id	sid	tid	token	lemma	pos
ejde-395	1	1	electronic	electronic	ADJ
ejde-395	1	2	journal	journal	NOUN
ejde-395	1	3	of	of	ADP
ejde-395	1	4	differential	differential	ADJ
ejde-395	1	5	equations	equation	NOUN
ejde-395	1	6	,	,	PUNCT
ejde-395	1	7	vol	vol	NOUN
ejde-395	1	8	.	.	PUNCT
ejde-395	1	9	2020	2020	NUM
ejde-395	1	10	(	(	PUNCT
ejde-395	1	11	2020	2020	NUM
ejde-395	1	12	)	)	PUNCT
ejde-395	1	13	,	,	PUNCT
ejde-395	1	14	no	no	INTJ
ejde-395	1	15	.	.	NOUN
ejde-395	1	16	14	14	NUM
ejde-395	1	17	,	,	PUNCT
ejde-395	1	18	pp	pp	PROPN
ejde-395	1	19	.	.	PUNCT
ejde-395	2	1	1–14	1–14	PROPN
ejde-395	2	2	.	.	PUNCT
ejde-395	3	1	issn	issn	PROPN
ejde-395	3	2	:	:	PUNCT
ejde-395	3	3	1072	1072	NUM
ejde-395	3	4	-	-	SYM
ejde-395	3	5	6691	6691	NUM
ejde-395	3	6	.	.	PUNCT
ejde-395	4	1	url	url	PROPN
ejde-395	4	2	:	:	PUNCT
ejde-395	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-395	4	4	or	or	CCONJ
ejde-395	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	PROPN
ejde-395	4	6	existence	existence	NOUN
ejde-395	4	7	of	of	ADP
ejde-395	4	8	rational	rational	ADJ
ejde-395	4	9	solutions	solution	NOUN
ejde-395	4	10	for	for	ADP
ejde-395	4	11	q	q	NOUN
ejde-395	4	12	-	-	PUNCT
ejde-395	4	13	difference	difference	NOUN
ejde-395	4	14	painlevé	painlevé	NOUN
ejde-395	4	15	equations	equation	NOUN
ejde-395	4	16	hong	hong	PROPN
ejde-395	4	17	yan	yan	PROPN
ejde-395	5	1	xu	xu	PROPN
ejde-395	5	2	,	,	PUNCT
ejde-395	5	3	jin	jin	PROPN
ejde-395	5	4	tu	tu	PROPN
ejde-395	5	5	abstract	abstract	PROPN
ejde-395	5	6	.	.	PUNCT
ejde-395	6	1	this	this	DET
ejde-395	6	2	article	article	NOUN
ejde-395	6	3	studies	study	VERB
ejde-395	6	4	properties	property	NOUN
ejde-395	6	5	of	of	ADP
ejde-395	6	6	meromorphic	meromorphic	ADJ
ejde-395	6	7	solutions	solution	NOUN
ejde-395	6	8	for	for	ADP
ejde-395	6	9	several	several	ADJ
ejde-395	6	10	types	type	NOUN
ejde-395	6	11	of	of	ADP
ejde-395	6	12	q	q	NOUN
ejde-395	6	13	-	-	PUNCT
ejde-395	6	14	difference	difference	NOUN
ejde-395	6	15	painlevé	painlevé	NOUN
ejde-395	6	16	equations	equation	NOUN
ejde-395	6	17	.	.	PUNCT
ejde-395	7	1	we	we	PRON
ejde-395	7	2	obtain	obtain	VERB
ejde-395	7	3	conditions	condition	NOUN
ejde-395	7	4	for	for	ADP
ejde-395	7	5	the	the	DET
ejde-395	7	6	existence	existence	NOUN
ejde-395	7	7	,	,	PUNCT
ejde-395	7	8	and	and	CCONJ
ejde-395	7	9	the	the	DET
ejde-395	7	10	form	form	NOUN
ejde-395	7	11	of	of	ADP
ejde-395	7	12	rational	rational	ADJ
ejde-395	7	13	solutions	solution	NOUN
ejde-395	7	14	for	for	ADP
ejde-395	7	15	two	two	NUM
ejde-395	7	16	classes	class	NOUN
ejde-395	7	17	of	of	ADP
ejde-395	7	18	q	q	NOUN
ejde-395	7	19	-	-	PUNCT
ejde-395	7	20	difference	difference	NOUN
ejde-395	7	21	painlevé	painlevé	NOUN
ejde-395	7	22	equations	equation	NOUN
ejde-395	7	23	.	.	PUNCT
ejde-395	8	1	also	also	ADV
ejde-395	8	2	for	for	ADP
ejde-395	8	3	a	a	DET
ejde-395	8	4	solution	solution	NOUN
ejde-395	8	5	f	f	X
ejde-395	8	6	we	we	PRON
ejde-395	8	7	obtain	obtain	VERB
ejde-395	8	8	results	result	NOUN
ejde-395	8	9	about	about	ADP
ejde-395	8	10	the	the	DET
ejde-395	8	11	fixed	fix	VERB
ejde-395	8	12	points	point	NOUN
ejde-395	8	13	,	,	PUNCT
ejde-395	8	14	the	the	DET
ejde-395	8	15	exponents	exponent	NOUN
ejde-395	8	16	of	of	ADP
ejde-395	8	17	convergence	convergence	NOUN
ejde-395	8	18	of	of	ADP
ejde-395	8	19	poles	pole	NOUN
ejde-395	8	20	of	of	ADP
ejde-395	8	21	f,∆qf	f,∆qf	NOUN
ejde-395	8	22	,	,	PUNCT
ejde-395	8	23	(	(	PUNCT
ejde-395	8	24	∆qf)/f	∆qf)/f	PROPN
ejde-395	8	25	.	.	PUNCT
ejde-395	9	1	our	our	PRON
ejde-395	9	2	results	result	NOUN
ejde-395	9	3	extend	extend	VERB
ejde-395	9	4	previous	previous	ADJ
ejde-395	9	5	theorems	theorem	NOUN
ejde-395	9	6	given	give	VERB
ejde-395	9	7	in	in	ADP
ejde-395	9	8	the	the	DET
ejde-395	9	9	references	reference	NOUN
ejde-395	9	10	.	.	PUNCT
ejde-395	10	1	1	1	X
ejde-395	10	2	.	.	X
ejde-395	10	3	introduction	introduction	NOUN
ejde-395	10	4	and	and	CCONJ
ejde-395	10	5	statement	statement	NOUN
ejde-395	10	6	of	of	ADP
ejde-395	10	7	main	main	ADJ
ejde-395	10	8	results	result	NOUN
ejde-395	10	9	painlevé	painlevé	VERB
ejde-395	10	10	equations	equation	NOUN
ejde-395	10	11	have	have	AUX
ejde-395	10	12	been	be	AUX
ejde-395	10	13	an	an	DET
ejde-395	10	14	important	important	ADJ
ejde-395	10	15	research	research	NOUN
ejde-395	10	16	subject	subject	NOUN
ejde-395	10	17	in	in	ADP
ejde-395	10	18	the	the	DET
ejde-395	10	19	field	field	NOUN
ejde-395	10	20	of	of	ADP
ejde-395	10	21	the	the	DET
ejde-395	10	22	mathematics	mathematic	NOUN
ejde-395	10	23	and	and	CCONJ
ejde-395	10	24	physics	physics	NOUN
ejde-395	10	25	,	,	PUNCT
ejde-395	10	26	and	and	CCONJ
ejde-395	10	27	they	they	PRON
ejde-395	10	28	occur	occur	VERB
ejde-395	10	29	in	in	ADP
ejde-395	10	30	many	many	ADJ
ejde-395	10	31	physical	physical	ADJ
ejde-395	10	32	situations	situation	NOUN
ejde-395	10	33	:	:	PUNCT
ejde-395	10	34	plasma	plasma	NOUN
ejde-395	10	35	physics	physics	NOUN
ejde-395	10	36	,	,	PUNCT
ejde-395	10	37	statistical	statistical	ADJ
ejde-395	10	38	mechanics	mechanic	NOUN
ejde-395	10	39	,	,	PUNCT
ejde-395	10	40	nonlinear	nonlinear	ADJ
ejde-395	10	41	waves	wave	NOUN
ejde-395	10	42	,	,	PUNCT
ejde-395	10	43	etc	etc	X
ejde-395	10	44	.	.	X
ejde-395	11	1	they	they	PRON
ejde-395	11	2	appear	appear	VERB
ejde-395	11	3	as	as	ADP
ejde-395	11	4	differential	differential	ADJ
ejde-395	11	5	painlevé	painlevé	NOUN
ejde-395	11	6	equation	equation	NOUN
ejde-395	11	7	,	,	PUNCT
ejde-395	11	8	discrete	discrete	ADJ
ejde-395	11	9	painlevé	painlevé	NOUN
ejde-395	11	10	equation	equation	NOUN
ejde-395	11	11	,	,	PUNCT
ejde-395	11	12	difference	difference	NOUN
ejde-395	11	13	painlevé	painlevé	NOUN
ejde-395	11	14	,	,	PUNCT
ejde-395	11	15	and	and	CCONJ
ejde-395	11	16	so	so	ADV
ejde-395	11	17	on	on	ADV
ejde-395	11	18	;	;	PUNCT
ejde-395	11	19	see	see	VERB
ejde-395	11	20	[	[	X
ejde-395	11	21	3	3	NUM
ejde-395	11	22	,	,	PUNCT
ejde-395	11	23	7	7	NUM
ejde-395	11	24	,	,	PUNCT
ejde-395	11	25	8	8	NUM
ejde-395	11	26	]	]	PUNCT
ejde-395	11	27	.	.	PUNCT
ejde-395	12	1	around	around	ADP
ejde-395	12	2	2006	2006	NUM
ejde-395	12	3	,	,	PUNCT
ejde-395	12	4	with	with	ADP
ejde-395	12	5	the	the	DET
ejde-395	12	6	development	development	NOUN
ejde-395	12	7	of	of	ADP
ejde-395	12	8	nevanlinna	nevanlinna	NOUN
ejde-395	12	9	theory	theory	NOUN
ejde-395	12	10	,	,	PUNCT
ejde-395	12	11	halburd	halburd	NOUN
ejde-395	12	12	-	-	PUNCT
ejde-395	12	13	korhonen	korhonen	PROPN
ejde-395	13	1	[	[	X
ejde-395	13	2	11	11	NUM
ejde-395	13	3	]	]	PUNCT
ejde-395	13	4	and	and	CCONJ
ejde-395	13	5	chiang	chiang	PROPN
ejde-395	13	6	-	-	PUNCT
ejde-395	13	7	feng	feng	PROPN
ejde-395	14	1	[	[	X
ejde-395	14	2	5	5	NUM
ejde-395	14	3	]	]	PUNCT
ejde-395	14	4	established	establish	VERB
ejde-395	14	5	independently	independently	ADV
ejde-395	14	6	important	important	ADJ
ejde-395	14	7	results	result	NOUN
ejde-395	14	8	about	about	ADP
ejde-395	14	9	the	the	DET
ejde-395	14	10	complex	complex	ADJ
ejde-395	14	11	difference	difference	NOUN
ejde-395	14	12	and	and	CCONJ
ejde-395	14	13	difference	difference	NOUN
ejde-395	14	14	operators	operator	NOUN
ejde-395	14	15	.	.	PUNCT
ejde-395	15	1	by	by	ADP
ejde-395	15	2	utilizing	utilize	VERB
ejde-395	15	3	these	these	DET
ejde-395	15	4	results	result	NOUN
ejde-395	15	5	,	,	PUNCT
ejde-395	15	6	halburdkorhonen	halburdkorhonen	NOUN
ejde-395	15	7	[	[	X
ejde-395	15	8	10	10	NUM
ejde-395	15	9	,	,	PUNCT
ejde-395	15	10	11	11	NUM
ejde-395	15	11	,	,	PUNCT
ejde-395	15	12	12	12	NUM
ejde-395	15	13	]	]	PUNCT
ejde-395	15	14	discussed	discuss	VERB
ejde-395	15	15	the	the	DET
ejde-395	15	16	equation	equation	NOUN
ejde-395	15	17	f(z	f(z	NOUN
ejde-395	15	18	+	+	CCONJ
ejde-395	15	19	1	1	X
ejde-395	15	20	)	)	PUNCT
ejde-395	15	21	+	+	CCONJ
ejde-395	16	1	f(z	f(z	NOUN
ejde-395	16	2	−	−	NOUN
ejde-395	16	3	1	1	NUM
ejde-395	16	4	)	)	PUNCT
ejde-395	16	5	=	=	SYM
ejde-395	16	6	r(z	r(z	NOUN
ejde-395	16	7	,	,	PUNCT
ejde-395	16	8	f	f	PROPN
ejde-395	16	9	)	)	PUNCT
ejde-395	16	10	,	,	PUNCT
ejde-395	16	11	(	(	PUNCT
ejde-395	16	12	1.1	1.1	NUM
ejde-395	16	13	)	)	PUNCT
ejde-395	16	14	where	where	SCONJ
ejde-395	16	15	r(z	r(z	NOUN
ejde-395	16	16	,	,	PUNCT
ejde-395	16	17	f	f	X
ejde-395	16	18	)	)	PUNCT
ejde-395	16	19	is	be	AUX
ejde-395	16	20	rational	rational	ADJ
ejde-395	16	21	in	in	ADP
ejde-395	16	22	f	f	NOUN
ejde-395	16	23	and	and	CCONJ
ejde-395	16	24	meromorphic	meromorphic	ADJ
ejde-395	16	25	in	in	ADP
ejde-395	16	26	z.	z.	PROPN
ejde-395	16	27	they	they	PRON
ejde-395	16	28	pointed	point	VERB
ejde-395	16	29	out	out	ADP
ejde-395	16	30	that	that	SCONJ
ejde-395	16	31	this	this	DET
ejde-395	16	32	equation	equation	NOUN
ejde-395	16	33	can	can	AUX
ejde-395	16	34	be	be	AUX
ejde-395	16	35	transformed	transform	VERB
ejde-395	16	36	into	into	ADP
ejde-395	16	37	difference	difference	NOUN
ejde-395	16	38	painlevé	painlevé	NOUN
ejde-395	16	39	i	i	PRON
ejde-395	16	40	equations	equation	VERB
ejde-395	16	41	f(z	f(z	VERB
ejde-395	16	42	+	+	CCONJ
ejde-395	16	43	1	1	X
ejde-395	16	44	)	)	PUNCT
ejde-395	17	1	+	+	CCONJ
ejde-395	17	2	f(z	f(z	NOUN
ejde-395	17	3	−	−	NOUN
ejde-395	17	4	1	1	NUM
ejde-395	17	5	)	)	PUNCT
ejde-395	17	6	=	=	SYM
ejde-395	17	7	az	az	PROPN
ejde-395	17	8	+	+	CCONJ
ejde-395	17	9	b	b	PROPN
ejde-395	17	10	f(z	f(z	PROPN
ejde-395	17	11	)	)	PUNCT
ejde-395	18	1	+	+	CCONJ
ejde-395	18	2	c	c	X
ejde-395	18	3	,	,	PUNCT
ejde-395	18	4	(	(	PUNCT
ejde-395	18	5	1.2	1.2	NUM
ejde-395	18	6	)	)	PUNCT
ejde-395	18	7	f(z	f(z	NOUN
ejde-395	18	8	+	+	CCONJ
ejde-395	18	9	1	1	X
ejde-395	18	10	)	)	PUNCT
ejde-395	18	11	+	+	NUM
ejde-395	18	12	f(z	f(z	NOUN
ejde-395	18	13	)	)	PUNCT
ejde-395	19	1	+	+	CCONJ
ejde-395	19	2	f(z	f(z	NOUN
ejde-395	19	3	−	−	NOUN
ejde-395	19	4	1	1	NUM
ejde-395	19	5	)	)	PUNCT
ejde-395	19	6	=	=	SYM
ejde-395	19	7	az	az	PROPN
ejde-395	19	8	+	+	CCONJ
ejde-395	19	9	b	b	PROPN
ejde-395	19	10	f(z	f(z	PROPN
ejde-395	19	11	)	)	PUNCT
ejde-395	20	1	+	+	CCONJ
ejde-395	20	2	c	c	X
ejde-395	20	3	,	,	PUNCT
ejde-395	20	4	(	(	PUNCT
ejde-395	20	5	1.3	1.3	NUM
ejde-395	20	6	)	)	PUNCT
ejde-395	20	7	and	and	CCONJ
ejde-395	20	8	into	into	ADP
ejde-395	20	9	difference	difference	NOUN
ejde-395	20	10	painlevé	painlevé	NOUN
ejde-395	20	11	ii	ii	PROPN
ejde-395	20	12	equations	equation	NOUN
ejde-395	20	13	f(z	f(z	VERB
ejde-395	20	14	+	+	CCONJ
ejde-395	20	15	1	1	X
ejde-395	20	16	)	)	PUNCT
ejde-395	20	17	+	+	CCONJ
ejde-395	20	18	f(z	f(z	NOUN
ejde-395	20	19	−	−	NOUN
ejde-395	20	20	1	1	NUM
ejde-395	20	21	)	)	PUNCT
ejde-395	20	22	=	=	SYM
ejde-395	20	23	(	(	PUNCT
ejde-395	20	24	az	az	PROPN
ejde-395	20	25	+	+	CCONJ
ejde-395	20	26	b)f(z	b)f(z	ADJ
ejde-395	20	27	)	)	PUNCT
ejde-395	21	1	+	+	SYM
ejde-395	21	2	c	c	NOUN
ejde-395	21	3	1−	1−	NUM
ejde-395	21	4	f(z)2	f(z)2	NOUN
ejde-395	21	5	.	.	PUNCT
ejde-395	22	1	(	(	PUNCT
ejde-395	22	2	1.4	1.4	NUM
ejde-395	22	3	)	)	PUNCT
ejde-395	22	4	in	in	ADP
ejde-395	22	5	2010	2010	NUM
ejde-395	22	6	,	,	PUNCT
ejde-395	22	7	ronkainen	ronkainen	NOUN
ejde-395	23	1	[	[	X
ejde-395	23	2	21	21	NUM
ejde-395	23	3	]	]	PUNCT
ejde-395	23	4	further	far	ADV
ejde-395	23	5	investigated	investigate	VERB
ejde-395	23	6	the	the	DET
ejde-395	23	7	meromorphic	meromorphic	ADJ
ejde-395	23	8	solutions	solution	NOUN
ejde-395	23	9	of	of	ADP
ejde-395	23	10	the	the	DET
ejde-395	23	11	equation	equation	NOUN
ejde-395	23	12	f(z	f(z	NOUN
ejde-395	23	13	+	+	CCONJ
ejde-395	23	14	1)f(z	1)f(z	NUM
ejde-395	23	15	−	−	NOUN
ejde-395	23	16	1	1	NUM
ejde-395	23	17	)	)	PUNCT
ejde-395	23	18	=	=	SYM
ejde-395	23	19	r(z	r(z	PROPN
ejde-395	23	20	,	,	PUNCT
ejde-395	23	21	f	f	NOUN
ejde-395	23	22	)	)	PUNCT
ejde-395	23	23	(	(	PUNCT
ejde-395	23	24	1.5	1.5	NUM
ejde-395	23	25	)	)	PUNCT
ejde-395	23	26	2010	2010	NUM
ejde-395	23	27	mathematics	mathematic	NOUN
ejde-395	23	28	subject	subject	NOUN
ejde-395	23	29	classification	classification	NOUN
ejde-395	23	30	.	.	PUNCT
ejde-395	24	1	39a13	39a13	NUM
ejde-395	24	2	,	,	PUNCT
ejde-395	24	3	30d35	30d35	NUM
ejde-395	24	4	.	.	PUNCT
ejde-395	25	1	key	key	ADJ
ejde-395	25	2	words	word	NOUN
ejde-395	25	3	and	and	CCONJ
ejde-395	25	4	phrases	phrase	NOUN
ejde-395	25	5	.	.	PUNCT
ejde-395	26	1	rational	rational	ADJ
ejde-395	26	2	solution	solution	NOUN
ejde-395	26	3	;	;	PUNCT
ejde-395	26	4	q	q	ADJ
ejde-395	26	5	-	-	PUNCT
ejde-395	26	6	difference	difference	NOUN
ejde-395	26	7	painlevé	painlevé	NOUN
ejde-395	26	8	equation	equation	NOUN
ejde-395	26	9	;	;	PUNCT
ejde-395	26	10	fixed	fix	VERB
ejde-395	26	11	point	point	NOUN
ejde-395	26	12	.	.	PUNCT
ejde-395	27	1	c	c	X
ejde-395	27	2	©	©	PROPN
ejde-395	27	3	2020	2020	NUM
ejde-395	27	4	texas	texas	PROPN
ejde-395	27	5	state	state	PROPN
ejde-395	27	6	university	university	PROPN
ejde-395	27	7	.	.	PUNCT
ejde-395	28	1	submitted	submit	VERB
ejde-395	28	2	january	january	PROPN
ejde-395	28	3	13	13	NUM
ejde-395	28	4	,	,	PUNCT
ejde-395	28	5	2019	2019	NUM
ejde-395	28	6	.	.	PUNCT
ejde-395	29	1	published	publish	VERB
ejde-395	29	2	february	february	PROPN
ejde-395	29	3	5	5	NUM
ejde-395	29	4	,	,	PUNCT
ejde-395	29	5	2020	2020	NUM
ejde-395	29	6	.	.	PUNCT
ejde-395	30	1	1	1	NUM
ejde-395	30	2	2	2	NUM
ejde-395	30	3	h.	h.	PROPN
ejde-395	30	4	y.	y.	PROPN
ejde-395	30	5	xu	xu	PROPN
ejde-395	30	6	,	,	PUNCT
ejde-395	30	7	j.	j.	PROPN
ejde-395	30	8	tu	tu	PROPN
ejde-395	30	9	ejde-2020/14	ejde-2020/14	VERB
ejde-395	30	10	where	where	SCONJ
ejde-395	30	11	r(z	r(z	NOUN
ejde-395	30	12	,	,	PUNCT
ejde-395	30	13	f	f	X
ejde-395	30	14	)	)	PUNCT
ejde-395	30	15	is	be	AUX
ejde-395	30	16	a	a	DET
ejde-395	30	17	rational	rational	ADJ
ejde-395	30	18	and	and	CCONJ
ejde-395	30	19	irreducible	irreducible	ADJ
ejde-395	30	20	in	in	ADP
ejde-395	30	21	f	f	PROPN
ejde-395	30	22	and	and	CCONJ
ejde-395	30	23	meromorphic	meromorphic	ADJ
ejde-395	30	24	in	in	ADP
ejde-395	30	25	z.	z.	PROPN
ejde-395	30	26	he	he	PRON
ejde-395	30	27	proved	prove	VERB
ejde-395	30	28	that	that	SCONJ
ejde-395	30	29	either	either	CCONJ
ejde-395	30	30	f	f	PROPN
ejde-395	30	31	satisfies	satisfy	VERB
ejde-395	30	32	the	the	DET
ejde-395	30	33	difference	difference	NOUN
ejde-395	30	34	riccati	riccati	NOUN
ejde-395	30	35	equation	equation	NOUN
ejde-395	30	36	f(z	f(z	VERB
ejde-395	30	37	+	+	CCONJ
ejde-395	30	38	1	1	X
ejde-395	30	39	)	)	PUNCT
ejde-395	30	40	=	=	NOUN
ejde-395	30	41	a(z)f(z	a(z)f(z	NOUN
ejde-395	30	42	)	)	PUNCT
ejde-395	31	1	+	+	ADJ
ejde-395	31	2	b(z	b(z	NOUN
ejde-395	31	3	)	)	PUNCT
ejde-395	31	4	f(z	f(z	PROPN
ejde-395	31	5	)	)	PUNCT
ejde-395	32	1	+	+	PUNCT
ejde-395	32	2	c(z	c(z	NUM
ejde-395	32	3	)	)	PUNCT
ejde-395	32	4	,	,	PUNCT
ejde-395	32	5	or	or	CCONJ
ejde-395	32	6	equation	equation	NOUN
ejde-395	32	7	(	(	PUNCT
ejde-395	32	8	1.5	1.5	NUM
ejde-395	32	9	)	)	PUNCT
ejde-395	32	10	can	can	AUX
ejde-395	32	11	be	be	AUX
ejde-395	32	12	transformed	transform	VERB
ejde-395	32	13	to	to	ADP
ejde-395	32	14	one	one	NUM
ejde-395	32	15	of	of	ADP
ejde-395	32	16	the	the	DET
ejde-395	32	17	following	follow	VERB
ejde-395	32	18	equations	equation	NOUN
ejde-395	32	19	f(z	f(z	VERB
ejde-395	33	1	+	+	CCONJ
ejde-395	33	2	1)f(z	1)f(z	NUM
ejde-395	33	3	−	−	NOUN
ejde-395	33	4	1	1	NUM
ejde-395	33	5	)	)	PUNCT
ejde-395	33	6	=	=	NOUN
ejde-395	33	7	η(z)f(z)2	η(z)f(z)2	NOUN
ejde-395	33	8	−	−	NOUN
ejde-395	33	9	λ(z)f(z	λ(z)f(z	NOUN
ejde-395	33	10	)	)	PUNCT
ejde-395	34	1	+	+	CCONJ
ejde-395	34	2	µ(z	µ(z	NOUN
ejde-395	34	3	)	)	PUNCT
ejde-395	34	4	(	(	PUNCT
ejde-395	34	5	f(z)−	f(z)−	PROPN
ejde-395	34	6	1)(f(z)−	1)(f(z)−	NUM
ejde-395	34	7	υ(z	υ(z	NOUN
ejde-395	34	8	)	)	PUNCT
ejde-395	34	9	)	)	PUNCT
ejde-395	34	10	,	,	PUNCT
ejde-395	34	11	f(z	f(z	NOUN
ejde-395	34	12	+	+	CCONJ
ejde-395	34	13	1)f(z	1)f(z	NUM
ejde-395	34	14	−	−	NOUN
ejde-395	34	15	1	1	NUM
ejde-395	34	16	)	)	PUNCT
ejde-395	34	17	=	=	NOUN
ejde-395	34	18	η(z)f(z)2	η(z)f(z)2	NOUN
ejde-395	34	19	−	−	NOUN
ejde-395	34	20	λ(z)f(z	λ(z)f(z	NOUN
ejde-395	34	21	)	)	PUNCT
ejde-395	34	22	f(z)−	f(z)−	NOUN
ejde-395	34	23	1	1	NUM
ejde-395	34	24	,	,	PUNCT
ejde-395	34	25	f(z	f(z	PROPN
ejde-395	34	26	+	+	CCONJ
ejde-395	34	27	1)f(z	1)f(z	NUM
ejde-395	34	28	−	−	NOUN
ejde-395	34	29	1	1	NUM
ejde-395	34	30	)	)	PUNCT
ejde-395	34	31	=	=	SYM
ejde-395	34	32	η(z)(f(z)−	η(z)(f(z)−	PROPN
ejde-395	34	33	λ(z	λ(z	NOUN
ejde-395	34	34	)	)	PUNCT
ejde-395	34	35	)	)	PUNCT
ejde-395	34	36	(	(	PUNCT
ejde-395	34	37	f(z)−	f(z)−	PROPN
ejde-395	34	38	1	1	NUM
ejde-395	34	39	)	)	PUNCT
ejde-395	34	40	,	,	PUNCT
ejde-395	34	41	f(z	f(z	PROPN
ejde-395	34	42	+	+	CCONJ
ejde-395	34	43	1)f(z	1)f(z	NUM
ejde-395	34	44	−	−	NOUN
ejde-395	34	45	1	1	NUM
ejde-395	34	46	)	)	PUNCT
ejde-395	34	47	=	=	PUNCT
ejde-395	35	1	h(z)f(z)m	h(z)f(z)m	PROPN
ejde-395	35	2	,	,	PUNCT
ejde-395	35	3	where	where	SCONJ
ejde-395	35	4	η(z	η(z	PROPN
ejde-395	35	5	)	)	PUNCT
ejde-395	35	6	,	,	PUNCT
ejde-395	35	7	λ(z	λ(z	NOUN
ejde-395	35	8	)	)	PUNCT
ejde-395	35	9	,	,	PUNCT
ejde-395	35	10	υ(z	υ(z	VERB
ejde-395	35	11	)	)	PUNCT
ejde-395	35	12	satisfy	satisfy	VERB
ejde-395	35	13	certain	certain	ADJ
ejde-395	35	14	conditions	condition	NOUN
ejde-395	35	15	.	.	PUNCT
ejde-395	36	1	generally	generally	ADV
ejde-395	36	2	speaking	speak	VERB
ejde-395	36	3	,	,	PUNCT
ejde-395	36	4	the	the	DET
ejde-395	36	5	above	above	ADJ
ejde-395	36	6	four	four	NUM
ejde-395	36	7	equation	equation	NOUN
ejde-395	36	8	can	can	AUX
ejde-395	36	9	be	be	AUX
ejde-395	36	10	called	call	VERB
ejde-395	36	11	as	as	SCONJ
ejde-395	36	12	the	the	DET
ejde-395	36	13	difference	difference	NOUN
ejde-395	36	14	painlevé	painlevé	VERB
ejde-395	36	15	iii	iii	NUM
ejde-395	36	16	equations	equation	NOUN
ejde-395	36	17	.	.	PUNCT
ejde-395	37	1	in	in	ADP
ejde-395	37	2	the	the	DET
ejde-395	37	3	past	past	ADJ
ejde-395	37	4	two	two	NUM
ejde-395	37	5	decades	decade	NOUN
ejde-395	37	6	,	,	PUNCT
ejde-395	37	7	many	many	ADJ
ejde-395	37	8	mathematicians	mathematician	NOUN
ejde-395	37	9	paid	pay	VERB
ejde-395	37	10	consideration	consideration	NOUN
ejde-395	37	11	attention	attention	NOUN
ejde-395	37	12	to	to	ADP
ejde-395	37	13	the	the	DET
ejde-395	37	14	value	value	NOUN
ejde-395	37	15	distribution	distribution	NOUN
ejde-395	37	16	of	of	ADP
ejde-395	37	17	solutions	solution	NOUN
ejde-395	37	18	for	for	ADP
ejde-395	37	19	complex	complex	ADJ
ejde-395	37	20	difference	difference	NOUN
ejde-395	37	21	equations	equation	NOUN
ejde-395	37	22	,	,	PUNCT
ejde-395	37	23	and	and	CCONJ
ejde-395	37	24	obtained	obtain	VERB
ejde-395	37	25	lots	lot	NOUN
ejde-395	37	26	of	of	ADP
ejde-395	37	27	important	important	ADJ
ejde-395	37	28	results	result	NOUN
ejde-395	37	29	on	on	ADP
ejde-395	37	30	the	the	DET
ejde-395	37	31	properties	property	NOUN
ejde-395	37	32	of	of	ADP
ejde-395	37	33	solutions	solution	NOUN
ejde-395	37	34	for	for	ADP
ejde-395	37	35	difference	difference	NOUN
ejde-395	37	36	painlevé	painlevé	NOUN
ejde-395	37	37	i	i	PROPN
ejde-395	37	38	-	-	PUNCT
ejde-395	37	39	iii	iii	NUM
ejde-395	37	40	equations	equation	NOUN
ejde-395	37	41	(	(	PUNCT
ejde-395	37	42	see	see	VERB
ejde-395	37	43	[	[	X
ejde-395	37	44	2	2	NUM
ejde-395	37	45	,	,	PUNCT
ejde-395	37	46	3	3	NUM
ejde-395	37	47	,	,	PUNCT
ejde-395	37	48	10	10	NUM
ejde-395	37	49	,	,	PUNCT
ejde-395	37	50	11	11	NUM
ejde-395	37	51	,	,	PUNCT
ejde-395	37	52	12	12	NUM
ejde-395	37	53	,	,	PUNCT
ejde-395	37	54	18	18	NUM
ejde-395	37	55	,	,	PUNCT
ejde-395	37	56	19	19	NUM
ejde-395	37	57	,	,	PUNCT
ejde-395	37	58	33	33	NUM
ejde-395	37	59	]	]	PUNCT
ejde-395	37	60	)	)	PUNCT
ejde-395	37	61	.	.	PUNCT
ejde-395	38	1	in	in	ADP
ejde-395	38	2	2010	2010	NUM
ejde-395	38	3	,	,	PUNCT
ejde-395	38	4	chen	chen	PROPN
ejde-395	38	5	-	-	PUNCT
ejde-395	38	6	shon	shon	PROPN
ejde-395	38	7	[	[	X
ejde-395	38	8	4	4	NUM
ejde-395	38	9	]	]	PUNCT
ejde-395	38	10	considered	consider	VERB
ejde-395	38	11	the	the	DET
ejde-395	38	12	difference	difference	NOUN
ejde-395	38	13	painlevé	painlevé	VERB
ejde-395	38	14	i	i	PRON
ejde-395	38	15	equation	equation	NOUN
ejde-395	38	16	(	(	PUNCT
ejde-395	38	17	1.2	1.2	NUM
ejde-395	38	18	)	)	PUNCT
ejde-395	38	19	and	and	CCONJ
ejde-395	38	20	obtained	obtain	VERB
ejde-395	38	21	the	the	DET
ejde-395	38	22	following	follow	VERB
ejde-395	38	23	theorem	theorem	VERB
ejde-395	38	24	.	.	PUNCT
ejde-395	38	25	theorem	theorem	VERB
ejde-395	38	26	1.1	1.1	NUM
ejde-395	38	27	(	(	PUNCT
ejde-395	38	28	see	see	VERB
ejde-395	38	29	[	[	X
ejde-395	38	30	4	4	NUM
ejde-395	38	31	,	,	PUNCT
ejde-395	38	32	theorem	theorem	VERB
ejde-395	38	33	4	4	NUM
ejde-395	38	34	]	]	PUNCT
ejde-395	38	35	)	)	PUNCT
ejde-395	38	36	.	.	PUNCT
ejde-395	39	1	let	let	VERB
ejde-395	39	2	a	a	DET
ejde-395	39	3	,	,	PUNCT
ejde-395	39	4	b	b	NOUN
ejde-395	39	5	,	,	PUNCT
ejde-395	39	6	c	c	AUX
ejde-395	39	7	be	be	AUX
ejde-395	39	8	constants	constant	NOUN
ejde-395	39	9	,	,	PUNCT
ejde-395	39	10	where	where	SCONJ
ejde-395	39	11	a	a	DET
ejde-395	39	12	,	,	PUNCT
ejde-395	39	13	b	b	NOUN
ejde-395	39	14	are	be	AUX
ejde-395	39	15	not	not	PART
ejde-395	39	16	both	both	ADV
ejde-395	39	17	equal	equal	ADJ
ejde-395	39	18	to	to	ADP
ejde-395	39	19	zero	zero	NUM
ejde-395	39	20	.	.	PUNCT
ejde-395	40	1	then	then	ADV
ejde-395	40	2	(	(	PUNCT
ejde-395	40	3	i	i	NOUN
ejde-395	40	4	)	)	PUNCT
ejde-395	40	5	if	if	SCONJ
ejde-395	40	6	a	a	PRON
ejde-395	40	7	6=	6=	NUM
ejde-395	40	8	0	0	NUM
ejde-395	40	9	,	,	PUNCT
ejde-395	40	10	then	then	ADV
ejde-395	40	11	(	(	PUNCT
ejde-395	40	12	1.2	1.2	NUM
ejde-395	40	13	)	)	PUNCT
ejde-395	40	14	has	have	VERB
ejde-395	40	15	no	no	DET
ejde-395	40	16	rational	rational	ADJ
ejde-395	40	17	solution	solution	NOUN
ejde-395	40	18	;	;	PUNCT
ejde-395	40	19	(	(	PUNCT
ejde-395	40	20	ii	ii	NOUN
ejde-395	40	21	)	)	PUNCT
ejde-395	40	22	if	if	SCONJ
ejde-395	40	23	a	a	PRON
ejde-395	40	24	=	=	NOUN
ejde-395	40	25	0	0	NUM
ejde-395	40	26	,	,	PUNCT
ejde-395	40	27	and	and	CCONJ
ejde-395	40	28	b	b	X
ejde-395	40	29	6=	6=	NUM
ejde-395	40	30	0	0	NUM
ejde-395	40	31	,	,	PUNCT
ejde-395	40	32	then	then	ADV
ejde-395	40	33	(	(	PUNCT
ejde-395	40	34	1.2	1.2	NUM
ejde-395	40	35	)	)	PUNCT
ejde-395	40	36	has	have	VERB
ejde-395	40	37	a	a	DET
ejde-395	40	38	nonzero	nonzero	ADJ
ejde-395	40	39	constant	constant	ADJ
ejde-395	40	40	solution	solution	NOUN
ejde-395	40	41	w(z	w(z	NOUN
ejde-395	40	42	)	)	PUNCT
ejde-395	40	43	=	=	SYM
ejde-395	41	1	a	a	NOUN
ejde-395	41	2	,	,	PUNCT
ejde-395	41	3	where	where	SCONJ
ejde-395	41	4	a	a	DET
ejde-395	41	5	satisfies	satisfie	NOUN
ejde-395	41	6	2a2	2a2	NUM
ejde-395	41	7	−	−	PROPN
ejde-395	41	8	ca−	ca−	SYM
ejde-395	41	9	b	b	NOUN
ejde-395	41	10	=	=	SYM
ejde-395	41	11	0	0	PROPN
ejde-395	41	12	.	.	PUNCT
ejde-395	42	1	the	the	DET
ejde-395	42	2	other	other	ADJ
ejde-395	42	3	rational	rational	ADJ
ejde-395	42	4	solution	solution	NOUN
ejde-395	42	5	is	be	AUX
ejde-395	42	6	w(z	w(z	PROPN
ejde-395	42	7	)	)	PUNCT
ejde-395	43	1	=	=	SYM
ejde-395	43	2	p	p	X
ejde-395	43	3	(	(	PUNCT
ejde-395	43	4	z	z	NOUN
ejde-395	43	5	)	)	PUNCT
ejde-395	43	6	q(z	q(z	PROPN
ejde-395	43	7	)	)	PUNCT
ejde-395	44	1	+	+	NOUN
ejde-395	44	2	a	a	X
ejde-395	44	3	,	,	PUNCT
ejde-395	44	4	where	where	SCONJ
ejde-395	44	5	p	p	PROPN
ejde-395	44	6	(	(	PUNCT
ejde-395	44	7	z	z	NOUN
ejde-395	44	8	)	)	PUNCT
ejde-395	44	9	and	and	CCONJ
ejde-395	44	10	q(z	q(z	PROPN
ejde-395	44	11	)	)	PUNCT
ejde-395	44	12	are	be	AUX
ejde-395	44	13	relatively	relatively	ADV
ejde-395	44	14	prime	prime	ADJ
ejde-395	44	15	polynomials	polynomial	NOUN
ejde-395	44	16	and	and	CCONJ
ejde-395	44	17	satisfy	satisfy	VERB
ejde-395	44	18	degp	degp	ADJ
ejde-395	44	19	<	<	X
ejde-395	44	20	degq	degq	NOUN
ejde-395	44	21	.	.	PUNCT
ejde-395	45	1	in	in	ADP
ejde-395	45	2	2014	2014	NUM
ejde-395	45	3	,	,	PUNCT
ejde-395	45	4	zhang	zhang	PROPN
ejde-395	45	5	-	-	PUNCT
ejde-395	45	6	yang	yang	PROPN
ejde-395	46	1	[	[	X
ejde-395	46	2	30	30	NUM
ejde-395	46	3	]	]	PUNCT
ejde-395	46	4	studied	study	VERB
ejde-395	46	5	the	the	DET
ejde-395	46	6	difference	difference	NOUN
ejde-395	46	7	painlevé	painlevé	NOUN
ejde-395	46	8	iii	iii	NUM
ejde-395	46	9	equations	equation	NOUN
ejde-395	46	10	with	with	ADP
ejde-395	46	11	the	the	DET
ejde-395	46	12	constant	constant	ADJ
ejde-395	46	13	coefficients	coefficient	NOUN
ejde-395	46	14	,	,	PUNCT
ejde-395	46	15	and	and	CCONJ
ejde-395	46	16	obtained	obtain	VERB
ejde-395	46	17	the	the	DET
ejde-395	46	18	following	following	ADJ
ejde-395	46	19	result	result	NOUN
ejde-395	46	20	.	.	PUNCT
ejde-395	47	1	theorem	theorem	VERB
ejde-395	47	2	1.2	1.2	NUM
ejde-395	47	3	(	(	PUNCT
ejde-395	47	4	[	[	X
ejde-395	47	5	30	30	NUM
ejde-395	47	6	]	]	PUNCT
ejde-395	47	7	)	)	PUNCT
ejde-395	47	8	.	.	PUNCT
ejde-395	48	1	if	if	SCONJ
ejde-395	48	2	f	f	PROPN
ejde-395	48	3	is	be	AUX
ejde-395	48	4	a	a	DET
ejde-395	48	5	transcendental	transcendental	ADJ
ejde-395	48	6	finite	finite	ADJ
ejde-395	48	7	-	-	PUNCT
ejde-395	48	8	order	order	NOUN
ejde-395	48	9	meromorphic	meromorphic	ADJ
ejde-395	48	10	solution	solution	NOUN
ejde-395	48	11	of	of	ADP
ejde-395	48	12	f(z+	f(z+	X
ejde-395	48	13	1)f(z−	1)f(z−	NUM
ejde-395	48	14	1)(f(z)−	1)(f(z)−	NUM
ejde-395	48	15	1	1	NUM
ejde-395	48	16	)	)	PUNCT
ejde-395	48	17	=	=	PUNCT
ejde-395	48	18	ηw(z	ηw(z	NOUN
ejde-395	48	19	)	)	PUNCT
ejde-395	48	20	or	or	CCONJ
ejde-395	48	21	f(z+	f(z+	NUM
ejde-395	48	22	1)f(z−	1)f(z−	NUM
ejde-395	48	23	1)(f(z)−	1)(f(z)−	NUM
ejde-395	48	24	1	1	NUM
ejde-395	48	25	)	)	PUNCT
ejde-395	48	26	=	=	SYM
ejde-395	48	27	f(z)2	f(z)2	NOUN
ejde-395	48	28	−	−	PROPN
ejde-395	48	29	λw(z	λw(z	NUM
ejde-395	48	30	)	)	PUNCT
ejde-395	48	31	,	,	PUNCT
ejde-395	48	32	where	where	SCONJ
ejde-395	48	33	η(6=	η(6=	PROPN
ejde-395	48	34	0	0	NUM
ejde-395	48	35	)	)	PUNCT
ejde-395	48	36	,	,	PUNCT
ejde-395	48	37	λ	λ	PROPN
ejde-395	48	38	(	(	PUNCT
ejde-395	48	39	6=	6=	ADP
ejde-395	48	40	0	0	NUM
ejde-395	48	41	,	,	PUNCT
ejde-395	48	42	1	1	NUM
ejde-395	48	43	)	)	PUNCT
ejde-395	48	44	are	be	AUX
ejde-395	48	45	constants	constant	NOUN
ejde-395	48	46	,	,	PUNCT
ejde-395	48	47	then	then	ADV
ejde-395	48	48	(	(	PUNCT
ejde-395	48	49	i	i	NOUN
ejde-395	48	50	)	)	PUNCT
ejde-395	48	51	λ(f	λ(f	PROPN
ejde-395	48	52	)	)	PUNCT
ejde-395	48	53	=	=	SYM
ejde-395	48	54	σ(f	σ(f	NOUN
ejde-395	48	55	)	)	PUNCT
ejde-395	48	56	;	;	PUNCT
ejde-395	48	57	(	(	PUNCT
ejde-395	48	58	ii	ii	NOUN
ejde-395	48	59	)	)	PUNCT
ejde-395	48	60	f	f	PROPN
ejde-395	48	61	has	have	VERB
ejde-395	48	62	at	at	ADP
ejde-395	48	63	most	most	ADJ
ejde-395	48	64	one	one	NUM
ejde-395	48	65	non	non	ADJ
ejde-395	48	66	-	-	ADJ
ejde-395	48	67	zero	zero	NUM
ejde-395	48	68	borel	borel	NOUN
ejde-395	48	69	exceptional	exceptional	ADJ
ejde-395	48	70	value	value	NOUN
ejde-395	48	71	for	for	ADP
ejde-395	48	72	σ(f	σ(f	NOUN
ejde-395	48	73	)	)	PUNCT
ejde-395	48	74	>	>	X
ejde-395	49	1	0	0	X
ejde-395	49	2	.	.	PUNCT
ejde-395	50	1	the	the	DET
ejde-395	50	2	logarithmic	logarithmic	ADJ
ejde-395	50	3	derivative	derivative	ADJ
ejde-395	50	4	lemma	lemma	PROPN
ejde-395	50	5	on	on	ADP
ejde-395	50	6	q	q	ADJ
ejde-395	50	7	-	-	PUNCT
ejde-395	50	8	difference	difference	NOUN
ejde-395	50	9	operators	operator	NOUN
ejde-395	50	10	was	be	AUX
ejde-395	50	11	established	establish	VERB
ejde-395	50	12	by	by	ADP
ejde-395	50	13	barnett	barnett	PROPN
ejde-395	50	14	,	,	PUNCT
ejde-395	50	15	halburd	halburd	PROPN
ejde-395	50	16	,	,	PUNCT
ejde-395	50	17	korhonen	korhonen	PROPN
ejde-395	50	18	and	and	CCONJ
ejde-395	50	19	morgan	morgan	PROPN
ejde-395	51	1	[	[	X
ejde-395	51	2	1	1	X
ejde-395	51	3	]	]	PUNCT
ejde-395	51	4	in	in	ADP
ejde-395	51	5	2007	2007	NUM
ejde-395	51	6	.	.	PUNCT
ejde-395	52	1	then	then	ADV
ejde-395	52	2	the	the	DET
ejde-395	52	3	interest	interest	NOUN
ejde-395	52	4	in	in	ADP
ejde-395	52	5	studying	study	VERB
ejde-395	52	6	the	the	DET
ejde-395	52	7	properties	property	NOUN
ejde-395	52	8	on	on	ADP
ejde-395	52	9	the	the	DET
ejde-395	52	10	existence	existence	NOUN
ejde-395	52	11	and	and	CCONJ
ejde-395	52	12	value	value	NOUN
ejde-395	52	13	distribution	distribution	NOUN
ejde-395	52	14	of	of	ADP
ejde-395	52	15	solutions	solution	NOUN
ejde-395	52	16	has	have	AUX
ejde-395	52	17	increased	increase	VERB
ejde-395	52	18	considerably	considerably	ADV
ejde-395	52	19	for	for	ADP
ejde-395	52	20	some	some	DET
ejde-395	52	21	q	q	ADJ
ejde-395	52	22	-	-	PUNCT
ejde-395	52	23	difference	difference	NOUN
ejde-395	52	24	equation	equation	NOUN
ejde-395	52	25	which	which	PRON
ejde-395	52	26	are	be	AUX
ejde-395	52	27	formed	form	VERB
ejde-395	52	28	by	by	ADP
ejde-395	52	29	replacing	replace	VERB
ejde-395	52	30	the	the	DET
ejde-395	52	31	qdifference	qdifference	NOUN
ejde-395	52	32	f(qz	f(qz	NOUN
ejde-395	52	33	)	)	PUNCT
ejde-395	52	34	,	,	PUNCT
ejde-395	52	35	q	q	PROPN
ejde-395	52	36	∈	∈	PROPN
ejde-395	52	37	c	c	X
ejde-395	52	38	\	\	X
ejde-395	52	39	{	{	PUNCT
ejde-395	52	40	0	0	NUM
ejde-395	52	41	,	,	PUNCT
ejde-395	52	42	1	1	NUM
ejde-395	52	43	}	}	PUNCT
ejde-395	52	44	with	with	ADP
ejde-395	52	45	f(z	f(z	PROPN
ejde-395	52	46	+	+	CCONJ
ejde-395	52	47	c	c	X
ejde-395	52	48	)	)	PUNCT
ejde-395	52	49	of	of	ADP
ejde-395	52	50	meromorphic	meromorphic	ADJ
ejde-395	52	51	function	function	NOUN
ejde-395	52	52	in	in	ADP
ejde-395	52	53	some	some	DET
ejde-395	52	54	expression	expression	NOUN
ejde-395	52	55	concerning	concern	VERB
ejde-395	52	56	complex	complex	ADJ
ejde-395	52	57	difference	difference	NOUN
ejde-395	52	58	equations	equation	NOUN
ejde-395	52	59	;	;	PUNCT
ejde-395	52	60	see	see	VERB
ejde-395	52	61	[	[	X
ejde-395	52	62	6	6	NUM
ejde-395	52	63	,	,	PUNCT
ejde-395	52	64	9	9	NUM
ejde-395	52	65	,	,	PUNCT
ejde-395	52	66	14	14	NUM
ejde-395	52	67	,	,	PUNCT
ejde-395	52	68	15	15	NUM
ejde-395	52	69	,	,	PUNCT
ejde-395	52	70	16	16	NUM
ejde-395	52	71	,	,	PUNCT
ejde-395	52	72	20	20	NUM
ejde-395	52	73	,	,	PUNCT
ejde-395	52	74	22	22	NUM
ejde-395	52	75	,	,	PUNCT
ejde-395	52	76	23	23	NUM
ejde-395	52	77	,	,	PUNCT
ejde-395	52	78	24	24	NUM
ejde-395	52	79	,	,	PUNCT
ejde-395	52	80	25	25	NUM
ejde-395	52	81	,	,	PUNCT
ejde-395	52	82	26	26	NUM
ejde-395	52	83	,	,	PUNCT
ejde-395	52	84	29	29	NUM
ejde-395	52	85	,	,	PUNCT
ejde-395	52	86	31	31	NUM
ejde-395	52	87	,	,	PUNCT
ejde-395	52	88	32	32	NUM
ejde-395	52	89	]	]	PUNCT
ejde-395	52	90	.	.	PUNCT
ejde-395	53	1	in	in	ADP
ejde-395	53	2	2015	2015	NUM
ejde-395	53	3	,	,	PUNCT
ejde-395	53	4	qi	qi	PROPN
ejde-395	53	5	-	-	PUNCT
ejde-395	53	6	yang	yang	PROPN
ejde-395	53	7	[	[	X
ejde-395	53	8	20	20	NUM
ejde-395	53	9	]	]	PUNCT
ejde-395	53	10	considered	consider	VERB
ejde-395	53	11	the	the	DET
ejde-395	53	12	equations	equation	NOUN
ejde-395	53	13	f(qz	f(qz	VERB
ejde-395	53	14	)	)	PUNCT
ejde-395	54	1	+	+	NUM
ejde-395	54	2	f	f	X
ejde-395	54	3	(	(	PUNCT
ejde-395	54	4	z	z	NOUN
ejde-395	54	5	q	q	NOUN
ejde-395	54	6	)	)	PUNCT
ejde-395	55	1	=	=	SYM
ejde-395	55	2	az	az	PROPN
ejde-395	55	3	+	+	CCONJ
ejde-395	55	4	b	b	PROPN
ejde-395	55	5	f(z	f(z	PROPN
ejde-395	55	6	)	)	PUNCT
ejde-395	56	1	+	+	CCONJ
ejde-395	56	2	c	c	X
ejde-395	56	3	,	,	PUNCT
ejde-395	56	4	(	(	PUNCT
ejde-395	56	5	1.6	1.6	NUM
ejde-395	56	6	)	)	PUNCT
ejde-395	56	7	ejde-2020/14	ejde-2020/14	NOUN
ejde-395	56	8	q	q	NOUN
ejde-395	56	9	-	-	PUNCT
ejde-395	56	10	difference	difference	NOUN
ejde-395	56	11	painlevé	painlevé	NOUN
ejde-395	56	12	equations	equation	NOUN
