	an	an	DET
ejpam-816	531	5	algebraic	algebraic	ADJ
ejpam-816	531	6	method	method	NOUN
ejpam-816	531	7	valid	valid	ADJ
ejpam-816	531	8	for	for	ADP
ejpam-816	531	9	arbitrary	arbitrary	ADJ
ejpam-816	531	10	αr	αr	NUM
ejpam-816	531	11	>	>	SYM
ejpam-816	531	12	0	0	PUNCT
ejpam-816	532	1	and	and	CCONJ
ejpam-816	532	2	βr	βr	INTJ
ejpam-816	532	3	>	>	NUM
ejpam-816	532	4	0	0	NUM
ejpam-816	532	5	;	;	PUNCT
ejpam-816	532	6	see	see	VERB
ejpam-816	532	7	also	also	ADV
ejpam-816	532	8	[	[	X
ejpam-816	532	9	12	12	NUM
ejpam-816	532	10	,	,	PUNCT
ejpam-816	532	11	pp	pp	ADJ
ejpam-816	532	12	.	.	PUNCT
ejpam-816	533	1	46–49	46–49	NUM
ejpam-816	533	2	]	]	PUNCT
ejpam-816	533	3	.	.	PUNCT
ejpam-816	534	1	we	we	PRON
ejpam-816	534	2	rewrite	rewrite	VERB
ejpam-816	534	3	the	the	DET
ejpam-816	534	4	inverse	inverse	NOUN
ejpam-816	534	5	factorial	factorial	NOUN
ejpam-816	534	6	expansion	expansion	NOUN
ejpam-816	534	7	(	(	PUNCT
ejpam-816	534	8	9	9	NUM
ejpam-816	534	9	)	)	PUNCT
ejpam-816	534	10	in	in	ADP
ejpam-816	534	11	the	the	DET
ejpam-816	534	12	form	form	NOUN
ejpam-816	534	13	g(s)γ(κs+	g(s)γ(κs+	PART
ejpam-816	534	14	ϑ′	ϑ′	NOUN
ejpam-816	534	15	)	)	PUNCT
ejpam-816	534	16	γ(s+	γ(s+	VERB
ejpam-816	534	17	1	1	NUM
ejpam-816	534	18	)	)	PUNCT
ejpam-816	534	19	=	=	PUNCT
ejpam-816	534	20	κa0(hκ	κa0(hκ	X
ejpam-816	534	21	κ)s	κ)s	X
ejpam-816	534	22	�	�	PROPN
ejpam-816	535	1	m−1	m−1	PROPN
ejpam-816	535	2	∑	∑	PUNCT
ejpam-816	535	3	j=0	j=0	PROPN
ejpam-816	535	4	c	c	PROPN
ejpam-816	535	5	j	j	PROPN
ejpam-816	535	6	(	(	PUNCT
ejpam-816	535	7	κs+	κs+	PROPN
ejpam-816	535	8	ϑ′	ϑ′	PROPN
ejpam-816	535	9	)	)	PUNCT
ejpam-816	535	10	j	j	PROPN
ejpam-816	535	11	+	+	CCONJ
ejpam-816	535	12	o(1	o(1	NOUN
ejpam-816	535	13	)	)	PUNCT
ejpam-816	535	14	(	(	PUNCT
ejpam-816	535	15	κs+	κs+	PROPN
ejpam-816	535	16	ϑ′)m	ϑ′)m	PROPN
ejpam-816	535	17	�	�	PROPN
ejpam-816	535	18	,	,	PUNCT
ejpam-816	535	19	(	(	PUNCT
ejpam-816	535	20	49	49	NUM
ejpam-816	535	21	)	)	PUNCT
ejpam-816	535	22	for	for	ADP
ejpam-816	535	23	|s|	|s|	PROPN
ejpam-816	535	24	→	→	SYM
ejpam-816	535	25	∞	∞	NUM
ejpam-816	535	26	uniformly	uniformly	ADV
ejpam-816	535	27	in	in	ADP
ejpam-816	535	28	|arg	|arg	NOUN
ejpam-816	535	29	s|	s|	VERB
ejpam-816	535	30	≤	≤	NUM
ejpam-816	535	31	π−	π−	PROPN
ejpam-816	535	32	ε	ε	PROPN
ejpam-816	535	33	,	,	PUNCT
ejpam-816	535	34	where	where	SCONJ
ejpam-816	535	35	g(s	g(	NOUN
ejpam-816	535	36	)	)	PUNCT
ejpam-816	535	37	is	be	AUX
ejpam-816	535	38	the	the	DET
ejpam-816	535	39	ratio	ratio	NOUN
ejpam-816	535	40	of	of	ADP
ejpam-816	535	41	gamma	gamma	NOUN
ejpam-816	535	42	functions	function	NOUN
ejpam-816	535	43	defined	define	VERB
ejpam-816	535	44	in	in	ADP
ejpam-816	535	45	(	(	PUNCT
ejpam-816	535	46	5	5	NUM
ejpam-816	535	47	)	)	PUNCT
ejpam-816	535	48	,	,	PUNCT
ejpam-816	535	49	(	(	PUNCT
ejpam-816	535	50	a	a	X
ejpam-816	535	51	)	)	PUNCT
ejpam-816	535	52	j	j	NOUN
ejpam-816	535	53	=	=	SYM
ejpam-816	535	54	γ(a+	γ(a+	NOUN
ejpam-816	535	55	j)/γ(a	j)/γ(a	ADV
ejpam-816	535	56	)	)	PUNCT
ejpam-816	535	57	and	and	CCONJ
ejpam-816	535	58	c	c	NOUN
ejpam-816	535	59	j	j	PROPN
ejpam-816	536	1	=	=	PUNCT
ejpam-816	536	2	a	a	DET
ejpam-816	536	3	j	j	PROPN
ejpam-816	536	4	/	/	SYM
ejpam-816	536	5	a0	a0	PROPN
ejpam-816	536	6	.	.	PUNCT
ejpam-816	537	1	introduction	introduction	NOUN
ejpam-816	537	2	of	of	ADP
ejpam-816	537	3	the	the	DET
ejpam-816	537	4	scaled	scale	VERB
ejpam-816	537	5	gamma	gamma	NOUN
ejpam-816	537	6	function	function	PROPN
ejpam-816	537	7	γ∗(z	γ∗(z	NOUN
ejpam-816	537	8	)	)	PUNCT
ejpam-816	537	9	defined	define	VERB
ejpam-816	537	10	by	by	ADP
ejpam-816	537	11	γ∗(z	γ∗(z	NOUN
ejpam-816	537	12	)	)	PUNCT
ejpam-816	537	13	:	:	PUNCT
ejpam-816	537	14	=	=	SYM
ejpam-816	537	15	γ(z)(2π)−	γ(z)(2π)−	PROPN
ejpam-816	537	16	1	1	NUM
ejpam-816	537	17	2	2	NUM
ejpam-816	537	18	ezz	ezz	NOUN
ejpam-816	537	19	1	1	NUM
ejpam-816	537	20	2	2	NUM
ejpam-816	537	21	−z	−z	NOUN
ejpam-816	537	22	references	reference	NOUN
ejpam-816	537	23	1026	1026	NUM
ejpam-816	537	24	leads	lead	VERB
ejpam-816	537	25	to	to	ADP
ejpam-816	537	26	the	the	DET
ejpam-816	537	27	representation	representation	NOUN
ejpam-816	537	28	γ(αs+	γ(αs+	X
ejpam-816	537	29	a	a	NOUN
ejpam-816	537	30	)	)	PUNCT
ejpam-816	537	31	=	=	SYM
ejpam-816	537	32	γ∗(αs+	γ∗(αs+	PROPN
ejpam-816	537	33	a)(2π	a)(2π	PROPN
ejpam-816	537	34	)	)	PUNCT
ejpam-816	537	35	1	1	NUM
ejpam-816	537	36	2	2	NUM
ejpam-816	537	37	e−αs(αs)αs+a−	e−αs(αs)αs+a−	NOUN
ejpam-816	537	38	1	1	NUM
ejpam-816	537	39	2	2	NUM
ejpam-816	537	40	e(αs	e(α	NOUN
ejpam-816	537	41	;	;	PUNCT
ejpam-816	537	42	a	a	X
ejpam-816	537	43	)	)	PUNCT
ejpam-816	537	44	,	,	PUNCT
ejpam-816	537	45	where	where	SCONJ
ejpam-816	537	46	e(αs	e(α	NOUN
ejpam-816	537	47	;	;	PUNCT
ejpam-816	537	48	a	a	X
ejpam-816	537	49	)	)	PUNCT
ejpam-816	537	50	=	=	SYM
ejpam-816	537	51	exp	exp	NOUN
ejpam-816	537	52	�	�	PROPN
ejpam-816	537	53	(	(	PUNCT
ejpam-816	537	54	αs+	αs+	NOUN
ejpam-816	537	55	a−	a−	PROPN
ejpam-816	537	56	1	1	NUM
ejpam-816	537	57	2	2	NUM
ejpam-816	537	58	)	)	PUNCT
ejpam-816	537	59	log	log	VERB
ejpam-816	537	60	�	�	PROPN
ejpam-816	537	61	1	1	NUM
ejpam-816	537	62	+	+	ADP
ejpam-816	537	63	a	a	DET
ejpam-816	537	64	αs	αs	PROPN
ejpam-816	537	65	�	�	PROPN
ejpam-816	537	66	−	−	PROPN
ejpam-816	537	67	a	a	DET
ejpam-816	537	68	�	�	PROPN
ejpam-816	537	69	.	.	PUNCT
ejpam-816	538	1	some	some	DET
ejpam-816	538	2	straightforward	straightforward	ADJ
ejpam-816	538	3	algebra	algebra	NOUN
ejpam-816	538	4	then	then	ADV
ejpam-816	538	5	shows	show	VERB
ejpam-816	538	6	that	that	SCONJ
ejpam-816	538	7	the	the	DET
ejpam-816	538	8	left	left	ADJ
ejpam-816	538	9	-	-	PUNCT
ejpam-816	538	10	hand	hand	NOUN
ejpam-816	538	11	side	side	NOUN
ejpam-816	538	12	of	of	ADP
ejpam-816	538	13	(	(	PUNCT
ejpam-816	538	14	49	49	NUM
ejpam-816	538	15	)	)	PUNCT
ejpam-816	538	16	becomes	become	VERB
ejpam-816	538	17	g(s)γ(κs+	g(s)γ(κs+	NOUN
ejpam-816	538	18	ϑ′	ϑ′	NOUN
ejpam-816	538	19	)	)	PUNCT
ejpam-816	538	20	γ(s+	γ(s+	ADJ
ejpam-816	538	21	1	1	NUM
ejpam-816	538	22	)	)	PUNCT
ejpam-816	538	23	=	=	PUNCT
ejpam-816	538	24	κa0(hκ	κa0(hκ	PROPN
ejpam-816	538	25	κ)sr(s)υ(s	κ)sr(s)υ(s	PROPN
ejpam-816	538	26	)	)	PUNCT
ejpam-816	538	27	,	,	PUNCT
ejpam-816	538	28	(	(	PUNCT
ejpam-816	538	29	50	50	NUM
ejpam-816	538	30	)	)	PUNCT
ejpam-816	538	31	where	where	SCONJ
ejpam-816	538	32	υ(s	υ(s	X
ejpam-816	538	33	)	)	PUNCT
ejpam-816	538	34	=	=	SYM
ejpam-816	538	35	∏p	∏p	NOUN
ejpam-816	538	36	r=1	r=1	NOUN
ejpam-816	538	37	γ	γ	X
ejpam-816	538	38	∗(αrs+	∗(αrs+	PROPN
ejpam-816	538	39	ar	ar	PROPN
ejpam-816	538	40	)	)	PUNCT
ejpam-816	538	41	∏q	∏q	VERB
ejpam-816	539	1	r=1	r=1	NOUN
ejpam-816	539	2	γ	γ	X
ejpam-816	539	3	∗(βrs+	∗(βrs+	ADJ
ejpam-816	539	4	br	br	NOUN
ejpam-816	539	5	)	)	PUNCT
ejpam-816	539	6	γ∗(κs+	γ∗(κs+	ADJ
ejpam-816	539	7	ϑ′	ϑ′	NOUN
ejpam-816	539	8	)	)	PUNCT
ejpam-816	539	9	γ∗(s+	γ∗(s+	NUM
ejpam-816	539	10	1	1	NUM
ejpam-816	539	11	)	)	PUNCT
ejpam-816	539	12	and	and	CCONJ
ejpam-816	539	13	r(s	r(s	NUM
ejpam-816	539	14	)	)	PUNCT
ejpam-816	539	15	=	=	SYM
ejpam-816	539	16	∏p	∏p	PROPN
ejpam-816	539	17	r=1	r=1	ADJ
ejpam-816	539	18	e(αrs	e(αrs	PROPN
ejpam-816	539	19	;	;	PUNCT
ejpam-816	539	20	ar	ar	NOUN
ejpam-816	539	21	)	)	PUNCT
ejpam-816	539	22	∏q	∏q	NOUN
ejpam-816	540	1	r=1	r=1	NOUN
ejpam-816	540	2	e(βrs	e(βrs	NOUN
ejpam-816	540	3	;	;	PUNCT
ejpam-816	540	4	br	br	X
ejpam-816	540	5	)	)	PUNCT
ejpam-816	540	6	e(κs;ϑ′	e(κs;ϑ′	NOUN
ejpam-816	540	7	)	)	PUNCT
ejpam-816	540	8	e(s	e(s	PROPN
ejpam-816	540	9	;	;	PUNCT
ejpam-816	540	10	1	1	NUM
ejpam-816	540	11	)	)	PUNCT
ejpam-816	540	12	.	.	PUNCT
ejpam-816	541	1	substitution	substitution	NOUN
ejpam-816	541	2	of	of	ADP
ejpam-816	541	3	(	(	PUNCT
ejpam-816	541	4	50	50	NUM
ejpam-816	541	5	)	)	PUNCT
ejpam-816	541	6	into	into	ADP
ejpam-816	541	7	(	(	PUNCT
ejpam-816	541	8	49	49	NUM
ejpam-816	541	9	)	)	PUNCT
ejpam-816	541	10	finally	finally	ADV
ejpam-816	541	11	produces	produce	VERB
ejpam-816	541	12	r(s)υ(s	r(s)υ(	NOUN
ejpam-816	541	13	)	)	PUNCT
ejpam-816	541	14	=	=	SYM
ejpam-816	542	1	m−1	m−1	PROPN
ejpam-816	542	2	∑	∑	PUNCT
ejpam-816	542	3	j=0	j=0	PROPN
ejpam-816	542	4	c	c	PROPN
ejpam-816	542	5	j	j	PROPN
ejpam-816	542	6	(	(	PUNCT
ejpam-816	542	7	κs+	κs+	PROPN
ejpam-816	542	8	ϑ′	ϑ′	PROPN
ejpam-816	542	9	)	)	PUNCT
ejpam-816	542	10	j	j	PROPN
ejpam-816	542	11	+	+	CCONJ
ejpam-816	542	12	o(1	o(1	NOUN
ejpam-816	542	13	)	)	PUNCT
ejpam-816	542	14	(	(	PUNCT
ejpam-816	542	15	κs+	κs+	PROPN
ejpam-816	542	16	ϑ′)m	ϑ′)m	PROPN
ejpam-816	542	17	(	(	PUNCT
ejpam-816	542	18	51	51	NUM
ejpam-816	542	19	)	)	PUNCT
ejpam-816	542	20	as	as	ADP
ejpam-816	542	21	|s|	|s|	NOUN
ejpam-816	542	22	→∞	→∞	PROPN
ejpam-816	542	23	in	in	ADP
ejpam-816	542	24	|arg	|arg	NOUN
ejpam-816	542	25	s|	s|	VERB
ejpam-816	542	26	≤	≤	NUM
ejpam-816	542	27	π−	π−	PROPN
ejpam-816	542	28	ε	ε	PROPN
ejpam-816	542	29	.	.	PUNCT
ejpam-816	542	30	now	now	ADV
ejpam-816	542	31	let	let	VERB
ejpam-816	542	32	χ	χ	X
ejpam-816	542	33	=	=	PUNCT
ejpam-816	542	34	(	(	PUNCT
ejpam-816	542	35	κs)−1	κs)−1	PRON
ejpam-816	542	36	and	and	CCONJ
ejpam-816	542	37	expand	expand	VERB
ejpam-816	542	38	r(s	r(s	NUM
ejpam-816	542	39	)	)	PUNCT
ejpam-816	542	40	and	and	CCONJ
ejpam-816	542	41	υ(s	υ(s	PROPN
ejpam-816	542	42	)	)	PUNCT
ejpam-816	542	43	for	for	ADP
ejpam-816	542	44	χ	χ	NOUN
ejpam-816	542	45	→	→	SYM
ejpam-816	542	46	0	0	NUM
ejpam-816	542	47	making	make	VERB
ejpam-816	542	48	use	use	NOUN
ejpam-816	542	49	of	of	ADP
ejpam-816	542	50	the	the	DET
ejpam-816	542	51	well	well	ADV
ejpam-816	542	52	-	-	PUNCT
ejpam-816	542	53	known	know	VERB
ejpam-816	542	54	expansion	expansion	NOUN
ejpam-816	543	1	[	[	X
ejpam-816	543	2	19	19	NUM
ejpam-816	543	3	,	,	PUNCT
ejpam-816	543	4	p.	p.	NOUN
ejpam-816	543	5	71	71	NUM
ejpam-816	543	6	]	]	PUNCT
ejpam-816	543	7	,	,	PUNCT
ejpam-816	543	8	[	[	X
ejpam-816	543	9	12	12	NUM
ejpam-816	543	10	,	,	PUNCT
ejpam-816	543	11	p.	p.	NOUN
ejpam-816	543	12	32	32	NUM
ejpam-816	543	13	]	]	PUNCT
ejpam-816	543	14	γ∗(z)∼	γ∗(z)∼	X
ejpam-816	543	15	∞	∞	PROPN
ejpam-816	543	16	∑	∑	PROPN
ejpam-816	543	17	k=0	k=0	X
ejpam-816	543	18	(	(	PUNCT
ejpam-816	543	19	−)kγkz−k	−)kγkz−k	NOUN
ejpam-816	543	20	(	(	PUNCT
ejpam-816	543	21	|z|	|z|	NOUN
ejpam-816	543	22	→∞	→∞	NOUN
ejpam-816	543	23	;	;	PUNCT
ejpam-816	543	24	|arg	|arg	VERB
ejpam-816	543	25	z|	z|	PROPN
ejpam-816	543	26	≤	≤	NOUN