ejde-395	56	13	3	3	NUM
ejde-395	56	14	which	which	PRON
ejde-395	56	15	can	can	AUX
ejde-395	56	16	be	be	AUX
ejde-395	56	17	seen	see	VERB
ejde-395	56	18	as	as	ADP
ejde-395	56	19	q	q	ADJ
ejde-395	56	20	-	-	PUNCT
ejde-395	56	21	difference	difference	NOUN
ejde-395	56	22	analogues	analogue	NOUN
ejde-395	56	23	of	of	ADP
ejde-395	56	24	(	(	PUNCT
ejde-395	56	25	1.2	1.2	NUM
ejde-395	56	26	)	)	PUNCT
ejde-395	56	27	,	,	PUNCT
ejde-395	56	28	and	and	CCONJ
ejde-395	56	29	obtained	obtain	VERB
ejde-395	56	30	the	the	DET
ejde-395	56	31	following	following	ADJ
ejde-395	56	32	result	result	NOUN
ejde-395	56	33	.	.	PUNCT
ejde-395	57	1	theorem	theorem	VERB
ejde-395	57	2	1.3	1.3	NUM
ejde-395	57	3	(	(	PUNCT
ejde-395	57	4	[	[	X
ejde-395	57	5	20	20	NUM
ejde-395	57	6	,	,	PUNCT
ejde-395	57	7	theorem	theorem	VERB
ejde-395	57	8	1.1	1.1	NUM
ejde-395	57	9	]	]	PUNCT
ejde-395	57	10	)	)	PUNCT
ejde-395	57	11	.	.	PUNCT
ejde-395	58	1	let	let	AUX
ejde-395	58	2	f(z	f(z	PROPN
ejde-395	58	3	)	)	PUNCT
ejde-395	58	4	be	be	AUX
ejde-395	58	5	a	a	DET
ejde-395	58	6	transcendental	transcendental	ADJ
ejde-395	58	7	meromorphic	meromorphic	ADJ
ejde-395	58	8	solution	solution	NOUN
ejde-395	58	9	with	with	ADP
ejde-395	58	10	zero	zero	NUM
ejde-395	58	11	order	order	NOUN
ejde-395	58	12	of	of	ADP
ejde-395	58	13	equation	equation	NOUN
ejde-395	58	14	(	(	PUNCT
ejde-395	58	15	1.6	1.6	NUM
ejde-395	58	16	)	)	PUNCT
ejde-395	58	17	,	,	PUNCT
ejde-395	58	18	and	and	CCONJ
ejde-395	58	19	let	let	VERB
ejde-395	58	20	a	a	DET
ejde-395	58	21	,	,	PUNCT
ejde-395	58	22	b	b	NOUN
ejde-395	58	23	,	,	PUNCT
ejde-395	58	24	c	c	AUX
ejde-395	58	25	be	be	AUX
ejde-395	58	26	constants	constant	NOUN
ejde-395	58	27	such	such	ADJ
ejde-395	58	28	that	that	SCONJ
ejde-395	58	29	a	a	PRON
ejde-395	58	30	,	,	PUNCT
ejde-395	58	31	b	b	NOUN
ejde-395	58	32	can	can	AUX
ejde-395	58	33	not	not	PART
ejde-395	58	34	vanish	vanish	VERB
ejde-395	58	35	simultaneously	simultaneously	ADV
ejde-395	58	36	.	.	PUNCT
ejde-395	59	1	then	then	ADV
ejde-395	59	2	(	(	PUNCT
ejde-395	59	3	i	i	NOUN
ejde-395	59	4	)	)	PUNCT
ejde-395	59	5	f(z	f(z	PROPN
ejde-395	59	6	)	)	PUNCT
ejde-395	59	7	has	have	VERB
ejde-395	59	8	infinitely	infinitely	ADV
ejde-395	59	9	many	many	ADJ
ejde-395	59	10	poles	pole	NOUN
ejde-395	59	11	.	.	PUNCT
ejde-395	60	1	(	(	PUNCT
ejde-395	60	2	ii	ii	NOUN
ejde-395	60	3	)	)	PUNCT
ejde-395	60	4	if	if	SCONJ
ejde-395	60	5	a	a	PRON
ejde-395	60	6	6=	6=	NUM
ejde-395	60	7	0	0	NUM
ejde-395	60	8	and	and	CCONJ
ejde-395	60	9	any	any	DET
ejde-395	60	10	d	d	PROPN
ejde-395	60	11	∈	∈	PROPN
ejde-395	60	12	c	c	NOUN
ejde-395	60	13	,	,	PUNCT
ejde-395	60	14	then	then	ADV
ejde-395	60	15	f(z)−	f(z)−	PROPN
ejde-395	60	16	d	d	PROPN
ejde-395	60	17	has	have	VERB
ejde-395	60	18	infinitely	infinitely	ADV
ejde-395	60	19	many	many	ADJ
ejde-395	60	20	zeros	zero	NOUN
ejde-395	60	21	.	.	PUNCT
ejde-395	61	1	(	(	PUNCT
ejde-395	61	2	iii	iii	X
ejde-395	61	3	)	)	PUNCT
ejde-395	61	4	if	if	SCONJ
ejde-395	61	5	a	a	DET
ejde-395	61	6	=	=	SYM
ejde-395	61	7	0	0	NUM
ejde-395	61	8	and	and	CCONJ
ejde-395	61	9	f(z	f(z	PROPN
ejde-395	61	10	)	)	PUNCT
ejde-395	61	11	takes	take	VERB
ejde-395	61	12	a	a	DET
ejde-395	61	13	finite	finite	ADJ
ejde-395	61	14	value	value	NOUN
ejde-395	61	15	a	a	DET
ejde-395	61	16	finitely	finitely	ADV
ejde-395	61	17	often	often	ADV
ejde-395	61	18	,	,	PUNCT
ejde-395	61	19	then	then	ADV
ejde-395	61	20	a	a	PRON
ejde-395	61	21	is	be	AUX
ejde-395	61	22	a	a	DET
ejde-395	61	23	solution	solution	NOUN
ejde-395	61	24	of	of	ADP
ejde-395	61	25	2z2	2z2	NUM
ejde-395	61	26	−	−	NOUN
ejde-395	61	27	cz	cz	NOUN
ejde-395	61	28	−	−	PROPN
ejde-395	61	29	b	b	NOUN
ejde-395	61	30	=	=	NOUN
ejde-395	61	31	0	0	PROPN
ejde-395	61	32	.	.	PUNCT
ejde-395	62	1	in	in	ADP
ejde-395	62	2	2018	2018	NUM
ejde-395	62	3	,	,	PUNCT
ejde-395	62	4	liu	liu	PROPN
ejde-395	62	5	-	-	PUNCT
ejde-395	62	6	zhang	zhang	PROPN
ejde-395	63	1	[	[	X
ejde-395	63	2	17	17	NUM
ejde-395	63	3	]	]	PUNCT
ejde-395	63	4	studied	study	VERB
ejde-395	63	5	the	the	DET
ejde-395	63	6	difference	difference	NOUN
ejde-395	63	7	equation	equation	NOUN
ejde-395	63	8	y	y	PROPN
ejde-395	63	9	(	(	PUNCT
ejde-395	63	10	ωz	ωz	NOUN
ejde-395	63	11	)	)	PUNCT
ejde-395	64	1	+	+	CCONJ
ejde-395	64	2	y	y	PROPN
ejde-395	64	3	(	(	PUNCT
ejde-395	64	4	z	z	NOUN
ejde-395	64	5	)	)	PUNCT
ejde-395	65	1	+	+	CCONJ
ejde-395	65	2	y	y	PROPN
ejde-395	65	3	(	(	PUNCT
ejde-395	65	4	z	z	PROPN
ejde-395	65	5	ω	ω	PROPN
ejde-395	65	6	)	)	PUNCT
ejde-395	66	1	=	=	SYM
ejde-395	66	2	v	v	X
ejde-395	66	3	(	(	PUNCT
ejde-395	66	4	z	z	NOUN
ejde-395	66	5	)	)	PUNCT
ejde-395	66	6	y	y	PROPN
ejde-395	66	7	(	(	PUNCT
ejde-395	66	8	z	z	NOUN
ejde-395	66	9	)	)	PUNCT
ejde-395	67	1	+	+	CCONJ
ejde-395	67	2	c	c	X
ejde-395	67	3	,	,	PUNCT
ejde-395	67	4	(	(	PUNCT
ejde-395	67	5	1.7	1.7	NUM
ejde-395	67	6	)	)	PUNCT
ejde-395	67	7	which	which	PRON
ejde-395	67	8	is	be	AUX
ejde-395	67	9	a	a	DET
ejde-395	67	10	q	q	ADJ
ejde-395	67	11	-	-	PUNCT
ejde-395	67	12	difference	difference	NOUN
ejde-395	67	13	analogues	analogue	NOUN
ejde-395	67	14	of	of	ADP
ejde-395	67	15	(	(	PUNCT
ejde-395	67	16	1.3	1.3	NUM
ejde-395	67	17	)	)	PUNCT
ejde-395	67	18	,	,	PUNCT
ejde-395	67	19	and	and	CCONJ
ejde-395	67	20	obtained	obtain	VERB
ejde-395	67	21	the	the	DET
ejde-395	67	22	following	following	ADJ
ejde-395	67	23	result	result	NOUN
ejde-395	67	24	.	.	PUNCT
ejde-395	68	1	theorem	theorem	VERB
ejde-395	68	2	1.4	1.4	NUM
ejde-395	68	3	(	(	PUNCT
ejde-395	68	4	[	[	NOUN
ejde-395	68	5	17	17	NUM
ejde-395	68	6	,	,	PUNCT
ejde-395	68	7	thereom	thereom	NOUN
ejde-395	68	8	1.2	1.2	NUM
ejde-395	68	9	]	]	PUNCT
ejde-395	68	10	)	)	PUNCT
ejde-395	68	11	.	.	PUNCT
ejde-395	69	1	let	let	VERB
ejde-395	69	2	c	c	NOUN
ejde-395	69	3	∈	∈	VERB
ejde-395	69	4	c\{0	c\{0	PROPN
ejde-395	69	5	}	}	PUNCT
ejde-395	69	6	,	,	PUNCT
ejde-395	69	7	|ω|	|ω|	ADP
ejde-395	69	8	6=	6=	ADP
ejde-395	69	9	1	1	NUM
ejde-395	69	10	,	,	PUNCT
ejde-395	69	11	and	and	CCONJ
ejde-395	69	12	v	v	X
ejde-395	69	13	(	(	PUNCT
ejde-395	69	14	z	z	NOUN
ejde-395	69	15	)	)	PUNCT
ejde-395	69	16	=	=	SYM
ejde-395	69	17	x(z	x(z	PROPN
ejde-395	69	18	)	)	PUNCT
ejde-395	69	19	b(z	b(z	NOUN
ejde-395	69	20	)	)	PUNCT
ejde-395	69	21	be	be	VERB
ejde-395	69	22	an	an	DET
ejde-395	69	23	irreducible	irreducible	ADJ
ejde-395	69	24	rational	rational	ADJ
ejde-395	69	25	function	function	NOUN
ejde-395	69	26	,	,	PUNCT
ejde-395	69	27	where	where	SCONJ
ejde-395	69	28	x(z	x(z	PROPN
ejde-395	69	29	)	)	PUNCT
ejde-395	69	30	and	and	CCONJ
ejde-395	69	31	b(z	b(z	NOUN
ejde-395	69	32	)	)	PUNCT
ejde-395	69	33	are	be	AUX
ejde-395	69	34	polynomials	polynomial	NOUN
ejde-395	69	35	with	with	ADP
ejde-395	69	36	degx(z	degx(z	NOUN
ejde-395	69	37	)	)	PUNCT
ejde-395	69	38	=	=	SYM
ejde-395	69	39	x	x	PUNCT
ejde-395	69	40	and	and	CCONJ
ejde-395	69	41	degb(z	degb(z	NOUN
ejde-395	69	42	)	)	PUNCT
ejde-395	69	43	=	=	SYM
ejde-395	69	44	b.	b.	PROPN
ejde-395	69	45	(	(	PUNCT
ejde-395	69	46	i	i	NOUN
ejde-395	69	47	)	)	PUNCT
ejde-395	69	48	suppose	suppose	VERB
ejde-395	69	49	that	that	SCONJ
ejde-395	69	50	x	x	PROPN
ejde-395	69	51	≥	≥	NUM
ejde-395	69	52	b	b	NUM
ejde-395	69	53	and	and	CCONJ
ejde-395	69	54	x−b	x−b	NOUN
ejde-395	69	55	is	be	AUX
ejde-395	69	56	zero	zero	NUM
ejde-395	69	57	or	or	CCONJ
ejde-395	69	58	an	an	DET
ejde-395	69	59	even	even	ADJ
ejde-395	69	60	number	number	NOUN
ejde-395	69	61	.	.	PUNCT
ejde-395	70	1	if	if	SCONJ
ejde-395	70	2	(	(	PUNCT
ejde-395	70	3	1.7	1.7	NUM
ejde-395	70	4	)	)	PUNCT
ejde-395	70	5	has	have	VERB
ejde-395	70	6	an	an	DET
ejde-395	70	7	irreducible	irreducible	ADJ
ejde-395	70	8	rational	rational	ADJ
ejde-395	70	9	solution	solution	NOUN
ejde-395	70	10	y	y	PROPN
ejde-395	70	11	(	(	PUNCT
ejde-395	70	12	z	z	NOUN
ejde-395	70	13	)	)	PUNCT
ejde-395	70	14	=	=	SYM
ejde-395	70	15	i(z	i(z	NOUN
ejde-395	70	16	)	)	PUNCT
ejde-395	70	17	j(z	j(z	PROPN
ejde-395	70	18	)	)	PUNCT
ejde-395	70	19	,	,	PUNCT
ejde-395	70	20	where	where	SCONJ
ejde-395	70	21	i(z	i(z	NOUN
ejde-395	70	22	)	)	PUNCT
ejde-395	70	23	and	and	CCONJ
ejde-395	70	24	j(z	j(z	PROPN
ejde-395	70	25	)	)	PUNCT
ejde-395	70	26	are	be	AUX
ejde-395	70	27	polynomials	polynomial	NOUN
ejde-395	70	28	with	with	ADP
ejde-395	70	29	deg	deg	PROPN
ejde-395	70	30	i(z	i(z	NOUN
ejde-395	70	31	)	)	PUNCT
ejde-395	71	1	=	=	SYM
ejde-395	72	1	i	i	PRON
ejde-395	72	2	and	and	CCONJ
ejde-395	72	3	deg	deg	VERB
ejde-395	72	4	j(z	j(z	PROPN
ejde-395	72	5	)	)	PUNCT
ejde-395	73	1	=	=	SYM
ejde-395	73	2	j	j	PROPN
ejde-395	73	3	,	,	PUNCT
ejde-395	73	4	then	then	ADV
ejde-395	73	5	i−	i−	PROPN
ejde-395	73	6	j	j	PROPN
ejde-395	73	7	=	=	SYM
ejde-395	73	8	x−b	x−b	PROPN
ejde-395	73	9	2	2	NUM
ejde-395	73	10	.	.	PUNCT
ejde-395	73	11	(	(	PUNCT
ejde-395	73	12	ii	ii	NOUN
ejde-395	73	13	)	)	PUNCT
ejde-395	73	14	suppose	suppose	VERB
ejde-395	73	15	that	that	SCONJ
ejde-395	73	16	x	x	PUNCT
ejde-395	73	17	<	<	X
ejde-395	73	18	b.	b.	PROPN
ejde-395	73	19	if	if	SCONJ
ejde-395	73	20	(	(	PUNCT
ejde-395	73	21	1.7	1.7	NUM
ejde-395	73	22	)	)	PUNCT
ejde-395	73	23	has	have	VERB
ejde-395	73	24	an	an	DET
ejde-395	73	25	irreducible	irreducible	ADJ
ejde-395	73	26	rational	rational	ADJ
ejde-395	73	27	solution	solution	NOUN
ejde-395	73	28	y	y	PROPN
ejde-395	73	29	(	(	PUNCT
ejde-395	73	30	z	z	NOUN
ejde-395	73	31	)	)	PUNCT
ejde-395	73	32	=	=	SYM
ejde-395	73	33	i(z	i(z	NOUN
ejde-395	73	34	)	)	PUNCT
ejde-395	73	35	j(z	j(z	PROPN
ejde-395	73	36	)	)	PUNCT
ejde-395	73	37	,	,	PUNCT
ejde-395	73	38	then	then	ADV
ejde-395	73	39	y	y	PROPN
ejde-395	73	40	(	(	PUNCT
ejde-395	73	41	z	z	NOUN
ejde-395	73	42	)	)	PUNCT
ejde-395	73	43	satisfies	satisfy	VERB
ejde-395	73	44	one	one	NUM
ejde-395	73	45	of	of	ADP
ejde-395	73	46	the	the	DET
ejde-395	73	47	following	follow	VERB
ejde-395	73	48	two	two	NUM
ejde-395	73	49	cases	case	NOUN
ejde-395	73	50	:	:	PUNCT
ejde-395	73	51	(	(	PUNCT
ejde-395	73	52	1	1	X
ejde-395	73	53	)	)	PUNCT
ejde-395	73	54	y	y	PROPN
ejde-395	73	55	(	(	PUNCT
ejde-395	73	56	z	z	NOUN
ejde-395	73	57	)	)	PUNCT
ejde-395	73	58	=	=	SYM
ejde-395	73	59	i(z	i(z	NOUN
ejde-395	73	60	)	)	PUNCT
ejde-395	73	61	j(z	j(z	PROPN
ejde-395	73	62	)	)	PUNCT
ejde-395	73	63	=	=	PUNCT
ejde-395	74	1	c	c	NOUN
ejde-395	74	2	3	3	NUM
ejde-395	74	3	+	+	NUM
ejde-395	74	4	t	t	PROPN
ejde-395	74	5	(	(	PUNCT
ejde-395	74	6	z	z	NOUN
ejde-395	74	7	)	)	PUNCT
ejde-395	74	8	d(z	d(z	PROPN
ejde-395	74	9	)	)	PUNCT
ejde-395	74	10	,	,	PUNCT
ejde-395	74	11	where	where	SCONJ
ejde-395	74	12	t	t	PROPN
ejde-395	74	13	(	(	PUNCT
ejde-395	74	14	z	z	NOUN
ejde-395	74	15	)	)	PUNCT
ejde-395	74	16	and	and	CCONJ
ejde-395	74	17	d(z	d(z	NOUN
ejde-395	74	18	)	)	PUNCT
ejde-395	74	19	are	be	AUX
ejde-395	74	20	polynomials	polynomial	NOUN
ejde-395	74	21	with	with	ADP
ejde-395	74	22	deg	deg	PROPN
ejde-395	74	23	t	t	PROPN
ejde-395	74	24	(	(	PUNCT
ejde-395	74	25	z	z	NOUN
ejde-395	74	26	)	)	PUNCT
ejde-395	74	27	=	=	SYM
ejde-395	74	28	t	t	PROPN
ejde-395	74	29	and	and	CCONJ
ejde-395	74	30	degd(z	degd(z	PROPN
ejde-395	74	31	)	)	PUNCT
ejde-395	75	1	=	=	SYM
ejde-395	75	2	d	d	NOUN
ejde-395	75	3	,	,	PUNCT
ejde-395	75	4	and	and	CCONJ
ejde-395	75	5	b−	b−	NOUN
ejde-395	75	6	x	x	PUNCT
ejde-395	76	1	=	=	PUNCT
ejde-395	76	2	d−	d−	PROPN
ejde-395	76	3	t.	t.	PROPN
ejde-395	76	4	(	(	PUNCT
ejde-395	76	5	2	2	NUM
ejde-395	76	6	)	)	PUNCT
ejde-395	76	7	i−	i−	PROPN
ejde-395	76	8	j	j	PROPN
ejde-395	76	9	=	=	SYM
ejde-395	76	10	x−	x−	PROPN
ejde-395	76	11	b.	b.	PROPN
ejde-395	76	12	motivated	motivate	VERB
ejde-395	76	13	by	by	ADP
ejde-395	76	14	the	the	DET
ejde-395	76	15	idea	idea	NOUN
ejde-395	77	1	[	[	X
ejde-395	77	2	17	17	NUM
ejde-395	77	3	]	]	PUNCT
ejde-395	77	4	and	and	CCONJ
ejde-395	77	5	[	[	X
ejde-395	77	6	20	20	NUM
ejde-395	77	7	,	,	PUNCT
ejde-395	77	8	30	30	NUM
ejde-395	77	9	]	]	PUNCT
ejde-395	77	10	,	,	PUNCT
ejde-395	77	11	we	we	PRON
ejde-395	77	12	investigate	investigate	VERB
ejde-395	77	13	some	some	DET
ejde-395	77	14	properties	property	NOUN
ejde-395	77	15	of	of	ADP
ejde-395	77	16	meromorphic	meromorphic	ADJ
ejde-395	77	17	solutions	solution	NOUN
ejde-395	77	18	of	of	ADP
ejde-395	77	19	the	the	DET
ejde-395	77	20	following	follow	VERB
ejde-395	77	21	two	two	NUM
ejde-395	77	22	equations	equation	NOUN
ejde-395	77	23	f(qz)f	f(qz)f	VERB
ejde-395	77	24	(	(	PUNCT
ejde-395	77	25	z	z	NOUN
ejde-395	77	26	q	q	NOUN
ejde-395	77	27	)	)	PUNCT
ejde-395	77	28	f(z)(f(z)−	f(z)(f(z)−	PROPN
ejde-395	77	29	1	1	NUM
ejde-395	77	30	)	)	PUNCT
ejde-395	77	31	=	=	SYM
ejde-395	77	32	µ	µ	X
ejde-395	77	33	,	,	PUNCT
ejde-395	77	34	(	(	PUNCT
ejde-395	77	35	1.8	1.8	NUM
ejde-395	77	36	)	)	PUNCT
ejde-395	77	37	f(qz)f	f(qz)f	PROPN
ejde-395	77	38	(	(	PUNCT
ejde-395	77	39	z	z	NOUN
ejde-395	77	40	q	q	NOUN
ejde-395	77	41	)	)	PUNCT
ejde-395	77	42	(	(	PUNCT
ejde-395	77	43	f(z)−	f(z)−	PROPN
ejde-395	77	44	1)2	1)2	NUM
ejde-395	77	45	=	=	SYM
ejde-395	77	46	(	(	PUNCT
ejde-395	77	47	f(z)−	f(z)−	PROPN
ejde-395	77	48	λ)2	λ)2	PROPN
ejde-395	77	49	,	,	PUNCT
ejde-395	77	50	(	(	PUNCT
ejde-395	77	51	1.9	1.9	NUM
ejde-395	77	52	)	)	PUNCT
ejde-395	77	53	which	which	PRON
ejde-395	77	54	can	can	AUX
ejde-395	77	55	be	be	AUX
ejde-395	77	56	seen	see	VERB
ejde-395	77	57	as	as	ADP
ejde-395	77	58	q	q	NOUN
ejde-395	77	59	-	-	PUNCT
ejde-395	77	60	difference	difference	NOUN
ejde-395	77	61	painlevé	painlevé	NOUN
ejde-395	77	62	iii	iii	NUM
ejde-395	77	63	equations	equation	NOUN
ejde-395	77	64	.	.	PUNCT
ejde-395	78	1	before	before	ADP
ejde-395	78	2	stating	state	VERB
ejde-395	78	3	our	our	PRON
ejde-395	78	4	main	main	ADJ
ejde-395	78	5	theorems	theorem	NOUN
ejde-395	78	6	,	,	PUNCT
ejde-395	78	7	let	let	VERB
ejde-395	78	8	us	we	PRON
ejde-395	78	9	introduce	introduce	VERB
ejde-395	78	10	some	some	DET
ejde-395	78	11	basic	basic	ADJ
ejde-395	78	12	notation	notation	NOUN
ejde-395	78	13	in	in	ADP
ejde-395	78	14	the	the	DET
ejde-395	78	15	theory	theory	NOUN
ejde-395	78	16	of	of	ADP
ejde-395	78	17	nevanlinna	nevanlinna	NOUN
ejde-395	78	18	value	value	NOUN
ejde-395	78	19	distribution	distribution	NOUN
ejde-395	78	20	(	(	PUNCT
ejde-395	78	21	see	see	VERB
ejde-395	78	22	hayman	hayman	PROPN
ejde-395	79	1	[	[	X
ejde-395	79	2	13	13	NUM
ejde-395	79	3	]	]	PUNCT
ejde-395	79	4	,	,	PUNCT
ejde-395	79	5	yang	yang	PROPN
ejde-395	80	1	[	[	X
ejde-395	80	2	27	27	NUM
ejde-395	80	3	]	]	PUNCT
ejde-395	80	4	and	and	CCONJ
ejde-395	80	5	yi	yi	PROPN
ejde-395	80	6	and	and	CCONJ
ejde-395	80	7	yang	yang	PROPN
ejde-395	81	1	[	[	X
ejde-395	81	2	28	28	NUM
ejde-395	81	3	]	]	NUM
ejde-395	81	4	)	)	PUNCT
ejde-395	81	5	.	.	PUNCT
ejde-395	82	1	we	we	PRON
ejde-395	82	2	denote	denote	VERB
ejde-395	82	3	σ(f	σ(f	PROPN
ejde-395	82	4	)	)	PUNCT
ejde-395	82	5	,	,	PUNCT
ejde-395	82	6	λ(f	λ(f	PROPN
ejde-395	82	7	)	)	PUNCT
ejde-395	82	8	and	and	CCONJ
ejde-395	82	9	λ	λ	NOUN
ejde-395	82	10	(	(	PUNCT
ejde-395	82	11	1	1	NUM
ejde-395	82	12	f	f	NOUN
ejde-395	82	13	)	)	PUNCT
ejde-395	82	14	by	by	ADP
ejde-395	82	15	the	the	DET
ejde-395	82	16	order	order	NOUN
ejde-395	82	17	,	,	PUNCT
ejde-395	82	18	the	the	DET
ejde-395	82	19	exponent	exponent	NOUN
ejde-395	82	20	of	of	ADP
ejde-395	82	21	convergence	convergence	NOUN
ejde-395	82	22	of	of	ADP
ejde-395	82	23	zeros	zero	NOUN
ejde-395	82	24	and	and	CCONJ
ejde-395	82	25	the	the	DET
ejde-395	82	26	exponent	exponent	NOUN
ejde-395	82	27	of	of	ADP
ejde-395	82	28	convergence	convergence	NOUN
ejde-395	82	29	of	of	ADP
ejde-395	82	30	poles	pole	NOUN
ejde-395	82	31	of	of	ADP
ejde-395	82	32	meromorphic	meromorphic	ADJ
ejde-395	82	33	function	function	NOUN
ejde-395	82	34	f(z	f(z	PROPN
ejde-395	82	35	)	)	PUNCT
ejde-395	82	36	,	,	PUNCT
ejde-395	82	37	respectively	respectively	ADV
ejde-395	82	38	,	,	PUNCT
ejde-395	82	39	and	and	CCONJ
ejde-395	82	40	τ(f	τ(f	PROPN
ejde-395	82	41	)	)	PUNCT
ejde-395	82	42	by	by	ADP
ejde-395	82	43	the	the	DET
ejde-395	82	44	exponent	exponent	NOUN
ejde-395	82	45	of	of	ADP
ejde-395	82	46	convergence	convergence	NOUN
ejde-395	82	47	of	of	ADP
ejde-395	82	48	fixed	fix	VERB
ejde-395	82	49	points	point	NOUN
ejde-395	82	50	of	of	ADP
ejde-395	82	51	f(z	f(z	PROPN
ejde-395	82	52	)	)	PUNCT
ejde-395	82	53	,	,	PUNCT
ejde-395	82	54	which	which	PRON
ejde-395	82	55	is	be	AUX
ejde-395	82	56	defined	define	VERB
ejde-395	82	57	as	as	ADP
ejde-395	82	58	τ(f	τ(f	NOUN
ejde-395	82	59	)	)	PUNCT
ejde-395	82	60	=	=	SYM
ejde-395	82	61	lim	lim	PROPN
ejde-395	82	62	sup	sup	NOUN
ejde-395	82	63	r→+∞	r→+∞	PROPN
ejde-395	82	64	logn(r	logn(r	PROPN
ejde-395	82	65	,	,	PUNCT
ejde-395	82	66	1	1	NUM
ejde-395	82	67	f(z)−z	f(z)−z	PROPN
ejde-395	82	68	)	)	PUNCT
ejde-395	82	69	log	log	NOUN
ejde-395	82	70	r	r	NOUN
ejde-395	82	71	.	.	PUNCT
ejde-395	83	1	in	in	ADP
ejde-395	83	2	addition	addition	NOUN
ejde-395	83	3	,	,	PUNCT
ejde-395	83	4	let	let	VERB
ejde-395	83	5	s(r	s(r	PROPN
ejde-395	83	6	,	,	PUNCT
ejde-395	83	7	f	f	X
ejde-395	83	8	)	)	PUNCT
ejde-395	83	9	be	be	VERB
ejde-395	83	10	any	any	DET
ejde-395	83	11	quantity	quantity	NOUN
ejde-395	83	12	satisfying	satisfy	VERB
ejde-395	83	13	s(r	s(r	PROPN
ejde-395	83	14	,	,	PUNCT
ejde-395	83	15	f	f	X
ejde-395	83	16	)	)	PUNCT
ejde-395	84	1	=	=	NOUN
ejde-395	84	2	o(t	o(t	NOUN
ejde-395	84	3	(	(	PUNCT
ejde-395	84	4	r	r	NOUN
ejde-395	84	5	,	,	PUNCT
ejde-395	84	6	f	f	NOUN
ejde-395	84	7	)	)	PUNCT
ejde-395	84	8	)	)	PUNCT
ejde-395	84	9	for	for	ADP
ejde-395	84	10	all	all	DET
ejde-395	84	11	r	r	NOUN
ejde-395	84	12	on	on	ADP
ejde-395	84	13	a	a	DET
ejde-395	84	14	set	set	ADJ
ejde-395	84	15	f	f	NOUN
ejde-395	84	16	of	of	ADP
ejde-395	84	17	logarithmic	logarithmic	ADJ
ejde-395	84	18	density	density	NOUN
ejde-395	84	19	1	1	NUM
ejde-395	84	20	,	,	PUNCT
ejde-395	84	21	the	the	DET
ejde-395	84	22	logarithmic	logarithmic	ADJ
ejde-395	84	23	density	density	NOUN
ejde-395	84	24	of	of	ADP
ejde-395	84	25	a	a	DET
ejde-395	84	26	set	set	NOUN
ejde-395	84	27	f	f	X
ejde-395	84	28	is	be	AUX
ejde-395	84	29	defined	define	VERB
ejde-395	84	30	as	as	ADP
ejde-395	84	31	lim	lim	PROPN
ejde-395	84	32	sup	sup	PROPN
ejde-395	84	33	r→∞	r→∞	NUM
ejde-395	84	34	1	1	NUM
ejde-395	84	35	log	log	NOUN
ejde-395	84	36	r	r	NOUN
ejde-395	84	37	∫	∫	NOUN
ejde-395	85	1	[	[	X
ejde-395	85	2	1,r]∩f	1,r]∩f	NUM
ejde-395	85	3	1	1	NUM
ejde-395	85	4	t	t	NOUN
ejde-395	85	5	dt	dt	PROPN
ejde-395	85	6	.	.	PROPN
ejde-395	85	7	4	4	NUM
ejde-395	85	8	h.	h.	PROPN
ejde-395	85	9	y.	y.	PROPN
ejde-395	85	10	xu	xu	PROPN
ejde-395	85	11	,	,	PUNCT
ejde-395	85	12	j.	j.	PROPN
ejde-395	85	13	tu	tu	PROPN
ejde-395	85	14	ejde-2020/14	ejde-2020/14	VERB
ejde-395	85	15	our	our	PRON
ejde-395	85	16	main	main	ADJ
ejde-395	85	17	results	result	NOUN
ejde-395	85	18	in	in	ADP
ejde-395	85	19	this	this	DET
ejde-395	85	20	paper	paper	NOUN
ejde-395	85	21	are	be	AUX
ejde-395	85	22	the	the	DET
ejde-395	85	23	following	following	NOUN
ejde-395	85	24	.	.	PUNCT
ejde-395	86	1	theorem	theorem	VERB
ejde-395	86	2	1.5	1.5	NUM
ejde-395	86	3	.	.	PUNCT
ejde-395	87	1	let	let	VERB
ejde-395	87	2	q(6=	q(6=	ADV
ejde-395	87	3	0	0	NUM
ejde-395	87	4	)	)	PUNCT
ejde-395	87	5	∈	∈	PROPN
ejde-395	87	6	c	c	X
ejde-395	87	7	,	,	PUNCT
ejde-395	87	8	|q|	|q|	VERB
ejde-395	87	9	6=	6=	ADP
ejde-395	87	10	1	1	NUM
ejde-395	87	11	,	,	PUNCT
ejde-395	87	12	and	and	CCONJ
ejde-395	87	13	µ(6=	µ(6=	PROPN
ejde-395	87	14	0	0	NUM
ejde-395	87	15	)	)	PUNCT
ejde-395	87	16	∈	∈	PROPN
ejde-395	87	17	c	c	NOUN
ejde-395	87	18	,	,	PUNCT
ejde-395	87	19	and	and	CCONJ
ejde-395	87	20	suppose	suppose	VERB
ejde-395	87	21	that	that	SCONJ
ejde-395	87	22	f(z	f(z	PROPN
ejde-395	87	23	)	)	PUNCT
ejde-395	87	24	is	be	AUX
ejde-395	87	25	a	a	DET
ejde-395	87	26	nonconstant	nonconstant	ADJ
ejde-395	87	27	rational	rational	ADJ
ejde-395	87	28	solution	solution	NOUN
ejde-395	87	29	of	of	ADP
ejde-395	87	30	equation	equation	NOUN
ejde-395	87	31	(	(	PUNCT
ejde-395	87	32	1.8	1.8	NUM
ejde-395	87	33	)	)	PUNCT
ejde-395	87	34	.	.	PUNCT
ejde-395	88	1	then	then	ADV
ejde-395	88	2	f(z	f(z	PROPN
ejde-395	88	3	)	)	PUNCT
ejde-395	88	4	can	can	AUX
ejde-395	88	5	be	be	AUX
ejde-395	88	6	represented	represent	VERB
ejde-395	88	7	in	in	ADP
ejde-395	88	8	the	the	DET
ejde-395	88	9	form	form	NOUN
ejde-395	88	10	f(z	f(z	PROPN
ejde-395	88	11	)	)	PUNCT
ejde-395	89	1	=	=	PUNCT
ejde-395	89	2	a(zn	a(zn	PROPN
ejde-395	89	3	+	+	CCONJ
ejde-395	89	4	b)2	b)2	PROPN
ejde-395	89	5	(	(	PUNCT
ejde-395	89	6	zn	zn	PROPN
ejde-395	89	7	+	+	NUM
ejde-395	89	8	q−nb)(zn	q−nb)(zn	PROPN
ejde-395	89	9	+	+	CCONJ
ejde-395	89	10	qnb	qnb	NOUN
ejde-395	89	11	)	)	PUNCT
ejde-395	89	12	,	,	PUNCT
ejde-395	89	13	and	and	CCONJ
ejde-395	89	14	a	a	PRON
ejde-395	89	15	=	=	X
ejde-395	89	16	q2n	q2n	PROPN
ejde-395	89	17	+	+	CCONJ
ejde-395	89	18	qn	qn	PROPN
ejde-395	89	19	+	+	NOUN
ejde-395	89	20	1	1	NUM
ejde-395	89	21	(	(	PUNCT
ejde-395	89	22	qn	qn	NOUN
ejde-395	89	23	+	+	X
ejde-395	89	24	1)2	1)2	NUM
ejde-395	89	25	,	,	PUNCT
ejde-395	89	26	µ	µ	NOUN
ejde-395	89	27	=	=	SYM
ejde-395	89	28	a3(a−	a3(a−	ADP
ejde-395	89	29	1	1	NUM
ejde-395	89	30	)	)	PUNCT
ejde-395	89	31	=	=	NOUN
ejde-395	90	1	−q	−q	ADJ
ejde-395	90	2	n(q2n	n(q2n	ADJ
ejde-395	90	3	+	+	SYM
ejde-395	90	4	qn	qn	PROPN
ejde-395	90	5	+	+	PROPN
ejde-395	90	6	1)3	1)3	PROPN
ejde-395	90	7	(	(	PUNCT
ejde-395	90	8	qn	qn	NOUN
ejde-395	90	9	+	+	PROPN
ejde-395	90	10	1)8	1)8	NUM
ejde-395	90	11	,	,	PUNCT
ejde-395	90	12	where	where	SCONJ
ejde-395	90	13	b	b	NOUN
ejde-395	90	14	is	be	AUX
ejde-395	90	15	an	an	DET
ejde-395	90	16	any	any	DET
ejde-395	90	17	nonzero	nonzero	NOUN
ejde-395	90	18	constant	constant	ADJ
ejde-395	90	19	and	and	CCONJ
ejde-395	90	20	n	n	PRON
ejde-395	90	21	∈	∈	PROPN
ejde-395	90	22	n+	n+	PROPN
ejde-395	90	23	;	;	PUNCT
ejde-395	90	24	example	example	NOUN
ejde-395	90	25	1.6	1.6	NUM
ejde-395	90	26	.	.	PUNCT
ejde-395	91	1	let	let	VERB
ejde-395	91	2	f(z	f(z	NOUN
ejde-395	91	3	)	)	PUNCT
ejde-395	91	4	=	=	PUNCT
ejde-395	92	1	7(z	7(z	NUM
ejde-395	93	1	+	+	CCONJ
ejde-395	93	2	1)2	1)2	NUM
ejde-395	93	3	9(2z	9(2z	NUM
ejde-395	94	1	+	+	CCONJ
ejde-395	94	2	1	1	NUM
ejde-395	94	3	)	)	PUNCT
ejde-395	94	4	(	(	PUNCT
ejde-395	94	5	z	z	NOUN
ejde-395	94	6	2	2	NUM
ejde-395	94	7	+	+	NUM
ejde-395	94	8	1	1	NUM
ejde-395	94	9	)	)	PUNCT
ejde-395	94	10	,	,	PUNCT
ejde-395	94	11	then	then	ADV
ejde-395	94	12	f(z	f(z	PROPN
ejde-395	94	13	)	)	PUNCT
ejde-395	94	14	satisfies	satisfy	VERB
ejde-395	94	15	the	the	DET
ejde-395	94	16	equation	equation	NOUN
ejde-395	94	17	f(2z)f	f(2z)f	ADP
ejde-395	94	18	(	(	PUNCT
ejde-395	94	19	z	z	NOUN
ejde-395	94	20	2	2	NUM
ejde-395	94	21	)	)	PUNCT
ejde-395	94	22	f(z)(f(z)−	f(z)(f(z)−	PROPN
ejde-395	94	23	1	1	NUM
ejde-395	94	24	)	)	PUNCT
ejde-395	94	25	=	=	PRON
ejde-395	95	1	−2	−2	NOUN
ejde-395	95	2	73	73	NUM
ejde-395	95	3	94	94	NUM
ejde-395	95	4	.	.	PUNCT
ejde-395	96	1	this	this	DET
ejde-395	96	2	example	example	NOUN
ejde-395	96	3	shows	show	VERB
ejde-395	96	4	that	that	SCONJ
ejde-395	96	5	our	our	PRON
ejde-395	96	6	conclusion	conclusion	NOUN
ejde-395	96	7	about	about	ADP
ejde-395	96	8	the	the	DET
ejde-395	96	9	form	form	NOUN
ejde-395	96	10	of	of	ADP
ejde-395	96	11	rational	rational	ADJ
ejde-395	96	12	solutions	solution	NOUN
ejde-395	96	13	for	for	ADP
ejde-395	96	14	equation	equation	NOUN
ejde-395	96	15	(	(	PUNCT
ejde-395	96	16	1.8	1.8	NUM
ejde-395	96	17	)	)	PUNCT
ejde-395	96	18	is	be	AUX
ejde-395	96	19	sharp	sharp	ADJ
ejde-395	96	20	.	.	PUNCT
ejde-395	97	1	theorem	theorem	VERB
ejde-395	97	2	1.7	1.7	NUM
ejde-395	97	3	.	.	PUNCT
ejde-395	98	1	let	let	VERB
ejde-395	98	2	q	q	PROPN
ejde-395	98	3	∈	∈	PROPN
ejde-395	98	4	c	c	NOUN
ejde-395	98	5	−	−	NOUN
ejde-395	98	6	{	{	PUNCT
ejde-395	98	7	0	0	NUM
ejde-395	98	8	,	,	PUNCT
ejde-395	98	9	1	1	NUM
ejde-395	98	10	}	}	PUNCT
ejde-395	98	11	and	and	CCONJ
ejde-395	98	12	µ(6=	µ(6=	PROPN
ejde-395	98	13	0	0	NUM
ejde-395	98	14	)	)	PUNCT
ejde-395	98	15	∈	∈	PROPN
ejde-395	98	16	c	c	NOUN
ejde-395	98	17	,	,	PUNCT
ejde-395	98	18	and	and	CCONJ
ejde-395	98	19	suppose	suppose	VERB
ejde-395	98	20	that	that	SCONJ
ejde-395	98	21	f(z	f(z	PROPN
ejde-395	98	22	)	)	PUNCT
ejde-395	98	23	is	be	AUX
ejde-395	98	24	a	a	DET
ejde-395	98	25	transcendental	transcendental	ADJ
ejde-395	98	26	meromorphic	meromorphic	ADJ
ejde-395	98	27	solution	solution	NOUN
ejde-395	98	28	with	with	ADP
ejde-395	98	29	zero	zero	NUM
ejde-395	98	30	order	order	NOUN
ejde-395	98	31	of	of	ADP
ejde-395	98	32	equation	equation	NOUN
ejde-395	98	33	(	(	PUNCT
ejde-395	98	34	1.8	1.8	NUM
ejde-395	98	35	)	)	PUNCT
ejde-395	98	36	.	.	PUNCT
ejde-395	99	1	then	then	ADV
ejde-395	99	2	(	(	PUNCT
ejde-395	99	3	i	i	NOUN
ejde-395	99	4	)	)	PUNCT
ejde-395	99	5	f(ηz	f(ηz	PROPN
ejde-395	99	6	)	)	PUNCT
ejde-395	99	7	has	have	VERB
ejde-395	99	8	infinitely	infinitely	ADV
ejde-395	99	9	many	many	ADJ
ejde-395	99	10	fixed	fix	VERB
ejde-395	99	11	-	-	PUNCT
ejde-395	99	12	points	point	NOUN
ejde-395	99	13	and	and	CCONJ
ejde-395	99	14	τ(f(ηz	τ(f(ηz	NOUN
ejde-395	99	15	)	)	PUNCT
ejde-395	99	16	)	)	PUNCT
ejde-395	100	1	=	=	SYM
ejde-395	100	2	σ(f	σ(f	NOUN
ejde-395	100	3	)	)	PUNCT
ejde-395	100	4	for	for	ADP
ejde-395	100	5	any	any	DET
ejde-395	100	6	η	η	PROPN
ejde-395	100	7	∈	∈	PROPN
ejde-395	100	8	c−	c−	NOUN
ejde-395	100	9	{	{	PUNCT
ejde-395	100	10	0	0	NUM
ejde-395	100	11	,	,	PUNCT
ejde-395	100	12	1	1	NUM
ejde-395	100	13	}	}	PUNCT
ejde-395	100	14	;	;	PUNCT
ejde-395	100	15	(	(	PUNCT
ejde-395	100	16	ii	ii	NOUN
ejde-395	100	17	)	)	PUNCT
ejde-395	100	18	f(z	f(z	PROPN
ejde-395	100	19	)	)	PUNCT
ejde-395	100	20	has	have	VERB
ejde-395	100	21	infinitely	infinitely	ADV
ejde-395	100	22	many	many	ADJ
ejde-395	100	23	zeros	zero	NOUN
ejde-395	100	24	and	and	CCONJ
ejde-395	100	25	poles	pole	NOUN
ejde-395	100	26	,	,	PUNCT
ejde-395	100	27	and	and	CCONJ
ejde-395	100	28	∆qf	∆qf	NOUN
ejde-395	100	29	,	,	PUNCT
ejde-395	100	30	(	(	PUNCT
ejde-395	100	31	∆qf)/f	∆qf)/f	PROPN
ejde-395	100	32	have	have	AUX
ejde-395	100	33	infinitely	infinitely	ADV
ejde-395	100	34	many	many	ADJ
ejde-395	100	35	poles	pole	NOUN
ejde-395	100	36	,	,	PUNCT
ejde-395	100	37	and	and	CCONJ
ejde-395	100	38	λ(f	λ(f	ADJ
ejde-395	101	1	)	)	PUNCT
ejde-395	101	2	=	=	PUNCT
ejde-395	101	3	λ	λ	NOUN
ejde-395	101	4	(	(	PUNCT
ejde-395	101	5	1	1	NUM
ejde-395	101	6	f	f	NOUN
ejde-395	101	7	)	)	PUNCT
ejde-395	102	1	=	=	PUNCT
ejde-395	102	2	λ	λ	X
ejde-395	102	3	(	(	PUNCT
ejde-395	102	4	1	1	NUM
ejde-395	102	5	∆qf	∆qf	NOUN
ejde-395	102	6	)	)	PUNCT
ejde-395	103	1	=	=	PUNCT
ejde-395	103	2	λ	λ	X
ejde-395	103	3	(	(	PUNCT
ejde-395	103	4	1	1	NUM
ejde-395	103	5	(	(	PUNCT
ejde-395	103	6	∆qf)/f	∆qf)/f	PROPN
ejde-395	103	7	)	)	PUNCT
ejde-395	103	8	.	.	PUNCT
ejde-395	104	1	theorem	theorem	VERB
ejde-395	104	2	1.8	1.8	NUM
ejde-395	104	3	.	.	PUNCT
ejde-395	105	1	let	let	VERB
ejde-395	105	2	q	q	X
ejde-395	105	3	,	,	PUNCT
ejde-395	105	4	λ	λ	PROPN
ejde-395	105	5	∈	∈	PROPN
ejde-395	105	6	c	c	NOUN
ejde-395	105	7	−	−	NOUN
ejde-395	105	8	{	{	PUNCT
ejde-395	105	9	0	0	NUM
ejde-395	105	10	,	,	PUNCT
ejde-395	105	11	1	1	NUM
ejde-395	105	12	}	}	PUNCT
ejde-395	105	13	and	and	CCONJ
ejde-395	105	14	|q|	|q|	VERB
ejde-395	105	15	6=	6=	PRON
ejde-395	105	16	1	1	NUM
ejde-395	105	17	.	.	PUNCT
ejde-395	106	1	if	if	SCONJ
ejde-395	106	2	(	(	PUNCT
ejde-395	106	3	1.9	1.9	NUM
ejde-395	106	4	)	)	PUNCT
ejde-395	106	5	has	have	VERB
ejde-395	106	6	a	a	DET
ejde-395	106	7	nonconstant	nonconstant	ADJ
ejde-395	106	8	rational	rational	ADJ
ejde-395	106	9	solution	solution	NOUN
ejde-395	106	10	f(z	f(z	NOUN
ejde-395	106	11	)	)	PUNCT
ejde-395	106	12	=	=	SYM
ejde-395	106	13	r(z	r(z	NOUN
ejde-395	106	14	)	)	PUNCT
ejde-395	107	1	=	=	PUNCT
ejde-395	107	2	p	p	X
ejde-395	107	3	(	(	PUNCT
ejde-395	107	4	z	z	NOUN
ejde-395	107	5	)	)	PUNCT
ejde-395	107	6	q(z	q(z	PROPN
ejde-395	107	7	)	)	PUNCT
ejde-395	108	1	=	=	VERB
ejde-395	108	2	apz	apz	VERB
ejde-395	108	3	p	p	NOUN
ejde-395	109	1	+	+	CCONJ
ejde-395	109	2	ap−1z	ap−1z	PROPN
ejde-395	109	3	p−1	p−1	PROPN
ejde-395	109	4	+	+	CCONJ
ejde-395	109	5	·	·	PUNCT
ejde-395	109	6	·	·	PUNCT
ejde-395	109	7	·	·	PUNCT
ejde-395	109	8	+	+	CCONJ
ejde-395	109	9	a1z	a1z	PROPN
ejde-395	109	10	+	+	CCONJ
ejde-395	109	11	a0	a0	NOUN
ejde-395	109	12	btzt	btzt	NOUN
ejde-395	109	13	+	+	CCONJ
ejde-395	109	14	bt−1zt−1	bt−1zt−1	NOUN
ejde-395	109	15	+	+	CCONJ
ejde-395	109	16	·	·	PUNCT
ejde-395	109	17	·	·	PUNCT
ejde-395	109	18	·	·	PUNCT
ejde-395	109	19	+	+	CCONJ
ejde-395	109	20	b1z	b1z	X
ejde-395	109	21	+	+	NUM
ejde-395	109	22	b0	b0	NOUN
ejde-395	109	23	,	,	PUNCT
ejde-395	109	24	then	then	ADV
ejde-395	109	25	p	p	PROPN
ejde-395	109	26	=	=	PROPN
ejde-395	109	27	t	t	PROPN
ejde-395	109	28	and	and	CCONJ
ejde-395	109	29	λ	λ	PROPN
ejde-395	109	30	=	=	PROPN
ejde-395	109	31	a2	a2	PROPN
ejde-395	109	32	,	,	PUNCT
ejde-395	109	33	where	where	SCONJ
ejde-395	109	34	a	a	DET
ejde-395	109	35	=	=	SYM
ejde-395	109	36	r(∞	r(∞	NOUN
ejde-395	109	37	)	)	PUNCT
ejde-395	109	38	=	=	SYM
ejde-395	109	39	ap	ap	PROPN
ejde-395	109	40	/	/	SYM
ejde-395	109	41	bp	bp	PROPN
ejde-395	109	42	.	.	PROPN
ejde-395	109	43	example	example	NOUN
ejde-395	110	1	1.9	1.9	NUM
ejde-395	110	2	.	.	PUNCT
ejde-395	111	1	let	let	VERB
ejde-395	111	2	a	a	DET
ejde-395	111	3	=	=	SYM
ejde-395	111	4	1/9	1/9	NUM
ejde-395	111	5	,	,	PUNCT
ejde-395	111	6	λ	λ	X
ejde-395	111	7	=	=	SYM
ejde-395	111	8	1/81	1/81	NUM
ejde-395	111	9	and	and	CCONJ
ejde-395	111	10	f(z	f(z	PROPN
ejde-395	111	11	)	)	PUNCT
ejde-395	111	12	=	=	SYM
ejde-395	112	1	1	1	NUM
ejde-395	112	2	9	9	NUM
ejde-395	112	3	(	(	PUNCT
ejde-395	112	4	z	z	NOUN
ejde-395	112	5	+	+	NOUN
ejde-395	112	6	1	1	NUM
ejde-395	112	7	z	z	NOUN
ejde-395	112	8	−	−	NOUN
ejde-395	112	9	1	1	NUM
ejde-395	112	10	)	)	SYM
ejde-395	112	11	2	2	NUM
ejde-395	112	12	,	,	PUNCT
ejde-395	112	13	then	then	ADV
ejde-395	112	14	f(z	f(z	PROPN
ejde-395	112	15	)	)	PUNCT
ejde-395	112	16	satisfies	satisfy	VERB
ejde-395	112	17	the	the	DET
ejde-395	112	18	difference	difference	NOUN
ejde-395	112	19	equation	equation	NOUN
ejde-395	112	20	f(2z)f	f(2z)f	ADP
ejde-395	112	21	(	(	PUNCT
ejde-395	112	22	z	z	NOUN
ejde-395	112	23	2	2	NUM
ejde-395	112	24	)	)	PUNCT
ejde-395	113	1	[	[	X
ejde-395	113	2	f(z)−	f(z)−	PROPN
ejde-395	113	3	1]2	1]2	NUM
ejde-395	113	4	=	=	PUNCT
ejde-395	114	1	[	[	PUNCT
ejde-395	114	2	f(z)−	f(z)−	PROPN
ejde-395	114	3	1	1	NUM
ejde-395	114	4	81	81	NUM
ejde-395	114	5	]	]	SYM
ejde-395	114	6	2	2	NUM
ejde-395	114	7	.	.	PUNCT
ejde-395	115	1	this	this	DET
ejde-395	115	2	example	example	NOUN
ejde-395	115	3	shows	show	VERB
ejde-395	115	4	that	that	SCONJ
ejde-395	115	5	our	our	PRON
ejde-395	115	6	conclusion	conclusion	NOUN
ejde-395	115	7	about	about	ADP
ejde-395	115	8	the	the	DET
ejde-395	115	9	form	form	NOUN
ejde-395	115	10	of	of	ADP
ejde-395	115	11	rational	rational	ADJ
ejde-395	115	12	solutions	solution	NOUN
ejde-395	115	13	for	for	ADP
ejde-395	115	14	equation	equation	NOUN
ejde-395	115	15	(	(	PUNCT
ejde-395	115	16	1.9	1.9	NUM
ejde-395	115	17	)	)	PUNCT
ejde-395	115	18	is	be	AUX
ejde-395	115	19	sharp	sharp	ADJ
ejde-395	115	20	to	to	ADP
ejde-395	115	21	a	a	DET
ejde-395	115	22	certain	certain	ADJ
ejde-395	115	23	extent	extent	NOUN
ejde-395	115	24	.	.	PUNCT
ejde-395	116	1	theorem	theorem	VERB
ejde-395	116	2	1.10	1.10	NUM
ejde-395	116	3	.	.	PUNCT
ejde-395	117	1	let	let	VERB
ejde-395	117	2	q	q	X
ejde-395	117	3	,	,	PUNCT
ejde-395	117	4	λ	λ	PROPN
ejde-395	117	5	∈	∈	PROPN
ejde-395	117	6	c	c	NOUN
ejde-395	117	7	−	−	NOUN
ejde-395	117	8	{	{	PUNCT
ejde-395	117	9	0	0	NUM
ejde-395	117	10	,	,	PUNCT
ejde-395	117	11	1	1	NUM
ejde-395	117	12	}	}	PUNCT
ejde-395	117	13	.	.	PUNCT
ejde-395	118	1	suppose	suppose	VERB
ejde-395	118	2	that	that	SCONJ
ejde-395	118	3	f(z	f(z	PROPN
ejde-395	118	4	)	)	PUNCT
ejde-395	118	5	is	be	AUX
ejde-395	118	6	a	a	DET
ejde-395	118	7	nonconstant	nonconstant	ADJ
ejde-395	118	8	meromorphic	meromorphic	ADJ
ejde-395	118	9	solution	solution	NOUN
ejde-395	118	10	with	with	ADP
ejde-395	118	11	zero	zero	NUM
ejde-395	118	12	order	order	NOUN
ejde-395	118	13	of	of	ADP
ejde-395	118	14	equation	equation	NOUN
ejde-395	118	15	(	(	PUNCT
ejde-395	118	16	1.9	1.9	NUM
ejde-395	118	17	)	)	PUNCT
ejde-395	118	18	.	.	PUNCT
ejde-395	119	1	then	then	ADV
ejde-395	119	2	(	(	PUNCT
ejde-395	119	3	i	i	NOUN
ejde-395	119	4	)	)	PUNCT
ejde-395	119	5	f(ηz	f(ηz	PROPN
ejde-395	119	6	)	)	PUNCT
ejde-395	119	7	has	have	VERB
ejde-395	119	8	infinitely	infinitely	ADV
ejde-395	119	9	many	many	ADJ
ejde-395	119	10	fixed	fix	VERB
ejde-395	119	11	-	-	PUNCT
ejde-395	119	12	points	point	NOUN
ejde-395	119	13	and	and	CCONJ
ejde-395	119	14	τ(f(ηz	τ(f(ηz	NOUN
ejde-395	119	15	)	)	PUNCT
ejde-395	119	16	)	)	PUNCT
ejde-395	120	1	=	=	SYM
ejde-395	120	2	σ(f	σ(f	NOUN
ejde-395	120	3	)	)	PUNCT
ejde-395	120	4	for	for	ADP
ejde-395	120	5	any	any	DET
ejde-395	120	6	η	η	PROPN
ejde-395	120	7	∈	∈	PROPN
ejde-395	120	8	c−	c−	NOUN
ejde-395	120	9	{	{	PUNCT
ejde-395	120	10	0	0	NUM
ejde-395	120	11	,	,	PUNCT
ejde-395	120	12	1	1	NUM
ejde-395	120	13	}	}	PUNCT
ejde-395	120	14	;	;	PUNCT
ejde-395	120	15	ejde-2020/14	ejde-2020/14	VERB
ejde-395	120	16	q	q	ADJ
ejde-395	120	17	-	-	PUNCT
ejde-395	120	18	difference	difference	NOUN
ejde-395	120	19	painlevé	painlevé	NOUN
ejde-395	120	20	equations	equation	NOUN
ejde-395	120	21	5	5	NUM
ejde-395	120	22	(	(	PUNCT
ejde-395	120	23	ii	ii	NOUN
ejde-395	120	24	)	)	PUNCT
ejde-395	120	25	f(z	f(z	PROPN
ejde-395	120	26	)	)	PUNCT
ejde-395	120	27	has	have	VERB
ejde-395	120	28	infinitely	infinitely	ADV
ejde-395	120	29	many	many	ADJ
ejde-395	120	30	zeros	zero	NOUN
ejde-395	120	31	and	and	CCONJ
ejde-395	120	32	poles	pole	NOUN
ejde-395	120	33	,	,	PUNCT
ejde-395	120	34	and	and	CCONJ
ejde-395	120	35	∆qf	∆qf	NOUN
ejde-395	120	36	,	,	PUNCT
ejde-395	120	37	∆qf	∆qf	X
ejde-395	120	38	f	f	PRON
ejde-395	120	39	have	have	VERB
ejde-395	120	40	infinitely	infinitely	ADV
ejde-395	120	41	many	many	ADJ
ejde-395	120	42	poles	pole	NOUN
ejde-395	120	43	,	,	PUNCT
ejde-395	120	44	and	and	CCONJ
ejde-395	120	45	λ(f	λ(f	ADJ
ejde-395	120	46	)	)	PUNCT
ejde-395	120	47	=	=	PUNCT
ejde-395	120	48	λ	λ	NOUN
ejde-395	120	49	(	(	PUNCT
ejde-395	120	50	1	1	NUM
ejde-395	120	51	f	f	NOUN
ejde-395	120	52	)	)	PUNCT
ejde-395	121	1	=	=	PUNCT
ejde-395	121	2	λ	λ	X
ejde-395	121	3	(	(	PUNCT
ejde-395	121	4	1	1	NUM
ejde-395	121	5	∆qf	∆qf	NOUN
ejde-395	121	6	)	)	PUNCT
ejde-395	122	1	=	=	PUNCT
ejde-395	122	2	λ	λ	X
ejde-395	122	3	(	(	PUNCT
ejde-395	122	4	1	1	NUM
ejde-395	122	5	(	(	PUNCT
ejde-395	122	6	∆qf)/f	∆qf)/f	PROPN
ejde-395	122	7	)	)	PUNCT
ejde-395	122	8	.	.	PUNCT
ejde-395	123	1	2	2	X
ejde-395	123	2	.	.	X
ejde-395	123	3	proof	proof	NOUN
ejde-395	123	4	of	of	ADP
ejde-395	123	5	theorem	theorem	ADJ
ejde-395	123	6	1.5	1.5	NUM
ejde-395	123	7	proof	proof	NOUN
ejde-395	123	8	.	.	PUNCT
ejde-395	124	1	let	let	VERB
ejde-395	124	2	f(z	f(z	NOUN
ejde-395	124	3	)	)	PUNCT
ejde-395	125	1	=	=	SYM
ejde-395	125	2	p	p	X
ejde-395	125	3	(	(	PUNCT
ejde-395	125	4	z)/q(z	z)/q(z	NOUN
ejde-395	125	5	)	)	PUNCT
ejde-395	125	6	be	be	AUX
ejde-395	125	7	a	a	DET
ejde-395	125	8	nonconstant	nonconstant	ADJ
ejde-395	125	9	rational	rational	ADJ
ejde-395	125	10	solution	solution	NOUN
ejde-395	125	11	of	of	ADP
ejde-395	125	12	(	(	PUNCT
ejde-395	125	13	1.8	1.8	NUM
ejde-395	125	14	)	)	PUNCT
ejde-395	125	15	,	,	PUNCT
ejde-395	125	16	where	where	SCONJ
ejde-395	125	17	p	p	PROPN
ejde-395	125	18	(	(	PUNCT
ejde-395	125	19	z	z	NOUN
ejde-395	125	20	)	)	PUNCT
ejde-395	125	21	,	,	PUNCT
ejde-395	125	22	q(z	q(z	PROPN
ejde-395	125	23	)	)	PUNCT
ejde-395	125	24	are	be	AUX
ejde-395	125	25	relatively	relatively	ADV
ejde-395	125	26	prime	prime	ADJ
ejde-395	125	27	polynomials	polynomial	NOUN
ejde-395	125	28	with	with	ADP
ejde-395	125	29	degrees	degree	NOUN
ejde-395	125	30	p	p	NOUN
ejde-395	125	31	and	and	CCONJ
ejde-395	125	32	t	t	NOUN
ejde-395	125	33	respectively	respectively	ADV
ejde-395	125	34	.	.	PUNCT
ejde-395	126	1	in	in	ADP
ejde-395	126	2	view	view	NOUN
ejde-395	126	3	of	of	ADP
ejde-395	126	4	(	(	PUNCT
ejde-395	126	5	1.8	1.8	NUM
ejde-395	126	6	)	)	PUNCT
ejde-395	126	7	,	,	PUNCT
ejde-395	126	8	it	it	PRON
ejde-395	126	9	follows	follow	VERB
ejde-395	126	10	that	that	SCONJ
ejde-395	127	1	p	p	PROPN
ejde-395	127	2	(	(	PUNCT
ejde-395	127	3	qz	qz	PROPN
ejde-395	127	4	)	)	PUNCT
ejde-395	127	5	q(qz	q(qz	PROPN
ejde-395	127	6	)	)	PUNCT
ejde-395	127	7	p	p	X
ejde-395	127	8	(	(	PUNCT
ejde-395	127	9	z	z	NOUN
ejde-395	127	10	q	q	NOUN
ejde-395	127	11	)	)	PUNCT
ejde-395	127	12	q	q	NOUN
ejde-395	127	13	(	(	PUNCT
ejde-395	127	14	z	z	NOUN
ejde-395	127	15	q	q	NOUN
ejde-395	127	16	)	)	PUNCT
ejde-395	127	17	p	p	X
ejde-395	127	18	(	(	PUNCT
ejde-395	127	19	z	z	NOUN
ejde-395	127	20	)	)	PUNCT
ejde-395	127	21	q(z	q(z	PROPN
ejde-395	127	22	)	)	PUNCT
ejde-395	127	23	p	p	NOUN
ejde-395	127	24	(	(	PUNCT
ejde-395	127	25	z)−q(z	z)−q(z	NOUN
ejde-395	127	26	)	)	PUNCT
ejde-395	127	27	q(z	q(z	PROPN
ejde-395	127	28	)	)	PUNCT
ejde-395	127	29	=	=	SYM
ejde-395	127	30	µ.	µ.	NOUN
ejde-395	127	31	(	(	PUNCT
ejde-395	127	32	2.1	2.1	NUM
ejde-395	127	33	)	)	PUNCT
ejde-395	127	34	without	without	ADP
ejde-395	127	35	loss	loss	NOUN
ejde-395	127	36	of	of	ADP
ejde-395	127	37	generality	generality	NOUN
ejde-395	127	38	,	,	PUNCT
ejde-395	127	39	we	we	PRON
ejde-395	127	40	assume	assume	VERB
ejde-395	127	41	that	that	SCONJ
ejde-395	127	42	the	the	DET
ejde-395	127	43	coefficients	coefficient	NOUN
ejde-395	127	44	of	of	ADP
ejde-395	127	45	the	the	DET
ejde-395	127	46	highest	high	ADJ
ejde-395	127	47	degree	degree	NOUN
ejde-395	127	48	terms	term	NOUN
ejde-395	127	49	of	of	ADP
ejde-395	127	50	p	p	NOUN
ejde-395	127	51	(	(	PUNCT
ejde-395	127	52	z	z	NOUN
ejde-395	127	53	)	)	PUNCT
ejde-395	127	54	and	and	CCONJ
ejde-395	127	55	q(z	q(z	PROPN
ejde-395	127	56	)	)	PUNCT
ejde-395	127	57	are	be	AUX
ejde-395	127	58	a(6=	a(6=	PROPN
ejde-395	127	59	0	0	NUM
ejde-395	127	60	)	)	PUNCT
ejde-395	127	61	and	and	CCONJ
ejde-395	127	62	1	1	NUM
ejde-395	127	63	respectively	respectively	ADV
ejde-395	127	64	,	,	PUNCT
ejde-395	127	65	and	and	CCONJ
ejde-395	127	66	set	set	VERB
ejde-395	127	67	s	s	PART
ejde-395	128	1	=	=	NOUN
ejde-395	128	2	p−	p−	NOUN
ejde-395	128	3	t.	t.	NOUN
ejde-395	128	4	if	if	SCONJ
ejde-395	128	5	s	s	VERB
ejde-395	128	6	>	>	X
ejde-395	128	7	0	0	PROPN
ejde-395	128	8	,	,	PUNCT
ejde-395	128	9	then	then	ADV
ejde-395	128	10	p	p	X
ejde-395	128	11	(	(	PUNCT
ejde-395	128	12	z)/q(z	z)/q(z	PROPN
ejde-395	128	13	)	)	PUNCT
ejde-395	128	14	=	=	SYM
ejde-395	128	15	azs(1	azs(1	NOUN
ejde-395	128	16	+	+	CCONJ
ejde-395	128	17	o(1	o(1	NOUN
ejde-395	128	18	)	)	PUNCT
ejde-395	128	19	)	)	PUNCT
ejde-395	128	20	as	as	ADP
ejde-395	128	21	|z|	|z|	NOUN
ejde-395	128	22	=	=	SYM
ejde-395	128	23	r	r	NOUN
ejde-395	128	24	→	→	SYM
ejde-395	128	25	∞.	∞.	PROPN
ejde-395	128	26	thus	thus	ADV
ejde-395	128	27	,	,	PUNCT
ejde-395	128	28	by	by	ADP
ejde-395	128	29	virtue	virtue	NOUN
ejde-395	128	30	of	of	ADP
ejde-395	128	31	(	(	PUNCT
ejde-395	128	32	2.1	2.1	NUM
ejde-395	128	33	)	)	PUNCT
ejde-395	128	34	,	,	PUNCT
ejde-395	128	35	it	it	PRON
ejde-395	128	36	follows	follow	VERB
ejde-395	128	37	that	that	SCONJ
ejde-395	128	38	a3z3s(1	a3z3s(1	PROPN
ejde-395	128	39	+	+	NUM
ejde-395	128	40	o(1))(azs(1	o(1))(azs(1	NOUN
ejde-395	128	41	+	+	CCONJ
ejde-395	128	42	o(1))−	o(1))−	NUM
ejde-395	128	43	1	1	NUM
ejde-395	128	44	)	)	PUNCT
ejde-395	128	45	=	=	SYM
ejde-395	128	46	µ	µ	NOUN
ejde-395	128	47	,	,	PUNCT
ejde-395	128	48	r	r	PROPN
ejde-395	128	49	→∞	→∞	NOUN
ejde-395	128	50	,	,	PUNCT
ejde-395	128	51	this	this	PRON
ejde-395	128	52	is	be	AUX
ejde-395	128	53	impossible	impossible	ADJ
ejde-395	128	54	for	for	ADP
ejde-395	128	55	a	a	DET
ejde-395	128	56	6=	6=	NUM
ejde-395	128	57	0	0	NUM
ejde-395	128	58	.	.	PUNCT
ejde-395	129	1	if	if	SCONJ
ejde-395	129	2	s	s	VERB
ejde-395	129	3	<	<	X
ejde-395	129	4	0	0	NUM
ejde-395	129	5	,	,	PUNCT
ejde-395	129	6	then	then	ADV
ejde-395	129	7	as	as	SCONJ
ejde-395	129	8	r	r	PROPN
ejde-395	129	9	→∞	→∞	NOUN
ejde-395	129	10	,	,	PUNCT
ejde-395	129	11	it	it	PRON
ejde-395	129	12	follows	follow	VERB
ejde-395	129	13	that	that	SCONJ
ejde-395	129	14	p	p	X
ejde-395	129	15	(	(	PUNCT
ejde-395	129	16	z	z	NOUN
ejde-395	129	17	)	)	PUNCT
ejde-395	129	18	q(z	q(z	PROPN
ejde-395	129	19	)	)	PUNCT
ejde-395	129	20	=	=	SYM
ejde-395	129	21	o(1	o(1	PROPN
ejde-395	129	22	)	)	PUNCT
ejde-395	129	23	and	and	CCONJ
ejde-395	129	24	p	p	PROPN
ejde-395	129	25	(	(	PUNCT
ejde-395	129	26	qz	qz	NOUN
ejde-395	129	27	)	)	PUNCT
ejde-395	129	28	q(qz	q(qz	NUM
ejde-395	129	29	)	)	PUNCT
ejde-395	129	30	=	=	SYM
ejde-395	129	31	o(1	o(1	PROPN
ejde-395	129	32	)	)	PUNCT
ejde-395	129	33	,	,	PUNCT
ejde-395	129	34	p	p	X
ejde-395	129	35	(	(	PUNCT
ejde-395	129	36	z	z	NOUN
ejde-395	129	37	q	q	NOUN
ejde-395	129	38	)	)	PUNCT
ejde-395	130	1	q	q	NOUN
ejde-395	130	2	(	(	PUNCT
ejde-395	130	3	z	z	NOUN
ejde-395	130	4	q	q	NOUN
ejde-395	130	5	)	)	PUNCT
ejde-395	130	6	=	=	SYM
ejde-395	130	7	o(1	o(1	NOUN
ejde-395	130	8	)	)	PUNCT
ejde-395	130	9	.	.	PUNCT
ejde-395	131	1	substituting	substitute	VERB
ejde-395	131	2	these	these	PRON
ejde-395	131	3	into	into	ADP
ejde-395	131	4	(	(	PUNCT
ejde-395	131	5	2.1	2.1	NUM
ejde-395	131	6	)	)	PUNCT
ejde-395	131	7	,	,	PUNCT
ejde-395	131	8	we	we	PRON
ejde-395	131	9	get	get	VERB
ejde-395	131	10	o(1	o(1	NOUN
ejde-395	131	11	)	)	PUNCT
ejde-395	131	12	=	=	SYM
ejde-395	131	13	µ	µ	NOUN
ejde-395	131	14	as	as	ADP
ejde-395	131	15	r	r	PROPN
ejde-395	131	16	→∞	→∞	NOUN
ejde-395	131	17	,	,	PUNCT
ejde-395	131	18	this	this	PRON
ejde-395	131	19	is	be	AUX
ejde-395	131	20	a	a	DET
ejde-395	131	21	contradiction	contradiction	NOUN
ejde-395	131	22	for	for	ADP
ejde-395	131	23	µ	µ	PRON
ejde-395	131	24	6=	6=	ADP
ejde-395	131	25	0	0	NUM
ejde-395	131	26	.	.	PUNCT
ejde-395	132	1	thus	thus	ADV
ejde-395	132	2	,	,	PUNCT
ejde-395	132	3	it	it	PRON
ejde-395	132	4	yields	yield	VERB
ejde-395	132	5	that	that	PRON
ejde-395	132	6	s	s	VERB
ejde-395	132	7	=	=	X
ejde-395	132	8	0	0	PROPN
ejde-395	132	9	and	and	CCONJ
ejde-395	132	10	p	p	NOUN
ejde-395	132	11	=	=	PROPN
ejde-395	132	12	t.	t.	NOUN
ejde-395	132	13	from	from	ADP
ejde-395	132	14	the	the	DET
ejde-395	132	15	assumptions	assumption	NOUN
ejde-395	132	16	of	of	ADP
ejde-395	132	17	this	this	DET
ejde-395	132	18	theorem	theorem	NOUN
ejde-395	132	19	,	,	PUNCT
ejde-395	132	20	we	we	PRON
ejde-395	132	21	know	know	VERB
ejde-395	132	22	that	that	SCONJ
ejde-395	132	23	the	the	DET
ejde-395	132	24	zeros	zero	NOUN
ejde-395	132	25	of	of	ADP
ejde-395	132	26	q(z	q(z	PROPN
ejde-395	132	27	)	)	PUNCT
ejde-395	132	28	are	be	AUX
ejde-395	132	29	not	not	PART
ejde-395	132	30	the	the	DET
ejde-395	132	31	zeros	zero	NOUN
ejde-395	132	32	of	of	ADP
ejde-395	132	33	p	p	PROPN
ejde-395	132	34	(	(	PUNCT
ejde-395	132	35	z	z	NOUN
ejde-395	132	36	)	)	PUNCT
ejde-395	132	37	and	and	CCONJ
ejde-395	132	38	p	p	X
ejde-395	132	39	(	(	PUNCT
ejde-395	132	40	z)−q(z	z)−q(z	NOUN
ejde-395	132	41	)	)	PUNCT
ejde-395	132	42	.	.	PUNCT
ejde-395	133	1	hence	hence	ADV
ejde-395	133	2	,	,	PUNCT
ejde-395	133	3	in	in	ADP
ejde-395	133	4	view	view	NOUN
ejde-395	133	5	of	of	ADP
ejde-395	133	6	(	(	PUNCT
ejde-395	133	7	2.2	2.2	NUM
ejde-395	133	8	)	)	PUNCT
ejde-395	133	9	,	,	PUNCT
ejde-395	133	10	it	it	PRON
ejde-395	133	11	follows	follow	VERB
ejde-395	133	12	that	that	SCONJ
ejde-395	133	13	all	all	DET
ejde-395	133	14	the	the	DET
ejde-395	133	15	zeros	zero	NOUN
ejde-395	133	16	of	of	ADP
ejde-395	133	17	q2(z	q2(z	NOUN
ejde-395	133	18	)	)	PUNCT
ejde-395	133	19	are	be	AUX
ejde-395	133	20	the	the	DET
ejde-395	133	21	zeros	zero	NOUN
ejde-395	133	22	of	of	ADP
ejde-395	133	23	p	p	PROPN
ejde-395	133	24	(	(	PUNCT
ejde-395	133	25	qz)p	qz)p	PROPN
ejde-395	133	26	(	(	PUNCT
ejde-395	133	27	z	z	NOUN
ejde-395	133	28	q	q	NOUN
ejde-395	133	29	)	)	PUNCT
ejde-395	133	30	.	.	PUNCT
ejde-395	134	1	since	since	SCONJ
ejde-395	134	2	degz[q(z)2	degz[q(z)2	NOUN
ejde-395	134	3	]	]	PUNCT
ejde-395	134	4	=	=	SYM
ejde-395	134	5	degz[p	degz[p	NOUN
ejde-395	134	6	(	(	PUNCT
ejde-395	134	7	qz)p	qz)p	PROPN
ejde-395	134	8	(	(	PUNCT
ejde-395	134	9	z	z	NOUN
ejde-395	134	10	q	q	NOUN
ejde-395	134	11	)	)	PUNCT
ejde-395	134	12	]	]	PUNCT
ejde-395	134	13	=	=	PUNCT
ejde-395	134	14	2p	2p	NOUN
ejde-395	134	15	,	,	PUNCT
ejde-395	134	16	then	then	ADV
ejde-395	134	17	it	it	PRON
ejde-395	134	18	yields	yield	VERB
ejde-395	134	19	from	from	ADP
ejde-395	134	20	(	(	PUNCT
ejde-395	134	21	2.1	2.1	NUM
ejde-395	134	22	)	)	PUNCT
ejde-395	135	1	that	that	PRON
ejde-395	135	2	p	p	X
ejde-395	135	3	(	(	PUNCT
ejde-395	135	4	qz)p	qz)p	PROPN
ejde-395	135	5	(	(	PUNCT
ejde-395	135	6	z	z	NOUN
ejde-395	135	7	q	q	NOUN
ejde-395	135	8	)	)	PUNCT
ejde-395	136	1	=	=	SYM
ejde-395	136	2	a2q(z)2	a2q(z)2	NUM
ejde-395	136	3	,	,	PUNCT
ejde-395	136	4	(	(	PUNCT
ejde-395	136	5	2.2	2.2	NUM
ejde-395	136	6	)	)	PUNCT
ejde-395	136	7	p	p	NOUN
ejde-395	136	8	(	(	PUNCT
ejde-395	136	9	z)(p	z)(p	X
ejde-395	136	10	(	(	PUNCT
ejde-395	136	11	z)−q(z	z)−q(z	NOUN
ejde-395	136	12	)	)	PUNCT
ejde-395	136	13	)	)	PUNCT
ejde-395	137	1	=	=	SYM
ejde-395	137	2	a(a−	a(a−	PROPN
ejde-395	137	3	1)q(qz)q	1)q(qz)q	NUM
ejde-395	137	4	(	(	PUNCT
ejde-395	137	5	z	z	NOUN
ejde-395	137	6	q	q	NOUN
ejde-395	137	7	)	)	PUNCT
ejde-395	137	8	.	.	PUNCT
ejde-395	138	1	(	(	PUNCT
ejde-395	138	2	2.3	2.3	NUM
ejde-395	138	3	)	)	PUNCT
ejde-395	138	4	next	next	ADV
ejde-395	138	5	,	,	PUNCT
ejde-395	138	6	we	we	PRON
ejde-395	138	7	confirm	confirm	VERB
ejde-395	138	8	that	that	SCONJ
ejde-395	138	9	the	the	DET
ejde-395	138	10	orders	order	NOUN
ejde-395	138	11	of	of	ADP
ejde-395	138	12	all	all	DET
ejde-395	138	13	the	the	DET
ejde-395	138	14	zeros	zero	NOUN
ejde-395	138	15	of	of	ADP
ejde-395	138	16	p	p	PROPN
ejde-395	138	17	(	(	PUNCT
ejde-395	138	18	z	z	NOUN
ejde-395	138	19	)	)	PUNCT
ejde-395	138	20	are	be	AUX
ejde-395	138	21	even	even	ADV
ejde-395	138	22	.	.	PUNCT
ejde-395	139	1	let	let	VERB
ejde-395	139	2	z0	z0	PROPN
ejde-395	139	3	be	be	AUX
ejde-395	139	4	a	a	DET
ejde-395	139	5	zero	zero	NUM
ejde-395	139	6	of	of	ADP
ejde-395	139	7	p	p	PROPN
ejde-395	139	8	(	(	PUNCT
ejde-395	139	9	z	z	NOUN
ejde-395	139	10	)	)	PUNCT
ejde-395	139	11	with	with	ADP
ejde-395	139	12	the	the	DET
ejde-395	139	13	order	order	NOUN
ejde-395	139	14	k.	k.	PROPN
ejde-395	140	1	if	if	SCONJ
ejde-395	140	2	z0	z0	PROPN
ejde-395	140	3	6=	6=	ADP
ejde-395	140	4	0	0	NUM
ejde-395	140	5	and	and	CCONJ
ejde-395	140	6	k	k	PROPN
ejde-395	140	7	is	be	AUX
ejde-395	140	8	an	an	DET
ejde-395	140	9	odd	odd	ADJ
ejde-395	140	10	integer	integer	NOUN
ejde-395	140	11	.	.	PUNCT
ejde-395	141	1	then	then	ADV
ejde-395	141	2	p	p	X
ejde-395	141	3	(	(	PUNCT
ejde-395	141	4	z	z	NOUN
ejde-395	141	5	)	)	PUNCT
ejde-395	141	6	has	have	VERB
ejde-395	141	7	the	the	DET
ejde-395	141	8	term	term	NOUN
ejde-395	141	9	(	(	PUNCT
ejde-395	141	10	z	z	NOUN
ejde-395	141	11	−	−	NOUN
ejde-395	141	12	z0)k	z0)k	NOUN
ejde-395	141	13	,	,	PUNCT
ejde-395	141	14	and	and	CCONJ
ejde-395	141	15	p	p	X
ejde-395	141	16	(	(	PUNCT
ejde-395	141	17	qz)p	qz)p	PROPN
ejde-395	141	18	(	(	PUNCT
ejde-395	141	19	z	z	NOUN
ejde-395	141	20	q	q	NOUN
ejde-395	141	21	)	)	PUNCT
ejde-395	141	22	has	have	VERB
ejde-395	141	23	the	the	DET
ejde-395	141	24	term	term	NOUN
ejde-395	141	25	(	(	PUNCT
ejde-395	141	26	z	z	NOUN
ejde-395	141	27	−	−	NOUN
ejde-395	141	28	qz0)k	qz0)k	NOUN
ejde-395	141	29	(	(	PUNCT
ejde-395	141	30	z	z	NOUN
ejde-395	141	31	−	−	PROPN
ejde-395	141	32	z0	z0	PROPN
ejde-395	141	33	q	q	PROPN
ejde-395	141	34	)	)	PUNCT
ejde-395	141	35	k	k	PROPN
ejde-395	141	36	.	.	PUNCT
ejde-395	142	1	(	(	PUNCT
ejde-395	142	2	2.4	2.4	NUM
ejde-395	142	3	)	)	PUNCT
ejde-395	142	4	it	it	PRON
ejde-395	142	5	means	mean	VERB
ejde-395	142	6	that	that	SCONJ
ejde-395	142	7	qz0	qz0	NOUN
ejde-395	142	8	and	and	CCONJ
ejde-395	142	9	z0	z0	PROPN
ejde-395	142	10	q	q	PROPN
ejde-395	142	11	are	be	AUX
ejde-395	142	12	both	both	PRON
ejde-395	142	13	zeros	zero	NOUN
ejde-395	142	14	of	of	ADP
ejde-395	142	15	p	p	PROPN
ejde-395	142	16	(	(	PUNCT
ejde-395	142	17	qz)p	qz)p	PROPN
ejde-395	142	18	(	(	PUNCT
ejde-395	142	19	z	z	NOUN
ejde-395	142	20	q	q	NOUN
ejde-395	142	21	)	)	PUNCT
ejde-395	142	22	with	with	ADP
ejde-395	142	23	the	the	DET
ejde-395	142	24	order	order	NOUN
ejde-395	142	25	at	at	ADP
ejde-395	142	26	least	least	ADJ
ejde-395	142	27	k.	k.	ADV
ejde-395	142	28	in	in	ADP
ejde-395	142	29	addition	addition	NOUN
ejde-395	142	30	,	,	PUNCT
ejde-395	142	31	since	since	SCONJ
ejde-395	142	32	p	p	X
ejde-395	142	33	(	(	PUNCT
ejde-395	142	34	z	z	NOUN
ejde-395	142	35	)	)	PUNCT
ejde-395	142	36	and	and	CCONJ
ejde-395	142	37	q(z	q(z	PROPN
ejde-395	142	38	)	)	PUNCT
ejde-395	142	39	are	be	AUX
ejde-395	142	40	relatively	relatively	ADV
ejde-395	142	41	prime	prime	ADJ
ejde-395	142	42	polynomials	polynomial	NOUN
ejde-395	142	43	,	,	PUNCT
ejde-395	142	44	in	in	ADP
ejde-395	142	45	view	view	NOUN
ejde-395	142	46	of	of	ADP
ejde-395	142	47	(	(	PUNCT
ejde-395	142	48	2.3	2.3	NUM
ejde-395	142	49	)	)	PUNCT
ejde-395	142	50	,	,	PUNCT
ejde-395	142	51	it	it	PRON
ejde-395	142	52	follows	follow	VERB
ejde-395	142	53	that	that	SCONJ
ejde-395	142	54	q(qz)q	q(qz)q	PROPN
ejde-395	142	55	(	(	PUNCT
ejde-395	142	56	z	z	NOUN
ejde-395	142	57	q	q	NOUN
ejde-395	142	58	)	)	PUNCT
ejde-395	142	59	has	have	VERB
ejde-395	142	60	the	the	DET
ejde-395	142	61	term	term	NOUN
ejde-395	142	62	(	(	PUNCT
ejde-395	142	63	z	z	NOUN
ejde-395	142	64	−	−	NOUN
ejde-395	142	65	z0)k	z0)k	NOUN
ejde-395	142	66	.	.	PUNCT
ejde-395	143	1	suppose	suppose	VERB
ejde-395	143	2	that	that	SCONJ
ejde-395	143	3	q(qz	q(qz	PROPN
ejde-395	143	4	)	)	PUNCT
ejde-395	143	5	and	and	CCONJ
ejde-395	143	6	q	q	X
ejde-395	143	7	(	(	PUNCT
ejde-395	143	8	z	z	NOUN
ejde-395	143	9	q	q	NOUN
ejde-395	143	10	)	)	PUNCT
ejde-395	143	11	have	have	VERB
ejde-395	143	12	the	the	DET
ejde-395	143	13	terms	term	NOUN
ejde-395	143	14	(	(	PUNCT
ejde-395	143	15	z	z	NOUN
ejde-395	143	16	−	−	NOUN
ejde-395	143	17	z0)m	z0)m	NOUN
ejde-395	143	18	and	and	CCONJ
ejde-395	143	19	(	(	PUNCT
ejde-395	143	20	z	z	NOUN
ejde-395	143	21	−	−	PROPN
ejde-395	143	22	z0)l	z0)l	PROPN
ejde-395	143	23	respectively	respectively	ADV
ejde-395	143	24	,	,	PUNCT
ejde-395	144	1	where	where	SCONJ
ejde-395	144	2	m	m	VERB
ejde-395	144	3	,	,	PUNCT
ejde-395	144	4	l	l	PROPN
ejde-395	144	5	∈	∈	PROPN
ejde-395	144	6	n	n	CCONJ
ejde-395	144	7	and	and	CCONJ
ejde-395	144	8	m+	m+	NUM
ejde-395	144	9	l	l	NOUN
ejde-395	144	10	=	=	PUNCT
ejde-395	144	11	k.	k.	PROPN
ejde-395	144	12	obviously	obviously	ADV
ejde-395	144	13	,	,	PUNCT
ejde-395	144	14	in	in	ADP
ejde-395	144	15	view	view	NOUN
ejde-395	144	16	of	of	ADP
ejde-395	144	17	(	(	PUNCT
ejde-395	144	18	2.4	2.4	NUM
ejde-395	144	19	)	)	PUNCT
ejde-395	144	20	,	,	PUNCT
ejde-395	144	21	we	we	PRON
ejde-395	144	22	have	have	VERB
ejde-395	144	23	m	m	PROPN
ejde-395	144	24	6=	6=	NUM
ejde-395	144	25	0	0	NUM
ejde-395	144	26	and	and	CCONJ
ejde-395	144	27	l	l	NOUN
ejde-395	144	28	6=	6=	ADP
ejde-395	144	29	0	0	NUM
ejde-395	144	30	.	.	PUNCT
ejde-395	145	1	thus	thus	ADV
ejde-395	145	2	,	,	PUNCT
ejde-395	145	3	q(z	q(z	PROPN
ejde-395	145	4	)	)	PUNCT
ejde-395	145	5	has	have	VERB
ejde-395	145	6	the	the	DET
ejde-395	145	7	term	term	NOUN
ejde-395	145	8	(	(	PUNCT
ejde-395	145	9	z−	z−	X
ejde-395	145	10	qz0)m(z−	qz0)m(z−	PROPN
ejde-395	145	11	z0	z0	PROPN
ejde-395	145	12	q	q	PROPN
ejde-395	145	13	)	)	PUNCT
ejde-395	145	14	l	l	NOUN
ejde-395	145	15	,	,	PUNCT
ejde-395	145	16	that	that	ADV
ejde-395	145	17	is	is	ADV
ejde-395	145	18	,	,	PUNCT
ejde-395	145	19	q(z)2	q(z)2	NOUN
ejde-395	145	20	has	have	VERB
ejde-395	145	21	the	the	DET
ejde-395	145	22	term	term	NOUN
ejde-395	145	23	(	(	PUNCT
ejde-395	145	24	z−	z−	X
ejde-395	145	25	qz0)2m(z−	qz0)2m(z−	PROPN
ejde-395	145	26	z0	z0	NOUN
ejde-395	145	27	q	q	PROPN
ejde-395	145	28	)	)	PUNCT
ejde-395	145	29	2l	2l	NUM
ejde-395	145	30	.	.	PUNCT
ejde-395	146	1	so	so	ADV
ejde-395	146	2	,	,	PUNCT
ejde-395	146	3	in	in	ADP
ejde-395	146	4	view	view	NOUN
ejde-395	146	5	of	of	ADP
ejde-395	146	6	(	(	PUNCT
ejde-395	146	7	2.3	2.3	NUM
ejde-395	146	8	)	)	PUNCT
ejde-395	146	9	,	,	PUNCT
ejde-395	146	10	it	it	PRON
ejde-395	146	11	follows	follow	VERB
ejde-395	146	12	that	that	SCONJ
ejde-395	146	13	p	p	X
ejde-395	146	14	(	(	PUNCT
ejde-395	146	15	qz)p	qz)p	PROPN
ejde-395	146	16	(	(	PUNCT
ejde-395	146	17	z	z	NOUN
ejde-395	146	18	q	q	NOUN
ejde-395	146	19	)	)	PUNCT
ejde-395	146	20	has	have	VERB
ejde-395	146	21	the	the	DET
ejde-395	146	22	term	term	NOUN
ejde-395	146	23	(	(	PUNCT
ejde-395	146	24	z	z	NOUN
ejde-395	146	25	−	−	PROPN
ejde-395	146	26	qz0)2m(z	qz0)2m(z	PROPN
ejde-395	146	27	−	−	PROPN
ejde-395	146	28	z0	z0	PROPN
ejde-395	146	29	q	q	PROPN
ejde-395	146	30	)	)	PUNCT
ejde-395	146	31	2l	2l	NUM
ejde-395	146	32	.	.	X
ejde-395	147	1	6	6	NUM
ejde-395	147	2	h.	h.	PROPN
ejde-395	147	3	y.	y.	PROPN
ejde-395	147	4	xu	xu	PROPN
ejde-395	147	5	,	,	PUNCT
ejde-395	147	6	j.	j.	PROPN
ejde-395	147	7	tu	tu	PROPN
ejde-395	147	8	ejde-2020/14	ejde-2020/14	PROPN
ejde-395	147	9	in	in	ADP
ejde-395	147	10	view	view	NOUN
ejde-395	147	11	of	of	ADP
ejde-395	147	12	m+	m+	NOUN
ejde-395	147	13	l	l	NOUN
ejde-395	147	14	=	=	PUNCT
ejde-395	148	1	k	k	PROPN
ejde-395	148	2	and	and	CCONJ
ejde-395	148	3	k	k	PROPN
ejde-395	148	4	is	be	AUX
ejde-395	148	5	an	an	DET
ejde-395	148	6	odd	odd	ADJ
ejde-395	148	7	integer	integer	NOUN
ejde-395	148	8	,	,	PUNCT
ejde-395	148	9	without	without	ADP
ejde-395	148	10	loss	loss	NOUN
ejde-395	148	11	of	of	ADP
ejde-395	148	12	generality	generality	NOUN
ejde-395	148	13	,	,	PUNCT
ejde-395	148	14	assume	assume	VERB
ejde-395	148	15	that	that	SCONJ
ejde-395	148	16	m	m	VERB
ejde-395	148	17	<	<	X
ejde-395	148	18	l.	l.	PROPN
ejde-395	148	19	thus	thus	ADV
ejde-395	148	20	,	,	PUNCT
ejde-395	148	21	2	2	NUM
ejde-395	148	22	m	m	NOUN
ejde-395	148	23	<	<	X
ejde-395	148	24	k	k	PROPN
ejde-395	148	25	and	and	CCONJ
ejde-395	148	26	2l	2l	PROPN
ejde-395	148	27	>	>	X
ejde-395	148	28	k.	k.	PROPN
ejde-395	149	1	thus	thus	ADV
ejde-395	149	2	,	,	PUNCT
ejde-395	149	3	qz0	qz0	PROPN
ejde-395	149	4	is	be	AUX
ejde-395	149	5	a	a	DET
ejde-395	149	6	zero	zero	NUM
ejde-395	149	7	of	of	ADP
ejde-395	149	8	p	p	PROPN
ejde-395	149	9	(	(	PUNCT
ejde-395	149	10	qz)p	qz)p	PROPN
ejde-395	149	11	(	(	PUNCT
ejde-395	149	12	z	z	NOUN
ejde-395	149	13	q	q	NOUN
ejde-395	149	14	)	)	PUNCT
ejde-395	149	15	with	with	ADP
ejde-395	149	16	the	the	DET
ejde-395	149	17	order	order	NOUN
ejde-395	149	18	2	2	NUM
ejde-395	149	19	m	m	NOUN
ejde-395	149	20	<	<	X
ejde-395	149	21	k	k	X
ejde-395	149	22	,	,	PUNCT
ejde-395	149	23	this	this	PRON
ejde-395	149	24	is	be	AUX
ejde-395	149	25	a	a	DET
ejde-395	149	26	contradiction	contradiction	NOUN
ejde-395	149	27	with	with	ADP
ejde-395	149	28	(	(	PUNCT
ejde-395	149	29	2.4	2.4	NUM
ejde-395	149	30	)	)	PUNCT
ejde-395	149	31	.	.	PUNCT
ejde-395	150	1	thus	thus	ADV
ejde-395	150	2	,	,	PUNCT
ejde-395	150	3	any	any	DET
ejde-395	150	4	nonzero	nonzero	ADJ
ejde-395	150	5	zeros	zero	NOUN
ejde-395	150	6	of	of	ADP
ejde-395	150	7	p	p	X
ejde-395	150	8	(	(	PUNCT
ejde-395	150	9	z	z	NOUN
ejde-395	150	10	)	)	PUNCT
ejde-395	150	11	have	have	VERB
ejde-395	150	12	even	even	ADV
ejde-395	150	13	orders	order	NOUN
ejde-395	150	14	.	.	PUNCT
ejde-395	151	1	if	if	SCONJ
ejde-395	151	2	0	0	NUM
ejde-395	151	3	is	be	AUX
ejde-395	151	4	a	a	DET
ejde-395	151	5	zero	zero	NUM
ejde-395	151	6	of	of	ADP
ejde-395	151	7	p	p	PROPN
ejde-395	151	8	(	(	PUNCT
ejde-395	151	9	z	z	NOUN
ejde-395	151	10	)	)	PUNCT
ejde-395	151	11	,	,	PUNCT
ejde-395	151	12	by	by	ADP
ejde-395	151	13	combining	combine	VERB
ejde-395	151	14	with	with	ADP
ejde-395	151	15	(	(	PUNCT
ejde-395	151	16	2.2	2.2	NUM
ejde-395	151	17	)	)	PUNCT
ejde-395	151	18	,	,	PUNCT
ejde-395	151	19	then	then	ADV
ejde-395	151	20	0	0	NUM
ejde-395	151	21	is	be	AUX
ejde-395	151	22	also	also	ADV
ejde-395	151	23	a	a	DET
ejde-395	151	24	zero	zero	NUM
ejde-395	151	25	of	of	ADP
ejde-395	151	26	q(z	q(z	PROPN
ejde-395	151	27	)	)	PUNCT
ejde-395	151	28	,	,	PUNCT
ejde-395	151	29	this	this	PRON
ejde-395	151	30	is	be	AUX
ejde-395	151	31	a	a	DET
ejde-395	151	32	contradiction	contradiction	NOUN
ejde-395	151	33	with	with	ADP
ejde-395	151	34	p	p	PROPN
ejde-395	151	35	(	(	PUNCT
ejde-395	151	36	z	z	NOUN
ejde-395	151	37	)	)	PUNCT
ejde-395	151	38	,	,	PUNCT
ejde-395	151	39	q(z	q(z	PROPN
ejde-395	151	40	)	)	PUNCT
ejde-395	151	41	being	be	AUX
ejde-395	151	42	relatively	relatively	ADV
ejde-395	151	43	prime	prime	ADJ
ejde-395	151	44	polynomials	polynomial	NOUN
ejde-395	151	45	.	.	PUNCT
ejde-395	152	1	therefore	therefore	ADV
ejde-395	152	2	,	,	PUNCT
ejde-395	152	3	all	all	DET
ejde-395	152	4	the	the	DET
ejde-395	152	5	zeros	zero	NOUN
ejde-395	152	6	of	of	ADP
ejde-395	152	7	p	p	PROPN
ejde-395	152	8	(	(	PUNCT
ejde-395	152	9	z	z	NOUN
ejde-395	152	10	)	)	PUNCT
ejde-395	152	11	are	be	AUX
ejde-395	152	12	nonzero	nonzero	NOUN
ejde-395	152	13	with	with	ADP
ejde-395	152	14	even	even	ADJ
ejde-395	152	15	orders	order	NOUN
ejde-395	152	16	.	.	PUNCT
ejde-395	153	1	let	let	VERB
ejde-395	153	2	p	p	NOUN
ejde-395	153	3	(	(	PUNCT
ejde-395	153	4	z	z	NOUN
ejde-395	153	5	)	)	PUNCT
ejde-395	153	6	=	=	SYM
ejde-395	153	7	ar(z)2	ar(z)2	PROPN
ejde-395	153	8	,	,	PUNCT
ejde-395	153	9	where	where	SCONJ
ejde-395	153	10	r(z	r(z	NOUN
ejde-395	153	11	)	)	PUNCT
ejde-395	153	12	=	=	PUNCT
ejde-395	154	1	zn	zn	X
ejde-395	154	2	+	+	PROPN
ejde-395	154	3	an−1z	an−1z	PROPN
ejde-395	154	4	n−1	n−1	PROPN
ejde-395	154	5	+	+	PROPN
ejde-395	154	6	an−2z	an−2z	PROPN
ejde-395	154	7	n−2	n−2	PROPN
ejde-395	154	8	+	+	CCONJ
ejde-395	154	9	·	·	PUNCT
ejde-395	154	10	·	·	PUNCT
ejde-395	154	11	·	·	PUNCT
ejde-395	154	12	+	+	ADJ
ejde-395	154	13	a1z	a1z	PROPN
ejde-395	154	14	+	+	ADJ
ejde-395	154	15	a0	a0	NOUN
ejde-395	154	16	,	,	PUNCT
ejde-395	154	17	and	and	CCONJ
ejde-395	154	18	a0	a0	NOUN
ejde-395	154	19	,	,	PUNCT
ejde-395	154	20	a1	a1	NOUN
ejde-395	154	21	,	,	PUNCT
ejde-395	154	22	.	.	PUNCT
ejde-395	154	23	.	.	PUNCT
ejde-395	154	24	.	.	PUNCT
ejde-395	155	1	,	,	PUNCT
ejde-395	155	2	an−1	an−1	PROPN
ejde-395	155	3	are	be	AUX
ejde-395	155	4	constants	constant	NOUN
ejde-395	155	5	.	.	PUNCT
ejde-395	156	1	since	since	SCONJ
ejde-395	156	2	0	0	NUM
ejde-395	156	3	is	be	AUX
ejde-395	156	4	not	not	PART
ejde-395	156	5	the	the	DET
ejde-395	156	6	zero	zero	NUM
ejde-395	156	7	of	of	ADP
ejde-395	156	8	p	p	X
ejde-395	156	9	(	(	PUNCT
ejde-395	156	10	z	z	NOUN
ejde-395	156	11	)	)	PUNCT
ejde-395	156	12	,	,	PUNCT
ejde-395	156	13	then	then	ADV
ejde-395	156	14	a0	a0	PROPN
ejde-395	156	15	6=	6=	PROPN
ejde-395	156	16	0	0	NUM
ejde-395	156	17	.	.	PUNCT
ejde-395	157	1	in	in	ADP
ejde-395	157	2	view	view	NOUN
ejde-395	157	3	of	of	ADP
ejde-395	157	4	(	(	PUNCT
ejde-395	157	5	2.2	2.2	NUM
ejde-395	157	6	)	)	PUNCT
ejde-395	157	7	and	and	CCONJ
ejde-395	157	8	(	(	PUNCT
ejde-395	157	9	2.3	2.3	NUM
ejde-395	157	10	)	)	PUNCT
ejde-395	157	11	,	,	PUNCT
ejde-395	157	12	it	it	PRON
ejde-395	157	13	yields	yield	VERB
ejde-395	157	14	q(z	q(z	PROPN
ejde-395	157	15	)	)	PUNCT
ejde-395	157	16	=	=	SYM
ejde-395	157	17	r(qz)r	r(qz)r	NOUN
ejde-395	157	18	(	(	PUNCT
ejde-395	157	19	z	z	NOUN
ejde-395	157	20	q	q	NOUN
ejde-395	157	21	)	)	PUNCT
ejde-395	157	22	and	and	CCONJ
ejde-395	157	23	ar(z)2	ar(z)2	PROPN
ejde-395	157	24	−	−	NOUN
ejde-395	157	25	r(qz)r	r(qz)r	NOUN
ejde-395	157	26	(	(	PUNCT
ejde-395	157	27	z	z	NOUN
ejde-395	157	28	q	q	NOUN
ejde-395	157	29	)	)	PUNCT
ejde-395	157	30	=	=	SYM
ejde-395	157	31	(	(	PUNCT
ejde-395	157	32	a−	a−	PROPN
ejde-395	157	33	1)r(q2z)r(q−2z	1)r(q2z)r(q−2z	NUM
ejde-395	157	34	)	)	PUNCT
ejde-395	157	35	.	.	PUNCT
ejde-395	158	1	denote	denote	PROPN
ejde-395	158	2	ϕ(z	ϕ(z	PROPN
ejde-395	158	3	)	)	PUNCT
ejde-395	159	1	=	=	PUNCT
ejde-395	159	2	ar(z)2	ar(z)2	PROPN
ejde-395	159	3	−	−	NOUN
ejde-395	159	4	r(qz)r(z	r(qz)r(z	NOUN
ejde-395	159	5	q	q	NOUN
ejde-395	159	6	)	)	PUNCT
ejde-395	159	7	−	−	PROPN
ejde-395	159	8	(	(	PUNCT
ejde-395	159	9	a−	a−	PROPN
ejde-395	159	10	1)r(q2z)r(q−2z	1)r(q2z)r(q−2z	NUM
ejde-395	159	11	)	)	PUNCT
ejde-395	159	12	.	.	PUNCT
ejde-395	160	1	thus	thus	ADV
ejde-395	160	2	,	,	PUNCT
ejde-395	160	3	ϕ(z	ϕ(z	PROPN
ejde-395	160	4	)	)	PUNCT
ejde-395	160	5	≡	≡	PROPN
ejde-395	160	6	0	0	NUM
ejde-395	160	7	.	.	PUNCT
ejde-395	161	1	substituting	substitute	VERB
ejde-395	161	2	r(z	r(z	NOUN
ejde-395	161	3	)	)	PUNCT
ejde-395	161	4	into	into	ADP
ejde-395	161	5	ϕ(z	ϕ(z	NOUN
ejde-395	161	6	)	)	PUNCT
ejde-395	161	7	,	,	PUNCT
ejde-395	161	8	then	then	ADV
ejde-395	161	9	we	we	PRON
ejde-395	161	10	give	give	VERB
ejde-395	161	11	the	the	DET
ejde-395	161	12	coefficients	coefficient	NOUN
ejde-395	161	13	of	of	ADP
ejde-395	161	14	term	term	NOUN
ejde-395	161	15	z2n−1	z2n−1	PROPN
ejde-395	161	16	,	,	PUNCT
ejde-395	161	17	z2n−2	z2n−2	PROPN
ejde-395	161	18	,	,	PUNCT
ejde-395	161	19	z2n−3	z2n−3	PROPN
ejde-395	161	20	,	,	PUNCT
ejde-395	161	21	z2n−4	z2n−4	PROPN
ejde-395	161	22	,	,	PUNCT
ejde-395	161	23	.	.	PUNCT
ejde-395	161	24	.	.	PUNCT
ejde-395	162	1	.	.	PUNCT
ejde-395	163	1	,	,	PUNCT
ejde-395	163	2	zn+1	zn+1	PROPN
ejde-395	163	3	as	as	SCONJ
ejde-395	163	4	follows	follow	VERB
ejde-395	163	5	b2n−1	b2n−1	PROPN
ejde-395	163	6	=	=	PUNCT
ejde-395	163	7	−an−1[a(q	−an−1[a(q	PROPN
ejde-395	163	8	+	+	CCONJ
ejde-395	163	9	q−1	q−1	PROPN
ejde-395	163	10	+	+	CCONJ
ejde-395	163	11	2)−	2)−	NUM
ejde-395	163	12	(	(	PUNCT
ejde-395	163	13	q	q	PROPN
ejde-395	164	1	+	+	NUM
ejde-395	164	2	q−1	q−1	PROPN
ejde-395	164	3	+	+	CCONJ
ejde-395	164	4	1)](q	1)](q	NUM
ejde-395	164	5	+	+	CCONJ
ejde-395	164	6	q−1	q−1	PROPN
ejde-395	164	7	−	−	NOUN
ejde-395	164	8	2	2	NUM
ejde-395	164	9	)	)	PUNCT
ejde-395	164	10	,	,	PUNCT
ejde-395	164	11	(	(	PUNCT
ejde-395	164	12	2.5	2.5	NUM
ejde-395	164	13	)	)	PUNCT
ejde-395	164	14	b2n−2	b2n−2	NOUN
ejde-395	164	15	=	=	PUNCT
ejde-395	164	16	−an−2[a(q2	−an−2[a(q2	PROPN
ejde-395	165	1	+	+	CCONJ
ejde-395	165	2	q−2	q−2	PROPN
ejde-395	165	3	+	+	PROPN
ejde-395	165	4	2)−	2)−	PROPN
ejde-395	165	5	(	(	PUNCT
ejde-395	165	6	q2	q2	NOUN
ejde-395	165	7	+	+	CCONJ
ejde-395	165	8	q−2	q−2	PROPN
ejde-395	165	9	+	+	CCONJ
ejde-395	165	10	1)](q2	1)](q2	NOUN
ejde-395	166	1	+	+	CCONJ
ejde-395	166	2	q−2	q−2	PROPN
ejde-395	166	3	−	−	PROPN
ejde-395	166	4	2	2	NUM
ejde-395	166	5	)	)	PUNCT
ejde-395	166	6	,	,	PUNCT