ejpam-816	543	27	π−	π−	PROPN
ejpam-816	543	28	ε	ε	PROPN
ejpam-816	543	29	)	)	PUNCT
ejpam-816	543	30	,	,	PUNCT
ejpam-816	543	31	where	where	SCONJ
ejpam-816	543	32	γk	γk	PROPN
ejpam-816	543	33	are	be	AUX
ejpam-816	543	34	the	the	DET
ejpam-816	543	35	stirling	stirling	NOUN
ejpam-816	543	36	coefficients	coefficient	NOUN
ejpam-816	543	37	.	.	PUNCT
ejpam-816	544	1	the	the	DET
ejpam-816	544	2	first	first	ADJ
ejpam-816	544	3	few	few	ADJ
ejpam-816	544	4	coefficients	coefficient	NOUN
ejpam-816	544	5	are	be	AUX
ejpam-816	544	6	given	give	VERB
ejpam-816	544	7	by	by	ADP
ejpam-816	544	8	γ0	γ0	NOUN
ejpam-816	544	9	=	=	SYM
ejpam-816	544	10	1	1	NUM
ejpam-816	544	11	,	,	PUNCT
ejpam-816	544	12	γ1	γ1	NOUN
ejpam-816	544	13	=	=	SYM
ejpam-816	544	14	−	−	PROPN
ejpam-816	544	15	1	1	NUM
ejpam-816	544	16	12	12	NUM
ejpam-816	544	17	,	,	PUNCT
ejpam-816	544	18	γ2	γ2	NOUN
ejpam-816	544	19	=	=	SYM
ejpam-816	544	20	1	1	NUM
ejpam-816	544	21	288	288	NUM
ejpam-816	544	22	,	,	PUNCT
ejpam-816	544	23	γ3	γ3	NOUN
ejpam-816	544	24	=	=	SYM
ejpam-816	544	25	139	139	NUM
ejpam-816	544	26	51840	51840	NUM
ejpam-816	544	27	,	,	PUNCT
ejpam-816	544	28	.	.	PUNCT
ejpam-816	544	29	.	.	PUNCT
ejpam-816	544	30	.	.	PUNCT
ejpam-816	544	31	.	.	PUNCT
ejpam-816	545	1	some	some	DET
ejpam-816	545	2	routine	routine	ADJ
ejpam-816	545	3	algebra	algebra	NOUN
ejpam-816	545	4	then	then	ADV
ejpam-816	545	5	yields	yield	VERB
ejpam-816	545	6	γ∗(αs+	γ∗(αs+	PROPN
ejpam-816	545	7	a	a	NOUN
ejpam-816	545	8	)	)	PUNCT
ejpam-816	545	9	=	=	SYM
ejpam-816	545	10	1−	1−	NUM
ejpam-816	545	11	γ1κχ	γ1κχ	PUNCT
ejpam-816	545	12	α	α	PROPN
ejpam-816	545	13	+	+	NOUN
ejpam-816	545	14	o(χ2	o(χ2	NOUN
ejpam-816	545	15	)	)	PUNCT
ejpam-816	545	16	,	,	PUNCT
ejpam-816	545	17	e(αs	e(αs	PROPN
ejpam-816	545	18	;	;	PUNCT
ejpam-816	545	19	a	a	X
ejpam-816	545	20	)	)	PUNCT
ejpam-816	545	21	=	=	SYM
ejpam-816	546	1	1	1	NUM
ejpam-816	546	2	+	+	CCONJ
ejpam-816	546	3	κχ	κχ	PROPN
ejpam-816	546	4	2α	2α	PROPN
ejpam-816	546	5	a(a−	a(a−	PROPN
ejpam-816	546	6	1	1	NUM
ejpam-816	546	7	)	)	PUNCT
ejpam-816	546	8	+	+	NOUN
ejpam-816	546	9	o(χ2	o(χ2	NOUN
ejpam-816	546	10	)	)	PUNCT
ejpam-816	546	11	,	,	PUNCT
ejpam-816	546	12	whence	whence	ADP
ejpam-816	546	13	r(s	r(s	PROPN
ejpam-816	546	14	)	)	PUNCT
ejpam-816	546	15	=	=	SYM
ejpam-816	547	1	1	1	NUM
ejpam-816	547	2	+	+	CCONJ
ejpam-816	547	3	κχ	κχ	PROPN
ejpam-816	547	4	2	2	NUM
ejpam-816	547	5	(	(	PUNCT
ejpam-816	547	6	p	p	NOUN
ejpam-816	547	7	∑	∑	PART
ejpam-816	547	8	r=1	r=1	NOUN
ejpam-816	547	9	ar(ar	ar(ar	NOUN
ejpam-816	547	10	−	−	PROPN
ejpam-816	547	11	1	1	X
ejpam-816	547	12	)	)	PUNCT
ejpam-816	547	13	αr	αr	ADP
ejpam-816	547	14	−	−	PROPN
ejpam-816	547	15	q	q	X
ejpam-816	547	16	∑	∑	PUNCT
ejpam-816	547	17	r=1	r=1	NOUN
ejpam-816	547	18	br(br	br(br	VERB
ejpam-816	547	19	−	−	PROPN
ejpam-816	547	20	1	1	NUM
ejpam-816	547	21	)	)	PUNCT
ejpam-816	547	22	βr	βr	ADP
ejpam-816	547	23	−	−	PROPN
ejpam-816	547	24	ϑ	ϑ	PROPN
ejpam-816	547	25	κ	κ	X
ejpam-816	547	26	(	(	PUNCT
ejpam-816	547	27	1−	1−	NUM
ejpam-816	547	28	ϑ	ϑ	NOUN
ejpam-816	547	29	)	)	PUNCT
ejpam-816	547	30	)	)	PUNCT
ejpam-816	548	1	+	+	VERB
ejpam-816	548	2	o(χ2	o(χ2	NOUN
ejpam-816	548	3	)	)	PUNCT
ejpam-816	548	4	,	,	PUNCT
ejpam-816	548	5	υ(s	υ(s	PROPN
ejpam-816	548	6	)	)	PUNCT
ejpam-816	548	7	=	=	SYM
ejpam-816	549	1	1	1	NUM
ejpam-816	549	2	+	+	CCONJ
ejpam-816	549	3	κχ	κχ	PROPN
ejpam-816	549	4	12	12	NUM
ejpam-816	549	5	(	(	PUNCT
ejpam-816	549	6	p	p	NOUN
ejpam-816	549	7	∑	∑	PUNCT
ejpam-816	549	8	r=1	r=1	NOUN
ejpam-816	549	9	1	1	NUM
ejpam-816	549	10	αr	αr	NUM
ejpam-816	549	11	−	−	PROPN
ejpam-816	549	12	q	q	X
ejpam-816	549	13	∑	∑	PUNCT
ejpam-816	549	14	r=1	r=1	NOUN
ejpam-816	549	15	1	1	NUM
ejpam-816	549	16	βr	βr	ADP
ejpam-816	549	17	+	+	NUM
ejpam-816	549	18	1	1	NUM
ejpam-816	549	19	κ	κ	NOUN
ejpam-816	549	20	−	−	NOUN
ejpam-816	549	21	1	1	NUM
ejpam-816	549	22	)	)	PUNCT
ejpam-816	549	23	+	+	NOUN
ejpam-816	549	24	o(χ2	o(χ2	NOUN
ejpam-816	549	25	)	)	PUNCT
ejpam-816	549	26	.	.	PUNCT
ejpam-816	550	1	references	reference	NOUN
ejpam-816	550	2	1027	1027	NUM
ejpam-816	550	3	upon	upon	SCONJ
ejpam-816	550	4	equating	equate	VERB
ejpam-816	550	5	coefficients	coefficient	NOUN
ejpam-816	550	6	of	of	ADP
ejpam-816	550	7	χ	χ	NOUN
ejpam-816	550	8	in	in	ADP
ejpam-816	550	9	(	(	PUNCT
ejpam-816	550	10	51	51	NUM
ejpam-816	550	11	)	)	PUNCT
ejpam-816	550	12	we	we	PRON
ejpam-816	550	13	obtain	obtain	VERB
ejpam-816	550	14	c1	c1	NOUN
ejpam-816	550	15	=	=	NOUN
ejpam-816	550	16	1	1	NUM
ejpam-816	550	17	2	2	NUM
ejpam-816	550	18	κ(a	κ(a	ADJ
ejpam-816	550	19	+	+	CCONJ
ejpam-816	550	20	1	1	NUM
ejpam-816	550	21	6	6	NUM
ejpam-816	550	22	b	b	NOUN
ejpam-816	550	23	)	)	PUNCT
ejpam-816	550	24	,	,	PUNCT
ejpam-816	550	25	(	(	PUNCT
ejpam-816	550	26	52	52	NUM
ejpam-816	550	27	)	)	PUNCT
ejpam-816	550	28	where	where	SCONJ
ejpam-816	550	29	a	a	DET
ejpam-816	550	30	=	=	SYM
ejpam-816	550	31	p	p	ADJ
ejpam-816	550	32	∑	∑	PUNCT
ejpam-816	550	33	r=1	r=1	NOUN
ejpam-816	550	34	ar(ar	ar(ar	NOUN
ejpam-816	550	35	−	−	PROPN
ejpam-816	550	36	1	1	X
ejpam-816	550	37	)	)	PUNCT
ejpam-816	550	38	αr	αr	ADP
ejpam-816	550	39	−	−	PROPN
ejpam-816	550	40	q	q	X
ejpam-816	550	41	∑	∑	PUNCT
ejpam-816	550	42	r=1	r=1	NOUN
ejpam-816	550	43	br(br	br(br	VERB
ejpam-816	550	44	−	−	PROPN
ejpam-816	550	45	1	1	NUM
ejpam-816	550	46	)	)	PUNCT
ejpam-816	550	47	βr	βr	ADP
ejpam-816	550	48	−	−	PROPN
ejpam-816	550	49	ϑ	ϑ	PROPN
ejpam-816	550	50	κ	κ	X
ejpam-816	550	51	(	(	PUNCT
ejpam-816	550	52	1−	1−	NUM
ejpam-816	550	53	ϑ	ϑ	NOUN
ejpam-816	550	54	)	)	PUNCT
ejpam-816	550	55	,	,	PUNCT
ejpam-816	550	56	b	b	X
ejpam-816	550	57	=	=	SYM
ejpam-816	550	58	p	p	ADJ
ejpam-816	550	59	∑	∑	PUNCT
ejpam-816	550	60	r=1	r=1	NOUN
ejpam-816	550	61	1	1	NUM
ejpam-816	550	62	αr	αr	NUM
ejpam-816	550	63	−	−	PROPN
ejpam-816	550	64	q	q	X
ejpam-816	550	65	∑	∑	PUNCT
ejpam-816	550	66	r=1	r=1	NOUN
ejpam-816	550	67	1	1	NUM
ejpam-816	550	68	βr	βr	ADP
ejpam-816	550	69	+	+	NUM
ejpam-816	550	70	1	1	NUM
ejpam-816	550	71	κ	κ	NOUN
ejpam-816	550	72	−	−	NOUN
ejpam-816	550	73	1	1	NUM
ejpam-816	550	74	.	.	PUNCT
ejpam-816	551	1	the	the	DET
ejpam-816	551	2	higher	high	ADJ
ejpam-816	551	3	coefficients	coefficient	NOUN
ejpam-816	551	4	are	be	AUX
ejpam-816	551	5	then	then	ADV
ejpam-816	551	6	obtained	obtain	VERB
ejpam-816	551	7	by	by	ADP
ejpam-816	551	8	continuation	continuation	NOUN
ejpam-816	551	9	of	of	ADP
ejpam-816	551	10	this	this	DET
ejpam-816	551	11	expansion	expansion	NOUN
ejpam-816	551	12	process	process	NOUN
ejpam-816	551	13	applied	apply	VERB
ejpam-816	551	14	to	to	ADP
ejpam-816	551	15	r(s	r(s	PROPN
ejpam-816	551	16	)	)	PUNCT
ejpam-816	551	17	and	and	CCONJ
ejpam-816	551	18	υ(s	υ(	NOUN
ejpam-816	551	19	)	)	PUNCT
ejpam-816	551	20	in	in	ADP
ejpam-816	551	21	(	(	PUNCT
ejpam-816	551	22	51	51	NUM
ejpam-816	551	23	)	)	PUNCT
ejpam-816	551	24	with	with	ADP
ejpam-816	551	25	the	the	DET
ejpam-816	551	26	help	help	NOUN
ejpam-816	551	27	of	of	ADP
ejpam-816	551	28	mathematica	mathematica	PROPN
ejpam-816	551	29	.	.	PUNCT
ejpam-816	552	1	in	in	ADP
ejpam-816	552	2	specific	specific	ADJ
ejpam-816	552	3	cases	case	NOUN
ejpam-816	552	4	(	(	PUNCT
ejpam-816	552	5	i.e.	i.e.	X
ejpam-816	552	6	,	,	PUNCT
ejpam-816	552	7	with	with	ADP
ejpam-816	552	8	numerical	numerical	ADJ
ejpam-816	552	9	values	value	NOUN
ejpam-816	552	10	for	for	ADP
ejpam-816	552	11	the	the	DET
ejpam-816	552	12	various	various	ADJ
ejpam-816	552	13	parameters	parameter	NOUN
ejpam-816	552	14	)	)	PUNCT
ejpam-816	552	15	it	it	PRON
ejpam-816	552	16	is	be	AUX
ejpam-816	552	17	possible	possible	ADJ
ejpam-816	552	18	to	to	PART
ejpam-816	552	19	generate	generate	VERB
ejpam-816	552	20	the	the	DET
ejpam-816	552	21	coefficients	coefficient	NOUN
ejpam-816	552	22	in	in	ADP
ejpam-816	552	23	this	this	DET
ejpam-816	552	24	manner	manner	NOUN
ejpam-816	552	25	quite	quite	ADV
ejpam-816	552	26	easily	easily	ADV
ejpam-816	552	27	.	.	PUNCT
ejpam-816	553	1	in	in	ADP
ejpam-816	553	2	our	our	PRON
ejpam-816	553	3	computations	computation	NOUN
ejpam-816	553	4	we	we	PRON
ejpam-816	553	5	have	have	AUX
ejpam-816	553	6	used	use	VERB
ejpam-816	553	7	up	up	ADP
ejpam-816	553	8	to	to	ADP
ejpam-816	553	9	a	a	DET
ejpam-816	553	10	maximum	maximum	NOUN
ejpam-816	553	11	of	of	ADP
ejpam-816	553	12	40	40	NUM
ejpam-816	553	13	coefficients	coefficient	NOUN
ejpam-816	553	14	.	.	PUNCT
ejpam-816	554	1	appendix	appendix	NOUN
ejpam-816	554	2	b.	b.	AUX
ejpam-816	555	1	the	the	DET
ejpam-816	555	2	asymptotic	asymptotic	ADJ
ejpam-816	555	3	expansion	expansion	NOUN
ejpam-816	555	4	of	of	ADP
ejpam-816	555	5	2ψ0(z	2ψ0(z	NUM
ejpam-816	555	6	)	)	PUNCT
ejpam-816	555	7	we	we	PRON
ejpam-816	555	8	demonstrate	demonstrate	VERB
ejpam-816	555	9	the	the	DET
ejpam-816	555	10	validity	validity	NOUN
ejpam-816	555	11	of	of	ADP
ejpam-816	555	12	the	the	DET
ejpam-816	555	13	assertion	assertion	NOUN
ejpam-816	555	14	in	in	ADP
ejpam-816	555	15	(	(	PUNCT
ejpam-816	555	16	19	19	NUM
ejpam-816	555	17	)	)	PUNCT
ejpam-816	555	18	concerning	concern	VERB
ejpam-816	555	19	the	the	DET
ejpam-816	555	20	asymptotic	asymptotic	ADJ
ejpam-816	555	21	expansion	expansion	NOUN
ejpam-816	555	22	of	of	ADP
ejpam-816	555	23	the	the	DET
ejpam-816	555	24	wright	wright	PROPN
ejpam-816	555	25	function	function	PROPN
ejpam-816	555	26	pψq(z	pψq(z	PROPN
ejpam-816	555	27	)	)	PUNCT
ejpam-816	555	28	as	as	ADP
ejpam-816	555	29	|z|	|z|	NOUN
ejpam-816	555	30	→	→	SYM
ejpam-816	555	31	∞	∞	NUM
ejpam-816	555	32	by	by	ADP
ejpam-816	555	33	considering	consider	VERB
ejpam-816	555	34	a	a	DET
ejpam-816	555	35	particular	particular	ADJ
ejpam-816	555	36	case	case	NOUN
ejpam-816	555	37	.	.	PUNCT
ejpam-816	556	1	let	let	VERB
ejpam-816	556	2	us	we	PRON
ejpam-816	556	3	take	take	VERB
ejpam-816	556	4	p	p	NOUN
ejpam-816	556	5	=	=	NOUN
ejpam-816	556	6	2	2	NUM
ejpam-816	556	7	,	,	PUNCT
ejpam-816	556	8	q	q	NOUN
ejpam-816	557	1	=	=	NOUN
ejpam-816	557	2	0	0	NUM
ejpam-816	557	3	with	with	SCONJ
ejpam-816	557	4	the	the	DET
ejpam-816	557	5	parameter	parameter	NOUN
ejpam-816	557	6	values	value	VERB
ejpam-816	557	7	α1	α1	PROPN
ejpam-816	557	8	=	=	SYM
ejpam-816	557	9	α2	α2	NOUN
ejpam-816	557	10	=	=	SYM
ejpam-816	557	11	1	1	NUM
ejpam-816	557	12	4	4	NUM
ejpam-816	557	13	and	and	CCONJ
ejpam-816	557	14	ν1	ν1	NOUN
ejpam-816	557	15	=	=	SYM
ejpam-816	557	16	ν2	ν2	NOUN
ejpam-816	557	17	=	=	SYM