ejde-395	166	7	(	(	PUNCT
ejde-395	166	8	2.6	2.6	NUM
ejde-395	166	9	)	)	PUNCT
ejde-395	166	10	b2n−3	b2n−3	PROPN
ejde-395	166	11	=	=	PUNCT
ejde-395	167	1	−an−2[a(q2	−an−2[a(q2	PROPN
ejde-395	168	1	+	+	CCONJ
ejde-395	168	2	q−2	q−2	PROPN
ejde-395	168	3	+	+	PROPN
ejde-395	168	4	2)−	2)−	PROPN
ejde-395	168	5	(	(	PUNCT
ejde-395	168	6	q2	q2	NOUN
ejde-395	168	7	+	+	CCONJ
ejde-395	168	8	q−2	q−2	PROPN
ejde-395	168	9	+	+	CCONJ
ejde-395	168	10	1)](q2	1)](q2	NOUN
ejde-395	169	1	+	+	CCONJ
ejde-395	169	2	q−2	q−2	PROPN
ejde-395	169	3	−	−	PROPN
ejde-395	169	4	2	2	NUM
ejde-395	169	5	)	)	PUNCT
ejde-395	170	1	+	+	NOUN
ejde-395	170	2	an−1an−2[a(q	an−1an−2[a(q	NOUN
ejde-395	170	3	+	+	CCONJ
ejde-395	170	4	q−1	q−1	PROPN
ejde-395	170	5	+	+	CCONJ
ejde-395	170	6	2)−	2)−	NUM
ejde-395	170	7	(	(	PUNCT
ejde-395	170	8	q	q	PROPN
ejde-395	170	9	+	+	NUM
ejde-395	170	10	q−1	q−1	PROPN
ejde-395	170	11	+	+	CCONJ
ejde-395	170	12	1)](q	1)](q	NUM
ejde-395	170	13	+	+	CCONJ
ejde-395	170	14	q−1	q−1	PROPN
ejde-395	170	15	−	−	NOUN
ejde-395	170	16	2	2	NUM
ejde-395	170	17	)	)	PUNCT
ejde-395	170	18	,	,	PUNCT
ejde-395	170	19	(	(	PUNCT
ejde-395	170	20	2.7	2.7	NUM
ejde-395	170	21	)	)	PUNCT
ejde-395	170	22	b2n−4	b2n−4	NOUN
ejde-395	170	23	=	=	SYM
ejde-395	170	24	−an−4	−an−4	X
ejde-395	170	25	[	[	PUNCT
ejde-395	170	26	a(q4	a(q4	NOUN
ejde-395	170	27	+	+	X
ejde-395	170	28	q−4	q−4	PROPN
ejde-395	170	29	+	+	NUM
ejde-395	170	30	2)−	2)−	PROPN
ejde-395	170	31	(	(	PUNCT
ejde-395	170	32	q4	q4	PROPN
ejde-395	170	33	+	+	CCONJ
ejde-395	170	34	q−4	q−4	PROPN
ejde-395	170	35	+	+	CCONJ
ejde-395	170	36	1)](q2	1)](q2	ADJ
ejde-395	171	1	+	+	CCONJ
ejde-395	171	2	q−2	q−2	PROPN
ejde-395	171	3	−	−	PROPN
ejde-395	171	4	2	2	NUM
ejde-395	171	5	)	)	PUNCT
ejde-395	171	6	+	+	NOUN
ejde-395	171	7	an−1an−3[a(q2	an−1an−3[a(q2	PROPN
ejde-395	171	8	+	+	CCONJ
ejde-395	171	9	q−2	q−2	PROPN
ejde-395	171	10	+	+	PROPN
ejde-395	171	11	2)−	2)−	PROPN
ejde-395	171	12	(	(	PUNCT
ejde-395	171	13	q2	q2	NOUN
ejde-395	171	14	+	+	CCONJ
ejde-395	171	15	q−2	q−2	PROPN
ejde-395	171	16	+	+	NOUN
ejde-395	171	17	1	1	NUM
ejde-395	171	18	)	)	PUNCT
ejde-395	171	19	]	]	PUNCT
ejde-395	172	1	(	(	PUNCT
ejde-395	172	2	q2	q2	NOUN
ejde-395	172	3	+	+	CCONJ
ejde-395	172	4	q−2	q−2	PROPN
ejde-395	172	5	−	−	PROPN
ejde-395	172	6	2	2	NUM
ejde-395	172	7	)	)	PUNCT
ejde-395	172	8	,	,	PUNCT
ejde-395	172	9	(	(	PUNCT
ejde-395	172	10	2.8	2.8	NUM
ejde-395	172	11	)	)	PUNCT
ejde-395	172	12	.	.	PUNCT
ejde-395	172	13	.	.	PUNCT
ejde-395	172	14	.	.	PUNCT
ejde-395	173	1	b2n−i	b2n−i	X
ejde-395	174	1	=	=	PUNCT
ejde-395	174	2	−an−i[a(qi	−an−i[a(qi	PROPN
ejde-395	174	3	+	+	NUM
ejde-395	174	4	q−i	q−i	NOUN
ejde-395	174	5	+	+	X
ejde-395	174	6	2)−	2)−	NUM
ejde-395	174	7	(	(	PUNCT
ejde-395	174	8	qi	qi	NOUN
ejde-395	174	9	+	+	NUM
ejde-395	174	10	q−i	q−i	NOUN
ejde-395	174	11	+	+	CCONJ
ejde-395	174	12	1)](qi	1)](qi	NUM
ejde-395	174	13	+	+	CCONJ
ejde-395	174	14	q−i	q−i	NOUN
ejde-395	174	15	−	−	NOUN
ejde-395	174	16	2	2	NUM
ejde-395	174	17	)	)	PUNCT
ejde-395	175	1	+	+	ADJ
ejde-395	175	2	an−1an−i+1[a(qi−2	an−1an−i+1[a(qi−2	NOUN
ejde-395	175	3	+	+	ADJ
ejde-395	175	4	q−(i−2	q−(i−2	NOUN
ejde-395	175	5	)	)	PUNCT
ejde-395	175	6	+	+	PROPN
ejde-395	176	1	2)−	2)−	NUM
ejde-395	176	2	(	(	PUNCT
ejde-395	176	3	qi−2	qi−2	NOUN
ejde-395	176	4	+	+	NUM
ejde-395	176	5	q−(i−2	q−(i−2	NOUN
ejde-395	176	6	)	)	PUNCT
ejde-395	176	7	+	+	CCONJ
ejde-395	176	8	1	1	NUM
ejde-395	176	9	)	)	PUNCT
ejde-395	176	10	]	]	PUNCT
ejde-395	176	11	×	×	NOUN
ejde-395	176	12	(	(	PUNCT
ejde-395	176	13	qi−2	qi−2	NOUN
ejde-395	176	14	+	+	NUM
ejde-395	176	15	q−(i−2	q−(i−2	NOUN
ejde-395	176	16	)	)	PUNCT
ejde-395	176	17	−	−	PROPN
ejde-395	176	18	2	2	NUM
ejde-395	176	19	)	)	PUNCT
ejde-395	176	20	+	+	CCONJ
ejde-395	176	21	·	·	PUNCT
ejde-395	176	22	·	·	PUNCT
ejde-395	176	23	·	·	PUNCT
ejde-395	176	24	+	+	X
ejde-395	176	25	an−	an−	X
ejde-395	176	26	[	[	PUNCT
ejde-395	176	27	i	i	NOUN
ejde-395	176	28	2	2	NUM
ejde-395	176	29	]	]	PUNCT
ejde-395	176	30	an−	an−	X
ejde-395	176	31	[	[	PUNCT
ejde-395	176	32	i	i	NOUN
ejde-395	176	33	2	2	NUM
ejde-395	176	34	]	]	X
ejde-395	176	35	+1	+1	X
ejde-395	176	36	[	[	PUNCT
ejde-395	176	37	a(q2	a(q2	NOUN
ejde-395	177	1	+	+	CCONJ
ejde-395	177	2	q−2	q−2	PROPN
ejde-395	177	3	+	+	NOUN
ejde-395	177	4	2	2	NUM
ejde-395	177	5	)	)	PUNCT
ejde-395	177	6	−	−	PROPN
ejde-395	177	7	(	(	PUNCT
ejde-395	177	8	q2	q2	NOUN
ejde-395	177	9	+	+	CCONJ
ejde-395	178	1	q−2	q−2	PROPN
ejde-395	178	2	+	+	NOUN
ejde-395	178	3	1	1	NUM
ejde-395	178	4	)	)	PUNCT
ejde-395	178	5	]	]	PUNCT
ejde-395	178	6	(	(	PUNCT
ejde-395	178	7	q2	q2	NOUN
ejde-395	178	8	+	+	CCONJ
ejde-395	178	9	q−2	q−2	PROPN
ejde-395	178	10	−	−	PROPN
ejde-395	178	11	2	2	NUM
ejde-395	178	12	)	)	PUNCT
ejde-395	178	13	,	,	PUNCT
ejde-395	178	14	(	(	PUNCT
ejde-395	178	15	2.9	2.9	NUM
ejde-395	178	16	)	)	PUNCT
ejde-395	178	17	.	.	PUNCT
ejde-395	178	18	.	.	PUNCT
ejde-395	179	1	.	.	PUNCT
ejde-395	180	1	bn+1	bn+1	X
ejde-395	180	2	=	=	PUNCT
ejde-395	181	1	−a1[a(qn−1	−a1[a(qn−1	PROPN
ejde-395	182	1	+	+	PUNCT
ejde-395	182	2	q−(n−1	q−(n−1	ADJ
ejde-395	182	3	)	)	PUNCT
ejde-395	183	1	+	+	SYM
ejde-395	183	2	2)−	2)−	NUM
ejde-395	183	3	(	(	PUNCT
ejde-395	183	4	qn−1	qn−1	PROPN
ejde-395	183	5	+	+	CCONJ
ejde-395	183	6	q−(n−1	q−(n−1	ADJ
ejde-395	183	7	)	)	PUNCT
ejde-395	184	1	+	+	NOUN
ejde-395	184	2	1	1	NUM
ejde-395	184	3	)	)	PUNCT
ejde-395	184	4	]	]	PUNCT
ejde-395	185	1	×	×	NOUN
ejde-395	185	2	(	(	PUNCT
ejde-395	185	3	qn−1	qn−1	PROPN
ejde-395	185	4	+	+	NUM
ejde-395	185	5	q−(n−1	q−(n−1	ADJ
ejde-395	185	6	)	)	PUNCT
ejde-395	185	7	−	−	PROPN
ejde-395	185	8	2	2	X
ejde-395	185	9	)	)	PUNCT
ejde-395	185	10	+	+	NOUN
ejde-395	185	11	an−1a2[a(qn−3	an−1a2[a(qn−3	PROPN
ejde-395	185	12	+	+	CCONJ
ejde-395	185	13	q−(n−3	q−(n−3	PROPN
ejde-395	185	14	)	)	PUNCT
ejde-395	185	15	+	+	CCONJ
ejde-395	185	16	2	2	X
ejde-395	185	17	)	)	PUNCT
ejde-395	185	18	−	−	PROPN
ejde-395	185	19	(	(	PUNCT
ejde-395	185	20	qn−3	qn−3	PROPN
ejde-395	185	21	+	+	CCONJ
ejde-395	185	22	q−(n−3	q−(n−3	ADJ
ejde-395	185	23	)	)	PUNCT
ejde-395	185	24	+	+	CCONJ
ejde-395	185	25	1)](qn−3	1)](qn−3	NUM
ejde-395	185	26	+	+	CCONJ
ejde-395	185	27	q−(n−3	q−(n−3	ADJ
ejde-395	185	28	)	)	PUNCT
ejde-395	185	29	−	−	PROPN
ejde-395	185	30	2	2	NUM
ejde-395	185	31	)	)	PUNCT
ejde-395	185	32	+	+	CCONJ
ejde-395	185	33	.	.	PUNCT
ejde-395	185	34	.	.	PUNCT
ejde-395	185	35	.	.	PUNCT
ejde-395	185	36	.	.	PUNCT
ejde-395	186	1	(	(	PUNCT
ejde-395	186	2	2.10	2.10	NUM
ejde-395	186	3	)	)	PUNCT
ejde-395	186	4	note	note	NOUN
ejde-395	186	5	that	that	SCONJ
ejde-395	186	6	if	if	SCONJ
ejde-395	186	7	i	i	PRON
ejde-395	186	8	is	be	AUX
ejde-395	186	9	an	an	DET
ejde-395	186	10	even	even	ADV
ejde-395	186	11	integer	integer	NOUN
ejde-395	186	12	in	in	ADP
ejde-395	186	13	(	(	PUNCT
ejde-395	186	14	2.9	2.9	NUM
ejde-395	186	15	)	)	PUNCT
ejde-395	186	16	,	,	PUNCT
ejde-395	186	17	then	then	ADV
ejde-395	186	18	an−	an−	NOUN
ejde-395	186	19	[	[	PUNCT
ejde-395	186	20	i	i	NOUN
ejde-395	186	21	2	2	NUM
ejde-395	186	22	]	]	PUNCT
ejde-395	186	23	an−	an−	X
ejde-395	186	24	[	[	PUNCT
ejde-395	186	25	i	i	NOUN
ejde-395	186	26	2	2	NUM
ejde-395	186	27	]	]	PUNCT
ejde-395	186	28	+1	+1	PRON
ejde-395	186	29	should	should	AUX
ejde-395	186	30	be	be	AUX
ejde-395	186	31	replaced	replace	VERB
ejde-395	186	32	by	by	ADP
ejde-395	186	33	an−	an−	PROPN
ejde-395	187	1	i	i	PRON
ejde-395	187	2	2−1an−	2−1an−	PROPN
ejde-395	187	3	i	i	PRON
ejde-395	187	4	2	2	NUM
ejde-395	187	5	+1	+1	NOUN
ejde-395	187	6	.	.	PUNCT
ejde-395	188	1	in	in	ADP
ejde-395	188	2	view	view	NOUN
ejde-395	188	3	of	of	ADP
ejde-395	188	4	(	(	PUNCT
ejde-395	188	5	2.5)-(2.10	2.5)-(2.10	NUM
ejde-395	188	6	)	)	PUNCT
ejde-395	188	7	,	,	PUNCT
ejde-395	188	8	we	we	PRON
ejde-395	188	9	conclude	conclude	VERB
ejde-395	188	10	that	that	SCONJ
ejde-395	188	11	there	there	PRON
ejde-395	188	12	are	be	VERB
ejde-395	188	13	at	at	ADP
ejde-395	188	14	most	most	ADJ
ejde-395	188	15	one	one	NUM
ejde-395	188	16	of	of	ADP
ejde-395	188	17	a1	a1	NOUN
ejde-395	188	18	,	,	PUNCT
ejde-395	188	19	a2	a2	PROPN
ejde-395	188	20	,	,	PUNCT
ejde-395	188	21	.	.	PUNCT
ejde-395	188	22	.	.	PUNCT
ejde-395	189	1	.	.	PUNCT
ejde-395	190	1	,	,	PUNCT
ejde-395	190	2	an−1	an−1	PROPN
ejde-395	190	3	can	can	AUX
ejde-395	190	4	be	be	AUX
ejde-395	190	5	equal	equal	ADJ
ejde-395	190	6	to	to	ADP
ejde-395	190	7	0	0	NUM
ejde-395	190	8	.	.	PUNCT
ejde-395	191	1	otherwise	otherwise	ADV
ejde-395	191	2	,	,	PUNCT
ejde-395	191	3	if	if	SCONJ
ejde-395	191	4	there	there	PRON
ejde-395	191	5	exist	exist	VERB
ejde-395	191	6	two	two	NUM
ejde-395	191	7	integers	integer	NOUN
ejde-395	191	8	i	i	PRON
ejde-395	191	9	,	,	PUNCT
ejde-395	191	10	j	j	PROPN
ejde-395	191	11	∈	∈	PROPN
ejde-395	191	12	n+	n+	NUM
ejde-395	192	1	such	such	ADJ
ejde-395	192	2	that	that	SCONJ
ejde-395	192	3	i	i	PRON
ejde-395	192	4	6=	6=	PROPN
ejde-395	192	5	j	j	PROPN
ejde-395	192	6	,	,	PUNCT
ejde-395	192	7	aj	aj	PROPN
ejde-395	192	8	6=	6=	PROPN
ejde-395	192	9	0	0	NUM
ejde-395	192	10	,	,	PUNCT
ejde-395	192	11	ai	ai	VERB
ejde-395	192	12	6=	6=	ADP
ejde-395	192	13	0	0	NUM
ejde-395	192	14	and	and	CCONJ
ejde-395	192	15	at	at	ADP
ejde-395	192	16	=	=	NOUN
ejde-395	192	17	0	0	NUM
ejde-395	192	18	for	for	ADP
ejde-395	192	19	t	t	NOUN
ejde-395	192	20	=	=	SYM
ejde-395	192	21	1	1	NUM
ejde-395	192	22	,	,	PUNCT
ejde-395	192	23	2	2	NUM
ejde-395	192	24	,	,	PUNCT
ejde-395	192	25	.	.	PUNCT
ejde-395	192	26	.	.	PUNCT
ejde-395	193	1	.	.	PUNCT
ejde-395	194	1	,	,	PUNCT
ejde-395	194	2	n−1	n−1	PROPN
ejde-395	194	3	,	,	PUNCT
ejde-395	194	4	t	t	PROPN
ejde-395	194	5	6=	6=	PROPN
ejde-395	195	1	i	i	PROPN
ejde-395	195	2	,	,	PUNCT
ejde-395	195	3	t	t	PROPN
ejde-395	195	4	6=	6=	PROPN
ejde-395	195	5	j.	j.	PROPN
ejde-395	195	6	from	from	ADP
ejde-395	195	7	(	(	PUNCT
ejde-395	195	8	2.5)-(2.10	2.5)-(2.10	NUM
ejde-395	195	9	)	)	PUNCT
ejde-395	195	10	,	,	PUNCT
ejde-395	195	11	we	we	PRON
ejde-395	195	12	have	have	VERB
ejde-395	195	13	a(qi	a(qi	NOUN
ejde-395	195	14	+	+	PUNCT
ejde-395	195	15	q−i	q−i	NOUN
ejde-395	195	16	+	+	X
ejde-395	195	17	2)−	2)−	NUM
ejde-395	195	18	(	(	PUNCT
ejde-395	195	19	qi	qi	NOUN
ejde-395	195	20	+	+	NUM
ejde-395	195	21	q−i	q−i	NOUN
ejde-395	195	22	+	+	CCONJ
ejde-395	195	23	1	1	NUM
ejde-395	195	24	)	)	PUNCT
ejde-395	195	25	≡	≡	PROPN
ejde-395	195	26	0	0	NUM
ejde-395	195	27	,	,	PUNCT
ejde-395	195	28	a(qj	a(qj	ADP
ejde-395	195	29	+	+	CCONJ
ejde-395	195	30	q−j	q−j	SYM
ejde-395	195	31	+	+	PROPN
ejde-395	195	32	2)−	2)−	NUM
ejde-395	195	33	(	(	PUNCT
ejde-395	195	34	qj	qj	PROPN
ejde-395	195	35	+	+	X
ejde-395	195	36	q−j	q−j	NUM
ejde-395	195	37	+	+	NOUN
ejde-395	195	38	1	1	NUM
ejde-395	195	39	)	)	PUNCT
ejde-395	195	40	≡	≡	PROPN
ejde-395	195	41	0	0	NUM
ejde-395	195	42	.	.	PUNCT
ejde-395	195	43	ejde-2020/14	ejde-2020/14	VERB
ejde-395	195	44	q	q	NOUN
ejde-395	195	45	-	-	PUNCT
ejde-395	195	46	difference	difference	NOUN
ejde-395	195	47	painlevé	painlevé	NOUN
ejde-395	195	48	equations	equation	NOUN
ejde-395	195	49	7	7	NUM
ejde-395	195	50	this	this	PRON
ejde-395	195	51	is	be	AUX
ejde-395	195	52	impossible	impossible	ADJ
ejde-395	195	53	as	as	SCONJ
ejde-395	195	54	|q|	|q|	VERB
ejde-395	195	55	6=	6=	PRON
ejde-395	195	56	1	1	NUM
ejde-395	195	57	.	.	PUNCT
ejde-395	196	1	thus	thus	ADV
ejde-395	196	2	,	,	PUNCT
ejde-395	196	3	without	without	ADP
ejde-395	196	4	loss	loss	NOUN
ejde-395	196	5	of	of	ADP
ejde-395	196	6	generality	generality	NOUN
ejde-395	196	7	,	,	PUNCT
ejde-395	196	8	we	we	PRON
ejde-395	196	9	assume	assume	VERB
ejde-395	196	10	that	that	SCONJ
ejde-395	196	11	an−1	an−1	ADV
ejde-395	196	12	6=	6=	NUM
ejde-395	196	13	0	0	NUM
ejde-395	196	14	and	and	CCONJ
ejde-395	196	15	ai	ai	VERB
ejde-395	196	16	=	=	NOUN
ejde-395	196	17	0	0	NUM
ejde-395	196	18	for	for	ADP
ejde-395	196	19	j	j	PROPN
ejde-395	196	20	=	=	SYM
ejde-395	196	21	1	1	NUM
ejde-395	196	22	,	,	PUNCT
ejde-395	196	23	2	2	NUM
ejde-395	196	24	,	,	PUNCT
ejde-395	196	25	.	.	PUNCT
ejde-395	196	26	.	.	PUNCT
ejde-395	197	1	.	.	PUNCT
ejde-395	198	1	,	,	PUNCT
ejde-395	199	1	n	n	CCONJ
ejde-395	199	2	−	−	PROPN
ejde-395	199	3	2	2	NUM
ejde-395	199	4	;	;	PUNCT
ejde-395	199	5	j	j	PROPN
ejde-395	199	6	6=	6=	PROPN
ejde-395	199	7	n	n	CCONJ
ejde-395	199	8	−	−	PROPN
ejde-395	199	9	1	1	NUM
ejde-395	199	10	.	.	PUNCT
ejde-395	200	1	then	then	ADV
ejde-395	200	2	,	,	PUNCT
ejde-395	200	3	in	in	ADP
ejde-395	200	4	view	view	NOUN
ejde-395	200	5	of	of	ADP
ejde-395	200	6	(	(	PUNCT
ejde-395	200	7	2.5	2.5	NUM
ejde-395	200	8	)	)	PUNCT
ejde-395	200	9	,	,	PUNCT
ejde-395	200	10	it	it	PRON
ejde-395	200	11	follows	follow	VERB
ejde-395	200	12	that	that	SCONJ
ejde-395	200	13	a	a	DET
ejde-395	200	14	=	=	NOUN
ejde-395	200	15	q2	q2	NOUN
ejde-395	200	16	+	+	CCONJ
ejde-395	200	17	q	q	PUNCT
ejde-395	201	1	+	+	NUM
ejde-395	201	2	1	1	NUM
ejde-395	201	3	(	(	PUNCT
ejde-395	201	4	q	q	NOUN
ejde-395	202	1	+	+	PROPN
ejde-395	202	2	1)2	1)2	NUM
ejde-395	202	3	.	.	PUNCT
ejde-395	203	1	(	(	PUNCT
ejde-395	203	2	2.11	2.11	NUM
ejde-395	203	3	)	)	PUNCT
ejde-395	203	4	thus	thus	ADV
ejde-395	203	5	,	,	PUNCT
ejde-395	203	6	r(z	r(z	PROPN
ejde-395	203	7	)	)	PUNCT
ejde-395	203	8	,	,	PUNCT
ejde-395	203	9	p	p	X
ejde-395	203	10	(	(	PUNCT
ejde-395	203	11	z	z	NOUN
ejde-395	203	12	)	)	PUNCT
ejde-395	203	13	can	can	AUX
ejde-395	203	14	be	be	AUX
ejde-395	203	15	represented	represent	VERB
ejde-395	203	16	in	in	ADP
ejde-395	203	17	the	the	DET
ejde-395	203	18	form	form	NOUN
ejde-395	203	19	r(z	r(z	NOUN
ejde-395	203	20	)	)	PUNCT
ejde-395	204	1	=	=	PUNCT
ejde-395	205	1	zn	zn	X
ejde-395	205	2	+	+	PROPN
ejde-395	205	3	an−1z	an−1z	PROPN
ejde-395	205	4	n−1	n−1	PROPN
ejde-395	205	5	+	+	NOUN
ejde-395	205	6	a0	a0	NOUN
ejde-395	205	7	,	,	PUNCT
ejde-395	205	8	p	p	X
ejde-395	205	9	(	(	PUNCT
ejde-395	205	10	z	z	NOUN
ejde-395	205	11	)	)	PUNCT
ejde-395	205	12	=	=	SYM
ejde-395	206	1	a[zn	a[zn	PROPN
ejde-395	206	2	+	+	PROPN
ejde-395	206	3	an−1z	an−1z	PROPN
ejde-395	206	4	n−1	n−1	PROPN
ejde-395	206	5	+	+	NOUN
ejde-395	206	6	a0]2	a0]2	ADJ
ejde-395	206	7	,	,	PUNCT
ejde-395	206	8	(	(	PUNCT
ejde-395	206	9	2.12	2.12	NUM
ejde-395	206	10	)	)	PUNCT
ejde-395	207	1	where	where	SCONJ
ejde-395	207	2	n	n	X
ejde-395	207	3	6=	6=	NUM
ejde-395	207	4	1	1	NUM
ejde-395	207	5	.	.	PUNCT
ejde-395	208	1	it	it	PRON
ejde-395	208	2	leads	lead	VERB
ejde-395	208	3	to	to	ADP
ejde-395	208	4	q(z	q(z	PROPN
ejde-395	208	5	)	)	PUNCT
ejde-395	208	6	=	=	PUNCT
ejde-395	208	7	(	(	PUNCT
ejde-395	208	8	qnzn	qnzn	NOUN
ejde-395	208	9	+	+	ADP
ejde-395	208	10	an−1q	an−1q	PROPN
ejde-395	208	11	n−1zn−1	n−1zn−1	NOUN
ejde-395	208	12	+	+	NOUN
ejde-395	208	13	a0)(q−nzn	a0)(q−nzn	ADV
ejde-395	208	14	+	+	ADJ
ejde-395	208	15	an−1q	an−1q	PROPN
ejde-395	208	16	−n+1zn−1	−n+1zn−1	PROPN
ejde-395	208	17	+	+	PROPN
ejde-395	208	18	a0	a0	NOUN
ejde-395	208	19	)	)	PUNCT
ejde-395	208	20	.	.	PUNCT
ejde-395	209	1	(	(	PUNCT
ejde-395	209	2	2.13	2.13	NUM
ejde-395	209	3	)	)	PUNCT
ejde-395	209	4	substituting	substituting	NOUN
ejde-395	209	5	(	(	PUNCT
ejde-395	209	6	2.12	2.12	NUM
ejde-395	209	7	)	)	PUNCT
ejde-395	209	8	and	and	CCONJ
ejde-395	209	9	(	(	PUNCT
ejde-395	209	10	2.13	2.13	NUM
ejde-395	209	11	)	)	PUNCT
ejde-395	209	12	into	into	ADP
ejde-395	209	13	ϕ(z	ϕ(z	NOUN
ejde-395	209	14	)	)	PUNCT
ejde-395	209	15	,	,	PUNCT
ejde-395	209	16	and	and	CCONJ
ejde-395	209	17	analyzing	analyze	VERB
ejde-395	209	18	the	the	DET
ejde-395	209	19	coefficients	coefficient	NOUN
ejde-395	209	20	of	of	ADP
ejde-395	209	21	the	the	DET
ejde-395	209	22	term	term	NOUN
ejde-395	209	23	zn	zn	PROPN
ejde-395	209	24	,	,	PUNCT
ejde-395	209	25	we	we	PRON
ejde-395	209	26	have	have	VERB
ejde-395	209	27	bn	bn	NOUN
ejde-395	209	28	=	=	SYM
ejde-395	209	29	−a0[a(qn	−a0[a(qn	PROPN
ejde-395	209	30	+	+	CCONJ
ejde-395	209	31	q−n	q−n	PROPN
ejde-395	209	32	+	+	PROPN
ejde-395	209	33	2)−	2)−	NUM
ejde-395	209	34	(	(	PUNCT
ejde-395	209	35	qn	qn	NOUN
ejde-395	209	36	+	+	X
ejde-395	209	37	q−n	q−n	PROPN
ejde-395	209	38	+	+	CCONJ
ejde-395	209	39	1)](qn	1)](qn	NUM
ejde-395	209	40	+	+	CCONJ
ejde-395	209	41	q−n	q−n	PROPN
ejde-395	209	42	−	−	PROPN
ejde-395	209	43	2	2	NUM
ejde-395	209	44	)	)	PUNCT
ejde-395	209	45	.	.	PUNCT
ejde-395	210	1	(	(	PUNCT
ejde-395	210	2	2.14	2.14	NUM
ejde-395	210	3	)	)	PUNCT
ejde-395	210	4	in	in	ADP
ejde-395	210	5	view	view	NOUN
ejde-395	210	6	of	of	ADP
ejde-395	210	7	(	(	PUNCT
ejde-395	210	8	2.11	2.11	NUM
ejde-395	210	9	)	)	PUNCT
ejde-395	210	10	,	,	PUNCT
ejde-395	210	11	|q|	|q|	VERB
ejde-395	210	12	6=	6=	ADP
ejde-395	210	13	1	1	NUM
ejde-395	210	14	and	and	CCONJ
ejde-395	210	15	n	n	CCONJ
ejde-395	210	16	6=	6=	NUM
ejde-395	210	17	1	1	NUM
ejde-395	210	18	,	,	PUNCT
ejde-395	210	19	it	it	PRON
ejde-395	210	20	follows	follow	VERB
ejde-395	210	21	that	that	SCONJ
ejde-395	210	22	a(qn	a(qn	PROPN
ejde-395	210	23	+	+	CCONJ
ejde-395	210	24	q−n	q−n	PROPN
ejde-395	210	25	+	+	PROPN
ejde-395	210	26	2)−	2)−	NUM
ejde-395	210	27	(	(	PUNCT
ejde-395	210	28	qn	qn	NOUN
ejde-395	210	29	+	+	X
ejde-395	210	30	q−n	q−n	PROPN
ejde-395	210	31	+	+	NOUN
ejde-395	210	32	1	1	NUM
ejde-395	210	33	)	)	PUNCT
ejde-395	210	34	6=	6=	ADP
ejde-395	210	35	0	0	NUM
ejde-395	210	36	.	.	PUNCT
ejde-395	211	1	thus	thus	ADV
ejde-395	211	2	,	,	PUNCT
ejde-395	211	3	by	by	ADP
ejde-395	211	4	combining	combine	VERB
ejde-395	211	5	with	with	ADP
ejde-395	211	6	a0	a0	PROPN
ejde-395	211	7	6=	6=	ADP
ejde-395	211	8	0	0	NUM
ejde-395	211	9	,	,	PUNCT
ejde-395	211	10	this	this	PRON
ejde-395	211	11	is	be	AUX
ejde-395	211	12	a	a	DET
ejde-395	211	13	contradiction	contradiction	NOUN
ejde-395	211	14	with	with	ADP
ejde-395	211	15	ϕ(z	ϕ(z	NOUN
ejde-395	211	16	)	)	PUNCT
ejde-395	211	17	≡	≡	PROPN
ejde-395	211	18	0	0	NUM
ejde-395	211	19	.	.	PUNCT
ejde-395	212	1	therefore	therefore	ADV
ejde-395	212	2	,	,	PUNCT
ejde-395	212	3	a1	a1	NOUN
ejde-395	212	4	=	=	SYM
ejde-395	212	5	a2	a2	PROPN
ejde-395	212	6	=	=	SYM
ejde-395	212	7	·	·	PUNCT
ejde-395	212	8	·	·	PUNCT
ejde-395	212	9	·	·	PUNCT
ejde-395	213	1	=	=	PUNCT
ejde-395	213	2	an−1	an−1	PROPN
ejde-395	213	3	≡	≡	PROPN
ejde-395	213	4	0	0	NUM
ejde-395	213	5	;	;	PUNCT
ejde-395	213	6	that	that	PRON
ejde-395	213	7	is	be	AUX
ejde-395	213	8	,	,	PUNCT
ejde-395	213	9	r(z	r(z	NOUN
ejde-395	213	10	)	)	PUNCT
ejde-395	213	11	=	=	PUNCT
ejde-395	214	1	zn	zn	PROPN
ejde-395	214	2	+	+	NUM
ejde-395	214	3	b	b	PROPN
ejde-395	214	4	,	,	PUNCT
ejde-395	214	5	p	p	X
ejde-395	214	6	(	(	PUNCT
ejde-395	214	7	z	z	NOUN
ejde-395	214	8	)	)	PUNCT
ejde-395	214	9	=	=	SYM
ejde-395	215	1	a(zn	a(zn	PROPN
ejde-395	215	2	+	+	CCONJ
ejde-395	215	3	b)2	b)2	ADJ
ejde-395	215	4	,	,	PUNCT
ejde-395	215	5	q(z	q(z	PROPN
ejde-395	215	6	)	)	PUNCT
ejde-395	215	7	=	=	PUNCT
ejde-395	216	1	(	(	PUNCT
ejde-395	216	2	qnzn	qnzn	NOUN
ejde-395	216	3	+	+	NUM
ejde-395	216	4	b)(q−nzn	b)(q−nzn	NOUN
ejde-395	216	5	+	+	CCONJ
ejde-395	216	6	b	b	NOUN
ejde-395	216	7	)	)	PUNCT
ejde-395	216	8	,	,	PUNCT
ejde-395	216	9	(	(	PUNCT
ejde-395	216	10	2.15	2.15	NUM
ejde-395	216	11	)	)	PUNCT
ejde-395	216	12	where	where	SCONJ
ejde-395	216	13	b	b	NOUN
ejde-395	216	14	is	be	AUX
ejde-395	216	15	an	an	DET
ejde-395	216	16	any	any	DET
ejde-395	216	17	nonzero	nonzero	NOUN
ejde-395	216	18	constant	constant	ADJ
ejde-395	216	19	.	.	PUNCT
ejde-395	217	1	substituting	substitute	VERB
ejde-395	217	2	(	(	PUNCT
ejde-395	217	3	2.15	2.15	NUM
ejde-395	217	4	)	)	PUNCT
ejde-395	217	5	into	into	ADP
ejde-395	217	6	ϕ(z	ϕ(z	NOUN
ejde-395	217	7	)	)	PUNCT
ejde-395	217	8	,	,	PUNCT
ejde-395	217	9	we	we	PRON
ejde-395	217	10	have	have	VERB
ejde-395	217	11	a	a	DET
ejde-395	217	12	=	=	PUNCT
ejde-395	217	13	q2n	q2n	PROPN
ejde-395	218	1	+	+	NUM
ejde-395	218	2	qn	qn	PROPN
ejde-395	218	3	+	+	NOUN
ejde-395	218	4	1	1	NUM
ejde-395	218	5	(	(	PUNCT
ejde-395	218	6	qn	qn	NOUN
ejde-395	218	7	+	+	X
ejde-395	218	8	1)2	1)2	NUM
ejde-395	218	9	.	.	PUNCT
ejde-395	219	1	(	(	PUNCT
ejde-395	219	2	2.16	2.16	NUM
ejde-395	219	3	)	)	PUNCT
ejde-395	219	4	thus	thus	ADV
ejde-395	219	5	,	,	PUNCT
ejde-395	219	6	substituting	substitute	VERB
ejde-395	219	7	(	(	PUNCT
ejde-395	219	8	2.15	2.15	NUM
ejde-395	219	9	)	)	PUNCT
ejde-395	219	10	and	and	CCONJ
ejde-395	219	11	(	(	PUNCT
ejde-395	219	12	2.16	2.16	NUM
ejde-395	219	13	)	)	PUNCT
ejde-395	219	14	into	into	ADP
ejde-395	219	15	(	(	PUNCT
ejde-395	219	16	2.1	2.1	NUM
ejde-395	219	17	)	)	PUNCT
ejde-395	219	18	,	,	PUNCT
ejde-395	219	19	we	we	PRON
ejde-395	219	20	obtain	obtain	VERB
ejde-395	219	21	µ	µ	X
ejde-395	219	22	=	=	SYM
ejde-395	219	23	a3(a−	a3(a−	ADP
ejde-395	219	24	1	1	NUM
ejde-395	219	25	)	)	PUNCT
ejde-395	219	26	=	=	NOUN
ejde-395	220	1	−q	−q	ADJ
ejde-395	220	2	n(q2n	n(q2n	ADJ
ejde-395	220	3	+	+	SYM
ejde-395	220	4	qn	qn	PROPN
ejde-395	220	5	+	+	PROPN
ejde-395	220	6	1)3	1)3	PROPN
ejde-395	220	7	(	(	PUNCT
ejde-395	220	8	qn	qn	NOUN
ejde-395	220	9	+	+	PROPN
ejde-395	220	10	1)8	1)8	NUM
ejde-395	220	11	.	.	PUNCT
ejde-395	221	1	this	this	PRON
ejde-395	221	2	completes	complete	VERB
ejde-395	221	3	the	the	DET
ejde-395	221	4	proof	proof	NOUN
ejde-395	221	5	of	of	ADP
ejde-395	221	6	theorem	theorem	ADJ
ejde-395	221	7	1.5	1.5	NUM
ejde-395	221	8	.	.	PUNCT
ejde-395	221	9	�	�	PROPN
ejde-395	221	10	3	3	NUM
ejde-395	221	11	.	.	PUNCT
ejde-395	221	12	proof	proof	NOUN
ejde-395	221	13	of	of	ADP
ejde-395	221	14	theorem	theorem	ADJ
ejde-395	221	15	1.7	1.7	NUM
ejde-395	221	16	the	the	DET
ejde-395	221	17	following	follow	VERB
ejde-395	221	18	lemmas	lemma	NOUN
ejde-395	221	19	are	be	AUX
ejde-395	221	20	necessary	necessary	ADJ
ejde-395	221	21	.	.	PUNCT
ejde-395	222	1	lemma	lemma	PROPN
ejde-395	222	2	3.1	3.1	NUM
ejde-395	222	3	(	(	PUNCT
ejde-395	222	4	[	[	X
ejde-395	222	5	1	1	NUM
ejde-395	222	6	,	,	PUNCT
ejde-395	222	7	theorem	theorem	VERB
ejde-395	222	8	2.5	2.5	NUM
ejde-395	222	9	]	]	PUNCT
ejde-395	222	10	)	)	PUNCT
ejde-395	222	11	.	.	PUNCT
ejde-395	223	1	let	let	VERB
ejde-395	223	2	f	f	PRON
ejde-395	223	3	be	be	AUX
ejde-395	223	4	a	a	DET
ejde-395	223	5	nonconstant	nonconstant	ADJ
ejde-395	223	6	zero	zero	NUM
ejde-395	223	7	-	-	PUNCT
ejde-395	223	8	order	order	NOUN
ejde-395	223	9	meromorphic	meromorphic	ADJ
ejde-395	223	10	solution	solution	NOUN
ejde-395	223	11	of	of	ADP
ejde-395	223	12	pq(z	pq(z	PROPN
ejde-395	223	13	,	,	PUNCT
ejde-395	223	14	f	f	X
ejde-395	223	15	)	)	PUNCT
ejde-395	223	16	=	=	SYM
ejde-395	223	17	0	0	NUM
ejde-395	223	18	,	,	PUNCT
ejde-395	223	19	where	where	SCONJ
ejde-395	223	20	pq(z	pq(z	NOUN
ejde-395	223	21	,	,	PUNCT
ejde-395	223	22	f	f	X
ejde-395	223	23	)	)	PUNCT
ejde-395	223	24	is	be	AUX
ejde-395	223	25	a	a	DET
ejde-395	223	26	q	q	ADJ
ejde-395	223	27	-	-	PUNCT
ejde-395	223	28	difference	difference	NOUN
ejde-395	223	29	polynomial	polynomial	NOUN
ejde-395	223	30	in	in	ADP
ejde-395	223	31	f(z	f(z	PROPN
ejde-395	223	32	)	)	PUNCT
ejde-395	223	33	.	.	PUNCT
ejde-395	224	1	if	if	SCONJ
ejde-395	224	2	pq(z	pq(z	NUM
ejde-395	224	3	,	,	PUNCT
ejde-395	224	4	a	a	PRON
ejde-395	224	5	)	)	PUNCT
ejde-395	224	6	6≡	6≡	NUM
ejde-395	224	7	0	0	NUM
ejde-395	224	8	for	for	ADP
ejde-395	224	9	slowly	slowly	ADV
ejde-395	224	10	moving	move	VERB
ejde-395	224	11	target	target	NOUN
ejde-395	224	12	a(z	a(z	NOUN
ejde-395	224	13	)	)	PUNCT
ejde-395	224	14	,	,	PUNCT
ejde-395	224	15	then	then	ADV
ejde-395	224	16	m	m	VERB
ejde-395	224	17	(	(	PUNCT
ejde-395	224	18	r	r	NOUN
ejde-395	224	19	,	,	PUNCT
ejde-395	224	20	1	1	NUM
ejde-395	224	21	f	f	NOUN
ejde-395	224	22	−	−	NOUN
ejde-395	224	23	a	a	X
ejde-395	224	24	)	)	PUNCT
ejde-395	224	25	=	=	SYM
ejde-395	224	26	s(r	s(r	PROPN
ejde-395	224	27	,	,	PUNCT
ejde-395	224	28	f	f	NOUN
ejde-395	224	29	)	)	PUNCT
ejde-395	224	30	.	.	PUNCT
ejde-395	225	1	lemma	lemma	PROPN
ejde-395	225	2	3.2	3.2	NUM
ejde-395	225	3	(	(	PUNCT
ejde-395	225	4	[	[	X
ejde-395	225	5	29	29	NUM
ejde-395	225	6	,	,	PUNCT
ejde-395	225	7	theorem	theorem	VERB
ejde-395	225	8	1.1	1.1	NUM
ejde-395	225	9	and	and	CCONJ
ejde-395	225	10	1.3	1.3	NUM
ejde-395	225	11	]	]	PUNCT
ejde-395	225	12	)	)	PUNCT
ejde-395	225	13	.	.	PUNCT
ejde-395	226	1	let	let	AUX
ejde-395	226	2	f(z	f(z	PROPN
ejde-395	226	3	)	)	PUNCT
ejde-395	226	4	be	be	AUX
ejde-395	226	5	a	a	DET
ejde-395	226	6	nonconstant	nonconstant	ADJ
ejde-395	226	7	zero	zero	NUM
ejde-395	226	8	-	-	PUNCT
ejde-395	226	9	order	order	NOUN
ejde-395	226	10	meromorphic	meromorphic	ADJ
ejde-395	226	11	function	function	NOUN
ejde-395	226	12	and	and	CCONJ
ejde-395	226	13	q	q	NOUN
ejde-395	226	14	∈	∈	PROPN
ejde-395	226	15	c	c	X
ejde-395	226	16	\	\	X
ejde-395	226	17	{	{	PUNCT
ejde-395	226	18	0	0	NUM
ejde-395	226	19	}	}	PUNCT
ejde-395	226	20	.	.	PUNCT
ejde-395	227	1	then	then	ADV
ejde-395	227	2	t	t	PROPN
ejde-395	227	3	(	(	PUNCT
ejde-395	227	4	r	r	NOUN
ejde-395	227	5	,	,	PUNCT
ejde-395	227	6	f(qz	f(qz	NOUN
ejde-395	227	7	)	)	PUNCT
ejde-395	227	8	)	)	PUNCT
ejde-395	228	1	=	=	PUNCT
ejde-395	228	2	(	(	PUNCT
ejde-395	228	3	1	1	NUM
ejde-395	228	4	+	+	NUM
ejde-395	228	5	o(1))t	o(1))t	PUNCT
ejde-395	228	6	(	(	PUNCT
ejde-395	228	7	r	r	NOUN
ejde-395	228	8	,	,	PUNCT
ejde-395	228	9	f(z	f(z	PROPN
ejde-395	228	10	)	)	PUNCT
ejde-395	228	11	)	)	PUNCT
ejde-395	228	12	,	,	PUNCT
ejde-395	228	13	n(r	n(r	NOUN
ejde-395	228	14	,	,	PUNCT
ejde-395	228	15	f(qz	f(qz	NOUN
ejde-395	228	16	)	)	PUNCT
ejde-395	228	17	)	)	PUNCT
ejde-395	229	1	=	=	PUNCT
ejde-395	229	2	(	(	PUNCT
ejde-395	229	3	1	1	NUM
ejde-395	229	4	+	+	NUM
ejde-395	229	5	o(1))n(r	o(1))n(r	NUM
ejde-395	229	6	,	,	PUNCT
ejde-395	229	7	f(z	f(z	PROPN
ejde-395	229	8	)	)	PUNCT
ejde-395	229	9	)	)	PUNCT
ejde-395	229	10	,	,	PUNCT
ejde-395	229	11	on	on	ADP
ejde-395	229	12	a	a	DET
ejde-395	229	13	set	set	NOUN
ejde-395	229	14	of	of	ADP
ejde-395	229	15	lower	low	ADJ
ejde-395	229	16	logarithmic	logarithmic	ADJ
ejde-395	229	17	density	density	NOUN
ejde-395	229	18	1	1	NUM
ejde-395	229	19	.	.	NOUN
ejde-395	229	20	8	8	NUM
ejde-395	229	21	h.	h.	PROPN
ejde-395	229	22	y.	y.	PROPN
ejde-395	229	23	xu	xu	PROPN
ejde-395	229	24	,	,	PUNCT
ejde-395	229	25	j.	j.	PROPN
ejde-395	229	26	tu	tu	PROPN
ejde-395	229	27	ejde-2020/14	ejde-2020/14	VERB
ejde-395	229	28	lemma	lemma	PROPN
ejde-395	229	29	3.3	3.3	NUM
ejde-395	229	30	(	(	PUNCT
ejde-395	229	31	[	[	X
ejde-395	229	32	15	15	NUM
ejde-395	229	33	,	,	PUNCT
ejde-395	229	34	theorem	theorem	VERB
ejde-395	229	35	2.5	2.5	NUM
ejde-395	229	36	]	]	PUNCT
ejde-395	229	37	)	)	PUNCT
ejde-395	229	38	.	.	PUNCT
ejde-395	230	1	let	let	VERB
ejde-395	230	2	f	f	PRON
ejde-395	230	3	be	be	AUX
ejde-395	230	4	a	a	DET
ejde-395	230	5	transcendental	transcendental	ADJ
ejde-395	230	6	meromorphic	meromorphic	ADJ
ejde-395	230	7	solution	solution	NOUN
ejde-395	230	8	of	of	ADP
ejde-395	230	9	order	order	NOUN
ejde-395	230	10	zero	zero	NUM
ejde-395	230	11	of	of	ADP
ejde-395	230	12	a	a	DET
ejde-395	230	13	q	q	ADJ
ejde-395	230	14	-	-	PUNCT
ejde-395	230	15	difference	difference	NOUN
ejde-395	230	16	equation	equation	NOUN
ejde-395	230	17	of	of	ADP
ejde-395	230	18	the	the	DET
ejde-395	230	19	form	form	NOUN
ejde-395	230	20	uq(z	uq(z	SYM
ejde-395	230	21	,	,	PUNCT
ejde-395	230	22	f)pq(z	f)pq(z	PROPN
ejde-395	230	23	,	,	PUNCT
ejde-395	230	24	f	f	X
ejde-395	230	25	)	)	PUNCT
ejde-395	230	26	=	=	SYM
ejde-395	230	27	qq(z	qq(z	NOUN
ejde-395	230	28	,	,	PUNCT
ejde-395	230	29	f	f	X
ejde-395	230	30	)	)	PUNCT
ejde-395	230	31	,	,	PUNCT
ejde-395	230	32	where	where	SCONJ
ejde-395	230	33	uq(z	uq(z	NUM
ejde-395	230	34	,	,	PUNCT
ejde-395	230	35	f	f	NOUN
ejde-395	230	36	)	)	PUNCT
ejde-395	230	37	,	,	PUNCT
ejde-395	230	38	pq(z	pq(z	NUM
ejde-395	230	39	,	,	PUNCT
ejde-395	230	40	f	f	X
ejde-395	230	41	)	)	PUNCT
ejde-395	230	42	and	and	CCONJ
ejde-395	230	43	qq(z	qq(z	NOUN
ejde-395	230	44	,	,	PUNCT
ejde-395	230	45	f	f	X
ejde-395	230	46	)	)	PUNCT
ejde-395	230	47	are	be	AUX
ejde-395	230	48	q	q	ADJ
ejde-395	230	49	-	-	PUNCT
ejde-395	230	50	difference	difference	NOUN
ejde-395	230	51	polynomials	polynomial	NOUN
ejde-395	230	52	such	such	ADJ
ejde-395	230	53	that	that	SCONJ
ejde-395	230	54	the	the	DET
ejde-395	230	55	total	total	ADJ
ejde-395	230	56	degree	degree	NOUN
ejde-395	230	57	deg	deg	PROPN
ejde-395	230	58	uq(z	uq(z	NUM
ejde-395	230	59	,	,	PUNCT
ejde-395	230	60	f	f	X
ejde-395	230	61	)	)	PUNCT
ejde-395	230	62	=	=	SYM
ejde-395	230	63	n	n	NOUN
ejde-395	230	64	in	in	ADP
ejde-395	230	65	f(z	f(z	PROPN
ejde-395	230	66	)	)	PUNCT
ejde-395	230	67	and	and	CCONJ
ejde-395	230	68	its	its	PRON
ejde-395	230	69	q	q	NOUN
ejde-395	230	70	-	-	NOUN
ejde-395	230	71	shifts	shift	NOUN
ejde-395	230	72	,	,	PUNCT
ejde-395	230	73	whereas	whereas	SCONJ
ejde-395	230	74	degqq(z	degqq(z	PROPN
ejde-395	230	75	,	,	PUNCT
ejde-395	230	76	f	f	NOUN
ejde-395	230	77	)	)	PUNCT
ejde-395	230	78	≤	≤	NOUN
ejde-395	230	79	n.	n.	NOUN
ejde-395	230	80	moreover	moreover	ADV
ejde-395	230	81	,	,	PUNCT
ejde-395	230	82	we	we	PRON
ejde-395	230	83	assume	assume	VERB
ejde-395	230	84	that	that	SCONJ
ejde-395	230	85	uq(z	uq(z	SYM
ejde-395	230	86	,	,	PUNCT
ejde-395	230	87	f	f	X
ejde-395	230	88	)	)	PUNCT
ejde-395	230	89	contains	contain	VERB
ejde-395	230	90	just	just	ADV
ejde-395	230	91	one	one	NUM
ejde-395	230	92	term	term	NOUN
ejde-395	230	93	of	of	ADP
ejde-395	230	94	maximal	maximal	ADJ
ejde-395	230	95	total	total	NOUN
ejde-395	230	96	degree	degree	NOUN
ejde-395	230	97	in	in	ADP
ejde-395	230	98	f(z	f(z	PROPN
ejde-395	230	99	)	)	PUNCT
ejde-395	230	100	and	and	CCONJ
ejde-395	230	101	its	its	PRON
ejde-395	230	102	q	q	NOUN
ejde-395	230	103	-	-	NOUN
ejde-395	230	104	shifts	shift	NOUN
ejde-395	230	105	.	.	PUNCT
ejde-395	231	1	then	then	ADV
ejde-395	231	2	m(r	m(r	PROPN
ejde-395	231	3	,	,	PUNCT
ejde-395	231	4	pq(z	pq(z	NUM
ejde-395	231	5	,	,	PUNCT
ejde-395	231	6	f	f	NOUN
ejde-395	231	7	)	)	PUNCT
ejde-395	231	8	)	)	PUNCT
ejde-395	232	1	=	=	SYM
ejde-395	232	2	s(r	s(r	PROPN
ejde-395	232	3	,	,	PUNCT
ejde-395	232	4	f	f	NOUN
ejde-395	232	5	)	)	PUNCT
ejde-395	232	6	.	.	PUNCT
ejde-395	233	1	remark	remark	VERB
ejde-395	233	2	3.4	3.4	NUM
ejde-395	233	3	.	.	PUNCT
ejde-395	234	1	for	for	ADP
ejde-395	234	2	q	q	PROPN
ejde-395	234	3	∈	∈	PROPN
ejde-395	234	4	c\{0	c\{0	PROPN
ejde-395	234	5	,	,	PUNCT
ejde-395	234	6	1	1	NUM
ejde-395	234	7	}	}	PUNCT
ejde-395	234	8	,	,	PUNCT
ejde-395	234	9	a	a	DET
ejde-395	234	10	polynomial	polynomial	NOUN
ejde-395	234	11	in	in	ADP
ejde-395	234	12	f(z	f(z	PROPN
ejde-395	234	13	)	)	PUNCT
ejde-395	234	14	and	and	CCONJ
ejde-395	234	15	finitely	finitely	ADV
ejde-395	234	16	many	many	ADJ
ejde-395	234	17	of	of	ADP
ejde-395	234	18	its	its	PRON
ejde-395	234	19	q	q	NOUN
ejde-395	234	20	-	-	PUNCT
ejde-395	234	21	shifts	shift	NOUN
ejde-395	234	22	f(qz	f(qz	NOUN
ejde-395	234	23	)	)	PUNCT
ejde-395	234	24	,	,	PUNCT
ejde-395	234	25	.	.	PUNCT
ejde-395	234	26	.	.	PUNCT
ejde-395	234	27	.	.	PUNCT
ejde-395	235	1	,	,	PUNCT
ejde-395	235	2	f(qnz	f(qnz	PROPN
ejde-395	235	3	)	)	PUNCT
ejde-395	235	4	with	with	ADP
ejde-395	235	5	meromorphic	meromorphic	ADJ
ejde-395	235	6	coefficients	coefficient	NOUN
ejde-395	235	7	in	in	ADP
ejde-395	235	8	the	the	DET
ejde-395	235	9	sense	sense	NOUN
ejde-395	235	10	that	that	SCONJ
ejde-395	235	11	their	their	PRON
ejde-395	235	12	nevanlinna	nevanlinna	ADJ
ejde-395	235	13	characteristic	characteristic	ADJ
ejde-395	235	14	functions	function	NOUN
ejde-395	235	15	are	be	AUX
ejde-395	235	16	o(t	o(t	NOUN
ejde-395	235	17	(	(	PUNCT
ejde-395	235	18	r	r	NOUN
ejde-395	235	19	,	,	PUNCT
ejde-395	235	20	f	f	NOUN
ejde-395	235	21	)	)	PUNCT
ejde-395	235	22	)	)	PUNCT
ejde-395	235	23	on	on	ADP
ejde-395	235	24	a	a	DET
ejde-395	235	25	set	set	ADJ
ejde-395	235	26	f	f	NOUN
ejde-395	235	27	of	of	ADP
ejde-395	235	28	logarithmic	logarithmic	ADJ
ejde-395	235	29	density	density	NOUN
ejde-395	235	30	1	1	NUM
ejde-395	235	31	,	,	PUNCT
ejde-395	235	32	can	can	AUX
ejde-395	235	33	be	be	AUX
ejde-395	235	34	called	call	VERB
ejde-395	235	35	as	as	ADP
ejde-395	235	36	a	a	DET
ejde-395	235	37	q	q	ADJ
ejde-395	235	38	-	-	PUNCT
ejde-395	235	39	difference	difference	NOUN
ejde-395	235	40	polynomial	polynomial	NOUN
ejde-395	235	41	of	of	ADP
ejde-395	235	42	f	f	PROPN
ejde-395	235	43	.	.	PUNCT
ejde-395	236	1	lemma	lemma	PROPN
ejde-395	236	2	3.5	3.5	NUM
ejde-395	236	3	(	(	PUNCT
ejde-395	236	4	valiron	valiron	NOUN
ejde-395	236	5	-	-	PUNCT
ejde-395	236	6	mohon’ko	mohon’ko	NOUN
ejde-395	237	1	[	[	X
ejde-395	237	2	28	28	NUM
ejde-395	237	3	]	]	NUM
ejde-395	237	4	)	)	PUNCT
ejde-395	237	5	.	.	PUNCT
ejde-395	238	1	let	let	AUX
ejde-395	238	2	f(z	f(z	PROPN
ejde-395	238	3	)	)	PUNCT
ejde-395	238	4	be	be	AUX
ejde-395	238	5	a	a	DET
ejde-395	238	6	meromorphic	meromorphic	ADJ
ejde-395	238	7	function	function	NOUN
ejde-395	238	8	.	.	PUNCT
ejde-395	239	1	then	then	ADV
ejde-395	239	2	for	for	ADP
ejde-395	239	3	all	all	DET
ejde-395	239	4	irreducible	irreducible	ADJ
ejde-395	239	5	rational	rational	ADJ
ejde-395	239	6	functions	function	NOUN
ejde-395	239	7	in	in	ADP
ejde-395	239	8	f	f	PROPN
ejde-395	239	9	,	,	PUNCT
ejde-395	239	10	r(z	r(z	PROPN
ejde-395	239	11	,	,	PUNCT
ejde-395	239	12	f(z	f(z	PROPN
ejde-395	239	13	)	)	PUNCT
ejde-395	239	14	)	)	PUNCT
ejde-395	240	1	=	=	PUNCT
ejde-395	240	2	∑m	∑m	PROPN
ejde-395	240	3	i=0	i=0	PROPN
ejde-395	240	4	ai(z)f(z)i∑n	ai(z)f(z)i∑n	NOUN
ejde-395	240	5	j=0	j=0	PROPN
ejde-395	240	6	bj(z)f(z)j	bj(z)f(z)j	VERB
ejde-395	240	7	,	,	PUNCT
ejde-395	240	8	with	with	ADP
ejde-395	240	9	meromorphic	meromorphic	ADJ
ejde-395	240	10	coefficients	coefficient	NOUN
ejde-395	240	11	ai(z	ai(z	NOUN
ejde-395	240	12	)	)	PUNCT
ejde-395	240	13	,	,	PUNCT
ejde-395	240	14	bj(z	bj(z	NOUN
ejde-395	240	15	)	)	PUNCT
ejde-395	240	16	,	,	PUNCT
ejde-395	240	17	the	the	DET
ejde-395	240	18	characteristic	characteristic	ADJ
ejde-395	240	19	function	function	NOUN
ejde-395	240	20	of	of	ADP
ejde-395	240	21	r(z	r(z	PROPN
ejde-395	240	22	,	,	PUNCT
ejde-395	240	23	f(z	f(z	PROPN
ejde-395	240	24	)	)	PUNCT
ejde-395	240	25	)	)	PUNCT
ejde-395	240	26	satisfies	satisfy	VERB
ejde-395	240	27	t	t	PROPN
ejde-395	240	28	(	(	PUNCT
ejde-395	240	29	r	r	NOUN
ejde-395	240	30	,	,	PUNCT
ejde-395	240	31	r(z	r(z	NOUN
ejde-395	240	32	,	,	PUNCT
ejde-395	240	33	f(z	f(z	PROPN
ejde-395	240	34	)	)	PUNCT
ejde-395	240	35	)	)	PUNCT
ejde-395	240	36	)	)	PUNCT
ejde-395	241	1	=	=	PRON
ejde-395	241	2	dt	dt	X
ejde-395	241	3	(	(	PUNCT
ejde-395	241	4	r	r	NOUN
ejde-395	241	5	,	,	PUNCT
ejde-395	241	6	f	f	NOUN
ejde-395	241	7	)	)	PUNCT
ejde-395	242	1	+	+	ADJ
ejde-395	242	2	o(ψ(r	o(ψ(r	NOUN
ejde-395	242	3	)	)	PUNCT
ejde-395	242	4	)	)	PUNCT
ejde-395	242	5	,	,	PUNCT
ejde-395	243	1	where	where	SCONJ
ejde-395	243	2	d	d	NOUN
ejde-395	243	3	=	=	SYM
ejde-395	243	4	max{m	max{m	PROPN
ejde-395	243	5	,	,	PUNCT
ejde-395	243	6	n	n	CCONJ
ejde-395	243	7	}	}	PUNCT
ejde-395	243	8	and	and	CCONJ
ejde-395	243	9	ψ(r	ψ(r	NOUN
ejde-395	243	10	)	)	PUNCT
ejde-395	243	11	=	=	SYM
ejde-395	243	12	maxi	maxi	ADJ
ejde-395	243	13	,	,	PUNCT
ejde-395	243	14	j{t	j{t	PROPN
ejde-395	243	15	(	(	PUNCT
ejde-395	243	16	r	r	NOUN
ejde-395	243	17	,	,	PUNCT
ejde-395	243	18	ai	ai	NOUN
ejde-395	243	19	)	)	PUNCT
ejde-395	243	20	,	,	PUNCT
ejde-395	243	21	t	t	PROPN
ejde-395	243	22	(	(	PUNCT
ejde-395	243	23	r	r	NOUN
ejde-395	243	24	,	,	PUNCT
ejde-395	243	25	bj	bj	NOUN
ejde-395	243	26	)	)	PUNCT
ejde-395	243	27	}	}	PUNCT
ejde-395	243	28	.	.	PUNCT
ejde-395	244	1	lemma	lemma	PROPN
ejde-395	244	2	3.6	3.6	NUM
ejde-395	244	3	(	(	PUNCT
ejde-395	244	4	[	[	X
ejde-395	244	5	1	1	NUM
ejde-395	244	6	,	,	PUNCT
ejde-395	244	7	theorem	theorem	VERB
ejde-395	244	8	1.1	1.1	NUM
ejde-395	244	9	]	]	PUNCT
ejde-395	244	10	)	)	PUNCT
ejde-395	244	11	.	.	PUNCT
ejde-395	245	1	let	let	AUX
ejde-395	245	2	f(z	f(z	PROPN
ejde-395	245	3	)	)	PUNCT
ejde-395	245	4	be	be	AUX
ejde-395	245	5	a	a	DET
ejde-395	245	6	nonconstant	nonconstant	ADJ
ejde-395	245	7	zero	zero	NUM
ejde-395	245	8	order	order	NOUN
ejde-395	245	9	meromorphic	meromorphic	ADJ
ejde-395	245	10	function	function	NOUN
ejde-395	245	11	and	and	CCONJ
ejde-395	245	12	q	q	NOUN
ejde-395	245	13	∈	∈	PROPN
ejde-395	245	14	c	c	X
ejde-395	245	15	\	\	X
ejde-395	245	16	{	{	PUNCT
ejde-395	245	17	0	0	NUM
ejde-395	245	18	}	}	PUNCT
ejde-395	245	19	.	.	PUNCT
ejde-395	246	1	then	then	ADV
ejde-395	246	2	m	m	VERB
ejde-395	246	3	(	(	PUNCT
ejde-395	246	4	r	r	NOUN
ejde-395	246	5	,	,	PUNCT
ejde-395	246	6	f(qz	f(qz	NOUN
ejde-395	246	7	)	)	PUNCT
ejde-395	246	8	f(z	f(z	PROPN
ejde-395	246	9	)	)	PUNCT
ejde-395	246	10	)	)	PUNCT
ejde-395	247	1	=	=	SYM
ejde-395	247	2	s(r	s(r	PROPN
ejde-395	247	3	,	,	PUNCT
ejde-395	247	4	f	f	NOUN
ejde-395	247	5	)	)	PUNCT
ejde-395	247	6	.	.	PUNCT
ejde-395	248	1	proof	proof	NOUN
ejde-395	248	2	of	of	ADP
ejde-395	248	3	theorem	theorem	NOUN
ejde-395	248	4	1.7	1.7	NUM
ejde-395	248	5	.	.	PUNCT
ejde-395	249	1	(	(	PUNCT
ejde-395	249	2	i	i	NOUN
ejde-395	249	3	)	)	PUNCT
ejde-395	249	4	let	let	AUX
ejde-395	249	5	f(z	f(z	PROPN
ejde-395	249	6	)	)	PUNCT
ejde-395	249	7	be	be	VERB
ejde-395	249	8	a	a	DET
ejde-395	249	9	transcendental	transcendental	ADJ
ejde-395	249	10	meromorphic	meromorphic	ADJ
ejde-395	249	11	function	function	NOUN
ejde-395	249	12	of	of	ADP
ejde-395	249	13	zero	zero	NUM
ejde-395	249	14	order	order	NOUN
ejde-395	249	15	.	.	PUNCT
ejde-395	250	1	for	for	ADP
ejde-395	250	2	any	any	DET
ejde-395	250	3	η	η	PROPN
ejde-395	250	4	∈	∈	PROPN
ejde-395	250	5	c−	c−	NOUN
ejde-395	250	6	{	{	PUNCT
ejde-395	250	7	0	0	NUM
ejde-395	250	8	,	,	PUNCT
ejde-395	250	9	1	1	NUM
ejde-395	250	10	}	}	PUNCT
ejde-395	250	11	,	,	PUNCT
ejde-395	250	12	substituting	substitute	VERB
ejde-395	250	13	ηz	ηz	ADV
ejde-395	250	14	into	into	ADP
ejde-395	250	15	(	(	PUNCT
ejde-395	250	16	1.8	1.8	NUM
ejde-395	250	17	)	)	PUNCT
ejde-395	250	18	,	,	PUNCT
ejde-395	250	19	we	we	PRON
ejde-395	250	20	have	have	VERB
ejde-395	250	21	f(qηz)f	f(qηz)f	VERB
ejde-395	250	22	(	(	PUNCT
ejde-395	250	23	ηz	ηz	PROPN
ejde-395	250	24	q	q	NOUN
ejde-395	250	25	)	)	PUNCT
ejde-395	250	26	f(ηz)(f(ηz)−	f(ηz)(f(ηz)−	PROPN
ejde-395	250	27	1	1	NUM
ejde-395	250	28	)	)	PUNCT
ejde-395	250	29	=	=	SYM
ejde-395	250	30	µ.	µ.	NOUN
ejde-395	250	31	(	(	PUNCT
ejde-395	250	32	3.1	3.1	NUM
ejde-395	250	33	)	)	PUNCT
ejde-395	250	34	denoting	denote	VERB
ejde-395	250	35	g(z	g(z	PROPN
ejde-395	250	36	)	)	PUNCT
ejde-395	250	37	=	=	SYM
ejde-395	250	38	f(ηz	f(ηz	PROPN
ejde-395	250	39	)	)	PUNCT
ejde-395	250	40	,	,	PUNCT
ejde-395	250	41	equation	equation	NOUN
ejde-395	250	42	(	(	PUNCT
ejde-395	250	43	3.1	3.1	NUM
ejde-395	250	44	)	)	PUNCT
ejde-395	250	45	can	can	AUX
ejde-395	250	46	be	be	AUX
ejde-395	250	47	represented	represent	VERB
ejde-395	250	48	as	as	ADP
ejde-395	250	49	g(qz)g	g(qz)g	NOUN
ejde-395	250	50	(	(	PUNCT
ejde-395	250	51	z	z	NOUN
ejde-395	250	52	q	q	NOUN
ejde-395	250	53	)	)	PUNCT
ejde-395	250	54	g(z)(g(z)−	g(z)(g(z)−	NOUN
ejde-395	250	55	1	1	NUM
ejde-395	250	56	)	)	PUNCT
ejde-395	250	57	=	=	VERB
ejde-395	251	1	µ.	µ.	NOUN
ejde-395	251	2	let	let	VERB
ejde-395	251	3	p1(z	p1(z	NUM
ejde-395	251	4	,	,	PUNCT
ejde-395	251	5	g	g	NOUN
ejde-395	251	6	)	)	PUNCT
ejde-395	251	7	:	:	PUNCT
ejde-395	251	8	=	=	SYM
ejde-395	251	9	g(qz)g	g(qz)g	NOUN
ejde-395	251	10	(	(	PUNCT
ejde-395	251	11	z	z	NOUN
ejde-395	251	12	q	q	NOUN
ejde-395	251	13	)	)	PUNCT
ejde-395	251	14	g(z)(g(z)−	g(z)(g(z)−	PROPN
ejde-395	251	15	1)−	1)−	PROPN
ejde-395	251	16	µ	µ	X
ejde-395	251	17	=	=	SYM
ejde-395	251	18	0	0	NUM
ejde-395	251	19	.	.	PUNCT
ejde-395	252	1	it	it	PRON
ejde-395	252	2	follows	follow	VERB
ejde-395	252	3	that	that	SCONJ
ejde-395	252	4	p1(z	p1(z	ADP
ejde-395	252	5	,	,	PUNCT
ejde-395	252	6	z	z	NOUN
ejde-395	252	7	)	)	PUNCT
ejde-395	252	8	=	=	PUNCT
ejde-395	253	1	z3(z	z3(z	PRON
ejde-395	253	2	−	−	PROPN
ejde-395	254	1	1)−	1)−	NUM
ejde-395	254	2	µ	µ	PRON
ejde-395	254	3	6≡	6≡	NUM
ejde-395	254	4	0	0	NUM
ejde-395	254	5	.	.	PUNCT
ejde-395	255	1	in	in	ADP
ejde-395	255	2	view	view	NOUN
ejde-395	255	3	of	of	ADP
ejde-395	255	4	p1(z	p1(z	PROPN
ejde-395	255	5	,	,	PUNCT
ejde-395	255	6	z	z	NOUN
ejde-395	255	7	)	)	PUNCT
ejde-395	255	8	6≡	6≡	NUM
ejde-395	255	9	0	0	NUM
ejde-395	255	10	,	,	PUNCT
ejde-395	255	11	by	by	ADP
ejde-395	255	12	lemma	lemma	PROPN
ejde-395	255	13	3.1	3.1	NUM
ejde-395	255	14	we	we	PRON
ejde-395	255	15	have	have	VERB
ejde-395	255	16	m	m	PROPN
ejde-395	255	17	(	(	PUNCT
ejde-395	255	18	r	r	NOUN
ejde-395	255	19	,	,	PUNCT
ejde-395	255	20	1	1	NUM
ejde-395	255	21	g(z)−	g(z)−	PROPN
ejde-395	255	22	z	z	NOUN
ejde-395	255	23	)	)	PUNCT
ejde-395	255	24	=	=	SYM
ejde-395	255	25	s(r	s(r	ADJ
ejde-395	255	26	,	,	PUNCT
ejde-395	255	27	g	g	NOUN
ejde-395	255	28	)	)	PUNCT
ejde-395	255	29	.	.	PUNCT
ejde-395	256	1	since	since	SCONJ
ejde-395	256	2	f	f	PROPN
ejde-395	256	3	is	be	AUX
ejde-395	256	4	of	of	ADP
ejde-395	256	5	zero	zero	NUM
ejde-395	256	6	order	order	NOUN
ejde-395	256	7	,	,	PUNCT
ejde-395	256	8	from	from	ADP
ejde-395	256	9	lemma	lemma	PROPN
ejde-395	256	10	3.2	3.2	NUM
ejde-395	256	11	,	,	PUNCT
ejde-395	256	12	it	it	PRON
ejde-395	256	13	follows	follow	VERB
ejde-395	256	14	that	that	SCONJ
ejde-395	257	1	n	n	PROPN
ejde-395	257	2	(	(	PUNCT
ejde-395	257	3	r	r	NOUN
ejde-395	257	4	,	,	PUNCT
ejde-395	257	5	1	1	NUM
ejde-395	257	6	f(ηz)−	f(ηz)−	X
ejde-395	257	7	z	z	NOUN
ejde-395	257	8	)	)	PUNCT
ejde-395	258	1	=	=	SYM
ejde-395	258	2	n	n	CCONJ
ejde-395	258	3	(	(	PUNCT
ejde-395	258	4	r	r	NOUN
ejde-395	258	5	,	,	PUNCT
ejde-395	258	6	1	1	NUM
ejde-395	258	7	g(z)−	g(z)−	PROPN
ejde-395	258	8	z	z	NOUN
ejde-395	258	9	)	)	PUNCT
ejde-395	259	1	=	=	SYM
ejde-395	259	2	t	t	PROPN
ejde-395	259	3	(	(	PUNCT
ejde-395	259	4	r	r	NOUN
ejde-395	259	5	,	,	PUNCT
ejde-395	259	6	g	g	NOUN
ejde-395	259	7	)	)	PUNCT
ejde-395	260	1	+	+	CCONJ
ejde-395	260	2	s(r	s(r	ADJ
ejde-395	260	3	,	,	PUNCT
ejde-395	260	4	g	g	NOUN
ejde-395	260	5	)	)	PUNCT
ejde-395	261	1	=	=	SYM
ejde-395	261	2	t	t	PROPN
ejde-395	261	3	(	(	PUNCT
ejde-395	261	4	r	r	NOUN
ejde-395	261	5	,	,	PUNCT
ejde-395	261	6	f(ηz	f(ηz	PROPN
ejde-395	261	7	)	)	PUNCT
ejde-395	261	8	)	)	PUNCT
ejde-395	262	1	+	+	CCONJ
ejde-395	262	2	s(r	s(r	ADJ
ejde-395	262	3	,	,	PUNCT
ejde-395	262	4	f(ηz	f(ηz	PROPN
ejde-395	262	5	)	)	PUNCT
ejde-395	262	6	)	)	PUNCT
ejde-395	263	1	=	=	SYM
ejde-395	263	2	t	t	PROPN
ejde-395	263	3	(	(	PUNCT
ejde-395	263	4	r	r	NOUN
ejde-395	263	5	,	,	PUNCT
ejde-395	263	6	f	f	NOUN
ejde-395	263	7	)	)	PUNCT
ejde-395	264	1	+	+	CCONJ
ejde-395	264	2	s(r	s(r	ADJ
ejde-395	264	3	,	,	PUNCT
ejde-395	264	4	f	f	NOUN
ejde-395	264	5	)	)	PUNCT
ejde-395	264	6	.	.	PUNCT
ejde-395	265	1	ejde-2020/14	ejde-2020/14	VERB
ejde-395	265	2	q	q	NOUN
ejde-395	265	3	-	-	PUNCT
ejde-395	265	4	difference	difference	NOUN
ejde-395	265	5	painlevé	painlevé	NOUN
ejde-395	265	6	equations	equation	NOUN
ejde-395	265	7	9	9	NUM
ejde-395	265	8	therefore	therefore	ADV
ejde-395	265	9	,	,	PUNCT
ejde-395	265	10	f(ηz	f(ηz	PROPN
ejde-395	265	11	)	)	PUNCT
ejde-395	265	12	has	have	VERB
ejde-395	265	13	infinitely	infinitely	ADV
ejde-395	265	14	many	many	ADJ
ejde-395	265	15	fixed	fix	VERB
ejde-395	265	16	points	point	NOUN
ejde-395	265	17	,	,	PUNCT
ejde-395	265	18	and	and	CCONJ
ejde-395	265	19	τ(f(ηz	τ(f(ηz	NOUN
ejde-395	265	20	)	)	PUNCT
ejde-395	265	21	)	)	PUNCT
ejde-395	266	1	=	=	SYM
ejde-395	266	2	σ(f	σ(f	NOUN
ejde-395	266	3	)	)	PUNCT
ejde-395	266	4	for	for	ADP
ejde-395	266	5	any	any	DET
ejde-395	266	6	η	η	PROPN
ejde-395	266	7	∈	∈	PROPN
ejde-395	266	8	c−	c−	NOUN
ejde-395	266	9	{	{	PUNCT
ejde-395	266	10	0	0	NUM
ejde-395	266	11	,	,	PUNCT
ejde-395	266	12	1	1	NUM
ejde-395	266	13	}	}	PUNCT
ejde-395	266	14	.	.	PUNCT
ejde-395	267	1	(	(	PUNCT
ejde-395	267	2	ii	ii	NOUN
ejde-395	267	3	)	)	PUNCT
ejde-395	267	4	since	since	SCONJ
ejde-395	267	5	f	f	PROPN
ejde-395	267	6	is	be	AUX
ejde-395	267	7	a	a	DET
ejde-395	267	8	transcendental	transcendental	ADJ
ejde-395	267	9	meromorphic	meromorphic	ADJ
ejde-395	267	10	solution	solution	NOUN
ejde-395	267	11	of	of	ADP
ejde-395	267	12	zero	zero	NUM
ejde-395	267	13	order	order	NOUN
ejde-395	267	14	.	.	PUNCT
ejde-395	268	1	in	in	ADP
ejde-395	268	2	view	view	NOUN
ejde-395	268	3	of	of	ADP
ejde-395	268	4	µ	µ	PRON
ejde-395	268	5	6=	6=	NUM
ejde-395	268	6	0	0	NUM
ejde-395	268	7	,	,	PUNCT
ejde-395	268	8	by	by	ADP
ejde-395	268	9	lemmas	lemmas	PROPN
ejde-395	268	10	3.2	3.2	NUM
ejde-395	268	11	-	-	SYM
ejde-395	268	12	3.6	3.6	NUM
ejde-395	268	13	,	,	PUNCT
ejde-395	268	14	4	4	NUM
ejde-395	268	15	t	t	NOUN
ejde-395	268	16	(	(	PUNCT
ejde-395	268	17	r	r	NOUN
ejde-395	268	18	,	,	PUNCT
ejde-395	268	19	f	f	NOUN
ejde-395	268	20	)	)	PUNCT
ejde-395	268	21	=	=	SYM
ejde-395	268	22	t	t	PROPN
ejde-395	268	23	(	(	PUNCT
ejde-395	268	24	r	r	PROPN
ejde-395	268	25	,	,	PUNCT
ejde-395	268	26	µ	µ	NOUN
ejde-395	268	27	f3(f	f3(f	NUM
ejde-395	268	28	−	−	NUM
ejde-395	268	29	1	1	NUM
ejde-395	268	30	)	)	PUNCT
ejde-395	268	31	)	)	PUNCT
ejde-395	269	1	+	+	VERB
ejde-395	269	2	o(1	o(1	NOUN
ejde-395	269	3	)	)	PUNCT
ejde-395	269	4	=	=	SYM
ejde-395	269	5	t	t	PROPN
ejde-395	269	6	(	(	PUNCT
ejde-395	269	7	r	r	NOUN
ejde-395	269	8	,	,	PUNCT
ejde-395	269	9	f(qz)f	f(qz)f	X
ejde-395	269	10	(	(	PUNCT
ejde-395	269	11	z	z	NOUN
ejde-395	269	12	q	q	NOUN
ejde-395	269	13	)	)	PUNCT
ejde-395	269	14	f(z)2	f(z)2	NOUN
ejde-395	269	15	)	)	PUNCT
ejde-395	269	16	+	+	NOUN
ejde-395	269	17	o(1	o(1	NOUN
ejde-395	269	18	)	)	PUNCT
ejde-395	269	19	≤	≤	NOUN
ejde-395	269	20	t	t	NOUN
ejde-395	269	21	(	(	PUNCT
ejde-395	269	22	r	r	NOUN
ejde-395	269	23	,	,	PUNCT
ejde-395	269	24	f(qz	f(qz	NOUN
ejde-395	269	25	)	)	PUNCT
ejde-395	269	26	f(z	f(z	PROPN
ejde-395	269	27	)	)	PUNCT
ejde-395	269	28	)	)	PUNCT
ejde-395	270	1	+	+	CCONJ
ejde-395	270	2	t	t	X
ejde-395	270	3	(	(	PUNCT
ejde-395	270	4	r	r	NOUN
ejde-395	270	5	,	,	PUNCT
ejde-395	270	6	f	f	X
ejde-395	270	7	(	(	PUNCT
ejde-395	270	8	z	z	NOUN
ejde-395	270	9	q	q	NOUN
ejde-395	270	10	)	)	PUNCT
ejde-395	270	11	f(z	f(z	PROPN
ejde-395	270	12	)	)	PUNCT
ejde-395	270	13	)	)	PUNCT
ejde-395	271	1	+	+	VERB
ejde-395	271	2	o(1	o(1	NOUN
ejde-395	271	3	)	)	PUNCT
ejde-395	271	4	≤	≤	NUM
ejde-395	271	5	2	2	NUM
ejde-395	271	6	t	t	NOUN
ejde-395	271	7	(	(	PUNCT
ejde-395	271	8	r	r	NOUN
ejde-395	271	9	,	,	PUNCT
ejde-395	271	10	f(qz	f(qz	NOUN
ejde-395	271	11	)	)	PUNCT
ejde-395	271	12	f(z	f(z	PROPN
ejde-395	271	13	)	)	PUNCT
ejde-395	271	14	)	)	PUNCT
ejde-395	272	1	+	+	CCONJ
ejde-395	272	2	s(r	s(r	ADJ
ejde-395	272	3	,	,	PUNCT
ejde-395	272	4	f	f	X
ejde-395	272	5	)	)	PUNCT
ejde-395	272	6	=	=	SYM
ejde-395	272	7	2	2	NUM
ejde-395	272	8	t	t	NOUN
ejde-395	272	9	(	(	PUNCT
ejde-395	272	10	r	r	NOUN
ejde-395	272	11	,	,	PUNCT
ejde-395	272	12	∆qf	∆qf	X
ejde-395	272	13	f	f	NOUN
ejde-395	272	14	)	)	PUNCT
ejde-395	273	1	+	+	CCONJ
ejde-395	273	2	s(r	s(r	ADJ
ejde-395	273	3	,	,	PUNCT
ejde-395	273	4	f	f	NOUN
ejde-395	273	5	)	)	PUNCT
ejde-395	273	6	;	;	PUNCT
ejde-395	273	7	that	that	PRON
ejde-395	273	8	is	be	AUX
ejde-395	273	9	,	,	PUNCT
ejde-395	273	10	2	2	NUM
ejde-395	273	11	t	t	NOUN
ejde-395	273	12	(	(	PUNCT
ejde-395	273	13	r	r	NOUN
ejde-395	273	14	,	,	PUNCT
ejde-395	273	15	f	f	NOUN
ejde-395	273	16	)	)	PUNCT
ejde-395	273	17	≤	≤	NOUN
ejde-395	273	18	t	t	NOUN
ejde-395	273	19	(	(	PUNCT
ejde-395	273	20	r	r	NOUN
ejde-395	273	21	,	,	PUNCT
ejde-395	273	22	∆qf	∆qf	X
ejde-395	273	23	f	f	NOUN
ejde-395	273	24	)	)	PUNCT
ejde-395	274	1	+	+	CCONJ
ejde-395	274	2	s(r	s(r	ADJ
ejde-395	274	3	,	,	PUNCT
ejde-395	274	4	f	f	NOUN
ejde-395	274	5	)	)	PUNCT
ejde-395	274	6	.	.	PUNCT
ejde-395	275	1	(	(	PUNCT
ejde-395	275	2	3.2	3.2	NUM
ejde-395	275	3	)	)	PUNCT
ejde-395	275	4	thus	thus	ADV
ejde-395	275	5	,	,	PUNCT
ejde-395	275	6	from	from	ADP
ejde-395	275	7	lemma	lemma	PROPN
ejde-395	275	8	3.6	3.6	NUM
ejde-395	275	9	and	and	CCONJ
ejde-395	275	10	(	(	PUNCT
ejde-395	275	11	3.2	3.2	NUM
ejde-395	275	12	)	)	PUNCT
ejde-395	275	13	,	,	PUNCT
ejde-395	275	14	we	we	PRON
ejde-395	275	15	conclude	conclude	VERB
ejde-395	275	16	that	that	SCONJ
ejde-395	275	17	n	n	PROPN
ejde-395	275	18	(	(	PUNCT
ejde-395	275	19	r	r	NOUN
ejde-395	275	20	,	,	PUNCT
ejde-395	275	21	∆qf	∆qf	X
ejde-395	275	22	f	f	NOUN
ejde-395	275	23	)	)	PUNCT
ejde-395	276	1	=	=	SYM
ejde-395	276	2	t	t	PROPN
ejde-395	276	3	(	(	PUNCT
ejde-395	276	4	r	r	NOUN
ejde-395	276	5	,	,	PUNCT
ejde-395	276	6	∆qf	∆qf	X
ejde-395	276	7	f	f	X
ejde-395	276	8	)	)	PUNCT
ejde-395	276	9	−m	−m	NOUN
ejde-395	276	10	(	(	PUNCT
ejde-395	276	11	r	r	NOUN
ejde-395	276	12	,	,	PUNCT
ejde-395	276	13	∆qf	∆qf	X
ejde-395	276	14	f	f	X
ejde-395	276	15	)	)	PUNCT
ejde-395	276	16	≥	≥	PROPN
ejde-395	276	17	2	2	NUM
ejde-395	276	18	t	t	NOUN
ejde-395	276	19	(	(	PUNCT
ejde-395	276	20	r	r	NOUN
ejde-395	276	21	,	,	PUNCT
ejde-395	276	22	f	f	NOUN
ejde-395	276	23	)	)	PUNCT
ejde-395	277	1	+	+	CCONJ
ejde-395	277	2	s(r	s(r	ADJ
ejde-395	277	3	,	,	PUNCT
ejde-395	277	4	f	f	NOUN
ejde-395	277	5	)	)	PUNCT
ejde-395	277	6	.	.	PUNCT
ejde-395	278	1	this	this	PRON
ejde-395	278	2	means	mean	VERB
ejde-395	278	3	that	that	SCONJ
ejde-395	278	4	∆qf	∆qf	NOUN
ejde-395	278	5	f	f	PROPN
ejde-395	278	6	has	have	VERB
ejde-395	278	7	infinitely	infinitely	ADV
ejde-395	278	8	many	many	ADJ
ejde-395	278	9	poles	pole	NOUN
ejde-395	278	10	,	,	PUNCT
ejde-395	278	11	and	and	CCONJ
ejde-395	278	12	λ	λ	X
ejde-395	278	13	(	(	PUNCT
ejde-395	278	14	1	1	NUM
ejde-395	278	15	∆qf	∆qf	NOUN
ejde-395	278	16	f	f	NOUN
ejde-395	278	17	)	)	PUNCT
ejde-395	278	18	=	=	SYM
ejde-395	278	19	σ(f	σ(f	NOUN
ejde-395	278	20	)	)	PUNCT
ejde-395	278	21	.	.	PUNCT
ejde-395	279	1	also	also	ADV
ejde-395	279	2	,	,	PUNCT
ejde-395	279	3	we	we	PRON
ejde-395	279	4	can	can	AUX
ejde-395	279	5	rewrite	rewrite	VERB
ejde-395	279	6	equation	equation	NOUN
ejde-395	279	7	(	(	PUNCT
ejde-395	279	8	1.8	1.8	NUM
ejde-395	279	9	)	)	PUNCT
ejde-395	279	10	as	as	ADP
ejde-395	279	11	f(qz)f	f(qz)f	X
ejde-395	279	12	(	(	PUNCT
ejde-395	279	13	z	z	NOUN
ejde-395	279	14	q	q	NOUN
ejde-395	279	15	)	)	PUNCT
ejde-395	280	1	=	=	SYM
ejde-395	280	2	(	(	PUNCT
ejde-395	280	3	∆qf	∆qf	NOUN
ejde-395	280	4	+	+	PUNCT
ejde-395	280	5	f)(∆q−1f	f)(∆q−1f	NOUN
ejde-395	281	1	+	+	X
ejde-395	281	2	f	f	X
ejde-395	281	3	)	)	PUNCT
ejde-395	281	4	=	=	SYM
ejde-395	281	5	µ	µ	X
ejde-395	281	6	f(f	f(f	PROPN
ejde-395	281	7	−	−	PROPN
ejde-395	281	8	1	1	NUM
ejde-395	281	9	)	)	PUNCT
ejde-395	281	10	;	;	PUNCT
ejde-395	281	11	that	that	PRON
ejde-395	281	12	is	be	AUX
ejde-395	281	13	,	,	PUNCT
ejde-395	281	14	∆qf∆q−1f	∆qf∆q−1f	PUNCT
ejde-395	281	15	+	+	CCONJ
ejde-395	281	16	(	(	PUNCT
ejde-395	281	17	∆qf	∆qf	NOUN
ejde-395	281	18	+	+	X
ejde-395	282	1	∆q−1f)f	∆q−1f)f	PROPN
ejde-395	282	2	=	=	SYM
ejde-395	282	3	µ−	µ−	PROPN
ejde-395	282	4	f4	f4	PROPN
ejde-395	282	5	+	+	CCONJ
ejde-395	282	6	f3	f3	ADJ
ejde-395	282	7	f(f	f(f	PROPN
ejde-395	282	8	−	−	PROPN
ejde-395	282	9	1	1	NUM
ejde-395	282	10	)	)	PUNCT
ejde-395	282	11	.	.	PUNCT
ejde-395	283	1	(	(	PUNCT
ejde-395	283	2	3.3	3.3	NUM
ejde-395	283	3	)	)	PUNCT
ejde-395	283	4	thus	thus	ADV
ejde-395	283	5	,	,	PUNCT
ejde-395	283	6	in	in	ADP
ejde-395	283	7	view	view	NOUN
ejde-395	283	8	of	of	ADP
ejde-395	283	9	lemmas	lemmas	PROPN
ejde-395	283	10	3.2	3.2	NUM
ejde-395	283	11	and	and	CCONJ
ejde-395	283	12	3.5	3.5	NUM
ejde-395	283	13	,	,	PUNCT
ejde-395	283	14	it	it	PRON
ejde-395	283	15	follows	follow	VERB
ejde-395	283	16	that	that	SCONJ
ejde-395	283	17	4	4	NUM
ejde-395	283	18	t	t	NOUN
ejde-395	283	19	(	(	PUNCT
ejde-395	283	20	r	r	NOUN
ejde-395	283	21	,	,	PUNCT
ejde-395	283	22	f	f	NOUN
ejde-395	283	23	)	)	PUNCT
ejde-395	284	1	=	=	SYM
ejde-395	284	2	t	t	PROPN
ejde-395	284	3	(	(	PUNCT
ejde-395	284	4	r	r	NOUN
ejde-395	284	5	,	,	PUNCT
ejde-395	284	6	µ−	µ−	PROPN
ejde-395	284	7	f4	f4	ADJ
ejde-395	284	8	+	+	CCONJ
ejde-395	284	9	f3	f3	ADJ
ejde-395	284	10	f(f	f(f	PROPN
ejde-395	284	11	−	−	PROPN
ejde-395	284	12	1	1	NUM
ejde-395	284	13	)	)	PUNCT
ejde-395	284	14	)	)	PUNCT
ejde-395	285	1	+	+	VERB
ejde-395	285	2	o(1	o(1	NOUN
ejde-395	285	3	)	)	PUNCT
ejde-395	285	4	=	=	SYM
ejde-395	285	5	t	t	PROPN
ejde-395	285	6	(	(	PUNCT
ejde-395	285	7	r,∆qf∆q−1f	r,∆qf∆q−1f	PROPN
ejde-395	285	8	)	)	PUNCT
ejde-395	285	9	+	+	CCONJ
ejde-395	285	10	(	(	PUNCT
ejde-395	285	11	∆qf	∆qf	NOUN
ejde-395	285	12	+	+	X
ejde-395	285	13	∆q−1f)f	∆q−1f)f	PROPN
ejde-395	285	14	)	)	PUNCT
ejde-395	285	15	+	+	NOUN
ejde-395	285	16	o(1	o(1	NOUN
ejde-395	285	17	)	)	PUNCT
ejde-395	285	18	≤	≤	NOUN
ejde-395	285	19	t	t	NOUN
ejde-395	285	20	(	(	PUNCT
ejde-395	285	21	r	r	NOUN
ejde-395	285	22	,	,	PUNCT
ejde-395	285	23	f	f	NOUN
ejde-395	285	24	)	)	PUNCT
ejde-395	286	1	+	+	CCONJ
ejde-395	286	2	2	2	NUM
ejde-395	286	3	t	t	NOUN
ejde-395	286	4	(	(	PUNCT
ejde-395	286	5	r,∆qf	r,∆qf	PROPN
ejde-395	286	6	)	)	PUNCT
ejde-395	287	1	+	+	CCONJ
ejde-395	287	2	2	2	NUM
ejde-395	287	3	t	t	NOUN
ejde-395	287	4	(	(	PUNCT
ejde-395	287	5	r,∆q−1f	r,∆q−1f	NOUN
ejde-395	287	6	)	)	PUNCT
ejde-395	287	7	+	+	NOUN
ejde-395	287	8	o(1	o(1	NOUN
ejde-395	287	9	)	)	PUNCT
ejde-395	287	10	≤	≤	NOUN
ejde-395	287	11	t	t	NOUN
ejde-395	287	12	(	(	PUNCT
ejde-395	287	13	r	r	NOUN
ejde-395	287	14	,	,	PUNCT
ejde-395	287	15	f	f	NOUN
ejde-395	287	16	)	)	PUNCT
ejde-395	288	1	+	+	CCONJ
ejde-395	288	2	4	4	NUM
ejde-395	288	3	t	t	NOUN
ejde-395	288	4	(	(	PUNCT
ejde-395	288	5	r,∆qf	r,∆qf	PROPN
ejde-395	288	6	)	)	PUNCT
ejde-395	289	1	+	+	CCONJ
ejde-395	289	2	s(r	s(r	ADJ
ejde-395	289	3	,	,	PUNCT
ejde-395	289	4	f	f	NOUN
ejde-395	289	5	)	)	PUNCT
ejde-395	289	6	;	;	PUNCT
ejde-395	289	7	that	that	PRON
ejde-395	289	8	is	be	AUX
ejde-395	289	9	,	,	PUNCT
ejde-395	289	10	3	3	NUM
ejde-395	289	11	4	4	NUM
ejde-395	289	12	t	t	NOUN
ejde-395	289	13	(	(	PUNCT
ejde-395	289	14	r	r	NOUN
ejde-395	289	15	,	,	PUNCT
ejde-395	289	16	f	f	NOUN
ejde-395	289	17	)	)	PUNCT
ejde-395	289	18	≤	≤	NOUN
ejde-395	289	19	t	t	PROPN
ejde-395	289	20	(	(	PUNCT
ejde-395	289	21	r,∆qf	r,∆qf	PROPN
ejde-395	289	22	)	)	PUNCT
ejde-395	290	1	+	+	CCONJ
ejde-395	290	2	s(r	s(r	ADJ
ejde-395	290	3	,	,	PUNCT
ejde-395	290	4	f	f	NOUN
ejde-395	290	5	)	)	PUNCT
ejde-395	290	6	.	.	PUNCT
ejde-395	291	1	(	(	PUNCT
ejde-395	291	2	3.4	3.4	NUM
ejde-395	291	3	)	)	PUNCT
ejde-395	291	4	on	on	ADP
ejde-395	291	5	the	the	DET
ejde-395	291	6	other	other	ADJ
ejde-395	291	7	hand	hand	NOUN
ejde-395	291	8	,	,	PUNCT
ejde-395	291	9	(	(	PUNCT
ejde-395	291	10	1.8	1.8	NUM
ejde-395	291	11	)	)	PUNCT
ejde-395	291	12	can	can	AUX
ejde-395	291	13	be	be	AUX
ejde-395	291	14	represented	represent	VERB
ejde-395	291	15	as	as	ADP
ejde-395	291	16	f(qz)f	f(qz)f	X
ejde-395	291	17	(	(	PUNCT
ejde-395	291	18	z	z	NOUN
ejde-395	291	19	q	q	NOUN
ejde-395	291	20	)	)	PUNCT
ejde-395	291	21	f(z)2	f(z)2	NOUN
ejde-395	291	22	=	=	SYM
ejde-395	291	23	µ+	µ+	PUNCT
ejde-395	291	24	f(qz)f	f(qz)f	X
ejde-395	291	25	(	(	PUNCT
ejde-395	291	26	z	z	NOUN
ejde-395	291	27	q	q	NOUN
ejde-395	291	28	)	)	PUNCT
ejde-395	291	29	f(z	f(z	PROPN
ejde-395	291	30	)	)	PUNCT
ejde-395	291	31	.	.	PUNCT
ejde-395	292	1	by	by	ADP
ejde-395	292	2	lemma	lemma	PROPN
ejde-395	292	3	3.3	3.3	NUM
ejde-395	292	4	,	,	PUNCT
ejde-395	292	5	we	we	PRON
ejde-395	292	6	obtain	obtain	VERB
ejde-395	292	7	m(r	m(r	PROPN
ejde-395	292	8	,	,	PUNCT
ejde-395	292	9	f	f	X
ejde-395	292	10	)	)	PUNCT
ejde-395	292	11	=	=	SYM
ejde-395	293	1	s(r	s(r	PROPN
ejde-395	293	2	,	,	PUNCT
ejde-395	293	3	f	f	NOUN
ejde-395	293	4	)	)	PUNCT
ejde-395	293	5	.	.	PUNCT
ejde-395	294	1	thus	thus	ADV
ejde-395	294	2	,	,	PUNCT
ejde-395	294	3	we	we	PRON
ejde-395	294	4	can	can	AUX
ejde-395	294	5	conclude	conclude	VERB
ejde-395	294	6	from	from	ADP
ejde-395	294	7	lemma	lemma	PROPN
ejde-395	294	8	3.6	3.6	NUM
ejde-395	294	9	that	that	DET
ejde-395	294	10	n(r,∆qf	n(r,∆qf	NOUN
ejde-395	294	11	)	)	PUNCT
ejde-395	294	12	=	=	SYM
ejde-395	294	13	t	t	PROPN
ejde-395	294	14	(	(	PUNCT
ejde-395	294	15	r,∆qf)−m(r,∆qf	r,∆qf)−m(r,∆qf	PROPN
ejde-395	294	16	)	)	PUNCT
ejde-395	294	17	≥	≥	PROPN
ejde-395	294	18	t	t	PROPN
ejde-395	294	19	(	(	PUNCT
ejde-395	294	20	r,∆qf)−	r,∆qf)−	PROPN
ejde-395	294	21	[	[	PUNCT
ejde-395	294	22	m(r	m(r	PROPN
ejde-395	294	23	,	,	PUNCT
ejde-395	294	24	f	f	X
ejde-395	294	25	)	)	PUNCT
ejde-395	295	1	+	+	NOUN
ejde-395	295	2	m	m	PROPN
ejde-395	295	3	(	(	PUNCT
ejde-395	295	4	r	r	NOUN
ejde-395	295	5	,	,	PUNCT
ejde-395	295	6	∆qf	∆qf	NOUN
ejde-395	295	7	f	f	NOUN
ejde-395	295	8	)	)	PUNCT
ejde-395	295	9	]	]	PUNCT
ejde-395	296	1	10	10	NUM
ejde-395	296	2	h.	h.	PROPN
ejde-395	296	3	y.	y.	PROPN
ejde-395	296	4	xu	xu	PROPN
ejde-395	296	5	,	,	PUNCT
ejde-395	296	6	j.	j.	PROPN
ejde-395	296	7	tu	tu	PROPN
ejde-395	296	8	ejde-2020/14	ejde-2020/14	PROPN
ejde-395	296	9	≥	≥	NUM
ejde-395	296	10	1	1	NUM
ejde-395	296	11	2	2	NUM
ejde-395	296	12	t	t	NOUN
ejde-395	296	13	(	(	PUNCT
ejde-395	296	14	r	r	NOUN
ejde-395	296	15	,	,	PUNCT
ejde-395	296	16	f	f	NOUN
ejde-395	296	17	)	)	PUNCT
ejde-395	297	1	+	+	CCONJ
ejde-395	297	2	s(r	s(r	ADJ
ejde-395	297	3	,	,	PUNCT
ejde-395	297	4	f	f	NOUN
ejde-395	297	5	)	)	PUNCT
ejde-395	297	6	,	,	PUNCT
ejde-395	297	7	which	which	PRON
ejde-395	297	8	implies	imply	VERB
ejde-395	297	9	that	that	SCONJ
ejde-395	297	10	∆qf	∆qf	NOUN
ejde-395	297	11	has	have	VERB
ejde-395	297	12	infinitely	infinitely	ADV
ejde-395	297	13	many	many	ADJ
ejde-395	297	14	poles	pole	NOUN
ejde-395	297	15	and	and	CCONJ
ejde-395	297	16	λ	λ	NOUN
ejde-395	297	17	(	(	PUNCT
ejde-395	297	18	1	1	NUM
ejde-395	297	19	∆qf	∆qf	NOUN
ejde-395	297	20	)	)	PUNCT
ejde-395	297	21	=	=	SYM
ejde-395	297	22	σ(f	σ(f	NOUN
ejde-395	297	23	)	)	PUNCT
ejde-395	297	24	.	.	PUNCT
ejde-395	298	1	since	since	SCONJ
ejde-395	298	2	m	m	PROPN
ejde-395	298	3	(	(	PUNCT
ejde-395	298	4	r	r	NOUN
ejde-395	298	5	,	,	PUNCT
ejde-395	298	6	1	1	NUM
ejde-395	298	7	f	f	NOUN
ejde-395	298	8	)	)	PUNCT
ejde-395	299	1	=	=	PUNCT
ejde-395	299	2	m	m	PROPN
ejde-395	299	3	(	(	PUNCT
ejde-395	299	4	r	r	NOUN
ejde-395	299	5	,	,	PUNCT
ejde-395	299	6	f(qz)f	f(qz)f	X
ejde-395	299	7	(	(	PUNCT
ejde-395	299	8	z	z	NOUN
ejde-395	299	9	q	q	NOUN
ejde-395	299	10	)	)	PUNCT
ejde-395	299	11	(	(	PUNCT
ejde-395	299	12	f	f	NOUN
ejde-395	300	1	−	−	PROPN
ejde-395	300	2	1	1	NUM
ejde-395	300	3	)	)	PUNCT
ejde-395	300	4	µ	µ	X
ejde-395	300	5	)	)	PUNCT
ejde-395	301	1	=	=	SYM
ejde-395	301	2	m	m	PROPN
ejde-395	301	3	(	(	PUNCT
ejde-395	301	4	r	r	NOUN
ejde-395	301	5	,	,	PUNCT
ejde-395	301	6	f(qz)f	f(qz)f	X
ejde-395	301	7	(	(	PUNCT
ejde-395	301	8	z	z	NOUN
ejde-395	301	9	q	q	NOUN
ejde-395	301	10	)	)	PUNCT
ejde-395	301	11	f2	f2	PROPN
ejde-395	301	12	f2(f	f2(f	PRON
ejde-395	301	13	−	−	PROPN
ejde-395	301	14	1	1	NUM
ejde-395	301	15	)	)	PUNCT
ejde-395	301	16	µ	µ	X
ejde-395	301	17	)	)	PUNCT
ejde-395	301	18	,	,	PUNCT
ejde-395	301	19	by	by	ADP
ejde-395	301	20	combining	combine	VERB
ejde-395	301	21	with	with	ADP
ejde-395	301	22	m(r	m(r	PROPN
ejde-395	301	23	,	,	PUNCT
ejde-395	301	24	f	f	X
ejde-395	301	25	)	)	PUNCT
ejde-395	302	1	=	=	SYM
ejde-395	302	2	s(r	s(r	PROPN
ejde-395	302	3	,	,	PUNCT
ejde-395	302	4	f	f	X
ejde-395	302	5	)	)	PUNCT
ejde-395	302	6	and	and	CCONJ
ejde-395	302	7	lemma	lemma	PROPN
ejde-395	302	8	3.6	3.6	NUM
ejde-395	302	9	,	,	PUNCT
ejde-395	302	10	it	it	PRON
ejde-395	302	11	follows	follow	VERB
ejde-395	302	12	that	that	SCONJ
ejde-395	302	13	m	m	VERB
ejde-395	302	14	(	(	PUNCT
ejde-395	302	15	r	r	NOUN
ejde-395	302	16	,	,	PUNCT
ejde-395	302	17	1	1	NUM
ejde-395	302	18	f	f	NOUN
ejde-395	302	19	)	)	PUNCT
ejde-395	303	1	=	=	SYM
ejde-395	303	2	s(r	s(r	PROPN
ejde-395	303	3	,	,	PUNCT
ejde-395	303	4	f	f	X
ejde-395	303	5	)	)	PUNCT
ejde-395	303	6	,	,	PUNCT
ejde-395	303	7	which	which	PRON
ejde-395	303	8	yields	yield	VERB
ejde-395	303	9	n	n	CCONJ
ejde-395	303	10	(	(	PUNCT
ejde-395	303	11	r	r	NOUN
ejde-395	303	12	,	,	PUNCT
ejde-395	303	13	1	1	NUM
ejde-395	303	14	f	f	NOUN
ejde-395	303	15	)	)	PUNCT
ejde-395	304	1	=	=	SYM
ejde-395	304	2	t	t	PROPN
ejde-395	304	3	(	(	PUNCT
ejde-395	304	4	r	r	NOUN
ejde-395	304	5	,	,	PUNCT
ejde-395	304	6	f	f	NOUN
ejde-395	304	7	)	)	PUNCT
ejde-395	305	1	+	+	CCONJ
ejde-395	305	2	s(r	s(r	ADJ
ejde-395	305	3	,	,	PUNCT
ejde-395	305	4	f	f	NOUN
ejde-395	305	5	)	)	PUNCT
ejde-395	305	6	,	,	PUNCT
ejde-395	305	7	n(r	n(r	NOUN
ejde-395	305	8	,	,	PUNCT
ejde-395	305	9	f	f	X
ejde-395	305	10	)	)	PUNCT
ejde-395	305	11	=	=	SYM
ejde-395	305	12	t	t	PROPN
ejde-395	305	13	(	(	PUNCT
ejde-395	305	14	r	r	NOUN
ejde-395	305	15	,	,	PUNCT
ejde-395	305	16	f	f	NOUN
ejde-395	305	17	)	)	PUNCT
ejde-395	306	1	+	+	CCONJ
ejde-395	306	2	s(r	s(r	ADJ
ejde-395	306	3	,	,	PUNCT
ejde-395	306	4	f	f	NOUN
ejde-395	306	5	)	)	PUNCT
ejde-395	306	6	,	,	PUNCT
ejde-395	306	7	which	which	PRON
ejde-395	306	8	implies	imply	VERB
ejde-395	306	9	that	that	SCONJ
ejde-395	306	10	f	f	PROPN
ejde-395	306	11	has	have	VERB
ejde-395	306	12	infinitely	infinitely	ADV
ejde-395	306	13	many	many	ADJ
ejde-395	306	14	poles	pole	NOUN
ejde-395	306	15	and	and	CCONJ
ejde-395	306	16	zeros	zero	NOUN
ejde-395	306	17	,	,	PUNCT
ejde-395	306	18	and	and	CCONJ
ejde-395	306	19	λ(f	λ(f	PROPN
ejde-395	307	1	)	)	PUNCT
ejde-395	307	2	=	=	PUNCT
ejde-395	307	3	λ	λ	NOUN
ejde-395	307	4	(	(	PUNCT
ejde-395	307	5	1	1	NUM
ejde-395	307	6	f	f	NOUN
ejde-395	307	7	)	)	PUNCT
ejde-395	307	8	=	=	SYM
ejde-395	307	9	σ(f	σ(f	NOUN
ejde-395	307	10	)	)	PUNCT
ejde-395	307	11	.	.	PUNCT
ejde-395	308	1	this	this	PRON
ejde-395	308	2	completes	complete	VERB
ejde-395	308	3	the	the	DET
ejde-395	308	4	proof	proof	NOUN
ejde-395	308	5	�	�	PROPN
ejde-395	308	6	4	4	X
ejde-395	308	7	.	.	PUNCT
ejde-395	308	8	proof	proof	NOUN
ejde-395	308	9	of	of	ADP
ejde-395	308	10	theorem	theorem	ADJ
ejde-395	308	11	1.8	1.8	NUM
ejde-395	308	12	suppose	suppose	VERB
ejde-395	308	13	that	that	SCONJ
ejde-395	308	14	f(z	f(z	NOUN
ejde-395	308	15	)	)	PUNCT
ejde-395	309	1	=	=	SYM
ejde-395	309	2	p	p	X
ejde-395	309	3	(	(	PUNCT
ejde-395	309	4	z)/q(z	z)/q(z	PROPN
ejde-395	309	5	)	)	PUNCT
ejde-395	309	6	is	be	AUX
ejde-395	309	7	a	a	DET
ejde-395	309	8	nonconstant	nonconstant	ADJ
ejde-395	309	9	rational	rational	ADJ
ejde-395	309	10	solution	solution	NOUN
ejde-395	309	11	of	of	ADP
ejde-395	309	12	equation	equation	NOUN
ejde-395	309	13	(	(	PUNCT
ejde-395	309	14	2.2	2.2	NUM
ejde-395	309	15	)	)	PUNCT
ejde-395	309	16	,	,	PUNCT
ejde-395	309	17	where	where	SCONJ
ejde-395	309	18	p	p	PROPN
ejde-395	309	19	(	(	PUNCT
ejde-395	309	20	z	z	NOUN
ejde-395	309	21	)	)	PUNCT
ejde-395	309	22	,	,	PUNCT
ejde-395	309	23	q(z	q(z	PROPN
ejde-395	309	24	)	)	PUNCT
ejde-395	309	25	are	be	AUX
ejde-395	309	26	relatively	relatively	ADV