ejpam-816	557	18	1	1	NUM
ejpam-816	557	19	8	8	NUM
ejpam-816	557	20	;	;	PUNCT
ejpam-816	557	21	that	that	PRON
ejpam-816	557	22	is	is	ADV
ejpam-816	557	23	,	,	PUNCT
ejpam-816	557	24	we	we	PRON
ejpam-816	557	25	consider	consider	VERB
ejpam-816	557	26	the	the	DET
ejpam-816	557	27	function	function	NOUN
ejpam-816	557	28	2ψ0(z	2ψ0(z	NUM
ejpam-816	557	29	)	)	PUNCT
ejpam-816	557	30	≡	≡	PROPN
ejpam-816	557	31	2ψ0	2ψ0	PROPN
ejpam-816	557	32	�	�	PROPN
ejpam-816	557	33	(	(	PUNCT
ejpam-816	557	34	1	1	NUM
ejpam-816	557	35	4	4	NUM
ejpam-816	557	36	,	,	PUNCT
ejpam-816	557	37	1	1	NUM
ejpam-816	557	38	8	8	NUM
ejpam-816	557	39	)	)	PUNCT
ejpam-816	557	40	,	,	PUNCT
ejpam-816	557	41	(	(	PUNCT
ejpam-816	557	42	1	1	NUM
ejpam-816	557	43	4	4	NUM
ejpam-816	557	44	,	,	PUNCT
ejpam-816	557	45	1	1	NUM
ejpam-816	557	46	8	8	NUM
ejpam-816	557	47	)	)	PUNCT
ejpam-816	557	48	;	;	PUNCT
ejpam-816	557	49	z	z	NOUN
ejpam-816	557	50	�	�	PROPN
ejpam-816	558	1	=	=	SYM
ejpam-816	558	2	∞	∞	PROPN
ejpam-816	558	3	∑	∑	PUNCT
ejpam-816	558	4	k=0	k=0	PROPN
ejpam-816	558	5	zk	zk	PROPN
ejpam-816	558	6	k	k	PROPN
ejpam-816	558	7	!	!	PUNCT
ejpam-816	558	8	γ2(1	γ2(1	PROPN
ejpam-816	558	9	4	4	NUM
ejpam-816	558	10	k+	k+	NOUN
ejpam-816	558	11	1	1	NUM
ejpam-816	558	12	8	8	NUM
ejpam-816	558	13	)	)	PUNCT
ejpam-816	558	14	.	.	PUNCT
ejpam-816	559	1	(	(	PUNCT
ejpam-816	559	2	53	53	NUM
ejpam-816	559	3	)	)	PUNCT
ejpam-816	559	4	from	from	ADP
ejpam-816	559	5	(	(	PUNCT
ejpam-816	559	6	7	7	NUM
ejpam-816	559	7	)	)	PUNCT
ejpam-816	559	8	,	,	PUNCT
ejpam-816	559	9	this	this	DET
ejpam-816	559	10	function	function	NOUN
ejpam-816	559	11	is	be	AUX
ejpam-816	559	12	associated	associate	VERB
ejpam-816	559	13	with	with	ADP
ejpam-816	559	14	the	the	DET
ejpam-816	559	15	parameters	parameter	NOUN
ejpam-816	559	16	κ	κ	X
ejpam-816	559	17	=	=	NOUN
ejpam-816	559	18	1	1	NUM
ejpam-816	559	19	2	2	NUM
ejpam-816	559	20	,	,	PUNCT
ejpam-816	559	21	h	h	NOUN
ejpam-816	559	22	=	=	NOUN
ejpam-816	559	23	1	1	NUM
ejpam-816	559	24	2	2	NUM
ejpam-816	559	25	and	and	CCONJ
ejpam-816	559	26	ϑ	ϑ	X
ejpam-816	559	27	=	=	X
ejpam-816	559	28	−3	−3	NOUN
ejpam-816	559	29	4	4	NUM
ejpam-816	559	30	.	.	PUNCT
ejpam-816	560	1	the	the	DET
ejpam-816	560	2	exponential	exponential	ADJ
ejpam-816	560	3	expansion	expansion	NOUN
ejpam-816	560	4	is	be	AUX
ejpam-816	560	5	,	,	PUNCT
ejpam-816	560	6	from	from	ADP
ejpam-816	560	7	(	(	PUNCT
ejpam-816	560	8	8)	8)	NUM
ejpam-816	560	9	and	and	CCONJ
ejpam-816	560	10	(	(	PUNCT
ejpam-816	560	11	10	10	NUM
ejpam-816	560	12	)	)	PUNCT
ejpam-816	560	13	,	,	PUNCT
ejpam-816	560	14	then	then	ADV
ejpam-816	560	15	given	give	VERB
ejpam-816	560	16	by	by	ADP
ejpam-816	560	17	e2,0(z	e2,0(z	PROPN
ejpam-816	560	18	)	)	PUNCT
ejpam-816	560	19	=	=	PUNCT
ejpam-816	561	1	z−3/4ez	z−3/4ez	PROPN
ejpam-816	561	2	∞	∞	PROPN
ejpam-816	561	3	∑	∑	PUNCT
ejpam-816	561	4	j=0	j=0	PROPN
ejpam-816	561	5	a	a	DET
ejpam-816	561	6	j	j	PROPN
ejpam-816	561	7	z	z	PROPN
ejpam-816	561	8	−	−	PROPN
ejpam-816	561	9	j	j	PROPN
ejpam-816	561	10	,	,	PUNCT
ejpam-816	561	11	z	z	NOUN
ejpam-816	561	12	=	=	SYM
ejpam-816	561	13	1	1	NUM
ejpam-816	561	14	8	8	NUM
ejpam-816	561	15	z2	z2	NUM
ejpam-816	561	16	,	,	PUNCT
ejpam-816	561	17	(	(	PUNCT
ejpam-816	561	18	54	54	NUM
ejpam-816	561	19	)	)	PUNCT
ejpam-816	561	20	where	where	SCONJ
ejpam-816	561	21	a0	a0	PROPN
ejpam-816	561	22	=	=	SYM
ejpam-816	561	23	29/4π	29/4π	PROPN
ejpam-816	561	24	;	;	PUNCT
ejpam-816	561	25	we	we	PRON
ejpam-816	561	26	have	have	AUX
ejpam-816	561	27	employed	employ	VERB
ejpam-816	561	28	coefficients	coefficient	NOUN
ejpam-816	561	29	with	with	ADP
ejpam-816	561	30	j	j	PROPN
ejpam-816	561	31	≤	≤	ADV
ejpam-816	561	32	28	28	NUM
ejpam-816	561	33	in	in	ADP
ejpam-816	561	34	our	our	PRON
ejpam-816	561	35	computations	computation	NOUN
ejpam-816	561	36	(	(	PUNCT
ejpam-816	561	37	see	see	VERB
ejpam-816	561	38	appendix	appendix	NOUN
ejpam-816	561	39	a	a	PRON
ejpam-816	561	40	)	)	PUNCT
ejpam-816	561	41	.	.	PUNCT
ejpam-816	562	1	the	the	DET
ejpam-816	562	2	first	first	ADJ
ejpam-816	562	3	ten	ten	NUM
ejpam-816	562	4	coefficients	coefficient	NOUN
ejpam-816	562	5	c	c	PROPN
ejpam-816	562	6	j	j	PROPN
ejpam-816	562	7	≡	≡	PROPN
ejpam-816	562	8	a	a	DET
ejpam-816	562	9	j	j	PROPN
ejpam-816	562	10	/	/	SYM
ejpam-816	562	11	a0	a0	PROPN
ejpam-816	562	12	for	for	ADP
ejpam-816	562	13	2ψ0(z	2ψ0(z	NUM
ejpam-816	562	14	)	)	PUNCT
ejpam-816	562	15	in	in	ADP
ejpam-816	562	16	(	(	PUNCT
ejpam-816	562	17	53	53	NUM
ejpam-816	562	18	)	)	PUNCT
ejpam-816	562	19	are	be	AUX
ejpam-816	562	20	listed	list	VERB
ejpam-816	562	21	in	in	ADP
ejpam-816	562	22	table	table	NOUN
ejpam-816	562	23	3	3	NUM
ejpam-816	562	24	.	.	PUNCT
ejpam-816	562	25	table	table	NOUN
ejpam-816	562	26	3	3	NUM
ejpam-816	562	27	:	:	PUNCT
ejpam-816	562	28	the	the	DET
ejpam-816	562	29	coefficients	coefficient	NOUN
ejpam-816	562	30	c	c	PROPN
ejpam-816	562	31	j	j	PROPN
ejpam-816	562	32	for	for	ADP
ejpam-816	562	33	1≤	1≤	NUM
ejpam-816	563	1	j	j	PROPN
ejpam-816	563	2	≤	≤	ADV
ejpam-816	563	3	10	10	NUM
ejpam-816	563	4	associated	associate	VERB
ejpam-816	563	5	with	with	ADP
ejpam-816	563	6	the	the	DET
ejpam-816	563	7	function	function	NOUN
ejpam-816	563	8	in	in	ADP
ejpam-816	563	9	(	(	PUNCT
ejpam-816	563	10	53	53	NUM
ejpam-816	563	11	)	)	PUNCT
ejpam-816	563	12	.	.	PUNCT
ejpam-816	564	1	j	j	PROPN
ejpam-816	564	2	c	c	PROPN
ejpam-816	564	3	j	j	PROPN
ejpam-816	564	4	j	j	PROPN
ejpam-816	564	5	c	c	PROPN
ejpam-816	564	6	j	j	PROPN
ejpam-816	564	7	1	1	NUM
ejpam-816	564	8	13	13	NUM
ejpam-816	564	9	16	16	NUM
ejpam-816	564	10	2	2	NUM
ejpam-816	564	11	729	729	NUM
ejpam-816	564	12	512	512	NUM
ejpam-816	564	13	3	3	NUM
ejpam-816	564	14	31575	31575	NUM
ejpam-816	564	15	8192	8192	NUM
ejpam-816	564	16	4	4	NUM
ejpam-816	564	17	7432635	7432635	NUM
ejpam-816	564	18	524288	524288	NUM
ejpam-816	564	19	5	5	NUM
ejpam-816	564	20	554191155	554191155	NUM
ejpam-816	564	21	8388608	8388608	NUM
ejpam-816	564	22	6	6	NUM
ejpam-816	564	23	100179200205	100179200205	NUM
ejpam-816	564	24	268435456	268435456	NUM
ejpam-816	564	25	7	7	NUM
ejpam-816	564	26	10645956497295	10645956497295	NUM
ejpam-816	564	27	4294967296	4294967296	NUM
ejpam-816	564	28	8	8	NUM
ejpam-816	564	29	10406881110208275	10406881110208275	NUM
ejpam-816	564	30	549755813888	549755813888	NUM
ejpam-816	564	31	9	9	NUM
ejpam-816	564	32	1437596137005803775	1437596137005803775	NUM
ejpam-816	564	33	8796093022208	8796093022208	NUM
ejpam-816	564	34	10	10	NUM
ejpam-816	564	35	443063017349580803175	443063017349580803175	NUM
ejpam-816	564	36	281474976710656	281474976710656	NUM
ejpam-816	564	37	references	reference	NOUN
ejpam-816	564	38	1028	1028	NUM
ejpam-816	564	39	from	from	ADP
ejpam-816	564	40	(	(	PUNCT
ejpam-816	564	41	11	11	NUM
ejpam-816	564	42	)	)	PUNCT
ejpam-816	564	43	,	,	PUNCT
ejpam-816	564	44	the	the	DET
ejpam-816	564	45	mellin	mellin	NOUN
ejpam-816	564	46	-	-	PUNCT
ejpam-816	564	47	barnes	barnes	NOUN
ejpam-816	564	48	integral	integral	ADJ
ejpam-816	564	49	representation	representation	NOUN
ejpam-816	564	50	for	for	ADP
ejpam-816	564	51	2ψ0(z	2ψ0(z	NUM
ejpam-816	564	52	)	)	PUNCT
ejpam-816	564	53	in	in	ADP
ejpam-816	564	54	(	(	PUNCT
ejpam-816	564	55	53	53	NUM
ejpam-816	564	56	)	)	PUNCT
ejpam-816	564	57	is	be	AUX
ejpam-816	564	58	given	give	VERB
ejpam-816	564	59	by	by	ADP
ejpam-816	564	60	2ψ0(z	2ψ0(z	NUM
ejpam-816	564	61	)	)	PUNCT
ejpam-816	564	62	=	=	SYM
ejpam-816	564	63	1	1	NUM
ejpam-816	564	64	2πi	2πi	NOUN
ejpam-816	564	65	∫	∫	PROPN
ejpam-816	564	66	∞i	∞i	NUM
ejpam-816	564	67	−∞i	−∞i	ADP
ejpam-816	565	1	γ(s)γ2(1	γ(s)γ2(1	NOUN
ejpam-816	565	2	8	8	NUM
ejpam-816	565	3	−	−	NOUN
ejpam-816	565	4	1	1	NUM
ejpam-816	565	5	4	4	NUM
ejpam-816	565	6	s)(ze∓πi)−sds	s)(ze∓πi)−sds	NUM
ejpam-816	565	7	(	(	PUNCT
ejpam-816	565	8	|arg(−z)|	|arg(−z)|	PUNCT
ejpam-816	565	9	<	<	X
ejpam-816	565	10	3	3	NUM
ejpam-816	565	11	4	4	NUM
ejpam-816	565	12	π	π	NOUN
ejpam-816	565	13	)	)	PUNCT
ejpam-816	565	14	,	,	PUNCT
ejpam-816	565	15	where	where	SCONJ
ejpam-816	565	16	the	the	DET
ejpam-816	565	17	upper	upper	ADJ
ejpam-816	565	18	or	or	CCONJ
ejpam-816	565	19	lower	low	ADJ
ejpam-816	565	20	sign	sign	NOUN
ejpam-816	565	21	is	be	AUX
ejpam-816	565	22	chosen	choose	VERB
ejpam-816	565	23	according	accord	VERB
ejpam-816	565	24	as	as	ADP
ejpam-816	565	25	arg	arg	NOUN
ejpam-816	565	26	z	z	NOUN
ejpam-816	565	27	>	>	X
ejpam-816	565	28	0	0	NUM
ejpam-816	565	29	or	or	CCONJ
ejpam-816	565	30	arg	arg	NOUN
ejpam-816	565	31	z	z	NOUN
ejpam-816	565	32	<	<	X
ejpam-816	565	33	0	0	NUM
ejpam-816	565	34	,	,	PUNCT
ejpam-816	565	35	respectively	respectively	ADV
ejpam-816	565	36	and	and	CCONJ
ejpam-816	565	37	the	the	DET
ejpam-816	565	38	integration	integration	NOUN
ejpam-816	565	39	path	path	NOUN
ejpam-816	565	40	separates	separate	VERB
ejpam-816	565	41	the	the	DET
ejpam-816	565	42	poles	pole	NOUN
ejpam-816	565	43	of	of	ADP
ejpam-816	565	44	γ(s	γ(	NOUN
ejpam-816	565	45	)	)	PUNCT
ejpam-816	565	46	from	from	ADP
ejpam-816	565	47	the	the	DET
ejpam-816	565	48	sequence	sequence	NOUN
ejpam-816	565	49	of	of	ADP
ejpam-816	565	50	double	double	ADJ
ejpam-816	565	51	poles	pole	NOUN
ejpam-816	565	52	of	of	ADP
ejpam-816	565	53	γ2(1	γ2(1	NOUN
ejpam-816	565	54	8	8	NUM
ejpam-816	565	55	−	−	NOUN
ejpam-816	565	56	1	1	NUM
ejpam-816	565	57	4	4	NUM
ejpam-816	565	58	s	s	NOUN
ejpam-816	565	59	)	)	PUNCT
ejpam-816	565	60	situated	situate	VERB
ejpam-816	565	61	at	at	ADP
ejpam-816	565	62	s	s	NOUN
ejpam-816	565	63	=	=	PUNCT
ejpam-816	565	64	4k+	4k+	NUM
ejpam-816	565	65	1	1	NUM
ejpam-816	565	66	2	2	NUM
ejpam-816	565	67	,	,	PUNCT
ejpam-816	565	68	k	k	PROPN
ejpam-816	565	69	=	=	PUNCT
ejpam-816	565	70	0,1,2	0,1,2	NUM
ejpam-816	565	71	,	,	PUNCT
ejpam-816	565	72	.	.	PUNCT
ejpam-816	565	73	.	.	PUNCT
ejpam-816	565	74	.	.	PUNCT
ejpam-816	565	75	.	.	PUNCT
ejpam-816	566	1	displacement	displacement	NOUN
ejpam-816	566	2	of	of	ADP
ejpam-816	566	3	the	the	DET
ejpam-816	566	4	integration	integration	NOUN
ejpam-816	566	5	path	path	NOUN
ejpam-816	566	6	over	over	ADP
ejpam-816	566	7	the	the	DET
ejpam-816	566	8	sequence	sequence	NOUN
ejpam-816	566	9	of	of	ADP
ejpam-816	566	10	double	double	ADJ
ejpam-816	566	11	poles	pole	NOUN
ejpam-816	566	12	and	and	CCONJ
ejpam-816	566	13	evaluation	evaluation	NOUN
ejpam-816	566	14	of	of	ADP
ejpam-816	566	15	the	the	DET
ejpam-816	566	16	residues	residue	NOUN
ejpam-816	566	17	leads	lead	VERB
ejpam-816	566	18	to	to	ADP
ejpam-816	566	19	the	the	DET
ejpam-816	566	20	algebraic	algebraic	ADJ
ejpam-816	566	21	expansion	expansion	NOUN
ejpam-816	566	22	h2,0(ze∓πi	h2,0(ze∓πi	PROPN
ejpam-816	566	23	)	)	PUNCT
ejpam-816	567	1	=	=	SYM
ejpam-816	567	2	−16	−16	PROPN
ejpam-816	567	3	∞	∞	PROPN
ejpam-816	567	4	∑	∑	PROPN
ejpam-816	567	5	k=0	k=0	PROPN
ejpam-816	567	6	γ(4k+	γ(4k+	PROPN
ejpam-816	567	7	1	1	NUM
ejpam-816	567	8	2	2	NUM
ejpam-816	567	9	)	)	PUNCT
ejpam-816	567	10	(	(	PUNCT
ejpam-816	567	11	k!)2	k!)2	PROPN
ejpam-816	567	12	(	(	PUNCT
ejpam-816	567	13	ze∓πi)−4k−	ze∓πi)−4k−	PROPN
ejpam-816	567	14	1	1	NUM
ejpam-816	567	15	2	2	NUM
ejpam-816	567	16	�	�	PROPN
ejpam-816	567	17	ψ(4k+	ψ(4k+	NOUN
ejpam-816	567	18	1	1	NUM
ejpam-816	567	19	2	2	NUM
ejpam-816	567	20	)	)	PUNCT
ejpam-816	567	21	−	−	PROPN
ejpam-816	567	22	1	1	NUM
ejpam-816	567	23	2	2	NUM
ejpam-816	567	24	ψ(k+	ψ(k+	PROPN
ejpam-816	567	25	1)−	1)−	PROPN
ejpam-816	567	26	log(ze∓πi	log(ze∓πi	PROPN
ejpam-816	567	27	)	)	PUNCT
ejpam-816	567	28	�	�	PROPN
ejpam-816	567	29	,	,	PUNCT
ejpam-816	567	30	(	(	PUNCT
ejpam-816	567	31	55	55	NUM
ejpam-816	567	32	)	)	PUNCT
ejpam-816	567	33	where	where	SCONJ
ejpam-816	567	34	ψ	ψ	ADP
ejpam-816	567	35	denotes	denote	VERB
ejpam-816	567	36	the	the	DET
ejpam-816	567	37	logarithmic	logarithmic	ADJ
ejpam-816	567	38	derivative	derivative	NOUN
ejpam-816	567	39	of	of	ADP
ejpam-816	567	40	the	the	DET
ejpam-816	567	41	gamma	gamma	NOUN
ejpam-816	567	42	function	function	NOUN
ejpam-816	567	43	;	;	PUNCT
ejpam-816	567	44	compare	compare	VERB
ejpam-816	567	45	(	(	PUNCT
ejpam-816	567	46	60	60	NUM
ejpam-816	567	47	)	)	PUNCT
ejpam-816	567	48	.	.	PUNCT
ejpam-816	568	1	theorems	theorems	PROPN
ejpam-816	568	2	1	1	NUM
ejpam-816	568	3	and	and	CCONJ
ejpam-816	568	4	2	2	NUM
ejpam-816	568	5	show	show	VERB
ejpam-816	568	6	that	that	SCONJ
ejpam-816	568	7	2ψ0(z	2ψ0(z	NUM
ejpam-816	568	8	)	)	PUNCT
ejpam-816	568	9	is	be	AUX
ejpam-816	568	10	exponentially	exponentially	ADV
ejpam-816	568	11	large	large	ADJ
ejpam-816	568	12	given	give	VERB
ejpam-816	568	13	by	by	ADP
ejpam-816	568	14	(	(	PUNCT
ejpam-816	568	15	54	54	NUM
ejpam-816	568	16	)	)	PUNCT
ejpam-816	568	17	in	in	ADP
ejpam-816	568	18	the	the	DET
ejpam-816	568	19	sector	sector	NOUN
ejpam-816	568	20	|arg	|arg	NOUN
ejpam-816	568	21	z|	z|	PROPN
ejpam-816	568	22	<	<	X
ejpam-816	568	23	1	1	NUM
ejpam-816	568	24	4	4	NUM
ejpam-816	568	25	π	π	NOUN
ejpam-816	568	26	,	,	PUNCT
ejpam-816	568	27	with	with	ADP
ejpam-816	568	28	the	the	DET
ejpam-816	568	29	dominant	dominant	ADJ
ejpam-816	568	30	expansion	expansion	NOUN
ejpam-816	568	31	in	in	ADP
ejpam-816	568	32	the	the	DET
ejpam-816	568	33	rest	rest	NOUN
ejpam-816	568	34	of	of	ADP
ejpam-816	568	35	the	the	DET
ejpam-816	568	36	z	z	NOUN
ejpam-816	568	37	-	-	PUNCT
ejpam-816	568	38	plane	plane	NOUN
ejpam-816	568	39	being	be	AUX
ejpam-816	568	40	the	the	DET
ejpam-816	568	41	algebraic	algebraic	ADJ
ejpam-816	568	42	expansion	expansion	NOUN
ejpam-816	568	43	in	in	ADP
ejpam-816	568	44	(	(	PUNCT
ejpam-816	568	45	55	55	NUM
ejpam-816	568	46	)	)	PUNCT
ejpam-816	568	47	.	.	PUNCT
ejpam-816	569	1	the	the	DET
ejpam-816	569	2	exponential	exponential	ADJ
ejpam-816	569	3	expansion	expansion	NOUN
ejpam-816	569	4	e2,0(z	e2,0(z	PROPN
ejpam-816	569	5	)	)	PUNCT
ejpam-816	569	6	,	,	PUNCT
ejpam-816	569	7	which	which	PRON
ejpam-816	569	8	is	be	AUX
ejpam-816	569	9	subdominant	subdominant	ADJ
ejpam-816	569	10	in	in	ADP
ejpam-816	569	11	the	the	DET
ejpam-816	569	12	sectors	sector	NOUN
ejpam-816	569	13	1	1	NUM
ejpam-816	569	14	4	4	NUM
ejpam-816	569	15	π	π	NOUN
ejpam-816	569	16	<	<	X
ejpam-816	569	17	|arg	|arg	VERB
ejpam-816	569	18	z|	z|	PROPN
ejpam-816	569	19	<	<	X
ejpam-816	569	20	3	3	NUM
ejpam-816	569	21	4	4	NUM
ejpam-816	569	22	π	π	NOUN
ejpam-816	569	23	,	,	PUNCT
ejpam-816	569	24	is	be	AUX
ejpam-816	569	25	maximally	maximally	ADV
ejpam-816	569	26	subdominant	subdominant	ADJ
ejpam-816	569	27	on	on	ADP
ejpam-816	569	28	the	the	DET
ejpam-816	569	29	rays	ray	NOUN
ejpam-816	569	30	(	(	PUNCT
ejpam-816	569	31	the	the	DET
ejpam-816	569	32	stokes	stokes	PROPN
ejpam-816	569	33	lines	line	NOUN
ejpam-816	569	34	)	)	PUNCT
ejpam-816	569	35	arg	arg	NOUN
ejpam-816	569	36	z	z	NOUN
ejpam-816	569	37	=	=	PUNCT
ejpam-816	569	38	±1	±1	VERB
ejpam-816	569	39	2	2	NUM
ejpam-816	569	40	π	π	NOUN
ejpam-816	569	41	.	.	PUNCT
ejpam-816	570	1	accordingly	accordingly	ADV
ejpam-816	570	2	,	,	PUNCT
ejpam-816	570	3	as	as	ADP
ejpam-816	570	4	|arg	|arg	VERB
ejpam-816	570	5	z|	z|	NOUN
ejpam-816	570	6	increases	increase	NOUN
ejpam-816	570	7	,	,	PUNCT
ejpam-816	570	8	the	the	DET
ejpam-816	570	9	expansion	expansion	NOUN
ejpam-816	570	10	e2,0(z	e2,0(z	PROPN
ejpam-816	570	11	)	)	PUNCT
ejpam-816	570	12	should	should	AUX
ejpam-816	570	13	undergo	undergo	VERB
ejpam-816	570	14	a	a	DET
ejpam-816	570	15	stokes	stoke	NOUN
ejpam-816	570	16	phenomenon	phenomenon	NOUN
ejpam-816	570	17	and	and	CCONJ
ejpam-816	570	18	switch	switch	VERB
ejpam-816	570	19	off	off	ADP
ejpam-816	570	20	smoothly	smoothly	ADV
ejpam-816	570	21	across	across	ADP
ejpam-816	570	22	the	the	DET
ejpam-816	570	23	rays	ray	NOUN
ejpam-816	570	24	arg	arg	VERB
ejpam-816	570	25	z	z	NOUN
ejpam-816	570	26	=	=	PUNCT
ejpam-816	570	27	±1	±1	VERB
ejpam-816	570	28	2	2	NUM
ejpam-816	570	29	π	π	NOUN
ejpam-816	570	30	,	,	PUNCT
ejpam-816	570	31	to	to	PART
ejpam-816	570	32	leave	leave	VERB
ejpam-816	570	33	the	the	DET
ejpam-816	570	34	algebraic	algebraic	ADJ
ejpam-816	570	35	expansion	expansion	NOUN
ejpam-816	570	36	h2,0(ze∓πi	h2,0(ze∓πi	PROPN
ejpam-816	570	37	)	)	PUNCT
ejpam-816	570	38	in	in	ADP
ejpam-816	570	39	the	the	DET
ejpam-816	570	40	sectors	sector	NOUN
ejpam-816	570	41	1	1	NUM
ejpam-816	570	42	2	2	NUM
ejpam-816	570	43	π	π	NOUN
ejpam-816	570	44	<	<	X
ejpam-816	570	45	|arg	|arg	VERB
ejpam-816	570	46	z|	z|	PROPN
ejpam-816	570	47	≤	≤	NOUN
ejpam-816	570	48	π	π	PROPN
ejpam-816	570	49	,	,	PUNCT
ejpam-816	570	50	as	as	SCONJ
ejpam-816	570	51	stated	state	VERB
ejpam-816	570	52	in	in	ADP
ejpam-816	570	53	(	(	PUNCT
ejpam-816	570	54	19	19	NUM
ejpam-816	570	55	)	)	PUNCT
ejpam-816	570	56	;	;	PUNCT
ejpam-816	570	57	that	that	PRON
ejpam-816	570	58	is	be	AUX
ejpam-816	570	59	2ψ0(z	2ψ0(z	NUM
ejpam-816	570	60	)	)	PUNCT
ejpam-816	570	61	∼	∼	NOUN
ejpam-816	570	62	¨	¨	NOUN
ejpam-816	570	63	e2,0(z	e2,0(z	NOUN
ejpam-816	570	64	)	)	PUNCT
ejpam-816	571	1	+	+	PROPN
ejpam-816	571	2	h2,0(ze∓πi	h2,0(ze∓πi	PROPN
ejpam-816	571	3	)	)	PUNCT
ejpam-816	571	4	in	in	ADP
ejpam-816	571	5	|arg	|arg	VERB
ejpam-816	571	6	z|	z|	PROPN
ejpam-816	571	7	≤	≤	NOUN
ejpam-816	571	8	1	1	NUM
ejpam-816	571	9	2	2	NUM
ejpam-816	571	10	π−	π−	PROPN
ejpam-816	571	11	ε	ε	PROPN
ejpam-816	571	12	h2,0(ze∓πi	h2,0(ze∓πi	PROPN
ejpam-816	571	13	)	)	PUNCT
ejpam-816	571	14	in	in	ADP
ejpam-816	571	15	1	1	NUM
ejpam-816	571	16	2	2	NUM
ejpam-816	571	17	π+	π+	PUNCT
ejpam-816	571	18	ε≤	ε≤	NOUN
ejpam-816	571	19	|arg	|arg	VERB
ejpam-816	571	20	z|	z|	ADJ
ejpam-816	571	21	≤	≤	NOUN
ejpam-816	571	22	π	π	X
ejpam-816	571	23	(	(	PUNCT
ejpam-816	571	24	56	56	NUM
ejpam-816	571	25	)	)	PUNCT
ejpam-816	571	26	as	as	ADP
ejpam-816	571	27	|z|	|z|	NOUN
ejpam-816	571	28	→∞.	→∞.	PUNCT
ejpam-816	571	29	to	to	PART
ejpam-816	571	30	demonstrate	demonstrate	VERB
ejpam-816	571	31	this	this	PRON
ejpam-816	572	1	,	,	PUNCT
ejpam-816	572	2	we	we	PRON
ejpam-816	572	3	set	set	VERB
ejpam-816	572	4	z	z	NOUN
ejpam-816	572	5	=	=	SYM
ejpam-816	572	6	|z|eiθ	|z|eiθ	PROPN
ejpam-816	572	7	and	and	CCONJ
ejpam-816	572	8	define	define	VERB
ejpam-816	572	9	the	the	DET
ejpam-816	572	10	stokes	stoke	NOUN
ejpam-816	572	11	multiplier	multiplier	ADV
ejpam-816	572	12	s(θ	s(θ	PROPN
ejpam-816	572	13	)	)	PUNCT
ejpam-816	572	14	(	(	PUNCT
ejpam-816	572	15	at	at	ADP
ejpam-816	572	16	fixed	fix	VERB
ejpam-816	572	17	|z|	|z|	NOUN
ejpam-816	572	18	)	)	PUNCT
ejpam-816	572	19	for	for	ADP
ejpam-816	572	20	the	the	DET
ejpam-816	572	21	stokes	stoke	NOUN
ejpam-816	572	22	line	line	NOUN
ejpam-816	572	23	arg	arg	NOUN
ejpam-816	572	24	z	z	NOUN
ejpam-816	572	25	=	=	SYM
ejpam-816	572	26	1	1	NUM
ejpam-816	572	27	2	2	NUM
ejpam-816	572	28	π	π	NOUN
ejpam-816	572	29	by	by	ADP
ejpam-816	572	30	2ψ0(z	2ψ0(z	NUM
ejpam-816	572	31	)	)	PUNCT
ejpam-816	573	1	=	=	NOUN
ejpam-816	573	2	h	h	NOUN
ejpam-816	573	3	opt	opt	VERB
ejpam-816	573	4	2,0	2,0	NUM
ejpam-816	573	5	(	(	PUNCT
ejpam-816	573	6	ze∓πi	ze∓πi	X
ejpam-816	573	7	)	)	PUNCT
ejpam-816	573	8	+	+	NUM
ejpam-816	573	9	a0z−3/4ez	a0z−3/4ez	NUM
ejpam-816	573	10	s(θ	s(θ	ADV
ejpam-816	573	11	)	)	PUNCT
ejpam-816	573	12	,	,	PUNCT
ejpam-816	573	13	where	where	SCONJ
ejpam-816	573	14	the	the	DET
ejpam-816	573	15	superscript	superscript	PROPN
ejpam-816	573	16	‘	'	PUNCT
ejpam-816	573	17	opt	opt	NOUN
ejpam-816	573	18	’	'	PUNCT
ejpam-816	573	19	denotes	denote	NOUN
ejpam-816	573	20	that	that	SCONJ
ejpam-816	573	21	the	the	DET
ejpam-816	573	22	algebraic	algebraic	ADJ
ejpam-816	573	23	expansion	expansion	NOUN
ejpam-816	573	24	is	be	AUX
ejpam-816	573	25	truncated	truncate	VERB
ejpam-816	573	26	at	at	ADP
ejpam-816	573	27	its	its	PRON
ejpam-816	573	28	optimal	optimal	ADJ
ejpam-816	573	29	truncation	truncation	NOUN
ejpam-816	573	30	point	point	NOUN
ejpam-816	573	31	and	and	CCONJ
ejpam-816	573	32	z	z	NOUN
ejpam-816	573	33	is	be	AUX
ejpam-816	573	34	defined	define	VERB
ejpam-816	573	35	in	in	ADP
ejpam-816	573	36	(	(	PUNCT
ejpam-816	573	37	54	54	NUM
ejpam-816	573	38	)	)	PUNCT
ejpam-816	573	39	.	.	PUNCT
ejpam-816	574	1	in	in	ADP
ejpam-816	574	2	the	the	DET
ejpam-816	574	3	first	first	ADJ
ejpam-816	574	4	half	half	NOUN
ejpam-816	574	5	of	of	ADP
ejpam-816	574	6	table	table	NOUN
ejpam-816	574	7	4	4	NUM
ejpam-816	574	8	we	we	PRON
ejpam-816	574	9	show	show	VERB
ejpam-816	574	10	the	the	DET
ejpam-816	574	11	values§	values§	NOUN
ejpam-816	574	12	of	of	ADP
ejpam-816	574	13	re	re	ADJ
ejpam-816	574	14	(	(	PUNCT
ejpam-816	574	15	s	s	NOUN
ejpam-816	574	16	)	)	PUNCT
ejpam-816	574	17	for	for	ADP
ejpam-816	574	18	varying	vary	VERB
ejpam-816	574	19	θ	θ	PROPN
ejpam-816	574	20	in	in	ADP
ejpam-816	574	21	the	the	DET
ejpam-816	574	22	neighbourhood	neighbourhood	NOUN
ejpam-816	574	23	of	of	ADP
ejpam-816	574	24	θ	θ	PROPN
ejpam-816	574	25	=	=	SYM
ejpam-816	574	26	1	1	NUM
ejpam-816	574	27	2	2	NUM