ejde-395	309	27	prime	prime	ADJ
ejde-395	309	28	polynomials	polynomial	NOUN
ejde-395	309	29	with	with	ADP
ejde-395	309	30	degz	degz	NOUN
ejde-395	309	31	p	p	PROPN
ejde-395	309	32	(	(	PUNCT
ejde-395	309	33	z	z	NOUN
ejde-395	309	34	)	)	PUNCT
ejde-395	309	35	=	=	SYM
ejde-395	309	36	p	p	NOUN
ejde-395	309	37	and	and	CCONJ
ejde-395	309	38	degz	degz	PROPN
ejde-395	309	39	q(z	q(z	PROPN
ejde-395	309	40	)	)	PUNCT
ejde-395	309	41	=	=	SYM
ejde-395	310	1	t.	t.	NOUN
ejde-395	310	2	substituting	substitute	VERB
ejde-395	310	3	this	this	PRON
ejde-395	310	4	into	into	ADP
ejde-395	310	5	(	(	PUNCT
ejde-395	310	6	1.9	1.9	NUM
ejde-395	310	7	)	)	PUNCT
ejde-395	310	8	,	,	PUNCT
ejde-395	310	9	we	we	PRON
ejde-395	310	10	have	have	VERB
ejde-395	310	11	p	p	PROPN
ejde-395	310	12	(	(	PUNCT
ejde-395	310	13	qz	qz	NOUN
ejde-395	310	14	)	)	PUNCT
ejde-395	310	15	q(qz	q(qz	PROPN
ejde-395	310	16	)	)	PUNCT
ejde-395	311	1	p	p	X
ejde-395	311	2	(	(	PUNCT
ejde-395	311	3	z	z	NOUN
ejde-395	311	4	q	q	NOUN
ejde-395	311	5	)	)	PUNCT
ejde-395	311	6	q	q	NOUN
ejde-395	311	7	(	(	PUNCT
ejde-395	311	8	z	z	NOUN
ejde-395	311	9	q	q	NOUN
ejde-395	311	10	)	)	PUNCT
ejde-395	311	11	(	(	PUNCT
ejde-395	311	12	p	p	X
ejde-395	311	13	(	(	PUNCT
ejde-395	311	14	z	z	NOUN
ejde-395	311	15	)	)	PUNCT
ejde-395	311	16	q(z	q(z	PROPN
ejde-395	311	17	)	)	PUNCT
ejde-395	311	18	−	−	NOUN
ejde-395	311	19	1	1	NUM
ejde-395	311	20	)	)	SYM
ejde-395	311	21	2	2	NUM
ejde-395	311	22	=	=	SYM
ejde-395	311	23	(	(	PUNCT
ejde-395	311	24	p	p	X
ejde-395	311	25	(	(	PUNCT
ejde-395	311	26	z	z	NOUN
ejde-395	311	27	)	)	PUNCT
ejde-395	311	28	q(z	q(z	PROPN
ejde-395	311	29	)	)	PUNCT
ejde-395	311	30	−	−	PROPN
ejde-395	312	1	λ	λ	NOUN
ejde-395	312	2	)	)	PUNCT
ejde-395	312	3	2	2	NUM
ejde-395	312	4	.	.	PUNCT
ejde-395	313	1	(	(	PUNCT
ejde-395	313	2	4.1	4.1	NUM
ejde-395	313	3	)	)	PUNCT
ejde-395	313	4	by	by	ADP
ejde-395	313	5	using	use	VERB
ejde-395	313	6	the	the	DET
ejde-395	313	7	same	same	ADJ
ejde-395	313	8	argument	argument	NOUN
ejde-395	313	9	as	as	ADP
ejde-395	313	10	in	in	ADP
ejde-395	313	11	the	the	DET
ejde-395	313	12	proof	proof	NOUN
ejde-395	313	13	of	of	ADP
ejde-395	313	14	theorem	theorem	ADJ
ejde-395	313	15	1.5	1.5	NUM
ejde-395	313	16	(	(	PUNCT
ejde-395	313	17	i	i	NOUN
ejde-395	313	18	)	)	PUNCT
ejde-395	313	19	,	,	PUNCT
ejde-395	313	20	we	we	PRON
ejde-395	313	21	obtain	obtain	VERB
ejde-395	313	22	p	p	NOUN
ejde-395	313	23	=	=	PUNCT
ejde-395	313	24	t.	t.	PROPN
ejde-395	313	25	suppose	suppose	VERB
ejde-395	313	26	that	that	SCONJ
ejde-395	313	27	λ	λ	PROPN
ejde-395	313	28	6=	6=	PROPN
ejde-395	313	29	a2	a2	PROPN
ejde-395	313	30	.	.	PUNCT
ejde-395	314	1	without	without	ADP
ejde-395	314	2	loss	loss	NOUN
ejde-395	314	3	of	of	ADP
ejde-395	314	4	generality	generality	NOUN
ejde-395	314	5	we	we	PRON
ejde-395	314	6	assume	assume	VERB
ejde-395	314	7	that	that	SCONJ
ejde-395	314	8	the	the	DET
ejde-395	314	9	coefficients	coefficient	NOUN
ejde-395	314	10	of	of	ADP
ejde-395	314	11	the	the	DET
ejde-395	314	12	highest	high	ADJ
ejde-395	314	13	degree	degree	NOUN
ejde-395	314	14	terms	term	NOUN
ejde-395	314	15	of	of	ADP
ejde-395	314	16	p	p	NOUN
ejde-395	314	17	(	(	PUNCT
ejde-395	314	18	z	z	NOUN
ejde-395	314	19	)	)	PUNCT
ejde-395	314	20	,	,	PUNCT
ejde-395	314	21	q(z	q(z	PROPN
ejde-395	314	22	)	)	PUNCT
ejde-395	314	23	are	be	AUX
ejde-395	314	24	a	a	PRON
ejde-395	314	25	and	and	CCONJ
ejde-395	314	26	1	1	NUM
ejde-395	314	27	,	,	PUNCT
ejde-395	314	28	respectively	respectively	ADV
ejde-395	314	29	.	.	PUNCT
ejde-395	315	1	in	in	ADP
ejde-395	315	2	view	view	NOUN
ejde-395	315	3	of	of	ADP
ejde-395	315	4	(	(	PUNCT
ejde-395	315	5	1.9	1.9	NUM
ejde-395	315	6	)	)	PUNCT
ejde-395	315	7	,	,	PUNCT
ejde-395	315	8	letting	let	VERB
ejde-395	315	9	|z|	|z|	NOUN
ejde-395	315	10	=	=	SYM
ejde-395	315	11	r	r	NOUN
ejde-395	315	12	→	→	SYM
ejde-395	315	13	+	+	ADJ
ejde-395	315	14	∞	∞	PROPN
ejde-395	315	15	yields	yield	NOUN
ejde-395	315	16	a2(a−	a2(a−	VERB
ejde-395	315	17	1)2	1)2	NUM
ejde-395	315	18	=	=	SYM
ejde-395	315	19	(	(	PUNCT
ejde-395	315	20	a−	a−	PROPN
ejde-395	315	21	λ)2	λ)2	NOUN
ejde-395	315	22	.	.	PUNCT
ejde-395	316	1	(	(	PUNCT
ejde-395	316	2	4.2	4.2	NUM
ejde-395	316	3	)	)	PUNCT
ejde-395	316	4	since	since	SCONJ
ejde-395	316	5	λ	λ	PROPN
ejde-395	316	6	6=	6=	PROPN
ejde-395	316	7	0	0	NUM
ejde-395	316	8	,	,	PUNCT
ejde-395	316	9	1	1	NUM
ejde-395	316	10	,	,	PUNCT
ejde-395	316	11	then	then	ADV
ejde-395	316	12	a	a	DET
ejde-395	316	13	6=	6=	NUM
ejde-395	316	14	0	0	NUM
ejde-395	316	15	,	,	PUNCT
ejde-395	316	16	1	1	NUM
ejde-395	316	17	,	,	PUNCT
ejde-395	316	18	λ	λ	NOUN
ejde-395	316	19	.	.	PUNCT
ejde-395	317	1	now	now	ADV
ejde-395	317	2	,	,	PUNCT
ejde-395	317	3	we	we	PRON
ejde-395	317	4	rewrite	rewrite	VERB
ejde-395	317	5	(	(	PUNCT
ejde-395	317	6	1.9	1.9	NUM
ejde-395	317	7	)	)	PUNCT
ejde-395	317	8	in	in	ADP
ejde-395	317	9	the	the	DET
ejde-395	317	10	form	form	NOUN
ejde-395	317	11	p	p	PROPN
ejde-395	317	12	(	(	PUNCT
ejde-395	317	13	qz	qz	NOUN
ejde-395	317	14	)	)	PUNCT
ejde-395	317	15	q(qz	q(qz	PROPN
ejde-395	317	16	)	)	PUNCT
ejde-395	318	1	p	p	X
ejde-395	318	2	(	(	PUNCT
ejde-395	318	3	z	z	NOUN
ejde-395	318	4	q	q	NOUN
ejde-395	318	5	)	)	PUNCT
ejde-395	318	6	q	q	NOUN
ejde-395	318	7	(	(	PUNCT
ejde-395	318	8	z	z	NOUN
ejde-395	318	9	q	q	NOUN
ejde-395	318	10	)	)	PUNCT
ejde-395	319	1	=	=	SYM
ejde-395	319	2	(	(	PUNCT
ejde-395	319	3	p	p	X
ejde-395	319	4	(	(	PUNCT
ejde-395	319	5	z)−	z)−	PROPN
ejde-395	319	6	λq(z	λq(z	NOUN
ejde-395	319	7	)	)	PUNCT
ejde-395	319	8	p	p	X
ejde-395	319	9	(	(	PUNCT
ejde-395	319	10	z)−q(z	z)−q(z	NOUN
ejde-395	319	11	)	)	PUNCT
ejde-395	319	12	)	)	PUNCT
ejde-395	319	13	2	2	X
ejde-395	319	14	.	.	PUNCT
ejde-395	320	1	since	since	SCONJ
ejde-395	320	2	degz[p	degz[p	PROPN
ejde-395	320	3	(	(	PUNCT
ejde-395	320	4	z)−	z)−	PROPN
ejde-395	320	5	λq(z	λq(z	PROPN
ejde-395	320	6	)	)	PUNCT
ejde-395	320	7	]	]	PUNCT
ejde-395	320	8	=	=	PUNCT
ejde-395	320	9	degz[p	degz[p	NOUN
ejde-395	320	10	(	(	PUNCT
ejde-395	320	11	z)−q(z	z)−q(z	NOUN
ejde-395	320	12	)	)	PUNCT
ejde-395	320	13	]	]	PUNCT
ejde-395	321	1	=	=	SYM
ejde-395	321	2	p	p	X
ejde-395	321	3	,	,	PUNCT
ejde-395	321	4	it	it	PRON
ejde-395	321	5	follows	follow	VERB
ejde-395	321	6	that	that	SCONJ
ejde-395	321	7	(	(	PUNCT
ejde-395	321	8	a−	a−	PROPN
ejde-395	321	9	λ)2p	λ)2p	X
ejde-395	321	10	(	(	PUNCT
ejde-395	321	11	qz)p	qz)p	PROPN
ejde-395	321	12	(	(	PUNCT
ejde-395	321	13	z	z	NOUN
ejde-395	321	14	q	q	NOUN
ejde-395	321	15	)	)	PUNCT
ejde-395	322	1	=	=	SYM
ejde-395	322	2	a2(p	a2(p	PROPN
ejde-395	322	3	(	(	PUNCT
ejde-395	322	4	z)−	z)−	PROPN
ejde-395	322	5	λq(z))2	λq(z))2	PROPN
ejde-395	322	6	,	,	PUNCT
ejde-395	322	7	(	(	PUNCT
ejde-395	322	8	4.3	4.3	NUM
ejde-395	322	9	)	)	PUNCT
ejde-395	322	10	(	(	PUNCT
ejde-395	322	11	a−	a−	PROPN
ejde-395	322	12	1)2q(qz)q	1)2q(qz)q	PROPN
ejde-395	322	13	(	(	PUNCT
ejde-395	322	14	z	z	NOUN
ejde-395	322	15	q	q	NOUN
ejde-395	322	16	)	)	PUNCT
ejde-395	323	1	=	=	SYM
ejde-395	323	2	(	(	PUNCT
ejde-395	323	3	p	p	X
ejde-395	323	4	(	(	PUNCT
ejde-395	323	5	z)−q(z))2	z)−q(z))2	NOUN
ejde-395	323	6	.	.	PUNCT
ejde-395	324	1	(	(	PUNCT
ejde-395	324	2	4.4	4.4	NUM
ejde-395	324	3	)	)	PUNCT
ejde-395	324	4	in	in	ADP
ejde-395	324	5	view	view	NOUN
ejde-395	324	6	of	of	ADP
ejde-395	324	7	(	(	PUNCT
ejde-395	324	8	4.3	4.3	NUM
ejde-395	324	9	)	)	PUNCT
ejde-395	324	10	and	and	CCONJ
ejde-395	324	11	(	(	PUNCT
ejde-395	324	12	4.4	4.4	NUM
ejde-395	324	13	)	)	PUNCT
ejde-395	324	14	,	,	PUNCT
ejde-395	324	15	it	it	PRON
ejde-395	324	16	is	be	AUX
ejde-395	324	17	easy	easy	ADJ
ejde-395	324	18	to	to	PART
ejde-395	324	19	see	see	VERB
ejde-395	324	20	that	that	SCONJ
ejde-395	324	21	0	0	NUM
ejde-395	324	22	is	be	AUX
ejde-395	324	23	not	not	PART
ejde-395	324	24	the	the	DET
ejde-395	324	25	zero	zero	NUM
ejde-395	324	26	of	of	ADP
ejde-395	324	27	p	p	X
ejde-395	324	28	(	(	PUNCT
ejde-395	324	29	z	z	NOUN
ejde-395	324	30	)	)	PUNCT
ejde-395	324	31	,	,	PUNCT
ejde-395	324	32	q(z	q(z	PROPN
ejde-395	324	33	)	)	PUNCT
ejde-395	324	34	.	.	PUNCT
ejde-395	325	1	otherwise	otherwise	ADV
ejde-395	325	2	,	,	PUNCT
ejde-395	325	3	if	if	SCONJ
ejde-395	325	4	0	0	NUM
ejde-395	325	5	is	be	AUX
ejde-395	325	6	a	a	DET
ejde-395	325	7	zero	zero	NUM
ejde-395	325	8	of	of	ADP
ejde-395	325	9	p	p	PROPN
ejde-395	325	10	(	(	PUNCT
ejde-395	325	11	z	z	NOUN
ejde-395	325	12	)	)	PUNCT
ejde-395	325	13	,	,	PUNCT
ejde-395	325	14	from	from	ADP
ejde-395	325	15	(	(	PUNCT
ejde-395	325	16	4.3	4.3	NUM
ejde-395	325	17	)	)	PUNCT
ejde-395	325	18	,	,	PUNCT
ejde-395	325	19	we	we	PRON
ejde-395	325	20	can	can	AUX
ejde-395	325	21	get	get	VERB
ejde-395	325	22	that	that	DET
ejde-395	325	23	0	0	NUM
ejde-395	325	24	is	be	AUX
ejde-395	325	25	also	also	ADV
ejde-395	325	26	a	a	DET
ejde-395	325	27	zero	zero	NUM
ejde-395	325	28	of	of	ADP
ejde-395	325	29	q(z	q(z	PROPN
ejde-395	325	30	)	)	PUNCT
ejde-395	325	31	,	,	PUNCT
ejde-395	325	32	this	this	PRON
ejde-395	325	33	is	be	AUX
ejde-395	325	34	a	a	DET
ejde-395	325	35	contradiction	contradiction	NOUN
ejde-395	325	36	with	with	ADP
ejde-395	325	37	the	the	DET
ejde-395	325	38	hypothesis	hypothesis	NOUN
ejde-395	325	39	of	of	ADP
ejde-395	325	40	p	p	NOUN
ejde-395	325	41	(	(	PUNCT
ejde-395	325	42	z	z	NOUN
ejde-395	325	43	)	)	PUNCT
ejde-395	325	44	,	,	PUNCT
ejde-395	325	45	q(z	q(z	PROPN
ejde-395	325	46	)	)	PUNCT
ejde-395	325	47	being	be	AUX
ejde-395	325	48	relatively	relatively	ADV
ejde-395	325	49	prime	prime	ADJ
ejde-395	325	50	polynomials	polynomial	NOUN
ejde-395	325	51	;	;	PUNCT
ejde-395	325	52	if	if	SCONJ
ejde-395	325	53	0	0	NUM
ejde-395	325	54	is	be	AUX
ejde-395	325	55	a	a	DET
ejde-395	325	56	zero	zero	NUM
ejde-395	325	57	of	of	ADP
ejde-395	325	58	q(z	q(z	PROPN
ejde-395	325	59	)	)	PUNCT
ejde-395	325	60	,	,	PUNCT
ejde-395	325	61	from	from	ADP
ejde-395	325	62	(	(	PUNCT
ejde-395	325	63	4.4	4.4	NUM
ejde-395	325	64	)	)	PUNCT
ejde-395	325	65	,	,	PUNCT
ejde-395	325	66	we	we	PRON
ejde-395	325	67	can	can	AUX
ejde-395	325	68	also	also	ADV
ejde-395	325	69	get	get	VERB
ejde-395	325	70	a	a	DET
ejde-395	325	71	contradiction	contradiction	NOUN
ejde-395	325	72	.	.	PUNCT
ejde-395	326	1	now	now	ADV
ejde-395	326	2	,	,	PUNCT
ejde-395	326	3	suppose	suppose	VERB
ejde-395	326	4	that	that	SCONJ
ejde-395	326	5	z0(6=	z0(6=	NOUN
ejde-395	326	6	0	0	X
ejde-395	326	7	)	)	PUNCT
ejde-395	326	8	is	be	AUX
ejde-395	326	9	a	a	DET
ejde-395	326	10	zero	zero	NUM
ejde-395	326	11	of	of	ADP
ejde-395	326	12	p	p	PROPN
ejde-395	326	13	(	(	PUNCT
ejde-395	326	14	z	z	NOUN
ejde-395	326	15	)	)	PUNCT
ejde-395	326	16	with	with	ADP
ejde-395	326	17	order	order	NOUN
ejde-395	326	18	k	k	NOUN
ejde-395	326	19	,	,	PUNCT
ejde-395	326	20	and	and	CCONJ
ejde-395	326	21	k	k	PROPN
ejde-395	326	22	is	be	AUX
ejde-395	326	23	an	an	DET
ejde-395	326	24	odd	odd	ADJ
ejde-395	326	25	integer	integer	NOUN
ejde-395	326	26	.	.	PUNCT
ejde-395	327	1	then	then	ADV
ejde-395	327	2	z0	z0	PROPN
ejde-395	327	3	/	/	SYM
ejde-395	327	4	q	q	PROPN
ejde-395	327	5	is	be	AUX
ejde-395	327	6	a	a	DET
ejde-395	327	7	zero	zero	NUM
ejde-395	327	8	of	of	ADP
ejde-395	327	9	p	p	PROPN
ejde-395	327	10	(	(	PUNCT
ejde-395	327	11	qz	qz	PROPN
ejde-395	327	12	)	)	PUNCT
ejde-395	327	13	with	with	ADP
ejde-395	327	14	order	order	NOUN
ejde-395	327	15	k.	k.	PROPN
ejde-395	328	1	however	however	ADV
ejde-395	328	2	,	,	PUNCT
ejde-395	328	3	in	in	ADP
ejde-395	328	4	view	view	NOUN
ejde-395	328	5	of	of	ADP
ejde-395	328	6	(	(	PUNCT
ejde-395	328	7	4.3	4.3	NUM
ejde-395	328	8	)	)	PUNCT
ejde-395	328	9	,	,	PUNCT
ejde-395	328	10	it	it	PRON
ejde-395	328	11	yields	yield	VERB
ejde-395	328	12	that	that	SCONJ
ejde-395	328	13	the	the	DET
ejde-395	328	14	orders	order	NOUN
ejde-395	328	15	of	of	ADP
ejde-395	328	16	the	the	DET
ejde-395	328	17	zeros	zero	NOUN
ejde-395	328	18	of	of	ADP
ejde-395	328	19	p	p	PROPN
ejde-395	328	20	(	(	PUNCT
ejde-395	328	21	qz)p	qz)p	PROPN
ejde-395	328	22	(	(	PUNCT
ejde-395	328	23	z	z	NOUN
ejde-395	328	24	/	/	SYM
ejde-395	328	25	q	q	NOUN
ejde-395	328	26	)	)	PUNCT
ejde-395	328	27	are	be	AUX
ejde-395	328	28	all	all	PRON
ejde-395	328	29	even	even	ADV
ejde-395	328	30	integers	integer	NOUN
ejde-395	328	31	,	,	PUNCT
ejde-395	328	32	thus	thus	ADV
ejde-395	328	33	,	,	PUNCT
ejde-395	328	34	z0	z0	PROPN
ejde-395	328	35	/	/	SYM
ejde-395	328	36	q	q	NOUN
ejde-395	328	37	must	must	AUX
ejde-395	328	38	be	be	AUX
ejde-395	328	39	a	a	DET
ejde-395	328	40	zero	zero	NUM
ejde-395	328	41	of	of	ADP
ejde-395	328	42	p	p	X
ejde-395	328	43	(	(	PUNCT
ejde-395	328	44	z	z	NOUN
ejde-395	328	45	/	/	SYM
ejde-395	328	46	q	q	NOUN
ejde-395	328	47	)	)	PUNCT
ejde-395	328	48	with	with	ADP
ejde-395	328	49	order	order	NOUN
ejde-395	328	50	l	l	NOUN
ejde-395	328	51	,	,	PUNCT
ejde-395	328	52	and	and	CCONJ
ejde-395	328	53	l	l	NOUN
ejde-395	328	54	is	be	AUX
ejde-395	328	55	an	an	DET
ejde-395	328	56	odd	odd	ADJ
ejde-395	328	57	integer	integer	NOUN
ejde-395	328	58	.	.	PUNCT
ejde-395	329	1	hence	hence	ADV
ejde-395	329	2	,	,	PUNCT
ejde-395	329	3	z0	z0	PROPN
ejde-395	329	4	/	/	SYM
ejde-395	329	5	q	q	PROPN
ejde-395	329	6	2	2	NUM
ejde-395	329	7	is	be	AUX
ejde-395	329	8	a	a	DET
ejde-395	329	9	zero	zero	NUM
ejde-395	329	10	of	of	ADP
ejde-395	329	11	p	p	PROPN
ejde-395	329	12	(	(	PUNCT
ejde-395	329	13	z	z	NOUN
ejde-395	329	14	)	)	PUNCT
ejde-395	329	15	with	with	ADP
ejde-395	329	16	the	the	DET
ejde-395	329	17	odd	odd	ADJ
ejde-395	329	18	order	order	NOUN
ejde-395	329	19	l.	l.	PROPN
ejde-395	329	20	thus	thus	ADV
ejde-395	329	21	,	,	PUNCT
ejde-395	329	22	continue	continue	VERB
ejde-395	329	23	this	this	DET
ejde-395	329	24	process	process	NOUN
ejde-395	329	25	,	,	PUNCT
ejde-395	329	26	we	we	PRON
ejde-395	329	27	obtain	obtain	VERB
ejde-395	329	28	that	that	PRON
ejde-395	329	29	z0	z0	PROPN
ejde-395	329	30	/	/	SYM
ejde-395	329	31	q	q	NOUN
ejde-395	329	32	m	m	VERB
ejde-395	329	33	are	be	AUX
ejde-395	329	34	the	the	DET
ejde-395	329	35	zeros	zero	NOUN
ejde-395	329	36	of	of	ADP
ejde-395	329	37	p	p	PROPN
ejde-395	329	38	(	(	PUNCT
ejde-395	329	39	z	z	NOUN
ejde-395	329	40	)	)	PUNCT
ejde-395	329	41	for	for	ADP
ejde-395	329	42	any	any	DET
ejde-395	329	43	integer	integer	NOUN
ejde-395	329	44	m.	m.	NOUN
ejde-395	329	45	this	this	PRON
ejde-395	329	46	is	be	AUX
ejde-395	329	47	impossible	impossible	ADJ
ejde-395	329	48	as	as	ADP
ejde-395	329	49	degz	degz	NOUN
ejde-395	329	50	p	p	PROPN
ejde-395	329	51	(	(	PUNCT
ejde-395	329	52	z	z	NOUN
ejde-395	329	53	)	)	PUNCT
ejde-395	329	54	=	=	SYM
ejde-395	329	55	p	p	NOUN
ejde-395	329	56	and	and	CCONJ
ejde-395	329	57	|q|	|q|	VERB
ejde-395	329	58	6=	6=	ADP
ejde-395	329	59	1	1	NUM
ejde-395	329	60	.	.	NUM
ejde-395	329	61	ejde-2020/14	ejde-2020/14	VERB
ejde-395	329	62	q	q	NOUN
ejde-395	329	63	-	-	PUNCT
ejde-395	329	64	difference	difference	NOUN
ejde-395	329	65	painlevé	painlevé	NOUN
ejde-395	329	66	equations	equation	NOUN
ejde-395	329	67	11	11	NUM
ejde-395	329	68	therefore	therefore	ADV
ejde-395	329	69	,	,	PUNCT
ejde-395	329	70	all	all	DET
ejde-395	329	71	the	the	DET
ejde-395	329	72	zeros	zero	NOUN
ejde-395	329	73	of	of	ADP
ejde-395	329	74	p	p	PROPN
ejde-395	329	75	(	(	PUNCT
ejde-395	329	76	z	z	NOUN
ejde-395	329	77	)	)	PUNCT
ejde-395	329	78	have	have	VERB
ejde-395	329	79	even	even	ADV
ejde-395	329	80	orders	order	NOUN
ejde-395	329	81	.	.	PUNCT
ejde-395	330	1	similarly	similarly	ADV
ejde-395	330	2	,	,	PUNCT
ejde-395	330	3	all	all	DET
ejde-395	330	4	the	the	DET
ejde-395	330	5	zeros	zero	NOUN
ejde-395	330	6	of	of	ADP
ejde-395	330	7	q(z	q(z	PROPN
ejde-395	330	8	)	)	PUNCT
ejde-395	330	9	have	have	VERB
ejde-395	330	10	even	even	ADV
ejde-395	330	11	orders	order	NOUN
ejde-395	330	12	.	.	PUNCT
ejde-395	331	1	thus	thus	ADV
ejde-395	331	2	,	,	PUNCT
ejde-395	331	3	set	set	VERB
ejde-395	331	4	p	p	NOUN
ejde-395	331	5	(	(	PUNCT
ejde-395	331	6	z	z	NOUN
ejde-395	331	7	)	)	PUNCT
ejde-395	331	8	=	=	SYM
ejde-395	331	9	aα(z)2	aα(z)2	NOUN
ejde-395	331	10	and	and	CCONJ
ejde-395	331	11	q(z	q(z	PROPN
ejde-395	331	12	)	)	PUNCT
ejde-395	332	1	=	=	SYM
ejde-395	332	2	β(z)2	β(z)2	PROPN
ejde-395	332	3	,	,	PUNCT
ejde-395	332	4	where	where	SCONJ
ejde-395	332	5	α(z	α(z	NOUN
ejde-395	332	6	)	)	PUNCT
ejde-395	332	7	=	=	PUNCT
ejde-395	332	8	zn	zn	X
ejde-395	332	9	+	+	PROPN
ejde-395	332	10	an−1z	an−1z	PROPN
ejde-395	332	11	n−1	n−1	PROPN
ejde-395	332	12	+	+	CCONJ
ejde-395	332	13	·	·	PUNCT
ejde-395	332	14	·	·	PUNCT
ejde-395	332	15	·	·	PUNCT
ejde-395	333	1	+	+	ADJ
ejde-395	333	2	a1z	a1z	PROPN
ejde-395	333	3	+	+	ADJ
ejde-395	333	4	a0	a0	NOUN
ejde-395	333	5	,	,	PUNCT
ejde-395	333	6	(	(	PUNCT
ejde-395	333	7	4.5	4.5	NUM
ejde-395	333	8	)	)	PUNCT
ejde-395	333	9	β(z	β(z	PROPN
ejde-395	333	10	)	)	PUNCT
ejde-395	333	11	=	=	PUNCT
ejde-395	334	1	zn	zn	X
ejde-395	334	2	+	+	PROPN
ejde-395	334	3	bn−1z	bn−1z	PROPN
ejde-395	334	4	n−1	n−1	PROPN
ejde-395	334	5	+	+	CCONJ
ejde-395	334	6	·	·	PUNCT
ejde-395	334	7	·	·	PUNCT
ejde-395	334	8	·	·	PUNCT
ejde-395	334	9	+	+	ADV
ejde-395	334	10	b1z	b1z	PROPN
ejde-395	334	11	+	+	ADJ
ejde-395	334	12	b0	b0	NOUN
ejde-395	334	13	,	,	PUNCT
ejde-395	334	14	(	(	PUNCT
ejde-395	334	15	4.6	4.6	NUM
ejde-395	334	16	)	)	PUNCT
ejde-395	334	17	and	and	CCONJ
ejde-395	334	18	a0	a0	PROPN
ejde-395	334	19	,	,	PUNCT
ejde-395	334	20	a1	a1	NOUN
ejde-395	334	21	,	,	PUNCT
ejde-395	334	22	.	.	PUNCT
ejde-395	334	23	.	.	PUNCT
ejde-395	335	1	.	.	PUNCT
ejde-395	336	1	,	,	PUNCT
ejde-395	336	2	an−1	an−1	ADJ
ejde-395	336	3	,	,	PUNCT
ejde-395	336	4	b0	b0	NOUN
ejde-395	336	5	,	,	PUNCT
ejde-395	336	6	b1	b1	NOUN
ejde-395	336	7	,	,	PUNCT
ejde-395	336	8	.	.	PUNCT
ejde-395	336	9	.	.	PUNCT
ejde-395	336	10	.	.	PUNCT
ejde-395	337	1	,	,	PUNCT
ejde-395	337	2	bn−1	bn−1	PRON
ejde-395	337	3	are	be	AUX
ejde-395	337	4	constants	constant	NOUN
ejde-395	337	5	.	.	PUNCT
ejde-395	338	1	obviously	obviously	ADV
ejde-395	338	2	,	,	PUNCT
ejde-395	338	3	a0	a0	PROPN
ejde-395	338	4	,	,	PUNCT
ejde-395	338	5	b0	b0	NOUN
ejde-395	338	6	can	can	AUX
ejde-395	338	7	not	not	PART
ejde-395	338	8	be	be	AUX
ejde-395	338	9	equal	equal	ADJ
ejde-395	338	10	to	to	ADP
ejde-395	338	11	0	0	NUM
ejde-395	338	12	simultaneously	simultaneously	ADV
ejde-395	338	13	.	.	PUNCT
ejde-395	339	1	then	then	ADV
ejde-395	339	2	,	,	PUNCT
ejde-395	339	3	in	in	ADP
ejde-395	339	4	view	view	NOUN
ejde-395	339	5	of	of	ADP
ejde-395	339	6	(	(	PUNCT
ejde-395	339	7	4.3	4.3	NUM
ejde-395	339	8	)	)	PUNCT
ejde-395	339	9	and	and	CCONJ
ejde-395	339	10	(	(	PUNCT
ejde-395	339	11	4.4	4.4	NUM
ejde-395	339	12	)	)	PUNCT
ejde-395	339	13	,	,	PUNCT
ejde-395	339	14	we	we	PRON
ejde-395	339	15	have	have	VERB
ejde-395	339	16	(	(	PUNCT
ejde-395	339	17	a−	a−	PROPN
ejde-395	339	18	λ)α(qz)α	λ)α(qz)α	NOUN
ejde-395	339	19	(	(	PUNCT
ejde-395	339	20	z	z	NOUN
ejde-395	339	21	q	q	NOUN
ejde-395	339	22	)	)	PUNCT
ejde-395	340	1	=	=	PUNCT
ejde-395	340	2	aα(z)2	aα(z)2	NOUN
ejde-395	340	3	−	−	NOUN
ejde-395	340	4	λβ(z)2	λβ(z)2	PROPN
ejde-395	340	5	,	,	PUNCT
ejde-395	340	6	(	(	PUNCT
ejde-395	340	7	4.7	4.7	NUM
ejde-395	340	8	)	)	PUNCT
ejde-395	340	9	(	(	PUNCT
ejde-395	340	10	a−	a−	PROPN
ejde-395	340	11	1)β(qz)β	1)β(qz)β	NUM
ejde-395	340	12	(	(	PUNCT
ejde-395	340	13	z	z	NOUN
ejde-395	340	14	q	q	NOUN
ejde-395	340	15	)	)	PUNCT
ejde-395	340	16	=	=	PUNCT
ejde-395	341	1	aα(z)2	aα(z)2	NOUN
ejde-395	341	2	−	−	PROPN
ejde-395	341	3	β(z)2	β(z)2	NOUN
ejde-395	341	4	.	.	PUNCT
ejde-395	342	1	(	(	PUNCT
ejde-395	342	2	4.8	4.8	NUM
ejde-395	342	3	)	)	PUNCT
ejde-395	342	4	substituting	substitute	VERB
ejde-395	342	5	(	(	PUNCT
ejde-395	342	6	4.5	4.5	NUM
ejde-395	342	7	)	)	PUNCT
ejde-395	342	8	and	and	CCONJ
ejde-395	342	9	(	(	PUNCT
ejde-395	342	10	4.6	4.6	NUM
ejde-395	342	11	)	)	PUNCT
ejde-395	342	12	into	into	ADP
ejde-395	342	13	the	the	DET
ejde-395	342	14	above	above	ADJ
ejde-395	342	15	equations	equation	NOUN
ejde-395	342	16	,	,	PUNCT
ejde-395	342	17	and	and	CCONJ
ejde-395	342	18	analyzing	analyze	VERB
ejde-395	342	19	the	the	DET
ejde-395	342	20	coefficients	coefficient	NOUN
ejde-395	342	21	of	of	ADP
ejde-395	342	22	terms	term	NOUN
ejde-395	342	23	z2n−1	z2n−1	PROPN
ejde-395	342	24	,	,	PUNCT
ejde-395	342	25	z2n−2	z2n−2	PROPN
ejde-395	342	26	,	,	PUNCT
ejde-395	342	27	.	.	PUNCT
ejde-395	342	28	.	.	PUNCT
ejde-395	343	1	.	.	PUNCT
ejde-395	344	1	,	,	PUNCT
ejde-395	344	2	we	we	PRON
ejde-395	344	3	can	can	AUX
ejde-395	344	4	deduce	deduce	VERB
ejde-395	344	5	that	that	PRON
ejde-395	344	6	(	(	PUNCT
ejde-395	344	7	a−	a−	X
ejde-395	344	8	λ)(q	λ)(q	PUNCT
ejde-395	345	1	+	+	CCONJ
ejde-395	345	2	q−1)an−1	q−1)an−1	PROPN
ejde-395	345	3	=	=	SYM
ejde-395	345	4	2aan−1	2aan−1	NUM
ejde-395	345	5	−	−	NOUN
ejde-395	345	6	2λbn−1	2λbn−1	NUM
ejde-395	345	7	,	,	PUNCT
ejde-395	345	8	(	(	PUNCT
ejde-395	345	9	4.9	4.9	NUM
ejde-395	345	10	)	)	PUNCT
ejde-395	345	11	(	(	PUNCT
ejde-395	345	12	a−	a−	PROPN
ejde-395	345	13	1)(q	1)(q	PROPN
ejde-395	346	1	+	+	CCONJ
ejde-395	346	2	q−1)bn−1	q−1)bn−1	PROPN
ejde-395	346	3	=	=	SYM
ejde-395	346	4	2aan−1	2aan−1	NUM
ejde-395	346	5	−	−	PROPN
ejde-395	346	6	2bn−1	2bn−1	NUM
ejde-395	346	7	,	,	PUNCT
ejde-395	346	8	(	(	PUNCT
ejde-395	346	9	4.10	4.10	NUM
ejde-395	346	10	)	)	PUNCT
ejde-395	346	11	(	(	PUNCT
ejde-395	346	12	a−	a−	X
ejde-395	346	13	λ)[(q2	λ)[(q2	NOUN
ejde-395	346	14	+	+	CCONJ
ejde-395	346	15	q−2)an−2	q−2)an−2	VERB
ejde-395	346	16	+	+	PROPN
ejde-395	346	17	a2	a2	PROPN
ejde-395	346	18	n−1	n−1	PROPN
ejde-395	346	19	]	]	X
ejde-395	346	20	=	=	SYM
ejde-395	346	21	a(2an−2	a(2an−2	X
ejde-395	347	1	+	+	SYM
ejde-395	347	2	a2	a2	PROPN
ejde-395	347	3	n−1)−	n−1)−	ADP
ejde-395	347	4	λ(2bn−2	λ(2bn−2	PROPN
ejde-395	347	5	+	+	ADJ
ejde-395	347	6	b2	b2	NOUN
ejde-395	347	7	n−1	n−1	PROPN
ejde-395	347	8	)	)	PUNCT
ejde-395	347	9	,	,	PUNCT
ejde-395	347	10	(	(	PUNCT
ejde-395	347	11	4.11	4.11	NUM
ejde-395	347	12	)	)	PUNCT
ejde-395	347	13	(	(	PUNCT
ejde-395	347	14	a−	a−	PROPN
ejde-395	347	15	1)[(q2	1)[(q2	NUM
ejde-395	347	16	+	+	CCONJ
ejde-395	347	17	q−2)bn−2	q−2)bn−2	PROPN
ejde-395	347	18	+	+	ADJ
ejde-395	347	19	b2	b2	NOUN
ejde-395	347	20	n−1	n−1	PROPN
ejde-395	347	21	]	]	X
ejde-395	347	22	=	=	SYM
ejde-395	347	23	a(2an−2	a(2an−2	X
ejde-395	347	24	+	+	SYM
ejde-395	347	25	a2	a2	PROPN
ejde-395	347	26	n−1)−	n−1)−	PROPN
ejde-395	347	27	(	(	PUNCT
ejde-395	347	28	2bn−2	2bn−2	NUM
ejde-395	347	29	+	+	NOUN
ejde-395	347	30	b2	b2	PROPN
ejde-395	347	31	n−1	n−1	PROPN
ejde-395	347	32	)	)	PUNCT
ejde-395	347	33	,	,	PUNCT
ejde-395	347	34	(	(	PUNCT
ejde-395	347	35	4.12	4.12	NUM
ejde-395	347	36	)	)	PUNCT
ejde-395	347	37	.	.	PUNCT
ejde-395	347	38	.	.	PUNCT
ejde-395	347	39	.	.	PUNCT
ejde-395	348	1	,	,	PUNCT
ejde-395	348	2	(	(	PUNCT
ejde-395	348	3	a−	a−	PROPN
ejde-395	348	4	λ)[(qi	λ)[(qi	X
ejde-395	349	1	+	+	CCONJ
ejde-395	349	2	q−i)an−i	q−i)an−i	ADV
ejde-395	349	3	+	+	CCONJ
ejde-395	349	4	(	(	PUNCT
ejde-395	349	5	qi−2	qi−2	NOUN
ejde-395	349	6	+	+	X
ejde-395	349	7	q−(i−2))an−1an−i+1	q−(i−2))an−1an−i+1	NOUN
ejde-395	349	8	+	+	X
ejde-395	349	9	.	.	PUNCT
ejde-395	349	10	.	.	PUNCT
ejde-395	349	11	.	.	PUNCT
ejde-395	350	1	+	+	CCONJ
ejde-395	350	2	(	(	PUNCT
ejde-395	350	3	q	q	X
ejde-395	350	4	+	+	CCONJ
ejde-395	350	5	q−1)an−	q−1)an−	ADJ
ejde-395	350	6	i−1	i−1	PROPN
ejde-395	350	7	2	2	NUM
ejde-395	350	8	an−	an−	PUNCT
ejde-395	350	9	i+1	i+1	NUM
ejde-395	350	10	2	2	NUM
ejde-395	350	11	]	]	PUNCT
ejde-395	350	12	=	=	PUNCT
ejde-395	351	1	a(2an−i	a(2an−i	PROPN
ejde-395	351	2	+	+	CCONJ
ejde-395	351	3	2an−1an−i+1	2an−1an−i+1	NUM
ejde-395	352	1	+	+	NUM
ejde-395	352	2	·	·	PUNCT
ejde-395	352	3	·	·	PUNCT
ejde-395	352	4	·	·	PUNCT
ejde-395	352	5	+	+	NUM
ejde-395	352	6	2an−	2an−	NUM
ejde-395	352	7	i−1	i−1	PROPN
ejde-395	352	8	2	2	NUM
ejde-395	352	9	an−	an−	PUNCT
ejde-395	352	10	i+1	i+1	NUM
ejde-395	352	11	2	2	X
ejde-395	352	12	)	)	PUNCT
ejde-395	352	13	−	−	NOUN
ejde-395	353	1	λ(2bn−i	λ(2bn−i	NOUN
ejde-395	353	2	+	+	CCONJ
ejde-395	353	3	2bn−1bn−i+1	2bn−1bn−i+1	NUM
ejde-395	353	4	+	+	CCONJ
ejde-395	353	5	·	·	PUNCT
ejde-395	353	6	·	·	PUNCT
ejde-395	353	7	·	·	PUNCT
ejde-395	354	1	+	+	SYM
ejde-395	354	2	2bn−	2bn−	NUM
ejde-395	354	3	i−1	i−1	PROPN
ejde-395	354	4	2	2	NUM
ejde-395	354	5	bn−	bn−	X
ejde-395	354	6	i+1	i+1	NUM
ejde-395	354	7	2	2	NUM
ejde-395	354	8	)	)	PUNCT
ejde-395	354	9	,	,	PUNCT
ejde-395	354	10	(	(	PUNCT
ejde-395	354	11	4.13	4.13	NUM
ejde-395	354	12	)	)	PUNCT
ejde-395	354	13	(	(	PUNCT
ejde-395	354	14	a−	a−	PROPN
ejde-395	354	15	1)[(qi	1)[(qi	NUM
ejde-395	354	16	+	+	CCONJ
ejde-395	354	17	q−i)bn−i	q−i)bn−i	ADJ
ejde-395	354	18	+	+	CCONJ
ejde-395	354	19	(	(	PUNCT
ejde-395	354	20	qi−2	qi−2	PROPN
ejde-395	354	21	+	+	X
ejde-395	354	22	q−(i−2))bn−1bn−i+1	q−(i−2))bn−1bn−i+1	NOUN
ejde-395	354	23	+	+	X
ejde-395	354	24	.	.	PUNCT
ejde-395	354	25	.	.	PUNCT
ejde-395	354	26	.	.	PUNCT
ejde-395	355	1	+	+	CCONJ
ejde-395	355	2	(	(	PUNCT
ejde-395	355	3	q	q	X
ejde-395	355	4	+	+	CCONJ
ejde-395	355	5	q−1)bn−	q−1)bn−	VERB
ejde-395	355	6	i−1	i−1	PROPN
ejde-395	355	7	2	2	NUM
ejde-395	355	8	bn−	bn−	X
ejde-395	355	9	i+1	i+1	NUM
ejde-395	355	10	2	2	NUM
ejde-395	355	11	]	]	PUNCT
ejde-395	355	12	=	=	PUNCT
ejde-395	356	1	a(2an−i	a(2an−i	PROPN
ejde-395	356	2	+	+	CCONJ
ejde-395	356	3	2an−1an−i+1	2an−1an−i+1	NUM
ejde-395	357	1	+	+	NUM
ejde-395	357	2	·	·	PUNCT
ejde-395	357	3	·	·	PUNCT
ejde-395	357	4	·	·	PUNCT
ejde-395	357	5	+	+	NUM
ejde-395	357	6	2an−	2an−	NUM
ejde-395	357	7	i−1	i−1	PROPN
ejde-395	357	8	2	2	NUM
ejde-395	357	9	an−	an−	PUNCT
ejde-395	357	10	i+1	i+1	NUM
ejde-395	357	11	2	2	NUM
ejde-395	357	12	)	)	PUNCT
ejde-395	357	13	−	−	PROPN
ejde-395	357	14	(	(	PUNCT
ejde-395	357	15	2bn−i	2bn−i	NUM
ejde-395	357	16	+	+	NUM
ejde-395	357	17	2bn−1bn−i+1	2bn−1bn−i+1	NUM
ejde-395	357	18	+	+	X
ejde-395	357	19	·	·	PUNCT
ejde-395	357	20	·	·	PUNCT
ejde-395	357	21	·	·	PUNCT
ejde-395	357	22	+	+	SYM
ejde-395	357	23	2bn−	2bn−	NUM
ejde-395	357	24	i−1	i−1	PROPN
ejde-395	357	25	2	2	NUM
ejde-395	357	26	bn−	bn−	X
ejde-395	357	27	i+1	i+1	NUM
ejde-395	357	28	2	2	NUM
ejde-395	357	29	)	)	PUNCT
ejde-395	357	30	,	,	PUNCT
ejde-395	357	31	(	(	PUNCT
ejde-395	357	32	4.14	4.14	NUM
ejde-395	357	33	)	)	PUNCT
ejde-395	357	34	.	.	PUNCT
ejde-395	357	35	.	.	PUNCT
ejde-395	357	36	.	.	PUNCT
ejde-395	358	1	,	,	PUNCT
ejde-395	358	2	(	(	PUNCT
ejde-395	358	3	a−	a−	PROPN
ejde-395	358	4	λ)[(qj	λ)[(qj	X
ejde-395	359	1	+	+	CCONJ
ejde-395	359	2	q−j)an−j	q−j)an−j	ADV
ejde-395	359	3	+	+	CCONJ
ejde-395	359	4	(	(	PUNCT
ejde-395	359	5	qj−2	qj−2	NOUN
ejde-395	359	6	+	+	CCONJ
ejde-395	359	7	q−(j−2))an−1an−j+1	q−(j−2))an−1an−j+1	PROPN
ejde-395	359	8	+	+	PRON
ejde-395	359	9	·	·	PUNCT
ejde-395	359	10	·	·	PUNCT
ejde-395	359	11	·	·	PUNCT
ejde-395	360	1	+	+	NUM
ejde-395	360	2	a2	a2	PROPN
ejde-395	360	3	n−	n−	NOUN
ejde-395	360	4	j	j	NOUN
ejde-395	360	5	2	2	NUM
ejde-395	360	6	]	]	PUNCT
ejde-395	360	7	=	=	PUNCT
ejde-395	361	1	a(2an−j	a(2an−j	ADV
ejde-395	361	2	+	+	CCONJ
ejde-395	361	3	2an−1an−j+1	2an−1an−j+1	NUM
ejde-395	361	4	+	+	PUNCT
ejde-395	361	5	·	·	PUNCT
ejde-395	361	6	·	·	PUNCT
ejde-395	361	7	·	·	PUNCT
ejde-395	361	8	+	+	NUM
ejde-395	361	9	a2	a2	PROPN
ejde-395	361	10	n−	n−	PROPN
ejde-395	361	11	j	j	PROPN
ejde-395	361	12	2	2	NUM
ejde-395	361	13	)	)	PUNCT
ejde-395	361	14	−	−	PROPN
ejde-395	361	15	λ(2bn−1bn−j+1	λ(2bn−1bn−j+1	NOUN
ejde-395	361	16	+	+	CCONJ
ejde-395	361	17	·	·	PUNCT
ejde-395	361	18	·	·	PUNCT
ejde-395	361	19	·	·	PUNCT
ejde-395	362	1	+	+	NUM
ejde-395	362	2	2b2	2b2	NUM
ejde-395	362	3	n−	n−	PROPN
ejde-395	362	4	j	j	PROPN
ejde-395	362	5	2	2	NUM
ejde-395	362	6	)	)	PUNCT
ejde-395	362	7	,	,	PUNCT
ejde-395	362	8	(	(	PUNCT
ejde-395	362	9	4.15	4.15	NUM
ejde-395	362	10	)	)	PUNCT
ejde-395	362	11	(	(	PUNCT
ejde-395	362	12	a−	a−	PROPN
ejde-395	362	13	1)[(qj	1)[(qj	NUM
ejde-395	362	14	+	+	CCONJ
ejde-395	362	15	q−j)bn−j	q−j)bn−j	X
ejde-395	362	16	+	+	CCONJ
ejde-395	362	17	(	(	PUNCT
ejde-395	362	18	qj−2	qj−2	PROPN
ejde-395	362	19	+	+	CCONJ
ejde-395	362	20	q−(j−2))bn−1bn−j+1	q−(j−2))bn−1bn−j+1	PROPN
ejde-395	362	21	+	+	X
ejde-395	362	22	·	·	PUNCT
ejde-395	362	23	·	·	PUNCT
ejde-395	362	24	·	·	PUNCT
ejde-395	362	25	+	+	NOUN
ejde-395	362	26	b2	b2	PROPN
ejde-395	362	27	n−	n−	NOUN
ejde-395	362	28	j	j	NOUN
ejde-395	362	29	2	2	NUM
ejde-395	362	30	]	]	PUNCT
ejde-395	362	31	=	=	PUNCT
ejde-395	363	1	a(2an−j	a(2an−j	ADV
ejde-395	363	2	+	+	CCONJ
ejde-395	363	3	2an−1an−j+1	2an−1an−j+1	NUM
ejde-395	363	4	+	+	PUNCT
ejde-395	363	5	·	·	PUNCT
ejde-395	363	6	·	·	PUNCT
ejde-395	363	7	·	·	PUNCT
ejde-395	363	8	+	+	NUM
ejde-395	363	9	a2	a2	PROPN
ejde-395	363	10	n−	n−	PROPN
ejde-395	363	11	j	j	PROPN
ejde-395	363	12	2	2	NUM
ejde-395	363	13	)	)	PUNCT
ejde-395	363	14	−	−	PROPN
ejde-395	363	15	(	(	PUNCT
ejde-395	363	16	2bn−1bn−j+1	2bn−1bn−j+1	NUM
ejde-395	363	17	+	+	NUM
ejde-395	363	18	·	·	PUNCT
ejde-395	363	19	·	·	PUNCT
ejde-395	363	20	·	·	PUNCT
ejde-395	363	21	+	+	NUM
ejde-395	363	22	2b2	2b2	NUM
ejde-395	363	23	n−	n−	PROPN
ejde-395	363	24	j	j	PROPN
ejde-395	363	25	2	2	NUM
ejde-395	363	26	)	)	PUNCT
ejde-395	363	27	,	,	PUNCT
ejde-395	363	28	(	(	PUNCT
ejde-395	363	29	4.16	4.16	NUM
ejde-395	363	30	)	)	PUNCT
ejde-395	363	31	.	.	PUNCT
ejde-395	363	32	.	.	PUNCT
ejde-395	364	1	.	.	PUNCT
ejde-395	365	1	,	,	PUNCT
ejde-395	365	2	where	where	SCONJ
ejde-395	365	3	i	i	PRON
ejde-395	365	4	is	be	AUX
ejde-395	365	5	an	an	DET
ejde-395	365	6	odd	odd	ADJ
ejde-395	365	7	integer	integer	NOUN
ejde-395	365	8	,	,	PUNCT
ejde-395	365	9	and	and	CCONJ
ejde-395	365	10	j	j	PROPN
ejde-395	365	11	is	be	AUX
ejde-395	365	12	an	an	DET
ejde-395	365	13	even	even	ADV
ejde-395	365	14	integer	integer	NOUN
ejde-395	365	15	.	.	PUNCT
ejde-395	366	1	assume	assume	VERB
ejde-395	366	2	that	that	SCONJ
ejde-395	366	3	there	there	PRON
ejde-395	366	4	exist	exist	VERB
ejde-395	366	5	a	a	DET
ejde-395	366	6	positive	positive	ADJ
ejde-395	366	7	integer	integer	NOUN
ejde-395	366	8	i	i	PROPN
ejde-395	366	9	∈	∈	PROPN
ejde-395	367	1	n+	n+	ADP
ejde-395	367	2	,	,	PUNCT
ejde-395	367	3	i	i	PRON
ejde-395	367	4	<	<	X
ejde-395	367	5	n	n	X
ejde-395	367	6	satisfying	satisfy	VERB
ejde-395	367	7	an−i	an−i	PROPN
ejde-395	367	8	6=	6=	ADP
ejde-395	367	9	0	0	NUM
ejde-395	367	10	and	and	CCONJ
ejde-395	367	11	an−j	an−j	ADV
ejde-395	367	12	=	=	SYM
ejde-395	367	13	0	0	NUM
ejde-395	367	14	for	for	ADP
ejde-395	367	15	any	any	DET
ejde-395	367	16	non	non	ADJ
ejde-395	367	17	-	-	ADJ
ejde-395	367	18	negative	negative	ADJ
ejde-395	367	19	integer	integer	NOUN
ejde-395	367	20	j	j	PROPN
ejde-395	367	21	<	<	X
ejde-395	367	22	i.	i.	PROPN
ejde-395	367	23	without	without	ADP
ejde-395	367	24	loss	loss	NOUN
ejde-395	367	25	of	of	ADP
ejde-395	367	26	generality	generality	NOUN
ejde-395	367	27	,	,	PUNCT
ejde-395	367	28	we	we	PRON
ejde-395	367	29	let	let	VERB
ejde-395	367	30	12	12	NUM
ejde-395	367	31	h.	h.	PROPN
ejde-395	367	32	y.	y.	PROPN
ejde-395	367	33	xu	xu	PROPN
ejde-395	367	34	,	,	PUNCT
ejde-395	367	35	j.	j.	PROPN
ejde-395	367	36	tu	tu	PROPN
ejde-395	367	37	ejde-2020/14	ejde-2020/14	PROPN
ejde-395	367	38	i	i	NOUN
ejde-395	367	39	=	=	NOUN
ejde-395	367	40	1	1	NUM
ejde-395	367	41	,	,	PUNCT
ejde-395	367	42	that	that	ADV
ejde-395	367	43	is	is	ADV