ejpam-816	574	28	π	π	NOUN
ejpam-816	574	29	when	when	SCONJ
ejpam-816	574	30	|z|	|z|	NOUN
ejpam-816	574	31	=	=	SYM
ejpam-816	574	32	15	15	NUM
ejpam-816	574	33	,	,	PUNCT
ejpam-816	574	34	where	where	SCONJ
ejpam-816	574	35	the	the	DET
ejpam-816	574	36	value	value	NOUN
ejpam-816	574	37	of	of	ADP
ejpam-816	574	38	2ψ0(z	2ψ0(z	NUM
ejpam-816	574	39	)	)	PUNCT
ejpam-816	574	40	has	have	AUX
ejpam-816	574	41	been	be	AUX
ejpam-816	574	42	computed	compute	VERB
ejpam-816	574	43	by	by	ADP
ejpam-816	574	44	high	high	ADJ
ejpam-816	574	45	-	-	PUNCT
ejpam-816	574	46	precision	precision	NOUN
ejpam-816	574	47	summation	summation	NOUN
ejpam-816	574	48	of	of	ADP
ejpam-816	574	49	(	(	PUNCT
ejpam-816	574	50	53	53	NUM
ejpam-816	574	51	)	)	PUNCT
ejpam-816	574	52	.	.	PUNCT
ejpam-816	575	1	the	the	DET
ejpam-816	575	2	second	second	ADJ
ejpam-816	575	3	half	half	NOUN
ejpam-816	575	4	of	of	ADP
ejpam-816	575	5	table	table	NOUN
ejpam-816	575	6	4	4	NUM
ejpam-816	575	7	displays	display	VERB
ejpam-816	575	8	the	the	DET
ejpam-816	575	9	absolute	absolute	ADJ
ejpam-816	575	10	error	error	NOUN
ejpam-816	575	11	in	in	ADP
ejpam-816	575	12	the	the	DET
ejpam-816	575	13	computation	computation	NOUN
ejpam-816	575	14	of	of	ADP
ejpam-816	575	15	2ψ0(z	2ψ0(z	NUM
ejpam-816	575	16	)	)	PUNCT
ejpam-816	575	17	using	use	VERB
ejpam-816	575	18	the	the	DET
ejpam-816	575	19	asymptotic	asymptotic	ADJ
ejpam-816	575	20	expansion	expansion	NOUN
ejpam-816	575	21	in	in	ADP
ejpam-816	575	22	(	(	PUNCT
ejpam-816	575	23	56	56	NUM
ejpam-816	575	24	)	)	PUNCT
ejpam-816	575	25	in	in	ADP
ejpam-816	575	26	the	the	DET
ejpam-816	575	27	sector	sector	NOUN
ejpam-816	575	28	1	1	NUM
ejpam-816	575	29	2	2	NUM
ejpam-816	575	30	π≤	π≤	NUM
ejpam-816	575	31	θ	θ	NOUN
ejpam-816	575	32	≤	≤	NUM
ejpam-816	575	33	3	3	NUM
ejpam-816	575	34	4	4	NUM
ejpam-816	575	35	π	π	NOUN
ejpam-816	575	36	with	with	ADP
ejpam-816	575	37	the	the	DET
ejpam-816	575	38	same	same	ADJ
ejpam-816	575	39	value	value	NOUN
ejpam-816	575	40	of	of	ADP
ejpam-816	575	41	|z|	|z|	NOUN
ejpam-816	575	42	.	.	PUNCT
ejpam-816	576	1	the	the	DET
ejpam-816	576	2	values	value	NOUN
ejpam-816	576	3	in	in	ADP
ejpam-816	576	4	the	the	DET
ejpam-816	576	5	column	column	NOUN
ejpam-816	576	6	labelled	label	VERB
ejpam-816	576	7	(	(	PUNCT
ejpam-816	576	8	a	a	X
ejpam-816	576	9	)	)	PUNCT
ejpam-816	576	10	were	be	AUX
ejpam-816	576	11	obtained	obtain	VERB
ejpam-816	576	12	using	use	VERB
ejpam-816	576	13	the	the	DET
ejpam-816	576	14	first	first	ADJ
ejpam-816	576	15	expansion	expansion	NOUN
ejpam-816	576	16	in	in	ADP
ejpam-816	576	17	(	(	PUNCT
ejpam-816	576	18	56	56	NUM
ejpam-816	576	19	)	)	PUNCT
ejpam-816	576	20	,	,	PUNCT
ejpam-816	576	21	that	that	PRON
ejpam-816	576	22	is	be	AUX
ejpam-816	576	23	with	with	ADP
ejpam-816	576	24	the	the	DET
ejpam-816	576	25	exponential	exponential	ADJ
ejpam-816	576	26	expansion	expansion	NOUN
ejpam-816	576	27	retained	retain	VERB
ejpam-816	576	28	in	in	ADP
ejpam-816	576	29	the	the	DET
ejpam-816	576	30	sector	sector	NOUN
ejpam-816	576	31	1	1	NUM
ejpam-816	576	32	2	2	NUM
ejpam-816	576	33	π	π	NOUN
ejpam-816	576	34	<	<	X
ejpam-816	576	35	θ	θ	X
ejpam-816	576	36	≤	≤	NUM
ejpam-816	576	37	3	3	NUM
ejpam-816	576	38	4	4	NUM
ejpam-816	576	39	π	π	NOUN
ejpam-816	576	40	,	,	PUNCT
ejpam-816	576	41	whereas	whereas	SCONJ
ejpam-816	576	42	those	those	PRON
ejpam-816	576	43	in	in	ADP
ejpam-816	576	44	the	the	DET
ejpam-816	576	45	column	column	NOUN
ejpam-816	576	46	labelled	label	VERB
ejpam-816	576	47	(	(	PUNCT
ejpam-816	576	48	b	b	NOUN
ejpam-816	576	49	)	)	PUNCT
ejpam-816	576	50	were	be	AUX
ejpam-816	576	51	obtained	obtain	VERB
ejpam-816	576	52	using	use	VERB
ejpam-816	576	53	the	the	DET
ejpam-816	576	54	second	second	ADJ
ejpam-816	576	55	expansion	expansion	NOUN
ejpam-816	576	56	in	in	ADP
ejpam-816	576	57	(	(	PUNCT
ejpam-816	576	58	56	56	NUM
ejpam-816	576	59	)	)	PUNCT
ejpam-816	576	60	.	.	PUNCT
ejpam-816	577	1	both	both	DET
ejpam-816	577	2	asymptotic	asymptotic	ADJ
ejpam-816	577	3	series	series	NOUN
ejpam-816	577	4	were	be	AUX
ejpam-816	577	5	truncated	truncate	VERB
ejpam-816	577	6	at	at	ADP
ejpam-816	577	7	their	their	PRON
ejpam-816	577	8	respective	respective	ADJ
ejpam-816	577	9	optimal	optimal	ADJ
ejpam-816	577	10	truncation	truncation	NOUN
ejpam-816	577	11	points	point	NOUN
ejpam-816	577	12	.	.	PUNCT
ejpam-816	578	1	the	the	DET
ejpam-816	578	2	first	first	ADJ
ejpam-816	578	3	half	half	NOUN
ejpam-816	578	4	of	of	ADP
ejpam-816	578	5	table	table	NOUN
ejpam-816	578	6	4	4	NUM
ejpam-816	578	7	confirms	confirm	VERB
ejpam-816	578	8	that	that	SCONJ
ejpam-816	578	9	the	the	DET
ejpam-816	578	10	exponential	exponential	ADJ
ejpam-816	578	11	expansion	expansion	NOUN
ejpam-816	578	12	e2,0(z	e2,0(z	NOUN
ejpam-816	578	13	)	)	PUNCT
ejpam-816	578	14	switches	switch	VERB
ejpam-816	578	15	off	off	ADP
ejpam-816	578	16	(	(	PUNCT
ejpam-816	578	17	as	as	ADP
ejpam-816	578	18	arg	arg	NOUN
ejpam-816	578	19	z	z	NOUN
ejpam-816	578	20	increases	increase	NOUN
ejpam-816	578	21	)	)	PUNCT
ejpam-816	578	22	across	across	ADP
ejpam-816	578	23	the	the	DET
ejpam-816	578	24	stokes	stoke	NOUN
ejpam-816	578	25	line	line	NOUN
ejpam-816	578	26	arg	arg	NOUN
ejpam-816	578	27	z	z	NOUN
ejpam-816	578	28	=	=	SYM
ejpam-816	578	29	1	1	NUM
ejpam-816	578	30	2	2	NUM
ejpam-816	578	31	π	π	NOUN
ejpam-816	578	32	to	to	PART
ejpam-816	578	33	leave	leave	VERB
ejpam-816	578	34	the	the	DET
ejpam-816	578	35	algebraic	algebraic	PROPN
ejpam-816	578	36	§	§	NOUN
ejpam-816	578	37	the	the	DET
ejpam-816	578	38	stokes	stoke	NOUN
ejpam-816	578	39	multiplier	multiplier	ADV
ejpam-816	578	40	s(θ	s(θ	PROPN
ejpam-816	578	41	)	)	PUNCT
ejpam-816	578	42	has	have	VERB
ejpam-816	578	43	a	a	DET
ejpam-816	578	44	small	small	ADJ
ejpam-816	578	45	imaginary	imaginary	ADJ
ejpam-816	578	46	part	part	NOUN
ejpam-816	578	47	that	that	SCONJ
ejpam-816	578	48	we	we	PRON
ejpam-816	578	49	do	do	AUX
ejpam-816	578	50	not	not	PART
ejpam-816	578	51	show	show	VERB
ejpam-816	578	52	.	.	PUNCT
ejpam-816	579	1	references	reference	NOUN
ejpam-816	579	2	1029	1029	NUM
ejpam-816	579	3	table	table	NOUN
ejpam-816	579	4	4	4	NUM
ejpam-816	579	5	:	:	PUNCT
ejpam-816	579	6	the	the	DET
ejpam-816	579	7	variation	variation	NOUN
ejpam-816	579	8	of	of	ADP
ejpam-816	579	9	the	the	DET
ejpam-816	579	10	real	real	ADJ
ejpam-816	579	11	part	part	NOUN
ejpam-816	579	12	of	of	ADP
ejpam-816	579	13	the	the	DET
ejpam-816	579	14	stokes	stoke	NOUN
ejpam-816	579	15	multiplier	multiplier	ADV
ejpam-816	579	16	s(θ	s(θ	PROPN
ejpam-816	579	17	)	)	PUNCT
ejpam-816	579	18	and	and	CCONJ
ejpam-816	579	19	the	the	DET
ejpam-816	579	20	absolute	absolute	ADJ
ejpam-816	579	21	error	error	NOUN
ejpam-816	579	22	in	in	ADP
ejpam-816	579	23	the	the	DET
ejpam-816	579	24	computation	computation	NOUN
ejpam-816	579	25	of	of	ADP
ejpam-816	579	26	2ψ0(z	2ψ0(z	NUM
ejpam-816	579	27	)	)	PUNCT
ejpam-816	579	28	for	for	ADP
ejpam-816	579	29	different	different	ADJ
ejpam-816	579	30	θ	θ	PROPN
ejpam-816	579	31	in	in	ADP
ejpam-816	579	32	the	the	DET
ejpam-816	579	33	sector	sector	NOUN
ejpam-816	579	34	1	1	NUM
ejpam-816	579	35	2	2	NUM
ejpam-816	579	36	π	π	NOUN
ejpam-816	579	37	≤	≤	NUM
ejpam-816	579	38	θ	θ	PROPN
ejpam-816	579	39	≤	≤	NUM
ejpam-816	579	40	3	3	NUM
ejpam-816	579	41	4	4	NUM
ejpam-816	579	42	π	π	NOUN
ejpam-816	579	43	when	when	SCONJ
ejpam-816	579	44	|z|	|z|	NOUN
ejpam-816	579	45	=	=	SYM
ejpam-816	579	46	15	15	NUM
ejpam-816	579	47	:	:	PUNCT
ejpam-816	579	48	(	(	PUNCT
ejpam-816	579	49	a	a	NOUN
ejpam-816	579	50	)	)	PUNCT
ejpam-816	579	51	with	with	ADP
ejpam-816	579	52	e2,0(z	e2,0(z	NOUN
ejpam-816	579	53	)	)	PUNCT
ejpam-816	579	54	and	and	CCONJ
ejpam-816	579	55	(	(	PUNCT
ejpam-816	579	56	b	b	NOUN
ejpam-816	579	57	)	)	PUNCT
ejpam-816	579	58	without	without	ADP
ejpam-816	579	59	e2,0(z	e2,0(z	PROPN
ejpam-816	579	60	)	)	PUNCT
ejpam-816	579	61	.	.	PUNCT
ejpam-816	580	1	θ	θ	X
ejpam-816	580	2	/	/	SYM
ejpam-816	580	3	π	π	NOUN
ejpam-816	580	4	re(s	re(s	X
ejpam-816	580	5	)	)	PUNCT
ejpam-816	580	6	θ	θ	PUNCT
ejpam-816	580	7	/	/	SYM
ejpam-816	580	8	π	π	PROPN
ejpam-816	580	9	re(s	re(s	X
ejpam-816	580	10	)	)	PUNCT
ejpam-816	580	11	θ	θ	PUNCT
ejpam-816	580	12	/	/	SYM
ejpam-816	580	13	π	π	PROPN
ejpam-816	580	14	|error|	|error|	PROPN
ejpam-816	580	15	(	(	PUNCT
ejpam-816	580	16	a	a	X
ejpam-816	580	17	)	)	PUNCT
ejpam-816	580	18	|error|	|error|	PROPN
ejpam-816	580	19	(	(	PUNCT
ejpam-816	580	20	b	b	NOUN
ejpam-816	580	21	)	)	PUNCT
ejpam-816	580	22	0.40	0.40	NUM
ejpam-816	580	23	0.97776	0.97776	NUM
ejpam-816	580	24	0.51	0.51	NUM
ejpam-816	580	25	0.32448	0.32448	NUM
ejpam-816	580	26	0.50	0.50	NUM
ejpam-816	580	27	4.010×	4.010×	NUM
ejpam-816	580	28	10−13	10−13	NOUN
ejpam-816	581	1	3.662×	3.662×	NUM
ejpam-816	581	2	10−13	10−13	NUM
ejpam-816	581	3	0.45	0.45	NUM
ejpam-816	581	4	0.94397	0.94397	NUM
ejpam-816	581	5	0.52	0.52	NUM
ejpam-816	581	6	0.20592	0.20592	NUM
ejpam-816	581	7	0.55	0.55	NUM
ejpam-816	581	8	2.819×	2.819×	PROPN
ejpam-816	581	9	10−12	10−12	PROPN
ejpam-816	581	10	1.324×	1.324×	PROPN
ejpam-816	581	11	10−13	10−13	PROPN
ejpam-816	581	12	0.47	0.47	NUM
ejpam-816	581	13	0.83063	0.83063	NUM
ejpam-816	581	14	0.53	0.53	NUM
ejpam-816	581	15	0.11579	0.11579	NUM
ejpam-816	581	16	0.60	0.60	NUM
ejpam-816	581	17	1.571×	1.571×	NUM
ejpam-816	581	18	10−10	10−10	NUM
ejpam-816	581	19	7.241×	7.241×	NUM
ejpam-816	581	20	10−14	10−14	NUM
ejpam-816	581	21	0.48	0.48	NUM
ejpam-816	581	22	0.72932	0.72932	NUM
ejpam-816	581	23	0.54	0.54	NUM
ejpam-816	581	24	0.05599	0.05599	NUM
ejpam-816	581	25	0.65	0.65	NUM
ejpam-816	581	26	7.955×	7.955×	NOUN
ejpam-816	581	27	10−8	10−8	NUM
ejpam-816	581	28	4.808×	4.808×	NUM
ejpam-816	582	1	10−14	10−14	NOUN
ejpam-816	582	2	0.49	0.49	NUM
ejpam-816	582	3	0.60226	0.60226	NUM
ejpam-816	582	4	0.55	0.55	NUM
ejpam-816	582	5	0.02191	0.02191	NUM
ejpam-816	582	6	0.70	0.70	NUM
ejpam-816	582	7	2.036×	2.036×	NUM
ejpam-816	582	8	10−4	10−4	NUM
ejpam-816	582	9	3.569×	3.569×	NUM
ejpam-816	582	10	10−14	10−14	NUM
ejpam-816	582	11	0.50	0.50	NUM
ejpam-816	582	12	0.46177	0.46177	NUM
ejpam-816	582	13	0.60	0.60	NUM
ejpam-816	582	14	0.00008	0.00008	NUM
ejpam-816	582	15	0.75	0.75	NUM
ejpam-816	582	16	1.222×	1.222×	NUM
ejpam-816	582	17	10−0	10−0	NUM
ejpam-816	582	18	2.854×	2.854×	NUM
ejpam-816	582	19	10−14	10−14	NUM
ejpam-816	582	20	expansion	expansion	NOUN
ejpam-816	582	21	h2,0(ze−πi	h2,0(ze−πi	NOUN
ejpam-816	582	22	)	)	PUNCT
ejpam-816	582	23	in	in	ADP
ejpam-816	582	24	the	the	DET
ejpam-816	582	25	remainder	remainder	NOUN
ejpam-816	582	26	of	of	ADP
ejpam-816	582	27	the	the	DET
ejpam-816	582	28	upper	upper	ADJ
ejpam-816	582	29	half	half	ADJ
ejpam-816	582	30	-	-	PUNCT
ejpam-816	582	31	plane	plane	NOUN
ejpam-816	582	32	;	;	PUNCT
ejpam-816	582	33	a	a	DET
ejpam-816	582	34	similar	similar	ADJ
ejpam-816	582	35	behaviour	behaviour	NOUN
ejpam-816	582	36	applies	apply	VERB
ejpam-816	582	37	across	across	ADP
ejpam-816	582	38	the	the	DET
ejpam-816	582	39	stokes	stoke	NOUN
ejpam-816	582	40	line	line	NOUN
ejpam-816	582	41	arg	arg	NOUN
ejpam-816	582	42	z	z	NOUN
ejpam-816	582	43	=	=	SYM
ejpam-816	582	44	−1	−1	NOUN
ejpam-816	582	45	2	2	NUM
ejpam-816	582	46	π	π	NOUN
ejpam-816	582	47	.	.	PUNCT
ejpam-816	583	1	the	the	DET
ejpam-816	583	2	values	value	NOUN
ejpam-816	583	3	of	of	ADP
ejpam-816	583	4	the	the	DET
ejpam-816	583	5	absolute	absolute	ADJ
ejpam-816	583	6	error	error	NOUN
ejpam-816	583	7	in	in	ADP
ejpam-816	583	8	the	the	DET
ejpam-816	583	9	second	second	ADJ
ejpam-816	583	10	half	half	NOUN
ejpam-816	583	11	of	of	ADP
ejpam-816	583	12	the	the	DET
ejpam-816	583	13	table	table	NOUN
ejpam-816	583	14	clearly	clearly	ADV
ejpam-816	583	15	indicate	indicate	VERB
ejpam-816	583	16	that	that	SCONJ
ejpam-816	583	17	a	a	DET
ejpam-816	583	18	uniform	uniform	ADJ
ejpam-816	583	19	accuracy	accuracy	NOUN
ejpam-816	583	20	over	over	ADP
ejpam-816	583	21	the	the	DET
ejpam-816	583	22	sector	sector	NOUN
ejpam-816	583	23	1	1	NUM
ejpam-816	583	24	2	2	NUM
ejpam-816	583	25	π	π	NOUN
ejpam-816	583	26	<	<	X
ejpam-816	583	27	θ	θ	X
ejpam-816	583	28	≤	≤	NUM
ejpam-816	583	29	3	3	NUM
ejpam-816	583	30	4	4	NUM
ejpam-816	583	31	π	π	NOUN
ejpam-816	583	32	is	be	AUX
ejpam-816	583	33	achievable	achievable	ADJ
ejpam-816	583	34	by	by	ADP
ejpam-816	583	35	discarding	discard	VERB
ejpam-816	583	36	the	the	DET
ejpam-816	583	37	exponential	exponential	ADJ
ejpam-816	583	38	expansion	expansion	NOUN
ejpam-816	583	39	in	in	ADP
ejpam-816	583	40	this	this	DET
ejpam-816	583	41	sector	sector	NOUN
ejpam-816	583	42	in	in	ADP
ejpam-816	583	43	accordance	accordance	NOUN
ejpam-816	583	44	with	with	ADP
ejpam-816	583	45	the	the	DET
ejpam-816	583	46	second	second	ADJ
ejpam-816	583	47	expansion	expansion	NOUN
ejpam-816	583	48	in	in	ADP
ejpam-816	583	49	(	(	PUNCT
ejpam-816	583	50	56	56	NUM
ejpam-816	583	51	)	)	PUNCT
ejpam-816	583	52	.	.	PUNCT
ejpam-816	584	1	we	we	PRON
ejpam-816	584	2	remark	remark	VERB
ejpam-816	584	3	that	that	SCONJ
ejpam-816	584	4	a	a	DET
ejpam-816	584	5	detailed	detailed	ADJ
ejpam-816	584	6	analysis	analysis	NOUN
ejpam-816	584	7	of	of	ADP
ejpam-816	584	8	the	the	DET
ejpam-816	584	9	stokes	stoke	NOUN
ejpam-816	584	10	multiplier	multipli	ADJ
ejpam-816	584	11	has	have	AUX
ejpam-816	584	12	been	be	AUX
ejpam-816	584	13	carried	carry	VERB
ejpam-816	584	14	out	out	ADP
ejpam-816	584	15	in	in	ADP
ejpam-816	584	16	[	[	X
ejpam-816	584	17	10	10	NUM
ejpam-816	584	18	]	]	PUNCT
ejpam-816	584	19	for	for	ADP
ejpam-816	584	20	the	the	DET
ejpam-816	584	21	more	more	ADV
ejpam-816	584	22	general	general	ADJ
ejpam-816	584	23	function	function	NOUN
ejpam-816	584	24	pψ0(z	pψ0(z	PROPN
ejpam-816	584	25	)	)	PUNCT
ejpam-816	584	26	with	with	ADP
ejpam-816	584	27	the	the	DET
ejpam-816	584	28	parameters	parameter	NOUN
ejpam-816	584	29	αr	αr	ADP
ejpam-816	584	30	=	=	SYM
ejpam-816	584	31	1	1	NUM
ejpam-816	584	32	/	/	SYM
ejpam-816	584	33	n	n	CCONJ
ejpam-816	584	34	(	(	PUNCT
ejpam-816	584	35	1	1	NUM
ejpam-816	584	36	≤	≤	NUM
ejpam-816	584	37	r	r	NOUN
ejpam-816	584	38	≤	≤	NOUN
ejpam-816	584	39	p	p	X
ejpam-816	584	40	)	)	PUNCT
ejpam-816	584	41	,	,	PUNCT
ejpam-816	584	42	for	for	ADP
ejpam-816	584	43	positive	positive	ADJ
ejpam-816	584	44	integer	integer	NOUN
ejpam-816	584	45	n	n	CCONJ
ejpam-816	584	46	,	,	PUNCT
ejpam-816	584	47	and	and	CCONJ
ejpam-816	584	48	general¶	general¶	PROPN
ejpam-816	584	49	ar	ar	PROPN
ejpam-816	584	50	(	(	PUNCT
ejpam-816	584	51	1	1	NUM
ejpam-816	584	52	≤	≤	NOUN
ejpam-816	584	53	r	r	NOUN
ejpam-816	584	54	≤	≤	NOUN
ejpam-816	584	55	p	p	X
ejpam-816	584	56	)	)	PUNCT
ejpam-816	584	57	.	.	PUNCT
ejpam-816	585	1	it	it	PRON
ejpam-816	585	2	was	be	AUX
ejpam-816	585	3	shown	show	VERB
ejpam-816	585	4	that	that	SCONJ
ejpam-816	585	5	for	for	ADP
ejpam-816	585	6	large	large	ADJ
ejpam-816	585	7	|z|	|z|	NOUN
ejpam-816	585	8	the	the	DET
ejpam-816	585	9	leading	lead	VERB
ejpam-816	585	10	behaviour	behaviour	NOUN
ejpam-816	585	11	of	of	ADP
ejpam-816	585	12	the	the	DET
ejpam-816	585	13	stokes	stoke	NOUN
ejpam-816	585	14	multiplier	multiplier	ADV
ejpam-816	585	15	s(θ	s(θ	PROPN
ejpam-816	585	16	)	)	PUNCT
ejpam-816	585	17	across	across	ADP
ejpam-816	585	18	the	the	DET
ejpam-816	585	19	stokes	stoke	NOUN
ejpam-816	585	20	lines	line	NOUN
ejpam-816	585	21	θ	θ	NOUN
ejpam-816	585	22	=	=	PUNCT
ejpam-816	585	23	±πκ	±πκ	PROPN
ejpam-816	585	24	is	be	AUX
ejpam-816	585	25	given	give	VERB
ejpam-816	585	26	by	by	ADP
ejpam-816	585	27	s(θ	s(θ	PROPN
ejpam-816	585	28	)	)	PUNCT
ejpam-816	585	29	≃	≃	VERB
ejpam-816	585	30	1	1	NUM
ejpam-816	585	31	2	2	NUM
ejpam-816	585	32	±	±	NUM
ejpam-816	585	33	1	1	NUM
ejpam-816	585	34	2	2	NUM
ejpam-816	585	35	erf	erf	NOUN
ejpam-816	586	1	[	[	X
ejpam-816	586	2	(	(	PUNCT
ejpam-816	586	3	θ	θ	NOUN
ejpam-816	586	4	∓πκ)(2κ	∓πκ)(2κ	NOUN
ejpam-816	586	5	/	/	SYM
ejpam-816	586	6	n)−1/2(|z|/n)1/(2κ	n)−1/2(|z|/n)1/(2κ	PROPN
ejpam-816	586	7	)	)	PUNCT
ejpam-816	586	8	]	]	PUNCT
ejpam-816	586	9	(	(	PUNCT
ejpam-816	586	10	|z|	|z|	NOUN
ejpam-816	586	11	→∞	→∞	NOUN
ejpam-816	586	12	)	)	PUNCT
ejpam-816	586	13	respectively	respectively	ADV
ejpam-816	586	14	,	,	PUNCT
ejpam-816	586	15	where	where	SCONJ
ejpam-816	586	16	erf	erf	NOUN
ejpam-816	586	17	denotes	denote	VERB
ejpam-816	586	18	the	the	DET
ejpam-816	586	19	error	error	NOUN
ejpam-816	586	20	function	function	NOUN
ejpam-816	586	21	and	and	CCONJ
ejpam-816	586	22	κ	κ	X
ejpam-816	586	23	=	=	SYM
ejpam-816	586	24	1−	1−	NUM
ejpam-816	586	25	(	(	PUNCT
ejpam-816	586	26	p	p	NOUN
ejpam-816	586	27	/	/	SYM
ejpam-816	586	28	n	n	CCONJ
ejpam-816	586	29	)	)	PUNCT
ejpam-816	586	30	.	.	PUNCT
ejpam-816	587	1	specialisation	specialisation	NOUN
ejpam-816	587	2	to	to	ADP
ejpam-816	587	3	the	the	DET
ejpam-816	587	4	values	value	NOUN
ejpam-816	587	5	p	p	X
ejpam-816	587	6	=	=	SYM
ejpam-816	587	7	2	2	NUM
ejpam-816	587	8	,	,	PUNCT
ejpam-816	587	9	n	n	NOUN
ejpam-816	587	10	=	=	SYM
ejpam-816	587	11	4	4	NUM
ejpam-816	587	12	,	,	PUNCT
ejpam-816	587	13	to	to	PART
ejpam-816	587	14	correspond	correspond	VERB
ejpam-816	587	15	to	to	ADP
ejpam-816	587	16	(	(	PUNCT
ejpam-816	587	17	53	53	NUM
ejpam-816	587	18	)	)	PUNCT
ejpam-816	587	19	,	,	PUNCT
ejpam-816	587	20	shows	show	VERB
ejpam-816	587	21	the	the	DET
ejpam-816	587	22	smooth	smooth	ADJ
ejpam-816	587	23	transition	transition	NOUN
ejpam-816	587	24	of	of	ADP
ejpam-816	587	25	s(θ	s(θ	PROPN
ejpam-816	587	26	)	)	PUNCT
ejpam-816	587	27	across	across	ADP
ejpam-816	587	28	the	the	DET
ejpam-816	587	29	stokes	stoke	NOUN
ejpam-816	587	30	lines	line	NOUN
ejpam-816	587	31	θ	θ	PROPN
ejpam-816	587	32	=	=	PRON
ejpam-816	587	33	±1	±1	VERB
ejpam-816	587	34	2	2	NUM
ejpam-816	587	35	π	π	NOUN
ejpam-816	587	36	,	,	PUNCT
ejpam-816	587	37	thereby	thereby	ADV
ejpam-816	587	38	confirming	confirm	VERB
ejpam-816	587	39	the	the	DET
ejpam-816	587	40	above	above	ADJ
ejpam-816	587	41	viewpoint	viewpoint	NOUN
ejpam-816	587	42	.	.	PUNCT
ejpam-816	588	1	appendix	appendix	VERB
ejpam-816	588	2	c.	c.	PROPN
ejpam-816	588	3	the	the	DET
ejpam-816	588	4	algebraic	algebraic	ADJ
ejpam-816	588	5	expansion	expansion	NOUN
ejpam-816	588	6	of	of	ADP
ejpam-816	588	7	jn(z	jn(z	NOUN
ejpam-816	588	8	)	)	PUNCT
ejpam-816	588	9	in	in	ADP
ejpam-816	588	10	the	the	DET
ejpam-816	588	11	case	case	NOUN
ejpam-816	588	12	of	of	ADP
ejpam-816	588	13	double	double	ADJ
ejpam-816	588	14	poles	pole	NOUN
ejpam-816	588	15	when	when	SCONJ
ejpam-816	588	16	some	some	PRON
ejpam-816	588	17	,	,	PUNCT
ejpam-816	588	18	or	or	CCONJ
ejpam-816	588	19	all	all	PRON
ejpam-816	588	20	,	,	PUNCT
ejpam-816	588	21	of	of	ADP
ejpam-816	588	22	the	the	DET
ejpam-816	588	23	poles	pole	NOUN
ejpam-816	588	24	in	in	ADP
ejpam-816	588	25	(	(	PUNCT
ejpam-816	588	26	12	12	NUM
ejpam-816	588	27	)	)	PUNCT
ejpam-816	588	28	are	be	AUX
ejpam-816	588	29	multiple	multiple	ADJ
ejpam-816	588	30	,	,	PUNCT
ejpam-816	588	31	the	the	DET
ejpam-816	588	32	analysis	analysis	NOUN
ejpam-816	588	33	of	of	ADP
ejpam-816	588	34	the	the	DET
ejpam-816	588	35	algebraic	algebraic	ADJ
ejpam-816	588	36	contributions	contribution	NOUN
ejpam-816	588	37	to	to	ADP
ejpam-816	588	38	the	the	DET
ejpam-816	588	39	integral	integral	ADJ
ejpam-816	588	40	jn(z	jn(z	NOUN
ejpam-816	588	41	)	)	PUNCT
ejpam-816	588	42	presented	present	VERB
ejpam-816	588	43	in	in	ADP
ejpam-816	588	44	section	section	NOUN
ejpam-816	588	45	4.2	4.2	NUM
ejpam-816	588	46	no	no	ADV
ejpam-816	588	47	longer	long	ADV
ejpam-816	588	48	applies	apply	VERB
ejpam-816	588	49	.	.	PUNCT
ejpam-816	589	1	the	the	DET
ejpam-816	589	2	treatment	treatment	NOUN
ejpam-816	589	3	of	of	ADP
ejpam-816	589	4	the	the	DET
ejpam-816	589	5	multiple	multiple	ADJ
ejpam-816	589	6	-	-	PUNCT
ejpam-816	589	7	pole	pole	NOUN
ejpam-816	589	8	case	case	NOUN
ejpam-816	589	9	in	in	ADP
ejpam-816	589	10	general	general	ADJ
ejpam-816	589	11	would	would	AUX
ejpam-816	589	12	be	be	AUX
ejpam-816	589	13	very	very	ADV
ejpam-816	589	14	tedious	tedious	ADJ
ejpam-816	589	15	.	.	PUNCT
ejpam-816	590	1	accordingly	accordingly	ADV
ejpam-816	590	2	,	,	PUNCT
ejpam-816	590	3	we	we	PRON
ejpam-816	590	4	demonstrate	demonstrate	VERB
ejpam-816	590	5	in	in	ADP
ejpam-816	590	6	the	the	DET
ejpam-816	590	7	case	case	NOUN
ejpam-816	590	8	n	n	NOUN
ejpam-816	590	9	=	=	SYM
ejpam-816	590	10	2	2	NUM
ejpam-816	590	11	when	when	SCONJ
ejpam-816	590	12	double	double	ADJ
ejpam-816	590	13	poles	pole	NOUN
ejpam-816	590	14	are	be	AUX
ejpam-816	590	15	present	present	ADJ
ejpam-816	590	16	that	that	SCONJ
ejpam-816	590	17	the	the	DET
ejpam-816	590	18	cancelation	cancelation	NOUN
ejpam-816	590	19	of	of	ADP
ejpam-816	590	20	the	the	DET
ejpam-816	590	21	algebraic	algebraic	ADJ
ejpam-816	590	22	expansions	expansion	NOUN
ejpam-816	590	23	associated	associate	VERB