ejde-395	367	44	,	,	PUNCT
ejde-395	367	45	an−1	an−1	PROPN
ejde-395	367	46	6=	6=	ADP
ejde-395	367	47	0	0	NUM
ejde-395	367	48	,	,	PUNCT
ejde-395	367	49	thus	thus	ADV
ejde-395	367	50	,	,	PUNCT
ejde-395	367	51	bn−1	bn−1	PRON
ejde-395	367	52	6=	6=	ADP
ejde-395	367	53	0	0	NUM
ejde-395	367	54	.	.	PUNCT
ejde-395	368	1	otherwise	otherwise	ADV
ejde-395	368	2	,	,	PUNCT
ejde-395	368	3	if	if	SCONJ
ejde-395	368	4	bn−1	bn−1	PRON
ejde-395	368	5	=	=	SYM
ejde-395	368	6	0	0	NUM
ejde-395	368	7	,	,	PUNCT
ejde-395	368	8	then	then	ADV
ejde-395	368	9	by	by	ADP
ejde-395	368	10	(	(	PUNCT
ejde-395	368	11	4.10	4.10	NUM
ejde-395	368	12	)	)	PUNCT
ejde-395	368	13	,	,	PUNCT
ejde-395	368	14	it	it	PRON
ejde-395	368	15	follows	follow	VERB
ejde-395	368	16	an−1	an−1	PROPN
ejde-395	368	17	=	=	SYM
ejde-395	368	18	0	0	NUM
ejde-395	368	19	,	,	PUNCT
ejde-395	368	20	a	a	DET
ejde-395	368	21	contradiction	contradiction	NOUN
ejde-395	368	22	.	.	PUNCT
ejde-395	369	1	in	in	ADP
ejde-395	369	2	view	view	NOUN
ejde-395	369	3	of	of	ADP
ejde-395	369	4	(	(	PUNCT
ejde-395	369	5	4.9)-(4.10	4.9)-(4.10	NOUN
ejde-395	369	6	)	)	PUNCT
ejde-395	369	7	,	,	PUNCT
ejde-395	369	8	it	it	PRON
ejde-395	369	9	yields	yield	VERB
ejde-395	369	10	(	(	PUNCT
ejde-395	369	11	an−1	an−1	PROPN
ejde-395	369	12	−bn−1)[(a−	−bn−1)[(a−	X
ejde-395	369	13	λ)aan−1	λ)aan−1	PROPN
ejde-395	369	14	−	−	PROPN
ejde-395	369	15	λ(a−	λ(a−	PROPN
ejde-395	369	16	1)bn−1	1)bn−1	NUM
ejde-395	369	17	]	]	X
ejde-395	369	18	=	=	SYM
ejde-395	369	19	0	0	NUM
ejde-395	369	20	,	,	PUNCT
ejde-395	369	21	(	(	PUNCT
ejde-395	369	22	4.17	4.17	NUM
ejde-395	369	23	)	)	PUNCT
ejde-395	369	24	which	which	PRON
ejde-395	369	25	leads	lead	VERB
ejde-395	369	26	to	to	ADP
ejde-395	369	27	either	either	CCONJ
ejde-395	369	28	an−1	an−1	PROPN
ejde-395	369	29	=	=	PUNCT
ejde-395	369	30	bn−1	bn−1	NOUN
ejde-395	369	31	or	or	CCONJ
ejde-395	369	32	(	(	PUNCT
ejde-395	369	33	a	a	DET
ejde-395	369	34	−	−	NOUN
ejde-395	369	35	λ)aan−1	λ)aan−1	PROPN
ejde-395	369	36	−	−	PROPN
ejde-395	369	37	λ(a	λ(a	NOUN
ejde-395	370	1	−	−	PROPN
ejde-395	371	1	1)bn−1	1)bn−1	PROPN
ejde-395	372	1	=	=	SYM
ejde-395	373	1	0	0	PROPN
ejde-395	373	2	.	.	PUNCT
ejde-395	374	1	if	if	SCONJ
ejde-395	374	2	an−1	an−1	PROPN
ejde-395	374	3	=	=	PUNCT
ejde-395	374	4	bn−1	bn−1	ADJ
ejde-395	374	5	,	,	PUNCT
ejde-395	374	6	we	we	PRON
ejde-395	374	7	can	can	AUX
ejde-395	374	8	deduce	deduce	VERB
ejde-395	374	9	from	from	ADP
ejde-395	374	10	(	(	PUNCT
ejde-395	374	11	4.10	4.10	NUM
ejde-395	374	12	)	)	PUNCT
ejde-395	374	13	that	that	PRON
ejde-395	374	14	q1	q1	VERB
ejde-395	374	15	+	+	CCONJ
ejde-395	374	16	q−1	q−1	PROPN
ejde-395	374	17	=	=	PUNCT
ejde-395	374	18	2	2	NUM
ejde-395	374	19	,	,	PUNCT
ejde-395	374	20	which	which	PRON
ejde-395	374	21	implies	imply	VERB
ejde-395	374	22	a	a	DET
ejde-395	374	23	contradiction	contradiction	NOUN
ejde-395	374	24	with	with	ADP
ejde-395	374	25	|q|	|q|	PROPN
ejde-395	374	26	6=	6=	PRON
ejde-395	374	27	1	1	NUM
ejde-395	374	28	.	.	PUNCT
ejde-395	375	1	thus	thus	ADV
ejde-395	375	2	,	,	PUNCT
ejde-395	375	3	it	it	PRON
ejde-395	375	4	yields	yield	VERB
ejde-395	375	5	that	that	SCONJ
ejde-395	375	6	an−1	an−1	PROPN
ejde-395	375	7	6=	6=	NUM
ejde-395	375	8	bn−1	bn−1	PRON
ejde-395	375	9	and	and	CCONJ
ejde-395	375	10	(	(	PUNCT
ejde-395	375	11	a−	a−	X
ejde-395	375	12	λ)aan−1	λ)aan−1	PROPN
ejde-395	375	13	=	=	PUNCT
ejde-395	375	14	λ(a−	λ(a−	PROPN
ejde-395	375	15	1)bn−1	1)bn−1	NUM
ejde-395	375	16	.	.	PUNCT
ejde-395	376	1	(	(	PUNCT
ejde-395	376	2	4.18	4.18	NUM
ejde-395	376	3	)	)	PUNCT
ejde-395	376	4	further	far	ADV
ejde-395	376	5	,	,	PUNCT
ejde-395	376	6	suppose	suppose	VERB
ejde-395	376	7	that	that	SCONJ
ejde-395	376	8	an−2	an−2	PROPN
ejde-395	376	9	6=	6=	PROPN
ejde-395	376	10	0	0	NUM
ejde-395	376	11	.	.	PUNCT
ejde-395	377	1	then	then	ADV
ejde-395	377	2	bn−2	bn−2	PROPN
ejde-395	377	3	6=	6=	PROPN
ejde-395	377	4	0	0	X
ejde-395	377	5	.	.	PUNCT
ejde-395	378	1	indeed	indeed	ADV
ejde-395	378	2	,	,	PUNCT
ejde-395	378	3	if	if	SCONJ
ejde-395	378	4	an−2	an−2	PROPN
ejde-395	378	5	=	=	SYM
ejde-395	378	6	0	0	NUM
ejde-395	378	7	,	,	PUNCT
ejde-395	378	8	then	then	ADV
ejde-395	378	9	from	from	ADP
ejde-395	378	10	(	(	PUNCT
ejde-395	378	11	4.11	4.11	NUM
ejde-395	378	12	)	)	PUNCT
ejde-395	378	13	and	and	CCONJ
ejde-395	378	14	(	(	PUNCT
ejde-395	378	15	4.12	4.12	NUM
ejde-395	378	16	)	)	PUNCT
ejde-395	378	17	,	,	PUNCT
ejde-395	378	18	we	we	PRON
ejde-395	378	19	have	have	VERB
ejde-395	378	20	bn−2	bn−2	PROPN
ejde-395	378	21	=	=	SYM
ejde-395	378	22	0	0	X
ejde-395	378	23	.	.	PUNCT
ejde-395	379	1	similarly	similarly	ADV
ejde-395	379	2	,	,	PUNCT
ejde-395	379	3	if	if	SCONJ
ejde-395	379	4	bn−2	bn−2	PROPN
ejde-395	379	5	=	=	SYM
ejde-395	379	6	0	0	NUM
ejde-395	379	7	,	,	PUNCT
ejde-395	379	8	then	then	ADV
ejde-395	379	9	an−2	an−2	PROPN
ejde-395	379	10	=	=	SYM
ejde-395	379	11	0	0	PROPN
ejde-395	379	12	.	.	PUNCT
ejde-395	380	1	in	in	ADP
ejde-395	380	2	view	view	NOUN
ejde-395	380	3	of	of	ADP
ejde-395	380	4	(	(	PUNCT
ejde-395	380	5	4.11	4.11	NUM
ejde-395	380	6	)	)	PUNCT
ejde-395	380	7	and	and	CCONJ
ejde-395	380	8	(	(	PUNCT
ejde-395	380	9	4.12	4.12	NUM
ejde-395	380	10	)	)	PUNCT
ejde-395	380	11	,	,	PUNCT
ejde-395	380	12	we	we	PRON
ejde-395	380	13	have	have	VERB
ejde-395	380	14	[	[	X
ejde-395	380	15	2(an−2	2(an−2	NUM
ejde-395	380	16	−bn−2	−bn−2	PRON
ejde-395	380	17	)	)	PUNCT
ejde-395	381	1	+	+	CCONJ
ejde-395	381	2	(	(	PUNCT
ejde-395	381	3	a2	a2	PROPN
ejde-395	381	4	n−1	n−1	PROPN
ejde-395	382	1	−b2	−b2	ADV
ejde-395	382	2	n−1)][(a−	n−1)][(a−	PROPN
ejde-395	383	1	λ)aan−2	λ)aan−2	PROPN
ejde-395	383	2	−	−	PROPN
ejde-395	383	3	λ(a−	λ(a−	PROPN
ejde-395	383	4	1)bn−2	1)bn−2	NUM
ejde-395	383	5	]	]	X
ejde-395	383	6	=	=	SYM
ejde-395	383	7	0	0	X
ejde-395	383	8	.	.	PUNCT
ejde-395	384	1	(	(	PUNCT
ejde-395	384	2	4.19	4.19	NUM
ejde-395	384	3	)	)	PUNCT
ejde-395	384	4	from	from	ADP
ejde-395	384	5	(	(	PUNCT
ejde-395	384	6	4.19	4.19	NUM
ejde-395	384	7	)	)	PUNCT
ejde-395	384	8	,	,	PUNCT
ejde-395	384	9	either	either	CCONJ
ejde-395	384	10	2(an−2−bn−2	2(an−2−bn−2	PROPN
ejde-395	384	11	)	)	PUNCT
ejde-395	384	12	+	+	CCONJ
ejde-395	384	13	(	(	PUNCT
ejde-395	384	14	a2	a2	PROPN
ejde-395	384	15	n−1−b2	n−1−b2	ADP
ejde-395	384	16	n−1	n−1	PROPN
ejde-395	384	17	)	)	PUNCT
ejde-395	384	18	=	=	SYM
ejde-395	384	19	0	0	NUM
ejde-395	384	20	or	or	CCONJ
ejde-395	384	21	(	(	PUNCT
ejde-395	384	22	a−λ)aan−2−λ(a−	a−λ)aan−2−λ(a−	PROPN
ejde-395	384	23	1)bn−2	1)bn−2	NUM
ejde-395	384	24	=	=	SYM
ejde-395	384	25	0	0	PROPN
ejde-395	384	26	.	.	PUNCT
ejde-395	385	1	if	if	SCONJ
ejde-395	385	2	2(an−2	2(an−2	NUM
ejde-395	385	3	−	−	PROPN
ejde-395	385	4	bn−2	bn−2	PROPN
ejde-395	385	5	)	)	PUNCT
ejde-395	385	6	+	+	CCONJ
ejde-395	385	7	(	(	PUNCT
ejde-395	385	8	a2	a2	PROPN
ejde-395	385	9	n−1	n−1	PROPN
ejde-395	385	10	−	−	PROPN
ejde-395	385	11	b2	b2	NOUN
ejde-395	385	12	n−1	n−1	PROPN
ejde-395	385	13	)	)	PUNCT
ejde-395	385	14	=	=	SYM
ejde-395	385	15	0	0	NUM
ejde-395	385	16	,	,	PUNCT
ejde-395	385	17	we	we	PRON
ejde-395	385	18	can	can	AUX
ejde-395	385	19	deduce	deduce	VERB
ejde-395	385	20	from	from	ADP
ejde-395	385	21	(	(	PUNCT
ejde-395	385	22	4.12	4.12	NUM
ejde-395	385	23	)	)	PUNCT
ejde-395	385	24	that	that	DET
ejde-395	385	25	q2	q2	NOUN
ejde-395	385	26	+	+	CCONJ
ejde-395	385	27	q−2	q−2	PROPN
ejde-395	385	28	=	=	SYM
ejde-395	385	29	2	2	NUM
ejde-395	385	30	,	,	PUNCT
ejde-395	385	31	which	which	PRON
ejde-395	385	32	implies	imply	VERB
ejde-395	385	33	a	a	DET
ejde-395	385	34	contradiction	contradiction	NOUN
ejde-395	385	35	with	with	ADP
ejde-395	385	36	|q|	|q|	PROPN
ejde-395	385	37	6=	6=	ADP
ejde-395	385	38	1	1	NUM
ejde-395	385	39	.	.	PUNCT
ejde-395	386	1	therefore	therefore	ADV
ejde-395	386	2	(	(	PUNCT
ejde-395	386	3	a−	a−	PROPN
ejde-395	386	4	λ)aan−2	λ)aan−2	PROPN
ejde-395	386	5	=	=	PUNCT
ejde-395	386	6	λ(a−	λ(a−	PROPN
ejde-395	386	7	1)bn−2	1)bn−2	NUM
ejde-395	386	8	.	.	PUNCT
ejde-395	387	1	(	(	PUNCT
ejde-395	387	2	4.20	4.20	NUM
ejde-395	387	3	)	)	PUNCT
ejde-395	387	4	it	it	PRON
ejde-395	387	5	follows	follow	VERB
ejde-395	387	6	from	from	ADP
ejde-395	387	7	(	(	PUNCT
ejde-395	387	8	4.18	4.18	NUM
ejde-395	387	9	)	)	PUNCT
ejde-395	387	10	and	and	CCONJ
ejde-395	387	11	(	(	PUNCT
ejde-395	387	12	4.20	4.20	NUM
ejde-395	387	13	)	)	PUNCT
ejde-395	387	14	that	that	SCONJ
ejde-395	387	15	(	(	PUNCT
ejde-395	387	16	a−	a−	PROPN
ejde-395	387	17	λ)2a2	λ)2a2	PROPN
ejde-395	387	18	=	=	SYM
ejde-395	388	1	λ2(a−	λ2(a−	X
ejde-395	388	2	1)2	1)2	NUM
ejde-395	388	3	.	.	PUNCT
ejde-395	389	1	combining	combine	VERB
ejde-395	389	2	this	this	PRON
ejde-395	389	3	with	with	ADP
ejde-395	389	4	(	(	PUNCT
ejde-395	389	5	4.2	4.2	NUM
ejde-395	389	6	)	)	PUNCT
ejde-395	389	7	yields	yield	NOUN
ejde-395	389	8	λ	λ	PROPN
ejde-395	389	9	=	=	SYM
ejde-395	389	10	a2	a2	PROPN
ejde-395	389	11	,	,	PUNCT
ejde-395	389	12	a	a	DET
ejde-395	389	13	contradiction	contradiction	NOUN
ejde-395	389	14	.	.	PUNCT
ejde-395	390	1	hence	hence	ADV
ejde-395	390	2	,	,	PUNCT
ejde-395	390	3	an−2	an−2	PROPN
ejde-395	390	4	=	=	PUNCT
ejde-395	390	5	0	0	PUNCT
ejde-395	390	6	and	and	CCONJ
ejde-395	390	7	bn−2	bn−2	PROPN
ejde-395	390	8	=	=	SYM
ejde-395	390	9	0	0	X
ejde-395	390	10	.	.	PUNCT
ejde-395	391	1	as	as	ADP
ejde-395	391	2	in	in	ADP
ejde-395	391	3	the	the	DET
ejde-395	391	4	above	above	ADJ
ejde-395	391	5	argument	argument	NOUN
ejde-395	391	6	,	,	PUNCT
ejde-395	391	7	it	it	PRON
ejde-395	391	8	follows	follow	VERB
ejde-395	391	9	that	that	SCONJ
ejde-395	391	10	an−3	an−3	PROPN
ejde-395	391	11	=	=	PRON
ejde-395	391	12	·	·	PUNCT
ejde-395	391	13	·	·	PUNCT
ejde-395	391	14	·	·	PUNCT
ejde-395	392	1	=	=	PUNCT
ejde-395	392	2	a1	a1	NOUN
ejde-395	392	3	=	=	SYM
ejde-395	392	4	0	0	NUM
ejde-395	392	5	and	and	CCONJ
ejde-395	392	6	bn−3	bn−3	PROPN
ejde-395	392	7	=	=	SYM
ejde-395	392	8	·	·	PUNCT
ejde-395	392	9	·	·	PUNCT
ejde-395	392	10	·	·	PUNCT
ejde-395	393	1	=	=	SYM
ejde-395	393	2	b1	b1	NOUN
ejde-395	393	3	=	=	SYM
ejde-395	393	4	0	0	NUM
ejde-395	393	5	.	.	PUNCT
ejde-395	394	1	thus	thus	ADV
ejde-395	394	2	,	,	PUNCT
ejde-395	394	3	an−3	an−3	PROPN
ejde-395	394	4	=	=	SYM
ejde-395	394	5	·	·	PUNCT
ejde-395	394	6	·	·	PUNCT
ejde-395	394	7	·	·	PUNCT
ejde-395	394	8	=	=	PUNCT
ejde-395	394	9	a1	a1	NOUN
ejde-395	394	10	=	=	SYM
ejde-395	394	11	0	0	NUM
ejde-395	394	12	and	and	CCONJ
ejde-395	394	13	bn−3	bn−3	PROPN
ejde-395	394	14	=	=	SYM
ejde-395	394	15	·	·	PUNCT
ejde-395	394	16	·	·	PUNCT
ejde-395	394	17	·	·	PUNCT
ejde-395	395	1	=	=	SYM
ejde-395	395	2	b1	b1	NOUN
ejde-395	395	3	=	=	SYM
ejde-395	395	4	0	0	X
ejde-395	395	5	.	.	PUNCT
ejde-395	396	1	since	since	SCONJ
ejde-395	396	2	0	0	NUM
ejde-395	396	3	is	be	AUX
ejde-395	396	4	not	not	PART
ejde-395	396	5	the	the	DET
ejde-395	396	6	zero	zero	NUM
ejde-395	396	7	of	of	ADP
ejde-395	396	8	p	p	X
ejde-395	396	9	(	(	PUNCT
ejde-395	396	10	z	z	NOUN
ejde-395	396	11	)	)	PUNCT
ejde-395	396	12	,	,	PUNCT
ejde-395	396	13	q(z	q(z	PROPN
ejde-395	396	14	)	)	PUNCT
ejde-395	396	15	,	,	PUNCT
ejde-395	396	16	it	it	PRON
ejde-395	396	17	follows	follow	VERB
ejde-395	396	18	that	that	DET
ejde-395	396	19	a0	a0	PROPN
ejde-395	396	20	6=	6=	ADP
ejde-395	396	21	0	0	NUM
ejde-395	396	22	and	and	CCONJ
ejde-395	396	23	b0	b0	NOUN
ejde-395	396	24	6=	6=	ADP
ejde-395	396	25	0	0	NUM
ejde-395	396	26	.	.	PUNCT
ejde-395	397	1	by	by	ADP
ejde-395	397	2	analyzing	analyze	VERB
ejde-395	397	3	the	the	DET
ejde-395	397	4	coefficients	coefficient	NOUN
ejde-395	397	5	of	of	ADP
ejde-395	397	6	the	the	DET
ejde-395	397	7	term	term	NOUN
ejde-395	397	8	zn	zn	NUM
ejde-395	397	9	,	,	PUNCT
ejde-395	397	10	we	we	PRON
ejde-395	397	11	deduce	deduce	VERB
ejde-395	397	12	that	that	SCONJ
ejde-395	397	13	(	(	PUNCT
ejde-395	397	14	a−	a−	PROPN
ejde-395	397	15	λ)aa0	λ)aa0	NOUN
ejde-395	397	16	=	=	SYM
ejde-395	397	17	λ(a−	λ(a−	PROPN
ejde-395	397	18	1)b0	1)b0	NUM
ejde-395	397	19	.	.	PUNCT
ejde-395	398	1	(	(	PUNCT
ejde-395	398	2	4.21	4.21	NUM
ejde-395	398	3	)	)	PUNCT
ejde-395	398	4	thus	thus	ADV
ejde-395	398	5	,	,	PUNCT
ejde-395	398	6	in	in	ADP
ejde-395	398	7	view	view	NOUN
ejde-395	398	8	of	of	ADP
ejde-395	398	9	(	(	PUNCT
ejde-395	398	10	4.18),(4.21	4.18),(4.21	NUM
ejde-395	398	11	)	)	PUNCT
ejde-395	398	12	and	and	CCONJ
ejde-395	398	13	(	(	PUNCT
ejde-395	398	14	4.2	4.2	NUM
ejde-395	398	15	)	)	PUNCT
ejde-395	398	16	,	,	PUNCT
ejde-395	398	17	it	it	PRON
ejde-395	398	18	yields	yield	VERB
ejde-395	398	19	λ	λ	PROPN
ejde-395	398	20	=	=	SYM
ejde-395	398	21	a2	a2	PROPN
ejde-395	398	22	,	,	PUNCT
ejde-395	398	23	a	a	DET
ejde-395	398	24	contradiction	contradiction	NOUN
ejde-395	398	25	.	.	PUNCT
ejde-395	399	1	hence	hence	ADV
ejde-395	399	2	,	,	PUNCT
ejde-395	399	3	we	we	PRON
ejde-395	399	4	conclude	conclude	VERB
ejde-395	399	5	a1	a1	NOUN
ejde-395	399	6	=	=	PROPN
ejde-395	399	7	a2	a2	PROPN
ejde-395	399	8	=	=	SYM
ejde-395	399	9	·	·	PUNCT
ejde-395	399	10	·	·	PUNCT
ejde-395	399	11	·	·	PUNCT
ejde-395	400	1	=	=	PUNCT
ejde-395	400	2	an−1	an−1	ADJ
ejde-395	400	3	=	=	SYM
ejde-395	400	4	0	0	NUM
ejde-395	400	5	and	and	CCONJ
ejde-395	400	6	b1	b1	NOUN
ejde-395	400	7	=	=	SYM
ejde-395	400	8	b2	b2	NOUN
ejde-395	400	9	=	=	SYM
ejde-395	400	10	·	·	PUNCT
ejde-395	400	11	·	·	PUNCT
ejde-395	400	12	·	·	PUNCT
ejde-395	401	1	=	=	PUNCT
ejde-395	401	2	bn−1	bn−1	ADJ
ejde-395	401	3	=	=	SYM
ejde-395	401	4	0	0	X
ejde-395	401	5	.	.	PUNCT
ejde-395	402	1	in	in	ADP
ejde-395	402	2	view	view	NOUN
ejde-395	402	3	of	of	ADP
ejde-395	402	4	(	(	PUNCT
ejde-395	402	5	4.9)-(4.16	4.9)-(4.16	NUM
ejde-395	402	6	)	)	PUNCT
ejde-395	402	7	,	,	PUNCT
ejde-395	402	8	it	it	PRON
ejde-395	402	9	is	be	AUX
ejde-395	402	10	easy	easy	ADJ
ejde-395	402	11	to	to	PART
ejde-395	402	12	deduce	deduce	VERB
ejde-395	402	13	that	that	DET
ejde-395	402	14	b1	b1	NOUN
ejde-395	402	15	=	=	SYM
ejde-395	402	16	b2	b2	NOUN
ejde-395	402	17	=	=	SYM
ejde-395	402	18	·	·	PUNCT
ejde-395	402	19	·	·	PUNCT
ejde-395	402	20	·	·	PUNCT
ejde-395	403	1	=	=	PUNCT
ejde-395	403	2	bn−1	bn−1	ADJ
ejde-395	403	3	=	=	SYM
ejde-395	403	4	0	0	NUM
ejde-395	403	5	.	.	PUNCT
ejde-395	404	1	thus	thus	ADV
ejde-395	404	2	,	,	PUNCT
ejde-395	404	3	α(z	α(z	NOUN
ejde-395	404	4	)	)	PUNCT
ejde-395	404	5	=	=	PUNCT
ejde-395	405	1	zn	zn	PROPN
ejde-395	405	2	+	+	PROPN
ejde-395	405	3	a0	a0	PROPN
ejde-395	405	4	,	,	PUNCT
ejde-395	405	5	β(z	β(z	PROPN
ejde-395	405	6	)	)	PUNCT
ejde-395	405	7	=	=	PUNCT
ejde-395	406	1	zn	zn	X
ejde-395	406	2	+	+	NOUN
ejde-395	406	3	b0	b0	PROPN
ejde-395	406	4	.	.	PUNCT
ejde-395	407	1	(	(	PUNCT
ejde-395	407	2	4.22	4.22	NUM
ejde-395	407	3	)	)	PUNCT
ejde-395	407	4	hence	hence	ADV
ejde-395	407	5	,	,	PUNCT
ejde-395	407	6	substituting	substitute	VERB
ejde-395	407	7	α	α	NOUN
ejde-395	407	8	,	,	PUNCT
ejde-395	407	9	β	β	X
ejde-395	407	10	into	into	ADP
ejde-395	407	11	(	(	PUNCT
ejde-395	407	12	4.7	4.7	NUM
ejde-395	407	13	)	)	PUNCT
ejde-395	407	14	and	and	CCONJ
ejde-395	407	15	(	(	PUNCT
ejde-395	407	16	4.8	4.8	NUM
ejde-395	407	17	)	)	PUNCT
ejde-395	407	18	,	,	PUNCT
ejde-395	407	19	by	by	ADP
ejde-395	407	20	comparing	compare	VERB
ejde-395	407	21	the	the	DET
ejde-395	407	22	coefficients	coefficient	NOUN
ejde-395	407	23	of	of	ADP
ejde-395	407	24	the	the	DET
ejde-395	407	25	terms	term	NOUN
ejde-395	407	26	zn	zn	NOUN
ejde-395	407	27	and	and	CCONJ
ejde-395	407	28	constant	constant	ADJ
ejde-395	407	29	,	,	PUNCT
ejde-395	407	30	we	we	PRON
ejde-395	407	31	have	have	VERB
ejde-395	407	32	(	(	PUNCT
ejde-395	407	33	a−	a−	X
ejde-395	407	34	λ)(qn	λ)(qn	X
ejde-395	408	1	+	+	CCONJ
ejde-395	408	2	q−n)a0	q−n)a0	PROPN
ejde-395	408	3	=	=	SYM
ejde-395	408	4	2aa0	2aa0	NUM
ejde-395	408	5	−	−	PROPN
ejde-395	408	6	2λb0	2λb0	NUM
ejde-395	408	7	,	,	PUNCT
ejde-395	408	8	(	(	PUNCT
ejde-395	408	9	a−	a−	PROPN
ejde-395	408	10	1)(qn	1)(qn	NUM
ejde-395	408	11	+	+	CCONJ
ejde-395	409	1	q−n)b0	q−n)b0	VERB
ejde-395	409	2	=	=	SYM
ejde-395	409	3	2aa0	2aa0	NUM
ejde-395	409	4	−	−	PROPN
ejde-395	409	5	2b0	2b0	NUM
ejde-395	409	6	,	,	PUNCT
ejde-395	409	7	(	(	PUNCT
ejde-395	409	8	a−	a−	X
ejde-395	409	9	λ)a2	λ)a2	NOUN
ejde-395	409	10	0	0	PUNCT
ejde-395	410	1	=	=	SYM
ejde-395	410	2	aa2	aa2	NOUN
ejde-395	410	3	0	0	PUNCT
ejde-395	411	1	−	−	PROPN
ejde-395	411	2	λb2	λb2	NOUN
ejde-395	411	3	0	0	NUM
ejde-395	411	4	,	,	PUNCT
ejde-395	411	5	(	(	PUNCT
ejde-395	411	6	a−	a−	PROPN
ejde-395	411	7	1)b2	1)b2	NOUN
ejde-395	411	8	0	0	PUNCT
ejde-395	412	1	=	=	SYM
ejde-395	412	2	aa2	aa2	NOUN
ejde-395	412	3	0	0	PUNCT
ejde-395	413	1	−b2	−b2	PROPN
ejde-395	413	2	0	0	NUM
ejde-395	413	3	.	.	PUNCT
ejde-395	414	1	then	then	ADV
ejde-395	414	2	it	it	PRON
ejde-395	414	3	follows	follow	VERB
ejde-395	414	4	that	that	DET
ejde-395	414	5	a0	a0	PROPN
ejde-395	414	6	=	=	PUNCT
ejde-395	414	7	b0	b0	PROPN
ejde-395	414	8	or	or	CCONJ
ejde-395	414	9	a0	a0	NOUN
ejde-395	414	10	=	=	PROPN
ejde-395	414	11	−b0	−b0	PROPN
ejde-395	414	12	.	.	PUNCT
ejde-395	415	1	if	if	SCONJ
ejde-395	415	2	a0	a0	PROPN
ejde-395	415	3	=	=	PUNCT
ejde-395	415	4	b0	b0	PROPN
ejde-395	415	5	,	,	PUNCT
ejde-395	415	6	then	then	ADV
ejde-395	415	7	qn	qn	PROPN
ejde-395	415	8	+	+	CCONJ
ejde-395	415	9	q−n	q−n	NOUN
ejde-395	415	10	=	=	SYM
ejde-395	415	11	2	2	NUM
ejde-395	415	12	is	be	AUX
ejde-395	415	13	a	a	DET
ejde-395	415	14	contradiction	contradiction	NOUN
ejde-395	415	15	.	.	PUNCT
ejde-395	416	1	if	if	SCONJ
ejde-395	416	2	a0	a0	PROPN
ejde-395	416	3	=	=	SYM
ejde-395	416	4	−b0	−b0	PROPN
ejde-395	416	5	,	,	PUNCT
ejde-395	416	6	then	then	ADV
ejde-395	416	7	λ(a	λ(a	VERB
ejde-395	416	8	−	−	PROPN
ejde-395	416	9	1)b0	1)b0	NUM
ejde-395	416	10	−	−	NOUN
ejde-395	416	11	a(a	a(a	PROPN
ejde-395	416	12	−	−	PROPN
ejde-395	417	1	λ)a0	λ)a0	PROPN
ejde-395	417	2	=	=	PROPN
ejde-395	417	3	0	0	PROPN
ejde-395	417	4	.	.	PUNCT
ejde-395	418	1	thus	thus	ADV
ejde-395	418	2	,	,	PUNCT
ejde-395	418	3	with	with	ADP
ejde-395	418	4	a	a	DET
ejde-395	418	5	view	view	NOUN
ejde-395	418	6	of	of	ADP
ejde-395	418	7	a0	a0	PROPN
ejde-395	418	8	6=	6=	ADP
ejde-395	418	9	0	0	NUM
ejde-395	418	10	,	,	PUNCT
ejde-395	418	11	this	this	PRON
ejde-395	418	12	yields	yield	NOUN
ejde-395	418	13	λ	λ	PROPN
ejde-395	418	14	=	=	SYM
ejde-395	418	15	a2	a2	PROPN
ejde-395	418	16	,	,	PUNCT
ejde-395	418	17	a	a	DET
ejde-395	418	18	contradiction	contradiction	NOUN
ejde-395	418	19	.	.	PUNCT
ejde-395	419	1	this	this	PRON
ejde-395	419	2	completes	complete	VERB
ejde-395	419	3	the	the	DET
ejde-395	419	4	proof	proof	NOUN
ejde-395	419	5	of	of	ADP
ejde-395	419	6	theorem	theorem	ADJ
ejde-395	419	7	1.8	1.8	NUM
ejde-395	419	8	.	.	PUNCT
ejde-395	420	1	for	for	ADP
ejde-395	420	2	the	the	DET
ejde-395	420	3	proof	proof	NOUN
ejde-395	420	4	of	of	ADP
ejde-395	420	5	theorem	theorem	NOUN
ejde-395	420	6	1.10	1.10	NUM
ejde-395	420	7	we	we	PRON
ejde-395	420	8	use	use	VERB
ejde-395	420	9	the	the	DET
ejde-395	420	10	same	same	ADJ
ejde-395	420	11	argument	argument	NOUN
ejde-395	420	12	as	as	ADP
ejde-395	420	13	in	in	ADP
ejde-395	420	14	the	the	DET
ejde-395	420	15	proof	proof	NOUN
ejde-395	420	16	of	of	ADP
ejde-395	420	17	theorem	theorem	ADJ
ejde-395	420	18	1.7	1.7	NUM
ejde-395	420	19	and	and	CCONJ
ejde-395	420	20	the	the	DET
ejde-395	420	21	conclusion	conclusion	NOUN
ejde-395	420	22	follows	follow	VERB
ejde-395	420	23	easily	easily	ADV
ejde-395	420	24	.	.	PUNCT
ejde-395	421	1	ejde-2020/14	ejde-2020/14	VERB
ejde-395	421	2	q	q	NOUN
ejde-395	421	3	-	-	PUNCT
ejde-395	421	4	difference	difference	NOUN
ejde-395	421	5	painlevé	painlevé	NOUN
ejde-395	421	6	equations	equation	NOUN
ejde-395	421	7	13	13	NUM
ejde-395	421	8	acknowledgments	acknowledgment	NOUN
ejde-395	421	9	.	.	PUNCT
ejde-395	422	1	this	this	DET
ejde-395	422	2	work	work	NOUN
ejde-395	422	3	was	be	AUX
ejde-395	422	4	supported	support	VERB
ejde-395	422	5	by	by	ADP
ejde-395	422	6	the	the	DET
ejde-395	422	7	national	national	ADJ
ejde-395	422	8	natural	natural	PROPN
ejde-395	422	9	science	science	PROPN
ejde-395	422	10	foundation	foundation	PROPN
ejde-395	422	11	of	of	ADP
ejde-395	422	12	china	china	PROPN
ejde-395	422	13	(	(	PUNCT
ejde-395	422	14	11561033	11561033	NUM
ejde-395	422	15	,	,	PUNCT
ejde-395	422	16	11561031	11561031	NUM
ejde-395	422	17	)	)	PUNCT
ejde-395	422	18	,	,	PUNCT
ejde-395	422	19	by	by	ADP
ejde-395	422	20	the	the	DET
ejde-395	422	21	natural	natural	ADJ
ejde-395	422	22	science	science	PROPN
ejde-395	422	23	foundation	foundation	PROPN
ejde-395	422	24	of	of	ADP
ejde-395	422	25	jiangxi	jiangxi	PROPN
ejde-395	422	26	province	province	PROPN
ejde-395	422	27	in	in	ADP
ejde-395	422	28	china	china	PROPN
ejde-395	422	29	(	(	PUNCT
ejde-395	422	30	20151bab201008	20151bab201008	PROPN
ejde-395	422	31	,	,	PUNCT
ejde-395	422	32	20181bab201001	20181bab201001	NUM
ejde-395	422	33	)	)	PUNCT
ejde-395	422	34	,	,	PUNCT
ejde-395	422	35	and	and	CCONJ
ejde-395	422	36	by	by	ADP
ejde-395	422	37	the	the	DET
ejde-395	422	38	foundation	foundation	NOUN
ejde-395	422	39	of	of	ADP
ejde-395	422	40	education	education	PROPN
ejde-395	422	41	department	department	PROPN
ejde-395	422	42	of	of	ADP
ejde-395	422	43	jiangxi	jiangxi	PROPN
ejde-395	422	44	(	(	PUNCT
ejde-395	422	45	gjj190876	gjj190876	NOUN
ejde-395	422	46	,	,	PUNCT
ejde-395	422	47	gjj191042	gjj191042	NOUN
ejde-395	422	48	,	,	PUNCT
ejde-395	422	49	gjj190895	gjj190895	VERB
ejde-395	422	50	)	)	PUNCT
ejde-395	422	51	of	of	ADP
ejde-395	422	52	china	china	PROPN
ejde-395	422	53	.	.	PUNCT
ejde-395	423	1	references	reference	NOUN
ejde-395	423	2	[	[	X
ejde-395	423	3	1	1	X
ejde-395	423	4	]	]	X
ejde-395	423	5	d.	d.	PROPN
ejde-395	423	6	c.	c.	PROPN
ejde-395	423	7	barnett	barnett	PROPN
ejde-395	423	8	,	,	PUNCT
ejde-395	423	9	r.	r.	PROPN
ejde-395	423	10	g.	g.	PROPN
ejde-395	423	11	halburd	halburd	PROPN
ejde-395	423	12	,	,	PUNCT
ejde-395	423	13	r.	r.	PROPN
ejde-395	423	14	j.	j.	PROPN
ejde-395	423	15	korhonen	korhonen	PROPN
ejde-395	423	16	,	,	PUNCT
ejde-395	423	17	w.	w.	PROPN
ejde-395	423	18	morgan	morgan	PROPN
ejde-395	423	19	;	;	PUNCT
ejde-395	423	20	nevanlinna	nevanlinna	NOUN
ejde-395	423	21	theory	theory	NOUN
ejde-395	423	22	for	for	ADP
ejde-395	423	23	the	the	DET
ejde-395	423	24	q	q	ADJ
ejde-395	423	25	-	-	PUNCT
ejde-395	423	26	difference	difference	NOUN
ejde-395	423	27	operator	operator	NOUN
ejde-395	423	28	and	and	CCONJ
ejde-395	423	29	meromorphic	meromorphic	ADJ
ejde-395	423	30	solutions	solution	NOUN
ejde-395	423	31	of	of	ADP
ejde-395	423	32	q	q	ADJ
ejde-395	423	33	-	-	PUNCT
ejde-395	423	34	difference	difference	NOUN
ejde-395	423	35	equations	equation	NOUN
ejde-395	423	36	,	,	PUNCT
ejde-395	423	37	proc	proc	NOUN
ejde-395	423	38	.	.	PUNCT
ejde-395	424	1	roy	roy	PROPN
ejde-395	424	2	.	.	PROPN
ejde-395	424	3	soc	soc	PROPN
ejde-395	424	4	.	.	PUNCT
ejde-395	425	1	edin	edin	NOUN
ejde-395	425	2	.	.	PUNCT
ejde-395	426	1	sect	sect	NOUN
ejde-395	426	2	.	.	PUNCT
ejde-395	427	1	a	a	DET
ejde-395	427	2	math	math	NOUN
ejde-395	427	3	.	.	PUNCT
ejde-395	427	4	,	,	PUNCT
ejde-395	427	5	137	137	NUM
ejde-395	427	6	(	(	PUNCT
ejde-395	427	7	2007	2007	NUM
ejde-395	427	8	)	)	PUNCT
ejde-395	427	9	,	,	PUNCT
ejde-395	427	10	457	457	NUM
ejde-395	427	11	-	-	SYM
ejde-395	427	12	474	474	NUM
ejde-395	427	13	.	.	PUNCT
ejde-395	428	1	[	[	X
ejde-395	428	2	2	2	X
ejde-395	428	3	]	]	PUNCT
ejde-395	428	4	h.	h.	PROPN
ejde-395	428	5	y.	y.	PROPN
ejde-395	428	6	chen	chen	PROPN
ejde-395	428	7	,	,	PUNCT
ejde-395	428	8	x.	x.	PROPN
ejde-395	428	9	m.	m.	PROPN
ejde-395	428	10	zheng	zheng	PROPN
ejde-395	428	11	;	;	PUNCT
ejde-395	428	12	the	the	DET
ejde-395	428	13	growth	growth	NOUN
ejde-395	428	14	of	of	ADP
ejde-395	428	15	meromorphic	meromorphic	ADJ
ejde-395	428	16	solutions	solution	NOUN
ejde-395	428	17	of	of	ADP
ejde-395	428	18	homogeneous	homogeneous	ADJ
ejde-395	428	19	and	and	CCONJ
ejde-395	428	20	nonhomogeneous	nonhomogeneous	ADJ
ejde-395	428	21	complex	complex	ADJ
ejde-395	428	22	linear	linear	ADJ
ejde-395	428	23	equations	equation	NOUN
ejde-395	428	24	for	for	ADP
ejde-395	428	25	composite	composite	ADJ
ejde-395	428	26	functions	function	NOUN
ejde-395	428	27	,	,	PUNCT
ejde-395	428	28	j.	j.	PROPN
ejde-395	428	29	jiangxi	jiangxi	PROPN
ejde-395	428	30	normal	normal	PROPN
ejde-395	428	31	university	university	PROPN
ejde-395	428	32	(	(	PUNCT
ejde-395	428	33	natural	natural	ADJ
ejde-395	428	34	sciences	science	NOUN
ejde-395	428	35	)	)	PUNCT
ejde-395	428	36	,	,	PUNCT
ejde-395	428	37	43	43	NUM
ejde-395	428	38	(	(	PUNCT
ejde-395	428	39	2019	2019	NUM
ejde-395	428	40	)	)	PUNCT
ejde-395	428	41	,	,	PUNCT
ejde-395	428	42	336	336	NUM
ejde-395	428	43	-	-	SYM
ejde-395	428	44	342	342	NUM
ejde-395	428	45	.	.	PUNCT
ejde-395	429	1	[	[	X
ejde-395	429	2	3	3	X
ejde-395	429	3	]	]	PUNCT
ejde-395	429	4	z.	z.	PROPN
ejde-395	429	5	x.	x.	PROPN
ejde-395	429	6	chen	chen	PROPN
ejde-395	429	7	;	;	PUNCT
ejde-395	429	8	complex	complex	ADJ
ejde-395	429	9	differences	difference	NOUN
ejde-395	429	10	and	and	CCONJ
ejde-395	429	11	difference	difference	NOUN
ejde-395	429	12	equations	equation	NOUN
ejde-395	429	13	,	,	PUNCT
ejde-395	429	14	mathematics	mathematics	PROPN
ejde-395	429	15	monograph	monograph	PROPN
ejde-395	429	16	series	series	PROPN
ejde-395	429	17	29	29	NUM
ejde-395	429	18	,	,	PUNCT
ejde-395	429	19	beijing	beijing	PROPN
ejde-395	429	20	:	:	PUNCT
ejde-395	429	21	science	science	NOUN
ejde-395	429	22	press	press	PROPN
ejde-395	429	23	,	,	PUNCT
ejde-395	429	24	2014	2014	NUM
ejde-395	429	25	.	.	PUNCT
ejde-395	430	1	[	[	X
ejde-395	430	2	4	4	X
ejde-395	430	3	]	]	PUNCT
ejde-395	430	4	z.	z.	PROPN
ejde-395	430	5	x.	x.	PROPN
ejde-395	430	6	chen	chen	PROPN
ejde-395	430	7	,	,	PUNCT
ejde-395	430	8	k.	k.	PROPN
ejde-395	430	9	h.	h.	PROPN
ejde-395	430	10	shon	shon	PROPN
ejde-395	430	11	;	;	PUNCT
ejde-395	430	12	value	value	NOUN
ejde-395	430	13	distribution	distribution	NOUN
ejde-395	430	14	of	of	ADP
ejde-395	430	15	meromorphic	meromorphic	ADJ
ejde-395	430	16	solutions	solution	NOUN
ejde-395	430	17	of	of	ADP
ejde-395	430	18	certain	certain	ADJ
ejde-395	430	19	difference	difference	NOUN
ejde-395	430	20	painlevé	painlevé	NOUN
ejde-395	430	21	equations	equation	NOUN
ejde-395	430	22	,	,	PUNCT
ejde-395	430	23	j.	j.	PROPN
ejde-395	430	24	math	math	PROPN
ejde-395	430	25	.	.	PUNCT
ejde-395	431	1	anal	anal	PROPN
ejde-395	431	2	.	.	PUNCT
ejde-395	432	1	appl	appl	PROPN
ejde-395	432	2	.	.	PROPN
ejde-395	432	3	,	,	PUNCT
ejde-395	432	4	364	364	NUM
ejde-395	432	5	(	(	PUNCT
ejde-395	432	6	2010	2010	NUM
ejde-395	432	7	)	)	PUNCT
ejde-395	432	8	,	,	PUNCT
ejde-395	432	9	556	556	NUM
ejde-395	432	10	-	-	SYM
ejde-395	432	11	566	566	NUM
ejde-395	432	12	.	.	PUNCT
ejde-395	433	1	[	[	X
ejde-395	433	2	5	5	X
ejde-395	433	3	]	]	X
ejde-395	433	4	y.	y.	PROPN
ejde-395	433	5	m.	m.	PROPN
ejde-395	433	6	chiang	chiang	PROPN
ejde-395	433	7	,	,	PUNCT
ejde-395	433	8	s.	s.	PROPN
ejde-395	433	9	j.	j.	PROPN
ejde-395	433	10	feng	feng	PROPN
ejde-395	433	11	;	;	PUNCT
ejde-395	433	12	on	on	ADP
ejde-395	433	13	the	the	DET
ejde-395	433	14	nevanlinna	nevanlinna	NOUN
ejde-395	433	15	characteristic	characteristic	NOUN
ejde-395	433	16	of	of	ADP
ejde-395	433	17	f(z	f(z	PROPN
ejde-395	433	18	+	+	CCONJ
ejde-395	433	19	η	η	NOUN
ejde-395	433	20	)	)	PUNCT
ejde-395	433	21	and	and	CCONJ
ejde-395	433	22	difference	difference	NOUN
ejde-395	433	23	equations	equation	NOUN
ejde-395	433	24	in	in	ADP
ejde-395	433	25	the	the	DET
ejde-395	433	26	complex	complex	ADJ
ejde-395	433	27	plane	plane	NOUN
ejde-395	433	28	,	,	PUNCT
ejde-395	433	29	ramanujan	ramanujan	PROPN
ejde-395	433	30	j.	j.	PROPN
ejde-395	433	31	,	,	PUNCT
ejde-395	433	32	16	16	NUM
ejde-395	433	33	(	(	PUNCT
ejde-395	433	34	2008	2008	NUM
ejde-395	433	35	)	)	PUNCT
ejde-395	433	36	,	,	PUNCT
ejde-395	433	37	105	105	NUM
ejde-395	433	38	-	-	SYM
ejde-395	433	39	129	129	NUM
ejde-395	433	40	.	.	PUNCT
ejde-395	434	1	[	[	X
ejde-395	434	2	6	6	NUM
ejde-395	434	3	]	]	X
ejde-395	434	4	y.	y.	PROPN
ejde-395	434	5	f.	f.	PROPN
ejde-395	434	6	du	du	PROPN
ejde-395	434	7	,	,	PUNCT
ejde-395	434	8	z.	z.	PROPN
ejde-395	434	9	s.	s.	PROPN
ejde-395	434	10	gao	gao	PROPN
ejde-395	434	11	,	,	PUNCT
ejde-395	434	12	j.	j.	PROPN
ejde-395	434	13	l.	l.	PROPN
ejde-395	434	14	zhang	zhang	PROPN
ejde-395	434	15	;	;	PUNCT
ejde-395	434	16	existence	existence	NOUN
ejde-395	434	17	of	of	ADP
ejde-395	434	18	zero	zero	NUM
ejde-395	434	19	-	-	PUNCT
ejde-395	434	20	order	order	NOUN
ejde-395	434	21	meromorphic	meromorphic	ADJ
ejde-395	434	22	solutions	solution	NOUN
ejde-395	434	23	of	of	ADP
ejde-395	434	24	certain	certain	ADJ
ejde-395	434	25	q	q	ADJ
ejde-395	434	26	-	-	PUNCT
ejde-395	434	27	difference	difference	NOUN
ejde-395	434	28	equations	equation	NOUN
ejde-395	434	29	,	,	PUNCT
ejde-395	434	30	journal	journal	NOUN
ejde-395	434	31	of	of	ADP
ejde-395	434	32	inequalities	inequality	NOUN
ejde-395	434	33	and	and	CCONJ
ejde-395	434	34	applications	application	NOUN
ejde-395	434	35	,	,	PUNCT
ejde-395	434	36	2018	2018	NUM
ejde-395	434	37	(	(	PUNCT
ejde-395	434	38	2018	2018	NUM
ejde-395	434	39	)	)	PUNCT
ejde-395	434	40	,	,	PUNCT
ejde-395	434	41	art	art	NOUN
ejde-395	434	42	.	.	PUNCT
ejde-395	435	1	i	i	PRON
ejde-395	435	2	d	d	PROPN
ejde-395	435	3	217	217	NUM
ejde-395	435	4	.	.	PUNCT
ejde-395	436	1	[	[	X
ejde-395	436	2	7	7	X
ejde-395	436	3	]	]	PUNCT
ejde-395	436	4	a.	a.	NOUN
ejde-395	436	5	s.	s.	PROPN
ejde-395	436	6	fokas	fokas	PROPN
ejde-395	436	7	;	;	PUNCT
ejde-395	436	8	from	from	ADP
ejde-395	436	9	continuous	continuous	ADJ
ejde-395	436	10	to	to	PART
ejde-395	436	11	discrete	discrete	VERB
ejde-395	436	12	painlevé	painlevé	NOUN
ejde-395	436	13	equations	equation	NOUN
ejde-395	436	14	,	,	PUNCT
ejde-395	436	15	j.	j.	PROPN
ejde-395	436	16	math	math	PROPN
ejde-395	436	17	.	.	PUNCT
ejde-395	437	1	anal	anal	PROPN
ejde-395	437	2	.	.	PUNCT
ejde-395	438	1	appl	appl	PROPN
ejde-395	438	2	.	.	PROPN
ejde-395	438	3	,	,	PUNCT
ejde-395	438	4	180	180	NUM
ejde-395	438	5	(	(	PUNCT
ejde-395	438	6	1993	1993	NUM
ejde-395	438	7	)	)	PUNCT
ejde-395	438	8	,	,	PUNCT
ejde-395	438	9	342	342	NUM
ejde-395	438	10	-	-	SYM
ejde-395	438	11	360	360	NUM
ejde-395	438	12	.	.	PUNCT
ejde-395	439	1	[	[	X
ejde-395	439	2	8	8	NUM
ejde-395	439	3	]	]	X
ejde-395	439	4	b.	b.	PROPN
ejde-395	439	5	grammaticos	grammaticos	PROPN
ejde-395	439	6	,	,	PUNCT
ejde-395	439	7	f.	f.	PROPN
ejde-395	439	8	w.	w.	PROPN
ejde-395	439	9	nijhoff	nijhoff	PROPN
ejde-395	439	10	,	,	PUNCT
ejde-395	439	11	a.	a.	NOUN
ejde-395	439	12	ramani	ramani	PROPN
ejde-395	439	13	;	;	PUNCT
ejde-395	439	14	discrete	discrete	ADJ
ejde-395	439	15	painlevé	painlevé	NOUN
ejde-395	439	16	equations	equation	NOUN
ejde-395	439	17	,	,	PUNCT
ejde-395	439	18	the	the	DET
ejde-395	439	19	painlevé	painlevé	NOUN
ejde-395	439	20	property	property	NOUN
ejde-395	439	21	,	,	PUNCT
ejde-395	439	22	crm	crm	NOUN
ejde-395	439	23	ser	ser	PROPN
ejde-395	439	24	.	.	PROPN
ejde-395	439	25	math	math	NOUN
ejde-395	439	26	.	.	PUNCT
ejde-395	440	1	phys	phy	NOUN
ejde-395	440	2	.	.	PUNCT
ejde-395	440	3	,	,	PUNCT
ejde-395	440	4	springer	springer	NOUN
ejde-395	440	5	,	,	PUNCT
ejde-395	440	6	new	new	PROPN