ejpam-816	590	24	with	with	ADP
ejpam-816	590	25	jn(z	jn(z	NOUN
ejpam-816	590	26	)	)	PUNCT
ejpam-816	590	27	continues	continue	VERB
ejpam-816	590	28	to	to	PART
ejpam-816	590	29	hold	hold	VERB
ejpam-816	590	30	in	in	ADP
ejpam-816	590	31	the	the	DET
ejpam-816	590	32	sector	sector	NOUN
ejpam-816	590	33	(	(	PUNCT
ejpam-816	590	34	34	34	NUM
ejpam-816	590	35	)	)	PUNCT
ejpam-816	590	36	,	,	PUNCT
ejpam-816	591	1	where	where	SCONJ
ejpam-816	591	2	m	m	VERB
ejpam-816	591	3	=	=	SYM
ejpam-816	591	4	m1	m1	PROPN
ejpam-816	591	5	+	+	NOUN
ejpam-816	591	6	m2	m2	PROPN
ejpam-816	591	7	.	.	PUNCT
ejpam-816	592	1	the	the	DET
ejpam-816	592	2	algebraic	algebraic	ADJ
ejpam-816	592	3	expansion	expansion	NOUN
ejpam-816	592	4	for	for	ADP
ejpam-816	592	5	the	the	DET
ejpam-816	592	6	wright	wright	PROPN
ejpam-816	592	7	function	function	PROPN
ejpam-816	592	8	2ψ0(z	2ψ0(z	NUM
ejpam-816	592	9	)	)	PUNCT
ejpam-816	592	10	associated	associate	VERB
ejpam-816	592	11	with	with	ADP
ejpam-816	592	12	the	the	DET
ejpam-816	592	13	parameters	parameter	NOUN
ejpam-816	592	14	αr	αr	ADP
ejpam-816	592	15	,	,	PUNCT
ejpam-816	592	16	ar	ar	PROPN
ejpam-816	592	17	(	(	PUNCT
ejpam-816	592	18	r	r	NOUN
ejpam-816	592	19	=	=	SYM
ejpam-816	592	20	1,2	1,2	NUM
ejpam-816	592	21	)	)	PUNCT
ejpam-816	592	22	as	as	ADP
ejpam-816	592	23	|z|	|z|	NOUN
ejpam-816	592	24	→	→	SYM
ejpam-816	592	25	∞	∞	PROPN
ejpam-816	592	26	is	be	AUX
ejpam-816	592	27	given	give	VERB
ejpam-816	592	28	by	by	ADP
ejpam-816	592	29	(	(	PUNCT
ejpam-816	592	30	16	16	NUM
ejpam-816	592	31	)	)	PUNCT
ejpam-816	592	32	with	with	ADP
ejpam-816	592	33	p	p	NOUN
ejpam-816	592	34	=	=	SYM
ejpam-816	592	35	2	2	NUM
ejpam-816	592	36	,	,	PUNCT
ejpam-816	592	37	q	q	NOUN
ejpam-816	592	38	=	=	NOUN
ejpam-816	592	39	0	0	NUM
ejpam-816	592	40	.	.	PUNCT
ejpam-816	593	1	the	the	DET
ejpam-816	593	2	form	form	NOUN
ejpam-816	593	3	of	of	ADP
ejpam-816	593	4	the	the	DET
ejpam-816	593	5	expansion	expansion	NOUN
ejpam-816	593	6	h2,0(ze−πi	h2,0(ze−πi	NOUN
ejpam-816	593	7	)	)	PUNCT
ejpam-816	593	8	in	in	ADP
ejpam-816	593	9	(	(	PUNCT
ejpam-816	593	10	13	13	NUM
ejpam-816	593	11	)	)	PUNCT
ejpam-816	593	12	and	and	CCONJ
ejpam-816	593	13	(	(	PUNCT
ejpam-816	593	14	14	14	NUM
ejpam-816	593	15	)	)	PUNCT
ejpam-816	593	16	has	have	VERB
ejpam-816	593	17	to	to	PART
ejpam-816	593	18	be	be	AUX
ejpam-816	593	19	modified	modify	VERB
ejpam-816	593	20	to	to	PART
ejpam-816	593	21	take	take	VERB
ejpam-816	593	22	into	into	ADP
ejpam-816	593	23	account	account	NOUN
ejpam-816	593	24	the	the	DET
ejpam-816	593	25	presence	presence	NOUN
ejpam-816	593	26	of	of	ADP
ejpam-816	593	27	the	the	DET
ejpam-816	593	28	double	double	ADJ
ejpam-816	593	29	poles	pole	NOUN
ejpam-816	593	30	.	.	PUNCT
ejpam-816	594	1	from	from	ADP
ejpam-816	594	2	the	the	DET
ejpam-816	594	3	mellin	mellin	PROPN
ejpam-816	594	4	-	-	PUNCT
ejpam-816	594	5	barnes	barnes	PROPN
ejpam-816	594	6	representation	representation	NOUN
ejpam-816	594	7	in	in	ADP
ejpam-816	594	8	(	(	PUNCT
ejpam-816	594	9	11	11	NUM
ejpam-816	594	10	)	)	PUNCT
ejpam-816	594	11	,	,	PUNCT
ejpam-816	594	12	we	we	PRON
ejpam-816	594	13	have	have	VERB
ejpam-816	594	14	2ψ0(z	2ψ0(z	NUM
ejpam-816	594	15	)	)	PUNCT
ejpam-816	595	1	=	=	SYM
ejpam-816	595	2	1	1	NUM
ejpam-816	595	3	2πi	2πi	NOUN
ejpam-816	595	4	∫	∫	PROPN
ejpam-816	595	5	∞i	∞i	NUM
ejpam-816	595	6	−∞i	−∞i	PUNCT
ejpam-816	596	1	γ(s)γ(a1	γ(s)γ(a1	ADP
ejpam-816	596	2	−α1s)γ(a2	−α1s)γ(a2	PROPN
ejpam-816	596	3	−α2s)(ze±πi)−sds	−α2s)(ze±πi)−sds	PUNCT
ejpam-816	597	1	(	(	PUNCT
ejpam-816	597	2	57	57	NUM
ejpam-816	597	3	)	)	PUNCT
ejpam-816	597	4	¶it	¶it	PROPN
ejpam-816	597	5	is	be	AUX
ejpam-816	597	6	assumed	assume	VERB
ejpam-816	597	7	the	the	DET
ejpam-816	597	8	parameters	parameter	NOUN
ejpam-816	597	9	are	be	AUX
ejpam-816	597	10	such	such	ADJ
ejpam-816	597	11	that	that	SCONJ
ejpam-816	597	12	only	only	ADJ
ejpam-816	597	13	simple	simple	ADJ
ejpam-816	597	14	poles	pole	NOUN
ejpam-816	597	15	arise	arise	VERB
ejpam-816	597	16	in	in	ADP
ejpam-816	597	17	the	the	DET
ejpam-816	597	18	corresponding	correspond	VERB
ejpam-816	597	19	integral	integral	ADJ
ejpam-816	597	20	(	(	PUNCT
ejpam-816	597	21	11	11	NUM
ejpam-816	597	22	)	)	PUNCT
ejpam-816	597	23	.	.	PUNCT
ejpam-816	598	1	references	reference	NOUN
ejpam-816	598	2	1030	1030	NUM
ejpam-816	598	3	valid	valid	NOUN
ejpam-816	598	4	in	in	ADP
ejpam-816	598	5	|arg(−z)|	|arg(−z)|	PUNCT
ejpam-816	598	6	<	<	X
ejpam-816	598	7	1	1	NUM
ejpam-816	598	8	2	2	NUM
ejpam-816	598	9	π(1	π(1	PROPN
ejpam-816	598	10	+	+	CCONJ
ejpam-816	598	11	α1	α1	PROPN
ejpam-816	598	12	+	+	CCONJ
ejpam-816	598	13	α2	α2	ADJ
ejpam-816	598	14	)	)	PUNCT
ejpam-816	598	15	,	,	PUNCT
ejpam-816	598	16	where	where	SCONJ
ejpam-816	598	17	the	the	DET
ejpam-816	598	18	upper	upper	ADJ
ejpam-816	598	19	or	or	CCONJ
ejpam-816	598	20	lower	low	ADJ
ejpam-816	598	21	sign	sign	NOUN
ejpam-816	598	22	is	be	AUX
ejpam-816	598	23	chosen	choose	VERB
ejpam-816	598	24	according	accord	VERB
ejpam-816	598	25	as	as	ADP
ejpam-816	598	26	arg	arg	NOUN
ejpam-816	598	27	z	z	NOUN
ejpam-816	598	28	>	>	X
ejpam-816	598	29	0	0	NUM
ejpam-816	598	30	or	or	CCONJ
ejpam-816	598	31	arg	arg	NOUN
ejpam-816	598	32	z	z	NOUN
ejpam-816	598	33	<	<	X
ejpam-816	598	34	0	0	NUM
ejpam-816	598	35	,	,	PUNCT
ejpam-816	598	36	respectively	respectively	ADV
ejpam-816	598	37	.	.	PUNCT
ejpam-816	599	1	the	the	DET
ejpam-816	599	2	two	two	NUM
ejpam-816	599	3	sequences	sequence	NOUN
ejpam-816	599	4	of	of	ADP
ejpam-816	599	5	poles	pole	NOUN
ejpam-816	599	6	that	that	PRON
ejpam-816	599	7	contribute	contribute	VERB
ejpam-816	599	8	to	to	ADP
ejpam-816	599	9	the	the	DET
ejpam-816	599	10	algebraic	algebraic	ADJ
ejpam-816	599	11	expansion	expansion	NOUN
ejpam-816	599	12	are	be	AUX
ejpam-816	599	13	,	,	PUNCT
ejpam-816	599	14	from	from	ADP
ejpam-816	599	15	(	(	PUNCT
ejpam-816	599	16	12	12	NUM
ejpam-816	599	17	)	)	PUNCT
ejpam-816	599	18	,	,	PUNCT
ejpam-816	599	19	sm	sm	PROPN
ejpam-816	599	20	,	,	PUNCT
ejpam-816	599	21	r	r	NOUN
ejpam-816	599	22	=	=	PUNCT
ejpam-816	599	23	(	(	PUNCT
ejpam-816	599	24	ar	ar	NOUN
ejpam-816	599	25	+	+	NOUN
ejpam-816	599	26	m)/αr	m)/αr	PROPN
ejpam-816	599	27	(	(	PUNCT
ejpam-816	599	28	r	r	NOUN
ejpam-816	599	29	=	=	SYM
ejpam-816	599	30	1,2	1,2	NUM
ejpam-816	599	31	;	;	PUNCT
ejpam-816	599	32	m	m	VERB
ejpam-816	599	33	=	=	NOUN
ejpam-816	599	34	0,1,2	0,1,2	NUM
ejpam-816	599	35	,	,	PUNCT
ejpam-816	599	36	.	.	PUNCT
ejpam-816	599	37	.	.	PUNCT
ejpam-816	599	38	.	.	PUNCT
ejpam-816	599	39	)	)	PUNCT
ejpam-816	600	1	,	,	PUNCT
ejpam-816	600	2	where	where	SCONJ
ejpam-816	600	3	we	we	PRON
ejpam-816	600	4	suppose	suppose	VERB
ejpam-816	600	5	for	for	ADP
ejpam-816	600	6	some	some	DET
ejpam-816	600	7	nonnegative	nonnegative	ADJ
ejpam-816	600	8	integers	integer	NOUN
ejpam-816	600	9	k	k	PROPN
ejpam-816	600	10	,	,	PUNCT
ejpam-816	600	11	ℓ	ℓ	PROPN
ejpam-816	600	12	that	that	SCONJ
ejpam-816	600	13	sk,1	sk,1	PROPN
ejpam-816	600	14	=	=	PUNCT
ejpam-816	600	15	a1	a1	PROPN
ejpam-816	600	16	+	+	CCONJ
ejpam-816	600	17	k	k	PROPN
ejpam-816	600	18	α1	α1	PROPN
ejpam-816	600	19	=	=	SYM
ejpam-816	600	20	a2	a2	PROPN
ejpam-816	600	21	+	+	CCONJ
ejpam-816	600	22	ℓ	ℓ	PROPN
ejpam-816	600	23	α2	α2	NOUN
ejpam-816	600	24	(	(	PUNCT
ejpam-816	600	25	58	58	NUM
ejpam-816	600	26	)	)	PUNCT
ejpam-816	600	27	for	for	ADP
ejpam-816	600	28	double	double	ADJ
ejpam-816	600	29	poles	pole	NOUN
ejpam-816	600	30	to	to	PART
ejpam-816	600	31	arise	arise	VERB
ejpam-816	600	32	.	.	PUNCT
ejpam-816	601	1	the	the	DET
ejpam-816	601	2	algebraic	algebraic	ADJ
ejpam-816	601	3	expansion	expansion	NOUN
ejpam-816	601	4	h2,0(ze−πi	h2,0(ze−πi	PROPN
ejpam-816	601	5	)	)	PUNCT
ejpam-816	601	6	,	,	PUNCT
ejpam-816	601	7	obtained	obtain	VERB
ejpam-816	601	8	by	by	ADP
ejpam-816	601	9	displacement	displacement	NOUN
ejpam-816	601	10	of	of	ADP
ejpam-816	601	11	the	the	DET
ejpam-816	601	12	integration	integration	NOUN
ejpam-816	601	13	path	path	NOUN
ejpam-816	601	14	in	in	ADP
ejpam-816	601	15	(	(	PUNCT
ejpam-816	601	16	57	57	NUM
ejpam-816	601	17	)	)	PUNCT
ejpam-816	601	18	to	to	ADP
ejpam-816	601	19	the	the	DET
ejpam-816	601	20	right	right	NOUN
ejpam-816	601	21	over	over	ADP
ejpam-816	601	22	the	the	DET
ejpam-816	601	23	above	above	ADJ
ejpam-816	601	24	poles	pole	NOUN
ejpam-816	601	25	,	,	PUNCT
ejpam-816	601	26	then	then	ADV
ejpam-816	601	27	becomes	become	VERB
ejpam-816	601	28	h2,0(ze−πi	h2,0(ze−πi	NOUN
ejpam-816	601	29	)	)	PUNCT
ejpam-816	601	30	=	=	SYM
ejpam-816	601	31	2	2	NUM
ejpam-816	601	32	∑	∑	PUNCT
ejpam-816	601	33	j=1	j=1	PROPN
ejpam-816	601	34	α−1	α−1	PROPN
ejpam-816	601	35	j	j	PROPN
ejpam-816	601	36	(	(	PUNCT
ejpam-816	601	37	ze−πi)−a	ze−πi)−a	PROPN
ejpam-816	601	38	j	j	PROPN
ejpam-816	601	39	/	/	SYM
ejpam-816	601	40	α	α	PROPN
ejpam-816	601	41	j	j	PROPN
ejpam-816	601	42	s′2,0(ze−πi	s′2,0(ze−πi	NOUN
ejpam-816	601	43	;	;	PUNCT
ejpam-816	601	44	j	j	X
ejpam-816	601	45	)	)	PUNCT
ejpam-816	602	1	+	+	PUNCT
ejpam-816	602	2	g(z	g(z	PROPN
ejpam-816	602	3	)	)	PUNCT
ejpam-816	602	4	(	(	PUNCT
ejpam-816	602	5	59	59	NUM
ejpam-816	602	6	)	)	PUNCT
ejpam-816	602	7	where	where	SCONJ
ejpam-816	602	8	the	the	DET
ejpam-816	602	9	prime	prime	ADJ
ejpam-816	602	10	denotes	denote	VERB
ejpam-816	602	11	the	the	DET
ejpam-816	602	12	deletion	deletion	NOUN
ejpam-816	602	13	of	of	ADP
ejpam-816	602	14	the	the	DET
ejpam-816	602	15	terms	term	NOUN
ejpam-816	602	16	in	in	ADP
ejpam-816	602	17	the	the	DET
ejpam-816	602	18	asymptotic	asymptotic	ADJ
ejpam-816	602	19	sum	sum	NOUN
ejpam-816	602	20	(	(	PUNCT
ejpam-816	602	21	14	14	NUM
ejpam-816	602	22	)	)	PUNCT
ejpam-816	602	23	corresponding	correspond	VERB
ejpam-816	602	24	to	to	ADP
ejpam-816	602	25	the	the	DET
ejpam-816	602	26	double	double	ADJ
ejpam-816	602	27	poles	pole	NOUN
ejpam-816	602	28	.	.	PUNCT
ejpam-816	603	1	the	the	DET
ejpam-816	603	2	contribution	contribution	NOUN
ejpam-816	603	3	g(z	g(z	PROPN
ejpam-816	603	4	)	)	PUNCT
ejpam-816	603	5	resulting	result	VERB
ejpam-816	603	6	from	from	ADP
ejpam-816	603	7	the	the	DET
ejpam-816	603	8	double	double	ADJ
ejpam-816	603	9	poles	pole	NOUN
ejpam-816	603	10	may	may	AUX
ejpam-816	603	11	be	be	AUX
ejpam-816	603	12	shown	show	VERB
ejpam-816	603	13	to	to	PART
ejpam-816	603	14	be	be	AUX
ejpam-816	603	15	g(z	g(z	ADJ
ejpam-816	603	16	)	)	PUNCT
ejpam-816	603	17	=	=	SYM
ejpam-816	603	18	1	1	NUM
ejpam-816	603	19	α1α2	α1α2	NOUN
ejpam-816	603	20	∑	∑	ADV
ejpam-816	603	21	k,ℓ	k,ℓ	PROPN
ejpam-816	603	22	(	(	PUNCT
ejpam-816	603	23	−)k+ℓ+1	−)k+ℓ+1	X
ejpam-816	603	24	k!ℓ	k!ℓ	PROPN
ejpam-816	603	25	!	!	PUNCT
ejpam-816	603	26	γ(sk,1)(ze−πi)−sk,1{ψ(sk,1)−α1ψ(k+1)−α2ψ(ℓ+1)−	γ(sk,1)(ze−πi)−sk,1{ψ(sk,1)−α1ψ(k+1)−α2ψ(ℓ+1)−	VERB
ejpam-816	603	27	log(ze−πi	log(ze−πi	NOUN
ejpam-816	603	28	)	)	PUNCT
ejpam-816	603	29	}	}	PUNCT
ejpam-816	603	30	,	,	PUNCT
ejpam-816	603	31	(	(	PUNCT
ejpam-816	603	32	60	60	NUM
ejpam-816	603	33	)	)	PUNCT
ejpam-816	603	34	where	where	SCONJ
ejpam-816	603	35	summation	summation	NOUN
ejpam-816	603	36	is	be	AUX
ejpam-816	603	37	over	over	ADP
ejpam-816	603	38	the	the	DET
ejpam-816	603	39	integers	integer	NOUN
ejpam-816	603	40	k	k	PROPN
ejpam-816	603	41	,	,	PUNCT
ejpam-816	603	42	ℓ	ℓ	NOUN
ejpam-816	603	43	satisfying	satisfying	NOUN
ejpam-816	603	44	(	(	PUNCT
ejpam-816	603	45	58	58	NUM
ejpam-816	603	46	)	)	PUNCT
ejpam-816	603	47	and	and	CCONJ
ejpam-816	603	48	ψ(z	ψ(z	PROPN
ejpam-816	603	49	)	)	PUNCT
ejpam-816	603	50	denotes	denote	VERB
ejpam-816	603	51	the	the	DET
ejpam-816	603	52	logarithmic	logarithmic	ADJ
ejpam-816	603	53	derivative	derivative	NOUN
ejpam-816	603	54	of	of	ADP
ejpam-816	603	55	the	the	DET
ejpam-816	603	56	gamma	gamma	NOUN
ejpam-816	603	57	function	function	NOUN
ejpam-816	603	58	.	.	PUNCT
ejpam-816	604	1	the	the	DET
ejpam-816	604	2	integral	integral	ADJ
ejpam-816	604	3	j2(z	j2(z	NOUN
ejpam-816	604	4	)	)	PUNCT
ejpam-816	604	5	is	be	AUX
ejpam-816	604	6	associated	associate	VERB
ejpam-816	604	7	with	with	ADP
ejpam-816	604	8	the	the	DET
ejpam-816	604	9	function	function	NOUN
ejpam-816	604	10	2ψ0(z	2ψ0(z	NUM
ejpam-816	604	11	)	)	PUNCT
ejpam-816	604	12	with	with	ADP
ejpam-816	604	13	the	the	DET
ejpam-816	604	14	parameters	parameter	NOUN
ejpam-816	604	15	αr	αr	ADP
ejpam-816	604	16	=	=	SYM
ejpam-816	604	17	mr/µr	mr/µr	NUM
ejpam-816	604	18	,	,	PUNCT
ejpam-816	604	19	ar	ar	NOUN
ejpam-816	604	20	=	=	NOUN
ejpam-816	604	21	νr/µr	νr/µr	NUM
ejpam-816	604	22	(	(	PUNCT
ejpam-816	604	23	r	r	NOUN
ejpam-816	604	24	=	=	SYM
ejpam-816	604	25	1,2	1,2	NUM
ejpam-816	604	26	)	)	PUNCT
ejpam-816	604	27	,	,	PUNCT
ejpam-816	604	28	where	where	SCONJ
ejpam-816	604	29	µr	µr	AUX
ejpam-816	604	30	are	be	AUX
ejpam-816	604	31	positive	positive	ADJ
ejpam-816	604	32	even	even	ADV
ejpam-816	604	33	integers	integer	NOUN
ejpam-816	604	34	.	.	PUNCT
ejpam-816	605	1	the	the	DET
ejpam-816	605	2	contribution	contribution	NOUN
ejpam-816	605	3	to	to	ADP
ejpam-816	605	4	the	the	DET
ejpam-816	605	5	algebraic	algebraic	ADJ
ejpam-816	605	6	expansion	expansion	NOUN
ejpam-816	605	7	of	of	ADP
ejpam-816	605	8	j2(z	j2(z	PROPN
ejpam-816	605	9	)	)	PUNCT
ejpam-816	605	10	from	from	ADP
ejpam-816	605	11	the	the	DET
ejpam-816	605	12	first	first	ADJ
ejpam-816	605	13	series	series	NOUN
ejpam-816	605	14	on	on	ADP
ejpam-816	605	15	the	the	DET
ejpam-816	605	16	right	right	ADJ
ejpam-816	605	17	-	-	PUNCT
ejpam-816	605	18	hand	hand	NOUN
ejpam-816	605	19	side	side	NOUN
ejpam-816	605	20	of	of	ADP
ejpam-816	605	21	(	(	PUNCT
ejpam-816	605	22	59	59	NUM
ejpam-816	605	23	)	)	PUNCT
ejpam-816	605	24	(	(	PUNCT
ejpam-816	605	25	resulting	result	VERB
ejpam-816	605	26	from	from	ADP
ejpam-816	605	27	the	the	DET
ejpam-816	605	28	simple	simple	ADJ
ejpam-816	605	29	poles	pole	NOUN
ejpam-816	605	30	)	)	PUNCT
ejpam-816	605	31	vanishes	vanish	VERB
ejpam-816	605	32	in	in	ADP
ejpam-816	605	33	the	the	DET
ejpam-816	605	34	sector	sector	NOUN
ejpam-816	605	35	(	(	PUNCT
ejpam-816	605	36	34	34	NUM
ejpam-816	605	37	)	)	PUNCT
ejpam-816	605	38	by	by	ADP
ejpam-816	605	39	virtue	virtue	NOUN
ejpam-816	605	40	of	of	ADP
ejpam-816	605	41	the	the	DET
ejpam-816	605	42	discussion	discussion	NOUN
ejpam-816	605	43	in	in	ADP
ejpam-816	605	44	section	section	NOUN
ejpam-816	605	45	4.2	4.2	NUM
ejpam-816	605	46	.	.	PUNCT
ejpam-816	606	1	to	to	PART
ejpam-816	606	2	deal	deal	VERB
ejpam-816	606	3	with	with	ADP
ejpam-816	606	4	the	the	DET
ejpam-816	606	5	contribution	contribution	NOUN
ejpam-816	606	6	from	from	ADP
ejpam-816	606	7	the	the	DET
ejpam-816	606	8	double	double	ADJ
ejpam-816	606	9	poles	pole	NOUN
ejpam-816	606	10	,	,	PUNCT
ejpam-816	606	11	we	we	PRON
ejpam-816	606	12	note	note	VERB
ejpam-816	606	13	that	that	SCONJ
ejpam-816	606	14	g(z	g(z	NOUN
ejpam-816	606	15	)	)	PUNCT
ejpam-816	606	16	may	may	AUX
ejpam-816	606	17	be	be	AUX
ejpam-816	606	18	written	write	VERB
ejpam-816	606	19	in	in	ADP
ejpam-816	606	20	the	the	DET
ejpam-816	606	21	form	form	NOUN
ejpam-816	606	22	g(z	g(z	ADJ
ejpam-816	606	23	)	)	PUNCT
ejpam-816	607	1	=	=	SYM
ejpam-816	607	2	∑	∑	PUNCT
ejpam-816	607	3	k,ℓ	k,ℓ	PROPN
ejpam-816	607	4	(	(	PUNCT
ejpam-816	607	5	ze−πi)−λk{ck,ℓ+	ze−πi)−λk{ck,ℓ+	PROPN
ejpam-816	607	6	dk,ℓ	dk,ℓ	NOUN
ejpam-816	607	7	log	log	NOUN
ejpam-816	607	8	(	(	PUNCT
ejpam-816	607	9	ze−πi	ze−πi	NOUN
ejpam-816	607	10	)	)	PUNCT
ejpam-816	607	11	}	}	PUNCT
ejpam-816	607	12	,	,	PUNCT
ejpam-816	607	13	where	where	SCONJ
ejpam-816	607	14	ck,ℓ	ck,ℓ	PUNCT
ejpam-816	607	15	and	and	CCONJ
ejpam-816	607	16	dk,ℓ	dk,ℓ	NOUN
ejpam-816	607	17	are	be	AUX
ejpam-816	607	18	coefficients	coefficient	NOUN
ejpam-816	607	19	independent	independent	ADJ
ejpam-816	607	20	of	of	ADP
ejpam-816	607	21	z	z	PROPN
ejpam-816	607	22	and	and	CCONJ
ejpam-816	607	23	λk	λk	ADP
ejpam-816	607	24	:	:	PUNCT
ejpam-816	607	25	=	=	SYM
ejpam-816	607	26	ν1	ν1	NOUN
ejpam-816	607	27	+	+	PROPN
ejpam-816	607	28	µ1k	µ1k	X
ejpam-816	607	29	m1	m1	NOUN
ejpam-816	607	30	=	=	PUNCT
ejpam-816	607	31	ν2	ν2	PROPN
ejpam-816	607	32	+	+	PROPN
ejpam-816	607	33	µ2ℓ	µ2ℓ	PROPN
ejpam-816	607	34	m2	m2	PROPN
ejpam-816	607	35	.	.	PUNCT
ejpam-816	608	1	(	(	PUNCT
ejpam-816	608	2	61	61	NUM
ejpam-816	608	3	)	)	PUNCT
ejpam-816	608	4	recalling	recall	VERB
ejpam-816	608	5	that	that	SCONJ
ejpam-816	608	6	e(x)≡	e(x)≡	PROPN
ejpam-816	608	7	exp(πi	exp(πi	ADV
ejpam-816	608	8	x	x	X
ejpam-816	608	9	)	)	PUNCT
ejpam-816	608	10	,	,	PUNCT
ejpam-816	608	11	we	we	PRON
ejpam-816	608	12	then	then	ADV
ejpam-816	608	13	see	see	VERB
ejpam-816	608	14	that	that	SCONJ
ejpam-816	608	15	e(ν1)g(ze(m1	e(ν1)g(ze(m1	NOUN
ejpam-816	608	16	)	)	PUNCT
ejpam-816	608	17	)	)	PUNCT
ejpam-816	609	1	=	=	PUNCT
ejpam-816	609	2	g(z	g(z	PROPN
ejpam-816	609	3	)	)	PUNCT
ejpam-816	610	1	+	+	ADJ
ejpam-816	610	2	πim1	πim1	PROPN
ejpam-816	610	3	∑	∑	ADP
ejpam-816	610	4	k,ℓ	k,ℓ	PROPN
ejpam-816	610	5	dk,ℓ(ze−πi)−λk	dk,ℓ(ze−πi)−λk	VERB
ejpam-816	610	6	.	.	PUNCT
ejpam-816	611	1	from	from	ADP
ejpam-816	611	2	(	(	PUNCT
ejpam-816	611	3	32	32	NUM
ejpam-816	611	4	)	)	PUNCT
ejpam-816	611	5	with	with	ADP
ejpam-816	611	6	n=	n=	ADJ
ejpam-816	611	7	2	2	NUM
ejpam-816	611	8	,	,	PUNCT
ejpam-816	611	9	the	the	DET
ejpam-816	611	10	contribution	contribution	NOUN
ejpam-816	611	11	to	to	ADP
ejpam-816	611	12	the	the	DET
ejpam-816	611	13	algebraic	algebraic	ADJ
ejpam-816	611	14	expansion	expansion	NOUN
ejpam-816	611	15	of	of	ADP
ejpam-816	611	16	j2(z	j2(z	PROPN
ejpam-816	611	17	)	)	PUNCT
ejpam-816	611	18	resulting	result	VERB
ejpam-816	611	19	from	from	ADP
ejpam-816	611	20	the	the	DET
ejpam-816	611	21	logarithmic	logarithmic	ADJ
ejpam-816	611	22	series	series	NOUN
ejpam-816	611	23	g(z	g(z	PROPN
ejpam-816	611	24	)	)	PUNCT
ejpam-816	611	25	in	in	ADP
ejpam-816	611	26	the	the	DET
ejpam-816	611	27	common	common	ADJ
ejpam-816	611	28	sector	sector	NOUN
ejpam-816	611	29	(	(	PUNCT
ejpam-816	611	30	34	34	NUM
ejpam-816	611	31	)	)	PUNCT
ejpam-816	611	32	is	be	AUX
ejpam-816	611	33	then	then	ADV
ejpam-816	611	34	g(z	g(z	ADJ
ejpam-816	611	35	)	)	PUNCT
ejpam-816	611	36	−	−	PROPN
ejpam-816	611	37	e(ν1)g(ze(m1))−	e(ν1)g(ze(m1))−	NOUN
ejpam-816	611	38	e(ν2)g(ze(m2	e(ν2)g(ze(m2	NUM
ejpam-816	611	39	)	)	PUNCT
ejpam-816	611	40	)	)	PUNCT
ejpam-816	612	1	+	+	CCONJ
ejpam-816	612	2	e(ν1	e(ν1	NOUN
ejpam-816	612	3	+	+	CCONJ
ejpam-816	612	4	ν2)g(ze(m1	ν2)g(ze(m1	NOUN
ejpam-816	612	5	+	+	NOUN
ejpam-816	612	6	m2	m2	NOUN
ejpam-816	612	7	)	)	PUNCT
ejpam-816	612	8	)	)	PUNCT
ejpam-816	612	9	references	reference	NOUN
ejpam-816	612	10	1031	1031	NUM
ejpam-816	612	11	=	=	SYM
ejpam-816	612	12	−πim1	−πim1	X
ejpam-816	612	13	∑	∑	PUNCT
ejpam-816	612	14	k,ℓ	k,ℓ	PROPN
ejpam-816	612	15	dk,ℓ(ze−πi)−λk	dk,ℓ(ze−πi)−λk	VERB
ejpam-816	612	16	−	−	PROPN
ejpam-816	612	17	e(ν2)g(ze(m2	e(ν2)g(ze(m2	NUM
ejpam-816	612	18	)	)	PUNCT
ejpam-816	612	19	)	)	PUNCT
ejpam-816	613	1	+	+	VERB
ejpam-816	613	2	e(ν2	e(ν2	NOUN
ejpam-816	613	3	)	)	PUNCT
ejpam-816	613	4	�	�	PROPN
ejpam-816	613	5	g(ze(m2	g(ze(m2	NOUN
ejpam-816	613	6	)	)	PUNCT
ejpam-816	613	7	)	)	PUNCT
ejpam-816	614	1	+	+	VERB
ejpam-816	614	2	πim1	πim1	PROPN
ejpam-816	614	3	∑	∑	PUNCT
ejpam-816	614	4	k,ℓ	k,ℓ	PROPN
ejpam-816	614	5	dk,ℓ(ze(m2	dk,ℓ(ze(m2	NUM
ejpam-816	614	6	−	−	PROPN
ejpam-816	614	7	1))−λk	1))−λk	NUM
ejpam-816	614	8	�	�	PROPN
ejpam-816	614	9	=	=	SYM
ejpam-816	614	10	πim1	πim1	PROPN
ejpam-816	614	11	∑	∑	ADP
ejpam-816	614	12	k,ℓ	k,ℓ	PROPN
ejpam-816	614	13	dk,ℓ(ze−πi)−λk	dk,ℓ(ze−πi)−λk	VERB
ejpam-816	614	14	{	{	PUNCT
ejpam-816	614	15	e(ν2	e(ν2	NOUN
ejpam-816	614	16	−m2λk)−	−m2λk)−	PROPN
ejpam-816	614	17	1	1	NUM
ejpam-816	614	18	}	}	PUNCT
ejpam-816	614	19	≡	≡	PROPN
ejpam-816	614	20	0	0	PUNCT
ejpam-816	614	21	since	since	SCONJ
ejpam-816	614	22	e(ν2	e(ν2	NOUN
ejpam-816	614	23	−	−	PROPN
ejpam-816	614	24	m2λk	m2λk	NOUN
ejpam-816	614	25	)	)	PUNCT
ejpam-816	614	26	=	=	SYM
ejpam-816	614	27	1	1	NUM
ejpam-816	614	28	by	by	ADP
ejpam-816	614	29	(	(	PUNCT
ejpam-816	614	30	61	61	NUM
ejpam-816	614	31	)	)	PUNCT
ejpam-816	614	32	.	.	PUNCT
ejpam-816	614	33	thus	thus	ADV
ejpam-816	614	34	,	,	PUNCT
ejpam-816	614	35	the	the	DET
ejpam-816	614	36	algebraic	algebraic	ADJ
ejpam-816	614	37	expansion	expansion	NOUN
ejpam-816	614	38	associated	associate	VERB
ejpam-816	614	39	with	with	ADP
ejpam-816	614	40	j2(z	j2(z	NOUN
ejpam-816	614	41	)	)	PUNCT
ejpam-816	614	42	when	when	SCONJ
ejpam-816	614	43	double	double	ADJ
ejpam-816	614	44	poles	pole	NOUN
ejpam-816	614	45	are	be	AUX
ejpam-816	614	46	present	present	ADJ
ejpam-816	614	47	similarly	similarly	ADV
ejpam-816	614	48	vanishes	vanish	VERB
ejpam-816	614	49	in	in	ADP
ejpam-816	614	50	the	the	DET
ejpam-816	614	51	sector	sector	NOUN
ejpam-816	614	52	(	(	PUNCT
ejpam-816	614	53	34	34	NUM
ejpam-816	614	54	)	)	PUNCT
ejpam-816	614	55	.	.	PUNCT