ejde-395	440	7	york	york	PROPN
ejde-395	440	8	,	,	PUNCT
ejde-395	440	9	1999	1999	NUM
ejde-395	440	10	,	,	PUNCT
ejde-395	440	11	pp	pp	ADJ
ejde-395	440	12	.	.	PUNCT
ejde-395	441	1	413	413	NUM
ejde-395	441	2	-	-	SYM
ejde-395	441	3	516	516	NUM
ejde-395	441	4	.	.	PUNCT
ejde-395	442	1	[	[	X
ejde-395	442	2	9	9	NUM
ejde-395	442	3	]	]	X
ejde-395	442	4	g.	g.	PROPN
ejde-395	442	5	g.	g.	PROPN
ejde-395	442	6	gundersen	gundersen	PROPN
ejde-395	442	7	,	,	PUNCT
ejde-395	442	8	j.	j.	PROPN
ejde-395	442	9	heittokangas	heittokangas	PROPN
ejde-395	442	10	,	,	PUNCT
ejde-395	442	11	i.	i.	PROPN
ejde-395	442	12	laine	laine	PROPN
ejde-395	442	13	,	,	PUNCT
ejde-395	442	14	j.	j.	PROPN
ejde-395	442	15	rieppo	rieppo	PROPN
ejde-395	442	16	,	,	PUNCT
ejde-395	442	17	d.	d.	PROPN
ejde-395	442	18	q.	q.	PROPN
ejde-395	442	19	yang	yang	PROPN
ejde-395	442	20	;	;	PUNCT
ejde-395	442	21	meromorphic	meromorphic	ADJ
ejde-395	442	22	solutions	solution	NOUN
ejde-395	442	23	of	of	ADP
ejde-395	442	24	generalized	generalized	ADJ
ejde-395	442	25	schröder	schröder	NOUN
ejde-395	442	26	equations	equation	NOUN
ejde-395	442	27	,	,	PUNCT
ejde-395	442	28	aequationes	aequatione	VERB
ejde-395	442	29	math	math	NOUN
ejde-395	442	30	.	.	PUNCT
ejde-395	443	1	63	63	NUM
ejde-395	443	2	(	(	PUNCT
ejde-395	443	3	2002	2002	NUM
ejde-395	443	4	)	)	PUNCT
ejde-395	443	5	,	,	PUNCT
ejde-395	443	6	110	110	NUM
ejde-395	443	7	-	-	SYM
ejde-395	443	8	135	135	NUM
ejde-395	443	9	.	.	PUNCT
ejde-395	444	1	[	[	X
ejde-395	444	2	10	10	NUM
ejde-395	444	3	]	]	X
ejde-395	444	4	r.	r.	PROPN
ejde-395	444	5	g.	g.	PROPN
ejde-395	444	6	halburd	halburd	PROPN
ejde-395	444	7	,	,	PUNCT
ejde-395	444	8	r.	r.	PROPN
ejde-395	444	9	j.	j.	PROPN
ejde-395	444	10	korhonen	korhonen	PROPN
ejde-395	444	11	;	;	PUNCT
ejde-395	444	12	difference	difference	NOUN
ejde-395	444	13	analogue	analogue	NOUN
ejde-395	444	14	of	of	ADP
ejde-395	444	15	the	the	DET
ejde-395	444	16	lemma	lemma	PROPN
ejde-395	444	17	on	on	ADP
ejde-395	444	18	the	the	DET
ejde-395	444	19	logarithmic	logarithmic	ADJ
ejde-395	444	20	derivative	derivative	NOUN
ejde-395	444	21	with	with	ADP
ejde-395	444	22	applications	application	NOUN
ejde-395	444	23	to	to	ADP
ejde-395	444	24	difference	difference	NOUN
ejde-395	444	25	equations	equation	NOUN
ejde-395	444	26	,	,	PUNCT
ejde-395	444	27	j.	j.	PROPN
ejde-395	444	28	math	math	PROPN
ejde-395	444	29	.	.	PUNCT
ejde-395	445	1	anal	anal	PROPN
ejde-395	445	2	.	.	PUNCT
ejde-395	446	1	appl	appl	PROPN
ejde-395	446	2	.	.	PROPN
ejde-395	446	3	,	,	PUNCT
ejde-395	446	4	314	314	NUM
ejde-395	446	5	(	(	PUNCT
ejde-395	446	6	2006	2006	NUM
ejde-395	446	7	)	)	PUNCT
ejde-395	446	8	,	,	PUNCT
ejde-395	446	9	477	477	NUM
ejde-395	446	10	-	-	SYM
ejde-395	446	11	487	487	NUM
ejde-395	446	12	.	.	PUNCT
ejde-395	447	1	[	[	X
ejde-395	447	2	11	11	NUM
ejde-395	447	3	]	]	PUNCT
ejde-395	447	4	r.	r.	PROPN
ejde-395	447	5	g.	g.	PROPN
ejde-395	447	6	halburd	halburd	PROPN
ejde-395	447	7	,	,	PUNCT
ejde-395	447	8	r.	r.	PROPN
ejde-395	447	9	j.	j.	PROPN
ejde-395	447	10	korhonen	korhonen	PROPN
ejde-395	447	11	;	;	PUNCT
ejde-395	447	12	finite	finite	VERB
ejde-395	447	13	order	order	NOUN
ejde-395	447	14	solutions	solution	NOUN
ejde-395	447	15	and	and	CCONJ
ejde-395	447	16	the	the	DET
ejde-395	447	17	discrete	discrete	ADJ
ejde-395	447	18	painlevé	painlevé	NOUN
ejde-395	447	19	equations	equation	NOUN
ejde-395	447	20	,	,	PUNCT
ejde-395	447	21	proc	proc	NOUN
ejde-395	447	22	.	.	PUNCT
ejde-395	448	1	london	london	PROPN
ejde-395	448	2	math	math	PROPN
ejde-395	448	3	.	.	PUNCT
ejde-395	449	1	soc	soc	PROPN
ejde-395	449	2	.	.	PUNCT
ejde-395	449	3	,	,	PUNCT
ejde-395	449	4	94	94	NUM
ejde-395	449	5	(	(	PUNCT
ejde-395	449	6	2007	2007	NUM
ejde-395	449	7	)	)	PUNCT
ejde-395	449	8	,	,	PUNCT
ejde-395	449	9	443	443	NUM
ejde-395	449	10	-	-	SYM
ejde-395	449	11	474	474	NUM
ejde-395	449	12	.	.	PUNCT
ejde-395	450	1	[	[	X
ejde-395	450	2	12	12	NUM
ejde-395	450	3	]	]	PUNCT
ejde-395	450	4	r.	r.	PROPN
ejde-395	450	5	g.	g.	PROPN
ejde-395	450	6	halburd	halburd	PROPN
ejde-395	450	7	,	,	PUNCT
ejde-395	450	8	r.	r.	PROPN
ejde-395	450	9	j.	j.	PROPN
ejde-395	450	10	korhonen	korhonen	PROPN
ejde-395	450	11	;	;	PUNCT
ejde-395	450	12	nevanlinna	nevanlinna	NOUN
ejde-395	450	13	theory	theory	NOUN
ejde-395	450	14	for	for	ADP
ejde-395	450	15	the	the	DET
ejde-395	450	16	difference	difference	NOUN
ejde-395	450	17	operator	operator	NOUN
ejde-395	450	18	,	,	PUNCT
ejde-395	450	19	ann	ann	PROPN
ejde-395	450	20	.	.	PUNCT
ejde-395	450	21	acad	acad	PROPN
ejde-395	450	22	.	.	PUNCT
ejde-395	451	1	sci	sci	PROPN
ejde-395	451	2	.	.	PUNCT
ejde-395	451	3	fenn	fenn	PROPN
ejde-395	451	4	.	.	PUNCT
ejde-395	451	5	math	math	PROPN
ejde-395	451	6	.	.	PUNCT
ejde-395	452	1	,	,	PUNCT
ejde-395	452	2	31	31	NUM
ejde-395	452	3	(	(	PUNCT
ejde-395	452	4	2006	2006	NUM
ejde-395	452	5	)	)	PUNCT
ejde-395	452	6	,	,	PUNCT
ejde-395	452	7	463	463	NUM
ejde-395	452	8	-	-	SYM
ejde-395	452	9	478	478	NUM
ejde-395	452	10	.	.	PUNCT
ejde-395	453	1	[	[	X
ejde-395	453	2	13	13	NUM
ejde-395	453	3	]	]	PUNCT
ejde-395	453	4	w.	w.	PROPN
ejde-395	453	5	k.	k.	PROPN
ejde-395	453	6	hayman	hayman	PROPN
ejde-395	453	7	;	;	PUNCT
ejde-395	453	8	meromorphic	meromorphic	ADJ
ejde-395	453	9	functions	function	NOUN
ejde-395	453	10	,	,	PUNCT
ejde-395	453	11	the	the	DET
ejde-395	453	12	clarendon	clarendon	PROPN
ejde-395	453	13	press	press	NOUN
ejde-395	453	14	,	,	PUNCT
ejde-395	453	15	oxford	oxford	PROPN
ejde-395	453	16	,	,	PUNCT
ejde-395	453	17	1964	1964	NUM
ejde-395	453	18	.	.	PUNCT
ejde-395	454	1	[	[	X
ejde-395	454	2	14	14	NUM
ejde-395	454	3	]	]	X
ejde-395	454	4	r.	r.	PROPN
ejde-395	454	5	korhonen	korhonen	PROPN
ejde-395	454	6	,	,	PUNCT
ejde-395	454	7	z.	z.	PROPN
ejde-395	454	8	t.	t.	PROPN
ejde-395	454	9	wen	wen	PROPN
ejde-395	454	10	;	;	PUNCT
ejde-395	454	11	existence	existence	NOUN
ejde-395	454	12	of	of	ADP
ejde-395	454	13	zero	zero	NUM
ejde-395	454	14	-	-	PUNCT
ejde-395	454	15	order	order	NOUN
ejde-395	454	16	meromorphic	meromorphic	ADJ
ejde-395	454	17	solutions	solution	NOUN
ejde-395	454	18	in	in	ADP
ejde-395	454	19	detecting	detect	VERB
ejde-395	454	20	qdifference	qdifference	NOUN
ejde-395	454	21	painlevé	painlevé	NOUN
ejde-395	454	22	equations	equation	NOUN
ejde-395	454	23	,	,	PUNCT
ejde-395	454	24	trans	trans	PROPN
ejde-395	454	25	.	.	PROPN
ejde-395	454	26	amer	amer	PROPN
ejde-395	454	27	.	.	PUNCT
ejde-395	454	28	math	math	PROPN
ejde-395	454	29	.	.	PUNCT
ejde-395	455	1	soc	soc	PROPN
ejde-395	455	2	.	.	PUNCT
ejde-395	455	3	,	,	PUNCT
ejde-395	455	4	368	368	NUM
ejde-395	455	5	(	(	PUNCT
ejde-395	455	6	7	7	NUM
ejde-395	455	7	)	)	PUNCT
ejde-395	455	8	(	(	PUNCT
ejde-395	455	9	2016	2016	NUM
ejde-395	455	10	)	)	PUNCT
ejde-395	455	11	,	,	PUNCT
ejde-395	455	12	4993	4993	NUM
ejde-395	455	13	-	-	SYM
ejde-395	455	14	5008	5008	NUM
ejde-395	455	15	.	.	PUNCT
ejde-395	456	1	[	[	X
ejde-395	456	2	15	15	NUM
ejde-395	456	3	]	]	X
ejde-395	456	4	i.	i.	NOUN
ejde-395	456	5	laine	laine	PROPN
ejde-395	456	6	,	,	PUNCT
ejde-395	456	7	c.	c.	PROPN
ejde-395	456	8	c.	c.	PROPN
ejde-395	456	9	yang	yang	PROPN
ejde-395	456	10	;	;	PUNCT
ejde-395	456	11	clunie	clunie	NOUN
ejde-395	456	12	theorems	theorem	NOUN
ejde-395	456	13	for	for	ADP
ejde-395	456	14	difference	difference	NOUN
ejde-395	456	15	and	and	CCONJ
ejde-395	456	16	q	q	ADJ
ejde-395	456	17	-	-	PUNCT
ejde-395	456	18	difference	difference	NOUN
ejde-395	456	19	polynomials	polynomial	NOUN
ejde-395	456	20	,	,	PUNCT
ejde-395	456	21	j.	j.	PROPN
ejde-395	456	22	london	london	PROPN
ejde-395	456	23	math	math	PROPN
ejde-395	456	24	.	.	PUNCT
ejde-395	457	1	soc	soc	PROPN
ejde-395	457	2	.	.	PUNCT
ejde-395	457	3	,	,	PUNCT
ejde-395	457	4	76	76	NUM
ejde-395	457	5	(	(	PUNCT
ejde-395	457	6	2	2	NUM
ejde-395	457	7	)	)	PUNCT
ejde-395	457	8	(	(	PUNCT
ejde-395	457	9	2007	2007	NUM
ejde-395	457	10	)	)	PUNCT
ejde-395	457	11	,	,	PUNCT
ejde-395	457	12	556	556	NUM
ejde-395	457	13	-	-	SYM
ejde-395	457	14	566	566	NUM
ejde-395	457	15	.	.	PUNCT
ejde-395	458	1	[	[	X
ejde-395	458	2	16	16	NUM
ejde-395	458	3	]	]	PUNCT
ejde-395	458	4	k.	k.	PROPN
ejde-395	458	5	liu	liu	PROPN
ejde-395	458	6	;	;	PUNCT
ejde-395	458	7	entire	entire	ADJ
ejde-395	458	8	solutions	solution	NOUN
ejde-395	458	9	of	of	ADP
ejde-395	458	10	fermat	fermat	PROPN
ejde-395	458	11	type	type	NOUN
ejde-395	458	12	q	q	ADJ
ejde-395	458	13	-	-	PUNCT
ejde-395	458	14	difference	difference	NOUN
ejde-395	458	15	differential	differential	NOUN
ejde-395	458	16	equations	equation	NOUN
ejde-395	458	17	,	,	PUNCT
ejde-395	458	18	electron	electron	NOUN
ejde-395	458	19	.	.	PUNCT
ejde-395	459	1	j.	j.	PROPN
ejde-395	459	2	diff	diff	PROPN
ejde-395	459	3	.	.	PUNCT
ejde-395	460	1	equ	equ	PROPN
ejde-395	460	2	.	.	PROPN
ejde-395	460	3	,	,	PUNCT
ejde-395	460	4	2013	2013	NUM
ejde-395	460	5	(	(	PUNCT
ejde-395	460	6	2013	2013	NUM
ejde-395	460	7	)	)	PUNCT
ejde-395	460	8	,	,	PUNCT
ejde-395	460	9	no	no	INTJ
ejde-395	460	10	.	.	NOUN
ejde-395	460	11	59	59	NUM
ejde-395	460	12	,	,	PUNCT
ejde-395	460	13	1	1	NUM
ejde-395	460	14	-	-	SYM
ejde-395	460	15	10	10	NUM
ejde-395	460	16	.	.	PUNCT
ejde-395	461	1	[	[	X
ejde-395	461	2	17	17	NUM
ejde-395	461	3	]	]	X
ejde-395	461	4	y.	y.	PROPN
ejde-395	461	5	liu	liu	PROPN
ejde-395	461	6	,	,	PUNCT
ejde-395	461	7	y.	y.	PROPN
ejde-395	461	8	q.	q.	PROPN
ejde-395	461	9	zhang	zhang	PROPN
ejde-395	461	10	;	;	PUNCT
ejde-395	461	11	some	some	DET
ejde-395	461	12	results	result	NOUN
ejde-395	461	13	of	of	ADP
ejde-395	461	14	ω−painlevé	ω−painlevé	ADJ
ejde-395	461	15	difference	difference	NOUN
ejde-395	461	16	equation	equation	NOUN
ejde-395	461	17	,	,	PUNCT
ejde-395	461	18	adv	adv	PROPN
ejde-395	461	19	.	.	PUNCT
ejde-395	461	20	differ	differ	VERB
ejde-395	461	21	.	.	PUNCT
ejde-395	462	1	equ	equ	PROPN
ejde-395	462	2	.	.	PROPN
ejde-395	462	3	,	,	PUNCT
ejde-395	462	4	2018	2018	NUM
ejde-395	462	5	(	(	PUNCT
ejde-395	462	6	2018	2018	NUM
ejde-395	462	7	)	)	PUNCT
ejde-395	462	8	,	,	PUNCT
ejde-395	462	9	art	art	NOUN
ejde-395	462	10	.	.	PUNCT
ejde-395	463	1	282	282	NUM
ejde-395	463	2	.	.	PUNCT
ejde-395	464	1	[	[	X
ejde-395	464	2	18	18	NUM
ejde-395	464	3	]	]	X
ejde-395	464	4	f.	f.	PROPN
ejde-395	464	5	lu	lu	PROPN
ejde-395	464	6	,	,	PUNCT
ejde-395	464	7	y.	y.	PROPN
ejde-395	464	8	f.	f.	PROPN
ejde-395	464	9	wang	wang	PROPN
ejde-395	464	10	,	,	PUNCT
ejde-395	464	11	w.	w.	PROPN
ejde-395	464	12	r.	r.	PROPN
ejde-395	464	13	lu	lu	PROPN
ejde-395	464	14	;	;	PUNCT
ejde-395	464	15	on	on	ADP
ejde-395	464	16	unicity	unicity	NOUN
ejde-395	464	17	of	of	ADP
ejde-395	464	18	meromorphic	meromorphic	ADJ
ejde-395	464	19	solutions	solution	NOUN
ejde-395	464	20	to	to	ADP
ejde-395	464	21	difference	difference	NOUN
ejde-395	464	22	painlevé	painlevé	NOUN
ejde-395	464	23	equation	equation	NOUN
ejde-395	464	24	,	,	PUNCT
ejde-395	464	25	math	math	NOUN
ejde-395	464	26	.	.	PUNCT
ejde-395	465	1	meth	meth	NOUN
ejde-395	465	2	.	.	PUNCT
ejde-395	466	1	appl	appl	PROPN
ejde-395	466	2	.	.	PUNCT
ejde-395	467	1	sci	sci	PROPN
ejde-395	467	2	.	.	PROPN
ejde-395	467	3	,	,	PUNCT
ejde-395	467	4	41	41	NUM
ejde-395	467	5	(	(	PUNCT
ejde-395	467	6	2018	2018	NUM
ejde-395	467	7	)	)	PUNCT
ejde-395	467	8	,	,	PUNCT
ejde-395	467	9	3093	3093	NUM
ejde-395	467	10	-	-	SYM
ejde-395	467	11	3102	3102	NUM
ejde-395	467	12	.	.	PUNCT
ejde-395	468	1	[	[	X
ejde-395	468	2	19	19	NUM
ejde-395	468	3	]	]	PUNCT
ejde-395	468	4	z.	z.	PROPN
ejde-395	468	5	t.	t.	PROPN
ejde-395	468	6	wen	wen	PROPN
ejde-395	468	7	;	;	PUNCT
ejde-395	468	8	meromorphic	meromorphic	ADJ
ejde-395	468	9	solutions	solution	NOUN
ejde-395	468	10	to	to	ADP
ejde-395	468	11	difference	difference	NOUN
ejde-395	468	12	painlevé	painlevé	NOUN
ejde-395	468	13	equations	equation	NOUN
ejde-395	468	14	i	i	PRON
ejde-395	468	15	and	and	CCONJ
ejde-395	468	16	ii	ii	PROPN
ejde-395	468	17	,	,	PUNCT
ejde-395	468	18	electronic	electronic	ADJ
ejde-395	468	19	j.	j.	PROPN
ejde-395	468	20	diff	diff	PROPN
ejde-395	468	21	.	.	PUNCT
ejde-395	469	1	equ	equ	PROPN
ejde-395	469	2	.	.	PROPN
ejde-395	469	3	,	,	PUNCT
ejde-395	469	4	2016	2016	NUM
ejde-395	469	5	(	(	PUNCT
ejde-395	469	6	2016	2016	NUM
ejde-395	469	7	)	)	PUNCT
ejde-395	469	8	,	,	PUNCT
ejde-395	469	9	art	art	NOUN
ejde-395	469	10	.	.	PUNCT
ejde-395	470	1	262	262	NUM
ejde-395	470	2	.	.	PUNCT
ejde-395	471	1	[	[	X
ejde-395	471	2	20	20	NUM
ejde-395	471	3	]	]	PUNCT
ejde-395	471	4	x.	x.	NOUN
ejde-395	471	5	g.	g.	PROPN
ejde-395	471	6	qi	qi	PROPN
ejde-395	471	7	,	,	PUNCT
ejde-395	471	8	l.	l.	PROPN
ejde-395	471	9	z.	z.	PROPN
ejde-395	471	10	yang	yang	PROPN
ejde-395	471	11	;	;	PUNCT
ejde-395	471	12	properties	property	NOUN
ejde-395	471	13	of	of	ADP
ejde-395	471	14	meromorphic	meromorphic	ADJ
ejde-395	471	15	solutions	solution	NOUN
ejde-395	471	16	of	of	ADP
ejde-395	471	17	q	q	ADJ
ejde-395	471	18	-	-	PUNCT
ejde-395	471	19	difference	difference	NOUN
ejde-395	471	20	equations	equation	NOUN
ejde-395	471	21	,	,	PUNCT
ejde-395	471	22	electron	electron	NOUN
ejde-395	471	23	.	.	PUNCT
ejde-395	472	1	j.	j.	PROPN
ejde-395	472	2	diff	diff	PROPN
ejde-395	472	3	.	.	PUNCT
ejde-395	473	1	equ	equ	PROPN
ejde-395	473	2	.	.	PROPN
ejde-395	473	3	,	,	PUNCT
ejde-395	473	4	2015	2015	NUM
ejde-395	473	5	(	(	PUNCT
ejde-395	473	6	2015	2015	NUM
ejde-395	473	7	)	)	PUNCT
ejde-395	473	8	,	,	PUNCT
ejde-395	473	9	no	no	INTJ
ejde-395	473	10	.	.	NOUN
ejde-395	473	11	59	59	NUM
ejde-395	473	12	,	,	PUNCT
ejde-395	473	13	pp	pp	ADJ
ejde-395	473	14	.	.	PUNCT
ejde-395	474	1	1	1	NUM
ejde-395	474	2	-	-	SYM
ejde-395	474	3	9	9	NUM
ejde-395	474	4	.	.	PUNCT
ejde-395	475	1	[	[	X
ejde-395	475	2	21	21	NUM
ejde-395	475	3	]	]	X
ejde-395	475	4	o.	o.	PROPN
ejde-395	475	5	ronkainen	ronkainen	PROPN
ejde-395	475	6	;	;	PUNCT
ejde-395	475	7	meromorphic	meromorphic	ADJ
ejde-395	475	8	solutions	solution	NOUN
ejde-395	475	9	of	of	ADP
ejde-395	475	10	difference	difference	NOUN
ejde-395	475	11	painlevé	painlevé	NOUN
ejde-395	475	12	equations	equation	NOUN
ejde-395	475	13	,	,	PUNCT
ejde-395	475	14	ph.d	ph.d	PROPN
ejde-395	475	15	.	.	PUNCT
ejde-395	476	1	thesis	thesis	PROPN
ejde-395	476	2	,	,	PUNCT
ejde-395	476	3	department	department	NOUN
ejde-395	476	4	of	of	ADP
ejde-395	476	5	physics	physics	PROPN
ejde-395	476	6	and	and	CCONJ
ejde-395	476	7	mathematics	mathematics	PROPN
ejde-395	476	8	,	,	PUNCT
ejde-395	476	9	university	university	NOUN
ejde-395	476	10	of	of	ADP
ejde-395	476	11	eastern	eastern	PROPN
ejde-395	476	12	finland	finland	PROPN
ejde-395	476	13	,	,	PUNCT
ejde-395	476	14	2010	2010	NUM
ejde-395	476	15	.	.	PUNCT
ejde-395	477	1	[	[	X
ejde-395	477	2	22	22	NUM
ejde-395	477	3	]	]	PUNCT
ejde-395	477	4	m.	m.	NOUN
ejde-395	477	5	ru	ru	PROPN
ejde-395	477	6	;	;	PUNCT
ejde-395	477	7	the	the	DET
ejde-395	477	8	recent	recent	ADJ
ejde-395	477	9	progress	progress	NOUN
ejde-395	477	10	in	in	ADP
ejde-395	477	11	nevanlinna	nevanlinna	NOUN
ejde-395	477	12	theory	theory	NOUN
ejde-395	477	13	,	,	PUNCT
ejde-395	477	14	j.	j.	PROPN
ejde-395	477	15	jiangxi	jiangxi	PROPN
ejde-395	477	16	normal	normal	PROPN
ejde-395	477	17	university	university	PROPN
ejde-395	477	18	(	(	PUNCT
ejde-395	477	19	natural	natural	ADJ
ejde-395	477	20	sciences	science	NOUN
ejde-395	477	21	)	)	PUNCT
ejde-395	477	22	,	,	PUNCT
ejde-395	477	23	42	42	NUM
ejde-395	477	24	(	(	PUNCT
ejde-395	477	25	2018	2018	NUM
ejde-395	477	26	)	)	PUNCT
ejde-395	477	27	,	,	PUNCT
ejde-395	477	28	1	1	NUM
ejde-395	477	29	-	-	SYM
ejde-395	477	30	11	11	NUM
ejde-395	477	31	.	.	PUNCT
ejde-395	478	1	[	[	X
ejde-395	478	2	23	23	NUM
ejde-395	478	3	]	]	PUNCT
ejde-395	478	4	h.	h.	PROPN
ejde-395	478	5	y.	y.	PROPN
ejde-395	478	6	xu	xu	PROPN
ejde-395	478	7	,	,	PUNCT
ejde-395	478	8	s.	s.	PROPN
ejde-395	478	9	y.	y.	PROPN
ejde-395	478	10	liu	liu	PROPN
ejde-395	478	11	,	,	PUNCT
ejde-395	478	12	x.	x.	PROPN
ejde-395	478	13	m.	m.	PROPN
ejde-395	478	14	zheng	zheng	PROPN
ejde-395	478	15	;	;	PUNCT
ejde-395	478	16	some	some	DET
ejde-395	478	17	properties	property	NOUN
ejde-395	478	18	of	of	ADP
ejde-395	478	19	meromorphic	meromorphic	ADJ
ejde-395	478	20	solutions	solution	NOUN
ejde-395	478	21	for	for	ADP
ejde-395	478	22	q	q	ADJ
ejde-395	478	23	-	-	PUNCT
ejde-395	478	24	difference	difference	NOUN
ejde-395	478	25	equations	equation	NOUN
ejde-395	478	26	,	,	PUNCT
ejde-395	478	27	electron	electron	NOUN
ejde-395	478	28	.	.	PUNCT
ejde-395	479	1	j.	j.	PROPN
ejde-395	479	2	diff	diff	PROPN
ejde-395	479	3	.	.	PUNCT
ejde-395	480	1	equ	equ	PROPN
ejde-395	480	2	.	.	PROPN
ejde-395	480	3	,	,	PUNCT
ejde-395	480	4	vol	vol	NOUN
ejde-395	480	5	.	.	PROPN
ejde-395	480	6	2017	2017	NUM
ejde-395	480	7	(	(	PUNCT
ejde-395	480	8	2017	2017	NUM
ejde-395	480	9	)	)	PUNCT
ejde-395	480	10	,	,	PUNCT
ejde-395	480	11	no	no	INTJ
ejde-395	480	12	.	.	NOUN
ejde-395	480	13	175	175	NUM
ejde-395	480	14	,	,	PUNCT
ejde-395	480	15	pp	pp	ADJ
ejde-395	480	16	.	.	PUNCT
ejde-395	481	1	1	1	NUM
ejde-395	481	2	-	-	SYM
ejde-395	481	3	12	12	NUM
ejde-395	481	4	.	.	PUNCT
ejde-395	482	1	[	[	X
ejde-395	482	2	24	24	NUM
ejde-395	482	3	]	]	X
ejde-395	482	4	h.	h.	PROPN
ejde-395	482	5	y.	y.	PROPN
ejde-395	482	6	xu	xu	PROPN
ejde-395	482	7	,	,	PUNCT
ejde-395	482	8	s.	s.	PROPN
ejde-395	482	9	y.	y.	PROPN
ejde-395	482	10	liu	liu	PROPN
ejde-395	482	11	,	,	PUNCT
ejde-395	482	12	q.	q.	PROPN
ejde-395	482	13	p.	p.	PROPN
ejde-395	482	14	li	li	PROPN
ejde-395	482	15	;	;	PUNCT
ejde-395	482	16	the	the	DET
ejde-395	482	17	existence	existence	NOUN
ejde-395	482	18	and	and	CCONJ
ejde-395	482	19	growth	growth	NOUN
ejde-395	482	20	of	of	ADP
ejde-395	482	21	solutions	solution	NOUN
ejde-395	482	22	for	for	ADP
ejde-395	482	23	several	several	ADJ
ejde-395	482	24	systems	system	NOUN
ejde-395	482	25	of	of	ADP
ejde-395	482	26	complex	complex	ADJ
ejde-395	482	27	nonlinear	nonlinear	ADJ
ejde-395	482	28	difference	difference	NOUN
ejde-395	482	29	equations	equation	NOUN
ejde-395	482	30	,	,	PUNCT
ejde-395	482	31	mediterr	mediterr	NOUN
ejde-395	482	32	.	.	PUNCT
ejde-395	483	1	j.	j.	PROPN
ejde-395	483	2	math	math	PROPN
ejde-395	483	3	.	.	PUNCT
ejde-395	483	4	,	,	PUNCT
ejde-395	483	5	16	16	NUM
ejde-395	483	6	(	(	PUNCT
ejde-395	483	7	2019	2019	NUM
ejde-395	483	8	)	)	PUNCT
ejde-395	483	9	,	,	PUNCT
ejde-395	483	10	art	art	NOUN
ejde-395	483	11	.	.	PUNCT
ejde-395	484	1	8	8	NUM
ejde-395	484	2	.	.	X
ejde-395	484	3	14	14	NUM
ejde-395	484	4	h.	h.	PROPN
ejde-395	484	5	y.	y.	PROPN
ejde-395	484	6	xu	xu	PROPN
ejde-395	484	7	,	,	PUNCT
ejde-395	484	8	j.	j.	PROPN
ejde-395	484	9	tu	tu	PROPN
ejde-395	484	10	ejde-2020/14	ejde-2020/14	PROPN
ejde-395	484	11	[	[	X
ejde-395	484	12	25	25	NUM
ejde-395	484	13	]	]	PUNCT
ejde-395	484	14	h.	h.	PROPN
ejde-395	484	15	y.	y.	PROPN
ejde-395	484	16	xu	xu	PROPN
ejde-395	484	17	,	,	PUNCT
ejde-395	484	18	s.	s.	PROPN
ejde-395	484	19	y.	y.	PROPN
ejde-395	484	20	liu	liu	PROPN
ejde-395	484	21	,	,	PUNCT
ejde-395	484	22	q.p	q.p	PROPN
ejde-395	484	23	.	.	PROPN
ejde-395	484	24	li	li	PROPN
ejde-395	484	25	;	;	PUNCT
ejde-395	484	26	entire	entire	ADJ
ejde-395	484	27	solutions	solution	NOUN
ejde-395	484	28	for	for	ADP
ejde-395	484	29	several	several	ADJ
ejde-395	484	30	systems	system	NOUN
ejde-395	484	31	of	of	ADP
ejde-395	484	32	nonlinear	nonlinear	ADJ
ejde-395	484	33	difference	difference	NOUN
ejde-395	484	34	and	and	CCONJ
ejde-395	484	35	partial	partial	ADJ
ejde-395	484	36	differential	differential	ADJ
ejde-395	484	37	-	-	PUNCT
ejde-395	484	38	difference	difference	NOUN
ejde-395	484	39	equations	equation	NOUN
ejde-395	484	40	of	of	ADP
ejde-395	484	41	fermat	fermat	NOUN
ejde-395	484	42	-	-	PUNCT
ejde-395	484	43	type	type	NOUN
ejde-395	484	44	,	,	PUNCT
ejde-395	484	45	journal	journal	NOUN
ejde-395	484	46	of	of	ADP
ejde-395	484	47	mathematical	mathematical	ADJ
ejde-395	484	48	analysis	analysis	NOUN
ejde-395	484	49	and	and	CCONJ
ejde-395	484	50	applications	application	NOUN
ejde-395	484	51	,	,	PUNCT
ejde-395	484	52	483	483	NUM
ejde-395	484	53	,	,	PUNCT
ejde-395	484	54	2020	2020	NUM
ejde-395	484	55	https://doi.org/10.1016/j.jmaa.2019.123641	https://doi.org/10.1016/j.jmaa.2019.123641	NOUN
ejde-395	484	56	.	.	PUNCT
ejde-395	485	1	[	[	X
ejde-395	485	2	26	26	NUM
ejde-395	485	3	]	]	X
ejde-395	485	4	h.	h.	PROPN
ejde-395	485	5	y.	y.	PROPN
ejde-395	485	6	xu	xu	PROPN
ejde-395	485	7	,	,	PUNCT
ejde-395	485	8	j.	j.	PROPN
ejde-395	485	9	tu	tu	PROPN
ejde-395	485	10	;	;	PUNCT
ejde-395	485	11	growth	growth	NOUN
ejde-395	485	12	of	of	ADP
ejde-395	485	13	solutions	solution	NOUN
ejde-395	485	14	to	to	ADP
ejde-395	485	15	systems	system	NOUN
ejde-395	485	16	of	of	ADP
ejde-395	485	17	q	q	ADJ
ejde-395	485	18	-	-	PUNCT
ejde-395	485	19	difference	difference	NOUN
ejde-395	485	20	differential	differential	NOUN
ejde-395	485	21	equations	equation	NOUN
ejde-395	485	22	,	,	PUNCT
ejde-395	485	23	electron	electron	NOUN
ejde-395	485	24	.	.	PUNCT
ejde-395	486	1	j.	j.	PROPN
ejde-395	486	2	diff	diff	PROPN
ejde-395	486	3	.	.	PUNCT
ejde-395	487	1	equ	equ	PROPN
ejde-395	487	2	.	.	PROPN
ejde-395	487	3	,	,	PUNCT
ejde-395	487	4	2016	2016	NUM
ejde-395	487	5	(	(	PUNCT
ejde-395	487	6	2016	2016	NUM
ejde-395	487	7	)	)	PUNCT
ejde-395	487	8	,	,	PUNCT
ejde-395	487	9	no	no	INTJ
ejde-395	487	10	.	.	NOUN
ejde-395	487	11	106	106	NUM
ejde-395	487	12	,	,	PUNCT
ejde-395	487	13	1	1	NUM
ejde-395	487	14	-	-	SYM
ejde-395	487	15	14	14	NUM
ejde-395	487	16	.	.	PUNCT
ejde-395	488	1	[	[	X
ejde-395	488	2	27	27	NUM
ejde-395	488	3	]	]	PUNCT
ejde-395	488	4	l.	l.	PROPN
ejde-395	488	5	yang	yang	PROPN
ejde-395	488	6	;	;	PUNCT
ejde-395	488	7	value	value	NOUN
ejde-395	488	8	distribution	distribution	NOUN
ejde-395	488	9	theory	theory	NOUN
ejde-395	488	10	,	,	PUNCT
ejde-395	488	11	springer	springer	NOUN
ejde-395	488	12	-	-	PUNCT
ejde-395	488	13	verlag	verlag	PROPN
ejde-395	488	14	.	.	PUNCT
ejde-395	489	1	berlin	berlin	PROPN
ejde-395	489	2	,	,	PUNCT
ejde-395	489	3	1993	1993	NUM
ejde-395	489	4	.	.	PUNCT
ejde-395	490	1	[	[	X
ejde-395	490	2	28	28	NUM
ejde-395	490	3	]	]	X
ejde-395	490	4	h.	h.	PROPN
ejde-395	490	5	x.	x.	PROPN
ejde-395	490	6	yi	yi	PROPN
ejde-395	490	7	,	,	PUNCT
ejde-395	490	8	c.	c.	PROPN
ejde-395	490	9	c.	c.	PROPN
ejde-395	490	10	yang	yang	PROPN
ejde-395	490	11	;	;	PUNCT
ejde-395	490	12	uniqueness	uniqueness	NOUN
ejde-395	490	13	theory	theory	NOUN
ejde-395	490	14	of	of	ADP
ejde-395	490	15	meromorphic	meromorphic	ADJ
ejde-395	490	16	functions	function	NOUN
ejde-395	490	17	,	,	PUNCT
ejde-395	490	18	kluwer	kluwer	NOUN
ejde-395	490	19	academic	academic	ADJ
ejde-395	490	20	publishers	publisher	NOUN
ejde-395	490	21	,	,	PUNCT
ejde-395	490	22	dordrecht	dordrecht	PROPN
ejde-395	490	23	,	,	PUNCT
ejde-395	490	24	2003	2003	NUM
ejde-395	490	25	;	;	PUNCT
ejde-395	490	26	chinese	chinese	ADJ
ejde-395	490	27	original	original	ADJ
ejde-395	490	28	:	:	PUNCT
ejde-395	490	29	science	science	NOUN
ejde-395	490	30	press	press	PROPN
ejde-395	490	31	,	,	PUNCT
ejde-395	490	32	beijing	beijing	PROPN
ejde-395	490	33	,	,	PUNCT
ejde-395	490	34	1995	1995	NUM
ejde-395	490	35	.	.	PUNCT
ejde-395	491	1	[	[	X
ejde-395	491	2	29	29	NUM
ejde-395	491	3	]	]	PUNCT
ejde-395	491	4	j.	j.	PROPN
ejde-395	491	5	l.	l.	PROPN
ejde-395	491	6	zhang	zhang	PROPN
ejde-395	491	7	,	,	PUNCT
ejde-395	491	8	r.	r.	PROPN
ejde-395	491	9	korhonen	korhonen	PROPN
ejde-395	491	10	;	;	PUNCT
ejde-395	491	11	on	on	ADP
ejde-395	491	12	the	the	DET
ejde-395	491	13	nevanlinna	nevanlinna	NOUN
ejde-395	491	14	characteristic	characteristic	NOUN
ejde-395	491	15	of	of	ADP
ejde-395	491	16	f(qz	f(qz	NOUN
ejde-395	491	17	)	)	PUNCT
ejde-395	491	18	and	and	CCONJ
ejde-395	491	19	its	its	PRON
ejde-395	491	20	applications	application	NOUN
ejde-395	491	21	,	,	PUNCT
ejde-395	491	22	j.	j.	PROPN
ejde-395	491	23	math	math	PROPN
ejde-395	491	24	.	.	PUNCT
ejde-395	492	1	anal	anal	PROPN
ejde-395	492	2	.	.	PUNCT
ejde-395	492	3	appl	appl	PROPN
ejde-395	492	4	.	.	PROPN
ejde-395	492	5	,	,	PUNCT
ejde-395	492	6	369	369	NUM
ejde-395	492	7	(	(	PUNCT
ejde-395	492	8	2010	2010	NUM
ejde-395	492	9	)	)	PUNCT
ejde-395	492	10	,	,	PUNCT
ejde-395	492	11	537	537	NUM
ejde-395	492	12	-	-	SYM
ejde-395	492	13	544	544	NUM
ejde-395	492	14	.	.	PUNCT
ejde-395	493	1	[	[	X
ejde-395	493	2	30	30	NUM
ejde-395	493	3	]	]	X
ejde-395	493	4	j.	j.	PROPN
ejde-395	493	5	l.	l.	PROPN
ejde-395	493	6	zhang	zhang	PROPN
ejde-395	493	7	,	,	PUNCT
ejde-395	493	8	l.	l.	PROPN
ejde-395	493	9	z.	z.	PROPN
ejde-395	493	10	yang	yang	PROPN
ejde-395	493	11	;	;	PUNCT
ejde-395	493	12	meromorphic	meromorphic	ADJ
ejde-395	493	13	solutions	solution	NOUN
ejde-395	493	14	of	of	ADP
ejde-395	493	15	painlevé	painlevé	NOUN
ejde-395	493	16	iii	iii	NUM
ejde-395	493	17	difference	difference	NOUN
ejde-395	493	18	equations	equation	NOUN
ejde-395	493	19	,	,	PUNCT
ejde-395	493	20	acta	acta	PROPN
ejde-395	493	21	math	math	PROPN
ejde-395	493	22	.	.	PUNCT
ejde-395	494	1	sin	sin	NOUN
ejde-395	494	2	.	.	PUNCT
ejde-395	495	1	57	57	NUM
ejde-395	495	2	(	(	PUNCT
ejde-395	495	3	2014	2014	NUM
ejde-395	495	4	)	)	PUNCT
ejde-395	495	5	,	,	PUNCT
ejde-395	495	6	181	181	NUM
ejde-395	495	7	-	-	SYM
ejde-395	495	8	188	188	NUM
ejde-395	495	9	.	.	PUNCT
ejde-395	496	1	[	[	X
ejde-395	496	2	31	31	NUM
ejde-395	496	3	]	]	PUNCT
ejde-395	496	4	x.	x.	NOUN
ejde-395	496	5	m.	m.	PROPN
ejde-395	496	6	zheng	zheng	PROPN
ejde-395	496	7	,	,	PUNCT
ejde-395	496	8	z.	z.	PROPN
ejde-395	496	9	x.	x.	PROPN
ejde-395	496	10	chen	chen	PROPN
ejde-395	496	11	;	;	PUNCT
ejde-395	496	12	on	on	ADP
ejde-395	496	13	properties	property	NOUN
ejde-395	496	14	of	of	ADP
ejde-395	496	15	q	q	ADJ
ejde-395	496	16	-	-	PUNCT
ejde-395	496	17	difference	difference	NOUN
ejde-395	496	18	equations	equation	NOUN
ejde-395	496	19	,	,	PUNCT
ejde-395	496	20	acta	acta	PROPN
ejde-395	496	21	math	math	PROPN
ejde-395	496	22	.	.	PUNCT
ejde-395	497	1	sci	sci	PROPN
ejde-395	497	2	.	.	PROPN
ejde-395	497	3	,	,	PUNCT
ejde-395	497	4	32b	32b	NOUN
ejde-395	497	5	(	(	PUNCT
ejde-395	497	6	2	2	NUM
ejde-395	497	7	)	)	PUNCT
ejde-395	497	8	(	(	PUNCT
ejde-395	497	9	2012	2012	NUM
ejde-395	497	10	)	)	PUNCT
ejde-395	497	11	,	,	PUNCT
ejde-395	497	12	724	724	NUM
ejde-395	497	13	-	-	SYM
ejde-395	497	14	734	734	NUM
ejde-395	497	15	.	.	PUNCT
ejde-395	498	1	[	[	X
ejde-395	498	2	32	32	NUM
ejde-395	498	3	]	]	PUNCT
ejde-395	498	4	x.	x.	NOUN
ejde-395	498	5	m.	m.	PROPN
ejde-395	498	6	zheng	zheng	PROPN
ejde-395	498	7	,	,	PUNCT
ejde-395	498	8	z.	z.	PROPN
ejde-395	498	9	x.	x.	PROPN
ejde-395	498	10	chen	chen	PROPN
ejde-395	498	11	;	;	PUNCT
ejde-395	498	12	some	some	DET
ejde-395	498	13	properties	property	NOUN
ejde-395	498	14	of	of	ADP
ejde-395	498	15	meromorphic	meromorphic	ADJ
ejde-395	498	16	solutions	solution	NOUN
ejde-395	498	17	of	of	ADP
ejde-395	498	18	q	q	ADJ
ejde-395	498	19	-	-	PUNCT
ejde-395	498	20	difference	difference	NOUN
ejde-395	498	21	equations	equation	NOUN
ejde-395	498	22	,	,	PUNCT
ejde-395	498	23	j.	j.	PROPN
ejde-395	498	24	math	math	PROPN
ejde-395	498	25	.	.	PUNCT
ejde-395	499	1	anal	anal	PROPN
ejde-395	499	2	.	.	PUNCT
ejde-395	499	3	appl	appl	PROPN
ejde-395	499	4	.	.	PROPN
ejde-395	499	5	,	,	PUNCT
ejde-395	499	6	361	361	NUM
ejde-395	499	7	(	(	PUNCT
ejde-395	499	8	2010	2010	NUM
ejde-395	499	9	)	)	PUNCT
ejde-395	499	10	,	,	PUNCT
ejde-395	499	11	472	472	NUM
ejde-395	499	12	-	-	SYM
ejde-395	499	13	480	480	NUM
ejde-395	499	14	.	.	PUNCT
ejde-395	500	1	[	[	X
ejde-395	500	2	33	33	NUM
ejde-395	500	3	]	]	PUNCT
ejde-395	500	4	j.	j.	PROPN
ejde-395	500	5	f.	f.	PROPN
ejde-395	500	6	zhong	zhong	PROPN
ejde-395	500	7	,	,	PUNCT
ejde-395	500	8	h.	h.	PROPN
ejde-395	500	9	f.	f.	PROPN
ejde-395	500	10	liu	liu	PROPN
ejde-395	500	11	;	;	PUNCT
ejde-395	500	12	the	the	DET
ejde-395	500	13	growth	growth	NOUN
ejde-395	500	14	of	of	ADP
ejde-395	500	15	meromorphic	meromorphic	ADJ
ejde-395	500	16	solutions	solution	NOUN
ejde-395	500	17	of	of	ADP
ejde-395	500	18	some	some	DET
ejde-395	500	19	type	type	NOUN
ejde-395	500	20	of	of	ADP
ejde-395	500	21	nonlinear	nonlinear	ADJ
ejde-395	500	22	difference	difference	NOUN
ejde-395	500	23	equations	equation	NOUN
ejde-395	500	24	,	,	PUNCT
ejde-395	500	25	j.	j.	PROPN
ejde-395	500	26	jiangxi	jiangxi	PROPN
ejde-395	500	27	normal	normal	PROPN
ejde-395	500	28	university	university	PROPN
ejde-395	500	29	(	(	PUNCT
ejde-395	500	30	natural	natural	ADJ
ejde-395	500	31	sciences	science	NOUN
ejde-395	500	32	)	)	PUNCT
ejde-395	500	33	,	,	PUNCT
ejde-395	500	34	43	43	NUM
ejde-395	500	35	(	(	PUNCT
ejde-395	500	36	2019	2019	NUM
ejde-395	500	37	)	)	PUNCT
ejde-395	500	38	,	,	PUNCT
ejde-395	500	39	508	508	NUM
ejde-395	500	40	-	-	SYM
ejde-395	500	41	512	512	NUM
ejde-395	500	42	.	.	PUNCT
ejde-395	501	1	hong	hong	PROPN
ejde-395	501	2	yan	yan	PROPN
ejde-395	501	3	xu	xu	PROPN
ejde-395	502	1	school	school	NOUN
ejde-395	502	2	of	of	ADP
ejde-395	502	3	mathematics	mathematic	NOUN
ejde-395	502	4	and	and	CCONJ
ejde-395	502	5	computer	computer	NOUN
ejde-395	502	6	science	science	NOUN
ejde-395	502	7	,	,	PUNCT
ejde-395	502	8	shangrao	shangrao	VERB
ejde-395	502	9	normal	normal	ADJ
ejde-395	502	10	university	university	NOUN
ejde-395	502	11	,	,	PUNCT
ejde-395	502	12	shangrao	shangrao	VERB
ejde-395	502	13	jiangxi	jiangxi	PROPN
ejde-395	502	14	334001	334001	NUM
ejde-395	502	15	,	,	PUNCT
ejde-395	502	16	china	china	PROPN
ejde-395	502	17	email	email	NOUN
ejde-395	502	18	address	address	NOUN
ejde-395	502	19	:	:	PUNCT
ejde-395	502	20	xhyhhh@126.com	xhyhhh@126.com	PROPN
ejde-395	502	21	jin	jin	PROPN
ejde-395	502	22	tu	tu	PROPN
ejde-395	502	23	department	department	PROPN
ejde-395	502	24	of	of	ADP
ejde-395	502	25	mathematics	mathematics	PROPN
ejde-395	502	26	,	,	PUNCT
ejde-395	502	27	jiangxi	jiangxi	PROPN
ejde-395	502	28	normal	normal	ADJ
ejde-395	502	29	university	university	PROPN
ejde-395	502	30	,	,	PUNCT
ejde-395	502	31	nanchan	nanchan	PROPN
ejde-395	502	32	,	,	PUNCT
ejde-395	502	33	jiangxi	jiangxi	PROPN
ejde-395	502	34	330022	330022	NUM
ejde-395	502	35	,	,	PUNCT
ejde-395	502	36	china	china	PROPN
ejde-395	502	37	email	email	NOUN
ejde-395	502	38	address	address	NOUN
ejde-395	502	39	:	:	PUNCT
ejde-395	503	1	tujin2008@sina.com	tujin2008@sina.com	X
ejde-395	503	2	1	1	NUM
ejde-395	503	3	.	.	PUNCT
ejde-395	503	4	introduction	introduction	NOUN
ejde-395	503	5	and	and	CCONJ
ejde-395	503	6	statement	statement	NOUN
ejde-395	503	7	of	of	ADP
ejde-395	503	8	main	main	ADJ
ejde-395	503	9	results	result	NOUN
ejde-395	503	10	2	2	NUM
ejde-395	503	11	.	.	PUNCT
ejde-395	503	12	proof	proof	NOUN
ejde-395	503	13	of	of	ADP
ejde-395	503	14	theorem	theorem	NOUN
ejde-395	503	15	?	?	PUNCT
ejde-395	503	16	?	?	PUNCT
ejde-395	504	1	3	3	X
ejde-395	504	2	.	.	X
ejde-395	504	3	proof	proof	NOUN
ejde-395	504	4	of	of	ADP
ejde-395	504	5	theorem	theorem	NOUN
ejde-395	504	6	?	?	PUNCT
ejde-395	504	7	?	?	PUNCT
ejde-395	505	1	4	4	X
ejde-395	505	2	.	.	X
ejde-395	505	3	proof	proof	NOUN
ejde-395	505	4	of	of	ADP
ejde-395	505	5	theorem	theorem	NOUN
ejde-395	505	6	?	?	PUNCT
ejde-395	505	7	?	?	PUNCT
ejde-395	506	1	acknowledgments	acknowledgment	NOUN
ejde-395	506	2	references	reference	NOUN